id	sid	tid	token	lemma	pos
ejpam-5085	1	1	european	european	PROPN
ejpam-5085	1	2	journal	journal	PROPN
ejpam-5085	1	3	of	of	ADP
ejpam-5085	1	4	pure	pure	ADJ
ejpam-5085	1	5	and	and	CCONJ
ejpam-5085	1	6	applied	apply	VERB
ejpam-5085	1	7	mathematics	mathematic	NOUN
ejpam-5085	1	8	vol	vol	NOUN
ejpam-5085	1	9	.	.	PROPN
ejpam-5085	2	1	17	17	NUM
ejpam-5085	2	2	,	,	PUNCT
ejpam-5085	2	3	no	no	INTJ
ejpam-5085	2	4	.	.	NOUN
ejpam-5085	2	5	2	2	NUM
ejpam-5085	2	6	,	,	PUNCT
ejpam-5085	2	7	2024	2024	NUM
ejpam-5085	2	8	,	,	PUNCT
ejpam-5085	2	9	1197	1197	NUM
ejpam-5085	2	10	-	-	SYM
ejpam-5085	2	11	1205	1205	NUM
ejpam-5085	2	12	issn	issn	PROPN
ejpam-5085	2	13	1307	1307	NUM
ejpam-5085	2	14	-	-	SYM
ejpam-5085	2	15	5543	5543	NUM
ejpam-5085	2	16	–	–	PUNCT
ejpam-5085	3	1	ejpam.com	ejpam.com	X
ejpam-5085	3	2	published	publish	VERB
ejpam-5085	3	3	by	by	ADP
ejpam-5085	3	4	new	new	PROPN
ejpam-5085	3	5	york	york	PROPN
ejpam-5085	3	6	business	business	PROPN
ejpam-5085	3	7	global	global	PROPN
ejpam-5085	3	8	on	on	ADP
ejpam-5085	3	9	the	the	DET
ejpam-5085	3	10	self	self	NOUN
ejpam-5085	3	11	-	-	PUNCT
ejpam-5085	3	12	injectivity	injectivity	NOUN
ejpam-5085	3	13	and	and	CCONJ
ejpam-5085	3	14	cm	cm	NOUN
ejpam-5085	3	15	-	-	PUNCT
ejpam-5085	3	16	free	free	ADJ
ejpam-5085	3	17	of	of	ADP
ejpam-5085	3	18	an	an	DET
ejpam-5085	3	19	artin	artin	PROPN
ejpam-5085	3	20	algebra	algebra	NOUN
ejpam-5085	3	21	with	with	ADP
ejpam-5085	3	22	radical	radical	ADJ
ejpam-5085	3	23	cubic	cubic	ADJ
ejpam-5085	3	24	zero	zero	NUM
ejpam-5085	3	25	mounir	mounir	PROPN
ejpam-5085	3	26	laaraj1,∗	laaraj1,∗	NOUN
ejpam-5085	3	27	,	,	PUNCT
ejpam-5085	3	28	seddik	seddik	ADJ
ejpam-5085	3	29	abdelalim1	abdelalim1	NOUN
ejpam-5085	3	30	1	1	NUM
ejpam-5085	3	31	laboratory	laboratory	NOUN
ejpam-5085	3	32	of	of	ADP
ejpam-5085	3	33	fundamental	fundamental	ADJ
ejpam-5085	3	34	and	and	CCONJ
ejpam-5085	3	35	applied	applied	ADJ
ejpam-5085	3	36	mathematics	mathematic	NOUN
ejpam-5085	3	37	(	(	PUNCT
ejpam-5085	3	38	lmfa	lmfa	NOUN
ejpam-5085	3	39	)	)	PUNCT
ejpam-5085	3	40	,	,	PUNCT
ejpam-5085	3	41	faculty	faculty	NOUN
ejpam-5085	3	42	of	of	ADP
ejpam-5085	3	43	sciences	science	NOUN
ejpam-5085	3	44	ain	ain	PROPN
ejpam-5085	3	45	chock	chock	PROPN
ejpam-5085	3	46	(	(	PUNCT
ejpam-5085	3	47	fsac	fsac	NOUN
ejpam-5085	3	48	)	)	PUNCT
ejpam-5085	3	49	,	,	PUNCT
ejpam-5085	3	50	university	university	PROPN
ejpam-5085	3	51	hassan	hassan	PROPN
ejpam-5085	3	52	ii	ii	PROPN
ejpam-5085	3	53	of	of	ADP
ejpam-5085	3	54	casablanca	casablanca	PROPN
ejpam-5085	3	55	(	(	PUNCT
ejpam-5085	3	56	univh2c	univh2c	PROPN
ejpam-5085	3	57	)	)	PUNCT
ejpam-5085	3	58	,	,	PUNCT
ejpam-5085	3	59	morocco	morocco	PROPN
ejpam-5085	3	60	.	.	PUNCT
ejpam-5085	4	1	abstract	abstract	ADJ
ejpam-5085	4	2	.	.	PUNCT
ejpam-5085	5	1	in	in	ADP
ejpam-5085	5	2	this	this	DET
ejpam-5085	5	3	paper	paper	NOUN
ejpam-5085	5	4	,	,	PUNCT
ejpam-5085	5	5	we	we	PRON
ejpam-5085	5	6	succeed	succeed	VERB
ejpam-5085	5	7	in	in	ADP
ejpam-5085	5	8	proving	prove	VERB
ejpam-5085	5	9	that	that	SCONJ
ejpam-5085	5	10	a	a	DET
ejpam-5085	5	11	connected	connected	ADJ
ejpam-5085	5	12	artin	artin	NOUN
ejpam-5085	5	13	algebra	algebra	NOUN
ejpam-5085	5	14	whose	whose	DET
ejpam-5085	5	15	jacobson	jacobson	PROPN
ejpam-5085	5	16	cubic	cubic	PROPN
ejpam-5085	5	17	radical	radical	PROPN
ejpam-5085	5	18	is	be	AUX
ejpam-5085	5	19	zero	zero	NUM
ejpam-5085	5	20	with	with	ADP
ejpam-5085	5	21	each	each	DET
ejpam-5085	5	22	simple	simple	ADJ
ejpam-5085	5	23	module	module	NOUN
ejpam-5085	5	24	and	and	CCONJ
ejpam-5085	5	25	each	each	DET
ejpam-5085	5	26	gorenstein	gorenstein	PROPN
ejpam-5085	5	27	projective	projective	NOUN
ejpam-5085	5	28	module	module	NOUN
ejpam-5085	5	29	having	have	VERB
ejpam-5085	5	30	the	the	DET
ejpam-5085	5	31	square	square	ADJ
ejpam-5085	5	32	radical	radical	NOUN
ejpam-5085	5	33	of	of	ADP
ejpam-5085	5	34	the	the	DET
ejpam-5085	5	35	cover	cover	NOUN
ejpam-5085	5	36	projective	projective	NOUN
ejpam-5085	5	37	of	of	ADP
ejpam-5085	5	38	its	its	PRON
ejpam-5085	5	39	first	first	ADJ
ejpam-5085	5	40	syzygy	syzygy	NOUN
ejpam-5085	5	41	to	to	PART
ejpam-5085	5	42	be	be	AUX
ejpam-5085	5	43	zero	zero	NUM
ejpam-5085	5	44	and	and	CCONJ
ejpam-5085	5	45	verifying	verify	VERB
ejpam-5085	5	46	the	the	DET
ejpam-5085	5	47	coincidence	coincidence	NOUN
ejpam-5085	5	48	covers	cover	NOUN
ejpam-5085	5	49	,	,	PUNCT
ejpam-5085	5	50	is	be	AUX
ejpam-5085	5	51	either	either	PRON
ejpam-5085	5	52	self	self	NOUN
ejpam-5085	5	53	-	-	PUNCT
ejpam-5085	5	54	injective	injective	ADJ
ejpam-5085	5	55	or	or	CCONJ
ejpam-5085	5	56	cm	cm	NOUN
ejpam-5085	5	57	-	-	PUNCT
ejpam-5085	5	58	free	free	ADJ
ejpam-5085	5	59	.	.	PUNCT
ejpam-5085	6	1	2020	2020	NUM
ejpam-5085	6	2	mathematics	mathematic	NOUN
ejpam-5085	6	3	subject	subject	NOUN
ejpam-5085	6	4	classifications	classification	NOUN
ejpam-5085	6	5	:	:	PUNCT
ejpam-5085	6	6	16p20	16p20	NUM
ejpam-5085	6	7	,	,	PUNCT
ejpam-5085	6	8	16p10	16p10	NUM
ejpam-5085	6	9	,	,	PUNCT
ejpam-5085	6	10	16g10	16g10	NUM
ejpam-5085	6	11	,	,	PUNCT
ejpam-5085	6	12	16n80	16n80	NUM
ejpam-5085	6	13	,	,	PUNCT
ejpam-5085	6	14	13h10	13h10	NUM
ejpam-5085	6	15	,	,	PUNCT
ejpam-5085	6	16	16e30	16e30	NUM
ejpam-5085	6	17	key	key	ADJ
ejpam-5085	6	18	words	word	NOUN
ejpam-5085	6	19	and	and	CCONJ
ejpam-5085	6	20	phrases	phrase	NOUN
ejpam-5085	6	21	:	:	PUNCT
ejpam-5085	6	22	artin	artin	PROPN
ejpam-5085	6	23	algebras	algebra	NOUN
ejpam-5085	6	24	,	,	PUNCT
ejpam-5085	6	25	representation	representation	NOUN
ejpam-5085	6	26	-	-	PUNCT
ejpam-5085	6	27	finite	finite	PROPN
ejpam-5085	6	28	algebras	algebra	NOUN
ejpam-5085	6	29	,	,	PUNCT
ejpam-5085	6	30	homological	homological	ADJ
ejpam-5085	6	31	algebra	algebra	NOUN
ejpam-5085	6	32	,	,	PUNCT
ejpam-5085	6	33	gorenstein	gorenstein	NOUN
ejpam-5085	6	34	algebra	algebra	PROPN
ejpam-5085	6	35	,	,	PUNCT
