id	sid	tid	token	lemma	pos
ejpam-2662	1	1	european	european	PROPN
ejpam-2662	1	2	journal	journal	PROPN
ejpam-2662	1	3	of	of	ADP
ejpam-2662	1	4	pure	pure	ADJ
ejpam-2662	1	5	and	and	CCONJ
ejpam-2662	1	6	applied	apply	VERB
ejpam-2662	1	7	mathematics	mathematic	NOUN
ejpam-2662	1	8	vol	vol	NOUN
ejpam-2662	1	9	.	.	PROPN
ejpam-2662	2	1	10	10	NUM
ejpam-2662	2	2	,	,	PUNCT
ejpam-2662	2	3	no	no	INTJ
ejpam-2662	2	4	.	.	NOUN
ejpam-2662	2	5	3	3	NUM
ejpam-2662	2	6	,	,	PUNCT
ejpam-2662	2	7	2017	2017	NUM
ejpam-2662	2	8	,	,	PUNCT
ejpam-2662	2	9	521	521	NUM
ejpam-2662	2	10	-	-	SYM
ejpam-2662	2	11	528	528	NUM
ejpam-2662	2	12	issn	issn	PROPN
ejpam-2662	2	13	1307	1307	NUM
ejpam-2662	2	14	-	-	SYM
ejpam-2662	2	15	5543	5543	NUM
ejpam-2662	2	16	–	–	PUNCT
ejpam-2662	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2662	2	18	published	publish	VERB
ejpam-2662	2	19	by	by	ADP
ejpam-2662	2	20	new	new	PROPN
ejpam-2662	2	21	york	york	PROPN
ejpam-2662	2	22	business	business	PROPN
ejpam-2662	2	23	global	global	ADJ
ejpam-2662	2	24	weakly	weakly	ADJ
ejpam-2662	2	25	g	g	NOUN
ejpam-2662	2	26	-	-	PUNCT
ejpam-2662	2	27	supplemented	supplement	VERB
ejpam-2662	2	28	modules	module	NOUN
ejpam-2662	2	29	celil	celil	NOUN
ejpam-2662	2	30	nebiyev1,∗	nebiyev1,∗	NOUN
ejpam-2662	2	31	,	,	PUNCT
ejpam-2662	2	32	hasan	hasan	PROPN
ejpam-2662	2	33	hüseyin	hüseyin	PROPN
ejpam-2662	2	34	ökten2	ökten2	VERB
ejpam-2662	2	35	1	1	NUM
ejpam-2662	2	36	department	department	NOUN
ejpam-2662	2	37	of	of	ADP
ejpam-2662	2	38	mathematics	mathematic	NOUN
ejpam-2662	2	39	,	,	PUNCT
ejpam-2662	2	40	ondokuz	ondokuz	PROPN
ejpam-2662	2	41	mayıs	mayıs	PROPN
ejpam-2662	2	42	university	university	PROPN
ejpam-2662	2	43	,	,	PUNCT
ejpam-2662	2	44	turkey	turkey	NOUN
ejpam-2662	2	45	2	2	NUM
ejpam-2662	2	46	technical	technical	ADJ
ejpam-2662	2	47	sciences	sciences	PROPN
ejpam-2662	2	48	vocational	vocational	ADJ
ejpam-2662	2	49	school	school	NOUN
ejpam-2662	2	50	,	,	PUNCT
ejpam-2662	2	51	amasya	amasya	NOUN
ejpam-2662	2	52	university	university	NOUN
ejpam-2662	2	53	,	,	PUNCT
ejpam-2662	2	54	turkey	turkey	PROPN
ejpam-2662	2	55	abstract	abstract	NOUN
ejpam-2662	2	56	.	.	PUNCT
ejpam-2662	3	1	in	in	ADP
ejpam-2662	3	2	this	this	DET
ejpam-2662	3	3	work	work	NOUN
ejpam-2662	3	4	,	,	PUNCT
ejpam-2662	3	5	we	we	PRON
ejpam-2662	3	6	define	define	VERB
ejpam-2662	3	7	weakly	weakly	ADJ
ejpam-2662	3	8	g	g	NOUN
ejpam-2662	3	9	-	-	PUNCT
ejpam-2662	3	10	supplemented	supplement	VERB
ejpam-2662	3	11	modules	module	NOUN
ejpam-2662	3	12	and	and	CCONJ
ejpam-2662	3	13	cofinitely	cofinitely	ADV
ejpam-2662	3	14	weak	weak	ADJ
ejpam-2662	3	15	g	g	NOUN
ejpam-2662	3	16	-	-	PUNCT
ejpam-2662	3	17	supplemented	supplement	VERB
ejpam-2662	3	18	modules	module	NOUN
ejpam-2662	3	19	.	.	PUNCT
ejpam-2662	4	1	we	we	PRON
ejpam-2662	4	2	investigate	investigate	VERB
ejpam-2662	4	3	some	some	DET
ejpam-2662	4	4	properties	property	NOUN
ejpam-2662	4	5	of	of	ADP
ejpam-2662	4	6	these	these	DET
ejpam-2662	4	7	modules	module	NOUN
ejpam-2662	4	8	.	.	PUNCT
ejpam-2662	5	1	we	we	PRON
ejpam-2662	5	2	show	show	VERB
ejpam-2662	5	3	that	that	SCONJ
ejpam-2662	5	4	the	the	DET
ejpam-2662	5	5	finite	finite	ADJ
ejpam-2662	5	6	sum	sum	NOUN
ejpam-2662	5	7	of	of	ADP
ejpam-2662	5	8	weakly	weakly	ADJ
ejpam-2662	5	9	g	g	NOUN
ejpam-2662	5	10	-	-	PUNCT
ejpam-2662	5	11	supplemented	supplement	VERB
ejpam-2662	5	12	modules	module	NOUN
ejpam-2662	5	13	is	be	AUX
ejpam-2662	5	14	weakly	weakly	ADJ
ejpam-2662	5	15	g	g	NOUN
ejpam-2662	5	16	-	-	PUNCT
ejpam-2662	5	17	supplemented	supplement	VERB
ejpam-2662	5	18	,	,	PUNCT
ejpam-2662	5	19	an	an	DET
ejpam-2662	5	20	arbitrary	arbitrary	ADJ
ejpam-2662	5	21	sum	sum	NOUN
ejpam-2662	5	22	of	of	ADP
ejpam-2662	5	23	cofinitely	cofinitely	ADV
ejpam-2662	5	24	weak	weak	ADJ
ejpam-2662	5	25	gsupplemented	gsupplemente	VERB
ejpam-2662	5	26	modules	module	NOUN
ejpam-2662	5	27	is	be	AUX
ejpam-2662	5	28	cofinitely	cofinitely	ADV
ejpam-2662	5	29	weak	weak	ADJ
ejpam-2662	5	30	g	g	NOUN
ejpam-2662	5	31	-	-	PUNCT
ejpam-2662	5	32	supplemented	supplement	VERB
ejpam-2662	5	33	.	.	PUNCT
ejpam-2662	6	1	we	we	PRON
ejpam-2662	6	2	also	also	ADV
ejpam-2662	6	3	define	define	VERB
ejpam-2662	6	4	g	g	NOUN
ejpam-2662	6	5	-	-	PUNCT
ejpam-2662	6	6	semilocal	semilocal	ADJ
ejpam-2662	6	7	modules	module	NOUN
ejpam-2662	6	8	and	and	CCONJ
ejpam-2662	6	9	give	give	VERB
ejpam-2662	6	10	some	some	DET
ejpam-2662	6	11	equivalencies	equivalencie	NOUN
ejpam-2662	6	12	for	for	ADP
ejpam-2662	6	13	weakly	weakly	ADJ
ejpam-2662	6	14	g	g	NOUN
ejpam-2662	6	15	-	-	PUNCT
ejpam-2662	6	16	supplemented	supplement	VERB
ejpam-2662	6	17	,	,	PUNCT
ejpam-2662	6	18	cofinitely	cofinitely	ADV
ejpam-2662	6	19	weak	weak	ADJ
ejpam-2662	6	20	g	g	NOUN
ejpam-2662	6	21	-	-	PUNCT
ejpam-2662	6	22	supplemented	supplement	VERB
ejpam-2662	6	23	and	and	CCONJ
ejpam-2662	6	24	g	g	NOUN
ejpam-2662	6	25	-	-	PUNCT
ejpam-2662	6	26	semilocal	semilocal	ADJ
ejpam-2662	6	27	modules	module	NOUN
ejpam-2662	6	28	.	.	PUNCT
ejpam-2662	7	1	2010	2010	NUM
ejpam-2662	7	2	mathematics	mathematic	NOUN
ejpam-2662	7	3	subject	subject	NOUN
ejpam-2662	7	4	classifications	classification	NOUN
ejpam-2662	7	5	:	:	PUNCT
ejpam-2662	7	6	16d60	16d60	NUM
ejpam-2662	7	7	,	,	PUNCT
ejpam-2662	7	8	16d80	16d80	NUM
ejpam-2662	7	9	key	key	ADJ
ejpam-2662	7	10	words	word	NOUN
ejpam-2662	7	11	and	and	CCONJ
ejpam-2662	7	12	phrases	phrase	NOUN
ejpam-2662	7	13	:	:	PUNCT
ejpam-2662	7	14	g	g	NOUN
ejpam-2662	7	15	-	-	PUNCT
ejpam-2662	7	16	small	small	ADJ
ejpam-2662	7	17	submodules	submodule	NOUN
ejpam-2662	7	18	,	,	PUNCT
ejpam-2662	7	19	generalized	generalized	ADJ
ejpam-2662	7	20	radical	radical	ADJ
ejpam-2662	7	21	,	,	PUNCT
ejpam-2662	7	22	g	g	NOUN
ejpam-2662	7	23	-	-	PUNCT
ejpam-2662	7	24	supplemented	supplement	VERB
ejpam-2662	7	25	modules	module	NOUN
ejpam-2662	7	26	,	,	PUNCT
ejpam-2662	7	27	weakly	weakly	ADV
ejpam-2662	7	28	supplemented	supplement	VERB
ejpam-2662	7	29	modules	module	NOUN
ejpam-2662	7	30	1	1	NUM
ejpam-2662	7	31	.	.	PUNCT
ejpam-2662	8	1	introduction	introduction	NOUN
ejpam-2662	8	2	throughout	throughout	ADP
ejpam-2662	8	3	this	this	DET
ejpam-2662	8	4	paper	paper	NOUN
ejpam-2662	8	5	all	all	DET
ejpam-2662	8	6	rings	ring	NOUN
ejpam-2662	8	7	have	have	VERB
ejpam-2662	8	8	an	an	DET
ejpam-2662	8	9	identity	identity	NOUN
ejpam-2662	8	10	and	and	CCONJ
ejpam-2662	8	11	all	all	DET
ejpam-2662	8	12	modules	module	NOUN
ejpam-2662	8	13	are	be	AUX
ejpam-2662	8	14	unital	unital	ADJ
ejpam-2662	8	15	left	leave	VERB
ejpam-2662	8	16	modules	module	NOUN
ejpam-2662	8	17	.	.	PUNCT
ejpam-2662	9	1	let	let	VERB
ejpam-2662	9	2	r	r	PRON
ejpam-2662	9	3	be	be	AUX
ejpam-2662	9	4	a	a	DET
ejpam-2662	9	5	ring	ring	NOUN
ejpam-2662	9	6	and	and	CCONJ
ejpam-2662	9	7	m	m	AUX
ejpam-2662	9	8	be	be	AUX
ejpam-2662	9	9	an	an	DET
ejpam-2662	9	10	r	r	NOUN
ejpam-2662	9	11	-	-	PUNCT
ejpam-2662	9	12	module	module	NOUN
ejpam-2662	9	13	.	.	PUNCT
ejpam-2662	10	1	we	we	PRON
ejpam-2662	10	2	denote	denote	VERB
ejpam-2662	10	3	a	a	DET
ejpam-2662	10	4	submodule	submodule	NOUN
ejpam-2662	10	5	n	n	PROPN
ejpam-2662	10	6	of	of	ADP
ejpam-2662	10	7	m	m	PRON
ejpam-2662	10	8	by	by	ADP
ejpam-2662	10	9	n	n	X
ejpam-2662	10	10	≤m	≤m	NOUN
ejpam-2662	10	11	.	.	PUNCT
ejpam-2662	11	1	if	if	SCONJ
ejpam-2662	11	2	m	m	NOUN
ejpam-2662	11	3	/	/	SYM
ejpam-2662	11	4	n	n	PROPN
ejpam-2662	11	5	is	be	AUX
ejpam-2662	11	6	finitely	finitely	ADV
ejpam-2662	11	7	generated	generate	VERB
ejpam-2662	11	8	for	for	ADP
ejpam-2662	11	9	n	n	X
ejpam-2662	11	10	≤m	≤m	NOUN
ejpam-2662	11	11	,	,	PUNCT
ejpam-2662	11	12	then	then	ADV
ejpam-2662	11	13	n	n	CCONJ
ejpam-2662	11	14	is	be	AUX
ejpam-2662	11	15	called	call	VERB
ejpam-2662	11	16	a	a	DET
ejpam-2662	11	17	cofinite	cofinite	NOUN
ejpam-2662	11	18	submodule	submodule	NOUN
ejpam-2662	11	19	of	of	ADP
ejpam-2662	11	20	m	m	PROPN
ejpam-2662	11	21	.	.	PUNCT
ejpam-2662	12	1	let	let	VERB
ejpam-2662	12	2	m	m	PRON
ejpam-2662	12	3	be	be	AUX
ejpam-2662	12	4	an	an	DET
ejpam-2662	12	5	r	r	NOUN
ejpam-2662	12	6	-	-	PUNCT
ejpam-2662	12	7	module	module	NOUN
ejpam-2662	12	8	and	and	CCONJ
ejpam-2662	12	9	t	t	NOUN
ejpam-2662	12	10	≤	≤	NUM
ejpam-2662	12	11	m	m	VERB
ejpam-2662	12	12	.	.	PUNCT
ejpam-2662	13	1	if	if	SCONJ
ejpam-2662	13	2	k	k	PROPN
ejpam-2662	13	3	=	=	PUNCT
ejpam-2662	13	4	0	0	NUM
ejpam-2662	13	5	for	for	ADP
ejpam-2662	13	6	every	every	DET
ejpam-2662	13	7	k	k	PROPN
ejpam-2662	13	8	≤	≤	PROPN
ejpam-2662	13	9	m	m	VERB
ejpam-2662	13	10	with	with	ADP
ejpam-2662	13	11	t	t	NOUN
ejpam-2662	13	12	∩k	∩k	NOUN
ejpam-2662	13	13	=	=	SYM
ejpam-2662	14	1	0	0	NUM
ejpam-2662	14	2	,	,	PUNCT
ejpam-2662	14	3	then	then	ADV
ejpam-2662	14	4	t	t	PROPN
ejpam-2662	14	5	is	be	AUX
ejpam-2662	14	6	called	call	VERB
ejpam-2662	14	7	an	an	DET
ejpam-2662	14	8	essential	essential	ADJ
ejpam-2662	14	9	submodule	submodule	NOUN
ejpam-2662	14	10	of	of	ADP
ejpam-2662	14	11	m	m	PROPN
ejpam-2662	14	12	and	and	CCONJ
ejpam-2662	14	13	it	it	PRON
ejpam-2662	14	14	is	be	AUX
ejpam-2662	14	15	denoted	denote	VERB
ejpam-2662	14	16	by	by	ADP
ejpam-2662	14	17	t	t	PROPN
ejpam-2662	14	18	e	e	X
ejpam-2662	14	19	m	m	NOUN
ejpam-2662	14	20	.	.	PUNCT
ejpam-2662	15	1	k	k	PROPN
ejpam-2662	15	2	is	be	AUX
ejpam-2662	15	3	called	call	VERB
ejpam-2662	15	4	a	a	DET
ejpam-2662	15	5	generalized	generalized	ADJ
ejpam-2662	15	6	small	small	ADJ
ejpam-2662	15	7	(	(	PUNCT
ejpam-2662	15	8	briefly	briefly	ADV
ejpam-2662	15	9	,	,	PUNCT
ejpam-2662	15	10	g	g	NOUN
ejpam-2662	15	11	-	-	PUNCT
ejpam-2662	15	12	small	small	ADJ
ejpam-2662	15	13	)	)	PUNCT
ejpam-2662	15	14	submodule	submodule	NOUN
ejpam-2662	15	15	of	of	ADP
ejpam-2662	15	16	m	m	PROPN
ejpam-2662	15	17	if	if	SCONJ
ejpam-2662	15	18	for	for	ADP
ejpam-2662	15	19	every	every	DET
ejpam-2662	15	20	t	t	NOUN
ejpam-2662	15	21	e	e	X
ejpam-2662	15	22	m	m	VERB
ejpam-2662	15	23	with	with	ADP
ejpam-2662	15	24	m	m	PROPN
ejpam-2662	15	25	=	=	SYM
ejpam-2662	15	26	k	k	X
ejpam-2662	16	1	+	+	PROPN
ejpam-2662	16	2	t	t	PROPN
ejpam-2662	16	3	implies	imply	VERB
ejpam-2662	16	4	that	that	SCONJ
ejpam-2662	16	5	t	t	NOUN
ejpam-2662	16	6	=	=	SYM
ejpam-2662	16	7	m	m	PROPN
ejpam-2662	16	8	,	,	PUNCT
ejpam-2662	16	9	this	this	PRON
ejpam-2662	16	10	is	be	AUX
ejpam-2662	16	11	written	write	VERB
ejpam-2662	16	12	by	by	ADP
ejpam-2662	16	13	k	k	PROPN
ejpam-2662	16	14	�	�	PROPN
ejpam-2662	16	15	g	g	PROPN
ejpam-2662	16	16	m	m	PROPN
ejpam-2662	16	17	(	(	PUNCT
ejpam-2662	16	18	in	in	ADP
ejpam-2662	16	19	[	[	X
ejpam-2662	16	20	5	5	NUM
ejpam-2662	16	21	]	]	PUNCT
ejpam-2662	16	22	,	,	PUNCT
ejpam-2662	16	23	it	it	PRON
ejpam-2662	16	24	is	be	AUX
ejpam-2662	16	25	called	call	VERB
ejpam-2662	16	26	an	an	DET
ejpam-2662	16	27	e	e	ADJ
ejpam-2662	16	28	-	-	ADJ
ejpam-2662	16	29	small	small	ADJ
ejpam-2662	16	30	submodule	submodule	NOUN
ejpam-2662	16	31	of	of	ADP
ejpam-2662	16	32	m	m	PROPN
ejpam-2662	16	33	and	and	CCONJ
ejpam-2662	16	34	denoted	denote	VERB
ejpam-2662	16	35	by	by	ADP
ejpam-2662	16	36	k	k	PROPN
ejpam-2662	16	37	�	�	PROPN
ejpam-2662	16	38	e	e	PROPN
ejpam-2662	16	39	m	m	PROPN
ejpam-2662	16	40	)	)	PUNCT
ejpam-2662	16	41	.	.	PUNCT
ejpam-2662	17	1	if	if	SCONJ
ejpam-2662	17	2	t	t	PROPN
ejpam-2662	17	3	is	be	AUX
ejpam-2662	17	4	both	both	PRON
ejpam-2662	17	5	essential	essential	ADJ
ejpam-2662	17	6	and	and	CCONJ
ejpam-2662	17	7	maximal	maximal	ADJ
ejpam-2662	17	8	submodule	submodule	NOUN
ejpam-2662	17	9	of	of	ADP
ejpam-2662	17	10	m	m	PROPN
ejpam-2662	17	11	,	,	PUNCT
ejpam-2662	17	12	then	then	ADV
ejpam-2662	17	13	t	t	PROPN
ejpam-2662	17	14	is	be	AUX
ejpam-2662	17	15	called	call	VERB
ejpam-2662	17	16	a	a	DET
ejpam-2662	17	17	generalized	generalize	VERB
ejpam-2662	17	18	maximal	maximal	ADJ
ejpam-2662	17	19	submodule	submodule	NOUN
ejpam-2662	17	20	of	of	ADP
ejpam-2662	17	21	m	m	PROPN
ejpam-2662	17	22	.	.	PUNCT
ejpam-2662	18	1	the	the	DET
ejpam-2662	18	2	intersection	intersection	NOUN
ejpam-2662	18	3	of	of	ADP
ejpam-2662	18	4	all	all	DET
ejpam-2662	18	5	generalized	generalize	VERB
ejpam-2662	18	6	maximal	maximal	ADJ
ejpam-2662	18	7	submodules	submodule	NOUN
ejpam-2662	18	8	of	of	ADP
ejpam-2662	18	9	m	m	PROPN
ejpam-2662	18	10	is	be	AUX
ejpam-2662	18	11	called	call	VERB
ejpam-2662	18	12	the	the	DET
ejpam-2662	18	13	generalized	generalized	ADJ
ejpam-2662	18	14	radical	radical	NOUN
ejpam-2662	18	15	of	of	ADP
ejpam-2662	18	16	m	m	PRON
ejpam-2662	18	17	and	and	CCONJ
ejpam-2662	18	18	it	it	PRON
ejpam-2662	18	19	is	be	AUX
ejpam-2662	18	20	denoted	denote	VERB
ejpam-2662	18	21	by	by	ADP
ejpam-2662	18	22	radgm	radgm	NOUN
ejpam-2662	18	23	(	(	PUNCT
ejpam-2662	18	24	in	in	ADP
ejpam-2662	18	25	[	[	X
ejpam-2662	18	26	5	5	NUM
ejpam-2662	18	27	]	]	PUNCT
ejpam-2662	18	28	,	,	PUNCT
ejpam-2662	18	29	it	it	PRON
ejpam-2662	18	30	is	be	AUX
ejpam-2662	18	31	denoted	denote	VERB
ejpam-2662	18	32	by	by	ADP
ejpam-2662	18	33	radem	radem	PROPN
ejpam-2662	18	34	)	)	PUNCT
ejpam-2662	18	35	.	.	PUNCT
ejpam-2662	19	1	if	if	SCONJ
ejpam-2662	19	2	m	m	NOUN
ejpam-2662	19	3	have	have	VERB
ejpam-2662	19	4	no	no	DET
ejpam-2662	19	5	generalized	generalize	VERB
ejpam-2662	19	6	maximal	maximal	ADJ
ejpam-2662	19	7	submodules	submodule	NOUN
ejpam-2662	19	8	,	,	PUNCT
ejpam-2662	19	9	then	then	ADV
ejpam-2662	19	10	the	the	DET
ejpam-2662	19	11	generalized	generalized	ADJ
ejpam-2662	19	12	radical	radical	NOUN
ejpam-2662	19	13	of	of	ADP
ejpam-2662	19	14	m	m	PROPN
ejpam-2662	19	15	is	be	AUX
ejpam-2662	19	16	defined	define	VERB
ejpam-2662	19	17	by	by	ADP
ejpam-2662	19	18	radgm	radgm	NOUN
ejpam-2662	19	19	=	=	NOUN
ejpam-2662	19	20	m	m	VERB
ejpam-2662	19	21	.	.	PUNCT
ejpam-2662	20	1	let	let	VERB
ejpam-2662	20	2	u	u	PRON
ejpam-2662	20	3	and	and	CCONJ
ejpam-2662	20	4	v	v	NOUN
ejpam-2662	20	5	be	be	AUX
ejpam-2662	20	6	submodules	submodule	NOUN
ejpam-2662	20	7	of	of	ADP
ejpam-2662	20	8	m	m	PROPN
ejpam-2662	20	9	.	.	PUNCT
ejpam-2662	21	1	if	if	SCONJ
ejpam-2662	21	2	m	m	VERB
ejpam-2662	21	3	=	=	VERB
ejpam-2662	21	4	u	u	NOUN
ejpam-2662	21	5	+	+	NOUN
ejpam-2662	21	6	v	v	NOUN
ejpam-2662	21	7	and	and	CCONJ
ejpam-2662	21	8	v	v	NOUN
ejpam-2662	21	9	is	be	AUX
ejpam-2662	21	10	minimal	minimal	ADJ
ejpam-2662	21	11	with	with	ADP
ejpam-2662	21	12	respect	respect	NOUN
ejpam-2662	21	13	to	to	ADP
ejpam-2662	21	14	this	this	DET
ejpam-2662	21	15	property	property	NOUN
ejpam-2662	21	16	,	,	PUNCT
ejpam-2662	21	17	or	or	CCONJ
ejpam-2662	21	18	equivalently	equivalently	ADV
ejpam-2662	21	19	,	,	PUNCT
ejpam-2662	21	20	m	m	VERB
ejpam-2662	21	21	=	=	VERB
ejpam-2662	21	22	u	u	NOUN
ejpam-2662	21	23	+	+	NOUN
ejpam-2662	21	24	v	v	NOUN
ejpam-2662	21	25	and	and	CCONJ
ejpam-2662	21	26	u	u	NOUN
ejpam-2662	21	27	∩v	∩v	PROPN
ejpam-2662	21	28	�	�	PROPN
ejpam-2662	21	29	v	v	ADP
ejpam-2662	21	30	,	,	PUNCT
ejpam-2662	21	31	then	then	ADV
ejpam-2662	21	32	v	v	NOUN
ejpam-2662	21	33	is	be	AUX
ejpam-2662	21	34	called	call	VERB
ejpam-2662	21	35	a	a	DET
ejpam-2662	21	36	supplement	supplement	NOUN
ejpam-2662	21	37	of	of	ADP
ejpam-2662	21	38	u	u	NOUN
ejpam-2662	21	39	in	in	ADP
ejpam-2662	21	40	m	m	PROPN
ejpam-2662	21	41	.	.	PUNCT
ejpam-2662	22	1	if	if	SCONJ
ejpam-2662	22	2	m	m	VERB
ejpam-2662	22	3	=	=	VERB
ejpam-2662	22	4	u	u	NOUN
ejpam-2662	22	5	+	+	NOUN
ejpam-2662	22	6	v	v	NOUN
ejpam-2662	22	7	and	and	CCONJ
ejpam-2662	22	8	m	m	PROPN
ejpam-2662	22	9	=	=	SYM
ejpam-2662	22	10	u	u	PROPN
ejpam-2662	22	11	+	+	PROPN
ejpam-2662	22	12	t	t	NOUN
ejpam-2662	22	13	with	with	ADP
ejpam-2662	22	14	t	t	PROPN
ejpam-2662	22	15	e	e	X
ejpam-2662	22	16	v	v	PROPN
ejpam-2662	22	17	implies	imply	VERB
ejpam-2662	22	18	that	that	SCONJ
ejpam-2662	22	19	t	t	NOUN
ejpam-2662	22	20	=	=	SYM
ejpam-2662	22	21	v	v	NOUN
ejpam-2662	22	22	,	,	PUNCT
ejpam-2662	22	23	or	or	CCONJ
ejpam-2662	22	24	equivalently	equivalently	ADV
ejpam-2662	22	25	,	,	PUNCT
ejpam-2662	22	26	m	m	VERB
ejpam-2662	22	27	=	=	SYM
ejpam-2662	22	28	u	u	NOUN
ejpam-2662	22	29	+	+	X
ejpam-2662	22	30	v	v	NOUN
ejpam-2662	22	31	and	and	CCONJ
ejpam-2662	22	32	u	u	NOUN
ejpam-2662	22	33	∩	∩	PROPN
ejpam-2662	22	34	v	v	ADP
ejpam-2662	22	35	�	�	PROPN
ejpam-2662	22	36	g	g	NOUN
ejpam-2662	22	37	v	v	NOUN
ejpam-2662	22	38	,	,	PUNCT
ejpam-2662	22	39	then	then	ADV
ejpam-2662	22	40	v	v	NOUN
ejpam-2662	22	41	is	be	AUX
ejpam-2662	22	42	called	call	VERB
ejpam-2662	22	43	a	a	DET
ejpam-2662	22	44	g	g	NOUN
ejpam-2662	22	45	-	-	PUNCT
