id	sid	tid	token	lemma	pos
ejpam-2406	1	1	compile	compile	NOUN
ejpam-2406	1	2	/	/	SYM
ejpam-2406	1	3	output.dvi	output.dvi	NOUN
ejpam-2406	1	4	european	european	ADJ
ejpam-2406	1	5	journal	journal	NOUN
ejpam-2406	1	6	of	of	ADP
ejpam-2406	1	7	pure	pure	ADJ
ejpam-2406	1	8	and	and	CCONJ
ejpam-2406	1	9	applied	apply	VERB
ejpam-2406	1	10	mathematics	mathematic	NOUN
ejpam-2406	1	11	vol	vol	NOUN
ejpam-2406	1	12	.	.	PROPN
ejpam-2406	1	13	8	8	NUM
ejpam-2406	1	14	,	,	PUNCT
ejpam-2406	1	15	no	no	INTJ
ejpam-2406	1	16	.	.	NOUN
ejpam-2406	1	17	2	2	NUM
ejpam-2406	1	18	,	,	PUNCT
ejpam-2406	1	19	2015	2015	NUM
ejpam-2406	1	20	,	,	PUNCT
ejpam-2406	1	21	172	172	NUM
ejpam-2406	1	22	-	-	SYM
ejpam-2406	1	23	184	184	NUM
ejpam-2406	1	24	issn	issn	PROPN
ejpam-2406	1	25	1307	1307	NUM
ejpam-2406	1	26	-	-	SYM
ejpam-2406	1	27	5543	5543	NUM
ejpam-2406	1	28	–	–	PUNCT
ejpam-2406	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2406	1	30	classical	classical	ADJ
ejpam-2406	1	31	quasi	quasi	ADJ
ejpam-2406	1	32	primary	primary	ADJ
ejpam-2406	1	33	elements	element	NOUN
ejpam-2406	1	34	in	in	ADP
ejpam-2406	1	35	lattice	lattice	PROPN
ejpam-2406	1	36	modules	module	NOUN
ejpam-2406	1	37	c.	c.	PROPN
ejpam-2406	1	38	s.	s.	PROPN
ejpam-2406	1	39	manjarekar	manjarekar	PROPN
ejpam-2406	1	40	1	1	NUM
ejpam-2406	1	41	,	,	PUNCT
ejpam-2406	1	42	u.	u.	PROPN
ejpam-2406	1	43	n.	n.	PROPN
ejpam-2406	1	44	kandale	kandale	PROPN
ejpam-2406	1	45	2,∗	2,∗	NUM
ejpam-2406	1	46	1	1	NUM
ejpam-2406	1	47	department	department	NOUN
ejpam-2406	1	48	of	of	ADP
ejpam-2406	1	49	mathematics	mathematics	PROPN
ejpam-2406	1	50	,	,	PUNCT
ejpam-2406	1	51	shivaji	shivaji	PROPN
ejpam-2406	1	52	university	university	PROPN
ejpam-2406	1	53	,	,	PUNCT
ejpam-2406	1	54	kolhapur	kolhapur	PROPN
ejpam-2406	1	55	,	,	PUNCT
ejpam-2406	1	56	india	india	PROPN
ejpam-2406	1	57	2	2	NUM
ejpam-2406	1	58	department	department	NOUN
ejpam-2406	1	59	of	of	ADP
ejpam-2406	1	60	general	general	ADJ
ejpam-2406	1	61	engineering	engineering	PROPN
ejpam-2406	1	62	,	,	PUNCT
ejpam-2406	1	63	sharad	sharad	PROPN
ejpam-2406	1	64	institute	institute	PROPN
ejpam-2406	1	65	,	,	PUNCT
ejpam-2406	1	66	shivaji	shivaji	PROPN
ejpam-2406	1	67	university	university	PROPN
ejpam-2406	1	68	,	,	PUNCT
ejpam-2406	1	69	kolhapur	kolhapur	PROPN
ejpam-2406	1	70	,	,	PUNCT
ejpam-2406	1	71	india	india	PROPN
ejpam-2406	1	72	abstract	abstract	NOUN
ejpam-2406	1	73	.	.	PUNCT
ejpam-2406	2	1	in	in	ADP
ejpam-2406	2	2	this	this	DET
ejpam-2406	2	3	paper	paper	NOUN
ejpam-2406	2	4	we	we	PRON
ejpam-2406	2	5	introduce	introduce	VERB
ejpam-2406	2	6	the	the	DET
ejpam-2406	2	7	notion	notion	NOUN
ejpam-2406	2	8	of	of	ADP
ejpam-2406	2	9	classical	classical	ADJ
ejpam-2406	2	10	primary	primary	ADJ
ejpam-2406	2	11	and	and	CCONJ
ejpam-2406	2	12	classical	classical	ADJ
ejpam-2406	2	13	quasi	quasi	ADJ
ejpam-2406	2	14	primary	primary	ADJ
ejpam-2406	2	15	elements	element	NOUN
ejpam-2406	2	16	in	in	ADP
ejpam-2406	2	17	lattice	lattice	NOUN
ejpam-2406	2	18	modules	module	NOUN
ejpam-2406	2	19	which	which	PRON
ejpam-2406	2	20	are	be	AUX
ejpam-2406	2	21	the	the	DET
ejpam-2406	2	22	generalization	generalization	NOUN
ejpam-2406	2	23	of	of	ADP
ejpam-2406	2	24	the	the	DET
ejpam-2406	2	25	concepts	concept	NOUN
ejpam-2406	2	26	in	in	ADP
ejpam-2406	2	27	submodules	submodule	NOUN
ejpam-2406	2	28	.	.	PUNCT
ejpam-2406	3	1	we	we	PRON
ejpam-2406	3	2	obtain	obtain	VERB
ejpam-2406	3	3	some	some	DET
ejpam-2406	3	4	characterizations	characterization	NOUN
ejpam-2406	3	5	of	of	ADP
ejpam-2406	3	6	classical	classical	ADJ
ejpam-2406	3	7	primary	primary	ADJ
ejpam-2406	3	8	and	and	CCONJ
ejpam-2406	3	9	classical	classical	ADJ
ejpam-2406	3	10	quasi	quasi	ADJ
ejpam-2406	3	11	primary	primary	ADJ
ejpam-2406	3	12	elements	element	NOUN
ejpam-2406	3	13	.we	.we	PUNCT
ejpam-2406	3	14	also	also	ADV
ejpam-2406	3	15	investigate	investigate	VERB
ejpam-2406	3	16	the	the	DET
ejpam-2406	3	17	decomposition	decomposition	NOUN
ejpam-2406	3	18	and	and	CCONJ
ejpam-2406	3	19	minimal	minimal	ADJ
ejpam-2406	3	20	decomposition	decomposition	NOUN
ejpam-2406	3	21	into	into	ADP
ejpam-2406	3	22	classical	classical	ADJ
ejpam-2406	3	23	quasi	quasi	ADJ
ejpam-2406	3	24	primary	primary	ADJ
ejpam-2406	3	25	elements	element	NOUN
ejpam-2406	3	26	.	.	PUNCT
ejpam-2406	4	1	2010	2010	NUM
ejpam-2406	4	2	mathematics	mathematic	NOUN
ejpam-2406	4	3	subject	subject	NOUN
ejpam-2406	4	4	classifications	classification	NOUN
ejpam-2406	4	5	:	:	PUNCT
ejpam-2406	4	6	13a99	13a99	NUM
ejpam-2406	4	7	key	key	ADJ
ejpam-2406	4	8	words	word	NOUN
ejpam-2406	4	9	and	and	CCONJ
ejpam-2406	4	10	phrases	phrase	NOUN
ejpam-2406	4	11	:	:	PUNCT
ejpam-2406	4	12	primary	primary	ADJ
ejpam-2406	4	13	element	element	NOUN
ejpam-2406	4	14	,	,	PUNCT
ejpam-2406	4	15	prime	prime	ADJ
ejpam-2406	4	16	element	element	NOUN
ejpam-2406	4	17	,	,	PUNCT
ejpam-2406	4	18	classical	classical	ADJ
ejpam-2406	4	19	quasi	quasi	ADJ
ejpam-2406	4	20	primary	primary	ADJ
ejpam-2406	4	21	element	element	NOUN
ejpam-2406	4	22	,	,	PUNCT
ejpam-2406	4	23	lattice	lattice	NOUN
ejpam-2406	4	24	modules	module	NOUN
ejpam-2406	4	25	.	.	PUNCT
ejpam-2406	5	1	1	1	X
ejpam-2406	5	2	.	.	X
ejpam-2406	5	3	introduction	introduction	NOUN
ejpam-2406	5	4	multiplicative	multiplicative	PROPN
ejpam-2406	5	5	lattice	lattice	PROPN
ejpam-2406	5	6	l	l	PROPN
ejpam-2406	5	7	is	be	AUX
ejpam-2406	5	8	a	a	DET
ejpam-2406	5	9	complete	complete	ADJ
ejpam-2406	5	10	lattice	lattice	NOUN
ejpam-2406	5	11	provided	provide	VERB
ejpam-2406	5	12	with	with	ADP
ejpam-2406	5	13	commutative	commutative	ADJ
ejpam-2406	5	14	,	,	PUNCT
ejpam-2406	5	15	associative	associative	ADJ
ejpam-2406	5	16	and	and	CCONJ
ejpam-2406	5	17	join	join	VERB
ejpam-2406	5	18	distributive	distributive	ADJ
ejpam-2406	5	19	multiplication	multiplication	NOUN
ejpam-2406	5	20	for	for	ADP
ejpam-2406	5	21	which	which	PRON
ejpam-2406	5	22	the	the	DET
ejpam-2406	5	23	largest	large	ADJ
ejpam-2406	5	24	element	element	NOUN
ejpam-2406	5	25	1	1	NUM
ejpam-2406	5	26	acts	act	NOUN
ejpam-2406	5	27	as	as	ADP
ejpam-2406	5	28	an	an	DET
ejpam-2406	5	29	multiplicative	multiplicative	ADJ
ejpam-2406	5	30	identity	identity	NOUN
ejpam-2406	5	31	.	.	PUNCT
ejpam-2406	6	1	a	a	DET
ejpam-2406	6	2	proper	proper	ADJ
ejpam-2406	6	3	element	element	NOUN
ejpam-2406	6	4	p	p	NOUN
ejpam-2406	6	5	of	of	ADP
ejpam-2406	6	6	l	l	NOUN
ejpam-2406	6	7	is	be	AUX
ejpam-2406	6	8	called	call	VERB
ejpam-2406	6	9	prime	prime	ADJ
ejpam-2406	6	10	element	element	NOUN
ejpam-2406	6	11	if	if	SCONJ
ejpam-2406	6	12	ab	ab	PROPN
ejpam-2406	6	13	¶	¶	PROPN
ejpam-2406	7	1	p	p	PROPN
ejpam-2406	7	2	implies	imply	VERB
ejpam-2406	7	3	a	a	DET
ejpam-2406	7	4	¶	¶	NOUN
ejpam-2406	7	5	p	p	NOUN
ejpam-2406	7	6	or	or	CCONJ
ejpam-2406	7	7	b	b	NOUN
ejpam-2406	7	8	¶	¶	PROPN
ejpam-2406	7	9	p	p	NOUN
ejpam-2406	7	10	for	for	ADP
ejpam-2406	7	11	a	a	DET
ejpam-2406	7	12	,	,	PUNCT
ejpam-2406	7	13	b	b	PROPN
ejpam-2406	7	14	∈	∈	PROPN
ejpam-2406	7	15	l	l	NOUN
ejpam-2406	7	16	and	and	CCONJ
ejpam-2406	7	17	is	be	AUX
ejpam-2406	7	18	called	call	VERB
ejpam-2406	7	19	primary	primary	ADJ
ejpam-2406	7	20	element	element	NOUN
ejpam-2406	7	21	if	if	SCONJ
ejpam-2406	7	22	ab	ab	PROPN
ejpam-2406	7	23	¶	¶	PROPN
ejpam-2406	7	24	p	p	PROPN
ejpam-2406	7	25	implies	imply	VERB
ejpam-2406	7	26	a	a	DET
ejpam-2406	7	27	¶	¶	NOUN
ejpam-2406	7	28	p	p	NOUN
ejpam-2406	7	29	or	or	CCONJ
ejpam-2406	7	30	bn	bn	ADP
ejpam-2406	7	31	¶	¶	NOUN
ejpam-2406	7	32	p	p	NOUN
ejpam-2406	7	33	for	for	ADP
ejpam-2406	7	34	some	some	DET
ejpam-2406	7	35	positive	positive	ADJ
ejpam-2406	7	36	integer	integer	NOUN
ejpam-2406	7	37	n.	n.	NOUN
ejpam-2406	7	38	for	for	ADP
ejpam-2406	7	39	a	a	DET
ejpam-2406	7	40	∈	∈	PROPN
ejpam-2406	7	41	l	l	NOUN
ejpam-2406	7	42	,	,	PUNCT
ejpam-2406	8	1	p	p	X
ejpam-2406	8	2	a	a	DET
ejpam-2406	8	3	=	=	SYM
ejpam-2406	8	4	∨{x	∨{x	NOUN
ejpam-2406	8	5	∈	∈	NOUN
ejpam-2406	8	6	l	l	NOUN
ejpam-2406	9	1	|	|	ADV
ejpam-2406	9	2	xn	xn	PROPN
ejpam-2406	9	3	¶	¶	PROPN
ejpam-2406	9	4	a	a	PRON
ejpam-2406	9	5	for	for	ADP
ejpam-2406	9	6	some	some	DET
ejpam-2406	9	7	integer	integer	NOUN
ejpam-2406	9	8	n	n	X
ejpam-2406	9	9	}	}	PUNCT
ejpam-2406	9	10	.	.	PUNCT
ejpam-2406	10	1	let	let	VERB
ejpam-2406	10	2	l	l	NOUN
ejpam-2406	10	3	be	be	AUX
ejpam-2406	10	4	a	a	DET
ejpam-2406	10	5	multiplicative	multiplicative	ADJ
ejpam-2406	10	6	lattice	lattice	NOUN
ejpam-2406	10	7	.	.	PUNCT
ejpam-2406	11	1	a	a	DET
ejpam-2406	11	2	lattice	lattice	NOUN
ejpam-2406	11	3	module	module	NOUN
ejpam-2406	11	4	over	over	ADP
ejpam-2406	11	5	l	l	NOUN
ejpam-2406	11	6	or	or	CCONJ
ejpam-2406	11	7	simply	simply	ADV
ejpam-2406	11	8	a	a	DET
ejpam-2406	11	9	lattice	lattice	NOUN
ejpam-2406	11	10	module	module	NOUN
ejpam-2406	11	11	is	be	AUX
ejpam-2406	11	12	defined	define	VERB
ejpam-2406	11	13	to	to	PART
ejpam-2406	11	14	be	be	AUX
ejpam-2406	11	15	a	a	DET
ejpam-2406	11	16	complete	complete	ADJ
ejpam-2406	11	17	lattice	lattice	NOUN
ejpam-2406	11	18	m	m	NOUN
ejpam-2406	11	19	with	with	ADP
ejpam-2406	11	20	multiplication	multiplication	NOUN
ejpam-2406	11	21	l	l	NOUN
ejpam-2406	11	22	×m	×m	NOUN
ejpam-2406	11	23	→	→	SYM
ejpam-2406	11	24	m	m	VERB
ejpam-2406	11	25	satisfying	satisfying	ADJ
ejpam-2406	11	26	,	,	PUNCT
ejpam-2406	11	27	(	(	PUNCT
ejpam-2406	11	28	i	i	NOUN
ejpam-2406	11	29	)	)	PUNCT
ejpam-2406	11	30	(	(	PUNCT
ejpam-2406	11	31	∨	∨	X
ejpam-2406	11	32	α	α	NOUN
ejpam-2406	11	33	aα)a=	aα)a=	ADP
ejpam-2406	11	34	∨	∨	NOUN
ejpam-2406	11	35	α	α	PROPN
ejpam-2406	11	36	aαa	aαa	VERB
ejpam-2406	11	37	∀aα	∀aα	NOUN
ejpam-2406	11	38	∈	∈	PROPN
ejpam-2406	11	39	l	l	NOUN
ejpam-2406	11	40	,	,	PUNCT
ejpam-2406	11	41	a∈	a∈	PROPN
ejpam-2406	11	42	m	m	VERB
ejpam-2406	11	43	for	for	ADP
ejpam-2406	11	44	some	some	DET
ejpam-2406	11	45	integer	integer	NOUN
ejpam-2406	11	46	(	(	PUNCT
ejpam-2406	11	47	ii	ii	NOUN
ejpam-2406	11	48	)	)	PUNCT
ejpam-2406	11	49	a(∨	a(∨	PUNCT
ejpam-2406	12	1	α	α	DET
ejpam-2406	12	2	aα	aα	NOUN
ejpam-2406	12	3	)	)	PUNCT
ejpam-2406	12	4	=	=	PUNCT
ejpam-2406	13	1	∨	∨	NUM
ejpam-2406	13	2	α	α	PRON
ejpam-2406	13	3	aaα	aaα	PRON
ejpam-2406	13	4	∀a	∀a	NOUN
ejpam-2406	13	5	∈	∈	PROPN
ejpam-2406	13	6	l	l	NOUN
ejpam-2406	13	7	,	,	PUNCT
ejpam-2406	13	8	aα	aα	NOUN
ejpam-2406	13	9	∈	∈	PROPN
ejpam-2406	13	10	m	m	NOUN
ejpam-2406	13	11	(	(	PUNCT
ejpam-2406	13	12	iii	iii	NOUN
ejpam-2406	13	13	)	)	PUNCT
ejpam-2406	13	14	(	(	PUNCT
ejpam-2406	13	15	ab)a=	ab)a=	ADP
ejpam-2406	13	16	a(ba	a(ba	NOUN
ejpam-2406	13	17	)	)	PUNCT
ejpam-2406	13	18	∀a	∀a	NOUN
ejpam-2406	13	19	,	,	PUNCT
ejpam-2406	13	20	b	b	X
ejpam-2406	13	21	∈	∈	PROPN
ejpam-2406	13	22	l	l	NOUN
ejpam-2406	13	23	,	,	PUNCT
ejpam-2406	13	24	a∈	a∈	PROPN
ejpam-2406	13	25	m	m	PROPN
ejpam-2406	13	26	(	(	PUNCT
ejpam-2406	13	27	iv	iv	X
ejpam-2406	13	28	)	)	PUNCT
ejpam-2406	13	29	ia=	ia=	NOUN
ejpam-2406	13	30	a	a	DET
ejpam-2406	13	31	∀a∈	∀a∈	NOUN
ejpam-2406	13	32	m	m	NOUN
ejpam-2406	13	33	(	(	PUNCT
ejpam-2406	13	34	v	v	NOUN
ejpam-2406	13	35	)	)	PUNCT
ejpam-2406	13	36	oa=	oa=	NOUN
ejpam-2406	13	37	om	om	NOUN
ejpam-2406	13	38	∀a∈	∀a∈	NOUN
ejpam-2406	13	39	m	m	VERB
ejpam-2406	13	40	where	where	SCONJ
ejpam-2406	13	41	om	om	PROPN
ejpam-2406	13	42	=	=	PROPN
ejpam-2406	13	43	gl	gl	PROPN
ejpam-2406	13	44	b(m	b(m	PROPN
ejpam-2406	13	45	)	)	PUNCT
ejpam-2406	13	46	.	.	PUNCT
ejpam-2406	14	1	∗corresponding	∗corresponde	VERB
ejpam-2406	14	2	author	author	NOUN
ejpam-2406	14	3	.	.	PUNCT
ejpam-2406	15	1	email	email	NOUN
ejpam-2406	15	2	addresses	address	NOUN
ejpam-2406	15	3	:	:	PUNCT
ejpam-2406	15	4	csmanjrekar@yahoo.co.in	csmanjrekar@yahoo.co.in	X
ejpam-2406	15	5	(	(	PUNCT
ejpam-2406	15	6	c.	c.	PROPN
ejpam-2406	15	7	manjarekar	manjarekar	PROPN
ejpam-2406	15	8	)	)	PUNCT
ejpam-2406	15	9	,	,	PUNCT
ejpam-2406	15	10	ujwalabiraje@gmail.com	ujwalabiraje@gmail.com	X
ejpam-2406	15	11	(	(	PUNCT
ejpam-2406	15	12	u.	u.	PROPN
ejpam-2406	15	13	kandale	kandale	PROPN
ejpam-2406	15	14	)	)	PUNCT
ejpam-2406	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2406	16	1	172	172	NUM
ejpam-2406	16	2	c	c	X
ejpam-2406	16	3	©	©	PROPN
ejpam-2406	16	4	2015	2015	NUM
ejpam-2406	16	5	ejpam	ejpam	VERB
ejpam-2406	16	6	all	all	DET
ejpam-2406	16	7	rights	right	NOUN
ejpam-2406	16	8	reserved	reserve	VERB
ejpam-2406	16	9	.	.	PUNCT
ejpam-2406	17	1	c.	c.	PROPN
ejpam-2406	17	2	manjarekar	manjarekar	PROPN
ejpam-2406	17	3	,	,	PUNCT
ejpam-2406	17	4	u.	u.	PROPN
ejpam-2406	17	5	kandale	kandale	PROPN
ejpam-2406	17	6	/	/	SYM
ejpam-2406	17	7	eur	eur	PROPN
ejpam-2406	17	8	.	.	PUNCT
ejpam-2406	18	1	j.	j.	PROPN
ejpam-2406	18	2	pure	pure	PROPN
ejpam-2406	18	3	appl	appl	PROPN
ejpam-2406	18	4	.	.	PROPN
ejpam-2406	18	5	math	math	PROPN
ejpam-2406	18	6	,	,	PUNCT
ejpam-2406	18	7	8	8	NUM
ejpam-2406	18	8	(	(	PUNCT
ejpam-2406	18	9	2015	2015	NUM
ejpam-2406	18	10	)	)	PUNCT
ejpam-2406	18	11	,	,	PUNCT
ejpam-2406	18	12	172	172	NUM
ejpam-2406	18	13	-	-	SYM
ejpam-2406	18	14	184	184	NUM
ejpam-2406	18	15	173	173	NUM
ejpam-2406	18	16	elements	element	NOUN
ejpam-2406	18	17	of	of	ADP
ejpam-2406	18	18	l	l	NOUN
ejpam-2406	18	19	will	will	AUX
ejpam-2406	18	20	generally	generally	ADV
ejpam-2406	18	21	be	be	AUX
ejpam-2406	18	22	denoted	denote	VERB
ejpam-2406	18	23	by	by	ADP
ejpam-2406	18	24	a	a	DET
ejpam-2406	18	25	,	,	PUNCT
ejpam-2406	18	26	b	b	PROPN
ejpam-2406	18	27	,	,	PUNCT
ejpam-2406	18	28	c	c	NOUN
ejpam-2406	18	29	,	,	PUNCT
ejpam-2406	18	30	.	.	PUNCT
ejpam-2406	18	31	.	.	PUNCT
ejpam-2406	19	1	.	.	PUNCT
ejpam-2406	20	1	except	except	SCONJ
ejpam-2406	20	2	that	that	SCONJ
ejpam-2406	20	3	the	the	DET
ejpam-2406	20	4	least	least	ADJ
ejpam-2406	20	5	element	element	NOUN
ejpam-2406	20	6	of	of	ADP
ejpam-2406	20	7	l	l	NOUN
ejpam-2406	20	8	will	will	AUX
ejpam-2406	20	9	be	be	AUX
ejpam-2406	20	10	denoted	denote	VERB
ejpam-2406	20	11	by	by	ADP
ejpam-2406	20	12	o	o	PROPN
ejpam-2406	20	13	and	and	CCONJ
ejpam-2406	20	14	greatest	great	ADJ
ejpam-2406	20	15	element	element	NOUN
ejpam-2406	20	16	of	of	ADP
ejpam-2406	20	17	l	l	NOUN
ejpam-2406	20	18	will	will	AUX
ejpam-2406	20	19	be	be	AUX
ejpam-2406	20	20	denoted	denote	VERB
ejpam-2406	20	21	by	by	ADP
ejpam-2406	20	22	1	1	NUM
ejpam-2406	20	23	.	.	PUNCT
ejpam-2406	21	1	the	the	DET
ejpam-2406	21	2	elements	element	NOUN
ejpam-2406	21	3	of	of	ADP
ejpam-2406	21	4	m	m	PROPN
ejpam-2406	21	5	will	will	AUX
ejpam-2406	21	6	generally	generally	ADV
ejpam-2406	21	7	be	be	AUX
ejpam-2406	21	8	denoted	denote	VERB
ejpam-2406	21	9	by	by	ADP
ejpam-2406	21	10	a	a	DET
ejpam-2406	21	11	,	,	PUNCT
ejpam-2406	21	12	b	b	NOUN
ejpam-2406	21	13	,	,	PUNCT
ejpam-2406	21	14	c	c	NOUN
ejpam-2406	21	15	,	,	PUNCT
ejpam-2406	21	16	.	.	PUNCT
ejpam-2406	21	17	.	.	PUNCT
ejpam-2406	22	1	.	.	PUNCT
ejpam-2406	23	1	except	except	SCONJ
ejpam-2406	23	2	that	that	SCONJ
ejpam-2406	23	3	the	the	DET
ejpam-2406	23	4	least	least	ADJ
ejpam-2406	23	5	element	element	NOUN
ejpam-2406	23	6	and	and	CCONJ
ejpam-2406	23	7	the	the	DET
ejpam-2406	23	8	greatest	great	ADJ
ejpam-2406	23	9	element	element	NOUN
ejpam-2406	23	10	of	of	ADP
ejpam-2406	23	11	m	m	PROPN
ejpam-2406	23	12	will	will	AUX
ejpam-2406	23	13	be	be	AUX
ejpam-2406	23	14	denoted	denote	VERB
ejpam-2406	23	15	by	by	ADP
ejpam-2406	23	16	om	om	PROPN
ejpam-2406	23	17	and	and	CCONJ
ejpam-2406	23	18	i	i	PRON
ejpam-2406	23	19	m	m	VERB
ejpam-2406	23	20	.	.	PUNCT
ejpam-2406	24	1	here	here	ADV
ejpam-2406	24	2	after	after	ADP
ejpam-2406	24	3	l	l	NOUN
ejpam-2406	24	4	will	will	AUX
ejpam-2406	24	5	be	be	AUX
ejpam-2406	24	6	a	a	DET
ejpam-2406	24	7	multiplicative	multiplicative	ADJ
ejpam-2406	24	8	lattice	lattice	NOUN
ejpam-2406	24	9	and	and	CCONJ
ejpam-2406	24	10	m	m	PROPN
ejpam-2406	24	11	will	will	AUX
ejpam-2406	24	12	be	be	AUX
ejpam-2406	24	13	a	a	DET
ejpam-2406	24	14	lattice	lattice	NOUN
ejpam-2406	24	15	module	module	NOUN
ejpam-2406	24	16	over	over	ADP
ejpam-2406	24	17	l.	l.	PROPN
ejpam-2406	24	18	as	as	ADP
ejpam-2406	24	19	in	in	ADP
ejpam-2406	24	20	the	the	DET
ejpam-2406	24	21	case	case	NOUN
ejpam-2406	24	22	of	of	ADP
ejpam-2406	24	23	commutative	commutative	ADJ
ejpam-2406	24	24	rings	ring	NOUN
ejpam-2406	24	25	,	,	PUNCT
ejpam-2406	24	26	there	there	PRON
ejpam-2406	24	27	are	be	VERB
ejpam-2406	24	28	residuation	residuation	ADJ
ejpam-2406	24	29	operations	operation	NOUN
ejpam-2406	24	30	in	in	ADP
ejpam-2406	24	31	lattice	lattice	NOUN
ejpam-2406	24	32	module	module	NOUN
ejpam-2406	24	33	.	.	PUNCT
ejpam-2406	25	1	for	for	ADP
ejpam-2406	25	2	a	a	DET
ejpam-2406	25	3	,	,	PUNCT
ejpam-2406	25	4	b	b	PROPN
ejpam-2406	25	5	∈	∈	PROPN
ejpam-2406	25	6	l	l	NOUN
ejpam-2406	25	7	and	and	CCONJ
ejpam-2406	25	8	a	a	DET
ejpam-2406	25	9	,	,	PUNCT
ejpam-2406	25	10	b	b	X
ejpam-2406	25	11	∈	∈	ADV
ejpam-2406	25	12	m	m	NOUN
ejpam-2406	25	13	,	,	PUNCT
ejpam-2406	25	14	•	•	ADV
ejpam-2406	25	15	a	a	PRON
ejpam-2406	25	16	:	:	PUNCT
ejpam-2406	25	17	b	b	NOUN
ejpam-2406	25	18	is	be	AUX
ejpam-2406	25	19	the	the	DET
ejpam-2406	25	20	join	join	NOUN
ejpam-2406	25	21	of	of	ADP
ejpam-2406	25	22	all	all	DET
ejpam-2406	25	23	elements	element	NOUN
ejpam-2406	25	24	c	c	NOUN
ejpam-2406	25	25	in	in	ADP
ejpam-2406	25	26	l	l	NOUN
ejpam-2406	25	27	such	such	ADJ
ejpam-2406	25	28	that	that	SCONJ
ejpam-2406	25	29	cb	cb	PROPN
ejpam-2406	25	30	¶	¶	PROPN
ejpam-2406	25	31	a	a	PROPN
ejpam-2406	25	32	,	,	PUNCT
ejpam-2406	25	33	•	•	ADP
ejpam-2406	25	34	a	a	PRON
ejpam-2406	25	35	:	:	PUNCT
ejpam-2406	25	36	b	b	NOUN
ejpam-2406	25	37	is	be	AUX
ejpam-2406	25	38	the	the	DET
ejpam-2406	25	39	join	join	NOUN
ejpam-2406	25	40	of	of	ADP
ejpam-2406	25	41	all	all	DET
ejpam-2406	25	42	elements	element	NOUN
ejpam-2406	25	43	c	c	NOUN
ejpam-2406	25	44	in	in	ADP
ejpam-2406	25	45	m	m	PRON
ejpam-2406	25	46	such	such	ADJ
ejpam-2406	25	47	that	that	SCONJ
ejpam-2406	25	48	bc	bc	PROPN
ejpam-2406	25	49	¶	¶	PROPN
ejpam-2406	25	50	a	a	PROPN
ejpam-2406	25	51	and	and	CCONJ
ejpam-2406	25	52	•	•	ADP
ejpam-2406	25	53	a	a	PRON
ejpam-2406	25	54	:	:	PUNCT
ejpam-2406	25	55	b	b	NOUN
ejpam-2406	25	56	is	be	AUX
ejpam-2406	25	57	the	the	DET
ejpam-2406	25	58	join	join	NOUN
ejpam-2406	25	59	of	of	ADP
ejpam-2406	25	60	all	all	DET
ejpam-2406	25	61	elements	element	NOUN
ejpam-2406	25	62	a	a	PRON
ejpam-2406	25	63	in	in	ADP
ejpam-2406	25	64	l	l	NOUN
ejpam-2406	25	65	such	such	ADJ
ejpam-2406	25	66	that	that	SCONJ
ejpam-2406	25	67	ab	ab	PROPN
ejpam-2406	25	68	¶	¶	PROPN
ejpam-2406	25	69	a.	a.	NOUN
ejpam-2406	25	70	an	an	DET
ejpam-2406	25	71	element	element	NOUN
ejpam-2406	25	72	n	n	PROPN
ejpam-2406	25	73	6=	6=	PROPN
ejpam-2406	25	74	i	i	PRON
ejpam-2406	25	75	m	m	VERB
ejpam-2406	25	76	of	of	ADP
ejpam-2406	25	77	a	a	DET
ejpam-2406	25	78	lattice	lattice	NOUN
ejpam-2406	25	79	module	module	NOUN
ejpam-2406	25	80	m	m	VERB
ejpam-2406	25	81	is	be	AUX
ejpam-2406	25	82	called	call	VERB
ejpam-2406	25	83	a	a	DET
ejpam-2406	25	84	prime	prime	ADJ
ejpam-2406	25	85	element	element	NOUN
ejpam-2406	25	86	if	if	SCONJ
ejpam-2406	25	87	whenever	whenever	ADV
ejpam-2406	25	88	aa¶	aa¶	ADV
ejpam-2406	25	89	n	n	VERB
ejpam-2406	25	90	where	where	SCONJ
ejpam-2406	25	91	a	a	DET
ejpam-2406	25	92	∈	∈	PROPN
ejpam-2406	25	93	l	l	NOUN
ejpam-2406	25	94	,	,	PUNCT
ejpam-2406	25	95	a	a	DET
ejpam-2406	25	96	∈	∈	NOUN
ejpam-2406	25	97	m	m	VERB
ejpam-2406	25	98	implies	imply	VERB
ejpam-2406	25	99	either	either	CCONJ
ejpam-2406	25	100	a	a	DET
ejpam-2406	25	101	¶	¶	PROPN
ejpam-2406	25	102	(	(	PUNCT
ejpam-2406	25	103	n	n	NUM
ejpam-2406	25	104	:	:	PUNCT
ejpam-2406	25	105	i	i	PRON
ejpam-2406	25	106	m	m	VERB
ejpam-2406	25	107	)	)	PUNCT
ejpam-2406	25	108	or	or	CCONJ
ejpam-2406	25	109	a	a	DET
ejpam-2406	25	110	¶	¶	NOUN
ejpam-2406	25	111	n	n	NOUN
ejpam-2406	25	112	.	.	PUNCT
ejpam-2406	26	1	an	an	DET
ejpam-2406	26	2	element	element	NOUN
ejpam-2406	26	3	n	n	PROPN
ejpam-2406	26	4	6=	6=	PROPN
ejpam-2406	26	5	i	i	PRON
ejpam-2406	26	6	m	m	VERB
ejpam-2406	26	7	of	of	ADP
ejpam-2406	26	8	a	a	DET
ejpam-2406	26	9	lattice	lattice	NOUN
ejpam-2406	26	10	module	module	NOUN
ejpam-2406	26	11	m	m	VERB
ejpam-2406	26	12	is	be	AUX
ejpam-2406	26	13	called	call	VERB
ejpam-2406	26	14	a	a	DET
ejpam-2406	26	15	primary	primary	ADJ
ejpam-2406	26	16	element	element	NOUN
ejpam-2406	26	17	if	if	SCONJ
ejpam-2406	26	18	whenever	whenever	SCONJ
ejpam-2406	26	19	aa	aa	PROPN
ejpam-2406	26	20	¶	¶	PROPN
ejpam-2406	26	21	n	n	PROPN
ejpam-2406	26	22	where	where	SCONJ
ejpam-2406	26	23	a	a	DET
ejpam-2406	26	24	∈	∈	PROPN
ejpam-2406	26	25	l	l	NOUN
ejpam-2406	26	26	,	,	PUNCT
ejpam-2406	26	27	a	a	DET
ejpam-2406	26	28	∈	∈	NOUN
ejpam-2406	26	29	m	m	VERB
ejpam-2406	26	30	implies	imply	VERB
ejpam-2406	26	31	either	either	CCONJ
ejpam-2406	26	32	a	a	DET
ejpam-2406	26	33	¶	¶	NOUN
ejpam-2406	26	34	n	n	NOUN
ejpam-2406	26	35	or	or	CCONJ
ejpam-2406	26	36	an	an	DET
ejpam-2406	26	37	¶	¶	NOUN
ejpam-2406	26	38	(	(	PUNCT
ejpam-2406	26	39	n	n	NUM
ejpam-2406	26	40	:	:	PUNCT
ejpam-2406	26	41	i	i	PRON
ejpam-2406	26	42	m	m	VERB
ejpam-2406	26	43	)	)	PUNCT
ejpam-2406	26	44	for	for	ADP
ejpam-2406	26	45	some	some	DET
ejpam-2406	26	46	positive	positive	ADJ
ejpam-2406	26	47	integer	integer	NOUN
ejpam-2406	26	48	n.	n.	NOUN
ejpam-2406	26	49	a	a	DET
ejpam-2406	26	50	lattice	lattice	NOUN
ejpam-2406	26	51	module	module	NOUN
ejpam-2406	26	52	m	m	VERB
ejpam-2406	26	53	is	be	AUX
ejpam-2406	26	54	called	call	VERB
ejpam-2406	26	55	a	a	DET
ejpam-2406	26	56	multiplication	multiplication	NOUN
ejpam-2406	26	57	lattice	lattice	NOUN
ejpam-2406	26	58	module	module	NOUN
ejpam-2406	26	59	if	if	SCONJ
ejpam-2406	26	60	for	for	ADP
ejpam-2406	26	61	any	any	DET
ejpam-2406	26	62	element	element	NOUN
ejpam-2406	26	63	n	n	PROPN
ejpam-2406	26	64	of	of	ADP
ejpam-2406	26	65	m	m	VERB
ejpam-2406	26	66	there	there	PRON
ejpam-2406	26	67	exists	exist	VERB
ejpam-2406	26	68	an	an	DET
ejpam-2406	26	69	element	element	NOUN
ejpam-2406	26	70	a	a	PRON
ejpam-2406	26	71	of	of	ADP
ejpam-2406	26	72	l	l	NOUN
ejpam-2406	27	1	such	such	ADJ
ejpam-2406	27	2	that	that	SCONJ
ejpam-2406	27	3	n	n	NOUN
ejpam-2406	27	4	=	=	NOUN
ejpam-2406	27	5	aim	aim	NOUN
ejpam-2406	27	6	.an	.an	PUNCT
ejpam-2406	27	7	element	element	NOUN
ejpam-2406	27	8	n	n	PROPN
ejpam-2406	27	9	6=	6=	PROPN
ejpam-2406	27	10	i	i	PRON
ejpam-2406	27	11	m	m	VERB
ejpam-2406	27	12	of	of	ADP
ejpam-2406	27	13	a	a	DET
ejpam-2406	27	14	lattice	lattice	NOUN
ejpam-2406	27	15	module	module	NOUN
ejpam-2406	27	16	m	m	NOUN
ejpam-2406	27	17	is	be	AUX
ejpam-2406	27	18	said	say	VERB
ejpam-2406	27	19	to	to	PART
ejpam-2406	27	20	have	have	VERB
ejpam-2406	27	21	primary	primary	ADJ
ejpam-2406	27	22	decomposition	decomposition	NOUN
ejpam-2406	27	23	if	if	SCONJ
ejpam-2406	27	24	there	there	PRON
ejpam-2406	27	25	exist	exist	VERB
ejpam-2406	27	26	primary	primary	ADJ
ejpam-2406	27	27	elements	element	NOUN
ejpam-2406	27	28	q1,q2	q1,q2	PROPN
ejpam-2406	27	29	,	,	PUNCT
ejpam-2406	27	30	.	.	PUNCT
ejpam-2406	27	31	.	.	PUNCT
ejpam-2406	28	1	.	.	PUNCT
ejpam-2406	29	1	,	,	PUNCT
ejpam-2406	29	2	qk	qk	AUX
ejpam-2406	29	3	such	such	ADJ
ejpam-2406	29	4	that	that	SCONJ
ejpam-2406	29	5	n	n	PROPN
ejpam-2406	29	6	=	=	PROPN
ejpam-2406	29	7	q1	q1	PROPN
ejpam-2406	29	8	∧q2	∧q2	VERB
ejpam-2406	29	9	∧	∧	PROPN
ejpam-2406	29	10	·	·	PUNCT
ejpam-2406	29	11	·	·	PUNCT
ejpam-2406	29	12	·	·	PUNCT
ejpam-2406	30	1	∧	∧	NOUN
ejpam-2406	30	2	qk	qk	NOUN
ejpam-2406	30	3	.	.	PUNCT
ejpam-2406	31	1	if	if	SCONJ
ejpam-2406	31	2	some	some	PRON
ejpam-2406	31	3	q	q	NOUN
ejpam-2406	31	4	i	i	PRON
ejpam-2406	31	5	contains	contain	VERB
ejpam-2406	31	6	the	the	DET
ejpam-2406	31	7	meet	meet	NOUN
ejpam-2406	31	8	of	of	ADP
ejpam-2406	31	9	remaining	remain	VERB
ejpam-2406	31	10	ones	one	NOUN
ejpam-2406	31	11	then	then	ADV
ejpam-2406	31	12	this	this	DET
ejpam-2406	31	13	q	q	NOUN
ejpam-2406	31	14	i	i	PRON
ejpam-2406	31	15	can	can	AUX
ejpam-2406	31	16	be	be	AUX
ejpam-2406	31	17	dropped	drop	VERB
ejpam-2406	31	18	from	from	ADP
ejpam-2406	31	19	the	the	DET
ejpam-2406	31	20	primary	primary	ADJ
ejpam-2406	31	21	decomposition	decomposition	NOUN
ejpam-2406	31	22	.	.	PUNCT
ejpam-2406	32	1	similarly	similarly	ADV
ejpam-2406	32	2	any	any	DET
ejpam-2406	32	3	other	other	ADJ
ejpam-2406	32	4	primary	primary	ADJ
ejpam-2406	32	5	component	component	NOUN
ejpam-2406	32	6	which	which	PRON
ejpam-2406	32	7	contains	contain	VERB
ejpam-2406	32	8	the	the	DET
ejpam-2406	32	9	meet	meet	NOUN
ejpam-2406	32	10	of	of	ADP
ejpam-2406	32	11	remaining	remain	VERB
ejpam-2406	32	12	ones	one	NOUN
ejpam-2406	32	13	can	can	AUX
ejpam-2406	32	14	be	be	AUX
ejpam-2406	32	15	dropped	drop	VERB
ejpam-2406	32	16	from	from	ADP
ejpam-2406	32	17	the	the	DET
ejpam-2406	32	18	primary	primary	ADJ
ejpam-2406	32	19	decomposition	decomposition	NOUN
ejpam-2406	32	20	.	.	PUNCT
ejpam-2406	33	1	if	if	SCONJ
ejpam-2406	33	2	such	such	ADJ
ejpam-2406	33	3	primary	primary	ADJ
ejpam-2406	33	4	components	component	NOUN
ejpam-2406	33	5	are	be	AUX
ejpam-2406	33	6	removed	remove	VERB
ejpam-2406	33	7	and	and	CCONJ
ejpam-2406	33	8	the	the	DET
ejpam-2406	33	9	primary	primary	ADJ
ejpam-2406	33	10	components	component	NOUN
ejpam-2406	33	11	with	with	ADP
ejpam-2406	33	12	same	same	ADJ
ejpam-2406	33	13	associated	associate	VERB
ejpam-2406	33	14	primes	prime	NOUN
ejpam-2406	33	15	are	be	AUX
ejpam-2406	33	16	combined	combine	VERB
ejpam-2406	33	17	then	then	ADV
ejpam-2406	33	18	we	we	PRON
ejpam-2406	33	19	get	get	VERB
ejpam-2406	33	20	a	a	DET
ejpam-2406	33	21	reduced	reduce	VERB
ejpam-2406	33	22	primary	primary	ADJ
ejpam-2406	33	23	decomposition	decomposition	NOUN
ejpam-2406	33	24	in	in	ADP
ejpam-2406	33	25	which	which	PRON
ejpam-2406	33	26	distinct	distinct	ADJ
ejpam-2406	33	27	primary	primary	ADJ
ejpam-2406	33	28	components	component	NOUN
ejpam-2406	33	29	are	be	AUX
ejpam-2406	33	30	associated	associate	VERB
ejpam-2406	33	31	with	with	ADP
ejpam-2406	33	32	distinct	distinct	ADJ
ejpam-2406	33	33	primes	prime	NOUN
ejpam-2406	33	34	such	such	DET
ejpam-2406	33	35	a	a	DET
ejpam-2406	33	36	primary	primary	ADJ
ejpam-2406	33	37	decomposition	decomposition	NOUN
ejpam-2406	33	38	is	be	AUX
ejpam-2406	33	39	called	call	VERB
ejpam-2406	33	40	a	a	DET
ejpam-2406	33	41	normal	normal	ADJ
ejpam-2406	33	42	decomposition	decomposition	NOUN
ejpam-2406	33	43	.	.	PUNCT
ejpam-2406	34	1	this	this	DET
ejpam-2406	34	2	decomposition	decomposition	NOUN
ejpam-2406	34	3	is	be	AUX
ejpam-2406	34	4	also	also	ADV
ejpam-2406	34	5	said	say	VERB
ejpam-2406	34	6	to	to	PART
ejpam-2406	34	7	be	be	AUX
ejpam-2406	34	8	reduced	reduce	VERB
ejpam-2406	34	9	.	.	PUNCT
ejpam-2406	35	1	this	this	DET
ejpam-2406	35	2	study	study	NOUN
ejpam-2406	35	3	is	be	AUX
ejpam-2406	35	4	carried	carry	VERB
ejpam-2406	35	5	out	out	ADP
ejpam-2406	35	6	by	by	ADP
ejpam-2406	35	7	d.	d.	PROPN
ejpam-2406	35	8	d.	d.	PROPN
ejpam-2406	35	9	anderson	anderson	PROPN
ejpam-2406	36	1	[	[	X
ejpam-2406	36	2	1	1	X
ejpam-2406	36	3	]	]	PUNCT
ejpam-2406	36	4	and	and	CCONJ
ejpam-2406	36	5	for	for	ADP
ejpam-2406	36	6	multiplicative	multiplicative	ADJ
ejpam-2406	36	7	lattices	lattice	NOUN
ejpam-2406	36	8	this	this	DET
ejpam-2406	36	9	work	work	NOUN
ejpam-2406	36	10	is	be	AUX
ejpam-2406	36	11	done	do	VERB
ejpam-2406	36	12	by	by	ADP
ejpam-2406	36	13	r.	r.	PROPN
ejpam-2406	36	14	p.	p.	PROPN
ejpam-2406	36	15	dilworth	dilworth	PROPN
ejpam-2406	37	1	[	[	X
ejpam-2406	37	2	2	2	NUM
ejpam-2406	37	3	]	]	PUNCT
ejpam-2406	37	4	.	.	PUNCT
ejpam-2406	38	1	2	2	X
ejpam-2406	38	2	.	.	X
ejpam-2406	38	3	classical	classical	ADJ
ejpam-2406	38	4	primary	primary	ADJ
ejpam-2406	38	5	and	and	CCONJ
ejpam-2406	38	6	classical	classical	ADJ
ejpam-2406	38	7	quasi	quasi	ADJ
ejpam-2406	38	8	primary	primary	ADJ
ejpam-2406	38	9	elements	element	NOUN
ejpam-2406	38	10	the	the	DET
ejpam-2406	38	11	notion	notion	NOUN
ejpam-2406	38	12	of	of	ADP
ejpam-2406	38	13	a	a	DET
ejpam-2406	38	14	quasi	quasi	ADJ
ejpam-2406	38	15	primary	primary	ADJ
ejpam-2406	38	16	ideal	ideal	NOUN
ejpam-2406	38	17	was	be	AUX
ejpam-2406	38	18	defined	define	VERB
ejpam-2406	38	19	by	by	ADP
ejpam-2406	38	20	fuchs	fuchs	PROPN
ejpam-2406	38	21	[	[	X
ejpam-2406	38	22	4	4	NUM
ejpam-2406	38	23	]	]	PUNCT
ejpam-2406	38	24	which	which	PRON
ejpam-2406	38	25	is	be	AUX
ejpam-2406	38	26	a	a	DET
ejpam-2406	38	27	generalization	generalization	NOUN
ejpam-2406	38	28	of	of	ADP
ejpam-2406	38	29	the	the	DET
ejpam-2406	38	30	notions	notion	NOUN
ejpam-2406	38	31	of	of	ADP
ejpam-2406	38	32	a	a	DET
ejpam-2406	38	33	primary	primary	ADJ
ejpam-2406	38	34	ideal	ideal	NOUN
ejpam-2406	38	35	.	.	PUNCT
ejpam-2406	39	1	the	the	DET
ejpam-2406	39	2	notions	notion	NOUN
ejpam-2406	39	3	of	of	ADP
ejpam-2406	39	4	quasi	quasi	NOUN
ejpam-2406	39	5	primary	primary	ADJ
ejpam-2406	39	6	,	,	PUNCT
ejpam-2406	39	7	classical	classical	ADJ
ejpam-2406	39	8	primary	primary	NOUN
ejpam-2406	39	9	,	,	PUNCT
ejpam-2406	39	10	classical	classical	ADJ
ejpam-2406	39	11	quasi	quasi	ADJ
ejpam-2406	39	12	primary	primary	ADJ
ejpam-2406	39	13	sub	sub	NOUN
ejpam-2406	39	14	modules	module	NOUN
ejpam-2406	39	15	are	be	AUX
ejpam-2406	39	16	studied	study	VERB
ejpam-2406	39	17	by	by	ADP
ejpam-2406	39	18	m	m	PROPN
ejpam-2406	39	19	behboodi	behboodi	PROPN
ejpam-2406	39	20	et	et	PROPN
ejpam-2406	39	21	al	al	PROPN
ejpam-2406	39	22	.	.	PUNCT
ejpam-2406	40	1	[	[	X
ejpam-2406	40	2	1	1	NUM
ejpam-2406	40	3	]	]	PUNCT
ejpam-2406	40	4	.	.	PUNCT
ejpam-2406	41	1	we	we	PRON
ejpam-2406	41	2	generalize	generalize	VERB
ejpam-2406	41	3	there	there	PRON
ejpam-2406	41	4	notions	notion	NOUN
ejpam-2406	41	5	for	for	ADP
ejpam-2406	41	6	multiplicative	multiplicative	ADJ
ejpam-2406	41	7	lattices	lattice	NOUN
ejpam-2406	41	8	and	and	CCONJ
ejpam-2406	41	9	lattice	lattice	NOUN
ejpam-2406	41	10	modules	module	NOUN
ejpam-2406	41	11	.	.	PUNCT
ejpam-2406	42	1	definition	definition	NOUN
ejpam-2406	42	2	1	1	NUM
ejpam-2406	42	3	.	.	PUNCT
ejpam-2406	43	1	an	an	DET
ejpam-2406	43	2	element	element	NOUN
ejpam-2406	43	3	q	q	NOUN
ejpam-2406	43	4	of	of	ADP
ejpam-2406	43	5	a	a	DET
ejpam-2406	43	6	multiplicative	multiplicative	ADJ
ejpam-2406	43	7	lattice	lattice	NOUN
ejpam-2406	43	8	l	l	NOUN
ejpam-2406	43	9	is	be	AUX
ejpam-2406	43	10	called	call	VERB
ejpam-2406	43	11	a	a	DET
ejpam-2406	43	12	classical	classical	ADJ
ejpam-2406	43	13	primary	primary	ADJ
ejpam-2406	43	14	element	element	NOUN
ejpam-2406	43	15	if	if	SCONJ
ejpam-2406	43	16	abr	abr	PROPN
ejpam-2406	43	17	¶	¶	PROPN
ejpam-2406	43	18	q	q	PROPN
ejpam-2406	43	19	where	where	SCONJ
ejpam-2406	43	20	a	a	PRON
ejpam-2406	43	21	,	,	PUNCT
ejpam-2406	43	22	b	b	PROPN
ejpam-2406	43	23	∈	∈	PROPN
ejpam-2406	43	24	l	l	NOUN
ejpam-2406	43	25	,	,	PUNCT
ejpam-2406	43	26	r	r	NOUN
ejpam-2406	43	27	∈	∈	PROPN
ejpam-2406	43	28	l	l	NOUN
ejpam-2406	43	29	implies	imply	VERB
ejpam-2406	43	30	that	that	SCONJ
ejpam-2406	43	31	either	either	CCONJ
ejpam-2406	43	32	ar	ar	PROPN
ejpam-2406	43	33	¶	¶	PROPN
ejpam-2406	43	34	q	q	PROPN
ejpam-2406	43	35	or	or	CCONJ
ejpam-2406	43	36	bkr	bkr	PROPN
ejpam-2406	43	37	¶	¶	PROPN
ejpam-2406	43	38	q	q	PROPN
ejpam-2406	43	39	for	for	ADP
ejpam-2406	43	40	some	some	DET
ejpam-2406	43	41	integer	integer	NOUN
ejpam-2406	43	42	k.	k.	PROPN
ejpam-2406	43	43	definition	definition	NOUN
ejpam-2406	43	44	2	2	NUM
ejpam-2406	43	45	.	.	PUNCT
ejpam-2406	43	46	an	an	DET
ejpam-2406	43	47	element	element	NOUN
ejpam-2406	43	48	q	q	NOUN
ejpam-2406	43	49	of	of	ADP
ejpam-2406	43	50	a	a	DET
ejpam-2406	43	51	multiplicative	multiplicative	ADJ
ejpam-2406	43	52	lattice	lattice	NOUN
ejpam-2406	43	53	l	l	NOUN
ejpam-2406	43	54	is	be	AUX
ejpam-2406	43	55	called	call	VERB
ejpam-2406	43	56	a	a	DET
ejpam-2406	43	57	classical	classical	ADJ
ejpam-2406	43	58	quasi	quasi	NOUN
ejpam-2406	43	59	primary	primary	ADJ
ejpam-2406	43	60	element	element	NOUN
ejpam-2406	43	61	if	if	SCONJ
ejpam-2406	43	62	abr	abr	PROPN
ejpam-2406	43	63	¶	¶	PROPN
ejpam-2406	43	64	q	q	PROPN
ejpam-2406	43	65	where	where	SCONJ
ejpam-2406	43	66	a	a	PRON
ejpam-2406	43	67	,	,	PUNCT
ejpam-2406	43	68	b	b	PROPN
ejpam-2406	43	69	∈	∈	PROPN
ejpam-2406	43	70	l	l	NOUN
ejpam-2406	43	71	,	,	PUNCT
ejpam-2406	43	72	r	r	NOUN
ejpam-2406	43	73	∈	∈	PROPN
ejpam-2406	43	74	l	l	NOUN
ejpam-2406	43	75	implies	imply	VERB
ejpam-2406	43	76	that	that	SCONJ
ejpam-2406	43	77	either	either	CCONJ
ejpam-2406	43	78	akr	akr	NOUN
ejpam-2406	43	79	¶	¶	PROPN
ejpam-2406	43	80	q	q	PROPN
ejpam-2406	43	81	or	or	CCONJ
ejpam-2406	43	82	bkr	bkr	PROPN
ejpam-2406	43	83	¶	¶	PROPN
ejpam-2406	43	84	q	q	PROPN
ejpam-2406	43	85	for	for	ADP
ejpam-2406	43	86	some	some	DET
ejpam-2406	43	87	integer	integer	NOUN
ejpam-2406	43	88	k.	k.	PROPN
ejpam-2406	43	89	definition	definition	NOUN
ejpam-2406	43	90	3	3	NUM
ejpam-2406	43	91	.	.	PUNCT
ejpam-2406	44	1	an	an	DET
ejpam-2406	44	2	element	element	NOUN
ejpam-2406	44	3	q	q	NOUN
ejpam-2406	44	4	of	of	ADP
ejpam-2406	44	5	a	a	DET
ejpam-2406	44	6	multiplicative	multiplicative	ADJ
ejpam-2406	44	7	lattice	lattice	NOUN
ejpam-2406	44	8	l	l	NOUN
ejpam-2406	44	9	is	be	AUX
ejpam-2406	44	10	called	call	VERB
ejpam-2406	44	11	a	a	DET
ejpam-2406	44	12	quasi	quasi	ADJ
ejpam-2406	44	13	primary	primary	ADJ
ejpam-2406	44	14	element	element	NOUN
ejpam-2406	44	15	if	if	SCONJ
ejpam-2406	44	16	radical	radical	ADJ
ejpam-2406	44	17	of	of	ADP
ejpam-2406	44	18	q	q	PROPN
ejpam-2406	44	19	is	be	AUX
ejpam-2406	44	20	a	a	DET
ejpam-2406	44	21	prime	prime	ADJ
ejpam-2406	44	22	element	element	NOUN
ejpam-2406	44	23	that	that	PRON
ejpam-2406	44	24	is	be	AUX
ejpam-2406	44	25	q	q	PUNCT
ejpam-2406	44	26	is	be	AUX
ejpam-2406	44	27	called	call	VERB
ejpam-2406	44	28	quasi	quasi	ADJ
ejpam-2406	44	29	primary	primary	NOUN
ejpam-2406	44	30	if	if	SCONJ
ejpam-2406	44	31	ab	ab	PROPN
ejpam-2406	44	32	¶	¶	PROPN
ejpam-2406	44	33	p	p	PROPN
ejpam-2406	44	34	q	q	X
ejpam-2406	44	35	where	where	SCONJ
ejpam-2406	44	36	a	a	DET
ejpam-2406	44	37	,	,	PUNCT
ejpam-2406	44	38	b	b	X
ejpam-2406	44	39	∈	∈	PROPN
ejpam-2406	44	40	l	l	NOUN
ejpam-2406	44	41	implies	imply	VERB
ejpam-2406	44	42	that	that	SCONJ
ejpam-2406	44	43	either	either	CCONJ
ejpam-2406	44	44	ak	ak	PROPN
ejpam-2406	44	45	¶	¶	PROPN
ejpam-2406	44	46	q	q	PROPN
ejpam-2406	44	47	or	or	CCONJ
ejpam-2406	44	48	bk	bk	PROPN
ejpam-2406	44	49	¶	¶	PROPN
ejpam-2406	44	50	q	q	NOUN
ejpam-2406	44	51	for	for	ADP
ejpam-2406	44	52	some	some	DET
ejpam-2406	44	53	integer	integer	PROPN
ejpam-2406	44	54	k.	k.	PROPN
ejpam-2406	44	55	c.	c.	PROPN
ejpam-2406	44	56	manjarekar	manjarekar	PROPN
ejpam-2406	44	57	,	,	PUNCT
ejpam-2406	44	58	u.	u.	PROPN
ejpam-2406	44	59	kandale	kandale	PROPN
ejpam-2406	44	60	/	/	SYM
ejpam-2406	44	61	eur	eur	PROPN
ejpam-2406	44	62	.	.	PUNCT
ejpam-2406	45	1	j.	j.	PROPN
ejpam-2406	45	2	pure	pure	PROPN
ejpam-2406	45	3	appl	appl	PROPN
ejpam-2406	45	4	.	.	PROPN
ejpam-2406	45	5	math	math	PROPN
ejpam-2406	45	6	,	,	PUNCT
ejpam-2406	45	7	8	8	NUM
ejpam-2406	45	8	(	(	PUNCT
ejpam-2406	45	9	2015	2015	NUM
ejpam-2406	45	10	)	)	PUNCT
ejpam-2406	45	11	,	,	PUNCT
ejpam-2406	45	12	172	172	NUM
ejpam-2406	45	13	-	-	SYM
ejpam-2406	45	14	184	184	NUM
ejpam-2406	45	15	174	174	NUM
ejpam-2406	45	16	definition	definition	NOUN
ejpam-2406	45	17	4	4	NUM
ejpam-2406	45	18	.	.	PUNCT
ejpam-2406	46	1	let	let	VERB
ejpam-2406	46	2	m	m	PRON
ejpam-2406	46	3	be	be	AUX
ejpam-2406	46	4	a	a	DET
ejpam-2406	46	5	lattice	lattice	NOUN
ejpam-2406	46	6	module	module	NOUN
ejpam-2406	46	7	over	over	ADP
ejpam-2406	46	8	a	a	DET
ejpam-2406	46	9	multiplicative	multiplicative	ADJ
ejpam-2406	46	10	lattice	lattice	NOUN
ejpam-2406	46	11	l	l	PROPN
ejpam-2406	46	12	a	a	DET
ejpam-2406	46	13	proper	proper	ADJ
ejpam-2406	46	14	element	element	NOUN
ejpam-2406	46	15	q	q	NOUN
ejpam-2406	46	16	of	of	ADP
ejpam-2406	46	17	m	m	PROPN
ejpam-2406	46	18	is	be	AUX
ejpam-2406	46	19	called	call	VERB
ejpam-2406	46	20	a	a	DET
ejpam-2406	46	21	classical	classical	ADJ
ejpam-2406	46	22	primary	primary	ADJ
ejpam-2406	46	23	element	element	NOUN
ejpam-2406	46	24	in	in	ADP
ejpam-2406	46	25	m	m	PROPN
ejpam-2406	46	26	if	if	SCONJ
ejpam-2406	46	27	abn	abn	NOUN
ejpam-2406	46	28	¶q	¶q	NOUN
ejpam-2406	47	1	where	where	SCONJ
ejpam-2406	47	2	a	a	DET
ejpam-2406	47	3	,	,	PUNCT
ejpam-2406	47	4	b	b	PROPN
ejpam-2406	47	5	∈	∈	PROPN
ejpam-2406	47	6	l	l	NOUN
ejpam-2406	47	7	,	,	PUNCT
ejpam-2406	47	8	n	n	PROPN
ejpam-2406	47	9	∈	∈	NOUN
ejpam-2406	47	10	m	m	VERB
ejpam-2406	47	11	then	then	ADV
ejpam-2406	47	12	either	either	CCONJ
ejpam-2406	47	13	an	an	DET
ejpam-2406	47	14	¶q	¶q	NOUN
ejpam-2406	47	15	or	or	CCONJ
ejpam-2406	47	16	bkn	bkn	PROPN
ejpam-2406	47	17	¶q	¶q	NOUN
ejpam-2406	47	18	for	for	ADP
ejpam-2406	47	19	some	some	DET
ejpam-2406	47	20	integer	integer	PROPN
ejpam-2406	47	21	k.	k.	PROPN
ejpam-2406	47	22	definition	definition	NOUN
ejpam-2406	47	23	5	5	NUM
ejpam-2406	47	24	.	.	PUNCT
ejpam-2406	48	1	a	a	DET
ejpam-2406	48	2	proper	proper	ADJ
ejpam-2406	48	3	element	element	NOUN
ejpam-2406	48	4	q	q	NOUN
ejpam-2406	48	5	of	of	ADP
ejpam-2406	48	6	m	m	PROPN
ejpam-2406	48	7	is	be	AUX
ejpam-2406	48	8	called	call	VERB
ejpam-2406	48	9	a	a	DET
ejpam-2406	48	10	classical	classical	ADJ
ejpam-2406	48	11	quasi	quasi	ADJ
ejpam-2406	48	12	primary	primary	ADJ
ejpam-2406	48	13	element	element	NOUN
ejpam-2406	48	14	in	in	ADP
ejpam-2406	48	15	m	m	PROPN
ejpam-2406	48	16	if	if	SCONJ
ejpam-2406	48	17	abn	abn	NOUN
ejpam-2406	48	18	¶q	¶q	NOUN
ejpam-2406	48	19	where	where	SCONJ
ejpam-2406	48	20	a	a	DET
ejpam-2406	48	21	,	,	PUNCT
ejpam-2406	48	22	b	b	PROPN
ejpam-2406	48	23	∈	∈	PROPN
ejpam-2406	48	24	l	l	NOUN
ejpam-2406	48	25	,	,	PUNCT
ejpam-2406	48	26	n	n	PROPN
ejpam-2406	49	1	∈	∈	NOUN
ejpam-2406	50	1	m	m	VERB
ejpam-2406	50	2	then	then	ADV
ejpam-2406	50	3	either	either	CCONJ
ejpam-2406	50	4	akn	akn	PROPN
ejpam-2406	50	5	¶q	¶q	PROPN
ejpam-2406	50	6	or	or	CCONJ
ejpam-2406	50	7	bkn	bkn	PROPN
ejpam-2406	50	8	¶q	¶q	NOUN
ejpam-2406	50	9	for	for	ADP
ejpam-2406	50	10	some	some	DET
ejpam-2406	50	11	integer	integer	PROPN
ejpam-2406	50	12	k.	k.	PROPN
ejpam-2406	50	13	definition	definition	NOUN
ejpam-2406	50	14	6	6	NUM
ejpam-2406	50	15	.	.	PUNCT
ejpam-2406	51	1	a	a	DET
ejpam-2406	51	2	proper	proper	ADJ
ejpam-2406	51	3	element	element	NOUN
ejpam-2406	51	4	q	q	NOUN
ejpam-2406	51	5	of	of	ADP
ejpam-2406	51	6	m	m	PROPN
ejpam-2406	51	7	is	be	AUX
ejpam-2406	51	8	called	call	VERB
ejpam-2406	51	9	a	a	DET
ejpam-2406	51	10	quasi	quasi	ADJ
ejpam-2406	51	11	primary	primary	ADJ
ejpam-2406	51	12	element	element	NOUN
ejpam-2406	51	13	if	if	SCONJ
ejpam-2406	51	14	p	p	PROPN
ejpam-2406	51	15	(	(	PUNCT
ejpam-2406	51	16	q	q	NOUN
ejpam-2406	51	17	:	:	PUNCT
ejpam-2406	51	18	i	i	PRON
ejpam-2406	51	19	m	m	PROPN
ejpam-2406	51	20	)	)	PUNCT
ejpam-2406	51	21	is	be	AUX
ejpam-2406	51	22	a	a	DET
ejpam-2406	51	23	prime	prime	ADJ
ejpam-2406	51	24	element	element	NOUN
ejpam-2406	51	25	of	of	ADP
ejpam-2406	51	26	l.	l.	PROPN
ejpam-2406	51	27	example	example	PROPN
ejpam-2406	52	1	1	1	X
ejpam-2406	52	2	.	.	PUNCT
ejpam-2406	53	1	let	let	AUX
ejpam-2406	53	2	r	r	PRON
ejpam-2406	53	3	be	be	AUX