ejpam-5085	6	36	jacobson	jacobson	PROPN
ejpam-5085	6	37	radical	radical	ADJ
ejpam-5085	6	38	introduction	introduction	NOUN
ejpam-5085	6	39	let	let	VERB
ejpam-5085	6	40	k	k	PRON
ejpam-5085	6	41	be	be	AUX
ejpam-5085	6	42	a	a	DET
ejpam-5085	6	43	commutative	commutative	ADJ
ejpam-5085	6	44	ring	ring	NOUN
ejpam-5085	6	45	and	and	CCONJ
ejpam-5085	6	46	a	a	DET
ejpam-5085	6	47	an	an	DET
ejpam-5085	6	48	artin	artin	PROPN
ejpam-5085	6	49	algebra	algebra	NOUN
ejpam-5085	6	50	over	over	ADP
ejpam-5085	6	51	k	k	PROPN
ejpam-5085	6	52	of	of	ADP
ejpam-5085	6	53	jacobson	jacobson	PROPN
ejpam-5085	6	54	radical	radical	PROPN
ejpam-5085	6	55	with	with	ADP
ejpam-5085	6	56	nilpotency	nilpotency	NOUN
ejpam-5085	6	57	index	index	NOUN
ejpam-5085	6	58	3	3	NUM
ejpam-5085	6	59	,	,	PUNCT
ejpam-5085	6	60	mod(a	mod(a	PROPN
ejpam-5085	6	61	)	)	PUNCT
ejpam-5085	6	62	will	will	AUX
ejpam-5085	6	63	be	be	AUX
ejpam-5085	6	64	the	the	DET
ejpam-5085	6	65	category	category	NOUN
ejpam-5085	6	66	of	of	ADP
ejpam-5085	6	67	finitely	finitely	ADV
ejpam-5085	6	68	generated	generate	VERB
ejpam-5085	6	69	modules	module	NOUN
ejpam-5085	6	70	over	over	ADP
ejpam-5085	6	71	a	a	PRON
ejpam-5085	6	72	and	and	CCONJ
ejpam-5085	6	73	all	all	DET
ejpam-5085	6	74	modules	module	NOUN
ejpam-5085	6	75	in	in	ADP
ejpam-5085	6	76	this	this	DET
ejpam-5085	6	77	work	work	NOUN
ejpam-5085	6	78	are	be	AUX
ejpam-5085	6	79	in	in	ADP
ejpam-5085	6	80	left	leave	VERB
ejpam-5085	6	81	in	in	ADP
ejpam-5085	6	82	the	the	DET
ejpam-5085	6	83	category	category	NOUN
ejpam-5085	6	84	mod(a	mod(a	PROPN
ejpam-5085	6	85	)	)	PUNCT
ejpam-5085	6	86	,	,	PUNCT
ejpam-5085	6	87	we	we	PRON
ejpam-5085	6	88	know	know	VERB
ejpam-5085	6	89	that	that	SCONJ
ejpam-5085	6	90	the	the	DET
ejpam-5085	6	91	non	non	ADJ
ejpam-5085	6	92	-	-	ADJ
ejpam-5085	6	93	isomorphic	isomorphic	ADJ
ejpam-5085	6	94	simple	simple	ADJ
ejpam-5085	6	95	a	a	PRON
ejpam-5085	6	96	-	-	PUNCT
ejpam-5085	6	97	modules	module	NOUN
ejpam-5085	6	98	are	be	AUX
ejpam-5085	6	99	in	in	ADP
ejpam-5085	6	100	finite	finite	ADJ
ejpam-5085	6	101	number	number	NOUN
ejpam-5085	6	102	and	and	CCONJ
ejpam-5085	6	103	denoted	denote	VERB
ejpam-5085	6	104	(	(	PUNCT
ejpam-5085	6	105	si)i∈i	si)i∈i	NUM
ejpam-5085	6	106	allowing	allow	VERB
ejpam-5085	6	107	us	we	PRON
ejpam-5085	6	108	to	to	PART
ejpam-5085	6	109	define	define	VERB
ejpam-5085	6	110	the	the	DET
ejpam-5085	6	111	extension	extension	NOUN
ejpam-5085	6	112	quiver	quiver	NOUN
ejpam-5085	6	113	denoted	denote	VERB
ejpam-5085	6	114	qa	qa	NOUN
ejpam-5085	6	115	according	accord	VERB
ejpam-5085	6	116	to	to	ADP
ejpam-5085	6	117	the	the	DET
ejpam-5085	6	118	condition	condition	NOUN
ejpam-5085	6	119	ext1a(si	ext1a(si	PROPN
ejpam-5085	6	120	,	,	PUNCT
ejpam-5085	6	121	sj	sj	PROPN
ejpam-5085	6	122	)	)	PUNCT
ejpam-5085	6	123	̸=	̸=	PROPN
ejpam-5085	6	124	0	0	NUM
ejpam-5085	6	125	by	by	ADP
ejpam-5085	6	126	defining	define	VERB
ejpam-5085	6	127	an	an	DET
ejpam-5085	6	128	arrow	arrow	NOUN
ejpam-5085	6	129	from	from	ADP
ejpam-5085	6	130	si	si	PROPN
ejpam-5085	6	131	to	to	PART
ejpam-5085	6	132	sj	sj	VERB
ejpam-5085	6	133	thus	thus	ADV
ejpam-5085	6	134	a	a	PRON
ejpam-5085	6	135	is	be	AUX
ejpam-5085	6	136	connected	connect	VERB
ejpam-5085	6	137	if	if	SCONJ
ejpam-5085	6	138	and	and	CCONJ
ejpam-5085	6	139	only	only	ADV
ejpam-5085	6	140	if	if	SCONJ
ejpam-5085	6	141	the	the	DET
ejpam-5085	6	142	algebra	algebra	NOUN
ejpam-5085	6	143	qa	qa	PROPN
ejpam-5085	6	144	is	be	AUX
ejpam-5085	6	145	connected	connect	VERB
ejpam-5085	6	146	.	.	PUNCT
ejpam-5085	7	1	we	we	PRON
ejpam-5085	7	2	also	also	ADV
ejpam-5085	7	3	recall	recall	VERB
ejpam-5085	7	4	that	that	PRON
ejpam-5085	7	5	extna(m	extna(m	NOUN
ejpam-5085	7	6	,	,	PUNCT
ejpam-5085	7	7	n	n	CCONJ
ejpam-5085	7	8	)	)	PUNCT
ejpam-5085	7	9	=	=	SYM
ejpam-5085	7	10	hn(homa(p∗	hn(homa(p∗	PROPN
ejpam-5085	7	11	,	,	PUNCT
ejpam-5085	7	12	n	n	CCONJ
ejpam-5085	7	13	)	)	PUNCT
ejpam-5085	7	14	)	)	PUNCT
ejpam-5085	7	15	is	be	AUX
ejpam-5085	7	16	the	the	DET
ejpam-5085	7	17	nth	nth	NOUN
ejpam-5085	7	18	cohomology	cohomology	NOUN
ejpam-5085	7	19	of	of	ADP
ejpam-5085	7	20	the	the	DET
ejpam-5085	7	21	cochain	cochain	NOUN
ejpam-5085	7	22	complex	complex	NOUN
ejpam-5085	7	23	of	of	ADP
ejpam-5085	7	24	k	k	NOUN
ejpam-5085	7	25	-	-	PUNCT
ejpam-5085	7	26	modules	module	NOUN
ejpam-5085	7	27	homa(p∗	homa(p∗	NOUN
ejpam-5085	7	28	,	,	PUNCT
ejpam-5085	7	29	n	n	CCONJ
ejpam-5085	7	30	)	)	PUNCT
ejpam-5085	7	31	which	which	PRON
ejpam-5085	7	32	is	be	AUX
ejpam-5085	7	33	:	:	PUNCT
ejpam-5085	7	34	·	·	PUNCT
ejpam-5085	7	35	·	·	PUNCT
ejpam-5085	7	36	·	·	PUNCT
ejpam-5085	8	1	//	//	PUNCT
ejpam-5085	8	2	0	0	NUM
ejpam-5085	8	3	//	//	SYM
ejpam-5085	8	4	homa(p0	homa(p0	PROPN
ejpam-5085	8	5	,	,	PUNCT
ejpam-5085	8	6	n	n	CCONJ
ejpam-5085	8	7	)	)	PUNCT
ejpam-5085	8	8	//	//	SYM
ejpam-5085	8	9	homa(p1	homa(p1	NOUN
ejpam-5085	8	10	,	,	PUNCT
ejpam-5085	8	11	n	n	CCONJ
ejpam-5085	8	12	)	)	PUNCT
ejpam-5085	8	13	//	//	X
ejpam-5085	8	14	homa(p2	homa(p2	ADJ
ejpam-5085	8	15	,	,	PUNCT
ejpam-5085	8	16	n	n	CCONJ
ejpam-5085	8	17	)	)	PUNCT
ejpam-5085	8	18	//	//	X
ejpam-5085	8	19	·	·	PUNCT
ejpam-5085	8	20	·	·	PUNCT
ejpam-5085	8	21	·	·	PUNCT
ejpam-5085	8	22	where	where	SCONJ
ejpam-5085	8	23	homa(pn	homa(pn	NOUN
ejpam-5085	8	24	,	,	PUNCT
ejpam-5085	8	25	n	n	CCONJ
ejpam-5085	8	26	)	)	PUNCT
ejpam-5085	8	27	is	be	AUX
ejpam-5085	8	28	in	in	ADP
ejpam-5085	8	29	degree	degree	NOUN
ejpam-5085	8	30	n	n	NOUN
ejpam-5085	8	31	and	and	CCONJ
ejpam-5085	8	32	p∗	p∗	VERB
ejpam-5085	8	33	the	the	DET
ejpam-5085	8	34	complex	complex	NOUN
ejpam-5085	8	35	deduced	deduce	VERB
ejpam-5085	8	36	from	from	ADP
ejpam-5085	8	37	the	the	DET
ejpam-5085	8	38	projective	projective	ADJ
ejpam-5085	8	39	resolution	resolution	NOUN
ejpam-5085	8	40	of	of	ADP
ejpam-5085	8	41	m	m	PROPN
ejpam-5085	8	42	,	,	PUNCT
ejpam-5085	8	43	where	where	SCONJ