ejpam-2662	22	46	supplement	supplement	NOUN
ejpam-2662	22	47	of	of	ADP
ejpam-2662	22	48	u	u	NOUN
ejpam-2662	22	49	in	in	ADP
ejpam-2662	22	50	m	m	PROPN
ejpam-2662	22	51	.	.	PUNCT
ejpam-2662	23	1	if	if	SCONJ
ejpam-2662	23	2	every	every	DET
ejpam-2662	23	3	submodule	submodule	NOUN
ejpam-2662	23	4	of	of	ADP
ejpam-2662	23	5	m	m	PROPN
ejpam-2662	23	6	has	have	VERB
ejpam-2662	23	7	a	a	DET
ejpam-2662	23	8	supplement	supplement	NOUN
ejpam-2662	23	9	in	in	ADP
ejpam-2662	23	10	∗corresponding	∗corresponde	VERB
ejpam-2662	23	11	author	author	NOUN
ejpam-2662	23	12	.	.	PUNCT
ejpam-2662	24	1	email	email	NOUN
ejpam-2662	24	2	addresses	address	NOUN
ejpam-2662	24	3	:	:	PUNCT
ejpam-2662	24	4	cnebiyev@omu.edu.tr	cnebiyev@omu.edu.tr	PROPN
ejpam-2662	24	5	(	(	PUNCT
ejpam-2662	24	6	c.	c.	PROPN
ejpam-2662	24	7	nebiyev	nebiyev	PROPN
ejpam-2662	24	8	)	)	PUNCT
ejpam-2662	24	9	,	,	PUNCT
ejpam-2662	24	10	hokten@gmail.com	hokten@gmail.com	X
ejpam-2662	25	1	(	(	PUNCT
ejpam-2662	25	2	h.	h.	PROPN
ejpam-2662	25	3	ökten	ökten	PROPN
ejpam-2662	25	4	)	)	PUNCT
ejpam-2662	25	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2662	26	1	521	521	NUM
ejpam-2662	26	2	c	c	NOUN
ejpam-2662	26	3	©	©	PROPN
ejpam-2662	26	4	2017	2017	NUM
ejpam-2662	26	5	ejpam	ejpam	VERB
ejpam-2662	26	6	all	all	DET
ejpam-2662	26	7	rights	right	NOUN
ejpam-2662	26	8	reserved	reserve	VERB
ejpam-2662	26	9	.	.	PUNCT
ejpam-2662	27	1	c.	c.	PROPN
ejpam-2662	27	2	nebiyev	nebiyev	PROPN
ejpam-2662	27	3	,	,	PUNCT
ejpam-2662	27	4	h.	h.	PROPN
ejpam-2662	27	5	ökten	ökten	PROPN
ejpam-2662	27	6	/	/	SYM
ejpam-2662	27	7	eur	eur	PROPN
ejpam-2662	27	8	.	.	PUNCT
ejpam-2662	28	1	j.	j.	PROPN
ejpam-2662	28	2	pure	pure	PROPN
ejpam-2662	28	3	appl	appl	PROPN
ejpam-2662	28	4	.	.	PROPN
ejpam-2662	28	5	math	math	PROPN
ejpam-2662	28	6	,	,	PUNCT
ejpam-2662	28	7	10	10	NUM
ejpam-2662	28	8	(	(	PUNCT
ejpam-2662	28	9	3	3	NUM
ejpam-2662	28	10	)	)	PUNCT
ejpam-2662	28	11	(	(	PUNCT
ejpam-2662	28	12	2017	2017	NUM
ejpam-2662	28	13	)	)	PUNCT
ejpam-2662	28	14	,	,	PUNCT
ejpam-2662	28	15	521	521	NUM
ejpam-2662	28	16	-	-	SYM
ejpam-2662	28	17	528	528	NUM
ejpam-2662	28	18	522	522	NUM
ejpam-2662	28	19	m	m	NOUN
ejpam-2662	28	20	,	,	PUNCT
ejpam-2662	28	21	then	then	ADV
ejpam-2662	28	22	m	m	VERB
ejpam-2662	28	23	is	be	AUX
ejpam-2662	28	24	called	call	VERB
ejpam-2662	28	25	a	a	DET
ejpam-2662	28	26	supplemented	supplement	VERB
ejpam-2662	28	27	module	module	NOUN
ejpam-2662	28	28	.	.	PUNCT
ejpam-2662	29	1	m	m	PROPN
ejpam-2662	29	2	is	be	AUX
ejpam-2662	29	3	called	call	VERB
ejpam-2662	29	4	a	a	DET
ejpam-2662	29	5	g	g	NOUN
ejpam-2662	29	6	-	-	PUNCT
ejpam-2662	29	7	supplemented	supplement	VERB
ejpam-2662	29	8	module	module	NOUN
ejpam-2662	29	9	,	,	PUNCT
ejpam-2662	29	10	if	if	SCONJ
ejpam-2662	29	11	every	every	DET
ejpam-2662	29	12	submodule	submodule	NOUN
ejpam-2662	29	13	of	of	ADP
ejpam-2662	29	14	m	m	PROPN
ejpam-2662	29	15	has	have	VERB
ejpam-2662	29	16	a	a	DET
ejpam-2662	29	17	g	g	NOUN
ejpam-2662	29	18	-	-	PUNCT
ejpam-2662	29	19	supplement	supplement	NOUN
ejpam-2662	29	20	in	in	ADP
ejpam-2662	29	21	m	m	PROPN
ejpam-2662	29	22	.	.	PUNCT
ejpam-2662	30	1	let	let	VERB
ejpam-2662	30	2	u	u	NOUN
ejpam-2662	30	3	,	,	PUNCT
ejpam-2662	30	4	v	v	NOUN
ejpam-2662	30	5	≤	≤	NOUN
ejpam-2662	30	6	m	m	NOUN
ejpam-2662	30	7	.	.	PUNCT
ejpam-2662	31	1	if	if	SCONJ
ejpam-2662	31	2	m	m	NOUN
ejpam-2662	31	3	=	=	VERB
ejpam-2662	31	4	u	u	NOUN
ejpam-2662	31	5	+	+	X
ejpam-2662	31	6	v	v	NOUN
ejpam-2662	31	7	and	and	CCONJ
ejpam-2662	31	8	u	u	NOUN
ejpam-2662	31	9	∩	∩	PROPN
ejpam-2662	31	10	v	v	ADP
ejpam-2662	31	11	�	�	PROPN
ejpam-2662	31	12	m	m	PROPN
ejpam-2662	31	13	,	,	PUNCT
ejpam-2662	31	14	then	then	ADV
ejpam-2662	31	15	v	v	NOUN
ejpam-2662	31	16	is	be	AUX
ejpam-2662	31	17	called	call	VERB
ejpam-2662	31	18	a	a	DET
ejpam-2662	31	19	weak	weak	ADJ
ejpam-2662	31	20	supplement	supplement	NOUN
ejpam-2662	31	21	of	of	ADP
ejpam-2662	31	22	u	u	NOUN
ejpam-2662	31	23	in	in	ADP
ejpam-2662	31	24	m	m	PROPN
ejpam-2662	31	25	.	.	PUNCT
ejpam-2662	32	1	if	if	SCONJ
ejpam-2662	32	2	every	every	DET
ejpam-2662	32	3	submodule	submodule	NOUN
ejpam-2662	32	4	of	of	ADP
ejpam-2662	32	5	m	m	PROPN
ejpam-2662	32	6	has	have	VERB
ejpam-2662	32	7	a	a	DET
ejpam-2662	32	8	weak	weak	ADJ
ejpam-2662	32	9	supplement	supplement	NOUN
ejpam-2662	32	10	in	in	ADP
ejpam-2662	32	11	m	m	PROPN
ejpam-2662	32	12	,	,	PUNCT
ejpam-2662	32	13	then	then	ADV
ejpam-2662	32	14	m	m	VERB
ejpam-2662	32	15	is	be	AUX
ejpam-2662	32	16	called	call	VERB
ejpam-2662	32	17	a	a	DET
ejpam-2662	32	18	weakly	weakly	ADJ
ejpam-2662	32	19	supplemented	supplement	VERB
ejpam-2662	32	20	module	module	NOUN
ejpam-2662	32	21	.	.	PUNCT
ejpam-2662	33	1	if	if	SCONJ
ejpam-2662	33	2	every	every	DET
ejpam-2662	33	3	cofinite	cofinite	NOUN
ejpam-2662	33	4	submodule	submodule	NOUN
ejpam-2662	33	5	of	of	ADP
ejpam-2662	33	6	m	m	PROPN
ejpam-2662	33	7	has	have	VERB
ejpam-2662	33	8	a	a	DET
ejpam-2662	33	9	weak	weak	ADJ
ejpam-2662	33	10	supplement	supplement	NOUN
ejpam-2662	33	11	in	in	ADP
ejpam-2662	33	12	m	m	PROPN
ejpam-2662	33	13	,	,	PUNCT
ejpam-2662	33	14	then	then	ADV
ejpam-2662	33	15	m	m	VERB
ejpam-2662	33	16	is	be	AUX
ejpam-2662	33	17	called	call	VERB
ejpam-2662	33	18	a	a	DET
ejpam-2662	33	19	cofinitely	cofinitely	ADV
ejpam-2662	33	20	weak	weak	ADJ
ejpam-2662	33	21	supplemented	supplement	VERB
ejpam-2662	33	22	module	module	NOUN
ejpam-2662	33	23	.	.	PUNCT
ejpam-2662	34	1	there	there	PRON
ejpam-2662	34	2	are	be	VERB
ejpam-2662	34	3	some	some	DET
ejpam-2662	34	4	important	important	ADJ
ejpam-2662	34	5	properties	property	NOUN
ejpam-2662	34	6	of	of	ADP
ejpam-2662	34	7	g	g	NOUN
ejpam-2662	34	8	-	-	PUNCT
ejpam-2662	34	9	small	small	ADJ
ejpam-2662	34	10	submodules	submodule	NOUN
ejpam-2662	34	11	in	in	ADP
ejpam-2662	34	12	[	[	X
ejpam-2662	34	13	1	1	NUM
ejpam-2662	34	14	,	,	PUNCT
ejpam-2662	34	15	3	3	NUM
ejpam-2662	34	16	,	,	PUNCT
ejpam-2662	34	17	4	4	NUM
ejpam-2662	34	18	]	]	PUNCT
ejpam-2662	34	19	and	and	CCONJ
ejpam-2662	34	20	[	[	X
ejpam-2662	34	21	5	5	NUM
ejpam-2662	34	22	]	]	PUNCT
ejpam-2662	34	23	.	.	PUNCT
ejpam-2662	35	1	lemma	lemma	PROPN
ejpam-2662	35	2	1	1	NUM
ejpam-2662	35	3	(	(	PUNCT
ejpam-2662	35	4	[	[	X
ejpam-2662	35	5	4	4	NUM
ejpam-2662	35	6	,	,	PUNCT
ejpam-2662	35	7	5	5	NUM
ejpam-2662	35	8	]	]	NUM
ejpam-2662	35	9	)	)	PUNCT
ejpam-2662	35	10	.	.	PUNCT
ejpam-2662	36	1	let	let	VERB
ejpam-2662	36	2	m	m	PRON
ejpam-2662	36	3	be	be	AUX
ejpam-2662	36	4	an	an	DET
ejpam-2662	36	5	r	r	NOUN
ejpam-2662	36	6	-	-	PUNCT
ejpam-2662	36	7	module	module	NOUN
ejpam-2662	36	8	and	and	CCONJ
ejpam-2662	36	9	k	k	NOUN
ejpam-2662	36	10	,	,	PUNCT
ejpam-2662	36	11	n	n	PRON
ejpam-2662	36	12	≤m	≤m	NOUN
ejpam-2662	36	13	.	.	PUNCT
ejpam-2662	37	1	the	the	DET
ejpam-2662	37	2	following	follow	VERB
ejpam-2662	37	3	conditions	condition	NOUN
ejpam-2662	37	4	are	be	AUX
ejpam-2662	37	5	hold	hold	ADJ
ejpam-2662	37	6	.	.	PUNCT
ejpam-2662	38	1	(	(	PUNCT
ejpam-2662	38	2	i	i	NOUN
ejpam-2662	38	3	)	)	PUNCT
ejpam-2662	38	4	if	if	SCONJ
ejpam-2662	38	5	k	k	PROPN
ejpam-2662	38	6	≤	≤	PROPN
ejpam-2662	38	7	n	n	CCONJ
ejpam-2662	38	8	and	and	CCONJ
ejpam-2662	38	9	n	n	PRON
ejpam-2662	38	10	�	�	PROPN
ejpam-2662	38	11	g	g	NOUN
ejpam-2662	38	12	m	m	PROPN
ejpam-2662	38	13	,	,	PUNCT
ejpam-2662	38	14	then	then	ADV
ejpam-2662	38	15	k	k	PROPN
ejpam-2662	38	16	�	�	PROPN
ejpam-2662	38	17	g	g	PROPN
ejpam-2662	38	18	m	m	PROPN
ejpam-2662	38	19	.	.	PUNCT
ejpam-2662	39	1	(	(	PUNCT
ejpam-2662	39	2	ii	ii	NOUN
ejpam-2662	39	3	)	)	PUNCT
ejpam-2662	39	4	if	if	SCONJ
ejpam-2662	39	5	k	k	PROPN
ejpam-2662	39	6	�	�	PROPN
ejpam-2662	39	7	g	g	PROPN
ejpam-2662	39	8	n	n	PROPN
ejpam-2662	39	9	,	,	PUNCT
ejpam-2662	39	10	then	then	ADV
ejpam-2662	39	11	k	k	PROPN
ejpam-2662	39	12	is	be	AUX
ejpam-2662	39	13	an	an	DET
ejpam-2662	39	14	g	g	NOUN
ejpam-2662	39	15	-	-	PUNCT
ejpam-2662	39	16	small	small	ADJ
ejpam-2662	39	17	submodule	submodule	NOUN
ejpam-2662	39	18	in	in	ADP
ejpam-2662	39	19	submodules	submodule	NOUN
ejpam-2662	39	20	of	of	ADP
ejpam-2662	39	21	m	m	PRON
ejpam-2662	39	22	which	which	PRON
ejpam-2662	39	23	contain	contain	VERB
ejpam-2662	39	24	n	n	PRON
ejpam-2662	39	25	.	.	PUNCT
ejpam-2662	40	1	(	(	PUNCT
ejpam-2662	40	2	iii	iii	X
ejpam-2662	40	3	)	)	PUNCT
ejpam-2662	40	4	if	if	SCONJ
ejpam-2662	40	5	f	f	PROPN
ejpam-2662	40	6	:	:	PUNCT
ejpam-2662	40	7	m	m	VERB
ejpam-2662	40	8	→	→	SYM
ejpam-2662	40	9	n	n	X
ejpam-2662	40	10	is	be	AUX
ejpam-2662	40	11	an	an	DET
ejpam-2662	40	12	r	r	NOUN
ejpam-2662	40	13	-	-	PUNCT
ejpam-2662	40	14	module	module	NOUN
ejpam-2662	40	15	homomorphism	homomorphism	NOUN
ejpam-2662	40	16	and	and	CCONJ
ejpam-2662	40	17	k	k	PROPN
ejpam-2662	40	18	�	�	PROPN
ejpam-2662	40	19	g	g	PROPN
ejpam-2662	40	20	m	m	PROPN
ejpam-2662	40	21	,	,	PUNCT
ejpam-2662	40	22	then	then	ADV
ejpam-2662	40	23	f	f	X
ejpam-2662	40	24	(	(	PUNCT
ejpam-2662	40	25	k)	k)	PROPN
ejpam-2662	40	26	�	�	PROPN
ejpam-2662	40	27	g	g	PROPN
ejpam-2662	40	28	n	n	PROPN
ejpam-2662	40	29	.	.	PUNCT
ejpam-2662	41	1	(	(	PUNCT
ejpam-2662	41	2	iv	iv	X
ejpam-2662	41	3	)	)	PUNCT
ejpam-2662	41	4	if	if	SCONJ
ejpam-2662	41	5	k	k	PROPN
ejpam-2662	41	6	�	�	PROPN
ejpam-2662	41	7	g	g	PROPN
ejpam-2662	41	8	l	l	PROPN
ejpam-2662	41	9	and	and	CCONJ
ejpam-2662	41	10	n	n	PRON
ejpam-2662	41	11	�	�	PROPN
ejpam-2662	41	12	g	g	PROPN
ejpam-2662	41	13	t	t	PROPN
ejpam-2662	41	14	for	for	ADP
ejpam-2662	41	15	l	l	PROPN
ejpam-2662	41	16	,	,	PUNCT
ejpam-2662	41	17	t	t	PROPN
ejpam-2662	41	18	≤m	≤m	PROPN
ejpam-2662	41	19	,	,	PUNCT
ejpam-2662	41	20	then	then	ADV
ejpam-2662	41	21	k	k	PROPN
ejpam-2662	41	22	+	+	CCONJ
ejpam-2662	41	23	n	n	PRON
ejpam-2662	41	24	�	�	PROPN
ejpam-2662	41	25	g	g	NOUN
ejpam-2662	41	26	l	l	NOUN
ejpam-2662	41	27	+	+	PROPN
ejpam-2662	41	28	t	t	NOUN
ejpam-2662	41	29	.	.	PUNCT
ejpam-2662	42	1	corollary	corollary	ADJ
ejpam-2662	42	2	1	1	NUM
ejpam-2662	42	3	.	.	PUNCT
ejpam-2662	43	1	let	let	VERB
ejpam-2662	43	2	m	m	PRON
ejpam-2662	43	3	be	be	AUX
ejpam-2662	43	4	an	an	DET
ejpam-2662	43	5	r	r	NOUN
ejpam-2662	43	6	-	-	PUNCT
ejpam-2662	43	7	module	module	NOUN
ejpam-2662	43	8	and	and	CCONJ
ejpam-2662	43	9	k	k	PROPN
ejpam-2662	43	10	≤	≤	PROPN
ejpam-2662	43	11	n	n	DET
ejpam-2662	43	12	≤m	≤m	NOUN
ejpam-2662	43	13	.	.	PUNCT
ejpam-2662	44	1	if	if	SCONJ
ejpam-2662	44	2	n	n	PRON
ejpam-2662	44	3	�	�	PROPN
ejpam-2662	44	4	g	g	NOUN
ejpam-2662	44	5	m	m	PROPN
ejpam-2662	44	6	,	,	PUNCT
ejpam-2662	44	7	then	then	ADV
ejpam-2662	44	8	n	n	CCONJ
ejpam-2662	44	9	/	/	SYM
ejpam-2662	44	10	k	k	PROPN
ejpam-2662	44	11	�	�	PROPN
ejpam-2662	44	12	g	g	PROPN
ejpam-2662	44	13	m	m	PROPN
ejpam-2662	44	14	/	/	SYM
ejpam-2662	44	15	k.	k.	PROPN
ejpam-2662	44	16	corollary	corollary	ADJ
ejpam-2662	45	1	2	2	NUM
ejpam-2662	45	2	.	.	PUNCT
ejpam-2662	46	1	let	let	VERB
ejpam-2662	46	2	m	m	PRON
ejpam-2662	46	3	be	be	AUX
ejpam-2662	46	4	an	an	DET
ejpam-2662	46	5	r	r	NOUN
ejpam-2662	46	6	-	-	PUNCT
ejpam-2662	46	7	module	module	NOUN
ejpam-2662	46	8	,	,	PUNCT
ejpam-2662	46	9	k	k	PROPN
ejpam-2662	46	10	�	�	PROPN
ejpam-2662	46	11	g	g	PROPN
ejpam-2662	46	12	m	m	PROPN
ejpam-2662	46	13	and	and	CCONJ
ejpam-2662	46	14	l	l	PROPN
ejpam-2662	46	15	≤m	≤m	NOUN
ejpam-2662	46	16	.	.	PUNCT
ejpam-2662	47	1	then	then	ADV
ejpam-2662	47	2	(	(	PUNCT
ejpam-2662	47	3	k	k	PROPN
ejpam-2662	47	4	+	+	NUM
ejpam-2662	47	5	l	l	NOUN
ejpam-2662	47	6	)	)	PUNCT
ejpam-2662	47	7	/l	/l	SYM
ejpam-2662	47	8	�	�	PROPN
ejpam-2662	47	9	g	g	PROPN
ejpam-2662	47	10	m	m	PROPN
ejpam-2662	47	11	/	/	SYM
ejpam-2662	47	12	l.	l.	PROPN
ejpam-2662	47	13	lemma	lemma	PROPN
ejpam-2662	47	14	2	2	NUM
ejpam-2662	47	15	(	(	PUNCT
ejpam-2662	47	16	[	[	X
ejpam-2662	47	17	1	1	NUM
ejpam-2662	47	18	]	]	PUNCT
ejpam-2662	47	19	)	)	PUNCT
ejpam-2662	47	20	.	.	PUNCT
ejpam-2662	48	1	let	let	VERB
ejpam-2662	48	2	m	m	PRON
ejpam-2662	48	3	be	be	AUX
ejpam-2662	48	4	an	an	DET
ejpam-2662	48	5	r	r	NOUN
ejpam-2662	48	6	-	-	PUNCT
ejpam-2662	48	7	module	module	NOUN
ejpam-2662	48	8	.	.	PUNCT
ejpam-2662	49	1	then	then	ADV
ejpam-2662	49	2	radgm	radgm	VERB
ejpam-2662	49	3	=	=	SYM
ejpam-2662	49	4	∑	∑	PUNCT
ejpam-2662	49	5	l	l	NOUN
ejpam-2662	49	6	�	�	PROPN
ejpam-2662	49	7	gm	gm	PROPN
ejpam-2662	49	8	l.	l.	PROPN
ejpam-2662	49	9	lemma	lemma	PROPN
ejpam-2662	49	10	3	3	NUM
ejpam-2662	49	11	(	(	PUNCT
ejpam-2662	49	12	[	[	X
ejpam-2662	49	13	1	1	NUM
ejpam-2662	49	14	]	]	PUNCT
ejpam-2662	49	15	)	)	PUNCT
ejpam-2662	49	16	.	.	PUNCT
ejpam-2662	50	1	let	let	VERB
ejpam-2662	50	2	m	m	PRON
ejpam-2662	50	3	be	be	AUX
ejpam-2662	50	4	an	an	DET
ejpam-2662	50	5	r	r	NOUN
ejpam-2662	50	6	-	-	PUNCT
ejpam-2662	50	7	module	module	NOUN
ejpam-2662	50	8	.	.	PUNCT
ejpam-2662	51	1	if	if	SCONJ
ejpam-2662	51	2	m	m	NOUN
ejpam-2662	51	3	has	have	VERB
ejpam-2662	51	4	at	at	ADV
ejpam-2662	51	5	least	least	ADJ
ejpam-2662	51	6	one	one	NUM
ejpam-2662	51	7	proper	proper	ADJ
ejpam-2662	51	8	essential	essential	ADJ
ejpam-2662	51	9	submodule	submodule	NOUN
ejpam-2662	51	10	and	and	CCONJ
ejpam-2662	51	11	every	every	DET
ejpam-2662	51	12	proper	proper	ADJ
ejpam-2662	51	13	essential	essential	ADJ
ejpam-2662	51	14	submodule	submodule	NOUN
ejpam-2662	51	15	of	of	ADP
ejpam-2662	51	16	m	m	PROPN
ejpam-2662	51	17	is	be	AUX
ejpam-2662	51	18	contained	contain	VERB
ejpam-2662	51	19	in	in	ADP
ejpam-2662	51	20	a	a	DET
ejpam-2662	51	21	generalized	generalized	ADJ
ejpam-2662	51	22	maximal	maximal	ADJ
ejpam-2662	51	23	submodule	submodule	NOUN
ejpam-2662	51	24	,	,	PUNCT
ejpam-2662	51	25	then	then	ADV
ejpam-2662	51	26	radgm	radgm	VERB
ejpam-2662	51	27	�	�	PROPN
ejpam-2662	51	28	g	g	NOUN
ejpam-2662	51	29	m	m	PROPN
ejpam-2662	51	30	.	.	PUNCT
ejpam-2662	52	1	lemma	lemma	PROPN
ejpam-2662	52	2	4	4	NUM
ejpam-2662	52	3	(	(	PUNCT
ejpam-2662	52	4	[	[	X
ejpam-2662	52	5	1	1	NUM
ejpam-2662	52	6	]	]	PUNCT
ejpam-2662	52	7	)	)	PUNCT
ejpam-2662	52	8	.	.	PUNCT
ejpam-2662	53	1	if	if	SCONJ
ejpam-2662	53	2	m	m	NOUN
ejpam-2662	53	3	is	be	AUX
ejpam-2662	53	4	a	a	DET
ejpam-2662	53	5	finitely	finitely	ADV
ejpam-2662	53	6	generated	generate	VERB
ejpam-2662	53	7	r	r	NOUN
ejpam-2662	53	8	-	-	PUNCT
ejpam-2662	53	9	module	module	NOUN
ejpam-2662	53	10	and	and	CCONJ
ejpam-2662	53	11	m	m	NOUN
ejpam-2662	53	12	has	have	VERB
ejpam-2662	53	13	at	at	ADV
ejpam-2662	53	14	least	least	ADJ
ejpam-2662	53	15	one	one	NUM
ejpam-2662	53	16	proper	proper	ADJ
ejpam-2662	53	17	essential	essential	ADJ
ejpam-2662	53	18	submodule	submodule	NOUN
ejpam-2662	53	19	,	,	PUNCT
ejpam-2662	53	20	then	then	ADV
ejpam-2662	53	21	every	every	DET
ejpam-2662	53	22	proper	proper	ADJ
ejpam-2662	53	23	essential	essential	ADJ
ejpam-2662	53	24	submodule	submodule	NOUN
ejpam-2662	53	25	of	of	ADP
ejpam-2662	53	26	m	m	PROPN
ejpam-2662	53	27	is	be	AUX
ejpam-2662	53	28	contained	contain	VERB
ejpam-2662	53	29	in	in	ADP
ejpam-2662	53	30	a	a	DET
ejpam-2662	53	31	generalized	generalized	ADJ
ejpam-2662	53	32	maximal	maximal	ADJ
ejpam-2662	53	33	submodule	submodule	NOUN
ejpam-2662	53	34	of	of	ADP
ejpam-2662	53	35	m	m	PROPN
ejpam-2662	53	36	.	.	PUNCT
ejpam-2662	54	1	2	2	X
ejpam-2662	54	2	.	.	X
ejpam-2662	54	3	weakly	weakly	ADJ
ejpam-2662	54	4	g	g	NOUN
ejpam-2662	54	5	-	-	PUNCT
ejpam-2662	54	6	supplemented	supplement	VERB
ejpam-2662	54	7	modules	module	NOUN
ejpam-2662	54	8	definition	definition	NOUN
ejpam-2662	54	9	1	1	NUM
ejpam-2662	54	10	.	.	PUNCT
ejpam-2662	55	1	let	let	VERB
ejpam-2662	55	2	m	m	PRON
ejpam-2662	55	3	be	be	AUX
ejpam-2662	55	4	an	an	DET
ejpam-2662	55	5	r	r	NOUN
ejpam-2662	55	6	-	-	PUNCT
ejpam-2662	55	7	module	module	NOUN
ejpam-2662	55	8	and	and	CCONJ
ejpam-2662	55	9	u	u	NOUN
ejpam-2662	55	10	,	,	PUNCT
ejpam-2662	55	11	v	v	NOUN
ejpam-2662	55	12	≤m	≤m	NOUN
ejpam-2662	55	13	.	.	PUNCT
ejpam-2662	56	1	if	if	SCONJ
ejpam-2662	56	2	m	m	NOUN
ejpam-2662	56	3	=	=	VERB
ejpam-2662	56	4	u	u	NOUN
ejpam-2662	56	5	+	+	X
ejpam-2662	56	6	v	v	NOUN
ejpam-2662	56	7	and	and	CCONJ
ejpam-2662	56	8	u	u	NOUN
ejpam-2662	56	9	∩	∩	PROPN
ejpam-2662	56	10	v	v	ADP
ejpam-2662	56	11	�	�	PROPN
ejpam-2662	56	12	g	g	NOUN
ejpam-2662	56	13	m	m	PROPN
ejpam-2662	56	14	,	,	PUNCT
ejpam-2662	56	15	then	then	ADV
ejpam-2662	56	16	v	v	NOUN
ejpam-2662	56	17	is	be	AUX
ejpam-2662	56	18	called	call	VERB
ejpam-2662	56	19	a	a	DET
ejpam-2662	56	20	weak	weak	ADJ
ejpam-2662	56	21	g	g	NOUN
ejpam-2662	56	22	-	-	PUNCT
ejpam-2662	56	23	supplement	supplement	NOUN
ejpam-2662	56	24	of	of	ADP
