id	sid	tid	token	lemma	pos
ejpam-2482	1	1	compile	compile	NOUN
ejpam-2482	1	2	/	/	SYM
ejpam-2482	1	3	output.dvi	output.dvi	NOUN
ejpam-2482	1	4	european	european	ADJ
ejpam-2482	1	5	journal	journal	NOUN
ejpam-2482	1	6	of	of	ADP
ejpam-2482	1	7	pure	pure	ADJ
ejpam-2482	1	8	and	and	CCONJ
ejpam-2482	1	9	applied	apply	VERB
ejpam-2482	1	10	mathematics	mathematic	NOUN
ejpam-2482	1	11	vol	vol	NOUN
ejpam-2482	1	12	.	.	PROPN
ejpam-2482	1	13	8	8	NUM
ejpam-2482	1	14	,	,	PUNCT
ejpam-2482	1	15	no	no	INTJ
ejpam-2482	1	16	.	.	NOUN
ejpam-2482	1	17	3	3	NUM
ejpam-2482	1	18	,	,	PUNCT
ejpam-2482	1	19	2015	2015	NUM
ejpam-2482	1	20	,	,	PUNCT
ejpam-2482	1	21	417	417	NUM
ejpam-2482	1	22	-	-	SYM
ejpam-2482	1	23	430	430	NUM
ejpam-2482	1	24	issn	issn	PROPN
ejpam-2482	1	25	1307	1307	NUM
ejpam-2482	1	26	-	-	SYM
ejpam-2482	1	27	5543	5543	NUM
ejpam-2482	1	28	–	–	PUNCT
ejpam-2482	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2482	1	30	classical	classical	ADJ
ejpam-2482	1	31	2	2	NUM
ejpam-2482	1	32	-	-	PUNCT
ejpam-2482	1	33	absorbing	absorb	VERB
ejpam-2482	1	34	submodules	submodule	NOUN
ejpam-2482	1	35	of	of	ADP
ejpam-2482	1	36	modules	module	NOUN
ejpam-2482	1	37	over	over	ADP
ejpam-2482	1	38	commutative	commutative	ADJ
ejpam-2482	1	39	rings	ring	NOUN
ejpam-2482	1	40	hojjat	hojjat	PROPN
ejpam-2482	1	41	mostafanasab1	mostafanasab1	PROPN
ejpam-2482	1	42	,	,	PUNCT
ejpam-2482	1	43	!	!	PUNCT
ejpam-2482	1	44	,	,	PUNCT
ejpam-2482	1	45	ünsal	ünsal	PROPN
ejpam-2482	1	46	tekir2	tekir2	PROPN
ejpam-2482	1	47	and	and	CCONJ
ejpam-2482	1	48	kürşat	kürşat	PROPN
ejpam-2482	1	49	hakan	hakan	PROPN
ejpam-2482	1	50	oral3	oral3	PROPN
ejpam-2482	1	51	1	1	NUM
ejpam-2482	1	52	department	department	NOUN
ejpam-2482	1	53	of	of	ADP
ejpam-2482	1	54	mathematics	mathematic	NOUN
ejpam-2482	1	55	and	and	CCONJ
ejpam-2482	1	56	applications	application	NOUN
ejpam-2482	1	57	,	,	PUNCT
ejpam-2482	1	58	university	university	NOUN
ejpam-2482	1	59	of	of	ADP
ejpam-2482	1	60	mohaghegh	mohaghegh	PROPN
ejpam-2482	1	61	ardabili	ardabili	PROPN
ejpam-2482	1	62	,	,	PUNCT
ejpam-2482	1	63	p.	p.	PROPN
ejpam-2482	1	64	o.	o.	PROPN
ejpam-2482	1	65	box	box	PROPN
ejpam-2482	1	66	179	179	NUM
ejpam-2482	1	67	,	,	PUNCT
ejpam-2482	1	68	ardabil	ardabil	VERB
ejpam-2482	1	69	,	,	PUNCT
ejpam-2482	1	70	iran	iran	PROPN
ejpam-2482	1	71	2	2	NUM
ejpam-2482	1	72	department	department	NOUN
ejpam-2482	1	73	of	of	ADP
ejpam-2482	1	74	mathematics	mathematic	NOUN
ejpam-2482	1	75	,	,	PUNCT
ejpam-2482	1	76	marmara	marmara	PROPN
ejpam-2482	1	77	university	university	PROPN
ejpam-2482	1	78	,	,	PUNCT
ejpam-2482	1	79	ziverbey	ziverbey	NOUN
ejpam-2482	1	80	,	,	PUNCT
ejpam-2482	1	81	goztepe	goztepe	NOUN
ejpam-2482	1	82	,	,	PUNCT
ejpam-2482	1	83	istanbul	istanbul	PROPN
ejpam-2482	1	84	34722	34722	NUM
ejpam-2482	1	85	,	,	PUNCT
ejpam-2482	1	86	turkey	turkey	PROPN
ejpam-2482	1	87	3	3	NUM
ejpam-2482	1	88	department	department	NOUN
ejpam-2482	1	89	of	of	ADP
ejpam-2482	1	90	mathematics	mathematic	NOUN
ejpam-2482	1	91	,	,	PUNCT
ejpam-2482	1	92	yildiz	yildiz	PROPN
ejpam-2482	1	93	technical	technical	PROPN
ejpam-2482	1	94	university	university	PROPN
ejpam-2482	1	95	,	,	PUNCT
ejpam-2482	1	96	davutpasa	davutpasa	NOUN
ejpam-2482	1	97	campus	campus	PROPN
ejpam-2482	1	98	,	,	PUNCT
ejpam-2482	1	99	esenler	esenler	NOUN
ejpam-2482	1	100	,	,	PUNCT
ejpam-2482	1	101	istanbul	istanbul	PROPN
ejpam-2482	1	102	,	,	PUNCT
ejpam-2482	1	103	turkey	turkey	PROPN
ejpam-2482	1	104	abstract	abstract	NOUN
ejpam-2482	1	105	.	.	PUNCT
ejpam-2482	2	1	in	in	ADP
ejpam-2482	2	2	this	this	DET
ejpam-2482	2	3	article	article	NOUN
ejpam-2482	2	4	,	,	PUNCT
ejpam-2482	2	5	all	all	DET
ejpam-2482	2	6	rings	ring	NOUN
ejpam-2482	2	7	are	be	AUX
ejpam-2482	2	8	commutative	commutative	ADJ
ejpam-2482	2	9	with	with	ADP
ejpam-2482	2	10	nonzero	nonzero	PROPN
ejpam-2482	2	11	identity	identity	NOUN
ejpam-2482	2	12	.	.	PUNCT
ejpam-2482	3	1	let	let	VERB
ejpam-2482	3	2	m	m	PRON
ejpam-2482	3	3	be	be	AUX
ejpam-2482	3	4	an	an	DET
ejpam-2482	3	5	r	r	NOUN
ejpam-2482	3	6	-	-	PUNCT
ejpam-2482	3	7	module	module	NOUN
ejpam-2482	3	8	.	.	PUNCT
ejpam-2482	4	1	a	a	DET
ejpam-2482	4	2	proper	proper	ADJ
ejpam-2482	4	3	submodule	submodule	NOUN
ejpam-2482	4	4	n	n	PROPN
ejpam-2482	4	5	of	of	ADP
ejpam-2482	4	6	m	m	PROPN
ejpam-2482	4	7	is	be	AUX
ejpam-2482	4	8	called	call	VERB
ejpam-2482	4	9	a	a	DET
ejpam-2482	4	10	classical	classical	ADJ
ejpam-2482	4	11	prime	prime	ADJ
ejpam-2482	4	12	submodule	submodule	NOUN
ejpam-2482	4	13	,	,	PUNCT
ejpam-2482	4	14	if	if	SCONJ
ejpam-2482	4	15	for	for	ADP
ejpam-2482	4	16	each	each	DET
ejpam-2482	4	17	m	m	NOUN
ejpam-2482	4	18	"	"	PUNCT
ejpam-2482	4	19	m	m	VERB
ejpam-2482	4	20	and	and	CCONJ
ejpam-2482	4	21	elements	element	NOUN
ejpam-2482	4	22	a	a	DET
ejpam-2482	4	23	,	,	PUNCT
ejpam-2482	4	24	b	b	NOUN
ejpam-2482	4	25	"	"	PUNCT
ejpam-2482	4	26	r	r	NOUN
ejpam-2482	4	27	,	,	PUNCT
ejpam-2482	4	28	abm	abm	PROPN
ejpam-2482	4	29	"	"	PUNCT
ejpam-2482	5	1	n	n	SYM
ejpam-2482	5	2	implies	imply	VERB
ejpam-2482	5	3	that	that	PRON
ejpam-2482	5	4	am	be	AUX
ejpam-2482	5	5	"	"	PUNCT
ejpam-2482	5	6	n	n	NOUN
ejpam-2482	5	7	or	or	CCONJ
ejpam-2482	5	8	bm	bm	PROPN
ejpam-2482	5	9	"	"	PUNCT
ejpam-2482	6	1	n	n	PROPN
ejpam-2482	6	2	.	.	PUNCT
ejpam-2482	7	1	we	we	PRON
ejpam-2482	7	2	introduce	introduce	VERB
ejpam-2482	7	3	the	the	DET
ejpam-2482	7	4	concept	concept	NOUN
ejpam-2482	7	5	of	of	ADP
ejpam-2482	7	6	"	"	PUNCT
ejpam-2482	7	7	classical	classical	ADJ
ejpam-2482	7	8	2	2	NUM
ejpam-2482	7	9	-	-	PUNCT
ejpam-2482	7	10	absorbing	absorbing	ADJ
ejpam-2482	7	11	submodules	submodule	NOUN
ejpam-2482	7	12	"	"	PUNCT
ejpam-2482	7	13	as	as	ADP
ejpam-2482	7	14	a	a	DET
ejpam-2482	7	15	generalization	generalization	NOUN
ejpam-2482	7	16	of	of	ADP
ejpam-2482	7	17	"	"	PUNCT
ejpam-2482	7	18	classical	classical	ADJ
ejpam-2482	7	19	prime	prime	ADJ
ejpam-2482	7	20	submodules	submodule	NOUN
ejpam-2482	7	21	"	"	PUNCT
ejpam-2482	7	22	.	.	PUNCT
ejpam-2482	8	1	we	we	PRON
ejpam-2482	8	2	say	say	VERB
ejpam-2482	8	3	that	that	SCONJ
ejpam-2482	8	4	a	a	DET
ejpam-2482	8	5	proper	proper	ADJ
ejpam-2482	8	6	submodule	submodule	NOUN
ejpam-2482	8	7	n	n	PROPN
ejpam-2482	8	8	of	of	ADP
ejpam-2482	8	9	m	m	PROPN
ejpam-2482	8	10	is	be	AUX
ejpam-2482	8	11	a	a	DET
ejpam-2482	8	12	classical	classical	ADJ
ejpam-2482	8	13	2	2	NUM
ejpam-2482	8	14	-	-	PUNCT
ejpam-2482	8	15	absorbing	absorb	VERB
ejpam-2482	8	16	submodule	submodule	NOUN
ejpam-2482	8	17	if	if	SCONJ
ejpam-2482	8	18	whenever	whenever	SCONJ
ejpam-2482	8	19	a	a	DET
ejpam-2482	8	20	,	,	PUNCT
ejpam-2482	8	21	b	b	NOUN
ejpam-2482	8	22	,	,	PUNCT
ejpam-2482	8	23	c	c	NOUN
ejpam-2482	8	24	"	"	PUNCT
ejpam-2482	8	25	r	r	NOUN
ejpam-2482	8	26	and	and	CCONJ
ejpam-2482	8	27	m	m	NOUN
ejpam-2482	8	28	"	"	PUNCT
ejpam-2482	8	29	m	m	VERB
ejpam-2482	8	30	with	with	ADP
ejpam-2482	8	31	abcm	abcm	NOUN
ejpam-2482	8	32	"	"	PUNCT
ejpam-2482	8	33	n	n	NOUN
ejpam-2482	8	34	,	,	PUNCT
ejpam-2482	8	35	then	then	ADV
ejpam-2482	8	36	abm	abm	PROPN
ejpam-2482	8	37	"	"	PUNCT
ejpam-2482	8	38	n	n	PROPN
ejpam-2482	8	39	or	or	CCONJ
ejpam-2482	8	40	acm	acm	PROPN
ejpam-2482	8	41	"	"	PUNCT
ejpam-2482	8	42	n	n	PROPN
ejpam-2482	8	43	or	or	CCONJ
ejpam-2482	8	44	bcm	bcm	NOUN
ejpam-2482	8	45	"	"	PUNCT
ejpam-2482	8	46	n	n	NOUN
ejpam-2482	8	47	.	.	PUNCT
ejpam-2482	9	1	2010	2010	NUM
ejpam-2482	9	2	mathematics	mathematic	NOUN
ejpam-2482	9	3	subject	subject	NOUN
ejpam-2482	9	4	classifications	classification	NOUN
ejpam-2482	9	5	:	:	PUNCT
ejpam-2482	9	6	13a15	13a15	NUM
ejpam-2482	9	7	,	,	PUNCT
ejpam-2482	9	8	13c99	13c99	NUM
ejpam-2482	9	9	,	,	PUNCT
ejpam-2482	9	10	13f05	13f05	NUM
ejpam-2482	9	11	key	key	ADJ
ejpam-2482	9	12	words	word	NOUN
ejpam-2482	9	13	and	and	CCONJ
ejpam-2482	9	14	phrases	phrase	NOUN
ejpam-2482	9	15	:	:	PUNCT
ejpam-2482	9	16	classical	classical	ADJ
ejpam-2482	9	17	prime	prime	ADJ
ejpam-2482	9	18	submodule	submodule	NOUN
ejpam-2482	9	19	,	,	PUNCT
ejpam-2482	9	20	classical	classical	ADJ
ejpam-2482	9	21	2	2	NUM
ejpam-2482	9	22	-	-	PUNCT
ejpam-2482	9	23	absorbing	absorb	VERB
ejpam-2482	9	24	submodule	submodule	NOUN
ejpam-2482	9	25	1	1	NUM
ejpam-2482	9	26	.	.	PUNCT
ejpam-2482	9	27	introduction	introduction	NOUN
ejpam-2482	9	28	throughout	throughout	ADP
ejpam-2482	9	29	this	this	DET
ejpam-2482	9	30	paper	paper	NOUN
ejpam-2482	10	1	,	,	PUNCT
ejpam-2482	10	2	we	we	PRON
ejpam-2482	10	3	assume	assume	VERB
ejpam-2482	10	4	that	that	SCONJ
ejpam-2482	10	5	all	all	DET
ejpam-2482	10	6	rings	ring	NOUN
ejpam-2482	10	7	are	be	AUX
ejpam-2482	10	8	commutative	commutative	ADJ
ejpam-2482	10	9	with	with	ADP
ejpam-2482	10	10	1	1	NUM
ejpam-2482	10	11	#	#	NOUN
ejpam-2482	10	12	=	=	SYM
ejpam-2482	10	13	0	0	NUM
ejpam-2482	10	14	.	.	PUNCT
ejpam-2482	11	1	let	let	VERB
ejpam-2482	11	2	r	r	PRON
ejpam-2482	11	3	be	be	AUX
ejpam-2482	11	4	a	a	DET
ejpam-2482	11	5	commutative	commutative	ADJ
ejpam-2482	11	6	ring	ring	NOUN
ejpam-2482	11	7	and	and	CCONJ
ejpam-2482	11	8	m	m	AUX
ejpam-2482	11	9	be	be	AUX
ejpam-2482	11	10	an	an	DET
ejpam-2482	11	11	r	r	NOUN
ejpam-2482	11	12	-	-	PUNCT
ejpam-2482	11	13	module	module	NOUN
ejpam-2482	11	14	.	.	PUNCT
ejpam-2482	12	1	a	a	DET
ejpam-2482	12	2	proper	proper	ADJ
ejpam-2482	12	3	submodule	submodule	NOUN
ejpam-2482	12	4	n	n	PROPN
ejpam-2482	12	5	of	of	ADP
ejpam-2482	12	6	m	m	PROPN
ejpam-2482	12	7	is	be	AUX
ejpam-2482	12	8	said	say	VERB
ejpam-2482	12	9	to	to	PART
ejpam-2482	12	10	be	be	AUX
ejpam-2482	12	11	a	a	DET
ejpam-2482	12	12	prime	prime	ADJ
ejpam-2482	12	13	submodule	submodule	NOUN
ejpam-2482	12	14	,	,	PUNCT
ejpam-2482	12	15	if	if	SCONJ
ejpam-2482	12	16	for	for	ADP
ejpam-2482	12	17	each	each	DET
ejpam-2482	12	18	element	element	NOUN
ejpam-2482	12	19	a	a	DET
ejpam-2482	12	20	"	"	PUNCT
ejpam-2482	12	21	r	r	NOUN
ejpam-2482	12	22	and	and	CCONJ
ejpam-2482	12	23	m	m	NOUN
ejpam-2482	12	24	"	"	PUNCT
ejpam-2482	12	25	m	m	PROPN
ejpam-2482	12	26	,	,	PUNCT
ejpam-2482	12	27	am	be	AUX
ejpam-2482	12	28	"	"	PUNCT
ejpam-2482	12	29	n	n	PRON
ejpam-2482	12	30	implies	imply	VERB
ejpam-2482	12	31	that	that	SCONJ
ejpam-2482	12	32	m	m	VERB
ejpam-2482	12	33	"	"	PUNCT
ejpam-2482	12	34	n	n	CCONJ
ejpam-2482	12	35	or	or	CCONJ
ejpam-2482	12	36	a	a	PRON
ejpam-2482	12	37	"	"	PUNCT
ejpam-2482	12	38	(	(	PUNCT
ejpam-2482	12	39	n	n	X
ejpam-2482	12	40	:	:	PUNCT
ejpam-2482	12	41	r	r	NOUN
ejpam-2482	12	42	m	m	NOUN
ejpam-2482	12	43	)	)	PUNCT
ejpam-2482	12	44	=	=	PRON
ejpam-2482	12	45	{	{	PUNCT
ejpam-2482	12	46	r	r	NOUN
ejpam-2482	12	47	"	"	PUNCT
ejpam-2482	12	48	r	r	NOUN
ejpam-2482	12	49	|	|	NOUN
ejpam-2482	12	50	rm	rm	PROPN
ejpam-2482	12	51	$	$	SYM
ejpam-2482	12	52	n	n	CCONJ
ejpam-2482	12	53	}	}	PUNCT
ejpam-2482	12	54	.	.	PUNCT
ejpam-2482	13	1	a	a	DET
ejpam-2482	13	2	proper	proper	ADJ
ejpam-2482	13	3	submodule	submodule	NOUN
ejpam-2482	13	4	n	n	PROPN
ejpam-2482	13	5	of	of	ADP
ejpam-2482	13	6	m	m	PROPN
ejpam-2482	13	7	is	be	AUX
ejpam-2482	13	8	called	call	VERB
ejpam-2482	13	9	a	a	DET
ejpam-2482	13	10	classical	classical	ADJ
ejpam-2482	13	11	prime	prime	ADJ
ejpam-2482	13	12	submodule	submodule	NOUN
ejpam-2482	13	13	,	,	PUNCT
ejpam-2482	13	14	if	if	SCONJ
ejpam-2482	13	15	for	for	ADP
ejpam-2482	13	16	each	each	DET
ejpam-2482	13	17	m	m	NOUN
ejpam-2482	13	18	"	"	PUNCT
ejpam-2482	13	19	m	m	PROPN
ejpam-2482	13	20	and	and	CCONJ
ejpam-2482	13	21	a	a	DET
ejpam-2482	13	22	,	,	PUNCT
ejpam-2482	13	23	b	b	NOUN
ejpam-2482	13	24	"	"	PUNCT
ejpam-2482	13	25	r	r	NOUN
ejpam-2482	13	26	,	,	PUNCT
ejpam-2482	13	27	abm	abm	PROPN
ejpam-2482	13	28	"	"	PUNCT
ejpam-2482	14	1	n	n	SYM
ejpam-2482	14	2	implies	imply	VERB
ejpam-2482	14	3	that	that	PRON
ejpam-2482	14	4	am	be	AUX
ejpam-2482	14	5	"	"	PUNCT
ejpam-2482	14	6	n	n	NOUN
ejpam-2482	14	7	or	or	CCONJ
ejpam-2482	14	8	bm	bm	PROPN
ejpam-2482	14	9	"	"	PUNCT
ejpam-2482	14	10	n	n	PROPN
ejpam-2482	14	11	.	.	PUNCT
ejpam-2482	15	1	this	this	DET
ejpam-2482	15	2	notion	notion	NOUN
ejpam-2482	15	3	of	of	ADP
ejpam-2482	15	4	classical	classical	ADJ
ejpam-2482	15	5	prime	prime	ADJ
ejpam-2482	15	6	submodules	submodule	NOUN
ejpam-2482	15	7	has	have	AUX
ejpam-2482	15	8	been	be	AUX
ejpam-2482	15	9	extensively	extensively	ADV
ejpam-2482	15	10	studied	study	VERB
ejpam-2482	15	11	by	by	ADP
ejpam-2482	15	12	behboodi	behboodi	NOUN
ejpam-2482	15	13	in	in	ADP
ejpam-2482	15	14	[	[	X
ejpam-2482	15	15	9	9	NUM
ejpam-2482	15	16	,	,	PUNCT
ejpam-2482	15	17	10	10	NUM
ejpam-2482	15	18	]	]	PUNCT
ejpam-2482	15	19	(	(	PUNCT
ejpam-2482	15	20	see	see	VERB
ejpam-2482	15	21	also	also	ADV
ejpam-2482	15	22	,	,	PUNCT
ejpam-2482	15	23	[	[	X
ejpam-2482	15	24	11	11	NUM
ejpam-2482	15	25	]	]	PUNCT
ejpam-2482	15	26	,	,	PUNCT
ejpam-2482	15	27	in	in	ADP
ejpam-2482	15	28	which	which	PRON
ejpam-2482	15	29	,	,	PUNCT
ejpam-2482	15	30	the	the	DET
ejpam-2482	15	31	notion	notion	NOUN
ejpam-2482	15	32	of	of	ADP
ejpam-2482	15	33	“	"	PUNCT
ejpam-2482	15	34	weakly	weakly	ADJ
ejpam-2482	15	35	prime	prime	ADJ
ejpam-2482	15	36	submodules	submodule	NOUN
ejpam-2482	15	37	”	"	PUNCT
ejpam-2482	15	38	is	be	AUX
ejpam-2482	15	39	investigated	investigate	VERB
ejpam-2482	15	40	)	)	PUNCT
ejpam-2482	15	41	.	.	PUNCT
ejpam-2482	16	1	for	for	ADP
ejpam-2482	16	2	more	more	ADJ
ejpam-2482	16	3	information	information	NOUN
ejpam-2482	16	4	on	on	ADP
ejpam-2482	16	5	weakly	weakly	ADJ
ejpam-2482	16	6	prime	prime	ADJ
ejpam-2482	16	7	submodules	submodule	NOUN
ejpam-2482	16	8	,	,	PUNCT
ejpam-2482	16	9	the	the	DET
ejpam-2482	16	10	reader	reader	NOUN
ejpam-2482	16	11	is	be	AUX
ejpam-2482	16	12	referred	refer	VERB
ejpam-2482	16	13	to	to	ADP
ejpam-2482	16	14	[	[	X
ejpam-2482	16	15	3	3	NUM
ejpam-2482	16	16	,	,	PUNCT
ejpam-2482	16	17	4	4	NUM
ejpam-2482	16	18	,	,	PUNCT
ejpam-2482	16	19	12	12	NUM
ejpam-2482	16	20	]	]	PUNCT
ejpam-2482	16	21	.	.	PUNCT
ejpam-2482	17	1	badawi	badawi	PROPN
ejpam-2482	17	2	gave	give	VERB
ejpam-2482	17	3	a	a	DET
ejpam-2482	17	4	generalization	generalization	NOUN
ejpam-2482	17	5	of	of	ADP
ejpam-2482	17	6	prime	prime	ADJ
ejpam-2482	17	7	ideals	ideal	NOUN
ejpam-2482	17	8	in	in	ADP
ejpam-2482	17	9	[	[	X
ejpam-2482	17	10	5	5	NUM
ejpam-2482	17	11	]	]	PUNCT
ejpam-2482	17	12	and	and	CCONJ
ejpam-2482	17	13	said	say	VERB
ejpam-2482	17	14	such	such	ADJ
ejpam-2482	17	15	ideals	ideal	NOUN
ejpam-2482	17	16	2	2	NUM
ejpam-2482	17	17	-	-	PUNCT
ejpam-2482	17	18	absorbing	absorbing	ADJ
ejpam-2482	17	19	ideals	ideal	NOUN
ejpam-2482	17	20	.	.	PUNCT
ejpam-2482	18	1	a	a	DET
ejpam-2482	18	2	proper	proper	ADJ
ejpam-2482	18	3	ideal	ideal	NOUN
ejpam-2482	18	4	i	i	PRON
ejpam-2482	18	5	of	of	ADP
ejpam-2482	18	6	r	r	NOUN
ejpam-2482	18	7	is	be	AUX
ejpam-2482	18	8	a	a	DET
ejpam-2482	18	9	2	2	NUM
ejpam-2482	18	10	-	-	PUNCT
ejpam-2482	18	11	absorbing	absorbing	ADJ
ejpam-2482	18	12	ideal	ideal	NOUN
ejpam-2482	18	13	of	of	ADP
ejpam-2482	18	14	r	r	NOUN
ejpam-2482	19	1	if	if	SCONJ
ejpam-2482	19	2	whenever	whenever	SCONJ
ejpam-2482	19	3	a	a	DET
ejpam-2482	19	4	,	,	PUNCT
ejpam-2482	19	5	b	b	NOUN
ejpam-2482	19	6	,	,	PUNCT
ejpam-2482	19	7	c	c	NOUN
ejpam-2482	19	8	"	"	PUNCT
ejpam-2482	19	9	r	r	NOUN
ejpam-2482	19	10	and	and	CCONJ
ejpam-2482	19	11	abc	abc	PROPN
ejpam-2482	19	12	"	"	PUNCT
ejpam-2482	19	13	i	i	PRON
ejpam-2482	19	14	,	,	PUNCT
ejpam-2482	19	15	then	then	ADV
ejpam-2482	19	16	ab	ab	PROPN
ejpam-2482	19	17	"	"	PUNCT
ejpam-2482	19	18	i	i	PROPN
ejpam-2482	19	19	or	or	CCONJ
ejpam-2482	19	20	ac	ac	PROPN
ejpam-2482	19	21	"	"	PUNCT
ejpam-2482	19	22	i	i	PRON
ejpam-2482	19	23	or	or	CCONJ
ejpam-2482	19	24	bc	bc	VERB
ejpam-2482	19	25	"	"	PUNCT
ejpam-2482	19	26	i	i	INTJ
ejpam-2482	19	27	.	.	PUNCT
ejpam-2482	20	1	he	he	PRON
ejpam-2482	20	2	proved	prove	VERB
ejpam-2482	20	3	that	that	SCONJ
ejpam-2482	20	4	i	i	PRON
ejpam-2482	20	5	is	be	AUX
ejpam-2482	20	6	a	a	DET
ejpam-2482	20	7	2	2	NUM
ejpam-2482	20	8	-	-	PUNCT
ejpam-2482	20	9	absorbing	absorbing	ADJ
ejpam-2482	20	10	ideal	ideal	NOUN
ejpam-2482	20	11	of	of	ADP
ejpam-2482	20	12	r	r	NOUN
ejpam-2482	20	13	if	if	SCONJ
ejpam-2482	20	14	and	and	CCONJ
ejpam-2482	20	15	only	only	ADV
ejpam-2482	20	16	if	if	SCONJ
ejpam-2482	20	17	!	!	PUNCT
ejpam-2482	20	18	corresponding	correspond	VERB
ejpam-2482	20	19	author	author	NOUN
ejpam-2482	20	20	.	.	PUNCT
ejpam-2482	21	1	email	email	NOUN
ejpam-2482	21	2	addresses	address	NOUN
ejpam-2482	21	3	:	:	PUNCT
ejpam-2482	21	4	h.mostafanasab@gmail.com	h.mostafanasab@gmail.com	X
ejpam-2482	21	5	(	(	PUNCT
ejpam-2482	21	6	h.	h.	PROPN
ejpam-2482	21	7	mostafanasab	mostafanasab	PROPN
ejpam-2482	21	8	)	)	PUNCT
ejpam-2482	21	9	,	,	PUNCT
ejpam-2482	21	10	utekir@marmara.edu.tr	utekir@marmara.edu.tr	PROPN
ejpam-2482	21	11	(	(	PUNCT
ejpam-2482	21	12	ü.	ü.	NOUN
ejpam-2482	21	13	tekir	tekir	NOUN
ejpam-2482	21	14	)	)	PUNCT
ejpam-2482	21	15	,	,	PUNCT
ejpam-2482	21	16	khoral@yildiz.edu.tr	khoral@yildiz.edu.tr	PROPN
ejpam-2482	21	17	(	(	PUNCT
ejpam-2482	21	18	k.	k.	PROPN
ejpam-2482	21	19	hakan	hakan	PROPN
ejpam-2482	21	20	oral	oral	PROPN
ejpam-2482	21	21	)	)	PUNCT
ejpam-2482	21	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2482	21	23	417	417	NUM
ejpam-2482	21	24	c%	c%	VERB
ejpam-2482	21	25	2015	2015	NUM
ejpam-2482	21	26	ejpam	ejpam	NOUN
ejpam-2482	21	27	all	all	DET
ejpam-2482	21	28	rights	right	NOUN
ejpam-2482	21	29	reserved	reserve	VERB
ejpam-2482	21	30	.	.	PUNCT
ejpam-2482	22	1	h.	h.	PROPN
ejpam-2482	22	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	22	3	,	,	PUNCT
ejpam-2482	22	4	ü.	ü.	NOUN
ejpam-2482	22	5	tekir	tekir	NOUN
ejpam-2482	22	6	and	and	CCONJ
ejpam-2482	22	7	k.	k.	PROPN
ejpam-2482	22	8	hakan	hakan	PROPN
ejpam-2482	22	9	oral	oral	PROPN
ejpam-2482	22	10	/	/	SYM
ejpam-2482	22	11	eur	eur	PROPN
ejpam-2482	22	12	.	.	PUNCT
ejpam-2482	23	1	j.	j.	PROPN
ejpam-2482	23	2	pure	pure	PROPN
ejpam-2482	23	3	appl	appl	PROPN
ejpam-2482	23	4	.	.	PROPN
ejpam-2482	23	5	math	math	PROPN
ejpam-2482	23	6	,	,	PUNCT
ejpam-2482	23	7	8	8	NUM
ejpam-2482	23	8	(	(	PUNCT
ejpam-2482	23	9	2015	2015	NUM
ejpam-2482	23	10	)	)	PUNCT
ejpam-2482	23	11	,	,	PUNCT
ejpam-2482	23	12	417	417	NUM
ejpam-2482	23	13	-	-	SYM
ejpam-2482	23	14	430	430	NUM
ejpam-2482	23	15	418	418	NUM
ejpam-2482	23	16	whenever	whenever	SCONJ
ejpam-2482	23	17	i1	i1	PROPN
ejpam-2482	23	18	,	,	PUNCT
ejpam-2482	23	19	i2	i2	PROPN
ejpam-2482	23	20	,	,	PUNCT
ejpam-2482	23	21	i3	i3	NOUN
ejpam-2482	23	22	are	be	AUX
ejpam-2482	23	23	ideals	ideal	NOUN
ejpam-2482	23	24	of	of	ADP
ejpam-2482	23	25	r	r	NOUN
ejpam-2482	23	26	with	with	ADP
ejpam-2482	23	27	i1	i1	PROPN
ejpam-2482	23	28	i2	i2	PROPN
ejpam-2482	23	29	i3	i3	PROPN
ejpam-2482	23	30	$	$	PROPN
ejpam-2482	23	31	i	i	PRON
ejpam-2482	23	32	,	,	PUNCT
ejpam-2482	23	33	then	then	ADV
ejpam-2482	23	34	i1	i1	PROPN
ejpam-2482	23	35	i2	i2	PROPN
ejpam-2482	23	36	$	$	SYM
ejpam-2482	23	37	i	i	PROPN
ejpam-2482	23	38	or	or	CCONJ
ejpam-2482	23	39	i1	i1	PROPN
ejpam-2482	23	40	i3	i3	PROPN
ejpam-2482	23	41	$	$	PROPN
ejpam-2482	23	42	i	i	PROPN
ejpam-2482	23	43	or	or	CCONJ
ejpam-2482	23	44	i2	i2	PROPN
ejpam-2482	23	45	i3	i3	PROPN
ejpam-2482	23	46	$	$	PROPN
ejpam-2482	23	47	i	i	PRON
ejpam-2482	23	48	.	.	PUNCT
ejpam-2482	24	1	anderson	anderson	PROPN
ejpam-2482	24	2	and	and	CCONJ
ejpam-2482	24	3	badawi	badawi	PROPN
ejpam-2482	25	1	[	[	X
ejpam-2482	25	2	2	2	NUM
ejpam-2482	25	3	]	]	PUNCT
ejpam-2482	25	4	generalized	generalize	VERB
ejpam-2482	25	5	the	the	DET
ejpam-2482	25	6	notion	notion	NOUN
ejpam-2482	25	7	of	of	ADP
ejpam-2482	25	8	2	2	NUM
ejpam-2482	25	9	-	-	PUNCT
ejpam-2482	25	10	absorbing	absorbing	ADJ
ejpam-2482	25	11	ideals	ideal	NOUN
ejpam-2482	25	12	to	to	ADP
ejpam-2482	25	13	n	n	CCONJ
ejpam-2482	25	14	-	-	PUNCT
ejpam-2482	25	15	absorbing	absorb	VERB
ejpam-2482	25	16	ideals	ideal	NOUN
ejpam-2482	25	17	.	.	PUNCT
ejpam-2482	26	1	a	a	DET
ejpam-2482	26	2	proper	proper	ADJ
ejpam-2482	26	3	ideal	ideal	NOUN
ejpam-2482	26	4	i	i	PRON
ejpam-2482	26	5	of	of	ADP
ejpam-2482	26	6	r	r	NOUN
ejpam-2482	26	7	is	be	AUX
ejpam-2482	26	8	called	call	VERB
ejpam-2482	26	9	an	an	DET
ejpam-2482	26	10	n	n	ADV
ejpam-2482	26	11	-	-	PUNCT
ejpam-2482	26	12	absorbing	absorbing	ADJ
ejpam-2482	26	13	(	(	PUNCT
ejpam-2482	26	14	resp	resp	NOUN
ejpam-2482	26	15	.	.	PUNCT
ejpam-2482	27	1	a	a	DET
ejpam-2482	27	2	strongly	strongly	ADV
ejpam-2482	27	3	n	n	CCONJ
ejpam-2482	27	4	-	-	PUNCT
ejpam-2482	27	5	absorbing	absorbing	ADJ
ejpam-2482	27	6	)	)	PUNCT
ejpam-2482	27	7	ideal	ideal	NOUN
ejpam-2482	27	8	if	if	SCONJ
ejpam-2482	27	9	whenever	whenever	SCONJ
ejpam-2482	27	10	x1	x1	PRON
ejpam-2482	27	11	·	·	PUNCT
ejpam-2482	27	12	·	·	PUNCT
ejpam-2482	27	13	·	·	PUNCT
ejpam-2482	27	14	xn+1	xn+1	X
ejpam-2482	28	1	"	"	PUNCT
ejpam-2482	28	2	i	i	PRON
ejpam-2482	28	3	for	for	ADP
ejpam-2482	28	4	x1	x1	PROPN
ejpam-2482	28	5	,	,	PUNCT
ejpam-2482	28	6	.	.	PUNCT
ejpam-2482	28	7	.	.	PUNCT
ejpam-2482	28	8	.	.	PUNCT
ejpam-2482	29	1	,	,	PUNCT
ejpam-2482	29	2	xn+1	xn+1	X
ejpam-2482	29	3	"	"	PUNCT
ejpam-2482	29	4	r	r	NOUN
ejpam-2482	29	5	(	(	PUNCT
ejpam-2482	29	6	resp	resp	NOUN
ejpam-2482	29	7	.	.	PUNCT
ejpam-2482	30	1	i1	i1	PROPN
ejpam-2482	30	2	.	.	PUNCT
ejpam-2482	30	3	.	.	PUNCT
ejpam-2482	30	4	.	.	PUNCT
ejpam-2482	31	1	in+1	in+1	VERB
ejpam-2482	31	2	$	$	PROPN
ejpam-2482	31	3	i	i	PRON
ejpam-2482	31	4	for	for	ADP
ejpam-2482	31	5	ideals	ideal	NOUN
ejpam-2482	31	6	i1	i1	PROPN
ejpam-2482	31	7	,	,	PUNCT
ejpam-2482	31	8	.	.	PUNCT
ejpam-2482	31	9	.	.	PUNCT
ejpam-2482	32	1	.	.	PUNCT
ejpam-2482	33	1	,	,	PUNCT
ejpam-2482	33	2	in+1	in+1	NOUN
ejpam-2482	33	3	of	of	ADP
ejpam-2482	33	4	r	r	NOUN
ejpam-2482	33	5	)	)	PUNCT
ejpam-2482	33	6	,	,	PUNCT
ejpam-2482	33	7	then	then	ADV
ejpam-2482	33	8	there	there	PRON
ejpam-2482	33	9	are	be	VERB
ejpam-2482	33	10	n	n	PRON
ejpam-2482	33	11	of	of	ADP
ejpam-2482	33	12	the	the	DET
ejpam-2482	33	13	xi	xi	X
ejpam-2482	33	14	’s	’s	PROPN
ejpam-2482	33	15	(	(	PUNCT
ejpam-2482	33	16	resp	resp	NOUN
ejpam-2482	33	17	.	.	PUNCT
ejpam-2482	34	1	n	n	PROPN
ejpam-2482	34	2	of	of	ADP
ejpam-2482	34	3	the	the	DET
ejpam-2482	34	4	ii	ii	PROPN
ejpam-2482	34	5	’s	’s	ADV
ejpam-2482	34	6	)	)	PUNCT
ejpam-2482	34	7	whose	whose	DET
ejpam-2482	34	8	product	product	NOUN
ejpam-2482	34	9	is	be	AUX
ejpam-2482	34	10	in	in	ADP
ejpam-2482	34	11	i	i	PRON
ejpam-2482	34	12	.	.	PUNCT
ejpam-2482	35	1	the	the	DET
ejpam-2482	35	2	reader	reader	NOUN
ejpam-2482	35	3	is	be	AUX
ejpam-2482	35	4	referred	refer	VERB
ejpam-2482	35	5	to	to	ADP
ejpam-2482	35	6	[	[	X
ejpam-2482	35	7	6–8	6–8	X
ejpam-2482	35	8	]	]	X
ejpam-2482	35	9	for	for	ADP
ejpam-2482	35	10	more	more	ADJ
ejpam-2482	35	11	concepts	concept	NOUN
ejpam-2482	35	12	related	relate	VERB
ejpam-2482	35	13	to	to	ADP
ejpam-2482	35	14	2	2	NUM
ejpam-2482	35	15	-	-	PUNCT
ejpam-2482	35	16	absorbing	absorbing	ADJ
ejpam-2482	35	17	ideals	ideal	NOUN
ejpam-2482	35	18	.	.	PUNCT
ejpam-2482	36	1	yousefian	yousefian	ADJ
ejpam-2482	36	2	darani	darani	PROPN
ejpam-2482	36	3	and	and	CCONJ
ejpam-2482	36	4	soheilnia	soheilnia	NOUN
ejpam-2482	36	5	in	in	ADP
ejpam-2482	36	6	[	[	PUNCT
ejpam-2482	36	7	13	13	NUM
ejpam-2482	36	8	]	]	PUNCT
ejpam-2482	36	9	extended	extend	VERB
ejpam-2482	36	10	2	2	NUM
ejpam-2482	36	11	-	-	PUNCT
ejpam-2482	36	12	absorbing	absorbing	ADJ
ejpam-2482	36	13	ideals	ideal	NOUN
ejpam-2482	36	14	to	to	ADP
ejpam-2482	36	15	2	2	NUM
ejpam-2482	36	16	-	-	PUNCT
ejpam-2482	36	17	absorbing	absorbing	ADJ
ejpam-2482	36	18	submodules	submodule	NOUN
ejpam-2482	36	19	.	.	PUNCT
ejpam-2482	37	1	a	a	DET
ejpam-2482	37	2	proper	proper	ADJ
ejpam-2482	37	3	submodule	submodule	NOUN
ejpam-2482	37	4	n	n	PROPN
ejpam-2482	37	5	of	of	ADP
ejpam-2482	37	6	m	m	PROPN
ejpam-2482	37	7	is	be	AUX
ejpam-2482	37	8	called	call	VERB
ejpam-2482	37	9	a	a	DET
ejpam-2482	37	10	2	2	NUM
ejpam-2482	37	11	-	-	PUNCT
ejpam-2482	37	12	absorbing	absorb	VERB
ejpam-2482	37	13	submodule	submodule	NOUN
ejpam-2482	37	14	of	of	ADP
ejpam-2482	37	15	m	m	PRON
ejpam-2482	37	16	if	if	SCONJ
ejpam-2482	37	17	whenever	whenever	SCONJ
ejpam-2482	37	18	abm	abm	PROPN
ejpam-2482	37	19	"	"	PUNCT
ejpam-2482	37	20	n	n	PROPN
ejpam-2482	37	21	for	for	ADP
ejpam-2482	37	22	some	some	DET
ejpam-2482	37	23	a	a	DET
ejpam-2482	37	24	,	,	PUNCT
ejpam-2482	37	25	b	b	NOUN
ejpam-2482	37	26	"	"	PUNCT
ejpam-2482	37	27	r	r	NOUN
ejpam-2482	37	28	and	and	CCONJ
ejpam-2482	37	29	m	m	NOUN
ejpam-2482	37	30	"	"	PUNCT
ejpam-2482	37	31	m	m	VERB
ejpam-2482	37	32	,	,	PUNCT
ejpam-2482	37	33	then	then	ADV
ejpam-2482	37	34	am	be	AUX
ejpam-2482	37	35	"	"	PUNCT
ejpam-2482	37	36	n	n	PROPN
ejpam-2482	37	37	or	or	CCONJ
ejpam-2482	37	38	bm	bm	PROPN
ejpam-2482	37	39	"	"	PUNCT
ejpam-2482	37	40	n	n	PROPN
ejpam-2482	37	41	or	or	CCONJ
ejpam-2482	37	42	ab	ab	PROPN
ejpam-2482	37	43	"	"	PUNCT
ejpam-2482	37	44	!	!	PUNCT
ejpam-2482	38	1	n	n	X
ejpam-2482	38	2	:	:	PUNCT
ejpam-2482	39	1	r	r	NOUN
ejpam-2482	39	2	m	m	NOUN
ejpam-2482	39	3	"	"	PUNCT
ejpam-2482	39	4	.	.	PUNCT
ejpam-2482	40	1	generally	generally	ADV
ejpam-2482	40	2	,	,	PUNCT
ejpam-2482	40	3	a	a	DET
ejpam-2482	40	4	proper	proper	ADJ
ejpam-2482	40	5	submodule	submodule	NOUN
ejpam-2482	40	6	n	n	PROPN
ejpam-2482	40	7	of	of	ADP
ejpam-2482	40	8	m	m	PROPN
ejpam-2482	40	9	is	be	AUX
ejpam-2482	40	10	called	call	VERB
ejpam-2482	40	11	an	an	DET
ejpam-2482	40	12	n	n	ADV
ejpam-2482	40	13	-	-	PUNCT
ejpam-2482	40	14	absorbing	absorb	VERB
ejpam-2482	40	15	submodule	submodule	NOUN
ejpam-2482	40	16	if	if	SCONJ
ejpam-2482	40	17	whenever	whenever	SCONJ
ejpam-2482	40	18	a1	a1	NOUN
ejpam-2482	40	19	.	.	PUNCT
ejpam-2482	40	20	.	.	PUNCT
ejpam-2482	40	21	.	.	PUNCT
ejpam-2482	41	1	anm	anm	INTJ
ejpam-2482	41	2	"	"	PUNCT
ejpam-2482	41	3	n	n	PROPN
ejpam-2482	41	4	for	for	ADP
ejpam-2482	41	5	a1	a1	NOUN
ejpam-2482	41	6	,	,	PUNCT
ejpam-2482	41	7	.	.	PUNCT
ejpam-2482	41	8	.	.	PUNCT
ejpam-2482	41	9	.	.	PUNCT
ejpam-2482	42	1	an	an	DET
ejpam-2482	42	2	"	"	PUNCT
ejpam-2482	42	3	r	r	NOUN
ejpam-2482	42	4	and	and	CCONJ
ejpam-2482	42	5	m	m	NOUN
ejpam-2482	42	6	"	"	PUNCT
ejpam-2482	42	7	m	m	VERB
ejpam-2482	42	8	,	,	PUNCT
ejpam-2482	42	9	then	then	ADV
ejpam-2482	42	10	either	either	CCONJ
ejpam-2482	42	11	a1	a1	NOUN
ejpam-2482	42	12	.	.	PUNCT
ejpam-2482	42	13	.	.	PUNCT
ejpam-2482	42	14	.	.	PUNCT
ejpam-2482	43	1	an	an	DET
ejpam-2482	43	2	"	"	PUNCT
ejpam-2482	43	3	(	(	PUNCT
ejpam-2482	43	4	n	n	NUM
ejpam-2482	43	5	:	:	PUNCT
ejpam-2482	43	6	r	r	NOUN
ejpam-2482	43	7	m	m	NOUN
ejpam-2482	43	8	)	)	PUNCT
ejpam-2482	43	9	or	or	CCONJ
ejpam-2482	43	10	there	there	PRON
ejpam-2482	43	11	are	be	VERB
ejpam-2482	43	12	n	n	X
ejpam-2482	43	13	&	&	CCONJ
ejpam-2482	43	14	1	1	NUM
ejpam-2482	43	15	of	of	ADP
ejpam-2482	43	16	ai	ai	PROPN
ejpam-2482	43	17	’s	’s	ADV
ejpam-2482	43	18	whose	whose	DET
ejpam-2482	43	19	product	product	NOUN
ejpam-2482	43	20	with	with	ADP
ejpam-2482	43	21	m	m	PROPN
ejpam-2482	43	22	is	be	AUX
ejpam-2482	43	23	in	in	ADP
ejpam-2482	43	24	n	n	PROPN
ejpam-2482	43	25	,	,	PUNCT
ejpam-2482	43	26	see	see	VERB
ejpam-2482	43	27	[	[	X
ejpam-2482	43	28	14	14	NUM
ejpam-2482	43	29	]	]	PUNCT
ejpam-2482	43	30	.	.	PUNCT
ejpam-2482	44	1	several	several	ADJ
ejpam-2482	44	2	authors	author	NOUN
ejpam-2482	44	3	investigated	investigate	VERB
ejpam-2482	44	4	properties	property	NOUN
ejpam-2482	44	5	of	of	ADP
ejpam-2482	44	6	2	2	NUM
ejpam-2482	44	7	-	-	PUNCT
ejpam-2482	44	8	absorbing	absorbing	ADJ
ejpam-2482	44	9	submodules	submodule	NOUN
ejpam-2482	44	10	,	,	PUNCT
ejpam-2482	44	11	for	for	ADP
ejpam-2482	44	12	example	example	NOUN
ejpam-2482	44	13	[	[	X
ejpam-2482	44	14	15	15	NUM
ejpam-2482	44	15	]	]	PUNCT
ejpam-2482	44	16	.	.	PUNCT
ejpam-2482	45	1	in	in	ADP
ejpam-2482	45	2	this	this	DET
ejpam-2482	45	3	paper	paper	NOUN
ejpam-2482	45	4	we	we	PRON
ejpam-2482	45	5	introduce	introduce	VERB
ejpam-2482	45	6	the	the	DET
ejpam-2482	45	7	definition	definition	NOUN
ejpam-2482	45	8	of	of	ADP
ejpam-2482	45	9	classical	classical	ADJ
ejpam-2482	45	10	2	2	NUM
ejpam-2482	45	11	-	-	PUNCT
ejpam-2482	45	12	absorbing	absorbing	ADJ
ejpam-2482	45	13	submodules	submodule	NOUN
ejpam-2482	45	14	.	.	PUNCT
ejpam-2482	46	1	a	a	DET
ejpam-2482	46	2	proper	proper	ADJ
ejpam-2482	46	3	submodule	submodule	NOUN
ejpam-2482	46	4	n	n	PROPN
ejpam-2482	46	5	of	of	ADP
ejpam-2482	46	6	an	an	DET
ejpam-2482	46	7	r	r	NOUN
ejpam-2482	46	8	-	-	PUNCT
ejpam-2482	46	9	module	module	NOUN
ejpam-2482	46	10	m	m	NOUN
ejpam-2482	46	11	is	be	AUX
ejpam-2482	46	12	called	call	VERB
ejpam-2482	46	13	classical	classical	ADJ
ejpam-2482	46	14	2	2	NUM
ejpam-2482	46	15	-	-	PUNCT
ejpam-2482	46	16	absorbing	absorb	VERB
ejpam-2482	46	17	submodule	submodule	NOUN
ejpam-2482	46	18	if	if	SCONJ
ejpam-2482	46	19	whenever	whenever	SCONJ
ejpam-2482	46	20	a	a	DET
ejpam-2482	46	21	,	,	PUNCT
ejpam-2482	46	22	b	b	NOUN
ejpam-2482	46	23	,	,	PUNCT
ejpam-2482	46	24	c	c	NOUN
ejpam-2482	46	25	"	"	PUNCT
ejpam-2482	46	26	r	r	NOUN
ejpam-2482	46	27	and	and	CCONJ
ejpam-2482	46	28	m	m	NOUN
ejpam-2482	46	29	"	"	PUNCT
ejpam-2482	46	30	m	m	VERB
ejpam-2482	46	31	with	with	ADP
ejpam-2482	46	32	abcm	abcm	NOUN
ejpam-2482	46	33	"	"	PUNCT
ejpam-2482	46	34	n	n	NOUN
ejpam-2482	46	35	,	,	PUNCT
ejpam-2482	46	36	then	then	ADV
ejpam-2482	46	37	abm	abm	PROPN
ejpam-2482	46	38	"	"	PUNCT
ejpam-2482	46	39	n	n	PROPN
ejpam-2482	46	40	or	or	CCONJ
ejpam-2482	46	41	acm	acm	PROPN
ejpam-2482	46	42	"	"	PUNCT
ejpam-2482	46	43	n	n	PROPN
ejpam-2482	46	44	or	or	CCONJ
ejpam-2482	46	45	bcm	bcm	NOUN
ejpam-2482	46	46	"	"	PUNCT
ejpam-2482	46	47	n	n	NOUN
ejpam-2482	46	48	.	.	PUNCT
ejpam-2482	47	1	clearly	clearly	ADV
ejpam-2482	47	2	,	,	PUNCT
ejpam-2482	47	3	every	every	DET
ejpam-2482	47	4	classical	classical	ADJ
ejpam-2482	47	5	prime	prime	ADJ
ejpam-2482	47	6	submodule	submodule	NOUN
ejpam-2482	47	7	is	be	AUX
ejpam-2482	47	8	a	a	DET
ejpam-2482	47	9	classical	classical	ADJ
ejpam-2482	47	10	2	2	NUM
ejpam-2482	47	11	-	-	PUNCT
ejpam-2482	47	12	absorbing	absorb	VERB
ejpam-2482	47	13	submodule	submodule	NOUN
ejpam-2482	47	14	.	.	PUNCT
ejpam-2482	48	1	we	we	PRON
ejpam-2482	48	2	show	show	VERB
ejpam-2482	48	3	that	that	SCONJ
ejpam-2482	48	4	every	every	DET
ejpam-2482	48	5	noetherian	noetherian	ADJ
ejpam-2482	48	6	r	r	NOUN
ejpam-2482	48	7	-	-	PUNCT
ejpam-2482	48	8	module	module	NOUN
ejpam-2482	48	9	m	m	NOUN
ejpam-2482	48	10	contains	contain	VERB
ejpam-2482	48	11	a	a	DET
ejpam-2482	48	12	finite	finite	ADJ
ejpam-2482	48	13	number	number	NOUN
ejpam-2482	48	14	of	of	ADP
ejpam-2482	48	15	minimal	minimal	ADJ
ejpam-2482	48	16	classical	classical	ADJ
ejpam-2482	48	17	2	2	NUM
ejpam-2482	48	18	-	-	PUNCT
ejpam-2482	48	19	absorbing	absorbing	ADJ
ejpam-2482	48	20	submodules	submodule	NOUN
ejpam-2482	48	21	(	(	PUNCT
ejpam-2482	48	22	theorem	theorem	NOUN
ejpam-2482	48	23	3	3	NUM
ejpam-2482	48	24	)	)	PUNCT
ejpam-2482	48	25	.	.	PUNCT
ejpam-2482	49	1	further	far	ADV
ejpam-2482	49	2	,	,	PUNCT
ejpam-2482	49	3	we	we	PRON
ejpam-2482	49	4	give	give	VERB
ejpam-2482	49	5	the	the	DET
ejpam-2482	49	6	relationship	relationship	NOUN
ejpam-2482	49	7	between	between	ADP
ejpam-2482	49	8	classical	classical	ADJ
ejpam-2482	49	9	2	2	NUM
ejpam-2482	49	10	-	-	PUNCT
ejpam-2482	49	11	absorbing	absorbing	ADJ
ejpam-2482	49	12	submodules	submodule	NOUN
ejpam-2482	49	13	,	,	PUNCT
ejpam-2482	49	14	classical	classical	ADJ
ejpam-2482	49	15	prime	prime	ADJ
ejpam-2482	49	16	submodules	submodule	NOUN
ejpam-2482	49	17	and	and	CCONJ
ejpam-2482	49	18	2	2	NUM
ejpam-2482	49	19	-	-	PUNCT
ejpam-2482	49	20	absorbing	absorbing	ADJ
ejpam-2482	49	21	submodules	submodule	NOUN
ejpam-2482	49	22	(	(	PUNCT
ejpam-2482	49	23	proposition	proposition	NOUN
ejpam-2482	49	24	2	2	NUM
ejpam-2482	49	25	,	,	PUNCT
ejpam-2482	49	26	proposition	proposition	NOUN
ejpam-2482	49	27	7	7	NUM
ejpam-2482	49	28	)	)	PUNCT
ejpam-2482	49	29	.	.	PUNCT
ejpam-2482	50	1	moreover	moreover	ADV
ejpam-2482	50	2	,	,	PUNCT
ejpam-2482	50	3	we	we	PRON
ejpam-2482	50	4	characterize	characterize	VERB
ejpam-2482	50	5	classical	classical	ADJ
ejpam-2482	50	6	2	2	NUM
ejpam-2482	50	7	-	-	PUNCT
ejpam-2482	50	8	absorbing	absorb	VERB
ejpam-2482	50	9	submodules	submodule	NOUN
ejpam-2482	50	10	in	in	ADP
ejpam-2482	50	11	(	(	PUNCT
ejpam-2482	50	12	theorem	theorem	ADJ
ejpam-2482	50	13	2	2	NUM
ejpam-2482	50	14	,	,	PUNCT
ejpam-2482	50	15	theorem	theorem	VERB
ejpam-2482	50	16	4	4	NUM
ejpam-2482	50	17	)	)	PUNCT
ejpam-2482	50	18	.	.	PUNCT
ejpam-2482	51	1	in	in	ADP
ejpam-2482	51	2	(	(	PUNCT
ejpam-2482	51	3	theorem	theorem	ADJ
ejpam-2482	51	4	7	7	NUM
ejpam-2482	51	5	,	,	PUNCT
ejpam-2482	51	6	theorem	theorem	ADJ
ejpam-2482	51	7	8)	8)	NUM
ejpam-2482	51	8	we	we	PRON
ejpam-2482	51	9	investigate	investigate	VERB
ejpam-2482	51	10	classical	classical	ADJ
ejpam-2482	51	11	2	2	NUM
ejpam-2482	51	12	-	-	PUNCT
ejpam-2482	51	13	absorbing	absorb	VERB
ejpam-2482	51	14	submodules	submodule	NOUN
ejpam-2482	51	15	of	of	ADP
ejpam-2482	51	16	a	a	DET
ejpam-2482	51	17	finite	finite	ADJ
ejpam-2482	51	18	direct	direct	ADJ
ejpam-2482	51	19	product	product	NOUN
ejpam-2482	51	20	of	of	ADP
ejpam-2482	51	21	modules	module	NOUN
ejpam-2482	51	22	.	.	PUNCT
ejpam-2482	52	1	2	2	X
ejpam-2482	52	2	.	.	X
ejpam-2482	52	3	characterizations	characterization	NOUN
ejpam-2482	52	4	of	of	ADP
ejpam-2482	52	5	classical	classical	ADJ
ejpam-2482	52	6	2	2	NUM
ejpam-2482	52	7	-	-	PUNCT
ejpam-2482	52	8	absorbing	absorb	VERB
ejpam-2482	52	9	submodules	submodule	NOUN
ejpam-2482	52	10	first	first	ADV
ejpam-2482	52	11	of	of	ADP
ejpam-2482	52	12	all	all	PRON
ejpam-2482	52	13	we	we	PRON
ejpam-2482	52	14	give	give	VERB
ejpam-2482	52	15	a	a	DET
ejpam-2482	52	16	module	module	NOUN
ejpam-2482	52	17	which	which	PRON
ejpam-2482	52	18	has	have	VERB
ejpam-2482	52	19	no	no	DET
ejpam-2482	52	20	classical	classical	ADJ
ejpam-2482	52	21	2	2	NUM
ejpam-2482	52	22	-	-	PUNCT
ejpam-2482	52	23	absorbing	absorb	VERB
ejpam-2482	52	24	submodule	submodule	NOUN
ejpam-2482	52	25	.	.	PUNCT
ejpam-2482	52	26	example	example	NOUN
ejpam-2482	53	1	1	1	NUM
ejpam-2482	53	2	.	.	PUNCT
ejpam-2482	53	3	let	let	VERB
ejpam-2482	53	4	p	p	PRON
ejpam-2482	53	5	be	be	AUX
ejpam-2482	53	6	a	a	DET
ejpam-2482	53	7	fixed	fix	VERB
ejpam-2482	53	8	prime	prime	ADJ
ejpam-2482	53	9	integer	integer	NOUN
ejpam-2482	53	10	and	and	CCONJ
ejpam-2482	53	11	!	!	PUNCT
ejpam-2482	53	12	0	0	PUNCT
ejpam-2482	54	1	=	=	PUNCT
ejpam-2482	54	2	!	!	PUNCT
ejpam-2482	54	3	'	'	PUNCT
ejpam-2482	55	1	{	{	PUNCT
ejpam-2482	55	2	0	0	NUM
ejpam-2482	55	3	}	}	PUNCT
ejpam-2482	55	4	.	.	PUNCT
ejpam-2482	56	1	then	then	ADV
ejpam-2482	56	2	e	e	X
ejpam-2482	56	3	!	!	PUNCT
ejpam-2482	57	1	p	p	NOUN
ejpam-2482	57	2	"	"	PUNCT
ejpam-2482	57	3	:	:	PUNCT
ejpam-2482	57	4	=	=	SYM
ejpam-2482	57	5	#	#	NOUN
ejpam-2482	57	6	!	!	PUNCT
ejpam-2482	57	7	"	"	PUNCT
ejpam-2482	58	1	"	"	PUNCT
ejpam-2482	58	2	/	/	SYM
ejpam-2482	58	3	#	#	NOUN
ejpam-2482	58	4	|	|	NOUN
ejpam-2482	58	5	!	!	PUNCT
ejpam-2482	58	6	=	=	PUNCT
ejpam-2482	59	1	r	r	NOUN
ejpam-2482	59	2	pn	pn	NOUN
ejpam-2482	59	3	+	+	NOUN
ejpam-2482	59	4	#	#	NOUN
ejpam-2482	59	5	for	for	ADP
ejpam-2482	59	6	some	some	DET
ejpam-2482	59	7	r	r	NOUN
ejpam-2482	59	8	"	"	PUNCT
ejpam-2482	59	9	#	#	NOUN
ejpam-2482	59	10	and	and	CCONJ
ejpam-2482	59	11	n	n	NOUN
ejpam-2482	59	12	"	"	PUNCT
ejpam-2482	59	13	!	!	PUNCT
ejpam-2482	59	14	0	0	PUNCT
ejpam-2482	60	1	$	$	PRON
ejpam-2482	60	2	is	be	AUX
ejpam-2482	60	3	a	a	DET
ejpam-2482	60	4	nonzero	nonzero	ADJ
ejpam-2482	60	5	submodule	submodule	NOUN
ejpam-2482	60	6	of	of	ADP
ejpam-2482	60	7	the	the	DET
ejpam-2482	60	8	#	#	SYM
ejpam-2482	60	9	-module	-module	NOUN
ejpam-2482	60	10	"	"	PUNCT
ejpam-2482	60	11	/	/	SYM
ejpam-2482	60	12	#	#	NOUN
ejpam-2482	60	13	.	.	PUNCT
ejpam-2482	61	1	for	for	ADP
ejpam-2482	61	2	each	each	DET
ejpam-2482	61	3	t	t	NOUN
ejpam-2482	61	4	"	"	PUNCT
ejpam-2482	61	5	!	!	PUNCT
ejpam-2482	61	6	0	0	NUM
ejpam-2482	61	7	,	,	PUNCT
ejpam-2482	61	8	set	set	VERB
ejpam-2482	61	9	gt	gt	INTJ
ejpam-2482	62	1	:	:	PUNCT
ejpam-2482	62	2	=	=	NOUN
ejpam-2482	62	3	#	#	NOUN
ejpam-2482	62	4	!	!	PUNCT
ejpam-2482	62	5	"	"	PUNCT
ejpam-2482	63	1	"	"	PUNCT
ejpam-2482	63	2	/	/	SYM
ejpam-2482	63	3	#	#	NOUN
ejpam-2482	63	4	|	|	NOUN
ejpam-2482	63	5	!	!	PUNCT
ejpam-2482	63	6	=	=	PUNCT
ejpam-2482	64	1	r	r	NOUN
ejpam-2482	64	2	pt	pt	NOUN
ejpam-2482	64	3	+	+	NOUN
ejpam-2482	64	4	#	#	NOUN
ejpam-2482	64	5	for	for	ADP
ejpam-2482	64	6	some	some	DET
ejpam-2482	64	7	r	r	NOUN
ejpam-2482	64	8	"	"	PUNCT
ejpam-2482	64	9	#	#	NOUN
ejpam-2482	64	10	$	$	NOUN
ejpam-2482	64	11	.	.	PUNCT
ejpam-2482	65	1	notice	notice	VERB
ejpam-2482	65	2	that	that	SCONJ
ejpam-2482	65	3	for	for	ADP
ejpam-2482	65	4	each	each	DET
ejpam-2482	65	5	t	t	NOUN
ejpam-2482	65	6	"	"	PUNCT
ejpam-2482	65	7	!	!	PUNCT
ejpam-2482	65	8	0	0	NUM
ejpam-2482	65	9	,	,	PUNCT
ejpam-2482	65	10	gt	gt	PROPN
ejpam-2482	65	11	is	be	AUX
ejpam-2482	65	12	a	a	DET
ejpam-2482	65	13	submodule	submodule	NOUN
ejpam-2482	65	14	of	of	ADP
ejpam-2482	65	15	e	e	NOUN
ejpam-2482	65	16	!	!	PUNCT
ejpam-2482	66	1	p	p	NOUN
ejpam-2482	66	2	"	"	PUNCT
ejpam-2482	66	3	generated	generate	VERB
ejpam-2482	66	4	by	by	ADP
ejpam-2482	66	5	1	1	NUM
ejpam-2482	66	6	pt	pt	NOUN
ejpam-2482	66	7	+	+	NOUN
ejpam-2482	66	8	#	#	NOUN
ejpam-2482	66	9	for	for	ADP
ejpam-2482	66	10	each	each	DET
ejpam-2482	66	11	t	t	NOUN
ejpam-2482	66	12	"	"	PUNCT
ejpam-2482	66	13	!	!	PUNCT
ejpam-2482	67	1	0	0	X
ejpam-2482	67	2	.	.	PUNCT
ejpam-2482	68	1	each	each	DET
ejpam-2482	68	2	proper	proper	ADJ
ejpam-2482	68	3	submodule	submodule	NOUN
ejpam-2482	68	4	of	of	ADP
ejpam-2482	68	5	e	e	PROPN
ejpam-2482	68	6	!	!	PUNCT
ejpam-2482	69	1	p	p	NOUN
ejpam-2482	69	2	"	"	PUNCT
ejpam-2482	69	3	is	be	AUX
ejpam-2482	69	4	equal	equal	ADJ
ejpam-2482	69	5	to	to	PART
ejpam-2482	69	6	gi	gi	VERB
ejpam-2482	69	7	for	for	ADP
ejpam-2482	69	8	some	some	DET
ejpam-2482	69	9	i	i	PRON
ejpam-2482	69	10	"	"	PUNCT
ejpam-2482	69	11	!	!	PUNCT
ejpam-2482	69	12	0	0	PUNCT
ejpam-2482	70	1	(	(	PUNCT
ejpam-2482	70	2	see	see	VERB
ejpam-2482	70	3	,	,	PUNCT
ejpam-2482	70	4	[	[	X
ejpam-2482	70	5	17	17	NUM
ejpam-2482	70	6	,	,	PUNCT
ejpam-2482	70	7	example	example	NOUN
ejpam-2482	70	8	7.10	7.10	NUM
ejpam-2482	70	9	]	]	PUNCT
ejpam-2482	70	10	)	)	PUNCT
ejpam-2482	70	11	.	.	PUNCT
ejpam-2482	71	1	however	however	ADV
ejpam-2482	71	2	,	,	PUNCT
ejpam-2482	71	3	no	no	DET
ejpam-2482	71	4	gt	gt	INTJ
ejpam-2482	71	5	is	be	AUX
ejpam-2482	71	6	a	a	DET
ejpam-2482	71	7	classical	classical	ADJ
ejpam-2482	71	8	2	2	NUM
ejpam-2482	71	9	-	-	PUNCT
ejpam-2482	71	10	absorbing	absorb	VERB
ejpam-2482	71	11	submodule	submodule	NOUN
ejpam-2482	71	12	of	of	ADP
ejpam-2482	71	13	e	e	PROPN
ejpam-2482	71	14	!	!	PUNCT
ejpam-2482	72	1	p	p	NOUN
ejpam-2482	72	2	"	"	PUNCT
ejpam-2482	72	3	.	.	PUNCT
ejpam-2482	73	1	indeed	indeed	ADV
ejpam-2482	73	2	,	,	PUNCT
ejpam-2482	73	3	1	1	NUM
ejpam-2482	73	4	pt+3	pt+3	VERB
ejpam-2482	73	5	+	+	NOUN
ejpam-2482	73	6	#	#	NOUN
ejpam-2482	73	7	"	"	PUNCT
ejpam-2482	73	8	e	e	NOUN
ejpam-2482	73	9	!	!	PUNCT
ejpam-2482	74	1	p	p	NOUN
ejpam-2482	74	2	"	"	PUNCT
ejpam-2482	74	3	.	.	PUNCT
ejpam-2482	75	1	then	then	ADV
ejpam-2482	75	2	p3	p3	PROPN
ejpam-2482	75	3	%	%	NOUN
ejpam-2482	75	4	1	1	NUM
ejpam-2482	75	5	pt+3	pt+3	VERB
ejpam-2482	75	6	+	+	NOUN
ejpam-2482	75	7	#	#	NOUN
ejpam-2482	75	8	&	&	CCONJ
ejpam-2482	75	9	=	=	SYM
ejpam-2482	75	10	1	1	NUM
ejpam-2482	75	11	pt	pt	NOUN
ejpam-2482	75	12	+	+	NOUN
ejpam-2482	75	13	#	#	NOUN
ejpam-2482	75	14	"	"	PUNCT
ejpam-2482	75	15	gt	gt	PROPN
ejpam-2482	75	16	but	but	CCONJ
ejpam-2482	75	17	p2	p2	PROPN
ejpam-2482	75	18	%	%	NOUN
ejpam-2482	75	19	1	1	NUM
ejpam-2482	76	1	pt+3	pt+3	VERB
ejpam-2482	76	2	+	+	NOUN
ejpam-2482	76	3	#	#	NOUN
ejpam-2482	76	4	&	&	CCONJ
ejpam-2482	76	5	=	=	SYM
ejpam-2482	76	6	1	1	NUM
ejpam-2482	76	7	pt+1	pt+1	NUM
ejpam-2482	77	1	+	+	NOUN
ejpam-2482	77	2	#	#	NOUN
ejpam-2482	77	3	/	/	SYM
ejpam-2482	77	4	"	"	PUNCT
ejpam-2482	77	5	gt	gt	PROPN
ejpam-2482	77	6	.	.	PUNCT
ejpam-2482	77	7	theorem	theorem	NOUN
ejpam-2482	77	8	1	1	NUM
ejpam-2482	77	9	.	.	PUNCT
ejpam-2482	78	1	let	let	VERB
ejpam-2482	78	2	f	f	NOUN
ejpam-2482	78	3	:	:	PUNCT
ejpam-2482	78	4	m	m	VERB
ejpam-2482	78	5	(	(	PUNCT
ejpam-2482	78	6	m	m	AUX
ejpam-2482	78	7	)	)	PUNCT
ejpam-2482	78	8	be	be	AUX
ejpam-2482	78	9	an	an	DET
ejpam-2482	78	10	epimorphism	epimorphism	NOUN
ejpam-2482	78	11	of	of	ADP
ejpam-2482	78	12	r	r	NOUN
ejpam-2482	78	13	-	-	PUNCT
ejpam-2482	78	14	modules	module	NOUN
ejpam-2482	78	15	.	.	PUNCT
ejpam-2482	79	1	(	(	PUNCT
ejpam-2482	79	2	i	i	NOUN
ejpam-2482	79	3	)	)	PUNCT
ejpam-2482	79	4	if	if	SCONJ
ejpam-2482	79	5	n	n	NUM
ejpam-2482	79	6	)	)	PUNCT
ejpam-2482	79	7	is	be	AUX
ejpam-2482	79	8	a	a	DET
ejpam-2482	79	9	classical	classical	ADJ
ejpam-2482	79	10	2	2	NUM