ejpam-5085	8	44	a	a	PRON
ejpam-5085	8	45	is	be	AUX
ejpam-5085	8	46	a	a	DET
ejpam-5085	8	47	k	k	NOUN
ejpam-5085	8	48	-	-	NOUN
ejpam-5085	8	49	algebra	algebra	NOUN
ejpam-5085	8	50	with	with	ADP
ejpam-5085	8	51	k	k	PROPN
ejpam-5085	8	52	is	be	AUX
ejpam-5085	8	53	a	a	DET
ejpam-5085	8	54	commutative	commutative	ADJ
ejpam-5085	8	55	ring	ring	NOUN
ejpam-5085	8	56	.	.	PUNCT
ejpam-5085	9	1	in	in	ADP
ejpam-5085	9	2	2012	2012	NUM
ejpam-5085	9	3	,	,	PUNCT
ejpam-5085	9	4	xiao	xiao	PROPN
ejpam-5085	9	5	-	-	PUNCT
ejpam-5085	9	6	wu	wu	PROPN
ejpam-5085	9	7	chen	chen	PROPN
ejpam-5085	9	8	classified	classify	VERB
ejpam-5085	9	9	the	the	DET
ejpam-5085	9	10	algebras	algebra	NOUN
ejpam-5085	9	11	whose	whose	DET
ejpam-5085	9	12	radical	radical	ADJ
ejpam-5085	9	13	square	square	NOUN
ejpam-5085	9	14	is	be	AUX
ejpam-5085	9	15	zero	zero	NUM
ejpam-5085	9	16	and	and	CCONJ
ejpam-5085	9	17	showed	show	VERB
ejpam-5085	9	18	∗corresponding	∗corresponde	VERB
ejpam-5085	9	19	author	author	NOUN
ejpam-5085	9	20	.	.	PUNCT
ejpam-5085	10	1	doi	doi	NOUN
ejpam-5085	10	2	:	:	PUNCT
ejpam-5085	10	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5085	https://doi.org/10.29020/nybg.ejpam.v17i2.5085	NUM
ejpam-5085	10	4	email	email	NOUN
ejpam-5085	10	5	addresses	address	NOUN
ejpam-5085	10	6	:	:	PUNCT
ejpam-5085	10	7	mounirlaaraj2@gmail.com	mounirlaaraj2@gmail.com	X
ejpam-5085	10	8	(	(	PUNCT
ejpam-5085	10	9	m.	m.	NOUN
ejpam-5085	10	10	laaraj	laaraj	PROPN
ejpam-5085	10	11	)	)	PUNCT
ejpam-5085	10	12	,	,	PUNCT
ejpam-5085	10	13	seddikabd@hotmail.com	seddikabd@hotmail.com	X
ejpam-5085	11	1	(	(	PUNCT
ejpam-5085	11	2	s.	s.	PROPN
ejpam-5085	11	3	abdelalim	abdelalim	PROPN
ejpam-5085	11	4	)	)	PUNCT
ejpam-5085	11	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5085	11	6	1197	1197	NUM
ejpam-5085	12	1	©	©	ADP
ejpam-5085	12	2	2024	2024	NUM
ejpam-5085	12	3	ejpam	ejpam	NOUN
ejpam-5085	12	4	all	all	DET
ejpam-5085	12	5	rights	right	NOUN
ejpam-5085	12	6	reserved	reserve	VERB
ejpam-5085	12	7	.	.	PUNCT
ejpam-5085	13	1	m.	m.	NOUN
ejpam-5085	13	2	laaraj	laaraj	PROPN
ejpam-5085	13	3	,	,	PUNCT
ejpam-5085	13	4	s.	s.	PROPN
ejpam-5085	13	5	abdelalim	abdelalim	PROPN
ejpam-5085	13	6	/	/	SYM
ejpam-5085	13	7	eur	eur	PROPN
ejpam-5085	13	8	.	.	PUNCT
ejpam-5085	14	1	j.	j.	PROPN
ejpam-5085	14	2	pure	pure	PROPN
ejpam-5085	14	3	appl	appl	PROPN
ejpam-5085	14	4	.	.	PROPN
ejpam-5085	14	5	math	math	PROPN
ejpam-5085	14	6	,	,	PUNCT
ejpam-5085	14	7	17	17	NUM
ejpam-5085	14	8	(	(	PUNCT
ejpam-5085	14	9	2	2	NUM
ejpam-5085	14	10	)	)	PUNCT
ejpam-5085	14	11	(	(	PUNCT
ejpam-5085	14	12	2024	2024	NUM
ejpam-5085	14	13	)	)	PUNCT
ejpam-5085	14	14	,	,	PUNCT
ejpam-5085	14	15	1197	1197	NUM
ejpam-5085	14	16	-	-	SYM
ejpam-5085	14	17	1205	1205	NUM
ejpam-5085	14	18	1198	1198	NUM
ejpam-5085	14	19	that	that	PRON
ejpam-5085	14	20	they	they	PRON
ejpam-5085	14	21	are	be	AUX
ejpam-5085	14	22	either	either	PRON
ejpam-5085	14	23	self	self	NOUN
ejpam-5085	14	24	-	-	PUNCT
ejpam-5085	14	25	injective	injective	ADJ
ejpam-5085	14	26	or	or	CCONJ
ejpam-5085	14	27	cm	cm	NOUN
ejpam-5085	14	28	-	-	PUNCT
ejpam-5085	14	29	free	free	ADJ
ejpam-5085	14	30	,	,	PUNCT
ejpam-5085	14	31	see	see	VERB
ejpam-5085	14	32	[	[	X
ejpam-5085	14	33	5	5	NUM
ejpam-5085	14	34	]	]	PUNCT
ejpam-5085	14	35	.	.	PUNCT
ejpam-5085	15	1	however	however	ADV
ejpam-5085	15	2	,	,	PUNCT
ejpam-5085	15	3	this	this	DET
ejpam-5085	15	4	result	result	NOUN
ejpam-5085	15	5	has	have	AUX
ejpam-5085	15	6	never	never	ADV
ejpam-5085	15	7	been	be	AUX
ejpam-5085	15	8	proven	prove	VERB
ejpam-5085	15	9	in	in	ADP
ejpam-5085	15	10	the	the	DET
ejpam-5085	15	11	case	case	NOUN
ejpam-5085	15	12	of	of	ADP
ejpam-5085	15	13	cube	cube	NOUN
ejpam-5085	15	14	radical	radical	ADJ
ejpam-5085	15	15	0	0	NUM
ejpam-5085	15	16	and	and	CCONJ
ejpam-5085	15	17	the	the	DET
ejpam-5085	15	18	same	same	ADJ
ejpam-5085	15	19	author	author	NOUN
ejpam-5085	15	20	pointed	point	VERB
ejpam-5085	15	21	out	out	ADP
ejpam-5085	15	22	that	that	SCONJ
ejpam-5085	15	23	it	it	PRON
ejpam-5085	15	24	is	be	AUX
ejpam-5085	15	25	false	false	ADJ
ejpam-5085	15	26	using	use	VERB
ejpam-5085	15	27	a	a	DET
ejpam-5085	15	28	counter	counter	NOUN
ejpam-5085	15	29	-	-	NOUN
ejpam-5085	15	30	example	example	NOUN
ejpam-5085	15	31	with	with	ADP
ejpam-5085	15	32	a	a	DET
ejpam-5085	15	33	non	non	ADJ
ejpam-5085	15	34	-	-	ADJ
ejpam-5085	15	35	zero	zero	NUM
ejpam-5085	15	36	square	square	ADJ
ejpam-5085	15	37	radical	radical	ADJ
ejpam-5085	15	38	algebra	algebra	NOUN
ejpam-5085	15	39	.	.	PUNCT
ejpam-5085	16	1	one	one	NUM
ejpam-5085	16	2	year	year	NOUN
ejpam-5085	16	3	later	later	ADV
ejpam-5085	16	4	,	,	PUNCT
ejpam-5085	16	5	luo	luo	PROPN
ejpam-5085	16	6	rong	rong	PROPN
ejpam-5085	16	7	proved	prove	VERB
ejpam-5085	16	8	that	that	SCONJ
ejpam-5085	16	9	all	all	DET
ejpam-5085	16	10	local	local	ADJ
ejpam-5085	16	11	algebras	algebra	NOUN
ejpam-5085	16	12	with	with	ADP
ejpam-5085	16	13	radical	radical	ADJ
ejpam-5085	16	14	cubic	cubic	ADJ
ejpam-5085	16	15	zero	zero	NUM
ejpam-5085	16	16	are	be	AUX
ejpam-5085	16	17	pcmfree	pcmfree	NOUN
ejpam-5085	16	18	,	,	PUNCT
ejpam-5085	16	19	see	see	VERB
ejpam-5085	16	20	[	[	X
ejpam-5085	16	21	2	2	X
ejpam-5085	16	22	]	]	PUNCT
ejpam-5085	16	23	.	.	PUNCT
ejpam-5085	17	1	an	an	DET
ejpam-5085	17	2	important	important	ADJ
ejpam-5085	17	3	invariant	invariant	NOUN
ejpam-5085	17	4	in	in	ADP
ejpam-5085	17	5	our	our	PRON
ejpam-5085	17	6	subject	subject	NOUN
ejpam-5085	17	7	is	be	AUX
ejpam-5085	17	8	the	the	DET
ejpam-5085	17	9	radical	radical	ADJ
ejpam-5085	17	10	square	square	NOUN
ejpam-5085	17	11	of	of	ADP
ejpam-5085	17	12	the	the	DET
ejpam-5085	17	13	projective	projective	ADJ
ejpam-5085	17	14	cover	cover	NOUN
ejpam-5085	17	15	of	of	ADP
ejpam-5085	17	16	the	the	DET
ejpam-5085	17	17	first	first	ADJ
ejpam-5085	17	18	syzygy	syzygy	NOUN
ejpam-5085	17	19	of	of	ADP
ejpam-5085	17	20	each	each	DET