ejpam-2662	56	25	u	u	NOUN
ejpam-2662	56	26	in	in	ADP
ejpam-2662	56	27	m	m	PROPN
ejpam-2662	56	28	.	.	PUNCT
ejpam-2662	57	1	if	if	SCONJ
ejpam-2662	57	2	every	every	DET
ejpam-2662	57	3	submodule	submodule	NOUN
ejpam-2662	57	4	of	of	ADP
ejpam-2662	57	5	m	m	PROPN
ejpam-2662	57	6	has	have	VERB
ejpam-2662	57	7	a	a	DET
ejpam-2662	57	8	weak	weak	ADJ
ejpam-2662	57	9	g	g	NOUN
ejpam-2662	57	10	-	-	PUNCT
ejpam-2662	57	11	supplement	supplement	NOUN
ejpam-2662	57	12	in	in	ADP
ejpam-2662	57	13	m	m	PROPN
ejpam-2662	57	14	,	,	PUNCT
ejpam-2662	57	15	then	then	ADV
ejpam-2662	57	16	m	m	VERB
ejpam-2662	57	17	is	be	AUX
ejpam-2662	57	18	called	call	VERB
ejpam-2662	57	19	a	a	DET
ejpam-2662	57	20	weakly	weakly	ADJ
ejpam-2662	57	21	g	g	NOUN
ejpam-2662	57	22	-	-	PUNCT
ejpam-2662	57	23	supplemented	supplement	VERB
ejpam-2662	57	24	module	module	NOUN
ejpam-2662	57	25	.	.	PUNCT
ejpam-2662	58	1	clearly	clearly	ADV
ejpam-2662	58	2	,	,	PUNCT
ejpam-2662	58	3	we	we	PRON
ejpam-2662	58	4	see	see	VERB
ejpam-2662	58	5	that	that	SCONJ
ejpam-2662	58	6	g	g	NOUN
ejpam-2662	58	7	-	-	PUNCT
ejpam-2662	58	8	supplemented	supplement	VERB
ejpam-2662	58	9	modules	module	NOUN
ejpam-2662	58	10	are	be	AUX
ejpam-2662	58	11	weakly	weakly	ADJ
ejpam-2662	58	12	g	g	NOUN
ejpam-2662	58	13	-	-	PUNCT
ejpam-2662	58	14	supplemented	supplement	VERB
ejpam-2662	58	15	.	.	PUNCT
ejpam-2662	59	1	we	we	PRON
ejpam-2662	59	2	also	also	ADV
ejpam-2662	59	3	see	see	VERB
ejpam-2662	59	4	that	that	SCONJ
ejpam-2662	59	5	every	every	DET
ejpam-2662	59	6	weakly	weakly	ADJ
ejpam-2662	59	7	supplemented	supplement	VERB
ejpam-2662	59	8	module	module	NOUN
ejpam-2662	59	9	is	be	AUX
ejpam-2662	59	10	weakly	weakly	ADJ
ejpam-2662	59	11	g	g	NOUN
ejpam-2662	59	12	-	-	PUNCT
ejpam-2662	59	13	supplemented	supplement	VERB
ejpam-2662	59	14	.	.	PUNCT
ejpam-2662	60	1	lemma	lemma	PROPN
ejpam-2662	60	2	5	5	X
ejpam-2662	60	3	.	.	PUNCT
ejpam-2662	61	1	let	let	VERB
ejpam-2662	61	2	m	m	PRON
ejpam-2662	61	3	be	be	AUX
ejpam-2662	61	4	an	an	DET
ejpam-2662	61	5	r	r	NOUN
ejpam-2662	61	6	-	-	PUNCT
ejpam-2662	61	7	module	module	NOUN
ejpam-2662	61	8	,	,	PUNCT
ejpam-2662	61	9	m1	m1	PROPN
ejpam-2662	61	10	≤m	≤m	PROPN
ejpam-2662	61	11	,	,	PUNCT
ejpam-2662	61	12	u	u	PROPN
ejpam-2662	61	13	≤m	≤m	PROPN
ejpam-2662	61	14	and	and	CCONJ
ejpam-2662	61	15	m1	m1	PROPN
ejpam-2662	61	16	be	be	AUX
ejpam-2662	61	17	a	a	DET
ejpam-2662	61	18	weakly	weakly	ADJ
ejpam-2662	61	19	g	g	NOUN
ejpam-2662	61	20	-	-	PUNCT
ejpam-2662	61	21	supplemented	supplement	VERB
ejpam-2662	61	22	module	module	NOUN
ejpam-2662	61	23	.	.	PUNCT
ejpam-2662	62	1	if	if	SCONJ
ejpam-2662	62	2	m1	m1	PROPN
ejpam-2662	62	3	+	+	CCONJ
ejpam-2662	62	4	u	u	NOUN
ejpam-2662	62	5	has	have	VERB
ejpam-2662	62	6	a	a	DET
ejpam-2662	62	7	weak	weak	ADJ
ejpam-2662	62	8	g	g	NOUN
ejpam-2662	62	9	-	-	PUNCT
ejpam-2662	62	10	supplement	supplement	NOUN
ejpam-2662	62	11	in	in	ADP
ejpam-2662	62	12	m	m	PROPN
ejpam-2662	62	13	,	,	PUNCT
ejpam-2662	62	14	then	then	ADV
ejpam-2662	62	15	u	u	NOUN
ejpam-2662	62	16	has	have	VERB
ejpam-2662	62	17	also	also	ADV
ejpam-2662	62	18	a	a	DET
ejpam-2662	62	19	weak	weak	ADJ
ejpam-2662	62	20	g	g	NOUN
ejpam-2662	62	21	-	-	PUNCT
ejpam-2662	62	22	supplement	supplement	NOUN
ejpam-2662	62	23	in	in	ADP
ejpam-2662	62	24	m	m	PROPN
ejpam-2662	62	25	.	.	PUNCT
ejpam-2662	63	1	c.	c.	PROPN
ejpam-2662	63	2	nebiyev	nebiyev	PROPN
ejpam-2662	63	3	,	,	PUNCT
ejpam-2662	63	4	h.	h.	PROPN
ejpam-2662	63	5	ökten	ökten	PROPN
ejpam-2662	63	6	/	/	SYM
ejpam-2662	63	7	eur	eur	PROPN
ejpam-2662	63	8	.	.	PUNCT
ejpam-2662	64	1	j.	j.	PROPN
ejpam-2662	64	2	pure	pure	PROPN
ejpam-2662	64	3	appl	appl	PROPN
ejpam-2662	64	4	.	.	PROPN
ejpam-2662	64	5	math	math	PROPN
ejpam-2662	64	6	,	,	PUNCT
ejpam-2662	64	7	10	10	NUM
ejpam-2662	64	8	(	(	PUNCT
ejpam-2662	64	9	3	3	NUM
ejpam-2662	64	10	)	)	PUNCT
ejpam-2662	64	11	(	(	PUNCT
ejpam-2662	64	12	2017	2017	NUM
ejpam-2662	64	13	)	)	PUNCT
ejpam-2662	64	14	,	,	PUNCT
ejpam-2662	64	15	521	521	NUM
ejpam-2662	64	16	-	-	SYM
ejpam-2662	64	17	528	528	NUM
ejpam-2662	64	18	523	523	NUM
ejpam-2662	64	19	proof	proof	NOUN
ejpam-2662	64	20	.	.	PUNCT
ejpam-2662	65	1	let	let	VERB
ejpam-2662	65	2	x	x	PRON
ejpam-2662	65	3	be	be	AUX
ejpam-2662	65	4	a	a	DET
ejpam-2662	65	5	weak	weak	ADJ
ejpam-2662	65	6	g	g	NOUN
ejpam-2662	65	7	-	-	PUNCT
ejpam-2662	65	8	supplement	supplement	NOUN
ejpam-2662	65	9	of	of	ADP
ejpam-2662	65	10	m1	m1	PROPN
ejpam-2662	65	11	+	+	CCONJ
ejpam-2662	65	12	u	u	NOUN
ejpam-2662	65	13	in	in	ADP
ejpam-2662	65	14	m	m	PROPN
ejpam-2662	65	15	.	.	PUNCT
ejpam-2662	66	1	then	then	ADV
ejpam-2662	66	2	m1	m1	PROPN
ejpam-2662	66	3	+	+	CCONJ
ejpam-2662	66	4	u	u	NOUN
ejpam-2662	66	5	+	+	NOUN
ejpam-2662	66	6	x	x	SYM
ejpam-2662	66	7	=	=	VERB
ejpam-2662	66	8	m	m	PRON
ejpam-2662	66	9	and	and	CCONJ
ejpam-2662	66	10	(	(	PUNCT
ejpam-2662	66	11	m1	m1	PROPN
ejpam-2662	66	12	+	+	CCONJ
ejpam-2662	66	13	u	u	NOUN
ejpam-2662	66	14	)	)	PUNCT
ejpam-2662	66	15	∩	∩	NOUN
ejpam-2662	66	16	x	x	SYM
ejpam-2662	66	17	�	�	PROPN
ejpam-2662	66	18	g	g	PROPN
ejpam-2662	66	19	m	m	PROPN
ejpam-2662	66	20	.	.	PUNCT
ejpam-2662	67	1	since	since	SCONJ
ejpam-2662	67	2	m1	m1	PROPN
ejpam-2662	67	3	is	be	AUX
ejpam-2662	67	4	weakly	weakly	ADJ
ejpam-2662	67	5	g	g	NOUN
ejpam-2662	67	6	-	-	PUNCT
ejpam-2662	67	7	supplemented	supplement	VERB
ejpam-2662	67	8	,	,	PUNCT
ejpam-2662	67	9	(	(	PUNCT
ejpam-2662	67	10	u	u	NOUN
ejpam-2662	67	11	+	+	NOUN
ejpam-2662	67	12	x	x	X
ejpam-2662	67	13	)	)	PUNCT
ejpam-2662	67	14	∩m1	∩m1	PUNCT
ejpam-2662	67	15	has	have	VERB
ejpam-2662	67	16	a	a	DET
ejpam-2662	67	17	weak	weak	ADJ
ejpam-2662	67	18	g	g	NOUN
ejpam-2662	67	19	-	-	PUNCT
ejpam-2662	67	20	supplement	supplement	NOUN
ejpam-2662	67	21	y	y	NOUN
ejpam-2662	67	22	in	in	ADP
ejpam-2662	67	23	m1	m1	PROPN
ejpam-2662	67	24	,	,	PUNCT
ejpam-2662	67	25	i.e.	i.e.	X
ejpam-2662	67	26	m1	m1	NOUN
ejpam-2662	67	27	∩	∩	NOUN
ejpam-2662	67	28	(	(	PUNCT
ejpam-2662	67	29	u	u	NOUN
ejpam-2662	67	30	+	+	NOUN
ejpam-2662	67	31	x	x	X
ejpam-2662	67	32	)	)	PUNCT
ejpam-2662	67	33	+	+	CCONJ
ejpam-2662	67	34	y	y	PROPN
ejpam-2662	67	35	=	=	SYM
ejpam-2662	67	36	m1	m1	PROPN
ejpam-2662	67	37	and	and	CCONJ
ejpam-2662	67	38	m1	m1	PROPN
ejpam-2662	67	39	∩	∩	NOUN
ejpam-2662	67	40	(	(	PUNCT
ejpam-2662	67	41	u	u	NOUN
ejpam-2662	67	42	+	+	NOUN
ejpam-2662	67	43	x	x	NOUN
ejpam-2662	67	44	)	)	PUNCT
ejpam-2662	67	45	∩	∩	PROPN
ejpam-2662	67	46	y	y	PROPN
ejpam-2662	67	47	�	�	PROPN
ejpam-2662	67	48	g	g	PROPN
ejpam-2662	67	49	m1	m1	PROPN
ejpam-2662	67	50	.	.	PUNCT
ejpam-2662	68	1	following	follow	VERB
ejpam-2662	68	2	this	this	PRON
ejpam-2662	68	3	,	,	PUNCT
ejpam-2662	68	4	we	we	PRON
ejpam-2662	68	5	have	have	VERB
ejpam-2662	68	6	m	m	NOUN
ejpam-2662	68	7	=	=	NOUN
ejpam-2662	68	8	m1	m1	NOUN
ejpam-2662	68	9	∩	∩	NOUN
ejpam-2662	68	10	(	(	PUNCT
ejpam-2662	68	11	u	u	NOUN
ejpam-2662	68	12	+	+	NOUN
ejpam-2662	68	13	x	x	X
ejpam-2662	68	14	)	)	PUNCT
ejpam-2662	69	1	+	+	CCONJ
ejpam-2662	69	2	y	y	PROPN
ejpam-2662	69	3	+	+	NUM
ejpam-2662	69	4	u	u	NOUN
ejpam-2662	69	5	+	+	NOUN
ejpam-2662	69	6	x	x	SYM
ejpam-2662	69	7	=	=	SYM
ejpam-2662	69	8	u	u	NOUN
ejpam-2662	69	9	+	+	NOUN
ejpam-2662	69	10	x	x	SYM
ejpam-2662	69	11	+	+	CCONJ
ejpam-2662	69	12	y	y	PROPN
ejpam-2662	69	13	and	and	CCONJ
ejpam-2662	69	14	u	u	PROPN
ejpam-2662	69	15	∩	∩	NOUN
ejpam-2662	69	16	(	(	PUNCT
ejpam-2662	69	17	x	x	SYM
ejpam-2662	69	18	+	+	NUM
ejpam-2662	69	19	y	y	PROPN
ejpam-2662	69	20	)	)	PUNCT
ejpam-2662	69	21	≤	≤	NUM
ejpam-2662	69	22	x	x	X
ejpam-2662	69	23	∩	∩	NOUN
ejpam-2662	69	24	(	(	PUNCT
ejpam-2662	69	25	u	u	NOUN
ejpam-2662	69	26	+	+	X
ejpam-2662	69	27	y	y	PROPN
ejpam-2662	69	28	)	)	PUNCT
ejpam-2662	70	1	+	+	CCONJ
ejpam-2662	70	2	y	y	PROPN
ejpam-2662	70	3	∩	∩	NOUN
ejpam-2662	70	4	(	(	PUNCT
ejpam-2662	70	5	u	u	NOUN
ejpam-2662	70	6	+	+	NOUN
ejpam-2662	70	7	x	x	NOUN
ejpam-2662	70	8	)	)	PUNCT
ejpam-2662	70	9	≤	≤	NUM
ejpam-2662	70	10	x	x	SYM
ejpam-2662	70	11	∩	∩	NOUN
ejpam-2662	70	12	(	(	PUNCT
ejpam-2662	70	13	m1	m1	PROPN
ejpam-2662	70	14	+	+	CCONJ
ejpam-2662	70	15	u	u	NOUN
ejpam-2662	70	16	)	)	PUNCT
ejpam-2662	70	17	+	+	CCONJ
ejpam-2662	70	18	y	y	PROPN
ejpam-2662	70	19	∩m1	∩m1	PROPN
ejpam-2662	70	20	∩	∩	PROPN
ejpam-2662	70	21	(	(	PUNCT
ejpam-2662	70	22	u	u	NOUN
ejpam-2662	70	23	+	+	X
ejpam-2662	70	24	x)	x)	PROPN
ejpam-2662	70	25	�	�	PROPN
ejpam-2662	70	26	g	g	NOUN
ejpam-2662	70	27	m.	m.	NOUN
ejpam-2662	70	28	hence	hence	ADV
ejpam-2662	70	29	x	x	PUNCT
ejpam-2662	71	1	+	+	CCONJ
ejpam-2662	71	2	y	y	NOUN
ejpam-2662	71	3	is	be	AUX
ejpam-2662	71	4	a	a	DET
ejpam-2662	71	5	weak	weak	ADJ
ejpam-2662	71	6	g	g	NOUN
ejpam-2662	71	7	-	-	PUNCT
ejpam-2662	71	8	supplement	supplement	NOUN
ejpam-2662	71	9	of	of	ADP
ejpam-2662	71	10	u	u	NOUN
ejpam-2662	71	11	in	in	ADP
ejpam-2662	71	12	m	m	PROPN
ejpam-2662	71	13	.	.	PUNCT
ejpam-2662	72	1	corollary	corollary	ADJ
ejpam-2662	72	2	3	3	X
ejpam-2662	72	3	.	.	PUNCT
ejpam-2662	73	1	let	let	VERB
ejpam-2662	73	2	m	m	PRON
ejpam-2662	73	3	be	be	AUX
ejpam-2662	73	4	an	an	DET
ejpam-2662	73	5	r	r	NOUN
ejpam-2662	73	6	-	-	PUNCT
ejpam-2662	73	7	module	module	NOUN
ejpam-2662	73	8	u	u	NOUN
ejpam-2662	73	9	≤	≤	X
ejpam-2662	73	10	m	m	PROPN
ejpam-2662	73	11	and	and	CCONJ
ejpam-2662	73	12	mi	mi	PROPN
ejpam-2662	73	13	≤	≤	PROPN
ejpam-2662	73	14	m	m	VERB
ejpam-2662	73	15	for	for	ADP
ejpam-2662	73	16	i	i	PROPN
ejpam-2662	73	17	=	=	SYM
ejpam-2662	73	18	1	1	NUM
ejpam-2662	73	19	,	,	PUNCT
ejpam-2662	73	20	2	2	NUM
ejpam-2662	73	21	,	,	PUNCT
ejpam-2662	73	22	.	.	PUNCT
ejpam-2662	73	23	.	.	PUNCT
ejpam-2662	74	1	.	.	PUNCT
ejpam-2662	75	1	,	,	PUNCT
ejpam-2662	75	2	n.	n.	VERB
ejpam-2662	75	3	if	if	SCONJ
ejpam-2662	75	4	u	u	PROPN
ejpam-2662	75	5	+	+	NOUN
ejpam-2662	75	6	m1+m2	m1+m2	X
ejpam-2662	75	7	+	+	NOUN
ejpam-2662	75	8	.	.	PUNCT
ejpam-2662	75	9	.	.	PUNCT
ejpam-2662	76	1	.+mn	.+mn	PROPN
ejpam-2662	76	2	has	have	VERB
ejpam-2662	76	3	a	a	DET
ejpam-2662	76	4	weak	weak	ADJ
ejpam-2662	76	5	g	g	NOUN
ejpam-2662	76	6	-	-	PUNCT
ejpam-2662	76	7	supplement	supplement	NOUN
ejpam-2662	76	8	in	in	ADP
ejpam-2662	76	9	m	m	PROPN
ejpam-2662	76	10	and	and	CCONJ
ejpam-2662	76	11	mi	mi	PROPN
ejpam-2662	76	12	is	be	AUX
ejpam-2662	76	13	a	a	DET
ejpam-2662	76	14	weakly	weakly	ADJ
ejpam-2662	76	15	g	g	NOUN
ejpam-2662	76	16	-	-	PUNCT
ejpam-2662	76	17	supplemented	supplement	VERB
ejpam-2662	76	18	module	module	NOUN
ejpam-2662	76	19	for	for	ADP
ejpam-2662	76	20	every	every	DET
ejpam-2662	76	21	i	i	NOUN
ejpam-2662	76	22	=	=	NOUN
ejpam-2662	76	23	1	1	NUM
ejpam-2662	76	24	,	,	PUNCT
ejpam-2662	76	25	2	2	NUM
ejpam-2662	76	26	,	,	PUNCT
ejpam-2662	76	27	.	.	PUNCT
ejpam-2662	76	28	.	.	PUNCT
ejpam-2662	77	1	.	.	PUNCT
ejpam-2662	78	1	,	,	PUNCT
ejpam-2662	78	2	n	n	CCONJ
ejpam-2662	78	3	,	,	PUNCT
ejpam-2662	78	4	then	then	ADV
ejpam-2662	78	5	u	u	NOUN
ejpam-2662	78	6	has	have	VERB
ejpam-2662	78	7	a	a	DET
ejpam-2662	78	8	weak	weak	ADJ
ejpam-2662	78	9	g	g	NOUN
ejpam-2662	78	10	-	-	PUNCT
ejpam-2662	78	11	supplement	supplement	NOUN
ejpam-2662	78	12	in	in	ADP
ejpam-2662	78	13	m	m	PROPN
ejpam-2662	78	14	.	.	PUNCT
ejpam-2662	79	1	proof	proof	NOUN
ejpam-2662	79	2	.	.	PUNCT
ejpam-2662	80	1	clear	clear	ADJ
ejpam-2662	80	2	from	from	ADP
ejpam-2662	80	3	lemma	lemma	PROPN
ejpam-2662	80	4	5	5	NUM
ejpam-2662	80	5	.	.	PUNCT
ejpam-2662	81	1	lemma	lemma	PROPN
ejpam-2662	81	2	6	6	NUM
ejpam-2662	81	3	.	.	PUNCT
ejpam-2662	82	1	let	let	VERB
ejpam-2662	82	2	m	m	NOUN
ejpam-2662	82	3	=	=	VERB
ejpam-2662	82	4	m1	m1	PROPN
ejpam-2662	82	5	+	+	CCONJ
ejpam-2662	82	6	m2	m2	PROPN
ejpam-2662	82	7	.	.	PUNCT
ejpam-2662	83	1	if	if	SCONJ
ejpam-2662	83	2	m1	m1	PROPN
ejpam-2662	83	3	and	and	CCONJ
ejpam-2662	83	4	m2	m2	PROPN
ejpam-2662	83	5	are	be	AUX
ejpam-2662	83	6	weakly	weakly	ADJ
ejpam-2662	83	7	g	g	NOUN
ejpam-2662	83	8	-	-	PUNCT
ejpam-2662	83	9	supplemented	supplement	VERB
ejpam-2662	83	10	modules	module	NOUN
ejpam-2662	83	11	,	,	PUNCT
ejpam-2662	83	12	then	then	ADV
ejpam-2662	83	13	m	m	VERB
ejpam-2662	83	14	is	be	AUX
ejpam-2662	83	15	a	a	DET
ejpam-2662	83	16	weakly	weakly	ADJ
ejpam-2662	83	17	g	g	NOUN
ejpam-2662	83	18	-	-	PUNCT
ejpam-2662	83	19	supplemented	supplement	VERB
ejpam-2662	83	20	module	module	NOUN
ejpam-2662	83	21	.	.	PUNCT
ejpam-2662	84	1	proof	proof	NOUN
ejpam-2662	84	2	.	.	PUNCT
ejpam-2662	85	1	clear	clear	ADJ
ejpam-2662	85	2	from	from	ADP
ejpam-2662	85	3	lemma	lemma	PROPN
ejpam-2662	85	4	5	5	NUM
ejpam-2662	85	5	.	.	PUNCT
ejpam-2662	85	6	corollary	corollary	ADJ
ejpam-2662	85	7	4	4	NUM
ejpam-2662	85	8	.	.	PUNCT
ejpam-2662	86	1	a	a	DET
ejpam-2662	86	2	finite	finite	ADJ
ejpam-2662	86	3	sum	sum	NOUN
ejpam-2662	86	4	of	of	ADP
ejpam-2662	86	5	weakly	weakly	ADJ
ejpam-2662	86	6	g	g	NOUN
ejpam-2662	86	7	-	-	PUNCT
ejpam-2662	86	8	supplemented	supplement	VERB
ejpam-2662	86	9	modules	module	NOUN
ejpam-2662	86	10	is	be	AUX
ejpam-2662	86	11	weakly	weakly	ADJ
ejpam-2662	86	12	g	g	NOUN
ejpam-2662	86	13	-	-	PUNCT
ejpam-2662	86	14	supplemented	supplement	VERB
ejpam-2662	86	15	.	.	PUNCT
ejpam-2662	87	1	proof	proof	NOUN
ejpam-2662	87	2	.	.	PUNCT
ejpam-2662	88	1	clear	clear	ADJ
ejpam-2662	88	2	from	from	ADP
ejpam-2662	88	3	lemma	lemma	PROPN
ejpam-2662	88	4	6	6	NUM
ejpam-2662	88	5	.	.	PUNCT
ejpam-2662	89	1	lemma	lemma	PROPN
ejpam-2662	89	2	7	7	X
ejpam-2662	89	3	.	.	PUNCT
ejpam-2662	90	1	let	let	VERB
ejpam-2662	90	2	m	m	PRON
ejpam-2662	90	3	be	be	AUX
ejpam-2662	90	4	an	an	DET
ejpam-2662	90	5	r	r	NOUN
ejpam-2662	90	6	-	-	PUNCT
ejpam-2662	90	7	module	module	NOUN
ejpam-2662	90	8	,	,	PUNCT
ejpam-2662	90	9	x	x	SYM
ejpam-2662	90	10	≤	≤	NUM
ejpam-2662	90	11	u	u	NOUN
ejpam-2662	90	12	≤	≤	X
ejpam-2662	90	13	m	m	PROPN
ejpam-2662	90	14	and	and	CCONJ
ejpam-2662	90	15	v	v	PART
ejpam-2662	90	16	be	be	AUX
ejpam-2662	90	17	a	a	DET
ejpam-2662	90	18	weak	weak	ADJ
ejpam-2662	90	19	g	g	NOUN
ejpam-2662	90	20	-	-	PUNCT
ejpam-2662	90	21	supplement	supplement	NOUN
ejpam-2662	90	22	of	of	ADP
ejpam-2662	90	23	u	u	NOUN
ejpam-2662	90	24	in	in	ADP
ejpam-2662	90	25	m	m	PROPN
ejpam-2662	90	26	.	.	PUNCT
ejpam-2662	91	1	then	then	ADV
ejpam-2662	91	2	(	(	PUNCT
ejpam-2662	91	3	v	v	NOUN
ejpam-2662	91	4	+	+	NOUN
ejpam-2662	91	5	x	x	NOUN
ejpam-2662	91	6	)	)	PUNCT
ejpam-2662	91	7	/x	/x	PUNCT
ejpam-2662	91	8	is	be	AUX
ejpam-2662	91	9	a	a	DET
ejpam-2662	91	10	weak	weak	ADJ
ejpam-2662	91	11	g	g	NOUN
ejpam-2662	91	12	-	-	PUNCT
ejpam-2662	91	13	supplement	supplement	NOUN
ejpam-2662	91	14	of	of	ADP
ejpam-2662	91	15	u	u	NOUN
ejpam-2662	91	16	/	/	SYM
ejpam-2662	91	17	x	x	PROPN
ejpam-2662	91	18	in	in	ADP
ejpam-2662	91	19	m	m	PROPN
ejpam-2662	91	20	/	/	SYM
ejpam-2662	91	21	x.	x.	NOUN
ejpam-2662	91	22	proof	proof	NOUN
ejpam-2662	91	23	.	.	PUNCT
ejpam-2662	92	1	since	since	SCONJ
ejpam-2662	92	2	v	v	NOUN
ejpam-2662	92	3	is	be	AUX
ejpam-2662	92	4	a	a	DET
ejpam-2662	92	5	weak	weak	ADJ
ejpam-2662	92	6	g	g	NOUN
ejpam-2662	92	7	-	-	PUNCT
ejpam-2662	92	8	supplement	supplement	NOUN
ejpam-2662	92	9	of	of	ADP
ejpam-2662	92	10	u	u	NOUN
ejpam-2662	92	11	in	in	ADP
ejpam-2662	92	12	m	m	PROPN
ejpam-2662	92	13	,	,	PUNCT
ejpam-2662	92	14	we	we	PRON
ejpam-2662	92	15	have	have	VERB
ejpam-2662	92	16	m	m	NOUN
ejpam-2662	92	17	=	=	PUNCT
ejpam-2662	92	18	u+v	u+v	PROPN
ejpam-2662	92	19	and	and	CCONJ
ejpam-2662	92	20	u∩v	u∩v	PROPN
ejpam-2662	92	21	�	�	PROPN
ejpam-2662	92	22	g	g	PROPN
ejpam-2662	92	23	m	m	PROPN
ejpam-2662	92	24	.	.	PUNCT
ejpam-2662	93	1	thus	thus	ADV
ejpam-2662	93	2	(	(	PUNCT
ejpam-2662	93	3	u	u	NOUN
ejpam-2662	93	4	∩	∩	NOUN
ejpam-2662	93	5	v	v	ADP
ejpam-2662	93	6	+	+	NOUN
ejpam-2662	93	7	x	x	NOUN
ejpam-2662	93	8	)	)	PUNCT
ejpam-2662	93	9	/x	/x	PUNCT
ejpam-2662	94	1	�	�	PROPN
ejpam-2662	94	2	g	g	NOUN
ejpam-2662	94	3	m	m	PROPN
ejpam-2662	94	4	/	/	SYM
ejpam-2662	94	5	x	x	VERB
ejpam-2662	94	6	by	by	ADP
ejpam-2662	94	7	lemma	lemma	PROPN
ejpam-2662	94	8	1	1	NUM
ejpam-2662	94	9	.	.	PUNCT
ejpam-2662	95	1	since	since	SCONJ
ejpam-2662	95	2	m	m	PROPN
ejpam-2662	95	3	=	=	SYM
ejpam-2662	95	4	u	u	PROPN
ejpam-2662	95	5	+	+	X
ejpam-2662	95	6	v	v	NUM
ejpam-2662	95	7	,	,	PUNCT
ejpam-2662	95	8	it	it	PRON
ejpam-2662	95	9	is	be	AUX
ejpam-2662	95	10	easy	easy	ADJ
ejpam-2662	95	11	to	to	PART
ejpam-2662	95	12	see	see	VERB
ejpam-2662	95	13	that	that	PRON
ejpam-2662	95	14	m	m	VERB
ejpam-2662	95	15	x	x	X
ejpam-2662	95	16	=	=	PUNCT
ejpam-2662	95	17	u+v	u+v	NUM
ejpam-2662	95	18	x	x	PUNCT
