id	sid	tid	token	lemma	pos
ejpam-3024	1	1	european	european	PROPN
ejpam-3024	1	2	journal	journal	PROPN
ejpam-3024	1	3	of	of	ADP
ejpam-3024	1	4	pure	pure	ADJ
ejpam-3024	1	5	and	and	CCONJ
ejpam-3024	1	6	applied	apply	VERB
ejpam-3024	1	7	mathematics	mathematic	NOUN
ejpam-3024	1	8	vol	vol	NOUN
ejpam-3024	1	9	.	.	PROPN
ejpam-3024	2	1	10	10	NUM
ejpam-3024	2	2	,	,	PUNCT
ejpam-3024	2	3	no	no	INTJ
ejpam-3024	2	4	.	.	NOUN
ejpam-3024	2	5	4	4	NUM
ejpam-3024	2	6	,	,	PUNCT
ejpam-3024	2	7	2017	2017	NUM
ejpam-3024	2	8	,	,	PUNCT
ejpam-3024	2	9	730	730	NUM
ejpam-3024	2	10	-	-	SYM
ejpam-3024	2	11	738	738	NUM
ejpam-3024	2	12	issn	issn	PROPN
ejpam-3024	2	13	1307	1307	NUM
ejpam-3024	2	14	-	-	SYM
ejpam-3024	2	15	5543	5543	NUM
ejpam-3024	2	16	–	–	PUNCT
ejpam-3024	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3024	2	18	published	publish	VERB
ejpam-3024	2	19	by	by	ADP
ejpam-3024	2	20	new	new	PROPN
ejpam-3024	2	21	york	york	PROPN
ejpam-3024	2	22	business	business	PROPN
ejpam-3024	2	23	global	global	ADJ
ejpam-3024	2	24	modules	module	NOUN
ejpam-3024	2	25	that	that	PRON
ejpam-3024	2	26	have	have	VERB
ejpam-3024	2	27	a	a	DET
ejpam-3024	2	28	δ	δ	NOUN
ejpam-3024	2	29	-	-	NOUN
ejpam-3024	2	30	supplement	supplement	NOUN
ejpam-3024	2	31	in	in	ADP
ejpam-3024	2	32	every	every	DET
ejpam-3024	2	33	extension	extension	NOUN
ejpam-3024	2	34	esra	esra	PROPN
ejpam-3024	2	35	öztürk	öztürk	PROPN
ejpam-3024	2	36	sözen1,∗	sözen1,∗	NOUN
ejpam-3024	2	37	,	,	PUNCT
ejpam-3024	2	38	şenol	şenol	ADJ
ejpam-3024	2	39	eren1	eren1	ADJ
ejpam-3024	2	40	1	1	NUM
ejpam-3024	2	41	ondokuz	ondokuz	PROPN
ejpam-3024	2	42	mayıs	mayıs	PROPN
ejpam-3024	2	43	university	university	PROPN
ejpam-3024	2	44	,	,	PUNCT
ejpam-3024	2	45	faculty	faculty	NOUN
ejpam-3024	2	46	of	of	ADP
ejpam-3024	2	47	science	science	NOUN
ejpam-3024	2	48	and	and	CCONJ
ejpam-3024	2	49	arts	arts	PROPN
ejpam-3024	2	50	department	department	PROPN
ejpam-3024	2	51	of	of	ADP
ejpam-3024	2	52	mathematics	mathematics	PROPN
ejpam-3024	2	53	,	,	PUNCT
ejpam-3024	2	54	turkey	turkey	PROPN
ejpam-3024	2	55	abstract	abstract	NOUN
ejpam-3024	2	56	.	.	PUNCT
ejpam-3024	3	1	let	let	VERB
ejpam-3024	3	2	r	r	PRON
ejpam-3024	3	3	be	be	AUX
ejpam-3024	3	4	a	a	DET
ejpam-3024	3	5	ring	ring	NOUN
ejpam-3024	3	6	and	and	CCONJ
ejpam-3024	3	7	m	m	AUX
ejpam-3024	3	8	be	be	AUX
ejpam-3024	3	9	a	a	DET
ejpam-3024	3	10	left	left	ADJ
ejpam-3024	3	11	r	r	NOUN
ejpam-3024	3	12	-	-	PUNCT
ejpam-3024	3	13	module	module	NOUN
ejpam-3024	3	14	.	.	PUNCT
ejpam-3024	4	1	in	in	ADP
ejpam-3024	4	2	this	this	DET
ejpam-3024	4	3	paper	paper	NOUN
ejpam-3024	4	4	,	,	PUNCT
ejpam-3024	4	5	we	we	PRON
ejpam-3024	4	6	define	define	VERB
ejpam-3024	4	7	modules	module	NOUN
ejpam-3024	4	8	with	with	ADP
ejpam-3024	4	9	the	the	DET
ejpam-3024	4	10	properties	property	NOUN
ejpam-3024	4	11	(	(	PUNCT
ejpam-3024	4	12	δ	δ	PROPN
ejpam-3024	4	13	-	-	PUNCT
ejpam-3024	4	14	e	e	NOUN
ejpam-3024	4	15	)	)	PUNCT
ejpam-3024	4	16	and	and	CCONJ
ejpam-3024	4	17	(	(	PUNCT
ejpam-3024	4	18	δ	δ	PROPN
ejpam-3024	4	19	-	-	PUNCT
ejpam-3024	4	20	ee	ee	PROPN
ejpam-3024	4	21	)	)	PUNCT
ejpam-3024	4	22	,	,	PUNCT
ejpam-3024	4	23	which	which	PRON
ejpam-3024	4	24	are	be	AUX
ejpam-3024	4	25	generalized	generalize	VERB
ejpam-3024	4	26	version	version	NOUN
ejpam-3024	4	27	of	of	ADP
ejpam-3024	4	28	zöschinger	zöschinger	NOUN
ejpam-3024	4	29	’s	’s	PART
ejpam-3024	4	30	modules	module	NOUN
ejpam-3024	4	31	with	with	ADP
ejpam-3024	4	32	the	the	DET
ejpam-3024	4	33	properties	property	NOUN
ejpam-3024	4	34	(	(	PUNCT
ejpam-3024	4	35	e	e	NOUN
ejpam-3024	4	36	)	)	PUNCT
ejpam-3024	4	37	and	and	CCONJ
ejpam-3024	4	38	(	(	PUNCT
ejpam-3024	4	39	ee	ee	PROPN
ejpam-3024	4	40	)	)	PUNCT
ejpam-3024	4	41	,	,	PUNCT
ejpam-3024	4	42	and	and	CCONJ
ejpam-3024	4	43	provide	provide	VERB
ejpam-3024	4	44	various	various	ADJ
ejpam-3024	4	45	properties	property	NOUN
ejpam-3024	4	46	of	of	ADP
ejpam-3024	4	47	these	these	DET
ejpam-3024	4	48	modules	module	NOUN
ejpam-3024	4	49	.	.	PUNCT
ejpam-3024	5	1	we	we	PRON
ejpam-3024	5	2	prove	prove	VERB
ejpam-3024	5	3	that	that	SCONJ
ejpam-3024	5	4	the	the	DET
ejpam-3024	5	5	class	class	NOUN
ejpam-3024	5	6	of	of	ADP
ejpam-3024	5	7	modules	module	NOUN
ejpam-3024	5	8	with	with	ADP
ejpam-3024	5	9	the	the	DET
ejpam-3024	5	10	property	property	NOUN
ejpam-3024	5	11	(	(	PUNCT
ejpam-3024	5	12	δ	δ	PROPN
ejpam-3024	5	13	-	-	PUNCT
ejpam-3024	5	14	e	e	NOUN
ejpam-3024	5	15	)	)	PUNCT
ejpam-3024	5	16	is	be	AUX
ejpam-3024	5	17	closed	close	VERB
ejpam-3024	5	18	under	under	ADP
ejpam-3024	5	19	direct	direct	ADJ
ejpam-3024	5	20	summands	summand	NOUN
ejpam-3024	5	21	and	and	CCONJ
ejpam-3024	5	22	finite	finite	VERB
ejpam-3024	5	23	direct	direct	ADJ
ejpam-3024	5	24	sums	sum	NOUN
ejpam-3024	5	25	.	.	PUNCT
ejpam-3024	6	1	it	it	PRON
ejpam-3024	6	2	is	be	AUX
ejpam-3024	6	3	shown	show	VERB
ejpam-3024	6	4	that	that	SCONJ
ejpam-3024	6	5	a	a	DET
ejpam-3024	6	6	module	module	NOUN
ejpam-3024	6	7	m	m	VERB
ejpam-3024	6	8	has	have	VERB
ejpam-3024	6	9	the	the	DET
ejpam-3024	6	10	property	property	NOUN
ejpam-3024	6	11	(	(	PUNCT
ejpam-3024	6	12	δ	δ	PROPN
ejpam-3024	6	13	-	-	PUNCT
ejpam-3024	6	14	ee	ee	NOUN
ejpam-3024	6	15	)	)	PUNCT
ejpam-3024	7	1	if	if	SCONJ
ejpam-3024	7	2	and	and	CCONJ
ejpam-3024	7	3	only	only	ADV
ejpam-3024	7	4	if	if	SCONJ
ejpam-3024	7	5	every	every	DET
ejpam-3024	7	6	submodule	submodule	NOUN
ejpam-3024	7	7	of	of	ADP
ejpam-3024	7	8	m	m	PROPN
ejpam-3024	7	9	has	have	VERB
ejpam-3024	7	10	the	the	DET
ejpam-3024	7	11	property	property	NOUN
ejpam-3024	7	12	(	(	PUNCT
ejpam-3024	7	13	δ	δ	PROPN
ejpam-3024	7	14	-	-	PUNCT
ejpam-3024	7	15	e	e	PROPN
ejpam-3024	7	16	)	)	PUNCT
ejpam-3024	7	17	.	.	PUNCT
ejpam-3024	8	1	it	it	PRON
ejpam-3024	8	2	is	be	AUX
ejpam-3024	8	3	a	a	DET
ejpam-3024	8	4	known	known	ADJ
ejpam-3024	8	5	fact	fact	NOUN
ejpam-3024	8	6	that	that	SCONJ
ejpam-3024	8	7	a	a	DET
ejpam-3024	8	8	ring	ring	NOUN
ejpam-3024	8	9	r	r	NOUN
ejpam-3024	8	10	is	be	AUX
ejpam-3024	8	11	perfect	perfect	ADJ
ejpam-3024	8	12	if	if	SCONJ
ejpam-3024	8	13	and	and	CCONJ
ejpam-3024	8	14	only	only	ADV
ejpam-3024	8	15	if	if	SCONJ
ejpam-3024	8	16	every	every	DET
ejpam-3024	8	17	left	left	ADJ
ejpam-3024	8	18	r	r	NOUN
ejpam-3024	8	19	-	-	PUNCT
ejpam-3024	8	20	module	module	NOUN
ejpam-3024	8	21	has	have	VERB
ejpam-3024	8	22	the	the	DET
ejpam-3024	8	23	property	property	NOUN
ejpam-3024	8	24	(	(	PUNCT
ejpam-3024	8	25	e	e	NOUN
ejpam-3024	8	26	)	)	PUNCT
ejpam-3024	8	27	.	.	PUNCT
ejpam-3024	9	1	as	as	ADP
ejpam-3024	9	2	a	a	DET
ejpam-3024	9	3	generalization	generalization	NOUN
ejpam-3024	9	4	of	of	ADP
ejpam-3024	9	5	this	this	PRON
ejpam-3024	9	6	,	,	PUNCT
ejpam-3024	9	7	we	we	PRON
ejpam-3024	9	8	prove	prove	VERB
ejpam-3024	9	9	that	that	SCONJ
ejpam-3024	9	10	if	if	SCONJ
ejpam-3024	9	11	r	r	NOUN
ejpam-3024	9	12	is	be	AUX
ejpam-3024	9	13	a	a	DET
ejpam-3024	9	14	δ	δ	NOUN
ejpam-3024	9	15	-	-	PUNCT
ejpam-3024	9	16	perfect	perfect	ADJ
ejpam-3024	9	17	ring	ring	NOUN
ejpam-3024	9	18	then	then	ADV
ejpam-3024	9	19	every	every	DET
ejpam-3024	9	20	left	left	ADJ
ejpam-3024	9	21	r	r	NOUN
ejpam-3024	9	22	-	-	PUNCT
ejpam-3024	9	23	module	module	NOUN
ejpam-3024	9	24	has	have	VERB
ejpam-3024	9	25	the	the	DET
ejpam-3024	9	26	property	property	NOUN
ejpam-3024	9	27	(	(	PUNCT
ejpam-3024	9	28	δ	δ	PROPN
ejpam-3024	9	29	-	-	PUNCT
ejpam-3024	9	30	e	e	PROPN
ejpam-3024	9	31	)	)	PUNCT
ejpam-3024	9	32	.	.	PUNCT
ejpam-3024	10	1	moreover	moreover	ADV
ejpam-3024	10	2	,	,	PUNCT
ejpam-3024	10	3	the	the	DET
ejpam-3024	10	4	converse	converse	NOUN
ejpam-3024	10	5	is	be	AUX
ejpam-3024	10	6	also	also	ADV
ejpam-3024	10	7	true	true	ADJ
ejpam-3024	10	8	on	on	ADP
ejpam-3024	10	9	δ	δ	NOUN
ejpam-3024	10	10	-	-	PUNCT
ejpam-3024	10	11	semiperfect	semiperfect	ADJ
ejpam-3024	10	12	rings	ring	NOUN
ejpam-3024	10	13	.	.	PUNCT
ejpam-3024	11	1	2010	2010	NUM
ejpam-3024	11	2	mathematics	mathematic	NOUN
ejpam-3024	11	3	subject	subject	NOUN
ejpam-3024	11	4	classifications	classification	NOUN
ejpam-3024	11	5	:	:	PUNCT
ejpam-3024	11	6	16d10	16d10	NUM
ejpam-3024	11	7	,	,	PUNCT
ejpam-3024	11	8	16d90	16d90	NUM
ejpam-3024	11	9	key	key	ADJ
ejpam-3024	11	10	words	word	NOUN
ejpam-3024	11	11	and	and	CCONJ
ejpam-3024	11	12	phrases	phrase	NOUN
ejpam-3024	11	13	:	:	PUNCT
ejpam-3024	11	14	supplement	supplement	NOUN
ejpam-3024	11	15	,	,	PUNCT
ejpam-3024	11	16	δ	δ	NOUN
ejpam-3024	11	17	-	-	PUNCT
ejpam-3024	11	18	supplement	supplement	NOUN
ejpam-3024	11	19	,	,	PUNCT
ejpam-3024	11	20	δ	δ	NOUN
ejpam-3024	11	21	-	-	PUNCT
ejpam-3024	11	22	perfect	perfect	ADJ
ejpam-3024	11	23	ring	ring	NOUN
ejpam-3024	11	24	,	,	PUNCT
ejpam-3024	11	25	δ	δ	PROPN
ejpam-3024	11	26	-	-	PUNCT
ejpam-3024	11	27	semiperfect	semiperfect	ADJ
ejpam-3024	11	28	ring	ring	NOUN
ejpam-3024	11	29	,	,	PUNCT
ejpam-3024	11	30	module	module	NOUN
ejpam-3024	11	31	extension	extension	NOUN
ejpam-3024	11	32	1	1	NUM
ejpam-3024	11	33	.	.	PUNCT
ejpam-3024	12	1	introduction	introduction	NOUN
ejpam-3024	12	2	in	in	ADP
ejpam-3024	12	3	this	this	DET
ejpam-3024	12	4	paper	paper	NOUN
ejpam-3024	12	5	r	r	NOUN
ejpam-3024	12	6	is	be	AUX
ejpam-3024	12	7	an	an	DET
ejpam-3024	12	8	associative	associative	ADJ
ejpam-3024	12	9	ring	ring	NOUN
ejpam-3024	12	10	with	with	ADP
ejpam-3024	12	11	identity	identity	NOUN
ejpam-3024	12	12	and	and	CCONJ
ejpam-3024	12	13	all	all	DET
ejpam-3024	12	14	modules	module	NOUN
ejpam-3024	12	15	are	be	AUX
ejpam-3024	12	16	unital	unital	ADJ
ejpam-3024	12	17	left	left	ADJ
ejpam-3024	12	18	r	r	NOUN
ejpam-3024	12	19	-	-	PUNCT
ejpam-3024	12	20	modules	module	NOUN
ejpam-3024	12	21	.	.	PUNCT
ejpam-3024	13	1	let	let	VERB
ejpam-3024	13	2	m	m	PRON
ejpam-3024	13	3	be	be	AUX
ejpam-3024	13	4	a	a	DET
ejpam-3024	13	5	module	module	NOUN
ejpam-3024	13	6	x	x	SYM
ejpam-3024	13	7	≤	≤	NOUN
ejpam-3024	13	8	m	m	VERB
ejpam-3024	13	9	means	mean	VERB
ejpam-3024	13	10	that	that	SCONJ
ejpam-3024	13	11	x	x	PRON
ejpam-3024	13	12	is	be	AUX
ejpam-3024	13	13	a	a	DET
ejpam-3024	13	14	submodule	submodule	NOUN
ejpam-3024	13	15	of	of	ADP
ejpam-3024	13	16	m	m	PROPN
ejpam-3024	13	17	or	or	CCONJ
ejpam-3024	13	18	m	m	VERB
ejpam-3024	13	19	is	be	AUX
ejpam-3024	13	20	an	an	DET
ejpam-3024	13	21	extension	extension	NOUN
ejpam-3024	13	22	of	of	ADP
ejpam-3024	13	23	x.	x.	NOUN
ejpam-3024	13	24	recall	recall	VERB
ejpam-3024	13	25	that	that	SCONJ
ejpam-3024	13	26	a	a	DET
ejpam-3024	13	27	submodule	submodule	NOUN
ejpam-3024	13	28	n	n	CCONJ
ejpam-3024	13	29	≤	≤	NOUN
ejpam-3024	13	30	m	m	VERB
ejpam-3024	13	31	is	be	AUX
ejpam-3024	13	32	called	call	VERB
ejpam-3024	13	33	small	small	ADJ
ejpam-3024	13	34	,	,	PUNCT
ejpam-3024	13	35	denoted	denote	VERB
ejpam-3024	13	36	by	by	ADP
ejpam-3024	13	37	n	n	PRON
ejpam-3024	13	38	�	�	PROPN
ejpam-3024	13	39	m	m	PROPN
ejpam-3024	13	40	,	,	PUNCT
ejpam-3024	13	41	if	if	SCONJ
ejpam-3024	13	42	n	n	PROPN
ejpam-3024	13	43	+	+	X
ejpam-3024	13	44	l	l	NOUN
ejpam-3024	14	1	6=	6=	NUM
ejpam-3024	14	2	m	m	PROPN
ejpam-3024	14	3	,	,	PUNCT
ejpam-3024	14	4	for	for	ADP
ejpam-3024	14	5	all	all	DET
ejpam-3024	14	6	proper	proper	ADJ
ejpam-3024	14	7	submodules	submodule	NOUN
ejpam-3024	14	8	l	l	NOUN
ejpam-3024	14	9	of	of	ADP
ejpam-3024	14	10	m.	m.	NOUN
ejpam-3024	14	11	we	we	PRON
ejpam-3024	14	12	call	call	VERB
ejpam-3024	14	13	t	t	PROPN
ejpam-3024	14	14	a	a	DET
ejpam-3024	14	15	supplement	supplement	NOUN
ejpam-3024	14	16	of	of	ADP
ejpam-3024	14	17	n	n	PROPN
ejpam-3024	14	18	in	in	ADP
ejpam-3024	14	19	m	m	PROPN
ejpam-3024	14	20	if	if	SCONJ
ejpam-3024	14	21	m	m	VERB
ejpam-3024	14	22	=	=	SYM
ejpam-3024	14	23	t	t	PROPN
ejpam-3024	14	24	+	+	CCONJ
ejpam-3024	14	25	n	n	PROPN
ejpam-3024	14	26	and	and	CCONJ
ejpam-3024	14	27	t	t	PROPN
ejpam-3024	14	28	∩	∩	NOUN
ejpam-3024	14	29	n	n	PART
ejpam-3024	14	30	is	be	AUX
ejpam-3024	14	31	small	small	ADJ
ejpam-3024	14	32	in	in	ADP
ejpam-3024	14	33	t.	t.	PROPN
ejpam-3024	14	34	a	a	DET
ejpam-3024	14	35	module	module	NOUN
ejpam-3024	14	36	m	m	VERB
ejpam-3024	14	37	is	be	AUX
ejpam-3024	14	38	called	call	VERB
ejpam-3024	14	39	supplemented	supplement	VERB
ejpam-3024	14	40	if	if	SCONJ
ejpam-3024	14	41	every	every	DET
ejpam-3024	14	42	submodule	submodule	NOUN
ejpam-3024	14	43	of	of	ADP
ejpam-3024	14	44	m	m	PROPN
ejpam-3024	14	45	has	have	VERB
ejpam-3024	14	46	a	a	DET
ejpam-3024	14	47	supplement	supplement	NOUN
ejpam-3024	14	48	in	in	ADP
ejpam-3024	14	49	m	m	PROPN
ejpam-3024	14	50	[	[	X
ejpam-3024	14	51	14	14	NUM
ejpam-3024	14	52	]	]	PUNCT
ejpam-3024	14	53	.	.	PUNCT
ejpam-3024	15	1	l	l	PROPN
ejpam-3024	15	2	≤m	≤m	PROPN
ejpam-3024	15	3	is	be	AUX
ejpam-3024	15	4	said	say	VERB
ejpam-3024	15	5	to	to	PART
ejpam-3024	15	6	be	be	AUX
ejpam-3024	15	7	essential	essential	ADJ
ejpam-3024	15	8	in	in	ADP
ejpam-3024	15	9	m	m	PROPN
ejpam-3024	15	10	,	,	PUNCT
ejpam-3024	15	11	denoted	denote	VERB
ejpam-3024	15	12	by	by	ADP
ejpam-3024	15	13	l	l	PROPN
ejpam-3024	15	14	em	em	PRON
ejpam-3024	15	15	,	,	PUNCT
ejpam-3024	15	16	if	if	SCONJ
ejpam-3024	15	17	l	l	PROPN
ejpam-3024	15	18	∩	∩	X
ejpam-3024	15	19	k	k	PROPN
ejpam-3024	15	20	6=	6=	PROPN
ejpam-3024	15	21	0	0	NUM
ejpam-3024	15	22	for	for	ADP
ejpam-3024	15	23	each	each	DET
ejpam-3024	15	24	nonzero	nonzero	PROPN
ejpam-3024	15	25	submodule	submodule	PROPN
ejpam-3024	15	26	k	k	PROPN
ejpam-3024	15	27	≤	≤	PROPN
ejpam-3024	15	28	m.	m.	NOUN
ejpam-3024	15	29	the	the	DET
ejpam-3024	15	30	singular	singular	PROPN
ejpam-3024	15	31	submodule	submodule	NOUN
ejpam-3024	15	32	of	of	ADP
ejpam-3024	15	33	a	a	DET
ejpam-3024	15	34	module	module	NOUN
ejpam-3024	15	35	m	m	VERB
ejpam-3024	15	36	(	(	PUNCT
ejpam-3024	15	37	denoted	denote	VERB
ejpam-3024	15	38	by	by	ADP
ejpam-3024	15	39	z(m	z(m	NOUN
ejpam-3024	15	40	)	)	PUNCT
ejpam-3024	15	41	)	)	PUNCT
ejpam-3024	16	1	is	be	AUX
ejpam-3024	16	2	z(m	z(m	NOUN
ejpam-3024	16	3	)	)	PUNCT
ejpam-3024	16	4	=	=	PRON
ejpam-3024	17	1	{	{	PUNCT
ejpam-3024	17	2	x	x	X
ejpam-3024	17	3	∈m	∈m	NOUN
ejpam-3024	17	4	|	|	ADV
ejpam-3024	17	5	ix	ix	ADV
ejpam-3024	17	6	=	=	NOUN
ejpam-3024	17	7	0	0	NUM
ejpam-3024	17	8	for	for	ADP
ejpam-3024	17	9	some	some	DET
ejpam-3024	17	10	ideal	ideal	NOUN
ejpam-3024	17	11	i	i	PRON
ejpam-3024	17	12	er	er	INTJ
ejpam-3024	17	13	}	}	PUNCT
ejpam-3024	17	14	.	.	PUNCT
ejpam-3024	18	1	a	a	DET
ejpam-3024	18	2	module	module	NOUN
ejpam-3024	18	3	m	m	VERB
ejpam-3024	18	4	is	be	AUX
ejpam-3024	18	5	called	call	VERB
ejpam-3024	18	6	singular	singular	ADJ
ejpam-3024	18	7	if	if	SCONJ
ejpam-3024	18	8	z(m	z(m	NOUN
ejpam-3024	18	9	)	)	PUNCT
ejpam-3024	18	10	=	=	VERB
ejpam-3024	18	11	m.	m.	NOUN
ejpam-3024	18	12	every	every	DET
ejpam-3024	18	13	submodule	submodule	NOUN
ejpam-3024	18	14	and	and	CCONJ
ejpam-3024	18	15	every	every	DET
ejpam-3024	18	16	factor	factor	NOUN
ejpam-3024	18	17	module	module	NOUN
ejpam-3024	18	18	of	of	ADP
ejpam-3024	18	19	a	a	DET
ejpam-3024	18	20	singular	singular	ADJ
ejpam-3024	18	21	module	module	NOUN
ejpam-3024	18	22	is	be	AUX
ejpam-3024	18	23	singular	singular	ADJ
ejpam-3024	18	24	.	.	PUNCT
ejpam-3024	19	1	we	we	PRON
ejpam-3024	19	2	refer	refer	VERB
ejpam-3024	19	3	to	to	ADP
ejpam-3024	19	4	[	[	X
ejpam-3024	19	5	6	6	NUM
ejpam-3024	19	6	]	]	PUNCT
ejpam-3024	19	7	for	for	ADP
ejpam-3024	19	8	the	the	DET
ejpam-3024	19	9	further	further	ADJ
ejpam-3024	19	10	properties	property	NOUN
ejpam-3024	19	11	of	of	ADP
ejpam-3024	19	12	singular	singular	ADJ
ejpam-3024	19	13	modules	module	NOUN
ejpam-3024	19	14	.	.	PUNCT
ejpam-3024	20	1	in	in	ADP
ejpam-3024	20	2	[	[	X
ejpam-3024	20	3	15	15	NUM
ejpam-3024	20	4	]	]	PUNCT
ejpam-3024	20	5	,	,	PUNCT
ejpam-3024	20	6	zhou	zhou	PROPN
ejpam-3024	20	7	introduced	introduce	VERB
ejpam-3024	20	8	the	the	DET
ejpam-3024	20	9	concept	concept	NOUN
ejpam-3024	20	10	of	of	ADP
ejpam-3024	20	11	δ	δ	NOUN
ejpam-3024	20	12	-	-	ADJ
ejpam-3024	20	13	small	small	ADJ
ejpam-3024	20	14	submodules	submodule	NOUN
ejpam-3024	20	15	as	as	ADP
ejpam-3024	20	16	a	a	DET
ejpam-3024	20	17	generalization	generalization	NOUN
ejpam-3024	20	18	of	of	ADP
ejpam-3024	20	19	small	small	ADJ
ejpam-3024	20	20	submodules	submodule	NOUN
ejpam-3024	20	21	.	.	PUNCT
ejpam-3024	21	1	a	a	DET
ejpam-3024	21	2	submodule	submodule	NOUN
ejpam-3024	21	3	n	n	PROPN
ejpam-3024	21	4	of	of	ADP
ejpam-3024	21	5	m	m	PROPN
ejpam-3024	21	6	is	be	AUX
ejpam-3024	21	7	said	say	VERB
ejpam-3024	21	8	to	to	PART
ejpam-3024	21	9	be	be	AUX
ejpam-3024	21	10	δ	δ	NOUN
ejpam-3024	21	11	-	-	ADJ
ejpam-3024	21	12	small	small	ADJ
ejpam-3024	21	13	in	in	ADP
ejpam-3024	21	14	m	m	PROPN
ejpam-3024	21	15	(	(	PUNCT
ejpam-3024	21	16	denoted	denote	VERB
ejpam-3024	21	17	by	by	ADP
ejpam-3024	21	18	n	n	DET
ejpam-3024	21	19	�	�	PROPN
ejpam-3024	21	20	δ	δ	PROPN
ejpam-3024	21	21	m	m	PROPN
ejpam-3024	21	22	)	)	PUNCT
ejpam-3024	21	23	if	if	SCONJ
ejpam-3024	21	24	whenever	whenever	SCONJ
ejpam-3024	21	25	m	m	VERB
ejpam-3024	21	26	=	=	SYM
ejpam-3024	21	27	n	n	PROPN
ejpam-3024	21	28	+	+	CCONJ
ejpam-3024	22	1	k	k	PROPN
ejpam-3024	22	2	and	and	CCONJ
ejpam-3024	22	3	m	m	PROPN
ejpam-3024	22	4	k	k	PROPN
ejpam-3024	22	5	is	be	AUX
ejpam-3024	22	6	singular	singular	ADJ
ejpam-3024	22	7	,	,	PUNCT
ejpam-3024	22	8	we	we	PRON
ejpam-3024	22	9	have	have	VERB
ejpam-3024	22	10	m	m	NOUN
ejpam-3024	22	11	=	=	PUNCT
ejpam-3024	22	12	k.	k.	PROPN
ejpam-3024	23	1	and	and	CCONJ
ejpam-3024	23	2	we	we	PRON
ejpam-3024	23	3	denote	denote	VERB
ejpam-3024	23	4	the	the	DET
ejpam-3024	23	5	sum	sum	NOUN
ejpam-3024	23	6	of	of	ADP
ejpam-3024	23	7	all	all	DET
ejpam-3024	23	8	δ	δ	NOUN
ejpam-3024	23	9	-	-	ADJ
ejpam-3024	23	10	small	small	ADJ
ejpam-3024	23	11	submodules	submodule	NOUN
ejpam-3024	23	12	of	of	ADP
ejpam-3024	23	13	m	m	PRON
ejpam-3024	23	14	by	by	ADP
ejpam-3024	23	15	δ(m	δ(m	PROPN
ejpam-3024	23	16	)	)	PUNCT
ejpam-3024	23	17	.	.	PUNCT
ejpam-3024	24	1	a	a	DET
ejpam-3024	24	2	submodule	submodule	PROPN
ejpam-3024	24	3	l	l	NOUN
ejpam-3024	24	4	of	of	ADP
ejpam-3024	24	5	m	m	PROPN
ejpam-3024	24	6	is	be	AUX
ejpam-3024	24	7	called	call	VERB
ejpam-3024	24	8	a	a	DET
ejpam-3024	24	9	δ	δ	NOUN
ejpam-3024	24	10	-	-	NOUN
ejpam-3024	24	11	supplement	supplement	NOUN
ejpam-3024	24	12	of	of	ADP
ejpam-3024	24	13	∗corresponding	∗corresponde	VERB
ejpam-3024	24	14	author	author	NOUN
ejpam-3024	24	15	.	.	PUNCT
ejpam-3024	25	1	email	email	NOUN
ejpam-3024	25	2	addresses	address	NOUN
ejpam-3024	25	3	:	:	PUNCT
ejpam-3024	25	4	esraozturk55@hotmail.com	esraozturk55@hotmail.com	X
ejpam-3024	25	5	(	(	PUNCT
ejpam-3024	25	6	e.	e.	PROPN
ejpam-3024	25	7	ö.	ö.	PROPN
ejpam-3024	25	8	sözen	sözen	PROPN
ejpam-3024	25	9	)	)	PUNCT
ejpam-3024	25	10	,	,	PUNCT
ejpam-3024	25	11	seren@omu.edu.tr	seren@omu.edu.tr	X
ejpam-3024	25	12	(	(	PUNCT
ejpam-3024	25	13	ş.	ş.	PROPN
ejpam-3024	25	14	eren	eren	PROPN
ejpam-3024	25	15	)	)	PUNCT
ejpam-3024	25	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3024	26	1	730	730	NUM
ejpam-3024	26	2	c	c	X
ejpam-3024	26	3	©	©	PROPN
ejpam-3024	26	4	2017	2017	NUM
ejpam-3024	26	5	ejpam	ejpam	VERB
ejpam-3024	26	6	all	all	DET
ejpam-3024	26	7	rights	right	NOUN
ejpam-3024	26	8	reserved	reserve	VERB
ejpam-3024	26	9	.	.	PUNCT
ejpam-3024	27	1	e.	e.	PROPN
ejpam-3024	27	2	ö.	ö.	PROPN
ejpam-3024	27	3	sözen	sözen	PROPN
ejpam-3024	27	4	,	,	PUNCT
ejpam-3024	27	5	ş.	ş.	PROPN
ejpam-3024	27	6	eren	eren	PROPN
ejpam-3024	27	7	/	/	SYM
ejpam-3024	27	8	eur	eur	PROPN
ejpam-3024	27	9	.	.	PUNCT
ejpam-3024	28	1	j.	j.	PROPN
ejpam-3024	28	2	pure	pure	PROPN