ejpam-5085	17	21	simple	simple	ADJ
ejpam-5085	17	22	a	a	DET
ejpam-5085	17	23	-	-	PUNCT
ejpam-5085	17	24	module	module	NOUN
ejpam-5085	17	25	and	and	CCONJ
ejpam-5085	17	26	each	each	PRON
ejpam-5085	17	27	gorenstein	gorenstein	NOUN
ejpam-5085	17	28	-	-	PUNCT
ejpam-5085	17	29	projective	projective	NOUN
ejpam-5085	17	30	a	a	NOUN
ejpam-5085	17	31	-	-	PUNCT
ejpam-5085	17	32	module	module	NOUN
ejpam-5085	17	33	that	that	PRON
ejpam-5085	17	34	we	we	PRON
ejpam-5085	17	35	consider	consider	VERB
ejpam-5085	17	36	here	here	ADV
ejpam-5085	17	37	to	to	PART
ejpam-5085	17	38	be	be	AUX
ejpam-5085	17	39	0	0	NUM
ejpam-5085	17	40	,	,	PUNCT
ejpam-5085	17	41	so	so	ADV
ejpam-5085	17	42	by	by	ADP
ejpam-5085	17	43	a	a	DET
ejpam-5085	17	44	formula	formula	NOUN
ejpam-5085	17	45	characterizing	characterize	VERB
ejpam-5085	17	46	the	the	DET
ejpam-5085	17	47	calculation	calculation	NOUN
ejpam-5085	17	48	of	of	ADP
ejpam-5085	17	49	the	the	DET
ejpam-5085	17	50	radical	radical	NOUN
ejpam-5085	17	51	of	of	ADP
ejpam-5085	17	52	syzygy	syzygy	NOUN
ejpam-5085	17	53	of	of	ADP
ejpam-5085	17	54	an	an	DET
ejpam-5085	17	55	indecomposable	indecomposable	ADJ
ejpam-5085	17	56	a	a	NOUN
ejpam-5085	17	57	-	-	PUNCT
ejpam-5085	17	58	module	module	NOUN
ejpam-5085	17	59	of	of	ADP
ejpam-5085	17	60	lowey	lowey	PROPN
ejpam-5085	17	61	length	length	NOUN
ejpam-5085	17	62	2	2	NUM
ejpam-5085	17	63	,	,	PUNCT
ejpam-5085	17	64	that	that	PRON
ejpam-5085	17	65	is	be	AUX
ejpam-5085	17	66	to	to	PART
ejpam-5085	17	67	say	say	VERB
ejpam-5085	17	68	from	from	ADP
ejpam-5085	17	69	the	the	DET
ejpam-5085	17	70	square	square	ADJ
ejpam-5085	17	71	radical	radical	ADJ
ejpam-5085	17	72	0	0	NUM
ejpam-5085	17	73	,	,	PUNCT
ejpam-5085	17	74	we	we	PRON
ejpam-5085	17	75	will	will	AUX
ejpam-5085	17	76	extend	extend	VERB
ejpam-5085	17	77	this	this	DET
ejpam-5085	17	78	calculation	calculation	NOUN
ejpam-5085	17	79	to	to	ADP
ejpam-5085	17	80	a	a	DET
ejpam-5085	17	81	gorenstein	gorenstein	NOUN
ejpam-5085	17	82	-	-	PUNCT
ejpam-5085	17	83	projective	projective	NOUN
ejpam-5085	17	84	a	a	NOUN
ejpam-5085	17	85	-	-	PUNCT
ejpam-5085	17	86	module	module	NOUN
ejpam-5085	17	87	and	and	CCONJ
ejpam-5085	17	88	by	by	ADP
ejpam-5085	17	89	characterization	characterization	NOUN
ejpam-5085	17	90	of	of	ADP
ejpam-5085	17	91	the	the	DET
ejpam-5085	17	92	latter	latter	ADJ
ejpam-5085	17	93	,	,	PUNCT
ejpam-5085	17	94	we	we	PRON
ejpam-5085	17	95	construct	construct	VERB
ejpam-5085	17	96	a	a	DET
ejpam-5085	17	97	family	family	NOUN
ejpam-5085	17	98	(	(	PUNCT
ejpam-5085	17	99	si)i∈j	si)i∈j	NUM
ejpam-5085	17	100	of	of	ADP
ejpam-5085	17	101	simple	simple	ADJ
ejpam-5085	17	102	a	a	DET
ejpam-5085	17	103	-	-	PUNCT
ejpam-5085	17	104	modules	module	NOUN
ejpam-5085	17	105	non	non	ADJ
ejpam-5085	17	106	-	-	ADJ
ejpam-5085	17	107	projective	projective	ADJ
ejpam-5085	17	108	and	and	CCONJ
ejpam-5085	17	109	gorenstein	gorenstein	NOUN
ejpam-5085	17	110	-	-	PUNCT
ejpam-5085	17	111	projective	projective	NOUN
ejpam-5085	17	112	and	and	CCONJ
ejpam-5085	17	113	the	the	DET
ejpam-5085	17	114	family	family	NOUN
ejpam-5085	17	115	(	(	PUNCT
ejpam-5085	17	116	pi)i∈j	pi)i∈j	NUM
ejpam-5085	17	117	of	of	ADP
ejpam-5085	17	118	projective	projective	ADJ
ejpam-5085	17	119	modules	module	NOUN
ejpam-5085	17	120	such	such	ADJ
ejpam-5085	17	121	that	that	SCONJ
ejpam-5085	17	122	each	each	DET
ejpam-5085	17	123	pi	pi	NOUN
ejpam-5085	17	124	is	be	AUX
ejpam-5085	17	125	associated	associate	VERB
ejpam-5085	17	126	to	to	ADP
ejpam-5085	17	127	si	si	PROPN
ejpam-5085	17	128	.	.	PUNCT
ejpam-5085	18	1	the	the	DET
ejpam-5085	18	2	quiver	quiver	PROPN
ejpam-5085	18	3	qa	qa	PROPN
ejpam-5085	18	4	will	will	AUX
ejpam-5085	18	5	be	be	AUX
ejpam-5085	18	6	connected	connect	VERB
ejpam-5085	18	7	,	,	PUNCT
ejpam-5085	18	8	which	which	PRON
ejpam-5085	18	9	implies	imply	VERB
ejpam-5085	18	10	the	the	DET
ejpam-5085	18	11	self	self	NOUN
ejpam-5085	18	12	-	-	PUNCT
ejpam-5085	18	13	injectivity	injectivity	NOUN
ejpam-5085	18	14	for	for	ADP
ejpam-5085	18	15	the	the	DET
ejpam-5085	18	16	algebra	algebra	NOUN
ejpam-5085	18	17	a	a	PRON
ejpam-5085	18	18	with	with	ADP
ejpam-5085	18	19	zero	zero	NUM
ejpam-5085	18	20	radical	radical	ADJ
ejpam-5085	18	21	cubic	cubic	NOUN
ejpam-5085	18	22	.	.	PUNCT
ejpam-5085	19	1	since	since	SCONJ
ejpam-5085	19	2	that	that	DET
ejpam-5085	19	3	assumption	assumption	NOUN
ejpam-5085	19	4	is	be	AUX
ejpam-5085	19	5	not	not	PART
ejpam-5085	19	6	always	always	ADV
ejpam-5085	19	7	true	true	ADJ
ejpam-5085	19	8	,	,	PUNCT
ejpam-5085	19	9	we	we	PRON
ejpam-5085	19	10	succeed	succeed	VERB
ejpam-5085	19	11	by	by	ADP
ejpam-5085	19	12	using	use	VERB
ejpam-5085	19	13	our	our	PRON
ejpam-5085	19	14	condition	condition	NOUN
ejpam-5085	19	15	,	,	PUNCT
ejpam-5085	19	16	to	to	PART
ejpam-5085	19	17	establish	establish	VERB
ejpam-5085	19	18	that	that	SCONJ
ejpam-5085	19	19	the	the	DET
ejpam-5085	19	20	property	property	NOUN
ejpam-5085	19	21	of	of	ADP
ejpam-5085	19	22	auto	auto	NOUN
ejpam-5085	19	23	-	-	PUNCT
ejpam-5085	19	24	injectivity	injectivity	NOUN
ejpam-5085	19	25	and	and	CCONJ
ejpam-5085	19	26	cm	cm	NOUN
ejpam-5085	19	27	-	-	PUNCT
ejpam-5085	19	28	free	free	ADJ
ejpam-5085	19	29	remain	remain	VERB
ejpam-5085	19	30	valid	valid	ADJ
ejpam-5085	19	31	.	.	PUNCT
ejpam-5085	20	1	if	if	SCONJ
ejpam-5085	20	2	m	m	NOUN
ejpam-5085	20	3	is	be	AUX
ejpam-5085	20	4	an	an	DET
ejpam-5085	20	5	a	a	DET
ejpam-5085	20	6	-	-	PUNCT
ejpam-5085	20	7	module	module	NOUN
ejpam-5085	20	8	,	,	PUNCT
ejpam-5085	20	9	we	we	PRON
ejpam-5085	20	10	note	note	VERB
ejpam-5085	20	11	ω(m	ω(m	NOUN
ejpam-5085	20	12	)	)	PUNCT
ejpam-5085	20	13	as	as	SCONJ
ejpam-5085	20	14	the	the	DET
ejpam-5085	20	15	first	first	ADJ
ejpam-5085	20	16	syzygy	syzygy	NOUN
ejpam-5085	20	17	of	of	ADP
ejpam-5085	20	18	m	m	PROPN
ejpam-5085	20	19	and	and	CCONJ
ejpam-5085	20	20	p	p	X