ejpam-2406	53	4	a	a	DET
ejpam-2406	53	5	integral	integral	ADJ
ejpam-2406	53	6	domain	domain	NOUN
ejpam-2406	53	7	and	and	CCONJ
ejpam-2406	53	8	l(r	l(r	PROPN
ejpam-2406	53	9	)	)	PUNCT
ejpam-2406	53	10	denote	denote	VERB
ejpam-2406	53	11	the	the	DET
ejpam-2406	53	12	set	set	NOUN
ejpam-2406	53	13	of	of	ADP
ejpam-2406	53	14	all	all	DET
ejpam-2406	53	15	ideals	ideal	NOUN
ejpam-2406	53	16	of	of	ADP
ejpam-2406	53	17	r.	r.	PROPN
ejpam-2406	53	18	then	then	ADV
ejpam-2406	53	19	l(r	l(r	PROPN
ejpam-2406	53	20	)	)	PUNCT
ejpam-2406	53	21	is	be	AUX
ejpam-2406	53	22	a	a	DET
ejpam-2406	53	23	multiplicative	multiplicative	ADJ
ejpam-2406	53	24	lattice	lattice	NOUN
ejpam-2406	53	25	.	.	PUNCT
ejpam-2406	54	1	let	let	VERB
ejpam-2406	54	2	f	f	NOUN
ejpam-2406	54	3	=	=	SYM
ejpam-2406	54	4	⊕	⊕	PROPN
ejpam-2406	55	1	λ∈∧	λ∈∧	X
ejpam-2406	55	2	rλ	rλ	VERB
ejpam-2406	55	3	be	be	AUX
ejpam-2406	55	4	a	a	DET
ejpam-2406	55	5	free	free	ADJ
ejpam-2406	55	6	r	r	NOUN
ejpam-2406	55	7	-	-	PUNCT
ejpam-2406	55	8	module	module	NOUN
ejpam-2406	55	9	and	and	CCONJ
ejpam-2406	55	10	let	let	VERB
ejpam-2406	55	11	m	m	PROPN
ejpam-2406	55	12	=	=	SYM
ejpam-2406	55	13	l(f	l(f	PROPN
ejpam-2406	55	14	)	)	PUNCT
ejpam-2406	55	15	denote	denote	VERB
ejpam-2406	55	16	the	the	DET
ejpam-2406	55	17	set	set	NOUN
ejpam-2406	55	18	of	of	ADP
ejpam-2406	55	19	all	all	DET
ejpam-2406	55	20	submodules	submodule	NOUN
ejpam-2406	55	21	of	of	ADP
ejpam-2406	55	22	f.	f.	PROPN
ejpam-2406	56	1	then	then	ADV
ejpam-2406	56	2	m	m	PROPN
ejpam-2406	56	3	is	be	AUX
ejpam-2406	56	4	a	a	DET
ejpam-2406	56	5	lattice	lattice	NOUN
ejpam-2406	56	6	module	module	NOUN
ejpam-2406	56	7	over	over	ADP
ejpam-2406	56	8	a	a	DET
ejpam-2406	56	9	multiplicative	multiplicative	ADJ
ejpam-2406	56	10	lattice	lattice	NOUN
ejpam-2406	56	11	l(r	l(r	PROPN
ejpam-2406	56	12	)	)	PUNCT
ejpam-2406	56	13	.	.	PUNCT
ejpam-2406	57	1	assume	assume	VERB
ejpam-2406	57	2	that	that	SCONJ
ejpam-2406	57	3	,	,	PUNCT
ejpam-2406	57	4	p	p	PRON
ejpam-2406	57	5	is	be	AUX
ejpam-2406	57	6	a	a	DET
ejpam-2406	57	7	nonzero	nonzero	ADJ
ejpam-2406	57	8	prime	prime	ADJ
ejpam-2406	57	9	ideal	ideal	NOUN
ejpam-2406	57	10	in	in	ADP
ejpam-2406	57	11	r.	r.	PROPN
ejpam-2406	57	12	let	let	VERB
ejpam-2406	57	13	n	n	PROPN
ejpam-2406	57	14	=	=	PROPN
ejpam-2406	57	15	⊕	⊕	PROPN
ejpam-2406	57	16	⋋∈∧	⋋∈∧	NOUN
ejpam-2406	57	17	a⋋	a⋋	NOUN
ejpam-2406	57	18	be	be	VERB
ejpam-2406	57	19	a	a	DET
ejpam-2406	57	20	proper	proper	ADJ
ejpam-2406	57	21	submodule	submodule	NOUN
ejpam-2406	57	22	of	of	ADP
ejpam-2406	57	23	f	f	PROPN
ejpam-2406	57	24	such	such	ADJ
ejpam-2406	57	25	that	that	PRON
ejpam-2406	57	26	for	for	ADP
ejpam-2406	57	27	every	every	DET
ejpam-2406	57	28	⋋	⋋	NUM
ejpam-2406	57	29	∈	∈	PROPN
ejpam-2406	57	30	∧	∧	NOUN
ejpam-2406	57	31	either	either	CCONJ
ejpam-2406	57	32	a⋋	a⋋	NOUN
ejpam-2406	57	33	=	=	PUNCT
ejpam-2406	57	34	p	p	NOUN
ejpam-2406	57	35	or	or	CCONJ
ejpam-2406	57	36	a⋋	a⋋	NOUN
ejpam-2406	57	37	=	=	SYM
ejpam-2406	57	38	(	(	PUNCT
ejpam-2406	57	39	0	0	NUM
ejpam-2406	57	40	)	)	PUNCT
ejpam-2406	57	41	.	.	PUNCT
ejpam-2406	58	1	then	then	ADV
ejpam-2406	58	2	n	n	PRON
ejpam-2406	58	3	is	be	AUX
ejpam-2406	58	4	a	a	DET
ejpam-2406	58	5	classical	classical	ADJ
ejpam-2406	58	6	primary	primary	ADJ
ejpam-2406	58	7	element	element	NOUN
ejpam-2406	58	8	of	of	ADP
ejpam-2406	58	9	m.	m.	NOUN
ejpam-2406	58	10	it	it	PRON
ejpam-2406	58	11	can	can	AUX
ejpam-2406	58	12	be	be	AUX
ejpam-2406	58	13	verified	verify	VERB
ejpam-2406	58	14	that	that	SCONJ
ejpam-2406	58	15	,	,	PUNCT
ejpam-2406	58	16	if	if	SCONJ
ejpam-2406	58	17	there	there	PRON
ejpam-2406	58	18	exist	exist	VERB
ejpam-2406	58	19	⋋1,⋋2	⋋1,⋋2	PROPN
ejpam-2406	58	20	∈	∈	NOUN
ejpam-2406	58	21	∧	∧	NOUN
ejpam-2406	58	22	such	such	ADJ
ejpam-2406	58	23	that	that	DET
ejpam-2406	58	24	a⋋1	a⋋1	NOUN
ejpam-2406	58	25	=	=	SYM
ejpam-2406	58	26	p	p	NOUN
ejpam-2406	58	27	and	and	CCONJ
ejpam-2406	58	28	a⋋2	a⋋2	PROPN
ejpam-2406	58	29	=	=	SYM
ejpam-2406	58	30	(	(	PUNCT
ejpam-2406	58	31	0	0	NUM
ejpam-2406	58	32	)	)	PUNCT
ejpam-2406	58	33	then	then	ADV
ejpam-2406	58	34	n	n	VERB
ejpam-2406	58	35	is	be	AUX
ejpam-2406	58	36	not	not	PART
ejpam-2406	58	37	a	a	DET
ejpam-2406	58	38	primary	primary	ADJ
ejpam-2406	58	39	element	element	NOUN
ejpam-2406	58	40	of	of	ADP
ejpam-2406	58	41	m	m	PROPN
ejpam-2406	58	42	,	,	PUNCT
ejpam-2406	58	43	see	see	VERB
ejpam-2406	58	44	[	[	X
ejpam-2406	58	45	1	1	NUM
ejpam-2406	58	46	]	]	PUNCT
ejpam-2406	58	47	.	.	PUNCT
ejpam-2406	58	48	example	example	NOUN
ejpam-2406	59	1	2	2	NUM
ejpam-2406	59	2	.	.	PUNCT
ejpam-2406	59	3	let	let	VERB
ejpam-2406	59	4	l(z	l(z	NOUN
ejpam-2406	59	5	)	)	PUNCT
ejpam-2406	59	6	denote	denote	VERB
ejpam-2406	59	7	the	the	DET
ejpam-2406	59	8	set	set	NOUN
ejpam-2406	59	9	of	of	ADP
ejpam-2406	59	10	all	all	DET
ejpam-2406	59	11	ideals	ideal	NOUN
ejpam-2406	59	12	of	of	ADP
ejpam-2406	59	13	z	z	PROPN
ejpam-2406	59	14	,	,	PUNCT
ejpam-2406	59	15	the	the	DET
ejpam-2406	59	16	set	set	NOUN
ejpam-2406	59	17	of	of	ADP
ejpam-2406	59	18	integers	integer	NOUN
ejpam-2406	59	19	.	.	PUNCT
ejpam-2406	60	1	if	if	SCONJ
ejpam-2406	60	2	p	p	NOUN
ejpam-2406	60	3	is	be	AUX
ejpam-2406	60	4	a	a	DET
ejpam-2406	60	5	prime	prime	ADJ
ejpam-2406	60	6	integer	integer	NOUN
ejpam-2406	60	7	then	then	ADV
ejpam-2406	60	8	z(p∞	z(p∞	PROPN
ejpam-2406	60	9	)	)	PUNCT
ejpam-2406	61	1	=	=	PRON
ejpam-2406	61	2	{	{	PUNCT
ejpam-2406	61	3	a	a	DET
ejpam-2406	61	4	pk	pk	NOUN
ejpam-2406	61	5	+	+	X
ejpam-2406	61	6	z	z	NOUN
ejpam-2406	61	7	|	|	ADV
ejpam-2406	61	8	a	a	X
ejpam-2406	61	9	,	,	PUNCT
ejpam-2406	61	10	k	k	PROPN
ejpam-2406	61	11	are	be	AUX
ejpam-2406	61	12	integers	integer	NOUN
ejpam-2406	61	13	andk	andk	NOUN
ejpam-2406	61	14	∈	∈	PROPN
ejpam-2406	61	15	z+	z+	PRON
ejpam-2406	61	16	}	}	PUNCT
ejpam-2406	61	17	is	be	AUX
ejpam-2406	61	18	a	a	DET
ejpam-2406	61	19	module	module	NOUN
ejpam-2406	61	20	over	over	ADP
ejpam-2406	61	21	z.	z.	PROPN
ejpam-2406	61	22	let	let	VERB
ejpam-2406	61	23	m	m	PROPN
ejpam-2406	61	24	=	=	VERB
ejpam-2406	61	25	l(z(p∞	l(z(p∞	PROPN
ejpam-2406	61	26	)	)	PUNCT
ejpam-2406	61	27	)	)	PUNCT
ejpam-2406	62	1	denote	denote	VERB
ejpam-2406	62	2	the	the	DET
ejpam-2406	62	3	set	set	NOUN
ejpam-2406	62	4	of	of	ADP
ejpam-2406	62	5	all	all	DET
ejpam-2406	62	6	submodules	submodule	NOUN
ejpam-2406	62	7	of	of	ADP
ejpam-2406	62	8	z(p∞	z(p∞	PROPN
ejpam-2406	62	9	)	)	PUNCT
ejpam-2406	62	10	.	.	PUNCT
ejpam-2406	63	1	then	then	ADV
ejpam-2406	63	2	m	m	PROPN
ejpam-2406	63	3	is	be	AUX
ejpam-2406	63	4	a	a	DET
ejpam-2406	63	5	lattice	lattice	NOUN
ejpam-2406	63	6	module	module	NOUN
ejpam-2406	63	7	over	over	ADP
ejpam-2406	63	8	a	a	DET
ejpam-2406	63	9	multiplicative	multiplicative	ADJ
ejpam-2406	63	10	lattice	lattice	NOUN
ejpam-2406	63	11	l(z	l(z	NOUN
ejpam-2406	63	12	)	)	PUNCT
ejpam-2406	63	13	.	.	PUNCT
ejpam-2406	64	1	every	every	DET
ejpam-2406	64	2	nonzero	nonzero	ADJ
ejpam-2406	64	3	proper	proper	ADJ
ejpam-2406	64	4	submodule	submodule	NOUN
ejpam-2406	64	5	of	of	ADP
ejpam-2406	64	6	z(p∞	z(p∞	PROPN
ejpam-2406	64	7	)	)	PUNCT
ejpam-2406	64	8	is	be	AUX
ejpam-2406	64	9	a	a	DET
ejpam-2406	64	10	classical	classical	ADJ
ejpam-2406	64	11	primary	primary	NOUN
ejpam-2406	64	12	but	but	CCONJ
ejpam-2406	64	13	not	not	PART
ejpam-2406	64	14	a	a	DET
ejpam-2406	64	15	primary	primary	ADJ
ejpam-2406	64	16	element	element	NOUN
ejpam-2406	64	17	of	of	ADP
ejpam-2406	64	18	m	m	PROPN
ejpam-2406	64	19	,	,	PUNCT
ejpam-2406	64	20	see	see	VERB
ejpam-2406	64	21	[	[	X
ejpam-2406	64	22	1	1	NUM
ejpam-2406	64	23	]	]	PUNCT
ejpam-2406	64	24	.	.	PUNCT
ejpam-2406	64	25	example	example	NOUN
ejpam-2406	65	1	3	3	X
ejpam-2406	65	2	.	.	PUNCT
ejpam-2406	65	3	let	let	VERB
ejpam-2406	65	4	r	r	NOUN
ejpam-2406	65	5	=	=	PUNCT
ejpam-2406	65	6	z	z	PROPN
ejpam-2406	65	7	and	and	CCONJ
ejpam-2406	65	8	m	m	PROPN
ejpam-2406	65	9	=	=	NOUN
ejpam-2406	66	1	q	q	X
ejpam-2406	66	2	where	where	SCONJ
ejpam-2406	66	3	q	q	NOUN
ejpam-2406	66	4	is	be	AUX
ejpam-2406	66	5	a	a	DET
ejpam-2406	66	6	module	module	NOUN
ejpam-2406	66	7	over	over	ADP
ejpam-2406	66	8	r	r	NOUN
ejpam-2406	66	9	=	=	PUNCT
ejpam-2406	66	10	z.	z.	PROPN
ejpam-2406	66	11	let	let	VERB
ejpam-2406	66	12	l(r	l(r	PROPN
ejpam-2406	66	13	)	)	PUNCT
ejpam-2406	67	1	denote	denote	VERB
ejpam-2406	67	2	the	the	DET
ejpam-2406	67	3	set	set	NOUN
ejpam-2406	67	4	of	of	ADP
ejpam-2406	67	5	all	all	DET
ejpam-2406	67	6	ideals	ideal	NOUN
ejpam-2406	67	7	of	of	ADP
ejpam-2406	67	8	z	z	PROPN
ejpam-2406	67	9	and	and	CCONJ
ejpam-2406	67	10	l(q	l(q	PROPN
ejpam-2406	67	11	)	)	PUNCT
ejpam-2406	67	12	denote	denote	VERB
ejpam-2406	67	13	the	the	DET
ejpam-2406	67	14	set	set	NOUN
ejpam-2406	67	15	of	of	ADP
ejpam-2406	67	16	submodules	submodule	NOUN
ejpam-2406	67	17	of	of	ADP
ejpam-2406	67	18	q.	q.	PROPN
ejpam-2406	67	19	then	then	ADV
ejpam-2406	67	20	l(q	l(q	PROPN
ejpam-2406	67	21	)	)	PUNCT
ejpam-2406	67	22	is	be	AUX
ejpam-2406	67	23	a	a	DET
ejpam-2406	67	24	lattice	lattice	NOUN
ejpam-2406	67	25	module	module	NOUN
ejpam-2406	67	26	over	over	ADP
ejpam-2406	67	27	l(r	l(r	PROPN
ejpam-2406	67	28	)	)	PUNCT
ejpam-2406	67	29	.	.	PUNCT
ejpam-2406	68	1	each	each	DET
ejpam-2406	68	2	proper	proper	ADJ
ejpam-2406	68	3	submodule	submodule	NOUN
ejpam-2406	68	4	n	n	PROPN
ejpam-2406	68	5	of	of	ADP
ejpam-2406	68	6	m	m	PROPN
ejpam-2406	68	7	is	be	AUX
ejpam-2406	68	8	a	a	DET
ejpam-2406	68	9	quasi	quasi	ADJ
ejpam-2406	68	10	primary	primary	ADJ
ejpam-2406	68	11	element	element	NOUN
ejpam-2406	68	12	since	since	ADV
ejpam-2406	68	13	,	,	PUNCT
ejpam-2406	68	14	p	p	X
ejpam-2406	68	15	(	(	PUNCT
ejpam-2406	68	16	n	n	NOUN
ejpam-2406	68	17	:	:	PUNCT
ejpam-2406	68	18	q	q	X
ejpam-2406	68	19	)	)	PUNCT
ejpam-2406	68	20	=	=	SYM
ejpam-2406	68	21	(	(	PUNCT
ejpam-2406	68	22	0	0	NUM
ejpam-2406	68	23	)	)	PUNCT
ejpam-2406	68	24	.	.	PUNCT
ejpam-2406	69	1	if	if	SCONJ
ejpam-2406	69	2	n	n	NOUN
ejpam-2406	69	3	=	=	SYM
ejpam-2406	69	4	z	z	PROPN
ejpam-2406	70	1	+	+	NOUN
ejpam-2406	70	2	z	z	NOUN
ejpam-2406	70	3	.(1	.(1	ADJ
ejpam-2406	71	1	5	5	NUM
ejpam-2406	71	2	)	)	PUNCT
ejpam-2406	71	3	,	,	PUNCT
ejpam-2406	71	4	the	the	DET
ejpam-2406	71	5	submodule	submodule	NOUN
ejpam-2406	71	6	of	of	ADP
ejpam-2406	71	7	m	m	AUX
ejpam-2406	71	8	generated	generate	VERB
ejpam-2406	71	9	by	by	ADP
ejpam-2406	71	10	{	{	PUNCT
ejpam-2406	71	11	1	1	NUM
ejpam-2406	71	12	,	,	PUNCT
ejpam-2406	71	13	1	1	NUM
ejpam-2406	71	14	5	5	NUM
ejpam-2406	71	15	}	}	PUNCT
ejpam-2406	71	16	,	,	PUNCT
ejpam-2406	71	17	then	then	ADV
ejpam-2406	71	18	2.3	2.3	NUM
ejpam-2406	71	19	〈	〈	NOUN
ejpam-2406	71	20	1	1	NUM
ejpam-2406	71	21	2.3	2.3	NUM
ejpam-2406	71	22	〉	〉	NOUN
ejpam-2406	71	23	⊆	⊆	NUM
ejpam-2406	71	24	n	n	CCONJ
ejpam-2406	71	25	,	,	PUNCT
ejpam-2406	71	26	but	but	CCONJ
ejpam-2406	71	27	for	for	ADP
ejpam-2406	71	28	each	each	DET
ejpam-2406	71	29	k	k	PROPN
ejpam-2406	71	30	≥	≥	NUM
ejpam-2406	71	31	1	1	NUM
ejpam-2406	71	32	,	,	PUNCT
ejpam-2406	71	33	2k	2k	NUM
ejpam-2406	71	34	〈	〈	PROPN
ejpam-2406	71	35	1	1	NUM
ejpam-2406	71	36	2.3	2.3	NUM
ejpam-2406	71	37	〉	〉	NOUN
ejpam-2406	71	38	6⊆	6⊆	NUM
ejpam-2406	71	39	n	n	PROPN
ejpam-2406	71	40	and	and	CCONJ
ejpam-2406	71	41	3k	3k	NUM
ejpam-2406	71	42	〈	〈	PROPN
ejpam-2406	71	43	1	1	NUM
ejpam-2406	71	44	2.3	2.3	NUM
ejpam-2406	71	45	〉	〉	NOUN
ejpam-2406	71	46	6⊆	6⊆	NUM
ejpam-2406	71	47	n.	n.	PROPN
ejpam-2406	71	48	thus	thus	ADV
ejpam-2406	71	49	,	,	PUNCT
ejpam-2406	71	50	n	n	PRON
ejpam-2406	71	51	is	be	AUX
ejpam-2406	71	52	not	not	PART
ejpam-2406	71	53	a	a	DET
ejpam-2406	71	54	classical	classical	ADJ
ejpam-2406	71	55	quasi	quasi	ADJ
ejpam-2406	71	56	primary	primary	ADJ
ejpam-2406	71	57	element	element	NOUN
ejpam-2406	71	58	of	of	ADP
ejpam-2406	71	59	l(q	l(q	PROPN
ejpam-2406	71	60	)	)	PUNCT
ejpam-2406	71	61	see	see	VERB
ejpam-2406	72	1	[	[	X
ejpam-2406	72	2	1	1	NUM
ejpam-2406	72	3	]	]	PUNCT
ejpam-2406	72	4	.	.	PUNCT
ejpam-2406	73	1	example	example	NOUN
ejpam-2406	74	1	4	4	X
ejpam-2406	74	2	.	.	PUNCT
ejpam-2406	75	1	let	let	AUX
ejpam-2406	75	2	r	r	NOUN
ejpam-2406	75	3	=	=	PUNCT
ejpam-2406	75	4	z	z	NOUN
ejpam-2406	75	5	,	,	PUNCT
ejpam-2406	75	6	m	m	VERB
ejpam-2406	75	7	=	=	SYM
ejpam-2406	75	8	z	z	PROPN
ejpam-2406	75	9	⊕	⊕	PROPN
ejpam-2406	75	10	z	z	PROPN
ejpam-2406	75	11	where	where	SCONJ
ejpam-2406	75	12	m	m	PRON
ejpam-2406	75	13	is	be	AUX
ejpam-2406	75	14	a	a	DET
ejpam-2406	75	15	module	module	NOUN
ejpam-2406	75	16	over	over	ADP
ejpam-2406	75	17	r	r	NOUN
ejpam-2406	75	18	=	=	SYM
ejpam-2406	75	19	z.let	z.let	NUM
ejpam-2406	75	20	l(r	l(r	PROPN
ejpam-2406	75	21	)	)	PUNCT
ejpam-2406	75	22	denote	denote	VERB
ejpam-2406	75	23	the	the	DET
ejpam-2406	75	24	set	set	NOUN
ejpam-2406	75	25	of	of	ADP
ejpam-2406	75	26	all	all	DET
ejpam-2406	75	27	ideals	ideal	NOUN
ejpam-2406	75	28	of	of	ADP
ejpam-2406	75	29	r	r	NOUN
ejpam-2406	75	30	and	and	CCONJ
ejpam-2406	75	31	l(m	l(m	PROPN
ejpam-2406	75	32	)	)	PUNCT
ejpam-2406	75	33	denote	denote	VERB
ejpam-2406	75	34	the	the	DET
ejpam-2406	75	35	set	set	NOUN
ejpam-2406	75	36	of	of	ADP
ejpam-2406	75	37	all	all	DET
ejpam-2406	75	38	submodules	submodule	NOUN
ejpam-2406	75	39	of	of	ADP
ejpam-2406	75	40	m.	m.	NOUN
ejpam-2406	75	41	then	then	ADV
ejpam-2406	75	42	l(m	l(m	PROPN
ejpam-2406	75	43	)	)	PUNCT
ejpam-2406	75	44	is	be	AUX
ejpam-2406	75	45	a	a	DET
ejpam-2406	75	46	lattice	lattice	NOUN
ejpam-2406	75	47	module	module	NOUN
ejpam-2406	75	48	over	over	ADP
ejpam-2406	75	49	l(r	l(r	PROPN
ejpam-2406	75	50	)	)	PUNCT
ejpam-2406	75	51	.	.	PUNCT
ejpam-2406	76	1	let	let	VERB
ejpam-2406	76	2	q	q	NOUN
ejpam-2406	76	3	=	=	SYM
ejpam-2406	76	4	pz	pz	PROPN
ejpam-2406	76	5	⊕	⊕	PROPN
ejpam-2406	76	6	(	(	PUNCT
ejpam-2406	76	7	0	0	NUM
ejpam-2406	76	8	)	)	PUNCT
ejpam-2406	76	9	,	,	PUNCT
ejpam-2406	76	10	for	for	ADP
ejpam-2406	76	11	some	some	DET
ejpam-2406	76	12	prime	prime	ADJ
ejpam-2406	76	13	number	number	NOUN
ejpam-2406	76	14	p.	p.	NOUN
ejpam-2406	77	1	then	then	ADV
ejpam-2406	77	2	q	q	X
ejpam-2406	77	3	is	be	AUX
ejpam-2406	77	4	a	a	DET
ejpam-2406	77	5	classical	classical	ADJ
ejpam-2406	77	6	quasi	quasi	ADJ
ejpam-2406	77	7	primary	primary	ADJ
ejpam-2406	77	8	element	element	NOUN
ejpam-2406	77	9	of	of	ADP
ejpam-2406	77	10	l(m	l(m	PROPN
ejpam-2406	77	11	)	)	PUNCT
ejpam-2406	77	12	but	but	CCONJ
ejpam-2406	77	13	it	it	PRON
ejpam-2406	77	14	is	be	AUX
ejpam-2406	77	15	not	not	PART
ejpam-2406	77	16	a	a	DET
ejpam-2406	77	17	primary	primary	ADJ
ejpam-2406	77	18	element	element	NOUN
ejpam-2406	77	19	of	of	ADP
ejpam-2406	77	20	l(m	l(m	PROPN
ejpam-2406	77	21	)	)	PUNCT
ejpam-2406	77	22	see	see	VERB
ejpam-2406	78	1	[	[	X
ejpam-2406	78	2	1	1	NUM
ejpam-2406	78	3	]	]	PUNCT
ejpam-2406	78	4	.	.	PUNCT
ejpam-2406	79	1	in	in	ADP
ejpam-2406	79	2	the	the	DET
ejpam-2406	79	3	next	next	ADJ
ejpam-2406	79	4	result	result	NOUN
ejpam-2406	79	5	we	we	PRON
ejpam-2406	79	6	obtain	obtain	VERB
ejpam-2406	79	7	characterizations	characterization	NOUN
ejpam-2406	79	8	of	of	ADP
ejpam-2406	79	9	primary	primary	ADJ
ejpam-2406	79	10	elements	element	NOUN
ejpam-2406	79	11	,	,	PUNCT
ejpam-2406	79	12	classical	classical	ADJ
ejpam-2406	79	13	primary	primary	ADJ
ejpam-2406	79	14	elements	element	NOUN
ejpam-2406	79	15	and	and	CCONJ
ejpam-2406	79	16	classical	classical	ADJ
ejpam-2406	79	17	quasi	quasi	ADJ
ejpam-2406	79	18	primary	primary	ADJ
ejpam-2406	79	19	elements	element	NOUN
ejpam-2406	79	20	of	of	ADP
ejpam-2406	79	21	a	a	DET
ejpam-2406	79	22	multiplicative	multiplicative	ADJ
ejpam-2406	79	23	lattice	lattice	NOUN
ejpam-2406	79	24	.	.	PUNCT
ejpam-2406	80	1	theorem	theorem	NOUN
ejpam-2406	80	2	1	1	X
ejpam-2406	80	3	.	.	PUNCT
ejpam-2406	80	4	consider	consider	VERB
ejpam-2406	80	5	the	the	DET
ejpam-2406	80	6	following	follow	VERB
ejpam-2406	80	7	statements	statement	NOUN
ejpam-2406	80	8	for	for	ADP
ejpam-2406	80	9	a	a	DET
ejpam-2406	80	10	proper	proper	ADJ
ejpam-2406	80	11	element	element	NOUN
ejpam-2406	80	12	q	q	PROPN
ejpam-2406	80	13	of	of	ADP
ejpam-2406	80	14	l	l	NOUN
ejpam-2406	80	15	,	,	PUNCT
ejpam-2406	80	16	(	(	PUNCT
ejpam-2406	80	17	i	i	NOUN
ejpam-2406	80	18	)	)	PUNCT
ejpam-2406	81	1	q	q	PUNCT
ejpam-2406	81	2	is	be	AUX
ejpam-2406	81	3	a	a	DET
ejpam-2406	81	4	primary	primary	ADJ
ejpam-2406	81	5	element	element	NOUN
ejpam-2406	81	6	(	(	PUNCT
ejpam-2406	81	7	ii	ii	NOUN
ejpam-2406	81	8	)	)	PUNCT
ejpam-2406	81	9	q	q	PUNCT
ejpam-2406	81	10	is	be	AUX
ejpam-2406	81	11	a	a	DET
ejpam-2406	81	12	classical	classical	ADJ
ejpam-2406	81	13	primary	primary	ADJ
ejpam-2406	81	14	element	element	NOUN
ejpam-2406	81	15	(	(	PUNCT
ejpam-2406	81	16	iii	iii	NOUN
ejpam-2406	81	17	)	)	PUNCT
ejpam-2406	81	18	(	(	PUNCT
ejpam-2406	81	19	q	q	NOUN
ejpam-2406	81	20	:	:	PUNCT
ejpam-2406	81	21	c	c	X
ejpam-2406	81	22	)	)	PUNCT
ejpam-2406	81	23	is	be	AUX
ejpam-2406	81	24	a	a	DET
ejpam-2406	81	25	primary	primary	ADJ
ejpam-2406	81	26	element	element	NOUN
ejpam-2406	81	27	for	for	ADP
ejpam-2406	81	28	each	each	DET
ejpam-2406	81	29	element	element	NOUN
ejpam-2406	81	30	c	c	PROPN
ejpam-2406	81	31	of	of	ADP
ejpam-2406	81	32	l	l	NOUN
ejpam-2406	81	33	such	such	ADJ
ejpam-2406	81	34	that	that	SCONJ
ejpam-2406	81	35	c	c	PROPN
ejpam-2406	81	36	�	�	PROPN
ejpam-2406	81	37	q	q	PROPN
ejpam-2406	81	38	(	(	PUNCT
ejpam-2406	81	39	iv	iv	X
ejpam-2406	81	40	)	)	PUNCT
ejpam-2406	81	41	q	q	PUNCT
ejpam-2406	81	42	is	be	AUX
ejpam-2406	81	43	a	a	DET
ejpam-2406	81	44	classical	classical	ADJ
ejpam-2406	81	45	quasi	quasi	ADJ
ejpam-2406	81	46	primary	primary	ADJ
ejpam-2406	81	47	element	element	NOUN
ejpam-2406	81	48	c.	c.	PROPN
ejpam-2406	81	49	manjarekar	manjarekar	PROPN
ejpam-2406	81	50	,	,	PUNCT
ejpam-2406	81	51	u.	u.	PROPN
ejpam-2406	81	52	kandale	kandale	PROPN
ejpam-2406	81	53	/	/	SYM
ejpam-2406	81	54	eur	eur	PROPN
ejpam-2406	81	55	.	.	PUNCT
ejpam-2406	82	1	j.	j.	PROPN
ejpam-2406	82	2	pure	pure	PROPN
ejpam-2406	82	3	appl	appl	PROPN
ejpam-2406	82	4	.	.	PROPN
ejpam-2406	82	5	math	math	PROPN
ejpam-2406	82	6	,	,	PUNCT
ejpam-2406	82	7	8	8	NUM
ejpam-2406	82	8	(	(	PUNCT
ejpam-2406	82	9	2015	2015	NUM
ejpam-2406	82	10	)	)	PUNCT
ejpam-2406	82	11	,	,	PUNCT
ejpam-2406	82	12	172	172	NUM
ejpam-2406	82	13	-	-	SYM
ejpam-2406	82	14	184	184	NUM
ejpam-2406	82	15	175	175	NUM
ejpam-2406	82	16	(	(	PUNCT
ejpam-2406	82	17	v	v	NOUN
ejpam-2406	82	18	)	)	PUNCT
ejpam-2406	82	19	p	p	NOUN
ejpam-2406	82	20	(	(	PUNCT
ejpam-2406	82	21	q	q	NOUN
ejpam-2406	82	22	:	:	PUNCT
ejpam-2406	82	23	c	c	X
ejpam-2406	82	24	)	)	PUNCT
ejpam-2406	82	25	is	be	AUX
ejpam-2406	82	26	a	a	DET
ejpam-2406	82	27	prime	prime	ADJ
ejpam-2406	82	28	element	element	NOUN
ejpam-2406	82	29	for	for	ADP
ejpam-2406	82	30	each	each	DET
ejpam-2406	82	31	element	element	NOUN
ejpam-2406	82	32	c	c	PROPN
ejpam-2406	82	33	of	of	ADP
ejpam-2406	82	34	l	l	NOUN
ejpam-2406	82	35	such	such	ADJ
ejpam-2406	82	36	that	that	SCONJ
ejpam-2406	82	37	c	c	PROPN
ejpam-2406	82	38	�	�	PROPN
ejpam-2406	82	39	q	q	PROPN
ejpam-2406	82	40	(	(	PUNCT
ejpam-2406	82	41	vi	vi	NOUN
ejpam-2406	82	42	)	)	PUNCT
ejpam-2406	82	43	q	q	PUNCT
ejpam-2406	82	44	is	be	AUX
ejpam-2406	82	45	a	a	DET
ejpam-2406	82	46	quasi	quasi	ADJ
ejpam-2406	82	47	primary	primary	ADJ
ejpam-2406	82	48	element	element	NOUN
ejpam-2406	82	49	that	that	PRON
ejpam-2406	82	50	is	be	AUX
ejpam-2406	82	51	p	p	NOUN
ejpam-2406	82	52	q	q	PROPN
ejpam-2406	82	53	=	=	X
ejpam-2406	82	54	p	p	X
ejpam-2406	82	55	(	(	PUNCT
ejpam-2406	82	56	q	q	NOUN
ejpam-2406	82	57	:	:	PUNCT
ejpam-2406	82	58	1	1	X
ejpam-2406	82	59	)	)	PUNCT
ejpam-2406	82	60	is	be	AUX
ejpam-2406	82	61	a	a	DET
ejpam-2406	82	62	prime	prime	ADJ
ejpam-2406	82	63	element	element	NOUN
ejpam-2406	82	64	(	(	PUNCT
ejpam-2406	82	65	vii	vii	PROPN
ejpam-2406	82	66	)	)	PUNCT
ejpam-2406	83	1	q	q	PUNCT
ejpam-2406	83	2	is	be	AUX
ejpam-2406	83	3	a	a	DET
ejpam-2406	83	4	power	power	NOUN
ejpam-2406	83	5	of	of	ADP
ejpam-2406	83	6	prime	prime	ADJ
ejpam-2406	83	7	element	element	NOUN
ejpam-2406	83	8	.	.	PUNCT
ejpam-2406	84	1	then	then	ADV
ejpam-2406	84	2	(	(	PUNCT
ejpam-2406	84	3	i)⇒	i)⇒	PROPN
ejpam-2406	84	4	(	(	PUNCT
ejpam-2406	84	5	ii	ii	NOUN
ejpam-2406	84	6	)	)	PUNCT
ejpam-2406	84	7	,	,	PUNCT
ejpam-2406	84	8	(	(	PUNCT
ejpam-2406	84	9	ii)⇒	ii)⇒	X
ejpam-2406	84	10	(	(	PUNCT
ejpam-2406	84	11	iii	iii	NOUN
ejpam-2406	84	12	)	)	PUNCT
ejpam-2406	84	13	,	,	PUNCT
ejpam-2406	84	14	(	(	PUNCT
ejpam-2406	84	15	iii)⇒	iii)⇒	PROPN
ejpam-2406	84	16	(	(	PUNCT
ejpam-2406	84	17	iv	iv	NUM
ejpam-2406	84	18	)	)	PUNCT
ejpam-2406	84	19	,	,	PUNCT
ejpam-2406	84	20	(	(	PUNCT
ejpam-2406	84	21	iv)⇒	iv)⇒	X
ejpam-2406	84	22	(	(	PUNCT
ejpam-2406	84	23	v	v	NOUN
ejpam-2406	84	24	)	)	PUNCT
ejpam-2406	84	25	,	,	PUNCT
ejpam-2406	84	26	(	(	PUNCT
ejpam-2406	84	27	v)⇒	v)⇒	X
ejpam-2406	84	28	(	(	PUNCT
ejpam-2406	84	29	vi	vi	NOUN
ejpam-2406	84	30	)	)	PUNCT
ejpam-2406	84	31	,	,	PUNCT
ejpam-2406	84	32	(	(	PUNCT
ejpam-2406	84	33	v)⇒	v)⇒	X
ejpam-2406	84	34	(	(	PUNCT
ejpam-2406	84	35	iv	iv	NUM
ejpam-2406	84	36	)	)	PUNCT
ejpam-2406	84	37	,	,	PUNCT
ejpam-2406	84	38	(	(	PUNCT
ejpam-2406	84	39	vii)⇒	vii)⇒	PROPN
ejpam-2406	84	40	(	(	PUNCT
ejpam-2406	84	41	vi	vi	NOUN
ejpam-2406	84	42	)	)	PUNCT
ejpam-2406	84	43	.	.	PUNCT
ejpam-2406	85	1	proof	proof	NOUN
ejpam-2406	85	2	.	.	PUNCT
ejpam-2406	86	1	(	(	PUNCT
ejpam-2406	86	2	i)⇒	i)⇒	PROPN
ejpam-2406	86	3	(	(	PUNCT
ejpam-2406	86	4	ii	ii	NOUN
ejpam-2406	86	5	)	)	PUNCT
ejpam-2406	86	6	suppose	suppose	VERB
ejpam-2406	86	7	,	,	PUNCT
ejpam-2406	86	8	q	q	X
ejpam-2406	86	9	is	be	AUX
ejpam-2406	86	10	a	a	DET
ejpam-2406	86	11	primary	primary	ADJ
ejpam-2406	86	12	element	element	NOUN
ejpam-2406	86	13	.	.	PUNCT
ejpam-2406	87	1	let	let	VERB
ejpam-2406	87	2	a	a	DET
ejpam-2406	87	3	,	,	PUNCT
ejpam-2406	87	4	b	b	PROPN
ejpam-2406	87	5	∈	∈	PROPN
ejpam-2406	87	6	l	l	NOUN
ejpam-2406	87	7	,	,	PUNCT
ejpam-2406	87	8	r	r	NOUN
ejpam-2406	87	9	∈	∈	PROPN
ejpam-2406	87	10	l	l	NOUN
ejpam-2406	87	11	such	such	ADJ
ejpam-2406	87	12	that	that	DET
ejpam-2406	87	13	abr	abr	PROPN
ejpam-2406	87	14	¶	¶	PROPN
ejpam-2406	87	15	q	q	PROPN
ejpam-2406	87	16	and	and	CCONJ
ejpam-2406	87	17	br	br	PROPN
ejpam-2406	87	18	6¶	6¶	NUM
ejpam-2406	87	19	q.	q.	NOUN
ejpam-2406	87	20	since	since	SCONJ
ejpam-2406	87	21	,	,	PUNCT
ejpam-2406	87	22	q	q	X
ejpam-2406	87	23	is	be	AUX
ejpam-2406	87	24	a	a	DET
ejpam-2406	87	25	primary	primary	ADJ
ejpam-2406	87	26	element	element	NOUN
ejpam-2406	87	27	,	,	PUNCT
ejpam-2406	87	28	abr	abr	VERB
ejpam-2406	87	29	¶	¶	PROPN
ejpam-2406	87	30	q	q	PROPN
ejpam-2406	87	31	,	,	PUNCT
ejpam-2406	87	32	br	br	PROPN
ejpam-2406	87	33	6¶	6¶	NUM
ejpam-2406	87	34	q	q	NOUN
ejpam-2406	87	35	implies	imply	VERB
ejpam-2406	87	36	ak	ak	PROPN
ejpam-2406	87	37	¶	¶	PROPN
ejpam-2406	87	38	q	q	PROPN
ejpam-2406	87	39	for	for	ADP
ejpam-2406	87	40	some	some	DET
ejpam-2406	87	41	positive	positive	ADJ
ejpam-2406	87	42	integer	integer	NOUN
ejpam-2406	87	43	k.	k.	PROPN
ejpam-2406	87	44	hence	hence	ADV
ejpam-2406	87	45	,	,	PUNCT
ejpam-2406	87	46	akr	akr	PROPN
ejpam-2406	87	47	¶	¶	PROPN
ejpam-2406	87	48	q.	q.	PROPN
ejpam-2406	87	49	thus	thus	ADV
ejpam-2406	87	50	,	,	PUNCT
ejpam-2406	87	51	q	q	PROPN
ejpam-2406	87	52	is	be	AUX
ejpam-2406	87	53	a	a	DET
ejpam-2406	87	54	classical	classical	ADJ
ejpam-2406	87	55	primary	primary	ADJ
ejpam-2406	87	56	element	element	NOUN
ejpam-2406	87	57	of	of	ADP
ejpam-2406	87	58	l.	l.	PROPN
ejpam-2406	87	59	(	(	PUNCT
ejpam-2406	87	60	ii)⇒	ii)⇒	PROPN
ejpam-2406	87	61	(	(	PUNCT
ejpam-2406	87	62	iii	iii	NOUN
ejpam-2406	87	63	)	)	PUNCT
ejpam-2406	87	64	suppose	suppose	VERB
ejpam-2406	87	65	,	,	PUNCT
ejpam-2406	87	66	q	q	X
ejpam-2406	87	67	is	be	AUX
ejpam-2406	87	68	a	a	DET
ejpam-2406	87	69	classical	classical	ADJ
ejpam-2406	87	70	primary	primary	ADJ
ejpam-2406	87	71	element	element	NOUN
ejpam-2406	87	72	of	of	ADP
ejpam-2406	87	73	l	l	NOUN
ejpam-2406	87	74	and	and	CCONJ
ejpam-2406	87	75	let	let	VERB
ejpam-2406	87	76	ab	ab	PROPN
ejpam-2406	87	77	¶	¶	PROPN
ejpam-2406	87	78	(	(	PUNCT
ejpam-2406	87	79	q	q	NOUN
ejpam-2406	87	80	:	:	PUNCT
ejpam-2406	87	81	c	c	X
ejpam-2406	87	82	)	)	PUNCT
ejpam-2406	87	83	,	,	PUNCT
ejpam-2406	87	84	a	a	DET
ejpam-2406	87	85	,	,	PUNCT
ejpam-2406	87	86	b	b	PROPN
ejpam-2406	87	87	∈	∈	PROPN
ejpam-2406	87	88	l.	l.	NOUN
ejpam-2406	87	89	then	then	ADV
ejpam-2406	87	90	(	(	PUNCT
ejpam-2406	87	91	ab)c	ab)c	PROPN
ejpam-2406	87	92	¶	¶	PROPN
ejpam-2406	87	93	q.	q.	PROPN
ejpam-2406	87	94	hence	hence	ADV
ejpam-2406	87	95	,	,	PUNCT
ejpam-2406	87	96	ac	ac	PROPN
ejpam-2406	87	97	¶	¶	PROPN
ejpam-2406	87	98	q	q	NOUN
ejpam-2406	87	99	or	or	CCONJ
ejpam-2406	87	100	bkc	bkc	PROPN
ejpam-2406	87	101	¶	¶	PROPN
ejpam-2406	87	102	q	q	PROPN
ejpam-2406	87	103	,	,	PUNCT
ejpam-2406	87	104	that	that	PRON
ejpam-2406	87	105	is	be	AUX
ejpam-2406	87	106	a	a	DET
ejpam-2406	87	107	¶	¶	NOUN
ejpam-2406	87	108	(	(	PUNCT
ejpam-2406	87	109	q	q	NOUN
ejpam-2406	87	110	:	:	PUNCT
ejpam-2406	87	111	c	c	X
ejpam-2406	87	112	)	)	PUNCT
ejpam-2406	87	113	or	or	CCONJ
ejpam-2406	87	114	bk	bk	VERB
ejpam-2406	87	115	¶	¶	PROPN
ejpam-2406	87	116	(	(	PUNCT
ejpam-2406	87	117	q	q	NOUN
ejpam-2406	87	118	:	:	PUNCT
ejpam-2406	87	119	c	c	X
ejpam-2406	87	120	)	)	PUNCT
ejpam-2406	87	121	for	for	ADP
ejpam-2406	87	122	some	some	DET
ejpam-2406	87	123	positive	positive	ADJ
ejpam-2406	87	124	integer	integer	NOUN
ejpam-2406	87	125	k.	k.	PROPN
ejpam-2406	88	1	therefore	therefore	ADV
ejpam-2406	88	2	,	,	PUNCT
ejpam-2406	88	3	(	(	PUNCT
ejpam-2406	88	4	q	q	NOUN
ejpam-2406	88	5	:	:	PUNCT
ejpam-2406	88	6	c	c	X
ejpam-2406	88	7	)	)	PUNCT
ejpam-2406	88	8	is	be	AUX
ejpam-2406	88	9	a	a	DET
ejpam-2406	88	10	primary	primary	ADJ
ejpam-2406	88	11	element	element	NOUN
ejpam-2406	88	12	for	for	ADP
ejpam-2406	88	13	each	each	DET
ejpam-2406	88	14	c	c	PROPN
ejpam-2406	88	15	6¶	6¶	NUM
ejpam-2406	88	16	q.	q.	NOUN
ejpam-2406	88	17	(	(	PUNCT
ejpam-2406	88	18	iii)⇒	iii)⇒	PROPN
ejpam-2406	88	19	(	(	PUNCT
ejpam-2406	88	20	i	i	NOUN
ejpam-2406	88	21	)	)	PUNCT
ejpam-2406	88	22	suppose	suppose	VERB
ejpam-2406	88	23	,	,	PUNCT
ejpam-2406	88	24	(	(	PUNCT
ejpam-2406	88	25	q	q	NOUN
ejpam-2406	88	26	:	:	PUNCT
ejpam-2406	88	27	c	c	X
ejpam-2406	88	28	)	)	PUNCT
ejpam-2406	88	29	is	be	AUX
ejpam-2406	88	30	a	a	DET
ejpam-2406	88	31	primary	primary	ADJ
ejpam-2406	88	32	element	element	NOUN
ejpam-2406	88	33	of	of	ADP
ejpam-2406	88	34	l	l	PROPN
ejpam-2406	88	35	,	,	PUNCT
ejpam-2406	88	36	for	for	SCONJ
ejpam-2406	88	37	each	each	DET
ejpam-2406	88	38	c	c	PROPN
ejpam-2406	88	39	6¶	6¶	NUM
ejpam-2406	88	40	q.	q.	NOUN
ejpam-2406	88	41	take	take	VERB
ejpam-2406	88	42	c	c	NOUN
ejpam-2406	89	1	=	=	SYM
ejpam-2406	89	2	1	1	X
ejpam-2406	89	3	.	.	PUNCT
ejpam-2406	90	1	then	then	ADV
ejpam-2406	90	2	,	,	PUNCT
ejpam-2406	90	3	(	(	PUNCT
ejpam-2406	90	4	q	q	NOUN
ejpam-2406	90	5	:	:	PUNCT
ejpam-2406	90	6	1	1	X
ejpam-2406	90	7	)	)	PUNCT
ejpam-2406	90	8	is	be	AUX
ejpam-2406	90	9	primary	primary	ADJ
ejpam-2406	90	10	.	.	PUNCT
ejpam-2406	91	1	let	let	VERB
ejpam-2406	91	2	ab	ab	PROPN
ejpam-2406	91	3	¶	¶	PROPN
ejpam-2406	91	4	q.	q.	PROPN
ejpam-2406	92	1	so	so	ADV
ejpam-2406	92	2	,	,	PUNCT
ejpam-2406	92	3	(	(	PUNCT
ejpam-2406	92	4	ab	ab	PROPN
ejpam-2406	92	5	)	)	PUNCT
ejpam-2406	92	6	¶	¶	PROPN
ejpam-2406	92	7	(	(	PUNCT
ejpam-2406	92	8	q	q	NOUN
ejpam-2406	92	9	:	:	PUNCT
ejpam-2406	92	10	1	1	NUM
ejpam-2406	92	11	)	)	PUNCT
ejpam-2406	92	12	and	and	CCONJ
ejpam-2406	92	13	a	a	DET
ejpam-2406	92	14	¶	¶	NOUN
ejpam-2406	92	15	(	(	PUNCT
ejpam-2406	92	16	q	q	NOUN
ejpam-2406	92	17	:	:	PUNCT
ejpam-2406	92	18	1	1	NUM
ejpam-2406	92	19	)	)	PUNCT
ejpam-2406	92	20	or	or	CCONJ
ejpam-2406	92	21	bk	bk	ADP
ejpam-2406	92	22	¶	¶	PROPN
ejpam-2406	92	23	(	(	PUNCT
ejpam-2406	92	24	q	q	NOUN
ejpam-2406	92	25	:	:	PUNCT
ejpam-2406	92	26	1	1	NUM
ejpam-2406	92	27	)	)	PUNCT
ejpam-2406	92	28	.	.	PUNCT
ejpam-2406	93	1	hence	hence	ADV
ejpam-2406	93	2	,	,	PUNCT
ejpam-2406	93	3	a	a	DET
ejpam-2406	93	4	¶	¶	NOUN
ejpam-2406	93	5	q	q	NOUN
ejpam-2406	93	6	or	or	CCONJ
ejpam-2406	93	7	bk	bk	PROPN
ejpam-2406	93	8	¶	¶	PROPN
ejpam-2406	93	9	q	q	PUNCT
ejpam-2406	93	10	and	and	CCONJ
ejpam-2406	93	11	q	q	NOUN
ejpam-2406	93	12	is	be	AUX
ejpam-2406	93	13	a	a	DET
ejpam-2406	93	14	primary	primary	ADJ
ejpam-2406	93	15	element	element	NOUN
ejpam-2406	93	16	.	.	PUNCT
ejpam-2406	94	1	that	that	ADV
ejpam-2406	94	2	is	is	ADV
ejpam-2406	94	3	(	(	PUNCT
ejpam-2406	94	4	i)⇒	i)⇒	PROPN
ejpam-2406	94	5	(	(	PUNCT
ejpam-2406	94	6	ii)⇒	ii)⇒	PROPN
ejpam-2406	94	7	(	(	PUNCT
ejpam-2406	94	8	iii)⇒	iii)⇒	PROPN
ejpam-2406	94	9	(	(	PUNCT
ejpam-2406	94	10	i	i	NOUN
ejpam-2406	94	11	)	)	PUNCT
ejpam-2406	94	12	.	.	PUNCT
ejpam-2406	95	1	(	(	PUNCT
ejpam-2406	95	2	iii)⇒	iii)⇒	PROPN
ejpam-2406	95	3	(	(	PUNCT
ejpam-2406	95	4	v	v	NOUN
ejpam-2406	95	5	)	)	PUNCT
ejpam-2406	95	6	suppose	suppose	VERB
ejpam-2406	95	7	,	,	PUNCT
ejpam-2406	95	8	(	(	PUNCT
ejpam-2406	95	9	q	q	NOUN
ejpam-2406	95	10	:	:	PUNCT
ejpam-2406	95	11	c	c	X
ejpam-2406	95	12	)	)	PUNCT
ejpam-2406	95	13	is	be	AUX
ejpam-2406	95	14	primary	primary	ADJ
ejpam-2406	95	15	,	,	PUNCT
ejpam-2406	95	16	for	for	ADP
ejpam-2406	95	17	any	any	DET
ejpam-2406	95	18	c	c	PROPN
ejpam-2406	95	19	6¶	6¶	NUM
ejpam-2406	95	20	q.	q.	NOUN
ejpam-2406	95	21	but	but	CCONJ
ejpam-2406	95	22	(	(	PUNCT
ejpam-2406	95	23	q	q	NOUN
ejpam-2406	95	24	:	:	PUNCT
ejpam-2406	95	25	c	c	X
ejpam-2406	95	26	)	)	PUNCT
ejpam-2406	95	27	is	be	AUX
ejpam-2406	95	28	a	a	DET
ejpam-2406	95	29	primary	primary	ADJ
ejpam-2406	95	30	implies	implie	NOUN
ejpam-2406	95	31	p	p	X
ejpam-2406	95	32	(	(	PUNCT
ejpam-2406	95	33	q	q	NOUN
ejpam-2406	95	34	:	:	PUNCT
ejpam-2406	95	35	c	c	X
ejpam-2406	95	36	)	)	PUNCT
ejpam-2406	95	37	is	be	AUX
ejpam-2406	95	38	prime	prime	ADJ
ejpam-2406	95	39	.	.	PUNCT
ejpam-2406	96	1	(	(	PUNCT
ejpam-2406	96	2	iv)⇒	iv)⇒	X
ejpam-2406	96	3	(	(	PUNCT
ejpam-2406	96	4	v	v	NOUN
ejpam-2406	96	5	)	)	PUNCT
ejpam-2406	96	6	suppose	suppose	VERB
ejpam-2406	96	7	,	,	PUNCT
ejpam-2406	96	8	q	q	X
ejpam-2406	96	9	is	be	AUX
ejpam-2406	96	10	a	a	DET
ejpam-2406	96	11	classical	classical	ADJ
ejpam-2406	96	12	quasi	quasi	ADJ
ejpam-2406	96	13	primary	primary	ADJ
ejpam-2406	96	14	element	element	NOUN
ejpam-2406	96	15	and	and	CCONJ
ejpam-2406	96	16	let	let	VERB
ejpam-2406	96	17	ab	ab	PROPN
ejpam-2406	96	18	¶	¶	PROPN
ejpam-2406	96	19	p	p	PROPN
ejpam-2406	96	20	(	(	PUNCT
ejpam-2406	96	21	q	q	NOUN
ejpam-2406	96	22	:	:	PUNCT
ejpam-2406	96	23	c	c	X
ejpam-2406	96	24	)	)	PUNCT
ejpam-2406	96	25	where	where	SCONJ
ejpam-2406	96	26	c	c	PROPN
ejpam-2406	96	27	6¶	6¶	NUM
ejpam-2406	96	28	q.	q.	NOUN
ejpam-2406	97	1	so	so	ADV
ejpam-2406	97	2	,	,	PUNCT
ejpam-2406	97	3	(	(	PUNCT
ejpam-2406	97	4	ab)k	ab)k	PROPN
ejpam-2406	97	5	¶	¶	PROPN
ejpam-2406	97	6	(	(	PUNCT
ejpam-2406	97	7	q	q	NOUN
ejpam-2406	97	8	:	:	PUNCT
ejpam-2406	97	9	c	c	X
ejpam-2406	97	10	)	)	PUNCT
ejpam-2406	97	11	for	for	ADP
ejpam-2406	97	12	some	some	DET
ejpam-2406	97	13	positive	positive	ADJ
ejpam-2406	97	14	integer	integer	NOUN
ejpam-2406	97	15	k.	k.	PROPN
ejpam-2406	98	1	that	that	PRON
ejpam-2406	98	2	is	be	AUX
ejpam-2406	98	3	ak	ak	PROPN
ejpam-2406	98	4	bkc	bkc	PROPN
ejpam-2406	98	5	¶	¶	PROPN
ejpam-2406	98	6	q.	q.	PROPN
ejpam-2406	98	7	as	as	SCONJ
ejpam-2406	98	8	q	q	PROPN
ejpam-2406	98	9	is	be	AUX
ejpam-2406	98	10	classical	classical	ADJ
ejpam-2406	98	11	primary	primary	NOUN
ejpam-2406	98	12	,	,	PUNCT
ejpam-2406	98	13	(	(	PUNCT
ejpam-2406	98	14	ak)t	ak)t	PROPN
ejpam-2406	98	15	c	c	PROPN
ejpam-2406	98	16	¶	¶	PROPN
ejpam-2406	98	17	q	q	PUNCT
ejpam-2406	98	18	or	or	CCONJ
ejpam-2406	98	19	(	(	PUNCT
ejpam-2406	98	20	bk)t	bk)t	PROPN
ejpam-2406	98	21	c	c	PROPN
ejpam-2406	98	22	¶	¶	PROPN
ejpam-2406	98	23	q.	q.	PROPN
ejpam-2406	98	24	that	that	PRON
ejpam-2406	98	25	is	be	AUX
ejpam-2406	98	26	amc	amc	PROPN
ejpam-2406	98	27	¶	¶	PROPN
ejpam-2406	98	28	q	q	PROPN
ejpam-2406	98	29	or	or	CCONJ
ejpam-2406	98	30	bmc	bmc	PROPN
ejpam-2406	98	31	¶	¶	PROPN
ejpam-2406	98	32	q	q	PROPN
ejpam-2406	98	33	where	where	SCONJ
ejpam-2406	98	34	m	m	VERB
ejpam-2406	98	35	=	=	PUNCT
ejpam-2406	98	36	kt	kt	PROPN
ejpam-2406	98	37	∈	∈	PROPN
ejpam-2406	98	38	z+	z+	PUNCT
ejpam-2406	98	39	.	.	PUNCT
ejpam-2406	99	1	this	this	PRON
ejpam-2406	99	2	shows	show	VERB
ejpam-2406	99	3	that	that	SCONJ
ejpam-2406	99	4	,	,	PUNCT
ejpam-2406	99	5	a	a	DET
ejpam-2406	99	6	¶	¶	NOUN
ejpam-2406	99	7	p	p	NOUN
ejpam-2406	99	8	(	(	PUNCT
ejpam-2406	99	9	q	q	NOUN
ejpam-2406	99	10	:	:	PUNCT
ejpam-2406	99	11	c	c	X
ejpam-2406	99	12	)	)	PUNCT
ejpam-2406	99	13	or	or	CCONJ
ejpam-2406	99	14	b	b	NOUN
ejpam-2406	99	15	¶	¶	NUM
ejpam-2406	99	16	p	p	NOUN
ejpam-2406	99	17	(	(	PUNCT
ejpam-2406	99	18	q	q	NOUN
ejpam-2406	99	19	:	:	PUNCT
ejpam-2406	99	20	c	c	X
ejpam-2406	99	21	)	)	PUNCT
ejpam-2406	99	22	.	.	PUNCT
ejpam-2406	100	1	therefore	therefore	ADV
ejpam-2406	100	2	,	,	PUNCT
ejpam-2406	100	3	p	p	X
ejpam-2406	100	4	(	(	PUNCT
ejpam-2406	100	5	q	q	NOUN
ejpam-2406	100	6	:	:	PUNCT
ejpam-2406	100	7	c	c	X
ejpam-2406	100	8	)	)	PUNCT
ejpam-2406	100	9	is	be	AUX
ejpam-2406	100	10	prime	prime	ADJ
ejpam-2406	100	11	.	.	PUNCT
ejpam-2406	101	1	(	(	PUNCT
ejpam-2406	101	2	v)⇒	v)⇒	PROPN
ejpam-2406	101	3	(	(	PUNCT
ejpam-2406	101	4	iv	iv	X
ejpam-2406	101	5	)	)	PUNCT
ejpam-2406	101	6	suppose	suppose	VERB
ejpam-2406	101	7	,	,	PUNCT
ejpam-2406	101	8	p	p	X
ejpam-2406	101	9	(	(	PUNCT
ejpam-2406	101	10	q	q	NOUN
ejpam-2406	101	11	:	:	PUNCT
ejpam-2406	101	12	c	c	X
ejpam-2406	101	13	)	)	PUNCT
ejpam-2406	101	14	is	be	AUX
ejpam-2406	101	15	prime	prime	ADJ
ejpam-2406	101	16	for	for	SCONJ
ejpam-2406	101	17	any	any	DET
ejpam-2406	101	18	c	c	PROPN
ejpam-2406	101	19	6¶	6¶	NUM
ejpam-2406	101	20	q.	q.	NOUN
ejpam-2406	101	21	let	let	AUX
ejpam-2406	101	22	abr	abr	PROPN
ejpam-2406	101	23	¶	¶	PROPN
ejpam-2406	101	24	q	q	PROPN
ejpam-2406	101	25	where	where	SCONJ
ejpam-2406	101	26	a	a	DET
ejpam-2406	101	27	,	,	PUNCT
ejpam-2406	101	28	b	b	NOUN
ejpam-2406	101	29	,	,	PUNCT
ejpam-2406	101	30	r	r	PROPN
ejpam-2406	101	31	∈	∈	PROPN
ejpam-2406	101	32	l.	l.	NOUN
ejpam-2406	101	33	we	we	PRON
ejpam-2406	101	34	have	have	VERB
ejpam-2406	101	35	,	,	PUNCT
ejpam-2406	101	36	ab	ab	PROPN
ejpam-2406	101	37	¶	¶	PROPN
ejpam-2406	101	38	(	(	PUNCT
ejpam-2406	101	39	q	q	NOUN
ejpam-2406	101	40	:	:	PUNCT
ejpam-2406	101	41	r)¶	r)¶	PROPN
ejpam-2406	101	42	p	p	X
ejpam-2406	101	43	(	(	PUNCT
ejpam-2406	101	44	q	q	NOUN
ejpam-2406	101	45	:	:	PUNCT
ejpam-2406	101	46	r	r	NOUN
ejpam-2406	101	47	)	)	PUNCT
ejpam-2406	101	48	.	.	PUNCT
ejpam-2406	102	1	let	let	VERB
ejpam-2406	102	2	r	r	PRON
ejpam-2406	102	3	6¶	6¶	NUM
ejpam-2406	102	4	q.	q.	NOUN
ejpam-2406	102	5	then	then	ADV
ejpam-2406	102	6	p	p	X
ejpam-2406	102	7	(	(	PUNCT
ejpam-2406	102	8	q	q	NOUN
ejpam-2406	102	9	:	:	PUNCT
ejpam-2406	102	10	r	r	X
ejpam-2406	102	11	)	)	PUNCT
ejpam-2406	102	12	is	be	AUX
ejpam-2406	102	13	prime	prime	ADJ
ejpam-2406	102	14	implies	imply	VERB
ejpam-2406	102	15	a	a	DET
ejpam-2406	102	16	¶	¶	PROPN
ejpam-2406	102	17	p	p	NOUN
ejpam-2406	102	18	(	(	PUNCT
ejpam-2406	102	19	q	q	NOUN
ejpam-2406	102	20	:	:	PUNCT
ejpam-2406	102	21	r	r	X
ejpam-2406	102	22	)	)	PUNCT
ejpam-2406	102	23	or	or	CCONJ
ejpam-2406	102	24	b	b	NOUN
ejpam-2406	102	25	¶	¶	NUM
ejpam-2406	102	26	p	p	NOUN
ejpam-2406	102	27	(	(	PUNCT
ejpam-2406	102	28	q	q	NOUN
ejpam-2406	102	29	:	:	PUNCT
ejpam-2406	102	30	r	r	NOUN
ejpam-2406	102	31	)	)	PUNCT
ejpam-2406	102	32	.	.	PUNCT
ejpam-2406	103	1	this	this	PRON
ejpam-2406	103	2	implies	imply	VERB
ejpam-2406	103	3	,	,	PUNCT
ejpam-2406	103	4	anr	anr	PROPN
ejpam-2406	103	5	¶	¶	PROPN
ejpam-2406	103	6	q	q	PROPN
ejpam-2406	103	7	or	or	CCONJ
ejpam-2406	103	8	bnr	bnr	PROPN
ejpam-2406	103	9	¶	¶	PROPN
ejpam-2406	103	10	q	q	PROPN
ejpam-2406	103	11	for	for	ADP
ejpam-2406	103	12	some	some	DET
ejpam-2406	103	13	positive	positive	ADJ
ejpam-2406	103	14	integer	integer	NOUN
ejpam-2406	103	15	n.	n.	PROPN
ejpam-2406	103	16	thus	thus	ADV
ejpam-2406	103	17	,	,	PUNCT
ejpam-2406	103	18	q	q	PROPN
ejpam-2406	103	19	is	be	AUX
ejpam-2406	103	20	a	a	DET
ejpam-2406	103	21	classical	classical	ADJ
ejpam-2406	103	22	quasi	quasi	ADJ
ejpam-2406	103	23	primary	primary	ADJ
ejpam-2406	103	24	element	element	NOUN
ejpam-2406	103	25	.	.	PUNCT
ejpam-2406	104	1	(	(	PUNCT
ejpam-2406	104	2	v)⇒	v)⇒	PROPN
ejpam-2406	104	3	(	(	PUNCT
ejpam-2406	104	4	vi	vi	NOUN
ejpam-2406	104	5	)	)	PUNCT
ejpam-2406	104	6	suppose	suppose	VERB
ejpam-2406	104	7	,	,	PUNCT
ejpam-2406	104	8	p	p	X
ejpam-2406	104	9	(	(	PUNCT
ejpam-2406	104	10	q	q	NOUN
ejpam-2406	104	11	:	:	PUNCT
ejpam-2406	104	12	c	c	X
ejpam-2406	104	13	)	)	PUNCT
ejpam-2406	104	14	is	be	AUX
ejpam-2406	104	15	prime	prime	ADJ
ejpam-2406	104	16	,	,	PUNCT
ejpam-2406	104	17	c	c	PROPN
ejpam-2406	104	18	6¶	6¶	NUM
ejpam-2406	104	19	q.	q.	NOUN
ejpam-2406	104	20	let	let	VERB
ejpam-2406	104	21	ab	ab	PROPN
ejpam-2406	104	22	¶	¶	PROPN
ejpam-2406	104	23	p	p	PROPN
ejpam-2406	105	1	q.	q.	PROPN
ejpam-2406	105	2	then	then	ADV
ejpam-2406	105	3	(	(	PUNCT
ejpam-2406	105	4	ab)k	ab)k	PROPN
ejpam-2406	105	5	¶	¶	PROPN
ejpam-2406	105	6	q	q	NOUN
ejpam-2406	105	7	for	for	ADP
ejpam-2406	105	8	some	some	DET
ejpam-2406	105	9	positive	positive	ADJ
ejpam-2406	105	10	integer	integer	NOUN
ejpam-2406	105	11	k.	k.	PROPN
ejpam-2406	105	12	take	take	VERB
ejpam-2406	105	13	c	c	NOUN
ejpam-2406	105	14	=	=	SYM
ejpam-2406	105	15	1	1	X
ejpam-2406	105	16	.	.	PUNCT
ejpam-2406	106	1	then	then	ADV
ejpam-2406	106	2	,	,	PUNCT
ejpam-2406	106	3	p	p	X
ejpam-2406	106	4	(	(	PUNCT
ejpam-2406	106	5	q	q	NOUN
ejpam-2406	106	6	:	:	PUNCT
ejpam-2406	106	7	1	1	X
ejpam-2406	106	8	)	)	PUNCT
ejpam-2406	106	9	is	be	AUX
ejpam-2406	106	10	prime	prime	ADJ
ejpam-2406	106	11	and	and	CCONJ
ejpam-2406	106	12	(	(	PUNCT
ejpam-2406	106	13	ab)k	ab)k	PROPN
ejpam-2406	106	14	¶	¶	PROPN
ejpam-2406	106	15	(	(	PUNCT
ejpam-2406	106	16	q	q	NOUN
ejpam-2406	106	17	:	:	PUNCT
ejpam-2406	106	18	1	1	NUM
ejpam-2406	106	19	)	)	PUNCT
ejpam-2406	106	20	,	,	PUNCT
ejpam-2406	106	21	that	that	PRON
ejpam-2406	106	22	is	is	ADV
ejpam-2406	106	23	ab	ab	PROPN
ejpam-2406	106	24	¶	¶	PROPN
ejpam-2406	106	25	p	p	PROPN
ejpam-2406	106	26	(	(	PUNCT
ejpam-2406	106	27	q	q	NOUN
ejpam-2406	106	28	:	:	PUNCT
ejpam-2406	106	29	1	1	X
ejpam-2406	106	30	)	)	PUNCT
ejpam-2406	106	31	which	which	PRON
ejpam-2406	106	32	is	be	AUX
ejpam-2406	106	33	prime	prime	ADJ
ejpam-2406	106	34	.	.	PUNCT
ejpam-2406	107	1	hence	hence	ADV
ejpam-2406	107	2	,	,	PUNCT
ejpam-2406	107	3	a	a	DET
ejpam-2406	107	4	¶	¶	NOUN
ejpam-2406	107	5	p	p	NOUN
ejpam-2406	107	6	(	(	PUNCT
ejpam-2406	107	7	q	q	NOUN
ejpam-2406	107	8	:	:	PUNCT
ejpam-2406	107	9	1	1	NUM
ejpam-2406	107	10	)	)	PUNCT
ejpam-2406	107	11	or	or	CCONJ
ejpam-2406	107	12	b	b	NOUN
ejpam-2406	107	13	¶	¶	NUM
ejpam-2406	107	14	p	p	NOUN
ejpam-2406	107	15	(	(	PUNCT
ejpam-2406	107	16	q	q	NOUN
ejpam-2406	107	17	:	:	PUNCT
ejpam-2406	107	18	1	1	NUM
ejpam-2406	107	19	)	)	PUNCT
ejpam-2406	107	20	.	.	PUNCT
ejpam-2406	108	1	therefore	therefore	ADV
ejpam-2406	108	2	,	,	PUNCT