ejpam-3024	28	3	appl	appl	PROPN
ejpam-3024	28	4	.	.	PROPN
ejpam-3024	28	5	math	math	PROPN
ejpam-3024	28	6	,	,	PUNCT
ejpam-3024	28	7	10	10	NUM
ejpam-3024	28	8	(	(	PUNCT
ejpam-3024	28	9	4	4	NUM
ejpam-3024	28	10	)	)	PUNCT
ejpam-3024	28	11	(	(	PUNCT
ejpam-3024	28	12	2017	2017	NUM
ejpam-3024	28	13	)	)	PUNCT
ejpam-3024	28	14	,	,	PUNCT
ejpam-3024	28	15	730	730	NUM
ejpam-3024	28	16	-	-	SYM
ejpam-3024	28	17	738	738	NUM
ejpam-3024	28	18	731	731	NUM
ejpam-3024	28	19	n	n	NOUN
ejpam-3024	28	20	in	in	ADP
ejpam-3024	28	21	m	m	PROPN
ejpam-3024	28	22	if	if	SCONJ
ejpam-3024	28	23	m	m	VERB
ejpam-3024	28	24	=	=	SYM
ejpam-3024	28	25	n	n	PROPN
ejpam-3024	28	26	+	+	CCONJ
ejpam-3024	28	27	l	l	NOUN
ejpam-3024	28	28	and	and	CCONJ
ejpam-3024	28	29	n	n	PROPN
ejpam-3024	28	30	∩	∩	ADJ
ejpam-3024	28	31	l	l	NOUN
ejpam-3024	28	32	�	�	PROPN
ejpam-3024	28	33	δ	δ	PROPN
ejpam-3024	28	34	l	l	NOUN
ejpam-3024	28	35	and	and	CCONJ
ejpam-3024	28	36	m	m	PROPN
ejpam-3024	28	37	is	be	AUX
ejpam-3024	28	38	called	call	VERB
ejpam-3024	28	39	δ	δ	NOUN
ejpam-3024	28	40	-	-	PUNCT
ejpam-3024	28	41	supplemented	supplement	VERB
ejpam-3024	28	42	in	in	ADP
ejpam-3024	28	43	case	case	NOUN
ejpam-3024	28	44	every	every	DET
ejpam-3024	28	45	submodule	submodule	NOUN
ejpam-3024	28	46	of	of	ADP
ejpam-3024	28	47	m	m	PROPN
ejpam-3024	28	48	has	have	VERB
ejpam-3024	28	49	a	a	DET
ejpam-3024	28	50	δ	δ	NOUN
ejpam-3024	28	51	-	-	PUNCT
ejpam-3024	28	52	supplement	supplement	NOUN
ejpam-3024	28	53	in	in	ADP
ejpam-3024	28	54	m	m	PROPN
ejpam-3024	28	55	[	[	X
ejpam-3024	28	56	7	7	NUM
ejpam-3024	28	57	]	]	PUNCT
ejpam-3024	28	58	.	.	PUNCT
ejpam-3024	29	1	for	for	ADP
ejpam-3024	29	2	a	a	DET
ejpam-3024	29	3	module	module	NOUN
ejpam-3024	29	4	m	m	PRON
ejpam-3024	29	5	consider	consider	VERB
ejpam-3024	29	6	the	the	DET
ejpam-3024	29	7	following	follow	VERB
ejpam-3024	29	8	conditions	condition	NOUN
ejpam-3024	29	9	:	:	PUNCT
ejpam-3024	29	10	(	(	PUNCT
ejpam-3024	29	11	e	e	NOUN
ejpam-3024	29	12	)	)	PUNCT
ejpam-3024	29	13	:	:	PUNCT
ejpam-3024	29	14	m	m	VERB
ejpam-3024	29	15	has	have	VERB
ejpam-3024	29	16	a	a	DET
ejpam-3024	29	17	supplement	supplement	NOUN
ejpam-3024	29	18	in	in	ADP
ejpam-3024	29	19	every	every	DET
ejpam-3024	29	20	extension	extension	NOUN
ejpam-3024	29	21	.	.	PUNCT
ejpam-3024	30	1	(	(	PUNCT
ejpam-3024	30	2	ee	ee	PROPN
ejpam-3024	30	3	)	)	PUNCT
ejpam-3024	30	4	:	:	PUNCT
ejpam-3024	30	5	m	m	VERB
ejpam-3024	30	6	has	have	VERB
ejpam-3024	30	7	ample	ample	ADJ
ejpam-3024	30	8	supplements	supplement	NOUN
ejpam-3024	30	9	in	in	ADP
ejpam-3024	30	10	every	every	DET
ejpam-3024	30	11	extension	extension	NOUN
ejpam-3024	30	12	.	.	PUNCT
ejpam-3024	31	1	the	the	DET
ejpam-3024	31	2	concept	concept	NOUN
ejpam-3024	31	3	of	of	ADP
ejpam-3024	31	4	these	these	DET
ejpam-3024	31	5	modules	module	NOUN
ejpam-3024	31	6	with	with	ADP
ejpam-3024	31	7	these	these	DET
ejpam-3024	31	8	properties	property	NOUN
ejpam-3024	31	9	was	be	AUX
ejpam-3024	31	10	first	first	ADV
ejpam-3024	31	11	introduced	introduce	VERB
ejpam-3024	31	12	by	by	ADP
ejpam-3024	31	13	zöschinger	zöschinger	NOUN
ejpam-3024	31	14	[	[	X
ejpam-3024	31	15	16	16	NUM
ejpam-3024	31	16	]	]	PUNCT
ejpam-3024	31	17	.	.	PUNCT
ejpam-3024	32	1	adapting	adapt	VERB
ejpam-3024	32	2	his	his	PRON
ejpam-3024	32	3	concept	concept	NOUN
ejpam-3024	32	4	in	in	ADP
ejpam-3024	32	5	[	[	X
ejpam-3024	32	6	4	4	NUM
ejpam-3024	32	7	]	]	PUNCT
ejpam-3024	32	8	,	,	PUNCT
ejpam-3024	32	9	çalışıcı	çalışıcı	NOUN
ejpam-3024	32	10	and	and	CCONJ
ejpam-3024	32	11	türkmen	türkman	NOUN
ejpam-3024	32	12	introduced	introduce	VERB
ejpam-3024	32	13	modules	module	NOUN
ejpam-3024	32	14	with	with	ADP
ejpam-3024	32	15	the	the	DET
ejpam-3024	32	16	properties	property	NOUN
ejpam-3024	32	17	(	(	PUNCT
ejpam-3024	32	18	ce	ce	PROPN
ejpam-3024	32	19	)	)	PUNCT
ejpam-3024	32	20	and	and	CCONJ
ejpam-3024	32	21	(	(	PUNCT
ejpam-3024	32	22	cee	cee	PROPN
ejpam-3024	32	23	)	)	PUNCT
ejpam-3024	32	24	as	as	ADP
ejpam-3024	32	25	a	a	DET
ejpam-3024	32	26	generalization	generalization	NOUN
ejpam-3024	32	27	of	of	ADP
ejpam-3024	32	28	the	the	DET
ejpam-3024	32	29	properties	property	NOUN
ejpam-3024	32	30	(	(	PUNCT
ejpam-3024	32	31	e	e	NOUN
ejpam-3024	32	32	)	)	PUNCT
ejpam-3024	32	33	and	and	CCONJ
ejpam-3024	32	34	(	(	PUNCT
ejpam-3024	32	35	ee	ee	PROPN
ejpam-3024	32	36	)	)	PUNCT
ejpam-3024	32	37	.	.	PUNCT
ejpam-3024	33	1	in	in	ADP
ejpam-3024	33	2	addition	addition	NOUN
ejpam-3024	33	3	,	,	PUNCT
ejpam-3024	33	4	in	in	ADP
ejpam-3024	33	5	[	[	PUNCT
ejpam-3024	33	6	9	9	NUM
ejpam-3024	33	7	]	]	PUNCT
ejpam-3024	33	8	the	the	DET
ejpam-3024	33	9	authors	author	NOUN
ejpam-3024	33	10	worked	work	VERB
ejpam-3024	33	11	on	on	ADP
ejpam-3024	33	12	modules	module	NOUN
ejpam-3024	33	13	that	that	PRON
ejpam-3024	33	14	have	have	VERB
ejpam-3024	33	15	a	a	DET
ejpam-3024	33	16	weak	weak	ADJ
ejpam-3024	33	17	supplement	supplement	NOUN
ejpam-3024	33	18	in	in	ADP
ejpam-3024	33	19	every	every	DET
ejpam-3024	33	20	extension	extension	NOUN
ejpam-3024	33	21	and	and	CCONJ
ejpam-3024	33	22	in	in	ADP
ejpam-3024	33	23	[	[	X
ejpam-3024	33	24	5	5	NUM
ejpam-3024	33	25	]	]	X
ejpam-3024	33	26	eryılmaz	eryılmaz	ADJ
ejpam-3024	33	27	introduced	introduce	VERB
ejpam-3024	33	28	modules	module	NOUN
ejpam-3024	33	29	that	that	PRON
ejpam-3024	33	30	have	have	VERB
ejpam-3024	33	31	a	a	DET
ejpam-3024	33	32	δ	δ	NOUN
ejpam-3024	33	33	-	-	NOUN
ejpam-3024	33	34	supplement	supplement	NOUN
ejpam-3024	33	35	in	in	ADP
ejpam-3024	33	36	every	every	DET
ejpam-3024	33	37	torsion	torsion	NOUN
ejpam-3024	33	38	extension	extension	NOUN
ejpam-3024	33	39	.	.	PUNCT
ejpam-3024	34	1	in	in	ADP
ejpam-3024	34	2	this	this	DET
ejpam-3024	34	3	paper	paper	NOUN
ejpam-3024	34	4	we	we	PRON
ejpam-3024	34	5	investigate	investigate	VERB
ejpam-3024	34	6	the	the	DET
ejpam-3024	34	7	structure	structure	NOUN
ejpam-3024	34	8	of	of	ADP
ejpam-3024	34	9	modules	module	NOUN
ejpam-3024	34	10	with	with	ADP
ejpam-3024	34	11	the	the	DET
ejpam-3024	34	12	properties	property	NOUN
ejpam-3024	34	13	(	(	PUNCT
ejpam-3024	34	14	δ	δ	PROPN
ejpam-3024	34	15	-	-	PUNCT
ejpam-3024	34	16	e	e	NOUN
ejpam-3024	34	17	)	)	PUNCT
ejpam-3024	34	18	and	and	CCONJ
ejpam-3024	34	19	(	(	PUNCT
ejpam-3024	34	20	δ	δ	PROPN
ejpam-3024	34	21	-	-	PUNCT
ejpam-3024	34	22	ee	ee	NOUN
ejpam-3024	34	23	)	)	PUNCT
ejpam-3024	34	24	as	as	ADP
ejpam-3024	34	25	a	a	DET
ejpam-3024	34	26	generalization	generalization	NOUN
ejpam-3024	34	27	of	of	ADP
ejpam-3024	34	28	zöschinger	zöschinger	PROPN
ejpam-3024	34	29	’s	’s	PART
ejpam-3024	34	30	modules	module	NOUN
ejpam-3024	34	31	with	with	ADP
ejpam-3024	34	32	the	the	DET
ejpam-3024	34	33	properties	property	NOUN
ejpam-3024	34	34	(	(	PUNCT
ejpam-3024	34	35	e	e	NOUN
ejpam-3024	34	36	)	)	PUNCT
ejpam-3024	34	37	and	and	CCONJ
ejpam-3024	34	38	(	(	PUNCT
ejpam-3024	34	39	ee	ee	PROPN
ejpam-3024	34	40	)	)	PUNCT
ejpam-3024	34	41	.	.	PUNCT
ejpam-3024	35	1	we	we	PRON
ejpam-3024	35	2	prove	prove	VERB
ejpam-3024	35	3	that	that	SCONJ
ejpam-3024	35	4	a	a	DET
ejpam-3024	35	5	module	module	NOUN
ejpam-3024	35	6	has	have	VERB
ejpam-3024	35	7	the	the	DET
ejpam-3024	35	8	property	property	NOUN
ejpam-3024	35	9	(	(	PUNCT
ejpam-3024	35	10	δ	δ	PROPN
ejpam-3024	35	11	-	-	PUNCT
ejpam-3024	35	12	ee	ee	NOUN
ejpam-3024	35	13	)	)	PUNCT
ejpam-3024	36	1	if	if	SCONJ
ejpam-3024	36	2	and	and	CCONJ
ejpam-3024	36	3	only	only	ADV
ejpam-3024	36	4	if	if	SCONJ
ejpam-3024	36	5	every	every	DET
ejpam-3024	36	6	submodule	submodule	NOUN
ejpam-3024	36	7	has	have	VERB
ejpam-3024	36	8	the	the	DET
ejpam-3024	36	9	property	property	NOUN
ejpam-3024	36	10	(	(	PUNCT
ejpam-3024	36	11	δ	δ	PROPN
ejpam-3024	36	12	-	-	PUNCT
ejpam-3024	36	13	e	e	PROPN
ejpam-3024	36	14	)	)	PUNCT
ejpam-3024	36	15	.	.	PUNCT
ejpam-3024	37	1	we	we	PRON
ejpam-3024	37	2	show	show	VERB
ejpam-3024	37	3	that	that	SCONJ
ejpam-3024	37	4	every	every	DET
ejpam-3024	37	5	direct	direct	ADJ
ejpam-3024	37	6	summand	summand	NOUN
ejpam-3024	37	7	and	and	CCONJ
ejpam-3024	37	8	δ	δ	NOUN
ejpam-3024	37	9	-	-	ADJ
ejpam-3024	37	10	small	small	ADJ
ejpam-3024	37	11	cover	cover	NOUN
ejpam-3024	37	12	of	of	ADP
ejpam-3024	37	13	m	m	PROPN
ejpam-3024	37	14	with	with	ADP
ejpam-3024	37	15	the	the	DET
ejpam-3024	37	16	property	property	NOUN
ejpam-3024	37	17	(	(	PUNCT
ejpam-3024	37	18	δ	δ	PROPN
ejpam-3024	37	19	-	-	PUNCT
ejpam-3024	37	20	e	e	PROPN
ejpam-3024	37	21	)	)	PUNCT
ejpam-3024	37	22	has	have	VERB
ejpam-3024	37	23	the	the	DET
ejpam-3024	37	24	property	property	NOUN
ejpam-3024	37	25	(	(	PUNCT
ejpam-3024	37	26	δ	δ	PROPN
ejpam-3024	37	27	-	-	PUNCT
ejpam-3024	37	28	e	e	NOUN
ejpam-3024	37	29	)	)	PUNCT
ejpam-3024	37	30	.	.	PUNCT
ejpam-3024	38	1	using	use	VERB
ejpam-3024	38	2	the	the	DET
ejpam-3024	38	3	property	property	NOUN
ejpam-3024	38	4	(	(	PUNCT
ejpam-3024	38	5	δ	δ	PROPN
ejpam-3024	38	6	-	-	PUNCT
ejpam-3024	38	7	e	e	PROPN
ejpam-3024	38	8	)	)	PUNCT
ejpam-3024	38	9	,	,	PUNCT
ejpam-3024	38	10	we	we	PRON
ejpam-3024	38	11	present	present	VERB
ejpam-3024	38	12	a	a	DET
ejpam-3024	38	13	relation	relation	NOUN
ejpam-3024	38	14	between	between	ADP
ejpam-3024	38	15	δ	δ	NOUN
ejpam-3024	38	16	-	-	PUNCT
ejpam-3024	38	17	perfect	perfect	ADJ
ejpam-3024	38	18	rings	ring	NOUN
ejpam-3024	38	19	and	and	CCONJ
ejpam-3024	38	20	modules	module	NOUN
ejpam-3024	38	21	with	with	ADP
ejpam-3024	38	22	the	the	DET
ejpam-3024	38	23	property	property	NOUN
ejpam-3024	38	24	(	(	PUNCT
ejpam-3024	38	25	δ	δ	PROPN
ejpam-3024	38	26	-	-	PUNCT
ejpam-3024	38	27	e	e	PROPN
ejpam-3024	38	28	)	)	PUNCT
ejpam-3024	38	29	,	,	PUNCT
ejpam-3024	38	30	which	which	PRON
ejpam-3024	38	31	are	be	AUX
ejpam-3024	38	32	a	a	DET
ejpam-3024	38	33	generalization	generalization	NOUN
ejpam-3024	38	34	of	of	ADP
ejpam-3024	38	35	perfect	perfect	ADJ
ejpam-3024	38	36	rings	ring	NOUN
ejpam-3024	38	37	,	,	PUNCT
ejpam-3024	38	38	that	that	ADV
ejpam-3024	38	39	is	is	ADV
ejpam-3024	38	40	,	,	PUNCT
ejpam-3024	38	41	r	r	NOUN
ejpam-3024	38	42	is	be	AUX
ejpam-3024	38	43	a	a	DET
ejpam-3024	38	44	δ	δ	NOUN
ejpam-3024	38	45	-	-	PUNCT
ejpam-3024	38	46	perfect	perfect	ADJ
ejpam-3024	38	47	ring	ring	NOUN
ejpam-3024	38	48	,	,	PUNCT
ejpam-3024	38	49	then	then	ADV
ejpam-3024	38	50	every	every	DET
ejpam-3024	38	51	left	left	ADJ
ejpam-3024	38	52	r	r	NOUN
ejpam-3024	38	53	-	-	PUNCT
ejpam-3024	38	54	module	module	NOUN
ejpam-3024	38	55	has	have	VERB
ejpam-3024	38	56	the	the	DET
ejpam-3024	38	57	property	property	NOUN
ejpam-3024	38	58	(	(	PUNCT
ejpam-3024	38	59	δ	δ	PROPN
ejpam-3024	38	60	-	-	PUNCT
ejpam-3024	38	61	e	e	PROPN
ejpam-3024	38	62	)	)	PUNCT
ejpam-3024	38	63	.	.	PUNCT
ejpam-3024	39	1	moreover	moreover	ADV
ejpam-3024	39	2	we	we	PRON
ejpam-3024	39	3	obtain	obtain	VERB
ejpam-3024	39	4	that	that	SCONJ
ejpam-3024	39	5	if	if	SCONJ
ejpam-3024	39	6	every	every	PRON
ejpam-3024	39	7	left	left	ADJ
ejpam-3024	39	8	r	r	NOUN
ejpam-3024	39	9	-	-	PUNCT
ejpam-3024	39	10	module	module	NOUN
ejpam-3024	39	11	has	have	VERB
ejpam-3024	39	12	the	the	DET
ejpam-3024	39	13	property	property	NOUN
ejpam-3024	39	14	(	(	PUNCT
ejpam-3024	39	15	δ	δ	PROPN
ejpam-3024	39	16	-	-	PUNCT
ejpam-3024	39	17	e	e	PROPN
ejpam-3024	39	18	)	)	PUNCT
ejpam-3024	39	19	,	,	PUNCT
ejpam-3024	39	20	then	then	ADV
ejpam-3024	39	21	r	r	NOUN
ejpam-3024	39	22	is	be	AUX
ejpam-3024	39	23	a	a	DET
ejpam-3024	39	24	δ	δ	NOUN
ejpam-3024	39	25	-	-	PUNCT
ejpam-3024	39	26	semiperfect	semiperfect	ADJ
ejpam-3024	39	27	ring	ring	NOUN
ejpam-3024	39	28	.	.	PUNCT
ejpam-3024	40	1	2	2	X
ejpam-3024	40	2	.	.	X
ejpam-3024	40	3	preliminaries	preliminary	NOUN
ejpam-3024	40	4	in	in	ADP
ejpam-3024	40	5	this	this	DET
ejpam-3024	40	6	section	section	NOUN
ejpam-3024	40	7	,	,	PUNCT
ejpam-3024	40	8	we	we	PRON
ejpam-3024	40	9	begin	begin	VERB
ejpam-3024	40	10	by	by	ADP
ejpam-3024	40	11	stating	state	VERB
ejpam-3024	40	12	the	the	DET
ejpam-3024	40	13	following	follow	VERB
ejpam-3024	40	14	lemmas	lemma	NOUN
ejpam-3024	40	15	and	and	CCONJ
ejpam-3024	40	16	theorems	theorem	NOUN
ejpam-3024	40	17	for	for	ADP
ejpam-3024	40	18	the	the	DET
ejpam-3024	40	19	completeness	completeness	NOUN
ejpam-3024	40	20	.	.	PUNCT
ejpam-3024	41	1	2.1	2.1	NUM
ejpam-3024	41	2	.	.	PUNCT
ejpam-3024	42	1	δ	δ	NOUN
ejpam-3024	42	2	-	-	ADJ
ejpam-3024	42	3	small	small	ADJ
ejpam-3024	42	4	submodues	submodue	NOUN
ejpam-3024	42	5	lemma	lemma	PROPN
ejpam-3024	43	1	1	1	X
ejpam-3024	43	2	.	.	PUNCT
ejpam-3024	44	1	(	(	PUNCT
ejpam-3024	44	2	[	[	X
ejpam-3024	44	3	15	15	NUM
ejpam-3024	44	4	,	,	PUNCT
ejpam-3024	44	5	lemma	lemma	PROPN
ejpam-3024	44	6	1.2	1.2	NUM
ejpam-3024	44	7	]	]	PUNCT
ejpam-3024	44	8	)	)	PUNCT
ejpam-3024	44	9	.	.	PUNCT
ejpam-3024	45	1	let	let	VERB
ejpam-3024	45	2	n	n	PRON
ejpam-3024	45	3	be	be	AUX
ejpam-3024	45	4	a	a	DET
ejpam-3024	45	5	submodule	submodule	NOUN
ejpam-3024	45	6	of	of	ADP
ejpam-3024	45	7	m	m	PROPN
ejpam-3024	45	8	.	.	PUNCT
ejpam-3024	46	1	the	the	DET
ejpam-3024	46	2	following	follow	VERB
ejpam-3024	46	3	are	be	AUX
ejpam-3024	46	4	equivalent	equivalent	ADJ
ejpam-3024	46	5	:	:	PUNCT
ejpam-3024	46	6	1	1	X
ejpam-3024	46	7	.	.	X
ejpam-3024	46	8	n	n	PROPN
ejpam-3024	46	9	�	�	PROPN
ejpam-3024	46	10	δ	δ	PROPN
ejpam-3024	46	11	m.	m.	NOUN
ejpam-3024	46	12	2	2	NUM
ejpam-3024	46	13	.	.	PUNCT
ejpam-3024	47	1	if	if	SCONJ
ejpam-3024	47	2	x	x	PROPN
ejpam-3024	47	3	+	+	NUM
ejpam-3024	47	4	n	n	PROPN
ejpam-3024	47	5	=	=	SYM
ejpam-3024	47	6	m	m	PROPN
ejpam-3024	47	7	,	,	PUNCT
ejpam-3024	47	8	then	then	ADV
ejpam-3024	47	9	m	m	VERB
ejpam-3024	47	10	=	=	SYM
ejpam-3024	47	11	x	x	SYM
ejpam-3024	47	12	⊕	⊕	PROPN
ejpam-3024	47	13	y	y	PROPN
ejpam-3024	47	14	for	for	ADP
ejpam-3024	47	15	a	a	DET
ejpam-3024	47	16	projective	projective	ADJ
ejpam-3024	47	17	semisimple	semisimple	NOUN
ejpam-3024	47	18	submodule	submodule	PROPN
ejpam-3024	47	19	y	y	PROPN
ejpam-3024	47	20	with	with	ADP
ejpam-3024	47	21	y	y	PROPN
ejpam-3024	47	22	⊆	⊆	NUM
ejpam-3024	47	23	n.	n.	NOUN
ejpam-3024	47	24	3	3	NUM
ejpam-3024	47	25	.	.	PUNCT
ejpam-3024	48	1	if	if	SCONJ
ejpam-3024	48	2	x	x	PUNCT
ejpam-3024	48	3	+	+	NOUN
ejpam-3024	48	4	n	n	NOUN
ejpam-3024	48	5	=	=	NOUN
ejpam-3024	48	6	m	m	NOUN
ejpam-3024	48	7	with	with	ADP
ejpam-3024	48	8	m	m	PROPN
ejpam-3024	48	9	x	x	PROPN
ejpam-3024	48	10	goldie	goldie	PROPN
ejpam-3024	48	11	torsion	torsion	PROPN
ejpam-3024	48	12	,	,	PUNCT
ejpam-3024	48	13	then	then	ADV
ejpam-3024	48	14	x	x	X
ejpam-3024	48	15	=	=	NOUN
ejpam-3024	48	16	m	m	PROPN
ejpam-3024	48	17	.	.	PUNCT
ejpam-3024	49	1	lemma	lemma	PROPN
ejpam-3024	49	2	2	2	NUM
ejpam-3024	49	3	.	.	PUNCT
ejpam-3024	50	1	(	(	PUNCT
ejpam-3024	50	2	[	[	X
ejpam-3024	50	3	15	15	NUM
ejpam-3024	50	4	,	,	PUNCT
ejpam-3024	50	5	lemma	lemma	PROPN
ejpam-3024	50	6	1.3	1.3	NUM
ejpam-3024	50	7	]	]	PUNCT
ejpam-3024	50	8	)	)	PUNCT
ejpam-3024	50	9	.	.	PUNCT
ejpam-3024	51	1	let	let	VERB
ejpam-3024	51	2	m	m	PRON
ejpam-3024	51	3	be	be	AUX
ejpam-3024	51	4	a	a	DET
ejpam-3024	51	5	module	module	NOUN
ejpam-3024	51	6	.	.	PUNCT
ejpam-3024	52	1	1	1	X
ejpam-3024	52	2	.	.	X
ejpam-3024	52	3	for	for	ADP
ejpam-3024	52	4	submodules	submodule	NOUN
ejpam-3024	52	5	n	n	NOUN
ejpam-3024	52	6	,	,	PUNCT
ejpam-3024	52	7	k	k	NOUN
ejpam-3024	52	8	,	,	PUNCT
ejpam-3024	52	9	l	l	NOUN
ejpam-3024	52	10	of	of	ADP
ejpam-3024	52	11	m	m	PROPN
ejpam-3024	52	12	with	with	ADP
ejpam-3024	52	13	k	k	PROPN
ejpam-3024	52	14	⊆	⊆	NUM
ejpam-3024	52	15	n	n	NOUN
ejpam-3024	52	16	,	,	PUNCT
ejpam-3024	52	17	we	we	PRON
ejpam-3024	52	18	have	have	VERB
ejpam-3024	52	19	(	(	PUNCT
ejpam-3024	52	20	a	a	NOUN
ejpam-3024	52	21	)	)	PUNCT
ejpam-3024	52	22	n	n	PRON
ejpam-3024	52	23	�	�	PROPN
ejpam-3024	52	24	δ	δ	PROPN
ejpam-3024	52	25	m	m	VERB
ejpam-3024	52	26	if	if	SCONJ
ejpam-3024	53	1	and	and	CCONJ
ejpam-3024	53	2	only	only	ADV
ejpam-3024	53	3	if	if	SCONJ
ejpam-3024	53	4	k	k	PROPN
ejpam-3024	53	5	�	�	PROPN
ejpam-3024	53	6	δ	δ	PROPN
ejpam-3024	53	7	m	m	PROPN
ejpam-3024	53	8	and	and	CCONJ
ejpam-3024	53	9	n	n	CCONJ
ejpam-3024	53	10	k	k	PROPN
ejpam-3024	53	11	�	�	PROPN
ejpam-3024	53	12	δ	δ	PROPN
ejpam-3024	53	13	m	m	PROPN
ejpam-3024	53	14	k	k	NOUN
ejpam-3024	53	15	.	.	PUNCT
ejpam-3024	54	1	(	(	PUNCT
ejpam-3024	54	2	b	b	X
ejpam-3024	54	3	)	)	PUNCT
ejpam-3024	54	4	n	n	PROPN
ejpam-3024	54	5	+	+	CCONJ
ejpam-3024	54	6	l	l	NOUN
ejpam-3024	54	7	�	�	PROPN
ejpam-3024	54	8	δ	δ	PROPN
ejpam-3024	54	9	m	m	VERB
ejpam-3024	54	10	if	if	SCONJ
ejpam-3024	54	11	and	and	CCONJ
ejpam-3024	54	12	only	only	ADV
ejpam-3024	54	13	if	if	SCONJ
ejpam-3024	54	14	n	n	PROPN
ejpam-3024	54	15	�	�	PROPN
ejpam-3024	54	16	δ	δ	PROPN
ejpam-3024	54	17	m	m	PROPN
ejpam-3024	54	18	and	and	CCONJ
ejpam-3024	54	19	l	l	PROPN
ejpam-3024	54	20	�	�	PROPN
ejpam-3024	54	21	δ	δ	PROPN
ejpam-3024	54	22	m.	m.	NOUN
ejpam-3024	54	23	2	2	NUM
ejpam-3024	54	24	.	.	PUNCT
ejpam-3024	55	1	if	if	SCONJ
ejpam-3024	55	2	k	k	PROPN
ejpam-3024	55	3	�	�	PROPN
ejpam-3024	55	4	δ	δ	PROPN
ejpam-3024	55	5	m	m	PROPN
ejpam-3024	55	6	and	and	CCONJ
ejpam-3024	55	7	f	f	X
ejpam-3024	55	8	:	:	PUNCT
ejpam-3024	55	9	m	m	VERB
ejpam-3024	55	10	−→	−→	ADJ
ejpam-3024	55	11	n	n	NOUN
ejpam-3024	55	12	is	be	AUX
ejpam-3024	55	13	a	a	DET
ejpam-3024	55	14	homomorphism	homomorphism	NOUN
ejpam-3024	55	15	,	,	PUNCT
ejpam-3024	55	16	then	then	ADV
ejpam-3024	55	17	f(k)	f(k)	PROPN
ejpam-3024	55	18	�	�	PROPN
ejpam-3024	55	19	δ	δ	PROPN
ejpam-3024	55	20	n.	n.	PROPN
ejpam-3024	55	21	in	in	ADP
ejpam-3024	55	22	particular	particular	ADJ
ejpam-3024	55	23	,	,	PUNCT
ejpam-3024	55	24	if	if	SCONJ
ejpam-3024	55	25	k	k	PROPN
ejpam-3024	55	26	<	<	X
ejpam-3024	55	27	<	<	X
ejpam-3024	55	28	δ	δ	PROPN
ejpam-3024	55	29	m	m	PROPN
ejpam-3024	55	30	⊆	⊆	NUM
ejpam-3024	55	31	n	n	CCONJ
ejpam-3024	55	32	,	,	PUNCT
ejpam-3024	55	33	then	then	ADV
ejpam-3024	55	34	k	k	PROPN
ejpam-3024	55	35	�	�	PROPN
ejpam-3024	55	36	δ	δ	PROPN
ejpam-3024	55	37	n.	n.	PROPN
ejpam-3024	55	38	e.	e.	PROPN
ejpam-3024	55	39	ö.	ö.	PROPN
ejpam-3024	55	40	sözen	sözen	PROPN
ejpam-3024	55	41	,	,	PUNCT
ejpam-3024	55	42	ş.	ş.	PROPN
ejpam-3024	55	43	eren	eren	PROPN
ejpam-3024	55	44	/	/	SYM
ejpam-3024	55	45	eur	eur	PROPN
ejpam-3024	55	46	.	.	PUNCT
ejpam-3024	56	1	j.	j.	PROPN
ejpam-3024	56	2	pure	pure	PROPN
ejpam-3024	56	3	appl	appl	PROPN
ejpam-3024	56	4	.	.	PROPN
ejpam-3024	56	5	math	math	PROPN
ejpam-3024	56	6	,	,	PUNCT
ejpam-3024	56	7	10	10	NUM
ejpam-3024	56	8	(	(	PUNCT
ejpam-3024	56	9	4	4	NUM
ejpam-3024	56	10	)	)	PUNCT
ejpam-3024	56	11	(	(	PUNCT
ejpam-3024	56	12	2017	2017	NUM
ejpam-3024	56	13	)	)	PUNCT
ejpam-3024	56	14	,	,	PUNCT
ejpam-3024	56	15	730	730	NUM
ejpam-3024	56	16	-	-	SYM
ejpam-3024	56	17	738	738	NUM
ejpam-3024	56	18	732	732	NUM
ejpam-3024	56	19	3	3	NUM
ejpam-3024	56	20	.	.	PUNCT
ejpam-3024	57	1	let	let	VERB
ejpam-3024	57	2	k1	k1	NOUN
ejpam-3024	57	3	⊆m1	⊆m1	PUNCT
ejpam-3024	57	4	⊆m	⊆m	NOUN
ejpam-3024	57	5	,	,	PUNCT
ejpam-3024	57	6	k2	k2	PROPN
ejpam-3024	57	7	⊆m2	⊆m2	VERB
ejpam-3024	57	8	⊆m	⊆m	NOUN
ejpam-3024	57	9	and	and	CCONJ
ejpam-3024	57	10	m	m	PROPN
ejpam-3024	57	11	=	=	ADJ
ejpam-3024	58	1	m1⊕m2	m1⊕m2	PROPN
ejpam-3024	58	2	.	.	PUNCT
ejpam-3024	59	1	then	then	ADV
ejpam-3024	59	2	k1⊕k2	k1⊕k2	PROPN
ejpam-3024	59	3	�	�	PROPN
ejpam-3024	59	4	δ	δ	PROPN
ejpam-3024	59	5	m1	m1	PROPN
ejpam-3024	59	6	⊕m2	⊕m2	PROPN
ejpam-3024	60	1	if	if	SCONJ
ejpam-3024	60	2	and	and	CCONJ
ejpam-3024	60	3	only	only	ADV
ejpam-3024	60	4	if	if	SCONJ
ejpam-3024	60	5	k1	k1	PROPN
ejpam-3024	60	6	�	�	PROPN
ejpam-3024	60	7	δ	δ	PROPN
