id	sid	tid	token	lemma	pos
ejpam-2366	1	1	european	european	PROPN
ejpam-2366	1	2	journal	journal	PROPN
ejpam-2366	1	3	of	of	ADP
ejpam-2366	1	4	pure	pure	ADJ
ejpam-2366	1	5	and	and	CCONJ
ejpam-2366	1	6	applied	apply	VERB
ejpam-2366	1	7	mathematics	mathematic	NOUN
ejpam-2366	1	8	vol	vol	NOUN
ejpam-2366	1	9	.	.	PUNCT
ejpam-2366	2	1	14	14	NUM
ejpam-2366	2	2	,	,	PUNCT
ejpam-2366	2	3	no	no	INTJ
ejpam-2366	2	4	.	.	NOUN
ejpam-2366	2	5	2	2	NUM
ejpam-2366	2	6	,	,	PUNCT
ejpam-2366	2	7	2021	2021	NUM
ejpam-2366	2	8	,	,	PUNCT
ejpam-2366	2	9	551	551	NUM
ejpam-2366	2	10	-	-	SYM
ejpam-2366	2	11	577	577	NUM
ejpam-2366	2	12	issn	issn	PROPN
ejpam-2366	2	13	1307	1307	NUM
ejpam-2366	2	14	-	-	SYM
ejpam-2366	2	15	5543	5543	NUM
ejpam-2366	2	16	–	–	PUNCT
ejpam-2366	2	17	ejpam.com	ejpam.com	X
ejpam-2366	2	18	published	publish	VERB
ejpam-2366	2	19	by	by	ADP
ejpam-2366	2	20	new	new	PROPN
ejpam-2366	2	21	york	york	PROPN
ejpam-2366	2	22	business	business	PROPN
ejpam-2366	2	23	global	global	PROPN
ejpam-2366	2	24	φ	φ	PROPN
ejpam-2366	2	25	-	-	NOUN
ejpam-2366	2	26	prime	prime	NOUN
ejpam-2366	2	27	and	and	CCONJ
ejpam-2366	2	28	φ	φ	VERB
ejpam-2366	2	29	-	-	ADJ
ejpam-2366	2	30	primary	primary	ADJ
ejpam-2366	2	31	elements	element	NOUN
ejpam-2366	2	32	in	in	ADP
ejpam-2366	2	33	lattice	lattice	NOUN
ejpam-2366	2	34	modules	module	NOUN
ejpam-2366	2	35	ashok	ashok	NOUN
ejpam-2366	2	36	v.	v.	ADP
ejpam-2366	2	37	bingi1,∗	bingi1,∗	PROPN
ejpam-2366	2	38	,	,	PUNCT
ejpam-2366	2	39	c.	c.	PROPN
ejpam-2366	2	40	s.	s.	PROPN
ejpam-2366	2	41	manjarekar2	manjarekar2	PROPN
ejpam-2366	3	1	1	1	NUM
ejpam-2366	3	2	department	department	NOUN
ejpam-2366	3	3	of	of	ADP
ejpam-2366	3	4	mathematics	mathematics	PROPN
ejpam-2366	3	5	,	,	PUNCT
ejpam-2366	3	6	st	st	PROPN
ejpam-2366	3	7	.	.	PROPN
ejpam-2366	3	8	xavier	xavier	PROPN
ejpam-2366	3	9	’s	’s	PROPN
ejpam-2366	3	10	college	college	PROPN
ejpam-2366	3	11	(	(	PUNCT
ejpam-2366	3	12	autonomous	autonomous	ADJ
ejpam-2366	3	13	)	)	PUNCT
ejpam-2366	3	14	,	,	PUNCT
ejpam-2366	3	15	mumbai–400001	mumbai–400001	PROPN
ejpam-2366	3	16	,	,	PUNCT
ejpam-2366	3	17	maharashtra	maharashtra	PROPN
ejpam-2366	3	18	,	,	PUNCT
ejpam-2366	3	19	india	india	PROPN
ejpam-2366	3	20	2	2	NUM
ejpam-2366	3	21	formerly	formerly	ADV
ejpam-2366	3	22	at	at	ADP
ejpam-2366	3	23	department	department	NOUN
ejpam-2366	3	24	of	of	ADP
ejpam-2366	3	25	mathematics	mathematics	PROPN
ejpam-2366	3	26	,	,	PUNCT
ejpam-2366	3	27	shivaji	shivaji	PROPN
ejpam-2366	3	28	university	university	PROPN
ejpam-2366	3	29	,	,	PUNCT
ejpam-2366	3	30	kolhapur–416004	kolhapur–416004	PROPN
ejpam-2366	3	31	,	,	PUNCT
ejpam-2366	3	32	maharashtra	maharashtra	PROPN
ejpam-2366	3	33	,	,	PUNCT
ejpam-2366	3	34	india	india	PROPN
ejpam-2366	3	35	abstract	abstract	NOUN
ejpam-2366	3	36	.	.	PUNCT
ejpam-2366	4	1	in	in	ADP
ejpam-2366	4	2	this	this	DET
ejpam-2366	4	3	paper	paper	NOUN
ejpam-2366	4	4	,	,	PUNCT
ejpam-2366	4	5	we	we	PRON
ejpam-2366	4	6	introduce	introduce	VERB
ejpam-2366	4	7	φ	φ	VERB
ejpam-2366	4	8	-	-	NOUN
ejpam-2366	4	9	prime	prime	NOUN
ejpam-2366	4	10	and	and	CCONJ
ejpam-2366	4	11	φ	φ	VERB
ejpam-2366	4	12	-	-	ADJ
ejpam-2366	4	13	primary	primary	ADJ
ejpam-2366	4	14	elements	element	NOUN
ejpam-2366	4	15	in	in	ADP
ejpam-2366	4	16	an	an	DET
ejpam-2366	4	17	l	l	NOUN
ejpam-2366	4	18	-	-	NOUN
ejpam-2366	4	19	module	module	NOUN
ejpam-2366	4	20	m	m	NOUN
ejpam-2366	4	21	.	.	PUNCT
ejpam-2366	5	1	many	many	ADJ
ejpam-2366	5	2	of	of	ADP
ejpam-2366	5	3	its	its	PRON
ejpam-2366	5	4	characterizations	characterization	NOUN
ejpam-2366	5	5	and	and	CCONJ
ejpam-2366	5	6	properties	property	NOUN
ejpam-2366	5	7	are	be	AUX
ejpam-2366	5	8	obtained	obtain	VERB
ejpam-2366	5	9	.	.	PUNCT
ejpam-2366	6	1	by	by	ADP
ejpam-2366	6	2	counter	counter	ADJ
ejpam-2366	6	3	examples	example	NOUN
ejpam-2366	6	4	,	,	PUNCT
ejpam-2366	6	5	it	it	PRON
ejpam-2366	6	6	is	be	AUX
ejpam-2366	6	7	shown	show	VERB
ejpam-2366	6	8	that	that	SCONJ
ejpam-2366	6	9	a	a	DET
ejpam-2366	6	10	φprime	φprime	NOUN
ejpam-2366	6	11	element	element	NOUN
ejpam-2366	6	12	of	of	ADP
ejpam-2366	6	13	m	m	PRON
ejpam-2366	6	14	need	need	AUX
ejpam-2366	6	15	not	not	PART
ejpam-2366	6	16	be	be	AUX
ejpam-2366	6	17	prime	prime	ADJ
ejpam-2366	6	18	,	,	PUNCT
ejpam-2366	6	19	a	a	DET
ejpam-2366	6	20	φ	φ	VERB
ejpam-2366	6	21	-	-	ADJ
ejpam-2366	6	22	primary	primary	ADJ
ejpam-2366	6	23	element	element	NOUN
ejpam-2366	6	24	of	of	ADP
ejpam-2366	6	25	m	m	PRON
ejpam-2366	6	26	need	need	AUX
ejpam-2366	6	27	not	not	PART
ejpam-2366	6	28	be	be	AUX
ejpam-2366	6	29	φ	φ	VERB
ejpam-2366	6	30	-	-	ADJ
ejpam-2366	6	31	prime	prime	NOUN
ejpam-2366	6	32	,	,	PUNCT
ejpam-2366	6	33	a	a	DET
ejpam-2366	6	34	φprimary	φprimary	ADJ
ejpam-2366	6	35	element	element	NOUN
ejpam-2366	6	36	of	of	ADP
ejpam-2366	6	37	m	m	PRON
ejpam-2366	6	38	need	need	AUX
ejpam-2366	6	39	not	not	PART
ejpam-2366	6	40	be	be	AUX
ejpam-2366	6	41	prime	prime	ADJ
ejpam-2366	6	42	and	and	CCONJ
ejpam-2366	6	43	a	a	DET
ejpam-2366	6	44	φ	φ	ADJ
ejpam-2366	6	45	-	-	ADJ
ejpam-2366	6	46	primary	primary	ADJ
ejpam-2366	6	47	element	element	NOUN
ejpam-2366	6	48	of	of	ADP
ejpam-2366	6	49	m	m	PRON
ejpam-2366	6	50	need	need	AUX
ejpam-2366	6	51	not	not	PART
ejpam-2366	6	52	be	be	AUX
ejpam-2366	6	53	primary	primary	ADJ
ejpam-2366	6	54	.	.	PUNCT
ejpam-2366	7	1	finally	finally	ADV
ejpam-2366	7	2	,	,	PUNCT
ejpam-2366	7	3	some	some	PRON
ejpam-2366	7	4	results	result	VERB
ejpam-2366	7	5	for	for	ADP
ejpam-2366	7	6	almost	almost	ADV
ejpam-2366	7	7	prime	prime	ADJ
ejpam-2366	7	8	and	and	CCONJ
ejpam-2366	7	9	almost	almost	ADV
ejpam-2366	7	10	primary	primary	ADJ
ejpam-2366	7	11	elements	element	NOUN
ejpam-2366	7	12	of	of	ADP
ejpam-2366	7	13	an	an	DET
ejpam-2366	7	14	l	l	NOUN
ejpam-2366	7	15	-	-	NOUN
ejpam-2366	7	16	module	module	NOUN
ejpam-2366	7	17	m	m	NOUN
ejpam-2366	7	18	with	with	ADP
ejpam-2366	7	19	their	their	PRON
ejpam-2366	7	20	characterizations	characterization	NOUN
ejpam-2366	7	21	are	be	AUX
ejpam-2366	7	22	obtained	obtain	VERB
ejpam-2366	7	23	.	.	PUNCT
ejpam-2366	8	1	also	also	ADV
ejpam-2366	8	2	,	,	PUNCT
ejpam-2366	8	3	we	we	PRON
ejpam-2366	8	4	introduce	introduce	VERB
ejpam-2366	8	5	the	the	DET
ejpam-2366	8	6	notions	notion	NOUN
ejpam-2366	8	7	of	of	ADP
ejpam-2366	8	8	n	n	CCONJ
ejpam-2366	8	9	-	-	PUNCT
ejpam-2366	8	10	potent	potent	ADJ
ejpam-2366	8	11	prime(respectively	prime(respectively	ADJ
ejpam-2366	8	12	n	n	CCONJ
ejpam-2366	8	13	-	-	PUNCT
ejpam-2366	8	14	potent	potent	ADJ
ejpam-2366	8	15	primary	primary	NOUN
ejpam-2366	8	16	)	)	PUNCT
ejpam-2366	8	17	elements	element	NOUN
ejpam-2366	8	18	in	in	ADP
ejpam-2366	8	19	l	l	PROPN
ejpam-2366	8	20	and	and	CCONJ
ejpam-2366	8	21	m	m	VERB
ejpam-2366	8	22	to	to	PART
ejpam-2366	8	23	obtain	obtain	VERB
ejpam-2366	8	24	interrelations	interrelation	NOUN
ejpam-2366	8	25	among	among	ADP
ejpam-2366	8	26	them	they	PRON
ejpam-2366	8	27	where	where	SCONJ
ejpam-2366	8	28	n	n	DET
ejpam-2366	8	29	>	>	X
ejpam-2366	8	30	2	2	NUM
ejpam-2366	8	31	.	.	NOUN
ejpam-2366	8	32	2020	2020	NUM
ejpam-2366	8	33	mathematics	mathematic	NOUN
ejpam-2366	8	34	subject	subject	NOUN
ejpam-2366	8	35	classifications	classification	NOUN
ejpam-2366	8	36	:	:	PUNCT
ejpam-2366	8	37	06d10	06d10	NUM
ejpam-2366	8	38	,	,	PUNCT
ejpam-2366	8	39	06e10	06e10	NUM
ejpam-2366	8	40	,	,	PUNCT
ejpam-2366	8	41	06e99	06e99	NOUN
ejpam-2366	8	42	,	,	PUNCT
ejpam-2366	8	43	06f10	06f10	NUM
ejpam-2366	8	44	,	,	PUNCT
ejpam-2366	8	45	06f99	06f99	X
ejpam-2366	8	46	key	key	ADJ
ejpam-2366	8	47	words	word	NOUN
ejpam-2366	8	48	and	and	CCONJ
ejpam-2366	8	49	phrases	phrase	NOUN
ejpam-2366	8	50	:	:	PUNCT
ejpam-2366	8	51	φ	φ	NUM
ejpam-2366	8	52	-	-	ADJ
ejpam-2366	8	53	prime	prime	ADJ
ejpam-2366	8	54	element	element	NOUN
ejpam-2366	8	55	,	,	PUNCT
ejpam-2366	8	56	φ	φ	PROPN
ejpam-2366	8	57	-	-	ADJ
ejpam-2366	8	58	primary	primary	ADJ
ejpam-2366	8	59	element	element	NOUN
ejpam-2366	8	60	,	,	PUNCT
ejpam-2366	8	61	almost	almost	ADV
ejpam-2366	8	62	prime	prime	ADJ
ejpam-2366	8	63	element	element	NOUN
ejpam-2366	8	64	,	,	PUNCT
ejpam-2366	8	65	almost	almost	ADV
ejpam-2366	8	66	primary	primary	ADJ
ejpam-2366	8	67	element	element	NOUN
ejpam-2366	8	68	,	,	PUNCT
ejpam-2366	8	69	n	n	CCONJ
ejpam-2366	8	70	-	-	PUNCT
ejpam-2366	8	71	potent	potent	ADJ
ejpam-2366	8	72	prime	prime	ADJ
ejpam-2366	8	73	element	element	NOUN
ejpam-2366	8	74	,	,	PUNCT
ejpam-2366	8	75	n	n	CCONJ
ejpam-2366	8	76	-	-	PUNCT
ejpam-2366	8	77	potent	potent	ADJ
ejpam-2366	8	78	primary	primary	ADJ
ejpam-2366	8	79	element	element	NOUN
ejpam-2366	8	80	1	1	NUM
ejpam-2366	8	81	.	.	PUNCT
ejpam-2366	8	82	introduction	introduction	NOUN
ejpam-2366	8	83	in	in	ADP
ejpam-2366	8	84	multiplicative	multiplicative	ADJ
ejpam-2366	8	85	lattices	lattice	NOUN
ejpam-2366	8	86	,	,	PUNCT
ejpam-2366	8	87	the	the	DET
ejpam-2366	8	88	study	study	NOUN
ejpam-2366	8	89	of	of	ADP
ejpam-2366	8	90	φ	φ	PROPN
ejpam-2366	8	91	-	-	NOUN
ejpam-2366	8	92	prime	prime	NOUN
ejpam-2366	8	93	and	and	CCONJ
ejpam-2366	8	94	φ	φ	VERB
ejpam-2366	8	95	-	-	ADJ
ejpam-2366	8	96	primary	primary	ADJ
ejpam-2366	8	97	elements	element	NOUN
ejpam-2366	8	98	is	be	AUX
ejpam-2366	8	99	done	do	VERB
ejpam-2366	8	100	by	by	ADP
ejpam-2366	8	101	c.	c.	PROPN
ejpam-2366	8	102	s.	s.	PROPN
ejpam-2366	8	103	manjarekar	manjarekar	PROPN
ejpam-2366	8	104	and	and	CCONJ
ejpam-2366	8	105	a.	a.	PROPN
ejpam-2366	8	106	v.	v.	ADP
ejpam-2366	8	107	bingi	bingi	PROPN
ejpam-2366	8	108	in	in	ADP
ejpam-2366	8	109	[	[	X
ejpam-2366	8	110	16	16	NUM
ejpam-2366	8	111	]	]	PUNCT
ejpam-2366	8	112	.	.	PUNCT
ejpam-2366	9	1	our	our	PRON
ejpam-2366	9	2	aim	aim	NOUN
ejpam-2366	9	3	is	be	AUX
ejpam-2366	9	4	to	to	PART
ejpam-2366	9	5	extend	extend	VERB
ejpam-2366	9	6	the	the	DET
ejpam-2366	9	7	notion	notion	NOUN
ejpam-2366	9	8	of	of	ADP
ejpam-2366	9	9	φ	φ	PROPN
ejpam-2366	9	10	-	-	NOUN
ejpam-2366	9	11	prime	prime	NOUN
ejpam-2366	9	12	and	and	CCONJ
ejpam-2366	9	13	φ	φ	VERB
ejpam-2366	9	14	-	-	ADJ
ejpam-2366	9	15	primary	primary	ADJ
ejpam-2366	9	16	elements	element	NOUN
ejpam-2366	9	17	in	in	ADP
ejpam-2366	9	18	a	a	DET
ejpam-2366	9	19	multiplicative	multiplicative	ADJ
ejpam-2366	9	20	lattice	lattice	NOUN
ejpam-2366	9	21	to	to	ADP
ejpam-2366	9	22	the	the	DET
ejpam-2366	9	23	notion	notion	NOUN
ejpam-2366	9	24	of	of	ADP
ejpam-2366	9	25	φ	φ	PROPN
ejpam-2366	9	26	-	-	NOUN
ejpam-2366	9	27	prime	prime	NOUN
ejpam-2366	9	28	and	and	CCONJ
ejpam-2366	9	29	φ	φ	VERB
ejpam-2366	9	30	-	-	ADJ
ejpam-2366	9	31	primary	primary	ADJ
ejpam-2366	9	32	elements	element	NOUN
ejpam-2366	9	33	in	in	ADP
ejpam-2366	9	34	a	a	DET
ejpam-2366	9	35	lattice	lattice	NOUN
ejpam-2366	9	36	module	module	NOUN
ejpam-2366	9	37	and	and	CCONJ
ejpam-2366	9	38	study	study	VERB
ejpam-2366	9	39	its	its	PRON
ejpam-2366	9	40	properties	property	NOUN
ejpam-2366	9	41	.	.	PUNCT
ejpam-2366	10	1	according	accord	VERB
ejpam-2366	10	2	to	to	ADP
ejpam-2366	10	3	[	[	X
ejpam-2366	10	4	1	1	NUM
ejpam-2366	10	5	]	]	PUNCT
ejpam-2366	10	6	,	,	PUNCT
ejpam-2366	10	7	a	a	DET
ejpam-2366	10	8	proper	proper	ADJ
ejpam-2366	10	9	element	element	NOUN
ejpam-2366	10	10	n	n	PROPN
ejpam-2366	10	11	of	of	ADP
ejpam-2366	10	12	an	an	DET
ejpam-2366	10	13	l	l	NOUN
ejpam-2366	10	14	-	-	NOUN
ejpam-2366	10	15	module	module	NOUN
ejpam-2366	10	16	m	m	NOUN
ejpam-2366	10	17	is	be	AUX
ejpam-2366	10	18	said	say	VERB
ejpam-2366	10	19	to	to	PART
ejpam-2366	10	20	be	be	AUX
ejpam-2366	10	21	prime	prime	ADJ
ejpam-2366	10	22	if	if	SCONJ
ejpam-2366	10	23	for	for	ADP
ejpam-2366	10	24	all	all	DET
ejpam-2366	10	25	a	a	DET
ejpam-2366	10	26	∈	∈	PROPN
ejpam-2366	10	27	m	m	NOUN
ejpam-2366	10	28	,	,	PUNCT
ejpam-2366	10	29	a	a	DET
ejpam-2366	10	30	∈	∈	PROPN
ejpam-2366	10	31	l	l	NOUN
ejpam-2366	10	32	,	,	PUNCT
ejpam-2366	10	33	aa	aa	PROPN
ejpam-2366	10	34	6	6	NUM
ejpam-2366	10	35	n	n	PRON
ejpam-2366	10	36	implies	imply	VERB
ejpam-2366	10	37	either	either	CCONJ
ejpam-2366	10	38	a	a	DET
ejpam-2366	10	39	6	6	NUM
ejpam-2366	10	40	n	n	NOUN
ejpam-2366	10	41	or	or	CCONJ
ejpam-2366	10	42	a	a	DET
ejpam-2366	10	43	6	6	NUM
ejpam-2366	10	44	(	(	PUNCT
ejpam-2366	10	45	n	n	NUM
ejpam-2366	10	46	:	:	PUNCT
ejpam-2366	10	47	i	i	PRON
ejpam-2366	10	48	m	m	PROPN
ejpam-2366	10	49	)	)	PUNCT
ejpam-2366	10	50	.	.	PUNCT
ejpam-2366	11	1	according	accord	VERB
ejpam-2366	11	2	to	to	ADP
ejpam-2366	11	3	[	[	X
ejpam-2366	11	4	10	10	NUM
ejpam-2366	11	5	]	]	PUNCT
ejpam-2366	11	6	,	,	PUNCT
ejpam-2366	11	7	a	a	DET
ejpam-2366	11	8	proper	proper	ADJ
ejpam-2366	11	9	element	element	NOUN
ejpam-2366	11	10	n	n	PROPN
ejpam-2366	11	11	of	of	ADP
ejpam-2366	11	12	an	an	DET
ejpam-2366	11	13	l	l	NOUN
ejpam-2366	11	14	-	-	NOUN
ejpam-2366	11	15	module	module	NOUN
ejpam-2366	11	16	m	m	NOUN
ejpam-2366	11	17	is	be	AUX
ejpam-2366	11	18	said	say	VERB
ejpam-2366	11	19	to	to	PART
ejpam-2366	11	20	be	be	AUX
ejpam-2366	11	21	primary	primary	ADJ
ejpam-2366	11	22	if	if	SCONJ
ejpam-2366	11	23	for	for	ADP
ejpam-2366	11	24	all	all	DET
ejpam-2366	11	25	a	a	DET
ejpam-2366	11	26	∈m	∈m	NOUN
ejpam-2366	11	27	,	,	PUNCT
ejpam-2366	11	28	a	a	DET
ejpam-2366	11	29	∈	∈	PROPN
ejpam-2366	11	30	l	l	NOUN
ejpam-2366	11	31	,	,	PUNCT
ejpam-2366	11	32	aa	aa	PROPN
ejpam-2366	11	33	6	6	NUM
ejpam-2366	11	34	n	n	PRON
ejpam-2366	11	35	implies	imply	VERB
ejpam-2366	11	36	either	either	CCONJ
ejpam-2366	11	37	a	a	DET
ejpam-2366	11	38	6	6	NUM
ejpam-2366	11	39	n	n	NOUN
ejpam-2366	11	40	or	or	CCONJ
ejpam-2366	11	41	a	a	DET
ejpam-2366	11	42	6	6	NUM
ejpam-2366	11	43	√	√	NUM
ejpam-2366	11	44	n	n	NOUN
ejpam-2366	11	45	:	:	PUNCT
ejpam-2366	11	46	i	i	PRON
ejpam-2366	11	47	m	m	VERB
ejpam-2366	11	48	.	.	PUNCT
ejpam-2366	12	1	by	by	ADP
ejpam-2366	12	2	restricting	restrict	VERB
ejpam-2366	12	3	where	where	SCONJ
ejpam-2366	12	4	aa	aa	NOUN
ejpam-2366	12	5	lies	lie	VERB
ejpam-2366	12	6	,	,	PUNCT
ejpam-2366	12	7	weakly	weakly	ADJ
ejpam-2366	12	8	prime	prime	ADJ
ejpam-2366	12	9	and	and	CCONJ
ejpam-2366	12	10	weakly	weakly	ADJ
ejpam-2366	12	11	primary	primary	ADJ
ejpam-2366	12	12	elements	element	NOUN
ejpam-2366	12	13	in	in	ADP
ejpam-2366	12	14	lattice	lattice	NOUN
ejpam-2366	12	15	modules	module	NOUN
ejpam-2366	12	16	are	be	AUX
ejpam-2366	12	17	studied	study	VERB
ejpam-2366	12	18	by	by	ADP
ejpam-2366	12	19	c.	c.	PROPN
ejpam-2366	12	20	s.	s.	PROPN
ejpam-2366	12	21	manjarekar	manjarekar	PROPN
ejpam-2366	12	22	et	et	PROPN
ejpam-2366	12	23	.	.	PUNCT
ejpam-2366	13	1	al	al	PROPN
ejpam-2366	13	2	.	.	PUNCT
ejpam-2366	14	1	in	in	ADP
ejpam-2366	14	2	[	[	X
ejpam-2366	14	3	19	19	NUM
ejpam-2366	14	4	]	]	PUNCT
ejpam-2366	14	5	and	and	CCONJ
ejpam-2366	14	6	[	[	X
ejpam-2366	14	7	20	20	NUM
ejpam-2366	14	8	]	]	PUNCT
ejpam-2366	14	9	,	,	PUNCT
ejpam-2366	14	10	respectively	respectively	ADV
ejpam-2366	14	11	.	.	PUNCT
ejpam-2366	15	1	a	a	DET
ejpam-2366	15	2	proper	proper	ADJ
ejpam-2366	15	3	element	element	NOUN
ejpam-2366	15	4	n	n	PROPN
ejpam-2366	15	5	of	of	ADP
ejpam-2366	15	6	an	an	DET
ejpam-2366	15	7	l	l	NOUN
ejpam-2366	15	8	-	-	NOUN
ejpam-2366	15	9	module	module	NOUN
ejpam-2366	15	10	m	m	NOUN
ejpam-2366	15	11	is	be	AUX
ejpam-2366	15	12	said	say	VERB
ejpam-2366	15	13	to	to	PART
ejpam-2366	15	14	be	be	AUX
ejpam-2366	15	15	weakly	weakly	ADV
ejpam-2366	15	16	prime	prime	ADJ
ejpam-2366	15	17	if	if	SCONJ
ejpam-2366	15	18	for	for	ADP
ejpam-2366	15	19	all	all	DET
ejpam-2366	15	20	a	a	DET
ejpam-2366	15	21	∈	∈	PROPN
ejpam-2366	15	22	m	m	NOUN
ejpam-2366	15	23	,	,	PUNCT
ejpam-2366	15	24	a	a	DET
ejpam-2366	15	25	∈	∈	PROPN
ejpam-2366	15	26	l	l	NOUN
ejpam-2366	15	27	,	,	PUNCT
ejpam-2366	15	28	om	om	PROPN
ejpam-2366	15	29	6=	6=	PROPN
ejpam-2366	15	30	aa	aa	PROPN
ejpam-2366	15	31	6	6	NUM
ejpam-2366	15	32	n	n	PRON
ejpam-2366	15	33	implies	imply	VERB
ejpam-2366	15	34	either	either	CCONJ
ejpam-2366	15	35	a	a	DET
ejpam-2366	15	36	6	6	NUM
ejpam-2366	15	37	n	n	NOUN
ejpam-2366	15	38	or	or	CCONJ
ejpam-2366	15	39	a	a	DET
ejpam-2366	15	40	6	6	NUM
ejpam-2366	15	41	(	(	PUNCT
ejpam-2366	15	42	n	n	NUM
ejpam-2366	15	43	:	:	PUNCT
ejpam-2366	15	44	i	i	PRON
ejpam-2366	15	45	m	m	PROPN
ejpam-2366	15	46	)	)	PUNCT
ejpam-2366	15	47	.	.	PUNCT
ejpam-2366	16	1	a	a	DET
ejpam-2366	16	2	proper	proper	ADJ
ejpam-2366	16	3	element	element	NOUN
ejpam-2366	16	4	n	n	PROPN
ejpam-2366	16	5	of	of	ADP
ejpam-2366	16	6	an	an	DET
ejpam-2366	16	7	l	l	NOUN
ejpam-2366	16	8	-	-	NOUN
ejpam-2366	16	9	module	module	NOUN
ejpam-2366	16	10	m	m	NOUN
ejpam-2366	16	11	is	be	AUX
ejpam-2366	16	12	said	say	VERB
ejpam-2366	16	13	to	to	PART
ejpam-2366	16	14	be	be	AUX
ejpam-2366	16	15	weakly	weakly	ADV
ejpam-2366	16	16	primary	primary	ADJ
ejpam-2366	16	17	if	if	SCONJ
ejpam-2366	16	18	for	for	ADP
ejpam-2366	16	19	all	all	DET
ejpam-2366	16	20	a	a	DET
ejpam-2366	16	21	∈	∈	PROPN
ejpam-2366	16	22	m	m	NOUN
ejpam-2366	16	23	,	,	PUNCT
ejpam-2366	16	24	a	a	DET
ejpam-2366	16	25	∈	∈	PROPN
ejpam-2366	16	26	l	l	NOUN
ejpam-2366	16	27	,	,	PUNCT
ejpam-2366	16	28	om	om	PROPN
ejpam-2366	16	29	6=	6=	PROPN
ejpam-2366	16	30	aa	aa	PROPN
ejpam-2366	16	31	6	6	NUM
ejpam-2366	16	32	n	n	PRON
ejpam-2366	16	33	implies	imply	VERB
ejpam-2366	16	34	either	either	CCONJ
ejpam-2366	16	35	a	a	DET
ejpam-2366	16	36	6	6	NUM
ejpam-2366	16	37	n	n	NOUN
ejpam-2366	16	38	∗corresponding	∗corresponde	VERB
ejpam-2366	16	39	author	author	NOUN
ejpam-2366	16	40	.	.	PUNCT
ejpam-2366	17	1	doi	doi	NOUN
ejpam-2366	17	2	:	:	PUNCT
ejpam-2366	17	3	https://doi.org/10.29020/nybg.ejpam.v14i2.2366	https://doi.org/10.29020/nybg.ejpam.v14i2.2366	PROPN
ejpam-2366	17	4	email	email	NOUN
ejpam-2366	17	5	addresses	address	NOUN
ejpam-2366	17	6	:	:	PUNCT
ejpam-2366	17	7	ashok.bingi@xaviers.edu	ashok.bingi@xaviers.edu	PROPN
ejpam-2366	17	8	(	(	PUNCT
ejpam-2366	17	9	ashok	ashok	NOUN
ejpam-2366	17	10	v.	v.	ADP
ejpam-2366	17	11	bingi	bingi	PROPN
ejpam-2366	17	12	)	)	PUNCT
ejpam-2366	17	13	,	,	PUNCT
ejpam-2366	17	14	csmanjrekar@yahoo.co.in	csmanjrekar@yahoo.co.in	X
ejpam-2366	17	15	(	(	PUNCT
ejpam-2366	17	16	c.	c.	PROPN
ejpam-2366	17	17	s.	s.	PROPN
ejpam-2366	17	18	manjarekar	manjarekar	PROPN
ejpam-2366	17	19	)	)	PUNCT
ejpam-2366	17	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2366	18	1	551	551	NUM
ejpam-2366	18	2	c	c	X
ejpam-2366	18	3	©	©	PROPN
ejpam-2366	18	4	2021	2021	NUM
ejpam-2366	18	5	ejpam	ejpam	VERB
ejpam-2366	18	6	all	all	DET
ejpam-2366	18	7	rights	right	NOUN
ejpam-2366	18	8	reserved	reserve	VERB
ejpam-2366	18	9	.	.	PUNCT
ejpam-2366	19	1	a.	a.	PROPN
ejpam-2366	19	2	v.	v.	PROPN
ejpam-2366	19	3	bingi	bingi	PROPN
ejpam-2366	19	4	,	,	PUNCT
ejpam-2366	19	5	c.	c.	PROPN
ejpam-2366	19	6	s.	s.	PROPN
ejpam-2366	19	7	manjarekar	manjarekar	PROPN
ejpam-2366	19	8	/	/	PROPN
ejpam-2366	19	9	eur	eur	PROPN
ejpam-2366	19	10	.	.	PUNCT
ejpam-2366	20	1	j.	j.	PROPN
ejpam-2366	20	2	pure	pure	PROPN
ejpam-2366	20	3	appl	appl	PROPN
ejpam-2366	20	4	.	.	PROPN
ejpam-2366	20	5	math	math	PROPN
ejpam-2366	20	6	,	,	PUNCT
ejpam-2366	20	7	14	14	NUM
ejpam-2366	20	8	(	(	PUNCT
ejpam-2366	20	9	2	2	NUM
ejpam-2366	20	10	)	)	PUNCT
ejpam-2366	20	11	(	(	PUNCT
ejpam-2366	20	12	2021	2021	NUM
ejpam-2366	20	13	)	)	PUNCT
ejpam-2366	20	14	,	,	PUNCT
ejpam-2366	20	15	551	551	NUM
ejpam-2366	20	16	-	-	SYM
ejpam-2366	20	17	577	577	NUM
ejpam-2366	20	18	552	552	NUM
ejpam-2366	20	19	or	or	CCONJ
ejpam-2366	20	20	a	a	DET
ejpam-2366	20	21	6	6	NUM
ejpam-2366	20	22	√	√	NUM
ejpam-2366	20	23	n	n	NOUN
ejpam-2366	20	24	:	:	PUNCT
ejpam-2366	20	25	i	i	PRON
ejpam-2366	20	26	m	m	VERB
ejpam-2366	20	27	.	.	PUNCT
ejpam-2366	21	1	keeping	keep	VERB
ejpam-2366	21	2	this	this	PRON
ejpam-2366	21	3	in	in	ADP
ejpam-2366	21	4	mind	mind	NOUN
ejpam-2366	21	5	,	,	PUNCT
ejpam-2366	21	6	in	in	ADP
ejpam-2366	21	7	this	this	DET
ejpam-2366	21	8	paper	paper	NOUN
ejpam-2366	21	9	we	we	PRON
ejpam-2366	21	10	define	define	VERB
ejpam-2366	21	11	and	and	CCONJ
ejpam-2366	21	12	study	study	VERB
ejpam-2366	21	13	φ	φ	VERB
ejpam-2366	21	14	-	-	NOUN
ejpam-2366	21	15	prime	prime	NOUN
ejpam-2366	21	16	and	and	CCONJ
ejpam-2366	21	17	φ	φ	VERB
ejpam-2366	21	18	-	-	ADJ
ejpam-2366	21	19	primary	primary	ADJ
ejpam-2366	21	20	elements	element	NOUN
ejpam-2366	21	21	of	of	ADP
ejpam-2366	21	22	an	an	DET
ejpam-2366	21	23	l	l	NOUN
ejpam-2366	21	24	-	-	NOUN
ejpam-2366	21	25	module	module	NOUN
ejpam-2366	21	26	m	m	NOUN
ejpam-2366	21	27	.	.	PUNCT
ejpam-2366	22	1	a	a	DET
ejpam-2366	22	2	multiplicative	multiplicative	ADJ
ejpam-2366	22	3	lattice	lattice	NOUN
ejpam-2366	22	4	l	l	NOUN
ejpam-2366	22	5	is	be	AUX
ejpam-2366	22	6	a	a	DET
ejpam-2366	22	7	complete	complete	ADJ
ejpam-2366	22	8	lattice	lattice	NOUN
ejpam-2366	22	9	provided	provide	VERB
ejpam-2366	22	10	with	with	ADP
ejpam-2366	22	11	commutative	commutative	ADJ
ejpam-2366	22	12	,	,	PUNCT
ejpam-2366	22	13	associative	associative	ADJ
ejpam-2366	22	14	and	and	CCONJ
ejpam-2366	22	15	join	join	VERB
ejpam-2366	22	16	distributive	distributive	ADJ
ejpam-2366	22	17	multiplication	multiplication	NOUN
ejpam-2366	22	18	in	in	ADP
ejpam-2366	22	19	which	which	PRON
ejpam-2366	22	20	the	the	DET
ejpam-2366	22	21	largest	large	ADJ
ejpam-2366	22	22	element	element	NOUN
ejpam-2366	22	23	1	1	NUM
ejpam-2366	22	24	acts	act	NOUN
ejpam-2366	22	25	as	as	ADP
ejpam-2366	22	26	a	a	DET
ejpam-2366	22	27	multiplicative	multiplicative	ADJ
ejpam-2366	22	28	identity	identity	NOUN
ejpam-2366	22	29	.	.	PUNCT
ejpam-2366	23	1	an	an	DET
ejpam-2366	23	2	element	element	NOUN
ejpam-2366	23	3	e	e	PROPN
ejpam-2366	23	4	∈	∈	PROPN
ejpam-2366	23	5	l	l	NOUN
ejpam-2366	23	6	is	be	AUX
ejpam-2366	23	7	called	call	VERB
ejpam-2366	23	8	meet	meet	ADJ
ejpam-2366	23	9	principal	principal	NOUN
ejpam-2366	23	10	if	if	SCONJ
ejpam-2366	23	11	a∧	a∧	NOUN
ejpam-2366	23	12	be	be	AUX
ejpam-2366	23	13	=	=	PUNCT
ejpam-2366	23	14	(	(	PUNCT
ejpam-2366	23	15	(	(	PUNCT
ejpam-2366	23	16	a	a	PRON
ejpam-2366	23	17	:	:	PUNCT
ejpam-2366	23	18	e)∧	e)∧	NOUN
ejpam-2366	23	19	b)e	b)e	NOUN
ejpam-2366	23	20	for	for	ADP
ejpam-2366	23	21	all	all	DET
ejpam-2366	23	22	a	a	PRON
ejpam-2366	23	23	,	,	PUNCT
ejpam-2366	23	24	b	b	PROPN
ejpam-2366	23	25	∈	∈	PROPN
ejpam-2366	23	26	l.	l.	NOUN
ejpam-2366	23	27	an	an	DET
ejpam-2366	23	28	element	element	NOUN
ejpam-2366	23	29	e	e	PROPN
ejpam-2366	23	30	∈	∈	PROPN
ejpam-2366	23	31	l	l	NOUN
ejpam-2366	23	32	is	be	AUX
ejpam-2366	23	33	called	call	VERB
ejpam-2366	23	34	join	join	NOUN
ejpam-2366	23	35	principal	principal	NOUN
ejpam-2366	23	36	if	if	SCONJ
ejpam-2366	23	37	(	(	PUNCT
ejpam-2366	23	38	ae	ae	PROPN
ejpam-2366	23	39	∨	∨	PROPN
ejpam-2366	23	40	b	b	PROPN
ejpam-2366	23	41	)	)	PUNCT
ejpam-2366	23	42	:	:	PUNCT
ejpam-2366	24	1	e	e	X
ejpam-2366	24	2	=	=	SYM
ejpam-2366	24	3	(	(	PUNCT
ejpam-2366	24	4	b	b	NOUN
ejpam-2366	24	5	:	:	PUNCT
ejpam-2366	24	6	e	e	X
ejpam-2366	24	7	)	)	PUNCT
ejpam-2366	24	8	∨	∨	NOUN
ejpam-2366	24	9	a	a	PRON
ejpam-2366	24	10	for	for	ADP
ejpam-2366	24	11	all	all	DET
ejpam-2366	24	12	a	a	PRON
ejpam-2366	24	13	,	,	PUNCT
ejpam-2366	24	14	b	b	PROPN
ejpam-2366	24	15	∈	∈	PROPN
ejpam-2366	24	16	l.	l.	NOUN
ejpam-2366	24	17	an	an	DET
ejpam-2366	24	18	element	element	NOUN
ejpam-2366	24	19	e	e	PROPN
ejpam-2366	24	20	∈	∈	PROPN
ejpam-2366	24	21	l	l	NOUN
ejpam-2366	24	22	is	be	AUX
ejpam-2366	24	23	called	call	VERB
ejpam-2366	24	24	principal	principal	ADJ
ejpam-2366	24	25	if	if	SCONJ
ejpam-2366	24	26	e	e	NOUN
ejpam-2366	24	27	is	be	AUX
ejpam-2366	24	28	both	both	PRON
ejpam-2366	24	29	meet	meet	VERB
ejpam-2366	24	30	principal	principal	NOUN
ejpam-2366	24	31	and	and	CCONJ
ejpam-2366	24	32	join	join	VERB
ejpam-2366	24	33	principal	principal	NOUN
ejpam-2366	24	34	.	.	PUNCT
ejpam-2366	25	1	an	an	DET
ejpam-2366	25	2	element	element	NOUN
ejpam-2366	25	3	a	a	DET
ejpam-2366	25	4	∈	∈	PROPN
ejpam-2366	25	5	l	l	NOUN
ejpam-2366	25	6	is	be	AUX
ejpam-2366	25	7	called	call	VERB
ejpam-2366	25	8	compact	compact	ADJ
ejpam-2366	25	9	if	if	SCONJ
ejpam-2366	25	10	for	for	ADP
ejpam-2366	25	11	x	x	X
ejpam-2366	25	12	⊆	⊆	NUM
ejpam-2366	25	13	l	l	NOUN
ejpam-2366	25	14	,	,	PUNCT
ejpam-2366	25	15	a	a	DET
ejpam-2366	25	16	6	6	NUM
ejpam-2366	25	17	∨x	∨x	NOUN
ejpam-2366	25	18	implies	imply	VERB
ejpam-2366	25	19	the	the	DET
ejpam-2366	25	20	existence	existence	NOUN
ejpam-2366	25	21	of	of	ADP
ejpam-2366	25	22	a	a	DET
ejpam-2366	25	23	finite	finite	ADJ
ejpam-2366	25	24	number	number	NOUN
ejpam-2366	25	25	of	of	ADP
ejpam-2366	25	26	elements	element	NOUN
ejpam-2366	25	27	a1	a1	NOUN
ejpam-2366	25	28	,	,	PUNCT
ejpam-2366	25	29	a2	a2	PROPN
ejpam-2366	25	30	,	,	PUNCT
ejpam-2366	25	31	·	·	PUNCT
ejpam-2366	25	32	·	·	PUNCT
ejpam-2366	26	1	·	·	PUNCT
ejpam-2366	26	2	,	,	PUNCT
ejpam-2366	26	3	an	an	DET
ejpam-2366	26	4	in	in	ADP
ejpam-2366	26	5	x	x	X
ejpam-2366	26	6	such	such	ADJ
ejpam-2366	26	7	that	that	SCONJ
ejpam-2366	26	8	a	a	DET
ejpam-2366	26	9	6	6	NUM
ejpam-2366	26	10	a1∨a2∨	a1∨a2∨	NOUN
ejpam-2366	26	11	·	·	PUNCT
ejpam-2366	26	12	·	·	PUNCT
ejpam-2366	26	13	·	·	PUNCT
ejpam-2366	26	14	∨an	∨an	PROPN
ejpam-2366	26	15	.	.	PUNCT
ejpam-2366	27	1	the	the	DET
ejpam-2366	27	2	set	set	NOUN
ejpam-2366	27	3	of	of	ADP
ejpam-2366	27	4	compact	compact	ADJ
ejpam-2366	27	5	elements	element	NOUN
ejpam-2366	27	6	of	of	ADP
ejpam-2366	27	7	l	l	NOUN
ejpam-2366	27	8	will	will	AUX
ejpam-2366	27	9	be	be	AUX
ejpam-2366	27	10	denoted	denote	VERB
ejpam-2366	27	11	by	by	ADP
ejpam-2366	27	12	l∗.	l∗.	NOUN
ejpam-2366	27	13	if	if	SCONJ
ejpam-2366	27	14	each	each	DET
ejpam-2366	27	15	element	element	NOUN
ejpam-2366	27	16	of	of	ADP
ejpam-2366	27	17	l	l	NOUN
ejpam-2366	27	18	is	be	AUX
ejpam-2366	27	19	a	a	DET
ejpam-2366	27	20	join	join	NOUN
ejpam-2366	27	21	of	of	ADP
ejpam-2366	27	22	compact	compact	ADJ
ejpam-2366	27	23	elements	element	NOUN
ejpam-2366	27	24	of	of	ADP
ejpam-2366	27	25	l	l	NOUN
ejpam-2366	27	26	,	,	PUNCT
ejpam-2366	27	27	then	then	ADV
ejpam-2366	27	28	l	l	NOUN
ejpam-2366	27	29	is	be	AUX
ejpam-2366	27	30	called	call	VERB
ejpam-2366	27	31	a	a	DET
ejpam-2366	27	32	compactly	compactly	ADV
ejpam-2366	27	33	generated	generate	VERB
ejpam-2366	27	34	lattice	lattice	NOUN
ejpam-2366	27	35	or	or	CCONJ
ejpam-2366	27	36	simply	simply	ADV
ejpam-2366	27	37	a	a	DET
ejpam-2366	27	38	cg	cg	NOUN
ejpam-2366	27	39	-	-	PUNCT
ejpam-2366	27	40	lattice	lattice	NOUN
ejpam-2366	27	41	.	.	PUNCT
ejpam-2366	28	1	l	l	NOUN
ejpam-2366	28	2	is	be	AUX
ejpam-2366	28	3	said	say	VERB
ejpam-2366	28	4	to	to	PART
ejpam-2366	28	5	be	be	AUX
ejpam-2366	28	6	a	a	DET
ejpam-2366	28	7	principally	principally	ADV
ejpam-2366	28	8	generated	generate	VERB
ejpam-2366	28	9	lattice	lattice	NOUN
ejpam-2366	28	10	or	or	CCONJ
ejpam-2366	28	11	simply	simply	ADV
ejpam-2366	28	12	a	a	DET
ejpam-2366	28	13	pg	pg	NOUN
ejpam-2366	28	14	-	-	PUNCT
ejpam-2366	28	15	lattice	lattice	NOUN
ejpam-2366	28	16	if	if	SCONJ
ejpam-2366	28	17	each	each	DET
ejpam-2366	28	18	element	element	NOUN
ejpam-2366	28	19	of	of	ADP
ejpam-2366	28	20	l	l	NOUN
ejpam-2366	28	21	is	be	AUX
ejpam-2366	28	22	a	a	DET
ejpam-2366	28	23	join	join	NOUN
ejpam-2366	28	24	of	of	ADP
ejpam-2366	28	25	principal	principal	ADJ
ejpam-2366	28	26	elements	element	NOUN
ejpam-2366	28	27	of	of	ADP
ejpam-2366	28	28	l.	l.	PROPN
ejpam-2366	28	29	throughout	throughout	ADP
ejpam-2366	28	30	this	this	DET
ejpam-2366	28	31	paper	paper	NOUN
ejpam-2366	28	32	,	,	PUNCT
ejpam-2366	28	33	l	l	NOUN
ejpam-2366	28	34	denotes	denote	VERB
ejpam-2366	28	35	a	a	DET
ejpam-2366	28	36	compactly	compactly	ADV
ejpam-2366	28	37	generated	generate	VERB
ejpam-2366	28	38	multiplicative	multiplicative	ADJ
ejpam-2366	28	39	lattice	lattice	NOUN
ejpam-2366	28	40	with	with	ADP
ejpam-2366	28	41	greatest	great	ADJ
ejpam-2366	28	42	compact	compact	ADJ
ejpam-2366	28	43	element	element	NOUN
ejpam-2366	28	44	1	1	NUM
ejpam-2366	28	45	in	in	ADP
ejpam-2366	28	46	which	which	PRON
ejpam-2366	28	47	every	every	DET
ejpam-2366	28	48	finite	finite	ADJ
ejpam-2366	28	49	product	product	NOUN
ejpam-2366	28	50	of	of	ADP
ejpam-2366	28	51	compact	compact	ADJ
ejpam-2366	28	52	elements	element	NOUN
ejpam-2366	28	53	is	be	AUX
ejpam-2366	28	54	compact	compact	ADJ
ejpam-2366	28	55	.	.	PUNCT
ejpam-2366	29	1	an	an	DET
ejpam-2366	29	2	element	element	NOUN
ejpam-2366	29	3	a	a	DET
ejpam-2366	29	4	∈	∈	PROPN
ejpam-2366	29	5	l	l	NOUN
ejpam-2366	29	6	is	be	AUX
ejpam-2366	29	7	said	say	VERB
ejpam-2366	29	8	to	to	PART
ejpam-2366	29	9	be	be	AUX
ejpam-2366	29	10	proper	proper	ADJ
ejpam-2366	29	11	if	if	SCONJ
ejpam-2366	29	12	a	a	DET
ejpam-2366	29	13	<	<	X
ejpam-2366	29	14	1	1	NUM
ejpam-2366	29	15	.	.	PUNCT
ejpam-2366	30	1	a	a	DET
ejpam-2366	30	2	proper	proper	ADJ
ejpam-2366	30	3	element	element	NOUN
ejpam-2366	30	4	m	m	PROPN
ejpam-2366	30	5	∈	∈	NOUN
ejpam-2366	30	6	l	l	NOUN
ejpam-2366	30	7	is	be	AUX
ejpam-2366	30	8	said	say	VERB
ejpam-2366	30	9	to	to	PART
ejpam-2366	30	10	be	be	AUX
ejpam-2366	30	11	maximal	maximal	ADJ
ejpam-2366	30	12	if	if	SCONJ
ejpam-2366	30	13	for	for	ADP
ejpam-2366	30	14	every	every	DET
ejpam-2366	30	15	element	element	NOUN
ejpam-2366	30	16	x	x	SYM
ejpam-2366	30	17	∈	∈	NOUN
ejpam-2366	30	18	l	l	NOUN
ejpam-2366	30	19	such	such	ADJ
ejpam-2366	30	20	that	that	SCONJ
ejpam-2366	30	21	m	m	VERB
ejpam-2366	30	22	<	<	X
ejpam-2366	30	23	x	x	SYM
ejpam-2366	30	24	6	6	NUM
ejpam-2366	30	25	1	1	NUM
ejpam-2366	30	26	implies	imply	VERB
ejpam-2366	30	27	x	x	PUNCT
ejpam-2366	30	28	=	=	SYM
ejpam-2366	30	29	1	1	X
ejpam-2366	30	30	.	.	PUNCT
ejpam-2366	30	31	a	a	DET
ejpam-2366	30	32	proper	proper	ADJ
ejpam-2366	30	33	element	element	NOUN
ejpam-2366	30	34	p	p	PROPN
ejpam-2366	30	35	∈	∈	PROPN
ejpam-2366	30	36	l	l	NOUN
ejpam-2366	30	37	is	be	AUX
ejpam-2366	30	38	called	call	VERB
ejpam-2366	30	39	a	a	DET
ejpam-2366	30	40	prime	prime	ADJ
ejpam-2366	30	41	element	element	NOUN
ejpam-2366	30	42	if	if	SCONJ
ejpam-2366	30	43	ab	ab	PROPN
ejpam-2366	30	44	6	6	NUM
ejpam-2366	30	45	p	p	PROPN
ejpam-2366	30	46	implies	imply	VERB
ejpam-2366	30	47	a	a	DET
ejpam-2366	30	48	6	6	NUM
ejpam-2366	30	49	p	p	NOUN
ejpam-2366	30	50	or	or	CCONJ
ejpam-2366	30	51	b	b	NOUN
ejpam-2366	30	52	6	6	NUM
ejpam-2366	30	53	p	p	NOUN
ejpam-2366	30	54	where	where	SCONJ
ejpam-2366	30	55	a	a	PRON
ejpam-2366	30	56	,	,	PUNCT
ejpam-2366	30	57	b	b	PROPN
ejpam-2366	30	58	∈	∈	PROPN
ejpam-2366	30	59	l	l	NOUN
ejpam-2366	30	60	and	and	CCONJ
ejpam-2366	30	61	is	be	AUX
ejpam-2366	30	62	called	call	VERB
ejpam-2366	30	63	a	a	DET
ejpam-2366	30	64	primary	primary	ADJ
ejpam-2366	30	65	element	element	NOUN
ejpam-2366	30	66	if	if	SCONJ
ejpam-2366	30	67	ab	ab	PROPN
ejpam-2366	30	68	6	6	NUM
ejpam-2366	30	69	p	p	PROPN
ejpam-2366	30	70	implies	imply	VERB
ejpam-2366	30	71	a	a	DET
ejpam-2366	30	72	6	6	NUM
ejpam-2366	30	73	p	p	NOUN
ejpam-2366	30	74	or	or	CCONJ
ejpam-2366	30	75	bn	bn	NUM
ejpam-2366	30	76	6	6	NUM
ejpam-2366	30	77	p	p	NOUN
ejpam-2366	30	78	for	for	ADP
ejpam-2366	30	79	some	some	DET
ejpam-2366	30	80	n	n	PRON
ejpam-2366	30	81	∈	∈	NOUN
ejpam-2366	30	82	z+	z+	NUM
ejpam-2366	30	83	where	where	SCONJ
ejpam-2366	30	84	a	a	DET
ejpam-2366	30	85	,	,	PUNCT
ejpam-2366	30	86	b	b	X
ejpam-2366	30	87	∈	∈	PROPN
ejpam-2366	30	88	l∗.	l∗.	NOUN
ejpam-2366	30	89	for	for	ADP
ejpam-2366	30	90	a	a	DET
ejpam-2366	30	91	,	,	PUNCT
ejpam-2366	30	92	b	b	PROPN
ejpam-2366	30	93	∈	∈	PROPN
ejpam-2366	30	94	l	l	NOUN
ejpam-2366	30	95	,	,	PUNCT
ejpam-2366	30	96	(	(	PUNCT
ejpam-2366	30	97	a	a	DET
ejpam-2366	30	98	:	:	PUNCT
ejpam-2366	30	99	b	b	X
ejpam-2366	30	100	)	)	PUNCT
ejpam-2366	30	101	=	=	SYM
ejpam-2366	31	1	∨{x	∨{x	NOUN
ejpam-2366	31	2	∈	∈	NOUN
ejpam-2366	31	3	l	l	NOUN
ejpam-2366	32	1	|	|	NOUN
ejpam-2366	32	2	xb	xb	PROPN
ejpam-2366	32	3	6	6	NUM
ejpam-2366	32	4	a	a	X
ejpam-2366	32	5	}	}	PUNCT
ejpam-2366	32	6	.	.	PUNCT
ejpam-2366	33	1	the	the	DET
ejpam-2366	33	2	radical	radical	NOUN
ejpam-2366	33	3	of	of	ADP
ejpam-2366	33	4	a	a	DET
ejpam-2366	33	5	∈	∈	PROPN
ejpam-2366	33	6	l	l	NOUN
ejpam-2366	33	7	is	be	AUX
ejpam-2366	33	8	denoted	denote	VERB
ejpam-2366	33	9	by	by	ADP
ejpam-2366	33	10	√	√	PROPN
ejpam-2366	33	11	a	a	PRON
ejpam-2366	33	12	and	and	CCONJ
ejpam-2366	33	13	is	be	AUX
ejpam-2366	33	14	defined	define	VERB
ejpam-2366	33	15	as	as	ADP
ejpam-2366	33	16	∨{x	∨{x	PROPN
ejpam-2366	33	17	∈	∈	PROPN
ejpam-2366	33	18	l∗	l∗	PROPN
ejpam-2366	34	1	|	|	ADV
ejpam-2366	34	2	xn	xn	PROPN
ejpam-2366	34	3	6	6	NUM
ejpam-2366	34	4	a	a	PRON
ejpam-2366	34	5	,	,	PUNCT
ejpam-2366	34	6	for	for	ADP
ejpam-2366	34	7	some	some	DET
ejpam-2366	34	8	n	n	PRON
ejpam-2366	34	9	∈	∈	NOUN
ejpam-2366	34	10	z+	z+	NUM
ejpam-2366	34	11	}	}	PUNCT
ejpam-2366	34	12	.	.	PUNCT
ejpam-2366	35	1	a	a	DET
ejpam-2366	35	2	multiplicative	multiplicative	ADJ
ejpam-2366	35	3	lattice	lattice	NOUN
ejpam-2366	35	4	is	be	AUX
ejpam-2366	35	5	called	call	VERB
ejpam-2366	35	6	as	as	ADP
ejpam-2366	35	7	a	a	DET
ejpam-2366	35	8	noether	noether	ADJ
ejpam-2366	35	9	lattice	lattice	NOUN
ejpam-2366	35	10	if	if	SCONJ
ejpam-2366	35	11	it	it	PRON
ejpam-2366	35	12	is	be	AUX
ejpam-2366	35	13	modular	modular	ADJ
ejpam-2366	35	14	,	,	PUNCT
ejpam-2366	35	15	principally	principally	ADV
ejpam-2366	35	16	generated	generate	VERB
ejpam-2366	35	17	and	and	CCONJ
ejpam-2366	35	18	satisfies	satisfy	VERB
ejpam-2366	35	19	the	the	DET
ejpam-2366	35	20	ascending	ascend	VERB
ejpam-2366	35	21	chain	chain	NOUN
ejpam-2366	35	22	condition	condition	NOUN
ejpam-2366	35	23	.	.	PUNCT
ejpam-2366	36	1	a	a	DET
ejpam-2366	36	2	proper	proper	ADJ
ejpam-2366	36	3	element	element	NOUN
ejpam-2366	36	4	a	a	DET
ejpam-2366	36	5	∈	∈	PROPN
ejpam-2366	36	6	l	l	NOUN
ejpam-2366	36	7	is	be	AUX
ejpam-2366	36	8	said	say	VERB
ejpam-2366	36	9	to	to	PART
ejpam-2366	36	10	be	be	AUX
ejpam-2366	36	11	nilpotent	nilpotent	ADJ
ejpam-2366	36	12	if	if	SCONJ
ejpam-2366	36	13	an	an	DET
ejpam-2366	36	14	=	=	NOUN
ejpam-2366	36	15	0	0	NUM
ejpam-2366	36	16	for	for	ADP
ejpam-2366	36	17	some	some	DET
ejpam-2366	36	18	n	n	PRON
ejpam-2366	36	19	∈	∈	NOUN
ejpam-2366	36	20	z+	z+	NUM
ejpam-2366	36	21	.	.	PUNCT
ejpam-2366	37	1	according	accord	VERB
ejpam-2366	37	2	to	to	ADP
ejpam-2366	37	3	[	[	X
ejpam-2366	37	4	9	9	NUM
ejpam-2366	37	5	]	]	PUNCT
ejpam-2366	37	6	,	,	PUNCT
ejpam-2366	37	7	a	a	DET
ejpam-2366	37	8	proper	proper	ADJ
ejpam-2366	37	9	element	element	NOUN
ejpam-2366	37	10	p	p	PROPN
ejpam-2366	37	11	∈	∈	PROPN
ejpam-2366	37	12	l	l	NOUN
ejpam-2366	37	13	is	be	AUX
ejpam-2366	37	14	said	say	VERB
ejpam-2366	37	15	to	to	PART
ejpam-2366	37	16	be	be	AUX
ejpam-2366	37	17	almost	almost	ADV
ejpam-2366	37	18	prime	prime	ADJ
ejpam-2366	37	19	if	if	SCONJ
ejpam-2366	37	20	for	for	ADP
ejpam-2366	37	21	all	all	DET
ejpam-2366	37	22	a	a	DET
ejpam-2366	37	23	,	,	PUNCT
ejpam-2366	37	24	b	b	PROPN
ejpam-2366	37	25	∈	∈	PROPN
ejpam-2366	37	26	l	l	NOUN
ejpam-2366	37	27	,	,	PUNCT
ejpam-2366	37	28	ab	ab	PROPN
ejpam-2366	37	29	6	6	NUM
ejpam-2366	37	30	p	p	NOUN
ejpam-2366	37	31	and	and	CCONJ
ejpam-2366	37	32	ab	ab	PROPN
ejpam-2366	37	33	p2	p2	PROPN
ejpam-2366	37	34	implies	imply	VERB
ejpam-2366	37	35	either	either	CCONJ
ejpam-2366	37	36	a	a	DET
ejpam-2366	37	37	6	6	NUM
ejpam-2366	37	38	p	p	NOUN
ejpam-2366	37	39	or	or	CCONJ
ejpam-2366	37	40	b	b	NUM
ejpam-2366	37	41	6	6	NUM
ejpam-2366	37	42	p	p	NOUN
ejpam-2366	37	43	and	and	CCONJ
ejpam-2366	37	44	according	accord	VERB
ejpam-2366	37	45	to	to	ADP
ejpam-2366	37	46	[	[	X
ejpam-2366	37	47	15	15	NUM
ejpam-2366	37	48	]	]	X
ejpam-2366	37	49	,	,	PUNCT
ejpam-2366	37	50	a	a	DET
ejpam-2366	37	51	proper	proper	ADJ
ejpam-2366	37	52	element	element	NOUN
ejpam-2366	37	53	p	p	PROPN
ejpam-2366	37	54	∈	∈	PROPN
ejpam-2366	37	55	l	l	NOUN
ejpam-2366	37	56	is	be	AUX
ejpam-2366	37	57	said	say	VERB
ejpam-2366	37	58	to	to	PART
ejpam-2366	37	59	be	be	AUX
ejpam-2366	37	60	almost	almost	ADV
ejpam-2366	37	61	primary	primary	ADJ
ejpam-2366	37	62	if	if	SCONJ
ejpam-2366	37	63	for	for	ADP
ejpam-2366	37	64	all	all	DET
ejpam-2366	37	65	a	a	DET
ejpam-2366	37	66	,	,	PUNCT
ejpam-2366	37	67	b	b	PROPN
ejpam-2366	37	68	∈	∈	PROPN
ejpam-2366	37	69	l	l	NOUN
ejpam-2366	37	70	,	,	PUNCT
ejpam-2366	37	71	ab	ab	PROPN
ejpam-2366	37	72	6	6	NUM
ejpam-2366	37	73	p	p	NOUN
ejpam-2366	37	74	and	and	CCONJ
ejpam-2366	37	75	ab	ab	PROPN
ejpam-2366	37	76	p2	p2	PROPN
ejpam-2366	37	77	implies	imply	VERB
ejpam-2366	37	78	either	either	CCONJ
ejpam-2366	37	79	a	a	DET
ejpam-2366	37	80	6	6	NUM
ejpam-2366	37	81	p	p	NOUN
ejpam-2366	37	82	or	or	CCONJ
ejpam-2366	37	83	b	b	NOUN
ejpam-2366	37	84	6	6	NUM
ejpam-2366	37	85	√	√	PROPN
ejpam-2366	37	86	p.	p.	NOUN
ejpam-2366	37	87	further	further	ADJ
ejpam-2366	37	88	study	study	NOUN
ejpam-2366	37	89	on	on	ADP
ejpam-2366	37	90	almost	almost	ADV
ejpam-2366	37	91	prime	prime	ADJ
ejpam-2366	37	92	and	and	CCONJ
ejpam-2366	37	93	almost	almost	ADV
ejpam-2366	37	94	primary	primary	ADJ
ejpam-2366	37	95	elements	element	NOUN
ejpam-2366	37	96	of	of	ADP
ejpam-2366	37	97	a	a	DET
ejpam-2366	37	98	multiplicative	multiplicative	ADJ
ejpam-2366	37	99	lattice	lattice	NOUN
ejpam-2366	37	100	l	l	NOUN
ejpam-2366	37	101	is	be	AUX
ejpam-2366	37	102	seen	see	VERB
ejpam-2366	37	103	in	in	ADP
ejpam-2366	37	104	[	[	X
ejpam-2366	37	105	16	16	NUM
ejpam-2366	37	106	]	]	PUNCT
ejpam-2366	37	107	,	,	PUNCT
ejpam-2366	38	1	[	[	X
ejpam-2366	38	2	5	5	NUM
ejpam-2366	38	3	]	]	PUNCT
ejpam-2366	38	4	and	and	CCONJ
ejpam-2366	38	5	[	[	X
ejpam-2366	38	6	4	4	NUM
ejpam-2366	38	7	]	]	PUNCT
ejpam-2366	38	8	.	.	PUNCT
ejpam-2366	39	1	according	accord	VERB
ejpam-2366	39	2	to	to	ADP
ejpam-2366	39	3	[	[	X
ejpam-2366	39	4	12	12	NUM
ejpam-2366	39	5	]	]	PUNCT
ejpam-2366	39	6	,	,	PUNCT
ejpam-2366	39	7	a	a	DET
ejpam-2366	39	8	proper	proper	ADJ
ejpam-2366	39	9	element	element	NOUN
ejpam-2366	39	10	q	q	PROPN
ejpam-2366	39	11	∈	∈	PROPN
ejpam-2366	39	12	l	l	NOUN
ejpam-2366	39	13	is	be	AUX
ejpam-2366	39	14	said	say	VERB
ejpam-2366	39	15	to	to	PART
ejpam-2366	39	16	be	be	AUX
ejpam-2366	39	17	2	2	NUM
ejpam-2366	39	18	-	-	ADJ
ejpam-2366	39	19	absorbing	absorb	VERB
ejpam-2366	39	20	if	if	SCONJ
ejpam-2366	39	21	for	for	ADP
ejpam-2366	39	22	all	all	DET
ejpam-2366	39	23	a	a	DET
ejpam-2366	39	24	,	,	PUNCT
ejpam-2366	39	25	b	b	NOUN
ejpam-2366	39	26	,	,	PUNCT
ejpam-2366	39	27	c	c	PROPN
ejpam-2366	39	28	∈	∈	PROPN
ejpam-2366	39	29	l	l	NOUN
ejpam-2366	39	30	,	,	PUNCT
ejpam-2366	39	31	abc	abc	PROPN
ejpam-2366	39	32	6	6	NUM
ejpam-2366	39	33	q	q	PROPN
ejpam-2366	39	34	implies	imply	VERB
ejpam-2366	39	35	either	either	CCONJ
ejpam-2366	39	36	ab	ab	PROPN
ejpam-2366	39	37	6	6	NUM
ejpam-2366	39	38	q	q	NOUN
ejpam-2366	39	39	or	or	CCONJ
ejpam-2366	39	40	bc	bc	PROPN
ejpam-2366	39	41	6	6	NUM
ejpam-2366	39	42	q	q	NOUN
ejpam-2366	39	43	or	or	CCONJ
ejpam-2366	39	44	ca	ca	PROPN
ejpam-2366	39	45	6	6	NUM
ejpam-2366	39	46	q.	q.	NOUN
ejpam-2366	39	47	according	accord	VERB
ejpam-2366	39	48	to	to	ADP
ejpam-2366	39	49	[	[	X
ejpam-2366	39	50	18	18	NUM
ejpam-2366	39	51	]	]	PUNCT
ejpam-2366	39	52	,	,	PUNCT
ejpam-2366	39	53	a	a	DET
ejpam-2366	39	54	proper	proper	ADJ
ejpam-2366	39	55	element	element	NOUN
ejpam-2366	39	56	q	q	PROPN
ejpam-2366	39	57	∈	∈	PROPN
ejpam-2366	39	58	l	l	NOUN
ejpam-2366	39	59	is	be	AUX
ejpam-2366	39	60	said	say	VERB
ejpam-2366	39	61	to	to	PART
ejpam-2366	39	62	be	be	AUX
ejpam-2366	39	63	2	2	NUM
ejpam-2366	39	64	-	-	PUNCT
ejpam-2366	39	65	absorbing	absorb	VERB
ejpam-2366	39	66	primary	primary	NOUN
ejpam-2366	39	67	if	if	SCONJ
ejpam-2366	39	68	for	for	ADP
ejpam-2366	39	69	all	all	DET
ejpam-2366	39	70	a	a	DET
ejpam-2366	39	71	,	,	PUNCT
ejpam-2366	39	72	b	b	NOUN
ejpam-2366	39	73	,	,	PUNCT
ejpam-2366	39	74	c	c	PROPN
ejpam-2366	39	75	∈	∈	PROPN
ejpam-2366	39	76	l	l	NOUN
ejpam-2366	39	77	,	,	PUNCT
ejpam-2366	39	78	abc	abc	PROPN
ejpam-2366	39	79	6	6	NUM
ejpam-2366	39	80	q	q	PROPN
ejpam-2366	39	81	implies	imply	VERB
ejpam-2366	39	82	either	either	CCONJ
ejpam-2366	39	83	ab	ab	PROPN
ejpam-2366	39	84	6	6	NUM
ejpam-2366	39	85	q	q	NOUN
ejpam-2366	39	86	or	or	CCONJ
ejpam-2366	39	87	bc	bc	PROPN
ejpam-2366	39	88	6	6	NUM
ejpam-2366	39	89	√	√	PROPN
ejpam-2366	39	90	q	q	NOUN
ejpam-2366	39	91	or	or	CCONJ
ejpam-2366	39	92	ca	ca	PROPN
ejpam-2366	39	93	6	6	NUM
ejpam-2366	39	94	√	√	NOUN
ejpam-2366	39	95	q.	q.	NOUN
ejpam-2366	39	96	the	the	DET
ejpam-2366	39	97	reader	reader	NOUN
ejpam-2366	39	98	is	be	AUX
ejpam-2366	39	99	referred	refer	VERB
ejpam-2366	39	100	to	to	ADP
ejpam-2366	39	101	[	[	X
ejpam-2366	39	102	2	2	NUM
ejpam-2366	39	103	]	]	PUNCT
ejpam-2366	39	104	,	,	PUNCT
ejpam-2366	39	105	[	[	X
ejpam-2366	39	106	3	3	NUM
ejpam-2366	39	107	]	]	PUNCT
ejpam-2366	39	108	and	and	CCONJ
ejpam-2366	39	109	[	[	X
ejpam-2366	39	110	9	9	NUM
ejpam-2366	39	111	]	]	PUNCT
ejpam-2366	39	112	for	for	ADP
ejpam-2366	39	113	general	general	ADJ
ejpam-2366	39	114	background	background	NOUN
ejpam-2366	39	115	and	and	CCONJ
ejpam-2366	39	116	terminology	terminology	NOUN
ejpam-2366	39	117	in	in	ADP
ejpam-2366	39	118	multiplicative	multiplicative	ADJ
ejpam-2366	39	119	lattices	lattice	NOUN
ejpam-2366	39	120	.	.	PUNCT
ejpam-2366	40	1	let	let	VERB
ejpam-2366	40	2	m	m	PRON
ejpam-2366	40	3	be	be	AUX
ejpam-2366	40	4	a	a	DET
ejpam-2366	40	5	complete	complete	ADJ
ejpam-2366	40	6	lattice	lattice	NOUN
ejpam-2366	40	7	and	and	CCONJ
ejpam-2366	40	8	l	l	NOUN
ejpam-2366	40	9	be	be	AUX
ejpam-2366	40	10	a	a	DET
ejpam-2366	40	11	multiplicative	multiplicative	ADJ
ejpam-2366	40	12	lattice	lattice	NOUN
ejpam-2366	40	13	.	.	PUNCT
ejpam-2366	41	1	then	then	ADV
ejpam-2366	41	2	m	m	PROPN
ejpam-2366	41	3	is	be	AUX
ejpam-2366	41	4	called	call	VERB
ejpam-2366	41	5	lmodule	lmodule	NOUN
ejpam-2366	41	6	or	or	CCONJ
ejpam-2366	41	7	module	module	NOUN
ejpam-2366	41	8	over	over	ADP
ejpam-2366	41	9	l	l	NOUN
ejpam-2366	41	10	if	if	SCONJ
ejpam-2366	41	11	there	there	PRON
ejpam-2366	41	12	is	be	VERB
ejpam-2366	41	13	a	a	DET
ejpam-2366	41	14	multiplication	multiplication	NOUN
ejpam-2366	41	15	between	between	ADP
ejpam-2366	41	16	elements	element	NOUN
ejpam-2366	41	17	of	of	ADP
ejpam-2366	41	18	l	l	NOUN
ejpam-2366	41	19	and	and	CCONJ
ejpam-2366	41	20	m	m	AUX
ejpam-2366	41	21	written	write	VERB
ejpam-2366	41	22	as	as	ADP
ejpam-2366	41	23	ab	ab	NUM
ejpam-2366	41	24	where	where	SCONJ
ejpam-2366	41	25	a	a	DET
ejpam-2366	41	26	∈	∈	PROPN
ejpam-2366	41	27	l	l	NOUN
ejpam-2366	41	28	and	and	CCONJ
ejpam-2366	41	29	b	b	NOUN
ejpam-2366	41	30	∈m	∈m	NOUN
ejpam-2366	41	31	which	which	PRON
ejpam-2366	41	32	satisfies	satisfy	VERB
ejpam-2366	41	33	the	the	DET
ejpam-2366	41	34	following	follow	VERB
ejpam-2366	41	35	properties	property	NOUN
ejpam-2366	41	36	:	:	PUNCT
ejpam-2366	41	37	1	1	NUM
ejpam-2366	41	38	©	©	NOUN
ejpam-2366	41	39	(	(	PUNCT
ejpam-2366	41	40	∨	∨	NOUN
ejpam-2366	41	41	α	α	NOUN
ejpam-2366	41	42	aα)a	aα)a	NOUN
ejpam-2366	41	43	=	=	SYM
ejpam-2366	41	44	∨	∨	NUM
ejpam-2366	41	45	α	α	NOUN
ejpam-2366	41	46	(	(	PUNCT
ejpam-2366	41	47	aα	aα	NOUN
ejpam-2366	41	48	a	a	NOUN
ejpam-2366	41	49	)	)	PUNCT
ejpam-2366	41	50	,	,	PUNCT
ejpam-2366	41	51	2	2	NUM
ejpam-2366	41	52	©	©	NOUN
ejpam-2366	41	53	a(∨	a(∨	X
ejpam-2366	41	54	α	α	NOUN
ejpam-2366	41	55	aα	aα	NOUN
ejpam-2366	41	56	)	)	PUNCT
ejpam-2366	41	57	=	=	PUNCT
ejpam-2366	42	1	∨	∨	NUM
ejpam-2366	42	2	α	α	NOUN
ejpam-2366	42	3	(	(	PUNCT
ejpam-2366	42	4	a	a	DET
ejpam-2366	42	5	aα	aα	NOUN
ejpam-2366	42	6	)	)	PUNCT
ejpam-2366	42	7	,	,	PUNCT
ejpam-2366	42	8	3	3	X
ejpam-2366	42	9	©	©	NOUN
ejpam-2366	42	10	(	(	PUNCT
ejpam-2366	42	11	ab)a	ab)a	PROPN
ejpam-2366	42	12	=	=	PUNCT
ejpam-2366	42	13	a(ba	a(ba	NOUN
ejpam-2366	42	14	)	)	PUNCT
ejpam-2366	42	15	,	,	PUNCT
ejpam-2366	42	16	4	4	NUM
ejpam-2366	42	17	©	©	ADP
ejpam-2366	42	18	1a	1a	NUM
ejpam-2366	42	19	=	=	SYM
ejpam-2366	42	20	a	a	PRON
ejpam-2366	42	21	,	,	PUNCT
ejpam-2366	42	22	5	5	NUM
ejpam-2366	42	23	©	©	NOUN
ejpam-2366	42	24	0a	0a	PROPN
ejpam-2366	42	25	=	=	SYM
ejpam-2366	42	26	om	om	PROPN
ejpam-2366	42	27	,	,	PUNCT
ejpam-2366	42	28	for	for	ADP
ejpam-2366	42	29	all	all	DET
ejpam-2366	42	30	a	a	DET
ejpam-2366	42	31	,	,	PUNCT
ejpam-2366	42	32	aα	aα	NOUN
ejpam-2366	42	33	,	,	PUNCT
ejpam-2366	42	34	b	b	X
ejpam-2366	42	35	∈	∈	PROPN
ejpam-2366	42	36	l	l	NOUN
ejpam-2366	42	37	and	and	CCONJ
ejpam-2366	42	38	a	a	DET
ejpam-2366	42	39	,	,	PUNCT
ejpam-2366	42	40	aα	aα	NOUN
ejpam-2366	42	41	∈	∈	PROPN
ejpam-2366	42	42	m	m	VERB
ejpam-2366	42	43	where	where	SCONJ
ejpam-2366	42	44	1	1	NUM
ejpam-2366	42	45	is	be	AUX
ejpam-2366	42	46	the	the	DET
ejpam-2366	42	47	supremum	supremum	NOUN
ejpam-2366	42	48	of	of	ADP
ejpam-2366	42	49	l	l	NOUN
ejpam-2366	42	50	and	and	CCONJ
ejpam-2366	42	51	0	0	NUM
ejpam-2366	42	52	is	be	AUX
ejpam-2366	42	53	the	the	DET
ejpam-2366	42	54	infimum	infimum	NOUN
ejpam-2366	42	55	of	of	ADP
ejpam-2366	42	56	l.	l.	NOUN
ejpam-2366	42	57	we	we	PRON
ejpam-2366	42	58	denote	denote	VERB
ejpam-2366	42	59	by	by	ADP
ejpam-2366	42	60	om	om	PROPN
ejpam-2366	42	61	and	and	CCONJ
ejpam-2366	42	62	i	i	PRON
ejpam-2366	42	63	m	m	VERB
ejpam-2366	42	64	for	for	ADP
ejpam-2366	42	65	the	the	DET
ejpam-2366	42	66	least	least	ADJ
ejpam-2366	42	67	element	element	NOUN
ejpam-2366	42	68	and	and	CCONJ
ejpam-2366	42	69	the	the	DET
ejpam-2366	42	70	greatest	great	ADJ
ejpam-2366	42	71	element	element	NOUN
ejpam-2366	42	72	of	of	ADP
ejpam-2366	42	73	m	m	PROPN
ejpam-2366	42	74	,	,	PUNCT
ejpam-2366	42	75	respectively	respectively	ADV
ejpam-2366	42	76	.	.	PUNCT
ejpam-2366	43	1	elements	element	NOUN
ejpam-2366	43	2	of	of	ADP
ejpam-2366	43	3	l	l	NOUN
ejpam-2366	43	4	will	will	AUX
ejpam-2366	43	5	generally	generally	ADV
ejpam-2366	43	6	be	be	AUX
ejpam-2366	43	7	denoted	denote	VERB
ejpam-2366	43	8	by	by	ADP
ejpam-2366	43	9	a	a	DET
ejpam-2366	43	10	,	,	PUNCT
ejpam-2366	43	11	b	b	PROPN
ejpam-2366	43	12	,	,	PUNCT
ejpam-2366	43	13	c	c	NOUN
ejpam-2366	43	14	,	,	PUNCT
ejpam-2366	43	15	·	·	PUNCT
ejpam-2366	43	16	·	·	PUNCT
ejpam-2366	43	17	·	·	PUNCT
ejpam-2366	43	18	and	and	CCONJ
ejpam-2366	43	19	elements	element	NOUN
ejpam-2366	43	20	of	of	ADP
ejpam-2366	43	21	m	m	PROPN
ejpam-2366	43	22	will	will	AUX
ejpam-2366	43	23	generally	generally	ADV
ejpam-2366	43	24	be	be	AUX
ejpam-2366	43	25	denoted	denote	VERB
ejpam-2366	43	26	by	by	ADP
ejpam-2366	43	27	a	a	DET
ejpam-2366	43	28	,	,	PUNCT
ejpam-2366	43	29	b	b	NOUN
ejpam-2366	43	30	,	,	PUNCT
ejpam-2366	43	31	c	c	NOUN
ejpam-2366	43	32	,	,	PUNCT
ejpam-2366	43	33	·	·	PUNCT
ejpam-2366	43	34	·	·	PUNCT
ejpam-2366	44	1	·	·	PUNCT
ejpam-2366	44	2	let	let	VERB
ejpam-2366	44	3	m	m	PRON
ejpam-2366	44	4	be	be	AUX
ejpam-2366	44	5	an	an	DET
ejpam-2366	44	6	l	l	NOUN
ejpam-2366	44	7	-	-	NOUN
ejpam-2366	44	8	module	module	NOUN
ejpam-2366	44	9	.	.	PUNCT
ejpam-2366	45	1	for	for	ADP
ejpam-2366	45	2	n	n	CCONJ
ejpam-2366	45	3	∈m	∈m	NOUN
ejpam-2366	45	4	and	and	CCONJ
ejpam-2366	45	5	a	a	DET
ejpam-2366	45	6	∈	∈	PROPN
ejpam-2366	45	7	l	l	NOUN
ejpam-2366	45	8	,	,	PUNCT
ejpam-2366	45	9	(	(	PUNCT
ejpam-2366	45	10	n	n	X
ejpam-2366	45	11	:	:	PUNCT
ejpam-2366	45	12	a	a	X
ejpam-2366	45	13	)	)	PUNCT
ejpam-2366	45	14	=	=	SYM
ejpam-2366	45	15	∨{x	∨{x	NOUN
ejpam-2366	45	16	∈m	∈m	NOUN
ejpam-2366	45	17	|	|	ADV
ejpam-2366	45	18	ax	ax	NOUN
ejpam-2366	45	19	6	6	NUM
ejpam-2366	45	20	n	n	CCONJ
ejpam-2366	45	21	}	}	PUNCT
ejpam-2366	45	22	.	.	PUNCT
ejpam-2366	46	1	for	for	ADP
ejpam-2366	46	2	a	a	DET
ejpam-2366	46	3	,	,	PUNCT
ejpam-2366	46	4	b	b	NOUN
ejpam-2366	46	5	∈m	∈m	NOUN
ejpam-2366	46	6	,	,	PUNCT
ejpam-2366	46	7	(	(	PUNCT
ejpam-2366	46	8	a	a	DET
ejpam-2366	46	9	:	:	PUNCT
ejpam-2366	46	10	b	b	X
ejpam-2366	46	11	)	)	PUNCT
ejpam-2366	46	12	=	=	SYM
ejpam-2366	46	13	∨{x	∨{x	NOUN
ejpam-2366	46	14	∈	∈	NOUN
ejpam-2366	46	15	l	l	NOUN
ejpam-2366	46	16	|	|	NOUN
ejpam-2366	46	17	xb	xb	PROPN
ejpam-2366	46	18	6	6	NUM
ejpam-2366	46	19	a	a	X
ejpam-2366	46	20	}	}	PUNCT
ejpam-2366	46	21	.	.	PUNCT
ejpam-2366	47	1	if	if	SCONJ
ejpam-2366	47	2	(	(	PUNCT
ejpam-2366	47	3	om	om	NOUN
ejpam-2366	47	4	:	:	PUNCT
ejpam-2366	47	5	i	i	PRON
ejpam-2366	47	6	m	m	VERB
ejpam-2366	47	7	)	)	PUNCT
ejpam-2366	48	1	=	=	SYM
ejpam-2366	48	2	0	0	NUM
ejpam-2366	48	3	,	,	PUNCT
ejpam-2366	48	4	then	then	ADV
ejpam-2366	48	5	m	m	VERB
ejpam-2366	48	6	is	be	AUX
ejpam-2366	48	7	called	call	VERB
ejpam-2366	48	8	a	a	DET
ejpam-2366	48	9	faithful	faithful	ADJ
ejpam-2366	48	10	l	l	NOUN
ejpam-2366	48	11	-	-	NOUN
ejpam-2366	48	12	module	module	NOUN
ejpam-2366	48	13	.	.	PUNCT
ejpam-2366	49	1	m	m	PROPN
ejpam-2366	49	2	is	be	AUX
ejpam-2366	49	3	called	call	VERB
ejpam-2366	49	4	a	a	DET
ejpam-2366	49	5	torsion	torsion	NOUN
ejpam-2366	49	6	free	free	ADJ
ejpam-2366	49	7	l	l	NOUN
ejpam-2366	49	8	-	-	NOUN
ejpam-2366	49	9	module	module	NOUN
ejpam-2366	49	10	if	if	SCONJ
ejpam-2366	49	11	for	for	ADP
ejpam-2366	49	12	all	all	DET
ejpam-2366	49	13	c	c	NOUN
ejpam-2366	49	14	∈	∈	PROPN
ejpam-2366	49	15	l	l	NOUN
ejpam-2366	49	16	,	,	PUNCT
ejpam-2366	49	17	b	b	PRON
ejpam-2366	49	18	∈m	∈m	NOUN
ejpam-2366	49	19	,	,	PUNCT
ejpam-2366	49	20	cb	cb	PROPN
ejpam-2366	49	21	=	=	SYM
ejpam-2366	49	22	om	om	PROPN
ejpam-2366	49	23	implies	imply	VERB
ejpam-2366	49	24	either	either	CCONJ
ejpam-2366	49	25	b	b	X
ejpam-2366	49	26	=	=	SYM
ejpam-2366	49	27	om	om	PROPN
ejpam-2366	49	28	or	or	CCONJ
ejpam-2366	49	29	c	c	NOUN
ejpam-2366	49	30	=	=	SYM
ejpam-2366	49	31	0	0	PROPN
ejpam-2366	49	32	.	.	PUNCT
ejpam-2366	50	1	an	an	DET
ejpam-2366	50	2	l	l	NOUN
ejpam-2366	50	3	-	-	NOUN
ejpam-2366	50	4	module	module	NOUN
ejpam-2366	50	5	m	m	NOUN
ejpam-2366	50	6	is	be	AUX
ejpam-2366	50	7	called	call	VERB
ejpam-2366	50	8	a	a	DET
ejpam-2366	50	9	multiplication	multiplication	NOUN
ejpam-2366	50	10	lattice	lattice	NOUN
ejpam-2366	50	11	module	module	NOUN
ejpam-2366	50	12	if	if	SCONJ
ejpam-2366	50	13	for	for	ADP
ejpam-2366	50	14	a.	a.	NOUN
ejpam-2366	50	15	v.	v.	PROPN
ejpam-2366	50	16	bingi	bingi	PROPN
ejpam-2366	50	17	,	,	PUNCT
ejpam-2366	50	18	c.	c.	PROPN
ejpam-2366	50	19	s.	s.	PROPN
ejpam-2366	50	20	manjarekar	manjarekar	PROPN
ejpam-2366	50	21	/	/	PROPN
ejpam-2366	50	22	eur	eur	PROPN
ejpam-2366	50	23	.	.	PUNCT
ejpam-2366	51	1	j.	j.	PROPN
ejpam-2366	51	2	pure	pure	PROPN
ejpam-2366	51	3	appl	appl	PROPN
ejpam-2366	51	4	.	.	PROPN
ejpam-2366	51	5	math	math	PROPN
ejpam-2366	51	6	,	,	PUNCT
ejpam-2366	51	7	14	14	NUM
ejpam-2366	51	8	(	(	PUNCT
ejpam-2366	51	9	2	2	NUM
ejpam-2366	51	10	)	)	PUNCT
ejpam-2366	51	11	(	(	PUNCT
ejpam-2366	51	12	2021	2021	NUM
ejpam-2366	51	13	)	)	PUNCT
ejpam-2366	51	14	,	,	PUNCT
ejpam-2366	51	15	551	551	NUM
ejpam-2366	51	16	-	-	SYM
ejpam-2366	51	17	577	577	NUM
ejpam-2366	51	18	553	553	NUM
ejpam-2366	51	19	every	every	DET
ejpam-2366	51	20	element	element	NOUN
ejpam-2366	51	21	n	n	PRON
ejpam-2366	51	22	∈	∈	NOUN
ejpam-2366	51	23	m	m	VERB
ejpam-2366	51	24	there	there	PRON
ejpam-2366	51	25	exists	exist	VERB
ejpam-2366	51	26	an	an	DET
ejpam-2366	51	27	element	element	NOUN
ejpam-2366	51	28	a	a	DET
ejpam-2366	51	29	∈	∈	NOUN
ejpam-2366	51	30	l	l	NOUN
ejpam-2366	51	31	such	such	ADJ
ejpam-2366	51	32	that	that	SCONJ
ejpam-2366	51	33	n	n	NOUN
ejpam-2366	51	34	=	=	NOUN
ejpam-2366	51	35	aim	aim	NOUN
ejpam-2366	51	36	.	.	PUNCT
ejpam-2366	52	1	by	by	ADP
ejpam-2366	52	2	proposition	proposition	NOUN
ejpam-2366	52	3	3	3	NUM
ejpam-2366	52	4	in	in	ADP
ejpam-2366	52	5	[	[	X
ejpam-2366	52	6	10	10	NUM
ejpam-2366	52	7	]	]	PUNCT
ejpam-2366	52	8	,	,	PUNCT
ejpam-2366	52	9	an	an	DET
ejpam-2366	52	10	l	l	NOUN
ejpam-2366	52	11	-	-	NOUN
ejpam-2366	52	12	module	module	NOUN
ejpam-2366	52	13	m	m	NOUN
ejpam-2366	52	14	is	be	AUX
ejpam-2366	52	15	a	a	DET
ejpam-2366	52	16	multiplication	multiplication	NOUN
ejpam-2366	52	17	lattice	lattice	NOUN
ejpam-2366	52	18	module	module	NOUN
ejpam-2366	52	19	if	if	SCONJ
ejpam-2366	52	20	and	and	CCONJ
ejpam-2366	52	21	only	only	ADV
ejpam-2366	52	22	if	if	SCONJ
ejpam-2366	52	23	n	n	ADV
ejpam-2366	52	24	=	=	SYM
ejpam-2366	52	25	(	(	PUNCT
ejpam-2366	52	26	n	n	X
ejpam-2366	52	27	:	:	PUNCT
ejpam-2366	52	28	i	i	PRON
ejpam-2366	52	29	m	m	VERB
ejpam-2366	52	30	)	)	PUNCT
ejpam-2366	53	1	i	i	PRON
ejpam-2366	53	2	m	m	VERB
ejpam-2366	53	3	∀n	∀n	NUM
ejpam-2366	53	4	∈m	∈m	NOUN
ejpam-2366	53	5	.	.	PUNCT
ejpam-2366	54	1	an	an	DET
ejpam-2366	54	2	element	element	NOUN
ejpam-2366	54	3	n	n	PRON
ejpam-2366	54	4	∈m	∈m	NOUN
ejpam-2366	54	5	is	be	AUX
ejpam-2366	54	6	called	call	VERB
ejpam-2366	54	7	meet	meet	ADJ
ejpam-2366	54	8	principal	principal	NOUN
ejpam-2366	54	9	if	if	SCONJ
ejpam-2366	54	10	(	(	PUNCT
ejpam-2366	54	11	b	b	PROPN
ejpam-2366	54	12	∧	∧	PROPN
ejpam-2366	54	13	(	(	PUNCT
ejpam-2366	54	14	b	b	NOUN
ejpam-2366	54	15	:	:	PUNCT
ejpam-2366	54	16	n))n	n))n	PROPN
ejpam-2366	54	17	=	=	PUNCT
ejpam-2366	54	18	bn	bn	PROPN
ejpam-2366	54	19	∧b	∧b	NOUN
ejpam-2366	54	20	for	for	ADP
ejpam-2366	54	21	all	all	DET
ejpam-2366	54	22	b	b	PROPN
ejpam-2366	54	23	∈	∈	PROPN
ejpam-2366	54	24	l	l	NOUN
ejpam-2366	54	25	,	,	PUNCT
ejpam-2366	54	26	b	b	DET
ejpam-2366	54	27	∈m	∈m	NOUN
ejpam-2366	54	28	.	.	PUNCT
ejpam-2366	55	1	an	an	DET
ejpam-2366	55	2	element	element	NOUN
ejpam-2366	55	3	n	n	PRON
ejpam-2366	55	4	∈m	∈m	NOUN
ejpam-2366	55	5	is	be	AUX
ejpam-2366	55	6	called	call	VERB
ejpam-2366	55	7	join	join	NOUN
ejpam-2366	55	8	principal	principal	NOUN
ejpam-2366	55	9	if	if	SCONJ
ejpam-2366	55	10	b	b	PROPN
ejpam-2366	55	11	∨	∨	X
ejpam-2366	55	12	(	(	PUNCT
ejpam-2366	55	13	b	b	NOUN
ejpam-2366	55	14	:	:	PUNCT
ejpam-2366	55	15	n	n	CCONJ
ejpam-2366	55	16	)	)	PUNCT
ejpam-2366	55	17	=	=	SYM
ejpam-2366	56	1	(	(	PUNCT
ejpam-2366	56	2	(	(	PUNCT
ejpam-2366	56	3	bn	bn	NUM
ejpam-2366	56	4	∨b	∨b	PROPN
ejpam-2366	56	5	)	)	PUNCT
ejpam-2366	56	6	:	:	PUNCT
ejpam-2366	57	1	n	n	CCONJ
ejpam-2366	57	2	)	)	PUNCT
ejpam-2366	57	3	for	for	ADP
ejpam-2366	57	4	all	all	DET
ejpam-2366	57	5	b	b	PROPN
ejpam-2366	57	6	∈	∈	PROPN
ejpam-2366	57	7	l	l	NOUN
ejpam-2366	57	8	,	,	PUNCT
ejpam-2366	57	9	b	b	DET
ejpam-2366	57	10	∈m	∈m	NOUN
ejpam-2366	57	11	.	.	PUNCT
ejpam-2366	58	1	an	an	DET
ejpam-2366	58	2	element	element	NOUN
ejpam-2366	58	3	n	n	PRON
ejpam-2366	58	4	∈m	∈m	NOUN
ejpam-2366	58	5	is	be	AUX
ejpam-2366	58	6	said	say	VERB
ejpam-2366	58	7	to	to	PART
ejpam-2366	58	8	be	be	AUX
ejpam-2366	58	9	principal	principal	ADJ
ejpam-2366	58	10	if	if	SCONJ
ejpam-2366	58	11	n	n	NOUN
ejpam-2366	58	12	is	be	AUX
ejpam-2366	58	13	both	both	PRON
ejpam-2366	58	14	meet	meet	VERB
ejpam-2366	58	15	principal	principal	NOUN
ejpam-2366	58	16	and	and	CCONJ
ejpam-2366	58	17	join	join	VERB
ejpam-2366	58	18	principal	principal	NOUN
ejpam-2366	58	19	.	.	PUNCT
ejpam-2366	59	1	m	m	PROPN
ejpam-2366	59	2	is	be	AUX
ejpam-2366	59	3	said	say	VERB
ejpam-2366	59	4	to	to	PART
ejpam-2366	59	5	be	be	AUX
ejpam-2366	59	6	a	a	DET
ejpam-2366	59	7	pg	pg	ADJ
ejpam-2366	59	8	-	-	PUNCT
ejpam-2366	59	9	lattice	lattice	NOUN
ejpam-2366	59	10	l	l	NOUN
ejpam-2366	59	11	-	-	NOUN
ejpam-2366	59	12	module	module	NOUN
ejpam-2366	59	13	if	if	SCONJ
ejpam-2366	59	14	each	each	DET
ejpam-2366	59	15	element	element	NOUN
ejpam-2366	59	16	of	of	ADP
ejpam-2366	59	17	m	m	PROPN
ejpam-2366	59	18	is	be	AUX
ejpam-2366	59	19	a	a	DET
ejpam-2366	59	20	join	join	NOUN
ejpam-2366	59	21	of	of	ADP
ejpam-2366	59	22	principal	principal	ADJ
ejpam-2366	59	23	elements	element	NOUN
ejpam-2366	59	24	of	of	ADP
ejpam-2366	59	25	m	m	PROPN
ejpam-2366	59	26	.	.	PUNCT
ejpam-2366	60	1	an	an	DET
ejpam-2366	60	2	element	element	NOUN
ejpam-2366	60	3	n	n	CCONJ
ejpam-2366	60	4	∈	∈	NOUN
ejpam-2366	60	5	m	m	VERB
ejpam-2366	60	6	is	be	AUX
ejpam-2366	60	7	called	call	VERB
ejpam-2366	60	8	compact	compact	ADJ
ejpam-2366	60	9	if	if	SCONJ
ejpam-2366	60	10	n	n	PROPN
ejpam-2366	60	11	6	6	NUM
ejpam-2366	60	12	∨	∨	NUM
ejpam-2366	60	13	α	α	DET
ejpam-2366	60	14	aα	aα	NOUN
ejpam-2366	60	15	implies	imply	VERB
ejpam-2366	60	16	n	n	ADV
ejpam-2366	60	17	6	6	NUM
ejpam-2366	60	18	aα1	aα1	NOUN
ejpam-2366	60	19	∨	∨	NUM
ejpam-2366	60	20	aα2	aα2	PROPN
ejpam-2366	60	21	∨	∨	NUM
ejpam-2366	60	22	·	·	PUNCT
ejpam-2366	60	23	·	·	PUNCT
ejpam-2366	60	24	·	·	PUNCT
ejpam-2366	61	1	∨	∨	NUM
ejpam-2366	61	2	aαn	aαn	VERB
ejpam-2366	61	3	for	for	ADP
ejpam-2366	61	4	some	some	DET
ejpam-2366	61	5	finite	finite	NOUN
ejpam-2366	61	6	subset	subset	NOUN
ejpam-2366	61	7	{	{	PUNCT
ejpam-2366	61	8	α1	α1	PROPN
ejpam-2366	61	9	,	,	PUNCT
ejpam-2366	61	10	α2	α2	ADJ
ejpam-2366	61	11	,	,	PUNCT
ejpam-2366	61	12	·	·	PUNCT
ejpam-2366	61	13	·	·	PUNCT
ejpam-2366	61	14	·	·	PUNCT
ejpam-2366	61	15	,	,	PUNCT
ejpam-2366	61	16	αn	αn	NOUN
ejpam-2366	61	17	}	}	PUNCT
ejpam-2366	61	18	.	.	PUNCT
ejpam-2366	62	1	the	the	DET
ejpam-2366	62	2	set	set	NOUN
ejpam-2366	62	3	of	of	ADP
ejpam-2366	62	4	compact	compact	ADJ
ejpam-2366	62	5	elements	element	NOUN
ejpam-2366	62	6	of	of	ADP
ejpam-2366	62	7	m	m	PROPN
ejpam-2366	62	8	is	be	AUX
ejpam-2366	62	9	denoted	denote	VERB
ejpam-2366	62	10	by	by	ADP
ejpam-2366	62	11	m∗.	m∗.	PROPN
ejpam-2366	62	12	if	if	SCONJ
ejpam-2366	62	13	each	each	DET
ejpam-2366	62	14	element	element	NOUN
ejpam-2366	62	15	of	of	ADP
ejpam-2366	62	16	m	m	PROPN
ejpam-2366	62	17	is	be	AUX
ejpam-2366	62	18	a	a	DET
ejpam-2366	62	19	join	join	NOUN
ejpam-2366	62	20	of	of	ADP
ejpam-2366	62	21	compact	compact	ADJ
ejpam-2366	62	22	elements	element	NOUN
ejpam-2366	62	23	of	of	ADP
ejpam-2366	62	24	m	m	PROPN
ejpam-2366	62	25	,	,	PUNCT
ejpam-2366	62	26	then	then	ADV
ejpam-2366	62	27	m	m	VERB
ejpam-2366	62	28	is	be	AUX
ejpam-2366	62	29	called	call	VERB
ejpam-2366	62	30	a	a	DET
ejpam-2366	62	31	cg	cg	NOUN
ejpam-2366	62	32	-	-	PUNCT
ejpam-2366	62	33	lattice	lattice	NOUN
ejpam-2366	62	34	l	l	NOUN
ejpam-2366	62	35	-	-	NOUN
ejpam-2366	62	36	module	module	NOUN
ejpam-2366	62	37	.	.	PUNCT
ejpam-2366	63	1	an	an	DET
ejpam-2366	63	2	element	element	NOUN
ejpam-2366	63	3	n	n	CCONJ
ejpam-2366	63	4	∈	∈	NOUN
ejpam-2366	63	5	m	m	VERB
ejpam-2366	63	6	is	be	AUX
ejpam-2366	63	7	said	say	VERB
ejpam-2366	63	8	to	to	PART
ejpam-2366	63	9	be	be	AUX
ejpam-2366	63	10	proper	proper	ADJ
ejpam-2366	63	11	if	if	SCONJ
ejpam-2366	63	12	n	n	NOUN
ejpam-2366	63	13	<	<	X
ejpam-2366	63	14	i	i	X
ejpam-2366	63	15	m	m	PROPN
ejpam-2366	63	16	.	.	PUNCT
ejpam-2366	64	1	a	a	DET
ejpam-2366	64	2	proper	proper	ADJ
ejpam-2366	64	3	element	element	NOUN
ejpam-2366	64	4	n	n	PRON
ejpam-2366	64	5	∈	∈	NOUN
ejpam-2366	64	6	m	m	VERB
ejpam-2366	64	7	is	be	AUX
ejpam-2366	64	8	said	say	VERB
ejpam-2366	64	9	to	to	PART
ejpam-2366	64	10	be	be	AUX
ejpam-2366	64	11	maximal	maximal	ADJ
ejpam-2366	64	12	if	if	SCONJ
ejpam-2366	64	13	whenever	whenever	SCONJ
ejpam-2366	64	14	there	there	PRON
ejpam-2366	64	15	exists	exist	VERB
ejpam-2366	64	16	an	an	DET
ejpam-2366	64	17	element	element	NOUN
ejpam-2366	64	18	b	b	PROPN
ejpam-2366	64	19	∈	∈	NOUN
ejpam-2366	64	20	m	m	VERB
ejpam-2366	64	21	such	such	ADJ
ejpam-2366	64	22	that	that	SCONJ
ejpam-2366	64	23	n	n	PROPN
ejpam-2366	64	24	6	6	NUM
ejpam-2366	64	25	b	b	NOUN
ejpam-2366	64	26	then	then	ADV
ejpam-2366	64	27	either	either	CCONJ
ejpam-2366	64	28	n	n	PROPN
ejpam-2366	64	29	=	=	SYM
ejpam-2366	64	30	b	b	PROPN
ejpam-2366	64	31	or	or	CCONJ
ejpam-2366	64	32	b	b	X
ejpam-2366	64	33	=	=	SYM
ejpam-2366	65	1	i	i	PRON
ejpam-2366	65	2	m	m	VERB
ejpam-2366	65	3	.	.	PUNCT
ejpam-2366	66	1	if	if	SCONJ
ejpam-2366	66	2	a	a	DET
ejpam-2366	66	3	proper	proper	ADJ
ejpam-2366	66	4	element	element	NOUN
ejpam-2366	66	5	n	n	CCONJ
ejpam-2366	66	6	∈	∈	NOUN
ejpam-2366	66	7	m	m	VERB
ejpam-2366	66	8	is	be	AUX
ejpam-2366	66	9	prime	prime	ADJ
ejpam-2366	66	10	,	,	PUNCT
ejpam-2366	66	11	then	then	ADV
ejpam-2366	66	12	(	(	PUNCT
ejpam-2366	66	13	n	n	X
ejpam-2366	66	14	:	:	PUNCT
ejpam-2366	67	1	i	i	PRON
ejpam-2366	67	2	m	m	VERB
ejpam-2366	67	3	)	)	PUNCT
ejpam-2366	68	1	∈	∈	PROPN
ejpam-2366	68	2	l	l	NOUN
ejpam-2366	68	3	is	be	AUX
ejpam-2366	68	4	prime	prime	ADJ
ejpam-2366	68	5	.	.	PUNCT
ejpam-2366	69	1	if	if	SCONJ
ejpam-2366	69	2	a	a	DET
ejpam-2366	69	3	proper	proper	ADJ
ejpam-2366	69	4	element	element	NOUN
ejpam-2366	69	5	n	n	CCONJ
ejpam-2366	69	6	∈	∈	NOUN
ejpam-2366	69	7	m	m	VERB
ejpam-2366	69	8	is	be	AUX
ejpam-2366	69	9	primary	primary	ADJ
ejpam-2366	69	10	,	,	PUNCT
ejpam-2366	69	11	then	then	ADV
ejpam-2366	69	12	√	√	VERB
ejpam-2366	69	13	n	n	NOUN
ejpam-2366	69	14	:	:	PUNCT
ejpam-2366	69	15	i	i	PRON
ejpam-2366	69	16	m	m	PROPN
ejpam-2366	69	17	∈	∈	NOUN
ejpam-2366	69	18	l	l	NOUN
ejpam-2366	69	19	is	be	AUX
ejpam-2366	69	20	prime	prime	ADJ
ejpam-2366	69	21	.	.	PUNCT
ejpam-2366	70	1	a	a	DET
ejpam-2366	70	2	proper	proper	ADJ
ejpam-2366	70	3	element	element	NOUN
ejpam-2366	70	4	n	n	PRON
ejpam-2366	70	5	∈	∈	NOUN
ejpam-2366	70	6	m	m	VERB
ejpam-2366	70	7	is	be	AUX
ejpam-2366	70	8	said	say	VERB
ejpam-2366	70	9	to	to	PART
ejpam-2366	70	10	be	be	AUX
ejpam-2366	70	11	a	a	DET
ejpam-2366	70	12	radical	radical	ADJ
ejpam-2366	70	13	element	element	NOUN
ejpam-2366	70	14	if	if	SCONJ
ejpam-2366	70	15	(	(	PUNCT
ejpam-2366	70	16	n	n	X
ejpam-2366	70	17	:	:	PUNCT
ejpam-2366	70	18	i	i	PRON
ejpam-2366	70	19	m	m	VERB
ejpam-2366	70	20	)	)	PUNCT
ejpam-2366	71	1	=	=	SYM
ejpam-2366	71	2	√	√	PROPN
ejpam-2366	72	1	n	n	NOUN
ejpam-2366	72	2	:	:	PUNCT
ejpam-2366	72	3	i	i	PRON
ejpam-2366	72	4	m	m	VERB
ejpam-2366	72	5	.	.	PUNCT
ejpam-2366	73	1	an	an	DET
ejpam-2366	73	2	l	l	NOUN
ejpam-2366	73	3	-	-	NOUN
ejpam-2366	73	4	module	module	NOUN
ejpam-2366	73	5	m	m	NOUN
ejpam-2366	73	6	is	be	AUX
ejpam-2366	73	7	said	say	VERB
ejpam-2366	73	8	to	to	PART
ejpam-2366	73	9	be	be	AUX
ejpam-2366	73	10	noetherian	noetherian	ADJ
ejpam-2366	73	11	,	,	PUNCT
ejpam-2366	73	12	if	if	SCONJ
ejpam-2366	73	13	m	m	NOUN
ejpam-2366	73	14	satisfies	satisfy	VERB
ejpam-2366	73	15	the	the	DET
ejpam-2366	73	16	ascending	ascend	VERB
ejpam-2366	73	17	chain	chain	NOUN
ejpam-2366	73	18	condition	condition	NOUN
ejpam-2366	73	19	,	,	PUNCT
ejpam-2366	73	20	is	be	AUX
ejpam-2366	73	21	modular	modular	ADJ
ejpam-2366	73	22	and	and	CCONJ
ejpam-2366	73	23	is	be	AUX
ejpam-2366	73	24	principally	principally	ADV
ejpam-2366	73	25	generated	generate	VERB
ejpam-2366	73	26	.	.	PUNCT
ejpam-2366	74	1	according	accord	VERB
ejpam-2366	74	2	to	to	ADP
ejpam-2366	74	3	[	[	X
ejpam-2366	74	4	17	17	NUM
ejpam-2366	74	5	]	]	PUNCT
ejpam-2366	74	6	,	,	PUNCT
ejpam-2366	74	7	a	a	DET
ejpam-2366	74	8	proper	proper	ADJ
ejpam-2366	74	9	element	element	NOUN
ejpam-2366	74	10	q	q	NOUN
ejpam-2366	74	11	of	of	ADP
ejpam-2366	74	12	an	an	DET
ejpam-2366	74	13	l	l	NOUN
ejpam-2366	74	14	-	-	NOUN
ejpam-2366	74	15	module	module	NOUN
ejpam-2366	74	16	m	m	NOUN
ejpam-2366	74	17	is	be	AUX
ejpam-2366	74	18	said	say	VERB
ejpam-2366	74	19	to	to	PART
ejpam-2366	74	20	be	be	AUX
ejpam-2366	74	21	2	2	NUM
ejpam-2366	74	22	-	-	ADJ
ejpam-2366	74	23	absorbing	absorb	VERB
ejpam-2366	74	24	if	if	SCONJ
ejpam-2366	74	25	for	for	ADP
ejpam-2366	74	26	all	all	DET
ejpam-2366	74	27	a	a	DET
ejpam-2366	74	28	,	,	PUNCT
ejpam-2366	74	29	b	b	PROPN
ejpam-2366	74	30	∈	∈	PROPN
ejpam-2366	74	31	l	l	NOUN
ejpam-2366	74	32	,	,	PUNCT
ejpam-2366	74	33	n	n	PROPN
ejpam-2366	74	34	∈	∈	NOUN
ejpam-2366	74	35	m	m	NOUN
ejpam-2366	74	36	,	,	PUNCT
ejpam-2366	74	37	abn	abn	PROPN
ejpam-2366	74	38	6	6	NUM
ejpam-2366	74	39	q	q	NOUN
ejpam-2366	74	40	implies	imply	VERB
ejpam-2366	74	41	either	either	CCONJ
ejpam-2366	74	42	ab	ab	PROPN
ejpam-2366	74	43	6	6	NUM
ejpam-2366	74	44	(	(	PUNCT
ejpam-2366	74	45	q	q	NOUN
ejpam-2366	74	46	:	:	PUNCT
ejpam-2366	74	47	i	i	PRON
ejpam-2366	74	48	m	m	VERB
ejpam-2366	74	49	)	)	PUNCT
ejpam-2366	74	50	or	or	CCONJ
ejpam-2366	74	51	bn	bn	NUM
ejpam-2366	74	52	6	6	NUM
ejpam-2366	74	53	q	q	NOUN
ejpam-2366	74	54	or	or	CCONJ
ejpam-2366	74	55	an	an	DET
ejpam-2366	74	56	6	6	NUM
ejpam-2366	74	57	q.	q.	NOUN
ejpam-2366	74	58	according	accord	VERB
ejpam-2366	74	59	to	to	ADP
ejpam-2366	74	60	[	[	X
ejpam-2366	74	61	6	6	NUM
ejpam-2366	74	62	]	]	PUNCT
ejpam-2366	74	63	,	,	PUNCT
ejpam-2366	74	64	a	a	DET
ejpam-2366	74	65	proper	proper	ADJ
ejpam-2366	74	66	element	element	NOUN
ejpam-2366	74	67	q	q	NOUN
ejpam-2366	74	68	of	of	ADP
ejpam-2366	74	69	an	an	DET
ejpam-2366	74	70	l	l	NOUN
ejpam-2366	74	71	-	-	NOUN
ejpam-2366	74	72	module	module	NOUN
ejpam-2366	74	73	m	m	NOUN
ejpam-2366	74	74	is	be	AUX
ejpam-2366	74	75	said	say	VERB
ejpam-2366	74	76	to	to	PART
ejpam-2366	74	77	be	be	AUX
ejpam-2366	74	78	2	2	NUM
ejpam-2366	74	79	-	-	PUNCT
ejpam-2366	74	80	absorbing	absorb	VERB
ejpam-2366	74	81	primary	primary	NOUN
ejpam-2366	74	82	if	if	SCONJ
ejpam-2366	74	83	for	for	ADP
ejpam-2366	74	84	all	all	DET
ejpam-2366	74	85	a	a	DET
ejpam-2366	74	86	,	,	PUNCT
ejpam-2366	74	87	b	b	PROPN
ejpam-2366	74	88	∈	∈	PROPN
ejpam-2366	74	89	l	l	NOUN
ejpam-2366	74	90	,	,	PUNCT
ejpam-2366	74	91	n	n	PRON
ejpam-2366	74	92	∈m	∈m	NOUN
ejpam-2366	74	93	,	,	PUNCT
ejpam-2366	74	94	abn	abn	PROPN
ejpam-2366	74	95	6	6	NUM
ejpam-2366	74	96	q	q	NOUN
ejpam-2366	74	97	implies	imply	VERB
ejpam-2366	74	98	either	either	CCONJ
ejpam-2366	74	99	ab	ab	PROPN
ejpam-2366	74	100	6	6	NUM
ejpam-2366	74	101	(	(	PUNCT
ejpam-2366	74	102	q	q	NOUN
ejpam-2366	74	103	:	:	PUNCT
ejpam-2366	74	104	i	i	PRON
ejpam-2366	74	105	m	m	VERB
ejpam-2366	74	106	)	)	PUNCT
ejpam-2366	74	107	or	or	CCONJ
ejpam-2366	74	108	bn	bn	NUM
ejpam-2366	74	109	6	6	NUM
ejpam-2366	74	110	(	(	PUNCT
ejpam-2366	74	111	√	√	INTJ
ejpam-2366	74	112	q	q	NOUN
ejpam-2366	74	113	:	:	PUNCT
ejpam-2366	74	114	i	i	PRON
ejpam-2366	74	115	m	m	VERB
ejpam-2366	74	116	)	)	PUNCT
ejpam-2366	74	117	i	i	PRON
ejpam-2366	74	118	m	m	VERB
ejpam-2366	74	119	or	or	CCONJ
ejpam-2366	74	120	an	an	DET
ejpam-2366	74	121	6	6	NUM
ejpam-2366	74	122	(	(	PUNCT
ejpam-2366	74	123	√	√	INTJ
ejpam-2366	74	124	q	q	NOUN
ejpam-2366	74	125	:	:	PUNCT
ejpam-2366	74	126	i	i	PRON
ejpam-2366	74	127	m	m	VERB
ejpam-2366	74	128	)	)	PUNCT
ejpam-2366	74	129	i	i	PRON
ejpam-2366	74	130	m	m	VERB
ejpam-2366	74	131	.	.	PUNCT
ejpam-2366	75	1	the	the	DET
ejpam-2366	75	2	reader	reader	NOUN
ejpam-2366	75	3	is	be	AUX
ejpam-2366	75	4	referred	refer	VERB
ejpam-2366	75	5	to	to	ADP
ejpam-2366	75	6	[	[	X
ejpam-2366	75	7	1	1	NUM
ejpam-2366	75	8	]	]	PUNCT
ejpam-2366	75	9	,	,	PUNCT
ejpam-2366	75	10	[	[	X
ejpam-2366	75	11	10	10	NUM
ejpam-2366	75	12	]	]	PUNCT
ejpam-2366	75	13	and	and	CCONJ
ejpam-2366	75	14	[	[	X
ejpam-2366	75	15	14	14	NUM
ejpam-2366	75	16	]	]	PUNCT
ejpam-2366	75	17	for	for	ADP
ejpam-2366	75	18	terminology	terminology	NOUN
ejpam-2366	75	19	in	in	ADP
ejpam-2366	75	20	lattice	lattice	NOUN
ejpam-2366	75	21	modules	module	NOUN
ejpam-2366	75	22	.	.	PUNCT
ejpam-2366	76	1	this	this	DET
ejpam-2366	76	2	paper	paper	NOUN
ejpam-2366	76	3	is	be	AUX
ejpam-2366	76	4	motivated	motivate	VERB
ejpam-2366	76	5	by	by	ADP
ejpam-2366	76	6	[	[	X
ejpam-2366	76	7	24	24	NUM
ejpam-2366	76	8	]	]	PUNCT
ejpam-2366	76	9	and	and	CCONJ
ejpam-2366	76	10	[	[	X
ejpam-2366	76	11	7	7	NUM
ejpam-2366	76	12	]	]	PUNCT
ejpam-2366	76	13	.	.	PUNCT
ejpam-2366	77	1	many	many	ADJ
ejpam-2366	77	2	of	of	ADP
ejpam-2366	77	3	the	the	DET
ejpam-2366	77	4	results	result	NOUN
ejpam-2366	77	5	obtained	obtain	VERB
ejpam-2366	77	6	in	in	ADP
ejpam-2366	77	7	this	this	DET
ejpam-2366	77	8	paper	paper	NOUN
ejpam-2366	77	9	are	be	AUX
ejpam-2366	77	10	lattice	lattice	NOUN
ejpam-2366	77	11	module	module	NOUN
ejpam-2366	77	12	version	version	NOUN
ejpam-2366	77	13	of	of	ADP
ejpam-2366	77	14	the	the	DET
ejpam-2366	77	15	results	result	NOUN
ejpam-2366	77	16	in	in	ADP
ejpam-2366	77	17	[	[	X
ejpam-2366	77	18	16	16	NUM
ejpam-2366	77	19	]	]	PUNCT
ejpam-2366	77	20	and	and	CCONJ
ejpam-2366	77	21	principal	principal	ADJ
ejpam-2366	77	22	elements	element	NOUN
ejpam-2366	77	23	of	of	ADP
ejpam-2366	77	24	m	m	NOUN
ejpam-2366	77	25	are	be	AUX
ejpam-2366	77	26	used	use	VERB
ejpam-2366	77	27	wherever	wherever	SCONJ
ejpam-2366	77	28	needed	need	VERB
ejpam-2366	77	29	with	with	ADP
ejpam-2366	77	30	some	some	DET
ejpam-2366	77	31	more	more	ADJ
ejpam-2366	77	32	conditions	condition	NOUN
ejpam-2366	77	33	on	on	ADP
ejpam-2366	77	34	m	m	PROPN
ejpam-2366	77	35	.	.	PUNCT
ejpam-2366	78	1	first	first	ADJ
ejpam-2366	78	2	section	section	NOUN
ejpam-2366	78	3	of	of	ADP
ejpam-2366	78	4	this	this	DET
ejpam-2366	78	5	paper	paper	NOUN
ejpam-2366	78	6	is	be	AUX
ejpam-2366	78	7	comprised	comprise	VERB
ejpam-2366	78	8	of	of	ADP
ejpam-2366	78	9	φprime	φprime	NOUN
ejpam-2366	78	10	and	and	CCONJ
ejpam-2366	78	11	φ	φ	VERB
ejpam-2366	78	12	-	-	ADJ
ejpam-2366	78	13	primary	primary	ADJ
ejpam-2366	78	14	elements	element	NOUN
ejpam-2366	78	15	of	of	ADP
ejpam-2366	78	16	an	an	DET
ejpam-2366	78	17	l	l	NOUN
ejpam-2366	78	18	-	-	NOUN
ejpam-2366	78	19	module	module	NOUN
ejpam-2366	78	20	m	m	NOUN
ejpam-2366	78	21	.	.	PUNCT
ejpam-2366	79	1	second	second	ADJ
ejpam-2366	79	2	section	section	NOUN
ejpam-2366	79	3	is	be	AUX
ejpam-2366	79	4	comprised	comprise	VERB
ejpam-2366	79	5	of	of	ADP
ejpam-2366	79	6	almost	almost	ADV
ejpam-2366	79	7	prime	prime	ADJ
ejpam-2366	79	8	and	and	CCONJ
ejpam-2366	79	9	almost	almost	ADV
ejpam-2366	79	10	primary	primary	ADJ
ejpam-2366	79	11	elements	element	NOUN
ejpam-2366	79	12	of	of	ADP
ejpam-2366	79	13	an	an	DET
ejpam-2366	79	14	l	l	NOUN
ejpam-2366	79	15	-	-	NOUN
ejpam-2366	79	16	module	module	NOUN
ejpam-2366	79	17	m	m	NOUN
ejpam-2366	79	18	.	.	PUNCT
ejpam-2366	80	1	by	by	ADP
ejpam-2366	80	2	counter	counter	ADJ
ejpam-2366	80	3	examples	example	NOUN
ejpam-2366	80	4	,	,	PUNCT
ejpam-2366	80	5	it	it	PRON
ejpam-2366	80	6	is	be	AUX
ejpam-2366	80	7	shown	show	VERB
ejpam-2366	80	8	that	that	SCONJ
ejpam-2366	80	9	a	a	DET
ejpam-2366	80	10	φ	φ	VERB
ejpam-2366	80	11	-	-	ADJ
ejpam-2366	80	12	prime	prime	ADJ
ejpam-2366	80	13	element	element	NOUN
ejpam-2366	80	14	of	of	ADP
ejpam-2366	80	15	m	m	PRON
ejpam-2366	80	16	need	need	AUX
ejpam-2366	80	17	not	not	PART
ejpam-2366	80	18	be	be	AUX
ejpam-2366	80	19	prime	prime	ADJ
ejpam-2366	80	20	(	(	PUNCT
ejpam-2366	80	21	see	see	VERB
ejpam-2366	80	22	example	example	NOUN
ejpam-2366	80	23	1	1	NUM
ejpam-2366	80	24	)	)	PUNCT
ejpam-2366	80	25	,	,	PUNCT
ejpam-2366	80	26	a	a	DET
ejpam-2366	80	27	φ	φ	VERB
ejpam-2366	80	28	-	-	ADJ
ejpam-2366	80	29	primary	primary	ADJ
ejpam-2366	80	30	element	element	NOUN
ejpam-2366	80	31	of	of	ADP
ejpam-2366	80	32	m	m	PRON
ejpam-2366	80	33	need	need	AUX
ejpam-2366	80	34	not	not	PART
ejpam-2366	80	35	be	be	AUX
ejpam-2366	80	36	φ	φ	VERB
ejpam-2366	80	37	-	-	ADJ
ejpam-2366	80	38	prime	prime	ADJ
ejpam-2366	80	39	(	(	PUNCT
ejpam-2366	80	40	see	see	VERB
ejpam-2366	80	41	example	example	NOUN
ejpam-2366	80	42	2	2	NUM
ejpam-2366	80	43	)	)	PUNCT
ejpam-2366	80	44	,	,	PUNCT
ejpam-2366	80	45	a	a	DET
ejpam-2366	80	46	φ	φ	VERB
ejpam-2366	80	47	-	-	ADJ
ejpam-2366	80	48	primary	primary	ADJ
ejpam-2366	80	49	element	element	NOUN
ejpam-2366	80	50	of	of	ADP
ejpam-2366	80	51	m	m	PRON
ejpam-2366	80	52	need	need	AUX
ejpam-2366	80	53	not	not	PART
ejpam-2366	80	54	be	be	AUX
ejpam-2366	80	55	prime	prime	ADJ
ejpam-2366	80	56	(	(	PUNCT
ejpam-2366	80	57	see	see	VERB
ejpam-2366	80	58	example	example	NOUN
ejpam-2366	80	59	3	3	NUM
ejpam-2366	80	60	)	)	PUNCT
ejpam-2366	80	61	and	and	CCONJ
ejpam-2366	80	62	a	a	DET
ejpam-2366	80	63	φ	φ	ADJ
ejpam-2366	80	64	-	-	ADJ
ejpam-2366	80	65	primary	primary	ADJ
ejpam-2366	80	66	element	element	NOUN
ejpam-2366	80	67	of	of	ADP
ejpam-2366	80	68	m	m	PRON
ejpam-2366	80	69	need	need	AUX
ejpam-2366	80	70	not	not	PART
ejpam-2366	80	71	be	be	AUX
ejpam-2366	80	72	primary	primary	ADJ
ejpam-2366	80	73	(	(	PUNCT
ejpam-2366	80	74	see	see	VERB
ejpam-2366	80	75	example	example	NOUN
ejpam-2366	80	76	4	4	NUM
ejpam-2366	80	77	)	)	PUNCT
ejpam-2366	80	78	.	.	PUNCT
ejpam-2366	81	1	we	we	PRON
ejpam-2366	81	2	define	define	VERB
ejpam-2366	81	3	2	2	NUM
ejpam-2366	81	4	-	-	PUNCT
ejpam-2366	81	5	potent	potent	ADJ
ejpam-2366	81	6	prime	prime	NOUN
ejpam-2366	81	7	and	and	CCONJ
ejpam-2366	81	8	2	2	NUM
ejpam-2366	81	9	-	-	PUNCT
ejpam-2366	81	10	potent	potent	ADJ
ejpam-2366	81	11	primary	primary	ADJ
ejpam-2366	81	12	elements	element	NOUN
ejpam-2366	81	13	in	in	ADP
ejpam-2366	81	14	an	an	DET
ejpam-2366	81	15	l	l	NOUN
ejpam-2366	81	16	-	-	NOUN
ejpam-2366	81	17	module	module	NOUN
ejpam-2366	81	18	m	m	NOUN
ejpam-2366	81	19	.	.	PUNCT
ejpam-2366	82	1	by	by	ADP
ejpam-2366	82	2	counter	counter	ADJ
ejpam-2366	82	3	examples	example	NOUN
ejpam-2366	82	4	,	,	PUNCT
ejpam-2366	82	5	it	it	PRON
ejpam-2366	82	6	is	be	AUX
ejpam-2366	82	7	shown	show	VERB
ejpam-2366	82	8	that	that	SCONJ
ejpam-2366	82	9	an	an	DET
ejpam-2366	82	10	almost	almost	ADV
ejpam-2366	82	11	primary	primary	ADJ
ejpam-2366	82	12	element	element	NOUN
ejpam-2366	82	13	of	of	ADP
ejpam-2366	82	14	m	m	PRON
ejpam-2366	82	15	need	need	AUX
ejpam-2366	82	16	not	not	PART
ejpam-2366	82	17	be	be	AUX
ejpam-2366	82	18	2	2	NUM
ejpam-2366	82	19	-	-	PUNCT
ejpam-2366	82	20	potent	potent	ADJ
ejpam-2366	82	21	prime	prime	NOUN
ejpam-2366	82	22	(	(	PUNCT
ejpam-2366	82	23	see	see	VERB
ejpam-2366	82	24	example	example	NOUN
ejpam-2366	82	25	5	5	NUM
ejpam-2366	82	26	)	)	PUNCT
ejpam-2366	82	27	and	and	CCONJ
ejpam-2366	82	28	a	a	DET
ejpam-2366	82	29	2	2	NUM
ejpam-2366	82	30	-	-	PUNCT
ejpam-2366	82	31	potent	potent	ADJ
ejpam-2366	82	32	prime	prime	ADJ
ejpam-2366	82	33	element	element	NOUN
ejpam-2366	82	34	of	of	ADP
ejpam-2366	82	35	m	m	PRON
ejpam-2366	82	36	which	which	PRON
ejpam-2366	82	37	is	be	AUX
ejpam-2366	82	38	almost	almost	ADV
ejpam-2366	82	39	primary	primary	ADJ
ejpam-2366	82	40	need	need	NOUN
ejpam-2366	82	41	not	not	PART
ejpam-2366	82	42	be	be	AUX
ejpam-2366	82	43	prime	prime	ADJ
ejpam-2366	82	44	(	(	PUNCT
ejpam-2366	82	45	see	see	VERB
ejpam-2366	82	46	example	example	NOUN
ejpam-2366	82	47	6	6	NUM
ejpam-2366	82	48	)	)	PUNCT
ejpam-2366	82	49	.	.	PUNCT
ejpam-2366	83	1	also	also	ADV
ejpam-2366	83	2	,	,	PUNCT
ejpam-2366	83	3	we	we	PRON
ejpam-2366	83	4	introduce	introduce	VERB
ejpam-2366	83	5	the	the	DET
ejpam-2366	83	6	notions	notion	NOUN
ejpam-2366	83	7	of	of	ADP
ejpam-2366	83	8	n	n	CCONJ
ejpam-2366	83	9	-	-	PUNCT
ejpam-2366	83	10	potent	potent	ADJ
ejpam-2366	83	11	prime	prime	NOUN
ejpam-2366	83	12	and	and	CCONJ
ejpam-2366	83	13	n	n	CCONJ
ejpam-2366	83	14	-	-	PUNCT
ejpam-2366	83	15	potent	potent	ADJ
ejpam-2366	83	16	primary	primary	ADJ
ejpam-2366	83	17	elements	element	NOUN
ejpam-2366	83	18	in	in	ADP
ejpam-2366	83	19	an	an	DET
ejpam-2366	83	20	l	l	NOUN
ejpam-2366	83	21	-	-	NOUN
ejpam-2366	83	22	module	module	NOUN
ejpam-2366	83	23	m	m	NOUN
ejpam-2366	83	24	where	where	SCONJ
ejpam-2366	83	25	n	n	X
ejpam-2366	83	26	>	>	X
ejpam-2366	83	27	2	2	X
ejpam-2366	83	28	.	.	X
ejpam-2366	84	1	we	we	PRON
ejpam-2366	84	2	find	find	VERB
ejpam-2366	84	3	condition(s	condition(s	NOUN
ejpam-2366	84	4	)	)	PUNCT
ejpam-2366	84	5	under	under	ADP
ejpam-2366	84	6	which	which	PRON
ejpam-2366	84	7	a	a	DET
ejpam-2366	84	8	φ	φ	NUM
ejpam-2366	84	9	-	-	ADJ
ejpam-2366	84	10	prime	prime	ADJ
ejpam-2366	84	11	element	element	NOUN
ejpam-2366	84	12	of	of	ADP
ejpam-2366	84	13	m	m	PROPN
ejpam-2366	84	14	is	be	AUX
ejpam-2366	84	15	prime	prime	ADJ
ejpam-2366	84	16	(	(	PUNCT
ejpam-2366	84	17	see	see	VERB
ejpam-2366	84	18	theorems	theorem	NOUN
ejpam-2366	84	19	5	5	NUM
ejpam-2366	84	20	-	-	SYM
ejpam-2366	84	21	10	10	NUM
ejpam-2366	84	22	)	)	PUNCT
ejpam-2366	84	23	.	.	PUNCT
ejpam-2366	85	1	also	also	ADV
ejpam-2366	85	2	,	,	PUNCT
ejpam-2366	85	3	we	we	PRON
ejpam-2366	85	4	find	find	VERB
ejpam-2366	85	5	condition(s	condition(s	NOUN
ejpam-2366	85	6	)	)	PUNCT
ejpam-2366	85	7	under	under	ADP
ejpam-2366	85	8	which	which	PRON
ejpam-2366	85	9	a	a	DET
ejpam-2366	85	10	φ	φ	NUM
ejpam-2366	85	11	-	-	ADJ
ejpam-2366	85	12	primary	primary	ADJ
ejpam-2366	85	13	element	element	NOUN
ejpam-2366	85	14	of	of	ADP
ejpam-2366	85	15	m	m	PROPN
ejpam-2366	85	16	is	be	AUX
ejpam-2366	85	17	primary	primary	ADJ
ejpam-2366	85	18	(	(	PUNCT
ejpam-2366	85	19	see	see	VERB
ejpam-2366	85	20	theorems	theorem	NOUN
ejpam-2366	85	21	15	15	NUM
ejpam-2366	85	22	-	-	SYM
ejpam-2366	85	23	23	23	NUM
ejpam-2366	85	24	)	)	PUNCT
ejpam-2366	85	25	.	.	PUNCT
ejpam-2366	86	1	absorbing	absorb	VERB
ejpam-2366	86	2	concepts	concept	NOUN
ejpam-2366	86	3	in	in	ADP
ejpam-2366	86	4	an	an	DET
ejpam-2366	86	5	l	l	NOUN
ejpam-2366	86	6	-	-	NOUN
ejpam-2366	86	7	module	module	NOUN
ejpam-2366	86	8	m	m	NOUN
ejpam-2366	86	9	are	be	AUX
ejpam-2366	86	10	related	relate	VERB
ejpam-2366	86	11	to	to	ADP
ejpam-2366	86	12	these	these	DET
ejpam-2366	86	13	notions	notion	NOUN
ejpam-2366	86	14	of	of	ADP
ejpam-2366	86	15	φ	φ	PROPN
ejpam-2366	86	16	-	-	NOUN
ejpam-2366	86	17	prime	prime	NOUN
ejpam-2366	86	18	and	and	CCONJ
ejpam-2366	86	19	φ	φ	VERB
ejpam-2366	86	20	-	-	NOUN