ejpam-2662	95	19	=	=	SYM
ejpam-2662	95	20	u	u	NOUN
ejpam-2662	95	21	x	x	NOUN
ejpam-2662	95	22	+	+	NUM
ejpam-2662	95	23	v+x	v+x	NOUN
ejpam-2662	95	24	x	x	X
ejpam-2662	95	25	and	and	CCONJ
ejpam-2662	95	26	u	u	NOUN
ejpam-2662	95	27	x	x	NOUN
ejpam-2662	95	28	∩	∩	ADJ
ejpam-2662	95	29	v+x	v+x	NOUN
ejpam-2662	95	30	x	x	X
ejpam-2662	96	1	=	=	SYM
ejpam-2662	96	2	u∩v+x	u∩v+x	NOUN
ejpam-2662	96	3	x	x	SYM
ejpam-2662	96	4	�	�	PROPN
ejpam-2662	96	5	g	g	NOUN
ejpam-2662	96	6	m	m	PROPN
ejpam-2662	96	7	x	x	NOUN
ejpam-2662	96	8	.	.	PUNCT
ejpam-2662	97	1	therefore	therefore	ADV
ejpam-2662	97	2	(	(	PUNCT
ejpam-2662	97	3	v	v	NOUN
ejpam-2662	97	4	+	+	NOUN
ejpam-2662	97	5	x	x	NOUN
ejpam-2662	97	6	)	)	PUNCT
ejpam-2662	97	7	/x	/x	PUNCT
ejpam-2662	97	8	is	be	AUX
ejpam-2662	97	9	a	a	DET
ejpam-2662	97	10	weak	weak	ADJ
ejpam-2662	97	11	g	g	NOUN
ejpam-2662	97	12	-	-	PUNCT
ejpam-2662	97	13	supplement	supplement	NOUN
ejpam-2662	97	14	of	of	ADP
ejpam-2662	97	15	u	u	NOUN
ejpam-2662	97	16	/	/	SYM
ejpam-2662	97	17	x	x	PROPN
ejpam-2662	97	18	in	in	ADP
ejpam-2662	97	19	m	m	PROPN
ejpam-2662	97	20	/	/	SYM
ejpam-2662	97	21	x.	x.	NOUN
ejpam-2662	97	22	theorem	theorem	VERB
ejpam-2662	97	23	8	8	NUM
ejpam-2662	97	24	.	.	PUNCT
ejpam-2662	98	1	if	if	SCONJ
ejpam-2662	98	2	m	m	NOUN
ejpam-2662	98	3	is	be	AUX
ejpam-2662	98	4	a	a	DET
ejpam-2662	98	5	weakly	weakly	ADJ
ejpam-2662	98	6	g	g	NOUN
ejpam-2662	98	7	-	-	PUNCT
ejpam-2662	98	8	supplemented	supplement	VERB
ejpam-2662	98	9	module	module	NOUN
ejpam-2662	98	10	,	,	PUNCT
ejpam-2662	98	11	then	then	ADV
ejpam-2662	98	12	every	every	DET
ejpam-2662	98	13	factor	factor	NOUN
ejpam-2662	98	14	module	module	NOUN
ejpam-2662	98	15	of	of	ADP
ejpam-2662	98	16	m	m	PROPN
ejpam-2662	98	17	is	be	AUX
ejpam-2662	98	18	weakly	weakly	ADJ
ejpam-2662	98	19	g	g	NOUN
ejpam-2662	98	20	-	-	PUNCT
ejpam-2662	98	21	supplemented	supplement	VERB
ejpam-2662	98	22	.	.	PUNCT
ejpam-2662	99	1	proof	proof	NOUN
ejpam-2662	99	2	.	.	PUNCT
ejpam-2662	100	1	clear	clear	ADJ
ejpam-2662	100	2	from	from	ADP
ejpam-2662	100	3	lemma	lemma	PROPN
ejpam-2662	100	4	7	7	NUM
ejpam-2662	100	5	.	.	PUNCT
ejpam-2662	100	6	corollary	corollary	ADJ
ejpam-2662	100	7	5	5	NUM
ejpam-2662	100	8	.	.	PUNCT
ejpam-2662	101	1	if	if	SCONJ
ejpam-2662	101	2	m	m	NOUN
ejpam-2662	101	3	is	be	AUX
ejpam-2662	101	4	a	a	DET
ejpam-2662	101	5	weakly	weakly	ADJ
ejpam-2662	101	6	g	g	NOUN
ejpam-2662	101	7	-	-	PUNCT
ejpam-2662	101	8	supplemented	supplement	VERB
ejpam-2662	101	9	module	module	NOUN
ejpam-2662	101	10	,	,	PUNCT
ejpam-2662	101	11	then	then	ADV
ejpam-2662	101	12	the	the	DET
ejpam-2662	101	13	homomorphic	homomorphic	ADJ
ejpam-2662	101	14	image	image	NOUN
ejpam-2662	101	15	of	of	ADP
ejpam-2662	101	16	m	m	NOUN
ejpam-2662	101	17	is	be	AUX
ejpam-2662	101	18	weakly	weakly	ADJ
ejpam-2662	101	19	g	g	NOUN
ejpam-2662	101	20	-	-	PUNCT
ejpam-2662	101	21	supplemented	supplement	VERB
ejpam-2662	101	22	.	.	PUNCT
ejpam-2662	102	1	definition	definition	NOUN
ejpam-2662	102	2	2	2	NUM
ejpam-2662	102	3	.	.	PUNCT
ejpam-2662	103	1	let	let	VERB
ejpam-2662	103	2	m	m	PRON
ejpam-2662	103	3	be	be	AUX
ejpam-2662	103	4	an	an	DET
ejpam-2662	103	5	r	r	NOUN
ejpam-2662	103	6	-	-	PUNCT
ejpam-2662	103	7	module	module	NOUN
ejpam-2662	103	8	.	.	PUNCT
ejpam-2662	104	1	if	if	SCONJ
ejpam-2662	104	2	m	m	NOUN
ejpam-2662	104	3	/	/	SYM
ejpam-2662	104	4	radgm	radgm	NOUN
ejpam-2662	104	5	is	be	AUX
ejpam-2662	104	6	semisimple	semisimple	ADJ
ejpam-2662	104	7	,	,	PUNCT
ejpam-2662	104	8	then	then	ADV
ejpam-2662	104	9	m	m	VERB
ejpam-2662	104	10	is	be	AUX
ejpam-2662	104	11	called	call	VERB
ejpam-2662	104	12	a	a	DET
ejpam-2662	104	13	g	g	NOUN
ejpam-2662	104	14	-	-	PUNCT
ejpam-2662	104	15	semilocal	semilocal	ADJ
ejpam-2662	104	16	module	module	NOUN
ejpam-2662	104	17	.	.	PUNCT
ejpam-2662	105	1	clearly	clearly	ADV
ejpam-2662	105	2	,	,	PUNCT
ejpam-2662	105	3	we	we	PRON
ejpam-2662	105	4	see	see	VERB
ejpam-2662	105	5	that	that	SCONJ
ejpam-2662	105	6	every	every	DET
ejpam-2662	105	7	semilocal	semilocal	ADJ
ejpam-2662	105	8	module	module	NOUN
ejpam-2662	105	9	is	be	AUX
ejpam-2662	105	10	g	g	NOUN
ejpam-2662	105	11	-	-	PUNCT
ejpam-2662	105	12	semilocal	semilocal	ADJ
ejpam-2662	105	13	.	.	PUNCT
ejpam-2662	106	1	lemma	lemma	PROPN
ejpam-2662	106	2	9	9	NUM
ejpam-2662	106	3	.	.	PUNCT
ejpam-2662	107	1	for	for	ADP
ejpam-2662	107	2	an	an	DET
ejpam-2662	107	3	r	r	NOUN
ejpam-2662	107	4	-	-	PUNCT
ejpam-2662	107	5	module	module	NOUN
ejpam-2662	107	6	m	m	NOUN
ejpam-2662	107	7	,	,	PUNCT
ejpam-2662	107	8	the	the	DET
ejpam-2662	107	9	following	follow	VERB
ejpam-2662	107	10	statements	statement	NOUN
ejpam-2662	107	11	are	be	AUX
ejpam-2662	107	12	equivalent	equivalent	ADJ
ejpam-2662	107	13	.	.	PUNCT
ejpam-2662	108	1	c.	c.	PROPN
ejpam-2662	108	2	nebiyev	nebiyev	PROPN
ejpam-2662	108	3	,	,	PUNCT
ejpam-2662	108	4	h.	h.	PROPN
ejpam-2662	108	5	ökten	ökten	PROPN
ejpam-2662	108	6	/	/	SYM
ejpam-2662	108	7	eur	eur	PROPN
ejpam-2662	108	8	.	.	PUNCT
ejpam-2662	109	1	j.	j.	PROPN
ejpam-2662	109	2	pure	pure	PROPN
ejpam-2662	109	3	appl	appl	PROPN
ejpam-2662	109	4	.	.	PROPN
ejpam-2662	109	5	math	math	PROPN
ejpam-2662	109	6	,	,	PUNCT
ejpam-2662	109	7	10	10	NUM
ejpam-2662	109	8	(	(	PUNCT
ejpam-2662	109	9	3	3	NUM
ejpam-2662	109	10	)	)	PUNCT
ejpam-2662	109	11	(	(	PUNCT
ejpam-2662	109	12	2017	2017	NUM
ejpam-2662	109	13	)	)	PUNCT
ejpam-2662	109	14	,	,	PUNCT
ejpam-2662	109	15	521	521	NUM
ejpam-2662	109	16	-	-	SYM
ejpam-2662	109	17	528	528	NUM
ejpam-2662	109	18	524	524	NUM
ejpam-2662	109	19	(	(	PUNCT
ejpam-2662	109	20	i	i	NOUN
ejpam-2662	109	21	)	)	PUNCT
ejpam-2662	109	22	m	m	VERB
ejpam-2662	109	23	is	be	AUX
ejpam-2662	109	24	g	g	NOUN
ejpam-2662	109	25	-	-	PUNCT
ejpam-2662	109	26	semilocal	semilocal	ADJ
ejpam-2662	109	27	.	.	PUNCT
ejpam-2662	110	1	(	(	PUNCT
ejpam-2662	110	2	ii	ii	NOUN
ejpam-2662	110	3	)	)	PUNCT
ejpam-2662	110	4	for	for	ADP
ejpam-2662	110	5	every	every	DET
ejpam-2662	110	6	u	u	NOUN
ejpam-2662	110	7	≤	≤	X
ejpam-2662	110	8	m	m	VERB
ejpam-2662	110	9	there	there	PRON
ejpam-2662	110	10	exists	exist	VERB
ejpam-2662	110	11	a	a	DET
ejpam-2662	110	12	submodule	submodule	NOUN
ejpam-2662	110	13	v	v	ADP
ejpam-2662	110	14	≤	≤	NUM
ejpam-2662	110	15	m	m	VERB
ejpam-2662	110	16	such	such	ADJ
ejpam-2662	110	17	that	that	SCONJ
ejpam-2662	110	18	u	u	PROPN
ejpam-2662	110	19	+	+	X
ejpam-2662	110	20	v	v	NOUN
ejpam-2662	110	21	=	=	SYM
ejpam-2662	110	22	m	m	ADJ
ejpam-2662	110	23	and	and	CCONJ
ejpam-2662	110	24	u	u	PROPN
ejpam-2662	110	25	∩	∩	NOUN
ejpam-2662	110	26	v	v	ADP
ejpam-2662	110	27	≤	≤	NUM
ejpam-2662	110	28	radgm	radgm	NOUN
ejpam-2662	110	29	.	.	PUNCT
ejpam-2662	111	1	(	(	PUNCT
ejpam-2662	111	2	iii	iii	X
ejpam-2662	111	3	)	)	PUNCT
ejpam-2662	111	4	there	there	PRON
ejpam-2662	111	5	exists	exist	VERB
ejpam-2662	111	6	a	a	DET
ejpam-2662	111	7	decomposition	decomposition	NOUN
ejpam-2662	111	8	m	m	NOUN
ejpam-2662	111	9	=	=	SYM
ejpam-2662	111	10	m1	m1	PROPN
ejpam-2662	111	11	⊕m2	⊕m2	NUM
ejpam-2662	111	12	such	such	ADJ
ejpam-2662	111	13	that	that	DET
ejpam-2662	111	14	m1	m1	PROPN
ejpam-2662	111	15	is	be	AUX
ejpam-2662	111	16	semisimple	semisimple	ADJ
ejpam-2662	111	17	,	,	PUNCT
ejpam-2662	111	18	radgm	radgm	NOUN
ejpam-2662	111	19	e	e	NOUN
ejpam-2662	111	20	m2	m2	PROPN
ejpam-2662	111	21	and	and	CCONJ
ejpam-2662	111	22	m2	m2	PROPN
ejpam-2662	111	23	/	/	SYM
ejpam-2662	111	24	radgm	radgm	NOUN
ejpam-2662	111	25	is	be	AUX
ejpam-2662	111	26	semisimple	semisimple	ADJ
ejpam-2662	111	27	.	.	PUNCT
ejpam-2662	112	1	proof	proof	NOUN
ejpam-2662	112	2	.	.	PUNCT
ejpam-2662	113	1	clear	clear	ADJ
ejpam-2662	113	2	from	from	ADP
ejpam-2662	113	3	[	[	X
ejpam-2662	113	4	2	2	NUM
ejpam-2662	113	5	,	,	PUNCT
ejpam-2662	113	6	proposition	proposition	NOUN
ejpam-2662	113	7	2.1	2.1	NUM
ejpam-2662	113	8	]	]	PUNCT
ejpam-2662	113	9	.	.	PUNCT
ejpam-2662	114	1	lemma	lemma	PROPN
ejpam-2662	114	2	10	10	NUM
ejpam-2662	114	3	.	.	PUNCT
ejpam-2662	115	1	any	any	DET
ejpam-2662	115	2	homomorphic	homomorphic	ADJ
ejpam-2662	115	3	image	image	NOUN
ejpam-2662	115	4	of	of	ADP
ejpam-2662	115	5	a	a	DET
ejpam-2662	115	6	g	g	NOUN
ejpam-2662	115	7	-	-	PUNCT
ejpam-2662	115	8	semilocal	semilocal	ADJ
ejpam-2662	115	9	module	module	NOUN
ejpam-2662	115	10	is	be	AUX
ejpam-2662	115	11	g	g	NOUN
ejpam-2662	115	12	-	-	PUNCT
ejpam-2662	115	13	semilocal	semilocal	ADJ
ejpam-2662	115	14	.	.	PUNCT
ejpam-2662	116	1	proof	proof	NOUN
ejpam-2662	116	2	.	.	PUNCT
ejpam-2662	117	1	let	let	VERB
ejpam-2662	117	2	m	m	PRON
ejpam-2662	117	3	and	and	CCONJ
ejpam-2662	117	4	n	n	ADV
ejpam-2662	117	5	be	be	VERB
ejpam-2662	117	6	r	r	NOUN
ejpam-2662	117	7	-	-	PUNCT
ejpam-2662	117	8	modules	module	NOUN
ejpam-2662	117	9	,	,	PUNCT
ejpam-2662	117	10	f	f	X
ejpam-2662	117	11	:	:	PUNCT
ejpam-2662	117	12	m	m	VERB
ejpam-2662	117	13	−→	−→	ADJ
ejpam-2662	117	14	n	n	AUX
ejpam-2662	117	15	be	be	AUX
ejpam-2662	117	16	an	an	DET
ejpam-2662	117	17	r	r	NOUN
ejpam-2662	117	18	-	-	PUNCT
ejpam-2662	117	19	module	module	NOUN
ejpam-2662	117	20	epimorphism	epimorphism	NOUN
ejpam-2662	117	21	and	and	CCONJ
ejpam-2662	117	22	m	m	AUX
ejpam-2662	117	23	be	be	AUX
ejpam-2662	117	24	g	g	NOUN
ejpam-2662	117	25	-	-	PUNCT
ejpam-2662	117	26	semilocal	semilocal	ADJ
ejpam-2662	117	27	.	.	PUNCT
ejpam-2662	118	1	since	since	SCONJ
ejpam-2662	118	2	m	m	PROPN
ejpam-2662	118	3	is	be	AUX
ejpam-2662	118	4	g	g	NOUN
ejpam-2662	118	5	-	-	PUNCT
ejpam-2662	118	6	semilocal	semilocal	ADJ
ejpam-2662	118	7	,	,	PUNCT
ejpam-2662	118	8	m	m	NOUN
ejpam-2662	118	9	/	/	SYM
ejpam-2662	118	10	radgm	radgm	NOUN
ejpam-2662	118	11	is	be	AUX
ejpam-2662	118	12	semisimple	semisimple	ADJ
ejpam-2662	118	13	.	.	PUNCT
ejpam-2662	119	1	let	let	VERB
ejpam-2662	119	2	ϕ	ϕ	NOUN
ejpam-2662	119	3	:	:	PUNCT
ejpam-2662	119	4	m	m	ADJ
ejpam-2662	119	5	/	/	SYM
ejpam-2662	119	6	radgm	radgm	VERB
ejpam-2662	119	7	−→	−→	NOUN
ejpam-2662	119	8	n	n	CCONJ
ejpam-2662	119	9	/	/	SYM
ejpam-2662	119	10	radgn	radgn	NOUN
ejpam-2662	119	11	,	,	PUNCT
ejpam-2662	119	12	x	x	PUNCT
ejpam-2662	120	1	+	+	CCONJ
ejpam-2662	120	2	radgm	radgm	VERB
ejpam-2662	120	3	−→	−→	NOUN
ejpam-2662	120	4	ϕ	ϕ	NOUN
ejpam-2662	120	5	(	(	PUNCT
ejpam-2662	120	6	x	x	SYM
ejpam-2662	120	7	+	+	NUM
ejpam-2662	120	8	radgm	radgm	NOUN
ejpam-2662	120	9	)	)	PUNCT
ejpam-2662	120	10	=	=	SYM
ejpam-2662	121	1	f	f	X
ejpam-2662	121	2	(	(	PUNCT
ejpam-2662	121	3	x	x	X
ejpam-2662	121	4	)	)	PUNCT
ejpam-2662	121	5	+	+	CCONJ
ejpam-2662	121	6	radgn	radgn	NOUN
ejpam-2662	121	7	be	be	AUX
ejpam-2662	121	8	a	a	DET
ejpam-2662	121	9	map	map	NOUN
ejpam-2662	121	10	.	.	PUNCT
ejpam-2662	122	1	it	it	PRON
ejpam-2662	122	2	easy	easy	ADJ
ejpam-2662	122	3	to	to	PART
ejpam-2662	122	4	check	check	VERB
ejpam-2662	122	5	that	that	PRON
ejpam-2662	122	6	ϕ	ϕ	NOUN
ejpam-2662	122	7	is	be	AUX
ejpam-2662	122	8	an	an	DET
ejpam-2662	122	9	r	r	NOUN
ejpam-2662	122	10	-	-	PUNCT
ejpam-2662	122	11	module	module	NOUN
ejpam-2662	122	12	epimorphism	epimorphism	NOUN
ejpam-2662	122	13	,	,	PUNCT
ejpam-2662	122	14	since	since	SCONJ
ejpam-2662	122	15	f	f	PROPN
ejpam-2662	122	16	(	(	PUNCT
ejpam-2662	122	17	radgm	radgm	NOUN
ejpam-2662	122	18	)	)	PUNCT
ejpam-2662	122	19	≤	≤	NOUN
ejpam-2662	122	20	radgn	radgn	NOUN
ejpam-2662	122	21	.	.	PUNCT
ejpam-2662	123	1	since	since	SCONJ
ejpam-2662	123	2	every	every	DET
ejpam-2662	123	3	homomorphic	homomorphic	ADJ
ejpam-2662	123	4	image	image	NOUN
ejpam-2662	123	5	of	of	ADP
ejpam-2662	123	6	a	a	DET
ejpam-2662	123	7	semisimple	semisimple	NOUN
ejpam-2662	123	8	module	module	NOUN
ejpam-2662	123	9	is	be	AUX
ejpam-2662	123	10	semisimple	semisimple	NOUN
ejpam-2662	123	11	,	,	PUNCT
ejpam-2662	123	12	n	n	CCONJ
ejpam-2662	123	13	/	/	SYM
ejpam-2662	123	14	radgn	radgn	NOUN
ejpam-2662	123	15	is	be	AUX
ejpam-2662	123	16	semisimple	semisimple	ADJ
ejpam-2662	123	17	.	.	PUNCT
ejpam-2662	124	1	hence	hence	ADV
ejpam-2662	124	2	n	n	ADV
ejpam-2662	124	3	is	be	AUX
ejpam-2662	124	4	g	g	NOUN
ejpam-2662	124	5	-	-	PUNCT
ejpam-2662	124	6	semilocal	semilocal	ADJ
ejpam-2662	124	7	.	.	PUNCT
ejpam-2662	125	1	lemma	lemma	PROPN
ejpam-2662	125	2	11	11	NUM
ejpam-2662	125	3	.	.	PUNCT
ejpam-2662	126	1	let	let	VERB
ejpam-2662	126	2	m	m	NOUN
ejpam-2662	126	3	=	=	VERB
ejpam-2662	126	4	m1	m1	PROPN
ejpam-2662	126	5	+	+	CCONJ
ejpam-2662	126	6	m2	m2	PROPN
ejpam-2662	126	7	.	.	PUNCT
ejpam-2662	127	1	if	if	SCONJ
ejpam-2662	127	2	m1	m1	PROPN
ejpam-2662	127	3	and	and	CCONJ
ejpam-2662	127	4	m2	m2	PROPN
ejpam-2662	127	5	are	be	AUX
ejpam-2662	127	6	g	g	NOUN
ejpam-2662	127	7	-	-	PUNCT
ejpam-2662	127	8	semilocal	semilocal	ADJ
ejpam-2662	127	9	,	,	PUNCT
ejpam-2662	127	10	then	then	ADV
ejpam-2662	127	11	m	m	PROPN
ejpam-2662	127	12	is	be	AUX
ejpam-2662	127	13	g	g	NOUN
ejpam-2662	127	14	-	-	PUNCT
ejpam-2662	127	15	semilocal	semilocal	ADJ
ejpam-2662	127	16	.	.	PUNCT
ejpam-2662	128	1	proof	proof	NOUN
ejpam-2662	128	2	.	.	PUNCT
ejpam-2662	129	1	since	since	SCONJ
ejpam-2662	129	2	m1	m1	PROPN
ejpam-2662	129	3	and	and	CCONJ
ejpam-2662	129	4	m2	m2	PROPN
ejpam-2662	129	5	are	be	AUX
ejpam-2662	129	6	g	g	NOUN
ejpam-2662	129	7	-	-	PUNCT
ejpam-2662	129	8	semilocal	semilocal	ADJ
ejpam-2662	129	9	,	,	PUNCT
ejpam-2662	129	10	m1	m1	NOUN
ejpam-2662	129	11	/	/	SYM
ejpam-2662	129	12	radgm1	radgm1	NOUN
ejpam-2662	129	13	and	and	CCONJ
ejpam-2662	129	14	m2	m2	PROPN
ejpam-2662	129	15	/	/	SYM
ejpam-2662	129	16	radgm2	radgm2	PROPN
ejpam-2662	129	17	are	be	AUX
ejpam-2662	129	18	semisimple	semisimple	ADJ
ejpam-2662	129	19	.	.	PUNCT
ejpam-2662	130	1	then	then	ADV
ejpam-2662	130	2	m1	m1	PROPN
ejpam-2662	130	3	radgm1	radgm1	NOUN
ejpam-2662	130	4	⊕	⊕	PROPN
ejpam-2662	131	1	m2	m2	PROPN
ejpam-2662	131	2	radgm2	radgm2	PROPN
ejpam-2662	131	3	is	be	AUX
ejpam-2662	131	4	semisimple	semisimple	ADJ
ejpam-2662	131	5	.	.	PUNCT
ejpam-2662	132	1	let	let	VERB
ejpam-2662	132	2	f	f	NOUN
ejpam-2662	132	3	:	:	PUNCT
ejpam-2662	133	1	m1	m1	PROPN
ejpam-2662	133	2	radgm1	radgm1	NOUN
ejpam-2662	133	3	⊕	⊕	PROPN
ejpam-2662	133	4	m2	m2	PROPN
ejpam-2662	134	1	radgm2	radgm2	PROPN
ejpam-2662	134	2	−→	−→	NOUN
ejpam-2662	134	3	m	m	VERB
ejpam-2662	134	4	radgm	radgm	NOUN
ejpam-2662	134	5	,	,	PUNCT
ejpam-2662	134	6	(	(	PUNCT
ejpam-2662	134	7	x1	x1	PROPN
ejpam-2662	134	8	+	+	NUM
ejpam-2662	134	9	radgm1	radgm1	NOUN
ejpam-2662	134	10	,	,	PUNCT
ejpam-2662	134	11	x2	x2	PROPN
ejpam-2662	134	12	+	+	NUM
ejpam-2662	134	13	radgm2	radgm2	ADJ
ejpam-2662	134	14	)	)	PUNCT
ejpam-2662	135	1	−→	−→	NOUN
ejpam-2662	135	2	f	f	X
ejpam-2662	135	3	(	(	PUNCT
ejpam-2662	135	4	x1	x1	PROPN
ejpam-2662	135	5	+	+	NUM
ejpam-2662	135	6	radgm1	radgm1	NOUN
ejpam-2662	135	7	,	,	PUNCT
ejpam-2662	135	8	x2	x2	PROPN
ejpam-2662	135	9	+	+	NUM
ejpam-2662	135	10	radgm2	radgm2	PROPN
ejpam-2662	135	11	)	)	PUNCT
ejpam-2662	136	1	=	=	SYM
ejpam-2662	137	1	x1	x1	PROPN
ejpam-2662	138	1	+	+	NUM
ejpam-2662	138	2	x2	x2	NOUN
ejpam-2662	138	3	+	+	CCONJ
ejpam-2662	138	4	radgm	radgm	NOUN
ejpam-2662	138	5	be	be	VERB
ejpam-2662	138	6	a	a	DET
ejpam-2662	138	7	map	map	NOUN
ejpam-2662	138	8	.	.	PUNCT
ejpam-2662	139	1	it	it	PRON
ejpam-2662	139	2	is	be	AUX
ejpam-2662	139	3	easy	easy	ADJ
ejpam-2662	139	4	to	to	PART
ejpam-2662	139	5	check	check	VERB
ejpam-2662	139	6	that	that	SCONJ
ejpam-2662	139	7	f	f	PROPN
ejpam-2662	139	8	is	be	AUX
ejpam-2662	139	9	an	an	DET
ejpam-2662	139	10	r	r	NOUN
ejpam-2662	139	11	-	-	PUNCT
ejpam-2662	139	12	module	module	NOUN
ejpam-2662	139	13	epimorphism	epimorphism	NOUN
ejpam-2662	139	14	.	.	PUNCT
ejpam-2662	140	1	since	since	SCONJ
ejpam-2662	140	2	every	every	DET
ejpam-2662	140	3	homomorphic	homomorphic	ADJ
ejpam-2662	140	4	image	image	NOUN
ejpam-2662	140	5	of	of	ADP
ejpam-2662	140	6	a	a	DET
ejpam-2662	140	7	semisimple	semisimple	NOUN
ejpam-2662	140	8	module	module	NOUN
ejpam-2662	140	9	is	be	AUX
ejpam-2662	140	10	semisimple	semisimple	NOUN
ejpam-2662	140	11	,	,	PUNCT
ejpam-2662	140	12	m	m	ADJ
ejpam-2662	140	13	/	/	SYM
ejpam-2662	140	14	radgm	radgm	NOUN
ejpam-2662	140	15	is	be	AUX
ejpam-2662	140	16	semisimple	semisimple	ADJ
ejpam-2662	140	17	.	.	PUNCT
ejpam-2662	141	1	hence	hence	ADV
ejpam-2662	141	2	m	m	PROPN
ejpam-2662	141	3	is	be	AUX
ejpam-2662	141	4	g	g	NOUN
ejpam-2662	141	5	-	-	PUNCT
ejpam-2662	141	6	semilocal	semilocal	ADJ
ejpam-2662	141	7	.	.	PUNCT
ejpam-2662	142	1	corollary	corollary	ADJ
ejpam-2662	142	2	6	6	NUM
ejpam-2662	142	3	.	.	PUNCT
ejpam-2662	143	1	let	let	VERB