ejpam-3024	60	8	m1	m1	PROPN
ejpam-3024	60	9	and	and	CCONJ
ejpam-3024	60	10	k2	k2	PROPN
ejpam-3024	60	11	�	�	PROPN
ejpam-3024	60	12	δ	δ	PROPN
ejpam-3024	60	13	m2	m2	PROPN
ejpam-3024	60	14	.	.	PROPN
ejpam-3024	60	15	2.2	2.2	NUM
ejpam-3024	60	16	.	.	PUNCT
ejpam-3024	61	1	δ	δ	NOUN
ejpam-3024	61	2	-	-	PUNCT
ejpam-3024	61	3	supplemented	supplement	VERB
ejpam-3024	61	4	modules	module	NOUN
ejpam-3024	61	5	lemma	lemma	PROPN
ejpam-3024	61	6	3	3	X
ejpam-3024	61	7	.	.	PUNCT
ejpam-3024	62	1	(	(	PUNCT
ejpam-3024	62	2	[	[	X
ejpam-3024	62	3	7	7	NUM
ejpam-3024	62	4	,	,	PUNCT
ejpam-3024	62	5	p	p	NOUN
ejpam-3024	62	6	rop.2.7	rop.2.7	NOUN
ejpam-3024	62	7	]	]	PUNCT
ejpam-3024	62	8	)	)	PUNCT
ejpam-3024	62	9	.	.	PUNCT
ejpam-3024	63	1	let	let	VERB
ejpam-3024	63	2	u	u	PRON
ejpam-3024	63	3	and	and	CCONJ
ejpam-3024	63	4	v	v	NOUN
ejpam-3024	63	5	be	be	AUX
ejpam-3024	63	6	submodules	submodule	NOUN
ejpam-3024	63	7	of	of	ADP
ejpam-3024	63	8	a	a	DET
ejpam-3024	63	9	module	module	NOUN
ejpam-3024	63	10	m.	m.	NOUN
ejpam-3024	63	11	assume	assume	VERB
ejpam-3024	63	12	that	that	SCONJ
ejpam-3024	63	13	v	v	NOUN
ejpam-3024	63	14	is	be	AUX
ejpam-3024	63	15	a	a	DET
ejpam-3024	63	16	δ	δ	NOUN
ejpam-3024	63	17	-	-	PUNCT
ejpam-3024	63	18	supplement	supplement	NOUN
ejpam-3024	63	19	of	of	ADP
ejpam-3024	63	20	u	u	NOUN
ejpam-3024	63	21	in	in	ADP
ejpam-3024	63	22	m.	m.	NOUN
ejpam-3024	63	23	then	then	ADV
ejpam-3024	63	24	1	1	X
ejpam-3024	63	25	.	.	PUNCT
ejpam-3024	64	1	if	if	SCONJ
ejpam-3024	64	2	w	w	PROPN
ejpam-3024	64	3	+	+	NOUN
ejpam-3024	64	4	v	v	NOUN
ejpam-3024	64	5	=	=	NOUN
ejpam-3024	64	6	m	m	VERB
ejpam-3024	64	7	for	for	ADP
ejpam-3024	64	8	some	some	DET
ejpam-3024	64	9	w	w	PROPN
ejpam-3024	64	10	⊆	⊆	NUM
ejpam-3024	64	11	u	u	NOUN
ejpam-3024	64	12	,	,	PUNCT
ejpam-3024	64	13	then	then	ADV
ejpam-3024	64	14	v	v	NOUN
ejpam-3024	64	15	is	be	AUX
ejpam-3024	64	16	a	a	DET
ejpam-3024	64	17	δ	δ	NOUN
ejpam-3024	64	18	-	-	PUNCT
ejpam-3024	64	19	supplement	supplement	NOUN
ejpam-3024	64	20	of	of	ADP
ejpam-3024	64	21	w	w	NOUN
ejpam-3024	64	22	in	in	ADP
ejpam-3024	64	23	m	m	PROPN
ejpam-3024	64	24	.	.	PUNCT
ejpam-3024	65	1	2	2	X
ejpam-3024	65	2	.	.	X
ejpam-3024	65	3	if	if	SCONJ
ejpam-3024	65	4	k	k	PROPN
ejpam-3024	65	5	�	�	PROPN
ejpam-3024	65	6	δ	δ	PROPN
ejpam-3024	65	7	m	m	PROPN
ejpam-3024	65	8	,	,	PUNCT
ejpam-3024	65	9	then	then	ADV
ejpam-3024	65	10	v	v	NOUN
ejpam-3024	65	11	is	be	AUX
ejpam-3024	65	12	a	a	DET
ejpam-3024	65	13	δ	δ	NOUN
ejpam-3024	65	14	-	-	PUNCT
ejpam-3024	65	15	supplement	supplement	NOUN
ejpam-3024	65	16	of	of	ADP
ejpam-3024	65	17	u	u	PROPN
ejpam-3024	65	18	+	+	PROPN
ejpam-3024	65	19	k	k	PROPN
ejpam-3024	65	20	in	in	ADP
ejpam-3024	65	21	m.	m.	NOUN
ejpam-3024	65	22	3	3	NUM
ejpam-3024	65	23	.	.	X
ejpam-3024	66	1	for	for	ADP
ejpam-3024	66	2	k	k	PROPN
ejpam-3024	66	3	�	�	PROPN
ejpam-3024	66	4	δ	δ	PROPN
ejpam-3024	66	5	m	m	VERB
ejpam-3024	66	6	we	we	PRON
ejpam-3024	66	7	have	have	VERB
ejpam-3024	66	8	k	k	PROPN
ejpam-3024	66	9	∩	∩	PROPN
ejpam-3024	66	10	v	v	ADP
ejpam-3024	66	11	�	�	PROPN
ejpam-3024	66	12	δ	δ	NOUN
ejpam-3024	66	13	v	v	NOUN
ejpam-3024	66	14	and	and	CCONJ
ejpam-3024	66	15	so	so	ADV
ejpam-3024	66	16	δ(v	δ(v	PROPN
ejpam-3024	66	17	)	)	PUNCT
ejpam-3024	67	1	=	=	SYM
ejpam-3024	67	2	v	v	ADP
ejpam-3024	67	3	∩	∩	ADJ
ejpam-3024	67	4	δ(m	δ(m	PROPN
ejpam-3024	67	5	)	)	PUNCT
ejpam-3024	67	6	.	.	PUNCT
ejpam-3024	68	1	4	4	X
ejpam-3024	68	2	.	.	X
ejpam-3024	68	3	for	for	ADP
ejpam-3024	68	4	l	l	NOUN
ejpam-3024	68	5	⊆	⊆	NUM
ejpam-3024	68	6	u	u	NOUN
ejpam-3024	68	7	,	,	PUNCT
ejpam-3024	68	8	v+l	v+l	PROPN
ejpam-3024	68	9	l	l	NOUN
ejpam-3024	68	10	is	be	AUX
ejpam-3024	68	11	a	a	DET
ejpam-3024	68	12	δ	δ	NOUN
ejpam-3024	68	13	-	-	PUNCT
ejpam-3024	68	14	supplement	supplement	NOUN
ejpam-3024	68	15	of	of	ADP
ejpam-3024	68	16	u	u	NOUN
ejpam-3024	68	17	l	l	NOUN
ejpam-3024	68	18	in	in	ADP
ejpam-3024	68	19	m	m	PROPN
ejpam-3024	68	20	l	l	NOUN
ejpam-3024	68	21	.	.	PUNCT
ejpam-3024	69	1	5	5	X
ejpam-3024	69	2	.	.	X
ejpam-3024	69	3	if	if	SCONJ
ejpam-3024	69	4	δ(m	δ(m	PROPN
ejpam-3024	69	5	)	)	PUNCT
ejpam-3024	69	6	�	�	PROPN
ejpam-3024	69	7	δ	δ	PROPN
ejpam-3024	69	8	m	m	PROPN
ejpam-3024	69	9	,	,	PUNCT
ejpam-3024	69	10	or	or	CCONJ
ejpam-3024	69	11	δ(m	δ(m	NUM
ejpam-3024	69	12	)	)	PUNCT
ejpam-3024	69	13	⊆	⊆	NUM
ejpam-3024	69	14	u	u	NOUN
ejpam-3024	69	15	and	and	CCONJ
ejpam-3024	69	16	if	if	SCONJ
ejpam-3024	69	17	p	p	X
ejpam-3024	69	18	:	:	PUNCT
ejpam-3024	69	19	m	m	VERB
ejpam-3024	69	20	−→	−→	ADJ
ejpam-3024	69	21	m	m	PROPN
ejpam-3024	69	22	δ(m	δ(m	PROPN
ejpam-3024	69	23	)	)	PUNCT
ejpam-3024	69	24	is	be	AUX
ejpam-3024	69	25	the	the	DET
ejpam-3024	69	26	canonical	canonical	ADJ
ejpam-3024	69	27	projection	projection	NOUN
ejpam-3024	69	28	,	,	PUNCT
ejpam-3024	69	29	then	then	ADV
ejpam-3024	69	30	m	m	PROPN
ejpam-3024	69	31	δ(m	δ(m	PROPN
ejpam-3024	69	32	)	)	PUNCT
ejpam-3024	70	1	=	=	SYM
ejpam-3024	70	2	p(u)⊕	p(u)⊕	PROPN
ejpam-3024	70	3	p(v	p(v	PROPN
ejpam-3024	70	4	)	)	PUNCT
ejpam-3024	70	5	.	.	PUNCT
ejpam-3024	71	1	in	in	ADP
ejpam-3024	71	2	[	[	X
ejpam-3024	71	3	7	7	NUM
ejpam-3024	71	4	]	]	PUNCT
ejpam-3024	71	5	,	,	PUNCT
ejpam-3024	71	6	a	a	DET
ejpam-3024	71	7	projective	projective	ADJ
ejpam-3024	71	8	module	module	NOUN
ejpam-3024	71	9	p	p	NOUN
ejpam-3024	71	10	is	be	AUX
ejpam-3024	71	11	called	call	VERB
ejpam-3024	71	12	a	a	DET
ejpam-3024	71	13	projective	projective	ADJ
ejpam-3024	71	14	δ	δ	NOUN
ejpam-3024	71	15	-	-	NOUN
ejpam-3024	71	16	cover	cover	NOUN
ejpam-3024	71	17	of	of	ADP
ejpam-3024	71	18	a	a	DET
ejpam-3024	71	19	module	module	NOUN
ejpam-3024	71	20	m	m	VERB
ejpam-3024	71	21	if	if	SCONJ
ejpam-3024	71	22	there	there	PRON
ejpam-3024	71	23	exists	exist	VERB
ejpam-3024	71	24	an	an	DET
ejpam-3024	71	25	epimorphism	epimorphism	NOUN
ejpam-3024	71	26	f	f	NOUN
ejpam-3024	71	27	:	:	PUNCT
ejpam-3024	71	28	p	p	X
ejpam-3024	71	29	−→m	−→m	PROPN
ejpam-3024	71	30	with	with	ADP
ejpam-3024	71	31	ker(f)	ker(f)	PROPN
ejpam-3024	71	32	�	�	PROPN
ejpam-3024	71	33	δ	δ	PROPN
ejpam-3024	71	34	m	m	PROPN
ejpam-3024	71	35	,	,	PUNCT
ejpam-3024	71	36	and	and	CCONJ
ejpam-3024	71	37	a	a	DET
ejpam-3024	71	38	ring	ring	NOUN
ejpam-3024	71	39	r	r	NOUN
ejpam-3024	71	40	is	be	AUX
ejpam-3024	71	41	called	call	VERB
ejpam-3024	71	42	δ	δ	NOUN
ejpam-3024	71	43	-	-	ADJ
ejpam-3024	71	44	perfect	perfect	ADJ
ejpam-3024	71	45	(	(	PUNCT
ejpam-3024	71	46	resp	resp	NOUN
ejpam-3024	71	47	.	.	PUNCT
ejpam-3024	71	48	,	,	PUNCT
ejpam-3024	71	49	δ	δ	NOUN
ejpam-3024	71	50	-	-	PUNCT
ejpam-3024	71	51	semiperfect	semiperfect	NOUN
ejpam-3024	71	52	)	)	PUNCT
ejpam-3024	71	53	if	if	SCONJ
ejpam-3024	71	54	every	every	DET
ejpam-3024	71	55	r	r	NOUN
ejpam-3024	71	56	-	-	PUNCT
ejpam-3024	71	57	module	module	NOUN
ejpam-3024	71	58	(	(	PUNCT
ejpam-3024	71	59	resp	resp	NOUN
ejpam-3024	71	60	.	.	PUNCT
ejpam-3024	72	1	,	,	PUNCT
ejpam-3024	72	2	every	every	DET
ejpam-3024	72	3	simple	simple	ADJ
ejpam-3024	72	4	r	r	NOUN
ejpam-3024	72	5	-	-	PUNCT
ejpam-3024	72	6	module	module	NOUN
ejpam-3024	72	7	)	)	PUNCT
ejpam-3024	72	8	has	have	VERB
ejpam-3024	72	9	a	a	DET
ejpam-3024	72	10	projective	projective	ADJ
ejpam-3024	72	11	δ	δ	NOUN
ejpam-3024	72	12	-	-	NOUN
ejpam-3024	72	13	cover	cover	NOUN
ejpam-3024	72	14	.	.	PUNCT
ejpam-3024	73	1	in	in	ADP
ejpam-3024	73	2	addition	addition	NOUN
ejpam-3024	73	3	,	,	PUNCT
ejpam-3024	73	4	a	a	DET
ejpam-3024	73	5	module	module	NOUN
ejpam-3024	73	6	m	m	VERB
ejpam-3024	73	7	is	be	AUX
ejpam-3024	73	8	called	call	VERB
ejpam-3024	73	9	δ	δ	NOUN
ejpam-3024	73	10	-	-	PUNCT
ejpam-3024	73	11	lifting	lift	VERB
ejpam-3024	73	12	if	if	SCONJ
ejpam-3024	73	13	for	for	ADP
ejpam-3024	73	14	any	any	DET
ejpam-3024	73	15	n	n	DET
ejpam-3024	73	16	≤m	≤m	NOUN
ejpam-3024	73	17	,	,	PUNCT
ejpam-3024	73	18	there	there	PRON
ejpam-3024	73	19	exists	exist	VERB
ejpam-3024	73	20	a	a	DET
ejpam-3024	73	21	decomposition	decomposition	NOUN
ejpam-3024	73	22	m	m	VERB
ejpam-3024	73	23	=	=	PUNCT
ejpam-3024	73	24	a⊕	a⊕	PROPN
ejpam-3024	73	25	b	b	NUM
ejpam-3024	73	26	such	such	ADJ
ejpam-3024	73	27	that	that	SCONJ
ejpam-3024	73	28	a	a	DET
ejpam-3024	73	29	≤	≤	NUM
ejpam-3024	73	30	n	n	CCONJ
ejpam-3024	73	31	and	and	CCONJ
ejpam-3024	73	32	n	n	PROPN
ejpam-3024	73	33	∩	∩	NOUN
ejpam-3024	73	34	b	b	PROPN
ejpam-3024	73	35	is	be	AUX
ejpam-3024	73	36	δ	δ	NOUN
ejpam-3024	73	37	-	-	ADJ
ejpam-3024	73	38	small	small	ADJ
ejpam-3024	73	39	in	in	ADP
ejpam-3024	73	40	b	b	PROPN
ejpam-3024	73	41	since	since	SCONJ
ejpam-3024	73	42	b	b	PROPN
ejpam-3024	73	43	is	be	AUX
ejpam-3024	73	44	a	a	DET
ejpam-3024	73	45	direct	direct	ADJ
ejpam-3024	73	46	summand	summand	NOUN
ejpam-3024	73	47	of	of	ADP
ejpam-3024	73	48	m.	m.	NOUN
ejpam-3024	73	49	theorem	theorem	VERB
ejpam-3024	73	50	4	4	NUM
ejpam-3024	73	51	.	.	PUNCT
ejpam-3024	74	1	[	[	X
ejpam-3024	74	2	7	7	NUM
ejpam-3024	74	3	,	,	PUNCT
ejpam-3024	74	4	theorem3.3].the	theorem3.3].the	DET
ejpam-3024	74	5	following	following	NOUN
ejpam-3024	74	6	are	be	AUX
ejpam-3024	74	7	equivalent	equivalent	ADJ
ejpam-3024	74	8	for	for	ADP
ejpam-3024	74	9	a	a	DET
ejpam-3024	74	10	ring	ring	NOUN
ejpam-3024	74	11	r	r	NOUN
ejpam-3024	74	12	:	:	PUNCT
ejpam-3024	74	13	1	1	X
ejpam-3024	74	14	.	.	X
ejpam-3024	74	15	r	r	NOUN
ejpam-3024	74	16	is	be	AUX
ejpam-3024	74	17	δ	δ	NOUN
ejpam-3024	74	18	-	-	PUNCT
ejpam-3024	74	19	semiperfect	semiperfect	ADJ
ejpam-3024	74	20	.	.	PUNCT
ejpam-3024	75	1	2	2	X
ejpam-3024	75	2	.	.	X
ejpam-3024	75	3	every	every	DET
ejpam-3024	75	4	finitely	finitely	ADV
ejpam-3024	75	5	generated	generate	VERB
ejpam-3024	75	6	module	module	NOUN
ejpam-3024	75	7	is	be	AUX
ejpam-3024	75	8	δ	δ	PROPN
ejpam-3024	75	9	-	-	PUNCT
ejpam-3024	75	10	supplemented	supplement	VERB
ejpam-3024	75	11	.	.	PUNCT
ejpam-3024	76	1	3	3	X
ejpam-3024	76	2	.	.	X
ejpam-3024	76	3	every	every	DET
ejpam-3024	76	4	finitely	finitely	ADV
ejpam-3024	76	5	generated	generate	VERB
ejpam-3024	76	6	projective	projective	ADJ
ejpam-3024	76	7	module	module	NOUN
ejpam-3024	76	8	is	be	AUX
ejpam-3024	76	9	δ	δ	PROPN
ejpam-3024	76	10	-	-	PUNCT
ejpam-3024	76	11	supplemented	supplement	VERB
ejpam-3024	76	12	.	.	PUNCT
ejpam-3024	77	1	4	4	X
ejpam-3024	77	2	.	.	X
ejpam-3024	77	3	every	every	DET
ejpam-3024	77	4	finitely	finitely	ADV
ejpam-3024	77	5	generated	generate	VERB
ejpam-3024	77	6	projective	projective	ADJ
ejpam-3024	77	7	module	module	NOUN
ejpam-3024	77	8	is	be	AUX
ejpam-3024	77	9	δ	δ	NOUN
ejpam-3024	77	10	-	-	PUNCT
ejpam-3024	77	11	lifting	lifting	NOUN
ejpam-3024	77	12	.	.	PUNCT
ejpam-3024	78	1	5	5	X
ejpam-3024	78	2	.	.	X
ejpam-3024	78	3	every	every	DET
ejpam-3024	78	4	left	leave	VERB
ejpam-3024	78	5	ideal	ideal	NOUN
ejpam-3024	78	6	of	of	ADP
ejpam-3024	78	7	r	r	NOUN
ejpam-3024	78	8	has	have	VERB
ejpam-3024	78	9	a	a	DET
ejpam-3024	78	10	δ	δ	NOUN
ejpam-3024	78	11	-	-	PUNCT
ejpam-3024	78	12	supplement	supplement	NOUN
ejpam-3024	78	13	in	in	ADP
ejpam-3024	78	14	rr	rr	PROPN
ejpam-3024	78	15	.	.	PUNCT
ejpam-3024	78	16	theorem	theorem	VERB
ejpam-3024	78	17	5	5	NUM
ejpam-3024	78	18	.	.	PUNCT
ejpam-3024	79	1	[	[	X
ejpam-3024	79	2	7	7	NUM
ejpam-3024	79	3	,	,	PUNCT
ejpam-3024	79	4	theorem	theorem	VERB
ejpam-3024	79	5	3.4	3.4	NUM
ejpam-3024	79	6	]	]	PUNCT
ejpam-3024	79	7	.	.	PUNCT
ejpam-3024	80	1	the	the	DET
ejpam-3024	80	2	following	follow	VERB
ejpam-3024	80	3	statements	statement	NOUN
ejpam-3024	80	4	are	be	AUX
ejpam-3024	80	5	equivqlent	equivqlent	ADJ
ejpam-3024	80	6	for	for	ADP
ejpam-3024	80	7	a	a	DET
ejpam-3024	80	8	ring	ring	NOUN
ejpam-3024	80	9	r	r	NOUN
ejpam-3024	80	10	:	:	PUNCT
ejpam-3024	80	11	1	1	X
ejpam-3024	80	12	.	.	X
ejpam-3024	80	13	r	r	NOUN
ejpam-3024	80	14	is	be	AUX
ejpam-3024	80	15	δ	δ	NOUN
ejpam-3024	80	16	-	-	NOUN
ejpam-3024	80	17	perfect	perfect	ADJ
ejpam-3024	80	18	.	.	PUNCT
ejpam-3024	81	1	2	2	X
ejpam-3024	81	2	.	.	X
ejpam-3024	81	3	every	every	DET
ejpam-3024	81	4	module	module	NOUN
ejpam-3024	81	5	is	be	AUX
ejpam-3024	81	6	δ	δ	PROPN
ejpam-3024	81	7	-	-	PUNCT
ejpam-3024	81	8	supplemented	supplement	VERB
ejpam-3024	81	9	.	.	PUNCT
ejpam-3024	82	1	3	3	X
ejpam-3024	82	2	.	.	X
ejpam-3024	82	3	every	every	DET
ejpam-3024	82	4	projective	projective	ADJ
ejpam-3024	82	5	module	module	NOUN
ejpam-3024	82	6	is	be	AUX
ejpam-3024	82	7	δ	δ	PROPN
ejpam-3024	82	8	-	-	PUNCT
ejpam-3024	82	9	supplemented	supplement	VERB
ejpam-3024	82	10	.	.	PUNCT
ejpam-3024	83	1	4	4	X
ejpam-3024	83	2	.	.	X
ejpam-3024	83	3	every	every	DET
ejpam-3024	83	4	projective	projective	ADJ
ejpam-3024	83	5	module	module	NOUN
ejpam-3024	83	6	is	be	AUX
ejpam-3024	83	7	δ	δ	NOUN
ejpam-3024	83	8	-	-	PUNCT
ejpam-3024	83	9	lifting	lifting	NOUN
ejpam-3024	83	10	.	.	PUNCT
ejpam-3024	84	1	e.	e.	PROPN
ejpam-3024	84	2	ö.	ö.	PROPN
ejpam-3024	84	3	sözen	sözen	PROPN
ejpam-3024	84	4	,	,	PUNCT
ejpam-3024	84	5	ş.	ş.	PROPN
ejpam-3024	84	6	eren	eren	PROPN
ejpam-3024	84	7	/	/	SYM
ejpam-3024	84	8	eur	eur	PROPN
ejpam-3024	84	9	.	.	PUNCT
ejpam-3024	85	1	j.	j.	PROPN
ejpam-3024	85	2	pure	pure	PROPN
ejpam-3024	85	3	appl	appl	PROPN
ejpam-3024	85	4	.	.	PROPN
ejpam-3024	85	5	math	math	PROPN
ejpam-3024	85	6	,	,	PUNCT
ejpam-3024	85	7	10	10	NUM
ejpam-3024	85	8	(	(	PUNCT
ejpam-3024	85	9	4	4	NUM
ejpam-3024	85	10	)	)	PUNCT
ejpam-3024	85	11	(	(	PUNCT
ejpam-3024	85	12	2017	2017	NUM
ejpam-3024	85	13	)	)	PUNCT
ejpam-3024	85	14	,	,	PUNCT
ejpam-3024	85	15	730	730	NUM
ejpam-3024	85	16	-	-	SYM
ejpam-3024	85	17	738	738	NUM
ejpam-3024	85	18	733	733	NUM
ejpam-3024	85	19	3	3	NUM
ejpam-3024	85	20	.	.	PUNCT
ejpam-3024	85	21	modules	module	NOUN
ejpam-3024	85	22	with	with	ADP
ejpam-3024	85	23	the	the	DET
ejpam-3024	85	24	properties	property	NOUN
ejpam-3024	85	25	(	(	PUNCT
ejpam-3024	85	26	δ	δ	PROPN
ejpam-3024	85	27	-	-	PUNCT
ejpam-3024	85	28	e	e	NOUN
ejpam-3024	85	29	)	)	PUNCT
ejpam-3024	85	30	and	and	CCONJ
ejpam-3024	85	31	(	(	PUNCT
ejpam-3024	85	32	δ	δ	PROPN
ejpam-3024	85	33	-	-	PUNCT
ejpam-3024	85	34	ee	ee	NOUN
ejpam-3024	85	35	)	)	PUNCT
ejpam-3024	85	36	in	in	ADP
ejpam-3024	85	37	this	this	DET
ejpam-3024	85	38	section	section	NOUN
ejpam-3024	85	39	,	,	PUNCT
ejpam-3024	85	40	we	we	PRON
ejpam-3024	85	41	define	define	VERB
ejpam-3024	85	42	the	the	DET
ejpam-3024	85	43	concept	concept	NOUN
ejpam-3024	85	44	of	of	ADP
ejpam-3024	85	45	modules	module	NOUN
ejpam-3024	85	46	with	with	ADP
ejpam-3024	85	47	the	the	DET
ejpam-3024	85	48	properties	property	NOUN
ejpam-3024	85	49	(	(	PUNCT
ejpam-3024	85	50	δ	δ	PROPN
ejpam-3024	85	51	-	-	PUNCT
ejpam-3024	85	52	e	e	NOUN
ejpam-3024	85	53	)	)	PUNCT
ejpam-3024	85	54	and	and	CCONJ
ejpam-3024	85	55	(	(	PUNCT
ejpam-3024	85	56	δ	δ	PROPN
ejpam-3024	85	57	-	-	PUNCT
ejpam-3024	85	58	ee	ee	PROPN
ejpam-3024	85	59	)	)	PUNCT
ejpam-3024	85	60	.	.	PUNCT
ejpam-3024	86	1	definition	definition	NOUN
ejpam-3024	86	2	1	1	NUM
ejpam-3024	86	3	.	.	PUNCT
ejpam-3024	87	1	a	a	DET
ejpam-3024	87	2	module	module	NOUN
ejpam-3024	87	3	m	m	VERB
ejpam-3024	87	4	has	have	VERB
ejpam-3024	87	5	the	the	DET
ejpam-3024	87	6	property	property	NOUN
ejpam-3024	87	7	(	(	PUNCT
ejpam-3024	87	8	δ	δ	PROPN
ejpam-3024	87	9	-	-	PUNCT
ejpam-3024	87	10	e	e	NOUN
ejpam-3024	87	11	)	)	PUNCT
ejpam-3024	87	12	if	if	SCONJ
ejpam-3024	87	13	it	it	PRON
ejpam-3024	87	14	has	have	VERB
ejpam-3024	87	15	a	a	DET
ejpam-3024	87	16	δ	δ	NOUN
ejpam-3024	87	17	-	-	PUNCT
ejpam-3024	87	18	supplement	supplement	NOUN
ejpam-3024	87	19	in	in	ADP
ejpam-3024	87	20	each	each	DET
ejpam-3024	87	21	module	module	NOUN
ejpam-3024	87	22	in	in	ADP
ejpam-3024	87	23	which	which	PRON
ejpam-3024	87	24	it	it	PRON
ejpam-3024	87	25	is	be	AUX
ejpam-3024	87	26	contained	contain	VERB
ejpam-3024	87	27	as	as	ADP
ejpam-3024	87	28	a	a	DET
ejpam-3024	87	29	submodule	submodule	NOUN
ejpam-3024	87	30	.	.	PUNCT
ejpam-3024	88	1	definition	definition	NOUN
ejpam-3024	88	2	2	2	NUM
ejpam-3024	88	3	.	.	PUNCT
ejpam-3024	89	1	a	a	DET
ejpam-3024	89	2	module	module	NOUN
ejpam-3024	89	3	m	m	VERB
ejpam-3024	89	4	has	have	VERB
ejpam-3024	89	5	the	the	DET
ejpam-3024	89	6	property	property	NOUN
ejpam-3024	89	7	(	(	PUNCT
ejpam-3024	89	8	δ	δ	PROPN
ejpam-3024	89	9	-	-	PUNCT
ejpam-3024	89	10	ee	ee	NOUN
ejpam-3024	89	11	)	)	PUNCT
ejpam-3024	89	12	if	if	SCONJ
ejpam-3024	89	13	it	it	PRON
ejpam-3024	89	14	has	have	VERB
ejpam-3024	89	15	ample	ample	ADJ
ejpam-3024	89	16	δ	δ	NOUN
ejpam-3024	89	17	-	-	PUNCT
ejpam-3024	89	18	supplements	supplement	NOUN
ejpam-3024	89	19	in	in	ADP
ejpam-3024	89	20	each	each	DET
ejpam-3024	89	21	module	module	NOUN
ejpam-3024	89	22	in	in	ADP
ejpam-3024	89	23	which	which	PRON
ejpam-3024	89	24	it	it	PRON
ejpam-3024	89	25	is	be	AUX
ejpam-3024	89	26	contained	contain	VERB
ejpam-3024	89	27	as	as	ADP
ejpam-3024	89	28	a	a	DET
ejpam-3024	89	29	submodule	submodule	NOUN
ejpam-3024	89	30	,	,	PUNCT
ejpam-3024	89	31	where	where	SCONJ
ejpam-3024	89	32	u	u	PROPN
ejpam-3024	89	33	≤	≤	X
ejpam-3024	89	34	m	m	VERB
ejpam-3024	89	35	has	have	VERB
ejpam-3024	89	36	ample	ample	ADJ
ejpam-3024	89	37	δ	δ	NOUN
ejpam-3024	89	38	-	-	PUNCT
ejpam-3024	89	39	supplements	supplement	NOUN
ejpam-3024	89	40	in	in	ADP
ejpam-3024	89	41	m	m	NOUN
ejpam-3024	89	42	if	if	SCONJ
ejpam-3024	89	43	for	for	ADP
ejpam-3024	89	44	every	every	DET
ejpam-3024	89	45	v	v	NOUN
ejpam-3024	89	46	≤m	≤m	NOUN
ejpam-3024	89	47	with	with	ADP
ejpam-3024	89	48	u	u	PROPN
ejpam-3024	89	49	+	+	X
ejpam-3024	89	50	v	v	NOUN
ejpam-3024	89	51	=	=	SYM
ejpam-3024	89	52	m	m	ADJ
ejpam-3024	89	53	,	,	PUNCT
ejpam-3024	89	54	there	there	PRON
ejpam-3024	89	55	is	be	VERB
ejpam-3024	89	56	a	a	DET
ejpam-3024	89	57	δ	δ	NOUN
ejpam-3024	89	58	-	-	PUNCT
ejpam-3024	89	59	supplement	supplement	NOUN
ejpam-3024	89	60	v	v	NOUN
ejpam-3024	89	61	′	′	NUM
ejpam-3024	89	62	of	of	ADP
ejpam-3024	89	63	u	u	NOUN
ejpam-3024	89	64	with	with	ADP
ejpam-3024	89	65	v	v	NOUN
ejpam-3024	89	66	′	′	NUM
ejpam-3024	89	67	≤	≤	NOUN
ejpam-3024	90	1	v.	v.	CCONJ
ejpam-3024	90	2	it	it	PRON
ejpam-3024	90	3	is	be	AUX
ejpam-3024	90	4	clear	clear	ADJ
ejpam-3024	90	5	that	that	SCONJ
ejpam-3024	90	6	every	every	DET
ejpam-3024	90	7	module	module	NOUN
ejpam-3024	90	8	with	with	ADP
ejpam-3024	90	9	the	the	DET
ejpam-3024	90	10	property	property	NOUN
ejpam-3024	90	11	(	(	PUNCT
ejpam-3024	90	12	e	e	NOUN
ejpam-3024	90	13	)	)	PUNCT
ejpam-3024	90	14	has	have	VERB
ejpam-3024	90	15	the	the	DET
ejpam-3024	90	16	property	property	NOUN
ejpam-3024	90	17	(	(	PUNCT
ejpam-3024	90	18	δ	δ	PROPN
ejpam-3024	90	19	-	-	PUNCT
ejpam-3024	90	20	e	e	PROPN
ejpam-3024	90	21	)	)	PUNCT
ejpam-3024	90	22	.	.	PUNCT
ejpam-3024	91	1	also	also	ADV
ejpam-3024	91	2	there	there	PRON
ejpam-3024	91	3	exists	exist	VERB
ejpam-3024	91	4	the	the	DET
ejpam-3024	91	5	same	same	ADJ
ejpam-3024	91	6	relation	relation	NOUN
ejpam-3024	91	7	between	between	ADP
ejpam-3024	91	8	modules	module	NOUN
ejpam-3024	91	9	with	with	ADP
ejpam-3024	91	10	the	the	DET
ejpam-3024	91	11	properties	property	NOUN
ejpam-3024	91	12	(	(	PUNCT
ejpam-3024	91	13	ee	ee	PROPN
ejpam-3024	91	14	)	)	PUNCT
ejpam-3024	91	15	and	and	CCONJ
ejpam-3024	91	16	(	(	PUNCT
ejpam-3024	91	17	δ	δ	PROPN
ejpam-3024	91	18	-	-	PUNCT
ejpam-3024	91	19	ee	ee	PROPN
ejpam-3024	91	20	)	)	PUNCT
ejpam-3024	91	21	.	.	PUNCT
ejpam-3024	92	1	at	at	ADP
ejpam-3024	92	2	the	the	DET
ejpam-3024	92	3	end	end	NOUN
ejpam-3024	92	4	of	of	ADP
ejpam-3024	92	5	this	this	DET
ejpam-3024	92	6	section	section	NOUN
ejpam-3024	92	7	,	,	PUNCT
ejpam-3024	92	8	we	we	PRON
ejpam-3024	92	9	shall	shall	AUX