ejpam-2482	79	11	-	-	PUNCT
ejpam-2482	79	12	absorbing	absorb	VERB
ejpam-2482	79	13	submodule	submodule	NOUN
ejpam-2482	79	14	of	of	ADP
ejpam-2482	79	15	m	m	PROPN
ejpam-2482	79	16	)	)	PUNCT
ejpam-2482	79	17	,	,	PUNCT
ejpam-2482	79	18	then	then	ADV
ejpam-2482	79	19	f	f	PROPN
ejpam-2482	79	20	&	&	CCONJ
ejpam-2482	79	21	1(n	1(n	NUM
ejpam-2482	79	22	)	)	PUNCT
ejpam-2482	79	23	)	)	PUNCT
ejpam-2482	79	24	is	be	AUX
ejpam-2482	79	25	a	a	DET
ejpam-2482	79	26	classical	classical	ADJ
ejpam-2482	79	27	2	2	NUM
ejpam-2482	79	28	-	-	PUNCT
ejpam-2482	79	29	absorbing	absorb	VERB
ejpam-2482	79	30	submodule	submodule	NOUN
ejpam-2482	79	31	of	of	ADP
ejpam-2482	79	32	m.	m.	PROPN
ejpam-2482	79	33	h.	h.	PROPN
ejpam-2482	79	34	mostafanasab	mostafanasab	VERB
ejpam-2482	79	35	,	,	PUNCT
ejpam-2482	79	36	ü.	ü.	NOUN
ejpam-2482	79	37	tekir	tekir	NOUN
ejpam-2482	79	38	and	and	CCONJ
ejpam-2482	79	39	k.	k.	PROPN
ejpam-2482	79	40	hakan	hakan	PROPN
ejpam-2482	79	41	oral	oral	PROPN
ejpam-2482	79	42	/	/	SYM
ejpam-2482	79	43	eur	eur	PROPN
ejpam-2482	79	44	.	.	PUNCT
ejpam-2482	80	1	j.	j.	PROPN
ejpam-2482	80	2	pure	pure	PROPN
ejpam-2482	80	3	appl	appl	PROPN
ejpam-2482	80	4	.	.	PROPN
ejpam-2482	80	5	math	math	PROPN
ejpam-2482	80	6	,	,	PUNCT
ejpam-2482	80	7	8	8	NUM
ejpam-2482	80	8	(	(	PUNCT
ejpam-2482	80	9	2015	2015	NUM
ejpam-2482	80	10	)	)	PUNCT
ejpam-2482	80	11	,	,	PUNCT
ejpam-2482	80	12	417	417	NUM
ejpam-2482	80	13	-	-	SYM
ejpam-2482	80	14	430	430	NUM
ejpam-2482	80	15	419	419	NUM
ejpam-2482	80	16	(	(	PUNCT
ejpam-2482	80	17	ii	ii	NOUN
ejpam-2482	80	18	)	)	PUNCT
ejpam-2482	80	19	if	if	SCONJ
ejpam-2482	80	20	n	n	PRON
ejpam-2482	80	21	is	be	AUX
ejpam-2482	80	22	a	a	DET
ejpam-2482	80	23	classical	classical	ADJ
ejpam-2482	80	24	2	2	NUM
ejpam-2482	80	25	-	-	PUNCT
ejpam-2482	80	26	absorbing	absorb	VERB
ejpam-2482	80	27	submodule	submodule	NOUN
ejpam-2482	80	28	of	of	ADP
ejpam-2482	80	29	m	m	PROPN
ejpam-2482	80	30	containing	contain	VERB
ejpam-2482	80	31	ker	ker	NOUN
ejpam-2482	80	32	(	(	PUNCT
ejpam-2482	80	33	f	f	PROPN
ejpam-2482	80	34	)	)	PUNCT
ejpam-2482	80	35	,	,	PUNCT
ejpam-2482	80	36	then	then	ADV
ejpam-2482	80	37	f	f	PROPN
ejpam-2482	80	38	(	(	PUNCT
ejpam-2482	80	39	n	n	CCONJ
ejpam-2482	80	40	)	)	PUNCT
ejpam-2482	80	41	is	be	AUX
ejpam-2482	80	42	a	a	DET
ejpam-2482	80	43	classical	classical	ADJ
ejpam-2482	80	44	2	2	NUM
ejpam-2482	80	45	-	-	PUNCT
ejpam-2482	80	46	absorbing	absorb	VERB
ejpam-2482	80	47	submodule	submodule	NOUN
ejpam-2482	80	48	of	of	ADP
ejpam-2482	80	49	m	m	PROPN
ejpam-2482	80	50	)	)	PUNCT
ejpam-2482	80	51	.	.	PUNCT
ejpam-2482	81	1	proof	proof	NOUN
ejpam-2482	81	2	.	.	PUNCT
ejpam-2482	82	1	(	(	PUNCT
ejpam-2482	82	2	i	i	NOUN
ejpam-2482	82	3	)	)	PUNCT
ejpam-2482	82	4	since	since	SCONJ
ejpam-2482	82	5	f	f	PROPN
ejpam-2482	82	6	is	be	AUX
ejpam-2482	82	7	epimorphism	epimorphism	NOUN
ejpam-2482	82	8	,	,	PUNCT
ejpam-2482	82	9	f	f	PROPN
ejpam-2482	82	10	&	&	CCONJ
ejpam-2482	82	11	1(n	1(n	NUM
ejpam-2482	82	12	)	)	PUNCT
ejpam-2482	82	13	)	)	PUNCT
ejpam-2482	82	14	is	be	AUX
ejpam-2482	82	15	a	a	DET
ejpam-2482	82	16	proper	proper	ADJ
ejpam-2482	82	17	submodule	submodule	NOUN
ejpam-2482	82	18	of	of	ADP
ejpam-2482	82	19	m	m	PROPN
ejpam-2482	82	20	.	.	PUNCT
ejpam-2482	83	1	let	let	VERB
ejpam-2482	83	2	a	a	DET
ejpam-2482	83	3	,	,	PUNCT
ejpam-2482	83	4	b	b	NOUN
ejpam-2482	83	5	,	,	PUNCT
ejpam-2482	83	6	c	c	NOUN
ejpam-2482	83	7	"	"	PUNCT
ejpam-2482	83	8	r	r	NOUN
ejpam-2482	83	9	and	and	CCONJ
ejpam-2482	83	10	m	m	PRON
ejpam-2482	83	11	"	"	PUNCT
ejpam-2482	83	12	m	m	VERB
ejpam-2482	83	13	such	such	ADJ
ejpam-2482	83	14	that	that	SCONJ
ejpam-2482	83	15	abcm	abcm	NOUN
ejpam-2482	83	16	"	"	PUNCT
ejpam-2482	83	17	f	f	PROPN
ejpam-2482	83	18	&	&	CCONJ
ejpam-2482	83	19	1(n	1(n	NUM
ejpam-2482	83	20	)	)	PUNCT
ejpam-2482	83	21	)	)	PUNCT
ejpam-2482	83	22	.	.	PUNCT
ejpam-2482	84	1	then	then	ADV
ejpam-2482	84	2	abc	abc	PROPN
ejpam-2482	84	3	f	f	PROPN
ejpam-2482	84	4	(	(	PUNCT
ejpam-2482	84	5	m	m	PROPN
ejpam-2482	84	6	)	)	PUNCT
ejpam-2482	84	7	"	"	PUNCT
ejpam-2482	84	8	n	n	CCONJ
ejpam-2482	84	9	)	)	PUNCT
ejpam-2482	84	10	.	.	PUNCT
ejpam-2482	85	1	hence	hence	ADV
ejpam-2482	85	2	ab	ab	PROPN
ejpam-2482	85	3	f	f	PROPN
ejpam-2482	85	4	(	(	PUNCT
ejpam-2482	85	5	m	m	PROPN
ejpam-2482	85	6	)	)	PUNCT
ejpam-2482	85	7	"	"	PUNCT
ejpam-2482	85	8	n	n	CCONJ
ejpam-2482	85	9	)	)	PUNCT
ejpam-2482	85	10	or	or	CCONJ
ejpam-2482	85	11	ac	ac	PROPN
ejpam-2482	85	12	f	f	PROPN
ejpam-2482	85	13	(	(	PUNCT
ejpam-2482	85	14	m	m	PROPN
ejpam-2482	85	15	)	)	PUNCT
ejpam-2482	85	16	"	"	PUNCT
ejpam-2482	85	17	n	n	CCONJ
ejpam-2482	85	18	)	)	PUNCT
ejpam-2482	85	19	or	or	CCONJ
ejpam-2482	85	20	bc	bc	PROPN
ejpam-2482	85	21	f	f	PROPN
ejpam-2482	85	22	(	(	PUNCT
ejpam-2482	85	23	m	m	PROPN
ejpam-2482	85	24	)	)	PUNCT
ejpam-2482	85	25	"	"	PUNCT
ejpam-2482	85	26	n	n	CCONJ
ejpam-2482	85	27	)	)	PUNCT
ejpam-2482	85	28	,	,	PUNCT
ejpam-2482	85	29	and	and	CCONJ
ejpam-2482	85	30	thus	thus	ADV
ejpam-2482	85	31	abm	abm	PROPN
ejpam-2482	85	32	"	"	PUNCT
ejpam-2482	85	33	f	f	PROPN
ejpam-2482	85	34	&	&	CCONJ
ejpam-2482	85	35	1(n	1(n	NUM
ejpam-2482	85	36	)	)	PUNCT
ejpam-2482	85	37	)	)	PUNCT
ejpam-2482	85	38	or	or	CCONJ
ejpam-2482	85	39	acm	acm	PROPN
ejpam-2482	85	40	"	"	PUNCT
ejpam-2482	85	41	f	f	PROPN
ejpam-2482	85	42	&	&	CCONJ
ejpam-2482	85	43	1(n	1(n	NUM
ejpam-2482	85	44	)	)	PUNCT
ejpam-2482	85	45	)	)	PUNCT
ejpam-2482	85	46	or	or	CCONJ
ejpam-2482	85	47	bcm	bcm	NOUN
ejpam-2482	85	48	"	"	PUNCT
ejpam-2482	85	49	f	f	PROPN
ejpam-2482	85	50	&	&	CCONJ
ejpam-2482	85	51	1(n	1(n	NUM
ejpam-2482	85	52	)	)	PUNCT
ejpam-2482	85	53	)	)	PUNCT
ejpam-2482	85	54	.	.	PUNCT
ejpam-2482	86	1	so	so	ADV
ejpam-2482	86	2	,	,	PUNCT
ejpam-2482	86	3	f	f	PROPN
ejpam-2482	86	4	&	&	CCONJ
ejpam-2482	86	5	1(n	1(n	NUM
ejpam-2482	86	6	)	)	PUNCT
ejpam-2482	86	7	)	)	PUNCT
ejpam-2482	86	8	is	be	AUX
ejpam-2482	86	9	a	a	DET
ejpam-2482	86	10	classical	classical	ADJ
ejpam-2482	86	11	2	2	NUM
ejpam-2482	86	12	-	-	PUNCT
ejpam-2482	86	13	absorbing	absorb	VERB
ejpam-2482	86	14	submodule	submodule	NOUN
ejpam-2482	86	15	of	of	ADP
ejpam-2482	86	16	m	m	PROPN
ejpam-2482	86	17	.	.	PUNCT
ejpam-2482	87	1	(	(	PUNCT
ejpam-2482	87	2	ii	ii	NOUN
ejpam-2482	87	3	)	)	PUNCT
ejpam-2482	87	4	let	let	VERB
ejpam-2482	87	5	a	a	DET
ejpam-2482	87	6	,	,	PUNCT
ejpam-2482	87	7	b	b	NOUN
ejpam-2482	87	8	,	,	PUNCT
ejpam-2482	87	9	c	c	NOUN
ejpam-2482	87	10	"	"	PUNCT
ejpam-2482	87	11	r	r	NOUN
ejpam-2482	87	12	and	and	CCONJ
ejpam-2482	87	13	m	m	NOUN
ejpam-2482	87	14	)	)	PUNCT
ejpam-2482	87	15	"	"	PUNCT
ejpam-2482	87	16	m	m	AUX
ejpam-2482	87	17	)	)	PUNCT
ejpam-2482	87	18	be	be	AUX
ejpam-2482	87	19	such	such	ADJ
ejpam-2482	87	20	that	that	DET
ejpam-2482	87	21	abcm	abcm	NOUN
ejpam-2482	87	22	)	)	PUNCT
ejpam-2482	87	23	"	"	PUNCT
ejpam-2482	87	24	f	f	PROPN
ejpam-2482	87	25	(	(	PUNCT
ejpam-2482	87	26	n	n	CCONJ
ejpam-2482	87	27	)	)	PUNCT
ejpam-2482	87	28	.	.	PUNCT
ejpam-2482	88	1	by	by	ADP
ejpam-2482	88	2	assumption	assumption	NOUN
ejpam-2482	88	3	there	there	PRON
ejpam-2482	88	4	exists	exist	VERB
ejpam-2482	88	5	m	m	VERB
ejpam-2482	88	6	"	"	PUNCT
ejpam-2482	88	7	m	m	VERB
ejpam-2482	88	8	such	such	ADJ
ejpam-2482	88	9	that	that	SCONJ
ejpam-2482	88	10	m	m	NOUN
ejpam-2482	88	11	)	)	PUNCT
ejpam-2482	89	1	=	=	SYM
ejpam-2482	89	2	f	f	PROPN
ejpam-2482	89	3	(	(	PUNCT
ejpam-2482	89	4	m	m	PROPN
ejpam-2482	89	5	)	)	PUNCT
ejpam-2482	89	6	and	and	CCONJ
ejpam-2482	89	7	so	so	ADV
ejpam-2482	89	8	f	f	X
ejpam-2482	89	9	(	(	PUNCT
ejpam-2482	89	10	abcm	abcm	NOUN
ejpam-2482	89	11	)	)	PUNCT
ejpam-2482	89	12	"	"	PUNCT
ejpam-2482	89	13	f	f	PROPN
ejpam-2482	89	14	(	(	PUNCT
ejpam-2482	89	15	n	n	CCONJ
ejpam-2482	89	16	)	)	PUNCT
ejpam-2482	89	17	.	.	PUNCT
ejpam-2482	90	1	since	since	SCONJ
ejpam-2482	90	2	ker	ker	PROPN
ejpam-2482	90	3	(	(	PUNCT
ejpam-2482	90	4	f	f	PROPN
ejpam-2482	90	5	)	)	PUNCT
ejpam-2482	90	6	$	$	SYM
ejpam-2482	90	7	n	n	NOUN
ejpam-2482	90	8	,	,	PUNCT
ejpam-2482	90	9	we	we	PRON
ejpam-2482	90	10	have	have	VERB
ejpam-2482	90	11	abcm	abcm	NOUN
ejpam-2482	90	12	"	"	PUNCT
ejpam-2482	90	13	n	n	NOUN
ejpam-2482	90	14	.	.	PUNCT
ejpam-2482	91	1	it	it	PRON
ejpam-2482	91	2	implies	imply	VERB
ejpam-2482	91	3	that	that	SCONJ
ejpam-2482	91	4	abm	abm	PROPN
ejpam-2482	91	5	"	"	PUNCT
ejpam-2482	91	6	n	n	PROPN
ejpam-2482	91	7	or	or	CCONJ
ejpam-2482	91	8	acm	acm	PROPN
ejpam-2482	91	9	"	"	PUNCT
ejpam-2482	91	10	n	n	PROPN
ejpam-2482	91	11	or	or	CCONJ
ejpam-2482	91	12	bcm	bcm	NOUN
ejpam-2482	91	13	"	"	PUNCT
ejpam-2482	91	14	n	n	NOUN
ejpam-2482	91	15	.	.	PUNCT
ejpam-2482	92	1	hence	hence	ADV
ejpam-2482	92	2	abm	abm	PROPN
ejpam-2482	92	3	)	)	PUNCT
ejpam-2482	92	4	"	"	PUNCT
ejpam-2482	93	1	f	f	PROPN
ejpam-2482	93	2	(	(	PUNCT
ejpam-2482	93	3	n	n	CCONJ
ejpam-2482	93	4	)	)	PUNCT
ejpam-2482	93	5	or	or	CCONJ
ejpam-2482	93	6	acm	acm	PROPN
ejpam-2482	93	7	)	)	PUNCT
ejpam-2482	93	8	"	"	PUNCT
ejpam-2482	93	9	f	f	PROPN
ejpam-2482	93	10	(	(	PUNCT
ejpam-2482	93	11	n	n	CCONJ
ejpam-2482	93	12	)	)	PUNCT
ejpam-2482	93	13	or	or	CCONJ
ejpam-2482	93	14	bcm	bcm	NOUN
ejpam-2482	93	15	)	)	PUNCT
ejpam-2482	93	16	"	"	PUNCT
ejpam-2482	93	17	f	f	PROPN
ejpam-2482	93	18	(	(	PUNCT
ejpam-2482	93	19	n	n	CCONJ
ejpam-2482	93	20	)	)	PUNCT
ejpam-2482	93	21	.	.	PUNCT
ejpam-2482	94	1	consequently	consequently	ADV
ejpam-2482	94	2	f	f	X
ejpam-2482	94	3	(	(	PUNCT
ejpam-2482	94	4	n	n	CCONJ
ejpam-2482	94	5	)	)	PUNCT
ejpam-2482	94	6	is	be	AUX
ejpam-2482	94	7	a	a	DET
ejpam-2482	94	8	classical	classical	ADJ
ejpam-2482	94	9	2	2	NUM
ejpam-2482	94	10	-	-	PUNCT
ejpam-2482	94	11	absorbing	absorb	VERB
ejpam-2482	94	12	submodule	submodule	NOUN
ejpam-2482	94	13	of	of	ADP
ejpam-2482	94	14	m	m	PROPN
ejpam-2482	94	15	)	)	PUNCT
ejpam-2482	94	16	.	.	PUNCT
ejpam-2482	95	1	as	as	ADP
ejpam-2482	95	2	an	an	DET
ejpam-2482	95	3	immediate	immediate	ADJ
ejpam-2482	95	4	consequence	consequence	NOUN
ejpam-2482	95	5	of	of	ADP
ejpam-2482	95	6	theorem	theorem	NOUN
ejpam-2482	95	7	1	1	NUM
ejpam-2482	95	8	we	we	PRON
ejpam-2482	95	9	have	have	VERB
ejpam-2482	95	10	the	the	DET
ejpam-2482	95	11	following	follow	VERB
ejpam-2482	95	12	corollary	corollary	NOUN
ejpam-2482	95	13	.	.	PUNCT
ejpam-2482	96	1	corollary	corollary	ADJ
ejpam-2482	96	2	1	1	NUM
ejpam-2482	96	3	.	.	PUNCT
ejpam-2482	97	1	let	let	VERB
ejpam-2482	97	2	m	m	PRON
ejpam-2482	97	3	be	be	AUX
ejpam-2482	97	4	an	an	DET
ejpam-2482	97	5	r	r	NOUN
ejpam-2482	97	6	-	-	PUNCT
ejpam-2482	97	7	module	module	NOUN
ejpam-2482	97	8	and	and	CCONJ
ejpam-2482	97	9	l	l	NOUN
ejpam-2482	97	10	$	$	SYM
ejpam-2482	97	11	n	n	PRON
ejpam-2482	97	12	be	be	VERB
ejpam-2482	97	13	submodules	submodule	NOUN
ejpam-2482	97	14	of	of	ADP
ejpam-2482	97	15	m.	m.	NOUN
ejpam-2482	97	16	then	then	ADV
ejpam-2482	97	17	n	n	PRON
ejpam-2482	97	18	is	be	AUX
ejpam-2482	97	19	a	a	DET
ejpam-2482	97	20	classical	classical	ADJ
ejpam-2482	97	21	2	2	NUM
ejpam-2482	97	22	-	-	PUNCT
ejpam-2482	97	23	absorbing	absorb	VERB
ejpam-2482	97	24	submodule	submodule	NOUN
ejpam-2482	97	25	of	of	ADP
ejpam-2482	97	26	m	m	PROPN
ejpam-2482	97	27	if	if	SCONJ
ejpam-2482	98	1	and	and	CCONJ
ejpam-2482	98	2	only	only	ADV
ejpam-2482	98	3	if	if	SCONJ
ejpam-2482	98	4	n	n	CCONJ
ejpam-2482	98	5	/	/	SYM
ejpam-2482	98	6	l	l	NOUN
ejpam-2482	98	7	is	be	AUX
ejpam-2482	98	8	a	a	DET
ejpam-2482	98	9	classical	classical	ADJ
ejpam-2482	98	10	2	2	NUM
ejpam-2482	98	11	-	-	PUNCT
ejpam-2482	98	12	absorbing	absorb	VERB
ejpam-2482	98	13	submodule	submodule	NOUN
ejpam-2482	98	14	of	of	ADP
ejpam-2482	98	15	m	m	PROPN
ejpam-2482	98	16	/	/	SYM
ejpam-2482	98	17	l.	l.	PROPN
ejpam-2482	98	18	proposition	proposition	NOUN
ejpam-2482	98	19	1	1	NUM
ejpam-2482	98	20	.	.	PUNCT
ejpam-2482	99	1	let	let	VERB
ejpam-2482	99	2	m	m	PRON
ejpam-2482	99	3	be	be	AUX
ejpam-2482	99	4	an	an	DET
ejpam-2482	99	5	r	r	NOUN
ejpam-2482	99	6	-	-	PUNCT
ejpam-2482	99	7	module	module	NOUN
ejpam-2482	99	8	and	and	CCONJ
ejpam-2482	99	9	n1	n1	NOUN
ejpam-2482	99	10	,	,	PUNCT
ejpam-2482	99	11	n2	n2	ADJ
ejpam-2482	99	12	be	be	AUX
ejpam-2482	99	13	classical	classical	ADJ
ejpam-2482	99	14	prime	prime	ADJ
ejpam-2482	99	15	submodules	submodule	NOUN
ejpam-2482	99	16	of	of	ADP
ejpam-2482	99	17	m.	m.	NOUN
ejpam-2482	99	18	then	then	ADV
ejpam-2482	99	19	n1	n1	PROPN
ejpam-2482	99	20	*	*	PUNCT
ejpam-2482	99	21	n2	n2	PROPN
ejpam-2482	99	22	is	be	AUX
ejpam-2482	99	23	a	a	DET
ejpam-2482	99	24	classical	classical	ADJ
ejpam-2482	99	25	2	2	NUM
ejpam-2482	99	26	-	-	PUNCT
ejpam-2482	99	27	absorbing	absorb	VERB
ejpam-2482	99	28	submodule	submodule	NOUN
ejpam-2482	99	29	of	of	ADP
ejpam-2482	99	30	m.	m.	NOUN
ejpam-2482	99	31	proof	proof	NOUN
ejpam-2482	99	32	.	.	PUNCT
ejpam-2482	100	1	let	let	VERB
ejpam-2482	100	2	for	for	ADP
ejpam-2482	100	3	some	some	PRON
ejpam-2482	100	4	a	a	DET
ejpam-2482	100	5	,	,	PUNCT
ejpam-2482	100	6	b	b	NOUN
ejpam-2482	100	7	,	,	PUNCT
ejpam-2482	100	8	c	c	NOUN
ejpam-2482	100	9	"	"	PUNCT
ejpam-2482	100	10	r	r	NOUN
ejpam-2482	100	11	and	and	CCONJ
ejpam-2482	100	12	m	m	NOUN
ejpam-2482	100	13	"	"	PUNCT
ejpam-2482	100	14	m	m	PROPN
ejpam-2482	100	15	,	,	PUNCT
ejpam-2482	100	16	abcm	abcm	ADJ
ejpam-2482	100	17	"	"	PUNCT
ejpam-2482	100	18	n1	n1	PROPN
ejpam-2482	100	19	*	*	PUNCT
ejpam-2482	100	20	n2	n2	PROPN
ejpam-2482	100	21	.	.	PUNCT
ejpam-2482	101	1	since	since	SCONJ
ejpam-2482	101	2	n1	n1	PROPN
ejpam-2482	101	3	is	be	AUX
ejpam-2482	101	4	a	a	DET
ejpam-2482	101	5	classical	classical	ADJ
ejpam-2482	101	6	prime	prime	ADJ
ejpam-2482	101	7	submodule	submodule	NOUN
ejpam-2482	101	8	,	,	PUNCT
ejpam-2482	101	9	then	then	ADV
ejpam-2482	101	10	we	we	PRON
ejpam-2482	101	11	may	may	AUX
ejpam-2482	101	12	assume	assume	VERB
ejpam-2482	101	13	that	that	PRON
ejpam-2482	101	14	am	be	AUX
ejpam-2482	101	15	"	"	PUNCT
ejpam-2482	101	16	n1	n1	PROPN
ejpam-2482	101	17	.	.	PUNCT
ejpam-2482	102	1	likewise	likewise	ADV
ejpam-2482	102	2	,	,	PUNCT
ejpam-2482	102	3	assume	assume	VERB
ejpam-2482	102	4	that	that	SCONJ
ejpam-2482	102	5	bm	bm	PROPN
ejpam-2482	102	6	"	"	PUNCT
ejpam-2482	102	7	n2	n2	PROPN
ejpam-2482	102	8	.	.	PUNCT
ejpam-2482	103	1	hence	hence	ADV
ejpam-2482	103	2	abm	abm	PROPN
ejpam-2482	103	3	"	"	PUNCT
ejpam-2482	103	4	n1	n1	PROPN
ejpam-2482	103	5	*	*	PUNCT
ejpam-2482	103	6	n2	n2	NOUN
ejpam-2482	103	7	which	which	PRON
ejpam-2482	103	8	implies	imply	VERB
ejpam-2482	103	9	n1	n1	PROPN
ejpam-2482	103	10	*	*	PUNCT
ejpam-2482	103	11	n2	n2	PROPN
ejpam-2482	103	12	is	be	AUX
ejpam-2482	103	13	a	a	DET
ejpam-2482	103	14	classical	classical	ADJ
ejpam-2482	103	15	2	2	NUM
ejpam-2482	103	16	-	-	PUNCT
ejpam-2482	103	17	absorbing	absorb	VERB
ejpam-2482	103	18	submodule	submodule	NOUN
ejpam-2482	103	19	.	.	PUNCT
ejpam-2482	104	1	proposition	proposition	NOUN
ejpam-2482	104	2	2	2	NUM
ejpam-2482	104	3	.	.	PUNCT
ejpam-2482	105	1	let	let	VERB
ejpam-2482	105	2	n	n	PRON
ejpam-2482	105	3	be	be	AUX
ejpam-2482	105	4	a	a	DET
ejpam-2482	105	5	proper	proper	ADJ
ejpam-2482	105	6	submodule	submodule	NOUN
ejpam-2482	105	7	of	of	ADP
ejpam-2482	105	8	an	an	DET
ejpam-2482	105	9	r	r	NOUN
ejpam-2482	105	10	-	-	PUNCT
ejpam-2482	105	11	module	module	NOUN
ejpam-2482	105	12	m.	m.	NOUN
ejpam-2482	105	13	(	(	PUNCT
ejpam-2482	105	14	i	i	NOUN
ejpam-2482	105	15	)	)	PUNCT
ejpam-2482	105	16	if	if	SCONJ
ejpam-2482	105	17	n	n	PRON
ejpam-2482	105	18	is	be	AUX
ejpam-2482	105	19	a	a	DET
ejpam-2482	105	20	2	2	NUM
ejpam-2482	105	21	-	-	PUNCT
ejpam-2482	105	22	absorbing	absorb	VERB
ejpam-2482	105	23	submodule	submodule	NOUN
ejpam-2482	105	24	of	of	ADP
ejpam-2482	105	25	m	m	PROPN
ejpam-2482	105	26	,	,	PUNCT
ejpam-2482	105	27	then	then	ADV
ejpam-2482	105	28	n	n	PRON
ejpam-2482	105	29	is	be	AUX
ejpam-2482	105	30	a	a	DET
ejpam-2482	105	31	classical	classical	ADJ
ejpam-2482	105	32	2	2	NUM
ejpam-2482	105	33	-	-	PUNCT
ejpam-2482	105	34	absorbing	absorb	VERB
ejpam-2482	105	35	submodule	submodule	NOUN
ejpam-2482	105	36	of	of	ADP
ejpam-2482	105	37	m.	m.	NOUN
ejpam-2482	105	38	(	(	PUNCT
ejpam-2482	105	39	ii	ii	NOUN
ejpam-2482	105	40	)	)	PUNCT
ejpam-2482	105	41	n	n	PRON
ejpam-2482	105	42	is	be	AUX
ejpam-2482	105	43	a	a	DET
ejpam-2482	105	44	classical	classical	ADJ
ejpam-2482	105	45	prime	prime	ADJ
ejpam-2482	105	46	submodule	submodule	NOUN
ejpam-2482	105	47	of	of	ADP
ejpam-2482	105	48	m	m	PROPN
ejpam-2482	105	49	if	if	SCONJ
ejpam-2482	106	1	and	and	CCONJ
ejpam-2482	106	2	only	only	ADV
ejpam-2482	106	3	if	if	SCONJ
ejpam-2482	106	4	n	n	PRON
ejpam-2482	106	5	is	be	AUX
ejpam-2482	106	6	a	a	DET
ejpam-2482	106	7	2	2	NUM
ejpam-2482	106	8	-	-	PUNCT
ejpam-2482	106	9	absorbing	absorb	VERB
ejpam-2482	106	10	submodule	submodule	NOUN
ejpam-2482	106	11	of	of	ADP
ejpam-2482	106	12	m	m	PROPN
ejpam-2482	106	13	and	and	CCONJ
ejpam-2482	106	14	(	(	PUNCT
ejpam-2482	106	15	n	n	X
ejpam-2482	106	16	:	:	PUNCT
ejpam-2482	106	17	r	r	NOUN
ejpam-2482	106	18	m	m	VERB
ejpam-2482	106	19	)	)	PUNCT
ejpam-2482	106	20	is	be	AUX
ejpam-2482	106	21	a	a	DET
ejpam-2482	106	22	prime	prime	ADJ
ejpam-2482	106	23	ideal	ideal	NOUN
ejpam-2482	106	24	of	of	ADP
ejpam-2482	106	25	r.	r.	PROPN
ejpam-2482	106	26	proof	proof	NOUN
ejpam-2482	106	27	.	.	PUNCT
ejpam-2482	107	1	(	(	PUNCT
ejpam-2482	107	2	i	i	NOUN
ejpam-2482	107	3	)	)	PUNCT
ejpam-2482	107	4	assume	assume	VERB
ejpam-2482	107	5	that	that	SCONJ
ejpam-2482	107	6	n	n	PRON
ejpam-2482	107	7	is	be	AUX
ejpam-2482	107	8	a	a	DET
ejpam-2482	107	9	2	2	NUM
ejpam-2482	107	10	-	-	PUNCT
ejpam-2482	107	11	absorbing	absorb	VERB
ejpam-2482	107	12	submodule	submodule	NOUN
ejpam-2482	107	13	of	of	ADP
ejpam-2482	107	14	m	m	PROPN
ejpam-2482	107	15	.	.	PUNCT
ejpam-2482	108	1	let	let	VERB
ejpam-2482	108	2	a	a	DET
ejpam-2482	108	3	,	,	PUNCT
ejpam-2482	108	4	b	b	NOUN
ejpam-2482	108	5	,	,	PUNCT
ejpam-2482	108	6	c	c	NOUN
ejpam-2482	108	7	"	"	PUNCT
ejpam-2482	108	8	r	r	NOUN
ejpam-2482	108	9	and	and	CCONJ
ejpam-2482	108	10	m	m	PRON
ejpam-2482	108	11	"	"	PUNCT
ejpam-2482	108	12	m	m	VERB
ejpam-2482	108	13	such	such	ADJ
ejpam-2482	108	14	that	that	SCONJ
ejpam-2482	108	15	abcm	abcm	NOUN
ejpam-2482	108	16	"	"	PUNCT
ejpam-2482	108	17	n	n	NOUN
ejpam-2482	108	18	.	.	PUNCT
ejpam-2482	109	1	therefore	therefore	ADV
ejpam-2482	109	2	either	either	CCONJ
ejpam-2482	109	3	acm	acm	PROPN
ejpam-2482	109	4	"	"	PUNCT
ejpam-2482	109	5	n	n	NOUN
ejpam-2482	109	6	or	or	CCONJ
ejpam-2482	109	7	bcm	bcm	NOUN
ejpam-2482	109	8	"	"	PUNCT
ejpam-2482	109	9	n	n	PROPN
ejpam-2482	109	10	or	or	CCONJ
ejpam-2482	109	11	ab	ab	PROPN
ejpam-2482	109	12	"	"	PUNCT
ejpam-2482	109	13	(	(	PUNCT
ejpam-2482	109	14	n	n	NUM
ejpam-2482	109	15	:	:	PUNCT
ejpam-2482	109	16	m	m	X
ejpam-2482	109	17	)	)	PUNCT
ejpam-2482	109	18	.	.	PUNCT
ejpam-2482	110	1	the	the	DET
ejpam-2482	110	2	first	first	ADJ
ejpam-2482	110	3	two	two	NUM
ejpam-2482	110	4	cases	case	NOUN
ejpam-2482	110	5	lead	lead	VERB
ejpam-2482	110	6	us	we	PRON
ejpam-2482	110	7	to	to	ADP
ejpam-2482	110	8	the	the	DET
ejpam-2482	110	9	claim	claim	NOUN
ejpam-2482	110	10	.	.	PUNCT
ejpam-2482	111	1	in	in	ADP
ejpam-2482	111	2	the	the	DET
ejpam-2482	111	3	third	third	ADJ
ejpam-2482	111	4	case	case	NOUN
ejpam-2482	111	5	we	we	PRON
ejpam-2482	111	6	have	have	VERB
ejpam-2482	111	7	that	that	DET
ejpam-2482	111	8	abm	abm	PROPN
ejpam-2482	111	9	"	"	PUNCT
ejpam-2482	111	10	n	n	NOUN
ejpam-2482	111	11	.	.	PUNCT
ejpam-2482	112	1	consequently	consequently	ADV
ejpam-2482	112	2	n	n	PROPN
ejpam-2482	112	3	is	be	AUX
ejpam-2482	112	4	a	a	DET
ejpam-2482	112	5	classical	classical	ADJ
ejpam-2482	112	6	2	2	NUM
ejpam-2482	112	7	-	-	PUNCT
ejpam-2482	112	8	absorbing	absorb	VERB
ejpam-2482	112	9	submodule	submodule	NOUN
ejpam-2482	112	10	.	.	PUNCT
ejpam-2482	113	1	(	(	PUNCT
ejpam-2482	113	2	ii	ii	X
ejpam-2482	113	3	)	)	PUNCT
ejpam-2482	113	4	it	it	PRON
ejpam-2482	113	5	is	be	AUX
ejpam-2482	113	6	evident	evident	ADJ
ejpam-2482	113	7	that	that	SCONJ
ejpam-2482	113	8	if	if	SCONJ
ejpam-2482	113	9	n	n	PRON
ejpam-2482	113	10	is	be	AUX
ejpam-2482	113	11	classical	classical	ADJ
ejpam-2482	113	12	prime	prime	NOUN
ejpam-2482	113	13	,	,	PUNCT
ejpam-2482	113	14	then	then	ADV
ejpam-2482	113	15	it	it	PRON
ejpam-2482	113	16	is	be	AUX
ejpam-2482	113	17	2	2	NUM
ejpam-2482	113	18	-	-	PUNCT
ejpam-2482	113	19	absorbing	absorbing	ADJ
ejpam-2482	113	20	.	.	PUNCT
ejpam-2482	114	1	also	also	ADV
ejpam-2482	114	2	,	,	PUNCT
ejpam-2482	114	3	[	[	X
ejpam-2482	114	4	3	3	NUM
ejpam-2482	114	5	,	,	PUNCT
ejpam-2482	114	6	lemma	lemma	PROPN
ejpam-2482	114	7	2.1	2.1	NUM
ejpam-2482	114	8	]	]	PUNCT
ejpam-2482	114	9	implies	imply	VERB
ejpam-2482	114	10	that	that	SCONJ
ejpam-2482	114	11	(	(	PUNCT
ejpam-2482	114	12	n	n	X
ejpam-2482	114	13	:	:	PUNCT
ejpam-2482	114	14	r	r	NOUN
ejpam-2482	114	15	m	m	VERB
ejpam-2482	114	16	)	)	PUNCT
ejpam-2482	114	17	is	be	AUX
ejpam-2482	114	18	a	a	DET
ejpam-2482	114	19	prime	prime	ADJ
ejpam-2482	114	20	ideal	ideal	NOUN
ejpam-2482	114	21	of	of	ADP
ejpam-2482	114	22	r.	r.	PROPN
ejpam-2482	114	23	assume	assume	VERB
ejpam-2482	114	24	that	that	SCONJ
ejpam-2482	114	25	n	n	PRON
ejpam-2482	114	26	is	be	AUX
ejpam-2482	114	27	a	a	DET
ejpam-2482	114	28	2	2	NUM
ejpam-2482	114	29	-	-	PUNCT
ejpam-2482	114	30	absorbing	absorb	VERB
ejpam-2482	114	31	submodule	submodule	NOUN
ejpam-2482	114	32	of	of	ADP
ejpam-2482	114	33	m	m	PROPN
ejpam-2482	114	34	and	and	CCONJ
ejpam-2482	114	35	(	(	PUNCT
ejpam-2482	114	36	n	n	X
ejpam-2482	114	37	:	:	PUNCT
ejpam-2482	114	38	r	r	NOUN
ejpam-2482	114	39	m	m	VERB
ejpam-2482	114	40	)	)	PUNCT
ejpam-2482	114	41	is	be	AUX
ejpam-2482	114	42	a	a	DET
ejpam-2482	114	43	prime	prime	ADJ
ejpam-2482	114	44	ideal	ideal	NOUN
ejpam-2482	114	45	of	of	ADP
ejpam-2482	114	46	r.	r.	PROPN
ejpam-2482	114	47	let	let	VERB
ejpam-2482	114	48	abm	abm	PROPN
ejpam-2482	114	49	"	"	PUNCT
ejpam-2482	114	50	n	n	PROPN
ejpam-2482	114	51	for	for	ADP
ejpam-2482	114	52	some	some	DET
ejpam-2482	114	53	a	a	DET
ejpam-2482	114	54	,	,	PUNCT
ejpam-2482	114	55	b	b	NOUN
ejpam-2482	114	56	"	"	PUNCT
ejpam-2482	114	57	r	r	NOUN
ejpam-2482	114	58	and	and	CCONJ
ejpam-2482	114	59	m	m	PRON
ejpam-2482	114	60	"	"	PUNCT
ejpam-2482	114	61	m	m	VERB
ejpam-2482	114	62	such	such	ADJ
ejpam-2482	114	63	that	that	SCONJ
ejpam-2482	114	64	neither	neither	PRON
ejpam-2482	114	65	am	be	AUX
ejpam-2482	114	66	"	"	PUNCT
ejpam-2482	114	67	n	n	X
ejpam-2482	114	68	nor	nor	CCONJ
ejpam-2482	114	69	bm	bm	PROPN
ejpam-2482	114	70	"	"	PUNCT
ejpam-2482	115	1	n	n	PROPN
ejpam-2482	115	2	.	.	PUNCT
ejpam-2482	116	1	then	then	ADV
ejpam-2482	116	2	ab	ab	PROPN
ejpam-2482	116	3	"	"	PUNCT
ejpam-2482	116	4	(	(	PUNCT
ejpam-2482	116	5	n	n	X
ejpam-2482	116	6	:	:	PUNCT
ejpam-2482	116	7	r	r	NOUN
ejpam-2482	116	8	m	m	PROPN
ejpam-2482	116	9	)	)	PUNCT
ejpam-2482	116	10	and	and	CCONJ
ejpam-2482	116	11	so	so	ADV
ejpam-2482	116	12	either	either	CCONJ
ejpam-2482	116	13	a	a	DET
ejpam-2482	116	14	"	"	PUNCT
ejpam-2482	116	15	(	(	PUNCT
ejpam-2482	116	16	n	n	NUM
ejpam-2482	116	17	:	:	PUNCT
ejpam-2482	116	18	r	r	NOUN
ejpam-2482	116	19	m	m	PROPN
ejpam-2482	116	20	)	)	PUNCT
ejpam-2482	116	21	or	or	CCONJ
ejpam-2482	116	22	b	b	X
ejpam-2482	116	23	"	"	PUNCT
ejpam-2482	116	24	(	(	PUNCT
ejpam-2482	116	25	n	n	X
ejpam-2482	116	26	:	:	PUNCT
ejpam-2482	116	27	r	r	NOUN
ejpam-2482	116	28	m).this	m).this	PROPN
ejpam-2482	116	29	contradiction	contradiction	NOUN
ejpam-2482	116	30	shows	show	VERB
ejpam-2482	116	31	that	that	SCONJ
ejpam-2482	116	32	n	n	PRON
ejpam-2482	116	33	is	be	AUX
ejpam-2482	116	34	classical	classical	ADJ
ejpam-2482	116	35	prime	prime	NOUN
ejpam-2482	116	36	.	.	PUNCT
ejpam-2482	117	1	he	he	PRON
ejpam-2482	117	2	following	follow	VERB
ejpam-2482	117	3	example	example	NOUN
ejpam-2482	117	4	shows	show	VERB
ejpam-2482	117	5	that	that	SCONJ
ejpam-2482	117	6	the	the	DET
ejpam-2482	117	7	converse	converse	NOUN
ejpam-2482	117	8	of	of	ADP
ejpam-2482	117	9	proposition	proposition	NOUN
ejpam-2482	117	10	2(i	2(i	NUM
ejpam-2482	117	11	)	)	PUNCT
ejpam-2482	117	12	is	be	AUX
ejpam-2482	117	13	not	not	PART
ejpam-2482	117	14	true	true	ADJ
ejpam-2482	117	15	.	.	PUNCT
ejpam-2482	118	1	example	example	NOUN
ejpam-2482	119	1	2	2	NUM
ejpam-2482	119	2	.	.	PUNCT
ejpam-2482	119	3	let	let	VERB
ejpam-2482	119	4	r	r	NOUN
ejpam-2482	119	5	=	=	SYM
ejpam-2482	119	6	#	#	NOUN
ejpam-2482	119	7	and	and	CCONJ
ejpam-2482	119	8	m	m	NOUN
ejpam-2482	119	9	=	=	ADJ
ejpam-2482	119	10	#	#	SYM
ejpam-2482	119	11	p	p	NOUN
ejpam-2482	119	12	'	'	PUNCT
ejpam-2482	119	13	#	#	SYM
ejpam-2482	119	14	q	q	NOUN
ejpam-2482	119	15	'	'	PUNCT
ejpam-2482	119	16	"	"	PUNCT
ejpam-2482	119	17	where	where	SCONJ
ejpam-2482	119	18	p	p	X
ejpam-2482	119	19	,	,	PUNCT
ejpam-2482	119	20	q	q	X
ejpam-2482	119	21	are	be	AUX
ejpam-2482	119	22	two	two	NUM
ejpam-2482	119	23	distinct	distinct	ADJ
ejpam-2482	119	24	prime	prime	ADJ
ejpam-2482	119	25	integers	integer	NOUN
ejpam-2482	119	26	.	.	PUNCT
ejpam-2482	120	1	one	one	PRON
ejpam-2482	120	2	can	can	AUX
ejpam-2482	120	3	easily	easily	ADV
ejpam-2482	120	4	see	see	VERB
ejpam-2482	120	5	that	that	SCONJ
ejpam-2482	120	6	the	the	DET
ejpam-2482	120	7	zero	zero	NUM
ejpam-2482	120	8	submodule	submodule	NOUN
ejpam-2482	120	9	of	of	ADP
ejpam-2482	120	10	m	m	PROPN
ejpam-2482	120	11	is	be	AUX
ejpam-2482	120	12	a	a	DET
ejpam-2482	120	13	classical	classical	ADJ
ejpam-2482	120	14	2	2	NUM
ejpam-2482	120	15	-	-	PUNCT
ejpam-2482	120	16	absorbing	absorb	VERB
ejpam-2482	120	17	submodule	submodule	NOUN
ejpam-2482	120	18	.	.	PUNCT
ejpam-2482	121	1	notice	notice	VERB
ejpam-2482	121	2	that	that	SCONJ
ejpam-2482	121	3	pq(1,1,0	pq(1,1,0	PROPN
ejpam-2482	121	4	)	)	PUNCT
ejpam-2482	121	5	=	=	SYM
ejpam-2482	121	6	(	(	PUNCT
ejpam-2482	121	7	0,0,0	0,0,0	NOUN
ejpam-2482	121	8	)	)	PUNCT
ejpam-2482	121	9	,	,	PUNCT
ejpam-2482	121	10	but	but	CCONJ
ejpam-2482	121	11	p(1,1,0	p(1,1,0	PROPN
ejpam-2482	121	12	)	)	PUNCT
ejpam-2482	122	1	#	#	SYM
ejpam-2482	122	2	=	=	SYM
ejpam-2482	122	3	(	(	PUNCT
ejpam-2482	122	4	0,0,0	0,0,0	NOUN
ejpam-2482	122	5	)	)	PUNCT
ejpam-2482	122	6	,	,	PUNCT
ejpam-2482	122	7	q(1,1,0	q(1,1,0	NUM
ejpam-2482	122	8	)	)	PUNCT
ejpam-2482	122	9	#	#	SYM
ejpam-2482	122	10	=	=	SYM
ejpam-2482	122	11	(	(	PUNCT
ejpam-2482	122	12	0,0,0	0,0,0	NOUN
ejpam-2482	122	13	)	)	PUNCT
ejpam-2482	122	14	and	and	CCONJ
ejpam-2482	122	15	pq(1,1,1	pq(1,1,1	ADP
ejpam-2482	122	16	)	)	PUNCT
ejpam-2482	122	17	#	#	NOUN
ejpam-2482	122	18	=	=	SYM
ejpam-2482	122	19	0	0	NUM
ejpam-2482	122	20	.	.	PUNCT
ejpam-2482	123	1	so	so	ADV
ejpam-2482	123	2	the	the	DET
ejpam-2482	123	3	zero	zero	NUM
ejpam-2482	123	4	submodule	submodule	NOUN
ejpam-2482	123	5	of	of	ADP
ejpam-2482	123	6	m	m	PROPN
ejpam-2482	123	7	is	be	AUX
ejpam-2482	123	8	not	not	PART
ejpam-2482	123	9	2	2	NUM
ejpam-2482	123	10	-	-	PUNCT
ejpam-2482	123	11	absorbing	absorbing	ADJ
ejpam-2482	123	12	.	.	PUNCT
ejpam-2482	124	1	also	also	ADV
ejpam-2482	124	2	,	,	PUNCT
ejpam-2482	124	3	part	part	NOUN
ejpam-2482	124	4	(	(	PUNCT
ejpam-2482	124	5	ii	ii	NOUN
ejpam-2482	124	6	)	)	PUNCT
ejpam-2482	124	7	of	of	ADP
ejpam-2482	124	8	proposition	proposition	NOUN
ejpam-2482	124	9	2	2	NUM
ejpam-2482	124	10	shows	show	VERB
ejpam-2482	124	11	that	that	SCONJ
ejpam-2482	124	12	the	the	DET
ejpam-2482	124	13	zero	zero	NUM
ejpam-2482	124	14	submodule	submodule	NOUN
ejpam-2482	124	15	is	be	AUX
ejpam-2482	124	16	not	not	PART
ejpam-2482	124	17	a	a	DET
ejpam-2482	124	18	classical	classical	ADJ
ejpam-2482	124	19	prime	prime	ADJ
ejpam-2482	124	20	submodule	submodule	NOUN
ejpam-2482	124	21	.	.	PUNCT
ejpam-2482	125	1	hence	hence	ADV
ejpam-2482	125	2	the	the	DET
ejpam-2482	125	3	two	two	NUM
ejpam-2482	125	4	concepts	concept	NOUN
ejpam-2482	125	5	of	of	ADP
ejpam-2482	125	6	classical	classical	ADJ
ejpam-2482	125	7	prime	prime	ADJ
ejpam-2482	125	8	submodules	submodule	NOUN
ejpam-2482	125	9	and	and	CCONJ
ejpam-2482	125	10	of	of	ADP
ejpam-2482	125	11	classical	classical	ADJ
ejpam-2482	125	12	2	2	NUM
ejpam-2482	125	13	-	-	PUNCT
ejpam-2482	125	14	absorbing	absorb	VERB
ejpam-2482	125	15	submodules	submodule	NOUN
ejpam-2482	125	16	are	be	AUX
ejpam-2482	125	17	different	different	ADJ
ejpam-2482	125	18	in	in	ADP
ejpam-2482	125	19	general	general	ADJ
ejpam-2482	125	20	.	.	PUNCT
ejpam-2482	126	1	h.	h.	PROPN
ejpam-2482	126	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	126	3	,	,	PUNCT
ejpam-2482	126	4	ü.	ü.	NOUN
ejpam-2482	126	5	tekir	tekir	NOUN
ejpam-2482	126	6	and	and	CCONJ
ejpam-2482	126	7	k.	k.	PROPN
ejpam-2482	126	8	hakan	hakan	PROPN
ejpam-2482	126	9	oral	oral	PROPN
ejpam-2482	126	10	/	/	SYM
ejpam-2482	126	11	eur	eur	PROPN
ejpam-2482	126	12	.	.	PUNCT
ejpam-2482	127	1	j.	j.	PROPN
ejpam-2482	127	2	pure	pure	PROPN
ejpam-2482	127	3	appl	appl	PROPN
ejpam-2482	127	4	.	.	PROPN
ejpam-2482	127	5	math	math	PROPN
ejpam-2482	127	6	,	,	PUNCT
ejpam-2482	127	7	8	8	NUM
ejpam-2482	127	8	(	(	PUNCT
ejpam-2482	127	9	2015	2015	NUM
ejpam-2482	127	10	)	)	PUNCT
ejpam-2482	127	11	,	,	PUNCT
ejpam-2482	127	12	417	417	NUM
ejpam-2482	127	13	-	-	SYM
ejpam-2482	127	14	430	430	NUM
ejpam-2482	127	15	420	420	NUM
ejpam-2482	127	16	let	let	VERB
ejpam-2482	127	17	m	m	PRON
ejpam-2482	127	18	be	be	AUX
ejpam-2482	127	19	an	an	DET
ejpam-2482	127	20	r	r	NOUN
ejpam-2482	127	21	-	-	PUNCT
ejpam-2482	127	22	module	module	NOUN
ejpam-2482	127	23	and	and	CCONJ
ejpam-2482	127	24	n	n	NOUN
ejpam-2482	127	25	a	a	DET
ejpam-2482	127	26	submodule	submodule	NOUN
ejpam-2482	127	27	of	of	ADP
ejpam-2482	127	28	m	m	PROPN
ejpam-2482	127	29	.	.	PUNCT
ejpam-2482	128	1	for	for	ADP
ejpam-2482	128	2	every	every	DET
ejpam-2482	128	3	a	a	DET
ejpam-2482	128	4	"	"	PUNCT
ejpam-2482	128	5	r	r	NOUN
ejpam-2482	128	6	,	,	PUNCT
ejpam-2482	128	7	{	{	PUNCT
ejpam-2482	128	8	m	m	NOUN
ejpam-2482	128	9	"	"	PUNCT
ejpam-2482	128	10	m	m	VERB
ejpam-2482	128	11	|	|	ADV
ejpam-2482	128	12	am	be	AUX
ejpam-2482	128	13	"	"	PUNCT
ejpam-2482	128	14	n	n	CCONJ
ejpam-2482	128	15	}	}	PUNCT
ejpam-2482	128	16	is	be	AUX
ejpam-2482	128	17	denoted	denote	VERB
ejpam-2482	128	18	by	by	ADP
ejpam-2482	128	19	(	(	PUNCT
ejpam-2482	128	20	n	n	X
ejpam-2482	128	21	:	:	PUNCT
ejpam-2482	128	22	r	r	NOUN
ejpam-2482	128	23	a	a	NOUN
ejpam-2482	128	24	)	)	PUNCT
ejpam-2482	128	25	.	.	PUNCT
ejpam-2482	129	1	it	it	PRON
ejpam-2482	129	2	is	be	AUX
ejpam-2482	129	3	easy	easy	ADJ
ejpam-2482	129	4	to	to	PART
ejpam-2482	129	5	see	see	VERB
ejpam-2482	129	6	that	that	PRON
ejpam-2482	129	7	(	(	PUNCT
ejpam-2482	129	8	n	n	X
ejpam-2482	129	9	:	:	PUNCT
ejpam-2482	129	10	m	m	NOUN
ejpam-2482	129	11	a	a	PRON
ejpam-2482	129	12	)	)	PUNCT
ejpam-2482	129	13	is	be	AUX
ejpam-2482	129	14	a	a	DET
ejpam-2482	129	15	submodule	submodule	NOUN
ejpam-2482	129	16	of	of	ADP
ejpam-2482	129	17	m	m	PROPN
ejpam-2482	129	18	containing	contain	VERB
ejpam-2482	129	19	n	n	X
ejpam-2482	129	20	.	.	PUNCT
ejpam-2482	130	1	theorem	theorem	NOUN
ejpam-2482	130	2	2	2	NUM
ejpam-2482	130	3	.	.	PUNCT
ejpam-2482	131	1	let	let	VERB
ejpam-2482	131	2	m	m	PRON
ejpam-2482	131	3	be	be	AUX
ejpam-2482	131	4	an	an	DET
ejpam-2482	131	5	r	r	NOUN
ejpam-2482	131	6	-	-	PUNCT
ejpam-2482	131	7	module	module	NOUN
ejpam-2482	131	8	and	and	CCONJ
ejpam-2482	131	9	n	n	CCONJ
ejpam-2482	131	10	be	be	VERB
ejpam-2482	131	11	a	a	DET
ejpam-2482	131	12	proper	proper	ADJ
ejpam-2482	131	13	submodule	submodule	NOUN
ejpam-2482	131	14	of	of	ADP
ejpam-2482	131	15	m.	m.	NOUN
ejpam-2482	131	16	the	the	DET
ejpam-2482	131	17	following	follow	VERB
ejpam-2482	131	18	conditions	condition	NOUN
ejpam-2482	131	19	are	be	AUX
ejpam-2482	131	20	equivalent	equivalent	ADJ
ejpam-2482	131	21	:	:	PUNCT
ejpam-2482	131	22	(	(	PUNCT
ejpam-2482	131	23	i	i	NOUN
ejpam-2482	131	24	)	)	PUNCT
ejpam-2482	131	25	n	n	PRON
ejpam-2482	131	26	is	be	AUX
ejpam-2482	131	27	classical	classical	ADJ
ejpam-2482	131	28	2	2	NUM
ejpam-2482	131	29	-	-	PUNCT
ejpam-2482	131	30	absorbing	absorbing	ADJ
ejpam-2482	131	31	;	;	PUNCT
ejpam-2482	131	32	(	(	PUNCT
ejpam-2482	131	33	ii	ii	NOUN
ejpam-2482	131	34	)	)	PUNCT
ejpam-2482	131	35	for	for	ADP
ejpam-2482	131	36	every	every	DET
ejpam-2482	131	37	a	a	DET
ejpam-2482	131	38	,	,	PUNCT
ejpam-2482	131	39	b	b	NOUN
ejpam-2482	131	40	,	,	PUNCT
ejpam-2482	131	41	c	c	NOUN
ejpam-2482	131	42	"	"	PUNCT
ejpam-2482	131	43	r	r	NOUN
ejpam-2482	131	44	,	,	PUNCT
ejpam-2482	131	45	(	(	PUNCT
ejpam-2482	131	46	n	n	X
ejpam-2482	131	47	:	:	PUNCT
ejpam-2482	131	48	m	m	PROPN
ejpam-2482	131	49	abc	abc	PROPN
ejpam-2482	131	50	)	)	PUNCT
ejpam-2482	131	51	=	=	PUNCT
ejpam-2482	132	1	(	(	PUNCT
ejpam-2482	132	2	n	n	X
ejpam-2482	132	3	:	:	PUNCT
ejpam-2482	132	4	m	m	VERB
ejpam-2482	132	5	ab	ab	PROPN
ejpam-2482	132	6	)	)	PUNCT
ejpam-2482	132	7	'	'	PUNCT
ejpam-2482	132	8	(	(	PUNCT
ejpam-2482	132	9	n	n	X
ejpam-2482	132	10	:	:	PUNCT
ejpam-2482	132	11	m	m	VERB
ejpam-2482	132	12	ac	ac	ADJ
ejpam-2482	132	13	)	)	PUNCT
ejpam-2482	132	14	'	'	PUNCT
ejpam-2482	132	15	(	(	PUNCT
ejpam-2482	132	16	n	n	X
ejpam-2482	132	17	:	:	PUNCT
ejpam-2482	132	18	m	m	PROPN
ejpam-2482	132	19	bc	bc	PROPN
ejpam-2482	132	20	)	)	PUNCT
ejpam-2482	132	21	;	;	PUNCT
ejpam-2482	132	22	(	(	PUNCT
ejpam-2482	132	23	iii	iii	X
ejpam-2482	132	24	)	)	PUNCT
ejpam-2482	132	25	for	for	ADP
ejpam-2482	132	26	every	every	DET
ejpam-2482	132	27	a	a	PROPN
ejpam-2482	132	28	,	,	PUNCT
ejpam-2482	132	29	b	b	NOUN
ejpam-2482	132	30	"	"	PUNCT
ejpam-2482	132	31	r	r	NOUN
ejpam-2482	132	32	and	and	CCONJ
ejpam-2482	132	33	m	m	PRON
ejpam-2482	132	34	"	"	PUNCT
ejpam-2482	132	35	m	m	VERB
ejpam-2482	132	36	with	with	ADP
ejpam-2482	132	37	abm	abm	PROPN
ejpam-2482	132	38	/	/	SYM
ejpam-2482	132	39	"	"	PUNCT
ejpam-2482	132	40	n	n	CCONJ
ejpam-2482	132	41	,	,	PUNCT
ejpam-2482	132	42	(	(	PUNCT
ejpam-2482	132	43	n	n	X
ejpam-2482	132	44	:	:	PUNCT
ejpam-2482	132	45	r	r	NOUN
ejpam-2482	132	46	abm	abm	PROPN
ejpam-2482	132	47	)	)	PUNCT
ejpam-2482	133	1	=	=	PUNCT
ejpam-2482	133	2	(	(	PUNCT
ejpam-2482	133	3	n	n	X
ejpam-2482	133	4	:	:	PUNCT
ejpam-2482	133	5	r	r	NOUN
ejpam-2482	133	6	am	am	NOUN
ejpam-2482	133	7	)	)	PUNCT
ejpam-2482	133	8	'	'	PUNCT
ejpam-2482	133	9	(	(	PUNCT
ejpam-2482	133	10	n	n	X
ejpam-2482	133	11	:	:	PUNCT
ejpam-2482	133	12	r	r	NOUN
ejpam-2482	133	13	bm	bm	PROPN
ejpam-2482	133	14	)	)	PUNCT
ejpam-2482	133	15	;	;	PUNCT
ejpam-2482	133	16	(	(	PUNCT
ejpam-2482	133	17	iv	iv	X
ejpam-2482	133	18	)	)	PUNCT
ejpam-2482	133	19	for	for	ADP
ejpam-2482	133	20	every	every	DET
ejpam-2482	133	21	a	a	PROPN
ejpam-2482	133	22	,	,	PUNCT
ejpam-2482	133	23	b	b	NOUN
ejpam-2482	133	24	"	"	PUNCT
ejpam-2482	133	25	r	r	NOUN
ejpam-2482	133	26	and	and	CCONJ
ejpam-2482	133	27	m	m	PRON
ejpam-2482	133	28	"	"	PUNCT
ejpam-2482	133	29	m	m	VERB
ejpam-2482	133	30	with	with	ADP
ejpam-2482	133	31	abm	abm	PROPN
ejpam-2482	133	32	/	/	SYM
ejpam-2482	133	33	"	"	PUNCT
ejpam-2482	133	34	n	n	CCONJ
ejpam-2482	133	35	,	,	PUNCT
ejpam-2482	133	36	(	(	PUNCT
ejpam-2482	133	37	n	n	X
ejpam-2482	133	38	:	:	PUNCT
ejpam-2482	133	39	r	r	NOUN
ejpam-2482	133	40	abm	abm	PROPN
ejpam-2482	133	41	)	)	PUNCT
ejpam-2482	134	1	=	=	PUNCT
ejpam-2482	134	2	(	(	PUNCT
ejpam-2482	134	3	n	n	X
ejpam-2482	134	4	:	:	PUNCT
ejpam-2482	134	5	r	r	NOUN
ejpam-2482	134	6	am	be	AUX
ejpam-2482	134	7	)	)	PUNCT
ejpam-2482	134	8	or	or	CCONJ
ejpam-2482	134	9	(	(	PUNCT
ejpam-2482	134	10	n	n	X
ejpam-2482	134	11	:	:	PUNCT
ejpam-2482	134	12	r	r	NOUN
ejpam-2482	134	13	abm	abm	PROPN
ejpam-2482	134	14	)	)	PUNCT
ejpam-2482	134	15	=	=	PUNCT
ejpam-2482	134	16	(	(	PUNCT
ejpam-2482	134	17	n	n	X
ejpam-2482	134	18	:	:	PUNCT
ejpam-2482	134	19	r	r	NOUN
ejpam-2482	134	20	bm	bm	PROPN
ejpam-2482	134	21	)	)	PUNCT
ejpam-2482	134	22	;	;	PUNCT
ejpam-2482	134	23	(	(	PUNCT
ejpam-2482	134	24	v	v	NOUN
ejpam-2482	134	25	)	)	PUNCT
ejpam-2482	134	26	for	for	ADP
ejpam-2482	134	27	every	every	DET
ejpam-2482	134	28	a	a	PROPN
ejpam-2482	134	29	,	,	PUNCT
ejpam-2482	134	30	b	b	NOUN
ejpam-2482	134	31	"	"	PUNCT
ejpam-2482	134	32	r	r	NOUN
ejpam-2482	134	33	and	and	CCONJ
ejpam-2482	134	34	every	every	DET
ejpam-2482	134	35	ideal	ideal	NOUN
ejpam-2482	134	36	i	i	PRON
ejpam-2482	134	37	of	of	ADP
ejpam-2482	134	38	r	r	NOUN
ejpam-2482	134	39	and	and	CCONJ
ejpam-2482	134	40	m	m	PRON
ejpam-2482	134	41	"	"	PUNCT
ejpam-2482	134	42	m	m	VERB
ejpam-2482	134	43	with	with	ADP
ejpam-2482	134	44	abim	abim	NOUN
ejpam-2482	134	45	$	$	SYM
ejpam-2482	134	46	n	n	CCONJ
ejpam-2482	134	47	,	,	PUNCT
ejpam-2482	134	48	either	either	CCONJ
ejpam-2482	134	49	abm	abm	PROPN
ejpam-2482	134	50	"	"	PUNCT
ejpam-2482	134	51	n	n	CCONJ
ejpam-2482	134	52	or	or	CCONJ
ejpam-2482	134	53	aim	aim	VERB
ejpam-2482	134	54	$	$	SYM
ejpam-2482	134	55	n	n	NOUN
ejpam-2482	134	56	or	or	CCONJ
ejpam-2482	134	57	bim	bim	VERB
ejpam-2482	134	58	$	$	SYM
ejpam-2482	134	59	n	n	NUM
ejpam-2482	134	60	;	;	PUNCT
ejpam-2482	134	61	(	(	PUNCT
ejpam-2482	134	62	vi	vi	NOUN
ejpam-2482	134	63	)	)	PUNCT
ejpam-2482	134	64	for	for	ADP
ejpam-2482	134	65	every	every	DET
ejpam-2482	134	66	a	a	DET
ejpam-2482	134	67	"	"	PUNCT
ejpam-2482	134	68	r	r	NOUN
ejpam-2482	134	69	and	and	CCONJ
ejpam-2482	134	70	every	every	DET
ejpam-2482	134	71	ideal	ideal	NOUN
ejpam-2482	134	72	i	i	PRON
ejpam-2482	134	73	of	of	ADP
ejpam-2482	134	74	r	r	NOUN
ejpam-2482	134	75	and	and	CCONJ
ejpam-2482	134	76	m	m	PRON
ejpam-2482	134	77	"	"	PUNCT
ejpam-2482	134	78	m	m	VERB
ejpam-2482	134	79	with	with	ADP
ejpam-2482	134	80	aim	aim	NOUN
ejpam-2482	134	81	#	#	SYM
ejpam-2482	134	82	$	$	SYM
ejpam-2482	134	83	n	n	NUM
ejpam-2482	134	84	,	,	PUNCT
ejpam-2482	134	85	(	(	PUNCT
ejpam-2482	134	86	n	n	X
ejpam-2482	134	87	:	:	PUNCT
ejpam-2482	134	88	r	r	NOUN
ejpam-2482	134	89	aim	aim	NOUN
ejpam-2482	134	90	)	)	PUNCT
ejpam-2482	134	91	=	=	SYM
ejpam-2482	134	92	(	(	PUNCT
ejpam-2482	134	93	n	n	X
ejpam-2482	134	94	:	:	PUNCT
ejpam-2482	134	95	r	r	NOUN
ejpam-2482	134	96	am	be	AUX
ejpam-2482	134	97	)	)	PUNCT
ejpam-2482	134	98	or	or	CCONJ
ejpam-2482	134	99	(	(	PUNCT
ejpam-2482	134	100	n	n	X
ejpam-2482	134	101	:	:	PUNCT
ejpam-2482	134	102	r	r	NOUN
ejpam-2482	134	103	aim	aim	NOUN
ejpam-2482	134	104	)	)	PUNCT
ejpam-2482	134	105	=	=	SYM
ejpam-2482	134	106	(	(	PUNCT
ejpam-2482	134	107	n	n	X
ejpam-2482	134	108	:	:	PUNCT
ejpam-2482	134	109	r	r	NOUN
ejpam-2482	134	110	i	i	NOUN
ejpam-2482	134	111	m	m	PROPN
ejpam-2482	134	112	)	)	PUNCT
ejpam-2482	134	113	;	;	PUNCT
ejpam-2482	134	114	(	(	PUNCT
ejpam-2482	134	115	vii	vii	PROPN
ejpam-2482	134	116	)	)	PUNCT
ejpam-2482	134	117	for	for	ADP
ejpam-2482	134	118	every	every	DET
ejpam-2482	134	119	a	a	DET
ejpam-2482	134	120	"	"	PUNCT
ejpam-2482	134	121	r	r	NOUN
ejpam-2482	134	122	and	and	CCONJ
ejpam-2482	134	123	every	every	DET
ejpam-2482	134	124	ideals	ideal	NOUN
ejpam-2482	134	125	i	i	PRON
ejpam-2482	134	126	,	,	PUNCT
ejpam-2482	134	127	j	j	PROPN
ejpam-2482	134	128	of	of	ADP
ejpam-2482	134	129	r	r	PROPN
ejpam-2482	134	130	and	and	CCONJ
ejpam-2482	134	131	m	m	PRON
ejpam-2482	134	132	"	"	PUNCT
ejpam-2482	134	133	m	m	VERB
ejpam-2482	134	134	with	with	ADP
ejpam-2482	134	135	aijm	aijm	ADJ
ejpam-2482	134	136	$	$	SYM
ejpam-2482	134	137	n	n	NUM
ejpam-2482	134	138	,	,	PUNCT
ejpam-2482	134	139	either	either	CCONJ
ejpam-2482	134	140	aim	aim	VERB
ejpam-2482	134	141	$	$	SYM
ejpam-2482	134	142	n	n	NOUN
ejpam-2482	134	143	or	or	CCONJ
ejpam-2482	134	144	ajm	ajm	VERB
ejpam-2482	134	145	$	$	SYM
ejpam-2482	134	146	n	n	PROPN
ejpam-2482	134	147	or	or	CCONJ
ejpam-2482	134	148	ijm	ijm	X
ejpam-2482	134	149	$	$	SYM
ejpam-2482	134	150	n	n	NUM
ejpam-2482	134	151	;	;	PUNCT
ejpam-2482	134	152	(	(	PUNCT
ejpam-2482	134	153	viii	viii	NOUN
ejpam-2482	134	154	)	)	PUNCT
ejpam-2482	134	155	for	for	ADP
ejpam-2482	134	156	every	every	DET
ejpam-2482	134	157	ideals	ideal	NOUN
ejpam-2482	134	158	i	i	PRON
ejpam-2482	134	159	,	,	PUNCT
ejpam-2482	134	160	j	j	PROPN
ejpam-2482	134	161	of	of	ADP
ejpam-2482	134	162	r	r	PROPN
ejpam-2482	134	163	and	and	CCONJ
ejpam-2482	134	164	m	m	PRON
ejpam-2482	134	165	"	"	PUNCT
ejpam-2482	134	166	m	m	VERB
ejpam-2482	134	167	with	with	ADP
ejpam-2482	134	168	ijm	ijm	PROPN
ejpam-2482	134	169	#	#	SYM
ejpam-2482	134	170	$	$	SYM
ejpam-2482	134	171	n	n	NUM
ejpam-2482	134	172	,	,	PUNCT
ejpam-2482	134	173	(	(	PUNCT
ejpam-2482	134	174	n	n	X
ejpam-2482	134	175	:	:	PUNCT
ejpam-2482	134	176	r	r	NOUN
ejpam-2482	134	177	ijm	ijm	PROPN
ejpam-2482	134	178	)	)	PUNCT
ejpam-2482	134	179	=	=	PUNCT
ejpam-2482	134	180	(	(	PUNCT
ejpam-2482	134	181	n	n	X
ejpam-2482	134	182	:	:	PUNCT
ejpam-2482	134	183	r	r	NOUN
ejpam-2482	134	184	i	i	NOUN
ejpam-2482	134	185	m	m	PROPN
ejpam-2482	134	186	)	)	PUNCT
ejpam-2482	134	187	or	or	CCONJ
ejpam-2482	134	188	(	(	PUNCT
ejpam-2482	134	189	n	n	X
ejpam-2482	134	190	:	:	PUNCT
ejpam-2482	134	191	r	r	NOUN