ejpam-2662	143	2	m	m	NOUN
ejpam-2662	143	3	=	=	VERB
ejpam-2662	143	4	m1	m1	PROPN
ejpam-2662	144	1	+	+	PROPN
ejpam-2662	144	2	m2	m2	PROPN
ejpam-2662	144	3	+	+	X
ejpam-2662	144	4	.	.	PUNCT
ejpam-2662	144	5	.	.	PUNCT
ejpam-2662	145	1	.+mn	.+mn	PROPN
ejpam-2662	145	2	.	.	PUNCT
ejpam-2662	146	1	if	if	SCONJ
ejpam-2662	146	2	mi	mi	PROPN
ejpam-2662	146	3	is	be	AUX
ejpam-2662	146	4	g	g	NOUN
ejpam-2662	146	5	-	-	PUNCT
ejpam-2662	146	6	semilocal	semilocal	ADJ
ejpam-2662	146	7	for	for	ADP
ejpam-2662	146	8	every	every	DET
ejpam-2662	146	9	i	i	NOUN
ejpam-2662	146	10	=	=	NOUN
ejpam-2662	146	11	1	1	NUM
ejpam-2662	146	12	,	,	PUNCT
ejpam-2662	146	13	2	2	NUM
ejpam-2662	146	14	,	,	PUNCT
ejpam-2662	146	15	.	.	PUNCT
ejpam-2662	147	1	.	.	PUNCT
ejpam-2662	148	1	.	.	PUNCT
ejpam-2662	149	1	,	,	PUNCT
ejpam-2662	149	2	n	n	CCONJ
ejpam-2662	149	3	,	,	PUNCT
ejpam-2662	149	4	then	then	ADV
ejpam-2662	149	5	m	m	VERB
ejpam-2662	149	6	is	be	AUX
ejpam-2662	149	7	g	g	NOUN
ejpam-2662	149	8	-	-	PUNCT
ejpam-2662	149	9	semilocal	semilocal	ADJ
ejpam-2662	149	10	.	.	PUNCT
ejpam-2662	150	1	proof	proof	NOUN
ejpam-2662	150	2	.	.	PUNCT
ejpam-2662	151	1	clear	clear	ADJ
ejpam-2662	151	2	from	from	ADP
ejpam-2662	151	3	lemma	lemma	PROPN
ejpam-2662	151	4	11	11	NUM
ejpam-2662	151	5	.	.	PUNCT
ejpam-2662	152	1	lemma	lemma	PROPN
ejpam-2662	152	2	12	12	NUM
ejpam-2662	152	3	.	.	PUNCT
ejpam-2662	153	1	if	if	SCONJ
ejpam-2662	153	2	m	m	NOUN
ejpam-2662	153	3	is	be	AUX
ejpam-2662	153	4	a	a	DET
ejpam-2662	153	5	weakly	weakly	ADJ
ejpam-2662	153	6	g	g	NOUN
ejpam-2662	153	7	-	-	PUNCT
ejpam-2662	153	8	supplemented	supplement	VERB
ejpam-2662	153	9	module	module	NOUN
ejpam-2662	153	10	,	,	PUNCT
ejpam-2662	153	11	then	then	ADV
ejpam-2662	153	12	m	m	PROPN
ejpam-2662	153	13	is	be	AUX
ejpam-2662	153	14	g	g	NOUN
ejpam-2662	153	15	-	-	PUNCT
ejpam-2662	153	16	semilocal	semilocal	ADJ
ejpam-2662	153	17	.	.	PUNCT
ejpam-2662	154	1	proof	proof	NOUN
ejpam-2662	154	2	.	.	PUNCT
ejpam-2662	155	1	let	let	VERB
ejpam-2662	155	2	u	u	PRON
ejpam-2662	155	3	/	/	SYM
ejpam-2662	155	4	radgm	radgm	NOUN
ejpam-2662	155	5	be	be	VERB
ejpam-2662	155	6	any	any	DET
ejpam-2662	155	7	submodule	submodule	NOUN
ejpam-2662	155	8	of	of	ADP
ejpam-2662	155	9	m	m	NOUN
ejpam-2662	155	10	/	/	SYM
ejpam-2662	155	11	radgm	radgm	NOUN
ejpam-2662	155	12	.	.	PUNCT
ejpam-2662	156	1	since	since	SCONJ
ejpam-2662	156	2	m	m	PROPN
ejpam-2662	156	3	is	be	AUX
ejpam-2662	156	4	weakly	weakly	ADJ
ejpam-2662	156	5	g	g	NOUN
ejpam-2662	156	6	-	-	PUNCT
ejpam-2662	156	7	supplemented	supplement	VERB
ejpam-2662	156	8	,	,	PUNCT
ejpam-2662	156	9	there	there	PRON
ejpam-2662	156	10	exists	exist	VERB
ejpam-2662	156	11	a	a	DET
ejpam-2662	156	12	submodule	submodule	NOUN
ejpam-2662	156	13	v	v	NOUN
ejpam-2662	156	14	of	of	ADP
ejpam-2662	156	15	m	m	PRON
ejpam-2662	156	16	such	such	ADJ
ejpam-2662	156	17	that	that	SCONJ
ejpam-2662	156	18	m	m	VERB
ejpam-2662	156	19	=	=	SYM
ejpam-2662	156	20	u	u	NOUN
ejpam-2662	156	21	+	+	NOUN
ejpam-2662	156	22	v	v	NOUN
ejpam-2662	156	23	and	and	CCONJ
ejpam-2662	156	24	u	u	NOUN
ejpam-2662	156	25	∩v	∩v	PROPN
ejpam-2662	156	26	�	�	PROPN
ejpam-2662	156	27	g	g	NOUN
ejpam-2662	156	28	m	m	PROPN
ejpam-2662	156	29	.	.	PUNCT
ejpam-2662	157	1	since	since	SCONJ
ejpam-2662	157	2	u	u	PROPN
ejpam-2662	157	3	∩v	∩v	PROPN
ejpam-2662	157	4	�	�	PROPN
ejpam-2662	157	5	g	g	NOUN
ejpam-2662	157	6	m	m	PROPN
ejpam-2662	157	7	,	,	PUNCT
ejpam-2662	157	8	then	then	ADV
ejpam-2662	157	9	by	by	ADP
ejpam-2662	157	10	lemma	lemma	PROPN
ejpam-2662	157	11	2	2	NUM
ejpam-2662	157	12	,	,	PUNCT
ejpam-2662	157	13	u	u	NOUN
ejpam-2662	157	14	∩	∩	NOUN
ejpam-2662	157	15	v	v	ADP
ejpam-2662	157	16	≤	≤	NUM
ejpam-2662	157	17	radgm	radgm	NOUN
ejpam-2662	157	18	.	.	PUNCT
ejpam-2662	158	1	then	then	ADV
ejpam-2662	158	2	by	by	ADP
ejpam-2662	158	3	m	m	NOUN
ejpam-2662	158	4	radgm	radgm	NOUN
ejpam-2662	158	5	=	=	SYM
ejpam-2662	158	6	u+v	u+v	NUM
ejpam-2662	158	7	radgm	radgm	NOUN
ejpam-2662	158	8	=	=	SYM
ejpam-2662	158	9	u	u	NOUN
ejpam-2662	158	10	radgm	radgm	NOUN
ejpam-2662	158	11	+	+	CCONJ
ejpam-2662	158	12	v+radgm	v+radgm	CCONJ
ejpam-2662	158	13	radgm	radgm	NOUN
ejpam-2662	158	14	and	and	CCONJ
ejpam-2662	158	15	u	u	NOUN
ejpam-2662	158	16	radgm	radgm	NOUN
ejpam-2662	158	17	∩v	∩v	NOUN
ejpam-2662	159	1	+	+	CCONJ
ejpam-2662	159	2	radgm	radgm	NOUN
ejpam-2662	159	3	radgm	radgm	NOUN
ejpam-2662	159	4	=	=	SYM
ejpam-2662	159	5	u	u	NOUN
ejpam-2662	159	6	∩	∩	NOUN
ejpam-2662	159	7	v	v	ADP
ejpam-2662	159	8	+	+	NUM
ejpam-2662	159	9	radgm	radgm	NOUN
ejpam-2662	159	10	radgm	radgm	NOUN
ejpam-2662	159	11	=	=	NOUN
ejpam-2662	159	12	radgm	radgm	NOUN
ejpam-2662	159	13	radgm	radgm	NOUN
ejpam-2662	159	14	=	=	SYM
ejpam-2662	159	15	0	0	NUM
ejpam-2662	159	16	,	,	PUNCT
ejpam-2662	159	17	m	m	VERB
ejpam-2662	159	18	radgm	radgm	NOUN
ejpam-2662	159	19	=	=	SYM
ejpam-2662	159	20	u	u	NOUN
ejpam-2662	159	21	radgm	radgm	VERB
ejpam-2662	159	22	⊕v	⊕v	NOUN
ejpam-2662	159	23	+	+	CCONJ
ejpam-2662	159	24	radgm	radgm	NOUN
ejpam-2662	159	25	radgm	radgm	NOUN
ejpam-2662	159	26	.	.	PUNCT
ejpam-2662	160	1	hence	hence	ADV
ejpam-2662	160	2	m	m	PROPN
ejpam-2662	160	3	is	be	AUX
ejpam-2662	160	4	g	g	NOUN
ejpam-2662	160	5	-	-	PUNCT
ejpam-2662	160	6	semilocal	semilocal	ADJ
ejpam-2662	160	7	.	.	PUNCT
ejpam-2662	161	1	c.	c.	PROPN
ejpam-2662	161	2	nebiyev	nebiyev	PROPN
ejpam-2662	161	3	,	,	PUNCT
ejpam-2662	161	4	h.	h.	PROPN
ejpam-2662	161	5	ökten	ökten	PROPN
ejpam-2662	161	6	/	/	SYM
ejpam-2662	161	7	eur	eur	PROPN
ejpam-2662	161	8	.	.	PUNCT
ejpam-2662	162	1	j.	j.	PROPN
ejpam-2662	162	2	pure	pure	PROPN
ejpam-2662	162	3	appl	appl	PROPN
ejpam-2662	162	4	.	.	PROPN
ejpam-2662	162	5	math	math	PROPN
ejpam-2662	162	6	,	,	PUNCT
ejpam-2662	162	7	10	10	NUM
ejpam-2662	162	8	(	(	PUNCT
ejpam-2662	162	9	3	3	NUM
ejpam-2662	162	10	)	)	PUNCT
ejpam-2662	162	11	(	(	PUNCT
ejpam-2662	162	12	2017	2017	NUM
ejpam-2662	162	13	)	)	PUNCT
ejpam-2662	162	14	,	,	PUNCT
ejpam-2662	162	15	521	521	NUM
ejpam-2662	162	16	-	-	SYM
ejpam-2662	162	17	528	528	NUM
ejpam-2662	162	18	525	525	NUM
ejpam-2662	162	19	lemma	lemma	PROPN
ejpam-2662	162	20	13	13	NUM
ejpam-2662	162	21	.	.	PUNCT
ejpam-2662	163	1	assume	assume	VERB
ejpam-2662	163	2	m	m	PRON
ejpam-2662	163	3	be	be	AUX
ejpam-2662	163	4	an	an	DET
ejpam-2662	163	5	r	r	NOUN
ejpam-2662	163	6	-	-	PUNCT
ejpam-2662	163	7	module	module	NOUN
ejpam-2662	163	8	and	and	CCONJ
ejpam-2662	163	9	radgm	radgm	NOUN
ejpam-2662	163	10	�	�	NOUN
ejpam-2662	163	11	g	g	NOUN
ejpam-2662	163	12	m	m	NOUN
ejpam-2662	163	13	.	.	PUNCT
ejpam-2662	164	1	if	if	SCONJ
ejpam-2662	164	2	m	m	NOUN
ejpam-2662	164	3	is	be	AUX
ejpam-2662	164	4	g	g	NOUN
ejpam-2662	164	5	-	-	PUNCT
ejpam-2662	164	6	semilocal	semilocal	ADJ
ejpam-2662	164	7	,	,	PUNCT
ejpam-2662	164	8	then	then	ADV
ejpam-2662	164	9	m	m	VERB
ejpam-2662	164	10	is	be	AUX
ejpam-2662	164	11	weakly	weakly	ADJ
ejpam-2662	164	12	g	g	NOUN
ejpam-2662	164	13	-	-	PUNCT
ejpam-2662	164	14	supplemented	supplement	VERB
ejpam-2662	164	15	.	.	PUNCT
ejpam-2662	165	1	proof	proof	NOUN
ejpam-2662	165	2	.	.	PUNCT
ejpam-2662	166	1	let	let	VERB
ejpam-2662	166	2	u	u	PRON
ejpam-2662	166	3	be	be	AUX
ejpam-2662	166	4	any	any	DET
ejpam-2662	166	5	submodule	submodule	NOUN
ejpam-2662	166	6	of	of	ADP
ejpam-2662	166	7	m	m	PROPN
ejpam-2662	166	8	.	.	PUNCT
ejpam-2662	167	1	since	since	SCONJ
ejpam-2662	167	2	m	m	PROPN
ejpam-2662	167	3	is	be	AUX
ejpam-2662	167	4	g	g	NOUN
ejpam-2662	167	5	-	-	PUNCT
ejpam-2662	167	6	semilocal	semilocal	ADJ
ejpam-2662	167	7	,	,	PUNCT
ejpam-2662	167	8	(	(	PUNCT
ejpam-2662	167	9	u	u	NOUN
ejpam-2662	167	10	+	+	X
ejpam-2662	167	11	radgm	radgm	NOUN
ejpam-2662	167	12	)	)	PUNCT
ejpam-2662	167	13	/radgm	/radgm	PRON
ejpam-2662	167	14	is	be	AUX
ejpam-2662	167	15	a	a	DET
ejpam-2662	167	16	direct	direct	ADJ
ejpam-2662	167	17	summand	summand	NOUN
ejpam-2662	167	18	of	of	ADP
ejpam-2662	167	19	m	m	NOUN
ejpam-2662	167	20	/	/	SYM
ejpam-2662	167	21	radgm	radgm	NOUN
ejpam-2662	167	22	.	.	PUNCT
ejpam-2662	168	1	then	then	ADV
ejpam-2662	168	2	there	there	PRON
ejpam-2662	168	3	exists	exist	VERB
ejpam-2662	168	4	a	a	DET
ejpam-2662	168	5	submodule	submodule	NOUN
ejpam-2662	168	6	v	v	NOUN
ejpam-2662	168	7	of	of	ADP
ejpam-2662	168	8	m	m	PRON
ejpam-2662	168	9	such	such	ADJ
ejpam-2662	168	10	that	that	DET
ejpam-2662	168	11	radgm	radgm	VERB
ejpam-2662	168	12	≤	≤	NUM
ejpam-2662	168	13	v	v	NOUN
ejpam-2662	168	14	and	and	CCONJ
ejpam-2662	168	15	m	m	VERB
ejpam-2662	168	16	radgm	radgm	NOUN
ejpam-2662	169	1	=	=	SYM
ejpam-2662	169	2	u+radgm	u+radgm	PRON
ejpam-2662	169	3	radgm	radgm	VERB
ejpam-2662	169	4	⊕	⊕	NOUN
ejpam-2662	169	5	v	v	ADP
ejpam-2662	169	6	radgm	radgm	NOUN
ejpam-2662	169	7	.	.	PUNCT
ejpam-2662	170	1	by	by	ADP
ejpam-2662	170	2	m	m	NOUN
ejpam-2662	170	3	radgm	radgm	NOUN
ejpam-2662	171	1	=	=	SYM
ejpam-2662	171	2	u+radgm	u+radgm	PRON
ejpam-2662	171	3	radgm	radgm	VERB
ejpam-2662	171	4	⊕	⊕	NOUN
ejpam-2662	171	5	v	v	ADP
ejpam-2662	171	6	radgm	radgm	NOUN
ejpam-2662	171	7	=	=	SYM
ejpam-2662	171	8	u+v	u+v	NUM
ejpam-2662	171	9	radgm	radgm	NOUN
ejpam-2662	171	10	,	,	PUNCT
ejpam-2662	171	11	m	m	VERB
ejpam-2662	171	12	=	=	SYM
ejpam-2662	171	13	u	u	PROPN
ejpam-2662	171	14	+	+	NOUN
ejpam-2662	171	15	v	v	NOUN
ejpam-2662	171	16	.	.	PUNCT
ejpam-2662	172	1	since	since	SCONJ
ejpam-2662	172	2	u	u	NOUN
ejpam-2662	172	3	∩	∩	NOUN
ejpam-2662	172	4	v	v	ADP
ejpam-2662	172	5	+	+	NUM
ejpam-2662	172	6	radgm	radgm	NOUN
ejpam-2662	172	7	radgm	radgm	NOUN
ejpam-2662	172	8	=	=	SYM
ejpam-2662	172	9	u	u	SYM
ejpam-2662	172	10	+	+	NOUN
ejpam-2662	172	11	radgm	radgm	NOUN
ejpam-2662	172	12	radgm	radgm	NOUN
ejpam-2662	172	13	∩	∩	NOUN
ejpam-2662	172	14	v	v	NOUN
ejpam-2662	172	15	radgm	radgm	NOUN
ejpam-2662	172	16	=	=	SYM
ejpam-2662	172	17	0	0	NUM
ejpam-2662	172	18	,	,	PUNCT
ejpam-2662	172	19	u	u	NOUN
ejpam-2662	172	20	∩	∩	NOUN
ejpam-2662	172	21	v	v	ADP
ejpam-2662	172	22	≤	≤	NUM
ejpam-2662	172	23	radgm	radgm	NOUN
ejpam-2662	172	24	�	�	PROPN
ejpam-2662	172	25	g	g	NOUN
ejpam-2662	172	26	m.	m.	NOUN
ejpam-2662	172	27	hence	hence	ADV
ejpam-2662	172	28	v	v	NOUN
ejpam-2662	172	29	is	be	AUX
ejpam-2662	172	30	a	a	DET
ejpam-2662	172	31	weak	weak	ADJ
ejpam-2662	172	32	g	g	NOUN
ejpam-2662	172	33	-	-	PUNCT
ejpam-2662	172	34	supplement	supplement	NOUN
ejpam-2662	172	35	of	of	ADP
ejpam-2662	172	36	u	u	NOUN
ejpam-2662	172	37	in	in	ADP
ejpam-2662	172	38	m	m	PROPN
ejpam-2662	172	39	.	.	PUNCT
ejpam-2662	173	1	corollary	corollary	ADJ
ejpam-2662	173	2	7	7	NUM
ejpam-2662	173	3	.	.	PUNCT
ejpam-2662	174	1	assume	assume	VERB
ejpam-2662	174	2	m	m	PRON
ejpam-2662	174	3	be	be	AUX
ejpam-2662	174	4	an	an	DET
ejpam-2662	174	5	r	r	NOUN
ejpam-2662	174	6	-	-	PUNCT
ejpam-2662	174	7	module	module	NOUN
ejpam-2662	174	8	with	with	ADP
ejpam-2662	174	9	radgm	radgm	NOUN
ejpam-2662	174	10	�	�	PROPN
ejpam-2662	174	11	g	g	NOUN
ejpam-2662	174	12	m	m	NOUN
ejpam-2662	174	13	.	.	PUNCT
ejpam-2662	175	1	then	then	ADV
ejpam-2662	175	2	m	m	PROPN
ejpam-2662	175	3	is	be	AUX
ejpam-2662	175	4	weakly	weakly	ADV
ejpam-2662	175	5	gsupplemented	gsupplemente	VERB
ejpam-2662	175	6	if	if	SCONJ
ejpam-2662	175	7	and	and	CCONJ
ejpam-2662	175	8	only	only	ADV
ejpam-2662	175	9	if	if	SCONJ
ejpam-2662	175	10	m	m	NOUN
ejpam-2662	175	11	is	be	AUX
ejpam-2662	175	12	g	g	NOUN
ejpam-2662	175	13	-	-	PUNCT
ejpam-2662	175	14	semilocal	semilocal	ADJ
ejpam-2662	175	15	.	.	PUNCT
ejpam-2662	176	1	proof	proof	NOUN
ejpam-2662	176	2	.	.	PUNCT
ejpam-2662	177	1	clear	clear	ADJ
ejpam-2662	177	2	from	from	ADP
ejpam-2662	177	3	lemma	lemma	PROPN
ejpam-2662	177	4	12	12	NUM
ejpam-2662	177	5	and	and	CCONJ
ejpam-2662	177	6	lemma	lemma	PROPN
ejpam-2662	177	7	13	13	NUM
ejpam-2662	177	8	.	.	PUNCT
ejpam-2662	178	1	lemma	lemma	PROPN
ejpam-2662	178	2	14	14	NUM
ejpam-2662	178	3	.	.	PUNCT
ejpam-2662	179	1	let	let	VERB
ejpam-2662	179	2	m	m	PRON
ejpam-2662	179	3	be	be	AUX
ejpam-2662	179	4	a	a	DET
ejpam-2662	179	5	finitely	finitely	ADV
ejpam-2662	179	6	generated	generate	VERB
ejpam-2662	179	7	r	r	NOUN
ejpam-2662	179	8	-	-	PUNCT
ejpam-2662	179	9	module	module	NOUN
ejpam-2662	179	10	.	.	PUNCT
ejpam-2662	180	1	then	then	ADV
ejpam-2662	180	2	radgm	radgm	VERB
ejpam-2662	180	3	�	�	PROPN
ejpam-2662	180	4	g	g	NOUN
ejpam-2662	180	5	m	m	NOUN
ejpam-2662	180	6	.	.	PUNCT
ejpam-2662	181	1	proof	proof	NOUN
ejpam-2662	181	2	.	.	PUNCT
ejpam-2662	182	1	if	if	SCONJ
ejpam-2662	182	2	m	m	NOUN
ejpam-2662	182	3	has	have	VERB
ejpam-2662	182	4	at	at	ADV
ejpam-2662	182	5	least	least	ADJ
ejpam-2662	182	6	one	one	NUM
ejpam-2662	182	7	proper	proper	ADJ
ejpam-2662	182	8	essential	essential	ADJ
ejpam-2662	182	9	submodule	submodule	NOUN
ejpam-2662	182	10	,	,	PUNCT
ejpam-2662	182	11	since	since	SCONJ
ejpam-2662	182	12	m	m	PROPN
ejpam-2662	182	13	is	be	AUX
ejpam-2662	182	14	finitely	finitely	ADV
ejpam-2662	182	15	generated	generate	VERB
ejpam-2662	182	16	,	,	PUNCT
ejpam-2662	182	17	by	by	ADP
ejpam-2662	182	18	lemma	lemma	PROPN
ejpam-2662	182	19	4	4	NUM
ejpam-2662	182	20	,	,	PUNCT
ejpam-2662	182	21	every	every	DET
ejpam-2662	182	22	proper	proper	ADJ
ejpam-2662	182	23	essential	essential	ADJ
ejpam-2662	182	24	submodule	submodule	NOUN
ejpam-2662	182	25	of	of	ADP
ejpam-2662	182	26	m	m	PROPN
ejpam-2662	182	27	is	be	AUX
ejpam-2662	182	28	contained	contain	VERB
ejpam-2662	182	29	in	in	ADP
ejpam-2662	182	30	a	a	DET
ejpam-2662	182	31	generalized	generalized	ADJ
ejpam-2662	182	32	maximal	maximal	ADJ
ejpam-2662	182	33	submodule	submodule	NOUN
ejpam-2662	182	34	of	of	ADP
ejpam-2662	182	35	m	m	PROPN
ejpam-2662	182	36	.	.	PUNCT
ejpam-2662	183	1	then	then	ADV
ejpam-2662	183	2	by	by	ADP
ejpam-2662	183	3	lemma	lemma	PROPN
ejpam-2662	183	4	3	3	NUM
ejpam-2662	183	5	,	,	PUNCT
ejpam-2662	183	6	radgm	radgm	NOUN
ejpam-2662	183	7	�	�	NOUN
ejpam-2662	183	8	g	g	NOUN
ejpam-2662	183	9	m	m	NOUN
ejpam-2662	183	10	.	.	PUNCT
ejpam-2662	184	1	if	if	SCONJ
ejpam-2662	184	2	m	m	NOUN
ejpam-2662	184	3	have	have	VERB
ejpam-2662	184	4	no	no	DET
ejpam-2662	184	5	proper	proper	ADJ
ejpam-2662	184	6	essential	essential	ADJ
ejpam-2662	184	7	submodules	submodule	NOUN
ejpam-2662	184	8	,	,	PUNCT
ejpam-2662	184	9	then	then	ADV
ejpam-2662	184	10	radgm	radgm	VERB
ejpam-2662	184	11	=	=	VERB
ejpam-2662	184	12	m	m	VERB
ejpam-2662	184	13	�	�	PROPN
ejpam-2662	184	14	g	g	PROPN
ejpam-2662	184	15	m	m	VERB
ejpam-2662	184	16	also	also	ADV
ejpam-2662	184	17	holds	hold	VERB
ejpam-2662	184	18	.	.	PUNCT
ejpam-2662	185	1	lemma	lemma	PROPN
ejpam-2662	185	2	15	15	NUM
ejpam-2662	185	3	.	.	PUNCT
ejpam-2662	186	1	let	let	VERB
ejpam-2662	186	2	m	m	PRON
ejpam-2662	186	3	be	be	AUX
ejpam-2662	186	4	a	a	DET
ejpam-2662	186	5	finitely	finitely	ADV
ejpam-2662	186	6	generated	generate	VERB
ejpam-2662	186	7	r	r	NOUN
ejpam-2662	186	8	-	-	PUNCT
ejpam-2662	186	9	module	module	NOUN
ejpam-2662	186	10	.	.	PUNCT
ejpam-2662	187	1	then	then	ADV
ejpam-2662	187	2	m	m	VERB
ejpam-2662	187	3	is	be	AUX
ejpam-2662	187	4	weakly	weakly	ADJ
ejpam-2662	187	5	g	g	NOUN
ejpam-2662	187	6	-	-	PUNCT
ejpam-2662	187	7	supplemented	supplement	VERB
ejpam-2662	187	8	if	if	SCONJ
ejpam-2662	187	9	and	and	CCONJ
ejpam-2662	187	10	only	only	ADV
ejpam-2662	187	11	if	if	SCONJ
ejpam-2662	187	12	m	m	NOUN
ejpam-2662	187	13	is	be	AUX
ejpam-2662	187	14	g	g	NOUN
ejpam-2662	187	15	-	-	PUNCT
ejpam-2662	187	16	semilocal	semilocal	ADJ
ejpam-2662	187	17	.	.	PUNCT
ejpam-2662	188	1	proof	proof	NOUN
ejpam-2662	188	2	.	.	PUNCT
ejpam-2662	189	1	by	by	ADP
ejpam-2662	189	2	lemma	lemma	PROPN
ejpam-2662	189	3	14	14	NUM
ejpam-2662	189	4	and	and	CCONJ
ejpam-2662	189	5	corollary	corollary	ADJ
ejpam-2662	189	6	7	7	NUM
ejpam-2662	189	7	,	,	PUNCT
ejpam-2662	189	8	this	this	PRON
ejpam-2662	189	9	is	be	AUX
ejpam-2662	189	10	clear	clear	ADJ
ejpam-2662	189	11	.	.	PUNCT
ejpam-2662	190	1	corollary	corollary	ADJ
ejpam-2662	190	2	8	8	NUM
ejpam-2662	190	3	.	.	PUNCT
ejpam-2662	191	1	rr	rr	PROPN
ejpam-2662	191	2	is	be	AUX
ejpam-2662	191	3	weakly	weakly	ADJ
ejpam-2662	191	4	g	g	NOUN
ejpam-2662	191	5	-	-	PUNCT
ejpam-2662	191	6	supplemented	supplement	VERB
ejpam-2662	191	7	if	if	SCONJ
ejpam-2662	191	8	and	and	CCONJ
ejpam-2662	191	9	only	only	ADV
ejpam-2662	191	10	if	if	SCONJ
ejpam-2662	191	11	rr	rr	PROPN
ejpam-2662	191	12	is	be	AUX
ejpam-2662	191	13	g	g	NOUN
ejpam-2662	191	14	-	-	PUNCT
ejpam-2662	191	15	semilocal	semilocal	ADJ
ejpam-2662	191	16	.	.	PUNCT