ejpam-2366	86	21	primary	primary	NOUN
ejpam-2366	86	22	in	in	ADP
ejpam-2366	86	23	m	m	PROPN
ejpam-2366	86	24	.	.	PUNCT
ejpam-2366	87	1	in	in	ADP
ejpam-2366	87	2	the	the	DET
ejpam-2366	87	3	last	last	ADJ
ejpam-2366	87	4	section	section	NOUN
ejpam-2366	87	5	of	of	ADP
ejpam-2366	87	6	this	this	DET
ejpam-2366	87	7	paper	paper	NOUN
ejpam-2366	87	8	,	,	PUNCT
ejpam-2366	87	9	many	many	ADJ
ejpam-2366	87	10	characterizations	characterization	NOUN
ejpam-2366	87	11	of	of	ADP
ejpam-2366	87	12	almost	almost	ADV
ejpam-2366	87	13	prime	prime	ADJ
ejpam-2366	87	14	and	and	CCONJ
ejpam-2366	87	15	almost	almost	ADV
ejpam-2366	87	16	primary	primary	ADJ
ejpam-2366	87	17	elements	element	NOUN
ejpam-2366	87	18	of	of	ADP
ejpam-2366	87	19	m	m	PROPN
ejpam-2366	87	20	are	be	AUX
ejpam-2366	87	21	obtained	obtain	VERB
ejpam-2366	87	22	.	.	PUNCT
ejpam-2366	88	1	by	by	ADP
ejpam-2366	88	2	a	a	DET
ejpam-2366	88	3	counter	counter	ADJ
ejpam-2366	88	4	example	example	NOUN
ejpam-2366	88	5	,	,	PUNCT
ejpam-2366	88	6	it	it	PRON
ejpam-2366	88	7	is	be	AUX
ejpam-2366	88	8	shown	show	VERB
ejpam-2366	88	9	that	that	SCONJ
ejpam-2366	88	10	an	an	DET
ejpam-2366	88	11	almost	almost	ADV
ejpam-2366	88	12	primary	primary	ADJ
ejpam-2366	88	13	element	element	NOUN
ejpam-2366	88	14	of	of	ADP
ejpam-2366	88	15	m	m	PRON
ejpam-2366	88	16	need	need	AUX
ejpam-2366	88	17	not	not	PART
ejpam-2366	88	18	be	be	AUX
ejpam-2366	88	19	idempotent	idempotent	ADJ
ejpam-2366	88	20	(	(	PUNCT
ejpam-2366	88	21	see	see	VERB
ejpam-2366	88	22	example	example	NOUN
ejpam-2366	88	23	7	7	NUM
ejpam-2366	88	24	)	)	PUNCT
ejpam-2366	88	25	.	.	PUNCT
ejpam-2366	89	1	by	by	ADP
ejpam-2366	89	2	a	a	DET
ejpam-2366	89	3	counter	counter	ADJ
ejpam-2366	89	4	example	example	NOUN
ejpam-2366	89	5	,	,	PUNCT
ejpam-2366	89	6	it	it	PRON
ejpam-2366	89	7	is	be	AUX
ejpam-2366	89	8	shown	show	VERB
ejpam-2366	89	9	that	that	SCONJ
ejpam-2366	89	10	an	an	DET
ejpam-2366	89	11	almost	almost	ADV
ejpam-2366	89	12	primary	primary	ADJ
ejpam-2366	89	13	element	element	NOUN
ejpam-2366	89	14	of	of	ADP
ejpam-2366	89	15	m	m	PRON
ejpam-2366	89	16	need	need	AUX
ejpam-2366	89	17	not	not	PART
ejpam-2366	89	18	be	be	AUX
ejpam-2366	89	19	weakly	weakly	ADV
ejpam-2366	89	20	primary	primary	ADJ
ejpam-2366	89	21	(	(	PUNCT
ejpam-2366	89	22	see	see	VERB
ejpam-2366	89	23	example	example	NOUN
ejpam-2366	89	24	8)	8)	NUM
ejpam-2366	89	25	.	.	PUNCT
ejpam-2366	90	1	finally	finally	ADV
ejpam-2366	90	2	,	,	PUNCT
ejpam-2366	90	3	we	we	PRON
ejpam-2366	90	4	show	show	VERB
ejpam-2366	90	5	that	that	SCONJ
ejpam-2366	90	6	if	if	SCONJ
ejpam-2366	90	7	an	an	DET
ejpam-2366	90	8	element	element	NOUN
ejpam-2366	90	9	in	in	ADP
ejpam-2366	90	10	m	m	PROPN
ejpam-2366	90	11	is	be	AUX
ejpam-2366	90	12	almost	almost	ADV
ejpam-2366	90	13	prime	prime	ADJ
ejpam-2366	90	14	(	(	PUNCT
ejpam-2366	90	15	respectively	respectively	ADV
ejpam-2366	90	16	almost	almost	ADV
ejpam-2366	90	17	primary	primary	ADJ
ejpam-2366	90	18	)	)	PUNCT
ejpam-2366	90	19	,	,	PUNCT
ejpam-2366	90	20	then	then	ADV
ejpam-2366	90	21	its	its	PRON
ejpam-2366	90	22	corresponding	corresponding	ADJ
ejpam-2366	90	23	element	element	NOUN
ejpam-2366	90	24	in	in	ADP
ejpam-2366	90	25	l	l	PROPN
ejpam-2366	90	26	is	be	AUX
ejpam-2366	90	27	also	also	ADV
ejpam-2366	90	28	almost	almost	ADV
ejpam-2366	90	29	prime	prime	ADJ
ejpam-2366	90	30	(	(	PUNCT
ejpam-2366	90	31	respectively	respectively	ADV
ejpam-2366	90	32	almost	almost	ADV
ejpam-2366	90	33	primary	primary	ADJ
ejpam-2366	90	34	)	)	PUNCT
ejpam-2366	90	35	and	and	CCONJ
ejpam-2366	90	36	vice	vice	NOUN
ejpam-2366	90	37	a.	a.	PROPN
ejpam-2366	90	38	v.	v.	PROPN
ejpam-2366	90	39	bingi	bingi	PROPN
ejpam-2366	90	40	,	,	PUNCT
ejpam-2366	90	41	c.	c.	PROPN
ejpam-2366	90	42	s.	s.	PROPN
ejpam-2366	90	43	manjarekar	manjarekar	PROPN
ejpam-2366	90	44	/	/	PROPN
ejpam-2366	90	45	eur	eur	PROPN
ejpam-2366	90	46	.	.	PUNCT
ejpam-2366	91	1	j.	j.	PROPN
ejpam-2366	91	2	pure	pure	PROPN
ejpam-2366	91	3	appl	appl	PROPN
ejpam-2366	91	4	.	.	PROPN
ejpam-2366	91	5	math	math	PROPN
ejpam-2366	91	6	,	,	PUNCT
ejpam-2366	91	7	14	14	NUM
ejpam-2366	91	8	(	(	PUNCT
ejpam-2366	91	9	2	2	NUM
ejpam-2366	91	10	)	)	PUNCT
ejpam-2366	91	11	(	(	PUNCT
ejpam-2366	91	12	2021	2021	NUM
ejpam-2366	91	13	)	)	PUNCT
ejpam-2366	91	14	,	,	PUNCT
ejpam-2366	91	15	551	551	NUM
ejpam-2366	91	16	-	-	SYM
ejpam-2366	91	17	577	577	NUM
ejpam-2366	91	18	554	554	NUM
ejpam-2366	91	19	versa	versa	ADV
ejpam-2366	91	20	.	.	PUNCT
ejpam-2366	92	1	2	2	X
ejpam-2366	92	2	.	.	X
ejpam-2366	92	3	φ	φ	NUM
ejpam-2366	92	4	-	-	NOUN
ejpam-2366	92	5	prime	prime	NOUN
ejpam-2366	92	6	and	and	CCONJ
ejpam-2366	92	7	φ	φ	VERB
ejpam-2366	92	8	-	-	ADJ
ejpam-2366	92	9	primary	primary	ADJ
ejpam-2366	92	10	elements	element	NOUN
ejpam-2366	92	11	in	in	ADP
ejpam-2366	92	12	m	m	DET
ejpam-2366	92	13	the	the	DET
ejpam-2366	92	14	study	study	NOUN
ejpam-2366	92	15	of	of	ADP
ejpam-2366	92	16	weakly	weakly	ADJ
ejpam-2366	92	17	prime	prime	ADJ
ejpam-2366	92	18	and	and	CCONJ
ejpam-2366	92	19	weakly	weakly	ADJ
ejpam-2366	92	20	primary	primary	ADJ
ejpam-2366	92	21	elements	element	NOUN
ejpam-2366	92	22	of	of	ADP
ejpam-2366	92	23	an	an	DET
ejpam-2366	92	24	l	l	NOUN
ejpam-2366	92	25	-	-	NOUN
ejpam-2366	92	26	module	module	NOUN
ejpam-2366	92	27	m	m	NOUN
ejpam-2366	92	28	is	be	AUX
ejpam-2366	92	29	carried	carry	VERB
ejpam-2366	92	30	out	out	ADP
ejpam-2366	92	31	by	by	ADP
ejpam-2366	92	32	a.	a.	PROPN
ejpam-2366	92	33	v.	v.	PROPN
ejpam-2366	92	34	bingi	bingi	PROPN
ejpam-2366	92	35	and	and	CCONJ
ejpam-2366	92	36	c.	c.	PROPN
ejpam-2366	92	37	s.	s.	PROPN
ejpam-2366	92	38	manjarekar	manjarekar	PROPN
ejpam-2366	92	39	in	in	ADP
ejpam-2366	92	40	[	[	X
ejpam-2366	92	41	8	8	NUM
ejpam-2366	92	42	]	]	PUNCT
ejpam-2366	92	43	.	.	PUNCT
ejpam-2366	93	1	also	also	ADV
ejpam-2366	93	2	,	,	PUNCT
ejpam-2366	93	3	the	the	DET
ejpam-2366	93	4	notion	notion	NOUN
ejpam-2366	93	5	of	of	ADP
ejpam-2366	93	6	an	an	DET
ejpam-2366	93	7	almost	almost	ADV
ejpam-2366	93	8	prime	prime	ADJ
ejpam-2366	93	9	element	element	NOUN
ejpam-2366	93	10	of	of	ADP
ejpam-2366	93	11	an	an	DET
ejpam-2366	93	12	l	l	NOUN
ejpam-2366	93	13	-	-	NOUN
ejpam-2366	93	14	module	module	NOUN
ejpam-2366	93	15	m	m	NOUN
ejpam-2366	93	16	is	be	AUX
ejpam-2366	93	17	seen	see	VERB
ejpam-2366	93	18	in	in	ADP
ejpam-2366	93	19	[	[	X
ejpam-2366	93	20	22	22	NUM
ejpam-2366	93	21	]	]	PUNCT
ejpam-2366	93	22	.	.	PUNCT
ejpam-2366	94	1	with	with	ADP
ejpam-2366	94	2	weakly	weakly	ADJ
ejpam-2366	94	3	prime	prime	ADJ
ejpam-2366	94	4	elements	element	NOUN
ejpam-2366	94	5	and	and	CCONJ
ejpam-2366	94	6	almost	almost	ADV
ejpam-2366	94	7	prime	prime	ADJ
ejpam-2366	94	8	elements	element	NOUN
ejpam-2366	94	9	of	of	ADP
ejpam-2366	94	10	an	an	DET
ejpam-2366	94	11	l	l	NOUN
ejpam-2366	94	12	-	-	NOUN
ejpam-2366	94	13	module	module	NOUN
ejpam-2366	94	14	m	m	NOUN
ejpam-2366	94	15	in	in	ADP
ejpam-2366	94	16	mind	mind	NOUN
ejpam-2366	94	17	,	,	PUNCT
ejpam-2366	94	18	we	we	PRON
ejpam-2366	94	19	begin	begin	VERB
ejpam-2366	94	20	with	with	ADP
ejpam-2366	94	21	introducing	introduce	VERB
ejpam-2366	94	22	the	the	DET
ejpam-2366	94	23	notion	notion	NOUN
ejpam-2366	94	24	of	of	ADP
ejpam-2366	94	25	a	a	DET
ejpam-2366	94	26	φ	φ	ADJ
ejpam-2366	94	27	-	-	ADJ
ejpam-2366	94	28	prime	prime	ADJ
ejpam-2366	94	29	element	element	NOUN
ejpam-2366	94	30	of	of	ADP
ejpam-2366	94	31	an	an	DET
ejpam-2366	94	32	l	l	NOUN
ejpam-2366	94	33	-	-	NOUN
ejpam-2366	94	34	module	module	NOUN
ejpam-2366	94	35	m	m	NOUN
ejpam-2366	94	36	.	.	PUNCT
ejpam-2366	95	1	definition	definition	NOUN
ejpam-2366	95	2	1	1	NUM
ejpam-2366	95	3	.	.	PUNCT
ejpam-2366	96	1	let	let	VERB
ejpam-2366	96	2	φ	φ	NOUN
ejpam-2366	96	3	:	:	PUNCT
ejpam-2366	96	4	m	m	AUX
ejpam-2366	96	5	−→	−→	ADJ
ejpam-2366	96	6	m	m	AUX
ejpam-2366	96	7	be	be	VERB
ejpam-2366	96	8	a	a	DET
ejpam-2366	96	9	function	function	NOUN
ejpam-2366	96	10	on	on	ADP
ejpam-2366	96	11	an	an	DET
ejpam-2366	96	12	l	l	NOUN
ejpam-2366	96	13	-	-	NOUN
ejpam-2366	96	14	module	module	NOUN
ejpam-2366	96	15	m	m	NOUN
ejpam-2366	96	16	.	.	PUNCT
ejpam-2366	97	1	a	a	DET
ejpam-2366	97	2	proper	proper	ADJ
ejpam-2366	97	3	element	element	NOUN
ejpam-2366	97	4	n	n	PRON
ejpam-2366	97	5	∈	∈	NOUN
ejpam-2366	97	6	m	m	VERB
ejpam-2366	97	7	is	be	AUX
ejpam-2366	97	8	said	say	VERB
ejpam-2366	97	9	to	to	PART
ejpam-2366	97	10	be	be	AUX
ejpam-2366	97	11	φ	φ	VERB
ejpam-2366	97	12	-	-	NOUN
ejpam-2366	97	13	prime	prime	NOUN
ejpam-2366	97	14	if	if	SCONJ
ejpam-2366	97	15	for	for	ADP
ejpam-2366	97	16	all	all	DET
ejpam-2366	97	17	a	a	DET
ejpam-2366	97	18	∈	∈	PROPN
ejpam-2366	97	19	l	l	NOUN
ejpam-2366	97	20	,	,	PUNCT
ejpam-2366	97	21	a	a	DET
ejpam-2366	97	22	∈	∈	NOUN
ejpam-2366	97	23	m	m	NOUN
ejpam-2366	97	24	,	,	PUNCT
ejpam-2366	97	25	aa	aa	PROPN
ejpam-2366	97	26	6	6	NUM
ejpam-2366	97	27	n	n	NOUN
ejpam-2366	97	28	and	and	CCONJ
ejpam-2366	97	29	aa	aa	PROPN
ejpam-2366	97	30	φ(n	φ(n	PROPN
ejpam-2366	97	31	)	)	PUNCT
ejpam-2366	97	32	implies	imply	VERB
ejpam-2366	97	33	either	either	CCONJ
ejpam-2366	97	34	a	a	DET
ejpam-2366	97	35	6	6	NUM
ejpam-2366	97	36	n	n	NOUN
ejpam-2366	97	37	or	or	CCONJ
ejpam-2366	97	38	a	a	DET
ejpam-2366	97	39	6	6	NUM
ejpam-2366	97	40	(	(	PUNCT
ejpam-2366	97	41	n	n	NUM
ejpam-2366	97	42	:	:	PUNCT
ejpam-2366	97	43	i	i	PRON
ejpam-2366	97	44	m	m	PROPN
ejpam-2366	97	45	)	)	PUNCT
ejpam-2366	97	46	.	.	PUNCT
ejpam-2366	98	1	now	now	ADV
ejpam-2366	98	2	if	if	SCONJ
ejpam-2366	98	3	φα	φα	X
ejpam-2366	98	4	:	:	PUNCT
ejpam-2366	98	5	m	m	VERB
ejpam-2366	98	6	−→m	−→m	NOUN
ejpam-2366	98	7	is	be	AUX
ejpam-2366	98	8	a	a	DET
ejpam-2366	98	9	function	function	NOUN
ejpam-2366	98	10	on	on	ADP
ejpam-2366	98	11	an	an	DET
ejpam-2366	98	12	l	l	NOUN
ejpam-2366	98	13	-	-	NOUN
ejpam-2366	98	14	module	module	NOUN
ejpam-2366	98	15	m	m	NOUN
ejpam-2366	98	16	,	,	PUNCT
ejpam-2366	98	17	then	then	ADV
ejpam-2366	98	18	φα	φα	NOUN
ejpam-2366	98	19	-	-	PUNCT
ejpam-2366	98	20	prime	prime	ADJ
ejpam-2366	98	21	elements	element	NOUN
ejpam-2366	98	22	of	of	ADP
ejpam-2366	98	23	m	m	NOUN
ejpam-2366	98	24	are	be	AUX
ejpam-2366	98	25	defined	define	VERB
ejpam-2366	98	26	by	by	ADP
ejpam-2366	98	27	following	follow	VERB
ejpam-2366	98	28	settings	setting	NOUN
ejpam-2366	98	29	in	in	ADP
ejpam-2366	98	30	the	the	DET
ejpam-2366	98	31	definition	definition	NOUN
ejpam-2366	98	32	1	1	NUM
ejpam-2366	98	33	of	of	ADP
ejpam-2366	98	34	a	a	DET
ejpam-2366	98	35	φ	φ	NUM
ejpam-2366	98	36	-	-	ADJ
ejpam-2366	98	37	prime	prime	ADJ
ejpam-2366	98	38	element	element	NOUN
ejpam-2366	98	39	.	.	PUNCT
ejpam-2366	99	1	•	•	NUM
ejpam-2366	100	1	φ0(n	φ0(n	PROPN
ejpam-2366	100	2	)	)	PUNCT
ejpam-2366	100	3	=	=	SYM
ejpam-2366	100	4	om	om	PROPN
ejpam-2366	100	5	.	.	PUNCT
ejpam-2366	101	1	then	then	ADV
ejpam-2366	101	2	n	n	DET
ejpam-2366	101	3	∈m	∈m	NOUN
ejpam-2366	101	4	is	be	AUX
ejpam-2366	101	5	called	call	VERB
ejpam-2366	101	6	a	a	DET
ejpam-2366	101	7	weakly	weakly	ADJ
ejpam-2366	101	8	prime	prime	ADJ
ejpam-2366	101	9	element	element	NOUN
ejpam-2366	101	10	.	.	PUNCT
ejpam-2366	102	1	•	•	NUM
ejpam-2366	102	2	φ2(n	φ2(n	X
ejpam-2366	102	3	)	)	PUNCT
ejpam-2366	102	4	=	=	SYM
ejpam-2366	102	5	(	(	PUNCT
ejpam-2366	102	6	n	n	X
ejpam-2366	102	7	:	:	PUNCT
ejpam-2366	102	8	i	i	PRON
ejpam-2366	102	9	m	m	PROPN
ejpam-2366	102	10	)	)	PUNCT
ejpam-2366	103	1	n	n	CCONJ
ejpam-2366	103	2	.	.	PUNCT
ejpam-2366	104	1	then	then	ADV
ejpam-2366	104	2	n	n	DET
ejpam-2366	104	3	∈m	∈m	NOUN
ejpam-2366	104	4	is	be	AUX
ejpam-2366	104	5	called	call	VERB
ejpam-2366	104	6	a	a	DET
ejpam-2366	104	7	2	2	NUM
ejpam-2366	104	8	-	-	PUNCT
ejpam-2366	104	9	almost	almost	ADV
ejpam-2366	104	10	prime	prime	ADJ
ejpam-2366	104	11	element	element	NOUN
ejpam-2366	104	12	or	or	CCONJ
ejpam-2366	104	13	a	a	DET
ejpam-2366	104	14	φ2	φ2	ADJ
ejpam-2366	104	15	-	-	PUNCT
ejpam-2366	104	16	prime	prime	NOUN
ejpam-2366	104	17	element	element	NOUN
ejpam-2366	104	18	or	or	CCONJ
ejpam-2366	104	19	simply	simply	ADV
ejpam-2366	104	20	an	an	DET
ejpam-2366	104	21	almost	almost	ADV
ejpam-2366	104	22	prime	prime	ADJ
ejpam-2366	104	23	element	element	NOUN
ejpam-2366	104	24	.	.	PUNCT
ejpam-2366	105	1	•	•	NUM
ejpam-2366	105	2	φn(n	φn(n	NUM
ejpam-2366	105	3	)	)	PUNCT
ejpam-2366	106	1	=	=	PUNCT
ejpam-2366	106	2	(	(	PUNCT
ejpam-2366	106	3	n	n	X
ejpam-2366	106	4	:	:	PUNCT
ejpam-2366	106	5	i	i	PRON
ejpam-2366	106	6	m	m	PROPN
ejpam-2366	106	7	)	)	PUNCT
ejpam-2366	106	8	n−1n	n−1n	NOUN
ejpam-2366	106	9	(	(	PUNCT
ejpam-2366	106	10	n	n	CCONJ
ejpam-2366	106	11	>	>	X
ejpam-2366	106	12	2	2	NUM
ejpam-2366	106	13	)	)	PUNCT
ejpam-2366	106	14	.	.	PUNCT
ejpam-2366	107	1	then	then	ADV
ejpam-2366	107	2	n	n	DET
ejpam-2366	107	3	∈m	∈m	NOUN
ejpam-2366	107	4	is	be	AUX
ejpam-2366	107	5	called	call	VERB
ejpam-2366	107	6	an	an	DET
ejpam-2366	107	7	n	n	ADV
ejpam-2366	107	8	-	-	PUNCT
ejpam-2366	107	9	almost	almost	ADV
ejpam-2366	107	10	prime	prime	ADJ
ejpam-2366	107	11	element	element	NOUN
ejpam-2366	107	12	or	or	CCONJ
ejpam-2366	107	13	a	a	DET
ejpam-2366	107	14	φn	φn	ADJ
ejpam-2366	107	15	-	-	PUNCT
ejpam-2366	107	16	prime	prime	ADJ
ejpam-2366	107	17	element	element	NOUN
ejpam-2366	107	18	(	(	PUNCT
ejpam-2366	107	19	n	n	CCONJ
ejpam-2366	107	20	>	>	X
ejpam-2366	107	21	2	2	NUM
ejpam-2366	107	22	)	)	PUNCT
ejpam-2366	107	23	.	.	PUNCT
ejpam-2366	108	1	•	•	NOUN
ejpam-2366	108	2	φω(n	φω(n	NUM
ejpam-2366	108	3	)	)	PUNCT
ejpam-2366	109	1	=	=	PUNCT
ejpam-2366	109	2	∧∞	∧∞	PRON
ejpam-2366	109	3	i=1(n	i=1(n	NOUN
ejpam-2366	109	4	:	:	PUNCT
ejpam-2366	109	5	i	i	PRON
ejpam-2366	109	6	m	m	VERB
ejpam-2366	109	7	)	)	PUNCT
ejpam-2366	109	8	in	in	ADP
ejpam-2366	109	9	.	.	PUNCT
ejpam-2366	110	1	then	then	ADV
ejpam-2366	110	2	n	n	X
ejpam-2366	110	3	∈	∈	NOUN
ejpam-2366	110	4	m	m	AUX
ejpam-2366	110	5	is	be	AUX
ejpam-2366	110	6	called	call	VERB
ejpam-2366	110	7	a	a	DET
ejpam-2366	110	8	ω	ω	ADJ
ejpam-2366	110	9	-	-	ADJ
ejpam-2366	110	10	prime	prime	ADJ
ejpam-2366	110	11	element	element	NOUN
ejpam-2366	110	12	or	or	CCONJ
ejpam-2366	110	13	φω	φω	NOUN
ejpam-2366	110	14	-	-	PUNCT
ejpam-2366	110	15	prime	prime	ADJ
ejpam-2366	110	16	element	element	NOUN
ejpam-2366	110	17	.	.	PUNCT
ejpam-2366	111	1	since	since	SCONJ
ejpam-2366	111	2	n\φ(n	n\φ(n	NOUN
ejpam-2366	111	3	)	)	PUNCT
ejpam-2366	111	4	=	=	PUNCT
ejpam-2366	111	5	n\(n	n\(n	ADP
ejpam-2366	111	6	∧	∧	PROPN
ejpam-2366	111	7	φ(n	φ(n	ADJ
ejpam-2366	111	8	)	)	PUNCT
ejpam-2366	111	9	)	)	PUNCT
ejpam-2366	111	10	,	,	PUNCT
ejpam-2366	111	11	so	so	CCONJ
ejpam-2366	111	12	without	without	ADP
ejpam-2366	111	13	loss	loss	NOUN
ejpam-2366	111	14	of	of	ADP
ejpam-2366	111	15	generality	generality	NOUN
ejpam-2366	111	16	,	,	PUNCT
ejpam-2366	111	17	throughout	throughout	ADP
ejpam-2366	111	18	this	this	DET
ejpam-2366	111	19	paper	paper	NOUN
ejpam-2366	111	20	,	,	PUNCT
ejpam-2366	111	21	we	we	PRON
ejpam-2366	111	22	assume	assume	VERB
ejpam-2366	111	23	that	that	SCONJ
ejpam-2366	111	24	φ(n	φ(n	NOUN
ejpam-2366	111	25	)	)	PUNCT
ejpam-2366	111	26	6	6	NUM
ejpam-2366	111	27	n	n	NOUN
ejpam-2366	111	28	.	.	PUNCT
ejpam-2366	112	1	definition	definition	NOUN
ejpam-2366	112	2	2	2	NUM
ejpam-2366	112	3	.	.	PUNCT
ejpam-2366	113	1	given	give	VERB
ejpam-2366	113	2	two	two	NUM
ejpam-2366	113	3	functions	function	NOUN
ejpam-2366	113	4	γ1	γ1	NOUN
ejpam-2366	113	5	,	,	PUNCT
ejpam-2366	113	6	γ2	γ2	PROPN
ejpam-2366	113	7	:	:	PUNCT
ejpam-2366	113	8	m	m	VERB
ejpam-2366	113	9	−→	−→	ADJ
ejpam-2366	113	10	m	m	VERB
ejpam-2366	113	11	on	on	ADP
ejpam-2366	113	12	an	an	DET
ejpam-2366	113	13	l	l	NOUN
ejpam-2366	113	14	-	-	NOUN
ejpam-2366	113	15	module	module	NOUN
ejpam-2366	113	16	m	m	NOUN
ejpam-2366	113	17	,	,	PUNCT
ejpam-2366	113	18	we	we	PRON
ejpam-2366	113	19	define	define	VERB
ejpam-2366	113	20	γ1	γ1	NOUN
ejpam-2366	113	21	6	6	NUM
ejpam-2366	113	22	γ2	γ2	NOUN
ejpam-2366	113	23	if	if	SCONJ
ejpam-2366	113	24	γ1(n	γ1(n	NOUN
ejpam-2366	113	25	)	)	PUNCT
ejpam-2366	113	26	6	6	NUM
ejpam-2366	113	27	γ2(n	γ2(n	PROPN
ejpam-2366	113	28	)	)	PUNCT
ejpam-2366	113	29	for	for	ADP
ejpam-2366	113	30	all	all	DET
ejpam-2366	113	31	n	n	PRON
ejpam-2366	113	32	∈m	∈m	NOUN
ejpam-2366	113	33	.	.	PUNCT
ejpam-2366	114	1	clearly	clearly	ADV
ejpam-2366	114	2	,	,	PUNCT
ejpam-2366	114	3	we	we	PRON
ejpam-2366	114	4	have	have	VERB
ejpam-2366	114	5	the	the	DET
ejpam-2366	114	6	following	follow	VERB
ejpam-2366	114	7	order	order	NOUN
ejpam-2366	114	8	:	:	PUNCT
ejpam-2366	114	9	φ0	φ0	PROPN
ejpam-2366	114	10	6	6	NUM
ejpam-2366	114	11	φω	φω	PART
ejpam-2366	114	12	6	6	NUM
ejpam-2366	114	13	·	·	PUNCT
ejpam-2366	114	14	·	·	PUNCT
ejpam-2366	114	15	·	·	PUNCT
ejpam-2366	114	16	6	6	NUM
ejpam-2366	114	17	φn+1	φn+1	NOUN
ejpam-2366	114	18	6	6	NUM
ejpam-2366	114	19	φn	φn	ADP
ejpam-2366	114	20	6	6	NUM
ejpam-2366	114	21	·	·	PUNCT
ejpam-2366	114	22	·	·	PUNCT
ejpam-2366	114	23	·	·	PUNCT
ejpam-2366	114	24	6	6	NUM
ejpam-2366	114	25	φ2	φ2	NOUN
ejpam-2366	114	26	now	now	ADV
ejpam-2366	114	27	before	before	ADP
ejpam-2366	114	28	obtaining	obtain	VERB
ejpam-2366	114	29	the	the	DET
ejpam-2366	114	30	characterizations	characterization	NOUN
ejpam-2366	114	31	of	of	ADP
ejpam-2366	114	32	a	a	DET
ejpam-2366	114	33	φ	φ	ADJ
ejpam-2366	114	34	-	-	ADJ
ejpam-2366	114	35	prime	prime	ADJ
ejpam-2366	114	36	element	element	NOUN
ejpam-2366	114	37	of	of	ADP
ejpam-2366	114	38	an	an	DET
ejpam-2366	114	39	l	l	NOUN
ejpam-2366	114	40	-	-	NOUN
ejpam-2366	114	41	module	module	NOUN
ejpam-2366	114	42	m	m	NOUN
ejpam-2366	114	43	,	,	PUNCT
ejpam-2366	114	44	we	we	PRON
ejpam-2366	114	45	state	state	VERB
ejpam-2366	114	46	the	the	DET
ejpam-2366	114	47	following	follow	VERB
ejpam-2366	114	48	essential	essential	ADJ
ejpam-2366	114	49	lemma	lemma	PROPN
ejpam-2366	114	50	which	which	PRON
ejpam-2366	114	51	is	be	AUX
ejpam-2366	114	52	outcome	outcome	NOUN
ejpam-2366	114	53	of	of	ADP
ejpam-2366	114	54	lemma	lemma	PROPN
ejpam-2366	114	55	2.3.13	2.3.13	NUM
ejpam-2366	114	56	from	from	ADP
ejpam-2366	114	57	[	[	X
ejpam-2366	114	58	11	11	NUM
ejpam-2366	114	59	]	]	PUNCT
ejpam-2366	114	60	.	.	PUNCT
ejpam-2366	115	1	lemma	lemma	PROPN
ejpam-2366	115	2	1	1	X
ejpam-2366	115	3	.	.	PUNCT
ejpam-2366	116	1	let	let	VERB
ejpam-2366	116	2	a1	a1	NOUN
ejpam-2366	116	3	,	,	PUNCT
ejpam-2366	116	4	a2	a2	PROPN
ejpam-2366	116	5	∈	∈	PROPN
ejpam-2366	116	6	l.	l.	PROPN
ejpam-2366	116	7	suppose	suppose	VERB
ejpam-2366	116	8	b	b	X
ejpam-2366	116	9	∈	∈	PROPN
ejpam-2366	116	10	l	l	NOUN
ejpam-2366	116	11	satisfies	satisfy	VERB
ejpam-2366	116	12	the	the	DET
ejpam-2366	116	13	following	follow	VERB
ejpam-2366	116	14	property	property	NOUN
ejpam-2366	116	15	:	:	PUNCT
ejpam-2366	116	16	(	(	PUNCT
ejpam-2366	116	17	∗	∗	NOUN
ejpam-2366	116	18	)	)	PUNCT
ejpam-2366	116	19	.	.	PUNCT
ejpam-2366	117	1	if	if	SCONJ
ejpam-2366	117	2	h	h	PROPN
ejpam-2366	117	3	∈	∈	PROPN
ejpam-2366	117	4	l∗	l∗	PROPN
ejpam-2366	117	5	with	with	ADP
ejpam-2366	117	6	h	h	PROPN
ejpam-2366	117	7	6	6	NUM
ejpam-2366	117	8	b	b	NOUN
ejpam-2366	117	9	,	,	PUNCT
ejpam-2366	117	10	then	then	ADV
ejpam-2366	117	11	either	either	CCONJ
ejpam-2366	117	12	h	h	NOUN
ejpam-2366	117	13	6	6	NUM
ejpam-2366	117	14	a1	a1	NOUN
ejpam-2366	117	15	or	or	CCONJ
ejpam-2366	117	16	h	h	NOUN
ejpam-2366	117	17	6	6	NUM
ejpam-2366	117	18	a2	a2	PROPN
ejpam-2366	117	19	.	.	PUNCT
ejpam-2366	118	1	then	then	ADV
ejpam-2366	118	2	either	either	CCONJ
ejpam-2366	118	3	b	b	X
ejpam-2366	118	4	6	6	NUM
ejpam-2366	118	5	a1	a1	NOUN
ejpam-2366	118	6	or	or	CCONJ
ejpam-2366	118	7	b	b	NOUN
ejpam-2366	118	8	6	6	NUM
ejpam-2366	118	9	a2	a2	PROPN
ejpam-2366	118	10	.	.	PUNCT
ejpam-2366	119	1	theorem	theorem	NOUN
ejpam-2366	119	2	1	1	NUM
ejpam-2366	119	3	.	.	PUNCT
ejpam-2366	120	1	let	let	VERB
ejpam-2366	120	2	m	m	PRON
ejpam-2366	120	3	be	be	AUX
ejpam-2366	120	4	a	a	DET
ejpam-2366	120	5	cg	cg	NOUN
ejpam-2366	120	6	-	-	PUNCT
ejpam-2366	120	7	lattice	lattice	NOUN
ejpam-2366	120	8	l	l	NOUN
ejpam-2366	120	9	-	-	NOUN
ejpam-2366	120	10	module	module	NOUN
ejpam-2366	120	11	,	,	PUNCT
ejpam-2366	120	12	n	n	PRON
ejpam-2366	120	13	∈m	∈m	NOUN
ejpam-2366	120	14	be	be	AUX
ejpam-2366	120	15	a	a	DET
ejpam-2366	120	16	proper	proper	ADJ
ejpam-2366	120	17	element	element	NOUN
ejpam-2366	120	18	and	and	CCONJ
ejpam-2366	120	19	φ	φ	NOUN
ejpam-2366	120	20	:	:	PUNCT
ejpam-2366	121	1	m	m	AUX
ejpam-2366	121	2	−→	−→	ADJ
ejpam-2366	121	3	m	m	AUX
ejpam-2366	121	4	be	be	VERB
ejpam-2366	121	5	a	a	DET
ejpam-2366	121	6	function	function	NOUN
ejpam-2366	121	7	on	on	ADP
ejpam-2366	121	8	m	m	PROPN
ejpam-2366	121	9	.	.	PUNCT
ejpam-2366	122	1	then	then	ADV
ejpam-2366	122	2	the	the	DET
ejpam-2366	122	3	following	follow	VERB
ejpam-2366	122	4	statements	statement	NOUN
ejpam-2366	122	5	are	be	AUX
ejpam-2366	122	6	equivalent	equivalent	ADJ
ejpam-2366	122	7	:	:	PUNCT
ejpam-2366	122	8	1	1	X
ejpam-2366	122	9	©	©	NOUN
ejpam-2366	122	10	n	n	NUM
ejpam-2366	122	11	is	be	AUX
ejpam-2366	122	12	a	a	DET
ejpam-2366	122	13	φ	φ	ADJ
ejpam-2366	122	14	-	-	ADJ
ejpam-2366	122	15	prime	prime	ADJ
ejpam-2366	122	16	element	element	NOUN
ejpam-2366	122	17	of	of	ADP
ejpam-2366	122	18	m	m	PROPN
ejpam-2366	122	19	.	.	PUNCT
ejpam-2366	123	1	a.	a.	PROPN
ejpam-2366	123	2	v.	v.	PROPN
ejpam-2366	123	3	bingi	bingi	PROPN
ejpam-2366	123	4	,	,	PUNCT
ejpam-2366	123	5	c.	c.	PROPN
ejpam-2366	123	6	s.	s.	PROPN
ejpam-2366	123	7	manjarekar	manjarekar	PROPN
ejpam-2366	123	8	/	/	PROPN
ejpam-2366	123	9	eur	eur	PROPN
ejpam-2366	123	10	.	.	PUNCT
ejpam-2366	124	1	j.	j.	PROPN
ejpam-2366	124	2	pure	pure	PROPN
ejpam-2366	124	3	appl	appl	PROPN
ejpam-2366	124	4	.	.	PROPN
ejpam-2366	124	5	math	math	PROPN
ejpam-2366	124	6	,	,	PUNCT
ejpam-2366	124	7	14	14	NUM
ejpam-2366	124	8	(	(	PUNCT
ejpam-2366	124	9	2	2	NUM
ejpam-2366	124	10	)	)	PUNCT
ejpam-2366	124	11	(	(	PUNCT
ejpam-2366	124	12	2021	2021	NUM
ejpam-2366	124	13	)	)	PUNCT
ejpam-2366	124	14	,	,	PUNCT
ejpam-2366	124	15	551	551	NUM
ejpam-2366	124	16	-	-	SYM
ejpam-2366	124	17	577	577	NUM
ejpam-2366	124	18	555	555	NUM
ejpam-2366	124	19	2	2	NUM
ejpam-2366	124	20	©	©	NOUN
ejpam-2366	124	21	for	for	ADP
ejpam-2366	124	22	every	every	DET
ejpam-2366	124	23	a	a	DET
ejpam-2366	124	24	∈m	∈m	NOUN
ejpam-2366	124	25	such	such	ADJ
ejpam-2366	124	26	that	that	SCONJ
ejpam-2366	124	27	a	a	DET
ejpam-2366	124	28	n	n	NOUN
ejpam-2366	124	29	,	,	PUNCT
ejpam-2366	124	30	either	either	CCONJ
ejpam-2366	124	31	(	(	PUNCT
ejpam-2366	124	32	n	n	X
ejpam-2366	124	33	:	:	PUNCT
ejpam-2366	124	34	a	a	X
ejpam-2366	124	35	)	)	PUNCT
ejpam-2366	124	36	=	=	SYM
ejpam-2366	124	37	(	(	PUNCT
ejpam-2366	124	38	n	n	X
ejpam-2366	124	39	:	:	PUNCT
ejpam-2366	124	40	i	i	PRON
ejpam-2366	124	41	m	m	VERB
ejpam-2366	124	42	)	)	PUNCT
ejpam-2366	124	43	or	or	CCONJ
ejpam-2366	124	44	(	(	PUNCT
ejpam-2366	124	45	n	n	X
ejpam-2366	124	46	:	:	PUNCT
ejpam-2366	124	47	a	a	X
ejpam-2366	124	48	)	)	PUNCT
ejpam-2366	124	49	=	=	SYM
ejpam-2366	124	50	(	(	PUNCT
ejpam-2366	124	51	φ(n	φ(n	PROPN
ejpam-2366	124	52	)	)	PUNCT
ejpam-2366	124	53	:	:	PUNCT
ejpam-2366	124	54	a	a	X
ejpam-2366	124	55	)	)	PUNCT
ejpam-2366	124	56	.	.	PUNCT
ejpam-2366	125	1	3	3	NUM
ejpam-2366	125	2	©	©	NOUN
ejpam-2366	125	3	for	for	ADP
ejpam-2366	125	4	every	every	DET
ejpam-2366	125	5	r	r	NOUN
ejpam-2366	125	6	∈	∈	NOUN
ejpam-2366	125	7	l	l	NOUN
ejpam-2366	125	8	such	such	ADJ
ejpam-2366	125	9	that	that	PRON
ejpam-2366	125	10	r	r	NOUN
ejpam-2366	125	11	(	(	PUNCT
ejpam-2366	125	12	n	n	NOUN
ejpam-2366	125	13	:	:	PUNCT
ejpam-2366	125	14	i	i	PRON
ejpam-2366	125	15	m	m	PROPN
ejpam-2366	125	16	)	)	PUNCT
ejpam-2366	125	17	,	,	PUNCT
ejpam-2366	125	18	either	either	CCONJ
ejpam-2366	125	19	(	(	PUNCT
ejpam-2366	125	20	n	n	NUM
ejpam-2366	125	21	:	:	PUNCT
ejpam-2366	125	22	r	r	X
ejpam-2366	125	23	)	)	PUNCT
ejpam-2366	125	24	=	=	SYM
ejpam-2366	125	25	n	n	NOUN
ejpam-2366	125	26	or	or	CCONJ
ejpam-2366	125	27	(	(	PUNCT
ejpam-2366	125	28	n	n	X
ejpam-2366	125	29	:	:	PUNCT
ejpam-2366	125	30	r	r	X
ejpam-2366	125	31	)	)	PUNCT
ejpam-2366	125	32	=	=	SYM
ejpam-2366	125	33	(	(	PUNCT
ejpam-2366	125	34	φ(n	φ(n	ADJ
ejpam-2366	125	35	)	)	PUNCT
ejpam-2366	125	36	:	:	PUNCT
ejpam-2366	125	37	r	r	X
ejpam-2366	125	38	)	)	PUNCT
ejpam-2366	125	39	.	.	PUNCT
ejpam-2366	126	1	4	4	NUM
ejpam-2366	126	2	©	©	NOUN
ejpam-2366	126	3	for	for	ADP
ejpam-2366	126	4	every	every	DET
ejpam-2366	126	5	r	r	NOUN
ejpam-2366	126	6	∈	∈	PROPN
ejpam-2366	126	7	l∗	l∗	NOUN
ejpam-2366	126	8	,	,	PUNCT
ejpam-2366	126	9	a	a	DET
ejpam-2366	126	10	∈m∗	∈m∗	NOUN
ejpam-2366	126	11	,	,	PUNCT
ejpam-2366	126	12	if	if	SCONJ
ejpam-2366	126	13	ra	ra	PROPN
ejpam-2366	126	14	6	6	NUM
ejpam-2366	126	15	n	n	NOUN
ejpam-2366	126	16	and	and	CCONJ
ejpam-2366	126	17	ra	ra	PROPN
ejpam-2366	126	18	φ(n	φ(n	PROPN
ejpam-2366	126	19	)	)	PUNCT
ejpam-2366	126	20	,	,	PUNCT
ejpam-2366	126	21	then	then	ADV
ejpam-2366	126	22	either	either	CCONJ
ejpam-2366	126	23	r	r	NOUN
ejpam-2366	126	24	6	6	NUM
ejpam-2366	126	25	(	(	PUNCT
ejpam-2366	126	26	n	n	NUM
ejpam-2366	126	27	:	:	PUNCT
ejpam-2366	126	28	i	i	PRON
ejpam-2366	126	29	m	m	VERB
ejpam-2366	126	30	)	)	PUNCT
ejpam-2366	126	31	or	or	CCONJ
ejpam-2366	126	32	a	a	DET
ejpam-2366	126	33	6	6	NUM
ejpam-2366	126	34	n	n	NOUN
ejpam-2366	126	35	.	.	PUNCT
ejpam-2366	127	1	proof	proof	NOUN
ejpam-2366	127	2	.	.	PUNCT
ejpam-2366	128	1	1	1	NUM
ejpam-2366	128	2	©	©	NOUN
ejpam-2366	128	3	=⇒	=⇒	NOUN
ejpam-2366	128	4	2	2	NUM
ejpam-2366	128	5	©	©	NOUN
ejpam-2366	128	6	.	.	PUNCT
ejpam-2366	128	7	suppose	suppose	VERB
ejpam-2366	128	8	1	1	NUM
ejpam-2366	128	9	©	©	PROPN
ejpam-2366	128	10	holds	hold	NOUN
ejpam-2366	128	11	.	.	PUNCT
ejpam-2366	129	1	let	let	VERB
ejpam-2366	129	2	a	a	DET
ejpam-2366	129	3	∈	∈	NOUN
ejpam-2366	129	4	m	m	AUX
ejpam-2366	129	5	be	be	AUX
ejpam-2366	129	6	such	such	ADJ
ejpam-2366	129	7	that	that	SCONJ
ejpam-2366	129	8	a	a	DET
ejpam-2366	129	9	n	n	NOUN
ejpam-2366	129	10	.	.	PUNCT
ejpam-2366	130	1	obviously	obviously	ADV
ejpam-2366	130	2	,	,	PUNCT
ejpam-2366	130	3	(	(	PUNCT
ejpam-2366	130	4	φ(n	φ(n	ADJ
ejpam-2366	130	5	)	)	PUNCT
ejpam-2366	130	6	:	:	PUNCT
ejpam-2366	130	7	a	a	X
ejpam-2366	130	8	)	)	PUNCT
ejpam-2366	130	9	6	6	NUM
ejpam-2366	130	10	(	(	PUNCT
ejpam-2366	130	11	n	n	NOUN
ejpam-2366	130	12	:	:	PUNCT
ejpam-2366	130	13	a	a	X
ejpam-2366	130	14	)	)	PUNCT
ejpam-2366	130	15	and	and	CCONJ
ejpam-2366	130	16	(	(	PUNCT
ejpam-2366	130	17	n	n	X
ejpam-2366	130	18	:	:	PUNCT
ejpam-2366	130	19	i	i	PRON
ejpam-2366	130	20	m	m	VERB
ejpam-2366	130	21	)	)	PUNCT
ejpam-2366	130	22	6	6	NUM
ejpam-2366	130	23	(	(	PUNCT
ejpam-2366	130	24	n	n	NOUN
ejpam-2366	130	25	:	:	PUNCT
ejpam-2366	130	26	a	a	X
ejpam-2366	130	27	)	)	PUNCT
ejpam-2366	130	28	.	.	PUNCT
ejpam-2366	131	1	let	let	VERB
ejpam-2366	131	2	a	a	DET
ejpam-2366	131	3	∈	∈	PROPN
ejpam-2366	131	4	l∗	l∗	NOUN
ejpam-2366	131	5	be	be	AUX
ejpam-2366	131	6	such	such	ADJ
ejpam-2366	131	7	that	that	SCONJ
ejpam-2366	131	8	a	a	DET
ejpam-2366	131	9	6	6	NUM
ejpam-2366	131	10	(	(	PUNCT
ejpam-2366	131	11	n	n	NOUN
ejpam-2366	131	12	:	:	PUNCT
ejpam-2366	131	13	a	a	X
ejpam-2366	131	14	)	)	PUNCT
ejpam-2366	131	15	.	.	PUNCT
ejpam-2366	132	1	then	then	ADV
ejpam-2366	132	2	aa	aa	PROPN
ejpam-2366	132	3	6	6	NUM
ejpam-2366	132	4	n	n	NOUN
ejpam-2366	132	5	.	.	PUNCT
ejpam-2366	133	1	if	if	SCONJ
ejpam-2366	133	2	aa	aa	NOUN
ejpam-2366	133	3	6	6	NUM
ejpam-2366	133	4	φ(n	φ(n	NOUN
ejpam-2366	133	5	)	)	PUNCT
ejpam-2366	133	6	,	,	PUNCT
ejpam-2366	133	7	then	then	ADV
ejpam-2366	133	8	a	a	DET
ejpam-2366	133	9	6	6	NUM
ejpam-2366	133	10	(	(	PUNCT
ejpam-2366	133	11	φ(n	φ(n	PROPN
ejpam-2366	133	12	)	)	PUNCT
ejpam-2366	133	13	:	:	PUNCT
ejpam-2366	133	14	a	a	X
ejpam-2366	133	15	)	)	PUNCT
ejpam-2366	133	16	.	.	PUNCT
ejpam-2366	134	1	if	if	SCONJ
ejpam-2366	134	2	aa	aa	PROPN
ejpam-2366	134	3	φ(n	φ(n	ADJ
ejpam-2366	134	4	)	)	PUNCT
ejpam-2366	134	5	,	,	PUNCT
ejpam-2366	134	6	then	then	ADV
ejpam-2366	134	7	since	since	SCONJ
ejpam-2366	134	8	n	n	PROPN
ejpam-2366	134	9	is	be	AUX
ejpam-2366	134	10	φ	φ	VERB
ejpam-2366	134	11	-	-	ADJ
ejpam-2366	134	12	prime	prime	NOUN
ejpam-2366	134	13	and	and	CCONJ
ejpam-2366	134	14	a	a	DET
ejpam-2366	134	15	n	n	NOUN
ejpam-2366	134	16	,	,	PUNCT
ejpam-2366	134	17	it	it	PRON
ejpam-2366	134	18	follows	follow	VERB
ejpam-2366	134	19	that	that	SCONJ
ejpam-2366	134	20	a	a	DET
ejpam-2366	134	21	6	6	NUM
ejpam-2366	134	22	(	(	PUNCT
ejpam-2366	134	23	n	n	NUM
ejpam-2366	134	24	:	:	PUNCT
ejpam-2366	134	25	i	i	PRON
ejpam-2366	134	26	m	m	PROPN
ejpam-2366	134	27	)	)	PUNCT
ejpam-2366	134	28	.	.	PUNCT
ejpam-2366	135	1	hence	hence	ADV
ejpam-2366	135	2	by	by	ADP
ejpam-2366	135	3	lemma	lemma	PROPN
ejpam-2366	135	4	1	1	NUM
ejpam-2366	135	5	,	,	PUNCT
ejpam-2366	135	6	either	either	CCONJ
ejpam-2366	135	7	(	(	PUNCT
ejpam-2366	135	8	n	n	X
ejpam-2366	135	9	:	:	PUNCT
ejpam-2366	135	10	a	a	X
ejpam-2366	135	11	)	)	PUNCT
ejpam-2366	135	12	6	6	NUM
ejpam-2366	135	13	(	(	PUNCT
ejpam-2366	135	14	φ(n	φ(n	PROPN
ejpam-2366	135	15	)	)	PUNCT
ejpam-2366	135	16	:	:	PUNCT
ejpam-2366	135	17	a	a	X
ejpam-2366	135	18	)	)	PUNCT
ejpam-2366	135	19	or	or	CCONJ
ejpam-2366	135	20	(	(	PUNCT
ejpam-2366	135	21	n	n	X
ejpam-2366	135	22	:	:	PUNCT
ejpam-2366	135	23	a	a	X
ejpam-2366	135	24	)	)	PUNCT
ejpam-2366	135	25	6	6	NUM
ejpam-2366	135	26	(	(	PUNCT
ejpam-2366	135	27	n	n	NUM
ejpam-2366	135	28	:	:	PUNCT
ejpam-2366	135	29	i	i	PRON
ejpam-2366	135	30	m	m	PROPN
ejpam-2366	135	31	)	)	PUNCT
ejpam-2366	135	32	.	.	PUNCT
ejpam-2366	136	1	thus	thus	ADV
ejpam-2366	136	2	either	either	CCONJ
ejpam-2366	136	3	(	(	PUNCT
ejpam-2366	136	4	n	n	X
ejpam-2366	136	5	:	:	PUNCT
ejpam-2366	136	6	a	a	X
ejpam-2366	136	7	)	)	PUNCT
ejpam-2366	136	8	=	=	SYM
ejpam-2366	136	9	(	(	PUNCT
ejpam-2366	136	10	φ(n	φ(n	PROPN
ejpam-2366	136	11	)	)	PUNCT
ejpam-2366	136	12	:	:	PUNCT
ejpam-2366	136	13	a	a	X
ejpam-2366	136	14	)	)	PUNCT
ejpam-2366	136	15	or	or	CCONJ
ejpam-2366	136	16	(	(	PUNCT
ejpam-2366	136	17	n	n	X
ejpam-2366	136	18	:	:	PUNCT
ejpam-2366	136	19	a	a	X
ejpam-2366	136	20	)	)	PUNCT
ejpam-2366	136	21	=	=	SYM
ejpam-2366	136	22	(	(	PUNCT
ejpam-2366	136	23	n	n	X
ejpam-2366	136	24	:	:	PUNCT
ejpam-2366	136	25	i	i	PRON
ejpam-2366	136	26	m	m	PROPN
ejpam-2366	136	27	)	)	PUNCT
ejpam-2366	136	28	.	.	PUNCT
ejpam-2366	137	1	2	2	NUM
ejpam-2366	137	2	©	©	NOUN
ejpam-2366	137	3	=⇒	=⇒	NOUN
ejpam-2366	137	4	3	3	NUM
ejpam-2366	137	5	©	©	NOUN
ejpam-2366	137	6	.	.	PUNCT
ejpam-2366	137	7	suppose	suppose	VERB
ejpam-2366	137	8	2	2	NUM
ejpam-2366	137	9	©	©	PROPN
ejpam-2366	137	10	holds	hold	NOUN
ejpam-2366	137	11	.	.	PUNCT
ejpam-2366	138	1	let	let	VERB
ejpam-2366	138	2	r	r	NOUN
ejpam-2366	138	3	(	(	PUNCT
ejpam-2366	138	4	n	n	NUM
ejpam-2366	138	5	:	:	PUNCT
ejpam-2366	138	6	i	i	PRON
ejpam-2366	138	7	m	m	VERB
ejpam-2366	138	8	)	)	PUNCT
ejpam-2366	138	9	for	for	ADP
ejpam-2366	138	10	r	r	PROPN
ejpam-2366	138	11	∈	∈	PROPN
ejpam-2366	138	12	l.	l.	NOUN
ejpam-2366	138	13	then	then	ADV
ejpam-2366	138	14	rim	rim	VERB
ejpam-2366	138	15	n	n	INTJ
ejpam-2366	138	16	.	.	PUNCT
ejpam-2366	139	1	using	use	VERB
ejpam-2366	139	2	2	2	NUM
ejpam-2366	139	3	©	©	NOUN
ejpam-2366	139	4	,	,	PUNCT
ejpam-2366	139	5	we	we	PRON
ejpam-2366	139	6	have	have	VERB
ejpam-2366	139	7	,	,	PUNCT
ejpam-2366	139	8	either	either	ADV
ejpam-2366	139	9	(	(	PUNCT
ejpam-2366	139	10	n	n	NUM
ejpam-2366	139	11	:	:	PUNCT
ejpam-2366	139	12	rim	rim	NOUN
ejpam-2366	139	13	)	)	PUNCT
ejpam-2366	139	14	=	=	PUNCT
ejpam-2366	140	1	(	(	PUNCT
ejpam-2366	140	2	n	n	X
ejpam-2366	140	3	:	:	PUNCT
ejpam-2366	140	4	i	i	PRON
ejpam-2366	140	5	m	m	VERB
ejpam-2366	140	6	)	)	PUNCT
ejpam-2366	140	7	or	or	CCONJ
ejpam-2366	140	8	(	(	PUNCT
ejpam-2366	140	9	n	n	NUM
ejpam-2366	140	10	:	:	PUNCT
ejpam-2366	140	11	rim	rim	NOUN
ejpam-2366	140	12	)	)	PUNCT
ejpam-2366	140	13	=	=	SYM
ejpam-2366	140	14	(	(	PUNCT
ejpam-2366	140	15	φ(n	φ(n	PROPN
ejpam-2366	140	16	)	)	PUNCT
ejpam-2366	140	17	:	:	PUNCT
ejpam-2366	140	18	rim	rim	NOUN
ejpam-2366	140	19	)	)	PUNCT
ejpam-2366	140	20	.	.	PUNCT
ejpam-2366	141	1	now	now	ADV
ejpam-2366	141	2	let	let	VERB
ejpam-2366	141	3	k	k	PROPN
ejpam-2366	141	4	6	6	NUM
ejpam-2366	141	5	(	(	PUNCT
ejpam-2366	141	6	n	n	NUM
ejpam-2366	141	7	:	:	PUNCT
ejpam-2366	141	8	r	r	X
ejpam-2366	141	9	)	)	PUNCT
ejpam-2366	141	10	for	for	ADP
ejpam-2366	141	11	k	k	PROPN
ejpam-2366	141	12	∈	∈	PROPN
ejpam-2366	141	13	m∗.	m∗.	PROPN
ejpam-2366	141	14	as	as	ADP
ejpam-2366	141	15	(	(	PUNCT
ejpam-2366	141	16	k	k	NOUN
ejpam-2366	141	17	:	:	PUNCT
ejpam-2366	141	18	i	i	PRON
ejpam-2366	141	19	m	m	VERB
ejpam-2366	141	20	)	)	PUNCT
ejpam-2366	141	21	i	i	PRON
ejpam-2366	141	22	m	m	VERB
ejpam-2366	141	23	6	6	NUM
ejpam-2366	141	24	k	k	NOUN
ejpam-2366	141	25	,	,	PUNCT
ejpam-2366	141	26	we	we	PRON
ejpam-2366	141	27	have	have	VERB
ejpam-2366	141	28	,	,	PUNCT
ejpam-2366	141	29	(	(	PUNCT
ejpam-2366	141	30	k	k	X
ejpam-2366	141	31	:	:	PUNCT
ejpam-2366	142	1	i	i	PRON
ejpam-2366	142	2	m	m	VERB
ejpam-2366	142	3	)	)	PUNCT
ejpam-2366	143	1	i	i	PRON
ejpam-2366	143	2	m	m	VERB
ejpam-2366	143	3	6	6	NUM
ejpam-2366	143	4	(	(	PUNCT
ejpam-2366	143	5	n	n	NUM
ejpam-2366	143	6	:	:	PUNCT
ejpam-2366	143	7	r	r	X
ejpam-2366	143	8	)	)	PUNCT
ejpam-2366	143	9	and	and	CCONJ
ejpam-2366	143	10	(	(	PUNCT
ejpam-2366	143	11	k	k	NOUN
ejpam-2366	143	12	:	:	PUNCT
ejpam-2366	143	13	i	i	PRON
ejpam-2366	143	14	m	m	VERB
ejpam-2366	143	15	)	)	PUNCT
ejpam-2366	144	1	i	i	PRON
ejpam-2366	144	2	m	m	VERB
ejpam-2366	144	3	∈	∈	PROPN
ejpam-2366	144	4	m∗.	m∗.	PROPN
ejpam-2366	144	5	clearly	clearly	ADV
ejpam-2366	144	6	,	,	PUNCT
ejpam-2366	144	7	k	k	PROPN
ejpam-2366	144	8	6	6	NUM
ejpam-2366	144	9	(	(	PUNCT
ejpam-2366	144	10	n	n	NUM
ejpam-2366	144	11	:	:	PUNCT
ejpam-2366	144	12	r	r	X
ejpam-2366	144	13	)	)	PUNCT
ejpam-2366	144	14	implies	imply	VERB
ejpam-2366	144	15	(	(	PUNCT
ejpam-2366	144	16	k	k	X
ejpam-2366	144	17	:	:	PUNCT
ejpam-2366	144	18	i	i	PRON
ejpam-2366	144	19	m	m	VERB
ejpam-2366	144	20	)	)	PUNCT
ejpam-2366	144	21	6	6	NUM
ejpam-2366	144	22	(	(	PUNCT
ejpam-2366	144	23	(	(	PUNCT
ejpam-2366	144	24	n	n	X
ejpam-2366	144	25	:	:	PUNCT
ejpam-2366	144	26	r	r	X
ejpam-2366	144	27	)	)	PUNCT
ejpam-2366	144	28	:	:	PUNCT
ejpam-2366	144	29	i	i	PRON
ejpam-2366	144	30	m	m	VERB
ejpam-2366	144	31	)	)	PUNCT
ejpam-2366	145	1	=	=	SYM
ejpam-2366	145	2	(	(	PUNCT
ejpam-2366	145	3	n	n	NOUN
ejpam-2366	145	4	:	:	PUNCT
ejpam-2366	145	5	rim	rim	NOUN
ejpam-2366	145	6	)	)	PUNCT
ejpam-2366	145	7	.	.	PUNCT
ejpam-2366	146	1	so	so	ADV
ejpam-2366	146	2	we	we	PRON
ejpam-2366	146	3	have	have	VERB
ejpam-2366	146	4	either	either	CCONJ
ejpam-2366	146	5	(	(	PUNCT
ejpam-2366	146	6	k	k	X
ejpam-2366	146	7	:	:	PUNCT
ejpam-2366	146	8	i	i	PRON
ejpam-2366	146	9	m	m	VERB
ejpam-2366	146	10	)	)	PUNCT
ejpam-2366	146	11	6	6	NUM
ejpam-2366	146	12	(	(	PUNCT
ejpam-2366	146	13	n	n	NUM
ejpam-2366	146	14	:	:	PUNCT
ejpam-2366	146	15	i	i	PRON
ejpam-2366	146	16	m	m	VERB
ejpam-2366	146	17	)	)	PUNCT
ejpam-2366	146	18	or	or	CCONJ
ejpam-2366	146	19	(	(	PUNCT
ejpam-2366	146	20	k	k	NOUN
ejpam-2366	146	21	:	:	PUNCT
ejpam-2366	146	22	i	i	PRON
ejpam-2366	146	23	m	m	VERB
ejpam-2366	146	24	)	)	PUNCT
ejpam-2366	146	25	6	6	NUM
ejpam-2366	146	26	(	(	PUNCT
ejpam-2366	146	27	φ(n	φ(n	ADJ
ejpam-2366	146	28	)	)	PUNCT
ejpam-2366	146	29	:	:	PUNCT
ejpam-2366	146	30	rim	rim	NOUN
ejpam-2366	146	31	)	)	PUNCT
ejpam-2366	147	1	=	=	SYM
ejpam-2366	147	2	(	(	PUNCT
ejpam-2366	147	3	φ(n	φ(n	ADJ
ejpam-2366	147	4	)	)	PUNCT
ejpam-2366	147	5	:	:	PUNCT
ejpam-2366	148	1	r	r	NOUN
ejpam-2366	148	2	:	:	PUNCT
ejpam-2366	148	3	i	i	PRON
ejpam-2366	148	4	m	m	PROPN
ejpam-2366	148	5	)	)	PUNCT
ejpam-2366	148	6	.	.	PUNCT
ejpam-2366	149	1	this	this	PRON
ejpam-2366	149	2	gives	give	VERB
ejpam-2366	149	3	either	either	PRON
ejpam-2366	149	4	(	(	PUNCT
ejpam-2366	149	5	k	k	NOUN
ejpam-2366	149	6	:	:	PUNCT
ejpam-2366	149	7	i	i	PRON
ejpam-2366	149	8	m	m	VERB
ejpam-2366	149	9	)	)	PUNCT
ejpam-2366	149	10	i	i	PRON
ejpam-2366	149	11	m	m	VERB
ejpam-2366	149	12	6	6	NUM
ejpam-2366	149	13	n	n	NOUN
ejpam-2366	149	14	or	or	CCONJ
ejpam-2366	149	15	(	(	PUNCT
ejpam-2366	149	16	k	k	NOUN
ejpam-2366	149	17	:	:	PUNCT
ejpam-2366	149	18	i	i	PRON
ejpam-2366	149	19	m	m	VERB
ejpam-2366	149	20	)	)	PUNCT
ejpam-2366	149	21	i	i	PRON
ejpam-2366	149	22	m	m	VERB
ejpam-2366	149	23	6	6	NUM
ejpam-2366	149	24	(	(	PUNCT
ejpam-2366	149	25	φ(n	φ(n	ADJ
ejpam-2366	149	26	)	)	PUNCT
ejpam-2366	149	27	:	:	PUNCT
ejpam-2366	150	1	r	r	X
ejpam-2366	150	2	)	)	PUNCT
ejpam-2366	150	3	.	.	PUNCT
ejpam-2366	151	1	this	this	PRON
ejpam-2366	151	2	implies	imply	VERB
ejpam-2366	151	3	that	that	SCONJ
ejpam-2366	151	4	either	either	ADV
ejpam-2366	151	5	(	(	PUNCT
ejpam-2366	151	6	n	n	NUM
ejpam-2366	151	7	:	:	PUNCT
ejpam-2366	151	8	r	r	X
ejpam-2366	151	9	)	)	PUNCT
ejpam-2366	151	10	6	6	NUM
ejpam-2366	151	11	n	n	NOUN
ejpam-2366	151	12	or	or	CCONJ
ejpam-2366	151	13	(	(	PUNCT
ejpam-2366	151	14	n	n	X
ejpam-2366	151	15	:	:	PUNCT
ejpam-2366	151	16	r	r	X
ejpam-2366	151	17	)	)	PUNCT
ejpam-2366	151	18	6	6	NUM
ejpam-2366	151	19	(	(	PUNCT
ejpam-2366	151	20	φ(n	φ(n	ADJ
ejpam-2366	151	21	)	)	PUNCT
ejpam-2366	151	22	:	:	PUNCT
ejpam-2366	151	23	r	r	X
ejpam-2366	151	24	)	)	PUNCT
ejpam-2366	151	25	,	,	PUNCT
ejpam-2366	151	26	by	by	ADP
ejpam-2366	151	27	lemma	lemma	PROPN
ejpam-2366	151	28	3.1	3.1	NUM
ejpam-2366	151	29	of	of	ADP
ejpam-2366	151	30	[	[	X
ejpam-2366	151	31	22	22	NUM
ejpam-2366	151	32	]	]	PUNCT
ejpam-2366	151	33	.	.	PUNCT
ejpam-2366	152	1	since	since	SCONJ
ejpam-2366	152	2	rn	rn	PROPN
ejpam-2366	152	3	6	6	NUM
ejpam-2366	152	4	n	n	PRON
ejpam-2366	152	5	gives	give	VERB
ejpam-2366	152	6	n	n	PRON
ejpam-2366	152	7	6	6	NUM
ejpam-2366	152	8	(	(	PUNCT
ejpam-2366	152	9	n	n	NUM
ejpam-2366	152	10	:	:	PUNCT
ejpam-2366	152	11	r	r	X
ejpam-2366	152	12	)	)	PUNCT
ejpam-2366	152	13	and	and	CCONJ
ejpam-2366	152	14	φ(n	φ(n	NOUN
ejpam-2366	152	15	)	)	PUNCT
ejpam-2366	152	16	6	6	NUM
ejpam-2366	152	17	n	n	PRON
ejpam-2366	152	18	gives	give	VERB
ejpam-2366	152	19	(	(	PUNCT
ejpam-2366	152	20	φ(n	φ(n	ADJ
ejpam-2366	152	21	)	)	PUNCT
ejpam-2366	152	22	:	:	PUNCT
ejpam-2366	152	23	r	r	X
ejpam-2366	152	24	)	)	PUNCT
ejpam-2366	152	25	6	6	NUM
ejpam-2366	152	26	(	(	PUNCT
ejpam-2366	152	27	n	n	NUM
ejpam-2366	152	28	:	:	PUNCT
ejpam-2366	152	29	r	r	X
ejpam-2366	152	30	)	)	PUNCT
ejpam-2366	152	31	,	,	PUNCT
ejpam-2366	152	32	it	it	PRON
ejpam-2366	152	33	follows	follow	VERB
ejpam-2366	152	34	that	that	SCONJ
ejpam-2366	152	35	either	either	CCONJ
ejpam-2366	152	36	(	(	PUNCT
ejpam-2366	152	37	n	n	NUM
ejpam-2366	152	38	:	:	PUNCT
ejpam-2366	152	39	r	r	X
ejpam-2366	152	40	)	)	PUNCT
ejpam-2366	152	41	=	=	SYM
ejpam-2366	152	42	n	n	NOUN
ejpam-2366	152	43	or	or	CCONJ
ejpam-2366	152	44	(	(	PUNCT
ejpam-2366	152	45	n	n	X
ejpam-2366	152	46	:	:	PUNCT
ejpam-2366	152	47	r	r	X
ejpam-2366	152	48	)	)	PUNCT
ejpam-2366	152	49	=	=	SYM
ejpam-2366	152	50	(	(	PUNCT
ejpam-2366	152	51	φ(n	φ(n	ADJ
ejpam-2366	152	52	)	)	PUNCT
ejpam-2366	152	53	:	:	PUNCT
ejpam-2366	153	1	r	r	X
ejpam-2366	153	2	)	)	PUNCT
ejpam-2366	153	3	.	.	PUNCT
ejpam-2366	154	1	3	3	NUM
ejpam-2366	154	2	©	©	NOUN
ejpam-2366	154	3	=⇒	=⇒	NOUN
ejpam-2366	154	4	4	4	NUM
ejpam-2366	154	5	©	©	NOUN
ejpam-2366	154	6	.	.	PUNCT
ejpam-2366	154	7	suppose	suppose	VERB
ejpam-2366	154	8	3	3	NUM
ejpam-2366	154	9	©	©	PROPN
ejpam-2366	154	10	holds	hold	NOUN
ejpam-2366	154	11	.	.	PUNCT
ejpam-2366	155	1	let	let	VERB
ejpam-2366	155	2	ra	ra	PROPN
ejpam-2366	155	3	6	6	NUM
ejpam-2366	155	4	n	n	NOUN
ejpam-2366	155	5	,	,	PUNCT
ejpam-2366	155	6	ra	ra	PROPN
ejpam-2366	155	7	φ(n	φ(n	PROPN
ejpam-2366	155	8	)	)	PUNCT
ejpam-2366	155	9	and	and	CCONJ
ejpam-2366	155	10	r	r	NOUN
ejpam-2366	155	11	(	(	PUNCT
ejpam-2366	155	12	n	n	NOUN
ejpam-2366	155	13	:	:	PUNCT
ejpam-2366	155	14	i	i	PRON
ejpam-2366	155	15	m	m	VERB
ejpam-2366	155	16	)	)	PUNCT
ejpam-2366	155	17	for	for	ADP
ejpam-2366	155	18	r	r	NOUN
ejpam-2366	155	19	∈	∈	PROPN
ejpam-2366	155	20	l∗	l∗	NOUN
ejpam-2366	155	21	,	,	PUNCT
ejpam-2366	155	22	a	a	DET
ejpam-2366	155	23	∈	∈	PROPN
ejpam-2366	155	24	m∗.	m∗.	PROPN
ejpam-2366	155	25	then	then	ADV
ejpam-2366	155	26	by	by	ADP
ejpam-2366	155	27	3	3	NUM
ejpam-2366	155	28	©	©	NOUN
ejpam-2366	155	29	,	,	PUNCT
ejpam-2366	155	30	we	we	PRON
ejpam-2366	155	31	have	have	VERB
ejpam-2366	155	32	either	either	CCONJ
ejpam-2366	155	33	(	(	PUNCT
ejpam-2366	155	34	n	n	NUM
ejpam-2366	155	35	:	:	PUNCT
ejpam-2366	155	36	r	r	X
ejpam-2366	155	37	)	)	PUNCT
ejpam-2366	155	38	=	=	SYM
ejpam-2366	155	39	(	(	PUNCT
ejpam-2366	155	40	φ(n	φ(n	ADJ
ejpam-2366	155	41	)	)	PUNCT
ejpam-2366	155	42	:	:	PUNCT
ejpam-2366	156	1	r	r	X
ejpam-2366	156	2	)	)	PUNCT
ejpam-2366	156	3	or	or	CCONJ
ejpam-2366	156	4	(	(	PUNCT
ejpam-2366	156	5	n	n	X
ejpam-2366	156	6	:	:	PUNCT
ejpam-2366	156	7	r	r	X
ejpam-2366	156	8	)	)	PUNCT
ejpam-2366	156	9	=	=	SYM
ejpam-2366	156	10	n	n	NOUN
ejpam-2366	156	11	.	.	PUNCT
ejpam-2366	157	1	if	if	SCONJ
ejpam-2366	157	2	(	(	PUNCT
ejpam-2366	157	3	n	n	X
ejpam-2366	157	4	:	:	PUNCT
ejpam-2366	157	5	r	r	X
ejpam-2366	157	6	)	)	PUNCT
ejpam-2366	157	7	=	=	SYM
ejpam-2366	157	8	(	(	PUNCT
ejpam-2366	157	9	φ(n	φ(n	ADJ
ejpam-2366	157	10	)	)	PUNCT
ejpam-2366	157	11	:	:	PUNCT
ejpam-2366	158	1	r	r	X
ejpam-2366	158	2	)	)	PUNCT
ejpam-2366	158	3	,	,	PUNCT
ejpam-2366	158	4	then	then	ADV
ejpam-2366	158	5	as	as	ADP
ejpam-2366	158	6	ra	ra	PROPN
ejpam-2366	158	7	6	6	NUM
ejpam-2366	158	8	n	n	NOUN
ejpam-2366	158	9	,	,	PUNCT
ejpam-2366	158	10	it	it	PRON
ejpam-2366	158	11	follows	follow	VERB
ejpam-2366	158	12	that	that	SCONJ
ejpam-2366	158	13	a	a	DET
ejpam-2366	158	14	6	6	NUM
ejpam-2366	158	15	(	(	PUNCT
ejpam-2366	158	16	φ(n	φ(n	ADJ
ejpam-2366	158	17	)	)	PUNCT
ejpam-2366	158	18	:	:	PUNCT
ejpam-2366	158	19	r	r	X
ejpam-2366	158	20	)	)	PUNCT
ejpam-2366	158	21	which	which	PRON
ejpam-2366	158	22	contradicts	contradict	VERB
ejpam-2366	158	23	ra	ra	PROPN
ejpam-2366	158	24	φ(n	φ(n	NOUN
ejpam-2366	158	25	)	)	PUNCT
ejpam-2366	158	26	and	and	CCONJ
ejpam-2366	158	27	so	so	ADV
ejpam-2366	158	28	we	we	PRON
ejpam-2366	158	29	must	must	AUX
ejpam-2366	158	30	have	have	VERB
ejpam-2366	158	31	(	(	PUNCT
ejpam-2366	158	32	n	n	NUM
ejpam-2366	158	33	:	:	PUNCT
ejpam-2366	158	34	r	r	X
ejpam-2366	158	35	)	)	PUNCT
ejpam-2366	158	36	=	=	SYM
ejpam-2366	159	1	n	n	PROPN
ejpam-2366	159	2	.	.	PUNCT
ejpam-2366	160	1	therefore	therefore	ADV
ejpam-2366	160	2	ra	ra	PROPN
ejpam-2366	160	3	6	6	NUM
ejpam-2366	160	4	n	n	ADV
ejpam-2366	160	5	gives	give	VERB
ejpam-2366	160	6	a	a	DET
ejpam-2366	160	7	6	6	NUM
ejpam-2366	160	8	n	n	NOUN
ejpam-2366	160	9	.	.	PUNCT
ejpam-2366	161	1	4	4	NUM
ejpam-2366	161	2	©	©	NOUN
ejpam-2366	161	3	=⇒	=⇒	NOUN
ejpam-2366	161	4	1	1	NUM
ejpam-2366	161	5	©	©	NOUN
ejpam-2366	161	6	.	.	PUNCT
ejpam-2366	161	7	suppose	suppose	VERB
ejpam-2366	161	8	4	4	NUM
ejpam-2366	161	9	©	©	PROPN
ejpam-2366	161	10	holds	hold	NOUN
ejpam-2366	161	11	.	.	PUNCT
ejpam-2366	162	1	let	let	VERB
ejpam-2366	162	2	aq	aq	VERB
ejpam-2366	162	3	6	6	NUM
ejpam-2366	162	4	n	n	NOUN
ejpam-2366	162	5	,	,	PUNCT
ejpam-2366	162	6	aq	aq	X
ejpam-2366	162	7	φ(n	φ(n	ADJ
ejpam-2366	162	8	)	)	PUNCT
ejpam-2366	162	9	and	and	CCONJ
ejpam-2366	162	10	q	q	ADJ
ejpam-2366	162	11	n	n	PROPN
ejpam-2366	162	12	for	for	ADP
ejpam-2366	162	13	a	a	DET
ejpam-2366	162	14	∈	∈	PROPN
ejpam-2366	162	15	l	l	NOUN
ejpam-2366	162	16	,	,	PUNCT
ejpam-2366	162	17	q	q	PRON
ejpam-2366	162	18	∈m	∈m	NOUN
ejpam-2366	162	19	.	.	PUNCT
ejpam-2366	163	1	as	as	SCONJ
ejpam-2366	163	2	l	l	PROPN
ejpam-2366	163	3	and	and	CCONJ
ejpam-2366	163	4	m	m	PROPN
ejpam-2366	163	5	are	be	AUX
ejpam-2366	163	6	compactly	compactly	ADV
ejpam-2366	163	7	generated	generate	VERB
ejpam-2366	163	8	,	,	PUNCT
ejpam-2366	163	9	there	there	PRON
ejpam-2366	163	10	exist	exist	VERB
ejpam-2366	163	11	x′	x′	PROPN
ejpam-2366	163	12	∈	∈	PROPN
ejpam-2366	163	13	l∗	l∗	PROPN
ejpam-2366	163	14	and	and	CCONJ
ejpam-2366	163	15	y	y	PROPN
ejpam-2366	163	16	,	,	PUNCT
ejpam-2366	163	17	y	y	PROPN
ejpam-2366	163	18	′	′	NUM
ejpam-2366	163	19	∈	∈	PROPN
ejpam-2366	163	20	m∗	m∗	VERB
ejpam-2366	163	21	such	such	ADJ
ejpam-2366	163	22	that	that	SCONJ
ejpam-2366	163	23	x′	x′	PROPN
ejpam-2366	163	24	6	6	NUM
ejpam-2366	163	25	a	a	NOUN
ejpam-2366	163	26	,	,	PUNCT
ejpam-2366	163	27	y	y	PROPN
ejpam-2366	163	28	6	6	NUM
ejpam-2366	163	29	q	q	NOUN
ejpam-2366	163	30	,	,	PUNCT
ejpam-2366	163	31	y	y	PROPN
ejpam-2366	163	32	′	′	NUM
ejpam-2366	163	33	6	6	NUM
ejpam-2366	163	34	q	q	NOUN
ejpam-2366	163	35	,	,	PUNCT
ejpam-2366	163	36	y	y	PROPN
ejpam-2366	163	37	′	′	NUM
ejpam-2366	163	38	n	n	PROPN
ejpam-2366	163	39	and	and	CCONJ
ejpam-2366	163	40	x′y	x′y	PROPN
ejpam-2366	163	41	′	′	NUM
ejpam-2366	163	42	φ(n	φ(n	PROPN
ejpam-2366	163	43	)	)	PUNCT
ejpam-2366	163	44	.	.	PUNCT
ejpam-2366	164	1	let	let	VERB
ejpam-2366	164	2	x	x	PRON
ejpam-2366	164	3	∈	∈	PROPN
ejpam-2366	164	4	l∗	l∗	NOUN
ejpam-2366	164	5	be	be	AUX
ejpam-2366	164	6	such	such	ADJ
ejpam-2366	164	7	that	that	SCONJ
ejpam-2366	164	8	x	x	PROPN
ejpam-2366	164	9	6	6	NUM
ejpam-2366	164	10	a.	a.	NOUN
ejpam-2366	164	11	then	then	ADV
ejpam-2366	164	12	(	(	PUNCT
ejpam-2366	164	13	x∨x′	x∨x′	PROPN
ejpam-2366	164	14	)	)	PUNCT
ejpam-2366	164	15	∈	∈	PROPN
ejpam-2366	164	16	l∗	l∗	PROPN
ejpam-2366	164	17	,	,	PUNCT
ejpam-2366	164	18	(	(	PUNCT
ejpam-2366	164	19	y	y	PROPN
ejpam-2366	164	20	∨y	∨y	PROPN
ejpam-2366	164	21	′	′	NOUN
ejpam-2366	164	22	)	)	PUNCT
ejpam-2366	164	23	∈m∗	∈m∗	NOUN
ejpam-2366	164	24	such	such	ADJ
ejpam-2366	164	25	that	that	SCONJ
ejpam-2366	164	26	(	(	PUNCT
ejpam-2366	164	27	x∨x′)(y	x∨x′)(y	PROPN
ejpam-2366	164	28	∨y	∨y	PROPN
ejpam-2366	164	29	′	′	NUM
ejpam-2366	164	30	)	)	PUNCT
ejpam-2366	164	31	6	6	NUM
ejpam-2366	164	32	aq	aq	NOUN
ejpam-2366	164	33	6	6	NUM
ejpam-2366	164	34	n	n	CCONJ
ejpam-2366	164	35	,	,	PUNCT
ejpam-2366	164	36	(	(	PUNCT
ejpam-2366	164	37	x∨x′)(y	x∨x′)(y	PROPN
ejpam-2366	164	38	∨y	∨y	PROPN
ejpam-2366	164	39	′	′	NOUN
ejpam-2366	164	40	)	)	PUNCT
ejpam-2366	164	41	φ(n	φ(n	NOUN
ejpam-2366	164	42	)	)	PUNCT
ejpam-2366	164	43	and	and	CCONJ
ejpam-2366	164	44	(	(	PUNCT
ejpam-2366	164	45	y	y	PROPN
ejpam-2366	164	46	∨	∨	NUM
ejpam-2366	164	47	y	y	PROPN
ejpam-2366	164	48	′	′	NUM
ejpam-2366	164	49	)	)	PUNCT
ejpam-2366	164	50	n	n	CCONJ
ejpam-2366	164	51	.	.	PUNCT
ejpam-2366	165	1	so	so	ADV
ejpam-2366	165	2	by	by	ADP
ejpam-2366	165	3	4	4	NUM
ejpam-2366	165	4	©	©	NOUN
ejpam-2366	165	5	,	,	PUNCT
ejpam-2366	165	6	(	(	PUNCT
ejpam-2366	165	7	x	x	PROPN
ejpam-2366	165	8	∨	∨	NUM
ejpam-2366	165	9	x′	x′	NUM
ejpam-2366	165	10	)	)	PUNCT
ejpam-2366	165	11	6	6	NUM
ejpam-2366	165	12	(	(	PUNCT
ejpam-2366	165	13	n	n	NUM
ejpam-2366	165	14	:	:	PUNCT
ejpam-2366	165	15	i	i	PRON
ejpam-2366	165	16	m	m	VERB
ejpam-2366	165	17	)	)	PUNCT
ejpam-2366	165	18	which	which	PRON
ejpam-2366	165	19	implies	imply	VERB
ejpam-2366	165	20	a	a	DET
ejpam-2366	165	21	6	6	NUM
ejpam-2366	165	22	(	(	PUNCT
ejpam-2366	165	23	n	n	NUM
ejpam-2366	165	24	:	:	PUNCT
ejpam-2366	165	25	i	i	PRON
ejpam-2366	165	26	m	m	PROPN
ejpam-2366	165	27	)	)	PUNCT
ejpam-2366	165	28	.	.	PUNCT
ejpam-2366	166	1	therefore	therefore	ADV
ejpam-2366	166	2	n	n	PROPN
ejpam-2366	166	3	is	be	AUX
ejpam-2366	166	4	φ	φ	VERB
ejpam-2366	166	5	-	-	NOUN
ejpam-2366	166	6	prime	prime	NOUN
ejpam-2366	166	7	.	.	PUNCT
ejpam-2366	167	1	the	the	DET
ejpam-2366	167	2	following	follow	VERB
ejpam-2366	167	3	2	2	NUM
ejpam-2366	167	4	corollaries	corollary	NOUN
ejpam-2366	167	5	are	be	AUX
ejpam-2366	167	6	consequences	consequence	NOUN
ejpam-2366	167	7	of	of	ADP
ejpam-2366	167	8	theorem	theorem	ADJ
ejpam-2366	167	9	1	1	NUM
ejpam-2366	167	10	.	.	PUNCT
ejpam-2366	167	11	corollary	corollary	ADJ
ejpam-2366	167	12	1	1	NUM
ejpam-2366	167	13	.	.	PUNCT
ejpam-2366	168	1	let	let	VERB
ejpam-2366	168	2	m	m	PRON
ejpam-2366	168	3	be	be	AUX
ejpam-2366	168	4	a	a	DET
ejpam-2366	168	5	cg	cg	NOUN
ejpam-2366	168	6	-	-	PUNCT
ejpam-2366	168	7	lattice	lattice	NOUN
ejpam-2366	168	8	l	l	NOUN
ejpam-2366	168	9	-	-	NOUN
ejpam-2366	168	10	module	module	NOUN
ejpam-2366	168	11	and	and	CCONJ
ejpam-2366	168	12	n	n	CCONJ
ejpam-2366	168	13	∈	∈	NOUN
ejpam-2366	168	14	m	m	AUX
ejpam-2366	168	15	be	be	VERB
ejpam-2366	168	16	a	a	DET
ejpam-2366	168	17	proper	proper	ADJ
ejpam-2366	168	18	element	element	NOUN
ejpam-2366	168	19	.	.	PUNCT
ejpam-2366	169	1	then	then	ADV
ejpam-2366	169	2	the	the	DET
ejpam-2366	169	3	following	follow	VERB
ejpam-2366	169	4	statements	statement	NOUN
ejpam-2366	169	5	are	be	AUX
ejpam-2366	169	6	equivalent	equivalent	ADJ
ejpam-2366	169	7	:	:	PUNCT
ejpam-2366	169	8	1	1	X
ejpam-2366	169	9	©	©	NOUN
ejpam-2366	169	10	n	n	NUM
ejpam-2366	169	11	is	be	AUX
ejpam-2366	169	12	a	a	DET
ejpam-2366	169	13	weakly	weakly	ADJ
ejpam-2366	169	14	prime	prime	ADJ
ejpam-2366	169	15	element	element	NOUN
ejpam-2366	169	16	of	of	ADP
ejpam-2366	169	17	m	m	PROPN
ejpam-2366	169	18	.	.	PUNCT
ejpam-2366	170	1	2	2	NUM
ejpam-2366	170	2	©	©	NOUN
ejpam-2366	170	3	for	for	ADP
ejpam-2366	170	4	every	every	DET
ejpam-2366	170	5	a	a	DET
ejpam-2366	170	6	∈	∈	NOUN
ejpam-2366	170	7	m	m	VERB
ejpam-2366	170	8	such	such	ADJ
ejpam-2366	170	9	that	that	SCONJ
ejpam-2366	170	10	a	a	DET
ejpam-2366	170	11	n	n	NOUN
ejpam-2366	170	12	,	,	PUNCT
ejpam-2366	170	13	either	either	CCONJ
ejpam-2366	170	14	(	(	PUNCT
ejpam-2366	170	15	n	n	X
ejpam-2366	170	16	:	:	PUNCT
ejpam-2366	170	17	a	a	X
ejpam-2366	170	18	)	)	PUNCT
ejpam-2366	170	19	=	=	SYM
ejpam-2366	170	20	(	(	PUNCT
ejpam-2366	170	21	n	n	X
ejpam-2366	170	22	:	:	PUNCT
ejpam-2366	170	23	i	i	PRON
ejpam-2366	170	24	m	m	VERB
ejpam-2366	170	25	)	)	PUNCT
ejpam-2366	170	26	or	or	CCONJ
ejpam-2366	170	27	(	(	PUNCT
ejpam-2366	170	28	n	n	X
ejpam-2366	170	29	:	:	PUNCT
ejpam-2366	170	30	a	a	X
ejpam-2366	170	31	)	)	PUNCT
ejpam-2366	170	32	=	=	SYM
ejpam-2366	170	33	(	(	PUNCT
ejpam-2366	170	34	om	om	INTJ
ejpam-2366	170	35	:	:	PUNCT
ejpam-2366	170	36	a	a	X
ejpam-2366	170	37	)	)	PUNCT
ejpam-2366	170	38	.	.	PUNCT
ejpam-2366	171	1	3	3	NUM
ejpam-2366	171	2	©	©	NOUN
ejpam-2366	171	3	for	for	ADP
ejpam-2366	171	4	every	every	DET
ejpam-2366	171	5	r	r	NOUN
ejpam-2366	171	6	∈	∈	NOUN
ejpam-2366	171	7	l	l	NOUN
ejpam-2366	171	8	such	such	ADJ
ejpam-2366	171	9	that	that	PRON
ejpam-2366	171	10	r	r	NOUN
ejpam-2366	171	11	(	(	PUNCT
ejpam-2366	171	12	n	n	NOUN
ejpam-2366	171	13	:	:	PUNCT
ejpam-2366	171	14	i	i	PRON
ejpam-2366	171	15	m	m	PROPN
ejpam-2366	171	16	)	)	PUNCT
ejpam-2366	171	17	,	,	PUNCT
ejpam-2366	171	18	either	either	CCONJ
ejpam-2366	171	19	(	(	PUNCT
ejpam-2366	171	20	n	n	NUM
ejpam-2366	171	21	:	:	PUNCT
ejpam-2366	171	22	r	r	X
ejpam-2366	171	23	)	)	PUNCT
ejpam-2366	171	24	=	=	SYM
ejpam-2366	171	25	n	n	NOUN
ejpam-2366	171	26	or	or	CCONJ
ejpam-2366	171	27	(	(	PUNCT
ejpam-2366	171	28	n	n	X
ejpam-2366	171	29	:	:	PUNCT
ejpam-2366	171	30	r	r	X
ejpam-2366	171	31	)	)	PUNCT
ejpam-2366	171	32	=	=	SYM
ejpam-2366	171	33	(	(	PUNCT
ejpam-2366	171	34	om	om	INTJ
ejpam-2366	171	35	:	:	PUNCT
ejpam-2366	171	36	r	r	X
ejpam-2366	171	37	)	)	PUNCT
ejpam-2366	171	38	.	.	PUNCT
ejpam-2366	172	1	4	4	NUM
ejpam-2366	172	2	©	©	NOUN
ejpam-2366	172	3	for	for	ADP
ejpam-2366	172	4	every	every	DET
ejpam-2366	172	5	r	r	NOUN
ejpam-2366	172	6	∈	∈	PROPN
ejpam-2366	172	7	l∗	l∗	NOUN
ejpam-2366	172	8	,	,	PUNCT
ejpam-2366	172	9	a	a	DET
ejpam-2366	172	10	∈m∗	∈m∗	NOUN
ejpam-2366	172	11	,	,	PUNCT
ejpam-2366	172	12	if	if	SCONJ
ejpam-2366	172	13	om	om	PROPN
ejpam-2366	172	14	6=	6=	PROPN
ejpam-2366	172	15	ra	ra	PROPN
ejpam-2366	172	16	6	6	NUM
ejpam-2366	172	17	n	n	NOUN
ejpam-2366	172	18	,	,	PUNCT
ejpam-2366	172	19	then	then	ADV
ejpam-2366	172	20	either	either	CCONJ
ejpam-2366	172	21	r	r	NOUN
ejpam-2366	172	22	6	6	NUM
ejpam-2366	172	23	(	(	PUNCT
ejpam-2366	172	24	n	n	NUM
ejpam-2366	172	25	:	:	PUNCT
ejpam-2366	172	26	i	i	PRON
ejpam-2366	172	27	m	m	VERB
ejpam-2366	172	28	)	)	PUNCT
ejpam-2366	172	29	or	or	CCONJ
ejpam-2366	172	30	a	a	DET
ejpam-2366	172	31	6	6	NUM
ejpam-2366	172	32	n	n	NOUN
ejpam-2366	172	33	.	.	PUNCT
ejpam-2366	173	1	a.	a.	PROPN
ejpam-2366	173	2	v.	v.	PROPN
ejpam-2366	173	3	bingi	bingi	PROPN
ejpam-2366	173	4	,	,	PUNCT
ejpam-2366	173	5	c.	c.	PROPN
ejpam-2366	173	6	s.	s.	PROPN
ejpam-2366	173	7	manjarekar	manjarekar	PROPN
ejpam-2366	173	8	/	/	PROPN
ejpam-2366	173	9	eur	eur	PROPN
ejpam-2366	173	10	.	.	PUNCT
ejpam-2366	174	1	j.	j.	PROPN
ejpam-2366	174	2	pure	pure	PROPN
ejpam-2366	174	3	appl	appl	PROPN
ejpam-2366	174	4	.	.	PROPN
ejpam-2366	174	5	math	math	PROPN
ejpam-2366	174	6	,	,	PUNCT
ejpam-2366	174	7	14	14	NUM
ejpam-2366	174	8	(	(	PUNCT
ejpam-2366	174	9	2	2	NUM
ejpam-2366	174	10	)	)	PUNCT
ejpam-2366	174	11	(	(	PUNCT
ejpam-2366	174	12	2021	2021	NUM
ejpam-2366	174	13	)	)	PUNCT
ejpam-2366	174	14	,	,	PUNCT
ejpam-2366	174	15	551	551	NUM
ejpam-2366	174	16	-	-	SYM
ejpam-2366	174	17	577	577	NUM
ejpam-2366	174	18	556	556	NUM
ejpam-2366	174	19	corollary	corollary	ADJ
ejpam-2366	174	20	2	2	NUM
ejpam-2366	174	21	.	.	PUNCT
ejpam-2366	175	1	let	let	VERB
ejpam-2366	175	2	m	m	PRON
ejpam-2366	175	3	be	be	AUX
ejpam-2366	175	4	a	a	DET
ejpam-2366	175	5	cg	cg	NOUN
ejpam-2366	175	6	-	-	PUNCT
ejpam-2366	175	7	lattice	lattice	NOUN
ejpam-2366	175	8	l	l	NOUN
ejpam-2366	175	9	-	-	NOUN
ejpam-2366	175	10	module	module	NOUN
ejpam-2366	175	11	and	and	CCONJ
ejpam-2366	175	12	n	n	CCONJ
ejpam-2366	175	13	∈	∈	NOUN
ejpam-2366	175	14	m	m	AUX
ejpam-2366	175	15	be	be	VERB
ejpam-2366	175	16	a	a	DET
ejpam-2366	175	17	proper	proper	ADJ
ejpam-2366	175	18	element	element	NOUN
ejpam-2366	175	19	.	.	PUNCT
ejpam-2366	176	1	then	then	ADV
ejpam-2366	176	2	the	the	DET
ejpam-2366	176	3	following	follow	VERB
ejpam-2366	176	4	statements	statement	NOUN
ejpam-2366	176	5	are	be	AUX
ejpam-2366	176	6	equivalent	equivalent	ADJ
ejpam-2366	176	7	:	:	PUNCT
ejpam-2366	176	8	1	1	X
ejpam-2366	176	9	©	©	NOUN
ejpam-2366	176	10	n	n	NUM
ejpam-2366	176	11	is	be	AUX
ejpam-2366	176	12	an	an	DET
ejpam-2366	176	13	almost	almost	ADV
ejpam-2366	176	14	prime	prime	ADJ
ejpam-2366	176	15	element	element	NOUN
ejpam-2366	176	16	of	of	ADP
ejpam-2366	176	17	m	m	PROPN
ejpam-2366	176	18	.	.	PUNCT
ejpam-2366	177	1	2	2	NUM
ejpam-2366	177	2	©	©	NOUN
ejpam-2366	177	3	for	for	ADP
ejpam-2366	177	4	every	every	DET
ejpam-2366	177	5	a	a	DET
ejpam-2366	177	6	∈m	∈m	NOUN
ejpam-2366	177	7	such	such	ADJ
ejpam-2366	177	8	that	that	SCONJ
ejpam-2366	177	9	a	a	DET
ejpam-2366	177	10	n	n	NOUN
ejpam-2366	177	11	,	,	PUNCT
ejpam-2366	177	12	either	either	CCONJ
ejpam-2366	177	13	(	(	PUNCT
ejpam-2366	177	14	n	n	X
ejpam-2366	177	15	:	:	PUNCT
ejpam-2366	177	16	a	a	X
ejpam-2366	177	17	)	)	PUNCT
ejpam-2366	177	18	=	=	SYM
ejpam-2366	177	19	(	(	PUNCT
ejpam-2366	177	20	(	(	PUNCT
ejpam-2366	177	21	n	n	X
ejpam-2366	177	22	:	:	PUNCT
ejpam-2366	177	23	i	i	PRON
ejpam-2366	177	24	m	m	PROPN
ejpam-2366	177	25	)	)	PUNCT
ejpam-2366	178	1	n	n	CCONJ
ejpam-2366	178	2	:	:	PUNCT
ejpam-2366	178	3	a	a	X
ejpam-2366	178	4	)	)	PUNCT
ejpam-2366	178	5	or	or	CCONJ
ejpam-2366	178	6	(	(	PUNCT
ejpam-2366	178	7	n	n	X
ejpam-2366	178	8	:	:	PUNCT
ejpam-2366	178	9	a	a	X
ejpam-2366	178	10	)	)	PUNCT
ejpam-2366	178	11	=	=	SYM
ejpam-2366	178	12	(	(	PUNCT
ejpam-2366	178	13	n	n	X
ejpam-2366	178	14	:	:	PUNCT
ejpam-2366	178	15	i	i	PRON
ejpam-2366	178	16	m	m	PROPN
ejpam-2366	178	17	)	)	PUNCT
ejpam-2366	178	18	.	.	PUNCT
ejpam-2366	179	1	3	3	NUM
ejpam-2366	179	2	©	©	NOUN
ejpam-2366	179	3	for	for	ADP
ejpam-2366	179	4	every	every	DET
ejpam-2366	179	5	r	r	NOUN
ejpam-2366	179	6	∈	∈	NOUN
ejpam-2366	179	7	l	l	NOUN
ejpam-2366	179	8	such	such	ADJ
ejpam-2366	179	9	that	that	DET
ejpam-2366	179	10	r	r	NOUN
ejpam-2366	179	11	(	(	PUNCT
ejpam-2366	179	12	n	n	NOUN
ejpam-2366	179	13	:	:	PUNCT
ejpam-2366	179	14	i	i	PRON
ejpam-2366	179	15	m	m	PROPN
ejpam-2366	179	16	)	)	PUNCT
ejpam-2366	179	17	,	,	PUNCT
ejpam-2366	179	18	either	either	CCONJ
ejpam-2366	179	19	(	(	PUNCT
ejpam-2366	179	20	n	n	NUM
ejpam-2366	179	21	:	:	PUNCT
ejpam-2366	179	22	r	r	X
ejpam-2366	179	23	)	)	PUNCT
ejpam-2366	179	24	=	=	SYM
ejpam-2366	179	25	(	(	PUNCT
ejpam-2366	179	26	(	(	PUNCT
ejpam-2366	179	27	n	n	X
ejpam-2366	179	28	:	:	PUNCT
ejpam-2366	179	29	i	i	PRON
ejpam-2366	179	30	m	m	PROPN
ejpam-2366	179	31	)	)	PUNCT
ejpam-2366	179	32	n	n	NOUN
ejpam-2366	179	33	:	:	PUNCT
ejpam-2366	179	34	r	r	X
ejpam-2366	179	35	)	)	PUNCT
ejpam-2366	179	36	or	or	CCONJ
ejpam-2366	179	37	(	(	PUNCT
ejpam-2366	179	38	n	n	X
ejpam-2366	179	39	:	:	PUNCT
ejpam-2366	179	40	r	r	X
ejpam-2366	179	41	)	)	PUNCT
ejpam-2366	179	42	=	=	SYM
ejpam-2366	179	43	n	n	NOUN
ejpam-2366	179	44	.	.	PUNCT
ejpam-2366	180	1	4	4	NUM
ejpam-2366	180	2	©	©	NOUN
ejpam-2366	180	3	for	for	ADP
ejpam-2366	180	4	every	every	DET
ejpam-2366	180	5	r	r	NOUN
ejpam-2366	180	6	∈	∈	PROPN
ejpam-2366	180	7	l∗	l∗	NOUN
ejpam-2366	180	8	,	,	PUNCT
ejpam-2366	180	9	a	a	DET
ejpam-2366	180	10	∈m∗	∈m∗	NOUN
ejpam-2366	180	11	,	,	PUNCT
ejpam-2366	180	12	if	if	SCONJ
ejpam-2366	180	13	ra	ra	PROPN
ejpam-2366	180	14	6	6	NUM
ejpam-2366	180	15	n	n	NOUN
ejpam-2366	180	16	and	and	CCONJ
ejpam-2366	180	17	ra	ra	PROPN
ejpam-2366	180	18	(	(	PUNCT
ejpam-2366	180	19	n	n	PROPN
ejpam-2366	180	20	:	:	PUNCT
ejpam-2366	180	21	i	i	PRON
ejpam-2366	180	22	m	m	PROPN
ejpam-2366	180	23	)	)	PUNCT
ejpam-2366	180	24	n	n	CCONJ
ejpam-2366	180	25	,	,	PUNCT
ejpam-2366	180	26	then	then	ADV
ejpam-2366	180	27	either	either	CCONJ
ejpam-2366	180	28	a	a	DET
ejpam-2366	180	29	6	6	NUM
ejpam-2366	180	30	n	n	NOUN
ejpam-2366	180	31	or	or	CCONJ
ejpam-2366	180	32	r	r	NOUN
ejpam-2366	180	33	6	6	NUM
ejpam-2366	180	34	(	(	PUNCT
ejpam-2366	180	35	n	n	NUM
ejpam-2366	180	36	:	:	PUNCT
ejpam-2366	180	37	i	i	PRON
ejpam-2366	180	38	m	m	PROPN
ejpam-2366	180	39	)	)	PUNCT
ejpam-2366	180	40	.	.	PUNCT
ejpam-2366	181	1	to	to	PART
ejpam-2366	181	2	obtain	obtain	VERB
ejpam-2366	181	3	the	the	DET
ejpam-2366	181	4	relation	relation	NOUN
ejpam-2366	181	5	among	among	ADP
ejpam-2366	181	6	prime	prime	ADJ
ejpam-2366	181	7	,	,	PUNCT
ejpam-2366	181	8	weakly	weakly	ADJ
ejpam-2366	181	9	prime	prime	ADJ
ejpam-2366	181	10	,	,	PUNCT
ejpam-2366	181	11	ω	ω	NOUN
ejpam-2366	181	12	-	-	NOUN
ejpam-2366	181	13	prime	prime	ADJ
ejpam-2366	181	14	,	,	PUNCT
ejpam-2366	181	15	n	n	CCONJ
ejpam-2366	181	16	-	-	PUNCT
ejpam-2366	181	17	almost	almost	ADV
ejpam-2366	181	18	prime	prime	ADJ
ejpam-2366	181	19	(	(	PUNCT
ejpam-2366	181	20	n	n	CCONJ
ejpam-2366	181	21	>	>	X
ejpam-2366	181	22	2	2	NUM
ejpam-2366	181	23	)	)	PUNCT
ejpam-2366	181	24	and	and	CCONJ
ejpam-2366	181	25	almost	almost	ADV
ejpam-2366	181	26	prime	prime	ADJ
ejpam-2366	181	27	elements	element	NOUN
ejpam-2366	181	28	of	of	ADP
ejpam-2366	181	29	an	an	DET
ejpam-2366	181	30	l	l	NOUN
ejpam-2366	181	31	-	-	NOUN
ejpam-2366	181	32	module	module	NOUN
ejpam-2366	181	33	m	m	NOUN
ejpam-2366	181	34	,	,	PUNCT
ejpam-2366	181	35	we	we	PRON
ejpam-2366	181	36	prove	prove	VERB
ejpam-2366	181	37	the	the	DET
ejpam-2366	181	38	following	follow	VERB
ejpam-2366	181	39	result	result	NOUN
ejpam-2366	181	40	.	.	PUNCT
ejpam-2366	182	1	theorem	theorem	NOUN
ejpam-2366	182	2	2	2	NUM
ejpam-2366	182	3	.	.	PUNCT
ejpam-2366	183	1	let	let	VERB
ejpam-2366	183	2	γ1	γ1	NOUN
ejpam-2366	183	3	,	,	PUNCT
ejpam-2366	183	4	γ2	γ2	PROPN
ejpam-2366	183	5	:	:	PUNCT
ejpam-2366	183	6	m	m	AUX
ejpam-2366	183	7	−→	−→	ADJ
ejpam-2366	183	8	m	m	AUX
ejpam-2366	183	9	be	be	VERB
ejpam-2366	183	10	functions	function	NOUN
ejpam-2366	183	11	on	on	ADP
ejpam-2366	183	12	an	an	DET
ejpam-2366	183	13	l	l	NOUN
ejpam-2366	183	14	-	-	NOUN
ejpam-2366	183	15	module	module	NOUN
ejpam-2366	183	16	m	m	NOUN
ejpam-2366	183	17	such	such	ADJ
ejpam-2366	183	18	that	that	DET
ejpam-2366	183	19	γ1	γ1	PROPN
ejpam-2366	183	20	6	6	NUM
ejpam-2366	183	21	γ2	γ2	NOUN
ejpam-2366	183	22	.	.	PUNCT
ejpam-2366	184	1	then	then	ADV
ejpam-2366	184	2	every	every	DET
ejpam-2366	184	3	proper	proper	ADJ
ejpam-2366	184	4	γ1	γ1	NOUN
ejpam-2366	184	5	-	-	PUNCT
ejpam-2366	184	6	prime	prime	ADJ
ejpam-2366	184	7	element	element	NOUN
ejpam-2366	184	8	of	of	ADP
ejpam-2366	184	9	m	m	PROPN
ejpam-2366	184	10	is	be	AUX
ejpam-2366	184	11	γ2	γ2	ADJ
ejpam-2366	184	12	-	-	PUNCT
ejpam-2366	184	13	prime	prime	NOUN
ejpam-2366	184	14	.	.	PUNCT
ejpam-2366	185	1	proof	proof	NOUN
ejpam-2366	185	2	.	.	PUNCT
ejpam-2366	186	1	let	let	VERB
ejpam-2366	186	2	a	a	DET
ejpam-2366	186	3	proper	proper	ADJ
ejpam-2366	186	4	element	element	NOUN
ejpam-2366	186	5	n	n	CCONJ
ejpam-2366	186	6	∈	∈	NOUN
ejpam-2366	186	7	m	m	AUX
ejpam-2366	186	8	be	be	VERB
ejpam-2366	186	9	γ1	γ1	NOUN
ejpam-2366	186	10	-	-	PUNCT
ejpam-2366	186	11	prime	prime	NOUN
ejpam-2366	186	12	.	.	PUNCT
ejpam-2366	187	1	assume	assume	VERB
ejpam-2366	187	2	that	that	SCONJ
ejpam-2366	187	3	aa	aa	PROPN
ejpam-2366	187	4	6	6	NUM
ejpam-2366	187	5	n	n	NOUN
ejpam-2366	187	6	and	and	CCONJ
ejpam-2366	187	7	aa	aa	NOUN
ejpam-2366	187	8	γ2(n	γ2(n	PROPN
ejpam-2366	187	9	)	)	PUNCT
ejpam-2366	187	10	for	for	ADP
ejpam-2366	187	11	a	a	DET
ejpam-2366	187	12	∈	∈	PROPN
ejpam-2366	187	13	l	l	NOUN
ejpam-2366	187	14	,	,	PUNCT
ejpam-2366	187	15	a	a	DET
ejpam-2366	187	16	∈m	∈m	NOUN
ejpam-2366	187	17	.	.	PUNCT
ejpam-2366	188	1	then	then	ADV
ejpam-2366	188	2	as	as	ADP
ejpam-2366	188	3	γ1	γ1	PROPN
ejpam-2366	188	4	6	6	NUM
ejpam-2366	188	5	γ2	γ2	PROPN
ejpam-2366	188	6	,	,	PUNCT
ejpam-2366	188	7	we	we	PRON
ejpam-2366	188	8	have	have	VERB
ejpam-2366	188	9	aa	aa	NOUN
ejpam-2366	188	10	γ1(n	γ1(n	NOUN
ejpam-2366	188	11	)	)	PUNCT
ejpam-2366	188	12	.	.	PUNCT
ejpam-2366	189	1	since	since	SCONJ
ejpam-2366	189	2	n	n	PROPN
ejpam-2366	189	3	is	be	AUX
ejpam-2366	189	4	γ1	γ1	NOUN
ejpam-2366	189	5	-	-	PUNCT
ejpam-2366	189	6	prime	prime	NOUN
ejpam-2366	189	7	,	,	PUNCT
ejpam-2366	189	8	it	it	PRON
ejpam-2366	189	9	follows	follow	VERB
ejpam-2366	189	10	that	that	SCONJ
ejpam-2366	189	11	either	either	CCONJ
ejpam-2366	189	12	a	a	DET
ejpam-2366	189	13	6	6	NUM
ejpam-2366	189	14	n	n	NOUN
ejpam-2366	189	15	or	or	CCONJ
ejpam-2366	189	16	a	a	DET
ejpam-2366	189	17	6	6	NUM
ejpam-2366	189	18	(	(	PUNCT
ejpam-2366	189	19	n	n	NUM
ejpam-2366	189	20	:	:	PUNCT
ejpam-2366	189	21	i	i	PRON
ejpam-2366	189	22	m	m	PROPN
ejpam-2366	189	23	)	)	PUNCT
ejpam-2366	189	24	and	and	CCONJ
ejpam-2366	189	25	hence	hence	ADV
ejpam-2366	189	26	n	n	PRON
ejpam-2366	189	27	is	be	AUX
ejpam-2366	189	28	γ2	γ2	ADJ
ejpam-2366	189	29	-	-	PUNCT
ejpam-2366	189	30	prime	prime	NOUN
ejpam-2366	189	31	.	.	PUNCT
ejpam-2366	190	1	theorem	theorem	NOUN
ejpam-2366	190	2	3	3	X
ejpam-2366	190	3	.	.	PUNCT
ejpam-2366	191	1	let	let	VERB
ejpam-2366	191	2	n	n	PRON
ejpam-2366	191	3	be	be	AUX
ejpam-2366	191	4	a	a	DET
ejpam-2366	191	5	proper	proper	ADJ
ejpam-2366	191	6	element	element	NOUN
ejpam-2366	191	7	of	of	ADP
ejpam-2366	191	8	an	an	DET
ejpam-2366	191	9	l	l	NOUN
ejpam-2366	191	10	-	-	NOUN
ejpam-2366	191	11	module	module	NOUN
ejpam-2366	191	12	m	m	NOUN
ejpam-2366	191	13	.	.	PUNCT
ejpam-2366	192	1	then	then	ADV
ejpam-2366	192	2	n	n	PRON
ejpam-2366	192	3	is	be	AUX
ejpam-2366	192	4	prime	prime	ADJ
ejpam-2366	192	5	implies	implie	NOUN
ejpam-2366	192	6	n	n	AUX
ejpam-2366	192	7	is	be	AUX
ejpam-2366	192	8	weakly	weakly	ADV
ejpam-2366	192	9	prime	prime	ADJ
ejpam-2366	192	10	,	,	PUNCT
ejpam-2366	192	11	n	n	X
ejpam-2366	192	12	is	be	AUX
ejpam-2366	192	13	weakly	weakly	ADJ
ejpam-2366	192	14	prime	prime	ADJ
ejpam-2366	192	15	implies	imply	VERB
ejpam-2366	192	16	n	n	AUX
ejpam-2366	192	17	is	be	AUX
ejpam-2366	192	18	ω	ω	NOUN
ejpam-2366	192	19	-	-	NOUN
ejpam-2366	192	20	prime	prime	NOUN
ejpam-2366	192	21	,	,	PUNCT
ejpam-2366	192	22	n	n	X
ejpam-2366	192	23	is	be	AUX
ejpam-2366	192	24	ω	ω	ADJ
ejpam-2366	192	25	-	-	ADJ
ejpam-2366	192	26	prime	prime	NOUN
ejpam-2366	192	27	implies	imply	VERB
ejpam-2366	192	28	n	n	VERB
ejpam-2366	192	29	is	be	AUX
ejpam-2366	192	30	n	n	ADV
ejpam-2366	192	31	-	-	PUNCT
ejpam-2366	192	32	almost	almost	ADV
ejpam-2366	192	33	prime	prime	ADJ
ejpam-2366	192	34	(	(	PUNCT
ejpam-2366	192	35	n	n	CCONJ
ejpam-2366	192	36	>	>	X
ejpam-2366	192	37	2	2	NUM
ejpam-2366	192	38	)	)	PUNCT
ejpam-2366	192	39	and	and	CCONJ
ejpam-2366	192	40	n	n	PROPN
ejpam-2366	192	41	is	be	AUX
ejpam-2366	192	42	n	n	ADV
ejpam-2366	192	43	-	-	PUNCT
ejpam-2366	192	44	almost	almost	ADV
ejpam-2366	192	45	prime	prime	ADJ
ejpam-2366	192	46	(	(	PUNCT
ejpam-2366	192	47	n	n	CCONJ
ejpam-2366	192	48	>	>	X
ejpam-2366	192	49	2	2	NUM
ejpam-2366	192	50	)	)	PUNCT
ejpam-2366	192	51	implies	imply	VERB
ejpam-2366	192	52	n	n	VERB
ejpam-2366	192	53	is	be	AUX
ejpam-2366	192	54	almost	almost	ADV
ejpam-2366	192	55	prime	prime	ADJ
ejpam-2366	192	56	.	.	PUNCT
ejpam-2366	193	1	proof	proof	NOUN
ejpam-2366	193	2	.	.	PUNCT
ejpam-2366	194	1	by	by	ADP
ejpam-2366	194	2	definition	definition	NOUN
ejpam-2366	194	3	,	,	PUNCT
ejpam-2366	194	4	every	every	DET
ejpam-2366	194	5	prime	prime	ADJ
ejpam-2366	194	6	element	element	NOUN
ejpam-2366	194	7	of	of	ADP
ejpam-2366	194	8	an	an	DET
ejpam-2366	194	9	l	l	NOUN
ejpam-2366	194	10	-	-	NOUN
ejpam-2366	194	11	module	module	NOUN
ejpam-2366	194	12	m	m	NOUN
ejpam-2366	194	13	is	be	AUX
ejpam-2366	194	14	weakly	weakly	ADV
ejpam-2366	194	15	prime	prime	ADJ
ejpam-2366	194	16	and	and	CCONJ
ejpam-2366	194	17	hence	hence	ADV
ejpam-2366	194	18	n	n	PRON
ejpam-2366	194	19	is	be	AUX
ejpam-2366	194	20	prime	prime	ADJ
ejpam-2366	194	21	implies	implie	NOUN
ejpam-2366	194	22	n	n	AUX
ejpam-2366	194	23	is	be	AUX
ejpam-2366	194	24	weakly	weakly	ADV
ejpam-2366	194	25	prime	prime	ADJ
ejpam-2366	194	26	.	.	PUNCT
ejpam-2366	195	1	the	the	DET
ejpam-2366	195	2	remaining	remain	VERB
ejpam-2366	195	3	implications	implication	NOUN
ejpam-2366	195	4	follow	follow	VERB
ejpam-2366	195	5	by	by	ADP
ejpam-2366	195	6	using	use	VERB
ejpam-2366	195	7	theorem	theorem	NOUN
ejpam-2366	195	8	2	2	NUM
ejpam-2366	195	9	to	to	ADP
ejpam-2366	195	10	the	the	DET
ejpam-2366	195	11	fact	fact	NOUN
ejpam-2366	195	12	that	that	SCONJ
ejpam-2366	195	13	φ0	φ0	PROPN
ejpam-2366	195	14	6	6	NUM
ejpam-2366	195	15	φω	φω	PART
ejpam-2366	195	16	6	6	NUM
ejpam-2366	195	17	·	·	PUNCT
ejpam-2366	195	18	·	·	PUNCT
ejpam-2366	195	19	·	·	PUNCT
ejpam-2366	195	20	6	6	NUM
ejpam-2366	195	21	φn+1	φn+1	NOUN
ejpam-2366	195	22	6	6	NUM
ejpam-2366	195	23	φn	φn	ADP
ejpam-2366	195	24	6	6	NUM
ejpam-2366	195	25	·	·	PUNCT
ejpam-2366	195	26	·	·	PUNCT
ejpam-2366	195	27	·	·	PUNCT
ejpam-2366	195	28	6	6	NUM
ejpam-2366	195	29	φ2	φ2	NOUN
ejpam-2366	195	30	.	.	PUNCT
ejpam-2366	196	1	from	from	ADP
ejpam-2366	196	2	the	the	DET
ejpam-2366	196	3	theorem	theorem	NOUN
ejpam-2366	196	4	3	3	NUM
ejpam-2366	196	5	,	,	PUNCT
ejpam-2366	196	6	we	we	PRON
ejpam-2366	196	7	get	get	VERB
ejpam-2366	196	8	the	the	DET
ejpam-2366	196	9	following	follow	VERB
ejpam-2366	196	10	characterization	characterization	NOUN
ejpam-2366	196	11	of	of	ADP
ejpam-2366	196	12	a	a	DET
ejpam-2366	196	13	ω	ω	ADJ
ejpam-2366	196	14	-	-	ADJ
ejpam-2366	196	15	prime	prime	ADJ
ejpam-2366	196	16	element	element	NOUN
ejpam-2366	196	17	of	of	ADP
ejpam-2366	196	18	an	an	DET
ejpam-2366	196	19	l	l	NOUN
ejpam-2366	196	20	-	-	NOUN
ejpam-2366	196	21	module	module	NOUN
ejpam-2366	196	22	m	m	NOUN
ejpam-2366	196	23	.	.	PUNCT
ejpam-2366	197	1	corollary	corollary	ADJ
ejpam-2366	197	2	3	3	X
ejpam-2366	197	3	.	.	PUNCT
ejpam-2366	198	1	let	let	VERB
ejpam-2366	198	2	n	n	PRON
ejpam-2366	198	3	be	be	AUX
ejpam-2366	198	4	a	a	DET
ejpam-2366	198	5	proper	proper	ADJ
ejpam-2366	198	6	element	element	NOUN
ejpam-2366	198	7	of	of	ADP
ejpam-2366	198	8	an	an	DET
ejpam-2366	198	9	l	l	NOUN
ejpam-2366	198	10	-	-	NOUN
ejpam-2366	198	11	module	module	NOUN
ejpam-2366	198	12	m	m	NOUN
ejpam-2366	198	13	.	.	PUNCT
ejpam-2366	199	1	then	then	ADV
ejpam-2366	199	2	n	n	PROPN
ejpam-2366	199	3	is	be	AUX
ejpam-2366	199	4	ω	ω	NOUN
ejpam-2366	199	5	-	-	NOUN
ejpam-2366	199	6	prime	prime	NOUN
ejpam-2366	199	7	if	if	SCONJ
ejpam-2366	200	1	and	and	CCONJ
ejpam-2366	200	2	only	only	ADV
ejpam-2366	200	3	if	if	SCONJ
ejpam-2366	200	4	n	n	PRON
ejpam-2366	200	5	is	be	AUX
ejpam-2366	200	6	n	n	ADV
ejpam-2366	200	7	-	-	PUNCT
ejpam-2366	200	8	almost	almost	ADV
ejpam-2366	200	9	prime	prime	NOUN
ejpam-2366	200	10	for	for	ADP
ejpam-2366	200	11	every	every	DET
ejpam-2366	200	12	n	n	NOUN
ejpam-2366	200	13	>	>	X
ejpam-2366	200	14	2	2	NUM
ejpam-2366	200	15	.	.	PUNCT
ejpam-2366	201	1	proof	proof	NOUN
ejpam-2366	201	2	.	.	PUNCT
ejpam-2366	202	1	assume	assume	VERB
ejpam-2366	202	2	that	that	SCONJ
ejpam-2366	202	3	n	n	PRON
ejpam-2366	202	4	∈	∈	PROPN
ejpam-2366	202	5	m	m	NOUN
ejpam-2366	202	6	is	be	AUX
ejpam-2366	202	7	n	n	ADV
ejpam-2366	202	8	-	-	PUNCT
ejpam-2366	202	9	almost	almost	ADV
ejpam-2366	202	10	prime	prime	NOUN
ejpam-2366	202	11	for	for	ADP
ejpam-2366	202	12	every	every	DET
ejpam-2366	202	13	n	n	NOUN
ejpam-2366	202	14	>	>	X
ejpam-2366	202	15	2	2	X
ejpam-2366	202	16	.	.	PUNCT
ejpam-2366	203	1	let	let	VERB
ejpam-2366	203	2	aa	aa	PROPN
ejpam-2366	203	3	6	6	NUM
ejpam-2366	203	4	n	n	NOUN
ejpam-2366	203	5	and	and	CCONJ
ejpam-2366	203	6	aa	aa	NOUN
ejpam-2366	203	7	∧∞	∧∞	ADJ
ejpam-2366	203	8	i=1(n	i=1(n	NOUN
ejpam-2366	203	9	:	:	PUNCT
ejpam-2366	204	1	i	i	PRON
ejpam-2366	204	2	m	m	VERB
ejpam-2366	204	3	)	)	PUNCT
ejpam-2366	204	4	in	in	ADP
ejpam-2366	204	5	for	for	ADP
ejpam-2366	204	6	a	a	DET
ejpam-2366	204	7	∈	∈	PROPN
ejpam-2366	204	8	l	l	NOUN
ejpam-2366	204	9	,	,	PUNCT
ejpam-2366	204	10	a	a	DET
ejpam-2366	204	11	∈	∈	NOUN
ejpam-2366	204	12	m	m	NOUN
ejpam-2366	204	13	.	.	PUNCT
ejpam-2366	205	1	then	then	ADV
ejpam-2366	205	2	aa	aa	INTJ
ejpam-2366	205	3	(	(	PUNCT
ejpam-2366	205	4	n	n	NOUN
ejpam-2366	205	5	:	:	PUNCT
ejpam-2366	205	6	i	i	PRON
ejpam-2366	205	7	m	m	PROPN
ejpam-2366	205	8	)	)	PUNCT
ejpam-2366	205	9	n−1n	n−1n	PROPN
ejpam-2366	205	10	for	for	ADP
ejpam-2366	205	11	some	some	DET
ejpam-2366	205	12	n	n	NOUN
ejpam-2366	205	13	>	>	X
ejpam-2366	205	14	2	2	NUM
ejpam-2366	205	15	.	.	PUNCT
ejpam-2366	205	16	since	since	SCONJ
ejpam-2366	205	17	n	n	NUM
ejpam-2366	205	18	is	be	AUX
ejpam-2366	205	19	n	n	ADV
ejpam-2366	205	20	-	-	PUNCT
ejpam-2366	205	21	almost	almost	ADV
ejpam-2366	205	22	prime	prime	ADJ
ejpam-2366	205	23	,	,	PUNCT
ejpam-2366	205	24	we	we	PRON
ejpam-2366	205	25	have	have	VERB
ejpam-2366	205	26	either	either	CCONJ
ejpam-2366	205	27	a	a	DET
ejpam-2366	205	28	6	6	NUM
ejpam-2366	205	29	(	(	PUNCT
ejpam-2366	205	30	n	n	NUM
ejpam-2366	205	31	:	:	PUNCT
ejpam-2366	205	32	i	i	PRON
ejpam-2366	205	33	m	m	VERB
ejpam-2366	205	34	)	)	PUNCT
ejpam-2366	205	35	or	or	CCONJ
ejpam-2366	205	36	a	a	DET
ejpam-2366	205	37	6	6	NUM
ejpam-2366	205	38	n	n	NOUN
ejpam-2366	205	39	and	and	CCONJ
ejpam-2366	205	40	hence	hence	ADV
ejpam-2366	205	41	n	n	PRON
ejpam-2366	205	42	is	be	AUX
ejpam-2366	205	43	ω	ω	NOUN
ejpam-2366	205	44	-	-	NOUN
ejpam-2366	205	45	prime	prime	NOUN
ejpam-2366	205	46	.	.	PUNCT
ejpam-2366	206	1	the	the	DET
ejpam-2366	206	2	converse	converse	NOUN
ejpam-2366	206	3	follows	follow	VERB
ejpam-2366	206	4	from	from	ADP
ejpam-2366	206	5	theorem	theorem	ADJ
ejpam-2366	206	6	3	3	NUM
ejpam-2366	206	7	.	.	PUNCT
ejpam-2366	206	8	before	before	ADP
ejpam-2366	206	9	going	go	VERB
ejpam-2366	206	10	to	to	ADP
ejpam-2366	206	11	the	the	DET
ejpam-2366	206	12	characterization	characterization	NOUN
ejpam-2366	206	13	of	of	ADP
ejpam-2366	206	14	an	an	DET
ejpam-2366	206	15	n	n	ADV
ejpam-2366	206	16	-	-	PUNCT
ejpam-2366	206	17	almost	almost	ADV
ejpam-2366	206	18	prime	prime	ADJ
ejpam-2366	206	19	element	element	NOUN
ejpam-2366	206	20	of	of	ADP
ejpam-2366	206	21	an	an	DET
ejpam-2366	206	22	l	l	NOUN
ejpam-2366	206	23	-	-	NOUN
ejpam-2366	206	24	module	module	NOUN
ejpam-2366	206	25	m	m	NOUN
ejpam-2366	206	26	,	,	PUNCT
ejpam-2366	206	27	we	we	PRON
ejpam-2366	206	28	recall	recall	VERB
ejpam-2366	206	29	the	the	DET
ejpam-2366	206	30	definition	definition	NOUN
ejpam-2366	206	31	of	of	ADP
ejpam-2366	206	32	the	the	DET
ejpam-2366	206	33	jacobson	jacobson	PROPN
ejpam-2366	206	34	radical	radical	PROPN
ejpam-2366	206	35	of	of	ADP
ejpam-2366	206	36	l.	l.	PROPN
ejpam-2366	206	37	according	accord	VERB
ejpam-2366	206	38	to	to	ADP
ejpam-2366	206	39	[	[	X
ejpam-2366	206	40	2	2	NUM
ejpam-2366	206	41	]	]	PUNCT
ejpam-2366	206	42	,	,	PUNCT
ejpam-2366	206	43	in	in	ADP
ejpam-2366	206	44	a	a	DET
ejpam-2366	206	45	multiplicative	multiplicative	ADJ
ejpam-2366	206	46	lattice	lattice	NOUN
ejpam-2366	206	47	l	l	NOUN
ejpam-2366	206	48	with	with	ADP
ejpam-2366	206	49	1	1	NUM
ejpam-2366	206	50	compact	compact	ADJ
ejpam-2366	206	51	,	,	PUNCT
ejpam-2366	206	52	the	the	DET
ejpam-2366	206	53	jacobson	jacobson	PROPN
ejpam-2366	206	54	radical	radical	PROPN
ejpam-2366	206	55	is	be	AUX
ejpam-2366	206	56	the	the	DET
ejpam-2366	206	57	element	element	NOUN
ejpam-2366	206	58	∧{m	∧{m	PROPN
ejpam-2366	206	59	∈	∈	PROPN
ejpam-2366	206	60	l	l	NOUN
ejpam-2366	207	1	|	|	ADV
ejpam-2366	207	2	m	m	VERB
ejpam-2366	207	3	is	be	AUX
ejpam-2366	207	4	a	a	DET
ejpam-2366	207	5	maximal	maximal	ADJ
ejpam-2366	207	6	element	element	NOUN
ejpam-2366	207	7	}	}	PUNCT
ejpam-2366	207	8	.	.	PUNCT
ejpam-2366	208	1	a.	a.	PROPN
ejpam-2366	208	2	v.	v.	PROPN
ejpam-2366	208	3	bingi	bingi	PROPN
ejpam-2366	208	4	,	,	PUNCT
ejpam-2366	208	5	c.	c.	PROPN
ejpam-2366	208	6	s.	s.	PROPN
ejpam-2366	208	7	manjarekar	manjarekar	PROPN
ejpam-2366	208	8	/	/	PROPN
ejpam-2366	208	9	eur	eur	PROPN
ejpam-2366	208	10	.	.	PUNCT
ejpam-2366	209	1	j.	j.	PROPN
ejpam-2366	209	2	pure	pure	PROPN
ejpam-2366	209	3	appl	appl	PROPN
ejpam-2366	209	4	.	.	PROPN
ejpam-2366	209	5	math	math	PROPN
ejpam-2366	209	6	,	,	PUNCT
ejpam-2366	209	7	14	14	NUM
ejpam-2366	209	8	(	(	PUNCT
ejpam-2366	209	9	2	2	NUM
ejpam-2366	209	10	)	)	PUNCT
ejpam-2366	209	11	(	(	PUNCT
ejpam-2366	209	12	2021	2021	NUM
ejpam-2366	209	13	)	)	PUNCT
ejpam-2366	209	14	,	,	PUNCT
ejpam-2366	209	15	551	551	NUM
ejpam-2366	209	16	-	-	SYM
ejpam-2366	209	17	577	577	NUM
ejpam-2366	209	18	557	557	NUM
ejpam-2366	209	19	theorem	theorem	NOUN
ejpam-2366	209	20	4	4	NUM
ejpam-2366	209	21	.	.	PUNCT
ejpam-2366	210	1	let	let	VERB
ejpam-2366	210	2	l	l	NOUN
ejpam-2366	210	3	be	be	AUX
ejpam-2366	210	4	a	a	DET
ejpam-2366	210	5	noether	noether	ADJ
ejpam-2366	210	6	lattice	lattice	NOUN
ejpam-2366	210	7	,	,	PUNCT
ejpam-2366	210	8	m	m	AUX
ejpam-2366	210	9	be	be	VERB
ejpam-2366	210	10	a	a	DET
ejpam-2366	210	11	torsion	torsion	NOUN
ejpam-2366	210	12	free	free	ADJ
ejpam-2366	210	13	noetherian	noetherian	ADJ
ejpam-2366	210	14	l	l	NOUN
ejpam-2366	210	15	-	-	NOUN
ejpam-2366	210	16	module	module	NOUN
ejpam-2366	210	17	and	and	CCONJ
ejpam-2366	210	18	f	f	PROPN
ejpam-2366	210	19	∈	∈	PROPN
ejpam-2366	210	20	l	l	NOUN
ejpam-2366	210	21	be	be	VERB
ejpam-2366	210	22	the	the	DET
ejpam-2366	210	23	jacobson	jacobson	PROPN
ejpam-2366	210	24	radical	radical	PROPN
ejpam-2366	210	25	.	.	PUNCT
ejpam-2366	211	1	then	then	ADV
ejpam-2366	211	2	a	a	DET
ejpam-2366	211	3	proper	proper	ADJ
ejpam-2366	211	4	element	element	NOUN
ejpam-2366	211	5	n	n	CCONJ
ejpam-2366	211	6	∈	∈	NOUN
ejpam-2366	211	7	m	m	VERB
ejpam-2366	211	8	such	such	ADJ
ejpam-2366	211	9	that	that	SCONJ
ejpam-2366	211	10	(	(	PUNCT
ejpam-2366	211	11	n	n	X
ejpam-2366	211	12	:	:	PUNCT
ejpam-2366	211	13	i	i	PRON
ejpam-2366	211	14	m	m	VERB
ejpam-2366	211	15	)	)	PUNCT
ejpam-2366	211	16	6	6	NUM
ejpam-2366	211	17	f	f	NOUN
ejpam-2366	211	18	is	be	AUX
ejpam-2366	211	19	n	n	ADV
ejpam-2366	211	20	-	-	PUNCT
ejpam-2366	211	21	almost	almost	ADV
ejpam-2366	211	22	prime	prime	NOUN
ejpam-2366	211	23	for	for	ADP
ejpam-2366	211	24	every	every	DET
ejpam-2366	211	25	n	n	NOUN
ejpam-2366	211	26	>	>	SYM
ejpam-2366	211	27	2	2	NUM
ejpam-2366	212	1	if	if	SCONJ
ejpam-2366	212	2	and	and	CCONJ
ejpam-2366	212	3	only	only	ADV
ejpam-2366	212	4	if	if	SCONJ
ejpam-2366	212	5	n	n	NOUN
ejpam-2366	212	6	is	be	AUX
ejpam-2366	212	7	prime	prime	ADJ
ejpam-2366	212	8	.	.	PUNCT
ejpam-2366	213	1	proof	proof	NOUN
ejpam-2366	213	2	.	.	PUNCT
ejpam-2366	214	1	assume	assume	VERB
ejpam-2366	214	2	that	that	SCONJ
ejpam-2366	214	3	n	n	PRON
ejpam-2366	214	4	∈	∈	PROPN
ejpam-2366	214	5	m	m	NOUN
ejpam-2366	214	6	is	be	AUX
ejpam-2366	214	7	n	n	ADV
ejpam-2366	214	8	-	-	PUNCT
ejpam-2366	214	9	almost	almost	ADV
ejpam-2366	214	10	prime	prime	NOUN
ejpam-2366	214	11	where	where	SCONJ
ejpam-2366	214	12	n	n	CCONJ
ejpam-2366	214	13	>	>	X
ejpam-2366	214	14	2	2	X
ejpam-2366	214	15	.	.	PUNCT
ejpam-2366	215	1	let	let	VERB
ejpam-2366	215	2	aa	aa	PROPN
ejpam-2366	215	3	6	6	NUM