ejpam-2482	134	192	ijm	ijm	PROPN
ejpam-2482	134	193	)	)	PUNCT
ejpam-2482	134	194	=	=	PUNCT
ejpam-2482	134	195	(	(	PUNCT
ejpam-2482	134	196	n	n	X
ejpam-2482	134	197	:	:	PUNCT
ejpam-2482	134	198	r	r	NOUN
ejpam-2482	134	199	jm	jm	PROPN
ejpam-2482	134	200	)	)	PUNCT
ejpam-2482	134	201	;	;	PUNCT
ejpam-2482	134	202	(	(	PUNCT
ejpam-2482	134	203	ix	ix	INTJ
ejpam-2482	134	204	)	)	PUNCT
ejpam-2482	134	205	for	for	ADP
ejpam-2482	134	206	every	every	DET
ejpam-2482	134	207	ideals	ideal	NOUN
ejpam-2482	134	208	i	i	PRON
ejpam-2482	134	209	,	,	PUNCT
ejpam-2482	134	210	j	j	PROPN
ejpam-2482	134	211	,	,	PUNCT
ejpam-2482	134	212	k	k	PROPN
ejpam-2482	134	213	of	of	ADP
ejpam-2482	134	214	r	r	NOUN
ejpam-2482	134	215	and	and	CCONJ
ejpam-2482	134	216	m	m	PRON
ejpam-2482	134	217	"	"	PUNCT
ejpam-2482	134	218	m	m	VERB
ejpam-2482	134	219	with	with	ADP
ejpam-2482	134	220	ijkm	ijkm	X
ejpam-2482	134	221	$	$	SYM
ejpam-2482	134	222	n	n	NUM
ejpam-2482	134	223	,	,	PUNCT
ejpam-2482	134	224	either	either	CCONJ
ejpam-2482	134	225	ijm	ijm	PROPN
ejpam-2482	134	226	$	$	SYM
ejpam-2482	134	227	n	n	NOUN
ejpam-2482	134	228	or	or	CCONJ
ejpam-2482	134	229	ikm	ikm	VERB
ejpam-2482	134	230	$	$	SYM
ejpam-2482	134	231	n	n	PROPN
ejpam-2482	134	232	or	or	CCONJ
ejpam-2482	134	233	jkm	jkm	PROPN
ejpam-2482	134	234	$	$	SYM
ejpam-2482	134	235	n	n	NUM
ejpam-2482	134	236	;	;	PUNCT
ejpam-2482	134	237	(	(	PUNCT
ejpam-2482	134	238	x	x	X
ejpam-2482	134	239	)	)	PUNCT
ejpam-2482	134	240	for	for	ADP
ejpam-2482	134	241	every	every	DET
ejpam-2482	134	242	m	m	NOUN
ejpam-2482	134	243	"	"	PUNCT
ejpam-2482	134	244	m\n	m\n	PROPN
ejpam-2482	134	245	,	,	PUNCT
ejpam-2482	134	246	(	(	PUNCT
ejpam-2482	134	247	n	n	X
ejpam-2482	134	248	:	:	PUNCT
ejpam-2482	134	249	r	r	NOUN
ejpam-2482	134	250	m	m	VERB
ejpam-2482	134	251	)	)	PUNCT
ejpam-2482	134	252	is	be	AUX
ejpam-2482	134	253	a	a	DET
ejpam-2482	134	254	2	2	NUM
ejpam-2482	134	255	-	-	PUNCT
ejpam-2482	134	256	absorbing	absorbing	ADJ
ejpam-2482	134	257	ideal	ideal	NOUN
ejpam-2482	134	258	of	of	ADP
ejpam-2482	134	259	r.	r.	PROPN
ejpam-2482	134	260	proof	proof	NOUN
ejpam-2482	134	261	.	.	PUNCT
ejpam-2482	135	1	(	(	PUNCT
ejpam-2482	135	2	i)+	i)+	X
ejpam-2482	135	3	(	(	PUNCT
ejpam-2482	135	4	ii	ii	NOUN
ejpam-2482	135	5	)	)	PUNCT
ejpam-2482	135	6	suppose	suppose	VERB
ejpam-2482	135	7	that	that	SCONJ
ejpam-2482	135	8	n	n	PRON
ejpam-2482	135	9	is	be	AUX
ejpam-2482	135	10	a	a	DET
ejpam-2482	135	11	classical	classical	ADJ
ejpam-2482	135	12	2	2	NUM
ejpam-2482	135	13	-	-	PUNCT
ejpam-2482	135	14	absorbing	absorb	VERB
ejpam-2482	135	15	submodule	submodule	NOUN
ejpam-2482	135	16	of	of	ADP
ejpam-2482	135	17	m	m	PROPN
ejpam-2482	135	18	.	.	PUNCT
ejpam-2482	136	1	let	let	VERB
ejpam-2482	136	2	m	m	VERB
ejpam-2482	136	3	"	"	PUNCT
ejpam-2482	136	4	!	!	PUNCT
ejpam-2482	137	1	n	n	X
ejpam-2482	137	2	:	:	PUNCT
ejpam-2482	138	1	m	m	VERB
ejpam-2482	138	2	abc	abc	PROPN
ejpam-2482	138	3	"	"	PUNCT
ejpam-2482	138	4	.	.	PUNCT
ejpam-2482	139	1	then	then	ADV
ejpam-2482	139	2	abcm	abcm	NOUN
ejpam-2482	139	3	"	"	PUNCT
ejpam-2482	139	4	n	n	NOUN
ejpam-2482	139	5	.	.	PUNCT
ejpam-2482	140	1	hence	hence	ADV
ejpam-2482	140	2	abm	abm	PROPN
ejpam-2482	140	3	"	"	PUNCT
ejpam-2482	140	4	n	n	PROPN
ejpam-2482	140	5	or	or	CCONJ
ejpam-2482	140	6	acm	acm	PROPN
ejpam-2482	140	7	"	"	PUNCT
ejpam-2482	140	8	n	n	PROPN
ejpam-2482	140	9	or	or	CCONJ
ejpam-2482	140	10	bcm	bcm	NOUN
ejpam-2482	140	11	"	"	PUNCT
ejpam-2482	140	12	n	n	NOUN
ejpam-2482	140	13	.	.	PUNCT
ejpam-2482	141	1	therefore	therefore	ADV
ejpam-2482	141	2	m	m	VERB
ejpam-2482	141	3	"	"	PUNCT
ejpam-2482	141	4	!	!	PUNCT
ejpam-2482	142	1	n	n	X
ejpam-2482	142	2	:	:	PUNCT
ejpam-2482	142	3	m	m	VERB
ejpam-2482	142	4	ab	ab	NOUN
ejpam-2482	142	5	"	"	PUNCT
ejpam-2482	142	6	or	or	CCONJ
ejpam-2482	142	7	m	m	PROPN
ejpam-2482	142	8	"	"	PUNCT
ejpam-2482	142	9	!	!	PUNCT
ejpam-2482	143	1	n	n	X
ejpam-2482	143	2	:	:	PUNCT
ejpam-2482	143	3	m	m	VERB
ejpam-2482	143	4	ac	ac	ADJ
ejpam-2482	143	5	"	"	PUNCT
ejpam-2482	143	6	or	or	CCONJ
ejpam-2482	143	7	m	m	PROPN
ejpam-2482	143	8	"	"	PUNCT
ejpam-2482	143	9	!	!	PUNCT
ejpam-2482	144	1	n	n	X
ejpam-2482	144	2	:	:	PUNCT
ejpam-2482	145	1	m	m	VERB
ejpam-2482	145	2	bc	bc	PROPN
ejpam-2482	145	3	"	"	PUNCT
ejpam-2482	145	4	.	.	PUNCT
ejpam-2482	146	1	consequently	consequently	ADV
ejpam-2482	146	2	,	,	PUNCT
ejpam-2482	146	3	!	!	PUNCT
ejpam-2482	147	1	n	n	X
ejpam-2482	147	2	:	:	PUNCT
ejpam-2482	148	1	m	m	VERB
ejpam-2482	148	2	abc	abc	NOUN
ejpam-2482	148	3	"	"	PUNCT
ejpam-2482	148	4	=	=	PUNCT
ejpam-2482	148	5	!	!	PUNCT
ejpam-2482	149	1	n	n	X
ejpam-2482	149	2	:	:	PUNCT
ejpam-2482	150	1	m	m	VERB
ejpam-2482	150	2	ab	ab	INTJ
ejpam-2482	150	3	"	"	PUNCT
ejpam-2482	150	4	'	'	PUNCT
ejpam-2482	150	5	!	!	PUNCT
ejpam-2482	151	1	n	n	X
ejpam-2482	151	2	:	:	PUNCT
ejpam-2482	151	3	m	m	VERB
ejpam-2482	151	4	ac	ac	ADJ
ejpam-2482	151	5	"	"	PUNCT
ejpam-2482	151	6	'	'	PUNCT
ejpam-2482	151	7	!	!	PUNCT
ejpam-2482	152	1	n	n	X
ejpam-2482	152	2	:	:	PUNCT
ejpam-2482	152	3	m	m	VERB
ejpam-2482	152	4	bc	bc	PROPN
ejpam-2482	152	5	"	"	PUNCT
ejpam-2482	152	6	.	.	PUNCT
ejpam-2482	153	1	(	(	PUNCT
ejpam-2482	153	2	ii)+	ii)+	NOUN
ejpam-2482	153	3	(	(	PUNCT
ejpam-2482	153	4	iii	iii	NOUN
ejpam-2482	153	5	)	)	PUNCT
ejpam-2482	153	6	let	let	AUX
ejpam-2482	153	7	abm	abm	PROPN
ejpam-2482	153	8	/	/	PUNCT
ejpam-2482	153	9	"	"	PUNCT
ejpam-2482	153	10	n	n	CCONJ
ejpam-2482	153	11	for	for	ADP
ejpam-2482	153	12	some	some	DET
ejpam-2482	153	13	a	a	DET
ejpam-2482	153	14	,	,	PUNCT
ejpam-2482	153	15	b	b	NOUN
ejpam-2482	153	16	"	"	PUNCT
ejpam-2482	153	17	r	r	NOUN
ejpam-2482	153	18	and	and	CCONJ
ejpam-2482	153	19	m	m	NOUN
ejpam-2482	153	20	"	"	PUNCT
ejpam-2482	153	21	m	m	VERB
ejpam-2482	153	22	.	.	PUNCT
ejpam-2482	153	23	assume	assume	VERB
ejpam-2482	153	24	that	that	SCONJ
ejpam-2482	153	25	x	x	PRON
ejpam-2482	153	26	"	"	PUNCT
ejpam-2482	153	27	(	(	PUNCT
ejpam-2482	153	28	n	n	X
ejpam-2482	153	29	:	:	PUNCT
ejpam-2482	153	30	r	r	NOUN
ejpam-2482	153	31	abm	abm	PROPN
ejpam-2482	153	32	)	)	PUNCT
ejpam-2482	153	33	.	.	PUNCT
ejpam-2482	154	1	then	then	ADV
ejpam-2482	154	2	abxm	abxm	VERB
ejpam-2482	154	3	"	"	PUNCT
ejpam-2482	154	4	n	n	CCONJ
ejpam-2482	154	5	,	,	PUNCT
ejpam-2482	154	6	and	and	CCONJ
ejpam-2482	154	7	so	so	ADV
ejpam-2482	154	8	m	m	VERB
ejpam-2482	154	9	"	"	PUNCT
ejpam-2482	154	10	(	(	PUNCT
ejpam-2482	154	11	n	n	X
ejpam-2482	154	12	:	:	PUNCT
ejpam-2482	154	13	m	m	PROPN
ejpam-2482	154	14	abx	abx	NOUN
ejpam-2482	154	15	)	)	PUNCT
ejpam-2482	154	16	.	.	PUNCT
ejpam-2482	155	1	since	since	SCONJ
ejpam-2482	155	2	abm	abm	PROPN
ejpam-2482	155	3	/	/	SYM
ejpam-2482	155	4	"	"	PUNCT
ejpam-2482	155	5	n	n	PROPN
ejpam-2482	155	6	,	,	PUNCT
ejpam-2482	155	7	m	m	PROPN
ejpam-2482	155	8	/	/	SYM
ejpam-2482	155	9	"	"	PUNCT
ejpam-2482	155	10	(	(	PUNCT
ejpam-2482	155	11	n	n	X
ejpam-2482	155	12	:	:	PUNCT
ejpam-2482	155	13	m	m	PROPN
ejpam-2482	155	14	ab	ab	NOUN
ejpam-2482	155	15	)	)	PUNCT
ejpam-2482	155	16	.	.	PUNCT
ejpam-2482	156	1	thus	thus	ADV
ejpam-2482	156	2	by	by	ADP
ejpam-2482	156	3	part	part	NOUN
ejpam-2482	156	4	(	(	PUNCT
ejpam-2482	156	5	i	i	NOUN
ejpam-2482	156	6	)	)	PUNCT
ejpam-2482	156	7	,	,	PUNCT
ejpam-2482	156	8	m	m	VERB
ejpam-2482	156	9	"	"	PUNCT
ejpam-2482	156	10	(	(	PUNCT
ejpam-2482	156	11	n	n	X
ejpam-2482	156	12	:	:	PUNCT
ejpam-2482	156	13	m	m	NOUN
ejpam-2482	156	14	ax	ax	NOUN
ejpam-2482	156	15	)	)	PUNCT
ejpam-2482	156	16	or	or	CCONJ
ejpam-2482	156	17	m	m	PRON
ejpam-2482	156	18	"	"	PUNCT
ejpam-2482	156	19	(	(	PUNCT
ejpam-2482	156	20	n	n	X
ejpam-2482	156	21	:	:	PUNCT
ejpam-2482	156	22	m	m	VERB
ejpam-2482	156	23	bx	bx	NOUN
ejpam-2482	156	24	)	)	PUNCT
ejpam-2482	156	25	,	,	PUNCT
ejpam-2482	156	26	whence	whence	NOUN
ejpam-2482	156	27	x	x	SYM
ejpam-2482	156	28	"	"	PUNCT
ejpam-2482	156	29	(	(	PUNCT
ejpam-2482	156	30	n	n	X
ejpam-2482	156	31	:	:	PUNCT
ejpam-2482	156	32	r	r	NOUN
ejpam-2482	156	33	am	be	AUX
ejpam-2482	156	34	)	)	PUNCT
ejpam-2482	156	35	or	or	CCONJ
ejpam-2482	156	36	x	x	X
ejpam-2482	156	37	"	"	PUNCT
ejpam-2482	156	38	(	(	PUNCT
ejpam-2482	156	39	n	n	X
ejpam-2482	156	40	:	:	PUNCT
ejpam-2482	156	41	r	r	NOUN
ejpam-2482	156	42	bm	bm	PROPN
ejpam-2482	156	43	)	)	PUNCT
ejpam-2482	156	44	.	.	PUNCT
ejpam-2482	157	1	therefore	therefore	ADV
ejpam-2482	157	2	(	(	PUNCT
ejpam-2482	157	3	n	n	X
ejpam-2482	157	4	:	:	PUNCT
ejpam-2482	157	5	r	r	NOUN
ejpam-2482	157	6	abm	abm	PROPN
ejpam-2482	157	7	)	)	PUNCT
ejpam-2482	157	8	=	=	PUNCT
ejpam-2482	157	9	(	(	PUNCT
ejpam-2482	157	10	n	n	X
ejpam-2482	157	11	:	:	PUNCT
ejpam-2482	157	12	r	r	NOUN
ejpam-2482	157	13	am	am	NOUN
ejpam-2482	157	14	)	)	PUNCT
ejpam-2482	157	15	'	'	PUNCT
ejpam-2482	157	16	(	(	PUNCT
ejpam-2482	157	17	n	n	X
ejpam-2482	157	18	:	:	PUNCT
ejpam-2482	157	19	r	r	NOUN
ejpam-2482	157	20	bm	bm	PROPN
ejpam-2482	157	21	)	)	PUNCT
ejpam-2482	157	22	.	.	PUNCT
ejpam-2482	158	1	(	(	PUNCT
ejpam-2482	158	2	iii)+	iii)+	PROPN
ejpam-2482	158	3	(	(	PUNCT
ejpam-2482	158	4	iv	iv	X
ejpam-2482	158	5	)	)	PUNCT
ejpam-2482	158	6	by	by	ADP
ejpam-2482	158	7	the	the	DET
ejpam-2482	158	8	fact	fact	NOUN
ejpam-2482	158	9	that	that	SCONJ
ejpam-2482	158	10	if	if	SCONJ
ejpam-2482	158	11	an	an	DET
ejpam-2482	158	12	ideal	ideal	NOUN
ejpam-2482	158	13	(	(	PUNCT
ejpam-2482	158	14	a	a	DET
ejpam-2482	158	15	subgroup	subgroup	NOUN
ejpam-2482	158	16	)	)	PUNCT
ejpam-2482	158	17	is	be	AUX
ejpam-2482	158	18	the	the	DET
ejpam-2482	158	19	union	union	NOUN
ejpam-2482	158	20	of	of	ADP
ejpam-2482	158	21	two	two	NUM
ejpam-2482	158	22	ideals	ideal	NOUN
ejpam-2482	158	23	(	(	PUNCT
ejpam-2482	158	24	two	two	NUM
ejpam-2482	158	25	subgroups	subgroup	NOUN
ejpam-2482	158	26	)	)	PUNCT
ejpam-2482	158	27	,	,	PUNCT
ejpam-2482	158	28	then	then	ADV
ejpam-2482	158	29	it	it	PRON
ejpam-2482	158	30	is	be	AUX
ejpam-2482	158	31	equal	equal	ADJ
ejpam-2482	158	32	to	to	ADP
ejpam-2482	158	33	one	one	NUM
ejpam-2482	158	34	of	of	ADP
ejpam-2482	158	35	them	they	PRON
ejpam-2482	158	36	.	.	PUNCT
ejpam-2482	159	1	(	(	PUNCT
ejpam-2482	159	2	iv)+	iv)+	NOUN
ejpam-2482	159	3	(	(	PUNCT
ejpam-2482	159	4	v	v	NOUN
ejpam-2482	159	5	)	)	PUNCT
ejpam-2482	159	6	let	let	VERB
ejpam-2482	159	7	for	for	ADP
ejpam-2482	159	8	some	some	PRON
ejpam-2482	159	9	a	a	PRON
ejpam-2482	159	10	,	,	PUNCT
ejpam-2482	159	11	b	b	NOUN
ejpam-2482	159	12	"	"	PUNCT
ejpam-2482	159	13	r	r	NOUN
ejpam-2482	159	14	,	,	PUNCT
ejpam-2482	159	15	an	an	DET
ejpam-2482	159	16	ideal	ideal	NOUN
ejpam-2482	159	17	i	i	PRON
ejpam-2482	159	18	of	of	ADP
ejpam-2482	159	19	r	r	NOUN
ejpam-2482	159	20	and	and	CCONJ
ejpam-2482	159	21	m	m	NOUN
ejpam-2482	159	22	"	"	PUNCT
ejpam-2482	159	23	m	m	PROPN
ejpam-2482	159	24	,	,	PUNCT
ejpam-2482	159	25	abim	abim	NOUN
ejpam-2482	159	26	$	$	SYM
ejpam-2482	159	27	n	n	NOUN
ejpam-2482	159	28	.	.	PUNCT
ejpam-2482	160	1	hence	hence	ADV
ejpam-2482	160	2	i	i	PRON
ejpam-2482	160	3	$	$	SYM
ejpam-2482	160	4	(	(	PUNCT
ejpam-2482	160	5	n	n	NUM
ejpam-2482	160	6	:	:	PUNCT
ejpam-2482	160	7	r	r	NOUN
ejpam-2482	160	8	abm	abm	PROPN
ejpam-2482	160	9	)	)	PUNCT
ejpam-2482	160	10	.	.	PUNCT
ejpam-2482	161	1	if	if	SCONJ
ejpam-2482	161	2	abm	abm	PROPN
ejpam-2482	161	3	"	"	PUNCT
ejpam-2482	161	4	n	n	PROPN
ejpam-2482	161	5	,	,	PUNCT
ejpam-2482	161	6	then	then	ADV
ejpam-2482	161	7	we	we	PRON
ejpam-2482	161	8	are	be	AUX
ejpam-2482	161	9	done	do	VERB
ejpam-2482	161	10	.	.	PUNCT
ejpam-2482	162	1	assume	assume	VERB
ejpam-2482	162	2	that	that	SCONJ
ejpam-2482	162	3	abm	abm	PROPN
ejpam-2482	162	4	/	/	PUNCT
ejpam-2482	162	5	"	"	PUNCT
ejpam-2482	162	6	n	n	NOUN
ejpam-2482	162	7	.	.	PUNCT
ejpam-2482	163	1	therefore	therefore	ADV
ejpam-2482	163	2	by	by	ADP
ejpam-2482	163	3	part	part	NOUN
ejpam-2482	163	4	(	(	PUNCT
ejpam-2482	163	5	iv	iv	X
ejpam-2482	163	6	)	)	PUNCT
ejpam-2482	163	7	we	we	PRON
ejpam-2482	163	8	have	have	VERB
ejpam-2482	163	9	that	that	SCONJ
ejpam-2482	163	10	i	i	PRON
ejpam-2482	163	11	$	$	SYM
ejpam-2482	163	12	(	(	PUNCT
ejpam-2482	163	13	n	n	NUM
ejpam-2482	163	14	:	:	PUNCT
ejpam-2482	163	15	r	r	NOUN
ejpam-2482	163	16	am	be	AUX
ejpam-2482	163	17	)	)	PUNCT
ejpam-2482	163	18	or	or	CCONJ
ejpam-2482	163	19	i	i	PRON
ejpam-2482	163	20	$	$	PROPN
ejpam-2482	163	21	(	(	PUNCT
ejpam-2482	163	22	n	n	NUM
ejpam-2482	163	23	:	:	PUNCT
ejpam-2482	163	24	r	r	NOUN
ejpam-2482	163	25	bm	bm	PROPN
ejpam-2482	163	26	)	)	PUNCT
ejpam-2482	163	27	,	,	PUNCT
ejpam-2482	163	28	i.e.	i.e.	X
ejpam-2482	163	29	,	,	PUNCT
ejpam-2482	163	30	aim	aim	VERB
ejpam-2482	163	31	$	$	SYM
ejpam-2482	163	32	n	n	NOUN
ejpam-2482	163	33	or	or	CCONJ
ejpam-2482	163	34	bim	bim	VERB
ejpam-2482	163	35	$	$	SYM
ejpam-2482	163	36	n	n	NOUN
ejpam-2482	163	37	.	.	PUNCT
ejpam-2482	164	1	(	(	PUNCT
ejpam-2482	164	2	v)+	v)+	NOUN
ejpam-2482	164	3	(	(	PUNCT
ejpam-2482	164	4	vi)+	vi)+	NOUN
ejpam-2482	164	5	(	(	PUNCT
ejpam-2482	164	6	vii)+	vii)+	PROPN
ejpam-2482	164	7	(	(	PUNCT
ejpam-2482	164	8	viii)+	viii)+	NUM
ejpam-2482	164	9	(	(	PUNCT
ejpam-2482	164	10	i	i	NOUN
ejpam-2482	164	11	x	x	X
ejpam-2482	164	12	)	)	PUNCT
ejpam-2482	164	13	have	have	AUX
ejpam-2482	164	14	proofs	proof	NOUN
ejpam-2482	164	15	similar	similar	ADJ
ejpam-2482	164	16	to	to	ADP
ejpam-2482	164	17	that	that	PRON
ejpam-2482	164	18	of	of	ADP
ejpam-2482	164	19	the	the	DET
ejpam-2482	164	20	previous	previous	ADJ
ejpam-2482	164	21	implications	implication	NOUN
ejpam-2482	164	22	.	.	PUNCT
ejpam-2482	165	1	h.	h.	PROPN
ejpam-2482	165	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	165	3	,	,	PUNCT
ejpam-2482	165	4	ü.	ü.	NOUN
ejpam-2482	165	5	tekir	tekir	NOUN
ejpam-2482	165	6	and	and	CCONJ
ejpam-2482	165	7	k.	k.	PROPN
ejpam-2482	165	8	hakan	hakan	PROPN
ejpam-2482	165	9	oral	oral	PROPN
ejpam-2482	165	10	/	/	SYM
ejpam-2482	165	11	eur	eur	PROPN
ejpam-2482	165	12	.	.	PUNCT
ejpam-2482	166	1	j.	j.	PROPN
ejpam-2482	166	2	pure	pure	PROPN
ejpam-2482	166	3	appl	appl	PROPN
ejpam-2482	166	4	.	.	PROPN
ejpam-2482	166	5	math	math	PROPN
ejpam-2482	166	6	,	,	PUNCT
ejpam-2482	166	7	8	8	NUM
ejpam-2482	166	8	(	(	PUNCT
ejpam-2482	166	9	2015	2015	NUM
ejpam-2482	166	10	)	)	PUNCT
ejpam-2482	166	11	,	,	PUNCT
ejpam-2482	166	12	417	417	NUM
ejpam-2482	166	13	-	-	SYM
ejpam-2482	166	14	430	430	NUM
ejpam-2482	166	15	421	421	NUM
ejpam-2482	166	16	(	(	PUNCT
ejpam-2482	166	17	i	i	PRON
ejpam-2482	166	18	x)+	x)+	PROPN
ejpam-2482	167	1	(	(	PUNCT
ejpam-2482	167	2	i	i	NOUN
ejpam-2482	167	3	)	)	PUNCT
ejpam-2482	167	4	is	be	AUX
ejpam-2482	167	5	trivial	trivial	ADJ
ejpam-2482	167	6	.	.	PUNCT
ejpam-2482	168	1	(	(	PUNCT
ejpam-2482	168	2	i	i	NOUN
ejpam-2482	168	3	x	x	NOUN
ejpam-2482	168	4	)	)	PUNCT
ejpam-2482	168	5	,	,	PUNCT
ejpam-2482	168	6	(	(	PUNCT
ejpam-2482	168	7	x	x	X
ejpam-2482	168	8	)	)	PUNCT
ejpam-2482	168	9	straightforward	straightforward	ADJ
ejpam-2482	168	10	.	.	PUNCT
ejpam-2482	169	1	corollary	corollary	ADJ
ejpam-2482	169	2	2	2	NUM
ejpam-2482	169	3	.	.	PUNCT
ejpam-2482	170	1	let	let	VERB
ejpam-2482	170	2	r	r	PRON
ejpam-2482	170	3	be	be	AUX
ejpam-2482	170	4	a	a	DET
ejpam-2482	170	5	ring	ring	NOUN
ejpam-2482	170	6	and	and	CCONJ
ejpam-2482	170	7	i	i	PRON
ejpam-2482	170	8	be	be	VERB
ejpam-2482	170	9	a	a	DET
ejpam-2482	170	10	proper	proper	ADJ
ejpam-2482	170	11	ideal	ideal	NOUN
ejpam-2482	170	12	of	of	ADP
ejpam-2482	170	13	r.	r.	PROPN
ejpam-2482	170	14	(	(	PUNCT
ejpam-2482	170	15	i	i	NOUN
ejpam-2482	170	16	)	)	PUNCT
ejpam-2482	170	17	ri	ri	PROPN
ejpam-2482	170	18	is	be	AUX
ejpam-2482	170	19	a	a	DET
ejpam-2482	170	20	classical	classical	ADJ
ejpam-2482	170	21	2	2	NUM
ejpam-2482	170	22	-	-	PUNCT
ejpam-2482	170	23	absorbing	absorb	VERB
ejpam-2482	170	24	submodule	submodule	NOUN
ejpam-2482	170	25	of	of	ADP
ejpam-2482	170	26	r	r	NOUN
ejpam-2482	170	27	if	if	SCONJ
ejpam-2482	171	1	and	and	CCONJ
ejpam-2482	171	2	only	only	ADV
ejpam-2482	171	3	if	if	SCONJ
ejpam-2482	171	4	i	i	PRON
ejpam-2482	171	5	is	be	AUX
ejpam-2482	171	6	a	a	DET
ejpam-2482	171	7	2	2	NUM
ejpam-2482	171	8	-	-	PUNCT
ejpam-2482	171	9	absorbing	absorbing	ADJ
ejpam-2482	171	10	ideal	ideal	NOUN
ejpam-2482	171	11	of	of	ADP
ejpam-2482	171	12	r.	r.	PROPN
ejpam-2482	171	13	(	(	PUNCT
ejpam-2482	171	14	ii	ii	PROPN
ejpam-2482	171	15	)	)	PUNCT
ejpam-2482	171	16	every	every	DET
ejpam-2482	171	17	proper	proper	ADJ
ejpam-2482	171	18	ideal	ideal	NOUN
ejpam-2482	171	19	of	of	ADP
ejpam-2482	171	20	r	r	NOUN
ejpam-2482	171	21	is	be	AUX
ejpam-2482	171	22	2	2	NUM
ejpam-2482	171	23	-	-	PUNCT
ejpam-2482	171	24	absorbing	absorbing	ADJ
ejpam-2482	171	25	if	if	SCONJ
ejpam-2482	171	26	and	and	CCONJ
ejpam-2482	171	27	only	only	ADV
ejpam-2482	171	28	if	if	SCONJ
ejpam-2482	171	29	for	for	ADP
ejpam-2482	171	30	every	every	DET
ejpam-2482	171	31	r	r	NOUN
ejpam-2482	171	32	-	-	PUNCT
ejpam-2482	171	33	module	module	NOUN
ejpam-2482	171	34	m	m	NOUN
ejpam-2482	171	35	and	and	CCONJ
ejpam-2482	171	36	every	every	DET
ejpam-2482	171	37	proper	proper	ADJ
ejpam-2482	171	38	submodule	submodule	NOUN
ejpam-2482	171	39	n	n	PROPN
ejpam-2482	171	40	of	of	ADP
ejpam-2482	171	41	m	m	PROPN
ejpam-2482	171	42	,	,	PUNCT
ejpam-2482	171	43	n	n	PRON
ejpam-2482	171	44	is	be	AUX
ejpam-2482	171	45	a	a	DET
ejpam-2482	171	46	classical	classical	ADJ
ejpam-2482	171	47	2	2	NUM
ejpam-2482	171	48	-	-	PUNCT
ejpam-2482	171	49	absorbing	absorb	VERB
ejpam-2482	171	50	submodule	submodule	NOUN
ejpam-2482	171	51	of	of	ADP
ejpam-2482	171	52	m.	m.	NOUN
ejpam-2482	171	53	proof	proof	NOUN
ejpam-2482	171	54	.	.	PUNCT
ejpam-2482	172	1	(	(	PUNCT
ejpam-2482	172	2	i	i	NOUN
ejpam-2482	172	3	)	)	PUNCT
ejpam-2482	172	4	let	let	VERB
ejpam-2482	172	5	i	i	PRON
ejpam-2482	172	6	be	be	AUX
ejpam-2482	172	7	a	a	DET
ejpam-2482	172	8	classical	classical	ADJ
ejpam-2482	172	9	2	2	NUM
ejpam-2482	172	10	-	-	PUNCT
ejpam-2482	172	11	absorbing	absorb	VERB
ejpam-2482	172	12	submodule	submodule	NOUN
ejpam-2482	172	13	of	of	ADP
ejpam-2482	172	14	r.	r.	PROPN
ejpam-2482	172	15	then	then	ADV
ejpam-2482	172	16	by	by	ADP
ejpam-2482	172	17	theorem	theorem	NOUN
ejpam-2482	172	18	2	2	NUM
ejpam-2482	172	19	,	,	PUNCT
ejpam-2482	172	20	(	(	PUNCT
ejpam-2482	172	21	i	i	PRON
ejpam-2482	172	22	:	:	PUNCT
ejpam-2482	172	23	r	r	NOUN
ejpam-2482	172	24	1	1	NUM
ejpam-2482	172	25	)	)	PUNCT
ejpam-2482	172	26	=	=	NOUN
ejpam-2482	173	1	i	i	PRON
ejpam-2482	173	2	is	be	AUX
ejpam-2482	173	3	a	a	DET
ejpam-2482	173	4	2	2	NUM
ejpam-2482	173	5	-	-	PUNCT
ejpam-2482	173	6	absorbing	absorbing	ADJ
ejpam-2482	173	7	ideal	ideal	NOUN
ejpam-2482	173	8	of	of	ADP
ejpam-2482	173	9	r.	r.	PROPN
ejpam-2482	173	10	for	for	ADP
ejpam-2482	173	11	the	the	DET
ejpam-2482	173	12	converse	converse	NOUN
ejpam-2482	173	13	see	see	VERB
ejpam-2482	173	14	part	part	NOUN
ejpam-2482	173	15	(	(	PUNCT
ejpam-2482	173	16	i	i	NOUN
ejpam-2482	173	17	)	)	PUNCT
ejpam-2482	173	18	of	of	ADP
ejpam-2482	173	19	proposition	proposition	NOUN
ejpam-2482	173	20	2	2	NUM
ejpam-2482	173	21	.	.	PUNCT
ejpam-2482	173	22	(	(	PUNCT
ejpam-2482	173	23	ii	ii	NOUN
ejpam-2482	173	24	)	)	PUNCT
ejpam-2482	173	25	assume	assume	VERB
ejpam-2482	173	26	that	that	SCONJ
ejpam-2482	173	27	every	every	DET
ejpam-2482	173	28	proper	proper	ADJ
ejpam-2482	173	29	ideal	ideal	NOUN
ejpam-2482	173	30	of	of	ADP
ejpam-2482	173	31	r	r	NOUN
ejpam-2482	173	32	is	be	AUX
ejpam-2482	173	33	2	2	NUM
ejpam-2482	173	34	-	-	PUNCT
ejpam-2482	173	35	absorbing	absorbing	ADJ
ejpam-2482	173	36	.	.	PUNCT
ejpam-2482	174	1	let	let	VERB
ejpam-2482	174	2	n	n	PRON
ejpam-2482	174	3	be	be	AUX
ejpam-2482	174	4	a	a	DET
ejpam-2482	174	5	proper	proper	ADJ
ejpam-2482	174	6	submodule	submodule	NOUN
ejpam-2482	174	7	of	of	ADP
ejpam-2482	174	8	an	an	DET
ejpam-2482	174	9	r	r	NOUN
ejpam-2482	174	10	-	-	PUNCT
ejpam-2482	174	11	module	module	NOUN
ejpam-2482	174	12	m	m	NOUN
ejpam-2482	174	13	.	.	PUNCT
ejpam-2482	175	1	since	since	SCONJ
ejpam-2482	175	2	for	for	ADP
ejpam-2482	175	3	every	every	DET
ejpam-2482	175	4	m	m	NOUN
ejpam-2482	175	5	"	"	PUNCT
ejpam-2482	175	6	m\n	m\n	NOUN
ejpam-2482	175	7	,	,	PUNCT
ejpam-2482	175	8	(	(	PUNCT
ejpam-2482	175	9	n	n	X
ejpam-2482	175	10	:	:	PUNCT
ejpam-2482	175	11	r	r	NOUN
ejpam-2482	175	12	m	m	VERB
ejpam-2482	175	13	)	)	PUNCT
ejpam-2482	175	14	is	be	AUX
ejpam-2482	175	15	a	a	DET
ejpam-2482	175	16	proper	proper	ADJ
ejpam-2482	175	17	ideal	ideal	NOUN
ejpam-2482	175	18	of	of	ADP
ejpam-2482	175	19	r	r	NOUN
ejpam-2482	175	20	,	,	PUNCT
ejpam-2482	175	21	then	then	ADV
ejpam-2482	175	22	it	it	PRON
ejpam-2482	175	23	is	be	AUX
ejpam-2482	175	24	a	a	DET
ejpam-2482	175	25	2	2	NUM
ejpam-2482	175	26	-	-	PUNCT
ejpam-2482	175	27	absorbing	absorbing	ADJ
ejpam-2482	175	28	ideal	ideal	NOUN
ejpam-2482	175	29	of	of	ADP
ejpam-2482	175	30	r.	r.	PROPN
ejpam-2482	175	31	hence	hence	ADV
ejpam-2482	175	32	by	by	ADP
ejpam-2482	175	33	theorem	theorem	NOUN
ejpam-2482	175	34	2	2	NUM
ejpam-2482	175	35	,	,	PUNCT
ejpam-2482	175	36	n	n	PRON
ejpam-2482	175	37	is	be	AUX
ejpam-2482	175	38	a	a	DET
ejpam-2482	175	39	classical	classical	ADJ
ejpam-2482	175	40	2	2	NUM
ejpam-2482	175	41	-	-	PUNCT
ejpam-2482	175	42	absorbing	absorb	VERB
ejpam-2482	175	43	submodule	submodule	NOUN
ejpam-2482	175	44	of	of	ADP
ejpam-2482	175	45	m	m	PROPN
ejpam-2482	175	46	.	.	PUNCT
ejpam-2482	176	1	we	we	PRON
ejpam-2482	176	2	have	have	VERB
ejpam-2482	176	3	the	the	DET
ejpam-2482	176	4	converse	converse	NOUN
ejpam-2482	176	5	immediately	immediately	ADV
ejpam-2482	176	6	by	by	ADP
ejpam-2482	176	7	part	part	NOUN
ejpam-2482	176	8	(	(	PUNCT
ejpam-2482	176	9	i	i	NOUN
ejpam-2482	176	10	)	)	PUNCT
ejpam-2482	176	11	.	.	PUNCT
ejpam-2482	177	1	proposition	proposition	NOUN
ejpam-2482	177	2	3	3	X
ejpam-2482	177	3	.	.	PUNCT
ejpam-2482	178	1	let	let	VERB
ejpam-2482	178	2	m	m	PRON
ejpam-2482	178	3	be	be	AUX
ejpam-2482	178	4	an	an	DET
ejpam-2482	178	5	r	r	NOUN
ejpam-2482	178	6	-	-	PUNCT
ejpam-2482	178	7	module	module	NOUN
ejpam-2482	178	8	and	and	CCONJ
ejpam-2482	178	9	(	(	PUNCT
ejpam-2482	178	10	ki	ki	INTJ
ejpam-2482	178	11	|	|	ADV
ejpam-2482	179	1	i	i	PRON
ejpam-2482	180	1	"	"	PUNCT
ejpam-2482	181	1	i	i	PRON
ejpam-2482	181	2	)	)	PUNCT
ejpam-2482	181	3	be	be	AUX
ejpam-2482	181	4	a	a	DET
ejpam-2482	181	5	chain	chain	NOUN
ejpam-2482	181	6	of	of	ADP
ejpam-2482	181	7	classical	classical	ADJ
ejpam-2482	181	8	2	2	NUM
ejpam-2482	181	9	-	-	PUNCT
ejpam-2482	181	10	absorbing	absorb	VERB
ejpam-2482	181	11	submodules	submodule	NOUN
ejpam-2482	181	12	of	of	ADP
ejpam-2482	181	13	m.	m.	NOUN
ejpam-2482	181	14	then	then	ADV
ejpam-2482	181	15	*	*	PUNCT
ejpam-2482	181	16	i"i	i"i	PROPN
ejpam-2482	181	17	ki	ki	PROPN
ejpam-2482	181	18	is	be	AUX
ejpam-2482	181	19	a	a	DET
ejpam-2482	181	20	classical	classical	ADJ
ejpam-2482	181	21	2	2	NUM
ejpam-2482	181	22	-	-	PUNCT
ejpam-2482	181	23	absorbing	absorb	VERB
ejpam-2482	181	24	submodule	submodule	NOUN
ejpam-2482	181	25	of	of	ADP
ejpam-2482	181	26	m.	m.	NOUN
ejpam-2482	181	27	proof	proof	NOUN
ejpam-2482	181	28	.	.	PUNCT
ejpam-2482	182	1	suppose	suppose	VERB
ejpam-2482	182	2	that	that	SCONJ
ejpam-2482	182	3	abcm	abcm	NOUN
ejpam-2482	182	4	"	"	PUNCT
ejpam-2482	182	5	*	*	PUNCT
ejpam-2482	182	6	i"i	i"i	PROPN
ejpam-2482	182	7	ki	ki	PROPN
ejpam-2482	182	8	for	for	ADP
ejpam-2482	182	9	some	some	DET
ejpam-2482	182	10	a	a	DET
ejpam-2482	182	11	,	,	PUNCT
ejpam-2482	182	12	b	b	NOUN
ejpam-2482	182	13	,	,	PUNCT
ejpam-2482	182	14	c	c	NOUN
ejpam-2482	182	15	"	"	PUNCT
ejpam-2482	182	16	r	r	NOUN
ejpam-2482	182	17	and	and	CCONJ
ejpam-2482	182	18	m	m	NOUN
ejpam-2482	182	19	"	"	PUNCT
ejpam-2482	182	20	m	m	VERB
ejpam-2482	182	21	.	.	PUNCT
ejpam-2482	182	22	assume	assume	VERB
ejpam-2482	182	23	that	that	SCONJ
ejpam-2482	182	24	abm	abm	PROPN
ejpam-2482	182	25	/	/	PUNCT
ejpam-2482	182	26	"	"	PUNCT
ejpam-2482	182	27	*	*	PUNCT
ejpam-2482	182	28	i"i	i"i	PROPN
ejpam-2482	182	29	ki	ki	PROPN
ejpam-2482	182	30	and	and	CCONJ
ejpam-2482	182	31	acm	acm	PROPN
ejpam-2482	182	32	/	/	SYM
ejpam-2482	182	33	"	"	PUNCT
ejpam-2482	182	34	*	*	PUNCT
ejpam-2482	182	35	i"i	i"i	PROPN
ejpam-2482	182	36	ki	ki	INTJ
ejpam-2482	182	37	.	.	PUNCT
ejpam-2482	183	1	then	then	ADV
ejpam-2482	183	2	there	there	PRON
ejpam-2482	183	3	are	be	VERB
ejpam-2482	183	4	t	t	PROPN
ejpam-2482	183	5	,	,	PUNCT
ejpam-2482	183	6	l	l	NOUN
ejpam-2482	183	7	"	"	PUNCT
ejpam-2482	183	8	i	i	PRON
ejpam-2482	183	9	where	where	SCONJ
ejpam-2482	183	10	abm	abm	PROPN
ejpam-2482	183	11	/	/	PUNCT
ejpam-2482	183	12	"	"	PUNCT
ejpam-2482	183	13	kt	kt	PROPN
ejpam-2482	183	14	and	and	CCONJ
ejpam-2482	183	15	acm	acm	PROPN
ejpam-2482	183	16	/	/	SYM
ejpam-2482	183	17	"	"	PUNCT
ejpam-2482	183	18	kl	kl	INTJ
ejpam-2482	183	19	.	.	PUNCT
ejpam-2482	184	1	hence	hence	ADV
ejpam-2482	184	2	,	,	PUNCT
ejpam-2482	184	3	for	for	ADP
ejpam-2482	184	4	every	every	DET
ejpam-2482	184	5	ks	ks	NOUN
ejpam-2482	184	6	$	$	SYM
ejpam-2482	184	7	kt	kt	NOUN
ejpam-2482	184	8	and	and	CCONJ
ejpam-2482	184	9	every	every	DET
ejpam-2482	184	10	kd	kd	PROPN
ejpam-2482	184	11	$	$	SYM
ejpam-2482	184	12	kl	kl	X
ejpam-2482	184	13	we	we	PRON
ejpam-2482	184	14	have	have	VERB
ejpam-2482	184	15	that	that	DET
ejpam-2482	184	16	abm	abm	PROPN
ejpam-2482	184	17	/	/	PUNCT
ejpam-2482	184	18	"	"	PUNCT
ejpam-2482	184	19	ks	ks	PROPN
ejpam-2482	184	20	and	and	CCONJ
ejpam-2482	184	21	acm	acm	PROPN
ejpam-2482	184	22	/	/	SYM
ejpam-2482	184	23	"	"	PUNCT
ejpam-2482	184	24	kd	kd	PROPN
ejpam-2482	184	25	.	.	PUNCT
ejpam-2482	185	1	thus	thus	ADV
ejpam-2482	185	2	,	,	PUNCT
ejpam-2482	185	3	for	for	ADP
ejpam-2482	185	4	every	every	DET
ejpam-2482	185	5	submodule	submodule	NOUN
ejpam-2482	185	6	kh	kh	PROPN
ejpam-2482	185	7	such	such	ADJ
ejpam-2482	185	8	that	that	SCONJ
ejpam-2482	185	9	kh	kh	PROPN
ejpam-2482	185	10	$	$	SYM
ejpam-2482	185	11	kt	kt	PROPN
ejpam-2482	185	12	and	and	CCONJ
ejpam-2482	185	13	kh	kh	PROPN
ejpam-2482	185	14	$	$	SYM
ejpam-2482	185	15	kl	kl	X
ejpam-2482	185	16	we	we	PRON
ejpam-2482	185	17	get	get	VERB
ejpam-2482	185	18	bcm	bcm	NOUN
ejpam-2482	185	19	"	"	PUNCT
ejpam-2482	185	20	kh	kh	PROPN
ejpam-2482	185	21	.	.	PUNCT
ejpam-2482	186	1	hence	hence	ADV
ejpam-2482	186	2	bcm	bcm	VERB
ejpam-2482	186	3	"	"	PUNCT
ejpam-2482	186	4	*	*	PUNCT
ejpam-2482	186	5	i"i	i"i	PROPN
ejpam-2482	186	6	ki	ki	PROPN
ejpam-2482	186	7	.	.	PUNCT
ejpam-2482	187	1	a	a	DET
ejpam-2482	187	2	classical	classical	ADJ
ejpam-2482	187	3	2	2	NUM
ejpam-2482	187	4	-	-	PUNCT
ejpam-2482	187	5	absorbing	absorb	VERB
ejpam-2482	187	6	submodule	submodule	NOUN
ejpam-2482	187	7	of	of	ADP
ejpam-2482	187	8	m	m	PROPN
ejpam-2482	187	9	is	be	AUX
ejpam-2482	187	10	called	call	VERB
ejpam-2482	187	11	minimal	minimal	ADJ
ejpam-2482	187	12	,	,	PUNCT
ejpam-2482	187	13	if	if	SCONJ
ejpam-2482	187	14	for	for	ADP
ejpam-2482	187	15	any	any	DET
ejpam-2482	187	16	classical	classical	ADJ
ejpam-2482	187	17	2	2	NUM
ejpam-2482	187	18	-	-	PUNCT
ejpam-2482	187	19	absorbing	absorb	VERB
ejpam-2482	187	20	submodule	submodule	NOUN
ejpam-2482	187	21	k	k	PROPN
ejpam-2482	187	22	of	of	ADP
ejpam-2482	187	23	m	m	PROPN
ejpam-2482	188	1	such	such	ADJ
ejpam-2482	188	2	that	that	SCONJ
ejpam-2482	188	3	k	k	PROPN
ejpam-2482	188	4	$	$	SYM
ejpam-2482	188	5	n	n	NOUN
ejpam-2482	188	6	,	,	PUNCT
ejpam-2482	188	7	then	then	ADV
ejpam-2482	188	8	k	k	PROPN
ejpam-2482	188	9	=	=	PUNCT
ejpam-2482	188	10	n	n	PROPN
ejpam-2482	188	11	.	.	PUNCT
ejpam-2482	189	1	let	let	VERB
ejpam-2482	189	2	l	l	NOUN
ejpam-2482	189	3	be	be	AUX
ejpam-2482	189	4	a	a	DET
ejpam-2482	189	5	classical	classical	ADJ
ejpam-2482	189	6	2	2	NUM
ejpam-2482	189	7	-	-	PUNCT
ejpam-2482	189	8	absorbing	absorb	VERB
ejpam-2482	189	9	submodule	submodule	NOUN
ejpam-2482	189	10	of	of	ADP
ejpam-2482	189	11	m	m	PROPN
ejpam-2482	189	12	.	.	PUNCT
ejpam-2482	190	1	set	set	VERB
ejpam-2482	190	2	!	!	PUNCT
ejpam-2482	191	1	=	=	PRON
ejpam-2482	192	1	(	(	PUNCT
ejpam-2482	192	2	k	k	X
ejpam-2482	192	3	|	|	ADV
ejpam-2482	192	4	k	k	PROPN
ejpam-2482	192	5	is	be	AUX
ejpam-2482	192	6	a	a	DET
ejpam-2482	192	7	classical	classical	ADJ
ejpam-2482	192	8	2	2	NUM
ejpam-2482	192	9	-	-	PUNCT
ejpam-2482	192	10	absorbing	absorb	VERB
ejpam-2482	192	11	submodule	submodule	NOUN
ejpam-2482	192	12	of	of	ADP
ejpam-2482	192	13	m	m	PROPN
ejpam-2482	192	14	and	and	CCONJ
ejpam-2482	192	15	k	k	PROPN
ejpam-2482	192	16	$	$	SYM
ejpam-2482	192	17	l	l	NOUN
ejpam-2482	192	18	)	)	PUNCT
ejpam-2482	192	19	.	.	PUNCT
ejpam-2482	193	1	if	if	SCONJ
ejpam-2482	193	2	(	(	PUNCT
ejpam-2482	193	3	ki	ki	X
ejpam-2482	193	4	:	:	PUNCT
ejpam-2482	193	5	i	i	PRON
ejpam-2482	193	6	"	"	PUNCT
ejpam-2482	193	7	i	i	PROPN
ejpam-2482	193	8	)	)	PUNCT
ejpam-2482	193	9	is	be	AUX
ejpam-2482	193	10	any	any	DET
ejpam-2482	193	11	chain	chain	NOUN
ejpam-2482	193	12	in	in	ADP
ejpam-2482	193	13	!	!	PUNCT
ejpam-2482	193	14	,	,	PUNCT
ejpam-2482	193	15	then	then	ADV
ejpam-2482	193	16	*	*	PUNCT
ejpam-2482	193	17	i"i	i"i	PROPN
ejpam-2482	193	18	ki	ki	PROPN
ejpam-2482	193	19	is	be	AUX
ejpam-2482	193	20	in	in	ADP
ejpam-2482	193	21	!	!	PUNCT
ejpam-2482	193	22	,	,	PUNCT
ejpam-2482	193	23	by	by	ADP
ejpam-2482	193	24	proposition	proposition	NOUN
ejpam-2482	193	25	3	3	NUM
ejpam-2482	193	26	.	.	PUNCT
ejpam-2482	193	27	by	by	ADP
ejpam-2482	193	28	zorn	zorn	PROPN
ejpam-2482	193	29	’s	’s	PART
ejpam-2482	193	30	lemma	lemma	PROPN
ejpam-2482	193	31	,	,	PUNCT
ejpam-2482	193	32	!	!	PUNCT
ejpam-2482	194	1	contains	contain	VERB
ejpam-2482	194	2	a	a	DET
ejpam-2482	194	3	minimal	minimal	ADJ
ejpam-2482	194	4	member	member	NOUN
ejpam-2482	194	5	which	which	PRON
ejpam-2482	194	6	is	be	AUX
ejpam-2482	194	7	clearly	clearly	ADV
ejpam-2482	194	8	a	a	DET
ejpam-2482	194	9	minimal	minimal	ADJ
ejpam-2482	194	10	classical	classical	ADJ
ejpam-2482	194	11	2	2	NUM
ejpam-2482	194	12	-	-	PUNCT
ejpam-2482	194	13	absorbing	absorb	VERB
ejpam-2482	194	14	submodule	submodule	NOUN
ejpam-2482	194	15	of	of	ADP
ejpam-2482	194	16	m	m	PROPN
ejpam-2482	194	17	.	.	PUNCT
ejpam-2482	195	1	thus	thus	ADV
ejpam-2482	195	2	,	,	PUNCT
ejpam-2482	195	3	every	every	DET
ejpam-2482	195	4	classical	classical	ADJ
ejpam-2482	195	5	2	2	NUM
ejpam-2482	195	6	-absorbing	-absorbing	NOUN
ejpam-2482	195	7	submodule	submodule	NOUN
ejpam-2482	195	8	of	of	ADP
ejpam-2482	195	9	m	m	PROPN
ejpam-2482	195	10	contains	contain	VERB
ejpam-2482	195	11	a	a	DET
ejpam-2482	195	12	minimal	minimal	ADJ
ejpam-2482	195	13	classical	classical	ADJ
ejpam-2482	195	14	2	2	NUM
ejpam-2482	195	15	-	-	PUNCT
ejpam-2482	195	16	absorbing	absorb	VERB
ejpam-2482	195	17	submodule	submodule	NOUN
ejpam-2482	195	18	of	of	ADP
ejpam-2482	195	19	m	m	PROPN
ejpam-2482	195	20	.	.	PUNCT
ejpam-2482	196	1	if	if	SCONJ
ejpam-2482	196	2	m	m	NOUN
ejpam-2482	196	3	is	be	AUX
ejpam-2482	196	4	a	a	DET
ejpam-2482	196	5	finitely	finitely	ADV
ejpam-2482	196	6	generated	generate	VERB
ejpam-2482	196	7	,	,	PUNCT
ejpam-2482	196	8	then	then	ADV
ejpam-2482	196	9	it	it	PRON
ejpam-2482	196	10	is	be	AUX
ejpam-2482	196	11	clear	clear	ADJ
ejpam-2482	196	12	that	that	SCONJ
ejpam-2482	196	13	m	m	NOUN
ejpam-2482	196	14	contains	contain	VERB
ejpam-2482	196	15	a	a	DET
ejpam-2482	196	16	minimal	minimal	ADJ
ejpam-2482	196	17	classical	classical	ADJ
ejpam-2482	196	18	2	2	NUM
ejpam-2482	196	19	-	-	PUNCT
ejpam-2482	196	20	absorbing	absorb	VERB
ejpam-2482	196	21	submodule	submodule	NOUN
ejpam-2482	196	22	.	.	PUNCT
ejpam-2482	197	1	theorem	theorem	NOUN
ejpam-2482	197	2	3	3	X
ejpam-2482	197	3	.	.	PUNCT
ejpam-2482	198	1	let	let	VERB
ejpam-2482	198	2	m	m	PRON
ejpam-2482	198	3	be	be	AUX
ejpam-2482	198	4	a	a	DET
ejpam-2482	198	5	noetherian	noetherian	ADJ
ejpam-2482	198	6	r	r	NOUN
ejpam-2482	198	7	-	-	PUNCT
ejpam-2482	198	8	module	module	NOUN
ejpam-2482	198	9	.	.	PUNCT
ejpam-2482	199	1	then	then	ADV
ejpam-2482	199	2	m	m	VERB
ejpam-2482	199	3	contains	contain	VERB
ejpam-2482	199	4	a	a	DET
ejpam-2482	199	5	finite	finite	ADJ
ejpam-2482	199	6	number	number	NOUN
ejpam-2482	199	7	of	of	ADP
ejpam-2482	199	8	minimal	minimal	ADJ
ejpam-2482	199	9	classical	classical	ADJ
ejpam-2482	199	10	2	2	NUM
ejpam-2482	199	11	-	-	PUNCT
ejpam-2482	199	12	absorbing	absorbing	ADJ
ejpam-2482	199	13	submodules	submodule	NOUN
ejpam-2482	199	14	.	.	PUNCT
ejpam-2482	200	1	proof	proof	NOUN
ejpam-2482	200	2	.	.	PUNCT
ejpam-2482	201	1	suppose	suppose	VERB
ejpam-2482	201	2	that	that	SCONJ
ejpam-2482	201	3	the	the	DET
ejpam-2482	201	4	result	result	NOUN
ejpam-2482	201	5	is	be	AUX
ejpam-2482	201	6	false	false	ADJ
ejpam-2482	201	7	.	.	PUNCT
ejpam-2482	202	1	let	let	VERB
ejpam-2482	202	2	!	!	PUNCT
ejpam-2482	203	1	denote	denote	VERB
ejpam-2482	203	2	the	the	DET
ejpam-2482	203	3	collection	collection	NOUN
ejpam-2482	203	4	of	of	ADP
ejpam-2482	203	5	proper	proper	ADJ
ejpam-2482	203	6	submodules	submodule	NOUN
ejpam-2482	203	7	n	n	PROPN
ejpam-2482	203	8	of	of	ADP
ejpam-2482	203	9	m	m	PRON
ejpam-2482	203	10	such	such	ADJ
ejpam-2482	203	11	that	that	SCONJ
ejpam-2482	203	12	the	the	DET
ejpam-2482	203	13	module	module	NOUN
ejpam-2482	203	14	m	m	PROPN
ejpam-2482	203	15	/	/	SYM
ejpam-2482	203	16	n	n	PROPN
ejpam-2482	203	17	has	have	VERB
ejpam-2482	203	18	an	an	DET
ejpam-2482	203	19	infinite	infinite	ADJ
ejpam-2482	203	20	number	number	NOUN
ejpam-2482	203	21	of	of	ADP
ejpam-2482	203	22	minimal	minimal	ADJ
ejpam-2482	203	23	classical	classical	ADJ
ejpam-2482	203	24	2	2	NUM
ejpam-2482	203	25	-	-	PUNCT
ejpam-2482	203	26	absorbing	absorbing	ADJ
ejpam-2482	203	27	submodules	submodule	NOUN
ejpam-2482	203	28	.	.	PUNCT
ejpam-2482	204	1	since	since	SCONJ
ejpam-2482	204	2	0	0	NUM
ejpam-2482	204	3	"	"	PUNCT
ejpam-2482	204	4	!	!	PUNCT
ejpam-2482	205	1	we	we	PRON
ejpam-2482	205	2	get	get	VERB
ejpam-2482	205	3	!	!	PUNCT
ejpam-2482	206	1	#	#	NOUN
ejpam-2482	206	2	=	=	SYM
ejpam-2482	206	3	$	$	SYM
ejpam-2482	206	4	.	.	PUNCT
ejpam-2482	207	1	therefore	therefore	ADV
ejpam-2482	207	2	!	!	PUNCT
ejpam-2482	207	3	has	have	VERB
ejpam-2482	207	4	a	a	DET
ejpam-2482	207	5	maximal	maximal	ADJ
ejpam-2482	207	6	member	member	NOUN
ejpam-2482	207	7	t	t	NOUN
ejpam-2482	207	8	,	,	PUNCT
ejpam-2482	207	9	since	since	SCONJ
ejpam-2482	207	10	m	m	PROPN
ejpam-2482	207	11	is	be	AUX
ejpam-2482	207	12	a	a	DET
ejpam-2482	207	13	noetherian	noetherian	ADJ
ejpam-2482	207	14	r	r	NOUN
ejpam-2482	207	15	-	-	PUNCT
ejpam-2482	207	16	module	module	NOUN
ejpam-2482	207	17	.	.	PUNCT
ejpam-2482	208	1	it	it	PRON
ejpam-2482	208	2	is	be	AUX
ejpam-2482	208	3	clear	clear	ADJ
ejpam-2482	208	4	that	that	SCONJ
ejpam-2482	208	5	t	t	PROPN
ejpam-2482	208	6	is	be	AUX
ejpam-2482	208	7	not	not	PART
ejpam-2482	208	8	a	a	DET
ejpam-2482	208	9	classical	classical	ADJ
ejpam-2482	208	10	2	2	NUM
ejpam-2482	208	11	-	-	PUNCT
ejpam-2482	208	12	absorbing	absorb	VERB
ejpam-2482	208	13	submodule	submodule	NOUN
ejpam-2482	208	14	.	.	PUNCT
ejpam-2482	209	1	therefore	therefore	ADV
ejpam-2482	209	2	,	,	PUNCT
ejpam-2482	209	3	there	there	PRON
ejpam-2482	209	4	exists	exist	VERB
ejpam-2482	209	5	an	an	DET
ejpam-2482	209	6	element	element	NOUN
ejpam-2482	209	7	m	m	NOUN
ejpam-2482	209	8	"	"	PUNCT
ejpam-2482	209	9	m\t	m\t	NOUN
ejpam-2482	209	10	and	and	CCONJ
ejpam-2482	209	11	ideals	ideal	NOUN
ejpam-2482	209	12	i	i	PRON
ejpam-2482	209	13	,	,	PUNCT
ejpam-2482	209	14	j	j	PROPN
ejpam-2482	209	15	,	,	PUNCT
ejpam-2482	209	16	k	k	PROPN
ejpam-2482	209	17	in	in	ADP
ejpam-2482	209	18	r	r	NOUN
ejpam-2482	209	19	such	such	ADJ
ejpam-2482	209	20	that	that	SCONJ
ejpam-2482	209	21	i	i	PRON
ejpam-2482	209	22	jkm	jkm	PROPN
ejpam-2482	209	23	$	$	SYM
ejpam-2482	209	24	t	t	PROPN
ejpam-2482	210	1	but	but	CCONJ
ejpam-2482	210	2	i	i	PRON
ejpam-2482	210	3	jm	jm	PROPN
ejpam-2482	210	4	#	#	SYM
ejpam-2482	210	5	$	$	SYM
ejpam-2482	210	6	t	t	NOUN
ejpam-2482	210	7	,	,	PUNCT
ejpam-2482	210	8	ikm	ikm	PROPN
ejpam-2482	210	9	#	#	SYM
ejpam-2482	210	10	$	$	SYM
ejpam-2482	210	11	t	t	PROPN
ejpam-2482	210	12	and	and	CCONJ
ejpam-2482	210	13	jkm	jkm	PROPN
ejpam-2482	210	14	#	#	SYM
ejpam-2482	210	15	$	$	SYM
ejpam-2482	210	16	t	t	NOUN
ejpam-2482	210	17	.	.	PUNCT
ejpam-2482	211	1	the	the	DET
ejpam-2482	211	2	maximality	maximality	NOUN
ejpam-2482	211	3	of	of	ADP
ejpam-2482	211	4	t	t	PROPN
ejpam-2482	211	5	implies	imply	VERB
ejpam-2482	211	6	that	that	SCONJ
ejpam-2482	211	7	m/	m/	NOUN
ejpam-2482	211	8	(	(	PUNCT
ejpam-2482	211	9	t	t	NOUN
ejpam-2482	211	10	+	+	CCONJ
ejpam-2482	211	11	i	i	PROPN
ejpam-2482	211	12	jm	jm	PROPN
ejpam-2482	211	13	)	)	PUNCT
ejpam-2482	211	14	,	,	PUNCT
ejpam-2482	211	15	m/	m/	NOUN
ejpam-2482	211	16	(	(	PUNCT
ejpam-2482	212	1	t	t	NOUN
ejpam-2482	212	2	+	+	CCONJ
ejpam-2482	212	3	ikm	ikm	PROPN
ejpam-2482	212	4	)	)	PUNCT
ejpam-2482	212	5	h.	h.	PROPN
ejpam-2482	212	6	mostafanasab	mostafanasab	VERB
ejpam-2482	212	7	,	,	PUNCT
ejpam-2482	212	8	ü.	ü.	NOUN
ejpam-2482	212	9	tekir	tekir	NOUN
ejpam-2482	212	10	and	and	CCONJ
ejpam-2482	212	11	k.	k.	PROPN
ejpam-2482	212	12	hakan	hakan	PROPN
ejpam-2482	212	13	oral	oral	PROPN
ejpam-2482	212	14	/	/	SYM
ejpam-2482	212	15	eur	eur	PROPN
ejpam-2482	212	16	.	.	PUNCT
ejpam-2482	213	1	j.	j.	PROPN
ejpam-2482	213	2	pure	pure	PROPN
ejpam-2482	213	3	appl	appl	PROPN
ejpam-2482	213	4	.	.	PROPN
ejpam-2482	213	5	math	math	PROPN
ejpam-2482	213	6	,	,	PUNCT
ejpam-2482	213	7	8	8	NUM
ejpam-2482	213	8	(	(	PUNCT
ejpam-2482	213	9	2015	2015	NUM
ejpam-2482	213	10	)	)	PUNCT
ejpam-2482	213	11	,	,	PUNCT
ejpam-2482	213	12	417	417	NUM
ejpam-2482	213	13	-	-	SYM
ejpam-2482	213	14	430	430	NUM
ejpam-2482	213	15	422	422	NUM
ejpam-2482	213	16	and	and	CCONJ
ejpam-2482	213	17	m/	m/	NOUN
ejpam-2482	213	18	(	(	PUNCT
ejpam-2482	213	19	t	t	PROPN
ejpam-2482	213	20	+	+	CCONJ
ejpam-2482	213	21	jkm	jkm	X
ejpam-2482	213	22	)	)	PUNCT
ejpam-2482	213	23	have	have	VERB
ejpam-2482	213	24	only	only	ADV
ejpam-2482	213	25	finitely	finitely	ADV
ejpam-2482	213	26	many	many	ADJ
ejpam-2482	213	27	minimal	minimal	ADJ
ejpam-2482	213	28	classical	classical	ADJ
ejpam-2482	213	29	2	2	NUM
ejpam-2482	213	30	-	-	PUNCT
ejpam-2482	213	31	absorbing	absorbing	ADJ
ejpam-2482	213	32	submodules	submodule	NOUN
ejpam-2482	213	33	.	.	PUNCT
ejpam-2482	214	1	suppose	suppose	VERB
ejpam-2482	214	2	p	p	X
ejpam-2482	214	3	/	/	SYM
ejpam-2482	214	4	t	t	PROPN
ejpam-2482	214	5	be	be	AUX
ejpam-2482	214	6	a	a	DET
ejpam-2482	214	7	minimal	minimal	ADJ
ejpam-2482	214	8	classical	classical	ADJ
ejpam-2482	214	9	2	2	NUM
ejpam-2482	214	10	-	-	PUNCT
ejpam-2482	214	11	absorbing	absorb	VERB
ejpam-2482	214	12	submodule	submodule	NOUN
ejpam-2482	214	13	of	of	ADP
ejpam-2482	214	14	m	m	PROPN
ejpam-2482	214	15	/	/	SYM
ejpam-2482	214	16	t	t	PROPN
ejpam-2482	214	17	.	.	PUNCT
ejpam-2482	215	1	so	so	ADV
ejpam-2482	216	1	i	i	PRON
ejpam-2482	216	2	jkm	jkm	PROPN
ejpam-2482	216	3	$	$	SYM
ejpam-2482	216	4	t	t	PROPN
ejpam-2482	216	5	$	$	SYM
ejpam-2482	216	6	p	p	NOUN
ejpam-2482	216	7	,	,	PUNCT
ejpam-2482	216	8	which	which	PRON
ejpam-2482	216	9	implies	imply	VERB
ejpam-2482	216	10	that	that	SCONJ
ejpam-2482	216	11	i	i	PRON
ejpam-2482	216	12	jm	jm	VERB
ejpam-2482	216	13	$	$	SYM
ejpam-2482	216	14	p	p	NOUN
ejpam-2482	216	15	or	or	CCONJ
ejpam-2482	216	16	ikm	ikm	VERB
ejpam-2482	216	17	$	$	SYM
ejpam-2482	216	18	p	p	PROPN
ejpam-2482	216	19	or	or	CCONJ
ejpam-2482	216	20	jkm	jkm	PROPN
ejpam-2482	216	21	$	$	PROPN
ejpam-2482	216	22	p.	p.	NOUN
ejpam-2482	216	23	thus	thus	ADV
ejpam-2482	216	24	p/	p/	NOUN
ejpam-2482	216	25	(	(	PUNCT
ejpam-2482	216	26	t	t	PROPN
ejpam-2482	216	27	+	+	CCONJ
ejpam-2482	216	28	i	i	PROPN
ejpam-2482	216	29	jm	jm	PROPN
ejpam-2482	216	30	)	)	PUNCT
ejpam-2482	216	31	is	be	AUX
ejpam-2482	216	32	a	a	DET
ejpam-2482	216	33	minimal	minimal	ADJ
ejpam-2482	216	34	classical	classical	ADJ
ejpam-2482	216	35	2	2	NUM
ejpam-2482	216	36	-	-	PUNCT
ejpam-2482	216	37	absorbing	absorb	VERB
ejpam-2482	216	38	submodule	submodule	NOUN
ejpam-2482	216	39	of	of	ADP
ejpam-2482	216	40	m/	m/	NOUN
ejpam-2482	216	41	(	(	PUNCT
ejpam-2482	216	42	t	t	NOUN
ejpam-2482	216	43	+	+	CCONJ
ejpam-2482	216	44	i	i	PROPN
ejpam-2482	216	45	jm	jm	PROPN
ejpam-2482	216	46	)	)	PUNCT
ejpam-2482	216	47	or	or	CCONJ
ejpam-2482	216	48	p/	p/	NOUN
ejpam-2482	216	49	(	(	PUNCT
ejpam-2482	216	50	t	t	PROPN
ejpam-2482	216	51	+	+	CCONJ
ejpam-2482	216	52	ikm	ikm	PROPN
ejpam-2482	216	53	)	)	PUNCT
ejpam-2482	216	54	is	be	AUX
ejpam-2482	216	55	a	a	DET
ejpam-2482	216	56	minimal	minimal	ADJ
ejpam-2482	216	57	classical	classical	ADJ
ejpam-2482	216	58	2	2	NUM
ejpam-2482	216	59	-	-	PUNCT
ejpam-2482	216	60	absorbing	absorb	VERB
ejpam-2482	216	61	submodule	submodule	NOUN
ejpam-2482	216	62	of	of	ADP
ejpam-2482	216	63	m/	m/	NOUN
ejpam-2482	216	64	(	(	PUNCT
ejpam-2482	216	65	t	t	NOUN
ejpam-2482	216	66	+	+	CCONJ
ejpam-2482	216	67	ikm	ikm	PROPN
ejpam-2482	216	68	)	)	PUNCT
ejpam-2482	216	69	or	or	CCONJ
ejpam-2482	216	70	p/	p/	NOUN