ejpam-3024	92	10	give	give	VERB
ejpam-3024	92	11	an	an	DET
ejpam-3024	92	12	example	example	NOUN
ejpam-3024	92	13	of	of	ADP
ejpam-3024	92	14	a	a	DET
ejpam-3024	92	15	module	module	NOUN
ejpam-3024	92	16	which	which	PRON
ejpam-3024	92	17	has	have	VERB
ejpam-3024	92	18	the	the	DET
ejpam-3024	92	19	property	property	NOUN
ejpam-3024	92	20	(	(	PUNCT
ejpam-3024	92	21	δ	δ	PROPN
ejpam-3024	92	22	-	-	PUNCT
ejpam-3024	92	23	e	e	NOUN
ejpam-3024	92	24	)	)	PUNCT
ejpam-3024	92	25	but	but	CCONJ
ejpam-3024	92	26	not	not	PART
ejpam-3024	92	27	(	(	PUNCT
ejpam-3024	92	28	e	e	NOUN
ejpam-3024	92	29	)	)	PUNCT
ejpam-3024	92	30	.	.	PUNCT
ejpam-3024	93	1	zöschinger	zöschinger	PROPN
ejpam-3024	93	2	proved	prove	VERB
ejpam-3024	93	3	in	in	ADP
ejpam-3024	93	4	[	[	X
ejpam-3024	93	5	16	16	NUM
ejpam-3024	93	6	]	]	PUNCT
ejpam-3024	93	7	that	that	SCONJ
ejpam-3024	93	8	a	a	DET
ejpam-3024	93	9	module	module	NOUN
ejpam-3024	93	10	has	have	VERB
ejpam-3024	93	11	the	the	DET
ejpam-3024	93	12	property	property	NOUN
ejpam-3024	93	13	(	(	PUNCT
ejpam-3024	93	14	ee	ee	PROPN
ejpam-3024	93	15	)	)	PUNCT
ejpam-3024	94	1	if	if	SCONJ
ejpam-3024	95	1	and	and	CCONJ
ejpam-3024	95	2	only	only	ADV
ejpam-3024	95	3	if	if	SCONJ
ejpam-3024	95	4	every	every	DET
ejpam-3024	95	5	submodule	submodule	NOUN
ejpam-3024	95	6	has	have	VERB
ejpam-3024	95	7	the	the	DET
ejpam-3024	95	8	property	property	NOUN
ejpam-3024	95	9	(	(	PUNCT
ejpam-3024	95	10	e).we	e).we	NOUN
ejpam-3024	95	11	give	give	VERB
ejpam-3024	95	12	an	an	DET
ejpam-3024	95	13	analogous	analogous	ADJ
ejpam-3024	95	14	characterization	characterization	NOUN
ejpam-3024	95	15	of	of	ADP
ejpam-3024	95	16	our	our	PRON
ejpam-3024	95	17	modules	module	NOUN
ejpam-3024	95	18	with	with	ADP
ejpam-3024	95	19	the	the	DET
ejpam-3024	95	20	following	follow	VERB
ejpam-3024	95	21	proposition	proposition	NOUN
ejpam-3024	95	22	.	.	PUNCT
ejpam-3024	96	1	proposition	proposition	NOUN
ejpam-3024	96	2	1	1	NUM
ejpam-3024	96	3	.	.	PUNCT
ejpam-3024	97	1	a	a	DET
ejpam-3024	97	2	module	module	NOUN
ejpam-3024	97	3	m	m	VERB
ejpam-3024	97	4	has	have	VERB
ejpam-3024	97	5	the	the	DET
ejpam-3024	97	6	property	property	NOUN
ejpam-3024	97	7	(	(	PUNCT
ejpam-3024	97	8	δ	δ	PROPN
ejpam-3024	97	9	-	-	PUNCT
ejpam-3024	97	10	ee	ee	NOUN
ejpam-3024	97	11	)	)	PUNCT
ejpam-3024	98	1	if	if	SCONJ
ejpam-3024	98	2	and	and	CCONJ
ejpam-3024	98	3	only	only	ADV
ejpam-3024	98	4	if	if	SCONJ
ejpam-3024	98	5	every	every	DET
ejpam-3024	98	6	submodule	submodule	NOUN
ejpam-3024	98	7	of	of	ADP
ejpam-3024	98	8	m	m	PROPN
ejpam-3024	98	9	has	have	VERB
ejpam-3024	98	10	the	the	DET
ejpam-3024	98	11	property	property	NOUN
ejpam-3024	98	12	(	(	PUNCT
ejpam-3024	98	13	δ	δ	PROPN
ejpam-3024	98	14	-	-	PUNCT
ejpam-3024	98	15	e	e	NOUN
ejpam-3024	98	16	)	)	PUNCT
ejpam-3024	98	17	.	.	PUNCT
ejpam-3024	99	1	proof	proof	NOUN
ejpam-3024	99	2	.	.	PUNCT
ejpam-3024	100	1	let	let	VERB
ejpam-3024	100	2	m	m	PRON
ejpam-3024	100	3	be	be	AUX
ejpam-3024	100	4	a	a	DET
ejpam-3024	100	5	module	module	NOUN
ejpam-3024	100	6	and	and	CCONJ
ejpam-3024	100	7	n	n	CCONJ
ejpam-3024	100	8	be	be	VERB
ejpam-3024	100	9	any	any	DET
ejpam-3024	100	10	extension	extension	NOUN
ejpam-3024	100	11	of	of	ADP
ejpam-3024	100	12	m.	m.	NOUN
ejpam-3024	100	13	suppose	suppose	VERB
ejpam-3024	101	1	that	that	SCONJ
ejpam-3024	101	2	for	for	ADP
ejpam-3024	101	3	a	a	DET
ejpam-3024	101	4	submodule	submodule	NOUN
ejpam-3024	101	5	x	x	SYM
ejpam-3024	101	6	≤	≤	NUM
ejpam-3024	101	7	n	n	CCONJ
ejpam-3024	101	8	,	,	PUNCT
ejpam-3024	101	9	x	x	PUNCT
ejpam-3024	101	10	+	+	NUM
ejpam-3024	101	11	m	m	AUX
ejpam-3024	101	12	=	=	VERB
ejpam-3024	101	13	n.	n.	NOUN
ejpam-3024	101	14	by	by	ADP
ejpam-3024	101	15	hypothesis	hypothesis	NOUN
ejpam-3024	101	16	,	,	PUNCT
ejpam-3024	101	17	the	the	DET
ejpam-3024	101	18	submodule	submodule	NOUN
ejpam-3024	101	19	x	x	INTJ
ejpam-3024	101	20	∩m	∩m	PROPN
ejpam-3024	101	21	of	of	ADP
ejpam-3024	101	22	m	m	PROPN
ejpam-3024	101	23	has	have	VERB
ejpam-3024	101	24	a	a	DET
ejpam-3024	101	25	δ	δ	NOUN
ejpam-3024	101	26	-	-	PUNCT
ejpam-3024	101	27	supplement	supplement	NOUN
ejpam-3024	101	28	v	v	NOUN
ejpam-3024	101	29	in	in	ADP
ejpam-3024	101	30	x	x	NOUN
ejpam-3024	101	31	,	,	PUNCT
ejpam-3024	101	32	that	that	ADV
ejpam-3024	101	33	is	is	ADV
ejpam-3024	101	34	,	,	PUNCT
ejpam-3024	101	35	(	(	PUNCT
ejpam-3024	101	36	x	x	PUNCT
ejpam-3024	101	37	∩m	∩m	PROPN
ejpam-3024	101	38	)	)	PUNCT
ejpam-3024	102	1	+	+	CCONJ
ejpam-3024	102	2	v	v	X
ejpam-3024	102	3	=	=	SYM
ejpam-3024	102	4	x	x	X
ejpam-3024	102	5	and	and	CCONJ
ejpam-3024	102	6	(	(	PUNCT
ejpam-3024	102	7	x	x	X
ejpam-3024	102	8	∩m	∩m	NOUN
ejpam-3024	102	9	)	)	PUNCT
ejpam-3024	102	10	∩	∩	PROPN
ejpam-3024	102	11	v	v	ADP
ejpam-3024	102	12	�	�	PROPN
ejpam-3024	102	13	δ	δ	NOUN
ejpam-3024	102	14	v	v	NOUN
ejpam-3024	102	15	.	.	PUNCT
ejpam-3024	103	1	then	then	ADV
ejpam-3024	103	2	,	,	PUNCT
ejpam-3024	103	3	n	n	PROPN
ejpam-3024	103	4	=	=	SYM
ejpam-3024	103	5	m	m	VERB
ejpam-3024	103	6	+	+	ADJ
ejpam-3024	103	7	x	x	X
ejpam-3024	103	8	=	=	VERB
ejpam-3024	103	9	m	m	VERB
ejpam-3024	103	10	+	+	X
ejpam-3024	104	1	[	[	X
ejpam-3024	104	2	(	(	PUNCT
ejpam-3024	104	3	x	x	X
ejpam-3024	104	4	∩m	∩m	PROPN
ejpam-3024	104	5	)	)	PUNCT
ejpam-3024	104	6	+	+	CCONJ
ejpam-3024	104	7	v	v	X
ejpam-3024	104	8	]	]	X
ejpam-3024	104	9	=	=	PUNCT
ejpam-3024	105	1	m	m	VERB
ejpam-3024	105	2	+	+	NOUN
ejpam-3024	105	3	v	v	NUM
ejpam-3024	105	4	and	and	CCONJ
ejpam-3024	105	5	m	m	PROPN
ejpam-3024	105	6	∩	∩	ADJ
ejpam-3024	105	7	v	v	NOUN
ejpam-3024	105	8	=	=	SYM
ejpam-3024	105	9	m	m	NOUN
ejpam-3024	105	10	∩	∩	NOUN
ejpam-3024	105	11	(	(	PUNCT
ejpam-3024	105	12	v	v	NOUN
ejpam-3024	105	13	∩x	∩x	NOUN
ejpam-3024	105	14	)	)	PUNCT
ejpam-3024	105	15	=	=	SYM
ejpam-3024	106	1	(	(	PUNCT
ejpam-3024	106	2	x	x	PUNCT
ejpam-3024	106	3	∩m	∩m	NOUN
ejpam-3024	106	4	)	)	PUNCT
ejpam-3024	106	5	∩	∩	PROPN
ejpam-3024	106	6	v	v	ADP
ejpam-3024	106	7	�	�	PROPN
ejpam-3024	106	8	δ	δ	PROPN
ejpam-3024	106	9	v.	v.	CCONJ
ejpam-3024	106	10	hence	hence	ADV
ejpam-3024	106	11	,	,	PUNCT
ejpam-3024	106	12	v	v	NOUN
ejpam-3024	106	13	is	be	AUX
ejpam-3024	106	14	a	a	DET
ejpam-3024	106	15	δ	δ	NOUN
ejpam-3024	106	16	-	-	PUNCT
ejpam-3024	106	17	supplement	supplement	NOUN
ejpam-3024	106	18	of	of	ADP
ejpam-3024	106	19	m	m	PROPN
ejpam-3024	106	20	in	in	ADP
ejpam-3024	106	21	n	n	CCONJ
ejpam-3024	106	22	such	such	ADJ
ejpam-3024	106	23	that	that	DET
ejpam-3024	106	24	v	v	NOUN
ejpam-3024	106	25	≤	≤	NUM
ejpam-3024	106	26	x.	x.	NOUN
ejpam-3024	106	27	conversely	conversely	ADV
ejpam-3024	106	28	,	,	PUNCT
ejpam-3024	106	29	let	let	VERB
ejpam-3024	106	30	u	u	PRON
ejpam-3024	106	31	be	be	AUX
ejpam-3024	106	32	a	a	DET
ejpam-3024	106	33	submodule	submodule	NOUN
ejpam-3024	106	34	of	of	ADP
ejpam-3024	106	35	m	m	PROPN
ejpam-3024	106	36	and	and	CCONJ
ejpam-3024	106	37	n	n	CCONJ
ejpam-3024	106	38	be	be	VERB
ejpam-3024	106	39	any	any	DET
ejpam-3024	106	40	module	module	NOUN
ejpam-3024	106	41	containing	contain	VERB
ejpam-3024	106	42	u.	u.	NOUN
ejpam-3024	106	43	then	then	ADV
ejpam-3024	106	44	we	we	PRON
ejpam-3024	106	45	can	can	AUX
ejpam-3024	106	46	draw	draw	VERB
ejpam-3024	106	47	the	the	DET
ejpam-3024	106	48	following	follow	VERB
ejpam-3024	106	49	pushout	pushout	NOUN
ejpam-3024	106	50	:	:	PUNCT
ejpam-3024	106	51	i1	i1	PROPN
ejpam-3024	106	52	and	and	CCONJ
ejpam-3024	106	53	i2	i2	PROPN
ejpam-3024	106	54	are	be	AUX
ejpam-3024	106	55	inclusion	inclusion	NOUN
ejpam-3024	106	56	homomorphisms	homomorphism	NOUN
ejpam-3024	106	57	in	in	ADP
ejpam-3024	106	58	this	this	DET
ejpam-3024	106	59	diagram	diagram	NOUN
ejpam-3024	106	60	.	.	PUNCT
ejpam-3024	107	1	additionally	additionally	ADV
ejpam-3024	107	2	α	α	X
ejpam-3024	107	3	:	:	PUNCT
ejpam-3024	107	4	m	m	VERB
ejpam-3024	107	5	−→	−→	ADJ
ejpam-3024	107	6	f	f	NOUN
ejpam-3024	107	7	and	and	CCONJ
ejpam-3024	107	8	β	β	X
ejpam-3024	107	9	:	:	PUNCT
ejpam-3024	107	10	n	n	CCONJ
ejpam-3024	107	11	−→	−→	NOUN
ejpam-3024	107	12	f	f	NOUN
ejpam-3024	107	13	are	be	AUX
ejpam-3024	107	14	monomorphisms	monomorphism	NOUN
ejpam-3024	107	15	by	by	ADP
ejpam-3024	107	16	the	the	DET
ejpam-3024	107	17	properties	property	NOUN
ejpam-3024	107	18	of	of	ADP
ejpam-3024	107	19	push	push	VERB
ejpam-3024	107	20	out	out	ADP
ejpam-3024	107	21	(	(	PUNCT
ejpam-3024	107	22	see	see	VERB
ejpam-3024	107	23	,	,	PUNCT
ejpam-3024	107	24	for	for	ADP
ejpam-3024	107	25	example	example	NOUN
ejpam-3024	107	26	,	,	PUNCT
ejpam-3024	107	27	[	[	X
ejpam-3024	107	28	11	11	NUM
ejpam-3024	107	29	,	,	PUNCT
ejpam-3024	107	30	exercise	exercise	VERB
ejpam-3024	107	31	5.10	5.10	NUM
ejpam-3024	107	32	]	]	PUNCT
ejpam-3024	107	33	)	)	PUNCT
ejpam-3024	107	34	.	.	PUNCT
ejpam-3024	108	1	let	let	VERB
ejpam-3024	108	2	α(m	α(m	PROPN
ejpam-3024	108	3	)	)	PUNCT
ejpam-3024	109	1	=	=	PUNCT
ejpam-3024	110	1	m	m	AUX
ejpam-3024	110	2	′	′	NUM
ejpam-3024	110	3	⊆	⊆	NUM
ejpam-3024	110	4	f	f	PROPN
ejpam-3024	110	5	and	and	CCONJ
ejpam-3024	110	6	β(n	β(n	NUM
ejpam-3024	110	7	)	)	PUNCT
ejpam-3024	110	8	=	=	SYM
ejpam-3024	111	1	n	n	CCONJ
ejpam-3024	112	1	′	′	NOUN
ejpam-3024	112	2	⊆	⊆	NUM
ejpam-3024	113	1	f.	f.	NOUN
ejpam-3024	114	1	then	then	ADV
ejpam-3024	114	2	it	it	PRON
ejpam-3024	114	3	can	can	AUX
ejpam-3024	114	4	be	be	AUX
ejpam-3024	114	5	easily	easily	ADV
ejpam-3024	114	6	shown	show	VERB
ejpam-3024	114	7	e.	e.	PROPN
ejpam-3024	114	8	ö.	ö.	PROPN
ejpam-3024	114	9	sözen	sözen	PROPN
ejpam-3024	114	10	,	,	PUNCT
ejpam-3024	114	11	ş.	ş.	PROPN
ejpam-3024	114	12	eren	eren	PROPN
ejpam-3024	114	13	/	/	SYM
ejpam-3024	114	14	eur	eur	PROPN
ejpam-3024	114	15	.	.	PUNCT
ejpam-3024	115	1	j.	j.	PROPN
ejpam-3024	115	2	pure	pure	PROPN
ejpam-3024	115	3	appl	appl	PROPN
ejpam-3024	115	4	.	.	PROPN
ejpam-3024	115	5	math	math	PROPN
ejpam-3024	115	6	,	,	PUNCT
ejpam-3024	115	7	10	10	NUM
ejpam-3024	115	8	(	(	PUNCT
ejpam-3024	115	9	4	4	NUM
ejpam-3024	115	10	)	)	PUNCT
ejpam-3024	115	11	(	(	PUNCT
ejpam-3024	115	12	2017	2017	NUM
ejpam-3024	115	13	)	)	PUNCT
ejpam-3024	115	14	,	,	PUNCT
ejpam-3024	115	15	730	730	NUM
ejpam-3024	115	16	-	-	SYM
ejpam-3024	115	17	738	738	NUM
ejpam-3024	115	18	734	734	NUM
ejpam-3024	115	19	that	that	PRON
ejpam-3024	115	20	f	f	AUX
ejpam-3024	116	1	=	=	NOUN
ejpam-3024	116	2	m	m	AUX
ejpam-3024	116	3	′	′	VERB
ejpam-3024	117	1	+	+	ADV
ejpam-3024	117	2	n	n	ADV
ejpam-3024	117	3	′	′	NOUN
ejpam-3024	117	4	.	.	PUNCT
ejpam-3024	118	1	so	so	ADV
ejpam-3024	118	2	by	by	ADP
ejpam-3024	118	3	using	use	VERB
ejpam-3024	118	4	hypothesis	hypothesis	NOUN
ejpam-3024	118	5	,	,	PUNCT
ejpam-3024	118	6	m	m	VERB
ejpam-3024	118	7	′	′	VERB
ejpam-3024	118	8	∼=	∼=	ADV
ejpam-3024	118	9	m	m	VERB
ejpam-3024	118	10	has	have	VERB
ejpam-3024	118	11	a	a	DET
ejpam-3024	118	12	δ	δ	NOUN
ejpam-3024	118	13	-	-	PUNCT
ejpam-3024	118	14	supplement	supplement	NOUN
ejpam-3024	118	15	v	v	NOUN
ejpam-3024	118	16	in	in	ADP
ejpam-3024	118	17	f	f	PROPN
ejpam-3024	118	18	such	such	DET
ejpam-3024	118	19	that	that	DET
ejpam-3024	118	20	v	v	NOUN
ejpam-3024	118	21	≤	≤	NUM
ejpam-3024	118	22	n	n	DET
ejpam-3024	118	23	′	′	NOUN
ejpam-3024	118	24	,	,	PUNCT
ejpam-3024	118	25	that	that	ADV
ejpam-3024	118	26	is	is	ADV
ejpam-3024	118	27	,	,	PUNCT
ejpam-3024	118	28	m	m	VERB
ejpam-3024	118	29	′	′	NOUN
ejpam-3024	119	1	+	+	CCONJ
ejpam-3024	119	2	v	v	NOUN
ejpam-3024	119	3	=	=	SYM
ejpam-3024	119	4	f	f	PROPN
ejpam-3024	119	5	and	and	CCONJ
ejpam-3024	119	6	m	m	PROPN
ejpam-3024	119	7	′	′	NUM
ejpam-3024	119	8	∩	∩	PROPN
ejpam-3024	119	9	v	v	ADP
ejpam-3024	119	10	�	�	PROPN
ejpam-3024	119	11	δ	δ	PROPN
ejpam-3024	119	12	v.	v.	CCONJ
ejpam-3024	119	13	hence	hence	ADV
ejpam-3024	119	14	,	,	PUNCT
ejpam-3024	119	15	(	(	PUNCT
ejpam-3024	119	16	m	m	VERB
ejpam-3024	119	17	′	′	NUM
ejpam-3024	119	18	∩n	∩n	NOUN
ejpam-3024	119	19	′	′	NUM
ejpam-3024	119	20	)	)	PUNCT
ejpam-3024	120	1	+	+	CCONJ
ejpam-3024	120	2	v	v	X
ejpam-3024	120	3	=	=	SYM
ejpam-3024	120	4	(	(	PUNCT
ejpam-3024	120	5	n	n	NOUN
ejpam-3024	120	6	′	′	NUM
ejpam-3024	121	1	∩m	∩m	NOUN
ejpam-3024	121	2	′	′	NUM
ejpam-3024	121	3	)	)	PUNCT
ejpam-3024	122	1	+	+	CCONJ
ejpam-3024	122	2	v	v	X
ejpam-3024	122	3	=	=	SYM
ejpam-3024	122	4	n	n	NOUN
ejpam-3024	122	5	′	′	NUM
ejpam-3024	122	6	∩	∩	NOUN
ejpam-3024	122	7	(	(	PUNCT
ejpam-3024	122	8	m	m	VERB
ejpam-3024	122	9	′	′	VERB
ejpam-3024	123	1	+	+	CCONJ
ejpam-3024	123	2	v	v	NOUN
ejpam-3024	123	3	)	)	PUNCT
ejpam-3024	123	4	=	=	SYM
ejpam-3024	124	1	n	n	NOUN
ejpam-3024	124	2	′	′	NUM
ejpam-3024	124	3	∩	∩	NOUN
ejpam-3024	124	4	f	f	PROPN
ejpam-3024	124	5	=	=	SYM
ejpam-3024	124	6	n	n	PROPN
ejpam-3024	124	7	′	′	NOUN
ejpam-3024	124	8	,	,	PUNCT
ejpam-3024	124	9	and	and	CCONJ
ejpam-3024	124	10	(	(	PUNCT
ejpam-3024	124	11	m	m	VERB
ejpam-3024	124	12	′	′	NUM
ejpam-3024	124	13	∩n	∩n	NOUN
ejpam-3024	124	14	′	′	NOUN
ejpam-3024	124	15	)	)	PUNCT
ejpam-3024	124	16	∩	∩	NOUN
ejpam-3024	124	17	v	v	NOUN
ejpam-3024	124	18	=	=	SYM
ejpam-3024	124	19	m	m	NOUN
ejpam-3024	124	20	′	′	NOUN
ejpam-3024	124	21	∩	∩	NOUN
ejpam-3024	124	22	(	(	PUNCT
ejpam-3024	124	23	n	n	ADV
ejpam-3024	124	24	′	′	NUM
ejpam-3024	124	25	∩	∩	NOUN
ejpam-3024	124	26	v	v	X
ejpam-3024	124	27	)	)	PUNCT
ejpam-3024	124	28	=	=	PUNCT
ejpam-3024	124	29	m	m	VERB
ejpam-3024	124	30	′	′	NUM
ejpam-3024	124	31	∩	∩	PROPN
ejpam-3024	124	32	v	v	ADP
ejpam-3024	124	33	�	�	PROPN
ejpam-3024	124	34	δ	δ	PROPN
ejpam-3024	124	35	v.	v.	NOUN
ejpam-3024	124	36	so	so	ADV
ejpam-3024	124	37	v	v	NOUN
ejpam-3024	124	38	is	be	AUX
ejpam-3024	124	39	a	a	DET
ejpam-3024	124	40	δ	δ	NOUN
ejpam-3024	124	41	-	-	PUNCT
ejpam-3024	124	42	supplement	supplement	NOUN
ejpam-3024	124	43	ofm	ofm	PROPN
ejpam-3024	124	44	′∩n	′∩n	PROPN
ejpam-3024	124	45	′	′	NUM
ejpam-3024	124	46	inn	inn	PROPN
ejpam-3024	124	47	′	′	NUM
ejpam-3024	124	48	.	.	PUNCT
ejpam-3024	125	1	now	now	ADV
ejpam-3024	125	2	we	we	PRON
ejpam-3024	125	3	will	will	AUX
ejpam-3024	125	4	show	show	VERB
ejpam-3024	125	5	that	that	PRON
ejpam-3024	125	6	β−1(v	β−1(v	PROPN
ejpam-3024	125	7	)	)	PUNCT
ejpam-3024	125	8	is	be	AUX
ejpam-3024	125	9	a	a	DET
ejpam-3024	125	10	δ	δ	NOUN
ejpam-3024	125	11	-	-	PUNCT
ejpam-3024	125	12	supplement	supplement	NOUN
ejpam-3024	125	13	of	of	ADP
ejpam-3024	125	14	u	u	NOUN
ejpam-3024	125	15	in	in	ADP
ejpam-3024	125	16	n.	n.	NOUN
ejpam-3024	125	17	we	we	PRON
ejpam-3024	125	18	have	have	VERB
ejpam-3024	125	19	an	an	DET
ejpam-3024	125	20	isomorphism	isomorphism	NOUN
ejpam-3024	125	21	∼	∼	NOUN
ejpam-3024	125	22	β	β	NOUN
ejpam-3024	125	23	:	:	PUNCT
ejpam-3024	125	24	n	n	CCONJ
ejpam-3024	125	25	−→	−→	NOUN
ejpam-3024	125	26	n	n	NOUN
ejpam-3024	125	27	′	′	NUM
ejpam-3024	125	28	defined	define	VERB
ejpam-3024	125	29	as	as	ADP
ejpam-3024	125	30	β(x	β(x	NOUN
ejpam-3024	125	31	)	)	PUNCT
ejpam-3024	125	32	=	=	SYM
ejpam-3024	125	33	∼	∼	NOUN
ejpam-3024	125	34	β(x	β(x	NOUN
ejpam-3024	125	35	)	)	PUNCT
ejpam-3024	125	36	for	for	ADP
ejpam-3024	125	37	all	all	DET
ejpam-3024	125	38	x	x	SYM
ejpam-3024	125	39	∈	∈	PROPN
ejpam-3024	125	40	n	n	CCONJ
ejpam-3024	125	41	,	,	PUNCT
ejpam-3024	125	42	since	since	SCONJ
ejpam-3024	125	43	β	β	X
ejpam-3024	125	44	is	be	AUX
ejpam-3024	125	45	a	a	DET
ejpam-3024	125	46	monomorphism	monomorphism	NOUN
ejpam-3024	125	47	.	.	PUNCT
ejpam-3024	126	1	using	use	VERB
ejpam-3024	126	2	this	this	PRON
ejpam-3024	126	3	,	,	PUNCT
ejpam-3024	126	4	we	we	PRON
ejpam-3024	126	5	obtain	obtain	VERB
ejpam-3024	126	6	∼	∼	NOUN
ejpam-3024	126	7	β−1(v	β−1(v	NOUN
ejpam-3024	126	8	)	)	PUNCT
ejpam-3024	126	9	is	be	AUX
ejpam-3024	126	10	a	a	DET
ejpam-3024	126	11	δ	δ	NOUN
ejpam-3024	126	12	-	-	PUNCT
ejpam-3024	126	13	supplement	supplement	NOUN
ejpam-3024	126	14	of	of	ADP
ejpam-3024	126	15	β−1(m	β−1(m	PROPN
ejpam-3024	127	1	′	′	NUM
ejpam-3024	127	2	∩n	∩n	PROPN
ejpam-3024	127	3	′	′	PROPN
ejpam-3024	127	4	)	)	PUNCT
ejpam-3024	127	5	in	in	ADP
ejpam-3024	127	6	∼	∼	NOUN
ejpam-3024	127	7	β−1(n	β−1(n	NOUN
ejpam-3024	127	8	′	′	NOUN
ejpam-3024	127	9	)	)	PUNCT
ejpam-3024	128	1	since	since	SCONJ
ejpam-3024	128	2	v	v	NOUN
ejpam-3024	128	3	is	be	AUX
ejpam-3024	128	4	a	a	DET
ejpam-3024	128	5	δ	δ	NOUN
ejpam-3024	128	6	-	-	PUNCT
ejpam-3024	128	7	supplement	supplement	NOUN
ejpam-3024	128	8	of	of	ADP
ejpam-3024	128	9	m	m	PROPN
ejpam-3024	128	10	′∩n	′∩n	PROPN
ejpam-3024	128	11	′	′	NUM
ejpam-3024	128	12	in	in	ADP
ejpam-3024	128	13	n	n	NOUN
ejpam-3024	128	14	′	′	NOUN
ejpam-3024	128	15	.	.	PUNCT
ejpam-3024	129	1	it	it	PRON
ejpam-3024	129	2	can	can	AUX
ejpam-3024	129	3	be	be	AUX
ejpam-3024	129	4	seen	see	VERB
ejpam-3024	129	5	that	that	SCONJ
ejpam-3024	129	6	∼	∼	NOUN
ejpam-3024	129	7	β−1(v	β−1(v	PUNCT
ejpam-3024	129	8	)	)	PUNCT
ejpam-3024	129	9	=	=	PUNCT
ejpam-3024	129	10	β−1(v	β−1(v	PROPN
ejpam-3024	129	11	)	)	PUNCT
ejpam-3024	129	12	,	,	PUNCT
ejpam-3024	129	13	∼	∼	NOUN
ejpam-3024	129	14	β−1(n	β−1(n	NOUN
ejpam-3024	129	15	′	′	NUM
ejpam-3024	129	16	)	)	PUNCT
ejpam-3024	130	1	=	=	SYM
ejpam-3024	130	2	n	n	NOUN
ejpam-3024	130	3	and	and	CCONJ
ejpam-3024	130	4	∼	∼	VERB
ejpam-3024	130	5	β−1(m	β−1(m	PROPN
ejpam-3024	130	6	′	′	NUM
ejpam-3024	130	7	∩n	∩n	NOUN
ejpam-3024	130	8	′	′	NUM
ejpam-3024	130	9	)	)	PUNCT
ejpam-3024	131	1	=	=	VERB
ejpam-3024	131	2	u.	u.	PROPN
ejpam-3024	131	3	thus	thus	ADV
ejpam-3024	131	4	β−1(v	β−1(v	VERB
ejpam-3024	131	5	)	)	PUNCT
ejpam-3024	131	6	is	be	AUX
ejpam-3024	131	7	a	a	DET
ejpam-3024	131	8	δ	δ	NOUN
ejpam-3024	131	9	-	-	PUNCT
ejpam-3024	131	10	supplement	supplement	NOUN
ejpam-3024	131	11	of	of	ADP
ejpam-3024	131	12	u	u	NOUN
ejpam-3024	131	13	in	in	ADP
ejpam-3024	131	14	n.	n.	PROPN
ejpam-3024	131	15	corollary	corollary	ADJ
ejpam-3024	131	16	1	1	NUM
ejpam-3024	131	17	.	.	PUNCT
ejpam-3024	131	18	a	a	DET
ejpam-3024	131	19	module	module	NOUN
ejpam-3024	131	20	with	with	ADP
ejpam-3024	131	21	the	the	DET
ejpam-3024	131	22	property	property	NOUN
ejpam-3024	131	23	(	(	PUNCT
ejpam-3024	131	24	δ	δ	PROPN
ejpam-3024	131	25	-	-	PUNCT
ejpam-3024	131	26	ee	ee	PROPN
ejpam-3024	131	27	)	)	PUNCT
ejpam-3024	131	28	has	have	VERB
ejpam-3024	131	29	the	the	DET
ejpam-3024	131	30	property	property	NOUN
ejpam-3024	131	31	(	(	PUNCT
ejpam-3024	131	32	δ	δ	PROPN
ejpam-3024	131	33	-	-	PUNCT
ejpam-3024	131	34	e	e	PROPN
ejpam-3024	131	35	)	)	PUNCT
ejpam-3024	131	36	and	and	CCONJ
ejpam-3024	131	37	it	it	PRON
ejpam-3024	131	38	is	be	AUX
ejpam-3024	131	39	also	also	ADV
ejpam-3024	131	40	δ	δ	PROPN
ejpam-3024	131	41	-	-	PUNCT
ejpam-3024	131	42	supplemented	supplement	VERB
ejpam-3024	131	43	.	.	PUNCT
ejpam-3024	132	1	recall	recall	NOUN
ejpam-3024	132	2	that	that	SCONJ
ejpam-3024	132	3	r	r	NOUN
ejpam-3024	132	4	is	be	AUX
ejpam-3024	132	5	a	a	DET
ejpam-3024	132	6	(	(	PUNCT
ejpam-3024	132	7	right	right	ADJ
ejpam-3024	132	8	)	)	PUNCT
ejpam-3024	132	9	δ	δ	PROPN
ejpam-3024	132	10	-	-	PUNCT
ejpam-3024	132	11	v	v	NOUN
ejpam-3024	132	12	ring	ring	NOUN
ejpam-3024	132	13	if	if	SCONJ
ejpam-3024	132	14	for	for	ADP
ejpam-3024	132	15	any	any	DET
ejpam-3024	132	16	right	right	ADJ
ejpam-3024	132	17	r	r	NOUN
ejpam-3024	132	18	-	-	PUNCT
ejpam-3024	132	19	module	module	NOUN
ejpam-3024	132	20	m	m	NOUN
ejpam-3024	132	21	,	,	PUNCT
ejpam-3024	132	22	δ(m	δ(m	PROPN
ejpam-3024	132	23	)	)	PUNCT
ejpam-3024	132	24	=	=	SYM
ejpam-3024	132	25	0	0	PUNCT
ejpam-3024	133	1	(	(	PUNCT
ejpam-3024	133	2	see	see	VERB
ejpam-3024	133	3	,	,	PUNCT
ejpam-3024	133	4	[	[	X
ejpam-3024	133	5	13	13	NUM
ejpam-3024	133	6	]	]	NUM
ejpam-3024	133	7	)	)	PUNCT
ejpam-3024	133	8	.	.	PUNCT