ejpam-5085	20	21	(	(	PUNCT
ejpam-5085	20	22	m	m	NOUN
ejpam-5085	20	23	)	)	PUNCT
ejpam-5085	20	24	as	as	ADP
ejpam-5085	20	25	the	the	DET
ejpam-5085	20	26	projective	projective	ADJ
ejpam-5085	20	27	cover	cover	NOUN
ejpam-5085	20	28	of	of	ADP
ejpam-5085	20	29	m	m	NOUN
ejpam-5085	20	30	with	with	ADP
ejpam-5085	20	31	ω(m	ω(m	NOUN
ejpam-5085	20	32	)	)	PUNCT
ejpam-5085	20	33	is	be	AUX
ejpam-5085	20	34	the	the	DET
ejpam-5085	20	35	kernel	kernel	NOUN
ejpam-5085	20	36	of	of	ADP
ejpam-5085	20	37	the	the	DET
ejpam-5085	20	38	essential	essential	ADJ
ejpam-5085	20	39	epimorphism	epimorphism	NOUN
ejpam-5085	20	40	:	:	PUNCT
ejpam-5085	20	41	p	p	X
ejpam-5085	20	42	(	(	PUNCT
ejpam-5085	20	43	m	m	NOUN
ejpam-5085	20	44	)	)	PUNCT
ejpam-5085	20	45	−→	−→	NOUN
ejpam-5085	20	46	m	m	VERB
ejpam-5085	20	47	ie	ie	X
ejpam-5085	20	48	p	p	PROPN
ejpam-5085	20	49	(	(	PUNCT
ejpam-5085	20	50	m)/rad(m	m)/rad(m	NOUN
ejpam-5085	20	51	)	)	PUNCT
ejpam-5085	20	52	≃	≃	DET
ejpam-5085	20	53	m	m	PROPN
ejpam-5085	20	54	/	/	SYM
ejpam-5085	20	55	rad(m	rad(m	ADJ
ejpam-5085	20	56	)	)	PUNCT
ejpam-5085	20	57	see	see	VERB
ejpam-5085	20	58	[	[	X
ejpam-5085	20	59	4	4	NUM
ejpam-5085	20	60	]	]	PUNCT
ejpam-5085	20	61	,	,	PUNCT
ejpam-5085	20	62	similarly	similarly	ADV
ejpam-5085	20	63	we	we	PRON
ejpam-5085	20	64	note	note	VERB
ejpam-5085	20	65	ω2(m	ω2(m	ADP
ejpam-5085	20	66	)	)	PUNCT
ejpam-5085	20	67	=	=	SYM
ejpam-5085	20	68	ω(ω(m	ω(ω(m	NOUN
ejpam-5085	20	69	)	)	PUNCT
ejpam-5085	20	70	)	)	PUNCT
ejpam-5085	20	71	.	.	PUNCT
ejpam-5085	21	1	in	in	ADP
ejpam-5085	21	2	the	the	DET
ejpam-5085	21	3	upcoming	upcoming	ADJ
ejpam-5085	21	4	parts	part	NOUN
ejpam-5085	21	5	of	of	ADP
ejpam-5085	21	6	the	the	DET
ejpam-5085	21	7	paper	paper	NOUN
ejpam-5085	21	8	,	,	PUNCT
ejpam-5085	21	9	we	we	PRON
ejpam-5085	21	10	start	start	VERB
ejpam-5085	21	11	by	by	ADP
ejpam-5085	21	12	discussing	discuss	VERB
ejpam-5085	21	13	some	some	DET
ejpam-5085	21	14	properties	property	NOUN
ejpam-5085	21	15	of	of	ADP
ejpam-5085	21	16	the	the	DET
ejpam-5085	21	17	gorensteinprojective	gorensteinprojective	ADJ
ejpam-5085	21	18	modules	module	NOUN
ejpam-5085	21	19	,	,	PUNCT
ejpam-5085	21	20	then	then	ADV
ejpam-5085	21	21	in	in	ADP
ejpam-5085	21	22	the	the	DET
ejpam-5085	21	23	case	case	NOUN
ejpam-5085	21	24	of	of	ADP
ejpam-5085	21	25	an	an	DET
ejpam-5085	21	26	artin	artin	PROPN
ejpam-5085	21	27	algebra	algebra	NOUN
ejpam-5085	21	28	a	a	PRON
ejpam-5085	21	29	whose	whose	DET
ejpam-5085	21	30	jacobson	jacobson	PROPN
ejpam-5085	21	31	cubic	cubic	PROPN
ejpam-5085	21	32	radical	radical	PROPN
ejpam-5085	21	33	is	be	AUX
ejpam-5085	21	34	zero	zero	NUM
ejpam-5085	21	35	while	while	SCONJ
ejpam-5085	21	36	considering	consider	VERB
ejpam-5085	21	37	a	a	DET
ejpam-5085	21	38	non	non	ADJ
ejpam-5085	21	39	-	-	ADJ
ejpam-5085	21	40	projective	projective	ADJ
ejpam-5085	21	41	and	and	CCONJ
ejpam-5085	21	42	indecomposable	indecomposable	ADJ
ejpam-5085	21	43	gorenstein	gorenstein	NOUN
ejpam-5085	21	44	-	-	PUNCT
ejpam-5085	21	45	projective	projective	NOUN
ejpam-5085	21	46	,	,	PUNCT
ejpam-5085	21	47	we	we	PRON
ejpam-5085	21	48	characterize	characterize	VERB
ejpam-5085	21	49	the	the	DET
ejpam-5085	21	50	radical	radical	NOUN
ejpam-5085	21	51	of	of	ADP
ejpam-5085	21	52	syzygy	syzygy	NOUN
ejpam-5085	21	53	of	of	ADP
ejpam-5085	21	54	an	an	DET
ejpam-5085	21	55	a	a	DET
ejpam-5085	21	56	-	-	PUNCT
ejpam-5085	21	57	module	module	NOUN
ejpam-5085	21	58	.	.	PUNCT
ejpam-5085	22	1	finally	finally	ADV
ejpam-5085	22	2	,	,	PUNCT
ejpam-5085	22	3	we	we	PRON
ejpam-5085	22	4	prove	prove	VERB
ejpam-5085	22	5	by	by	ADP
ejpam-5085	22	6	using	use	VERB
ejpam-5085	22	7	our	our	PRON
ejpam-5085	22	8	condition	condition	NOUN
ejpam-5085	22	9	,	,	PUNCT
ejpam-5085	22	10	that	that	SCONJ
ejpam-5085	22	11	the	the	DET
ejpam-5085	22	12	properties	property	NOUN
ejpam-5085	22	13	of	of	ADP
ejpam-5085	22	14	self	self	NOUN
ejpam-5085	22	15	-	-	PUNCT
ejpam-5085	22	16	injectivity	injectivity	NOUN
ejpam-5085	22	17	and	and	CCONJ
ejpam-5085	22	18	cm	cm	NOUN
ejpam-5085	22	19	-	-	PUNCT
ejpam-5085	22	20	free	free	ADJ
ejpam-5085	22	21	remain	remain	VERB
ejpam-5085	22	22	true	true	ADJ
ejpam-5085	22	23	.	.	PUNCT
ejpam-5085	23	1	1	1	X
ejpam-5085	23	2	.	.	X
ejpam-5085	23	3	gorenstein	gorenstein	ADJ
ejpam-5085	23	4	-	-	PUNCT
ejpam-5085	23	5	projective	projective	NOUN
ejpam-5085	23	6	modules	module	NOUN
ejpam-5085	23	7	1.1	1.1	NUM
ejpam-5085	23	8	definition	definition	NOUN
ejpam-5085	23	9	.	.	PUNCT
ejpam-5085	24	1	recall	recall	VERB
ejpam-5085	24	2	that	that	SCONJ
ejpam-5085	24	3	the	the	DET
ejpam-5085	24	4	infinite	infinite	ADJ
ejpam-5085	24	5	sequence	sequence	NOUN
ejpam-5085	24	6	of	of	ADP
ejpam-5085	24	7	amodules	amodule	NOUN
ejpam-5085	24	8	(	(	PUNCT
ejpam-5085	24	9	cn)n∈z	cn)n∈z	NUM
ejpam-5085	24	10	:	:	PUNCT
ejpam-5085	24	11	·	·	PUNCT
ejpam-5085	24	12	·	·	PUNCT
ejpam-5085	24	13	·	·	PUNCT
ejpam-5085	25	1	//	//	NUM
ejpam-5085	25	2	cn−1	cn−1	PROPN
ejpam-5085	25	3	dn−1	dn−1	PROPN
ejpam-5085	25	4	//	//	PROPN
ejpam-5085	26	1	cn	cn	PROPN
ejpam-5085	27	1	dn	dn	PROPN
ejpam-5085	27	2	//	//	NUM
ejpam-5085	27	3	cn+1	cn+1	PROPN
ejpam-5085	27	4	dn+1	dn+1	X
ejpam-5085	27	5	//	//	X
ejpam-5085	27	6	·	·	PUNCT
ejpam-5085	27	7	·	·	PUNCT
ejpam-5085	27	8	·	·	PUNCT
ejpam-5085	27	9	is	be	AUX
ejpam-5085	27	10	called	call	VERB
ejpam-5085	27	11	complex	complex	ADJ
ejpam-5085	27	12	and	and	CCONJ
ejpam-5085	27	13	denoted	denote	VERB
ejpam-5085	27	14	c⋆	c⋆	ADV
ejpam-5085	27	15	if	if	SCONJ
ejpam-5085	27	16	im(dn−1	im(dn−1	NUM
ejpam-5085	27	17	)	)	PUNCT
ejpam-5085	27	18	⊆	⊆	NUM
ejpam-5085	27	19	ker(dn	ker(dn	X
ejpam-5085	27	20	)	)	PUNCT
ejpam-5085	27	21	.	.	PUNCT
ejpam-5085	28	1	denote	denote	VERB
ejpam-5085	28	2	bn(c⋆	bn(c⋆	NOUN
ejpam-5085	28	3	)	)	PUNCT
ejpam-5085	29	1	=	=	SYM
ejpam-5085	29	2	im(dn−1	im(dn−1	PROPN
ejpam-5085	29	3	)	)	PUNCT