ejpam-2482	216	71	(	(	PUNCT
ejpam-2482	216	72	t	t	PROPN
ejpam-2482	216	73	+	+	CCONJ
ejpam-2482	216	74	jkm	jkm	PROPN
ejpam-2482	216	75	)	)	PUNCT
ejpam-2482	216	76	is	be	AUX
ejpam-2482	216	77	a	a	DET
ejpam-2482	216	78	minimal	minimal	ADJ
ejpam-2482	216	79	classical	classical	ADJ
ejpam-2482	216	80	2	2	NUM
ejpam-2482	216	81	-	-	PUNCT
ejpam-2482	216	82	absorbing	absorb	VERB
ejpam-2482	216	83	submodule	submodule	NOUN
ejpam-2482	216	84	of	of	ADP
ejpam-2482	216	85	m/	m/	NOUN
ejpam-2482	216	86	(	(	PUNCT
ejpam-2482	216	87	t	t	PROPN
ejpam-2482	216	88	+	+	CCONJ
ejpam-2482	216	89	jkm	jkm	PROPN
ejpam-2482	216	90	)	)	PUNCT
ejpam-2482	216	91	.	.	PUNCT
ejpam-2482	217	1	thus	thus	ADV
ejpam-2482	217	2	,	,	PUNCT
ejpam-2482	217	3	there	there	PRON
ejpam-2482	217	4	are	be	VERB
ejpam-2482	217	5	only	only	ADV
ejpam-2482	217	6	a	a	DET
ejpam-2482	217	7	finite	finite	ADJ
ejpam-2482	217	8	number	number	NOUN
ejpam-2482	217	9	of	of	ADP
ejpam-2482	217	10	possibilities	possibility	NOUN
ejpam-2482	217	11	for	for	ADP
ejpam-2482	217	12	the	the	DET
ejpam-2482	217	13	submodule	submodule	PROPN
ejpam-2482	217	14	p.	p.	NOUN
ejpam-2482	217	15	this	this	PRON
ejpam-2482	217	16	is	be	AUX
ejpam-2482	217	17	a	a	DET
ejpam-2482	217	18	contradiction	contradiction	NOUN
ejpam-2482	217	19	.	.	PUNCT
ejpam-2482	218	1	we	we	PRON
ejpam-2482	218	2	recall	recall	VERB
ejpam-2482	218	3	from	from	ADP
ejpam-2482	218	4	[	[	X
ejpam-2482	218	5	5	5	NUM
ejpam-2482	218	6	]	]	PUNCT
ejpam-2482	218	7	that	that	SCONJ
ejpam-2482	218	8	if	if	SCONJ
ejpam-2482	218	9	i	i	PRON
ejpam-2482	218	10	is	be	AUX
ejpam-2482	218	11	a	a	DET
ejpam-2482	218	12	2	2	NUM
ejpam-2482	218	13	-	-	PUNCT
ejpam-2482	218	14	absorbing	absorbing	ADJ
ejpam-2482	218	15	ideal	ideal	NOUN
ejpam-2482	218	16	of	of	ADP
ejpam-2482	218	17	a	a	DET
ejpam-2482	218	18	ring	ring	NOUN
ejpam-2482	218	19	r	r	NOUN
ejpam-2482	218	20	,	,	PUNCT
ejpam-2482	218	21	then	then	ADV
ejpam-2482	218	22	either	either	CCONJ
ejpam-2482	218	23	i	i	PRON
ejpam-2482	218	24	=	=	NOUN
ejpam-2482	218	25	p	p	X
ejpam-2482	218	26	where	where	SCONJ
ejpam-2482	218	27	p	p	NOUN
ejpam-2482	218	28	is	be	AUX
ejpam-2482	218	29	a	a	DET
ejpam-2482	218	30	prime	prime	ADJ
ejpam-2482	218	31	ideal	ideal	NOUN
ejpam-2482	218	32	of	of	ADP
ejpam-2482	218	33	r	r	NOUN
ejpam-2482	218	34	or	or	CCONJ
ejpam-2482	218	35	i	i	NOUN
ejpam-2482	218	36	=	=	SYM
ejpam-2482	218	37	p1	p1	PROPN
ejpam-2482	218	38	*	*	PUNCT
ejpam-2482	218	39	p2	p2	PROPN
ejpam-2482	218	40	where	where	SCONJ
ejpam-2482	218	41	p1	p1	NOUN
ejpam-2482	218	42	,	,	PUNCT
ejpam-2482	218	43	p2	p2	PROPN
ejpam-2482	218	44	are	be	AUX
ejpam-2482	218	45	the	the	DET
ejpam-2482	218	46	only	only	ADJ
ejpam-2482	218	47	distinct	distinct	ADJ
ejpam-2482	218	48	minimal	minimal	ADJ
ejpam-2482	218	49	prime	prime	ADJ
ejpam-2482	218	50	ideals	ideal	NOUN
ejpam-2482	218	51	of	of	ADP
ejpam-2482	218	52	i	i	PRON
ejpam-2482	218	53	.	.	PUNCT
ejpam-2482	219	1	corollary	corollary	ADJ
ejpam-2482	219	2	3	3	X
ejpam-2482	219	3	.	.	PUNCT
ejpam-2482	220	1	let	let	AUX
ejpam-2482	220	2	n	n	PRON
ejpam-2482	220	3	be	be	AUX
ejpam-2482	220	4	a	a	DET
ejpam-2482	220	5	classical	classical	ADJ
ejpam-2482	220	6	2	2	NUM
ejpam-2482	220	7	-	-	PUNCT
ejpam-2482	220	8	absorbing	absorb	VERB
ejpam-2482	220	9	submodule	submodule	NOUN
ejpam-2482	220	10	of	of	ADP
ejpam-2482	220	11	an	an	DET
ejpam-2482	220	12	r	r	NOUN
ejpam-2482	220	13	-	-	PUNCT
ejpam-2482	220	14	module	module	NOUN
ejpam-2482	220	15	m.	m.	NOUN
ejpam-2482	220	16	suppose	suppose	VERB
ejpam-2482	220	17	that	that	SCONJ
ejpam-2482	220	18	m	m	VERB
ejpam-2482	220	19	"	"	PUNCT
ejpam-2482	220	20	m\n	m\n	NOUN
ejpam-2482	220	21	and	and	CCONJ
ejpam-2482	220	22	*	*	PUNCT
ejpam-2482	220	23	(	(	PUNCT
ejpam-2482	220	24	n	n	X
ejpam-2482	220	25	:	:	PUNCT
ejpam-2482	220	26	r	r	NOUN
ejpam-2482	220	27	m	m	NOUN
ejpam-2482	220	28	)	)	PUNCT
ejpam-2482	221	1	=	=	PUNCT
ejpam-2482	222	1	p	p	NOUN
ejpam-2482	222	2	where	where	SCONJ
ejpam-2482	222	3	p	p	NOUN
ejpam-2482	222	4	is	be	AUX
ejpam-2482	222	5	a	a	DET
ejpam-2482	222	6	prime	prime	ADJ
ejpam-2482	222	7	ideal	ideal	NOUN
ejpam-2482	222	8	of	of	ADP
ejpam-2482	222	9	r	r	NOUN
ejpam-2482	222	10	and	and	CCONJ
ejpam-2482	222	11	(	(	PUNCT
ejpam-2482	222	12	n	n	X
ejpam-2482	222	13	:	:	PUNCT
ejpam-2482	222	14	r	r	NOUN
ejpam-2482	222	15	m	m	NOUN
ejpam-2482	222	16	)	)	PUNCT
ejpam-2482	223	1	#	#	NOUN
ejpam-2482	223	2	=	=	SYM
ejpam-2482	223	3	p.	p.	NOUN
ejpam-2482	223	4	then	then	ADV
ejpam-2482	223	5	for	for	ADP
ejpam-2482	223	6	each	each	PRON
ejpam-2482	223	7	x	x	PUNCT
ejpam-2482	223	8	"	"	PUNCT
ejpam-2482	223	9	*	*	PUNCT
ejpam-2482	223	10	(	(	PUNCT
ejpam-2482	223	11	n	n	X
ejpam-2482	223	12	:	:	PUNCT
ejpam-2482	223	13	r	r	NOUN
ejpam-2482	223	14	m)\(n	m)\(n	NOUN
ejpam-2482	223	15	:	:	PUNCT
ejpam-2482	223	16	r	r	NOUN
ejpam-2482	223	17	m	m	PROPN
ejpam-2482	223	18	)	)	PUNCT
ejpam-2482	223	19	,	,	PUNCT
ejpam-2482	223	20	(	(	PUNCT
ejpam-2482	223	21	n	n	X
ejpam-2482	223	22	:	:	PUNCT
ejpam-2482	223	23	r	r	NOUN
ejpam-2482	223	24	xm	xm	PROPN
ejpam-2482	223	25	)	)	PUNCT
ejpam-2482	223	26	is	be	AUX
ejpam-2482	223	27	a	a	DET
ejpam-2482	223	28	prime	prime	ADJ
ejpam-2482	223	29	ideal	ideal	NOUN
ejpam-2482	223	30	of	of	ADP
ejpam-2482	223	31	r	r	NOUN
ejpam-2482	223	32	containing	contain	VERB
ejpam-2482	223	33	p.	p.	NOUN
ejpam-2482	223	34	furthermore	furthermore	ADV
ejpam-2482	223	35	,	,	PUNCT
ejpam-2482	223	36	either	either	CCONJ
ejpam-2482	223	37	(	(	PUNCT
ejpam-2482	223	38	n	n	X
ejpam-2482	223	39	:	:	PUNCT
ejpam-2482	223	40	r	r	NOUN
ejpam-2482	223	41	xm	xm	PROPN
ejpam-2482	223	42	)	)	PUNCT
ejpam-2482	223	43	$	$	SYM
ejpam-2482	223	44	(	(	PUNCT
ejpam-2482	223	45	n	n	NUM
ejpam-2482	223	46	:	:	PUNCT
ejpam-2482	223	47	r	r	NOUN
ejpam-2482	223	48	ym	ym	PROPN
ejpam-2482	223	49	)	)	PUNCT
ejpam-2482	223	50	or	or	CCONJ
ejpam-2482	223	51	(	(	PUNCT
ejpam-2482	223	52	n	n	X
ejpam-2482	223	53	:	:	PUNCT
ejpam-2482	223	54	r	r	NOUN
ejpam-2482	223	55	ym	ym	PROPN
ejpam-2482	223	56	)	)	PUNCT
ejpam-2482	223	57	$	$	SYM
ejpam-2482	223	58	(	(	PUNCT
ejpam-2482	223	59	n	n	NUM
ejpam-2482	223	60	:	:	PUNCT
ejpam-2482	223	61	r	r	NOUN
ejpam-2482	223	62	xm	xm	PROPN
ejpam-2482	223	63	)	)	PUNCT
ejpam-2482	223	64	for	for	ADP
ejpam-2482	223	65	every	every	DET
ejpam-2482	223	66	x	x	SYM
ejpam-2482	223	67	,	,	PUNCT
ejpam-2482	223	68	y	y	PROPN
ejpam-2482	223	69	"	"	PUNCT
ejpam-2482	223	70	*	*	PUNCT
ejpam-2482	223	71	(	(	PUNCT
ejpam-2482	223	72	n	n	X
ejpam-2482	223	73	:	:	PUNCT
ejpam-2482	223	74	r	r	NOUN
ejpam-2482	223	75	m)\(n	m)\(n	NOUN
ejpam-2482	223	76	:	:	PUNCT
ejpam-2482	223	77	r	r	NOUN
ejpam-2482	223	78	m	m	PROPN
ejpam-2482	223	79	)	)	PUNCT
ejpam-2482	223	80	.	.	PUNCT
ejpam-2482	224	1	proof	proof	NOUN
ejpam-2482	224	2	.	.	PUNCT
ejpam-2482	225	1	by	by	ADP
ejpam-2482	225	2	theorem	theorem	NOUN
ejpam-2482	225	3	2	2	NUM
ejpam-2482	225	4	and	and	CCONJ
ejpam-2482	225	5	[	[	X
ejpam-2482	225	6	5	5	NUM
ejpam-2482	225	7	,	,	PUNCT
ejpam-2482	225	8	theorem	theorem	VERB
ejpam-2482	225	9	2.5	2.5	NUM
ejpam-2482	225	10	]	]	PUNCT
ejpam-2482	225	11	.	.	PUNCT
ejpam-2482	226	1	corollary	corollary	ADJ
ejpam-2482	226	2	4	4	NUM
ejpam-2482	226	3	.	.	PUNCT
ejpam-2482	227	1	let	let	AUX
ejpam-2482	227	2	n	n	PRON
ejpam-2482	227	3	be	be	AUX
ejpam-2482	227	4	a	a	DET
ejpam-2482	227	5	classical	classical	ADJ
ejpam-2482	227	6	2	2	NUM
ejpam-2482	227	7	-	-	PUNCT
ejpam-2482	227	8	absorbing	absorb	VERB
ejpam-2482	227	9	submodule	submodule	NOUN
ejpam-2482	227	10	of	of	ADP
ejpam-2482	227	11	an	an	DET
ejpam-2482	227	12	r	r	NOUN
ejpam-2482	227	13	-	-	PUNCT
ejpam-2482	227	14	module	module	NOUN
ejpam-2482	227	15	m.	m.	NOUN
ejpam-2482	227	16	suppose	suppose	VERB
ejpam-2482	227	17	that	that	SCONJ
ejpam-2482	227	18	m	m	VERB
ejpam-2482	227	19	"	"	PUNCT
ejpam-2482	227	20	m\n	m\n	NOUN
ejpam-2482	227	21	and	and	CCONJ
ejpam-2482	227	22	*	*	PUNCT
ejpam-2482	227	23	(	(	PUNCT
ejpam-2482	227	24	n	n	X
ejpam-2482	227	25	:	:	PUNCT
ejpam-2482	227	26	r	r	NOUN
ejpam-2482	227	27	m	m	NOUN
ejpam-2482	227	28	)	)	PUNCT
ejpam-2482	227	29	=	=	SYM
ejpam-2482	227	30	p1	p1	NOUN
ejpam-2482	227	31	*	*	PUNCT
ejpam-2482	227	32	p2	p2	PROPN
ejpam-2482	227	33	where	where	SCONJ
ejpam-2482	227	34	p1	p1	NOUN
ejpam-2482	227	35	and	and	CCONJ
ejpam-2482	227	36	p2	p2	PROPN
ejpam-2482	227	37	are	be	AUX
ejpam-2482	227	38	the	the	DET
ejpam-2482	227	39	only	only	ADJ
ejpam-2482	227	40	nonzero	nonzero	X
ejpam-2482	227	41	distinct	distinct	ADJ
ejpam-2482	227	42	prime	prime	ADJ
ejpam-2482	227	43	ideals	ideal	NOUN
ejpam-2482	227	44	of	of	ADP
ejpam-2482	227	45	r	r	NOUN
ejpam-2482	227	46	that	that	PRON
ejpam-2482	227	47	are	be	AUX
ejpam-2482	227	48	minimal	minimal	ADJ
ejpam-2482	227	49	over	over	ADP
ejpam-2482	227	50	(	(	PUNCT
ejpam-2482	227	51	n	n	X
ejpam-2482	227	52	:	:	PUNCT
ejpam-2482	227	53	r	r	NOUN
ejpam-2482	227	54	m	m	PROPN
ejpam-2482	227	55	)	)	PUNCT
ejpam-2482	227	56	.	.	PUNCT
ejpam-2482	228	1	then	then	ADV
ejpam-2482	228	2	for	for	ADP
ejpam-2482	228	3	each	each	PRON
ejpam-2482	228	4	x	x	PUNCT
ejpam-2482	228	5	"	"	PUNCT
ejpam-2482	228	6	*	*	PUNCT
ejpam-2482	228	7	(	(	PUNCT
ejpam-2482	228	8	n	n	X
ejpam-2482	228	9	:	:	PUNCT
ejpam-2482	228	10	r	r	NOUN
ejpam-2482	228	11	m)\(n	m)\(n	NOUN
ejpam-2482	228	12	:	:	PUNCT
ejpam-2482	228	13	r	r	NOUN
ejpam-2482	228	14	m	m	PROPN
ejpam-2482	228	15	)	)	PUNCT
ejpam-2482	228	16	,	,	PUNCT
ejpam-2482	228	17	(	(	PUNCT
ejpam-2482	228	18	n	n	X
ejpam-2482	228	19	:	:	PUNCT
ejpam-2482	228	20	r	r	NOUN
ejpam-2482	228	21	xm	xm	PROPN
ejpam-2482	228	22	)	)	PUNCT
ejpam-2482	228	23	is	be	AUX
ejpam-2482	228	24	a	a	DET
ejpam-2482	228	25	prime	prime	ADJ
ejpam-2482	228	26	ideal	ideal	NOUN
ejpam-2482	228	27	of	of	ADP
ejpam-2482	228	28	r	r	NOUN
ejpam-2482	228	29	containing	contain	VERB
ejpam-2482	228	30	p1	p1	NOUN
ejpam-2482	228	31	and	and	CCONJ
ejpam-2482	228	32	p2	p2	NOUN
ejpam-2482	228	33	.	.	PUNCT
ejpam-2482	229	1	furthermore	furthermore	ADV
ejpam-2482	229	2	,	,	PUNCT
ejpam-2482	229	3	either	either	CCONJ
ejpam-2482	229	4	(	(	PUNCT
ejpam-2482	229	5	n	n	X
ejpam-2482	229	6	:	:	PUNCT
ejpam-2482	229	7	r	r	NOUN
ejpam-2482	229	8	xm	xm	PROPN
ejpam-2482	229	9	)	)	PUNCT
ejpam-2482	229	10	$	$	SYM
ejpam-2482	229	11	(	(	PUNCT
ejpam-2482	229	12	n	n	NUM
ejpam-2482	229	13	:	:	PUNCT
ejpam-2482	229	14	r	r	NOUN
ejpam-2482	229	15	ym	ym	PROPN
ejpam-2482	229	16	)	)	PUNCT
ejpam-2482	229	17	or	or	CCONJ
ejpam-2482	229	18	(	(	PUNCT
ejpam-2482	229	19	n	n	X
ejpam-2482	229	20	:	:	PUNCT
ejpam-2482	229	21	r	r	NOUN
ejpam-2482	229	22	ym	ym	PROPN
ejpam-2482	229	23	)	)	PUNCT
ejpam-2482	229	24	$	$	SYM
ejpam-2482	229	25	(	(	PUNCT
ejpam-2482	229	26	n	n	NUM
ejpam-2482	229	27	:	:	PUNCT
ejpam-2482	229	28	r	r	NOUN
ejpam-2482	229	29	xm	xm	PROPN
ejpam-2482	229	30	)	)	PUNCT
ejpam-2482	229	31	for	for	ADP
ejpam-2482	229	32	every	every	DET
ejpam-2482	229	33	x	x	SYM
ejpam-2482	229	34	,	,	PUNCT
ejpam-2482	229	35	y	y	PROPN
ejpam-2482	229	36	"	"	PUNCT
ejpam-2482	229	37	*	*	PUNCT
ejpam-2482	229	38	(	(	PUNCT
ejpam-2482	229	39	n	n	X
ejpam-2482	229	40	:	:	PUNCT
ejpam-2482	229	41	r	r	NOUN
ejpam-2482	229	42	m)\(n	m)\(n	NOUN
ejpam-2482	229	43	:	:	PUNCT
ejpam-2482	229	44	r	r	NOUN
ejpam-2482	229	45	m	m	PROPN
ejpam-2482	229	46	)	)	PUNCT
ejpam-2482	229	47	.	.	PUNCT
ejpam-2482	230	1	proof	proof	NOUN
ejpam-2482	230	2	.	.	PUNCT
ejpam-2482	231	1	by	by	ADP
ejpam-2482	231	2	theorem	theorem	NOUN
ejpam-2482	231	3	2	2	NUM
ejpam-2482	231	4	and	and	CCONJ
ejpam-2482	231	5	[	[	X
ejpam-2482	231	6	5	5	NUM
ejpam-2482	231	7	,	,	PUNCT
ejpam-2482	231	8	theorem	theorem	VERB
ejpam-2482	231	9	2.6	2.6	NUM
ejpam-2482	231	10	]	]	PUNCT
ejpam-2482	231	11	.	.	PUNCT
ejpam-2482	232	1	an	an	DET
ejpam-2482	232	2	r	r	NOUN
ejpam-2482	232	3	-	-	PUNCT
ejpam-2482	232	4	module	module	NOUN
ejpam-2482	232	5	m	m	NOUN
ejpam-2482	232	6	is	be	AUX
ejpam-2482	232	7	called	call	VERB
ejpam-2482	232	8	a	a	DET
ejpam-2482	232	9	multiplication	multiplication	NOUN
ejpam-2482	232	10	module	module	NOUN
ejpam-2482	232	11	if	if	SCONJ
ejpam-2482	232	12	every	every	DET
ejpam-2482	232	13	submodule	submodule	NOUN
ejpam-2482	232	14	n	n	PROPN
ejpam-2482	232	15	of	of	ADP
ejpam-2482	232	16	m	m	PROPN
ejpam-2482	232	17	has	have	VERB
ejpam-2482	232	18	the	the	DET
ejpam-2482	232	19	form	form	NOUN
ejpam-2482	232	20	i	i	PRON
ejpam-2482	232	21	m	m	VERB
ejpam-2482	232	22	for	for	ADP
ejpam-2482	232	23	some	some	DET
ejpam-2482	232	24	ideal	ideal	NOUN
ejpam-2482	232	25	i	i	PRON
ejpam-2482	232	26	of	of	ADP
ejpam-2482	232	27	r.	r.	PROPN
ejpam-2482	232	28	let	let	VERB
ejpam-2482	232	29	n	n	PROPN
ejpam-2482	232	30	and	and	CCONJ
ejpam-2482	232	31	k	k	PROPN
ejpam-2482	232	32	be	be	AUX
ejpam-2482	232	33	submodules	submodule	NOUN
ejpam-2482	232	34	of	of	ADP
ejpam-2482	232	35	a	a	DET
ejpam-2482	232	36	multiplication	multiplication	NOUN
ejpam-2482	232	37	r	r	NOUN
ejpam-2482	232	38	-	-	PUNCT
ejpam-2482	232	39	module	module	NOUN
ejpam-2482	232	40	m	m	NOUN
ejpam-2482	232	41	with	with	ADP
ejpam-2482	232	42	n	n	PROPN
ejpam-2482	232	43	=	=	PROPN
ejpam-2482	232	44	i1	i1	PROPN
ejpam-2482	232	45	m	m	PROPN
ejpam-2482	232	46	and	and	CCONJ
ejpam-2482	232	47	k	k	PROPN
ejpam-2482	232	48	=	=	PROPN
ejpam-2482	232	49	i2	i2	PROPN
ejpam-2482	232	50	m	m	PROPN
ejpam-2482	232	51	for	for	ADP
ejpam-2482	232	52	some	some	DET
ejpam-2482	232	53	ideals	ideal	NOUN
ejpam-2482	232	54	i1	i1	PROPN
ejpam-2482	232	55	and	and	CCONJ
ejpam-2482	232	56	i2	i2	PROPN
ejpam-2482	232	57	of	of	ADP
ejpam-2482	232	58	r.	r.	PROPN
ejpam-2482	232	59	the	the	DET
ejpam-2482	232	60	product	product	NOUN
ejpam-2482	232	61	of	of	ADP
ejpam-2482	232	62	n	n	PROPN
ejpam-2482	232	63	and	and	CCONJ
ejpam-2482	232	64	k	k	PROPN
ejpam-2482	232	65	denoted	denote	VERB
ejpam-2482	232	66	by	by	ADP
ejpam-2482	232	67	nk	nk	PROPN
ejpam-2482	232	68	is	be	AUX
ejpam-2482	232	69	defined	define	VERB
ejpam-2482	232	70	by	by	ADP
ejpam-2482	232	71	nk	nk	PROPN
ejpam-2482	232	72	=	=	PROPN
ejpam-2482	232	73	i1	i1	PROPN
ejpam-2482	232	74	i2	i2	PROPN
ejpam-2482	232	75	m	m	PROPN
ejpam-2482	232	76	.	.	PUNCT
ejpam-2482	233	1	then	then	ADV
ejpam-2482	233	2	by	by	ADP
ejpam-2482	233	3	[	[	X
ejpam-2482	233	4	1	1	NUM
ejpam-2482	233	5	,	,	PUNCT
ejpam-2482	233	6	theorem	theorem	VERB
ejpam-2482	233	7	3.4	3.4	NUM
ejpam-2482	233	8	]	]	PUNCT
ejpam-2482	233	9	,	,	PUNCT
ejpam-2482	233	10	the	the	DET
ejpam-2482	233	11	product	product	NOUN
ejpam-2482	233	12	of	of	ADP
ejpam-2482	233	13	n	n	PROPN
ejpam-2482	233	14	and	and	CCONJ
ejpam-2482	233	15	k	k	PROPN
ejpam-2482	233	16	is	be	AUX
ejpam-2482	233	17	independent	independent	ADJ
ejpam-2482	233	18	of	of	ADP
ejpam-2482	233	19	presentations	presentation	NOUN
ejpam-2482	233	20	of	of	ADP
ejpam-2482	233	21	n	n	PRON
ejpam-2482	233	22	and	and	CCONJ
ejpam-2482	233	23	k	k	PROPN
ejpam-2482	233	24	.	.	PUNCT
ejpam-2482	234	1	proposition	proposition	NOUN
ejpam-2482	234	2	4	4	NUM
ejpam-2482	234	3	.	.	PUNCT
ejpam-2482	235	1	let	let	VERB
ejpam-2482	235	2	m	m	PRON
ejpam-2482	235	3	be	be	AUX
ejpam-2482	235	4	a	a	DET
ejpam-2482	235	5	multiplication	multiplication	NOUN
ejpam-2482	235	6	r	r	NOUN
ejpam-2482	235	7	-	-	PUNCT
ejpam-2482	235	8	module	module	NOUN
ejpam-2482	235	9	and	and	CCONJ
ejpam-2482	235	10	n	n	CCONJ
ejpam-2482	235	11	be	be	VERB
ejpam-2482	235	12	a	a	DET
ejpam-2482	235	13	proper	proper	ADJ
ejpam-2482	235	14	submodule	submodule	NOUN
ejpam-2482	235	15	of	of	ADP
ejpam-2482	235	16	m.	m.	NOUN
ejpam-2482	235	17	the	the	DET
ejpam-2482	235	18	following	follow	VERB
ejpam-2482	235	19	conditions	condition	NOUN
ejpam-2482	235	20	are	be	AUX
ejpam-2482	235	21	equivalent	equivalent	ADJ
ejpam-2482	235	22	:	:	PUNCT
ejpam-2482	235	23	(	(	PUNCT
ejpam-2482	235	24	i	i	NOUN
ejpam-2482	235	25	)	)	PUNCT
ejpam-2482	235	26	n	n	PRON
ejpam-2482	235	27	is	be	AUX
ejpam-2482	235	28	a	a	DET
ejpam-2482	235	29	classical	classical	ADJ
ejpam-2482	235	30	2	2	NUM
ejpam-2482	235	31	-	-	PUNCT
ejpam-2482	235	32	absorbing	absorb	VERB
ejpam-2482	235	33	submodule	submodule	NOUN
ejpam-2482	235	34	of	of	ADP
ejpam-2482	235	35	m	m	PROPN
ejpam-2482	235	36	;	;	PUNCT
ejpam-2482	235	37	(	(	PUNCT
ejpam-2482	235	38	ii	ii	NOUN
ejpam-2482	235	39	)	)	PUNCT
ejpam-2482	235	40	if	if	SCONJ
ejpam-2482	235	41	n1n2n3	n1n2n3	NOUN
ejpam-2482	235	42	m	m	VERB
ejpam-2482	235	43	$	$	SYM
ejpam-2482	235	44	n	n	NUM
ejpam-2482	235	45	for	for	ADP
ejpam-2482	235	46	some	some	DET
ejpam-2482	235	47	submodules	submodule	NOUN
ejpam-2482	235	48	n1	n1	NOUN
ejpam-2482	235	49	,	,	PUNCT
ejpam-2482	235	50	n2	n2	NOUN
ejpam-2482	235	51	,	,	PUNCT
ejpam-2482	235	52	n3	n3	NOUN
ejpam-2482	235	53	of	of	ADP
ejpam-2482	235	54	m	m	PROPN
ejpam-2482	235	55	and	and	CCONJ
ejpam-2482	235	56	m	m	PRON
ejpam-2482	235	57	"	"	PUNCT
ejpam-2482	235	58	m	m	PROPN
ejpam-2482	235	59	,	,	PUNCT
ejpam-2482	235	60	then	then	ADV
ejpam-2482	235	61	either	either	CCONJ
ejpam-2482	235	62	n1n2	n1n2	NOUN
ejpam-2482	235	63	m	m	VERB
ejpam-2482	235	64	$	$	SYM
ejpam-2482	235	65	n	n	ADJ
ejpam-2482	235	66	or	or	CCONJ
ejpam-2482	235	67	n1n3	n1n3	NOUN
ejpam-2482	235	68	m	m	VERB
ejpam-2482	235	69	$	$	SYM
ejpam-2482	235	70	n	n	NOUN
ejpam-2482	235	71	or	or	CCONJ
ejpam-2482	235	72	n2n3	n2n3	ADP
ejpam-2482	235	73	m	m	VERB
ejpam-2482	235	74	$	$	NOUN
ejpam-2482	235	75	n.	n.	NOUN
ejpam-2482	235	76	proof	proof	NOUN
ejpam-2482	235	77	.	.	PUNCT
ejpam-2482	236	1	(	(	PUNCT
ejpam-2482	236	2	i	i	NOUN
ejpam-2482	236	3	)	)	PUNCT
ejpam-2482	237	1	+	+	CCONJ
ejpam-2482	237	2	(	(	PUNCT
ejpam-2482	237	3	ii	ii	NOUN
ejpam-2482	237	4	)	)	PUNCT
ejpam-2482	237	5	let	let	VERB
ejpam-2482	237	6	n1n2n3	n1n2n3	PROPN
ejpam-2482	237	7	m	m	VERB
ejpam-2482	237	8	$	$	SYM
ejpam-2482	237	9	n	n	NOUN
ejpam-2482	237	10	for	for	ADP
ejpam-2482	237	11	some	some	DET
ejpam-2482	237	12	submodules	submodule	NOUN
ejpam-2482	237	13	n1	n1	NOUN
ejpam-2482	237	14	,	,	PUNCT
ejpam-2482	237	15	n2	n2	NOUN
ejpam-2482	237	16	,	,	PUNCT
ejpam-2482	237	17	n3	n3	NOUN
ejpam-2482	237	18	of	of	ADP
ejpam-2482	237	19	m	m	PROPN
ejpam-2482	237	20	and	and	CCONJ
ejpam-2482	237	21	m	m	PRON
ejpam-2482	237	22	"	"	PUNCT
ejpam-2482	237	23	m	m	VERB
ejpam-2482	237	24	.	.	PUNCT
ejpam-2482	238	1	since	since	SCONJ
ejpam-2482	238	2	m	m	PROPN
ejpam-2482	238	3	is	be	AUX
ejpam-2482	238	4	multiplication	multiplication	NOUN
ejpam-2482	238	5	,	,	PUNCT
ejpam-2482	238	6	there	there	PRON
ejpam-2482	238	7	are	be	VERB
ejpam-2482	238	8	ideals	ideal	NOUN
ejpam-2482	238	9	i1	i1	PROPN
ejpam-2482	238	10	,	,	PUNCT
ejpam-2482	238	11	i2	i2	PROPN
ejpam-2482	238	12	,	,	PUNCT
ejpam-2482	238	13	i3	i3	NOUN
ejpam-2482	238	14	of	of	ADP
ejpam-2482	238	15	r	r	NOUN
ejpam-2482	238	16	such	such	ADJ
ejpam-2482	238	17	that	that	DET
ejpam-2482	238	18	n1	n1	PROPN
ejpam-2482	238	19	=	=	PROPN
ejpam-2482	238	20	i1	i1	PROPN
ejpam-2482	238	21	m	m	PROPN
ejpam-2482	238	22	,	,	PUNCT
ejpam-2482	238	23	n2	n2	PROPN
ejpam-2482	238	24	=	=	PROPN
ejpam-2482	238	25	i2	i2	PROPN
ejpam-2482	238	26	m	m	PROPN
ejpam-2482	238	27	and	and	CCONJ
ejpam-2482	238	28	n3	n3	NOUN
ejpam-2482	238	29	=	=	SYM
ejpam-2482	238	30	i3	i3	PROPN
ejpam-2482	238	31	m	m	PROPN
ejpam-2482	238	32	.	.	PUNCT
ejpam-2482	239	1	therefore	therefore	ADV
ejpam-2482	239	2	i1	i1	PROPN
ejpam-2482	239	3	i2	i2	PROPN
ejpam-2482	239	4	i3	i3	PROPN
ejpam-2482	239	5	m	m	VERB
ejpam-2482	239	6	$	$	SYM
ejpam-2482	239	7	n	n	NOUN
ejpam-2482	239	8	,	,	PUNCT
ejpam-2482	239	9	and	and	CCONJ
ejpam-2482	239	10	so	so	ADV
ejpam-2482	239	11	either	either	CCONJ
ejpam-2482	239	12	i1	i1	PROPN
ejpam-2482	239	13	i2	i2	PROPN
ejpam-2482	239	14	m	m	PROPN
ejpam-2482	239	15	$	$	SYM
ejpam-2482	239	16	n	n	NOUN
ejpam-2482	239	17	or	or	CCONJ
ejpam-2482	239	18	i1	i1	PROPN
ejpam-2482	239	19	i3	i3	PROPN
ejpam-2482	239	20	m	m	VERB
ejpam-2482	239	21	$	$	SYM
ejpam-2482	239	22	n	n	NUM
ejpam-2482	239	23	or	or	CCONJ
ejpam-2482	239	24	i2	i2	PROPN
ejpam-2482	239	25	i3	i3	PROPN
ejpam-2482	239	26	m	m	PROPN
ejpam-2482	239	27	$	$	SYM
ejpam-2482	239	28	n	n	NUM
ejpam-2482	239	29	.	.	PUNCT
ejpam-2482	240	1	hence	hence	ADV
ejpam-2482	240	2	n1n2	n1n2	VERB
ejpam-2482	240	3	m	m	VERB
ejpam-2482	240	4	$	$	SYM
ejpam-2482	240	5	n	n	ADJ
ejpam-2482	240	6	or	or	CCONJ
ejpam-2482	240	7	n1n3	n1n3	NOUN
ejpam-2482	240	8	m	m	VERB
ejpam-2482	240	9	$	$	SYM
ejpam-2482	240	10	n	n	NOUN
ejpam-2482	240	11	or	or	CCONJ
ejpam-2482	240	12	n2n3	n2n3	ADP
ejpam-2482	240	13	m	m	PROPN
ejpam-2482	240	14	$	$	SYM
ejpam-2482	240	15	n	n	NOUN
ejpam-2482	240	16	.	.	PUNCT
ejpam-2482	241	1	(	(	PUNCT
ejpam-2482	241	2	ii	ii	NOUN
ejpam-2482	241	3	)	)	PUNCT
ejpam-2482	242	1	+	+	CCONJ
ejpam-2482	242	2	(	(	PUNCT
ejpam-2482	242	3	i	i	NOUN
ejpam-2482	242	4	)	)	PUNCT
ejpam-2482	242	5	suppose	suppose	VERB
ejpam-2482	242	6	that	that	SCONJ
ejpam-2482	242	7	i1	i1	PROPN
ejpam-2482	242	8	i2	i2	PROPN
ejpam-2482	242	9	i3	i3	PROPN
ejpam-2482	242	10	m	m	PROPN
ejpam-2482	242	11	$	$	SYM
ejpam-2482	242	12	n	n	NUM
ejpam-2482	242	13	for	for	ADP
ejpam-2482	242	14	some	some	DET
ejpam-2482	242	15	ideals	ideal	NOUN
ejpam-2482	242	16	i1	i1	PROPN
ejpam-2482	242	17	,	,	PUNCT
ejpam-2482	242	18	i2	i2	PROPN
ejpam-2482	242	19	,	,	PUNCT
ejpam-2482	242	20	i3	i3	NOUN
ejpam-2482	242	21	of	of	ADP
ejpam-2482	242	22	r	r	NOUN
ejpam-2482	242	23	and	and	CCONJ
ejpam-2482	242	24	some	some	DET
ejpam-2482	242	25	m	m	VERB
ejpam-2482	242	26	"	"	PUNCT
ejpam-2482	242	27	m	m	VERB
ejpam-2482	242	28	.	.	PUNCT
ejpam-2482	243	1	it	it	PRON
ejpam-2482	243	2	is	be	AUX
ejpam-2482	243	3	sufficient	sufficient	ADJ
ejpam-2482	243	4	to	to	PART
ejpam-2482	243	5	set	set	VERB
ejpam-2482	243	6	n1	n1	PROPN
ejpam-2482	243	7	:	:	PUNCT
ejpam-2482	243	8	=	=	SYM
ejpam-2482	243	9	i1	i1	PROPN
ejpam-2482	243	10	m	m	PROPN
ejpam-2482	243	11	,	,	PUNCT
ejpam-2482	243	12	n2	n2	ADJ
ejpam-2482	243	13	:	:	PUNCT
ejpam-2482	243	14	=	=	SYM
ejpam-2482	243	15	i2	i2	PROPN
ejpam-2482	243	16	m	m	PROPN
ejpam-2482	243	17	and	and	CCONJ
ejpam-2482	243	18	n3	n3	NOUN
ejpam-2482	243	19	=	=	SYM
ejpam-2482	243	20	i3	i3	PROPN
ejpam-2482	243	21	m	m	PROPN
ejpam-2482	243	22	in	in	ADP
ejpam-2482	243	23	part	part	NOUN
ejpam-2482	243	24	(	(	PUNCT
ejpam-2482	243	25	ii	ii	NOUN
ejpam-2482	243	26	)	)	PUNCT
ejpam-2482	243	27	.	.	PUNCT
ejpam-2482	244	1	h.	h.	PROPN
ejpam-2482	244	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	244	3	,	,	PUNCT
ejpam-2482	244	4	ü.	ü.	NOUN
ejpam-2482	244	5	tekir	tekir	NOUN
ejpam-2482	244	6	and	and	CCONJ
ejpam-2482	244	7	k.	k.	PROPN
ejpam-2482	244	8	hakan	hakan	PROPN
ejpam-2482	244	9	oral	oral	PROPN
ejpam-2482	244	10	/	/	SYM
ejpam-2482	244	11	eur	eur	PROPN
ejpam-2482	244	12	.	.	PUNCT
ejpam-2482	245	1	j.	j.	PROPN
ejpam-2482	245	2	pure	pure	PROPN
ejpam-2482	245	3	appl	appl	PROPN
ejpam-2482	245	4	.	.	PROPN
ejpam-2482	245	5	math	math	PROPN
ejpam-2482	245	6	,	,	PUNCT
ejpam-2482	245	7	8	8	NUM
ejpam-2482	245	8	(	(	PUNCT
ejpam-2482	245	9	2015	2015	NUM
ejpam-2482	245	10	)	)	PUNCT
ejpam-2482	245	11	,	,	PUNCT
ejpam-2482	245	12	417	417	NUM
ejpam-2482	245	13	-	-	SYM
ejpam-2482	245	14	430	430	NUM
ejpam-2482	245	15	423	423	NUM
ejpam-2482	245	16	in	in	ADP
ejpam-2482	245	17	[	[	X
ejpam-2482	245	18	16	16	NUM
ejpam-2482	245	19	]	]	PUNCT
ejpam-2482	245	20	,	,	PUNCT
ejpam-2482	245	21	quartararo	quartararo	PROPN
ejpam-2482	245	22	et	et	PROPN
ejpam-2482	245	23	al	al	PROPN
ejpam-2482	245	24	.	.	PROPN
ejpam-2482	245	25	said	say	VERB
ejpam-2482	245	26	that	that	SCONJ
ejpam-2482	245	27	a	a	DET
ejpam-2482	245	28	commutative	commutative	ADJ
ejpam-2482	245	29	ring	ring	NOUN
ejpam-2482	245	30	r	r	NOUN
ejpam-2482	245	31	is	be	AUX
ejpam-2482	245	32	a	a	DET
ejpam-2482	245	33	u	u	NOUN
ejpam-2482	245	34	-	-	NOUN
ejpam-2482	245	35	ring	ring	NOUN
ejpam-2482	245	36	provided	provide	VERB
ejpam-2482	245	37	r	r	NOUN
ejpam-2482	245	38	has	have	VERB
ejpam-2482	245	39	the	the	DET
ejpam-2482	245	40	property	property	NOUN
ejpam-2482	245	41	that	that	PRON
ejpam-2482	245	42	an	an	DET
ejpam-2482	245	43	ideal	ideal	NOUN
ejpam-2482	245	44	contained	contain	VERB
ejpam-2482	245	45	in	in	ADP
ejpam-2482	245	46	a	a	DET
ejpam-2482	245	47	finite	finite	ADJ
ejpam-2482	245	48	union	union	NOUN
ejpam-2482	245	49	of	of	ADP
ejpam-2482	245	50	ideals	ideal	NOUN
ejpam-2482	245	51	must	must	AUX
ejpam-2482	245	52	be	be	AUX
ejpam-2482	245	53	contained	contain	VERB
ejpam-2482	245	54	in	in	ADP
ejpam-2482	245	55	one	one	NUM
ejpam-2482	245	56	of	of	ADP
ejpam-2482	245	57	those	those	DET
ejpam-2482	245	58	ideals	ideal	NOUN
ejpam-2482	245	59	;	;	PUNCT
ejpam-2482	245	60	and	and	CCONJ
ejpam-2482	245	61	a	a	DET
ejpam-2482	245	62	um	um	INTJ
ejpam-2482	245	63	-	-	PUNCT
ejpam-2482	245	64	ring	ring	NOUN
ejpam-2482	245	65	is	be	AUX
ejpam-2482	245	66	a	a	DET
ejpam-2482	245	67	ring	ring	NOUN
ejpam-2482	245	68	r	r	NOUN
ejpam-2482	245	69	with	with	ADP
ejpam-2482	245	70	the	the	DET
ejpam-2482	245	71	property	property	NOUN
ejpam-2482	245	72	that	that	PRON
ejpam-2482	245	73	an	an	DET
ejpam-2482	245	74	r	r	NOUN
ejpam-2482	245	75	-	-	PUNCT
ejpam-2482	245	76	module	module	NOUN
ejpam-2482	245	77	which	which	PRON
ejpam-2482	245	78	is	be	AUX
ejpam-2482	245	79	equal	equal	ADJ
ejpam-2482	245	80	to	to	ADP
ejpam-2482	245	81	a	a	DET
ejpam-2482	245	82	finite	finite	ADJ
ejpam-2482	245	83	union	union	NOUN
ejpam-2482	245	84	of	of	ADP
ejpam-2482	245	85	submodules	submodule	NOUN
ejpam-2482	245	86	must	must	AUX
ejpam-2482	245	87	be	be	AUX
ejpam-2482	245	88	equal	equal	ADJ
ejpam-2482	245	89	to	to	ADP
ejpam-2482	245	90	one	one	NUM
ejpam-2482	245	91	of	of	ADP
ejpam-2482	245	92	them	they	PRON
ejpam-2482	245	93	.	.	PUNCT
ejpam-2482	246	1	they	they	PRON
ejpam-2482	246	2	show	show	VERB
ejpam-2482	246	3	that	that	SCONJ
ejpam-2482	246	4	every	every	DET
ejpam-2482	246	5	bézout	bézout	PROPN
ejpam-2482	246	6	ring	ring	NOUN
ejpam-2482	246	7	is	be	AUX
ejpam-2482	246	8	a	a	DET
ejpam-2482	246	9	u	u	NOUN
ejpam-2482	246	10	-	-	NOUN
ejpam-2482	246	11	ring	ring	NOUN
ejpam-2482	246	12	.	.	PUNCT
ejpam-2482	247	1	moreover	moreover	ADV
ejpam-2482	247	2	,	,	PUNCT
ejpam-2482	247	3	they	they	PRON
ejpam-2482	247	4	proved	prove	VERB
ejpam-2482	247	5	that	that	SCONJ
ejpam-2482	247	6	every	every	DET
ejpam-2482	247	7	prüfer	prüfer	NOUN
ejpam-2482	247	8	domain	domain	NOUN
ejpam-2482	247	9	is	be	AUX
ejpam-2482	247	10	a	a	DET
ejpam-2482	247	11	u	u	NOUN
ejpam-2482	247	12	-	-	NOUN
ejpam-2482	247	13	domain	domain	NOUN
ejpam-2482	247	14	.	.	PUNCT
ejpam-2482	248	1	also	also	ADV
ejpam-2482	248	2	,	,	PUNCT
ejpam-2482	248	3	any	any	DET
ejpam-2482	248	4	ring	ring	NOUN
ejpam-2482	248	5	which	which	PRON
ejpam-2482	248	6	contains	contain	VERB
ejpam-2482	248	7	an	an	DET
ejpam-2482	248	8	infinite	infinite	ADJ
ejpam-2482	248	9	field	field	NOUN
ejpam-2482	248	10	as	as	ADP
ejpam-2482	248	11	a	a	DET
ejpam-2482	248	12	subring	subring	NOUN
ejpam-2482	248	13	is	be	AUX
ejpam-2482	248	14	a	a	DET
ejpam-2482	248	15	u	u	NOUN
ejpam-2482	248	16	-	-	NOUN
ejpam-2482	248	17	ring	ring	NOUN
ejpam-2482	248	18	,	,	PUNCT
ejpam-2482	248	19	[	[	X
ejpam-2482	248	20	17	17	NUM
ejpam-2482	248	21	,	,	PUNCT
ejpam-2482	248	22	exercise	exercise	VERB
ejpam-2482	248	23	3.63	3.63	NUM
ejpam-2482	248	24	]	]	PUNCT
ejpam-2482	248	25	.	.	PUNCT
ejpam-2482	249	1	theorem	theorem	ADJ
ejpam-2482	249	2	4	4	NUM
ejpam-2482	249	3	.	.	PUNCT
ejpam-2482	250	1	let	let	VERB
ejpam-2482	250	2	r	r	PRON
ejpam-2482	250	3	be	be	AUX
ejpam-2482	250	4	a	a	DET
ejpam-2482	250	5	um	um	INTJ
ejpam-2482	250	6	-	-	PUNCT
ejpam-2482	250	7	ring	ring	NOUN
ejpam-2482	250	8	,	,	PUNCT
ejpam-2482	250	9	m	m	VERB
ejpam-2482	250	10	be	be	VERB
ejpam-2482	250	11	an	an	DET
ejpam-2482	250	12	r	r	NOUN
ejpam-2482	250	13	-	-	PUNCT
ejpam-2482	250	14	module	module	NOUN
ejpam-2482	250	15	and	and	CCONJ
ejpam-2482	250	16	n	n	CCONJ
ejpam-2482	250	17	be	be	VERB
ejpam-2482	250	18	a	a	DET
ejpam-2482	250	19	proper	proper	ADJ
ejpam-2482	250	20	submodule	submodule	NOUN
ejpam-2482	250	21	of	of	ADP
ejpam-2482	250	22	m.	m.	NOUN
ejpam-2482	250	23	the	the	DET
ejpam-2482	250	24	following	follow	VERB
ejpam-2482	250	25	conditions	condition	NOUN
ejpam-2482	250	26	are	be	AUX
ejpam-2482	250	27	equivalent	equivalent	ADJ
ejpam-2482	250	28	:	:	PUNCT
ejpam-2482	250	29	(	(	PUNCT
ejpam-2482	250	30	i	i	NOUN
ejpam-2482	250	31	)	)	PUNCT
ejpam-2482	250	32	n	n	PRON
ejpam-2482	250	33	is	be	AUX
ejpam-2482	250	34	classical	classical	ADJ
ejpam-2482	250	35	2	2	NUM
ejpam-2482	250	36	-	-	PUNCT
ejpam-2482	250	37	absorbing	absorbing	ADJ
ejpam-2482	250	38	;	;	PUNCT
ejpam-2482	250	39	(	(	PUNCT
ejpam-2482	250	40	ii	ii	NOUN
ejpam-2482	250	41	)	)	PUNCT
ejpam-2482	250	42	for	for	ADP
ejpam-2482	250	43	every	every	DET
ejpam-2482	250	44	a	a	DET
ejpam-2482	250	45	,	,	PUNCT
ejpam-2482	250	46	b	b	NOUN
ejpam-2482	250	47	,	,	PUNCT
ejpam-2482	250	48	c	c	NOUN
ejpam-2482	250	49	"	"	PUNCT
ejpam-2482	250	50	r	r	NOUN
ejpam-2482	250	51	,	,	PUNCT
ejpam-2482	250	52	(	(	PUNCT
ejpam-2482	250	53	n	n	X
ejpam-2482	250	54	:	:	PUNCT
ejpam-2482	250	55	m	m	PROPN
ejpam-2482	250	56	abc	abc	PROPN
ejpam-2482	250	57	)	)	PUNCT
ejpam-2482	251	1	=	=	PUNCT
ejpam-2482	251	2	(	(	PUNCT
ejpam-2482	251	3	n	n	X
ejpam-2482	251	4	:	:	PUNCT
ejpam-2482	251	5	m	m	PROPN
ejpam-2482	251	6	ab	ab	ADJ
ejpam-2482	251	7	)	)	PUNCT
ejpam-2482	251	8	or	or	CCONJ
ejpam-2482	251	9	(	(	PUNCT
ejpam-2482	251	10	n	n	X
ejpam-2482	251	11	:	:	PUNCT
ejpam-2482	251	12	m	m	PROPN
ejpam-2482	251	13	abc	abc	PROPN
ejpam-2482	251	14	)	)	PUNCT
ejpam-2482	251	15	=	=	PUNCT
ejpam-2482	251	16	(	(	PUNCT
ejpam-2482	251	17	n	n	X
ejpam-2482	251	18	:	:	PUNCT
ejpam-2482	251	19	m	m	VERB
ejpam-2482	251	20	ac	ac	ADJ
ejpam-2482	251	21	)	)	PUNCT
ejpam-2482	251	22	or	or	CCONJ
ejpam-2482	251	23	(	(	PUNCT
ejpam-2482	251	24	n	n	X
ejpam-2482	251	25	:	:	PUNCT
ejpam-2482	251	26	m	m	PROPN
ejpam-2482	251	27	abc	abc	PROPN
ejpam-2482	251	28	)	)	PUNCT
ejpam-2482	252	1	=	=	PUNCT
ejpam-2482	252	2	(	(	PUNCT
ejpam-2482	252	3	n	n	X
ejpam-2482	252	4	:	:	PUNCT
ejpam-2482	252	5	m	m	PROPN
ejpam-2482	252	6	bc	bc	PROPN
ejpam-2482	252	7	)	)	PUNCT
ejpam-2482	252	8	;	;	PUNCT
ejpam-2482	252	9	(	(	PUNCT
ejpam-2482	252	10	iii	iii	X
ejpam-2482	252	11	)	)	PUNCT
ejpam-2482	252	12	for	for	ADP
ejpam-2482	252	13	every	every	DET
ejpam-2482	252	14	a	a	DET
ejpam-2482	252	15	,	,	PUNCT
ejpam-2482	252	16	b	b	NOUN
ejpam-2482	252	17	,	,	PUNCT
ejpam-2482	252	18	c	c	NOUN
ejpam-2482	252	19	"	"	PUNCT
ejpam-2482	252	20	r	r	NOUN
ejpam-2482	252	21	and	and	CCONJ
ejpam-2482	252	22	every	every	DET
ejpam-2482	252	23	submodule	submodule	NOUN
ejpam-2482	252	24	l	l	NOUN
ejpam-2482	252	25	of	of	ADP
ejpam-2482	252	26	m	m	PROPN
ejpam-2482	252	27	,	,	PUNCT
ejpam-2482	252	28	abcl	abcl	NOUN
ejpam-2482	252	29	$	$	SYM
ejpam-2482	252	30	n	n	PRON
ejpam-2482	252	31	implies	imply	VERB
ejpam-2482	252	32	that	that	SCONJ
ejpam-2482	252	33	abl	abl	PROPN
ejpam-2482	252	34	$	$	SYM
ejpam-2482	252	35	n	n	NOUN
ejpam-2482	252	36	or	or	CCONJ
ejpam-2482	252	37	acl	acl	PROPN
ejpam-2482	252	38	$	$	SYM
ejpam-2482	252	39	n	n	NOUN
ejpam-2482	252	40	or	or	CCONJ
ejpam-2482	252	41	bcl	bcl	NOUN
ejpam-2482	252	42	$	$	SYM
ejpam-2482	252	43	n	n	NUM
ejpam-2482	252	44	;	;	PUNCT
ejpam-2482	252	45	(	(	PUNCT
ejpam-2482	252	46	iv	iv	X
ejpam-2482	252	47	)	)	PUNCT
ejpam-2482	252	48	for	for	ADP
ejpam-2482	252	49	every	every	DET
ejpam-2482	252	50	a	a	PROPN
ejpam-2482	252	51	,	,	PUNCT
ejpam-2482	252	52	b	b	NOUN
ejpam-2482	252	53	"	"	PUNCT
ejpam-2482	252	54	r	r	NOUN
ejpam-2482	252	55	and	and	CCONJ
ejpam-2482	252	56	every	every	DET
ejpam-2482	252	57	submodule	submodule	NOUN
ejpam-2482	252	58	l	l	NOUN
ejpam-2482	252	59	of	of	ADP
ejpam-2482	252	60	m	m	PROPN
ejpam-2482	252	61	with	with	ADP
ejpam-2482	252	62	abl	abl	PROPN
ejpam-2482	252	63	#	#	SYM
ejpam-2482	252	64	$	$	SYM
ejpam-2482	252	65	n	n	NUM
ejpam-2482	252	66	,	,	PUNCT
ejpam-2482	252	67	(	(	PUNCT
ejpam-2482	252	68	n	n	X
ejpam-2482	252	69	:	:	PUNCT
ejpam-2482	252	70	r	r	NOUN
ejpam-2482	252	71	abl	abl	PROPN
ejpam-2482	252	72	)	)	PUNCT
ejpam-2482	252	73	=	=	PUNCT
ejpam-2482	253	1	(	(	PUNCT
ejpam-2482	253	2	n	n	X
ejpam-2482	253	3	:	:	PUNCT
ejpam-2482	253	4	r	r	NOUN
ejpam-2482	253	5	al	al	PROPN
ejpam-2482	253	6	)	)	PUNCT
ejpam-2482	253	7	or	or	CCONJ
ejpam-2482	253	8	(	(	PUNCT
ejpam-2482	253	9	n	n	X
ejpam-2482	253	10	:	:	PUNCT
ejpam-2482	253	11	r	r	NOUN
ejpam-2482	253	12	abl	abl	PROPN
ejpam-2482	253	13	)	)	PUNCT
ejpam-2482	253	14	=	=	PUNCT
ejpam-2482	253	15	(	(	PUNCT
ejpam-2482	253	16	n	n	X
ejpam-2482	253	17	:	:	PUNCT
ejpam-2482	253	18	r	r	NOUN
ejpam-2482	253	19	bl	bl	PROPN
ejpam-2482	253	20	)	)	PUNCT
ejpam-2482	253	21	;	;	PUNCT
ejpam-2482	253	22	(	(	PUNCT
ejpam-2482	253	23	v	v	NOUN
ejpam-2482	253	24	)	)	PUNCT
ejpam-2482	253	25	for	for	ADP
ejpam-2482	253	26	every	every	PRON
ejpam-2482	253	27	a	a	PROPN
ejpam-2482	253	28	,	,	PUNCT
ejpam-2482	253	29	b	b	NOUN
ejpam-2482	253	30	"	"	PUNCT
ejpam-2482	253	31	r	r	NOUN
ejpam-2482	253	32	,	,	PUNCT
ejpam-2482	253	33	every	every	DET
ejpam-2482	253	34	ideal	ideal	NOUN
ejpam-2482	253	35	i	i	PRON
ejpam-2482	253	36	of	of	ADP
ejpam-2482	253	37	r	r	NOUN
ejpam-2482	253	38	and	and	CCONJ
ejpam-2482	253	39	every	every	DET
ejpam-2482	253	40	submodule	submodule	NOUN
ejpam-2482	253	41	l	l	NOUN
ejpam-2482	253	42	of	of	ADP
ejpam-2482	253	43	m	m	PROPN
ejpam-2482	253	44	,	,	PUNCT
ejpam-2482	253	45	abi	abi	PROPN
ejpam-2482	253	46	l	l	PROPN
ejpam-2482	253	47	$	$	SYM
ejpam-2482	253	48	n	n	PRON
ejpam-2482	253	49	implies	imply	VERB
ejpam-2482	253	50	that	that	SCONJ
ejpam-2482	253	51	abl	abl	PROPN
ejpam-2482	253	52	$	$	SYM
ejpam-2482	253	53	n	n	NOUN
ejpam-2482	253	54	or	or	CCONJ
ejpam-2482	253	55	ai	ai	VERB
ejpam-2482	253	56	l	l	NOUN
ejpam-2482	253	57	$	$	SYM
ejpam-2482	253	58	n	n	NOUN
ejpam-2482	253	59	or	or	CCONJ
ejpam-2482	253	60	bi	bi	NOUN
ejpam-2482	253	61	l	l	NOUN
ejpam-2482	253	62	$	$	SYM
ejpam-2482	253	63	n	n	NUM
ejpam-2482	253	64	;	;	PUNCT
ejpam-2482	253	65	(	(	PUNCT
ejpam-2482	253	66	vi	vi	NOUN
ejpam-2482	253	67	)	)	PUNCT
ejpam-2482	253	68	for	for	ADP
ejpam-2482	253	69	every	every	PRON
ejpam-2482	253	70	a	a	DET
ejpam-2482	253	71	"	"	PUNCT
ejpam-2482	253	72	r	r	NOUN
ejpam-2482	253	73	,	,	PUNCT
ejpam-2482	253	74	every	every	DET
ejpam-2482	253	75	ideal	ideal	NOUN
ejpam-2482	253	76	i	i	PRON
ejpam-2482	253	77	of	of	ADP
ejpam-2482	253	78	r	r	NOUN
ejpam-2482	253	79	and	and	CCONJ
ejpam-2482	253	80	every	every	DET
ejpam-2482	253	81	submodule	submodule	NOUN
ejpam-2482	253	82	l	l	NOUN
ejpam-2482	253	83	of	of	ADP
ejpam-2482	253	84	m	m	PROPN
ejpam-2482	253	85	with	with	ADP
ejpam-2482	253	86	ai	ai	PROPN
ejpam-2482	253	87	l	l	NOUN
ejpam-2482	253	88	#	#	SYM
ejpam-2482	253	89	$	$	SYM
ejpam-2482	253	90	n	n	NUM
ejpam-2482	253	91	,	,	PUNCT
ejpam-2482	253	92	(	(	PUNCT
ejpam-2482	253	93	n	n	X
ejpam-2482	253	94	:	:	PUNCT
ejpam-2482	253	95	r	r	AUX
ejpam-2482	253	96	ai	ai	PROPN
ejpam-2482	253	97	l	l	NOUN
ejpam-2482	253	98	)	)	PUNCT
ejpam-2482	253	99	=	=	PUNCT
ejpam-2482	253	100	(	(	PUNCT
ejpam-2482	253	101	n	n	X
ejpam-2482	253	102	:	:	PUNCT
ejpam-2482	253	103	r	r	NOUN
ejpam-2482	253	104	al	al	PROPN
ejpam-2482	253	105	)	)	PUNCT
ejpam-2482	253	106	or	or	CCONJ
ejpam-2482	253	107	(	(	PUNCT
ejpam-2482	253	108	n	n	X
ejpam-2482	253	109	:	:	PUNCT
ejpam-2482	253	110	r	r	AUX
ejpam-2482	253	111	ai	ai	PROPN
ejpam-2482	253	112	l	l	NOUN
ejpam-2482	253	113	)	)	PUNCT
ejpam-2482	253	114	=	=	PUNCT
ejpam-2482	253	115	(	(	PUNCT
ejpam-2482	253	116	n	n	X
ejpam-2482	253	117	:	:	PUNCT
ejpam-2482	253	118	r	r	NOUN
ejpam-2482	253	119	i	i	NOUN
ejpam-2482	253	120	l	l	NOUN
ejpam-2482	253	121	)	)	PUNCT
ejpam-2482	253	122	;	;	PUNCT
ejpam-2482	253	123	(	(	PUNCT
ejpam-2482	253	124	vii	vii	PROPN
ejpam-2482	253	125	)	)	PUNCT
ejpam-2482	253	126	for	for	ADP
ejpam-2482	253	127	every	every	PRON
ejpam-2482	253	128	a	a	DET
ejpam-2482	253	129	"	"	PUNCT
ejpam-2482	253	130	r	r	NOUN
ejpam-2482	253	131	,	,	PUNCT
ejpam-2482	253	132	every	every	DET
ejpam-2482	253	133	ideals	ideal	NOUN
ejpam-2482	253	134	i	i	PRON
ejpam-2482	253	135	,	,	PUNCT
ejpam-2482	253	136	j	j	PROPN
ejpam-2482	253	137	of	of	ADP
ejpam-2482	253	138	r	r	NOUN
ejpam-2482	253	139	and	and	CCONJ
ejpam-2482	253	140	every	every	DET
ejpam-2482	253	141	submodule	submodule	NOUN
ejpam-2482	253	142	l	l	NOUN
ejpam-2482	253	143	of	of	ADP
ejpam-2482	253	144	m	m	PROPN
ejpam-2482	253	145	,	,	PUNCT
ejpam-2482	253	146	aij	aij	PROPN
ejpam-2482	253	147	l	l	PROPN
ejpam-2482	253	148	$	$	SYM
ejpam-2482	253	149	n	n	PRON
ejpam-2482	253	150	implies	imply	VERB
ejpam-2482	253	151	that	that	SCONJ
ejpam-2482	253	152	ai	ai	VERB
ejpam-2482	253	153	l	l	NOUN
ejpam-2482	253	154	$	$	SYM
ejpam-2482	253	155	n	n	NOUN
ejpam-2482	253	156	or	or	CCONJ
ejpam-2482	253	157	aj	aj	PROPN
ejpam-2482	253	158	l	l	PROPN
ejpam-2482	253	159	$	$	SYM
ejpam-2482	253	160	n	n	NOUN
ejpam-2482	253	161	or	or	CCONJ
ejpam-2482	253	162	ij	ij	INTJ
ejpam-2482	253	163	l	l	NOUN
ejpam-2482	253	164	$	$	SYM
ejpam-2482	253	165	n	n	NUM
ejpam-2482	253	166	;	;	PUNCT
ejpam-2482	253	167	(	(	PUNCT
ejpam-2482	253	168	viii	viii	NOUN
ejpam-2482	253	169	)	)	PUNCT
ejpam-2482	253	170	for	for	ADP
ejpam-2482	253	171	every	every	DET
ejpam-2482	253	172	ideals	ideal	NOUN
ejpam-2482	253	173	i	i	PRON
ejpam-2482	253	174	,	,	PUNCT
ejpam-2482	253	175	j	j	PROPN
ejpam-2482	253	176	of	of	ADP
ejpam-2482	253	177	r	r	NOUN
ejpam-2482	253	178	and	and	CCONJ
ejpam-2482	253	179	every	every	DET
ejpam-2482	253	180	submodule	submodule	NOUN
ejpam-2482	253	181	l	l	NOUN
ejpam-2482	253	182	of	of	ADP
ejpam-2482	253	183	m	m	PROPN
ejpam-2482	253	184	with	with	ADP
ejpam-2482	253	185	ij	ij	NOUN
ejpam-2482	253	186	l	l	NOUN
ejpam-2482	253	187	#	#	SYM
ejpam-2482	253	188	$	$	SYM
ejpam-2482	253	189	n	n	NUM
ejpam-2482	253	190	,	,	PUNCT
ejpam-2482	253	191	(	(	PUNCT
ejpam-2482	253	192	n	n	X
ejpam-2482	253	193	:	:	PUNCT
ejpam-2482	253	194	r	r	NOUN
ejpam-2482	253	195	ij	ij	NUM
ejpam-2482	253	196	l	l	NOUN
ejpam-2482	253	197	)	)	PUNCT
ejpam-2482	253	198	=	=	PUNCT
ejpam-2482	253	199	(	(	PUNCT
ejpam-2482	253	200	n	n	X
ejpam-2482	253	201	:	:	PUNCT
ejpam-2482	253	202	r	r	NOUN
ejpam-2482	253	203	i	i	NOUN
ejpam-2482	253	204	l	l	NOUN
ejpam-2482	253	205	)	)	PUNCT
ejpam-2482	253	206	or	or	CCONJ
ejpam-2482	253	207	(	(	PUNCT
ejpam-2482	253	208	n	n	X
ejpam-2482	253	209	:	:	PUNCT
ejpam-2482	253	210	r	r	NOUN
ejpam-2482	253	211	ij	ij	NUM
ejpam-2482	253	212	l	l	NOUN
ejpam-2482	253	213	)	)	PUNCT
ejpam-2482	253	214	=	=	PUNCT
ejpam-2482	253	215	(	(	PUNCT
ejpam-2482	253	216	n	n	X
ejpam-2482	253	217	:	:	PUNCT
ejpam-2482	253	218	r	r	NOUN
ejpam-2482	253	219	j	j	PROPN
ejpam-2482	253	220	l	l	NOUN
ejpam-2482	253	221	)	)	PUNCT
ejpam-2482	253	222	;	;	PUNCT
ejpam-2482	253	223	(	(	PUNCT
ejpam-2482	253	224	ix	ix	INTJ
ejpam-2482	253	225	)	)	PUNCT
ejpam-2482	253	226	for	for	ADP
ejpam-2482	253	227	every	every	DET
ejpam-2482	253	228	ideals	ideal	NOUN
ejpam-2482	253	229	i	i	PRON
ejpam-2482	253	230	,	,	PUNCT
ejpam-2482	253	231	j	j	PROPN
ejpam-2482	253	232	,	,	PUNCT
ejpam-2482	253	233	k	k	PROPN
ejpam-2482	253	234	of	of	ADP
ejpam-2482	253	235	r	r	NOUN
ejpam-2482	253	236	and	and	CCONJ
ejpam-2482	253	237	every	every	DET
ejpam-2482	253	238	submodule	submodule	NOUN
ejpam-2482	253	239	l	l	NOUN
ejpam-2482	253	240	of	of	ADP
ejpam-2482	253	241	m	m	PROPN
ejpam-2482	253	242	,	,	PUNCT
ejpam-2482	253	243	ijk	ijk	PROPN
ejpam-2482	253	244	l	l	PROPN
ejpam-2482	253	245	$	$	SYM
ejpam-2482	253	246	n	n	PRON
ejpam-2482	253	247	implies	imply	VERB
ejpam-2482	253	248	that	that	SCONJ
ejpam-2482	253	249	ij	ij	NOUN
ejpam-2482	253	250	l	l	NOUN
ejpam-2482	253	251	$	$	SYM
ejpam-2482	253	252	n	n	NUM
ejpam-2482	253	253	or	or	CCONJ
ejpam-2482	253	254	ik	ik	PROPN
ejpam-2482	253	255	l	l	NOUN
ejpam-2482	253	256	$	$	SYM
ejpam-2482	253	257	n	n	NOUN
ejpam-2482	253	258	or	or	CCONJ
ejpam-2482	253	259	jk	jk	ADP
ejpam-2482	253	260	l	l	NOUN
ejpam-2482	253	261	$	$	SYM
ejpam-2482	253	262	n	n	NUM
ejpam-2482	253	263	;	;	PUNCT
ejpam-2482	253	264	(	(	PUNCT
ejpam-2482	253	265	x	x	X
ejpam-2482	253	266	)	)	PUNCT
ejpam-2482	253	267	for	for	ADP
ejpam-2482	253	268	every	every	DET
ejpam-2482	253	269	submodule	submodule	NOUN
ejpam-2482	253	270	l	l	NOUN
ejpam-2482	253	271	of	of	ADP
ejpam-2482	253	272	m	m	PRON
ejpam-2482	253	273	not	not	PART
ejpam-2482	253	274	contained	contain	VERB
ejpam-2482	253	275	in	in	ADP
ejpam-2482	253	276	n	n	CCONJ
ejpam-2482	253	277	,	,	PUNCT
ejpam-2482	253	278	(	(	PUNCT
ejpam-2482	253	279	n	n	X
ejpam-2482	253	280	:	:	PUNCT
ejpam-2482	253	281	r	r	NOUN
ejpam-2482	253	282	l	l	NOUN
ejpam-2482	253	283	)	)	PUNCT
ejpam-2482	253	284	is	be	AUX
ejpam-2482	253	285	a	a	DET
ejpam-2482	253	286	2	2	NUM
ejpam-2482	253	287	-	-	PUNCT
ejpam-2482	253	288	absorbing	absorbing	ADJ