ejpam-2662	192	1	proof	proof	NOUN
ejpam-2662	192	2	.	.	PUNCT
ejpam-2662	193	1	by	by	ADP
ejpam-2662	193	2	lemma	lemma	PROPN
ejpam-2662	193	3	15	15	NUM
ejpam-2662	193	4	,	,	PUNCT
ejpam-2662	193	5	this	this	PRON
ejpam-2662	193	6	is	be	AUX
ejpam-2662	193	7	clear	clear	ADJ
ejpam-2662	193	8	.	.	PUNCT
ejpam-2662	194	1	proposition	proposition	NOUN
ejpam-2662	194	2	1	1	NUM
ejpam-2662	194	3	.	.	PUNCT
ejpam-2662	195	1	let	let	VERB
ejpam-2662	195	2	m	m	PRON
ejpam-2662	195	3	be	be	AUX
ejpam-2662	195	4	a	a	DET
ejpam-2662	195	5	weakly	weakly	ADJ
ejpam-2662	195	6	g	g	NOUN
ejpam-2662	195	7	-	-	PUNCT
ejpam-2662	195	8	supplemented	supplement	VERB
ejpam-2662	195	9	r	r	NOUN
ejpam-2662	195	10	-	-	PUNCT
ejpam-2662	195	11	module	module	NOUN
ejpam-2662	195	12	.	.	PUNCT
ejpam-2662	196	1	then	then	ADV
ejpam-2662	196	2	for	for	ADP
ejpam-2662	196	3	every	every	DET
ejpam-2662	196	4	u	u	NOUN
ejpam-2662	196	5	,	,	PUNCT
ejpam-2662	196	6	v	v	ADP
ejpam-2662	196	7	≤m	≤m	NOUN
ejpam-2662	196	8	with	with	ADP
ejpam-2662	196	9	m	m	PROPN
ejpam-2662	196	10	=	=	SYM
ejpam-2662	196	11	u	u	PROPN
ejpam-2662	197	1	+	+	X
ejpam-2662	197	2	v	v	NUM
ejpam-2662	197	3	,	,	PUNCT
ejpam-2662	197	4	there	there	PRON
ejpam-2662	197	5	exists	exist	VERB
ejpam-2662	197	6	a	a	DET
ejpam-2662	197	7	weak	weak	ADJ
ejpam-2662	197	8	g	g	NOUN
ejpam-2662	197	9	-	-	PUNCT
ejpam-2662	197	10	supplement	supplement	NOUN
ejpam-2662	197	11	k	k	NOUN
ejpam-2662	197	12	of	of	ADP
ejpam-2662	197	13	u	u	PROPN
ejpam-2662	197	14	in	in	ADP
ejpam-2662	197	15	m	m	PROPN
ejpam-2662	197	16	with	with	ADP
ejpam-2662	197	17	k	k	PROPN
ejpam-2662	197	18	≤	≤	PROPN
ejpam-2662	197	19	v	v	NOUN
ejpam-2662	197	20	.	.	PUNCT
ejpam-2662	198	1	proof	proof	NOUN
ejpam-2662	198	2	.	.	PUNCT
ejpam-2662	199	1	assume	assume	VERB
ejpam-2662	199	2	u	u	PROPN
ejpam-2662	199	3	,	,	PUNCT
ejpam-2662	199	4	v	v	ADP
ejpam-2662	199	5	≤m	≤m	NOUN
ejpam-2662	199	6	with	with	ADP
ejpam-2662	199	7	m	m	PROPN
ejpam-2662	199	8	=	=	SYM
ejpam-2662	199	9	u	u	NOUN
ejpam-2662	199	10	+	+	NOUN
ejpam-2662	199	11	v	v	NOUN
ejpam-2662	199	12	.	.	PUNCT
ejpam-2662	200	1	since	since	SCONJ
ejpam-2662	200	2	m	m	PROPN
ejpam-2662	200	3	is	be	AUX
ejpam-2662	200	4	weakly	weakly	ADJ
ejpam-2662	200	5	g	g	NOUN
ejpam-2662	200	6	-	-	PUNCT
ejpam-2662	200	7	supplemented	supplement	VERB
ejpam-2662	200	8	,	,	PUNCT
ejpam-2662	200	9	u	u	PROPN
ejpam-2662	200	10	∩v	∩v	NOUN
ejpam-2662	200	11	has	have	VERB
ejpam-2662	200	12	a	a	DET
ejpam-2662	200	13	weak	weak	ADJ
ejpam-2662	200	14	g	g	NOUN
ejpam-2662	200	15	-	-	PUNCT
ejpam-2662	200	16	supplement	supplement	NOUN
ejpam-2662	200	17	t	t	NOUN
ejpam-2662	200	18	in	in	ADP
ejpam-2662	200	19	m	m	PROPN
ejpam-2662	200	20	.	.	PUNCT
ejpam-2662	201	1	in	in	ADP
ejpam-2662	201	2	this	this	DET
ejpam-2662	201	3	case	case	NOUN
ejpam-2662	201	4	,	,	PUNCT
ejpam-2662	201	5	m	m	VERB
ejpam-2662	201	6	=	=	NOUN
ejpam-2662	201	7	u∩v	u∩v	PROPN
ejpam-2662	201	8	+	+	NOUN
ejpam-2662	201	9	t	t	NOUN
ejpam-2662	201	10	and	and	CCONJ
ejpam-2662	201	11	u∩v	u∩v	PROPN
ejpam-2662	201	12	∩t	∩t	PROPN
ejpam-2662	201	13	�	�	PROPN
ejpam-2662	201	14	g	g	PROPN
ejpam-2662	201	15	m	m	PROPN
ejpam-2662	201	16	.	.	PUNCT
ejpam-2662	202	1	since	since	SCONJ
ejpam-2662	202	2	m	m	PROPN
ejpam-2662	202	3	=	=	SYM
ejpam-2662	202	4	u	u	PROPN
ejpam-2662	202	5	+	+	NOUN
ejpam-2662	202	6	v	v	NOUN
ejpam-2662	202	7	=	=	SYM
ejpam-2662	202	8	u	u	NOUN
ejpam-2662	202	9	∩v	∩v	NOUN
ejpam-2662	203	1	+	+	NOUN
ejpam-2662	203	2	t	t	PROPN
ejpam-2662	203	3	,	,	PUNCT
ejpam-2662	203	4	m	m	VERB
ejpam-2662	203	5	=	=	SYM
ejpam-2662	203	6	u	u	NOUN
ejpam-2662	203	7	+	+	NOUN
ejpam-2662	203	8	v	v	NOUN
ejpam-2662	203	9	∩t	∩t	NOUN
ejpam-2662	203	10	.	.	PUNCT
ejpam-2662	204	1	let	let	VERB
ejpam-2662	204	2	k	k	NOUN
ejpam-2662	204	3	=	=	PUNCT
ejpam-2662	204	4	v	v	PROPN
ejpam-2662	204	5	∩t	∩t	NOUN
ejpam-2662	204	6	.	.	PUNCT
ejpam-2662	205	1	then	then	ADV
ejpam-2662	205	2	m	m	VERB
ejpam-2662	205	3	=	=	SYM
ejpam-2662	205	4	u	u	NOUN
ejpam-2662	205	5	+	+	NOUN
ejpam-2662	205	6	v	v	NOUN
ejpam-2662	205	7	∩t	∩t	NOUN
ejpam-2662	205	8	=	=	PUNCT
ejpam-2662	205	9	u	u	PROPN
ejpam-2662	206	1	+	+	PROPN
ejpam-2662	206	2	k	k	PROPN
ejpam-2662	206	3	and	and	CCONJ
ejpam-2662	206	4	u	u	PROPN
ejpam-2662	206	5	∩	∩	NOUN
ejpam-2662	206	6	k	k	PROPN
ejpam-2662	206	7	=	=	SYM
ejpam-2662	206	8	u	u	PROPN
ejpam-2662	206	9	∩	∩	NOUN
ejpam-2662	206	10	v	v	ADP
ejpam-2662	206	11	∩	∩	NOUN
ejpam-2662	206	12	t	t	PROPN
ejpam-2662	206	13	�	�	PROPN
ejpam-2662	206	14	g	g	PROPN
ejpam-2662	206	15	m	m	PROPN
ejpam-2662	206	16	.	.	PUNCT
ejpam-2662	207	1	hence	hence	ADV
ejpam-2662	207	2	k	k	PROPN
ejpam-2662	207	3	is	be	AUX
ejpam-2662	207	4	a	a	DET
ejpam-2662	207	5	weak	weak	ADJ
ejpam-2662	207	6	g	g	NOUN
ejpam-2662	207	7	-	-	PUNCT
ejpam-2662	207	8	supplement	supplement	NOUN
ejpam-2662	207	9	of	of	ADP
ejpam-2662	207	10	u	u	NOUN
ejpam-2662	207	11	in	in	ADP
ejpam-2662	207	12	m	m	PROPN
ejpam-2662	207	13	with	with	ADP
ejpam-2662	207	14	k	k	PROPN
ejpam-2662	207	15	≤	≤	PROPN
ejpam-2662	207	16	v	v	NOUN
ejpam-2662	207	17	.	.	PUNCT
ejpam-2662	207	18	example	example	NOUN
ejpam-2662	208	1	1	1	NUM
ejpam-2662	208	2	.	.	PUNCT
ejpam-2662	208	3	let	let	VERB
ejpam-2662	208	4	p	p	NOUN
ejpam-2662	208	5	and	and	CCONJ
ejpam-2662	208	6	q	q	NOUN
ejpam-2662	208	7	be	be	AUX
ejpam-2662	208	8	prime	prime	ADJ
ejpam-2662	208	9	numbers	number	NOUN
ejpam-2662	208	10	and	and	CCONJ
ejpam-2662	208	11	consider	consider	VERB
ejpam-2662	208	12	the	the	DET
ejpam-2662	208	13	ring	ring	NOUN
ejpam-2662	208	14	r	r	NOUN
ejpam-2662	208	15	=	=	SYM
ejpam-2662	208	16	zp	zp	PROPN
ejpam-2662	208	17	,	,	PUNCT
ejpam-2662	208	18	q	q	NOUN
ejpam-2662	208	19	=	=	X
ejpam-2662	208	20	{	{	PUNCT
ejpam-2662	208	21	a	a	DET
ejpam-2662	208	22	b	b	NOUN
ejpam-2662	209	1	|	|	ADV
ejpam-2662	209	2	a	a	NOUN
ejpam-2662	209	3	,	,	PUNCT
ejpam-2662	209	4	b	b	PROPN
ejpam-2662	209	5	∈	∈	PROPN
ejpam-2662	209	6	z	z	PROPN
ejpam-2662	209	7	,	,	PUNCT
ejpam-2662	209	8	b	b	PROPN
ejpam-2662	209	9	6=	6=	PROPN
ejpam-2662	209	10	0	0	NUM
ejpam-2662	209	11	,	,	PUNCT
ejpam-2662	209	12	p	p	NOUN
ejpam-2662	209	13	6	6	NUM
ejpam-2662	209	14	|b	|b	NOUN
ejpam-2662	209	15	and	and	CCONJ
ejpam-2662	209	16	q	q	PROPN
ejpam-2662	209	17	6	6	NUM
ejpam-2662	209	18	|b	|b	NOUN
ejpam-2662	209	19	}	}	PUNCT
ejpam-2662	209	20	.	.	PUNCT
ejpam-2662	210	1	by	by	ADP
ejpam-2662	210	2	[	[	X
ejpam-2662	210	3	2	2	NUM
ejpam-2662	210	4	,	,	PUNCT
ejpam-2662	210	5	remark	remark	VERB
ejpam-2662	210	6	3.3	3.3	NUM
ejpam-2662	210	7	]	]	PUNCT
ejpam-2662	210	8	,	,	PUNCT
ejpam-2662	210	9	rr	rr	PROPN
ejpam-2662	210	10	is	be	AUX
ejpam-2662	210	11	weakly	weakly	ADV
ejpam-2662	210	12	supplemented	supplement	VERB
ejpam-2662	210	13	but	but	CCONJ
ejpam-2662	210	14	not	not	PART
ejpam-2662	210	15	supplemented	supplement	VERB
ejpam-2662	210	16	.	.	PUNCT
ejpam-2662	211	1	since	since	SCONJ
ejpam-2662	211	2	every	every	DET
ejpam-2662	211	3	nonzero	nonzero	PROPN
ejpam-2662	211	4	submodule	submodule	PROPN
ejpam-2662	211	5	of	of	ADP
ejpam-2662	211	6	rr	rr	PROPN
ejpam-2662	211	7	is	be	AUX
ejpam-2662	211	8	essential	essential	ADJ
ejpam-2662	211	9	in	in	ADP
ejpam-2662	211	10	rr	rr	PROPN
ejpam-2662	211	11	,	,	PUNCT
ejpam-2662	211	12	rr	rr	PROPN
ejpam-2662	211	13	is	be	AUX
ejpam-2662	211	14	weakly	weakly	ADJ
ejpam-2662	211	15	g	g	NOUN
ejpam-2662	211	16	-	-	PUNCT
ejpam-2662	211	17	supplemented	supplemented	ADJ
ejpam-2662	211	18	but	but	CCONJ
ejpam-2662	211	19	not	not	PART
ejpam-2662	211	20	g	g	NOUN
ejpam-2662	211	21	-	-	PUNCT
ejpam-2662	211	22	supplemented	supplement	VERB
ejpam-2662	211	23	.	.	PUNCT
ejpam-2662	212	1	c.	c.	PROPN
ejpam-2662	212	2	nebiyev	nebiyev	PROPN
ejpam-2662	212	3	,	,	PUNCT
ejpam-2662	212	4	h.	h.	PROPN
ejpam-2662	212	5	ökten	ökten	PROPN
ejpam-2662	212	6	/	/	SYM
ejpam-2662	212	7	eur	eur	PROPN
ejpam-2662	212	8	.	.	PUNCT
ejpam-2662	213	1	j.	j.	PROPN
ejpam-2662	213	2	pure	pure	PROPN
ejpam-2662	213	3	appl	appl	PROPN
ejpam-2662	213	4	.	.	PROPN
ejpam-2662	213	5	math	math	PROPN
ejpam-2662	213	6	,	,	PUNCT
ejpam-2662	213	7	10	10	NUM
ejpam-2662	213	8	(	(	PUNCT
ejpam-2662	213	9	3	3	NUM
ejpam-2662	213	10	)	)	PUNCT
ejpam-2662	213	11	(	(	PUNCT
ejpam-2662	213	12	2017	2017	NUM
ejpam-2662	213	13	)	)	PUNCT
ejpam-2662	213	14	,	,	PUNCT
ejpam-2662	213	15	521	521	NUM
ejpam-2662	213	16	-	-	SYM
ejpam-2662	213	17	528	528	NUM
ejpam-2662	213	18	526	526	NUM
ejpam-2662	213	19	3	3	NUM
ejpam-2662	213	20	.	.	PUNCT
ejpam-2662	213	21	cofinitely	cofinitely	ADV
ejpam-2662	213	22	weak	weak	ADJ
ejpam-2662	213	23	g	g	NOUN
ejpam-2662	213	24	-	-	PUNCT
ejpam-2662	213	25	supplemented	supplement	VERB
ejpam-2662	213	26	modules	module	NOUN
ejpam-2662	213	27	definition	definition	NOUN
ejpam-2662	213	28	3	3	X
ejpam-2662	213	29	.	.	PUNCT
ejpam-2662	214	1	let	let	VERB
ejpam-2662	214	2	m	m	PRON
ejpam-2662	214	3	be	be	AUX
ejpam-2662	214	4	an	an	DET
ejpam-2662	214	5	r	r	NOUN
ejpam-2662	214	6	-	-	PUNCT
ejpam-2662	214	7	module	module	NOUN
ejpam-2662	214	8	.	.	PUNCT
ejpam-2662	215	1	if	if	SCONJ
ejpam-2662	215	2	every	every	DET
ejpam-2662	215	3	cofinite	cofinite	NOUN
ejpam-2662	215	4	submodule	submodule	NOUN
ejpam-2662	215	5	of	of	ADP
ejpam-2662	215	6	m	m	PROPN
ejpam-2662	215	7	has	have	VERB
ejpam-2662	215	8	a	a	DET
ejpam-2662	215	9	weak	weak	ADJ
ejpam-2662	215	10	g	g	NOUN
ejpam-2662	215	11	-	-	PUNCT
ejpam-2662	215	12	supplement	supplement	NOUN
ejpam-2662	215	13	in	in	ADP
ejpam-2662	215	14	m	m	PROPN
ejpam-2662	215	15	,	,	PUNCT
ejpam-2662	215	16	then	then	ADV
ejpam-2662	215	17	m	m	VERB
ejpam-2662	215	18	is	be	AUX
ejpam-2662	215	19	called	call	VERB
ejpam-2662	215	20	a	a	DET
ejpam-2662	215	21	cofinitely	cofinitely	ADV
ejpam-2662	215	22	weak	weak	ADJ
ejpam-2662	215	23	g	g	NOUN
ejpam-2662	215	24	-	-	PUNCT
ejpam-2662	215	25	supplemented	supplement	VERB
ejpam-2662	215	26	module	module	NOUN
ejpam-2662	215	27	.	.	PUNCT
ejpam-2662	216	1	clearly	clearly	ADV
ejpam-2662	216	2	we	we	PRON
ejpam-2662	216	3	see	see	VERB
ejpam-2662	216	4	that	that	SCONJ
ejpam-2662	216	5	every	every	DET
ejpam-2662	216	6	weakly	weakly	ADJ
ejpam-2662	216	7	g	g	NOUN
ejpam-2662	216	8	-	-	PUNCT
ejpam-2662	216	9	supplemented	supplement	VERB
ejpam-2662	216	10	module	module	NOUN
ejpam-2662	216	11	is	be	AUX
ejpam-2662	216	12	cofinitely	cofinitely	ADV
ejpam-2662	216	13	weak	weak	ADJ
ejpam-2662	216	14	gsupplemented	gsupplemente	VERB
ejpam-2662	216	15	.	.	PUNCT
ejpam-2662	217	1	lemma	lemma	PROPN
ejpam-2662	217	2	16	16	NUM
ejpam-2662	217	3	.	.	PUNCT
ejpam-2662	218	1	assume	assume	VERB
ejpam-2662	218	2	m	m	PRON
ejpam-2662	218	3	be	be	AUX
ejpam-2662	218	4	a	a	DET
ejpam-2662	218	5	finitely	finitely	ADV
ejpam-2662	218	6	generated	generate	VERB
ejpam-2662	218	7	r	r	NOUN
ejpam-2662	218	8	-	-	PUNCT
ejpam-2662	218	9	module	module	NOUN
ejpam-2662	218	10	.	.	PUNCT
ejpam-2662	219	1	if	if	SCONJ
ejpam-2662	219	2	m	m	NOUN
ejpam-2662	219	3	is	be	AUX
ejpam-2662	219	4	cofinitely	cofinitely	ADV
ejpam-2662	219	5	weak	weak	ADJ
ejpam-2662	219	6	gsupplemented	gsupplemente	VERB
ejpam-2662	219	7	,	,	PUNCT
ejpam-2662	219	8	then	then	ADV
ejpam-2662	219	9	m	m	VERB
ejpam-2662	219	10	is	be	AUX
ejpam-2662	219	11	weakly	weakly	ADJ
ejpam-2662	219	12	g	g	NOUN
ejpam-2662	219	13	-	-	PUNCT
ejpam-2662	219	14	supplemented	supplement	VERB
ejpam-2662	219	15	.	.	PUNCT
ejpam-2662	220	1	proof	proof	NOUN
ejpam-2662	220	2	.	.	PUNCT
ejpam-2662	221	1	clear	clear	ADJ
ejpam-2662	221	2	,	,	PUNCT
ejpam-2662	221	3	since	since	SCONJ
ejpam-2662	221	4	every	every	DET
ejpam-2662	221	5	submodule	submodule	NOUN
ejpam-2662	221	6	of	of	ADP
ejpam-2662	221	7	m	m	PROPN
ejpam-2662	221	8	is	be	AUX
ejpam-2662	221	9	cofinite	cofinite	VERB
ejpam-2662	221	10	.	.	PUNCT
ejpam-2662	222	1	lemma	lemma	PROPN
ejpam-2662	222	2	17	17	NUM
ejpam-2662	222	3	.	.	PUNCT
ejpam-2662	223	1	let	let	VERB
ejpam-2662	223	2	m	m	PRON
ejpam-2662	223	3	be	be	AUX
ejpam-2662	223	4	a	a	DET
ejpam-2662	223	5	cofinitely	cofinitely	ADV
ejpam-2662	223	6	weak	weak	ADJ
ejpam-2662	223	7	g	g	NOUN
ejpam-2662	223	8	-	-	PUNCT
ejpam-2662	223	9	supplemented	supplement	VERB
ejpam-2662	223	10	module	module	NOUN
ejpam-2662	223	11	.	.	PUNCT
ejpam-2662	224	1	then	then	ADV
ejpam-2662	224	2	every	every	DET
ejpam-2662	224	3	factor	factor	NOUN
ejpam-2662	224	4	module	module	NOUN
ejpam-2662	224	5	of	of	ADP
ejpam-2662	224	6	m	m	PROPN
ejpam-2662	224	7	is	be	AUX
ejpam-2662	224	8	cofinitely	cofinitely	ADV
ejpam-2662	224	9	weak	weak	ADJ
ejpam-2662	224	10	g	g	NOUN
ejpam-2662	224	11	-	-	PUNCT
ejpam-2662	224	12	supplemented	supplement	VERB
ejpam-2662	224	13	.	.	PUNCT
ejpam-2662	225	1	proof	proof	NOUN
ejpam-2662	225	2	.	.	PUNCT
ejpam-2662	226	1	let	let	VERB
ejpam-2662	226	2	m	m	PRON
ejpam-2662	226	3	/	/	SYM
ejpam-2662	226	4	x	x	VERB
ejpam-2662	226	5	be	be	VERB
ejpam-2662	226	6	any	any	DET
ejpam-2662	226	7	factor	factor	NOUN
ejpam-2662	226	8	module	module	NOUN
ejpam-2662	226	9	of	of	ADP
ejpam-2662	226	10	m	m	PROPN
ejpam-2662	226	11	and	and	CCONJ
ejpam-2662	226	12	u	u	NOUN
ejpam-2662	226	13	/	/	SYM
ejpam-2662	226	14	x	x	AUX
ejpam-2662	226	15	be	be	VERB
ejpam-2662	226	16	a	a	DET
ejpam-2662	226	17	cofinite	cofinite	NOUN
ejpam-2662	226	18	submodule	submodule	NOUN
ejpam-2662	226	19	of	of	ADP
ejpam-2662	226	20	m	m	PROPN
ejpam-2662	226	21	/	/	SYM
ejpam-2662	226	22	x.	x.	NOUN
ejpam-2662	226	23	since	since	SCONJ
ejpam-2662	226	24	m	m	VERB
ejpam-2662	226	25	u	u	NOUN
ejpam-2662	226	26	∼=	∼=	PROPN
ejpam-2662	226	27	m	m	NOUN
ejpam-2662	226	28	/	/	SYM
ejpam-2662	226	29	x	x	SYM
ejpam-2662	226	30	u	u	NOUN
ejpam-2662	226	31	/	/	SYM
ejpam-2662	226	32	x	x	SYM
ejpam-2662	226	33	,	,	PUNCT
ejpam-2662	226	34	u	u	NOUN
ejpam-2662	226	35	is	be	AUX
ejpam-2662	226	36	a	a	DET
ejpam-2662	226	37	cofinite	cofinite	NOUN
ejpam-2662	226	38	submodule	submodule	NOUN
ejpam-2662	226	39	of	of	ADP
ejpam-2662	226	40	m	m	PROPN
ejpam-2662	226	41	.	.	PUNCT
ejpam-2662	227	1	since	since	SCONJ
ejpam-2662	227	2	m	m	PROPN
ejpam-2662	227	3	is	be	AUX
ejpam-2662	227	4	cofinitely	cofinitely	ADV
ejpam-2662	227	5	weak	weak	ADJ
ejpam-2662	227	6	g	g	NOUN
ejpam-2662	227	7	-	-	PUNCT
ejpam-2662	227	8	supplemented	supplement	VERB
ejpam-2662	227	9	,	,	PUNCT
ejpam-2662	227	10	u	u	NOUN
ejpam-2662	227	11	has	have	VERB
ejpam-2662	227	12	a	a	DET
ejpam-2662	227	13	weak	weak	ADJ
ejpam-2662	227	14	g	g	NOUN
ejpam-2662	227	15	-	-	PUNCT
ejpam-2662	227	16	supplement	supplement	NOUN
ejpam-2662	227	17	v	v	NOUN
ejpam-2662	227	18	in	in	ADP
ejpam-2662	227	19	m	m	PROPN
ejpam-2662	227	20	.	.	PUNCT
ejpam-2662	228	1	then	then	ADV
ejpam-2662	228	2	by	by	ADP
ejpam-2662	228	3	lemma	lemma	PROPN
ejpam-2662	228	4	7	7	NUM
ejpam-2662	228	5	,	,	PUNCT
ejpam-2662	228	6	(	(	PUNCT
ejpam-2662	228	7	v	v	NOUN
ejpam-2662	228	8	+	+	NOUN
ejpam-2662	228	9	x	x	NOUN
ejpam-2662	228	10	)	)	PUNCT
ejpam-2662	228	11	/x	/x	PUNCT
ejpam-2662	228	12	is	be	AUX
ejpam-2662	228	13	a	a	DET
ejpam-2662	228	14	weak	weak	ADJ
ejpam-2662	228	15	g	g	NOUN
ejpam-2662	228	16	-	-	PUNCT
ejpam-2662	228	17	supplement	supplement	NOUN
ejpam-2662	228	18	of	of	ADP
ejpam-2662	228	19	u	u	NOUN
ejpam-2662	228	20	/	/	SYM
ejpam-2662	228	21	x	x	PROPN
ejpam-2662	228	22	in	in	ADP
ejpam-2662	228	23	m	m	PROPN
ejpam-2662	228	24	/	/	SYM
ejpam-2662	228	25	x.	x.	NOUN
ejpam-2662	228	26	hence	hence	PROPN
ejpam-2662	228	27	m	m	PROPN
ejpam-2662	228	28	/	/	SYM
ejpam-2662	228	29	x	x	VERB
ejpam-2662	228	30	is	be	AUX
ejpam-2662	228	31	cofinitely	cofinitely	ADV
ejpam-2662	228	32	weak	weak	ADJ
ejpam-2662	228	33	g	g	NOUN
ejpam-2662	228	34	-	-	PUNCT
ejpam-2662	228	35	supplemented	supplement	VERB
ejpam-2662	228	36	.	.	PUNCT
ejpam-2662	229	1	corollary	corollary	ADJ
ejpam-2662	229	2	9	9	NUM
ejpam-2662	229	3	.	.	PUNCT
ejpam-2662	230	1	any	any	DET
ejpam-2662	230	2	homomorphic	homomorphic	ADJ
ejpam-2662	230	3	image	image	NOUN
ejpam-2662	230	4	of	of	ADP
ejpam-2662	230	5	a	a	DET
ejpam-2662	230	6	cofinitely	cofinitely	ADV
ejpam-2662	230	7	weak	weak	ADJ
ejpam-2662	230	8	g	g	NOUN
ejpam-2662	230	9	-	-	PUNCT
ejpam-2662	230	10	supplemented	supplement	VERB
ejpam-2662	230	11	module	module	NOUN
ejpam-2662	230	12	is	be	AUX
ejpam-2662	230	13	cofinitely	cofinitely	ADV
ejpam-2662	230	14	weak	weak	ADJ
ejpam-2662	230	15	g	g	NOUN
ejpam-2662	230	16	-	-	PUNCT
ejpam-2662	230	17	supplemented	supplement	VERB
ejpam-2662	230	18	.	.	PUNCT
ejpam-2662	231	1	proof	proof	NOUN
ejpam-2662	231	2	.	.	PUNCT
ejpam-2662	232	1	clear	clear	ADJ