ejpam-2366	215	4	n	n	NOUN
ejpam-2366	215	5	for	for	ADP
ejpam-2366	215	6	a	a	DET
ejpam-2366	215	7	∈	∈	PROPN
ejpam-2366	215	8	l	l	NOUN
ejpam-2366	215	9	,	,	PUNCT
ejpam-2366	215	10	a	a	DET
ejpam-2366	215	11	∈	∈	NOUN
ejpam-2366	215	12	m	m	VERB
ejpam-2366	215	13	.	.	PUNCT
ejpam-2366	216	1	if	if	SCONJ
ejpam-2366	216	2	aa	aa	PROPN
ejpam-2366	216	3	(	(	PUNCT
ejpam-2366	216	4	n	n	NOUN
ejpam-2366	216	5	:	:	PUNCT
ejpam-2366	216	6	i	i	PRON
ejpam-2366	216	7	m	m	PROPN
ejpam-2366	216	8	)	)	PUNCT
ejpam-2366	216	9	n−1n	n−1n	PROPN
ejpam-2366	216	10	for	for	ADP
ejpam-2366	216	11	n	n	PROPN
ejpam-2366	216	12	>	>	X
ejpam-2366	216	13	2	2	NUM
ejpam-2366	216	14	,	,	PUNCT
ejpam-2366	216	15	then	then	ADV
ejpam-2366	216	16	as	as	SCONJ
ejpam-2366	216	17	n	n	PROPN
ejpam-2366	216	18	is	be	AUX
ejpam-2366	216	19	n	n	ADV
ejpam-2366	216	20	-	-	PUNCT
ejpam-2366	216	21	almost	almost	ADV
ejpam-2366	216	22	prime	prime	ADJ
ejpam-2366	216	23	,	,	PUNCT
ejpam-2366	216	24	we	we	PRON
ejpam-2366	216	25	have	have	VERB
ejpam-2366	216	26	either	either	CCONJ
ejpam-2366	216	27	a	a	DET
ejpam-2366	216	28	6	6	NUM
ejpam-2366	216	29	n	n	NOUN
ejpam-2366	216	30	or	or	CCONJ
ejpam-2366	216	31	a	a	DET
ejpam-2366	216	32	6	6	NUM
ejpam-2366	216	33	(	(	PUNCT
ejpam-2366	216	34	n	n	NUM
ejpam-2366	216	35	:	:	PUNCT
ejpam-2366	216	36	i	i	PRON
ejpam-2366	216	37	m	m	PROPN
ejpam-2366	216	38	)	)	PUNCT
ejpam-2366	216	39	.	.	PUNCT
ejpam-2366	217	1	if	if	SCONJ
ejpam-2366	217	2	aa	aa	NOUN
ejpam-2366	217	3	6	6	NUM
ejpam-2366	217	4	(	(	PUNCT
ejpam-2366	217	5	n	n	NUM
ejpam-2366	217	6	:	:	PUNCT
ejpam-2366	217	7	i	i	PRON
ejpam-2366	217	8	m	m	PROPN
ejpam-2366	217	9	)	)	PUNCT
ejpam-2366	217	10	n−1n	n−1n	PROPN
ejpam-2366	217	11	for	for	ADP
ejpam-2366	217	12	all	all	DET
ejpam-2366	217	13	n	n	PRON
ejpam-2366	217	14	>	>	X
ejpam-2366	217	15	2	2	NUM
ejpam-2366	217	16	,	,	PUNCT
ejpam-2366	217	17	then	then	ADV
ejpam-2366	217	18	as	as	ADP
ejpam-2366	217	19	(	(	PUNCT
ejpam-2366	217	20	n	n	X
ejpam-2366	217	21	:	:	PUNCT
ejpam-2366	217	22	i	i	PRON
ejpam-2366	217	23	m	m	VERB
ejpam-2366	217	24	)	)	PUNCT
ejpam-2366	217	25	6	6	NUM
ejpam-2366	217	26	f	f	NOUN
ejpam-2366	217	27	,	,	PUNCT
ejpam-2366	217	28	from	from	ADP
ejpam-2366	217	29	corollary	corollary	ADJ
ejpam-2366	217	30	3.3	3.3	NUM
ejpam-2366	217	31	of	of	ADP
ejpam-2366	217	32	[	[	X
ejpam-2366	217	33	13	13	NUM
ejpam-2366	217	34	]	]	PUNCT
ejpam-2366	217	35	,	,	PUNCT
ejpam-2366	217	36	it	it	PRON
ejpam-2366	217	37	follows	follow	VERB
ejpam-2366	217	38	that	that	SCONJ
ejpam-2366	217	39	aa	aa	PROPN
ejpam-2366	217	40	6	6	NUM
ejpam-2366	217	41	∧∞	∧∞	ADV
ejpam-2366	217	42	n=1(n	n=1(n	NUM
ejpam-2366	217	43	:	:	PUNCT
ejpam-2366	217	44	i	i	PRON
ejpam-2366	217	45	m	m	VERB
ejpam-2366	217	46	)	)	PUNCT
ejpam-2366	217	47	nn	nn	PROPN
ejpam-2366	218	1	=	=	SYM
ejpam-2366	218	2	om	om	PROPN
ejpam-2366	218	3	and	and	CCONJ
ejpam-2366	218	4	thus	thus	ADV
ejpam-2366	218	5	aa	aa	ADJ
ejpam-2366	218	6	=	=	SYM
ejpam-2366	218	7	om	om	PROPN
ejpam-2366	218	8	.	.	PUNCT
ejpam-2366	219	1	since	since	SCONJ
ejpam-2366	219	2	m	m	PROPN
ejpam-2366	219	3	is	be	AUX
ejpam-2366	219	4	torsion	torsion	NOUN
ejpam-2366	219	5	free	free	ADJ
ejpam-2366	219	6	,	,	PUNCT
ejpam-2366	219	7	we	we	PRON
ejpam-2366	219	8	have	have	VERB
ejpam-2366	219	9	either	either	CCONJ
ejpam-2366	219	10	a	a	DET
ejpam-2366	219	11	=	=	X
ejpam-2366	219	12	om	om	PROPN
ejpam-2366	219	13	or	or	CCONJ
ejpam-2366	219	14	a	a	DET
ejpam-2366	219	15	=	=	SYM
ejpam-2366	219	16	0	0	NUM
ejpam-2366	219	17	which	which	PRON
ejpam-2366	219	18	implies	imply	VERB
ejpam-2366	219	19	either	either	CCONJ
ejpam-2366	219	20	a	a	DET
ejpam-2366	219	21	6	6	NUM
ejpam-2366	219	22	n	n	NOUN
ejpam-2366	219	23	or	or	CCONJ
ejpam-2366	219	24	a	a	DET
ejpam-2366	219	25	6	6	NUM
ejpam-2366	219	26	(	(	PUNCT
ejpam-2366	219	27	n	n	NUM
ejpam-2366	219	28	:	:	PUNCT
ejpam-2366	219	29	i	i	PRON
ejpam-2366	219	30	m	m	PROPN
ejpam-2366	219	31	)	)	PUNCT
ejpam-2366	219	32	and	and	CCONJ
ejpam-2366	219	33	hence	hence	ADV
ejpam-2366	219	34	n	n	PRON
ejpam-2366	219	35	is	be	AUX
ejpam-2366	219	36	prime	prime	ADJ
ejpam-2366	219	37	.	.	PUNCT
ejpam-2366	220	1	the	the	DET
ejpam-2366	220	2	converse	converse	NOUN
ejpam-2366	220	3	follows	follow	VERB
ejpam-2366	220	4	from	from	ADP
ejpam-2366	220	5	theorem	theorem	ADJ
ejpam-2366	220	6	3	3	NUM
ejpam-2366	220	7	.	.	PUNCT
ejpam-2366	220	8	clearly	clearly	ADV
ejpam-2366	220	9	,	,	PUNCT
ejpam-2366	220	10	every	every	DET
ejpam-2366	220	11	prime	prime	ADJ
ejpam-2366	220	12	element	element	NOUN
ejpam-2366	220	13	of	of	ADP
ejpam-2366	220	14	an	an	DET
ejpam-2366	220	15	l	l	NOUN
ejpam-2366	220	16	-	-	NOUN
ejpam-2366	220	17	module	module	NOUN
ejpam-2366	220	18	m	m	NOUN
ejpam-2366	220	19	is	be	AUX
ejpam-2366	220	20	φ	φ	NOUN
ejpam-2366	220	21	-	-	NOUN
ejpam-2366	220	22	prime	prime	NOUN
ejpam-2366	220	23	.	.	PUNCT
ejpam-2366	221	1	but	but	CCONJ
ejpam-2366	221	2	the	the	DET
ejpam-2366	221	3	converse	converse	NOUN
ejpam-2366	221	4	is	be	AUX
ejpam-2366	221	5	not	not	PART
ejpam-2366	221	6	true	true	ADJ
ejpam-2366	221	7	which	which	PRON
ejpam-2366	221	8	is	be	AUX
ejpam-2366	221	9	shown	show	VERB
ejpam-2366	221	10	in	in	ADP
ejpam-2366	221	11	the	the	DET
ejpam-2366	221	12	following	follow	VERB
ejpam-2366	221	13	example	example	NOUN
ejpam-2366	221	14	by	by	ADP
ejpam-2366	221	15	taking	take	VERB
ejpam-2366	221	16	φ(n	φ(n	NOUN
ejpam-2366	221	17	)	)	PUNCT
ejpam-2366	221	18	=	=	PUNCT
ejpam-2366	221	19	(	(	PUNCT
ejpam-2366	221	20	n	n	X
ejpam-2366	221	21	:	:	PUNCT
ejpam-2366	221	22	i	i	PRON
ejpam-2366	221	23	m	m	PROPN
ejpam-2366	221	24	)	)	PUNCT
ejpam-2366	221	25	n	n	PROPN
ejpam-2366	221	26	for	for	ADP
ejpam-2366	221	27	convenience	convenience	NOUN
ejpam-2366	221	28	.	.	PUNCT
ejpam-2366	222	1	example	example	NOUN
ejpam-2366	223	1	1	1	NUM
ejpam-2366	223	2	.	.	PUNCT
ejpam-2366	224	1	if	if	SCONJ
ejpam-2366	224	2	z	z	NOUN
ejpam-2366	224	3	is	be	AUX
ejpam-2366	224	4	the	the	DET
ejpam-2366	224	5	ring	ring	NOUN
ejpam-2366	224	6	of	of	ADP
ejpam-2366	224	7	integers	integer	NOUN
ejpam-2366	224	8	,	,	PUNCT
ejpam-2366	224	9	then	then	ADV
ejpam-2366	224	10	z24	z24	PROPN
ejpam-2366	224	11	is	be	AUX
ejpam-2366	224	12	a	a	DET
ejpam-2366	224	13	z−module	z−module	NOUN
ejpam-2366	224	14	.	.	PUNCT
ejpam-2366	225	1	assume	assume	VERB
ejpam-2366	225	2	that	that	SCONJ
ejpam-2366	225	3	(	(	PUNCT
ejpam-2366	225	4	k	k	X
ejpam-2366	225	5	)	)	PUNCT
ejpam-2366	225	6	denotes	denote	VERB
ejpam-2366	225	7	the	the	DET
ejpam-2366	225	8	cyclic	cyclic	ADJ
ejpam-2366	225	9	ideal	ideal	NOUN
ejpam-2366	225	10	of	of	ADP
ejpam-2366	225	11	z	z	PROPN
ejpam-2366	225	12	generated	generate	VERB
ejpam-2366	225	13	by	by	ADP
ejpam-2366	225	14	k	k	PROPN
ejpam-2366	225	15	∈	∈	PROPN
ejpam-2366	225	16	z	z	PROPN
ejpam-2366	225	17	and	and	CCONJ
ejpam-2366	225	18	<	<	X
ejpam-2366	225	19	t	t	X
ejpam-2366	225	20	>	>	X
ejpam-2366	225	21	denotes	denote	VERB
ejpam-2366	225	22	the	the	DET
ejpam-2366	225	23	cyclic	cyclic	PROPN
ejpam-2366	225	24	submodule	submodule	NOUN
ejpam-2366	225	25	of	of	ADP
ejpam-2366	225	26	z−module	z−module	PROPN
ejpam-2366	225	27	z24	z24	X
ejpam-2366	225	28	where	where	SCONJ
ejpam-2366	225	29	t	t	PROPN
ejpam-2366	225	30	∈	∈	PROPN
ejpam-2366	225	31	z24	z24	PROPN
ejpam-2366	225	32	.	.	PUNCT
ejpam-2366	225	33	suppose	suppose	VERB
ejpam-2366	225	34	that	that	SCONJ
ejpam-2366	225	35	l	l	NOUN
ejpam-2366	225	36	=	=	SYM
ejpam-2366	225	37	l(z	l(z	NOUN
ejpam-2366	225	38	)	)	PUNCT
ejpam-2366	225	39	is	be	AUX
ejpam-2366	225	40	the	the	DET
ejpam-2366	225	41	set	set	NOUN
ejpam-2366	225	42	of	of	ADP
ejpam-2366	225	43	all	all	DET
ejpam-2366	225	44	ideals	ideal	NOUN
ejpam-2366	225	45	of	of	ADP
ejpam-2366	225	46	z	z	NOUN
ejpam-2366	225	47	and	and	CCONJ
ejpam-2366	225	48	m	m	PROPN
ejpam-2366	225	49	=	=	ADJ
ejpam-2366	225	50	l(z24	l(z24	NOUN
ejpam-2366	225	51	)	)	PUNCT
ejpam-2366	225	52	is	be	AUX
ejpam-2366	225	53	the	the	DET
ejpam-2366	225	54	set	set	NOUN
ejpam-2366	225	55	of	of	ADP
ejpam-2366	225	56	all	all	DET
ejpam-2366	225	57	submodules	submodule	NOUN
ejpam-2366	225	58	of	of	ADP
ejpam-2366	225	59	z−module	z−module	NOUN
ejpam-2366	225	60	z24	z24	PROPN
ejpam-2366	225	61	.	.	PUNCT
ejpam-2366	226	1	the	the	DET
ejpam-2366	226	2	multiplication	multiplication	NOUN
ejpam-2366	226	3	between	between	ADP
ejpam-2366	226	4	elements	element	NOUN
ejpam-2366	226	5	of	of	ADP
ejpam-2366	226	6	l	l	NOUN
ejpam-2366	226	7	and	and	CCONJ
ejpam-2366	226	8	m	m	PROPN
ejpam-2366	226	9	is	be	AUX
ejpam-2366	226	10	given	give	VERB
ejpam-2366	226	11	by	by	ADP
ejpam-2366	226	12	(	(	PUNCT
ejpam-2366	226	13	ki	ki	PROPN
ejpam-2366	226	14	)	)	PUNCT
ejpam-2366	226	15	<	<	X
ejpam-2366	226	16	tj	tj	X
ejpam-2366	226	17	>	>	PUNCT
ejpam-2366	226	18	=	=	X
ejpam-2366	226	19	<	<	X
ejpam-2366	226	20	kitj	kitj	X
ejpam-2366	226	21	>	>	X
ejpam-2366	226	22	for	for	ADP
ejpam-2366	226	23	every	every	DET
ejpam-2366	226	24	(	(	PUNCT
ejpam-2366	226	25	ki	ki	PROPN
ejpam-2366	226	26	)	)	PUNCT
ejpam-2366	226	27	∈	∈	PROPN
ejpam-2366	226	28	l	l	NOUN
ejpam-2366	226	29	and	and	CCONJ
ejpam-2366	226	30	<	<	X
ejpam-2366	226	31	tj	tj	X
ejpam-2366	226	32	>	>	X
ejpam-2366	226	33	∈m	∈m	NOUN
ejpam-2366	227	1	where	where	SCONJ
ejpam-2366	227	2	ki	ki	PROPN
ejpam-2366	227	3	,	,	PUNCT
ejpam-2366	227	4	tj	tj	PROPN
ejpam-2366	227	5	∈	∈	PROPN
ejpam-2366	227	6	z.	z.	PROPN
ejpam-2366	227	7	then	then	ADV
ejpam-2366	227	8	m	m	PROPN
ejpam-2366	227	9	is	be	AUX
ejpam-2366	227	10	a	a	DET
ejpam-2366	227	11	lattice	lattice	NOUN
ejpam-2366	227	12	module	module	NOUN
ejpam-2366	227	13	over	over	ADP
ejpam-2366	227	14	l	l	NOUN
ejpam-2366	228	1	[	[	X
ejpam-2366	228	2	[	[	X
ejpam-2366	228	3	22	22	NUM
ejpam-2366	228	4	]	]	PUNCT
ejpam-2366	228	5	,	,	PUNCT
ejpam-2366	228	6	example	example	NOUN
ejpam-2366	228	7	2.5	2.5	NUM
ejpam-2366	228	8	]	]	PUNCT
ejpam-2366	228	9	.	.	PUNCT
ejpam-2366	229	1	let	let	VERB
ejpam-2366	229	2	n	n	PRON
ejpam-2366	229	3	be	be	AUX
ejpam-2366	229	4	the	the	DET
ejpam-2366	229	5	cyclic	cyclic	ADJ
ejpam-2366	229	6	submodule	submodule	NOUN
ejpam-2366	229	7	of	of	ADP
ejpam-2366	229	8	m	m	AUX
ejpam-2366	229	9	generated	generate	VERB
ejpam-2366	229	10	by	by	ADP
ejpam-2366	229	11	0	0	PROPN
ejpam-2366	229	12	.	.	PUNCT
ejpam-2366	230	1	it	it	PRON
ejpam-2366	230	2	is	be	AUX
ejpam-2366	230	3	easy	easy	ADJ
ejpam-2366	230	4	to	to	PART
ejpam-2366	230	5	see	see	VERB
ejpam-2366	230	6	that	that	PRON
ejpam-2366	230	7	om	om	PROPN
ejpam-2366	230	8	=	=	NOUN
ejpam-2366	230	9	<	<	X
ejpam-2366	230	10	0	0	PUNCT
ejpam-2366	230	11	>	>	PUNCT
ejpam-2366	230	12	=	=	SYM
ejpam-2366	230	13	n	n	X
ejpam-2366	230	14	is	be	AUX
ejpam-2366	230	15	weakly	weakly	ADV
ejpam-2366	230	16	prime	prime	ADJ
ejpam-2366	230	17	and	and	CCONJ
ejpam-2366	230	18	hence	hence	ADV
ejpam-2366	230	19	almost	almost	ADV
ejpam-2366	230	20	prime	prime	ADJ
ejpam-2366	230	21	(	(	PUNCT
ejpam-2366	230	22	φ2	φ2	NOUN
ejpam-2366	230	23	-	-	PUNCT
ejpam-2366	230	24	prime	prime	NOUN
ejpam-2366	230	25	)	)	PUNCT
ejpam-2366	230	26	while	while	SCONJ
ejpam-2366	230	27	n	n	PRON
ejpam-2366	230	28	is	be	AUX
ejpam-2366	230	29	not	not	PART
ejpam-2366	230	30	prime	prime	ADJ
ejpam-2366	230	31	,	,	PUNCT
ejpam-2366	230	32	since	since	SCONJ
ejpam-2366	230	33	(	(	PUNCT
ejpam-2366	230	34	2	2	X
ejpam-2366	230	35	)	)	PUNCT
ejpam-2366	230	36	<	<	X
ejpam-2366	230	37	12	12	NUM
ejpam-2366	230	38	>	>	SYM
ejpam-2366	230	39	6	6	NUM
ejpam-2366	230	40	n	n	NOUN
ejpam-2366	230	41	but	but	CCONJ
ejpam-2366	230	42	<	<	X
ejpam-2366	230	43	12	12	NUM
ejpam-2366	230	44	>	>	SYM
ejpam-2366	230	45	n	n	PROPN
ejpam-2366	230	46	and	and	CCONJ
ejpam-2366	230	47	(	(	PUNCT
ejpam-2366	230	48	2	2	NUM
ejpam-2366	230	49	)	)	PUNCT
ejpam-2366	230	50	(	(	PUNCT
ejpam-2366	230	51	n	n	X
ejpam-2366	230	52	:	:	PUNCT
ejpam-2366	230	53	i	i	PRON
ejpam-2366	230	54	m	m	VERB
ejpam-2366	230	55	)	)	PUNCT
ejpam-2366	231	1	=	=	SYM
ejpam-2366	231	2	(	(	PUNCT
ejpam-2366	231	3	0	0	NUM
ejpam-2366	231	4	)	)	PUNCT
ejpam-2366	231	5	where	where	SCONJ
ejpam-2366	231	6	i	i	PRON
ejpam-2366	231	7	m	m	VERB
ejpam-2366	231	8	=	=	ADJ
ejpam-2366	231	9	<	<	X
ejpam-2366	231	10	1	1	NUM
ejpam-2366	231	11	>	>	PUNCT
ejpam-2366	231	12	.	.	PUNCT
ejpam-2366	232	1	now	now	ADV
ejpam-2366	232	2	we	we	PRON
ejpam-2366	232	3	obtain	obtain	VERB
ejpam-2366	232	4	six	six	NUM
ejpam-2366	232	5	results	result	NOUN
ejpam-2366	232	6	that	that	PRON
ejpam-2366	232	7	show	show	VERB
ejpam-2366	232	8	under	under	ADP
ejpam-2366	232	9	which	which	DET
ejpam-2366	232	10	condition(s	condition(s	NOUN
ejpam-2366	232	11	)	)	PUNCT
ejpam-2366	232	12	a	a	DET
ejpam-2366	232	13	φ	φ	VERB
ejpam-2366	232	14	-	-	ADJ
ejpam-2366	232	15	prime	prime	ADJ
ejpam-2366	232	16	element	element	NOUN
ejpam-2366	232	17	of	of	ADP
ejpam-2366	232	18	an	an	DET
ejpam-2366	232	19	l	l	NOUN
ejpam-2366	232	20	-	-	NOUN
ejpam-2366	232	21	module	module	NOUN
ejpam-2366	232	22	m	m	NOUN
ejpam-2366	232	23	is	be	AUX
ejpam-2366	232	24	prime	prime	ADJ
ejpam-2366	232	25	.	.	PUNCT
ejpam-2366	233	1	but	but	CCONJ
ejpam-2366	233	2	before	before	ADP
ejpam-2366	233	3	that	that	PRON
ejpam-2366	233	4	we	we	PRON
ejpam-2366	233	5	prove	prove	VERB
ejpam-2366	233	6	the	the	DET
ejpam-2366	233	7	required	require	VERB
ejpam-2366	233	8	cancellation	cancellation	NOUN
ejpam-2366	233	9	laws	law	NOUN
ejpam-2366	233	10	of	of	ADP
ejpam-2366	233	11	m	m	PRON
ejpam-2366	233	12	in	in	ADP
ejpam-2366	233	13	the	the	DET
ejpam-2366	233	14	form	form	NOUN
ejpam-2366	233	15	of	of	ADP
ejpam-2366	233	16	following	follow	VERB
ejpam-2366	233	17	lemmas	lemmas	PROPN
ejpam-2366	233	18	.	.	PUNCT
ejpam-2366	234	1	lemma	lemma	PROPN
ejpam-2366	234	2	2	2	X
ejpam-2366	234	3	.	.	PUNCT
ejpam-2366	235	1	let	let	VERB
ejpam-2366	235	2	m	m	PRON
ejpam-2366	235	3	be	be	AUX
ejpam-2366	235	4	a	a	DET
ejpam-2366	235	5	torsion	torsion	NOUN
ejpam-2366	235	6	free	free	ADJ
ejpam-2366	235	7	l	l	NOUN
ejpam-2366	235	8	-	-	NOUN
ejpam-2366	235	9	module	module	NOUN
ejpam-2366	235	10	and	and	CCONJ
ejpam-2366	235	11	om	om	PROPN
ejpam-2366	235	12	6=	6=	PROPN
ejpam-2366	235	13	a	a	DET
ejpam-2366	235	14	∈m	∈m	NOUN
ejpam-2366	235	15	be	be	AUX
ejpam-2366	235	16	a	a	DET
ejpam-2366	235	17	weak	weak	ADJ
ejpam-2366	235	18	join	join	NOUN
ejpam-2366	235	19	principal	principal	ADJ
ejpam-2366	235	20	element	element	NOUN
ejpam-2366	235	21	.	.	PUNCT
ejpam-2366	236	1	then	then	ADV
ejpam-2366	236	2	aa	aa	PROPN
ejpam-2366	236	3	6	6	NUM
ejpam-2366	236	4	ba	ba	NOUN
ejpam-2366	236	5	implies	imply	VERB
ejpam-2366	236	6	a	a	DET
ejpam-2366	236	7	6	6	NUM
ejpam-2366	236	8	b	b	NOUN
ejpam-2366	236	9	for	for	ADP
ejpam-2366	236	10	a	a	DET
ejpam-2366	236	11	,	,	PUNCT
ejpam-2366	236	12	b	b	PROPN
ejpam-2366	236	13	∈	∈	PROPN
ejpam-2366	236	14	l	l	NOUN
ejpam-2366	236	15	where	where	SCONJ
ejpam-2366	236	16	b	b	X
ejpam-2366	236	17	6=	6=	NUM
ejpam-2366	236	18	0	0	NUM
ejpam-2366	236	19	.	.	PUNCT
ejpam-2366	237	1	proof	proof	NOUN
ejpam-2366	237	2	.	.	PUNCT
ejpam-2366	238	1	let	let	VERB
ejpam-2366	238	2	aa	aa	PROPN
ejpam-2366	238	3	6	6	NUM
ejpam-2366	238	4	ba	ba	NOUN
ejpam-2366	238	5	and	and	CCONJ
ejpam-2366	238	6	om	om	PROPN
ejpam-2366	238	7	6=	6=	PROPN
ejpam-2366	238	8	a	a	DET
ejpam-2366	238	9	∈m	∈m	NOUN
ejpam-2366	238	10	be	be	AUX
ejpam-2366	238	11	a	a	DET
ejpam-2366	238	12	weak	weak	ADJ
ejpam-2366	238	13	join	join	NOUN
ejpam-2366	238	14	principal	principal	ADJ
ejpam-2366	238	15	element	element	NOUN
ejpam-2366	238	16	for	for	ADP
ejpam-2366	238	17	a	a	DET
ejpam-2366	238	18	,	,	PUNCT
ejpam-2366	238	19	b	b	PROPN
ejpam-2366	238	20	∈	∈	PROPN
ejpam-2366	238	21	l.	l.	NOUN
ejpam-2366	238	22	as	as	SCONJ
ejpam-2366	238	23	m	m	PROPN
ejpam-2366	238	24	is	be	AUX
ejpam-2366	238	25	a	a	DET
ejpam-2366	238	26	torsion	torsion	NOUN
ejpam-2366	238	27	free	free	ADJ
ejpam-2366	238	28	l	l	NOUN
ejpam-2366	238	29	-	-	NOUN
ejpam-2366	238	30	module	module	NOUN
ejpam-2366	238	31	,	,	PUNCT
ejpam-2366	238	32	we	we	PRON
ejpam-2366	238	33	have	have	VERB
ejpam-2366	238	34	(	(	PUNCT
ejpam-2366	238	35	om	om	NOUN
ejpam-2366	238	36	:	:	PUNCT
ejpam-2366	238	37	a	a	X
ejpam-2366	238	38	)	)	PUNCT
ejpam-2366	238	39	=	=	SYM
ejpam-2366	239	1	0	0	X
ejpam-2366	239	2	.	.	PUNCT
ejpam-2366	240	1	then	then	ADV
ejpam-2366	240	2	clearly	clearly	ADV
ejpam-2366	240	3	,	,	PUNCT
ejpam-2366	240	4	a	a	PRON
ejpam-2366	240	5	=	=	X
ejpam-2366	240	6	a	a	DET
ejpam-2366	240	7	∨	∨	NOUN
ejpam-2366	240	8	0	0	NUM
ejpam-2366	240	9	=	=	SYM
ejpam-2366	240	10	a	a	DET
ejpam-2366	240	11	∨	∨	NOUN
ejpam-2366	240	12	(	(	PUNCT
ejpam-2366	240	13	om	om	PROPN
ejpam-2366	240	14	:	:	PUNCT
ejpam-2366	240	15	a	a	X
ejpam-2366	240	16	)	)	PUNCT
ejpam-2366	240	17	=	=	SYM
ejpam-2366	240	18	(	(	PUNCT
ejpam-2366	240	19	aa	aa	NOUN
ejpam-2366	240	20	:	:	PUNCT
ejpam-2366	240	21	a	a	X
ejpam-2366	240	22	)	)	PUNCT
ejpam-2366	240	23	6	6	NUM
ejpam-2366	240	24	(	(	PUNCT
ejpam-2366	240	25	ba	ba	NOUN
ejpam-2366	240	26	:	:	PUNCT
ejpam-2366	240	27	a	a	X
ejpam-2366	240	28	)	)	PUNCT
ejpam-2366	240	29	=	=	SYM
ejpam-2366	240	30	b	b	PROPN
ejpam-2366	240	31	∨	∨	X
ejpam-2366	240	32	(	(	PUNCT
ejpam-2366	240	33	om	om	PROPN
ejpam-2366	240	34	:	:	PUNCT
ejpam-2366	240	35	a	a	X
ejpam-2366	240	36	)	)	PUNCT
ejpam-2366	240	37	=	=	SYM
ejpam-2366	240	38	b	b	PROPN
ejpam-2366	240	39	∨	∨	NUM
ejpam-2366	240	40	0	0	NUM
ejpam-2366	240	41	=	=	SYM
ejpam-2366	240	42	b	b	NOUN
ejpam-2366	240	43	which	which	PRON
ejpam-2366	240	44	implies	imply	VERB
ejpam-2366	240	45	a	a	DET
ejpam-2366	240	46	6	6	NUM
ejpam-2366	240	47	b.	b.	NOUN
ejpam-2366	240	48	lemma	lemma	PROPN
ejpam-2366	240	49	3	3	X
ejpam-2366	240	50	.	.	PUNCT
ejpam-2366	241	1	let	let	VERB
ejpam-2366	241	2	m	m	PRON
ejpam-2366	241	3	be	be	AUX
ejpam-2366	241	4	a	a	DET
ejpam-2366	241	5	torsion	torsion	NOUN
ejpam-2366	241	6	free	free	ADJ
ejpam-2366	241	7	l	l	NOUN
ejpam-2366	241	8	-	-	NOUN
ejpam-2366	241	9	module	module	NOUN
ejpam-2366	241	10	and	and	CCONJ
ejpam-2366	241	11	om	om	PROPN
ejpam-2366	241	12	6=	6=	PROPN
ejpam-2366	241	13	a	a	DET
ejpam-2366	241	14	∈m	∈m	NOUN
ejpam-2366	241	15	be	be	AUX
ejpam-2366	241	16	a	a	DET
ejpam-2366	241	17	weak	weak	ADJ
ejpam-2366	241	18	join	join	NOUN
ejpam-2366	241	19	principal	principal	ADJ
ejpam-2366	241	20	element	element	NOUN
ejpam-2366	241	21	.	.	PUNCT
ejpam-2366	242	1	then	then	ADV
ejpam-2366	242	2	aa	aa	NOUN
ejpam-2366	242	3	=	=	SYM
ejpam-2366	242	4	ba	ba	PROPN
ejpam-2366	242	5	implies	imply	VERB
ejpam-2366	242	6	a	a	DET
ejpam-2366	242	7	=	=	SYM
ejpam-2366	242	8	b	b	PROPN
ejpam-2366	242	9	for	for	ADP
ejpam-2366	242	10	a	a	DET
ejpam-2366	242	11	,	,	PUNCT
ejpam-2366	242	12	b	b	PROPN
ejpam-2366	242	13	∈	∈	PROPN
ejpam-2366	242	14	l	l	NOUN
ejpam-2366	242	15	where	where	SCONJ
ejpam-2366	242	16	a	a	PRON
ejpam-2366	242	17	6=	6=	NUM
ejpam-2366	242	18	0	0	NUM
ejpam-2366	242	19	,	,	PUNCT
ejpam-2366	242	20	b	b	PROPN
ejpam-2366	242	21	6=	6=	ADP
ejpam-2366	242	22	0	0	NUM
ejpam-2366	242	23	.	.	PUNCT
ejpam-2366	243	1	proof	proof	NOUN
ejpam-2366	243	2	.	.	PUNCT
ejpam-2366	244	1	the	the	DET
ejpam-2366	244	2	proof	proof	NOUN
ejpam-2366	244	3	is	be	AUX
ejpam-2366	244	4	obvious	obvious	ADJ
ejpam-2366	244	5	.	.	PUNCT
ejpam-2366	245	1	now	now	ADV
ejpam-2366	245	2	we	we	PRON
ejpam-2366	245	3	have	have	VERB
ejpam-2366	245	4	a	a	DET
ejpam-2366	245	5	characterization	characterization	NOUN
ejpam-2366	245	6	of	of	ADP
ejpam-2366	245	7	a	a	DET
ejpam-2366	245	8	φ	φ	ADJ
ejpam-2366	245	9	-	-	ADJ
ejpam-2366	245	10	prime	prime	ADJ
ejpam-2366	245	11	element	element	NOUN
ejpam-2366	245	12	of	of	ADP
ejpam-2366	245	13	an	an	DET
ejpam-2366	245	14	l	l	NOUN
ejpam-2366	245	15	-	-	NOUN
ejpam-2366	245	16	module	module	NOUN
ejpam-2366	245	17	m	m	NOUN
ejpam-2366	245	18	.	.	PUNCT
ejpam-2366	246	1	theorem	theorem	ADJ
ejpam-2366	246	2	5	5	NUM
ejpam-2366	246	3	.	.	PUNCT
ejpam-2366	247	1	let	let	VERB
ejpam-2366	247	2	m	m	PRON
ejpam-2366	247	3	be	be	AUX
ejpam-2366	247	4	a	a	DET
ejpam-2366	247	5	torsion	torsion	NOUN
ejpam-2366	247	6	free	free	ADJ
ejpam-2366	247	7	l	l	NOUN
ejpam-2366	247	8	-	-	NOUN
ejpam-2366	247	9	module	module	NOUN
ejpam-2366	247	10	and	and	CCONJ
ejpam-2366	247	11	om	om	PROPN
ejpam-2366	247	12	6=	6=	PROPN
ejpam-2366	247	13	n	n	CCONJ
ejpam-2366	247	14	<	<	X
ejpam-2366	247	15	i	i	PRON
ejpam-2366	247	16	m	m	VERB
ejpam-2366	247	17	be	be	VERB
ejpam-2366	247	18	a	a	DET
ejpam-2366	247	19	weak	weak	ADJ
ejpam-2366	247	20	join	join	NOUN
ejpam-2366	247	21	principal	principal	ADJ
ejpam-2366	247	22	element	element	NOUN
ejpam-2366	247	23	of	of	ADP
ejpam-2366	247	24	m	m	PROPN
ejpam-2366	247	25	.	.	PUNCT
ejpam-2366	248	1	then	then	ADV
ejpam-2366	248	2	n	n	PROPN
ejpam-2366	248	3	is	be	AUX
ejpam-2366	248	4	φ	φ	NOUN
ejpam-2366	248	5	-	-	NOUN
ejpam-2366	248	6	prime	prime	NOUN
ejpam-2366	248	7	for	for	ADP
ejpam-2366	248	8	some	some	DET
ejpam-2366	248	9	φ	φ	NUM
ejpam-2366	248	10	6	6	NUM
ejpam-2366	248	11	φ2	φ2	PROPN
ejpam-2366	248	12	if	if	SCONJ
ejpam-2366	248	13	and	and	CCONJ
ejpam-2366	248	14	only	only	ADV
ejpam-2366	248	15	if	if	SCONJ
ejpam-2366	248	16	n	n	PRON
ejpam-2366	248	17	is	be	AUX
ejpam-2366	248	18	prime	prime	ADJ
ejpam-2366	248	19	.	.	PUNCT
ejpam-2366	249	1	a.	a.	PROPN
ejpam-2366	249	2	v.	v.	PROPN
ejpam-2366	249	3	bingi	bingi	PROPN
ejpam-2366	249	4	,	,	PUNCT
ejpam-2366	249	5	c.	c.	PROPN
ejpam-2366	249	6	s.	s.	PROPN
ejpam-2366	249	7	manjarekar	manjarekar	PROPN
ejpam-2366	249	8	/	/	PROPN
ejpam-2366	249	9	eur	eur	PROPN
ejpam-2366	249	10	.	.	PUNCT
ejpam-2366	250	1	j.	j.	PROPN
ejpam-2366	250	2	pure	pure	PROPN
ejpam-2366	250	3	appl	appl	PROPN
ejpam-2366	250	4	.	.	PROPN
ejpam-2366	250	5	math	math	PROPN
ejpam-2366	250	6	,	,	PUNCT
ejpam-2366	250	7	14	14	NUM
ejpam-2366	250	8	(	(	PUNCT
ejpam-2366	250	9	2	2	NUM
ejpam-2366	250	10	)	)	PUNCT
ejpam-2366	250	11	(	(	PUNCT
ejpam-2366	250	12	2021	2021	NUM
ejpam-2366	250	13	)	)	PUNCT
ejpam-2366	250	14	,	,	PUNCT
ejpam-2366	250	15	551	551	NUM
ejpam-2366	250	16	-	-	SYM
ejpam-2366	250	17	577	577	NUM
ejpam-2366	250	18	558	558	NUM
ejpam-2366	250	19	proof	proof	NOUN
ejpam-2366	250	20	.	.	PUNCT
ejpam-2366	251	1	assume	assume	VERB
ejpam-2366	251	2	that	that	SCONJ
ejpam-2366	251	3	n	n	PRON
ejpam-2366	251	4	∈	∈	PROPN
ejpam-2366	251	5	m	m	VERB
ejpam-2366	251	6	is	be	AUX
ejpam-2366	251	7	a	a	DET
ejpam-2366	251	8	prime	prime	ADJ
ejpam-2366	251	9	element	element	NOUN
ejpam-2366	251	10	.	.	PUNCT
ejpam-2366	252	1	then	then	ADV
ejpam-2366	252	2	obviously	obviously	ADV
ejpam-2366	252	3	,	,	PUNCT
ejpam-2366	252	4	n	n	PROPN
ejpam-2366	252	5	is	be	AUX
ejpam-2366	252	6	φ	φ	NOUN
ejpam-2366	252	7	-	-	NOUN
ejpam-2366	252	8	prime	prime	NOUN
ejpam-2366	252	9	for	for	ADP
ejpam-2366	252	10	every	every	DET
ejpam-2366	252	11	φ	φ	NOUN
ejpam-2366	252	12	and	and	CCONJ
ejpam-2366	252	13	hence	hence	ADV
ejpam-2366	252	14	for	for	ADP
ejpam-2366	252	15	some	some	DET
ejpam-2366	252	16	φ	φ	NUM
ejpam-2366	252	17	6	6	NUM
ejpam-2366	252	18	φ2	φ2	PROPN
ejpam-2366	252	19	.	.	PUNCT
ejpam-2366	253	1	conversely	conversely	ADV
ejpam-2366	253	2	,	,	PUNCT
ejpam-2366	253	3	let	let	VERB
ejpam-2366	253	4	n	n	PRON
ejpam-2366	253	5	be	be	AUX
ejpam-2366	253	6	φ	φ	VERB
ejpam-2366	253	7	-	-	NOUN
ejpam-2366	253	8	prime	prime	NOUN
ejpam-2366	253	9	for	for	ADP
ejpam-2366	253	10	some	some	DET
ejpam-2366	253	11	φ	φ	PROPN
ejpam-2366	253	12	6	6	NUM
ejpam-2366	253	13	φ2	φ2	PROPN
ejpam-2366	253	14	.	.	PUNCT
ejpam-2366	254	1	then	then	ADV
ejpam-2366	254	2	by	by	ADP
ejpam-2366	254	3	theorem	theorem	NOUN
ejpam-2366	254	4	2	2	NUM
ejpam-2366	254	5	,	,	PUNCT
ejpam-2366	254	6	n	n	X
ejpam-2366	254	7	is	be	AUX
ejpam-2366	254	8	φ2	φ2	NOUN
ejpam-2366	254	9	-	-	PUNCT
ejpam-2366	254	10	prime	prime	NOUN
ejpam-2366	254	11	.	.	PUNCT
ejpam-2366	255	1	let	let	VERB
ejpam-2366	255	2	aa	aa	PROPN
ejpam-2366	255	3	6	6	NUM
ejpam-2366	255	4	n	n	NOUN
ejpam-2366	255	5	for	for	ADP
ejpam-2366	255	6	a	a	DET
ejpam-2366	255	7	∈	∈	PROPN
ejpam-2366	255	8	l	l	NOUN
ejpam-2366	255	9	,	,	PUNCT
ejpam-2366	255	10	a	a	DET
ejpam-2366	255	11	∈m	∈m	NOUN
ejpam-2366	255	12	.	.	PUNCT
ejpam-2366	256	1	if	if	SCONJ
ejpam-2366	256	2	aa	aa	PROPN
ejpam-2366	256	3	φ2(n	φ2(n	VERB
ejpam-2366	256	4	)	)	PUNCT
ejpam-2366	256	5	,	,	PUNCT
ejpam-2366	256	6	then	then	ADV
ejpam-2366	256	7	as	as	SCONJ
ejpam-2366	256	8	n	n	PRON
ejpam-2366	256	9	is	be	AUX
ejpam-2366	256	10	φ2	φ2	ADJ
ejpam-2366	256	11	-	-	PUNCT
ejpam-2366	256	12	prime	prime	NOUN
ejpam-2366	256	13	,	,	PUNCT
ejpam-2366	256	14	we	we	PRON
ejpam-2366	256	15	have	have	VERB
ejpam-2366	256	16	either	either	CCONJ
ejpam-2366	256	17	a	a	DET
ejpam-2366	256	18	6	6	NUM
ejpam-2366	256	19	n	n	NOUN
ejpam-2366	256	20	or	or	CCONJ
ejpam-2366	256	21	a	a	DET
ejpam-2366	256	22	6	6	NUM
ejpam-2366	256	23	(	(	PUNCT
ejpam-2366	256	24	n	n	NUM
ejpam-2366	256	25	:	:	PUNCT
ejpam-2366	256	26	i	i	PRON
ejpam-2366	256	27	m	m	PROPN
ejpam-2366	256	28	)	)	PUNCT
ejpam-2366	256	29	.	.	PUNCT
ejpam-2366	257	1	next	next	ADV
ejpam-2366	257	2	,	,	PUNCT
ejpam-2366	257	3	assume	assume	VERB
ejpam-2366	257	4	that	that	SCONJ
ejpam-2366	257	5	aa	aa	PROPN
ejpam-2366	257	6	6	6	NUM
ejpam-2366	257	7	φ2(n	φ2(n	NUM
ejpam-2366	257	8	)	)	PUNCT
ejpam-2366	257	9	.	.	PUNCT
ejpam-2366	258	1	if	if	SCONJ
ejpam-2366	258	2	a(a∨n	a(a∨n	ADV
ejpam-2366	258	3	)	)	PUNCT
ejpam-2366	258	4	φ2(n	φ2(n	NOUN
ejpam-2366	258	5	)	)	PUNCT
ejpam-2366	258	6	,	,	PUNCT
ejpam-2366	258	7	then	then	ADV
ejpam-2366	258	8	as	as	ADP
ejpam-2366	258	9	a(a∨n	a(a∨n	ADJ
ejpam-2366	258	10	)	)	PUNCT
ejpam-2366	258	11	6	6	NUM
ejpam-2366	258	12	n	n	NOUN
ejpam-2366	258	13	and	and	CCONJ
ejpam-2366	258	14	n	n	PROPN
ejpam-2366	258	15	is	be	AUX
ejpam-2366	258	16	φ2	φ2	ADJ
ejpam-2366	258	17	-	-	PUNCT
ejpam-2366	258	18	prime	prime	NOUN
ejpam-2366	258	19	,	,	PUNCT
ejpam-2366	258	20	we	we	PRON
ejpam-2366	258	21	have	have	VERB
ejpam-2366	258	22	either	either	CCONJ
ejpam-2366	258	23	(	(	PUNCT
ejpam-2366	258	24	a∨n	a∨n	PROPN
ejpam-2366	258	25	)	)	PUNCT
ejpam-2366	258	26	6	6	NUM
ejpam-2366	258	27	n	n	NUM
ejpam-2366	258	28	or	or	CCONJ
ejpam-2366	258	29	a	a	DET
ejpam-2366	258	30	6	6	NUM
ejpam-2366	258	31	(	(	PUNCT
ejpam-2366	258	32	n	n	NUM
ejpam-2366	258	33	:	:	PUNCT
ejpam-2366	258	34	i	i	PRON
ejpam-2366	258	35	m	m	PROPN
ejpam-2366	258	36	)	)	PUNCT
ejpam-2366	258	37	and	and	CCONJ
ejpam-2366	258	38	hence	hence	ADV
ejpam-2366	258	39	either	either	CCONJ
ejpam-2366	258	40	a	a	DET
ejpam-2366	258	41	6	6	NUM
ejpam-2366	258	42	n	n	NOUN
ejpam-2366	258	43	or	or	CCONJ
ejpam-2366	258	44	a	a	DET
ejpam-2366	258	45	6	6	NUM
ejpam-2366	258	46	(	(	PUNCT
ejpam-2366	258	47	n	n	NUM
ejpam-2366	258	48	:	:	PUNCT
ejpam-2366	258	49	i	i	PRON
ejpam-2366	258	50	m	m	PROPN
ejpam-2366	258	51	)	)	PUNCT
ejpam-2366	258	52	.	.	PUNCT
ejpam-2366	259	1	finally	finally	ADV
ejpam-2366	259	2	,	,	PUNCT
ejpam-2366	259	3	if	if	SCONJ
ejpam-2366	259	4	a(a	a(a	PROPN
ejpam-2366	259	5	∨n	∨n	VERB
ejpam-2366	259	6	)	)	PUNCT
ejpam-2366	259	7	6	6	NUM
ejpam-2366	259	8	φ2(n	φ2(n	NUM
ejpam-2366	259	9	)	)	PUNCT
ejpam-2366	259	10	,	,	PUNCT
ejpam-2366	259	11	then	then	ADV
ejpam-2366	259	12	an	an	DET
ejpam-2366	259	13	6	6	NUM
ejpam-2366	259	14	(	(	PUNCT
ejpam-2366	259	15	n	n	NUM
ejpam-2366	259	16	:	:	PUNCT
ejpam-2366	259	17	i	i	PRON
ejpam-2366	259	18	m	m	PROPN
ejpam-2366	259	19	)	)	PUNCT
ejpam-2366	259	20	n	n	NUM
ejpam-2366	259	21	which	which	PRON
ejpam-2366	259	22	implies	imply	VERB
ejpam-2366	259	23	a	a	DET
ejpam-2366	259	24	6	6	NUM
ejpam-2366	259	25	(	(	PUNCT
ejpam-2366	259	26	n	n	NUM
ejpam-2366	259	27	:	:	PUNCT
ejpam-2366	259	28	i	i	PRON
ejpam-2366	259	29	m	m	PROPN
ejpam-2366	259	30	)	)	PUNCT
ejpam-2366	259	31	,	,	PUNCT
ejpam-2366	259	32	by	by	ADP
ejpam-2366	259	33	lemma	lemma	PROPN
ejpam-2366	259	34	2	2	NUM
ejpam-2366	259	35	and	and	CCONJ
ejpam-2366	259	36	hence	hence	ADV
ejpam-2366	259	37	n	n	PRON
ejpam-2366	259	38	is	be	AUX
ejpam-2366	259	39	prime	prime	ADJ
ejpam-2366	259	40	.	.	PUNCT
ejpam-2366	260	1	now	now	ADV
ejpam-2366	260	2	we	we	PRON
ejpam-2366	260	3	show	show	VERB
ejpam-2366	260	4	that	that	SCONJ
ejpam-2366	260	5	the	the	DET
ejpam-2366	260	6	theorem	theorem	NOUN
ejpam-2366	260	7	5	5	NUM
ejpam-2366	260	8	can	can	AUX
ejpam-2366	260	9	also	also	ADV
ejpam-2366	260	10	be	be	AUX
ejpam-2366	260	11	achieved	achieve	VERB
ejpam-2366	260	12	by	by	ADP
ejpam-2366	260	13	changing	change	VERB
ejpam-2366	260	14	the	the	DET
ejpam-2366	260	15	conditions	condition	NOUN
ejpam-2366	260	16	on	on	ADP
ejpam-2366	260	17	m	m	PRON
ejpam-2366	260	18	and	and	CCONJ
ejpam-2366	260	19	l.	l.	PROPN
ejpam-2366	260	20	according	accord	VERB
ejpam-2366	260	21	to	to	ADP
ejpam-2366	260	22	[	[	X
ejpam-2366	260	23	23	23	NUM
ejpam-2366	260	24	]	]	PUNCT
ejpam-2366	260	25	,	,	PUNCT
ejpam-2366	260	26	in	in	ADP
ejpam-2366	260	27	a	a	DET
ejpam-2366	260	28	noether	noether	ADJ
ejpam-2366	260	29	lattice	lattice	PROPN
ejpam-2366	260	30	l	l	PROPN
ejpam-2366	260	31	,	,	PUNCT
ejpam-2366	260	32	an	an	DET
ejpam-2366	260	33	element	element	NOUN
ejpam-2366	260	34	a	a	DET
ejpam-2366	260	35	∈	∈	PROPN
ejpam-2366	260	36	l	l	NOUN
ejpam-2366	260	37	is	be	AUX
ejpam-2366	260	38	said	say	VERB
ejpam-2366	260	39	to	to	PART
ejpam-2366	260	40	satisfy	satisfy	VERB
ejpam-2366	260	41	the	the	DET
ejpam-2366	260	42	restricted	restricted	ADJ
ejpam-2366	260	43	cancellation	cancellation	NOUN
ejpam-2366	260	44	law	law	NOUN
ejpam-2366	260	45	(	(	PUNCT
ejpam-2366	260	46	rcl	rcl	NOUN
ejpam-2366	260	47	)	)	PUNCT
ejpam-2366	260	48	if	if	SCONJ
ejpam-2366	260	49	for	for	ADP
ejpam-2366	260	50	all	all	DET
ejpam-2366	260	51	b	b	NOUN
ejpam-2366	260	52	,	,	PUNCT
ejpam-2366	260	53	c	c	PROPN
ejpam-2366	260	54	∈	∈	PROPN
ejpam-2366	260	55	l	l	NOUN
ejpam-2366	260	56	,	,	PUNCT
ejpam-2366	260	57	ab	ab	PROPN
ejpam-2366	260	58	=	=	PUNCT
ejpam-2366	260	59	ac	ac	PROPN
ejpam-2366	260	60	6=	6=	ADP
ejpam-2366	260	61	0	0	NUM
ejpam-2366	260	62	implies	imply	VERB
ejpam-2366	260	63	b	b	PROPN
ejpam-2366	260	64	=	=	SYM
ejpam-2366	260	65	c.	c.	PROPN
ejpam-2366	260	66	theorem	theorem	VERB
ejpam-2366	260	67	6	6	NUM
ejpam-2366	260	68	.	.	PUNCT
ejpam-2366	261	1	let	let	VERB
ejpam-2366	261	2	l	l	NOUN
ejpam-2366	261	3	be	be	AUX
ejpam-2366	261	4	a	a	DET
ejpam-2366	261	5	noether	noether	ADJ
ejpam-2366	261	6	pg	pg	NOUN
ejpam-2366	261	7	-	-	PUNCT
ejpam-2366	261	8	lattice	lattice	NOUN
ejpam-2366	261	9	and	and	CCONJ
ejpam-2366	261	10	m	m	AUX
ejpam-2366	261	11	be	be	AUX
ejpam-2366	261	12	a	a	DET
ejpam-2366	261	13	faithful	faithful	ADJ
ejpam-2366	261	14	multiplication	multiplication	NOUN
ejpam-2366	261	15	pg	pg	NOUN
ejpam-2366	261	16	-	-	PUNCT
ejpam-2366	261	17	lattice	lattice	NOUN
ejpam-2366	261	18	l	l	NOUN
ejpam-2366	261	19	-	-	NOUN
ejpam-2366	261	20	module	module	NOUN
ejpam-2366	261	21	with	with	ADP
ejpam-2366	261	22	i	i	PRON
ejpam-2366	261	23	m	m	VERB
ejpam-2366	261	24	compact	compact	ADJ
ejpam-2366	261	25	.	.	PUNCT
ejpam-2366	262	1	let	let	VERB
ejpam-2366	262	2	n	n	PRON
ejpam-2366	262	3	be	be	AUX
ejpam-2366	262	4	a	a	DET
ejpam-2366	262	5	proper	proper	ADJ
ejpam-2366	262	6	element	element	NOUN
ejpam-2366	262	7	of	of	ADP
ejpam-2366	262	8	m	m	PRON
ejpam-2366	262	9	such	such	ADJ
ejpam-2366	262	10	that	that	DET
ejpam-2366	262	11	0	0	NUM
ejpam-2366	263	1	6=	6=	NUM
ejpam-2366	263	2	(	(	PUNCT
ejpam-2366	263	3	n	n	X
ejpam-2366	263	4	:	:	PUNCT
ejpam-2366	263	5	i	i	PRON
ejpam-2366	263	6	m	m	VERB
ejpam-2366	263	7	)	)	PUNCT
ejpam-2366	263	8	∈	∈	PROPN
ejpam-2366	263	9	l	l	NOUN
ejpam-2366	263	10	satisfies	satisfy	VERB
ejpam-2366	263	11	the	the	DET
ejpam-2366	263	12	restricted	restricted	ADJ
ejpam-2366	263	13	cancellation	cancellation	NOUN
ejpam-2366	263	14	law	law	NOUN
ejpam-2366	263	15	(	(	PUNCT
ejpam-2366	263	16	rcl	rcl	NOUN
ejpam-2366	263	17	)	)	PUNCT
ejpam-2366	263	18	and	and	CCONJ
ejpam-2366	263	19	is	be	AUX
ejpam-2366	263	20	a	a	DET
ejpam-2366	263	21	non	non	ADJ
ejpam-2366	263	22	-	-	ADJ
ejpam-2366	263	23	nilpotent	nilpotent	ADJ
ejpam-2366	263	24	element	element	NOUN
ejpam-2366	263	25	.	.	PUNCT
ejpam-2366	264	1	then	then	ADV
ejpam-2366	264	2	n	n	PROPN
ejpam-2366	264	3	is	be	AUX
ejpam-2366	264	4	φ	φ	NOUN
ejpam-2366	264	5	-	-	NOUN
ejpam-2366	264	6	prime	prime	NOUN
ejpam-2366	264	7	for	for	ADP
ejpam-2366	264	8	some	some	DET
ejpam-2366	264	9	φ	φ	NUM
ejpam-2366	264	10	6	6	NUM
ejpam-2366	264	11	φ2	φ2	PROPN
ejpam-2366	264	12	if	if	SCONJ
ejpam-2366	264	13	and	and	CCONJ
ejpam-2366	264	14	only	only	ADV
ejpam-2366	264	15	if	if	SCONJ
ejpam-2366	264	16	n	n	NOUN
ejpam-2366	264	17	is	be	AUX
ejpam-2366	264	18	prime	prime	ADJ
ejpam-2366	264	19	.	.	PUNCT
ejpam-2366	265	1	proof	proof	NOUN
ejpam-2366	265	2	.	.	PUNCT
ejpam-2366	266	1	assume	assume	VERB
ejpam-2366	266	2	that	that	SCONJ
ejpam-2366	266	3	n	n	PRON
ejpam-2366	266	4	∈	∈	PROPN
ejpam-2366	266	5	m	m	VERB
ejpam-2366	266	6	is	be	AUX
ejpam-2366	266	7	a	a	DET
ejpam-2366	266	8	prime	prime	ADJ
ejpam-2366	266	9	element	element	NOUN
ejpam-2366	266	10	.	.	PUNCT
ejpam-2366	267	1	then	then	ADV
ejpam-2366	267	2	obviously	obviously	ADV
ejpam-2366	267	3	,	,	PUNCT
ejpam-2366	267	4	n	n	PROPN
ejpam-2366	267	5	is	be	AUX
ejpam-2366	267	6	φ	φ	NOUN
ejpam-2366	267	7	-	-	NOUN
ejpam-2366	267	8	prime	prime	NOUN
ejpam-2366	267	9	for	for	ADP
ejpam-2366	267	10	every	every	DET
ejpam-2366	267	11	φ	φ	NOUN
ejpam-2366	267	12	and	and	CCONJ
ejpam-2366	267	13	hence	hence	ADV
ejpam-2366	267	14	for	for	ADP
ejpam-2366	267	15	some	some	DET
ejpam-2366	267	16	φ	φ	NUM
ejpam-2366	267	17	6	6	NUM
ejpam-2366	267	18	φ2	φ2	PROPN
ejpam-2366	267	19	.	.	PUNCT
ejpam-2366	268	1	conversely	conversely	ADV
ejpam-2366	268	2	,	,	PUNCT
ejpam-2366	268	3	let	let	VERB
ejpam-2366	268	4	n	n	PRON
ejpam-2366	268	5	be	be	AUX
ejpam-2366	268	6	φ	φ	VERB
ejpam-2366	268	7	-	-	NOUN
ejpam-2366	268	8	prime	prime	NOUN
ejpam-2366	268	9	for	for	ADP
ejpam-2366	268	10	some	some	DET
ejpam-2366	268	11	φ	φ	PROPN
ejpam-2366	268	12	6	6	NUM
ejpam-2366	268	13	φ2	φ2	PROPN
ejpam-2366	268	14	.	.	PUNCT
ejpam-2366	269	1	then	then	ADV
ejpam-2366	269	2	by	by	ADP
ejpam-2366	269	3	theorem	theorem	NOUN
ejpam-2366	269	4	2	2	NUM
ejpam-2366	269	5	,	,	PUNCT
ejpam-2366	269	6	n	n	X
ejpam-2366	269	7	is	be	AUX
ejpam-2366	269	8	φ2	φ2	NOUN
ejpam-2366	269	9	-	-	PUNCT
ejpam-2366	269	10	prime	prime	NOUN
ejpam-2366	269	11	.	.	PUNCT
ejpam-2366	270	1	let	let	VERB
ejpam-2366	270	2	aa	aa	PROPN
ejpam-2366	270	3	6	6	NUM
ejpam-2366	270	4	n	n	NOUN
ejpam-2366	270	5	for	for	ADP
ejpam-2366	270	6	a	a	DET
ejpam-2366	270	7	∈	∈	PROPN
ejpam-2366	270	8	l	l	NOUN
ejpam-2366	270	9	,	,	PUNCT
ejpam-2366	270	10	a	a	DET
ejpam-2366	270	11	∈m	∈m	NOUN
ejpam-2366	270	12	.	.	PUNCT
ejpam-2366	271	1	if	if	SCONJ
ejpam-2366	271	2	aa	aa	PROPN
ejpam-2366	271	3	φ2(n	φ2(n	VERB
ejpam-2366	271	4	)	)	PUNCT
ejpam-2366	271	5	,	,	PUNCT
ejpam-2366	271	6	then	then	ADV
ejpam-2366	271	7	as	as	SCONJ
ejpam-2366	271	8	n	n	PRON
ejpam-2366	271	9	is	be	AUX
ejpam-2366	271	10	φ2	φ2	ADJ
ejpam-2366	271	11	-	-	PUNCT
ejpam-2366	271	12	prime	prime	NOUN
ejpam-2366	271	13	,	,	PUNCT
ejpam-2366	271	14	we	we	PRON
ejpam-2366	271	15	have	have	VERB
ejpam-2366	271	16	either	either	CCONJ
ejpam-2366	271	17	a	a	DET
ejpam-2366	271	18	6	6	NUM
ejpam-2366	271	19	n	n	NOUN
ejpam-2366	271	20	or	or	CCONJ
ejpam-2366	271	21	a	a	DET
ejpam-2366	271	22	6	6	NUM
ejpam-2366	271	23	(	(	PUNCT
ejpam-2366	271	24	n	n	NUM
ejpam-2366	271	25	:	:	PUNCT
ejpam-2366	271	26	i	i	PRON
ejpam-2366	271	27	m	m	PROPN
ejpam-2366	271	28	)	)	PUNCT
ejpam-2366	271	29	.	.	PUNCT
ejpam-2366	272	1	next	next	ADV
ejpam-2366	272	2	,	,	PUNCT
ejpam-2366	272	3	assume	assume	VERB
ejpam-2366	272	4	that	that	SCONJ
ejpam-2366	272	5	aa	aa	PROPN
ejpam-2366	272	6	6	6	NUM
ejpam-2366	272	7	φ2(n	φ2(n	NUM
ejpam-2366	272	8	)	)	PUNCT
ejpam-2366	272	9	.	.	PUNCT
ejpam-2366	273	1	if	if	SCONJ
ejpam-2366	273	2	a(a∨n	a(a∨n	ADV
ejpam-2366	273	3	)	)	PUNCT
ejpam-2366	273	4	φ2(n	φ2(n	NOUN
ejpam-2366	273	5	)	)	PUNCT
ejpam-2366	273	6	,	,	PUNCT
ejpam-2366	273	7	then	then	ADV
ejpam-2366	273	8	as	as	ADP
ejpam-2366	273	9	a(a∨n	a(a∨n	ADJ
ejpam-2366	273	10	)	)	PUNCT
ejpam-2366	273	11	6	6	NUM
ejpam-2366	273	12	n	n	NOUN
ejpam-2366	273	13	and	and	CCONJ
ejpam-2366	273	14	n	n	PROPN
ejpam-2366	273	15	is	be	AUX
ejpam-2366	273	16	φ2	φ2	ADJ
ejpam-2366	273	17	-	-	PUNCT
ejpam-2366	273	18	prime	prime	NOUN
ejpam-2366	273	19	,	,	PUNCT
ejpam-2366	273	20	we	we	PRON
ejpam-2366	273	21	have	have	VERB
ejpam-2366	273	22	either	either	CCONJ
ejpam-2366	273	23	(	(	PUNCT
ejpam-2366	273	24	a∨n	a∨n	PROPN
ejpam-2366	273	25	)	)	PUNCT
ejpam-2366	273	26	6	6	NUM
ejpam-2366	273	27	n	n	NUM
ejpam-2366	273	28	or	or	CCONJ
ejpam-2366	273	29	a	a	DET
ejpam-2366	273	30	6	6	NUM
ejpam-2366	273	31	(	(	PUNCT
ejpam-2366	273	32	n	n	NUM
ejpam-2366	273	33	:	:	PUNCT
ejpam-2366	273	34	i	i	PRON
ejpam-2366	273	35	m	m	PROPN
ejpam-2366	273	36	)	)	PUNCT
ejpam-2366	273	37	and	and	CCONJ
ejpam-2366	273	38	hence	hence	ADV
ejpam-2366	273	39	either	either	CCONJ
ejpam-2366	273	40	a	a	DET
ejpam-2366	273	41	6	6	NUM
ejpam-2366	273	42	n	n	NOUN
ejpam-2366	273	43	or	or	CCONJ
ejpam-2366	273	44	a	a	DET
ejpam-2366	273	45	6	6	NUM
ejpam-2366	273	46	(	(	PUNCT
ejpam-2366	273	47	n	n	NUM
ejpam-2366	273	48	:	:	PUNCT
ejpam-2366	273	49	i	i	PRON
ejpam-2366	273	50	m	m	PROPN
ejpam-2366	273	51	)	)	PUNCT
ejpam-2366	273	52	.	.	PUNCT
ejpam-2366	274	1	finally	finally	ADV
ejpam-2366	274	2	,	,	PUNCT
ejpam-2366	274	3	if	if	SCONJ
ejpam-2366	274	4	a(a∨n	a(a∨n	ADJ
ejpam-2366	274	5	)	)	PUNCT
ejpam-2366	274	6	6	6	NUM
ejpam-2366	274	7	φ2(n	φ2(n	NUM
ejpam-2366	274	8	)	)	PUNCT
ejpam-2366	274	9	,	,	PUNCT
ejpam-2366	274	10	then	then	ADV
ejpam-2366	274	11	an	an	DET
ejpam-2366	274	12	6	6	NUM
ejpam-2366	274	13	(	(	PUNCT
ejpam-2366	274	14	n	n	NUM
ejpam-2366	274	15	:	:	PUNCT
ejpam-2366	274	16	i	i	PRON
ejpam-2366	274	17	m	m	PROPN
ejpam-2366	274	18	)	)	PUNCT
ejpam-2366	274	19	n	n	NUM
ejpam-2366	274	20	which	which	PRON
ejpam-2366	274	21	implies	imply	VERB
ejpam-2366	274	22	a(n	a(n	ADV
ejpam-2366	274	23	:	:	PUNCT
ejpam-2366	274	24	i	i	PRON
ejpam-2366	274	25	m	m	VERB
ejpam-2366	274	26	)	)	PUNCT
ejpam-2366	275	1	i	i	PRON
ejpam-2366	275	2	m	m	VERB
ejpam-2366	275	3	6	6	NUM
ejpam-2366	275	4	(	(	PUNCT
ejpam-2366	275	5	n	n	NUM
ejpam-2366	275	6	:	:	PUNCT
ejpam-2366	275	7	i	i	PRON
ejpam-2366	275	8	m	m	NOUN
ejpam-2366	275	9	)	)	PUNCT
ejpam-2366	275	10	2im	2im	NOUN
ejpam-2366	275	11	,	,	PUNCT
ejpam-2366	275	12	since	since	SCONJ
ejpam-2366	275	13	m	m	PROPN
ejpam-2366	275	14	is	be	AUX
ejpam-2366	275	15	a	a	DET
ejpam-2366	275	16	multiplication	multiplication	NOUN
ejpam-2366	275	17	lattice	lattice	NOUN
ejpam-2366	275	18	l	l	NOUN
ejpam-2366	275	19	module	module	NOUN
ejpam-2366	275	20	.	.	PUNCT
ejpam-2366	276	1	as	as	SCONJ
ejpam-2366	276	2	i	i	PRON
ejpam-2366	276	3	m	m	VERB
ejpam-2366	276	4	is	be	AUX
ejpam-2366	276	5	compact	compact	ADJ
ejpam-2366	276	6	,	,	PUNCT
ejpam-2366	276	7	this	this	PRON
ejpam-2366	276	8	gives	give	VERB
ejpam-2366	276	9	a(n	a(n	ADV
ejpam-2366	276	10	:	:	PUNCT
ejpam-2366	276	11	i	i	PRON
ejpam-2366	276	12	m	m	VERB
ejpam-2366	276	13	)	)	PUNCT
ejpam-2366	276	14	6	6	NUM
ejpam-2366	276	15	(	(	PUNCT
ejpam-2366	276	16	n	n	NUM
ejpam-2366	276	17	:	:	PUNCT
ejpam-2366	276	18	i	i	PRON
ejpam-2366	276	19	m	m	VERB
ejpam-2366	276	20	)	)	PUNCT
ejpam-2366	276	21	2	2	NUM
ejpam-2366	276	22	6=	6=	NUM
ejpam-2366	276	23	0	0	NUM
ejpam-2366	276	24	,	,	PUNCT
ejpam-2366	276	25	by	by	ADP
ejpam-2366	276	26	theorem	theorem	NOUN
ejpam-2366	276	27	5	5	NUM
ejpam-2366	276	28	of	of	ADP
ejpam-2366	276	29	[	[	X
ejpam-2366	276	30	10	10	NUM
ejpam-2366	276	31	]	]	PUNCT
ejpam-2366	276	32	.	.	PUNCT
ejpam-2366	277	1	this	this	PRON
ejpam-2366	277	2	implies	imply	VERB
ejpam-2366	277	3	a	a	DET
ejpam-2366	277	4	6	6	NUM
ejpam-2366	277	5	(	(	PUNCT
ejpam-2366	277	6	n	n	NUM
ejpam-2366	277	7	:	:	PUNCT
ejpam-2366	277	8	i	i	PRON
ejpam-2366	277	9	m	m	PROPN
ejpam-2366	277	10	)	)	PUNCT
ejpam-2366	277	11	,	,	PUNCT
ejpam-2366	277	12	by	by	ADP
ejpam-2366	277	13	lemma	lemma	PROPN
ejpam-2366	277	14	1.11	1.11	NUM
ejpam-2366	277	15	of	of	ADP
ejpam-2366	277	16	[	[	X
ejpam-2366	277	17	23	23	NUM
ejpam-2366	277	18	]	]	PUNCT
ejpam-2366	277	19	and	and	CCONJ
ejpam-2366	277	20	hence	hence	ADV
ejpam-2366	277	21	n	n	PRON
ejpam-2366	277	22	is	be	AUX
ejpam-2366	277	23	prime	prime	ADJ
ejpam-2366	277	24	.	.	PUNCT
ejpam-2366	278	1	now	now	ADV
ejpam-2366	278	2	we	we	PRON
ejpam-2366	278	3	define	define	VERB
ejpam-2366	278	4	a	a	DET
ejpam-2366	278	5	2	2	NUM
ejpam-2366	278	6	-	-	PUNCT
ejpam-2366	278	7	potent	potent	ADJ
ejpam-2366	278	8	prime	prime	ADJ
ejpam-2366	278	9	element	element	NOUN
ejpam-2366	278	10	in	in	ADP
ejpam-2366	278	11	an	an	DET
ejpam-2366	278	12	l	l	NOUN
ejpam-2366	278	13	-	-	NOUN
ejpam-2366	278	14	module	module	NOUN
ejpam-2366	278	15	m	m	NOUN
ejpam-2366	278	16	.	.	PUNCT
ejpam-2366	279	1	definition	definition	NOUN
ejpam-2366	279	2	3	3	NUM
ejpam-2366	279	3	.	.	PUNCT
ejpam-2366	280	1	a	a	DET
ejpam-2366	280	2	proper	proper	ADJ
ejpam-2366	280	3	element	element	NOUN
ejpam-2366	280	4	n	n	PRON
ejpam-2366	280	5	∈m	∈m	NOUN
ejpam-2366	280	6	is	be	AUX
ejpam-2366	280	7	said	say	VERB
ejpam-2366	280	8	to	to	PART
ejpam-2366	280	9	be	be	AUX
ejpam-2366	280	10	2	2	NUM
ejpam-2366	280	11	-	-	PUNCT
ejpam-2366	280	12	potent	potent	ADJ
ejpam-2366	280	13	prime	prime	NOUN
ejpam-2366	280	14	if	if	SCONJ
ejpam-2366	280	15	for	for	ADP
ejpam-2366	280	16	all	all	DET
ejpam-2366	280	17	a	a	DET
ejpam-2366	280	18	∈	∈	PROPN
ejpam-2366	280	19	l	l	NOUN
ejpam-2366	280	20	,	,	PUNCT
ejpam-2366	280	21	a	a	DET
ejpam-2366	280	22	∈	∈	NOUN
ejpam-2366	280	23	m	m	VERB
ejpam-2366	280	24	,	,	PUNCT
ejpam-2366	280	25	aa	aa	ADV
ejpam-2366	280	26	6	6	NUM
ejpam-2366	280	27	(	(	PUNCT
ejpam-2366	280	28	n	n	NUM
ejpam-2366	280	29	:	:	PUNCT
ejpam-2366	280	30	i	i	PRON
ejpam-2366	280	31	m	m	PROPN
ejpam-2366	280	32	)	)	PUNCT
ejpam-2366	280	33	n	n	PRON
ejpam-2366	280	34	implies	imply	VERB
ejpam-2366	280	35	either	either	CCONJ
ejpam-2366	280	36	a	a	DET
ejpam-2366	280	37	6	6	NUM
ejpam-2366	280	38	(	(	PUNCT
ejpam-2366	280	39	n	n	NUM
ejpam-2366	280	40	:	:	PUNCT
ejpam-2366	280	41	i	i	PRON
ejpam-2366	280	42	m	m	VERB
ejpam-2366	280	43	)	)	PUNCT
ejpam-2366	280	44	or	or	CCONJ
ejpam-2366	280	45	a	a	DET
ejpam-2366	280	46	6	6	NUM
ejpam-2366	280	47	n	n	NOUN
ejpam-2366	280	48	.	.	PUNCT
ejpam-2366	281	1	theorem	theorem	ADJ
ejpam-2366	281	2	7	7	NUM
ejpam-2366	281	3	.	.	PUNCT
ejpam-2366	282	1	let	let	VERB
ejpam-2366	282	2	a	a	DET
ejpam-2366	282	3	proper	proper	ADJ
ejpam-2366	282	4	element	element	NOUN
ejpam-2366	282	5	n	n	PROPN
ejpam-2366	282	6	of	of	ADP
ejpam-2366	282	7	an	an	DET
ejpam-2366	282	8	l	l	NOUN
ejpam-2366	282	9	-	-	NOUN
ejpam-2366	282	10	module	module	NOUN
ejpam-2366	282	11	m	m	NOUN
ejpam-2366	282	12	be	be	VERB
ejpam-2366	282	13	2	2	NUM
ejpam-2366	282	14	-	-	PUNCT
ejpam-2366	282	15	potent	potent	ADJ
ejpam-2366	282	16	prime	prime	NOUN
ejpam-2366	282	17	.	.	PUNCT
ejpam-2366	283	1	then	then	ADV
ejpam-2366	283	2	n	n	PROPN
ejpam-2366	283	3	is	be	AUX
ejpam-2366	283	4	φ	φ	NOUN
ejpam-2366	283	5	-	-	NOUN
ejpam-2366	283	6	prime	prime	NOUN
ejpam-2366	283	7	for	for	ADP
ejpam-2366	283	8	some	some	DET
ejpam-2366	283	9	φ	φ	NUM
ejpam-2366	283	10	6	6	NUM
ejpam-2366	283	11	φ2	φ2	PROPN
ejpam-2366	283	12	if	if	SCONJ
ejpam-2366	283	13	and	and	CCONJ
ejpam-2366	283	14	only	only	ADV
ejpam-2366	283	15	if	if	SCONJ
ejpam-2366	283	16	n	n	NOUN
ejpam-2366	283	17	is	be	AUX
ejpam-2366	283	18	prime	prime	ADJ
ejpam-2366	283	19	.	.	PUNCT
ejpam-2366	284	1	proof	proof	NOUN
ejpam-2366	284	2	.	.	PUNCT
ejpam-2366	285	1	assume	assume	VERB
ejpam-2366	285	2	that	that	SCONJ
ejpam-2366	285	3	n	n	PRON
ejpam-2366	285	4	∈	∈	PROPN
ejpam-2366	285	5	m	m	VERB
ejpam-2366	285	6	is	be	AUX
ejpam-2366	285	7	a	a	DET
ejpam-2366	285	8	prime	prime	ADJ
ejpam-2366	285	9	element	element	NOUN
ejpam-2366	285	10	.	.	PUNCT
ejpam-2366	286	1	then	then	ADV
ejpam-2366	286	2	obviously	obviously	ADV
ejpam-2366	286	3	,	,	PUNCT
ejpam-2366	286	4	n	n	PROPN
ejpam-2366	286	5	is	be	AUX
ejpam-2366	286	6	φ	φ	NOUN
ejpam-2366	286	7	-	-	NOUN
ejpam-2366	286	8	prime	prime	NOUN
ejpam-2366	286	9	for	for	ADP
ejpam-2366	286	10	every	every	DET
ejpam-2366	286	11	φ	φ	NOUN
ejpam-2366	286	12	and	and	CCONJ
ejpam-2366	286	13	hence	hence	ADV
ejpam-2366	286	14	for	for	ADP
ejpam-2366	286	15	some	some	DET
ejpam-2366	286	16	φ	φ	NUM
ejpam-2366	286	17	6	6	NUM
ejpam-2366	286	18	φ2	φ2	PROPN
ejpam-2366	286	19	.	.	PUNCT
ejpam-2366	287	1	conversely	conversely	ADV
ejpam-2366	287	2	,	,	PUNCT
ejpam-2366	287	3	let	let	VERB
ejpam-2366	287	4	n	n	PRON
ejpam-2366	287	5	be	be	AUX
ejpam-2366	287	6	φ	φ	VERB
ejpam-2366	287	7	-	-	NOUN
ejpam-2366	287	8	prime	prime	NOUN
ejpam-2366	287	9	for	for	ADP
ejpam-2366	287	10	some	some	DET
ejpam-2366	287	11	φ	φ	PROPN
ejpam-2366	287	12	6	6	NUM
ejpam-2366	287	13	φ2	φ2	PROPN
ejpam-2366	287	14	.	.	PUNCT
ejpam-2366	288	1	then	then	ADV
ejpam-2366	288	2	by	by	ADP
ejpam-2366	288	3	theorem	theorem	NOUN
ejpam-2366	288	4	2	2	NUM
ejpam-2366	288	5	,	,	PUNCT
ejpam-2366	288	6	n	n	PRON
ejpam-2366	288	7	∈	∈	NOUN
ejpam-2366	288	8	m	m	VERB
ejpam-2366	288	9	is	be	AUX
ejpam-2366	288	10	φ2	φ2	ADJ
ejpam-2366	288	11	-	-	PUNCT
ejpam-2366	288	12	prime	prime	NOUN
ejpam-2366	288	13	.	.	PUNCT
ejpam-2366	289	1	let	let	VERB
ejpam-2366	289	2	aa	aa	PROPN
ejpam-2366	289	3	6	6	NUM
ejpam-2366	289	4	n	n	NOUN
ejpam-2366	289	5	for	for	ADP
ejpam-2366	289	6	a	a	DET
ejpam-2366	289	7	∈	∈	PROPN
ejpam-2366	289	8	l	l	NOUN
ejpam-2366	289	9	,	,	PUNCT
ejpam-2366	289	10	a	a	DET
ejpam-2366	289	11	∈	∈	NOUN
ejpam-2366	289	12	m	m	VERB
ejpam-2366	289	13	.	.	PUNCT
ejpam-2366	290	1	if	if	SCONJ
ejpam-2366	290	2	aa	aa	PROPN
ejpam-2366	290	3	(	(	PUNCT
ejpam-2366	290	4	n	n	NOUN
ejpam-2366	290	5	:	:	PUNCT
ejpam-2366	290	6	i	i	PRON
ejpam-2366	290	7	m	m	PROPN
ejpam-2366	290	8	)	)	PUNCT
ejpam-2366	290	9	n	n	CCONJ
ejpam-2366	290	10	,	,	PUNCT
ejpam-2366	290	11	then	then	ADV
ejpam-2366	290	12	as	as	SCONJ
ejpam-2366	290	13	n	n	PRON
ejpam-2366	290	14	is	be	AUX
ejpam-2366	290	15	φ2	φ2	ADJ
ejpam-2366	290	16	-	-	PUNCT
ejpam-2366	290	17	prime	prime	NOUN
ejpam-2366	290	18	,	,	PUNCT
ejpam-2366	290	19	we	we	PRON
ejpam-2366	290	20	have	have	VERB
ejpam-2366	290	21	either	either	CCONJ
ejpam-2366	290	22	a	a	DET
ejpam-2366	290	23	6	6	NUM
ejpam-2366	290	24	(	(	PUNCT
ejpam-2366	290	25	n	n	NUM
ejpam-2366	290	26	:	:	PUNCT
ejpam-2366	290	27	i	i	PRON
ejpam-2366	290	28	m	m	VERB
ejpam-2366	290	29	)	)	PUNCT
ejpam-2366	290	30	or	or	CCONJ
ejpam-2366	290	31	a	a	DET
ejpam-2366	290	32	6	6	NUM
ejpam-2366	290	33	n	n	NOUN
ejpam-2366	290	34	.	.	PUNCT
ejpam-2366	291	1	if	if	SCONJ
ejpam-2366	291	2	aa	aa	NOUN
ejpam-2366	291	3	6	6	NUM
ejpam-2366	291	4	(	(	PUNCT
ejpam-2366	291	5	n	n	NUM
ejpam-2366	291	6	:	:	PUNCT
ejpam-2366	291	7	i	i	PRON
ejpam-2366	291	8	m	m	PROPN
ejpam-2366	291	9	)	)	PUNCT
ejpam-2366	291	10	n	n	CCONJ
ejpam-2366	291	11	,	,	PUNCT
ejpam-2366	291	12	then	then	ADV
ejpam-2366	291	13	as	as	SCONJ
ejpam-2366	291	14	n	n	NOUN
ejpam-2366	291	15	is	be	AUX
ejpam-2366	291	16	2	2	NUM
ejpam-2366	291	17	-	-	PUNCT
ejpam-2366	291	18	potent	potent	ADJ
ejpam-2366	291	19	prime	prime	NOUN
ejpam-2366	291	20	,	,	PUNCT
ejpam-2366	291	21	we	we	PRON
ejpam-2366	291	22	have	have	VERB
ejpam-2366	291	23	either	either	CCONJ
ejpam-2366	291	24	a	a	DET
ejpam-2366	291	25	6	6	NUM
ejpam-2366	291	26	(	(	PUNCT
ejpam-2366	291	27	n	n	NUM
ejpam-2366	291	28	:	:	PUNCT
ejpam-2366	291	29	i	i	PRON
ejpam-2366	291	30	m	m	VERB
ejpam-2366	291	31	)	)	PUNCT
ejpam-2366	291	32	or	or	CCONJ
ejpam-2366	291	33	a	a	DET
ejpam-2366	291	34	6	6	NUM
ejpam-2366	291	35	n	n	NOUN
ejpam-2366	291	36	and	and	CCONJ
ejpam-2366	291	37	hence	hence	ADV
ejpam-2366	291	38	n	n	PRON
ejpam-2366	291	39	is	be	AUX
ejpam-2366	291	40	prime	prime	ADJ
ejpam-2366	291	41	.	.	PUNCT
ejpam-2366	292	1	now	now	ADV
ejpam-2366	292	2	we	we	PRON
ejpam-2366	292	3	define	define	VERB
ejpam-2366	292	4	a	a	DET
ejpam-2366	292	5	n	n	ADV
ejpam-2366	292	6	-	-	PUNCT
ejpam-2366	292	7	potent	potent	ADJ
ejpam-2366	292	8	prime	prime	ADJ
ejpam-2366	292	9	element	element	NOUN
ejpam-2366	292	10	in	in	ADP
ejpam-2366	292	11	an	an	DET
ejpam-2366	292	12	l	l	NOUN
ejpam-2366	292	13	-	-	NOUN
ejpam-2366	292	14	module	module	NOUN
ejpam-2366	292	15	m	m	NOUN
ejpam-2366	292	16	where	where	SCONJ
ejpam-2366	292	17	n	n	X
ejpam-2366	292	18	>	>	X
ejpam-2366	292	19	2	2	X
ejpam-2366	292	20	.	.	X
ejpam-2366	292	21	definition	definition	NOUN
ejpam-2366	292	22	4	4	NUM
ejpam-2366	292	23	.	.	PUNCT
ejpam-2366	293	1	let	let	VERB
ejpam-2366	293	2	n	n	PRON
ejpam-2366	293	3	>	>	X
ejpam-2366	293	4	2	2	NUM
ejpam-2366	293	5	and	and	CCONJ
ejpam-2366	293	6	n	n	PRON
ejpam-2366	293	7	∈	∈	PROPN
ejpam-2366	293	8	z+	z+	NUM
ejpam-2366	293	9	.	.	PUNCT
ejpam-2366	294	1	a	a	DET
ejpam-2366	294	2	proper	proper	ADJ
ejpam-2366	294	3	element	element	NOUN
ejpam-2366	294	4	n	n	PRON
ejpam-2366	294	5	∈	∈	NOUN
ejpam-2366	294	6	m	m	VERB
ejpam-2366	294	7	is	be	AUX
ejpam-2366	294	8	said	say	VERB
ejpam-2366	294	9	to	to	PART
ejpam-2366	294	10	be	be	AUX
ejpam-2366	294	11	n	n	PRON
ejpam-2366	294	12	-	-	PUNCT
ejpam-2366	294	13	potent	potent	ADJ
ejpam-2366	294	14	prime	prime	NOUN
ejpam-2366	294	15	if	if	SCONJ
ejpam-2366	294	16	for	for	ADP
ejpam-2366	294	17	all	all	DET
ejpam-2366	294	18	a	a	DET
ejpam-2366	294	19	∈	∈	PROPN
ejpam-2366	294	20	l	l	NOUN
ejpam-2366	294	21	,	,	PUNCT
ejpam-2366	294	22	a	a	DET
ejpam-2366	294	23	∈	∈	NOUN
ejpam-2366	294	24	m	m	VERB
ejpam-2366	294	25	,	,	PUNCT
ejpam-2366	294	26	aa	aa	ADV
ejpam-2366	294	27	6	6	NUM
ejpam-2366	294	28	(	(	PUNCT
ejpam-2366	294	29	n	n	NUM
ejpam-2366	294	30	:	:	PUNCT
ejpam-2366	295	1	i	i	PRON
ejpam-2366	295	2	m	m	PROPN
ejpam-2366	295	3	)	)	PUNCT
ejpam-2366	295	4	n−1n	n−1n	NOUN
ejpam-2366	295	5	implies	imply	VERB
ejpam-2366	295	6	either	either	CCONJ
ejpam-2366	295	7	a	a	DET
ejpam-2366	295	8	6	6	NUM
ejpam-2366	295	9	(	(	PUNCT
ejpam-2366	295	10	n	n	NUM
ejpam-2366	295	11	:	:	PUNCT
ejpam-2366	295	12	i	i	PRON
ejpam-2366	295	13	m	m	VERB
ejpam-2366	295	14	)	)	PUNCT
ejpam-2366	295	15	or	or	CCONJ
ejpam-2366	295	16	a	a	DET
ejpam-2366	295	17	6	6	NUM
ejpam-2366	295	18	n	n	NOUN
ejpam-2366	295	19	.	.	PUNCT
ejpam-2366	296	1	a.	a.	PROPN
ejpam-2366	296	2	v.	v.	PROPN
ejpam-2366	296	3	bingi	bingi	PROPN
ejpam-2366	296	4	,	,	PUNCT
ejpam-2366	296	5	c.	c.	PROPN
ejpam-2366	296	6	s.	s.	PROPN
ejpam-2366	296	7	manjarekar	manjarekar	PROPN
ejpam-2366	296	8	/	/	PROPN
ejpam-2366	296	9	eur	eur	PROPN
ejpam-2366	296	10	.	.	PUNCT
ejpam-2366	297	1	j.	j.	PROPN
ejpam-2366	297	2	pure	pure	PROPN
ejpam-2366	297	3	appl	appl	PROPN
ejpam-2366	297	4	.	.	PROPN
ejpam-2366	297	5	math	math	PROPN
ejpam-2366	297	6	,	,	PUNCT
ejpam-2366	297	7	14	14	NUM
ejpam-2366	297	8	(	(	PUNCT
ejpam-2366	297	9	2	2	NUM
ejpam-2366	297	10	)	)	PUNCT
ejpam-2366	297	11	(	(	PUNCT
ejpam-2366	297	12	2021	2021	NUM
ejpam-2366	297	13	)	)	PUNCT
ejpam-2366	297	14	,	,	PUNCT
ejpam-2366	297	15	551	551	NUM
ejpam-2366	297	16	-	-	SYM
ejpam-2366	297	17	577	577	NUM
ejpam-2366	297	18	559	559	NUM
ejpam-2366	297	19	theorem	theorem	NOUN
ejpam-2366	297	20	8	8	NUM
ejpam-2366	297	21	.	.	PUNCT
ejpam-2366	298	1	a	a	DET
ejpam-2366	298	2	proper	proper	ADJ
ejpam-2366	298	3	element	element	NOUN
ejpam-2366	298	4	n	n	PROPN
ejpam-2366	298	5	of	of	ADP
ejpam-2366	298	6	an	an	DET
ejpam-2366	298	7	l	l	NOUN
ejpam-2366	298	8	-	-	NOUN
ejpam-2366	298	9	module	module	NOUN
ejpam-2366	298	10	m	m	NOUN
ejpam-2366	298	11	is	be	AUX
ejpam-2366	298	12	φ	φ	NOUN
ejpam-2366	298	13	-	-	NOUN
ejpam-2366	298	14	prime	prime	NOUN
ejpam-2366	298	15	for	for	ADP
ejpam-2366	298	16	some	some	DET
ejpam-2366	298	17	φ	φ	NOUN
ejpam-2366	298	18	6	6	NUM
ejpam-2366	298	19	φn	φn	ADP
ejpam-2366	298	20	where	where	SCONJ
ejpam-2366	298	21	n	n	X
ejpam-2366	298	22	>	>	X
ejpam-2366	298	23	2	2	NUM
ejpam-2366	298	24	if	if	SCONJ
ejpam-2366	298	25	and	and	CCONJ
ejpam-2366	298	26	only	only	ADV
ejpam-2366	298	27	if	if	SCONJ
ejpam-2366	298	28	n	n	PRON
ejpam-2366	298	29	is	be	AUX
ejpam-2366	298	30	prime	prime	ADJ
ejpam-2366	298	31	,	,	PUNCT
ejpam-2366	298	32	provided	provide	VERB
ejpam-2366	298	33	n	n	PRON
ejpam-2366	298	34	is	be	AUX
ejpam-2366	298	35	k	k	ADJ
ejpam-2366	298	36	-	-	PUNCT
ejpam-2366	298	37	potent	potent	ADJ
ejpam-2366	298	38	prime	prime	NOUN
ejpam-2366	298	39	for	for	ADP
ejpam-2366	298	40	some	some	DET
ejpam-2366	298	41	k	k	PROPN
ejpam-2366	298	42	6	6	NUM
ejpam-2366	298	43	n.	n.	NOUN
ejpam-2366	298	44	proof	proof	NOUN
ejpam-2366	298	45	.	.	PUNCT
ejpam-2366	299	1	assume	assume	VERB
ejpam-2366	299	2	that	that	SCONJ
ejpam-2366	299	3	n	n	PRON
ejpam-2366	299	4	∈	∈	PROPN
ejpam-2366	299	5	m	m	VERB
ejpam-2366	299	6	is	be	AUX
ejpam-2366	299	7	a	a	DET
ejpam-2366	299	8	prime	prime	ADJ
ejpam-2366	299	9	element	element	NOUN
ejpam-2366	299	10	.	.	PUNCT
ejpam-2366	300	1	then	then	ADV
ejpam-2366	300	2	obviously	obviously	ADV
ejpam-2366	300	3	,	,	PUNCT
ejpam-2366	300	4	n	n	PROPN
ejpam-2366	300	5	is	be	AUX
ejpam-2366	300	6	φ	φ	NOUN
ejpam-2366	300	7	-	-	NOUN
ejpam-2366	300	8	prime	prime	NOUN
ejpam-2366	300	9	for	for	ADP
ejpam-2366	300	10	every	every	DET
ejpam-2366	300	11	φ	φ	NOUN
ejpam-2366	300	12	and	and	CCONJ
ejpam-2366	300	13	hence	hence	ADV
ejpam-2366	300	14	for	for	ADP
ejpam-2366	300	15	some	some	DET
ejpam-2366	300	16	φ	φ	NOUN
ejpam-2366	300	17	6	6	NUM
ejpam-2366	300	18	φn	φn	ADP
ejpam-2366	300	19	where	where	SCONJ
ejpam-2366	300	20	n	n	AUX
ejpam-2366	300	21	>	>	X
ejpam-2366	300	22	2	2	X
ejpam-2366	300	23	.	.	PUNCT
ejpam-2366	301	1	conversely	conversely	ADV
ejpam-2366	301	2	,	,	PUNCT
ejpam-2366	301	3	let	let	VERB
ejpam-2366	301	4	n	n	PRON
ejpam-2366	301	5	be	be	AUX
ejpam-2366	301	6	φ	φ	VERB
ejpam-2366	301	7	-	-	NOUN
ejpam-2366	301	8	prime	prime	NOUN
ejpam-2366	301	9	for	for	ADP
ejpam-2366	301	10	some	some	DET
ejpam-2366	301	11	φ	φ	NOUN
ejpam-2366	301	12	6	6	NUM
ejpam-2366	301	13	φn	φn	ADP
ejpam-2366	301	14	where	where	SCONJ
ejpam-2366	301	15	n	n	AUX
ejpam-2366	301	16	>	>	X
ejpam-2366	301	17	2	2	X
ejpam-2366	301	18	.	.	PUNCT
ejpam-2366	301	19	then	then	ADV
ejpam-2366	301	20	by	by	ADP
ejpam-2366	301	21	theorem	theorem	NOUN
ejpam-2366	301	22	2	2	NUM
ejpam-2366	301	23	,	,	PUNCT
ejpam-2366	301	24	n	n	PRON
ejpam-2366	301	25	∈	∈	NOUN
ejpam-2366	301	26	m	m	VERB
ejpam-2366	301	27	is	be	AUX
ejpam-2366	301	28	φn	φn	ADJ
ejpam-2366	301	29	-	-	PUNCT
ejpam-2366	301	30	prime	prime	NOUN
ejpam-2366	301	31	.	.	PUNCT
ejpam-2366	302	1	let	let	VERB
ejpam-2366	302	2	aa	aa	PROPN
ejpam-2366	302	3	6	6	NUM
ejpam-2366	302	4	n	n	NOUN
ejpam-2366	302	5	for	for	ADP
ejpam-2366	302	6	a	a	DET
ejpam-2366	302	7	∈	∈	PROPN
ejpam-2366	302	8	l	l	NOUN
ejpam-2366	302	9	,	,	PUNCT
ejpam-2366	302	10	a	a	DET
ejpam-2366	302	11	∈m	∈m	NOUN
ejpam-2366	302	12	.	.	PUNCT
ejpam-2366	303	1	if	if	SCONJ
ejpam-2366	303	2	aa	aa	PROPN
ejpam-2366	303	3	φk(n	φk(n	NUM
ejpam-2366	303	4	)	)	PUNCT
ejpam-2366	303	5	,	,	PUNCT
ejpam-2366	303	6	then	then	ADV
ejpam-2366	303	7	aa	aa	PROPN
ejpam-2366	303	8	φn(n	φn(n	PROPN
ejpam-2366	303	9	)	)	PUNCT
ejpam-2366	303	10	as	as	SCONJ
ejpam-2366	303	11	k	k	PROPN
ejpam-2366	303	12	6	6	NUM
ejpam-2366	303	13	n.	n.	NOUN
ejpam-2366	303	14	since	since	SCONJ
ejpam-2366	303	15	n	n	PROPN
ejpam-2366	303	16	is	be	AUX
ejpam-2366	303	17	φn	φn	ADJ
ejpam-2366	303	18	-	-	PUNCT
ejpam-2366	303	19	prime	prime	NOUN
ejpam-2366	303	20	,	,	PUNCT
ejpam-2366	303	21	we	we	PRON
ejpam-2366	303	22	have	have	VERB
ejpam-2366	303	23	either	either	CCONJ
ejpam-2366	303	24	a	a	DET
ejpam-2366	303	25	6	6	NUM
ejpam-2366	303	26	(	(	PUNCT
ejpam-2366	303	27	n	n	NUM
ejpam-2366	303	28	:	:	PUNCT
ejpam-2366	303	29	i	i	PRON
ejpam-2366	303	30	m	m	VERB
ejpam-2366	303	31	)	)	PUNCT
ejpam-2366	303	32	or	or	CCONJ
ejpam-2366	303	33	a	a	DET
ejpam-2366	303	34	6	6	NUM
ejpam-2366	303	35	n	n	NOUN
ejpam-2366	303	36	.	.	PUNCT
ejpam-2366	304	1	if	if	SCONJ
ejpam-2366	304	2	aa	aa	PROPN
ejpam-2366	304	3	6	6	NUM
ejpam-2366	304	4	φk(n	φk(n	NUM
ejpam-2366	304	5	)	)	PUNCT
ejpam-2366	304	6	,	,	PUNCT
ejpam-2366	304	7	then	then	ADV
ejpam-2366	304	8	as	as	SCONJ
ejpam-2366	304	9	n	n	NOUN
ejpam-2366	304	10	is	be	AUX
ejpam-2366	304	11	k	k	ADJ
ejpam-2366	304	12	-	-	PUNCT
ejpam-2366	304	13	potent	potent	ADJ
ejpam-2366	304	14	prime	prime	NOUN
ejpam-2366	304	15	,	,	PUNCT
ejpam-2366	304	16	we	we	PRON
ejpam-2366	304	17	have	have	VERB
ejpam-2366	304	18	either	either	CCONJ
ejpam-2366	304	19	a	a	DET
ejpam-2366	304	20	6	6	NUM
ejpam-2366	304	21	(	(	PUNCT
ejpam-2366	304	22	n	n	NUM
ejpam-2366	304	23	:	:	PUNCT
ejpam-2366	304	24	i	i	PRON
ejpam-2366	304	25	m	m	VERB
ejpam-2366	304	26	)	)	PUNCT
ejpam-2366	304	27	or	or	CCONJ
ejpam-2366	304	28	a	a	DET
ejpam-2366	304	29	6	6	NUM
ejpam-2366	304	30	n	n	NOUN
ejpam-2366	304	31	and	and	CCONJ
ejpam-2366	304	32	hence	hence	ADV
ejpam-2366	304	33	n	n	PRON
ejpam-2366	304	34	is	be	AUX
ejpam-2366	304	35	prime	prime	ADJ
ejpam-2366	304	36	.	.	PUNCT
ejpam-2366	305	1	the	the	DET
ejpam-2366	305	2	following	follow	VERB
ejpam-2366	305	3	corollary	corollary	NOUN
ejpam-2366	305	4	is	be	AUX
ejpam-2366	305	5	outcome	outcome	NOUN
ejpam-2366	305	6	of	of	ADP
ejpam-2366	305	7	theorems	theorem	NOUN
ejpam-2366	305	8	5	5	NUM
ejpam-2366	305	9	,	,	PUNCT
ejpam-2366	305	10	6	6	NUM
ejpam-2366	305	11	and	and	CCONJ
ejpam-2366	305	12	7	7	NUM
ejpam-2366	305	13	.	.	PUNCT
ejpam-2366	305	14	corollary	corollary	ADJ
ejpam-2366	305	15	4	4	NUM
ejpam-2366	305	16	.	.	PUNCT
ejpam-2366	306	1	an	an	DET
ejpam-2366	306	2	almost	almost	ADV
ejpam-2366	306	3	prime	prime	ADJ
ejpam-2366	306	4	element	element	NOUN
ejpam-2366	306	5	n	n	PROPN
ejpam-2366	306	6	of	of	ADP
ejpam-2366	306	7	an	an	DET
ejpam-2366	306	8	l	l	NOUN
ejpam-2366	306	9	-	-	NOUN
ejpam-2366	306	10	module	module	NOUN
ejpam-2366	306	11	m	m	NOUN
ejpam-2366	306	12	is	be	AUX
ejpam-2366	306	13	prime	prime	ADJ
ejpam-2366	306	14	if	if	SCONJ
ejpam-2366	306	15	one	one	NUM
ejpam-2366	306	16	the	the	DET
ejpam-2366	306	17	following	following	ADJ
ejpam-2366	306	18	statements	statement	NOUN
ejpam-2366	306	19	hold	hold	VERB
ejpam-2366	306	20	true	true	ADJ
ejpam-2366	306	21	:	:	PUNCT
ejpam-2366	306	22	(	(	PUNCT
ejpam-2366	306	23	i	i	NOUN
ejpam-2366	306	24	)	)	PUNCT
ejpam-2366	306	25	m	m	VERB
ejpam-2366	306	26	is	be	AUX
ejpam-2366	306	27	torsion	torsion	NOUN
ejpam-2366	306	28	free	free	ADJ
ejpam-2366	306	29	and	and	CCONJ
ejpam-2366	306	30	om	om	PROPN
ejpam-2366	306	31	6=	6=	PROPN
ejpam-2366	306	32	n	n	CCONJ
ejpam-2366	306	33	<	<	X
ejpam-2366	306	34	i	i	X
ejpam-2366	306	35	m	m	VERB
ejpam-2366	306	36	is	be	AUX
ejpam-2366	306	37	a	a	DET
ejpam-2366	306	38	weak	weak	ADJ
ejpam-2366	306	39	join	join	NOUN
ejpam-2366	306	40	principal	principal	ADJ
ejpam-2366	306	41	element	element	NOUN
ejpam-2366	306	42	.	.	PUNCT
ejpam-2366	307	1	(	(	PUNCT
ejpam-2366	307	2	ii	ii	NOUN
ejpam-2366	307	3	)	)	PUNCT
ejpam-2366	308	1	n	n	PRON
ejpam-2366	308	2	is	be	AUX
ejpam-2366	308	3	a	a	DET
ejpam-2366	308	4	2	2	NUM
ejpam-2366	308	5	-	-	PUNCT
ejpam-2366	308	6	potent	potent	ADJ
ejpam-2366	308	7	prime	prime	ADJ
ejpam-2366	308	8	element	element	NOUN
ejpam-2366	308	9	.	.	PUNCT
ejpam-2366	309	1	(	(	PUNCT
ejpam-2366	309	2	iii	iii	X
ejpam-2366	309	3	)	)	PUNCT
ejpam-2366	309	4	l	l	NOUN
ejpam-2366	309	5	is	be	AUX
ejpam-2366	309	6	a	a	DET
ejpam-2366	309	7	noether	noether	ADJ
ejpam-2366	309	8	pg	pg	NOUN
ejpam-2366	309	9	-	-	PUNCT
ejpam-2366	309	10	lattice	lattice	PROPN
ejpam-2366	309	11	,	,	PUNCT
ejpam-2366	309	12	m	m	VERB
ejpam-2366	309	13	is	be	AUX
ejpam-2366	309	14	a	a	DET
ejpam-2366	309	15	faithful	faithful	ADJ
ejpam-2366	309	16	multiplication	multiplication	NOUN
ejpam-2366	309	17	pg	pg	NOUN
ejpam-2366	309	18	-	-	PUNCT
ejpam-2366	309	19	lattice	lattice	VERB
ejpam-2366	309	20	with	with	ADP
ejpam-2366	309	21	i	i	PRON
ejpam-2366	309	22	m	m	VERB
ejpam-2366	309	23	compact	compact	ADJ
ejpam-2366	309	24	,	,	PUNCT
ejpam-2366	309	25	0	0	NUM
ejpam-2366	309	26	6=	6=	NUM
ejpam-2366	309	27	(	(	PUNCT
ejpam-2366	309	28	n	n	X
ejpam-2366	309	29	:	:	PUNCT
ejpam-2366	309	30	i	i	PRON
ejpam-2366	309	31	m	m	VERB
ejpam-2366	309	32	)	)	PUNCT
ejpam-2366	309	33	∈	∈	PROPN
ejpam-2366	309	34	l	l	NOUN
ejpam-2366	309	35	satisfies	satisfy	VERB
ejpam-2366	309	36	the	the	DET
ejpam-2366	309	37	restricted	restricted	ADJ
ejpam-2366	309	38	cancellation	cancellation	NOUN
ejpam-2366	309	39	law	law	NOUN
ejpam-2366	309	40	(	(	PUNCT
ejpam-2366	309	41	rcl	rcl	NOUN
ejpam-2366	309	42	)	)	PUNCT
ejpam-2366	309	43	and	and	CCONJ
ejpam-2366	309	44	is	be	AUX
ejpam-2366	309	45	a	a	DET
ejpam-2366	309	46	nonnilpotent	nonnilpotent	ADJ
ejpam-2366	309	47	element	element	NOUN
ejpam-2366	309	48	.	.	PUNCT
ejpam-2366	310	1	theorem	theorem	VERB
ejpam-2366	310	2	9	9	NUM
ejpam-2366	310	3	.	.	PUNCT
ejpam-2366	311	1	let	let	VERB
ejpam-2366	311	2	a	a	DET
ejpam-2366	311	3	proper	proper	ADJ
ejpam-2366	311	4	element	element	NOUN
ejpam-2366	311	5	n	n	PROPN
ejpam-2366	311	6	of	of	ADP
ejpam-2366	311	7	an	an	DET
ejpam-2366	311	8	l	l	NOUN
ejpam-2366	311	9	-	-	NOUN
ejpam-2366	311	10	module	module	NOUN
ejpam-2366	311	11	m	m	NOUN
ejpam-2366	311	12	be	be	VERB
ejpam-2366	311	13	φ	φ	VERB
ejpam-2366	311	14	-	-	NOUN
ejpam-2366	311	15	prime	prime	NOUN
ejpam-2366	311	16	.	.	PUNCT
ejpam-2366	312	1	if	if	SCONJ
ejpam-2366	312	2	φ(n	φ(n	NOUN
ejpam-2366	312	3	)	)	PUNCT
ejpam-2366	312	4	is	be	AUX
ejpam-2366	312	5	prime	prime	ADJ
ejpam-2366	312	6	,	,	PUNCT
ejpam-2366	312	7	then	then	ADV
ejpam-2366	312	8	n	n	PROPN
ejpam-2366	312	9	is	be	AUX
ejpam-2366	312	10	prime	prime	ADJ
ejpam-2366	312	11	.	.	PUNCT
ejpam-2366	313	1	proof	proof	NOUN
ejpam-2366	313	2	.	.	PUNCT
ejpam-2366	314	1	let	let	VERB
ejpam-2366	314	2	aa	aa	PROPN
ejpam-2366	314	3	6	6	NUM
ejpam-2366	314	4	n	n	NOUN
ejpam-2366	314	5	for	for	ADP
ejpam-2366	314	6	a	a	DET
ejpam-2366	314	7	∈	∈	PROPN
ejpam-2366	314	8	l	l	NOUN
ejpam-2366	314	9	,	,	PUNCT
ejpam-2366	314	10	a	a	DET
ejpam-2366	314	11	∈	∈	NOUN
ejpam-2366	314	12	m	m	VERB
ejpam-2366	314	13	.	.	PUNCT
ejpam-2366	315	1	if	if	SCONJ
ejpam-2366	315	2	aa	aa	PROPN
ejpam-2366	315	3	φ(n	φ(n	ADJ
ejpam-2366	315	4	)	)	PUNCT
ejpam-2366	315	5	,	,	PUNCT
ejpam-2366	315	6	then	then	ADV
ejpam-2366	315	7	as	as	SCONJ
ejpam-2366	315	8	n	n	PROPN
ejpam-2366	315	9	is	be	AUX
ejpam-2366	315	10	φ	φ	VERB
ejpam-2366	315	11	-	-	NOUN
ejpam-2366	315	12	prime	prime	NOUN
ejpam-2366	315	13	,	,	PUNCT
ejpam-2366	315	14	we	we	PRON
ejpam-2366	315	15	have	have	VERB
ejpam-2366	315	16	either	either	CCONJ
ejpam-2366	315	17	a	a	DET
ejpam-2366	315	18	6	6	NUM
ejpam-2366	315	19	(	(	PUNCT
ejpam-2366	315	20	n	n	NUM
ejpam-2366	315	21	:	:	PUNCT
ejpam-2366	315	22	i	i	PRON
ejpam-2366	315	23	m	m	VERB
ejpam-2366	315	24	)	)	PUNCT
ejpam-2366	315	25	or	or	CCONJ
ejpam-2366	315	26	a	a	DET
ejpam-2366	315	27	6	6	NUM
ejpam-2366	315	28	n	n	NOUN
ejpam-2366	316	1	and	and	CCONJ
ejpam-2366	316	2	we	we	PRON
ejpam-2366	316	3	are	be	AUX
ejpam-2366	316	4	done	do	VERB
ejpam-2366	316	5	.	.	PUNCT
ejpam-2366	317	1	if	if	SCONJ
ejpam-2366	317	2	aa	aa	NOUN
ejpam-2366	317	3	6	6	NUM
ejpam-2366	317	4	φ(n	φ(n	NOUN
ejpam-2366	317	5	)	)	PUNCT
ejpam-2366	317	6	,	,	PUNCT
ejpam-2366	317	7	then	then	ADV
ejpam-2366	317	8	as	as	SCONJ
ejpam-2366	317	9	φ(n	φ(n	NOUN
ejpam-2366	317	10	)	)	PUNCT
ejpam-2366	317	11	is	be	AUX
ejpam-2366	317	12	prime	prime	ADJ
ejpam-2366	317	13	,	,	PUNCT
ejpam-2366	317	14	we	we	PRON
ejpam-2366	317	15	have	have	AUX
ejpam-2366	317	16	either	either	CCONJ
ejpam-2366	317	17	aim	aim	VERB
ejpam-2366	317	18	6	6	NUM
ejpam-2366	317	19	φ(n	φ(n	NOUN
ejpam-2366	317	20	)	)	PUNCT
ejpam-2366	317	21	or	or	CCONJ
ejpam-2366	317	22	a	a	DET
ejpam-2366	317	23	6	6	NUM
ejpam-2366	317	24	φ(n	φ(n	NOUN
ejpam-2366	317	25	)	)	PUNCT
ejpam-2366	317	26	.	.	PUNCT
ejpam-2366	318	1	this	this	PRON
ejpam-2366	318	2	implies	imply	VERB
ejpam-2366	318	3	that	that	SCONJ
ejpam-2366	318	4	either	either	CCONJ
ejpam-2366	318	5	aim	aim	VERB
ejpam-2366	318	6	6	6	NUM
ejpam-2366	318	7	n	n	NOUN
ejpam-2366	318	8	or	or	CCONJ
ejpam-2366	318	9	a	a	DET
ejpam-2366	318	10	6	6	NUM
ejpam-2366	318	11	n	n	NOUN
ejpam-2366	318	12	because	because	SCONJ
ejpam-2366	318	13	φ(n	φ(n	NOUN
ejpam-2366	318	14	)	)	PUNCT
ejpam-2366	318	15	6	6	NUM
ejpam-2366	318	16	n	n	NOUN
ejpam-2366	318	17	.	.	PUNCT
ejpam-2366	319	1	hence	hence	ADV
ejpam-2366	319	2	n	n	PROPN
ejpam-2366	319	3	is	be	AUX
ejpam-2366	319	4	prime	prime	ADJ
ejpam-2366	319	5	.	.	PUNCT
ejpam-2366	320	1	theorem	theorem	ADJ
ejpam-2366	320	2	10	10	NUM
ejpam-2366	320	3	.	.	PUNCT
ejpam-2366	321	1	let	let	VERB
ejpam-2366	321	2	a	a	DET
ejpam-2366	321	3	proper	proper	ADJ
ejpam-2366	321	4	element	element	NOUN
ejpam-2366	321	5	n	n	PROPN
ejpam-2366	321	6	of	of	ADP
ejpam-2366	321	7	an	an	DET
ejpam-2366	321	8	l	l	NOUN
ejpam-2366	321	9	-	-	NOUN
ejpam-2366	321	10	module	module	NOUN
ejpam-2366	321	11	m	m	NOUN
ejpam-2366	321	12	be	be	VERB
ejpam-2366	321	13	φ	φ	VERB
ejpam-2366	321	14	-	-	NOUN
ejpam-2366	321	15	prime	prime	NOUN
ejpam-2366	321	16	.	.	PUNCT
ejpam-2366	322	1	if	if	SCONJ
ejpam-2366	322	2	(	(	PUNCT
ejpam-2366	322	3	n	n	X
ejpam-2366	322	4	:	:	PUNCT
ejpam-2366	322	5	i	i	PRON
ejpam-2366	322	6	m	m	VERB
ejpam-2366	322	7	)	)	PUNCT
ejpam-2366	322	8	n	n	PRON
ejpam-2366	322	9	φ(n	φ(n	NOUN
ejpam-2366	322	10	)	)	PUNCT
ejpam-2366	322	11	,	,	PUNCT
ejpam-2366	322	12	then	then	ADV
ejpam-2366	322	13	n	n	PROPN
ejpam-2366	322	14	is	be	AUX
ejpam-2366	322	15	prime	prime	ADJ
ejpam-2366	322	16	.	.	PUNCT
ejpam-2366	323	1	proof	proof	NOUN
ejpam-2366	323	2	.	.	PUNCT
ejpam-2366	324	1	let	let	VERB
ejpam-2366	324	2	aa	aa	PROPN
ejpam-2366	324	3	6	6	NUM
ejpam-2366	324	4	n	n	NOUN
ejpam-2366	324	5	for	for	ADP
ejpam-2366	324	6	a	a	DET
ejpam-2366	324	7	∈	∈	PROPN
ejpam-2366	324	8	l	l	NOUN
ejpam-2366	324	9	,	,	PUNCT
ejpam-2366	324	10	a	a	DET
ejpam-2366	324	11	∈	∈	NOUN
ejpam-2366	324	12	m	m	VERB
ejpam-2366	324	13	.	.	PUNCT
ejpam-2366	325	1	if	if	SCONJ
ejpam-2366	325	2	aa	aa	PROPN
ejpam-2366	325	3	φ(n	φ(n	ADJ
ejpam-2366	325	4	)	)	PUNCT
ejpam-2366	325	5	,	,	PUNCT
ejpam-2366	325	6	then	then	ADV
ejpam-2366	325	7	as	as	SCONJ
ejpam-2366	325	8	n	n	PROPN
ejpam-2366	325	9	is	be	AUX
ejpam-2366	325	10	φ	φ	VERB
ejpam-2366	325	11	-	-	NOUN
ejpam-2366	325	12	prime	prime	NOUN
ejpam-2366	325	13	,	,	PUNCT
ejpam-2366	325	14	we	we	PRON
ejpam-2366	325	15	have	have	VERB
ejpam-2366	325	16	either	either	CCONJ
ejpam-2366	325	17	a	a	DET
ejpam-2366	325	18	6	6	NUM
ejpam-2366	325	19	(	(	PUNCT
ejpam-2366	325	20	n	n	NUM
ejpam-2366	325	21	:	:	PUNCT
ejpam-2366	325	22	i	i	PRON
ejpam-2366	325	23	m	m	VERB
ejpam-2366	325	24	)	)	PUNCT
ejpam-2366	325	25	or	or	CCONJ
ejpam-2366	325	26	a	a	DET
ejpam-2366	325	27	6	6	NUM
ejpam-2366	325	28	n	n	NOUN
ejpam-2366	325	29	.	.	PUNCT
ejpam-2366	326	1	so	so	ADV
ejpam-2366	326	2	assume	assume	VERB
ejpam-2366	326	3	that	that	SCONJ
ejpam-2366	326	4	aa	aa	NOUN
ejpam-2366	326	5	6	6	NUM
ejpam-2366	326	6	φ(n	φ(n	NOUN
ejpam-2366	326	7	)	)	PUNCT
ejpam-2366	326	8	.	.	PUNCT
ejpam-2366	327	1	first	first	ADV
ejpam-2366	327	2	suppose	suppose	VERB
ejpam-2366	327	3	an	an	DET
ejpam-2366	327	4	φ(n	φ(n	NOUN
ejpam-2366	327	5	)	)	PUNCT
ejpam-2366	327	6	.	.	PUNCT
ejpam-2366	328	1	then	then	ADV
ejpam-2366	328	2	an0	an0	PROPN
ejpam-2366	328	3	φ(n	φ(n	PROPN
ejpam-2366	328	4	)	)	PUNCT
ejpam-2366	328	5	for	for	ADP
ejpam-2366	328	6	some	some	DET
ejpam-2366	328	7	n0	n0	NUM
ejpam-2366	328	8	6	6	NUM
ejpam-2366	328	9	n	n	NOUN
ejpam-2366	328	10	in	in	ADP
ejpam-2366	328	11	m	m	PROPN
ejpam-2366	328	12	.	.	PUNCT
ejpam-2366	329	1	since	since	SCONJ
ejpam-2366	329	2	n	n	PROPN
ejpam-2366	329	3	is	be	AUX
ejpam-2366	329	4	φ	φ	VERB
ejpam-2366	329	5	-	-	ADJ
ejpam-2366	329	6	prime	prime	ADJ
ejpam-2366	329	7	,	,	PUNCT
ejpam-2366	329	8	a(a∨n0	a(a∨n0	NOUN
ejpam-2366	329	9	)	)	PUNCT
ejpam-2366	329	10	=	=	PUNCT
ejpam-2366	329	11	aa∨an0	aa∨an0	PROPN
ejpam-2366	329	12	6	6	NUM
ejpam-2366	329	13	n	n	CCONJ
ejpam-2366	329	14	and	and	CCONJ
ejpam-2366	329	15	a(a	a(a	PROPN
ejpam-2366	329	16	∨	∨	PROPN
ejpam-2366	329	17	n0	n0	NUM
ejpam-2366	329	18	)	)	PUNCT
ejpam-2366	329	19	φ(n	φ(n	NOUN
ejpam-2366	329	20	)	)	PUNCT
ejpam-2366	329	21	,	,	PUNCT
ejpam-2366	329	22	we	we	PRON
ejpam-2366	329	23	have	have	VERB
ejpam-2366	329	24	either	either	CCONJ
ejpam-2366	329	25	a	a	DET
ejpam-2366	329	26	6	6	NUM
ejpam-2366	329	27	(	(	PUNCT
ejpam-2366	329	28	n	n	NUM
ejpam-2366	329	29	:	:	PUNCT
ejpam-2366	329	30	i	i	PRON
ejpam-2366	329	31	m	m	VERB
ejpam-2366	329	32	)	)	PUNCT
ejpam-2366	329	33	or	or	CCONJ
ejpam-2366	329	34	(	(	PUNCT
ejpam-2366	329	35	a	a	DET
ejpam-2366	329	36	∨	∨	NUM
ejpam-2366	329	37	n0	n0	NUM
ejpam-2366	329	38	)	)	PUNCT
ejpam-2366	329	39	6	6	NUM
ejpam-2366	329	40	n	n	NOUN
ejpam-2366	329	41	and	and	CCONJ
ejpam-2366	329	42	hence	hence	ADV
ejpam-2366	329	43	either	either	CCONJ
ejpam-2366	329	44	a	a	DET
ejpam-2366	329	45	6	6	NUM
ejpam-2366	329	46	(	(	PUNCT
ejpam-2366	329	47	n	n	NUM
ejpam-2366	329	48	:	:	PUNCT
ejpam-2366	329	49	i	i	PRON
ejpam-2366	329	50	m	m	VERB
ejpam-2366	329	51	)	)	PUNCT
ejpam-2366	329	52	or	or	CCONJ
ejpam-2366	329	53	a	a	DET
ejpam-2366	329	54	6	6	NUM
ejpam-2366	329	55	n	n	NOUN
ejpam-2366	329	56	.	.	PUNCT
ejpam-2366	330	1	next	next	ADV
ejpam-2366	330	2	,	,	PUNCT
ejpam-2366	330	3	assume	assume	VERB
ejpam-2366	330	4	that	that	SCONJ
ejpam-2366	330	5	an	an	DET
ejpam-2366	330	6	6	6	NUM
ejpam-2366	330	7	φ(n	φ(n	NOUN
ejpam-2366	330	8	)	)	PUNCT
ejpam-2366	330	9	.	.	PUNCT
ejpam-2366	331	1	if	if	SCONJ
ejpam-2366	331	2	(	(	PUNCT
ejpam-2366	331	3	n	n	X
ejpam-2366	331	4	:	:	PUNCT
ejpam-2366	331	5	i	i	PRON
ejpam-2366	331	6	m	m	VERB
ejpam-2366	331	7	)	)	PUNCT
ejpam-2366	331	8	a	a	DET
ejpam-2366	331	9	φ(n	φ(n	NOUN
ejpam-2366	331	10	)	)	PUNCT
ejpam-2366	331	11	,	,	PUNCT
ejpam-2366	331	12	then	then	ADV
ejpam-2366	331	13	k0a	k0a	ADJ
ejpam-2366	331	14	φ(n	φ(n	NOUN
ejpam-2366	331	15	)	)	PUNCT
ejpam-2366	331	16	for	for	ADP
ejpam-2366	331	17	some	some	DET
ejpam-2366	331	18	k0	k0	PROPN
ejpam-2366	331	19	6	6	NUM
ejpam-2366	331	20	(	(	PUNCT
ejpam-2366	331	21	n	n	NUM
ejpam-2366	331	22	:	:	PUNCT
ejpam-2366	331	23	i	i	PRON
ejpam-2366	331	24	m	m	VERB
ejpam-2366	331	25	)	)	PUNCT
ejpam-2366	331	26	in	in	ADP
ejpam-2366	331	27	l.	l.	PROPN
ejpam-2366	331	28	since	since	SCONJ
ejpam-2366	331	29	n	n	PROPN
ejpam-2366	331	30	is	be	AUX
ejpam-2366	331	31	φ	φ	VERB
ejpam-2366	331	32	-	-	NOUN
ejpam-2366	331	33	prime	prime	NOUN
ejpam-2366	331	34	,	,	PUNCT
ejpam-2366	331	35	(	(	PUNCT
ejpam-2366	331	36	a	a	DET
ejpam-2366	331	37	∨	∨	NUM
ejpam-2366	331	38	k0)a	k0)a	NOUN
ejpam-2366	331	39	6	6	NUM
ejpam-2366	331	40	n	n	NOUN
ejpam-2366	331	41	and	and	CCONJ
ejpam-2366	331	42	(	(	PUNCT
ejpam-2366	331	43	a∨k0)a	a∨k0)a	PROPN
ejpam-2366	331	44	φ(n	φ(n	ADJ
ejpam-2366	331	45	)	)	PUNCT
ejpam-2366	331	46	,	,	PUNCT
ejpam-2366	331	47	we	we	PRON
ejpam-2366	331	48	have	have	VERB
ejpam-2366	331	49	either	either	CCONJ
ejpam-2366	331	50	(	(	PUNCT
ejpam-2366	331	51	a∨k0	a∨k0	NUM
ejpam-2366	331	52	)	)	PUNCT
ejpam-2366	331	53	6	6	NUM
ejpam-2366	331	54	(	(	PUNCT
ejpam-2366	331	55	n	n	NUM
ejpam-2366	331	56	:	:	PUNCT
ejpam-2366	331	57	i	i	PRON
ejpam-2366	331	58	m	m	VERB
ejpam-2366	331	59	)	)	PUNCT
ejpam-2366	331	60	or	or	CCONJ
ejpam-2366	331	61	a	a	DET
ejpam-2366	331	62	6	6	NUM
ejpam-2366	331	63	n	n	NOUN
ejpam-2366	331	64	and	and	CCONJ
ejpam-2366	331	65	hence	hence	ADV
ejpam-2366	331	66	either	either	CCONJ
ejpam-2366	331	67	a	a	DET
ejpam-2366	331	68	6	6	NUM
ejpam-2366	331	69	(	(	PUNCT
ejpam-2366	331	70	n	n	NUM
ejpam-2366	331	71	:	:	PUNCT
ejpam-2366	331	72	i	i	PRON
ejpam-2366	331	73	m	m	VERB
ejpam-2366	331	74	)	)	PUNCT
ejpam-2366	331	75	or	or	CCONJ
ejpam-2366	331	76	a	a	DET
ejpam-2366	331	77	6	6	NUM
ejpam-2366	331	78	n	n	NOUN
ejpam-2366	331	79	.	.	PUNCT
ejpam-2366	332	1	now	now	ADV
ejpam-2366	332	2	let	let	VERB
ejpam-2366	332	3	(	(	PUNCT
ejpam-2366	332	4	n	n	X
ejpam-2366	332	5	:	:	PUNCT
ejpam-2366	332	6	i	i	PRON
ejpam-2366	332	7	m	m	VERB
ejpam-2366	332	8	)	)	PUNCT
ejpam-2366	332	9	a	a	DET
ejpam-2366	332	10	6	6	NUM
ejpam-2366	332	11	φ(n	φ(n	NOUN
ejpam-2366	332	12	)	)	PUNCT
ejpam-2366	332	13	.	.	PUNCT
ejpam-2366	333	1	by	by	ADP
ejpam-2366	333	2	hypothesis	hypothesis	NOUN
ejpam-2366	333	3	,	,	PUNCT
ejpam-2366	333	4	as	as	ADP
ejpam-2366	333	5	(	(	PUNCT
ejpam-2366	333	6	n	n	X
ejpam-2366	333	7	:	:	PUNCT
ejpam-2366	333	8	i	i	PRON
ejpam-2366	333	9	m	m	VERB
ejpam-2366	333	10	)	)	PUNCT
ejpam-2366	333	11	n	n	PRON
ejpam-2366	333	12	φ(n	φ(n	NOUN
ejpam-2366	333	13	)	)	PUNCT
ejpam-2366	333	14	,	,	PUNCT
ejpam-2366	333	15	there	there	PRON
ejpam-2366	333	16	exist	exist	VERB
ejpam-2366	333	17	k	k	PROPN
ejpam-2366	333	18	6	6	NUM
ejpam-2366	333	19	(	(	PUNCT
ejpam-2366	333	20	n	n	NUM
ejpam-2366	333	21	:	:	PUNCT
ejpam-2366	333	22	i	i	PRON
ejpam-2366	333	23	m	m	VERB
ejpam-2366	333	24	)	)	PUNCT
ejpam-2366	333	25	in	in	ADP
ejpam-2366	333	26	l	l	NOUN
ejpam-2366	333	27	and	and	CCONJ
ejpam-2366	333	28	n0	n0	NUM
ejpam-2366	333	29	6	6	NUM
ejpam-2366	333	30	n	n	NOUN
ejpam-2366	333	31	in	in	ADP
ejpam-2366	333	32	m	m	PRON
ejpam-2366	333	33	such	such	ADJ
ejpam-2366	333	34	that	that	DET
ejpam-2366	333	35	kn0	kn0	NOUN
ejpam-2366	333	36	φ(n	φ(n	PROPN
ejpam-2366	333	37	)	)	PUNCT
ejpam-2366	333	38	.	.	PUNCT
ejpam-2366	334	1	since	since	SCONJ
ejpam-2366	334	2	n	n	PROPN
ejpam-2366	334	3	is	be	AUX
ejpam-2366	334	4	φ	φ	VERB
ejpam-2366	334	5	-	-	NOUN
ejpam-2366	334	6	prime	prime	NOUN
ejpam-2366	334	7	,	,	PUNCT
ejpam-2366	334	8	(	(	PUNCT
ejpam-2366	334	9	a	a	DET
ejpam-2366	334	10	∨	∨	NOUN
ejpam-2366	334	11	k)(a	k)(a	PRON
ejpam-2366	334	12	∨n0	∨n0	NOUN
ejpam-2366	334	13	)	)	PUNCT
ejpam-2366	334	14	6	6	NUM
ejpam-2366	334	15	n	n	NOUN
ejpam-2366	334	16	and	and	CCONJ
ejpam-2366	334	17	(	(	PUNCT
ejpam-2366	334	18	a	a	DET
ejpam-2366	334	19	∨	∨	NOUN
ejpam-2366	334	20	k)(a	k)(a	PRON
ejpam-2366	334	21	∨n0	∨n0	NOUN
ejpam-2366	334	22	)	)	PUNCT
ejpam-2366	334	23	φ(n	φ(n	NOUN
ejpam-2366	334	24	)	)	PUNCT
ejpam-2366	334	25	,	,	PUNCT
ejpam-2366	334	26	we	we	PRON
ejpam-2366	334	27	have	have	VERB
ejpam-2366	334	28	either	either	CCONJ
ejpam-2366	334	29	(	(	PUNCT
ejpam-2366	334	30	a	a	DET
ejpam-2366	334	31	∨	∨	NUM
ejpam-2366	334	32	k	k	NOUN
ejpam-2366	334	33	)	)	PUNCT
ejpam-2366	334	34	6	6	NUM
ejpam-2366	334	35	(	(	PUNCT
ejpam-2366	334	36	n	n	NUM
ejpam-2366	334	37	:	:	PUNCT
ejpam-2366	334	38	i	i	PRON
ejpam-2366	334	39	m	m	VERB
ejpam-2366	334	40	)	)	PUNCT
ejpam-2366	334	41	or	or	CCONJ
ejpam-2366	334	42	(	(	PUNCT
ejpam-2366	334	43	a	a	DET
ejpam-2366	334	44	∨n0	∨n0	NOUN
ejpam-2366	334	45	)	)	PUNCT
ejpam-2366	334	46	6	6	NUM
ejpam-2366	334	47	n	n	NOUN
ejpam-2366	334	48	and	and	CCONJ
ejpam-2366	334	49	hence	hence	ADV
ejpam-2366	334	50	either	either	CCONJ
ejpam-2366	334	51	a	a	DET
ejpam-2366	334	52	6	6	NUM
ejpam-2366	334	53	(	(	PUNCT
ejpam-2366	334	54	n	n	NUM
ejpam-2366	334	55	:	:	PUNCT
ejpam-2366	334	56	i	i	PRON
ejpam-2366	334	57	m	m	VERB
ejpam-2366	334	58	)	)	PUNCT
ejpam-2366	334	59	or	or	CCONJ
ejpam-2366	334	60	a	a	DET
ejpam-2366	334	61	6	6	NUM
ejpam-2366	334	62	n	n	NOUN
ejpam-2366	334	63	.	.	PUNCT
ejpam-2366	335	1	therefore	therefore	ADV
ejpam-2366	335	2	n	n	PROPN
ejpam-2366	335	3	is	be	AUX
ejpam-2366	335	4	prime	prime	ADJ
ejpam-2366	335	5	.	.	PUNCT
ejpam-2366	336	1	the	the	DET
ejpam-2366	336	2	consequences	consequence	NOUN
ejpam-2366	336	3	of	of	ADP
ejpam-2366	336	4	theorem	theorem	ADJ
ejpam-2366	336	5	10	10	NUM
ejpam-2366	336	6	are	be	AUX
ejpam-2366	336	7	presented	present	VERB
ejpam-2366	336	8	in	in	ADP
ejpam-2366	336	9	the	the	DET
ejpam-2366	336	10	following	follow	VERB
ejpam-2366	336	11	corollaries	corollary	NOUN
ejpam-2366	336	12	.	.	PUNCT
ejpam-2366	337	1	a.	a.	PROPN
ejpam-2366	337	2	v.	v.	PROPN
ejpam-2366	337	3	bingi	bingi	PROPN
ejpam-2366	337	4	,	,	PUNCT
ejpam-2366	337	5	c.	c.	PROPN
ejpam-2366	337	6	s.	s.	PROPN
ejpam-2366	337	7	manjarekar	manjarekar	PROPN
ejpam-2366	337	8	/	/	PROPN
ejpam-2366	337	9	eur	eur	PROPN
ejpam-2366	337	10	.	.	PUNCT
ejpam-2366	338	1	j.	j.	PROPN
ejpam-2366	338	2	pure	pure	PROPN
ejpam-2366	338	3	appl	appl	PROPN
ejpam-2366	338	4	.	.	PROPN
ejpam-2366	338	5	math	math	PROPN
ejpam-2366	338	6	,	,	PUNCT
ejpam-2366	338	7	14	14	NUM
ejpam-2366	338	8	(	(	PUNCT
ejpam-2366	338	9	2	2	NUM
ejpam-2366	338	10	)	)	PUNCT
ejpam-2366	338	11	(	(	PUNCT
ejpam-2366	338	12	2021	2021	NUM
ejpam-2366	338	13	)	)	PUNCT
ejpam-2366	338	14	,	,	PUNCT
ejpam-2366	338	15	551	551	NUM
ejpam-2366	338	16	-	-	SYM