ejpam-2482	253	289	ideal	ideal	NOUN
ejpam-2482	253	290	of	of	ADP
ejpam-2482	253	291	r.	r.	PROPN
ejpam-2482	253	292	proof	proof	NOUN
ejpam-2482	253	293	.	.	PUNCT
ejpam-2482	254	1	similar	similar	ADJ
ejpam-2482	254	2	to	to	ADP
ejpam-2482	254	3	the	the	DET
ejpam-2482	254	4	proof	proof	NOUN
ejpam-2482	254	5	of	of	ADP
ejpam-2482	254	6	theorem	theorem	ADJ
ejpam-2482	254	7	2	2	NUM
ejpam-2482	254	8	.	.	PUNCT
ejpam-2482	254	9	proposition	proposition	NOUN
ejpam-2482	254	10	5	5	NUM
ejpam-2482	254	11	.	.	PUNCT
ejpam-2482	255	1	let	let	VERB
ejpam-2482	255	2	r	r	PRON
ejpam-2482	255	3	be	be	AUX
ejpam-2482	255	4	a	a	DET
ejpam-2482	255	5	um	um	INTJ
ejpam-2482	255	6	-	-	PUNCT
ejpam-2482	255	7	ring	ring	NOUN
ejpam-2482	255	8	and	and	CCONJ
ejpam-2482	255	9	n	n	CCONJ
ejpam-2482	255	10	be	be	VERB
ejpam-2482	255	11	a	a	DET
ejpam-2482	255	12	proper	proper	ADJ
ejpam-2482	255	13	submodule	submodule	NOUN
ejpam-2482	255	14	of	of	ADP
ejpam-2482	255	15	an	an	DET
ejpam-2482	255	16	r	r	NOUN
ejpam-2482	255	17	-	-	PUNCT
ejpam-2482	255	18	module	module	NOUN
ejpam-2482	255	19	m.	m.	NOUN
ejpam-2482	255	20	then	then	ADV
ejpam-2482	255	21	n	n	PRON
ejpam-2482	255	22	is	be	AUX
ejpam-2482	255	23	a	a	DET
ejpam-2482	255	24	classical	classical	ADJ
ejpam-2482	255	25	2	2	NUM
ejpam-2482	255	26	-	-	PUNCT
ejpam-2482	255	27	absorbing	absorb	VERB
ejpam-2482	255	28	submodule	submodule	NOUN
ejpam-2482	255	29	of	of	ADP
ejpam-2482	255	30	m	m	PROPN
ejpam-2482	255	31	if	if	SCONJ
ejpam-2482	256	1	and	and	CCONJ
ejpam-2482	256	2	only	only	ADV
ejpam-2482	256	3	if	if	SCONJ
ejpam-2482	256	4	n	n	PRON
ejpam-2482	256	5	is	be	AUX
ejpam-2482	256	6	a	a	DET
ejpam-2482	256	7	3	3	NUM
ejpam-2482	256	8	-	-	PUNCT
ejpam-2482	256	9	absorbing	absorb	VERB
ejpam-2482	256	10	submodule	submodule	NOUN
ejpam-2482	256	11	of	of	ADP
ejpam-2482	256	12	m	m	PROPN
ejpam-2482	256	13	and	and	CCONJ
ejpam-2482	256	14	(	(	PUNCT
ejpam-2482	256	15	n	n	X
ejpam-2482	256	16	:	:	PUNCT
ejpam-2482	256	17	r	r	NOUN
ejpam-2482	256	18	m	m	VERB
ejpam-2482	256	19	)	)	PUNCT
ejpam-2482	256	20	is	be	AUX
ejpam-2482	256	21	a	a	DET
ejpam-2482	256	22	2	2	NUM
ejpam-2482	256	23	-	-	PUNCT
ejpam-2482	256	24	absorbing	absorbing	ADJ
ejpam-2482	256	25	ideal	ideal	NOUN
ejpam-2482	256	26	of	of	ADP
ejpam-2482	256	27	r.	r.	PROPN
ejpam-2482	256	28	proof	proof	NOUN
ejpam-2482	256	29	.	.	PUNCT
ejpam-2482	257	1	it	it	PRON
ejpam-2482	257	2	is	be	AUX
ejpam-2482	257	3	trivial	trivial	ADJ
ejpam-2482	257	4	that	that	SCONJ
ejpam-2482	257	5	if	if	SCONJ
ejpam-2482	257	6	n	n	PRON
ejpam-2482	257	7	is	be	AUX
ejpam-2482	257	8	classical	classical	ADJ
ejpam-2482	257	9	2	2	NUM
ejpam-2482	257	10	-	-	PUNCT
ejpam-2482	257	11	absorbing	absorbing	ADJ
ejpam-2482	257	12	,	,	PUNCT
ejpam-2482	257	13	then	then	ADV
ejpam-2482	257	14	it	it	PRON
ejpam-2482	257	15	is	be	AUX
ejpam-2482	257	16	3	3	NUM
ejpam-2482	257	17	-	-	ADJ
ejpam-2482	257	18	absorbing	absorbing	ADJ
ejpam-2482	257	19	.	.	PUNCT
ejpam-2482	258	1	also	also	ADV
ejpam-2482	258	2	,	,	PUNCT
ejpam-2482	258	3	theorem	theorem	VERB
ejpam-2482	258	4	4	4	NUM
ejpam-2482	258	5	implies	imply	VERB
ejpam-2482	258	6	that	that	SCONJ
ejpam-2482	258	7	(	(	PUNCT
ejpam-2482	258	8	n	n	X
ejpam-2482	258	9	:	:	PUNCT
ejpam-2482	258	10	r	r	NOUN
ejpam-2482	258	11	m	m	VERB
ejpam-2482	258	12	)	)	PUNCT
ejpam-2482	258	13	is	be	AUX
ejpam-2482	258	14	a	a	DET
ejpam-2482	258	15	2	2	NUM
ejpam-2482	258	16	-	-	PUNCT
ejpam-2482	258	17	absorbing	absorbing	ADJ
ejpam-2482	258	18	ideal	ideal	NOUN
ejpam-2482	258	19	of	of	ADP
ejpam-2482	258	20	r.	r.	PROPN
ejpam-2482	258	21	now	now	ADV
ejpam-2482	258	22	,	,	PUNCT
ejpam-2482	258	23	assume	assume	VERB
ejpam-2482	258	24	that	that	SCONJ
ejpam-2482	258	25	n	n	PRON
ejpam-2482	258	26	is	be	AUX
ejpam-2482	258	27	a	a	DET
ejpam-2482	258	28	3	3	NUM
ejpam-2482	258	29	-	-	PUNCT
ejpam-2482	258	30	absorbing	absorb	VERB
ejpam-2482	258	31	submodule	submodule	NOUN
ejpam-2482	258	32	of	of	ADP
ejpam-2482	258	33	m	m	PROPN
ejpam-2482	258	34	and	and	CCONJ
ejpam-2482	258	35	(	(	PUNCT
ejpam-2482	258	36	n	n	X
ejpam-2482	258	37	:	:	PUNCT
ejpam-2482	258	38	r	r	NOUN
ejpam-2482	258	39	m	m	VERB
ejpam-2482	258	40	)	)	PUNCT
ejpam-2482	258	41	is	be	AUX
ejpam-2482	258	42	a	a	DET
ejpam-2482	258	43	2	2	NUM
ejpam-2482	258	44	-	-	PUNCT
ejpam-2482	258	45	absorbing	absorbing	ADJ
ejpam-2482	258	46	ideal	ideal	NOUN
ejpam-2482	258	47	of	of	ADP
ejpam-2482	258	48	r.	r.	PROPN
ejpam-2482	258	49	let	let	VERB
ejpam-2482	258	50	a1a2a3	a1a2a3	PROPN
ejpam-2482	258	51	m	m	NOUN
ejpam-2482	258	52	"	"	PUNCT
ejpam-2482	258	53	n	n	NOUN
ejpam-2482	258	54	for	for	ADP
ejpam-2482	258	55	some	some	DET
ejpam-2482	258	56	a1	a1	NOUN
ejpam-2482	258	57	,	,	PUNCT
ejpam-2482	258	58	a2	a2	PROPN
ejpam-2482	258	59	,	,	PUNCT
ejpam-2482	258	60	a3	a3	NOUN
ejpam-2482	258	61	"	"	PUNCT
ejpam-2482	258	62	r	r	NOUN
ejpam-2482	258	63	and	and	CCONJ
ejpam-2482	258	64	m	m	PRON
ejpam-2482	258	65	"	"	PUNCT
ejpam-2482	259	1	m	m	VERB
ejpam-2482	259	2	such	such	ADJ
ejpam-2482	259	3	that	that	SCONJ
ejpam-2482	259	4	neither	neither	CCONJ
ejpam-2482	259	5	a1a2	a1a2	PROPN
ejpam-2482	259	6	m	m	NOUN
ejpam-2482	259	7	"	"	PUNCT
ejpam-2482	259	8	n	n	CCONJ
ejpam-2482	259	9	nor	nor	CCONJ
ejpam-2482	259	10	a1a3	a1a3	ADP
ejpam-2482	259	11	m	m	NOUN
ejpam-2482	259	12	"	"	PUNCT
ejpam-2482	259	13	n	n	PROPN
ejpam-2482	259	14	nor	nor	CCONJ
ejpam-2482	259	15	a2a3	a2a3	NOUN
ejpam-2482	259	16	m	m	NOUN
ejpam-2482	259	17	"	"	PUNCT
ejpam-2482	259	18	n	n	PROPN
ejpam-2482	259	19	.	.	PUNCT
ejpam-2482	260	1	then	then	ADV
ejpam-2482	260	2	a1a2a3	a1a2a3	VERB
ejpam-2482	260	3	"	"	PUNCT
ejpam-2482	260	4	(	(	PUNCT
ejpam-2482	260	5	n	n	NUM
ejpam-2482	260	6	:	:	PUNCT
ejpam-2482	260	7	r	r	NOUN
ejpam-2482	260	8	m	m	NOUN
ejpam-2482	260	9	)	)	PUNCT
ejpam-2482	260	10	h.	h.	PROPN
ejpam-2482	260	11	mostafanasab	mostafanasab	PROPN
ejpam-2482	260	12	,	,	PUNCT
ejpam-2482	260	13	ü.	ü.	NOUN
ejpam-2482	260	14	tekir	tekir	NOUN
ejpam-2482	260	15	and	and	CCONJ
ejpam-2482	260	16	k.	k.	PROPN
ejpam-2482	260	17	hakan	hakan	PROPN
ejpam-2482	260	18	oral	oral	PROPN
ejpam-2482	260	19	/	/	SYM
ejpam-2482	260	20	eur	eur	PROPN
ejpam-2482	260	21	.	.	PUNCT
ejpam-2482	261	1	j.	j.	PROPN
ejpam-2482	261	2	pure	pure	PROPN
ejpam-2482	261	3	appl	appl	PROPN
ejpam-2482	261	4	.	.	PROPN
ejpam-2482	261	5	math	math	PROPN
ejpam-2482	261	6	,	,	PUNCT
ejpam-2482	261	7	8	8	NUM
ejpam-2482	261	8	(	(	PUNCT
ejpam-2482	261	9	2015	2015	NUM
ejpam-2482	261	10	)	)	PUNCT
ejpam-2482	261	11	,	,	PUNCT
ejpam-2482	261	12	417	417	NUM
ejpam-2482	261	13	-	-	SYM
ejpam-2482	261	14	430	430	NUM
ejpam-2482	261	15	424	424	NUM
ejpam-2482	261	16	and	and	CCONJ
ejpam-2482	261	17	so	so	ADV
ejpam-2482	261	18	either	either	CCONJ
ejpam-2482	261	19	a1a2	a1a2	ADP
ejpam-2482	261	20	"	"	PUNCT
ejpam-2482	261	21	(	(	PUNCT
ejpam-2482	261	22	n	n	X
ejpam-2482	261	23	:	:	PUNCT
ejpam-2482	261	24	r	r	NOUN
ejpam-2482	261	25	m	m	PROPN
ejpam-2482	261	26	)	)	PUNCT
ejpam-2482	261	27	or	or	CCONJ
ejpam-2482	261	28	a1a3	a1a3	ADP
ejpam-2482	261	29	"	"	PUNCT
ejpam-2482	261	30	(	(	PUNCT
ejpam-2482	261	31	n	n	X
ejpam-2482	261	32	:	:	PUNCT
ejpam-2482	261	33	r	r	NOUN
ejpam-2482	261	34	m	m	PROPN
ejpam-2482	261	35	)	)	PUNCT
ejpam-2482	261	36	or	or	CCONJ
ejpam-2482	261	37	a2a3	a2a3	VERB
ejpam-2482	261	38	"	"	PUNCT
ejpam-2482	261	39	(	(	PUNCT
ejpam-2482	261	40	n	n	X
ejpam-2482	261	41	:	:	PUNCT
ejpam-2482	261	42	r	r	NOUN
ejpam-2482	261	43	m	m	PROPN
ejpam-2482	261	44	)	)	PUNCT
ejpam-2482	261	45	.	.	PUNCT
ejpam-2482	262	1	this	this	DET
ejpam-2482	262	2	contradiction	contradiction	NOUN
ejpam-2482	262	3	shows	show	VERB
ejpam-2482	262	4	that	that	SCONJ
ejpam-2482	262	5	n	n	PRON
ejpam-2482	262	6	is	be	AUX
ejpam-2482	262	7	classical	classical	ADJ
ejpam-2482	262	8	2	2	NUM
ejpam-2482	262	9	-	-	PUNCT
ejpam-2482	262	10	absorbing	absorbing	ADJ
ejpam-2482	262	11	.	.	PUNCT
ejpam-2482	263	1	proposition	proposition	NOUN
ejpam-2482	263	2	6	6	NUM
ejpam-2482	263	3	.	.	PUNCT
ejpam-2482	264	1	let	let	VERB
ejpam-2482	264	2	m	m	PRON
ejpam-2482	264	3	be	be	AUX
ejpam-2482	264	4	an	an	DET
ejpam-2482	264	5	r	r	NOUN
ejpam-2482	264	6	-	-	PUNCT
ejpam-2482	264	7	module	module	NOUN
ejpam-2482	264	8	and	and	CCONJ
ejpam-2482	264	9	n	n	CCONJ
ejpam-2482	264	10	be	be	VERB
ejpam-2482	264	11	a	a	DET
ejpam-2482	264	12	classical	classical	ADJ
ejpam-2482	264	13	2	2	NUM
ejpam-2482	264	14	-	-	PUNCT
ejpam-2482	264	15	absorbing	absorb	VERB
ejpam-2482	264	16	submodule	submodule	NOUN
ejpam-2482	264	17	of	of	ADP
ejpam-2482	264	18	m.	m.	NOUN
ejpam-2482	264	19	the	the	DET
ejpam-2482	264	20	following	follow	VERB
ejpam-2482	264	21	conditions	condition	NOUN
ejpam-2482	264	22	hold	hold	VERB
ejpam-2482	264	23	:	:	PUNCT
ejpam-2482	264	24	(	(	PUNCT
ejpam-2482	264	25	i	i	NOUN
ejpam-2482	264	26	)	)	PUNCT
ejpam-2482	264	27	for	for	ADP
ejpam-2482	264	28	every	every	DET
ejpam-2482	264	29	a	a	DET
ejpam-2482	264	30	,	,	PUNCT
ejpam-2482	264	31	b	b	NOUN
ejpam-2482	264	32	,	,	PUNCT
ejpam-2482	264	33	c	c	NOUN
ejpam-2482	264	34	"	"	PUNCT
ejpam-2482	264	35	r	r	NOUN
ejpam-2482	264	36	and	and	CCONJ
ejpam-2482	264	37	m	m	NOUN
ejpam-2482	264	38	"	"	PUNCT
ejpam-2482	264	39	m	m	PROPN
ejpam-2482	264	40	,	,	PUNCT
ejpam-2482	264	41	(	(	PUNCT
ejpam-2482	264	42	n	n	X
ejpam-2482	264	43	:	:	PUNCT
ejpam-2482	264	44	r	r	NOUN
ejpam-2482	264	45	abcm	abcm	NOUN
ejpam-2482	264	46	)	)	PUNCT
ejpam-2482	264	47	=	=	PUNCT
ejpam-2482	264	48	(	(	PUNCT
ejpam-2482	264	49	n	n	X
ejpam-2482	264	50	:	:	PUNCT
ejpam-2482	264	51	r	r	NOUN
ejpam-2482	264	52	abm	abm	PROPN
ejpam-2482	264	53	)	)	PUNCT
ejpam-2482	264	54	'	'	PUNCT
ejpam-2482	264	55	(	(	PUNCT
ejpam-2482	264	56	n	n	X
ejpam-2482	264	57	:	:	PUNCT
ejpam-2482	264	58	r	r	NOUN
ejpam-2482	264	59	acm	acm	PROPN
ejpam-2482	264	60	)	)	PUNCT
ejpam-2482	264	61	'	'	PUNCT
ejpam-2482	264	62	(	(	PUNCT
ejpam-2482	264	63	n	n	X
ejpam-2482	264	64	:	:	PUNCT
ejpam-2482	264	65	r	r	NOUN
ejpam-2482	264	66	bcm	bcm	NOUN
ejpam-2482	264	67	)	)	PUNCT
ejpam-2482	264	68	;	;	PUNCT
ejpam-2482	264	69	(	(	PUNCT
ejpam-2482	264	70	ii	ii	NOUN
ejpam-2482	264	71	)	)	PUNCT
ejpam-2482	264	72	if	if	SCONJ
ejpam-2482	264	73	r	r	NOUN
ejpam-2482	264	74	is	be	AUX
ejpam-2482	264	75	a	a	DET
ejpam-2482	264	76	u	u	NOUN
ejpam-2482	264	77	-	-	NOUN
ejpam-2482	264	78	ring	ring	NOUN
ejpam-2482	264	79	,	,	PUNCT
ejpam-2482	264	80	then	then	ADV
ejpam-2482	264	81	for	for	ADP
ejpam-2482	264	82	every	every	DET
ejpam-2482	264	83	a	a	DET
ejpam-2482	264	84	,	,	PUNCT
ejpam-2482	264	85	b	b	NOUN
ejpam-2482	264	86	,	,	PUNCT
ejpam-2482	264	87	c	c	NOUN
ejpam-2482	264	88	"	"	PUNCT
ejpam-2482	264	89	r	r	NOUN
ejpam-2482	264	90	and	and	CCONJ
ejpam-2482	264	91	m	m	NOUN
ejpam-2482	264	92	"	"	PUNCT
ejpam-2482	264	93	m	m	PROPN
ejpam-2482	264	94	,	,	PUNCT
ejpam-2482	264	95	(	(	PUNCT
ejpam-2482	264	96	n	n	X
ejpam-2482	264	97	:	:	PUNCT
ejpam-2482	264	98	r	r	NOUN
ejpam-2482	264	99	abcm	abcm	NOUN
ejpam-2482	264	100	)	)	PUNCT
ejpam-2482	264	101	=	=	PUNCT
ejpam-2482	264	102	(	(	PUNCT
ejpam-2482	264	103	n	n	X
ejpam-2482	264	104	:	:	PUNCT
ejpam-2482	264	105	r	r	NOUN
ejpam-2482	264	106	abm	abm	PROPN
ejpam-2482	264	107	)	)	PUNCT
ejpam-2482	264	108	or	or	CCONJ
ejpam-2482	264	109	(	(	PUNCT
ejpam-2482	264	110	n	n	X
ejpam-2482	264	111	:	:	PUNCT
ejpam-2482	264	112	r	r	NOUN
ejpam-2482	264	113	abcm	abcm	NOUN
ejpam-2482	264	114	)	)	PUNCT
ejpam-2482	264	115	=	=	PUNCT
ejpam-2482	264	116	(	(	PUNCT
ejpam-2482	264	117	n	n	X
ejpam-2482	264	118	:	:	PUNCT
ejpam-2482	264	119	r	r	NOUN
ejpam-2482	264	120	acm	acm	PROPN
ejpam-2482	264	121	)	)	PUNCT
ejpam-2482	264	122	or	or	CCONJ
ejpam-2482	264	123	(	(	PUNCT
ejpam-2482	264	124	n	n	X
ejpam-2482	264	125	:	:	PUNCT
ejpam-2482	264	126	r	r	NOUN
ejpam-2482	264	127	abcm	abcm	NOUN
ejpam-2482	264	128	)	)	PUNCT
ejpam-2482	264	129	=	=	PUNCT
ejpam-2482	264	130	(	(	PUNCT
ejpam-2482	264	131	n	n	X
ejpam-2482	264	132	:	:	PUNCT
ejpam-2482	264	133	r	r	NOUN
ejpam-2482	264	134	bcm	bcm	NOUN
ejpam-2482	264	135	)	)	PUNCT
ejpam-2482	264	136	.	.	PUNCT
ejpam-2482	265	1	proof	proof	NOUN
ejpam-2482	265	2	.	.	PUNCT
ejpam-2482	266	1	(	(	PUNCT
ejpam-2482	266	2	i	i	NOUN
ejpam-2482	266	3	)	)	PUNCT
ejpam-2482	266	4	let	let	VERB
ejpam-2482	266	5	a	a	DET
ejpam-2482	266	6	,	,	PUNCT
ejpam-2482	266	7	b	b	NOUN
ejpam-2482	266	8	,	,	PUNCT
ejpam-2482	266	9	c	c	NOUN
ejpam-2482	266	10	"	"	PUNCT
ejpam-2482	266	11	r	r	NOUN
ejpam-2482	266	12	and	and	CCONJ
ejpam-2482	266	13	m	m	NOUN
ejpam-2482	266	14	"	"	PUNCT
ejpam-2482	267	1	m	m	VERB
ejpam-2482	267	2	.	.	PUNCT
ejpam-2482	268	1	suppose	suppose	VERB
ejpam-2482	268	2	that	that	SCONJ
ejpam-2482	268	3	r	r	NOUN
ejpam-2482	268	4	"	"	PUNCT
ejpam-2482	268	5	(	(	PUNCT
ejpam-2482	268	6	n	n	X
ejpam-2482	268	7	:	:	PUNCT
ejpam-2482	268	8	r	r	NOUN
ejpam-2482	268	9	abcm	abcm	NOUN
ejpam-2482	268	10	)	)	PUNCT
ejpam-2482	268	11	.	.	PUNCT
ejpam-2482	269	1	then	then	ADV
ejpam-2482	269	2	abc(rm	abc(rm	NOUN
ejpam-2482	269	3	)	)	PUNCT
ejpam-2482	269	4	"	"	PUNCT
ejpam-2482	270	1	n	n	CCONJ
ejpam-2482	270	2	.	.	PUNCT
ejpam-2482	271	1	so	so	ADV
ejpam-2482	271	2	,	,	PUNCT
ejpam-2482	271	3	either	either	PRON
ejpam-2482	271	4	ab(rm	ab(rm	NOUN
ejpam-2482	271	5	)	)	PUNCT
ejpam-2482	271	6	"	"	PUNCT
ejpam-2482	271	7	n	n	CCONJ
ejpam-2482	271	8	or	or	CCONJ
ejpam-2482	271	9	ac(rm	ac(rm	NOUN
ejpam-2482	271	10	)	)	PUNCT
ejpam-2482	271	11	"	"	PUNCT
ejpam-2482	271	12	n	n	CCONJ
ejpam-2482	271	13	or	or	CCONJ
ejpam-2482	271	14	bc(rm	bc(rm	NOUN
ejpam-2482	271	15	)	)	PUNCT
ejpam-2482	271	16	"	"	PUNCT
ejpam-2482	272	1	n	n	X
ejpam-2482	272	2	.	.	PUNCT
ejpam-2482	273	1	therefore	therefore	ADV
ejpam-2482	273	2	,	,	PUNCT
ejpam-2482	273	3	either	either	CCONJ
ejpam-2482	273	4	r	r	NOUN
ejpam-2482	273	5	"	"	PUNCT
ejpam-2482	273	6	(	(	PUNCT
ejpam-2482	273	7	n	n	X
ejpam-2482	273	8	:	:	PUNCT
ejpam-2482	273	9	r	r	NOUN
ejpam-2482	273	10	abm	abm	PROPN
ejpam-2482	273	11	)	)	PUNCT
ejpam-2482	273	12	or	or	CCONJ
ejpam-2482	273	13	r	r	NOUN
ejpam-2482	273	14	"	"	PUNCT
ejpam-2482	273	15	(	(	PUNCT
ejpam-2482	273	16	n	n	X
ejpam-2482	273	17	:	:	PUNCT
ejpam-2482	273	18	r	r	NOUN
ejpam-2482	273	19	acm	acm	PROPN
ejpam-2482	273	20	)	)	PUNCT
ejpam-2482	273	21	or	or	CCONJ
ejpam-2482	273	22	r	r	NOUN
ejpam-2482	273	23	"	"	PUNCT
ejpam-2482	273	24	(	(	PUNCT
ejpam-2482	273	25	n	n	X
ejpam-2482	273	26	:	:	PUNCT
ejpam-2482	273	27	r	r	NOUN
ejpam-2482	273	28	bcm	bcm	NOUN
ejpam-2482	273	29	)	)	PUNCT
ejpam-2482	273	30	.	.	PUNCT
ejpam-2482	274	1	consequently	consequently	ADV
ejpam-2482	274	2	(	(	PUNCT
ejpam-2482	274	3	n	n	X
ejpam-2482	274	4	:	:	PUNCT
ejpam-2482	274	5	r	r	NOUN
ejpam-2482	274	6	abcm	abcm	NOUN
ejpam-2482	274	7	)	)	PUNCT
ejpam-2482	274	8	=	=	PUNCT
ejpam-2482	274	9	(	(	PUNCT
ejpam-2482	274	10	n	n	X
ejpam-2482	274	11	:	:	PUNCT
ejpam-2482	274	12	r	r	NOUN
ejpam-2482	274	13	abm	abm	PROPN
ejpam-2482	274	14	)	)	PUNCT
ejpam-2482	274	15	'	'	PUNCT
ejpam-2482	274	16	(	(	PUNCT
ejpam-2482	274	17	n	n	X
ejpam-2482	274	18	:	:	PUNCT
ejpam-2482	274	19	r	r	NOUN
ejpam-2482	274	20	acm	acm	PROPN
ejpam-2482	274	21	)	)	PUNCT
ejpam-2482	274	22	'	'	PUNCT
ejpam-2482	274	23	(	(	PUNCT
ejpam-2482	274	24	n	n	X
ejpam-2482	274	25	:	:	PUNCT
ejpam-2482	274	26	r	r	NOUN
ejpam-2482	274	27	bcm	bcm	NOUN
ejpam-2482	274	28	)	)	PUNCT
ejpam-2482	274	29	.	.	PUNCT
ejpam-2482	275	1	(	(	PUNCT
ejpam-2482	275	2	ii	ii	NOUN
ejpam-2482	275	3	)	)	PUNCT
ejpam-2482	275	4	use	use	VERB
ejpam-2482	275	5	part	part	NOUN
ejpam-2482	275	6	(	(	PUNCT
ejpam-2482	275	7	i	i	NOUN
ejpam-2482	275	8	)	)	PUNCT
ejpam-2482	275	9	.	.	PUNCT
ejpam-2482	276	1	proposition	proposition	NOUN
ejpam-2482	276	2	7	7	NUM
ejpam-2482	276	3	.	.	PUNCT
ejpam-2482	277	1	let	let	VERB
ejpam-2482	277	2	r	r	PRON
ejpam-2482	277	3	be	be	AUX
ejpam-2482	277	4	a	a	DET
ejpam-2482	277	5	um	um	INTJ
ejpam-2482	277	6	-	-	PUNCT
ejpam-2482	277	7	ring	ring	NOUN
ejpam-2482	277	8	,	,	PUNCT
ejpam-2482	277	9	m	m	VERB
ejpam-2482	277	10	be	be	VERB
ejpam-2482	277	11	a	a	DET
ejpam-2482	277	12	multiplication	multiplication	NOUN
ejpam-2482	277	13	r	r	NOUN
ejpam-2482	277	14	-	-	PUNCT
ejpam-2482	277	15	module	module	NOUN
ejpam-2482	277	16	and	and	CCONJ
ejpam-2482	277	17	n	n	CCONJ
ejpam-2482	277	18	be	be	VERB
ejpam-2482	277	19	a	a	DET
ejpam-2482	277	20	proper	proper	ADJ
ejpam-2482	277	21	submodule	submodule	NOUN
ejpam-2482	277	22	of	of	ADP
ejpam-2482	277	23	m.	m.	NOUN
ejpam-2482	277	24	the	the	DET
ejpam-2482	277	25	following	follow	VERB
ejpam-2482	277	26	conditions	condition	NOUN
ejpam-2482	277	27	are	be	AUX
ejpam-2482	277	28	equivalent	equivalent	ADJ
ejpam-2482	277	29	:	:	PUNCT
ejpam-2482	277	30	(	(	PUNCT
ejpam-2482	277	31	i	i	NOUN
ejpam-2482	277	32	)	)	PUNCT
ejpam-2482	277	33	n	n	PRON
ejpam-2482	277	34	is	be	AUX
ejpam-2482	277	35	a	a	DET
ejpam-2482	277	36	classical	classical	ADJ
ejpam-2482	277	37	2	2	NUM
ejpam-2482	277	38	-	-	PUNCT
ejpam-2482	277	39	absorbing	absorb	VERB
ejpam-2482	277	40	submodule	submodule	NOUN
ejpam-2482	277	41	of	of	ADP
ejpam-2482	277	42	m	m	PROPN
ejpam-2482	277	43	;	;	PUNCT
ejpam-2482	277	44	(	(	PUNCT
ejpam-2482	277	45	ii	ii	NOUN
ejpam-2482	277	46	)	)	PUNCT
ejpam-2482	277	47	if	if	SCONJ
ejpam-2482	277	48	n1n2n3n4	n1n2n3n4	PROPN
ejpam-2482	277	49	$	$	SYM
ejpam-2482	277	50	n	n	NOUN
ejpam-2482	277	51	for	for	ADP
ejpam-2482	277	52	some	some	DET
ejpam-2482	277	53	submodules	submodule	NOUN
ejpam-2482	277	54	n1	n1	NOUN
ejpam-2482	277	55	,	,	PUNCT
ejpam-2482	277	56	n2	n2	NOUN
ejpam-2482	277	57	,	,	PUNCT
ejpam-2482	277	58	n3	n3	PROPN
ejpam-2482	277	59	,	,	PUNCT
ejpam-2482	277	60	n4	n4	PROPN
ejpam-2482	277	61	of	of	ADP
ejpam-2482	277	62	m	m	PROPN
ejpam-2482	277	63	,	,	PUNCT
ejpam-2482	277	64	then	then	ADV
ejpam-2482	277	65	either	either	PRON
ejpam-2482	277	66	n1n2n4	n1n2n4	NOUN
ejpam-2482	277	67	$	$	SYM
ejpam-2482	277	68	n	n	NOUN
ejpam-2482	277	69	or	or	CCONJ
ejpam-2482	277	70	n1n3n4	n1n3n4	PROPN
ejpam-2482	277	71	$	$	SYM
ejpam-2482	277	72	n	n	NOUN
ejpam-2482	277	73	or	or	CCONJ
ejpam-2482	277	74	n2n3n4	n2n3n4	PROPN
ejpam-2482	277	75	$	$	SYM
ejpam-2482	277	76	n	n	NUM
ejpam-2482	277	77	;	;	PUNCT
ejpam-2482	277	78	(	(	PUNCT
ejpam-2482	277	79	iii	iii	X
ejpam-2482	277	80	)	)	PUNCT
ejpam-2482	277	81	if	if	SCONJ
ejpam-2482	277	82	n1n2n3	n1n2n3	ADP
ejpam-2482	277	83	$	$	SYM
ejpam-2482	277	84	n	n	NOUN
ejpam-2482	277	85	for	for	ADP
ejpam-2482	277	86	some	some	DET
ejpam-2482	277	87	submodules	submodule	NOUN
ejpam-2482	277	88	n1	n1	NOUN
ejpam-2482	277	89	,	,	PUNCT
ejpam-2482	277	90	n2	n2	NOUN
ejpam-2482	277	91	,	,	PUNCT
ejpam-2482	277	92	n3	n3	NOUN
ejpam-2482	277	93	of	of	ADP
ejpam-2482	277	94	m	m	PROPN
ejpam-2482	277	95	,	,	PUNCT
ejpam-2482	277	96	then	then	ADV
ejpam-2482	277	97	either	either	CCONJ
ejpam-2482	277	98	n1n2	n1n2	ADV
ejpam-2482	277	99	$	$	SYM
ejpam-2482	277	100	n	n	NOUN
ejpam-2482	277	101	or	or	CCONJ
ejpam-2482	277	102	n1n3	n1n3	PRON
ejpam-2482	277	103	$	$	SYM
ejpam-2482	277	104	n	n	NOUN
ejpam-2482	277	105	or	or	CCONJ
ejpam-2482	277	106	n2n3	n2n3	ADP
ejpam-2482	277	107	$	$	SYM
ejpam-2482	277	108	n	n	NUM
ejpam-2482	277	109	;	;	PUNCT
ejpam-2482	277	110	(	(	PUNCT
ejpam-2482	277	111	iv	iv	X
ejpam-2482	277	112	)	)	PUNCT
ejpam-2482	277	113	n	n	PRON
ejpam-2482	277	114	is	be	AUX
ejpam-2482	277	115	a	a	DET
ejpam-2482	277	116	2	2	NUM
ejpam-2482	277	117	-	-	PUNCT
ejpam-2482	277	118	absorbing	absorb	VERB
ejpam-2482	277	119	submodule	submodule	NOUN
ejpam-2482	277	120	of	of	ADP
ejpam-2482	277	121	m	m	PROPN
ejpam-2482	277	122	;	;	PUNCT
ejpam-2482	277	123	(	(	PUNCT
ejpam-2482	277	124	v	v	NOUN
ejpam-2482	277	125	)	)	PUNCT
ejpam-2482	277	126	(	(	PUNCT
ejpam-2482	277	127	n	n	X
ejpam-2482	277	128	:	:	PUNCT
ejpam-2482	277	129	r	r	NOUN
ejpam-2482	277	130	m	m	VERB
ejpam-2482	277	131	)	)	PUNCT
ejpam-2482	277	132	is	be	AUX
ejpam-2482	277	133	a	a	DET
ejpam-2482	277	134	2	2	NUM
ejpam-2482	277	135	-	-	PUNCT
ejpam-2482	277	136	absorbing	absorbing	ADJ
ejpam-2482	277	137	ideal	ideal	NOUN
ejpam-2482	277	138	of	of	ADP
ejpam-2482	277	139	r.	r.	PROPN
ejpam-2482	277	140	proof	proof	NOUN
ejpam-2482	277	141	.	.	PUNCT
ejpam-2482	278	1	(	(	PUNCT
ejpam-2482	278	2	i)+	i)+	X
ejpam-2482	278	3	(	(	PUNCT
ejpam-2482	278	4	ii	ii	NOUN
ejpam-2482	278	5	)	)	PUNCT
ejpam-2482	278	6	let	let	VERB
ejpam-2482	278	7	n1n2n3n4	n1n2n3n4	PROPN
ejpam-2482	278	8	$	$	SYM
ejpam-2482	278	9	n	n	NOUN
ejpam-2482	278	10	for	for	ADP
ejpam-2482	278	11	some	some	DET
ejpam-2482	278	12	submodules	submodule	NOUN
ejpam-2482	278	13	n1	n1	NOUN
ejpam-2482	278	14	,	,	PUNCT
ejpam-2482	278	15	n2	n2	NOUN
ejpam-2482	278	16	,	,	PUNCT
ejpam-2482	278	17	n3	n3	PROPN
ejpam-2482	278	18	,	,	PUNCT
ejpam-2482	278	19	n4	n4	PROPN
ejpam-2482	278	20	of	of	ADP
ejpam-2482	278	21	m	m	PROPN
ejpam-2482	278	22	.	.	PUNCT
ejpam-2482	279	1	since	since	SCONJ
ejpam-2482	279	2	m	m	PROPN
ejpam-2482	279	3	is	be	AUX
ejpam-2482	279	4	multiplication	multiplication	NOUN
ejpam-2482	279	5	,	,	PUNCT
ejpam-2482	279	6	there	there	PRON
ejpam-2482	279	7	are	be	VERB
ejpam-2482	279	8	ideals	ideal	NOUN
ejpam-2482	279	9	i1	i1	PROPN
ejpam-2482	279	10	,	,	PUNCT
ejpam-2482	279	11	i2	i2	PROPN
ejpam-2482	279	12	,	,	PUNCT
ejpam-2482	279	13	i3	i3	NOUN
ejpam-2482	279	14	of	of	ADP
ejpam-2482	279	15	r	r	NOUN
ejpam-2482	279	16	such	such	ADJ
ejpam-2482	279	17	that	that	DET
ejpam-2482	279	18	n1	n1	PROPN
ejpam-2482	279	19	=	=	PROPN
ejpam-2482	279	20	i1	i1	PROPN
ejpam-2482	279	21	m	m	PROPN
ejpam-2482	279	22	,	,	PUNCT
ejpam-2482	279	23	n2	n2	PROPN
ejpam-2482	279	24	=	=	PROPN
ejpam-2482	279	25	i2	i2	PROPN
ejpam-2482	279	26	m	m	PROPN
ejpam-2482	279	27	and	and	CCONJ
ejpam-2482	279	28	n3	n3	NOUN
ejpam-2482	279	29	=	=	SYM
ejpam-2482	279	30	i3	i3	PROPN
ejpam-2482	279	31	m	m	PROPN
ejpam-2482	279	32	.	.	PUNCT
ejpam-2482	280	1	therefore	therefore	ADV
ejpam-2482	280	2	i1	i1	PROPN
ejpam-2482	280	3	i2	i2	PROPN
ejpam-2482	280	4	i3n4	i3n4	PROPN
ejpam-2482	280	5	$	$	SYM
ejpam-2482	280	6	n	n	NOUN
ejpam-2482	280	7	,	,	PUNCT
ejpam-2482	280	8	and	and	CCONJ
ejpam-2482	280	9	so	so	ADV
ejpam-2482	280	10	i1	i1	PROPN
ejpam-2482	280	11	i2n4	i2n4	PROPN
ejpam-2482	280	12	$	$	SYM
ejpam-2482	280	13	n	n	NOUN
ejpam-2482	280	14	or	or	CCONJ
ejpam-2482	280	15	i1	i1	PROPN
ejpam-2482	280	16	i3n4	i3n4	PROPN
ejpam-2482	280	17	$	$	SYM
ejpam-2482	280	18	n	n	NOUN
ejpam-2482	280	19	or	or	CCONJ
ejpam-2482	280	20	i2	i2	PROPN
ejpam-2482	280	21	i3n4	i3n4	NOUN
ejpam-2482	280	22	$	$	SYM
ejpam-2482	280	23	n	n	NOUN
ejpam-2482	280	24	.	.	PUNCT
ejpam-2482	281	1	thus	thus	ADV
ejpam-2482	281	2	by	by	ADP
ejpam-2482	281	3	theorem	theorem	NOUN
ejpam-2482	281	4	4	4	NUM
ejpam-2482	281	5	,	,	PUNCT
ejpam-2482	281	6	either	either	CCONJ
ejpam-2482	281	7	n1n2n4	n1n2n4	NOUN
ejpam-2482	281	8	$	$	SYM
ejpam-2482	281	9	n	n	NOUN
ejpam-2482	281	10	or	or	CCONJ
ejpam-2482	281	11	n1n3n4	n1n3n4	PROPN
ejpam-2482	281	12	$	$	SYM
ejpam-2482	281	13	n	n	NOUN
ejpam-2482	281	14	or	or	CCONJ
ejpam-2482	281	15	n2n3n4	n2n3n4	ADJ
ejpam-2482	281	16	$	$	SYM
ejpam-2482	281	17	n	n	NOUN
ejpam-2482	281	18	.	.	PUNCT
ejpam-2482	282	1	(	(	PUNCT
ejpam-2482	282	2	ii)+	ii)+	NOUN
ejpam-2482	282	3	(	(	PUNCT
ejpam-2482	282	4	iii	iii	NOUN
ejpam-2482	282	5	)	)	PUNCT
ejpam-2482	282	6	is	be	AUX
ejpam-2482	282	7	easy	easy	ADJ
ejpam-2482	282	8	.	.	PUNCT
ejpam-2482	283	1	(	(	PUNCT
ejpam-2482	283	2	iii)+	iii)+	PROPN
ejpam-2482	283	3	(	(	PUNCT
ejpam-2482	283	4	iv	iv	X
ejpam-2482	283	5	)	)	PUNCT
ejpam-2482	283	6	suppose	suppose	VERB
ejpam-2482	283	7	that	that	SCONJ
ejpam-2482	283	8	i1	i1	PROPN
ejpam-2482	283	9	i2k	i2k	CCONJ
ejpam-2482	283	10	$	$	SYM
ejpam-2482	283	11	n	n	NOUN
ejpam-2482	283	12	for	for	ADP
ejpam-2482	283	13	some	some	DET
ejpam-2482	283	14	ideals	ideal	NOUN
ejpam-2482	283	15	i1	i1	PROPN
ejpam-2482	283	16	,	,	PUNCT
ejpam-2482	283	17	i2	i2	PROPN
ejpam-2482	283	18	of	of	ADP
ejpam-2482	283	19	r	r	NOUN
ejpam-2482	283	20	and	and	CCONJ
ejpam-2482	283	21	some	some	DET
ejpam-2482	283	22	submodule	submodule	NOUN
ejpam-2482	283	23	k	k	PROPN
ejpam-2482	283	24	of	of	ADP
ejpam-2482	283	25	m	m	PROPN
ejpam-2482	283	26	.	.	PUNCT
ejpam-2482	284	1	it	it	PRON
ejpam-2482	284	2	is	be	AUX
ejpam-2482	284	3	sufficient	sufficient	ADJ
ejpam-2482	284	4	to	to	PART
ejpam-2482	284	5	set	set	VERB
ejpam-2482	284	6	n1	n1	PROPN
ejpam-2482	284	7	:	:	PUNCT
ejpam-2482	284	8	=	=	SYM
ejpam-2482	284	9	i1	i1	PROPN
ejpam-2482	284	10	m	m	PROPN
ejpam-2482	284	11	,	,	PUNCT
ejpam-2482	284	12	n2	n2	ADJ
ejpam-2482	284	13	:	:	PUNCT
ejpam-2482	284	14	=	=	SYM
ejpam-2482	284	15	i2	i2	PROPN
ejpam-2482	284	16	m	m	PROPN
ejpam-2482	284	17	and	and	CCONJ
ejpam-2482	284	18	n3	n3	NOUN
ejpam-2482	284	19	=	=	SYM
ejpam-2482	284	20	k	k	PROPN
ejpam-2482	284	21	in	in	ADP
ejpam-2482	284	22	part	part	NOUN
ejpam-2482	284	23	(	(	PUNCT
ejpam-2482	284	24	iii	iii	NOUN
ejpam-2482	284	25	)	)	PUNCT
ejpam-2482	284	26	.	.	PUNCT
ejpam-2482	285	1	(	(	PUNCT
ejpam-2482	285	2	iv)+	iv)+	NOUN
ejpam-2482	285	3	(	(	PUNCT
ejpam-2482	285	4	i	i	NOUN
ejpam-2482	285	5	)	)	PUNCT
ejpam-2482	285	6	by	by	ADP
ejpam-2482	285	7	part	part	NOUN
ejpam-2482	285	8	(	(	PUNCT
ejpam-2482	285	9	i	i	NOUN
ejpam-2482	285	10	)	)	PUNCT
ejpam-2482	285	11	of	of	ADP
ejpam-2482	285	12	proposition	proposition	NOUN
ejpam-2482	285	13	2	2	NUM
ejpam-2482	285	14	.	.	PUNCT
ejpam-2482	285	15	(	(	PUNCT
ejpam-2482	285	16	iv)+	iv)+	NOUN
ejpam-2482	285	17	(	(	PUNCT
ejpam-2482	285	18	v	v	NOUN
ejpam-2482	285	19	)	)	PUNCT
ejpam-2482	285	20	by	by	ADP
ejpam-2482	285	21	[	[	X
ejpam-2482	285	22	15	15	NUM
ejpam-2482	285	23	,	,	PUNCT
ejpam-2482	285	24	theorem	theorem	VERB
ejpam-2482	285	25	2.3	2.3	NUM
ejpam-2482	285	26	]	]	PUNCT
ejpam-2482	285	27	.	.	PUNCT
ejpam-2482	286	1	(	(	PUNCT
ejpam-2482	286	2	v)+	v)+	NOUN
ejpam-2482	286	3	(	(	PUNCT
ejpam-2482	286	4	iv	iv	X
ejpam-2482	286	5	)	)	PUNCT
ejpam-2482	286	6	let	let	VERB
ejpam-2482	286	7	i1	i1	PROPN
ejpam-2482	286	8	i2k	i2k	ADP
ejpam-2482	286	9	$	$	SYM
ejpam-2482	286	10	n	n	NOUN
ejpam-2482	286	11	for	for	ADP
ejpam-2482	286	12	some	some	DET
ejpam-2482	286	13	ideals	ideal	NOUN
ejpam-2482	286	14	i1	i1	PROPN
ejpam-2482	286	15	,	,	PUNCT
ejpam-2482	286	16	i2	i2	PROPN
ejpam-2482	286	17	of	of	ADP
ejpam-2482	286	18	r	r	NOUN
ejpam-2482	286	19	and	and	CCONJ
ejpam-2482	286	20	some	some	DET
ejpam-2482	286	21	submodule	submodule	NOUN
ejpam-2482	286	22	k	k	PROPN
ejpam-2482	286	23	of	of	ADP
ejpam-2482	286	24	m	m	PROPN
ejpam-2482	286	25	.	.	PUNCT
ejpam-2482	287	1	since	since	SCONJ
ejpam-2482	287	2	m	m	PROPN
ejpam-2482	287	3	is	be	AUX
ejpam-2482	287	4	multiplication	multiplication	NOUN
ejpam-2482	287	5	,	,	PUNCT
ejpam-2482	287	6	then	then	ADV
ejpam-2482	287	7	there	there	PRON
ejpam-2482	287	8	is	be	VERB
ejpam-2482	287	9	an	an	DET
ejpam-2482	287	10	ideal	ideal	ADJ
ejpam-2482	287	11	i3	i3	NOUN
ejpam-2482	287	12	of	of	ADP
ejpam-2482	287	13	r	r	NOUN
ejpam-2482	287	14	such	such	ADJ
ejpam-2482	287	15	that	that	SCONJ
ejpam-2482	287	16	k	k	PROPN
ejpam-2482	287	17	=	=	PUNCT
ejpam-2482	287	18	i3	i3	PROPN
ejpam-2482	287	19	m	m	PROPN
ejpam-2482	287	20	.	.	PUNCT
ejpam-2482	288	1	hence	hence	ADV
ejpam-2482	288	2	i1	i1	PROPN
ejpam-2482	288	3	i2	i2	PROPN
ejpam-2482	288	4	i3	i3	PROPN
ejpam-2482	288	5	$	$	SYM
ejpam-2482	288	6	(	(	PUNCT
ejpam-2482	288	7	n	n	NUM
ejpam-2482	288	8	:	:	PUNCT
ejpam-2482	288	9	r	r	NOUN
ejpam-2482	288	10	m)which	m)which	NOUN
ejpam-2482	288	11	implies	imply	VERB
ejpam-2482	288	12	that	that	SCONJ
ejpam-2482	288	13	either	either	CCONJ
ejpam-2482	288	14	i1	i1	PROPN
ejpam-2482	288	15	i2	i2	PROPN
ejpam-2482	288	16	$	$	SYM
ejpam-2482	288	17	(	(	PUNCT
ejpam-2482	288	18	n	n	NUM
ejpam-2482	288	19	:	:	PUNCT
ejpam-2482	288	20	r	r	NOUN
ejpam-2482	288	21	m	m	PROPN
ejpam-2482	288	22	)	)	PUNCT
ejpam-2482	288	23	or	or	CCONJ
ejpam-2482	288	24	i1	i1	PROPN
ejpam-2482	288	25	i3	i3	PROPN
ejpam-2482	288	26	$	$	PROPN
ejpam-2482	288	27	(	(	PUNCT
ejpam-2482	288	28	n	n	NUM
ejpam-2482	288	29	:	:	PUNCT
ejpam-2482	288	30	r	r	NOUN
ejpam-2482	288	31	m	m	NOUN
ejpam-2482	288	32	)	)	PUNCT
ejpam-2482	288	33	or	or	CCONJ
ejpam-2482	288	34	i2	i2	PROPN
ejpam-2482	288	35	i3	i3	PROPN
ejpam-2482	288	36	$	$	SYM
ejpam-2482	288	37	(	(	PUNCT
ejpam-2482	288	38	n	n	NUM
ejpam-2482	288	39	:	:	PUNCT
ejpam-2482	288	40	r	r	NOUN
ejpam-2482	288	41	m	m	PROPN
ejpam-2482	288	42	)	)	PUNCT
ejpam-2482	288	43	.	.	PUNCT
ejpam-2482	289	1	if	if	SCONJ
ejpam-2482	289	2	i1	i1	PROPN
ejpam-2482	289	3	i2	i2	PROPN
ejpam-2482	289	4	$	$	SYM
ejpam-2482	289	5	(	(	PUNCT
ejpam-2482	289	6	n	n	NUM
ejpam-2482	289	7	:	:	PUNCT
ejpam-2482	289	8	r	r	NOUN
ejpam-2482	289	9	m	m	PROPN
ejpam-2482	289	10	)	)	PUNCT
ejpam-2482	289	11	,	,	PUNCT
ejpam-2482	289	12	then	then	ADV
ejpam-2482	289	13	we	we	PRON
ejpam-2482	289	14	are	be	AUX
ejpam-2482	289	15	done	do	VERB
ejpam-2482	289	16	.	.	PUNCT
ejpam-2482	290	1	so	so	ADV
ejpam-2482	290	2	,	,	PUNCT
ejpam-2482	290	3	suppose	suppose	VERB
ejpam-2482	290	4	that	that	SCONJ
ejpam-2482	290	5	i1	i1	PROPN
ejpam-2482	290	6	i3	i3	PROPN
ejpam-2482	290	7	$	$	SYM
ejpam-2482	290	8	(	(	PUNCT
ejpam-2482	290	9	n	n	NUM
ejpam-2482	290	10	:	:	PUNCT
ejpam-2482	290	11	r	r	NOUN
ejpam-2482	290	12	m	m	PROPN
ejpam-2482	290	13	)	)	PUNCT
ejpam-2482	290	14	.	.	PUNCT
ejpam-2482	291	1	thus	thus	ADV
ejpam-2482	291	2	i1	i1	PROPN
ejpam-2482	291	3	i3	i3	PROPN
ejpam-2482	291	4	m	m	PROPN
ejpam-2482	291	5	=	=	PUNCT
ejpam-2482	291	6	i1k	i1k	ADJ
ejpam-2482	291	7	$	$	SYM
ejpam-2482	291	8	n	n	NOUN
ejpam-2482	291	9	.	.	PUNCT
ejpam-2482	292	1	similarly	similarly	ADV
ejpam-2482	292	2	if	if	SCONJ
ejpam-2482	292	3	i2	i2	PROPN
ejpam-2482	292	4	i3	i3	VERB
ejpam-2482	292	5	$	$	SYM
ejpam-2482	292	6	(	(	PUNCT
ejpam-2482	292	7	n	n	NUM
ejpam-2482	292	8	:	:	PUNCT
ejpam-2482	292	9	r	r	NOUN
ejpam-2482	292	10	m	m	PROPN
ejpam-2482	292	11	)	)	PUNCT
ejpam-2482	292	12	,	,	PUNCT
ejpam-2482	292	13	then	then	ADV
ejpam-2482	292	14	we	we	PRON
ejpam-2482	292	15	have	have	VERB
ejpam-2482	292	16	i2k	i2k	ADP
ejpam-2482	292	17	$	$	SYM
ejpam-2482	292	18	n	n	NOUN
ejpam-2482	292	19	.	.	PUNCT
ejpam-2482	293	1	h.	h.	PROPN
ejpam-2482	293	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	293	3	,	,	PUNCT
ejpam-2482	293	4	ü.	ü.	NOUN
ejpam-2482	293	5	tekir	tekir	NOUN
ejpam-2482	293	6	and	and	CCONJ
ejpam-2482	293	7	k.	k.	PROPN
ejpam-2482	293	8	hakan	hakan	PROPN
ejpam-2482	293	9	oral	oral	PROPN
ejpam-2482	293	10	/	/	SYM
ejpam-2482	293	11	eur	eur	PROPN
ejpam-2482	293	12	.	.	PUNCT
ejpam-2482	294	1	j.	j.	PROPN
ejpam-2482	294	2	pure	pure	PROPN
ejpam-2482	294	3	appl	appl	PROPN
ejpam-2482	294	4	.	.	PROPN
ejpam-2482	294	5	math	math	PROPN
ejpam-2482	294	6	,	,	PUNCT
ejpam-2482	294	7	8	8	NUM
ejpam-2482	294	8	(	(	PUNCT
ejpam-2482	294	9	2015	2015	NUM
ejpam-2482	294	10	)	)	PUNCT
ejpam-2482	294	11	,	,	PUNCT
ejpam-2482	294	12	417	417	NUM
ejpam-2482	294	13	-	-	SYM
ejpam-2482	294	14	430	430	NUM
ejpam-2482	294	15	425	425	NUM
ejpam-2482	294	16	definition	definition	NOUN
ejpam-2482	294	17	1	1	NUM
ejpam-2482	294	18	.	.	PUNCT
ejpam-2482	295	1	let	let	VERB
ejpam-2482	295	2	r	r	PRON
ejpam-2482	295	3	be	be	AUX
ejpam-2482	295	4	a	a	DET
ejpam-2482	295	5	um	um	INTJ
ejpam-2482	295	6	-	-	PUNCT
ejpam-2482	295	7	ring	ring	NOUN
ejpam-2482	295	8	,	,	PUNCT
ejpam-2482	295	9	m	m	VERB
ejpam-2482	295	10	be	be	VERB
ejpam-2482	295	11	an	an	DET
ejpam-2482	295	12	r	r	NOUN
ejpam-2482	295	13	-	-	PUNCT
ejpam-2482	295	14	module	module	NOUN
ejpam-2482	295	15	and	and	CCONJ
ejpam-2482	295	16	s	s	VERB
ejpam-2482	295	17	be	be	AUX
ejpam-2482	295	18	a	a	DET
ejpam-2482	295	19	subset	subset	NOUN
ejpam-2482	295	20	of	of	ADP
ejpam-2482	295	21	m\{0	m\{0	NOUN
ejpam-2482	295	22	}	}	PUNCT
ejpam-2482	295	23	.	.	PUNCT
ejpam-2482	296	1	if	if	SCONJ
ejpam-2482	296	2	for	for	ADP
ejpam-2482	296	3	all	all	DET
ejpam-2482	296	4	ideals	ideal	NOUN
ejpam-2482	296	5	i	i	PRON
ejpam-2482	296	6	,	,	PUNCT
ejpam-2482	296	7	j	j	PROPN
ejpam-2482	296	8	,	,	PUNCT
ejpam-2482	296	9	q	q	NOUN
ejpam-2482	296	10	of	of	ADP
ejpam-2482	296	11	r	r	NOUN
ejpam-2482	296	12	and	and	CCONJ
ejpam-2482	296	13	all	all	DET
ejpam-2482	296	14	submodules	submodule	NOUN
ejpam-2482	296	15	k	k	NOUN
ejpam-2482	296	16	,	,	PUNCT
ejpam-2482	296	17	l	l	NOUN
ejpam-2482	296	18	of	of	ADP
ejpam-2482	296	19	m	m	PRON
ejpam-2482	296	20	,	,	PUNCT
ejpam-2482	296	21	(	(	PUNCT
ejpam-2482	296	22	k	k	X
ejpam-2482	296	23	+	+	CCONJ
ejpam-2482	296	24	i	i	PRON
ejpam-2482	296	25	j	j	PROPN
ejpam-2482	296	26	l	l	NOUN
ejpam-2482	296	27	)	)	PUNCT
ejpam-2482	296	28	*	*	PUNCT
ejpam-2482	296	29	s	s	VERB
ejpam-2482	296	30	#	#	NOUN
ejpam-2482	296	31	=	=	NOUN
ejpam-2482	296	32	.	.	PUNCT
ejpam-2482	297	1	and	and	CCONJ
ejpam-2482	297	2	(	(	PUNCT
ejpam-2482	297	3	k	k	PROPN
ejpam-2482	297	4	+	+	PROPN
ejpam-2482	297	5	iql	iql	NOUN
ejpam-2482	297	6	)	)	PUNCT
ejpam-2482	297	7	*	*	PUNCT
ejpam-2482	297	8	s	s	VERB
ejpam-2482	297	9	#	#	NOUN
ejpam-2482	297	10	=	=	NOUN
ejpam-2482	297	11	.	.	PUNCT
ejpam-2482	298	1	and	and	CCONJ
ejpam-2482	298	2	(	(	PUNCT
ejpam-2482	298	3	k	k	PROPN
ejpam-2482	298	4	+	+	NUM
ejpam-2482	298	5	jql	jql	NOUN
ejpam-2482	298	6	)	)	PUNCT
ejpam-2482	298	7	*	*	PUNCT
ejpam-2482	298	8	s	s	VERB
ejpam-2482	298	9	#	#	NOUN
ejpam-2482	298	10	=	=	PRON
ejpam-2482	298	11	.	.	PUNCT
ejpam-2482	299	1	implies	imply	VERB
ejpam-2482	299	2	(	(	PUNCT
ejpam-2482	299	3	k	k	X
ejpam-2482	299	4	+	+	CCONJ
ejpam-2482	299	5	i	i	PRON
ejpam-2482	299	6	jql	jql	VERB
ejpam-2482	299	7	)	)	PUNCT
ejpam-2482	299	8	*	*	PUNCT
ejpam-2482	299	9	s	s	VERB
ejpam-2482	299	10	#	#	NOUN
ejpam-2482	299	11	=	=	PRON
ejpam-2482	299	12	.	.	PUNCT
ejpam-2482	300	1	,	,	PUNCT
ejpam-2482	300	2	then	then	ADV
ejpam-2482	300	3	the	the	DET
ejpam-2482	300	4	subset	subset	NOUN
ejpam-2482	300	5	s	s	X
ejpam-2482	300	6	is	be	AUX
ejpam-2482	300	7	called	call	VERB
ejpam-2482	300	8	classical	classical	ADJ
ejpam-2482	300	9	2	2	NUM
ejpam-2482	300	10	-	-	PUNCT
ejpam-2482	300	11	absorbing	absorbing	ADJ
ejpam-2482	300	12	m	m	NOUN
ejpam-2482	300	13	-	-	PUNCT
ejpam-2482	300	14	closed	closed	ADJ
ejpam-2482	300	15	.	.	PUNCT
ejpam-2482	301	1	proposition	proposition	NOUN
ejpam-2482	301	2	8	8	NUM
ejpam-2482	301	3	.	.	PUNCT
ejpam-2482	302	1	let	let	VERB
ejpam-2482	302	2	r	r	PRON
ejpam-2482	302	3	be	be	AUX
ejpam-2482	302	4	a	a	DET
ejpam-2482	302	5	um	um	INTJ
ejpam-2482	302	6	-	-	PUNCT
ejpam-2482	302	7	ring	ring	NOUN
ejpam-2482	302	8	,	,	PUNCT
ejpam-2482	302	9	m	m	VERB
ejpam-2482	302	10	be	be	VERB
ejpam-2482	302	11	r	r	NOUN
ejpam-2482	302	12	-	-	PUNCT
ejpam-2482	302	13	module	module	NOUN
ejpam-2482	302	14	and	and	CCONJ
ejpam-2482	302	15	n	n	NOUN
ejpam-2482	302	16	a	a	DET
ejpam-2482	302	17	submodule	submodule	NOUN
ejpam-2482	302	18	of	of	ADP
ejpam-2482	302	19	m.	m.	NOUN
ejpam-2482	302	20	then	then	ADV
ejpam-2482	302	21	n	n	PRON
ejpam-2482	302	22	is	be	AUX
ejpam-2482	302	23	a	a	DET
ejpam-2482	302	24	classical	classical	ADJ
ejpam-2482	302	25	2	2	NUM
ejpam-2482	302	26	-	-	PUNCT
ejpam-2482	302	27	absorbing	absorb	VERB
ejpam-2482	302	28	submodule	submodule	NOUN
ejpam-2482	303	1	if	if	SCONJ
ejpam-2482	303	2	and	and	CCONJ
ejpam-2482	303	3	only	only	ADV
ejpam-2482	303	4	if	if	SCONJ
ejpam-2482	303	5	m\n	m\n	NOUN
ejpam-2482	303	6	is	be	AUX
ejpam-2482	303	7	a	a	DET
ejpam-2482	303	8	classical	classical	ADJ
ejpam-2482	303	9	2	2	NUM
ejpam-2482	303	10	-	-	PUNCT
ejpam-2482	303	11	absorbing	absorbing	ADJ
ejpam-2482	303	12	m	m	NOUN
ejpam-2482	303	13	-	-	PUNCT
ejpam-2482	303	14	closed	closed	ADJ
ejpam-2482	303	15	.	.	PUNCT
ejpam-2482	304	1	proof	proof	NOUN
ejpam-2482	304	2	.	.	PUNCT
ejpam-2482	305	1	suppose	suppose	VERB
ejpam-2482	305	2	that	that	SCONJ
ejpam-2482	305	3	n	n	PRON
ejpam-2482	305	4	is	be	AUX
ejpam-2482	305	5	a	a	DET
ejpam-2482	305	6	classical	classical	ADJ
ejpam-2482	305	7	2	2	NUM
ejpam-2482	305	8	-	-	PUNCT
ejpam-2482	305	9	absorbing	absorb	VERB
ejpam-2482	305	10	submodule	submodule	NOUN
ejpam-2482	305	11	of	of	ADP
ejpam-2482	305	12	m	m	PROPN
ejpam-2482	305	13	and	and	CCONJ
ejpam-2482	305	14	i	i	PRON
ejpam-2482	305	15	,	,	PUNCT
ejpam-2482	305	16	j	j	PROPN
ejpam-2482	305	17	,	,	PUNCT
ejpam-2482	305	18	q	q	PROPN
ejpam-2482	305	19	are	be	AUX
ejpam-2482	305	20	ideals	ideal	NOUN
ejpam-2482	305	21	of	of	ADP
ejpam-2482	305	22	r	r	NOUN
ejpam-2482	305	23	and	and	CCONJ
ejpam-2482	305	24	k	k	PROPN
ejpam-2482	305	25	,	,	PUNCT
ejpam-2482	305	26	l	l	NOUN
ejpam-2482	305	27	are	be	AUX
ejpam-2482	305	28	submodules	submodule	NOUN
ejpam-2482	305	29	of	of	ADP
ejpam-2482	305	30	m	m	NOUN
ejpam-2482	305	31	such	such	ADJ
ejpam-2482	305	32	that	that	SCONJ
ejpam-2482	305	33	(	(	PUNCT
ejpam-2482	305	34	k	k	X
ejpam-2482	306	1	+	+	CCONJ
ejpam-2482	306	2	i	i	NOUN
ejpam-2482	306	3	j	j	PROPN
ejpam-2482	306	4	l	l	NOUN
ejpam-2482	306	5	)	)	PUNCT
ejpam-2482	306	6	*	*	PUNCT
ejpam-2482	306	7	s	s	VERB
ejpam-2482	306	8	#	#	NOUN
ejpam-2482	306	9	=	=	NOUN
ejpam-2482	306	10	.	.	PUNCT
ejpam-2482	307	1	and	and	CCONJ
ejpam-2482	307	2	(	(	PUNCT
ejpam-2482	307	3	k	k	PROPN
ejpam-2482	307	4	+	+	PROPN
ejpam-2482	307	5	iql	iql	NOUN
ejpam-2482	307	6	)	)	PUNCT
ejpam-2482	307	7	*	*	PUNCT
ejpam-2482	307	8	s	s	VERB
ejpam-2482	307	9	#	#	NOUN
ejpam-2482	307	10	=	=	NOUN
ejpam-2482	307	11	.	.	PUNCT
ejpam-2482	308	1	and	and	CCONJ
ejpam-2482	308	2	(	(	PUNCT
ejpam-2482	308	3	k	k	PROPN
ejpam-2482	308	4	+	+	NUM
ejpam-2482	308	5	jql	jql	NOUN
ejpam-2482	308	6	)	)	PUNCT
ejpam-2482	308	7	*	*	PUNCT
ejpam-2482	308	8	s	s	VERB
ejpam-2482	308	9	#	#	NOUN
ejpam-2482	308	10	=	=	NOUN
ejpam-2482	308	11	.	.	PUNCT
ejpam-2482	309	1	where	where	SCONJ
ejpam-2482	309	2	s	s	VERB
ejpam-2482	309	3	=	=	PUNCT
ejpam-2482	309	4	m\n	m\n	NOUN
ejpam-2482	309	5	.	.	PUNCT
ejpam-2482	310	1	assume	assume	VERB
ejpam-2482	310	2	that	that	SCONJ
ejpam-2482	310	3	(	(	PUNCT
ejpam-2482	310	4	k	k	X
ejpam-2482	310	5	+	+	CCONJ
ejpam-2482	310	6	i	i	PRON
ejpam-2482	310	7	jql	jql	VERB
ejpam-2482	310	8	)	)	PUNCT
ejpam-2482	310	9	*	*	PUNCT
ejpam-2482	310	10	s	s	X
ejpam-2482	310	11	=	=	PUNCT
ejpam-2482	310	12	..	..	PUNCT
ejpam-2482	311	1	then	then	ADV
ejpam-2482	311	2	k	k	PROPN
ejpam-2482	312	1	+	+	CCONJ
ejpam-2482	312	2	i	i	PRON
ejpam-2482	312	3	jql	jql	VERB
ejpam-2482	312	4	$	$	SYM
ejpam-2482	312	5	n	n	NOUN
ejpam-2482	313	1	and	and	CCONJ
ejpam-2482	313	2	so	so	ADV
ejpam-2482	313	3	k	k	PROPN
ejpam-2482	313	4	$	$	SYM
ejpam-2482	313	5	n	n	PROPN
ejpam-2482	314	1	and	and	CCONJ
ejpam-2482	314	2	i	i	PRON
ejpam-2482	314	3	jql	jql	VERB
ejpam-2482	314	4	$	$	SYM
ejpam-2482	314	5	n	n	NOUN
ejpam-2482	314	6	.	.	PUNCT
ejpam-2482	315	1	since	since	SCONJ
ejpam-2482	315	2	n	n	NUM
ejpam-2482	315	3	is	be	AUX
ejpam-2482	315	4	a	a	DET
ejpam-2482	315	5	classical	classical	ADJ
ejpam-2482	315	6	2	2	NUM
ejpam-2482	315	7	-	-	PUNCT
ejpam-2482	315	8	absorbing	absorb	VERB
ejpam-2482	315	9	submodule	submodule	NOUN
ejpam-2482	315	10	,	,	PUNCT
ejpam-2482	315	11	we	we	PRON
ejpam-2482	315	12	get	get	VERB
ejpam-2482	315	13	i	i	PRON
ejpam-2482	315	14	j	j	PROPN
ejpam-2482	315	15	l	l	NOUN
ejpam-2482	315	16	$	$	SYM
ejpam-2482	315	17	n	n	NUM
ejpam-2482	315	18	or	or	CCONJ
ejpam-2482	315	19	iql	iql	VERB
ejpam-2482	315	20	$	$	SYM
ejpam-2482	315	21	n	n	NOUN
ejpam-2482	315	22	or	or	CCONJ
ejpam-2482	315	23	jql	jql	VERB
ejpam-2482	315	24	$	$	SYM
ejpam-2482	315	25	n	n	NOUN
ejpam-2482	315	26	.	.	PUNCT
ejpam-2482	316	1	if	if	SCONJ
ejpam-2482	316	2	i	i	PRON
ejpam-2482	316	3	j	j	PROPN
ejpam-2482	316	4	l	l	NOUN
ejpam-2482	316	5	$	$	SYM
ejpam-2482	316	6	n	n	NOUN
ejpam-2482	316	7	,	,	PUNCT
ejpam-2482	316	8	then	then	ADV
ejpam-2482	316	9	we	we	PRON
ejpam-2482	316	10	get	get	VERB
ejpam-2482	316	11	(	(	PUNCT
ejpam-2482	316	12	k	k	X
ejpam-2482	317	1	+	+	CCONJ
ejpam-2482	317	2	i	i	NOUN
ejpam-2482	317	3	j	j	PROPN
ejpam-2482	317	4	l	l	NOUN
ejpam-2482	317	5	)	)	PUNCT
ejpam-2482	317	6	*	*	PUNCT
ejpam-2482	317	7	s	s	X
ejpam-2482	317	8	=	=	PUNCT
ejpam-2482	317	9	.	.	PUNCT
ejpam-2482	317	10	,	,	PUNCT
ejpam-2482	317	11	since	since	SCONJ
ejpam-2482	317	12	k	k	PROPN
ejpam-2482	317	13	$	$	SYM
ejpam-2482	317	14	n	n	NOUN
ejpam-2482	317	15	.	.	PUNCT
ejpam-2482	318	1	this	this	PRON
ejpam-2482	318	2	is	be	AUX
ejpam-2482	318	3	a	a	DET
ejpam-2482	318	4	contradiction	contradiction	NOUN
ejpam-2482	318	5	.	.	PUNCT
ejpam-2482	319	1	by	by	ADP
ejpam-2482	319	2	the	the	DET
ejpam-2482	319	3	other	other	ADJ
ejpam-2482	319	4	cases	case	NOUN
ejpam-2482	319	5	we	we	PRON
ejpam-2482	319	6	get	get	VERB
ejpam-2482	319	7	similar	similar	ADJ
ejpam-2482	319	8	contradictions	contradiction	NOUN
ejpam-2482	319	9	.	.	PUNCT
ejpam-2482	320	1	now	now	ADV
ejpam-2482	320	2	for	for	ADP
ejpam-2482	320	3	the	the	DET
ejpam-2482	320	4	converse	converse	NOUN
ejpam-2482	320	5	suppose	suppose	VERB
ejpam-2482	320	6	that	that	SCONJ
ejpam-2482	320	7	s	s	VERB
ejpam-2482	320	8	=	=	SYM
ejpam-2482	320	9	m\n	m\n	NOUN