ejpam-5085	29	4	,	,	PUNCT
ejpam-5085	29	5	zn(c⋆	zn(c⋆	NUM
ejpam-5085	29	6	)	)	PUNCT
ejpam-5085	29	7	=	=	SYM
ejpam-5085	29	8	ker(dn	ker(dn	X
ejpam-5085	29	9	)	)	PUNCT
ejpam-5085	29	10	and	and	CCONJ
ejpam-5085	29	11	hn(c⋆	hn(c⋆	NOUN
ejpam-5085	29	12	)	)	PUNCT
ejpam-5085	29	13	=	=	SYM
ejpam-5085	29	14	zn(c⋆)/b	zn(c⋆)/b	NOUN
ejpam-5085	29	15	n(c⋆	n(c⋆	NOUN
ejpam-5085	29	16	)	)	PUNCT
ejpam-5085	29	17	where	where	SCONJ
ejpam-5085	29	18	zn(c⋆	zn(c⋆	NOUN
ejpam-5085	29	19	)	)	PUNCT
ejpam-5085	29	20	is	be	AUX
ejpam-5085	29	21	called	call	VERB
ejpam-5085	29	22	cocycle	cocycle	NOUN
ejpam-5085	29	23	and	and	CCONJ
ejpam-5085	29	24	the	the	DET
ejpam-5085	29	25	complex	complex	NOUN
ejpam-5085	29	26	c⋆	c⋆	ADV
ejpam-5085	29	27	is	be	AUX
ejpam-5085	29	28	called	call	VERB
ejpam-5085	29	29	acyclic	acyclic	ADJ
ejpam-5085	29	30	if	if	SCONJ
ejpam-5085	29	31	it	it	PRON
ejpam-5085	29	32	is	be	AUX
ejpam-5085	29	33	an	an	DET
ejpam-5085	29	34	exact	exact	ADJ
ejpam-5085	29	35	sequence	sequence	NOUN
ejpam-5085	29	36	,	,	PUNCT
ejpam-5085	29	37	i.e.	i.e.	X
ejpam-5085	29	38	hn(c⋆	hn(c⋆	NOUN
ejpam-5085	29	39	)	)	PUNCT
ejpam-5085	29	40	=	=	SYM
ejpam-5085	29	41	0	0	NUM
ejpam-5085	29	42	for	for	ADP
ejpam-5085	29	43	all	all	DET
ejpam-5085	29	44	n.	n.	PROPN
ejpam-5085	29	45	1.2	1.2	NUM
ejpam-5085	29	46	remark	remark	NOUN
ejpam-5085	29	47	.	.	PUNCT
ejpam-5085	30	1	if	if	SCONJ
ejpam-5085	30	2	the	the	DET
ejpam-5085	30	3	cn	cn	PROPN
ejpam-5085	30	4	’s	’s	PART
ejpam-5085	30	5	are	be	AUX
ejpam-5085	30	6	projective	projective	ADJ
ejpam-5085	30	7	for	for	ADP
ejpam-5085	30	8	all	all	DET
ejpam-5085	30	9	n	n	PRON
ejpam-5085	30	10	and	and	CCONJ
ejpam-5085	30	11	hom(c⋆	hom(c⋆	PROPN
ejpam-5085	30	12	,	,	PUNCT
ejpam-5085	30	13	a	a	PRON
ejpam-5085	30	14	)	)	PUNCT
ejpam-5085	30	15	is	be	AUX
ejpam-5085	30	16	acylic	acylic	ADJ
ejpam-5085	30	17	,	,	PUNCT
ejpam-5085	30	18	then	then	ADV
ejpam-5085	30	19	c⋆	c⋆	ADV
ejpam-5085	30	20	is	be	AUX
ejpam-5085	30	21	called	call	VERB
ejpam-5085	30	22	totally	totally	ADV
ejpam-5085	30	23	acyclic	acyclic	ADJ
ejpam-5085	30	24	.	.	PUNCT
ejpam-5085	31	1	m.	m.	NOUN
ejpam-5085	31	2	laaraj	laaraj	PROPN
ejpam-5085	31	3	,	,	PUNCT
ejpam-5085	31	4	s.	s.	PROPN
ejpam-5085	31	5	abdelalim	abdelalim	PROPN
ejpam-5085	31	6	/	/	SYM
ejpam-5085	31	7	eur	eur	PROPN
ejpam-5085	31	8	.	.	PUNCT
ejpam-5085	32	1	j.	j.	PROPN
ejpam-5085	32	2	pure	pure	PROPN
ejpam-5085	32	3	appl	appl	PROPN
ejpam-5085	32	4	.	.	PROPN
ejpam-5085	32	5	math	math	PROPN
ejpam-5085	32	6	,	,	PUNCT
ejpam-5085	32	7	17	17	NUM
ejpam-5085	32	8	(	(	PUNCT
ejpam-5085	32	9	2	2	NUM
ejpam-5085	32	10	)	)	PUNCT
ejpam-5085	32	11	(	(	PUNCT
ejpam-5085	32	12	2024	2024	NUM
ejpam-5085	32	13	)	)	PUNCT
ejpam-5085	32	14	,	,	PUNCT
ejpam-5085	32	15	1197	1197	NUM
ejpam-5085	32	16	-	-	SYM
ejpam-5085	32	17	1205	1205	NUM
ejpam-5085	32	18	1199	1199	NUM
ejpam-5085	32	19	1.3	1.3	NUM
ejpam-5085	32	20	definition	definition	NOUN
ejpam-5085	32	21	.	.	PUNCT
ejpam-5085	33	1	an	an	DET
ejpam-5085	33	2	a	a	DET
ejpam-5085	33	3	-	-	PUNCT
ejpam-5085	33	4	module	module	NOUN
ejpam-5085	33	5	m	m	NOUN
ejpam-5085	33	6	in	in	ADP
ejpam-5085	33	7	mod(a	mod(a	PROPN
ejpam-5085	33	8	)	)	PUNCT
ejpam-5085	33	9	is	be	AUX
ejpam-5085	33	10	said	say	VERB
ejpam-5085	33	11	gorenstein	gorenstein	ADJ
ejpam-5085	33	12	-	-	PUNCT
ejpam-5085	33	13	projective	projective	NOUN
ejpam-5085	33	14	provided	provide	VERB
ejpam-5085	33	15	that	that	SCONJ
ejpam-5085	33	16	there	there	PRON
ejpam-5085	33	17	is	be	VERB
ejpam-5085	33	18	a	a	DET
ejpam-5085	33	19	totally	totally	ADV
ejpam-5085	33	20	acyclic	acyclic	ADJ
ejpam-5085	33	21	complex	complex	ADJ
ejpam-5085	33	22	(	(	PUNCT
ejpam-5085	33	23	p⋆	p⋆	NOUN
ejpam-5085	33	24	)	)	PUNCT
ejpam-5085	33	25	of	of	ADP
ejpam-5085	33	26	projective	projective	ADJ
ejpam-5085	33	27	modules	module	NOUN
ejpam-5085	33	28	such	such	ADJ
ejpam-5085	33	29	that	that	SCONJ
ejpam-5085	33	30	its	its	PRON
ejpam-5085	33	31	0	0	NUM
ejpam-5085	33	32	-	-	PUNCT
ejpam-5085	33	33	th	th	X
ejpam-5085	33	34	cocycle	cocycle	NOUN
ejpam-5085	33	35	z0(p⋆	z0(p⋆	PROPN
ejpam-5085	33	36	)	)	PUNCT
ejpam-5085	33	37	is	be	AUX
ejpam-5085	33	38	isomorphic	isomorphic	ADJ
ejpam-5085	33	39	to	to	ADP
ejpam-5085	33	40	m	m	PROPN
ejpam-5085	33	41	.	.	PUNCT
ejpam-5085	34	1	1.4	1.4	NUM
ejpam-5085	34	2	example	example	NOUN
ejpam-5085	34	3	.	.	PUNCT
ejpam-5085	35	1	any	any	DET
ejpam-5085	35	2	a	a	DET
ejpam-5085	35	3	-	-	PUNCT
ejpam-5085	35	4	module	module	NOUN
ejpam-5085	35	5	p	p	NOUN
ejpam-5085	35	6	projective	projective	NOUN
ejpam-5085	35	7	is	be	AUX
ejpam-5085	35	8	a	a	DET
ejpam-5085	35	9	gorenstein	gorenstein	ADJ
ejpam-5085	35	10	-	-	PUNCT
ejpam-5085	35	11	projective	projective	NOUN
ejpam-5085	35	12	module	module	NOUN
ejpam-5085	35	13	;	;	PUNCT
ejpam-5085	35	14	just	just	ADV
ejpam-5085	35	15	consider	consider	VERB
ejpam-5085	35	16	the	the	DET
ejpam-5085	35	17	exact	exact	ADJ
ejpam-5085	35	18	sequence	sequence	NOUN
ejpam-5085	35	19	p⋆	p⋆	NOUN
ejpam-5085	35	20	:	:	PUNCT
ejpam-5085	35	21	·	·	PUNCT
ejpam-5085	35	22	·	·	PUNCT
ejpam-5085	35	23	·	·	PUNCT
ejpam-5085	36	1	//	//	PUNCT
ejpam-5085	36	2	0	0	NUM
ejpam-5085	37	1	//	//	PUNCT
ejpam-5085	37	2	p	p	PROPN
ejpam-5085	37	3	idp	idp	PROPN
ejpam-5085	37	4	//	//	PROPN
ejpam-5085	37	5	p	p	PROPN
ejpam-5085	37	6	//	//	PROPN
ejpam-5085	37	7	0	0	NUM
ejpam-5085	37	8	//	//	PROPN
ejpam-5085	37	9	·	·	PUNCT
ejpam-5085	37	10	·	·	PUNCT
ejpam-5085	37	11	·	·	PUNCT
ejpam-5085	38	1	and	and	CCONJ
ejpam-5085	38	2	we	we	PRON
ejpam-5085	38	3	have	have	VERB
ejpam-5085	38	4	z0(p⋆	z0(p⋆	NUM
ejpam-5085	38	5	)	)	PUNCT
ejpam-5085	38	6	≃	≃	NOUN
ejpam-5085	38	7	p	p	NOUN
ejpam-5085	38	8	.	.	PUNCT
ejpam-5085	39	1	over	over	ADP
ejpam-5085	39	2	the	the	DET
ejpam-5085	39	3	algebra	algebra	NOUN
ejpam-5085	39	4	z/4z	z/4z	NUM
ejpam-5085	39	5	,	,	PUNCT
ejpam-5085	39	6	the	the	DET
ejpam-5085	39	7	complex	complex	NOUN