ejpam-3024	134	1	proposition	proposition	NOUN
ejpam-3024	134	2	2	2	NUM
ejpam-3024	134	3	.	.	PUNCT
ejpam-3024	135	1	let	let	VERB
ejpam-3024	135	2	r	r	NOUN
ejpam-3024	135	3	be	be	AUX
ejpam-3024	135	4	δ	δ	NOUN
ejpam-3024	135	5	-	-	PUNCT
ejpam-3024	135	6	v	v	NOUN
ejpam-3024	135	7	ring	ring	NOUN
ejpam-3024	135	8	and	and	CCONJ
ejpam-3024	135	9	m	m	AUX
ejpam-3024	135	10	be	be	AUX
ejpam-3024	135	11	an	an	DET
ejpam-3024	135	12	r	r	NOUN
ejpam-3024	135	13	-	-	PUNCT
ejpam-3024	135	14	module	module	NOUN
ejpam-3024	135	15	.	.	PUNCT
ejpam-3024	136	1	then	then	ADV
ejpam-3024	136	2	the	the	DET
ejpam-3024	136	3	following	follow	VERB
ejpam-3024	136	4	statements	statement	NOUN
ejpam-3024	136	5	are	be	AUX
ejpam-3024	136	6	equivalent	equivalent	ADJ
ejpam-3024	136	7	:	:	PUNCT
ejpam-3024	136	8	1	1	X
ejpam-3024	136	9	.	.	X
ejpam-3024	136	10	m	m	PROPN
ejpam-3024	136	11	has	have	AUX
ejpam-3024	136	12	the	the	DET
ejpam-3024	136	13	property	property	NOUN
ejpam-3024	136	14	(	(	PUNCT
ejpam-3024	136	15	δ	δ	PROPN
ejpam-3024	136	16	-	-	PUNCT
ejpam-3024	136	17	e	e	PROPN
ejpam-3024	136	18	)	)	PUNCT
ejpam-3024	136	19	.	.	PUNCT
ejpam-3024	137	1	2	2	X
ejpam-3024	137	2	.	.	X
ejpam-3024	137	3	m	m	PROPN
ejpam-3024	137	4	is	be	AUX
ejpam-3024	137	5	injective	injective	ADJ
ejpam-3024	137	6	.	.	PUNCT
ejpam-3024	138	1	proof	proof	NOUN
ejpam-3024	138	2	.	.	PUNCT
ejpam-3024	139	1	(	(	PUNCT
ejpam-3024	139	2	1	1	X
ejpam-3024	139	3	)	)	PUNCT
ejpam-3024	139	4	=	=	NOUN
ejpam-3024	139	5	⇒	⇒	NOUN
ejpam-3024	139	6	(	(	PUNCT
ejpam-3024	139	7	2	2	NUM
ejpam-3024	139	8	)	)	PUNCT
ejpam-3024	139	9	:	:	PUNCT
ejpam-3024	139	10	suppose	suppose	VERB
ejpam-3024	139	11	that	that	SCONJ
ejpam-3024	139	12	m	m	PROPN
ejpam-3024	139	13	has	have	VERB
ejpam-3024	139	14	the	the	DET
ejpam-3024	139	15	property	property	NOUN
ejpam-3024	139	16	(	(	PUNCT
ejpam-3024	139	17	δ	δ	PROPN
ejpam-3024	139	18	-	-	PUNCT
ejpam-3024	139	19	e	e	NOUN
ejpam-3024	139	20	)	)	PUNCT
ejpam-3024	139	21	.	.	PUNCT
ejpam-3024	140	1	let	let	VERB
ejpam-3024	140	2	n	n	PRON
ejpam-3024	140	3	be	be	AUX
ejpam-3024	140	4	any	any	DET
ejpam-3024	140	5	extension	extension	NOUN
ejpam-3024	140	6	of	of	ADP
ejpam-3024	140	7	m.	m.	NOUN
ejpam-3024	140	8	so	so	ADV
ejpam-3024	140	9	,	,	PUNCT
ejpam-3024	140	10	there	there	PRON
ejpam-3024	140	11	exists	exist	VERB
ejpam-3024	140	12	a	a	DET
ejpam-3024	140	13	δ	δ	NOUN
ejpam-3024	140	14	-	-	PUNCT
ejpam-3024	140	15	supplement	supplement	NOUN
ejpam-3024	140	16	v	v	NOUN
ejpam-3024	140	17	of	of	ADP
ejpam-3024	140	18	m	m	PROPN
ejpam-3024	140	19	in	in	ADP
ejpam-3024	140	20	n	n	CCONJ
ejpam-3024	140	21	,	,	PUNCT
ejpam-3024	140	22	that	that	ADV
ejpam-3024	140	23	is	be	AUX
ejpam-3024	140	24	,	,	PUNCT
ejpam-3024	140	25	m	m	VERB
ejpam-3024	140	26	+	+	NOUN
ejpam-3024	140	27	v	v	NOUN
ejpam-3024	140	28	=	=	SYM
ejpam-3024	140	29	n	n	NOUN
ejpam-3024	140	30	and	and	CCONJ
ejpam-3024	140	31	m	m	PROPN
ejpam-3024	140	32	∩v	∩v	NOUN
ejpam-3024	140	33	�	�	PROPN
ejpam-3024	140	34	δ	δ	PROPN
ejpam-3024	140	35	v	v	NOUN
ejpam-3024	141	1	and	and	CCONJ
ejpam-3024	141	2	so	so	ADV
ejpam-3024	141	3	m	m	NOUN
ejpam-3024	141	4	∩	∩	NOUN
ejpam-3024	141	5	v	v	ADP
ejpam-3024	141	6	≤	≤	NUM
ejpam-3024	141	7	δ(v	δ(v	PROPN
ejpam-3024	141	8	)	)	PUNCT
ejpam-3024	141	9	.	.	PUNCT
ejpam-3024	142	1	since	since	SCONJ
ejpam-3024	142	2	r	r	NOUN
ejpam-3024	142	3	is	be	AUX
ejpam-3024	142	4	a	a	DET
ejpam-3024	142	5	δ	δ	PROPN
ejpam-3024	142	6	-	-	PUNCT
ejpam-3024	142	7	v	v	NOUN
ejpam-3024	142	8	ring	ring	NOUN
ejpam-3024	142	9	,	,	PUNCT
ejpam-3024	142	10	δ(v	δ(v	PROPN
ejpam-3024	142	11	)	)	PUNCT
ejpam-3024	143	1	=	=	PUNCT
ejpam-3024	143	2	0	0	X
ejpam-3024	143	3	.	.	PUNCT
ejpam-3024	144	1	so	so	ADV
ejpam-3024	144	2	,	,	PUNCT
ejpam-3024	144	3	n	n	PROPN
ejpam-3024	144	4	=	=	SYM
ejpam-3024	144	5	m	m	VERB
ejpam-3024	144	6	⊕	⊕	PROPN
ejpam-3024	144	7	v.	v.	CCONJ
ejpam-3024	144	8	therefore	therefore	ADV
ejpam-3024	144	9	,	,	PUNCT
ejpam-3024	144	10	m	m	VERB
ejpam-3024	144	11	is	be	AUX
ejpam-3024	144	12	injective	injective	ADJ
ejpam-3024	144	13	.	.	PUNCT
ejpam-3024	145	1	(	(	PUNCT
ejpam-3024	145	2	2	2	X
ejpam-3024	145	3	)	)	PUNCT
ejpam-3024	145	4	=	=	NOUN
ejpam-3024	145	5	⇒	⇒	NOUN
ejpam-3024	145	6	(	(	PUNCT
ejpam-3024	145	7	1	1	NUM
ejpam-3024	145	8	)	)	PUNCT
ejpam-3024	145	9	:	:	PUNCT
ejpam-3024	145	10	is	be	AUX
ejpam-3024	145	11	clear	clear	ADJ
ejpam-3024	145	12	.	.	PUNCT
ejpam-3024	146	1	now	now	ADV
ejpam-3024	146	2	we	we	PRON
ejpam-3024	146	3	show	show	VERB
ejpam-3024	146	4	that	that	SCONJ
ejpam-3024	146	5	the	the	DET
ejpam-3024	146	6	property	property	NOUN
ejpam-3024	146	7	(	(	PUNCT
ejpam-3024	146	8	δ	δ	PROPN
ejpam-3024	146	9	-	-	PUNCT
ejpam-3024	146	10	e	e	NOUN
ejpam-3024	146	11	)	)	PUNCT
ejpam-3024	146	12	is	be	AUX
ejpam-3024	146	13	preserved	preserve	VERB
ejpam-3024	146	14	by	by	ADP
ejpam-3024	146	15	direct	direct	ADJ
ejpam-3024	146	16	summands	summand	NOUN
ejpam-3024	146	17	in	in	ADP
ejpam-3024	146	18	the	the	DET
ejpam-3024	146	19	following	follow	VERB
ejpam-3024	146	20	proposition	proposition	NOUN
ejpam-3024	146	21	:	:	PUNCT
ejpam-3024	146	22	proposition	proposition	NOUN
ejpam-3024	146	23	3	3	NUM
ejpam-3024	146	24	.	.	PUNCT
ejpam-3024	147	1	every	every	DET
ejpam-3024	147	2	direct	direct	ADJ
ejpam-3024	147	3	summand	summand	NOUN
ejpam-3024	147	4	of	of	ADP
ejpam-3024	147	5	any	any	DET
ejpam-3024	147	6	module	module	NOUN
ejpam-3024	147	7	with	with	ADP
ejpam-3024	147	8	the	the	DET
ejpam-3024	147	9	property	property	NOUN
ejpam-3024	147	10	(	(	PUNCT
ejpam-3024	147	11	δ	δ	PROPN
ejpam-3024	147	12	-	-	PUNCT
ejpam-3024	147	13	e	e	PROPN
ejpam-3024	147	14	)	)	PUNCT
ejpam-3024	147	15	has	have	VERB
ejpam-3024	147	16	the	the	DET
ejpam-3024	147	17	property	property	NOUN
ejpam-3024	147	18	(	(	PUNCT
ejpam-3024	147	19	δ	δ	PROPN
ejpam-3024	147	20	-	-	PUNCT
ejpam-3024	147	21	e	e	NOUN
ejpam-3024	147	22	)	)	PUNCT
ejpam-3024	147	23	.	.	PUNCT
ejpam-3024	148	1	proof	proof	NOUN
ejpam-3024	148	2	.	.	PUNCT
ejpam-3024	149	1	let	let	VERB
ejpam-3024	149	2	m	m	PRON
ejpam-3024	149	3	be	be	AUX
ejpam-3024	149	4	a	a	DET
ejpam-3024	149	5	module	module	NOUN
ejpam-3024	149	6	with	with	ADP
ejpam-3024	149	7	the	the	DET
ejpam-3024	149	8	property	property	NOUN
ejpam-3024	149	9	(	(	PUNCT
ejpam-3024	149	10	δ	δ	PROPN
ejpam-3024	149	11	-	-	PUNCT
ejpam-3024	149	12	e	e	PROPN
ejpam-3024	149	13	)	)	PUNCT
ejpam-3024	149	14	,	,	PUNCT
ejpam-3024	149	15	u	u	PRON
ejpam-3024	149	16	be	be	VERB
ejpam-3024	149	17	a	a	DET
ejpam-3024	149	18	direct	direct	ADJ
ejpam-3024	149	19	summand	summand	NOUN
ejpam-3024	149	20	of	of	ADP
ejpam-3024	149	21	m	m	PROPN
ejpam-3024	149	22	and	and	CCONJ
ejpam-3024	149	23	n	n	CCONJ
ejpam-3024	149	24	be	be	VERB
ejpam-3024	149	25	any	any	DET
ejpam-3024	149	26	extension	extension	NOUN
ejpam-3024	149	27	of	of	ADP
ejpam-3024	149	28	u.	u.	NOUN
ejpam-3024	149	29	then	then	ADV
ejpam-3024	149	30	there	there	PRON
ejpam-3024	149	31	exists	exist	VERB
ejpam-3024	149	32	a	a	DET
ejpam-3024	149	33	submodule	submodule	NOUN
ejpam-3024	149	34	a	a	PRON
ejpam-3024	149	35	of	of	ADP
ejpam-3024	149	36	m	m	PRON
ejpam-3024	149	37	such	such	ADJ
ejpam-3024	149	38	that	that	SCONJ
ejpam-3024	149	39	m	m	VERB
ejpam-3024	149	40	=	=	SYM
ejpam-3024	149	41	u	u	PROPN
ejpam-3024	149	42	⊕	⊕	PROPN
ejpam-3024	149	43	a.	a.	NOUN
ejpam-3024	149	44	by	by	ADP
ejpam-3024	149	45	hypothesis	hypothesis	NOUN
ejpam-3024	149	46	,	,	PUNCT
ejpam-3024	149	47	m	m	VERB
ejpam-3024	149	48	has	have	VERB
ejpam-3024	149	49	a	a	DET
ejpam-3024	149	50	δ	δ	NOUN
ejpam-3024	149	51	-	-	PUNCT
ejpam-3024	149	52	supplement	supplement	NOUN
ejpam-3024	149	53	v	v	NOUN
ejpam-3024	149	54	in	in	ADP
ejpam-3024	149	55	a	a	DET
ejpam-3024	149	56	⊕n	⊕n	NOUN
ejpam-3024	149	57	such	such	ADJ
ejpam-3024	149	58	that	that	SCONJ
ejpam-3024	149	59	(	(	PUNCT
ejpam-3024	149	60	a	a	DET
ejpam-3024	149	61	⊕	⊕	PROPN
ejpam-3024	149	62	u	u	NOUN
ejpam-3024	149	63	)	)	PUNCT
ejpam-3024	149	64	+	+	CCONJ
ejpam-3024	149	65	v	v	NOUN
ejpam-3024	149	66	=	=	PUNCT
ejpam-3024	149	67	a	a	DET
ejpam-3024	149	68	⊕n	⊕n	NOUN
ejpam-3024	149	69	and	and	CCONJ
ejpam-3024	149	70	(	(	PUNCT
ejpam-3024	149	71	a⊕	a⊕	PROPN
ejpam-3024	149	72	u	u	NOUN
ejpam-3024	149	73	)	)	PUNCT
ejpam-3024	149	74	∩	∩	NOUN
ejpam-3024	149	75	v	v	ADP
ejpam-3024	149	76	<	<	X
ejpam-3024	149	77	<	<	X
ejpam-3024	149	78	δ	δ	X
ejpam-3024	149	79	v.	v.	CCONJ
ejpam-3024	149	80	let	let	VERB
ejpam-3024	149	81	g	g	NOUN
ejpam-3024	149	82	:	:	PUNCT
ejpam-3024	149	83	a⊕n	a⊕n	PROPN
ejpam-3024	149	84	−→	−→	PROPN
ejpam-3024	149	85	n	n	PRON
ejpam-3024	149	86	be	be	VERB
ejpam-3024	149	87	the	the	DET
ejpam-3024	149	88	projection	projection	NOUN
ejpam-3024	149	89	onto	onto	ADP
ejpam-3024	149	90	n.	n.	NOUN
ejpam-3024	149	91	then	then	ADV
ejpam-3024	149	92	n	n	PROPN
ejpam-3024	149	93	=	=	SYM
ejpam-3024	149	94	g(a⊕n	g(a⊕n	PROPN
ejpam-3024	149	95	)	)	PUNCT
ejpam-3024	150	1	=	=	PUNCT
ejpam-3024	150	2	g((a⊕	g((a⊕	NOUN
ejpam-3024	150	3	u	u	NOUN
ejpam-3024	150	4	)	)	PUNCT
ejpam-3024	151	1	+	+	NUM
ejpam-3024	151	2	v	v	NOUN
ejpam-3024	151	3	)	)	PUNCT
ejpam-3024	152	1	=	=	PUNCT
ejpam-3024	152	2	g(a⊕	g(a⊕	PROPN
ejpam-3024	152	3	u	u	NOUN
ejpam-3024	152	4	)	)	PUNCT
ejpam-3024	153	1	+	+	CCONJ
ejpam-3024	153	2	g(v	g(v	X
ejpam-3024	153	3	)	)	PUNCT
ejpam-3024	153	4	=	=	SYM
ejpam-3024	153	5	u	u	PROPN
ejpam-3024	153	6	+	+	X
ejpam-3024	153	7	g(v	g(v	PROPN
ejpam-3024	153	8	)	)	PUNCT
ejpam-3024	153	9	,	,	PUNCT
ejpam-3024	153	10	and	and	CCONJ
ejpam-3024	153	11	g((a⊕	g((a⊕	ADJ
ejpam-3024	153	12	u	u	NOUN
ejpam-3024	153	13	)	)	PUNCT
ejpam-3024	153	14	∩	∩	NOUN
ejpam-3024	153	15	v	v	NOUN
ejpam-3024	153	16	)	)	PUNCT
ejpam-3024	153	17	=	=	SYM
ejpam-3024	153	18	u	u	NOUN
ejpam-3024	153	19	∩	∩	NOUN
ejpam-3024	153	20	g(v	g(v	PROPN
ejpam-3024	153	21	)	)	PUNCT
ejpam-3024	153	22	�	�	PROPN
ejpam-3024	153	23	δ	δ	PROPN
ejpam-3024	153	24	g(v	g(v	PROPN
ejpam-3024	153	25	)	)	PUNCT
ejpam-3024	153	26	.	.	PUNCT
ejpam-3024	154	1	hence	hence	ADV
ejpam-3024	154	2	,	,	PUNCT
ejpam-3024	154	3	g(v	g(v	PROPN
ejpam-3024	154	4	)	)	PUNCT
ejpam-3024	154	5	is	be	AUX
ejpam-3024	154	6	a	a	DET
ejpam-3024	154	7	δ	δ	NOUN
ejpam-3024	154	8	-	-	PUNCT
ejpam-3024	154	9	supplement	supplement	NOUN
ejpam-3024	154	10	of	of	ADP
ejpam-3024	154	11	u	u	NOUN
ejpam-3024	154	12	in	in	ADP
ejpam-3024	154	13	n.	n.	PROPN
ejpam-3024	154	14	e.	e.	PROPN
ejpam-3024	154	15	ö.	ö.	PROPN
ejpam-3024	154	16	sözen	sözen	PROPN
ejpam-3024	154	17	,	,	PUNCT
ejpam-3024	154	18	ş.	ş.	PROPN
ejpam-3024	154	19	eren	eren	PROPN
ejpam-3024	154	20	/	/	SYM
ejpam-3024	154	21	eur	eur	PROPN
ejpam-3024	154	22	.	.	PUNCT
ejpam-3024	155	1	j.	j.	PROPN
ejpam-3024	155	2	pure	pure	PROPN
ejpam-3024	155	3	appl	appl	PROPN
ejpam-3024	155	4	.	.	PROPN
ejpam-3024	155	5	math	math	PROPN
ejpam-3024	155	6	,	,	PUNCT
ejpam-3024	155	7	10	10	NUM
ejpam-3024	155	8	(	(	PUNCT
ejpam-3024	155	9	4	4	NUM
ejpam-3024	155	10	)	)	PUNCT
ejpam-3024	155	11	(	(	PUNCT
ejpam-3024	155	12	2017	2017	NUM
ejpam-3024	155	13	)	)	PUNCT
ejpam-3024	155	14	,	,	PUNCT
ejpam-3024	155	15	730	730	NUM
ejpam-3024	155	16	-	-	SYM
ejpam-3024	155	17	738	738	NUM
ejpam-3024	155	18	735	735	NUM
ejpam-3024	155	19	proposition	proposition	NOUN
ejpam-3024	155	20	4	4	NUM
ejpam-3024	155	21	.	.	PUNCT
ejpam-3024	156	1	let	let	VERB
ejpam-3024	156	2	a	a	DET
ejpam-3024	156	3	≤	≤	PROPN
ejpam-3024	156	4	b.	b.	NOUN
ejpam-3024	157	1	if	if	SCONJ
ejpam-3024	157	2	a	a	PRON
ejpam-3024	157	3	and	and	CCONJ
ejpam-3024	157	4	b	b	NOUN
ejpam-3024	157	5	a	a	PRON
ejpam-3024	157	6	have	have	VERB
ejpam-3024	157	7	the	the	DET
ejpam-3024	157	8	property	property	NOUN
ejpam-3024	157	9	(	(	PUNCT
ejpam-3024	157	10	δ	δ	PROPN
ejpam-3024	157	11	-	-	PUNCT
ejpam-3024	157	12	e	e	PROPN
ejpam-3024	157	13	)	)	PUNCT
ejpam-3024	157	14	,	,	PUNCT
ejpam-3024	157	15	so	so	ADV
ejpam-3024	157	16	does	do	VERB
ejpam-3024	157	17	b.	b.	PROPN
ejpam-3024	157	18	proof	proof	NOUN
ejpam-3024	157	19	.	.	PUNCT
ejpam-3024	158	1	let	let	VERB
ejpam-3024	158	2	n	n	PRON
ejpam-3024	158	3	be	be	AUX
ejpam-3024	158	4	any	any	DET
ejpam-3024	158	5	extension	extension	NOUN
ejpam-3024	158	6	of	of	ADP
ejpam-3024	158	7	b.	b.	PROPN
ejpam-3024	159	1	so	so	ADV
ejpam-3024	159	2	,	,	PUNCT
ejpam-3024	159	3	there	there	PRON
ejpam-3024	159	4	is	be	VERB
ejpam-3024	159	5	a	a	DET
ejpam-3024	159	6	δ	δ	NOUN
ejpam-3024	159	7	-	-	PUNCT
ejpam-3024	159	8	supplement	supplement	NOUN
ejpam-3024	159	9	v	v	ADP
ejpam-3024	159	10	a	a	PRON
ejpam-3024	159	11	of	of	ADP
ejpam-3024	159	12	b	b	NOUN
ejpam-3024	159	13	a	a	NOUN
ejpam-3024	159	14	in	in	ADP
ejpam-3024	159	15	n	n	PROPN
ejpam-3024	159	16	a	a	PRON
ejpam-3024	159	17	and	and	CCONJ
ejpam-3024	159	18	a	a	DET
ejpam-3024	159	19	δ	δ	NOUN
ejpam-3024	159	20	-	-	PUNCT
ejpam-3024	159	21	supplement	supplement	NOUN
ejpam-3024	159	22	t	t	NOUN
ejpam-3024	159	23	of	of	ADP
ejpam-3024	159	24	a	a	DET
ejpam-3024	159	25	in	in	ADP
ejpam-3024	160	1	v.	v.	CCONJ
ejpam-3024	161	1	we	we	PRON
ejpam-3024	161	2	have	have	VERB
ejpam-3024	161	3	δ	δ	NOUN
ejpam-3024	161	4	-	-	ADJ
ejpam-3024	161	5	small	small	ADJ
ejpam-3024	161	6	epimorphisms	epimorphism	NOUN
ejpam-3024	161	7	f	f	X
ejpam-3024	161	8	:	:	PUNCT
ejpam-3024	161	9	t	t	X
ejpam-3024	161	10	−→	−→	NOUN
ejpam-3024	161	11	v	v	PROPN
ejpam-3024	161	12	a	a	PRON
ejpam-3024	161	13	and	and	CCONJ
ejpam-3024	161	14	g	g	NOUN
ejpam-3024	161	15	:	:	PUNCT
ejpam-3024	161	16	va	va	PROPN
ejpam-3024	162	1	−→	−→	NOUN
ejpam-3024	162	2	n	n	PROPN
ejpam-3024	162	3	b	b	PROPN
ejpam-3024	162	4	that	that	DET
ejpam-3024	162	5	ker	ker	PROPN
ejpam-3024	163	1	f	f	PROPN
ejpam-3024	163	2	=	=	SYM
ejpam-3024	163	3	t	t	PROPN
ejpam-3024	163	4	∩	∩	PROPN
ejpam-3024	163	5	a	a	DET
ejpam-3024	163	6	�	�	PROPN
ejpam-3024	163	7	δ	δ	PROPN
ejpam-3024	163	8	t	t	PROPN
ejpam-3024	163	9	and	and	CCONJ
ejpam-3024	163	10	ker	ker	NOUN
ejpam-3024	163	11	g	g	PROPN
ejpam-3024	163	12	=	=	PROPN
ejpam-3024	163	13	v	v	PROPN
ejpam-3024	163	14	a	a	DET
ejpam-3024	163	15	∩	∩	ADJ
ejpam-3024	163	16	b	b	X
ejpam-3024	163	17	a	a	DET
ejpam-3024	163	18	�	�	PROPN
ejpam-3024	163	19	δ	δ	PROPN
ejpam-3024	163	20	v	v	ADP
ejpam-3024	163	21	a	a	PRON
ejpam-3024	163	22	.	.	PUNCT
ejpam-3024	164	1	then	then	ADV
ejpam-3024	164	2	,	,	PUNCT
ejpam-3024	164	3	g	g	PROPN
ejpam-3024	164	4	◦	◦	NOUN
ejpam-3024	164	5	f	f	X
ejpam-3024	164	6	:	:	PUNCT
ejpam-3024	164	7	t	t	X
ejpam-3024	164	8	−→	−→	NOUN
ejpam-3024	164	9	n	n	PROPN
ejpam-3024	164	10	b	b	PROPN
ejpam-3024	164	11	is	be	AUX
ejpam-3024	164	12	a	a	DET
ejpam-3024	164	13	δ	δ	NOUN
ejpam-3024	164	14	-	-	ADJ
ejpam-3024	164	15	small	small	ADJ
ejpam-3024	164	16	epimorphism	epimorphism	NOUN
ejpam-3024	164	17	such	such	ADJ
ejpam-3024	164	18	that	that	SCONJ
ejpam-3024	164	19	t	t	NOUN
ejpam-3024	164	20	∩b	∩b	NOUN
ejpam-3024	165	1	=	=	PRON
ejpam-3024	165	2	ker	ker	NOUN
ejpam-3024	165	3	(	(	PUNCT
ejpam-3024	165	4	g	g	PROPN
ejpam-3024	165	5	◦	◦	NOUN
ejpam-3024	165	6	f)	f)	SYM
ejpam-3024	165	7	�	�	NOUN
ejpam-3024	165	8	δ	δ	NOUN
ejpam-3024	165	9	t.	t.	PROPN
ejpam-3024	165	10	moreover	moreover	ADV
ejpam-3024	165	11	,	,	PUNCT
ejpam-3024	165	12	we	we	PRON
ejpam-3024	165	13	have	have	VERB
ejpam-3024	165	14	b	b	NOUN
ejpam-3024	165	15	+	+	NOUN
ejpam-3024	165	16	t	t	NOUN
ejpam-3024	165	17	=	=	SYM
ejpam-3024	165	18	(	(	PUNCT
ejpam-3024	165	19	b	b	X
ejpam-3024	165	20	+	+	NOUN
ejpam-3024	165	21	a	a	X
ejpam-3024	165	22	)	)	PUNCT
ejpam-3024	166	1	+	+	NUM
ejpam-3024	166	2	t	t	NOUN
ejpam-3024	166	3	=	=	SYM
ejpam-3024	166	4	b	b	PROPN
ejpam-3024	166	5	+	+	CCONJ
ejpam-3024	166	6	(	(	PUNCT
ejpam-3024	166	7	a+	a+	PUNCT
ejpam-3024	166	8	t	t	NOUN
ejpam-3024	166	9	)	)	PUNCT
ejpam-3024	167	1	=	=	PUNCT
ejpam-3024	168	1	b	b	X
ejpam-3024	168	2	+	+	NUM
ejpam-3024	168	3	v	v	NOUN
ejpam-3024	168	4	=	=	SYM
ejpam-3024	168	5	n	n	CCONJ
ejpam-3024	168	6	since	since	SCONJ
ejpam-3024	168	7	v	v	NOUN
ejpam-3024	168	8	a	a	PRON
ejpam-3024	168	9	is	be	AUX
ejpam-3024	168	10	a	a	DET
ejpam-3024	168	11	δ	δ	NOUN
ejpam-3024	168	12	-	-	PUNCT
ejpam-3024	168	13	supplement	supplement	NOUN
ejpam-3024	168	14	of	of	ADP
ejpam-3024	168	15	b	b	NOUN
ejpam-3024	168	16	a	a	NOUN
ejpam-3024	168	17	in	in	ADP
ejpam-3024	168	18	n	n	PROPN
ejpam-3024	168	19	a	a	NOUN
ejpam-3024	168	20	.	.	PUNCT
ejpam-3024	169	1	this	this	PRON
ejpam-3024	169	2	completes	complete	VERB
ejpam-3024	169	3	the	the	DET
ejpam-3024	169	4	proof	proof	NOUN
ejpam-3024	169	5	.	.	PUNCT
ejpam-3024	170	1	corollary	corollary	ADJ
ejpam-3024	170	2	2	2	NUM
ejpam-3024	170	3	.	.	PUNCT
ejpam-3024	171	1	if	if	SCONJ
ejpam-3024	171	2	m1	m1	PROPN
ejpam-3024	171	3	and	and	CCONJ
ejpam-3024	171	4	m2	m2	PROPN
ejpam-3024	171	5	have	have	VERB
ejpam-3024	171	6	the	the	DET
ejpam-3024	171	7	property	property	NOUN
ejpam-3024	171	8	(	(	PUNCT
ejpam-3024	171	9	δ	δ	PROPN
ejpam-3024	171	10	-	-	PUNCT
ejpam-3024	171	11	e	e	PROPN
ejpam-3024	171	12	)	)	PUNCT
ejpam-3024	171	13	,	,	PUNCT
ejpam-3024	171	14	so	so	ADV
ejpam-3024	171	15	does	do	VERB
ejpam-3024	171	16	m1	m1	PROPN
ejpam-3024	171	17	⊕m2	⊕m2	PROPN
ejpam-3024	171	18	.	.	PUNCT
ejpam-3024	172	1	proof	proof	NOUN
ejpam-3024	172	2	.	.	PUNCT
ejpam-3024	173	1	let	let	VERB
ejpam-3024	173	2	0	0	NUM
ejpam-3024	173	3	−→	−→	NOUN
ejpam-3024	173	4	m1	m1	PROPN
ejpam-3024	173	5	−→	−→	NOUN
ejpam-3024	173	6	m1	m1	PROPN
ejpam-3024	173	7	⊕m2	⊕m2	PROPN
ejpam-3024	173	8	−→	−→	NOUN
ejpam-3024	173	9	m2	m2	PROPN
ejpam-3024	173	10	−→	−→	NOUN
ejpam-3024	173	11	0	0	NUM
ejpam-3024	173	12	be	be	AUX
ejpam-3024	173	13	a	a	DET
ejpam-3024	173	14	short	short	ADJ
ejpam-3024	173	15	exact	exact	ADJ
ejpam-3024	173	16	sequence	sequence	NOUN
ejpam-3024	173	17	.	.	PUNCT
ejpam-3024	174	1	result	result	NOUN
ejpam-3024	174	2	follows	follow	VERB
ejpam-3024	174	3	by	by	ADP
ejpam-3024	174	4	proposition	proposition	NOUN
ejpam-3024	174	5	4	4	NUM
ejpam-3024	174	6	.	.	PUNCT
ejpam-3024	174	7	proposition	proposition	NOUN
ejpam-3024	174	8	5	5	NUM
ejpam-3024	174	9	.	.	PUNCT
ejpam-3024	175	1	let	let	VERB
ejpam-3024	175	2	0	0	NUM
ejpam-3024	176	1	−→	−→	NOUN
ejpam-3024	176	2	k	k	INTJ
ejpam-3024	176	3	−→	−→	NOUN
ejpam-3024	176	4	m	m	VERB
ejpam-3024	176	5	−→	−→	ADJ
ejpam-3024	176	6	l	l	NOUN
ejpam-3024	176	7	−→	−→	NOUN
ejpam-3024	176	8	0	0	NUM
ejpam-3024	176	9	be	be	AUX
ejpam-3024	176	10	a	a	DET
ejpam-3024	176	11	short	short	ADJ
ejpam-3024	176	12	exact	exact	ADJ
ejpam-3024	176	13	sequence	sequence	NOUN
ejpam-3024	176	14	.	.	PUNCT
ejpam-3024	177	1	if	if	SCONJ
ejpam-3024	177	2	k	k	PROPN
ejpam-3024	177	3	and	and	CCONJ
ejpam-3024	177	4	l	l	PROPN
ejpam-3024	177	5	have	have	VERB
ejpam-3024	177	6	the	the	DET
ejpam-3024	177	7	property	property	NOUN
ejpam-3024	177	8	(	(	PUNCT
ejpam-3024	177	9	δ	δ	PROPN
ejpam-3024	177	10	-	-	PUNCT
ejpam-3024	177	11	e	e	PROPN
ejpam-3024	177	12	)	)	PUNCT
ejpam-3024	177	13	,	,	PUNCT
ejpam-3024	177	14	so	so	ADV
ejpam-3024	177	15	does	do	AUX
ejpam-3024	177	16	m.	m.	NOUN
ejpam-3024	177	17	if	if	SCONJ
ejpam-3024	177	18	the	the	DET
ejpam-3024	177	19	sequence	sequence	NOUN
ejpam-3024	177	20	splits	split	VERB
ejpam-3024	177	21	the	the	DET
ejpam-3024	177	22	converse	converse	NOUN
ejpam-3024	177	23	is	be	AUX
ejpam-3024	177	24	also	also	ADV
ejpam-3024	177	25	true	true	ADJ
ejpam-3024	177	26	.	.	PUNCT
ejpam-3024	178	1	proof	proof	NOUN
ejpam-3024	178	2	.	.	PUNCT
ejpam-3024	179	1	let	let	VERB
ejpam-3024	179	2	n	n	PRON
ejpam-3024	179	3	be	be	AUX
ejpam-3024	179	4	any	any	DET
ejpam-3024	179	5	extension	extension	NOUN
ejpam-3024	179	6	of	of	ADP