ejpam-2662	232	2	from	from	ADP
ejpam-2662	232	3	lemma	lemma	PROPN
ejpam-2662	232	4	17	17	NUM
ejpam-2662	232	5	.	.	PUNCT
ejpam-2662	233	1	lemma	lemma	PROPN
ejpam-2662	233	2	18	18	NUM
ejpam-2662	233	3	.	.	PUNCT
ejpam-2662	234	1	let	let	VERB
ejpam-2662	234	2	m	m	PRON
ejpam-2662	234	3	be	be	AUX
ejpam-2662	234	4	an	an	DET
ejpam-2662	234	5	r	r	NOUN
ejpam-2662	234	6	-	-	PUNCT
ejpam-2662	234	7	module	module	NOUN
ejpam-2662	234	8	,	,	PUNCT
ejpam-2662	234	9	m1	m1	PROPN
ejpam-2662	234	10	≤	≤	NUM
ejpam-2662	234	11	m	m	VERB
ejpam-2662	234	12	,	,	PUNCT
ejpam-2662	234	13	u	u	PRON
ejpam-2662	234	14	be	be	VERB
ejpam-2662	234	15	a	a	DET
ejpam-2662	234	16	cofinite	cofinite	NOUN
ejpam-2662	234	17	submodule	submodule	NOUN
ejpam-2662	234	18	of	of	ADP
ejpam-2662	234	19	m	m	PROPN
ejpam-2662	234	20	and	and	CCONJ
ejpam-2662	234	21	m1	m1	PROPN
ejpam-2662	234	22	be	be	AUX
ejpam-2662	234	23	a	a	DET
ejpam-2662	234	24	cofinitely	cofinitely	ADV
ejpam-2662	234	25	weak	weak	ADJ
ejpam-2662	234	26	g	g	NOUN
ejpam-2662	234	27	-	-	PUNCT
ejpam-2662	234	28	supplemented	supplement	VERB
ejpam-2662	234	29	module	module	NOUN
ejpam-2662	234	30	.	.	PUNCT
ejpam-2662	235	1	if	if	SCONJ
ejpam-2662	235	2	m1	m1	PROPN
ejpam-2662	235	3	+	+	CCONJ
ejpam-2662	235	4	u	u	NOUN
ejpam-2662	235	5	has	have	VERB
ejpam-2662	235	6	a	a	DET
ejpam-2662	235	7	weak	weak	ADJ
ejpam-2662	235	8	g	g	NOUN
ejpam-2662	235	9	-	-	PUNCT
ejpam-2662	235	10	supplement	supplement	NOUN
ejpam-2662	235	11	in	in	ADP
ejpam-2662	235	12	m	m	PROPN
ejpam-2662	235	13	,	,	PUNCT
ejpam-2662	235	14	then	then	ADV
ejpam-2662	235	15	so	so	ADV
ejpam-2662	235	16	does	do	VERB
ejpam-2662	235	17	u	u	PRON
ejpam-2662	235	18	.	.	PUNCT
ejpam-2662	236	1	proof	proof	NOUN
ejpam-2662	236	2	.	.	PUNCT
ejpam-2662	237	1	let	let	VERB
ejpam-2662	237	2	x	x	PRON
ejpam-2662	237	3	be	be	AUX
ejpam-2662	237	4	a	a	DET
ejpam-2662	237	5	weak	weak	ADJ
ejpam-2662	237	6	g	g	NOUN
ejpam-2662	237	7	-	-	PUNCT
ejpam-2662	237	8	supplement	supplement	NOUN
ejpam-2662	237	9	of	of	ADP
ejpam-2662	237	10	m1	m1	PROPN
ejpam-2662	237	11	+	+	CCONJ
ejpam-2662	237	12	u	u	NOUN
ejpam-2662	237	13	in	in	ADP
ejpam-2662	237	14	m	m	PROPN
ejpam-2662	237	15	.	.	PUNCT
ejpam-2662	238	1	then	then	ADV
ejpam-2662	238	2	m1	m1	PROPN
ejpam-2662	238	3	+	+	CCONJ
ejpam-2662	238	4	u	u	NOUN
ejpam-2662	238	5	+	+	NOUN
ejpam-2662	238	6	x	x	SYM
ejpam-2662	238	7	=	=	VERB
ejpam-2662	238	8	m	m	PRON
ejpam-2662	238	9	and	and	CCONJ
ejpam-2662	238	10	(	(	PUNCT
ejpam-2662	238	11	m1	m1	PROPN
ejpam-2662	238	12	+	+	CCONJ
ejpam-2662	238	13	u	u	NOUN
ejpam-2662	238	14	)	)	PUNCT
ejpam-2662	238	15	∩	∩	NOUN
ejpam-2662	238	16	x	x	SYM
ejpam-2662	238	17	�	�	PROPN
ejpam-2662	238	18	g	g	PROPN
ejpam-2662	238	19	m	m	PROPN
ejpam-2662	238	20	.	.	PUNCT
ejpam-2662	239	1	since	since	SCONJ
ejpam-2662	239	2	u	u	NOUN
ejpam-2662	239	3	is	be	AUX
ejpam-2662	239	4	a	a	DET
ejpam-2662	239	5	cofinite	cofinite	NOUN
ejpam-2662	239	6	submodule	submodule	NOUN
ejpam-2662	239	7	of	of	ADP
ejpam-2662	239	8	m	m	PROPN
ejpam-2662	239	9	,	,	PUNCT
ejpam-2662	239	10	u	u	PROPN
ejpam-2662	239	11	+	+	NOUN
ejpam-2662	239	12	x	x	VERB
ejpam-2662	239	13	is	be	AUX
ejpam-2662	239	14	also	also	ADV
ejpam-2662	239	15	a	a	DET
ejpam-2662	239	16	cofinite	cofinite	NOUN
ejpam-2662	239	17	submodule	submodule	NOUN
ejpam-2662	239	18	of	of	ADP
ejpam-2662	239	19	m	m	PROPN
ejpam-2662	239	20	.	.	PUNCT
ejpam-2662	240	1	then	then	ADV
ejpam-2662	240	2	by	by	ADP
ejpam-2662	240	3	m1	m1	PROPN
ejpam-2662	240	4	m1∩(u+x	m1∩(u+x	NOUN
ejpam-2662	240	5	)	)	PUNCT
ejpam-2662	240	6	∼=	∼=	PROPN
ejpam-2662	240	7	m1+u+x	m1+u+x	NOUN
ejpam-2662	240	8	u+x	u+x	NUM
ejpam-2662	240	9	=	=	SYM
ejpam-2662	240	10	m	m	X
ejpam-2662	240	11	u+x	u+x	NUM
ejpam-2662	240	12	,	,	PUNCT
ejpam-2662	240	13	m1	m1	PROPN
ejpam-2662	240	14	∩	∩	NOUN
ejpam-2662	240	15	(	(	PUNCT
ejpam-2662	240	16	u	u	NOUN
ejpam-2662	240	17	+	+	NOUN
ejpam-2662	240	18	x	x	X
ejpam-2662	240	19	)	)	PUNCT
ejpam-2662	240	20	is	be	AUX
ejpam-2662	240	21	a	a	DET
ejpam-2662	240	22	cofinite	cofinite	NOUN
ejpam-2662	240	23	submodule	submodule	NOUN
ejpam-2662	240	24	of	of	ADP
ejpam-2662	240	25	m1	m1	PROPN
ejpam-2662	240	26	.	.	PUNCT
ejpam-2662	241	1	since	since	SCONJ
ejpam-2662	241	2	m1	m1	PROPN
ejpam-2662	241	3	is	be	AUX
ejpam-2662	241	4	cofinitely	cofinitely	ADV
ejpam-2662	241	5	weak	weak	ADJ
ejpam-2662	241	6	g	g	NOUN
ejpam-2662	241	7	-	-	PUNCT
ejpam-2662	241	8	supplemented	supplement	VERB
ejpam-2662	241	9	,	,	PUNCT
ejpam-2662	241	10	m1	m1	PROPN
ejpam-2662	241	11	∩	∩	NOUN
ejpam-2662	241	12	(	(	PUNCT
ejpam-2662	241	13	u	u	NOUN
ejpam-2662	241	14	+	+	NOUN
ejpam-2662	241	15	x	x	X
ejpam-2662	241	16	)	)	PUNCT
ejpam-2662	241	17	has	have	VERB
ejpam-2662	241	18	a	a	DET
ejpam-2662	241	19	weak	weak	ADJ
ejpam-2662	241	20	g	g	NOUN
ejpam-2662	241	21	-	-	PUNCT
ejpam-2662	241	22	supplement	supplement	NOUN
ejpam-2662	241	23	y	y	NOUN
ejpam-2662	241	24	in	in	ADP
ejpam-2662	241	25	m1	m1	PROPN
ejpam-2662	241	26	,	,	PUNCT
ejpam-2662	241	27	i.e.	i.e.	X
ejpam-2662	241	28	m1	m1	NOUN
ejpam-2662	241	29	∩	∩	NOUN
ejpam-2662	241	30	(	(	PUNCT
ejpam-2662	241	31	u	u	NOUN
ejpam-2662	241	32	+	+	NOUN
ejpam-2662	241	33	x	x	X
ejpam-2662	241	34	)	)	PUNCT
ejpam-2662	241	35	+	+	CCONJ
ejpam-2662	241	36	y	y	PROPN
ejpam-2662	241	37	=	=	SYM
ejpam-2662	241	38	m1	m1	PROPN
ejpam-2662	241	39	and	and	CCONJ
ejpam-2662	241	40	m1	m1	PROPN
ejpam-2662	241	41	∩	∩	NOUN
ejpam-2662	241	42	(	(	PUNCT
ejpam-2662	241	43	u	u	NOUN
ejpam-2662	241	44	+	+	NOUN
ejpam-2662	241	45	x	x	NOUN
ejpam-2662	241	46	)	)	PUNCT
ejpam-2662	241	47	∩	∩	PROPN
ejpam-2662	241	48	y	y	PROPN
ejpam-2662	241	49	�	�	PROPN
ejpam-2662	241	50	g	g	PROPN
ejpam-2662	241	51	m1	m1	PROPN
ejpam-2662	241	52	.	.	PUNCT
ejpam-2662	242	1	following	follow	VERB
ejpam-2662	242	2	this	this	PRON
ejpam-2662	242	3	,	,	PUNCT
ejpam-2662	242	4	we	we	PRON
ejpam-2662	242	5	have	have	VERB
ejpam-2662	242	6	m	m	NOUN
ejpam-2662	242	7	=	=	NOUN
ejpam-2662	242	8	m1	m1	NOUN
ejpam-2662	242	9	∩	∩	NOUN
ejpam-2662	242	10	(	(	PUNCT
ejpam-2662	242	11	u	u	NOUN
ejpam-2662	242	12	+	+	NOUN
ejpam-2662	242	13	x	x	X
ejpam-2662	242	14	)	)	PUNCT
ejpam-2662	243	1	+	+	CCONJ
ejpam-2662	243	2	y	y	PROPN
ejpam-2662	243	3	+	+	NUM
ejpam-2662	243	4	u	u	NOUN
ejpam-2662	243	5	+	+	NOUN
ejpam-2662	243	6	x	x	SYM
ejpam-2662	243	7	=	=	SYM
ejpam-2662	243	8	u	u	NOUN
ejpam-2662	243	9	+	+	NOUN
ejpam-2662	243	10	x	x	SYM
ejpam-2662	243	11	+	+	CCONJ
ejpam-2662	243	12	y	y	PROPN
ejpam-2662	243	13	and	and	CCONJ
ejpam-2662	243	14	u	u	PROPN
ejpam-2662	243	15	∩	∩	NOUN
ejpam-2662	243	16	(	(	PUNCT
ejpam-2662	243	17	x	x	SYM
ejpam-2662	243	18	+	+	NUM
ejpam-2662	243	19	y	y	PROPN
ejpam-2662	243	20	)	)	PUNCT
ejpam-2662	243	21	≤	≤	NUM
ejpam-2662	243	22	x	x	X
ejpam-2662	243	23	∩	∩	NOUN
ejpam-2662	243	24	(	(	PUNCT
ejpam-2662	243	25	u	u	NOUN
ejpam-2662	243	26	+	+	X
ejpam-2662	243	27	y	y	PROPN
ejpam-2662	243	28	)	)	PUNCT
ejpam-2662	244	1	+	+	CCONJ
ejpam-2662	244	2	y	y	PROPN
ejpam-2662	244	3	∩	∩	NOUN
ejpam-2662	244	4	(	(	PUNCT
ejpam-2662	244	5	u	u	NOUN
ejpam-2662	244	6	+	+	NOUN
ejpam-2662	244	7	x	x	NOUN
ejpam-2662	244	8	)	)	PUNCT
ejpam-2662	244	9	≤	≤	NUM
ejpam-2662	244	10	x	x	SYM
ejpam-2662	244	11	∩	∩	NOUN
ejpam-2662	244	12	(	(	PUNCT
ejpam-2662	244	13	m1	m1	PROPN
ejpam-2662	244	14	+	+	CCONJ
ejpam-2662	244	15	u	u	NOUN
ejpam-2662	244	16	)	)	PUNCT
ejpam-2662	244	17	+	+	CCONJ
ejpam-2662	244	18	y	y	PROPN
ejpam-2662	244	19	∩m1	∩m1	PROPN
ejpam-2662	244	20	∩	∩	PROPN
ejpam-2662	244	21	(	(	PUNCT
ejpam-2662	244	22	u	u	NOUN
ejpam-2662	244	23	+	+	X
ejpam-2662	244	24	x)	x)	PROPN
ejpam-2662	244	25	�	�	PROPN
ejpam-2662	244	26	g	g	NOUN
ejpam-2662	244	27	m.	m.	NOUN
ejpam-2662	244	28	hence	hence	ADV
ejpam-2662	244	29	x	x	PUNCT
ejpam-2662	245	1	+	+	CCONJ
ejpam-2662	245	2	y	y	NOUN
ejpam-2662	245	3	is	be	AUX
ejpam-2662	245	4	a	a	DET
ejpam-2662	245	5	weak	weak	ADJ
ejpam-2662	245	6	g	g	NOUN
ejpam-2662	245	7	-	-	PUNCT
ejpam-2662	245	8	supplement	supplement	NOUN
ejpam-2662	245	9	of	of	ADP
ejpam-2662	245	10	u	u	NOUN
ejpam-2662	245	11	in	in	ADP
ejpam-2662	245	12	m	m	PROPN
ejpam-2662	245	13	.	.	PUNCT
ejpam-2662	246	1	corollary	corollary	ADJ
ejpam-2662	246	2	10	10	NUM
ejpam-2662	246	3	.	.	PUNCT
ejpam-2662	247	1	let	let	VERB
ejpam-2662	247	2	m	m	PRON
ejpam-2662	247	3	be	be	AUX
ejpam-2662	247	4	an	an	DET
ejpam-2662	247	5	r	r	NOUN
ejpam-2662	247	6	-	-	PUNCT
ejpam-2662	247	7	module	module	NOUN
ejpam-2662	247	8	,	,	PUNCT
ejpam-2662	247	9	u	u	PRON
ejpam-2662	247	10	be	be	VERB
ejpam-2662	247	11	a	a	DET
ejpam-2662	247	12	cofinite	cofinite	NOUN
ejpam-2662	247	13	submodule	submodule	NOUN
ejpam-2662	247	14	of	of	ADP
ejpam-2662	247	15	m	m	PROPN
ejpam-2662	247	16	and	and	CCONJ
ejpam-2662	247	17	mi	mi	PROPN
ejpam-2662	247	18	≤m	≤m	PROPN
ejpam-2662	247	19	for	for	ADP
ejpam-2662	247	20	i	i	PROPN
ejpam-2662	247	21	=	=	NOUN
ejpam-2662	247	22	1	1	NUM
ejpam-2662	247	23	,	,	PUNCT
ejpam-2662	247	24	2	2	NUM
ejpam-2662	247	25	,	,	PUNCT
ejpam-2662	247	26	.	.	PUNCT
ejpam-2662	247	27	.	.	PUNCT
ejpam-2662	248	1	.	.	PUNCT
ejpam-2662	249	1	,	,	PUNCT
ejpam-2662	249	2	n.	n.	VERB
ejpam-2662	249	3	if	if	SCONJ
ejpam-2662	249	4	u	u	PROPN
ejpam-2662	249	5	+	+	X
ejpam-2662	249	6	m1	m1	PROPN
ejpam-2662	249	7	+	+	NUM
ejpam-2662	249	8	m2	m2	PROPN
ejpam-2662	249	9	+	+	X
ejpam-2662	249	10	.	.	PUNCT
ejpam-2662	249	11	.	.	PUNCT
ejpam-2662	249	12	.	.	PUNCT
ejpam-2662	250	1	+	+	CCONJ
ejpam-2662	250	2	mn	mn	PROPN
ejpam-2662	250	3	has	have	VERB
ejpam-2662	250	4	a	a	DET
ejpam-2662	250	5	weak	weak	ADJ
ejpam-2662	250	6	g	g	NOUN
ejpam-2662	250	7	-	-	PUNCT
ejpam-2662	250	8	supplement	supplement	NOUN
ejpam-2662	250	9	in	in	ADP
ejpam-2662	250	10	m	m	PROPN
ejpam-2662	250	11	and	and	CCONJ
ejpam-2662	250	12	mi	mi	PROPN
ejpam-2662	250	13	is	be	AUX
ejpam-2662	250	14	a	a	DET
ejpam-2662	250	15	cofinitely	cofinitely	ADV
ejpam-2662	250	16	weak	weak	ADJ
ejpam-2662	250	17	g	g	NOUN
ejpam-2662	250	18	-	-	PUNCT
ejpam-2662	250	19	supplemented	supplement	VERB
ejpam-2662	250	20	module	module	NOUN
ejpam-2662	250	21	for	for	ADP
ejpam-2662	250	22	every	every	DET
ejpam-2662	250	23	i	i	NOUN
ejpam-2662	250	24	=	=	NOUN
ejpam-2662	250	25	1	1	NUM
ejpam-2662	250	26	,	,	PUNCT
ejpam-2662	250	27	2	2	NUM
ejpam-2662	250	28	,	,	PUNCT
ejpam-2662	250	29	.	.	PUNCT
ejpam-2662	250	30	.	.	PUNCT
ejpam-2662	251	1	.	.	PUNCT
ejpam-2662	252	1	,	,	PUNCT
ejpam-2662	252	2	n	n	CCONJ
ejpam-2662	252	3	,	,	PUNCT
ejpam-2662	252	4	then	then	ADV
ejpam-2662	252	5	u	u	NOUN
ejpam-2662	252	6	has	have	VERB
ejpam-2662	252	7	a	a	DET
ejpam-2662	252	8	weak	weak	ADJ
ejpam-2662	252	9	g	g	NOUN
ejpam-2662	252	10	-	-	PUNCT
ejpam-2662	252	11	supplement	supplement	NOUN
ejpam-2662	252	12	in	in	ADP
ejpam-2662	252	13	m	m	PROPN
ejpam-2662	252	14	.	.	PUNCT
ejpam-2662	253	1	c.	c.	PROPN
ejpam-2662	253	2	nebiyev	nebiyev	PROPN
ejpam-2662	253	3	,	,	PUNCT
ejpam-2662	253	4	h.	h.	PROPN
ejpam-2662	253	5	ökten	ökten	PROPN
ejpam-2662	253	6	/	/	SYM
ejpam-2662	253	7	eur	eur	PROPN
ejpam-2662	253	8	.	.	PUNCT
ejpam-2662	254	1	j.	j.	PROPN
ejpam-2662	254	2	pure	pure	PROPN
ejpam-2662	254	3	appl	appl	PROPN
ejpam-2662	254	4	.	.	PROPN
ejpam-2662	254	5	math	math	PROPN
ejpam-2662	254	6	,	,	PUNCT
ejpam-2662	254	7	10	10	NUM
ejpam-2662	254	8	(	(	PUNCT
ejpam-2662	254	9	3	3	NUM
ejpam-2662	254	10	)	)	PUNCT
ejpam-2662	254	11	(	(	PUNCT
ejpam-2662	254	12	2017	2017	NUM
ejpam-2662	254	13	)	)	PUNCT
ejpam-2662	254	14	,	,	PUNCT
ejpam-2662	254	15	521	521	NUM
ejpam-2662	254	16	-	-	SYM
ejpam-2662	254	17	528	528	NUM
ejpam-2662	254	18	527	527	NUM
ejpam-2662	254	19	proof	proof	NOUN
ejpam-2662	254	20	.	.	PUNCT
ejpam-2662	255	1	clear	clear	ADJ
ejpam-2662	255	2	from	from	ADP
ejpam-2662	255	3	lemma	lemma	PROPN
ejpam-2662	255	4	18	18	NUM
ejpam-2662	255	5	.	.	PUNCT
ejpam-2662	256	1	lemma	lemma	PROPN
ejpam-2662	256	2	19	19	NUM
ejpam-2662	256	3	.	.	PUNCT
ejpam-2662	257	1	any	any	DET
ejpam-2662	257	2	sum	sum	NOUN
ejpam-2662	257	3	of	of	ADP
ejpam-2662	257	4	cofinitely	cofinitely	ADV
ejpam-2662	257	5	weak	weak	ADJ
ejpam-2662	257	6	g	g	NOUN
ejpam-2662	257	7	-	-	PUNCT
ejpam-2662	257	8	supplemented	supplement	VERB
ejpam-2662	257	9	modules	module	NOUN
ejpam-2662	257	10	is	be	AUX
ejpam-2662	257	11	cofinitely	cofinitely	ADV
ejpam-2662	257	12	weak	weak	ADJ
ejpam-2662	257	13	gsupplemented	gsupplemente	VERB
ejpam-2662	257	14	.	.	PUNCT
ejpam-2662	258	1	proof	proof	NOUN
ejpam-2662	258	2	.	.	PUNCT
ejpam-2662	259	1	let	let	VERB
ejpam-2662	259	2	{	{	PUNCT
ejpam-2662	259	3	mi}i∈i	mi}i∈i	VERB
ejpam-2662	259	4	be	be	AUX
ejpam-2662	259	5	a	a	DET
ejpam-2662	259	6	family	family	NOUN
ejpam-2662	259	7	of	of	ADP
ejpam-2662	259	8	cofinitely	cofinitely	ADV
ejpam-2662	259	9	weak	weak	ADJ
ejpam-2662	259	10	g	g	NOUN
ejpam-2662	259	11	-	-	PUNCT
ejpam-2662	259	12	supplemented	supplement	VERB
ejpam-2662	259	13	submodules	submodule	NOUN
ejpam-2662	259	14	of	of	ADP
ejpam-2662	259	15	an	an	DET
ejpam-2662	259	16	r	r	NOUN
ejpam-2662	259	17	-	-	PUNCT
ejpam-2662	259	18	module	module	NOUN
ejpam-2662	259	19	m	m	NOUN
ejpam-2662	259	20	and	and	CCONJ
ejpam-2662	259	21	m	m	PROPN
ejpam-2662	259	22	=	=	PUNCT
ejpam-2662	259	23	∑	∑	PROPN
ejpam-2662	259	24	i∈i	i∈i	PROPN
ejpam-2662	259	25	mi	mi	PROPN
ejpam-2662	259	26	.	.	PROPN
ejpam-2662	259	27	let	let	VERB
ejpam-2662	259	28	u	u	PRON
ejpam-2662	259	29	be	be	AUX
ejpam-2662	259	30	any	any	DET
ejpam-2662	259	31	cofinite	cofinite	NOUN
ejpam-2662	259	32	submodule	submodule	NOUN
ejpam-2662	259	33	of	of	ADP
ejpam-2662	259	34	m	m	PROPN
ejpam-2662	259	35	.	.	PUNCT
ejpam-2662	260	1	since	since	SCONJ
ejpam-2662	260	2	u	u	NOUN
ejpam-2662	260	3	is	be	AUX
ejpam-2662	260	4	cofinite	cofinite	NOUN
ejpam-2662	260	5	submodule	submodule	NOUN
ejpam-2662	260	6	of	of	ADP
ejpam-2662	260	7	m	m	PROPN
ejpam-2662	260	8	,	,	PUNCT
ejpam-2662	260	9	there	there	PRON
ejpam-2662	260	10	exists	exist	VERB
ejpam-2662	260	11	a	a	DET
ejpam-2662	260	12	finite	finite	NOUN
ejpam-2662	260	13	subset	subset	NOUN
ejpam-2662	260	14	{	{	PUNCT
ejpam-2662	260	15	i1	i1	PROPN
ejpam-2662	260	16	,	,	PUNCT
ejpam-2662	260	17	i2	i2	PROPN
ejpam-2662	260	18	,	,	PUNCT
ejpam-2662	260	19	.	.	PUNCT
ejpam-2662	260	20	.	.	PUNCT
ejpam-2662	261	1	.	.	PUNCT
ejpam-2662	262	1	,	,	PUNCT
ejpam-2662	262	2	in	in	ADP
ejpam-2662	262	3	}	}	PUNCT
ejpam-2662	262	4	of	of	ADP
ejpam-2662	262	5	i	i	PRON
ejpam-2662	262	6	such	such	ADJ
ejpam-2662	262	7	that	that	SCONJ
ejpam-2662	262	8	m	m	VERB
ejpam-2662	262	9	=	=	SYM
ejpam-2662	262	10	u+mi1	u+mi1	PROPN
ejpam-2662	262	11	+	+	PROPN
ejpam-2662	262	12	mi2	mi2	PROPN
ejpam-2662	262	13	+	+	PROPN
ejpam-2662	262	14	.	.	PUNCT
ejpam-2662	262	15	.	.	PUNCT
ejpam-2662	262	16	.+min	.+min	PROPN
ejpam-2662	262	17	.	.	PUNCT
ejpam-2662	263	1	since	since	SCONJ
ejpam-2662	263	2	u+mi1	u+mi1	PROPN
ejpam-2662	263	3	+	+	PROPN
ejpam-2662	263	4	mi2	mi2	PROPN
ejpam-2662	263	5	+	+	PROPN
ejpam-2662	263	6	.	.	PUNCT
ejpam-2662	263	7	.	.	PUNCT
ejpam-2662	264	1	.+min	.+min	PROPN
ejpam-2662	264	2	has	have	VERB
ejpam-2662	264	3	a	a	DET
ejpam-2662	264	4	weak	weak	ADJ
ejpam-2662	264	5	g	g	NOUN
ejpam-2662	264	6	-	-	PUNCT
ejpam-2662	264	7	supplement	supplement	NOUN
ejpam-2662	264	8	0	0	NUM
ejpam-2662	264	9	in	in	ADP
ejpam-2662	264	10	m	m	PROPN
ejpam-2662	264	11	and	and	CCONJ
ejpam-2662	264	12	mik	mik	PROPN
ejpam-2662	264	13	is	be	AUX
ejpam-2662	264	14	cofinitely	cofinitely	ADV
ejpam-2662	264	15	weak	weak	ADJ
ejpam-2662	264	16	g	g	NOUN
ejpam-2662	264	17	-	-	PUNCT
ejpam-2662	264	18	supplemented	supplement	VERB
ejpam-2662	264	19	for	for	ADP
ejpam-2662	264	20	k	k	PROPN
ejpam-2662	264	21	=	=	SYM
ejpam-2662	264	22	1	1	NUM
ejpam-2662	264	23	,	,	PUNCT
ejpam-2662	264	24	2	2	NUM
ejpam-2662	264	25	,	,	PUNCT
ejpam-2662	264	26	.	.	PUNCT
ejpam-2662	264	27	.	.	PUNCT
ejpam-2662	265	1	.	.	PUNCT
ejpam-2662	266	1	,	,	PUNCT
ejpam-2662	266	2	n	n	CCONJ
ejpam-2662	266	3	,	,	PUNCT
ejpam-2662	266	4	then	then	ADV
ejpam-2662	266	5	by	by	ADP
ejpam-2662	266	6	corollary	corollary	ADJ
ejpam-2662	266	7	10	10	NUM
ejpam-2662	266	8	,	,	PUNCT
ejpam-2662	266	9	u	u	NOUN
ejpam-2662	266	10	has	have	VERB
ejpam-2662	266	11	a	a	DET
ejpam-2662	266	12	weak	weak	ADJ
ejpam-2662	266	13	g	g	NOUN
ejpam-2662	266	14	-	-	PUNCT
ejpam-2662	266	15	supplement	supplement	NOUN
ejpam-2662	266	16	in	in	ADP
ejpam-2662	266	17	m	m	PROPN
ejpam-2662	266	18	.	.	PUNCT
ejpam-2662	267	1	proposition	proposition	NOUN
ejpam-2662	267	2	2	2	NUM