ejpam-2406	108	3	a	a	DET
ejpam-2406	108	4	¶	¶	NOUN
ejpam-2406	108	5	p	p	NOUN
ejpam-2406	108	6	q	q	PROPN
ejpam-2406	108	7	or	or	CCONJ
ejpam-2406	108	8	b	b	NOUN
ejpam-2406	108	9	¶	¶	NOUN
ejpam-2406	108	10	p	p	NOUN
ejpam-2406	108	11	q	q	PROPN
ejpam-2406	109	1	and	and	CCONJ
ejpam-2406	109	2	p	p	NOUN
ejpam-2406	109	3	q	q	PROPN
ejpam-2406	109	4	is	be	AUX
ejpam-2406	109	5	prime	prime	ADJ
ejpam-2406	109	6	.	.	PUNCT
ejpam-2406	110	1	(	(	PUNCT
ejpam-2406	110	2	vii)⇒	vii)⇒	PROPN
ejpam-2406	110	3	(	(	PUNCT
ejpam-2406	110	4	vi	vi	NOUN
ejpam-2406	110	5	)	)	PUNCT
ejpam-2406	110	6	suppose	suppose	VERB
ejpam-2406	110	7	,	,	PUNCT
ejpam-2406	110	8	q	q	X
ejpam-2406	110	9	is	be	AUX
ejpam-2406	110	10	a	a	DET
ejpam-2406	110	11	power	power	NOUN
ejpam-2406	110	12	of	of	ADP
ejpam-2406	110	13	a	a	DET
ejpam-2406	110	14	prime	prime	ADJ
ejpam-2406	110	15	element	element	NOUN
ejpam-2406	110	16	and	and	CCONJ
ejpam-2406	110	17	q	q	NOUN
ejpam-2406	110	18	=	=	NOUN
ejpam-2406	110	19	pk	pk	NOUN
ejpam-2406	110	20	where	where	SCONJ
ejpam-2406	110	21	p	p	NOUN
ejpam-2406	110	22	is	be	AUX
ejpam-2406	110	23	prime	prime	ADJ
ejpam-2406	110	24	and	and	CCONJ
ejpam-2406	110	25	k	k	PROPN
ejpam-2406	110	26	is	be	AUX
ejpam-2406	110	27	positive	positive	ADJ
ejpam-2406	110	28	integer	integer	NOUN
ejpam-2406	110	29	.	.	PUNCT
ejpam-2406	111	1	we	we	PRON
ejpam-2406	111	2	prove	prove	VERB
ejpam-2406	111	3	that	that	SCONJ
ejpam-2406	111	4	,	,	PUNCT
ejpam-2406	111	5	p	p	PRON
ejpam-2406	111	6	q	q	NOUN
ejpam-2406	111	7	is	be	AUX
ejpam-2406	111	8	prime	prime	ADJ
ejpam-2406	111	9	.	.	PUNCT
ejpam-2406	112	1	let	let	VERB
ejpam-2406	112	2	ab	ab	PROPN
ejpam-2406	112	3	¶	¶	PROPN
ejpam-2406	112	4	p	p	PROPN
ejpam-2406	113	1	q.	q.	PROPN
ejpam-2406	113	2	then	then	ADV
ejpam-2406	113	3	(	(	PUNCT
ejpam-2406	113	4	ab)m	ab)m	X
ejpam-2406	113	5	¶	¶	PROPN
ejpam-2406	113	6	q	q	NOUN
ejpam-2406	114	1	=	=	SYM
ejpam-2406	114	2	pk	pk	NOUN
ejpam-2406	114	3	¶	¶	PROPN
ejpam-2406	114	4	p	p	PROPN
ejpam-2406	114	5	,	,	PUNCT
ejpam-2406	114	6	for	for	ADP
ejpam-2406	114	7	some	some	DET
ejpam-2406	114	8	positive	positive	ADJ
ejpam-2406	114	9	integer	integer	NOUN
ejpam-2406	114	10	m.	m.	NOUN
ejpam-2406	114	11	then	then	ADV
ejpam-2406	114	12	am	be	AUX
ejpam-2406	114	13	¶	¶	PROPN
ejpam-2406	114	14	p	p	NOUN
ejpam-2406	114	15	or	or	CCONJ
ejpam-2406	114	16	bm	bm	PROPN
ejpam-2406	114	17	¶	¶	PROPN
ejpam-2406	115	1	p.	p.	PROPN
ejpam-2406	116	1	so	so	ADV
ejpam-2406	116	2	,	,	PUNCT
ejpam-2406	116	3	a	a	DET
ejpam-2406	116	4	¶	¶	NOUN
ejpam-2406	116	5	p	p	NOUN
ejpam-2406	116	6	or	or	CCONJ
ejpam-2406	116	7	b	b	NOUN
ejpam-2406	116	8	¶	¶	NUM
ejpam-2406	116	9	p	p	NOUN
ejpam-2406	116	10	and	and	CCONJ
ejpam-2406	116	11	hence	hence	ADV
ejpam-2406	116	12	,	,	PUNCT
ejpam-2406	116	13	ak	ak	PROPN
ejpam-2406	116	14	¶	¶	PROPN
ejpam-2406	116	15	pk	pk	NOUN
ejpam-2406	116	16	or	or	CCONJ
ejpam-2406	116	17	bk	bk	VERB
ejpam-2406	116	18	¶	¶	NOUN
ejpam-2406	116	19	pk	pk	NOUN
ejpam-2406	116	20	=	=	SYM
ejpam-2406	116	21	q.	q.	NOUN
ejpam-2406	116	22	this	this	PRON
ejpam-2406	116	23	shows	show	VERB
ejpam-2406	116	24	that	that	SCONJ
ejpam-2406	116	25	a	a	DET
ejpam-2406	116	26	¶	¶	PROPN
ejpam-2406	116	27	p	p	NOUN
ejpam-2406	116	28	q	q	PROPN
ejpam-2406	116	29	or	or	CCONJ
ejpam-2406	116	30	b	b	NOUN
ejpam-2406	116	31	¶	¶	NOUN
ejpam-2406	116	32	p	p	NOUN
ejpam-2406	116	33	q	q	PROPN
ejpam-2406	117	1	and	and	CCONJ
ejpam-2406	117	2	p	p	NOUN
ejpam-2406	117	3	q	q	NOUN
ejpam-2406	117	4	is	be	AUX
ejpam-2406	117	5	a	a	DET
ejpam-2406	117	6	prime	prime	ADJ
ejpam-2406	117	7	element	element	NOUN
ejpam-2406	117	8	.	.	PUNCT
ejpam-2406	118	1	we	we	PRON
ejpam-2406	118	2	now	now	ADV
ejpam-2406	118	3	prove	prove	VERB
ejpam-2406	118	4	the	the	DET
ejpam-2406	118	5	characterizations	characterization	NOUN
ejpam-2406	118	6	of	of	ADP
ejpam-2406	118	7	a	a	DET
ejpam-2406	118	8	classical	classical	ADJ
ejpam-2406	118	9	primary	primary	ADJ
ejpam-2406	118	10	element	element	NOUN
ejpam-2406	118	11	and	and	CCONJ
ejpam-2406	118	12	a	a	DET
ejpam-2406	118	13	classical	classical	ADJ
ejpam-2406	118	14	quasi	quasi	ADJ
ejpam-2406	118	15	primary	primary	ADJ
ejpam-2406	118	16	element	element	NOUN
ejpam-2406	118	17	of	of	ADP
ejpam-2406	118	18	a	a	DET
ejpam-2406	118	19	lattice	lattice	NOUN
ejpam-2406	118	20	module	module	NOUN
ejpam-2406	118	21	m.	m.	NOUN
ejpam-2406	118	22	these	these	DET
ejpam-2406	118	23	results	result	NOUN
ejpam-2406	118	24	establish	establish	VERB
ejpam-2406	118	25	the	the	DET
ejpam-2406	118	26	relation	relation	NOUN
ejpam-2406	118	27	between	between	ADP
ejpam-2406	118	28	a	a	DET
ejpam-2406	118	29	classical	classical	ADJ
ejpam-2406	118	30	c.	c.	NOUN
ejpam-2406	118	31	manjarekar	manjarekar	PROPN
ejpam-2406	118	32	,	,	PUNCT
ejpam-2406	118	33	u.	u.	PROPN
ejpam-2406	118	34	kandale	kandale	PROPN
ejpam-2406	118	35	/	/	SYM
ejpam-2406	118	36	eur	eur	PROPN
ejpam-2406	118	37	.	.	PUNCT
ejpam-2406	119	1	j.	j.	PROPN
ejpam-2406	119	2	pure	pure	PROPN
ejpam-2406	119	3	appl	appl	PROPN
ejpam-2406	119	4	.	.	PROPN
ejpam-2406	119	5	math	math	PROPN
ejpam-2406	119	6	,	,	PUNCT
ejpam-2406	119	7	8	8	NUM
ejpam-2406	119	8	(	(	PUNCT
ejpam-2406	119	9	2015	2015	NUM
ejpam-2406	119	10	)	)	PUNCT
ejpam-2406	119	11	,	,	PUNCT
ejpam-2406	119	12	172	172	NUM
ejpam-2406	119	13	-	-	SYM
ejpam-2406	119	14	184	184	NUM
ejpam-2406	119	15	176	176	NUM
ejpam-2406	119	16	primary	primary	ADJ
ejpam-2406	119	17	element	element	NOUN
ejpam-2406	119	18	of	of	ADP
ejpam-2406	119	19	a	a	DET
ejpam-2406	119	20	lattice	lattice	NOUN
ejpam-2406	119	21	module	module	NOUN
ejpam-2406	119	22	and	and	CCONJ
ejpam-2406	119	23	a	a	DET
ejpam-2406	119	24	primary	primary	ADJ
ejpam-2406	119	25	element	element	NOUN
ejpam-2406	119	26	of	of	ADP
ejpam-2406	119	27	a	a	DET
ejpam-2406	119	28	multiplicative	multiplicative	ADJ
ejpam-2406	119	29	lattice	lattice	NOUN
ejpam-2406	119	30	and	and	CCONJ
ejpam-2406	119	31	also	also	ADV
ejpam-2406	119	32	the	the	DET
ejpam-2406	119	33	relation	relation	NOUN
ejpam-2406	119	34	between	between	ADP
ejpam-2406	119	35	a	a	DET
ejpam-2406	119	36	classical	classical	ADJ
ejpam-2406	119	37	quasi	quasi	ADJ
ejpam-2406	119	38	primary	primary	ADJ
ejpam-2406	119	39	element	element	NOUN
ejpam-2406	119	40	of	of	ADP
ejpam-2406	119	41	a	a	DET
ejpam-2406	119	42	lattice	lattice	NOUN
ejpam-2406	119	43	module	module	NOUN
ejpam-2406	119	44	and	and	CCONJ
ejpam-2406	119	45	a	a	DET
ejpam-2406	119	46	quasi	quasi	ADJ
ejpam-2406	119	47	primary	primary	ADJ
ejpam-2406	119	48	element	element	NOUN
ejpam-2406	119	49	of	of	ADP
ejpam-2406	119	50	a	a	DET
ejpam-2406	119	51	multiplicative	multiplicative	ADJ
ejpam-2406	119	52	lattice	lattice	NOUN
ejpam-2406	119	53	.	.	PUNCT
ejpam-2406	120	1	theorem	theorem	NOUN
ejpam-2406	120	2	2	2	NUM
ejpam-2406	120	3	.	.	PUNCT
ejpam-2406	121	1	let	let	VERB
ejpam-2406	121	2	m	m	PRON
ejpam-2406	121	3	be	be	AUX
ejpam-2406	121	4	a	a	DET
ejpam-2406	121	5	lattice	lattice	NOUN
ejpam-2406	121	6	module	module	NOUN
ejpam-2406	121	7	and	and	CCONJ
ejpam-2406	121	8	q	q	NOUN
ejpam-2406	121	9	be	be	AUX
ejpam-2406	121	10	a	a	DET
ejpam-2406	121	11	proper	proper	ADJ
ejpam-2406	121	12	element	element	NOUN
ejpam-2406	121	13	of	of	ADP
ejpam-2406	121	14	m.	m.	NOUN
ejpam-2406	121	15	then	then	ADV
ejpam-2406	121	16	(	(	PUNCT
ejpam-2406	121	17	i	i	NOUN
ejpam-2406	121	18	)	)	PUNCT
ejpam-2406	121	19	q	q	PUNCT
ejpam-2406	121	20	is	be	AUX
ejpam-2406	121	21	a	a	DET
ejpam-2406	121	22	classical	classical	ADJ
ejpam-2406	121	23	primary	primary	ADJ
ejpam-2406	121	24	element	element	NOUN
ejpam-2406	122	1	if	if	SCONJ
ejpam-2406	122	2	and	and	CCONJ
ejpam-2406	122	3	only	only	ADV
ejpam-2406	122	4	if	if	SCONJ
ejpam-2406	122	5	for	for	ADP
ejpam-2406	122	6	every	every	DET
ejpam-2406	122	7	element	element	NOUN
ejpam-2406	122	8	n	n	PROPN
ejpam-2406	122	9	of	of	ADP
ejpam-2406	122	10	m	m	PRON
ejpam-2406	122	11	such	such	ADJ
ejpam-2406	122	12	that	that	SCONJ
ejpam-2406	122	13	n	n	PROPN
ejpam-2406	122	14	6¶q	6¶q	NUM
ejpam-2406	122	15	,	,	PUNCT
ejpam-2406	122	16	(	(	PUNCT
ejpam-2406	122	17	q	q	NOUN
ejpam-2406	122	18	:	:	PUNCT
ejpam-2406	122	19	n	n	CCONJ
ejpam-2406	122	20	)	)	PUNCT
ejpam-2406	122	21	is	be	AUX
ejpam-2406	122	22	a	a	DET
ejpam-2406	122	23	primary	primary	ADJ
ejpam-2406	122	24	element	element	NOUN
ejpam-2406	122	25	of	of	ADP
ejpam-2406	122	26	l.	l.	PROPN
ejpam-2406	122	27	(	(	PUNCT
ejpam-2406	122	28	ii	ii	PROPN
ejpam-2406	122	29	)	)	PUNCT
ejpam-2406	122	30	q	q	PUNCT
ejpam-2406	122	31	is	be	AUX
ejpam-2406	122	32	a	a	DET
ejpam-2406	122	33	classical	classical	ADJ
ejpam-2406	122	34	quasi	quasi	NOUN
ejpam-2406	122	35	primary	primary	NOUN
ejpam-2406	122	36	if	if	SCONJ
ejpam-2406	122	37	and	and	CCONJ
ejpam-2406	122	38	only	only	ADV
ejpam-2406	122	39	if	if	SCONJ
ejpam-2406	122	40	for	for	ADP
ejpam-2406	122	41	every	every	DET
ejpam-2406	122	42	element	element	NOUN
ejpam-2406	122	43	n	n	PRON
ejpam-2406	122	44	∈	∈	NOUN
ejpam-2406	122	45	m	m	VERB
ejpam-2406	122	46	such	such	ADJ
ejpam-2406	122	47	that	that	SCONJ
ejpam-2406	122	48	n	n	PROPN
ejpam-2406	122	49	6¶	6¶	NUM
ejpam-2406	122	50	q	q	NOUN
ejpam-2406	122	51	,	,	PUNCT
ejpam-2406	122	52	(	(	PUNCT
ejpam-2406	122	53	q	q	NOUN
ejpam-2406	122	54	:	:	PUNCT
ejpam-2406	122	55	n	n	CCONJ
ejpam-2406	122	56	)	)	PUNCT
ejpam-2406	122	57	is	be	AUX
ejpam-2406	122	58	quasi	quasi	ADJ
ejpam-2406	122	59	primary	primary	ADJ
ejpam-2406	122	60	element	element	NOUN
ejpam-2406	122	61	of	of	ADP
ejpam-2406	122	62	l.	l.	PROPN
ejpam-2406	122	63	proof	proof	PROPN
ejpam-2406	122	64	.	.	PUNCT
ejpam-2406	123	1	(	(	PUNCT
ejpam-2406	123	2	i	i	NOUN
ejpam-2406	123	3	)	)	PUNCT
ejpam-2406	123	4	suppose	suppose	VERB
ejpam-2406	123	5	,	,	PUNCT
ejpam-2406	123	6	q	q	X
ejpam-2406	123	7	is	be	AUX
ejpam-2406	123	8	a	a	DET
ejpam-2406	123	9	classical	classical	ADJ
ejpam-2406	123	10	primary	primary	ADJ
ejpam-2406	123	11	element	element	NOUN
ejpam-2406	123	12	of	of	ADP
ejpam-2406	123	13	m	m	PROPN
ejpam-2406	123	14	and	and	CCONJ
ejpam-2406	123	15	n	n	DET
ejpam-2406	123	16	6¶	6¶	NUM
ejpam-2406	123	17	q.	q.	NOUN
ejpam-2406	123	18	let	let	VERB
ejpam-2406	123	19	ab	ab	PROPN
ejpam-2406	123	20	¶	¶	PROPN
ejpam-2406	123	21	(	(	PUNCT
ejpam-2406	123	22	q	q	NOUN
ejpam-2406	123	23	:	:	PUNCT
ejpam-2406	123	24	n	n	CCONJ
ejpam-2406	123	25	)	)	PUNCT
ejpam-2406	123	26	.	.	PUNCT
ejpam-2406	124	1	since	since	SCONJ
ejpam-2406	124	2	,	,	PUNCT
ejpam-2406	124	3	q	q	X
ejpam-2406	124	4	is	be	AUX
ejpam-2406	124	5	a	a	DET
ejpam-2406	124	6	classical	classical	ADJ
ejpam-2406	124	7	primary	primary	ADJ
ejpam-2406	124	8	element	element	NOUN
ejpam-2406	124	9	of	of	ADP
ejpam-2406	124	10	m	m	PROPN
ejpam-2406	124	11	,	,	PUNCT
ejpam-2406	124	12	an	an	DET
ejpam-2406	124	13	¶	¶	PROPN
ejpam-2406	124	14	q	q	PUNCT
ejpam-2406	124	15	or	or	CCONJ
ejpam-2406	124	16	bkn	bkn	PROPN
ejpam-2406	124	17	¶	¶	PROPN
ejpam-2406	124	18	q	q	PROPN
ejpam-2406	124	19	for	for	ADP
ejpam-2406	124	20	some	some	DET
ejpam-2406	124	21	positive	positive	ADJ
ejpam-2406	124	22	integer	integer	NOUN
ejpam-2406	124	23	k.	k.	PROPN
ejpam-2406	125	1	that	that	PRON
ejpam-2406	125	2	is	be	AUX
ejpam-2406	125	3	a	a	DET
ejpam-2406	125	4	¶	¶	NOUN
ejpam-2406	125	5	(	(	PUNCT
ejpam-2406	125	6	q	q	NOUN
ejpam-2406	125	7	:	:	PUNCT
ejpam-2406	125	8	n	n	CCONJ
ejpam-2406	125	9	)	)	PUNCT
ejpam-2406	125	10	or	or	CCONJ
ejpam-2406	125	11	bk	bk	VERB
ejpam-2406	125	12	¶	¶	PROPN
ejpam-2406	125	13	(	(	PUNCT
ejpam-2406	125	14	q	q	NOUN
ejpam-2406	125	15	:	:	PUNCT
ejpam-2406	125	16	n	n	CCONJ
ejpam-2406	125	17	)	)	PUNCT
ejpam-2406	125	18	.	.	PUNCT
ejpam-2406	126	1	hence	hence	ADV
ejpam-2406	126	2	,	,	PUNCT
ejpam-2406	126	3	(	(	PUNCT
ejpam-2406	126	4	q	q	NOUN
ejpam-2406	126	5	:	:	PUNCT
ejpam-2406	126	6	n	n	CCONJ
ejpam-2406	126	7	)	)	PUNCT
ejpam-2406	126	8	is	be	AUX
ejpam-2406	126	9	a	a	DET
ejpam-2406	126	10	primary	primary	ADJ
ejpam-2406	126	11	element	element	NOUN
ejpam-2406	126	12	of	of	ADP
ejpam-2406	126	13	l.	l.	PROPN
ejpam-2406	126	14	conversely	conversely	ADV
ejpam-2406	126	15	,	,	PUNCT
ejpam-2406	126	16	suppose	suppose	VERB
ejpam-2406	126	17	(	(	PUNCT
ejpam-2406	126	18	q	q	NOUN
ejpam-2406	126	19	:	:	PUNCT
ejpam-2406	126	20	n	n	CCONJ
ejpam-2406	126	21	)	)	PUNCT
ejpam-2406	126	22	is	be	AUX
ejpam-2406	126	23	a	a	DET
ejpam-2406	126	24	primary	primary	ADJ
ejpam-2406	126	25	element	element	NOUN
ejpam-2406	126	26	of	of	ADP
ejpam-2406	126	27	l	l	NOUN
ejpam-2406	126	28	for	for	ADP
ejpam-2406	126	29	any	any	DET
ejpam-2406	126	30	n	n	PRON
ejpam-2406	126	31	∈	∈	NOUN
ejpam-2406	126	32	m	m	VERB
ejpam-2406	126	33	such	such	ADJ
ejpam-2406	126	34	that	that	SCONJ
ejpam-2406	126	35	n	n	PROPN
ejpam-2406	126	36	6¶	6¶	NUM
ejpam-2406	126	37	q.	q.	NOUN
ejpam-2406	126	38	let	let	VERB
ejpam-2406	126	39	abn	abn	PROPN
ejpam-2406	126	40	¶	¶	PROPN
ejpam-2406	126	41	q.	q.	PROPN
ejpam-2406	126	42	then	then	ADV
ejpam-2406	126	43	,	,	PUNCT
ejpam-2406	126	44	ab	ab	PROPN
ejpam-2406	126	45	¶	¶	PROPN
ejpam-2406	126	46	(	(	PUNCT
ejpam-2406	126	47	q	q	NOUN
ejpam-2406	126	48	:	:	PUNCT
ejpam-2406	126	49	n	n	CCONJ
ejpam-2406	126	50	)	)	PUNCT
ejpam-2406	126	51	,	,	PUNCT
ejpam-2406	126	52	which	which	PRON
ejpam-2406	126	53	is	be	AUX
ejpam-2406	126	54	primary	primary	ADJ
ejpam-2406	126	55	.	.	PUNCT
ejpam-2406	127	1	so	so	ADV
ejpam-2406	127	2	,	,	PUNCT
ejpam-2406	127	3	a	a	DET
ejpam-2406	127	4	¶	¶	NOUN
ejpam-2406	127	5	(	(	PUNCT
ejpam-2406	127	6	q	q	NOUN
ejpam-2406	127	7	:	:	PUNCT
ejpam-2406	127	8	n	n	CCONJ
ejpam-2406	127	9	)	)	PUNCT
ejpam-2406	127	10	or	or	CCONJ
ejpam-2406	127	11	bk	bk	VERB
ejpam-2406	127	12	¶	¶	PROPN
ejpam-2406	127	13	(	(	PUNCT
ejpam-2406	127	14	q	q	NOUN
ejpam-2406	127	15	:	:	PUNCT
ejpam-2406	127	16	n	n	CCONJ
ejpam-2406	127	17	)	)	PUNCT
ejpam-2406	127	18	.	.	PUNCT
ejpam-2406	128	1	that	that	PRON
ejpam-2406	128	2	is	be	AUX
ejpam-2406	128	3	an	an	DET
ejpam-2406	128	4	¶	¶	PROPN
ejpam-2406	128	5	q	q	PUNCT
ejpam-2406	128	6	or	or	CCONJ
ejpam-2406	128	7	bkn	bkn	PROPN
ejpam-2406	128	8	¶	¶	PROPN
ejpam-2406	128	9	q.	q.	PROPN
ejpam-2406	128	10	suppose	suppose	VERB
ejpam-2406	128	11	,	,	PUNCT
ejpam-2406	128	12	n	n	PROPN
ejpam-2406	128	13	¶	¶	PROPN
ejpam-2406	128	14	q.	q.	PROPN
ejpam-2406	128	15	then	then	ADV
ejpam-2406	128	16	for	for	ADP
ejpam-2406	128	17	any	any	DET
ejpam-2406	128	18	a	a	DET
ejpam-2406	128	19	∈	∈	PROPN
ejpam-2406	128	20	l	l	NOUN
ejpam-2406	128	21	,	,	PUNCT
ejpam-2406	128	22	an	an	DET
ejpam-2406	128	23	¶	¶	PROPN
ejpam-2406	128	24	n	n	NOUN
ejpam-2406	128	25	¶	¶	PROPN
ejpam-2406	128	26	q	q	PROPN
ejpam-2406	128	27	implies	imply	VERB
ejpam-2406	128	28	(	(	PUNCT
ejpam-2406	128	29	q	q	NOUN
ejpam-2406	128	30	:	:	PUNCT
ejpam-2406	128	31	n	n	X
ejpam-2406	128	32	)	)	PUNCT
ejpam-2406	128	33	=	=	SYM
ejpam-2406	128	34	1	1	NUM
ejpam-2406	128	35	and	and	CCONJ
ejpam-2406	128	36	hence	hence	ADV
ejpam-2406	128	37	ab	ab	PROPN
ejpam-2406	128	38	¶	¶	PROPN
ejpam-2406	128	39	(	(	PUNCT
ejpam-2406	128	40	q	q	NOUN
ejpam-2406	128	41	:	:	PUNCT
ejpam-2406	128	42	n	n	X
ejpam-2406	128	43	)	)	PUNCT
ejpam-2406	129	1	=	=	SYM
ejpam-2406	129	2	1	1	X
ejpam-2406	129	3	.	.	PUNCT
ejpam-2406	130	1	so	so	ADV
ejpam-2406	130	2	,	,	PUNCT
ejpam-2406	130	3	a	a	DET
ejpam-2406	130	4	¶	¶	NOUN
ejpam-2406	130	5	(	(	PUNCT
ejpam-2406	130	6	q	q	NOUN
ejpam-2406	130	7	:	:	PUNCT
ejpam-2406	130	8	n	n	CCONJ
ejpam-2406	130	9	)	)	PUNCT
ejpam-2406	130	10	,	,	PUNCT
ejpam-2406	130	11	b	b	X
ejpam-2406	130	12	¶	¶	PROPN
ejpam-2406	130	13	(	(	PUNCT
ejpam-2406	130	14	q	q	NOUN
ejpam-2406	130	15	:	:	PUNCT
ejpam-2406	130	16	n	n	CCONJ
ejpam-2406	130	17	)	)	PUNCT
ejpam-2406	130	18	which	which	PRON
ejpam-2406	130	19	shows	show	VERB
ejpam-2406	130	20	that	that	SCONJ
ejpam-2406	130	21	an	an	DET
ejpam-2406	130	22	¶	¶	NOUN
ejpam-2406	130	23	q	q	NOUN
ejpam-2406	130	24	and	and	CCONJ
ejpam-2406	130	25	bn	bn	ADP
ejpam-2406	130	26	¶	¶	PROPN
ejpam-2406	130	27	q	q	NOUN
ejpam-2406	130	28	,	,	PUNCT
ejpam-2406	130	29	when	when	SCONJ
ejpam-2406	130	30	abn	abn	PROPN
ejpam-2406	130	31	¶q	¶q	PROPN
ejpam-2406	130	32	.	.	PUNCT
ejpam-2406	131	1	hence	hence	ADV
ejpam-2406	131	2	,	,	PUNCT
ejpam-2406	131	3	q	q	PUNCT
ejpam-2406	131	4	is	be	AUX
ejpam-2406	131	5	a	a	DET
ejpam-2406	131	6	classical	classical	ADJ
ejpam-2406	131	7	primary	primary	ADJ
ejpam-2406	131	8	element	element	NOUN
ejpam-2406	131	9	of	of	ADP
ejpam-2406	131	10	m.	m.	NOUN
ejpam-2406	131	11	(	(	PUNCT
ejpam-2406	131	12	ii	ii	NOUN
ejpam-2406	131	13	)	)	PUNCT
ejpam-2406	131	14	let	let	VERB
ejpam-2406	131	15	q	q	NOUN
ejpam-2406	131	16	be	be	AUX
ejpam-2406	131	17	a	a	DET
ejpam-2406	131	18	classical	classical	ADJ
ejpam-2406	131	19	quasi	quasi	ADJ
ejpam-2406	131	20	primary	primary	ADJ
ejpam-2406	131	21	element	element	NOUN
ejpam-2406	131	22	and	and	CCONJ
ejpam-2406	131	23	let	let	VERB
ejpam-2406	131	24	ab	ab	PROPN
ejpam-2406	131	25	¶	¶	PROPN
ejpam-2406	131	26	p	p	PROPN
ejpam-2406	131	27	(	(	PUNCT
ejpam-2406	131	28	q	q	NOUN
ejpam-2406	131	29	:	:	PUNCT
ejpam-2406	131	30	n	n	CCONJ
ejpam-2406	131	31	)	)	PUNCT
ejpam-2406	131	32	where	where	SCONJ
ejpam-2406	131	33	n	n	PRON
ejpam-2406	131	34	6¶	6¶	NUM
ejpam-2406	131	35	q.	q.	NOUN
ejpam-2406	131	36	then	then	ADV
ejpam-2406	131	37	,	,	PUNCT
ejpam-2406	131	38	(	(	PUNCT
ejpam-2406	131	39	ab)k	ab)k	PROPN
ejpam-2406	131	40	¶	¶	PROPN
ejpam-2406	131	41	(	(	PUNCT
ejpam-2406	131	42	q	q	NOUN
ejpam-2406	131	43	:	:	PUNCT
ejpam-2406	131	44	n	n	CCONJ
ejpam-2406	131	45	)	)	PUNCT
ejpam-2406	131	46	for	for	ADP
ejpam-2406	131	47	some	some	DET
ejpam-2406	131	48	positive	positive	ADJ
ejpam-2406	131	49	integer	integer	NOUN
ejpam-2406	131	50	k.	k.	PROPN
ejpam-2406	131	51	since	since	ADV
ejpam-2406	131	52	,	,	PUNCT
ejpam-2406	131	53	q	q	X
ejpam-2406	131	54	is	be	AUX
ejpam-2406	131	55	a	a	DET
ejpam-2406	131	56	classical	classical	ADJ
ejpam-2406	131	57	quasi	quasi	ADJ
ejpam-2406	131	58	primary	primary	ADJ
ejpam-2406	131	59	element	element	NOUN
ejpam-2406	131	60	of	of	ADP
ejpam-2406	131	61	m	m	PROPN
ejpam-2406	131	62	,	,	PUNCT
ejpam-2406	131	63	ak	ak	PROPN
ejpam-2406	131	64	bkn	bkn	PROPN
ejpam-2406	131	65	¶	¶	PROPN
ejpam-2406	131	66	q	q	PROPN
ejpam-2406	131	67	implies	imply	VERB
ejpam-2406	131	68	(	(	PUNCT
ejpam-2406	131	69	ak)l	ak)l	NOUN
ejpam-2406	131	70	n	n	NOUN
ejpam-2406	131	71	¶	¶	NOUN
ejpam-2406	131	72	q	q	PUNCT
ejpam-2406	131	73	or	or	CCONJ
ejpam-2406	131	74	(	(	PUNCT
ejpam-2406	131	75	bk)l	bk)l	NOUN
ejpam-2406	131	76	n	n	NUM
ejpam-2406	131	77	¶	¶	NUM
ejpam-2406	131	78	q.	q.	NOUN
ejpam-2406	131	79	that	that	PRON
ejpam-2406	131	80	is	be	AUX
ejpam-2406	131	81	ann	ann	PROPN
ejpam-2406	131	82	¶	¶	PROPN
ejpam-2406	131	83	q	q	PROPN
ejpam-2406	131	84	or	or	CCONJ
ejpam-2406	131	85	bnn	bnn	PROPN
ejpam-2406	131	86	¶	¶	PROPN
ejpam-2406	131	87	q	q	PROPN
ejpam-2406	131	88	for	for	ADP
ejpam-2406	131	89	some	some	DET
ejpam-2406	131	90	n	n	PRON
ejpam-2406	131	91	∈	∈	PROPN
ejpam-2406	131	92	z+	z+	NUM
ejpam-2406	131	93	.	.	PUNCT
ejpam-2406	132	1	hence	hence	ADV
ejpam-2406	132	2	,	,	PUNCT
ejpam-2406	132	3	a	a	DET
ejpam-2406	132	4	¶	¶	NOUN
ejpam-2406	132	5	p	p	NOUN
ejpam-2406	132	6	(	(	PUNCT
ejpam-2406	132	7	q	q	NOUN
ejpam-2406	132	8	:	:	PUNCT
ejpam-2406	132	9	n	n	CCONJ
ejpam-2406	132	10	)	)	PUNCT
ejpam-2406	132	11	or	or	CCONJ
ejpam-2406	132	12	b	b	NOUN
ejpam-2406	132	13	¶	¶	NUM
ejpam-2406	132	14	p	p	NOUN
ejpam-2406	132	15	(	(	PUNCT
ejpam-2406	132	16	q	q	NOUN
ejpam-2406	132	17	:	:	PUNCT
ejpam-2406	132	18	n	n	CCONJ
ejpam-2406	132	19	)	)	PUNCT
ejpam-2406	132	20	and	and	CCONJ
ejpam-2406	132	21	p	p	X
ejpam-2406	132	22	(	(	PUNCT
ejpam-2406	132	23	q	q	NOUN
ejpam-2406	132	24	:	:	PUNCT
ejpam-2406	132	25	n	n	CCONJ
ejpam-2406	132	26	)	)	PUNCT
ejpam-2406	132	27	is	be	AUX
ejpam-2406	132	28	prime	prime	ADJ
ejpam-2406	132	29	.	.	PUNCT
ejpam-2406	133	1	thus	thus	ADV
ejpam-2406	133	2	,	,	PUNCT
ejpam-2406	133	3	(	(	PUNCT
ejpam-2406	133	4	q	q	NOUN
ejpam-2406	133	5	:	:	PUNCT
ejpam-2406	133	6	n	n	CCONJ
ejpam-2406	133	7	)	)	PUNCT
ejpam-2406	133	8	is	be	AUX
ejpam-2406	133	9	a	a	DET
ejpam-2406	133	10	quasi	quasi	ADJ
ejpam-2406	133	11	primary	primary	ADJ
ejpam-2406	133	12	element	element	NOUN
ejpam-2406	133	13	of	of	ADP
ejpam-2406	133	14	l.	l.	PROPN
ejpam-2406	133	15	suppose	suppose	VERB
ejpam-2406	133	16	,	,	PUNCT
ejpam-2406	133	17	(	(	PUNCT
ejpam-2406	133	18	q	q	NOUN
ejpam-2406	133	19	:	:	PUNCT
ejpam-2406	133	20	n	n	CCONJ
ejpam-2406	133	21	)	)	PUNCT
ejpam-2406	133	22	is	be	AUX
ejpam-2406	133	23	a	a	DET
ejpam-2406	133	24	quasi	quasi	ADJ
ejpam-2406	133	25	primary	primary	ADJ
ejpam-2406	133	26	element	element	NOUN
ejpam-2406	133	27	.	.	PUNCT
ejpam-2406	134	1	let	let	VERB
ejpam-2406	134	2	abn	abn	NOUN
ejpam-2406	134	3	¶q	¶q	NOUN
ejpam-2406	134	4	where	where	SCONJ
ejpam-2406	134	5	a	a	DET
ejpam-2406	134	6	,	,	PUNCT
ejpam-2406	134	7	b	b	PROPN
ejpam-2406	134	8	∈	∈	PROPN
ejpam-2406	134	9	l	l	NOUN
ejpam-2406	134	10	and	and	CCONJ
ejpam-2406	134	11	for	for	ADP
ejpam-2406	134	12	each	each	DET
ejpam-2406	134	13	element	element	NOUN
ejpam-2406	134	14	n	n	CCONJ
ejpam-2406	134	15	6¶	6¶	NUM
ejpam-2406	134	16	q.	q.	NOUN
ejpam-2406	134	17	then	then	ADV
ejpam-2406	134	18	ab	ab	PROPN
ejpam-2406	134	19	¶	¶	PROPN
ejpam-2406	134	20	(	(	PUNCT
ejpam-2406	134	21	q	q	NOUN
ejpam-2406	134	22	:	:	PUNCT
ejpam-2406	134	23	n	n	NUM
ejpam-2406	134	24	)	)	PUNCT
ejpam-2406	134	25	¶	¶	PROPN
ejpam-2406	134	26	p	p	NOUN
ejpam-2406	134	27	(	(	PUNCT
ejpam-2406	134	28	q	q	NOUN
ejpam-2406	134	29	:	:	PUNCT
ejpam-2406	134	30	n	n	CCONJ
ejpam-2406	134	31	)	)	PUNCT
ejpam-2406	134	32	)	)	PUNCT
ejpam-2406	134	33	.	.	PUNCT
ejpam-2406	135	1	since	since	SCONJ
ejpam-2406	135	2	,	,	PUNCT
ejpam-2406	135	3	(	(	PUNCT
ejpam-2406	135	4	q	q	NOUN
ejpam-2406	135	5	:	:	PUNCT
ejpam-2406	135	6	n	n	CCONJ
ejpam-2406	135	7	)	)	PUNCT
ejpam-2406	135	8	is	be	AUX
ejpam-2406	135	9	quasi	quasi	NOUN
ejpam-2406	135	10	primary	primary	NOUN
ejpam-2406	135	11	,	,	PUNCT
ejpam-2406	135	12	p	p	X
ejpam-2406	135	13	(	(	PUNCT
ejpam-2406	135	14	q	q	NOUN
ejpam-2406	135	15	:	:	PUNCT
ejpam-2406	135	16	n	n	CCONJ
ejpam-2406	135	17	)	)	PUNCT
ejpam-2406	135	18	is	be	AUX
ejpam-2406	135	19	prime	prime	ADJ
ejpam-2406	135	20	.	.	PUNCT
ejpam-2406	136	1	so	so	ADV
ejpam-2406	136	2	that	that	SCONJ
ejpam-2406	136	3	ak	ak	PROPN
ejpam-2406	136	4	¶	¶	PROPN
ejpam-2406	136	5	(	(	PUNCT
ejpam-2406	136	6	q	q	NOUN
ejpam-2406	136	7	:	:	PUNCT
ejpam-2406	136	8	n	n	CCONJ
ejpam-2406	136	9	)	)	PUNCT
ejpam-2406	136	10	or	or	CCONJ
ejpam-2406	136	11	bk	bk	VERB
ejpam-2406	136	12	¶	¶	PROPN
ejpam-2406	136	13	(	(	PUNCT
ejpam-2406	136	14	q	q	NOUN
ejpam-2406	136	15	:	:	PUNCT
ejpam-2406	136	16	n	n	CCONJ
ejpam-2406	136	17	)	)	PUNCT
ejpam-2406	136	18	.	.	PUNCT
ejpam-2406	137	1	that	that	PRON
ejpam-2406	137	2	is	be	AUX
ejpam-2406	137	3	,	,	PUNCT
ejpam-2406	137	4	akn	akn	PROPN
ejpam-2406	137	5	¶	¶	PROPN
ejpam-2406	137	6	q	q	PROPN
ejpam-2406	137	7	or	or	CCONJ
ejpam-2406	137	8	bkn	bkn	PROPN
ejpam-2406	137	9	¶	¶	PROPN
ejpam-2406	137	10	q.	q.	PROPN
ejpam-2406	137	11	hence	hence	ADV
ejpam-2406	137	12	,	,	PUNCT
ejpam-2406	137	13	q	q	PROPN
ejpam-2406	137	14	is	be	AUX
ejpam-2406	137	15	a	a	DET
ejpam-2406	137	16	classical	classical	ADJ
ejpam-2406	137	17	quasi	quasi	ADJ
ejpam-2406	137	18	primary	primary	ADJ
ejpam-2406	137	19	element	element	NOUN
ejpam-2406	137	20	.	.	PUNCT
ejpam-2406	138	1	if	if	SCONJ
ejpam-2406	138	2	n	n	X
ejpam-2406	138	3	¶	¶	PROPN
ejpam-2406	138	4	q	q	PROPN
ejpam-2406	138	5	,	,	PUNCT
ejpam-2406	138	6	(	(	PUNCT
ejpam-2406	138	7	q	q	NOUN
ejpam-2406	138	8	:	:	PUNCT
ejpam-2406	138	9	n	n	X
ejpam-2406	138	10	)	)	PUNCT
ejpam-2406	139	1	=	=	SYM
ejpam-2406	139	2	1	1	X
ejpam-2406	139	3	.	.	PUNCT
ejpam-2406	140	1	in	in	ADP
ejpam-2406	140	2	this	this	DET
ejpam-2406	140	3	case	case	NOUN
ejpam-2406	140	4	abn	abn	PROPN
ejpam-2406	140	5	¶	¶	PROPN
ejpam-2406	140	6	q	q	PROPN
ejpam-2406	140	7	implies	imply	VERB
ejpam-2406	140	8	ab	ab	PROPN
ejpam-2406	140	9	¶	¶	PROPN
ejpam-2406	140	10	(	(	PUNCT
ejpam-2406	140	11	q	q	NOUN
ejpam-2406	140	12	:	:	PUNCT
ejpam-2406	140	13	n	n	X
ejpam-2406	140	14	)	)	PUNCT
ejpam-2406	141	1	=	=	SYM
ejpam-2406	141	2	1	1	NUM
ejpam-2406	141	3	and	and	CCONJ
ejpam-2406	141	4	obviously	obviously	ADV
ejpam-2406	141	5	a	a	DET
ejpam-2406	141	6	¶	¶	NOUN
ejpam-2406	141	7	(	(	PUNCT
ejpam-2406	141	8	q	q	NOUN
ejpam-2406	141	9	:	:	PUNCT
ejpam-2406	141	10	n	n	CCONJ
ejpam-2406	141	11	)	)	PUNCT
ejpam-2406	141	12	,	,	PUNCT
ejpam-2406	141	13	b	b	X
ejpam-2406	141	14	¶	¶	PROPN
ejpam-2406	141	15	(	(	PUNCT
ejpam-2406	141	16	q	q	NOUN
ejpam-2406	141	17	:	:	PUNCT
ejpam-2406	141	18	n	n	CCONJ
ejpam-2406	141	19	)	)	PUNCT
ejpam-2406	141	20	.	.	PUNCT
ejpam-2406	142	1	consequently	consequently	ADV
ejpam-2406	142	2	,	,	PUNCT
ejpam-2406	142	3	an	an	DET
ejpam-2406	142	4	¶q	¶q	NOUN
ejpam-2406	142	5	,	,	PUNCT
ejpam-2406	142	6	bn	bn	X
ejpam-2406	142	7	¶q	¶q	NOUN
ejpam-2406	142	8	and	and	CCONJ
ejpam-2406	142	9	q	q	NOUN
ejpam-2406	142	10	is	be	AUX
ejpam-2406	142	11	a	a	DET
ejpam-2406	142	12	classical	classical	ADJ
ejpam-2406	142	13	quasi	quasi	ADJ
ejpam-2406	142	14	primary	primary	ADJ
ejpam-2406	142	15	element	element	NOUN
ejpam-2406	142	16	.	.	PUNCT
ejpam-2406	143	1	the	the	DET
ejpam-2406	143	2	following	follow	VERB
ejpam-2406	143	3	theorem	theorem	NOUN
ejpam-2406	143	4	is	be	AUX
ejpam-2406	143	5	obvious	obvious	ADJ
ejpam-2406	143	6	.	.	PUNCT
ejpam-2406	144	1	theorem	theorem	NOUN
ejpam-2406	144	2	3	3	X
ejpam-2406	144	3	.	.	PUNCT
ejpam-2406	145	1	let	let	VERB
ejpam-2406	145	2	m	m	PRON
ejpam-2406	145	3	be	be	AUX
ejpam-2406	145	4	a	a	DET
ejpam-2406	145	5	l	l	NOUN
ejpam-2406	145	6	-	-	NOUN
ejpam-2406	145	7	module	module	NOUN
ejpam-2406	145	8	and	and	CCONJ
ejpam-2406	145	9	q	q	NOUN
ejpam-2406	145	10	be	be	AUX
ejpam-2406	145	11	a	a	DET
ejpam-2406	145	12	proper	proper	ADJ
ejpam-2406	145	13	element	element	NOUN
ejpam-2406	145	14	of	of	ADP
ejpam-2406	145	15	m.	m.	NOUN
ejpam-2406	145	16	(	(	PUNCT
ejpam-2406	145	17	i	i	NOUN
ejpam-2406	145	18	)	)	PUNCT
ejpam-2406	145	19	the	the	DET
ejpam-2406	145	20	following	follow	VERB
ejpam-2406	145	21	statements	statement	NOUN
ejpam-2406	145	22	are	be	AUX
ejpam-2406	145	23	equivalent	equivalent	ADJ
ejpam-2406	145	24	,	,	PUNCT
ejpam-2406	145	25	(	(	PUNCT
ejpam-2406	145	26	a	a	X
ejpam-2406	145	27	)	)	PUNCT
ejpam-2406	145	28	q	q	NOUN
ejpam-2406	145	29	is	be	AUX
ejpam-2406	145	30	a	a	DET
ejpam-2406	145	31	classical	classical	ADJ
ejpam-2406	145	32	primary	primary	ADJ
ejpam-2406	145	33	element	element	NOUN
ejpam-2406	145	34	.	.	PUNCT
ejpam-2406	146	1	(	(	PUNCT
ejpam-2406	146	2	b	b	X
ejpam-2406	146	3	)	)	PUNCT
ejpam-2406	146	4	for	for	ADP
ejpam-2406	146	5	every	every	DET
ejpam-2406	146	6	a	a	PROPN
ejpam-2406	146	7	,	,	PUNCT
ejpam-2406	146	8	b	b	PROPN
ejpam-2406	146	9	∈	∈	PROPN
ejpam-2406	146	10	l	l	NOUN
ejpam-2406	146	11	and	and	CCONJ
ejpam-2406	146	12	n	n	CCONJ
ejpam-2406	146	13	∈	∈	PROPN
ejpam-2406	146	14	m	m	PROPN
ejpam-2406	146	15	,	,	PUNCT
ejpam-2406	146	16	abn	abn	PROPN
ejpam-2406	146	17	¶	¶	PROPN
ejpam-2406	146	18	q	q	PROPN
ejpam-2406	146	19	implies	imply	VERB
ejpam-2406	146	20	that	that	SCONJ
ejpam-2406	146	21	either	either	CCONJ
ejpam-2406	146	22	an	an	DET
ejpam-2406	146	23	¶	¶	PROPN
ejpam-2406	146	24	q	q	PUNCT
ejpam-2406	146	25	or	or	CCONJ
ejpam-2406	146	26	bkn	bkn	PROPN
ejpam-2406	146	27	¶	¶	PROPN
ejpam-2406	146	28	q	q	PROPN
ejpam-2406	146	29	for	for	ADP
ejpam-2406	146	30	some	some	DET
ejpam-2406	146	31	k	k	PROPN
ejpam-2406	146	32	∈	∈	PROPN
ejpam-2406	146	33	z+	z+	NUM
ejpam-2406	146	34	(	(	PUNCT
ejpam-2406	146	35	c	c	NOUN
ejpam-2406	146	36	)	)	PUNCT
ejpam-2406	146	37	for	for	ADP
ejpam-2406	146	38	every	every	DET
ejpam-2406	146	39	n	n	NOUN
ejpam-2406	146	40	∈	∈	NOUN
ejpam-2406	146	41	m	m	VERB
ejpam-2406	146	42	where	where	SCONJ
ejpam-2406	146	43	n	n	PROPN
ejpam-2406	146	44	6¶q	6¶q	NUM
ejpam-2406	146	45	,	,	PUNCT
ejpam-2406	146	46	(	(	PUNCT
ejpam-2406	146	47	q	q	NOUN
ejpam-2406	146	48	:	:	PUNCT
ejpam-2406	146	49	n	n	CCONJ
ejpam-2406	146	50	)	)	PUNCT
ejpam-2406	146	51	is	be	AUX
ejpam-2406	146	52	a	a	DET
ejpam-2406	146	53	primary	primary	ADJ
ejpam-2406	146	54	element	element	NOUN
ejpam-2406	146	55	of	of	ADP
ejpam-2406	146	56	l.	l.	PROPN
ejpam-2406	146	57	(	(	PUNCT
ejpam-2406	146	58	ii	ii	PROPN
ejpam-2406	146	59	)	)	PUNCT
ejpam-2406	146	60	the	the	DET
ejpam-2406	146	61	following	follow	VERB
ejpam-2406	146	62	statements	statement	NOUN
ejpam-2406	146	63	are	be	AUX
ejpam-2406	146	64	equivalent	equivalent	ADJ
ejpam-2406	146	65	.	.	PUNCT
ejpam-2406	147	1	(	(	PUNCT
ejpam-2406	147	2	a	a	X
ejpam-2406	147	3	)	)	PUNCT
ejpam-2406	147	4	q	q	NOUN
ejpam-2406	147	5	is	be	AUX
ejpam-2406	147	6	a	a	DET
ejpam-2406	147	7	classical	classical	ADJ
ejpam-2406	147	8	quasi	quasi	ADJ
ejpam-2406	147	9	primary	primary	ADJ
ejpam-2406	147	10	element	element	NOUN
ejpam-2406	147	11	.	.	PUNCT
ejpam-2406	148	1	(	(	PUNCT
ejpam-2406	148	2	b	b	X
ejpam-2406	148	3	)	)	PUNCT
ejpam-2406	148	4	for	for	ADP
ejpam-2406	148	5	every	every	DET
ejpam-2406	148	6	a	a	PROPN
ejpam-2406	148	7	,	,	PUNCT
ejpam-2406	148	8	b	b	PROPN
ejpam-2406	148	9	∈	∈	PROPN
ejpam-2406	148	10	l	l	NOUN
ejpam-2406	148	11	and	and	CCONJ
ejpam-2406	148	12	n	n	CCONJ
ejpam-2406	148	13	∈	∈	PROPN
ejpam-2406	148	14	m	m	PROPN
ejpam-2406	148	15	,	,	PUNCT
ejpam-2406	148	16	abn	abn	PROPN
ejpam-2406	148	17	¶	¶	PROPN
ejpam-2406	148	18	q	q	PROPN
ejpam-2406	148	19	implies	imply	VERB
ejpam-2406	148	20	either	either	CCONJ
ejpam-2406	148	21	akn	akn	PROPN
ejpam-2406	148	22	¶	¶	PROPN
ejpam-2406	148	23	q	q	PROPN
ejpam-2406	148	24	or	or	CCONJ
ejpam-2406	148	25	bkn	bkn	PROPN
ejpam-2406	148	26	¶	¶	PROPN
ejpam-2406	148	27	q	q	PROPN
ejpam-2406	148	28	for	for	ADP
ejpam-2406	148	29	some	some	DET
ejpam-2406	148	30	k	k	PROPN
ejpam-2406	148	31	∈	∈	PROPN
ejpam-2406	148	32	z+	z+	NUM
ejpam-2406	148	33	c.	c.	PROPN
ejpam-2406	148	34	manjarekar	manjarekar	PROPN
ejpam-2406	148	35	,	,	PUNCT
ejpam-2406	148	36	u.	u.	PROPN
ejpam-2406	148	37	kandale	kandale	PROPN
ejpam-2406	148	38	/	/	SYM
ejpam-2406	148	39	eur	eur	PROPN
ejpam-2406	148	40	.	.	PUNCT
ejpam-2406	149	1	j.	j.	PROPN
ejpam-2406	149	2	pure	pure	PROPN
ejpam-2406	149	3	appl	appl	PROPN
ejpam-2406	149	4	.	.	PROPN
ejpam-2406	149	5	math	math	PROPN
ejpam-2406	149	6	,	,	PUNCT
ejpam-2406	149	7	8	8	NUM
ejpam-2406	149	8	(	(	PUNCT
ejpam-2406	149	9	2015	2015	NUM
ejpam-2406	149	10	)	)	PUNCT
ejpam-2406	149	11	,	,	PUNCT
ejpam-2406	149	12	172	172	NUM
ejpam-2406	149	13	-	-	SYM
ejpam-2406	149	14	184	184	NUM
ejpam-2406	149	15	177	177	NUM
ejpam-2406	149	16	(	(	PUNCT
ejpam-2406	149	17	c	c	NOUN
ejpam-2406	149	18	)	)	PUNCT
ejpam-2406	149	19	for	for	ADP
ejpam-2406	149	20	every	every	DET
ejpam-2406	149	21	n	n	PRON
ejpam-2406	149	22	∈	∈	PROPN
ejpam-2406	149	23	m	m	NOUN
ejpam-2406	149	24	,	,	PUNCT
ejpam-2406	149	25	where	where	SCONJ
ejpam-2406	149	26	n	n	PRON
ejpam-2406	149	27	6¶q	6¶q	NUM
ejpam-2406	149	28	,	,	PUNCT
ejpam-2406	149	29	(	(	PUNCT
ejpam-2406	149	30	q	q	NOUN
ejpam-2406	149	31	:	:	PUNCT
ejpam-2406	149	32	n	n	CCONJ
ejpam-2406	149	33	)	)	PUNCT
ejpam-2406	149	34	is	be	AUX
ejpam-2406	149	35	a	a	DET
ejpam-2406	149	36	quasi	quasi	ADJ
ejpam-2406	149	37	primary	primary	ADJ
ejpam-2406	149	38	element	element	NOUN
ejpam-2406	149	39	of	of	ADP
ejpam-2406	149	40	l.	l.	PROPN
ejpam-2406	149	41	theorem	theorem	PROPN
ejpam-2406	149	42	4	4	X
ejpam-2406	149	43	.	.	PUNCT
ejpam-2406	150	1	let	let	VERB
ejpam-2406	150	2	m	m	PRON
ejpam-2406	150	3	be	be	AUX
ejpam-2406	150	4	a	a	DET
ejpam-2406	150	5	lattice	lattice	NOUN
ejpam-2406	150	6	module	module	NOUN
ejpam-2406	150	7	and	and	CCONJ
ejpam-2406	150	8	q	q	NOUN
ejpam-2406	150	9	be	be	AUX
ejpam-2406	150	10	a	a	DET
ejpam-2406	150	11	classical	classical	ADJ
ejpam-2406	150	12	primary	primary	NOUN
ejpam-2406	150	13	(	(	PUNCT
ejpam-2406	150	14	or	or	CCONJ
ejpam-2406	150	15	classical	classical	ADJ
ejpam-2406	150	16	quasi	quasi	ADJ
ejpam-2406	150	17	primary	primary	NOUN
ejpam-2406	150	18	)	)	PUNCT
ejpam-2406	150	19	element	element	NOUN
ejpam-2406	150	20	of	of	ADP
ejpam-2406	150	21	m.	m.	NOUN
ejpam-2406	150	22	then	then	ADV
ejpam-2406	150	23	{	{	PUNCT
ejpam-2406	150	24	p(q	p(q	PROPN
ejpam-2406	150	25	:	:	PUNCT
ejpam-2406	150	26	n	n	CCONJ
ejpam-2406	150	27	)	)	PUNCT
ejpam-2406	151	1	|	|	ADV
ejpam-2406	151	2	n	n	ADV
ejpam-2406	151	3	6¶q	6¶q	PRON
ejpam-2406	151	4	}	}	PUNCT
ejpam-2406	151	5	is	be	AUX
ejpam-2406	151	6	a	a	DET
ejpam-2406	151	7	chain	chain	NOUN
ejpam-2406	151	8	of	of	ADP
ejpam-2406	151	9	prime	prime	ADJ
ejpam-2406	151	10	element	element	NOUN
ejpam-2406	151	11	of	of	ADP
ejpam-2406	151	12	l.	l.	PROPN
ejpam-2406	151	13	proof	proof	PROPN
ejpam-2406	151	14	.	.	PUNCT
ejpam-2406	152	1	for	for	ADP
ejpam-2406	152	2	each	each	DET
ejpam-2406	152	3	m1	m1	NOUN
ejpam-2406	152	4	,	,	PUNCT
ejpam-2406	152	5	m2	m2	PROPN
ejpam-2406	152	6	6¶	6¶	NUM
ejpam-2406	152	7	q	q	NOUN
ejpam-2406	152	8	,	,	PUNCT
ejpam-2406	152	9	we	we	PRON
ejpam-2406	152	10	show	show	VERB
ejpam-2406	152	11	that	that	SCONJ
ejpam-2406	152	12	p	p	X
ejpam-2406	152	13	(	(	PUNCT
ejpam-2406	152	14	q	q	NOUN
ejpam-2406	152	15	:	:	PUNCT
ejpam-2406	152	16	m1	m1	NOUN
ejpam-2406	152	17	)	)	PUNCT
ejpam-2406	152	18	∧	∧	NOUN
ejpam-2406	152	19	p	p	NOUN
ejpam-2406	152	20	(	(	PUNCT
ejpam-2406	152	21	q	q	NOUN
ejpam-2406	152	22	:	:	PUNCT
ejpam-2406	152	23	m2	m2	PROPN
ejpam-2406	152	24	)	)	PUNCT
ejpam-2406	152	25	¶	¶	PROPN
ejpam-2406	152	26	p	p	NOUN
ejpam-2406	152	27	(	(	PUNCT
ejpam-2406	152	28	q	q	NOUN
ejpam-2406	152	29	:	:	PUNCT
ejpam-2406	152	30	(	(	PUNCT
ejpam-2406	152	31	m1	m1	PROPN
ejpam-2406	152	32	∨m2	∨m2	NOUN
ejpam-2406	152	33	)	)	PUNCT
ejpam-2406	152	34	)	)	PUNCT
ejpam-2406	152	35	.	.	PUNCT
ejpam-2406	153	1	let	let	VERB
ejpam-2406	153	2	x	x	X
ejpam-2406	153	3	¶	¶	PROPN
ejpam-2406	153	4	p	p	X
ejpam-2406	153	5	(	(	PUNCT
ejpam-2406	153	6	q	q	NOUN
ejpam-2406	153	7	:	:	PUNCT
ejpam-2406	153	8	m1)∧	m1)∧	PROPN
ejpam-2406	153	9	p	p	X
ejpam-2406	153	10	(	(	PUNCT
ejpam-2406	153	11	q	q	NOUN
ejpam-2406	153	12	:	:	PUNCT
ejpam-2406	153	13	m2	m2	PROPN
ejpam-2406	153	14	)	)	PUNCT
ejpam-2406	153	15	.	.	PUNCT
ejpam-2406	154	1	then	then	ADV
ejpam-2406	154	2	x	x	X
ejpam-2406	154	3	¶	¶	PROPN
ejpam-2406	154	4	p	p	X
ejpam-2406	154	5	(	(	PUNCT
ejpam-2406	154	6	q	q	NOUN
ejpam-2406	154	7	:	:	PUNCT
ejpam-2406	154	8	m1	m1	NOUN
ejpam-2406	154	9	)	)	PUNCT
ejpam-2406	154	10	and	and	CCONJ
ejpam-2406	154	11	x	x	SYM
ejpam-2406	154	12	¶	¶	NOUN
ejpam-2406	154	13	p	p	X
ejpam-2406	154	14	(	(	PUNCT
ejpam-2406	154	15	q	q	NOUN
ejpam-2406	154	16	:	:	PUNCT
ejpam-2406	154	17	m2	m2	PROPN
ejpam-2406	154	18	)	)	PUNCT
ejpam-2406	154	19	.	.	PUNCT
ejpam-2406	155	1	so	so	ADV
ejpam-2406	155	2	xn1	xn1	DET
ejpam-2406	155	3	m1	m1	PROPN
ejpam-2406	155	4	¶q	¶q	PROPN
ejpam-2406	155	5	,	,	PUNCT
ejpam-2406	155	6	xn2	xn2	PROPN
ejpam-2406	155	7	m2	m2	PROPN
ejpam-2406	155	8	¶q	¶q	NOUN
ejpam-2406	155	9	for	for	ADP
ejpam-2406	155	10	some	some	DET
ejpam-2406	155	11	integers	integer	NOUN
ejpam-2406	155	12	n1	n1	NOUN
ejpam-2406	155	13	,	,	PUNCT
ejpam-2406	155	14	n2	n2	ADJ
ejpam-2406	155	15	and	and	CCONJ
ejpam-2406	155	16	let	let	VERB
ejpam-2406	155	17	n=	n=	ADJ
ejpam-2406	155	18	max{n1	max{n1	NOUN
ejpam-2406	155	19	,	,	PUNCT
ejpam-2406	155	20	n2	n2	ADJ
ejpam-2406	155	21	}	}	PUNCT
ejpam-2406	155	22	.	.	PUNCT
ejpam-2406	156	1	hence	hence	ADV
ejpam-2406	156	2	xn(m1	xn(m1	NOUN
ejpam-2406	156	3	∨m2)¶q	∨m2)¶q	NOUN
ejpam-2406	156	4	.	.	PUNCT
ejpam-2406	157	1	that	that	PRON
ejpam-2406	157	2	is	is	ADV
ejpam-2406	157	3	x	x	X
ejpam-2406	157	4	¶	¶	PROPN
ejpam-2406	157	5	p	p	NOUN
ejpam-2406	157	6	(	(	PUNCT
ejpam-2406	157	7	q	q	NOUN
ejpam-2406	157	8	:	:	PUNCT
ejpam-2406	157	9	(	(	PUNCT
ejpam-2406	157	10	m1	m1	PROPN
ejpam-2406	157	11	∨m2	∨m2	NOUN
ejpam-2406	157	12	)	)	PUNCT
ejpam-2406	157	13	)	)	PUNCT
ejpam-2406	158	1	and	and	CCONJ
ejpam-2406	158	2	we	we	PRON
ejpam-2406	158	3	have	have	VERB
ejpam-2406	158	4	æ	æ	X
ejpam-2406	159	1	(	(	PUNCT
ejpam-2406	159	2	q	q	NOUN
ejpam-2406	159	3	:	:	PUNCT
ejpam-2406	159	4	m1)∧	m1)∧	PROPN
ejpam-2406	159	5	æ	æ	X
ejpam-2406	159	6	(	(	PUNCT
ejpam-2406	159	7	q	q	NOUN
ejpam-2406	159	8	:	:	PUNCT
ejpam-2406	159	9	m2)¶	m2)¶	PROPN
ejpam-2406	159	10	æ	æ	PROPN
ejpam-2406	159	11	(	(	PUNCT
ejpam-2406	159	12	q	q	NOUN
ejpam-2406	159	13	:	:	PUNCT
ejpam-2406	159	14	(	(	PUNCT
ejpam-2406	159	15	m1	m1	PROPN
ejpam-2406	159	16	∨m2	∨m2	NOUN
ejpam-2406	159	17	)	)	PUNCT
ejpam-2406	159	18	)	)	PUNCT
ejpam-2406	159	19	.	.	PUNCT
ejpam-2406	160	1	since	since	SCONJ
ejpam-2406	160	2	q	q	PROPN
ejpam-2406	160	3	is	be	AUX
ejpam-2406	160	4	classical	classical	ADJ
ejpam-2406	160	5	primary	primary	NOUN
ejpam-2406	160	6	and	and	CCONJ
ejpam-2406	160	7	m1	m1	PROPN
ejpam-2406	160	8	∨	∨	NUM
ejpam-2406	160	9	m2	m2	PROPN
ejpam-2406	160	10	6¶	6¶	NUM
ejpam-2406	160	11	q	q	NOUN
ejpam-2406	160	12	,	,	PUNCT
ejpam-2406	160	13	p	p	X
ejpam-2406	160	14	(	(	PUNCT
ejpam-2406	160	15	q	q	NOUN
ejpam-2406	160	16	:	:	PUNCT
ejpam-2406	160	17	(	(	PUNCT
ejpam-2406	160	18	m1	m1	PROPN
ejpam-2406	160	19	∨m2	∨m2	NOUN
ejpam-2406	160	20	)	)	PUNCT
ejpam-2406	160	21	)	)	PUNCT
ejpam-2406	160	22	is	be	AUX
ejpam-2406	160	23	prime	prime	ADJ
ejpam-2406	160	24	by	by	ADP
ejpam-2406	160	25	theorem	theorem	NOUN
ejpam-2406	160	26	1	1	NUM
ejpam-2406	160	27	,	,	PUNCT
ejpam-2406	160	28	we	we	PRON
ejpam-2406	160	29	conclude	conclude	VERB
ejpam-2406	160	30	that	that	SCONJ
ejpam-2406	160	31	,	,	PUNCT
ejpam-2406	160	32	p	p	X
ejpam-2406	160	33	(	(	PUNCT
ejpam-2406	160	34	q	q	NOUN
ejpam-2406	160	35	:	:	PUNCT
ejpam-2406	160	36	m1	m1	NOUN
ejpam-2406	160	37	)	)	PUNCT
ejpam-2406	160	38	¶	¶	PROPN
ejpam-2406	160	39	p	p	NOUN
ejpam-2406	160	40	(	(	PUNCT
ejpam-2406	160	41	q	q	NOUN
ejpam-2406	160	42	:	:	PUNCT
ejpam-2406	160	43	(	(	PUNCT
ejpam-2406	160	44	m1	m1	PROPN
ejpam-2406	160	45	∨m2	∨m2	NOUN
ejpam-2406	160	46	)	)	PUNCT
ejpam-2406	160	47	)	)	PUNCT
ejpam-2406	160	48	or	or	CCONJ
ejpam-2406	160	49	p	p	X
ejpam-2406	160	50	(	(	PUNCT
ejpam-2406	160	51	q	q	NOUN
ejpam-2406	160	52	:	:	PUNCT
ejpam-2406	160	53	m2	m2	PROPN
ejpam-2406	160	54	)	)	PUNCT
ejpam-2406	160	55	¶	¶	PROPN
ejpam-2406	160	56	p	p	NOUN
ejpam-2406	160	57	(	(	PUNCT
ejpam-2406	160	58	q	q	NOUN
ejpam-2406	160	59	:	:	PUNCT
ejpam-2406	160	60	(	(	PUNCT
ejpam-2406	160	61	m1	m1	PROPN
ejpam-2406	160	62	∨m2	∨m2	NOUN
ejpam-2406	160	63	)	)	PUNCT
ejpam-2406	160	64	)	)	PUNCT
ejpam-2406	160	65	.	.	PUNCT
ejpam-2406	161	1	suppose	suppose	VERB
ejpam-2406	161	2	p	p	X
ejpam-2406	161	3	(	(	PUNCT
ejpam-2406	161	4	q	q	NOUN
ejpam-2406	161	5	:	:	PUNCT
ejpam-2406	161	6	m1)¶	m1)¶	PROPN
ejpam-2406	161	7	p	p	X
ejpam-2406	161	8	(	(	PUNCT
ejpam-2406	161	9	q	q	NOUN
ejpam-2406	161	10	:	:	PUNCT
ejpam-2406	161	11	(	(	PUNCT
ejpam-2406	161	12	m1	m1	PROPN
ejpam-2406	161	13	∨m2	∨m2	NOUN
ejpam-2406	161	14	)	)	PUNCT
ejpam-2406	161	15	)	)	PUNCT
ejpam-2406	161	16	.	.	PUNCT
ejpam-2406	162	1	then	then	ADV
ejpam-2406	162	2	∨{x	∨{x	PROPN
ejpam-2406	162	3	∈	∈	PROPN
ejpam-2406	162	4	l	l	NOUN