ejpam-3024	179	7	m.	m.	NOUN
ejpam-3024	179	8	so	so	SCONJ
ejpam-3024	179	9	n	n	CCONJ
ejpam-3024	179	10	k	k	PROPN
ejpam-3024	179	11	is	be	AUX
ejpam-3024	179	12	an	an	DET
ejpam-3024	179	13	extension	extension	NOUN
ejpam-3024	179	14	of	of	ADP
ejpam-3024	179	15	m	m	PROPN
ejpam-3024	179	16	k	k	NOUN
ejpam-3024	179	17	and	and	CCONJ
ejpam-3024	179	18	is	be	AUX
ejpam-3024	179	19	is	be	AUX
ejpam-3024	179	20	a	a	DET
ejpam-3024	179	21	well	well	ADV
ejpam-3024	179	22	known	know	VERB
ejpam-3024	179	23	fact	fact	NOUN
ejpam-3024	179	24	that	that	SCONJ
ejpam-3024	179	25	m	m	VERB
ejpam-3024	179	26	k	k	NOUN
ejpam-3024	179	27	∼=	∼=	PROPN
ejpam-3024	179	28	l.	l.	NOUN
ejpam-3024	179	29	then	then	ADV
ejpam-3024	179	30	there	there	PRON
ejpam-3024	179	31	exists	exist	VERB
ejpam-3024	179	32	a	a	DET
ejpam-3024	179	33	δ	δ	NOUN
ejpam-3024	179	34	-	-	PUNCT
ejpam-3024	179	35	supplement	supplement	NOUN
ejpam-3024	179	36	v	v	X
ejpam-3024	179	37	k	k	PROPN
ejpam-3024	179	38	for	for	ADP
ejpam-3024	179	39	m	m	PROPN
ejpam-3024	179	40	k	k	NOUN
ejpam-3024	179	41	in	in	ADP
ejpam-3024	179	42	n	n	PROPN
ejpam-3024	179	43	k	k	NOUN
ejpam-3024	179	44	,	,	PUNCT
ejpam-3024	179	45	that	that	PRON
ejpam-3024	179	46	means	mean	VERB
ejpam-3024	179	47	m	m	VERB
ejpam-3024	179	48	k	k	NOUN
ejpam-3024	180	1	+	+	X
ejpam-3024	180	2	v	v	X
ejpam-3024	180	3	k	k	NOUN
ejpam-3024	180	4	=	=	PUNCT
ejpam-3024	180	5	n	n	CCONJ
ejpam-3024	180	6	k	k	PROPN
ejpam-3024	180	7	and	and	CCONJ
ejpam-3024	180	8	m	m	PROPN
ejpam-3024	180	9	k	k	NOUN
ejpam-3024	180	10	∩	∩	PROPN
ejpam-3024	180	11	v	v	ADP
ejpam-3024	180	12	k	k	PROPN
ejpam-3024	180	13	�	�	PROPN
ejpam-3024	180	14	δ	δ	PROPN
ejpam-3024	180	15	v	v	ADP
ejpam-3024	180	16	k	k	PROPN
ejpam-3024	180	17	for	for	ADP
ejpam-3024	180	18	some	some	PRON
ejpam-3024	180	19	v	v	NOUN
ejpam-3024	180	20	k	k	PROPN
ejpam-3024	180	21	≤	≤	PROPN
ejpam-3024	181	1	n	n	PRON
ejpam-3024	181	2	k	k	PROPN
ejpam-3024	181	3	.	.	PUNCT
ejpam-3024	182	1	since	since	SCONJ
ejpam-3024	182	2	k	k	PROPN
ejpam-3024	182	3	≤	≤	PROPN
ejpam-3024	182	4	v	v	NOUN
ejpam-3024	182	5	and	and	CCONJ
ejpam-3024	182	6	k	k	PROPN
ejpam-3024	182	7	has	have	VERB
ejpam-3024	182	8	the	the	DET
ejpam-3024	182	9	property	property	NOUN
ejpam-3024	182	10	(	(	PUNCT
ejpam-3024	182	11	δ	δ	PROPN
ejpam-3024	182	12	-	-	PUNCT
ejpam-3024	182	13	e	e	PROPN
ejpam-3024	182	14	)	)	PUNCT
ejpam-3024	182	15	,	,	PUNCT
ejpam-3024	182	16	k+k	k+k	PROPN
ejpam-3024	182	17	′	′	NUM
ejpam-3024	182	18	=	=	SYM
ejpam-3024	182	19	v	v	NOUN
ejpam-3024	182	20	,	,	PUNCT
ejpam-3024	182	21	k∩k	k∩k	NOUN
ejpam-3024	182	22	′	′	NUM
ejpam-3024	182	23	�	�	PROPN
ejpam-3024	182	24	δ	δ	PROPN
ejpam-3024	182	25	k	k	NOUN
ejpam-3024	182	26	′	′	NUM
ejpam-3024	182	27	for	for	ADP
ejpam-3024	182	28	some	some	DET
ejpam-3024	182	29	k	k	PROPN
ejpam-3024	182	30	′	′	NOUN
ejpam-3024	182	31	≤	≤	NOUN
ejpam-3024	182	32	v.	v.	ADP
ejpam-3024	182	33	hence	hence	ADV
ejpam-3024	182	34	,	,	PUNCT
ejpam-3024	182	35	n	n	PROPN
ejpam-3024	182	36	=	=	SYM
ejpam-3024	182	37	m+v	m+v	X
ejpam-3024	182	38	=	=	SYM
ejpam-3024	182	39	m+k+k	m+k+k	NOUN
ejpam-3024	182	40	′	′	NUM
ejpam-3024	183	1	=	=	SYM
ejpam-3024	183	2	m+k	m+k	NUM
ejpam-3024	184	1	′	′	NOUN
ejpam-3024	184	2	.	.	PUNCT
ejpam-3024	185	1	now	now	ADV
ejpam-3024	185	2	we	we	PRON
ejpam-3024	185	3	claim	claim	VERB
ejpam-3024	185	4	that	that	SCONJ
ejpam-3024	185	5	m	m	VERB
ejpam-3024	185	6	∩	∩	ADJ
ejpam-3024	185	7	k	k	PROPN
ejpam-3024	185	8	′	′	NUM
ejpam-3024	185	9	�	�	PROPN
ejpam-3024	185	10	δ	δ	PROPN
ejpam-3024	185	11	k	k	NOUN
ejpam-3024	185	12	′	′	NUM
ejpam-3024	185	13	.	.	PUNCT
ejpam-3024	186	1	for	for	ADP
ejpam-3024	186	2	this	this	PRON
ejpam-3024	186	3	let	let	VERB
ejpam-3024	186	4	m	m	PRON
ejpam-3024	186	5	∩	∩	ADJ
ejpam-3024	186	6	k	k	ADJ
ejpam-3024	187	1	′	′	NUM
ejpam-3024	188	1	+	+	NUM
ejpam-3024	188	2	t	t	X
ejpam-3024	188	3	=	=	SYM
ejpam-3024	188	4	k	k	NOUN
ejpam-3024	188	5	′	′	NOUN
ejpam-3024	188	6	with	with	ADP
ejpam-3024	188	7	k	k	PROPN
ejpam-3024	189	1	′	′	PROPN
ejpam-3024	189	2	t	t	PROPN
ejpam-3024	189	3	is	be	AUX
ejpam-3024	189	4	singular	singular	ADJ
ejpam-3024	189	5	.	.	PUNCT
ejpam-3024	190	1	k	k	PROPN
ejpam-3024	191	1	+	+	CCONJ
ejpam-3024	191	2	m	m	VERB
ejpam-3024	191	3	∩k	∩k	NOUN
ejpam-3024	191	4	′	′	NUM
ejpam-3024	192	1	+	+	CCONJ
ejpam-3024	192	2	t	t	X
ejpam-3024	193	1	=	=	SYM
ejpam-3024	193	2	k	k	PROPN
ejpam-3024	194	1	+	+	CCONJ
ejpam-3024	194	2	k	k	PROPN
ejpam-3024	194	3	′	′	NOUN
ejpam-3024	194	4	and	and	CCONJ
ejpam-3024	194	5	by	by	ADP
ejpam-3024	194	6	the	the	DET
ejpam-3024	194	7	modular	modular	ADJ
ejpam-3024	194	8	law	law	NOUN
ejpam-3024	194	9	(	(	PUNCT
ejpam-3024	194	10	k	k	PROPN
ejpam-3024	195	1	+	+	CCONJ
ejpam-3024	195	2	k	k	PROPN
ejpam-3024	195	3	′	′	NOUN
ejpam-3024	195	4	)	)	PUNCT
ejpam-3024	196	1	∩m	∩m	PROPN
ejpam-3024	197	1	+	+	NUM
ejpam-3024	197	2	t	t	X
ejpam-3024	197	3	=	=	PUNCT
ejpam-3024	197	4	v.	v.	ADP
ejpam-3024	197	5	following	follow	VERB
ejpam-3024	197	6	this	this	PRON
ejpam-3024	197	7	,	,	PUNCT
ejpam-3024	197	8	v	v	ADP
ejpam-3024	197	9	∩m	∩m	PROPN
ejpam-3024	198	1	+	+	NUM
ejpam-3024	198	2	t	t	NOUN
ejpam-3024	198	3	=	=	SYM
ejpam-3024	198	4	v	v	NOUN
ejpam-3024	198	5	is	be	AUX
ejpam-3024	198	6	obtained	obtain	VERB
ejpam-3024	198	7	.	.	PUNCT
ejpam-3024	199	1	it	it	PRON
ejpam-3024	199	2	can	can	AUX
ejpam-3024	199	3	be	be	AUX
ejpam-3024	199	4	easily	easily	ADV
ejpam-3024	199	5	seen	see	VERB
ejpam-3024	199	6	written	write	VERB
ejpam-3024	199	7	that	that	PRON
ejpam-3024	199	8	v	v	ADP
ejpam-3024	199	9	∩m	∩m	PROPN
ejpam-3024	199	10	k	k	PROPN
ejpam-3024	200	1	+	+	CCONJ
ejpam-3024	200	2	t+k	t+k	NUM
ejpam-3024	200	3	k	k	NOUN
ejpam-3024	200	4	=	=	X
ejpam-3024	200	5	v	v	PROPN
ejpam-3024	200	6	k	k	NOUN
ejpam-3024	200	7	,	,	PUNCT
ejpam-3024	200	8	additionally	additionally	ADV
ejpam-3024	200	9	,	,	PUNCT
ejpam-3024	200	10	v	v	NOUN
ejpam-3024	200	11	t+k	t+k	PROPN
ejpam-3024	200	12	is	be	AUX
ejpam-3024	200	13	singular	singular	ADJ
ejpam-3024	200	14	since	since	SCONJ
ejpam-3024	200	15	,	,	PUNCT
ejpam-3024	200	16	v	v	ADP
ejpam-3024	200	17	t	t	NOUN
ejpam-3024	200	18	+	+	NOUN
ejpam-3024	200	19	k	k	PROPN
ejpam-3024	200	20	=	=	PUNCT
ejpam-3024	201	1	k	k	PROPN
ejpam-3024	202	1	+	+	PROPN
ejpam-3024	202	2	k	k	PROPN
ejpam-3024	202	3	′	′	NUM
ejpam-3024	202	4	t	t	PROPN
ejpam-3024	203	1	+	+	NOUN
ejpam-3024	203	2	k	k	PROPN
ejpam-3024	203	3	=	=	SYM
ejpam-3024	203	4	k	k	PROPN
ejpam-3024	204	1	+	+	CCONJ
ejpam-3024	204	2	(	(	PUNCT
ejpam-3024	204	3	k	k	NOUN
ejpam-3024	204	4	′	′	PROPN
ejpam-3024	204	5	+	+	NUM
ejpam-3024	204	6	t	t	NOUN
ejpam-3024	204	7	)	)	PUNCT
ejpam-3024	204	8	t	t	PROPN
ejpam-3024	205	1	+	+	PROPN
ejpam-3024	205	2	k	k	X
ejpam-3024	205	3	=	=	X
ejpam-3024	205	4	(	(	PUNCT
ejpam-3024	205	5	t	t	PROPN
ejpam-3024	205	6	+	+	PROPN
ejpam-3024	205	7	k	k	NOUN
ejpam-3024	205	8	)	)	PUNCT
ejpam-3024	206	1	+	+	NOUN
ejpam-3024	206	2	k	k	NOUN
ejpam-3024	206	3	′	′	NUM
ejpam-3024	206	4	t	t	PROPN
ejpam-3024	207	1	+	+	NOUN
ejpam-3024	207	2	k	k	PROPN
ejpam-3024	207	3	∼=	∼=	PROPN
ejpam-3024	207	4	k	k	NOUN
ejpam-3024	207	5	′	′	NOUN
ejpam-3024	207	6	(	(	PUNCT
ejpam-3024	207	7	t	t	PROPN
ejpam-3024	207	8	+	+	PROPN
ejpam-3024	207	9	k	k	NOUN
ejpam-3024	207	10	)	)	PUNCT
ejpam-3024	207	11	∩k	∩k	NOUN
ejpam-3024	207	12	′	′	NUM
ejpam-3024	208	1	=	=	PUNCT
ejpam-3024	208	2	k	k	NOUN
ejpam-3024	209	1	′	′	NUM
ejpam-3024	209	2	t	t	NOUN
ejpam-3024	210	1	+	+	CCONJ
ejpam-3024	210	2	(	(	PUNCT
ejpam-3024	210	3	k	k	PROPN
ejpam-3024	210	4	∩k	∩k	PROPN
ejpam-3024	210	5	′	′	NOUN
ejpam-3024	210	6	)	)	PUNCT
ejpam-3024	210	7	≤	≤	PUNCT
ejpam-3024	211	1	k	k	NOUN
ejpam-3024	211	2	′	′	NUM
ejpam-3024	211	3	t	t	PROPN
ejpam-3024	211	4	and	and	CCONJ
ejpam-3024	211	5	m	m	PROPN
ejpam-3024	211	6	k	k	NOUN
ejpam-3024	211	7	∩	∩	PROPN
ejpam-3024	211	8	v	v	ADP
ejpam-3024	211	9	k	k	PROPN
ejpam-3024	211	10	�	�	PROPN
ejpam-3024	211	11	δ	δ	PROPN
ejpam-3024	211	12	v	v	ADP
ejpam-3024	211	13	k	k	PROPN
ejpam-3024	211	14	.	.	PUNCT
ejpam-3024	212	1	so	so	ADV
ejpam-3024	212	2	t+k	t+k	NUM
ejpam-3024	213	1	k	k	NOUN
ejpam-3024	213	2	=	=	X
ejpam-3024	213	3	v	v	PROPN
ejpam-3024	213	4	k	k	PROPN
ejpam-3024	213	5	and	and	CCONJ
ejpam-3024	213	6	of	of	ADP
ejpam-3024	213	7	course	course	NOUN
ejpam-3024	213	8	t	t	PROPN
ejpam-3024	214	1	+	+	NOUN
ejpam-3024	214	2	k	k	PROPN
ejpam-3024	214	3	=	=	SYM
ejpam-3024	214	4	v	v	PROPN
ejpam-3024	214	5	.	.	PUNCT
ejpam-3024	215	1	(	(	PUNCT
ejpam-3024	215	2	t	t	NOUN
ejpam-3024	216	1	+	+	NOUN
ejpam-3024	216	2	k)∩k	k)∩k	PROPN
ejpam-3024	216	3	′	′	NUM
ejpam-3024	217	1	=	=	PUNCT
ejpam-3024	218	1	k	k	NOUN
ejpam-3024	218	2	′	′	NOUN
ejpam-3024	218	3	can	can	AUX
ejpam-3024	218	4	be	be	AUX
ejpam-3024	218	5	seen	see	VERB
ejpam-3024	218	6	and	and	CCONJ
ejpam-3024	218	7	by	by	ADP
ejpam-3024	218	8	the	the	DET
ejpam-3024	218	9	modular	modular	PROPN
ejpam-3024	218	10	lae	lae	PROPN
ejpam-3024	218	11	,	,	PUNCT
ejpam-3024	218	12	t	t	PROPN
ejpam-3024	219	1	+	+	CCONJ
ejpam-3024	219	2	(	(	PUNCT
ejpam-3024	219	3	k	k	PROPN
ejpam-3024	219	4	∩k	∩k	PROPN
ejpam-3024	219	5	′	′	NUM
ejpam-3024	219	6	)	)	PUNCT
ejpam-3024	220	1	=	=	NOUN
ejpam-3024	221	1	k	k	X
ejpam-3024	221	2	′	′	NOUN
ejpam-3024	221	3	is	be	AUX
ejpam-3024	221	4	obtained	obtain	VERB
ejpam-3024	221	5	.	.	PUNCT
ejpam-3024	222	1	this	this	PRON
ejpam-3024	222	2	provides	provide	VERB
ejpam-3024	222	3	t	t	NOUN
ejpam-3024	222	4	=	=	PUNCT
ejpam-3024	222	5	k	k	NOUN
ejpam-3024	223	1	′	′	VERB
ejpam-3024	223	2	since	since	SCONJ
ejpam-3024	223	3	k	k	PROPN
ejpam-3024	223	4	∩k	∩k	PROPN
ejpam-3024	223	5	′	′	VERB
ejpam-3024	224	1	<	<	X
ejpam-3024	224	2	<	<	X
ejpam-3024	224	3	δ	δ	X
ejpam-3024	224	4	k	k	NOUN
ejpam-3024	224	5	′	′	NOUN
ejpam-3024	225	1	and	and	CCONJ
ejpam-3024	225	2	k	k	PROPN
ejpam-3024	225	3	′	′	PROPN
ejpam-3024	225	4	t	t	PROPN
ejpam-3024	225	5	is	be	AUX
ejpam-3024	225	6	singular	singular	ADJ
ejpam-3024	225	7	.	.	PUNCT
ejpam-3024	226	1	moreover	moreover	ADV
ejpam-3024	226	2	,	,	PUNCT
ejpam-3024	226	3	suppose	suppose	VERB
ejpam-3024	226	4	that	that	SCONJ
ejpam-3024	226	5	the	the	DET
ejpam-3024	226	6	sequence	sequence	NOUN
ejpam-3024	226	7	splits	split	VERB
ejpam-3024	226	8	,	,	PUNCT
ejpam-3024	226	9	then	then	ADV
ejpam-3024	226	10	k	k	PROPN
ejpam-3024	226	11	and	and	CCONJ
ejpam-3024	226	12	l	l	PROPN
ejpam-3024	226	13	have	have	VERB
ejpam-3024	226	14	the	the	DET
ejpam-3024	226	15	property	property	NOUN
ejpam-3024	226	16	(	(	PUNCT
ejpam-3024	226	17	δ	δ	PROPN
ejpam-3024	226	18	-	-	PUNCT
ejpam-3024	226	19	e	e	NOUN
ejpam-3024	226	20	)	)	PUNCT
ejpam-3024	226	21	by	by	ADP
ejpam-3024	226	22	corollary	corollary	ADJ
ejpam-3024	226	23	2	2	NUM
ejpam-3024	226	24	.	.	PUNCT
ejpam-3024	226	25	corollary	corollary	ADJ
ejpam-3024	226	26	3	3	X
ejpam-3024	226	27	.	.	PUNCT
ejpam-3024	227	1	let	let	VERB
ejpam-3024	227	2	mi	mi	PROPN
ejpam-3024	227	3	(	(	PUNCT
ejpam-3024	227	4	i	i	NOUN
ejpam-3024	227	5	=	=	NOUN
ejpam-3024	227	6	1	1	NUM
ejpam-3024	227	7	,	,	PUNCT
ejpam-3024	227	8	2	2	NUM
ejpam-3024	227	9	,	,	PUNCT
ejpam-3024	227	10	...	...	PUNCT
ejpam-3024	227	11	,	,	PUNCT
ejpam-3024	227	12	n	n	CCONJ
ejpam-3024	227	13	)	)	PUNCT
ejpam-3024	227	14	be	be	AUX
ejpam-3024	227	15	any	any	DET
ejpam-3024	227	16	finite	finite	ADJ
ejpam-3024	227	17	collection	collection	NOUN
ejpam-3024	227	18	of	of	ADP
ejpam-3024	227	19	modules	module	NOUN
ejpam-3024	227	20	and	and	CCONJ
ejpam-3024	227	21	m	m	NOUN
ejpam-3024	227	22	=	=	PROPN
ejpam-3024	227	23	m1	m1	PROPN
ejpam-3024	227	24	⊕	⊕	PROPN
ejpam-3024	227	25	m2⊕	m2⊕	ADP
ejpam-3024	227	26	...	...	PUNCT
ejpam-3024	228	1	⊕	⊕	PROPN
ejpam-3024	228	2	mn	mn	PROPN
ejpam-3024	228	3	.	.	PUNCT
ejpam-3024	229	1	then	then	ADV
ejpam-3024	229	2	m	m	PROPN
ejpam-3024	229	3	has	have	VERB
ejpam-3024	229	4	the	the	DET
ejpam-3024	229	5	property	property	NOUN
ejpam-3024	229	6	(	(	PUNCT
ejpam-3024	229	7	δ	δ	PROPN
ejpam-3024	229	8	-	-	PUNCT
ejpam-3024	229	9	e	e	NOUN
ejpam-3024	229	10	)	)	PUNCT
ejpam-3024	229	11	if	if	SCONJ
ejpam-3024	230	1	and	and	CCONJ
ejpam-3024	230	2	only	only	ADV
ejpam-3024	230	3	if	if	SCONJ
ejpam-3024	230	4	mi	mi	PROPN
ejpam-3024	230	5	has	have	VERB
ejpam-3024	230	6	the	the	DET
ejpam-3024	230	7	property	property	NOUN
ejpam-3024	230	8	(	(	PUNCT
ejpam-3024	230	9	δ	δ	PROPN
ejpam-3024	230	10	-	-	PUNCT
ejpam-3024	230	11	e	e	NOUN
ejpam-3024	230	12	)	)	PUNCT
ejpam-3024	230	13	for	for	ADP
ejpam-3024	230	14	each	each	DET
ejpam-3024	230	15	i	i	NOUN
ejpam-3024	230	16	=	=	NOUN
ejpam-3024	230	17	1	1	NUM
ejpam-3024	230	18	,	,	PUNCT
ejpam-3024	230	19	2	2	NUM
ejpam-3024	230	20	,	,	PUNCT
ejpam-3024	230	21	...	...	PUNCT
ejpam-3024	230	22	,	,	PUNCT
ejpam-3024	230	23	n.	n.	NOUN
ejpam-3024	230	24	proof	proof	NOUN
ejpam-3024	230	25	.	.	PUNCT
ejpam-3024	231	1	it	it	PRON
ejpam-3024	231	2	can	can	AUX
ejpam-3024	231	3	be	be	AUX
ejpam-3024	231	4	proved	prove	VERB
ejpam-3024	231	5	easily	easily	ADV
ejpam-3024	231	6	for	for	ADP
ejpam-3024	231	7	n	n	NOUN
ejpam-3024	231	8	=	=	SYM
ejpam-3024	231	9	2	2	NUM
ejpam-3024	231	10	by	by	ADP
ejpam-3024	231	11	using	use	VERB
ejpam-3024	231	12	the	the	DET
ejpam-3024	231	13	previous	previous	ADJ
ejpam-3024	231	14	theorem	theorem	NOUN
ejpam-3024	231	15	and	and	CCONJ
ejpam-3024	231	16	can	can	AUX
ejpam-3024	231	17	be	be	AUX
ejpam-3024	231	18	generalized	generalize	VERB
ejpam-3024	231	19	on	on	ADP
ejpam-3024	231	20	n.	n.	NOUN
ejpam-3024	231	21	we	we	PRON
ejpam-3024	231	22	give	give	VERB
ejpam-3024	231	23	the	the	DET
ejpam-3024	231	24	following	follow	VERB
ejpam-3024	231	25	known	know	VERB
ejpam-3024	231	26	lemma	lemma	PROPN
ejpam-3024	231	27	for	for	ADP
ejpam-3024	231	28	the	the	DET
ejpam-3024	231	29	completeness	completeness	NOUN
ejpam-3024	231	30	.	.	PUNCT
ejpam-3024	232	1	e.	e.	PROPN
ejpam-3024	232	2	ö.	ö.	PROPN
ejpam-3024	232	3	sözen	sözen	PROPN
ejpam-3024	232	4	,	,	PUNCT
ejpam-3024	232	5	ş.	ş.	PROPN
ejpam-3024	232	6	eren	eren	PROPN
ejpam-3024	232	7	/	/	SYM
ejpam-3024	232	8	eur	eur	PROPN
ejpam-3024	232	9	.	.	PUNCT
ejpam-3024	233	1	j.	j.	PROPN
ejpam-3024	233	2	pure	pure	PROPN
ejpam-3024	233	3	appl	appl	PROPN
ejpam-3024	233	4	.	.	PROPN
ejpam-3024	233	5	math	math	PROPN
ejpam-3024	233	6	,	,	PUNCT
ejpam-3024	233	7	10	10	NUM
ejpam-3024	233	8	(	(	PUNCT
ejpam-3024	233	9	4	4	NUM
ejpam-3024	233	10	)	)	PUNCT
ejpam-3024	233	11	(	(	PUNCT
ejpam-3024	233	12	2017	2017	NUM
ejpam-3024	233	13	)	)	PUNCT
ejpam-3024	233	14	,	,	PUNCT
ejpam-3024	233	15	730	730	NUM
ejpam-3024	233	16	-	-	SYM
ejpam-3024	233	17	738	738	NUM
ejpam-3024	233	18	736	736	NUM
ejpam-3024	233	19	lemma	lemma	PROPN
ejpam-3024	233	20	6	6	NUM
ejpam-3024	233	21	.	.	PUNCT
ejpam-3024	234	1	every	every	DET
ejpam-3024	234	2	simple	simple	ADJ
ejpam-3024	234	3	submodule	submodule	NOUN
ejpam-3024	234	4	s	s	PROPN
ejpam-3024	234	5	of	of	ADP
ejpam-3024	234	6	a	a	DET
ejpam-3024	234	7	module	module	NOUN
ejpam-3024	234	8	m	m	NOUN
ejpam-3024	234	9	is	be	AUX
ejpam-3024	234	10	either	either	CCONJ
ejpam-3024	234	11	a	a	DET
ejpam-3024	234	12	direct	direct	ADJ
ejpam-3024	234	13	summand	summand	NOUN
ejpam-3024	234	14	of	of	ADP
ejpam-3024	234	15	m	m	NOUN
ejpam-3024	234	16	or	or	CCONJ
ejpam-3024	234	17	small	small	ADJ
ejpam-3024	234	18	in	in	ADP
ejpam-3024	234	19	m	m	PROPN
ejpam-3024	234	20	(	(	PUNCT
ejpam-3024	234	21	see	see	VERB
ejpam-3024	234	22	in	in	ADP
ejpam-3024	234	23	[	[	X
ejpam-3024	234	24	10	10	NUM
ejpam-3024	234	25	]	]	SYM
ejpam-3024	234	26	)	)	PUNCT
ejpam-3024	234	27	proposition	proposition	NOUN
ejpam-3024	234	28	6	6	NUM
ejpam-3024	234	29	.	.	PUNCT
ejpam-3024	235	1	every	every	DET
ejpam-3024	235	2	simple	simple	ADJ
ejpam-3024	235	3	module	module	NOUN
ejpam-3024	235	4	has	have	VERB
ejpam-3024	235	5	the	the	DET
ejpam-3024	235	6	property	property	NOUN
ejpam-3024	235	7	(	(	PUNCT
ejpam-3024	235	8	δ	δ	PROPN
ejpam-3024	235	9	-	-	PUNCT
ejpam-3024	235	10	e	e	NOUN
ejpam-3024	235	11	)	)	PUNCT
ejpam-3024	235	12	.	.	PUNCT
ejpam-3024	236	1	proof	proof	NOUN
ejpam-3024	236	2	.	.	PUNCT
ejpam-3024	237	1	let	let	VERB
ejpam-3024	237	2	s	s	PRON
ejpam-3024	237	3	be	be	AUX
ejpam-3024	237	4	a	a	DET
ejpam-3024	237	5	simple	simple	ADJ
ejpam-3024	237	6	module	module	NOUN
ejpam-3024	237	7	and	and	CCONJ
ejpam-3024	237	8	n	n	CCONJ
ejpam-3024	237	9	be	be	VERB
ejpam-3024	237	10	any	any	DET
ejpam-3024	237	11	extension	extension	NOUN
ejpam-3024	237	12	of	of	ADP
ejpam-3024	237	13	s.	s.	PROPN
ejpam-3024	237	14	then	then	ADV
ejpam-3024	237	15	by	by	ADP
ejpam-3024	237	16	lemma	lemma	PROPN
ejpam-3024	237	17	4	4	NUM
ejpam-3024	237	18	,	,	PUNCT
ejpam-3024	237	19	s	s	VERB
ejpam-3024	237	20	�	�	PROPN
ejpam-3024	237	21	n	n	PROPN
ejpam-3024	237	22	and	and	CCONJ
ejpam-3024	237	23	so	so	ADV
ejpam-3024	237	24	s	s	VERB
ejpam-3024	237	25	�	�	PROPN
ejpam-3024	237	26	δ	δ	PROPN
ejpam-3024	237	27	n	n	NOUN
ejpam-3024	237	28	or	or	CCONJ
ejpam-3024	237	29	s	s	PROPN
ejpam-3024	237	30	⊕	⊕	PROPN
ejpam-3024	237	31	s′	s′	VERB
ejpam-3024	237	32	=	=	PUNCT
ejpam-3024	237	33	n	n	CCONJ
ejpam-3024	237	34	for	for	ADP
ejpam-3024	237	35	a	a	DET
ejpam-3024	237	36	submodule	submodule	NOUN
ejpam-3024	237	37	s	s	PART
ejpam-3024	237	38	′	′	NOUN
ejpam-3024	237	39	≤	≤	NUM
ejpam-3024	237	40	n.	n.	NOUN
ejpam-3024	237	41	if	if	SCONJ
ejpam-3024	237	42	s	s	PROPN
ejpam-3024	237	43	�	�	PROPN
ejpam-3024	237	44	δ	δ	PROPN
ejpam-3024	237	45	n	n	CCONJ
ejpam-3024	237	46	,	,	PUNCT
ejpam-3024	237	47	then	then	ADV
ejpam-3024	237	48	n	n	PRON
ejpam-3024	237	49	is	be	AUX
ejpam-3024	237	50	a	a	DET
ejpam-3024	237	51	δ	δ	NOUN
ejpam-3024	237	52	-	-	PUNCT
ejpam-3024	237	53	supplement	supplement	NOUN
ejpam-3024	237	54	of	of	ADP
ejpam-3024	237	55	s	s	NOUN
ejpam-3024	237	56	in	in	ADP
ejpam-3024	237	57	n	n	PRON
ejpam-3024	237	58	or	or	CCONJ
ejpam-3024	237	59	if	if	SCONJ
ejpam-3024	237	60	s	s	VERB
ejpam-3024	237	61	is	be	AUX
ejpam-3024	237	62	a	a	DET
ejpam-3024	237	63	direct	direct	ADJ
ejpam-3024	237	64	summand	summand	NOUN
ejpam-3024	237	65	of	of	ADP
ejpam-3024	237	66	n	n	PROPN
ejpam-3024	237	67	then	then	ADV
ejpam-3024	237	68	s	s	VERB
ejpam-3024	238	1	′	′	NOUN
ejpam-3024	238	2	is	be	AUX
ejpam-3024	238	3	a	a	DET
ejpam-3024	238	4	δ	δ	NOUN
ejpam-3024	238	5	-	-	PUNCT
ejpam-3024	238	6	supplement	supplement	NOUN
ejpam-3024	238	7	of	of	ADP
ejpam-3024	238	8	s	s	NOUN
ejpam-3024	238	9	in	in	ADP
ejpam-3024	238	10	n	n	PROPN
ejpam-3024	238	11	.	.	PUNCT
ejpam-3024	239	1	so	so	ADV
ejpam-3024	239	2	in	in	ADP
ejpam-3024	239	3	each	each	DET
ejpam-3024	239	4	case	case	NOUN
ejpam-3024	239	5	s	s	AUX
ejpam-3024	239	6	has	have	VERB
ejpam-3024	239	7	a	a	DET
ejpam-3024	239	8	δ	δ	NOUN
ejpam-3024	239	9	-	-	PUNCT
ejpam-3024	239	10	supplement	supplement	NOUN
ejpam-3024	239	11	in	in	ADP
ejpam-3024	239	12	n	n	PROPN
ejpam-3024	239	13	.	.	PUNCT
ejpam-3024	240	1	this	this	PRON
ejpam-3024	240	2	means	mean	VERB
ejpam-3024	240	3	that	that	SCONJ
ejpam-3024	240	4	s	s	VERB
ejpam-3024	240	5	has	have	VERB
ejpam-3024	240	6	the	the	DET
ejpam-3024	240	7	property	property	NOUN
ejpam-3024	240	8	(	(	PUNCT
ejpam-3024	240	9	δ	δ	PROPN
ejpam-3024	240	10	-	-	PUNCT
ejpam-3024	240	11	e	e	NOUN
ejpam-3024	240	12	)	)	PUNCT
ejpam-3024	240	13	.	.	PUNCT
ejpam-3024	241	1	theorem	theorem	VERB
ejpam-3024	241	2	7	7	NUM
ejpam-3024	241	3	.	.	PUNCT
ejpam-3024	242	1	every	every	DET
ejpam-3024	242	2	module	module	NOUN
ejpam-3024	242	3	with	with	ADP
ejpam-3024	242	4	composition	composition	NOUN
ejpam-3024	242	5	series	series	NOUN
ejpam-3024	242	6	has	have	VERB