ejpam-5085	39	8	:	:	PUNCT
ejpam-5085	39	9	·	·	PUNCT
ejpam-5085	39	10	·	·	PUNCT
ejpam-5085	39	11	·	·	PUNCT
ejpam-5085	40	1	//	//	SYM
ejpam-5085	40	2	z/4z	z/4z	NUM
ejpam-5085	40	3	//	//	NUM
ejpam-5085	40	4	z/4z	z/4z	NUM
ejpam-5085	40	5	//	//	NUM
ejpam-5085	40	6	z/4z	z/4z	NUM
ejpam-5085	40	7	//	//	NOUN
ejpam-5085	40	8	·	·	PUNCT
ejpam-5085	40	9	·	·	PUNCT
ejpam-5085	40	10	·	·	PUNCT
ejpam-5085	40	11	defined	define	VERB
ejpam-5085	40	12	by	by	ADP
ejpam-5085	40	13	multiplication	multiplication	NOUN
ejpam-5085	40	14	by	by	ADP
ejpam-5085	40	15	2	2	NUM
ejpam-5085	40	16	is	be	AUX
ejpam-5085	40	17	acyclic	acyclic	ADJ
ejpam-5085	40	18	and	and	CCONJ
ejpam-5085	40	19	it	it	PRON
ejpam-5085	40	20	remains	remain	VERB
ejpam-5085	40	21	exact	exact	ADJ
ejpam-5085	40	22	by	by	ADP
ejpam-5085	40	23	applying	apply	VERB
ejpam-5085	40	24	the	the	DET
ejpam-5085	40	25	functor	functor	PROPN
ejpam-5085	40	26	hom(−	hom(−	PROPN
ejpam-5085	40	27	,	,	PUNCT
ejpam-5085	40	28	p	p	NOUN
ejpam-5085	40	29	)	)	PUNCT
ejpam-5085	40	30	with	with	ADP
ejpam-5085	40	31	p	p	X
ejpam-5085	40	32	a	a	DET
ejpam-5085	40	33	projective	projective	ADJ
ejpam-5085	40	34	module	module	NOUN
ejpam-5085	40	35	,	,	PUNCT
ejpam-5085	40	36	then	then	ADV
ejpam-5085	40	37	2z/4z	2z/4z	NUM
ejpam-5085	40	38	is	be	AUX
ejpam-5085	40	39	a	a	DET
ejpam-5085	40	40	gorenstein	gorenstein	NOUN
ejpam-5085	40	41	-	-	PUNCT
ejpam-5085	40	42	projective	projective	NOUN
ejpam-5085	40	43	but	but	CCONJ
ejpam-5085	40	44	not	not	PART
ejpam-5085	40	45	projective	projective	ADJ
ejpam-5085	40	46	as	as	ADP
ejpam-5085	40	47	z/4z	z/4z	NOUN
ejpam-5085	40	48	-	-	NOUN
ejpam-5085	40	49	module	module	NOUN
ejpam-5085	40	50	.	.	PUNCT
ejpam-5085	41	1	1.5	1.5	NUM
ejpam-5085	41	2	remark	remark	NOUN
ejpam-5085	41	3	.	.	PUNCT
ejpam-5085	42	1	the	the	DET
ejpam-5085	42	2	full	full	ADJ
ejpam-5085	42	3	subcategory	subcategory	NOUN
ejpam-5085	42	4	of	of	ADP
ejpam-5085	42	5	the	the	DET
ejpam-5085	42	6	finite	finite	ADJ
ejpam-5085	42	7	type	type	NOUN
ejpam-5085	42	8	a	a	DET
ejpam-5085	42	9	-	-	PUNCT
ejpam-5085	42	10	module	module	NOUN
ejpam-5085	42	11	category	category	NOUN
ejpam-5085	42	12	constituted	constitute	VERB
ejpam-5085	42	13	by	by	ADP
ejpam-5085	42	14	the	the	DET
ejpam-5085	42	15	gorenstein	gorenstein	ADJ
ejpam-5085	42	16	-	-	PUNCT
ejpam-5085	42	17	projective	projective	NOUN
ejpam-5085	42	18	modules	module	NOUN
ejpam-5085	42	19	is	be	AUX
ejpam-5085	42	20	denoted	denote	VERB
ejpam-5085	42	21	a	a	DET
ejpam-5085	42	22	-	-	PUNCT
ejpam-5085	42	23	gproj	gproj	NOUN
ejpam-5085	42	24	and	and	CCONJ
ejpam-5085	42	25	the	the	DET
ejpam-5085	42	26	subcategory	subcategory	NOUN
ejpam-5085	42	27	of	of	ADP
ejpam-5085	42	28	projective	projective	ADJ
ejpam-5085	42	29	a	a	PRON
ejpam-5085	42	30	-	-	PUNCT
ejpam-5085	42	31	modules	module	NOUN
ejpam-5085	42	32	is	be	AUX
ejpam-5085	42	33	included	include	VERB
ejpam-5085	42	34	in	in	ADP
ejpam-5085	42	35	a	a	DET
ejpam-5085	42	36	-	-	PUNCT
ejpam-5085	42	37	gproj	gproj	NOUN
ejpam-5085	42	38	.	.	PUNCT
ejpam-5085	43	1	denote	denote	VERB
ejpam-5085	43	2	by	by	ADP
ejpam-5085	43	3	⊥a	⊥a	PROPN
ejpam-5085	43	4	the	the	DET
ejpam-5085	43	5	full	full	ADJ
ejpam-5085	43	6	subcategory	subcategory	PROPN
ejpam-5085	43	7	ofa	ofa	PROPN
ejpam-5085	43	8	-	-	PUNCT
ejpam-5085	43	9	mod	mod	PROPN
ejpam-5085	43	10	consisting	consist	VERB
ejpam-5085	43	11	by	by	ADP
ejpam-5085	43	12	modulesm	modulesm	ADJ
ejpam-5085	43	13	such	such	ADJ
ejpam-5085	43	14	that	that	SCONJ
ejpam-5085	43	15	extia(m	extia(m	NOUN
ejpam-5085	43	16	,	,	PUNCT
ejpam-5085	43	17	a	a	PRON
ejpam-5085	43	18	)	)	PUNCT
ejpam-5085	43	19	=	=	SYM
ejpam-5085	43	20	0	0	NUM
ejpam-5085	44	1	for	for	ADP
ejpam-5085	44	2	all	all	PRON
ejpam-5085	44	3	i	i	PRON
ejpam-5085	44	4	≥	≥	VERB
ejpam-5085	44	5	1	1	NUM
ejpam-5085	44	6	.	.	PUNCT
ejpam-5085	44	7	recall	recall	VERB
ejpam-5085	44	8	the	the	DET
ejpam-5085	44	9	following	follow	VERB
ejpam-5085	44	10	lemma	lemma	PROPN
ejpam-5085	44	11	,	,	PUNCT
ejpam-5085	44	12	see	see	VERB
ejpam-5085	44	13	[	[	X
ejpam-5085	44	14	3	3	NUM
ejpam-5085	44	15	]	]	PUNCT
ejpam-5085	44	16	.	.	PUNCT
ejpam-5085	45	1	1.6	1.6	NUM
ejpam-5085	45	2	lemma	lemma	PROPN
ejpam-5085	45	3	.	.	PUNCT
ejpam-5085	46	1	let	let	AUX
ejpam-5085	46	2	(	(	PUNCT
ejpam-5085	46	3	p⋆	p⋆	X
ejpam-5085	46	4	)	)	PUNCT
ejpam-5085	46	5	be	be	VERB
ejpam-5085	46	6	a	a	DET
ejpam-5085	46	7	complex	complex	NOUN
ejpam-5085	46	8	of	of	ADP
ejpam-5085	46	9	projective	projective	ADJ
ejpam-5085	46	10	a	a	PRON
ejpam-5085	46	11	-	-	PUNCT
ejpam-5085	46	12	modules	module	NOUN
ejpam-5085	46	13	.	.	PUNCT
ejpam-5085	47	1	then	then	ADV
ejpam-5085	47	2	the	the	DET
ejpam-5085	47	3	following	follow	VERB
ejpam-5085	47	4	statements	statement	NOUN
ejpam-5085	47	5	are	be	AUX
ejpam-5085	47	6	equivalent	equivalent	ADJ
ejpam-5085	47	7	:	:	PUNCT
ejpam-5085	47	8	(	(	PUNCT
ejpam-5085	47	9	1	1	X
ejpam-5085	47	10	)	)	PUNCT
ejpam-5085	47	11	the	the	DET
ejpam-5085	47	12	complex	complex	ADJ
ejpam-5085	47	13	(	(	PUNCT
ejpam-5085	47	14	p⋆	p⋆	X
ejpam-5085	47	15	)	)	PUNCT
ejpam-5085	47	16	is	be	AUX
ejpam-5085	47	17	totally	totally	ADV
ejpam-5085	47	18	acyclic	acyclic	ADJ
ejpam-5085	47	19	.	.	PUNCT
ejpam-5085	48	1	(	(	PUNCT
ejpam-5085	48	2	2	2	X
ejpam-5085	48	3	)	)	PUNCT
ejpam-5085	48	4	the	the	DET
ejpam-5085	48	5	complex	complex	ADJ
ejpam-5085	48	6	(	(	PUNCT
ejpam-5085	48	7	p⋆	p⋆	X
ejpam-5085	48	8	)	)	PUNCT
ejpam-5085	48	9	is	be	AUX
ejpam-5085	48	10	acyclic	acyclic	ADJ
ejpam-5085	48	11	and	and	CCONJ
ejpam-5085	48	12	each	each	DET
ejpam-5085	48	13	cocycle	cocycle	NOUN
ejpam-5085	48	14	zi(p⋆	zi(p⋆	NUM
ejpam-5085	48	15	)	)	PUNCT
ejpam-5085	48	16	lies	lie	VERB
ejpam-5085	48	17	in	in	ADP
ejpam-5085	48	18	⊥a	⊥a	PROPN
ejpam-5085	48	19	;	;	PUNCT
ejpam-5085	48	20	(	(	PUNCT
ejpam-5085	48	21	3	3	X
ejpam-5085	48	22	)	)	PUNCT
ejpam-5085	48	23	the	the	DET