ejpam-2406	163	1	|	|	INTJ
ejpam-2406	163	2	xk1	xk1	PROPN
ejpam-2406	163	3	m1	m1	PROPN
ejpam-2406	163	4	¶q	¶q	PROPN
ejpam-2406	163	5	,	,	PUNCT
ejpam-2406	163	6	k1	k1	PROPN
ejpam-2406	163	7	∈	∈	PROPN
ejpam-2406	163	8	z+}¶	z+}¶	NUM
ejpam-2406	163	9	∨{x	∨{x	NOUN
ejpam-2406	163	10	∈	∈	NOUN
ejpam-2406	163	11	l	l	NOUN
ejpam-2406	164	1	|	|	ADV
ejpam-2406	164	2	xk2	xk2	NOUN
ejpam-2406	164	3	m1	m1	PROPN
ejpam-2406	164	4	∨	∨	NUM
ejpam-2406	164	5	xk2	xk2	PROPN
ejpam-2406	164	6	m2	m2	PROPN
ejpam-2406	164	7	¶q	¶q	PROPN
ejpam-2406	164	8	}	}	PUNCT
ejpam-2406	164	9	=	=	SYM
ejpam-2406	164	10	∨{x	∨{x	NOUN
ejpam-2406	165	1	∈	∈	NOUN
ejpam-2406	165	2	l	l	NOUN
ejpam-2406	165	3	|	|	ADV
ejpam-2406	165	4	xk2	xk2	PROPN
ejpam-2406	165	5	m1	m1	PROPN
ejpam-2406	165	6	¶	¶	PROPN
ejpam-2406	165	7	and	and	CCONJ
ejpam-2406	165	8	xk2	xk2	PROPN
ejpam-2406	165	9	m2	m2	PROPN
ejpam-2406	165	10	¶q	¶q	PROPN
ejpam-2406	165	11	}	}	PUNCT
ejpam-2406	165	12	.	.	PUNCT
ejpam-2406	166	1	hence	hence	ADV
ejpam-2406	166	2	xk1	xk1	PROPN
ejpam-2406	166	3	m1	m1	PROPN
ejpam-2406	166	4	¶q	¶q	NOUN
ejpam-2406	166	5	implies	imply	VERB
ejpam-2406	166	6	xk2	xk2	PROPN
ejpam-2406	166	7	m2	m2	PROPN
ejpam-2406	166	8	¶q	¶q	NOUN
ejpam-2406	166	9	for	for	ADP
ejpam-2406	166	10	some	some	DET
ejpam-2406	166	11	integers	integer	NOUN
ejpam-2406	166	12	k1	k1	NOUN
ejpam-2406	166	13	,	,	PUNCT
ejpam-2406	166	14	k2	k2	NOUN
ejpam-2406	166	15	.	.	PUNCT
ejpam-2406	167	1	therefore	therefore	ADV
ejpam-2406	167	2	,	,	PUNCT
ejpam-2406	167	3	∨{x	∨{x	PROPN
ejpam-2406	167	4	∈	∈	PROPN
ejpam-2406	167	5	l	l	NOUN
ejpam-2406	168	1	|	|	INTJ
ejpam-2406	168	2	xk1	xk1	PROPN
ejpam-2406	168	3	m1	m1	PROPN
ejpam-2406	168	4	¶q}¶	¶q}¶	PRON
ejpam-2406	168	5	∨{x	∨{x	NOUN
ejpam-2406	168	6	∈	∈	NOUN
ejpam-2406	168	7	l	l	NOUN
ejpam-2406	169	1	|	|	ADV
ejpam-2406	169	2	xk2	xk2	PROPN
ejpam-2406	169	3	m2	m2	PROPN
ejpam-2406	169	4	¶q	¶q	PROPN
ejpam-2406	169	5	}	}	PUNCT
ejpam-2406	169	6	.	.	PUNCT
ejpam-2406	170	1	consequently	consequently	ADV
ejpam-2406	170	2	,	,	PUNCT
ejpam-2406	170	3	p	p	X
ejpam-2406	170	4	(	(	PUNCT
ejpam-2406	170	5	q	q	NOUN
ejpam-2406	170	6	:	:	PUNCT
ejpam-2406	170	7	m1	m1	NOUN
ejpam-2406	170	8	)	)	PUNCT
ejpam-2406	170	9	¶	¶	PROPN
ejpam-2406	170	10	p	p	NOUN
ejpam-2406	170	11	(	(	PUNCT
ejpam-2406	170	12	q	q	NOUN
ejpam-2406	170	13	:	:	PUNCT
ejpam-2406	170	14	m2	m2	PROPN
ejpam-2406	170	15	)	)	PUNCT
ejpam-2406	170	16	.	.	PUNCT
ejpam-2406	171	1	similarly	similarly	ADV
ejpam-2406	171	2	,	,	PUNCT
ejpam-2406	171	3	p	p	X
ejpam-2406	171	4	(	(	PUNCT
ejpam-2406	171	5	q	q	NOUN
ejpam-2406	171	6	:	:	PUNCT
ejpam-2406	171	7	m2	m2	PROPN
ejpam-2406	171	8	)	)	PUNCT
ejpam-2406	171	9	¶	¶	PROPN
ejpam-2406	171	10	p	p	NOUN
ejpam-2406	171	11	(	(	PUNCT
ejpam-2406	171	12	q	q	NOUN
ejpam-2406	171	13	:	:	PUNCT
ejpam-2406	171	14	(	(	PUNCT
ejpam-2406	171	15	m1	m1	PROPN
ejpam-2406	171	16	∨m2	∨m2	NOUN
ejpam-2406	171	17	)	)	PUNCT
ejpam-2406	171	18	)	)	PUNCT
ejpam-2406	171	19	implies	imply	VERB
ejpam-2406	171	20	p	p	X
ejpam-2406	171	21	(	(	PUNCT
ejpam-2406	171	22	q	q	NOUN
ejpam-2406	171	23	:	:	PUNCT
ejpam-2406	171	24	m2	m2	PROPN
ejpam-2406	171	25	)	)	PUNCT
ejpam-2406	171	26	¶	¶	PROPN
ejpam-2406	171	27	p	p	NOUN
ejpam-2406	171	28	(	(	PUNCT
ejpam-2406	171	29	q	q	NOUN
ejpam-2406	171	30	:	:	PUNCT
ejpam-2406	171	31	m1	m1	NOUN
ejpam-2406	171	32	)	)	PUNCT
ejpam-2406	171	33	.	.	PUNCT
ejpam-2406	172	1	thus	thus	ADV
ejpam-2406	172	2	p	p	X
ejpam-2406	172	3	(	(	PUNCT
ejpam-2406	172	4	q	q	NOUN
ejpam-2406	172	5	:	:	PUNCT
ejpam-2406	172	6	m1	m1	NOUN
ejpam-2406	172	7	)	)	PUNCT
ejpam-2406	172	8	¶	¶	PROPN
ejpam-2406	172	9	p	p	NOUN
ejpam-2406	172	10	(	(	PUNCT
ejpam-2406	172	11	q	q	NOUN
ejpam-2406	172	12	:	:	PUNCT
ejpam-2406	172	13	m2)or	m2)or	NOUN
ejpam-2406	172	14	p	p	NOUN
ejpam-2406	172	15	(	(	PUNCT
ejpam-2406	172	16	q	q	NOUN
ejpam-2406	172	17	:	:	PUNCT
ejpam-2406	172	18	m2	m2	PROPN
ejpam-2406	172	19	)	)	PUNCT
ejpam-2406	172	20	¶	¶	PROPN
ejpam-2406	172	21	p	p	NOUN
ejpam-2406	172	22	(	(	PUNCT
ejpam-2406	172	23	q	q	NOUN
ejpam-2406	172	24	:	:	PUNCT
ejpam-2406	172	25	m1	m1	NOUN
ejpam-2406	172	26	)	)	PUNCT
ejpam-2406	172	27	.	.	PUNCT
ejpam-2406	173	1	hence	hence	ADV
ejpam-2406	173	2	{	{	PUNCT
ejpam-2406	173	3	p(q	p(q	PROPN
ejpam-2406	173	4	:	:	PUNCT
ejpam-2406	173	5	n	n	CCONJ
ejpam-2406	173	6	)	)	PUNCT
ejpam-2406	174	1	|	|	ADV
ejpam-2406	174	2	n	n	ADV
ejpam-2406	174	3	6¶q	6¶q	PRON
ejpam-2406	174	4	}	}	PUNCT
ejpam-2406	174	5	is	be	AUX
ejpam-2406	174	6	a	a	DET
ejpam-2406	174	7	chain	chain	NOUN
ejpam-2406	174	8	of	of	ADP
ejpam-2406	174	9	prime	prime	ADJ
ejpam-2406	174	10	elements	element	NOUN
ejpam-2406	174	11	of	of	ADP
ejpam-2406	174	12	l.	l.	PROPN
ejpam-2406	174	13	we	we	PRON
ejpam-2406	174	14	now	now	ADV
ejpam-2406	174	15	obtain	obtain	VERB
ejpam-2406	174	16	the	the	DET
ejpam-2406	174	17	characterizations	characterization	NOUN
ejpam-2406	174	18	of	of	ADP
ejpam-2406	174	19	a	a	DET
ejpam-2406	174	20	classical	classical	ADJ
ejpam-2406	174	21	primary	primary	ADJ
ejpam-2406	174	22	element	element	NOUN
ejpam-2406	174	23	,	,	PUNCT
ejpam-2406	174	24	a	a	DET
ejpam-2406	174	25	primary	primary	ADJ
ejpam-2406	174	26	element	element	NOUN
ejpam-2406	174	27	of	of	ADP
ejpam-2406	174	28	a	a	DET
ejpam-2406	174	29	lattice	lattice	NOUN
ejpam-2406	174	30	module	module	NOUN
ejpam-2406	174	31	and	and	CCONJ
ejpam-2406	174	32	a	a	DET
ejpam-2406	174	33	primary	primary	ADJ
ejpam-2406	174	34	element	element	NOUN
ejpam-2406	174	35	of	of	ADP
ejpam-2406	174	36	a	a	DET
ejpam-2406	174	37	multiplicative	multiplicative	ADJ
ejpam-2406	174	38	lattice	lattice	NOUN
ejpam-2406	174	39	.	.	PUNCT
ejpam-2406	175	1	theorem	theorem	NOUN
ejpam-2406	175	2	5	5	NUM
ejpam-2406	175	3	.	.	PUNCT
ejpam-2406	176	1	let	let	VERB
ejpam-2406	176	2	m	m	PRON
ejpam-2406	176	3	be	be	AUX
ejpam-2406	176	4	a	a	DET
ejpam-2406	176	5	multiplication	multiplication	NOUN
ejpam-2406	176	6	l	l	NOUN
ejpam-2406	176	7	-	-	NOUN
ejpam-2406	176	8	module	module	NOUN
ejpam-2406	176	9	and	and	CCONJ
ejpam-2406	176	10	q	q	NOUN
ejpam-2406	176	11	be	be	AUX
ejpam-2406	176	12	a	a	DET
ejpam-2406	176	13	proper	proper	ADJ
ejpam-2406	176	14	element	element	NOUN
ejpam-2406	176	15	of	of	ADP
ejpam-2406	176	16	m.	m.	NOUN
ejpam-2406	176	17	the	the	DET
ejpam-2406	176	18	following	follow	VERB
ejpam-2406	176	19	statements	statement	NOUN
ejpam-2406	176	20	are	be	AUX
ejpam-2406	176	21	equivalent	equivalent	ADJ
ejpam-2406	176	22	,	,	PUNCT
ejpam-2406	176	23	(	(	PUNCT
ejpam-2406	176	24	i	i	NOUN
ejpam-2406	176	25	)	)	PUNCT
ejpam-2406	177	1	q	q	PUNCT
ejpam-2406	177	2	is	be	AUX
ejpam-2406	177	3	a	a	DET
ejpam-2406	177	4	classical	classical	ADJ
ejpam-2406	177	5	primary	primary	ADJ
ejpam-2406	177	6	element	element	NOUN
ejpam-2406	177	7	of	of	ADP
ejpam-2406	177	8	m.	m.	NOUN
ejpam-2406	177	9	(	(	PUNCT
ejpam-2406	177	10	ii	ii	NOUN
ejpam-2406	177	11	)	)	PUNCT
ejpam-2406	177	12	q	q	PUNCT
ejpam-2406	177	13	is	be	AUX
ejpam-2406	177	14	a	a	DET
ejpam-2406	177	15	primary	primary	ADJ
ejpam-2406	177	16	element	element	NOUN
ejpam-2406	177	17	(	(	PUNCT
ejpam-2406	177	18	iii	iii	NOUN
ejpam-2406	177	19	)	)	PUNCT
ejpam-2406	177	20	(	(	PUNCT
ejpam-2406	177	21	q	q	NOUN
ejpam-2406	177	22	:	:	PUNCT
ejpam-2406	177	23	i	i	PRON
ejpam-2406	177	24	m	m	PROPN
ejpam-2406	177	25	)	)	PUNCT
ejpam-2406	177	26	is	be	AUX
ejpam-2406	177	27	a	a	DET
ejpam-2406	177	28	primary	primary	ADJ
ejpam-2406	177	29	element	element	NOUN
ejpam-2406	177	30	of	of	ADP
ejpam-2406	177	31	l	l	PROPN
ejpam-2406	177	32	(	(	PUNCT
ejpam-2406	177	33	iv	iv	X
ejpam-2406	177	34	)	)	PUNCT
ejpam-2406	177	35	q	q	NOUN
ejpam-2406	178	1	=	=	PUNCT
ejpam-2406	178	2	qim	qim	NOUN
ejpam-2406	178	3	where	where	SCONJ
ejpam-2406	178	4	q	q	NOUN
ejpam-2406	178	5	is	be	AUX
ejpam-2406	178	6	primary	primary	ADJ
ejpam-2406	178	7	element	element	NOUN
ejpam-2406	178	8	of	of	ADP
ejpam-2406	178	9	l	l	NOUN
ejpam-2406	178	10	,	,	PUNCT
ejpam-2406	178	11	is	be	AUX
ejpam-2406	178	12	maximal	maximal	ADJ
ejpam-2406	178	13	with	with	ADP
ejpam-2406	178	14	respect	respect	NOUN
ejpam-2406	178	15	to	to	ADP
ejpam-2406	178	16	this	this	DET
ejpam-2406	178	17	property	property	NOUN
ejpam-2406	178	18	i.e.	i.e.	X
ejpam-2406	178	19	aim	aim	VERB
ejpam-2406	178	20	=	=	SYM
ejpam-2406	178	21	q	q	PROPN
ejpam-2406	178	22	implies	imply	VERB
ejpam-2406	178	23	a	a	DET
ejpam-2406	178	24	¶	¶	PROPN
ejpam-2406	178	25	q	q	NOUN
ejpam-2406	178	26	,	,	PUNCT
ejpam-2406	178	27	a	a	DET
ejpam-2406	178	28	∈	∈	NOUN
ejpam-2406	178	29	l.	l.	NOUN
ejpam-2406	178	30	proof	proof	NOUN
ejpam-2406	178	31	.	.	PUNCT
ejpam-2406	179	1	(	(	PUNCT
ejpam-2406	179	2	i)⇒	i)⇒	PROPN
ejpam-2406	179	3	(	(	PUNCT
ejpam-2406	179	4	ii	ii	NOUN
ejpam-2406	179	5	)	)	PUNCT
ejpam-2406	179	6	assume	assume	VERB
ejpam-2406	179	7	that	that	SCONJ
ejpam-2406	179	8	q	q	NOUN
ejpam-2406	179	9	is	be	AUX
ejpam-2406	179	10	a	a	DET
ejpam-2406	179	11	classical	classical	ADJ
ejpam-2406	179	12	primary	primary	ADJ
ejpam-2406	179	13	element	element	NOUN
ejpam-2406	179	14	of	of	ADP
ejpam-2406	179	15	m.	m.	NOUN
ejpam-2406	179	16	let	let	PROPN
ejpam-2406	179	17	,	,	PUNCT
ejpam-2406	179	18	an	an	DET
ejpam-2406	179	19	¶	¶	PROPN
ejpam-2406	179	20	q	q	NOUN
ejpam-2406	179	21	,	,	PUNCT
ejpam-2406	179	22	a	a	DET
ejpam-2406	179	23	∈	∈	PROPN
ejpam-2406	179	24	l	l	NOUN
ejpam-2406	179	25	,	,	PUNCT
ejpam-2406	179	26	n	n	PROPN
ejpam-2406	179	27	∈	∈	NOUN
ejpam-2406	179	28	m	m	NOUN
ejpam-2406	179	29	and	and	CCONJ
ejpam-2406	179	30	n	n	PRON
ejpam-2406	179	31	6¶	6¶	NUM
ejpam-2406	179	32	q.	q.	NOUN
ejpam-2406	179	33	since	since	ADV
ejpam-2406	179	34	,	,	PUNCT
ejpam-2406	179	35	m	m	VERB
ejpam-2406	179	36	is	be	AUX
ejpam-2406	179	37	a	a	DET
ejpam-2406	179	38	multiplication	multiplication	NOUN
ejpam-2406	179	39	module	module	NOUN
ejpam-2406	179	40	,	,	PUNCT
ejpam-2406	179	41	n	n	NOUN
ejpam-2406	179	42	=	=	PUNCT
ejpam-2406	179	43	bim	bim	NOUN
ejpam-2406	179	44	for	for	ADP
ejpam-2406	179	45	some	some	DET
ejpam-2406	179	46	b	b	PROPN
ejpam-2406	179	47	∈	∈	PROPN
ejpam-2406	179	48	l.	l.	NOUN
ejpam-2406	179	49	hence	hence	ADV
ejpam-2406	179	50	,	,	PUNCT
ejpam-2406	179	51	abim	abim	NOUN
ejpam-2406	179	52	¶q	¶q	NOUN
ejpam-2406	179	53	and	and	CCONJ
ejpam-2406	179	54	bim	bim	NOUN
ejpam-2406	179	55	6¶q	6¶q	NUM
ejpam-2406	179	56	,	,	PUNCT
ejpam-2406	180	1	i.e.	i.e.	X
ejpam-2406	180	2	ab	ab	PROPN
ejpam-2406	180	3	¶	¶	PROPN
ejpam-2406	180	4	(	(	PUNCT
ejpam-2406	180	5	q	q	NOUN
ejpam-2406	180	6	:	:	PUNCT
ejpam-2406	180	7	i	i	PRON
ejpam-2406	180	8	m	m	PROPN
ejpam-2406	180	9	)	)	PUNCT
ejpam-2406	180	10	and	and	CCONJ
ejpam-2406	180	11	b	b	X
ejpam-2406	180	12	6¶	6¶	NUM
ejpam-2406	180	13	(	(	PUNCT
ejpam-2406	180	14	q	q	NOUN
ejpam-2406	180	15	:	:	PUNCT
ejpam-2406	180	16	i	i	PRON
ejpam-2406	180	17	m	m	PROPN
ejpam-2406	180	18	)	)	PUNCT
ejpam-2406	180	19	.	.	PUNCT
ejpam-2406	181	1	by	by	ADP
ejpam-2406	181	2	theorem	theorem	NOUN
ejpam-2406	181	3	3	3	NUM
ejpam-2406	181	4	,	,	PUNCT
ejpam-2406	181	5	(	(	PUNCT
ejpam-2406	181	6	q	q	NOUN
ejpam-2406	181	7	:	:	PUNCT
ejpam-2406	181	8	i	i	PRON
ejpam-2406	181	9	m	m	PROPN
ejpam-2406	181	10	)	)	PUNCT
ejpam-2406	181	11	is	be	AUX
ejpam-2406	181	12	a	a	DET
ejpam-2406	181	13	primary	primary	ADJ
ejpam-2406	181	14	element	element	NOUN
ejpam-2406	181	15	of	of	ADP
ejpam-2406	181	16	l.	l.	PROPN
ejpam-2406	181	17	hence	hence	PROPN
ejpam-2406	181	18	,	,	PUNCT
ejpam-2406	181	19	ak	ak	PROPN
ejpam-2406	182	1	i	i	PROPN
ejpam-2406	182	2	m	m	VERB
ejpam-2406	182	3	¶q	¶q	ADJ
ejpam-2406	182	4	for	for	ADP
ejpam-2406	182	5	some	some	DET
ejpam-2406	182	6	k	k	PROPN
ejpam-2406	182	7	∈	∈	PROPN
ejpam-2406	182	8	z+	z+	PUNCT
ejpam-2406	182	9	.	.	PUNCT
ejpam-2406	183	1	thus	thus	ADV
ejpam-2406	183	2	,	,	PUNCT
ejpam-2406	183	3	q	q	PROPN
ejpam-2406	183	4	is	be	AUX
ejpam-2406	183	5	primary	primary	ADJ
ejpam-2406	183	6	element	element	NOUN
ejpam-2406	183	7	of	of	ADP
ejpam-2406	183	8	m.	m.	PROPN
ejpam-2406	183	9	c.	c.	PROPN
ejpam-2406	183	10	manjarekar	manjarekar	PROPN
ejpam-2406	183	11	,	,	PUNCT
ejpam-2406	183	12	u.	u.	PROPN
ejpam-2406	183	13	kandale	kandale	PROPN
ejpam-2406	183	14	/	/	SYM
ejpam-2406	183	15	eur	eur	PROPN
ejpam-2406	183	16	.	.	PUNCT
ejpam-2406	184	1	j.	j.	PROPN
ejpam-2406	184	2	pure	pure	PROPN
ejpam-2406	184	3	appl	appl	PROPN
ejpam-2406	184	4	.	.	PROPN
ejpam-2406	184	5	math	math	PROPN
ejpam-2406	184	6	,	,	PUNCT
ejpam-2406	184	7	8	8	NUM
ejpam-2406	184	8	(	(	PUNCT
ejpam-2406	184	9	2015	2015	NUM
ejpam-2406	184	10	)	)	PUNCT
ejpam-2406	184	11	,	,	PUNCT
ejpam-2406	184	12	172	172	NUM
ejpam-2406	184	13	-	-	SYM
ejpam-2406	184	14	184	184	NUM
ejpam-2406	184	15	178	178	NUM
ejpam-2406	184	16	(	(	PUNCT
ejpam-2406	184	17	ii)⇒	ii)⇒	X
ejpam-2406	184	18	(	(	PUNCT
ejpam-2406	184	19	iii	iii	NOUN
ejpam-2406	184	20	)	)	PUNCT
ejpam-2406	184	21	assume	assume	VERB
ejpam-2406	184	22	that	that	SCONJ
ejpam-2406	184	23	,	,	PUNCT
ejpam-2406	184	24	q	q	X
ejpam-2406	184	25	is	be	AUX
ejpam-2406	184	26	a	a	DET
ejpam-2406	184	27	primary	primary	ADJ
ejpam-2406	184	28	element	element	NOUN
ejpam-2406	184	29	of	of	ADP
ejpam-2406	184	30	m.	m.	NOUN
ejpam-2406	184	31	let	let	VERB
ejpam-2406	184	32	ab	ab	PROPN
ejpam-2406	184	33	¶	¶	PROPN
ejpam-2406	184	34	(	(	PUNCT
ejpam-2406	184	35	q	q	NOUN
ejpam-2406	184	36	:	:	PUNCT
ejpam-2406	184	37	i	i	PRON
ejpam-2406	184	38	m	m	PROPN
ejpam-2406	184	39	)	)	PUNCT
ejpam-2406	184	40	.	.	PUNCT
ejpam-2406	185	1	then	then	ADV
ejpam-2406	185	2	,	,	PUNCT
ejpam-2406	185	3	abim	abim	PROPN
ejpam-2406	185	4	¶	¶	PROPN
ejpam-2406	185	5	q.	q.	PROPN
ejpam-2406	185	6	since	since	SCONJ
ejpam-2406	185	7	,	,	PUNCT
ejpam-2406	185	8	q	q	X
ejpam-2406	185	9	is	be	AUX
ejpam-2406	185	10	a	a	DET
ejpam-2406	185	11	primary	primary	ADJ
ejpam-2406	185	12	element	element	NOUN
ejpam-2406	185	13	of	of	ADP
ejpam-2406	185	14	m	m	PROPN
ejpam-2406	185	15	,	,	PUNCT
ejpam-2406	185	16	either	either	CCONJ
ejpam-2406	185	17	bim	bim	PROPN
ejpam-2406	185	18	¶	¶	PROPN
ejpam-2406	185	19	or	or	CCONJ
ejpam-2406	185	20	ak	ak	PROPN
ejpam-2406	185	21	i	i	NOUN
ejpam-2406	185	22	m	m	PROPN
ejpam-2406	185	23	¶	¶	PROPN
ejpam-2406	185	24	q.	q.	PROPN
ejpam-2406	186	1	so	so	ADV
ejpam-2406	186	2	,	,	PUNCT
ejpam-2406	186	3	b	b	PROPN
ejpam-2406	186	4	¶	¶	PROPN
ejpam-2406	186	5	(	(	PUNCT
ejpam-2406	186	6	q	q	NOUN
ejpam-2406	186	7	:	:	PUNCT
ejpam-2406	186	8	i	i	PRON
ejpam-2406	186	9	m	m	VERB
ejpam-2406	186	10	)	)	PUNCT
ejpam-2406	186	11	or	or	CCONJ
ejpam-2406	186	12	ak	ak	PROPN
ejpam-2406	186	13	¶	¶	PROPN
ejpam-2406	186	14	(	(	PUNCT
ejpam-2406	186	15	q	q	NOUN
ejpam-2406	186	16	:	:	PUNCT
ejpam-2406	186	17	i	i	PRON
ejpam-2406	186	18	m	m	PROPN
ejpam-2406	186	19	)	)	PUNCT
ejpam-2406	186	20	and	and	CCONJ
ejpam-2406	186	21	(	(	PUNCT
ejpam-2406	186	22	q	q	NOUN
ejpam-2406	186	23	:	:	PUNCT
ejpam-2406	186	24	i	i	PRON
ejpam-2406	186	25	m	m	PROPN
ejpam-2406	186	26	)	)	PUNCT
ejpam-2406	186	27	is	be	AUX
ejpam-2406	186	28	a	a	DET
ejpam-2406	186	29	primary	primary	ADJ
ejpam-2406	186	30	element	element	NOUN
ejpam-2406	186	31	of	of	ADP
ejpam-2406	186	32	l.	l.	PROPN
ejpam-2406	186	33	(	(	PUNCT
ejpam-2406	186	34	iii)⇒	iii)⇒	PROPN
ejpam-2406	186	35	(	(	PUNCT
ejpam-2406	186	36	iv	iv	X
ejpam-2406	186	37	)	)	PUNCT
ejpam-2406	186	38	assume	assume	VERB
ejpam-2406	186	39	that	that	SCONJ
ejpam-2406	186	40	,	,	PUNCT
ejpam-2406	186	41	q	q	X
ejpam-2406	186	42	=	=	X
ejpam-2406	186	43	(	(	PUNCT
ejpam-2406	186	44	q	q	NOUN
ejpam-2406	186	45	:	:	PUNCT
ejpam-2406	186	46	i	i	PRON
ejpam-2406	186	47	m	m	PROPN
ejpam-2406	186	48	)	)	PUNCT
ejpam-2406	186	49	is	be	AUX
ejpam-2406	186	50	a	a	DET
ejpam-2406	186	51	primary	primary	ADJ
ejpam-2406	186	52	element	element	NOUN
ejpam-2406	186	53	of	of	ADP
ejpam-2406	186	54	l.	l.	PROPN
ejpam-2406	186	55	since	since	ADV
ejpam-2406	186	56	,	,	PUNCT
ejpam-2406	186	57	m	m	PROPN
ejpam-2406	186	58	is	be	AUX
ejpam-2406	186	59	a	a	DET
ejpam-2406	186	60	multiplication	multiplication	NOUN
ejpam-2406	186	61	module	module	NOUN
ejpam-2406	186	62	,	,	PUNCT
ejpam-2406	186	63	q	q	NOUN
ejpam-2406	186	64	=	=	PUNCT
ejpam-2406	186	65	aim	aim	VERB
ejpam-2406	186	66	for	for	ADP
ejpam-2406	186	67	somea	somea	ADJ
ejpam-2406	186	68	∈	∈	PROPN
ejpam-2406	186	69	l.	l.	NOUN
ejpam-2406	186	70	we	we	PRON
ejpam-2406	186	71	have	have	VERB
ejpam-2406	186	72	,	,	PUNCT
ejpam-2406	186	73	qim	qim	PROPN
ejpam-2406	186	74	¶	¶	PROPN
ejpam-2406	186	75	q	q	PROPN
ejpam-2406	186	76	and	and	CCONJ
ejpam-2406	186	77	a	a	DET
ejpam-2406	186	78	¶	¶	NOUN
ejpam-2406	186	79	(	(	PUNCT
ejpam-2406	186	80	q	q	NOUN
ejpam-2406	186	81	:	:	PUNCT
ejpam-2406	186	82	i	i	PRON
ejpam-2406	186	83	m	m	VERB
ejpam-2406	186	84	)	)	PUNCT
ejpam-2406	187	1	=	=	SYM
ejpam-2406	187	2	q.	q.	NOUN
ejpam-2406	188	1	so	so	ADV
ejpam-2406	188	2	q	q	NOUN
ejpam-2406	188	3	=	=	PUNCT
ejpam-2406	188	4	aim	aim	VERB
ejpam-2406	188	5	¶	¶	PROPN
ejpam-2406	188	6	qim	qim	PROPN
ejpam-2406	188	7	.	.	PUNCT
ejpam-2406	189	1	thus	thus	ADV
ejpam-2406	189	2	,	,	PUNCT
ejpam-2406	189	3	q	q	X
ejpam-2406	189	4	=	=	PUNCT
ejpam-2406	189	5	qim	qim	NOUN
ejpam-2406	189	6	,	,	PUNCT
ejpam-2406	189	7	q	q	X
ejpam-2406	189	8	is	be	AUX
ejpam-2406	189	9	primary	primary	ADJ
ejpam-2406	189	10	and	and	CCONJ
ejpam-2406	189	11	bim	bim	NOUN
ejpam-2406	190	1	=	=	NOUN
ejpam-2406	190	2	q⇒	q⇒	PROPN
ejpam-2406	190	3	b	b	PROPN
ejpam-2406	190	4	¶	¶	PROPN
ejpam-2406	190	5	q.	q.	PROPN
ejpam-2406	190	6	(	(	PUNCT
ejpam-2406	190	7	iv)⇒	iv)⇒	X
ejpam-2406	190	8	(	(	PUNCT
ejpam-2406	190	9	i	i	NOUN
ejpam-2406	190	10	)	)	PUNCT
ejpam-2406	190	11	suppose	suppose	VERB
ejpam-2406	190	12	,	,	PUNCT
ejpam-2406	190	13	q	q	NOUN
ejpam-2406	190	14	=	=	PUNCT
ejpam-2406	190	15	qim	qim	NOUN
ejpam-2406	190	16	where	where	SCONJ
ejpam-2406	190	17	q	q	NOUN
ejpam-2406	190	18	is	be	AUX
ejpam-2406	190	19	primary	primary	ADJ
ejpam-2406	190	20	element	element	NOUN
ejpam-2406	190	21	which	which	PRON
ejpam-2406	190	22	is	be	AUX
ejpam-2406	190	23	maximal	maximal	ADJ
ejpam-2406	190	24	w.r.t	w.r.t	NOUN
ejpam-2406	190	25	.	.	PUNCT
ejpam-2406	191	1	this	this	DET
ejpam-2406	191	2	property	property	NOUN
ejpam-2406	191	3	.	.	PUNCT
ejpam-2406	192	1	let	let	VERB
ejpam-2406	192	2	,	,	PUNCT
ejpam-2406	192	3	abn	abn	PROPN
ejpam-2406	192	4	¶	¶	PROPN
ejpam-2406	192	5	q	q	PROPN
ejpam-2406	192	6	where	where	SCONJ
ejpam-2406	192	7	a	a	DET
ejpam-2406	192	8	,	,	PUNCT
ejpam-2406	192	9	b	b	PROPN
ejpam-2406	192	10	∈	∈	PROPN
ejpam-2406	192	11	l	l	NOUN
ejpam-2406	192	12	and	and	CCONJ
ejpam-2406	192	13	n	n	PRON
ejpam-2406	192	14	∈	∈	NOUN
ejpam-2406	192	15	such	such	ADJ
ejpam-2406	192	16	that	that	PRON
ejpam-2406	192	17	bn	bn	ADJ
ejpam-2406	192	18	6¶	6¶	NUM
ejpam-2406	192	19	q.	q.	NOUN
ejpam-2406	192	20	since	since	ADV
ejpam-2406	192	21	,	,	PUNCT
ejpam-2406	192	22	m	m	VERB
ejpam-2406	192	23	is	be	AUX
ejpam-2406	192	24	a	a	DET
ejpam-2406	192	25	multiplication	multiplication	NOUN
ejpam-2406	192	26	l	l	NOUN
ejpam-2406	192	27	-	-	NOUN
ejpam-2406	192	28	module	module	NOUN
ejpam-2406	192	29	n	n	NOUN
ejpam-2406	192	30	=	=	PROPN
ejpam-2406	192	31	cim	cim	PROPN
ejpam-2406	192	32	for	for	ADP
ejpam-2406	192	33	somec	somec	PROPN
ejpam-2406	192	34	∈	∈	PROPN
ejpam-2406	192	35	l.	l.	NOUN
ejpam-2406	192	36	thus	thus	ADV
ejpam-2406	192	37	abcim	abcim	VERB
ejpam-2406	193	1	¶	¶	PROPN
ejpam-2406	193	2	q	q	NOUN
ejpam-2406	193	3	and	and	CCONJ
ejpam-2406	193	4	hence	hence	ADV
ejpam-2406	193	5	abc	abc	PROPN
ejpam-2406	193	6	¶	¶	PROPN
ejpam-2406	193	7	(	(	PUNCT
ejpam-2406	193	8	q	q	NOUN
ejpam-2406	193	9	:	:	PUNCT
ejpam-2406	193	10	i	i	PRON
ejpam-2406	193	11	m	m	VERB
ejpam-2406	193	12	)	)	PUNCT
ejpam-2406	194	1	¶	¶	PROPN
ejpam-2406	194	2	q.	q.	PROPN
ejpam-2406	194	3	since	since	ADV
ejpam-2406	194	4	,	,	PUNCT
ejpam-2406	194	5	bcim	bcim	PROPN
ejpam-2406	194	6	6¶	6¶	NUM
ejpam-2406	194	7	q	q	NOUN
ejpam-2406	194	8	,	,	PUNCT
ejpam-2406	194	9	we	we	PRON
ejpam-2406	194	10	have	have	AUX
ejpam-2406	194	11	,	,	PUNCT
ejpam-2406	194	12	bc	bc	PROPN
ejpam-2406	194	13	6¶	6¶	NUM
ejpam-2406	194	14	(	(	PUNCT
ejpam-2406	194	15	q	q	NOUN
ejpam-2406	194	16	:	:	PUNCT
ejpam-2406	194	17	i	i	PRON
ejpam-2406	194	18	m	m	VERB
ejpam-2406	194	19	)	)	PUNCT
ejpam-2406	194	20	¶	¶	PROPN
ejpam-2406	194	21	q.	q.	PROPN
ejpam-2406	194	22	as	as	ADP
ejpam-2406	194	23	,	,	PUNCT
ejpam-2406	194	24	q	q	X
ejpam-2406	194	25	is	be	AUX
ejpam-2406	194	26	primary	primary	ADJ
ejpam-2406	194	27	and	and	CCONJ
ejpam-2406	194	28	abc	abc	PROPN
ejpam-2406	194	29	¶	¶	PROPN
ejpam-2406	194	30	q	q	PROPN
ejpam-2406	194	31	withbc	withbc	PROPN
ejpam-2406	194	32	6¶	6¶	NUM
ejpam-2406	194	33	q	q	NOUN
ejpam-2406	194	34	we	we	PRON
ejpam-2406	194	35	have	have	VERB
ejpam-2406	194	36	,	,	PUNCT
ejpam-2406	194	37	ak	ak	PROPN
ejpam-2406	194	38	¶	¶	PROPN
ejpam-2406	194	39	q	q	PROPN
ejpam-2406	194	40	for	for	ADP
ejpam-2406	194	41	some	some	DET
ejpam-2406	194	42	k	k	PROPN
ejpam-2406	194	43	∈	∈	PROPN
ejpam-2406	194	44	z+	z+	PUNCT
ejpam-2406	194	45	.	.	PUNCT
ejpam-2406	195	1	this	this	PRON
ejpam-2406	195	2	implies	imply	VERB
ejpam-2406	195	3	that	that	SCONJ
ejpam-2406	195	4	,	,	PUNCT
ejpam-2406	195	5	akn	akn	PROPN
ejpam-2406	195	6	¶	¶	PROPN
ejpam-2406	195	7	qim	qim	PROPN
ejpam-2406	195	8	=	=	PUNCT
ejpam-2406	195	9	q	q	NOUN
ejpam-2406	196	1	and	and	CCONJ
ejpam-2406	196	2	so	so	ADV
ejpam-2406	196	3	q	q	X
ejpam-2406	196	4	is	be	AUX
ejpam-2406	196	5	a	a	DET
ejpam-2406	196	6	classical	classical	ADJ
ejpam-2406	196	7	primary	primary	ADJ
ejpam-2406	196	8	element	element	NOUN
ejpam-2406	196	9	of	of	ADP
ejpam-2406	196	10	m.	m.	NOUN
ejpam-2406	196	11	in	in	ADP
ejpam-2406	196	12	the	the	DET
ejpam-2406	196	13	next	next	ADJ
ejpam-2406	196	14	result	result	NOUN
ejpam-2406	196	15	we	we	PRON
ejpam-2406	196	16	have	have	VERB
ejpam-2406	196	17	the	the	DET
ejpam-2406	196	18	important	important	ADJ
ejpam-2406	196	19	relation	relation	NOUN
ejpam-2406	196	20	between	between	ADP
ejpam-2406	196	21	a	a	DET
ejpam-2406	196	22	classical	classical	ADJ
ejpam-2406	196	23	quasi	quasi	ADJ
ejpam-2406	196	24	primary	primary	ADJ
ejpam-2406	196	25	element	element	NOUN
ejpam-2406	196	26	of	of	ADP
ejpam-2406	196	27	a	a	DET
ejpam-2406	196	28	lattice	lattice	NOUN
ejpam-2406	196	29	module	module	NOUN
ejpam-2406	196	30	and	and	CCONJ
ejpam-2406	196	31	a	a	DET
ejpam-2406	196	32	classical	classical	ADJ
ejpam-2406	196	33	quasi	quasi	ADJ
ejpam-2406	196	34	primary	primary	ADJ
ejpam-2406	196	35	element	element	NOUN
ejpam-2406	196	36	of	of	ADP
ejpam-2406	196	37	a	a	DET
ejpam-2406	196	38	multiplicative	multiplicative	ADJ
ejpam-2406	196	39	lattice	lattice	NOUN
ejpam-2406	196	40	.	.	PUNCT
ejpam-2406	197	1	theorem	theorem	VERB
ejpam-2406	197	2	6	6	NUM
ejpam-2406	197	3	.	.	PUNCT
ejpam-2406	198	1	let	let	VERB
ejpam-2406	198	2	m	m	PRON
ejpam-2406	198	3	be	be	AUX
ejpam-2406	198	4	a	a	DET
ejpam-2406	198	5	multiplication	multiplication	NOUN
ejpam-2406	198	6	lattice	lattice	NOUN
ejpam-2406	198	7	module	module	NOUN
ejpam-2406	198	8	and	and	CCONJ
ejpam-2406	198	9	q	q	NOUN
ejpam-2406	198	10	be	be	AUX
ejpam-2406	198	11	a	a	DET
ejpam-2406	198	12	proper	proper	ADJ
ejpam-2406	198	13	element	element	NOUN
ejpam-2406	198	14	of	of	ADP
ejpam-2406	198	15	m.	m.	NOUN
ejpam-2406	198	16	the	the	DET
ejpam-2406	198	17	following	follow	VERB
ejpam-2406	198	18	statements	statement	NOUN
ejpam-2406	198	19	are	be	AUX
ejpam-2406	198	20	equivalent	equivalent	ADJ
ejpam-2406	198	21	,	,	PUNCT
ejpam-2406	198	22	(	(	PUNCT
ejpam-2406	198	23	i	i	NOUN
ejpam-2406	198	24	)	)	PUNCT
ejpam-2406	199	1	q	q	PUNCT
ejpam-2406	199	2	is	be	AUX
ejpam-2406	199	3	a	a	DET
ejpam-2406	199	4	classical	classical	ADJ
ejpam-2406	199	5	quasi	quasi	ADJ
ejpam-2406	199	6	primary	primary	ADJ
ejpam-2406	199	7	element	element	NOUN
ejpam-2406	199	8	.	.	PUNCT
ejpam-2406	200	1	(	(	PUNCT
ejpam-2406	200	2	ii	ii	NOUN
ejpam-2406	200	3	)	)	PUNCT
ejpam-2406	200	4	q	q	NOUN
ejpam-2406	201	1	=	=	PUNCT
ejpam-2406	201	2	(	(	PUNCT
ejpam-2406	201	3	q	q	NOUN
ejpam-2406	201	4	:	:	PUNCT
ejpam-2406	201	5	i	i	PRON
ejpam-2406	201	6	m	m	PROPN
ejpam-2406	201	7	)	)	PUNCT
ejpam-2406	201	8	is	be	AUX
ejpam-2406	201	9	a	a	DET
ejpam-2406	201	10	classical	classical	ADJ
ejpam-2406	201	11	quasi	quasi	ADJ
ejpam-2406	201	12	primary	primary	ADJ
ejpam-2406	201	13	element	element	NOUN
ejpam-2406	201	14	of	of	ADP
ejpam-2406	201	15	l.	l.	PROPN
ejpam-2406	201	16	(	(	PUNCT
ejpam-2406	201	17	iii	iii	PROPN
ejpam-2406	201	18	)	)	PUNCT
ejpam-2406	201	19	q	q	NOUN
ejpam-2406	202	1	=	=	PUNCT
ejpam-2406	202	2	qim	qim	NOUN
ejpam-2406	202	3	where	where	SCONJ
ejpam-2406	202	4	q	q	NOUN
ejpam-2406	202	5	is	be	AUX
ejpam-2406	202	6	a	a	DET
ejpam-2406	202	7	classical	classical	ADJ
ejpam-2406	202	8	quasi	quasi	ADJ
ejpam-2406	202	9	primary	primary	ADJ
ejpam-2406	202	10	element	element	NOUN
ejpam-2406	202	11	which	which	PRON
ejpam-2406	202	12	is	be	AUX
ejpam-2406	202	13	maximal	maximal	ADJ
ejpam-2406	202	14	w.r.t	w.r.t	ADJ
ejpam-2406	202	15	this	this	DET
ejpam-2406	202	16	property	property	NOUN
ejpam-2406	202	17	.	.	PUNCT
ejpam-2406	203	1	(	(	PUNCT
ejpam-2406	203	2	i.e.	i.e.	X
ejpam-2406	203	3	aim	aim	VERB
ejpam-2406	203	4	=	=	SYM
ejpam-2406	203	5	q⇒	q⇒	X
ejpam-2406	203	6	a	a	DET
ejpam-2406	203	7	¶	¶	PROPN
ejpam-2406	203	8	q	q	NOUN
ejpam-2406	203	9	)	)	PUNCT
ejpam-2406	203	10	proof	proof	NOUN
ejpam-2406	203	11	.	.	PUNCT
ejpam-2406	204	1	(	(	PUNCT
ejpam-2406	204	2	i)⇒	i)⇒	PROPN
ejpam-2406	204	3	(	(	PUNCT
ejpam-2406	204	4	ii	ii	NOUN
ejpam-2406	204	5	)	)	PUNCT
ejpam-2406	204	6	suppose	suppose	VERB
ejpam-2406	204	7	,	,	PUNCT
ejpam-2406	204	8	q	q	X
ejpam-2406	204	9	is	be	AUX
ejpam-2406	204	10	a	a	DET
ejpam-2406	204	11	classical	classical	ADJ
ejpam-2406	204	12	quasi	quasi	ADJ
ejpam-2406	204	13	primary	primary	ADJ
ejpam-2406	204	14	element	element	NOUN
ejpam-2406	204	15	of	of	ADP
ejpam-2406	204	16	m.	m.	NOUN
ejpam-2406	204	17	let	let	VERB
ejpam-2406	204	18	,	,	PUNCT
ejpam-2406	204	19	abr	abr	VERB
ejpam-2406	204	20	¶	¶	PROPN
ejpam-2406	204	21	q	q	PROPN
ejpam-2406	204	22	,	,	PUNCT
ejpam-2406	204	23	a	a	DET
ejpam-2406	204	24	,	,	PUNCT
ejpam-2406	204	25	b	b	NOUN
ejpam-2406	204	26	,	,	PUNCT
ejpam-2406	204	27	r	r	PROPN
ejpam-2406	204	28	∈	∈	PROPN
ejpam-2406	204	29	l.	l.	NOUN
ejpam-2406	204	30	this	this	PRON
ejpam-2406	204	31	gives	give	VERB
ejpam-2406	204	32	,	,	PUNCT
ejpam-2406	204	33	abr	abr	VERB
ejpam-2406	204	34	i	i	PRON
ejpam-2406	204	35	m	m	PROPN
ejpam-2406	204	36	¶	¶	PROPN
ejpam-2406	204	37	q.	q.	PROPN
ejpam-2406	204	38	by	by	ADP
ejpam-2406	204	39	classical	classical	ADJ
ejpam-2406	204	40	quasi	quasi	ADJ
ejpam-2406	204	41	primality	primality	NOUN
ejpam-2406	204	42	of	of	ADP
ejpam-2406	204	43	q	q	PROPN
ejpam-2406	204	44	,	,	PUNCT
ejpam-2406	204	45	we	we	PRON
ejpam-2406	204	46	have	have	AUX
ejpam-2406	204	47	,	,	PUNCT
ejpam-2406	204	48	either	either	CCONJ
ejpam-2406	204	49	(	(	PUNCT
ejpam-2406	204	50	ab)k	ab)k	PROPN
ejpam-2406	204	51	i	i	PROPN
ejpam-2406	204	52	m	m	VERB
ejpam-2406	204	53	¶	¶	NUM
ejpam-2406	204	54	q	q	NOUN
ejpam-2406	204	55	or	or	CCONJ
ejpam-2406	204	56	rk	rk	VERB
ejpam-2406	204	57	i	i	NOUN
ejpam-2406	204	58	m	m	VERB
ejpam-2406	204	59	¶	¶	NOUN
ejpam-2406	204	60	q	q	NOUN
ejpam-2406	204	61	for	for	ADP
ejpam-2406	204	62	some	some	DET
ejpam-2406	204	63	k	k	PROPN
ejpam-2406	204	64	∈	∈	PROPN
ejpam-2406	204	65	z+	z+	X
ejpam-2406	204	66	.	.	PUNCT
ejpam-2406	205	1	i.e.	i.e.	X
ejpam-2406	205	2	(	(	PUNCT
ejpam-2406	205	3	ab)k	ab)k	PROPN
ejpam-2406	205	4	¶	¶	PROPN
ejpam-2406	205	5	(	(	PUNCT
ejpam-2406	205	6	q	q	NOUN
ejpam-2406	205	7	:	:	PUNCT
ejpam-2406	205	8	i	i	PRON
ejpam-2406	205	9	m	m	VERB
ejpam-2406	205	10	)	)	PUNCT
ejpam-2406	205	11	or	or	CCONJ
ejpam-2406	205	12	rk	rk	PROPN
ejpam-2406	205	13	¶	¶	PROPN
ejpam-2406	205	14	(	(	PUNCT
ejpam-2406	205	15	q	q	NOUN
ejpam-2406	205	16	:	:	PUNCT
ejpam-2406	205	17	i	i	PRON
ejpam-2406	205	18	m	m	PROPN
ejpam-2406	205	19	)	)	PUNCT
ejpam-2406	205	20	.	.	PUNCT
ejpam-2406	206	1	as	as	SCONJ
ejpam-2406	206	2	,	,	PUNCT
ejpam-2406	206	3	q	q	X
ejpam-2406	206	4	is	be	AUX
ejpam-2406	206	5	a	a	DET
ejpam-2406	206	6	classical	classical	ADJ
ejpam-2406	206	7	quasi	quasi	ADJ
ejpam-2406	206	8	primary	primary	ADJ
ejpam-2406	206	9	element	element	NOUN
ejpam-2406	206	10	and	and	CCONJ
ejpam-2406	206	11	i	i	PRON
ejpam-2406	206	12	m	m	VERB
ejpam-2406	206	13	6¶	6¶	NUM
ejpam-2406	206	14	q	q	NOUN
ejpam-2406	206	15	,	,	PUNCT
ejpam-2406	206	16	(	(	PUNCT
ejpam-2406	206	17	q	q	NOUN
ejpam-2406	206	18	:	:	PUNCT
ejpam-2406	206	19	i	i	PRON
ejpam-2406	206	20	m	m	PROPN
ejpam-2406	206	21	)	)	PUNCT
ejpam-2406	206	22	is	be	AUX
ejpam-2406	206	23	a	a	DET
ejpam-2406	206	24	quasi	quasi	ADJ
ejpam-2406	206	25	primary	primary	ADJ
ejpam-2406	206	26	element	element	NOUN
ejpam-2406	206	27	of	of	ADP
ejpam-2406	206	28	l	l	NOUN
ejpam-2406	206	29	i.e.	i.e.	X
ejpam-2406	206	30	p	p	X
ejpam-2406	206	31	(	(	PUNCT
ejpam-2406	206	32	q	q	NOUN
ejpam-2406	206	33	:	:	PUNCT
ejpam-2406	206	34	i	i	PRON
ejpam-2406	206	35	m	m	PROPN
ejpam-2406	206	36	)	)	PUNCT
ejpam-2406	206	37	is	be	AUX
ejpam-2406	206	38	a	a	DET
ejpam-2406	206	39	prime	prime	ADJ
ejpam-2406	206	40	element	element	NOUN
ejpam-2406	206	41	of	of	ADP
ejpam-2406	206	42	l	l	PROPN
ejpam-2406	206	43	,	,	PUNCT
ejpam-2406	206	44	by	by	ADP
ejpam-2406	206	45	theorem	theorem	NOUN
ejpam-2406	206	46	5	5	NUM
ejpam-2406	206	47	.	.	PUNCT
ejpam-2406	206	48	hence	hence	ADV
ejpam-2406	206	49	abr	abr	VERB
ejpam-2406	206	50	i	i	PRON
ejpam-2406	206	51	m	m	PROPN
ejpam-2406	206	52	¶	¶	PROPN
ejpam-2406	206	53	q	q	PROPN
ejpam-2406	206	54	implies	imply	VERB
ejpam-2406	206	55	ab	ab	PROPN
ejpam-2406	206	56	¶	¶	PROPN
ejpam-2406	206	57	p	p	PROPN
ejpam-2406	206	58	(	(	PUNCT
ejpam-2406	206	59	q	q	NOUN
ejpam-2406	206	60	:	:	PUNCT
ejpam-2406	206	61	i	i	PRON
ejpam-2406	206	62	m	m	VERB
ejpam-2406	206	63	)	)	PUNCT
ejpam-2406	206	64	or	or	CCONJ
ejpam-2406	206	65	r	r	NOUN
ejpam-2406	206	66	¶	¶	PROPN
ejpam-2406	206	67	p	p	NOUN
ejpam-2406	206	68	(	(	PUNCT
ejpam-2406	206	69	q	q	NOUN
ejpam-2406	206	70	:	:	PUNCT
ejpam-2406	206	71	i	i	PRON
ejpam-2406	206	72	m	m	PROPN
ejpam-2406	206	73	)	)	PUNCT
ejpam-2406	206	74	.	.	PUNCT
ejpam-2406	207	1	thus	thus	ADV
ejpam-2406	207	2	again	again	ADV
ejpam-2406	207	3	,	,	PUNCT
ejpam-2406	207	4	a	a	DET
ejpam-2406	207	5	¶	¶	NOUN
ejpam-2406	207	6	p	p	NOUN
ejpam-2406	207	7	(	(	PUNCT
ejpam-2406	207	8	q	q	NOUN
ejpam-2406	207	9	:	:	PUNCT
ejpam-2406	207	10	i	i	PRON
ejpam-2406	207	11	m	m	VERB
ejpam-2406	207	12	)	)	PUNCT
ejpam-2406	207	13	or	or	CCONJ
ejpam-2406	207	14	b	b	NUM
ejpam-2406	207	15	¶	¶	NOUN
ejpam-2406	207	16	p	p	PROPN
ejpam-2406	207	17	q	q	PROPN
ejpam-2406	207	18	:	:	PUNCT
ejpam-2406	207	19	i	i	PRON
ejpam-2406	207	20	m	m	VERB
ejpam-2406	207	21	.	.	PUNCT
ejpam-2406	208	1	so	so	ADV
ejpam-2406	208	2	ak	ak	PROPN
ejpam-2406	208	3	¶	¶	PROPN
ejpam-2406	208	4	(	(	PUNCT
ejpam-2406	208	5	q	q	NOUN
ejpam-2406	208	6	:	:	PUNCT
ejpam-2406	208	7	i	i	PRON
ejpam-2406	208	8	m	m	VERB
ejpam-2406	208	9	)	)	PUNCT
ejpam-2406	208	10	or	or	CCONJ
ejpam-2406	208	11	bk	bk	VERB
ejpam-2406	208	12	¶	¶	PROPN
ejpam-2406	208	13	(	(	PUNCT
ejpam-2406	208	14	q	q	NOUN
ejpam-2406	208	15	:	:	PUNCT
ejpam-2406	208	16	i	i	PRON
ejpam-2406	208	17	m	m	PROPN
ejpam-2406	208	18	)	)	PUNCT
ejpam-2406	208	19	.	.	PUNCT
ejpam-2406	209	1	consequently	consequently	ADV
ejpam-2406	209	2	,	,	PUNCT
ejpam-2406	209	3	akr	akr	PROPN
ejpam-2406	209	4	¶	¶	PROPN
ejpam-2406	209	5	(	(	PUNCT
ejpam-2406	209	6	q	q	NOUN
ejpam-2406	209	7	:	:	PUNCT
ejpam-2406	209	8	i	i	PRON
ejpam-2406	209	9	m	m	VERB
ejpam-2406	209	10	)	)	PUNCT
ejpam-2406	209	11	or	or	CCONJ
ejpam-2406	209	12	bkr	bkr	NUM
ejpam-2406	209	13	¶	¶	PROPN
ejpam-2406	209	14	(	(	PUNCT
ejpam-2406	209	15	q	q	NOUN
ejpam-2406	209	16	:	:	PUNCT
ejpam-2406	209	17	i	i	PRON
ejpam-2406	209	18	m	m	VERB
ejpam-2406	209	19	)	)	PUNCT
ejpam-2406	209	20	i.e.	i.e.	X
ejpam-2406	209	21	akr	akr	NOUN
ejpam-2406	209	22	¶	¶	PROPN
ejpam-2406	209	23	q	q	PROPN
ejpam-2406	209	24	or	or	CCONJ
ejpam-2406	209	25	bkr	bkr	PROPN
ejpam-2406	209	26	¶	¶	PROPN
ejpam-2406	209	27	q.	q.	PROPN
ejpam-2406	209	28	hence	hence	ADV
ejpam-2406	209	29	,	,	PUNCT
ejpam-2406	209	30	q	q	PROPN
ejpam-2406	209	31	is	be	AUX
ejpam-2406	209	32	classical	classical	ADJ
ejpam-2406	209	33	quasi	quasi	NOUN
ejpam-2406	209	34	primary	primary	NOUN
ejpam-2406	209	35	.	.	PUNCT
ejpam-2406	210	1	(	(	PUNCT
ejpam-2406	210	2	ii)⇒	ii)⇒	X
ejpam-2406	210	3	(	(	PUNCT
ejpam-2406	210	4	iii	iii	NOUN
ejpam-2406	210	5	)	)	PUNCT
ejpam-2406	210	6	suppose	suppose	VERB
ejpam-2406	210	7	,	,	PUNCT
ejpam-2406	210	8	q	q	X
ejpam-2406	210	9	=	=	X
ejpam-2406	210	10	(	(	PUNCT
ejpam-2406	210	11	q	q	NOUN
ejpam-2406	210	12	:	:	PUNCT
ejpam-2406	210	13	i	i	PRON
ejpam-2406	210	14	m	m	PROPN
ejpam-2406	210	15	)	)	PUNCT
ejpam-2406	210	16	is	be	AUX
ejpam-2406	210	17	a	a	DET
ejpam-2406	210	18	classical	classical	ADJ
ejpam-2406	210	19	quasi	quasi	ADJ
ejpam-2406	210	20	primary	primary	ADJ
ejpam-2406	210	21	element	element	NOUN
ejpam-2406	210	22	of	of	ADP
ejpam-2406	210	23	l.	l.	PROPN
ejpam-2406	210	24	since	since	ADV
ejpam-2406	210	25	,	,	PUNCT
ejpam-2406	210	26	m	m	PROPN
ejpam-2406	210	27	is	be	AUX
ejpam-2406	210	28	a	a	DET
ejpam-2406	210	29	multiplication	multiplication	NOUN
ejpam-2406	210	30	module	module	NOUN
ejpam-2406	210	31	,	,	PUNCT
ejpam-2406	210	32	q	q	NOUN
ejpam-2406	210	33	=	=	PUNCT
ejpam-2406	210	34	aim	aim	VERB
ejpam-2406	210	35	for	for	ADP
ejpam-2406	210	36	some	some	PRON
ejpam-2406	210	37	a	a	DET
ejpam-2406	210	38	∈	∈	PROPN
ejpam-2406	210	39	l.	l.	NOUN
ejpam-2406	210	40	we	we	PRON
ejpam-2406	210	41	have	have	VERB
ejpam-2406	210	42	,	,	PUNCT
ejpam-2406	210	43	qim	qim	PROPN
ejpam-2406	210	44	¶	¶	PROPN
ejpam-2406	210	45	q	q	PROPN
ejpam-2406	210	46	and	and	CCONJ
ejpam-2406	210	47	a	a	DET
ejpam-2406	210	48	¶	¶	NOUN
ejpam-2406	210	49	(	(	PUNCT
ejpam-2406	210	50	q	q	NOUN
ejpam-2406	210	51	:	:	PUNCT
ejpam-2406	210	52	i	i	PRON
ejpam-2406	210	53	m	m	VERB
ejpam-2406	210	54	)	)	PUNCT
ejpam-2406	211	1	=	=	SYM
ejpam-2406	211	2	q.	q.	PROPN
ejpam-2406	211	3	thus	thus	ADV
ejpam-2406	211	4	,	,	PUNCT
ejpam-2406	211	5	aim	aim	VERB
ejpam-2406	211	6	=	=	PUNCT
ejpam-2406	211	7	q	q	NOUN
ejpam-2406	211	8	gives	give	VERB
ejpam-2406	211	9	a	a	DET
ejpam-2406	211	10	¶	¶	NOUN
ejpam-2406	211	11	q.	q.	NOUN
ejpam-2406	212	1	so	so	ADV
ejpam-2406	212	2	,	,	PUNCT
ejpam-2406	212	3	q	q	PROPN
ejpam-2406	212	4	is	be	AUX
ejpam-2406	212	5	maximal	maximal	ADJ
ejpam-2406	212	6	w.r.t	w.r.t	NOUN
ejpam-2406	212	7	.	.	PUNCT
ejpam-2406	213	1	q	q	NOUN
ejpam-2406	214	1	=	=	PUNCT
ejpam-2406	214	2	qim	qim	NOUN
ejpam-2406	214	3	,	,	PUNCT
ejpam-2406	214	4	(	(	PUNCT
ejpam-2406	214	5	q	q	PROPN
ejpam-2406	214	6	∈	∈	PROPN
ejpam-2406	214	7	l	l	NOUN
ejpam-2406	214	8	)	)	PUNCT
ejpam-2406	214	9	(	(	PUNCT
ejpam-2406	214	10	iii)⇒	iii)⇒	PROPN
ejpam-2406	214	11	(	(	PUNCT
ejpam-2406	214	12	i	i	NOUN
ejpam-2406	214	13	)	)	PUNCT
ejpam-2406	214	14	suppose	suppose	VERB
ejpam-2406	214	15	,	,	PUNCT
ejpam-2406	214	16	q	q	NOUN
ejpam-2406	214	17	=	=	PUNCT
ejpam-2406	214	18	qim	qim	NOUN
ejpam-2406	214	19	where	where	SCONJ
ejpam-2406	214	20	q	q	NOUN
ejpam-2406	214	21	is	be	AUX
ejpam-2406	214	22	classical	classical	ADJ
ejpam-2406	214	23	quasi	quasi	ADJ
ejpam-2406	214	24	primary	primary	ADJ
ejpam-2406	214	25	element	element	NOUN
ejpam-2406	214	26	which	which	PRON
ejpam-2406	214	27	is	be	AUX
ejpam-2406	214	28	maximal	maximal	ADJ
ejpam-2406	214	29	w.r.t	w.r.t	NOUN
ejpam-2406	214	30	.	.	PUNCT
ejpam-2406	215	1	this	this	DET
ejpam-2406	215	2	property	property	NOUN
ejpam-2406	215	3	.	.	PUNCT
ejpam-2406	216	1	so	so	ADV
ejpam-2406	216	2	,	,	PUNCT
ejpam-2406	216	3	aim	aim	VERB
ejpam-2406	216	4	=	=	PUNCT
ejpam-2406	216	5	q	q	PROPN
ejpam-2406	216	6	implies	imply	VERB
ejpam-2406	216	7	a	a	DET
ejpam-2406	216	8	¶	¶	PROPN
ejpam-2406	216	9	q.	q.	NOUN
ejpam-2406	216	10	we	we	PRON
ejpam-2406	216	11	show	show	VERB
ejpam-2406	216	12	that	that	SCONJ
ejpam-2406	216	13	,	,	PUNCT
ejpam-2406	216	14	q	q	X
ejpam-2406	216	15	is	be	AUX
ejpam-2406	216	16	a	a	DET
ejpam-2406	216	17	classical	classical	ADJ
ejpam-2406	216	18	quasi	quasi	ADJ
ejpam-2406	216	19	primary	primary	ADJ
ejpam-2406	216	20	element	element	NOUN
ejpam-2406	216	21	of	of	ADP
ejpam-2406	216	22	m.	m.	NOUN
ejpam-2406	216	23	let	let	VERB
ejpam-2406	216	24	abn	abn	PROPN
ejpam-2406	216	25	¶	¶	PROPN
ejpam-2406	216	26	q	q	PROPN
ejpam-2406	217	1	where	where	SCONJ
ejpam-2406	217	2	a	a	PRON
ejpam-2406	217	3	,	,	PUNCT
ejpam-2406	217	4	b	b	PROPN
ejpam-2406	217	5	∈	∈	PROPN
ejpam-2406	217	6	l	l	NOUN
ejpam-2406	217	7	,	,	PUNCT
ejpam-2406	217	8	n	n	PROPN
ejpam-2406	217	9	∈	∈	PROPN
ejpam-2406	217	10	m	m	VERB
ejpam-2406	217	11	.	.	PUNCT
ejpam-2406	217	12	suppose	suppose	VERB
ejpam-2406	217	13	,	,	PUNCT
ejpam-2406	217	14	bkn	bkn	PROPN
ejpam-2406	217	15	6¶	6¶	NUM
ejpam-2406	217	16	q	q	NOUN
ejpam-2406	217	17	for	for	ADP
ejpam-2406	217	18	any	any	DET
ejpam-2406	217	19	integer	integer	NOUN
ejpam-2406	217	20	k.	k.	PROPN
ejpam-2406	217	21	since	since	SCONJ
ejpam-2406	217	22	m	m	PROPN
ejpam-2406	217	23	is	be	AUX
ejpam-2406	217	24	a	a	DET
ejpam-2406	217	25	c.	c.	PROPN
ejpam-2406	217	26	manjarekar	manjarekar	NOUN
ejpam-2406	217	27	,	,	PUNCT
ejpam-2406	217	28	u.	u.	PROPN
ejpam-2406	217	29	kandale	kandale	PROPN
ejpam-2406	217	30	/	/	SYM
ejpam-2406	217	31	eur	eur	PROPN
ejpam-2406	217	32	.	.	PUNCT
ejpam-2406	218	1	j.	j.	PROPN
ejpam-2406	218	2	pure	pure	PROPN
ejpam-2406	218	3	appl	appl	PROPN
ejpam-2406	218	4	.	.	PROPN
ejpam-2406	218	5	math	math	PROPN
ejpam-2406	218	6	,	,	PUNCT
ejpam-2406	218	7	8	8	NUM
ejpam-2406	218	8	(	(	PUNCT
ejpam-2406	218	9	2015	2015	NUM
ejpam-2406	218	10	)	)	PUNCT
ejpam-2406	218	11	,	,	PUNCT
ejpam-2406	218	12	172	172	NUM
ejpam-2406	218	13	-	-	SYM
ejpam-2406	218	14	184	184	NUM
ejpam-2406	218	15	179	179	NUM
ejpam-2406	218	16	multiplication	multiplication	NOUN
ejpam-2406	218	17	l	l	NOUN
ejpam-2406	218	18	-	-	NOUN
ejpam-2406	218	19	module	module	NOUN
ejpam-2406	218	20	.	.	PUNCT
ejpam-2406	219	1	n	n	PROPN
ejpam-2406	219	2	=	=	SYM
ejpam-2406	219	3	cim	cim	PROPN
ejpam-2406	219	4	for	for	ADP
ejpam-2406	219	5	some	some	DET
ejpam-2406	219	6	c	c	PROPN
ejpam-2406	219	7	∈	∈	PROPN
ejpam-2406	219	8	l.	l.	PROPN
ejpam-2406	219	9	thus	thus	ADV
ejpam-2406	219	10	,	,	PUNCT
ejpam-2406	219	11	abcim	abcim	PROPN
ejpam-2406	219	12	¶	¶	PROPN
ejpam-2406	219	13	q	q	PROPN
ejpam-2406	219	14	i.e.	i.e.	X
ejpam-2406	219	15	abc	abc	PROPN
ejpam-2406	219	16	¶	¶	PROPN
ejpam-2406	219	17	(	(	PUNCT
ejpam-2406	219	18	q	q	NOUN
ejpam-2406	219	19	:	:	PUNCT
ejpam-2406	219	20	i	i	PRON
ejpam-2406	219	21	m	m	VERB
ejpam-2406	219	22	)	)	PUNCT
ejpam-2406	220	1	¶	¶	PROPN
ejpam-2406	220	2	q	q	PROPN
ejpam-2406	220	3	where	where	SCONJ
ejpam-2406	220	4	q	q	NOUN
ejpam-2406	220	5	is	be	AUX
ejpam-2406	220	6	a	a	DET
ejpam-2406	220	7	classical	classical	ADJ
ejpam-2406	220	8	quasi	quasi	ADJ
ejpam-2406	220	9	primary	primary	ADJ
ejpam-2406	220	10	element	element	NOUN
ejpam-2406	220	11	of	of	ADP