ejpam-3024	242	7	the	the	DET
ejpam-3024	242	8	property	property	NOUN
ejpam-3024	242	9	(	(	PUNCT
ejpam-3024	242	10	δ	δ	PROPN
ejpam-3024	242	11	-	-	PUNCT
ejpam-3024	242	12	e	e	NOUN
ejpam-3024	242	13	)	)	PUNCT
ejpam-3024	242	14	.	.	PUNCT
ejpam-3024	243	1	proof	proof	NOUN
ejpam-3024	243	2	.	.	PUNCT
ejpam-3024	244	1	let	let	VERB
ejpam-3024	244	2	0	0	NUM
ejpam-3024	245	1	=	=	SYM
ejpam-3024	245	2	m0	m0	NOUN
ejpam-3024	245	3	≤m1	≤m1	X
ejpam-3024	245	4	≤m2	≤m2	VERB
ejpam-3024	245	5	≤	≤	NUM
ejpam-3024	245	6	...	...	PUNCT
ejpam-3024	246	1	≤mn−1	≤mn−1	ADJ
ejpam-3024	246	2	≤mn	≤mn	NOUN
ejpam-3024	246	3	=	=	PUNCT
ejpam-3024	246	4	m	m	AUX
ejpam-3024	246	5	be	be	VERB
ejpam-3024	246	6	any	any	DET
ejpam-3024	246	7	composition	composition	NOUN
ejpam-3024	246	8	series	series	NOUN
ejpam-3024	246	9	of	of	ADP
ejpam-3024	246	10	a	a	DET
ejpam-3024	246	11	module	module	NOUN
ejpam-3024	246	12	m.	m.	NOUN
ejpam-3024	246	13	we	we	PRON
ejpam-3024	246	14	shall	shall	AUX
ejpam-3024	246	15	prove	prove	VERB
ejpam-3024	246	16	the	the	DET
ejpam-3024	246	17	theorem	theorem	NOUN
ejpam-3024	246	18	by	by	ADP
ejpam-3024	246	19	induction	induction	NOUN
ejpam-3024	246	20	on	on	ADP
ejpam-3024	246	21	nεn	nεn	PROPN
ejpam-3024	246	22	.	.	PUNCT
ejpam-3024	247	1	if	if	SCONJ
ejpam-3024	247	2	n	n	NUM
ejpam-3024	247	3	=	=	SYM
ejpam-3024	247	4	1	1	NUM
ejpam-3024	247	5	,	,	PUNCT
ejpam-3024	247	6	then	then	ADV
ejpam-3024	247	7	m	m	VERB
ejpam-3024	247	8	=	=	ADJ
ejpam-3024	247	9	m1	m1	PROPN
ejpam-3024	247	10	is	be	AUX
ejpam-3024	247	11	simple	simple	ADJ
ejpam-3024	247	12	,	,	PUNCT
ejpam-3024	247	13	and	and	CCONJ
ejpam-3024	247	14	so	so	ADV
ejpam-3024	247	15	m	m	NOUN
ejpam-3024	247	16	has	have	VERB
ejpam-3024	247	17	the	the	DET
ejpam-3024	247	18	property	property	NOUN
ejpam-3024	247	19	(	(	PUNCT
ejpam-3024	247	20	δ	δ	PROPN
ejpam-3024	247	21	-	-	PUNCT
ejpam-3024	247	22	e	e	NOUN
ejpam-3024	247	23	)	)	PUNCT
ejpam-3024	247	24	by	by	ADP
ejpam-3024	247	25	proposition	proposition	NOUN
ejpam-3024	247	26	6	6	NUM
ejpam-3024	247	27	.	.	PUNCT
ejpam-3024	247	28	assume	assume	VERB
ejpam-3024	247	29	that	that	SCONJ
ejpam-3024	247	30	this	this	PRON
ejpam-3024	247	31	is	be	AUX
ejpam-3024	247	32	true	true	ADJ
ejpam-3024	247	33	for	for	ADP
ejpam-3024	247	34	each	each	DET
ejpam-3024	247	35	k	k	PROPN
ejpam-3024	247	36	≤	≤	PROPN
ejpam-3024	247	37	n−	n−	PROPN
ejpam-3024	247	38	1.then	1.then	PROPN
ejpam-3024	247	39	mn−1	mn−1	PROPN
ejpam-3024	247	40	has	have	VERB
ejpam-3024	247	41	the	the	DET
ejpam-3024	247	42	property	property	NOUN
ejpam-3024	247	43	(	(	PUNCT
ejpam-3024	247	44	δ	δ	PROPN
ejpam-3024	247	45	-	-	PUNCT
ejpam-3024	247	46	e	e	PROPN
ejpam-3024	247	47	)	)	PUNCT
ejpam-3024	247	48	.	.	PUNCT
ejpam-3024	248	1	since	since	SCONJ
ejpam-3024	248	2	mn	mn	PROPN
ejpam-3024	248	3	mn−1	mn−1	PROPN
ejpam-3024	248	4	has	have	VERB
ejpam-3024	248	5	the	the	DET
ejpam-3024	248	6	property	property	NOUN
ejpam-3024	248	7	(	(	PUNCT
ejpam-3024	248	8	δ	δ	PROPN
ejpam-3024	248	9	-	-	PUNCT
ejpam-3024	248	10	e	e	NOUN
ejpam-3024	248	11	)	)	PUNCT
ejpam-3024	248	12	as	as	ADP
ejpam-3024	248	13	a	a	DET
ejpam-3024	248	14	simple	simple	ADJ
ejpam-3024	248	15	module	module	NOUN
ejpam-3024	248	16	,	,	PUNCT
ejpam-3024	248	17	m	m	VERB
ejpam-3024	248	18	has	have	VERB
ejpam-3024	248	19	the	the	DET
ejpam-3024	248	20	property	property	NOUN
ejpam-3024	248	21	(	(	PUNCT
ejpam-3024	248	22	δ	δ	PROPN
ejpam-3024	248	23	-	-	PUNCT
ejpam-3024	248	24	e	e	NOUN
ejpam-3024	248	25	)	)	PUNCT
ejpam-3024	248	26	by	by	ADP
ejpam-3024	248	27	proposition	proposition	NOUN
ejpam-3024	248	28	4	4	NUM
ejpam-3024	248	29	.	.	PUNCT
ejpam-3024	248	30	corollary	corollary	ADJ
ejpam-3024	248	31	4	4	NUM
ejpam-3024	248	32	.	.	PUNCT
ejpam-3024	248	33	a	a	DET
ejpam-3024	248	34	finitely	finitely	ADV
ejpam-3024	248	35	generated	generate	VERB
ejpam-3024	248	36	semisimple	semisimple	NOUN
ejpam-3024	248	37	module	module	NOUN
ejpam-3024	248	38	has	have	VERB
ejpam-3024	248	39	the	the	DET
ejpam-3024	248	40	property	property	NOUN
ejpam-3024	248	41	(	(	PUNCT
ejpam-3024	248	42	δ	δ	PROPN
ejpam-3024	248	43	-	-	PUNCT
ejpam-3024	248	44	e	e	PROPN
ejpam-3024	248	45	)	)	PUNCT
ejpam-3024	248	46	.	.	PUNCT
ejpam-3024	249	1	in	in	ADP
ejpam-3024	249	2	the	the	DET
ejpam-3024	249	3	following	follow	VERB
ejpam-3024	249	4	proposition	proposition	NOUN
ejpam-3024	249	5	we	we	PRON
ejpam-3024	249	6	will	will	AUX
ejpam-3024	249	7	prove	prove	VERB
ejpam-3024	249	8	that	that	SCONJ
ejpam-3024	249	9	modules	module	NOUN
ejpam-3024	249	10	with	with	ADP
ejpam-3024	249	11	the	the	DET
ejpam-3024	249	12	property	property	NOUN
ejpam-3024	249	13	(	(	PUNCT
ejpam-3024	249	14	δ	δ	PROPN
ejpam-3024	249	15	-	-	PUNCT
ejpam-3024	249	16	e	e	NOUN
ejpam-3024	249	17	)	)	PUNCT
ejpam-3024	249	18	are	be	AUX
ejpam-3024	249	19	closed	close	VERB
ejpam-3024	249	20	onder	onder	PROPN
ejpam-3024	249	21	factor	factor	NOUN
ejpam-3024	249	22	modules	module	NOUN
ejpam-3024	249	23	,	,	PUNCT
ejpam-3024	249	24	under	under	ADP
ejpam-3024	249	25	a	a	DET
ejpam-3024	249	26	special	special	ADJ
ejpam-3024	249	27	condition	condition	NOUN
ejpam-3024	249	28	.	.	PUNCT
ejpam-3024	250	1	proposition	proposition	NOUN
ejpam-3024	250	2	7	7	NUM
ejpam-3024	250	3	.	.	PUNCT
ejpam-3024	250	4	let	let	VERB
ejpam-3024	250	5	a	a	DET
ejpam-3024	250	6	≤	≤	NUM
ejpam-3024	250	7	b	b	NOUN
ejpam-3024	250	8	≤	≤	NUM
ejpam-3024	250	9	c	c	NOUN
ejpam-3024	250	10	with	with	ADP
ejpam-3024	250	11	c	c	PROPN
ejpam-3024	250	12	a	a	DET
ejpam-3024	250	13	injective	injective	NOUN
ejpam-3024	250	14	.	.	PUNCT
ejpam-3024	251	1	if	if	SCONJ
ejpam-3024	251	2	b	b	PROPN
ejpam-3024	251	3	has	have	VERB
ejpam-3024	251	4	the	the	DET
ejpam-3024	251	5	property	property	NOUN
ejpam-3024	251	6	(	(	PUNCT
ejpam-3024	251	7	δ	δ	PROPN
ejpam-3024	251	8	-	-	PUNCT
ejpam-3024	251	9	e	e	PROPN
ejpam-3024	251	10	)	)	PUNCT
ejpam-3024	251	11	,	,	PUNCT
ejpam-3024	251	12	so	so	ADV
ejpam-3024	251	13	does	do	VERB
ejpam-3024	251	14	b	b	PROPN
ejpam-3024	251	15	a	a	PRON
ejpam-3024	251	16	.	.	PUNCT
ejpam-3024	252	1	proof	proof	NOUN
ejpam-3024	252	2	.	.	PUNCT
ejpam-3024	253	1	let	let	VERB
ejpam-3024	253	2	n	n	PRON
ejpam-3024	253	3	be	be	AUX
ejpam-3024	253	4	any	any	DET
ejpam-3024	253	5	extension	extension	NOUN
ejpam-3024	253	6	of	of	ADP
ejpam-3024	253	7	b	b	NOUN
ejpam-3024	253	8	a	a	NOUN
ejpam-3024	253	9	.	.	PUNCT
ejpam-3024	254	1	so	so	ADV
ejpam-3024	254	2	we	we	PRON
ejpam-3024	254	3	have	have	VERB
ejpam-3024	254	4	the	the	DET
ejpam-3024	254	5	following	following	ADJ
ejpam-3024	254	6	commutative	commutative	ADJ
ejpam-3024	254	7	diagram	diagram	NOUN
ejpam-3024	254	8	with	with	ADP
ejpam-3024	254	9	exact	exact	ADJ
ejpam-3024	254	10	rows	row	NOUN
ejpam-3024	254	11	since	since	SCONJ
ejpam-3024	254	12	c	c	PROPN
ejpam-3024	254	13	a	a	PRON
ejpam-3024	254	14	is	be	AUX
ejpam-3024	254	15	injective	injective	ADJ
ejpam-3024	254	16	,	,	PUNCT
ejpam-3024	254	17	(	(	PUNCT
ejpam-3024	254	18	see	see	VERB
ejpam-3024	254	19	in	in	ADP
ejpam-3024	254	20	[	[	X
ejpam-3024	254	21	10	10	NUM
ejpam-3024	254	22	]	]	NUM
ejpam-3024	254	23	)	)	PUNCT
ejpam-3024	254	24	.	.	PUNCT
ejpam-3024	255	1	since	since	SCONJ
ejpam-3024	255	2	h	h	NOUN
ejpam-3024	255	3	is	be	AUX
ejpam-3024	255	4	monic	monic	ADJ
ejpam-3024	255	5	and	and	CCONJ
ejpam-3024	255	6	b	b	PROPN
ejpam-3024	255	7	has	have	VERB
ejpam-3024	255	8	the	the	DET
ejpam-3024	255	9	property	property	NOUN
ejpam-3024	255	10	(	(	PUNCT
ejpam-3024	255	11	δ	δ	PROPN
ejpam-3024	255	12	-	-	PUNCT
ejpam-3024	255	13	e	e	PROPN
ejpam-3024	255	14	)	)	PUNCT
ejpam-3024	255	15	,	,	PUNCT
ejpam-3024	255	16	b	b	X
ejpam-3024	255	17	∼=	∼=	ADP
ejpam-3024	255	18	h(b	h(b	PROPN
ejpam-3024	255	19	)	)	PUNCT
ejpam-3024	255	20	has	have	VERB
ejpam-3024	255	21	a	a	DET
ejpam-3024	255	22	δ	δ	NOUN
ejpam-3024	255	23	-	-	PUNCT
ejpam-3024	255	24	supplement	supplement	NOUN
ejpam-3024	255	25	v	v	NOUN
ejpam-3024	255	26	in	in	ADP
ejpam-3024	255	27	p	p	X
ejpam-3024	255	28	,	,	PUNCT
ejpam-3024	255	29	that	that	ADV
ejpam-3024	255	30	is	is	ADV
ejpam-3024	255	31	,	,	PUNCT
ejpam-3024	255	32	h(b	h(b	PROPN
ejpam-3024	255	33	)	)	PUNCT
ejpam-3024	256	1	+	+	SYM
ejpam-3024	256	2	v	v	X
ejpam-3024	256	3	=	=	SYM
ejpam-3024	256	4	p	p	NOUN
ejpam-3024	256	5	and	and	CCONJ
ejpam-3024	256	6	h(b)∩	h(b)∩	VERB
ejpam-3024	256	7	v	v	NUM
ejpam-3024	256	8	�	�	NOUN
ejpam-3024	256	9	δ	δ	PROPN
ejpam-3024	256	10	v.	v.	CCONJ
ejpam-3024	256	11	we	we	PRON
ejpam-3024	256	12	claim	claim	VERB
ejpam-3024	256	13	that	that	SCONJ
ejpam-3024	256	14	g(v	g(v	PROPN
ejpam-3024	256	15	)	)	PUNCT
ejpam-3024	256	16	is	be	AUX
ejpam-3024	256	17	a	a	DET
ejpam-3024	256	18	δ	δ	NOUN
ejpam-3024	256	19	-	-	PUNCT
ejpam-3024	256	20	supplement	supplement	NOUN
ejpam-3024	256	21	of	of	ADP
ejpam-3024	256	22	b	b	NOUN
ejpam-3024	256	23	a	a	PRON
ejpam-3024	256	24	in	in	ADP
ejpam-3024	256	25	n.	n.	PROPN
ejpam-3024	256	26	b	b	PROPN
ejpam-3024	257	1	a	a	DET
ejpam-3024	257	2	+	+	X
ejpam-3024	257	3	g(v	g(v	X
ejpam-3024	257	4	)	)	PUNCT
ejpam-3024	257	5	=	=	SYM
ejpam-3024	257	6	(	(	PUNCT
ejpam-3024	257	7	fσ)(b	fσ)(b	PROPN
ejpam-3024	257	8	)	)	PUNCT
ejpam-3024	258	1	+	+	CCONJ
ejpam-3024	258	2	g(v	g(v	X
ejpam-3024	258	3	)	)	PUNCT
ejpam-3024	258	4	=	=	SYM
ejpam-3024	258	5	g(h(b	g(h(b	PROPN
ejpam-3024	258	6	)	)	PUNCT
ejpam-3024	258	7	)	)	PUNCT
ejpam-3024	259	1	+	+	CCONJ
ejpam-3024	259	2	g(v	g(v	X
ejpam-3024	259	3	)	)	PUNCT
ejpam-3024	259	4	=	=	SYM
ejpam-3024	259	5	g(p	g(p	X
ejpam-3024	259	6	)	)	PUNCT
ejpam-3024	259	7	=	=	SYM
ejpam-3024	259	8	n	n	CCONJ
ejpam-3024	259	9	,	,	PUNCT
ejpam-3024	259	10	and	and	CCONJ
ejpam-3024	259	11	b	b	X
ejpam-3024	259	12	a	a	DET
ejpam-3024	259	13	∩	∩	ADJ
ejpam-3024	259	14	g(v	g(v	X
ejpam-3024	259	15	)	)	PUNCT
ejpam-3024	259	16	=	=	SYM
ejpam-3024	259	17	f(σ(b	f(σ(b	NOUN
ejpam-3024	259	18	)	)	PUNCT
ejpam-3024	259	19	)	)	PUNCT
ejpam-3024	259	20	∩	∩	NOUN
ejpam-3024	259	21	g(v	g(v	PROPN
ejpam-3024	259	22	)	)	PUNCT
ejpam-3024	259	23	=	=	SYM
ejpam-3024	259	24	g[h(b	g[h(b	ADJ
ejpam-3024	259	25	)	)	PUNCT
ejpam-3024	259	26	∩	∩	PROPN
ejpam-3024	259	27	v	v	X
ejpam-3024	259	28	]	]	PUNCT
ejpam-3024	259	29	�	�	PROPN
ejpam-3024	259	30	δ	δ	PROPN
ejpam-3024	259	31	g(v	g(v	PROPN
ejpam-3024	259	32	)	)	PUNCT
ejpam-3024	259	33	references	reference	NOUN
ejpam-3024	259	34	737	737	NUM
ejpam-3024	259	35	since	since	SCONJ
ejpam-3024	259	36	h(b	h(b	PROPN
ejpam-3024	259	37	)	)	PUNCT
ejpam-3024	259	38	∩	∩	PROPN
ejpam-3024	259	39	v	v	ADP
ejpam-3024	259	40	�	�	PROPN
ejpam-3024	259	41	δ	δ	NOUN
ejpam-3024	259	42	v	v	NOUN
ejpam-3024	259	43	and	and	CCONJ
ejpam-3024	259	44	g	g	PROPN
ejpam-3024	259	45	is	be	AUX
ejpam-3024	259	46	a	a	DET
ejpam-3024	259	47	homomorphism	homomorphism	NOUN
ejpam-3024	259	48	.	.	PUNCT
ejpam-3024	260	1	a	a	DET
ejpam-3024	260	2	ring	ring	NOUN
ejpam-3024	260	3	r	r	NOUN
ejpam-3024	260	4	is	be	AUX
ejpam-3024	260	5	left	leave	VERB
ejpam-3024	260	6	perfect	perfect	ADJ
ejpam-3024	260	7	if	if	SCONJ
ejpam-3024	260	8	and	and	CCONJ
ejpam-3024	260	9	only	only	ADV
ejpam-3024	260	10	if	if	SCONJ
ejpam-3024	260	11	every	every	DET
ejpam-3024	260	12	left	left	ADJ
ejpam-3024	260	13	r	r	NOUN
ejpam-3024	260	14	-	-	PUNCT
ejpam-3024	260	15	module	module	NOUN
ejpam-3024	260	16	has	have	VERB
ejpam-3024	260	17	the	the	DET
ejpam-3024	260	18	property	property	NOUN
ejpam-3024	260	19	(	(	PUNCT
ejpam-3024	260	20	e	e	NOUN
ejpam-3024	260	21	)	)	PUNCT
ejpam-3024	260	22	(	(	PUNCT
ejpam-3024	260	23	see	see	VERB
ejpam-3024	260	24	[	[	X
ejpam-3024	260	25	16	16	NUM
ejpam-3024	260	26	]	]	PUNCT
ejpam-3024	260	27	)	)	PUNCT
ejpam-3024	260	28	.	.	PUNCT
ejpam-3024	261	1	now	now	ADV
ejpam-3024	261	2	we	we	PRON
ejpam-3024	261	3	show	show	VERB
ejpam-3024	261	4	only	only	ADV
ejpam-3024	261	5	one	one	NUM
ejpam-3024	261	6	side	side	NOUN
ejpam-3024	261	7	of	of	ADP
ejpam-3024	261	8	this	this	DET
ejpam-3024	261	9	fact	fact	NOUN
ejpam-3024	261	10	is	be	AUX
ejpam-3024	261	11	valid	valid	ADJ
ejpam-3024	261	12	for	for	ADP
ejpam-3024	261	13	δ	δ	NOUN
ejpam-3024	261	14	-	-	PUNCT
ejpam-3024	261	15	perfect	perfect	ADJ
ejpam-3024	261	16	rings	ring	NOUN
ejpam-3024	261	17	.	.	PUNCT
ejpam-3024	262	1	proposition	proposition	NOUN
ejpam-3024	262	2	8	8	NUM
ejpam-3024	262	3	.	.	PUNCT
ejpam-3024	263	1	if	if	SCONJ
ejpam-3024	263	2	r	r	NOUN
ejpam-3024	263	3	is	be	AUX
ejpam-3024	263	4	a	a	DET
ejpam-3024	263	5	δ	δ	NOUN
ejpam-3024	263	6	-	-	PUNCT
ejpam-3024	263	7	perfect	perfect	ADJ
ejpam-3024	263	8	ring	ring	NOUN
ejpam-3024	263	9	,	,	PUNCT
ejpam-3024	263	10	then	then	ADV
ejpam-3024	263	11	every	every	DET
ejpam-3024	263	12	left	left	ADJ
ejpam-3024	263	13	r	r	NOUN
ejpam-3024	263	14	-	-	PUNCT
ejpam-3024	263	15	module	module	NOUN
ejpam-3024	263	16	has	have	VERB
ejpam-3024	263	17	the	the	DET
ejpam-3024	263	18	property	property	NOUN
ejpam-3024	263	19	(	(	PUNCT
ejpam-3024	263	20	δ	δ	PROPN
ejpam-3024	263	21	-	-	PUNCT
ejpam-3024	263	22	e	e	NOUN
ejpam-3024	263	23	)	)	PUNCT
ejpam-3024	263	24	.	.	PUNCT
ejpam-3024	264	1	proof	proof	NOUN
ejpam-3024	264	2	.	.	PUNCT
ejpam-3024	265	1	suppose	suppose	VERB
ejpam-3024	265	2	that	that	SCONJ
ejpam-3024	265	3	a	a	DET
ejpam-3024	265	4	ring	ring	NOUN
ejpam-3024	265	5	r	r	NOUN
ejpam-3024	265	6	is	be	AUX
ejpam-3024	265	7	δ	δ	NOUN
ejpam-3024	265	8	-	-	NOUN
ejpam-3024	265	9	perfect	perfect	ADJ
ejpam-3024	265	10	.	.	PUNCT
ejpam-3024	266	1	let	let	VERB
ejpam-3024	266	2	m	m	PRON
ejpam-3024	266	3	be	be	AUX
ejpam-3024	266	4	an	an	DET
ejpam-3024	266	5	r	r	NOUN
ejpam-3024	266	6	-	-	PUNCT
ejpam-3024	266	7	module	module	NOUN
ejpam-3024	266	8	and	and	CCONJ
ejpam-3024	266	9	n	n	CCONJ
ejpam-3024	266	10	be	be	VERB
ejpam-3024	266	11	any	any	DET
ejpam-3024	266	12	extension	extension	NOUN
ejpam-3024	266	13	of	of	ADP
ejpam-3024	266	14	m.	m.	NOUN
ejpam-3024	266	15	n	n	CCONJ
ejpam-3024	266	16	is	be	AUX
ejpam-3024	266	17	δ	δ	NOUN
ejpam-3024	266	18	-	-	PUNCT
ejpam-3024	266	19	supplemented	supplement	VERB
ejpam-3024	266	20	since	since	SCONJ
ejpam-3024	266	21	r	r	NOUN
ejpam-3024	266	22	is	be	AUX
ejpam-3024	266	23	δ	δ	NOUN
ejpam-3024	266	24	-	-	NOUN
ejpam-3024	266	25	perfect	perfect	ADJ
ejpam-3024	266	26	.	.	PUNCT
ejpam-3024	267	1	so	so	ADV
ejpam-3024	267	2	m	m	PROPN
ejpam-3024	267	3	has	have	VERB
ejpam-3024	267	4	a	a	DET
ejpam-3024	267	5	δ	δ	NOUN
ejpam-3024	267	6	-	-	PUNCT
ejpam-3024	267	7	supplemented	supplement	VERB
ejpam-3024	267	8	in	in	ADP
ejpam-3024	267	9	n	n	PRON
ejpam-3024	267	10	as	as	ADP
ejpam-3024	267	11	a	a	DET
ejpam-3024	267	12	submodule	submodule	NOUN
ejpam-3024	267	13	of	of	ADP
ejpam-3024	267	14	n.	n.	PROPN
ejpam-3024	267	15	hence	hence	ADV
ejpam-3024	267	16	,	,	PUNCT
ejpam-3024	267	17	m	m	VERB
ejpam-3024	267	18	has	have	VERB
ejpam-3024	267	19	the	the	DET
ejpam-3024	267	20	property	property	NOUN
ejpam-3024	267	21	(	(	PUNCT
ejpam-3024	267	22	δ	δ	PROPN
ejpam-3024	267	23	-	-	PUNCT
ejpam-3024	267	24	e	e	NOUN
ejpam-3024	267	25	)	)	PUNCT
ejpam-3024	267	26	.	.	PUNCT
ejpam-3024	268	1	proposition	proposition	NOUN
ejpam-3024	268	2	9	9	NUM
ejpam-3024	268	3	.	.	PUNCT
ejpam-3024	269	1	let	let	VERB
ejpam-3024	269	2	r	r	PRON
ejpam-3024	269	3	be	be	AUX
ejpam-3024	269	4	a	a	DET
ejpam-3024	269	5	ring	ring	NOUN
ejpam-3024	269	6	.	.	PUNCT
ejpam-3024	270	1	if	if	SCONJ
ejpam-3024	270	2	every	every	DET
ejpam-3024	270	3	left	left	ADJ
ejpam-3024	270	4	r	r	NOUN
ejpam-3024	270	5	-	-	PUNCT
ejpam-3024	270	6	module	module	NOUN
ejpam-3024	270	7	has	have	VERB
ejpam-3024	270	8	the	the	DET
ejpam-3024	270	9	property	property	NOUN
ejpam-3024	270	10	(	(	PUNCT
ejpam-3024	270	11	δ	δ	PROPN
ejpam-3024	270	12	-	-	PUNCT
ejpam-3024	270	13	e	e	PROPN
ejpam-3024	270	14	)	)	PUNCT
ejpam-3024	270	15	,	,	PUNCT
ejpam-3024	270	16	then	then	ADV
ejpam-3024	270	17	r	r	NOUN
ejpam-3024	270	18	is	be	AUX
ejpam-3024	270	19	a	a	DET
ejpam-3024	270	20	δ	δ	NOUN
ejpam-3024	270	21	-	-	PUNCT
ejpam-3024	270	22	semiperfect	semiperfect	ADJ
ejpam-3024	270	23	ring	ring	NOUN
ejpam-3024	270	24	.	.	PUNCT
ejpam-3024	271	1	proof	proof	NOUN
ejpam-3024	271	2	.	.	PUNCT
ejpam-3024	272	1	since	since	SCONJ
ejpam-3024	272	2	every	every	DET
ejpam-3024	272	3	left	left	ADJ
ejpam-3024	272	4	r	r	NOUN
ejpam-3024	272	5	-	-	PUNCT
ejpam-3024	272	6	module	module	NOUN
ejpam-3024	272	7	has	have	VERB
ejpam-3024	272	8	the	the	DET
ejpam-3024	272	9	property	property	NOUN
ejpam-3024	272	10	(	(	PUNCT
ejpam-3024	272	11	δ	δ	PROPN
ejpam-3024	272	12	-	-	PUNCT
ejpam-3024	272	13	e	e	PROPN
ejpam-3024	272	14	)	)	PUNCT
ejpam-3024	272	15	,	,	PUNCT
ejpam-3024	272	16	every	every	DET
ejpam-3024	272	17	ideal	ideal	NOUN
ejpam-3024	272	18	of	of	ADP
ejpam-3024	272	19	r	r	NOUN
ejpam-3024	272	20	also	also	ADV
ejpam-3024	272	21	has	have	VERB
ejpam-3024	272	22	the	the	DET
ejpam-3024	272	23	property	property	NOUN
ejpam-3024	272	24	(	(	PUNCT
ejpam-3024	272	25	δ	δ	PROPN
ejpam-3024	272	26	-	-	PUNCT
ejpam-3024	272	27	e	e	NOUN
ejpam-3024	272	28	)	)	PUNCT
ejpam-3024	272	29	as	as	ADP
ejpam-3024	272	30	a	a	DET
ejpam-3024	272	31	submodule	submodule	NOUN
ejpam-3024	272	32	of	of	ADP
ejpam-3024	272	33	rr	rr	PROPN
ejpam-3024	272	34	.	.	PUNCT
ejpam-3024	273	1	so	so	ADV
ejpam-3024	273	2	every	every	DET
ejpam-3024	273	3	ideal	ideal	NOUN
ejpam-3024	273	4	of	of	ADP
ejpam-3024	273	5	r	r	NOUN
ejpam-3024	273	6	has	have	VERB
ejpam-3024	273	7	a	a	DET
ejpam-3024	273	8	δ	δ	NOUN
ejpam-3024	273	9	-	-	PUNCT
ejpam-3024	273	10	supplement	supplement	NOUN
ejpam-3024	273	11	in	in	ADP
ejpam-3024	273	12	rr	rr	NOUN
ejpam-3024	273	13	.	.	PUNCT
ejpam-3024	274	1	hence	hence	ADV
ejpam-3024	274	2	r	r	NOUN
ejpam-3024	274	3	is	be	AUX
ejpam-3024	274	4	δ	δ	NOUN
ejpam-3024	274	5	-	-	PUNCT
ejpam-3024	274	6	semiperfect	semiperfect	NOUN
ejpam-3024	274	7	by	by	ADP
ejpam-3024	274	8	[	[	X
ejpam-3024	274	9	6	6	NUM
ejpam-3024	274	10	,	,	PUNCT
ejpam-3024	274	11	theorem	theorem	VERB
ejpam-3024	274	12	3.3	3.3	NUM
ejpam-3024	274	13	]	]	PUNCT
ejpam-3024	274	14	.	.	PUNCT
ejpam-3024	275	1	example	example	NOUN
ejpam-3024	276	1	1	1	NUM
ejpam-3024	276	2	.	.	PUNCT
ejpam-3024	276	3	let	let	VERB
ejpam-3024	276	4	f	f	PRON
ejpam-3024	276	5	be	be	AUX
ejpam-3024	276	6	a	a	DET
ejpam-3024	276	7	field	field	NOUN
ejpam-3024	276	8	,	,	PUNCT
ejpam-3024	276	9	i	i	PRON
ejpam-3024	276	10	=	=	PUNCT
ejpam-3024	276	11	(	(	PUNCT
ejpam-3024	276	12	f	f	NOUN
ejpam-3024	276	13	f	f	PROPN
ejpam-3024	276	14	0	0	NUM
ejpam-3024	276	15	f	f	PROPN
ejpam-3024	276	16	)	)	PUNCT
ejpam-3024	276	17	,	,	PUNCT
ejpam-3024	276	18	r	r	NOUN
ejpam-3024	276	19	=	=	SYM
ejpam-3024	276	20	{	{	PUNCT
ejpam-3024	276	21	(	(	PUNCT
ejpam-3024	276	22	x1	x1	PROPN
ejpam-3024	276	23	,	,	PUNCT
ejpam-3024	276	24	...	...	PUNCT
ejpam-3024	276	25	,	,	PUNCT
ejpam-3024	276	26	xn	xn	PROPN
ejpam-3024	276	27	,	,	PUNCT
ejpam-3024	276	28	x	x	X
ejpam-3024	276	29	,	,	PUNCT
ejpam-3024	276	30	x	x	X
ejpam-3024	276	31	,	,	PUNCT
ejpam-3024	276	32	...	...	PUNCT
ejpam-3024	276	33	)	)	PUNCT
ejpam-3024	277	1	|	|	ADV
ejpam-3024	277	2	n	n	ADV
ejpam-3024	277	3	ε	ε	PROPN
ejpam-3024	277	4	n	n	CCONJ
ejpam-3024	277	5	,	,	PUNCT
ejpam-3024	277	6	xi	xi	PROPN
ejpam-3024	277	7	ε	ε	PROPN
ejpam-3024	277	8	m2(f	m2(f	PROPN
ejpam-3024	277	9	)	)	PUNCT
ejpam-3024	277	10	,	,	PUNCT
ejpam-3024	277	11	x	x	PUNCT
ejpam-3024	277	12	ε	ε	PROPN
ejpam-3024	277	13	i	i	PRON
ejpam-3024	277	14	}	}	PUNCT
ejpam-3024	277	15	with	with	ADP
ejpam-3024	277	16	component	component	NOUN
ejpam-3024	277	17	-	-	PUNCT
ejpam-3024	277	18	wise	wise	ADJ