ejpam-2366	338	17	577	577	NUM
ejpam-2366	338	18	560	560	NUM
ejpam-2366	338	19	corollary	corollary	ADJ
ejpam-2366	338	20	5	5	NUM
ejpam-2366	338	21	.	.	PUNCT
ejpam-2366	339	1	if	if	SCONJ
ejpam-2366	339	2	a	a	DET
ejpam-2366	339	3	proper	proper	ADJ
ejpam-2366	339	4	element	element	NOUN
ejpam-2366	339	5	n	n	NOUN
ejpam-2366	339	6	of	of	ADP
ejpam-2366	339	7	a	a	DET
ejpam-2366	339	8	multiplication	multiplication	NOUN
ejpam-2366	339	9	lattice	lattice	NOUN
ejpam-2366	339	10	l	l	NOUN
ejpam-2366	339	11	-	-	NOUN
ejpam-2366	339	12	module	module	NOUN
ejpam-2366	339	13	m	m	NOUN
ejpam-2366	339	14	is	be	AUX
ejpam-2366	339	15	φ	φ	ADJ
ejpam-2366	339	16	-	-	ADJ
ejpam-2366	339	17	prime	prime	ADJ
ejpam-2366	339	18	but	but	CCONJ
ejpam-2366	339	19	not	not	PART
ejpam-2366	339	20	prime	prime	ADJ
ejpam-2366	339	21	,	,	PUNCT
ejpam-2366	339	22	then	then	ADV
ejpam-2366	339	23	(	(	PUNCT
ejpam-2366	339	24	n	n	X
ejpam-2366	339	25	:	:	PUNCT
ejpam-2366	339	26	i	i	PRON
ejpam-2366	339	27	m	m	NOUN
ejpam-2366	339	28	)	)	PUNCT
ejpam-2366	339	29	2im	2im	NOUN
ejpam-2366	339	30	6	6	NUM
ejpam-2366	339	31	φ(n	φ(n	NOUN
ejpam-2366	339	32	)	)	PUNCT
ejpam-2366	339	33	.	.	PUNCT
ejpam-2366	340	1	proof	proof	NOUN
ejpam-2366	340	2	.	.	PUNCT
ejpam-2366	341	1	since	since	SCONJ
ejpam-2366	341	2	m	m	PROPN
ejpam-2366	341	3	is	be	AUX
ejpam-2366	341	4	a	a	DET
ejpam-2366	341	5	multiplication	multiplication	NOUN
ejpam-2366	341	6	lattice	lattice	NOUN
ejpam-2366	341	7	l	l	NOUN
ejpam-2366	341	8	-	-	NOUN
ejpam-2366	341	9	module	module	NOUN
ejpam-2366	341	10	,	,	PUNCT
ejpam-2366	341	11	by	by	ADP
ejpam-2366	341	12	proposition	proposition	NOUN
ejpam-2366	341	13	3	3	NUM
ejpam-2366	341	14	of	of	ADP
ejpam-2366	341	15	[	[	X
ejpam-2366	341	16	10	10	NUM
ejpam-2366	341	17	]	]	PUNCT
ejpam-2366	341	18	,	,	PUNCT
ejpam-2366	341	19	we	we	PRON
ejpam-2366	341	20	have	have	VERB
ejpam-2366	341	21	n	n	NOUN
ejpam-2366	341	22	=	=	SYM
ejpam-2366	341	23	(	(	PUNCT
ejpam-2366	341	24	n	n	X
ejpam-2366	341	25	:	:	PUNCT
ejpam-2366	341	26	i	i	PRON
ejpam-2366	341	27	m	m	VERB
ejpam-2366	341	28	)	)	PUNCT
ejpam-2366	341	29	i	i	PRON
ejpam-2366	341	30	m	m	VERB
ejpam-2366	341	31	.	.	PUNCT
ejpam-2366	342	1	so	so	ADV
ejpam-2366	342	2	(	(	PUNCT
ejpam-2366	342	3	n	n	X
ejpam-2366	342	4	:	:	PUNCT
ejpam-2366	342	5	i	i	PRON
ejpam-2366	342	6	m	m	NOUN
ejpam-2366	342	7	)	)	PUNCT
ejpam-2366	342	8	2im	2im	NOUN
ejpam-2366	342	9	=	=	SYM
ejpam-2366	342	10	(	(	PUNCT
ejpam-2366	342	11	n	n	X
ejpam-2366	342	12	:	:	PUNCT
ejpam-2366	342	13	i	i	PRON
ejpam-2366	342	14	m	m	VERB
ejpam-2366	342	15	)	)	PUNCT
ejpam-2366	342	16	n	n	CCONJ
ejpam-2366	342	17	6	6	NUM
ejpam-2366	342	18	φ(n	φ(n	ADJ
ejpam-2366	342	19	)	)	PUNCT
ejpam-2366	342	20	by	by	ADP
ejpam-2366	342	21	theorem	theorem	ADJ
ejpam-2366	342	22	10	10	NUM
ejpam-2366	342	23	.	.	PUNCT
ejpam-2366	343	1	corollary	corollary	ADJ
ejpam-2366	343	2	6	6	NUM
ejpam-2366	343	3	.	.	PUNCT
ejpam-2366	344	1	if	if	SCONJ
ejpam-2366	344	2	a	a	DET
ejpam-2366	344	3	proper	proper	ADJ
ejpam-2366	344	4	element	element	NOUN
ejpam-2366	344	5	n	n	PROPN
ejpam-2366	344	6	of	of	ADP
ejpam-2366	344	7	an	an	DET
ejpam-2366	344	8	l	l	NOUN
ejpam-2366	344	9	-	-	NOUN
ejpam-2366	344	10	module	module	NOUN
ejpam-2366	344	11	m	m	NOUN
ejpam-2366	344	12	is	be	AUX
ejpam-2366	344	13	weakly	weakly	ADJ
ejpam-2366	344	14	prime	prime	ADJ
ejpam-2366	344	15	such	such	ADJ
ejpam-2366	344	16	that	that	PRON
ejpam-2366	344	17	(	(	PUNCT
ejpam-2366	344	18	n	n	X
ejpam-2366	344	19	:	:	PUNCT
ejpam-2366	344	20	i	i	PRON
ejpam-2366	344	21	m	m	PROPN
ejpam-2366	344	22	)	)	PUNCT
ejpam-2366	344	23	n	n	PROPN
ejpam-2366	344	24	6=	6=	ADP
ejpam-2366	344	25	om	om	PROPN
ejpam-2366	344	26	,	,	PUNCT
ejpam-2366	344	27	then	then	ADV
ejpam-2366	344	28	n	n	PRON
ejpam-2366	344	29	is	be	AUX
ejpam-2366	344	30	prime	prime	ADJ
ejpam-2366	344	31	.	.	PUNCT
ejpam-2366	345	1	proof	proof	NOUN
ejpam-2366	345	2	.	.	PUNCT
ejpam-2366	346	1	the	the	DET
ejpam-2366	346	2	proof	proof	NOUN
ejpam-2366	346	3	is	be	AUX
ejpam-2366	346	4	obvious	obvious	ADJ
ejpam-2366	346	5	.	.	PUNCT
ejpam-2366	347	1	corollary	corollary	ADJ
ejpam-2366	347	2	7	7	NUM
ejpam-2366	347	3	.	.	PUNCT
ejpam-2366	348	1	if	if	SCONJ
ejpam-2366	348	2	a	a	DET
ejpam-2366	348	3	proper	proper	ADJ
ejpam-2366	348	4	element	element	NOUN
ejpam-2366	348	5	n	n	PROPN
ejpam-2366	348	6	of	of	ADP
ejpam-2366	348	7	an	an	DET
ejpam-2366	348	8	l	l	NOUN
ejpam-2366	348	9	-	-	NOUN
ejpam-2366	348	10	module	module	NOUN
ejpam-2366	348	11	m	m	NOUN
ejpam-2366	348	12	is	be	AUX
ejpam-2366	348	13	φ	φ	NOUN
ejpam-2366	348	14	-	-	ADJ
ejpam-2366	348	15	prime	prime	NOUN
ejpam-2366	348	16	such	such	ADJ
ejpam-2366	348	17	that	that	SCONJ
ejpam-2366	348	18	φ	φ	PROPN
ejpam-2366	348	19	6	6	NUM
ejpam-2366	348	20	φ3	φ3	NOUN
ejpam-2366	348	21	,	,	PUNCT
ejpam-2366	348	22	then	then	ADV
ejpam-2366	348	23	n	n	PROPN
ejpam-2366	348	24	is	be	AUX
ejpam-2366	348	25	ω	ω	NOUN
ejpam-2366	348	26	-	-	NOUN
ejpam-2366	348	27	prime	prime	NOUN
ejpam-2366	348	28	.	.	PUNCT
ejpam-2366	349	1	proof	proof	NOUN
ejpam-2366	349	2	.	.	PUNCT
ejpam-2366	350	1	if	if	SCONJ
ejpam-2366	350	2	n	n	NOUN
ejpam-2366	350	3	is	be	AUX
ejpam-2366	350	4	prime	prime	ADJ
ejpam-2366	350	5	,	,	PUNCT
ejpam-2366	350	6	then	then	ADV
ejpam-2366	350	7	by	by	ADP
ejpam-2366	350	8	theorem	theorem	NOUN
ejpam-2366	350	9	3	3	NUM
ejpam-2366	350	10	,	,	PUNCT
ejpam-2366	350	11	n	n	X
ejpam-2366	350	12	is	be	AUX
ejpam-2366	350	13	ω	ω	NOUN
ejpam-2366	350	14	-	-	NOUN
ejpam-2366	350	15	prime	prime	NOUN
ejpam-2366	350	16	.	.	PUNCT
ejpam-2366	351	1	so	so	ADV
ejpam-2366	351	2	assume	assume	VERB
ejpam-2366	351	3	that	that	SCONJ
ejpam-2366	351	4	n	n	PRON
ejpam-2366	351	5	is	be	AUX
ejpam-2366	351	6	not	not	PART
ejpam-2366	351	7	prime	prime	ADJ
ejpam-2366	351	8	.	.	PUNCT
ejpam-2366	352	1	then	then	ADV
ejpam-2366	352	2	by	by	ADP
ejpam-2366	352	3	theorem	theorem	ADJ
ejpam-2366	352	4	10	10	NUM
ejpam-2366	352	5	and	and	CCONJ
ejpam-2366	352	6	hypothesis	hypothesis	NOUN
ejpam-2366	352	7	,	,	PUNCT
ejpam-2366	352	8	we	we	PRON
ejpam-2366	352	9	get	get	VERB
ejpam-2366	352	10	(	(	PUNCT
ejpam-2366	352	11	n	n	X
ejpam-2366	352	12	:	:	PUNCT
ejpam-2366	352	13	i	i	PRON
ejpam-2366	352	14	m	m	VERB
ejpam-2366	352	15	)	)	PUNCT
ejpam-2366	352	16	2n	2n	NUM
ejpam-2366	352	17	6	6	NUM
ejpam-2366	352	18	(	(	PUNCT
ejpam-2366	352	19	n	n	NUM
ejpam-2366	352	20	:	:	PUNCT
ejpam-2366	352	21	i	i	PRON
ejpam-2366	352	22	m	m	VERB
ejpam-2366	352	23	)	)	PUNCT
ejpam-2366	352	24	n	n	CCONJ
ejpam-2366	352	25	6	6	NUM
ejpam-2366	352	26	φ(n	φ(n	ADJ
ejpam-2366	352	27	)	)	PUNCT
ejpam-2366	352	28	6	6	NUM
ejpam-2366	352	29	(	(	PUNCT
ejpam-2366	352	30	n	n	NUM
ejpam-2366	352	31	:	:	PUNCT
ejpam-2366	352	32	i	i	PRON
ejpam-2366	352	33	m	m	VERB
ejpam-2366	352	34	)	)	PUNCT
ejpam-2366	352	35	2n	2n	NUM
ejpam-2366	352	36	and	and	CCONJ
ejpam-2366	352	37	so	so	ADV
ejpam-2366	352	38	φ(n	φ(n	ADJ
ejpam-2366	352	39	)	)	PUNCT
ejpam-2366	352	40	=	=	PUNCT
ejpam-2366	352	41	(	(	PUNCT
ejpam-2366	352	42	n	n	X
ejpam-2366	352	43	:	:	PUNCT
ejpam-2366	352	44	i	i	PRON
ejpam-2366	352	45	m	m	VERB
ejpam-2366	352	46	)	)	PUNCT
ejpam-2366	352	47	2n	2n	NUM
ejpam-2366	353	1	=	=	SYM
ejpam-2366	353	2	(	(	PUNCT
ejpam-2366	353	3	n	n	X
ejpam-2366	353	4	:	:	PUNCT
ejpam-2366	353	5	i	i	PRON
ejpam-2366	353	6	m	m	PROPN
ejpam-2366	353	7	)	)	PUNCT
ejpam-2366	353	8	n	n	X
ejpam-2366	353	9	.	.	PUNCT
ejpam-2366	354	1	now	now	ADV
ejpam-2366	354	2	consider	consider	VERB
ejpam-2366	354	3	(	(	PUNCT
ejpam-2366	354	4	n	n	NUM
ejpam-2366	354	5	:	:	PUNCT
ejpam-2366	354	6	i	i	PRON
ejpam-2366	354	7	m	m	VERB
ejpam-2366	354	8	)	)	PUNCT
ejpam-2366	354	9	3n	3n	NOUN
ejpam-2366	354	10	=	=	SYM
ejpam-2366	354	11	(	(	PUNCT
ejpam-2366	354	12	(	(	PUNCT
ejpam-2366	354	13	n	n	X
ejpam-2366	354	14	:	:	PUNCT
ejpam-2366	354	15	i	i	PRON
ejpam-2366	354	16	m	m	VERB
ejpam-2366	354	17	)	)	PUNCT
ejpam-2366	354	18	(	(	PUNCT
ejpam-2366	354	19	n	n	X
ejpam-2366	354	20	:	:	PUNCT
ejpam-2366	354	21	i	i	PRON
ejpam-2366	354	22	m	m	VERB
ejpam-2366	354	23	)	)	PUNCT
ejpam-2366	354	24	2)n	2)n	NUM
ejpam-2366	354	25	=	=	SYM
ejpam-2366	354	26	(	(	PUNCT
ejpam-2366	354	27	n	n	X
ejpam-2366	354	28	:	:	PUNCT
ejpam-2366	354	29	i	i	PRON
ejpam-2366	354	30	m	m	VERB
ejpam-2366	354	31	)	)	PUNCT
ejpam-2366	354	32	(	(	PUNCT
ejpam-2366	354	33	(	(	PUNCT
ejpam-2366	354	34	n	n	X
ejpam-2366	354	35	:	:	PUNCT
ejpam-2366	354	36	i	i	PRON
ejpam-2366	354	37	m	m	VERB
ejpam-2366	354	38	)	)	PUNCT
ejpam-2366	354	39	2n	2n	NUM
ejpam-2366	354	40	)	)	PUNCT
ejpam-2366	355	1	=	=	PUNCT
ejpam-2366	355	2	(	(	PUNCT
ejpam-2366	355	3	n	n	X
ejpam-2366	355	4	:	:	PUNCT
ejpam-2366	355	5	i	i	PRON
ejpam-2366	355	6	m	m	VERB
ejpam-2366	355	7	)	)	PUNCT
ejpam-2366	355	8	(	(	PUNCT
ejpam-2366	355	9	(	(	PUNCT
ejpam-2366	355	10	n	n	X
ejpam-2366	355	11	:	:	PUNCT
ejpam-2366	355	12	i	i	PRON
ejpam-2366	355	13	m	m	PROPN
ejpam-2366	355	14	)	)	PUNCT
ejpam-2366	355	15	n	n	CCONJ
ejpam-2366	355	16	)	)	PUNCT
ejpam-2366	355	17	=	=	SYM
ejpam-2366	355	18	(	(	PUNCT
ejpam-2366	355	19	(	(	PUNCT
ejpam-2366	355	20	n	n	X
ejpam-2366	355	21	:	:	PUNCT
ejpam-2366	355	22	i	i	PRON
ejpam-2366	355	23	m	m	VERB
ejpam-2366	355	24	)	)	PUNCT
ejpam-2366	355	25	(	(	PUNCT
ejpam-2366	355	26	n	n	X
ejpam-2366	355	27	:	:	PUNCT
ejpam-2366	355	28	i	i	PRON
ejpam-2366	355	29	m	m	PROPN
ejpam-2366	355	30	)	)	PUNCT
ejpam-2366	355	31	)	)	PUNCT
ejpam-2366	356	1	n	n	NOUN
ejpam-2366	356	2	=	=	SYM
ejpam-2366	356	3	(	(	PUNCT
ejpam-2366	356	4	n	n	X
ejpam-2366	356	5	:	:	PUNCT
ejpam-2366	356	6	i	i	PRON
ejpam-2366	356	7	m	m	VERB
ejpam-2366	356	8	)	)	PUNCT
ejpam-2366	356	9	2n	2n	NUM
ejpam-2366	356	10	=	=	PUNCT
ejpam-2366	356	11	φ(n	φ(n	NOUN
ejpam-2366	356	12	)	)	PUNCT
ejpam-2366	356	13	and	and	CCONJ
ejpam-2366	356	14	so	so	ADV
ejpam-2366	356	15	on	on	ADV
ejpam-2366	356	16	.	.	PUNCT
ejpam-2366	357	1	hence	hence	ADV
ejpam-2366	357	2	φ(n	φ(n	ADJ
ejpam-2366	357	3	)	)	PUNCT
ejpam-2366	357	4	=	=	PUNCT
ejpam-2366	357	5	(	(	PUNCT
ejpam-2366	357	6	n	n	X
ejpam-2366	357	7	:	:	PUNCT
ejpam-2366	357	8	i	i	PRON
ejpam-2366	357	9	m	m	PROPN
ejpam-2366	357	10	)	)	PUNCT
ejpam-2366	357	11	n−1n	n−1n	PROPN
ejpam-2366	357	12	for	for	ADP
ejpam-2366	357	13	every	every	DET
ejpam-2366	357	14	n	n	NOUN
ejpam-2366	357	15	>	>	X
ejpam-2366	357	16	2	2	NUM
ejpam-2366	357	17	.	.	PUNCT
ejpam-2366	357	18	consequently	consequently	ADV
ejpam-2366	357	19	,	,	PUNCT
ejpam-2366	357	20	n	n	PROPN
ejpam-2366	357	21	is	be	AUX
ejpam-2366	357	22	n	n	ADV
ejpam-2366	357	23	-	-	PUNCT
ejpam-2366	357	24	almost	almost	ADV
ejpam-2366	357	25	prime	prime	NOUN
ejpam-2366	357	26	for	for	ADP
ejpam-2366	357	27	every	every	DET
ejpam-2366	357	28	n	n	NOUN
ejpam-2366	357	29	>	>	SYM
ejpam-2366	357	30	2	2	NUM
ejpam-2366	357	31	and	and	CCONJ
ejpam-2366	357	32	thus	thus	ADV
ejpam-2366	357	33	n	n	PRON
ejpam-2366	357	34	is	be	AUX
ejpam-2366	357	35	ω	ω	NOUN
ejpam-2366	357	36	-	-	NOUN
ejpam-2366	357	37	prime	prime	NOUN
ejpam-2366	357	38	by	by	ADP
ejpam-2366	357	39	corollary	corollary	ADJ
ejpam-2366	357	40	3	3	NUM
ejpam-2366	357	41	.	.	PUNCT
ejpam-2366	357	42	corollary	corollary	ADJ
ejpam-2366	357	43	8	8	NUM
ejpam-2366	357	44	.	.	PUNCT
ejpam-2366	358	1	if	if	SCONJ
ejpam-2366	358	2	a	a	DET
ejpam-2366	358	3	proper	proper	ADJ
ejpam-2366	358	4	element	element	NOUN
ejpam-2366	358	5	n	n	NOUN
ejpam-2366	358	6	of	of	ADP
ejpam-2366	358	7	a	a	DET
ejpam-2366	358	8	multiplication	multiplication	NOUN
ejpam-2366	358	9	lattice	lattice	NOUN
ejpam-2366	358	10	l	l	NOUN
ejpam-2366	358	11	-	-	NOUN
ejpam-2366	358	12	module	module	NOUN
ejpam-2366	358	13	m	m	NOUN
ejpam-2366	358	14	is	be	AUX
ejpam-2366	358	15	φ	φ	ADJ
ejpam-2366	358	16	-	-	ADJ
ejpam-2366	358	17	prime	prime	ADJ
ejpam-2366	358	18	but	but	CCONJ
ejpam-2366	358	19	not	not	PART
ejpam-2366	358	20	prime	prime	ADJ
ejpam-2366	358	21	,	,	PUNCT
ejpam-2366	358	22	then	then	ADV
ejpam-2366	358	23	√	√	VERB
ejpam-2366	358	24	n	n	NOUN
ejpam-2366	358	25	:	:	PUNCT
ejpam-2366	358	26	i	i	PRON
ejpam-2366	358	27	m	m	VERB
ejpam-2366	358	28	=	=	ADJ
ejpam-2366	358	29	√	√	ADP
ejpam-2366	358	30	φ(n	φ(n	NOUN
ejpam-2366	358	31	)	)	PUNCT
ejpam-2366	358	32	:	:	PUNCT
ejpam-2366	359	1	i	i	PRON
ejpam-2366	359	2	m	m	VERB
ejpam-2366	359	3	.	.	PUNCT
ejpam-2366	360	1	proof	proof	NOUN
ejpam-2366	360	2	.	.	PUNCT
ejpam-2366	361	1	by	by	ADP
ejpam-2366	361	2	corollary	corollary	ADJ
ejpam-2366	361	3	5	5	NUM
ejpam-2366	361	4	,	,	PUNCT
ejpam-2366	361	5	we	we	PRON
ejpam-2366	361	6	have	have	AUX
ejpam-2366	361	7	(	(	PUNCT
ejpam-2366	361	8	n	n	X
ejpam-2366	361	9	:	:	PUNCT
ejpam-2366	361	10	i	i	PRON
ejpam-2366	361	11	m	m	NOUN
ejpam-2366	361	12	)	)	PUNCT
ejpam-2366	361	13	2im	2im	NOUN
ejpam-2366	361	14	6	6	NUM
ejpam-2366	361	15	φ(n	φ(n	NOUN
ejpam-2366	361	16	)	)	PUNCT
ejpam-2366	361	17	which	which	PRON
ejpam-2366	361	18	implies	imply	VERB
ejpam-2366	361	19	(	(	PUNCT
ejpam-2366	361	20	n	n	X
ejpam-2366	361	21	:	:	PUNCT
ejpam-2366	361	22	i	i	PRON
ejpam-2366	361	23	m	m	VERB
ejpam-2366	361	24	)	)	PUNCT
ejpam-2366	361	25	6√	6√	VERB
ejpam-2366	361	26	φ(n	φ(n	NOUN
ejpam-2366	361	27	)	)	PUNCT
ejpam-2366	361	28	:	:	PUNCT
ejpam-2366	362	1	i	i	PRON
ejpam-2366	362	2	m	m	VERB
ejpam-2366	362	3	.	.	PUNCT
ejpam-2366	363	1	hence	hence	ADV
ejpam-2366	363	2	√	√	PROPN
ejpam-2366	363	3	n	n	NOUN
ejpam-2366	363	4	:	:	PUNCT
ejpam-2366	363	5	i	i	PRON
ejpam-2366	363	6	m	m	VERB
ejpam-2366	363	7	6	6	NUM
ejpam-2366	363	8	√√	√√	ADV
ejpam-2366	363	9	φ(n	φ(n	ADJ
ejpam-2366	363	10	)	)	PUNCT
ejpam-2366	363	11	:	:	PUNCT
ejpam-2366	364	1	i	i	PRON
ejpam-2366	364	2	m	m	VERB
ejpam-2366	364	3	=	=	ADJ
ejpam-2366	364	4	√	√	ADP
ejpam-2366	364	5	φ(n	φ(n	NOUN
ejpam-2366	364	6	)	)	PUNCT
ejpam-2366	364	7	:	:	PUNCT
ejpam-2366	365	1	i	i	PRON
ejpam-2366	365	2	m	m	VERB
ejpam-2366	365	3	,	,	PUNCT
ejpam-2366	365	4	by	by	ADP
ejpam-2366	365	5	property	property	NOUN
ejpam-2366	365	6	(	(	PUNCT
ejpam-2366	365	7	p3	p3	PROPN
ejpam-2366	365	8	)	)	PUNCT
ejpam-2366	365	9	of	of	ADP
ejpam-2366	365	10	radicals	radical	NOUN
ejpam-2366	365	11	in	in	ADP
ejpam-2366	365	12	[	[	X
ejpam-2366	365	13	21	21	NUM
ejpam-2366	365	14	]	]	PUNCT
ejpam-2366	365	15	.	.	PUNCT
ejpam-2366	366	1	also	also	ADV
ejpam-2366	366	2	,	,	PUNCT
ejpam-2366	366	3	as	as	ADP
ejpam-2366	366	4	φ(n	φ(n	NOUN
ejpam-2366	366	5	)	)	PUNCT
ejpam-2366	366	6	6	6	NUM
ejpam-2366	366	7	n	n	NOUN
ejpam-2366	366	8	,	,	PUNCT
ejpam-2366	366	9	we	we	PRON
ejpam-2366	366	10	have	have	VERB
ejpam-2366	366	11	√	√	VERB
ejpam-2366	366	12	φ(n	φ(n	NOUN
ejpam-2366	366	13	)	)	PUNCT
ejpam-2366	366	14	:	:	PUNCT
ejpam-2366	367	1	i	i	PRON
ejpam-2366	367	2	m	m	VERB
ejpam-2366	367	3	6	6	NUM
ejpam-2366	367	4	√	√	NUM
ejpam-2366	367	5	n	n	NOUN
ejpam-2366	367	6	:	:	PUNCT
ejpam-2366	367	7	i	i	PRON
ejpam-2366	367	8	m	m	VERB
ejpam-2366	367	9	and	and	CCONJ
ejpam-2366	367	10	thus	thus	ADV
ejpam-2366	367	11	√	√	NUM
ejpam-2366	367	12	n	n	NOUN
ejpam-2366	367	13	:	:	PUNCT
ejpam-2366	367	14	i	i	PRON
ejpam-2366	367	15	m	m	VERB
ejpam-2366	367	16	=	=	ADJ
ejpam-2366	367	17	√	√	ADP
ejpam-2366	367	18	φ(n	φ(n	NOUN
ejpam-2366	367	19	)	)	PUNCT
ejpam-2366	367	20	:	:	PUNCT
ejpam-2366	368	1	i	i	PRON
ejpam-2366	368	2	m	m	VERB
ejpam-2366	368	3	.	.	PUNCT
ejpam-2366	369	1	corollary	corollary	ADJ
ejpam-2366	369	2	9	9	NUM
ejpam-2366	369	3	.	.	PUNCT
ejpam-2366	370	1	if	if	SCONJ
ejpam-2366	370	2	a	a	DET
ejpam-2366	370	3	proper	proper	ADJ
ejpam-2366	370	4	element	element	NOUN
ejpam-2366	370	5	n	n	NOUN
ejpam-2366	370	6	of	of	ADP
ejpam-2366	370	7	a	a	DET
ejpam-2366	370	8	multiplication	multiplication	NOUN
ejpam-2366	370	9	lattice	lattice	NOUN
ejpam-2366	370	10	l	l	NOUN
ejpam-2366	370	11	-	-	NOUN
ejpam-2366	370	12	module	module	NOUN
ejpam-2366	370	13	m	m	NOUN
ejpam-2366	370	14	is	be	AUX
ejpam-2366	370	15	φ	φ	ADJ
ejpam-2366	370	16	-	-	NOUN
ejpam-2366	370	17	prime	prime	NOUN
ejpam-2366	370	18	,	,	PUNCT
ejpam-2366	370	19	then	then	ADV
ejpam-2366	370	20	either	either	CCONJ
ejpam-2366	370	21	√	√	ADP
ejpam-2366	370	22	φ(n	φ(n	NOUN
ejpam-2366	370	23	)	)	PUNCT
ejpam-2366	370	24	:	:	PUNCT
ejpam-2366	371	1	i	i	PRON
ejpam-2366	371	2	m	m	VERB
ejpam-2366	371	3	6	6	NUM
ejpam-2366	371	4	(	(	PUNCT
ejpam-2366	371	5	n	n	NUM
ejpam-2366	371	6	:	:	PUNCT
ejpam-2366	371	7	i	i	PRON
ejpam-2366	371	8	m	m	VERB
ejpam-2366	371	9	)	)	PUNCT
ejpam-2366	371	10	or	or	CCONJ
ejpam-2366	371	11	(	(	PUNCT
ejpam-2366	371	12	n	n	X
ejpam-2366	371	13	:	:	PUNCT
ejpam-2366	371	14	i	i	PRON
ejpam-2366	371	15	m	m	VERB
ejpam-2366	371	16	)	)	PUNCT
ejpam-2366	371	17	6	6	NUM
ejpam-2366	371	18	√	√	ADP
ejpam-2366	371	19	φ(n	φ(n	NOUN
ejpam-2366	371	20	)	)	PUNCT
ejpam-2366	371	21	:	:	PUNCT
ejpam-2366	371	22	i	i	PRON
ejpam-2366	371	23	m	m	VERB
ejpam-2366	371	24	.	.	PUNCT
ejpam-2366	372	1	proof	proof	NOUN
ejpam-2366	372	2	.	.	PUNCT
ejpam-2366	373	1	the	the	DET
ejpam-2366	373	2	proof	proof	NOUN
ejpam-2366	373	3	is	be	AUX
ejpam-2366	373	4	obvious	obvious	ADJ
ejpam-2366	373	5	.	.	PUNCT
ejpam-2366	374	1	now	now	ADV
ejpam-2366	374	2	we	we	PRON
ejpam-2366	374	3	introduce	introduce	VERB
ejpam-2366	374	4	the	the	DET
ejpam-2366	374	5	notion	notion	NOUN
ejpam-2366	374	6	of	of	ADP
ejpam-2366	374	7	φ	φ	VERB
ejpam-2366	374	8	-	-	ADJ
ejpam-2366	374	9	primary	primary	ADJ
ejpam-2366	374	10	element	element	NOUN
ejpam-2366	374	11	of	of	ADP
ejpam-2366	374	12	an	an	DET
ejpam-2366	374	13	l	l	NOUN
ejpam-2366	374	14	-	-	NOUN
ejpam-2366	374	15	module	module	NOUN
ejpam-2366	374	16	m	m	NOUN
ejpam-2366	374	17	.	.	PUNCT
ejpam-2366	375	1	definition	definition	NOUN
ejpam-2366	375	2	5	5	NUM
ejpam-2366	375	3	.	.	PUNCT
ejpam-2366	376	1	let	let	VERB
ejpam-2366	376	2	φ	φ	NOUN
ejpam-2366	376	3	:	:	PUNCT
ejpam-2366	376	4	m	m	AUX
ejpam-2366	376	5	−→	−→	ADJ
ejpam-2366	376	6	m	m	AUX
ejpam-2366	376	7	be	be	VERB
ejpam-2366	376	8	a	a	DET
ejpam-2366	376	9	function	function	NOUN
ejpam-2366	376	10	on	on	ADP
ejpam-2366	376	11	an	an	DET
ejpam-2366	376	12	l	l	NOUN
ejpam-2366	376	13	-	-	NOUN
ejpam-2366	376	14	module	module	NOUN
ejpam-2366	376	15	m	m	NOUN
ejpam-2366	376	16	.	.	PUNCT
ejpam-2366	377	1	a	a	DET
ejpam-2366	377	2	proper	proper	ADJ
ejpam-2366	377	3	element	element	NOUN
ejpam-2366	377	4	n	n	PRON
ejpam-2366	377	5	∈m	∈m	NOUN
ejpam-2366	377	6	is	be	AUX
ejpam-2366	377	7	said	say	VERB
ejpam-2366	377	8	to	to	PART
ejpam-2366	377	9	be	be	AUX
ejpam-2366	377	10	φ	φ	VERB
ejpam-2366	377	11	-	-	ADJ
ejpam-2366	377	12	primary	primary	ADJ
ejpam-2366	377	13	if	if	SCONJ
ejpam-2366	377	14	for	for	ADP
ejpam-2366	377	15	all	all	DET
ejpam-2366	377	16	a	a	DET
ejpam-2366	377	17	∈	∈	PROPN
ejpam-2366	377	18	l	l	NOUN
ejpam-2366	377	19	,	,	PUNCT
ejpam-2366	377	20	a	a	DET
ejpam-2366	377	21	∈m	∈m	NOUN
ejpam-2366	377	22	,	,	PUNCT
ejpam-2366	377	23	aa	aa	NOUN
ejpam-2366	377	24	6	6	NUM
ejpam-2366	377	25	n	n	NOUN
ejpam-2366	377	26	and	and	CCONJ
ejpam-2366	377	27	aa	aa	PROPN
ejpam-2366	377	28	φ(n	φ(n	PROPN
ejpam-2366	377	29	)	)	PUNCT
ejpam-2366	377	30	implies	imply	VERB
ejpam-2366	377	31	either	either	CCONJ
ejpam-2366	377	32	a	a	DET
ejpam-2366	377	33	6	6	NUM
ejpam-2366	377	34	n	n	NOUN
ejpam-2366	377	35	or	or	CCONJ
ejpam-2366	377	36	an	an	DET
ejpam-2366	377	37	6	6	NUM
ejpam-2366	377	38	(	(	PUNCT
ejpam-2366	377	39	n	n	NUM
ejpam-2366	377	40	:	:	PUNCT
ejpam-2366	377	41	i	i	PRON
ejpam-2366	377	42	m	m	VERB
ejpam-2366	377	43	)	)	PUNCT
ejpam-2366	377	44	for	for	ADP
ejpam-2366	377	45	some	some	DET
ejpam-2366	377	46	n	n	PRON
ejpam-2366	377	47	∈	∈	NOUN
ejpam-2366	377	48	z+	z+	PUNCT
ejpam-2366	377	49	.	.	PUNCT
ejpam-2366	378	1	now	now	ADV
ejpam-2366	378	2	if	if	SCONJ
ejpam-2366	378	3	φα	φα	X
ejpam-2366	378	4	:	:	PUNCT
ejpam-2366	378	5	m	m	AUX
ejpam-2366	378	6	−→	−→	ADJ
ejpam-2366	378	7	m	m	VERB
ejpam-2366	378	8	is	be	AUX
ejpam-2366	378	9	a	a	DET
ejpam-2366	378	10	function	function	NOUN
ejpam-2366	378	11	on	on	ADP
ejpam-2366	378	12	an	an	DET
ejpam-2366	378	13	l	l	NOUN
ejpam-2366	378	14	-	-	NOUN
ejpam-2366	378	15	module	module	NOUN
ejpam-2366	378	16	m	m	NOUN
ejpam-2366	378	17	,	,	PUNCT
ejpam-2366	378	18	then	then	ADV
ejpam-2366	378	19	φα	φα	NOUN
ejpam-2366	378	20	-	-	PUNCT
ejpam-2366	378	21	primary	primary	ADJ
ejpam-2366	378	22	elements	element	NOUN
ejpam-2366	378	23	of	of	ADP
ejpam-2366	378	24	m	m	NOUN
ejpam-2366	378	25	are	be	AUX
ejpam-2366	378	26	defined	define	VERB
ejpam-2366	378	27	by	by	ADP
ejpam-2366	378	28	following	follow	VERB
ejpam-2366	378	29	settings	setting	NOUN
ejpam-2366	378	30	in	in	ADP
ejpam-2366	378	31	the	the	DET
ejpam-2366	378	32	definition	definition	NOUN
ejpam-2366	378	33	5	5	NUM
ejpam-2366	378	34	of	of	ADP
ejpam-2366	378	35	a	a	DET
ejpam-2366	378	36	φ	φ	ADJ
ejpam-2366	378	37	-	-	ADJ
ejpam-2366	378	38	primary	primary	ADJ
ejpam-2366	378	39	element	element	NOUN
ejpam-2366	378	40	.	.	PUNCT
ejpam-2366	379	1	•	•	NUM
ejpam-2366	380	1	φ0(n	φ0(n	PROPN
ejpam-2366	380	2	)	)	PUNCT
ejpam-2366	380	3	=	=	SYM
ejpam-2366	380	4	om	om	PROPN
ejpam-2366	380	5	.	.	PUNCT
ejpam-2366	381	1	then	then	ADV
ejpam-2366	381	2	n	n	DET
ejpam-2366	381	3	∈m	∈m	NOUN
ejpam-2366	381	4	is	be	AUX
ejpam-2366	381	5	called	call	VERB
ejpam-2366	381	6	a	a	DET
ejpam-2366	381	7	weakly	weakly	ADJ
ejpam-2366	381	8	primary	primary	ADJ
ejpam-2366	381	9	element	element	NOUN
ejpam-2366	381	10	.	.	PUNCT
ejpam-2366	382	1	•	•	NUM
ejpam-2366	382	2	φ2(n	φ2(n	X
ejpam-2366	382	3	)	)	PUNCT
ejpam-2366	382	4	=	=	SYM
ejpam-2366	382	5	(	(	PUNCT
ejpam-2366	382	6	n	n	X
ejpam-2366	382	7	:	:	PUNCT
ejpam-2366	382	8	i	i	PRON
ejpam-2366	382	9	m	m	PROPN
ejpam-2366	382	10	)	)	PUNCT
ejpam-2366	383	1	n	n	PROPN
ejpam-2366	383	2	.	.	PUNCT
ejpam-2366	384	1	then	then	ADV
ejpam-2366	384	2	n	n	X
ejpam-2366	384	3	∈	∈	NOUN
ejpam-2366	384	4	m	m	VERB
ejpam-2366	384	5	is	be	AUX
ejpam-2366	384	6	called	call	VERB
ejpam-2366	384	7	a	a	DET
ejpam-2366	384	8	2	2	NUM
ejpam-2366	384	9	-	-	PUNCT
ejpam-2366	384	10	almost	almost	ADV
ejpam-2366	384	11	primary	primary	ADJ
ejpam-2366	384	12	element	element	NOUN
ejpam-2366	384	13	or	or	CCONJ
ejpam-2366	384	14	a	a	DET
ejpam-2366	384	15	φ2	φ2	NOUN
ejpam-2366	384	16	-	-	PUNCT
ejpam-2366	384	17	primary	primary	ADJ
ejpam-2366	384	18	element	element	NOUN
ejpam-2366	384	19	or	or	CCONJ
ejpam-2366	384	20	simply	simply	ADV
ejpam-2366	384	21	an	an	DET
ejpam-2366	384	22	almost	almost	ADV
ejpam-2366	384	23	primary	primary	ADJ
ejpam-2366	384	24	element	element	NOUN
ejpam-2366	384	25	.	.	PUNCT
ejpam-2366	385	1	a.	a.	PROPN
ejpam-2366	385	2	v.	v.	PROPN
ejpam-2366	385	3	bingi	bingi	PROPN
ejpam-2366	385	4	,	,	PUNCT
ejpam-2366	385	5	c.	c.	PROPN
ejpam-2366	385	6	s.	s.	PROPN
ejpam-2366	385	7	manjarekar	manjarekar	PROPN
ejpam-2366	385	8	/	/	PROPN
ejpam-2366	385	9	eur	eur	PROPN
ejpam-2366	385	10	.	.	PUNCT
ejpam-2366	386	1	j.	j.	PROPN
ejpam-2366	386	2	pure	pure	PROPN
ejpam-2366	386	3	appl	appl	PROPN
ejpam-2366	386	4	.	.	PROPN
ejpam-2366	386	5	math	math	PROPN
ejpam-2366	386	6	,	,	PUNCT
ejpam-2366	386	7	14	14	NUM
ejpam-2366	386	8	(	(	PUNCT
ejpam-2366	386	9	2	2	NUM
ejpam-2366	386	10	)	)	PUNCT
ejpam-2366	386	11	(	(	PUNCT
ejpam-2366	386	12	2021	2021	NUM
ejpam-2366	386	13	)	)	PUNCT
ejpam-2366	386	14	,	,	PUNCT
ejpam-2366	386	15	551	551	NUM
ejpam-2366	386	16	-	-	SYM
ejpam-2366	386	17	577	577	NUM
ejpam-2366	386	18	561	561	NUM
ejpam-2366	386	19	•	•	NOUN
ejpam-2366	386	20	φn(n	φn(n	NUM
ejpam-2366	386	21	)	)	PUNCT
ejpam-2366	386	22	=	=	PUNCT
ejpam-2366	386	23	(	(	PUNCT
ejpam-2366	386	24	n	n	X
ejpam-2366	386	25	:	:	PUNCT
ejpam-2366	386	26	i	i	PRON
ejpam-2366	386	27	m	m	PROPN
ejpam-2366	386	28	)	)	PUNCT
ejpam-2366	386	29	n−1n	n−1n	NOUN
ejpam-2366	386	30	(	(	PUNCT
ejpam-2366	386	31	n	n	CCONJ
ejpam-2366	386	32	>	>	X
ejpam-2366	386	33	2	2	NUM
ejpam-2366	386	34	)	)	PUNCT
ejpam-2366	386	35	.	.	PUNCT
ejpam-2366	387	1	then	then	ADV
ejpam-2366	387	2	n	n	X
ejpam-2366	387	3	∈	∈	NOUN
ejpam-2366	387	4	m	m	VERB
ejpam-2366	387	5	is	be	AUX
ejpam-2366	387	6	called	call	VERB
ejpam-2366	387	7	an	an	DET
ejpam-2366	387	8	n	n	ADV
ejpam-2366	387	9	-	-	PUNCT
ejpam-2366	387	10	almost	almost	ADV
ejpam-2366	387	11	primary	primary	ADJ
ejpam-2366	387	12	element	element	NOUN
ejpam-2366	387	13	or	or	CCONJ
ejpam-2366	387	14	a	a	DET
ejpam-2366	387	15	φn	φn	ADJ
ejpam-2366	387	16	-	-	PUNCT
ejpam-2366	387	17	primary	primary	ADJ
ejpam-2366	387	18	element	element	NOUN
ejpam-2366	387	19	(	(	PUNCT
ejpam-2366	387	20	n	n	CCONJ
ejpam-2366	387	21	>	>	X
ejpam-2366	387	22	2	2	NUM
ejpam-2366	387	23	)	)	PUNCT
ejpam-2366	387	24	.	.	PUNCT
ejpam-2366	388	1	•	•	NOUN
ejpam-2366	388	2	φω(n	φω(n	NUM
ejpam-2366	388	3	)	)	PUNCT
ejpam-2366	389	1	=	=	PUNCT
ejpam-2366	389	2	∧∞	∧∞	PRON
ejpam-2366	389	3	i=1(n	i=1(n	NOUN
ejpam-2366	389	4	:	:	PUNCT
ejpam-2366	389	5	i	i	PRON
ejpam-2366	389	6	m	m	VERB
ejpam-2366	389	7	)	)	PUNCT
ejpam-2366	389	8	in	in	ADP
ejpam-2366	389	9	.	.	PUNCT
ejpam-2366	390	1	then	then	ADV
ejpam-2366	390	2	n	n	X
ejpam-2366	390	3	∈	∈	NOUN
ejpam-2366	390	4	m	m	AUX
ejpam-2366	390	5	is	be	AUX
ejpam-2366	390	6	called	call	VERB
ejpam-2366	390	7	a	a	DET
ejpam-2366	390	8	ω	ω	ADJ
ejpam-2366	390	9	-	-	ADJ
ejpam-2366	390	10	primary	primary	ADJ
ejpam-2366	390	11	element	element	NOUN
ejpam-2366	390	12	or	or	CCONJ
ejpam-2366	390	13	φωprimary	φωprimary	ADJ
ejpam-2366	390	14	element	element	NOUN
ejpam-2366	390	15	.	.	PUNCT
ejpam-2366	391	1	clearly	clearly	ADV
ejpam-2366	391	2	,	,	PUNCT
ejpam-2366	391	3	every	every	DET
ejpam-2366	391	4	φ	φ	VERB
ejpam-2366	391	5	-	-	ADJ
ejpam-2366	391	6	prime	prime	ADJ
ejpam-2366	391	7	element	element	NOUN
ejpam-2366	391	8	of	of	ADP
ejpam-2366	391	9	an	an	DET
ejpam-2366	391	10	l	l	NOUN
ejpam-2366	391	11	-	-	NOUN
ejpam-2366	391	12	module	module	NOUN
ejpam-2366	391	13	m	m	NOUN
ejpam-2366	391	14	is	be	AUX
ejpam-2366	391	15	φ	φ	VERB
ejpam-2366	391	16	-	-	ADJ
ejpam-2366	391	17	primary	primary	ADJ
ejpam-2366	391	18	but	but	CCONJ
ejpam-2366	391	19	the	the	DET
ejpam-2366	391	20	converse	converse	NOUN
ejpam-2366	391	21	is	be	AUX
ejpam-2366	391	22	not	not	PART
ejpam-2366	391	23	true	true	ADJ
ejpam-2366	391	24	as	as	SCONJ
ejpam-2366	391	25	shown	show	VERB
ejpam-2366	391	26	in	in	ADP
ejpam-2366	391	27	the	the	DET
ejpam-2366	391	28	following	follow	VERB
ejpam-2366	391	29	example	example	NOUN
ejpam-2366	391	30	by	by	ADP
ejpam-2366	391	31	taking	take	VERB
ejpam-2366	391	32	φ(n	φ(n	NOUN
ejpam-2366	391	33	)	)	PUNCT
ejpam-2366	391	34	=	=	PUNCT
ejpam-2366	391	35	(	(	PUNCT
ejpam-2366	391	36	n	n	X
ejpam-2366	391	37	:	:	PUNCT
ejpam-2366	391	38	i	i	PRON
ejpam-2366	391	39	m	m	PROPN
ejpam-2366	391	40	)	)	PUNCT
ejpam-2366	391	41	n	n	PROPN
ejpam-2366	391	42	for	for	ADP
ejpam-2366	391	43	convenience	convenience	NOUN
ejpam-2366	391	44	.	.	PUNCT
ejpam-2366	392	1	example	example	NOUN
ejpam-2366	393	1	2	2	NUM
ejpam-2366	393	2	.	.	X
ejpam-2366	393	3	consider	consider	VERB
ejpam-2366	393	4	the	the	DET
ejpam-2366	393	5	lattice	lattice	NOUN
ejpam-2366	393	6	module	module	NOUN
ejpam-2366	393	7	as	as	ADP
ejpam-2366	393	8	in	in	ADP
ejpam-2366	393	9	example	example	NOUN
ejpam-2366	393	10	1	1	X
ejpam-2366	393	11	.	.	PUNCT
ejpam-2366	394	1	let	let	VERB
ejpam-2366	394	2	n	n	PRON
ejpam-2366	394	3	be	be	AUX
ejpam-2366	394	4	the	the	DET
ejpam-2366	394	5	cyclic	cyclic	ADJ
ejpam-2366	394	6	submodule	submodule	NOUN
ejpam-2366	394	7	of	of	ADP
ejpam-2366	394	8	m	m	AUX
ejpam-2366	394	9	generated	generate	VERB
ejpam-2366	394	10	by	by	ADP
ejpam-2366	394	11	4	4	NUM
ejpam-2366	394	12	.	.	PUNCT
ejpam-2366	395	1	it	it	PRON
ejpam-2366	395	2	is	be	AUX
ejpam-2366	395	3	easy	easy	ADJ
ejpam-2366	395	4	to	to	PART
ejpam-2366	395	5	see	see	VERB
ejpam-2366	395	6	that	that	SCONJ
ejpam-2366	395	7	the	the	DET
ejpam-2366	395	8	element	element	NOUN
ejpam-2366	395	9	n	n	NOUN
ejpam-2366	395	10	=	=	NOUN
ejpam-2366	395	11	<	<	X
ejpam-2366	395	12	4	4	NUM
ejpam-2366	395	13	>	>	X
ejpam-2366	395	14	is	be	AUX
ejpam-2366	395	15	almost	almost	ADV
ejpam-2366	395	16	primary	primary	ADJ
ejpam-2366	395	17	(	(	PUNCT
ejpam-2366	395	18	φ2	φ2	NOUN
ejpam-2366	395	19	-	-	PUNCT
ejpam-2366	395	20	primary	primary	NOUN
ejpam-2366	395	21	)	)	PUNCT
ejpam-2366	395	22	but	but	CCONJ
ejpam-2366	395	23	n	n	PRON
ejpam-2366	395	24	is	be	AUX
ejpam-2366	395	25	not	not	PART
ejpam-2366	395	26	almost	almost	ADV
ejpam-2366	395	27	prime	prime	ADJ
ejpam-2366	395	28	(	(	PUNCT
ejpam-2366	395	29	φ2	φ2	NOUN
ejpam-2366	395	30	-	-	PUNCT
ejpam-2366	395	31	prime	prime	NOUN
ejpam-2366	395	32	)	)	PUNCT
ejpam-2366	395	33	because	because	SCONJ
ejpam-2366	395	34	(	(	PUNCT
ejpam-2366	395	35	2	2	X
ejpam-2366	395	36	)	)	PUNCT
ejpam-2366	395	37	<	<	X
ejpam-2366	395	38	6	6	NUM
ejpam-2366	395	39	>	>	SYM
ejpam-2366	395	40	6	6	NUM
ejpam-2366	395	41	n	n	NOUN
ejpam-2366	395	42	,	,	PUNCT
ejpam-2366	395	43	(	(	PUNCT
ejpam-2366	395	44	2	2	X
ejpam-2366	395	45	)	)	PUNCT
ejpam-2366	395	46	<	<	X
ejpam-2366	395	47	6	6	NUM
ejpam-2366	395	48	>	>	SYM
ejpam-2366	395	49	φ2(n	φ2(n	PROPN
ejpam-2366	395	50	)	)	PUNCT
ejpam-2366	395	51	=	=	NOUN
ejpam-2366	395	52	<	<	X
ejpam-2366	395	53	8	8	NUM
ejpam-2366	395	54	>	>	PUNCT
ejpam-2366	395	55	but	but	CCONJ
ejpam-2366	395	56	<	<	X
ejpam-2366	395	57	6	6	NUM
ejpam-2366	395	58	>	>	SYM
ejpam-2366	395	59	n	n	PROPN
ejpam-2366	395	60	and	and	CCONJ
ejpam-2366	395	61	(	(	PUNCT
ejpam-2366	395	62	2	2	NUM
ejpam-2366	395	63	)	)	PUNCT
ejpam-2366	395	64	(	(	PUNCT
ejpam-2366	395	65	n	n	X
ejpam-2366	395	66	:	:	PUNCT
ejpam-2366	395	67	i	i	PRON
ejpam-2366	395	68	m	m	VERB
ejpam-2366	395	69	)	)	PUNCT
ejpam-2366	396	1	=	=	PUNCT
ejpam-2366	396	2	(	(	PUNCT
ejpam-2366	396	3	4	4	NUM
ejpam-2366	396	4	)	)	PUNCT
ejpam-2366	396	5	where	where	SCONJ
ejpam-2366	396	6	i	i	PRON
ejpam-2366	396	7	m	m	VERB
ejpam-2366	396	8	=	=	ADJ
ejpam-2366	396	9	<	<	X
ejpam-2366	396	10	1	1	NUM
ejpam-2366	396	11	>	>	PUNCT
ejpam-2366	396	12	.	.	PUNCT
ejpam-2366	397	1	clearly	clearly	ADV
ejpam-2366	397	2	,	,	PUNCT
ejpam-2366	397	3	every	every	DET
ejpam-2366	397	4	prime	prime	ADJ
ejpam-2366	397	5	element	element	NOUN
ejpam-2366	397	6	of	of	ADP
ejpam-2366	397	7	an	an	DET
ejpam-2366	397	8	l	l	NOUN
ejpam-2366	397	9	-	-	NOUN
ejpam-2366	397	10	module	module	NOUN
ejpam-2366	397	11	m	m	NOUN
ejpam-2366	397	12	is	be	AUX
ejpam-2366	397	13	φ	φ	VERB
ejpam-2366	397	14	-	-	NOUN
ejpam-2366	397	15	primary	primary	NOUN
ejpam-2366	397	16	.	.	PUNCT
ejpam-2366	398	1	but	but	CCONJ
ejpam-2366	398	2	the	the	DET
ejpam-2366	398	3	converse	converse	NOUN
ejpam-2366	398	4	is	be	AUX
ejpam-2366	398	5	not	not	PART
ejpam-2366	398	6	true	true	ADJ
ejpam-2366	398	7	which	which	PRON
ejpam-2366	398	8	is	be	AUX
ejpam-2366	398	9	shown	show	VERB
ejpam-2366	398	10	in	in	ADP
ejpam-2366	398	11	the	the	DET
ejpam-2366	398	12	following	follow	VERB
ejpam-2366	398	13	example	example	NOUN
ejpam-2366	398	14	by	by	ADP
ejpam-2366	398	15	taking	take	VERB
ejpam-2366	398	16	φ(n	φ(n	NOUN
ejpam-2366	398	17	)	)	PUNCT
ejpam-2366	398	18	=	=	PUNCT
ejpam-2366	398	19	(	(	PUNCT
ejpam-2366	398	20	n	n	X
ejpam-2366	398	21	:	:	PUNCT
ejpam-2366	398	22	i	i	PRON
ejpam-2366	398	23	m	m	PROPN
ejpam-2366	398	24	)	)	PUNCT
ejpam-2366	398	25	n	n	PROPN
ejpam-2366	398	26	for	for	ADP
ejpam-2366	398	27	convenience	convenience	NOUN
ejpam-2366	398	28	.	.	PUNCT
ejpam-2366	399	1	example	example	NOUN
ejpam-2366	400	1	3	3	X
ejpam-2366	400	2	.	.	X
ejpam-2366	400	3	consider	consider	VERB
ejpam-2366	400	4	the	the	DET
ejpam-2366	400	5	lattice	lattice	NOUN
ejpam-2366	400	6	module	module	NOUN
ejpam-2366	400	7	as	as	ADP
ejpam-2366	400	8	in	in	ADP
ejpam-2366	400	9	example	example	NOUN
ejpam-2366	400	10	1	1	X
ejpam-2366	400	11	.	.	PUNCT
ejpam-2366	401	1	let	let	VERB
ejpam-2366	401	2	n	n	PRON
ejpam-2366	401	3	be	be	AUX
ejpam-2366	401	4	the	the	DET
ejpam-2366	401	5	cyclic	cyclic	ADJ
ejpam-2366	401	6	submodule	submodule	NOUN
ejpam-2366	401	7	of	of	ADP
ejpam-2366	401	8	m	m	AUX
ejpam-2366	401	9	generated	generate	VERB
ejpam-2366	401	10	by	by	ADP
ejpam-2366	401	11	0	0	PROPN
ejpam-2366	401	12	.	.	PUNCT
ejpam-2366	402	1	it	it	PRON
ejpam-2366	402	2	is	be	AUX
ejpam-2366	402	3	easy	easy	ADJ
ejpam-2366	402	4	to	to	PART
ejpam-2366	402	5	see	see	VERB
ejpam-2366	402	6	that	that	SCONJ
ejpam-2366	402	7	the	the	DET
ejpam-2366	402	8	element	element	NOUN
ejpam-2366	402	9	n	n	NOUN
ejpam-2366	402	10	=	=	NOUN
ejpam-2366	402	11	<	<	X
ejpam-2366	402	12	0	0	NUM
ejpam-2366	402	13	>	>	PUNCT
ejpam-2366	402	14	=	=	PUNCT
ejpam-2366	402	15	om	om	PROPN
ejpam-2366	402	16	is	be	AUX
ejpam-2366	402	17	almost	almost	ADV
ejpam-2366	402	18	primary	primary	ADJ
ejpam-2366	402	19	(	(	PUNCT
ejpam-2366	402	20	φ2	φ2	NOUN
ejpam-2366	402	21	-	-	PUNCT
ejpam-2366	402	22	primary	primary	NOUN
ejpam-2366	402	23	)	)	PUNCT
ejpam-2366	402	24	but	but	CCONJ
ejpam-2366	402	25	n	n	PRON
ejpam-2366	402	26	is	be	AUX
ejpam-2366	402	27	not	not	PART
ejpam-2366	402	28	prime	prime	ADJ
ejpam-2366	402	29	.	.	PUNCT
ejpam-2366	403	1	the	the	DET
ejpam-2366	403	2	analogous	analogous	ADJ
ejpam-2366	403	3	results	result	NOUN
ejpam-2366	403	4	(	(	PUNCT
ejpam-2366	403	5	from	from	ADP
ejpam-2366	403	6	the	the	DET
ejpam-2366	403	7	results	result	NOUN
ejpam-2366	403	8	of	of	ADP
ejpam-2366	403	9	φ	φ	ADJ
ejpam-2366	403	10	-	-	ADJ
ejpam-2366	403	11	prime	prime	ADJ
ejpam-2366	403	12	elements	element	NOUN
ejpam-2366	403	13	of	of	ADP
ejpam-2366	403	14	m	m	PROPN
ejpam-2366	403	15	)	)	PUNCT
ejpam-2366	403	16	for	for	ADP
ejpam-2366	403	17	φ	φ	VERB
ejpam-2366	403	18	-	-	ADJ
ejpam-2366	403	19	primary	primary	ADJ
ejpam-2366	403	20	elements	element	NOUN
ejpam-2366	403	21	of	of	ADP
ejpam-2366	403	22	m	m	NOUN
ejpam-2366	403	23	are	be	AUX
ejpam-2366	403	24	stated	state	VERB
ejpam-2366	403	25	below	below	ADP
ejpam-2366	403	26	whose	whose	DET
ejpam-2366	403	27	proofs	proof	NOUN
ejpam-2366	403	28	being	be	AUX
ejpam-2366	403	29	on	on	ADP
ejpam-2366	403	30	similar	similar	ADJ
ejpam-2366	403	31	arguments	argument	NOUN
ejpam-2366	403	32	are	be	AUX
ejpam-2366	403	33	omitted	omit	VERB
ejpam-2366	403	34	.	.	PUNCT
ejpam-2366	404	1	we	we	PRON
ejpam-2366	404	2	begin	begin	VERB
ejpam-2366	404	3	with	with	ADP
ejpam-2366	404	4	the	the	DET
ejpam-2366	404	5	characterizations	characterization	NOUN
ejpam-2366	404	6	of	of	ADP
ejpam-2366	404	7	a	a	DET
ejpam-2366	404	8	φ	φ	ADJ
ejpam-2366	404	9	-	-	ADJ
ejpam-2366	404	10	primary	primary	ADJ
ejpam-2366	404	11	element	element	NOUN
ejpam-2366	404	12	of	of	ADP
ejpam-2366	404	13	an	an	DET
ejpam-2366	404	14	l	l	NOUN
ejpam-2366	404	15	-	-	NOUN
ejpam-2366	404	16	module	module	NOUN
ejpam-2366	404	17	m	m	NOUN
ejpam-2366	404	18	.	.	PUNCT
ejpam-2366	405	1	theorem	theorem	ADJ
ejpam-2366	405	2	11	11	NUM
ejpam-2366	405	3	.	.	PUNCT
ejpam-2366	406	1	let	let	VERB
ejpam-2366	406	2	m	m	PRON
ejpam-2366	406	3	be	be	AUX
ejpam-2366	406	4	a	a	DET
ejpam-2366	406	5	cg	cg	NOUN
ejpam-2366	406	6	-	-	PUNCT
ejpam-2366	406	7	lattice	lattice	NOUN
ejpam-2366	406	8	l	l	NOUN
ejpam-2366	406	9	-	-	NOUN
ejpam-2366	406	10	module	module	NOUN
ejpam-2366	406	11	,	,	PUNCT
ejpam-2366	406	12	n	n	CCONJ
ejpam-2366	406	13	∈	∈	NOUN
ejpam-2366	406	14	m	m	AUX
ejpam-2366	406	15	be	be	VERB
ejpam-2366	406	16	a	a	DET
ejpam-2366	406	17	proper	proper	ADJ
ejpam-2366	406	18	element	element	NOUN
ejpam-2366	406	19	and	and	CCONJ
ejpam-2366	406	20	φ	φ	NOUN
ejpam-2366	406	21	:	:	PUNCT
ejpam-2366	407	1	m	m	VERB
ejpam-2366	407	2	−→m	−→m	VERB
ejpam-2366	407	3	be	be	AUX
ejpam-2366	407	4	a	a	DET
ejpam-2366	407	5	function	function	NOUN
ejpam-2366	407	6	on	on	ADP
ejpam-2366	407	7	m	m	PROPN
ejpam-2366	407	8	.	.	PUNCT
ejpam-2366	408	1	then	then	ADV
ejpam-2366	408	2	the	the	DET
ejpam-2366	408	3	following	follow	VERB
ejpam-2366	408	4	statements	statement	NOUN
ejpam-2366	408	5	are	be	AUX
ejpam-2366	408	6	equivalent	equivalent	ADJ
ejpam-2366	408	7	:	:	PUNCT
ejpam-2366	408	8	(	(	PUNCT
ejpam-2366	408	9	i	i	NOUN
ejpam-2366	408	10	)	)	PUNCT
ejpam-2366	408	11	n	n	PRON
ejpam-2366	408	12	is	be	AUX
ejpam-2366	408	13	a	a	DET
ejpam-2366	408	14	φ	φ	ADJ
ejpam-2366	408	15	-	-	ADJ
ejpam-2366	408	16	primary	primary	ADJ
ejpam-2366	408	17	element	element	NOUN
ejpam-2366	408	18	of	of	ADP
ejpam-2366	408	19	m	m	PROPN
ejpam-2366	408	20	.	.	PUNCT
ejpam-2366	409	1	(	(	PUNCT
ejpam-2366	409	2	ii	ii	NOUN
ejpam-2366	409	3	)	)	PUNCT
ejpam-2366	409	4	for	for	ADP
ejpam-2366	409	5	every	every	DET
ejpam-2366	409	6	a	a	DET
ejpam-2366	409	7	∈m	∈m	NOUN
ejpam-2366	409	8	such	such	ADJ
ejpam-2366	409	9	that	that	SCONJ
ejpam-2366	409	10	a	a	DET
ejpam-2366	409	11	n	n	NOUN
ejpam-2366	409	12	,	,	PUNCT
ejpam-2366	409	13	either	either	CCONJ
ejpam-2366	409	14	(	(	PUNCT
ejpam-2366	409	15	n	n	X
ejpam-2366	409	16	:	:	PUNCT
ejpam-2366	409	17	a	a	X
ejpam-2366	409	18	)	)	PUNCT
ejpam-2366	409	19	6	6	NUM
ejpam-2366	409	20	√	√	NOUN
ejpam-2366	410	1	n	n	NOUN
ejpam-2366	410	2	:	:	PUNCT
ejpam-2366	410	3	i	i	PRON
ejpam-2366	410	4	m	m	VERB
ejpam-2366	410	5	or	or	CCONJ
ejpam-2366	410	6	(	(	PUNCT
ejpam-2366	410	7	n	n	X
ejpam-2366	410	8	:	:	PUNCT
ejpam-2366	410	9	a	a	X
ejpam-2366	410	10	)	)	PUNCT
ejpam-2366	410	11	=	=	SYM
ejpam-2366	410	12	(	(	PUNCT
ejpam-2366	410	13	φ(n	φ(n	PROPN
ejpam-2366	410	14	)	)	PUNCT
ejpam-2366	410	15	:	:	PUNCT
ejpam-2366	410	16	a	a	X
ejpam-2366	410	17	)	)	PUNCT
ejpam-2366	410	18	.	.	PUNCT
ejpam-2366	411	1	(	(	PUNCT
ejpam-2366	411	2	iii	iii	X
ejpam-2366	411	3	)	)	PUNCT
ejpam-2366	411	4	for	for	ADP
ejpam-2366	411	5	every	every	DET
ejpam-2366	411	6	r	r	NOUN
ejpam-2366	411	7	∈	∈	NOUN
ejpam-2366	411	8	l	l	NOUN
ejpam-2366	411	9	such	such	ADJ
ejpam-2366	411	10	that	that	DET
ejpam-2366	411	11	r	r	NOUN
ejpam-2366	411	12	√	√	NOUN
ejpam-2366	411	13	n	n	NOUN
ejpam-2366	411	14	:	:	PUNCT
ejpam-2366	412	1	i	i	PRON
ejpam-2366	412	2	m	m	VERB
ejpam-2366	412	3	,	,	PUNCT
ejpam-2366	412	4	either	either	CCONJ
ejpam-2366	412	5	(	(	PUNCT
ejpam-2366	412	6	n	n	NUM
ejpam-2366	412	7	:	:	PUNCT
ejpam-2366	412	8	r	r	X
ejpam-2366	412	9	)	)	PUNCT
ejpam-2366	412	10	=	=	SYM
ejpam-2366	412	11	n	n	NOUN
ejpam-2366	412	12	or	or	CCONJ
ejpam-2366	412	13	(	(	PUNCT
ejpam-2366	412	14	n	n	X
ejpam-2366	412	15	:	:	PUNCT
ejpam-2366	412	16	r	r	X
ejpam-2366	412	17	)	)	PUNCT
ejpam-2366	412	18	=	=	SYM
ejpam-2366	412	19	(	(	PUNCT
ejpam-2366	412	20	φ(n	φ(n	ADJ
ejpam-2366	412	21	)	)	PUNCT
ejpam-2366	412	22	:	:	PUNCT
ejpam-2366	413	1	r	r	X
ejpam-2366	413	2	)	)	PUNCT
ejpam-2366	413	3	.	.	PUNCT
ejpam-2366	414	1	(	(	PUNCT
ejpam-2366	414	2	iv	iv	X
ejpam-2366	414	3	)	)	PUNCT
ejpam-2366	414	4	for	for	ADP
ejpam-2366	414	5	every	every	DET
ejpam-2366	414	6	r	r	NOUN
ejpam-2366	414	7	∈	∈	PROPN
ejpam-2366	414	8	l∗	l∗	NOUN
ejpam-2366	414	9	,	,	PUNCT
ejpam-2366	414	10	a	a	DET
ejpam-2366	414	11	∈m∗	∈m∗	NOUN
ejpam-2366	414	12	,	,	PUNCT
ejpam-2366	414	13	if	if	SCONJ
ejpam-2366	414	14	ra	ra	PROPN
ejpam-2366	414	15	6	6	NUM
ejpam-2366	414	16	n	n	NOUN
ejpam-2366	414	17	and	and	CCONJ
ejpam-2366	414	18	ra	ra	PROPN
ejpam-2366	414	19	φ(n	φ(n	PROPN
ejpam-2366	414	20	)	)	PUNCT
ejpam-2366	414	21	,	,	PUNCT
ejpam-2366	414	22	then	then	ADV
ejpam-2366	414	23	either	either	CCONJ
ejpam-2366	414	24	r	r	NOUN
ejpam-2366	414	25	6	6	NUM
ejpam-2366	414	26	√	√	NUM
ejpam-2366	414	27	n	n	NOUN
ejpam-2366	414	28	:	:	PUNCT
ejpam-2366	414	29	i	i	PRON
ejpam-2366	414	30	m	m	VERB
ejpam-2366	414	31	or	or	CCONJ
ejpam-2366	414	32	a	a	DET
ejpam-2366	414	33	6	6	NUM
ejpam-2366	414	34	n	n	NOUN
ejpam-2366	414	35	.	.	PUNCT
ejpam-2366	415	1	the	the	DET
ejpam-2366	415	2	following	follow	VERB
ejpam-2366	415	3	2	2	NUM
ejpam-2366	415	4	corollaries	corollary	NOUN
ejpam-2366	415	5	are	be	AUX
ejpam-2366	415	6	consequences	consequence	NOUN
ejpam-2366	415	7	of	of	ADP
ejpam-2366	415	8	theorem	theorem	ADJ
ejpam-2366	415	9	11	11	NUM
ejpam-2366	415	10	.	.	PUNCT
ejpam-2366	416	1	corollary	corollary	ADJ
ejpam-2366	416	2	10	10	NUM
ejpam-2366	416	3	.	.	PUNCT
ejpam-2366	417	1	let	let	VERB
ejpam-2366	417	2	m	m	PRON
ejpam-2366	417	3	be	be	AUX
ejpam-2366	417	4	a	a	DET
ejpam-2366	417	5	cg	cg	NOUN
ejpam-2366	417	6	-	-	PUNCT
ejpam-2366	417	7	lattice	lattice	NOUN
ejpam-2366	417	8	l	l	NOUN
ejpam-2366	417	9	-	-	NOUN
ejpam-2366	417	10	module	module	NOUN
ejpam-2366	417	11	and	and	CCONJ
ejpam-2366	417	12	n	n	CCONJ
ejpam-2366	417	13	∈	∈	NOUN
ejpam-2366	417	14	m	m	AUX
ejpam-2366	417	15	be	be	VERB
ejpam-2366	417	16	a	a	DET
ejpam-2366	417	17	proper	proper	ADJ
ejpam-2366	417	18	element	element	NOUN
ejpam-2366	417	19	.	.	PUNCT
ejpam-2366	418	1	then	then	ADV
ejpam-2366	418	2	the	the	DET
ejpam-2366	418	3	following	follow	VERB
ejpam-2366	418	4	statements	statement	NOUN
ejpam-2366	418	5	are	be	AUX
ejpam-2366	418	6	equivalent	equivalent	ADJ
ejpam-2366	418	7	:	:	PUNCT
ejpam-2366	418	8	1	1	X
ejpam-2366	418	9	©	©	NOUN
ejpam-2366	418	10	n	n	NUM
ejpam-2366	418	11	is	be	AUX
ejpam-2366	418	12	a	a	DET
ejpam-2366	418	13	weakly	weakly	ADJ
ejpam-2366	418	14	primary	primary	ADJ
ejpam-2366	418	15	element	element	NOUN
ejpam-2366	418	16	of	of	ADP
ejpam-2366	418	17	m	m	PROPN
ejpam-2366	418	18	.	.	PUNCT
ejpam-2366	419	1	2	2	NUM
ejpam-2366	419	2	©	©	NOUN
ejpam-2366	419	3	for	for	ADP
ejpam-2366	419	4	every	every	DET
ejpam-2366	419	5	a	a	DET
ejpam-2366	419	6	∈	∈	NOUN
ejpam-2366	419	7	m	m	VERB
ejpam-2366	419	8	such	such	ADJ
ejpam-2366	419	9	that	that	SCONJ
ejpam-2366	419	10	a	a	DET
ejpam-2366	419	11	n	n	NOUN
ejpam-2366	419	12	,	,	PUNCT
ejpam-2366	419	13	either	either	CCONJ
ejpam-2366	419	14	(	(	PUNCT
ejpam-2366	419	15	n	n	X
ejpam-2366	419	16	:	:	PUNCT
ejpam-2366	419	17	a	a	X
ejpam-2366	419	18	)	)	PUNCT
ejpam-2366	419	19	6	6	NUM
ejpam-2366	419	20	√	√	NOUN
ejpam-2366	419	21	n	n	NOUN
ejpam-2366	419	22	:	:	PUNCT
ejpam-2366	419	23	i	i	PRON
ejpam-2366	419	24	m	m	VERB
ejpam-2366	419	25	or	or	CCONJ
ejpam-2366	419	26	(	(	PUNCT
ejpam-2366	419	27	n	n	X
ejpam-2366	419	28	:	:	PUNCT
ejpam-2366	419	29	a	a	X
ejpam-2366	419	30	)	)	PUNCT
ejpam-2366	419	31	=	=	SYM
ejpam-2366	419	32	(	(	PUNCT
ejpam-2366	419	33	om	om	INTJ
ejpam-2366	419	34	:	:	PUNCT
ejpam-2366	419	35	a	a	X
ejpam-2366	419	36	)	)	PUNCT
ejpam-2366	419	37	.	.	PUNCT
ejpam-2366	420	1	3	3	NUM
ejpam-2366	420	2	©	©	NOUN
ejpam-2366	420	3	for	for	ADP
ejpam-2366	420	4	every	every	DET
ejpam-2366	420	5	r	r	NOUN
ejpam-2366	420	6	∈	∈	NOUN
ejpam-2366	420	7	l	l	NOUN
ejpam-2366	420	8	such	such	ADJ
ejpam-2366	420	9	that	that	DET
ejpam-2366	420	10	r	r	NOUN
ejpam-2366	420	11	√	√	NOUN
ejpam-2366	420	12	n	n	NOUN
ejpam-2366	420	13	:	:	PUNCT
ejpam-2366	420	14	i	i	PRON
ejpam-2366	420	15	m	m	VERB
ejpam-2366	420	16	,	,	PUNCT
ejpam-2366	420	17	either	either	CCONJ
ejpam-2366	420	18	(	(	PUNCT
ejpam-2366	420	19	n	n	NUM
ejpam-2366	420	20	:	:	PUNCT
ejpam-2366	420	21	r	r	X
ejpam-2366	420	22	)	)	PUNCT
ejpam-2366	420	23	=	=	SYM
ejpam-2366	420	24	n	n	NOUN
ejpam-2366	420	25	or	or	CCONJ
ejpam-2366	420	26	(	(	PUNCT
ejpam-2366	420	27	n	n	X
ejpam-2366	420	28	:	:	PUNCT
ejpam-2366	420	29	r	r	X
ejpam-2366	420	30	)	)	PUNCT
ejpam-2366	420	31	=	=	SYM
ejpam-2366	420	32	(	(	PUNCT
ejpam-2366	420	33	om	om	INTJ
ejpam-2366	420	34	:	:	PUNCT
ejpam-2366	420	35	r	r	X
ejpam-2366	420	36	)	)	PUNCT
ejpam-2366	420	37	.	.	PUNCT
ejpam-2366	421	1	a.	a.	PROPN
ejpam-2366	421	2	v.	v.	PROPN
ejpam-2366	421	3	bingi	bingi	PROPN
ejpam-2366	421	4	,	,	PUNCT
ejpam-2366	421	5	c.	c.	PROPN
ejpam-2366	421	6	s.	s.	PROPN
ejpam-2366	421	7	manjarekar	manjarekar	PROPN
ejpam-2366	421	8	/	/	PROPN
ejpam-2366	421	9	eur	eur	PROPN
ejpam-2366	421	10	.	.	PUNCT
ejpam-2366	422	1	j.	j.	PROPN
ejpam-2366	422	2	pure	pure	PROPN
ejpam-2366	422	3	appl	appl	PROPN
ejpam-2366	422	4	.	.	PROPN
ejpam-2366	422	5	math	math	PROPN
ejpam-2366	422	6	,	,	PUNCT
ejpam-2366	422	7	14	14	NUM
ejpam-2366	422	8	(	(	PUNCT
ejpam-2366	422	9	2	2	NUM
ejpam-2366	422	10	)	)	PUNCT
ejpam-2366	422	11	(	(	PUNCT
ejpam-2366	422	12	2021	2021	NUM
ejpam-2366	422	13	)	)	PUNCT
ejpam-2366	422	14	,	,	PUNCT
ejpam-2366	422	15	551	551	NUM
ejpam-2366	422	16	-	-	SYM
ejpam-2366	422	17	577	577	NUM
ejpam-2366	422	18	562	562	NUM
ejpam-2366	422	19	4	4	NUM
ejpam-2366	422	20	©	©	NOUN
ejpam-2366	422	21	for	for	ADP
ejpam-2366	422	22	every	every	DET
ejpam-2366	422	23	r	r	NOUN
ejpam-2366	422	24	∈	∈	PROPN
ejpam-2366	422	25	l∗	l∗	NOUN
ejpam-2366	422	26	,	,	PUNCT
ejpam-2366	422	27	a	a	DET
ejpam-2366	422	28	∈m∗	∈m∗	NOUN
ejpam-2366	422	29	,	,	PUNCT
ejpam-2366	422	30	if	if	SCONJ
ejpam-2366	422	31	om	om	PROPN
ejpam-2366	422	32	6=	6=	PROPN
ejpam-2366	422	33	ra	ra	PROPN
ejpam-2366	422	34	6	6	NUM
ejpam-2366	422	35	n	n	NOUN
ejpam-2366	422	36	,	,	PUNCT
ejpam-2366	422	37	then	then	ADV
ejpam-2366	422	38	either	either	CCONJ
ejpam-2366	422	39	r	r	NOUN
ejpam-2366	422	40	6	6	NUM
ejpam-2366	422	41	√	√	NUM
ejpam-2366	422	42	n	n	NOUN
ejpam-2366	422	43	:	:	PUNCT
ejpam-2366	422	44	i	i	PRON
ejpam-2366	422	45	m	m	VERB
ejpam-2366	422	46	or	or	CCONJ
ejpam-2366	422	47	a	a	DET
ejpam-2366	422	48	6	6	NUM
ejpam-2366	422	49	n	n	NOUN
ejpam-2366	422	50	.	.	PUNCT
ejpam-2366	423	1	corollary	corollary	ADJ
ejpam-2366	423	2	11	11	NUM
ejpam-2366	423	3	.	.	PUNCT
ejpam-2366	424	1	let	let	VERB
ejpam-2366	424	2	m	m	PRON
ejpam-2366	424	3	be	be	AUX
ejpam-2366	424	4	a	a	DET
ejpam-2366	424	5	cg	cg	NOUN
ejpam-2366	424	6	-	-	PUNCT
ejpam-2366	424	7	lattice	lattice	NOUN
ejpam-2366	424	8	l	l	NOUN
ejpam-2366	424	9	-	-	NOUN
ejpam-2366	424	10	module	module	NOUN
ejpam-2366	424	11	and	and	CCONJ
ejpam-2366	424	12	n	n	CCONJ
ejpam-2366	424	13	∈	∈	NOUN
ejpam-2366	424	14	m	m	AUX
ejpam-2366	424	15	be	be	VERB
ejpam-2366	424	16	a	a	DET
ejpam-2366	424	17	proper	proper	ADJ
ejpam-2366	424	18	element	element	NOUN
ejpam-2366	424	19	.	.	PUNCT
ejpam-2366	425	1	then	then	ADV
ejpam-2366	425	2	the	the	DET
ejpam-2366	425	3	following	follow	VERB
ejpam-2366	425	4	statements	statement	NOUN
ejpam-2366	425	5	are	be	AUX
ejpam-2366	425	6	equivalent	equivalent	ADJ
ejpam-2366	425	7	:	:	PUNCT
ejpam-2366	425	8	1	1	X
ejpam-2366	425	9	©	©	NOUN
ejpam-2366	425	10	n	n	NUM
ejpam-2366	425	11	is	be	AUX
ejpam-2366	425	12	an	an	DET
ejpam-2366	425	13	almost	almost	ADV
ejpam-2366	425	14	primary	primary	ADJ
ejpam-2366	425	15	element	element	NOUN
ejpam-2366	425	16	of	of	ADP
ejpam-2366	425	17	m	m	PROPN
ejpam-2366	425	18	.	.	PUNCT
ejpam-2366	426	1	2	2	NUM
ejpam-2366	426	2	©	©	NOUN
ejpam-2366	426	3	for	for	ADP
ejpam-2366	426	4	every	every	DET
ejpam-2366	426	5	a	a	DET
ejpam-2366	426	6	∈m	∈m	NOUN
ejpam-2366	426	7	such	such	ADJ
ejpam-2366	426	8	that	that	SCONJ
ejpam-2366	426	9	a	a	DET
ejpam-2366	426	10	n	n	NOUN
ejpam-2366	426	11	,	,	PUNCT
ejpam-2366	426	12	either	either	CCONJ
ejpam-2366	426	13	(	(	PUNCT
ejpam-2366	426	14	n	n	X
ejpam-2366	426	15	:	:	PUNCT
ejpam-2366	426	16	a	a	X
ejpam-2366	426	17	)	)	PUNCT
ejpam-2366	426	18	=	=	SYM
ejpam-2366	426	19	(	(	PUNCT
ejpam-2366	426	20	(	(	PUNCT
ejpam-2366	426	21	n	n	X
ejpam-2366	426	22	:	:	PUNCT
ejpam-2366	426	23	i	i	PRON
ejpam-2366	426	24	m	m	PROPN
ejpam-2366	426	25	)	)	PUNCT
ejpam-2366	427	1	n	n	CCONJ
ejpam-2366	427	2	:	:	PUNCT
ejpam-2366	427	3	a	a	X
ejpam-2366	427	4	)	)	PUNCT
ejpam-2366	427	5	or	or	CCONJ
ejpam-2366	427	6	(	(	PUNCT
ejpam-2366	427	7	n	n	X
ejpam-2366	427	8	:	:	PUNCT
ejpam-2366	427	9	a	a	X
ejpam-2366	427	10	)	)	PUNCT
ejpam-2366	427	11	6√	6√	VERB
ejpam-2366	427	12	n	n	NOUN
ejpam-2366	427	13	:	:	PUNCT
ejpam-2366	427	14	i	i	PRON
ejpam-2366	427	15	m	m	VERB
ejpam-2366	427	16	.	.	PUNCT
ejpam-2366	428	1	3	3	NUM
ejpam-2366	428	2	©	©	NOUN
ejpam-2366	428	3	for	for	ADP
ejpam-2366	428	4	every	every	DET
ejpam-2366	428	5	r	r	NOUN
ejpam-2366	428	6	∈	∈	NOUN
ejpam-2366	428	7	l	l	NOUN
ejpam-2366	428	8	such	such	ADJ
ejpam-2366	428	9	that	that	DET
ejpam-2366	428	10	r	r	NOUN
ejpam-2366	428	11	√	√	NOUN
ejpam-2366	428	12	n	n	NOUN
ejpam-2366	428	13	:	:	PUNCT
ejpam-2366	428	14	i	i	PRON
ejpam-2366	428	15	m	m	VERB
ejpam-2366	428	16	,	,	PUNCT
ejpam-2366	428	17	either	either	CCONJ
ejpam-2366	428	18	(	(	PUNCT
ejpam-2366	428	19	n	n	NUM
ejpam-2366	428	20	:	:	PUNCT
ejpam-2366	428	21	r	r	X
ejpam-2366	428	22	)	)	PUNCT
ejpam-2366	428	23	=	=	SYM
ejpam-2366	428	24	(	(	PUNCT
ejpam-2366	428	25	(	(	PUNCT
ejpam-2366	428	26	n	n	X
ejpam-2366	428	27	:	:	PUNCT
ejpam-2366	428	28	i	i	PRON
ejpam-2366	428	29	m	m	PROPN
ejpam-2366	428	30	)	)	PUNCT
ejpam-2366	428	31	n	n	NOUN
ejpam-2366	428	32	:	:	PUNCT
ejpam-2366	428	33	r	r	X
ejpam-2366	428	34	)	)	PUNCT
ejpam-2366	428	35	or	or	CCONJ
ejpam-2366	428	36	(	(	PUNCT
ejpam-2366	428	37	n	n	X
ejpam-2366	428	38	:	:	PUNCT
ejpam-2366	428	39	r	r	X
ejpam-2366	428	40	)	)	PUNCT
ejpam-2366	428	41	=	=	SYM
ejpam-2366	428	42	n	n	NOUN
ejpam-2366	428	43	.	.	PUNCT
ejpam-2366	429	1	4	4	NUM
ejpam-2366	429	2	©	©	NOUN
ejpam-2366	429	3	for	for	ADP
ejpam-2366	429	4	every	every	DET
ejpam-2366	429	5	r	r	NOUN
ejpam-2366	429	6	∈	∈	PROPN
ejpam-2366	429	7	l∗	l∗	NOUN
ejpam-2366	429	8	,	,	PUNCT
ejpam-2366	429	9	a	a	DET
ejpam-2366	429	10	∈	∈	PROPN
ejpam-2366	429	11	m∗	m∗	NOUN
ejpam-2366	429	12	,	,	PUNCT
ejpam-2366	429	13	if	if	SCONJ
ejpam-2366	429	14	ra	ra	PROPN
ejpam-2366	429	15	6	6	NUM
ejpam-2366	429	16	n	n	NOUN
ejpam-2366	429	17	and	and	CCONJ
ejpam-2366	429	18	ra	ra	PROPN
ejpam-2366	429	19	(	(	PUNCT
ejpam-2366	429	20	n	n	PROPN
ejpam-2366	429	21	:	:	PUNCT
ejpam-2366	429	22	i	i	PRON
ejpam-2366	429	23	m	m	PROPN
ejpam-2366	429	24	)	)	PUNCT
ejpam-2366	429	25	n	n	CCONJ
ejpam-2366	429	26	,	,	PUNCT
ejpam-2366	429	27	then	then	ADV
ejpam-2366	429	28	either	either	CCONJ
ejpam-2366	429	29	r	r	NOUN
ejpam-2366	429	30	6√	6√	NOUN
ejpam-2366	429	31	n	n	NOUN
ejpam-2366	429	32	:	:	PUNCT
ejpam-2366	429	33	i	i	PRON
ejpam-2366	429	34	m	m	VERB
ejpam-2366	429	35	or	or	CCONJ
ejpam-2366	429	36	a	a	DET
ejpam-2366	429	37	6	6	NUM
ejpam-2366	429	38	n	n	NOUN
ejpam-2366	429	39	.	.	PUNCT
ejpam-2366	430	1	to	to	PART
ejpam-2366	430	2	obtain	obtain	VERB
ejpam-2366	430	3	the	the	DET
ejpam-2366	430	4	relation	relation	NOUN
ejpam-2366	430	5	among	among	ADP
ejpam-2366	430	6	primary	primary	ADJ
ejpam-2366	430	7	,	,	PUNCT
ejpam-2366	430	8	weakly	weakly	ADJ
ejpam-2366	430	9	primary	primary	ADJ
ejpam-2366	430	10	,	,	PUNCT
ejpam-2366	430	11	ω	ω	NOUN
ejpam-2366	430	12	-	-	NOUN
ejpam-2366	430	13	primary	primary	ADJ
ejpam-2366	430	14	,	,	PUNCT
ejpam-2366	430	15	n	n	CCONJ
ejpam-2366	430	16	-	-	PUNCT
ejpam-2366	430	17	almost	almost	ADV
ejpam-2366	430	18	primary	primary	ADJ
ejpam-2366	430	19	(	(	PUNCT
ejpam-2366	430	20	n	n	CCONJ
ejpam-2366	430	21	>	>	X
ejpam-2366	430	22	2	2	NUM
ejpam-2366	430	23	)	)	PUNCT
ejpam-2366	430	24	and	and	CCONJ
ejpam-2366	430	25	almost	almost	ADV
ejpam-2366	430	26	primary	primary	ADJ
ejpam-2366	430	27	elements	element	NOUN
ejpam-2366	430	28	of	of	ADP
ejpam-2366	430	29	an	an	DET
ejpam-2366	430	30	l	l	NOUN
ejpam-2366	430	31	-	-	NOUN
ejpam-2366	430	32	module	module	NOUN
ejpam-2366	430	33	m	m	NOUN
ejpam-2366	430	34	,	,	PUNCT
ejpam-2366	430	35	we	we	PRON
ejpam-2366	430	36	have	have	VERB
ejpam-2366	430	37	the	the	DET
ejpam-2366	430	38	following	follow	VERB
ejpam-2366	430	39	result	result	NOUN
ejpam-2366	430	40	.	.	PUNCT
ejpam-2366	431	1	theorem	theorem	NOUN
ejpam-2366	431	2	12	12	NUM
ejpam-2366	431	3	.	.	PUNCT
ejpam-2366	432	1	let	let	VERB
ejpam-2366	432	2	γ1	γ1	NOUN
ejpam-2366	432	3	,	,	PUNCT
ejpam-2366	432	4	γ2	γ2	PROPN
ejpam-2366	432	5	:	:	PUNCT
ejpam-2366	432	6	m	m	VERB
ejpam-2366	432	7	−→m	−→m	NOUN
ejpam-2366	432	8	be	be	AUX
ejpam-2366	432	9	functions	function	NOUN
ejpam-2366	432	10	on	on	ADP
ejpam-2366	432	11	an	an	DET
ejpam-2366	432	12	l	l	NOUN
ejpam-2366	432	13	-	-	NOUN
ejpam-2366	432	14	module	module	NOUN
ejpam-2366	432	15	m	m	NOUN
ejpam-2366	432	16	such	such	ADJ
ejpam-2366	432	17	that	that	DET
ejpam-2366	432	18	γ1	γ1	PROPN
ejpam-2366	432	19	6	6	NUM
ejpam-2366	432	20	γ2	γ2	NOUN
ejpam-2366	432	21	.	.	PUNCT
ejpam-2366	433	1	then	then	ADV
ejpam-2366	433	2	every	every	DET
ejpam-2366	433	3	proper	proper	ADJ
ejpam-2366	433	4	γ1	γ1	NOUN
ejpam-2366	433	5	-	-	PUNCT
ejpam-2366	433	6	primary	primary	ADJ
ejpam-2366	433	7	element	element	NOUN
ejpam-2366	433	8	of	of	ADP
ejpam-2366	433	9	m	m	PROPN
ejpam-2366	433	10	is	be	AUX
ejpam-2366	433	11	γ2	γ2	NOUN
ejpam-2366	433	12	-	-	PUNCT
ejpam-2366	433	13	primary	primary	NOUN
ejpam-2366	433	14	.	.	PUNCT
ejpam-2366	434	1	theorem	theorem	NOUN
ejpam-2366	434	2	13	13	NUM
ejpam-2366	434	3	.	.	PUNCT
ejpam-2366	435	1	let	let	VERB
ejpam-2366	435	2	n	n	PRON
ejpam-2366	435	3	be	be	AUX
ejpam-2366	435	4	a	a	DET
ejpam-2366	435	5	proper	proper	ADJ
ejpam-2366	435	6	element	element	NOUN
ejpam-2366	435	7	of	of	ADP
ejpam-2366	435	8	an	an	DET
ejpam-2366	435	9	l	l	NOUN
ejpam-2366	435	10	-	-	NOUN
ejpam-2366	435	11	module	module	NOUN
ejpam-2366	435	12	m	m	NOUN
ejpam-2366	435	13	.	.	PUNCT
ejpam-2366	436	1	then	then	ADV
ejpam-2366	436	2	n	n	PRON
ejpam-2366	436	3	is	be	AUX
ejpam-2366	436	4	primary	primary	ADJ
ejpam-2366	436	5	implies	implie	NOUN
ejpam-2366	436	6	n	n	VERB
ejpam-2366	436	7	is	be	AUX
ejpam-2366	436	8	weakly	weakly	ADV
ejpam-2366	436	9	primary	primary	ADJ
ejpam-2366	436	10	,	,	PUNCT
ejpam-2366	436	11	n	n	X
ejpam-2366	436	12	is	be	AUX
ejpam-2366	436	13	weakly	weakly	ADV
ejpam-2366	436	14	primary	primary	ADJ
ejpam-2366	436	15	implies	implie	NOUN
ejpam-2366	436	16	n	n	AUX
ejpam-2366	436	17	is	be	AUX
ejpam-2366	436	18	ω	ω	NOUN
ejpam-2366	436	19	-	-	NOUN
ejpam-2366	436	20	primary	primary	ADJ
ejpam-2366	436	21	,	,	PUNCT
ejpam-2366	436	22	n	n	X
ejpam-2366	436	23	is	be	AUX
ejpam-2366	436	24	ω	ω	NOUN
ejpam-2366	436	25	-	-	ADJ
ejpam-2366	436	26	primary	primary	ADJ
ejpam-2366	436	27	implies	imply	VERB
ejpam-2366	436	28	n	n	VERB
ejpam-2366	436	29	is	be	AUX
ejpam-2366	436	30	n	n	ADV
ejpam-2366	436	31	-	-	PUNCT
ejpam-2366	436	32	almost	almost	ADV
ejpam-2366	436	33	primary	primary	ADJ
ejpam-2366	436	34	(	(	PUNCT
ejpam-2366	436	35	n	n	CCONJ
ejpam-2366	436	36	>	>	X
ejpam-2366	436	37	2	2	NUM
ejpam-2366	436	38	)	)	PUNCT
ejpam-2366	436	39	,	,	PUNCT
ejpam-2366	436	40	n	n	PROPN
ejpam-2366	436	41	is	be	AUX
ejpam-2366	436	42	n	n	ADV
ejpam-2366	436	43	-	-	PUNCT
ejpam-2366	436	44	almost	almost	ADV
ejpam-2366	436	45	primary	primary	ADJ
ejpam-2366	436	46	(	(	PUNCT
ejpam-2366	436	47	n	n	CCONJ
ejpam-2366	436	48	>	>	X
ejpam-2366	436	49	2	2	NUM
ejpam-2366	436	50	)	)	PUNCT
ejpam-2366	436	51	implies	imply	VERB
ejpam-2366	436	52	n	n	VERB
ejpam-2366	436	53	is	be	AUX
ejpam-2366	436	54	almost	almost	ADV
ejpam-2366	436	55	primary	primary	ADJ
ejpam-2366	436	56	.	.	PUNCT
ejpam-2366	437	1	from	from	ADP
ejpam-2366	437	2	the	the	DET
ejpam-2366	437	3	theorem	theorem	NOUN
ejpam-2366	437	4	13	13	NUM
ejpam-2366	437	5	,	,	PUNCT
ejpam-2366	437	6	we	we	PRON
ejpam-2366	437	7	get	get	VERB
ejpam-2366	437	8	the	the	DET
ejpam-2366	437	9	following	follow	VERB
ejpam-2366	437	10	characterization	characterization	NOUN
ejpam-2366	437	11	of	of	ADP
ejpam-2366	437	12	a	a	DET
ejpam-2366	437	13	ω	ω	ADJ
ejpam-2366	437	14	-	-	ADJ
ejpam-2366	437	15	primary	primary	ADJ
ejpam-2366	437	16	element	element	NOUN
ejpam-2366	437	17	of	of	ADP
ejpam-2366	437	18	an	an	DET
ejpam-2366	437	19	l	l	NOUN
ejpam-2366	437	20	-	-	NOUN
ejpam-2366	437	21	module	module	NOUN
ejpam-2366	437	22	m	m	NOUN
ejpam-2366	437	23	.	.	PUNCT
ejpam-2366	438	1	corollary	corollary	ADJ
ejpam-2366	438	2	12	12	NUM
ejpam-2366	438	3	.	.	PUNCT
ejpam-2366	439	1	let	let	VERB
ejpam-2366	439	2	n	n	PRON
ejpam-2366	439	3	∈m	∈m	VERB
ejpam-2366	439	4	be	be	AUX
ejpam-2366	439	5	a	a	DET
ejpam-2366	439	6	proper	proper	ADJ
ejpam-2366	439	7	element	element	NOUN
ejpam-2366	439	8	of	of	ADP
ejpam-2366	439	9	an	an	DET
ejpam-2366	439	10	l	l	NOUN
ejpam-2366	439	11	-	-	NOUN
ejpam-2366	439	12	module	module	NOUN
ejpam-2366	439	13	m	m	NOUN
ejpam-2366	439	14	.	.	PUNCT
ejpam-2366	440	1	then	then	ADV
ejpam-2366	440	2	n	n	PROPN
ejpam-2366	440	3	is	be	AUX
ejpam-2366	440	4	ω	ω	NOUN
ejpam-2366	440	5	-	-	NOUN
ejpam-2366	440	6	primary	primary	ADJ
ejpam-2366	440	7	if	if	SCONJ
ejpam-2366	441	1	and	and	CCONJ
ejpam-2366	441	2	only	only	ADV
ejpam-2366	441	3	if	if	SCONJ
ejpam-2366	441	4	n	n	PRON
ejpam-2366	441	5	is	be	AUX
ejpam-2366	441	6	n	n	ADV
ejpam-2366	441	7	-	-	PUNCT
ejpam-2366	441	8	almost	almost	ADV
ejpam-2366	441	9	primary	primary	ADJ
ejpam-2366	441	10	for	for	ADP
ejpam-2366	441	11	every	every	DET
ejpam-2366	441	12	n	n	NOUN
ejpam-2366	441	13	>	>	X
ejpam-2366	441	14	2	2	NUM
ejpam-2366	441	15	.	.	PUNCT
ejpam-2366	442	1	the	the	DET
ejpam-2366	442	2	following	follow	VERB
ejpam-2366	442	3	theorem	theorem	NOUN
ejpam-2366	442	4	gives	give	VERB
ejpam-2366	442	5	the	the	DET
ejpam-2366	442	6	characterization	characterization	NOUN
ejpam-2366	442	7	of	of	ADP
ejpam-2366	442	8	an	an	DET
ejpam-2366	442	9	n	n	ADV
ejpam-2366	442	10	-	-	PUNCT
ejpam-2366	442	11	almost	almost	ADV
ejpam-2366	442	12	primary	primary	ADJ
ejpam-2366	442	13	element	element	NOUN
ejpam-2366	442	14	of	of	ADP
ejpam-2366	442	15	an	an	DET
ejpam-2366	442	16	l	l	NOUN
ejpam-2366	442	17	-	-	NOUN
ejpam-2366	442	18	module	module	NOUN
ejpam-2366	442	19	m	m	NOUN
ejpam-2366	442	20	.	.	PUNCT
ejpam-2366	443	1	theorem	theorem	ADJ
ejpam-2366	443	2	14	14	NUM
ejpam-2366	443	3	.	.	PUNCT
ejpam-2366	444	1	let	let	VERB
ejpam-2366	444	2	l	l	NOUN
ejpam-2366	444	3	be	be	AUX
ejpam-2366	444	4	a	a	DET
ejpam-2366	444	5	noether	noether	ADJ
ejpam-2366	444	6	lattice	lattice	NOUN
ejpam-2366	444	7	,	,	PUNCT
ejpam-2366	444	8	m	m	AUX
ejpam-2366	444	9	be	be	VERB
ejpam-2366	444	10	a	a	DET
ejpam-2366	444	11	torsion	torsion	NOUN
ejpam-2366	444	12	free	free	ADJ
ejpam-2366	444	13	noetherian	noetherian	ADJ
ejpam-2366	444	14	l	l	NOUN
ejpam-2366	444	15	-	-	NOUN
ejpam-2366	444	16	module	module	NOUN
ejpam-2366	444	17	and	and	CCONJ
ejpam-2366	444	18	f	f	PROPN
ejpam-2366	444	19	∈	∈	PROPN
ejpam-2366	444	20	l	l	NOUN
ejpam-2366	444	21	be	be	VERB
ejpam-2366	444	22	the	the	DET
ejpam-2366	444	23	jacobson	jacobson	PROPN
ejpam-2366	444	24	radical	radical	PROPN
ejpam-2366	444	25	.	.	PUNCT
ejpam-2366	445	1	then	then	ADV
ejpam-2366	445	2	a	a	DET
ejpam-2366	445	3	proper	proper	ADJ
ejpam-2366	445	4	element	element	NOUN
ejpam-2366	445	5	n	n	CCONJ
ejpam-2366	445	6	∈	∈	NOUN
ejpam-2366	445	7	m	m	VERB
ejpam-2366	445	8	such	such	ADJ
ejpam-2366	445	9	that	that	SCONJ
ejpam-2366	445	10	(	(	PUNCT
ejpam-2366	445	11	n	n	X
ejpam-2366	445	12	:	:	PUNCT
ejpam-2366	445	13	i	i	PRON
ejpam-2366	445	14	m	m	VERB
ejpam-2366	445	15	)	)	PUNCT
ejpam-2366	445	16	6	6	NUM
ejpam-2366	445	17	f	f	NOUN
ejpam-2366	445	18	is	be	AUX
ejpam-2366	445	19	n	n	ADV
ejpam-2366	445	20	-	-	PUNCT
ejpam-2366	445	21	almost	almost	ADV
ejpam-2366	445	22	primary	primary	ADJ
ejpam-2366	445	23	for	for	ADP
ejpam-2366	445	24	every	every	DET
ejpam-2366	445	25	n	n	NOUN
ejpam-2366	445	26	>	>	SYM
ejpam-2366	445	27	2	2	NUM
ejpam-2366	445	28	if	if	SCONJ
ejpam-2366	445	29	and	and	CCONJ
ejpam-2366	445	30	only	only	ADV
ejpam-2366	445	31	if	if	SCONJ
ejpam-2366	445	32	n	n	PRON
ejpam-2366	445	33	is	be	AUX
ejpam-2366	445	34	primary	primary	ADJ
ejpam-2366	445	35	.	.	PUNCT
ejpam-2366	446	1	clearly	clearly	ADV
ejpam-2366	446	2	,	,	PUNCT
ejpam-2366	446	3	every	every	DET
ejpam-2366	446	4	primary	primary	ADJ
ejpam-2366	446	5	element	element	NOUN
ejpam-2366	446	6	of	of	ADP
ejpam-2366	446	7	an	an	DET
ejpam-2366	446	8	l	l	NOUN
ejpam-2366	446	9	-	-	NOUN
ejpam-2366	446	10	module	module	NOUN
ejpam-2366	446	11	m	m	NOUN
ejpam-2366	446	12	is	be	AUX
ejpam-2366	446	13	φ	φ	VERB
ejpam-2366	446	14	-	-	NOUN
ejpam-2366	446	15	primary	primary	NOUN
ejpam-2366	446	16	.	.	PUNCT
ejpam-2366	447	1	but	but	CCONJ
ejpam-2366	447	2	the	the	DET
ejpam-2366	447	3	converse	converse	NOUN
ejpam-2366	447	4	is	be	AUX
ejpam-2366	447	5	not	not	PART
ejpam-2366	447	6	true	true	ADJ
ejpam-2366	447	7	which	which	PRON
ejpam-2366	447	8	is	be	AUX
ejpam-2366	447	9	shown	show	VERB
ejpam-2366	447	10	in	in	ADP
ejpam-2366	447	11	the	the	DET
ejpam-2366	447	12	following	follow	VERB
ejpam-2366	447	13	example	example	NOUN
ejpam-2366	447	14	by	by	ADP
ejpam-2366	447	15	taking	take	VERB
ejpam-2366	447	16	φ(n	φ(n	NOUN
ejpam-2366	447	17	)	)	PUNCT
ejpam-2366	447	18	=	=	PUNCT
ejpam-2366	447	19	(	(	PUNCT
ejpam-2366	447	20	n	n	X
ejpam-2366	447	21	:	:	PUNCT
ejpam-2366	447	22	i	i	PRON
ejpam-2366	447	23	m	m	PROPN
ejpam-2366	447	24	)	)	PUNCT
ejpam-2366	447	25	n	n	PROPN
ejpam-2366	447	26	for	for	ADP
ejpam-2366	447	27	convenience	convenience	NOUN
ejpam-2366	447	28	.	.	PUNCT
ejpam-2366	448	1	example	example	NOUN
ejpam-2366	449	1	4	4	NUM
ejpam-2366	449	2	.	.	PUNCT
ejpam-2366	450	1	if	if	SCONJ
ejpam-2366	450	2	z	z	NOUN
ejpam-2366	450	3	is	be	AUX
ejpam-2366	450	4	the	the	DET
ejpam-2366	450	5	ring	ring	NOUN
ejpam-2366	450	6	of	of	ADP
ejpam-2366	450	7	integers	integer	NOUN
ejpam-2366	450	8	,	,	PUNCT
ejpam-2366	450	9	then	then	ADV
ejpam-2366	450	10	z30	z30	PROPN
ejpam-2366	450	11	is	be	AUX
ejpam-2366	450	12	a	a	DET
ejpam-2366	450	13	z−module	z−module	NOUN
ejpam-2366	450	14	.	.	PUNCT
ejpam-2366	451	1	assume	assume	VERB
ejpam-2366	451	2	that	that	SCONJ
ejpam-2366	451	3	(	(	PUNCT
ejpam-2366	451	4	k	k	X
ejpam-2366	451	5	)	)	PUNCT
ejpam-2366	451	6	denotes	denote	VERB
ejpam-2366	451	7	the	the	DET
ejpam-2366	451	8	cyclic	cyclic	ADJ
ejpam-2366	451	9	ideal	ideal	NOUN
ejpam-2366	451	10	of	of	ADP
ejpam-2366	451	11	z	z	PROPN
ejpam-2366	451	12	generated	generate	VERB
ejpam-2366	451	13	by	by	ADP
ejpam-2366	451	14	k	k	PROPN
ejpam-2366	451	15	∈	∈	PROPN
ejpam-2366	451	16	z	z	PROPN
ejpam-2366	451	17	and	and	CCONJ
ejpam-2366	451	18	<	<	X
ejpam-2366	451	19	t	t	X
ejpam-2366	451	20	>	>	X
ejpam-2366	451	21	denotes	denote	VERB
ejpam-2366	451	22	the	the	DET
ejpam-2366	451	23	cyclic	cyclic	PROPN
ejpam-2366	451	24	submodule	submodule	NOUN
ejpam-2366	451	25	of	of	ADP
ejpam-2366	451	26	z−module	z−module	PROPN
ejpam-2366	451	27	z30	z30	PROPN
ejpam-2366	451	28	where	where	SCONJ
ejpam-2366	451	29	t	t	PROPN
ejpam-2366	451	30	∈	∈	PROPN
ejpam-2366	451	31	z30	z30	PROPN
ejpam-2366	451	32	.	.	PUNCT
ejpam-2366	451	33	suppose	suppose	VERB
ejpam-2366	451	34	that	that	SCONJ
ejpam-2366	451	35	l	l	NOUN
ejpam-2366	451	36	=	=	SYM
ejpam-2366	451	37	l(z	l(z	NOUN
ejpam-2366	451	38	)	)	PUNCT
ejpam-2366	451	39	is	be	AUX
ejpam-2366	451	40	the	the	DET
ejpam-2366	451	41	set	set	NOUN
ejpam-2366	451	42	of	of	ADP
ejpam-2366	451	43	all	all	DET
ejpam-2366	451	44	ideals	ideal	NOUN
ejpam-2366	451	45	of	of	ADP
ejpam-2366	451	46	z	z	NOUN
ejpam-2366	451	47	and	and	CCONJ
ejpam-2366	451	48	m	m	PROPN
ejpam-2366	451	49	=	=	PUNCT
ejpam-2366	451	50	l(z30	l(z30	NOUN
ejpam-2366	451	51	)	)	PUNCT
ejpam-2366	451	52	is	be	AUX
ejpam-2366	451	53	the	the	DET
ejpam-2366	451	54	set	set	NOUN
ejpam-2366	451	55	of	of	ADP
ejpam-2366	451	56	all	all	DET
ejpam-2366	451	57	submodules	submodule	NOUN
ejpam-2366	451	58	of	of	ADP
ejpam-2366	451	59	z−module	z−module	PROPN
ejpam-2366	451	60	z30	z30	PROPN
ejpam-2366	451	61	.	.	PUNCT
ejpam-2366	452	1	the	the	DET
ejpam-2366	452	2	multiplication	multiplication	NOUN
ejpam-2366	452	3	between	between	ADP
ejpam-2366	452	4	a.	a.	NOUN
ejpam-2366	452	5	v.	v.	PROPN
ejpam-2366	452	6	bingi	bingi	PROPN
ejpam-2366	452	7	,	,	PUNCT
ejpam-2366	452	8	c.	c.	PROPN
ejpam-2366	452	9	s.	s.	PROPN
ejpam-2366	452	10	manjarekar	manjarekar	PROPN
ejpam-2366	452	11	/	/	PROPN
ejpam-2366	452	12	eur	eur	PROPN
ejpam-2366	452	13	.	.	PUNCT
ejpam-2366	453	1	j.	j.	PROPN
ejpam-2366	453	2	pure	pure	PROPN
ejpam-2366	453	3	appl	appl	PROPN
ejpam-2366	453	4	.	.	PROPN
ejpam-2366	453	5	math	math	PROPN
ejpam-2366	453	6	,	,	PUNCT
ejpam-2366	453	7	14	14	NUM
ejpam-2366	453	8	(	(	PUNCT
ejpam-2366	453	9	2	2	NUM
ejpam-2366	453	10	)	)	PUNCT
ejpam-2366	453	11	(	(	PUNCT
ejpam-2366	453	12	2021	2021	NUM
ejpam-2366	453	13	)	)	PUNCT
ejpam-2366	453	14	,	,	PUNCT
ejpam-2366	453	15	551	551	NUM
ejpam-2366	453	16	-	-	SYM
ejpam-2366	453	17	577	577	NUM
ejpam-2366	453	18	563	563	NUM
ejpam-2366	453	19	elements	element	NOUN
ejpam-2366	453	20	of	of	ADP
ejpam-2366	453	21	l	l	NOUN
ejpam-2366	453	22	and	and	CCONJ
ejpam-2366	453	23	m	m	PROPN
ejpam-2366	453	24	is	be	AUX
ejpam-2366	453	25	given	give	VERB
ejpam-2366	453	26	by	by	ADP
ejpam-2366	453	27	(	(	PUNCT
ejpam-2366	453	28	ki	ki	PROPN
ejpam-2366	453	29	)	)	PUNCT
ejpam-2366	453	30	<	<	X
ejpam-2366	453	31	tj	tj	X
ejpam-2366	453	32	>	>	PUNCT
ejpam-2366	453	33	=	=	X
ejpam-2366	453	34	<	<	X
ejpam-2366	453	35	kitj	kitj	X
ejpam-2366	453	36	>	>	X
ejpam-2366	453	37	for	for	ADP
ejpam-2366	453	38	every	every	DET
ejpam-2366	453	39	(	(	PUNCT
ejpam-2366	453	40	ki	ki	PROPN
ejpam-2366	453	41	)	)	PUNCT
ejpam-2366	453	42	∈	∈	PROPN
ejpam-2366	453	43	l	l	NOUN
ejpam-2366	453	44	and	and	CCONJ
ejpam-2366	453	45	<	<	X
ejpam-2366	453	46	tj	tj	X
ejpam-2366	453	47	>	>	X
ejpam-2366	453	48	∈m	∈m	NOUN
ejpam-2366	453	49	where	where	SCONJ
ejpam-2366	453	50	ki	ki	PROPN
ejpam-2366	453	51	,	,	PUNCT
ejpam-2366	453	52	tj	tj	PROPN
ejpam-2366	453	53	∈	∈	PROPN
ejpam-2366	453	54	z.	z.	PROPN
ejpam-2366	454	1	then	then	ADV
ejpam-2366	454	2	m	m	PROPN
ejpam-2366	454	3	is	be	AUX
ejpam-2366	454	4	a	a	DET
ejpam-2366	454	5	lattice	lattice	NOUN
ejpam-2366	454	6	module	module	NOUN
ejpam-2366	454	7	over	over	ADP
ejpam-2366	454	8	l.	l.	PROPN
ejpam-2366	454	9	let	let	VERB
ejpam-2366	454	10	n	n	PRON
ejpam-2366	454	11	be	be	AUX
ejpam-2366	454	12	the	the	DET
ejpam-2366	454	13	cyclic	cyclic	ADJ
ejpam-2366	454	14	submodule	submodule	NOUN
ejpam-2366	454	15	of	of	ADP
ejpam-2366	454	16	m	m	AUX
ejpam-2366	454	17	generated	generate	VERB
ejpam-2366	454	18	by	by	ADP
ejpam-2366	454	19	6	6	NUM
ejpam-2366	454	20	.	.	PUNCT
ejpam-2366	455	1	it	it	PRON
ejpam-2366	455	2	is	be	AUX
ejpam-2366	455	3	easy	easy	ADJ
ejpam-2366	455	4	to	to	PART
ejpam-2366	455	5	see	see	VERB
ejpam-2366	455	6	that	that	PRON
ejpam-2366	455	7	n	n	NOUN
ejpam-2366	455	8	=	=	NOUN
ejpam-2366	455	9	<	<	X
ejpam-2366	455	10	6	6	NUM
ejpam-2366	455	11	>	>	X
ejpam-2366	455	12	is	be	AUX
ejpam-2366	455	13	almost	almost	ADV
ejpam-2366	455	14	primary	primary	ADJ
ejpam-2366	455	15	(	(	PUNCT
ejpam-2366	455	16	φ2	φ2	NOUN
ejpam-2366	455	17	-	-	PUNCT
ejpam-2366	455	18	primary	primary	NOUN
ejpam-2366	455	19	)	)	PUNCT
ejpam-2366	455	20	while	while	SCONJ
ejpam-2366	455	21	n	n	PRON
ejpam-2366	455	22	is	be	AUX
ejpam-2366	455	23	not	not	PART
ejpam-2366	455	24	primary	primary	ADJ
ejpam-2366	455	25	,	,	PUNCT
ejpam-2366	455	26	since	since	SCONJ
ejpam-2366	455	27	(	(	PUNCT
ejpam-2366	455	28	3	3	X
ejpam-2366	455	29	)	)	PUNCT
ejpam-2366	455	30	<	<	X
ejpam-2366	455	31	2	2	NUM
ejpam-2366	455	32	>	>	SYM
ejpam-2366	455	33	6	6	NUM
ejpam-2366	455	34	n	n	NOUN
ejpam-2366	455	35	but	but	CCONJ
ejpam-2366	455	36	<	<	X
ejpam-2366	455	37	2	2	NUM
ejpam-2366	455	38	>	>	SYM
ejpam-2366	455	39	n	n	NOUN
ejpam-2366	455	40	and	and	CCONJ
ejpam-2366	455	41	(	(	PUNCT
ejpam-2366	455	42	3)n	3)n	NUM
ejpam-2366	455	43	(	(	PUNCT
ejpam-2366	455	44	n	n	NUM
ejpam-2366	455	45	:	:	PUNCT
ejpam-2366	455	46	i	i	PRON
ejpam-2366	455	47	m	m	VERB
ejpam-2366	455	48	)	)	PUNCT
ejpam-2366	455	49	=	=	PUNCT
ejpam-2366	455	50	(	(	PUNCT
ejpam-2366	455	51	6	6	NUM
ejpam-2366	455	52	)	)	PUNCT
ejpam-2366	455	53	for	for	ADP
ejpam-2366	455	54	every	every	DET
ejpam-2366	455	55	n	n	PRON
ejpam-2366	455	56	∈	∈	NOUN
ejpam-2366	455	57	z+	z+	NUM
ejpam-2366	455	58	where	where	SCONJ
ejpam-2366	455	59	i	i	PRON
ejpam-2366	455	60	m	m	VERB
ejpam-2366	455	61	=	=	ADJ
ejpam-2366	455	62	<	<	X
ejpam-2366	455	63	1	1	NUM
ejpam-2366	455	64	>	>	PUNCT
ejpam-2366	455	65	.	.	PUNCT
ejpam-2366	456	1	in	in	ADP
ejpam-2366	456	2	the	the	DET
ejpam-2366	456	3	following	follow	VERB
ejpam-2366	456	4	successive	successive	ADJ
ejpam-2366	456	5	nine	nine	NUM
ejpam-2366	456	6	theorems	theorem	NOUN
ejpam-2366	456	7	,	,	PUNCT
ejpam-2366	456	8	we	we	PRON
ejpam-2366	456	9	show	show	VERB
ejpam-2366	456	10	under	under	ADP
ejpam-2366	456	11	which	which	DET
ejpam-2366	456	12	condition(s	condition(s	NOUN
ejpam-2366	456	13	)	)	PUNCT
ejpam-2366	456	14	a	a	DET
ejpam-2366	456	15	φprimary	φprimary	ADJ
ejpam-2366	456	16	element	element	NOUN
ejpam-2366	456	17	of	of	ADP
ejpam-2366	456	18	an	an	DET
ejpam-2366	456	19	l	l	NOUN
ejpam-2366	456	20	-	-	NOUN
ejpam-2366	456	21	module	module	NOUN
ejpam-2366	456	22	m	m	NOUN
ejpam-2366	456	23	is	be	AUX
ejpam-2366	456	24	primary	primary	ADJ
ejpam-2366	456	25	.	.	PUNCT
ejpam-2366	457	1	now	now	ADV
ejpam-2366	457	2	we	we	PRON
ejpam-2366	457	3	have	have	VERB
ejpam-2366	457	4	a	a	DET
ejpam-2366	457	5	characterization	characterization	NOUN
ejpam-2366	457	6	of	of	ADP
ejpam-2366	457	7	a	a	DET
ejpam-2366	457	8	φ	φ	ADJ
ejpam-2366	457	9	-	-	ADJ
ejpam-2366	457	10	primary	primary	ADJ
ejpam-2366	457	11	element	element	NOUN
ejpam-2366	457	12	of	of	ADP
ejpam-2366	457	13	an	an	DET
ejpam-2366	457	14	l	l	NOUN
ejpam-2366	457	15	-	-	NOUN
ejpam-2366	457	16	module	module	NOUN
ejpam-2366	457	17	m	m	NOUN
ejpam-2366	457	18	.	.	PUNCT
ejpam-2366	458	1	theorem	theorem	ADJ
ejpam-2366	458	2	15	15	NUM
ejpam-2366	458	3	.	.	PUNCT
ejpam-2366	459	1	let	let	VERB
ejpam-2366	459	2	m	m	PRON
ejpam-2366	459	3	be	be	AUX
ejpam-2366	459	4	a	a	DET
ejpam-2366	459	5	torsion	torsion	NOUN
ejpam-2366	459	6	free	free	ADJ
ejpam-2366	459	7	l	l	NOUN
ejpam-2366	459	8	-	-	NOUN
ejpam-2366	459	9	module	module	NOUN
ejpam-2366	459	10	and	and	CCONJ
ejpam-2366	459	11	om	om	PROPN
ejpam-2366	459	12	6=	6=	PROPN
ejpam-2366	459	13	n	n	CCONJ
ejpam-2366	459	14	<	<	X
ejpam-2366	459	15	i	i	PRON
ejpam-2366	459	16	m	m	VERB
ejpam-2366	459	17	be	be	VERB
ejpam-2366	459	18	a	a	DET
ejpam-2366	459	19	weak	weak	ADJ
ejpam-2366	459	20	join	join	NOUN
ejpam-2366	459	21	principal	principal	ADJ
ejpam-2366	459	22	element	element	NOUN
ejpam-2366	459	23	of	of	ADP
ejpam-2366	459	24	an	an	DET
ejpam-2366	459	25	l	l	NOUN
ejpam-2366	459	26	-	-	NOUN
ejpam-2366	459	27	module	module	NOUN
ejpam-2366	459	28	m	m	NOUN
ejpam-2366	459	29	.	.	PUNCT
ejpam-2366	460	1	then	then	ADV
ejpam-2366	460	2	n	n	PROPN
ejpam-2366	460	3	is	be	AUX
ejpam-2366	460	4	φ	φ	NOUN
ejpam-2366	460	5	-	-	NOUN
ejpam-2366	460	6	primary	primary	ADJ
ejpam-2366	460	7	for	for	ADP
ejpam-2366	460	8	some	some	DET
ejpam-2366	460	9	φ	φ	NUM
ejpam-2366	460	10	6	6	NUM
ejpam-2366	460	11	φ2	φ2	PROPN
ejpam-2366	460	12	if	if	SCONJ
ejpam-2366	460	13	and	and	CCONJ
ejpam-2366	460	14	only	only	ADV
ejpam-2366	460	15	if	if	SCONJ
ejpam-2366	460	16	n	n	PRON
ejpam-2366	460	17	is	be	AUX
ejpam-2366	460	18	primary	primary	ADJ
ejpam-2366	460	19	.	.	PUNCT
ejpam-2366	461	1	the	the	DET
ejpam-2366	461	2	following	follow	VERB
ejpam-2366	461	3	result	result	NOUN
ejpam-2366	461	4	shows	show	VERB
ejpam-2366	461	5	that	that	SCONJ
ejpam-2366	461	6	the	the	DET
ejpam-2366	461	7	theorem	theorem	NOUN
ejpam-2366	461	8	15	15	NUM
ejpam-2366	461	9	can	can	AUX
ejpam-2366	461	10	also	also	ADV
ejpam-2366	461	11	be	be	AUX
ejpam-2366	461	12	achieved	achieve	VERB
ejpam-2366	461	13	by	by	ADP
ejpam-2366	461	14	changing	change	VERB
ejpam-2366	461	15	the	the	DET
ejpam-2366	461	16	conditions	condition	NOUN
ejpam-2366	461	17	on	on	ADP
ejpam-2366	461	18	m	m	PROPN
ejpam-2366	461	19	and	and	CCONJ
ejpam-2366	461	20	l.	l.	PROPN
ejpam-2366	461	21	theorem	theorem	VERB
ejpam-2366	461	22	16	16	NUM
ejpam-2366	461	23	.	.	PUNCT
ejpam-2366	462	1	let	let	VERB
ejpam-2366	462	2	l	l	NOUN
ejpam-2366	462	3	be	be	AUX
ejpam-2366	462	4	a	a	DET
ejpam-2366	462	5	noether	noether	ADJ
ejpam-2366	462	6	pg	pg	NOUN
ejpam-2366	462	7	-	-	PUNCT
ejpam-2366	462	8	lattice	lattice	NOUN
ejpam-2366	462	9	and	and	CCONJ
ejpam-2366	462	10	m	m	AUX
ejpam-2366	462	11	be	be	AUX
ejpam-2366	462	12	a	a	DET
ejpam-2366	462	13	faithful	faithful	ADJ
ejpam-2366	462	14	multiplication	multiplication	NOUN
ejpam-2366	462	15	pg	pg	NOUN
ejpam-2366	462	16	-	-	PUNCT
ejpam-2366	462	17	lattice	lattice	NOUN
ejpam-2366	462	18	l	l	NOUN
ejpam-2366	462	19	-	-	NOUN
ejpam-2366	462	20	module	module	NOUN
ejpam-2366	462	21	with	with	ADP
ejpam-2366	462	22	i	i	PRON
ejpam-2366	462	23	m	m	VERB
ejpam-2366	462	24	compact	compact	ADJ
ejpam-2366	462	25	.	.	PUNCT
ejpam-2366	463	1	let	let	VERB
ejpam-2366	463	2	n	n	PRON
ejpam-2366	463	3	be	be	AUX
ejpam-2366	463	4	a	a	DET
ejpam-2366	463	5	proper	proper	ADJ
ejpam-2366	463	6	element	element	NOUN
ejpam-2366	463	7	of	of	ADP
ejpam-2366	463	8	m	m	PRON
ejpam-2366	463	9	such	such	ADJ
ejpam-2366	463	10	that	that	DET
ejpam-2366	463	11	0	0	NUM
ejpam-2366	464	1	6=	6=	NUM
ejpam-2366	464	2	(	(	PUNCT
ejpam-2366	464	3	n	n	X
ejpam-2366	464	4	:	:	PUNCT
ejpam-2366	464	5	i	i	PRON
ejpam-2366	464	6	m	m	VERB
ejpam-2366	464	7	)	)	PUNCT
ejpam-2366	464	8	∈	∈	PROPN
ejpam-2366	464	9	l	l	NOUN
ejpam-2366	464	10	satisfies	satisfy	VERB
ejpam-2366	464	11	the	the	DET
ejpam-2366	464	12	restricted	restricted	ADJ
ejpam-2366	464	13	cancellation	cancellation	NOUN
ejpam-2366	464	14	law	law	NOUN
ejpam-2366	464	15	(	(	PUNCT
ejpam-2366	464	16	rcl	rcl	NOUN
ejpam-2366	464	17	)	)	PUNCT
ejpam-2366	464	18	and	and	CCONJ
ejpam-2366	464	19	is	be	AUX
ejpam-2366	464	20	a	a	DET
ejpam-2366	464	21	non	non	ADJ
ejpam-2366	464	22	-	-	ADJ
ejpam-2366	464	23	nilpotent	nilpotent	ADJ
ejpam-2366	464	24	element	element	NOUN
ejpam-2366	464	25	.	.	PUNCT
ejpam-2366	465	1	then	then	ADV
ejpam-2366	465	2	n	n	PROPN
ejpam-2366	465	3	is	be	AUX
ejpam-2366	465	4	φ	φ	NOUN
ejpam-2366	465	5	-	-	NOUN
ejpam-2366	465	6	primary	primary	ADJ
ejpam-2366	465	7	for	for	ADP
ejpam-2366	465	8	some	some	DET
ejpam-2366	465	9	φ	φ	NUM
ejpam-2366	465	10	6	6	NUM
ejpam-2366	465	11	φ2	φ2	PROPN
ejpam-2366	465	12	if	if	SCONJ
ejpam-2366	465	13	and	and	CCONJ
ejpam-2366	465	14	only	only	ADV
ejpam-2366	465	15	if	if	SCONJ
ejpam-2366	465	16	n	n	PRON
ejpam-2366	465	17	is	be	AUX
ejpam-2366	465	18	primary	primary	ADJ
ejpam-2366	465	19	.	.	PUNCT
ejpam-2366	466	1	now	now	ADV
ejpam-2366	466	2	we	we	PRON
ejpam-2366	466	3	define	define	VERB
ejpam-2366	466	4	a	a	DET
ejpam-2366	466	5	2	2	NUM
ejpam-2366	466	6	-	-	PUNCT
ejpam-2366	466	7	potent	potent	ADJ
ejpam-2366	466	8	primary	primary	ADJ
ejpam-2366	466	9	element	element	NOUN
ejpam-2366	466	10	in	in	ADP
ejpam-2366	466	11	an	an	DET
ejpam-2366	466	12	l	l	NOUN
ejpam-2366	466	13	-	-	NOUN
ejpam-2366	466	14	module	module	NOUN
ejpam-2366	466	15	m	m	NOUN
ejpam-2366	466	16	.	.	PUNCT
ejpam-2366	467	1	definition	definition	NOUN
ejpam-2366	467	2	6	6	NUM
ejpam-2366	467	3	.	.	PUNCT
ejpam-2366	468	1	a	a	DET
ejpam-2366	468	2	proper	proper	ADJ
ejpam-2366	468	3	element	element	NOUN
ejpam-2366	468	4	n	n	PRON
ejpam-2366	468	5	∈	∈	NOUN
ejpam-2366	468	6	m	m	VERB
ejpam-2366	468	7	is	be	AUX
ejpam-2366	468	8	said	say	VERB
ejpam-2366	468	9	to	to	PART
ejpam-2366	468	10	be	be	AUX
ejpam-2366	468	11	2	2	NUM
ejpam-2366	468	12	-	-	PUNCT
ejpam-2366	468	13	potent	potent	ADJ
ejpam-2366	468	14	primary	primary	NOUN
ejpam-2366	468	15	if	if	SCONJ
ejpam-2366	468	16	for	for	ADP
ejpam-2366	468	17	all	all	DET
ejpam-2366	468	18	a	a	DET
ejpam-2366	468	19	∈	∈	PROPN
ejpam-2366	468	20	l	l	NOUN
ejpam-2366	468	21	,	,	PUNCT
ejpam-2366	468	22	a	a	DET
ejpam-2366	468	23	∈m	∈m	NOUN
ejpam-2366	468	24	,	,	PUNCT
ejpam-2366	468	25	aa	aa	NOUN
ejpam-2366	468	26	6	6	NUM
ejpam-2366	468	27	(	(	PUNCT
ejpam-2366	468	28	n	n	NUM
ejpam-2366	468	29	:	:	PUNCT
ejpam-2366	468	30	i	i	PRON
ejpam-2366	468	31	m	m	PROPN
ejpam-2366	468	32	)	)	PUNCT
ejpam-2366	468	33	n	n	PRON
ejpam-2366	468	34	implies	imply	VERB
ejpam-2366	468	35	either	either	CCONJ
ejpam-2366	468	36	a	a	DET
ejpam-2366	468	37	6	6	NUM
ejpam-2366	468	38	n	n	NOUN
ejpam-2366	468	39	or	or	CCONJ
ejpam-2366	468	40	am	be	AUX
ejpam-2366	468	41	6	6	NUM
ejpam-2366	468	42	(	(	PUNCT
ejpam-2366	468	43	n	n	NUM
ejpam-2366	468	44	:	:	PUNCT
ejpam-2366	468	45	i	i	PRON
ejpam-2366	468	46	m	m	VERB
ejpam-2366	468	47	)	)	PUNCT
ejpam-2366	468	48	for	for	ADP
ejpam-2366	468	49	some	some	DET
ejpam-2366	468	50	m	m	NOUN
ejpam-2366	468	51	∈	∈	NOUN
ejpam-2366	468	52	z+	z+	NUM
ejpam-2366	468	53	.	.	PUNCT
ejpam-2366	469	1	theorem	theorem	VERB
ejpam-2366	469	2	17	17	NUM
ejpam-2366	469	3	.	.	PUNCT
ejpam-2366	470	1	let	let	VERB
ejpam-2366	470	2	a	a	DET
ejpam-2366	470	3	proper	proper	ADJ
ejpam-2366	470	4	element	element	NOUN
ejpam-2366	470	5	n	n	PROPN
ejpam-2366	470	6	of	of	ADP
ejpam-2366	470	7	an	an	DET
ejpam-2366	470	8	l	l	NOUN
ejpam-2366	470	9	-	-	NOUN
ejpam-2366	470	10	module	module	NOUN
ejpam-2366	470	11	m	m	NOUN
ejpam-2366	470	12	be	be	VERB
ejpam-2366	470	13	2	2	NUM
ejpam-2366	470	14	-	-	PUNCT
ejpam-2366	470	15	potent	potent	ADJ
ejpam-2366	470	16	primary	primary	NOUN
ejpam-2366	470	17	.	.	PUNCT
ejpam-2366	471	1	then	then	ADV
ejpam-2366	471	2	n	n	PROPN
ejpam-2366	471	3	is	be	AUX
ejpam-2366	471	4	φ	φ	NOUN
ejpam-2366	471	5	-	-	NOUN
ejpam-2366	471	6	primary	primary	ADJ
ejpam-2366	471	7	for	for	ADP
ejpam-2366	471	8	some	some	DET