ejpam-2406	220	12	l.	l.	PROPN
ejpam-2406	220	13	now	now	ADV
ejpam-2406	220	14	,	,	PUNCT
ejpam-2406	220	15	abc	abc	PROPN
ejpam-2406	220	16	¶	¶	PROPN
ejpam-2406	220	17	q	q	PROPN
ejpam-2406	220	18	and	and	CCONJ
ejpam-2406	220	19	bkcim	bkcim	PROPN
ejpam-2406	220	20	6¶q	6¶q	PROPN
ejpam-2406	220	21	implies	imply	VERB
ejpam-2406	220	22	bkc	bkc	NOUN
ejpam-2406	220	23	6¶	6¶	NUM
ejpam-2406	220	24	(	(	PUNCT
ejpam-2406	220	25	q	q	NOUN
ejpam-2406	220	26	:	:	PUNCT
ejpam-2406	220	27	i	i	PRON
ejpam-2406	220	28	m	m	VERB
ejpam-2406	220	29	)	)	PUNCT
ejpam-2406	221	1	=	=	PUNCT
ejpam-2406	221	2	q	q	PROPN
ejpam-2406	222	1	for	for	ADP
ejpam-2406	222	2	any	any	DET
ejpam-2406	222	3	k.	k.	NOUN
ejpam-2406	222	4	therefore	therefore	ADV
ejpam-2406	222	5	we	we	PRON
ejpam-2406	222	6	have	have	VERB
ejpam-2406	222	7	akc	akc	PROPN
ejpam-2406	222	8	¶	¶	PROPN
ejpam-2406	222	9	q	q	NOUN
ejpam-2406	222	10	for	for	ADP
ejpam-2406	222	11	some	some	DET
ejpam-2406	222	12	integer	integer	NOUN
ejpam-2406	222	13	k.	k.	PROPN
ejpam-2406	223	1	so	so	ADV
ejpam-2406	223	2	,	,	PUNCT
ejpam-2406	223	3	akcim	akcim	PROPN
ejpam-2406	223	4	¶	¶	PROPN
ejpam-2406	223	5	qim	qim	PROPN
ejpam-2406	223	6	,	,	PUNCT
ejpam-2406	223	7	i.e.	i.e.	X
ejpam-2406	223	8	akn	akn	PROPN
ejpam-2406	223	9	¶	¶	PROPN
ejpam-2406	223	10	qim	qim	PROPN
ejpam-2406	224	1	=	=	X
ejpam-2406	224	2	q.	q.	PROPN
ejpam-2406	224	3	consequently	consequently	ADV
ejpam-2406	224	4	,	,	PUNCT
ejpam-2406	224	5	q	q	X
ejpam-2406	224	6	is	be	AUX
ejpam-2406	224	7	a	a	DET
ejpam-2406	224	8	classical	classical	ADJ
ejpam-2406	224	9	quasi	quasi	ADJ
ejpam-2406	224	10	primary	primary	ADJ
ejpam-2406	224	11	element	element	NOUN
ejpam-2406	224	12	of	of	ADP
ejpam-2406	224	13	m.	m.	NOUN
ejpam-2406	224	14	3	3	NUM
ejpam-2406	224	15	.	.	PUNCT
ejpam-2406	224	16	classical	classical	ADJ
ejpam-2406	224	17	quasi	quasi	ADJ
ejpam-2406	224	18	primary	primary	ADJ
ejpam-2406	224	19	decomposition	decomposition	NOUN
ejpam-2406	224	20	of	of	ADP
ejpam-2406	224	21	elements	element	NOUN
ejpam-2406	224	22	the	the	DET
ejpam-2406	224	23	study	study	NOUN
ejpam-2406	224	24	of	of	ADP
ejpam-2406	224	25	decomposition	decomposition	NOUN
ejpam-2406	224	26	into	into	ADP
ejpam-2406	224	27	classical	classical	ADJ
ejpam-2406	224	28	primary	primary	ADJ
ejpam-2406	224	29	submodules	submodule	NOUN
ejpam-2406	224	30	was	be	AUX
ejpam-2406	224	31	introduced	introduce	VERB
ejpam-2406	224	32	in	in	ADP
ejpam-2406	224	33	[	[	X
ejpam-2406	224	34	3	3	NUM
ejpam-2406	224	35	]	]	PUNCT
ejpam-2406	224	36	.	.	PUNCT
ejpam-2406	225	1	further	further	ADJ
ejpam-2406	225	2	investigation	investigation	NOUN
ejpam-2406	225	3	of	of	ADP
ejpam-2406	225	4	decomposition	decomposition	NOUN
ejpam-2406	225	5	of	of	ADP
ejpam-2406	225	6	submodules	submodule	NOUN
ejpam-2406	225	7	into	into	ADP
ejpam-2406	225	8	classical	classical	ADJ
ejpam-2406	225	9	primary	primary	ADJ
ejpam-2406	225	10	submodules	submodule	NOUN
ejpam-2406	225	11	is	be	AUX
ejpam-2406	225	12	carried	carry	VERB
ejpam-2406	225	13	out	out	ADP
ejpam-2406	225	14	by	by	ADP
ejpam-2406	225	15	behboodi	behboodi	NOUN
ejpam-2406	225	16	et	et	PROPN
ejpam-2406	225	17	al	al	PROPN
ejpam-2406	225	18	.	.	PUNCT
ejpam-2406	226	1	[	[	X
ejpam-2406	226	2	1	1	NUM
ejpam-2406	226	3	]	]	PUNCT
ejpam-2406	226	4	.	.	PUNCT
ejpam-2406	227	1	we	we	PRON
ejpam-2406	227	2	carry	carry	VERB
ejpam-2406	227	3	out	out	ADP
ejpam-2406	227	4	this	this	DET
ejpam-2406	227	5	study	study	NOUN
ejpam-2406	227	6	for	for	ADP
ejpam-2406	227	7	lattice	lattice	NOUN
ejpam-2406	227	8	modules	module	NOUN
ejpam-2406	227	9	.	.	PUNCT
ejpam-2406	228	1	the	the	DET
ejpam-2406	228	2	next	next	ADJ
ejpam-2406	228	3	result	result	NOUN
ejpam-2406	228	4	shows	show	VERB
ejpam-2406	228	5	when	when	SCONJ
ejpam-2406	228	6	the	the	DET
ejpam-2406	228	7	element	element	NOUN
ejpam-2406	228	8	having	have	VERB
ejpam-2406	228	9	a	a	DET
ejpam-2406	228	10	primary	primary	ADJ
ejpam-2406	228	11	decomposition	decomposition	NOUN
ejpam-2406	228	12	is	be	AUX
ejpam-2406	228	13	classical	classical	ADJ
ejpam-2406	228	14	quasi	quasi	ADJ
ejpam-2406	228	15	primary	primary	ADJ
ejpam-2406	228	16	element	element	NOUN
ejpam-2406	228	17	.	.	PUNCT
ejpam-2406	229	1	theorem	theorem	VERB
ejpam-2406	229	2	7	7	NUM
ejpam-2406	229	3	.	.	PUNCT
ejpam-2406	230	1	let	let	VERB
ejpam-2406	230	2	m	m	PRON
ejpam-2406	230	3	be	be	AUX
ejpam-2406	230	4	an	an	DET
ejpam-2406	230	5	l	l	NOUN
ejpam-2406	230	6	-	-	NOUN
ejpam-2406	230	7	module	module	NOUN
ejpam-2406	230	8	and	and	CCONJ
ejpam-2406	230	9	let	let	VERB
ejpam-2406	230	10	q	q	NOUN
ejpam-2406	230	11	=	=	PUNCT
ejpam-2406	230	12	q1	q1	PROPN
ejpam-2406	230	13	∧q2	∧q2	VERB
ejpam-2406	230	14	∧	∧	PROPN
ejpam-2406	230	15	·	·	PUNCT
ejpam-2406	230	16	·	·	PUNCT
ejpam-2406	230	17	·	·	PUNCT
ejpam-2406	231	1	∧qn	∧qn	PROPN
ejpam-2406	231	2	be	be	VERB
ejpam-2406	231	3	a	a	DET
ejpam-2406	231	4	primary	primary	ADJ
ejpam-2406	231	5	decomposition	decomposition	NOUN
ejpam-2406	231	6	of	of	ADP
ejpam-2406	231	7	q	q	NOUN
ejpam-2406	231	8	with	with	ADP
ejpam-2406	231	9	pi	pi	NOUN
ejpam-2406	231	10	=	=	PUNCT
ejpam-2406	231	11	p	p	X
ejpam-2406	231	12	(	(	PUNCT
ejpam-2406	231	13	q	q	NOUN
ejpam-2406	231	14	i	i	PRON
ejpam-2406	231	15	:	:	PUNCT
ejpam-2406	231	16	i	i	PRON
ejpam-2406	231	17	m	m	VERB
ejpam-2406	231	18	)	)	PUNCT
ejpam-2406	231	19	.	.	PUNCT
ejpam-2406	232	1	if	if	SCONJ
ejpam-2406	232	2	p1	p1	PROPN
ejpam-2406	232	3	¶	¶	PROPN
ejpam-2406	232	4	p2	p2	PROPN
ejpam-2406	232	5	¶	¶	PROPN
ejpam-2406	232	6	·	·	PUNCT
ejpam-2406	232	7	·	·	PUNCT
ejpam-2406	232	8	·	·	PUNCT
ejpam-2406	232	9	¶	¶	PROPN
ejpam-2406	232	10	pn	pn	PROPN
ejpam-2406	232	11	then	then	ADV
ejpam-2406	232	12	q	q	X
ejpam-2406	232	13	is	be	AUX
ejpam-2406	232	14	a	a	DET
ejpam-2406	232	15	classical	classical	ADJ
ejpam-2406	232	16	p1	p1	NOUN
ejpam-2406	232	17	-	-	PUNCT
ejpam-2406	232	18	quasi	quasi	ADJ
ejpam-2406	232	19	primary	primary	ADJ
ejpam-2406	232	20	element	element	NOUN
ejpam-2406	232	21	.	.	PUNCT
ejpam-2406	233	1	proof	proof	NOUN
ejpam-2406	233	2	.	.	PUNCT
ejpam-2406	234	1	assume	assume	VERB
ejpam-2406	234	2	that	that	SCONJ
ejpam-2406	234	3	,	,	PUNCT
ejpam-2406	234	4	abn	abn	PROPN
ejpam-2406	234	5	¶q	¶q	PROPN
ejpam-2406	234	6	,	,	PUNCT
ejpam-2406	234	7	where	where	SCONJ
ejpam-2406	234	8	a	a	DET
ejpam-2406	234	9	,	,	PUNCT
ejpam-2406	234	10	b	b	PROPN
ejpam-2406	234	11	∈	∈	PROPN
ejpam-2406	234	12	l	l	NOUN
ejpam-2406	234	13	,	,	PUNCT
ejpam-2406	234	14	n	n	PROPN
ejpam-2406	234	15	6¶q	6¶q	NUM
ejpam-2406	234	16	.	.	PUNCT
ejpam-2406	235	1	then	then	ADV
ejpam-2406	235	2	,	,	PUNCT
ejpam-2406	235	3	n	n	PROPN
ejpam-2406	236	1	6¶q	6¶q	NOUN
ejpam-2406	236	2	i	i	PRON
ejpam-2406	236	3	,	,	PUNCT
ejpam-2406	236	4	for	for	ADP
ejpam-2406	236	5	some	some	DET
ejpam-2406	236	6	i	i	PRON
ejpam-2406	236	7	(	(	PUNCT
ejpam-2406	236	8	1¶	1¶	NOUN
ejpam-2406	236	9	i	i	PROPN
ejpam-2406	236	10	¶	¶	PROPN
ejpam-2406	236	11	n	n	CCONJ
ejpam-2406	236	12	)	)	PUNCT
ejpam-2406	236	13	.	.	PUNCT
ejpam-2406	237	1	suppose	suppose	VERB
ejpam-2406	237	2	,	,	PUNCT
ejpam-2406	237	3	t	t	PROPN
ejpam-2406	237	4	(	(	PUNCT
ejpam-2406	237	5	1¶	1¶	PROPN
ejpam-2406	237	6	t	t	PROPN
ejpam-2406	237	7	¶	¶	PROPN
ejpam-2406	237	8	n	n	CCONJ
ejpam-2406	237	9	)	)	PUNCT
ejpam-2406	237	10	is	be	AUX
ejpam-2406	237	11	the	the	DET
ejpam-2406	237	12	smallest	small	ADJ
ejpam-2406	237	13	number	number	NOUN
ejpam-2406	237	14	such	such	ADJ
ejpam-2406	237	15	that	that	SCONJ
ejpam-2406	237	16	n	n	PROPN
ejpam-2406	237	17	6¶q	6¶q	NUM
ejpam-2406	237	18	t	t	NOUN
ejpam-2406	237	19	.	.	PUNCT
ejpam-2406	238	1	thus	thus	ADV
ejpam-2406	238	2	,	,	PUNCT
ejpam-2406	238	3	n	n	PRON
ejpam-2406	238	4	¶q1∧q2∧	¶q1∧q2∧	ADJ
ejpam-2406	238	5	·	·	PUNCT
ejpam-2406	238	6	·	·	PUNCT
ejpam-2406	238	7	·	·	PUNCT
ejpam-2406	238	8	∧q	∧q	PROPN
ejpam-2406	238	9	t−1	t−1	PROPN
ejpam-2406	238	10	.	.	PUNCT
ejpam-2406	239	1	we	we	PRON
ejpam-2406	239	2	have	have	VERB
ejpam-2406	239	3	abn	abn	PROPN
ejpam-2406	239	4	¶	¶	PROPN
ejpam-2406	239	5	q	q	PROPN
ejpam-2406	239	6	t	t	PROPN
ejpam-2406	239	7	and	and	CCONJ
ejpam-2406	239	8	q	q	PROPN
ejpam-2406	239	9	t	t	PROPN
ejpam-2406	239	10	is	be	AUX
ejpam-2406	239	11	pt	pt	NOUN
ejpam-2406	239	12	primary	primary	NOUN
ejpam-2406	239	13	.	.	PUNCT
ejpam-2406	240	1	hence	hence	ADV
ejpam-2406	240	2	,	,	PUNCT
ejpam-2406	240	3	(	(	PUNCT
ejpam-2406	240	4	ab)k1	ab)k1	PROPN
ejpam-2406	240	5	i	i	NOUN
ejpam-2406	240	6	m	m	VERB
ejpam-2406	240	7	¶	¶	PROPN
ejpam-2406	240	8	q	q	PROPN
ejpam-2406	241	1	t	t	PROPN
ejpam-2406	241	2	for	for	ADP
ejpam-2406	241	3	some	some	DET
ejpam-2406	241	4	k1	k1	NOUN
ejpam-2406	241	5	∈	∈	PROPN
ejpam-2406	241	6	z+	z+	NUM
ejpam-2406	241	7	implies	imply	VERB
ejpam-2406	241	8	ab	ab	PROPN
ejpam-2406	241	9	¶	¶	PROPN
ejpam-2406	241	10	p	p	PROPN
ejpam-2406	241	11	(	(	PUNCT
ejpam-2406	241	12	q	q	PROPN
ejpam-2406	241	13	t	t	NOUN
ejpam-2406	241	14	:	:	PUNCT
ejpam-2406	241	15	i	i	PRON
ejpam-2406	241	16	m	m	VERB
ejpam-2406	241	17	)	)	PUNCT
ejpam-2406	242	1	=	=	SYM
ejpam-2406	242	2	pt	pt	X
ejpam-2406	242	3	.	.	PUNCT
ejpam-2406	243	1	thus	thus	ADV
ejpam-2406	243	2	,	,	PUNCT
ejpam-2406	243	3	a	a	DET
ejpam-2406	243	4	¶	¶	PROPN
ejpam-2406	243	5	pt	pt	NOUN
ejpam-2406	243	6	or	or	CCONJ
ejpam-2406	243	7	b	b	NOUN
ejpam-2406	243	8	¶	¶	PROPN
ejpam-2406	243	9	pt	pt	PROPN
ejpam-2406	243	10	.	.	PUNCT
ejpam-2406	244	1	now	now	ADV
ejpam-2406	244	2	pt	pt	X
ejpam-2406	245	1	¶	¶	PROPN
ejpam-2406	245	2	pt+1	pt+1	PROPN
ejpam-2406	245	3	¶	¶	PROPN
ejpam-2406	245	4	·	·	PUNCT
ejpam-2406	245	5	·	·	PUNCT
ejpam-2406	245	6	·	·	PUNCT
ejpam-2406	245	7	¶	¶	PROPN
ejpam-2406	245	8	pn	pn	PROPN
ejpam-2406	245	9	.	.	PROPN
ejpam-2406	245	10	suppose	suppose	VERB
ejpam-2406	245	11	,	,	PUNCT
ejpam-2406	245	12	a	a	DET
ejpam-2406	245	13	¶	¶	NOUN
ejpam-2406	245	14	pt	pt	X
ejpam-2406	245	15	=	=	SYM
ejpam-2406	245	16	p	p	X
ejpam-2406	245	17	(	(	PUNCT
ejpam-2406	245	18	q	q	PROPN
ejpam-2406	245	19	t	t	NOUN
ejpam-2406	245	20	:	:	PUNCT
ejpam-2406	245	21	i	i	PRON
ejpam-2406	245	22	m	m	PROPN
ejpam-2406	245	23	)	)	PUNCT
ejpam-2406	245	24	.	.	PUNCT
ejpam-2406	246	1	consequently	consequently	ADV
ejpam-2406	246	2	ak	ak	PROPN
ejpam-2406	246	3	i	i	PROPN
ejpam-2406	246	4	m	m	PROPN
ejpam-2406	246	5	¶	¶	PROPN
ejpam-2406	246	6	q	q	PROPN
ejpam-2406	246	7	t	t	PROPN
ejpam-2406	246	8	,	,	PUNCT
ejpam-2406	246	9	for	for	ADP
ejpam-2406	246	10	some	some	DET
ejpam-2406	246	11	integer	integer	NOUN
ejpam-2406	246	12	k.	k.	PROPN
ejpam-2406	247	1	if	if	SCONJ
ejpam-2406	247	2	b	b	PROPN
ejpam-2406	247	3	¶	¶	PROPN
ejpam-2406	247	4	pt	pt	X
ejpam-2406	247	5	=	=	SYM
ejpam-2406	247	6	p	p	X
ejpam-2406	247	7	(	(	PUNCT
ejpam-2406	247	8	q	q	PROPN
ejpam-2406	247	9	t	t	NOUN
ejpam-2406	247	10	:	:	PUNCT
ejpam-2406	247	11	i	i	PRON
ejpam-2406	247	12	m	m	VERB
ejpam-2406	247	13	)	)	PUNCT
ejpam-2406	248	1	we	we	PRON
ejpam-2406	248	2	have	have	VERB
ejpam-2406	248	3	bk	bk	INTJ
ejpam-2406	248	4	i	i	NOUN
ejpam-2406	248	5	m	m	PROPN
ejpam-2406	248	6	¶	¶	PROPN
ejpam-2406	248	7	q	q	PROPN
ejpam-2406	248	8	t	t	PROPN
ejpam-2406	248	9	.	.	PUNCT
ejpam-2406	249	1	thus	thus	ADV
ejpam-2406	249	2	ak	ak	PROPN
ejpam-2406	249	3	i	i	PROPN
ejpam-2406	249	4	m	m	PROPN
ejpam-2406	249	5	¶	¶	PROPN
ejpam-2406	249	6	q	q	PROPN
ejpam-2406	250	1	t	t	PROPN
ejpam-2406	250	2	or	or	CCONJ
ejpam-2406	250	3	bk	bk	INTJ
ejpam-2406	250	4	i	i	NOUN
ejpam-2406	250	5	m	m	PROPN
ejpam-2406	250	6	¶	¶	PROPN
ejpam-2406	250	7	q	q	PROPN
ejpam-2406	250	8	t	t	PROPN
ejpam-2406	250	9	for	for	ADP
ejpam-2406	250	10	some	some	DET
ejpam-2406	250	11	k	k	PROPN
ejpam-2406	250	12	∈	∈	PROPN
ejpam-2406	250	13	z+	z+	NUM
ejpam-2406	250	14	where	where	SCONJ
ejpam-2406	250	15	t	t	PROPN
ejpam-2406	250	16	is	be	AUX
ejpam-2406	250	17	the	the	DET
ejpam-2406	250	18	smallest	small	ADJ
ejpam-2406	250	19	positive	positive	ADJ
ejpam-2406	250	20	integer	integer	NOUN
ejpam-2406	250	21	such	such	DET
ejpam-2406	250	22	that	that	SCONJ
ejpam-2406	250	23	n	n	PROPN
ejpam-2406	250	24	6¶q	6¶q	NUM
ejpam-2406	250	25	t	t	NOUN
ejpam-2406	250	26	.	.	PUNCT
ejpam-2406	251	1	we	we	PRON
ejpam-2406	251	2	have	have	VERB
ejpam-2406	251	3	n	n	PROPN
ejpam-2406	251	4	6¶q	6¶q	NUM
ejpam-2406	251	5	t+1	t+1	PROPN
ejpam-2406	251	6	,	,	PUNCT
ejpam-2406	251	7	.	.	PUNCT
ejpam-2406	251	8	.	.	PUNCT
ejpam-2406	252	1	.	.	PUNCT
ejpam-2406	253	1	,	,	PUNCT
ejpam-2406	253	2	n	n	PROPN
ejpam-2406	253	3	6¶qn	6¶qn	NUM
ejpam-2406	253	4	,	,	PUNCT
ejpam-2406	253	5	ak	ak	PROPN
ejpam-2406	254	1	i	i	PROPN
ejpam-2406	254	2	m	m	VERB
ejpam-2406	254	3	¶q	¶q	PROPN
ejpam-2406	254	4	t	t	NOUN
ejpam-2406	254	5	,	,	PUNCT
ejpam-2406	254	6	q	q	PROPN
ejpam-2406	254	7	t+1	t+1	PROPN
ejpam-2406	254	8	,	,	PUNCT
ejpam-2406	254	9	.	.	PUNCT
ejpam-2406	254	10	.	.	PUNCT
ejpam-2406	254	11	.	.	PUNCT
ejpam-2406	255	1	,	,	PUNCT
ejpam-2406	255	2	qn	qn	NOUN
ejpam-2406	255	3	or	or	CCONJ
ejpam-2406	255	4	bk	bk	INTJ
ejpam-2406	255	5	i	i	NOUN
ejpam-2406	255	6	m	m	VERB
ejpam-2406	255	7	¶q	¶q	ADJ
ejpam-2406	255	8	t	t	NOUN
ejpam-2406	255	9	,	,	PUNCT
ejpam-2406	255	10	q	q	PROPN
ejpam-2406	255	11	t+1	t+1	PROPN
ejpam-2406	255	12	,	,	PUNCT
ejpam-2406	255	13	.	.	PUNCT
ejpam-2406	255	14	.	.	PUNCT
ejpam-2406	255	15	.	.	PUNCT
ejpam-2406	256	1	,	,	PUNCT
ejpam-2406	256	2	qn	qn	INTJ
ejpam-2406	256	3	.	.	PROPN
ejpam-2406	256	4	hence	hence	PROPN
ejpam-2406	256	5	ak	ak	PROPN
ejpam-2406	257	1	i	i	PRON
ejpam-2406	257	2	m	m	VERB
ejpam-2406	257	3	¶q	¶q	PROPN
ejpam-2406	257	4	t	t	NUM
ejpam-2406	257	5	∧q	∧q	PROPN
ejpam-2406	257	6	t+1∧	t+1∧	NOUN
ejpam-2406	257	7	·	·	PUNCT
ejpam-2406	257	8	·	·	PUNCT
ejpam-2406	257	9	·	·	PUNCT
ejpam-2406	257	10	∧qn	∧qn	PROPN
ejpam-2406	257	11	or	or	CCONJ
ejpam-2406	257	12	bk	bk	INTJ
ejpam-2406	257	13	i	i	NOUN
ejpam-2406	257	14	m	m	VERB
ejpam-2406	257	15	¶q	¶q	ADJ
ejpam-2406	257	16	t	t	NUM
ejpam-2406	257	17	∧q	∧q	PROPN
ejpam-2406	257	18	t+1∧	t+1∧	NOUN
ejpam-2406	257	19	·	·	PUNCT
ejpam-2406	257	20	·	·	PUNCT
ejpam-2406	258	1	·	·	PUNCT
ejpam-2406	258	2	∧qn	∧qn	PROPN
ejpam-2406	258	3	for	for	ADP
ejpam-2406	258	4	some	some	DET
ejpam-2406	258	5	k	k	PROPN
ejpam-2406	258	6	∈	∈	PROPN
ejpam-2406	258	7	z+	z+	PUNCT
ejpam-2406	258	8	.	.	PUNCT
ejpam-2406	259	1	but	but	CCONJ
ejpam-2406	259	2	,	,	PUNCT
ejpam-2406	259	3	n	n	PROPN
ejpam-2406	259	4	¶	¶	PROPN
ejpam-2406	259	5	q1	q1	PROPN
ejpam-2406	259	6	∧q2	∧q2	VERB
ejpam-2406	259	7	∧	∧	PROPN
ejpam-2406	259	8	·	·	PUNCT
ejpam-2406	259	9	·	·	PUNCT
ejpam-2406	259	10	·	·	PUNCT
ejpam-2406	259	11	∧q	∧q	PROPN
ejpam-2406	259	12	t−1	t−1	PROPN
ejpam-2406	259	13	.	.	PUNCT
ejpam-2406	260	1	it	it	PRON
ejpam-2406	260	2	follows	follow	VERB
ejpam-2406	260	3	that	that	SCONJ
ejpam-2406	260	4	,	,	PUNCT
ejpam-2406	260	5	akn	akn	PROPN
ejpam-2406	260	6	¶	¶	PROPN
ejpam-2406	260	7	q1	q1	PROPN
ejpam-2406	260	8	∧q2	∧q2	VERB
ejpam-2406	260	9	∧	∧	PROPN
ejpam-2406	260	10	·	·	PUNCT
ejpam-2406	260	11	·	·	PUNCT
ejpam-2406	260	12	·	·	PUNCT
ejpam-2406	261	1	∧qn	∧qn	PROPN
ejpam-2406	261	2	=	=	PUNCT
ejpam-2406	261	3	q	q	PROPN
ejpam-2406	261	4	or	or	CCONJ
ejpam-2406	261	5	bkn	bkn	PROPN
ejpam-2406	261	6	¶q1	¶q1	PROPN
ejpam-2406	261	7	∧q2	∧q2	VERB
ejpam-2406	261	8	∧	∧	PROPN
ejpam-2406	261	9	·	·	PUNCT
ejpam-2406	261	10	·	·	PUNCT
ejpam-2406	261	11	·	·	PUNCT
ejpam-2406	261	12	∧qn	∧qn	PROPN
ejpam-2406	261	13	.	.	PUNCT
ejpam-2406	262	1	if	if	SCONJ
ejpam-2406	262	2	n	n	X
ejpam-2406	262	3	¶q	¶q	NOUN
ejpam-2406	262	4	,	,	PUNCT
ejpam-2406	262	5	abn	abn	PROPN
ejpam-2406	262	6	¶q	¶q	NOUN
ejpam-2406	262	7	implies	imply	VERB
ejpam-2406	262	8	an	an	DET
ejpam-2406	262	9	¶q	¶q	PROPN
ejpam-2406	262	10	,	,	PUNCT
ejpam-2406	262	11	bn	bn	X
ejpam-2406	262	12	¶q	¶q	NOUN
ejpam-2406	262	13	.	.	PUNCT
ejpam-2406	263	1	also	also	ADV
ejpam-2406	263	2	,	,	PUNCT
ejpam-2406	263	3	p	p	X
ejpam-2406	263	4	(	(	PUNCT
ejpam-2406	263	5	q	q	NOUN
ejpam-2406	263	6	:	:	PUNCT
ejpam-2406	263	7	i	i	PRON
ejpam-2406	263	8	m	m	VERB
ejpam-2406	263	9	)	)	PUNCT
ejpam-2406	264	1	=	=	SYM
ejpam-2406	264	2	p	p	X
ejpam-2406	264	3	(	(	PUNCT
ejpam-2406	264	4	q1	q1	PROPN
ejpam-2406	264	5	∧q2	∧q2	VERB
ejpam-2406	264	6	∧	∧	PROPN
ejpam-2406	264	7	·	·	PUNCT
ejpam-2406	264	8	·	·	PUNCT
ejpam-2406	264	9	·	·	PUNCT
ejpam-2406	264	10	∧qn	∧qn	PROPN
ejpam-2406	264	11	)	)	PUNCT
ejpam-2406	264	12	:	:	PUNCT
ejpam-2406	265	1	i	i	PRON
ejpam-2406	265	2	m	m	VERB
ejpam-2406	265	3	=	=	NOUN
ejpam-2406	265	4	p1	p1	PROPN
ejpam-2406	265	5	.	.	PUNCT
ejpam-2406	266	1	therefore	therefore	ADV
ejpam-2406	266	2	,	,	PUNCT
ejpam-2406	266	3	q	q	X
ejpam-2406	266	4	is	be	AUX
ejpam-2406	266	5	a	a	DET
ejpam-2406	266	6	classical	classical	ADJ
ejpam-2406	266	7	p1quasi	p1quasi	NOUN
ejpam-2406	266	8	primary	primary	ADJ
ejpam-2406	266	9	element	element	NOUN
ejpam-2406	266	10	.	.	PUNCT
ejpam-2406	267	1	remark	remark	NOUN
ejpam-2406	267	2	1	1	NUM
ejpam-2406	267	3	.	.	PUNCT
ejpam-2406	268	1	the	the	DET
ejpam-2406	268	2	following	follow	VERB
ejpam-2406	268	3	example	example	NOUN
ejpam-2406	268	4	shows	show	VERB
ejpam-2406	268	5	that	that	SCONJ
ejpam-2406	268	6	the	the	DET
ejpam-2406	268	7	above	above	ADJ
ejpam-2406	268	8	theorem	theorem	NOUN
ejpam-2406	268	9	is	be	AUX
ejpam-2406	268	10	not	not	PART
ejpam-2406	268	11	necessarily	necessarily	ADV
ejpam-2406	268	12	true	true	ADJ
ejpam-2406	268	13	if	if	SCONJ
ejpam-2406	268	14	q1,q2	q1,q2	PROPN
ejpam-2406	268	15	,	,	PUNCT
ejpam-2406	268	16	.	.	PUNCT
ejpam-2406	268	17	.	.	PUNCT
ejpam-2406	268	18	.	.	PUNCT
ejpam-2406	269	1	,	,	PUNCT
ejpam-2406	269	2	qn	qn	PROPN
ejpam-2406	269	3	are	be	AUX
ejpam-2406	269	4	only	only	ADV
ejpam-2406	269	5	assured	assure	VERB
ejpam-2406	269	6	to	to	PART
ejpam-2406	269	7	be	be	AUX
ejpam-2406	269	8	classical	classical	ADJ
ejpam-2406	269	9	(	(	PUNCT
ejpam-2406	269	10	quasi	quasi	ADJ
ejpam-2406	269	11	)	)	PUNCT
ejpam-2406	269	12	primary	primary	ADJ
ejpam-2406	269	13	elements	element	NOUN
ejpam-2406	269	14	.	.	PUNCT
ejpam-2406	270	1	example	example	NOUN
ejpam-2406	271	1	5	5	NUM
ejpam-2406	271	2	.	.	PUNCT
ejpam-2406	272	1	let	let	VERB
ejpam-2406	272	2	r	r	NOUN
ejpam-2406	272	3	=	=	PUNCT
ejpam-2406	272	4	z	z	NOUN
ejpam-2406	272	5	,	,	PUNCT
ejpam-2406	272	6	m	m	VERB
ejpam-2406	273	1	=	=	ADJ
ejpam-2406	273	2	z2	z2	PROPN
ejpam-2406	273	3	⊕	⊕	PROPN
ejpam-2406	273	4	z3	z3	PROPN
ejpam-2406	273	5	⊕	⊕	PROPN
ejpam-2406	274	1	z	z	PROPN
ejpam-2406	274	2	then	then	ADV
ejpam-2406	274	3	m	m	VERB
ejpam-2406	274	4	is	be	AUX
ejpam-2406	274	5	a	a	DET
ejpam-2406	274	6	z	z	NOUN
ejpam-2406	274	7	-	-	PUNCT
ejpam-2406	274	8	module	module	NOUN
ejpam-2406	274	9	.	.	PUNCT
ejpam-2406	275	1	let	let	AUX
ejpam-2406	275	2	l(r	l(r	PROPN
ejpam-2406	275	3	)	)	PUNCT
ejpam-2406	275	4	denote	denote	VERB
ejpam-2406	275	5	the	the	DET
ejpam-2406	275	6	set	set	NOUN
ejpam-2406	275	7	of	of	ADP
ejpam-2406	275	8	all	all	DET
ejpam-2406	275	9	ideals	ideal	NOUN
ejpam-2406	275	10	of	of	ADP
ejpam-2406	275	11	r	r	NOUN
ejpam-2406	275	12	and	and	CCONJ
ejpam-2406	275	13	l(m	l(m	PROPN
ejpam-2406	275	14	)	)	PUNCT
ejpam-2406	275	15	denote	denote	VERB
ejpam-2406	275	16	the	the	DET
ejpam-2406	275	17	set	set	NOUN
ejpam-2406	275	18	of	of	ADP
ejpam-2406	275	19	all	all	DET
ejpam-2406	275	20	submodules	submodule	NOUN
ejpam-2406	275	21	of	of	ADP
ejpam-2406	275	22	m.	m.	NOUN
ejpam-2406	275	23	then	then	ADV
ejpam-2406	275	24	l(m	l(m	PROPN
ejpam-2406	275	25	)	)	PUNCT
ejpam-2406	275	26	is	be	AUX
ejpam-2406	275	27	a	a	DET
ejpam-2406	275	28	module	module	NOUN
ejpam-2406	275	29	over	over	ADP
ejpam-2406	275	30	l(r	l(r	PROPN
ejpam-2406	275	31	)	)	PUNCT
ejpam-2406	275	32	where	where	SCONJ
ejpam-2406	275	33	l(r	l(r	PROPN
ejpam-2406	275	34	)	)	PUNCT
ejpam-2406	275	35	is	be	AUX
ejpam-2406	275	36	a	a	DET
ejpam-2406	275	37	multiplicative	multiplicative	ADJ
ejpam-2406	275	38	lattice	lattice	NOUN
ejpam-2406	275	39	.	.	PUNCT
ejpam-2406	276	1	let	let	VERB
ejpam-2406	276	2	q1	q1	PROPN
ejpam-2406	276	3	=	=	SYM
ejpam-2406	276	4	z2	z2	PROPN
ejpam-2406	276	5	⊕	⊕	PROPN
ejpam-2406	276	6	(	(	PUNCT
ejpam-2406	276	7	0)⊕	0)⊕	NUM
ejpam-2406	276	8	(	(	PUNCT
ejpam-2406	276	9	0	0	NUM
ejpam-2406	276	10	)	)	PUNCT
ejpam-2406	276	11	.	.	PUNCT
ejpam-2406	277	1	q2	q2	NOUN
ejpam-2406	277	2	=	=	SYM
ejpam-2406	277	3	(	(	PUNCT
ejpam-2406	277	4	0)⊕	0)⊕	NUM
ejpam-2406	277	5	z3	z3	PROPN
ejpam-2406	277	6	⊕	⊕	PROPN
ejpam-2406	277	7	(	(	PUNCT
ejpam-2406	277	8	0	0	NUM
ejpam-2406	277	9	)	)	PUNCT
ejpam-2406	277	10	.	.	PUNCT
ejpam-2406	278	1	then	then	ADV
ejpam-2406	278	2	q1	q1	PROPN
ejpam-2406	278	3	,	,	PUNCT
ejpam-2406	278	4	q2	q2	PROPN
ejpam-2406	278	5	,	,	PUNCT
ejpam-2406	278	6	are	be	AUX
ejpam-2406	278	7	elements	element	NOUN
ejpam-2406	278	8	of	of	ADP
ejpam-2406	278	9	l(m	l(m	PROPN
ejpam-2406	278	10	)	)	PUNCT
ejpam-2406	278	11	.	.	PUNCT
ejpam-2406	279	1	it	it	PRON
ejpam-2406	279	2	can	can	AUX
ejpam-2406	279	3	be	be	AUX
ejpam-2406	279	4	shown	show	VERB
ejpam-2406	279	5	that	that	SCONJ
ejpam-2406	279	6	q1	q1	PROPN
ejpam-2406	279	7	and	and	CCONJ
ejpam-2406	279	8	q2	q2	NOUN
ejpam-2406	279	9	are	be	AUX
ejpam-2406	279	10	classical	classical	ADJ
ejpam-2406	279	11	(	(	PUNCT
ejpam-2406	279	12	quasi	quasi	ADJ
ejpam-2406	279	13	)	)	PUNCT
ejpam-2406	279	14	primary	primary	ADJ
ejpam-2406	279	15	elements	element	NOUN
ejpam-2406	279	16	of	of	ADP
ejpam-2406	279	17	l(m	l(m	PROPN
ejpam-2406	279	18	)	)	PUNCT
ejpam-2406	279	19	.	.	PUNCT
ejpam-2406	280	1	also	also	ADV
ejpam-2406	280	2	,	,	PUNCT
ejpam-2406	280	3	(	(	PUNCT
ejpam-2406	280	4	0	0	X
ejpam-2406	280	5	)	)	PUNCT
ejpam-2406	280	6	=	=	NOUN
ejpam-2406	280	7	q1	q1	NOUN
ejpam-2406	280	8	∩q2	∩q2	NOUN
ejpam-2406	280	9	and	and	CCONJ
ejpam-2406	280	10	p	p	PROPN
ejpam-2406	280	11	(	(	PUNCT
ejpam-2406	280	12	q1	q1	PROPN
ejpam-2406	280	13	:	:	PUNCT
ejpam-2406	280	14	m	m	X
ejpam-2406	280	15	)	)	PUNCT
ejpam-2406	281	1	=	=	SYM
ejpam-2406	281	2	p	p	X
ejpam-2406	281	3	(	(	PUNCT
ejpam-2406	281	4	q2	q2	NOUN
ejpam-2406	281	5	:	:	PUNCT
ejpam-2406	281	6	m	m	X
ejpam-2406	281	7	)	)	PUNCT
ejpam-2406	281	8	=	=	SYM
ejpam-2406	281	9	(	(	PUNCT
ejpam-2406	281	10	0	0	NUM
ejpam-2406	281	11	)	)	PUNCT
ejpam-2406	281	12	.	.	PUNCT
ejpam-2406	282	1	obviously	obviously	ADV
ejpam-2406	282	2	,	,	PUNCT
ejpam-2406	282	3	2×3(z2⊕z3⊕(0	2×3(z2⊕z3⊕(0	NUM
ejpam-2406	282	4	)	)	PUNCT
ejpam-2406	282	5	)	)	PUNCT
ejpam-2406	283	1	=	=	PUNCT
ejpam-2406	283	2	(	(	PUNCT
ejpam-2406	283	3	0	0	NUM
ejpam-2406	283	4	)	)	PUNCT
ejpam-2406	283	5	.	.	PUNCT
ejpam-2406	284	1	also	also	ADV
ejpam-2406	284	2	,	,	PUNCT
ejpam-2406	284	3	for	for	ADP
ejpam-2406	284	4	each	each	DET
ejpam-2406	284	5	k	k	PROPN
ejpam-2406	284	6	≥	≥	NUM
ejpam-2406	284	7	1,2k(z2⊕z3⊕(0	1,2k(z2⊕z3⊕(0	NUM
ejpam-2406	284	8	)	)	PUNCT
ejpam-2406	284	9	)	)	PUNCT
ejpam-2406	284	10	6⊆	6⊆	NOUN
ejpam-2406	284	11	(	(	PUNCT
ejpam-2406	284	12	0	0	NUM
ejpam-2406	284	13	)	)	PUNCT
ejpam-2406	284	14	and	and	CCONJ
ejpam-2406	284	15	3k(z2⊕z3⊕(0	3k(z2⊕z3⊕(0	NUM
ejpam-2406	284	16	)	)	PUNCT
ejpam-2406	284	17	)	)	PUNCT
ejpam-2406	285	1	6⊆	6⊆	NOUN
ejpam-2406	285	2	(	(	PUNCT
ejpam-2406	285	3	0	0	NUM
ejpam-2406	285	4	)	)	PUNCT
ejpam-2406	285	5	.	.	PUNCT
ejpam-2406	286	1	thus	thus	ADV
ejpam-2406	286	2	,	,	PUNCT
ejpam-2406	286	3	(	(	PUNCT
ejpam-2406	286	4	0	0	X
ejpam-2406	286	5	)	)	PUNCT
ejpam-2406	286	6	⊂	⊂	ADJ
ejpam-2406	286	7	m	m	VERB
ejpam-2406	286	8	is	be	AUX
ejpam-2406	286	9	not	not	PART
ejpam-2406	286	10	a	a	DET
ejpam-2406	286	11	classical	classical	ADJ
ejpam-2406	286	12	(	(	PUNCT
ejpam-2406	286	13	quasi	quasi	ADJ
ejpam-2406	286	14	)	)	PUNCT
ejpam-2406	286	15	primary	primary	ADJ
ejpam-2406	286	16	element	element	NOUN
ejpam-2406	286	17	.	.	PUNCT
ejpam-2406	287	1	remark	remark	NOUN
ejpam-2406	287	2	2	2	NUM
ejpam-2406	287	3	.	.	PUNCT
ejpam-2406	288	1	we	we	PRON
ejpam-2406	288	2	shall	shall	AUX
ejpam-2406	288	3	show	show	VERB
ejpam-2406	288	4	that	that	SCONJ
ejpam-2406	288	5	the	the	DET
ejpam-2406	288	6	converse	converse	NOUN
ejpam-2406	288	7	of	of	ADP
ejpam-2406	288	8	theorem	theorem	NOUN
ejpam-2406	288	9	7	7	NUM
ejpam-2406	288	10	is	be	AUX
ejpam-2406	288	11	also	also	ADV
ejpam-2406	288	12	true	true	ADJ
ejpam-2406	288	13	when	when	SCONJ
ejpam-2406	288	14	decomposition	decomposition	NOUN
ejpam-2406	288	15	q1	q1	PROPN
ejpam-2406	288	16	∧	∧	PROPN
ejpam-2406	288	17	q2	q2	PROPN
ejpam-2406	288	18	∧	∧	PROPN
ejpam-2406	288	19	·	·	PUNCT
ejpam-2406	288	20	·	·	PUNCT
ejpam-2406	288	21	·	·	PUNCT
ejpam-2406	289	1	∧qn	∧qn	PROPN
ejpam-2406	289	2	is	be	AUX
ejpam-2406	289	3	a	a	DET
ejpam-2406	289	4	reduced	reduce	VERB
ejpam-2406	289	5	primary	primary	ADJ
ejpam-2406	289	6	decomposition	decomposition	NOUN
ejpam-2406	289	7	.	.	PUNCT
ejpam-2406	290	1	theorem	theorem	VERB
ejpam-2406	290	2	8	8	NUM
ejpam-2406	290	3	.	.	PUNCT
ejpam-2406	291	1	let	let	VERB
ejpam-2406	291	2	q	q	PART
ejpam-2406	291	3	be	be	AUX
ejpam-2406	291	4	a	a	DET
ejpam-2406	291	5	p	p	NOUN
ejpam-2406	291	6	-	-	PUNCT
ejpam-2406	291	7	primary	primary	ADJ
ejpam-2406	291	8	element	element	NOUN
ejpam-2406	291	9	of	of	ADP
ejpam-2406	291	10	a	a	DET
ejpam-2406	291	11	lattice	lattice	NOUN
ejpam-2406	291	12	module	module	NOUN
ejpam-2406	291	13	m	m	PROPN
ejpam-2406	291	14	and	and	CCONJ
ejpam-2406	291	15	n	n	ADV
ejpam-2406	291	16	be	be	VERB
ejpam-2406	291	17	an	an	DET
ejpam-2406	291	18	element	element	NOUN
ejpam-2406	291	19	of	of	ADP
ejpam-2406	291	20	m.	m.	NOUN
ejpam-2406	291	21	if	if	SCONJ
ejpam-2406	291	22	n	n	PROPN
ejpam-2406	291	23	6¶q	6¶q	NOUN
ejpam-2406	292	1	then	then	ADV
ejpam-2406	292	2	(	(	PUNCT
ejpam-2406	292	3	q	q	NOUN
ejpam-2406	292	4	:	:	PUNCT
ejpam-2406	292	5	n	n	CCONJ
ejpam-2406	292	6	)	)	PUNCT
ejpam-2406	292	7	is	be	AUX
ejpam-2406	292	8	a	a	DET
ejpam-2406	292	9	p	p	NOUN
ejpam-2406	292	10	-	-	PUNCT
ejpam-2406	292	11	primary	primary	ADJ
ejpam-2406	292	12	element	element	NOUN
ejpam-2406	292	13	.	.	PUNCT
ejpam-2406	293	1	c.	c.	PROPN
ejpam-2406	293	2	manjarekar	manjarekar	PROPN
ejpam-2406	293	3	,	,	PUNCT
ejpam-2406	293	4	u.	u.	PROPN
ejpam-2406	293	5	kandale	kandale	PROPN
ejpam-2406	293	6	/	/	SYM
ejpam-2406	293	7	eur	eur	PROPN
ejpam-2406	293	8	.	.	PUNCT
ejpam-2406	294	1	j.	j.	PROPN
ejpam-2406	294	2	pure	pure	PROPN
ejpam-2406	294	3	appl	appl	PROPN
ejpam-2406	294	4	.	.	PROPN
ejpam-2406	294	5	math	math	PROPN
ejpam-2406	294	6	,	,	PUNCT
ejpam-2406	294	7	8	8	NUM
ejpam-2406	294	8	(	(	PUNCT
ejpam-2406	294	9	2015	2015	NUM
ejpam-2406	294	10	)	)	PUNCT
ejpam-2406	294	11	,	,	PUNCT
ejpam-2406	294	12	172	172	NUM
ejpam-2406	294	13	-	-	SYM
ejpam-2406	294	14	184	184	NUM
ejpam-2406	294	15	180	180	NUM
ejpam-2406	294	16	proof	proof	NOUN
ejpam-2406	294	17	.	.	PUNCT
ejpam-2406	295	1	first	first	ADV
ejpam-2406	295	2	we	we	PRON
ejpam-2406	295	3	show	show	VERB
ejpam-2406	295	4	that	that	SCONJ
ejpam-2406	295	5	(	(	PUNCT
ejpam-2406	295	6	q	q	NOUN
ejpam-2406	295	7	:	:	PUNCT
ejpam-2406	295	8	n	n	CCONJ
ejpam-2406	295	9	)	)	PUNCT
ejpam-2406	295	10	is	be	AUX
ejpam-2406	295	11	a	a	DET
ejpam-2406	295	12	primary	primary	ADJ
ejpam-2406	295	13	element	element	NOUN
ejpam-2406	295	14	.	.	PUNCT
ejpam-2406	296	1	let	let	VERB
ejpam-2406	296	2	a	a	DET
ejpam-2406	296	3	,	,	PUNCT
ejpam-2406	296	4	b	b	PROPN
ejpam-2406	296	5	∈	∈	PROPN
ejpam-2406	296	6	l	l	NOUN
ejpam-2406	296	7	,	,	PUNCT
ejpam-2406	296	8	ab	ab	PROPN
ejpam-2406	296	9	¶	¶	PROPN
ejpam-2406	296	10	(	(	PUNCT
ejpam-2406	296	11	q	q	NOUN
ejpam-2406	296	12	:	:	PUNCT
ejpam-2406	296	13	n	n	CCONJ
ejpam-2406	296	14	)	)	PUNCT
ejpam-2406	296	15	and	and	CCONJ
ejpam-2406	296	16	suppose	suppose	VERB
ejpam-2406	296	17	a	a	DET
ejpam-2406	296	18	6¶	6¶	NUM
ejpam-2406	296	19	(	(	PUNCT
ejpam-2406	296	20	q	q	NOUN
ejpam-2406	296	21	:	:	PUNCT
ejpam-2406	296	22	n	n	CCONJ
ejpam-2406	296	23	)	)	PUNCT
ejpam-2406	296	24	.	.	PUNCT
ejpam-2406	297	1	also	also	ADV
ejpam-2406	297	2	as	as	SCONJ
ejpam-2406	297	3	ab	ab	PROPN
ejpam-2406	297	4	¶	¶	PROPN
ejpam-2406	297	5	(	(	PUNCT
ejpam-2406	297	6	q	q	NOUN
ejpam-2406	297	7	:	:	PUNCT
ejpam-2406	297	8	n	n	CCONJ
ejpam-2406	297	9	)	)	PUNCT
ejpam-2406	297	10	,	,	PUNCT
ejpam-2406	297	11	abn	abn	NOUN
ejpam-2406	297	12	¶q	¶q	NOUN
ejpam-2406	297	13	with	with	ADP
ejpam-2406	297	14	an	an	DET
ejpam-2406	297	15	6¶q	6¶q	NOUN
ejpam-2406	297	16	and	and	CCONJ
ejpam-2406	297	17	q	q	NOUN
ejpam-2406	297	18	is	be	AUX
ejpam-2406	297	19	a	a	DET
ejpam-2406	297	20	primary	primary	ADJ
ejpam-2406	297	21	element	element	NOUN
ejpam-2406	297	22	implies	imply	VERB
ejpam-2406	297	23	that	that	SCONJ
ejpam-2406	298	1	bn	bn	PROPN
ejpam-2406	298	2	¶	¶	INTJ
ejpam-2406	298	3	(	(	PUNCT
ejpam-2406	298	4	q	q	NOUN
ejpam-2406	298	5	:	:	PUNCT
ejpam-2406	298	6	i	i	PRON
ejpam-2406	298	7	m	m	VERB
ejpam-2406	298	8	)	)	PUNCT
ejpam-2406	298	9	for	for	ADP
ejpam-2406	298	10	some	some	DET
ejpam-2406	298	11	integer	integer	NOUN
ejpam-2406	298	12	n.	n.	NOUN
ejpam-2406	298	13	but	but	CCONJ
ejpam-2406	298	14	bn	bn	INTJ
ejpam-2406	298	15	i	i	NOUN
ejpam-2406	298	16	m	m	VERB
ejpam-2406	298	17	¶q	¶q	NOUN
ejpam-2406	298	18	implies	imply	VERB
ejpam-2406	298	19	bnn	bnn	PROPN
ejpam-2406	298	20	¶q	¶q	PROPN
ejpam-2406	298	21	and	and	CCONJ
ejpam-2406	298	22	we	we	PRON
ejpam-2406	298	23	have	have	VERB
ejpam-2406	298	24	b	b	NUM
ejpam-2406	298	25	¶	¶	NUM
ejpam-2406	298	26	p	p	NOUN
ejpam-2406	298	27	(	(	PUNCT
ejpam-2406	298	28	q	q	NOUN
ejpam-2406	298	29	:	:	PUNCT
ejpam-2406	298	30	n	n	CCONJ
ejpam-2406	298	31	)	)	PUNCT
ejpam-2406	298	32	.	.	PUNCT
ejpam-2406	299	1	therefore	therefore	ADV
ejpam-2406	299	2	,	,	PUNCT
ejpam-2406	299	3	(	(	PUNCT
ejpam-2406	299	4	q	q	NOUN
ejpam-2406	299	5	:	:	PUNCT
ejpam-2406	299	6	n	n	CCONJ
ejpam-2406	299	7	)	)	PUNCT
ejpam-2406	299	8	is	be	AUX
ejpam-2406	299	9	a	a	DET
ejpam-2406	299	10	primary	primary	ADJ
ejpam-2406	299	11	element	element	NOUN
ejpam-2406	299	12	of	of	ADP
ejpam-2406	299	13	l.	l.	PROPN
ejpam-2406	299	14	now	now	ADV
ejpam-2406	299	15	since	since	SCONJ
ejpam-2406	299	16	n	n	PROPN
ejpam-2406	299	17	6¶q	6¶q	NUM
ejpam-2406	299	18	,	,	PUNCT
ejpam-2406	299	19	there	there	PRON
ejpam-2406	299	20	exists	exist	VERB
ejpam-2406	299	21	a¶	a¶	PRON
ejpam-2406	299	22	i	i	PRON
ejpam-2406	299	23	m	m	VERB
ejpam-2406	299	24	and	and	CCONJ
ejpam-2406	299	25	a¶	a¶	X
ejpam-2406	299	26	n	n	PRON
ejpam-2406	299	27	such	such	ADJ
ejpam-2406	299	28	that	that	SCONJ
ejpam-2406	299	29	a	a	DET
ejpam-2406	299	30	6¶q	6¶q	NOUN
ejpam-2406	299	31	.	.	PUNCT
ejpam-2406	300	1	let	let	VERB
ejpam-2406	300	2	a	a	DET
ejpam-2406	300	3	¶	¶	PROPN
ejpam-2406	300	4	p	p	NOUN
ejpam-2406	300	5	(	(	PUNCT
ejpam-2406	300	6	q	q	NOUN
ejpam-2406	300	7	:	:	PUNCT
ejpam-2406	300	8	n	n	CCONJ
ejpam-2406	300	9	)	)	PUNCT
ejpam-2406	300	10	.	.	PUNCT
ejpam-2406	301	1	then	then	ADV
ejpam-2406	301	2	ann	ann	PROPN
ejpam-2406	301	3	¶q	¶q	PROPN
ejpam-2406	301	4	and	and	CCONJ
ejpam-2406	301	5	ana¶q	ana¶q	NOUN
ejpam-2406	301	6	.	.	PUNCT
ejpam-2406	302	1	but	but	CCONJ
ejpam-2406	302	2	a	a	DET
ejpam-2406	302	3	6¶q	6¶q	NOUN
ejpam-2406	302	4	and	and	CCONJ
ejpam-2406	302	5	q	q	NOUN
ejpam-2406	302	6	is	be	AUX
ejpam-2406	302	7	primary	primary	ADJ
ejpam-2406	302	8	implies	imply	VERB
ejpam-2406	302	9	that	that	SCONJ
ejpam-2406	302	10	(	(	PUNCT
ejpam-2406	302	11	an)k	an)k	PROPN
ejpam-2406	302	12	=	=	PRON
ejpam-2406	302	13	am	be	AUX
ejpam-2406	302	14	¶	¶	NOUN
ejpam-2406	302	15	(	(	PUNCT
ejpam-2406	302	16	q	q	NOUN
ejpam-2406	302	17	:	:	PUNCT
ejpam-2406	302	18	i	i	PRON
ejpam-2406	302	19	m	m	VERB
ejpam-2406	302	20	)	)	PUNCT
ejpam-2406	302	21	for	for	ADP
ejpam-2406	302	22	some	some	DET
ejpam-2406	302	23	integer	integer	NOUN
ejpam-2406	302	24	m.	m.	NOUN
ejpam-2406	302	25	that	that	PRON
ejpam-2406	302	26	is	be	AUX
ejpam-2406	302	27	a	a	DET
ejpam-2406	302	28	¶	¶	PROPN
ejpam-2406	302	29	p	p	NOUN
ejpam-2406	302	30	(	(	PUNCT
ejpam-2406	302	31	q	q	NOUN
ejpam-2406	302	32	:	:	PUNCT
ejpam-2406	302	33	i	i	PRON
ejpam-2406	302	34	m	m	VERB
ejpam-2406	302	35	)	)	PUNCT
ejpam-2406	303	1	=	=	SYM
ejpam-2406	304	1	p	p	NOUN
ejpam-2406	304	2	and	and	CCONJ
ejpam-2406	304	3	p	p	X
ejpam-2406	304	4	(	(	PUNCT
ejpam-2406	304	5	q	q	NOUN
ejpam-2406	304	6	:	:	PUNCT
ejpam-2406	304	7	n	n	NUM
ejpam-2406	304	8	)	)	PUNCT
ejpam-2406	304	9	¶	¶	PROPN
ejpam-2406	304	10	p.	p.	NOUN
ejpam-2406	305	1	conversely	conversely	ADV
ejpam-2406	305	2	,	,	PUNCT
ejpam-2406	305	3	let	let	VERB
ejpam-2406	305	4	a	a	DET
ejpam-2406	305	5	¶	¶	PROPN
ejpam-2406	305	6	p	p	NOUN
ejpam-2406	305	7	(	(	PUNCT
ejpam-2406	305	8	q	q	NOUN
ejpam-2406	305	9	:	:	PUNCT
ejpam-2406	305	10	i	i	PRON
ejpam-2406	305	11	m	m	VERB
ejpam-2406	305	12	)	)	PUNCT
ejpam-2406	306	1	=	=	SYM
ejpam-2406	307	1	p.	p.	NOUN
ejpam-2406	307	2	hence	hence	ADV
ejpam-2406	307	3	,	,	PUNCT
ejpam-2406	307	4	an	an	DET
ejpam-2406	307	5	i	i	NOUN
ejpam-2406	307	6	m	m	PROPN
ejpam-2406	307	7	¶	¶	NOUN
ejpam-2406	307	8	q	q	NOUN
ejpam-2406	307	9	for	for	ADP
ejpam-2406	307	10	some	some	DET
ejpam-2406	307	11	integern	integern	NOUN
ejpam-2406	307	12	.	.	PUNCT
ejpam-2406	308	1	so	so	ADV
ejpam-2406	308	2	ann	ann	PROPN
ejpam-2406	308	3	¶	¶	PROPN
ejpam-2406	308	4	q	q	PROPN
ejpam-2406	308	5	for	for	ADP
ejpam-2406	308	6	some	some	DET
ejpam-2406	308	7	integer	integer	NOUN
ejpam-2406	308	8	n.	n.	NOUN
ejpam-2406	308	9	thus	thus	ADV
ejpam-2406	308	10	an	an	DET
ejpam-2406	308	11	¶	¶	NOUN
ejpam-2406	308	12	(	(	PUNCT
ejpam-2406	308	13	q	q	NOUN
ejpam-2406	308	14	:	:	PUNCT
ejpam-2406	308	15	n	n	CCONJ
ejpam-2406	308	16	)	)	PUNCT
ejpam-2406	308	17	and	and	CCONJ
ejpam-2406	308	18	a	a	DET
ejpam-2406	308	19	¶	¶	NOUN
ejpam-2406	308	20	p	p	NOUN
ejpam-2406	308	21	(	(	PUNCT
ejpam-2406	308	22	q	q	NOUN
ejpam-2406	308	23	:	:	PUNCT
ejpam-2406	308	24	n	n	CCONJ
ejpam-2406	308	25	)	)	PUNCT
ejpam-2406	308	26	.	.	PUNCT
ejpam-2406	309	1	this	this	PRON
ejpam-2406	309	2	shows	show	VERB
ejpam-2406	309	3	that	that	SCONJ
ejpam-2406	309	4	p	p	PROPN
ejpam-2406	309	5	¶	¶	PROPN
ejpam-2406	309	6	p	p	NOUN
ejpam-2406	309	7	(	(	PUNCT
ejpam-2406	309	8	q	q	NOUN
ejpam-2406	309	9	:	:	PUNCT
ejpam-2406	309	10	n	n	CCONJ
ejpam-2406	309	11	)	)	PUNCT
ejpam-2406	309	12	and	and	CCONJ
ejpam-2406	309	13	we	we	PRON
ejpam-2406	309	14	have	have	VERB
ejpam-2406	309	15	p	p	NOUN
ejpam-2406	309	16	(	(	PUNCT
ejpam-2406	309	17	q	q	NOUN
ejpam-2406	309	18	:	:	PUNCT
ejpam-2406	309	19	n	n	X
ejpam-2406	309	20	)	)	PUNCT
ejpam-2406	309	21	=	=	VERB
ejpam-2406	310	1	p.	p.	NOUN
ejpam-2406	310	2	therefore	therefore	ADV
ejpam-2406	310	3	,	,	PUNCT
ejpam-2406	310	4	(	(	PUNCT
ejpam-2406	310	5	q	q	NOUN
ejpam-2406	310	6	:	:	PUNCT
ejpam-2406	310	7	n	n	CCONJ
ejpam-2406	310	8	)	)	PUNCT
ejpam-2406	310	9	is	be	AUX
ejpam-2406	310	10	a	a	DET
ejpam-2406	310	11	p	p	NOUN
ejpam-2406	310	12	-	-	PUNCT
ejpam-2406	310	13	primary	primary	ADJ
ejpam-2406	310	14	element	element	NOUN
ejpam-2406	310	15	.	.	PUNCT
ejpam-2406	311	1	we	we	PRON
ejpam-2406	311	2	now	now	ADV
ejpam-2406	311	3	establish	establish	VERB
ejpam-2406	311	4	the	the	DET
ejpam-2406	311	5	characterization	characterization	NOUN
ejpam-2406	311	6	of	of	ADP
ejpam-2406	311	7	an	an	DET
ejpam-2406	311	8	associated	associated	ADJ
ejpam-2406	311	9	prime	prime	NOUN
ejpam-2406	311	10	of	of	ADP
ejpam-2406	311	11	an	an	DET
ejpam-2406	311	12	element	element	NOUN
ejpam-2406	311	13	of	of	ADP
ejpam-2406	311	14	a	a	DET
ejpam-2406	311	15	lattice	lattice	NOUN
ejpam-2406	311	16	module	module	NOUN
ejpam-2406	311	17	having	have	VERB
ejpam-2406	311	18	a	a	DET
ejpam-2406	311	19	primary	primary	ADJ
ejpam-2406	311	20	decomposition	decomposition	NOUN
ejpam-2406	311	21	.	.	PUNCT
ejpam-2406	312	1	theorem	theorem	NOUN
ejpam-2406	312	2	9	9	NUM
ejpam-2406	312	3	.	.	PUNCT
ejpam-2406	313	1	let	let	VERB
ejpam-2406	313	2	n	n	PRON
ejpam-2406	313	3	6=	6=	NUM
ejpam-2406	314	1	i	i	PRON
ejpam-2406	314	2	m	m	AUX
ejpam-2406	314	3	be	be	VERB
ejpam-2406	314	4	an	an	DET
ejpam-2406	314	5	element	element	NOUN
ejpam-2406	314	6	of	of	ADP
ejpam-2406	314	7	a	a	DET
ejpam-2406	314	8	lattice	lattice	NOUN
ejpam-2406	314	9	module	module	NOUN
ejpam-2406	314	10	m	m	PROPN
ejpam-2406	314	11	and	and	CCONJ
ejpam-2406	314	12	assume	assume	VERB
ejpam-2406	314	13	that	that	SCONJ
ejpam-2406	314	14	n	n	PRON
ejpam-2406	314	15	has	have	VERB
ejpam-2406	314	16	a	a	DET
ejpam-2406	314	17	primary	primary	ADJ
ejpam-2406	314	18	decomposition	decomposition	NOUN
ejpam-2406	314	19	.	.	PUNCT
ejpam-2406	315	1	let	let	VERB
ejpam-2406	315	2	n	n	PRON
ejpam-2406	315	3	=	=	PROPN
ejpam-2406	315	4	q1	q1	PROPN
ejpam-2406	315	5	∧q2	∧q2	VERB
ejpam-2406	315	6	∧	∧	PROPN
ejpam-2406	315	7	·	·	PUNCT
ejpam-2406	315	8	·	·	PUNCT
ejpam-2406	315	9	·	·	PUNCT
ejpam-2406	316	1	∧qk	∧qk	NOUN
ejpam-2406	316	2	be	be	AUX
ejpam-2406	316	3	a	a	DET
ejpam-2406	316	4	reduced	reduce	VERB
ejpam-2406	316	5	primary	primary	ADJ
ejpam-2406	316	6	decomposition	decomposition	NOUN
ejpam-2406	316	7	of	of	ADP
ejpam-2406	316	8	n	n	PROPN
ejpam-2406	316	9	and	and	CCONJ
ejpam-2406	316	10	p	p	NOUN
ejpam-2406	316	11	be	be	AUX
ejpam-2406	316	12	prime	prime	ADJ
ejpam-2406	316	13	element	element	NOUN
ejpam-2406	316	14	of	of	ADP
ejpam-2406	316	15	l.	l.	PROPN
ejpam-2406	316	16	then	then	ADV
ejpam-2406	316	17	following	follow	VERB
ejpam-2406	316	18	statements	statement	NOUN
ejpam-2406	316	19	are	be	AUX
ejpam-2406	316	20	equivalent	equivalent	ADJ
ejpam-2406	316	21	,	,	PUNCT
ejpam-2406	316	22	(	(	PUNCT
ejpam-2406	316	23	i	i	NOUN
ejpam-2406	316	24	)	)	PUNCT
ejpam-2406	317	1	p	p	X
ejpam-2406	318	1	=	=	PUNCT
ejpam-2406	318	2	p	p	X
ejpam-2406	318	3	q	q	X
ejpam-2406	319	1	i	i	NOUN
ejpam-2406	319	2	for	for	ADP
ejpam-2406	319	3	some	some	DET
ejpam-2406	319	4	i	i	PROPN
ejpam-2406	319	5	(	(	PUNCT
ejpam-2406	319	6	ii	ii	PROPN
ejpam-2406	319	7	)	)	PUNCT
ejpam-2406	319	8	(	(	PUNCT
ejpam-2406	319	9	n	n	X
ejpam-2406	319	10	:	:	PUNCT
ejpam-2406	319	11	x	x	X
ejpam-2406	319	12	)	)	PUNCT
ejpam-2406	319	13	is	be	AUX
ejpam-2406	319	14	a	a	DET
ejpam-2406	319	15	p	p	NOUN
ejpam-2406	319	16	-	-	PUNCT
ejpam-2406	319	17	primary	primary	ADJ
ejpam-2406	319	18	element	element	NOUN
ejpam-2406	319	19	of	of	ADP
ejpam-2406	319	20	l	l	NOUN
ejpam-2406	319	21	for	for	ADP
ejpam-2406	319	22	some	some	PRON
ejpam-2406	319	23	x	x	SYM
ejpam-2406	319	24	6¶	6¶	NUM
ejpam-2406	319	25	n.	n.	NOUN
ejpam-2406	319	26	proof	proof	NOUN
ejpam-2406	319	27	.	.	PUNCT
ejpam-2406	320	1	(	(	PUNCT
ejpam-2406	320	2	i)⇒	i)⇒	PROPN
ejpam-2406	320	3	(	(	PUNCT
ejpam-2406	320	4	ii	ii	NOUN
ejpam-2406	320	5	)	)	PUNCT
ejpam-2406	320	6	let	let	VERB
ejpam-2406	320	7	n	n	NOUN
ejpam-2406	320	8	=	=	PROPN
ejpam-2406	320	9	q1	q1	PROPN
ejpam-2406	320	10	∧	∧	PROPN
ejpam-2406	320	11	q2	q2	PROPN
ejpam-2406	320	12	∧	∧	PROPN
ejpam-2406	320	13	·	·	PUNCT
ejpam-2406	320	14	·	·	PUNCT
ejpam-2406	320	15	·	·	PUNCT
ejpam-2406	321	1	∧	∧	NOUN
ejpam-2406	321	2	qk	qk	PART
ejpam-2406	321	3	be	be	AUX
ejpam-2406	321	4	a	a	DET
ejpam-2406	321	5	reduced	reduce	VERB
ejpam-2406	321	6	primary	primary	ADJ
ejpam-2406	321	7	decomposition	decomposition	NOUN
ejpam-2406	321	8	of	of	ADP
ejpam-2406	321	9	n.	n.	PROPN
ejpam-2406	321	10	first	first	ADV
ejpam-2406	321	11	suppose	suppose	VERB
ejpam-2406	321	12	that	that	SCONJ