ejpam-2662	267	3	.	.	PUNCT
ejpam-2662	268	1	let	let	VERB
ejpam-2662	268	2	r	r	PRON
ejpam-2662	268	3	be	be	AUX
ejpam-2662	268	4	a	a	DET
ejpam-2662	268	5	ring	ring	NOUN
ejpam-2662	268	6	.	.	PUNCT
ejpam-2662	269	1	the	the	DET
ejpam-2662	269	2	following	follow	VERB
ejpam-2662	269	3	statements	statement	NOUN
ejpam-2662	269	4	are	be	AUX
ejpam-2662	269	5	equivalent	equivalent	ADJ
ejpam-2662	269	6	.	.	PUNCT
ejpam-2662	270	1	(	(	PUNCT
ejpam-2662	270	2	1	1	X
ejpam-2662	270	3	)	)	PUNCT
ejpam-2662	270	4	rr	rr	NOUN
ejpam-2662	270	5	is	be	AUX
ejpam-2662	270	6	g	g	NOUN
ejpam-2662	270	7	-	-	PUNCT
ejpam-2662	270	8	semilocal	semilocal	ADJ
ejpam-2662	270	9	.	.	PUNCT
ejpam-2662	271	1	(	(	PUNCT
ejpam-2662	271	2	2	2	X
ejpam-2662	271	3	)	)	PUNCT
ejpam-2662	271	4	rr	rr	NOUN
ejpam-2662	271	5	is	be	AUX
ejpam-2662	271	6	weakly	weakly	ADJ
ejpam-2662	271	7	g	g	NOUN
ejpam-2662	271	8	-	-	PUNCT
ejpam-2662	271	9	supplemented	supplement	VERB
ejpam-2662	271	10	.	.	PUNCT
ejpam-2662	272	1	(	(	PUNCT
ejpam-2662	272	2	3	3	X
ejpam-2662	272	3	)	)	PUNCT
ejpam-2662	272	4	every	every	DET
ejpam-2662	272	5	finitely	finitely	ADV
ejpam-2662	272	6	generated	generate	VERB
ejpam-2662	272	7	r	r	NOUN
ejpam-2662	272	8	-	-	PUNCT
ejpam-2662	272	9	module	module	NOUN
ejpam-2662	272	10	is	be	AUX
ejpam-2662	272	11	g	g	NOUN
ejpam-2662	272	12	-	-	PUNCT
ejpam-2662	272	13	semilocal	semilocal	ADJ
ejpam-2662	272	14	.	.	PUNCT
ejpam-2662	273	1	(	(	PUNCT
ejpam-2662	273	2	4	4	X
ejpam-2662	273	3	)	)	PUNCT
ejpam-2662	273	4	every	every	DET
ejpam-2662	273	5	finitely	finitely	ADV
ejpam-2662	273	6	generated	generate	VERB
ejpam-2662	273	7	r	r	NOUN
ejpam-2662	273	8	-	-	PUNCT
ejpam-2662	273	9	module	module	NOUN
ejpam-2662	273	10	is	be	AUX
ejpam-2662	273	11	weakly	weakly	ADJ
ejpam-2662	273	12	g	g	NOUN
ejpam-2662	273	13	-	-	PUNCT
ejpam-2662	273	14	supplemented	supplement	VERB
ejpam-2662	273	15	.	.	PUNCT
ejpam-2662	274	1	(	(	PUNCT
ejpam-2662	274	2	5	5	NUM
ejpam-2662	274	3	)	)	PUNCT
ejpam-2662	274	4	r(i	r(i	NOUN
ejpam-2662	274	5	)	)	PUNCT
ejpam-2662	274	6	is	be	AUX
ejpam-2662	274	7	cofinitely	cofinitely	ADV
ejpam-2662	274	8	weak	weak	ADJ
ejpam-2662	274	9	g	g	NOUN
ejpam-2662	274	10	-	-	PUNCT
ejpam-2662	274	11	supplemented	supplement	VERB
ejpam-2662	274	12	for	for	ADP
ejpam-2662	274	13	every	every	DET
ejpam-2662	274	14	index	index	NOUN
ejpam-2662	274	15	set	set	VERB
ejpam-2662	274	16	i.	i.	NOUN
ejpam-2662	274	17	(	(	PUNCT
ejpam-2662	274	18	6	6	NUM
ejpam-2662	274	19	)	)	PUNCT
ejpam-2662	274	20	every	every	DET
ejpam-2662	274	21	r	r	NOUN
ejpam-2662	274	22	-	-	PUNCT
ejpam-2662	274	23	module	module	NOUN
ejpam-2662	274	24	is	be	AUX
ejpam-2662	274	25	cofinitely	cofinitely	ADV
ejpam-2662	274	26	weak	weak	ADJ
ejpam-2662	274	27	g	g	NOUN
ejpam-2662	274	28	-	-	PUNCT
ejpam-2662	274	29	supplemented	supplement	VERB
ejpam-2662	274	30	.	.	PUNCT
ejpam-2662	275	1	proof	proof	NOUN
ejpam-2662	275	2	.	.	PUNCT
ejpam-2662	276	1	(	(	PUNCT
ejpam-2662	276	2	1)⇔	1)⇔	NUM
ejpam-2662	276	3	(	(	PUNCT
ejpam-2662	276	4	2	2	NUM
ejpam-2662	276	5	)	)	PUNCT
ejpam-2662	276	6	clear	clear	ADJ
ejpam-2662	276	7	from	from	ADP
ejpam-2662	276	8	corollary	corollary	ADJ
ejpam-2662	276	9	8	8	NUM
ejpam-2662	276	10	.	.	PUNCT
ejpam-2662	277	1	(	(	PUNCT
ejpam-2662	277	2	1)⇒	1)⇒	NUM
ejpam-2662	277	3	(	(	PUNCT
ejpam-2662	277	4	3	3	NUM
ejpam-2662	277	5	)	)	PUNCT
ejpam-2662	277	6	assume	assume	VERB
ejpam-2662	277	7	m	m	PRON
ejpam-2662	277	8	be	be	AUX
ejpam-2662	277	9	a	a	DET
ejpam-2662	277	10	finitely	finitely	ADV
ejpam-2662	277	11	generated	generate	VERB
ejpam-2662	277	12	r	r	NOUN
ejpam-2662	277	13	-	-	PUNCT
ejpam-2662	277	14	module	module	NOUN
ejpam-2662	277	15	and	and	CCONJ
ejpam-2662	277	16	let	let	VERB
ejpam-2662	277	17	m	m	NOUN
ejpam-2662	277	18	=	=	VERB
ejpam-2662	277	19	〈	〈	PROPN
ejpam-2662	277	20	m2,m2	m2,m2	PROPN
ejpam-2662	277	21	,	,	PUNCT
ejpam-2662	277	22	.	.	PUNCT
ejpam-2662	277	23	.	.	PUNCT
ejpam-2662	278	1	.	.	PUNCT
ejpam-2662	279	1	,	,	PUNCT
ejpam-2662	279	2	mn	mn	PROPN
ejpam-2662	279	3	〉	〉	PROPN
ejpam-2662	279	4	.	.	PUNCT
ejpam-2662	280	1	then	then	ADV
ejpam-2662	280	2	m	m	VERB
ejpam-2662	280	3	=	=	PROPN
ejpam-2662	280	4	rm1	rm1	PROPN
ejpam-2662	281	1	+	+	PROPN
ejpam-2662	281	2	rm2	rm2	PROPN
ejpam-2662	281	3	+	+	PUNCT
ejpam-2662	281	4	.	.	PUNCT
ejpam-2662	281	5	.	.	PUNCT
ejpam-2662	282	1	.+rmn	.+rmn	PROPN
ejpam-2662	282	2	.	.	PUNCT
ejpam-2662	283	1	since	since	SCONJ
ejpam-2662	283	2	rr	rr	PROPN
ejpam-2662	283	3	is	be	AUX
ejpam-2662	283	4	g	g	NOUN
ejpam-2662	283	5	-	-	PUNCT
ejpam-2662	283	6	semilocal	semilocal	ADJ
ejpam-2662	283	7	and	and	CCONJ
ejpam-2662	283	8	rmi	rmi	NOUN
ejpam-2662	283	9	(	(	PUNCT
ejpam-2662	283	10	i	i	NOUN
ejpam-2662	283	11	=	=	NOUN
ejpam-2662	283	12	1	1	NUM
ejpam-2662	283	13	,	,	PUNCT
ejpam-2662	283	14	2	2	NUM
ejpam-2662	283	15	,	,	PUNCT
ejpam-2662	283	16	.	.	PUNCT
ejpam-2662	283	17	.	.	PUNCT
ejpam-2662	284	1	.	.	PUNCT
ejpam-2662	285	1	,	,	PUNCT
ejpam-2662	285	2	n	n	CCONJ
ejpam-2662	285	3	)	)	PUNCT
ejpam-2662	285	4	is	be	AUX
ejpam-2662	285	5	an	an	DET
ejpam-2662	285	6	homomorphic	homomorphic	ADJ
ejpam-2662	285	7	image	image	NOUN
ejpam-2662	285	8	of	of	ADP
ejpam-2662	285	9	rr	rr	NOUN
ejpam-2662	285	10	,	,	PUNCT
ejpam-2662	285	11	by	by	ADP
ejpam-2662	285	12	lemma	lemma	PROPN
ejpam-2662	285	13	10	10	NUM
ejpam-2662	285	14	,	,	PUNCT
ejpam-2662	285	15	rmi	rmi	NOUN
ejpam-2662	285	16	is	be	AUX
ejpam-2662	285	17	g	g	NOUN
ejpam-2662	285	18	-	-	PUNCT
ejpam-2662	285	19	semilocal	semilocal	ADJ
ejpam-2662	285	20	.	.	PUNCT
ejpam-2662	286	1	then	then	ADV
ejpam-2662	286	2	by	by	ADP
ejpam-2662	286	3	corollary	corollary	ADJ
ejpam-2662	286	4	6	6	NUM
ejpam-2662	286	5	,	,	PUNCT
ejpam-2662	286	6	m	m	VERB
ejpam-2662	286	7	is	be	AUX
ejpam-2662	286	8	g	g	NOUN
ejpam-2662	286	9	-	-	PUNCT
ejpam-2662	286	10	semilocal	semilocal	ADJ
ejpam-2662	286	11	.	.	PUNCT
ejpam-2662	287	1	(	(	PUNCT
ejpam-2662	287	2	3)⇔	3)⇔	NUM
ejpam-2662	287	3	(	(	PUNCT
ejpam-2662	287	4	4	4	NUM
ejpam-2662	287	5	)	)	PUNCT
ejpam-2662	287	6	obtained	obtain	VERB
ejpam-2662	287	7	from	from	ADP
ejpam-2662	287	8	lemma	lemma	PROPN
ejpam-2662	287	9	15	15	NUM
ejpam-2662	287	10	.	.	PUNCT
ejpam-2662	288	1	(	(	PUNCT
ejpam-2662	288	2	4	4	X
ejpam-2662	288	3	)	)	PUNCT
ejpam-2662	288	4	⇒	⇒	NOUN
ejpam-2662	288	5	(	(	PUNCT
ejpam-2662	288	6	5	5	NUM
ejpam-2662	288	7	)	)	PUNCT
ejpam-2662	288	8	by	by	ADP
ejpam-2662	288	9	hypothesis	hypothesis	NOUN
ejpam-2662	288	10	,	,	PUNCT
ejpam-2662	288	11	rr	rr	PROPN
ejpam-2662	288	12	is	be	AUX
ejpam-2662	288	13	weakly	weakly	ADJ
ejpam-2662	288	14	g	g	NOUN
ejpam-2662	288	15	-	-	PUNCT
ejpam-2662	288	16	supplemented	supplement	VERB
ejpam-2662	288	17	.	.	PUNCT
ejpam-2662	289	1	hence	hence	ADV
ejpam-2662	289	2	rr	rr	PROPN
ejpam-2662	289	3	is	be	AUX
ejpam-2662	289	4	cofinitely	cofinitely	ADV
ejpam-2662	289	5	weak	weak	ADJ
ejpam-2662	289	6	g	g	NOUN
ejpam-2662	289	7	-	-	PUNCT
ejpam-2662	289	8	supplemented	supplement	VERB
ejpam-2662	289	9	.	.	PUNCT
ejpam-2662	290	1	because	because	SCONJ
ejpam-2662	290	2	of	of	ADP
ejpam-2662	290	3	this	this	PRON
ejpam-2662	290	4	,	,	PUNCT
ejpam-2662	290	5	by	by	ADP
ejpam-2662	290	6	lemma	lemma	PROPN
ejpam-2662	290	7	19	19	NUM
ejpam-2662	290	8	,	,	PUNCT
ejpam-2662	290	9	r(i	r(i	NOUN
ejpam-2662	290	10	)	)	PUNCT
ejpam-2662	290	11	is	be	AUX
ejpam-2662	290	12	cofinitely	cofinitely	ADV
ejpam-2662	290	13	weak	weak	ADJ
ejpam-2662	290	14	g	g	NOUN
ejpam-2662	290	15	-	-	PUNCT
ejpam-2662	290	16	supplemented	supplement	VERB
ejpam-2662	290	17	for	for	ADP
ejpam-2662	290	18	every	every	DET
ejpam-2662	290	19	index	index	NOUN
ejpam-2662	290	20	set	set	VERB
ejpam-2662	290	21	i.	i.	NOUN
ejpam-2662	290	22	(	(	PUNCT
ejpam-2662	290	23	5)⇒	5)⇒	NUM
ejpam-2662	290	24	(	(	PUNCT
ejpam-2662	290	25	6	6	NUM
ejpam-2662	290	26	)	)	PUNCT
ejpam-2662	290	27	clear	clear	ADJ
ejpam-2662	290	28	from	from	ADP
ejpam-2662	290	29	corollary	corollary	ADJ
ejpam-2662	290	30	9	9	NUM
ejpam-2662	290	31	,	,	PUNCT
ejpam-2662	290	32	since	since	SCONJ
ejpam-2662	290	33	every	every	DET
ejpam-2662	290	34	r	r	NOUN
ejpam-2662	290	35	-	-	PUNCT
ejpam-2662	290	36	module	module	NOUN
ejpam-2662	290	37	is	be	AUX
ejpam-2662	290	38	rr	rr	NOUN
ejpam-2662	290	39	-	-	PUNCT
ejpam-2662	290	40	generated	generate	VERB
ejpam-2662	290	41	.	.	PUNCT
ejpam-2662	291	1	(	(	PUNCT
ejpam-2662	291	2	6	6	NUM
ejpam-2662	291	3	)	)	PUNCT
ejpam-2662	291	4	⇒	⇒	NOUN
ejpam-2662	291	5	(	(	PUNCT
ejpam-2662	291	6	2	2	NUM
ejpam-2662	291	7	)	)	PUNCT
ejpam-2662	291	8	by	by	ADP
ejpam-2662	291	9	hypothesis	hypothesis	NOUN
ejpam-2662	291	10	,	,	PUNCT
ejpam-2662	291	11	rr	rr	PROPN
ejpam-2662	291	12	is	be	AUX
ejpam-2662	291	13	cofinitely	cofinitely	ADV
ejpam-2662	291	14	weak	weak	ADJ
ejpam-2662	291	15	g	g	NOUN
ejpam-2662	291	16	-	-	PUNCT
ejpam-2662	291	17	supplemented	supplement	VERB
ejpam-2662	291	18	.	.	PUNCT
ejpam-2662	292	1	since	since	SCONJ
ejpam-2662	292	2	rr	rr	PROPN
ejpam-2662	292	3	is	be	AUX
ejpam-2662	292	4	finitely	finitely	ADV
ejpam-2662	292	5	generated	generate	VERB
ejpam-2662	292	6	,	,	PUNCT
ejpam-2662	292	7	by	by	ADP
ejpam-2662	292	8	lemma	lemma	PROPN
ejpam-2662	292	9	16	16	NUM
ejpam-2662	292	10	,	,	PUNCT
ejpam-2662	292	11	rr	rr	PROPN
ejpam-2662	292	12	is	be	AUX
ejpam-2662	292	13	weakly	weakly	ADJ
ejpam-2662	292	14	g	g	NOUN
ejpam-2662	292	15	-	-	PUNCT
ejpam-2662	292	16	supplemented	supplement	VERB
ejpam-2662	292	17	.	.	PUNCT
ejpam-2662	293	1	proposition	proposition	NOUN
ejpam-2662	293	2	3	3	NUM
ejpam-2662	293	3	.	.	PUNCT
ejpam-2662	294	1	let	let	VERB
ejpam-2662	294	2	m	m	PRON
ejpam-2662	294	3	be	be	AUX
ejpam-2662	294	4	weakly	weakly	ADV
ejpam-2662	294	5	g	g	NOUN
ejpam-2662	294	6	-	-	PUNCT
ejpam-2662	294	7	supplemented	supplement	VERB
ejpam-2662	294	8	r	r	NOUN
ejpam-2662	294	9	-	-	PUNCT
ejpam-2662	294	10	module	module	NOUN
ejpam-2662	294	11	and	and	CCONJ
ejpam-2662	294	12	u	u	NOUN
ejpam-2662	294	13	be	be	VERB
ejpam-2662	294	14	a	a	DET
ejpam-2662	294	15	cofinite	cofinite	NOUN
ejpam-2662	294	16	submodule	submodule	NOUN
ejpam-2662	294	17	of	of	ADP
ejpam-2662	294	18	m	m	PROPN
ejpam-2662	294	19	.	.	PUNCT
ejpam-2662	295	1	then	then	ADV
ejpam-2662	295	2	for	for	ADP
ejpam-2662	295	3	every	every	DET
ejpam-2662	295	4	v	v	PRON
ejpam-2662	295	5	≤m	≤m	NOUN
ejpam-2662	295	6	with	with	ADP
ejpam-2662	295	7	m	m	PROPN
ejpam-2662	295	8	=	=	SYM
ejpam-2662	295	9	u	u	PROPN
ejpam-2662	295	10	+	+	NOUN
ejpam-2662	295	11	v	v	NOUN
ejpam-2662	295	12	and	and	CCONJ
ejpam-2662	295	13	u	u	NOUN
ejpam-2662	295	14	∩	∩	NOUN
ejpam-2662	295	15	v	v	NOUN
ejpam-2662	295	16	is	be	AUX
ejpam-2662	295	17	a	a	DET
ejpam-2662	295	18	cofinite	cofinite	NOUN
ejpam-2662	295	19	submodule	submodule	NOUN
ejpam-2662	295	20	of	of	ADP
ejpam-2662	295	21	m	m	PROPN
ejpam-2662	295	22	,	,	PUNCT
ejpam-2662	295	23	there	there	PRON
ejpam-2662	295	24	exists	exist	VERB
ejpam-2662	295	25	a	a	DET
ejpam-2662	295	26	weak	weak	ADJ
ejpam-2662	295	27	g	g	NOUN
ejpam-2662	295	28	-	-	PUNCT
ejpam-2662	295	29	supplement	supplement	NOUN
ejpam-2662	295	30	k	k	NOUN
ejpam-2662	295	31	of	of	ADP
ejpam-2662	295	32	u	u	PROPN
ejpam-2662	295	33	with	with	ADP
ejpam-2662	295	34	k	k	PROPN
ejpam-2662	295	35	≤	≤	PROPN
ejpam-2662	295	36	v	v	NOUN
ejpam-2662	295	37	.	.	PUNCT
ejpam-2662	296	1	proof	proof	NOUN
ejpam-2662	296	2	.	.	PUNCT
ejpam-2662	297	1	similar	similar	ADJ
ejpam-2662	297	2	to	to	ADP
ejpam-2662	297	3	proof	proof	NOUN
ejpam-2662	297	4	of	of	ADP
ejpam-2662	297	5	proposition	proposition	NOUN
ejpam-2662	297	6	1	1	NUM
ejpam-2662	297	7	.	.	PUNCT
ejpam-2662	298	1	references	reference	NOUN
ejpam-2662	298	2	528	528	NUM
ejpam-2662	298	3	references	reference	NOUN
ejpam-2662	298	4	[	[	X
ejpam-2662	298	5	1	1	NUM
ejpam-2662	298	6	]	]	PUNCT
ejpam-2662	298	7	b.	b.	PROPN
ejpam-2662	298	8	koşar	koşar	PROPN
ejpam-2662	298	9	,	,	PUNCT
ejpam-2662	298	10	c.	c.	PROPN
ejpam-2662	298	11	nebiyev	nebiyev	PROPN
ejpam-2662	298	12	,	,	PUNCT
ejpam-2662	298	13	and	and	CCONJ
ejpam-2662	298	14	n.	n.	PROPN
ejpam-2662	298	15	sökmez	sökmez	NOUN
ejpam-2662	298	16	.	.	PUNCT
ejpam-2662	299	1	g	g	NOUN
ejpam-2662	299	2	-	-	PUNCT
ejpam-2662	299	3	supplemented	supplement	VERB
ejpam-2662	299	4	modules	module	NOUN
ejpam-2662	299	5	.	.	PUNCT
ejpam-2662	300	1	ukrainian	ukrainian	ADJ
ejpam-2662	300	2	mathematical	mathematical	ADJ
ejpam-2662	300	3	journal	journal	NOUN
ejpam-2662	300	4	,	,	PUNCT
ejpam-2662	300	5	67(6):861–864	67(6):861–864	PROPN
ejpam-2662	300	6	,	,	PUNCT
ejpam-2662	300	7	2015	2015	NUM
ejpam-2662	300	8	.	.	PUNCT
ejpam-2662	301	1	[	[	X
ejpam-2662	301	2	2	2	NUM
ejpam-2662	301	3	]	]	PUNCT
ejpam-2662	301	4	c.	c.	PROPN
ejpam-2662	301	5	lomp	lomp	PROPN
ejpam-2662	301	6	.	.	PUNCT
ejpam-2662	302	1	on	on	ADP
ejpam-2662	302	2	semilocal	semilocal	ADJ
ejpam-2662	302	3	modules	module	NOUN
ejpam-2662	302	4	and	and	CCONJ
ejpam-2662	302	5	rings	ring	NOUN
ejpam-2662	302	6	.	.	PUNCT
ejpam-2662	303	1	communications	communication	NOUN
ejpam-2662	303	2	in	in	ADP
ejpam-2662	303	3	algebra	algebra	NOUN
ejpam-2662	303	4	,	,	PUNCT
ejpam-2662	303	5	27(4):1921	27(4):1921	NUM
ejpam-2662	303	6	–	–	PUNCT
ejpam-2662	303	7	1935	1935	NUM
ejpam-2662	303	8	,	,	PUNCT
ejpam-2662	303	9	1999	1999	NUM
ejpam-2662	303	10	.	.	PUNCT
ejpam-2662	304	1	[	[	X
ejpam-2662	304	2	3	3	X
ejpam-2662	304	3	]	]	PUNCT
ejpam-2662	304	4	t.	t.	PROPN
ejpam-2662	304	5	c.	c.	PROPN
ejpam-2662	304	6	quynh	quynh	PROPN
ejpam-2662	304	7	and	and	CCONJ
ejpam-2662	304	8	p.	p.	NOUN
ejpam-2662	304	9	h.	h.	PROPN
ejpam-2662	304	10	tin	tin	PROPN
ejpam-2662	304	11	.	.	PUNCT
ejpam-2662	305	1	some	some	DET
ejpam-2662	305	2	properties	property	NOUN
ejpam-2662	305	3	of	of	ADP
ejpam-2662	305	4	e	e	NOUN
ejpam-2662	305	5	-	-	VERB
ejpam-2662	305	6	supplemented	supplement	VERB
ejpam-2662	305	7	and	and	CCONJ
ejpam-2662	305	8	e	e	NOUN
ejpam-2662	305	9	-	-	ADJ
ejpam-2662	305	10	lifting	lift	VERB
ejpam-2662	305	11	modules	module	NOUN
ejpam-2662	305	12	.	.	PUNCT
ejpam-2662	306	1	vietnam	vietnam	PROPN
ejpam-2662	306	2	journal	journal	PROPN
ejpam-2662	306	3	of	of	ADP
ejpam-2662	306	4	mathematics	mathematic	NOUN
ejpam-2662	306	5	,	,	PUNCT
ejpam-2662	306	6	41(3):303–312	41(3):303–312	PROPN
ejpam-2662	306	7	,	,	PUNCT
ejpam-2662	306	8	2013	2013	NUM
ejpam-2662	306	9	.	.	PUNCT
ejpam-2662	307	1	[	[	X
ejpam-2662	307	2	4	4	NUM
ejpam-2662	307	3	]	]	X
ejpam-2662	307	4	n.	n.	NOUN
ejpam-2662	307	5	sökmez	sökmez	PROPN
ejpam-2662	307	6	,	,	PUNCT
ejpam-2662	307	7	b.	b.	PROPN
ejpam-2662	307	8	koşar	koşar	PROPN
ejpam-2662	307	9	,	,	PUNCT
ejpam-2662	307	10	and	and	CCONJ
ejpam-2662	307	11	c.	c.	PROPN
ejpam-2662	307	12	nebiyev	nebiyev	PROPN
ejpam-2662	307	13	.	.	PUNCT
ejpam-2662	308	1	genelleştirilmiş	genelleştirilmiş	PROPN
ejpam-2662	308	2	küçük	küçük	PROPN
ejpam-2662	308	3	alt	alt	VERB
ejpam-2662	308	4	modüller	modüller	PRON
ejpam-2662	308	5	,	,	PUNCT
ejpam-2662	308	6	2010	2010	NUM
ejpam-2662	308	7	.	.	PUNCT
ejpam-2662	309	1	presented	present	VERB
ejpam-2662	309	2	at	at	ADP
ejpam-2662	309	3	the	the	DET
ejpam-2662	309	4	xxiii	xxiii	PROPN
ejpam-2662	309	5	.	.	PUNCT
ejpam-2662	310	1	ulusal	ulusal	PROPN
ejpam-2662	310	2	matematik	matematik	PROPN
ejpam-2662	310	3	sempozyumu	sempozyumu	PROPN
ejpam-2662	310	4	,	,	PUNCT
ejpam-2662	310	5	erciyes	erciye	NOUN
ejpam-2662	310	6	üniversitesi	üniversitesi	PROPN
ejpam-2662	310	7	,	,	PUNCT
ejpam-2662	310	8	kayseritürkiye	kayseritürkiye	X
ejpam-2662	310	9	.	.	PUNCT
ejpam-2662	311	1	[	[	X
ejpam-2662	311	2	5	5	X
ejpam-2662	311	3	]	]	PUNCT
ejpam-2662	311	4	d.	d.	PROPN
ejpam-2662	311	5	x.	x.	PROPN
ejpam-2662	311	6	zhou	zhou	PROPN
ejpam-2662	311	7	and	and	CCONJ
ejpam-2662	311	8	x.	x.	PROPN
ejpam-2662	311	9	r.	r.	PROPN
ejpam-2662	311	10	zhang	zhang	PROPN
ejpam-2662	311	11	.	.	PUNCT
ejpam-2662	312	1	small	small	ADJ
ejpam-2662	312	2	-	-	PUNCT
ejpam-2662	312	3	essential	essential	ADJ
ejpam-2662	312	4	submodules	submodule	NOUN
ejpam-2662	312	5	and	and	CCONJ
ejpam-2662	312	6	morita	morita	PROPN
ejpam-2662	312	7	duality	duality	PROPN
ejpam-2662	312	8	.	.	PUNCT
ejpam-2662	313	1	southeast	southeast	ADJ
ejpam-2662	313	2	asian	asian	ADJ
ejpam-2662	313	3	bulletin	bulletin	NOUN
ejpam-2662	313	4	of	of	ADP
ejpam-2662	313	5	mathematics	mathematic	NOUN
ejpam-2662	313	6	,	,	PUNCT
ejpam-2662	313	7	35(6):1051–1062	35(6):1051–1062	NUM
ejpam-2662	313	8	,	,	PUNCT
ejpam-2662	313	9	2011	2011	NUM
ejpam-2662	313	10	.	.	PUNCT