ejpam-2366	471	9	φ	φ	NUM
ejpam-2366	471	10	6	6	NUM
ejpam-2366	471	11	φ2	φ2	PROPN
ejpam-2366	471	12	if	if	SCONJ
ejpam-2366	471	13	and	and	CCONJ
ejpam-2366	471	14	only	only	ADV
ejpam-2366	471	15	if	if	SCONJ
ejpam-2366	471	16	n	n	PRON
ejpam-2366	471	17	is	be	AUX
ejpam-2366	471	18	primary	primary	ADJ
ejpam-2366	471	19	.	.	PUNCT
ejpam-2366	472	1	clearly	clearly	ADV
ejpam-2366	472	2	,	,	PUNCT
ejpam-2366	472	3	every	every	DET
ejpam-2366	472	4	2	2	NUM
ejpam-2366	472	5	-	-	PUNCT
ejpam-2366	472	6	potent	potent	ADJ
ejpam-2366	472	7	prime	prime	ADJ
ejpam-2366	472	8	element	element	NOUN
ejpam-2366	472	9	of	of	ADP
ejpam-2366	472	10	an	an	DET
ejpam-2366	472	11	l	l	NOUN
ejpam-2366	472	12	-	-	NOUN
ejpam-2366	472	13	module	module	NOUN
ejpam-2366	472	14	m	m	NOUN
ejpam-2366	472	15	is	be	AUX
ejpam-2366	472	16	2	2	NUM
ejpam-2366	472	17	-	-	PUNCT
ejpam-2366	472	18	potent	potent	ADJ
ejpam-2366	472	19	primary	primary	NOUN
ejpam-2366	472	20	.	.	PUNCT
ejpam-2366	473	1	theorem	theorem	NOUN
ejpam-2366	473	2	18	18	NUM
ejpam-2366	473	3	.	.	PUNCT
ejpam-2366	474	1	let	let	VERB
ejpam-2366	474	2	a	a	DET
ejpam-2366	474	3	proper	proper	ADJ
ejpam-2366	474	4	element	element	NOUN
ejpam-2366	474	5	n	n	PROPN
ejpam-2366	474	6	of	of	ADP
ejpam-2366	474	7	an	an	DET
ejpam-2366	474	8	l	l	NOUN
ejpam-2366	474	9	-	-	NOUN
ejpam-2366	474	10	module	module	NOUN
ejpam-2366	474	11	m	m	NOUN
ejpam-2366	474	12	be	be	VERB
ejpam-2366	474	13	2	2	NUM
ejpam-2366	474	14	-	-	PUNCT
ejpam-2366	474	15	potent	potent	ADJ
ejpam-2366	474	16	prime	prime	NOUN
ejpam-2366	474	17	.	.	PUNCT
ejpam-2366	475	1	then	then	ADV
ejpam-2366	475	2	n	n	PROPN
ejpam-2366	475	3	is	be	AUX
ejpam-2366	475	4	φ	φ	NOUN
ejpam-2366	475	5	-	-	NOUN
ejpam-2366	475	6	primary	primary	ADJ
ejpam-2366	475	7	for	for	ADP
ejpam-2366	475	8	some	some	DET
ejpam-2366	475	9	φ	φ	NUM
ejpam-2366	475	10	6	6	NUM
ejpam-2366	475	11	φ2	φ2	PROPN
ejpam-2366	475	12	if	if	SCONJ
ejpam-2366	475	13	and	and	CCONJ
ejpam-2366	475	14	only	only	ADV
ejpam-2366	475	15	if	if	SCONJ
ejpam-2366	475	16	n	n	PRON
ejpam-2366	475	17	is	be	AUX
ejpam-2366	475	18	primary	primary	ADJ
ejpam-2366	475	19	.	.	PUNCT
ejpam-2366	476	1	now	now	ADV
ejpam-2366	476	2	we	we	PRON
ejpam-2366	476	3	define	define	VERB
ejpam-2366	476	4	a	a	DET
ejpam-2366	476	5	n	n	ADV
ejpam-2366	476	6	-	-	PUNCT
ejpam-2366	476	7	potent	potent	ADJ
ejpam-2366	476	8	primary	primary	ADJ
ejpam-2366	476	9	element	element	NOUN
ejpam-2366	476	10	in	in	ADP
ejpam-2366	476	11	an	an	DET
ejpam-2366	476	12	l	l	NOUN
ejpam-2366	476	13	-	-	NOUN
ejpam-2366	476	14	module	module	NOUN
ejpam-2366	476	15	m	m	NOUN
ejpam-2366	476	16	where	where	SCONJ
ejpam-2366	476	17	n	n	X
ejpam-2366	476	18	>	>	X
ejpam-2366	476	19	2	2	X
ejpam-2366	476	20	.	.	PUNCT
ejpam-2366	476	21	definition	definition	NOUN
ejpam-2366	476	22	7	7	NUM
ejpam-2366	476	23	.	.	PUNCT
ejpam-2366	477	1	let	let	VERB
ejpam-2366	477	2	n	n	PRON
ejpam-2366	477	3	>	>	X
ejpam-2366	477	4	2	2	NUM
ejpam-2366	477	5	and	and	CCONJ
ejpam-2366	477	6	n	n	PRON
ejpam-2366	477	7	∈	∈	PROPN
ejpam-2366	477	8	z+	z+	NUM
ejpam-2366	477	9	.	.	PUNCT
ejpam-2366	478	1	a	a	DET
ejpam-2366	478	2	proper	proper	ADJ
ejpam-2366	478	3	element	element	NOUN
ejpam-2366	478	4	n	n	PRON
ejpam-2366	478	5	∈	∈	NOUN
ejpam-2366	478	6	m	m	VERB
ejpam-2366	478	7	is	be	AUX
ejpam-2366	478	8	said	say	VERB
ejpam-2366	478	9	to	to	PART
ejpam-2366	478	10	be	be	AUX
ejpam-2366	478	11	npotent	npotent	ADJ
ejpam-2366	478	12	primary	primary	ADJ
ejpam-2366	478	13	if	if	SCONJ
ejpam-2366	478	14	for	for	ADP
ejpam-2366	478	15	all	all	DET
ejpam-2366	478	16	a	a	DET
ejpam-2366	478	17	∈	∈	PROPN
ejpam-2366	478	18	l	l	NOUN
ejpam-2366	478	19	,	,	PUNCT
ejpam-2366	478	20	a	a	DET
ejpam-2366	478	21	∈	∈	NOUN
ejpam-2366	478	22	m	m	VERB
ejpam-2366	478	23	,	,	PUNCT
ejpam-2366	478	24	aa	aa	ADV
ejpam-2366	478	25	6	6	NUM
ejpam-2366	478	26	(	(	PUNCT
ejpam-2366	478	27	n	n	NUM
ejpam-2366	478	28	:	:	PUNCT
ejpam-2366	478	29	i	i	PRON
ejpam-2366	478	30	m	m	PROPN
ejpam-2366	478	31	)	)	PUNCT
ejpam-2366	478	32	n−1n	n−1n	NOUN
ejpam-2366	478	33	implies	imply	VERB
ejpam-2366	478	34	either	either	CCONJ
ejpam-2366	478	35	a	a	DET
ejpam-2366	478	36	6	6	NUM
ejpam-2366	478	37	n	n	NOUN
ejpam-2366	478	38	or	or	CCONJ
ejpam-2366	478	39	am	be	AUX
ejpam-2366	478	40	6	6	NUM
ejpam-2366	478	41	(	(	PUNCT
ejpam-2366	478	42	n	n	NUM
ejpam-2366	478	43	:	:	PUNCT
ejpam-2366	478	44	i	i	PRON
ejpam-2366	478	45	m	m	VERB
ejpam-2366	478	46	)	)	PUNCT
ejpam-2366	478	47	for	for	ADP
ejpam-2366	478	48	some	some	DET
ejpam-2366	478	49	m	m	NOUN
ejpam-2366	478	50	∈	∈	NOUN
ejpam-2366	478	51	z+	z+	NUM
ejpam-2366	478	52	.	.	PUNCT
ejpam-2366	479	1	theorem	theorem	VERB
ejpam-2366	479	2	19	19	NUM
ejpam-2366	479	3	.	.	PUNCT
ejpam-2366	480	1	a	a	DET
ejpam-2366	480	2	proper	proper	ADJ
ejpam-2366	480	3	element	element	NOUN
ejpam-2366	480	4	n	n	PROPN
ejpam-2366	480	5	of	of	ADP
ejpam-2366	480	6	an	an	DET
ejpam-2366	480	7	l	l	NOUN
ejpam-2366	480	8	-	-	NOUN
ejpam-2366	480	9	module	module	NOUN
ejpam-2366	480	10	m	m	NOUN
ejpam-2366	480	11	is	be	AUX
ejpam-2366	480	12	φ	φ	NOUN
ejpam-2366	480	13	-	-	NOUN
ejpam-2366	480	14	primary	primary	ADJ
ejpam-2366	480	15	for	for	ADP
ejpam-2366	480	16	some	some	DET
ejpam-2366	480	17	φ	φ	NOUN
ejpam-2366	480	18	6	6	NUM
ejpam-2366	480	19	φn	φn	ADP
ejpam-2366	480	20	where	where	SCONJ
ejpam-2366	480	21	n	n	X
ejpam-2366	480	22	>	>	X
ejpam-2366	480	23	2	2	NUM
ejpam-2366	480	24	if	if	SCONJ
ejpam-2366	480	25	and	and	CCONJ
ejpam-2366	480	26	only	only	ADV
ejpam-2366	480	27	if	if	SCONJ
ejpam-2366	480	28	n	n	PRON
ejpam-2366	480	29	is	be	AUX
ejpam-2366	480	30	primary	primary	ADJ
ejpam-2366	480	31	,	,	PUNCT
ejpam-2366	480	32	provided	provide	VERB
ejpam-2366	480	33	n	n	PRON
ejpam-2366	480	34	is	be	AUX
ejpam-2366	480	35	k	k	ADJ
ejpam-2366	480	36	-	-	PUNCT
ejpam-2366	480	37	potent	potent	ADJ
ejpam-2366	480	38	primary	primary	NOUN
ejpam-2366	480	39	for	for	ADP
ejpam-2366	480	40	some	some	DET
ejpam-2366	480	41	k	k	PROPN
ejpam-2366	480	42	6	6	NUM
ejpam-2366	480	43	n.	n.	NOUN
ejpam-2366	480	44	clearly	clearly	ADV
ejpam-2366	480	45	,	,	PUNCT
ejpam-2366	480	46	every	every	DET
ejpam-2366	480	47	n	n	CCONJ
ejpam-2366	480	48	-	-	PUNCT
ejpam-2366	480	49	potent	potent	ADJ
ejpam-2366	480	50	prime	prime	ADJ
ejpam-2366	480	51	element	element	NOUN
ejpam-2366	480	52	of	of	ADP
ejpam-2366	480	53	an	an	DET
ejpam-2366	480	54	l	l	NOUN
ejpam-2366	480	55	-	-	NOUN
ejpam-2366	480	56	module	module	NOUN
ejpam-2366	480	57	m	m	NOUN
ejpam-2366	480	58	is	be	AUX
ejpam-2366	480	59	n	n	CCONJ
ejpam-2366	480	60	-	-	PUNCT
ejpam-2366	480	61	potent	potent	ADJ
ejpam-2366	480	62	primary	primary	NOUN
ejpam-2366	480	63	.	.	PUNCT
ejpam-2366	481	1	theorem	theorem	NOUN
ejpam-2366	481	2	20	20	NUM
ejpam-2366	481	3	.	.	PUNCT
ejpam-2366	482	1	a	a	DET
ejpam-2366	482	2	proper	proper	ADJ
ejpam-2366	482	3	element	element	NOUN
ejpam-2366	482	4	n	n	PROPN
ejpam-2366	482	5	of	of	ADP
ejpam-2366	482	6	an	an	DET
ejpam-2366	482	7	l	l	NOUN
ejpam-2366	482	8	-	-	NOUN
ejpam-2366	482	9	module	module	NOUN
ejpam-2366	482	10	m	m	NOUN
ejpam-2366	482	11	is	be	AUX
ejpam-2366	482	12	φ	φ	NOUN
ejpam-2366	482	13	-	-	NOUN
ejpam-2366	482	14	primary	primary	ADJ
ejpam-2366	482	15	for	for	ADP
ejpam-2366	482	16	some	some	DET
ejpam-2366	482	17	φ	φ	NOUN
ejpam-2366	482	18	6	6	NUM
ejpam-2366	482	19	φn	φn	ADP
ejpam-2366	482	20	where	where	SCONJ
ejpam-2366	482	21	n	n	X
ejpam-2366	482	22	>	>	X
ejpam-2366	482	23	2	2	NUM
ejpam-2366	482	24	if	if	SCONJ
ejpam-2366	482	25	and	and	CCONJ
ejpam-2366	482	26	only	only	ADV
ejpam-2366	482	27	if	if	SCONJ
ejpam-2366	482	28	n	n	PRON
ejpam-2366	482	29	is	be	AUX
ejpam-2366	482	30	primary	primary	ADJ
ejpam-2366	482	31	,	,	PUNCT
ejpam-2366	482	32	provided	provide	VERB
ejpam-2366	482	33	n	n	PRON
ejpam-2366	482	34	is	be	AUX
ejpam-2366	482	35	k	k	ADJ
ejpam-2366	482	36	-	-	PUNCT
ejpam-2366	482	37	potent	potent	ADJ
ejpam-2366	482	38	prime	prime	NOUN
ejpam-2366	482	39	for	for	ADP
ejpam-2366	482	40	some	some	PRON
ejpam-2366	482	41	k	k	PROPN
ejpam-2366	482	42	6	6	NUM
ejpam-2366	482	43	n.	n.	NOUN
ejpam-2366	482	44	a.	a.	NOUN
ejpam-2366	483	1	v.	v.	PROPN
ejpam-2366	483	2	bingi	bingi	PROPN
ejpam-2366	483	3	,	,	PUNCT
ejpam-2366	483	4	c.	c.	PROPN
ejpam-2366	483	5	s.	s.	PROPN
ejpam-2366	483	6	manjarekar	manjarekar	PROPN
ejpam-2366	483	7	/	/	PROPN
ejpam-2366	483	8	eur	eur	PROPN
ejpam-2366	483	9	.	.	PUNCT
ejpam-2366	484	1	j.	j.	PROPN
ejpam-2366	484	2	pure	pure	PROPN
ejpam-2366	484	3	appl	appl	PROPN
ejpam-2366	484	4	.	.	PROPN
ejpam-2366	484	5	math	math	PROPN
ejpam-2366	484	6	,	,	PUNCT
ejpam-2366	484	7	14	14	NUM
ejpam-2366	484	8	(	(	PUNCT
ejpam-2366	484	9	2	2	NUM
ejpam-2366	484	10	)	)	PUNCT
ejpam-2366	484	11	(	(	PUNCT
ejpam-2366	484	12	2021	2021	NUM
ejpam-2366	484	13	)	)	PUNCT
ejpam-2366	484	14	,	,	PUNCT
ejpam-2366	484	15	551	551	NUM
ejpam-2366	484	16	-	-	SYM
ejpam-2366	484	17	577	577	NUM
ejpam-2366	484	18	564	564	NUM
ejpam-2366	484	19	the	the	DET
ejpam-2366	484	20	following	follow	VERB
ejpam-2366	484	21	corollary	corollary	NOUN
ejpam-2366	484	22	is	be	AUX
ejpam-2366	484	23	outcome	outcome	NOUN
ejpam-2366	484	24	of	of	ADP
ejpam-2366	484	25	theorems	theorem	NOUN
ejpam-2366	484	26	15	15	NUM
ejpam-2366	484	27	,	,	PUNCT
ejpam-2366	484	28	16	16	NUM
ejpam-2366	484	29	,	,	PUNCT
ejpam-2366	484	30	17	17	NUM
ejpam-2366	484	31	and	and	CCONJ
ejpam-2366	484	32	18	18	NUM
ejpam-2366	484	33	.	.	PUNCT
ejpam-2366	484	34	corollary	corollary	ADJ
ejpam-2366	484	35	13	13	NUM
ejpam-2366	484	36	.	.	PUNCT
ejpam-2366	485	1	an	an	DET
ejpam-2366	485	2	almost	almost	ADV
ejpam-2366	485	3	primary	primary	ADJ
ejpam-2366	485	4	element	element	NOUN
ejpam-2366	485	5	n	n	PROPN
ejpam-2366	485	6	of	of	ADP
ejpam-2366	485	7	an	an	DET
ejpam-2366	485	8	l	l	NOUN
ejpam-2366	485	9	-	-	NOUN
ejpam-2366	485	10	module	module	NOUN
ejpam-2366	485	11	m	m	NOUN
ejpam-2366	485	12	is	be	AUX
ejpam-2366	485	13	primary	primary	ADJ
ejpam-2366	485	14	if	if	SCONJ
ejpam-2366	485	15	one	one	NUM
ejpam-2366	485	16	the	the	DET
ejpam-2366	485	17	following	following	ADJ
ejpam-2366	485	18	statements	statement	NOUN
ejpam-2366	485	19	hold	hold	VERB
ejpam-2366	485	20	true	true	ADJ
ejpam-2366	485	21	:	:	PUNCT
ejpam-2366	485	22	(	(	PUNCT
ejpam-2366	485	23	i	i	NOUN
ejpam-2366	485	24	)	)	PUNCT
ejpam-2366	485	25	m	m	VERB
ejpam-2366	485	26	is	be	AUX
ejpam-2366	485	27	torsion	torsion	NOUN
ejpam-2366	485	28	free	free	ADJ
ejpam-2366	485	29	and	and	CCONJ
ejpam-2366	485	30	om	om	PROPN
ejpam-2366	485	31	6=	6=	PROPN
ejpam-2366	485	32	n	n	CCONJ
ejpam-2366	485	33	<	<	X
ejpam-2366	485	34	i	i	X
ejpam-2366	485	35	m	m	VERB
ejpam-2366	485	36	is	be	AUX
ejpam-2366	485	37	a	a	DET
ejpam-2366	485	38	weak	weak	ADJ
ejpam-2366	485	39	join	join	NOUN
ejpam-2366	485	40	principal	principal	ADJ
ejpam-2366	485	41	element	element	NOUN
ejpam-2366	485	42	.	.	PUNCT
ejpam-2366	486	1	(	(	PUNCT
ejpam-2366	486	2	ii	ii	NOUN
ejpam-2366	486	3	)	)	PUNCT
ejpam-2366	487	1	n	n	PRON
ejpam-2366	487	2	is	be	AUX
ejpam-2366	487	3	a	a	DET
ejpam-2366	487	4	2	2	NUM
ejpam-2366	487	5	-	-	PUNCT
ejpam-2366	487	6	potent	potent	ADJ
ejpam-2366	487	7	primary	primary	ADJ
ejpam-2366	487	8	element	element	NOUN
ejpam-2366	487	9	.	.	PUNCT
ejpam-2366	488	1	(	(	PUNCT
ejpam-2366	488	2	iii	iii	NOUN
ejpam-2366	488	3	)	)	PUNCT
ejpam-2366	489	1	n	n	PRON
ejpam-2366	489	2	is	be	AUX
ejpam-2366	489	3	a	a	DET
ejpam-2366	489	4	2	2	NUM
ejpam-2366	489	5	-	-	PUNCT
ejpam-2366	489	6	potent	potent	ADJ
ejpam-2366	489	7	prime	prime	ADJ
ejpam-2366	489	8	element	element	NOUN
ejpam-2366	489	9	.	.	PUNCT
ejpam-2366	490	1	(	(	PUNCT
ejpam-2366	490	2	iv	iv	X
ejpam-2366	490	3	)	)	PUNCT
ejpam-2366	490	4	l	l	NOUN
ejpam-2366	490	5	is	be	AUX
ejpam-2366	490	6	a	a	DET
ejpam-2366	490	7	noether	noether	ADJ
ejpam-2366	490	8	pg	pg	NOUN
ejpam-2366	490	9	-	-	PUNCT
ejpam-2366	490	10	lattice	lattice	PROPN
ejpam-2366	490	11	,	,	PUNCT
ejpam-2366	490	12	m	m	VERB
ejpam-2366	490	13	is	be	AUX
ejpam-2366	490	14	a	a	DET
ejpam-2366	490	15	faithful	faithful	ADJ
ejpam-2366	490	16	multiplication	multiplication	NOUN
ejpam-2366	490	17	pg	pg	NOUN
ejpam-2366	490	18	-	-	PUNCT
ejpam-2366	490	19	lattice	lattice	VERB
ejpam-2366	490	20	with	with	ADP
ejpam-2366	490	21	i	i	PRON
ejpam-2366	490	22	m	m	VERB
ejpam-2366	490	23	compact	compact	ADJ
ejpam-2366	490	24	,	,	PUNCT
ejpam-2366	490	25	0	0	NUM
ejpam-2366	490	26	6=	6=	NUM
ejpam-2366	490	27	(	(	PUNCT
ejpam-2366	490	28	n	n	X
ejpam-2366	490	29	:	:	PUNCT
ejpam-2366	490	30	i	i	PRON
ejpam-2366	490	31	m	m	VERB
ejpam-2366	490	32	)	)	PUNCT
ejpam-2366	490	33	∈	∈	PROPN
ejpam-2366	490	34	l	l	NOUN
ejpam-2366	490	35	satisfies	satisfy	VERB
ejpam-2366	490	36	the	the	DET
ejpam-2366	490	37	restricted	restricted	ADJ
ejpam-2366	490	38	cancellation	cancellation	NOUN
ejpam-2366	490	39	law	law	NOUN
ejpam-2366	490	40	(	(	PUNCT
ejpam-2366	490	41	rcl	rcl	NOUN
ejpam-2366	490	42	)	)	PUNCT
ejpam-2366	490	43	and	and	CCONJ
ejpam-2366	490	44	is	be	AUX
ejpam-2366	490	45	a	a	DET
ejpam-2366	490	46	nonnilpotent	nonnilpotent	ADJ
ejpam-2366	490	47	element	element	NOUN
ejpam-2366	490	48	.	.	PUNCT
ejpam-2366	491	1	from	from	ADP
ejpam-2366	491	2	the	the	DET
ejpam-2366	491	3	following	following	ADJ
ejpam-2366	491	4	examples	example	NOUN
ejpam-2366	491	5	,	,	PUNCT
ejpam-2366	491	6	it	it	PRON
ejpam-2366	491	7	is	be	AUX
ejpam-2366	491	8	clear	clear	ADJ
ejpam-2366	491	9	that	that	SCONJ
ejpam-2366	491	10	,	,	PUNCT
ejpam-2366	491	11	an	an	DET
ejpam-2366	491	12	almost	almost	ADV
ejpam-2366	491	13	primary	primary	ADJ
ejpam-2366	491	14	element	element	NOUN
ejpam-2366	491	15	of	of	ADP
ejpam-2366	491	16	an	an	DET
ejpam-2366	491	17	l	l	NOUN
ejpam-2366	491	18	module	module	NOUN
ejpam-2366	491	19	m	m	PRON
ejpam-2366	491	20	need	need	AUX
ejpam-2366	491	21	not	not	PART
ejpam-2366	491	22	be	be	AUX
ejpam-2366	491	23	2	2	NUM
ejpam-2366	491	24	-	-	PUNCT
ejpam-2366	491	25	potent	potent	ADJ
ejpam-2366	491	26	prime	prime	NOUN
ejpam-2366	491	27	and	and	CCONJ
ejpam-2366	491	28	a	a	DET
ejpam-2366	491	29	2	2	NUM
ejpam-2366	491	30	-	-	PUNCT
ejpam-2366	491	31	potent	potent	ADJ
ejpam-2366	491	32	prime	prime	ADJ
ejpam-2366	491	33	element	element	NOUN
ejpam-2366	491	34	of	of	ADP
ejpam-2366	491	35	an	an	DET
ejpam-2366	491	36	l	l	NOUN
ejpam-2366	491	37	module	module	NOUN
ejpam-2366	491	38	m	m	VERB
ejpam-2366	491	39	which	which	PRON
ejpam-2366	491	40	is	be	AUX
ejpam-2366	491	41	almost	almost	ADV
ejpam-2366	491	42	primary	primary	ADJ
ejpam-2366	491	43	need	need	AUX
ejpam-2366	491	44	not	not	PART
ejpam-2366	491	45	be	be	AUX
ejpam-2366	491	46	prime	prime	ADJ
ejpam-2366	491	47	.	.	PUNCT
ejpam-2366	491	48	example	example	NOUN
ejpam-2366	492	1	5	5	NUM
ejpam-2366	492	2	.	.	PUNCT
ejpam-2366	492	3	consider	consider	VERB
ejpam-2366	492	4	the	the	DET
ejpam-2366	492	5	lattice	lattice	NOUN
ejpam-2366	492	6	module	module	NOUN
ejpam-2366	492	7	as	as	ADP
ejpam-2366	492	8	in	in	ADP
ejpam-2366	492	9	example	example	NOUN
ejpam-2366	492	10	4	4	X
ejpam-2366	492	11	.	.	PUNCT
ejpam-2366	493	1	let	let	VERB
ejpam-2366	493	2	n	n	PRON
ejpam-2366	493	3	be	be	AUX
ejpam-2366	493	4	the	the	DET
ejpam-2366	493	5	cyclic	cyclic	ADJ
ejpam-2366	493	6	submodule	submodule	NOUN
ejpam-2366	493	7	of	of	ADP
ejpam-2366	493	8	m	m	AUX
ejpam-2366	493	9	generated	generate	VERB
ejpam-2366	493	10	by	by	ADP
ejpam-2366	493	11	6	6	NUM
ejpam-2366	493	12	.	.	PUNCT
ejpam-2366	494	1	it	it	PRON
ejpam-2366	494	2	is	be	AUX
ejpam-2366	494	3	easy	easy	ADJ
ejpam-2366	494	4	to	to	PART
ejpam-2366	494	5	see	see	VERB
ejpam-2366	494	6	that	that	SCONJ
ejpam-2366	494	7	the	the	DET
ejpam-2366	494	8	element	element	NOUN
ejpam-2366	494	9	n	n	NOUN
ejpam-2366	494	10	=	=	NOUN
ejpam-2366	494	11	<	<	X
ejpam-2366	494	12	6	6	NUM
ejpam-2366	494	13	>	>	X
ejpam-2366	494	14	is	be	AUX
ejpam-2366	494	15	almost	almost	ADV
ejpam-2366	494	16	primary	primary	ADJ
ejpam-2366	494	17	but	but	CCONJ
ejpam-2366	494	18	not	not	PART
ejpam-2366	494	19	2	2	NUM
ejpam-2366	494	20	-	-	PUNCT
ejpam-2366	494	21	potent	potent	ADJ
ejpam-2366	494	22	prime	prime	NOUN
ejpam-2366	494	23	.	.	PUNCT
ejpam-2366	494	24	example	example	NOUN
ejpam-2366	495	1	6	6	NUM
ejpam-2366	495	2	.	.	PUNCT
ejpam-2366	496	1	if	if	SCONJ
ejpam-2366	496	2	z	z	NOUN
ejpam-2366	496	3	is	be	AUX
ejpam-2366	496	4	the	the	DET
ejpam-2366	496	5	ring	ring	NOUN
ejpam-2366	496	6	of	of	ADP
ejpam-2366	496	7	integers	integer	NOUN
ejpam-2366	496	8	,	,	PUNCT
ejpam-2366	496	9	then	then	ADV
ejpam-2366	496	10	z8	z8	NOUN
ejpam-2366	496	11	is	be	AUX
ejpam-2366	496	12	a	a	DET
ejpam-2366	496	13	z−module	z−module	NOUN
ejpam-2366	496	14	.	.	PUNCT
ejpam-2366	497	1	assume	assume	VERB
ejpam-2366	497	2	that	that	SCONJ
ejpam-2366	497	3	(	(	PUNCT
ejpam-2366	497	4	k	k	X
ejpam-2366	497	5	)	)	PUNCT
ejpam-2366	497	6	denotes	denote	VERB
ejpam-2366	497	7	the	the	DET
ejpam-2366	497	8	cyclic	cyclic	ADJ
ejpam-2366	497	9	ideal	ideal	NOUN
ejpam-2366	497	10	of	of	ADP
ejpam-2366	497	11	z	z	PROPN
ejpam-2366	497	12	generated	generate	VERB
ejpam-2366	497	13	by	by	ADP
ejpam-2366	497	14	k	k	PROPN
ejpam-2366	497	15	∈	∈	PROPN
ejpam-2366	497	16	z	z	PROPN
ejpam-2366	497	17	and	and	CCONJ
ejpam-2366	497	18	<	<	X
ejpam-2366	497	19	t	t	X
ejpam-2366	497	20	>	>	X
ejpam-2366	497	21	denotes	denote	VERB
ejpam-2366	497	22	the	the	DET
ejpam-2366	497	23	cyclic	cyclic	PROPN
ejpam-2366	497	24	submodule	submodule	NOUN
ejpam-2366	497	25	of	of	ADP
ejpam-2366	497	26	z−module	z−module	PROPN
ejpam-2366	497	27	z8	z8	NOUN
ejpam-2366	497	28	where	where	SCONJ
ejpam-2366	497	29	t	t	PROPN
ejpam-2366	497	30	∈	∈	PROPN
ejpam-2366	497	31	z8	z8	PROPN
ejpam-2366	497	32	.	.	PUNCT
ejpam-2366	498	1	suppose	suppose	VERB
ejpam-2366	498	2	that	that	SCONJ
ejpam-2366	498	3	l	l	NOUN
ejpam-2366	498	4	=	=	SYM
ejpam-2366	498	5	l(z	l(z	NOUN
ejpam-2366	498	6	)	)	PUNCT
ejpam-2366	498	7	is	be	AUX
ejpam-2366	498	8	the	the	DET
ejpam-2366	498	9	set	set	NOUN
ejpam-2366	498	10	of	of	ADP
ejpam-2366	498	11	all	all	DET
ejpam-2366	498	12	ideals	ideal	NOUN
ejpam-2366	498	13	of	of	ADP
ejpam-2366	498	14	z	z	NOUN
ejpam-2366	498	15	and	and	CCONJ
ejpam-2366	498	16	m	m	PROPN
ejpam-2366	498	17	=	=	ADJ
ejpam-2366	498	18	l(z8	l(z8	NOUN
ejpam-2366	498	19	)	)	PUNCT
ejpam-2366	498	20	is	be	AUX
ejpam-2366	498	21	the	the	DET
ejpam-2366	498	22	set	set	NOUN
ejpam-2366	498	23	of	of	ADP
ejpam-2366	498	24	all	all	DET
ejpam-2366	498	25	submodules	submodule	NOUN
ejpam-2366	498	26	of	of	ADP
ejpam-2366	498	27	z−module	z−module	PROPN
ejpam-2366	498	28	z8	z8	NOUN
ejpam-2366	498	29	.	.	PUNCT
ejpam-2366	499	1	the	the	DET
ejpam-2366	499	2	multiplication	multiplication	NOUN
ejpam-2366	499	3	between	between	ADP
ejpam-2366	499	4	elements	element	NOUN
ejpam-2366	499	5	of	of	ADP
ejpam-2366	499	6	l	l	NOUN
ejpam-2366	499	7	and	and	CCONJ
ejpam-2366	499	8	m	m	PROPN
ejpam-2366	499	9	is	be	AUX
ejpam-2366	499	10	given	give	VERB
ejpam-2366	499	11	by	by	ADP
ejpam-2366	499	12	(	(	PUNCT
ejpam-2366	499	13	ki	ki	PROPN
ejpam-2366	499	14	)	)	PUNCT
ejpam-2366	499	15	<	<	X
ejpam-2366	499	16	tj	tj	X
ejpam-2366	499	17	>	>	PUNCT
ejpam-2366	499	18	=	=	X
ejpam-2366	499	19	<	<	X
ejpam-2366	499	20	kitj	kitj	X
ejpam-2366	499	21	>	>	X
ejpam-2366	499	22	for	for	ADP
ejpam-2366	499	23	every	every	DET
ejpam-2366	499	24	(	(	PUNCT
ejpam-2366	499	25	ki	ki	PROPN
ejpam-2366	499	26	)	)	PUNCT
ejpam-2366	499	27	∈	∈	PROPN
ejpam-2366	499	28	l	l	NOUN
ejpam-2366	499	29	and	and	CCONJ
ejpam-2366	499	30	<	<	X
ejpam-2366	499	31	tj	tj	X
ejpam-2366	499	32	>	>	X
ejpam-2366	499	33	∈m	∈m	NOUN
ejpam-2366	500	1	where	where	SCONJ
ejpam-2366	500	2	ki	ki	PROPN
ejpam-2366	500	3	,	,	PUNCT
ejpam-2366	500	4	tj	tj	PROPN
ejpam-2366	500	5	∈	∈	PROPN
ejpam-2366	500	6	z.	z.	PROPN
ejpam-2366	500	7	then	then	ADV
ejpam-2366	500	8	m	m	PROPN
ejpam-2366	500	9	is	be	AUX
ejpam-2366	500	10	a	a	DET
ejpam-2366	500	11	lattice	lattice	NOUN
ejpam-2366	500	12	module	module	NOUN
ejpam-2366	500	13	over	over	ADP
ejpam-2366	500	14	l.	l.	PROPN
ejpam-2366	500	15	let	let	VERB
ejpam-2366	500	16	n	n	PRON
ejpam-2366	500	17	be	be	AUX
ejpam-2366	500	18	the	the	DET
ejpam-2366	500	19	cyclic	cyclic	ADJ
ejpam-2366	500	20	submodule	submodule	NOUN
ejpam-2366	500	21	of	of	ADP
ejpam-2366	500	22	m	m	AUX
ejpam-2366	500	23	generated	generate	VERB
ejpam-2366	500	24	by	by	ADP
ejpam-2366	500	25	4	4	NUM
ejpam-2366	500	26	.	.	PUNCT
ejpam-2366	501	1	it	it	PRON
ejpam-2366	501	2	is	be	AUX
ejpam-2366	501	3	easy	easy	ADJ
ejpam-2366	501	4	to	to	PART
ejpam-2366	501	5	see	see	VERB
ejpam-2366	501	6	that	that	PRON
ejpam-2366	501	7	n	n	NOUN
ejpam-2366	501	8	=	=	NOUN
ejpam-2366	501	9	<	<	X
ejpam-2366	501	10	4	4	NUM
ejpam-2366	501	11	>	>	X
ejpam-2366	501	12	is	be	AUX
ejpam-2366	501	13	almost	almost	ADV
ejpam-2366	501	14	primary	primary	ADJ
ejpam-2366	501	15	(	(	PUNCT
ejpam-2366	501	16	φ2	φ2	NOUN
ejpam-2366	501	17	-	-	PUNCT
ejpam-2366	501	18	primary	primary	NOUN
ejpam-2366	501	19	)	)	PUNCT
ejpam-2366	501	20	and	and	CCONJ
ejpam-2366	501	21	2	2	NUM
ejpam-2366	501	22	-	-	PUNCT
ejpam-2366	501	23	potent	potent	ADJ
ejpam-2366	501	24	prime	prime	NOUN
ejpam-2366	501	25	but	but	CCONJ
ejpam-2366	501	26	not	not	PART
ejpam-2366	501	27	prime	prime	ADJ
ejpam-2366	501	28	.	.	PUNCT
ejpam-2366	502	1	theorem	theorem	PROPN
ejpam-2366	502	2	21	21	NUM
ejpam-2366	502	3	.	.	PUNCT
ejpam-2366	503	1	let	let	VERB
ejpam-2366	503	2	a	a	DET
ejpam-2366	503	3	proper	proper	ADJ
ejpam-2366	503	4	element	element	NOUN
ejpam-2366	503	5	n	n	PROPN
ejpam-2366	503	6	of	of	ADP
ejpam-2366	503	7	an	an	DET
ejpam-2366	503	8	l	l	NOUN
ejpam-2366	503	9	-	-	NOUN
ejpam-2366	503	10	module	module	NOUN
ejpam-2366	503	11	m	m	NOUN
ejpam-2366	503	12	be	be	VERB
ejpam-2366	503	13	φ	φ	VERB
ejpam-2366	503	14	-	-	NOUN
ejpam-2366	503	15	primary	primary	NOUN
ejpam-2366	503	16	.	.	PUNCT
ejpam-2366	504	1	if	if	SCONJ
ejpam-2366	504	2	φ(n	φ(n	NOUN
ejpam-2366	504	3	)	)	PUNCT
ejpam-2366	504	4	is	be	AUX
ejpam-2366	504	5	primary	primary	ADJ
ejpam-2366	504	6	,	,	PUNCT
ejpam-2366	504	7	then	then	ADV
ejpam-2366	504	8	n	n	PROPN
ejpam-2366	504	9	is	be	AUX
ejpam-2366	504	10	primary	primary	ADJ
ejpam-2366	504	11	.	.	PUNCT
ejpam-2366	505	1	theorem	theorem	PROPN
ejpam-2366	505	2	22	22	NUM
ejpam-2366	505	3	.	.	PUNCT
ejpam-2366	506	1	let	let	VERB
ejpam-2366	506	2	a	a	DET
ejpam-2366	506	3	proper	proper	ADJ
ejpam-2366	506	4	element	element	NOUN
ejpam-2366	506	5	n	n	PROPN
ejpam-2366	506	6	of	of	ADP
ejpam-2366	506	7	an	an	DET
ejpam-2366	506	8	l	l	NOUN
ejpam-2366	506	9	-	-	NOUN
ejpam-2366	506	10	module	module	NOUN
ejpam-2366	506	11	m	m	NOUN
ejpam-2366	506	12	be	be	VERB
ejpam-2366	506	13	φ	φ	VERB
ejpam-2366	506	14	-	-	NOUN
ejpam-2366	506	15	primary	primary	NOUN
ejpam-2366	506	16	.	.	PUNCT
ejpam-2366	507	1	if	if	SCONJ
ejpam-2366	507	2	(	(	PUNCT
ejpam-2366	507	3	n	n	X
ejpam-2366	507	4	:	:	PUNCT
ejpam-2366	507	5	i	i	PRON
ejpam-2366	507	6	m	m	VERB
ejpam-2366	507	7	)	)	PUNCT
ejpam-2366	507	8	n	n	PRON
ejpam-2366	507	9	φ(n	φ(n	NOUN
ejpam-2366	507	10	)	)	PUNCT
ejpam-2366	507	11	,	,	PUNCT
ejpam-2366	507	12	then	then	ADV
ejpam-2366	507	13	n	n	PROPN
ejpam-2366	507	14	is	be	AUX
ejpam-2366	507	15	primary	primary	ADJ
ejpam-2366	507	16	.	.	PUNCT
ejpam-2366	508	1	the	the	DET
ejpam-2366	508	2	consequences	consequence	NOUN
ejpam-2366	508	3	of	of	ADP
ejpam-2366	508	4	theorem	theorem	NOUN
ejpam-2366	508	5	22	22	NUM
ejpam-2366	508	6	are	be	AUX
ejpam-2366	508	7	presented	present	VERB
ejpam-2366	508	8	in	in	ADP
ejpam-2366	508	9	the	the	DET
ejpam-2366	508	10	form	form	NOUN
ejpam-2366	508	11	of	of	ADP
ejpam-2366	508	12	following	follow	VERB
ejpam-2366	508	13	corollaries	corollary	NOUN
ejpam-2366	508	14	.	.	PUNCT
ejpam-2366	509	1	corollary	corollary	ADJ
ejpam-2366	509	2	14	14	NUM
ejpam-2366	509	3	.	.	PUNCT
ejpam-2366	510	1	if	if	SCONJ
ejpam-2366	510	2	a	a	DET
ejpam-2366	510	3	proper	proper	ADJ
ejpam-2366	510	4	element	element	NOUN
ejpam-2366	510	5	n	n	NOUN
ejpam-2366	510	6	of	of	ADP
ejpam-2366	510	7	a	a	DET
ejpam-2366	510	8	multiplication	multiplication	NOUN
ejpam-2366	510	9	lattice	lattice	NOUN
ejpam-2366	510	10	l	l	NOUN
ejpam-2366	510	11	-	-	NOUN
ejpam-2366	510	12	module	module	NOUN
ejpam-2366	510	13	m	m	NOUN
ejpam-2366	510	14	is	be	AUX
ejpam-2366	510	15	φ	φ	VERB
ejpam-2366	510	16	-	-	ADJ
ejpam-2366	510	17	primary	primary	ADJ
ejpam-2366	510	18	but	but	CCONJ
ejpam-2366	510	19	not	not	PART
ejpam-2366	510	20	primary	primary	ADJ
ejpam-2366	510	21	,	,	PUNCT
ejpam-2366	510	22	then	then	ADV
ejpam-2366	510	23	(	(	PUNCT
ejpam-2366	510	24	n	n	X
ejpam-2366	510	25	:	:	PUNCT
ejpam-2366	510	26	i	i	PRON
ejpam-2366	510	27	m	m	NOUN
ejpam-2366	510	28	)	)	PUNCT
ejpam-2366	510	29	2im	2im	NOUN
ejpam-2366	510	30	6	6	NUM
ejpam-2366	510	31	φ(n	φ(n	NOUN
ejpam-2366	510	32	)	)	PUNCT
ejpam-2366	510	33	.	.	PUNCT
ejpam-2366	511	1	corollary	corollary	ADJ
ejpam-2366	511	2	15	15	NUM
ejpam-2366	511	3	.	.	PUNCT
ejpam-2366	512	1	if	if	SCONJ
ejpam-2366	512	2	a	a	DET
ejpam-2366	512	3	proper	proper	ADJ
ejpam-2366	512	4	element	element	NOUN
ejpam-2366	512	5	n	n	PROPN
ejpam-2366	512	6	of	of	ADP
ejpam-2366	512	7	an	an	DET
ejpam-2366	512	8	l	l	NOUN
ejpam-2366	512	9	-	-	NOUN
ejpam-2366	512	10	module	module	NOUN
ejpam-2366	512	11	m	m	NOUN
ejpam-2366	512	12	is	be	AUX
ejpam-2366	512	13	weakly	weakly	ADV
ejpam-2366	512	14	primary	primary	ADJ
ejpam-2366	512	15	such	such	ADJ
ejpam-2366	512	16	that	that	SCONJ
ejpam-2366	512	17	(	(	PUNCT
ejpam-2366	512	18	n	n	X
ejpam-2366	512	19	:	:	PUNCT
ejpam-2366	512	20	i	i	PRON
ejpam-2366	512	21	m	m	PROPN
ejpam-2366	512	22	)	)	PUNCT
ejpam-2366	512	23	n	n	PROPN
ejpam-2366	512	24	6=	6=	ADP
ejpam-2366	512	25	om	om	PROPN
ejpam-2366	512	26	,	,	PUNCT
ejpam-2366	512	27	then	then	ADV
ejpam-2366	512	28	n	n	PROPN
ejpam-2366	512	29	is	be	AUX
ejpam-2366	512	30	primary	primary	ADJ
ejpam-2366	512	31	.	.	PUNCT
ejpam-2366	513	1	corollary	corollary	ADJ
ejpam-2366	513	2	16	16	NUM
ejpam-2366	513	3	.	.	PUNCT
ejpam-2366	514	1	if	if	SCONJ
ejpam-2366	514	2	a	a	DET
ejpam-2366	514	3	proper	proper	ADJ
ejpam-2366	514	4	element	element	NOUN
ejpam-2366	514	5	n	n	PROPN
ejpam-2366	514	6	of	of	ADP
ejpam-2366	514	7	an	an	DET
ejpam-2366	514	8	l	l	NOUN
ejpam-2366	514	9	-	-	NOUN
ejpam-2366	514	10	module	module	NOUN
ejpam-2366	514	11	m	m	NOUN
ejpam-2366	514	12	is	be	AUX
ejpam-2366	514	13	φ	φ	VERB
ejpam-2366	514	14	-	-	ADJ
ejpam-2366	514	15	primary	primary	ADJ
ejpam-2366	514	16	such	such	ADJ
ejpam-2366	514	17	that	that	SCONJ
ejpam-2366	514	18	φ	φ	PROPN
ejpam-2366	514	19	6	6	NUM
ejpam-2366	514	20	φ3	φ3	NOUN
ejpam-2366	514	21	,	,	PUNCT
ejpam-2366	514	22	then	then	ADV
ejpam-2366	514	23	n	n	PROPN
ejpam-2366	514	24	is	be	AUX
ejpam-2366	514	25	ω	ω	NOUN
ejpam-2366	514	26	-	-	NOUN
ejpam-2366	514	27	primary	primary	NOUN
ejpam-2366	514	28	.	.	PUNCT
ejpam-2366	515	1	a.	a.	PROPN
ejpam-2366	515	2	v.	v.	PROPN
ejpam-2366	515	3	bingi	bingi	PROPN
ejpam-2366	515	4	,	,	PUNCT
ejpam-2366	515	5	c.	c.	PROPN
ejpam-2366	515	6	s.	s.	PROPN
ejpam-2366	515	7	manjarekar	manjarekar	PROPN
ejpam-2366	515	8	/	/	PROPN
ejpam-2366	515	9	eur	eur	PROPN
ejpam-2366	515	10	.	.	PUNCT
ejpam-2366	516	1	j.	j.	PROPN
ejpam-2366	516	2	pure	pure	PROPN
ejpam-2366	516	3	appl	appl	PROPN
ejpam-2366	516	4	.	.	PROPN
ejpam-2366	516	5	math	math	PROPN
ejpam-2366	516	6	,	,	PUNCT
ejpam-2366	516	7	14	14	NUM
ejpam-2366	516	8	(	(	PUNCT
ejpam-2366	516	9	2	2	NUM
ejpam-2366	516	10	)	)	PUNCT
ejpam-2366	516	11	(	(	PUNCT
ejpam-2366	516	12	2021	2021	NUM
ejpam-2366	516	13	)	)	PUNCT
ejpam-2366	516	14	,	,	PUNCT
ejpam-2366	516	15	551	551	NUM
ejpam-2366	516	16	-	-	SYM
ejpam-2366	516	17	577	577	NUM
ejpam-2366	516	18	565	565	NUM
ejpam-2366	516	19	corollary	corollary	ADJ
ejpam-2366	516	20	17	17	NUM
ejpam-2366	516	21	.	.	PUNCT
ejpam-2366	517	1	if	if	SCONJ
ejpam-2366	517	2	a	a	DET
ejpam-2366	517	3	proper	proper	ADJ
ejpam-2366	517	4	element	element	NOUN
ejpam-2366	517	5	n	n	NOUN
ejpam-2366	517	6	of	of	ADP
ejpam-2366	517	7	a	a	DET
ejpam-2366	517	8	multiplication	multiplication	NOUN
ejpam-2366	517	9	lattice	lattice	NOUN
ejpam-2366	517	10	l	l	NOUN
ejpam-2366	517	11	-	-	NOUN
ejpam-2366	517	12	module	module	NOUN
ejpam-2366	517	13	m	m	NOUN
ejpam-2366	517	14	is	be	AUX
ejpam-2366	517	15	φ	φ	VERB
ejpam-2366	517	16	-	-	ADJ
ejpam-2366	517	17	primary	primary	ADJ
ejpam-2366	517	18	but	but	CCONJ
ejpam-2366	517	19	not	not	PART
ejpam-2366	517	20	primary	primary	ADJ
ejpam-2366	517	21	,	,	PUNCT
ejpam-2366	517	22	then	then	ADV
ejpam-2366	517	23	√	√	VERB
ejpam-2366	517	24	n	n	NOUN
ejpam-2366	517	25	:	:	PUNCT
ejpam-2366	517	26	i	i	PRON
ejpam-2366	517	27	m	m	VERB
ejpam-2366	517	28	=	=	ADJ
ejpam-2366	517	29	√	√	ADP
ejpam-2366	517	30	φ(n	φ(n	NOUN
ejpam-2366	517	31	)	)	PUNCT
ejpam-2366	517	32	:	:	PUNCT
ejpam-2366	518	1	i	i	PRON
ejpam-2366	518	2	m	m	VERB
ejpam-2366	518	3	.	.	PUNCT
ejpam-2366	519	1	corollary	corollary	ADJ
ejpam-2366	519	2	18	18	NUM
ejpam-2366	519	3	.	.	PUNCT
ejpam-2366	520	1	if	if	SCONJ
ejpam-2366	520	2	a	a	DET
ejpam-2366	520	3	proper	proper	ADJ
ejpam-2366	520	4	element	element	NOUN
ejpam-2366	520	5	n	n	NOUN
ejpam-2366	520	6	of	of	ADP
ejpam-2366	520	7	a	a	DET
ejpam-2366	520	8	multiplication	multiplication	NOUN
ejpam-2366	520	9	lattice	lattice	NOUN
ejpam-2366	520	10	l	l	NOUN
ejpam-2366	520	11	-	-	NOUN
ejpam-2366	520	12	module	module	NOUN
ejpam-2366	520	13	m	m	NOUN
ejpam-2366	520	14	is	be	AUX
ejpam-2366	520	15	φ	φ	VERB
ejpam-2366	520	16	-	-	NOUN
ejpam-2366	520	17	primary	primary	ADJ
ejpam-2366	520	18	,	,	PUNCT
ejpam-2366	520	19	then	then	ADV
ejpam-2366	520	20	either	either	CCONJ
ejpam-2366	520	21	√	√	ADP
ejpam-2366	520	22	φ(n	φ(n	NOUN
ejpam-2366	520	23	)	)	PUNCT
ejpam-2366	520	24	:	:	PUNCT
ejpam-2366	521	1	i	i	PRON
ejpam-2366	521	2	m	m	VERB
ejpam-2366	521	3	6	6	NUM
ejpam-2366	521	4	(	(	PUNCT
ejpam-2366	521	5	n	n	NUM
ejpam-2366	521	6	:	:	PUNCT
ejpam-2366	521	7	i	i	PRON
ejpam-2366	521	8	m	m	VERB
ejpam-2366	521	9	)	)	PUNCT
ejpam-2366	521	10	or	or	CCONJ
ejpam-2366	521	11	(	(	PUNCT
ejpam-2366	521	12	n	n	X
ejpam-2366	521	13	:	:	PUNCT
ejpam-2366	521	14	i	i	PRON
ejpam-2366	521	15	m	m	VERB
ejpam-2366	521	16	)	)	PUNCT
ejpam-2366	521	17	6	6	NUM
ejpam-2366	521	18	√	√	ADP
ejpam-2366	521	19	φ(n	φ(n	NOUN
ejpam-2366	521	20	)	)	PUNCT
ejpam-2366	521	21	:	:	PUNCT
ejpam-2366	522	1	i	i	PRON
ejpam-2366	522	2	m	m	VERB
ejpam-2366	522	3	.	.	PUNCT
ejpam-2366	523	1	theorem	theorem	ADJ
ejpam-2366	523	2	23	23	NUM
ejpam-2366	523	3	.	.	PUNCT
ejpam-2366	524	1	let	let	VERB
ejpam-2366	524	2	a	a	DET
ejpam-2366	524	3	proper	proper	ADJ
ejpam-2366	524	4	element	element	NOUN
ejpam-2366	524	5	n	n	PROPN
ejpam-2366	524	6	of	of	ADP
ejpam-2366	524	7	an	an	DET
ejpam-2366	524	8	l	l	NOUN
ejpam-2366	524	9	-	-	NOUN
ejpam-2366	524	10	module	module	NOUN
ejpam-2366	524	11	m	m	NOUN
ejpam-2366	524	12	be	be	VERB
ejpam-2366	524	13	φ	φ	VERB
ejpam-2366	524	14	-	-	NOUN
ejpam-2366	524	15	primary	primary	NOUN
ejpam-2366	524	16	.	.	PUNCT
ejpam-2366	525	1	if	if	SCONJ
ejpam-2366	525	2	(	(	PUNCT
ejpam-2366	525	3	√	√	NOUN
ejpam-2366	525	4	n	n	NOUN
ejpam-2366	525	5	:	:	PUNCT
ejpam-2366	525	6	i	i	PRON
ejpam-2366	525	7	m	m	VERB
ejpam-2366	525	8	)	)	PUNCT
ejpam-2366	525	9	n	n	PRON
ejpam-2366	525	10	φ(n	φ(n	NOUN
ejpam-2366	525	11	)	)	PUNCT
ejpam-2366	525	12	,	,	PUNCT
ejpam-2366	525	13	then	then	ADV
ejpam-2366	525	14	n	n	PROPN
ejpam-2366	525	15	is	be	AUX
ejpam-2366	525	16	primary	primary	ADJ
ejpam-2366	525	17	.	.	PUNCT
ejpam-2366	526	1	proof	proof	NOUN
ejpam-2366	526	2	.	.	PUNCT
ejpam-2366	527	1	just	just	ADV
ejpam-2366	527	2	mimic	mimic	VERB
ejpam-2366	527	3	the	the	DET
ejpam-2366	527	4	proof	proof	NOUN
ejpam-2366	527	5	of	of	ADP
ejpam-2366	527	6	theorem	theorem	ADJ
ejpam-2366	527	7	10	10	NUM
ejpam-2366	527	8	.	.	PUNCT
ejpam-2366	528	1	now	now	ADV
ejpam-2366	528	2	,	,	PUNCT
ejpam-2366	528	3	the	the	DET
ejpam-2366	528	4	interrelations	interrelation	NOUN
ejpam-2366	528	5	among	among	ADP
ejpam-2366	528	6	prime	prime	ADJ
ejpam-2366	528	7	,	,	PUNCT
ejpam-2366	528	8	primary	primary	ADJ
ejpam-2366	528	9	,	,	PUNCT
ejpam-2366	528	10	2	2	NUM
ejpam-2366	528	11	-	-	PUNCT
ejpam-2366	528	12	absorbing	absorbing	ADJ
ejpam-2366	528	13	and	and	CCONJ
ejpam-2366	528	14	2	2	NUM
ejpam-2366	528	15	-	-	PUNCT
ejpam-2366	528	16	absorbing	absorbing	ADJ
ejpam-2366	528	17	primary	primary	ADJ
ejpam-2366	528	18	elements	element	NOUN
ejpam-2366	528	19	of	of	ADP
ejpam-2366	528	20	an	an	DET
ejpam-2366	528	21	l	l	NOUN
ejpam-2366	528	22	-	-	NOUN
ejpam-2366	528	23	module	module	NOUN
ejpam-2366	528	24	m	m	NOUN
ejpam-2366	528	25	are	be	AUX
ejpam-2366	528	26	given	give	VERB
ejpam-2366	528	27	in	in	ADP
ejpam-2366	528	28	following	follow	VERB
ejpam-2366	528	29	theorems	theorem	NOUN
ejpam-2366	528	30	whose	whose	DET
ejpam-2366	528	31	proofs	proof	NOUN
ejpam-2366	528	32	being	be	AUX
ejpam-2366	528	33	obvious	obvious	ADJ
ejpam-2366	528	34	are	be	AUX
ejpam-2366	528	35	omitted	omit	VERB
ejpam-2366	528	36	.	.	PUNCT
ejpam-2366	529	1	theorem	theorem	VERB
ejpam-2366	529	2	24	24	NUM
ejpam-2366	529	3	.	.	PUNCT
ejpam-2366	530	1	every	every	DET
ejpam-2366	530	2	prime	prime	ADJ
ejpam-2366	530	3	element	element	NOUN
ejpam-2366	530	4	of	of	ADP
ejpam-2366	530	5	an	an	DET
ejpam-2366	530	6	l	l	NOUN
ejpam-2366	530	7	-	-	NOUN
ejpam-2366	530	8	module	module	NOUN
ejpam-2366	530	9	m	m	NOUN
ejpam-2366	530	10	is	be	AUX
ejpam-2366	530	11	primary	primary	ADJ
ejpam-2366	530	12	and	and	CCONJ
ejpam-2366	530	13	2	2	NUM
ejpam-2366	530	14	-	-	PUNCT
ejpam-2366	530	15	absorbing	absorbing	ADJ
ejpam-2366	530	16	.	.	PUNCT
ejpam-2366	531	1	theorem	theorem	NOUN
ejpam-2366	531	2	25	25	NUM
ejpam-2366	531	3	.	.	PUNCT
ejpam-2366	532	1	if	if	SCONJ
ejpam-2366	532	2	q	q	NOUN
ejpam-2366	532	3	is	be	AUX
ejpam-2366	532	4	a	a	DET
ejpam-2366	532	5	primary	primary	ADJ
ejpam-2366	532	6	element	element	NOUN
ejpam-2366	532	7	of	of	ADP
ejpam-2366	532	8	an	an	DET
ejpam-2366	532	9	l	l	NOUN
ejpam-2366	532	10	-	-	NOUN
ejpam-2366	532	11	module	module	NOUN
ejpam-2366	532	12	m	m	NOUN
ejpam-2366	532	13	,	,	PUNCT
ejpam-2366	532	14	then	then	ADV
ejpam-2366	532	15	√	√	VERB
ejpam-2366	532	16	q	q	NOUN
ejpam-2366	532	17	:	:	PUNCT
ejpam-2366	532	18	i	i	PRON
ejpam-2366	532	19	m	m	VERB
ejpam-2366	532	20	is	be	AUX
ejpam-2366	532	21	a	a	DET
ejpam-2366	532	22	prime	prime	ADJ
ejpam-2366	532	23	element	element	NOUN
ejpam-2366	532	24	and	and	CCONJ
ejpam-2366	532	25	hence	hence	ADV
ejpam-2366	532	26	a	a	DET
ejpam-2366	532	27	2	2	NUM
ejpam-2366	532	28	-	-	PUNCT
ejpam-2366	532	29	absorbing	absorbing	ADJ
ejpam-2366	532	30	element	element	NOUN
ejpam-2366	532	31	of	of	ADP
ejpam-2366	532	32	l.	l.	PROPN
ejpam-2366	532	33	also	also	ADV
ejpam-2366	532	34	,	,	PUNCT
ejpam-2366	532	35	it	it	PRON
ejpam-2366	532	36	is	be	AUX
ejpam-2366	532	37	a	a	DET
ejpam-2366	532	38	2	2	NUM
ejpam-2366	532	39	-	-	PUNCT
ejpam-2366	532	40	absorbing	absorbing	ADJ
ejpam-2366	532	41	primary	primary	ADJ
ejpam-2366	532	42	element	element	NOUN
ejpam-2366	532	43	of	of	ADP
ejpam-2366	532	44	l.	l.	PROPN
ejpam-2366	532	45	theorem	theorem	PROPN
ejpam-2366	532	46	26	26	NUM
ejpam-2366	532	47	.	.	PUNCT
ejpam-2366	533	1	if	if	SCONJ
ejpam-2366	533	2	q	q	NOUN
ejpam-2366	533	3	is	be	AUX
ejpam-2366	533	4	a	a	DET
ejpam-2366	533	5	2	2	NUM
ejpam-2366	533	6	-	-	PUNCT
ejpam-2366	533	7	absorbing	absorbing	ADJ
ejpam-2366	533	8	element	element	NOUN
ejpam-2366	533	9	of	of	ADP
ejpam-2366	533	10	an	an	DET
ejpam-2366	533	11	l	l	NOUN
ejpam-2366	533	12	-	-	NOUN
ejpam-2366	533	13	module	module	NOUN
ejpam-2366	533	14	m	m	NOUN
ejpam-2366	533	15	,	,	PUNCT
ejpam-2366	533	16	then	then	ADV
ejpam-2366	533	17	both	both	DET
ejpam-2366	533	18	√	√	ADJ
ejpam-2366	533	19	q	q	NOUN
ejpam-2366	533	20	:	:	PUNCT
ejpam-2366	534	1	i	i	PRON
ejpam-2366	534	2	m	m	VERB
ejpam-2366	534	3	and	and	CCONJ
ejpam-2366	534	4	(	(	PUNCT
ejpam-2366	534	5	q	q	NOUN
ejpam-2366	534	6	:	:	PUNCT
ejpam-2366	534	7	i	i	PRON
ejpam-2366	534	8	m	m	VERB
ejpam-2366	534	9	)	)	PUNCT
ejpam-2366	534	10	are	be	AUX
ejpam-2366	534	11	2	2	NUM
ejpam-2366	534	12	-	-	PUNCT
ejpam-2366	534	13	absorbing	absorbing	ADJ
ejpam-2366	534	14	elements	element	NOUN
ejpam-2366	534	15	of	of	ADP
ejpam-2366	534	16	l.	l.	PROPN
ejpam-2366	534	17	also	also	ADV
ejpam-2366	534	18	,	,	PUNCT
ejpam-2366	534	19	they	they	PRON
ejpam-2366	534	20	are	be	AUX
ejpam-2366	534	21	2	2	NUM
ejpam-2366	534	22	-	-	PUNCT
ejpam-2366	534	23	absorbing	absorbing	ADJ
ejpam-2366	534	24	primary	primary	ADJ
ejpam-2366	534	25	elements	element	NOUN
ejpam-2366	534	26	of	of	ADP
ejpam-2366	534	27	l.	l.	PROPN
ejpam-2366	534	28	theorem	theorem	PROPN
ejpam-2366	534	29	27	27	NUM
ejpam-2366	534	30	.	.	PUNCT
ejpam-2366	535	1	let	let	VERB
ejpam-2366	535	2	l	l	NOUN
ejpam-2366	535	3	be	be	AUX
ejpam-2366	535	4	a	a	DET
ejpam-2366	535	5	pg	pg	NOUN
ejpam-2366	535	6	-	-	PUNCT
ejpam-2366	535	7	lattice	lattice	NOUN
ejpam-2366	535	8	and	and	CCONJ
ejpam-2366	535	9	m	m	AUX
ejpam-2366	535	10	be	be	AUX
ejpam-2366	535	11	a	a	DET
ejpam-2366	535	12	faithful	faithful	ADJ
ejpam-2366	535	13	multiplication	multiplication	NOUN
ejpam-2366	535	14	pg	pg	ADJ
ejpam-2366	535	15	-	-	PUNCT
ejpam-2366	535	16	lattice	lattice	NOUN
ejpam-2366	535	17	lmodule	lmodule	NOUN
ejpam-2366	535	18	with	with	ADP
ejpam-2366	535	19	i	i	PROPN
ejpam-2366	535	20	m	m	VERB
ejpam-2366	535	21	compact	compact	ADJ
ejpam-2366	535	22	.	.	PUNCT
ejpam-2366	536	1	if	if	SCONJ
ejpam-2366	536	2	q	q	NOUN
ejpam-2366	536	3	is	be	AUX
ejpam-2366	536	4	a	a	DET
ejpam-2366	536	5	2	2	NUM
ejpam-2366	536	6	-	-	PUNCT
ejpam-2366	536	7	absorbing	absorbing	ADJ
ejpam-2366	536	8	primary	primary	ADJ
ejpam-2366	536	9	element	element	NOUN
ejpam-2366	536	10	of	of	ADP
ejpam-2366	536	11	m	m	PROPN
ejpam-2366	536	12	,	,	PUNCT
ejpam-2366	536	13	then	then	ADV
ejpam-2366	536	14	(	(	PUNCT
ejpam-2366	536	15	q	q	NOUN
ejpam-2366	536	16	:	:	PUNCT
ejpam-2366	536	17	i	i	PRON
ejpam-2366	536	18	m	m	PROPN
ejpam-2366	536	19	)	)	PUNCT
ejpam-2366	536	20	is	be	AUX
ejpam-2366	536	21	a	a	DET
ejpam-2366	536	22	2	2	NUM
ejpam-2366	536	23	-	-	PUNCT
ejpam-2366	536	24	absorbing	absorbing	ADJ
ejpam-2366	536	25	primary	primary	ADJ
ejpam-2366	536	26	element	element	NOUN
ejpam-2366	536	27	of	of	ADP
ejpam-2366	536	28	l	l	NOUN
ejpam-2366	536	29	and	and	CCONJ
ejpam-2366	536	30	√	√	ADJ
ejpam-2366	536	31	q	q	NOUN
ejpam-2366	536	32	:	:	PUNCT
ejpam-2366	536	33	i	i	PRON
ejpam-2366	536	34	m	m	VERB
ejpam-2366	536	35	is	be	AUX
ejpam-2366	536	36	a	a	DET
ejpam-2366	536	37	2	2	NUM
ejpam-2366	536	38	-	-	PUNCT
ejpam-2366	536	39	absorbing	absorbing	ADJ
ejpam-2366	536	40	element	element	NOUN
ejpam-2366	536	41	of	of	ADP
ejpam-2366	536	42	l.	l.	PROPN
ejpam-2366	536	43	proof	proof	PROPN
ejpam-2366	536	44	.	.	PUNCT
ejpam-2366	537	1	let	let	VERB
ejpam-2366	537	2	abc	abc	PROPN
ejpam-2366	537	3	6	6	NUM
ejpam-2366	537	4	(	(	PUNCT
ejpam-2366	537	5	q	q	NOUN
ejpam-2366	537	6	:	:	PUNCT
ejpam-2366	537	7	i	i	PRON
ejpam-2366	537	8	m	m	VERB
ejpam-2366	537	9	)	)	PUNCT
ejpam-2366	537	10	for	for	ADP
ejpam-2366	537	11	a	a	DET
ejpam-2366	537	12	,	,	PUNCT
ejpam-2366	537	13	b	b	NOUN
ejpam-2366	537	14	,	,	PUNCT
ejpam-2366	537	15	c	c	PROPN
ejpam-2366	537	16	∈	∈	PROPN
ejpam-2366	537	17	l.	l.	NOUN
ejpam-2366	537	18	then	then	ADV
ejpam-2366	537	19	as	as	ADP
ejpam-2366	537	20	ab(cim	ab(cim	PROPN
ejpam-2366	537	21	)	)	PUNCT
ejpam-2366	537	22	6	6	NUM
ejpam-2366	537	23	q	q	NOUN
ejpam-2366	537	24	and	and	CCONJ
ejpam-2366	537	25	q	q	NOUN
ejpam-2366	537	26	is	be	AUX
ejpam-2366	537	27	a	a	DET
ejpam-2366	537	28	2	2	NUM
ejpam-2366	537	29	-	-	PUNCT
ejpam-2366	537	30	absorbing	absorbing	ADJ
ejpam-2366	537	31	primary	primary	ADJ
ejpam-2366	537	32	element	element	NOUN
ejpam-2366	537	33	of	of	ADP
ejpam-2366	537	34	m	m	PROPN
ejpam-2366	537	35	,	,	PUNCT
ejpam-2366	537	36	we	we	PRON
ejpam-2366	537	37	have	have	AUX
ejpam-2366	537	38	,	,	PUNCT
ejpam-2366	537	39	either	either	CCONJ
ejpam-2366	537	40	ab	ab	PROPN
ejpam-2366	537	41	6	6	NUM
ejpam-2366	537	42	(	(	PUNCT
ejpam-2366	537	43	q	q	NOUN
ejpam-2366	537	44	:	:	PUNCT
ejpam-2366	537	45	i	i	PRON
ejpam-2366	537	46	m	m	PROPN
ejpam-2366	537	47	)	)	PUNCT
ejpam-2366	537	48	or	or	CCONJ
ejpam-2366	537	49	a(cim	a(cim	PROPN
ejpam-2366	537	50	)	)	PUNCT
ejpam-2366	537	51	6	6	NUM
ejpam-2366	537	52	(	(	PUNCT
ejpam-2366	537	53	√	√	INTJ
ejpam-2366	537	54	q	q	NOUN
ejpam-2366	537	55	:	:	PUNCT
ejpam-2366	537	56	i	i	PRON
ejpam-2366	537	57	m	m	VERB
ejpam-2366	537	58	)	)	PUNCT
ejpam-2366	537	59	i	i	PRON
ejpam-2366	537	60	m	m	VERB
ejpam-2366	537	61	or	or	CCONJ
ejpam-2366	537	62	b(cim	b(cim	NOUN
ejpam-2366	537	63	)	)	PUNCT
ejpam-2366	537	64	6	6	NUM
ejpam-2366	537	65	(	(	PUNCT
ejpam-2366	537	66	√	√	INTJ
ejpam-2366	537	67	q	q	NOUN
ejpam-2366	537	68	:	:	PUNCT
ejpam-2366	537	69	i	i	PRON
ejpam-2366	537	70	m	m	VERB
ejpam-2366	537	71	)	)	PUNCT
ejpam-2366	537	72	i	i	PRON
ejpam-2366	537	73	m	m	VERB
ejpam-2366	537	74	.	.	PUNCT
ejpam-2366	538	1	since	since	SCONJ
ejpam-2366	538	2	i	i	PRON
ejpam-2366	538	3	m	m	VERB
ejpam-2366	538	4	is	be	AUX
ejpam-2366	538	5	compact	compact	ADJ
ejpam-2366	538	6	,	,	PUNCT
ejpam-2366	538	7	by	by	ADP
ejpam-2366	538	8	theorem	theorem	NOUN
ejpam-2366	538	9	5	5	NUM
ejpam-2366	538	10	of	of	ADP
ejpam-2366	538	11	[	[	X
ejpam-2366	538	12	10	10	NUM
ejpam-2366	538	13	]	]	PUNCT
ejpam-2366	538	14	,	,	PUNCT
ejpam-2366	538	15	it	it	PRON
ejpam-2366	538	16	follows	follow	VERB
ejpam-2366	538	17	that	that	SCONJ
ejpam-2366	538	18	,	,	PUNCT
ejpam-2366	538	19	either	either	CCONJ
ejpam-2366	538	20	ab	ab	PROPN
ejpam-2366	538	21	6	6	NUM
ejpam-2366	538	22	(	(	PUNCT
ejpam-2366	538	23	q	q	NOUN
ejpam-2366	538	24	:	:	PUNCT
ejpam-2366	538	25	i	i	PRON
ejpam-2366	538	26	m	m	VERB
ejpam-2366	538	27	)	)	PUNCT
ejpam-2366	538	28	or	or	CCONJ
ejpam-2366	538	29	ac	ac	ADV
ejpam-2366	538	30	6	6	NUM
ejpam-2366	538	31	√	√	PROPN
ejpam-2366	538	32	q	q	NOUN
ejpam-2366	538	33	:	:	PUNCT
ejpam-2366	538	34	i	i	PRON
ejpam-2366	538	35	m	m	VERB
ejpam-2366	538	36	or	or	CCONJ
ejpam-2366	538	37	bc	bc	PROPN
ejpam-2366	538	38	6	6	NUM
ejpam-2366	538	39	√	√	PROPN
ejpam-2366	539	1	q	q	NOUN
ejpam-2366	540	1	:	:	PUNCT
ejpam-2366	541	1	i	i	PRON
ejpam-2366	541	2	m	m	VERB
ejpam-2366	541	3	and	and	CCONJ
ejpam-2366	541	4	hence	hence	ADV
ejpam-2366	541	5	(	(	PUNCT
ejpam-2366	541	6	q	q	NOUN
ejpam-2366	541	7	:	:	PUNCT
ejpam-2366	541	8	i	i	PRON
ejpam-2366	541	9	m	m	PROPN
ejpam-2366	541	10	)	)	PUNCT
ejpam-2366	541	11	is	be	AUX
ejpam-2366	541	12	a	a	DET
ejpam-2366	541	13	2	2	NUM
ejpam-2366	541	14	-	-	PUNCT
ejpam-2366	541	15	absorbing	absorbing	ADJ
ejpam-2366	541	16	primary	primary	ADJ
ejpam-2366	541	17	element	element	NOUN
ejpam-2366	541	18	of	of	ADP
ejpam-2366	541	19	l.	l.	NOUN
ejpam-2366	541	20	by	by	ADP
ejpam-2366	541	21	theorem	theorem	VERB
ejpam-2366	541	22	2.4	2.4	NUM
ejpam-2366	541	23	in	in	ADP
ejpam-2366	541	24	[	[	X
ejpam-2366	541	25	18	18	NUM
ejpam-2366	541	26	]	]	PUNCT
ejpam-2366	541	27	,	,	PUNCT
ejpam-2366	541	28	it	it	PRON
ejpam-2366	541	29	follows	follow	VERB
ejpam-2366	541	30	that	that	PRON
ejpam-2366	541	31	√	√	PROPN
ejpam-2366	542	1	q	q	NOUN
ejpam-2366	542	2	:	:	PUNCT
ejpam-2366	542	3	i	i	PRON
ejpam-2366	542	4	m	m	VERB
ejpam-2366	542	5	is	be	AUX
ejpam-2366	542	6	a	a	DET
ejpam-2366	542	7	2	2	NUM
ejpam-2366	542	8	-	-	PUNCT
ejpam-2366	542	9	absorbing	absorbing	ADJ
ejpam-2366	542	10	element	element	NOUN
ejpam-2366	542	11	of	of	ADP
ejpam-2366	542	12	l.	l.	NOUN
ejpam-2366	542	13	by	by	ADP
ejpam-2366	542	14	relating	relate	VERB
ejpam-2366	542	15	the	the	DET
ejpam-2366	542	16	absorbing	absorbing	ADJ
ejpam-2366	542	17	concepts	concept	NOUN
ejpam-2366	542	18	with	with	ADP
ejpam-2366	542	19	φ	φ	NOUN
ejpam-2366	542	20	-	-	ADJ
ejpam-2366	542	21	prime	prime	NOUN
ejpam-2366	542	22	and	and	CCONJ
ejpam-2366	542	23	φ	φ	VERB
ejpam-2366	542	24	-	-	ADJ
ejpam-2366	542	25	primary	primary	ADJ
ejpam-2366	542	26	elements	element	NOUN
ejpam-2366	542	27	of	of	ADP
ejpam-2366	542	28	an	an	DET
ejpam-2366	542	29	lmodule	lmodule	NOUN
ejpam-2366	542	30	m	m	VERB
ejpam-2366	542	31	,	,	PUNCT
ejpam-2366	542	32	we	we	PRON
ejpam-2366	542	33	obtain	obtain	VERB
ejpam-2366	542	34	the	the	DET
ejpam-2366	542	35	following	follow	VERB
ejpam-2366	542	36	results	result	NOUN
ejpam-2366	542	37	.	.	PUNCT
ejpam-2366	543	1	theorem	theorem	NOUN
ejpam-2366	543	2	28	28	NUM
ejpam-2366	543	3	.	.	PUNCT
ejpam-2366	544	1	let	let	VERB
ejpam-2366	544	2	a	a	DET
ejpam-2366	544	3	proper	proper	ADJ
ejpam-2366	544	4	element	element	NOUN
ejpam-2366	544	5	n	n	PROPN
ejpam-2366	544	6	of	of	ADP
ejpam-2366	544	7	an	an	DET
ejpam-2366	544	8	l	l	NOUN
ejpam-2366	544	9	-	-	NOUN
ejpam-2366	544	10	module	module	NOUN
ejpam-2366	544	11	m	m	NOUN
ejpam-2366	544	12	be	be	VERB
ejpam-2366	544	13	φ	φ	VERB
ejpam-2366	544	14	-	-	NOUN
ejpam-2366	544	15	prime	prime	NOUN
ejpam-2366	544	16	.	.	PUNCT
ejpam-2366	545	1	if	if	SCONJ
ejpam-2366	545	2	(	(	PUNCT
ejpam-2366	545	3	n	n	X
ejpam-2366	545	4	:	:	PUNCT
ejpam-2366	545	5	i	i	PRON
ejpam-2366	545	6	m	m	VERB
ejpam-2366	545	7	)	)	PUNCT
ejpam-2366	545	8	n	n	PRON
ejpam-2366	545	9	φ(n	φ(n	NOUN
ejpam-2366	545	10	)	)	PUNCT
ejpam-2366	545	11	,	,	PUNCT
ejpam-2366	545	12	then	then	ADV
ejpam-2366	545	13	n	n	PRON
ejpam-2366	545	14	is	be	AUX
ejpam-2366	545	15	primary	primary	ADJ
ejpam-2366	545	16	and	and	CCONJ
ejpam-2366	545	17	2	2	NUM
ejpam-2366	545	18	-	-	PUNCT
ejpam-2366	545	19	absorbing	absorbing	ADJ
ejpam-2366	545	20	.	.	PUNCT
ejpam-2366	546	1	also	also	ADV
ejpam-2366	546	2	,	,	PUNCT
ejpam-2366	546	3	then	then	ADV
ejpam-2366	546	4	both	both	DET
ejpam-2366	546	5	√	√	ADJ
ejpam-2366	546	6	n	n	NOUN
ejpam-2366	546	7	:	:	PUNCT
ejpam-2366	546	8	i	i	PRON
ejpam-2366	546	9	m	m	VERB
ejpam-2366	546	10	and	and	CCONJ
ejpam-2366	546	11	(	(	PUNCT
ejpam-2366	546	12	n	n	X
ejpam-2366	546	13	:	:	PUNCT
ejpam-2366	546	14	i	i	PRON
ejpam-2366	546	15	m	m	VERB
ejpam-2366	546	16	)	)	PUNCT
ejpam-2366	546	17	are	be	AUX
ejpam-2366	546	18	2	2	NUM
ejpam-2366	546	19	-	-	PUNCT
ejpam-2366	546	20	absorbing	absorbing	ADJ
ejpam-2366	546	21	and	and	CCONJ
ejpam-2366	546	22	hence	hence	ADV
ejpam-2366	546	23	2	2	NUM
ejpam-2366	546	24	-	-	PUNCT
ejpam-2366	546	25	absorbing	absorbing	ADJ
ejpam-2366	546	26	primary	primary	ADJ
ejpam-2366	546	27	elements	element	NOUN
ejpam-2366	546	28	of	of	ADP
ejpam-2366	546	29	l.	l.	PROPN
ejpam-2366	546	30	proof	proof	PROPN
ejpam-2366	546	31	.	.	PUNCT
ejpam-2366	547	1	the	the	DET
ejpam-2366	547	2	proof	proof	NOUN
ejpam-2366	547	3	follows	follow	VERB
ejpam-2366	547	4	from	from	ADP
ejpam-2366	547	5	theorems	theorem	NOUN
ejpam-2366	547	6	10	10	NUM
ejpam-2366	547	7	,	,	PUNCT
ejpam-2366	547	8	24	24	NUM
ejpam-2366	547	9	and	and	CCONJ
ejpam-2366	547	10	26	26	NUM
ejpam-2366	547	11	.	.	PUNCT
ejpam-2366	548	1	clearly	clearly	ADV
ejpam-2366	548	2	,	,	PUNCT
ejpam-2366	548	3	every	every	DET
ejpam-2366	548	4	primary	primary	ADJ
ejpam-2366	548	5	element	element	NOUN
ejpam-2366	548	6	of	of	ADP
ejpam-2366	548	7	a	a	DET
ejpam-2366	548	8	multiplication	multiplication	NOUN
ejpam-2366	548	9	l	l	NOUN
ejpam-2366	548	10	-	-	NOUN
ejpam-2366	548	11	module	module	NOUN
ejpam-2366	548	12	m	m	NOUN
ejpam-2366	548	13	is	be	AUX
ejpam-2366	548	14	2	2	NUM
ejpam-2366	548	15	-	-	PUNCT
ejpam-2366	548	16	absorbing	absorb	VERB
ejpam-2366	548	17	primary	primary	NOUN
ejpam-2366	548	18	.	.	PUNCT
ejpam-2366	549	1	theorem	theorem	NOUN
ejpam-2366	549	2	29	29	NUM
ejpam-2366	549	3	.	.	PUNCT
ejpam-2366	550	1	let	let	VERB
ejpam-2366	550	2	a	a	DET
ejpam-2366	550	3	proper	proper	ADJ
ejpam-2366	550	4	element	element	NOUN
ejpam-2366	550	5	n	n	NOUN
ejpam-2366	550	6	of	of	ADP
ejpam-2366	550	7	a	a	DET
ejpam-2366	550	8	multiplication	multiplication	NOUN
ejpam-2366	550	9	l	l	NOUN
ejpam-2366	550	10	-	-	NOUN
ejpam-2366	550	11	module	module	NOUN
ejpam-2366	550	12	m	m	NOUN
ejpam-2366	550	13	be	be	VERB
ejpam-2366	550	14	φ	φ	VERB
ejpam-2366	550	15	-	-	NOUN
ejpam-2366	550	16	prime	prime	NOUN
ejpam-2366	550	17	.	.	PUNCT
ejpam-2366	551	1	if	if	SCONJ
ejpam-2366	551	2	(	(	PUNCT
ejpam-2366	551	3	n	n	X
ejpam-2366	551	4	:	:	PUNCT
ejpam-2366	551	5	i	i	PRON
ejpam-2366	551	6	m	m	VERB
ejpam-2366	551	7	)	)	PUNCT
ejpam-2366	551	8	n	n	PRON
ejpam-2366	551	9	φ(n	φ(n	NOUN
ejpam-2366	551	10	)	)	PUNCT
ejpam-2366	551	11	,	,	PUNCT
ejpam-2366	551	12	then	then	ADV
ejpam-2366	551	13	n	n	PROPN
ejpam-2366	551	14	is	be	AUX
ejpam-2366	551	15	2	2	NUM
ejpam-2366	551	16	-	-	PUNCT
ejpam-2366	551	17	absorbing	absorb	VERB
ejpam-2366	551	18	primary	primary	NOUN
ejpam-2366	551	19	.	.	PUNCT
ejpam-2366	552	1	also	also	ADV
ejpam-2366	552	2	,	,	PUNCT
ejpam-2366	552	3	then	then	ADV
ejpam-2366	552	4	(	(	PUNCT
ejpam-2366	552	5	n	n	X
ejpam-2366	552	6	:	:	PUNCT
ejpam-2366	552	7	i	i	PRON
ejpam-2366	552	8	m	m	PROPN
ejpam-2366	552	9	)	)	PUNCT
ejpam-2366	552	10	is	be	AUX
ejpam-2366	552	11	a	a	DET
ejpam-2366	552	12	2	2	NUM
ejpam-2366	552	13	-	-	PUNCT
ejpam-2366	552	14	absorbing	absorbing	ADJ
ejpam-2366	552	15	primary	primary	ADJ
ejpam-2366	552	16	element	element	NOUN
ejpam-2366	552	17	of	of	ADP
ejpam-2366	552	18	l	l	NOUN
ejpam-2366	552	19	provided	provide	VERB
ejpam-2366	552	20	m	m	VERB
ejpam-2366	552	21	is	be	AUX
ejpam-2366	552	22	a	a	DET
ejpam-2366	552	23	faithful	faithful	ADJ
ejpam-2366	552	24	pg	pg	NOUN
ejpam-2366	552	25	-	-	PUNCT
ejpam-2366	552	26	lattice	lattice	NOUN
ejpam-2366	552	27	with	with	ADP
ejpam-2366	552	28	i	i	PRON
ejpam-2366	552	29	m	m	VERB
ejpam-2366	552	30	compact	compact	ADJ
ejpam-2366	552	31	and	and	CCONJ
ejpam-2366	552	32	l	l	NOUN
ejpam-2366	552	33	as	as	ADP
ejpam-2366	552	34	a	a	DET
ejpam-2366	552	35	pg	pg	NOUN
ejpam-2366	552	36	-	-	PUNCT
ejpam-2366	552	37	lattice	lattice	NOUN
ejpam-2366	552	38	.	.	PUNCT
ejpam-2366	553	1	further	far	ADV
ejpam-2366	553	2	,	,	PUNCT
ejpam-2366	553	3	√	√	PROPN
ejpam-2366	553	4	n	n	NOUN
ejpam-2366	553	5	:	:	PUNCT
ejpam-2366	553	6	i	i	PRON
ejpam-2366	553	7	m	m	VERB
ejpam-2366	553	8	is	be	AUX
ejpam-2366	553	9	a	a	DET
ejpam-2366	553	10	2	2	NUM
ejpam-2366	553	11	-	-	PUNCT
ejpam-2366	553	12	absorbing	absorbing	ADJ
ejpam-2366	553	13	element	element	NOUN
ejpam-2366	553	14	of	of	ADP
ejpam-2366	553	15	l.	l.	PROPN
ejpam-2366	553	16	a.	a.	PROPN
ejpam-2366	553	17	v.	v.	PROPN
ejpam-2366	553	18	bingi	bingi	PROPN
ejpam-2366	553	19	,	,	PUNCT
ejpam-2366	553	20	c.	c.	PROPN
ejpam-2366	553	21	s.	s.	PROPN
ejpam-2366	553	22	manjarekar	manjarekar	PROPN
ejpam-2366	553	23	/	/	PROPN
ejpam-2366	553	24	eur	eur	PROPN
ejpam-2366	553	25	.	.	PUNCT
ejpam-2366	554	1	j.	j.	PROPN
ejpam-2366	554	2	pure	pure	PROPN
ejpam-2366	554	3	appl	appl	PROPN
ejpam-2366	554	4	.	.	PROPN
ejpam-2366	554	5	math	math	PROPN
ejpam-2366	554	6	,	,	PUNCT
ejpam-2366	554	7	14	14	NUM
ejpam-2366	554	8	(	(	PUNCT
ejpam-2366	554	9	2	2	NUM
ejpam-2366	554	10	)	)	PUNCT
ejpam-2366	554	11	(	(	PUNCT
ejpam-2366	554	12	2021	2021	NUM
ejpam-2366	554	13	)	)	PUNCT
ejpam-2366	554	14	,	,	PUNCT
ejpam-2366	554	15	551	551	NUM
ejpam-2366	554	16	-	-	SYM
ejpam-2366	554	17	577	577	NUM
ejpam-2366	554	18	566	566	NUM
ejpam-2366	554	19	proof	proof	NOUN
ejpam-2366	554	20	.	.	PUNCT
ejpam-2366	555	1	the	the	DET
ejpam-2366	555	2	proof	proof	NOUN
ejpam-2366	555	3	follows	follow	VERB
ejpam-2366	555	4	from	from	ADP
ejpam-2366	555	5	theorems	theorem	NOUN
ejpam-2366	555	6	10	10	NUM
ejpam-2366	555	7	,	,	PUNCT
ejpam-2366	555	8	24	24	NUM
ejpam-2366	555	9	and	and	CCONJ
ejpam-2366	555	10	27	27	NUM
ejpam-2366	555	11	.	.	PUNCT
ejpam-2366	556	1	theorem	theorem	NOUN
ejpam-2366	556	2	30	30	NUM
ejpam-2366	556	3	.	.	PUNCT
ejpam-2366	557	1	let	let	VERB
ejpam-2366	557	2	a	a	DET
ejpam-2366	557	3	proper	proper	ADJ
ejpam-2366	557	4	element	element	NOUN
ejpam-2366	557	5	n	n	NOUN
ejpam-2366	557	6	of	of	ADP
ejpam-2366	557	7	a	a	DET
ejpam-2366	557	8	multiplication	multiplication	NOUN
ejpam-2366	557	9	l	l	NOUN
ejpam-2366	557	10	-	-	NOUN
ejpam-2366	557	11	module	module	NOUN
ejpam-2366	557	12	m	m	NOUN
ejpam-2366	557	13	be	be	VERB
ejpam-2366	557	14	φ	φ	VERB
ejpam-2366	557	15	-	-	NOUN
ejpam-2366	557	16	primary	primary	NOUN
ejpam-2366	557	17	.	.	PUNCT
ejpam-2366	558	1	if	if	SCONJ
ejpam-2366	558	2	(	(	PUNCT
ejpam-2366	558	3	n	n	X
ejpam-2366	558	4	:	:	PUNCT
ejpam-2366	558	5	i	i	PRON
ejpam-2366	558	6	m	m	VERB
ejpam-2366	558	7	)	)	PUNCT
ejpam-2366	558	8	n	n	PRON
ejpam-2366	558	9	φ(n	φ(n	NOUN
ejpam-2366	558	10	)	)	PUNCT
ejpam-2366	558	11	,	,	PUNCT
ejpam-2366	558	12	then	then	ADV
ejpam-2366	558	13	n	n	PROPN
ejpam-2366	558	14	is	be	AUX
ejpam-2366	558	15	2	2	NUM
ejpam-2366	558	16	-	-	PUNCT
ejpam-2366	558	17	absorbing	absorb	VERB
ejpam-2366	558	18	primary	primary	NOUN
ejpam-2366	558	19	.	.	PUNCT
ejpam-2366	559	1	proof	proof	NOUN
ejpam-2366	559	2	.	.	PUNCT
ejpam-2366	560	1	the	the	DET
ejpam-2366	560	2	proof	proof	NOUN
ejpam-2366	560	3	follows	follow	VERB
ejpam-2366	560	4	from	from	ADP
ejpam-2366	560	5	theorem	theorem	ADJ
ejpam-2366	560	6	22	22	NUM
ejpam-2366	560	7	.	.	PUNCT
ejpam-2366	561	1	theorem	theorem	NOUN
ejpam-2366	561	2	31	31	NUM
ejpam-2366	561	3	.	.	PUNCT
ejpam-2366	562	1	let	let	VERB
ejpam-2366	562	2	l	l	NOUN
ejpam-2366	562	3	be	be	AUX
ejpam-2366	562	4	a	a	DET
ejpam-2366	562	5	pg	pg	NOUN
ejpam-2366	562	6	-	-	PUNCT
ejpam-2366	562	7	lattice	lattice	NOUN
ejpam-2366	562	8	and	and	CCONJ
ejpam-2366	562	9	m	m	AUX
ejpam-2366	562	10	be	be	AUX
ejpam-2366	562	11	a	a	DET
ejpam-2366	562	12	faithful	faithful	ADJ
ejpam-2366	562	13	multiplication	multiplication	NOUN
ejpam-2366	562	14	pg	pg	ADJ
ejpam-2366	562	15	-	-	PUNCT
ejpam-2366	562	16	lattice	lattice	NOUN
ejpam-2366	562	17	lmodule	lmodule	NOUN
ejpam-2366	562	18	with	with	ADP
ejpam-2366	562	19	i	i	PRON
ejpam-2366	562	20	m	m	VERB
ejpam-2366	562	21	compact	compact	ADJ
ejpam-2366	562	22	.	.	PUNCT
ejpam-2366	563	1	let	let	VERB
ejpam-2366	563	2	a	a	DET
ejpam-2366	563	3	proper	proper	ADJ
ejpam-2366	563	4	element	element	NOUN
ejpam-2366	563	5	n	n	PROPN
ejpam-2366	563	6	of	of	ADP
ejpam-2366	563	7	an	an	DET
ejpam-2366	563	8	l	l	NOUN
ejpam-2366	563	9	-	-	NOUN
ejpam-2366	563	10	module	module	NOUN
ejpam-2366	563	11	m	m	NOUN
ejpam-2366	563	12	be	be	VERB
ejpam-2366	563	13	φ	φ	VERB
ejpam-2366	563	14	-	-	NOUN
ejpam-2366	563	15	primary	primary	NOUN
ejpam-2366	563	16	.	.	PUNCT
ejpam-2366	564	1	if	if	SCONJ
ejpam-2366	564	2	(	(	PUNCT
ejpam-2366	564	3	n	n	X
ejpam-2366	564	4	:	:	PUNCT
ejpam-2366	564	5	i	i	PRON
ejpam-2366	564	6	m	m	VERB
ejpam-2366	564	7	)	)	PUNCT
ejpam-2366	564	8	n	n	PRON
ejpam-2366	564	9	φ(n	φ(n	NOUN
ejpam-2366	564	10	)	)	PUNCT
ejpam-2366	564	11	,	,	PUNCT
ejpam-2366	564	12	then	then	ADV
ejpam-2366	564	13	(	(	PUNCT
ejpam-2366	564	14	n	n	X
ejpam-2366	564	15	:	:	PUNCT
ejpam-2366	564	16	i	i	PRON
ejpam-2366	564	17	m	m	PROPN
ejpam-2366	564	18	)	)	PUNCT
ejpam-2366	564	19	is	be	AUX
ejpam-2366	564	20	a	a	DET
ejpam-2366	564	21	2	2	NUM
ejpam-2366	564	22	-	-	PUNCT
ejpam-2366	564	23	absorbing	absorbing	ADJ
ejpam-2366	564	24	primary	primary	ADJ
ejpam-2366	564	25	element	element	NOUN
ejpam-2366	564	26	of	of	ADP
ejpam-2366	564	27	l	l	PROPN
ejpam-2366	564	28	and	and	CCONJ
ejpam-2366	564	29	√	√	PROPN
ejpam-2366	564	30	n	n	NOUN
ejpam-2366	564	31	:	:	PUNCT
ejpam-2366	565	1	i	i	PRON
ejpam-2366	565	2	m	m	VERB
ejpam-2366	565	3	is	be	AUX
ejpam-2366	565	4	a	a	DET
ejpam-2366	565	5	2	2	NUM
ejpam-2366	565	6	-	-	PUNCT
ejpam-2366	565	7	absorbing	absorbing	ADJ
ejpam-2366	565	8	element	element	NOUN
ejpam-2366	565	9	of	of	ADP
ejpam-2366	565	10	l.	l.	PROPN
ejpam-2366	565	11	proof	proof	PROPN
ejpam-2366	565	12	.	.	PUNCT
ejpam-2366	566	1	the	the	DET
ejpam-2366	566	2	proof	proof	NOUN
ejpam-2366	566	3	follows	follow	VERB
ejpam-2366	566	4	from	from	ADP
ejpam-2366	566	5	theorems	theorem	NOUN
ejpam-2366	566	6	30	30	NUM
ejpam-2366	566	7	and	and	CCONJ
ejpam-2366	566	8	27	27	NUM
ejpam-2366	566	9	.	.	PUNCT
ejpam-2366	567	1	the	the	DET
ejpam-2366	567	2	following	follow	VERB
ejpam-2366	567	3	results	result	NOUN
ejpam-2366	567	4	are	be	AUX
ejpam-2366	567	5	obtained	obtain	VERB
ejpam-2366	567	6	by	by	ADP
ejpam-2366	567	7	relating	relate	VERB
ejpam-2366	567	8	the	the	DET
ejpam-2366	567	9	absorbing	absorbing	ADJ
ejpam-2366	567	10	concepts	concept	NOUN
ejpam-2366	567	11	with	with	ADP
ejpam-2366	567	12	almost	almost	ADV
ejpam-2366	567	13	prime	prime	ADJ
ejpam-2366	567	14	and	and	CCONJ
ejpam-2366	567	15	almost	almost	ADV
ejpam-2366	567	16	primary	primary	ADJ
ejpam-2366	567	17	elements	element	NOUN
ejpam-2366	567	18	of	of	ADP
ejpam-2366	567	19	an	an	DET
ejpam-2366	567	20	l	l	NOUN
ejpam-2366	567	21	-	-	NOUN
ejpam-2366	567	22	module	module	NOUN
ejpam-2366	567	23	m	m	NOUN
ejpam-2366	567	24	.	.	PUNCT
ejpam-2366	568	1	theorem	theorem	ADJ
ejpam-2366	568	2	32	32	NUM
ejpam-2366	568	3	.	.	PUNCT
ejpam-2366	569	1	let	let	VERB
ejpam-2366	569	2	m	m	PRON
ejpam-2366	569	3	be	be	AUX
ejpam-2366	569	4	a	a	DET
ejpam-2366	569	5	torsion	torsion	NOUN
ejpam-2366	569	6	free	free	ADJ
ejpam-2366	569	7	l	l	NOUN
ejpam-2366	569	8	-	-	NOUN
ejpam-2366	569	9	module	module	NOUN
ejpam-2366	569	10	and	and	CCONJ
ejpam-2366	569	11	om	om	PROPN
ejpam-2366	569	12	6=	6=	PROPN
ejpam-2366	569	13	n	n	CCONJ
ejpam-2366	569	14	<	<	X
ejpam-2366	569	15	i	i	PRON
ejpam-2366	569	16	m	m	VERB
ejpam-2366	569	17	be	be	VERB
ejpam-2366	569	18	a	a	DET
ejpam-2366	569	19	weak	weak	ADJ
ejpam-2366	569	20	join	join	NOUN
ejpam-2366	569	21	principal	principal	ADJ
ejpam-2366	569	22	element	element	NOUN
ejpam-2366	569	23	of	of	ADP
ejpam-2366	569	24	m	m	PROPN
ejpam-2366	569	25	.	.	PUNCT
ejpam-2366	570	1	if	if	SCONJ
ejpam-2366	570	2	n	n	PRON
ejpam-2366	570	3	is	be	AUX
ejpam-2366	570	4	almost	almost	ADV
ejpam-2366	570	5	prime	prime	ADJ
ejpam-2366	570	6	,	,	PUNCT
ejpam-2366	570	7	then	then	ADV
ejpam-2366	570	8	n	n	PRON
ejpam-2366	570	9	is	be	AUX
ejpam-2366	570	10	primary	primary	ADJ
ejpam-2366	570	11	and	and	CCONJ
ejpam-2366	570	12	2	2	NUM
ejpam-2366	570	13	-	-	PUNCT
ejpam-2366	570	14	absorbing	absorbing	ADJ
ejpam-2366	570	15	.	.	PUNCT
ejpam-2366	571	1	also	also	ADV
ejpam-2366	571	2	,	,	PUNCT
ejpam-2366	571	3	then	then	ADV
ejpam-2366	571	4	both	both	DET
ejpam-2366	571	5	√	√	ADJ
ejpam-2366	571	6	n	n	NOUN
ejpam-2366	571	7	:	:	PUNCT
ejpam-2366	571	8	i	i	PRON
ejpam-2366	571	9	m	m	VERB
ejpam-2366	571	10	and	and	CCONJ
ejpam-2366	571	11	(	(	PUNCT
ejpam-2366	571	12	n	n	X
ejpam-2366	571	13	:	:	PUNCT
ejpam-2366	571	14	i	i	PRON
ejpam-2366	571	15	m	m	VERB
ejpam-2366	571	16	)	)	PUNCT
ejpam-2366	571	17	are	be	AUX
ejpam-2366	571	18	2	2	NUM
ejpam-2366	571	19	-	-	PUNCT
ejpam-2366	571	20	absorbing	absorbing	ADJ
ejpam-2366	571	21	and	and	CCONJ
ejpam-2366	571	22	hence	hence	ADV
ejpam-2366	571	23	2	2	NUM
ejpam-2366	571	24	-	-	PUNCT
ejpam-2366	571	25	absorbing	absorbing	ADJ
ejpam-2366	571	26	primary	primary	ADJ
ejpam-2366	571	27	elements	element	NOUN
ejpam-2366	571	28	of	of	ADP
ejpam-2366	571	29	l.	l.	PROPN
ejpam-2366	571	30	proof	proof	PROPN
ejpam-2366	571	31	.	.	PUNCT
ejpam-2366	572	1	the	the	DET
ejpam-2366	572	2	proof	proof	NOUN
ejpam-2366	572	3	follows	follow	VERB
ejpam-2366	572	4	from	from	ADP
ejpam-2366	572	5	theorems	theorem	NOUN
ejpam-2366	572	6	5	5	NUM
ejpam-2366	572	7	,	,	PUNCT
ejpam-2366	572	8	24	24	NUM
ejpam-2366	572	9	and	and	CCONJ
ejpam-2366	572	10	26	26	NUM
ejpam-2366	572	11	.	.	PUNCT
ejpam-2366	573	1	theorem	theorem	VERB
ejpam-2366	573	2	33	33	NUM
ejpam-2366	573	3	.	.	PUNCT
ejpam-2366	574	1	let	let	VERB
ejpam-2366	574	2	m	m	PRON
ejpam-2366	574	3	be	be	AUX
ejpam-2366	574	4	a	a	PRON
ejpam-2366	574	5	torsion	torsion	NOUN
ejpam-2366	574	6	free	free	ADJ
ejpam-2366	574	7	,	,	PUNCT
ejpam-2366	574	8	multiplication	multiplication	NOUN
ejpam-2366	574	9	l	l	NOUN
ejpam-2366	574	10	-	-	NOUN
ejpam-2366	574	11	module	module	NOUN
ejpam-2366	574	12	and	and	CCONJ
ejpam-2366	574	13	om	om	PROPN
ejpam-2366	574	14	6=	6=	PROPN
ejpam-2366	574	15	n	n	CCONJ
ejpam-2366	574	16	<	<	X
ejpam-2366	575	1	i	i	PRON
ejpam-2366	575	2	m	m	AUX
ejpam-2366	575	3	be	be	VERB
ejpam-2366	575	4	a	a	DET
ejpam-2366	575	5	weak	weak	ADJ
ejpam-2366	575	6	join	join	NOUN
ejpam-2366	575	7	principal	principal	ADJ
ejpam-2366	575	8	element	element	NOUN
ejpam-2366	575	9	of	of	ADP
ejpam-2366	575	10	m	m	PROPN
ejpam-2366	575	11	.	.	PUNCT
ejpam-2366	576	1	if	if	SCONJ
ejpam-2366	576	2	n	n	PRON
ejpam-2366	576	3	is	be	AUX
ejpam-2366	576	4	almost	almost	ADV
ejpam-2366	576	5	prime	prime	ADJ
ejpam-2366	576	6	,	,	PUNCT
ejpam-2366	576	7	then	then	ADV
ejpam-2366	576	8	n	n	PROPN
ejpam-2366	576	9	is	be	AUX
ejpam-2366	576	10	2	2	NUM
ejpam-2366	576	11	-	-	PUNCT
ejpam-2366	576	12	absorbing	absorb	VERB
ejpam-2366	576	13	primary	primary	NOUN
ejpam-2366	576	14	.	.	PUNCT
ejpam-2366	577	1	also	also	ADV
ejpam-2366	577	2	,	,	PUNCT
ejpam-2366	577	3	then	then	ADV
ejpam-2366	577	4	(	(	PUNCT
ejpam-2366	577	5	n	n	X
ejpam-2366	577	6	:	:	PUNCT
ejpam-2366	577	7	i	i	PRON
ejpam-2366	577	8	m	m	PROPN
ejpam-2366	577	9	)	)	PUNCT
ejpam-2366	577	10	is	be	AUX
ejpam-2366	577	11	a	a	DET
ejpam-2366	577	12	2	2	NUM
ejpam-2366	577	13	-	-	PUNCT
ejpam-2366	577	14	absorbing	absorbing	ADJ
ejpam-2366	577	15	primary	primary	ADJ
ejpam-2366	577	16	element	element	NOUN
ejpam-2366	577	17	of	of	ADP
ejpam-2366	577	18	l	l	NOUN
ejpam-2366	577	19	provided	provide	VERB
ejpam-2366	577	20	m	m	VERB
ejpam-2366	577	21	is	be	AUX
ejpam-2366	577	22	a	a	DET
ejpam-2366	577	23	faithful	faithful	ADJ
ejpam-2366	577	24	pglattice	pglattice	NOUN
ejpam-2366	577	25	with	with	ADP
ejpam-2366	577	26	i	i	PRON
ejpam-2366	577	27	m	m	VERB
ejpam-2366	577	28	compact	compact	ADJ
ejpam-2366	577	29	and	and	CCONJ
ejpam-2366	577	30	l	l	NOUN
ejpam-2366	577	31	as	as	ADP
ejpam-2366	577	32	a	a	DET
ejpam-2366	577	33	pg	pg	NOUN
ejpam-2366	577	34	-	-	PUNCT
ejpam-2366	577	35	lattice	lattice	NOUN
ejpam-2366	577	36	.	.	PUNCT
ejpam-2366	578	1	further	far	ADV
ejpam-2366	578	2	,	,	PUNCT
ejpam-2366	578	3	√	√	PROPN
ejpam-2366	578	4	n	n	NOUN
ejpam-2366	578	5	:	:	PUNCT
ejpam-2366	578	6	i	i	PRON
ejpam-2366	578	7	m	m	VERB
ejpam-2366	578	8	is	be	AUX
ejpam-2366	578	9	a	a	DET
ejpam-2366	578	10	2	2	NUM
ejpam-2366	578	11	-	-	PUNCT
ejpam-2366	578	12	absorbing	absorbing	ADJ
ejpam-2366	578	13	element	element	NOUN
ejpam-2366	578	14	of	of	ADP
ejpam-2366	578	15	l.	l.	PROPN
ejpam-2366	578	16	proof	proof	PROPN
ejpam-2366	578	17	.	.	PUNCT
ejpam-2366	579	1	the	the	DET
ejpam-2366	579	2	proof	proof	NOUN
ejpam-2366	579	3	follows	follow	VERB
ejpam-2366	579	4	from	from	ADP
ejpam-2366	579	5	theorems	theorem	NOUN
ejpam-2366	579	6	5	5	NUM
ejpam-2366	579	7	,	,	PUNCT
ejpam-2366	579	8	24	24	NUM
ejpam-2366	579	9	and	and	CCONJ
ejpam-2366	579	10	27	27	NUM
ejpam-2366	579	11	.	.	PUNCT
ejpam-2366	580	1	theorem	theorem	VERB
ejpam-2366	580	2	34	34	NUM
ejpam-2366	580	3	.	.	PUNCT
ejpam-2366	581	1	let	let	VERB
ejpam-2366	581	2	m	m	PRON
ejpam-2366	581	3	be	be	AUX
ejpam-2366	581	4	a	a	PRON
ejpam-2366	581	5	torsion	torsion	NOUN
ejpam-2366	581	6	free	free	ADJ
ejpam-2366	581	7	,	,	PUNCT
ejpam-2366	581	8	multiplication	multiplication	NOUN
ejpam-2366	581	9	l	l	NOUN
ejpam-2366	581	10	-	-	NOUN
ejpam-2366	581	11	module	module	NOUN
ejpam-2366	581	12	and	and	CCONJ
ejpam-2366	581	13	om	om	PROPN
ejpam-2366	581	14	6=	6=	PROPN
ejpam-2366	581	15	n	n	CCONJ
ejpam-2366	581	16	<	<	X
ejpam-2366	582	1	i	i	PRON
ejpam-2366	582	2	m	m	AUX
ejpam-2366	582	3	be	be	VERB
ejpam-2366	582	4	a	a	DET
ejpam-2366	582	5	weak	weak	ADJ
ejpam-2366	582	6	join	join	NOUN
ejpam-2366	582	7	principal	principal	ADJ
ejpam-2366	582	8	element	element	NOUN
ejpam-2366	582	9	of	of	ADP
ejpam-2366	582	10	m	m	PROPN
ejpam-2366	582	11	.	.	PUNCT
ejpam-2366	583	1	if	if	SCONJ
ejpam-2366	583	2	n	n	PRON
ejpam-2366	583	3	is	be	AUX
ejpam-2366	583	4	almost	almost	ADV
ejpam-2366	583	5	primary	primary	ADJ
ejpam-2366	583	6	,	,	PUNCT
ejpam-2366	583	7	then	then	ADV
ejpam-2366	583	8	n	n	PROPN
ejpam-2366	583	9	is	be	AUX
ejpam-2366	583	10	2	2	NUM
ejpam-2366	583	11	-	-	PUNCT
ejpam-2366	583	12	absorbing	absorb	VERB
ejpam-2366	583	13	primary	primary	NOUN
ejpam-2366	583	14	.	.	PUNCT
ejpam-2366	584	1	proof	proof	NOUN
ejpam-2366	584	2	.	.	PUNCT
ejpam-2366	585	1	the	the	DET
ejpam-2366	585	2	proof	proof	NOUN
ejpam-2366	585	3	follows	follow	VERB
ejpam-2366	585	4	from	from	ADP
ejpam-2366	585	5	theorem	theorem	ADJ
ejpam-2366	585	6	15	15	NUM
ejpam-2366	585	7	.	.	PUNCT
ejpam-2366	586	1	theorem	theorem	VERB
ejpam-2366	586	2	35	35	NUM
ejpam-2366	586	3	.	.	PUNCT
ejpam-2366	587	1	let	let	VERB
ejpam-2366	587	2	m	m	PRON
ejpam-2366	587	3	be	be	AUX
ejpam-2366	587	4	a	a	DET
ejpam-2366	587	5	torsion	torsion	NOUN
ejpam-2366	587	6	free	free	ADJ
ejpam-2366	587	7	,	,	PUNCT
ejpam-2366	587	8	faithful	faithful	ADJ
ejpam-2366	587	9	,	,	PUNCT
ejpam-2366	587	10	multiplication	multiplication	NOUN
ejpam-2366	587	11	pg	pg	NOUN
ejpam-2366	587	12	-	-	PUNCT
ejpam-2366	587	13	lattice	lattice	NOUN
ejpam-2366	587	14	l	l	NOUN
ejpam-2366	587	15	-	-	NOUN
ejpam-2366	587	16	module	module	NOUN
ejpam-2366	587	17	with	with	ADP
ejpam-2366	587	18	i	i	PRON
ejpam-2366	587	19	m	m	VERB
ejpam-2366	587	20	compact	compact	ADJ
ejpam-2366	587	21	and	and	CCONJ
ejpam-2366	587	22	l	l	NOUN
ejpam-2366	587	23	be	be	AUX
ejpam-2366	587	24	a	a	DET
ejpam-2366	587	25	pg	pg	NOUN
ejpam-2366	587	26	-	-	PUNCT
ejpam-2366	587	27	lattice	lattice	NOUN
ejpam-2366	587	28	.	.	PUNCT
ejpam-2366	588	1	let	let	VERB
ejpam-2366	588	2	om	om	PROPN
ejpam-2366	588	3	6=	6=	PROPN
ejpam-2366	588	4	n	n	CCONJ
ejpam-2366	588	5	<	<	X
ejpam-2366	589	1	i	i	PRON
ejpam-2366	589	2	m	m	AUX
ejpam-2366	589	3	be	be	VERB
ejpam-2366	589	4	a	a	DET
ejpam-2366	589	5	weak	weak	ADJ
ejpam-2366	589	6	join	join	NOUN
ejpam-2366	589	7	principal	principal	ADJ
ejpam-2366	589	8	element	element	NOUN
ejpam-2366	589	9	of	of	ADP
ejpam-2366	589	10	m	m	PROPN
ejpam-2366	589	11	.	.	PUNCT
ejpam-2366	590	1	if	if	SCONJ
ejpam-2366	590	2	n	n	PRON
ejpam-2366	590	3	is	be	AUX
ejpam-2366	590	4	almost	almost	ADV
ejpam-2366	590	5	primary	primary	ADJ
ejpam-2366	590	6	,	,	PUNCT
ejpam-2366	590	7	then	then	ADV
ejpam-2366	590	8	(	(	PUNCT
ejpam-2366	590	9	n	n	X
ejpam-2366	590	10	:	:	PUNCT
ejpam-2366	590	11	i	i	PRON
ejpam-2366	590	12	m	m	PROPN
ejpam-2366	590	13	)	)	PUNCT
ejpam-2366	590	14	is	be	AUX
ejpam-2366	590	15	a	a	DET
ejpam-2366	590	16	2	2	NUM
ejpam-2366	590	17	-	-	PUNCT
ejpam-2366	590	18	absorbing	absorbing	ADJ
ejpam-2366	590	19	primary	primary	ADJ
ejpam-2366	590	20	element	element	NOUN
ejpam-2366	590	21	of	of	ADP
ejpam-2366	590	22	l	l	PROPN
ejpam-2366	590	23	and√	and√	X
ejpam-2366	590	24	n	n	NOUN
ejpam-2366	590	25	:	:	PUNCT
ejpam-2366	590	26	i	i	PRON
ejpam-2366	590	27	m	m	VERB
ejpam-2366	590	28	is	be	AUX
ejpam-2366	590	29	a	a	DET
ejpam-2366	590	30	2	2	NUM
ejpam-2366	590	31	-	-	PUNCT
ejpam-2366	590	32	absorbing	absorbing	ADJ
ejpam-2366	590	33	element	element	NOUN
ejpam-2366	590	34	of	of	ADP
ejpam-2366	590	35	l.	l.	PROPN
ejpam-2366	590	36	proof	proof	PROPN
ejpam-2366	590	37	.	.	PUNCT
ejpam-2366	591	1	the	the	DET
ejpam-2366	591	2	proof	proof	NOUN
ejpam-2366	591	3	follows	follow	VERB
ejpam-2366	591	4	from	from	ADP
ejpam-2366	591	5	theorems	theorem	NOUN
ejpam-2366	591	6	34	34	NUM
ejpam-2366	591	7	and	and	CCONJ
ejpam-2366	591	8	27	27	NUM
ejpam-2366	591	9	.	.	PUNCT
ejpam-2366	592	1	a.	a.	PROPN
ejpam-2366	592	2	v.	v.	PROPN
ejpam-2366	592	3	bingi	bingi	PROPN
ejpam-2366	592	4	,	,	PUNCT
ejpam-2366	592	5	c.	c.	PROPN
ejpam-2366	592	6	s.	s.	PROPN
ejpam-2366	592	7	manjarekar	manjarekar	PROPN
ejpam-2366	592	8	/	/	PROPN
ejpam-2366	592	9	eur	eur	PROPN
ejpam-2366	592	10	.	.	PUNCT
ejpam-2366	593	1	j.	j.	PROPN
ejpam-2366	593	2	pure	pure	PROPN
ejpam-2366	593	3	appl	appl	PROPN
ejpam-2366	593	4	.	.	PROPN
ejpam-2366	593	5	math	math	PROPN
ejpam-2366	593	6	,	,	PUNCT
ejpam-2366	593	7	14	14	NUM
ejpam-2366	593	8	(	(	PUNCT
ejpam-2366	593	9	2	2	NUM
ejpam-2366	593	10	)	)	PUNCT
ejpam-2366	593	11	(	(	PUNCT
ejpam-2366	593	12	2021	2021	NUM
ejpam-2366	593	13	)	)	PUNCT
ejpam-2366	593	14	,	,	PUNCT
ejpam-2366	593	15	551	551	NUM
ejpam-2366	593	16	-	-	SYM
ejpam-2366	593	17	577	577	NUM
ejpam-2366	593	18	567	567	NUM
ejpam-2366	593	19	3	3	NUM
ejpam-2366	593	20	.	.	PUNCT
ejpam-2366	593	21	almost	almost	ADV
ejpam-2366	593	22	prime	prime	ADJ
ejpam-2366	593	23	and	and	CCONJ
ejpam-2366	593	24	almost	almost	ADV
ejpam-2366	593	25	primary	primary	ADJ
ejpam-2366	593	26	elements	element	NOUN
ejpam-2366	593	27	in	in	ADP
ejpam-2366	593	28	m	m	PROPN
ejpam-2366	593	29	in	in	ADP
ejpam-2366	593	30	this	this	DET
ejpam-2366	593	31	section	section	NOUN
ejpam-2366	593	32	,	,	PUNCT
ejpam-2366	593	33	we	we	PRON
ejpam-2366	593	34	will	will	AUX
ejpam-2366	593	35	obtain	obtain	VERB
ejpam-2366	593	36	some	some	DET
ejpam-2366	593	37	more	more	ADJ
ejpam-2366	593	38	results	result	NOUN
ejpam-2366	593	39	on	on	ADP
ejpam-2366	593	40	an	an	DET
ejpam-2366	593	41	almost	almost	ADV
ejpam-2366	593	42	prime	prime	ADJ
ejpam-2366	593	43	(	(	PUNCT
ejpam-2366	593	44	respectively	respectively	ADV
ejpam-2366	593	45	almost	almost	ADV
ejpam-2366	593	46	primary	primary	ADJ
ejpam-2366	593	47	)	)	PUNCT
ejpam-2366	593	48	element	element	NOUN
ejpam-2366	593	49	of	of	ADP
ejpam-2366	593	50	an	an	DET
ejpam-2366	593	51	l	l	NOUN
ejpam-2366	593	52	-	-	NOUN
ejpam-2366	593	53	module	module	NOUN
ejpam-2366	593	54	m	m	NOUN
ejpam-2366	593	55	by	by	ADP
ejpam-2366	593	56	relating	relate	VERB
ejpam-2366	593	57	it	it	PRON
ejpam-2366	593	58	with	with	ADP
ejpam-2366	593	59	an	an	DET
ejpam-2366	593	60	idempotent	idempotent	ADJ
ejpam-2366	593	61	element	element	NOUN
ejpam-2366	593	62	and	and	CCONJ
ejpam-2366	593	63	a	a	DET
ejpam-2366	593	64	weakly	weakly	ADJ
ejpam-2366	593	65	prime	prime	NOUN
ejpam-2366	593	66	(	(	PUNCT
ejpam-2366	593	67	respectively	respectively	ADV
ejpam-2366	593	68	weakly	weakly	ADJ
ejpam-2366	593	69	primary	primary	ADJ
ejpam-2366	593	70	)	)	PUNCT
ejpam-2366	593	71	element	element	NOUN
ejpam-2366	593	72	of	of	ADP
ejpam-2366	593	73	an	an	DET
ejpam-2366	593	74	l	l	NOUN
ejpam-2366	593	75	-	-	NOUN
ejpam-2366	593	76	module	module	NOUN
ejpam-2366	593	77	m	m	NOUN
ejpam-2366	593	78	.	.	PUNCT
ejpam-2366	594	1	also	also	ADV
ejpam-2366	594	2	,	,	PUNCT
ejpam-2366	594	3	many	many	ADJ
ejpam-2366	594	4	characterizations	characterization	NOUN
ejpam-2366	594	5	of	of	ADP
ejpam-2366	594	6	an	an	DET
ejpam-2366	594	7	almost	almost	ADV
ejpam-2366	594	8	prime	prime	ADJ
ejpam-2366	594	9	and	and	CCONJ
ejpam-2366	594	10	almost	almost	ADV
ejpam-2366	594	11	primary	primary	ADJ
ejpam-2366	594	12	element	element	NOUN
ejpam-2366	594	13	of	of	ADP
ejpam-2366	594	14	an	an	DET
ejpam-2366	594	15	l	l	NOUN
ejpam-2366	594	16	-	-	NOUN
ejpam-2366	594	17	module	module	NOUN
ejpam-2366	594	18	m	m	NOUN
ejpam-2366	594	19	are	be	AUX
ejpam-2366	594	20	obtained	obtain	VERB
ejpam-2366	594	21	.	.	PUNCT
ejpam-2366	595	1	finally	finally	ADV
ejpam-2366	595	2	,	,	PUNCT
ejpam-2366	595	3	we	we	PRON
ejpam-2366	595	4	define	define	VERB
ejpam-2366	595	5	n	n	CCONJ
ejpam-2366	595	6	-	-	PUNCT
ejpam-2366	595	7	potent	potent	ADJ
ejpam-2366	595	8	prime(respectively	prime(respectively	ADJ
ejpam-2366	595	9	n	n	CCONJ
ejpam-2366	595	10	-	-	PUNCT
ejpam-2366	595	11	potent	potent	ADJ
ejpam-2366	595	12	primary	primary	NOUN
ejpam-2366	595	13	)	)	PUNCT
ejpam-2366	595	14	elements	element	NOUN
ejpam-2366	595	15	in	in	ADP
ejpam-2366	595	16	l	l	NOUN
ejpam-2366	595	17	and	and	CCONJ
ejpam-2366	595	18	these	these	DET
ejpam-2366	595	19	notions	notion	NOUN
ejpam-2366	595	20	are	be	AUX
ejpam-2366	595	21	related	relate	VERB
ejpam-2366	595	22	with	with	ADP
ejpam-2366	595	23	n	n	X
ejpam-2366	595	24	-	-	PUNCT
ejpam-2366	595	25	potent	potent	ADJ
ejpam-2366	595	26	prime(respectively	prime(respectively	ADJ
ejpam-2366	595	27	n	n	CCONJ
ejpam-2366	595	28	-	-	PUNCT
ejpam-2366	595	29	potent	potent	ADJ
ejpam-2366	595	30	primary	primary	NOUN
ejpam-2366	595	31	)	)	PUNCT
ejpam-2366	595	32	elements	element	NOUN
ejpam-2366	595	33	in	in	ADP
ejpam-2366	595	34	m	m	PROPN
ejpam-2366	595	35	where	where	SCONJ
ejpam-2366	595	36	n	n	CCONJ
ejpam-2366	595	37	>	>	X
ejpam-2366	595	38	2	2	X
ejpam-2366	595	39	.	.	PUNCT
ejpam-2366	595	40	clearly	clearly	ADV
ejpam-2366	595	41	,	,	PUNCT
ejpam-2366	595	42	every	every	DET
ejpam-2366	595	43	almost	almost	ADV
ejpam-2366	595	44	prime	prime	ADJ
ejpam-2366	595	45	element	element	NOUN
ejpam-2366	595	46	of	of	ADP
ejpam-2366	595	47	an	an	DET
ejpam-2366	595	48	l	l	NOUN
ejpam-2366	595	49	-	-	NOUN
ejpam-2366	595	50	module	module	NOUN
ejpam-2366	595	51	m	m	NOUN
ejpam-2366	595	52	is	be	AUX
ejpam-2366	595	53	almost	almost	ADV
ejpam-2366	595	54	primary	primary	ADJ
ejpam-2366	595	55	but	but	CCONJ
ejpam-2366	595	56	the	the	DET
ejpam-2366	595	57	converse	converse	NOUN
ejpam-2366	595	58	need	need	AUX
ejpam-2366	595	59	not	not	PART
ejpam-2366	595	60	be	be	AUX
ejpam-2366	595	61	true	true	ADJ
ejpam-2366	595	62	as	as	SCONJ
ejpam-2366	595	63	seen	see	VERB
ejpam-2366	595	64	in	in	ADP
ejpam-2366	595	65	example	example	NOUN
ejpam-2366	596	1	2	2	X
ejpam-2366	596	2	.	.	PUNCT
ejpam-2366	597	1	it	it	PRON
ejpam-2366	597	2	is	be	AUX
ejpam-2366	597	3	easy	easy	ADJ
ejpam-2366	597	4	to	to	PART
ejpam-2366	597	5	see	see	VERB
ejpam-2366	597	6	that	that	SCONJ
ejpam-2366	597	7	converse	converse	NOUN
ejpam-2366	597	8	holds	hold	VERB
ejpam-2366	597	9	for	for	ADP
ejpam-2366	597	10	radical	radical	ADJ
ejpam-2366	597	11	elements	element	NOUN
ejpam-2366	597	12	of	of	ADP
ejpam-2366	597	13	an	an	DET
ejpam-2366	597	14	l	l	NOUN
ejpam-2366	597	15	-	-	NOUN
ejpam-2366	597	16	module	module	NOUN
ejpam-2366	597	17	m	m	NOUN
ejpam-2366	597	18	.	.	PUNCT
ejpam-2366	598	1	every	every	DET
ejpam-2366	598	2	prime	prime	ADJ
ejpam-2366	598	3	element	element	NOUN
ejpam-2366	598	4	of	of	ADP
ejpam-2366	598	5	an	an	DET
ejpam-2366	598	6	l	l	NOUN
ejpam-2366	598	7	-	-	NOUN
ejpam-2366	598	8	module	module	NOUN
ejpam-2366	598	9	m	m	NOUN
ejpam-2366	598	10	is	be	AUX
ejpam-2366	598	11	almost	almost	ADV
ejpam-2366	598	12	prime	prime	ADJ
ejpam-2366	598	13	and	and	CCONJ
ejpam-2366	598	14	every	every	DET
ejpam-2366	598	15	primary	primary	ADJ
ejpam-2366	598	16	element	element	NOUN
ejpam-2366	598	17	of	of	ADP
ejpam-2366	598	18	an	an	DET
ejpam-2366	598	19	l	l	NOUN
ejpam-2366	598	20	-	-	NOUN
ejpam-2366	598	21	module	module	NOUN
ejpam-2366	598	22	m	m	NOUN
ejpam-2366	598	23	is	be	AUX
ejpam-2366	598	24	almost	almost	ADV
ejpam-2366	598	25	primary	primary	ADJ
ejpam-2366	598	26	but	but	CCONJ
ejpam-2366	598	27	their	their	PRON
ejpam-2366	598	28	converses	converse	NOUN
ejpam-2366	598	29	are	be	AUX
ejpam-2366	598	30	not	not	PART
ejpam-2366	598	31	true	true	ADJ
ejpam-2366	598	32	as	as	SCONJ
ejpam-2366	598	33	seen	see	VERB
ejpam-2366	598	34	in	in	ADP
ejpam-2366	598	35	example	example	NOUN
ejpam-2366	598	36	1	1	NUM
ejpam-2366	598	37	and	and	CCONJ
ejpam-2366	598	38	example	example	NOUN
ejpam-2366	598	39	4	4	NUM
ejpam-2366	598	40	,	,	PUNCT
ejpam-2366	598	41	respectively	respectively	ADV
ejpam-2366	598	42	.	.	PUNCT
ejpam-2366	599	1	also	also	ADV
ejpam-2366	599	2	,	,	PUNCT
ejpam-2366	599	3	every	every	DET
ejpam-2366	599	4	prime	prime	ADJ
ejpam-2366	599	5	element	element	NOUN
ejpam-2366	599	6	of	of	ADP
ejpam-2366	599	7	an	an	DET
ejpam-2366	599	8	l	l	NOUN
ejpam-2366	599	9	-	-	NOUN
ejpam-2366	599	10	module	module	NOUN
ejpam-2366	599	11	m	m	NOUN
ejpam-2366	599	12	is	be	AUX
ejpam-2366	599	13	almost	almost	ADV
ejpam-2366	599	14	primary	primary	ADJ
ejpam-2366	599	15	.	.	PUNCT
ejpam-2366	600	1	according	accord	VERB
ejpam-2366	600	2	to	to	ADP
ejpam-2366	600	3	definition	definition	NOUN
ejpam-2366	600	4	2.6	2.6	NUM
ejpam-2366	600	5	of	of	ADP
ejpam-2366	600	6	[	[	X
ejpam-2366	600	7	22	22	NUM
ejpam-2366	600	8	]	]	PUNCT
ejpam-2366	600	9	,	,	PUNCT
ejpam-2366	600	10	an	an	DET
ejpam-2366	600	11	idempotent	idempotent	ADJ
ejpam-2366	600	12	element	element	NOUN
ejpam-2366	600	13	of	of	ADP
ejpam-2366	600	14	an	an	DET
ejpam-2366	600	15	l	l	NOUN
ejpam-2366	600	16	-	-	NOUN
ejpam-2366	600	17	module	module	NOUN
ejpam-2366	600	18	m	m	NOUN
ejpam-2366	600	19	is	be	AUX
ejpam-2366	600	20	defined	define	VERB
ejpam-2366	600	21	in	in	ADP
ejpam-2366	600	22	the	the	DET
ejpam-2366	600	23	following	following	ADJ
ejpam-2366	600	24	way	way	NOUN
ejpam-2366	600	25	.	.	PUNCT
ejpam-2366	601	1	definition	definition	NOUN
ejpam-2366	601	2	8	8	NUM
ejpam-2366	601	3	.	.	PUNCT
ejpam-2366	602	1	a	a	DET
ejpam-2366	602	2	proper	proper	ADJ
ejpam-2366	602	3	element	element	NOUN
ejpam-2366	602	4	n	n	PROPN
ejpam-2366	602	5	of	of	ADP
ejpam-2366	602	6	an	an	DET