ejpam-2482	320	10	is	be	AUX
ejpam-2482	320	11	a	a	DET
ejpam-2482	320	12	classical	classical	ADJ
ejpam-2482	320	13	2	2	NUM
ejpam-2482	320	14	-	-	PUNCT
ejpam-2482	320	15	absorbing	absorbing	ADJ
ejpam-2482	320	16	m	m	NOUN
ejpam-2482	320	17	-	-	PUNCT
ejpam-2482	320	18	closed	closed	ADJ
ejpam-2482	320	19	and	and	CCONJ
ejpam-2482	320	20	assume	assume	VERB
ejpam-2482	320	21	that	that	SCONJ
ejpam-2482	320	22	i	i	PRON
ejpam-2482	320	23	jql	jql	VERB
ejpam-2482	320	24	$	$	SYM
ejpam-2482	320	25	n	n	NOUN
ejpam-2482	320	26	for	for	ADP
ejpam-2482	320	27	some	some	DET
ejpam-2482	320	28	ideals	ideal	NOUN
ejpam-2482	320	29	i	i	PRON
ejpam-2482	320	30	,	,	PUNCT
ejpam-2482	320	31	j	j	PROPN
ejpam-2482	320	32	,	,	PUNCT
ejpam-2482	320	33	q	q	NOUN
ejpam-2482	320	34	of	of	ADP
ejpam-2482	320	35	r	r	NOUN
ejpam-2482	320	36	and	and	CCONJ
ejpam-2482	320	37	submodule	submodule	PROPN
ejpam-2482	320	38	l	l	NOUN
ejpam-2482	320	39	of	of	ADP
ejpam-2482	320	40	m	m	PROPN
ejpam-2482	320	41	.	.	PUNCT
ejpam-2482	321	1	then	then	ADV
ejpam-2482	321	2	we	we	PRON
ejpam-2482	321	3	get	get	VERB
ejpam-2482	321	4	for	for	ADP
ejpam-2482	321	5	submodule	submodule	NOUN
ejpam-2482	321	6	k	k	PROPN
ejpam-2482	322	1	=	=	PUNCT
ejpam-2482	323	1	(	(	PUNCT
ejpam-2482	323	2	0	0	NUM
ejpam-2482	323	3	)	)	PUNCT
ejpam-2482	323	4	,	,	PUNCT
ejpam-2482	324	1	k	k	PROPN
ejpam-2482	325	1	+	+	CCONJ
ejpam-2482	325	2	i	i	PRON
ejpam-2482	325	3	jql	jql	VERB
ejpam-2482	325	4	$	$	SYM
ejpam-2482	325	5	n	n	NOUN
ejpam-2482	325	6	.	.	PUNCT
ejpam-2482	326	1	thus	thus	ADV
ejpam-2482	326	2	(	(	PUNCT
ejpam-2482	326	3	k	k	X
ejpam-2482	326	4	+	+	CCONJ
ejpam-2482	326	5	i	i	PRON
ejpam-2482	326	6	jql	jql	VERB
ejpam-2482	326	7	)	)	PUNCT
ejpam-2482	326	8	*	*	PUNCT
ejpam-2482	326	9	s	s	X
ejpam-2482	326	10	=	=	PUNCT
ejpam-2482	326	11	..	..	PUNCT
ejpam-2482	326	12	since	since	SCONJ
ejpam-2482	326	13	s	s	PROPN
ejpam-2482	326	14	is	be	AUX
ejpam-2482	326	15	a	a	DET
ejpam-2482	326	16	classical	classical	ADJ
ejpam-2482	326	17	2	2	NUM
ejpam-2482	326	18	-	-	PUNCT
ejpam-2482	326	19	absorbing	absorbing	ADJ
ejpam-2482	326	20	m	m	NOUN
ejpam-2482	326	21	-	-	PUNCT
ejpam-2482	326	22	closed	closed	ADJ
ejpam-2482	326	23	,	,	PUNCT
ejpam-2482	326	24	(	(	PUNCT
ejpam-2482	326	25	k	k	X
ejpam-2482	327	1	+	+	CCONJ
ejpam-2482	327	2	i	i	NOUN
ejpam-2482	327	3	j	j	PROPN
ejpam-2482	327	4	l	l	NOUN
ejpam-2482	327	5	)	)	PUNCT
ejpam-2482	327	6	*	*	PUNCT
ejpam-2482	327	7	s	s	X
ejpam-2482	327	8	=	=	PUNCT
ejpam-2482	327	9	.	.	PUNCT
ejpam-2482	328	1	or	or	CCONJ
ejpam-2482	328	2	(	(	PUNCT
ejpam-2482	328	3	k	k	PROPN
ejpam-2482	328	4	+	+	PROPN
ejpam-2482	328	5	iql	iql	NOUN
ejpam-2482	328	6	)	)	PUNCT
ejpam-2482	328	7	*	*	PUNCT
ejpam-2482	329	1	s	s	X
ejpam-2482	329	2	=	=	PUNCT
ejpam-2482	329	3	.	.	PUNCT
ejpam-2482	330	1	or	or	CCONJ
ejpam-2482	330	2	(	(	PUNCT
ejpam-2482	330	3	k	k	PROPN
ejpam-2482	330	4	+	+	NUM
ejpam-2482	330	5	jql	jql	NOUN
ejpam-2482	330	6	)	)	PUNCT
ejpam-2482	330	7	*	*	PUNCT
ejpam-2482	331	1	s	s	X
ejpam-2482	331	2	=	=	PUNCT
ejpam-2482	331	3	..	..	PUNCT
ejpam-2482	332	1	hence	hence	ADV
ejpam-2482	332	2	i	i	INTJ
ejpam-2482	332	3	j	j	PROPN
ejpam-2482	332	4	l	l	NOUN
ejpam-2482	332	5	$	$	SYM
ejpam-2482	332	6	n	n	NUM
ejpam-2482	332	7	or	or	CCONJ
ejpam-2482	332	8	iql	iql	VERB
ejpam-2482	332	9	$	$	SYM
ejpam-2482	332	10	n	n	NOUN
ejpam-2482	332	11	or	or	CCONJ
ejpam-2482	332	12	jql	jql	VERB
ejpam-2482	332	13	$	$	SYM
ejpam-2482	332	14	n	n	NOUN
ejpam-2482	332	15	.	.	PUNCT
ejpam-2482	333	1	so	so	ADV
ejpam-2482	333	2	n	n	PRON
ejpam-2482	333	3	is	be	AUX
ejpam-2482	333	4	a	a	DET
ejpam-2482	333	5	classical	classical	ADJ
ejpam-2482	333	6	2	2	NUM
ejpam-2482	333	7	-	-	PUNCT
ejpam-2482	333	8	absorbing	absorb	VERB
ejpam-2482	333	9	submodule	submodule	NOUN
ejpam-2482	333	10	.	.	PUNCT
ejpam-2482	334	1	proposition	proposition	NOUN
ejpam-2482	334	2	9	9	NUM
ejpam-2482	334	3	.	.	PUNCT
ejpam-2482	335	1	let	let	VERB
ejpam-2482	335	2	r	r	PRON
ejpam-2482	335	3	be	be	AUX
ejpam-2482	335	4	a	a	DET
ejpam-2482	335	5	um	um	INTJ
ejpam-2482	335	6	-	-	PUNCT
ejpam-2482	335	7	ring	ring	NOUN
ejpam-2482	335	8	,	,	PUNCT
ejpam-2482	335	9	m	m	VERB
ejpam-2482	335	10	be	be	VERB
ejpam-2482	335	11	an	an	DET
ejpam-2482	335	12	r	r	NOUN
ejpam-2482	335	13	-	-	PUNCT
ejpam-2482	335	14	module	module	NOUN
ejpam-2482	335	15	,	,	PUNCT
ejpam-2482	335	16	n	n	CCONJ
ejpam-2482	335	17	a	a	DET
ejpam-2482	335	18	submodule	submodule	NOUN
ejpam-2482	335	19	of	of	ADP
ejpam-2482	335	20	m	m	PROPN
ejpam-2482	335	21	and	and	CCONJ
ejpam-2482	335	22	s	s	PART
ejpam-2482	335	23	=	=	ADJ
ejpam-2482	335	24	m\n	m\n	NOUN
ejpam-2482	335	25	.	.	PUNCT
ejpam-2482	336	1	the	the	DET
ejpam-2482	336	2	following	follow	VERB
ejpam-2482	336	3	conditions	condition	NOUN
ejpam-2482	336	4	are	be	AUX
ejpam-2482	336	5	equivalent	equivalent	ADJ
ejpam-2482	336	6	:	:	PUNCT
ejpam-2482	336	7	(	(	PUNCT
ejpam-2482	336	8	i	i	NOUN
ejpam-2482	336	9	)	)	PUNCT
ejpam-2482	336	10	n	n	PRON
ejpam-2482	336	11	is	be	AUX
ejpam-2482	336	12	a	a	DET
ejpam-2482	336	13	classical	classical	ADJ
ejpam-2482	336	14	2	2	NUM
ejpam-2482	336	15	-	-	PUNCT
ejpam-2482	336	16	absorbing	absorb	VERB
ejpam-2482	336	17	submodule	submodule	NOUN
ejpam-2482	336	18	of	of	ADP
ejpam-2482	336	19	m	m	PROPN
ejpam-2482	336	20	;	;	PUNCT
ejpam-2482	336	21	(	(	PUNCT
ejpam-2482	336	22	ii	ii	NOUN
ejpam-2482	336	23	)	)	PUNCT
ejpam-2482	336	24	s	s	VERB
ejpam-2482	336	25	is	be	AUX
ejpam-2482	336	26	a	a	DET
ejpam-2482	336	27	classical	classical	ADJ
ejpam-2482	336	28	2	2	NUM
ejpam-2482	336	29	-	-	PUNCT
ejpam-2482	336	30	absorbing	absorbing	ADJ
ejpam-2482	336	31	m	m	NOUN
ejpam-2482	336	32	-	-	PUNCT
ejpam-2482	336	33	closed	closed	ADJ
ejpam-2482	336	34	;	;	PUNCT
ejpam-2482	336	35	(	(	PUNCT
ejpam-2482	336	36	iii	iii	NOUN
ejpam-2482	336	37	)	)	PUNCT
ejpam-2482	336	38	for	for	ADP
ejpam-2482	336	39	every	every	DET
ejpam-2482	336	40	ideals	ideal	NOUN
ejpam-2482	336	41	i	i	PRON
ejpam-2482	336	42	,	,	PUNCT
ejpam-2482	336	43	j	j	PROPN
ejpam-2482	336	44	,	,	PUNCT
ejpam-2482	336	45	q	q	NOUN
ejpam-2482	336	46	of	of	ADP
ejpam-2482	336	47	r	r	NOUN
ejpam-2482	336	48	and	and	CCONJ
ejpam-2482	336	49	every	every	DET
ejpam-2482	336	50	submodule	submodule	NOUN
ejpam-2482	336	51	l	l	NOUN
ejpam-2482	336	52	of	of	ADP
ejpam-2482	336	53	m	m	PROPN
ejpam-2482	336	54	,	,	PUNCT
ejpam-2482	336	55	if	if	SCONJ
ejpam-2482	336	56	i	i	PRON
ejpam-2482	336	57	j	j	VERB
ejpam-2482	337	1	l	l	NOUN
ejpam-2482	337	2	*	*	PUNCT
ejpam-2482	337	3	s	s	VERB
ejpam-2482	337	4	#	#	NOUN
ejpam-2482	337	5	=	=	NOUN
ejpam-2482	337	6	.	.	PUNCT
ejpam-2482	338	1	and	and	CCONJ
ejpam-2482	338	2	iql	iql	AUX
ejpam-2482	338	3	*	*	PUNCT
ejpam-2482	338	4	s	s	PART
ejpam-2482	338	5	#	#	NOUN
ejpam-2482	338	6	=	=	NOUN
ejpam-2482	338	7	.	.	PUNCT
ejpam-2482	339	1	and	and	CCONJ
ejpam-2482	339	2	jql	jql	VERB
ejpam-2482	339	3	*	*	PUNCT
ejpam-2482	339	4	s	s	VERB
ejpam-2482	339	5	#	#	NOUN
ejpam-2482	339	6	=	=	PRON
ejpam-2482	339	7	.	.	PUNCT
ejpam-2482	339	8	,	,	PUNCT
ejpam-2482	339	9	then	then	ADV
ejpam-2482	339	10	ijql	ijql	ADP
ejpam-2482	339	11	*	*	PUNCT
ejpam-2482	339	12	s	s	PART
ejpam-2482	339	13	#	#	NOUN
ejpam-2482	339	14	=	=	NOUN
ejpam-2482	339	15	.	.	PUNCT
ejpam-2482	339	16	;	;	PUNCT
ejpam-2482	339	17	(	(	PUNCT
ejpam-2482	339	18	iv	iv	X
ejpam-2482	339	19	)	)	PUNCT
ejpam-2482	339	20	for	for	ADP
ejpam-2482	339	21	every	every	DET
ejpam-2482	339	22	ideals	ideal	NOUN
ejpam-2482	340	1	i	i	PRON
ejpam-2482	340	2	,	,	PUNCT
ejpam-2482	340	3	j	j	PROPN
ejpam-2482	340	4	,	,	PUNCT
ejpam-2482	340	5	q	q	NOUN
ejpam-2482	340	6	of	of	ADP
ejpam-2482	340	7	r	r	NOUN
ejpam-2482	340	8	and	and	CCONJ
ejpam-2482	340	9	every	every	DET
ejpam-2482	340	10	m	m	NOUN
ejpam-2482	340	11	"	"	PUNCT
ejpam-2482	340	12	m	m	PROPN
ejpam-2482	340	13	,	,	PUNCT
ejpam-2482	340	14	if	if	SCONJ
ejpam-2482	340	15	i	i	PRON
ejpam-2482	340	16	jm	jm	VERB
ejpam-2482	340	17	*	*	PUNCT
ejpam-2482	340	18	s	s	PART
ejpam-2482	340	19	#	#	NOUN
ejpam-2482	340	20	=	=	NOUN
ejpam-2482	340	21	.	.	PUNCT
ejpam-2482	341	1	and	and	CCONJ
ejpam-2482	341	2	iqm	iqm	PROPN
ejpam-2482	341	3	*	*	PUNCT
ejpam-2482	341	4	s	s	PART
ejpam-2482	341	5	#	#	NOUN
ejpam-2482	341	6	=	=	NOUN
ejpam-2482	341	7	.	.	PUNCT
ejpam-2482	342	1	and	and	CCONJ
ejpam-2482	342	2	jqm	jqm	PROPN
ejpam-2482	342	3	*	*	SYM
ejpam-2482	342	4	s	s	PART
ejpam-2482	342	5	#	#	NOUN
ejpam-2482	342	6	=	=	PRON
ejpam-2482	342	7	.	.	PUNCT
ejpam-2482	343	1	,	,	PUNCT
ejpam-2482	343	2	then	then	ADV
ejpam-2482	343	3	ijqm	ijqm	NOUN
ejpam-2482	343	4	*	*	PROPN
ejpam-2482	343	5	s	s	PART
ejpam-2482	343	6	#	#	NOUN
ejpam-2482	343	7	=	=	NOUN
ejpam-2482	343	8	..	..	PUNCT
ejpam-2482	343	9	proof	proof	NOUN
ejpam-2482	343	10	.	.	PUNCT
ejpam-2482	344	1	it	it	PRON
ejpam-2482	344	2	follows	follow	VERB
ejpam-2482	344	3	from	from	ADP
ejpam-2482	344	4	the	the	DET
ejpam-2482	344	5	previous	previous	ADJ
ejpam-2482	344	6	proposition	proposition	NOUN
ejpam-2482	344	7	,	,	PUNCT
ejpam-2482	344	8	theorem	theorem	VERB
ejpam-2482	344	9	2	2	NUM
ejpam-2482	344	10	and	and	CCONJ
ejpam-2482	344	11	theorem	theorem	VERB
ejpam-2482	344	12	4	4	NUM
ejpam-2482	344	13	.	.	PUNCT
ejpam-2482	344	14	theorem	theorem	NOUN
ejpam-2482	344	15	5	5	NUM
ejpam-2482	344	16	.	.	PUNCT
ejpam-2482	345	1	let	let	VERB
ejpam-2482	345	2	r	r	PRON
ejpam-2482	345	3	be	be	AUX
ejpam-2482	345	4	a	a	DET
ejpam-2482	345	5	um	um	INTJ
ejpam-2482	345	6	-	-	PUNCT
ejpam-2482	345	7	ring	ring	NOUN
ejpam-2482	345	8	,	,	PUNCT
ejpam-2482	345	9	m	m	VERB
ejpam-2482	345	10	be	be	VERB
ejpam-2482	345	11	an	an	DET
ejpam-2482	345	12	r	r	NOUN
ejpam-2482	345	13	-	-	PUNCT
ejpam-2482	345	14	module	module	NOUN
ejpam-2482	345	15	and	and	CCONJ
ejpam-2482	345	16	s	s	VERB
ejpam-2482	345	17	be	be	AUX
ejpam-2482	345	18	a	a	DET
ejpam-2482	345	19	classical	classical	ADJ
ejpam-2482	345	20	2	2	NUM
ejpam-2482	345	21	-	-	PUNCT
ejpam-2482	345	22	absorbing	absorbing	ADJ
ejpam-2482	345	23	m	m	NOUN
ejpam-2482	345	24	-	-	PUNCT
ejpam-2482	345	25	closed	closed	ADJ
ejpam-2482	345	26	.	.	PUNCT
ejpam-2482	346	1	then	then	ADV
ejpam-2482	346	2	the	the	DET
ejpam-2482	346	3	set	set	NOUN
ejpam-2482	346	4	of	of	ADP
ejpam-2482	346	5	all	all	DET
ejpam-2482	346	6	submodules	submodule	NOUN
ejpam-2482	346	7	of	of	ADP
ejpam-2482	346	8	m	m	PRON
ejpam-2482	346	9	which	which	PRON
ejpam-2482	346	10	are	be	AUX
ejpam-2482	346	11	disjoint	disjoint	ADJ
ejpam-2482	346	12	from	from	ADP
ejpam-2482	346	13	s	s	PRON
ejpam-2482	346	14	has	have	VERB
ejpam-2482	346	15	at	at	ADV
ejpam-2482	346	16	least	least	ADV
ejpam-2482	346	17	one	one	NUM
ejpam-2482	346	18	maximal	maximal	ADJ
ejpam-2482	346	19	element	element	NOUN
ejpam-2482	346	20	.	.	PUNCT
ejpam-2482	347	1	any	any	DET
ejpam-2482	347	2	such	such	ADJ
ejpam-2482	347	3	maximal	maximal	ADJ
ejpam-2482	347	4	element	element	NOUN
ejpam-2482	347	5	is	be	AUX
ejpam-2482	347	6	a	a	DET
ejpam-2482	347	7	classical	classical	ADJ
ejpam-2482	347	8	2	2	NUM
ejpam-2482	347	9	-	-	PUNCT
ejpam-2482	347	10	absorbing	absorb	VERB
ejpam-2482	347	11	submodule	submodule	NOUN
ejpam-2482	347	12	.	.	PUNCT
ejpam-2482	348	1	proof	proof	NOUN
ejpam-2482	348	2	.	.	PUNCT
ejpam-2482	349	1	let	let	VERB
ejpam-2482	349	2	"	"	PUNCT
ejpam-2482	349	3	=	=	PRON
ejpam-2482	349	4	{	{	PUNCT
ejpam-2482	349	5	n	n	NOUN
ejpam-2482	349	6	|	|	ADV
ejpam-2482	349	7	n	n	ADV
ejpam-2482	349	8	is	be	AUX
ejpam-2482	349	9	a	a	DET
ejpam-2482	349	10	submodule	submodule	NOUN
ejpam-2482	349	11	of	of	ADP
ejpam-2482	349	12	m	m	PROPN
ejpam-2482	349	13	and	and	CCONJ
ejpam-2482	349	14	n	n	PROPN
ejpam-2482	349	15	*	*	PUNCT
ejpam-2482	349	16	s	s	PART
ejpam-2482	349	17	=	=	NOUN
ejpam-2482	349	18	.	.	PUNCT
ejpam-2482	349	19	}	}	PUNCT
ejpam-2482	349	20	.	.	PUNCT
ejpam-2482	350	1	then	then	ADV
ejpam-2482	350	2	(	(	PUNCT
ejpam-2482	350	3	0	0	NUM
ejpam-2482	350	4	)	)	PUNCT
ejpam-2482	350	5	"	"	PUNCT
ejpam-2482	350	6	"	"	PUNCT
ejpam-2482	350	7	#	#	PROPN
ejpam-2482	350	8	=	=	PUNCT
ejpam-2482	350	9	..	..	PUNCT
ejpam-2482	350	10	since	since	SCONJ
ejpam-2482	350	11	"	"	PUNCT
ejpam-2482	350	12	is	be	AUX
ejpam-2482	350	13	partially	partially	ADV
ejpam-2482	350	14	ordered	order	VERB
ejpam-2482	350	15	by	by	ADP
ejpam-2482	350	16	using	use	VERB
ejpam-2482	350	17	zorn	zorn	PROPN
ejpam-2482	350	18	’s	’s	PART
ejpam-2482	350	19	lemma	lemma	PROPN
ejpam-2482	350	20	we	we	PRON
ejpam-2482	350	21	get	get	VERB
ejpam-2482	350	22	at	at	ADP
ejpam-2482	350	23	least	least	ADJ
ejpam-2482	350	24	a	a	DET
ejpam-2482	350	25	maximal	maximal	ADJ
ejpam-2482	350	26	element	element	NOUN
ejpam-2482	350	27	of	of	ADP
ejpam-2482	350	28	"	"	PUNCT
ejpam-2482	350	29	,	,	PUNCT
ejpam-2482	350	30	say	say	VERB
ejpam-2482	350	31	p	p	X
ejpam-2482	350	32	,	,	PUNCT
ejpam-2482	350	33	with	with	ADP
ejpam-2482	350	34	property	property	NOUN
ejpam-2482	350	35	p	p	NOUN
ejpam-2482	350	36	*	*	X
ejpam-2482	350	37	s	s	X
ejpam-2482	350	38	=	=	X
ejpam-2482	350	39	..	..	PUNCT
ejpam-2482	350	40	now	now	ADV
ejpam-2482	350	41	we	we	PRON
ejpam-2482	350	42	will	will	AUX
ejpam-2482	350	43	show	show	VERB
ejpam-2482	350	44	that	that	SCONJ
ejpam-2482	350	45	p	p	NOUN
ejpam-2482	350	46	is	be	AUX
ejpam-2482	350	47	classical	classical	ADJ
ejpam-2482	350	48	2	2	NUM
ejpam-2482	350	49	-	-	PUNCT
ejpam-2482	350	50	absorbing	absorbing	ADJ
ejpam-2482	350	51	.	.	PUNCT
ejpam-2482	351	1	suppose	suppose	VERB
ejpam-2482	351	2	that	that	SCONJ
ejpam-2482	351	3	i	i	PRON
ejpam-2482	351	4	jql	jql	VERB
ejpam-2482	351	5	$	$	SYM
ejpam-2482	351	6	p	p	NOUN
ejpam-2482	351	7	for	for	ADP
ejpam-2482	351	8	ideals	ideal	NOUN
ejpam-2482	351	9	i	i	PRON
ejpam-2482	351	10	,	,	PUNCT
ejpam-2482	351	11	j	j	PROPN
ejpam-2482	351	12	,	,	PUNCT
ejpam-2482	351	13	q	q	NOUN
ejpam-2482	351	14	of	of	ADP
ejpam-2482	351	15	r	r	NOUN
ejpam-2482	351	16	and	and	CCONJ
ejpam-2482	351	17	submodule	submodule	PROPN
ejpam-2482	351	18	l	l	NOUN
ejpam-2482	351	19	of	of	ADP
ejpam-2482	351	20	m	m	PROPN
ejpam-2482	351	21	.	.	PUNCT
ejpam-2482	352	1	assume	assume	VERB
ejpam-2482	352	2	that	that	SCONJ
ejpam-2482	352	3	i	i	PRON
ejpam-2482	353	1	j	j	PROPN
ejpam-2482	353	2	l	l	NOUN
ejpam-2482	353	3	#	#	SYM
ejpam-2482	353	4	$	$	SYM
ejpam-2482	353	5	p	p	NOUN
ejpam-2482	353	6	or	or	CCONJ
ejpam-2482	353	7	iql	iql	NOUN
ejpam-2482	353	8	#	#	SYM
ejpam-2482	353	9	$	$	SYM
ejpam-2482	353	10	p	p	NOUN
ejpam-2482	353	11	or	or	CCONJ
ejpam-2482	353	12	jql	jql	VERB
ejpam-2482	354	1	#	#	SYM
ejpam-2482	354	2	$	$	NOUN
ejpam-2482	354	3	p.	p.	NOUN
ejpam-2482	354	4	then	then	ADV
ejpam-2482	354	5	by	by	ADP
ejpam-2482	354	6	the	the	DET
ejpam-2482	354	7	maximality	maximality	NOUN
ejpam-2482	354	8	of	of	ADP
ejpam-2482	354	9	p	p	X
ejpam-2482	354	10	we	we	PRON
ejpam-2482	354	11	get	get	VERB
ejpam-2482	354	12	(	(	PUNCT
ejpam-2482	354	13	i	i	PRON
ejpam-2482	354	14	j	j	NOUN
ejpam-2482	354	15	l	l	NOUN
ejpam-2482	355	1	+	+	CCONJ
ejpam-2482	355	2	p	p	X
ejpam-2482	355	3	)	)	PUNCT
ejpam-2482	355	4	*	*	PUNCT
ejpam-2482	355	5	s	s	VERB
ejpam-2482	355	6	#	#	NOUN
ejpam-2482	355	7	=	=	NOUN
ejpam-2482	355	8	.	.	PUNCT
ejpam-2482	356	1	and	and	CCONJ
ejpam-2482	356	2	(	(	PUNCT
ejpam-2482	356	3	iql	iql	NOUN
ejpam-2482	356	4	+	+	CCONJ
ejpam-2482	356	5	p	p	X
ejpam-2482	356	6	)	)	PUNCT
ejpam-2482	356	7	*	*	PUNCT
ejpam-2482	356	8	s	s	VERB
ejpam-2482	356	9	#	#	NOUN
ejpam-2482	356	10	=	=	NOUN
ejpam-2482	356	11	.	.	PUNCT
ejpam-2482	357	1	and	and	CCONJ
ejpam-2482	357	2	(	(	PUNCT
ejpam-2482	357	3	jql	jql	X
ejpam-2482	357	4	+	+	CCONJ
ejpam-2482	357	5	p	p	X
ejpam-2482	357	6	)	)	PUNCT
ejpam-2482	357	7	*	*	PUNCT
ejpam-2482	357	8	s	s	VERB
ejpam-2482	357	9	#	#	NOUN
ejpam-2482	357	10	=	=	NOUN
ejpam-2482	357	11	..	..	PUNCT
ejpam-2482	357	12	since	since	SCONJ
ejpam-2482	357	13	s	s	PROPN
ejpam-2482	357	14	is	be	AUX
ejpam-2482	357	15	a	a	DET
ejpam-2482	357	16	classical	classical	ADJ
ejpam-2482	357	17	2	2	NUM
ejpam-2482	357	18	-	-	PUNCT
ejpam-2482	357	19	absorbing	absorb	VERB
ejpam-2482	357	20	m	m	NOUN
ejpam-2482	357	21	-	-	PUNCT
ejpam-2482	357	22	closed	closed	ADJ
ejpam-2482	357	23	we	we	PRON
ejpam-2482	357	24	have	have	VERB
ejpam-2482	357	25	(	(	PUNCT
ejpam-2482	357	26	i	i	PRON
ejpam-2482	357	27	jql	jql	VERB
ejpam-2482	357	28	+	+	CCONJ
ejpam-2482	357	29	p	p	X
ejpam-2482	357	30	)	)	PUNCT
ejpam-2482	357	31	*	*	PUNCT
ejpam-2482	357	32	s	s	VERB
ejpam-2482	357	33	#	#	NOUN
ejpam-2482	357	34	=	=	NOUN
ejpam-2482	357	35	..	..	PUNCT
ejpam-2482	358	1	hence	hence	ADV
ejpam-2482	358	2	p	p	X
ejpam-2482	358	3	*	*	PUNCT
ejpam-2482	358	4	s	s	PART
ejpam-2482	358	5	#	#	NOUN
ejpam-2482	358	6	=	=	PRON
ejpam-2482	358	7	.	.	PUNCT
ejpam-2482	358	8	,	,	PUNCT
ejpam-2482	358	9	which	which	PRON
ejpam-2482	358	10	is	be	AUX
ejpam-2482	358	11	a	a	DET
ejpam-2482	358	12	contradiction	contradiction	NOUN
ejpam-2482	358	13	.	.	PUNCT
ejpam-2482	359	1	thus	thus	ADV
ejpam-2482	359	2	p	p	PRON
ejpam-2482	359	3	is	be	AUX
ejpam-2482	359	4	a	a	DET
ejpam-2482	359	5	classical	classical	ADJ
ejpam-2482	359	6	2	2	NUM
ejpam-2482	359	7	-	-	PUNCT
ejpam-2482	359	8	absorbing	absorb	VERB
ejpam-2482	359	9	submodule	submodule	NOUN
ejpam-2482	359	10	of	of	ADP
ejpam-2482	359	11	m	m	PROPN
ejpam-2482	359	12	.	.	PUNCT
ejpam-2482	360	1	h.	h.	PROPN
ejpam-2482	360	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	360	3	,	,	PUNCT
ejpam-2482	360	4	ü.	ü.	NOUN
ejpam-2482	360	5	tekir	tekir	NOUN
ejpam-2482	360	6	and	and	CCONJ
ejpam-2482	360	7	k.	k.	PROPN
ejpam-2482	360	8	hakan	hakan	PROPN
ejpam-2482	360	9	oral	oral	PROPN
ejpam-2482	360	10	/	/	SYM
ejpam-2482	360	11	eur	eur	PROPN
ejpam-2482	360	12	.	.	PUNCT
ejpam-2482	361	1	j.	j.	PROPN
ejpam-2482	361	2	pure	pure	PROPN
ejpam-2482	361	3	appl	appl	PROPN
ejpam-2482	361	4	.	.	PROPN
ejpam-2482	361	5	math	math	PROPN
ejpam-2482	361	6	,	,	PUNCT
ejpam-2482	361	7	8	8	NUM
ejpam-2482	361	8	(	(	PUNCT
ejpam-2482	361	9	2015	2015	NUM
ejpam-2482	361	10	)	)	PUNCT
ejpam-2482	361	11	,	,	PUNCT
ejpam-2482	361	12	417	417	NUM
ejpam-2482	361	13	-	-	SYM
ejpam-2482	361	14	430	430	NUM
ejpam-2482	361	15	426	426	NUM
ejpam-2482	361	16	theorem	theorem	NOUN
ejpam-2482	361	17	6	6	NUM
ejpam-2482	361	18	.	.	PUNCT
ejpam-2482	362	1	let	let	VERB
ejpam-2482	362	2	r	r	PRON
ejpam-2482	362	3	be	be	AUX
ejpam-2482	362	4	a	a	DET
ejpam-2482	362	5	um	um	INTJ
ejpam-2482	362	6	-	-	PUNCT
ejpam-2482	362	7	ring	ring	NOUN
ejpam-2482	362	8	and	and	CCONJ
ejpam-2482	362	9	m	m	AUX
ejpam-2482	362	10	be	be	AUX
ejpam-2482	362	11	an	an	DET
ejpam-2482	362	12	r	r	NOUN
ejpam-2482	362	13	-	-	PUNCT
ejpam-2482	362	14	module	module	NOUN
ejpam-2482	362	15	.	.	PUNCT
ejpam-2482	363	1	(	(	PUNCT
ejpam-2482	363	2	i	i	NOUN
ejpam-2482	363	3	)	)	PUNCT
ejpam-2482	363	4	if	if	SCONJ
ejpam-2482	363	5	f	f	PROPN
ejpam-2482	363	6	is	be	AUX
ejpam-2482	363	7	a	a	DET
ejpam-2482	363	8	flat	flat	ADJ
ejpam-2482	363	9	r	r	NOUN
ejpam-2482	363	10	-	-	PUNCT
ejpam-2482	363	11	module	module	NOUN
ejpam-2482	363	12	and	and	CCONJ
ejpam-2482	363	13	n	n	NOUN
ejpam-2482	363	14	is	be	AUX
ejpam-2482	363	15	a	a	DET
ejpam-2482	363	16	classical	classical	ADJ
ejpam-2482	363	17	2	2	NUM
ejpam-2482	363	18	-	-	PUNCT
ejpam-2482	363	19	absorbing	absorb	VERB
ejpam-2482	363	20	submodule	submodule	NOUN
ejpam-2482	363	21	of	of	ADP
ejpam-2482	363	22	m	m	PRON
ejpam-2482	363	23	such	such	ADJ
ejpam-2482	363	24	that	that	SCONJ
ejpam-2482	363	25	f	f	PROPN
ejpam-2482	363	26	/	/	SYM
ejpam-2482	363	27	n	n	PROPN
ejpam-2482	363	28	#	#	SYM
ejpam-2482	363	29	=	=	SYM
ejpam-2482	363	30	f	f	X
ejpam-2482	363	31	/m	/m	PUNCT
ejpam-2482	363	32	,	,	PUNCT
ejpam-2482	363	33	then	then	ADV
ejpam-2482	363	34	f	f	PROPN
ejpam-2482	363	35	/	/	SYM
ejpam-2482	363	36	n	n	PROPN
ejpam-2482	363	37	is	be	AUX
ejpam-2482	363	38	a	a	DET
ejpam-2482	363	39	classical	classical	ADJ
ejpam-2482	363	40	2	2	NUM
ejpam-2482	363	41	-	-	PUNCT
ejpam-2482	363	42	absorbing	absorb	VERB
ejpam-2482	363	43	submodule	submodule	NOUN
ejpam-2482	363	44	of	of	ADP
ejpam-2482	363	45	f	f	PROPN
ejpam-2482	363	46	/m	/m	PUNCT
ejpam-2482	363	47	.	.	PUNCT
ejpam-2482	364	1	(	(	PUNCT
ejpam-2482	364	2	ii	ii	NOUN
ejpam-2482	364	3	)	)	PUNCT
ejpam-2482	364	4	suppose	suppose	VERB
ejpam-2482	364	5	that	that	SCONJ
ejpam-2482	364	6	f	f	PROPN
ejpam-2482	364	7	is	be	AUX
ejpam-2482	364	8	a	a	DET
ejpam-2482	364	9	faithfully	faithfully	ADV
ejpam-2482	364	10	flat	flat	ADJ
ejpam-2482	364	11	r	r	NOUN
ejpam-2482	364	12	-	-	PUNCT
ejpam-2482	364	13	module	module	NOUN
ejpam-2482	364	14	.	.	PUNCT
ejpam-2482	365	1	then	then	ADV
ejpam-2482	365	2	n	n	PRON
ejpam-2482	365	3	is	be	AUX
ejpam-2482	365	4	a	a	DET
ejpam-2482	365	5	classical	classical	ADJ
ejpam-2482	365	6	2	2	NUM
ejpam-2482	365	7	-	-	PUNCT
ejpam-2482	365	8	absorbing	absorb	VERB
ejpam-2482	365	9	submodule	submodule	NOUN
ejpam-2482	365	10	of	of	ADP
ejpam-2482	365	11	m	m	PROPN
ejpam-2482	365	12	if	if	SCONJ
ejpam-2482	366	1	and	and	CCONJ
ejpam-2482	366	2	only	only	ADV
ejpam-2482	366	3	if	if	SCONJ
ejpam-2482	366	4	f	f	PROPN
ejpam-2482	366	5	/	/	SYM
ejpam-2482	366	6	n	n	PROPN
ejpam-2482	366	7	is	be	AUX
ejpam-2482	366	8	a	a	DET
ejpam-2482	366	9	classical	classical	ADJ
ejpam-2482	366	10	2	2	NUM
ejpam-2482	366	11	-	-	PUNCT
ejpam-2482	366	12	absorbing	absorb	VERB
ejpam-2482	366	13	submodule	submodule	NOUN
ejpam-2482	366	14	of	of	ADP
ejpam-2482	366	15	f	f	PROPN
ejpam-2482	366	16	/m	/m	PUNCT
ejpam-2482	366	17	.	.	PUNCT
ejpam-2482	367	1	proof	proof	NOUN
ejpam-2482	367	2	.	.	PUNCT
ejpam-2482	368	1	(	(	PUNCT
ejpam-2482	368	2	i	i	NOUN
ejpam-2482	368	3	)	)	PUNCT
ejpam-2482	368	4	let	let	VERB
ejpam-2482	368	5	a	a	DET
ejpam-2482	368	6	,	,	PUNCT
ejpam-2482	368	7	b	b	NOUN
ejpam-2482	368	8	,	,	PUNCT
ejpam-2482	369	1	c	c	PROPN
ejpam-2482	369	2	"	"	PUNCT
ejpam-2482	369	3	r.	r.	PROPN
ejpam-2482	370	1	then	then	ADV
ejpam-2482	370	2	we	we	PRON
ejpam-2482	370	3	get	get	VERB
ejpam-2482	370	4	by	by	ADP
ejpam-2482	370	5	theorem	theorem	NOUN
ejpam-2482	370	6	4	4	NUM
ejpam-2482	370	7	,	,	PUNCT
ejpam-2482	370	8	!	!	PUNCT
ejpam-2482	371	1	n	n	X
ejpam-2482	371	2	:	:	PUNCT
ejpam-2482	372	1	m	m	VERB
ejpam-2482	372	2	abc	abc	NOUN
ejpam-2482	372	3	"	"	PUNCT
ejpam-2482	372	4	=	=	PUNCT
ejpam-2482	372	5	!	!	PUNCT
ejpam-2482	373	1	n	n	X
ejpam-2482	373	2	:	:	PUNCT
ejpam-2482	373	3	m	m	VERB
ejpam-2482	373	4	ab	ab	NOUN
ejpam-2482	373	5	"	"	PUNCT
ejpam-2482	373	6	or	or	CCONJ
ejpam-2482	373	7	!	!	PUNCT
ejpam-2482	374	1	n	n	X
ejpam-2482	374	2	:	:	PUNCT
ejpam-2482	375	1	m	m	VERB
ejpam-2482	375	2	abc	abc	NOUN
ejpam-2482	375	3	"	"	PUNCT
ejpam-2482	375	4	=	=	PUNCT
ejpam-2482	375	5	!	!	PUNCT
ejpam-2482	376	1	n	n	X
ejpam-2482	376	2	:	:	PUNCT
ejpam-2482	376	3	m	m	VERB
ejpam-2482	376	4	ac	ac	ADJ
ejpam-2482	376	5	"	"	PUNCT
ejpam-2482	376	6	or	or	CCONJ
ejpam-2482	376	7	!	!	PUNCT
ejpam-2482	377	1	n	n	X
ejpam-2482	377	2	:	:	PUNCT
ejpam-2482	378	1	m	m	VERB
ejpam-2482	378	2	abc	abc	NOUN
ejpam-2482	378	3	"	"	PUNCT
ejpam-2482	378	4	=	=	PUNCT
ejpam-2482	378	5	!	!	PUNCT
ejpam-2482	379	1	n	n	X
ejpam-2482	379	2	:	:	PUNCT
ejpam-2482	380	1	m	m	VERB
ejpam-2482	380	2	bc	bc	PROPN
ejpam-2482	380	3	"	"	PUNCT
ejpam-2482	380	4	.	.	PUNCT
ejpam-2482	381	1	assume	assume	VERB
ejpam-2482	381	2	that	that	PRON
ejpam-2482	381	3	!	!	PUNCT
ejpam-2482	382	1	n	n	X
ejpam-2482	382	2	:	:	PUNCT
ejpam-2482	383	1	m	m	VERB
ejpam-2482	383	2	abc	abc	NOUN
ejpam-2482	383	3	"	"	PUNCT
ejpam-2482	383	4	=	=	PUNCT
ejpam-2482	383	5	!	!	PUNCT
ejpam-2482	384	1	n	n	X
ejpam-2482	384	2	:	:	PUNCT
ejpam-2482	385	1	m	m	VERB
ejpam-2482	385	2	ab	ab	INTJ
ejpam-2482	385	3	"	"	PUNCT
ejpam-2482	385	4	.	.	PUNCT
ejpam-2482	386	1	then	then	ADV
ejpam-2482	386	2	by	by	ADP
ejpam-2482	386	3	[	[	X
ejpam-2482	386	4	4	4	NUM
ejpam-2482	386	5	,	,	PUNCT
ejpam-2482	386	6	lemma	lemma	PROPN
ejpam-2482	386	7	3.2	3.2	NUM
ejpam-2482	386	8	]	]	PUNCT
ejpam-2482	386	9	,	,	PUNCT
ejpam-2482	386	10	!	!	PUNCT
ejpam-2482	387	1	f	f	PROPN
ejpam-2482	387	2	/	/	SYM
ejpam-2482	388	1	n	n	PROPN
ejpam-2482	388	2	:	:	PUNCT
ejpam-2482	388	3	f	f	X
ejpam-2482	388	4	/	/	SYM
ejpam-2482	388	5	m	m	VERB
ejpam-2482	388	6	abc	abc	NOUN
ejpam-2482	388	7	"	"	PUNCT
ejpam-2482	388	8	=	=	PROPN
ejpam-2482	388	9	f	f	PROPN
ejpam-2482	388	10	/	/	PUNCT
ejpam-2482	388	11	!	!	PUNCT
ejpam-2482	389	1	n	n	X
ejpam-2482	389	2	:	:	PUNCT
ejpam-2482	390	1	m	m	VERB
ejpam-2482	390	2	abc	abc	NOUN
ejpam-2482	390	3	"	"	PUNCT
ejpam-2482	390	4	=	=	PROPN
ejpam-2482	390	5	f	f	PROPN
ejpam-2482	390	6	/	/	PUNCT
ejpam-2482	390	7	!	!	PUNCT
ejpam-2482	391	1	n	n	X
ejpam-2482	391	2	:	:	PUNCT
ejpam-2482	392	1	m	m	VERB
ejpam-2482	392	2	ab	ab	INTJ
ejpam-2482	392	3	"	"	PUNCT
ejpam-2482	392	4	=	=	PUNCT
ejpam-2482	392	5	!	!	PUNCT
ejpam-2482	393	1	f	f	PROPN
ejpam-2482	393	2	/	/	SYM
ejpam-2482	394	1	n	n	PROPN
ejpam-2482	394	2	:	:	PUNCT
ejpam-2482	394	3	f	f	X
ejpam-2482	394	4	/	/	SYM
ejpam-2482	394	5	m	m	VERB
ejpam-2482	394	6	ab	ab	NOUN
ejpam-2482	394	7	"	"	PUNCT
ejpam-2482	394	8	.	.	PUNCT
ejpam-2482	395	1	again	again	ADV
ejpam-2482	395	2	theorem	theorem	VERB
ejpam-2482	395	3	4	4	NUM
ejpam-2482	395	4	implies	imply	VERB
ejpam-2482	395	5	that	that	SCONJ
ejpam-2482	395	6	f	f	PROPN
ejpam-2482	395	7	/	/	SYM
ejpam-2482	395	8	n	n	PROPN
ejpam-2482	395	9	is	be	AUX
ejpam-2482	395	10	a	a	DET
ejpam-2482	395	11	classical	classical	ADJ
ejpam-2482	395	12	2	2	NUM
ejpam-2482	395	13	-	-	PUNCT
ejpam-2482	395	14	absorbing	absorb	VERB
ejpam-2482	395	15	submodule	submodule	NOUN
ejpam-2482	395	16	of	of	ADP
ejpam-2482	395	17	f	f	PROPN
ejpam-2482	395	18	/m	/m	PUNCT
ejpam-2482	395	19	.	.	PUNCT
ejpam-2482	396	1	(	(	PUNCT
ejpam-2482	396	2	ii	ii	NOUN
ejpam-2482	396	3	)	)	PUNCT
ejpam-2482	396	4	let	let	VERB
ejpam-2482	396	5	n	n	PRON
ejpam-2482	396	6	be	be	AUX
ejpam-2482	396	7	a	a	DET
ejpam-2482	396	8	classical	classical	ADJ
ejpam-2482	396	9	2	2	NUM
ejpam-2482	396	10	-	-	PUNCT
ejpam-2482	396	11	absorbing	absorb	VERB
ejpam-2482	396	12	submodule	submodule	NOUN
ejpam-2482	396	13	of	of	ADP
ejpam-2482	396	14	m	m	PRON
ejpam-2482	396	15	and	and	CCONJ
ejpam-2482	396	16	assume	assume	VERB
ejpam-2482	396	17	that	that	SCONJ
ejpam-2482	396	18	f	f	PROPN
ejpam-2482	396	19	/	/	SYM
ejpam-2482	396	20	n	n	PROPN
ejpam-2482	397	1	=	=	SYM
ejpam-2482	397	2	f	f	PROPN
ejpam-2482	397	3	/	/	SYM
ejpam-2482	397	4	m	m	PROPN
ejpam-2482	397	5	.	.	PUNCT
ejpam-2482	398	1	then	then	ADV
ejpam-2482	398	2	0	0	NUM
ejpam-2482	399	1	(	(	PUNCT
ejpam-2482	399	2	f	f	PROPN
ejpam-2482	399	3	/	/	SYM
ejpam-2482	399	4	n	n	PROPN
ejpam-2482	399	5	$	$	SYM
ejpam-2482	399	6	(	(	PUNCT
ejpam-2482	399	7	f	f	PROPN
ejpam-2482	399	8	/	/	SYM
ejpam-2482	399	9	m	m	PROPN
ejpam-2482	399	10	(	(	PUNCT
ejpam-2482	399	11	0	0	NUM
ejpam-2482	399	12	is	be	AUX
ejpam-2482	399	13	an	an	DET
ejpam-2482	399	14	exact	exact	ADJ
ejpam-2482	399	15	sequence	sequence	NOUN
ejpam-2482	399	16	.	.	PUNCT
ejpam-2482	400	1	since	since	SCONJ
ejpam-2482	400	2	f	f	PROPN
ejpam-2482	400	3	is	be	AUX
ejpam-2482	400	4	a	a	DET
ejpam-2482	400	5	faithfully	faithfully	ADV
ejpam-2482	400	6	flat	flat	ADJ
ejpam-2482	400	7	module	module	NOUN
ejpam-2482	400	8	,	,	PUNCT
ejpam-2482	400	9	0	0	NUM
ejpam-2482	400	10	(	(	PUNCT
ejpam-2482	400	11	n	n	DET
ejpam-2482	400	12	$	$	SYM
ejpam-2482	400	13	(	(	PUNCT
ejpam-2482	400	14	m	m	AUX
ejpam-2482	400	15	(	(	PUNCT
ejpam-2482	400	16	0	0	NUM
ejpam-2482	400	17	is	be	AUX
ejpam-2482	400	18	an	an	DET
ejpam-2482	400	19	exact	exact	ADJ
ejpam-2482	400	20	sequence	sequence	NOUN
ejpam-2482	400	21	.	.	PUNCT
ejpam-2482	401	1	so	so	ADV
ejpam-2482	401	2	n	n	NOUN
ejpam-2482	401	3	=	=	SYM
ejpam-2482	401	4	m	m	PROPN
ejpam-2482	401	5	,	,	PUNCT
ejpam-2482	401	6	which	which	PRON
ejpam-2482	401	7	is	be	AUX
ejpam-2482	401	8	a	a	DET
ejpam-2482	401	9	contradiction	contradiction	NOUN
ejpam-2482	401	10	.	.	PUNCT
ejpam-2482	402	1	so	so	ADV
ejpam-2482	402	2	f	f	PROPN
ejpam-2482	402	3	/	/	SYM
ejpam-2482	402	4	n	n	PROPN
ejpam-2482	402	5	#	#	SYM
ejpam-2482	402	6	=	=	SYM
ejpam-2482	402	7	f	f	PROPN
ejpam-2482	402	8	/m	/m	PUNCT
ejpam-2482	402	9	.	.	PUNCT
ejpam-2482	403	1	then	then	ADV
ejpam-2482	403	2	f	f	PROPN
ejpam-2482	403	3	/	/	SYM
ejpam-2482	403	4	n	n	PROPN
ejpam-2482	403	5	is	be	AUX
ejpam-2482	403	6	a	a	DET
ejpam-2482	403	7	classical	classical	ADJ
ejpam-2482	403	8	2	2	NUM
ejpam-2482	403	9	-	-	PUNCT
ejpam-2482	403	10	absorbing	absorb	VERB
ejpam-2482	403	11	submodule	submodule	NOUN
ejpam-2482	403	12	by	by	ADP
ejpam-2482	403	13	(	(	PUNCT
ejpam-2482	403	14	1	1	NUM
ejpam-2482	403	15	)	)	PUNCT
ejpam-2482	403	16	.	.	PUNCT
ejpam-2482	404	1	now	now	ADV
ejpam-2482	404	2	for	for	ADP
ejpam-2482	404	3	conversely	conversely	ADV
ejpam-2482	404	4	,	,	PUNCT
ejpam-2482	404	5	let	let	VERB
ejpam-2482	404	6	f	f	PRON
ejpam-2482	404	7	/	/	SYM
ejpam-2482	404	8	n	n	CCONJ
ejpam-2482	404	9	be	be	AUX
ejpam-2482	404	10	a	a	DET
ejpam-2482	404	11	classical	classical	ADJ
ejpam-2482	404	12	2	2	NUM
ejpam-2482	404	13	-	-	PUNCT
ejpam-2482	404	14	absorbing	absorb	VERB
ejpam-2482	404	15	submodule	submodule	NOUN
ejpam-2482	404	16	of	of	ADP
ejpam-2482	404	17	f	f	PROPN
ejpam-2482	404	18	/	/	SYM
ejpam-2482	404	19	m	m	PROPN
ejpam-2482	404	20	.	.	PUNCT
ejpam-2482	405	1	we	we	PRON
ejpam-2482	405	2	have	have	VERB
ejpam-2482	405	3	f	f	PROPN
ejpam-2482	405	4	/	/	SYM
ejpam-2482	405	5	n	n	PROPN
ejpam-2482	405	6	#	#	SYM
ejpam-2482	405	7	=	=	SYM
ejpam-2482	405	8	f	f	PROPN
ejpam-2482	405	9	/	/	SYM
ejpam-2482	405	10	m	m	PROPN
ejpam-2482	405	11	and	and	CCONJ
ejpam-2482	405	12	so	so	ADV
ejpam-2482	405	13	n	n	ADV
ejpam-2482	405	14	#	#	SYM
ejpam-2482	405	15	=	=	NOUN
ejpam-2482	405	16	m	m	VERB
ejpam-2482	405	17	.	.	PUNCT
ejpam-2482	406	1	let	let	VERB
ejpam-2482	406	2	a	a	DET
ejpam-2482	406	3	,	,	PUNCT
ejpam-2482	406	4	b	b	NOUN
ejpam-2482	406	5	,	,	PUNCT
ejpam-2482	406	6	c	c	PROPN
ejpam-2482	406	7	"	"	PUNCT
ejpam-2482	406	8	r.	r.	PROPN
ejpam-2482	406	9	then	then	ADV
ejpam-2482	406	10	!	!	PUNCT
ejpam-2482	407	1	f	f	PROPN
ejpam-2482	407	2	/	/	SYM
ejpam-2482	407	3	n	n	PROPN
ejpam-2482	407	4	:	:	PUNCT
ejpam-2482	407	5	f	f	X
ejpam-2482	407	6	/	/	SYM
ejpam-2482	407	7	m	m	VERB
ejpam-2482	407	8	abc	abc	NOUN
ejpam-2482	407	9	"	"	PUNCT
ejpam-2482	407	10	=	=	PUNCT
ejpam-2482	407	11	!	!	PUNCT
ejpam-2482	408	1	f	f	PROPN
ejpam-2482	408	2	/	/	SYM
ejpam-2482	409	1	n	n	PROPN
ejpam-2482	409	2	:	:	PUNCT
ejpam-2482	409	3	f	f	X
ejpam-2482	409	4	/	/	SYM
ejpam-2482	409	5	m	m	VERB
ejpam-2482	409	6	ab	ab	NOUN
ejpam-2482	409	7	"	"	PUNCT
ejpam-2482	409	8	or	or	CCONJ
ejpam-2482	409	9	!	!	PUNCT
ejpam-2482	410	1	f	f	PROPN
ejpam-2482	410	2	/	/	SYM
ejpam-2482	410	3	n	n	PROPN
ejpam-2482	410	4	:	:	PUNCT
ejpam-2482	410	5	f	f	X
ejpam-2482	410	6	/	/	SYM
ejpam-2482	410	7	m	m	VERB
ejpam-2482	410	8	abc	abc	NOUN
ejpam-2482	410	9	"	"	PUNCT
ejpam-2482	410	10	=	=	PUNCT
ejpam-2482	410	11	!	!	PUNCT
ejpam-2482	411	1	f	f	PROPN
ejpam-2482	411	2	/	/	SYM
ejpam-2482	412	1	n	n	PROPN
ejpam-2482	412	2	:	:	PUNCT
ejpam-2482	412	3	f	f	X
ejpam-2482	412	4	/	/	SYM
ejpam-2482	412	5	m	m	VERB
ejpam-2482	412	6	ac	ac	ADJ
ejpam-2482	412	7	"	"	PUNCT
ejpam-2482	412	8	or	or	CCONJ
ejpam-2482	412	9	!	!	PUNCT
ejpam-2482	413	1	f	f	PROPN
ejpam-2482	413	2	/	/	SYM
ejpam-2482	413	3	n	n	PROPN
ejpam-2482	413	4	:	:	PUNCT
ejpam-2482	413	5	f	f	X
ejpam-2482	413	6	/	/	SYM
ejpam-2482	413	7	m	m	VERB
ejpam-2482	413	8	abc	abc	NOUN
ejpam-2482	413	9	"	"	PUNCT
ejpam-2482	413	10	=	=	PUNCT
ejpam-2482	413	11	!	!	PUNCT
ejpam-2482	414	1	f	f	PROPN
ejpam-2482	414	2	/	/	SYM
ejpam-2482	415	1	n	n	PROPN
ejpam-2482	415	2	:	:	PUNCT
ejpam-2482	415	3	f	f	X
ejpam-2482	415	4	/	/	SYM
ejpam-2482	415	5	m	m	VERB
ejpam-2482	415	6	bc	bc	PROPN
ejpam-2482	415	7	"	"	PUNCT
ejpam-2482	415	8	by	by	ADP
ejpam-2482	415	9	theorem	theorem	NOUN
ejpam-2482	415	10	4	4	NUM
ejpam-2482	415	11	.	.	PUNCT
ejpam-2482	415	12	assume	assume	VERB
ejpam-2482	415	13	that	that	PRON
ejpam-2482	415	14	!	!	PUNCT
ejpam-2482	416	1	f	f	PROPN
ejpam-2482	416	2	/	/	SYM
ejpam-2482	416	3	n	n	PROPN
ejpam-2482	416	4	:	:	PUNCT
ejpam-2482	416	5	f	f	X
ejpam-2482	416	6	/	/	SYM
ejpam-2482	416	7	m	m	VERB
ejpam-2482	416	8	abc	abc	NOUN
ejpam-2482	416	9	"	"	PUNCT
ejpam-2482	416	10	=	=	PUNCT
ejpam-2482	416	11	!	!	PUNCT
ejpam-2482	417	1	f	f	PROPN
ejpam-2482	417	2	/	/	SYM
ejpam-2482	418	1	n	n	PROPN
ejpam-2482	418	2	:	:	PUNCT
ejpam-2482	418	3	f	f	X
ejpam-2482	418	4	/	/	SYM
ejpam-2482	418	5	m	m	VERB
ejpam-2482	418	6	ab	ab	NOUN
ejpam-2482	418	7	"	"	PUNCT
ejpam-2482	418	8	.	.	PUNCT
ejpam-2482	419	1	hence	hence	ADV
ejpam-2482	419	2	f	f	PROPN
ejpam-2482	419	3	/	/	PUNCT
ejpam-2482	419	4	!	!	PUNCT
ejpam-2482	420	1	n	n	X
ejpam-2482	420	2	:	:	PUNCT
ejpam-2482	421	1	m	m	VERB
ejpam-2482	421	2	ab	ab	INTJ
ejpam-2482	421	3	"	"	PUNCT
ejpam-2482	421	4	=	=	PUNCT
ejpam-2482	421	5	!	!	PUNCT
ejpam-2482	422	1	f	f	PROPN
ejpam-2482	422	2	/	/	SYM
ejpam-2482	423	1	n	n	PROPN
ejpam-2482	423	2	:	:	PUNCT
ejpam-2482	423	3	f	f	X
ejpam-2482	423	4	/	/	SYM
ejpam-2482	423	5	m	m	VERB
ejpam-2482	423	6	ab	ab	NOUN
ejpam-2482	423	7	"	"	PUNCT
ejpam-2482	423	8	=	=	PUNCT
ejpam-2482	423	9	!	!	PUNCT
ejpam-2482	424	1	f	f	PROPN
ejpam-2482	424	2	/	/	SYM
ejpam-2482	425	1	n	n	PROPN
ejpam-2482	425	2	:	:	PUNCT
ejpam-2482	425	3	f	f	X
ejpam-2482	425	4	/	/	SYM
ejpam-2482	425	5	m	m	VERB
ejpam-2482	425	6	abc	abc	NOUN
ejpam-2482	425	7	"	"	PUNCT
ejpam-2482	425	8	=	=	PROPN
ejpam-2482	425	9	f	f	PROPN
ejpam-2482	425	10	/	/	PUNCT
ejpam-2482	425	11	!	!	PUNCT
ejpam-2482	426	1	n	n	X
ejpam-2482	426	2	:	:	PUNCT
ejpam-2482	427	1	m	m	VERB
ejpam-2482	427	2	abc	abc	PROPN
ejpam-2482	427	3	"	"	PUNCT
ejpam-2482	427	4	.	.	PUNCT
ejpam-2482	428	1	so	so	ADV
ejpam-2482	428	2	0	0	PUNCT
ejpam-2482	429	1	(	(	PUNCT
ejpam-2482	429	2	f	f	PROPN
ejpam-2482	429	3	/	/	PUNCT
ejpam-2482	429	4	!	!	PUNCT
ejpam-2482	430	1	n	n	X
ejpam-2482	430	2	:	:	PUNCT
ejpam-2482	431	1	m	m	VERB
ejpam-2482	431	2	ab	ab	INTJ
ejpam-2482	431	3	"	"	PUNCT
ejpam-2482	431	4	$	$	SYM
ejpam-2482	431	5	(	(	PUNCT
ejpam-2482	431	6	f	f	PROPN
ejpam-2482	431	7	/	/	PUNCT
ejpam-2482	431	8	!	!	PUNCT
ejpam-2482	432	1	n	n	X
ejpam-2482	432	2	:	:	PUNCT
ejpam-2482	432	3	m	m	VERB
ejpam-2482	432	4	abc	abc	PROPN
ejpam-2482	432	5	"	"	PUNCT
ejpam-2482	432	6	(	(	PUNCT
ejpam-2482	432	7	0	0	NUM
ejpam-2482	432	8	is	be	AUX
ejpam-2482	432	9	an	an	DET
ejpam-2482	432	10	exact	exact	ADJ
ejpam-2482	432	11	sequence	sequence	NOUN
ejpam-2482	432	12	.	.	PUNCT
ejpam-2482	433	1	since	since	SCONJ
ejpam-2482	433	2	f	f	PROPN
ejpam-2482	433	3	is	be	AUX
ejpam-2482	433	4	a	a	DET
ejpam-2482	433	5	faithfully	faithfully	ADV
ejpam-2482	433	6	flat	flat	ADJ
ejpam-2482	433	7	module	module	NOUN
ejpam-2482	433	8	,	,	PUNCT
ejpam-2482	433	9	0	0	NUM
ejpam-2482	433	10	(	(	PUNCT
ejpam-2482	433	11	!	!	PUNCT
ejpam-2482	434	1	n	n	X
ejpam-2482	434	2	:	:	PUNCT
ejpam-2482	434	3	m	m	VERB
ejpam-2482	434	4	ab	ab	INTJ
ejpam-2482	434	5	"	"	PUNCT
ejpam-2482	434	6	$	$	SYM
ejpam-2482	434	7	(	(	PUNCT
ejpam-2482	434	8	!	!	PUNCT
ejpam-2482	435	1	n	n	X
ejpam-2482	435	2	:	:	PUNCT
ejpam-2482	435	3	m	m	VERB
ejpam-2482	435	4	abc	abc	PROPN
ejpam-2482	435	5	"	"	PUNCT
ejpam-2482	435	6	(	(	PUNCT
ejpam-2482	435	7	0	0	NUM
ejpam-2482	435	8	is	be	AUX
ejpam-2482	435	9	an	an	DET
ejpam-2482	435	10	exact	exact	ADJ
ejpam-2482	435	11	sequence	sequence	NOUN
ejpam-2482	435	12	which	which	PRON
ejpam-2482	435	13	implies	imply	VERB
ejpam-2482	435	14	that	that	PRON
ejpam-2482	435	15	!	!	PUNCT
ejpam-2482	436	1	n	n	X
ejpam-2482	436	2	:	:	PUNCT
ejpam-2482	437	1	m	m	VERB
ejpam-2482	437	2	ab	ab	INTJ
ejpam-2482	437	3	"	"	PUNCT
ejpam-2482	437	4	=	=	PUNCT
ejpam-2482	437	5	!	!	PUNCT
ejpam-2482	438	1	n	n	X
ejpam-2482	438	2	:	:	PUNCT
ejpam-2482	439	1	m	m	VERB
ejpam-2482	439	2	abc	abc	PROPN
ejpam-2482	439	3	"	"	PUNCT
ejpam-2482	439	4	.	.	PUNCT
ejpam-2482	440	1	consequently	consequently	ADV
ejpam-2482	440	2	n	n	PRON
ejpam-2482	440	3	is	be	AUX
ejpam-2482	440	4	a	a	DET
ejpam-2482	440	5	classical	classical	ADJ
ejpam-2482	440	6	2	2	NUM
ejpam-2482	440	7	-	-	PUNCT
ejpam-2482	440	8	absorbing	absorb	VERB
ejpam-2482	440	9	submodule	submodule	NOUN
ejpam-2482	440	10	of	of	ADP
ejpam-2482	440	11	m	m	PRON
ejpam-2482	440	12	by	by	ADP
ejpam-2482	440	13	theorem	theorem	ADJ
ejpam-2482	440	14	4	4	NUM
ejpam-2482	440	15	.	.	PUNCT
ejpam-2482	440	16	corollary	corollary	ADJ
ejpam-2482	440	17	5	5	NUM
ejpam-2482	440	18	.	.	PUNCT
ejpam-2482	441	1	let	let	VERB
ejpam-2482	441	2	r	r	PRON
ejpam-2482	441	3	be	be	AUX
ejpam-2482	441	4	a	a	DET
ejpam-2482	441	5	um	um	INTJ
ejpam-2482	441	6	-	-	PUNCT
ejpam-2482	441	7	ring	ring	NOUN
ejpam-2482	441	8	,	,	PUNCT
ejpam-2482	441	9	m	m	VERB
ejpam-2482	441	10	be	be	VERB
ejpam-2482	441	11	an	an	DET
ejpam-2482	441	12	r	r	NOUN
ejpam-2482	441	13	-	-	PUNCT
ejpam-2482	441	14	module	module	NOUN
ejpam-2482	441	15	and	and	CCONJ
ejpam-2482	441	16	x	x	AUX
ejpam-2482	441	17	be	be	AUX
ejpam-2482	441	18	an	an	DET
ejpam-2482	441	19	indeterminate	indeterminate	NOUN
ejpam-2482	441	20	.	.	PUNCT
ejpam-2482	442	1	if	if	SCONJ
ejpam-2482	442	2	n	n	PRON
ejpam-2482	442	3	is	be	AUX
ejpam-2482	442	4	a	a	DET
ejpam-2482	442	5	classical	classical	ADJ
ejpam-2482	442	6	2	2	NUM
ejpam-2482	442	7	-	-	PUNCT
ejpam-2482	442	8	absorbing	absorb	VERB
ejpam-2482	442	9	submodule	submodule	NOUN
ejpam-2482	442	10	of	of	ADP
ejpam-2482	442	11	m	m	PROPN
ejpam-2482	442	12	,	,	PUNCT
ejpam-2482	442	13	then	then	ADV
ejpam-2482	442	14	n[x	n[x	ADJ
ejpam-2482	442	15	]	]	PUNCT
ejpam-2482	442	16	is	be	AUX
ejpam-2482	442	17	a	a	DET
ejpam-2482	442	18	classical	classical	ADJ
ejpam-2482	442	19	2	2	NUM
ejpam-2482	442	20	-	-	PUNCT
ejpam-2482	442	21	absorbing	absorb	VERB
ejpam-2482	442	22	submodule	submodule	NOUN
ejpam-2482	442	23	of	of	ADP
ejpam-2482	442	24	m[x	m[x	NOUN
ejpam-2482	442	25	]	]	PUNCT
ejpam-2482	442	26	.	.	PUNCT
ejpam-2482	443	1	proof	proof	NOUN
ejpam-2482	443	2	.	.	PUNCT
ejpam-2482	444	1	assume	assume	VERB
ejpam-2482	444	2	that	that	SCONJ
ejpam-2482	444	3	n	n	PRON
ejpam-2482	444	4	is	be	AUX
ejpam-2482	444	5	a	a	DET
ejpam-2482	444	6	classical	classical	ADJ
ejpam-2482	444	7	2	2	NUM
ejpam-2482	444	8	-	-	PUNCT
ejpam-2482	444	9	absorbing	absorb	VERB
ejpam-2482	444	10	submodule	submodule	NOUN
ejpam-2482	444	11	of	of	ADP
ejpam-2482	444	12	m	m	PROPN
ejpam-2482	444	13	.	.	PUNCT
ejpam-2482	445	1	notice	notice	VERB
ejpam-2482	445	2	that	that	SCONJ
ejpam-2482	445	3	r[x	r[x	NOUN
ejpam-2482	445	4	]	]	PUNCT
ejpam-2482	445	5	is	be	AUX
ejpam-2482	445	6	a	a	DET
ejpam-2482	445	7	flat	flat	ADJ
ejpam-2482	445	8	r	r	NOUN
ejpam-2482	445	9	-	-	PUNCT
ejpam-2482	445	10	module	module	NOUN
ejpam-2482	445	11	.	.	PUNCT
ejpam-2482	446	1	so	so	ADV
ejpam-2482	446	2	by	by	ADP
ejpam-2482	446	3	theorem	theorem	NOUN
ejpam-2482	446	4	6	6	NUM
ejpam-2482	446	5	,	,	PUNCT
ejpam-2482	446	6	r[x	r[x	NOUN
ejpam-2482	446	7	]	]	PUNCT
ejpam-2482	446	8	/	/	SYM
ejpam-2482	447	1	n	n	CCONJ
ejpam-2482	447	2	0	0	NUM
ejpam-2482	447	3	n[x	n[x	NOUN
ejpam-2482	447	4	]	]	PUNCT
ejpam-2482	447	5	is	be	AUX
ejpam-2482	447	6	a	a	DET
ejpam-2482	447	7	classical	classical	ADJ
ejpam-2482	447	8	2	2	NUM
ejpam-2482	447	9	-	-	PUNCT
ejpam-2482	447	10	absorbing	absorb	VERB
ejpam-2482	447	11	submodule	submodule	NOUN
ejpam-2482	447	12	of	of	ADP
ejpam-2482	447	13	r[x	r[x	NOUN
ejpam-2482	447	14	]	]	X
ejpam-2482	447	15	/m	/m	SYM
ejpam-2482	447	16	0	0	NUM
ejpam-2482	447	17	m[x	m[x	NOUN
ejpam-2482	447	18	]	]	PUNCT
ejpam-2482	447	19	.	.	PUNCT
ejpam-2482	448	1	for	for	ADP
ejpam-2482	448	2	an	an	DET
ejpam-2482	448	3	r	r	NOUN
ejpam-2482	448	4	-	-	PUNCT
ejpam-2482	448	5	module	module	NOUN
ejpam-2482	448	6	m	m	NOUN
ejpam-2482	448	7	,	,	PUNCT
ejpam-2482	448	8	the	the	DET
ejpam-2482	448	9	set	set	NOUN
ejpam-2482	448	10	of	of	ADP
ejpam-2482	448	11	zero	zero	NUM
ejpam-2482	448	12	-	-	PUNCT
ejpam-2482	448	13	divisors	divisor	NOUN
ejpam-2482	448	14	of	of	ADP
ejpam-2482	448	15	m	m	PROPN
ejpam-2482	448	16	is	be	AUX
ejpam-2482	448	17	denoted	denote	VERB
ejpam-2482	448	18	by	by	ADP
ejpam-2482	448	19	zr(m	zr(m	NOUN
ejpam-2482	448	20	)	)	PUNCT
ejpam-2482	448	21	.	.	PUNCT
ejpam-2482	449	1	proposition	proposition	NOUN
ejpam-2482	449	2	10	10	NUM
ejpam-2482	449	3	.	.	PUNCT
ejpam-2482	450	1	let	let	VERB
ejpam-2482	450	2	m	m	PRON
ejpam-2482	450	3	be	be	AUX
ejpam-2482	450	4	an	an	DET
ejpam-2482	450	5	r	r	NOUN
ejpam-2482	450	6	-	-	PUNCT
ejpam-2482	450	7	module	module	NOUN
ejpam-2482	450	8	,	,	PUNCT
ejpam-2482	450	9	n	n	PRON
ejpam-2482	450	10	be	be	VERB
ejpam-2482	450	11	a	a	DET
ejpam-2482	450	12	submodule	submodule	NOUN
ejpam-2482	450	13	and	and	CCONJ
ejpam-2482	450	14	s	s	AUX
ejpam-2482	450	15	be	be	AUX
ejpam-2482	450	16	a	a	DET
ejpam-2482	450	17	multiplicative	multiplicative	ADJ
ejpam-2482	450	18	subset	subset	NOUN
ejpam-2482	450	19	of	of	ADP
ejpam-2482	450	20	r.	r.	PROPN
ejpam-2482	450	21	(	(	PUNCT
ejpam-2482	450	22	i	i	NOUN