ejpam-2406	321	13	,	,	PUNCT
ejpam-2406	321	14	p	p	X
ejpam-2406	321	15	=	=	NOUN
ejpam-2406	321	16	p	p	X
ejpam-2406	321	17	q	q	X
ejpam-2406	321	18	i	i	NOUN
ejpam-2406	321	19	for	for	ADP
ejpam-2406	321	20	some	some	DET
ejpam-2406	321	21	i.	i.	NOUN
ejpam-2406	321	22	without	without	ADP
ejpam-2406	321	23	loss	loss	NOUN
ejpam-2406	321	24	of	of	ADP
ejpam-2406	321	25	generality	generality	NOUN
ejpam-2406	321	26	we	we	PRON
ejpam-2406	321	27	can	can	AUX
ejpam-2406	321	28	assume	assume	VERB
ejpam-2406	321	29	that	that	SCONJ
ejpam-2406	321	30	p	p	NOUN
ejpam-2406	321	31	=	=	X
ejpam-2406	321	32	p	p	X
ejpam-2406	321	33	(	(	PUNCT
ejpam-2406	321	34	q1	q1	PROPN
ejpam-2406	321	35	:	:	PUNCT
ejpam-2406	321	36	i	i	PRON
ejpam-2406	321	37	m	m	VERB
ejpam-2406	321	38	)	)	PUNCT
ejpam-2406	321	39	where	where	SCONJ
ejpam-2406	321	40	pi	pi	NOUN
ejpam-2406	321	41	=	=	PUNCT
ejpam-2406	321	42	p	p	X
ejpam-2406	321	43	(	(	PUNCT
ejpam-2406	321	44	q	q	NOUN
ejpam-2406	322	1	i	i	PRON
ejpam-2406	322	2	:	:	PUNCT
ejpam-2406	322	3	i	i	PRON
ejpam-2406	322	4	m	m	VERB
ejpam-2406	322	5	)	)	PUNCT
ejpam-2406	323	1	i	i	NOUN
ejpam-2406	323	2	=	=	SYM
ejpam-2406	323	3	1,2	1,2	NUM
ejpam-2406	323	4	,	,	PUNCT
ejpam-2406	323	5	.	.	PUNCT
ejpam-2406	323	6	.	.	PUNCT
ejpam-2406	324	1	.	.	PUNCT
ejpam-2406	325	1	,	,	PUNCT
ejpam-2406	325	2	k.	k.	PROPN
ejpam-2406	325	3	we	we	PRON
ejpam-2406	325	4	prove	prove	VERB
ejpam-2406	325	5	that	that	SCONJ
ejpam-2406	325	6	,	,	PUNCT
ejpam-2406	325	7	(	(	PUNCT
ejpam-2406	325	8	n	n	X
ejpam-2406	325	9	:	:	PUNCT
ejpam-2406	325	10	x	x	X
ejpam-2406	325	11	)	)	PUNCT
ejpam-2406	325	12	is	be	AUX
ejpam-2406	325	13	a	a	DET
ejpam-2406	325	14	p	p	NOUN
ejpam-2406	325	15	-	-	PUNCT
ejpam-2406	325	16	primary	primary	ADJ
ejpam-2406	325	17	element	element	NOUN
ejpam-2406	325	18	of	of	ADP
ejpam-2406	325	19	l	l	NOUN
ejpam-2406	325	20	for	for	ADP
ejpam-2406	325	21	some	some	DET
ejpam-2406	325	22	x	x	SYM
ejpam-2406	325	23	6¶	6¶	NUM
ejpam-2406	325	24	n	n	NOUN
ejpam-2406	325	25	.	.	PUNCT
ejpam-2406	326	1	since	since	SCONJ
ejpam-2406	326	2	the	the	DET
ejpam-2406	326	3	decomposition	decomposition	NOUN
ejpam-2406	326	4	is	be	AUX
ejpam-2406	326	5	reduced	reduce	VERB
ejpam-2406	326	6	q	q	PROPN
ejpam-2406	326	7	i	i	PROPN
ejpam-2406	326	8	�	�	PROPN
ejpam-2406	326	9	q1	q1	PROPN
ejpam-2406	326	10	∧	∧	PROPN
ejpam-2406	326	11	q2	q2	PROPN
ejpam-2406	326	12	∧	∧	PROPN
ejpam-2406	326	13	·	·	PUNCT
ejpam-2406	326	14	·	·	PUNCT
ejpam-2406	327	1	·	·	PUNCT
ejpam-2406	327	2	∧	∧	NOUN
ejpam-2406	327	3	q	q	PROPN
ejpam-2406	327	4	i−1	i−1	PROPN
ejpam-2406	327	5	∧	∧	PROPN
ejpam-2406	327	6	q	q	PROPN
ejpam-2406	328	1	i+1	i+1	SYM
ejpam-2406	328	2	∧	∧	PROPN
ejpam-2406	328	3	·	·	PUNCT
ejpam-2406	328	4	·	·	PUNCT
ejpam-2406	328	5	·	·	PUNCT
ejpam-2406	328	6	∧	∧	NOUN
ejpam-2406	328	7	qk	qk	NOUN
ejpam-2406	328	8	for	for	ADP
ejpam-2406	328	9	i	i	PROPN
ejpam-2406	328	10	=	=	NOUN
ejpam-2406	328	11	1,2	1,2	NUM
ejpam-2406	328	12	,	,	PUNCT
ejpam-2406	328	13	.	.	PUNCT
ejpam-2406	328	14	.	.	PUNCT
ejpam-2406	328	15	.	.	PUNCT
ejpam-2406	329	1	,	,	PUNCT
ejpam-2406	329	2	k.	k.	PROPN
ejpam-2406	329	3	in	in	ADP
ejpam-2406	329	4	particular	particular	ADJ
ejpam-2406	329	5	,	,	PUNCT
ejpam-2406	329	6	q1	q1	PROPN
ejpam-2406	329	7	�	�	PROPN
ejpam-2406	329	8	q2	q2	PROPN
ejpam-2406	329	9	∧q3	∧q3	PROPN
ejpam-2406	329	10	∧	∧	PROPN
ejpam-2406	329	11	·	·	PUNCT
ejpam-2406	329	12	·	·	PUNCT
ejpam-2406	329	13	·	·	PUNCT
ejpam-2406	330	1	∧qk	∧qk	NOUN
ejpam-2406	330	2	.	.	PUNCT
ejpam-2406	331	1	so	so	ADV
ejpam-2406	331	2	there	there	PRON
ejpam-2406	331	3	exists	exist	VERB
ejpam-2406	331	4	x	x	PROPN
ejpam-2406	331	5	¶	¶	PROPN
ejpam-2406	331	6	q2	q2	PROPN
ejpam-2406	331	7	∧q3	∧q3	PROPN
ejpam-2406	331	8	∧	∧	PROPN
ejpam-2406	331	9	·	·	PUNCT
ejpam-2406	331	10	·	·	PUNCT
ejpam-2406	331	11	·	·	PUNCT
ejpam-2406	332	1	∧qk	∧qk	VERB
ejpam-2406	332	2	such	such	ADJ
ejpam-2406	332	3	that	that	SCONJ
ejpam-2406	332	4	x	x	X
ejpam-2406	333	1	6¶q1	6¶q1	PROPN
ejpam-2406	333	2	and	and	CCONJ
ejpam-2406	333	3	hence	hence	ADV
ejpam-2406	333	4	x	x	PRON
ejpam-2406	333	5	6¶	6¶	NUM
ejpam-2406	333	6	n	n	CCONJ
ejpam-2406	333	7	=	=	NOUN
ejpam-2406	333	8	q1	q1	NOUN
ejpam-2406	333	9	∧q2	∧q2	VERB
ejpam-2406	333	10	∧	∧	PROPN
ejpam-2406	333	11	·	·	PUNCT
ejpam-2406	333	12	·	·	PUNCT
ejpam-2406	333	13	·	·	PUNCT
ejpam-2406	333	14	∧qk	∧qk	NOUN
ejpam-2406	333	15	.	.	PUNCT
ejpam-2406	334	1	also	also	ADV
ejpam-2406	334	2	(	(	PUNCT
ejpam-2406	334	3	n	n	X
ejpam-2406	334	4	:	:	PUNCT
ejpam-2406	334	5	x	x	X
ejpam-2406	334	6	)	)	PUNCT
ejpam-2406	334	7	=	=	SYM
ejpam-2406	334	8	(	(	PUNCT
ejpam-2406	334	9	q1	q1	PROPN
ejpam-2406	334	10	∧q2	∧q2	VERB
ejpam-2406	334	11	∧	∧	PROPN
ejpam-2406	334	12	·	·	PUNCT
ejpam-2406	334	13	·	·	PUNCT
ejpam-2406	334	14	·	·	PUNCT
ejpam-2406	334	15	∧qk	∧qk	NOUN
ejpam-2406	334	16	)	)	PUNCT
ejpam-2406	334	17	:	:	PUNCT
ejpam-2406	335	1	x	x	X
ejpam-2406	335	2	=	=	SYM
ejpam-2406	335	3	(	(	PUNCT
ejpam-2406	335	4	q1	q1	INTJ
ejpam-2406	335	5	:	:	PUNCT
ejpam-2406	335	6	x	x	X
ejpam-2406	335	7	)	)	PUNCT
ejpam-2406	335	8	∧	∧	PROPN
ejpam-2406	335	9	(	(	PUNCT
ejpam-2406	335	10	q2	q2	NOUN
ejpam-2406	335	11	:	:	PUNCT
ejpam-2406	335	12	x	x	X
ejpam-2406	335	13	)	)	PUNCT
ejpam-2406	335	14	∧	∧	NOUN
ejpam-2406	335	15	·	·	PUNCT
ejpam-2406	335	16	·	·	PUNCT
ejpam-2406	335	17	·	·	PUNCT
ejpam-2406	336	1	∧	∧	NOUN
ejpam-2406	336	2	(	(	PUNCT
ejpam-2406	336	3	qk	qk	NOUN
ejpam-2406	336	4	:	:	PUNCT
ejpam-2406	336	5	x	x	X
ejpam-2406	336	6	)	)	PUNCT
ejpam-2406	336	7	.	.	PUNCT
ejpam-2406	337	1	for	for	ADP
ejpam-2406	337	2	i	i	PRON
ejpam-2406	337	3	=	=	NOUN
ejpam-2406	337	4	2,3	2,3	NUM
ejpam-2406	337	5	,	,	PUNCT
ejpam-2406	337	6	.	.	PUNCT
ejpam-2406	337	7	.	.	PUNCT
ejpam-2406	337	8	.	.	PUNCT
ejpam-2406	338	1	,	,	PUNCT
ejpam-2406	338	2	k	k	PROPN
ejpam-2406	338	3	we	we	PRON
ejpam-2406	338	4	show	show	VERB
ejpam-2406	338	5	that	that	SCONJ
ejpam-2406	338	6	(	(	PUNCT
ejpam-2406	338	7	q	q	NOUN
ejpam-2406	338	8	i	i	PRON
ejpam-2406	338	9	:	:	PUNCT
ejpam-2406	338	10	x	x	X
ejpam-2406	338	11	)	)	PUNCT
ejpam-2406	339	1	=	=	SYM
ejpam-2406	339	2	1	1	X
ejpam-2406	339	3	.	.	PUNCT
ejpam-2406	340	1	since	since	SCONJ
ejpam-2406	340	2	x	x	PROPN
ejpam-2406	340	3	¶	¶	PROPN
ejpam-2406	340	4	q2	q2	PROPN
ejpam-2406	340	5	∧q3	∧q3	PROPN
ejpam-2406	340	6	·	·	PUNCT
ejpam-2406	340	7	·	·	PUNCT
ejpam-2406	340	8	·	·	PUNCT
ejpam-2406	340	9	∧qk	∧qk	NOUN
ejpam-2406	340	10	,	,	PUNCT
ejpam-2406	340	11	we	we	PRON
ejpam-2406	340	12	have	have	VERB
ejpam-2406	340	13	x	x	X
ejpam-2406	340	14	¶	¶	PROPN
ejpam-2406	340	15	q	q	PROPN
ejpam-2406	340	16	i	i	PROPN
ejpam-2406	340	17	for	for	ADP
ejpam-2406	340	18	all	all	DET
ejpam-2406	340	19	i	i	PRON
ejpam-2406	340	20	=	=	NOUN
ejpam-2406	340	21	2	2	NUM
ejpam-2406	340	22	,	,	PUNCT
ejpam-2406	340	23	.	.	PUNCT
ejpam-2406	340	24	.	.	PUNCT
ejpam-2406	341	1	.	.	PUNCT
ejpam-2406	342	1	,	,	PUNCT
ejpam-2406	342	2	k.	k.	PROPN
ejpam-2406	342	3	then	then	ADV
ejpam-2406	342	4	ax	ax	VERB
ejpam-2406	342	5	¶	¶	PROPN
ejpam-2406	342	6	q	q	PROPN
ejpam-2406	342	7	i	i	PROPN
ejpam-2406	342	8	for	for	ADP
ejpam-2406	342	9	all	all	DET
ejpam-2406	342	10	a	a	DET
ejpam-2406	342	11	∈	∈	ADJ
ejpam-2406	342	12	l	l	NOUN
ejpam-2406	342	13	and	and	CCONJ
ejpam-2406	342	14	for	for	ADP
ejpam-2406	342	15	all	all	DET
ejpam-2406	342	16	i	i	NOUN
ejpam-2406	342	17	=	=	NOUN
ejpam-2406	342	18	2,3	2,3	NUM
ejpam-2406	342	19	,	,	PUNCT
ejpam-2406	342	20	.	.	PUNCT
ejpam-2406	342	21	.	.	PUNCT
ejpam-2406	342	22	.	.	PUNCT
ejpam-2406	343	1	,	,	PUNCT
ejpam-2406	343	2	k.	k.	PROPN
ejpam-2406	344	1	that	that	PRON
ejpam-2406	344	2	is	be	AUX
ejpam-2406	344	3	a	a	DET
ejpam-2406	344	4	¶	¶	NOUN
ejpam-2406	344	5	(	(	PUNCT
ejpam-2406	344	6	q	q	NOUN
ejpam-2406	344	7	i	i	PRON
ejpam-2406	344	8	:	:	PUNCT
ejpam-2406	344	9	x	x	X
ejpam-2406	344	10	)	)	PUNCT
ejpam-2406	344	11	for	for	ADP
ejpam-2406	344	12	all	all	DET
ejpam-2406	344	13	i	i	PRON
ejpam-2406	344	14	=	=	NOUN
ejpam-2406	344	15	2,3	2,3	NUM
ejpam-2406	344	16	,	,	PUNCT
ejpam-2406	344	17	.	.	PUNCT
ejpam-2406	344	18	.	.	PUNCT
ejpam-2406	345	1	.	.	PUNCT
ejpam-2406	346	1	,	,	PUNCT
ejpam-2406	346	2	k.	k.	PROPN
ejpam-2406	347	1	so	so	ADV
ejpam-2406	347	2	1	1	NUM
ejpam-2406	347	3	¶	¶	NOUN
ejpam-2406	347	4	(	(	PUNCT
ejpam-2406	347	5	q	q	NOUN
ejpam-2406	347	6	i	i	PRON
ejpam-2406	347	7	:	:	PUNCT
ejpam-2406	347	8	x	x	X
ejpam-2406	347	9	)	)	PUNCT
ejpam-2406	347	10	.	.	PUNCT
ejpam-2406	348	1	but	but	CCONJ
ejpam-2406	348	2	(	(	PUNCT
ejpam-2406	348	3	q	q	NOUN
ejpam-2406	348	4	i	i	PRON
ejpam-2406	348	5	:	:	PUNCT
ejpam-2406	348	6	x	x	X
ejpam-2406	348	7	)	)	PUNCT
ejpam-2406	348	8	¶	¶	NOUN
ejpam-2406	348	9	1	1	NUM
ejpam-2406	348	10	implies	imply	VERB
ejpam-2406	348	11	(	(	PUNCT
ejpam-2406	348	12	q	q	NOUN
ejpam-2406	348	13	i	i	PRON
ejpam-2406	348	14	:	:	PUNCT
ejpam-2406	348	15	x	x	X
ejpam-2406	348	16	)	)	PUNCT
ejpam-2406	348	17	=	=	SYM
ejpam-2406	348	18	1	1	NUM
ejpam-2406	348	19	for	for	ADP
ejpam-2406	348	20	i	i	PRON
ejpam-2406	348	21	=	=	NOUN
ejpam-2406	348	22	2,3	2,3	NUM
ejpam-2406	348	23	,	,	PUNCT
ejpam-2406	348	24	.	.	PUNCT
ejpam-2406	348	25	.	.	PUNCT
ejpam-2406	348	26	.	.	PUNCT
ejpam-2406	349	1	,	,	PUNCT
ejpam-2406	349	2	k.	k.	PROPN
ejpam-2406	349	3	hence	hence	ADV
ejpam-2406	349	4	,	,	PUNCT
ejpam-2406	349	5	(	(	PUNCT
ejpam-2406	349	6	n	n	CCONJ
ejpam-2406	349	7	:	:	PUNCT
ejpam-2406	349	8	x	x	X
ejpam-2406	349	9	)	)	PUNCT
ejpam-2406	349	10	=	=	SYM
ejpam-2406	349	11	(	(	PUNCT
ejpam-2406	349	12	q1	q1	INTJ
ejpam-2406	349	13	:	:	PUNCT
ejpam-2406	349	14	x	x	X
ejpam-2406	349	15	)	)	PUNCT
ejpam-2406	349	16	∧1∧	∧1∧	ADP
ejpam-2406	349	17	·	·	PUNCT
ejpam-2406	349	18	·	·	PUNCT
ejpam-2406	349	19	·	·	PUNCT
ejpam-2406	349	20	∧1=	∧1=	X
ejpam-2406	349	21	(	(	PUNCT
ejpam-2406	349	22	q1	q1	NOUN
ejpam-2406	349	23	:	:	PUNCT
ejpam-2406	349	24	x	x	X
ejpam-2406	349	25	)	)	PUNCT
ejpam-2406	349	26	.	.	PUNCT
ejpam-2406	350	1	so	so	ADV
ejpam-2406	350	2	by	by	ADP
ejpam-2406	350	3	the	the	DET
ejpam-2406	350	4	above	above	ADJ
ejpam-2406	350	5	result	result	NOUN
ejpam-2406	350	6	,	,	PUNCT
ejpam-2406	350	7	(	(	PUNCT
ejpam-2406	350	8	q1	q1	INTJ
ejpam-2406	350	9	:	:	PUNCT
ejpam-2406	350	10	x	x	X
ejpam-2406	350	11	)	)	PUNCT
ejpam-2406	350	12	is	be	AUX
ejpam-2406	350	13	p	p	ADJ
ejpam-2406	350	14	-	-	PUNCT
ejpam-2406	350	15	primary	primary	ADJ
ejpam-2406	350	16	element	element	NOUN
ejpam-2406	350	17	implies	imply	VERB
ejpam-2406	350	18	(	(	PUNCT
ejpam-2406	350	19	n	n	X
ejpam-2406	350	20	:	:	PUNCT
ejpam-2406	350	21	x	x	X
ejpam-2406	350	22	)	)	PUNCT
ejpam-2406	350	23	is	be	AUX
ejpam-2406	350	24	a	a	DET
ejpam-2406	350	25	p	p	NOUN
ejpam-2406	350	26	-	-	PUNCT
ejpam-2406	350	27	primary	primary	ADJ
ejpam-2406	350	28	element	element	NOUN
ejpam-2406	350	29	of	of	ADP
ejpam-2406	350	30	l	l	NOUN
ejpam-2406	350	31	where	where	SCONJ
ejpam-2406	350	32	x	x	PUNCT
ejpam-2406	350	33	6¶	6¶	NUM
ejpam-2406	350	34	n	n	X
ejpam-2406	350	35	.	.	PUNCT
ejpam-2406	351	1	(	(	PUNCT
ejpam-2406	351	2	ii)⇒	ii)⇒	PROPN
ejpam-2406	351	3	(	(	PUNCT
ejpam-2406	351	4	i	i	NOUN
ejpam-2406	351	5	)	)	PUNCT
ejpam-2406	351	6	assume	assume	VERB
ejpam-2406	351	7	that	that	SCONJ
ejpam-2406	351	8	(	(	PUNCT
ejpam-2406	351	9	n	n	X
ejpam-2406	351	10	:	:	PUNCT
ejpam-2406	351	11	x	x	X
ejpam-2406	351	12	)	)	PUNCT
ejpam-2406	351	13	is	be	AUX
ejpam-2406	351	14	a	a	DET
ejpam-2406	351	15	p	p	NOUN
ejpam-2406	351	16	-	-	PUNCT
ejpam-2406	351	17	primary	primary	ADJ
ejpam-2406	351	18	element	element	NOUN
ejpam-2406	351	19	of	of	ADP
ejpam-2406	351	20	l	l	NOUN
ejpam-2406	351	21	for	for	ADP
ejpam-2406	351	22	some	some	DET
ejpam-2406	351	23	x	x	SYM
ejpam-2406	351	24	6¶	6¶	NUM
ejpam-2406	351	25	n	n	NOUN
ejpam-2406	351	26	,	,	PUNCT
ejpam-2406	351	27	x	x	PUNCT
ejpam-2406	351	28	∈	∈	NOUN
ejpam-2406	351	29	m	m	VERB
ejpam-2406	351	30	.	.	PUNCT
ejpam-2406	352	1	we	we	PRON
ejpam-2406	352	2	prove	prove	VERB
ejpam-2406	352	3	that	that	SCONJ
ejpam-2406	352	4	p	p	NOUN
ejpam-2406	352	5	q	q	X
ejpam-2406	353	1	i	i	PRON
ejpam-2406	353	2	=	=	PUNCT
ejpam-2406	353	3	p	p	NOUN
ejpam-2406	353	4	for	for	ADP
ejpam-2406	353	5	some	some	DET
ejpam-2406	353	6	i.	i.	NOUN
ejpam-2406	353	7	we	we	PRON
ejpam-2406	353	8	have	have	VERB
ejpam-2406	353	9	,	,	PUNCT
ejpam-2406	353	10	p	p	X
ejpam-2406	353	11	=	=	PUNCT
ejpam-2406	353	12	æ	æ	X
ejpam-2406	353	13	(	(	PUNCT
ejpam-2406	353	14	n	n	NOUN
ejpam-2406	353	15	:	:	PUNCT
ejpam-2406	353	16	x	x	X
ejpam-2406	353	17	)	)	PUNCT
ejpam-2406	354	1	=	=	PUNCT
ejpam-2406	354	2	æ	æ	X
ejpam-2406	355	1	[	[	X
ejpam-2406	355	2	(	(	PUNCT
ejpam-2406	355	3	q1	q1	PROPN
ejpam-2406	355	4	∧q2	∧q2	VERB
ejpam-2406	355	5	∧	∧	PROPN
ejpam-2406	355	6	·	·	PUNCT
ejpam-2406	355	7	·	·	PUNCT
ejpam-2406	355	8	·	·	PUNCT
ejpam-2406	355	9	∧qk	∧qk	NOUN
ejpam-2406	355	10	)	)	PUNCT
ejpam-2406	355	11	:	:	PUNCT
ejpam-2406	356	1	x	x	X
ejpam-2406	356	2	]	]	PUNCT
ejpam-2406	357	1	=	=	PUNCT
ejpam-2406	357	2	æ	æ	X
ejpam-2406	357	3	(	(	PUNCT
ejpam-2406	357	4	q1	q1	INTJ
ejpam-2406	357	5	:	:	PUNCT
ejpam-2406	357	6	x	x	X
ejpam-2406	357	7	)	)	PUNCT
ejpam-2406	357	8	∧	∧	PROPN
ejpam-2406	357	9	æ	æ	X
ejpam-2406	357	10	(	(	PUNCT
ejpam-2406	357	11	q2	q2	NOUN
ejpam-2406	357	12	:	:	PUNCT
ejpam-2406	357	13	x	x	X
ejpam-2406	357	14	)	)	PUNCT
ejpam-2406	357	15	∧	∧	NOUN
ejpam-2406	357	16	·	·	PUNCT
ejpam-2406	357	17	·	·	PUNCT
ejpam-2406	357	18	·	·	PUNCT
ejpam-2406	358	1	∧	∧	NOUN
ejpam-2406	358	2	æ	æ	X
ejpam-2406	358	3	(	(	PUNCT
ejpam-2406	358	4	qk	qk	NOUN
ejpam-2406	358	5	:	:	PUNCT
ejpam-2406	358	6	x	x	X
ejpam-2406	358	7	)	)	PUNCT
ejpam-2406	358	8	.	.	PUNCT
ejpam-2406	359	1	we	we	PRON
ejpam-2406	359	2	claim	claim	VERB
ejpam-2406	359	3	that	that	SCONJ
ejpam-2406	359	4	for	for	ADP
ejpam-2406	359	5	each	each	DET
ejpam-2406	359	6	i	i	PRON
ejpam-2406	359	7	,	,	PUNCT
ejpam-2406	359	8	p	p	X
ejpam-2406	359	9	(	(	PUNCT
ejpam-2406	359	10	q	q	NOUN
ejpam-2406	359	11	i	i	PRON
ejpam-2406	359	12	:	:	PUNCT
ejpam-2406	359	13	x	x	X
ejpam-2406	359	14	)	)	PUNCT
ejpam-2406	359	15	=	=	SYM
ejpam-2406	359	16	pi	pi	NOUN
ejpam-2406	359	17	or	or	CCONJ
ejpam-2406	359	18	1	1	NUM
ejpam-2406	359	19	and	and	CCONJ
ejpam-2406	359	20	equal	equal	ADJ
ejpam-2406	359	21	to	to	AUX
ejpam-2406	359	22	pi	pi	VERB
ejpam-2406	359	23	for	for	ADP
ejpam-2406	359	24	at	at	ADV
ejpam-2406	359	25	least	least	ADV
ejpam-2406	359	26	one	one	NUM
ejpam-2406	359	27	i.	i.	NOUN
ejpam-2406	359	28	we	we	PRON
ejpam-2406	359	29	have	have	VERB
ejpam-2406	359	30	,	,	PUNCT
ejpam-2406	359	31	x	x	PROPN
ejpam-2406	359	32	6¶	6¶	NUM
ejpam-2406	359	33	n	n	NOUN
ejpam-2406	359	34	=	=	PROPN
ejpam-2406	359	35	q1	q1	PROPN
ejpam-2406	359	36	∧q2	∧q2	VERB
ejpam-2406	359	37	∧	∧	PROPN
ejpam-2406	359	38	·	·	PUNCT
ejpam-2406	359	39	·	·	PUNCT
ejpam-2406	359	40	·	·	PUNCT
ejpam-2406	360	1	∧qk	∧qk	PROPN
ejpam-2406	360	2	implies	imply	VERB
ejpam-2406	360	3	x	x	X
ejpam-2406	360	4	6¶	6¶	NUM
ejpam-2406	360	5	q	q	NOUN
ejpam-2406	360	6	i	i	PRON
ejpam-2406	360	7	for	for	ADP
ejpam-2406	360	8	at	at	ADV
ejpam-2406	360	9	least	least	ADV
ejpam-2406	360	10	one	one	NUM
ejpam-2406	360	11	i	i	NOUN
ejpam-2406	360	12	(	(	PUNCT
ejpam-2406	360	13	1	1	NUM
ejpam-2406	360	14	¶	¶	NUM
ejpam-2406	360	15	i	i	PRON
ejpam-2406	360	16	¶	¶	PROPN
ejpam-2406	360	17	k	k	PROPN
ejpam-2406	360	18	)	)	PUNCT
ejpam-2406	360	19	.	.	PUNCT
ejpam-2406	361	1	suppose	suppose	VERB
ejpam-2406	361	2	,	,	PUNCT
ejpam-2406	361	3	x	x	PROPN
ejpam-2406	361	4	6¶	6¶	NUM
ejpam-2406	361	5	qr	qr	NOUN
ejpam-2406	361	6	(	(	PUNCT
ejpam-2406	361	7	1	1	NUM
ejpam-2406	361	8	¶	¶	NUM
ejpam-2406	361	9	r	r	NOUN
ejpam-2406	361	10	¶	¶	PROPN
ejpam-2406	361	11	k	k	NOUN
ejpam-2406	361	12	)	)	PUNCT
ejpam-2406	361	13	and	and	CCONJ
ejpam-2406	361	14	x	x	PROPN
ejpam-2406	361	15	¶	¶	PROPN
ejpam-2406	361	16	q1	q1	PROPN
ejpam-2406	361	17	∧	∧	PROPN
ejpam-2406	361	18	q2	q2	PROPN
ejpam-2406	361	19	∧	∧	PROPN
ejpam-2406	361	20	·	·	PUNCT
ejpam-2406	361	21	·	·	PUNCT
ejpam-2406	361	22	·	·	PUNCT
ejpam-2406	362	1	∧	∧	NOUN
ejpam-2406	362	2	qr−1	qr−1	PROPN
ejpam-2406	362	3	∧	∧	PROPN
ejpam-2406	362	4	qr+1	qr+1	PROPN
ejpam-2406	362	5	∧	∧	PROPN
ejpam-2406	362	6	.	.	PUNCT
ejpam-2406	362	7	.	.	PUNCT
ejpam-2406	363	1	.qk	.qk	PUNCT
ejpam-2406	364	1	that	that	PRON
ejpam-2406	364	2	is	is	ADV
ejpam-2406	364	3	x	x	X
ejpam-2406	364	4	¶	¶	PROPN
ejpam-2406	364	5	∧q	∧q	PROPN
ejpam-2406	365	1	i	i	PRON
ejpam-2406	365	2	,	,	PUNCT
ejpam-2406	365	3	where	where	SCONJ
ejpam-2406	365	4	(	(	PUNCT
ejpam-2406	365	5	i	i	NOUN
ejpam-2406	365	6	6=	6=	NOUN
ejpam-2406	365	7	r	r	NOUN
ejpam-2406	365	8	)	)	PUNCT
ejpam-2406	365	9	.	.	PUNCT
ejpam-2406	366	1	c.	c.	PROPN
ejpam-2406	366	2	manjarekar	manjarekar	PROPN
ejpam-2406	366	3	,	,	PUNCT
ejpam-2406	366	4	u.	u.	PROPN
ejpam-2406	366	5	kandale	kandale	PROPN
ejpam-2406	366	6	/	/	SYM
ejpam-2406	366	7	eur	eur	PROPN
ejpam-2406	366	8	.	.	PUNCT
ejpam-2406	367	1	j.	j.	PROPN
ejpam-2406	367	2	pure	pure	PROPN
ejpam-2406	367	3	appl	appl	PROPN
ejpam-2406	367	4	.	.	PROPN
ejpam-2406	367	5	math	math	PROPN
ejpam-2406	367	6	,	,	PUNCT
ejpam-2406	367	7	8	8	NUM
ejpam-2406	367	8	(	(	PUNCT
ejpam-2406	367	9	2015	2015	NUM
ejpam-2406	367	10	)	)	PUNCT
ejpam-2406	367	11	,	,	PUNCT
ejpam-2406	367	12	172	172	NUM
ejpam-2406	367	13	-	-	SYM
ejpam-2406	367	14	184	184	NUM
ejpam-2406	367	15	181	181	NUM
ejpam-2406	367	16	let	let	VERB
ejpam-2406	367	17	a	a	DET
ejpam-2406	367	18	¶	¶	NOUN
ejpam-2406	367	19	(	(	PUNCT
ejpam-2406	367	20	q	q	NOUN
ejpam-2406	367	21	i	i	PRON
ejpam-2406	367	22	:	:	PUNCT
ejpam-2406	367	23	x	x	X
ejpam-2406	367	24	)	)	PUNCT
ejpam-2406	367	25	,	,	PUNCT
ejpam-2406	367	26	a	a	DET
ejpam-2406	367	27	∈	∈	PROPN
ejpam-2406	367	28	l.	l.	NOUN
ejpam-2406	367	29	since	since	ADV
ejpam-2406	367	30	,	,	PUNCT
ejpam-2406	367	31	x	x	PROPN
ejpam-2406	367	32	¶	¶	NUM
ejpam-2406	367	33	∧q	∧q	PROPN
ejpam-2406	368	1	i	i	PRON
ejpam-2406	368	2	.	.	PUNCT
ejpam-2406	369	1	we	we	PRON
ejpam-2406	369	2	have	have	VERB
ejpam-2406	369	3	,	,	PUNCT
ejpam-2406	369	4	ax	ax	NOUN
ejpam-2406	369	5	¶	¶	PROPN
ejpam-2406	369	6	q	q	PROPN
ejpam-2406	369	7	i	i	PROPN
ejpam-2406	369	8	for	for	ADP
ejpam-2406	369	9	all	all	DET
ejpam-2406	369	10	i	i	PRON
ejpam-2406	369	11	6=	6=	NOUN
ejpam-2406	369	12	r	r	NOUN
ejpam-2406	369	13	and	and	CCONJ
ejpam-2406	369	14	a	a	DET
ejpam-2406	369	15	∈	∈	PROPN
ejpam-2406	369	16	l.	l.	NOUN
ejpam-2406	369	17	hence	hence	ADV
ejpam-2406	369	18	,	,	PUNCT
ejpam-2406	369	19	a	a	DET
ejpam-2406	369	20	¶	¶	NOUN
ejpam-2406	369	21	p	p	NOUN
ejpam-2406	369	22	(	(	PUNCT
ejpam-2406	369	23	q	q	NOUN
ejpam-2406	369	24	i	i	PRON
ejpam-2406	369	25	:	:	PUNCT
ejpam-2406	369	26	x	x	X
ejpam-2406	369	27	)	)	PUNCT
ejpam-2406	369	28	for	for	ADP
ejpam-2406	369	29	all	all	DET
ejpam-2406	369	30	a	a	DET
ejpam-2406	369	31	∈	∈	PROPN
ejpam-2406	369	32	l.	l.	NOUN
ejpam-2406	369	33	in	in	ADP
ejpam-2406	369	34	particular	particular	ADJ
ejpam-2406	369	35	,	,	PUNCT
ejpam-2406	369	36	1	1	NUM
ejpam-2406	369	37	¶	¶	NOUN
ejpam-2406	369	38	p	p	NOUN
ejpam-2406	369	39	(	(	PUNCT
ejpam-2406	369	40	q	q	NOUN
ejpam-2406	369	41	i	i	PRON
ejpam-2406	369	42	:	:	PUNCT
ejpam-2406	369	43	x	x	X
ejpam-2406	369	44	)	)	PUNCT
ejpam-2406	369	45	for	for	ADP
ejpam-2406	369	46	all	all	DET
ejpam-2406	369	47	i	i	PRON
ejpam-2406	369	48	6=	6=	PROPN
ejpam-2406	369	49	r.	r.	PROPN
ejpam-2406	370	1	but	but	CCONJ
ejpam-2406	370	2	,	,	PUNCT
ejpam-2406	371	1	p	p	X
ejpam-2406	371	2	(	(	PUNCT
ejpam-2406	371	3	q	q	NOUN
ejpam-2406	371	4	i	i	PRON
ejpam-2406	371	5	:	:	PUNCT
ejpam-2406	371	6	x	x	X
ejpam-2406	371	7	)	)	PUNCT
ejpam-2406	371	8	¶	¶	NOUN
ejpam-2406	371	9	1	1	NUM
ejpam-2406	371	10	for	for	ADP
ejpam-2406	371	11	all	all	DET
ejpam-2406	371	12	i	i	PRON
ejpam-2406	371	13	6=	6=	PROPN
ejpam-2406	371	14	r.	r.	PROPN
ejpam-2406	371	15	therefore	therefore	ADV
ejpam-2406	371	16	,	,	PUNCT
ejpam-2406	371	17	p	p	X
ejpam-2406	371	18	(	(	PUNCT
ejpam-2406	371	19	q	q	NOUN
ejpam-2406	371	20	i	i	PRON
ejpam-2406	371	21	:	:	PUNCT
ejpam-2406	371	22	x	x	X
ejpam-2406	371	23	)	)	PUNCT
ejpam-2406	371	24	=	=	SYM
ejpam-2406	371	25	1	1	NUM
ejpam-2406	371	26	for	for	ADP
ejpam-2406	371	27	all	all	DET
ejpam-2406	371	28	i	i	PRON
ejpam-2406	371	29	6=	6=	PROPN
ejpam-2406	371	30	r.	r.	NOUN
ejpam-2406	371	31	for	for	ADP
ejpam-2406	371	32	i	i	PROPN
ejpam-2406	371	33	=	=	SYM
ejpam-2406	371	34	r	r	NOUN
ejpam-2406	371	35	,	,	PUNCT
ejpam-2406	371	36	x	x	PROPN
ejpam-2406	371	37	6¶	6¶	NUM
ejpam-2406	371	38	qr	qr	NOUN
ejpam-2406	371	39	.	.	PUNCT
ejpam-2406	372	1	let	let	VERB
ejpam-2406	372	2	a	a	DET
ejpam-2406	372	3	¶	¶	PROPN
ejpam-2406	372	4	p	p	NOUN
ejpam-2406	372	5	(	(	PUNCT
ejpam-2406	372	6	qr	qr	NOUN
ejpam-2406	372	7	:	:	PUNCT
ejpam-2406	372	8	x	x	X
ejpam-2406	372	9	)	)	PUNCT
ejpam-2406	372	10	.	.	PUNCT
ejpam-2406	373	1	hence	hence	ADV
ejpam-2406	373	2	,	,	PUNCT
ejpam-2406	373	3	anx	anx	PROPN
ejpam-2406	373	4	¶qr	¶qr	PROPN
ejpam-2406	373	5	,	,	PUNCT
ejpam-2406	373	6	for	for	ADP
ejpam-2406	373	7	some	some	DET
ejpam-2406	373	8	positive	positive	ADJ
ejpam-2406	373	9	integer	integer	NOUN
ejpam-2406	373	10	n	n	CCONJ
ejpam-2406	373	11	,	,	PUNCT
ejpam-2406	373	12	where	where	SCONJ
ejpam-2406	373	13	x	x	PROPN
ejpam-2406	373	14	6¶qr	6¶qr	NUM
ejpam-2406	373	15	.	.	PUNCT
ejpam-2406	374	1	as	as	SCONJ
ejpam-2406	374	2	qr	qr	PROPN
ejpam-2406	374	3	is	be	AUX
ejpam-2406	374	4	primary	primary	ADJ
ejpam-2406	374	5	,	,	PUNCT
ejpam-2406	374	6	an	an	DET
ejpam-2406	374	7	¶	¶	PROPN
ejpam-2406	374	8	p	p	NOUN
ejpam-2406	374	9	(	(	PUNCT
ejpam-2406	374	10	qr	qr	INTJ
ejpam-2406	374	11	:	:	PUNCT
ejpam-2406	374	12	i	i	PRON
ejpam-2406	374	13	m	m	VERB
ejpam-2406	374	14	)	)	PUNCT
ejpam-2406	375	1	=	=	NOUN
ejpam-2406	375	2	pr	pr	NOUN
ejpam-2406	375	3	.	.	PUNCT
ejpam-2406	376	1	thus	thus	ADV
ejpam-2406	376	2	,	,	PUNCT
ejpam-2406	376	3	a	a	DET
ejpam-2406	376	4	¶	¶	NOUN
ejpam-2406	376	5	pr	pr	NOUN
ejpam-2406	376	6	,	,	PUNCT
ejpam-2406	376	7	since	since	SCONJ
ejpam-2406	376	8	pr	pr	NOUN
ejpam-2406	376	9	is	be	AUX
ejpam-2406	376	10	prime	prime	ADJ
ejpam-2406	376	11	and	and	CCONJ
ejpam-2406	376	12	we	we	PRON
ejpam-2406	376	13	have	have	VERB
ejpam-2406	376	14	,	,	PUNCT
ejpam-2406	376	15	p	p	X
ejpam-2406	376	16	(	(	PUNCT
ejpam-2406	376	17	qr	qr	NOUN
ejpam-2406	376	18	:	:	PUNCT
ejpam-2406	376	19	x	x	SYM
ejpam-2406	376	20	)	)	PUNCT
ejpam-2406	376	21	¶	¶	INTJ
ejpam-2406	376	22	pr	pr	NOUN
ejpam-2406	376	23	.	.	PUNCT
ejpam-2406	377	1	on	on	ADP
ejpam-2406	377	2	the	the	DET
ejpam-2406	377	3	other	other	ADJ
ejpam-2406	377	4	hand	hand	NOUN
ejpam-2406	377	5	,	,	PUNCT
ejpam-2406	377	6	let	let	VERB
ejpam-2406	377	7	a	a	DET
ejpam-2406	377	8	¶	¶	NOUN
ejpam-2406	377	9	pr	pr	NOUN
ejpam-2406	378	1	=	=	NOUN
ejpam-2406	378	2	p	p	X
ejpam-2406	378	3	qr	qr	NOUN
ejpam-2406	378	4	=	=	SYM
ejpam-2406	378	5	p	p	X
ejpam-2406	378	6	(	(	PUNCT
ejpam-2406	378	7	qr	qr	NOUN
ejpam-2406	378	8	:	:	PUNCT
ejpam-2406	378	9	i	i	PRON
ejpam-2406	378	10	m	m	PROPN
ejpam-2406	378	11	)	)	PUNCT
ejpam-2406	378	12	.	.	PUNCT
ejpam-2406	379	1	hence	hence	ADV
ejpam-2406	379	2	,	,	PUNCT
ejpam-2406	379	3	an	an	DET
ejpam-2406	379	4	¶	¶	PROPN
ejpam-2406	379	5	(	(	PUNCT
ejpam-2406	379	6	qr	qr	NOUN
ejpam-2406	379	7	:	:	PUNCT
ejpam-2406	379	8	i	i	PRON
ejpam-2406	379	9	m	m	VERB
ejpam-2406	379	10	)	)	PUNCT
ejpam-2406	379	11	for	for	ADP
ejpam-2406	379	12	some	some	DET
ejpam-2406	379	13	positive	positive	ADJ
ejpam-2406	379	14	integer	integer	NOUN
ejpam-2406	379	15	n.	n.	NOUN
ejpam-2406	379	16	that	that	PRON
ejpam-2406	379	17	is	be	AUX
ejpam-2406	379	18	an	an	DET
ejpam-2406	379	19	i	i	NOUN
ejpam-2406	379	20	m	m	NOUN
ejpam-2406	379	21	¶	¶	PROPN
ejpam-2406	379	22	qr	qr	NOUN
ejpam-2406	379	23	and	and	CCONJ
ejpam-2406	379	24	therefore	therefore	ADV
ejpam-2406	379	25	,	,	PUNCT
ejpam-2406	379	26	anx	anx	PROPN
ejpam-2406	379	27	¶	¶	PROPN
ejpam-2406	379	28	qr	qr	PROPN
ejpam-2406	379	29	,	,	PUNCT
ejpam-2406	379	30	for	for	ADP
ejpam-2406	379	31	some	some	DET
ejpam-2406	379	32	positive	positive	ADJ
ejpam-2406	379	33	integer	integer	NOUN
ejpam-2406	379	34	n.	n.	NOUN
ejpam-2406	379	35	consequently	consequently	ADV
ejpam-2406	379	36	,	,	PUNCT
ejpam-2406	379	37	an	an	DET
ejpam-2406	379	38	¶	¶	PROPN
ejpam-2406	379	39	(	(	PUNCT
ejpam-2406	379	40	qr	qr	NOUN
ejpam-2406	379	41	:	:	PUNCT
ejpam-2406	379	42	x	x	X
ejpam-2406	379	43	)	)	PUNCT
ejpam-2406	379	44	and	and	CCONJ
ejpam-2406	379	45	hence	hence	ADV
ejpam-2406	379	46	a	a	DET
ejpam-2406	379	47	¶	¶	NOUN
ejpam-2406	379	48	p	p	NOUN
ejpam-2406	379	49	(	(	PUNCT
ejpam-2406	379	50	qr	qr	NOUN
ejpam-2406	379	51	:	:	PUNCT
ejpam-2406	379	52	x	x	X
ejpam-2406	379	53	)	)	PUNCT
ejpam-2406	379	54	.	.	PUNCT
ejpam-2406	380	1	this	this	PRON
ejpam-2406	380	2	gives	give	VERB
ejpam-2406	380	3	pr	pr	NOUN
ejpam-2406	380	4	¶	¶	PROPN
ejpam-2406	380	5	p	p	NOUN
ejpam-2406	380	6	(	(	PUNCT
ejpam-2406	380	7	qr	qr	NOUN
ejpam-2406	380	8	:	:	PUNCT
ejpam-2406	380	9	x	x	X
ejpam-2406	380	10	)	)	PUNCT
ejpam-2406	380	11	.	.	PUNCT
ejpam-2406	381	1	hence	hence	ADV
ejpam-2406	381	2	,	,	PUNCT
ejpam-2406	381	3	p	p	X
ejpam-2406	381	4	(	(	PUNCT
ejpam-2406	381	5	qr	qr	NOUN
ejpam-2406	381	6	:	:	PUNCT
ejpam-2406	381	7	x	x	X
ejpam-2406	381	8	)	)	PUNCT
ejpam-2406	381	9	=	=	SYM
ejpam-2406	381	10	pr	pr	X
ejpam-2406	381	11	where	where	SCONJ
ejpam-2406	381	12	x	x	PUNCT
ejpam-2406	381	13	6¶	6¶	NUM
ejpam-2406	381	14	qr	qr	NOUN
ejpam-2406	381	15	.	.	PUNCT
ejpam-2406	382	1	we	we	PRON
ejpam-2406	382	2	have	have	AUX
ejpam-2406	382	3	shown	show	VERB
ejpam-2406	382	4	that	that	SCONJ
ejpam-2406	382	5	for	for	ADP
ejpam-2406	382	6	each	each	DET
ejpam-2406	382	7	i	i	PRON
ejpam-2406	382	8	,	,	PUNCT
ejpam-2406	382	9	p	p	X
ejpam-2406	382	10	(	(	PUNCT
ejpam-2406	382	11	q	q	NOUN
ejpam-2406	382	12	i	i	PRON
ejpam-2406	382	13	:	:	PUNCT
ejpam-2406	382	14	x	x	X
ejpam-2406	382	15	)	)	PUNCT
ejpam-2406	383	1	=	=	SYM
ejpam-2406	383	2	pi	pi	NOUN
ejpam-2406	383	3	or	or	CCONJ
ejpam-2406	383	4	1	1	NUM
ejpam-2406	383	5	and	and	CCONJ
ejpam-2406	383	6	is	be	AUX
ejpam-2406	383	7	equal	equal	ADJ
ejpam-2406	383	8	to	to	PART
ejpam-2406	383	9	pi	pi	VERB
ejpam-2406	383	10	for	for	ADP
ejpam-2406	383	11	at	at	ADV
ejpam-2406	383	12	least	least	ADV
ejpam-2406	383	13	one	one	NUM
ejpam-2406	383	14	i	i	PRON
ejpam-2406	383	15	,	,	PUNCT
ejpam-2406	383	16	since	since	SCONJ
ejpam-2406	383	17	x	x	X
ejpam-2406	383	18	6¶	6¶	NUM
ejpam-2406	383	19	n	n	NOUN
ejpam-2406	383	20	.	.	PUNCT
ejpam-2406	384	1	then	then	ADV
ejpam-2406	384	2	,	,	PUNCT
ejpam-2406	384	3	p	p	X
ejpam-2406	384	4	=	=	PUNCT
ejpam-2406	384	5	p	p	X
ejpam-2406	384	6	(	(	PUNCT
ejpam-2406	384	7	n	n	NOUN
ejpam-2406	384	8	:	:	PUNCT
ejpam-2406	384	9	x	x	X
ejpam-2406	384	10	)	)	PUNCT
ejpam-2406	385	1	=	=	SYM
ejpam-2406	385	2	p	p	X
ejpam-2406	385	3	(	(	PUNCT
ejpam-2406	385	4	q1	q1	PROPN
ejpam-2406	385	5	:	:	PUNCT
ejpam-2406	385	6	x	x	X
ejpam-2406	385	7	)	)	PUNCT
ejpam-2406	385	8	∧	∧	NOUN
ejpam-2406	385	9	·	·	PUNCT
ejpam-2406	385	10	·	·	PUNCT
ejpam-2406	385	11	·	·	PUNCT
ejpam-2406	386	1	∧p(qk	∧p(qk	NOUN
ejpam-2406	386	2	:	:	PUNCT
ejpam-2406	386	3	x	x	X
ejpam-2406	386	4	)	)	PUNCT
ejpam-2406	386	5	is	be	AUX
ejpam-2406	386	6	the	the	DET
ejpam-2406	386	7	meet	meet	NOUN
ejpam-2406	386	8	of	of	ADP
ejpam-2406	386	9	some	some	PRON
ejpam-2406	386	10	of	of	ADP
ejpam-2406	386	11	the	the	DET
ejpam-2406	386	12	prime	prime	ADJ
ejpam-2406	386	13	elements	element	NOUN
ejpam-2406	386	14	p1	p1	NOUN
ejpam-2406	386	15	,	,	PUNCT
ejpam-2406	386	16	p2	p2	NOUN
ejpam-2406	386	17	,	,	PUNCT
ejpam-2406	386	18	.	.	PUNCT
ejpam-2406	386	19	.	.	PUNCT
ejpam-2406	387	1	.	.	PUNCT
ejpam-2406	388	1	,	,	PUNCT
ejpam-2406	388	2	pl	pl	PROPN
ejpam-2406	388	3	(	(	PUNCT
ejpam-2406	388	4	1¶	1¶	PROPN
ejpam-2406	388	5	l	l	PROPN
ejpam-2406	388	6	¶	¶	PROPN
ejpam-2406	388	7	k	k	NOUN
ejpam-2406	388	8	)	)	PUNCT
ejpam-2406	388	9	.	.	PUNCT
ejpam-2406	389	1	that	that	PRON
ejpam-2406	389	2	is	be	AUX
ejpam-2406	389	3	p	p	NOUN
ejpam-2406	389	4	=	=	PUNCT
ejpam-2406	389	5	p	p	X
ejpam-2406	389	6	(	(	PUNCT
ejpam-2406	389	7	n	n	NOUN
ejpam-2406	389	8	:	:	PUNCT
ejpam-2406	389	9	x	x	X
ejpam-2406	389	10	)	)	PUNCT
ejpam-2406	389	11	=	=	SYM
ejpam-2406	389	12	p1∧p2∧	p1∧p2∧	PROPN
ejpam-2406	389	13	·	·	PUNCT
ejpam-2406	389	14	·	·	PUNCT
ejpam-2406	389	15	·	·	PUNCT
ejpam-2406	389	16	∧	∧	NOUN
ejpam-2406	389	17	pl	pl	X
ejpam-2406	389	18	.	.	PUNCT
ejpam-2406	390	1	we	we	PRON
ejpam-2406	390	2	show	show	VERB
ejpam-2406	390	3	that	that	SCONJ
ejpam-2406	390	4	p	p	X
ejpam-2406	390	5	=	=	PUNCT
ejpam-2406	390	6	pi	pi	NOUN
ejpam-2406	390	7	for	for	ADP
ejpam-2406	390	8	some	some	DET
ejpam-2406	390	9	i.	i.	NOUN
ejpam-2406	390	10	we	we	PRON
ejpam-2406	390	11	have	have	VERB
ejpam-2406	390	12	,	,	PUNCT
ejpam-2406	390	13	p	p	PROPN
ejpam-2406	390	14	¶	¶	NUM
ejpam-2406	390	15	pi	pi	NOUN
ejpam-2406	390	16	i	i	NOUN
ejpam-2406	390	17	=	=	NOUN
ejpam-2406	390	18	1,2	1,2	NUM
ejpam-2406	390	19	,	,	PUNCT
ejpam-2406	390	20	.	.	PUNCT
ejpam-2406	390	21	.	.	PUNCT
ejpam-2406	391	1	.	.	PUNCT
ejpam-2406	392	1	,	,	PUNCT
ejpam-2406	392	2	l.	l.	PROPN
ejpam-2406	392	3	if	if	SCONJ
ejpam-2406	392	4	for	for	ADP
ejpam-2406	392	5	each	each	DET
ejpam-2406	392	6	i	i	PRON
ejpam-2406	392	7	p	p	PROPN
ejpam-2406	392	8	6=	6=	NUM
ejpam-2406	392	9	pi	pi	NOUN
ejpam-2406	392	10	then	then	ADV
ejpam-2406	392	11	pi	pi	VERB
ejpam-2406	392	12	6¶	6¶	NUM
ejpam-2406	392	13	p	p	NOUN
ejpam-2406	392	14	for	for	ADP
ejpam-2406	392	15	all	all	DET
ejpam-2406	392	16	i	i	NOUN
ejpam-2406	392	17	=	=	SYM
ejpam-2406	392	18	1,2	1,2	NUM
ejpam-2406	392	19	,	,	PUNCT
ejpam-2406	392	20	.	.	PUNCT
ejpam-2406	392	21	.	.	PUNCT
ejpam-2406	393	1	.	.	PUNCT
ejpam-2406	394	1	,	,	PUNCT
ejpam-2406	394	2	l.	l.	PROPN
ejpam-2406	394	3	this	this	PRON
ejpam-2406	394	4	implies	imply	VERB
ejpam-2406	394	5	that	that	SCONJ
ejpam-2406	394	6	there	there	PRON
ejpam-2406	394	7	exist	exist	VERB
ejpam-2406	394	8	x	x	PUNCT
ejpam-2406	395	1	i	i	PRON
ejpam-2406	395	2	¶	¶	VERB
ejpam-2406	395	3	pi	pi	NOUN
ejpam-2406	395	4	such	such	ADJ
ejpam-2406	395	5	that	that	SCONJ
ejpam-2406	395	6	x	x	X
ejpam-2406	396	1	i	i	PRON
ejpam-2406	396	2	6¶	6¶	NUM
ejpam-2406	396	3	p	p	NOUN
ejpam-2406	396	4	for	for	ADP
ejpam-2406	396	5	all	all	DET
ejpam-2406	396	6	i	i	NOUN
ejpam-2406	396	7	=	=	SYM
ejpam-2406	396	8	1,2	1,2	NUM
ejpam-2406	396	9	,	,	PUNCT
ejpam-2406	396	10	.	.	PUNCT
ejpam-2406	396	11	.	.	PUNCT
ejpam-2406	396	12	.	.	PUNCT
ejpam-2406	397	1	,	,	PUNCT
ejpam-2406	397	2	l.	l.	PROPN
ejpam-2406	397	3	then	then	ADV
ejpam-2406	397	4	,	,	PUNCT
ejpam-2406	397	5	x1	x1	PROPN
ejpam-2406	398	1	x2	x2	PROPN
ejpam-2406	398	2	.	.	PUNCT
ejpam-2406	398	3	.	.	PUNCT
ejpam-2406	398	4	.	.	PUNCT
ejpam-2406	399	1	x	x	X
ejpam-2406	399	2	l	l	NOUN
ejpam-2406	399	3	¶	¶	PROPN
ejpam-2406	399	4	p1	p1	PROPN
ejpam-2406	399	5	∧	∧	PROPN
ejpam-2406	399	6	p2	p2	NOUN
ejpam-2406	399	7	∧	∧	PROPN
ejpam-2406	399	8	·	·	PUNCT
ejpam-2406	399	9	·	·	PUNCT
ejpam-2406	399	10	·	·	PUNCT
ejpam-2406	400	1	∧	∧	NOUN
ejpam-2406	400	2	pl	pl	NOUN
ejpam-2406	400	3	=	=	SYM
ejpam-2406	400	4	p.	p.	NOUN
ejpam-2406	400	5	this	this	PRON
ejpam-2406	400	6	shows	show	VERB
ejpam-2406	400	7	that	that	SCONJ
ejpam-2406	400	8	x	x	PUNCT
ejpam-2406	401	1	i	i	PRON
ejpam-2406	401	2	¶	¶	VERB
ejpam-2406	401	3	p	p	NOUN
ejpam-2406	401	4	for	for	ADP
ejpam-2406	401	5	at	at	ADV
ejpam-2406	401	6	least	least	ADV
ejpam-2406	401	7	one	one	NUM
ejpam-2406	401	8	i	i	NOUN
ejpam-2406	401	9	(	(	PUNCT
ejpam-2406	401	10	1	1	NUM
ejpam-2406	401	11	¶	¶	NUM
ejpam-2406	401	12	i	i	PRON
ejpam-2406	401	13	¶	¶	PROPN
ejpam-2406	401	14	k	k	NOUN
ejpam-2406	401	15	)	)	PUNCT
ejpam-2406	401	16	a	a	DET
ejpam-2406	401	17	contradiction	contradiction	NOUN
ejpam-2406	401	18	.	.	PUNCT
ejpam-2406	402	1	hence	hence	ADV
ejpam-2406	402	2	,	,	PUNCT
ejpam-2406	402	3	p	p	NOUN
ejpam-2406	402	4	=	=	NOUN
ejpam-2406	402	5	pi	pi	NOUN
ejpam-2406	402	6	for	for	ADP
ejpam-2406	402	7	at	at	ADV
ejpam-2406	402	8	least	least	ADV
ejpam-2406	402	9	one	one	NUM
ejpam-2406	402	10	i.	i.	NOUN
ejpam-2406	402	11	we	we	PRON
ejpam-2406	402	12	have	have	VERB
ejpam-2406	402	13	the	the	DET
ejpam-2406	402	14	characterization	characterization	NOUN
ejpam-2406	402	15	of	of	ADP
ejpam-2406	402	16	a	a	DET
ejpam-2406	402	17	classical	classical	ADJ
ejpam-2406	402	18	quasi	quasi	ADJ
ejpam-2406	402	19	primary	primary	ADJ
ejpam-2406	402	20	element	element	NOUN
ejpam-2406	402	21	of	of	ADP
ejpam-2406	402	22	a	a	DET
ejpam-2406	402	23	lattice	lattice	NOUN
ejpam-2406	402	24	module	module	NOUN
ejpam-2406	402	25	in	in	ADP
ejpam-2406	402	26	terms	term	NOUN
ejpam-2406	402	27	of	of	ADP
ejpam-2406	402	28	a	a	DET
ejpam-2406	402	29	chain	chain	NOUN
ejpam-2406	402	30	of	of	ADP
ejpam-2406	402	31	its	its	PRON
ejpam-2406	402	32	associated	associated	ADJ
ejpam-2406	402	33	primes	prime	NOUN
ejpam-2406	402	34	.	.	PUNCT
ejpam-2406	403	1	theorem	theorem	NOUN
ejpam-2406	403	2	10	10	NUM
ejpam-2406	403	3	.	.	PUNCT
ejpam-2406	404	1	let	let	VERB
ejpam-2406	404	2	m	m	PRON
ejpam-2406	404	3	be	be	AUX
ejpam-2406	404	4	a	a	DET
ejpam-2406	404	5	l	l	NOUN
ejpam-2406	404	6	-	-	NOUN
ejpam-2406	404	7	module	module	NOUN
ejpam-2406	404	8	and	and	CCONJ
ejpam-2406	404	9	q	q	NOUN
ejpam-2406	404	10	be	be	AUX
ejpam-2406	404	11	a	a	DET
ejpam-2406	404	12	proper	proper	ADJ
ejpam-2406	404	13	element	element	NOUN
ejpam-2406	404	14	of	of	ADP
ejpam-2406	404	15	m.	m.	NOUN
ejpam-2406	404	16	let	let	VERB
ejpam-2406	405	1	q	q	NOUN
ejpam-2406	405	2	=	=	PUNCT
ejpam-2406	405	3	q1∧q2∧	q1∧q2∧	NOUN
ejpam-2406	405	4	·	·	PUNCT
ejpam-2406	405	5	·	·	PUNCT
ejpam-2406	405	6	·	·	PUNCT
ejpam-2406	405	7	∧qn	∧qn	PROPN
ejpam-2406	405	8	with	with	ADP
ejpam-2406	405	9	pi	pi	NOUN
ejpam-2406	405	10	=	=	SYM
ejpam-2406	405	11	p	p	X
ejpam-2406	405	12	(	(	PUNCT
ejpam-2406	405	13	q	q	NOUN
ejpam-2406	406	1	i	i	PRON
ejpam-2406	406	2	:	:	PUNCT
ejpam-2406	406	3	i	i	PRON
ejpam-2406	406	4	m	m	VERB
ejpam-2406	406	5	)	)	PUNCT
ejpam-2406	406	6	be	be	VERB
ejpam-2406	406	7	a	a	DET
ejpam-2406	406	8	reduced	reduce	VERB
ejpam-2406	406	9	primary	primary	ADJ
ejpam-2406	406	10	decomposition	decomposition	NOUN
ejpam-2406	406	11	of	of	ADP
ejpam-2406	406	12	q.	q.	PROPN
ejpam-2406	406	13	then	then	ADV
ejpam-2406	406	14	q	q	X
ejpam-2406	406	15	is	be	AUX
ejpam-2406	406	16	a	a	DET
ejpam-2406	406	17	classical	classical	ADJ
ejpam-2406	406	18	quasi	quasi	ADJ
ejpam-2406	406	19	primary	primary	ADJ
ejpam-2406	406	20	element	element	NOUN
ejpam-2406	406	21	if	if	SCONJ
ejpam-2406	406	22	and	and	CCONJ
ejpam-2406	406	23	only	only	ADV
ejpam-2406	406	24	if	if	SCONJ
ejpam-2406	406	25	{	{	PUNCT
ejpam-2406	406	26	p1	p1	NOUN
ejpam-2406	406	27	,	,	PUNCT
ejpam-2406	406	28	p2	p2	NOUN
ejpam-2406	406	29	,	,	PUNCT
ejpam-2406	406	30	.	.	PUNCT
ejpam-2406	406	31	.	.	PUNCT
ejpam-2406	407	1	.	.	PUNCT
ejpam-2406	408	1	,	,	PUNCT
ejpam-2406	408	2	pn	pn	PROPN
ejpam-2406	408	3	}	}	PUNCT
ejpam-2406	408	4	is	be	AUX
ejpam-2406	408	5	a	a	DET
ejpam-2406	408	6	chain	chain	NOUN
ejpam-2406	408	7	of	of	ADP
ejpam-2406	408	8	prime	prime	ADJ
ejpam-2406	408	9	elements	element	NOUN
ejpam-2406	408	10	of	of	ADP
ejpam-2406	408	11	l.	l.	PROPN
ejpam-2406	408	12	in	in	ADP
ejpam-2406	408	13	that	that	DET
ejpam-2406	408	14	case	case	NOUN
ejpam-2406	408	15	,	,	PUNCT
ejpam-2406	408	16	radical	radical	ADJ
ejpam-2406	408	17	of	of	ADP
ejpam-2406	408	18	(	(	PUNCT
ejpam-2406	408	19	q	q	NOUN
ejpam-2406	408	20	:	:	PUNCT
ejpam-2406	408	21	i	i	PRON
ejpam-2406	408	22	m	m	PROPN
ejpam-2406	408	23	)	)	PUNCT
ejpam-2406	408	24	is	be	AUX
ejpam-2406	408	25	the	the	DET
ejpam-2406	408	26	smallest	small	ADJ
ejpam-2406	408	27	of	of	ADP
ejpam-2406	408	28	the	the	DET
ejpam-2406	408	29	primes	prime	NOUN
ejpam-2406	408	30	p1	p1	NOUN
ejpam-2406	408	31	,	,	PUNCT
ejpam-2406	408	32	p2	p2	NOUN
ejpam-2406	408	33	,	,	PUNCT
ejpam-2406	408	34	.	.	PUNCT
ejpam-2406	408	35	.	.	PUNCT
ejpam-2406	409	1	.	.	PUNCT
ejpam-2406	410	1	,	,	PUNCT
ejpam-2406	410	2	pn	pn	PROPN
ejpam-2406	410	3	.	.	PROPN
ejpam-2406	410	4	proof	proof	NOUN
ejpam-2406	410	5	.	.	PUNCT
ejpam-2406	411	1	since	since	SCONJ
ejpam-2406	411	2	,	,	PUNCT
ejpam-2406	411	3	q	q	PROPN
ejpam-2406	411	4	=	=	ADJ
ejpam-2406	411	5	q1	q1	NOUN
ejpam-2406	411	6	∧q2	∧q2	VERB
ejpam-2406	411	7	∧	∧	PROPN
ejpam-2406	411	8	·	·	PUNCT
ejpam-2406	411	9	·	·	PUNCT
ejpam-2406	411	10	·	·	PUNCT
ejpam-2406	412	1	∧qn	∧qn	PROPN
ejpam-2406	412	2	is	be	AUX
ejpam-2406	412	3	a	a	DET
ejpam-2406	412	4	reduced	reduce	VERB
ejpam-2406	412	5	primary	primary	ADJ
ejpam-2406	412	6	decomposition	decomposition	NOUN
ejpam-2406	412	7	of	of	ADP
ejpam-2406	412	8	q	q	NOUN
ejpam-2406	412	9	by	by	ADP
ejpam-2406	412	10	theorem	theorem	NOUN
ejpam-2406	412	11	7	7	NUM
ejpam-2406	412	12	for	for	ADP
ejpam-2406	412	13	each	each	DET
ejpam-2406	412	14	i	i	PRON
ejpam-2406	412	15	(	(	PUNCT
ejpam-2406	412	16	1	1	NUM
ejpam-2406	412	17	¶	¶	NUM
ejpam-2406	412	18	i	i	PROPN
ejpam-2406	412	19	¶	¶	PROPN
ejpam-2406	412	20	n	n	CCONJ
ejpam-2406	412	21	)	)	PUNCT
ejpam-2406	412	22	,	,	PUNCT
ejpam-2406	412	23	pi	pi	NOUN
ejpam-2406	412	24	=	=	PUNCT
ejpam-2406	412	25	p	p	X
ejpam-2406	412	26	(	(	PUNCT
ejpam-2406	412	27	q	q	NOUN
ejpam-2406	412	28	:	:	PUNCT
ejpam-2406	412	29	ai	ai	VERB
ejpam-2406	412	30	)	)	PUNCT
ejpam-2406	412	31	for	for	ADP
ejpam-2406	412	32	some	some	PRON
ejpam-2406	412	33	ai	ai	VERB
ejpam-2406	412	34	6¶	6¶	NUM
ejpam-2406	412	35	q	q	NOUN
ejpam-2406	412	36	where	where	SCONJ
ejpam-2406	412	37	pi	pi	NOUN
ejpam-2406	412	38	=	=	PUNCT
ejpam-2406	412	39	p	p	X
ejpam-2406	412	40	(	(	PUNCT
ejpam-2406	412	41	q	q	NOUN
ejpam-2406	413	1	i	i	PRON
ejpam-2406	413	2	:	:	PUNCT
ejpam-2406	413	3	i	i	PRON
ejpam-2406	413	4	m	m	PROPN
ejpam-2406	413	5	)	)	PUNCT
ejpam-2406	413	6	.	.	PUNCT
ejpam-2406	414	1	assume	assume	VERB
ejpam-2406	414	2	that	that	SCONJ
ejpam-2406	414	3	,	,	PUNCT
ejpam-2406	414	4	q	q	X
ejpam-2406	414	5	is	be	AUX
ejpam-2406	414	6	a	a	DET
ejpam-2406	414	7	classical	classical	ADJ
ejpam-2406	414	8	quasi	quasi	ADJ
ejpam-2406	414	9	primary	primary	ADJ
ejpam-2406	414	10	element	element	NOUN
ejpam-2406	414	11	.	.	PUNCT
ejpam-2406	415	1	we	we	PRON
ejpam-2406	415	2	show	show	VERB
ejpam-2406	415	3	that	that	SCONJ
ejpam-2406	415	4	{	{	PUNCT
ejpam-2406	415	5	p1	p1	NOUN
ejpam-2406	415	6	,	,	PUNCT
ejpam-2406	415	7	p2	p2	NOUN
ejpam-2406	415	8	,	,	PUNCT
ejpam-2406	415	9	.	.	PUNCT
ejpam-2406	415	10	.	.	PUNCT
ejpam-2406	415	11	.	.	PUNCT
ejpam-2406	416	1	,	,	PUNCT
ejpam-2406	416	2	pn	pn	PROPN
ejpam-2406	416	3	}	}	PUNCT
ejpam-2406	416	4	is	be	AUX
ejpam-2406	416	5	the	the	DET
ejpam-2406	416	6	chain	chain	NOUN
ejpam-2406	416	7	of	of	ADP
ejpam-2406	416	8	prime	prime	ADJ
ejpam-2406	416	9	elements	element	NOUN
ejpam-2406	416	10	of	of	ADP
ejpam-2406	416	11	l.	l.	PROPN
ejpam-2406	416	12	assume	assume	VERB
ejpam-2406	416	13	that	that	SCONJ
ejpam-2406	416	14	,	,	PUNCT
ejpam-2406	416	15	it	it	PRON
ejpam-2406	416	16	is	be	AUX
ejpam-2406	416	17	not	not	PART
ejpam-2406	416	18	a	a	DET
ejpam-2406	416	19	chain	chain	NOUN
ejpam-2406	416	20	.	.	PUNCT
ejpam-2406	417	1	then	then	ADV