ejpam-2366	602	7	l	l	NOUN
ejpam-2366	602	8	-	-	NOUN
ejpam-2366	602	9	module	module	NOUN
ejpam-2366	602	10	m	m	NOUN
ejpam-2366	602	11	is	be	AUX
ejpam-2366	602	12	said	say	VERB
ejpam-2366	602	13	to	to	PART
ejpam-2366	602	14	be	be	AUX
ejpam-2366	602	15	idempotent	idempotent	ADJ
ejpam-2366	602	16	if	if	SCONJ
ejpam-2366	602	17	(	(	PUNCT
ejpam-2366	602	18	n	n	X
ejpam-2366	602	19	:	:	PUNCT
ejpam-2366	602	20	i	i	PRON
ejpam-2366	602	21	m	m	VERB
ejpam-2366	602	22	)	)	PUNCT
ejpam-2366	602	23	n	n	NOUN
ejpam-2366	602	24	=	=	SYM
ejpam-2366	602	25	n	n	PROPN
ejpam-2366	602	26	.	.	PUNCT
ejpam-2366	603	1	clearly	clearly	ADV
ejpam-2366	603	2	,	,	PUNCT
ejpam-2366	603	3	every	every	DET
ejpam-2366	603	4	idempotent	idempotent	ADJ
ejpam-2366	603	5	element	element	NOUN
ejpam-2366	603	6	of	of	ADP
ejpam-2366	603	7	an	an	DET
ejpam-2366	603	8	l	l	NOUN
ejpam-2366	603	9	-	-	NOUN
ejpam-2366	603	10	module	module	NOUN
ejpam-2366	603	11	m	m	NOUN
ejpam-2366	603	12	is	be	AUX
ejpam-2366	603	13	almost	almost	ADV
ejpam-2366	603	14	prime	prime	ADJ
ejpam-2366	603	15	and	and	CCONJ
ejpam-2366	603	16	hence	hence	ADV
ejpam-2366	603	17	almost	almost	ADV
ejpam-2366	603	18	primary	primary	ADJ
ejpam-2366	603	19	.	.	PUNCT
ejpam-2366	604	1	but	but	CCONJ
ejpam-2366	604	2	an	an	DET
ejpam-2366	604	3	almost	almost	ADV
ejpam-2366	604	4	primary	primary	ADJ
ejpam-2366	604	5	element	element	NOUN
ejpam-2366	604	6	of	of	ADP
ejpam-2366	604	7	an	an	DET
ejpam-2366	604	8	l	l	NOUN
ejpam-2366	604	9	-	-	NOUN
ejpam-2366	604	10	module	module	NOUN
ejpam-2366	604	11	m	m	NOUN
ejpam-2366	604	12	need	need	AUX
ejpam-2366	604	13	not	not	PART
ejpam-2366	604	14	be	be	AUX
ejpam-2366	604	15	idempotent	idempotent	ADJ
ejpam-2366	604	16	as	as	SCONJ
ejpam-2366	604	17	shown	show	VERB
ejpam-2366	604	18	in	in	ADP
ejpam-2366	604	19	the	the	DET
ejpam-2366	604	20	following	follow	VERB
ejpam-2366	604	21	example	example	NOUN
ejpam-2366	604	22	.	.	PUNCT
ejpam-2366	605	1	example	example	NOUN
ejpam-2366	606	1	7	7	NUM
ejpam-2366	606	2	.	.	X
ejpam-2366	606	3	consider	consider	VERB
ejpam-2366	606	4	the	the	DET
ejpam-2366	606	5	lattice	lattice	NOUN
ejpam-2366	606	6	module	module	NOUN
ejpam-2366	606	7	as	as	ADP
ejpam-2366	606	8	in	in	ADP
ejpam-2366	606	9	example	example	NOUN
ejpam-2366	606	10	6	6	NUM
ejpam-2366	606	11	.	.	PUNCT
ejpam-2366	607	1	let	let	VERB
ejpam-2366	607	2	n	n	PRON
ejpam-2366	607	3	be	be	AUX
ejpam-2366	607	4	the	the	DET
ejpam-2366	607	5	cyclic	cyclic	ADJ
ejpam-2366	607	6	submodule	submodule	NOUN
ejpam-2366	607	7	of	of	ADP
ejpam-2366	607	8	m	m	AUX
ejpam-2366	607	9	generated	generate	VERB
ejpam-2366	607	10	by	by	ADP
ejpam-2366	607	11	4	4	NUM
ejpam-2366	607	12	.	.	PUNCT
ejpam-2366	608	1	it	it	PRON
ejpam-2366	608	2	is	be	AUX
ejpam-2366	608	3	easy	easy	ADJ
ejpam-2366	608	4	to	to	PART
ejpam-2366	608	5	see	see	VERB
ejpam-2366	608	6	that	that	SCONJ
ejpam-2366	608	7	the	the	DET
ejpam-2366	608	8	element	element	NOUN
ejpam-2366	608	9	n	n	NOUN
ejpam-2366	608	10	=	=	NOUN
ejpam-2366	608	11	<	<	X
ejpam-2366	608	12	4	4	NUM
ejpam-2366	608	13	>	>	X
ejpam-2366	608	14	is	be	AUX
ejpam-2366	608	15	almost	almost	ADV
ejpam-2366	608	16	primary	primary	ADJ
ejpam-2366	608	17	but	but	CCONJ
ejpam-2366	608	18	not	not	PART
ejpam-2366	608	19	idempotent	idempotent	ADJ
ejpam-2366	608	20	.	.	PUNCT
ejpam-2366	609	1	theorem	theorem	NOUN
ejpam-2366	609	2	36	36	NUM
ejpam-2366	609	3	.	.	PUNCT
ejpam-2366	610	1	let	let	VERB
ejpam-2366	610	2	l	l	NOUN
ejpam-2366	610	3	be	be	AUX
ejpam-2366	610	4	a	a	DET
ejpam-2366	610	5	pg	pg	NOUN
ejpam-2366	610	6	-	-	PUNCT
ejpam-2366	610	7	lattice	lattice	NOUN
ejpam-2366	610	8	and	and	CCONJ
ejpam-2366	610	9	m	m	AUX
ejpam-2366	610	10	be	be	AUX
ejpam-2366	610	11	a	a	DET
ejpam-2366	610	12	faithful	faithful	ADJ
ejpam-2366	610	13	multiplication	multiplication	NOUN
ejpam-2366	610	14	pg	pg	ADJ
ejpam-2366	610	15	-	-	PUNCT
ejpam-2366	610	16	lattice	lattice	NOUN
ejpam-2366	610	17	lmodule	lmodule	NOUN
ejpam-2366	610	18	with	with	ADP
ejpam-2366	610	19	i	i	PROPN
ejpam-2366	610	20	m	m	VERB
ejpam-2366	610	21	compact	compact	ADJ
ejpam-2366	610	22	.	.	PUNCT
ejpam-2366	611	1	for	for	ADP
ejpam-2366	611	2	an	an	DET
ejpam-2366	611	3	idempotent	idempotent	ADJ
ejpam-2366	611	4	element	element	NOUN
ejpam-2366	611	5	n	n	CCONJ
ejpam-2366	611	6	∈	∈	NOUN
ejpam-2366	611	7	m	m	VERB
ejpam-2366	611	8	,	,	PUNCT
ejpam-2366	611	9	(	(	PUNCT
ejpam-2366	611	10	√	√	INTJ
ejpam-2366	611	11	(	(	PUNCT
ejpam-2366	611	12	n	n	NOUN
ejpam-2366	611	13	:	:	PUNCT
ejpam-2366	611	14	i	i	PRON
ejpam-2366	611	15	m	m	PROPN
ejpam-2366	611	16	)	)	PUNCT
ejpam-2366	611	17	n	n	CCONJ
ejpam-2366	611	18	:	:	PUNCT
ejpam-2366	611	19	i	i	PRON
ejpam-2366	611	20	m	m	VERB
ejpam-2366	611	21	)	)	PUNCT
ejpam-2366	611	22	n	n	NOUN
ejpam-2366	611	23	=	=	SYM
ejpam-2366	611	24	(	(	PUNCT
ejpam-2366	611	25	n	n	X
ejpam-2366	611	26	:	:	PUNCT
ejpam-2366	611	27	i	i	PRON
ejpam-2366	611	28	m	m	PROPN
ejpam-2366	611	29	)	)	PUNCT
ejpam-2366	611	30	n	n	NOUN
ejpam-2366	611	31	.	.	PUNCT
ejpam-2366	612	1	proof	proof	NOUN
ejpam-2366	612	2	.	.	PUNCT
ejpam-2366	613	1	as	as	SCONJ
ejpam-2366	613	2	n	n	ADP
ejpam-2366	613	3	<	<	X
ejpam-2366	613	4	i	i	X
ejpam-2366	613	5	m	m	VERB
ejpam-2366	613	6	is	be	AUX
ejpam-2366	613	7	idempotent	idempotent	ADJ
ejpam-2366	613	8	,	,	PUNCT
ejpam-2366	613	9	n	n	PRON
ejpam-2366	613	10	is	be	AUX
ejpam-2366	613	11	almost	almost	ADV
ejpam-2366	613	12	prime	prime	ADJ
ejpam-2366	613	13	(	(	PUNCT
ejpam-2366	613	14	φ2	φ2	NOUN
ejpam-2366	613	15	−	−	PROPN
ejpam-2366	613	16	prime	prime	NOUN
ejpam-2366	613	17	)	)	PUNCT
ejpam-2366	613	18	.	.	PUNCT
ejpam-2366	614	1	since	since	SCONJ
ejpam-2366	614	2	m	m	PROPN
ejpam-2366	614	3	is	be	AUX
ejpam-2366	614	4	a	a	DET
ejpam-2366	614	5	multiplication	multiplication	NOUN
ejpam-2366	614	6	lattice	lattice	NOUN
ejpam-2366	614	7	l	l	NOUN
ejpam-2366	614	8	-	-	NOUN
ejpam-2366	614	9	module	module	NOUN
ejpam-2366	614	10	,	,	PUNCT
ejpam-2366	614	11	we	we	PRON
ejpam-2366	614	12	have	have	VERB
ejpam-2366	614	13	(	(	PUNCT
ejpam-2366	614	14	n	n	X
ejpam-2366	614	15	:	:	PUNCT
ejpam-2366	614	16	i	i	PRON
ejpam-2366	614	17	m	m	NOUN
ejpam-2366	614	18	)	)	PUNCT
ejpam-2366	614	19	2im	2im	NOUN
ejpam-2366	615	1	=	=	SYM
ejpam-2366	615	2	(	(	PUNCT
ejpam-2366	615	3	n	n	X
ejpam-2366	615	4	:	:	PUNCT
ejpam-2366	615	5	i	i	PRON
ejpam-2366	615	6	m	m	PROPN
ejpam-2366	615	7	)	)	PUNCT
ejpam-2366	615	8	n	n	NUM
ejpam-2366	615	9	which	which	PRON
ejpam-2366	615	10	implies	imply	VERB
ejpam-2366	615	11	(	(	PUNCT
ejpam-2366	615	12	n	n	X
ejpam-2366	615	13	:	:	PUNCT
ejpam-2366	615	14	i	i	PRON
ejpam-2366	615	15	m	m	VERB
ejpam-2366	615	16	)	)	PUNCT
ejpam-2366	615	17	6	6	NUM
ejpam-2366	615	18	√	√	NUM
ejpam-2366	615	19	(	(	PUNCT
ejpam-2366	615	20	n	n	NUM
ejpam-2366	615	21	:	:	PUNCT
ejpam-2366	615	22	i	i	PRON
ejpam-2366	615	23	m	m	PROPN
ejpam-2366	615	24	)	)	PUNCT
ejpam-2366	615	25	n	n	CCONJ
ejpam-2366	615	26	:	:	PUNCT
ejpam-2366	615	27	i	i	PRON
ejpam-2366	615	28	m	m	VERB
ejpam-2366	615	29	.	.	PUNCT
ejpam-2366	616	1	thus	thus	ADV
ejpam-2366	616	2	(	(	PUNCT
ejpam-2366	616	3	n	n	X
ejpam-2366	616	4	:	:	PUNCT
ejpam-2366	616	5	i	i	PRON
ejpam-2366	616	6	m	m	PROPN
ejpam-2366	616	7	)	)	PUNCT
ejpam-2366	616	8	n	n	PROPN
ejpam-2366	616	9	6	6	NUM
ejpam-2366	616	10	(	(	PUNCT
ejpam-2366	616	11	√	√	NUM
ejpam-2366	616	12	(	(	PUNCT
ejpam-2366	616	13	n	n	NUM
ejpam-2366	616	14	:	:	PUNCT
ejpam-2366	616	15	i	i	PRON
ejpam-2366	616	16	m	m	PROPN
ejpam-2366	616	17	)	)	PUNCT
ejpam-2366	616	18	n	n	CCONJ
ejpam-2366	616	19	:	:	PUNCT
ejpam-2366	616	20	i	i	PRON
ejpam-2366	616	21	m	m	PROPN
ejpam-2366	616	22	)	)	PUNCT
ejpam-2366	616	23	n	n	X
ejpam-2366	616	24	.	.	PUNCT
ejpam-2366	617	1	now	now	ADV
ejpam-2366	617	2	to	to	PART
ejpam-2366	617	3	prove	prove	VERB
ejpam-2366	617	4	that	that	SCONJ
ejpam-2366	617	5	(	(	PUNCT
ejpam-2366	617	6	√	√	INTJ
ejpam-2366	617	7	(	(	PUNCT
ejpam-2366	617	8	n	n	NOUN
ejpam-2366	617	9	:	:	PUNCT
ejpam-2366	617	10	i	i	PRON
ejpam-2366	617	11	m	m	PROPN
ejpam-2366	617	12	)	)	PUNCT
ejpam-2366	617	13	n	n	CCONJ
ejpam-2366	617	14	:	:	PUNCT
ejpam-2366	617	15	i	i	PRON
ejpam-2366	617	16	m	m	VERB
ejpam-2366	617	17	)	)	PUNCT
ejpam-2366	617	18	n	n	PROPN
ejpam-2366	617	19	6	6	NUM
ejpam-2366	617	20	(	(	PUNCT
ejpam-2366	617	21	n	n	NUM
ejpam-2366	617	22	:	:	PUNCT
ejpam-2366	617	23	i	i	PRON
ejpam-2366	617	24	m	m	PROPN
ejpam-2366	617	25	)	)	PUNCT
ejpam-2366	617	26	n	n	CCONJ
ejpam-2366	617	27	,	,	PUNCT
ejpam-2366	617	28	let	let	VERB
ejpam-2366	617	29	a	a	DET
ejpam-2366	617	30	6	6	NUM
ejpam-2366	617	31	√	√	NUM
ejpam-2366	617	32	(	(	PUNCT
ejpam-2366	617	33	n	n	NUM
ejpam-2366	617	34	:	:	PUNCT
ejpam-2366	617	35	i	i	PRON
ejpam-2366	617	36	m	m	PROPN
ejpam-2366	617	37	)	)	PUNCT
ejpam-2366	618	1	n	n	CCONJ
ejpam-2366	618	2	:	:	PUNCT
ejpam-2366	619	1	i	i	PRON
ejpam-2366	619	2	m	m	VERB
ejpam-2366	619	3	for	for	ADP
ejpam-2366	619	4	a	a	DET
ejpam-2366	619	5	∈	∈	PROPN
ejpam-2366	619	6	l.	l.	NOUN
ejpam-2366	619	7	if	if	SCONJ
ejpam-2366	619	8	a	a	DET
ejpam-2366	619	9	6	6	NUM
ejpam-2366	619	10	(	(	PUNCT
ejpam-2366	619	11	n	n	NUM
ejpam-2366	619	12	:	:	PUNCT
ejpam-2366	619	13	i	i	PRON
ejpam-2366	619	14	m	m	PROPN
ejpam-2366	619	15	)	)	PUNCT
ejpam-2366	619	16	,	,	PUNCT
ejpam-2366	619	17	then	then	ADV
ejpam-2366	619	18	we	we	PRON
ejpam-2366	619	19	are	be	AUX
ejpam-2366	619	20	done	do	VERB
ejpam-2366	619	21	.	.	PUNCT
ejpam-2366	620	1	so	so	ADV
ejpam-2366	620	2	let	let	VERB
ejpam-2366	620	3	a	a	DET
ejpam-2366	620	4	(	(	PUNCT
ejpam-2366	620	5	n	n	NOUN
ejpam-2366	620	6	:	:	PUNCT
ejpam-2366	620	7	i	i	PRON
ejpam-2366	620	8	m	m	PROPN
ejpam-2366	620	9	)	)	PUNCT
ejpam-2366	620	10	.	.	PUNCT
ejpam-2366	621	1	then	then	ADV
ejpam-2366	621	2	as	as	SCONJ
ejpam-2366	621	3	n	n	NOUN
ejpam-2366	621	4	is	be	AUX
ejpam-2366	621	5	φ2	φ2	PROPN
ejpam-2366	621	6	−	−	PROPN
ejpam-2366	621	7	prime	prime	NOUN
ejpam-2366	621	8	,	,	PUNCT
ejpam-2366	621	9	by	by	ADP
ejpam-2366	621	10	theorem	theorem	NOUN
ejpam-2366	621	11	1	1	NUM
ejpam-2366	621	12	,	,	PUNCT
ejpam-2366	621	13	we	we	PRON
ejpam-2366	621	14	have	have	VERB
ejpam-2366	621	15	either	either	CCONJ
ejpam-2366	621	16	(	(	PUNCT
ejpam-2366	621	17	n	n	X
ejpam-2366	621	18	:	:	PUNCT
ejpam-2366	621	19	a	a	X
ejpam-2366	621	20	)	)	PUNCT
ejpam-2366	621	21	=	=	SYM
ejpam-2366	621	22	n	n	NOUN
ejpam-2366	621	23	or	or	CCONJ
ejpam-2366	621	24	(	(	PUNCT
ejpam-2366	621	25	n	n	X
ejpam-2366	621	26	:	:	PUNCT
ejpam-2366	621	27	a	a	X
ejpam-2366	621	28	)	)	PUNCT
ejpam-2366	621	29	=	=	SYM
ejpam-2366	621	30	(	(	PUNCT
ejpam-2366	621	31	(	(	PUNCT
ejpam-2366	621	32	n	n	X
ejpam-2366	621	33	:	:	PUNCT
ejpam-2366	621	34	i	i	PRON
ejpam-2366	621	35	m	m	PROPN
ejpam-2366	621	36	)	)	PUNCT
ejpam-2366	621	37	n	n	CCONJ
ejpam-2366	621	38	:	:	PUNCT
ejpam-2366	621	39	a	a	X
ejpam-2366	621	40	)	)	PUNCT
ejpam-2366	621	41	.	.	PUNCT
ejpam-2366	622	1	let	let	VERB
ejpam-2366	622	2	(	(	PUNCT
ejpam-2366	622	3	n	n	X
ejpam-2366	622	4	:	:	PUNCT
ejpam-2366	622	5	a	a	X
ejpam-2366	622	6	)	)	PUNCT
ejpam-2366	622	7	=	=	SYM
ejpam-2366	622	8	n	n	NOUN
ejpam-2366	622	9	and	and	CCONJ
ejpam-2366	622	10	n	n	ADV
ejpam-2366	622	11	be	be	VERB
ejpam-2366	622	12	the	the	DET
ejpam-2366	622	13	least	least	ADV
ejpam-2366	622	14	positive	positive	ADJ
ejpam-2366	622	15	integer	integer	NOUN
ejpam-2366	622	16	such	such	DET
ejpam-2366	622	17	that	that	SCONJ
ejpam-2366	622	18	an	an	DET
ejpam-2366	622	19	6	6	NUM
ejpam-2366	622	20	(	(	PUNCT
ejpam-2366	622	21	(	(	PUNCT
ejpam-2366	622	22	n	n	X
ejpam-2366	622	23	:	:	PUNCT
ejpam-2366	622	24	i	i	PRON
ejpam-2366	622	25	m	m	PROPN
ejpam-2366	622	26	)	)	PUNCT
ejpam-2366	622	27	n	n	CCONJ
ejpam-2366	622	28	:	:	PUNCT
ejpam-2366	622	29	i	i	PRON
ejpam-2366	622	30	m	m	PROPN
ejpam-2366	622	31	)	)	PUNCT
ejpam-2366	622	32	.	.	PUNCT
ejpam-2366	623	1	if	if	SCONJ
ejpam-2366	623	2	n	n	NOUN
ejpam-2366	623	3	=	=	SYM
ejpam-2366	623	4	1	1	NUM
ejpam-2366	623	5	,	,	PUNCT
ejpam-2366	623	6	then	then	ADV
ejpam-2366	623	7	aim	aim	VERB
ejpam-2366	623	8	6	6	NUM
ejpam-2366	623	9	(	(	PUNCT
ejpam-2366	623	10	n	n	NUM
ejpam-2366	623	11	:	:	PUNCT
ejpam-2366	623	12	i	i	PRON
ejpam-2366	623	13	m	m	VERB
ejpam-2366	623	14	)	)	PUNCT
ejpam-2366	623	15	n	n	NOUN
ejpam-2366	623	16	=	=	SYM
ejpam-2366	623	17	(	(	PUNCT
ejpam-2366	623	18	n	n	X
ejpam-2366	623	19	:	:	PUNCT
ejpam-2366	623	20	i	i	PRON
ejpam-2366	623	21	m	m	NOUN
ejpam-2366	623	22	)	)	PUNCT
ejpam-2366	623	23	2im	2im	NOUN
ejpam-2366	623	24	.	.	PUNCT
ejpam-2366	624	1	as	as	SCONJ
ejpam-2366	624	2	i	i	PRON
ejpam-2366	624	3	m	m	VERB
ejpam-2366	624	4	is	be	AUX
ejpam-2366	624	5	compact	compact	ADJ
ejpam-2366	624	6	,	,	PUNCT
ejpam-2366	624	7	by	by	ADP
ejpam-2366	624	8	theorem	theorem	NOUN
ejpam-2366	624	9	5	5	NUM
ejpam-2366	624	10	of	of	ADP
ejpam-2366	624	11	[	[	X
ejpam-2366	624	12	10	10	NUM
ejpam-2366	624	13	]	]	PUNCT
ejpam-2366	624	14	,	,	PUNCT
ejpam-2366	624	15	we	we	PRON
ejpam-2366	624	16	have	have	VERB
ejpam-2366	624	17	a	a	DET
ejpam-2366	624	18	6	6	NUM
ejpam-2366	624	19	(	(	PUNCT
ejpam-2366	624	20	n	n	NUM
ejpam-2366	624	21	:	:	PUNCT
ejpam-2366	624	22	i	i	PRON
ejpam-2366	624	23	m	m	VERB
ejpam-2366	624	24	)	)	PUNCT
ejpam-2366	624	25	2	2	NUM
ejpam-2366	624	26	6	6	NUM
ejpam-2366	624	27	(	(	PUNCT
ejpam-2366	624	28	n	n	NUM
ejpam-2366	624	29	:	:	PUNCT
ejpam-2366	624	30	i	i	PRON
ejpam-2366	624	31	m	m	VERB
ejpam-2366	624	32	)	)	PUNCT
ejpam-2366	624	33	which	which	PRON
ejpam-2366	624	34	contradicts	contradict	VERB
ejpam-2366	624	35	a	a	DET
ejpam-2366	624	36	(	(	PUNCT
ejpam-2366	624	37	n	n	NOUN
ejpam-2366	624	38	:	:	PUNCT
ejpam-2366	624	39	i	i	PRON
ejpam-2366	624	40	m	m	PROPN
ejpam-2366	624	41	)	)	PUNCT
ejpam-2366	624	42	.	.	PUNCT
ejpam-2366	625	1	so	so	ADV
ejpam-2366	625	2	assume	assume	VERB
ejpam-2366	625	3	that	that	SCONJ
ejpam-2366	625	4	n	n	X
ejpam-2366	625	5	>	>	X
ejpam-2366	625	6	2	2	X
ejpam-2366	625	7	.	.	PUNCT
ejpam-2366	625	8	then	then	ADV
ejpam-2366	625	9	anim	anim	NOUN
ejpam-2366	625	10	6	6	NUM
ejpam-2366	625	11	(	(	PUNCT
ejpam-2366	625	12	n	n	NUM
ejpam-2366	625	13	:	:	PUNCT
ejpam-2366	625	14	i	i	PRON
ejpam-2366	625	15	m	m	PROPN
ejpam-2366	625	16	)	)	PUNCT
ejpam-2366	625	17	n	n	PROPN
ejpam-2366	625	18	6	6	NUM
ejpam-2366	625	19	n	n	NOUN
ejpam-2366	625	20	with	with	ADP
ejpam-2366	625	21	akim	akim	PROPN
ejpam-2366	625	22	(	(	PUNCT
ejpam-2366	625	23	n	n	PROPN
ejpam-2366	625	24	:	:	PUNCT
ejpam-2366	625	25	i	i	PRON
ejpam-2366	625	26	m	m	PROPN
ejpam-2366	625	27	)	)	PUNCT
ejpam-2366	625	28	n	n	PROPN
ejpam-2366	625	29	for	for	ADP
ejpam-2366	625	30	every	every	DET
ejpam-2366	625	31	k	k	PROPN
ejpam-2366	625	32	6	6	NUM
ejpam-2366	625	33	(	(	PUNCT
ejpam-2366	625	34	n	n	CCONJ
ejpam-2366	625	35	−	−	PROPN
ejpam-2366	625	36	1	1	NUM
ejpam-2366	625	37	)	)	PUNCT
ejpam-2366	625	38	.	.	PUNCT
ejpam-2366	626	1	since	since	SCONJ
ejpam-2366	626	2	a.	a.	PROPN
ejpam-2366	626	3	v.	v.	PROPN
ejpam-2366	626	4	bingi	bingi	PROPN
ejpam-2366	626	5	,	,	PUNCT
ejpam-2366	626	6	c.	c.	PROPN
ejpam-2366	626	7	s.	s.	PROPN
ejpam-2366	626	8	manjarekar	manjarekar	PROPN
ejpam-2366	626	9	/	/	PROPN
ejpam-2366	626	10	eur	eur	PROPN
ejpam-2366	626	11	.	.	PUNCT
ejpam-2366	627	1	j.	j.	PROPN
ejpam-2366	627	2	pure	pure	PROPN
ejpam-2366	627	3	appl	appl	PROPN
ejpam-2366	627	4	.	.	PROPN
ejpam-2366	627	5	math	math	PROPN
ejpam-2366	627	6	,	,	PUNCT
ejpam-2366	627	7	14	14	NUM
ejpam-2366	627	8	(	(	PUNCT
ejpam-2366	627	9	2	2	NUM
ejpam-2366	627	10	)	)	PUNCT
ejpam-2366	627	11	(	(	PUNCT
ejpam-2366	627	12	2021	2021	NUM
ejpam-2366	627	13	)	)	PUNCT
ejpam-2366	627	14	,	,	PUNCT
ejpam-2366	627	15	551	551	NUM
ejpam-2366	627	16	-	-	SYM
ejpam-2366	627	17	577	577	NUM
ejpam-2366	627	18	568	568	NUM
ejpam-2366	627	19	a(an−1im	a(an−1im	ADV
ejpam-2366	627	20	)	)	PUNCT
ejpam-2366	627	21	6	6	NUM
ejpam-2366	627	22	n	n	NOUN
ejpam-2366	627	23	,	,	PUNCT
ejpam-2366	627	24	we	we	PRON
ejpam-2366	627	25	have	have	AUX
ejpam-2366	627	26	an−1im	an−1im	PROPN
ejpam-2366	627	27	6	6	NUM
ejpam-2366	627	28	(	(	PUNCT
ejpam-2366	627	29	n	n	NOUN
ejpam-2366	627	30	:	:	PUNCT
ejpam-2366	627	31	a	a	X
ejpam-2366	627	32	)	)	PUNCT
ejpam-2366	627	33	=	=	SYM
ejpam-2366	627	34	n	n	NOUN
ejpam-2366	627	35	with	with	ADP
ejpam-2366	627	36	an−1im	an−1im	PROPN
ejpam-2366	627	37	(	(	PUNCT
ejpam-2366	627	38	n	n	NUM
ejpam-2366	627	39	:	:	PUNCT
ejpam-2366	627	40	i	i	PRON
ejpam-2366	627	41	m	m	PROPN
ejpam-2366	627	42	)	)	PUNCT
ejpam-2366	627	43	n	n	CCONJ
ejpam-2366	627	44	.	.	PUNCT
ejpam-2366	628	1	if	if	SCONJ
ejpam-2366	628	2	n	n	NOUN
ejpam-2366	628	3	=	=	SYM
ejpam-2366	628	4	2	2	NUM
ejpam-2366	628	5	,	,	PUNCT
ejpam-2366	628	6	then	then	ADV
ejpam-2366	628	7	aim	aim	VERB
ejpam-2366	628	8	6	6	NUM
ejpam-2366	628	9	n	n	NUM
ejpam-2366	628	10	which	which	PRON
ejpam-2366	628	11	contradicts	contradict	VERB
ejpam-2366	628	12	a	a	DET
ejpam-2366	628	13	(	(	PUNCT
ejpam-2366	628	14	n	n	NOUN
ejpam-2366	628	15	:	:	PUNCT
ejpam-2366	628	16	i	i	PRON
ejpam-2366	628	17	m	m	PROPN
ejpam-2366	628	18	)	)	PUNCT
ejpam-2366	628	19	.	.	PUNCT
ejpam-2366	629	1	if	if	SCONJ
ejpam-2366	629	2	n	n	PROPN
ejpam-2366	629	3	>	>	X
ejpam-2366	629	4	3	3	NUM
ejpam-2366	629	5	,	,	PUNCT
ejpam-2366	629	6	then	then	ADV
ejpam-2366	629	7	a(an−2im	a(an−2im	NOUN
ejpam-2366	629	8	)	)	PUNCT
ejpam-2366	629	9	6	6	NUM
ejpam-2366	629	10	n	n	NOUN
ejpam-2366	629	11	but	but	CCONJ
ejpam-2366	629	12	a(an−2im	a(an−2im	PROPN
ejpam-2366	629	13	)	)	PUNCT
ejpam-2366	629	14	(	(	PUNCT
ejpam-2366	629	15	n	n	X
ejpam-2366	629	16	:	:	PUNCT
ejpam-2366	629	17	i	i	PRON
ejpam-2366	629	18	m	m	PROPN
ejpam-2366	629	19	)	)	PUNCT
ejpam-2366	629	20	n	n	CCONJ
ejpam-2366	629	21	.	.	PUNCT
ejpam-2366	630	1	as	as	SCONJ
ejpam-2366	630	2	n	n	PRON
ejpam-2366	630	3	is	be	AUX
ejpam-2366	630	4	almost	almost	ADV
ejpam-2366	630	5	prime	prime	ADJ
ejpam-2366	630	6	,	,	PUNCT
ejpam-2366	630	7	we	we	PRON
ejpam-2366	630	8	have	have	VERB
ejpam-2366	630	9	either	either	CCONJ
ejpam-2366	630	10	a	a	DET
ejpam-2366	630	11	6	6	NUM
ejpam-2366	630	12	(	(	PUNCT
ejpam-2366	630	13	n	n	NUM
ejpam-2366	630	14	:	:	PUNCT
ejpam-2366	630	15	i	i	PRON
ejpam-2366	630	16	m	m	VERB
ejpam-2366	630	17	)	)	PUNCT
ejpam-2366	630	18	or	or	CCONJ
ejpam-2366	630	19	an−2im	an−2im	NUM
ejpam-2366	630	20	6	6	NUM
ejpam-2366	630	21	n	n	NOUN
ejpam-2366	630	22	.	.	PUNCT
ejpam-2366	631	1	as	as	ADP
ejpam-2366	631	2	a	a	DET
ejpam-2366	631	3	6	6	NUM
ejpam-2366	631	4	(	(	PUNCT
ejpam-2366	631	5	n	n	NUM
ejpam-2366	631	6	:	:	PUNCT
ejpam-2366	631	7	i	i	PRON
ejpam-2366	631	8	m	m	PROPN
ejpam-2366	631	9	)	)	PUNCT
ejpam-2366	631	10	is	be	AUX
ejpam-2366	631	11	a	a	DET
ejpam-2366	631	12	contradiction	contradiction	NOUN
ejpam-2366	631	13	,	,	PUNCT
ejpam-2366	631	14	let	let	VERB
ejpam-2366	631	15	an−2im	an−2im	NOUN
ejpam-2366	631	16	6	6	NUM
ejpam-2366	631	17	n	n	NOUN
ejpam-2366	631	18	.	.	PUNCT
ejpam-2366	632	1	then	then	ADV
ejpam-2366	632	2	a(an−3im	a(an−3im	ADJ
ejpam-2366	632	3	)	)	PUNCT
ejpam-2366	632	4	6	6	NUM
ejpam-2366	632	5	n	n	NOUN
ejpam-2366	632	6	but	but	CCONJ
ejpam-2366	632	7	a(an−3im	a(an−3im	ADJ
ejpam-2366	632	8	)	)	PUNCT
ejpam-2366	632	9	(	(	PUNCT
ejpam-2366	632	10	n	n	X
ejpam-2366	632	11	:	:	PUNCT
ejpam-2366	632	12	i	i	PRON
ejpam-2366	632	13	m	m	PROPN
ejpam-2366	632	14	)	)	PUNCT
ejpam-2366	632	15	n	n	CCONJ
ejpam-2366	632	16	.	.	PUNCT
ejpam-2366	633	1	as	as	SCONJ
ejpam-2366	633	2	n	n	PRON
ejpam-2366	633	3	is	be	AUX
ejpam-2366	633	4	almost	almost	ADV
ejpam-2366	633	5	prime	prime	ADJ
ejpam-2366	633	6	,	,	PUNCT
ejpam-2366	633	7	we	we	PRON
ejpam-2366	633	8	have	have	VERB
ejpam-2366	633	9	either	either	CCONJ
ejpam-2366	633	10	a	a	DET
ejpam-2366	633	11	6	6	NUM
ejpam-2366	633	12	(	(	PUNCT
ejpam-2366	633	13	n	n	NUM
ejpam-2366	633	14	:	:	PUNCT
ejpam-2366	633	15	i	i	PRON
ejpam-2366	633	16	m	m	VERB
ejpam-2366	633	17	)	)	PUNCT
ejpam-2366	633	18	or	or	CCONJ
ejpam-2366	633	19	an−3im	an−3im	NUM
ejpam-2366	633	20	6	6	NUM
ejpam-2366	633	21	n	n	NOUN
ejpam-2366	633	22	.	.	PUNCT
ejpam-2366	634	1	continuing	continue	VERB
ejpam-2366	634	2	this	this	DET
ejpam-2366	634	3	process	process	NOUN
ejpam-2366	634	4	we	we	PRON
ejpam-2366	634	5	conclude	conclude	VERB
ejpam-2366	634	6	that	that	SCONJ
ejpam-2366	634	7	a	a	DET
ejpam-2366	634	8	6	6	NUM
ejpam-2366	634	9	(	(	PUNCT
ejpam-2366	634	10	n	n	NUM
ejpam-2366	634	11	:	:	PUNCT
ejpam-2366	634	12	i	i	PRON
ejpam-2366	634	13	m	m	VERB
ejpam-2366	634	14	)	)	PUNCT
ejpam-2366	634	15	which	which	PRON
ejpam-2366	634	16	contradicts	contradict	VERB
ejpam-2366	634	17	a	a	DET
ejpam-2366	634	18	(	(	PUNCT
ejpam-2366	634	19	n	n	NOUN
ejpam-2366	634	20	:	:	PUNCT
ejpam-2366	634	21	i	i	PRON
ejpam-2366	634	22	m	m	PROPN
ejpam-2366	634	23	)	)	PUNCT
ejpam-2366	634	24	.	.	PUNCT
ejpam-2366	635	1	hence	hence	ADV
ejpam-2366	635	2	we	we	PRON
ejpam-2366	635	3	must	must	AUX
ejpam-2366	635	4	have	have	VERB
ejpam-2366	635	5	(	(	PUNCT
ejpam-2366	635	6	n	n	X
ejpam-2366	635	7	:	:	PUNCT
ejpam-2366	635	8	a	a	X
ejpam-2366	635	9	)	)	PUNCT
ejpam-2366	635	10	=	=	SYM
ejpam-2366	635	11	(	(	PUNCT
ejpam-2366	635	12	(	(	PUNCT
ejpam-2366	635	13	n	n	X
ejpam-2366	635	14	:	:	PUNCT
ejpam-2366	635	15	i	i	PRON
ejpam-2366	635	16	m	m	PROPN
ejpam-2366	635	17	)	)	PUNCT
ejpam-2366	636	1	n	n	CCONJ
ejpam-2366	636	2	:	:	PUNCT
ejpam-2366	636	3	a	a	X
ejpam-2366	636	4	)	)	PUNCT
ejpam-2366	636	5	.	.	PUNCT
ejpam-2366	637	1	then	then	ADV
ejpam-2366	637	2	an	an	DET
ejpam-2366	637	3	6	6	NUM
ejpam-2366	637	4	a(n	a(n	NOUN
ejpam-2366	637	5	:	:	PUNCT
ejpam-2366	637	6	a	a	X
ejpam-2366	637	7	)	)	PUNCT
ejpam-2366	637	8	=	=	NOUN
ejpam-2366	637	9	a((n	a((n	NOUN
ejpam-2366	637	10	:	:	PUNCT
ejpam-2366	637	11	i	i	PRON
ejpam-2366	637	12	m	m	VERB
ejpam-2366	637	13	)	)	PUNCT
ejpam-2366	638	1	n	n	CCONJ
ejpam-2366	638	2	:	:	PUNCT
ejpam-2366	638	3	a	a	X
ejpam-2366	638	4	)	)	PUNCT
ejpam-2366	638	5	6	6	NUM
ejpam-2366	638	6	(	(	PUNCT
ejpam-2366	638	7	n	n	NUM
ejpam-2366	638	8	:	:	PUNCT
ejpam-2366	638	9	i	i	PRON
ejpam-2366	638	10	m	m	PROPN
ejpam-2366	638	11	)	)	PUNCT
ejpam-2366	638	12	n	n	NUM
ejpam-2366	638	13	which	which	PRON
ejpam-2366	638	14	implies	imply	VERB
ejpam-2366	638	15	a	a	DET
ejpam-2366	638	16	6	6	NUM
ejpam-2366	638	17	(	(	PUNCT
ejpam-2366	638	18	(	(	PUNCT
ejpam-2366	638	19	n	n	X
ejpam-2366	638	20	:	:	PUNCT
ejpam-2366	638	21	i	i	PRON
ejpam-2366	638	22	m	m	PROPN
ejpam-2366	638	23	)	)	PUNCT
ejpam-2366	638	24	n	n	CCONJ
ejpam-2366	638	25	:	:	PUNCT
ejpam-2366	638	26	n	n	X
ejpam-2366	638	27	)	)	PUNCT
ejpam-2366	638	28	and	and	CCONJ
ejpam-2366	638	29	so√	so√	NOUN
ejpam-2366	638	30	(	(	PUNCT
ejpam-2366	638	31	n	n	X
ejpam-2366	638	32	:	:	PUNCT
ejpam-2366	638	33	i	i	PRON
ejpam-2366	638	34	m	m	PROPN
ejpam-2366	638	35	)	)	PUNCT
ejpam-2366	639	1	n	n	CCONJ
ejpam-2366	639	2	:	:	PUNCT
ejpam-2366	640	1	i	i	PRON
ejpam-2366	640	2	m	m	VERB
ejpam-2366	640	3	6	6	NUM
ejpam-2366	640	4	(	(	PUNCT
ejpam-2366	640	5	(	(	PUNCT
ejpam-2366	640	6	n	n	X
ejpam-2366	640	7	:	:	PUNCT
ejpam-2366	640	8	i	i	PRON
ejpam-2366	640	9	m	m	PROPN
ejpam-2366	640	10	)	)	PUNCT
ejpam-2366	640	11	n	n	CCONJ
ejpam-2366	640	12	:	:	PUNCT
ejpam-2366	640	13	n	n	CCONJ
ejpam-2366	640	14	)	)	PUNCT
ejpam-2366	640	15	.	.	PUNCT
ejpam-2366	641	1	it	it	PRON
ejpam-2366	641	2	follows	follow	VERB
ejpam-2366	641	3	that	that	SCONJ
ejpam-2366	641	4	(	(	PUNCT
ejpam-2366	641	5	√	√	INTJ
ejpam-2366	641	6	(	(	PUNCT
ejpam-2366	641	7	n	n	NOUN
ejpam-2366	641	8	:	:	PUNCT
ejpam-2366	641	9	i	i	PRON
ejpam-2366	641	10	m	m	PROPN
ejpam-2366	641	11	)	)	PUNCT
ejpam-2366	641	12	n	n	CCONJ
ejpam-2366	641	13	:	:	PUNCT
ejpam-2366	641	14	i	i	PRON
ejpam-2366	641	15	m	m	VERB
ejpam-2366	641	16	)	)	PUNCT
ejpam-2366	641	17	n	n	PROPN
ejpam-2366	641	18	6	6	NUM
ejpam-2366	641	19	(	(	PUNCT
ejpam-2366	641	20	n	n	NUM
ejpam-2366	641	21	:	:	PUNCT
ejpam-2366	641	22	i	i	PRON
ejpam-2366	641	23	m	m	PROPN
ejpam-2366	641	24	)	)	PUNCT
ejpam-2366	641	25	n	n	CCONJ
ejpam-2366	641	26	and	and	CCONJ
ejpam-2366	641	27	hence	hence	ADV
ejpam-2366	641	28	(	(	PUNCT
ejpam-2366	641	29	√	√	INTJ
ejpam-2366	641	30	(	(	PUNCT
ejpam-2366	641	31	n	n	NOUN
ejpam-2366	641	32	:	:	PUNCT
ejpam-2366	641	33	i	i	PRON
ejpam-2366	641	34	m	m	PROPN
ejpam-2366	641	35	)	)	PUNCT
ejpam-2366	641	36	n	n	CCONJ
ejpam-2366	641	37	:	:	PUNCT
ejpam-2366	641	38	i	i	PRON
ejpam-2366	641	39	m	m	VERB
ejpam-2366	641	40	)	)	PUNCT
ejpam-2366	641	41	n	n	NOUN
ejpam-2366	641	42	=	=	SYM
ejpam-2366	641	43	(	(	PUNCT
ejpam-2366	641	44	n	n	X
ejpam-2366	641	45	:	:	PUNCT
ejpam-2366	641	46	i	i	PRON
ejpam-2366	641	47	m	m	PROPN
ejpam-2366	641	48	)	)	PUNCT
ejpam-2366	641	49	n	n	CCONJ
ejpam-2366	641	50	.	.	PUNCT
ejpam-2366	642	1	from	from	ADP
ejpam-2366	642	2	following	follow	VERB
ejpam-2366	642	3	example	example	NOUN
ejpam-2366	642	4	,	,	PUNCT
ejpam-2366	642	5	it	it	PRON
ejpam-2366	642	6	is	be	AUX
ejpam-2366	642	7	clear	clear	ADJ
ejpam-2366	642	8	that	that	SCONJ
ejpam-2366	642	9	an	an	DET
ejpam-2366	642	10	almost	almost	ADV
ejpam-2366	642	11	primary	primary	ADJ
ejpam-2366	642	12	element	element	NOUN
ejpam-2366	642	13	of	of	ADP
ejpam-2366	642	14	an	an	DET
ejpam-2366	642	15	l	l	NOUN
ejpam-2366	642	16	-	-	NOUN
ejpam-2366	642	17	module	module	NOUN
ejpam-2366	642	18	m	m	NOUN
ejpam-2366	642	19	need	need	AUX
ejpam-2366	642	20	not	not	PART
ejpam-2366	642	21	be	be	AUX
ejpam-2366	642	22	weakly	weakly	ADV
ejpam-2366	642	23	primary	primary	ADJ
ejpam-2366	642	24	.	.	PUNCT
ejpam-2366	642	25	example	example	NOUN
ejpam-2366	643	1	8	8	NUM
ejpam-2366	643	2	.	.	PUNCT
ejpam-2366	643	3	consider	consider	VERB
ejpam-2366	643	4	the	the	DET
ejpam-2366	643	5	lattice	lattice	NOUN
ejpam-2366	643	6	module	module	NOUN
ejpam-2366	643	7	as	as	ADP
ejpam-2366	643	8	in	in	ADP
ejpam-2366	643	9	example	example	NOUN
ejpam-2366	643	10	4	4	X
ejpam-2366	643	11	.	.	PUNCT
ejpam-2366	644	1	let	let	VERB
ejpam-2366	644	2	n	n	PRON
ejpam-2366	644	3	be	be	AUX
ejpam-2366	644	4	the	the	DET
ejpam-2366	644	5	cyclic	cyclic	ADJ
ejpam-2366	644	6	submodule	submodule	NOUN
ejpam-2366	644	7	of	of	ADP
ejpam-2366	644	8	m	m	AUX
ejpam-2366	644	9	generated	generate	VERB
ejpam-2366	644	10	by	by	ADP
ejpam-2366	644	11	6	6	NUM
ejpam-2366	644	12	.	.	PUNCT
ejpam-2366	645	1	it	it	PRON
ejpam-2366	645	2	is	be	AUX
ejpam-2366	645	3	easy	easy	ADJ
ejpam-2366	645	4	to	to	PART
ejpam-2366	645	5	see	see	VERB
ejpam-2366	645	6	that	that	SCONJ
ejpam-2366	645	7	the	the	DET
ejpam-2366	645	8	element	element	NOUN
ejpam-2366	645	9	n	n	NOUN
ejpam-2366	645	10	=	=	NOUN
ejpam-2366	645	11	<	<	X
ejpam-2366	645	12	6	6	NUM
ejpam-2366	645	13	>	>	X
ejpam-2366	645	14	is	be	AUX
ejpam-2366	645	15	almost	almost	ADV
ejpam-2366	645	16	primary	primary	ADJ
ejpam-2366	645	17	(	(	PUNCT
ejpam-2366	645	18	φ2	φ2	NOUN
ejpam-2366	645	19	-	-	PUNCT
ejpam-2366	645	20	primary	primary	NOUN
ejpam-2366	645	21	)	)	PUNCT
ejpam-2366	645	22	but	but	CCONJ
ejpam-2366	645	23	not	not	PART
ejpam-2366	645	24	weakly	weakly	ADV
ejpam-2366	645	25	primary	primary	ADJ
ejpam-2366	645	26	.	.	PUNCT
ejpam-2366	646	1	before	before	ADP
ejpam-2366	646	2	obtaining	obtain	VERB
ejpam-2366	646	3	the	the	DET
ejpam-2366	646	4	characterization	characterization	NOUN
ejpam-2366	646	5	of	of	ADP
ejpam-2366	646	6	an	an	DET
ejpam-2366	646	7	almost	almost	ADV
ejpam-2366	646	8	primary	primary	ADJ
ejpam-2366	646	9	element	element	NOUN
ejpam-2366	646	10	of	of	ADP
ejpam-2366	646	11	an	an	DET
ejpam-2366	646	12	l	l	NOUN
ejpam-2366	646	13	-	-	NOUN
ejpam-2366	646	14	module	module	NOUN
ejpam-2366	646	15	m	m	NOUN
ejpam-2366	646	16	in	in	ADP
ejpam-2366	646	17	terms	term	NOUN
ejpam-2366	646	18	of	of	ADP
ejpam-2366	646	19	a	a	DET
ejpam-2366	646	20	weakly	weakly	ADJ
ejpam-2366	646	21	primary	primary	ADJ
ejpam-2366	646	22	element	element	NOUN
ejpam-2366	646	23	of	of	ADP
ejpam-2366	646	24	m	m	PROPN
ejpam-2366	646	25	,	,	PUNCT
ejpam-2366	646	26	we	we	PRON
ejpam-2366	646	27	recall	recall	VERB
ejpam-2366	646	28	the	the	DET
ejpam-2366	646	29	definition	definition	NOUN
ejpam-2366	646	30	of	of	ADP
ejpam-2366	646	31	a	a	DET
ejpam-2366	646	32	local	local	ADJ
ejpam-2366	646	33	module	module	NOUN
ejpam-2366	646	34	m	m	PROPN
ejpam-2366	646	35	.	.	PUNCT
ejpam-2366	647	1	according	accord	VERB
ejpam-2366	647	2	to	to	ADP
ejpam-2366	647	3	[	[	X
ejpam-2366	647	4	1	1	NUM
ejpam-2366	647	5	]	]	PUNCT
ejpam-2366	647	6	,	,	PUNCT
ejpam-2366	647	7	an	an	DET
ejpam-2366	647	8	l	l	NOUN
ejpam-2366	647	9	-	-	NOUN
ejpam-2366	647	10	module	module	NOUN
ejpam-2366	647	11	m	m	NOUN
ejpam-2366	647	12	is	be	AUX
ejpam-2366	647	13	said	say	VERB
ejpam-2366	647	14	to	to	PART
ejpam-2366	647	15	be	be	AUX
ejpam-2366	647	16	a	a	DET
ejpam-2366	647	17	local	local	ADJ
ejpam-2366	647	18	module	module	NOUN
ejpam-2366	647	19	if	if	SCONJ
ejpam-2366	647	20	it	it	PRON
ejpam-2366	647	21	has	have	VERB
ejpam-2366	647	22	a	a	DET
ejpam-2366	647	23	unique	unique	ADJ
ejpam-2366	647	24	maximal	maximal	ADJ
ejpam-2366	647	25	element	element	NOUN
ejpam-2366	647	26	.	.	PUNCT
ejpam-2366	648	1	theorem	theorem	VERB
ejpam-2366	648	2	37	37	NUM
ejpam-2366	648	3	.	.	PUNCT
ejpam-2366	649	1	let	let	VERB
ejpam-2366	649	2	m	m	PRON
ejpam-2366	649	3	be	be	AUX
ejpam-2366	649	4	a	a	DET
ejpam-2366	649	5	local	local	ADJ
ejpam-2366	649	6	l	l	NOUN
ejpam-2366	649	7	-	-	NOUN
ejpam-2366	649	8	module	module	NOUN
ejpam-2366	649	9	with	with	ADP
ejpam-2366	649	10	a	a	DET
ejpam-2366	649	11	unique	unique	ADJ
ejpam-2366	649	12	maximal	maximal	ADJ
ejpam-2366	649	13	element	element	NOUN
ejpam-2366	649	14	q	q	PROPN
ejpam-2366	649	15	∈	∈	PROPN
ejpam-2366	649	16	m	m	VERB
ejpam-2366	649	17	such	such	ADJ
ejpam-2366	649	18	that	that	SCONJ
ejpam-2366	649	19	(	(	PUNCT
ejpam-2366	649	20	q	q	NOUN
ejpam-2366	649	21	:	:	PUNCT
ejpam-2366	649	22	i	i	PRON
ejpam-2366	649	23	m	m	VERB
ejpam-2366	649	24	)	)	PUNCT
ejpam-2366	649	25	q	q	NOUN
ejpam-2366	650	1	=	=	PUNCT
ejpam-2366	650	2	om	om	PROPN
ejpam-2366	650	3	.	.	PUNCT
ejpam-2366	651	1	then	then	ADV
ejpam-2366	651	2	a	a	DET
ejpam-2366	651	3	proper	proper	ADJ
ejpam-2366	651	4	element	element	NOUN
ejpam-2366	651	5	n	n	PRON
ejpam-2366	651	6	∈m	∈m	NOUN
ejpam-2366	651	7	is	be	AUX
ejpam-2366	651	8	almost	almost	ADV
ejpam-2366	651	9	primary	primary	ADJ
ejpam-2366	651	10	if	if	SCONJ
ejpam-2366	652	1	and	and	CCONJ
ejpam-2366	652	2	only	only	ADV
ejpam-2366	652	3	if	if	SCONJ
ejpam-2366	652	4	n	n	PRON
ejpam-2366	652	5	is	be	AUX
ejpam-2366	652	6	weakly	weakly	ADV
ejpam-2366	652	7	primary	primary	ADJ
ejpam-2366	652	8	.	.	PUNCT
ejpam-2366	653	1	proof	proof	NOUN
ejpam-2366	653	2	.	.	PUNCT
ejpam-2366	654	1	assume	assume	VERB
ejpam-2366	654	2	that	that	SCONJ
ejpam-2366	654	3	a	a	DET
ejpam-2366	654	4	proper	proper	ADJ
ejpam-2366	654	5	element	element	NOUN
ejpam-2366	654	6	n	n	CCONJ
ejpam-2366	654	7	∈	∈	NOUN
ejpam-2366	654	8	m	m	VERB
ejpam-2366	654	9	is	be	AUX
ejpam-2366	654	10	almost	almost	ADV
ejpam-2366	654	11	primary	primary	ADJ
ejpam-2366	654	12	.	.	PUNCT
ejpam-2366	655	1	then	then	ADV
ejpam-2366	655	2	n	n	PROPN
ejpam-2366	655	3	6	6	NUM
ejpam-2366	655	4	q.	q.	NOUN
ejpam-2366	655	5	it	it	PRON
ejpam-2366	655	6	follows	follow	VERB
ejpam-2366	655	7	that	that	PRON
ejpam-2366	655	8	(	(	PUNCT
ejpam-2366	655	9	n	n	X
ejpam-2366	655	10	:	:	PUNCT
ejpam-2366	655	11	i	i	PRON
ejpam-2366	655	12	m	m	PROPN
ejpam-2366	655	13	)	)	PUNCT
ejpam-2366	655	14	n	n	PROPN
ejpam-2366	655	15	6	6	NUM
ejpam-2366	655	16	(	(	PUNCT
ejpam-2366	655	17	q	q	NOUN
ejpam-2366	655	18	:	:	PUNCT
ejpam-2366	655	19	i	i	PRON
ejpam-2366	655	20	m	m	VERB
ejpam-2366	655	21	)	)	PUNCT
ejpam-2366	655	22	q	q	NOUN
ejpam-2366	656	1	=	=	PUNCT
ejpam-2366	656	2	om	om	PROPN
ejpam-2366	656	3	and	and	CCONJ
ejpam-2366	656	4	hence	hence	ADV
ejpam-2366	656	5	(	(	PUNCT
ejpam-2366	656	6	n	n	X
ejpam-2366	656	7	:	:	PUNCT
ejpam-2366	656	8	i	i	PRON
ejpam-2366	656	9	m	m	VERB
ejpam-2366	656	10	)	)	PUNCT
ejpam-2366	657	1	n	n	PROPN
ejpam-2366	657	2	=	=	SYM
ejpam-2366	657	3	om	om	PROPN
ejpam-2366	657	4	.	.	PUNCT
ejpam-2366	658	1	let	let	VERB
ejpam-2366	658	2	om	om	PROPN
ejpam-2366	658	3	6=	6=	NOUN
ejpam-2366	658	4	aa	aa	PROPN
ejpam-2366	658	5	6	6	NUM
ejpam-2366	658	6	n	n	NOUN
ejpam-2366	658	7	for	for	ADP
ejpam-2366	658	8	a	a	DET
ejpam-2366	658	9	∈	∈	PROPN
ejpam-2366	658	10	l	l	NOUN
ejpam-2366	658	11	,	,	PUNCT
ejpam-2366	658	12	a	a	DET
ejpam-2366	658	13	∈	∈	NOUN
ejpam-2366	658	14	m	m	NOUN
ejpam-2366	658	15	.	.	PUNCT
ejpam-2366	659	1	as	as	SCONJ
ejpam-2366	659	2	aa	aa	PROPN
ejpam-2366	659	3	6	6	NUM
ejpam-2366	659	4	n	n	NOUN
ejpam-2366	659	5	,	,	PUNCT
ejpam-2366	659	6	aa	aa	INTJ
ejpam-2366	659	7	(	(	PUNCT
ejpam-2366	659	8	n	n	NOUN
ejpam-2366	659	9	:	:	PUNCT
ejpam-2366	659	10	i	i	PRON
ejpam-2366	659	11	m	m	VERB
ejpam-2366	659	12	)	)	PUNCT
ejpam-2366	659	13	n	n	NOUN
ejpam-2366	659	14	=	=	SYM
ejpam-2366	659	15	om	om	PROPN
ejpam-2366	659	16	and	and	CCONJ
ejpam-2366	659	17	n	n	PRON
ejpam-2366	659	18	is	be	AUX
ejpam-2366	659	19	almost	almost	ADV
ejpam-2366	659	20	primary	primary	ADJ
ejpam-2366	659	21	,	,	PUNCT
ejpam-2366	659	22	we	we	PRON
ejpam-2366	659	23	have	have	VERB
ejpam-2366	659	24	either	either	CCONJ
ejpam-2366	659	25	a	a	DET
ejpam-2366	659	26	6	6	NUM
ejpam-2366	659	27	n	n	NOUN
ejpam-2366	659	28	or	or	CCONJ
ejpam-2366	659	29	a	a	DET
ejpam-2366	659	30	6	6	NUM
ejpam-2366	659	31	√	√	NUM
ejpam-2366	659	32	n	n	NOUN
ejpam-2366	659	33	:	:	PUNCT
ejpam-2366	659	34	i	i	PRON
ejpam-2366	659	35	m	m	VERB
ejpam-2366	659	36	and	and	CCONJ
ejpam-2366	659	37	hence	hence	ADV
ejpam-2366	659	38	n	n	PRON
ejpam-2366	659	39	is	be	AUX
ejpam-2366	659	40	weakly	weakly	ADV
ejpam-2366	659	41	primary	primary	ADJ
ejpam-2366	659	42	.	.	PUNCT
ejpam-2366	660	1	the	the	DET
ejpam-2366	660	2	converse	converse	NOUN
ejpam-2366	660	3	is	be	AUX
ejpam-2366	660	4	obvious	obvious	ADJ
ejpam-2366	660	5	from	from	ADP
ejpam-2366	660	6	theorem	theorem	ADJ
ejpam-2366	660	7	13	13	NUM
ejpam-2366	660	8	.	.	PUNCT
ejpam-2366	661	1	now	now	ADV
ejpam-2366	661	2	we	we	PRON
ejpam-2366	661	3	prove	prove	VERB
ejpam-2366	661	4	the	the	DET
ejpam-2366	661	5	result	result	NOUN
ejpam-2366	661	6	required	require	VERB
ejpam-2366	661	7	to	to	PART
ejpam-2366	661	8	show	show	VERB
ejpam-2366	661	9	that	that	SCONJ
ejpam-2366	661	10	if	if	SCONJ
ejpam-2366	661	11	an	an	DET
ejpam-2366	661	12	element	element	NOUN
ejpam-2366	661	13	in	in	ADP
ejpam-2366	661	14	m	m	PROPN
ejpam-2366	661	15	(	(	PUNCT
ejpam-2366	661	16	or	or	CCONJ
ejpam-2366	661	17	l	l	NOUN
ejpam-2366	661	18	)	)	PUNCT
ejpam-2366	661	19	is	be	AUX
ejpam-2366	661	20	almost	almost	ADV
ejpam-2366	661	21	primary	primary	ADJ
ejpam-2366	661	22	,	,	PUNCT
ejpam-2366	661	23	then	then	ADV
ejpam-2366	661	24	its	its	PRON
ejpam-2366	661	25	corresponding	corresponding	ADJ
ejpam-2366	661	26	element	element	NOUN
ejpam-2366	661	27	in	in	ADP
ejpam-2366	661	28	l	l	PROPN
ejpam-2366	661	29	(	(	PUNCT
ejpam-2366	661	30	or	or	CCONJ
ejpam-2366	661	31	m	m	VERB
ejpam-2366	661	32	)	)	PUNCT
ejpam-2366	661	33	is	be	AUX
ejpam-2366	661	34	also	also	ADV
ejpam-2366	661	35	almost	almost	ADV
ejpam-2366	661	36	primary	primary	ADJ
ejpam-2366	661	37	.	.	PUNCT
ejpam-2366	662	1	lemma	lemma	PROPN
ejpam-2366	662	2	4	4	X
ejpam-2366	662	3	.	.	PUNCT
ejpam-2366	663	1	let	let	VERB
ejpam-2366	663	2	m	m	PRON
ejpam-2366	663	3	be	be	AUX
ejpam-2366	663	4	a	a	DET
ejpam-2366	663	5	torsion	torsion	NOUN
ejpam-2366	663	6	free	free	ADJ
ejpam-2366	663	7	multiplication	multiplication	NOUN
ejpam-2366	663	8	lattice	lattice	PROPN
ejpam-2366	663	9	l	l	NOUN
ejpam-2366	663	10	-	-	NOUN
ejpam-2366	663	11	module	module	NOUN
ejpam-2366	664	1	and	and	CCONJ
ejpam-2366	664	2	i	i	PRON
ejpam-2366	664	3	m	m	VERB
ejpam-2366	664	4	be	be	VERB
ejpam-2366	664	5	a	a	DET
ejpam-2366	664	6	weak	weak	ADJ
ejpam-2366	664	7	join	join	NOUN
ejpam-2366	664	8	principal	principal	ADJ
ejpam-2366	664	9	element	element	NOUN
ejpam-2366	664	10	of	of	ADP
ejpam-2366	664	11	m	m	PROPN
ejpam-2366	664	12	.	.	PUNCT
ejpam-2366	665	1	let	let	VERB
ejpam-2366	665	2	n	n	PRON
ejpam-2366	665	3	be	be	AUX
ejpam-2366	665	4	a	a	DET
ejpam-2366	665	5	proper	proper	ADJ
ejpam-2366	665	6	element	element	NOUN
ejpam-2366	665	7	of	of	ADP
ejpam-2366	665	8	m	m	PROPN
ejpam-2366	665	9	.	.	PUNCT
ejpam-2366	666	1	then	then	ADV
ejpam-2366	666	2	a(n	a(n	ADV
ejpam-2366	666	3	:	:	PUNCT
ejpam-2366	667	1	i	i	PRON
ejpam-2366	667	2	m	m	VERB
ejpam-2366	667	3	)	)	PUNCT
ejpam-2366	668	1	=	=	SYM
ejpam-2366	668	2	(	(	PUNCT
ejpam-2366	668	3	an	an	PRON
ejpam-2366	668	4	:	:	PUNCT
ejpam-2366	668	5	i	i	PRON
ejpam-2366	668	6	m	m	PROPN
ejpam-2366	668	7	)	)	PUNCT
ejpam-2366	668	8	for	for	ADP
ejpam-2366	668	9	a	a	DET
ejpam-2366	668	10	∈	∈	PROPN
ejpam-2366	668	11	l.	l.	NOUN
ejpam-2366	668	12	proof	proof	NOUN
ejpam-2366	668	13	.	.	PUNCT
ejpam-2366	669	1	since	since	SCONJ
ejpam-2366	669	2	m	m	PROPN
ejpam-2366	669	3	is	be	AUX
ejpam-2366	669	4	a	a	DET
ejpam-2366	669	5	multiplication	multiplication	NOUN
ejpam-2366	669	6	lattice	lattice	NOUN
ejpam-2366	669	7	l	l	NOUN
ejpam-2366	669	8	-	-	NOUN
ejpam-2366	669	9	module	module	NOUN
ejpam-2366	669	10	,	,	PUNCT
ejpam-2366	669	11	n	n	NOUN
ejpam-2366	669	12	=	=	SYM
ejpam-2366	669	13	(	(	PUNCT
ejpam-2366	669	14	n	n	X
ejpam-2366	669	15	:	:	PUNCT
ejpam-2366	669	16	i	i	PRON
ejpam-2366	669	17	m	m	VERB
ejpam-2366	669	18	)	)	PUNCT
ejpam-2366	669	19	i	i	PRON
ejpam-2366	669	20	m	m	VERB
ejpam-2366	669	21	.	.	PUNCT
ejpam-2366	670	1	then	then	ADV
ejpam-2366	670	2	a(n	a(n	ADV
ejpam-2366	670	3	:	:	PUNCT
ejpam-2366	670	4	i	i	PRON
ejpam-2366	670	5	m	m	VERB
ejpam-2366	670	6	)	)	PUNCT
ejpam-2366	671	1	i	i	PRON
ejpam-2366	671	2	m	m	VERB
ejpam-2366	671	3	=	=	VERB
ejpam-2366	671	4	an	an	PROPN
ejpam-2366	671	5	=	=	X
ejpam-2366	671	6	(	(	PUNCT
ejpam-2366	671	7	an	an	PRON
ejpam-2366	671	8	:	:	PUNCT
ejpam-2366	671	9	i	i	PRON
ejpam-2366	671	10	m	m	VERB
ejpam-2366	671	11	)	)	PUNCT
ejpam-2366	672	1	i	i	PRON
ejpam-2366	672	2	m	m	VERB
ejpam-2366	673	1	and	and	CCONJ
ejpam-2366	673	2	so	so	ADV
ejpam-2366	673	3	the	the	DET
ejpam-2366	673	4	result	result	NOUN
ejpam-2366	673	5	follows	follow	VERB
ejpam-2366	673	6	by	by	ADP
ejpam-2366	673	7	lemma	lemma	PROPN
ejpam-2366	673	8	3	3	NUM
ejpam-2366	673	9	.	.	PUNCT
ejpam-2366	673	10	theorem	theorem	VERB
ejpam-2366	673	11	38	38	NUM
ejpam-2366	673	12	.	.	PUNCT
ejpam-2366	674	1	let	let	VERB
ejpam-2366	674	2	l	l	NOUN
ejpam-2366	674	3	be	be	AUX
ejpam-2366	674	4	a	a	DET
ejpam-2366	674	5	pg	pg	NOUN
ejpam-2366	674	6	-	-	PUNCT
ejpam-2366	674	7	lattice	lattice	NOUN
ejpam-2366	674	8	and	and	CCONJ
ejpam-2366	674	9	m	m	AUX
ejpam-2366	674	10	be	be	AUX
ejpam-2366	674	11	a	a	DET
ejpam-2366	674	12	faithful	faithful	ADJ
ejpam-2366	674	13	multiplication	multiplication	NOUN
ejpam-2366	674	14	torsion	torsion	NOUN
ejpam-2366	674	15	free	free	ADJ
ejpam-2366	674	16	pglattice	pglattice	NOUN
ejpam-2366	674	17	l	l	NOUN
ejpam-2366	674	18	-	-	NOUN
ejpam-2366	674	19	module	module	NOUN
ejpam-2366	674	20	with	with	ADP
ejpam-2366	674	21	i	i	PRON
ejpam-2366	674	22	m	m	VERB
ejpam-2366	674	23	compact	compact	ADJ
ejpam-2366	674	24	.	.	PUNCT
ejpam-2366	675	1	let	let	VERB
ejpam-2366	675	2	i	i	PRON
ejpam-2366	675	3	m	m	AUX
ejpam-2366	675	4	be	be	AUX
ejpam-2366	675	5	a	a	DET
ejpam-2366	675	6	weak	weak	ADJ
ejpam-2366	675	7	join	join	NOUN
ejpam-2366	675	8	principal	principal	ADJ
ejpam-2366	675	9	element	element	NOUN
ejpam-2366	675	10	and	and	CCONJ
ejpam-2366	675	11	n	n	CCONJ
ejpam-2366	675	12	be	be	VERB
ejpam-2366	675	13	a	a	DET
ejpam-2366	675	14	proper	proper	ADJ
ejpam-2366	675	15	element	element	NOUN
ejpam-2366	675	16	of	of	ADP
ejpam-2366	675	17	m	m	PROPN
ejpam-2366	675	18	.	.	PUNCT
ejpam-2366	676	1	then	then	ADV
ejpam-2366	676	2	the	the	DET
ejpam-2366	676	3	following	follow	VERB
ejpam-2366	676	4	statements	statement	NOUN
ejpam-2366	676	5	are	be	AUX
ejpam-2366	676	6	equivalent	equivalent	ADJ
ejpam-2366	676	7	:	:	PUNCT
ejpam-2366	676	8	a.	a.	PROPN
ejpam-2366	676	9	v.	v.	PROPN
ejpam-2366	676	10	bingi	bingi	PROPN
ejpam-2366	676	11	,	,	PUNCT
ejpam-2366	676	12	c.	c.	PROPN
ejpam-2366	676	13	s.	s.	PROPN
ejpam-2366	676	14	manjarekar	manjarekar	PROPN
ejpam-2366	676	15	/	/	PROPN
ejpam-2366	676	16	eur	eur	PROPN
ejpam-2366	676	17	.	.	PUNCT
ejpam-2366	677	1	j.	j.	PROPN
ejpam-2366	677	2	pure	pure	PROPN
ejpam-2366	677	3	appl	appl	PROPN
ejpam-2366	677	4	.	.	PROPN
ejpam-2366	677	5	math	math	PROPN
ejpam-2366	677	6	,	,	PUNCT
ejpam-2366	677	7	14	14	NUM
ejpam-2366	677	8	(	(	PUNCT
ejpam-2366	677	9	2	2	NUM
ejpam-2366	677	10	)	)	PUNCT
ejpam-2366	677	11	(	(	PUNCT
ejpam-2366	677	12	2021	2021	NUM
ejpam-2366	677	13	)	)	PUNCT
ejpam-2366	677	14	,	,	PUNCT
ejpam-2366	677	15	551	551	NUM
ejpam-2366	677	16	-	-	SYM
ejpam-2366	677	17	577	577	NUM
ejpam-2366	677	18	569	569	NUM
ejpam-2366	677	19	1	1	NUM
ejpam-2366	677	20	©	©	PROPN
ejpam-2366	677	21	n	n	NUM
ejpam-2366	677	22	is	be	AUX
ejpam-2366	677	23	an	an	DET
ejpam-2366	677	24	almost	almost	ADV
ejpam-2366	677	25	primary	primary	ADJ
ejpam-2366	677	26	element	element	NOUN
ejpam-2366	677	27	of	of	ADP
ejpam-2366	677	28	m	m	PROPN
ejpam-2366	677	29	.	.	PUNCT
ejpam-2366	678	1	2	2	NUM
ejpam-2366	678	2	©	©	NOUN
ejpam-2366	678	3	(	(	PUNCT
ejpam-2366	678	4	n	n	NOUN
ejpam-2366	678	5	:	:	PUNCT
ejpam-2366	678	6	i	i	PRON
ejpam-2366	678	7	m	m	PROPN
ejpam-2366	678	8	)	)	PUNCT
ejpam-2366	678	9	is	be	AUX
ejpam-2366	678	10	an	an	DET
ejpam-2366	678	11	almost	almost	ADV
ejpam-2366	678	12	primary	primary	ADJ
ejpam-2366	678	13	element	element	NOUN
ejpam-2366	678	14	of	of	ADP
ejpam-2366	678	15	l.	l.	PROPN
ejpam-2366	678	16	3	3	NUM
ejpam-2366	678	17	©	©	PROPN
ejpam-2366	678	18	n	n	NOUN
ejpam-2366	678	19	=	=	X
ejpam-2366	678	20	qim	qim	NOUN
ejpam-2366	678	21	for	for	ADP
ejpam-2366	678	22	some	some	DET
ejpam-2366	678	23	almost	almost	ADV
ejpam-2366	678	24	primary	primary	ADJ
ejpam-2366	678	25	element	element	NOUN
ejpam-2366	678	26	q	q	PROPN
ejpam-2366	678	27	∈	∈	PROPN
ejpam-2366	678	28	l	l	NOUN
ejpam-2366	678	29	which	which	PRON
ejpam-2366	678	30	is	be	AUX
ejpam-2366	678	31	maximal	maximal	ADJ
ejpam-2366	678	32	in	in	ADP
ejpam-2366	678	33	the	the	DET
ejpam-2366	678	34	sense	sense	NOUN
ejpam-2366	678	35	that	that	SCONJ
ejpam-2366	678	36	if	if	SCONJ
ejpam-2366	678	37	aim	aim	VERB
ejpam-2366	678	38	=	=	SYM
ejpam-2366	678	39	n	n	CCONJ
ejpam-2366	678	40	,	,	PUNCT
ejpam-2366	678	41	then	then	ADV
ejpam-2366	678	42	a	a	DET
ejpam-2366	678	43	6	6	NUM
ejpam-2366	678	44	q	q	NOUN
ejpam-2366	678	45	where	where	SCONJ
ejpam-2366	678	46	a	a	DET
ejpam-2366	678	47	∈	∈	PROPN
ejpam-2366	678	48	l.	l.	NOUN
ejpam-2366	678	49	proof	proof	NOUN
ejpam-2366	678	50	.	.	PUNCT
ejpam-2366	679	1	1	1	NUM
ejpam-2366	679	2	©	©	NOUN
ejpam-2366	679	3	=⇒	=⇒	NOUN
ejpam-2366	679	4	2	2	NUM
ejpam-2366	679	5	©	©	NOUN
ejpam-2366	679	6	.	.	PUNCT
ejpam-2366	679	7	assume	assume	VERB
ejpam-2366	679	8	that	that	SCONJ
ejpam-2366	679	9	n	n	PRON
ejpam-2366	679	10	is	be	AUX
ejpam-2366	679	11	an	an	DET
ejpam-2366	679	12	almost	almost	ADV
ejpam-2366	679	13	primary	primary	ADJ
ejpam-2366	679	14	element	element	NOUN
ejpam-2366	679	15	of	of	ADP
ejpam-2366	679	16	m	m	PROPN
ejpam-2366	679	17	.	.	PUNCT
ejpam-2366	680	1	let	let	VERB
ejpam-2366	680	2	ab	ab	PROPN
ejpam-2366	680	3	6	6	NUM
ejpam-2366	680	4	(	(	PUNCT
ejpam-2366	680	5	n	n	NUM
ejpam-2366	680	6	:	:	PUNCT
ejpam-2366	680	7	i	i	PRON
ejpam-2366	680	8	m	m	PROPN
ejpam-2366	680	9	)	)	PUNCT
ejpam-2366	680	10	and	and	CCONJ
ejpam-2366	680	11	ab	ab	PROPN
ejpam-2366	680	12	(	(	PUNCT
ejpam-2366	680	13	n	n	PROPN
ejpam-2366	680	14	:	:	PUNCT
ejpam-2366	680	15	i	i	PRON
ejpam-2366	680	16	m	m	VERB
ejpam-2366	680	17	)	)	PUNCT
ejpam-2366	680	18	2	2	NUM
ejpam-2366	680	19	for	for	ADP
ejpam-2366	680	20	a	a	DET
ejpam-2366	680	21	,	,	PUNCT
ejpam-2366	680	22	b	b	PROPN
ejpam-2366	680	23	∈	∈	PROPN
ejpam-2366	680	24	l.	l.	NOUN
ejpam-2366	680	25	then	then	ADV
ejpam-2366	680	26	abim	abim	PROPN
ejpam-2366	680	27	6	6	NUM
ejpam-2366	680	28	n	n	NOUN
ejpam-2366	680	29	.	.	PUNCT
ejpam-2366	681	1	if	if	SCONJ
ejpam-2366	681	2	abim	abim	NOUN
ejpam-2366	681	3	6	6	NUM
ejpam-2366	681	4	(	(	PUNCT
ejpam-2366	681	5	n	n	NUM
ejpam-2366	681	6	:	:	PUNCT
ejpam-2366	681	7	i	i	PRON
ejpam-2366	681	8	m	m	PROPN
ejpam-2366	681	9	)	)	PUNCT
ejpam-2366	681	10	n	n	CCONJ
ejpam-2366	681	11	,	,	PUNCT
ejpam-2366	681	12	then	then	ADV
ejpam-2366	681	13	by	by	ADP
ejpam-2366	681	14	lemma	lemma	PROPN
ejpam-2366	681	15	4	4	NUM
ejpam-2366	681	16	,	,	PUNCT
ejpam-2366	681	17	we	we	PRON
ejpam-2366	681	18	have	have	VERB
ejpam-2366	681	19	ab	ab	PROPN
ejpam-2366	681	20	6	6	NUM
ejpam-2366	681	21	(	(	PUNCT
ejpam-2366	681	22	(	(	PUNCT
ejpam-2366	681	23	n	n	X
ejpam-2366	681	24	:	:	PUNCT
ejpam-2366	681	25	i	i	PRON
ejpam-2366	681	26	m	m	PROPN
ejpam-2366	681	27	)	)	PUNCT
ejpam-2366	681	28	n	n	CCONJ
ejpam-2366	681	29	:	:	PUNCT
ejpam-2366	682	1	i	i	PRON
ejpam-2366	682	2	m	m	VERB
ejpam-2366	682	3	)	)	PUNCT
ejpam-2366	683	1	=	=	SYM
ejpam-2366	683	2	(	(	PUNCT
ejpam-2366	683	3	n	n	X
ejpam-2366	683	4	:	:	PUNCT
ejpam-2366	683	5	i	i	PRON
ejpam-2366	683	6	m	m	VERB
ejpam-2366	683	7	)	)	PUNCT
ejpam-2366	683	8	(	(	PUNCT
ejpam-2366	683	9	n	n	X
ejpam-2366	683	10	:	:	PUNCT
ejpam-2366	683	11	i	i	PRON
ejpam-2366	683	12	m	m	VERB
ejpam-2366	683	13	)	)	PUNCT
ejpam-2366	683	14	which	which	PRON
ejpam-2366	683	15	contradicts	contradict	VERB
ejpam-2366	683	16	ab	ab	PROPN
ejpam-2366	683	17	(	(	PUNCT
ejpam-2366	683	18	n	n	PROPN
ejpam-2366	683	19	:	:	PUNCT
ejpam-2366	683	20	i	i	PRON
ejpam-2366	683	21	m	m	VERB
ejpam-2366	683	22	)	)	PUNCT
ejpam-2366	683	23	2	2	X
ejpam-2366	683	24	.	.	PUNCT
ejpam-2366	684	1	so	so	ADV
ejpam-2366	684	2	let	let	VERB
ejpam-2366	684	3	a(bim	a(bim	PROPN
ejpam-2366	684	4	)	)	PUNCT
ejpam-2366	685	1	(	(	PUNCT
ejpam-2366	685	2	n	n	X
ejpam-2366	685	3	:	:	PUNCT
ejpam-2366	685	4	i	i	PRON
ejpam-2366	685	5	m	m	PROPN
ejpam-2366	685	6	)	)	PUNCT
ejpam-2366	685	7	n	n	PROPN
ejpam-2366	685	8	.	.	PUNCT
ejpam-2366	686	1	then	then	ADV
ejpam-2366	686	2	as	as	SCONJ
ejpam-2366	686	3	n	n	PRON
ejpam-2366	686	4	is	be	AUX
ejpam-2366	686	5	almost	almost	ADV
ejpam-2366	686	6	primary	primary	ADJ
ejpam-2366	686	7	,	,	PUNCT
ejpam-2366	686	8	we	we	PRON
ejpam-2366	686	9	have	have	VERB
ejpam-2366	686	10	either	either	CCONJ
ejpam-2366	686	11	a	a	DET
ejpam-2366	686	12	6	6	NUM
ejpam-2366	686	13	√	√	NUM
ejpam-2366	687	1	n	n	NOUN
ejpam-2366	687	2	:	:	PUNCT
ejpam-2366	687	3	i	i	PRON
ejpam-2366	687	4	m	m	VERB
ejpam-2366	687	5	or	or	CCONJ
ejpam-2366	687	6	bim	bim	VERB
ejpam-2366	687	7	6	6	NUM
ejpam-2366	687	8	n	n	NOUN
ejpam-2366	687	9	and	and	CCONJ
ejpam-2366	687	10	thus	thus	ADV
ejpam-2366	687	11	(	(	PUNCT
ejpam-2366	687	12	n	n	X
ejpam-2366	687	13	:	:	PUNCT
ejpam-2366	687	14	i	i	PRON
ejpam-2366	687	15	m	m	PROPN
ejpam-2366	687	16	)	)	PUNCT
ejpam-2366	687	17	is	be	AUX
ejpam-2366	687	18	an	an	DET
ejpam-2366	687	19	almost	almost	ADV
ejpam-2366	687	20	primary	primary	ADJ
ejpam-2366	687	21	element	element	NOUN
ejpam-2366	687	22	of	of	ADP
ejpam-2366	687	23	l.	l.	PROPN
ejpam-2366	687	24	2	2	NUM
ejpam-2366	687	25	©	©	PROPN
ejpam-2366	687	26	=⇒	=⇒	NOUN
ejpam-2366	687	27	3	3	NUM
ejpam-2366	687	28	©	©	PROPN
ejpam-2366	687	29	.	.	PUNCT
ejpam-2366	688	1	assume	assume	VERB
ejpam-2366	688	2	that	that	SCONJ
ejpam-2366	688	3	(	(	PUNCT
ejpam-2366	688	4	n	n	X
ejpam-2366	688	5	:	:	PUNCT
ejpam-2366	688	6	i	i	PRON
ejpam-2366	688	7	m	m	VERB
ejpam-2366	688	8	)	)	PUNCT
ejpam-2366	689	1	=	=	PRON
ejpam-2366	689	2	q	q	X
ejpam-2366	689	3	is	be	AUX
ejpam-2366	689	4	an	an	DET
ejpam-2366	689	5	almost	almost	ADV
ejpam-2366	689	6	primary	primary	ADJ
ejpam-2366	689	7	element	element	NOUN
ejpam-2366	689	8	of	of	ADP
ejpam-2366	689	9	l.	l.	PROPN
ejpam-2366	689	10	then	then	ADV
ejpam-2366	689	11	qim	qim	PROPN
ejpam-2366	689	12	6	6	NUM
ejpam-2366	689	13	n	n	NOUN
ejpam-2366	689	14	.	.	PUNCT
ejpam-2366	690	1	since	since	SCONJ
ejpam-2366	690	2	m	m	PROPN
ejpam-2366	690	3	is	be	AUX
ejpam-2366	690	4	a	a	DET
ejpam-2366	690	5	multiplication	multiplication	NOUN
ejpam-2366	690	6	lattice	lattice	NOUN
ejpam-2366	690	7	module	module	NOUN
ejpam-2366	690	8	,	,	PUNCT
ejpam-2366	690	9	n	n	NOUN
ejpam-2366	690	10	=	=	PRON
ejpam-2366	690	11	aim	aim	VERB
ejpam-2366	690	12	for	for	ADP
ejpam-2366	690	13	some	some	DET
ejpam-2366	690	14	a	a	DET
ejpam-2366	690	15	∈	∈	NOUN
ejpam-2366	690	16	l.	l.	NOUN
ejpam-2366	690	17	so	so	SCONJ
ejpam-2366	690	18	a	a	DET
ejpam-2366	690	19	6	6	NUM
ejpam-2366	690	20	(	(	PUNCT
ejpam-2366	690	21	n	n	NUM
ejpam-2366	690	22	:	:	PUNCT
ejpam-2366	690	23	i	i	PRON
ejpam-2366	690	24	m	m	VERB
ejpam-2366	690	25	)	)	PUNCT
ejpam-2366	691	1	=	=	SYM
ejpam-2366	691	2	q	q	X
ejpam-2366	691	3	and	and	CCONJ
ejpam-2366	691	4	thus	thus	ADV
ejpam-2366	691	5	n	n	CCONJ
ejpam-2366	691	6	=	=	PRON
ejpam-2366	691	7	aim	aim	VERB
ejpam-2366	691	8	6	6	NUM
ejpam-2366	691	9	qim	qim	NOUN
ejpam-2366	691	10	.	.	PUNCT
ejpam-2366	692	1	hence	hence	ADV
ejpam-2366	692	2	n	n	NOUN
ejpam-2366	692	3	=	=	PUNCT
ejpam-2366	692	4	qim	qim	NOUN
ejpam-2366	692	5	for	for	ADP
ejpam-2366	692	6	some	some	DET
ejpam-2366	692	7	almost	almost	ADV
ejpam-2366	692	8	primary	primary	ADJ
ejpam-2366	692	9	element	element	NOUN
ejpam-2366	692	10	q	q	PROPN
ejpam-2366	692	11	∈	∈	PROPN
ejpam-2366	692	12	l	l	NOUN
ejpam-2366	692	13	which	which	PRON
ejpam-2366	692	14	is	be	AUX
ejpam-2366	692	15	maximal	maximal	ADJ
ejpam-2366	692	16	in	in	ADP
ejpam-2366	692	17	the	the	DET
ejpam-2366	692	18	sense	sense	NOUN
ejpam-2366	693	1	that	that	SCONJ
ejpam-2366	693	2	if	if	SCONJ
ejpam-2366	693	3	aim	aim	VERB
ejpam-2366	693	4	=	=	SYM
ejpam-2366	693	5	n	n	CCONJ
ejpam-2366	693	6	,	,	PUNCT
ejpam-2366	693	7	then	then	ADV
ejpam-2366	693	8	a	a	DET
ejpam-2366	693	9	6	6	NUM
ejpam-2366	693	10	q.	q.	NOUN
ejpam-2366	693	11	3	3	NUM
ejpam-2366	693	12	©	©	NOUN
ejpam-2366	693	13	=⇒	=⇒	NOUN
ejpam-2366	693	14	1	1	NUM
ejpam-2366	693	15	©	©	NOUN
ejpam-2366	693	16	.	.	PUNCT
ejpam-2366	693	17	suppose	suppose	VERB
ejpam-2366	693	18	n	n	PROPN
ejpam-2366	693	19	=	=	PUNCT
ejpam-2366	693	20	qim	qim	NOUN
ejpam-2366	693	21	for	for	ADP
ejpam-2366	693	22	some	some	DET
ejpam-2366	693	23	almost	almost	ADV
ejpam-2366	693	24	primary	primary	ADJ
ejpam-2366	693	25	element	element	NOUN
ejpam-2366	693	26	q	q	PROPN
ejpam-2366	693	27	∈	∈	PROPN
ejpam-2366	693	28	l	l	NOUN
ejpam-2366	693	29	which	which	PRON
ejpam-2366	693	30	is	be	AUX
ejpam-2366	693	31	maximal	maximal	ADJ
ejpam-2366	693	32	in	in	ADP
ejpam-2366	693	33	the	the	DET
ejpam-2366	693	34	sense	sense	NOUN
ejpam-2366	693	35	that	that	SCONJ
ejpam-2366	693	36	if	if	SCONJ
ejpam-2366	693	37	aim	aim	VERB
ejpam-2366	693	38	=	=	SYM
ejpam-2366	693	39	n	n	CCONJ
ejpam-2366	693	40	,	,	PUNCT
ejpam-2366	693	41	then	then	ADV
ejpam-2366	693	42	a	a	DET
ejpam-2366	693	43	6	6	NUM
ejpam-2366	693	44	q	q	NOUN
ejpam-2366	693	45	where	where	SCONJ
ejpam-2366	693	46	a	a	DET
ejpam-2366	693	47	∈	∈	PROPN
ejpam-2366	693	48	l.	l.	NOUN
ejpam-2366	693	49	then	then	ADV
ejpam-2366	693	50	q	q	PROPN
ejpam-2366	693	51	6	6	NUM
ejpam-2366	693	52	(	(	PUNCT
ejpam-2366	693	53	n	n	NUM
ejpam-2366	693	54	:	:	PUNCT
ejpam-2366	693	55	i	i	PRON
ejpam-2366	693	56	m	m	PROPN
ejpam-2366	693	57	)	)	PUNCT
ejpam-2366	693	58	.	.	PUNCT
ejpam-2366	694	1	now	now	ADV
ejpam-2366	694	2	,	,	PUNCT
ejpam-2366	694	3	let	let	VERB
ejpam-2366	694	4	rx	rx	VERB
ejpam-2366	694	5	6	6	NUM
ejpam-2366	694	6	n	n	NOUN
ejpam-2366	694	7	,	,	PUNCT
ejpam-2366	694	8	rx	rx	VERB
ejpam-2366	694	9	(	(	PUNCT
ejpam-2366	694	10	n	n	X
ejpam-2366	694	11	:	:	PUNCT
ejpam-2366	694	12	i	i	PRON
ejpam-2366	694	13	m	m	PROPN
ejpam-2366	694	14	)	)	PUNCT
ejpam-2366	694	15	n	n	PROPN
ejpam-2366	694	16	and	and	CCONJ
ejpam-2366	694	17	x	x	SYM
ejpam-2366	694	18	n	n	PROPN
ejpam-2366	694	19	for	for	ADP
ejpam-2366	694	20	r	r	PROPN
ejpam-2366	694	21	∈	∈	PROPN
ejpam-2366	694	22	l	l	NOUN
ejpam-2366	694	23	,	,	PUNCT
ejpam-2366	694	24	x	x	SYM
ejpam-2366	694	25	∈	∈	PROPN
ejpam-2366	694	26	m	m	VERB
ejpam-2366	694	27	.	.	PUNCT
ejpam-2366	695	1	since	since	SCONJ
ejpam-2366	695	2	m	m	PROPN
ejpam-2366	695	3	is	be	AUX
ejpam-2366	695	4	a	a	DET
ejpam-2366	695	5	multiplication	multiplication	NOUN
ejpam-2366	695	6	lattice	lattice	NOUN
ejpam-2366	695	7	module	module	NOUN
ejpam-2366	695	8	,	,	PUNCT
ejpam-2366	695	9	x	x	SYM
ejpam-2366	695	10	=	=	SYM
ejpam-2366	695	11	cim	cim	NOUN
ejpam-2366	695	12	for	for	ADP
ejpam-2366	695	13	some	some	DET
ejpam-2366	695	14	c	c	PROPN
ejpam-2366	695	15	∈	∈	PROPN
ejpam-2366	695	16	l.	l.	PROPN
ejpam-2366	695	17	then	then	ADV
ejpam-2366	695	18	rc	rc	PROPN
ejpam-2366	695	19	6	6	NUM
ejpam-2366	695	20	(	(	PUNCT
ejpam-2366	695	21	n	n	NUM
ejpam-2366	695	22	:	:	PUNCT
ejpam-2366	695	23	i	i	PRON
ejpam-2366	695	24	m	m	VERB
ejpam-2366	695	25	)	)	PUNCT
ejpam-2366	695	26	6	6	NUM
ejpam-2366	695	27	q	q	NOUN
ejpam-2366	695	28	,	,	PUNCT
ejpam-2366	695	29	using	use	VERB
ejpam-2366	695	30	maximality	maximality	NOUN
ejpam-2366	695	31	of	of	ADP
ejpam-2366	695	32	q	q	NOUN
ejpam-2366	695	33	to	to	ADP
ejpam-2366	695	34	n	n	NOUN
ejpam-2366	695	35	=	=	SYM
ejpam-2366	695	36	(	(	PUNCT
ejpam-2366	695	37	n	n	X
ejpam-2366	695	38	:	:	PUNCT
ejpam-2366	695	39	i	i	PRON
ejpam-2366	695	40	m	m	VERB
ejpam-2366	695	41	)	)	PUNCT
ejpam-2366	696	1	i	i	PRON
ejpam-2366	696	2	m	m	VERB
ejpam-2366	696	3	(	(	PUNCT
ejpam-2366	696	4	by	by	ADP
ejpam-2366	696	5	proposition	proposition	NOUN
ejpam-2366	696	6	3	3	NUM
ejpam-2366	696	7	of	of	ADP
ejpam-2366	696	8	[	[	X
ejpam-2366	696	9	10	10	NUM
ejpam-2366	696	10	]	]	NUM
ejpam-2366	696	11	)	)	PUNCT
ejpam-2366	696	12	.	.	PUNCT
ejpam-2366	697	1	if	if	SCONJ
ejpam-2366	697	2	rc	rc	PROPN
ejpam-2366	697	3	6	6	NUM
ejpam-2366	697	4	q2	q2	NOUN
ejpam-2366	697	5	,	,	PUNCT
ejpam-2366	697	6	then	then	ADV
ejpam-2366	697	7	rx	rx	VERB
ejpam-2366	697	8	6	6	NUM
ejpam-2366	697	9	qn	qn	NOUN
ejpam-2366	697	10	6	6	NUM
ejpam-2366	697	11	(	(	PUNCT
ejpam-2366	697	12	n	n	NUM
ejpam-2366	697	13	:	:	PUNCT
ejpam-2366	697	14	i	i	PRON
ejpam-2366	697	15	m	m	PROPN
ejpam-2366	697	16	)	)	PUNCT
ejpam-2366	697	17	n	n	CCONJ
ejpam-2366	697	18	,	,	PUNCT
ejpam-2366	697	19	a	a	DET
ejpam-2366	697	20	contradiction	contradiction	NOUN
ejpam-2366	697	21	.	.	PUNCT
ejpam-2366	698	1	so	so	ADV
ejpam-2366	698	2	rc	rc	PROPN
ejpam-2366	698	3	q2	q2	PROPN
ejpam-2366	698	4	.	.	PUNCT
ejpam-2366	699	1	also	also	ADV
ejpam-2366	699	2	,	,	PUNCT
ejpam-2366	699	3	c	c	NOUN
ejpam-2366	699	4	q	q	NOUN
ejpam-2366	699	5	because	because	SCONJ
ejpam-2366	699	6	if	if	SCONJ
ejpam-2366	699	7	c	c	PROPN
ejpam-2366	699	8	6	6	NUM
ejpam-2366	699	9	q	q	NOUN
ejpam-2366	699	10	,	,	PUNCT
ejpam-2366	699	11	then	then	ADV
ejpam-2366	699	12	x	x	SYM
ejpam-2366	699	13	6	6	NUM
ejpam-2366	699	14	n	n	NOUN
ejpam-2366	699	15	,	,	PUNCT
ejpam-2366	699	16	a	a	DET
ejpam-2366	699	17	contradiction	contradiction	NOUN
ejpam-2366	699	18	.	.	PUNCT
ejpam-2366	700	1	now	now	ADV
ejpam-2366	700	2	,	,	PUNCT
ejpam-2366	700	3	as	as	SCONJ
ejpam-2366	700	4	rc	rc	PROPN
ejpam-2366	700	5	6	6	NUM
ejpam-2366	700	6	q	q	PROPN
ejpam-2366	700	7	,	,	PUNCT
ejpam-2366	700	8	rc	rc	PROPN
ejpam-2366	700	9	q2	q2	PROPN
ejpam-2366	700	10	,	,	PUNCT
ejpam-2366	700	11	c	c	PROPN
ejpam-2366	700	12	q	q	NOUN
ejpam-2366	700	13	and	and	CCONJ
ejpam-2366	700	14	q	q	NOUN
ejpam-2366	700	15	is	be	AUX
ejpam-2366	700	16	almost	almost	ADV
ejpam-2366	700	17	primary	primary	ADJ
ejpam-2366	700	18	,	,	PUNCT
ejpam-2366	700	19	we	we	PRON
ejpam-2366	700	20	have	have	AUX
ejpam-2366	700	21	,	,	PUNCT
ejpam-2366	700	22	r	r	NOUN
ejpam-2366	700	23	6	6	NUM
ejpam-2366	700	24	√	√	NOUN
ejpam-2366	700	25	q	q	NOUN
ejpam-2366	700	26	which	which	PRON
ejpam-2366	700	27	implies	imply	VERB
ejpam-2366	700	28	r	r	NOUN
ejpam-2366	700	29	6	6	NUM
ejpam-2366	700	30	√	√	NUM
ejpam-2366	700	31	n	n	NOUN
ejpam-2366	700	32	:	:	PUNCT
ejpam-2366	700	33	i	i	PRON
ejpam-2366	700	34	m	m	VERB
ejpam-2366	700	35	and	and	CCONJ
ejpam-2366	700	36	hence	hence	ADV
ejpam-2366	700	37	n	n	ADV
ejpam-2366	700	38	is	be	AUX
ejpam-2366	700	39	almost	almost	ADV
ejpam-2366	700	40	primary	primary	ADJ
ejpam-2366	700	41	theorem	theorem	NOUN
ejpam-2366	700	42	39	39	NUM
ejpam-2366	700	43	.	.	PUNCT
ejpam-2366	701	1	let	let	VERB
ejpam-2366	701	2	l	l	NOUN
ejpam-2366	701	3	be	be	AUX
ejpam-2366	701	4	a	a	DET
ejpam-2366	701	5	pg	pg	NOUN
ejpam-2366	701	6	-	-	PUNCT
ejpam-2366	701	7	lattice	lattice	NOUN
ejpam-2366	701	8	and	and	CCONJ
ejpam-2366	701	9	m	m	AUX
ejpam-2366	701	10	be	be	AUX
ejpam-2366	701	11	a	a	DET
ejpam-2366	701	12	faithful	faithful	ADJ
ejpam-2366	701	13	multiplication	multiplication	NOUN
ejpam-2366	701	14	torsion	torsion	NOUN
ejpam-2366	701	15	free	free	ADJ
ejpam-2366	701	16	pglattice	pglattice	NOUN
ejpam-2366	701	17	l	l	NOUN
ejpam-2366	701	18	-	-	NOUN
ejpam-2366	701	19	module	module	NOUN
ejpam-2366	701	20	with	with	ADP
ejpam-2366	701	21	i	i	PRON
ejpam-2366	701	22	m	m	VERB
ejpam-2366	701	23	compact	compact	ADJ
ejpam-2366	701	24	.	.	PUNCT
ejpam-2366	702	1	let	let	VERB
ejpam-2366	702	2	i	i	PRON
ejpam-2366	702	3	m	m	AUX
ejpam-2366	702	4	be	be	AUX
ejpam-2366	702	5	a	a	DET
ejpam-2366	702	6	weak	weak	ADJ
ejpam-2366	702	7	join	join	NOUN
ejpam-2366	702	8	principal	principal	ADJ
ejpam-2366	702	9	element	element	NOUN
ejpam-2366	702	10	and	and	CCONJ
ejpam-2366	702	11	n	n	CCONJ
ejpam-2366	702	12	be	be	VERB
ejpam-2366	702	13	a	a	DET
ejpam-2366	702	14	proper	proper	ADJ
ejpam-2366	702	15	element	element	NOUN
ejpam-2366	702	16	in	in	ADP
ejpam-2366	702	17	m	m	PROPN
ejpam-2366	702	18	.	.	PUNCT
ejpam-2366	703	1	then	then	ADV
ejpam-2366	703	2	the	the	DET
ejpam-2366	703	3	following	follow	VERB
ejpam-2366	703	4	statements	statement	NOUN
ejpam-2366	703	5	are	be	AUX
ejpam-2366	703	6	equivalent	equivalent	ADJ
ejpam-2366	703	7	:	:	PUNCT
ejpam-2366	703	8	1	1	X
ejpam-2366	703	9	©	©	NOUN
ejpam-2366	703	10	n	n	NUM
ejpam-2366	703	11	is	be	AUX
ejpam-2366	703	12	an	an	DET
ejpam-2366	703	13	almost	almost	ADV
ejpam-2366	703	14	primary	primary	ADJ
ejpam-2366	703	15	element	element	NOUN
ejpam-2366	703	16	of	of	ADP
ejpam-2366	703	17	m	m	PROPN
ejpam-2366	703	18	.	.	PUNCT
ejpam-2366	704	1	2	2	NUM
ejpam-2366	704	2	©	©	NOUN
ejpam-2366	704	3	(	(	PUNCT
ejpam-2366	704	4	n	n	NOUN
ejpam-2366	704	5	:	:	PUNCT
ejpam-2366	704	6	i	i	PRON
ejpam-2366	704	7	m	m	PROPN
ejpam-2366	704	8	)	)	PUNCT
ejpam-2366	704	9	is	be	AUX
ejpam-2366	704	10	an	an	DET
ejpam-2366	704	11	almost	almost	ADV
ejpam-2366	704	12	primary	primary	ADJ
ejpam-2366	704	13	element	element	NOUN
ejpam-2366	704	14	of	of	ADP
ejpam-2366	704	15	l.	l.	PROPN
ejpam-2366	704	16	3	3	NUM
ejpam-2366	704	17	©	©	PROPN
ejpam-2366	704	18	n	n	NOUN
ejpam-2366	704	19	=	=	X
ejpam-2366	704	20	qim	qim	NOUN
ejpam-2366	704	21	for	for	ADP
ejpam-2366	704	22	some	some	DET
ejpam-2366	704	23	almost	almost	ADV
ejpam-2366	704	24	primary	primary	ADJ
ejpam-2366	704	25	element	element	NOUN
ejpam-2366	704	26	q	q	PROPN
ejpam-2366	704	27	∈	∈	PROPN
ejpam-2366	704	28	l.	l.	NOUN
ejpam-2366	704	29	proof	proof	NOUN
ejpam-2366	704	30	.	.	PUNCT
ejpam-2366	705	1	1	1	NUM
ejpam-2366	705	2	©	©	NOUN
ejpam-2366	705	3	=⇒	=⇒	NOUN
ejpam-2366	705	4	2	2	NUM
ejpam-2366	705	5	©	©	NOUN
ejpam-2366	705	6	follows	follow	VERB
ejpam-2366	705	7	from	from	ADP
ejpam-2366	705	8	1	1	NUM
ejpam-2366	705	9	©	©	NOUN
ejpam-2366	705	10	=⇒	=⇒	NOUN
ejpam-2366	705	11	2	2	NUM
ejpam-2366	705	12	©	©	NOUN
ejpam-2366	705	13	in	in	ADP
ejpam-2366	705	14	the	the	DET
ejpam-2366	705	15	proof	proof	NOUN
ejpam-2366	705	16	of	of	ADP
ejpam-2366	705	17	theorem	theorem	ADJ
ejpam-2366	705	18	38	38	NUM
ejpam-2366	705	19	.	.	PUNCT
ejpam-2366	706	1	2	2	NUM
ejpam-2366	706	2	©	©	NOUN
ejpam-2366	706	3	=⇒	=⇒	NOUN
ejpam-2366	706	4	1	1	NUM
ejpam-2366	706	5	©	©	PROPN
ejpam-2366	706	6	.	.	PUNCT
ejpam-2366	706	7	assume	assume	VERB
ejpam-2366	706	8	that	that	SCONJ
ejpam-2366	706	9	(	(	PUNCT
ejpam-2366	706	10	n	n	X
ejpam-2366	706	11	:	:	PUNCT
ejpam-2366	706	12	i	i	PRON
ejpam-2366	706	13	m	m	PROPN
ejpam-2366	706	14	)	)	PUNCT
ejpam-2366	706	15	is	be	AUX
ejpam-2366	706	16	an	an	DET
ejpam-2366	706	17	almost	almost	ADV
ejpam-2366	706	18	primary	primary	ADJ
ejpam-2366	706	19	element	element	NOUN
ejpam-2366	706	20	of	of	ADP
ejpam-2366	706	21	l.	l.	PROPN
ejpam-2366	706	22	let	let	AUX
ejpam-2366	706	23	rq	rq	VERB
ejpam-2366	706	24	6	6	NUM
ejpam-2366	706	25	n	n	NOUN
ejpam-2366	706	26	and	and	CCONJ
ejpam-2366	706	27	rq	rq	X
ejpam-2366	706	28	(	(	PUNCT
ejpam-2366	706	29	n	n	X
ejpam-2366	706	30	:	:	PUNCT
ejpam-2366	706	31	i	i	PRON
ejpam-2366	706	32	m	m	PROPN
ejpam-2366	706	33	)	)	PUNCT
ejpam-2366	706	34	n	n	PROPN
ejpam-2366	706	35	for	for	ADP
ejpam-2366	706	36	r	r	PROPN
ejpam-2366	706	37	∈	∈	PROPN
ejpam-2366	706	38	l	l	NOUN
ejpam-2366	706	39	,	,	PUNCT
ejpam-2366	706	40	q	q	PRON
ejpam-2366	706	41	∈m	∈m	NOUN
ejpam-2366	706	42	.	.	PUNCT
ejpam-2366	707	1	then	then	ADV
ejpam-2366	707	2	(	(	PUNCT
ejpam-2366	707	3	rq	rq	INTJ
ejpam-2366	707	4	:	:	PUNCT
ejpam-2366	707	5	i	i	PRON
ejpam-2366	707	6	m	m	VERB
ejpam-2366	707	7	)	)	PUNCT
ejpam-2366	707	8	6	6	NUM
ejpam-2366	707	9	(	(	PUNCT
ejpam-2366	707	10	n	n	NUM
ejpam-2366	707	11	:	:	PUNCT
ejpam-2366	707	12	i	i	PRON
ejpam-2366	707	13	m	m	PROPN
ejpam-2366	707	14	)	)	PUNCT
ejpam-2366	707	15	and	and	CCONJ
ejpam-2366	707	16	so	so	ADV
ejpam-2366	707	17	by	by	ADP
ejpam-2366	707	18	lemma	lemma	PROPN
ejpam-2366	707	19	4	4	NUM
ejpam-2366	707	20	,	,	PUNCT
ejpam-2366	707	21	we	we	PRON
ejpam-2366	707	22	have	have	VERB
ejpam-2366	707	23	r(q	r(q	NOUN
ejpam-2366	707	24	:	:	PUNCT
ejpam-2366	707	25	i	i	PRON
ejpam-2366	707	26	m	m	VERB
ejpam-2366	707	27	)	)	PUNCT
ejpam-2366	708	1	=	=	PUNCT
ejpam-2366	708	2	(	(	PUNCT
ejpam-2366	708	3	rq	rq	INTJ
ejpam-2366	708	4	:	:	PUNCT
ejpam-2366	708	5	i	i	PRON
ejpam-2366	708	6	m	m	VERB
ejpam-2366	708	7	)	)	PUNCT
ejpam-2366	708	8	6	6	NUM
ejpam-2366	708	9	(	(	PUNCT
ejpam-2366	708	10	n	n	NUM
ejpam-2366	708	11	:	:	PUNCT
ejpam-2366	708	12	i	i	PRON
ejpam-2366	708	13	m	m	PROPN
ejpam-2366	708	14	)	)	PUNCT
ejpam-2366	708	15	.	.	PUNCT
ejpam-2366	709	1	if	if	SCONJ
ejpam-2366	709	2	r(q	r(q	PROPN
ejpam-2366	709	3	:	:	PUNCT
ejpam-2366	709	4	i	i	PRON
ejpam-2366	709	5	m	m	VERB
ejpam-2366	709	6	)	)	PUNCT
ejpam-2366	709	7	6	6	NUM
ejpam-2366	709	8	(	(	PUNCT
ejpam-2366	709	9	n	n	NUM
ejpam-2366	709	10	:	:	PUNCT
ejpam-2366	709	11	i	i	PRON
ejpam-2366	709	12	m	m	VERB
ejpam-2366	709	13	)	)	PUNCT
ejpam-2366	709	14	2	2	NUM
ejpam-2366	709	15	=	=	SYM
ejpam-2366	709	16	(	(	PUNCT
ejpam-2366	709	17	(	(	PUNCT
ejpam-2366	709	18	n	n	X
ejpam-2366	709	19	:	:	PUNCT
ejpam-2366	709	20	i	i	PRON
ejpam-2366	709	21	m	m	PROPN
ejpam-2366	709	22	)	)	PUNCT
ejpam-2366	709	23	n	n	CCONJ
ejpam-2366	709	24	:	:	PUNCT
ejpam-2366	709	25	i	i	PRON
ejpam-2366	709	26	m	m	PROPN
ejpam-2366	709	27	)	)	PUNCT
ejpam-2366	709	28	,	,	PUNCT
ejpam-2366	709	29	then	then	ADV
ejpam-2366	709	30	r(q	r(q	NOUN
ejpam-2366	709	31	:	:	PUNCT
ejpam-2366	710	1	i	i	PRON
ejpam-2366	710	2	m	m	VERB
ejpam-2366	710	3	)	)	PUNCT
ejpam-2366	711	1	i	i	PRON
ejpam-2366	711	2	m	m	VERB
ejpam-2366	711	3	6	6	NUM
ejpam-2366	711	4	(	(	PUNCT
ejpam-2366	711	5	n	n	NUM
ejpam-2366	711	6	:	:	PUNCT
ejpam-2366	711	7	i	i	PRON
ejpam-2366	711	8	m	m	PROPN
ejpam-2366	711	9	)	)	PUNCT
ejpam-2366	711	10	n	n	NUM
ejpam-2366	711	11	which	which	PRON
ejpam-2366	711	12	implies	imply	VERB
ejpam-2366	711	13	rq	rq	X
ejpam-2366	711	14	6	6	NUM
ejpam-2366	711	15	(	(	PUNCT
ejpam-2366	711	16	n	n	NUM
ejpam-2366	711	17	:	:	PUNCT
ejpam-2366	711	18	i	i	PRON
ejpam-2366	711	19	m	m	PROPN
ejpam-2366	711	20	)	)	PUNCT
ejpam-2366	711	21	n	n	CCONJ
ejpam-2366	711	22	,	,	PUNCT
ejpam-2366	711	23	a	a	DET
ejpam-2366	711	24	contradiction	contradiction	NOUN
ejpam-2366	711	25	.	.	PUNCT
ejpam-2366	712	1	if	if	SCONJ
ejpam-2366	712	2	r(q	r(q	PROPN
ejpam-2366	712	3	:	:	PUNCT
ejpam-2366	712	4	i	i	PRON
ejpam-2366	712	5	m	m	VERB
ejpam-2366	712	6	)	)	PUNCT
ejpam-2366	712	7	(	(	PUNCT
ejpam-2366	712	8	n	n	X
ejpam-2366	712	9	:	:	PUNCT
ejpam-2366	712	10	i	i	PRON
ejpam-2366	712	11	m	m	VERB
ejpam-2366	712	12	)	)	PUNCT
ejpam-2366	712	13	2	2	NUM
ejpam-2366	712	14	,	,	PUNCT
ejpam-2366	712	15	then	then	ADV
ejpam-2366	712	16	as	as	ADP
ejpam-2366	712	17	r(q	r(q	PROPN
ejpam-2366	712	18	:	:	PUNCT
ejpam-2366	712	19	i	i	PRON
ejpam-2366	712	20	m	m	VERB
ejpam-2366	712	21	)	)	PUNCT
ejpam-2366	712	22	6	6	NUM
ejpam-2366	712	23	(	(	PUNCT
ejpam-2366	712	24	n	n	NUM
ejpam-2366	712	25	:	:	PUNCT
ejpam-2366	712	26	i	i	PRON
ejpam-2366	712	27	m	m	PROPN
ejpam-2366	712	28	)	)	PUNCT
ejpam-2366	712	29	and	and	CCONJ
ejpam-2366	712	30	(	(	PUNCT
ejpam-2366	712	31	n	n	X
ejpam-2366	712	32	:	:	PUNCT
ejpam-2366	712	33	i	i	PRON
ejpam-2366	712	34	m	m	PROPN
ejpam-2366	712	35	)	)	PUNCT
ejpam-2366	712	36	is	be	AUX
ejpam-2366	712	37	almost	almost	ADV
ejpam-2366	712	38	primary	primary	ADJ
ejpam-2366	712	39	,	,	PUNCT
ejpam-2366	712	40	we	we	PRON
ejpam-2366	712	41	have	have	VERB
ejpam-2366	712	42	either	either	CCONJ
ejpam-2366	712	43	r	r	NOUN
ejpam-2366	712	44	6	6	NUM
ejpam-2366	712	45	√	√	NUM
ejpam-2366	712	46	n	n	NOUN
ejpam-2366	712	47	:	:	PUNCT
ejpam-2366	712	48	i	i	PRON
ejpam-2366	712	49	m	m	VERB
ejpam-2366	712	50	or	or	CCONJ
ejpam-2366	712	51	(	(	PUNCT
ejpam-2366	712	52	q	q	NOUN
ejpam-2366	712	53	:	:	PUNCT
ejpam-2366	712	54	i	i	PRON
ejpam-2366	712	55	m	m	VERB
ejpam-2366	712	56	)	)	PUNCT
ejpam-2366	712	57	6	6	NUM
ejpam-2366	712	58	(	(	PUNCT
ejpam-2366	712	59	n	n	NUM
ejpam-2366	712	60	:	:	PUNCT
ejpam-2366	712	61	i	i	PRON
ejpam-2366	712	62	m	m	VERB
ejpam-2366	712	63	)	)	PUNCT
ejpam-2366	712	64	which	which	PRON
ejpam-2366	712	65	implies	imply	VERB
ejpam-2366	712	66	either	either	CCONJ
ejpam-2366	712	67	r	r	NOUN
ejpam-2366	712	68	6	6	NUM
ejpam-2366	712	69	√	√	NUM
ejpam-2366	712	70	n	n	NOUN
ejpam-2366	712	71	:	:	PUNCT
ejpam-2366	712	72	i	i	PRON
ejpam-2366	712	73	m	m	VERB
ejpam-2366	712	74	or	or	CCONJ
ejpam-2366	712	75	q	q	PROPN
ejpam-2366	712	76	6	6	NUM
ejpam-2366	712	77	n	n	NOUN
ejpam-2366	712	78	and	and	CCONJ
ejpam-2366	712	79	thus	thus	ADV
ejpam-2366	712	80	n	n	PRON
ejpam-2366	712	81	is	be	AUX
ejpam-2366	712	82	an	an	DET
ejpam-2366	712	83	almost	almost	ADV
ejpam-2366	712	84	primary	primary	ADJ
ejpam-2366	712	85	element	element	NOUN
ejpam-2366	712	86	of	of	ADP
ejpam-2366	712	87	m	m	PROPN
ejpam-2366	712	88	.	.	PUNCT
ejpam-2366	713	1	2	2	NUM
ejpam-2366	713	2	©	©	NOUN
ejpam-2366	713	3	=⇒	=⇒	NOUN
ejpam-2366	713	4	3	3	NUM
ejpam-2366	713	5	©	©	NOUN
ejpam-2366	713	6	.	.	PUNCT
ejpam-2366	713	7	suppose	suppose	VERB
ejpam-2366	713	8	(	(	PUNCT
ejpam-2366	713	9	n	n	X
ejpam-2366	713	10	:	:	PUNCT
ejpam-2366	713	11	i	i	PRON
ejpam-2366	713	12	m	m	PROPN
ejpam-2366	713	13	)	)	PUNCT
ejpam-2366	713	14	is	be	AUX
ejpam-2366	713	15	an	an	DET
ejpam-2366	713	16	almost	almost	ADV
ejpam-2366	713	17	primary	primary	ADJ
ejpam-2366	713	18	element	element	NOUN
ejpam-2366	713	19	of	of	ADP
ejpam-2366	713	20	l.	l.	PROPN
ejpam-2366	713	21	since	since	SCONJ
ejpam-2366	713	22	m	m	PROPN
ejpam-2366	713	23	is	be	AUX
ejpam-2366	713	24	a	a	DET
ejpam-2366	713	25	multiplication	multiplication	NOUN
ejpam-2366	713	26	lattice	lattice	NOUN
ejpam-2366	713	27	l	l	NOUN
ejpam-2366	713	28	-	-	NOUN
ejpam-2366	713	29	module	module	NOUN
ejpam-2366	713	30	,	,	PUNCT
ejpam-2366	713	31	n	n	NOUN
ejpam-2366	713	32	=	=	SYM
ejpam-2366	713	33	(	(	PUNCT
ejpam-2366	713	34	n	n	X
ejpam-2366	713	35	:	:	PUNCT
ejpam-2366	713	36	i	i	PRON
ejpam-2366	713	37	m	m	VERB
ejpam-2366	713	38	)	)	PUNCT
ejpam-2366	714	1	i	i	PRON
ejpam-2366	714	2	m	m	VERB
ejpam-2366	714	3	and	and	CCONJ
ejpam-2366	714	4	hence	hence	ADV
ejpam-2366	714	5	3	3	NUM
ejpam-2366	714	6	©	©	PROPN
ejpam-2366	714	7	holds	hold	NOUN
ejpam-2366	714	8	.	.	PUNCT
ejpam-2366	715	1	a.	a.	PROPN
ejpam-2366	715	2	v.	v.	PROPN
ejpam-2366	715	3	bingi	bingi	PROPN
ejpam-2366	715	4	,	,	PUNCT
ejpam-2366	715	5	c.	c.	PROPN
ejpam-2366	715	6	s.	s.	PROPN
ejpam-2366	715	7	manjarekar	manjarekar	PROPN
ejpam-2366	715	8	/	/	PROPN
ejpam-2366	715	9	eur	eur	PROPN
ejpam-2366	715	10	.	.	PUNCT
ejpam-2366	716	1	j.	j.	PROPN
ejpam-2366	716	2	pure	pure	PROPN
ejpam-2366	716	3	appl	appl	PROPN
ejpam-2366	716	4	.	.	PROPN
ejpam-2366	716	5	math	math	PROPN
ejpam-2366	716	6	,	,	PUNCT
ejpam-2366	716	7	14	14	NUM
ejpam-2366	716	8	(	(	PUNCT
ejpam-2366	716	9	2	2	NUM
ejpam-2366	716	10	)	)	PUNCT
ejpam-2366	716	11	(	(	PUNCT
ejpam-2366	716	12	2021	2021	NUM
ejpam-2366	716	13	)	)	PUNCT
ejpam-2366	716	14	,	,	PUNCT
ejpam-2366	716	15	551	551	NUM
ejpam-2366	716	16	-	-	SYM
ejpam-2366	716	17	577	577	NUM
ejpam-2366	716	18	570	570	NUM
ejpam-2366	716	19	3	3	NUM
ejpam-2366	716	20	©	©	NOUN
ejpam-2366	716	21	=⇒	=⇒	NOUN
ejpam-2366	716	22	2	2	NUM
ejpam-2366	716	23	©	©	NOUN
ejpam-2366	716	24	.	.	PUNCT
ejpam-2366	716	25	suppose	suppose	VERB
ejpam-2366	716	26	n	n	PROPN
ejpam-2366	716	27	=	=	PUNCT
ejpam-2366	716	28	qim	qim	NOUN
ejpam-2366	716	29	for	for	ADP
ejpam-2366	716	30	some	some	DET
ejpam-2366	716	31	almost	almost	ADV
ejpam-2366	716	32	primary	primary	ADJ
ejpam-2366	716	33	element	element	NOUN
ejpam-2366	716	34	q	q	PROPN
ejpam-2366	716	35	∈	∈	PROPN
ejpam-2366	716	36	l.	l.	NOUN
ejpam-2366	716	37	as	as	SCONJ
ejpam-2366	716	38	m	m	PROPN
ejpam-2366	716	39	is	be	AUX
ejpam-2366	716	40	a	a	DET
ejpam-2366	716	41	multiplication	multiplication	NOUN
ejpam-2366	716	42	lattice	lattice	NOUN
ejpam-2366	716	43	l	l	NOUN
ejpam-2366	716	44	-	-	NOUN
ejpam-2366	716	45	module	module	NOUN
ejpam-2366	716	46	,	,	PUNCT
ejpam-2366	716	47	n	n	NOUN
ejpam-2366	716	48	=	=	SYM
ejpam-2366	716	49	(	(	PUNCT
ejpam-2366	716	50	n	n	X
ejpam-2366	716	51	:	:	PUNCT
ejpam-2366	716	52	i	i	PRON
ejpam-2366	716	53	m	m	VERB
ejpam-2366	716	54	)	)	PUNCT
ejpam-2366	717	1	i	i	PRON
ejpam-2366	717	2	m	m	VERB
ejpam-2366	717	3	.	.	PUNCT
ejpam-2366	718	1	since	since	SCONJ
ejpam-2366	718	2	i	i	PRON
ejpam-2366	718	3	m	m	VERB
ejpam-2366	718	4	is	be	AUX
ejpam-2366	718	5	compact	compact	ADJ
ejpam-2366	718	6	,	,	PUNCT
ejpam-2366	718	7	2	2	NUM
ejpam-2366	718	8	©	©	PROPN
ejpam-2366	718	9	holds	hold	NOUN
ejpam-2366	718	10	by	by	ADP
ejpam-2366	718	11	theorem	theorem	NOUN
ejpam-2366	718	12	5	5	NUM
ejpam-2366	718	13	of	of	ADP
ejpam-2366	718	14	[	[	X
ejpam-2366	718	15	10	10	NUM
ejpam-2366	718	16	]	]	PUNCT
ejpam-2366	718	17	.	.	PUNCT
ejpam-2366	719	1	now	now	ADV
ejpam-2366	719	2	we	we	PRON
ejpam-2366	719	3	relate	relate	VERB
ejpam-2366	719	4	the	the	DET
ejpam-2366	719	5	almost	almost	ADV
ejpam-2366	719	6	primary	primary	ADJ
ejpam-2366	719	7	element	element	NOUN
ejpam-2366	719	8	n	n	CCONJ
ejpam-2366	719	9	∈	∈	NOUN
ejpam-2366	719	10	m	m	VERB
ejpam-2366	719	11	with	with	ADP
ejpam-2366	719	12	rad(n	rad(n	NOUN
ejpam-2366	719	13	)	)	PUNCT
ejpam-2366	719	14	∈	∈	PROPN
ejpam-2366	719	15	m	m	NOUN
ejpam-2366	719	16	,	,	PUNCT
ejpam-2366	719	17	the	the	DET
ejpam-2366	719	18	radical	radical	NOUN
ejpam-2366	719	19	of	of	ADP
ejpam-2366	719	20	n	n	PROPN
ejpam-2366	719	21	.	.	PUNCT
ejpam-2366	720	1	according	accord	VERB
ejpam-2366	720	2	to	to	ADP
ejpam-2366	720	3	definition	definition	NOUN
ejpam-2366	720	4	3.1	3.1	NUM
ejpam-2366	720	5	in	in	ADP
ejpam-2366	720	6	[	[	X
ejpam-2366	720	7	17	17	NUM
ejpam-2366	720	8	]	]	PUNCT
ejpam-2366	720	9	,	,	PUNCT
ejpam-2366	720	10	the	the	DET
ejpam-2366	720	11	radical	radical	NOUN
ejpam-2366	720	12	of	of	ADP
ejpam-2366	720	13	a	a	DET
ejpam-2366	720	14	proper	proper	ADJ
ejpam-2366	720	15	element	element	NOUN
ejpam-2366	720	16	n	n	NOUN
ejpam-2366	720	17	in	in	ADP
ejpam-2366	720	18	an	an	DET
ejpam-2366	720	19	l	l	NOUN
ejpam-2366	720	20	module	module	NOUN
ejpam-2366	720	21	m	m	NOUN
ejpam-2366	720	22	is	be	AUX
ejpam-2366	720	23	defined	define	VERB
ejpam-2366	720	24	as	as	ADP
ejpam-2366	720	25	∧{p	∧{p	PROPN
ejpam-2366	720	26	∈m	∈m	NOUN
ejpam-2366	720	27	|	|	ADV
ejpam-2366	720	28	p	p	NOUN
ejpam-2366	720	29	is	be	AUX
ejpam-2366	720	30	a	a	DET
ejpam-2366	720	31	prime	prime	ADJ
ejpam-2366	720	32	element	element	NOUN
ejpam-2366	720	33	and	and	CCONJ
ejpam-2366	720	34	n	n	PRON
ejpam-2366	720	35	6	6	NUM
ejpam-2366	720	36	p	p	NOUN
ejpam-2366	720	37	}	}	PUNCT
ejpam-2366	720	38	and	and	CCONJ
ejpam-2366	720	39	is	be	AUX
ejpam-2366	720	40	denoted	denote	VERB
ejpam-2366	720	41	as	as	ADP
ejpam-2366	720	42	rad(n	rad(n	NOUN
ejpam-2366	720	43	)	)	PUNCT
ejpam-2366	720	44	.	.	PUNCT
ejpam-2366	721	1	using	use	VERB
ejpam-2366	721	2	theorem	theorem	ADJ
ejpam-2366	721	3	3.6	3.6	NUM
ejpam-2366	721	4	of	of	ADP
ejpam-2366	721	5	[	[	X
ejpam-2366	721	6	17	17	NUM
ejpam-2366	721	7	]	]	PUNCT
ejpam-2366	721	8	,	,	PUNCT
ejpam-2366	721	9	we	we	PRON
ejpam-2366	721	10	have	have	VERB
ejpam-2366	721	11	the	the	DET
ejpam-2366	721	12	following	follow	VERB
ejpam-2366	721	13	interesting	interesting	ADJ
ejpam-2366	721	14	characterization	characterization	NOUN
ejpam-2366	721	15	of	of	ADP
ejpam-2366	721	16	an	an	DET
ejpam-2366	721	17	almost	almost	ADV
ejpam-2366	721	18	primary	primary	ADJ
ejpam-2366	721	19	element	element	NOUN
ejpam-2366	721	20	of	of	ADP
ejpam-2366	721	21	m	m	PROPN
ejpam-2366	721	22	.	.	PUNCT
ejpam-2366	722	1	theorem	theorem	ADJ
ejpam-2366	722	2	40	40	NUM
ejpam-2366	722	3	.	.	PUNCT
ejpam-2366	723	1	let	let	VERB
ejpam-2366	723	2	l	l	NOUN
ejpam-2366	723	3	be	be	AUX
ejpam-2366	723	4	a	a	DET
ejpam-2366	723	5	pg	pg	NOUN
ejpam-2366	723	6	-	-	PUNCT
ejpam-2366	723	7	lattice	lattice	NOUN
ejpam-2366	723	8	and	and	CCONJ
ejpam-2366	723	9	m	m	AUX
ejpam-2366	723	10	be	be	AUX
ejpam-2366	723	11	a	a	DET
ejpam-2366	723	12	faithful	faithful	ADJ
ejpam-2366	723	13	multiplication	multiplication	NOUN
ejpam-2366	723	14	torsion	torsion	NOUN
ejpam-2366	723	15	free	free	ADJ
ejpam-2366	723	16	pglattice	pglattice	NOUN
ejpam-2366	723	17	l	l	NOUN
ejpam-2366	723	18	-	-	NOUN
ejpam-2366	723	19	module	module	NOUN
ejpam-2366	723	20	with	with	ADP
ejpam-2366	723	21	i	i	PRON
ejpam-2366	723	22	m	m	VERB
ejpam-2366	723	23	compact	compact	ADJ
ejpam-2366	723	24	.	.	PUNCT
ejpam-2366	724	1	let	let	VERB
ejpam-2366	724	2	i	i	PRON
ejpam-2366	724	3	m	m	VERB
ejpam-2366	724	4	∈m	∈m	NOUN
ejpam-2366	724	5	be	be	AUX
ejpam-2366	724	6	a	a	DET
ejpam-2366	724	7	weak	weak	ADJ
ejpam-2366	724	8	join	join	NOUN
ejpam-2366	724	9	principal	principal	ADJ
ejpam-2366	724	10	element	element	NOUN
ejpam-2366	724	11	.	.	PUNCT
ejpam-2366	725	1	then	then	ADV
ejpam-2366	725	2	a	a	DET
ejpam-2366	725	3	proper	proper	ADJ
ejpam-2366	725	4	element	element	NOUN
ejpam-2366	725	5	p	p	NOUN
ejpam-2366	725	6	∈m	∈m	NOUN
ejpam-2366	725	7	is	be	AUX
ejpam-2366	725	8	almost	almost	ADV
ejpam-2366	725	9	primary	primary	ADJ
ejpam-2366	725	10	(	(	PUNCT
ejpam-2366	725	11	φ2−primary	φ2−primary	NOUN
ejpam-2366	725	12	)	)	PUNCT
ejpam-2366	726	1	if	if	SCONJ
ejpam-2366	726	2	and	and	CCONJ
ejpam-2366	726	3	only	only	ADV
ejpam-2366	726	4	if	if	SCONJ
ejpam-2366	726	5	whenever	whenever	SCONJ
ejpam-2366	726	6	n	n	NOUN
ejpam-2366	726	7	=	=	VERB
ejpam-2366	726	8	aim	aim	NOUN
ejpam-2366	726	9	and	and	CCONJ
ejpam-2366	726	10	k	k	X
ejpam-2366	726	11	=	=	X
ejpam-2366	727	1	bim	bim	NOUN
ejpam-2366	727	2	in	in	ADP
ejpam-2366	727	3	m	m	PROPN
ejpam-2366	727	4	are	be	AUX
ejpam-2366	727	5	such	such	ADJ
ejpam-2366	727	6	that	that	DET
ejpam-2366	727	7	abim	abim	NOUN
ejpam-2366	727	8	6	6	NUM
ejpam-2366	727	9	p	p	NOUN
ejpam-2366	727	10	and	and	CCONJ
ejpam-2366	727	11	abim	abim	NOUN
ejpam-2366	727	12	(	(	PUNCT
ejpam-2366	727	13	p	p	X
ejpam-2366	727	14	:	:	PUNCT
ejpam-2366	727	15	i	i	PRON
ejpam-2366	727	16	m	m	PROPN
ejpam-2366	727	17	)	)	PUNCT
ejpam-2366	728	1	p	p	NOUN
ejpam-2366	728	2	then	then	ADV
ejpam-2366	728	3	either	either	CCONJ
ejpam-2366	728	4	n	n	PROPN
ejpam-2366	728	5	6	6	NUM
ejpam-2366	728	6	p	p	NOUN
ejpam-2366	728	7	or	or	CCONJ
ejpam-2366	728	8	k	k	PROPN
ejpam-2366	728	9	6	6	NUM
ejpam-2366	728	10	rad(p	rad(p	PROPN
ejpam-2366	728	11	)	)	PUNCT
ejpam-2366	728	12	for	for	ADP
ejpam-2366	728	13	a	a	DET
ejpam-2366	728	14	,	,	PUNCT
ejpam-2366	728	15	b	b	PROPN
ejpam-2366	728	16	∈	∈	PROPN
ejpam-2366	728	17	l.	l.	NOUN
ejpam-2366	728	18	proof	proof	PROPN
ejpam-2366	728	19	.	.	PUNCT
ejpam-2366	729	1	assume	assume	VERB
ejpam-2366	729	2	that	that	SCONJ
ejpam-2366	729	3	p	p	PROPN
ejpam-2366	729	4	∈	∈	PROPN
ejpam-2366	729	5	m	m	VERB
ejpam-2366	729	6	is	be	AUX
ejpam-2366	729	7	almost	almost	ADV
ejpam-2366	729	8	primary	primary	ADJ
ejpam-2366	729	9	.	.	PUNCT
ejpam-2366	730	1	let	let	VERB
ejpam-2366	730	2	n	n	NOUN
ejpam-2366	730	3	=	=	NOUN
ejpam-2366	730	4	aim	aim	VERB
ejpam-2366	730	5	and	and	CCONJ
ejpam-2366	730	6	k	k	X
ejpam-2366	730	7	=	=	X
ejpam-2366	731	1	bim	bim	NOUN