ejpam-2482	450	23	)	)	PUNCT
ejpam-2482	450	24	if	if	SCONJ
ejpam-2482	450	25	n	n	PRON
ejpam-2482	450	26	is	be	AUX
ejpam-2482	450	27	a	a	DET
ejpam-2482	450	28	classical	classical	ADJ
ejpam-2482	450	29	2	2	NUM
ejpam-2482	450	30	-	-	PUNCT
ejpam-2482	450	31	absorbing	absorb	VERB
ejpam-2482	450	32	submodule	submodule	NOUN
ejpam-2482	450	33	of	of	ADP
ejpam-2482	450	34	m	m	PRON
ejpam-2482	450	35	such	such	ADJ
ejpam-2482	450	36	that	that	PRON
ejpam-2482	450	37	!	!	PUNCT
ejpam-2482	451	1	n	n	X
ejpam-2482	451	2	:	:	PUNCT
ejpam-2482	451	3	r	r	NOUN
ejpam-2482	451	4	m	m	VERB
ejpam-2482	451	5	"	"	PUNCT
ejpam-2482	452	1	*	*	PUNCT
ejpam-2482	452	2	s	s	PART
ejpam-2482	452	3	=	=	PUNCT
ejpam-2482	452	4	.	.	PUNCT
ejpam-2482	452	5	,	,	PUNCT
ejpam-2482	452	6	then	then	ADV
ejpam-2482	452	7	s&1n	s&1n	PROPN
ejpam-2482	452	8	is	be	AUX
ejpam-2482	452	9	a	a	DET
ejpam-2482	452	10	classical	classical	ADJ
ejpam-2482	452	11	2	2	NUM
ejpam-2482	452	12	-	-	PUNCT
ejpam-2482	452	13	absorbing	absorb	VERB
ejpam-2482	452	14	submodule	submodule	NOUN
ejpam-2482	452	15	of	of	ADP
ejpam-2482	452	16	s&1	s&1	NOUN
ejpam-2482	452	17	m.	m.	PROPN
ejpam-2482	452	18	h.	h.	PROPN
ejpam-2482	452	19	mostafanasab	mostafanasab	VERB
ejpam-2482	452	20	,	,	PUNCT
ejpam-2482	452	21	ü.	ü.	NOUN
ejpam-2482	452	22	tekir	tekir	NOUN
ejpam-2482	452	23	and	and	CCONJ
ejpam-2482	452	24	k.	k.	PROPN
ejpam-2482	452	25	hakan	hakan	PROPN
ejpam-2482	452	26	oral	oral	PROPN
ejpam-2482	452	27	/	/	SYM
ejpam-2482	452	28	eur	eur	PROPN
ejpam-2482	452	29	.	.	PUNCT
ejpam-2482	453	1	j.	j.	PROPN
ejpam-2482	453	2	pure	pure	PROPN
ejpam-2482	453	3	appl	appl	PROPN
ejpam-2482	453	4	.	.	PROPN
ejpam-2482	453	5	math	math	PROPN
ejpam-2482	453	6	,	,	PUNCT
ejpam-2482	453	7	8	8	NUM
ejpam-2482	453	8	(	(	PUNCT
ejpam-2482	453	9	2015	2015	NUM
ejpam-2482	453	10	)	)	PUNCT
ejpam-2482	453	11	,	,	PUNCT
ejpam-2482	453	12	417	417	NUM
ejpam-2482	453	13	-	-	SYM
ejpam-2482	453	14	430	430	NUM
ejpam-2482	453	15	427	427	NUM
ejpam-2482	453	16	(	(	PUNCT
ejpam-2482	453	17	ii	ii	NOUN
ejpam-2482	453	18	)	)	PUNCT
ejpam-2482	453	19	if	if	SCONJ
ejpam-2482	453	20	s&1n	s&1n	PROPN
ejpam-2482	453	21	is	be	AUX
ejpam-2482	453	22	a	a	DET
ejpam-2482	453	23	classical	classical	ADJ
ejpam-2482	453	24	2	2	NUM
ejpam-2482	453	25	-	-	PUNCT
ejpam-2482	453	26	absorbing	absorb	VERB
ejpam-2482	453	27	submodule	submodule	NOUN
ejpam-2482	453	28	of	of	ADP
ejpam-2482	453	29	s&1	s&1	NOUN
ejpam-2482	453	30	m	m	NOUN
ejpam-2482	453	31	such	such	ADJ
ejpam-2482	453	32	that	that	SCONJ
ejpam-2482	453	33	zr(m	zr(m	NOUN
ejpam-2482	453	34	/	/	SYM
ejpam-2482	453	35	n)*s	n)*s	NOUN
ejpam-2482	453	36	=	=	NOUN
ejpam-2482	453	37	.	.	PUNCT
ejpam-2482	453	38	,	,	PUNCT
ejpam-2482	453	39	then	then	ADV
ejpam-2482	453	40	n	n	PRON
ejpam-2482	453	41	is	be	AUX
ejpam-2482	453	42	a	a	DET
ejpam-2482	453	43	classical	classical	ADJ
ejpam-2482	453	44	2	2	NUM
ejpam-2482	453	45	-	-	PUNCT
ejpam-2482	453	46	absorbing	absorb	VERB
ejpam-2482	453	47	submodule	submodule	NOUN
ejpam-2482	453	48	of	of	ADP
ejpam-2482	453	49	m.	m.	NOUN
ejpam-2482	453	50	proof	proof	NOUN
ejpam-2482	453	51	.	.	PUNCT
ejpam-2482	454	1	(	(	PUNCT
ejpam-2482	454	2	i	i	NOUN
ejpam-2482	454	3	)	)	PUNCT
ejpam-2482	454	4	let	let	VERB
ejpam-2482	454	5	n	n	PRON
ejpam-2482	454	6	be	be	AUX
ejpam-2482	454	7	a	a	DET
ejpam-2482	454	8	classical	classical	ADJ
ejpam-2482	454	9	2	2	NUM
ejpam-2482	454	10	-	-	PUNCT
ejpam-2482	454	11	absorbing	absorb	VERB
ejpam-2482	454	12	submodule	submodule	NOUN
ejpam-2482	454	13	of	of	ADP
ejpam-2482	454	14	m	m	PROPN
ejpam-2482	454	15	and	and	CCONJ
ejpam-2482	454	16	!	!	PUNCT
ejpam-2482	455	1	n	n	X
ejpam-2482	455	2	:	:	PUNCT
ejpam-2482	455	3	r	r	NOUN
ejpam-2482	455	4	m	m	VERB
ejpam-2482	455	5	"	"	PUNCT
ejpam-2482	455	6	*	*	PUNCT
ejpam-2482	455	7	s	s	X
ejpam-2482	455	8	=	=	X
ejpam-2482	455	9	..	..	PUNCT
ejpam-2482	455	10	suppose	suppose	VERB
ejpam-2482	455	11	that	that	SCONJ
ejpam-2482	455	12	a1	a1	NOUN
ejpam-2482	455	13	s1	s1	PROPN
ejpam-2482	455	14	a2	a2	PROPN
ejpam-2482	455	15	s2	s2	PROPN
ejpam-2482	455	16	a3	a3	NOUN
ejpam-2482	455	17	s3	s3	PROPN
ejpam-2482	455	18	m	m	PROPN
ejpam-2482	455	19	s4	s4	PROPN
ejpam-2482	455	20	"	"	PUNCT
ejpam-2482	455	21	s&1n	s&1n	PROPN
ejpam-2482	455	22	.	.	PUNCT
ejpam-2482	456	1	then	then	ADV
ejpam-2482	456	2	there	there	PRON
ejpam-2482	456	3	exist	exist	VERB
ejpam-2482	456	4	n	n	CCONJ
ejpam-2482	456	5	"	"	PUNCT
ejpam-2482	456	6	n	n	PROPN
ejpam-2482	456	7	and	and	CCONJ
ejpam-2482	456	8	s	s	AUX
ejpam-2482	456	9	"	"	PUNCT
ejpam-2482	456	10	s	s	VERB
ejpam-2482	456	11	such	such	ADJ
ejpam-2482	456	12	that	that	DET
ejpam-2482	456	13	a1	a1	NOUN
ejpam-2482	456	14	s1	s1	PROPN
ejpam-2482	456	15	a2	a2	PROPN
ejpam-2482	456	16	s2	s2	PROPN
ejpam-2482	456	17	a3	a3	NOUN
ejpam-2482	456	18	s3	s3	PROPN
ejpam-2482	456	19	m	m	PROPN
ejpam-2482	456	20	s4	s4	PROPN
ejpam-2482	456	21	=	=	SYM
ejpam-2482	456	22	n	n	NUM
ejpam-2482	456	23	s	s	NOUN
ejpam-2482	456	24	.	.	PUNCT
ejpam-2482	457	1	therefore	therefore	ADV
ejpam-2482	457	2	there	there	PRON
ejpam-2482	457	3	exists	exist	VERB
ejpam-2482	457	4	an	an	DET
ejpam-2482	457	5	s	s	NOUN
ejpam-2482	457	6	)	)	PUNCT
ejpam-2482	457	7	"	"	PUNCT
ejpam-2482	457	8	s	s	VERB
ejpam-2482	457	9	such	such	ADJ
ejpam-2482	457	10	that	that	DET
ejpam-2482	457	11	s)sa1a2a3m=	s)sa1a2a3m=	ADJ
ejpam-2482	457	12	s)s1s2s3s4n	s)s1s2s3s4n	PROPN
ejpam-2482	457	13	"	"	PUNCT
ejpam-2482	457	14	n	n	NOUN
ejpam-2482	457	15	.	.	PUNCT
ejpam-2482	458	1	so	so	ADV
ejpam-2482	458	2	a1a2a3	a1a2a3	ADJ
ejpam-2482	458	3	(	(	PUNCT
ejpam-2482	458	4	s	s	NOUN
ejpam-2482	458	5	!	!	PUNCT
ejpam-2482	458	6	m	m	PUNCT
ejpam-2482	458	7	)	)	PUNCT
ejpam-2482	458	8	"	"	PUNCT
ejpam-2482	458	9	n	n	CCONJ
ejpam-2482	458	10	for	for	ADP
ejpam-2482	458	11	s	s	PROPN
ejpam-2482	458	12	!	!	PUNCT
ejpam-2482	458	13	=	=	PUNCT
ejpam-2482	458	14	s)s	s)s	X
ejpam-2482	458	15	.	.	PUNCT
ejpam-2482	459	1	since	since	SCONJ
ejpam-2482	459	2	n	n	NUM
ejpam-2482	459	3	is	be	AUX
ejpam-2482	459	4	a	a	DET
ejpam-2482	459	5	classical	classical	ADJ
ejpam-2482	459	6	2	2	NUM
ejpam-2482	459	7	-	-	PUNCT
ejpam-2482	459	8	absorbing	absorb	VERB
ejpam-2482	459	9	submodule	submodule	NOUN
ejpam-2482	459	10	we	we	PRON
ejpam-2482	459	11	get	get	VERB
ejpam-2482	459	12	a1a2	a1a2	INTJ
ejpam-2482	459	13	(	(	PUNCT
ejpam-2482	459	14	s	s	NOUN
ejpam-2482	459	15	!	!	PUNCT
ejpam-2482	459	16	m	m	PUNCT
ejpam-2482	459	17	)	)	PUNCT
ejpam-2482	459	18	"	"	PUNCT
ejpam-2482	459	19	n	n	CCONJ
ejpam-2482	459	20	or	or	CCONJ
ejpam-2482	459	21	a1a3	a1a3	PROPN
ejpam-2482	459	22	(	(	PUNCT
ejpam-2482	459	23	s	s	NOUN
ejpam-2482	459	24	!	!	PUNCT
ejpam-2482	459	25	m	m	PUNCT
ejpam-2482	459	26	)	)	PUNCT
ejpam-2482	459	27	"	"	PUNCT
ejpam-2482	459	28	n	n	CCONJ
ejpam-2482	459	29	or	or	CCONJ
ejpam-2482	459	30	a2a3	a2a3	PROPN
ejpam-2482	459	31	(	(	PUNCT
ejpam-2482	459	32	s	s	NOUN
ejpam-2482	459	33	!	!	PUNCT
ejpam-2482	459	34	m	m	PUNCT
ejpam-2482	459	35	)	)	PUNCT
ejpam-2482	459	36	"	"	PUNCT
ejpam-2482	459	37	n	n	CCONJ
ejpam-2482	459	38	.	.	PUNCT
ejpam-2482	460	1	thus	thus	ADV
ejpam-2482	460	2	a1a2	a1a2	ADP
ejpam-2482	460	3	m	m	PROPN
ejpam-2482	460	4	s1s2s4	s1s2s4	NOUN
ejpam-2482	460	5	=	=	PUNCT
ejpam-2482	460	6	a1a2(s	a1a2(s	PROPN
ejpam-2482	460	7	!	!	PUNCT
ejpam-2482	460	8	m	m	VERB
ejpam-2482	460	9	)	)	PUNCT
ejpam-2482	460	10	s1s2s4s	s1s2s4s	PROPN
ejpam-2482	460	11	!	!	PUNCT
ejpam-2482	460	12	"	"	PUNCT
ejpam-2482	461	1	s&1n	s&1n	NUM
ejpam-2482	461	2	or	or	CCONJ
ejpam-2482	461	3	a1a3	a1a3	NOUN
ejpam-2482	461	4	m	m	NOUN
ejpam-2482	461	5	s1s3s4	s1s3s4	NOUN
ejpam-2482	461	6	"	"	PUNCT
ejpam-2482	461	7	s&1n	s&1n	PROPN
ejpam-2482	461	8	or	or	CCONJ
ejpam-2482	461	9	a2a3	a2a3	NOUN
ejpam-2482	461	10	m	m	VERB
ejpam-2482	461	11	s2s3s4	s2s3s4	VERB
ejpam-2482	461	12	"	"	PUNCT
ejpam-2482	461	13	s&1n	s&1n	PROPN
ejpam-2482	461	14	.	.	PUNCT
ejpam-2482	462	1	(	(	PUNCT
ejpam-2482	462	2	ii	ii	NOUN
ejpam-2482	462	3	)	)	PUNCT
ejpam-2482	462	4	assume	assume	VERB
ejpam-2482	462	5	that	that	SCONJ
ejpam-2482	462	6	s&1n	s&1n	PROPN
ejpam-2482	462	7	is	be	AUX
ejpam-2482	462	8	a	a	DET
ejpam-2482	462	9	classical	classical	ADJ
ejpam-2482	462	10	2	2	NUM
ejpam-2482	462	11	-	-	PUNCT
ejpam-2482	462	12	absorbing	absorb	VERB
ejpam-2482	462	13	submodule	submodule	NOUN
ejpam-2482	462	14	of	of	ADP
ejpam-2482	462	15	s&1	s&1	NOUN
ejpam-2482	462	16	m	m	PROPN
ejpam-2482	462	17	and	and	CCONJ
ejpam-2482	462	18	zr(m	zr(m	NOUN
ejpam-2482	462	19	/	/	SYM
ejpam-2482	462	20	n)*s	n)*s	NOUN
ejpam-2482	462	21	=	=	X
ejpam-2482	462	22	..	..	PUNCT
ejpam-2482	462	23	let	let	VERB
ejpam-2482	462	24	a	a	DET
ejpam-2482	462	25	,	,	PUNCT
ejpam-2482	462	26	b	b	NOUN
ejpam-2482	462	27	,	,	PUNCT
ejpam-2482	462	28	c	c	NOUN
ejpam-2482	462	29	"	"	PUNCT
ejpam-2482	462	30	r	r	NOUN
ejpam-2482	462	31	and	and	CCONJ
ejpam-2482	462	32	m	m	PRON
ejpam-2482	462	33	"	"	PUNCT
ejpam-2482	462	34	m	m	VERB
ejpam-2482	462	35	such	such	ADJ
ejpam-2482	462	36	that	that	SCONJ
ejpam-2482	462	37	abcm	abcm	NOUN
ejpam-2482	462	38	"	"	PUNCT
ejpam-2482	462	39	n	n	NOUN
ejpam-2482	462	40	.	.	PUNCT
ejpam-2482	463	1	then	then	ADV
ejpam-2482	463	2	a	a	DET
ejpam-2482	463	3	1	1	NUM
ejpam-2482	463	4	b	b	SYM
ejpam-2482	463	5	1	1	NUM
ejpam-2482	463	6	c	c	NOUN
ejpam-2482	463	7	1	1	NUM
ejpam-2482	463	8	m	m	NOUN
ejpam-2482	463	9	1	1	NUM
ejpam-2482	463	10	"	"	PUNCT
ejpam-2482	463	11	s&1n	s&1n	PROPN
ejpam-2482	463	12	.	.	PUNCT
ejpam-2482	464	1	therefore	therefore	ADV
ejpam-2482	464	2	a	a	DET
ejpam-2482	464	3	1	1	NUM
ejpam-2482	464	4	b	b	SYM
ejpam-2482	464	5	1	1	NUM
ejpam-2482	464	6	m	m	NOUN
ejpam-2482	464	7	1	1	NUM
ejpam-2482	464	8	"	"	PUNCT
ejpam-2482	464	9	s&1n	s&1n	PROPN
ejpam-2482	464	10	or	or	CCONJ
ejpam-2482	464	11	a	a	DET
ejpam-2482	464	12	1	1	NUM
ejpam-2482	464	13	c	c	NOUN
ejpam-2482	464	14	1	1	NUM
ejpam-2482	464	15	m	m	NOUN
ejpam-2482	464	16	1	1	NUM
ejpam-2482	464	17	"	"	PUNCT
ejpam-2482	464	18	s&1n	s&1n	PROPN
ejpam-2482	464	19	or	or	CCONJ
ejpam-2482	464	20	b	b	NUM
ejpam-2482	464	21	1	1	NUM
ejpam-2482	464	22	c	c	NOUN
ejpam-2482	464	23	1	1	NUM
ejpam-2482	464	24	m	m	NOUN
ejpam-2482	464	25	1	1	NUM
ejpam-2482	464	26	"	"	PUNCT
ejpam-2482	464	27	s&1n	s&1n	PROPN
ejpam-2482	464	28	.	.	PUNCT
ejpam-2482	465	1	we	we	PRON
ejpam-2482	465	2	may	may	AUX
ejpam-2482	465	3	assume	assume	VERB
ejpam-2482	465	4	that	that	SCONJ
ejpam-2482	465	5	a	a	DET
ejpam-2482	465	6	1	1	NUM
ejpam-2482	465	7	b	b	SYM
ejpam-2482	465	8	1	1	NUM
ejpam-2482	465	9	m	m	NOUN
ejpam-2482	465	10	1	1	NUM
ejpam-2482	465	11	"	"	PUNCT
ejpam-2482	465	12	s&1n	s&1n	PROPN
ejpam-2482	465	13	.	.	PUNCT
ejpam-2482	466	1	so	so	ADV
ejpam-2482	466	2	there	there	PRON
ejpam-2482	466	3	exists	exist	VERB
ejpam-2482	466	4	u	u	NOUN
ejpam-2482	466	5	"	"	PUNCT
ejpam-2482	466	6	s	s	VERB
ejpam-2482	466	7	such	such	ADJ
ejpam-2482	466	8	that	that	PRON
ejpam-2482	466	9	uabm	uabm	PROPN
ejpam-2482	466	10	"	"	PUNCT
ejpam-2482	466	11	n	n	NOUN
ejpam-2482	466	12	.	.	PUNCT
ejpam-2482	467	1	but	but	CCONJ
ejpam-2482	467	2	zr(m	zr(m	NUM
ejpam-2482	467	3	/	/	SYM
ejpam-2482	467	4	n	n	CCONJ
ejpam-2482	467	5	)	)	PUNCT
ejpam-2482	467	6	*	*	PUNCT
ejpam-2482	468	1	s	s	PART
ejpam-2482	468	2	=	=	PUNCT
ejpam-2482	468	3	.	.	PUNCT
ejpam-2482	468	4	,	,	PUNCT
ejpam-2482	468	5	whence	whence	PROPN
ejpam-2482	468	6	abm	abm	PROPN
ejpam-2482	468	7	"	"	PUNCT
ejpam-2482	468	8	n	n	PROPN
ejpam-2482	468	9	.	.	PUNCT
ejpam-2482	469	1	consequently	consequently	ADV
ejpam-2482	469	2	n	n	PROPN
ejpam-2482	469	3	is	be	AUX
ejpam-2482	469	4	a	a	DET
ejpam-2482	469	5	classical	classical	ADJ
ejpam-2482	469	6	2	2	NUM
ejpam-2482	469	7	-	-	PUNCT
ejpam-2482	469	8	absorbing	absorb	VERB
ejpam-2482	469	9	submodule	submodule	NOUN
ejpam-2482	469	10	of	of	ADP
ejpam-2482	469	11	m	m	PROPN
ejpam-2482	469	12	.	.	PUNCT
ejpam-2482	470	1	let	let	VERB
ejpam-2482	470	2	ri	ri	PRON
ejpam-2482	470	3	be	be	AUX
ejpam-2482	470	4	a	a	DET
ejpam-2482	470	5	commutative	commutative	ADJ
ejpam-2482	470	6	ring	ring	NOUN
ejpam-2482	470	7	with	with	ADP
ejpam-2482	470	8	identity	identity	NOUN
ejpam-2482	470	9	and	and	CCONJ
ejpam-2482	470	10	mi	mi	PROPN
ejpam-2482	470	11	be	be	AUX
ejpam-2482	470	12	an	an	DET
ejpam-2482	470	13	ri	ri	NOUN
ejpam-2482	470	14	-	-	PUNCT
ejpam-2482	470	15	module	module	NOUN
ejpam-2482	470	16	,	,	PUNCT
ejpam-2482	470	17	for	for	ADP
ejpam-2482	470	18	i	i	PROPN
ejpam-2482	470	19	=	=	SYM
ejpam-2482	470	20	1,2	1,2	NUM
ejpam-2482	470	21	.	.	PUNCT
ejpam-2482	471	1	let	let	VERB
ejpam-2482	471	2	r	r	NOUN
ejpam-2482	471	3	=	=	SYM
ejpam-2482	471	4	r1	r1	PROPN
ejpam-2482	471	5	1	1	NUM
ejpam-2482	471	6	r2	r2	NOUN
ejpam-2482	471	7	.	.	PUNCT
ejpam-2482	472	1	then	then	ADV
ejpam-2482	472	2	m	m	VERB
ejpam-2482	472	3	=	=	SYM
ejpam-2482	472	4	m1	m1	PROPN
ejpam-2482	472	5	1	1	NUM
ejpam-2482	472	6	m2	m2	PROPN
ejpam-2482	472	7	is	be	AUX
ejpam-2482	472	8	an	an	DET
ejpam-2482	472	9	r	r	NOUN
ejpam-2482	472	10	-	-	PUNCT
ejpam-2482	472	11	module	module	NOUN
ejpam-2482	472	12	and	and	CCONJ
ejpam-2482	472	13	each	each	DET
ejpam-2482	472	14	submodule	submodule	NOUN
ejpam-2482	472	15	of	of	ADP
ejpam-2482	472	16	m	m	PROPN
ejpam-2482	472	17	is	be	AUX
ejpam-2482	472	18	in	in	ADP
ejpam-2482	472	19	the	the	DET
ejpam-2482	472	20	form	form	NOUN
ejpam-2482	472	21	of	of	ADP
ejpam-2482	472	22	n	n	NOUN
ejpam-2482	472	23	=	=	SYM
ejpam-2482	472	24	n1	n1	PROPN
ejpam-2482	472	25	1	1	NUM
ejpam-2482	472	26	n2	n2	NOUN
ejpam-2482	472	27	for	for	ADP
ejpam-2482	472	28	some	some	DET
ejpam-2482	472	29	submodules	submodule	NOUN
ejpam-2482	472	30	n1	n1	NOUN
ejpam-2482	472	31	of	of	ADP
ejpam-2482	472	32	m1	m1	PROPN
ejpam-2482	472	33	and	and	CCONJ
ejpam-2482	472	34	n2	n2	NOUN
ejpam-2482	472	35	of	of	ADP
ejpam-2482	472	36	m2	m2	PROPN
ejpam-2482	472	37	.	.	PUNCT
ejpam-2482	473	1	theorem	theorem	VERB
ejpam-2482	473	2	7	7	NUM
ejpam-2482	473	3	.	.	PUNCT
ejpam-2482	474	1	let	let	AUX
ejpam-2482	474	2	r	r	NOUN
ejpam-2482	474	3	=	=	SYM
ejpam-2482	474	4	r1	r1	PROPN
ejpam-2482	474	5	1	1	NUM
ejpam-2482	474	6	r2	r2	NOUN
ejpam-2482	474	7	be	be	VERB
ejpam-2482	474	8	a	a	DET
ejpam-2482	474	9	decomposable	decomposable	ADJ
ejpam-2482	474	10	ring	ring	NOUN
ejpam-2482	474	11	and	and	CCONJ
ejpam-2482	474	12	m	m	PROPN
ejpam-2482	474	13	=	=	ADJ
ejpam-2482	474	14	m1	m1	PROPN
ejpam-2482	474	15	1m2	1m2	NUM
ejpam-2482	474	16	be	be	AUX
ejpam-2482	474	17	an	an	DET
ejpam-2482	474	18	r	r	NOUN
ejpam-2482	474	19	-	-	PUNCT
ejpam-2482	474	20	module	module	NOUN
ejpam-2482	474	21	where	where	SCONJ
ejpam-2482	474	22	m1	m1	PROPN
ejpam-2482	474	23	is	be	AUX
ejpam-2482	474	24	an	an	DET
ejpam-2482	474	25	r1	r1	NOUN
ejpam-2482	474	26	-	-	PUNCT
ejpam-2482	474	27	module	module	NOUN
ejpam-2482	474	28	and	and	CCONJ
ejpam-2482	474	29	m2	m2	PROPN
ejpam-2482	474	30	is	be	AUX
ejpam-2482	474	31	an	an	DET
ejpam-2482	474	32	r2	r2	NOUN
ejpam-2482	474	33	-	-	PUNCT
ejpam-2482	474	34	module	module	NOUN
ejpam-2482	474	35	.	.	PUNCT
ejpam-2482	475	1	suppose	suppose	VERB
ejpam-2482	475	2	that	that	SCONJ
ejpam-2482	475	3	n	n	PROPN
ejpam-2482	475	4	=	=	SYM
ejpam-2482	475	5	n1	n1	ADJ
ejpam-2482	475	6	1	1	NUM
ejpam-2482	475	7	n2	n2	NOUN
ejpam-2482	475	8	is	be	AUX
ejpam-2482	475	9	a	a	DET
ejpam-2482	475	10	proper	proper	ADJ
ejpam-2482	475	11	submodule	submodule	NOUN
ejpam-2482	475	12	of	of	ADP
ejpam-2482	475	13	m.	m.	NOUN
ejpam-2482	475	14	then	then	ADV
ejpam-2482	475	15	the	the	DET
ejpam-2482	475	16	following	follow	VERB
ejpam-2482	475	17	conditions	condition	NOUN
ejpam-2482	475	18	are	be	AUX
ejpam-2482	475	19	equivalent	equivalent	ADJ
ejpam-2482	475	20	:	:	PUNCT
ejpam-2482	475	21	(	(	PUNCT
ejpam-2482	475	22	i	i	NOUN
ejpam-2482	475	23	)	)	PUNCT
ejpam-2482	475	24	n	n	PRON
ejpam-2482	475	25	is	be	AUX
ejpam-2482	475	26	a	a	DET
ejpam-2482	475	27	classical	classical	ADJ
ejpam-2482	475	28	2	2	NUM
ejpam-2482	475	29	-	-	PUNCT
ejpam-2482	475	30	absorbing	absorb	VERB
ejpam-2482	475	31	submodule	submodule	NOUN
ejpam-2482	475	32	of	of	ADP
ejpam-2482	475	33	m	m	PROPN
ejpam-2482	475	34	;	;	PUNCT
ejpam-2482	475	35	(	(	PUNCT
ejpam-2482	475	36	ii	ii	NOUN
ejpam-2482	475	37	)	)	PUNCT
ejpam-2482	475	38	either	either	CCONJ
ejpam-2482	475	39	n1	n1	PROPN
ejpam-2482	475	40	=	=	SYM
ejpam-2482	475	41	m1	m1	PROPN
ejpam-2482	475	42	and	and	CCONJ
ejpam-2482	475	43	n2	n2	NOUN
ejpam-2482	475	44	is	be	AUX
ejpam-2482	475	45	a	a	DET
ejpam-2482	475	46	classical	classical	ADJ
ejpam-2482	475	47	2	2	NUM
ejpam-2482	475	48	-	-	PUNCT
ejpam-2482	475	49	absorbing	absorb	VERB
ejpam-2482	475	50	submodule	submodule	NOUN
ejpam-2482	475	51	of	of	ADP
ejpam-2482	475	52	m2	m2	PROPN
ejpam-2482	475	53	or	or	CCONJ
ejpam-2482	475	54	n2	n2	NOUN
ejpam-2482	476	1	=	=	PROPN
ejpam-2482	476	2	m2	m2	PROPN
ejpam-2482	476	3	and	and	CCONJ
ejpam-2482	476	4	n1	n1	PROPN
ejpam-2482	476	5	is	be	AUX
ejpam-2482	476	6	a	a	DET
ejpam-2482	476	7	classical	classical	ADJ
ejpam-2482	476	8	2	2	NUM
ejpam-2482	476	9	-	-	PUNCT
ejpam-2482	476	10	absorbing	absorb	VERB
ejpam-2482	476	11	submodule	submodule	NOUN
ejpam-2482	476	12	of	of	ADP
ejpam-2482	476	13	m1	m1	PROPN
ejpam-2482	476	14	or	or	CCONJ
ejpam-2482	476	15	n1	n1	NOUN
ejpam-2482	476	16	,	,	PUNCT
ejpam-2482	476	17	n2	n2	NOUN
ejpam-2482	476	18	are	be	AUX
ejpam-2482	476	19	classical	classical	ADJ
ejpam-2482	476	20	prime	prime	ADJ
ejpam-2482	476	21	submodules	submodule	NOUN
ejpam-2482	476	22	of	of	ADP
ejpam-2482	476	23	m1	m1	PROPN
ejpam-2482	476	24	,	,	PUNCT
ejpam-2482	476	25	m2	m2	PROPN
ejpam-2482	476	26	,	,	PUNCT
ejpam-2482	476	27	respectively	respectively	ADV
ejpam-2482	476	28	.	.	PUNCT
ejpam-2482	477	1	proof	proof	NOUN
ejpam-2482	477	2	.	.	PUNCT
ejpam-2482	478	1	(	(	PUNCT
ejpam-2482	478	2	i)+	i)+	X
ejpam-2482	478	3	(	(	PUNCT
ejpam-2482	478	4	ii	ii	NOUN
ejpam-2482	478	5	)	)	PUNCT
ejpam-2482	478	6	suppose	suppose	VERB
ejpam-2482	478	7	that	that	SCONJ
ejpam-2482	478	8	n	n	PRON
ejpam-2482	478	9	is	be	AUX
ejpam-2482	478	10	a	a	DET
ejpam-2482	478	11	classical	classical	ADJ
ejpam-2482	478	12	2	2	NUM
ejpam-2482	478	13	-	-	PUNCT
ejpam-2482	478	14	absorbing	absorb	VERB
ejpam-2482	478	15	submodule	submodule	NOUN
ejpam-2482	478	16	of	of	ADP
ejpam-2482	478	17	m	m	PRON
ejpam-2482	478	18	such	such	ADJ
ejpam-2482	478	19	that	that	DET
ejpam-2482	478	20	n2	n2	NOUN
ejpam-2482	478	21	=	=	PROPN
ejpam-2482	478	22	m2	m2	PROPN
ejpam-2482	478	23	.	.	PROPN
ejpam-2482	479	1	from	from	ADP
ejpam-2482	479	2	our	our	PRON
ejpam-2482	479	3	hypothesis	hypothesis	NOUN
ejpam-2482	479	4	,	,	PUNCT
ejpam-2482	479	5	n	n	PRON
ejpam-2482	479	6	is	be	AUX
ejpam-2482	479	7	proper	proper	ADJ
ejpam-2482	479	8	,	,	PUNCT
ejpam-2482	479	9	so	so	ADV
ejpam-2482	479	10	n1	n1	ADJ
ejpam-2482	479	11	#	#	NOUN
ejpam-2482	479	12	=	=	SYM
ejpam-2482	479	13	m1	m1	NOUN
ejpam-2482	479	14	.	.	PUNCT
ejpam-2482	480	1	set	set	VERB
ejpam-2482	480	2	m	m	PROPN
ejpam-2482	480	3	)	)	PUNCT
ejpam-2482	481	1	=	=	PUNCT
ejpam-2482	481	2	m	m	PRON
ejpam-2482	481	3	{	{	PUNCT
ejpam-2482	481	4	0}1m2	0}1m2	NUM
ejpam-2482	481	5	.	.	PUNCT
ejpam-2482	482	1	hence	hence	ADV
ejpam-2482	482	2	n	n	CCONJ
ejpam-2482	482	3	)	)	PUNCT
ejpam-2482	482	4	=	=	SYM
ejpam-2482	483	1	n	n	CCONJ
ejpam-2482	483	2	{	{	PUNCT
ejpam-2482	483	3	0}1m2	0}1m2	X
ejpam-2482	483	4	is	be	AUX
ejpam-2482	483	5	a	a	DET
ejpam-2482	483	6	classical	classical	ADJ
ejpam-2482	483	7	2	2	NUM
ejpam-2482	483	8	-	-	PUNCT
ejpam-2482	483	9	absorbing	absorb	VERB
ejpam-2482	483	10	submodule	submodule	NOUN
ejpam-2482	483	11	of	of	ADP
ejpam-2482	483	12	m	m	PROPN
ejpam-2482	483	13	)	)	PUNCT
ejpam-2482	483	14	by	by	ADP
ejpam-2482	483	15	corollary	corollary	ADJ
ejpam-2482	483	16	1	1	NUM
ejpam-2482	483	17	.	.	PUNCT
ejpam-2482	484	1	also	also	ADV
ejpam-2482	484	2	observe	observe	VERB
ejpam-2482	484	3	that	that	SCONJ
ejpam-2482	484	4	m	m	NOUN
ejpam-2482	484	5	)	)	PUNCT
ejpam-2482	484	6	2=	2=	NUM
ejpam-2482	484	7	m1	m1	NOUN
ejpam-2482	484	8	and	and	CCONJ
ejpam-2482	484	9	n	n	NOUN
ejpam-2482	484	10	)	)	PUNCT
ejpam-2482	484	11	2=	2=	NUM
ejpam-2482	484	12	n1	n1	NOUN
ejpam-2482	484	13	.	.	PUNCT
ejpam-2482	485	1	thus	thus	ADV
ejpam-2482	485	2	n1	n1	PROPN
ejpam-2482	485	3	is	be	AUX
ejpam-2482	485	4	a	a	DET
ejpam-2482	485	5	classical	classical	ADJ
ejpam-2482	485	6	2	2	NUM
ejpam-2482	485	7	-	-	PUNCT
ejpam-2482	485	8	absorbing	absorb	VERB
ejpam-2482	485	9	submodule	submodule	NOUN
ejpam-2482	485	10	of	of	ADP
ejpam-2482	485	11	m1	m1	PROPN
ejpam-2482	485	12	.	.	PUNCT
ejpam-2482	486	1	suppose	suppose	VERB
ejpam-2482	486	2	that	that	SCONJ
ejpam-2482	486	3	n1	n1	ADJ
ejpam-2482	486	4	#	#	NOUN
ejpam-2482	486	5	=	=	SYM
ejpam-2482	486	6	m1	m1	PROPN
ejpam-2482	486	7	and	and	CCONJ
ejpam-2482	486	8	n2	n2	ADJ
ejpam-2482	486	9	#	#	PROPN
ejpam-2482	486	10	=	=	SYM
ejpam-2482	486	11	m2	m2	PROPN
ejpam-2482	486	12	.	.	PUNCT
ejpam-2482	487	1	we	we	PRON
ejpam-2482	487	2	show	show	VERB
ejpam-2482	487	3	that	that	SCONJ
ejpam-2482	487	4	n1	n1	PROPN
ejpam-2482	487	5	is	be	AUX
ejpam-2482	487	6	a	a	DET
ejpam-2482	487	7	classical	classical	ADJ
ejpam-2482	487	8	prime	prime	ADJ
ejpam-2482	487	9	submodule	submodule	NOUN
ejpam-2482	487	10	of	of	ADP
ejpam-2482	487	11	m1	m1	PROPN
ejpam-2482	487	12	.	.	PUNCT
ejpam-2482	488	1	since	since	SCONJ
ejpam-2482	488	2	n2	n2	ADJ
ejpam-2482	488	3	#	#	PROPN
ejpam-2482	488	4	=	=	SYM
ejpam-2482	488	5	m2	m2	PROPN
ejpam-2482	488	6	,	,	PUNCT
ejpam-2482	488	7	there	there	PRON
ejpam-2482	488	8	exists	exist	VERB
ejpam-2482	488	9	m2	m2	PROPN
ejpam-2482	488	10	"	"	PUNCT
ejpam-2482	488	11	m2\n2	m2\n2	PROPN
ejpam-2482	488	12	.	.	PUNCT
ejpam-2482	489	1	let	let	VERB
ejpam-2482	489	2	abm1	abm1	PROPN
ejpam-2482	489	3	"	"	PUNCT
ejpam-2482	489	4	n1	n1	PROPN
ejpam-2482	489	5	for	for	ADP
ejpam-2482	489	6	some	some	DET
ejpam-2482	489	7	a	a	PRON
ejpam-2482	489	8	,	,	PUNCT
ejpam-2482	489	9	b	b	NOUN
ejpam-2482	489	10	"	"	PUNCT
ejpam-2482	489	11	r1	r1	NOUN
ejpam-2482	489	12	and	and	CCONJ
ejpam-2482	489	13	m1	m1	PROPN
ejpam-2482	489	14	"	"	PUNCT
ejpam-2482	489	15	m1	m1	PROPN
ejpam-2482	489	16	.	.	PUNCT
ejpam-2482	490	1	thus	thus	ADV
ejpam-2482	490	2	(	(	PUNCT
ejpam-2482	490	3	a	a	PRON
ejpam-2482	490	4	,	,	PUNCT
ejpam-2482	490	5	1)(b	1)(b	NUM
ejpam-2482	490	6	,	,	PUNCT
ejpam-2482	490	7	1)(1,0)(m1	1)(1,0)(m1	NUM
ejpam-2482	490	8	,	,	PUNCT
ejpam-2482	490	9	m2	m2	PROPN
ejpam-2482	490	10	)	)	PUNCT
ejpam-2482	490	11	=	=	PUNCT
ejpam-2482	490	12	(	(	PUNCT
ejpam-2482	490	13	abm1	abm1	PROPN
ejpam-2482	490	14	,	,	PUNCT
ejpam-2482	490	15	0	0	NUM
ejpam-2482	490	16	)	)	PUNCT
ejpam-2482	490	17	"	"	PUNCT
ejpam-2482	491	1	n	n	PROPN
ejpam-2482	491	2	=	=	SYM
ejpam-2482	491	3	n1	n1	PROPN
ejpam-2482	491	4	1	1	NUM
ejpam-2482	491	5	n2	n2	NOUN
ejpam-2482	491	6	.	.	PUNCT
ejpam-2482	492	1	so	so	ADV
ejpam-2482	492	2	either	either	CCONJ
ejpam-2482	492	3	(	(	PUNCT
ejpam-2482	492	4	a	a	PRON
ejpam-2482	492	5	,	,	PUNCT
ejpam-2482	492	6	1)(1,0)(m1	1)(1,0)(m1	NOUN
ejpam-2482	492	7	,	,	PUNCT
ejpam-2482	492	8	m2	m2	PROPN
ejpam-2482	492	9	)	)	PUNCT
ejpam-2482	492	10	=	=	PRON
ejpam-2482	492	11	(	(	PUNCT
ejpam-2482	492	12	am1	am1	PROPN
ejpam-2482	492	13	,	,	PUNCT
ejpam-2482	492	14	0	0	NUM
ejpam-2482	492	15	)	)	PUNCT
ejpam-2482	492	16	"	"	PUNCT
ejpam-2482	492	17	n	n	CCONJ
ejpam-2482	492	18	or	or	CCONJ
ejpam-2482	492	19	(	(	PUNCT
ejpam-2482	492	20	b	b	NOUN
ejpam-2482	492	21	,	,	PUNCT
ejpam-2482	492	22	1)(1,0)(m1	1)(1,0)(m1	NUM
ejpam-2482	492	23	,	,	PUNCT
ejpam-2482	492	24	m2	m2	PROPN
ejpam-2482	492	25	)	)	PUNCT
ejpam-2482	492	26	=	=	PUNCT
ejpam-2482	492	27	(	(	PUNCT
ejpam-2482	492	28	bm1	bm1	PROPN
ejpam-2482	492	29	,	,	PUNCT
ejpam-2482	492	30	0	0	NUM
ejpam-2482	492	31	)	)	PUNCT
ejpam-2482	492	32	"	"	PUNCT
ejpam-2482	492	33	n	n	CCONJ
ejpam-2482	492	34	.	.	PUNCT
ejpam-2482	493	1	hence	hence	ADV
ejpam-2482	493	2	either	either	CCONJ
ejpam-2482	493	3	am1	am1	PROPN
ejpam-2482	493	4	"	"	PUNCT
ejpam-2482	493	5	n1	n1	PROPN
ejpam-2482	493	6	or	or	CCONJ
ejpam-2482	493	7	bm1	bm1	ADJ
ejpam-2482	493	8	"	"	PUNCT
ejpam-2482	493	9	n1	n1	NOUN
ejpam-2482	493	10	which	which	PRON
ejpam-2482	493	11	shows	show	VERB
ejpam-2482	493	12	that	that	SCONJ
ejpam-2482	493	13	n1	n1	PROPN
ejpam-2482	493	14	is	be	AUX
ejpam-2482	493	15	a	a	DET
ejpam-2482	493	16	classical	classical	ADJ
ejpam-2482	493	17	prime	prime	ADJ
ejpam-2482	493	18	submodule	submodule	NOUN
ejpam-2482	493	19	of	of	ADP
ejpam-2482	493	20	m1	m1	PROPN
ejpam-2482	493	21	.	.	PUNCT
ejpam-2482	494	1	similarly	similarly	ADV
ejpam-2482	494	2	we	we	PRON
ejpam-2482	494	3	can	can	AUX
ejpam-2482	494	4	show	show	VERB
ejpam-2482	494	5	that	that	DET
ejpam-2482	494	6	n2	n2	NOUN
ejpam-2482	494	7	is	be	AUX
ejpam-2482	494	8	a	a	DET
ejpam-2482	494	9	classical	classical	ADJ
ejpam-2482	494	10	prime	prime	ADJ
ejpam-2482	494	11	submodule	submodule	NOUN
ejpam-2482	494	12	of	of	ADP
ejpam-2482	494	13	m2	m2	PROPN
ejpam-2482	494	14	.	.	PUNCT
ejpam-2482	495	1	(	(	PUNCT
ejpam-2482	495	2	ii	ii	NOUN
ejpam-2482	495	3	)	)	PUNCT
ejpam-2482	496	1	+	+	CCONJ
ejpam-2482	496	2	(	(	PUNCT
ejpam-2482	496	3	i	i	NOUN
ejpam-2482	496	4	)	)	PUNCT
ejpam-2482	496	5	suppose	suppose	VERB
ejpam-2482	496	6	that	that	SCONJ
ejpam-2482	496	7	n	n	PROPN
ejpam-2482	496	8	=	=	SYM
ejpam-2482	496	9	n1	n1	PROPN
ejpam-2482	496	10	1	1	NUM
ejpam-2482	496	11	m2	m2	PROPN
ejpam-2482	496	12	where	where	SCONJ
ejpam-2482	496	13	n1	n1	PROPN
ejpam-2482	496	14	is	be	AUX
ejpam-2482	496	15	a	a	DET
ejpam-2482	496	16	classical	classical	ADJ
ejpam-2482	496	17	2	2	NUM
ejpam-2482	496	18	-	-	PUNCT
ejpam-2482	496	19	absorbing	absorbing	ADJ
ejpam-2482	496	20	(	(	PUNCT
ejpam-2482	496	21	resp	resp	NOUN
ejpam-2482	496	22	.	.	PUNCT
ejpam-2482	497	1	classical	classical	ADJ
ejpam-2482	497	2	prime	prime	ADJ
ejpam-2482	497	3	)	)	PUNCT
ejpam-2482	497	4	submodule	submodule	NOUN
ejpam-2482	497	5	of	of	ADP
ejpam-2482	497	6	m1	m1	PROPN
ejpam-2482	497	7	.	.	PUNCT
ejpam-2482	498	1	then	then	ADV
ejpam-2482	498	2	it	it	PRON
ejpam-2482	498	3	is	be	AUX
ejpam-2482	498	4	clear	clear	ADJ
ejpam-2482	498	5	that	that	SCONJ
ejpam-2482	498	6	n	n	X
ejpam-2482	498	7	is	be	AUX
ejpam-2482	498	8	a	a	DET
ejpam-2482	498	9	classical	classical	ADJ
ejpam-2482	498	10	2	2	NUM
ejpam-2482	498	11	-	-	PUNCT
ejpam-2482	498	12	absorbing	absorbing	ADJ
ejpam-2482	498	13	(	(	PUNCT
ejpam-2482	498	14	resp	resp	NOUN
ejpam-2482	498	15	.	.	PUNCT
ejpam-2482	499	1	classical	classical	ADJ
ejpam-2482	499	2	prime	prime	ADJ
ejpam-2482	499	3	)	)	PUNCT
ejpam-2482	499	4	submodule	submodule	NOUN
ejpam-2482	499	5	of	of	ADP
ejpam-2482	499	6	m	m	PROPN
ejpam-2482	499	7	.	.	PUNCT
ejpam-2482	500	1	now	now	ADV
ejpam-2482	500	2	,	,	PUNCT
ejpam-2482	500	3	assume	assume	VERB
ejpam-2482	500	4	that	that	SCONJ
ejpam-2482	500	5	n	n	NOUN
ejpam-2482	500	6	=	=	SYM
ejpam-2482	500	7	n1	n1	PROPN
ejpam-2482	500	8	1	1	NUM
ejpam-2482	500	9	n2	n2	NOUN
ejpam-2482	500	10	where	where	SCONJ
ejpam-2482	500	11	n1	n1	PROPN
ejpam-2482	500	12	and	and	CCONJ
ejpam-2482	500	13	n2	n2	NOUN
ejpam-2482	500	14	are	be	AUX
ejpam-2482	500	15	classical	classical	ADJ
ejpam-2482	500	16	prime	prime	ADJ
ejpam-2482	500	17	submodules	submodule	NOUN
ejpam-2482	500	18	of	of	ADP
ejpam-2482	500	19	m1	m1	PROPN
ejpam-2482	500	20	and	and	CCONJ
ejpam-2482	500	21	m2	m2	PROPN
ejpam-2482	500	22	,	,	PUNCT
ejpam-2482	500	23	respectively	respectively	ADV
ejpam-2482	500	24	.	.	PUNCT
ejpam-2482	501	1	hence	hence	ADV
ejpam-2482	501	2	(	(	PUNCT
ejpam-2482	501	3	n1	n1	PROPN
ejpam-2482	501	4	1	1	NUM
ejpam-2482	501	5	m2	m2	PROPN
ejpam-2482	501	6	)	)	PUNCT
ejpam-2482	501	7	*	*	PUNCT
ejpam-2482	502	1	(	(	PUNCT
ejpam-2482	502	2	m1	m1	PROPN
ejpam-2482	502	3	1	1	NUM
ejpam-2482	502	4	n2	n2	NOUN
ejpam-2482	502	5	)	)	PUNCT
ejpam-2482	502	6	=	=	SYM
ejpam-2482	502	7	n1	n1	ADJ
ejpam-2482	502	8	1	1	NUM
ejpam-2482	502	9	n2	n2	NOUN
ejpam-2482	502	10	=	=	PUNCT
ejpam-2482	502	11	n	n	X
ejpam-2482	502	12	is	be	AUX
ejpam-2482	502	13	a	a	DET
ejpam-2482	502	14	classical	classical	ADJ
ejpam-2482	502	15	2	2	NUM
ejpam-2482	502	16	-	-	PUNCT
ejpam-2482	502	17	absorbing	absorb	VERB
ejpam-2482	502	18	submodule	submodule	NOUN
ejpam-2482	502	19	of	of	ADP
ejpam-2482	502	20	m	m	PRON
ejpam-2482	502	21	,	,	PUNCT
ejpam-2482	502	22	by	by	ADP
ejpam-2482	502	23	proposition	proposition	NOUN
ejpam-2482	502	24	1	1	NUM
ejpam-2482	502	25	.	.	PUNCT
ejpam-2482	503	1	h.	h.	PROPN
ejpam-2482	503	2	mostafanasab	mostafanasab	PROPN
ejpam-2482	503	3	,	,	PUNCT
ejpam-2482	503	4	ü.	ü.	NOUN
ejpam-2482	503	5	tekir	tekir	NOUN
ejpam-2482	503	6	and	and	CCONJ
ejpam-2482	503	7	k.	k.	PROPN
ejpam-2482	503	8	hakan	hakan	PROPN
ejpam-2482	503	9	oral	oral	PROPN
ejpam-2482	503	10	/	/	SYM
ejpam-2482	503	11	eur	eur	PROPN
ejpam-2482	503	12	.	.	PUNCT
ejpam-2482	504	1	j.	j.	PROPN
ejpam-2482	504	2	pure	pure	PROPN
ejpam-2482	504	3	appl	appl	PROPN
ejpam-2482	504	4	.	.	PROPN
ejpam-2482	504	5	math	math	PROPN
ejpam-2482	504	6	,	,	PUNCT
ejpam-2482	504	7	8	8	NUM
ejpam-2482	504	8	(	(	PUNCT
ejpam-2482	504	9	2015	2015	NUM
ejpam-2482	504	10	)	)	PUNCT
ejpam-2482	504	11	,	,	PUNCT
ejpam-2482	504	12	417	417	NUM
ejpam-2482	504	13	-	-	SYM
ejpam-2482	504	14	430	430	NUM
ejpam-2482	504	15	428	428	NUM
ejpam-2482	504	16	lemma	lemma	PROPN
ejpam-2482	504	17	1	1	NUM
ejpam-2482	504	18	.	.	PUNCT
ejpam-2482	505	1	let	let	VERB
ejpam-2482	505	2	r=	r=	ADJ
ejpam-2482	505	3	r11r21	r11r21	VERB
ejpam-2482	505	4	·	·	PUNCT
ejpam-2482	505	5	·	·	PUNCT
ejpam-2482	505	6	·	·	PUNCT
ejpam-2482	505	7	1rn	1rn	NOUN
ejpam-2482	505	8	be	be	VERB
ejpam-2482	505	9	a	a	DET
ejpam-2482	505	10	decomposable	decomposable	ADJ
ejpam-2482	505	11	ring	ring	NOUN
ejpam-2482	505	12	and	and	CCONJ
ejpam-2482	505	13	m	m	NOUN
ejpam-2482	505	14	=	=	VERB
ejpam-2482	505	15	m11m21	m11m21	NOUN
ejpam-2482	505	16	·	·	PUNCT
ejpam-2482	505	17	·	·	PUNCT
ejpam-2482	505	18	·	·	PUNCT
ejpam-2482	505	19	1mn	1mn	X
ejpam-2482	505	20	be	be	AUX
ejpam-2482	505	21	an	an	DET
ejpam-2482	505	22	r	r	NOUN
ejpam-2482	505	23	-	-	PUNCT
ejpam-2482	505	24	module	module	NOUN
ejpam-2482	505	25	where	where	SCONJ
ejpam-2482	505	26	for	for	ADP
ejpam-2482	505	27	every	every	DET
ejpam-2482	505	28	13	13	NUM
ejpam-2482	505	29	i	i	NOUN
ejpam-2482	505	30	3	3	NUM
ejpam-2482	505	31	n	n	CCONJ
ejpam-2482	505	32	,	,	PUNCT
ejpam-2482	505	33	mi	mi	PROPN
ejpam-2482	505	34	is	be	AUX
ejpam-2482	505	35	an	an	DET
ejpam-2482	505	36	ri	ri	NOUN
ejpam-2482	505	37	-	-	PUNCT
ejpam-2482	505	38	module	module	NOUN
ejpam-2482	505	39	,	,	PUNCT
ejpam-2482	505	40	respectively	respectively	ADV
ejpam-2482	505	41	.	.	PUNCT
ejpam-2482	506	1	a	a	DET
ejpam-2482	506	2	proper	proper	ADJ
ejpam-2482	506	3	submodule	submodule	NOUN
ejpam-2482	506	4	n	n	PROPN
ejpam-2482	506	5	of	of	ADP
ejpam-2482	506	6	m	m	PROPN
ejpam-2482	506	7	is	be	AUX
ejpam-2482	506	8	a	a	DET
ejpam-2482	506	9	classical	classical	ADJ
ejpam-2482	506	10	prime	prime	ADJ
ejpam-2482	506	11	submodule	submodule	NOUN
ejpam-2482	506	12	of	of	ADP
ejpam-2482	506	13	m	m	PROPN
ejpam-2482	506	14	if	if	SCONJ
ejpam-2482	507	1	and	and	CCONJ
ejpam-2482	507	2	only	only	ADV
ejpam-2482	507	3	if	if	SCONJ
ejpam-2482	507	4	n	n	PROPN
ejpam-2482	507	5	=	=	SYM
ejpam-2482	507	6	1n	1n	NUM
ejpam-2482	507	7	i=1ni	i=1ni	NUM
ejpam-2482	507	8	such	such	ADJ
ejpam-2482	507	9	that	that	PRON
ejpam-2482	507	10	for	for	ADP
ejpam-2482	507	11	some	some	DET
ejpam-2482	507	12	k	k	NOUN
ejpam-2482	507	13	"	"	PUNCT
ejpam-2482	507	14	{	{	PUNCT
ejpam-2482	507	15	1,2	1,2	NUM
ejpam-2482	507	16	,	,	PUNCT
ejpam-2482	507	17	.	.	PUNCT
ejpam-2482	507	18	.	.	PUNCT
ejpam-2482	508	1	.	.	PUNCT
ejpam-2482	509	1	,	,	PUNCT
ejpam-2482	509	2	n	n	CCONJ
ejpam-2482	509	3	}	}	PUNCT
ejpam-2482	509	4	,	,	PUNCT
ejpam-2482	509	5	nk	nk	PROPN
ejpam-2482	509	6	is	be	AUX
ejpam-2482	509	7	a	a	DET
ejpam-2482	509	8	classical	classical	ADJ
ejpam-2482	509	9	prime	prime	ADJ
ejpam-2482	509	10	submodule	submodule	NOUN
ejpam-2482	509	11	of	of	ADP
ejpam-2482	509	12	mk	mk	PROPN
ejpam-2482	509	13	,	,	PUNCT
ejpam-2482	509	14	and	and	CCONJ
ejpam-2482	509	15	ni	ni	PROPN
ejpam-2482	509	16	=	=	PROPN
ejpam-2482	509	17	mi	mi	PROPN
ejpam-2482	509	18	for	for	ADP
ejpam-2482	509	19	every	every	DET
ejpam-2482	509	20	i	i	NOUN
ejpam-2482	509	21	"	"	PUNCT
ejpam-2482	509	22	{	{	PUNCT
ejpam-2482	509	23	1,2	1,2	NUM
ejpam-2482	509	24	,	,	PUNCT
ejpam-2482	509	25	.	.	PUNCT
ejpam-2482	509	26	.	.	PUNCT
ejpam-2482	510	1	.	.	PUNCT
ejpam-2482	510	2	,	,	PUNCT
ejpam-2482	510	3	n}\{k	n}\{k	ADV
ejpam-2482	510	4	}	}	PUNCT
ejpam-2482	510	5	.	.	PUNCT
ejpam-2482	511	1	proof	proof	NOUN
ejpam-2482	511	2	.	.	PUNCT
ejpam-2482	512	1	(	(	PUNCT
ejpam-2482	512	2	+	+	ADV
ejpam-2482	512	3	)	)	PUNCT
ejpam-2482	512	4	let	let	VERB
ejpam-2482	512	5	n	n	PRON
ejpam-2482	512	6	be	be	AUX
ejpam-2482	512	7	a	a	DET
ejpam-2482	512	8	classical	classical	ADJ
ejpam-2482	512	9	prime	prime	ADJ
ejpam-2482	512	10	submodule	submodule	NOUN
ejpam-2482	512	11	of	of	ADP
ejpam-2482	512	12	m	m	PROPN
ejpam-2482	512	13	.	.	PUNCT
ejpam-2482	513	1	we	we	PRON
ejpam-2482	513	2	know	know	VERB
ejpam-2482	513	3	n	n	NOUN
ejpam-2482	513	4	=	=	SYM
ejpam-2482	513	5	1n	1n	NUM
ejpam-2482	513	6	i=1ni	i=1ni	PUNCT
ejpam-2482	513	7	where	where	SCONJ
ejpam-2482	513	8	for	for	ADP
ejpam-2482	513	9	every	every	DET
ejpam-2482	513	10	13	13	NUM
ejpam-2482	513	11	i	i	NOUN
ejpam-2482	513	12	3	3	NUM
ejpam-2482	513	13	n	n	CCONJ
ejpam-2482	513	14	,	,	PUNCT
ejpam-2482	513	15	ni	ni	PROPN
ejpam-2482	513	16	is	be	AUX
ejpam-2482	513	17	a	a	DET
ejpam-2482	513	18	submodule	submodule	NOUN
ejpam-2482	513	19	of	of	ADP
ejpam-2482	513	20	mi	mi	PROPN
ejpam-2482	513	21	,	,	PUNCT
ejpam-2482	513	22	respectively	respectively	ADV
ejpam-2482	513	23	.	.	PUNCT
ejpam-2482	514	1	assume	assume	VERB
ejpam-2482	514	2	that	that	SCONJ
ejpam-2482	514	3	nr	nr	PRON
ejpam-2482	514	4	is	be	AUX
ejpam-2482	514	5	a	a	DET
ejpam-2482	514	6	proper	proper	ADJ
ejpam-2482	514	7	submodule	submodule	NOUN
ejpam-2482	514	8	of	of	ADP
ejpam-2482	514	9	mr	mr	PROPN
ejpam-2482	514	10	and	and	CCONJ
ejpam-2482	514	11	ns	ns	PROPN
ejpam-2482	514	12	is	be	AUX
ejpam-2482	514	13	a	a	DET
ejpam-2482	514	14	proper	proper	ADJ
ejpam-2482	514	15	submodule	submodule	NOUN
ejpam-2482	514	16	of	of	ADP
ejpam-2482	514	17	ms	ms	NOUN
ejpam-2482	514	18	for	for	ADP
ejpam-2482	514	19	some	some	DET
ejpam-2482	514	20	1	1	NUM
ejpam-2482	514	21	3	3	NUM
ejpam-2482	514	22	r	r	NOUN
ejpam-2482	514	23	<	<	X
ejpam-2482	514	24	s	s	PROPN
ejpam-2482	514	25	3	3	NUM
ejpam-2482	514	26	n.	n.	NOUN
ejpam-2482	514	27	so	so	ADV
ejpam-2482	514	28	,	,	PUNCT
ejpam-2482	514	29	there	there	PRON
ejpam-2482	514	30	are	be	VERB
ejpam-2482	514	31	mr	mr	PROPN
ejpam-2482	514	32	"	"	PUNCT
ejpam-2482	514	33	mr\nr	mr\nr	PROPN
ejpam-2482	514	34	and	and	CCONJ
ejpam-2482	514	35	ms	ms	NOUN
ejpam-2482	514	36	"	"	PUNCT
ejpam-2482	514	37	ms\ns	ms\ns	PROPN
ejpam-2482	514	38	.	.	PUNCT
ejpam-2482	515	1	since	since	SCONJ
ejpam-2482	515	2	(	(	PUNCT
ejpam-2482	515	3	0	0	NUM
ejpam-2482	515	4	,	,	PUNCT
ejpam-2482	515	5	.	.	PUNCT
ejpam-2482	515	6	.	.	PUNCT
ejpam-2482	515	7	.	.	PUNCT
ejpam-2482	516	1	,	,	PUNCT
ejpam-2482	516	2	0	0	NUM
ejpam-2482	516	3	,	,	PUNCT
ejpam-2482	516	4	r	r	X
ejpam-2482	516	5	-	-	PUNCT
ejpam-2482	516	6	th	th	X
ejpam-2482	516	7	+	+	NOUN
ejpam-2482	516	8	,	,	PUNCT
ejpam-2482	516	9	-	-	PUNCT
ejpam-2482	516	10	.	.	PUNCT
ejpam-2482	517	1	1rr	1rr	ADJ
ejpam-2482	517	2	,	,	PUNCT
ejpam-2482	517	3	0	0	NUM
ejpam-2482	517	4	,	,	PUNCT
ejpam-2482	517	5	.	.	PUNCT
ejpam-2482	517	6	.	.	PUNCT
ejpam-2482	518	1	.	.	PUNCT
ejpam-2482	519	1	,	,	PUNCT
ejpam-2482	519	2	0)(0	0)(0	NUM
ejpam-2482	519	3	,	,	PUNCT
ejpam-2482	519	4	.	.	PUNCT
ejpam-2482	519	5	.	.	PUNCT
ejpam-2482	520	1	.	.	PUNCT
ejpam-2482	521	1	,	,	PUNCT
ejpam-2482	521	2	0	0	NUM
ejpam-2482	521	3	,	,	PUNCT
ejpam-2482	521	4	s	s	X
ejpam-2482	521	5	-	-	PUNCT
ejpam-2482	521	6	th	th	X
ejpam-2482	521	7	+	+	NOUN
ejpam-2482	521	8	,	,	PUNCT
ejpam-2482	521	9	-	-	PUNCT
ejpam-2482	521	10	.	.	PUNCT
ejpam-2482	522	1	1rs	1rs	ADJ
ejpam-2482	522	2	,	,	PUNCT
ejpam-2482	522	3	0	0	NUM
ejpam-2482	522	4	,	,	PUNCT
ejpam-2482	522	5	.	.	PUNCT
ejpam-2482	522	6	.	.	PUNCT
ejpam-2482	523	1	.	.	PUNCT
ejpam-2482	524	1	,	,	PUNCT
ejpam-2482	524	2	0)(0	0)(0	NUM
ejpam-2482	524	3	,	,	PUNCT
ejpam-2482	524	4	.	.	PUNCT
ejpam-2482	524	5	.	.	PUNCT
ejpam-2482	525	1	.	.	PUNCT
ejpam-2482	526	1	,	,	PUNCT
ejpam-2482	526	2	0	0	NUM
ejpam-2482	526	3	,	,	PUNCT
ejpam-2482	526	4	r	r	X
ejpam-2482	526	5	-	-	PUNCT
ejpam-2482	526	6	th	th	X
ejpam-2482	526	7	+	+	NOUN
ejpam-2482	526	8	,	,	PUNCT
ejpam-2482	526	9	-	-	PUNCT
ejpam-2482	526	10	.	.	PUNCT
ejpam-2482	527	1	mr	mr	PROPN
ejpam-2482	527	2	,	,	PUNCT
ejpam-2482	527	3	0	0	NUM
ejpam-2482	527	4	,	,	PUNCT
ejpam-2482	527	5	.	.	PUNCT
ejpam-2482	527	6	.	.	PUNCT
ejpam-2482	528	1	.	.	PUNCT
ejpam-2482	529	1	,	,	PUNCT
ejpam-2482	529	2	0	0	NUM
ejpam-2482	529	3	,	,	PUNCT
ejpam-2482	529	4	s	s	X
ejpam-2482	529	5	-	-	PUNCT
ejpam-2482	529	6	th	th	X
ejpam-2482	529	7	+	+	NOUN
ejpam-2482	529	8	,	,	PUNCT
ejpam-2482	529	9	-	-	PUNCT
ejpam-2482	529	10	.	.	PUNCT
ejpam-2482	530	1	ms	ms	NOUN
ejpam-2482	530	2	,	,	PUNCT
ejpam-2482	530	3	0	0	NUM
ejpam-2482	530	4	,	,	PUNCT
ejpam-2482	530	5	.	.	PUNCT
ejpam-2482	530	6	.	.	PUNCT
ejpam-2482	531	1	.	.	PUNCT
ejpam-2482	532	1	,	,	PUNCT
ejpam-2482	532	2	0	0	X
ejpam-2482	532	3	)	)	PUNCT
ejpam-2482	532	4	=(	=(	NOUN
ejpam-2482	532	5	0	0	NUM
ejpam-2482	532	6	,	,	PUNCT
ejpam-2482	532	7	.	.	PUNCT
ejpam-2482	532	8	.	.	PUNCT
ejpam-2482	533	1	.	.	PUNCT
ejpam-2482	534	1	,	,	PUNCT
ejpam-2482	534	2	0	0	X
ejpam-2482	534	3	)	)	PUNCT
ejpam-2482	534	4	"	"	PUNCT
ejpam-2482	534	5	n	n	CCONJ
ejpam-2482	534	6	,	,	PUNCT
ejpam-2482	534	7	then	then	ADV
ejpam-2482	534	8	either	either	CCONJ
ejpam-2482	534	9	(	(	PUNCT
ejpam-2482	534	10	0	0	NUM
ejpam-2482	534	11	,	,	PUNCT
ejpam-2482	534	12	.	.	PUNCT
ejpam-2482	534	13	.	.	PUNCT
ejpam-2482	535	1	.	.	PUNCT
ejpam-2482	536	1	,	,	PUNCT
ejpam-2482	536	2	0	0	NUM
ejpam-2482	536	3	,	,	PUNCT
ejpam-2482	536	4	r	r	X
ejpam-2482	536	5	-	-	PUNCT
ejpam-2482	536	6	th	th	X
ejpam-2482	536	7	+	+	NOUN
ejpam-2482	536	8	,	,	PUNCT
ejpam-2482	536	9	-	-	PUNCT
ejpam-2482	536	10	.	.	PUNCT
ejpam-2482	537	1	1rr	1rr	ADJ
ejpam-2482	537	2	,	,	PUNCT
ejpam-2482	537	3	0	0	NUM
ejpam-2482	537	4	,	,	PUNCT
ejpam-2482	537	5	.	.	PUNCT
ejpam-2482	537	6	.	.	PUNCT
ejpam-2482	538	1	.	.	PUNCT
ejpam-2482	539	1	,	,	PUNCT
ejpam-2482	539	2	0)(0	0)(0	NUM
ejpam-2482	539	3	,	,	PUNCT
ejpam-2482	539	4	.	.	PUNCT
ejpam-2482	539	5	.	.	PUNCT
ejpam-2482	540	1	.	.	PUNCT
ejpam-2482	541	1	,	,	PUNCT
ejpam-2482	541	2	0	0	NUM
ejpam-2482	541	3	,	,	PUNCT
ejpam-2482	541	4	r	r	X
ejpam-2482	541	5	-	-	PUNCT
ejpam-2482	541	6	th	th	X
ejpam-2482	541	7	+	+	NOUN
ejpam-2482	541	8	,	,	PUNCT
ejpam-2482	541	9	-	-	PUNCT
ejpam-2482	541	10	.	.	PUNCT
ejpam-2482	542	1	mr	mr	PROPN
ejpam-2482	542	2	,	,	PUNCT
ejpam-2482	542	3	0	0	NUM
ejpam-2482	542	4	,	,	PUNCT
ejpam-2482	542	5	.	.	PUNCT
ejpam-2482	542	6	.	.	PUNCT
ejpam-2482	543	1	.	.	PUNCT
ejpam-2482	544	1	,	,	PUNCT
ejpam-2482	544	2	0	0	NUM
ejpam-2482	544	3	,	,	PUNCT
ejpam-2482	544	4	s	s	X
ejpam-2482	544	5	-	-	PUNCT
ejpam-2482	544	6	th	th	X
ejpam-2482	544	7	+	+	NOUN
ejpam-2482	544	8	,	,	PUNCT
ejpam-2482	544	9	-	-	PUNCT
ejpam-2482	544	10	.	.	PUNCT
ejpam-2482	545	1	ms	ms	NOUN
ejpam-2482	545	2	,	,	PUNCT
ejpam-2482	545	3	0	0	NUM
ejpam-2482	545	4	,	,	PUNCT
ejpam-2482	545	5	.	.	PUNCT
ejpam-2482	545	6	.	.	PUNCT
ejpam-2482	546	1	.	.	PUNCT
ejpam-2482	547	1	,	,	PUNCT
ejpam-2482	547	2	0	0	X
ejpam-2482	547	3	)	)	PUNCT
ejpam-2482	547	4	=(	=(	NOUN
ejpam-2482	547	5	0	0	NUM
ejpam-2482	547	6	,	,	PUNCT
ejpam-2482	547	7	.	.	PUNCT
ejpam-2482	547	8	.	.	PUNCT
ejpam-2482	548	1	.	.	PUNCT
ejpam-2482	549	1	,	,	PUNCT
ejpam-2482	549	2	0	0	NUM
ejpam-2482	549	3	,	,	PUNCT
ejpam-2482	549	4	r	r	X
ejpam-2482	549	5	-	-	PUNCT
ejpam-2482	549	6	th	th	X
ejpam-2482	549	7	+	+	NOUN
ejpam-2482	549	8	,	,	PUNCT
ejpam-2482	549	9	-	-	PUNCT
ejpam-2482	549	10	.	.	PUNCT
ejpam-2482	550	1	mr	mr	PROPN
ejpam-2482	550	2	,	,	PUNCT
ejpam-2482	550	3	0	0	NUM
ejpam-2482	550	4	,	,	PUNCT
ejpam-2482	550	5	.	.	PUNCT
ejpam-2482	550	6	.	.	PUNCT
ejpam-2482	551	1	.	.	PUNCT
ejpam-2482	552	1	,	,	PUNCT
ejpam-2482	552	2	0	0	X
ejpam-2482	552	3	)	)	PUNCT
ejpam-2482	552	4	"	"	PUNCT
ejpam-2482	552	5	n	n	CCONJ
ejpam-2482	552	6	or	or	CCONJ
ejpam-2482	552	7	(	(	PUNCT
ejpam-2482	552	8	0	0	NUM
ejpam-2482	552	9	,	,	PUNCT
ejpam-2482	552	10	.	.	PUNCT
ejpam-2482	552	11	.	.	PUNCT
ejpam-2482	553	1	.	.	PUNCT
ejpam-2482	554	1	,	,	PUNCT
ejpam-2482	554	2	0	0	NUM
ejpam-2482	554	3	,	,	PUNCT
ejpam-2482	554	4	s	s	X
ejpam-2482	554	5	-	-	PUNCT
ejpam-2482	554	6	th	th	X
ejpam-2482	554	7	+	+	NOUN
ejpam-2482	554	8	,	,	PUNCT
ejpam-2482	554	9	-	-	PUNCT