ejpam-2406	417	2	pi	pi	VERB
ejpam-2406	417	3	6¶	6¶	NUM
ejpam-2406	418	1	p	p	NOUN
ejpam-2406	418	2	j	j	PROPN
ejpam-2406	418	3	and	and	CCONJ
ejpam-2406	418	4	p	p	PROPN
ejpam-2406	418	5	j	j	PROPN
ejpam-2406	418	6	6¶	6¶	NUM
ejpam-2406	418	7	pi	pi	NOUN
ejpam-2406	418	8	for	for	ADP
ejpam-2406	418	9	some	some	DET
ejpam-2406	418	10	i	i	PRON
ejpam-2406	418	11	6=	6=	PROPN
ejpam-2406	418	12	j.	j.	PROPN
ejpam-2406	418	13	select	select	VERB
ejpam-2406	418	14	a	a	DET
ejpam-2406	418	15	¶	¶	NOUN
ejpam-2406	418	16	pi	pi	NOUN
ejpam-2406	418	17	such	such	ADJ
ejpam-2406	418	18	that	that	SCONJ
ejpam-2406	418	19	a	a	DET
ejpam-2406	418	20	6¶	6¶	NUM
ejpam-2406	418	21	p	p	PROPN
ejpam-2406	418	22	j	j	PROPN
ejpam-2406	418	23	and	and	CCONJ
ejpam-2406	418	24	b	b	PROPN
ejpam-2406	418	25	¶	¶	PROPN
ejpam-2406	418	26	p	p	PROPN
ejpam-2406	418	27	j	j	PROPN
ejpam-2406	418	28	such	such	ADJ
ejpam-2406	418	29	that	that	DET
ejpam-2406	418	30	b	b	PROPN
ejpam-2406	418	31	6¶	6¶	NUM
ejpam-2406	418	32	pi	pi	NOUN
ejpam-2406	418	33	.	.	PUNCT
ejpam-2406	419	1	i.e.	i.e.	X
ejpam-2406	419	2	a	a	DET
ejpam-2406	419	3	¶	¶	PROPN
ejpam-2406	419	4	p	p	NOUN
ejpam-2406	419	5	(	(	PUNCT
ejpam-2406	419	6	q	q	NOUN
ejpam-2406	419	7	i	i	X
ejpam-2406	419	8	:	:	PUNCT
ejpam-2406	419	9	i	i	NOUN
ejpam-2406	419	10	m	m	PROPN
ejpam-2406	419	11	)	)	PUNCT
ejpam-2406	419	12	,	,	PUNCT
ejpam-2406	419	13	a	a	DET
ejpam-2406	419	14	6¶	6¶	NUM
ejpam-2406	419	15	æ(q	æ(q	PROPN
ejpam-2406	419	16	j	j	PROPN
ejpam-2406	419	17	:	:	PUNCT
ejpam-2406	419	18	i	i	PRON
ejpam-2406	419	19	m	m	PROPN
ejpam-2406	419	20	)	)	PUNCT
ejpam-2406	419	21	and	and	CCONJ
ejpam-2406	419	22	b	b	X
ejpam-2406	419	23	¶	¶	PROPN
ejpam-2406	419	24	æ	æ	PROPN
ejpam-2406	419	25	(	(	PUNCT
ejpam-2406	419	26	q	q	PROPN
ejpam-2406	419	27	j	j	NOUN
ejpam-2406	419	28	:	:	PUNCT
ejpam-2406	419	29	i	i	PROPN
ejpam-2406	419	30	m	m	PROPN
ejpam-2406	419	31	)	)	PUNCT
ejpam-2406	419	32	,	,	PUNCT
ejpam-2406	419	33	b	b	X
ejpam-2406	419	34	6¶p(q	6¶p(q	NUM
ejpam-2406	419	35	i	i	NOUN
ejpam-2406	419	36	:	:	PUNCT
ejpam-2406	419	37	i	i	NOUN
ejpam-2406	419	38	m	m	PROPN
ejpam-2406	419	39	)	)	PUNCT
ejpam-2406	419	40	.	.	PUNCT
ejpam-2406	420	1	since	since	SCONJ
ejpam-2406	420	2	pi	pi	NOUN
ejpam-2406	420	3	=	=	PROPN
ejpam-2406	420	4	p	p	X
ejpam-2406	420	5	(	(	PUNCT
ejpam-2406	420	6	q	q	NOUN
ejpam-2406	420	7	:	:	PUNCT
ejpam-2406	420	8	ai	ai	VERB
ejpam-2406	420	9	)	)	PUNCT
ejpam-2406	420	10	,	,	PUNCT
ejpam-2406	420	11	ai	ai	VERB
ejpam-2406	420	12	6¶q	6¶q	PUNCT
ejpam-2406	420	13	for	for	ADP
ejpam-2406	420	14	each	each	DET
ejpam-2406	420	15	i	i	NOUN
ejpam-2406	420	16	=	=	NOUN
ejpam-2406	420	17	1,2	1,2	NUM
ejpam-2406	420	18	,	,	PUNCT
ejpam-2406	420	19	.	.	PUNCT
ejpam-2406	420	20	.	.	PUNCT
ejpam-2406	421	1	.	.	PUNCT
ejpam-2406	422	1	,	,	PUNCT
ejpam-2406	422	2	n	n	CCONJ
ejpam-2406	422	3	,	,	PUNCT
ejpam-2406	422	4	we	we	PRON
ejpam-2406	422	5	have	have	VERB
ejpam-2406	422	6	,	,	PUNCT
ejpam-2406	422	7	a	a	DET
ejpam-2406	422	8	¶	¶	NOUN
ejpam-2406	422	9	p	p	NOUN
ejpam-2406	422	10	(	(	PUNCT
ejpam-2406	422	11	q	q	NOUN
ejpam-2406	422	12	i	i	X
ejpam-2406	422	13	:	:	PUNCT
ejpam-2406	422	14	i	i	PRON
ejpam-2406	422	15	m	m	VERB
ejpam-2406	422	16	)	)	PUNCT
ejpam-2406	423	1	=	=	SYM
ejpam-2406	423	2	p	p	X
ejpam-2406	423	3	(	(	PUNCT
ejpam-2406	423	4	q	q	NOUN
ejpam-2406	423	5	:	:	PUNCT
ejpam-2406	423	6	ai	ai	VERB
ejpam-2406	423	7	)	)	PUNCT
ejpam-2406	423	8	and	and	CCONJ
ejpam-2406	424	1	a	a	DET
ejpam-2406	424	2	6¶æ(q	6¶æ(q	NOUN
ejpam-2406	424	3	:	:	PUNCT
ejpam-2406	424	4	a	a	DET
ejpam-2406	424	5	j	j	NOUN
ejpam-2406	424	6	)	)	PUNCT
ejpam-2406	424	7	.	.	PUNCT
ejpam-2406	425	1	similarly	similarly	ADV
ejpam-2406	425	2	,	,	PUNCT
ejpam-2406	425	3	b	b	PROPN
ejpam-2406	425	4	¶	¶	PROPN
ejpam-2406	425	5	æ	æ	PROPN
ejpam-2406	426	1	(	(	PUNCT
ejpam-2406	426	2	q	q	PROPN
ejpam-2406	426	3	j	j	NOUN
ejpam-2406	426	4	:	:	PUNCT
ejpam-2406	426	5	i	i	PRON
ejpam-2406	426	6	m	m	VERB
ejpam-2406	426	7	)	)	PUNCT
ejpam-2406	427	1	=	=	SYM
ejpam-2406	428	1	æ	æ	X
ejpam-2406	428	2	(	(	PUNCT
ejpam-2406	428	3	q	q	NOUN
ejpam-2406	428	4	:	:	PUNCT
ejpam-2406	428	5	a	a	DET
ejpam-2406	428	6	j	j	NOUN
ejpam-2406	428	7	)	)	PUNCT
ejpam-2406	428	8	and	and	CCONJ
ejpam-2406	428	9	b	b	X
ejpam-2406	428	10	6¶	6¶	NUM
ejpam-2406	428	11	p(q	p(q	NOUN
ejpam-2406	428	12	:	:	PUNCT
ejpam-2406	428	13	ai	ai	NOUN
ejpam-2406	428	14	)	)	PUNCT
ejpam-2406	428	15	.	.	PUNCT
ejpam-2406	429	1	this	this	PRON
ejpam-2406	429	2	shows	show	VERB
ejpam-2406	429	3	that	that	SCONJ
ejpam-2406	429	4	aki	aki	PROPN
ejpam-2406	429	5	ai	ai	PROPN
ejpam-2406	429	6	¶	¶	PROPN
ejpam-2406	429	7	q	q	NOUN
ejpam-2406	429	8	for	for	ADP
ejpam-2406	429	9	some	some	DET
ejpam-2406	429	10	integer	integer	NOUN
ejpam-2406	429	11	ki	ki	PROPN
ejpam-2406	429	12	and	and	CCONJ
ejpam-2406	429	13	aka	aka	ADV
ejpam-2406	429	14	j	j	PROPN
ejpam-2406	429	15	6¶	6¶	NUM
ejpam-2406	429	16	q	q	NOUN
ejpam-2406	429	17	for	for	ADP
ejpam-2406	429	18	any	any	DET
ejpam-2406	429	19	k.	k.	PROPN
ejpam-2406	429	20	similarly	similarly	ADV
ejpam-2406	429	21	,	,	PUNCT
ejpam-2406	429	22	bk	bk	VERB
ejpam-2406	429	23	j	j	PROPN
ejpam-2406	429	24	a	a	DET
ejpam-2406	429	25	j	j	PROPN
ejpam-2406	429	26	¶	¶	PROPN
ejpam-2406	429	27	q	q	NOUN
ejpam-2406	429	28	for	for	ADP
ejpam-2406	429	29	some	some	DET
ejpam-2406	429	30	integer	integer	NOUN
ejpam-2406	429	31	k	k	PROPN
ejpam-2406	429	32	j	j	PROPN
ejpam-2406	429	33	and	and	CCONJ
ejpam-2406	429	34	bkai	bkai	PROPN
ejpam-2406	429	35	6¶	6¶	NUM
ejpam-2406	429	36	q	q	NOUN
ejpam-2406	429	37	for	for	ADP
ejpam-2406	429	38	any	any	DET
ejpam-2406	429	39	k.	k.	NOUN
ejpam-2406	429	40	thus	thus	ADV
ejpam-2406	429	41	aki	aki	PROPN
ejpam-2406	429	42	ai	ai	PROPN
ejpam-2406	429	43	∨	∨	NOUN
ejpam-2406	429	44	bk	bk	ADP
ejpam-2406	429	45	j	j	PROPN
ejpam-2406	429	46	a	a	DET
ejpam-2406	429	47	j	j	PROPN
ejpam-2406	429	48	¶	¶	PROPN
ejpam-2406	429	49	q	q	PROPN
ejpam-2406	429	50	and	and	CCONJ
ejpam-2406	429	51	aka	aka	ADV
ejpam-2406	429	52	j	j	PROPN
ejpam-2406	429	53	∨	∨	PROPN
ejpam-2406	429	54	bkai	bkai	PROPN
ejpam-2406	429	55	6¶	6¶	NUM
ejpam-2406	429	56	q	q	NOUN
ejpam-2406	429	57	for	for	ADP
ejpam-2406	429	58	any	any	DET
ejpam-2406	429	59	k.	k.	NOUN
ejpam-2406	429	60	let	let	VERB
ejpam-2406	429	61	k	k	NOUN
ejpam-2406	429	62	=	=	PUNCT
ejpam-2406	429	63	max{ki	max{ki	X
ejpam-2406	429	64	,	,	PUNCT
ejpam-2406	429	65	k	k	PROPN
ejpam-2406	429	66	j	j	PROPN
ejpam-2406	429	67	}	}	PUNCT
ejpam-2406	429	68	.	.	PUNCT
ejpam-2406	430	1	then	then	ADV
ejpam-2406	430	2	ak	ak	PROPN
ejpam-2406	430	3	bkai	bkai	PROPN
ejpam-2406	430	4	∨	∨	PROPN
ejpam-2406	430	5	bkaka	bkaka	PROPN
ejpam-2406	430	6	j	j	PROPN
ejpam-2406	430	7	=	=	SYM
ejpam-2406	430	8	ak	ak	PROPN
ejpam-2406	430	9	bk(a	bk(a	PUNCT
ejpam-2406	430	10	j	j	PROPN
ejpam-2406	430	11	∨	∨	NUM
ejpam-2406	430	12	ai	ai	PROPN
ejpam-2406	430	13	)	)	PUNCT
ejpam-2406	430	14	¶	¶	PROPN
ejpam-2406	430	15	q.	q.	PROPN
ejpam-2406	430	16	since	since	SCONJ
ejpam-2406	430	17	,	,	PUNCT
ejpam-2406	430	18	q	q	X
ejpam-2406	430	19	is	be	AUX
ejpam-2406	430	20	a	a	DET
ejpam-2406	430	21	classical	classical	ADJ
ejpam-2406	430	22	quasi	quasi	ADJ
ejpam-2406	430	23	primary	primary	ADJ
ejpam-2406	430	24	element	element	NOUN
ejpam-2406	430	25	of	of	ADP
ejpam-2406	430	26	m	m	PROPN
ejpam-2406	430	27	,	,	PUNCT
ejpam-2406	430	28	it	it	PRON
ejpam-2406	430	29	follows	follow	VERB
ejpam-2406	430	30	that	that	SCONJ
ejpam-2406	430	31	(	(	PUNCT
ejpam-2406	430	32	ak)l(ai	ak)l(ai	PROPN
ejpam-2406	430	33	∨	∨	NUM
ejpam-2406	430	34	a	a	DET
ejpam-2406	430	35	j	j	PROPN
ejpam-2406	430	36	)	)	PUNCT
ejpam-2406	430	37	¶	¶	PROPN
ejpam-2406	430	38	q	q	PROPN
ejpam-2406	430	39	or	or	CCONJ
ejpam-2406	430	40	(	(	PUNCT
ejpam-2406	430	41	bk)l(ai	bk)l(ai	PROPN
ejpam-2406	430	42	∨	∨	NUM
ejpam-2406	430	43	a	a	DET
ejpam-2406	430	44	j	j	PROPN
ejpam-2406	430	45	)	)	PUNCT
ejpam-2406	430	46	¶	¶	PROPN
ejpam-2406	430	47	q	q	PROPN
ejpam-2406	430	48	i.e.	i.e.	X
ejpam-2406	430	49	as(ai	as(ai	PRON
ejpam-2406	430	50	∨	∨	NOUN
ejpam-2406	430	51	a	a	DET
ejpam-2406	430	52	j	j	PROPN
ejpam-2406	430	53	)	)	PUNCT
ejpam-2406	430	54	¶	¶	PROPN
ejpam-2406	430	55	q	q	PUNCT
ejpam-2406	430	56	or	or	CCONJ
ejpam-2406	430	57	bs(ai	bs(ai	PROPN
ejpam-2406	430	58	∨	∨	NUM
ejpam-2406	430	59	a	a	DET
ejpam-2406	430	60	j	j	PROPN
ejpam-2406	430	61	)	)	PUNCT
ejpam-2406	430	62	¶	¶	PROPN
ejpam-2406	430	63	q	q	NOUN
ejpam-2406	430	64	for	for	ADP
ejpam-2406	430	65	some	some	DET
ejpam-2406	430	66	integer	integer	NOUN
ejpam-2406	430	67	s.	s.	PROPN
ejpam-2406	430	68	therefore	therefore	ADV
ejpam-2406	430	69	,	,	PUNCT
ejpam-2406	430	70	as	as	SCONJ
ejpam-2406	430	71	¶	¶	PROPN
ejpam-2406	430	72	(	(	PUNCT
ejpam-2406	430	73	q	q	NOUN
ejpam-2406	430	74	:	:	PUNCT
ejpam-2406	430	75	a	a	DET
ejpam-2406	430	76	j	j	NOUN
ejpam-2406	430	77	)	)	PUNCT
ejpam-2406	430	78	or	or	CCONJ
ejpam-2406	430	79	bs	bs	ADJ
ejpam-2406	430	80	¶	¶	PROPN
ejpam-2406	430	81	(	(	PUNCT
ejpam-2406	430	82	q	q	NOUN
ejpam-2406	430	83	:	:	PUNCT
ejpam-2406	430	84	ai	ai	VERB
ejpam-2406	430	85	)	)	PUNCT
ejpam-2406	430	86	for	for	ADP
ejpam-2406	430	87	some	some	DET
ejpam-2406	430	88	integer	integer	NOUN
ejpam-2406	430	89	s.	s.	PROPN
ejpam-2406	430	90	hence	hence	PROPN
ejpam-2406	430	91	,	,	PUNCT
ejpam-2406	430	92	a	a	DET
ejpam-2406	430	93	¶	¶	NOUN
ejpam-2406	430	94	p	p	PROPN
ejpam-2406	430	95	j	j	PROPN
ejpam-2406	430	96	or	or	CCONJ
ejpam-2406	430	97	b	b	PROPN
ejpam-2406	430	98	¶	¶	NUM
ejpam-2406	430	99	pi	pi	NOUN
ejpam-2406	430	100	,	,	PUNCT
ejpam-2406	430	101	which	which	PRON
ejpam-2406	430	102	is	be	AUX
ejpam-2406	430	103	a	a	DET
ejpam-2406	430	104	contradiction	contradiction	NOUN
ejpam-2406	430	105	.	.	PUNCT
ejpam-2406	431	1	thus	thus	ADV
ejpam-2406	431	2	,	,	PUNCT
ejpam-2406	431	3	{	{	PUNCT
ejpam-2406	431	4	p1	p1	NOUN
ejpam-2406	431	5	,	,	PUNCT
ejpam-2406	431	6	p2	p2	NOUN
ejpam-2406	431	7	,	,	PUNCT
ejpam-2406	431	8	.	.	PUNCT
ejpam-2406	431	9	.	.	PUNCT
ejpam-2406	432	1	.	.	PUNCT
ejpam-2406	433	1	,	,	PUNCT
ejpam-2406	433	2	pn	pn	PROPN
ejpam-2406	433	3	}	}	PUNCT
ejpam-2406	433	4	is	be	AUX
ejpam-2406	433	5	a	a	DET
ejpam-2406	433	6	chain	chain	NOUN
ejpam-2406	433	7	of	of	ADP
ejpam-2406	433	8	prime	prime	ADJ
ejpam-2406	433	9	elements	element	NOUN
ejpam-2406	433	10	of	of	ADP
ejpam-2406	433	11	l.	l.	PROPN
ejpam-2406	433	12	converse	converse	PROPN
ejpam-2406	433	13	follows	follow	VERB
ejpam-2406	433	14	by	by	ADP
ejpam-2406	433	15	theorem	theorem	ADJ
ejpam-2406	433	16	7	7	NUM
ejpam-2406	433	17	.	.	NOUN
ejpam-2406	433	18	remark	remark	NOUN
ejpam-2406	433	19	3	3	NUM
ejpam-2406	433	20	.	.	PUNCT
ejpam-2406	434	1	we	we	PRON
ejpam-2406	434	2	note	note	VERB
ejpam-2406	434	3	that	that	SCONJ
ejpam-2406	434	4	theorem	theorem	NOUN
ejpam-2406	434	5	8	8	NUM
ejpam-2406	434	6	is	be	AUX
ejpam-2406	434	7	not	not	PART
ejpam-2406	434	8	necessarily	necessarily	ADV
ejpam-2406	434	9	true	true	ADJ
ejpam-2406	434	10	if	if	SCONJ
ejpam-2406	434	11	the	the	DET
ejpam-2406	434	12	primary	primary	ADJ
ejpam-2406	434	13	decomposition	decomposition	NOUN
ejpam-2406	434	14	q	q	NOUN
ejpam-2406	435	1	=	=	VERB
ejpam-2406	435	2	q1	q1	NOUN
ejpam-2406	435	3	∧q2	∧q2	VERB
ejpam-2406	435	4	∧	∧	PROPN
ejpam-2406	435	5	·	·	PUNCT
ejpam-2406	435	6	·	·	PUNCT
ejpam-2406	435	7	·	·	PUNCT
ejpam-2406	436	1	∧qn	∧qn	PROPN
ejpam-2406	436	2	is	be	AUX
ejpam-2406	436	3	not	not	PART
ejpam-2406	436	4	minimal	minimal	ADJ
ejpam-2406	436	5	.	.	PUNCT
ejpam-2406	436	6	example	example	NOUN
ejpam-2406	437	1	6	6	NUM
ejpam-2406	437	2	.	.	PUNCT
ejpam-2406	438	1	let	let	VERB
ejpam-2406	438	2	r	r	NOUN
ejpam-2406	438	3	=	=	SYM
ejpam-2406	438	4	z	z	NOUN
ejpam-2406	438	5	,	,	PUNCT
ejpam-2406	438	6	m	m	VERB
ejpam-2406	438	7	=	=	SYM
ejpam-2406	438	8	z	z	PROPN
ejpam-2406	438	9	⊕	⊕	PROPN
ejpam-2406	438	10	z.	z.	PROPN
ejpam-2406	438	11	let	let	VERB
ejpam-2406	438	12	l(r	l(r	PROPN
ejpam-2406	438	13	)	)	PUNCT
ejpam-2406	438	14	denote	denote	VERB
ejpam-2406	438	15	the	the	DET
ejpam-2406	438	16	set	set	NOUN
ejpam-2406	438	17	of	of	ADP
ejpam-2406	438	18	all	all	DET
ejpam-2406	438	19	ideals	ideal	NOUN
ejpam-2406	438	20	of	of	ADP
ejpam-2406	438	21	r	r	NOUN
ejpam-2406	438	22	and	and	CCONJ
ejpam-2406	438	23	l(m	l(m	PROPN
ejpam-2406	438	24	)	)	PUNCT
ejpam-2406	438	25	denote	denote	VERB
ejpam-2406	438	26	the	the	DET
ejpam-2406	438	27	set	set	NOUN
ejpam-2406	438	28	of	of	ADP
ejpam-2406	438	29	all	all	DET
ejpam-2406	438	30	sub	sub	NOUN
ejpam-2406	438	31	modules	module	NOUN
ejpam-2406	438	32	of	of	ADP
ejpam-2406	438	33	a	a	DET
ejpam-2406	438	34	module	module	NOUN
ejpam-2406	438	35	m	m	VERB
ejpam-2406	438	36	over	over	ADP
ejpam-2406	438	37	r	r	NOUN
ejpam-2406	438	38	=	=	PUNCT
ejpam-2406	438	39	z.	z.	PROPN
ejpam-2406	438	40	then	then	ADV
ejpam-2406	438	41	l(m	l(m	PROPN
ejpam-2406	438	42	)	)	PUNCT
ejpam-2406	438	43	is	be	AUX
ejpam-2406	438	44	an	an	DET
ejpam-2406	438	45	l	l	NOUN
ejpam-2406	438	46	-	-	NOUN
ejpam-2406	438	47	module	module	NOUN
ejpam-2406	438	48	over	over	ADP
ejpam-2406	438	49	l(r	l(r	PROPN
ejpam-2406	438	50	)	)	PUNCT
ejpam-2406	438	51	.	.	PUNCT
ejpam-2406	439	1	let	let	VERB
ejpam-2406	439	2	c.	c.	PROPN
ejpam-2406	439	3	manjarekar	manjarekar	PROPN
ejpam-2406	439	4	,	,	PUNCT
ejpam-2406	439	5	u.	u.	PROPN
ejpam-2406	439	6	kandale	kandale	PROPN
ejpam-2406	439	7	/	/	SYM
ejpam-2406	439	8	eur	eur	PROPN
ejpam-2406	439	9	.	.	PUNCT
ejpam-2406	440	1	j.	j.	PROPN
ejpam-2406	440	2	pure	pure	PROPN
ejpam-2406	440	3	appl	appl	PROPN
ejpam-2406	440	4	.	.	PROPN
ejpam-2406	440	5	math	math	PROPN
ejpam-2406	440	6	,	,	PUNCT
ejpam-2406	440	7	8	8	NUM
ejpam-2406	440	8	(	(	PUNCT
ejpam-2406	440	9	2015	2015	NUM
ejpam-2406	440	10	)	)	PUNCT
ejpam-2406	440	11	,	,	PUNCT
ejpam-2406	440	12	172	172	NUM
ejpam-2406	440	13	-	-	SYM
ejpam-2406	440	14	184	184	NUM
ejpam-2406	440	15	182	182	NUM
ejpam-2406	440	16	q1	q1	NOUN
ejpam-2406	440	17	=	=	SYM
ejpam-2406	440	18	2z	2z	NUM
ejpam-2406	440	19	⊕	⊕	PROPN
ejpam-2406	440	20	z	z	NOUN
ejpam-2406	440	21	,	,	PUNCT
ejpam-2406	440	22	q2	q2	NOUN
ejpam-2406	440	23	=	=	SYM
ejpam-2406	440	24	z	z	PROPN
ejpam-2406	440	25	⊕	⊕	PROPN
ejpam-2406	440	26	3z	3z	NUM
ejpam-2406	440	27	,	,	PUNCT
ejpam-2406	440	28	q3	q3	NOUN
ejpam-2406	440	29	=	=	PROPN
ejpam-2406	440	30	z	z	PROPN
ejpam-2406	440	31	⊕	⊕	PROPN
ejpam-2406	440	32	(	(	PUNCT
ejpam-2406	440	33	0	0	NUM
ejpam-2406	440	34	)	)	PUNCT
ejpam-2406	440	35	,	,	PUNCT
ejpam-2406	440	36	q4	q4	PROPN
ejpam-2406	440	37	=	=	SYM
ejpam-2406	440	38	(	(	PUNCT
ejpam-2406	440	39	0)⊕	0)⊕	NUM
ejpam-2406	440	40	z.	z.	PROPN
ejpam-2406	440	41	then	then	ADV
ejpam-2406	440	42	,	,	PUNCT
ejpam-2406	440	43	q1	q1	PROPN
ejpam-2406	440	44	,	,	PUNCT
ejpam-2406	440	45	q2	q2	PROPN
ejpam-2406	440	46	,	,	PUNCT
ejpam-2406	440	47	q3	q3	PROPN
ejpam-2406	440	48	,	,	PUNCT
ejpam-2406	440	49	q4	q4	PROPN
ejpam-2406	440	50	are	be	AUX
ejpam-2406	440	51	primary	primary	ADJ
ejpam-2406	440	52	sub	sub	NOUN
ejpam-2406	440	53	modules	module	NOUN
ejpam-2406	440	54	of	of	ADP
ejpam-2406	440	55	m	m	PRON
ejpam-2406	440	56	and	and	CCONJ
ejpam-2406	440	57	hence	hence	ADV
ejpam-2406	440	58	,	,	PUNCT
ejpam-2406	440	59	these	these	PRON
ejpam-2406	440	60	are	be	AUX
ejpam-2406	440	61	the	the	DET
ejpam-2406	440	62	elements	element	NOUN
ejpam-2406	440	63	of	of	ADP
ejpam-2406	440	64	a	a	DET
ejpam-2406	440	65	lattice	lattice	NOUN
ejpam-2406	440	66	module	module	NOUN
ejpam-2406	440	67	l(m	l(m	PROPN
ejpam-2406	440	68	)	)	PUNCT
ejpam-2406	440	69	with	with	ADP
ejpam-2406	440	70	p	p	PROPN
ejpam-2406	440	71	(	(	PUNCT
ejpam-2406	440	72	q	q	NOUN
ejpam-2406	440	73	i	i	PRON
ejpam-2406	440	74	:	:	PUNCT
ejpam-2406	440	75	m	m	X
ejpam-2406	440	76	)	)	PUNCT
ejpam-2406	441	1	=	=	SYM
ejpam-2406	441	2	2z	2z	NUM
ejpam-2406	441	3	,	,	PUNCT
ejpam-2406	441	4	p	p	X
ejpam-2406	441	5	(	(	PUNCT
ejpam-2406	441	6	q2	q2	NOUN
ejpam-2406	441	7	:	:	PUNCT
ejpam-2406	441	8	m	m	X
ejpam-2406	441	9	)	)	PUNCT
ejpam-2406	441	10	=	=	SYM
ejpam-2406	441	11	3z	3z	NUM
ejpam-2406	441	12	and	and	CCONJ
ejpam-2406	441	13	p	p	X
ejpam-2406	441	14	(	(	PUNCT
ejpam-2406	441	15	q	q	NOUN
ejpam-2406	441	16	i	i	PRON
ejpam-2406	441	17	:	:	PUNCT
ejpam-2406	441	18	m	m	X
ejpam-2406	441	19	)	)	PUNCT
ejpam-2406	442	1	=	=	SYM
ejpam-2406	442	2	p	p	X
ejpam-2406	442	3	(	(	PUNCT
ejpam-2406	442	4	q4	q4	PROPN
ejpam-2406	442	5	:	:	PUNCT
ejpam-2406	442	6	m	m	X
ejpam-2406	442	7	)	)	PUNCT
ejpam-2406	442	8	=	=	SYM
ejpam-2406	442	9	(	(	PUNCT
ejpam-2406	442	10	0	0	NUM
ejpam-2406	442	11	)	)	PUNCT
ejpam-2406	442	12	.	.	PUNCT
ejpam-2406	443	1	also	also	ADV
ejpam-2406	443	2	,	,	PUNCT
ejpam-2406	443	3	(	(	PUNCT
ejpam-2406	443	4	0	0	X
ejpam-2406	443	5	)	)	PUNCT
ejpam-2406	443	6	=	=	NOUN
ejpam-2406	443	7	q1∩q2∩q3∩q4	q1∩q2∩q3∩q4	NOUN
ejpam-2406	443	8	and	and	CCONJ
ejpam-2406	443	9	(	(	PUNCT
ejpam-2406	443	10	0	0	NUM
ejpam-2406	443	11	)	)	PUNCT
ejpam-2406	443	12	is	be	AUX
ejpam-2406	443	13	a	a	DET
ejpam-2406	443	14	classical	classical	ADJ
ejpam-2406	443	15	quasi	quasi	ADJ
ejpam-2406	443	16	primary	primary	ADJ
ejpam-2406	443	17	sub	sub	NOUN
ejpam-2406	443	18	module	module	NOUN
ejpam-2406	443	19	of	of	ADP
ejpam-2406	443	20	m	m	PROPN
ejpam-2406	443	21	and	and	CCONJ
ejpam-2406	443	22	hence	hence	ADV
ejpam-2406	443	23	a	a	DET
ejpam-2406	443	24	classical	classical	ADJ
ejpam-2406	443	25	quasi	quasi	ADJ
ejpam-2406	443	26	primary	primary	ADJ
ejpam-2406	443	27	element	element	NOUN
ejpam-2406	443	28	of	of	ADP
ejpam-2406	443	29	l(m	l(m	PROPN
ejpam-2406	443	30	)	)	PUNCT
ejpam-2406	443	31	.	.	PUNCT
ejpam-2406	444	1	but	but	CCONJ
ejpam-2406	444	2	{	{	PUNCT
ejpam-2406	444	3	(	(	PUNCT
ejpam-2406	444	4	0	0	NUM
ejpam-2406	444	5	)	)	PUNCT
ejpam-2406	444	6	,	,	PUNCT
ejpam-2406	444	7	2z	2z	NUM
ejpam-2406	444	8	,	,	PUNCT
ejpam-2406	444	9	3z	3z	NUM
ejpam-2406	444	10	}	}	PUNCT
ejpam-2406	444	11	is	be	AUX
ejpam-2406	444	12	not	not	PART
ejpam-2406	444	13	a	a	DET
ejpam-2406	444	14	chain	chain	NOUN
ejpam-2406	444	15	of	of	ADP
ejpam-2406	444	16	prime	prime	ADJ
ejpam-2406	444	17	ideals	ideal	NOUN
ejpam-2406	444	18	of	of	ADP
ejpam-2406	444	19	r	r	NOUN
ejpam-2406	444	20	i.e.	i.e.	X
ejpam-2406	444	21	(	(	PUNCT
ejpam-2406	444	22	0	0	NUM
ejpam-2406	444	23	)	)	PUNCT
ejpam-2406	444	24	,	,	PUNCT
ejpam-2406	444	25	2z	2z	NUM
ejpam-2406	444	26	,	,	PUNCT
ejpam-2406	444	27	3z	3z	NUM
ejpam-2406	444	28	is	be	AUX
ejpam-2406	444	29	not	not	PART
ejpam-2406	444	30	a	a	DET
ejpam-2406	444	31	chain	chain	NOUN
ejpam-2406	444	32	of	of	ADP
ejpam-2406	444	33	prime	prime	ADJ
ejpam-2406	444	34	elements	element	NOUN
ejpam-2406	444	35	of	of	ADP
ejpam-2406	444	36	l(r	l(r	PROPN
ejpam-2406	444	37	)	)	PUNCT
ejpam-2406	444	38	.	.	PUNCT
ejpam-2406	445	1	definition	definition	NOUN
ejpam-2406	445	2	7	7	NUM
ejpam-2406	445	3	.	.	PUNCT
ejpam-2406	446	1	let	let	VERB
ejpam-2406	446	2	n	n	PRON
ejpam-2406	446	3	be	be	AUX
ejpam-2406	446	4	a	a	DET
ejpam-2406	446	5	proper	proper	ADJ
ejpam-2406	446	6	element	element	NOUN
ejpam-2406	446	7	of	of	ADP
ejpam-2406	446	8	a	a	DET
ejpam-2406	446	9	lattice	lattice	NOUN
ejpam-2406	446	10	module	module	NOUN
ejpam-2406	446	11	m	m	PROPN
ejpam-2406	446	12	over	over	ADP
ejpam-2406	446	13	l.	l.	PROPN
ejpam-2406	446	14	a	a	DET
ejpam-2406	446	15	classical	classical	ADJ
ejpam-2406	446	16	primary	primary	NOUN
ejpam-2406	446	17	(	(	PUNCT
ejpam-2406	446	18	respectively	respectively	ADV
ejpam-2406	446	19	classical	classical	ADJ
ejpam-2406	446	20	quasi	quasi	ADJ
ejpam-2406	446	21	primary	primary	NOUN
ejpam-2406	446	22	)	)	PUNCT
ejpam-2406	446	23	decomposition	decomposition	NOUN
ejpam-2406	446	24	of	of	ADP
ejpam-2406	446	25	n	n	PROPN
ejpam-2406	446	26	is	be	AUX
ejpam-2406	446	27	an	an	DET
ejpam-2406	446	28	expression	expression	NOUN
ejpam-2406	446	29	n	n	NOUN
ejpam-2406	446	30	=	=	SYM
ejpam-2406	446	31	n∧	n∧	NUM
ejpam-2406	447	1	i=1	i=1	PROPN
ejpam-2406	448	1	q	q	PROPN
ejpam-2406	449	1	i	i	PRON
ejpam-2406	449	2	where	where	SCONJ
ejpam-2406	449	3	each	each	PRON
ejpam-2406	449	4	q	q	X
ejpam-2406	450	1	i	i	PRON
ejpam-2406	450	2	is	be	AUX
ejpam-2406	450	3	classical	classical	ADJ
ejpam-2406	450	4	primary	primary	NOUN
ejpam-2406	450	5	(	(	PUNCT
ejpam-2406	450	6	respectively	respectively	ADV
ejpam-2406	450	7	classical	classical	ADJ
ejpam-2406	450	8	quasi	quasi	ADJ
ejpam-2406	450	9	primary	primary	NOUN
ejpam-2406	450	10	)	)	PUNCT
ejpam-2406	450	11	element	element	NOUN
ejpam-2406	450	12	of	of	ADP
ejpam-2406	450	13	m.the	m.the	DET
ejpam-2406	450	14	decomposition	decomposition	NOUN
ejpam-2406	450	15	is	be	AUX
ejpam-2406	450	16	called	call	VERB
ejpam-2406	450	17	reduced	reduce	VERB
ejpam-2406	450	18	if	if	SCONJ
ejpam-2406	450	19	it	it	PRON
ejpam-2406	450	20	satisfies	satisfy	VERB
ejpam-2406	450	21	the	the	DET
ejpam-2406	450	22	following	follow	VERB
ejpam-2406	450	23	two	two	NUM
ejpam-2406	450	24	conditions	condition	NOUN
ejpam-2406	450	25	,	,	PUNCT
ejpam-2406	450	26	(	(	PUNCT
ejpam-2406	450	27	i	i	NOUN
ejpam-2406	450	28	)	)	PUNCT
ejpam-2406	450	29	no	no	DET
ejpam-2406	450	30	q	q	PROPN
ejpam-2406	450	31	i1	i1	PROPN
ejpam-2406	450	32	∧q	∧q	PROPN
ejpam-2406	450	33	i2	i2	PROPN
ejpam-2406	450	34	∧	∧	PROPN
ejpam-2406	450	35	·	·	PUNCT
ejpam-2406	450	36	·	·	PUNCT
ejpam-2406	451	1	·	·	PUNCT
ejpam-2406	451	2	∧q	∧q	PROPN
ejpam-2406	451	3	i	i	PRON
ejpam-2406	451	4	t	t	PROPN
ejpam-2406	451	5	is	be	AUX
ejpam-2406	451	6	classical	classical	ADJ
ejpam-2406	451	7	primary	primary	NOUN
ejpam-2406	451	8	(	(	PUNCT
ejpam-2406	451	9	respectively	respectively	ADV
ejpam-2406	451	10	classical	classical	ADJ
ejpam-2406	451	11	quasi	quasi	ADJ
ejpam-2406	451	12	primary	primary	NOUN
ejpam-2406	451	13	)	)	PUNCT
ejpam-2406	451	14	element	element	NOUN
ejpam-2406	451	15	where	where	SCONJ
ejpam-2406	451	16	(	(	PUNCT
ejpam-2406	451	17	i1	i1	PROPN
ejpam-2406	451	18	,	,	PUNCT
ejpam-2406	451	19	i2	i2	PROPN
ejpam-2406	451	20	,	,	PUNCT
ejpam-2406	451	21	.	.	PUNCT
ejpam-2406	451	22	.	.	PUNCT
ejpam-2406	452	1	.	.	PUNCT
ejpam-2406	453	1	,	,	PUNCT
ejpam-2406	453	2	it	it	PRON
ejpam-2406	453	3	)	)	PUNCT
ejpam-2406	453	4	⊆	⊆	X
ejpam-2406	453	5	{	{	PUNCT
ejpam-2406	453	6	1,2	1,2	NUM
ejpam-2406	453	7	,	,	PUNCT
ejpam-2406	453	8	.	.	PUNCT
ejpam-2406	453	9	.	.	PUNCT
ejpam-2406	453	10	.	.	PUNCT
ejpam-2406	453	11	,	,	PUNCT
ejpam-2406	453	12	n	n	CCONJ
ejpam-2406	453	13	}	}	PUNCT
ejpam-2406	453	14	for	for	ADP
ejpam-2406	453	15	t	t	PROPN
ejpam-2406	453	16	¾	¾	PROPN
ejpam-2406	453	17	2	2	NUM
ejpam-2406	453	18	with	with	ADP
ejpam-2406	453	19	i1	i1	PROPN
ejpam-2406	453	20	<	<	X
ejpam-2406	453	21	i2	i2	PROPN
ejpam-2406	453	22	<	<	X
ejpam-2406	453	23	·	·	PUNCT
ejpam-2406	453	24	·	·	PUNCT
ejpam-2406	453	25	·	·	PUNCT
ejpam-2406	453	26	<	<	X
ejpam-2406	453	27	it	it	PRON
ejpam-2406	453	28	(	(	PUNCT
ejpam-2406	453	29	ii	ii	NOUN
ejpam-2406	453	30	)	)	PUNCT
ejpam-2406	453	31	for	for	ADP
ejpam-2406	453	32	each	each	DET
ejpam-2406	453	33	j	j	PROPN
ejpam-2406	453	34	,	,	PUNCT
ejpam-2406	453	35	q	q	PROPN
ejpam-2406	454	1	j	j	PROPN
ejpam-2406	454	2	∧	∧	PROPN
ejpam-2406	454	3	i	i	PROPN
ejpam-2406	454	4	6=	6=	PROPN
ejpam-2406	455	1	j	j	PROPN
ejpam-2406	455	2	q	q	X
ejpam-2406	456	1	i	i	PRON
ejpam-2406	456	2	corresponding	correspond	VERB
ejpam-2406	456	3	to	to	ADP
ejpam-2406	456	4	the	the	DET
ejpam-2406	456	5	above	above	ADJ
ejpam-2406	456	6	definition	definition	NOUN
ejpam-2406	456	7	by	by	ADP
ejpam-2406	456	8	theorem	theorem	NOUN
ejpam-2406	456	9	2	2	NUM
ejpam-2406	456	10	we	we	PRON
ejpam-2406	456	11	have	have	VERB
ejpam-2406	456	12	a	a	DET
ejpam-2406	456	13	list	list	NOUN
ejpam-2406	456	14	of	of	ADP
ejpam-2406	456	15	prime	prime	ADJ
ejpam-2406	456	16	elements	element	NOUN
ejpam-2406	456	17	p	p	X
ejpam-2406	456	18	(	(	PUNCT
ejpam-2406	456	19	q1	q1	PROPN
ejpam-2406	456	20	:	:	PUNCT
ejpam-2406	456	21	i	i	PRON
ejpam-2406	456	22	m	m	VERB
ejpam-2406	456	23	)	)	PUNCT
ejpam-2406	456	24	,	,	PUNCT
ejpam-2406	456	25	.	.	PUNCT
ejpam-2406	456	26	.	.	PUNCT
ejpam-2406	456	27	.	.	PUNCT
ejpam-2406	457	1	p	p	X
ejpam-2406	457	2	(	(	PUNCT
ejpam-2406	457	3	qn	qn	NOUN
ejpam-2406	457	4	:	:	PUNCT
ejpam-2406	457	5	i	i	PROPN
ejpam-2406	457	6	m	m	PROPN
ejpam-2406	457	7	)	)	PUNCT
ejpam-2406	457	8	.	.	PUNCT
ejpam-2406	458	1	among	among	ADP
ejpam-2406	458	2	reduced	reduced	ADJ
ejpam-2406	458	3	classical	classical	ADJ
ejpam-2406	458	4	primary	primary	NOUN
ejpam-2406	458	5	(	(	PUNCT
ejpam-2406	458	6	resp	resp	NOUN
ejpam-2406	458	7	classical	classical	ADJ
ejpam-2406	458	8	quasi	quasi	NOUN
ejpam-2406	458	9	primary	primary	NOUN
ejpam-2406	458	10	)	)	PUNCT
ejpam-2406	458	11	decomposition	decomposition	NOUN
ejpam-2406	458	12	,	,	PUNCT
ejpam-2406	458	13	any	any	DET
ejpam-2406	458	14	one	one	NOUN
ejpam-2406	458	15	that	that	PRON
ejpam-2406	458	16	has	have	VERB
ejpam-2406	458	17	the	the	DET
ejpam-2406	458	18	least	least	ADJ
ejpam-2406	458	19	number	number	NOUN
ejpam-2406	458	20	of	of	ADP
ejpam-2406	458	21	distinct	distinct	ADJ
ejpam-2406	458	22	primes	prime	NOUN
ejpam-2406	458	23	will	will	AUX
ejpam-2406	458	24	be	be	AUX
ejpam-2406	458	25	called	call	VERB
ejpam-2406	458	26	minimal	minimal	ADJ
ejpam-2406	458	27	.	.	PUNCT
ejpam-2406	459	1	it	it	PRON
ejpam-2406	459	2	is	be	AUX
ejpam-2406	459	3	clear	clear	ADJ
ejpam-2406	459	4	that	that	SCONJ
ejpam-2406	459	5	,	,	PUNCT
ejpam-2406	459	6	every	every	DET
ejpam-2406	459	7	primary	primary	ADJ
ejpam-2406	459	8	decomposition	decomposition	NOUN
ejpam-2406	459	9	of	of	ADP
ejpam-2406	459	10	an	an	DET
ejpam-2406	459	11	element	element	NOUN
ejpam-2406	459	12	n	n	PROPN
ejpam-2406	459	13	of	of	ADP
ejpam-2406	459	14	m	m	PROPN
ejpam-2406	459	15	is	be	AUX
ejpam-2406	459	16	called	call	VERB
ejpam-2406	459	17	classical	classical	ADJ
ejpam-2406	459	18	primary	primary	NOUN
ejpam-2406	459	19	but	but	CCONJ
ejpam-2406	459	20	the	the	DET
ejpam-2406	459	21	converse	converse	NOUN
ejpam-2406	459	22	is	be	AUX
ejpam-2406	459	23	not	not	PART
ejpam-2406	459	24	always	always	ADV
ejpam-2406	459	25	true	true	ADJ
ejpam-2406	459	26	.	.	PUNCT
ejpam-2406	460	1	the	the	DET
ejpam-2406	460	2	next	next	ADJ
ejpam-2406	460	3	result	result	NOUN
ejpam-2406	460	4	is	be	AUX
ejpam-2406	460	5	useful	useful	ADJ
ejpam-2406	460	6	in	in	ADP
ejpam-2406	460	7	proving	prove	VERB
ejpam-2406	460	8	the	the	DET
ejpam-2406	460	9	uniqueness	uniqueness	NOUN
ejpam-2406	460	10	of	of	ADP
ejpam-2406	460	11	associated	associated	ADJ
ejpam-2406	460	12	primes	prime	NOUN
ejpam-2406	460	13	of	of	ADP
ejpam-2406	460	14	an	an	DET
ejpam-2406	460	15	element	element	NOUN
ejpam-2406	460	16	of	of	ADP
ejpam-2406	460	17	a	a	DET
ejpam-2406	460	18	lattice	lattice	NOUN
ejpam-2406	460	19	module	module	NOUN
ejpam-2406	460	20	with	with	ADP
ejpam-2406	460	21	a	a	DET
ejpam-2406	460	22	primary	primary	ADJ
ejpam-2406	460	23	decomposition	decomposition	NOUN
ejpam-2406	460	24	.	.	PUNCT
ejpam-2406	461	1	theorem	theorem	NOUN
ejpam-2406	461	2	11	11	NUM
ejpam-2406	461	3	.	.	PUNCT
ejpam-2406	462	1	let	let	VERB
ejpam-2406	462	2	n	n	PRON
ejpam-2406	462	3	=	=	VERB
ejpam-2406	462	4	q1∧q2∧	q1∧q2∧	NOUN
ejpam-2406	462	5	·	·	PUNCT
ejpam-2406	462	6	·	·	PUNCT
ejpam-2406	462	7	·	·	PUNCT
ejpam-2406	462	8	∧qk	∧qk	NOUN
ejpam-2406	462	9	be	be	AUX
ejpam-2406	462	10	a	a	DET
ejpam-2406	462	11	reduced	reduce	VERB
ejpam-2406	462	12	primary	primary	ADJ
ejpam-2406	462	13	decomposition	decomposition	NOUN
ejpam-2406	462	14	of	of	ADP
ejpam-2406	462	15	a	a	DET
ejpam-2406	462	16	lattice	lattice	NOUN
ejpam-2406	462	17	module	module	NOUN
ejpam-2406	462	18	m	m	PROPN
ejpam-2406	462	19	over	over	ADP
ejpam-2406	462	20	l.	l.	PROPN
ejpam-2406	462	21	then	then	ADV
ejpam-2406	462	22	every	every	DET
ejpam-2406	462	23	minimal	minimal	ADJ
ejpam-2406	462	24	prime	prime	ADJ
ejpam-2406	462	25	divisor	divisor	NOUN
ejpam-2406	462	26	of	of	ADP
ejpam-2406	462	27	n	n	PROPN
ejpam-2406	462	28	is	be	AUX
ejpam-2406	462	29	a	a	DET
ejpam-2406	462	30	prime	prime	ADJ
ejpam-2406	462	31	divisor	divisor	NOUN
ejpam-2406	462	32	of	of	ADP
ejpam-2406	462	33	n.	n.	PROPN
ejpam-2406	462	34	proof	proof	NOUN
ejpam-2406	462	35	.	.	PUNCT
ejpam-2406	463	1	let	let	VERB
ejpam-2406	463	2	pi	pi	NOUN
ejpam-2406	463	3	=	=	PUNCT
ejpam-2406	463	4	p	p	X
ejpam-2406	463	5	(	(	PUNCT
ejpam-2406	463	6	q	q	NOUN
ejpam-2406	463	7	i	i	PRON
ejpam-2406	463	8	:	:	PUNCT
ejpam-2406	463	9	i	i	PRON
ejpam-2406	463	10	m	m	PROPN
ejpam-2406	463	11	)	)	PUNCT
ejpam-2406	463	12	.	.	PUNCT
ejpam-2406	464	1	then	then	ADV
ejpam-2406	464	2	p1	p1	PROPN
ejpam-2406	464	3	,	,	PUNCT
ejpam-2406	464	4	p2	p2	NOUN
ejpam-2406	464	5	,	,	PUNCT
ejpam-2406	464	6	.	.	PUNCT
ejpam-2406	464	7	.	.	PUNCT
ejpam-2406	464	8	.	.	PUNCT
ejpam-2406	465	1	,	,	PUNCT
ejpam-2406	465	2	pk	pk	NOUN
ejpam-2406	465	3	are	be	AUX
ejpam-2406	465	4	the	the	DET
ejpam-2406	465	5	prime	prime	ADJ
ejpam-2406	465	6	elements	element	NOUN
ejpam-2406	465	7	which	which	PRON
ejpam-2406	465	8	are	be	AUX
ejpam-2406	465	9	called	call	VERB
ejpam-2406	465	10	prime	prime	ADJ
ejpam-2406	465	11	divisors	divisor	NOUN
ejpam-2406	465	12	of	of	ADP
ejpam-2406	465	13	n	n	PRON
ejpam-2406	465	14	or	or	CCONJ
ejpam-2406	465	15	associated	associated	ADJ
ejpam-2406	465	16	primes	prime	NOUN
ejpam-2406	465	17	of	of	ADP
ejpam-2406	465	18	n.	n.	NOUN
ejpam-2406	465	19	we	we	PRON
ejpam-2406	465	20	have	have	VERB
ejpam-2406	465	21	æ	æ	X
ejpam-2406	465	22	(	(	PUNCT
ejpam-2406	465	23	n	n	NUM
ejpam-2406	465	24	:	:	PUNCT
ejpam-2406	465	25	i	i	PRON
ejpam-2406	465	26	m	m	VERB
ejpam-2406	465	27	)	)	PUNCT
ejpam-2406	466	1	=	=	SYM
ejpam-2406	466	2	æ	æ	X
ejpam-2406	466	3	(	(	PUNCT
ejpam-2406	466	4	q1	q1	PROPN
ejpam-2406	466	5	∧q2	∧q2	VERB
ejpam-2406	466	6	∧	∧	PROPN
ejpam-2406	466	7	·	·	PUNCT
ejpam-2406	466	8	·	·	PUNCT
ejpam-2406	466	9	·	·	PUNCT
ejpam-2406	466	10	∧qk	∧qk	NOUN
ejpam-2406	466	11	)	)	PUNCT
ejpam-2406	466	12	:	:	PUNCT
ejpam-2406	467	1	i	i	PRON
ejpam-2406	467	2	m	m	VERB
ejpam-2406	467	3	=	=	ADJ
ejpam-2406	467	4	æ	æ	X
ejpam-2406	467	5	(	(	PUNCT
ejpam-2406	467	6	q1	q1	PROPN
ejpam-2406	467	7	:	:	PUNCT
ejpam-2406	467	8	i	i	PRON
ejpam-2406	467	9	m	m	VERB
ejpam-2406	467	10	)	)	PUNCT
ejpam-2406	467	11	∧	∧	PROPN
ejpam-2406	467	12	æ	æ	X
ejpam-2406	467	13	(	(	PUNCT
ejpam-2406	467	14	q2	q2	NOUN
ejpam-2406	467	15	:	:	PUNCT
ejpam-2406	467	16	i	i	PRON
ejpam-2406	467	17	m	m	VERB
ejpam-2406	467	18	)	)	PUNCT
ejpam-2406	467	19	∧	∧	PROPN
ejpam-2406	467	20	·	·	PUNCT
ejpam-2406	467	21	·	·	PUNCT
ejpam-2406	467	22	·	·	PUNCT
ejpam-2406	468	1	∧	∧	NOUN
ejpam-2406	468	2	æ	æ	X
ejpam-2406	468	3	(	(	PUNCT
ejpam-2406	468	4	qk	qk	INTJ
ejpam-2406	468	5	:	:	PUNCT
ejpam-2406	468	6	i	i	PRON
ejpam-2406	468	7	m	m	VERB
ejpam-2406	468	8	)	)	PUNCT
ejpam-2406	469	1	=	=	NOUN
ejpam-2406	469	2	p1	p1	NOUN
ejpam-2406	469	3	∧	∧	NOUN
ejpam-2406	469	4	p2	p2	NOUN
ejpam-2406	469	5	∧	∧	PROPN
ejpam-2406	469	6	·	·	PUNCT
ejpam-2406	469	7	·	·	PUNCT
ejpam-2406	469	8	·	·	PUNCT
ejpam-2406	469	9	∧	∧	NOUN
ejpam-2406	469	10	pk	pk	PROPN
ejpam-2406	469	11	.	.	PUNCT
ejpam-2406	470	1	if	if	SCONJ
ejpam-2406	470	2	a	a	DET
ejpam-2406	470	3	¶	¶	PROPN
ejpam-2406	470	4	p1p2p3	p1p2p3	NOUN
ejpam-2406	470	5	.	.	PUNCT
ejpam-2406	471	1	.	.	PUNCT
ejpam-2406	471	2	.	.	PUNCT
ejpam-2406	472	1	pk	pk	NOUN
ejpam-2406	472	2	then	then	ADV
ejpam-2406	472	3	a	a	DET
ejpam-2406	472	4	¶	¶	PROPN
ejpam-2406	472	5	pi	pi	NOUN
ejpam-2406	472	6	for	for	ADP
ejpam-2406	472	7	each	each	DET
ejpam-2406	472	8	i	i	NOUN
ejpam-2406	472	9	=	=	NOUN
ejpam-2406	472	10	1,2	1,2	NUM
ejpam-2406	472	11	,	,	PUNCT
ejpam-2406	472	12	.	.	PUNCT
ejpam-2406	472	13	.	.	PUNCT
ejpam-2406	472	14	.	.	PUNCT
ejpam-2406	473	1	,	,	PUNCT
ejpam-2406	473	2	n.	n.	NOUN
ejpam-2406	473	3	hence	hence	ADV
ejpam-2406	474	1	a	a	DET
ejpam-2406	474	2	¶	¶	NOUN
ejpam-2406	474	3	p	p	NOUN
ejpam-2406	474	4	(	(	PUNCT
ejpam-2406	474	5	q	q	NOUN
ejpam-2406	474	6	i	i	X
ejpam-2406	474	7	:	:	PUNCT
ejpam-2406	474	8	i	i	PRON
ejpam-2406	474	9	m	m	VERB
ejpam-2406	474	10	)	)	PUNCT
ejpam-2406	474	11	for	for	ADP
ejpam-2406	474	12	each	each	DET
ejpam-2406	474	13	i.	i.	NOUN
ejpam-2406	474	14	that	that	PRON
ejpam-2406	474	15	is	be	AUX
ejpam-2406	474	16	a	a	PRON
ejpam-2406	474	17	¶	¶	PROPN
ejpam-2406	474	18	p	p	NOUN
ejpam-2406	474	19	(	(	PUNCT
ejpam-2406	474	20	q1	q1	PROPN
ejpam-2406	474	21	:	:	PUNCT
ejpam-2406	474	22	i	i	PRON
ejpam-2406	474	23	m	m	VERB
ejpam-2406	474	24	)	)	PUNCT
ejpam-2406	474	25	∧	∧	PROPN
ejpam-2406	474	26	p	p	NOUN
ejpam-2406	474	27	(	(	PUNCT
ejpam-2406	474	28	q2	q2	NOUN
ejpam-2406	474	29	:	:	PUNCT
ejpam-2406	474	30	i	i	PRON
ejpam-2406	474	31	m	m	VERB
ejpam-2406	474	32	)	)	PUNCT
ejpam-2406	474	33	∧	∧	PROPN
ejpam-2406	474	34	.	.	PUNCT
ejpam-2406	474	35	.	.	PUNCT
ejpam-2406	474	36	.	.	PUNCT
ejpam-2406	475	1	p	p	X
ejpam-2406	475	2	(	(	PUNCT
ejpam-2406	475	3	qk	qk	NOUN
ejpam-2406	475	4	:	:	PUNCT
ejpam-2406	475	5	i	i	PRON
ejpam-2406	475	6	m	m	VERB
ejpam-2406	475	7	)	)	PUNCT
ejpam-2406	476	1	=	=	SYM
ejpam-2406	476	2	p	p	X
ejpam-2406	476	3	(	(	PUNCT
ejpam-2406	476	4	n	n	NOUN
ejpam-2406	476	5	:	:	PUNCT
ejpam-2406	476	6	i	i	PRON
ejpam-2406	476	7	m	m	PROPN
ejpam-2406	476	8	)	)	PUNCT
ejpam-2406	476	9	.	.	PUNCT
ejpam-2406	477	1	so	so	ADV
ejpam-2406	477	2	an	an	DET
ejpam-2406	477	3	¶	¶	PROPN
ejpam-2406	477	4	(	(	PUNCT
ejpam-2406	477	5	n	n	NUM
ejpam-2406	477	6	:	:	PUNCT
ejpam-2406	477	7	i	i	PRON
ejpam-2406	477	8	m	m	VERB
ejpam-2406	477	9	)	)	PUNCT
ejpam-2406	477	10	for	for	ADP
ejpam-2406	477	11	some	some	DET
ejpam-2406	477	12	positive	positive	ADJ
ejpam-2406	477	13	integer	integer	NOUN
ejpam-2406	477	14	n.	n.	NOUN
ejpam-2406	477	15	if	if	SCONJ
ejpam-2406	477	16	p	p	NOUN
ejpam-2406	477	17	is	be	AUX
ejpam-2406	477	18	any	any	DET
ejpam-2406	477	19	prime	prime	ADJ
ejpam-2406	477	20	element	element	NOUN
ejpam-2406	477	21	of	of	ADP
ejpam-2406	477	22	l	l	NOUN
ejpam-2406	477	23	containing	contain	VERB
ejpam-2406	477	24	(	(	PUNCT
ejpam-2406	477	25	n	n	NUM
ejpam-2406	477	26	:	:	PUNCT
ejpam-2406	477	27	i	i	PRON
ejpam-2406	477	28	m	m	VERB
ejpam-2406	477	29	)	)	PUNCT
ejpam-2406	477	30	then	then	ADV
ejpam-2406	477	31	an	an	DET
ejpam-2406	477	32	¶	¶	NOUN
ejpam-2406	477	33	p	p	NOUN
ejpam-2406	477	34	and	and	CCONJ
ejpam-2406	477	35	hence	hence	ADV
ejpam-2406	477	36	a	a	DET
ejpam-2406	477	37	¶	¶	NOUN
ejpam-2406	477	38	p.	p.	NOUN
ejpam-2406	477	39	then	then	ADV
ejpam-2406	477	40	p1p2	p1p2	PROPN
ejpam-2406	477	41	.	.	PUNCT
ejpam-2406	477	42	.	.	PUNCT
ejpam-2406	477	43	.	.	PUNCT
ejpam-2406	478	1	pk	pk	NOUN
ejpam-2406	478	2	¶	¶	NOUN
ejpam-2406	478	3	p	p	X
ejpam-2406	479	1	whenever	whenever	SCONJ
ejpam-2406	479	2	(	(	PUNCT
ejpam-2406	479	3	n	n	X
ejpam-2406	479	4	:	:	PUNCT
ejpam-2406	479	5	i	i	PRON
ejpam-2406	479	6	m	m	VERB
ejpam-2406	479	7	)	)	PUNCT
ejpam-2406	479	8	¶	¶	PROPN
ejpam-2406	479	9	p.	p.	NOUN
ejpam-2406	479	10	this	this	PRON
ejpam-2406	479	11	shows	show	VERB
ejpam-2406	479	12	that	that	SCONJ
ejpam-2406	479	13	pi	pi	PROPN
ejpam-2406	479	14	¶	¶	PROPN
ejpam-2406	479	15	p	p	NOUN
ejpam-2406	479	16	for	for	ADP
ejpam-2406	479	17	some	some	DET
ejpam-2406	479	18	i.	i.	NOUN
ejpam-2406	479	19	if	if	SCONJ
ejpam-2406	479	20	p	p	NOUN
ejpam-2406	479	21	is	be	AUX
ejpam-2406	479	22	a	a	DET
ejpam-2406	479	23	minimal	minimal	ADJ
ejpam-2406	479	24	prime	prime	ADJ
ejpam-2406	479	25	element	element	NOUN
ejpam-2406	479	26	containing	contain	VERB
ejpam-2406	479	27	(	(	PUNCT
ejpam-2406	479	28	n	n	NUM
ejpam-2406	479	29	:	:	PUNCT
ejpam-2406	479	30	i	i	PRON
ejpam-2406	479	31	m	m	VERB
ejpam-2406	479	32	)	)	PUNCT
ejpam-2406	479	33	then	then	ADV
ejpam-2406	479	34	pi	pi	PROPN
ejpam-2406	479	35	¶	¶	PROPN
ejpam-2406	479	36	p	p	NOUN
ejpam-2406	479	37	for	for	ADP
ejpam-2406	479	38	some	some	DET
ejpam-2406	479	39	i.	i.	NOUN
ejpam-2406	479	40	also	also	ADV
ejpam-2406	479	41	pi	pi	PROPN
ejpam-2406	479	42	contains	contain	VERB
ejpam-2406	479	43	(	(	PUNCT
ejpam-2406	479	44	n	n	X
ejpam-2406	479	45	:	:	PUNCT
ejpam-2406	479	46	i	i	PRON
ejpam-2406	479	47	m	m	PROPN
ejpam-2406	479	48	)	)	PUNCT
ejpam-2406	479	49	,	,	PUNCT
ejpam-2406	479	50	but	but	CCONJ
ejpam-2406	479	51	p	p	NOUN
ejpam-2406	479	52	is	be	AUX
ejpam-2406	479	53	minimal	minimal	ADJ
ejpam-2406	479	54	such	such	ADJ
ejpam-2406	479	55	element	element	NOUN
ejpam-2406	479	56	.	.	PUNCT
ejpam-2406	480	1	hence	hence	ADV
ejpam-2406	480	2	pi	pi	NOUN
ejpam-2406	481	1	=	=	SYM
ejpam-2406	481	2	p.	p.	NOUN
ejpam-2406	481	3	thus	thus	ADV
ejpam-2406	481	4	every	every	DET
ejpam-2406	481	5	minimal	minimal	ADJ
ejpam-2406	481	6	prime	prime	ADJ
ejpam-2406	481	7	divisors	divisor	NOUN
ejpam-2406	481	8	of	of	ADP
ejpam-2406	481	9	n	n	PROPN
ejpam-2406	481	10	is	be	AUX
ejpam-2406	481	11	a	a	DET
ejpam-2406	481	12	prime	prime	ADJ
ejpam-2406	481	13	divisor	divisor	NOUN
ejpam-2406	481	14	of	of	ADP
ejpam-2406	481	15	n	n	NUM
ejpam-2406	481	16	and	and	CCONJ
ejpam-2406	481	17	is	be	AUX
ejpam-2406	481	18	minimal	minimal	ADJ
ejpam-2406	481	19	in	in	ADP
ejpam-2406	481	20	the	the	DET
ejpam-2406	481	21	set	set	NOUN
ejpam-2406	481	22	of	of	ADP
ejpam-2406	481	23	prime	prime	ADJ
ejpam-2406	481	24	divisors	divisor	NOUN
ejpam-2406	481	25	of	of	ADP
ejpam-2406	481	26	n.	n.	NOUN
ejpam-2406	481	27	the	the	DET
ejpam-2406	481	28	next	next	ADJ
ejpam-2406	481	29	result	result	NOUN
ejpam-2406	481	30	we	we	PRON
ejpam-2406	481	31	prove	prove	VERB
ejpam-2406	481	32	the	the	DET
ejpam-2406	481	33	important	important	ADJ
ejpam-2406	481	34	property	property	NOUN
ejpam-2406	481	35	of	of	ADP
ejpam-2406	481	36	uniqueness	uniqueness	NOUN
ejpam-2406	481	37	of	of	ADP
ejpam-2406	481	38	associated	associated	ADJ
ejpam-2406	481	39	primes	prime	NOUN
ejpam-2406	481	40	of	of	ADP
ejpam-2406	481	41	an	an	DET
ejpam-2406	481	42	element	element	NOUN
ejpam-2406	481	43	having	have	VERB
ejpam-2406	481	44	classical	classical	ADJ
ejpam-2406	481	45	quasi	quasi	ADJ
ejpam-2406	481	46	primary	primary	ADJ
ejpam-2406	481	47	decomposition	decomposition	NOUN
ejpam-2406	481	48	.	.	PUNCT
ejpam-2406	482	1	c.	c.	PROPN
ejpam-2406	482	2	manjarekar	manjarekar	PROPN
ejpam-2406	482	3	,	,	PUNCT
ejpam-2406	482	4	u.	u.	PROPN
ejpam-2406	482	5	kandale	kandale	PROPN
ejpam-2406	482	6	/	/	SYM
ejpam-2406	482	7	eur	eur	PROPN
ejpam-2406	482	8	.	.	PUNCT
ejpam-2406	483	1	j.	j.	PROPN
ejpam-2406	483	2	pure	pure	PROPN
ejpam-2406	483	3	appl	appl	PROPN
ejpam-2406	483	4	.	.	PROPN
ejpam-2406	483	5	math	math	PROPN
ejpam-2406	483	6	,	,	PUNCT
ejpam-2406	483	7	8	8	NUM
ejpam-2406	483	8	(	(	PUNCT
ejpam-2406	483	9	2015	2015	NUM
ejpam-2406	483	10	)	)	PUNCT
ejpam-2406	483	11	,	,	PUNCT
ejpam-2406	483	12	172	172	NUM
ejpam-2406	483	13	-	-	SYM
ejpam-2406	483	14	184	184	NUM
ejpam-2406	483	15	183	183	NUM
ejpam-2406	483	16	theorem	theorem	NOUN
ejpam-2406	483	17	12	12	NUM
ejpam-2406	483	18	.	.	PUNCT
ejpam-2406	484	1	let	let	VERB
ejpam-2406	484	2	l	l	NOUN
ejpam-2406	484	3	be	be	AUX
ejpam-2406	484	4	a	a	DET
ejpam-2406	484	5	noetherian	noetherian	ADJ
ejpam-2406	484	6	lattice	lattice	NOUN
ejpam-2406	484	7	and	and	CCONJ
ejpam-2406	484	8	m	m	AUX
ejpam-2406	484	9	be	be	AUX
ejpam-2406	484	10	a	a	DET