ejpam-2366	731	2	in	in	ADP
ejpam-2366	731	3	m	m	PROPN
ejpam-2366	731	4	be	be	VERB
ejpam-2366	731	5	such	such	ADJ
ejpam-2366	731	6	that	that	DET
ejpam-2366	731	7	abim	abim	NOUN
ejpam-2366	731	8	6	6	NUM
ejpam-2366	731	9	p	p	NOUN
ejpam-2366	731	10	and	and	CCONJ
ejpam-2366	731	11	abim	abim	NOUN
ejpam-2366	731	12	(	(	PUNCT
ejpam-2366	731	13	p	p	X
ejpam-2366	731	14	:	:	PUNCT
ejpam-2366	731	15	i	i	PRON
ejpam-2366	731	16	m	m	PROPN
ejpam-2366	731	17	)	)	PUNCT
ejpam-2366	731	18	p	p	NOUN
ejpam-2366	731	19	for	for	ADP
ejpam-2366	731	20	a	a	DET
ejpam-2366	731	21	,	,	PUNCT
ejpam-2366	731	22	b	b	PROPN
ejpam-2366	731	23	∈	∈	PROPN
ejpam-2366	731	24	l.	l.	NOUN
ejpam-2366	731	25	since	since	SCONJ
ejpam-2366	731	26	m	m	PROPN
ejpam-2366	731	27	is	be	AUX
ejpam-2366	731	28	a	a	DET
ejpam-2366	731	29	multiplication	multiplication	NOUN
ejpam-2366	731	30	lattice	lattice	NOUN
ejpam-2366	731	31	l	l	NOUN
ejpam-2366	731	32	-	-	NOUN
ejpam-2366	731	33	module	module	NOUN
ejpam-2366	731	34	,	,	PUNCT
ejpam-2366	731	35	we	we	PRON
ejpam-2366	731	36	have	have	VERB
ejpam-2366	731	37	a	a	DET
ejpam-2366	731	38	=	=	X
ejpam-2366	731	39	(	(	PUNCT
ejpam-2366	731	40	n	n	NOUN
ejpam-2366	731	41	:	:	PUNCT
ejpam-2366	731	42	i	i	PRON
ejpam-2366	731	43	m	m	PROPN
ejpam-2366	731	44	)	)	PUNCT
ejpam-2366	731	45	and	and	CCONJ
ejpam-2366	732	1	b	b	X
ejpam-2366	732	2	=	=	SYM
ejpam-2366	732	3	(	(	PUNCT
ejpam-2366	732	4	k	k	NOUN
ejpam-2366	732	5	:	:	PUNCT
ejpam-2366	732	6	i	i	PRON
ejpam-2366	732	7	m	m	VERB
ejpam-2366	732	8	)	)	PUNCT
ejpam-2366	732	9	and	and	CCONJ
ejpam-2366	732	10	so	so	ADV
ejpam-2366	732	11	(	(	PUNCT
ejpam-2366	732	12	k	k	X
ejpam-2366	732	13	:	:	PUNCT
ejpam-2366	732	14	i	i	PRON
ejpam-2366	732	15	m	m	VERB
ejpam-2366	732	16	)	)	PUNCT
ejpam-2366	732	17	(	(	PUNCT
ejpam-2366	732	18	n	n	X
ejpam-2366	732	19	:	:	PUNCT
ejpam-2366	732	20	i	i	PRON
ejpam-2366	732	21	m	m	VERB
ejpam-2366	732	22	)	)	PUNCT
ejpam-2366	732	23	i	i	PRON
ejpam-2366	732	24	m	m	VERB
ejpam-2366	732	25	=	=	VERB
ejpam-2366	732	26	abim	abim	ADJ
ejpam-2366	732	27	6	6	NUM
ejpam-2366	732	28	p	p	NOUN
ejpam-2366	732	29	and	and	CCONJ
ejpam-2366	732	30	(	(	PUNCT
ejpam-2366	732	31	k	k	NOUN
ejpam-2366	732	32	:	:	PUNCT
ejpam-2366	732	33	i	i	PRON
ejpam-2366	732	34	m	m	VERB
ejpam-2366	732	35	)	)	PUNCT
ejpam-2366	732	36	(	(	PUNCT
ejpam-2366	732	37	n	n	X
ejpam-2366	732	38	:	:	PUNCT
ejpam-2366	732	39	i	i	PRON
ejpam-2366	732	40	m	m	VERB
ejpam-2366	732	41	)	)	PUNCT
ejpam-2366	733	1	i	i	PRON
ejpam-2366	733	2	m	m	VERB
ejpam-2366	733	3	(	(	PUNCT
ejpam-2366	733	4	p	p	X
ejpam-2366	733	5	:	:	PUNCT
ejpam-2366	733	6	i	i	PRON
ejpam-2366	733	7	m	m	VERB
ejpam-2366	733	8	)	)	PUNCT
ejpam-2366	734	1	p	p	NOUN
ejpam-2366	734	2	.	.	PUNCT
ejpam-2366	735	1	as	as	SCONJ
ejpam-2366	735	2	p	p	PROPN
ejpam-2366	735	3	∈	∈	PROPN
ejpam-2366	735	4	m	m	VERB
ejpam-2366	735	5	is	be	AUX
ejpam-2366	735	6	almost	almost	ADV
ejpam-2366	735	7	primary	primary	ADJ
ejpam-2366	735	8	,	,	PUNCT
ejpam-2366	735	9	we	we	PRON
ejpam-2366	735	10	have	have	VERB
ejpam-2366	735	11	either	either	CCONJ
ejpam-2366	735	12	(	(	PUNCT
ejpam-2366	735	13	n	n	X
ejpam-2366	735	14	:	:	PUNCT
ejpam-2366	735	15	i	i	PRON
ejpam-2366	735	16	m	m	VERB
ejpam-2366	735	17	)	)	PUNCT
ejpam-2366	736	1	i	i	PRON
ejpam-2366	736	2	m	m	VERB
ejpam-2366	736	3	6	6	NUM
ejpam-2366	736	4	p	p	NOUN
ejpam-2366	736	5	or	or	CCONJ
ejpam-2366	736	6	(	(	PUNCT
ejpam-2366	736	7	k	k	NOUN
ejpam-2366	736	8	:	:	PUNCT
ejpam-2366	736	9	i	i	PRON
ejpam-2366	736	10	m	m	VERB
ejpam-2366	736	11	)	)	PUNCT
ejpam-2366	736	12	6	6	NUM
ejpam-2366	736	13	√	√	NOUN
ejpam-2366	737	1	p	p	X
ejpam-2366	737	2	:	:	PUNCT
ejpam-2366	737	3	i	i	PRON
ejpam-2366	737	4	m	m	VERB
ejpam-2366	737	5	which	which	PRON
ejpam-2366	737	6	implies	imply	VERB
ejpam-2366	737	7	either	either	CCONJ
ejpam-2366	737	8	n	n	PROPN
ejpam-2366	737	9	=	=	SYM
ejpam-2366	737	10	(	(	PUNCT
ejpam-2366	737	11	n	n	X
ejpam-2366	737	12	:	:	PUNCT
ejpam-2366	737	13	i	i	PRON
ejpam-2366	737	14	m	m	VERB
ejpam-2366	737	15	)	)	PUNCT
ejpam-2366	738	1	i	i	PRON
ejpam-2366	738	2	m	m	VERB
ejpam-2366	738	3	6	6	NUM
ejpam-2366	738	4	p	p	NOUN
ejpam-2366	738	5	or	or	CCONJ
ejpam-2366	738	6	k	k	NOUN
ejpam-2366	738	7	=	=	SYM
ejpam-2366	739	1	(	(	PUNCT
ejpam-2366	739	2	k	k	NOUN
ejpam-2366	739	3	:	:	PUNCT
ejpam-2366	739	4	i	i	PRON
ejpam-2366	739	5	m	m	VERB
ejpam-2366	739	6	)	)	PUNCT
ejpam-2366	740	1	i	i	PRON
ejpam-2366	740	2	m	m	VERB
ejpam-2366	740	3	6	6	NUM
ejpam-2366	740	4	(	(	PUNCT
ejpam-2366	740	5	√	√	PROPN
ejpam-2366	740	6	p	p	NOUN
ejpam-2366	740	7	:	:	PUNCT
ejpam-2366	740	8	i	i	PRON
ejpam-2366	740	9	m	m	VERB
ejpam-2366	740	10	)	)	PUNCT
ejpam-2366	741	1	i	i	PRON
ejpam-2366	741	2	m	m	VERB
ejpam-2366	741	3	=	=	ADJ
ejpam-2366	741	4	rad(p	rad(p	PROPN
ejpam-2366	741	5	)	)	PUNCT
ejpam-2366	741	6	by	by	ADP
ejpam-2366	741	7	theorem	theorem	VERB
ejpam-2366	741	8	3.6	3.6	NUM
ejpam-2366	741	9	of	of	ADP
ejpam-2366	741	10	[	[	X
ejpam-2366	741	11	17	17	NUM
ejpam-2366	741	12	]	]	PUNCT
ejpam-2366	741	13	.	.	PUNCT
ejpam-2366	742	1	conversely	conversely	ADV
ejpam-2366	742	2	,	,	PUNCT
ejpam-2366	742	3	assume	assume	VERB
ejpam-2366	742	4	that	that	SCONJ
ejpam-2366	742	5	abim	abim	NOUN
ejpam-2366	742	6	6	6	NUM
ejpam-2366	742	7	p	p	NOUN
ejpam-2366	742	8	and	and	CCONJ
ejpam-2366	742	9	abim	abim	NOUN
ejpam-2366	742	10	(	(	PUNCT
ejpam-2366	742	11	p	p	X
ejpam-2366	742	12	:	:	PUNCT
ejpam-2366	742	13	i	i	PRON
ejpam-2366	742	14	m	m	VERB
ejpam-2366	742	15	)	)	PUNCT
ejpam-2366	742	16	p	p	NOUN
ejpam-2366	742	17	implies	imply	VERB
ejpam-2366	742	18	either	either	CCONJ
ejpam-2366	742	19	n	n	PROPN
ejpam-2366	742	20	6	6	NUM
ejpam-2366	742	21	p	p	NOUN
ejpam-2366	742	22	or	or	CCONJ
ejpam-2366	742	23	k	k	PROPN
ejpam-2366	742	24	6	6	NUM
ejpam-2366	742	25	rad(p	rad(p	PROPN
ejpam-2366	742	26	)	)	PUNCT
ejpam-2366	742	27	where	where	SCONJ
ejpam-2366	742	28	n	n	NOUN
ejpam-2366	742	29	=	=	SYM
ejpam-2366	742	30	aim	aim	NOUN
ejpam-2366	742	31	and	and	CCONJ
ejpam-2366	742	32	k	k	PROPN
ejpam-2366	743	1	=	=	NOUN
ejpam-2366	743	2	bim	bim	NOUN
ejpam-2366	743	3	are	be	AUX
ejpam-2366	743	4	in	in	ADP
ejpam-2366	743	5	m	m	PROPN
ejpam-2366	743	6	for	for	ADP
ejpam-2366	743	7	a	a	DET
ejpam-2366	743	8	,	,	PUNCT
ejpam-2366	743	9	b	b	PROPN
ejpam-2366	743	10	∈	∈	PROPN
ejpam-2366	743	11	l.	l.	NOUN
ejpam-2366	743	12	let	let	VERB
ejpam-2366	743	13	rs	rs	X
ejpam-2366	743	14	6	6	NUM
ejpam-2366	743	15	(	(	PUNCT
ejpam-2366	743	16	p	p	X
ejpam-2366	743	17	:	:	PUNCT
ejpam-2366	743	18	i	i	PRON
ejpam-2366	743	19	m	m	PROPN
ejpam-2366	743	20	)	)	PUNCT
ejpam-2366	743	21	and	and	CCONJ
ejpam-2366	743	22	rs	rs	INTJ
ejpam-2366	743	23	(	(	PUNCT
ejpam-2366	743	24	p	p	X
ejpam-2366	743	25	:	:	PUNCT
ejpam-2366	743	26	i	i	PRON
ejpam-2366	743	27	m	m	VERB
ejpam-2366	743	28	)	)	PUNCT
ejpam-2366	743	29	2	2	NUM
ejpam-2366	743	30	where	where	SCONJ
ejpam-2366	743	31	s	s	VERB
ejpam-2366	743	32	=	=	VERB
ejpam-2366	743	33	rim	rim	NOUN
ejpam-2366	743	34	and	and	CCONJ
ejpam-2366	743	35	q	q	NOUN
ejpam-2366	744	1	=	=	NOUN
ejpam-2366	744	2	sim	sim	NOUN
ejpam-2366	744	3	are	be	AUX
ejpam-2366	744	4	in	in	ADP
ejpam-2366	744	5	m	m	PROPN
ejpam-2366	744	6	for	for	ADP
ejpam-2366	744	7	r	r	NOUN
ejpam-2366	744	8	,	,	PUNCT
ejpam-2366	744	9	s	s	NOUN
ejpam-2366	744	10	∈	∈	PROPN
ejpam-2366	744	11	l.	l.	NOUN
ejpam-2366	744	12	if	if	SCONJ
ejpam-2366	744	13	rsim	rsim	NOUN
ejpam-2366	744	14	6	6	NUM
ejpam-2366	744	15	(	(	PUNCT
ejpam-2366	744	16	p	p	X
ejpam-2366	744	17	:	:	PUNCT
ejpam-2366	744	18	i	i	PRON
ejpam-2366	744	19	m	m	VERB
ejpam-2366	744	20	)	)	PUNCT
ejpam-2366	744	21	p	p	NOUN
ejpam-2366	744	22	,	,	PUNCT
ejpam-2366	744	23	then	then	ADV
ejpam-2366	744	24	since	since	SCONJ
ejpam-2366	744	25	m	m	PROPN
ejpam-2366	744	26	is	be	AUX
ejpam-2366	744	27	a	a	DET
ejpam-2366	744	28	multiplication	multiplication	NOUN
ejpam-2366	744	29	lattice	lattice	NOUN
ejpam-2366	744	30	l	l	NOUN
ejpam-2366	744	31	-	-	NOUN
ejpam-2366	744	32	module	module	NOUN
ejpam-2366	744	33	,	,	PUNCT
ejpam-2366	744	34	we	we	PRON
ejpam-2366	744	35	have	have	VERB
ejpam-2366	744	36	rsim	rsim	NOUN
ejpam-2366	744	37	6	6	NUM
ejpam-2366	744	38	(	(	PUNCT
ejpam-2366	744	39	p	p	X
ejpam-2366	744	40	:	:	PUNCT
ejpam-2366	744	41	i	i	PROPN
ejpam-2366	744	42	m	m	NOUN
ejpam-2366	744	43	)	)	PUNCT
ejpam-2366	744	44	2im	2im	NOUN
ejpam-2366	744	45	.	.	PUNCT
ejpam-2366	745	1	so	so	ADV
ejpam-2366	745	2	by	by	ADP
ejpam-2366	745	3	theorem	theorem	NOUN
ejpam-2366	745	4	5	5	NUM
ejpam-2366	745	5	of	of	ADP
ejpam-2366	745	6	[	[	X
ejpam-2366	745	7	10	10	NUM
ejpam-2366	745	8	]	]	PUNCT
ejpam-2366	745	9	,	,	PUNCT
ejpam-2366	745	10	we	we	PRON
ejpam-2366	745	11	have	have	VERB
ejpam-2366	745	12	rs	r	VERB
ejpam-2366	745	13	6	6	NUM
ejpam-2366	745	14	(	(	PUNCT
ejpam-2366	745	15	p	p	X
ejpam-2366	745	16	:	:	PUNCT
ejpam-2366	745	17	i	i	PRON
ejpam-2366	745	18	m	m	VERB
ejpam-2366	745	19	)	)	PUNCT
ejpam-2366	745	20	2	2	NUM
ejpam-2366	745	21	,	,	PUNCT
ejpam-2366	745	22	a	a	DET
ejpam-2366	745	23	contradiction	contradiction	NOUN
ejpam-2366	745	24	.	.	PUNCT
ejpam-2366	746	1	so	so	ADV
ejpam-2366	746	2	let	let	VERB
ejpam-2366	746	3	rsim	rsim	NOUN
ejpam-2366	746	4	(	(	PUNCT
ejpam-2366	746	5	p	p	X
ejpam-2366	746	6	:	:	PUNCT
ejpam-2366	746	7	i	i	PRON
ejpam-2366	746	8	m	m	PROPN
ejpam-2366	746	9	)	)	PUNCT
ejpam-2366	746	10	p	p	NOUN
ejpam-2366	746	11	.	.	PUNCT
ejpam-2366	747	1	since	since	SCONJ
ejpam-2366	747	2	rsim	rsim	NOUN
ejpam-2366	747	3	6	6	NUM
ejpam-2366	747	4	p	p	NOUN
ejpam-2366	747	5	,	,	PUNCT
ejpam-2366	747	6	by	by	ADP
ejpam-2366	747	7	hypothesis	hypothesis	NOUN
ejpam-2366	747	8	,	,	PUNCT
ejpam-2366	747	9	we	we	PRON
ejpam-2366	747	10	have	have	VERB
ejpam-2366	747	11	either	either	CCONJ
ejpam-2366	747	12	s	s	VERB
ejpam-2366	747	13	6	6	NUM
ejpam-2366	747	14	p	p	NOUN
ejpam-2366	747	15	or	or	CCONJ
ejpam-2366	747	16	q	q	PROPN
ejpam-2366	747	17	6	6	NUM
ejpam-2366	747	18	rad(p	rad(p	PROPN
ejpam-2366	747	19	)	)	PUNCT
ejpam-2366	747	20	which	which	PRON
ejpam-2366	747	21	implies	imply	VERB
ejpam-2366	747	22	either	either	CCONJ
ejpam-2366	747	23	rim	rim	VERB
ejpam-2366	747	24	6	6	NUM
ejpam-2366	747	25	p	p	NOUN
ejpam-2366	747	26	or	or	CCONJ
ejpam-2366	747	27	sim	sim	ADJ
ejpam-2366	747	28	6	6	NUM
ejpam-2366	747	29	rad(p	rad(p	PROPN
ejpam-2366	747	30	)	)	PUNCT
ejpam-2366	748	1	=	=	PUNCT
ejpam-2366	748	2	(	(	PUNCT
ejpam-2366	748	3	√	√	INTJ
ejpam-2366	748	4	p	p	X
ejpam-2366	748	5	:	:	PUNCT
ejpam-2366	748	6	i	i	PRON
ejpam-2366	748	7	m	m	VERB
ejpam-2366	748	8	)	)	PUNCT
ejpam-2366	749	1	i	i	PRON
ejpam-2366	749	2	m	m	VERB
ejpam-2366	749	3	,	,	PUNCT
ejpam-2366	749	4	by	by	ADP
ejpam-2366	749	5	theorem	theorem	VERB
ejpam-2366	749	6	3.6	3.6	NUM
ejpam-2366	749	7	of	of	ADP
ejpam-2366	749	8	[	[	X
ejpam-2366	749	9	17	17	NUM
ejpam-2366	749	10	]	]	PUNCT
ejpam-2366	749	11	.	.	PUNCT
ejpam-2366	750	1	so	so	ADV
ejpam-2366	750	2	either	either	DET
ejpam-2366	750	3	r	r	NOUN
ejpam-2366	750	4	6	6	NUM
ejpam-2366	750	5	(	(	PUNCT
ejpam-2366	750	6	p	p	X
ejpam-2366	750	7	:	:	PUNCT
ejpam-2366	750	8	i	i	PRON
ejpam-2366	750	9	m	m	VERB
ejpam-2366	750	10	)	)	PUNCT
ejpam-2366	750	11	or	or	CCONJ
ejpam-2366	750	12	s	s	VERB
ejpam-2366	750	13	6	6	NUM
ejpam-2366	750	14	√	√	NOUN
ejpam-2366	750	15	p	p	NOUN
ejpam-2366	750	16	:	:	PUNCT
ejpam-2366	750	17	i	i	PRON
ejpam-2366	750	18	m	m	VERB
ejpam-2366	750	19	,	,	PUNCT
ejpam-2366	750	20	by	by	ADP
ejpam-2366	750	21	theorem	theorem	NOUN
ejpam-2366	750	22	5	5	NUM
ejpam-2366	750	23	of	of	ADP
ejpam-2366	750	24	[	[	X
ejpam-2366	750	25	10	10	NUM
ejpam-2366	750	26	]	]	PUNCT
ejpam-2366	750	27	.	.	PUNCT
ejpam-2366	751	1	thus	thus	ADV
ejpam-2366	751	2	(	(	PUNCT
ejpam-2366	751	3	p	p	X
ejpam-2366	751	4	:	:	PUNCT
ejpam-2366	751	5	i	i	PRON
ejpam-2366	751	6	m	m	PROPN
ejpam-2366	751	7	)	)	PUNCT
ejpam-2366	751	8	is	be	AUX
ejpam-2366	751	9	an	an	DET
ejpam-2366	751	10	almost	almost	ADV
ejpam-2366	751	11	primary	primary	ADJ
ejpam-2366	751	12	element	element	NOUN
ejpam-2366	751	13	of	of	ADP
ejpam-2366	751	14	l	l	NOUN
ejpam-2366	751	15	and	and	CCONJ
ejpam-2366	751	16	hence	hence	ADV
ejpam-2366	751	17	by	by	ADP
ejpam-2366	751	18	theorem	theorem	NOUN
ejpam-2366	751	19	39	39	NUM
ejpam-2366	751	20	,	,	PUNCT
ejpam-2366	751	21	p	p	NOUN
ejpam-2366	751	22	is	be	AUX
ejpam-2366	751	23	an	an	DET
ejpam-2366	751	24	almost	almost	ADV
ejpam-2366	751	25	primary	primary	ADJ
ejpam-2366	751	26	element	element	NOUN
ejpam-2366	751	27	of	of	ADP
ejpam-2366	751	28	m	m	PROPN
ejpam-2366	751	29	.	.	PUNCT
ejpam-2366	752	1	now	now	ADV
ejpam-2366	752	2	we	we	PRON
ejpam-2366	752	3	show	show	VERB
ejpam-2366	752	4	that	that	SCONJ
ejpam-2366	752	5	lemma	lemma	PROPN
ejpam-2366	752	6	4	4	NUM
ejpam-2366	752	7	can	can	AUX
ejpam-2366	752	8	also	also	ADV
ejpam-2366	752	9	be	be	AUX
ejpam-2366	752	10	achieved	achieve	VERB
ejpam-2366	752	11	by	by	ADP
ejpam-2366	752	12	changing	change	VERB
ejpam-2366	752	13	the	the	DET
ejpam-2366	752	14	conditions	condition	NOUN
ejpam-2366	752	15	on	on	ADP
ejpam-2366	752	16	m	m	NOUN
ejpam-2366	752	17	and	and	CCONJ
ejpam-2366	752	18	i	i	PRON
ejpam-2366	752	19	m	m	PROPN
ejpam-2366	752	20	.	.	PUNCT
ejpam-2366	753	1	lemma	lemma	PROPN
ejpam-2366	753	2	5	5	X
ejpam-2366	753	3	.	.	PUNCT
ejpam-2366	754	1	let	let	VERB
ejpam-2366	754	2	l	l	NOUN
ejpam-2366	754	3	be	be	AUX
ejpam-2366	754	4	a	a	DET
ejpam-2366	754	5	pg	pg	NOUN
ejpam-2366	754	6	-	-	PUNCT
ejpam-2366	754	7	lattice	lattice	NOUN
ejpam-2366	754	8	and	and	CCONJ
ejpam-2366	754	9	m	m	AUX
ejpam-2366	754	10	be	be	AUX
ejpam-2366	754	11	a	a	DET
ejpam-2366	754	12	faithful	faithful	ADJ
ejpam-2366	754	13	multiplication	multiplication	NOUN
ejpam-2366	754	14	pg	pg	NOUN
ejpam-2366	754	15	-	-	PUNCT
ejpam-2366	754	16	lattice	lattice	NOUN
ejpam-2366	754	17	l	l	NOUN
ejpam-2366	754	18	-	-	NOUN
ejpam-2366	754	19	module	module	NOUN
ejpam-2366	754	20	with	with	ADP
ejpam-2366	754	21	i	i	PRON
ejpam-2366	754	22	m	m	VERB
ejpam-2366	754	23	compact	compact	ADJ
ejpam-2366	754	24	.	.	PUNCT
ejpam-2366	755	1	let	let	VERB
ejpam-2366	755	2	n	n	PRON
ejpam-2366	755	3	be	be	AUX
ejpam-2366	755	4	a	a	DET
ejpam-2366	755	5	proper	proper	ADJ
ejpam-2366	755	6	element	element	NOUN
ejpam-2366	755	7	of	of	ADP
ejpam-2366	755	8	m	m	PROPN
ejpam-2366	755	9	.	.	PUNCT
ejpam-2366	756	1	then	then	ADV
ejpam-2366	756	2	a(n	a(n	ADV
ejpam-2366	756	3	:	:	PUNCT
ejpam-2366	757	1	i	i	PRON
ejpam-2366	757	2	m	m	VERB
ejpam-2366	757	3	)	)	PUNCT
ejpam-2366	758	1	=	=	SYM
ejpam-2366	758	2	(	(	PUNCT
ejpam-2366	758	3	an	an	PRON
ejpam-2366	758	4	:	:	PUNCT
ejpam-2366	758	5	i	i	PRON
ejpam-2366	758	6	m	m	PROPN
ejpam-2366	758	7	)	)	PUNCT
ejpam-2366	758	8	for	for	ADP
ejpam-2366	758	9	a	a	DET
ejpam-2366	758	10	∈	∈	PROPN
ejpam-2366	758	11	l.	l.	NOUN
ejpam-2366	758	12	proof	proof	NOUN
ejpam-2366	758	13	.	.	PUNCT
ejpam-2366	759	1	since	since	SCONJ
ejpam-2366	759	2	m	m	PROPN
ejpam-2366	759	3	is	be	AUX
ejpam-2366	759	4	a	a	DET
ejpam-2366	759	5	multiplication	multiplication	NOUN
ejpam-2366	759	6	lattice	lattice	NOUN
ejpam-2366	759	7	l	l	NOUN
ejpam-2366	759	8	-	-	NOUN
ejpam-2366	759	9	module	module	NOUN
ejpam-2366	759	10	,	,	PUNCT
ejpam-2366	759	11	n	n	NOUN
ejpam-2366	759	12	=	=	SYM
ejpam-2366	759	13	(	(	PUNCT
ejpam-2366	759	14	n	n	X
ejpam-2366	759	15	:	:	PUNCT
ejpam-2366	759	16	i	i	PRON
ejpam-2366	759	17	m	m	VERB
ejpam-2366	759	18	)	)	PUNCT
ejpam-2366	759	19	i	i	PRON
ejpam-2366	759	20	m	m	VERB
ejpam-2366	759	21	.	.	PUNCT
ejpam-2366	760	1	then	then	ADV
ejpam-2366	760	2	a(n	a(n	ADV
ejpam-2366	760	3	:	:	PUNCT
ejpam-2366	760	4	i	i	PRON
ejpam-2366	760	5	m	m	VERB
ejpam-2366	760	6	)	)	PUNCT
ejpam-2366	761	1	i	i	PRON
ejpam-2366	761	2	m	m	VERB
ejpam-2366	761	3	=	=	VERB
ejpam-2366	761	4	an	an	PROPN
ejpam-2366	761	5	=	=	X
ejpam-2366	761	6	(	(	PUNCT
ejpam-2366	761	7	an	an	PRON
ejpam-2366	761	8	:	:	PUNCT
ejpam-2366	761	9	i	i	PRON
ejpam-2366	761	10	m	m	VERB
ejpam-2366	761	11	)	)	PUNCT
ejpam-2366	762	1	i	i	PRON
ejpam-2366	762	2	m	m	VERB
ejpam-2366	762	3	and	and	CCONJ
ejpam-2366	762	4	we	we	PRON
ejpam-2366	762	5	are	be	AUX
ejpam-2366	762	6	done	do	VERB
ejpam-2366	762	7	,	,	PUNCT
ejpam-2366	762	8	by	by	ADP
ejpam-2366	762	9	theorem	theorem	NOUN
ejpam-2366	762	10	5	5	NUM
ejpam-2366	762	11	of	of	ADP
ejpam-2366	762	12	[	[	X
ejpam-2366	762	13	10	10	NUM
ejpam-2366	762	14	]	]	PUNCT
ejpam-2366	762	15	.	.	PUNCT
ejpam-2366	763	1	lemma	lemma	PROPN
ejpam-2366	763	2	5	5	NUM
ejpam-2366	763	3	is	be	AUX
ejpam-2366	763	4	lemma	lemma	PROPN
ejpam-2366	763	5	3.5	3.5	NUM
ejpam-2366	763	6	of	of	ADP
ejpam-2366	763	7	[	[	X
ejpam-2366	763	8	22	22	NUM
ejpam-2366	763	9	]	]	PUNCT
ejpam-2366	763	10	.	.	PUNCT
ejpam-2366	764	1	in	in	ADP
ejpam-2366	764	2	view	view	NOUN
ejpam-2366	764	3	of	of	ADP
ejpam-2366	764	4	lemma	lemma	PROPN
ejpam-2366	764	5	5	5	NUM
ejpam-2366	764	6	,	,	PUNCT
ejpam-2366	764	7	the	the	DET
ejpam-2366	764	8	theorems	theorem	NOUN
ejpam-2366	764	9	38	38	NUM
ejpam-2366	764	10	,	,	PUNCT
ejpam-2366	764	11	39	39	NUM
ejpam-2366	764	12	and	and	CCONJ
ejpam-2366	764	13	40	40	NUM
ejpam-2366	764	14	can	can	AUX
ejpam-2366	764	15	be	be	AUX
ejpam-2366	764	16	restated	restate	VERB
ejpam-2366	764	17	in	in	ADP
ejpam-2366	764	18	the	the	DET
ejpam-2366	764	19	following	following	ADJ
ejpam-2366	764	20	way	way	NOUN
ejpam-2366	764	21	.	.	PUNCT
ejpam-2366	765	1	a.	a.	PROPN
ejpam-2366	765	2	v.	v.	PROPN
ejpam-2366	765	3	bingi	bingi	PROPN
ejpam-2366	765	4	,	,	PUNCT
ejpam-2366	765	5	c.	c.	PROPN
ejpam-2366	765	6	s.	s.	PROPN
ejpam-2366	765	7	manjarekar	manjarekar	PROPN
ejpam-2366	765	8	/	/	PROPN
ejpam-2366	765	9	eur	eur	PROPN
ejpam-2366	765	10	.	.	PUNCT
ejpam-2366	766	1	j.	j.	PROPN
ejpam-2366	766	2	pure	pure	PROPN
ejpam-2366	766	3	appl	appl	PROPN
ejpam-2366	766	4	.	.	PROPN
ejpam-2366	766	5	math	math	PROPN
ejpam-2366	766	6	,	,	PUNCT
ejpam-2366	766	7	14	14	NUM
ejpam-2366	766	8	(	(	PUNCT
ejpam-2366	766	9	2	2	NUM
ejpam-2366	766	10	)	)	PUNCT
ejpam-2366	766	11	(	(	PUNCT
ejpam-2366	766	12	2021	2021	NUM
ejpam-2366	766	13	)	)	PUNCT
ejpam-2366	766	14	,	,	PUNCT
ejpam-2366	766	15	551	551	NUM
ejpam-2366	766	16	-	-	SYM
ejpam-2366	766	17	577	577	NUM
ejpam-2366	766	18	571	571	NUM
ejpam-2366	766	19	theorem	theorem	VERB
ejpam-2366	766	20	41	41	NUM
ejpam-2366	766	21	.	.	PUNCT
ejpam-2366	767	1	let	let	VERB
ejpam-2366	767	2	l	l	NOUN
ejpam-2366	767	3	be	be	AUX
ejpam-2366	767	4	a	a	DET
ejpam-2366	767	5	pg	pg	NOUN
ejpam-2366	767	6	-	-	PUNCT
ejpam-2366	767	7	lattice	lattice	NOUN
ejpam-2366	767	8	and	and	CCONJ
ejpam-2366	767	9	m	m	AUX
ejpam-2366	767	10	be	be	AUX
ejpam-2366	767	11	a	a	DET
ejpam-2366	767	12	faithful	faithful	ADJ
ejpam-2366	767	13	multiplication	multiplication	NOUN
ejpam-2366	767	14	pg	pg	ADJ
ejpam-2366	767	15	-	-	PUNCT
ejpam-2366	767	16	lattice	lattice	NOUN
ejpam-2366	767	17	lmodule	lmodule	NOUN
ejpam-2366	767	18	with	with	ADP
ejpam-2366	767	19	i	i	PRON
ejpam-2366	767	20	m	m	VERB
ejpam-2366	767	21	compact	compact	ADJ
ejpam-2366	767	22	.	.	PUNCT
ejpam-2366	768	1	let	let	VERB
ejpam-2366	768	2	n	n	PRON
ejpam-2366	768	3	be	be	AUX
ejpam-2366	768	4	a	a	DET
ejpam-2366	768	5	proper	proper	ADJ
ejpam-2366	768	6	element	element	NOUN
ejpam-2366	768	7	of	of	ADP
ejpam-2366	768	8	an	an	DET
ejpam-2366	768	9	l	l	NOUN
ejpam-2366	768	10	-	-	NOUN
ejpam-2366	768	11	module	module	NOUN
ejpam-2366	768	12	m	m	NOUN
ejpam-2366	768	13	.	.	PUNCT
ejpam-2366	769	1	then	then	ADV
ejpam-2366	769	2	the	the	DET
ejpam-2366	769	3	following	follow	VERB
ejpam-2366	769	4	statements	statement	NOUN
ejpam-2366	769	5	are	be	AUX
ejpam-2366	769	6	equivalent	equivalent	ADJ
ejpam-2366	769	7	:	:	PUNCT
ejpam-2366	769	8	1	1	X
ejpam-2366	769	9	©	©	NOUN
ejpam-2366	769	10	n	n	NUM
ejpam-2366	769	11	is	be	AUX
ejpam-2366	769	12	an	an	DET
ejpam-2366	769	13	almost	almost	ADV
ejpam-2366	769	14	primary	primary	ADJ
ejpam-2366	769	15	element	element	NOUN
ejpam-2366	769	16	of	of	ADP
ejpam-2366	769	17	m	m	PROPN
ejpam-2366	769	18	.	.	PUNCT
ejpam-2366	770	1	2	2	NUM
ejpam-2366	770	2	©	©	NOUN
ejpam-2366	770	3	(	(	PUNCT
ejpam-2366	770	4	n	n	NOUN
ejpam-2366	770	5	:	:	PUNCT
ejpam-2366	770	6	i	i	PRON
ejpam-2366	770	7	m	m	PROPN
ejpam-2366	770	8	)	)	PUNCT
ejpam-2366	770	9	is	be	AUX
ejpam-2366	770	10	an	an	DET
ejpam-2366	770	11	almost	almost	ADV
ejpam-2366	770	12	primary	primary	ADJ
ejpam-2366	770	13	element	element	NOUN
ejpam-2366	770	14	of	of	ADP
ejpam-2366	770	15	l.	l.	PROPN
ejpam-2366	770	16	3	3	NUM
ejpam-2366	770	17	©	©	PROPN
ejpam-2366	770	18	n	n	NOUN
ejpam-2366	770	19	=	=	X
ejpam-2366	770	20	qim	qim	NOUN
ejpam-2366	770	21	for	for	ADP
ejpam-2366	770	22	some	some	DET
ejpam-2366	770	23	almost	almost	ADV
ejpam-2366	770	24	primary	primary	ADJ
ejpam-2366	770	25	element	element	NOUN
ejpam-2366	770	26	q	q	PROPN
ejpam-2366	770	27	∈	∈	PROPN
ejpam-2366	770	28	l	l	NOUN
ejpam-2366	770	29	which	which	PRON
ejpam-2366	770	30	is	be	AUX
ejpam-2366	770	31	maximal	maximal	ADJ
ejpam-2366	770	32	in	in	ADP
ejpam-2366	770	33	the	the	DET
ejpam-2366	770	34	sense	sense	NOUN
ejpam-2366	770	35	that	that	SCONJ
ejpam-2366	770	36	if	if	SCONJ
ejpam-2366	770	37	aim	aim	VERB
ejpam-2366	770	38	=	=	SYM
ejpam-2366	770	39	n	n	CCONJ
ejpam-2366	770	40	,	,	PUNCT
ejpam-2366	770	41	then	then	ADV
ejpam-2366	770	42	a	a	DET
ejpam-2366	770	43	6	6	NUM
ejpam-2366	770	44	q	q	NOUN
ejpam-2366	770	45	where	where	SCONJ
ejpam-2366	770	46	a	a	DET
ejpam-2366	770	47	∈	∈	PROPN
ejpam-2366	770	48	l.	l.	NOUN
ejpam-2366	770	49	theorem	theorem	VERB
ejpam-2366	770	50	42	42	NUM
ejpam-2366	770	51	.	.	PUNCT
ejpam-2366	771	1	let	let	VERB
ejpam-2366	771	2	l	l	NOUN
ejpam-2366	771	3	be	be	AUX
ejpam-2366	771	4	a	a	DET
ejpam-2366	771	5	pg	pg	NOUN
ejpam-2366	771	6	-	-	PUNCT
ejpam-2366	771	7	lattice	lattice	NOUN
ejpam-2366	771	8	and	and	CCONJ
ejpam-2366	771	9	m	m	AUX
ejpam-2366	771	10	be	be	AUX
ejpam-2366	771	11	a	a	DET
ejpam-2366	771	12	faithful	faithful	ADJ
ejpam-2366	771	13	multiplication	multiplication	NOUN
ejpam-2366	771	14	pg	pg	ADJ
ejpam-2366	771	15	-	-	PUNCT
ejpam-2366	771	16	lattice	lattice	NOUN
ejpam-2366	771	17	lmodule	lmodule	NOUN
ejpam-2366	771	18	with	with	ADP
ejpam-2366	771	19	i	i	PRON
ejpam-2366	771	20	m	m	VERB
ejpam-2366	771	21	compact	compact	ADJ
ejpam-2366	771	22	.	.	PUNCT
ejpam-2366	772	1	let	let	VERB
ejpam-2366	772	2	n	n	PRON
ejpam-2366	772	3	be	be	AUX
ejpam-2366	772	4	a	a	DET
ejpam-2366	772	5	proper	proper	ADJ
ejpam-2366	772	6	element	element	NOUN
ejpam-2366	772	7	of	of	ADP
ejpam-2366	772	8	an	an	DET
ejpam-2366	772	9	l	l	NOUN
ejpam-2366	772	10	-	-	NOUN
ejpam-2366	772	11	module	module	NOUN
ejpam-2366	772	12	m	m	NOUN
ejpam-2366	772	13	.	.	PUNCT
ejpam-2366	773	1	then	then	ADV
ejpam-2366	773	2	the	the	DET
ejpam-2366	773	3	following	follow	VERB
ejpam-2366	773	4	statements	statement	NOUN
ejpam-2366	773	5	are	be	AUX
ejpam-2366	773	6	equivalent	equivalent	ADJ
ejpam-2366	773	7	:	:	PUNCT
ejpam-2366	773	8	1	1	X
ejpam-2366	773	9	©	©	NOUN
ejpam-2366	773	10	n	n	NUM
ejpam-2366	773	11	is	be	AUX
ejpam-2366	773	12	an	an	DET
ejpam-2366	773	13	almost	almost	ADV
ejpam-2366	773	14	primary	primary	ADJ
ejpam-2366	773	15	element	element	NOUN
ejpam-2366	773	16	of	of	ADP
ejpam-2366	773	17	m	m	PROPN
ejpam-2366	773	18	.	.	PUNCT
ejpam-2366	774	1	2	2	NUM
ejpam-2366	774	2	©	©	NOUN
ejpam-2366	774	3	(	(	PUNCT
ejpam-2366	774	4	n	n	NOUN
ejpam-2366	774	5	:	:	PUNCT
ejpam-2366	774	6	i	i	PRON
ejpam-2366	774	7	m	m	PROPN
ejpam-2366	774	8	)	)	PUNCT
ejpam-2366	774	9	is	be	AUX
ejpam-2366	774	10	an	an	DET
ejpam-2366	774	11	almost	almost	ADV
ejpam-2366	774	12	primary	primary	ADJ
ejpam-2366	774	13	element	element	NOUN
ejpam-2366	774	14	of	of	ADP
ejpam-2366	774	15	l.	l.	PROPN
ejpam-2366	774	16	3	3	NUM
ejpam-2366	774	17	©	©	PROPN
ejpam-2366	774	18	n	n	NOUN
ejpam-2366	774	19	=	=	X
ejpam-2366	774	20	qim	qim	NOUN
ejpam-2366	774	21	for	for	ADP
ejpam-2366	774	22	some	some	DET
ejpam-2366	774	23	almost	almost	ADV
ejpam-2366	774	24	primary	primary	ADJ
ejpam-2366	774	25	element	element	NOUN
ejpam-2366	774	26	q	q	PROPN
ejpam-2366	774	27	∈	∈	PROPN
ejpam-2366	774	28	l.	l.	PROPN
ejpam-2366	774	29	theorem	theorem	VERB
ejpam-2366	774	30	43	43	NUM
ejpam-2366	774	31	.	.	PUNCT
ejpam-2366	775	1	let	let	VERB
ejpam-2366	775	2	l	l	NOUN
ejpam-2366	775	3	be	be	AUX
ejpam-2366	775	4	a	a	DET
ejpam-2366	775	5	pg	pg	NOUN
ejpam-2366	775	6	-	-	PUNCT
ejpam-2366	775	7	lattice	lattice	NOUN
ejpam-2366	775	8	and	and	CCONJ
ejpam-2366	775	9	m	m	AUX
ejpam-2366	775	10	be	be	AUX
ejpam-2366	775	11	a	a	DET
ejpam-2366	775	12	faithful	faithful	ADJ
ejpam-2366	775	13	multiplication	multiplication	NOUN
ejpam-2366	775	14	pg	pg	ADJ
ejpam-2366	775	15	-	-	PUNCT
ejpam-2366	775	16	lattice	lattice	NOUN
ejpam-2366	775	17	lmodule	lmodule	NOUN
ejpam-2366	775	18	with	with	ADP
ejpam-2366	775	19	i	i	PROPN
ejpam-2366	775	20	m	m	VERB
ejpam-2366	775	21	compact	compact	ADJ
ejpam-2366	775	22	.	.	PUNCT
ejpam-2366	776	1	then	then	ADV
ejpam-2366	776	2	a	a	DET
ejpam-2366	776	3	proper	proper	ADJ
ejpam-2366	776	4	element	element	NOUN
ejpam-2366	776	5	p	p	NOUN
ejpam-2366	776	6	∈m	∈m	NOUN
ejpam-2366	776	7	is	be	AUX
ejpam-2366	776	8	almost	almost	ADV
ejpam-2366	776	9	primary	primary	ADJ
ejpam-2366	776	10	(	(	PUNCT
ejpam-2366	776	11	φ2−primary	φ2−primary	NOUN
ejpam-2366	776	12	)	)	PUNCT
ejpam-2366	777	1	if	if	SCONJ
ejpam-2366	778	1	and	and	CCONJ
ejpam-2366	778	2	only	only	ADV
ejpam-2366	778	3	if	if	SCONJ
ejpam-2366	778	4	whenever	whenever	SCONJ
ejpam-2366	778	5	n	n	NOUN
ejpam-2366	778	6	=	=	VERB
ejpam-2366	778	7	aim	aim	NOUN
ejpam-2366	778	8	and	and	CCONJ
ejpam-2366	778	9	k	k	X
ejpam-2366	778	10	=	=	X
ejpam-2366	778	11	bim	bim	NOUN
ejpam-2366	778	12	in	in	ADP
ejpam-2366	778	13	m	m	PROPN
ejpam-2366	778	14	are	be	AUX
ejpam-2366	778	15	such	such	ADJ
ejpam-2366	778	16	that	that	DET
ejpam-2366	778	17	abim	abim	NOUN
ejpam-2366	778	18	6	6	NUM
ejpam-2366	778	19	p	p	NOUN
ejpam-2366	778	20	and	and	CCONJ
ejpam-2366	778	21	abim	abim	NOUN
ejpam-2366	778	22	(	(	PUNCT
ejpam-2366	778	23	p	p	X
ejpam-2366	778	24	:	:	PUNCT
ejpam-2366	778	25	i	i	PRON
ejpam-2366	778	26	m	m	PROPN
ejpam-2366	778	27	)	)	PUNCT
ejpam-2366	779	1	p	p	NOUN
ejpam-2366	779	2	then	then	ADV
ejpam-2366	779	3	either	either	CCONJ
ejpam-2366	779	4	n	n	PROPN
ejpam-2366	779	5	6	6	NUM
ejpam-2366	779	6	p	p	NOUN
ejpam-2366	779	7	or	or	CCONJ
ejpam-2366	779	8	k	k	PROPN
ejpam-2366	779	9	6	6	NUM
ejpam-2366	779	10	rad(p	rad(p	PROPN
ejpam-2366	779	11	)	)	PUNCT
ejpam-2366	779	12	for	for	ADP
ejpam-2366	779	13	a	a	DET
ejpam-2366	779	14	,	,	PUNCT
ejpam-2366	779	15	b	b	PROPN
ejpam-2366	779	16	∈	∈	PROPN
ejpam-2366	779	17	l.	l.	NOUN
ejpam-2366	779	18	the	the	DET
ejpam-2366	779	19	following	following	ADJ
ejpam-2366	779	20	result	result	NOUN
ejpam-2366	779	21	is	be	AUX
ejpam-2366	779	22	a	a	DET
ejpam-2366	779	23	consequence	consequence	NOUN
ejpam-2366	779	24	of	of	ADP
ejpam-2366	779	25	the	the	DET
ejpam-2366	779	26	theorem	theorem	ADJ
ejpam-2366	779	27	42	42	NUM
ejpam-2366	779	28	.	.	PUNCT
ejpam-2366	780	1	corollary	corollary	ADJ
ejpam-2366	780	2	19	19	NUM
ejpam-2366	780	3	.	.	PUNCT
ejpam-2366	781	1	let	let	VERB
ejpam-2366	781	2	l	l	NOUN
ejpam-2366	781	3	be	be	AUX
ejpam-2366	781	4	a	a	DET
ejpam-2366	781	5	pg	pg	NOUN
ejpam-2366	781	6	-	-	PUNCT
ejpam-2366	781	7	lattice	lattice	NOUN
ejpam-2366	781	8	and	and	CCONJ
ejpam-2366	781	9	m	m	AUX
ejpam-2366	781	10	be	be	AUX
ejpam-2366	781	11	a	a	DET
ejpam-2366	781	12	faithful	faithful	ADJ
ejpam-2366	781	13	multiplication	multiplication	NOUN
ejpam-2366	781	14	pg	pg	ADJ
ejpam-2366	781	15	-	-	PUNCT
ejpam-2366	781	16	lattice	lattice	NOUN
ejpam-2366	781	17	lmodule	lmodule	NOUN
ejpam-2366	781	18	with	with	ADP
ejpam-2366	781	19	i	i	PROPN
ejpam-2366	781	20	m	m	VERB
ejpam-2366	781	21	compact	compact	ADJ
ejpam-2366	781	22	.	.	PUNCT
ejpam-2366	782	1	then	then	ADV
ejpam-2366	782	2	a	a	DET
ejpam-2366	782	3	proper	proper	ADJ
ejpam-2366	782	4	element	element	NOUN
ejpam-2366	782	5	n	n	PROPN
ejpam-2366	782	6	of	of	ADP
ejpam-2366	782	7	an	an	DET
ejpam-2366	782	8	l	l	NOUN
ejpam-2366	782	9	-	-	NOUN
ejpam-2366	782	10	module	module	NOUN
ejpam-2366	782	11	m	m	NOUN
ejpam-2366	782	12	is	be	AUX
ejpam-2366	782	13	almost	almost	ADV
ejpam-2366	782	14	primary	primary	ADJ
ejpam-2366	782	15	if	if	SCONJ
ejpam-2366	782	16	and	and	CCONJ
ejpam-2366	782	17	only	only	ADV
ejpam-2366	782	18	if	if	SCONJ
ejpam-2366	782	19	(	(	PUNCT
ejpam-2366	782	20	n	n	X
ejpam-2366	782	21	:	:	PUNCT
ejpam-2366	782	22	i	i	PRON
ejpam-2366	782	23	m	m	PROPN
ejpam-2366	782	24	)	)	PUNCT
ejpam-2366	782	25	is	be	AUX
ejpam-2366	782	26	an	an	DET
ejpam-2366	782	27	almost	almost	ADV
ejpam-2366	782	28	primary	primary	ADJ
ejpam-2366	782	29	element	element	NOUN
ejpam-2366	782	30	of	of	ADP
ejpam-2366	782	31	l.	l.	PROPN
ejpam-2366	782	32	the	the	DET
ejpam-2366	782	33	analogous	analogous	ADJ
ejpam-2366	782	34	results	result	NOUN
ejpam-2366	782	35	(	(	PUNCT
ejpam-2366	782	36	from	from	ADP
ejpam-2366	782	37	the	the	DET
ejpam-2366	782	38	results	result	NOUN
ejpam-2366	782	39	of	of	ADP
ejpam-2366	782	40	almost	almost	ADV
ejpam-2366	782	41	primary	primary	ADJ
ejpam-2366	782	42	elements	element	NOUN
ejpam-2366	782	43	of	of	ADP
ejpam-2366	782	44	m	m	PROPN
ejpam-2366	782	45	)	)	PUNCT
ejpam-2366	782	46	for	for	ADP
ejpam-2366	782	47	almost	almost	ADV
ejpam-2366	782	48	prime	prime	ADJ
ejpam-2366	782	49	elements	element	NOUN
ejpam-2366	782	50	of	of	ADP
ejpam-2366	782	51	m	m	NOUN
ejpam-2366	782	52	are	be	AUX
ejpam-2366	782	53	as	as	SCONJ
ejpam-2366	782	54	follows	follow	VERB
ejpam-2366	782	55	.	.	PUNCT
ejpam-2366	783	1	in	in	ADP
ejpam-2366	783	2	example	example	NOUN
ejpam-2366	783	3	2.5	2.5	NUM
ejpam-2366	783	4	of	of	ADP
ejpam-2366	783	5	[	[	X
ejpam-2366	783	6	22	22	NUM
ejpam-2366	783	7	]	]	PUNCT
ejpam-2366	783	8	,	,	PUNCT
ejpam-2366	783	9	it	it	PRON
ejpam-2366	783	10	is	be	AUX
ejpam-2366	783	11	shown	show	VERB
ejpam-2366	783	12	that	that	SCONJ
ejpam-2366	783	13	an	an	DET
ejpam-2366	783	14	almost	almost	ADV
ejpam-2366	783	15	prime	prime	ADJ
ejpam-2366	783	16	element	element	NOUN
ejpam-2366	783	17	of	of	ADP
ejpam-2366	783	18	an	an	DET
ejpam-2366	783	19	l	l	NOUN
ejpam-2366	783	20	-	-	NOUN
ejpam-2366	783	21	module	module	NOUN
ejpam-2366	783	22	m	m	NOUN
ejpam-2366	783	23	need	need	AUX
ejpam-2366	783	24	not	not	PART
ejpam-2366	783	25	be	be	AUX
ejpam-2366	783	26	weakly	weakly	ADV
ejpam-2366	783	27	prime	prime	ADJ
ejpam-2366	783	28	.	.	PUNCT
ejpam-2366	784	1	the	the	DET
ejpam-2366	784	2	following	follow	VERB
ejpam-2366	784	3	characterization	characterization	NOUN
ejpam-2366	784	4	of	of	ADP
ejpam-2366	784	5	an	an	DET
ejpam-2366	784	6	almost	almost	ADV
ejpam-2366	784	7	prime	prime	ADJ
ejpam-2366	784	8	element	element	NOUN
ejpam-2366	784	9	of	of	ADP
ejpam-2366	784	10	an	an	DET
ejpam-2366	784	11	l	l	NOUN
ejpam-2366	784	12	-	-	NOUN
ejpam-2366	784	13	module	module	NOUN
ejpam-2366	784	14	m	m	NOUN
ejpam-2366	784	15	shows	show	VERB
ejpam-2366	784	16	that	that	SCONJ
ejpam-2366	784	17	under	under	ADP
ejpam-2366	784	18	a	a	DET
ejpam-2366	784	19	certain	certain	ADJ
ejpam-2366	784	20	condition	condition	NOUN
ejpam-2366	784	21	,	,	PUNCT
ejpam-2366	784	22	an	an	DET
ejpam-2366	784	23	almost	almost	ADV
ejpam-2366	784	24	prime	prime	ADJ
ejpam-2366	784	25	element	element	NOUN
ejpam-2366	784	26	of	of	ADP
ejpam-2366	784	27	an	an	DET
ejpam-2366	784	28	l	l	NOUN
ejpam-2366	784	29	-	-	NOUN
ejpam-2366	784	30	module	module	NOUN
ejpam-2366	784	31	m	m	NOUN
ejpam-2366	784	32	is	be	AUX
ejpam-2366	784	33	weakly	weakly	ADV
ejpam-2366	784	34	prime	prime	ADJ
ejpam-2366	784	35	.	.	PUNCT
ejpam-2366	785	1	theorem	theorem	VERB
ejpam-2366	785	2	44	44	NUM
ejpam-2366	785	3	.	.	PUNCT
ejpam-2366	786	1	let	let	VERB
ejpam-2366	786	2	m	m	PRON
ejpam-2366	786	3	be	be	AUX
ejpam-2366	786	4	a	a	DET
ejpam-2366	786	5	local	local	ADJ
ejpam-2366	786	6	l	l	NOUN
ejpam-2366	786	7	-	-	NOUN
ejpam-2366	786	8	module	module	NOUN
ejpam-2366	786	9	with	with	ADP
ejpam-2366	786	10	a	a	DET
ejpam-2366	786	11	unique	unique	ADJ
ejpam-2366	786	12	maximal	maximal	ADJ
ejpam-2366	786	13	element	element	NOUN
ejpam-2366	786	14	q	q	PROPN
ejpam-2366	786	15	∈	∈	PROPN
ejpam-2366	786	16	m	m	VERB
ejpam-2366	786	17	such	such	ADJ
ejpam-2366	786	18	that	that	SCONJ
ejpam-2366	786	19	(	(	PUNCT
ejpam-2366	786	20	q	q	NOUN
ejpam-2366	786	21	:	:	PUNCT
ejpam-2366	786	22	i	i	PRON
ejpam-2366	786	23	m	m	VERB
ejpam-2366	786	24	)	)	PUNCT
ejpam-2366	786	25	q	q	NOUN
ejpam-2366	787	1	=	=	PUNCT
ejpam-2366	787	2	om	om	PROPN
ejpam-2366	787	3	.	.	PUNCT
ejpam-2366	788	1	then	then	ADV
ejpam-2366	788	2	a	a	DET
ejpam-2366	788	3	proper	proper	ADJ
ejpam-2366	788	4	element	element	NOUN
ejpam-2366	788	5	n	n	PRON
ejpam-2366	788	6	∈m	∈m	NOUN
ejpam-2366	788	7	is	be	AUX
ejpam-2366	788	8	almost	almost	ADV
ejpam-2366	788	9	prime	prime	ADJ
ejpam-2366	788	10	if	if	SCONJ
ejpam-2366	789	1	and	and	CCONJ
ejpam-2366	789	2	only	only	ADV
ejpam-2366	789	3	if	if	SCONJ
ejpam-2366	789	4	n	n	PRON
ejpam-2366	789	5	is	be	AUX
ejpam-2366	789	6	weakly	weakly	ADV
ejpam-2366	789	7	prime	prime	ADJ
ejpam-2366	789	8	.	.	PUNCT
ejpam-2366	790	1	proof	proof	NOUN
ejpam-2366	790	2	.	.	PUNCT
ejpam-2366	791	1	assume	assume	VERB
ejpam-2366	791	2	that	that	SCONJ
ejpam-2366	791	3	a	a	DET
ejpam-2366	791	4	proper	proper	ADJ
ejpam-2366	791	5	element	element	NOUN
ejpam-2366	791	6	n	n	PRON
ejpam-2366	791	7	∈m	∈m	NOUN
ejpam-2366	791	8	is	be	AUX
ejpam-2366	791	9	almost	almost	ADV
ejpam-2366	791	10	prime	prime	ADJ
ejpam-2366	791	11	.	.	PUNCT
ejpam-2366	792	1	then	then	ADV
ejpam-2366	792	2	n	n	PROPN
ejpam-2366	792	3	6	6	NUM
ejpam-2366	792	4	q.	q.	NOUN
ejpam-2366	792	5	it	it	PRON
ejpam-2366	792	6	follows	follow	VERB
ejpam-2366	792	7	that	that	PRON
ejpam-2366	792	8	(	(	PUNCT
ejpam-2366	792	9	n	n	X
ejpam-2366	792	10	:	:	PUNCT
ejpam-2366	792	11	i	i	PRON
ejpam-2366	792	12	m	m	PROPN
ejpam-2366	792	13	)	)	PUNCT
ejpam-2366	792	14	n	n	PROPN
ejpam-2366	792	15	6	6	NUM
ejpam-2366	792	16	(	(	PUNCT
ejpam-2366	792	17	q	q	NOUN
ejpam-2366	792	18	:	:	PUNCT
ejpam-2366	792	19	i	i	PRON
ejpam-2366	792	20	m	m	VERB
ejpam-2366	792	21	)	)	PUNCT
ejpam-2366	792	22	q	q	NOUN
ejpam-2366	793	1	=	=	PUNCT
ejpam-2366	793	2	om	om	PROPN
ejpam-2366	793	3	and	and	CCONJ
ejpam-2366	793	4	hence	hence	ADV
ejpam-2366	793	5	(	(	PUNCT
ejpam-2366	793	6	n	n	X
ejpam-2366	793	7	:	:	PUNCT
ejpam-2366	793	8	i	i	PRON
ejpam-2366	793	9	m	m	VERB
ejpam-2366	793	10	)	)	PUNCT
ejpam-2366	794	1	n	n	PROPN
ejpam-2366	794	2	=	=	SYM
ejpam-2366	794	3	om	om	PROPN
ejpam-2366	794	4	.	.	PUNCT
ejpam-2366	795	1	let	let	VERB
ejpam-2366	795	2	om	om	PROPN
ejpam-2366	795	3	6=	6=	NOUN
ejpam-2366	795	4	aa	aa	PROPN
ejpam-2366	795	5	6	6	NUM
ejpam-2366	795	6	n	n	NOUN
ejpam-2366	795	7	for	for	ADP
ejpam-2366	795	8	a	a	DET
ejpam-2366	795	9	∈	∈	PROPN
ejpam-2366	795	10	l	l	NOUN
ejpam-2366	795	11	,	,	PUNCT
ejpam-2366	795	12	a	a	DET
ejpam-2366	795	13	∈	∈	NOUN
ejpam-2366	795	14	m	m	NOUN
ejpam-2366	795	15	.	.	PUNCT
ejpam-2366	796	1	as	as	SCONJ
ejpam-2366	796	2	aa	aa	PROPN
ejpam-2366	796	3	6	6	NUM
ejpam-2366	796	4	n	n	NOUN
ejpam-2366	796	5	,	,	PUNCT
ejpam-2366	796	6	aa	aa	INTJ
ejpam-2366	796	7	(	(	PUNCT
ejpam-2366	796	8	n	n	NOUN
ejpam-2366	796	9	:	:	PUNCT
ejpam-2366	796	10	i	i	PRON
ejpam-2366	796	11	m	m	VERB
ejpam-2366	796	12	)	)	PUNCT
ejpam-2366	796	13	n	n	NOUN
ejpam-2366	796	14	=	=	SYM
ejpam-2366	796	15	om	om	PROPN
ejpam-2366	796	16	and	and	CCONJ
ejpam-2366	796	17	n	n	PRON
ejpam-2366	796	18	is	be	AUX
ejpam-2366	796	19	almost	almost	ADV
ejpam-2366	796	20	prime	prime	ADJ
ejpam-2366	796	21	,	,	PUNCT
ejpam-2366	796	22	we	we	PRON
ejpam-2366	796	23	have	have	VERB
ejpam-2366	796	24	either	either	CCONJ
ejpam-2366	796	25	a	a	DET
ejpam-2366	796	26	6	6	NUM
ejpam-2366	796	27	n	n	NOUN
ejpam-2366	796	28	or	or	CCONJ
ejpam-2366	796	29	a	a	DET
ejpam-2366	796	30	6	6	NUM
ejpam-2366	796	31	(	(	PUNCT
ejpam-2366	796	32	n	n	NUM
ejpam-2366	796	33	:	:	PUNCT
ejpam-2366	796	34	i	i	PRON
ejpam-2366	796	35	m	m	PROPN
ejpam-2366	796	36	)	)	PUNCT
ejpam-2366	796	37	and	and	CCONJ
ejpam-2366	796	38	hence	hence	ADV
ejpam-2366	796	39	n	n	PRON
ejpam-2366	796	40	is	be	AUX
ejpam-2366	796	41	weakly	weakly	ADV
ejpam-2366	796	42	prime	prime	ADJ
ejpam-2366	796	43	.	.	PUNCT
ejpam-2366	797	1	the	the	DET
ejpam-2366	797	2	converse	converse	NOUN
ejpam-2366	797	3	is	be	AUX
ejpam-2366	797	4	obvious	obvious	ADJ
ejpam-2366	797	5	from	from	ADP
ejpam-2366	797	6	theorem	theorem	ADJ
ejpam-2366	797	7	3	3	NUM
ejpam-2366	797	8	.	.	PUNCT
ejpam-2366	798	1	the	the	DET
ejpam-2366	798	2	following	follow	VERB
ejpam-2366	798	3	result	result	NOUN
ejpam-2366	798	4	shows	show	VERB
ejpam-2366	798	5	that	that	SCONJ
ejpam-2366	798	6	if	if	SCONJ
ejpam-2366	798	7	an	an	DET
ejpam-2366	798	8	element	element	NOUN
ejpam-2366	798	9	in	in	ADP
ejpam-2366	798	10	m	m	PROPN
ejpam-2366	798	11	(	(	PUNCT
ejpam-2366	798	12	or	or	CCONJ
ejpam-2366	798	13	l	l	NOUN
ejpam-2366	798	14	)	)	PUNCT
ejpam-2366	798	15	is	be	AUX
ejpam-2366	798	16	almost	almost	ADV
ejpam-2366	798	17	prime	prime	ADJ
ejpam-2366	798	18	,	,	PUNCT
ejpam-2366	798	19	then	then	ADV
ejpam-2366	798	20	its	its	PRON
ejpam-2366	798	21	corresponding	corresponding	ADJ
ejpam-2366	798	22	element	element	NOUN
ejpam-2366	798	23	in	in	ADP
ejpam-2366	798	24	l	l	PROPN
ejpam-2366	798	25	(	(	PUNCT
ejpam-2366	798	26	or	or	CCONJ
ejpam-2366	798	27	m	m	VERB
ejpam-2366	798	28	)	)	PUNCT
ejpam-2366	798	29	is	be	AUX
ejpam-2366	798	30	also	also	ADV
ejpam-2366	798	31	almost	almost	ADV
ejpam-2366	798	32	prime	prime	ADJ
ejpam-2366	798	33	.	.	PUNCT
ejpam-2366	799	1	a.	a.	PROPN
ejpam-2366	799	2	v.	v.	PROPN
ejpam-2366	799	3	bingi	bingi	PROPN
ejpam-2366	799	4	,	,	PUNCT
ejpam-2366	799	5	c.	c.	PROPN
ejpam-2366	799	6	s.	s.	PROPN
ejpam-2366	799	7	manjarekar	manjarekar	PROPN
ejpam-2366	799	8	/	/	PROPN
ejpam-2366	799	9	eur	eur	PROPN
ejpam-2366	799	10	.	.	PUNCT
ejpam-2366	800	1	j.	j.	PROPN
ejpam-2366	800	2	pure	pure	PROPN
ejpam-2366	800	3	appl	appl	PROPN
ejpam-2366	800	4	.	.	PROPN
ejpam-2366	800	5	math	math	PROPN
ejpam-2366	800	6	,	,	PUNCT
ejpam-2366	800	7	14	14	NUM
ejpam-2366	800	8	(	(	PUNCT
ejpam-2366	800	9	2	2	NUM
ejpam-2366	800	10	)	)	PUNCT
ejpam-2366	800	11	(	(	PUNCT
ejpam-2366	800	12	2021	2021	NUM
ejpam-2366	800	13	)	)	PUNCT
ejpam-2366	800	14	,	,	PUNCT
ejpam-2366	800	15	551	551	NUM
ejpam-2366	800	16	-	-	SYM
ejpam-2366	800	17	577	577	NUM
ejpam-2366	800	18	572	572	NUM
ejpam-2366	800	19	theorem	theorem	VERB
ejpam-2366	800	20	45	45	NUM
ejpam-2366	800	21	.	.	PUNCT
ejpam-2366	801	1	let	let	VERB
ejpam-2366	801	2	l	l	NOUN
ejpam-2366	801	3	be	be	AUX
ejpam-2366	801	4	a	a	DET
ejpam-2366	801	5	pg	pg	NOUN
ejpam-2366	801	6	-	-	PUNCT
ejpam-2366	801	7	lattice	lattice	NOUN
ejpam-2366	801	8	and	and	CCONJ
ejpam-2366	801	9	m	m	AUX
ejpam-2366	801	10	be	be	AUX
ejpam-2366	801	11	a	a	DET
ejpam-2366	801	12	faithful	faithful	ADJ
ejpam-2366	801	13	multiplication	multiplication	NOUN
ejpam-2366	801	14	torsion	torsion	NOUN
ejpam-2366	801	15	free	free	ADJ
ejpam-2366	801	16	pglattice	pglattice	NOUN
ejpam-2366	801	17	l	l	NOUN
ejpam-2366	801	18	-	-	NOUN
ejpam-2366	801	19	module	module	NOUN
ejpam-2366	801	20	with	with	ADP
ejpam-2366	801	21	i	i	PRON
ejpam-2366	801	22	m	m	VERB
ejpam-2366	801	23	compact	compact	ADJ
ejpam-2366	801	24	.	.	PUNCT
ejpam-2366	802	1	let	let	VERB
ejpam-2366	802	2	i	i	PRON
ejpam-2366	802	3	m	m	AUX
ejpam-2366	802	4	be	be	AUX
ejpam-2366	802	5	a	a	DET
ejpam-2366	802	6	weak	weak	ADJ
ejpam-2366	802	7	join	join	NOUN
ejpam-2366	802	8	principal	principal	ADJ
ejpam-2366	802	9	element	element	NOUN
ejpam-2366	802	10	and	and	CCONJ
ejpam-2366	802	11	n	n	CCONJ
ejpam-2366	802	12	be	be	VERB
ejpam-2366	802	13	a	a	DET
ejpam-2366	802	14	proper	proper	ADJ
ejpam-2366	802	15	element	element	NOUN
ejpam-2366	802	16	of	of	ADP
ejpam-2366	802	17	m	m	PROPN
ejpam-2366	802	18	.	.	PUNCT
ejpam-2366	803	1	then	then	ADV
ejpam-2366	803	2	the	the	DET
ejpam-2366	803	3	following	follow	VERB
ejpam-2366	803	4	statements	statement	NOUN
ejpam-2366	803	5	are	be	AUX
ejpam-2366	803	6	equivalent	equivalent	ADJ
ejpam-2366	803	7	:	:	PUNCT
ejpam-2366	803	8	1	1	X
ejpam-2366	803	9	©	©	NOUN
ejpam-2366	803	10	n	n	NUM
ejpam-2366	803	11	is	be	AUX
ejpam-2366	803	12	an	an	DET
ejpam-2366	803	13	almost	almost	ADV
ejpam-2366	803	14	prime	prime	ADJ
ejpam-2366	803	15	element	element	NOUN
ejpam-2366	803	16	of	of	ADP
ejpam-2366	803	17	m	m	PROPN
ejpam-2366	803	18	.	.	PUNCT
ejpam-2366	804	1	2	2	NUM
ejpam-2366	804	2	©	©	NOUN
ejpam-2366	804	3	(	(	PUNCT
ejpam-2366	804	4	n	n	NOUN
ejpam-2366	804	5	:	:	PUNCT
ejpam-2366	804	6	i	i	PRON
ejpam-2366	804	7	m	m	PROPN
ejpam-2366	804	8	)	)	PUNCT
ejpam-2366	804	9	is	be	AUX
ejpam-2366	804	10	an	an	DET
ejpam-2366	804	11	almost	almost	ADV
ejpam-2366	804	12	prime	prime	ADJ
ejpam-2366	804	13	element	element	NOUN
ejpam-2366	804	14	of	of	ADP
ejpam-2366	804	15	l.	l.	PROPN
ejpam-2366	804	16	3	3	NUM
ejpam-2366	804	17	©	©	PROPN
ejpam-2366	804	18	n	n	NOUN
ejpam-2366	804	19	=	=	X
ejpam-2366	804	20	qim	qim	NOUN
ejpam-2366	804	21	for	for	ADP
ejpam-2366	804	22	some	some	DET
ejpam-2366	804	23	almost	almost	ADV
ejpam-2366	804	24	prime	prime	ADJ
ejpam-2366	804	25	element	element	NOUN
ejpam-2366	804	26	q	q	PROPN
ejpam-2366	804	27	∈	∈	PROPN
ejpam-2366	804	28	l	l	NOUN
ejpam-2366	804	29	which	which	PRON
ejpam-2366	804	30	is	be	AUX
ejpam-2366	804	31	maximal	maximal	ADJ
ejpam-2366	804	32	in	in	ADP
ejpam-2366	804	33	the	the	DET
ejpam-2366	804	34	sense	sense	NOUN
ejpam-2366	804	35	that	that	SCONJ
ejpam-2366	804	36	if	if	SCONJ
ejpam-2366	804	37	aim	aim	VERB
ejpam-2366	804	38	=	=	SYM
ejpam-2366	804	39	n	n	CCONJ
ejpam-2366	804	40	,	,	PUNCT
ejpam-2366	804	41	then	then	ADV
ejpam-2366	804	42	a	a	DET
ejpam-2366	804	43	6	6	NUM
ejpam-2366	804	44	q	q	NOUN
ejpam-2366	804	45	where	where	SCONJ
ejpam-2366	804	46	a	a	DET
ejpam-2366	804	47	∈	∈	PROPN
ejpam-2366	804	48	l.	l.	NOUN
ejpam-2366	804	49	proof	proof	NOUN
ejpam-2366	804	50	.	.	PUNCT
ejpam-2366	805	1	1	1	NUM
ejpam-2366	805	2	©	©	NOUN
ejpam-2366	805	3	=⇒	=⇒	NOUN
ejpam-2366	805	4	2	2	NUM
ejpam-2366	805	5	©	©	NOUN
ejpam-2366	805	6	.	.	PUNCT
ejpam-2366	805	7	assume	assume	VERB
ejpam-2366	805	8	that	that	SCONJ
ejpam-2366	805	9	n	n	PRON
ejpam-2366	805	10	is	be	AUX
ejpam-2366	805	11	an	an	DET
ejpam-2366	805	12	almost	almost	ADV
ejpam-2366	805	13	prime	prime	ADJ
ejpam-2366	805	14	element	element	NOUN
ejpam-2366	805	15	of	of	ADP
ejpam-2366	805	16	m	m	PROPN
ejpam-2366	805	17	.	.	PUNCT
ejpam-2366	806	1	let	let	VERB
ejpam-2366	806	2	ab	ab	PROPN
ejpam-2366	806	3	6	6	NUM
ejpam-2366	806	4	(	(	PUNCT
ejpam-2366	806	5	n	n	NUM
ejpam-2366	806	6	:	:	PUNCT
ejpam-2366	806	7	i	i	PRON
ejpam-2366	806	8	m	m	PROPN
ejpam-2366	806	9	)	)	PUNCT
ejpam-2366	806	10	and	and	CCONJ
ejpam-2366	806	11	ab	ab	PROPN
ejpam-2366	806	12	(	(	PUNCT
ejpam-2366	806	13	n	n	PROPN
ejpam-2366	806	14	:	:	PUNCT
ejpam-2366	806	15	i	i	PRON
ejpam-2366	806	16	m	m	VERB
ejpam-2366	806	17	)	)	PUNCT
ejpam-2366	806	18	2	2	NUM
ejpam-2366	806	19	for	for	ADP
ejpam-2366	806	20	a	a	DET
ejpam-2366	806	21	,	,	PUNCT
ejpam-2366	806	22	b	b	PROPN
ejpam-2366	806	23	∈	∈	PROPN
ejpam-2366	806	24	l.	l.	NOUN
ejpam-2366	806	25	then	then	ADV
ejpam-2366	806	26	abim	abim	PROPN
ejpam-2366	806	27	6	6	NUM
ejpam-2366	806	28	n	n	NOUN
ejpam-2366	806	29	.	.	PUNCT
ejpam-2366	807	1	if	if	SCONJ
ejpam-2366	807	2	abim	abim	NOUN
ejpam-2366	807	3	6	6	NUM
ejpam-2366	807	4	(	(	PUNCT
ejpam-2366	807	5	n	n	NUM
ejpam-2366	807	6	:	:	PUNCT
ejpam-2366	807	7	i	i	PRON
ejpam-2366	807	8	m	m	PROPN
ejpam-2366	807	9	)	)	PUNCT
ejpam-2366	807	10	n	n	CCONJ
ejpam-2366	807	11	,	,	PUNCT
ejpam-2366	807	12	then	then	ADV
ejpam-2366	807	13	by	by	ADP
ejpam-2366	807	14	lemma	lemma	PROPN
ejpam-2366	807	15	4	4	NUM
ejpam-2366	807	16	,	,	PUNCT
ejpam-2366	807	17	we	we	PRON
ejpam-2366	807	18	have	have	VERB
ejpam-2366	807	19	ab	ab	PROPN
ejpam-2366	807	20	6	6	NUM
ejpam-2366	807	21	(	(	PUNCT
ejpam-2366	807	22	(	(	PUNCT
ejpam-2366	807	23	n	n	X
ejpam-2366	807	24	:	:	PUNCT
ejpam-2366	807	25	i	i	PRON
ejpam-2366	807	26	m	m	PROPN
ejpam-2366	807	27	)	)	PUNCT
ejpam-2366	807	28	n	n	CCONJ
ejpam-2366	807	29	:	:	PUNCT
ejpam-2366	808	1	i	i	PRON
ejpam-2366	808	2	m	m	VERB
ejpam-2366	808	3	)	)	PUNCT
ejpam-2366	809	1	=	=	SYM
ejpam-2366	809	2	(	(	PUNCT
ejpam-2366	809	3	n	n	X
ejpam-2366	809	4	:	:	PUNCT
ejpam-2366	809	5	i	i	PRON
ejpam-2366	809	6	m	m	VERB
ejpam-2366	809	7	)	)	PUNCT
ejpam-2366	809	8	(	(	PUNCT
ejpam-2366	809	9	n	n	X
ejpam-2366	809	10	:	:	PUNCT
ejpam-2366	809	11	i	i	PRON
ejpam-2366	809	12	m	m	VERB
ejpam-2366	809	13	)	)	PUNCT
ejpam-2366	809	14	which	which	PRON
ejpam-2366	809	15	contradicts	contradict	VERB
ejpam-2366	809	16	ab	ab	PROPN
ejpam-2366	809	17	(	(	PUNCT
ejpam-2366	809	18	n	n	PROPN
ejpam-2366	809	19	:	:	PUNCT
ejpam-2366	809	20	i	i	PRON
ejpam-2366	809	21	m	m	VERB
ejpam-2366	809	22	)	)	PUNCT
ejpam-2366	809	23	2	2	X
ejpam-2366	809	24	.	.	PUNCT
ejpam-2366	810	1	so	so	ADV
ejpam-2366	810	2	let	let	VERB
ejpam-2366	810	3	a(bim	a(bim	PROPN
ejpam-2366	810	4	)	)	PUNCT
ejpam-2366	811	1	(	(	PUNCT
ejpam-2366	811	2	n	n	X
ejpam-2366	811	3	:	:	PUNCT
ejpam-2366	811	4	i	i	PRON
ejpam-2366	811	5	m	m	PROPN
ejpam-2366	811	6	)	)	PUNCT
ejpam-2366	811	7	n	n	PROPN
ejpam-2366	811	8	.	.	PUNCT
ejpam-2366	812	1	then	then	ADV
ejpam-2366	812	2	as	as	SCONJ
ejpam-2366	812	3	n	n	PRON
ejpam-2366	812	4	is	be	AUX
ejpam-2366	812	5	almost	almost	ADV
ejpam-2366	812	6	prime	prime	ADJ
ejpam-2366	812	7	,	,	PUNCT
ejpam-2366	812	8	we	we	PRON
ejpam-2366	812	9	have	have	VERB
ejpam-2366	812	10	either	either	CCONJ
ejpam-2366	812	11	a	a	DET
ejpam-2366	812	12	6	6	NUM
ejpam-2366	812	13	(	(	PUNCT
ejpam-2366	812	14	n	n	NUM
ejpam-2366	812	15	:	:	PUNCT
ejpam-2366	812	16	i	i	PRON
ejpam-2366	812	17	m	m	VERB
ejpam-2366	812	18	)	)	PUNCT
ejpam-2366	812	19	or	or	CCONJ
ejpam-2366	812	20	bim	bim	VERB
ejpam-2366	812	21	6	6	NUM
ejpam-2366	812	22	n	n	NOUN
ejpam-2366	812	23	and	and	CCONJ
ejpam-2366	812	24	thus	thus	ADV
ejpam-2366	812	25	(	(	PUNCT
ejpam-2366	812	26	n	n	X
ejpam-2366	812	27	:	:	PUNCT
ejpam-2366	812	28	i	i	PRON
ejpam-2366	812	29	m	m	PROPN
ejpam-2366	812	30	)	)	PUNCT
ejpam-2366	812	31	is	be	AUX
ejpam-2366	812	32	an	an	DET
ejpam-2366	812	33	almost	almost	ADV
ejpam-2366	812	34	prime	prime	ADJ
ejpam-2366	812	35	element	element	NOUN
ejpam-2366	812	36	of	of	ADP
ejpam-2366	812	37	l.	l.	PROPN
ejpam-2366	812	38	2	2	NUM
ejpam-2366	812	39	©	©	PROPN
ejpam-2366	812	40	=⇒	=⇒	NOUN
ejpam-2366	812	41	3	3	NUM
ejpam-2366	812	42	©	©	PROPN
ejpam-2366	812	43	.	.	PUNCT
ejpam-2366	813	1	assume	assume	VERB
ejpam-2366	813	2	that	that	SCONJ
ejpam-2366	813	3	(	(	PUNCT
ejpam-2366	813	4	n	n	X
ejpam-2366	813	5	:	:	PUNCT
ejpam-2366	813	6	i	i	PRON
ejpam-2366	813	7	m	m	VERB
ejpam-2366	813	8	)	)	PUNCT
ejpam-2366	814	1	=	=	PRON
ejpam-2366	814	2	q	q	X
ejpam-2366	814	3	is	be	AUX
ejpam-2366	814	4	an	an	DET
ejpam-2366	814	5	almost	almost	ADV
ejpam-2366	814	6	prime	prime	ADJ
ejpam-2366	814	7	element	element	NOUN
ejpam-2366	814	8	of	of	ADP
ejpam-2366	814	9	l.	l.	PROPN
ejpam-2366	814	10	then	then	ADV
ejpam-2366	814	11	qim	qim	PROPN
ejpam-2366	814	12	6	6	NUM
ejpam-2366	814	13	n	n	NOUN
ejpam-2366	814	14	.	.	PUNCT
ejpam-2366	815	1	since	since	SCONJ
ejpam-2366	815	2	m	m	PROPN
ejpam-2366	815	3	is	be	AUX
ejpam-2366	815	4	a	a	DET
ejpam-2366	815	5	multiplication	multiplication	NOUN
ejpam-2366	815	6	lattice	lattice	NOUN
ejpam-2366	815	7	module	module	NOUN
ejpam-2366	815	8	,	,	PUNCT
ejpam-2366	815	9	n	n	NOUN
ejpam-2366	815	10	=	=	PRON
ejpam-2366	815	11	aim	aim	VERB
ejpam-2366	815	12	for	for	ADP
ejpam-2366	815	13	some	some	DET
ejpam-2366	815	14	a	a	DET
ejpam-2366	815	15	∈	∈	NOUN
ejpam-2366	815	16	l.	l.	NOUN
ejpam-2366	815	17	so	so	SCONJ
ejpam-2366	815	18	a	a	DET
ejpam-2366	815	19	6	6	NUM
ejpam-2366	815	20	(	(	PUNCT
ejpam-2366	815	21	n	n	NUM
ejpam-2366	815	22	:	:	PUNCT
ejpam-2366	815	23	i	i	PRON
ejpam-2366	815	24	m	m	VERB
ejpam-2366	815	25	)	)	PUNCT
ejpam-2366	816	1	=	=	SYM
ejpam-2366	816	2	q	q	X
ejpam-2366	816	3	and	and	CCONJ
ejpam-2366	816	4	thus	thus	ADV
ejpam-2366	816	5	n	n	CCONJ
ejpam-2366	816	6	=	=	PRON
ejpam-2366	816	7	aim	aim	VERB
ejpam-2366	816	8	6	6	NUM
ejpam-2366	816	9	qim	qim	NOUN
ejpam-2366	816	10	.	.	PUNCT
ejpam-2366	817	1	hence	hence	ADV
ejpam-2366	817	2	n	n	NOUN
ejpam-2366	817	3	=	=	PUNCT
ejpam-2366	817	4	qim	qim	NOUN
ejpam-2366	817	5	for	for	ADP
ejpam-2366	817	6	some	some	DET
ejpam-2366	817	7	almost	almost	ADV
ejpam-2366	817	8	prime	prime	ADJ
ejpam-2366	817	9	element	element	NOUN
ejpam-2366	817	10	q	q	PROPN
ejpam-2366	817	11	∈	∈	PROPN
ejpam-2366	817	12	l	l	NOUN
ejpam-2366	817	13	which	which	PRON
ejpam-2366	817	14	is	be	AUX
ejpam-2366	817	15	maximal	maximal	ADJ
ejpam-2366	817	16	in	in	ADP
ejpam-2366	817	17	the	the	DET
ejpam-2366	817	18	sense	sense	NOUN
ejpam-2366	818	1	that	that	SCONJ
ejpam-2366	818	2	if	if	SCONJ
ejpam-2366	818	3	aim	aim	VERB
ejpam-2366	818	4	=	=	SYM
ejpam-2366	818	5	n	n	CCONJ
ejpam-2366	818	6	,	,	PUNCT
ejpam-2366	818	7	then	then	ADV
ejpam-2366	818	8	a	a	DET
ejpam-2366	818	9	6	6	NUM
ejpam-2366	818	10	q.	q.	NOUN
ejpam-2366	818	11	3	3	NUM
ejpam-2366	818	12	©	©	NOUN
ejpam-2366	818	13	=⇒	=⇒	NOUN
ejpam-2366	818	14	1	1	NUM
ejpam-2366	818	15	©	©	NOUN
ejpam-2366	818	16	.	.	PUNCT
ejpam-2366	818	17	suppose	suppose	VERB
ejpam-2366	818	18	n	n	PROPN
ejpam-2366	818	19	=	=	PUNCT
ejpam-2366	818	20	qim	qim	NOUN
ejpam-2366	818	21	for	for	ADP
ejpam-2366	818	22	some	some	DET
ejpam-2366	818	23	almost	almost	ADV
ejpam-2366	818	24	prime	prime	ADJ
ejpam-2366	818	25	element	element	NOUN
ejpam-2366	818	26	q	q	PROPN
ejpam-2366	818	27	∈	∈	PROPN
ejpam-2366	818	28	l	l	NOUN
ejpam-2366	818	29	which	which	PRON
ejpam-2366	818	30	is	be	AUX
ejpam-2366	818	31	maximal	maximal	ADJ
ejpam-2366	818	32	in	in	ADP
ejpam-2366	818	33	the	the	DET
ejpam-2366	818	34	sense	sense	NOUN
ejpam-2366	818	35	that	that	SCONJ
ejpam-2366	818	36	if	if	SCONJ
ejpam-2366	818	37	aim	aim	VERB
ejpam-2366	818	38	=	=	SYM
ejpam-2366	818	39	n	n	CCONJ
ejpam-2366	818	40	,	,	PUNCT
ejpam-2366	818	41	then	then	ADV
ejpam-2366	818	42	a	a	DET
ejpam-2366	818	43	6	6	NUM
ejpam-2366	818	44	q	q	NOUN
ejpam-2366	818	45	where	where	SCONJ
ejpam-2366	818	46	a	a	DET
ejpam-2366	818	47	∈	∈	PROPN
ejpam-2366	818	48	l.	l.	NOUN
ejpam-2366	818	49	then	then	ADV
ejpam-2366	818	50	q	q	PROPN
ejpam-2366	818	51	6	6	NUM
ejpam-2366	818	52	(	(	PUNCT
ejpam-2366	818	53	n	n	NUM
ejpam-2366	818	54	:	:	PUNCT
ejpam-2366	818	55	i	i	PRON
ejpam-2366	818	56	m	m	PROPN
ejpam-2366	818	57	)	)	PUNCT
ejpam-2366	818	58	.	.	PUNCT
ejpam-2366	819	1	now	now	ADV
ejpam-2366	819	2	,	,	PUNCT
ejpam-2366	819	3	let	let	VERB
ejpam-2366	819	4	rx	rx	VERB
ejpam-2366	819	5	6	6	NUM
ejpam-2366	819	6	n	n	NOUN
ejpam-2366	819	7	,	,	PUNCT
ejpam-2366	819	8	rx	rx	VERB
ejpam-2366	819	9	(	(	PUNCT
ejpam-2366	819	10	n	n	X
ejpam-2366	819	11	:	:	PUNCT
ejpam-2366	819	12	i	i	PRON
ejpam-2366	819	13	m	m	PROPN
ejpam-2366	819	14	)	)	PUNCT
ejpam-2366	819	15	n	n	PROPN
ejpam-2366	819	16	and	and	CCONJ
ejpam-2366	819	17	x	x	SYM
ejpam-2366	819	18	n	n	PROPN
ejpam-2366	819	19	for	for	ADP
ejpam-2366	819	20	r	r	PROPN
ejpam-2366	819	21	∈	∈	PROPN
ejpam-2366	819	22	l	l	NOUN
ejpam-2366	819	23	,	,	PUNCT
ejpam-2366	819	24	x	x	SYM
ejpam-2366	819	25	∈	∈	PROPN
ejpam-2366	819	26	m	m	VERB
ejpam-2366	819	27	.	.	PUNCT
ejpam-2366	820	1	since	since	SCONJ
ejpam-2366	820	2	m	m	PROPN
ejpam-2366	820	3	is	be	AUX
ejpam-2366	820	4	a	a	DET
ejpam-2366	820	5	multiplication	multiplication	NOUN
ejpam-2366	820	6	lattice	lattice	NOUN
ejpam-2366	820	7	module	module	NOUN
ejpam-2366	820	8	,	,	PUNCT
ejpam-2366	820	9	x	x	SYM
ejpam-2366	820	10	=	=	SYM
ejpam-2366	820	11	cim	cim	NOUN
ejpam-2366	820	12	for	for	ADP
ejpam-2366	820	13	some	some	DET
ejpam-2366	820	14	c	c	PROPN
ejpam-2366	820	15	∈	∈	PROPN
ejpam-2366	820	16	l.	l.	PROPN
ejpam-2366	820	17	then	then	ADV
ejpam-2366	820	18	rc	rc	PROPN
ejpam-2366	820	19	6	6	NUM
ejpam-2366	820	20	(	(	PUNCT
ejpam-2366	820	21	n	n	NUM
ejpam-2366	820	22	:	:	PUNCT
ejpam-2366	820	23	i	i	PRON
ejpam-2366	820	24	m	m	VERB
ejpam-2366	820	25	)	)	PUNCT
ejpam-2366	820	26	6	6	NUM
ejpam-2366	820	27	q	q	NOUN
ejpam-2366	820	28	,	,	PUNCT
ejpam-2366	820	29	using	use	VERB
ejpam-2366	820	30	maximality	maximality	NOUN
ejpam-2366	820	31	of	of	ADP
ejpam-2366	820	32	q	q	NOUN
ejpam-2366	820	33	to	to	ADP
ejpam-2366	820	34	n	n	NOUN
ejpam-2366	820	35	=	=	SYM
ejpam-2366	820	36	(	(	PUNCT
ejpam-2366	820	37	n	n	X
ejpam-2366	820	38	:	:	PUNCT
ejpam-2366	820	39	i	i	PRON
ejpam-2366	820	40	m	m	VERB
ejpam-2366	820	41	)	)	PUNCT
ejpam-2366	821	1	i	i	PRON
ejpam-2366	821	2	m	m	VERB
ejpam-2366	821	3	(	(	PUNCT
ejpam-2366	821	4	by	by	ADP
ejpam-2366	821	5	proposition	proposition	NOUN
ejpam-2366	821	6	3	3	NUM
ejpam-2366	821	7	of	of	ADP
ejpam-2366	821	8	[	[	X
ejpam-2366	821	9	10	10	NUM
ejpam-2366	821	10	]	]	NUM
ejpam-2366	821	11	)	)	PUNCT
ejpam-2366	821	12	.	.	PUNCT
ejpam-2366	822	1	if	if	SCONJ
ejpam-2366	822	2	rc	rc	PROPN
ejpam-2366	822	3	6	6	NUM
ejpam-2366	822	4	q2	q2	NOUN
ejpam-2366	822	5	,	,	PUNCT
ejpam-2366	822	6	then	then	ADV
ejpam-2366	822	7	rx	rx	VERB
ejpam-2366	822	8	6	6	NUM
ejpam-2366	822	9	qn	qn	NOUN
ejpam-2366	822	10	6	6	NUM
ejpam-2366	822	11	(	(	PUNCT
ejpam-2366	822	12	n	n	NUM
ejpam-2366	822	13	:	:	PUNCT
ejpam-2366	822	14	i	i	PRON
ejpam-2366	822	15	m	m	PROPN
ejpam-2366	822	16	)	)	PUNCT
ejpam-2366	822	17	n	n	CCONJ
ejpam-2366	822	18	,	,	PUNCT
ejpam-2366	822	19	a	a	DET
ejpam-2366	822	20	contradiction	contradiction	NOUN
ejpam-2366	822	21	.	.	PUNCT
ejpam-2366	823	1	so	so	ADV
ejpam-2366	823	2	rc	rc	PROPN
ejpam-2366	823	3	q2	q2	PROPN
ejpam-2366	823	4	.	.	PUNCT
ejpam-2366	824	1	also	also	ADV
ejpam-2366	824	2	,	,	PUNCT
ejpam-2366	824	3	c	c	NOUN
ejpam-2366	824	4	q	q	NOUN
ejpam-2366	824	5	because	because	SCONJ
ejpam-2366	824	6	if	if	SCONJ
ejpam-2366	824	7	c	c	PROPN
ejpam-2366	824	8	6	6	NUM
ejpam-2366	824	9	q	q	NOUN
ejpam-2366	824	10	,	,	PUNCT
ejpam-2366	824	11	then	then	ADV
ejpam-2366	824	12	x	x	SYM
ejpam-2366	824	13	6	6	NUM
ejpam-2366	824	14	n	n	NOUN
ejpam-2366	824	15	,	,	PUNCT
ejpam-2366	824	16	a	a	DET
ejpam-2366	824	17	contradiction	contradiction	NOUN
ejpam-2366	824	18	.	.	PUNCT
ejpam-2366	825	1	now	now	ADV
ejpam-2366	825	2	,	,	PUNCT
ejpam-2366	825	3	as	as	SCONJ
ejpam-2366	825	4	rc	rc	PROPN
ejpam-2366	825	5	6	6	NUM
ejpam-2366	825	6	q	q	PROPN
ejpam-2366	825	7	,	,	PUNCT
ejpam-2366	825	8	rc	rc	PROPN
ejpam-2366	825	9	q2	q2	PROPN
ejpam-2366	825	10	,	,	PUNCT
ejpam-2366	825	11	c	c	PROPN
ejpam-2366	825	12	q	q	NOUN
ejpam-2366	825	13	and	and	CCONJ
ejpam-2366	825	14	q	q	NOUN
ejpam-2366	825	15	is	be	AUX
ejpam-2366	825	16	almost	almost	ADV
ejpam-2366	825	17	prime	prime	ADJ
ejpam-2366	825	18	,	,	PUNCT
ejpam-2366	825	19	we	we	PRON
ejpam-2366	825	20	have	have	VERB
ejpam-2366	825	21	,	,	PUNCT
ejpam-2366	825	22	r	r	NOUN
ejpam-2366	825	23	6	6	NUM
ejpam-2366	825	24	q	q	NOUN
ejpam-2366	825	25	which	which	PRON
ejpam-2366	825	26	implies	imply	VERB
ejpam-2366	825	27	r	r	NOUN
ejpam-2366	825	28	6	6	NUM
ejpam-2366	825	29	(	(	PUNCT
ejpam-2366	825	30	n	n	NUM
ejpam-2366	825	31	:	:	PUNCT
ejpam-2366	825	32	i	i	PRON
ejpam-2366	825	33	m	m	PROPN
ejpam-2366	825	34	)	)	PUNCT
ejpam-2366	825	35	and	and	CCONJ
ejpam-2366	825	36	hence	hence	ADV
ejpam-2366	825	37	n	n	X
ejpam-2366	825	38	is	be	AUX
ejpam-2366	825	39	almost	almost	ADV
ejpam-2366	825	40	prime	prime	ADJ
ejpam-2366	825	41	theorem	theorem	NOUN
ejpam-2366	825	42	46	46	NUM
ejpam-2366	825	43	.	.	PUNCT
ejpam-2366	826	1	let	let	VERB
ejpam-2366	826	2	l	l	NOUN
ejpam-2366	826	3	be	be	AUX
ejpam-2366	826	4	a	a	DET
ejpam-2366	826	5	pg	pg	NOUN
ejpam-2366	826	6	-	-	PUNCT
ejpam-2366	826	7	lattice	lattice	NOUN
ejpam-2366	826	8	and	and	CCONJ
ejpam-2366	826	9	m	m	AUX
ejpam-2366	826	10	be	be	AUX
ejpam-2366	826	11	a	a	DET
ejpam-2366	826	12	faithful	faithful	ADJ
ejpam-2366	826	13	multiplication	multiplication	NOUN
ejpam-2366	826	14	torsion	torsion	NOUN
ejpam-2366	826	15	free	free	ADJ
ejpam-2366	826	16	pglattice	pglattice	NOUN
ejpam-2366	826	17	l	l	NOUN
ejpam-2366	826	18	-	-	NOUN
ejpam-2366	826	19	module	module	NOUN
ejpam-2366	826	20	with	with	ADP
ejpam-2366	826	21	i	i	PRON
ejpam-2366	826	22	m	m	VERB
ejpam-2366	826	23	compact	compact	ADJ
ejpam-2366	826	24	.	.	PUNCT
ejpam-2366	827	1	let	let	VERB
ejpam-2366	827	2	i	i	PRON
ejpam-2366	827	3	m	m	AUX
ejpam-2366	827	4	be	be	AUX
ejpam-2366	827	5	a	a	DET
ejpam-2366	827	6	weak	weak	ADJ
ejpam-2366	827	7	join	join	NOUN
ejpam-2366	827	8	principal	principal	ADJ
ejpam-2366	827	9	element	element	NOUN
ejpam-2366	827	10	and	and	CCONJ
ejpam-2366	827	11	n	n	CCONJ
ejpam-2366	827	12	be	be	VERB
ejpam-2366	827	13	a	a	DET
ejpam-2366	827	14	proper	proper	ADJ
ejpam-2366	827	15	element	element	NOUN
ejpam-2366	827	16	of	of	ADP
ejpam-2366	827	17	m	m	PROPN
ejpam-2366	827	18	.	.	PUNCT
ejpam-2366	828	1	then	then	ADV
ejpam-2366	828	2	the	the	DET
ejpam-2366	828	3	following	follow	VERB
ejpam-2366	828	4	statements	statement	NOUN
ejpam-2366	828	5	are	be	AUX
ejpam-2366	828	6	equivalent	equivalent	ADJ
ejpam-2366	828	7	:	:	PUNCT
ejpam-2366	828	8	1	1	X
ejpam-2366	828	9	©	©	NOUN
ejpam-2366	828	10	n	n	NUM
ejpam-2366	828	11	is	be	AUX
ejpam-2366	828	12	an	an	DET
ejpam-2366	828	13	almost	almost	ADV
ejpam-2366	828	14	prime	prime	ADJ
ejpam-2366	828	15	element	element	NOUN
ejpam-2366	828	16	of	of	ADP
ejpam-2366	828	17	m	m	PROPN
ejpam-2366	828	18	.	.	PUNCT
ejpam-2366	829	1	2	2	NUM
ejpam-2366	829	2	©	©	NOUN
ejpam-2366	829	3	(	(	PUNCT
ejpam-2366	829	4	n	n	NOUN
ejpam-2366	829	5	:	:	PUNCT
ejpam-2366	829	6	i	i	PRON
ejpam-2366	829	7	m	m	PROPN
ejpam-2366	829	8	)	)	PUNCT
ejpam-2366	829	9	is	be	AUX
ejpam-2366	829	10	an	an	DET
ejpam-2366	829	11	almost	almost	ADV
ejpam-2366	829	12	prime	prime	ADJ
ejpam-2366	829	13	element	element	NOUN
ejpam-2366	829	14	of	of	ADP
ejpam-2366	829	15	l.	l.	PROPN
ejpam-2366	829	16	3	3	NUM
ejpam-2366	829	17	©	©	PROPN
ejpam-2366	829	18	n	n	NOUN
ejpam-2366	829	19	=	=	X
ejpam-2366	829	20	qim	qim	NOUN
ejpam-2366	829	21	for	for	ADP
ejpam-2366	829	22	some	some	DET
ejpam-2366	829	23	almost	almost	ADV
ejpam-2366	829	24	prime	prime	ADJ
ejpam-2366	829	25	element	element	NOUN
ejpam-2366	829	26	q	q	PROPN
ejpam-2366	829	27	∈	∈	PROPN
ejpam-2366	829	28	l.	l.	NOUN
ejpam-2366	829	29	proof	proof	NOUN
ejpam-2366	829	30	.	.	PUNCT
ejpam-2366	830	1	1	1	NUM
ejpam-2366	830	2	©	©	NOUN
ejpam-2366	830	3	=⇒	=⇒	NOUN
ejpam-2366	830	4	2	2	NUM
ejpam-2366	830	5	©	©	NOUN
ejpam-2366	830	6	follows	follow	VERB
ejpam-2366	830	7	from	from	ADP
ejpam-2366	830	8	1	1	NUM
ejpam-2366	830	9	©	©	NOUN
ejpam-2366	830	10	=⇒	=⇒	NOUN
ejpam-2366	830	11	2	2	NUM
ejpam-2366	830	12	©	©	NOUN
ejpam-2366	830	13	in	in	ADP
ejpam-2366	830	14	the	the	DET
ejpam-2366	830	15	proof	proof	NOUN
ejpam-2366	830	16	of	of	ADP
ejpam-2366	830	17	theorem	theorem	ADJ
ejpam-2366	830	18	45	45	NUM
ejpam-2366	830	19	.	.	NOUN
ejpam-2366	831	1	2	2	NUM
ejpam-2366	831	2	©	©	NOUN
ejpam-2366	831	3	=⇒	=⇒	NOUN
ejpam-2366	831	4	1	1	NUM
ejpam-2366	831	5	©	©	PROPN
ejpam-2366	831	6	.	.	PUNCT
ejpam-2366	831	7	assume	assume	VERB
ejpam-2366	831	8	that	that	SCONJ
ejpam-2366	831	9	(	(	PUNCT
ejpam-2366	831	10	n	n	X
ejpam-2366	831	11	:	:	PUNCT
ejpam-2366	831	12	i	i	PRON
ejpam-2366	831	13	m	m	PROPN
ejpam-2366	831	14	)	)	PUNCT
ejpam-2366	831	15	is	be	AUX
ejpam-2366	831	16	an	an	DET
ejpam-2366	831	17	almost	almost	ADV
ejpam-2366	831	18	prime	prime	ADJ
ejpam-2366	831	19	element	element	NOUN
ejpam-2366	831	20	of	of	ADP
ejpam-2366	831	21	l.	l.	PROPN
ejpam-2366	831	22	let	let	AUX
ejpam-2366	831	23	rq	rq	VERB
ejpam-2366	831	24	6	6	NUM
ejpam-2366	831	25	n	n	NOUN
ejpam-2366	831	26	and	and	CCONJ
ejpam-2366	831	27	rq	rq	X
ejpam-2366	831	28	(	(	PUNCT
ejpam-2366	831	29	n	n	X
ejpam-2366	831	30	:	:	PUNCT
ejpam-2366	831	31	i	i	PRON
ejpam-2366	831	32	m	m	PROPN
ejpam-2366	831	33	)	)	PUNCT
ejpam-2366	831	34	n	n	PROPN
ejpam-2366	831	35	for	for	ADP
ejpam-2366	831	36	r	r	PROPN
ejpam-2366	831	37	∈	∈	PROPN
ejpam-2366	831	38	l	l	NOUN
ejpam-2366	831	39	,	,	PUNCT
ejpam-2366	831	40	q	q	PRON
ejpam-2366	831	41	∈m	∈m	NOUN
ejpam-2366	831	42	.	.	PUNCT
ejpam-2366	832	1	then	then	ADV
ejpam-2366	832	2	(	(	PUNCT
ejpam-2366	832	3	rq	rq	INTJ
ejpam-2366	832	4	:	:	PUNCT
ejpam-2366	832	5	i	i	PRON
ejpam-2366	832	6	m	m	VERB
ejpam-2366	832	7	)	)	PUNCT
ejpam-2366	832	8	6	6	NUM
ejpam-2366	832	9	(	(	PUNCT
ejpam-2366	832	10	n	n	NUM
ejpam-2366	832	11	:	:	PUNCT
ejpam-2366	832	12	i	i	PRON
ejpam-2366	832	13	m	m	PROPN
ejpam-2366	832	14	)	)	PUNCT
ejpam-2366	832	15	and	and	CCONJ
ejpam-2366	832	16	so	so	ADV
ejpam-2366	832	17	by	by	ADP
ejpam-2366	832	18	lemma	lemma	PROPN
ejpam-2366	832	19	4	4	NUM
ejpam-2366	832	20	,	,	PUNCT
ejpam-2366	832	21	we	we	PRON
ejpam-2366	832	22	have	have	VERB
ejpam-2366	832	23	r(q	r(q	NOUN
ejpam-2366	832	24	:	:	PUNCT
ejpam-2366	832	25	i	i	PRON
ejpam-2366	832	26	m	m	VERB
ejpam-2366	832	27	)	)	PUNCT
ejpam-2366	833	1	=	=	PUNCT
ejpam-2366	833	2	(	(	PUNCT
ejpam-2366	833	3	rq	rq	INTJ
ejpam-2366	833	4	:	:	PUNCT
ejpam-2366	833	5	i	i	PRON
ejpam-2366	833	6	m	m	VERB
ejpam-2366	833	7	)	)	PUNCT
ejpam-2366	833	8	6	6	NUM
ejpam-2366	833	9	(	(	PUNCT
ejpam-2366	833	10	n	n	NUM
ejpam-2366	833	11	:	:	PUNCT
ejpam-2366	833	12	i	i	PRON
ejpam-2366	833	13	m	m	PROPN
ejpam-2366	833	14	)	)	PUNCT
ejpam-2366	833	15	.	.	PUNCT
ejpam-2366	834	1	if	if	SCONJ
ejpam-2366	834	2	r(q	r(q	PROPN
ejpam-2366	834	3	:	:	PUNCT
ejpam-2366	834	4	i	i	PRON
ejpam-2366	834	5	m	m	VERB
ejpam-2366	834	6	)	)	PUNCT
ejpam-2366	834	7	6	6	NUM
ejpam-2366	834	8	(	(	PUNCT
ejpam-2366	834	9	n	n	NUM
ejpam-2366	834	10	:	:	PUNCT
ejpam-2366	834	11	i	i	PRON
ejpam-2366	834	12	m	m	VERB
ejpam-2366	834	13	)	)	PUNCT
ejpam-2366	834	14	2	2	NUM
ejpam-2366	834	15	=	=	SYM
ejpam-2366	834	16	(	(	PUNCT
ejpam-2366	834	17	(	(	PUNCT
ejpam-2366	834	18	n	n	X
ejpam-2366	834	19	:	:	PUNCT
ejpam-2366	834	20	i	i	PRON
ejpam-2366	834	21	m	m	PROPN
ejpam-2366	834	22	)	)	PUNCT
ejpam-2366	834	23	n	n	CCONJ
ejpam-2366	834	24	:	:	PUNCT
ejpam-2366	834	25	i	i	PRON
ejpam-2366	834	26	m	m	PROPN
ejpam-2366	834	27	)	)	PUNCT
ejpam-2366	834	28	,	,	PUNCT
ejpam-2366	834	29	then	then	ADV
ejpam-2366	834	30	r(q	r(q	NOUN
ejpam-2366	834	31	:	:	PUNCT
ejpam-2366	835	1	i	i	PRON
ejpam-2366	835	2	m	m	VERB
ejpam-2366	835	3	)	)	PUNCT
ejpam-2366	836	1	i	i	PRON
ejpam-2366	836	2	m	m	VERB
ejpam-2366	836	3	6	6	NUM
ejpam-2366	836	4	(	(	PUNCT
ejpam-2366	836	5	n	n	NUM
ejpam-2366	836	6	:	:	PUNCT
ejpam-2366	836	7	i	i	PRON
ejpam-2366	836	8	m	m	PROPN
ejpam-2366	836	9	)	)	PUNCT
ejpam-2366	836	10	n	n	NUM
ejpam-2366	836	11	which	which	PRON
ejpam-2366	836	12	implies	imply	VERB
ejpam-2366	836	13	rq	rq	X
ejpam-2366	836	14	6	6	NUM
ejpam-2366	836	15	(	(	PUNCT
ejpam-2366	836	16	n	n	NUM
ejpam-2366	836	17	:	:	PUNCT
ejpam-2366	836	18	i	i	PRON
ejpam-2366	836	19	m	m	PROPN
ejpam-2366	836	20	)	)	PUNCT
ejpam-2366	836	21	n	n	CCONJ
ejpam-2366	836	22	,	,	PUNCT
ejpam-2366	836	23	a	a	DET
ejpam-2366	836	24	contradiction	contradiction	NOUN
ejpam-2366	836	25	.	.	PUNCT
ejpam-2366	837	1	if	if	SCONJ
ejpam-2366	837	2	r(q	r(q	PROPN
ejpam-2366	837	3	:	:	PUNCT
ejpam-2366	837	4	i	i	PRON
ejpam-2366	837	5	m	m	VERB
ejpam-2366	837	6	)	)	PUNCT
ejpam-2366	837	7	(	(	PUNCT
ejpam-2366	837	8	n	n	X
ejpam-2366	837	9	:	:	PUNCT
ejpam-2366	837	10	i	i	PRON
ejpam-2366	837	11	m	m	VERB
ejpam-2366	837	12	)	)	PUNCT
ejpam-2366	837	13	2	2	NUM
ejpam-2366	837	14	,	,	PUNCT
ejpam-2366	837	15	then	then	ADV
ejpam-2366	837	16	as	as	ADP
ejpam-2366	837	17	r(q	r(q	PROPN
ejpam-2366	837	18	:	:	PUNCT
ejpam-2366	837	19	i	i	PRON
ejpam-2366	837	20	m	m	VERB
ejpam-2366	837	21	)	)	PUNCT
ejpam-2366	837	22	6	6	NUM
ejpam-2366	837	23	(	(	PUNCT
ejpam-2366	837	24	n	n	NUM
ejpam-2366	837	25	:	:	PUNCT
ejpam-2366	837	26	i	i	PRON
ejpam-2366	837	27	m	m	PROPN
ejpam-2366	837	28	)	)	PUNCT
ejpam-2366	837	29	and	and	CCONJ
ejpam-2366	837	30	(	(	PUNCT
ejpam-2366	837	31	n	n	X
ejpam-2366	837	32	:	:	PUNCT
ejpam-2366	837	33	i	i	PRON
ejpam-2366	837	34	m	m	PROPN
ejpam-2366	837	35	)	)	PUNCT
ejpam-2366	837	36	is	be	AUX
ejpam-2366	837	37	almost	almost	ADV
ejpam-2366	837	38	prime	prime	ADJ
ejpam-2366	837	39	,	,	PUNCT
ejpam-2366	837	40	we	we	PRON
ejpam-2366	837	41	a.	a.	VERB
ejpam-2366	837	42	v.	v.	PROPN
ejpam-2366	837	43	bingi	bingi	PROPN
ejpam-2366	837	44	,	,	PUNCT
ejpam-2366	837	45	c.	c.	PROPN
ejpam-2366	837	46	s.	s.	PROPN
ejpam-2366	837	47	manjarekar	manjarekar	PROPN
ejpam-2366	837	48	/	/	PROPN
ejpam-2366	837	49	eur	eur	PROPN
ejpam-2366	837	50	.	.	PUNCT
ejpam-2366	838	1	j.	j.	PROPN
ejpam-2366	838	2	pure	pure	PROPN
ejpam-2366	838	3	appl	appl	PROPN
ejpam-2366	838	4	.	.	PROPN
ejpam-2366	838	5	math	math	PROPN
ejpam-2366	838	6	,	,	PUNCT
ejpam-2366	838	7	14	14	NUM
ejpam-2366	838	8	(	(	PUNCT
ejpam-2366	838	9	2	2	NUM
ejpam-2366	838	10	)	)	PUNCT
ejpam-2366	838	11	(	(	PUNCT
ejpam-2366	838	12	2021	2021	NUM
ejpam-2366	838	13	)	)	PUNCT
ejpam-2366	839	1	,	,	PUNCT
ejpam-2366	839	2	551	551	NUM
ejpam-2366	839	3	-	-	SYM
ejpam-2366	839	4	577	577	NUM
ejpam-2366	839	5	573	573	NUM
ejpam-2366	839	6	have	have	VERB
ejpam-2366	839	7	either	either	CCONJ
ejpam-2366	839	8	r	r	NOUN
ejpam-2366	839	9	6	6	NUM
ejpam-2366	839	10	(	(	PUNCT
ejpam-2366	839	11	n	n	NUM
ejpam-2366	839	12	:	:	PUNCT
ejpam-2366	839	13	i	i	PRON
ejpam-2366	839	14	m	m	VERB
ejpam-2366	839	15	)	)	PUNCT
ejpam-2366	839	16	or	or	CCONJ
ejpam-2366	839	17	(	(	PUNCT
ejpam-2366	839	18	q	q	NOUN
ejpam-2366	839	19	:	:	PUNCT
ejpam-2366	839	20	i	i	PRON
ejpam-2366	839	21	m	m	VERB
ejpam-2366	839	22	)	)	PUNCT
ejpam-2366	839	23	6	6	NUM
ejpam-2366	839	24	(	(	PUNCT
ejpam-2366	839	25	n	n	NUM
ejpam-2366	839	26	:	:	PUNCT
ejpam-2366	839	27	i	i	PRON
ejpam-2366	839	28	m	m	VERB
ejpam-2366	839	29	)	)	PUNCT
ejpam-2366	839	30	which	which	PRON
ejpam-2366	839	31	implies	imply	VERB
ejpam-2366	839	32	either	either	CCONJ
ejpam-2366	839	33	r	r	NOUN
ejpam-2366	839	34	6	6	NUM
ejpam-2366	839	35	(	(	PUNCT
ejpam-2366	839	36	n	n	NUM
ejpam-2366	839	37	:	:	PUNCT
ejpam-2366	839	38	i	i	PRON
ejpam-2366	839	39	m	m	VERB
ejpam-2366	839	40	)	)	PUNCT
ejpam-2366	839	41	or	or	CCONJ
ejpam-2366	839	42	q	q	ADJ
ejpam-2366	839	43	6	6	NUM
ejpam-2366	839	44	n	n	NOUN
ejpam-2366	839	45	and	and	CCONJ
ejpam-2366	839	46	thus	thus	ADV
ejpam-2366	839	47	n	n	PRON
ejpam-2366	839	48	is	be	AUX
ejpam-2366	839	49	an	an	DET
ejpam-2366	839	50	almost	almost	ADV
ejpam-2366	839	51	prime	prime	ADJ
ejpam-2366	839	52	element	element	NOUN
ejpam-2366	839	53	of	of	ADP
ejpam-2366	839	54	m	m	PROPN
ejpam-2366	839	55	.	.	PUNCT
ejpam-2366	840	1	2	2	NUM
ejpam-2366	840	2	©	©	NOUN
ejpam-2366	840	3	=⇒	=⇒	NOUN
ejpam-2366	840	4	3	3	NUM
ejpam-2366	840	5	©	©	NOUN
ejpam-2366	840	6	.	.	PUNCT
ejpam-2366	840	7	suppose	suppose	VERB
ejpam-2366	840	8	(	(	PUNCT
ejpam-2366	840	9	n	n	X
ejpam-2366	840	10	:	:	PUNCT
ejpam-2366	840	11	i	i	PRON
ejpam-2366	840	12	m	m	PROPN
ejpam-2366	840	13	)	)	PUNCT
ejpam-2366	840	14	is	be	AUX
ejpam-2366	840	15	an	an	DET
ejpam-2366	840	16	almost	almost	ADV
ejpam-2366	840	17	prime	prime	ADJ
ejpam-2366	840	18	element	element	NOUN
ejpam-2366	840	19	of	of	ADP
ejpam-2366	840	20	l.	l.	PROPN
ejpam-2366	840	21	since	since	SCONJ
ejpam-2366	840	22	m	m	PROPN
ejpam-2366	840	23	is	be	AUX
ejpam-2366	840	24	a	a	DET
ejpam-2366	840	25	multiplication	multiplication	NOUN
ejpam-2366	840	26	lattice	lattice	NOUN
ejpam-2366	840	27	l	l	NOUN
ejpam-2366	840	28	-	-	NOUN
ejpam-2366	840	29	module	module	NOUN
ejpam-2366	840	30	,	,	PUNCT
ejpam-2366	840	31	n	n	NOUN
ejpam-2366	840	32	=	=	SYM
ejpam-2366	840	33	(	(	PUNCT
ejpam-2366	840	34	n	n	X
ejpam-2366	840	35	:	:	PUNCT
ejpam-2366	840	36	i	i	PRON
ejpam-2366	840	37	m	m	VERB
ejpam-2366	840	38	)	)	PUNCT
ejpam-2366	841	1	i	i	PRON
ejpam-2366	841	2	m	m	VERB
ejpam-2366	841	3	and	and	CCONJ
ejpam-2366	841	4	hence	hence	ADV
ejpam-2366	841	5	3	3	NUM
ejpam-2366	841	6	©	©	PROPN
ejpam-2366	841	7	holds	hold	NOUN
ejpam-2366	841	8	.	.	PUNCT
ejpam-2366	842	1	3	3	NUM
ejpam-2366	842	2	©	©	NOUN
ejpam-2366	842	3	=⇒	=⇒	NOUN
ejpam-2366	842	4	2	2	NUM
ejpam-2366	842	5	©	©	NOUN
ejpam-2366	842	6	.	.	PUNCT
ejpam-2366	842	7	suppose	suppose	VERB
ejpam-2366	842	8	n	n	PROPN
ejpam-2366	842	9	=	=	PUNCT
ejpam-2366	842	10	qim	qim	NOUN
ejpam-2366	842	11	for	for	ADP
ejpam-2366	842	12	some	some	DET
ejpam-2366	842	13	almost	almost	ADV
ejpam-2366	842	14	prime	prime	ADJ
ejpam-2366	842	15	element	element	NOUN
ejpam-2366	842	16	q	q	PROPN
ejpam-2366	842	17	∈	∈	PROPN
ejpam-2366	842	18	l.	l.	NOUN
ejpam-2366	842	19	as	as	SCONJ
ejpam-2366	842	20	m	m	PROPN
ejpam-2366	842	21	is	be	AUX
ejpam-2366	842	22	a	a	DET
ejpam-2366	842	23	multiplication	multiplication	NOUN
ejpam-2366	842	24	lattice	lattice	NOUN
ejpam-2366	842	25	l	l	NOUN
ejpam-2366	842	26	-	-	NOUN
ejpam-2366	842	27	module	module	NOUN
ejpam-2366	842	28	,	,	PUNCT
ejpam-2366	842	29	n	n	NOUN
ejpam-2366	842	30	=	=	SYM
ejpam-2366	842	31	(	(	PUNCT
ejpam-2366	842	32	n	n	X
ejpam-2366	842	33	:	:	PUNCT
ejpam-2366	842	34	i	i	PRON
ejpam-2366	842	35	m	m	VERB
ejpam-2366	842	36	)	)	PUNCT
ejpam-2366	843	1	i	i	PRON
ejpam-2366	843	2	m	m	VERB
ejpam-2366	843	3	.	.	PUNCT
ejpam-2366	844	1	since	since	SCONJ
ejpam-2366	844	2	i	i	PRON
ejpam-2366	844	3	m	m	VERB
ejpam-2366	844	4	is	be	AUX
ejpam-2366	844	5	compact	compact	ADJ
ejpam-2366	844	6	,	,	PUNCT
ejpam-2366	844	7	2	2	NUM
ejpam-2366	844	8	©	©	PROPN
ejpam-2366	844	9	holds	hold	NOUN
ejpam-2366	844	10	by	by	ADP
ejpam-2366	844	11	theorem	theorem	NOUN
ejpam-2366	844	12	5	5	NUM
ejpam-2366	844	13	of	of	ADP
ejpam-2366	844	14	[	[	X
ejpam-2366	844	15	10	10	NUM
ejpam-2366	844	16	]	]	PUNCT
ejpam-2366	844	17	.	.	PUNCT
ejpam-2366	845	1	the	the	DET
ejpam-2366	845	2	following	following	ADJ
ejpam-2366	845	3	result	result	NOUN
ejpam-2366	845	4	is	be	AUX
ejpam-2366	845	5	another	another	DET
ejpam-2366	845	6	characterization	characterization	NOUN
ejpam-2366	845	7	of	of	ADP
ejpam-2366	845	8	an	an	DET
ejpam-2366	845	9	almost	almost	ADV
ejpam-2366	845	10	prime	prime	ADJ
ejpam-2366	845	11	element	element	NOUN
ejpam-2366	845	12	of	of	ADP
ejpam-2366	845	13	an	an	DET
ejpam-2366	845	14	lmodule	lmodule	NOUN
ejpam-2366	845	15	m	m	NOUN
ejpam-2366	845	16	.	.	PUNCT
ejpam-2366	846	1	theorem	theorem	PROPN
ejpam-2366	846	2	47	47	NUM
ejpam-2366	846	3	.	.	PUNCT
ejpam-2366	847	1	let	let	VERB
ejpam-2366	847	2	l	l	NOUN
ejpam-2366	847	3	be	be	AUX
ejpam-2366	847	4	a	a	DET
ejpam-2366	847	5	pg	pg	NOUN
ejpam-2366	847	6	-	-	PUNCT
ejpam-2366	847	7	lattice	lattice	NOUN
ejpam-2366	847	8	and	and	CCONJ
ejpam-2366	847	9	m	m	AUX
ejpam-2366	847	10	be	be	AUX
ejpam-2366	847	11	a	a	DET
ejpam-2366	847	12	faithful	faithful	ADJ
ejpam-2366	847	13	multiplication	multiplication	NOUN
ejpam-2366	847	14	torsion	torsion	NOUN
ejpam-2366	847	15	free	free	ADJ
ejpam-2366	847	16	pglattice	pglattice	NOUN
ejpam-2366	847	17	l	l	NOUN
ejpam-2366	847	18	-	-	NOUN
ejpam-2366	847	19	module	module	NOUN
ejpam-2366	847	20	with	with	ADP
ejpam-2366	847	21	i	i	PRON
ejpam-2366	847	22	m	m	VERB
ejpam-2366	847	23	compact	compact	ADJ
ejpam-2366	847	24	.	.	PUNCT
ejpam-2366	848	1	let	let	VERB
ejpam-2366	848	2	i	i	PRON
ejpam-2366	848	3	m	m	AUX
ejpam-2366	848	4	be	be	AUX
ejpam-2366	848	5	a	a	DET
ejpam-2366	848	6	weak	weak	ADJ
ejpam-2366	848	7	join	join	NOUN
ejpam-2366	848	8	principal	principal	ADJ
ejpam-2366	848	9	element	element	NOUN
ejpam-2366	848	10	.	.	PUNCT
ejpam-2366	849	1	then	then	ADV
ejpam-2366	849	2	a	a	DET
ejpam-2366	849	3	proper	proper	ADJ
ejpam-2366	849	4	element	element	NOUN
ejpam-2366	849	5	p	p	PROPN
ejpam-2366	849	6	∈	∈	PROPN
ejpam-2366	849	7	m	m	VERB
ejpam-2366	849	8	is	be	AUX
ejpam-2366	849	9	almost	almost	ADV
ejpam-2366	849	10	prime	prime	ADJ
ejpam-2366	849	11	(	(	PUNCT
ejpam-2366	849	12	φ2	φ2	NOUN
ejpam-2366	849	13	−	−	PROPN
ejpam-2366	849	14	prime	prime	NOUN
ejpam-2366	849	15	)	)	PUNCT
ejpam-2366	849	16	if	if	SCONJ
ejpam-2366	849	17	and	and	CCONJ
ejpam-2366	849	18	only	only	ADV
ejpam-2366	849	19	if	if	SCONJ
ejpam-2366	849	20	whenever	whenever	SCONJ
ejpam-2366	849	21	n	n	NOUN
ejpam-2366	849	22	=	=	VERB
ejpam-2366	849	23	aim	aim	NOUN
ejpam-2366	849	24	and	and	CCONJ
ejpam-2366	849	25	k	k	X
ejpam-2366	850	1	=	=	X
ejpam-2366	850	2	bim	bim	NOUN
ejpam-2366	850	3	in	in	ADP
ejpam-2366	850	4	m	m	PROPN
ejpam-2366	850	5	are	be	AUX
ejpam-2366	850	6	such	such	ADJ
ejpam-2366	850	7	that	that	DET
ejpam-2366	850	8	abim	abim	NOUN
ejpam-2366	850	9	6	6	NUM
ejpam-2366	850	10	p	p	NOUN
ejpam-2366	850	11	and	and	CCONJ
ejpam-2366	850	12	abim	abim	NOUN
ejpam-2366	850	13	(	(	PUNCT
ejpam-2366	850	14	p	p	X
ejpam-2366	850	15	:	:	PUNCT
ejpam-2366	850	16	i	i	PRON
ejpam-2366	850	17	m	m	PROPN
ejpam-2366	850	18	)	)	PUNCT
ejpam-2366	851	1	p	p	NOUN
ejpam-2366	851	2	then	then	ADV
ejpam-2366	851	3	either	either	CCONJ
ejpam-2366	851	4	n	n	PROPN
ejpam-2366	851	5	6	6	NUM
ejpam-2366	851	6	p	p	NOUN
ejpam-2366	851	7	or	or	CCONJ
ejpam-2366	851	8	k	k	PROPN
ejpam-2366	851	9	6	6	NUM
ejpam-2366	851	10	p	p	NOUN
ejpam-2366	851	11	for	for	ADP
ejpam-2366	851	12	a	a	DET
ejpam-2366	851	13	,	,	PUNCT
ejpam-2366	851	14	b	b	PROPN
ejpam-2366	851	15	∈	∈	PROPN
ejpam-2366	851	16	l.	l.	NOUN
ejpam-2366	851	17	proof	proof	PROPN
ejpam-2366	851	18	.	.	PUNCT
ejpam-2366	852	1	assume	assume	VERB
ejpam-2366	852	2	that	that	SCONJ
ejpam-2366	852	3	p	p	PROPN
ejpam-2366	852	4	∈m	∈m	NOUN
ejpam-2366	852	5	is	be	AUX
ejpam-2366	852	6	almost	almost	ADV
ejpam-2366	852	7	prime	prime	ADJ
ejpam-2366	852	8	.	.	PUNCT
ejpam-2366	853	1	let	let	VERB
ejpam-2366	853	2	n	n	NOUN
ejpam-2366	853	3	=	=	NOUN
ejpam-2366	853	4	aim	aim	VERB
ejpam-2366	853	5	and	and	CCONJ
ejpam-2366	853	6	k	k	X
ejpam-2366	853	7	=	=	X
ejpam-2366	854	1	bim	bim	NOUN
ejpam-2366	854	2	in	in	ADP
ejpam-2366	854	3	m	m	PROPN
ejpam-2366	854	4	be	be	VERB
ejpam-2366	854	5	such	such	ADJ
ejpam-2366	854	6	that	that	DET
ejpam-2366	854	7	abim	abim	NOUN
ejpam-2366	854	8	6	6	NUM
ejpam-2366	854	9	p	p	NOUN
ejpam-2366	854	10	and	and	CCONJ
ejpam-2366	854	11	abim	abim	NOUN
ejpam-2366	854	12	(	(	PUNCT
ejpam-2366	854	13	p	p	X
ejpam-2366	854	14	:	:	PUNCT
ejpam-2366	854	15	i	i	PRON
ejpam-2366	854	16	m	m	PROPN
ejpam-2366	854	17	)	)	PUNCT
ejpam-2366	854	18	p	p	NOUN
ejpam-2366	854	19	for	for	ADP
ejpam-2366	854	20	a	a	DET
ejpam-2366	854	21	,	,	PUNCT
ejpam-2366	854	22	b	b	PROPN
ejpam-2366	854	23	∈	∈	PROPN
ejpam-2366	854	24	l.	l.	NOUN
ejpam-2366	854	25	since	since	SCONJ
ejpam-2366	854	26	m	m	PROPN
ejpam-2366	854	27	is	be	AUX
ejpam-2366	854	28	a	a	DET
ejpam-2366	854	29	multiplication	multiplication	NOUN
ejpam-2366	854	30	lattice	lattice	NOUN
ejpam-2366	854	31	lmodule	lmodule	NOUN
ejpam-2366	854	32	,	,	PUNCT
ejpam-2366	854	33	we	we	PRON
ejpam-2366	854	34	have	have	VERB
ejpam-2366	854	35	a	a	DET
ejpam-2366	854	36	=	=	X
ejpam-2366	854	37	(	(	PUNCT
ejpam-2366	854	38	n	n	NOUN
ejpam-2366	854	39	:	:	PUNCT
ejpam-2366	854	40	i	i	PRON
ejpam-2366	854	41	m	m	PROPN
ejpam-2366	854	42	)	)	PUNCT
ejpam-2366	855	1	and	and	CCONJ
ejpam-2366	855	2	b	b	X
ejpam-2366	855	3	=	=	SYM
ejpam-2366	855	4	(	(	PUNCT
ejpam-2366	855	5	k	k	NOUN
ejpam-2366	855	6	:	:	PUNCT
ejpam-2366	855	7	i	i	PRON
ejpam-2366	855	8	m	m	VERB
ejpam-2366	855	9	)	)	PUNCT
ejpam-2366	855	10	and	and	CCONJ
ejpam-2366	855	11	so	so	ADV
ejpam-2366	855	12	(	(	PUNCT
ejpam-2366	855	13	k	k	X
ejpam-2366	855	14	:	:	PUNCT
ejpam-2366	855	15	i	i	PRON
ejpam-2366	855	16	m	m	VERB
ejpam-2366	855	17	)	)	PUNCT
ejpam-2366	855	18	(	(	PUNCT
ejpam-2366	855	19	n	n	X
ejpam-2366	855	20	:	:	PUNCT
ejpam-2366	855	21	i	i	PRON
ejpam-2366	855	22	m	m	VERB
ejpam-2366	855	23	)	)	PUNCT
ejpam-2366	856	1	i	i	PRON
ejpam-2366	856	2	m	m	VERB
ejpam-2366	856	3	=	=	VERB
ejpam-2366	856	4	abim	abim	ADJ
ejpam-2366	856	5	6	6	NUM
ejpam-2366	856	6	p	p	NOUN
ejpam-2366	856	7	and	and	CCONJ
ejpam-2366	856	8	(	(	PUNCT
ejpam-2366	856	9	k	k	NOUN
ejpam-2366	856	10	:	:	PUNCT
ejpam-2366	856	11	i	i	PRON
ejpam-2366	856	12	m	m	VERB
ejpam-2366	856	13	)	)	PUNCT
ejpam-2366	856	14	(	(	PUNCT
ejpam-2366	856	15	n	n	X
ejpam-2366	856	16	:	:	PUNCT
ejpam-2366	856	17	i	i	PRON
ejpam-2366	856	18	m	m	VERB
ejpam-2366	856	19	)	)	PUNCT
ejpam-2366	857	1	i	i	PRON
ejpam-2366	857	2	m	m	VERB
ejpam-2366	857	3	(	(	PUNCT
ejpam-2366	857	4	p	p	X
ejpam-2366	857	5	:	:	PUNCT
ejpam-2366	857	6	i	i	PRON
ejpam-2366	857	7	m	m	VERB
ejpam-2366	857	8	)	)	PUNCT
ejpam-2366	858	1	p	p	NOUN
ejpam-2366	858	2	.	.	PUNCT
ejpam-2366	859	1	as	as	SCONJ
ejpam-2366	859	2	p	p	PROPN
ejpam-2366	859	3	∈	∈	PROPN
ejpam-2366	859	4	m	m	VERB