ejpam-2482	554	10	.	.	PUNCT
ejpam-2482	555	1	1rs	1rs	ADJ
ejpam-2482	555	2	,	,	PUNCT
ejpam-2482	555	3	0	0	NUM
ejpam-2482	555	4	,	,	PUNCT
ejpam-2482	555	5	.	.	PUNCT
ejpam-2482	555	6	.	.	PUNCT
ejpam-2482	556	1	.	.	PUNCT
ejpam-2482	557	1	,	,	PUNCT
ejpam-2482	557	2	0)(0	0)(0	NUM
ejpam-2482	557	3	,	,	PUNCT
ejpam-2482	557	4	.	.	PUNCT
ejpam-2482	557	5	.	.	PUNCT
ejpam-2482	558	1	.	.	PUNCT
ejpam-2482	559	1	,	,	PUNCT
ejpam-2482	559	2	0	0	NUM
ejpam-2482	559	3	,	,	PUNCT
ejpam-2482	559	4	r	r	X
ejpam-2482	559	5	-	-	PUNCT
ejpam-2482	559	6	th	th	X
ejpam-2482	559	7	+	+	NOUN
ejpam-2482	559	8	,	,	PUNCT
ejpam-2482	559	9	-	-	PUNCT
ejpam-2482	559	10	.	.	PUNCT
ejpam-2482	560	1	mr	mr	PROPN
ejpam-2482	560	2	,	,	PUNCT
ejpam-2482	560	3	0	0	NUM
ejpam-2482	560	4	,	,	PUNCT
ejpam-2482	560	5	.	.	PUNCT
ejpam-2482	560	6	.	.	PUNCT
ejpam-2482	561	1	.	.	PUNCT
ejpam-2482	562	1	,	,	PUNCT
ejpam-2482	562	2	0	0	NUM
ejpam-2482	562	3	,	,	PUNCT
ejpam-2482	562	4	s	s	X
ejpam-2482	562	5	-	-	PUNCT
ejpam-2482	562	6	th	th	X
ejpam-2482	562	7	+	+	NOUN
ejpam-2482	562	8	,	,	PUNCT
ejpam-2482	562	9	-	-	PUNCT
ejpam-2482	562	10	.	.	PUNCT
ejpam-2482	563	1	ms	ms	NOUN
ejpam-2482	563	2	,	,	PUNCT
ejpam-2482	563	3	0	0	NUM
ejpam-2482	563	4	,	,	PUNCT
ejpam-2482	563	5	.	.	PUNCT
ejpam-2482	563	6	.	.	PUNCT
ejpam-2482	564	1	.	.	PUNCT
ejpam-2482	565	1	,	,	PUNCT
ejpam-2482	565	2	0	0	X
ejpam-2482	565	3	)	)	PUNCT
ejpam-2482	565	4	=(	=(	NOUN
ejpam-2482	565	5	0	0	NUM
ejpam-2482	565	6	,	,	PUNCT
ejpam-2482	565	7	.	.	PUNCT
ejpam-2482	565	8	.	.	PUNCT
ejpam-2482	566	1	.	.	PUNCT
ejpam-2482	567	1	,	,	PUNCT
ejpam-2482	567	2	0	0	NUM
ejpam-2482	567	3	,	,	PUNCT
ejpam-2482	567	4	s	s	X
ejpam-2482	567	5	-	-	PUNCT
ejpam-2482	567	6	th	th	X
ejpam-2482	567	7	+	+	NOUN
ejpam-2482	567	8	,	,	PUNCT
ejpam-2482	567	9	-	-	PUNCT
ejpam-2482	567	10	.	.	PUNCT
ejpam-2482	568	1	ms	ms	NOUN
ejpam-2482	568	2	,	,	PUNCT
ejpam-2482	568	3	0	0	NUM
ejpam-2482	568	4	,	,	PUNCT
ejpam-2482	568	5	.	.	PUNCT
ejpam-2482	568	6	.	.	PUNCT
ejpam-2482	569	1	.	.	PUNCT
ejpam-2482	570	1	,	,	PUNCT
ejpam-2482	570	2	0	0	X
ejpam-2482	570	3	)	)	PUNCT
ejpam-2482	570	4	"	"	PUNCT
ejpam-2482	570	5	n	n	CCONJ
ejpam-2482	570	6	,	,	PUNCT
ejpam-2482	570	7	which	which	PRON
ejpam-2482	570	8	is	be	AUX
ejpam-2482	570	9	a	a	DET
ejpam-2482	570	10	contradiction	contradiction	NOUN
ejpam-2482	570	11	.	.	PUNCT
ejpam-2482	571	1	hence	hence	ADV
ejpam-2482	571	2	exactly	exactly	ADV
ejpam-2482	571	3	one	one	NUM
ejpam-2482	571	4	of	of	ADP
ejpam-2482	571	5	the	the	DET
ejpam-2482	571	6	ni	ni	PROPN
ejpam-2482	571	7	’s	’s	PART
ejpam-2482	571	8	is	be	AUX
ejpam-2482	571	9	proper	proper	ADJ
ejpam-2482	571	10	,	,	PUNCT
ejpam-2482	571	11	say	say	VERB
ejpam-2482	571	12	nk	nk	PROPN
ejpam-2482	571	13	.	.	PUNCT
ejpam-2482	572	1	now	now	ADV
ejpam-2482	572	2	,	,	PUNCT
ejpam-2482	572	3	we	we	PRON
ejpam-2482	572	4	show	show	VERB
ejpam-2482	572	5	that	that	SCONJ
ejpam-2482	572	6	nk	nk	PROPN
ejpam-2482	572	7	is	be	AUX
ejpam-2482	572	8	a	a	DET
ejpam-2482	572	9	classical	classical	ADJ
ejpam-2482	572	10	prime	prime	ADJ
ejpam-2482	572	11	submodule	submodule	NOUN
ejpam-2482	572	12	of	of	ADP
ejpam-2482	572	13	mk	mk	PROPN
ejpam-2482	572	14	.	.	PUNCT
ejpam-2482	573	1	let	let	VERB
ejpam-2482	573	2	abmk	abmk	PROPN
ejpam-2482	573	3	"	"	PUNCT
ejpam-2482	573	4	nk	nk	PROPN
ejpam-2482	573	5	for	for	ADP
ejpam-2482	573	6	some	some	DET
ejpam-2482	573	7	a	a	PRON
ejpam-2482	573	8	,	,	PUNCT
ejpam-2482	573	9	b	b	NOUN
ejpam-2482	573	10	"	"	PUNCT
ejpam-2482	573	11	rk	rk	PROPN
ejpam-2482	573	12	and	and	CCONJ
ejpam-2482	573	13	mk	mk	PROPN
ejpam-2482	573	14	"	"	PUNCT
ejpam-2482	573	15	mk	mk	PROPN
ejpam-2482	573	16	.	.	PUNCT
ejpam-2482	574	1	therefore	therefore	ADV
ejpam-2482	574	2	(	(	PUNCT
ejpam-2482	574	3	0	0	NUM
ejpam-2482	574	4	,	,	PUNCT
ejpam-2482	574	5	.	.	PUNCT
ejpam-2482	574	6	.	.	PUNCT
ejpam-2482	574	7	.	.	PUNCT
ejpam-2482	575	1	,	,	PUNCT
ejpam-2482	575	2	0	0	NUM
ejpam-2482	575	3	,	,	PUNCT
ejpam-2482	575	4	k	k	X
ejpam-2482	575	5	-	-	PUNCT
ejpam-2482	575	6	th	th	X
ejpam-2482	575	7	+	+	NOUN
ejpam-2482	575	8	,	,	PUNCT
ejpam-2482	575	9	-	-	PUNCT
ejpam-2482	575	10	.	.	PUNCT
ejpam-2482	576	1	a	a	PRON
ejpam-2482	576	2	,	,	PUNCT
ejpam-2482	576	3	0	0	NUM
ejpam-2482	576	4	,	,	PUNCT
ejpam-2482	576	5	.	.	PUNCT
ejpam-2482	576	6	.	.	PUNCT
ejpam-2482	577	1	.	.	PUNCT
ejpam-2482	578	1	,	,	PUNCT
ejpam-2482	578	2	0)(0	0)(0	NUM
ejpam-2482	578	3	,	,	PUNCT
ejpam-2482	578	4	.	.	PUNCT
ejpam-2482	578	5	.	.	PUNCT
ejpam-2482	579	1	.	.	PUNCT
ejpam-2482	580	1	,	,	PUNCT
ejpam-2482	580	2	0	0	NUM
ejpam-2482	580	3	,	,	PUNCT
ejpam-2482	580	4	k	k	X
ejpam-2482	580	5	-	-	PUNCT
ejpam-2482	580	6	th	th	X
ejpam-2482	580	7	+	+	NOUN
ejpam-2482	580	8	,	,	PUNCT
ejpam-2482	580	9	-	-	PUNCT
ejpam-2482	580	10	.	.	PUNCT
ejpam-2482	581	1	b	b	PROPN
ejpam-2482	581	2	,	,	PUNCT
ejpam-2482	581	3	0	0	NUM
ejpam-2482	581	4	,	,	PUNCT
ejpam-2482	581	5	.	.	PUNCT
ejpam-2482	581	6	.	.	PUNCT
ejpam-2482	582	1	.	.	PUNCT
ejpam-2482	583	1	,	,	PUNCT
ejpam-2482	583	2	0)(0	0)(0	NUM
ejpam-2482	583	3	,	,	PUNCT
ejpam-2482	583	4	.	.	PUNCT
ejpam-2482	583	5	.	.	PUNCT
ejpam-2482	584	1	.	.	PUNCT
ejpam-2482	585	1	,	,	PUNCT
ejpam-2482	585	2	0	0	NUM
ejpam-2482	585	3	,	,	PUNCT
ejpam-2482	585	4	k	k	X
ejpam-2482	585	5	-	-	PUNCT
ejpam-2482	585	6	th	th	X
ejpam-2482	585	7	+	+	NOUN
ejpam-2482	585	8	,	,	PUNCT
ejpam-2482	585	9	-	-	PUNCT
ejpam-2482	585	10	.	.	PUNCT
ejpam-2482	586	1	mk	mk	PROPN
ejpam-2482	586	2	,	,	PUNCT
ejpam-2482	586	3	0	0	NUM
ejpam-2482	586	4	,	,	PUNCT
ejpam-2482	586	5	.	.	PUNCT
ejpam-2482	586	6	.	.	PUNCT
ejpam-2482	586	7	.	.	PUNCT
ejpam-2482	587	1	,	,	PUNCT
ejpam-2482	587	2	0	0	X
ejpam-2482	587	3	)	)	PUNCT
ejpam-2482	587	4	=(	=(	NOUN
ejpam-2482	587	5	0	0	NUM
ejpam-2482	587	6	,	,	PUNCT
ejpam-2482	587	7	.	.	PUNCT
ejpam-2482	587	8	.	.	PUNCT
ejpam-2482	588	1	.	.	PUNCT
ejpam-2482	589	1	,	,	PUNCT
ejpam-2482	589	2	0	0	NUM
ejpam-2482	589	3	,	,	PUNCT
ejpam-2482	589	4	k	k	X
ejpam-2482	589	5	-	-	PUNCT
ejpam-2482	589	6	th	th	X
ejpam-2482	589	7	+	+	NOUN
ejpam-2482	589	8	,	,	PUNCT
ejpam-2482	589	9	.	.	PUNCT
ejpam-2482	590	1	abmk	abmk	PROPN
ejpam-2482	590	2	,	,	PUNCT
ejpam-2482	590	3	0	0	NUM
ejpam-2482	590	4	,	,	PUNCT
ejpam-2482	590	5	.	.	PUNCT
ejpam-2482	590	6	.	.	PUNCT
ejpam-2482	590	7	.	.	PUNCT
ejpam-2482	591	1	,	,	PUNCT
ejpam-2482	591	2	0	0	X
ejpam-2482	591	3	)	)	PUNCT
ejpam-2482	591	4	"	"	PUNCT
ejpam-2482	591	5	n	n	CCONJ
ejpam-2482	591	6	,	,	PUNCT
ejpam-2482	591	7	and	and	CCONJ
ejpam-2482	591	8	so	so	ADV
ejpam-2482	591	9	(	(	PUNCT
ejpam-2482	591	10	0	0	NUM
ejpam-2482	591	11	,	,	PUNCT
ejpam-2482	591	12	.	.	PUNCT
ejpam-2482	591	13	.	.	PUNCT
ejpam-2482	591	14	.	.	PUNCT
ejpam-2482	592	1	,	,	PUNCT
ejpam-2482	592	2	0	0	NUM
ejpam-2482	592	3	,	,	PUNCT
ejpam-2482	592	4	k	k	X
ejpam-2482	592	5	-	-	PUNCT
ejpam-2482	592	6	th	th	X
ejpam-2482	592	7	+	+	NOUN
ejpam-2482	592	8	,	,	PUNCT
ejpam-2482	592	9	-	-	PUNCT
ejpam-2482	592	10	.	.	PUNCT
ejpam-2482	593	1	a	a	PRON
ejpam-2482	593	2	,	,	PUNCT
ejpam-2482	593	3	0	0	NUM
ejpam-2482	593	4	,	,	PUNCT
ejpam-2482	593	5	.	.	PUNCT
ejpam-2482	593	6	.	.	PUNCT
ejpam-2482	594	1	.	.	PUNCT
ejpam-2482	595	1	,	,	PUNCT
ejpam-2482	595	2	0)(0	0)(0	NUM
ejpam-2482	595	3	,	,	PUNCT
ejpam-2482	595	4	.	.	PUNCT
ejpam-2482	595	5	.	.	PUNCT
ejpam-2482	596	1	.	.	PUNCT
ejpam-2482	597	1	,	,	PUNCT
ejpam-2482	597	2	0	0	NUM
ejpam-2482	597	3	,	,	PUNCT
ejpam-2482	597	4	k	k	X
ejpam-2482	597	5	-	-	PUNCT
ejpam-2482	597	6	th	th	X
ejpam-2482	597	7	+	+	NOUN
ejpam-2482	597	8	,	,	PUNCT
ejpam-2482	597	9	-	-	PUNCT
ejpam-2482	597	10	.	.	PUNCT
ejpam-2482	598	1	mk	mk	PROPN
ejpam-2482	598	2	,	,	PUNCT
ejpam-2482	598	3	0	0	NUM
ejpam-2482	598	4	,	,	PUNCT
ejpam-2482	598	5	.	.	PUNCT
ejpam-2482	598	6	.	.	PUNCT
ejpam-2482	598	7	.	.	PUNCT
ejpam-2482	599	1	,	,	PUNCT
ejpam-2482	599	2	0	0	X
ejpam-2482	599	3	)	)	PUNCT
ejpam-2482	599	4	=	=	SYM
ejpam-2482	599	5	(	(	PUNCT
ejpam-2482	599	6	0	0	NUM
ejpam-2482	599	7	,	,	PUNCT
ejpam-2482	599	8	.	.	PUNCT
ejpam-2482	599	9	.	.	PUNCT
ejpam-2482	600	1	.	.	PUNCT
ejpam-2482	601	1	,	,	PUNCT
ejpam-2482	601	2	0	0	NUM
ejpam-2482	601	3	,	,	PUNCT
ejpam-2482	601	4	k	k	X
ejpam-2482	601	5	-	-	PUNCT
ejpam-2482	601	6	th	th	X
ejpam-2482	601	7	+	+	NOUN
ejpam-2482	601	8	,	,	PUNCT
ejpam-2482	601	9	-	-	PUNCT
ejpam-2482	601	10	.	.	PUNCT
ejpam-2482	602	1	amk	amk	PROPN
ejpam-2482	602	2	,	,	PUNCT
ejpam-2482	602	3	0	0	NUM
ejpam-2482	602	4	,	,	PUNCT
ejpam-2482	602	5	.	.	PUNCT
ejpam-2482	602	6	.	.	PUNCT
ejpam-2482	603	1	.	.	PUNCT
ejpam-2482	604	1	,	,	PUNCT
ejpam-2482	604	2	0	0	X
ejpam-2482	604	3	)	)	PUNCT
ejpam-2482	604	4	"	"	PUNCT
ejpam-2482	604	5	n	n	CCONJ
ejpam-2482	604	6	or	or	CCONJ
ejpam-2482	604	7	(	(	PUNCT
ejpam-2482	604	8	0	0	NUM
ejpam-2482	604	9	,	,	PUNCT
ejpam-2482	604	10	.	.	PUNCT
ejpam-2482	604	11	.	.	PUNCT
ejpam-2482	605	1	.	.	PUNCT
ejpam-2482	606	1	,	,	PUNCT
ejpam-2482	606	2	0	0	NUM
ejpam-2482	606	3	,	,	PUNCT
ejpam-2482	606	4	k	k	X
ejpam-2482	606	5	-	-	PUNCT
ejpam-2482	606	6	th	th	X
ejpam-2482	606	7	+	+	NOUN
ejpam-2482	606	8	,	,	PUNCT
ejpam-2482	606	9	-	-	PUNCT
ejpam-2482	606	10	.	.	PUNCT
ejpam-2482	607	1	b	b	PROPN
ejpam-2482	607	2	,	,	PUNCT
ejpam-2482	607	3	0	0	NUM
ejpam-2482	607	4	,	,	PUNCT
ejpam-2482	607	5	.	.	PUNCT
ejpam-2482	607	6	.	.	PUNCT
ejpam-2482	608	1	.	.	PUNCT
ejpam-2482	609	1	,	,	PUNCT
ejpam-2482	609	2	0)(0	0)(0	NUM
ejpam-2482	609	3	,	,	PUNCT
ejpam-2482	609	4	.	.	PUNCT
ejpam-2482	609	5	.	.	PUNCT
ejpam-2482	610	1	.	.	PUNCT
ejpam-2482	611	1	,	,	PUNCT
ejpam-2482	611	2	0	0	NUM
ejpam-2482	611	3	,	,	PUNCT
ejpam-2482	611	4	k	k	X
ejpam-2482	611	5	-	-	PUNCT
ejpam-2482	611	6	th	th	X
ejpam-2482	611	7	+	+	NOUN
ejpam-2482	611	8	,	,	PUNCT
ejpam-2482	611	9	-	-	PUNCT
ejpam-2482	611	10	.	.	PUNCT
ejpam-2482	612	1	mk	mk	PROPN
ejpam-2482	612	2	,	,	PUNCT
ejpam-2482	612	3	0	0	NUM
ejpam-2482	612	4	,	,	PUNCT
ejpam-2482	612	5	.	.	PUNCT
ejpam-2482	612	6	.	.	PUNCT
ejpam-2482	612	7	.	.	PUNCT
ejpam-2482	613	1	,	,	PUNCT
ejpam-2482	613	2	0	0	X
ejpam-2482	613	3	)	)	PUNCT
ejpam-2482	613	4	=	=	SYM
ejpam-2482	613	5	(	(	PUNCT
ejpam-2482	613	6	0	0	NUM
ejpam-2482	613	7	,	,	PUNCT
ejpam-2482	613	8	.	.	PUNCT
ejpam-2482	613	9	.	.	PUNCT
ejpam-2482	614	1	.	.	PUNCT
ejpam-2482	615	1	,	,	PUNCT
ejpam-2482	615	2	0	0	NUM
ejpam-2482	615	3	,	,	PUNCT
ejpam-2482	615	4	k	k	X
ejpam-2482	615	5	-	-	PUNCT
ejpam-2482	615	6	th	th	X
ejpam-2482	615	7	+	+	NOUN
ejpam-2482	615	8	,	,	PUNCT
ejpam-2482	615	9	-	-	PUNCT
ejpam-2482	615	10	.	.	PUNCT
ejpam-2482	616	1	bmk	bmk	PROPN
ejpam-2482	616	2	,	,	PUNCT
ejpam-2482	616	3	0	0	NUM
ejpam-2482	616	4	,	,	PUNCT
ejpam-2482	616	5	.	.	PUNCT
ejpam-2482	616	6	.	.	PUNCT
ejpam-2482	617	1	.	.	PUNCT
ejpam-2482	618	1	,	,	PUNCT
ejpam-2482	618	2	0	0	X
ejpam-2482	618	3	)	)	PUNCT
ejpam-2482	618	4	"	"	PUNCT
ejpam-2482	618	5	n	n	NOUN
ejpam-2482	618	6	.	.	PUNCT
ejpam-2482	619	1	thus	thus	ADV
ejpam-2482	619	2	amk	amk	PROPN
ejpam-2482	619	3	"	"	PUNCT
ejpam-2482	619	4	nk	nk	PROPN
ejpam-2482	619	5	or	or	CCONJ
ejpam-2482	619	6	bmk	bmk	PROPN
ejpam-2482	619	7	"	"	PUNCT
ejpam-2482	619	8	nk	nk	PROPN
ejpam-2482	619	9	which	which	PRON
ejpam-2482	619	10	implies	imply	VERB
ejpam-2482	619	11	that	that	SCONJ
ejpam-2482	619	12	nk	nk	PROPN
ejpam-2482	619	13	is	be	AUX
ejpam-2482	619	14	a	a	DET
ejpam-2482	619	15	classical	classical	ADJ
ejpam-2482	619	16	prime	prime	ADJ
ejpam-2482	619	17	submodule	submodule	NOUN
ejpam-2482	619	18	of	of	ADP
ejpam-2482	619	19	mk	mk	PROPN
ejpam-2482	619	20	.	.	PUNCT
ejpam-2482	620	1	(	(	PUNCT
ejpam-2482	620	2	4	4	X
ejpam-2482	620	3	)	)	PUNCT
ejpam-2482	620	4	is	be	AUX
ejpam-2482	620	5	easy	easy	ADJ
ejpam-2482	620	6	.	.	PUNCT
ejpam-2482	621	1	references	reference	NOUN
ejpam-2482	621	2	429	429	NUM
ejpam-2482	621	3	theorem	theorem	NOUN
ejpam-2482	621	4	8	8	NUM
ejpam-2482	621	5	.	.	PUNCT
ejpam-2482	622	1	let	let	VERB
ejpam-2482	622	2	r=	r=	ADJ
ejpam-2482	622	3	r1	r1	PROPN
ejpam-2482	622	4	1	1	NUM
ejpam-2482	622	5	r2	r2	PROPN
ejpam-2482	622	6	1	1	NUM
ejpam-2482	622	7	·	·	PUNCT
ejpam-2482	622	8	·	·	PUNCT
ejpam-2482	622	9	·	·	PUNCT
ejpam-2482	622	10	1	1	NUM
ejpam-2482	622	11	rn	rn	PROPN
ejpam-2482	622	12	(	(	PUNCT
ejpam-2482	622	13	23	23	NUM
ejpam-2482	622	14	n<5	n<5	NOUN
ejpam-2482	622	15	)	)	PUNCT
ejpam-2482	622	16	be	be	VERB
ejpam-2482	622	17	a	a	DET
ejpam-2482	622	18	decomposable	decomposable	ADJ
ejpam-2482	622	19	ring	ring	NOUN
ejpam-2482	622	20	and	and	CCONJ
ejpam-2482	622	21	m	m	NOUN
ejpam-2482	622	22	=	=	ADJ
ejpam-2482	622	23	m1	m1	PROPN
ejpam-2482	622	24	1	1	NUM
ejpam-2482	622	25	m2	m2	PROPN
ejpam-2482	622	26	1	1	NUM
ejpam-2482	622	27	·	·	PUNCT
ejpam-2482	622	28	·	·	PUNCT
ejpam-2482	622	29	·	·	PUNCT
ejpam-2482	622	30	1	1	NUM
ejpam-2482	622	31	mn	mn	NOUN
ejpam-2482	622	32	be	be	AUX
ejpam-2482	622	33	an	an	DET
ejpam-2482	622	34	r	r	NOUN
ejpam-2482	622	35	-	-	PUNCT
ejpam-2482	622	36	module	module	NOUN
ejpam-2482	622	37	where	where	SCONJ
ejpam-2482	622	38	for	for	ADP
ejpam-2482	622	39	every	every	DET
ejpam-2482	622	40	1	1	NUM
ejpam-2482	622	41	3	3	NUM
ejpam-2482	622	42	i	i	NOUN
ejpam-2482	622	43	3	3	NUM
ejpam-2482	622	44	n	n	CCONJ
ejpam-2482	622	45	,	,	PUNCT
ejpam-2482	622	46	mi	mi	PROPN
ejpam-2482	622	47	is	be	AUX
ejpam-2482	622	48	an	an	DET
ejpam-2482	622	49	ri	ri	NOUN
ejpam-2482	622	50	-	-	PUNCT
ejpam-2482	622	51	module	module	NOUN
ejpam-2482	622	52	,	,	PUNCT
ejpam-2482	622	53	respectively	respectively	ADV
ejpam-2482	622	54	.	.	PUNCT
ejpam-2482	623	1	for	for	ADP
ejpam-2482	623	2	a	a	DET
ejpam-2482	623	3	proper	proper	ADJ
ejpam-2482	623	4	submodule	submodule	NOUN
ejpam-2482	623	5	n	n	PROPN
ejpam-2482	623	6	of	of	ADP
ejpam-2482	623	7	m	m	PRON
ejpam-2482	623	8	the	the	DET
ejpam-2482	623	9	following	follow	VERB
ejpam-2482	623	10	conditions	condition	NOUN
ejpam-2482	623	11	are	be	AUX
ejpam-2482	623	12	equivalent	equivalent	ADJ
ejpam-2482	623	13	:	:	PUNCT
ejpam-2482	623	14	(	(	PUNCT
ejpam-2482	623	15	i	i	NOUN
ejpam-2482	623	16	)	)	PUNCT
ejpam-2482	623	17	n	n	PRON
ejpam-2482	623	18	is	be	AUX
ejpam-2482	623	19	a	a	DET
ejpam-2482	623	20	classical	classical	ADJ
ejpam-2482	623	21	2	2	NUM
ejpam-2482	623	22	-	-	PUNCT
ejpam-2482	623	23	absorbing	absorb	VERB
ejpam-2482	623	24	submodule	submodule	NOUN
ejpam-2482	623	25	of	of	ADP
ejpam-2482	623	26	m	m	PROPN
ejpam-2482	623	27	;	;	PUNCT
ejpam-2482	623	28	(	(	PUNCT
ejpam-2482	623	29	ii	ii	NOUN
ejpam-2482	623	30	)	)	PUNCT
ejpam-2482	623	31	either	either	CCONJ
ejpam-2482	623	32	n	n	PROPN
ejpam-2482	623	33	=	=	SYM
ejpam-2482	623	34	1n	1n	NUM
ejpam-2482	623	35	t=1nt	t=1nt	ADP
ejpam-2482	623	36	such	such	ADJ
ejpam-2482	623	37	that	that	PRON
ejpam-2482	623	38	for	for	ADP
ejpam-2482	623	39	some	some	DET
ejpam-2482	623	40	k	k	NOUN
ejpam-2482	623	41	"	"	PUNCT
ejpam-2482	623	42	{	{	PUNCT
ejpam-2482	623	43	1,2	1,2	NUM
ejpam-2482	623	44	,	,	PUNCT
ejpam-2482	623	45	.	.	PUNCT
ejpam-2482	623	46	.	.	PUNCT
ejpam-2482	624	1	.	.	PUNCT
ejpam-2482	625	1	,	,	PUNCT
ejpam-2482	625	2	n	n	CCONJ
ejpam-2482	625	3	}	}	PUNCT
ejpam-2482	625	4	,	,	PUNCT
ejpam-2482	625	5	nk	nk	PROPN
ejpam-2482	625	6	is	be	AUX
ejpam-2482	625	7	a	a	DET
ejpam-2482	625	8	classical	classical	ADJ
ejpam-2482	625	9	2	2	NUM
ejpam-2482	625	10	-	-	PUNCT
ejpam-2482	625	11	absorbing	absorb	VERB
ejpam-2482	625	12	submodule	submodule	NOUN
ejpam-2482	625	13	of	of	ADP
ejpam-2482	625	14	mk	mk	PROPN
ejpam-2482	625	15	,	,	PUNCT
ejpam-2482	625	16	and	and	CCONJ
ejpam-2482	625	17	nt	not	PART
ejpam-2482	625	18	=	=	PROPN
ejpam-2482	625	19	mt	mt	PROPN
ejpam-2482	625	20	for	for	ADP
ejpam-2482	625	21	every	every	DET
ejpam-2482	625	22	t	t	NOUN
ejpam-2482	625	23	"	"	PUNCT
ejpam-2482	625	24	{	{	PUNCT
ejpam-2482	625	25	1,2	1,2	NUM
ejpam-2482	625	26	,	,	PUNCT
ejpam-2482	625	27	.	.	PUNCT
ejpam-2482	625	28	.	.	PUNCT
ejpam-2482	626	1	.	.	PUNCT
ejpam-2482	627	1	,	,	PUNCT
ejpam-2482	627	2	n}\{k	n}\{k	ADV
ejpam-2482	627	3	}	}	PUNCT
ejpam-2482	627	4	or	or	CCONJ
ejpam-2482	627	5	n	n	NOUN
ejpam-2482	627	6	=	=	SYM
ejpam-2482	627	7	1n	1n	NUM
ejpam-2482	627	8	t=1nt	t=1nt	ADP
ejpam-2482	627	9	such	such	ADJ
ejpam-2482	627	10	that	that	PRON
ejpam-2482	627	11	for	for	ADP
ejpam-2482	627	12	some	some	DET
ejpam-2482	627	13	k	k	NOUN
ejpam-2482	627	14	,	,	PUNCT
ejpam-2482	627	15	m	m	VERB
ejpam-2482	627	16	"	"	PUNCT
ejpam-2482	627	17	{	{	PUNCT
ejpam-2482	627	18	1,2	1,2	NUM
ejpam-2482	627	19	,	,	PUNCT
ejpam-2482	627	20	.	.	PUNCT
ejpam-2482	627	21	.	.	PUNCT
ejpam-2482	628	1	.	.	PUNCT
ejpam-2482	629	1	,	,	PUNCT
ejpam-2482	629	2	n	n	CCONJ
ejpam-2482	629	3	}	}	PUNCT
ejpam-2482	629	4	,	,	PUNCT
ejpam-2482	629	5	nk	nk	PROPN
ejpam-2482	629	6	is	be	AUX
ejpam-2482	629	7	a	a	DET
ejpam-2482	629	8	classical	classical	ADJ
ejpam-2482	629	9	prime	prime	ADJ
ejpam-2482	629	10	submodule	submodule	NOUN
ejpam-2482	629	11	of	of	ADP
ejpam-2482	629	12	mk	mk	PROPN
ejpam-2482	629	13	,	,	PUNCT
ejpam-2482	629	14	nm	nm	PROPN
ejpam-2482	629	15	is	be	AUX
ejpam-2482	629	16	a	a	DET
ejpam-2482	629	17	classical	classical	ADJ
ejpam-2482	629	18	prime	prime	ADJ
ejpam-2482	629	19	submodule	submodule	NOUN
ejpam-2482	629	20	of	of	ADP
ejpam-2482	629	21	mm	mm	PROPN
ejpam-2482	629	22	,	,	PUNCT
ejpam-2482	629	23	and	and	CCONJ
ejpam-2482	629	24	nt	not	PART
ejpam-2482	629	25	=	=	PROPN
ejpam-2482	629	26	mt	mt	PROPN
ejpam-2482	629	27	for	for	ADP
ejpam-2482	629	28	every	every	DET
ejpam-2482	629	29	t	t	NOUN
ejpam-2482	629	30	"	"	PUNCT
ejpam-2482	629	31	{	{	PUNCT
ejpam-2482	629	32	1,2	1,2	NUM
ejpam-2482	629	33	,	,	PUNCT
ejpam-2482	629	34	.	.	PUNCT
ejpam-2482	629	35	.	.	PUNCT
ejpam-2482	630	1	.	.	PUNCT
ejpam-2482	631	1	,	,	PUNCT
ejpam-2482	631	2	n}\{k	n}\{k	PROPN
ejpam-2482	631	3	,	,	PUNCT
ejpam-2482	631	4	m	m	VERB
ejpam-2482	631	5	}	}	PUNCT
ejpam-2482	631	6	.	.	PUNCT
ejpam-2482	632	1	proof	proof	NOUN
ejpam-2482	632	2	.	.	PUNCT
ejpam-2482	633	1	we	we	PRON
ejpam-2482	633	2	argue	argue	VERB
ejpam-2482	633	3	induction	induction	NOUN
ejpam-2482	633	4	on	on	ADP
ejpam-2482	633	5	n.	n.	NOUN
ejpam-2482	633	6	for	for	ADP
ejpam-2482	633	7	n	n	NOUN
ejpam-2482	633	8	=	=	SYM
ejpam-2482	633	9	2	2	NUM
ejpam-2482	633	10	the	the	DET
ejpam-2482	633	11	result	result	NOUN
ejpam-2482	633	12	holds	hold	VERB
ejpam-2482	633	13	by	by	ADP
ejpam-2482	633	14	theorem	theorem	NOUN
ejpam-2482	633	15	7	7	NUM
ejpam-2482	633	16	.	.	PUNCT
ejpam-2482	633	17	then	then	ADV
ejpam-2482	633	18	let	let	VERB
ejpam-2482	633	19	33	33	NUM
ejpam-2482	633	20	n<5	n<5	NOUN
ejpam-2482	633	21	and	and	CCONJ
ejpam-2482	633	22	suppose	suppose	VERB
ejpam-2482	633	23	that	that	SCONJ
ejpam-2482	633	24	the	the	DET
ejpam-2482	633	25	result	result	NOUN
ejpam-2482	633	26	is	be	AUX
ejpam-2482	633	27	valid	valid	ADJ
ejpam-2482	633	28	when	when	SCONJ
ejpam-2482	633	29	k	k	PROPN
ejpam-2482	633	30	=	=	SYM
ejpam-2482	633	31	m1	m1	PROPN
ejpam-2482	633	32	1	1	NUM
ejpam-2482	633	33	·	·	PUNCT
ejpam-2482	633	34	·	·	PUNCT
ejpam-2482	633	35	·	·	PUNCT
ejpam-2482	633	36	1mn&1	1mn&1	NUM
ejpam-2482	633	37	.	.	PUNCT
ejpam-2482	634	1	we	we	PRON
ejpam-2482	634	2	show	show	VERB
ejpam-2482	634	3	that	that	SCONJ
ejpam-2482	634	4	the	the	DET
ejpam-2482	634	5	result	result	NOUN
ejpam-2482	634	6	holds	hold	VERB
ejpam-2482	634	7	when	when	SCONJ
ejpam-2482	634	8	m	m	VERB
ejpam-2482	634	9	=	=	SYM
ejpam-2482	634	10	k	k	PROPN
ejpam-2482	634	11	1mn	1mn	PROPN
ejpam-2482	634	12	.	.	PUNCT
ejpam-2482	635	1	by	by	ADP
ejpam-2482	635	2	theorem	theorem	NOUN
ejpam-2482	635	3	7	7	NUM
ejpam-2482	635	4	,	,	PUNCT
ejpam-2482	635	5	n	n	PRON
ejpam-2482	635	6	is	be	AUX
ejpam-2482	635	7	a	a	DET
ejpam-2482	635	8	classical	classical	ADJ
ejpam-2482	635	9	2	2	NUM
ejpam-2482	635	10	-	-	PUNCT
ejpam-2482	635	11	absorbing	absorb	VERB
ejpam-2482	635	12	submodule	submodule	NOUN
ejpam-2482	635	13	of	of	ADP
ejpam-2482	635	14	m	m	PROPN
ejpam-2482	635	15	if	if	SCONJ
ejpam-2482	636	1	and	and	CCONJ
ejpam-2482	636	2	only	only	ADV
ejpam-2482	636	3	if	if	SCONJ
ejpam-2482	636	4	either	either	PRON
ejpam-2482	636	5	n	n	ADV
ejpam-2482	636	6	=	=	PUNCT
ejpam-2482	636	7	l1mn	l1mn	PUNCT
ejpam-2482	636	8	for	for	ADP
ejpam-2482	636	9	some	some	DET
ejpam-2482	636	10	classical	classical	ADJ
ejpam-2482	636	11	2	2	NUM
ejpam-2482	636	12	-	-	PUNCT
ejpam-2482	636	13	absorbing	absorb	VERB
ejpam-2482	636	14	submodule	submodule	NOUN
ejpam-2482	636	15	l	l	NOUN
ejpam-2482	636	16	of	of	ADP
ejpam-2482	636	17	k	k	PROPN
ejpam-2482	636	18	or	or	CCONJ
ejpam-2482	636	19	n	n	PROPN
ejpam-2482	636	20	=	=	SYM
ejpam-2482	636	21	k	k	PROPN
ejpam-2482	636	22	1	1	NUM
ejpam-2482	636	23	ln	ln	NOUN
ejpam-2482	636	24	for	for	ADP
ejpam-2482	636	25	some	some	DET
ejpam-2482	636	26	classical	classical	ADJ
ejpam-2482	636	27	2	2	NUM
ejpam-2482	636	28	-	-	PUNCT
ejpam-2482	636	29	absorbing	absorb	VERB
ejpam-2482	636	30	submodule	submodule	NOUN
ejpam-2482	636	31	ln	ln	NOUN
ejpam-2482	636	32	of	of	ADP
ejpam-2482	636	33	mn	mn	PROPN
ejpam-2482	636	34	or	or	CCONJ
ejpam-2482	636	35	n	n	NOUN
ejpam-2482	636	36	=	=	SYM
ejpam-2482	636	37	l	l	NOUN
ejpam-2482	636	38	1	1	NUM
ejpam-2482	636	39	ln	ln	ADV
ejpam-2482	636	40	for	for	ADP
ejpam-2482	636	41	some	some	DET
ejpam-2482	636	42	classical	classical	ADJ
ejpam-2482	636	43	prime	prime	ADJ
ejpam-2482	636	44	submodule	submodule	NOUN
ejpam-2482	636	45	l	l	NOUN
ejpam-2482	636	46	of	of	ADP
ejpam-2482	636	47	k	k	PROPN
ejpam-2482	636	48	and	and	CCONJ
ejpam-2482	636	49	some	some	DET
ejpam-2482	636	50	classical	classical	ADJ
ejpam-2482	636	51	prime	prime	ADJ
ejpam-2482	636	52	submodule	submodule	NOUN
ejpam-2482	636	53	ln	ln	PROPN
ejpam-2482	636	54	of	of	ADP
ejpam-2482	636	55	mn	mn	PROPN
ejpam-2482	636	56	.	.	PROPN
ejpam-2482	636	57	notice	notice	VERB
ejpam-2482	636	58	that	that	SCONJ
ejpam-2482	636	59	by	by	ADP
ejpam-2482	636	60	lemma	lemma	PROPN
ejpam-2482	636	61	1	1	NUM
ejpam-2482	636	62	,	,	PUNCT
ejpam-2482	636	63	a	a	DET
ejpam-2482	636	64	proper	proper	ADJ
ejpam-2482	636	65	submodule	submodule	NOUN
ejpam-2482	636	66	l	l	NOUN
ejpam-2482	636	67	of	of	ADP
ejpam-2482	636	68	k	k	PROPN
ejpam-2482	636	69	is	be	AUX
ejpam-2482	636	70	a	a	DET
ejpam-2482	636	71	classical	classical	ADJ
ejpam-2482	636	72	prime	prime	ADJ
ejpam-2482	636	73	submodule	submodule	NOUN
ejpam-2482	636	74	of	of	ADP
ejpam-2482	636	75	k	k	PROPN
ejpam-2482	637	1	if	if	SCONJ
ejpam-2482	638	1	and	and	CCONJ
ejpam-2482	638	2	only	only	ADV
ejpam-2482	638	3	if	if	SCONJ
ejpam-2482	638	4	l	l	NOUN
ejpam-2482	638	5	=	=	SYM
ejpam-2482	638	6	1n&1	1n&1	NUM
ejpam-2482	638	7	t=1nt	t=1nt	ADP
ejpam-2482	638	8	such	such	ADJ
ejpam-2482	638	9	that	that	SCONJ
ejpam-2482	638	10	for	for	ADP
ejpam-2482	638	11	some	some	DET
ejpam-2482	638	12	k	k	NOUN
ejpam-2482	638	13	"	"	PUNCT
ejpam-2482	638	14	{	{	PUNCT
ejpam-2482	638	15	1,2	1,2	NUM
ejpam-2482	638	16	,	,	PUNCT
ejpam-2482	638	17	.	.	PUNCT
ejpam-2482	638	18	.	.	PUNCT
ejpam-2482	639	1	.	.	PUNCT
ejpam-2482	640	1	,	,	PUNCT
ejpam-2482	640	2	n	n	CCONJ
ejpam-2482	640	3	&	&	CCONJ
ejpam-2482	640	4	1	1	NUM
ejpam-2482	640	5	}	}	PUNCT
ejpam-2482	640	6	,	,	PUNCT
ejpam-2482	640	7	nk	nk	PROPN
ejpam-2482	640	8	is	be	AUX
ejpam-2482	640	9	a	a	DET
ejpam-2482	640	10	classical	classical	ADJ
ejpam-2482	640	11	prime	prime	ADJ
ejpam-2482	640	12	submodule	submodule	NOUN
ejpam-2482	640	13	of	of	ADP
ejpam-2482	640	14	mk	mk	PROPN
ejpam-2482	640	15	,	,	PUNCT
ejpam-2482	640	16	and	and	CCONJ
ejpam-2482	640	17	nt	not	PART
ejpam-2482	640	18	=	=	PROPN
ejpam-2482	640	19	mt	mt	PROPN
ejpam-2482	640	20	for	for	ADP
ejpam-2482	640	21	every	every	DET
ejpam-2482	640	22	t	t	NOUN
ejpam-2482	640	23	"	"	PUNCT
ejpam-2482	640	24	{	{	PUNCT
ejpam-2482	640	25	1,2	1,2	NUM
ejpam-2482	640	26	,	,	PUNCT
ejpam-2482	640	27	.	.	PUNCT
ejpam-2482	640	28	.	.	PUNCT
ejpam-2482	641	1	.	.	PUNCT
ejpam-2482	642	1	,	,	PUNCT
ejpam-2482	642	2	n	n	CCONJ
ejpam-2482	642	3	&	&	CCONJ
ejpam-2482	642	4	1}\{k	1}\{k	NUM
ejpam-2482	642	5	}	}	PUNCT
ejpam-2482	642	6	.	.	PUNCT
ejpam-2482	643	1	consequently	consequently	ADV
ejpam-2482	643	2	we	we	PRON
ejpam-2482	643	3	reach	reach	VERB
ejpam-2482	643	4	the	the	DET
ejpam-2482	643	5	claim	claim	NOUN
ejpam-2482	643	6	.	.	PUNCT
ejpam-2482	644	1	references	reference	NOUN
ejpam-2482	644	2	[	[	X
ejpam-2482	644	3	1	1	NUM
ejpam-2482	644	4	]	]	X
ejpam-2482	644	5	r.	r.	PROPN
ejpam-2482	644	6	ameri	ameri	PROPN
ejpam-2482	644	7	.	.	PUNCT
ejpam-2482	645	1	on	on	ADP
ejpam-2482	645	2	the	the	DET
ejpam-2482	645	3	prime	prime	ADJ
ejpam-2482	645	4	submodules	submodule	NOUN
ejpam-2482	645	5	of	of	ADP
ejpam-2482	645	6	multiplication	multiplication	NOUN
ejpam-2482	645	7	modules	module	NOUN
ejpam-2482	645	8	,	,	PUNCT
ejpam-2482	645	9	international	international	ADJ
ejpam-2482	645	10	journal	journal	NOUN
ejpam-2482	645	11	of	of	ADP
ejpam-2482	645	12	mathematics	mathematics	PROPN
ejpam-2482	645	13	and	and	CCONJ
ejpam-2482	645	14	mathematical	mathematical	ADJ
ejpam-2482	645	15	sciences	science	NOUN
ejpam-2482	645	16	,	,	PUNCT
ejpam-2482	645	17	27	27	NUM
ejpam-2482	645	18	,	,	PUNCT
ejpam-2482	645	19	1715–1724	1715–1724	NUM
ejpam-2482	645	20	.	.	PUNCT
ejpam-2482	645	21	2003	2003	NUM
ejpam-2482	645	22	.	.	PUNCT
ejpam-2482	646	1	[	[	X
ejpam-2482	646	2	2	2	X
ejpam-2482	646	3	]	]	PUNCT
ejpam-2482	646	4	d.	d.	PROPN
ejpam-2482	646	5	f.	f.	PROPN
ejpam-2482	646	6	anderson	anderson	PROPN
ejpam-2482	646	7	and	and	CCONJ
ejpam-2482	646	8	a.	a.	PROPN
ejpam-2482	646	9	badawi	badawi	PROPN
ejpam-2482	646	10	.	.	PUNCT
ejpam-2482	647	1	on	on	ADP
ejpam-2482	647	2	n	n	CCONJ
ejpam-2482	647	3	-	-	PUNCT
ejpam-2482	647	4	absorbing	absorbing	ADJ
ejpam-2482	647	5	ideals	ideal	NOUN
ejpam-2482	647	6	of	of	ADP
ejpam-2482	647	7	commutative	commutative	ADJ
ejpam-2482	647	8	rings	ring	NOUN
ejpam-2482	647	9	,	,	PUNCT
ejpam-2482	647	10	comunications	comunication	NOUN
ejpam-2482	647	11	in	in	ADP
ejpam-2482	647	12	algebra	algebra	NOUN
ejpam-2482	647	13	,	,	PUNCT
ejpam-2482	647	14	39	39	NUM
ejpam-2482	647	15	,	,	PUNCT
ejpam-2482	647	16	1646–1672	1646–1672	NUM
ejpam-2482	647	17	.	.	NOUN
ejpam-2482	647	18	2011	2011	NUM
ejpam-2482	647	19	.	.	PUNCT
ejpam-2482	648	1	[	[	X
ejpam-2482	648	2	3	3	NUM
ejpam-2482	648	3	]	]	PUNCT
ejpam-2482	648	4	a.	a.	NOUN
ejpam-2482	648	5	azizi	azizi	PROPN
ejpam-2482	648	6	.	.	PUNCT
ejpam-2482	649	1	on	on	ADP
ejpam-2482	649	2	prime	prime	ADJ
ejpam-2482	649	3	and	and	CCONJ
ejpam-2482	649	4	weakly	weakly	ADJ
ejpam-2482	649	5	prime	prime	ADJ
ejpam-2482	649	6	submodules	submodule	NOUN
ejpam-2482	649	7	,	,	PUNCT
ejpam-2482	649	8	vietnam	vietnam	PROPN
ejpam-2482	649	9	journal	journal	NOUN
ejpam-2482	649	10	of	of	ADP
ejpam-2482	649	11	mathematics	mathematics	PROPN
ejpam-2482	649	12	,	,	PUNCT
ejpam-2482	649	13	36(3	36(3	NUM
ejpam-2482	649	14	)	)	PUNCT
ejpam-2482	649	15	,	,	PUNCT
ejpam-2482	649	16	315–325	315–325	NUM
ejpam-2482	649	17	.	.	NOUN
ejpam-2482	649	18	2008	2008	NUM
ejpam-2482	649	19	.	.	PUNCT
ejpam-2482	650	1	[	[	X
ejpam-2482	650	2	4	4	NUM
ejpam-2482	650	3	]	]	PUNCT
ejpam-2482	650	4	a.	a.	NOUN
ejpam-2482	650	5	azizi	azizi	PROPN
ejpam-2482	650	6	.	.	PUNCT
ejpam-2482	651	1	weakly	weakly	ADJ
ejpam-2482	651	2	prime	prime	ADJ
ejpam-2482	651	3	submodules	submodule	NOUN
ejpam-2482	651	4	and	and	CCONJ
ejpam-2482	651	5	prime	prime	ADJ
ejpam-2482	651	6	submodules	submodule	NOUN
ejpam-2482	651	7	,	,	PUNCT
ejpam-2482	651	8	glasgow	glasgow	PROPN
ejpam-2482	651	9	mathematical	mathematical	ADJ
ejpam-2482	651	10	journal	journal	NOUN
ejpam-2482	651	11	,	,	PUNCT
ejpam-2482	651	12	48	48	NUM
ejpam-2482	651	13	,	,	PUNCT
ejpam-2482	651	14	343–346	343–346	NUM
ejpam-2482	651	15	.	.	PUNCT
ejpam-2482	651	16	2006	2006	NUM
ejpam-2482	651	17	.	.	PUNCT
ejpam-2482	652	1	[	[	X
ejpam-2482	652	2	5	5	NUM
ejpam-2482	652	3	]	]	PUNCT
ejpam-2482	652	4	a.	a.	NOUN
ejpam-2482	652	5	badawi	badawi	PROPN
ejpam-2482	652	6	.	.	PUNCT
ejpam-2482	653	1	on	on	ADP
ejpam-2482	653	2	2	2	NUM
ejpam-2482	653	3	-	-	PUNCT
ejpam-2482	653	4	absorbing	absorbing	ADJ
ejpam-2482	653	5	ideals	ideal	NOUN
ejpam-2482	653	6	of	of	ADP
ejpam-2482	653	7	commutative	commutative	ADJ
ejpam-2482	653	8	rings	ring	NOUN
ejpam-2482	653	9	,	,	PUNCT
ejpam-2482	653	10	bulletin	bulletin	NOUN
ejpam-2482	653	11	of	of	ADP
ejpam-2482	653	12	the	the	DET
ejpam-2482	653	13	australian	australian	ADJ
ejpam-2482	653	14	mathematical	mathematical	ADJ
ejpam-2482	653	15	society	society	NOUN
ejpam-2482	653	16	,	,	PUNCT
ejpam-2482	653	17	75	75	NUM
ejpam-2482	653	18	,	,	PUNCT
ejpam-2482	653	19	417–429	417–429	NUM
ejpam-2482	653	20	.	.	PUNCT
ejpam-2482	653	21	2007	2007	NUM
ejpam-2482	653	22	.	.	PUNCT
ejpam-2482	654	1	[	[	X
ejpam-2482	654	2	6	6	NUM
ejpam-2482	654	3	]	]	PUNCT
ejpam-2482	654	4	a.	a.	NOUN
ejpam-2482	654	5	badawi	badawi	PROPN
ejpam-2482	654	6	,	,	PUNCT
ejpam-2482	654	7	ü.	ü.	NOUN
ejpam-2482	654	8	tekir	tekir	NOUN
ejpam-2482	654	9	,	,	PUNCT
ejpam-2482	654	10	and	and	CCONJ
ejpam-2482	654	11	e.	e.	PROPN
ejpam-2482	654	12	yetkin	yetkin	PROPN
ejpam-2482	654	13	.	.	PUNCT
ejpam-2482	655	1	on	on	ADP
ejpam-2482	655	2	2	2	NUM
ejpam-2482	655	3	-	-	PUNCT
ejpam-2482	655	4	absorbing	absorbing	ADJ
ejpam-2482	655	5	primary	primary	ADJ
ejpam-2482	655	6	ideals	ideal	NOUN
ejpam-2482	655	7	in	in	ADP
ejpam-2482	655	8	commutative	commutative	ADJ
ejpam-2482	655	9	rings	ring	NOUN
ejpam-2482	655	10	,	,	PUNCT
ejpam-2482	655	11	bulletin	bulletin	NOUN
ejpam-2482	655	12	of	of	ADP
ejpam-2482	655	13	the	the	DET
ejpam-2482	655	14	korean	korean	ADJ
ejpam-2482	655	15	mathematical	mathematical	ADJ
ejpam-2482	655	16	society	society	NOUN
ejpam-2482	655	17	,	,	PUNCT
ejpam-2482	655	18	51(4	51(4	NUM
ejpam-2482	655	19	)	)	PUNCT
ejpam-2482	655	20	,	,	PUNCT
ejpam-2482	655	21	1163–1173	1163–1173	NUM
ejpam-2482	655	22	.	.	PUNCT
ejpam-2482	655	23	2014	2014	NUM
ejpam-2482	655	24	.	.	PUNCT
ejpam-2482	656	1	[	[	X
ejpam-2482	656	2	7	7	NUM
ejpam-2482	656	3	]	]	PUNCT
ejpam-2482	656	4	a.	a.	NOUN
ejpam-2482	656	5	badawi	badawi	PROPN
ejpam-2482	656	6	,	,	PUNCT
ejpam-2482	656	7	e.	e.	PROPN
ejpam-2482	656	8	yetkin	yetkin	PROPN
ejpam-2482	656	9	,	,	PUNCT
ejpam-2482	656	10	and	and	CCONJ
ejpam-2482	656	11	ü.	ü.	NOUN
ejpam-2482	656	12	tekir	tekir	NOUN
ejpam-2482	656	13	.	.	PUNCT
ejpam-2482	657	1	on	on	ADP
ejpam-2482	657	2	weakly	weakly	ADJ
ejpam-2482	657	3	2	2	NUM
ejpam-2482	657	4	-	-	PUNCT
ejpam-2482	657	5	absorbing	absorbing	ADJ
ejpam-2482	657	6	primary	primary	ADJ
ejpam-2482	657	7	ideals	ideal	NOUN
ejpam-2482	657	8	of	of	ADP
ejpam-2482	657	9	commutative	commutative	ADJ
ejpam-2482	657	10	rings	ring	NOUN
ejpam-2482	657	11	,	,	PUNCT
ejpam-2482	657	12	journal	journal	NOUN
ejpam-2482	657	13	of	of	ADP
ejpam-2482	657	14	the	the	DET
ejpam-2482	657	15	korean	korean	PROPN
ejpam-2482	657	16	mathematical	mathematical	ADJ
ejpam-2482	657	17	society	society	NOUN
ejpam-2482	657	18	,	,	PUNCT
ejpam-2482	657	19	52(1	52(1	NOUN
ejpam-2482	657	20	)	)	PUNCT
ejpam-2482	657	21	,	,	PUNCT
ejpam-2482	657	22	97–111	97–111	NUM
ejpam-2482	657	23	.	.	NOUN
ejpam-2482	657	24	2015	2015	NUM
ejpam-2482	657	25	.	.	PUNCT
ejpam-2482	658	1	[	[	X
ejpam-2482	658	2	8	8	NUM
ejpam-2482	658	3	]	]	PUNCT
ejpam-2482	658	4	a.	a.	NOUN
ejpam-2482	658	5	badawi	badawi	PROPN
ejpam-2482	658	6	and	and	CCONJ
ejpam-2482	658	7	a.	a.	NOUN
ejpam-2482	658	8	yousefian	yousefian	PROPN
ejpam-2482	658	9	darani	darani	PROPN
ejpam-2482	658	10	.	.	PUNCT
ejpam-2482	659	1	on	on	ADP
ejpam-2482	659	2	weakly	weakly	ADJ
ejpam-2482	659	3	2	2	NUM
ejpam-2482	659	4	-	-	PUNCT
ejpam-2482	659	5	absorbing	absorbing	ADJ
ejpam-2482	659	6	ideals	ideal	NOUN
ejpam-2482	659	7	of	of	ADP
ejpam-2482	659	8	commutative	commutative	ADJ
ejpam-2482	659	9	rings	ring	NOUN
ejpam-2482	659	10	,	,	PUNCT
ejpam-2482	659	11	houston	houston	PROPN
ejpam-2482	659	12	journal	journal	PROPN
ejpam-2482	659	13	of	of	ADP
ejpam-2482	659	14	mathematics	mathematic	NOUN
ejpam-2482	659	15	,	,	PUNCT
ejpam-2482	659	16	39	39	NUM
ejpam-2482	659	17	,	,	PUNCT
ejpam-2482	659	18	441–452	441–452	NUM
ejpam-2482	659	19	.	.	NOUN
ejpam-2482	659	20	2013	2013	NUM
ejpam-2482	659	21	.	.	PUNCT
ejpam-2482	660	1	references	reference	NOUN
ejpam-2482	660	2	430	430	NUM
ejpam-2482	660	3	[	[	SYM
ejpam-2482	660	4	9	9	NUM
ejpam-2482	660	5	]	]	PUNCT
ejpam-2482	660	6	m.	m.	NOUN
ejpam-2482	660	7	behboodi	behboodi	NOUN
ejpam-2482	660	8	.	.	PUNCT
ejpam-2482	661	1	a	a	DET
ejpam-2482	661	2	generalization	generalization	NOUN
ejpam-2482	661	3	of	of	ADP
ejpam-2482	661	4	bear	bear	PROPN
ejpam-2482	661	5	’s	’s	PART
ejpam-2482	661	6	lower	low	ADJ
ejpam-2482	661	7	nilradical	nilradical	ADJ
ejpam-2482	661	8	for	for	ADP
ejpam-2482	661	9	modules	module	NOUN
ejpam-2482	661	10	,	,	PUNCT
ejpam-2482	661	11	journal	journal	NOUN
ejpam-2482	661	12	of	of	ADP
ejpam-2482	661	13	algebra	algebra	NOUN
ejpam-2482	661	14	and	and	CCONJ
ejpam-2482	661	15	its	its	PRON
ejpam-2482	661	16	applications	application	NOUN
ejpam-2482	661	17	,	,	PUNCT
ejpam-2482	661	18	6(2	6(2	NUM
ejpam-2482	661	19	)	)	PUNCT
ejpam-2482	661	20	,	,	PUNCT
ejpam-2482	661	21	337	337	NUM
ejpam-2482	661	22	-	-	SYM
ejpam-2482	661	23	353	353	NUM
ejpam-2482	661	24	.	.	PUNCT
ejpam-2482	661	25	2007	2007	NUM
ejpam-2482	661	26	.	.	PUNCT
ejpam-2482	662	1	[	[	X
ejpam-2482	662	2	10	10	NUM
ejpam-2482	662	3	]	]	PUNCT
ejpam-2482	662	4	m.	m.	NOUN
ejpam-2482	662	5	behboodi	behboodi	NOUN
ejpam-2482	662	6	.	.	PUNCT
ejpam-2482	663	1	on	on	ADP
ejpam-2482	663	2	weakly	weakly	ADJ
ejpam-2482	663	3	prime	prime	ADJ
ejpam-2482	663	4	radical	radical	NOUN
ejpam-2482	663	5	of	of	ADP
ejpam-2482	663	6	modules	module	NOUN
ejpam-2482	663	7	and	and	CCONJ
ejpam-2482	663	8	semi	semi	ADJ
ejpam-2482	663	9	-	-	ADJ
ejpam-2482	663	10	compatible	compatible	ADJ
ejpam-2482	663	11	modules	module	NOUN
ejpam-2482	663	12	,	,	PUNCT
ejpam-2482	663	13	acta	acta	PROPN
ejpam-2482	663	14	mathematical	mathematical	PROPN
ejpam-2482	663	15	hungarica	hungarica	PROPN
ejpam-2482	663	16	,	,	PUNCT
ejpam-2482	663	17	113(3	113(3	NUM
ejpam-2482	663	18	)	)	PUNCT
ejpam-2482	663	19	,	,	PUNCT
ejpam-2482	663	20	239	239	NUM
ejpam-2482	663	21	-	-	SYM
ejpam-2482	663	22	250	250	NUM
ejpam-2482	663	23	.	.	PUNCT
ejpam-2482	664	1	2006	2006	NUM
ejpam-2482	664	2	.	.	PUNCT
ejpam-2482	665	1	[	[	X
ejpam-2482	665	2	11	11	NUM
ejpam-2482	665	3	]	]	PUNCT
ejpam-2482	665	4	m.	m.	NOUN
ejpam-2482	665	5	behboodi	behboodi	NOUN
ejpam-2482	665	6	and	and	CCONJ
ejpam-2482	665	7	h.	h.	PROPN
ejpam-2482	665	8	koohy	koohy	PROPN
ejpam-2482	665	9	.	.	PUNCT
ejpam-2482	666	1	weakly	weakly	ADJ
ejpam-2482	666	2	prime	prime	ADJ
ejpam-2482	666	3	modules	module	NOUN
ejpam-2482	666	4	,	,	PUNCT
ejpam-2482	666	5	vietnam	vietnam	PROPN
ejpam-2482	666	6	journal	journal	NOUN
ejpam-2482	666	7	of	of	ADP
ejpam-2482	666	8	mathematics	mathematic	NOUN
ejpam-2482	666	9	,	,	PUNCT
ejpam-2482	666	10	32(2	32(2	NUM
ejpam-2482	666	11	)	)	PUNCT
ejpam-2482	666	12	,	,	PUNCT
ejpam-2482	666	13	185	185	NUM
ejpam-2482	666	14	-	-	SYM
ejpam-2482	666	15	195	195	NUM
ejpam-2482	666	16	.	.	NOUN
ejpam-2482	666	17	2004	2004	NUM
ejpam-2482	666	18	.	.	PUNCT
ejpam-2482	667	1	[	[	X
ejpam-2482	667	2	12	12	NUM
ejpam-2482	667	3	]	]	PUNCT
ejpam-2482	667	4	m.	m.	NOUN
ejpam-2482	667	5	behboodi	behboodi	NOUN
ejpam-2482	667	6	and	and	CCONJ
ejpam-2482	667	7	s.	s.	PROPN
ejpam-2482	667	8	h.	h.	PROPN
ejpam-2482	667	9	shojaee	shojaee	PROPN
ejpam-2482	667	10	.	.	PUNCT
ejpam-2482	668	1	on	on	ADP
ejpam-2482	668	2	chains	chain	NOUN
ejpam-2482	668	3	of	of	ADP
ejpam-2482	668	4	classical	classical	ADJ
ejpam-2482	668	5	prime	prime	ADJ
ejpam-2482	668	6	submodules	submodule	NOUN
ejpam-2482	668	7	and	and	CCONJ
ejpam-2482	668	8	dimension	dimension	NOUN
ejpam-2482	668	9	theory	theory	NOUN
ejpam-2482	668	10	of	of	ADP
ejpam-2482	668	11	modules	module	NOUN
ejpam-2482	668	12	,	,	PUNCT
ejpam-2482	668	13	bulletin	bulletin	NOUN
ejpam-2482	668	14	of	of	ADP
ejpam-2482	668	15	the	the	DET
ejpam-2482	668	16	iranian	iranian	PROPN
ejpam-2482	668	17	mathematical	mathematical	ADJ
ejpam-2482	668	18	society	society	NOUN
ejpam-2482	668	19	,	,	PUNCT
ejpam-2482	668	20	36(1	36(1	NUM
ejpam-2482	668	21	)	)	PUNCT
ejpam-2482	668	22	,	,	PUNCT
ejpam-2482	668	23	149–166	149–166	NUM
ejpam-2482	668	24	.	.	PUNCT
ejpam-2482	668	25	2010	2010	NUM
ejpam-2482	668	26	.	.	PUNCT
ejpam-2482	669	1	[	[	X
ejpam-2482	669	2	13	13	NUM
ejpam-2482	669	3	]	]	PUNCT
ejpam-2482	669	4	a.	a.	NOUN
ejpam-2482	669	5	y.	y.	PROPN
ejpam-2482	669	6	darani	darani	PROPN
ejpam-2482	669	7	and	and	CCONJ
ejpam-2482	669	8	f.	f.	PROPN
ejpam-2482	669	9	soheilnia	soheilnia	PROPN
ejpam-2482	669	10	.	.	PUNCT
ejpam-2482	670	1	2	2	NUM
ejpam-2482	670	2	-	-	PUNCT
ejpam-2482	670	3	absorbing	absorbing	ADJ
ejpam-2482	670	4	and	and	CCONJ
ejpam-2482	670	5	weakly	weakly	ADJ
ejpam-2482	670	6	2	2	NUM
ejpam-2482	670	7	-	-	PUNCT
ejpam-2482	670	8	absorbing	absorbing	ADJ
ejpam-2482	670	9	submodules	submodule	NOUN
ejpam-2482	670	10	,	,	PUNCT
ejpam-2482	670	11	thai	thai	PROPN
ejpam-2482	670	12	journal	journal	PROPN
ejpam-2482	670	13	of	of	ADP
ejpam-2482	670	14	mathematics	mathematic	NOUN
ejpam-2482	670	15	,	,	PUNCT
ejpam-2482	670	16	9(3	9(3	NUM
ejpam-2482	670	17	)	)	PUNCT
ejpam-2482	670	18	,	,	PUNCT
ejpam-2482	670	19	577–584	577–584	NUM
ejpam-2482	670	20	.	.	NOUN
ejpam-2482	670	21	2011	2011	NUM
ejpam-2482	670	22	.	.	PUNCT
ejpam-2482	671	1	[	[	X
ejpam-2482	671	2	14	14	NUM
ejpam-2482	671	3	]	]	PUNCT
ejpam-2482	671	4	a.	a.	NOUN
ejpam-2482	671	5	y.	y.	PROPN
ejpam-2482	671	6	darani	darani	PROPN
ejpam-2482	671	7	and	and	CCONJ
ejpam-2482	671	8	f.	f.	PROPN
ejpam-2482	671	9	soheilnia	soheilnia	PROPN
ejpam-2482	671	10	.	.	PUNCT
ejpam-2482	672	1	on	on	ADP
ejpam-2482	672	2	n	n	CCONJ
ejpam-2482	672	3	-	-	PUNCT
ejpam-2482	672	4	absorbing	absorb	VERB
ejpam-2482	672	5	submodules	submodule	NOUN
ejpam-2482	672	6	,	,	PUNCT
ejpam-2482	672	7	mathematical	mathematical	ADJ
ejpam-2482	672	8	communications	communication	NOUN
ejpam-2482	672	9	,	,	PUNCT
ejpam-2482	672	10	17	17	NUM
ejpam-2482	672	11	,	,	PUNCT
ejpam-2482	672	12	547	547	NUM
ejpam-2482	672	13	-	-	SYM
ejpam-2482	672	14	557	557	NUM
ejpam-2482	672	15	.	.	NOUN
ejpam-2482	672	16	2012	2012	NUM
ejpam-2482	672	17	.	.	PUNCT
ejpam-2482	673	1	[	[	X
ejpam-2482	673	2	15	15	NUM
ejpam-2482	673	3	]	]	X
ejpam-2482	673	4	sh	sh	PROPN
ejpam-2482	673	5	.	.	PROPN
ejpam-2482	673	6	payrovi	payrovi	PROPN
ejpam-2482	673	7	and	and	CCONJ
ejpam-2482	673	8	s.	s.	PROPN
ejpam-2482	673	9	babaei	babaei	PROPN
ejpam-2482	673	10	.	.	PUNCT
ejpam-2482	674	1	on	on	ADP
ejpam-2482	674	2	2	2	NUM
ejpam-2482	674	3	-	-	PUNCT
ejpam-2482	674	4	absorbing	absorbing	ADJ
ejpam-2482	674	5	submodules	submodule	NOUN
ejpam-2482	674	6	,	,	PUNCT
ejpam-2482	674	7	algebra	algebra	NOUN
ejpam-2482	674	8	colloquium	colloquium	NOUN
ejpam-2482	674	9	,	,	PUNCT
ejpam-2482	674	10	19	19	NUM
ejpam-2482	674	11	,	,	PUNCT
ejpam-2482	674	12	913–920	913–920	NUM
ejpam-2482	674	13	.	.	PUNCT
ejpam-2482	674	14	2012	2012	NUM
ejpam-2482	674	15	.	.	PUNCT
ejpam-2482	675	1	[	[	X
ejpam-2482	675	2	16	16	NUM
ejpam-2482	675	3	]	]	X
ejpam-2482	675	4	p.	p.	NOUN
ejpam-2482	675	5	quartararo	quartararo	NOUN
ejpam-2482	675	6	and	and	CCONJ
ejpam-2482	675	7	h.	h.	PROPN
ejpam-2482	675	8	s.	s.	PROPN
ejpam-2482	675	9	butts	butts	PROPN
ejpam-2482	675	10	.	.	PUNCT
ejpam-2482	676	1	finite	finite	PROPN
ejpam-2482	676	2	unions	union	NOUN
ejpam-2482	676	3	of	of	ADP
ejpam-2482	676	4	ideals	ideal	NOUN
ejpam-2482	676	5	and	and	CCONJ
ejpam-2482	676	6	modules	module	NOUN
ejpam-2482	676	7	,	,	PUNCT
ejpam-2482	676	8	proceedings	proceeding	NOUN
ejpam-2482	676	9	of	of	ADP
ejpam-2482	676	10	the	the	DET
ejpam-2482	676	11	american	american	PROPN
ejpam-2482	676	12	mathematical	mathematical	PROPN
ejpam-2482	676	13	society	society	NOUN
ejpam-2482	676	14	,	,	PUNCT
ejpam-2482	676	15	52	52	NUM
ejpam-2482	676	16	,	,	PUNCT
ejpam-2482	676	17	91	91	NUM
ejpam-2482	676	18	-	-	SYM
ejpam-2482	676	19	96	96	NUM
ejpam-2482	676	20	.	.	PUNCT
ejpam-2482	676	21	1975	1975	NUM
ejpam-2482	676	22	.	.	PUNCT
ejpam-2482	677	1	[	[	X
ejpam-2482	677	2	17	17	NUM
ejpam-2482	677	3	]	]	X
ejpam-2482	677	4	r.y	r.y	PROPN
ejpam-2482	677	5	.	.	PROPN
ejpam-2482	677	6	sharp	sharp	PROPN
ejpam-2482	677	7	.	.	PUNCT
ejpam-2482	678	1	steps	step	NOUN
ejpam-2482	678	2	in	in	ADP
ejpam-2482	678	3	commutative	commutative	ADJ
ejpam-2482	678	4	algebra	algebra	NOUN
ejpam-2482	678	5	,	,	PUNCT
ejpam-2482	678	6	second	second	ADJ
ejpam-2482	678	7	edition	edition	NOUN
ejpam-2482	678	8	,	,	PUNCT
ejpam-2482	678	9	cambridge	cambridge	PROPN
ejpam-2482	678	10	university	university	PROPN
ejpam-2482	678	11	press	press	PROPN
ejpam-2482	678	12	,	,	PUNCT
ejpam-2482	678	13	cambridge	cambridge	PROPN
ejpam-2482	678	14	,	,	PUNCT
ejpam-2482	678	15	2000	2000	NUM
ejpam-2482	678	16	.	.	PUNCT