ejpam-3024	277	19	operations	operation	NOUN
ejpam-3024	277	20	,	,	PUNCT
ejpam-3024	277	21	r	r	NOUN
ejpam-3024	277	22	is	be	AUX
ejpam-3024	277	23	a	a	DET
ejpam-3024	277	24	ring	ring	NOUN
ejpam-3024	277	25	.	.	PUNCT
ejpam-3024	278	1	by	by	ADP
ejpam-3024	278	2	example	example	NOUN
ejpam-3024	278	3	4.3	4.3	NUM
ejpam-3024	278	4	in	in	ADP
ejpam-3024	278	5	[	[	X
ejpam-3024	278	6	15	15	NUM
ejpam-3024	278	7	]	]	PUNCT
ejpam-3024	278	8	,	,	PUNCT
ejpam-3024	278	9	r	r	NOUN
ejpam-3024	278	10	is	be	AUX
ejpam-3024	278	11	a	a	DET
ejpam-3024	278	12	δ	δ	NOUN
ejpam-3024	278	13	-	-	PUNCT
ejpam-3024	278	14	perfect	perfect	ADJ
ejpam-3024	278	15	ring	ring	NOUN
ejpam-3024	278	16	that	that	PRON
ejpam-3024	278	17	is	be	AUX
ejpam-3024	278	18	not	not	PART
ejpam-3024	278	19	perfect	perfect	ADJ
ejpam-3024	278	20	.	.	PUNCT
ejpam-3024	279	1	and	and	CCONJ
ejpam-3024	279	2	so	so	ADV
ejpam-3024	279	3	rr	rr	PROPN
ejpam-3024	279	4	is	be	AUX
ejpam-3024	279	5	an	an	DET
ejpam-3024	279	6	example	example	NOUN
ejpam-3024	279	7	of	of	ADP
ejpam-3024	279	8	a	a	DET
ejpam-3024	279	9	module	module	NOUN
ejpam-3024	279	10	that	that	PRON
ejpam-3024	279	11	has	have	VERB
ejpam-3024	279	12	the	the	DET
ejpam-3024	279	13	property	property	NOUN
ejpam-3024	279	14	(	(	PUNCT
ejpam-3024	279	15	δ	δ	PROPN
ejpam-3024	279	16	-	-	PUNCT
ejpam-3024	279	17	e	e	NOUN
ejpam-3024	279	18	)	)	PUNCT
ejpam-3024	279	19	but	but	CCONJ
ejpam-3024	279	20	not	not	PART
ejpam-3024	279	21	have	have	VERB
ejpam-3024	279	22	the	the	DET
ejpam-3024	279	23	property	property	NOUN
ejpam-3024	279	24	(	(	PUNCT
ejpam-3024	279	25	e	e	NOUN
ejpam-3024	279	26	)	)	PUNCT
ejpam-3024	279	27	.	.	PUNCT
ejpam-3024	280	1	acknowledgements	acknowledgement	VERB
ejpam-3024	280	2	the	the	DET
ejpam-3024	280	3	authors	author	NOUN
ejpam-3024	280	4	sincerely	sincerely	ADV
ejpam-3024	280	5	thank	thank	VERB
ejpam-3024	280	6	the	the	DET
ejpam-3024	280	7	reviewers	reviewer	NOUN
ejpam-3024	280	8	for	for	ADP
ejpam-3024	280	9	the	the	DET
ejpam-3024	280	10	valuable	valuable	ADJ
ejpam-3024	280	11	suggestions	suggestion	NOUN
ejpam-3024	280	12	and	and	CCONJ
ejpam-3024	280	13	comments	comment	NOUN
ejpam-3024	280	14	.	.	PUNCT
ejpam-3024	281	1	references	reference	NOUN
ejpam-3024	281	2	[	[	X
ejpam-3024	281	3	1	1	NUM
ejpam-3024	281	4	]	]	X
ejpam-3024	281	5	f.w	f.w	PROPN
ejpam-3024	281	6	.	.	PROPN
ejpam-3024	281	7	anderson	anderson	PROPN
ejpam-3024	281	8	and	and	CCONJ
ejpam-3024	281	9	k.r	k.r	PROPN
ejpam-3024	281	10	.	.	PROPN
ejpam-3024	281	11	fuller	full	ADJ
ejpam-3024	281	12	.	.	PUNCT
ejpam-3024	282	1	rings	ring	NOUN
ejpam-3024	282	2	and	and	CCONJ
ejpam-3024	282	3	categories	category	NOUN
ejpam-3024	282	4	of	of	ADP
ejpam-3024	282	5	modules	module	NOUN
ejpam-3024	282	6	.	.	PUNCT
ejpam-3024	283	1	vol	vol	NOUN
ejpam-3024	283	2	.	.	PROPN
ejpam-3024	283	3	13	13	NUM
ejpam-3024	283	4	of	of	ADP
ejpam-3024	283	5	graduate	graduate	ADJ
ejpam-3024	283	6	texts	text	NOUN
ejpam-3024	283	7	in	in	ADP
ejpam-3024	283	8	mathematics	mathematic	NOUN
ejpam-3024	283	9	,	,	PUNCT
ejpam-3024	283	10	springer	springer	NOUN
ejpam-3024	283	11	,	,	PUNCT
ejpam-3024	283	12	new	new	PROPN
ejpam-3024	283	13	york	york	PROPN
ejpam-3024	283	14	,	,	PUNCT
ejpam-3024	283	15	ny	ny	PROPN
ejpam-3024	283	16	,	,	PUNCT
ejpam-3024	283	17	usa,1974	usa,1974	PROPN
ejpam-3024	283	18	.	.	PUNCT
ejpam-3024	284	1	[	[	X
ejpam-3024	284	2	2	2	X
ejpam-3024	284	3	]	]	PUNCT
ejpam-3024	284	4	e.	e.	PROPN
ejpam-3024	284	5	büyükaşık	büyükaşık	PROPN
ejpam-3024	284	6	and	and	CCONJ
ejpam-3024	284	7	c.	c.	PROPN
ejpam-3024	284	8	lomp	lomp	PROPN
ejpam-3024	284	9	.	.	PUNCT
ejpam-3024	285	1	when	when	SCONJ
ejpam-3024	285	2	δ	δ	NOUN
ejpam-3024	285	3	-	-	PUNCT
ejpam-3024	285	4	semiperfect	semiperfect	ADJ
ejpam-3024	285	5	rings	ring	NOUN
ejpam-3024	285	6	are	be	AUX
ejpam-3024	285	7	semiperfect	semiperfect	ADJ
ejpam-3024	285	8	.	.	PUNCT
ejpam-3024	286	1	turkish	turkish	ADJ
ejpam-3024	286	2	j.	j.	PROPN
ejpam-3024	286	3	math	math	PROPN
ejpam-3024	286	4	.	.	PUNCT
ejpam-3024	287	1	34	34	NUM
ejpam-3024	287	2	,	,	PUNCT
ejpam-3024	287	3	317	317	NUM
ejpam-3024	287	4	-	-	SYM
ejpam-3024	287	5	324	324	NUM
ejpam-3024	287	6	,	,	PUNCT
ejpam-3024	287	7	2010	2010	NUM
ejpam-3024	287	8	.	.	PUNCT
ejpam-3024	288	1	[	[	X
ejpam-3024	288	2	3	3	X
ejpam-3024	288	3	]	]	PUNCT
ejpam-3024	288	4	j.	j.	PROPN
ejpam-3024	288	5	clark	clark	PROPN
ejpam-3024	288	6	,	,	PUNCT
ejpam-3024	288	7	c.	c.	PROPN
ejpam-3024	288	8	lomp	lomp	PROPN
ejpam-3024	288	9	,	,	PUNCT
ejpam-3024	288	10	n.	n.	PROPN
ejpam-3024	288	11	vanaja	vanaja	PROPN
ejpam-3024	288	12	and	and	CCONJ
ejpam-3024	288	13	r.	r.	PROPN
ejpam-3024	288	14	wisbauer	wisbauer	PROPN
ejpam-3024	288	15	.	.	PUNCT
ejpam-3024	289	1	lifting	lift	VERB
ejpam-3024	289	2	modules	module	NOUN
ejpam-3024	289	3	.	.	PUNCT
ejpam-3024	290	1	supplements	supplement	NOUN
ejpam-3024	290	2	and	and	CCONJ
ejpam-3024	290	3	projectivity	projectivity	NOUN
ejpam-3024	290	4	in	in	ADP
ejpam-3024	290	5	module	module	NOUN
ejpam-3024	290	6	theory	theory	NOUN
ejpam-3024	290	7	,	,	PUNCT
ejpam-3024	290	8	ser.frontiers	ser.frontier	NOUN
ejpam-3024	290	9	in	in	ADP
ejpam-3024	290	10	mathematics	mathematic	NOUN
ejpam-3024	290	11	.	.	PUNCT
ejpam-3024	291	1	basel	basel	PROPN
ejpam-3024	291	2	:	:	PUNCT
ejpam-3024	291	3	birkhauser	birkhauser	PROPN
ejpam-3024	291	4	,	,	PUNCT
ejpam-3024	291	5	2006	2006	NUM
ejpam-3024	291	6	.	.	PUNCT
ejpam-3024	292	1	[	[	X
ejpam-3024	292	2	4	4	X
ejpam-3024	292	3	]	]	X
ejpam-3024	292	4	h.	h.	PROPN
ejpam-3024	292	5	çalışıcı	çalışıcı	PROPN
ejpam-3024	292	6	and	and	CCONJ
ejpam-3024	292	7	e.	e.	PROPN
ejpam-3024	292	8	türkmen	türkman	NOUN
ejpam-3024	292	9	.	.	PUNCT
ejpam-3024	293	1	modules	module	NOUN
ejpam-3024	293	2	that	that	PRON
ejpam-3024	293	3	have	have	VERB
ejpam-3024	293	4	supplement	supplement	NOUN
ejpam-3024	293	5	in	in	ADP
ejpam-3024	293	6	every	every	DET
ejpam-3024	293	7	cofinite	cofinite	NOUN
ejpam-3024	293	8	extension	extension	NOUN
ejpam-3024	293	9	.	.	PUNCT
ejpam-3024	294	1	georgian	georgian	PROPN
ejpam-3024	294	2	math	math	PROPN
ejpam-3024	294	3	.	.	PUNCT
ejpam-3024	295	1	j.	j.	PROPN
ejpam-3024	295	2	,	,	PUNCT
ejpam-3024	295	3	vol	vol	NOUN
ejpam-3024	295	4	.	.	PROPN
ejpam-3024	295	5	19	19	NUM
ejpam-3024	295	6	,	,	PUNCT
ejpam-3024	295	7	no	no	INTJ
ejpam-3024	295	8	.	.	NOUN
ejpam-3024	295	9	2	2	NUM
ejpam-3024	295	10	,	,	PUNCT
ejpam-3024	295	11	pp	pp	ADJ
ejpam-3024	295	12	.	.	PUNCT
ejpam-3024	296	1	209	209	NUM
ejpam-3024	296	2	-	-	SYM
ejpam-3024	296	3	216	216	NUM
ejpam-3024	296	4	,	,	PUNCT
ejpam-3024	296	5	2012	2012	NUM
ejpam-3024	296	6	.	.	PUNCT
ejpam-3024	297	1	[	[	X
ejpam-3024	297	2	5	5	NUM
ejpam-3024	297	3	]	]	X
ejpam-3024	297	4	f.	f.	PROPN
ejpam-3024	297	5	eryılmaz	eryılmaz	PROPN
ejpam-3024	297	6	.	.	PUNCT
ejpam-3024	298	1	modules	module	NOUN
ejpam-3024	298	2	that	that	PRON
ejpam-3024	298	3	have	have	VERB
ejpam-3024	298	4	a	a	DET
ejpam-3024	298	5	δ	δ	NOUN
ejpam-3024	298	6	-	-	NOUN
ejpam-3024	298	7	supplement	supplement	NOUN
ejpam-3024	298	8	in	in	ADP
ejpam-3024	298	9	every	every	DET
ejpam-3024	298	10	torsion	torsion	NOUN
ejpam-3024	298	11	extension	extension	NOUN
ejpam-3024	298	12	.	.	PUNCT
ejpam-3024	299	1	turkish	turkish	ADJ
ejpam-3024	299	2	journal	journal	PROPN
ejpam-3024	299	3	of	of	ADP
ejpam-3024	299	4	science	science	PROPN
ejpam-3024	299	5	&	&	CCONJ
ejpam-3024	299	6	technology	technology	PROPN
ejpam-3024	299	7	,	,	PUNCT
ejpam-3024	299	8	vol	vol	NOUN
ejpam-3024	299	9	.	.	NOUN
ejpam-3024	299	10	11	11	NUM
ejpam-3024	299	11	issue	issue	NOUN
ejpam-3024	299	12	2	2	NUM
ejpam-3024	299	13	,	,	PUNCT
ejpam-3024	299	14	p35	p35	NOUN
ejpam-3024	299	15	-	-	SYM
ejpam-3024	299	16	38	38	NUM
ejpam-3024	299	17	.	.	PUNCT
ejpam-3024	300	1	4p	4p	NUM
ejpam-3024	300	2	,	,	PUNCT
ejpam-3024	300	3	2016	2016	NUM
ejpam-3024	300	4	.	.	PUNCT
ejpam-3024	301	1	references	reference	NOUN
ejpam-3024	301	2	738	738	NUM
ejpam-3024	301	3	[	[	SYM
ejpam-3024	301	4	6	6	NUM
ejpam-3024	301	5	]	]	PUNCT
ejpam-3024	301	6	k.	k.	PROPN
ejpam-3024	301	7	r.	r.	PROPN
ejpam-3024	301	8	gooderal	gooderal	PROPN
ejpam-3024	301	9	.	.	PUNCT
ejpam-3024	302	1	ring	ring	NOUN
ejpam-3024	302	2	theory	theory	NOUN
ejpam-3024	302	3	:	:	PUNCT
ejpam-3024	302	4	nonsingular	nonsingular	ADJ
ejpam-3024	302	5	rings	ring	NOUN
ejpam-3024	302	6	and	and	CCONJ
ejpam-3024	302	7	modules	module	NOUN
ejpam-3024	302	8	.	.	PUNCT
ejpam-3024	303	1	dekker	dekker	PROPN
ejpam-3024	303	2	,	,	PUNCT
ejpam-3024	303	3	new	new	PROPN
ejpam-3024	303	4	york	york	PROPN
ejpam-3024	303	5	,	,	PUNCT
ejpam-3024	303	6	1976	1976	NUM
ejpam-3024	303	7	.	.	PUNCT
ejpam-3024	304	1	[	[	X
ejpam-3024	304	2	7	7	X
ejpam-3024	304	3	]	]	X
ejpam-3024	304	4	m.	m.	NOUN
ejpam-3024	304	5	t.	t.	PROPN
ejpam-3024	304	6	koşan	koşan	PROPN
ejpam-3024	304	7	,	,	PUNCT
ejpam-3024	304	8	δ	δ	PROPN
ejpam-3024	304	9	-	-	PUNCT
ejpam-3024	304	10	lifting	lifting	NOUN
ejpam-3024	304	11	and	and	CCONJ
ejpam-3024	304	12	δ	δ	NOUN
ejpam-3024	304	13	-	-	PUNCT
ejpam-3024	304	14	supplemented	supplement	VERB
ejpam-3024	304	15	modules	module	NOUN
ejpam-3024	304	16	.	.	PUNCT
ejpam-3024	305	1	algebra	algebra	NOUN
ejpam-3024	305	2	colloquium	colloquium	NOUN
ejpam-3024	305	3	,	,	PUNCT
ejpam-3024	305	4	14	14	NUM
ejpam-3024	305	5	(	(	PUNCT
ejpam-3024	305	6	1	1	NUM
ejpam-3024	305	7	)	)	PUNCT
ejpam-3024	305	8	,	,	PUNCT
ejpam-3024	305	9	5360	5360	NUM
ejpam-3024	305	10	,	,	PUNCT
ejpam-3024	305	11	2007	2007	NUM
ejpam-3024	305	12	.	.	PUNCT
ejpam-3024	306	1	[	[	X
ejpam-3024	306	2	8	8	NUM
ejpam-3024	306	3	]	]	PUNCT
ejpam-3024	306	4	m.	m.	NOUN
ejpam-3024	306	5	j.	j.	PROPN
ejpam-3024	306	6	nematollahi	nematollahi	PROPN
ejpam-3024	306	7	.	.	PUNCT
ejpam-3024	307	1	on	on	ADP
ejpam-3024	307	2	δ	δ	NOUN
ejpam-3024	307	3	-	-	PUNCT
ejpam-3024	307	4	supplemented	supplement	VERB
ejpam-3024	307	5	modules	module	NOUN
ejpam-3024	307	6	.	.	PUNCT
ejpam-3024	308	1	tarbiat	tarbiat	PROPN
ejpam-3024	308	2	moallem	moallem	PROPN
ejpam-3024	308	3	university	university	PROPN
ejpam-3024	308	4	,	,	PUNCT
ejpam-3024	308	5	20	20	NUM
ejpam-3024	308	6	th	th	NOUN
ejpam-3024	308	7	seminar	seminar	NOUN
ejpam-3024	308	8	on	on	ADP
ejpam-3024	308	9	algebra	algebra	NOUN
ejpam-3024	308	10	,	,	PUNCT
ejpam-3024	308	11	(	(	PUNCT
ejpam-3024	308	12	apr	apr	NOUN
ejpam-3024	308	13	.	.	PROPN
ejpam-3024	309	1	22	22	NUM
ejpam-3024	309	2	-	-	SYM
ejpam-3024	309	3	23	23	NUM
ejpam-3024	309	4	)	)	PUNCT
ejpam-3024	309	5	,	,	PUNCT
ejpam-3024	309	6	pp	pp	ADP
ejpam-3024	309	7	.	.	PUNCT
ejpam-3024	310	1	155	155	NUM
ejpam-3024	310	2	-	-	SYM
ejpam-3024	310	3	158	158	NUM
ejpam-3024	310	4	,	,	PUNCT
ejpam-3024	310	5	2009	2009	NUM
ejpam-3024	310	6	.	.	PUNCT
ejpam-3024	311	1	[	[	X
ejpam-3024	311	2	9	9	NUM
ejpam-3024	311	3	]	]	X
ejpam-3024	311	4	e.	e.	PROPN
ejpam-3024	311	5	önal	önal	PROPN
ejpam-3024	311	6	,	,	PUNCT
ejpam-3024	311	7	h.çalışıcı	h.çalışıcı	PROPN
ejpam-3024	311	8	and	and	CCONJ
ejpam-3024	311	9	e.	e.	PROPN
ejpam-3024	311	10	türkmen	türkman	NOUN
ejpam-3024	311	11	.	.	PUNCT
ejpam-3024	312	1	modules	module	NOUN
ejpam-3024	312	2	that	that	PRON
ejpam-3024	312	3	have	have	VERB
ejpam-3024	312	4	a	a	DET
ejpam-3024	312	5	weak	weak	ADJ
ejpam-3024	312	6	supplement	supplement	NOUN
ejpam-3024	312	7	in	in	ADP
ejpam-3024	312	8	every	every	DET
ejpam-3024	312	9	extension	extension	NOUN
ejpam-3024	312	10	.	.	PUNCT
ejpam-3024	313	1	miskolc	miskolc	ADJ
ejpam-3024	313	2	mathematical	mathematical	ADJ
ejpam-3024	313	3	notes	note	NOUN
ejpam-3024	313	4	,	,	PUNCT
ejpam-3024	313	5	vol	vol	NOUN
ejpam-3024	313	6	.	.	PROPN
ejpam-3024	313	7	17	17	NUM
ejpam-3024	313	8	,	,	PUNCT
ejpam-3024	313	9	no	no	INTJ
ejpam-3024	313	10	.	.	NOUN
ejpam-3024	313	11	1	1	NUM
ejpam-3024	313	12	,	,	PUNCT
ejpam-3024	313	13	pp	pp	ADJ
ejpam-3024	313	14	.	.	PUNCT
ejpam-3024	314	1	471–481	471–481	NUM
ejpam-3024	314	2	,	,	PUNCT
ejpam-3024	314	3	2016	2016	NUM
ejpam-3024	314	4	.	.	PUNCT
ejpam-3024	315	1	[	[	X
ejpam-3024	315	2	10	10	NUM
ejpam-3024	315	3	]	]	X
ejpam-3024	315	4	s.	s.	PROPN
ejpam-3024	315	5	özdemir	özdemir	PROPN
ejpam-3024	315	6	.	.	PUNCT
ejpam-3024	316	1	rad	rad	NOUN
ejpam-3024	316	2	-	-	ADJ
ejpam-3024	316	3	supplementing	supplement	VERB
ejpam-3024	316	4	modules	module	NOUN
ejpam-3024	316	5	.	.	PUNCT
ejpam-3024	317	1	j.	j.	PROPN
ejpam-3024	317	2	korean	korean	PROPN
ejpam-3024	317	3	math	math	PROPN
ejpam-3024	317	4	.	.	PUNCT
ejpam-3024	318	1	soc	soc	PROPN
ejpam-3024	318	2	.	.	PUNCT
ejpam-3024	319	1	,	,	PUNCT
ejpam-3024	319	2	vol	vol	NOUN
ejpam-3024	319	3	.	.	PROPN
ejpam-3024	320	1	53	53	NUM
ejpam-3024	320	2	,	,	PUNCT
ejpam-3024	320	3	no	no	INTJ
ejpam-3024	320	4	.	.	NOUN
ejpam-3024	320	5	2	2	NUM
ejpam-3024	320	6	,	,	PUNCT
ejpam-3024	320	7	pp	pp	ADJ
ejpam-3024	320	8	.	.	PUNCT
ejpam-3024	321	1	403	403	NUM
ejpam-3024	321	2	-	-	SYM
ejpam-3024	321	3	414	414	NUM
ejpam-3024	321	4	,	,	PUNCT
ejpam-3024	321	5	2016	2016	NUM
ejpam-3024	321	6	.	.	PUNCT
ejpam-3024	322	1	[	[	X
ejpam-3024	322	2	11	11	NUM
ejpam-3024	322	3	]	]	PUNCT
ejpam-3024	322	4	j.	j.	PROPN
ejpam-3024	322	5	j.	j.	PROPN
ejpam-3024	322	6	rotman	rotman	PROPN
ejpam-3024	322	7	.	.	PUNCT
ejpam-3024	323	1	an	an	DET
ejpam-3024	323	2	introduction	introduction	NOUN
ejpam-3024	323	3	to	to	ADP
ejpam-3024	323	4	homological	homological	ADJ
ejpam-3024	323	5	algebra	algebra	NOUN
ejpam-3024	323	6	.	.	PUNCT
ejpam-3024	324	1	universitext	universitext	PROPN
ejpam-3024	324	2	,	,	PUNCT
ejpam-3024	324	3	new	new	PROPN
ejpam-3024	324	4	york	york	PROPN
ejpam-3024	324	5	:	:	PUNCT
ejpam-3024	324	6	springer	springer	NOUN
ejpam-3024	324	7	,	,	PUNCT
ejpam-3024	324	8	2009	2009	NUM
ejpam-3024	324	9	.	.	PUNCT
ejpam-3024	325	1	[	[	X
ejpam-3024	325	2	12	12	NUM
ejpam-3024	325	3	]	]	X
ejpam-3024	325	4	d.w	d.w	PROPN
ejpam-3024	325	5	.	.	PROPN
ejpam-3024	325	6	sharpe	sharpe	PROPN
ejpam-3024	325	7	and	and	CCONJ
ejpam-3024	325	8	p.	p.	PROPN
ejpam-3024	325	9	vamos	vamos	PROPN
ejpam-3024	325	10	.	.	PUNCT
ejpam-3024	326	1	injective	injective	ADJ
ejpam-3024	326	2	modules	module	NOUN
ejpam-3024	326	3	.	.	PUNCT
ejpam-3024	327	1	ser	ser	PROPN
ejpam-3024	327	2	.	.	PUNCT
ejpam-3024	328	1	cambridge	cambridge	PROPN
ejpam-3024	328	2	tracts	tract	NOUN
ejpam-3024	328	3	in	in	ADP
ejpam-3024	328	4	mathematicsand	mathematicsand	NOUN
ejpam-3024	328	5	mathematical	mathematical	ADJ
ejpam-3024	328	6	physics	physics	PROPN
ejpam-3024	328	7	.	.	PUNCT
ejpam-3024	329	1	cambridge	cambridge	PROPN
ejpam-3024	329	2	:	:	PUNCT
ejpam-3024	329	3	at	at	ADP
ejpam-3024	329	4	the	the	DET
ejpam-3024	329	5	university	university	NOUN
ejpam-3024	329	6	press	press	NOUN
ejpam-3024	329	7	,	,	PUNCT
ejpam-3024	329	8	vol	vol	NOUN
ejpam-3024	329	9	.	.	PROPN
ejpam-3024	329	10	62	62	NUM
ejpam-3024	329	11	,	,	PUNCT
ejpam-3024	329	12	1962	1962	NUM
ejpam-3024	329	13	.	.	PUNCT
ejpam-3024	330	1	[	[	X
ejpam-3024	330	2	13	13	NUM
ejpam-3024	330	3	]	]	PUNCT
ejpam-3024	330	4	b.	b.	NOUN
ejpam-3024	330	5	ungor	ungor	PROPN
ejpam-3024	330	6	,	,	PUNCT
ejpam-3024	330	7	s.	s.	PROPN
ejpam-3024	330	8	halıcıoğlu	halıcıoğlu	PROPN
ejpam-3024	330	9	and	and	CCONJ
ejpam-3024	330	10	a.	a.	NOUN
ejpam-3024	330	11	harmancı	harmancı	PROPN
ejpam-3024	330	12	.	.	PUNCT
ejpam-3024	331	1	on	on	ADP
ejpam-3024	331	2	a	a	DET
ejpam-3024	331	3	class	class	NOUN
ejpam-3024	331	4	of	of	ADP
ejpam-3024	331	5	δ	δ	NOUN
ejpam-3024	331	6	-	-	PUNCT
ejpam-3024	331	7	supplemented	supplement	VERB
ejpam-3024	331	8	modules	module	NOUN
ejpam-3024	331	9	.	.	PUNCT
ejpam-3024	332	1	bull	bull	NOUN
ejpam-3024	332	2	.	.	PUNCT
ejpam-3024	333	1	malays	malays	PROPN
ejpam-3024	333	2	.	.	PUNCT
ejpam-3024	334	1	math	math	NOUN
ejpam-3024	334	2	.	.	PUNCT
ejpam-3024	335	1	sci	sci	PROPN
ejpam-3024	335	2	.	.	PROPN
ejpam-3024	335	3	soc	soc	PROPN
ejpam-3024	335	4	.	.	PUNCT
ejpam-3024	335	5	,	,	PUNCT
ejpam-3024	335	6	(	(	PUNCT
ejpam-3024	335	7	2	2	NUM
ejpam-3024	335	8	)	)	PUNCT
ejpam-3024	335	9	,	,	PUNCT
ejpam-3024	335	10	37(3	37(3	NUM
ejpam-3024	335	11	)	)	PUNCT
ejpam-3024	335	12	,	,	PUNCT
ejpam-3024	335	13	703	703	NUM
ejpam-3024	335	14	-	-	SYM
ejpam-3024	335	15	717	717	NUM
ejpam-3024	335	16	,	,	PUNCT
ejpam-3024	335	17	2014	2014	NUM
ejpam-3024	335	18	.	.	PUNCT
ejpam-3024	336	1	[	[	X
ejpam-3024	336	2	14	14	NUM
ejpam-3024	336	3	]	]	X
ejpam-3024	336	4	r.	r.	PROPN
ejpam-3024	336	5	wisbauer	wisbauer	PROPN
ejpam-3024	336	6	.	.	PUNCT
ejpam-3024	337	1	foundations	foundation	NOUN
ejpam-3024	337	2	of	of	ADP
ejpam-3024	337	3	module	module	NOUN
ejpam-3024	337	4	theory	theory	NOUN
ejpam-3024	337	5	and	and	CCONJ
ejpam-3024	337	6	ring	ring	NOUN
ejpam-3024	337	7	theory	theory	NOUN
ejpam-3024	337	8	,	,	PUNCT
ejpam-3024	337	9	vol	vol	NOUN
ejpam-3024	337	10	.	.	PROPN
ejpam-3024	337	11	3	3	NUM
ejpam-3024	337	12	of	of	ADP
ejpam-3024	337	13	algebra	algebra	NOUN
ejpam-3024	337	14	,	,	PUNCT
ejpam-3024	337	15	logic	logic	NOUN
ejpam-3024	337	16	and	and	CCONJ
ejpam-3024	337	17	applications	application	NOUN
ejpam-3024	337	18	,	,	PUNCT
ejpam-3024	337	19	gordon	gordon	PROPN
ejpam-3024	337	20	and	and	CCONJ
ejpam-3024	337	21	breach	breach	VERB
ejpam-3024	337	22	science	science	NOUN
ejpam-3024	337	23	,	,	PUNCT
ejpam-3024	337	24	philadelphia	philadelphia	PROPN
ejpam-3024	337	25	,	,	PUNCT
ejpam-3024	337	26	pa	pa	PROPN
ejpam-3024	337	27	,	,	PUNCT
ejpam-3024	337	28	usa	usa	PROPN
ejpam-3024	337	29	,	,	PUNCT
ejpam-3024	337	30	german	german	ADJ
ejpam-3024	337	31	edition	edition	NOUN
ejpam-3024	337	32	,	,	PUNCT
ejpam-3024	337	33	1991.y	1991.y	PROPN
ejpam-3024	337	34	.	.	PUNCT
ejpam-3024	338	1	[	[	X
ejpam-3024	338	2	15	15	NUM
ejpam-3024	338	3	]	]	X
ejpam-3024	338	4	zhou	zhou	X
ejpam-3024	338	5	,	,	PUNCT
ejpam-3024	338	6	generalizations	generalization	NOUN
ejpam-3024	338	7	of	of	ADP
ejpam-3024	338	8	perfect	perfect	ADJ
ejpam-3024	338	9	,	,	PUNCT
ejpam-3024	338	10	semiperfect	semiperfect	ADJ
ejpam-3024	338	11	and	and	CCONJ
ejpam-3024	338	12	semiregular	semiregular	PROPN
ejpam-3024	338	13	rings	ring	NOUN
ejpam-3024	338	14	,	,	PUNCT
ejpam-3024	338	15	algebra	algebra	NOUN
ejpam-3024	338	16	colloquium	colloquium	NOUN
ejpam-3024	338	17	,	,	PUNCT
ejpam-3024	338	18	7(3	7(3	NUM
ejpam-3024	338	19	)	)	PUNCT
ejpam-3024	338	20	,	,	PUNCT
ejpam-3024	338	21	305	305	NUM
ejpam-3024	338	22	-	-	SYM
ejpam-3024	338	23	318	318	NUM
ejpam-3024	338	24	,	,	PUNCT
ejpam-3024	338	25	2000	2000	NUM
ejpam-3024	338	26	.	.	PUNCT
ejpam-3024	339	1	[	[	X
ejpam-3024	339	2	16	16	NUM
ejpam-3024	339	3	]	]	X
ejpam-3024	339	4	h.	h.	PROPN
ejpam-3024	339	5	zöschinger	zöschinger	PROPN
ejpam-3024	339	6	.	.	PUNCT
ejpam-3024	340	1	komplementierte	komplementierte	PROPN
ejpam-3024	340	2	moduln	moduln	ADV
ejpam-3024	340	3	,	,	PUNCT
ejpam-3024	340	4	die	die	VERB
ejpam-3024	340	5	in	in	ADP
ejpam-3024	340	6	jeder	jeder	PROPN
ejpam-3024	340	7	erweiterung	erweiterung	PROPN
ejpam-3024	340	8	ein	ein	PROPN
ejpam-3024	340	9	komplement	komplement	PROPN
ejpam-3024	340	10	haben	haben	PROPN
ejpam-3024	340	11	,	,	PUNCT
ejpam-3024	340	12	math	math	NOUN
ejpam-3024	340	13	.	.	PUNCT
ejpam-3024	341	1	scand	scand	PROPN
ejpam-3024	341	2	.	.	PROPN
ejpam-3024	341	3	,	,	PUNCT
ejpam-3024	341	4	vol	vol	NOUN
ejpam-3024	341	5	.	.	PROPN
ejpam-3024	341	6	35	35	NUM
ejpam-3024	341	7	,	,	PUNCT
ejpam-3024	341	8	pp	pp	ADJ
ejpam-3024	341	9	.	.	PUNCT
ejpam-3024	342	1	267	267	NUM
ejpam-3024	342	2	-	-	SYM
ejpam-3024	342	3	287	287	NUM
ejpam-3024	342	4	,	,	PUNCT
ejpam-3024	342	5	1975	1975	NUM
ejpam-3024	342	6	.	.	PUNCT