ejpam-2366	859	5	is	be	AUX
ejpam-2366	859	6	almost	almost	ADV
ejpam-2366	859	7	prime	prime	ADJ
ejpam-2366	859	8	,	,	PUNCT
ejpam-2366	859	9	we	we	PRON
ejpam-2366	859	10	have	have	VERB
ejpam-2366	859	11	either	either	CCONJ
ejpam-2366	859	12	(	(	PUNCT
ejpam-2366	859	13	n	n	X
ejpam-2366	859	14	:	:	PUNCT
ejpam-2366	859	15	i	i	PRON
ejpam-2366	859	16	m	m	VERB
ejpam-2366	859	17	)	)	PUNCT
ejpam-2366	860	1	i	i	PRON
ejpam-2366	860	2	m	m	VERB
ejpam-2366	860	3	6	6	NUM
ejpam-2366	860	4	p	p	NOUN
ejpam-2366	860	5	or	or	CCONJ
ejpam-2366	860	6	(	(	PUNCT
ejpam-2366	860	7	k	k	NOUN
ejpam-2366	860	8	:	:	PUNCT
ejpam-2366	860	9	i	i	PRON
ejpam-2366	860	10	m	m	VERB
ejpam-2366	860	11	)	)	PUNCT
ejpam-2366	860	12	6	6	NUM
ejpam-2366	860	13	(	(	PUNCT
ejpam-2366	860	14	p	p	X
ejpam-2366	860	15	:	:	PUNCT
ejpam-2366	860	16	i	i	PRON
ejpam-2366	860	17	m	m	VERB
ejpam-2366	860	18	)	)	PUNCT
ejpam-2366	860	19	which	which	PRON
ejpam-2366	860	20	implies	imply	VERB
ejpam-2366	860	21	either	either	CCONJ
ejpam-2366	860	22	n	n	PROPN
ejpam-2366	860	23	=	=	SYM
ejpam-2366	860	24	(	(	PUNCT
ejpam-2366	860	25	n	n	X
ejpam-2366	860	26	:	:	PUNCT
ejpam-2366	860	27	i	i	PRON
ejpam-2366	860	28	m	m	VERB
ejpam-2366	860	29	)	)	PUNCT
ejpam-2366	861	1	i	i	PRON
ejpam-2366	861	2	m	m	VERB
ejpam-2366	861	3	6	6	NUM
ejpam-2366	861	4	p	p	NOUN
ejpam-2366	861	5	or	or	CCONJ
ejpam-2366	861	6	k	k	NOUN
ejpam-2366	861	7	=	=	SYM
ejpam-2366	862	1	(	(	PUNCT
ejpam-2366	862	2	k	k	NOUN
ejpam-2366	862	3	:	:	PUNCT
ejpam-2366	862	4	i	i	PRON
ejpam-2366	862	5	m	m	VERB
ejpam-2366	862	6	)	)	PUNCT
ejpam-2366	863	1	i	i	PRON
ejpam-2366	863	2	m	m	VERB
ejpam-2366	863	3	6	6	NUM
ejpam-2366	863	4	p	p	NOUN
ejpam-2366	863	5	.	.	PUNCT
ejpam-2366	864	1	conversely	conversely	ADV
ejpam-2366	864	2	,	,	PUNCT
ejpam-2366	864	3	assume	assume	VERB
ejpam-2366	864	4	that	that	SCONJ
ejpam-2366	864	5	abim	abim	NOUN
ejpam-2366	864	6	6	6	NUM
ejpam-2366	864	7	p	p	NOUN
ejpam-2366	864	8	and	and	CCONJ
ejpam-2366	864	9	abim	abim	NOUN
ejpam-2366	864	10	(	(	PUNCT
ejpam-2366	864	11	p	p	X
ejpam-2366	864	12	:	:	PUNCT
ejpam-2366	864	13	i	i	PRON
ejpam-2366	864	14	m	m	VERB
ejpam-2366	864	15	)	)	PUNCT
ejpam-2366	864	16	p	p	NOUN
ejpam-2366	864	17	implies	imply	VERB
ejpam-2366	864	18	either	either	CCONJ
ejpam-2366	864	19	n	n	PROPN
ejpam-2366	864	20	6	6	NUM
ejpam-2366	864	21	p	p	NOUN
ejpam-2366	864	22	or	or	CCONJ
ejpam-2366	864	23	k	k	PROPN
ejpam-2366	864	24	6	6	NUM
ejpam-2366	864	25	p	p	NOUN
ejpam-2366	864	26	where	where	SCONJ
ejpam-2366	864	27	n	n	NOUN
ejpam-2366	864	28	=	=	SYM
ejpam-2366	864	29	aim	aim	NOUN
ejpam-2366	864	30	and	and	CCONJ
ejpam-2366	864	31	k	k	PROPN
ejpam-2366	864	32	=	=	NOUN
ejpam-2366	864	33	bim	bim	NOUN
ejpam-2366	864	34	are	be	AUX
ejpam-2366	864	35	in	in	ADP
ejpam-2366	864	36	m	m	PROPN
ejpam-2366	864	37	for	for	ADP
ejpam-2366	864	38	a	a	DET
ejpam-2366	864	39	,	,	PUNCT
ejpam-2366	864	40	b	b	PROPN
ejpam-2366	864	41	∈	∈	PROPN
ejpam-2366	864	42	l.	l.	NOUN
ejpam-2366	864	43	let	let	VERB
ejpam-2366	864	44	rs	rs	X
ejpam-2366	864	45	6	6	NUM
ejpam-2366	864	46	(	(	PUNCT
ejpam-2366	864	47	p	p	X
ejpam-2366	864	48	:	:	PUNCT
ejpam-2366	864	49	i	i	PRON
ejpam-2366	864	50	m	m	PROPN
ejpam-2366	864	51	)	)	PUNCT
ejpam-2366	864	52	and	and	CCONJ
ejpam-2366	864	53	rs	rs	INTJ
ejpam-2366	864	54	(	(	PUNCT
ejpam-2366	864	55	p	p	X
ejpam-2366	864	56	:	:	PUNCT
ejpam-2366	864	57	i	i	PRON
ejpam-2366	864	58	m	m	VERB
ejpam-2366	864	59	)	)	PUNCT
ejpam-2366	864	60	2	2	NUM
ejpam-2366	864	61	where	where	SCONJ
ejpam-2366	864	62	s	s	VERB
ejpam-2366	864	63	=	=	VERB
ejpam-2366	864	64	rim	rim	NOUN
ejpam-2366	864	65	and	and	CCONJ
ejpam-2366	864	66	q	q	NOUN
ejpam-2366	865	1	=	=	NOUN
ejpam-2366	865	2	sim	sim	NOUN
ejpam-2366	865	3	are	be	AUX
ejpam-2366	865	4	in	in	ADP
ejpam-2366	865	5	m	m	PROPN
ejpam-2366	865	6	for	for	ADP
ejpam-2366	865	7	r	r	NOUN
ejpam-2366	865	8	,	,	PUNCT
ejpam-2366	865	9	s	s	NOUN
ejpam-2366	865	10	∈	∈	PROPN
ejpam-2366	865	11	l.	l.	NOUN
ejpam-2366	865	12	if	if	SCONJ
ejpam-2366	865	13	rsim	rsim	NOUN
ejpam-2366	865	14	6	6	NUM
ejpam-2366	865	15	(	(	PUNCT
ejpam-2366	865	16	p	p	X
ejpam-2366	865	17	:	:	PUNCT
ejpam-2366	865	18	i	i	PRON
ejpam-2366	865	19	m	m	VERB
ejpam-2366	865	20	)	)	PUNCT
ejpam-2366	865	21	p	p	NOUN
ejpam-2366	865	22	,	,	PUNCT
ejpam-2366	865	23	then	then	ADV
ejpam-2366	865	24	since	since	SCONJ
ejpam-2366	865	25	m	m	PROPN
ejpam-2366	865	26	is	be	AUX
ejpam-2366	865	27	a	a	DET
ejpam-2366	865	28	multiplication	multiplication	NOUN
ejpam-2366	865	29	lattice	lattice	NOUN
ejpam-2366	865	30	l	l	NOUN
ejpam-2366	865	31	-	-	NOUN
ejpam-2366	865	32	module	module	NOUN
ejpam-2366	865	33	,	,	PUNCT
ejpam-2366	865	34	we	we	PRON
ejpam-2366	865	35	have	have	VERB
ejpam-2366	865	36	rsim	rsim	NOUN
ejpam-2366	865	37	6	6	NUM
ejpam-2366	865	38	(	(	PUNCT
ejpam-2366	865	39	p	p	X
ejpam-2366	865	40	:	:	PUNCT
ejpam-2366	865	41	i	i	PROPN
ejpam-2366	865	42	m	m	NOUN
ejpam-2366	865	43	)	)	PUNCT
ejpam-2366	865	44	2im	2im	NOUN
ejpam-2366	865	45	.	.	PUNCT
ejpam-2366	866	1	so	so	ADV
ejpam-2366	866	2	by	by	ADP
ejpam-2366	866	3	theorem	theorem	NOUN
ejpam-2366	866	4	5	5	NUM
ejpam-2366	866	5	of	of	ADP
ejpam-2366	866	6	[	[	X
ejpam-2366	866	7	10	10	NUM
ejpam-2366	866	8	]	]	PUNCT
ejpam-2366	866	9	,	,	PUNCT
ejpam-2366	866	10	we	we	PRON
ejpam-2366	866	11	have	have	VERB
ejpam-2366	866	12	rs	r	VERB
ejpam-2366	866	13	6	6	NUM
ejpam-2366	866	14	(	(	PUNCT
ejpam-2366	866	15	p	p	X
ejpam-2366	866	16	:	:	PUNCT
ejpam-2366	866	17	i	i	PRON
ejpam-2366	866	18	m	m	VERB
ejpam-2366	866	19	)	)	PUNCT
ejpam-2366	866	20	2	2	NUM
ejpam-2366	866	21	,	,	PUNCT
ejpam-2366	866	22	a	a	DET
ejpam-2366	866	23	contradiction	contradiction	NOUN
ejpam-2366	866	24	.	.	PUNCT
ejpam-2366	867	1	so	so	ADV
ejpam-2366	867	2	let	let	VERB
ejpam-2366	867	3	rsim	rsim	NOUN
ejpam-2366	867	4	(	(	PUNCT
ejpam-2366	867	5	p	p	X
ejpam-2366	867	6	:	:	PUNCT
ejpam-2366	867	7	i	i	PRON
ejpam-2366	867	8	m	m	PROPN
ejpam-2366	867	9	)	)	PUNCT
ejpam-2366	867	10	p	p	NOUN
ejpam-2366	867	11	.	.	PUNCT
ejpam-2366	868	1	since	since	SCONJ
ejpam-2366	868	2	rsim	rsim	NOUN
ejpam-2366	868	3	6	6	NUM
ejpam-2366	868	4	p	p	NOUN
ejpam-2366	868	5	,	,	PUNCT
ejpam-2366	868	6	by	by	ADP
ejpam-2366	868	7	hypothesis	hypothesis	NOUN
ejpam-2366	868	8	,	,	PUNCT
ejpam-2366	868	9	we	we	PRON
ejpam-2366	868	10	have	have	VERB
ejpam-2366	868	11	either	either	CCONJ
ejpam-2366	868	12	s	s	VERB
ejpam-2366	868	13	6	6	NUM
ejpam-2366	868	14	p	p	NOUN
ejpam-2366	868	15	or	or	CCONJ
ejpam-2366	868	16	q	q	NOUN
ejpam-2366	868	17	6	6	NUM
ejpam-2366	868	18	p	p	NOUN
ejpam-2366	868	19	which	which	PRON
ejpam-2366	868	20	implies	imply	VERB
ejpam-2366	868	21	either	either	CCONJ
ejpam-2366	868	22	rim	rim	VERB
ejpam-2366	868	23	6	6	NUM
ejpam-2366	868	24	p	p	NOUN
ejpam-2366	868	25	or	or	CCONJ
ejpam-2366	868	26	sim	sim	VERB
ejpam-2366	868	27	6	6	NUM
ejpam-2366	868	28	p	p	NOUN
ejpam-2366	869	1	and	and	CCONJ
ejpam-2366	869	2	so	so	ADV
ejpam-2366	869	3	either	either	DET
ejpam-2366	869	4	r	r	NOUN
ejpam-2366	869	5	6	6	NUM
ejpam-2366	869	6	(	(	PUNCT
ejpam-2366	869	7	p	p	X
ejpam-2366	869	8	:	:	PUNCT
ejpam-2366	869	9	i	i	PRON
ejpam-2366	869	10	m	m	VERB
ejpam-2366	869	11	)	)	PUNCT
ejpam-2366	869	12	or	or	CCONJ
ejpam-2366	869	13	s	s	PRON
ejpam-2366	869	14	6	6	NUM
ejpam-2366	869	15	(	(	PUNCT
ejpam-2366	869	16	p	p	X
ejpam-2366	869	17	:	:	PUNCT
ejpam-2366	869	18	i	i	PRON
ejpam-2366	869	19	m	m	PROPN
ejpam-2366	869	20	)	)	PUNCT
ejpam-2366	869	21	.	.	PUNCT
ejpam-2366	870	1	thus	thus	ADV
ejpam-2366	870	2	(	(	PUNCT
ejpam-2366	870	3	p	p	X
ejpam-2366	870	4	:	:	PUNCT
ejpam-2366	870	5	i	i	PRON
ejpam-2366	870	6	m	m	PROPN
ejpam-2366	870	7	)	)	PUNCT
ejpam-2366	870	8	is	be	AUX
ejpam-2366	870	9	an	an	DET
ejpam-2366	870	10	almost	almost	ADV
ejpam-2366	870	11	prime	prime	ADJ
ejpam-2366	870	12	element	element	NOUN
ejpam-2366	870	13	of	of	ADP
ejpam-2366	870	14	l	l	NOUN
ejpam-2366	870	15	and	and	CCONJ
ejpam-2366	870	16	hence	hence	ADV
ejpam-2366	870	17	by	by	ADP
ejpam-2366	870	18	theorem	theorem	NOUN
ejpam-2366	870	19	46	46	NUM
ejpam-2366	870	20	,	,	PUNCT
ejpam-2366	870	21	p	p	NOUN
ejpam-2366	870	22	is	be	AUX
ejpam-2366	870	23	an	an	DET
ejpam-2366	870	24	almost	almost	ADV
ejpam-2366	870	25	prime	prime	ADJ
ejpam-2366	870	26	element	element	NOUN
ejpam-2366	870	27	of	of	ADP
ejpam-2366	870	28	m	m	PROPN
ejpam-2366	870	29	.	.	PUNCT
ejpam-2366	871	1	in	in	ADP
ejpam-2366	871	2	view	view	NOUN
ejpam-2366	871	3	of	of	ADP
ejpam-2366	871	4	lemma	lemma	PROPN
ejpam-2366	871	5	5	5	NUM
ejpam-2366	871	6	,	,	PUNCT
ejpam-2366	871	7	the	the	DET
ejpam-2366	871	8	theorems	theorem	NOUN
ejpam-2366	871	9	45	45	NUM
ejpam-2366	871	10	,	,	PUNCT
ejpam-2366	871	11	46	46	NUM
ejpam-2366	871	12	and	and	CCONJ
ejpam-2366	871	13	47	47	NUM
ejpam-2366	871	14	can	can	AUX
ejpam-2366	871	15	be	be	AUX
ejpam-2366	871	16	restated	restate	VERB
ejpam-2366	871	17	in	in	ADP
ejpam-2366	871	18	the	the	DET
ejpam-2366	871	19	following	following	ADJ
ejpam-2366	871	20	way	way	NOUN
ejpam-2366	871	21	.	.	PUNCT
ejpam-2366	872	1	theorem	theorem	VERB
ejpam-2366	872	2	48	48	NUM
ejpam-2366	872	3	.	.	PUNCT
ejpam-2366	873	1	let	let	VERB
ejpam-2366	873	2	l	l	NOUN
ejpam-2366	873	3	be	be	AUX
ejpam-2366	873	4	a	a	DET
ejpam-2366	873	5	pg	pg	NOUN
ejpam-2366	873	6	-	-	PUNCT
ejpam-2366	873	7	lattice	lattice	NOUN
ejpam-2366	873	8	and	and	CCONJ
ejpam-2366	873	9	m	m	AUX
ejpam-2366	873	10	be	be	AUX
ejpam-2366	873	11	a	a	DET
ejpam-2366	873	12	faithful	faithful	ADJ
ejpam-2366	873	13	multiplication	multiplication	NOUN
ejpam-2366	873	14	pg	pg	ADJ
ejpam-2366	873	15	-	-	PUNCT
ejpam-2366	873	16	lattice	lattice	NOUN
ejpam-2366	873	17	lmodule	lmodule	NOUN
ejpam-2366	873	18	with	with	ADP
ejpam-2366	873	19	i	i	PRON
ejpam-2366	873	20	m	m	VERB
ejpam-2366	873	21	compact	compact	ADJ
ejpam-2366	873	22	.	.	PUNCT
ejpam-2366	874	1	let	let	VERB
ejpam-2366	874	2	n	n	PRON
ejpam-2366	874	3	be	be	AUX
ejpam-2366	874	4	a	a	DET
ejpam-2366	874	5	proper	proper	ADJ
ejpam-2366	874	6	element	element	NOUN
ejpam-2366	874	7	of	of	ADP
ejpam-2366	874	8	an	an	DET
ejpam-2366	874	9	l	l	NOUN
ejpam-2366	874	10	-	-	NOUN
ejpam-2366	874	11	module	module	NOUN
ejpam-2366	874	12	m	m	NOUN
ejpam-2366	874	13	.	.	PUNCT
ejpam-2366	875	1	then	then	ADV
ejpam-2366	875	2	the	the	DET
ejpam-2366	875	3	following	follow	VERB
ejpam-2366	875	4	statements	statement	NOUN
ejpam-2366	875	5	are	be	AUX
ejpam-2366	875	6	equivalent	equivalent	ADJ
ejpam-2366	875	7	:	:	PUNCT
ejpam-2366	875	8	1	1	X
ejpam-2366	875	9	©	©	NOUN
ejpam-2366	875	10	n	n	NUM
ejpam-2366	875	11	is	be	AUX
ejpam-2366	875	12	an	an	DET
ejpam-2366	875	13	almost	almost	ADV
ejpam-2366	875	14	prime	prime	ADJ
ejpam-2366	875	15	element	element	NOUN
ejpam-2366	875	16	of	of	ADP
ejpam-2366	875	17	m	m	PROPN
ejpam-2366	875	18	.	.	PUNCT
ejpam-2366	876	1	2	2	NUM
ejpam-2366	876	2	©	©	NOUN
ejpam-2366	876	3	(	(	PUNCT
ejpam-2366	876	4	n	n	NOUN
ejpam-2366	876	5	:	:	PUNCT
ejpam-2366	876	6	i	i	PRON
ejpam-2366	876	7	m	m	PROPN
ejpam-2366	876	8	)	)	PUNCT
ejpam-2366	876	9	is	be	AUX
ejpam-2366	876	10	an	an	DET
ejpam-2366	876	11	almost	almost	ADV
ejpam-2366	876	12	prime	prime	ADJ
ejpam-2366	876	13	element	element	NOUN
ejpam-2366	876	14	of	of	ADP
ejpam-2366	876	15	l.	l.	PROPN
ejpam-2366	876	16	3	3	NUM
ejpam-2366	876	17	©	©	PROPN
ejpam-2366	876	18	n	n	NOUN
ejpam-2366	876	19	=	=	X
ejpam-2366	876	20	qim	qim	NOUN
ejpam-2366	876	21	for	for	ADP
ejpam-2366	876	22	some	some	DET
ejpam-2366	876	23	almost	almost	ADV
ejpam-2366	876	24	prime	prime	ADJ
ejpam-2366	876	25	element	element	NOUN
ejpam-2366	876	26	q	q	PROPN
ejpam-2366	876	27	∈	∈	PROPN
ejpam-2366	876	28	l	l	NOUN
ejpam-2366	876	29	which	which	PRON
ejpam-2366	876	30	is	be	AUX
ejpam-2366	876	31	maximal	maximal	ADJ
ejpam-2366	876	32	in	in	ADP
ejpam-2366	876	33	the	the	DET
ejpam-2366	876	34	sense	sense	NOUN
ejpam-2366	876	35	that	that	SCONJ
ejpam-2366	876	36	if	if	SCONJ
ejpam-2366	876	37	aim	aim	VERB
ejpam-2366	876	38	=	=	SYM
ejpam-2366	876	39	n	n	CCONJ
ejpam-2366	876	40	,	,	PUNCT
ejpam-2366	876	41	then	then	ADV
ejpam-2366	876	42	a	a	DET
ejpam-2366	876	43	6	6	NUM
ejpam-2366	876	44	q	q	NOUN
ejpam-2366	876	45	where	where	SCONJ
ejpam-2366	876	46	a	a	DET
ejpam-2366	876	47	∈	∈	PROPN
ejpam-2366	876	48	l.	l.	NOUN
ejpam-2366	876	49	theorem	theorem	VERB
ejpam-2366	876	50	49	49	NUM
ejpam-2366	876	51	.	.	PUNCT
ejpam-2366	877	1	let	let	VERB
ejpam-2366	877	2	l	l	NOUN
ejpam-2366	877	3	be	be	AUX
ejpam-2366	877	4	a	a	DET
ejpam-2366	877	5	pg	pg	NOUN
ejpam-2366	877	6	-	-	PUNCT
ejpam-2366	877	7	lattice	lattice	NOUN
ejpam-2366	877	8	and	and	CCONJ
ejpam-2366	877	9	m	m	AUX
ejpam-2366	877	10	be	be	AUX
ejpam-2366	877	11	a	a	DET
ejpam-2366	877	12	faithful	faithful	ADJ
ejpam-2366	877	13	multiplication	multiplication	NOUN
ejpam-2366	877	14	pg	pg	ADJ
ejpam-2366	877	15	-	-	PUNCT
ejpam-2366	877	16	lattice	lattice	NOUN
ejpam-2366	877	17	lmodule	lmodule	NOUN
ejpam-2366	877	18	with	with	ADP
ejpam-2366	877	19	i	i	PRON
ejpam-2366	877	20	m	m	VERB
ejpam-2366	877	21	compact	compact	ADJ
ejpam-2366	877	22	.	.	PUNCT
ejpam-2366	878	1	let	let	VERB
ejpam-2366	878	2	n	n	PRON
ejpam-2366	878	3	be	be	AUX
ejpam-2366	878	4	a	a	DET
ejpam-2366	878	5	proper	proper	ADJ
ejpam-2366	878	6	element	element	NOUN
ejpam-2366	878	7	of	of	ADP
ejpam-2366	878	8	an	an	DET
ejpam-2366	878	9	l	l	NOUN
ejpam-2366	878	10	-	-	NOUN
ejpam-2366	878	11	module	module	NOUN
ejpam-2366	878	12	m	m	NOUN
ejpam-2366	878	13	.	.	PUNCT
ejpam-2366	879	1	then	then	ADV
ejpam-2366	879	2	the	the	DET
ejpam-2366	879	3	following	follow	VERB
ejpam-2366	879	4	statements	statement	NOUN
ejpam-2366	879	5	are	be	AUX
ejpam-2366	879	6	equivalent	equivalent	ADJ
ejpam-2366	879	7	:	:	PUNCT
ejpam-2366	879	8	a.	a.	PROPN
ejpam-2366	879	9	v.	v.	PROPN
ejpam-2366	879	10	bingi	bingi	PROPN
ejpam-2366	879	11	,	,	PUNCT
ejpam-2366	879	12	c.	c.	PROPN
ejpam-2366	879	13	s.	s.	PROPN
ejpam-2366	879	14	manjarekar	manjarekar	PROPN
ejpam-2366	879	15	/	/	PROPN
ejpam-2366	879	16	eur	eur	PROPN
ejpam-2366	879	17	.	.	PUNCT
ejpam-2366	880	1	j.	j.	PROPN
ejpam-2366	880	2	pure	pure	PROPN
ejpam-2366	880	3	appl	appl	PROPN
ejpam-2366	880	4	.	.	PROPN
ejpam-2366	880	5	math	math	PROPN
ejpam-2366	880	6	,	,	PUNCT
ejpam-2366	880	7	14	14	NUM
ejpam-2366	880	8	(	(	PUNCT
ejpam-2366	880	9	2	2	NUM
ejpam-2366	880	10	)	)	PUNCT
ejpam-2366	880	11	(	(	PUNCT
ejpam-2366	880	12	2021	2021	NUM
ejpam-2366	880	13	)	)	PUNCT
ejpam-2366	880	14	,	,	PUNCT
ejpam-2366	880	15	551	551	NUM
ejpam-2366	880	16	-	-	SYM
ejpam-2366	880	17	577	577	NUM
ejpam-2366	880	18	574	574	NUM
ejpam-2366	880	19	1	1	NUM
ejpam-2366	880	20	©	©	PROPN
ejpam-2366	880	21	n	n	NUM
ejpam-2366	880	22	is	be	AUX
ejpam-2366	880	23	an	an	DET
ejpam-2366	880	24	almost	almost	ADV
ejpam-2366	880	25	prime	prime	ADJ
ejpam-2366	880	26	element	element	NOUN
ejpam-2366	880	27	of	of	ADP
ejpam-2366	880	28	m	m	PROPN
ejpam-2366	880	29	.	.	PUNCT
ejpam-2366	881	1	2	2	NUM
ejpam-2366	881	2	©	©	NOUN
ejpam-2366	881	3	(	(	PUNCT
ejpam-2366	881	4	n	n	NOUN
ejpam-2366	881	5	:	:	PUNCT
ejpam-2366	881	6	i	i	PRON
ejpam-2366	881	7	m	m	PROPN
ejpam-2366	881	8	)	)	PUNCT
ejpam-2366	881	9	is	be	AUX
ejpam-2366	881	10	an	an	DET
ejpam-2366	881	11	almost	almost	ADV
ejpam-2366	881	12	prime	prime	ADJ
ejpam-2366	881	13	element	element	NOUN
ejpam-2366	881	14	of	of	ADP
ejpam-2366	881	15	l.	l.	PROPN
ejpam-2366	881	16	3	3	NUM
ejpam-2366	881	17	©	©	PROPN
ejpam-2366	881	18	n	n	NOUN
ejpam-2366	881	19	=	=	X
ejpam-2366	881	20	qim	qim	NOUN
ejpam-2366	881	21	for	for	ADP
ejpam-2366	881	22	some	some	DET
ejpam-2366	881	23	almost	almost	ADV
ejpam-2366	881	24	prime	prime	ADJ
ejpam-2366	881	25	element	element	NOUN
ejpam-2366	881	26	q	q	PROPN
ejpam-2366	881	27	∈	∈	PROPN
ejpam-2366	881	28	l.	l.	NOUN
ejpam-2366	881	29	theorem	theorem	VERB
ejpam-2366	881	30	49	49	NUM
ejpam-2366	881	31	is	be	AUX
ejpam-2366	881	32	theorem	theorem	VERB
ejpam-2366	881	33	3.8	3.8	NUM
ejpam-2366	881	34	of	of	ADP
ejpam-2366	881	35	[	[	X
ejpam-2366	881	36	22	22	NUM
ejpam-2366	881	37	]	]	PUNCT
ejpam-2366	881	38	.	.	PUNCT
ejpam-2366	882	1	theorem	theorem	VERB
ejpam-2366	882	2	50	50	NUM
ejpam-2366	882	3	.	.	PUNCT
ejpam-2366	883	1	let	let	VERB
ejpam-2366	883	2	l	l	NOUN
ejpam-2366	883	3	be	be	AUX
ejpam-2366	883	4	a	a	DET
ejpam-2366	883	5	pg	pg	NOUN
ejpam-2366	883	6	-	-	PUNCT
ejpam-2366	883	7	lattice	lattice	NOUN
ejpam-2366	883	8	and	and	CCONJ
ejpam-2366	883	9	m	m	AUX
ejpam-2366	883	10	be	be	AUX
ejpam-2366	883	11	a	a	DET
ejpam-2366	883	12	faithful	faithful	ADJ
ejpam-2366	883	13	multiplication	multiplication	NOUN
ejpam-2366	883	14	pg	pg	ADJ
ejpam-2366	883	15	-	-	PUNCT
ejpam-2366	883	16	lattice	lattice	NOUN
ejpam-2366	883	17	lmodule	lmodule	NOUN
ejpam-2366	883	18	with	with	ADP
ejpam-2366	883	19	i	i	PROPN
ejpam-2366	883	20	m	m	VERB
ejpam-2366	883	21	compact	compact	ADJ
ejpam-2366	883	22	.	.	PUNCT
ejpam-2366	884	1	then	then	ADV
ejpam-2366	884	2	a	a	DET
ejpam-2366	884	3	proper	proper	ADJ
ejpam-2366	884	4	element	element	NOUN
ejpam-2366	884	5	p	p	PROPN
ejpam-2366	884	6	∈	∈	PROPN
ejpam-2366	884	7	m	m	VERB
ejpam-2366	884	8	is	be	AUX
ejpam-2366	884	9	almost	almost	ADV
ejpam-2366	884	10	prime	prime	ADJ
ejpam-2366	884	11	(	(	PUNCT
ejpam-2366	884	12	φ2	φ2	NOUN
ejpam-2366	884	13	−	−	PROPN
ejpam-2366	884	14	prime	prime	NOUN
ejpam-2366	884	15	)	)	PUNCT
ejpam-2366	884	16	if	if	SCONJ
ejpam-2366	884	17	and	and	CCONJ
ejpam-2366	884	18	only	only	ADV
ejpam-2366	884	19	if	if	SCONJ
ejpam-2366	884	20	whenever	whenever	SCONJ
ejpam-2366	884	21	n	n	NOUN
ejpam-2366	884	22	=	=	VERB
ejpam-2366	884	23	aim	aim	NOUN
ejpam-2366	884	24	and	and	CCONJ
ejpam-2366	884	25	k	k	X
ejpam-2366	885	1	=	=	X
ejpam-2366	885	2	bim	bim	NOUN
ejpam-2366	885	3	in	in	ADP
ejpam-2366	885	4	m	m	PROPN
ejpam-2366	885	5	are	be	AUX
ejpam-2366	885	6	such	such	ADJ
ejpam-2366	885	7	that	that	DET
ejpam-2366	885	8	abim	abim	NOUN
ejpam-2366	885	9	6	6	NUM
ejpam-2366	885	10	p	p	NOUN
ejpam-2366	885	11	and	and	CCONJ
ejpam-2366	885	12	abim	abim	NOUN
ejpam-2366	885	13	(	(	PUNCT
ejpam-2366	885	14	p	p	X
ejpam-2366	885	15	:	:	PUNCT
ejpam-2366	885	16	i	i	PRON
ejpam-2366	885	17	m	m	PROPN
ejpam-2366	885	18	)	)	PUNCT
ejpam-2366	886	1	p	p	NOUN
ejpam-2366	886	2	then	then	ADV
ejpam-2366	886	3	either	either	CCONJ
ejpam-2366	886	4	n	n	PROPN
ejpam-2366	886	5	6	6	NUM
ejpam-2366	886	6	p	p	NOUN
ejpam-2366	886	7	or	or	CCONJ
ejpam-2366	886	8	k	k	PROPN
ejpam-2366	886	9	6	6	NUM
ejpam-2366	886	10	p	p	NOUN
ejpam-2366	886	11	for	for	ADP
ejpam-2366	886	12	a	a	PRON
ejpam-2366	886	13	,	,	PUNCT
ejpam-2366	886	14	b	b	PROPN
ejpam-2366	886	15	∈	∈	PROPN
ejpam-2366	886	16	l.	l.	NOUN
ejpam-2366	886	17	theorem	theorem	VERB
ejpam-2366	886	18	50	50	NUM
ejpam-2366	886	19	is	be	AUX
ejpam-2366	886	20	theorem	theorem	VERB
ejpam-2366	886	21	3.14	3.14	NUM
ejpam-2366	886	22	of	of	ADP
ejpam-2366	886	23	[	[	X
ejpam-2366	886	24	22	22	NUM
ejpam-2366	886	25	]	]	PUNCT
ejpam-2366	886	26	.	.	PUNCT
ejpam-2366	887	1	the	the	DET
ejpam-2366	887	2	following	following	ADJ
ejpam-2366	887	3	result	result	NOUN
ejpam-2366	887	4	is	be	AUX
ejpam-2366	887	5	a	a	DET
ejpam-2366	887	6	consequence	consequence	NOUN
ejpam-2366	887	7	of	of	ADP
ejpam-2366	887	8	the	the	DET
ejpam-2366	887	9	theorem	theorem	ADJ
ejpam-2366	887	10	49	49	NUM
ejpam-2366	887	11	.	.	PUNCT
ejpam-2366	888	1	corollary	corollary	ADJ
ejpam-2366	888	2	20	20	NUM
ejpam-2366	888	3	.	.	PUNCT
ejpam-2366	889	1	let	let	VERB
ejpam-2366	889	2	l	l	NOUN
ejpam-2366	889	3	be	be	AUX
ejpam-2366	889	4	a	a	DET
ejpam-2366	889	5	pg	pg	NOUN
ejpam-2366	889	6	-	-	PUNCT
ejpam-2366	889	7	lattice	lattice	NOUN
ejpam-2366	889	8	and	and	CCONJ
ejpam-2366	889	9	m	m	AUX
ejpam-2366	889	10	be	be	AUX
ejpam-2366	889	11	a	a	DET
ejpam-2366	889	12	faithful	faithful	ADJ
ejpam-2366	889	13	multiplication	multiplication	NOUN
ejpam-2366	889	14	pg	pg	ADJ
ejpam-2366	889	15	-	-	PUNCT
ejpam-2366	889	16	lattice	lattice	NOUN
ejpam-2366	889	17	lmodule	lmodule	NOUN
ejpam-2366	889	18	with	with	ADP
ejpam-2366	889	19	i	i	PROPN
ejpam-2366	889	20	m	m	VERB
ejpam-2366	889	21	compact	compact	ADJ
ejpam-2366	889	22	.	.	PUNCT
ejpam-2366	890	1	then	then	ADV
ejpam-2366	890	2	a	a	DET
ejpam-2366	890	3	proper	proper	ADJ
ejpam-2366	890	4	element	element	NOUN
ejpam-2366	890	5	n	n	PROPN
ejpam-2366	890	6	of	of	ADP
ejpam-2366	890	7	an	an	DET
ejpam-2366	890	8	l	l	NOUN
ejpam-2366	890	9	-	-	NOUN
ejpam-2366	890	10	module	module	NOUN
ejpam-2366	890	11	m	m	NOUN
ejpam-2366	890	12	is	be	AUX
ejpam-2366	890	13	almost	almost	ADV
ejpam-2366	890	14	prime	prime	ADJ
ejpam-2366	890	15	if	if	SCONJ
ejpam-2366	891	1	and	and	CCONJ
ejpam-2366	891	2	only	only	ADV
ejpam-2366	891	3	if	if	SCONJ
ejpam-2366	891	4	(	(	PUNCT
ejpam-2366	891	5	n	n	X
ejpam-2366	891	6	:	:	PUNCT
ejpam-2366	891	7	i	i	PRON
ejpam-2366	891	8	m	m	PROPN
ejpam-2366	891	9	)	)	PUNCT
ejpam-2366	891	10	is	be	AUX
ejpam-2366	891	11	an	an	DET
ejpam-2366	891	12	almost	almost	ADV
ejpam-2366	891	13	prime	prime	ADJ
ejpam-2366	891	14	element	element	NOUN
ejpam-2366	891	15	of	of	ADP
ejpam-2366	891	16	l.	l.	PROPN
ejpam-2366	891	17	according	accord	VERB
ejpam-2366	891	18	to	to	ADP
ejpam-2366	891	19	[	[	X
ejpam-2366	891	20	16	16	NUM
ejpam-2366	891	21	]	]	X
ejpam-2366	891	22	,	,	PUNCT
ejpam-2366	891	23	a	a	DET
ejpam-2366	891	24	proper	proper	ADJ
ejpam-2366	891	25	element	element	NOUN
ejpam-2366	891	26	q	q	PROPN
ejpam-2366	891	27	∈	∈	PROPN
ejpam-2366	891	28	l	l	NOUN
ejpam-2366	891	29	is	be	AUX
ejpam-2366	891	30	said	say	VERB
ejpam-2366	891	31	to	to	PART
ejpam-2366	891	32	be	be	AUX
ejpam-2366	891	33	2	2	NUM
ejpam-2366	891	34	-	-	PUNCT
ejpam-2366	891	35	potent	potent	ADJ
ejpam-2366	891	36	prime	prime	NOUN
ejpam-2366	891	37	if	if	SCONJ
ejpam-2366	891	38	for	for	ADP
ejpam-2366	891	39	all	all	DET
ejpam-2366	891	40	a	a	DET
ejpam-2366	891	41	,	,	PUNCT
ejpam-2366	891	42	b	b	PROPN
ejpam-2366	891	43	∈	∈	PROPN
ejpam-2366	891	44	l	l	NOUN
ejpam-2366	891	45	,	,	PUNCT
ejpam-2366	891	46	ab	ab	PROPN
ejpam-2366	891	47	6	6	NUM
ejpam-2366	891	48	q2	q2	NOUN
ejpam-2366	891	49	implies	imply	VERB
ejpam-2366	891	50	either	either	CCONJ
ejpam-2366	891	51	a	a	DET
ejpam-2366	891	52	6	6	NUM
ejpam-2366	891	53	q	q	NOUN
ejpam-2366	891	54	or	or	CCONJ
ejpam-2366	891	55	b	b	NUM
ejpam-2366	891	56	6	6	NUM
ejpam-2366	891	57	q	q	NOUN
ejpam-2366	891	58	and	and	CCONJ
ejpam-2366	891	59	a	a	DET
ejpam-2366	891	60	proper	proper	ADJ
ejpam-2366	891	61	element	element	NOUN
ejpam-2366	891	62	q	q	PROPN
ejpam-2366	891	63	∈	∈	PROPN
ejpam-2366	891	64	l	l	NOUN
ejpam-2366	891	65	is	be	AUX
ejpam-2366	891	66	said	say	VERB
ejpam-2366	891	67	to	to	PART
ejpam-2366	891	68	be	be	AUX
ejpam-2366	891	69	2	2	NUM
ejpam-2366	891	70	-	-	PUNCT
ejpam-2366	891	71	potent	potent	ADJ
ejpam-2366	891	72	primary	primary	NOUN
ejpam-2366	891	73	if	if	SCONJ
ejpam-2366	891	74	for	for	ADP
ejpam-2366	891	75	all	all	DET
ejpam-2366	891	76	a	a	DET
ejpam-2366	891	77	,	,	PUNCT
ejpam-2366	891	78	b	b	PROPN
ejpam-2366	891	79	∈	∈	PROPN
ejpam-2366	891	80	l	l	NOUN
ejpam-2366	891	81	,	,	PUNCT
ejpam-2366	891	82	ab	ab	PROPN
ejpam-2366	891	83	6	6	NUM
ejpam-2366	891	84	q2	q2	NOUN
ejpam-2366	891	85	implies	imply	VERB
ejpam-2366	891	86	either	either	CCONJ
ejpam-2366	891	87	a	a	DET
ejpam-2366	891	88	6	6	NUM
ejpam-2366	891	89	q	q	NOUN
ejpam-2366	891	90	or	or	CCONJ
ejpam-2366	891	91	b	b	NOUN
ejpam-2366	891	92	6	6	NUM
ejpam-2366	891	93	√	√	PROPN
ejpam-2366	891	94	q.	q.	NOUN
ejpam-2366	891	95	in	in	ADP
ejpam-2366	891	96	view	view	NOUN
ejpam-2366	891	97	of	of	ADP
ejpam-2366	891	98	these	these	DET
ejpam-2366	891	99	definitions	definition	NOUN
ejpam-2366	891	100	,	,	PUNCT
ejpam-2366	891	101	we	we	PRON
ejpam-2366	891	102	define	define	VERB
ejpam-2366	891	103	n	n	CCONJ
ejpam-2366	891	104	-	-	PUNCT
ejpam-2366	891	105	potent	potent	ADJ
ejpam-2366	891	106	prime	prime	NOUN
ejpam-2366	891	107	and	and	CCONJ
ejpam-2366	891	108	n	n	CCONJ
ejpam-2366	891	109	-	-	PUNCT
ejpam-2366	891	110	potent	potent	ADJ
ejpam-2366	891	111	primary	primary	ADJ
ejpam-2366	891	112	elements	element	NOUN
ejpam-2366	891	113	(	(	PUNCT
ejpam-2366	891	114	where	where	SCONJ
ejpam-2366	891	115	n	n	CCONJ
ejpam-2366	891	116	>	>	X
ejpam-2366	891	117	2	2	NUM
ejpam-2366	891	118	)	)	PUNCT
ejpam-2366	891	119	in	in	ADP
ejpam-2366	891	120	a	a	DET
ejpam-2366	891	121	multiplicative	multiplicative	ADJ
ejpam-2366	891	122	lattice	lattice	NOUN
ejpam-2366	891	123	l	l	NOUN
ejpam-2366	891	124	in	in	ADP
ejpam-2366	891	125	following	follow	VERB
ejpam-2366	891	126	way	way	NOUN
ejpam-2366	891	127	.	.	PUNCT
ejpam-2366	892	1	definition	definition	NOUN
ejpam-2366	892	2	9	9	NUM
ejpam-2366	892	3	.	.	PUNCT
ejpam-2366	893	1	let	let	VERB
ejpam-2366	893	2	n	n	PRON
ejpam-2366	893	3	>	>	X
ejpam-2366	893	4	2	2	NUM
ejpam-2366	893	5	and	and	CCONJ
ejpam-2366	893	6	n	n	PRON
ejpam-2366	893	7	∈	∈	PROPN
ejpam-2366	893	8	z+	z+	NUM
ejpam-2366	893	9	.	.	PUNCT
ejpam-2366	894	1	a	a	DET
ejpam-2366	894	2	proper	proper	ADJ
ejpam-2366	894	3	element	element	NOUN
ejpam-2366	894	4	q	q	PROPN
ejpam-2366	894	5	∈	∈	PROPN
ejpam-2366	894	6	l	l	NOUN
ejpam-2366	894	7	is	be	AUX
ejpam-2366	894	8	said	say	VERB
ejpam-2366	894	9	to	to	PART
ejpam-2366	894	10	be	be	AUX
ejpam-2366	894	11	n	n	PRON
ejpam-2366	894	12	-	-	PUNCT
ejpam-2366	894	13	potent	potent	ADJ
ejpam-2366	894	14	prime	prime	NOUN
ejpam-2366	894	15	if	if	SCONJ
ejpam-2366	894	16	for	for	ADP
ejpam-2366	894	17	all	all	DET
ejpam-2366	894	18	a	a	DET
ejpam-2366	894	19	,	,	PUNCT
ejpam-2366	894	20	b	b	PROPN
ejpam-2366	894	21	∈	∈	PROPN
ejpam-2366	894	22	l	l	NOUN
ejpam-2366	894	23	,	,	PUNCT
ejpam-2366	894	24	ab	ab	PROPN
ejpam-2366	894	25	6	6	NUM
ejpam-2366	894	26	qn	qn	NOUN
ejpam-2366	894	27	implies	imply	VERB
ejpam-2366	894	28	either	either	CCONJ
ejpam-2366	894	29	a	a	DET
ejpam-2366	894	30	6	6	NUM
ejpam-2366	894	31	q	q	NOUN
ejpam-2366	894	32	or	or	CCONJ
ejpam-2366	894	33	b	b	NUM
ejpam-2366	894	34	6	6	NUM
ejpam-2366	894	35	q.	q.	NOUN
ejpam-2366	894	36	definition	definition	NOUN
ejpam-2366	894	37	10	10	NUM
ejpam-2366	894	38	.	.	PUNCT
ejpam-2366	895	1	let	let	VERB
ejpam-2366	895	2	n	n	PRON
ejpam-2366	895	3	>	>	X
ejpam-2366	895	4	2	2	NUM
ejpam-2366	895	5	and	and	CCONJ
ejpam-2366	895	6	n	n	PRON
ejpam-2366	895	7	∈	∈	PROPN
ejpam-2366	895	8	z+	z+	NUM
ejpam-2366	895	9	.	.	PUNCT
ejpam-2366	896	1	a	a	DET
ejpam-2366	896	2	proper	proper	ADJ
ejpam-2366	896	3	element	element	NOUN
ejpam-2366	896	4	q	q	PROPN
ejpam-2366	896	5	∈	∈	PROPN
ejpam-2366	896	6	l	l	NOUN
ejpam-2366	896	7	is	be	AUX
ejpam-2366	896	8	said	say	VERB
ejpam-2366	896	9	to	to	PART
ejpam-2366	896	10	be	be	AUX
ejpam-2366	896	11	n	n	PRON
ejpam-2366	896	12	-	-	PUNCT
ejpam-2366	896	13	potent	potent	ADJ
ejpam-2366	896	14	primary	primary	NOUN
ejpam-2366	896	15	if	if	SCONJ
ejpam-2366	896	16	for	for	ADP
ejpam-2366	896	17	all	all	DET
ejpam-2366	896	18	a	a	DET
ejpam-2366	896	19	,	,	PUNCT
ejpam-2366	896	20	b	b	PROPN
ejpam-2366	896	21	∈	∈	PROPN
ejpam-2366	896	22	l	l	NOUN
ejpam-2366	896	23	,	,	PUNCT
ejpam-2366	896	24	ab	ab	PROPN
ejpam-2366	896	25	6	6	NUM
ejpam-2366	896	26	qn	qn	NOUN
ejpam-2366	896	27	implies	imply	VERB
ejpam-2366	896	28	either	either	CCONJ
ejpam-2366	896	29	a	a	DET
ejpam-2366	896	30	6	6	NUM
ejpam-2366	896	31	q	q	NOUN
ejpam-2366	896	32	or	or	CCONJ
ejpam-2366	896	33	b	b	NOUN
ejpam-2366	896	34	6	6	NUM
ejpam-2366	896	35	√	√	PROPN
ejpam-2366	896	36	q.	q.	NOUN
ejpam-2366	896	37	now	now	ADV
ejpam-2366	896	38	we	we	PRON
ejpam-2366	896	39	show	show	VERB
ejpam-2366	896	40	that	that	SCONJ
ejpam-2366	896	41	if	if	SCONJ
ejpam-2366	896	42	an	an	DET
ejpam-2366	896	43	element	element	NOUN
ejpam-2366	896	44	in	in	ADP
ejpam-2366	896	45	m	m	PROPN
ejpam-2366	896	46	is	be	AUX
ejpam-2366	896	47	n	n	CCONJ
ejpam-2366	896	48	-	-	PUNCT
ejpam-2366	896	49	potent	potent	ADJ
ejpam-2366	896	50	prime	prime	NOUN
ejpam-2366	896	51	(	(	PUNCT
ejpam-2366	896	52	respectively	respectively	ADV
ejpam-2366	896	53	n	n	CCONJ
ejpam-2366	896	54	-	-	PUNCT
ejpam-2366	896	55	potent	potent	ADJ
ejpam-2366	896	56	primary	primary	NOUN
ejpam-2366	896	57	)	)	PUNCT
ejpam-2366	896	58	,	,	PUNCT
ejpam-2366	896	59	then	then	ADV
ejpam-2366	896	60	its	its	PRON
ejpam-2366	896	61	corresponding	corresponding	ADJ
ejpam-2366	896	62	element	element	NOUN
ejpam-2366	896	63	in	in	ADP
ejpam-2366	896	64	l	l	PROPN
ejpam-2366	896	65	is	be	AUX
ejpam-2366	896	66	also	also	ADV
ejpam-2366	896	67	n	n	CCONJ
ejpam-2366	896	68	-	-	PUNCT
ejpam-2366	896	69	potent	potent	ADJ
ejpam-2366	896	70	prime	prime	NOUN
ejpam-2366	896	71	(	(	PUNCT
ejpam-2366	896	72	respectively	respectively	ADV
ejpam-2366	896	73	n	n	CCONJ
ejpam-2366	896	74	-	-	PUNCT
ejpam-2366	896	75	potent	potent	ADJ
ejpam-2366	896	76	primary	primary	NOUN
ejpam-2366	896	77	)	)	PUNCT
ejpam-2366	896	78	and	and	CCONJ
ejpam-2366	896	79	vice	vice	NOUN
ejpam-2366	896	80	-	-	NOUN
ejpam-2366	896	81	versa	versa	ADJ
ejpam-2366	896	82	where	where	SCONJ
ejpam-2366	896	83	n	n	X
ejpam-2366	896	84	>	>	X
ejpam-2366	896	85	2	2	X
ejpam-2366	896	86	.	.	PUNCT
ejpam-2366	896	87	theorem	theorem	NOUN
ejpam-2366	896	88	51	51	NUM
ejpam-2366	896	89	.	.	PUNCT
ejpam-2366	897	1	let	let	VERB
ejpam-2366	897	2	l	l	NOUN
ejpam-2366	897	3	be	be	AUX
ejpam-2366	897	4	a	a	DET
ejpam-2366	897	5	pg	pg	NOUN
ejpam-2366	897	6	-	-	PUNCT
ejpam-2366	897	7	lattice	lattice	NOUN
ejpam-2366	897	8	and	and	CCONJ
ejpam-2366	897	9	m	m	AUX
ejpam-2366	897	10	be	be	AUX
ejpam-2366	897	11	a	a	DET
ejpam-2366	897	12	faithful	faithful	ADJ
ejpam-2366	897	13	multiplication	multiplication	NOUN
ejpam-2366	897	14	pg	pg	ADJ
ejpam-2366	897	15	-	-	PUNCT
ejpam-2366	897	16	lattice	lattice	NOUN
ejpam-2366	897	17	lmodule	lmodule	NOUN
ejpam-2366	897	18	with	with	ADP
ejpam-2366	897	19	i	i	PRON
ejpam-2366	897	20	m	m	VERB
ejpam-2366	897	21	compact	compact	ADJ
ejpam-2366	897	22	.	.	PUNCT
ejpam-2366	898	1	let	let	VERB
ejpam-2366	898	2	n	n	PRON
ejpam-2366	898	3	be	be	AUX
ejpam-2366	898	4	a	a	DET
ejpam-2366	898	5	proper	proper	ADJ
ejpam-2366	898	6	element	element	NOUN
ejpam-2366	898	7	of	of	ADP
ejpam-2366	898	8	an	an	DET
ejpam-2366	898	9	l	l	NOUN
ejpam-2366	898	10	-	-	NOUN
ejpam-2366	898	11	module	module	NOUN
ejpam-2366	898	12	m	m	NOUN
ejpam-2366	898	13	and	and	CCONJ
ejpam-2366	898	14	n	n	CCONJ
ejpam-2366	898	15	>	>	X
ejpam-2366	899	1	2	2	X
ejpam-2366	899	2	.	.	PUNCT
ejpam-2366	900	1	then	then	ADV
ejpam-2366	900	2	the	the	DET
ejpam-2366	900	3	following	following	ADJ
ejpam-2366	900	4	statements	statement	NOUN
ejpam-2366	900	5	are	be	AUX
ejpam-2366	900	6	equivalent	equivalent	ADJ
ejpam-2366	900	7	:	:	PUNCT
ejpam-2366	900	8	1	1	X
ejpam-2366	900	9	©	©	NOUN
ejpam-2366	900	10	n	n	NUM
ejpam-2366	900	11	is	be	AUX
ejpam-2366	900	12	a	a	DET
ejpam-2366	900	13	n	n	CCONJ
ejpam-2366	900	14	-	-	PUNCT
ejpam-2366	900	15	potent	potent	ADJ
ejpam-2366	900	16	prime	prime	ADJ
ejpam-2366	900	17	element	element	NOUN
ejpam-2366	900	18	of	of	ADP
ejpam-2366	900	19	m	m	PROPN
ejpam-2366	900	20	.	.	PUNCT
ejpam-2366	901	1	2	2	NUM
ejpam-2366	901	2	©	©	NOUN
ejpam-2366	901	3	(	(	PUNCT
ejpam-2366	901	4	n	n	NOUN
ejpam-2366	901	5	:	:	PUNCT
ejpam-2366	901	6	i	i	PRON
ejpam-2366	901	7	m	m	PROPN
ejpam-2366	901	8	)	)	PUNCT
ejpam-2366	901	9	is	be	AUX
ejpam-2366	901	10	a	a	DET
ejpam-2366	901	11	n	n	CCONJ
ejpam-2366	901	12	-	-	PUNCT
ejpam-2366	901	13	potent	potent	ADJ
ejpam-2366	901	14	prime	prime	ADJ
ejpam-2366	901	15	element	element	NOUN
ejpam-2366	901	16	of	of	ADP
ejpam-2366	901	17	l.	l.	PROPN
ejpam-2366	901	18	3	3	NUM
ejpam-2366	901	19	©	©	PROPN
ejpam-2366	901	20	n	n	NOUN
ejpam-2366	901	21	=	=	X
ejpam-2366	901	22	qim	qim	NOUN
ejpam-2366	901	23	for	for	ADP
ejpam-2366	901	24	some	some	DET
ejpam-2366	901	25	n	n	CCONJ
ejpam-2366	901	26	-	-	PUNCT
ejpam-2366	901	27	potent	potent	ADJ
ejpam-2366	901	28	prime	prime	ADJ
ejpam-2366	901	29	element	element	NOUN
ejpam-2366	901	30	q	q	PROPN
ejpam-2366	901	31	∈	∈	PROPN
ejpam-2366	901	32	l.	l.	PROPN
ejpam-2366	901	33	a.	a.	PROPN
ejpam-2366	901	34	v.	v.	PROPN
ejpam-2366	901	35	bingi	bingi	PROPN
ejpam-2366	901	36	,	,	PUNCT
ejpam-2366	901	37	c.	c.	PROPN
ejpam-2366	901	38	s.	s.	PROPN
ejpam-2366	901	39	manjarekar	manjarekar	PROPN
ejpam-2366	901	40	/	/	PROPN
ejpam-2366	901	41	eur	eur	PROPN
ejpam-2366	901	42	.	.	PUNCT
ejpam-2366	902	1	j.	j.	PROPN
ejpam-2366	902	2	pure	pure	PROPN
ejpam-2366	902	3	appl	appl	PROPN
ejpam-2366	902	4	.	.	PROPN
ejpam-2366	902	5	math	math	PROPN
ejpam-2366	902	6	,	,	PUNCT
ejpam-2366	902	7	14	14	NUM
ejpam-2366	902	8	(	(	PUNCT
ejpam-2366	902	9	2	2	NUM
ejpam-2366	902	10	)	)	PUNCT
ejpam-2366	902	11	(	(	PUNCT
ejpam-2366	902	12	2021	2021	NUM
ejpam-2366	902	13	)	)	PUNCT
ejpam-2366	902	14	,	,	PUNCT
ejpam-2366	902	15	551	551	NUM
ejpam-2366	902	16	-	-	SYM
ejpam-2366	902	17	577	577	NUM
ejpam-2366	902	18	575	575	NUM
ejpam-2366	902	19	proof	proof	NOUN
ejpam-2366	902	20	.	.	PUNCT
ejpam-2366	903	1	since	since	SCONJ
ejpam-2366	903	2	m	m	PROPN
ejpam-2366	903	3	is	be	AUX
ejpam-2366	903	4	a	a	DET
ejpam-2366	903	5	multiplication	multiplication	NOUN
ejpam-2366	903	6	lattice	lattice	NOUN
ejpam-2366	903	7	l	l	NOUN
ejpam-2366	903	8	-	-	NOUN
ejpam-2366	903	9	module	module	NOUN
ejpam-2366	903	10	,	,	PUNCT
ejpam-2366	903	11	by	by	ADP
ejpam-2366	903	12	proposition	proposition	NOUN
ejpam-2366	903	13	3	3	NUM
ejpam-2366	903	14	of	of	ADP
ejpam-2366	903	15	[	[	X
ejpam-2366	903	16	10	10	NUM
ejpam-2366	903	17	]	]	PUNCT
ejpam-2366	903	18	,	,	PUNCT
ejpam-2366	903	19	we	we	PRON
ejpam-2366	903	20	have	have	VERB
ejpam-2366	903	21	n	n	NOUN
ejpam-2366	903	22	=	=	SYM
ejpam-2366	903	23	(	(	PUNCT
ejpam-2366	903	24	n	n	X
ejpam-2366	903	25	:	:	PUNCT
ejpam-2366	903	26	i	i	PRON
ejpam-2366	903	27	m	m	VERB
ejpam-2366	903	28	)	)	PUNCT
ejpam-2366	903	29	i	i	PRON
ejpam-2366	903	30	m	m	VERB
ejpam-2366	903	31	.	.	PUNCT
ejpam-2366	904	1	1	1	NUM
ejpam-2366	904	2	©	©	NOUN
ejpam-2366	904	3	=⇒	=⇒	NOUN
ejpam-2366	904	4	2	2	NUM
ejpam-2366	904	5	©	©	NOUN
ejpam-2366	904	6	.	.	PUNCT
ejpam-2366	904	7	assume	assume	VERB
ejpam-2366	904	8	that	that	SCONJ
ejpam-2366	904	9	n	n	PRON
ejpam-2366	904	10	is	be	AUX
ejpam-2366	904	11	a	a	DET
ejpam-2366	904	12	n	n	CCONJ
ejpam-2366	904	13	-	-	PUNCT
ejpam-2366	904	14	potent	potent	ADJ
ejpam-2366	904	15	prime	prime	ADJ
ejpam-2366	904	16	element	element	NOUN
ejpam-2366	904	17	of	of	ADP
ejpam-2366	904	18	m	m	PROPN
ejpam-2366	904	19	.	.	PUNCT
ejpam-2366	905	1	let	let	VERB
ejpam-2366	905	2	ab	ab	PROPN
ejpam-2366	905	3	6	6	NUM
ejpam-2366	905	4	(	(	PUNCT
ejpam-2366	905	5	n	n	NUM
ejpam-2366	905	6	:	:	PUNCT
ejpam-2366	905	7	i	i	PRON
ejpam-2366	905	8	m	m	PROPN
ejpam-2366	905	9	)	)	PUNCT
ejpam-2366	905	10	n	n	PROPN
ejpam-2366	905	11	for	for	ADP
ejpam-2366	905	12	a	a	DET
ejpam-2366	905	13	,	,	PUNCT
ejpam-2366	905	14	b	b	PROPN
ejpam-2366	905	15	∈	∈	PROPN
ejpam-2366	905	16	l.	l.	NOUN
ejpam-2366	905	17	then	then	ADV
ejpam-2366	905	18	a(bim	a(bim	PROPN
ejpam-2366	905	19	)	)	PUNCT
ejpam-2366	905	20	6	6	NUM
ejpam-2366	905	21	(	(	PUNCT
ejpam-2366	905	22	n	n	NUM
ejpam-2366	905	23	:	:	PUNCT
ejpam-2366	905	24	i	i	PRON
ejpam-2366	905	25	m	m	NOUN
ejpam-2366	905	26	)	)	PUNCT
ejpam-2366	905	27	n−1n	n−1n	NOUN
ejpam-2366	905	28	.	.	PUNCT
ejpam-2366	906	1	as	as	SCONJ
ejpam-2366	906	2	n	n	NUM
ejpam-2366	906	3	is	be	AUX
ejpam-2366	906	4	n	n	ADV
ejpam-2366	906	5	-	-	PUNCT
ejpam-2366	906	6	potent	potent	ADJ
ejpam-2366	906	7	prime	prime	NOUN
ejpam-2366	906	8	,	,	PUNCT
ejpam-2366	906	9	we	we	PRON
ejpam-2366	906	10	have	have	VERB
ejpam-2366	906	11	either	either	CCONJ
ejpam-2366	906	12	a	a	DET
ejpam-2366	906	13	6	6	NUM
ejpam-2366	906	14	(	(	PUNCT
ejpam-2366	906	15	n	n	NUM
ejpam-2366	906	16	:	:	PUNCT
ejpam-2366	906	17	i	i	PRON
ejpam-2366	906	18	m	m	VERB
ejpam-2366	906	19	)	)	PUNCT
ejpam-2366	906	20	or	or	CCONJ
ejpam-2366	906	21	bim	bim	VERB
ejpam-2366	906	22	6	6	NUM
ejpam-2366	906	23	n	n	NOUN
ejpam-2366	906	24	and	and	CCONJ
ejpam-2366	906	25	thus	thus	ADV
ejpam-2366	906	26	(	(	PUNCT
ejpam-2366	906	27	n	n	X
ejpam-2366	906	28	:	:	PUNCT
ejpam-2366	906	29	i	i	PRON
ejpam-2366	906	30	m	m	PROPN
ejpam-2366	906	31	)	)	PUNCT
ejpam-2366	906	32	is	be	AUX
ejpam-2366	906	33	a	a	DET
ejpam-2366	906	34	n	n	CCONJ
ejpam-2366	906	35	-	-	PUNCT
ejpam-2366	906	36	potent	potent	ADJ
ejpam-2366	906	37	prime	prime	ADJ
ejpam-2366	906	38	element	element	NOUN
ejpam-2366	906	39	of	of	ADP
ejpam-2366	906	40	l.	l.	PROPN
ejpam-2366	906	41	2	2	NUM
ejpam-2366	906	42	©	©	PROPN
ejpam-2366	906	43	=⇒	=⇒	NOUN
ejpam-2366	906	44	1	1	NUM
ejpam-2366	906	45	©	©	PROPN
ejpam-2366	906	46	.	.	PUNCT
ejpam-2366	907	1	assume	assume	VERB
ejpam-2366	907	2	that	that	SCONJ
ejpam-2366	907	3	(	(	PUNCT
ejpam-2366	907	4	n	n	X
ejpam-2366	907	5	:	:	PUNCT
ejpam-2366	907	6	i	i	PRON
ejpam-2366	907	7	m	m	PROPN
ejpam-2366	907	8	)	)	PUNCT
ejpam-2366	907	9	is	be	AUX
ejpam-2366	907	10	a	a	DET
ejpam-2366	907	11	n	n	CCONJ
ejpam-2366	907	12	-	-	PUNCT
ejpam-2366	907	13	potent	potent	ADJ
ejpam-2366	907	14	prime	prime	ADJ
ejpam-2366	907	15	element	element	NOUN
ejpam-2366	907	16	of	of	ADP
ejpam-2366	907	17	l.	l.	PROPN
ejpam-2366	907	18	let	let	VERB
ejpam-2366	907	19	ax	ax	NOUN
ejpam-2366	907	20	6	6	NUM
ejpam-2366	907	21	(	(	PUNCT
ejpam-2366	907	22	n	n	NUM
ejpam-2366	907	23	:	:	PUNCT
ejpam-2366	907	24	i	i	PRON
ejpam-2366	907	25	m	m	PROPN
ejpam-2366	907	26	)	)	PUNCT
ejpam-2366	907	27	n−1n	n−1n	PROPN
ejpam-2366	907	28	for	for	ADP
ejpam-2366	907	29	a	a	DET
ejpam-2366	907	30	∈	∈	PROPN
ejpam-2366	907	31	l	l	NOUN
ejpam-2366	907	32	and	and	CCONJ
ejpam-2366	907	33	x	x	NOUN
ejpam-2366	907	34	∈m	∈m	NOUN
ejpam-2366	907	35	.	.	PUNCT
ejpam-2366	908	1	m	m	AUX
ejpam-2366	908	2	being	be	AUX
ejpam-2366	908	3	a	a	DET
ejpam-2366	908	4	multiplication	multiplication	NOUN
ejpam-2366	908	5	lattice	lattice	NOUN
ejpam-2366	908	6	l	l	NOUN
ejpam-2366	908	7	-	-	NOUN
ejpam-2366	908	8	module	module	NOUN
ejpam-2366	908	9	,	,	PUNCT
ejpam-2366	908	10	we	we	PRON
ejpam-2366	908	11	have	have	VERB
ejpam-2366	908	12	x	x	NOUN
ejpam-2366	908	13	=	=	SYM
ejpam-2366	908	14	cim	cim	NOUN
ejpam-2366	908	15	for	for	ADP
ejpam-2366	908	16	some	some	DET
ejpam-2366	908	17	c	c	PROPN
ejpam-2366	908	18	∈	∈	PROPN
ejpam-2366	908	19	l.	l.	PROPN
ejpam-2366	908	20	clearly	clearly	ADV
ejpam-2366	908	21	,	,	PUNCT
ejpam-2366	908	22	a(cim	a(cim	PROPN
ejpam-2366	908	23	)	)	PUNCT
ejpam-2366	908	24	6	6	NUM
ejpam-2366	908	25	(	(	PUNCT
ejpam-2366	908	26	n	n	NUM
ejpam-2366	908	27	:	:	PUNCT
ejpam-2366	908	28	i	i	PRON
ejpam-2366	908	29	m	m	VERB
ejpam-2366	908	30	)	)	PUNCT
ejpam-2366	908	31	nim	nim	PROPN
ejpam-2366	908	32	.	.	PUNCT
ejpam-2366	909	1	this	this	PRON
ejpam-2366	909	2	implies	imply	VERB
ejpam-2366	909	3	that	that	SCONJ
ejpam-2366	909	4	ac	ac	PROPN
ejpam-2366	909	5	6	6	NUM
ejpam-2366	909	6	(	(	PUNCT
ejpam-2366	909	7	n	n	NUM
ejpam-2366	909	8	:	:	PUNCT
ejpam-2366	909	9	i	i	PRON
ejpam-2366	909	10	m	m	PROPN
ejpam-2366	909	11	)	)	PUNCT
ejpam-2366	909	12	n	n	CCONJ
ejpam-2366	909	13	by	by	ADP
ejpam-2366	909	14	theorem	theorem	NOUN
ejpam-2366	909	15	5	5	NUM
ejpam-2366	909	16	of	of	ADP
ejpam-2366	909	17	[	[	X
ejpam-2366	909	18	10	10	NUM
ejpam-2366	909	19	]	]	PUNCT
ejpam-2366	909	20	.	.	PUNCT
ejpam-2366	910	1	as	as	ADP
ejpam-2366	910	2	(	(	PUNCT
ejpam-2366	910	3	n	n	X
ejpam-2366	910	4	:	:	PUNCT
ejpam-2366	910	5	i	i	PRON
ejpam-2366	910	6	m	m	PROPN
ejpam-2366	910	7	)	)	PUNCT
ejpam-2366	910	8	is	be	AUX
ejpam-2366	910	9	a	a	DET
ejpam-2366	910	10	n	n	CCONJ
ejpam-2366	910	11	-	-	PUNCT
ejpam-2366	910	12	potent	potent	ADJ
ejpam-2366	910	13	prime	prime	NOUN
ejpam-2366	910	14	,	,	PUNCT
ejpam-2366	910	15	we	we	PRON
ejpam-2366	910	16	have	have	VERB
ejpam-2366	910	17	either	either	CCONJ
ejpam-2366	910	18	a	a	DET
ejpam-2366	910	19	6	6	NUM
ejpam-2366	910	20	(	(	PUNCT
ejpam-2366	910	21	n	n	NUM
ejpam-2366	910	22	:	:	PUNCT
ejpam-2366	910	23	i	i	PRON
ejpam-2366	910	24	m	m	VERB
ejpam-2366	910	25	)	)	PUNCT
ejpam-2366	910	26	or	or	CCONJ
ejpam-2366	910	27	c	c	PROPN
ejpam-2366	910	28	6	6	NUM
ejpam-2366	910	29	(	(	PUNCT
ejpam-2366	910	30	n	n	NUM
ejpam-2366	910	31	:	:	PUNCT
ejpam-2366	910	32	i	i	PRON
ejpam-2366	910	33	m	m	VERB
ejpam-2366	910	34	)	)	PUNCT
ejpam-2366	910	35	which	which	PRON
ejpam-2366	910	36	implies	imply	VERB
ejpam-2366	910	37	either	either	CCONJ
ejpam-2366	910	38	a	a	DET
ejpam-2366	910	39	6	6	NUM
ejpam-2366	910	40	(	(	PUNCT
ejpam-2366	910	41	n	n	NUM
ejpam-2366	910	42	:	:	PUNCT
ejpam-2366	910	43	i	i	PRON
ejpam-2366	910	44	m	m	VERB
ejpam-2366	910	45	)	)	PUNCT
ejpam-2366	910	46	or	or	CCONJ
ejpam-2366	910	47	x	x	X
ejpam-2366	910	48	=	=	SYM
ejpam-2366	910	49	cim	cim	NOUN
ejpam-2366	910	50	6	6	NUM
ejpam-2366	910	51	(	(	PUNCT
ejpam-2366	910	52	n	n	NUM
ejpam-2366	910	53	:	:	PUNCT
ejpam-2366	910	54	i	i	PRON
ejpam-2366	910	55	m	m	VERB
ejpam-2366	910	56	)	)	PUNCT
ejpam-2366	911	1	i	i	PRON
ejpam-2366	911	2	m	m	VERB
ejpam-2366	911	3	=	=	SYM
ejpam-2366	911	4	n	n	PROPN
ejpam-2366	911	5	and	and	CCONJ
ejpam-2366	911	6	thus	thus	ADV
ejpam-2366	911	7	n	n	PRON
ejpam-2366	911	8	is	be	AUX
ejpam-2366	911	9	a	a	DET
ejpam-2366	911	10	n	n	CCONJ
ejpam-2366	911	11	-	-	PUNCT
ejpam-2366	911	12	potent	potent	ADJ
ejpam-2366	911	13	prime	prime	ADJ
ejpam-2366	911	14	element	element	NOUN
ejpam-2366	911	15	of	of	ADP
ejpam-2366	911	16	m	m	PROPN
ejpam-2366	911	17	.	.	PUNCT
ejpam-2366	912	1	2	2	NUM
ejpam-2366	912	2	©	©	NOUN
ejpam-2366	912	3	=⇒	=⇒	NOUN
ejpam-2366	912	4	3	3	NUM
ejpam-2366	912	5	©	©	NOUN
ejpam-2366	912	6	.	.	PUNCT
ejpam-2366	912	7	suppose	suppose	VERB
ejpam-2366	912	8	q	q	X
ejpam-2366	913	1	=	=	SYM
ejpam-2366	913	2	(	(	PUNCT
ejpam-2366	913	3	n	n	NOUN
ejpam-2366	913	4	:	:	PUNCT
ejpam-2366	913	5	i	i	PRON
ejpam-2366	913	6	m	m	PROPN
ejpam-2366	913	7	)	)	PUNCT
ejpam-2366	913	8	is	be	AUX
ejpam-2366	913	9	a	a	DET
ejpam-2366	913	10	n	n	CCONJ
ejpam-2366	913	11	-	-	PUNCT
ejpam-2366	913	12	potent	potent	ADJ
ejpam-2366	913	13	prime	prime	ADJ
ejpam-2366	913	14	element	element	NOUN
ejpam-2366	913	15	of	of	ADP
ejpam-2366	913	16	l.	l.	PROPN
ejpam-2366	913	17	since	since	SCONJ
ejpam-2366	913	18	m	m	PROPN
ejpam-2366	913	19	is	be	AUX
ejpam-2366	913	20	a	a	DET
ejpam-2366	913	21	multiplication	multiplication	NOUN
ejpam-2366	913	22	lattice	lattice	NOUN
ejpam-2366	913	23	l	l	NOUN
ejpam-2366	913	24	-	-	NOUN
ejpam-2366	913	25	module	module	NOUN
ejpam-2366	913	26	,	,	PUNCT
ejpam-2366	913	27	n	n	NOUN
ejpam-2366	913	28	=	=	SYM
ejpam-2366	913	29	(	(	PUNCT
ejpam-2366	913	30	n	n	X
ejpam-2366	913	31	:	:	PUNCT
ejpam-2366	913	32	i	i	PRON
ejpam-2366	913	33	m	m	VERB
ejpam-2366	913	34	)	)	PUNCT
ejpam-2366	914	1	i	i	PRON
ejpam-2366	914	2	m	m	VERB
ejpam-2366	914	3	=	=	ADJ
ejpam-2366	914	4	qim	qim	NOUN
ejpam-2366	914	5	and	and	CCONJ
ejpam-2366	914	6	hence	hence	ADV
ejpam-2366	914	7	3	3	NUM
ejpam-2366	914	8	©	©	PROPN
ejpam-2366	914	9	holds	hold	NOUN
ejpam-2366	914	10	.	.	PUNCT
ejpam-2366	915	1	3	3	NUM
ejpam-2366	915	2	©	©	NOUN
ejpam-2366	915	3	=⇒	=⇒	NOUN
ejpam-2366	915	4	2	2	NUM
ejpam-2366	915	5	©	©	NOUN
ejpam-2366	915	6	.	.	PUNCT
ejpam-2366	915	7	suppose	suppose	VERB
ejpam-2366	915	8	n	n	PROPN
ejpam-2366	915	9	=	=	PUNCT
ejpam-2366	915	10	qim	qim	NOUN
ejpam-2366	915	11	for	for	ADP
ejpam-2366	915	12	some	some	DET
ejpam-2366	915	13	n	n	CCONJ
ejpam-2366	915	14	-	-	PUNCT
ejpam-2366	915	15	potent	potent	ADJ
ejpam-2366	915	16	prime	prime	ADJ
ejpam-2366	915	17	element	element	NOUN
ejpam-2366	915	18	q	q	PROPN
ejpam-2366	915	19	∈	∈	PROPN
ejpam-2366	915	20	l.	l.	NOUN
ejpam-2366	915	21	as	as	SCONJ
ejpam-2366	915	22	m	m	PROPN
ejpam-2366	915	23	is	be	AUX
ejpam-2366	915	24	a	a	DET
ejpam-2366	915	25	multiplication	multiplication	NOUN
ejpam-2366	915	26	lattice	lattice	NOUN
ejpam-2366	915	27	l	l	NOUN
ejpam-2366	915	28	-	-	NOUN
ejpam-2366	915	29	module	module	NOUN
ejpam-2366	915	30	,	,	PUNCT
ejpam-2366	915	31	n	n	NOUN
ejpam-2366	915	32	=	=	SYM
ejpam-2366	915	33	(	(	PUNCT
ejpam-2366	915	34	n	n	X
ejpam-2366	915	35	:	:	PUNCT
ejpam-2366	915	36	i	i	PRON
ejpam-2366	915	37	m	m	VERB
ejpam-2366	915	38	)	)	PUNCT
ejpam-2366	916	1	i	i	PRON
ejpam-2366	916	2	m	m	VERB
ejpam-2366	916	3	.	.	PUNCT
ejpam-2366	917	1	since	since	SCONJ
ejpam-2366	917	2	i	i	PRON
ejpam-2366	917	3	m	m	VERB
ejpam-2366	917	4	is	be	AUX
ejpam-2366	917	5	compact	compact	ADJ
ejpam-2366	917	6	,	,	PUNCT
ejpam-2366	917	7	2	2	NUM
ejpam-2366	917	8	©	©	PROPN
ejpam-2366	917	9	holds	hold	NOUN
ejpam-2366	917	10	by	by	ADP
ejpam-2366	917	11	theorem	theorem	NOUN
ejpam-2366	917	12	5	5	NUM
ejpam-2366	917	13	of	of	ADP
ejpam-2366	917	14	[	[	X
ejpam-2366	917	15	10	10	NUM
ejpam-2366	917	16	]	]	PUNCT
ejpam-2366	917	17	.	.	PUNCT
ejpam-2366	918	1	theorem	theorem	VERB
ejpam-2366	918	2	52	52	NUM
ejpam-2366	918	3	.	.	PUNCT
ejpam-2366	919	1	let	let	VERB
ejpam-2366	919	2	l	l	NOUN
ejpam-2366	919	3	be	be	AUX
ejpam-2366	919	4	a	a	DET
ejpam-2366	919	5	pg	pg	NOUN
ejpam-2366	919	6	-	-	PUNCT
ejpam-2366	919	7	lattice	lattice	NOUN
ejpam-2366	919	8	and	and	CCONJ
ejpam-2366	919	9	m	m	AUX
ejpam-2366	919	10	be	be	AUX
ejpam-2366	919	11	a	a	DET
ejpam-2366	919	12	faithful	faithful	ADJ
ejpam-2366	919	13	multiplication	multiplication	NOUN
ejpam-2366	919	14	pg	pg	ADJ
ejpam-2366	919	15	-	-	PUNCT
ejpam-2366	919	16	lattice	lattice	NOUN
ejpam-2366	919	17	lmodule	lmodule	NOUN
ejpam-2366	919	18	with	with	ADP
ejpam-2366	919	19	i	i	PRON
ejpam-2366	919	20	m	m	VERB
ejpam-2366	919	21	compact	compact	ADJ
ejpam-2366	919	22	.	.	PUNCT
ejpam-2366	920	1	let	let	VERB
ejpam-2366	920	2	n	n	PRON
ejpam-2366	920	3	be	be	AUX
ejpam-2366	920	4	a	a	DET
ejpam-2366	920	5	proper	proper	ADJ
ejpam-2366	920	6	element	element	NOUN
ejpam-2366	920	7	of	of	ADP
ejpam-2366	920	8	an	an	DET
ejpam-2366	920	9	l	l	NOUN
ejpam-2366	920	10	-	-	NOUN
ejpam-2366	920	11	module	module	NOUN
ejpam-2366	920	12	m	m	NOUN
ejpam-2366	920	13	and	and	CCONJ
ejpam-2366	920	14	n	n	CCONJ
ejpam-2366	920	15	>	>	X
ejpam-2366	921	1	2	2	X
ejpam-2366	921	2	.	.	PUNCT
ejpam-2366	922	1	then	then	ADV
ejpam-2366	922	2	the	the	DET
ejpam-2366	922	3	following	following	ADJ
ejpam-2366	922	4	statements	statement	NOUN
ejpam-2366	922	5	are	be	AUX
ejpam-2366	922	6	equivalent	equivalent	ADJ
ejpam-2366	922	7	:	:	PUNCT
ejpam-2366	922	8	1	1	X
ejpam-2366	922	9	©	©	NOUN
ejpam-2366	922	10	n	n	NUM
ejpam-2366	922	11	is	be	AUX
ejpam-2366	922	12	a	a	DET
ejpam-2366	922	13	n	n	CCONJ
ejpam-2366	922	14	-	-	PUNCT
ejpam-2366	922	15	potent	potent	ADJ
ejpam-2366	922	16	primary	primary	ADJ
ejpam-2366	922	17	element	element	NOUN
ejpam-2366	922	18	of	of	ADP
ejpam-2366	922	19	m	m	PROPN
ejpam-2366	922	20	.	.	PUNCT
ejpam-2366	923	1	2	2	NUM
ejpam-2366	923	2	©	©	NOUN
ejpam-2366	923	3	(	(	PUNCT
ejpam-2366	923	4	n	n	NOUN
ejpam-2366	923	5	:	:	PUNCT
ejpam-2366	923	6	i	i	PRON
ejpam-2366	923	7	m	m	PROPN
ejpam-2366	923	8	)	)	PUNCT
ejpam-2366	923	9	is	be	AUX
ejpam-2366	923	10	a	a	DET
ejpam-2366	923	11	n	n	CCONJ
ejpam-2366	923	12	-	-	PUNCT
ejpam-2366	923	13	potent	potent	ADJ
ejpam-2366	923	14	primary	primary	ADJ
ejpam-2366	923	15	element	element	NOUN
ejpam-2366	923	16	of	of	ADP
ejpam-2366	923	17	l.	l.	PROPN
ejpam-2366	923	18	3	3	NUM
ejpam-2366	923	19	©	©	PROPN
ejpam-2366	923	20	n	n	NOUN
ejpam-2366	923	21	=	=	X
ejpam-2366	923	22	qim	qim	NOUN
ejpam-2366	923	23	for	for	ADP
ejpam-2366	923	24	some	some	DET
ejpam-2366	923	25	n	n	CCONJ
ejpam-2366	923	26	-	-	PUNCT
ejpam-2366	923	27	potent	potent	ADJ
ejpam-2366	923	28	primary	primary	ADJ
ejpam-2366	923	29	element	element	NOUN
ejpam-2366	923	30	q	q	PROPN
ejpam-2366	923	31	∈	∈	PROPN
ejpam-2366	923	32	l.	l.	NOUN
ejpam-2366	923	33	proof	proof	NOUN
ejpam-2366	923	34	.	.	PUNCT
ejpam-2366	924	1	just	just	ADV
ejpam-2366	924	2	mimic	mimic	VERB
ejpam-2366	924	3	the	the	DET
ejpam-2366	924	4	proof	proof	NOUN
ejpam-2366	924	5	of	of	ADP
ejpam-2366	924	6	theorem	theorem	NOUN
ejpam-2366	924	7	51	51	NUM
ejpam-2366	924	8	.	.	PUNCT
ejpam-2366	925	1	we	we	PRON
ejpam-2366	925	2	conclude	conclude	VERB
ejpam-2366	925	3	this	this	DET
ejpam-2366	925	4	paper	paper	NOUN
ejpam-2366	925	5	with	with	ADP
ejpam-2366	925	6	following	follow	VERB
ejpam-2366	925	7	2	2	NUM
ejpam-2366	925	8	results	result	NOUN
ejpam-2366	925	9	which	which	PRON
ejpam-2366	925	10	are	be	AUX
ejpam-2366	925	11	outcomes	outcome	NOUN
ejpam-2366	925	12	of	of	ADP
ejpam-2366	925	13	theorems	theorem	NOUN
ejpam-2366	925	14	51	51	NUM
ejpam-2366	925	15	and	and	CCONJ
ejpam-2366	925	16	52	52	NUM
ejpam-2366	925	17	,	,	PUNCT
ejpam-2366	925	18	respectively	respectively	ADV
ejpam-2366	925	19	.	.	PUNCT
ejpam-2366	926	1	corollary	corollary	ADJ
ejpam-2366	926	2	21	21	NUM
ejpam-2366	926	3	.	.	PUNCT
ejpam-2366	927	1	let	let	VERB
ejpam-2366	927	2	l	l	NOUN
ejpam-2366	927	3	be	be	AUX
ejpam-2366	927	4	a	a	DET
ejpam-2366	927	5	pg	pg	NOUN
ejpam-2366	927	6	-	-	PUNCT
ejpam-2366	927	7	lattice	lattice	NOUN
ejpam-2366	927	8	and	and	CCONJ
ejpam-2366	927	9	m	m	AUX
ejpam-2366	927	10	be	be	AUX
ejpam-2366	927	11	a	a	DET
ejpam-2366	927	12	faithful	faithful	ADJ
ejpam-2366	927	13	multiplication	multiplication	NOUN
ejpam-2366	927	14	pg	pg	ADJ
ejpam-2366	927	15	-	-	PUNCT
ejpam-2366	927	16	lattice	lattice	NOUN
ejpam-2366	927	17	lmodule	lmodule	NOUN
ejpam-2366	927	18	with	with	ADP
ejpam-2366	927	19	i	i	PROPN
ejpam-2366	927	20	m	m	VERB
ejpam-2366	927	21	compact	compact	ADJ
ejpam-2366	927	22	.	.	PUNCT
ejpam-2366	928	1	then	then	ADV
ejpam-2366	928	2	a	a	DET
ejpam-2366	928	3	proper	proper	ADJ
ejpam-2366	928	4	element	element	NOUN
ejpam-2366	928	5	n	n	PROPN
ejpam-2366	928	6	of	of	ADP
ejpam-2366	928	7	an	an	DET
ejpam-2366	928	8	l	l	NOUN
ejpam-2366	928	9	-	-	NOUN
ejpam-2366	928	10	module	module	NOUN
ejpam-2366	928	11	m	m	NOUN
ejpam-2366	928	12	is	be	AUX
ejpam-2366	928	13	2	2	NUM
ejpam-2366	928	14	-	-	PUNCT
ejpam-2366	928	15	potent	potent	ADJ
ejpam-2366	928	16	prime	prime	NOUN
ejpam-2366	928	17	if	if	SCONJ
ejpam-2366	928	18	and	and	CCONJ
ejpam-2366	928	19	only	only	ADV
ejpam-2366	928	20	if	if	SCONJ
ejpam-2366	928	21	(	(	PUNCT
ejpam-2366	928	22	n	n	X
ejpam-2366	928	23	:	:	PUNCT
ejpam-2366	928	24	i	i	PRON
ejpam-2366	928	25	m	m	PROPN
ejpam-2366	928	26	)	)	PUNCT
ejpam-2366	928	27	is	be	AUX
ejpam-2366	928	28	a	a	DET
ejpam-2366	928	29	2	2	NUM
ejpam-2366	928	30	-	-	PUNCT
ejpam-2366	928	31	potent	potent	ADJ
ejpam-2366	928	32	prime	prime	ADJ
ejpam-2366	928	33	element	element	NOUN
ejpam-2366	928	34	of	of	ADP
ejpam-2366	928	35	l.	l.	PROPN
ejpam-2366	928	36	corollary	corollary	PROPN
ejpam-2366	928	37	22	22	PROPN
ejpam-2366	928	38	.	.	PUNCT
ejpam-2366	929	1	let	let	VERB
ejpam-2366	929	2	l	l	NOUN
ejpam-2366	929	3	be	be	AUX
ejpam-2366	929	4	a	a	DET
ejpam-2366	929	5	pg	pg	NOUN
ejpam-2366	929	6	-	-	PUNCT
ejpam-2366	929	7	lattice	lattice	NOUN
ejpam-2366	929	8	and	and	CCONJ
ejpam-2366	929	9	m	m	AUX
ejpam-2366	929	10	be	be	AUX
ejpam-2366	929	11	a	a	DET
ejpam-2366	929	12	faithful	faithful	ADJ
ejpam-2366	929	13	multiplication	multiplication	NOUN
ejpam-2366	929	14	pg	pg	ADJ
ejpam-2366	929	15	-	-	PUNCT
ejpam-2366	929	16	lattice	lattice	NOUN
ejpam-2366	929	17	lmodule	lmodule	NOUN
ejpam-2366	929	18	with	with	ADP
ejpam-2366	929	19	i	i	PROPN
ejpam-2366	929	20	m	m	VERB
ejpam-2366	929	21	compact	compact	ADJ
ejpam-2366	929	22	.	.	PUNCT
ejpam-2366	930	1	then	then	ADV
ejpam-2366	930	2	a	a	DET
ejpam-2366	930	3	proper	proper	ADJ
ejpam-2366	930	4	element	element	NOUN
ejpam-2366	930	5	n	n	PROPN
ejpam-2366	930	6	of	of	ADP
ejpam-2366	930	7	an	an	DET
ejpam-2366	930	8	l	l	NOUN
ejpam-2366	930	9	-	-	NOUN
ejpam-2366	930	10	module	module	NOUN
ejpam-2366	930	11	m	m	NOUN
ejpam-2366	930	12	is	be	AUX
ejpam-2366	930	13	2	2	NUM
ejpam-2366	930	14	-	-	PUNCT
ejpam-2366	930	15	potent	potent	ADJ
ejpam-2366	930	16	primary	primary	NOUN
ejpam-2366	930	17	if	if	SCONJ
ejpam-2366	930	18	and	and	CCONJ
ejpam-2366	930	19	only	only	ADV
ejpam-2366	930	20	if	if	SCONJ
ejpam-2366	930	21	(	(	PUNCT
ejpam-2366	930	22	n	n	X
ejpam-2366	930	23	:	:	PUNCT
ejpam-2366	930	24	i	i	PRON
ejpam-2366	930	25	m	m	PROPN
ejpam-2366	930	26	)	)	PUNCT
ejpam-2366	930	27	is	be	AUX
ejpam-2366	930	28	a	a	DET
ejpam-2366	930	29	2	2	NUM
ejpam-2366	930	30	-	-	PUNCT
ejpam-2366	930	31	potent	potent	ADJ
ejpam-2366	930	32	primary	primary	ADJ
ejpam-2366	930	33	element	element	NOUN
ejpam-2366	930	34	of	of	ADP
ejpam-2366	930	35	l.	l.	PROPN
ejpam-2366	930	36	note	note	PROPN
ejpam-2366	930	37	:	:	PUNCT
ejpam-2366	930	38	this	this	DET
ejpam-2366	930	39	paper	paper	NOUN
ejpam-2366	930	40	is	be	AUX
ejpam-2366	930	41	a	a	DET
ejpam-2366	930	42	part	part	NOUN
ejpam-2366	930	43	of	of	ADP
ejpam-2366	930	44	the	the	DET
ejpam-2366	930	45	first	first	ADJ
ejpam-2366	930	46	author	author	NOUN
ejpam-2366	930	47	’s	’s	PART
ejpam-2366	930	48	ph.d	ph.d	PROPN
ejpam-2366	930	49	.	.	PUNCT
ejpam-2366	931	1	thesis	thesis	NOUN
ejpam-2366	931	2	,	,	PUNCT
ejpam-2366	931	3	submitted	submit	VERB
ejpam-2366	931	4	in	in	ADP
ejpam-2366	931	5	2015	2015	NUM
ejpam-2366	931	6	to	to	ADP
ejpam-2366	931	7	shivaji	shivaji	PROPN
ejpam-2366	931	8	university	university	PROPN
ejpam-2366	931	9	,	,	PUNCT
ejpam-2366	931	10	kolhapur	kolhapur	PROPN
ejpam-2366	931	11	,	,	PUNCT
ejpam-2366	931	12	maharashtra	maharashtra	PROPN
ejpam-2366	931	13	,	,	PUNCT
ejpam-2366	931	14	india	india	PROPN
ejpam-2366	931	15	.	.	PUNCT
ejpam-2366	931	16	references	reference	VERB
ejpam-2366	931	17	576	576	NUM
ejpam-2366	931	18	acknowledgements	acknowledgement	NOUN
ejpam-2366	931	19	the	the	DET
ejpam-2366	931	20	authors	author	NOUN
ejpam-2366	931	21	wish	wish	VERB
ejpam-2366	931	22	to	to	PART
ejpam-2366	931	23	thank	thank	VERB
ejpam-2366	931	24	the	the	DET
ejpam-2366	931	25	referee	referee	NOUN
ejpam-2366	931	26	for	for	ADP
ejpam-2366	931	27	his	his	PRON
ejpam-2366	931	28	assistance	assistance	NOUN
ejpam-2366	931	29	in	in	ADP
ejpam-2366	931	30	making	make	VERB
ejpam-2366	931	31	this	this	DET
ejpam-2366	931	32	paper	paper	NOUN
ejpam-2366	931	33	accessible	accessible	ADJ
ejpam-2366	931	34	to	to	ADP
ejpam-2366	931	35	a	a	DET
ejpam-2366	931	36	broader	broad	ADJ
ejpam-2366	931	37	audience	audience	NOUN
ejpam-2366	931	38	.	.	PUNCT
ejpam-2366	932	1	references	reference	NOUN
ejpam-2366	932	2	[	[	X
ejpam-2366	932	3	1	1	NUM
ejpam-2366	932	4	]	]	PUNCT
ejpam-2366	932	5	eaman	eaman	NOUN
ejpam-2366	932	6	a	a	DET
ejpam-2366	932	7	al	al	PROPN
ejpam-2366	932	8	-	-	PUNCT
ejpam-2366	932	9	khouja	khouja	PROPN
ejpam-2366	932	10	.	.	PUNCT
ejpam-2366	933	1	maximal	maximal	ADJ
ejpam-2366	933	2	elements	element	NOUN
ejpam-2366	933	3	and	and	CCONJ
ejpam-2366	933	4	prime	prime	ADJ
ejpam-2366	933	5	elements	element	NOUN
ejpam-2366	933	6	in	in	ADP
ejpam-2366	933	7	lattice	lattice	NOUN
ejpam-2366	933	8	modules	module	NOUN
ejpam-2366	933	9	.	.	PUNCT
ejpam-2366	934	1	damascus	damascus	PROPN
ejpam-2366	934	2	university	university	PROPN
ejpam-2366	934	3	for	for	ADP
ejpam-2366	934	4	basic	basic	ADJ
ejpam-2366	934	5	sciences	science	NOUN
ejpam-2366	934	6	,	,	PUNCT
ejpam-2366	934	7	19(2):9–20	19(2):9–20	NUM
ejpam-2366	934	8	,	,	PUNCT
ejpam-2366	934	9	2003	2003	NUM
ejpam-2366	934	10	.	.	PUNCT
ejpam-2366	935	1	[	[	X
ejpam-2366	935	2	2	2	NUM
ejpam-2366	935	3	]	]	SYM
ejpam-2366	935	4	francisco	francisco	PROPN
ejpam-2366	935	5	alarcon	alarcon	PROPN
ejpam-2366	935	6	,	,	PUNCT
ejpam-2366	935	7	dd	dd	PROPN
ejpam-2366	935	8	anderson	anderson	PROPN
ejpam-2366	935	9	,	,	PUNCT
ejpam-2366	935	10	and	and	CCONJ
ejpam-2366	935	11	c	c	PROPN
ejpam-2366	935	12	jayaram	jayaram	PROPN
ejpam-2366	935	13	.	.	PUNCT
ejpam-2366	936	1	some	some	DET
ejpam-2366	936	2	results	result	NOUN
ejpam-2366	936	3	on	on	ADP
ejpam-2366	936	4	abstract	abstract	ADJ
ejpam-2366	936	5	commutative	commutative	ADJ
ejpam-2366	936	6	ideal	ideal	PROPN
ejpam-2366	936	7	theory	theory	NOUN
ejpam-2366	936	8	.	.	PUNCT
ejpam-2366	937	1	periodica	periodica	PROPN
ejpam-2366	937	2	mathematica	mathematica	PROPN
ejpam-2366	937	3	hungarica	hungarica	PROPN
ejpam-2366	937	4	,	,	PUNCT
ejpam-2366	937	5	30(1):1–26	30(1):1–26	PROPN
ejpam-2366	937	6	,	,	PUNCT
ejpam-2366	937	7	1995	1995	NUM
ejpam-2366	937	8	.	.	PUNCT
ejpam-2366	938	1	[	[	X
ejpam-2366	938	2	3	3	X
ejpam-2366	938	3	]	]	X
ejpam-2366	938	4	dd	dd	PROPN
ejpam-2366	938	5	anderson	anderson	PROPN
ejpam-2366	938	6	.	.	PUNCT
ejpam-2366	939	1	abstract	abstract	PROPN
ejpam-2366	939	2	commutative	commutative	ADJ
ejpam-2366	939	3	ideal	ideal	PROPN
ejpam-2366	939	4	theory	theory	NOUN
ejpam-2366	939	5	without	without	ADP
ejpam-2366	939	6	chain	chain	NOUN
ejpam-2366	939	7	condition	condition	NOUN
ejpam-2366	939	8	.	.	PUNCT
ejpam-2366	940	1	algebra	algebra	NOUN
ejpam-2366	940	2	universalis	universali	VERB
ejpam-2366	940	3	,	,	PUNCT
ejpam-2366	940	4	6(2):131–145	6(2):131–145	NUM
ejpam-2366	940	5	,	,	PUNCT
ejpam-2366	940	6	1976	1976	NUM
ejpam-2366	940	7	.	.	PUNCT
ejpam-2366	941	1	[	[	X
ejpam-2366	941	2	4	4	NUM
ejpam-2366	941	3	]	]	X
ejpam-2366	941	4	sachin	sachin	ADJ
ejpam-2366	941	5	ballal	ballal	PROPN
ejpam-2366	941	6	,	,	PUNCT
ejpam-2366	941	7	machchhindra	machchhindra	PROPN
ejpam-2366	941	8	gophane	gophane	PROPN
ejpam-2366	941	9	,	,	PUNCT
ejpam-2366	941	10	and	and	CCONJ
ejpam-2366	941	11	vilas	vilas	PROPN
ejpam-2366	941	12	kharat	kharat	PROPN
ejpam-2366	941	13	.	.	PUNCT
ejpam-2366	942	1	on	on	ADP
ejpam-2366	942	2	weakly	weakly	ADJ
ejpam-2366	942	3	primary	primary	ADJ
ejpam-2366	942	4	elements	element	NOUN
ejpam-2366	942	5	in	in	ADP
ejpam-2366	942	6	multiplicative	multiplicative	ADJ
ejpam-2366	942	7	lattices	lattice	NOUN
ejpam-2366	942	8	.	.	PUNCT
ejpam-2366	943	1	southeast	southeast	ADJ
ejpam-2366	943	2	asian	asian	ADJ
ejpam-2366	943	3	bulletin	bulletin	NOUN
ejpam-2366	943	4	of	of	ADP
ejpam-2366	943	5	mathematics	mathematic	NOUN
ejpam-2366	943	6	,	,	PUNCT
ejpam-2366	943	7	40(1):439	40(1):439	NOUN
ejpam-2366	943	8	–	–	PUNCT
ejpam-2366	943	9	449	449	NUM
ejpam-2366	943	10	,	,	PUNCT
ejpam-2366	943	11	2016	2016	NUM
ejpam-2366	943	12	.	.	PUNCT
ejpam-2366	944	1	[	[	X
ejpam-2366	944	2	5	5	NUM
ejpam-2366	944	3	]	]	X
ejpam-2366	944	4	sachin	sachin	ADJ
ejpam-2366	944	5	ballal	ballal	PROPN
ejpam-2366	944	6	and	and	CCONJ
ejpam-2366	944	7	vilas	vilas	PROPN
ejpam-2366	944	8	kharat	kharat	PROPN
ejpam-2366	944	9	.	.	PUNCT
ejpam-2366	945	1	on	on	ADP
ejpam-2366	945	2	generalization	generalization	NOUN
ejpam-2366	945	3	of	of	ADP
ejpam-2366	945	4	prime	prime	ADJ
ejpam-2366	945	5	,	,	PUNCT
ejpam-2366	945	6	weakly	weakly	ADJ
ejpam-2366	945	7	prime	prime	NOUN
ejpam-2366	945	8	and	and	CCONJ
ejpam-2366	945	9	almost	almost	ADV
ejpam-2366	945	10	prime	prime	ADJ
ejpam-2366	945	11	elements	element	NOUN
ejpam-2366	945	12	in	in	ADP
ejpam-2366	945	13	multiplicative	multiplicative	ADJ
ejpam-2366	945	14	lattices	lattice	NOUN
ejpam-2366	945	15	.	.	PUNCT
ejpam-2366	946	1	int	int	NOUN
ejpam-2366	946	2	.	.	PUNCT
ejpam-2366	947	1	j.	j.	PROPN
ejpam-2366	947	2	algebra	algebra	PROPN
ejpam-2366	947	3	,	,	PUNCT
ejpam-2366	947	4	8(9):439–449	8(9):439–449	NOUN
ejpam-2366	947	5	,	,	PUNCT
ejpam-2366	947	6	2014	2014	NUM
ejpam-2366	947	7	.	.	PUNCT
ejpam-2366	948	1	[	[	X
ejpam-2366	948	2	6	6	NUM
ejpam-2366	948	3	]	]	X
ejpam-2366	948	4	sachin	sachin	PROPN
ejpam-2366	948	5	ballal	ballal	PROPN
ejpam-2366	948	6	and	and	CCONJ
ejpam-2366	948	7	vilas	vilas	PROPN
ejpam-2366	948	8	kharat	kharat	PROPN
ejpam-2366	948	9	.	.	PUNCT
ejpam-2366	949	1	on	on	ADP
ejpam-2366	949	2	φ	φ	VERB
ejpam-2366	949	3	-	-	ADJ
ejpam-2366	949	4	absorbing	absorbing	ADJ
ejpam-2366	949	5	primary	primary	ADJ
ejpam-2366	949	6	elements	element	NOUN
ejpam-2366	949	7	in	in	ADP
ejpam-2366	949	8	lattice	lattice	NOUN
ejpam-2366	949	9	modules	module	NOUN
ejpam-2366	949	10	.	.	PUNCT
ejpam-2366	950	1	algebra	algebra	NOUN
ejpam-2366	950	2	,	,	PUNCT
ejpam-2366	950	3	2015:1–6	2015:1–6	PROPN
ejpam-2366	950	4	,	,	PUNCT
ejpam-2366	950	5	2015	2015	NUM
ejpam-2366	950	6	.	.	PUNCT
ejpam-2366	951	1	[	[	X
ejpam-2366	951	2	7	7	X
ejpam-2366	951	3	]	]	X
ejpam-2366	951	4	malik	malik	PROPN
ejpam-2366	951	5	bataineh	bataineh	PROPN
ejpam-2366	951	6	and	and	CCONJ
ejpam-2366	951	7	s	s	VERB
ejpam-2366	951	8	kuhail	kuhail	NOUN
ejpam-2366	951	9	.	.	PUNCT
ejpam-2366	952	1	generalizations	generalization	NOUN
ejpam-2366	952	2	of	of	ADP
ejpam-2366	952	3	primary	primary	ADJ
ejpam-2366	952	4	ideals	ideal	NOUN
ejpam-2366	952	5	and	and	CCONJ
ejpam-2366	952	6	submodules	submodule	NOUN
ejpam-2366	952	7	.	.	PUNCT
ejpam-2366	953	1	international	international	ADJ
ejpam-2366	953	2	journal	journal	PROPN
ejpam-2366	953	3	of	of	ADP
ejpam-2366	953	4	contemporary	contemporary	PROPN
ejpam-2366	953	5	mathematical	mathematical	PROPN
ejpam-2366	953	6	sciences	sciences	PROPN
ejpam-2366	953	7	,	,	PUNCT
ejpam-2366	953	8	6(17):811–824	6(17):811–824	NUM
ejpam-2366	953	9	,	,	PUNCT
ejpam-2366	953	10	2011	2011	NUM
ejpam-2366	953	11	.	.	PUNCT
ejpam-2366	954	1	[	[	X
ejpam-2366	954	2	8	8	NUM
ejpam-2366	954	3	]	]	X
ejpam-2366	954	4	ashok	ashok	NOUN
ejpam-2366	954	5	v	v	ADP
ejpam-2366	954	6	bingi	bingi	PROPN
ejpam-2366	954	7	and	and	CCONJ
ejpam-2366	954	8	cs	cs	PROPN
ejpam-2366	954	9	manjarekar	manjarekar	NOUN
ejpam-2366	954	10	.	.	PUNCT
ejpam-2366	955	1	weakly	weakly	ADJ
ejpam-2366	955	2	prime	prime	ADJ
ejpam-2366	955	3	and	and	CCONJ
ejpam-2366	955	4	weakly	weakly	ADJ
ejpam-2366	955	5	primary	primary	ADJ
ejpam-2366	955	6	elements	element	NOUN
ejpam-2366	955	7	in	in	ADP
ejpam-2366	955	8	multiplication	multiplication	NOUN
ejpam-2366	955	9	lattice	lattice	NOUN
ejpam-2366	955	10	modules	module	NOUN
ejpam-2366	955	11	.	.	PUNCT
ejpam-2366	956	1	(	(	PUNCT
ejpam-2366	956	2	to	to	PART
ejpam-2366	956	3	appear	appear	VERB
ejpam-2366	956	4	)	)	PUNCT
ejpam-2366	956	5	.	.	PUNCT
ejpam-2366	957	1	[	[	X
ejpam-2366	957	2	9	9	NUM
ejpam-2366	957	3	]	]	X
ejpam-2366	957	4	fethi	fethi	ADJ
ejpam-2366	957	5	çallıalp	çallıalp	PROPN
ejpam-2366	957	6	,	,	PUNCT
ejpam-2366	957	7	c	c	PROPN
ejpam-2366	957	8	jayaram	jayaram	PROPN
ejpam-2366	957	9	,	,	PUNCT
ejpam-2366	957	10	and	and	CCONJ
ejpam-2366	957	11	ünsal	ünsal	PROPN
ejpam-2366	957	12	tekir	tekir	NOUN
ejpam-2366	957	13	.	.	PUNCT
ejpam-2366	958	1	weakly	weakly	ADJ
ejpam-2366	958	2	prime	prime	ADJ
ejpam-2366	958	3	elements	element	NOUN
ejpam-2366	958	4	in	in	ADP
ejpam-2366	958	5	multiplicative	multiplicative	ADJ
ejpam-2366	958	6	lattices	lattice	NOUN
ejpam-2366	958	7	.	.	PUNCT
ejpam-2366	959	1	communications	communication	NOUN
ejpam-2366	959	2	in	in	ADP
ejpam-2366	959	3	algebra	algebra	NOUN
ejpam-2366	959	4	,	,	PUNCT
ejpam-2366	959	5	40(8):2825–2840	40(8):2825–2840	NUM
ejpam-2366	959	6	,	,	PUNCT
ejpam-2366	959	7	2012	2012	NUM
ejpam-2366	959	8	.	.	PUNCT
ejpam-2366	960	1	[	[	X
ejpam-2366	960	2	10	10	NUM
ejpam-2366	960	3	]	]	X
ejpam-2366	960	4	fethi	fethi	ADJ
ejpam-2366	960	5	çallıalp	çallıalp	NOUN
ejpam-2366	960	6	and	and	CCONJ
ejpam-2366	960	7	ünsal	ünsal	PROPN
ejpam-2366	960	8	tekir	tekir	NOUN
ejpam-2366	960	9	.	.	PUNCT
ejpam-2366	961	1	multiplication	multiplication	NOUN
ejpam-2366	961	2	lattice	lattice	NOUN
ejpam-2366	961	3	modules	module	NOUN
ejpam-2366	961	4	.	.	PUNCT
ejpam-2366	962	1	iranian	iranian	ADJ
ejpam-2366	962	2	journal	journal	PROPN
ejpam-2366	962	3	of	of	ADP
ejpam-2366	962	4	science	science	NOUN
ejpam-2366	962	5	and	and	CCONJ
ejpam-2366	962	6	technology	technology	NOUN
ejpam-2366	962	7	,	,	PUNCT
ejpam-2366	962	8	35(4):309–313	35(4):309–313	NUM
ejpam-2366	962	9	,	,	PUNCT
ejpam-2366	962	10	2011	2011	NUM
ejpam-2366	962	11	.	.	PUNCT
ejpam-2366	963	1	[	[	X
ejpam-2366	963	2	11	11	NUM
ejpam-2366	963	3	]	]	X
ejpam-2366	963	4	dustin	dustin	PROPN
ejpam-2366	963	5	scott	scott	PROPN
ejpam-2366	963	6	culhan	culhan	PROPN
ejpam-2366	963	7	.	.	PUNCT
ejpam-2366	964	1	associated	associate	VERB
ejpam-2366	964	2	primes	prime	NOUN
ejpam-2366	964	3	and	and	CCONJ
ejpam-2366	964	4	primal	primal	ADJ
ejpam-2366	964	5	decomposition	decomposition	NOUN
ejpam-2366	964	6	in	in	ADP
ejpam-2366	964	7	modules	module	NOUN
ejpam-2366	964	8	and	and	CCONJ
ejpam-2366	964	9	lattice	lattice	NOUN
ejpam-2366	964	10	modules	module	NOUN
ejpam-2366	964	11	,	,	PUNCT
ejpam-2366	964	12	and	and	CCONJ
ejpam-2366	964	13	their	their	PRON
ejpam-2366	964	14	duals	dual	NOUN
ejpam-2366	964	15	.	.	PUNCT
ejpam-2366	965	1	university	university	NOUN
ejpam-2366	965	2	of	of	ADP
ejpam-2366	965	3	michigan	michigan	PROPN
ejpam-2366	965	4	press	press	PROPN
ejpam-2366	965	5	,	,	PUNCT
ejpam-2366	965	6	university	university	PROPN
ejpam-2366	965	7	of	of	ADP
ejpam-2366	965	8	california	california	PROPN
ejpam-2366	965	9	,	,	PUNCT
ejpam-2366	965	10	riverside	riverside	PROPN
ejpam-2366	965	11	,	,	PUNCT
ejpam-2366	965	12	2005	2005	NUM
ejpam-2366	965	13	.	.	PUNCT
ejpam-2366	966	1	[	[	X
ejpam-2366	966	2	12	12	NUM
ejpam-2366	966	3	]	]	X
ejpam-2366	966	4	c	c	PROPN
ejpam-2366	966	5	jayaram	jayaram	PROPN
ejpam-2366	966	6	,	,	PUNCT
ejpam-2366	966	7	ünsal	ünsal	PROPN
ejpam-2366	966	8	tekir	tekir	NOUN
ejpam-2366	966	9	,	,	PUNCT
ejpam-2366	966	10	and	and	CCONJ
ejpam-2366	966	11	ece	ece	PROPN
ejpam-2366	966	12	yetkin	yetkin	PROPN
ejpam-2366	966	13	.	.	PUNCT
ejpam-2366	967	1	2	2	NUM
ejpam-2366	967	2	-	-	PUNCT
ejpam-2366	967	3	absorbing	absorbing	ADJ
ejpam-2366	967	4	and	and	CCONJ
ejpam-2366	967	5	weakly	weakly	ADJ
ejpam-2366	967	6	2	2	NUM
ejpam-2366	967	7	-	-	PUNCT
ejpam-2366	967	8	absorbing	absorbing	ADJ
ejpam-2366	967	9	elements	element	NOUN
ejpam-2366	967	10	in	in	ADP
ejpam-2366	967	11	multiplicative	multiplicative	ADJ
ejpam-2366	967	12	lattices	lattice	NOUN
ejpam-2366	967	13	.	.	PUNCT
ejpam-2366	968	1	communications	communication	NOUN
ejpam-2366	968	2	in	in	ADP
ejpam-2366	968	3	algebra	algebra	NOUN
ejpam-2366	968	4	,	,	PUNCT
ejpam-2366	968	5	42(6):2338–2353	42(6):2338–2353	PROPN
ejpam-2366	968	6	,	,	PUNCT
ejpam-2366	968	7	2014	2014	NUM
ejpam-2366	968	8	.	.	PUNCT
ejpam-2366	969	1	[	[	X
ejpam-2366	969	2	13	13	NUM
ejpam-2366	969	3	]	]	X
ejpam-2366	969	4	ew	ew	PROPN
ejpam-2366	969	5	johnson	johnson	PROPN
ejpam-2366	969	6	and	and	CCONJ
ejpam-2366	969	7	ja	ja	PROPN
ejpam-2366	969	8	johnson	johnson	PROPN
ejpam-2366	969	9	.	.	PUNCT
ejpam-2366	970	1	lattice	lattice	PROPN
ejpam-2366	970	2	modules	module	NOUN
ejpam-2366	970	3	over	over	ADP
ejpam-2366	970	4	semi	semi	ADJ
ejpam-2366	970	5	-	-	ADJ
ejpam-2366	970	6	local	local	ADJ
ejpam-2366	970	7	noether	noether	ADJ
ejpam-2366	970	8	lattices	lattice	NOUN
ejpam-2366	970	9	.	.	PUNCT
ejpam-2366	971	1	fundamenta	fundamenta	PROPN
ejpam-2366	971	2	mathematicae	mathematicae	PROPN
ejpam-2366	971	3	,	,	PUNCT
ejpam-2366	971	4	68(2):187–201	68(2):187–201	NOUN
ejpam-2366	971	5	,	,	PUNCT
ejpam-2366	971	6	1970	1970	NUM
ejpam-2366	971	7	.	.	PUNCT
ejpam-2366	972	1	references	reference	NOUN
ejpam-2366	972	2	577	577	NUM
ejpam-2366	972	3	[	[	X
ejpam-2366	972	4	14	14	NUM
ejpam-2366	972	5	]	]	X
ejpam-2366	972	6	j	j	PROPN
ejpam-2366	972	7	johnson	johnson	PROPN
ejpam-2366	972	8	.	.	PUNCT
ejpam-2366	973	1	a	a	DET
ejpam-2366	973	2	-	-	PUNCT
ejpam-2366	973	3	adic	adic	ADJ
ejpam-2366	973	4	completions	completion	NOUN
ejpam-2366	973	5	of	of	ADP
ejpam-2366	973	6	noetherian	noetherian	ADJ
ejpam-2366	973	7	lattice	lattice	NOUN
ejpam-2366	973	8	modules	module	NOUN
ejpam-2366	973	9	.	.	PUNCT
ejpam-2366	974	1	fundamenta	fundamenta	PROPN
ejpam-2366	974	2	mathematicae	mathematicae	PROPN
ejpam-2366	974	3	,	,	PUNCT
ejpam-2366	974	4	66:347–373	66:347–373	PROPN
ejpam-2366	974	5	,	,	PUNCT
ejpam-2366	974	6	1970	1970	NUM
ejpam-2366	974	7	.	.	PUNCT
ejpam-2366	975	1	[	[	X
ejpam-2366	975	2	15	15	NUM
ejpam-2366	975	3	]	]	X
ejpam-2366	975	4	zeliha	zeliha	PROPN
ejpam-2366	975	5	kılıç.	kılıç.	PROPN
ejpam-2366	975	6	almost	almost	ADV
ejpam-2366	975	7	primary	primary	ADJ
ejpam-2366	975	8	elements	element	NOUN
ejpam-2366	975	9	in	in	ADP
ejpam-2366	975	10	multiplicative	multiplicative	ADJ
ejpam-2366	975	11	lattices	lattice	NOUN
ejpam-2366	975	12	.	.	PUNCT
ejpam-2366	976	1	international	international	ADJ
ejpam-2366	976	2	journal	journal	NOUN
ejpam-2366	976	3	of	of	ADP
ejpam-2366	976	4	algebra	algebra	PROPN
ejpam-2366	976	5	,	,	PUNCT
ejpam-2366	976	6	7(18):881–888	7(18):881–888	NUM
ejpam-2366	976	7	,	,	PUNCT
ejpam-2366	976	8	2013	2013	NUM
ejpam-2366	976	9	.	.	PUNCT
ejpam-2366	977	1	[	[	X
ejpam-2366	977	2	16	16	NUM
ejpam-2366	977	3	]	]	X
ejpam-2366	977	4	cs	cs	PROPN
ejpam-2366	977	5	manjarekar	manjarekar	NOUN
ejpam-2366	977	6	and	and	CCONJ
ejpam-2366	977	7	av	av	PROPN
ejpam-2366	977	8	bingi	bingi	PROPN
ejpam-2366	977	9	.	.	PUNCT
ejpam-2366	978	1	φ	φ	PROPN
ejpam-2366	978	2	-	-	NOUN
ejpam-2366	978	3	prime	prime	NOUN
ejpam-2366	978	4	and	and	CCONJ
ejpam-2366	978	5	φ	φ	VERB
ejpam-2366	978	6	-	-	ADJ
ejpam-2366	978	7	primary	primary	ADJ
ejpam-2366	978	8	elements	element	NOUN
ejpam-2366	978	9	in	in	ADP
ejpam-2366	978	10	multiplicative	multiplicative	ADJ
ejpam-2366	978	11	lattices	lattice	NOUN
ejpam-2366	978	12	.	.	PUNCT
ejpam-2366	979	1	algebra	algebra	NOUN
ejpam-2366	979	2	,	,	PUNCT
ejpam-2366	979	3	2014:1–7	2014:1–7	PROPN
ejpam-2366	979	4	,	,	PUNCT
ejpam-2366	979	5	2014	2014	NUM
ejpam-2366	979	6	.	.	PUNCT
ejpam-2366	980	1	[	[	X
ejpam-2366	980	2	17	17	NUM
ejpam-2366	980	3	]	]	X
ejpam-2366	980	4	cs	cs	PROPN
ejpam-2366	980	5	manjarekar	manjarekar	NOUN
ejpam-2366	980	6	and	and	CCONJ
ejpam-2366	980	7	av	av	PROPN
ejpam-2366	980	8	bingi	bingi	PROPN
ejpam-2366	980	9	.	.	PUNCT
ejpam-2366	981	1	absorbing	absorb	VERB
ejpam-2366	981	2	elements	element	NOUN
ejpam-2366	981	3	in	in	ADP
ejpam-2366	981	4	lattice	lattice	NOUN
ejpam-2366	981	5	modules	module	NOUN
ejpam-2366	981	6	.	.	PUNCT
ejpam-2366	982	1	international	international	ADJ
ejpam-2366	982	2	electronic	electronic	ADJ
ejpam-2366	982	3	journal	journal	NOUN
ejpam-2366	982	4	of	of	ADP
ejpam-2366	982	5	algebra	algebra	PROPN
ejpam-2366	982	6	,	,	PUNCT
ejpam-2366	982	7	19(19):58–76	19(19):58–76	NUM
ejpam-2366	982	8	,	,	PUNCT
ejpam-2366	982	9	2016	2016	NUM
ejpam-2366	982	10	.	.	PUNCT
ejpam-2366	983	1	[	[	X
ejpam-2366	983	2	18	18	NUM
ejpam-2366	983	3	]	]	X
ejpam-2366	983	4	cs	cs	PROPN
ejpam-2366	983	5	manjarekar	manjarekar	NOUN
ejpam-2366	983	6	and	and	CCONJ
ejpam-2366	983	7	av	av	PROPN
ejpam-2366	983	8	bingi	bingi	PROPN
ejpam-2366	983	9	.	.	PUNCT
ejpam-2366	984	1	on	on	ADP
ejpam-2366	984	2	2	2	NUM
ejpam-2366	984	3	-	-	PUNCT
ejpam-2366	984	4	absorbing	absorb	VERB
ejpam-2366	984	5	primary	primary	ADJ
ejpam-2366	984	6	and	and	CCONJ
ejpam-2366	984	7	weakly	weakly	ADJ
ejpam-2366	984	8	2	2	NUM
ejpam-2366	984	9	-	-	PUNCT
ejpam-2366	984	10	absorbing	absorbing	ADJ
ejpam-2366	984	11	primary	primary	ADJ
ejpam-2366	984	12	elements	element	NOUN
ejpam-2366	984	13	in	in	ADP
ejpam-2366	984	14	multiplicative	multiplicative	ADJ
ejpam-2366	984	15	lattices	lattice	NOUN
ejpam-2366	984	16	.	.	PUNCT
ejpam-2366	985	1	trans	trans	PROPN
ejpam-2366	985	2	.	.	PUNCT
ejpam-2366	986	1	algebra	algebra	PROPN
ejpam-2366	986	2	appl	appl	PROPN
ejpam-2366	986	3	.	.	PROPN
ejpam-2366	986	4	,	,	PUNCT
ejpam-2366	986	5	2:1–13	2:1–13	NUM
ejpam-2366	986	6	,	,	PUNCT
ejpam-2366	986	7	2016	2016	NUM
ejpam-2366	986	8	.	.	PUNCT
ejpam-2366	987	1	[	[	X
ejpam-2366	987	2	19	19	NUM
ejpam-2366	987	3	]	]	X
ejpam-2366	987	4	cs	cs	PROPN
ejpam-2366	987	5	manjarekar	manjarekar	PROPN
ejpam-2366	987	6	and	and	CCONJ
ejpam-2366	987	7	un	un	PROPN
ejpam-2366	987	8	kandale	kandale	PROPN
ejpam-2366	987	9	.	.	PUNCT
ejpam-2366	988	1	weakly	weakly	ADJ
ejpam-2366	988	2	prime	prime	ADJ
ejpam-2366	988	3	elements	element	NOUN
ejpam-2366	988	4	in	in	ADP
ejpam-2366	988	5	lattice	lattice	NOUN
ejpam-2366	988	6	modules	module	NOUN
ejpam-2366	988	7	.	.	PUNCT
ejpam-2366	989	1	international	international	ADJ
ejpam-2366	989	2	journal	journal	PROPN
ejpam-2366	989	3	of	of	ADP
ejpam-2366	989	4	scientific	scientific	ADJ
ejpam-2366	989	5	and	and	CCONJ
ejpam-2366	989	6	research	research	NOUN
ejpam-2366	989	7	publications	publication	NOUN
ejpam-2366	989	8	,	,	PUNCT
ejpam-2366	989	9	3(8):1–6	3(8):1–6	NUM
ejpam-2366	989	10	,	,	PUNCT
ejpam-2366	989	11	2013	2013	NUM
ejpam-2366	989	12	.	.	PUNCT
ejpam-2366	990	1	[	[	X
ejpam-2366	990	2	20	20	NUM
ejpam-2366	990	3	]	]	X
ejpam-2366	990	4	cs	cs	PROPN
ejpam-2366	990	5	manjarekar	manjarekar	PROPN
ejpam-2366	990	6	and	and	CCONJ
ejpam-2366	990	7	un	un	PROPN
ejpam-2366	990	8	kandale	kandale	PROPN
ejpam-2366	990	9	.	.	PUNCT
ejpam-2366	991	1	residuation	residuation	NOUN
ejpam-2366	991	2	properties	property	NOUN
ejpam-2366	991	3	and	and	CCONJ
ejpam-2366	991	4	weakly	weakly	ADJ
ejpam-2366	991	5	primary	primary	ADJ
ejpam-2366	991	6	elements	element	NOUN
ejpam-2366	991	7	in	in	ADP
ejpam-2366	991	8	lattice	lattice	NOUN
ejpam-2366	991	9	modules	module	NOUN
ejpam-2366	991	10	.	.	PUNCT
ejpam-2366	992	1	algebra	algebra	NOUN
ejpam-2366	992	2	,	,	PUNCT
ejpam-2366	992	3	2014:1–4	2014:1–4	NOUN
ejpam-2366	992	4	,	,	PUNCT
ejpam-2366	992	5	2014	2014	NUM
ejpam-2366	992	6	.	.	PUNCT
ejpam-2366	993	1	[	[	X
ejpam-2366	993	2	21	21	NUM
ejpam-2366	993	3	]	]	X
ejpam-2366	993	4	nk	nk	PROPN
ejpam-2366	993	5	thakare	thakare	NOUN
ejpam-2366	993	6	and	and	CCONJ
ejpam-2366	993	7	cs	cs	PROPN
ejpam-2366	993	8	manjarekar	manjarekar	NOUN
ejpam-2366	993	9	.	.	PUNCT
ejpam-2366	994	1	radicals	radical	NOUN
ejpam-2366	994	2	and	and	CCONJ
ejpam-2366	994	3	uniqueness	uniqueness	NOUN
ejpam-2366	994	4	theorem	theorem	VERB
ejpam-2366	994	5	in	in	ADP
ejpam-2366	994	6	multiplicative	multiplicative	ADJ
ejpam-2366	994	7	lattices	lattice	NOUN
ejpam-2366	994	8	with	with	ADP
ejpam-2366	994	9	chain	chain	NOUN
ejpam-2366	994	10	conditions	condition	NOUN
ejpam-2366	994	11	.	.	PUNCT
ejpam-2366	995	1	studia	studia	PROPN
ejpam-2366	995	2	scientifica	scientifica	PROPN
ejpam-2366	995	3	mathematicarum	mathematicarum	PROPN
ejpam-2366	995	4	hungarica	hungarica	PROPN
ejpam-2366	995	5	,	,	PUNCT
ejpam-2366	995	6	18:13	18:13	NUM
ejpam-2366	995	7	–	–	PUNCT
ejpam-2366	995	8	19	19	NUM
ejpam-2366	995	9	,	,	PUNCT
ejpam-2366	995	10	1983	1983	NUM
ejpam-2366	995	11	.	.	PUNCT
ejpam-2366	996	1	[	[	X
ejpam-2366	996	2	22	22	NUM
ejpam-2366	996	3	]	]	X
ejpam-2366	996	4	emel	emel	X
ejpam-2366	996	5	aslankarayigit	aslankarayigit	ADJ
ejpam-2366	996	6	ugurlu	ugurlu	ADJ
ejpam-2366	996	7	,	,	PUNCT
ejpam-2366	996	8	fethi	fethi	ADJ
ejpam-2366	996	9	callialp	callialp	NOUN
ejpam-2366	996	10	,	,	PUNCT
ejpam-2366	996	11	and	and	CCONJ
ejpam-2366	996	12	unsal	unsal	PROPN
ejpam-2366	996	13	tekir	tekir	PROPN
ejpam-2366	996	14	.	.	PUNCT
ejpam-2366	997	1	prime	prime	ADJ
ejpam-2366	997	2	,	,	PUNCT
ejpam-2366	997	3	weakly	weakly	ADJ
ejpam-2366	997	4	prime	prime	NOUN
ejpam-2366	997	5	and	and	CCONJ
ejpam-2366	997	6	almost	almost	ADV
ejpam-2366	997	7	prime	prime	ADJ
ejpam-2366	997	8	elements	element	NOUN
ejpam-2366	997	9	in	in	ADP
ejpam-2366	997	10	multiplication	multiplication	NOUN
ejpam-2366	997	11	lattice	lattice	NOUN
ejpam-2366	997	12	modules	module	NOUN
ejpam-2366	997	13	.	.	PUNCT
ejpam-2366	998	1	open	open	ADJ
ejpam-2366	998	2	mathematics	mathematic	NOUN
ejpam-2366	998	3	,	,	PUNCT
ejpam-2366	998	4	14(1):673–680	14(1):673–680	PROPN
ejpam-2366	998	5	,	,	PUNCT
ejpam-2366	998	6	2016	2016	NUM
ejpam-2366	998	7	.	.	PUNCT
ejpam-2366	999	1	[	[	X
ejpam-2366	999	2	23	23	NUM
ejpam-2366	999	3	]	]	PUNCT
ejpam-2366	999	4	jane	jane	NOUN
ejpam-2366	999	5	wells	wells	PROPN
ejpam-2366	999	6	.	.	PUNCT
ejpam-2366	1000	1	the	the	DET
ejpam-2366	1000	2	restricted	restrict	VERB
ejpam-2366	1000	3	cancellation	cancellation	NOUN
ejpam-2366	1000	4	law	law	NOUN
ejpam-2366	1000	5	in	in	ADP
ejpam-2366	1000	6	a	a	DET
ejpam-2366	1000	7	noether	noether	ADJ
ejpam-2366	1000	8	lattice	lattice	NOUN
ejpam-2366	1000	9	.	.	PUNCT
ejpam-2366	1001	1	fundamenta	fundamenta	PROPN
ejpam-2366	1001	2	mathematicae	mathematicae	PROPN
ejpam-2366	1001	3	,	,	PUNCT
ejpam-2366	1001	4	3(75):235–247	3(75):235–247	NUM
ejpam-2366	1001	5	,	,	PUNCT
ejpam-2366	1001	6	1972	1972	NUM
ejpam-2366	1001	7	.	.	PUNCT
ejpam-2366	1002	1	[	[	X
ejpam-2366	1002	2	24	24	NUM
ejpam-2366	1002	3	]	]	SYM
ejpam-2366	1002	4	naser	naser	PROPN
ejpam-2366	1002	5	zamani	zamani	PROPN
ejpam-2366	1002	6	.	.	PUNCT
ejpam-2366	1002	7	ϕ-prime	ϕ-prime	PROPN
ejpam-2366	1002	8	submodules	submodule	NOUN
ejpam-2366	1002	9	.	.	PUNCT
ejpam-2366	1003	1	glasgow	glasgow	PROPN
ejpam-2366	1003	2	mathematical	mathematical	ADJ
ejpam-2366	1003	3	journal	journal	NOUN
ejpam-2366	1003	4	,	,	PUNCT
ejpam-2366	1003	5	52(2):253–259	52(2):253–259	NUM
ejpam-2366	1003	6	,	,	PUNCT
ejpam-2366	1003	7	2010	2010	NUM
ejpam-2366	1003	8	.	.	PUNCT