ejpam-2406	484	11	module	module	NOUN
ejpam-2406	484	12	over	over	ADP
ejpam-2406	484	13	l.	l.	PROPN
ejpam-2406	484	14	let	let	VERB
ejpam-2406	484	15	n	n	PRON
ejpam-2406	484	16	be	be	AUX
ejpam-2406	484	17	a	a	DET
ejpam-2406	484	18	proper	proper	ADJ
ejpam-2406	484	19	element	element	NOUN
ejpam-2406	484	20	of	of	ADP
ejpam-2406	484	21	m	m	PROPN
ejpam-2406	484	22	and	and	CCONJ
ejpam-2406	484	23	n	n	PROPN
ejpam-2406	484	24	=	=	PROPN
ejpam-2406	484	25	q1	q1	PROPN
ejpam-2406	484	26	∧q2	∧q2	VERB
ejpam-2406	484	27	∧	∧	PROPN
ejpam-2406	484	28	·	·	PUNCT
ejpam-2406	484	29	·	·	PUNCT
ejpam-2406	484	30	·	·	PUNCT
ejpam-2406	485	1	∧qn	∧qn	PROPN
ejpam-2406	485	2	with	with	ADP
ejpam-2406	485	3	p	p	PROPN
ejpam-2406	485	4	(	(	PUNCT
ejpam-2406	485	5	q	q	NOUN
ejpam-2406	485	6	i	i	PRON
ejpam-2406	485	7	:	:	PUNCT
ejpam-2406	485	8	i	i	PRON
ejpam-2406	485	9	m	m	VERB
ejpam-2406	485	10	)	)	PUNCT
ejpam-2406	486	1	=	=	SYM
ejpam-2406	487	1	pi	pi	NOUN
ejpam-2406	487	2	for	for	ADP
ejpam-2406	487	3	i	i	PROPN
ejpam-2406	487	4	=	=	SYM
ejpam-2406	487	5	1,2	1,2	NUM
ejpam-2406	487	6	,	,	PUNCT
ejpam-2406	487	7	.	.	PUNCT
ejpam-2406	487	8	.	.	PUNCT
ejpam-2406	488	1	.	.	PUNCT
ejpam-2406	489	1	,	,	PUNCT
ejpam-2406	489	2	n	n	PRON
ejpam-2406	489	3	be	be	VERB
ejpam-2406	489	4	a	a	DET
ejpam-2406	489	5	reduced	reduce	VERB
ejpam-2406	489	6	classical	classical	ADJ
ejpam-2406	489	7	quasi	quasi	ADJ
ejpam-2406	489	8	primary	primary	ADJ
ejpam-2406	489	9	decomposition	decomposition	NOUN
ejpam-2406	489	10	of	of	ADP
ejpam-2406	489	11	n.	n.	NOUN
ejpam-2406	489	12	then	then	ADV
ejpam-2406	489	13	,	,	PUNCT
ejpam-2406	489	14	{	{	PUNCT
ejpam-2406	489	15	pi	pi	NOUN
ejpam-2406	490	1	|	|	INTJ
ejpam-2406	490	2	i	i	NOUN
ejpam-2406	490	3	=	=	NOUN
ejpam-2406	490	4	1,2	1,2	NUM
ejpam-2406	490	5	,	,	PUNCT
ejpam-2406	490	6	.	.	PUNCT
ejpam-2406	490	7	.	.	PUNCT
ejpam-2406	490	8	.	.	PUNCT
ejpam-2406	491	1	,	,	PUNCT
ejpam-2406	491	2	n}=	n}=	PROPN
ejpam-2406	491	3	min(n	min(n	PROPN
ejpam-2406	491	4	:	:	PUNCT
ejpam-2406	491	5	i	i	PRON
ejpam-2406	491	6	m	m	VERB
ejpam-2406	491	7	)	)	PUNCT
ejpam-2406	491	8	}	}	PUNCT
ejpam-2406	491	9	and	and	CCONJ
ejpam-2406	491	10	the	the	DET
ejpam-2406	491	11	set	set	NOUN
ejpam-2406	491	12	{	{	PUNCT
ejpam-2406	491	13	pi	pi	NOUN
ejpam-2406	492	1	|	|	ADV
ejpam-2406	492	2	i	i	NOUN
ejpam-2406	492	3	=	=	NOUN
ejpam-2406	492	4	1,2	1,2	NUM
ejpam-2406	492	5	,	,	PUNCT
ejpam-2406	492	6	.	.	PUNCT
ejpam-2406	492	7	.	.	PUNCT
ejpam-2406	493	1	.	.	PUNCT
ejpam-2406	494	1	,	,	PUNCT
ejpam-2406	494	2	n	n	CCONJ
ejpam-2406	494	3	}	}	PUNCT
ejpam-2406	494	4	is	be	AUX
ejpam-2406	494	5	uniquely	uniquely	ADV
ejpam-2406	494	6	determined	determine	VERB
ejpam-2406	494	7	.	.	PUNCT
ejpam-2406	495	1	proof	proof	NOUN
ejpam-2406	495	2	.	.	PUNCT
ejpam-2406	496	1	first	first	ADV
ejpam-2406	496	2	we	we	PRON
ejpam-2406	496	3	show	show	VERB
ejpam-2406	496	4	that	that	SCONJ
ejpam-2406	496	5	,	,	PUNCT
ejpam-2406	496	6	min(n	min(n	PROPN
ejpam-2406	496	7	:	:	PUNCT
ejpam-2406	496	8	i	i	PRON
ejpam-2406	496	9	m	m	VERB
ejpam-2406	496	10	)	)	PUNCT
ejpam-2406	497	1	⊆	⊆	NUM
ejpam-2406	497	2	{	{	PUNCT
ejpam-2406	497	3	pi	pi	NOUN
ejpam-2406	498	1	|	|	ADV
ejpam-2406	498	2	i	i	NOUN
ejpam-2406	498	3	=	=	NOUN
ejpam-2406	498	4	1,2,3	1,2,3	NUM
ejpam-2406	498	5	,	,	PUNCT
ejpam-2406	498	6	.	.	PUNCT
ejpam-2406	498	7	.	.	PUNCT
ejpam-2406	499	1	.	.	PUNCT
ejpam-2406	499	2	,	,	PUNCT
ejpam-2406	499	3	n	n	CCONJ
ejpam-2406	499	4	}	}	PUNCT
ejpam-2406	499	5	.	.	PUNCT
ejpam-2406	500	1	let	let	VERB
ejpam-2406	500	2	p	p	PRON
ejpam-2406	500	3	be	be	AUX
ejpam-2406	500	4	a	a	DET
ejpam-2406	500	5	minimal	minimal	ADJ
ejpam-2406	500	6	prime	prime	NOUN
ejpam-2406	500	7	of	of	ADP
ejpam-2406	500	8	(	(	PUNCT
ejpam-2406	500	9	n	n	X
ejpam-2406	500	10	:	:	PUNCT
ejpam-2406	500	11	i	i	PRON
ejpam-2406	500	12	m	m	PROPN
ejpam-2406	500	13	)	)	PUNCT
ejpam-2406	500	14	.	.	PUNCT
ejpam-2406	501	1	then	then	ADV
ejpam-2406	501	2	p	p	PROPN
ejpam-2406	501	3	is	be	AUX
ejpam-2406	501	4	a	a	DET
ejpam-2406	501	5	minimal	minimal	ADJ
ejpam-2406	501	6	member	member	NOUN
ejpam-2406	501	7	of	of	ADP
ejpam-2406	501	8	associated	associated	ADJ
ejpam-2406	501	9	primes	prime	NOUN
ejpam-2406	501	10	of	of	ADP
ejpam-2406	501	11	n.	n.	NOUN
ejpam-2406	501	12	but	but	CCONJ
ejpam-2406	501	13	p	p	NOUN
ejpam-2406	501	14	=	=	NOUN
ejpam-2406	501	15	pi	pi	NOUN
ejpam-2406	501	16	for	for	ADP
ejpam-2406	501	17	some	some	DET
ejpam-2406	501	18	i	i	PRON
ejpam-2406	501	19	if	if	VERB
ejpam-2406	502	1	and	and	CCONJ
ejpam-2406	502	2	only	only	ADV
ejpam-2406	502	3	if	if	SCONJ
ejpam-2406	502	4	there	there	PRON
ejpam-2406	502	5	exists	exist	VERB
ejpam-2406	502	6	a	a	DET
ejpam-2406	502	7	6¶	6¶	NUM
ejpam-2406	502	8	n	n	NOUN
ejpam-2406	502	9	in	in	ADP
ejpam-2406	502	10	m	m	PRON
ejpam-2406	502	11	such	such	ADJ
ejpam-2406	502	12	that	that	SCONJ
ejpam-2406	502	13	(	(	PUNCT
ejpam-2406	502	14	n	n	X
ejpam-2406	502	15	:	:	PUNCT
ejpam-2406	502	16	a	a	X
ejpam-2406	502	17	)	)	PUNCT
ejpam-2406	502	18	p	p	NOUN
ejpam-2406	502	19	-	-	PUNCT
ejpam-2406	502	20	primary	primary	NOUN
ejpam-2406	502	21	.	.	PUNCT
ejpam-2406	503	1	thus	thus	ADV
ejpam-2406	503	2	,	,	PUNCT
ejpam-2406	503	3	p	p	X
ejpam-2406	503	4	=	=	PUNCT
ejpam-2406	503	5	p	p	X
ejpam-2406	503	6	(	(	PUNCT
ejpam-2406	503	7	n	n	NOUN
ejpam-2406	503	8	:	:	PUNCT
ejpam-2406	503	9	a	a	X
ejpam-2406	503	10	)	)	PUNCT
ejpam-2406	503	11	=	=	SYM
ejpam-2406	503	12	p	p	X
ejpam-2406	503	13	(	(	PUNCT
ejpam-2406	503	14	q	q	NOUN
ejpam-2406	503	15	:	:	PUNCT
ejpam-2406	503	16	i	i	PRON
ejpam-2406	503	17	m	m	VERB
ejpam-2406	503	18	)	)	PUNCT
ejpam-2406	503	19	for	for	ADP
ejpam-2406	503	20	some	some	PRON
ejpam-2406	503	21	a	a	DET
ejpam-2406	503	22	6¶	6¶	NUM
ejpam-2406	503	23	n	n	NOUN
ejpam-2406	503	24	.	.	PUNCT
ejpam-2406	504	1	renumber	renumber	PROPN
ejpam-2406	504	2	the	the	DET
ejpam-2406	504	3	q	q	X
ejpam-2406	505	1	i	i	PRON
ejpam-2406	505	2	such	such	ADJ
ejpam-2406	505	3	that	that	SCONJ
ejpam-2406	505	4	a	a	DET
ejpam-2406	505	5	6¶	6¶	NUM
ejpam-2406	505	6	q	q	NOUN
ejpam-2406	505	7	i	i	PRON
ejpam-2406	505	8	for	for	ADP
ejpam-2406	505	9	1	1	NUM
ejpam-2406	505	10	¶	¶	NUM
ejpam-2406	505	11	i	i	PRON
ejpam-2406	505	12	¶	¶	PROPN
ejpam-2406	505	13	j	j	PROPN
ejpam-2406	505	14	and	and	CCONJ
ejpam-2406	505	15	a	a	DET
ejpam-2406	505	16	¶	¶	NOUN
ejpam-2406	505	17	q	q	PROPN
ejpam-2406	506	1	i	i	PROPN
ejpam-2406	506	2	for	for	ADP
ejpam-2406	506	3	j	j	PROPN
ejpam-2406	506	4	+	+	CCONJ
ejpam-2406	506	5	1	1	NUM
ejpam-2406	506	6	¶	¶	NUM
ejpam-2406	506	7	i	i	NOUN
ejpam-2406	506	8	¶	¶	PROPN
ejpam-2406	506	9	n.	n.	PROPN
ejpam-2406	506	10	since	since	SCONJ
ejpam-2406	506	11	pi	pi	PROPN
ejpam-2406	506	12	=	=	PROPN
ejpam-2406	506	13	p	p	X
ejpam-2406	506	14	(	(	PUNCT
ejpam-2406	506	15	q	q	NOUN
ejpam-2406	507	1	i	i	PRON
ejpam-2406	507	2	:	:	PUNCT
ejpam-2406	507	3	i	i	NOUN
ejpam-2406	507	4	m	m	PROPN
ejpam-2406	507	5	)	)	PUNCT
ejpam-2406	507	6	,	,	PUNCT
ejpam-2406	507	7	pi	pi	NOUN
ejpam-2406	507	8	ki	ki	PROPN
ejpam-2406	508	1	i	i	PRON
ejpam-2406	508	2	m	m	VERB
ejpam-2406	508	3	¶	¶	PROPN
ejpam-2406	508	4	q	q	PROPN
ejpam-2406	509	1	i	i	PROPN
ejpam-2406	509	2	for	for	ADP
ejpam-2406	509	3	some	some	DET
ejpam-2406	509	4	integer	integer	NOUN
ejpam-2406	509	5	ki	ki	PROPN
ejpam-2406	509	6	,	,	PUNCT
ejpam-2406	509	7	(	(	PUNCT
ejpam-2406	509	8	1	1	NUM
ejpam-2406	509	9	¶	¶	NUM
ejpam-2406	509	10	i	i	PROPN
ejpam-2406	509	11	¶	¶	PROPN
ejpam-2406	509	12	n	n	CCONJ
ejpam-2406	509	13	)	)	PUNCT
ejpam-2406	509	14	.	.	PUNCT
ejpam-2406	510	1	therefore	therefore	ADV
ejpam-2406	510	2	,	,	PUNCT
ejpam-2406	510	3	(	(	PUNCT
ejpam-2406	510	4	j∧	j∧	ADV
ejpam-2406	510	5	i=1	i=1	PROPN
ejpam-2406	511	1	pi	pi	NOUN
ejpam-2406	511	2	ki	ki	PROPN
ejpam-2406	511	3	)	)	PUNCT
ejpam-2406	512	1	a¶	a¶	ADP
ejpam-2406	512	2	n∧	n∧	NUM
ejpam-2406	512	3	i=1	i=1	PROPN
ejpam-2406	513	1	q	q	PROPN
ejpam-2406	514	1	i	i	NOUN
ejpam-2406	514	2	=	=	PUNCT
ejpam-2406	514	3	n	n	PROPN
ejpam-2406	514	4	and	and	CCONJ
ejpam-2406	514	5	so	so	ADV
ejpam-2406	514	6	j∧	j∧	ADJ
ejpam-2406	515	1	i=1	i=1	PROPN
ejpam-2406	516	1	pi	pi	INTJ
ejpam-2406	516	2	ki	ki	PROPN
ejpam-2406	516	3	¶	¶	PROPN
ejpam-2406	516	4	(	(	PUNCT
ejpam-2406	516	5	n	n	CCONJ
ejpam-2406	516	6	:	:	PUNCT
ejpam-2406	516	7	a	a	X
ejpam-2406	516	8	)	)	PUNCT
ejpam-2406	516	9	¶	¶	PROPN
ejpam-2406	516	10	p.	p.	NOUN
ejpam-2406	516	11	since	since	SCONJ
ejpam-2406	516	12	p	p	PROPN
ejpam-2406	516	13	is	be	AUX
ejpam-2406	516	14	prime	prime	ADJ
ejpam-2406	516	15	,	,	PUNCT
ejpam-2406	516	16	pt	pt	X
ejpam-2406	516	17	¶	¶	NOUN
ejpam-2406	516	18	p	p	NOUN
ejpam-2406	516	19	for	for	ADP
ejpam-2406	516	20	some	some	DET
ejpam-2406	516	21	t	t	PROPN
ejpam-2406	516	22	¶	¶	PROPN
ejpam-2406	516	23	j.	j.	PROPN
ejpam-2406	516	24	as	as	ADP
ejpam-2406	516	25	,	,	PUNCT
ejpam-2406	516	26	(	(	PUNCT
ejpam-2406	516	27	n	n	X
ejpam-2406	516	28	:	:	PUNCT
ejpam-2406	516	29	i	i	PRON
ejpam-2406	516	30	m	m	VERB
ejpam-2406	516	31	)	)	PUNCT
ejpam-2406	516	32	¶	¶	PROPN
ejpam-2406	516	33	p	p	NOUN
ejpam-2406	516	34	(	(	PUNCT
ejpam-2406	516	35	n	n	NUM
ejpam-2406	516	36	:	:	PUNCT
ejpam-2406	516	37	i	i	PRON
ejpam-2406	516	38	m	m	VERB
ejpam-2406	516	39	)	)	PUNCT
ejpam-2406	516	40	¶	¶	PROPN
ejpam-2406	516	41	p	p	NOUN
ejpam-2406	516	42	(	(	PUNCT
ejpam-2406	516	43	q	q	PROPN
ejpam-2406	516	44	t	t	NOUN
ejpam-2406	516	45	:	:	PUNCT
ejpam-2406	516	46	i	i	PRON
ejpam-2406	516	47	m	m	VERB
ejpam-2406	516	48	)	)	PUNCT
ejpam-2406	517	1	=	=	SYM
ejpam-2406	517	2	pt	pt	PROPN
ejpam-2406	517	3	and	and	CCONJ
ejpam-2406	517	4	p	p	NOUN
ejpam-2406	517	5	is	be	AUX
ejpam-2406	517	6	a	a	DET
ejpam-2406	517	7	minimal	minimal	ADJ
ejpam-2406	517	8	prime	prime	NOUN
ejpam-2406	517	9	of	of	ADP
ejpam-2406	517	10	(	(	PUNCT
ejpam-2406	517	11	n	n	X
ejpam-2406	517	12	:	:	PUNCT
ejpam-2406	517	13	i	i	PRON
ejpam-2406	517	14	m	m	PROPN
ejpam-2406	517	15	)	)	PUNCT
ejpam-2406	517	16	,	,	PUNCT
ejpam-2406	517	17	we	we	PRON
ejpam-2406	517	18	conclude	conclude	VERB
ejpam-2406	517	19	that	that	SCONJ
ejpam-2406	517	20	p	p	PRON
ejpam-2406	517	21	=	=	NOUN
ejpam-2406	517	22	pt	pt	X
ejpam-2406	517	23	.	.	PUNCT
ejpam-2406	518	1	now	now	ADV
ejpam-2406	518	2	it	it	PRON
ejpam-2406	518	3	is	be	AUX
ejpam-2406	518	4	sufficient	sufficient	ADJ
ejpam-2406	518	5	to	to	PART
ejpam-2406	518	6	show	show	VERB
ejpam-2406	518	7	that	that	SCONJ
ejpam-2406	518	8	each	each	DET
ejpam-2406	518	9	pi(1	pi(1	PROPN
ejpam-2406	518	10	¶	¶	PROPN
ejpam-2406	518	11	i	i	PROPN
ejpam-2406	518	12	¶	¶	PROPN
ejpam-2406	518	13	n	n	CCONJ
ejpam-2406	518	14	)	)	PUNCT
ejpam-2406	518	15	is	be	AUX
ejpam-2406	518	16	a	a	DET
ejpam-2406	518	17	minimal	minimal	ADJ
ejpam-2406	518	18	prime	prime	NOUN
ejpam-2406	518	19	of	of	ADP
ejpam-2406	518	20	(	(	PUNCT
ejpam-2406	518	21	n	n	X
ejpam-2406	518	22	:	:	PUNCT
ejpam-2406	518	23	i	i	PRON
ejpam-2406	518	24	m	m	PROPN
ejpam-2406	518	25	)	)	PUNCT
ejpam-2406	518	26	.	.	PUNCT
ejpam-2406	519	1	without	without	ADP
ejpam-2406	519	2	loss	loss	NOUN
ejpam-2406	519	3	of	of	ADP
ejpam-2406	519	4	generality	generality	NOUN
ejpam-2406	519	5	,	,	PUNCT
ejpam-2406	519	6	we	we	PRON
ejpam-2406	519	7	may	may	AUX
ejpam-2406	519	8	take	take	VERB
ejpam-2406	519	9	i	i	NOUN
ejpam-2406	519	10	=	=	NOUN
ejpam-2406	519	11	1	1	X
ejpam-2406	519	12	.	.	PUNCT
ejpam-2406	520	1	clearly	clearly	ADV
ejpam-2406	520	2	(	(	PUNCT
ejpam-2406	520	3	n	n	X
ejpam-2406	520	4	:	:	PUNCT
ejpam-2406	520	5	i	i	PRON
ejpam-2406	520	6	m	m	VERB
ejpam-2406	520	7	)	)	PUNCT
ejpam-2406	520	8	¶	¶	PROPN
ejpam-2406	520	9	æ	æ	PROPN
ejpam-2406	521	1	(	(	PUNCT
ejpam-2406	521	2	n	n	X
ejpam-2406	521	3	:	:	PUNCT
ejpam-2406	521	4	i	i	PRON
ejpam-2406	521	5	m	m	VERB
ejpam-2406	521	6	)	)	PUNCT
ejpam-2406	522	1	=	=	SYM
ejpam-2406	522	2	æ	æ	X
ejpam-2406	522	3	(	(	PUNCT
ejpam-2406	522	4	q1	q1	PROPN
ejpam-2406	522	5	∧q2	∧q2	VERB
ejpam-2406	522	6	∧	∧	PROPN
ejpam-2406	522	7	·	·	PUNCT
ejpam-2406	522	8	·	·	PUNCT
ejpam-2406	522	9	·	·	PUNCT
ejpam-2406	523	1	∧qn	∧qn	PROPN
ejpam-2406	523	2	:	:	PUNCT
ejpam-2406	523	3	m	m	X
ejpam-2406	523	4	)	)	PUNCT
ejpam-2406	524	1	=	=	SYM
ejpam-2406	524	2	n∧	n∧	NUM
ejpam-2406	524	3	i=1	i=1	PROPN
ejpam-2406	525	1	æ	æ	X
ejpam-2406	526	1	(	(	PUNCT
ejpam-2406	526	2	q	q	NOUN
ejpam-2406	526	3	i	i	X
ejpam-2406	526	4	:	:	PUNCT
ejpam-2406	526	5	i	i	PROPN
ejpam-2406	526	6	m	m	VERB
ejpam-2406	526	7	)	)	PUNCT
ejpam-2406	526	8	¶	¶	PROPN
ejpam-2406	526	9	p1	p1	PROPN
ejpam-2406	526	10	.	.	PUNCT
ejpam-2406	527	1	on	on	ADP
ejpam-2406	527	2	the	the	DET
ejpam-2406	527	3	contrary	contrary	NOUN
ejpam-2406	527	4	,	,	PUNCT
ejpam-2406	527	5	suppose	suppose	VERB
ejpam-2406	527	6	that	that	SCONJ
ejpam-2406	527	7	p1	p1	NOUN
ejpam-2406	527	8	is	be	AUX
ejpam-2406	527	9	not	not	PART
ejpam-2406	527	10	a	a	DET
ejpam-2406	527	11	minimal	minimal	ADJ
ejpam-2406	527	12	prime	prime	NOUN
ejpam-2406	527	13	of	of	ADP
ejpam-2406	527	14	(	(	PUNCT
ejpam-2406	527	15	n	n	X
ejpam-2406	527	16	:	:	PUNCT
ejpam-2406	527	17	i	i	PRON
ejpam-2406	527	18	m	m	PROPN
ejpam-2406	527	19	)	)	PUNCT
ejpam-2406	527	20	.	.	PUNCT
ejpam-2406	528	1	thus	thus	ADV
ejpam-2406	528	2	∃	∃	PROPN
ejpam-2406	528	3	an	an	DET
ejpam-2406	528	4	i	i	PROPN
ejpam-2406	528	5	∈	∈	PROPN
ejpam-2406	528	6	{	{	PUNCT
ejpam-2406	528	7	1,2	1,2	NUM
ejpam-2406	528	8	,	,	PUNCT
ejpam-2406	528	9	.	.	PUNCT
ejpam-2406	528	10	.	.	PUNCT
ejpam-2406	528	11	.	.	PUNCT
ejpam-2406	528	12	,	,	PUNCT
ejpam-2406	528	13	n	n	CCONJ
ejpam-2406	528	14	}	}	PUNCT
ejpam-2406	528	15	such	such	ADJ
ejpam-2406	528	16	that	that	DET
ejpam-2406	528	17	pi	pi	NOUN
ejpam-2406	528	18	is	be	AUX
ejpam-2406	528	19	minimal	minimal	ADJ
ejpam-2406	528	20	prime	prime	NOUN
ejpam-2406	528	21	of	of	ADP
ejpam-2406	528	22	(	(	PUNCT
ejpam-2406	528	23	n	n	X
ejpam-2406	528	24	:	:	PUNCT
ejpam-2406	528	25	i	i	PRON
ejpam-2406	528	26	m	m	VERB
ejpam-2406	528	27	)	)	PUNCT
ejpam-2406	528	28	with	with	ADP
ejpam-2406	528	29	pi	pi	NOUN
ejpam-2406	528	30	<	<	X
ejpam-2406	528	31	p1	p1	PROPN
ejpam-2406	528	32	(	(	PUNCT
ejpam-2406	528	33	since	since	SCONJ
ejpam-2406	528	34	min(n	min(n	PROPN
ejpam-2406	528	35	:	:	PUNCT
ejpam-2406	528	36	i	i	PRON
ejpam-2406	528	37	m	m	VERB
ejpam-2406	528	38	)	)	PUNCT
ejpam-2406	529	1	⊆	⊆	NUM
ejpam-2406	529	2	{	{	PUNCT
ejpam-2406	529	3	pi	pi	NOUN
ejpam-2406	530	1	|	|	ADV
ejpam-2406	530	2	i	i	NOUN
ejpam-2406	530	3	=	=	NOUN
ejpam-2406	530	4	1,2,3	1,2,3	NUM
ejpam-2406	530	5	,	,	PUNCT
ejpam-2406	530	6	.	.	PUNCT
ejpam-2406	530	7	.	.	PUNCT
ejpam-2406	531	1	.	.	PUNCT
ejpam-2406	531	2	,	,	PUNCT
ejpam-2406	532	1	n	n	CCONJ
ejpam-2406	532	2	}	}	PUNCT
ejpam-2406	532	3	)	)	PUNCT
ejpam-2406	532	4	.	.	PUNCT
ejpam-2406	533	1	again	again	ADV
ejpam-2406	533	2	without	without	ADP
ejpam-2406	533	3	loss	loss	NOUN
ejpam-2406	533	4	of	of	ADP
ejpam-2406	533	5	generality	generality	NOUN
ejpam-2406	533	6	,	,	PUNCT
ejpam-2406	533	7	we	we	PRON
ejpam-2406	533	8	may	may	AUX
ejpam-2406	533	9	take	take	VERB
ejpam-2406	533	10	i	i	NOUN
ejpam-2406	533	11	=	=	NOUN
ejpam-2406	533	12	2	2	X
ejpam-2406	533	13	.	.	PUNCT
ejpam-2406	534	1	thus	thus	ADV
ejpam-2406	534	2	(	(	PUNCT
ejpam-2406	534	3	n	n	X
ejpam-2406	534	4	:	:	PUNCT
ejpam-2406	534	5	i	i	PRON
ejpam-2406	534	6	m	m	VERB
ejpam-2406	534	7	)	)	PUNCT
ejpam-2406	534	8	¶	¶	PROPN
ejpam-2406	534	9	p2	p2	PROPN
ejpam-2406	534	10	<	<	X
ejpam-2406	534	11	p1	p1	PROPN
ejpam-2406	534	12	.	.	PUNCT
ejpam-2406	535	1	by	by	ADP
ejpam-2406	535	2	[	[	X
ejpam-2406	535	3	5	5	NUM
ejpam-2406	535	4	]	]	PUNCT
ejpam-2406	535	5	,	,	PUNCT
ejpam-2406	535	6	each	each	DET
ejpam-2406	535	7	q	q	NOUN
ejpam-2406	535	8	i	i	PRON
ejpam-2406	535	9	has	have	VERB
ejpam-2406	535	10	a	a	DET
ejpam-2406	535	11	minimal	minimal	ADJ
ejpam-2406	535	12	primary	primary	ADJ
ejpam-2406	535	13	decomposition	decomposition	NOUN
ejpam-2406	535	14	.	.	PUNCT
ejpam-2406	536	1	suppose	suppose	VERB
ejpam-2406	536	2	that	that	SCONJ
ejpam-2406	536	3	,	,	PUNCT
ejpam-2406	536	4	q1	q1	PROPN
ejpam-2406	536	5	=	=	SYM
ejpam-2406	536	6	q11	q11	NOUN
ejpam-2406	536	7	∧	∧	PROPN
ejpam-2406	536	8	·	·	PUNCT
ejpam-2406	536	9	·	·	PUNCT
ejpam-2406	536	10	·	·	PUNCT
ejpam-2406	537	1	∧q1s	∧q1s	PROPN
ejpam-2406	537	2	with	with	ADP
ejpam-2406	537	3	æ	æ	PROPN
ejpam-2406	537	4	(	(	PUNCT
ejpam-2406	537	5	q1	q1	PROPN
ejpam-2406	537	6	j	j	PROPN
ejpam-2406	537	7	:	:	PUNCT
ejpam-2406	537	8	i	i	PRON
ejpam-2406	537	9	m	m	VERB
ejpam-2406	537	10	)	)	PUNCT
ejpam-2406	538	1	=	=	SYM
ejpam-2406	538	2	p1	p1	PROPN
ejpam-2406	538	3	j	j	PROPN
ejpam-2406	538	4	(	(	PUNCT
ejpam-2406	538	5	1	1	NUM
ejpam-2406	538	6	¶	¶	NUM
ejpam-2406	538	7	j	j	PROPN
ejpam-2406	538	8	¶	¶	PROPN
ejpam-2406	538	9	s	s	PART
ejpam-2406	538	10	)	)	PUNCT
ejpam-2406	538	11	and	and	CCONJ
ejpam-2406	538	12	q2	q2	NOUN
ejpam-2406	538	13	=	=	SYM
ejpam-2406	538	14	q21	q21	PROPN
ejpam-2406	538	15	∧	∧	PROPN
ejpam-2406	538	16	·	·	PUNCT
ejpam-2406	538	17	·	·	PUNCT
ejpam-2406	538	18	·	·	PUNCT
ejpam-2406	539	1	∧q2	∧q2	NOUN
ejpam-2406	539	2	t	t	NOUN
ejpam-2406	539	3	with	with	ADP
ejpam-2406	539	4	æ	æ	PROPN
ejpam-2406	539	5	(	(	PUNCT
ejpam-2406	539	6	q2	q2	PROPN
ejpam-2406	539	7	j	j	PROPN
ejpam-2406	539	8	:	:	PUNCT
ejpam-2406	539	9	i	i	PRON
ejpam-2406	539	10	m	m	VERB
ejpam-2406	539	11	)	)	PUNCT
ejpam-2406	540	1	=	=	PUNCT
ejpam-2406	540	2	p2	p2	PROPN
ejpam-2406	540	3	j	j	PROPN
ejpam-2406	540	4	(	(	PUNCT
ejpam-2406	540	5	1¶	1¶	PROPN
ejpam-2406	540	6	j	j	PROPN
ejpam-2406	540	7	¶	¶	PROPN
ejpam-2406	540	8	t	t	PROPN
ejpam-2406	540	9	)	)	PUNCT
ejpam-2406	540	10	are	be	AUX
ejpam-2406	540	11	a	a	DET
ejpam-2406	540	12	reduced	reduce	VERB
ejpam-2406	540	13	primary	primary	ADJ
ejpam-2406	540	14	decompositions	decomposition	NOUN
ejpam-2406	540	15	of	of	ADP
ejpam-2406	540	16	q1	q1	PROPN
ejpam-2406	540	17	and	and	CCONJ
ejpam-2406	540	18	q2	q2	NOUN
ejpam-2406	540	19	respectively	respectively	ADV
ejpam-2406	540	20	.	.	PUNCT
ejpam-2406	541	1	by	by	ADP
ejpam-2406	541	2	theorem	theorem	NOUN
ejpam-2406	541	3	8	8	NUM
ejpam-2406	541	4	{	{	PUNCT
ejpam-2406	541	5	p1	p1	PROPN
ejpam-2406	541	6	j	j	PROPN
ejpam-2406	542	1	|	|	ADV
ejpam-2406	542	2	1	1	NUM
ejpam-2406	542	3	¶	¶	NUM
ejpam-2406	542	4	j	j	PROPN
ejpam-2406	542	5	¶	¶	PROPN
ejpam-2406	542	6	s	s	PROPN
ejpam-2406	542	7	}	}	PUNCT
ejpam-2406	542	8	and	and	CCONJ
ejpam-2406	542	9	{	{	PUNCT
ejpam-2406	542	10	p2	p2	PROPN
ejpam-2406	542	11	j	j	PROPN
ejpam-2406	542	12	|	|	ADV
ejpam-2406	543	1	1	1	NUM
ejpam-2406	543	2	¶	¶	NUM
ejpam-2406	543	3	j	j	PROPN
ejpam-2406	543	4	¶	¶	PROPN
ejpam-2406	543	5	t	t	PROPN
ejpam-2406	543	6	}	}	PUNCT
ejpam-2406	543	7	are	be	AUX
ejpam-2406	543	8	chains	chain	NOUN
ejpam-2406	543	9	of	of	ADP
ejpam-2406	543	10	prime	prime	ADJ
ejpam-2406	543	11	elements	element	NOUN
ejpam-2406	543	12	.	.	PUNCT
ejpam-2406	544	1	without	without	ADP
ejpam-2406	544	2	loss	loss	NOUN
ejpam-2406	544	3	of	of	ADP
ejpam-2406	544	4	generality	generality	NOUN
ejpam-2406	544	5	,	,	PUNCT
ejpam-2406	544	6	we	we	PRON
ejpam-2406	544	7	can	can	AUX
ejpam-2406	544	8	assume	assume	VERB
ejpam-2406	544	9	that	that	SCONJ
ejpam-2406	544	10	,	,	PUNCT
ejpam-2406	544	11	p11	p11	ADJ
ejpam-2406	544	12	⊆	⊆	NUM
ejpam-2406	544	13	p12	p12	NOUN
ejpam-2406	544	14	⊆	⊆	NUM
ejpam-2406	544	15	·	·	PUNCT
ejpam-2406	544	16	·	·	PUNCT
ejpam-2406	544	17	·	·	PUNCT
ejpam-2406	545	1	⊆	⊆	NUM
ejpam-2406	545	2	p1s	p1	NOUN
ejpam-2406	545	3	and	and	CCONJ
ejpam-2406	545	4	p21	p21	NOUN
ejpam-2406	545	5	⊆	⊆	NUM
ejpam-2406	545	6	p22	p22	NOUN
ejpam-2406	545	7	⊆	⊆	NUM
ejpam-2406	545	8	·	·	PUNCT
ejpam-2406	545	9	·	·	PUNCT
ejpam-2406	545	10	·	·	PUNCT
ejpam-2406	546	1	⊆	⊆	NUM
ejpam-2406	546	2	p2	p2	NOUN
ejpam-2406	546	3	t	t	NOUN
ejpam-2406	546	4	.	.	PUNCT
ejpam-2406	547	1	we	we	PRON
ejpam-2406	547	2	thus	thus	ADV
ejpam-2406	547	3	get	get	VERB
ejpam-2406	547	4	p1	p1	NOUN
ejpam-2406	547	5	=	=	SYM
ejpam-2406	547	6	p11	p11	NOUN
ejpam-2406	547	7	and	and	CCONJ
ejpam-2406	547	8	p2	p2	PROPN
ejpam-2406	547	9	=	=	SYM
ejpam-2406	547	10	p21	p21	NOUN
ejpam-2406	547	11	,	,	PUNCT
ejpam-2406	547	12	since	since	SCONJ
ejpam-2406	547	13	p1	p1	PROPN
ejpam-2406	547	14	=	=	SYM
ejpam-2406	547	15	æ	æ	PROPN
ejpam-2406	547	16	(	(	PUNCT
ejpam-2406	547	17	q1	q1	PROPN
ejpam-2406	547	18	:	:	PUNCT
ejpam-2406	547	19	i	i	PRON
ejpam-2406	547	20	m	m	VERB
ejpam-2406	547	21	)	)	PUNCT
ejpam-2406	548	1	=	=	SYM
ejpam-2406	549	1	æ	æ	X
ejpam-2406	549	2	(	(	PUNCT
ejpam-2406	549	3	q11	q11	NOUN
ejpam-2406	549	4	∧	∧	PROPN
ejpam-2406	549	5	·	·	PUNCT
ejpam-2406	549	6	·	·	PUNCT
ejpam-2406	549	7	·	·	PUNCT
ejpam-2406	549	8	∧q1s	∧q1s	NUM
ejpam-2406	549	9	)	)	PUNCT
ejpam-2406	549	10	:	:	PUNCT
ejpam-2406	550	1	i	i	PRON
ejpam-2406	550	2	m	m	VERB
ejpam-2406	550	3	=	=	VERB
ejpam-2406	550	4	s∧	s∧	ADJ
ejpam-2406	550	5	i=1	i=1	PROPN
ejpam-2406	551	1	æ	æ	X
ejpam-2406	551	2	(	(	PUNCT
ejpam-2406	551	3	q1i	q1i	NOUN
ejpam-2406	551	4	:	:	PUNCT
ejpam-2406	551	5	i	i	PRON
ejpam-2406	551	6	m	m	VERB
ejpam-2406	551	7	)	)	PUNCT
ejpam-2406	552	1	=	=	SYM
ejpam-2406	552	2	p11	p11	NOUN
ejpam-2406	552	3	and	and	CCONJ
ejpam-2406	552	4	p2	p2	PROPN
ejpam-2406	552	5	=	=	SYM
ejpam-2406	552	6	æ	æ	PROPN
ejpam-2406	552	7	(	(	PUNCT
ejpam-2406	552	8	q2	q2	NOUN
ejpam-2406	552	9	:	:	PUNCT
ejpam-2406	552	10	i	i	PRON
ejpam-2406	552	11	m	m	VERB
ejpam-2406	552	12	)	)	PUNCT
ejpam-2406	553	1	=	=	SYM
ejpam-2406	554	1	æ	æ	X
ejpam-2406	554	2	(	(	PUNCT
ejpam-2406	554	3	q21	q21	PROPN
ejpam-2406	554	4	∧	∧	PROPN
ejpam-2406	554	5	·	·	PUNCT
ejpam-2406	554	6	·	·	PUNCT
ejpam-2406	554	7	·	·	PUNCT
ejpam-2406	555	1	∧q2	∧q2	NUM
ejpam-2406	555	2	t	t	NUM
ejpam-2406	555	3	)	)	PUNCT
ejpam-2406	555	4	:	:	PUNCT
ejpam-2406	556	1	i	i	PRON
ejpam-2406	556	2	m	m	VERB
ejpam-2406	556	3	=	=	VERB
ejpam-2406	556	4	t∧	t∧	NOUN
ejpam-2406	556	5	i=1	i=1	PROPN
ejpam-2406	556	6	æ	æ	X
ejpam-2406	556	7	(	(	PUNCT
ejpam-2406	556	8	q2i	q2i	PROPN
ejpam-2406	556	9	:	:	PUNCT
ejpam-2406	556	10	i	i	PRON
ejpam-2406	556	11	m	m	VERB
ejpam-2406	556	12	)	)	PUNCT
ejpam-2406	557	1	=	=	SYM
ejpam-2406	557	2	p21	p21	NOUN
ejpam-2406	557	3	.	.	PUNCT
ejpam-2406	558	1	it	it	PRON
ejpam-2406	558	2	follows	follow	VERB
ejpam-2406	558	3	that	that	SCONJ
ejpam-2406	558	4	,	,	PUNCT
ejpam-2406	558	5	p21	p21	NOUN
ejpam-2406	558	6	⊆	⊆	NUM
ejpam-2406	558	7	p11	p11	NOUN
ejpam-2406	558	8	⊆	⊆	NUM
ejpam-2406	558	9	p12	p12	NOUN
ejpam-2406	558	10	⊆	⊆	NUM
ejpam-2406	558	11	·	·	PUNCT
ejpam-2406	558	12	·	·	PUNCT
ejpam-2406	558	13	·	·	PUNCT
ejpam-2406	559	1	⊆	⊆	NUM
ejpam-2406	559	2	p1s	p1	NOUN
ejpam-2406	559	3	and	and	CCONJ
ejpam-2406	559	4	so	so	ADV
ejpam-2406	559	5	by	by	ADP
ejpam-2406	559	6	theorem	theorem	NOUN
ejpam-2406	559	7	8	8	NUM
ejpam-2406	559	8	,	,	PUNCT
ejpam-2406	559	9	q1	q1	NOUN
ejpam-2406	559	10	′	′	NOUN
ejpam-2406	559	11	=	=	PUNCT
ejpam-2406	559	12	q21∧q11∧	q21∧q11∧	NOUN
ejpam-2406	559	13	·	·	PUNCT
ejpam-2406	559	14	·	·	PUNCT
ejpam-2406	559	15	·	·	PUNCT
ejpam-2406	559	16	∧q1s	∧q1s	PROPN
ejpam-2406	559	17	is	be	AUX
ejpam-2406	559	18	a	a	DET
ejpam-2406	559	19	classical	classical	ADJ
ejpam-2406	559	20	quasi	quasi	ADJ
ejpam-2406	559	21	primary	primary	ADJ
ejpam-2406	559	22	element	element	NOUN
ejpam-2406	559	23	of	of	ADP
ejpam-2406	559	24	m	m	PROPN
ejpam-2406	559	25	with	with	ADP
ejpam-2406	559	26	q	q	PROPN
ejpam-2406	559	27	(	(	PUNCT
ejpam-2406	559	28	q1	q1	PROPN
ejpam-2406	559	29	′	′	NUM
ejpam-2406	559	30	:	:	PUNCT
ejpam-2406	560	1	i	i	PRON
ejpam-2406	560	2	m	m	VERB
ejpam-2406	560	3	)	)	PUNCT
ejpam-2406	561	1	=	=	SYM
ejpam-2406	561	2	p21	p21	NOUN
ejpam-2406	561	3	=	=	NOUN
ejpam-2406	561	4	p2	p2	NOUN
ejpam-2406	561	5	.	.	PUNCT
ejpam-2406	562	1	on	on	ADP
ejpam-2406	562	2	the	the	DET
ejpam-2406	562	3	other	other	ADJ
ejpam-2406	562	4	hand	hand	NOUN
ejpam-2406	562	5	,	,	PUNCT
ejpam-2406	562	6	n	n	PROPN
ejpam-2406	562	7	=	=	PROPN
ejpam-2406	562	8	q1	q1	PROPN
ejpam-2406	562	9	∧	∧	PROPN
ejpam-2406	562	10	·	·	PUNCT
ejpam-2406	562	11	·	·	PUNCT
ejpam-2406	562	12	·	·	PUNCT
ejpam-2406	562	13	∧qn	∧qn	PROPN
ejpam-2406	562	14	=	=	PUNCT
ejpam-2406	562	15	(	(	PUNCT
ejpam-2406	562	16	q11	q11	NOUN
ejpam-2406	562	17	∧	∧	PROPN
ejpam-2406	562	18	·	·	PUNCT
ejpam-2406	562	19	·	·	PUNCT
ejpam-2406	562	20	·	·	PUNCT
ejpam-2406	562	21	∧q1s)∧	∧q1s)∧	NOUN
ejpam-2406	562	22	(	(	PUNCT
ejpam-2406	562	23	q21	q21	NOUN
ejpam-2406	562	24	∧	∧	PROPN
ejpam-2406	562	25	·	·	PUNCT
ejpam-2406	562	26	·	·	PUNCT
ejpam-2406	562	27	·	·	PUNCT
ejpam-2406	562	28	∧q2t)∧q3	∧q2t)∧q3	X
ejpam-2406	562	29	·	·	PUNCT
ejpam-2406	562	30	·	·	PUNCT
ejpam-2406	562	31	·	·	PUNCT
ejpam-2406	562	32	∧qn	∧qn	PROPN
ejpam-2406	562	33	=(	=(	NOUN
ejpam-2406	562	34	q21	q21	PROPN
ejpam-2406	562	35	∧q11	∧q11	PROPN
ejpam-2406	562	36	∧	∧	PROPN
ejpam-2406	562	37	·	·	PUNCT
ejpam-2406	562	38	·	·	PUNCT
ejpam-2406	562	39	·	·	PUNCT
ejpam-2406	562	40	∧q1s)∧	∧q1s)∧	NOUN
ejpam-2406	562	41	(	(	PUNCT
ejpam-2406	562	42	q21	q21	NOUN
ejpam-2406	562	43	∧	∧	PROPN
ejpam-2406	562	44	·	·	PUNCT
ejpam-2406	562	45	·	·	PUNCT
ejpam-2406	562	46	·	·	PUNCT
ejpam-2406	562	47	∧q2t)∧	∧q2t)∧	NUM
ejpam-2406	562	48	(	(	PUNCT
ejpam-2406	562	49	q3	q3	NOUN
ejpam-2406	562	50	∧	∧	PROPN
ejpam-2406	562	51	·	·	PUNCT
ejpam-2406	562	52	·	·	PUNCT
ejpam-2406	562	53	·	·	PUNCT
ejpam-2406	562	54	∧qn	∧qn	PROPN
ejpam-2406	562	55	)	)	PUNCT
ejpam-2406	562	56	.	.	PUNCT
ejpam-2406	563	1	thus	thus	ADV
ejpam-2406	563	2	,	,	PUNCT
ejpam-2406	563	3	n	n	PROPN
ejpam-2406	563	4	=	=	NOUN
ejpam-2406	563	5	q	q	NOUN
ejpam-2406	563	6	′	′	NUM
ejpam-2406	563	7	1	1	NUM
ejpam-2406	563	8	∧q2	∧q2	VERB
ejpam-2406	563	9	∧	∧	PROPN
ejpam-2406	563	10	·	·	PUNCT
ejpam-2406	563	11	·	·	PUNCT
ejpam-2406	563	12	·	·	PUNCT
ejpam-2406	564	1	∧qn	∧qn	PROPN
ejpam-2406	564	2	is	be	AUX
ejpam-2406	564	3	a	a	DET
ejpam-2406	564	4	classical	classical	ADJ
ejpam-2406	564	5	quasi	quasi	ADJ
ejpam-2406	564	6	primary	primary	ADJ
ejpam-2406	564	7	decomposition	decomposition	NOUN
ejpam-2406	564	8	of	of	ADP
ejpam-2406	564	9	n	n	PROPN
ejpam-2406	564	10	with	with	ADP
ejpam-2406	564	11	q	q	PROPN
ejpam-2406	564	12	(	(	PUNCT
ejpam-2406	564	13	q	q	NOUN
ejpam-2406	564	14	′	′	NOUN
ejpam-2406	564	15	1	1	NUM
ejpam-2406	564	16	:	:	PUNCT
ejpam-2406	564	17	i	i	PRON
ejpam-2406	564	18	m	m	VERB
ejpam-2406	564	19	)	)	PUNCT
ejpam-2406	565	1	=	=	SYM
ejpam-2406	565	2	p	p	X
ejpam-2406	565	3	(	(	PUNCT
ejpam-2406	565	4	q2	q2	NOUN
ejpam-2406	565	5	:	:	PUNCT
ejpam-2406	565	6	i	i	PRON
ejpam-2406	565	7	m	m	VERB
ejpam-2406	565	8	)	)	PUNCT
ejpam-2406	566	1	=	=	NOUN
ejpam-2406	566	2	p2	p2	PROPN
ejpam-2406	566	3	and	and	CCONJ
ejpam-2406	566	4	p	p	X
ejpam-2406	566	5	(	(	PUNCT
ejpam-2406	566	6	q	q	NOUN
ejpam-2406	567	1	i	i	X
ejpam-2406	567	2	:	:	PUNCT
ejpam-2406	567	3	i	i	PRON
ejpam-2406	567	4	m	m	VERB
ejpam-2406	567	5	)	)	PUNCT
ejpam-2406	568	1	=	=	SYM
ejpam-2406	569	1	pi	pi	NOUN
ejpam-2406	569	2	for	for	ADP
ejpam-2406	569	3	i	i	PRON
ejpam-2406	569	4	=	=	NOUN
ejpam-2406	569	5	3	3	NUM
ejpam-2406	569	6	,	,	PUNCT
ejpam-2406	569	7	.	.	PUNCT
ejpam-2406	569	8	.	.	PUNCT
ejpam-2406	569	9	.	.	PUNCT
ejpam-2406	570	1	n.	n.	INTJ
ejpam-2406	570	2	we	we	PRON
ejpam-2406	570	3	note	note	VERB
ejpam-2406	570	4	that	that	SCONJ
ejpam-2406	570	5	if	if	SCONJ
ejpam-2406	570	6	∃	∃	PROPN
ejpam-2406	570	7	another	another	PRON
ejpam-2406	570	8	q	q	X
ejpam-2406	571	1	i	i	PRON
ejpam-2406	571	2	(	(	PUNCT
ejpam-2406	571	3	3	3	NUM
ejpam-2406	571	4	¶	¶	PROPN
ejpam-2406	571	5	i	i	PROPN
ejpam-2406	571	6	¶	¶	PROPN
ejpam-2406	571	7	n	n	CCONJ
ejpam-2406	571	8	)	)	PUNCT
ejpam-2406	571	9	such	such	ADJ
ejpam-2406	571	10	that	that	SCONJ
ejpam-2406	571	11	p	p	X
ejpam-2406	571	12	(	(	PUNCT
ejpam-2406	571	13	q	q	NOUN
ejpam-2406	571	14	i	i	PRON
ejpam-2406	571	15	:	:	PUNCT
ejpam-2406	571	16	i	i	PRON
ejpam-2406	571	17	m	m	VERB
ejpam-2406	571	18	)	)	PUNCT
ejpam-2406	572	1	=	=	SYM
ejpam-2406	572	2	pi	pi	NOUN
ejpam-2406	572	3	=	=	PROPN
ejpam-2406	572	4	p1	p1	NOUN
ejpam-2406	572	5	then	then	ADV
ejpam-2406	572	6	by	by	ADP
ejpam-2406	572	7	similar	similar	ADJ
ejpam-2406	572	8	arguments	argument	NOUN
ejpam-2406	572	9	we	we	PRON
ejpam-2406	572	10	can	can	AUX
ejpam-2406	572	11	replace	replace	VERB
ejpam-2406	572	12	it	it	PRON
ejpam-2406	572	13	references	reference	NOUN
ejpam-2406	572	14	184	184	NUM
ejpam-2406	572	15	by	by	ADP
ejpam-2406	572	16	q	q	PROPN
ejpam-2406	572	17	′	′	NUM
ejpam-2406	573	1	i	i	PRON
ejpam-2406	573	2	such	such	ADJ
ejpam-2406	573	3	that	that	PRON
ejpam-2406	573	4	q	q	NOUN
ejpam-2406	573	5	(	(	PUNCT
ejpam-2406	573	6	q	q	NOUN
ejpam-2406	573	7	′	′	INTJ
ejpam-2406	574	1	i	i	PRON
ejpam-2406	574	2	:	:	PUNCT
ejpam-2406	574	3	i	i	PRON
ejpam-2406	574	4	m	m	VERB
ejpam-2406	574	5	)	)	PUNCT
ejpam-2406	575	1	=	=	SYM
ejpam-2406	575	2	p	p	X
ejpam-2406	575	3	(	(	PUNCT
ejpam-2406	575	4	q2	q2	NOUN
ejpam-2406	575	5	:	:	PUNCT
ejpam-2406	575	6	i	i	PRON
ejpam-2406	575	7	m	m	VERB
ejpam-2406	575	8	)	)	PUNCT
ejpam-2406	576	1	=	=	PUNCT
ejpam-2406	576	2	p2	p2	NOUN
ejpam-2406	576	3	.	.	PUNCT
ejpam-2406	577	1	now	now	ADV
ejpam-2406	577	2	,	,	PUNCT
ejpam-2406	577	3	by	by	ADP
ejpam-2406	577	4	using	use	VERB
ejpam-2406	577	5	this	this	DET
ejpam-2406	577	6	decomposition	decomposition	NOUN
ejpam-2406	577	7	we	we	PRON
ejpam-2406	577	8	can	can	AUX
ejpam-2406	577	9	obtain	obtain	VERB
ejpam-2406	577	10	a	a	DET
ejpam-2406	577	11	reduced	reduced	ADJ
ejpam-2406	577	12	classical	classical	ADJ
ejpam-2406	577	13	quasi	quasi	ADJ
ejpam-2406	577	14	primary	primary	ADJ
ejpam-2406	577	15	decomposition	decomposition	NOUN
ejpam-2406	577	16	,	,	PUNCT
ejpam-2406	577	17	n	n	NOUN
ejpam-2406	577	18	=	=	PUNCT
ejpam-2406	577	19	q	q	SYM
ejpam-2406	577	20	′′	′′	PROPN
ejpam-2406	577	21	1	1	NUM
ejpam-2406	577	22	∧	∧	PROPN
ejpam-2406	577	23	q	q	PROPN
ejpam-2406	577	24	′′	′′	PROPN
ejpam-2406	577	25	2	2	NUM
ejpam-2406	577	26	∧	∧	PROPN
ejpam-2406	577	27	·	·	PUNCT
ejpam-2406	577	28	·	·	PUNCT
ejpam-2406	577	29	·	·	PUNCT
ejpam-2406	578	1	∧	∧	NOUN
ejpam-2406	578	2	q	q	X
ejpam-2406	578	3	′′	′′	PROPN
ejpam-2406	578	4	k	k	PROPN
ejpam-2406	578	5	such	such	ADJ
ejpam-2406	578	6	that	that	DET
ejpam-2406	578	7	p1	p1	PROPN
ejpam-2406	578	8	/∈	/∈	PUNCT
ejpam-2406	578	9	{	{	PUNCT
ejpam-2406	578	10	q	q	X
ejpam-2406	578	11	(	(	PUNCT
ejpam-2406	578	12	q	q	PUNCT
ejpam-2406	578	13	′′	′′	NOUN
ejpam-2406	579	1	i	i	PRON
ejpam-2406	579	2	:	:	PUNCT
ejpam-2406	579	3	i	i	PRON
ejpam-2406	579	4	m	m	VERB
ejpam-2406	579	5	)	)	PUNCT
ejpam-2406	580	1	|	|	ADV
ejpam-2406	580	2	i	i	PRON
ejpam-2406	580	3	=	=	NOUN
ejpam-2406	580	4	1,2,3,4	1,2,3,4	NUM
ejpam-2406	580	5	,	,	PUNCT
ejpam-2406	580	6	.	.	PUNCT
ejpam-2406	580	7	.	.	PUNCT
ejpam-2406	580	8	.	.	PUNCT
ejpam-2406	581	1	,	,	PUNCT
ejpam-2406	581	2	k	k	X
ejpam-2406	581	3	}	}	PUNCT
ejpam-2406	581	4	⊆	⊆	NUM
ejpam-2406	581	5	{	{	PUNCT
ejpam-2406	581	6	pi	pi	NOUN
ejpam-2406	582	1	|	|	ADV
ejpam-2406	582	2	i	i	NOUN
ejpam-2406	582	3	=	=	NOUN
ejpam-2406	582	4	2	2	NUM
ejpam-2406	582	5	,	,	PUNCT
ejpam-2406	582	6	.	.	PUNCT
ejpam-2406	582	7	.	.	PUNCT
ejpam-2406	583	1	.	.	PUNCT
ejpam-2406	584	1	,	,	PUNCT
ejpam-2406	585	1	n	n	CCONJ
ejpam-2406	585	2	}	}	PUNCT
ejpam-2406	586	1	,	,	PUNCT
ejpam-2406	586	2	contrary	contrary	ADV
ejpam-2406	586	3	with	with	ADP
ejpam-2406	586	4	the	the	DET
ejpam-2406	586	5	irrenduntness	irrenduntness	NOUN
ejpam-2406	586	6	of	of	ADP
ejpam-2406	586	7	the	the	DET
ejpam-2406	586	8	decomposition	decomposition	NOUN
ejpam-2406	586	9	n	n	PRON
ejpam-2406	586	10	=	=	NOUN
ejpam-2406	586	11	q1,∧q2	q1,∧q2	PROPN
ejpam-2406	586	12	∧	∧	NOUN
ejpam-2406	586	13	.	.	PUNCT
ejpam-2406	586	14	.	.	PUNCT
ejpam-2406	587	1	.	.	PUNCT
ejpam-2406	588	1	,	,	PUNCT
ejpam-2406	588	2	∧qn	∧qn	PROPN
ejpam-2406	588	3	with	with	ADP
ejpam-2406	588	4	{	{	PUNCT
ejpam-2406	588	5	æ	æ	X
ejpam-2406	588	6	(	(	PUNCT
ejpam-2406	588	7	q	q	NOUN
ejpam-2406	588	8	i	i	X
ejpam-2406	588	9	:	:	PUNCT
ejpam-2406	588	10	i	i	PRON
ejpam-2406	588	11	m	m	VERB
ejpam-2406	588	12	)	)	PUNCT
ejpam-2406	589	1	|	|	ADV
ejpam-2406	589	2	i	i	PRON
ejpam-2406	589	3	=	=	NOUN
ejpam-2406	589	4	1,2,3	1,2,3	NUM
ejpam-2406	589	5	,	,	PUNCT
ejpam-2406	589	6	.	.	PUNCT
ejpam-2406	589	7	.	.	PUNCT
ejpam-2406	589	8	.	.	PUNCT
ejpam-2406	590	1	,	,	PUNCT
ejpam-2406	590	2	n}=	n}=	ADJ
ejpam-2406	590	3	{	{	PUNCT
ejpam-2406	590	4	pi	pi	NOUN
ejpam-2406	591	1	|	|	ADV
ejpam-2406	591	2	i	i	NOUN
ejpam-2406	591	3	=	=	NOUN
ejpam-2406	591	4	1,2	1,2	NUM
ejpam-2406	591	5	.	.	PUNCT
ejpam-2406	591	6	.	.	PUNCT
ejpam-2406	592	1	.	.	PUNCT
ejpam-2406	592	2	,	,	PUNCT
ejpam-2406	592	3	n	n	CCONJ
ejpam-2406	592	4	}	}	PUNCT
ejpam-2406	592	5	.	.	PUNCT
ejpam-2406	593	1	thus	thus	ADV
ejpam-2406	593	2	,	,	PUNCT
ejpam-2406	593	3	{	{	PUNCT
ejpam-2406	593	4	pi	pi	NOUN
ejpam-2406	593	5	|	|	INTJ
ejpam-2406	593	6	i	i	NOUN
ejpam-2406	593	7	=	=	NOUN
ejpam-2406	593	8	1,2	1,2	NUM
ejpam-2406	593	9	,	,	PUNCT
ejpam-2406	593	10	.	.	PUNCT
ejpam-2406	593	11	.	.	PUNCT
ejpam-2406	593	12	.	.	PUNCT
ejpam-2406	594	1	,	,	PUNCT
ejpam-2406	594	2	n}=	n}=	PROPN
ejpam-2406	594	3	min(n	min(n	PROPN
ejpam-2406	594	4	:	:	PUNCT
ejpam-2406	594	5	i	i	PRON
ejpam-2406	594	6	m	m	PROPN
ejpam-2406	594	7	)	)	PUNCT
ejpam-2406	594	8	.	.	PUNCT
ejpam-2406	595	1	acknowledgements	acknowledgement	NOUN
ejpam-2406	595	2	the	the	DET
ejpam-2406	595	3	authors	author	NOUN
ejpam-2406	595	4	thank	thank	VERB
ejpam-2406	595	5	the	the	DET
ejpam-2406	595	6	readers	reader	NOUN
ejpam-2406	595	7	of	of	ADP
ejpam-2406	595	8	european	european	PROPN
ejpam-2406	595	9	journal	journal	PROPN
ejpam-2406	595	10	of	of	ADP
ejpam-2406	595	11	pure	pure	ADJ
ejpam-2406	595	12	and	and	CCONJ
ejpam-2406	595	13	applied	applied	ADJ
ejpam-2406	595	14	mathematics	mathematic	NOUN
ejpam-2406	595	15	,	,	PUNCT
ejpam-2406	595	16	for	for	ADP
ejpam-2406	595	17	making	make	VERB
ejpam-2406	595	18	our	our	PRON
ejpam-2406	595	19	journal	journal	NOUN
ejpam-2406	595	20	successful	successful	ADJ
ejpam-2406	595	21	.	.	PUNCT
ejpam-2406	596	1	we	we	PRON
ejpam-2406	596	2	dedicate	dedicate	VERB
ejpam-2406	596	3	this	this	DET
ejpam-2406	596	4	research	research	NOUN
ejpam-2406	596	5	article	article	NOUN
ejpam-2406	596	6	to	to	ADP
ejpam-2406	596	7	prof	prof	PROPN
ejpam-2406	596	8	dr	dr	PROPN
ejpam-2406	596	9	n	n	PROPN
ejpam-2406	596	10	k	k	PROPN
ejpam-2406	596	11	thakare	thakare	NOUN
ejpam-2406	596	12	on	on	ADP
ejpam-2406	596	13	his	his	PRON
ejpam-2406	596	14	76	76	NUM
ejpam-2406	596	15	birthday	birthday	NOUN
ejpam-2406	596	16	.	.	PUNCT
ejpam-2406	597	1	references	reference	NOUN
ejpam-2406	597	2	[	[	X
ejpam-2406	597	3	1	1	NUM
ejpam-2406	597	4	]	]	PUNCT
ejpam-2406	597	5	m.	m.	NOUN
ejpam-2406	597	6	behboodi	behboodi	PROPN
ejpam-2406	597	7	,	,	PUNCT
ejpam-2406	597	8	r.	r.	PROPN
ejpam-2406	597	9	jahani	jahani	PROPN
ejpam-2406	597	10	-	-	PUNCT
ejpam-2406	597	11	nezhad	nezhad	VERB
ejpam-2406	597	12	,	,	PUNCT
ejpam-2406	597	13	and	and	CCONJ
ejpam-2406	597	14	m.	m.	PROPN
ejpam-2406	597	15	h.	h.	PROPN
ejpam-2406	597	16	naderi	naderi	PROPN
ejpam-2406	597	17	.	.	PUNCT
ejpam-2406	598	1	classical	classical	ADJ
ejpam-2406	598	2	quasi	quasi	ADJ
ejpam-2406	598	3	primary	primary	ADJ
ejpam-2406	598	4	submodules	submodule	NOUN
ejpam-2406	598	5	,	,	PUNCT
ejpam-2406	598	6	bulletin	bulletin	NOUN
ejpam-2406	598	7	of	of	ADP
ejpam-2406	598	8	the	the	DET
ejpam-2406	598	9	iranian	iranian	PROPN
ejpam-2406	598	10	mathematical	mathematical	PROPN
ejpam-2406	598	11	society	society	NOUN
ejpam-2406	598	12	,	,	PUNCT
ejpam-2406	598	13	37(4	37(4	PROPN
ejpam-2406	598	14	)	)	PUNCT
ejpam-2406	598	15	,	,	PUNCT
ejpam-2406	598	16	51	51	NUM
ejpam-2406	598	17	-	-	SYM
ejpam-2406	598	18	71	71	NUM
ejpam-2406	598	19	.	.	PUNCT
ejpam-2406	598	20	2011	2011	NUM
ejpam-2406	598	21	.	.	PUNCT
ejpam-2406	599	1	[	[	X
ejpam-2406	599	2	2	2	NUM
ejpam-2406	599	3	]	]	PUNCT
ejpam-2406	599	4	m.	m.	NOUN
ejpam-2406	599	5	behboodi	behboodi	NOUN
ejpam-2406	599	6	and	and	CCONJ
ejpam-2406	599	7	m.	m.	NOUN
ejpam-2406	599	8	baziar	baziar	PROPN
ejpam-2406	599	9	.	.	PUNCT
ejpam-2406	600	1	classical	classical	ADJ
ejpam-2406	600	2	primary	primary	ADJ
ejpam-2406	600	3	submodules	submodule	NOUN
ejpam-2406	600	4	and	and	CCONJ
ejpam-2406	600	5	decomposition	decomposition	NOUN
ejpam-2406	600	6	theory	theory	NOUN
ejpam-2406	600	7	of	of	ADP
ejpam-2406	600	8	modules	module	NOUN
ejpam-2406	600	9	,	,	PUNCT
ejpam-2406	600	10	journal	journal	NOUN
ejpam-2406	600	11	of	of	ADP
ejpam-2406	600	12	algebra	algebra	PROPN
ejpam-2406	600	13	application	application	NOUN
ejpam-2406	600	14	,	,	PUNCT
ejpam-2406	600	15	8(3	8(3	NUM
ejpam-2406	600	16	)	)	PUNCT
ejpam-2406	600	17	,	,	PUNCT
ejpam-2406	600	18	351	351	NUM
ejpam-2406	600	19	-	-	SYM
ejpam-2406	600	20	362	362	NUM
ejpam-2406	600	21	.	.	PUNCT
ejpam-2406	600	22	2009	2009	NUM
ejpam-2406	600	23	.	.	PUNCT
ejpam-2406	601	1	[	[	X
ejpam-2406	601	2	3	3	X
ejpam-2406	601	3	]	]	X
ejpam-2406	601	4	r.	r.	PROPN
ejpam-2406	601	5	p.	p.	PROPN
ejpam-2406	601	6	dilworth	dilworth	PROPN
ejpam-2406	601	7	.	.	PUNCT
ejpam-2406	602	1	abstract	abstract	ADJ
ejpam-2406	602	2	commutative	commutative	ADJ
ejpam-2406	602	3	ideal	ideal	PROPN
ejpam-2406	602	4	theory	theory	NOUN
ejpam-2406	602	5	,	,	PUNCT
ejpam-2406	602	6	pacific	pacific	PROPN
ejpam-2406	602	7	j.	j.	PROPN
ejpam-2406	602	8	math	math	PROPN
ejpam-2406	602	9	.	.	PUNCT
ejpam-2406	602	10	,	,	PUNCT
ejpam-2406	602	11	12	12	NUM
ejpam-2406	602	12	,	,	PUNCT
ejpam-2406	602	13	481	481	NUM
ejpam-2406	602	14	-	-	SYM
ejpam-2406	602	15	498	498	NUM
ejpam-2406	602	16	.	.	PUNCT
ejpam-2406	603	1	1962	1962	NUM
ejpam-2406	603	2	.	.	PUNCT
ejpam-2406	604	1	[	[	X
ejpam-2406	604	2	4	4	X
ejpam-2406	604	3	]	]	PUNCT
ejpam-2406	604	4	l.	l.	PROPN
ejpam-2406	604	5	fuchs	fuchs	PROPN
ejpam-2406	604	6	.	.	PUNCT
ejpam-2406	605	1	on	on	ADP
ejpam-2406	605	2	quasi	quasi	ADJ
ejpam-2406	605	3	primary	primary	ADJ
ejpam-2406	605	4	ideals	ideal	NOUN
ejpam-2406	605	5	,	,	PUNCT
ejpam-2406	605	6	acta	acta	PROPN
ejpam-2406	605	7	scientiarum	scientiarum	PROPN
ejpam-2406	605	8	mathematicarum	mathematicarum	PROPN
ejpam-2406	605	9	,	,	PUNCT
ejpam-2406	605	10	11	11	NUM
ejpam-2406	605	11	,	,	PUNCT
ejpam-2406	605	12	174	174	NUM
ejpam-2406	605	13	-	-	SYM
ejpam-2406	605	14	183	183	NUM
ejpam-2406	605	15	.	.	PUNCT
ejpam-2406	605	16	1947	1947	NUM
ejpam-2406	605	17	.	.	PUNCT
ejpam-2406	606	1	[	[	X
ejpam-2406	606	2	5	5	NUM
ejpam-2406	606	3	]	]	PUNCT
ejpam-2406	606	4	r.	r.	PROPN
ejpam-2406	606	5	y.	y.	PROPN
ejpam-2406	606	6	sharp	sharp	PROPN
ejpam-2406	606	7	.	.	PUNCT
ejpam-2406	607	1	steps	step	NOUN
ejpam-2406	607	2	in	in	ADP
ejpam-2406	607	3	commutative	commutative	ADJ
ejpam-2406	607	4	algebra	algebra	NOUN
ejpam-2406	607	5	,	,	PUNCT
ejpam-2406	607	6	london	london	PROPN
ejpam-2406	607	7	mathematatical	mathematatical	ADJ
ejpam-2406	607	8	society	society	PROPN
ejpam-2406	607	9	,	,	PUNCT
ejpam-2406	607	10	cambridge	cambridge	PROPN
ejpam-2406	607	11	university	university	PROPN
ejpam-2406	607	12	press	press	PROPN
ejpam-2406	607	13	,	,	PUNCT
ejpam-2406	607	14	cambridge	cambridge	PROPN
ejpam-2406	607	15	,	,	PUNCT
ejpam-2406	607	16	1990	1990	NUM
ejpam-2406	607	17	.	.	PUNCT