ejpam-5085	48	24	complex	complex	ADJ
ejpam-5085	48	25	hom((p⋆	hom((p⋆	NOUN
ejpam-5085	48	26	)	)	PUNCT
ejpam-5085	48	27	,	,	PUNCT
ejpam-5085	48	28	a	a	PRON
ejpam-5085	48	29	)	)	PUNCT
ejpam-5085	48	30	is	be	AUX
ejpam-5085	48	31	totally	totally	ADV
ejpam-5085	48	32	acyclic	acyclic	ADJ
ejpam-5085	48	33	.	.	PUNCT
ejpam-5085	49	1	we	we	PRON
ejpam-5085	49	2	note	note	VERB
ejpam-5085	49	3	we	we	PRON
ejpam-5085	49	4	will	will	AUX
ejpam-5085	49	5	need	need	VERB
ejpam-5085	49	6	the	the	DET
ejpam-5085	49	7	corollary	corollary	ADJ
ejpam-5085	49	8	and	and	CCONJ
ejpam-5085	49	9	proposition	proposition	NOUN
ejpam-5085	49	10	stated	state	VERB
ejpam-5085	49	11	in	in	ADP
ejpam-5085	49	12	[	[	X
ejpam-5085	49	13	1	1	NUM
ejpam-5085	49	14	]	]	PUNCT
ejpam-5085	49	15	thereafter	thereafter	ADV
ejpam-5085	49	16	which	which	PRON
ejpam-5085	49	17	says	say	VERB
ejpam-5085	49	18	the	the	DET
ejpam-5085	49	19	following	following	NOUN
ejpam-5085	49	20	,	,	PUNCT
ejpam-5085	49	21	1.7	1.7	NUM
ejpam-5085	49	22	corollary	corollary	NOUN
ejpam-5085	49	23	.	.	PUNCT
ejpam-5085	50	1	if	if	SCONJ
ejpam-5085	50	2	m	m	NOUN
ejpam-5085	50	3	is	be	AUX
ejpam-5085	50	4	a	a	DET
ejpam-5085	50	5	gorenstein	gorenstein	ADJ
ejpam-5085	50	6	-	-	PUNCT
ejpam-5085	50	7	projective	projective	NOUN
ejpam-5085	50	8	module	module	NOUN
ejpam-5085	50	9	,	,	PUNCT
ejpam-5085	50	10	then	then	ADV
ejpam-5085	50	11	ext1a(m	ext1a(m	ADJ
ejpam-5085	50	12	,	,	PUNCT
ejpam-5085	50	13	l	l	NOUN
ejpam-5085	50	14	)	)	PUNCT
ejpam-5085	50	15	=	=	SYM
ejpam-5085	50	16	0	0	NUM
ejpam-5085	50	17	for	for	ADP
ejpam-5085	50	18	all	all	DET
ejpam-5085	50	19	module	module	NOUN
ejpam-5085	50	20	l	l	NOUN
ejpam-5085	50	21	of	of	ADP
ejpam-5085	50	22	finite	finite	PROPN
ejpam-5085	50	23	projective	projective	PROPN
ejpam-5085	50	24	dimension	dimension	NOUN
ejpam-5085	50	25	.	.	PUNCT
ejpam-5085	51	1	1.8	1.8	NUM
ejpam-5085	51	2	proposition	proposition	NOUN
ejpam-5085	51	3	.	.	PUNCT
ejpam-5085	52	1	let	let	VERB
ejpam-5085	52	2	m	m	PRON
ejpam-5085	52	3	in	in	ADP
ejpam-5085	52	4	mod(a	mod(a	PROPN
ejpam-5085	52	5	)	)	PUNCT
ejpam-5085	52	6	,	,	PUNCT
ejpam-5085	52	7	then	then	ADV
ejpam-5085	52	8	m	m	PROPN
ejpam-5085	52	9	is	be	AUX
ejpam-5085	52	10	a	a	DET
ejpam-5085	52	11	gorenstein	gorenstein	ADJ
ejpam-5085	52	12	-	-	PUNCT
ejpam-5085	52	13	projective	projective	NOUN
ejpam-5085	52	14	module	module	NOUN
ejpam-5085	52	15	if	if	SCONJ
ejpam-5085	52	16	and	and	CCONJ
ejpam-5085	52	17	only	only	ADV
ejpam-5085	52	18	if	if	SCONJ
ejpam-5085	52	19	there	there	PRON
ejpam-5085	52	20	exists	exist	VERB
ejpam-5085	52	21	a	a	DET
ejpam-5085	52	22	long	long	ADJ
ejpam-5085	52	23	exact	exact	ADJ
ejpam-5085	52	24	sequence	sequence	NOUN
ejpam-5085	52	25	:	:	PUNCT
ejpam-5085	52	26	0	0	NUM
ejpam-5085	52	27	//m	//m	SYM
ejpam-5085	52	28	//	//	NUM
ejpam-5085	52	29	p0	p0	PROPN
ejpam-5085	52	30	//	//	PROPN
ejpam-5085	52	31	p1	p1	PROPN
ejpam-5085	52	32	//	//	PROPN
ejpam-5085	52	33	p2	p2	PROPN
ejpam-5085	52	34	//	//	X
ejpam-5085	52	35	·	·	PUNCT
ejpam-5085	52	36	·	·	PUNCT
ejpam-5085	52	37	·	·	PUNCT
ejpam-5085	52	38	with	with	ADP
ejpam-5085	52	39	pi	pi	NOUN
ejpam-5085	52	40	are	be	AUX
ejpam-5085	52	41	the	the	DET
ejpam-5085	52	42	projective	projective	ADJ
ejpam-5085	52	43	modules	module	NOUN
ejpam-5085	52	44	and	and	CCONJ
ejpam-5085	52	45	each	each	DET
ejpam-5085	52	46	cocycle	cocycle	NOUN
ejpam-5085	52	47	in	in	ADP
ejpam-5085	52	48	⊥a	⊥a	PROPN
ejpam-5085	52	49	.	.	PUNCT
ejpam-5085	53	1	proof	proof	NOUN
ejpam-5085	53	2	.	.	PUNCT
ejpam-5085	54	1	by	by	ADP
ejpam-5085	54	2	definition	definition	NOUN
ejpam-5085	54	3	m	m	VERB
ejpam-5085	54	4	is	be	AUX
ejpam-5085	54	5	in	in	ADP
ejpam-5085	54	6	a	a	DET
ejpam-5085	54	7	-	-	PUNCT
ejpam-5085	54	8	gproj	gproj	NOUN
ejpam-5085	54	9	then	then	ADV
ejpam-5085	54	10	,	,	PUNCT
ejpam-5085	54	11	there	there	PRON
ejpam-5085	54	12	exists	exist	VERB
ejpam-5085	54	13	a	a	DET
ejpam-5085	54	14	totally	totally	ADV
ejpam-5085	54	15	acyclic	acyclic	ADJ
ejpam-5085	54	16	complex	complex	ADJ
ejpam-5085	54	17	p⋆	p⋆	NOUN
ejpam-5085	54	18	such	such	ADJ
ejpam-5085	54	19	that	that	SCONJ
ejpam-5085	54	20	m	m	VERB
ejpam-5085	54	21	≃	≃	ADJ
ejpam-5085	54	22	z0(p⋆	z0(p⋆	PROPN
ejpam-5085	54	23	)	)	PUNCT
ejpam-5085	54	24	and	and	CCONJ
ejpam-5085	54	25	we	we	PRON
ejpam-5085	54	26	have	have	VERB
ejpam-5085	54	27	:	:	PUNCT
ejpam-5085	54	28	0	0	NUM
ejpam-5085	54	29	//m	//m	SYM
ejpam-5085	54	30	//	//	NUM
ejpam-5085	54	31	p0	p0	PROPN
ejpam-5085	54	32	//	//	PROPN
ejpam-5085	54	33	p1	p1	PROPN
ejpam-5085	54	34	//	//	PROPN
ejpam-5085	54	35	p2	p2	PROPN
ejpam-5085	54	36	//	//	X
ejpam-5085	54	37	·	·	PUNCT
ejpam-5085	54	38	·	·	PUNCT
ejpam-5085	54	39	·	·	PUNCT
ejpam-5085	54	40	m.	m.	NOUN
ejpam-5085	54	41	laaraj	laaraj	PROPN
ejpam-5085	54	42	,	,	PUNCT
ejpam-5085	54	43	s.	s.	PROPN
ejpam-5085	54	44	abdelalim	abdelalim	PROPN
ejpam-5085	54	45	/	/	SYM
ejpam-5085	54	46	eur	eur	PROPN
ejpam-5085	54	47	.	.	PUNCT
ejpam-5085	55	1	j.	j.	PROPN
ejpam-5085	55	2	pure	pure	PROPN
ejpam-5085	55	3	appl	appl	PROPN
ejpam-5085	55	4	.	.	PROPN
ejpam-5085	55	5	math	math	PROPN
ejpam-5085	55	6	,	,	PUNCT
ejpam-5085	55	7	17	17	NUM
ejpam-5085	55	8	(	(	PUNCT
ejpam-5085	55	9	2	2	NUM
ejpam-5085	55	10	)	)	PUNCT
ejpam-5085	55	11	(	(	PUNCT
ejpam-5085	55	12	2024	2024	NUM
ejpam-5085	55	13	)	)	PUNCT
ejpam-5085	55	14	,	,	PUNCT
ejpam-5085	55	15	1197	1197	NUM
ejpam-5085	55	16	-	-	SYM
ejpam-5085	55	17	1205	1205	NUM
ejpam-5085	55	18	1200	1200	NUM
ejpam-5085	55	19	.	.	PUNCT
ejpam-5085	56	1	now	now	ADV
ejpam-5085	56	2	for	for	ADP
ejpam-5085	56	3	the	the	DET
ejpam-5085	56	4	reciprocal	reciprocal	ADJ
ejpam-5085	56	5	,	,	PUNCT
ejpam-5085	56	6	we	we	PRON
ejpam-5085	56	7	consider	consider	VERB
ejpam-5085	56	8	·	·	PUNCT
ejpam-5085	56	9	·	·	PUNCT
ejpam-5085	56	10	·	·	PUNCT
ejpam-5085	57	1	//	//	NUM
ejpam-5085	57	2	q2	q2	PROPN
ejpam-5085	57	3	//	//	PROPN
ejpam-5085	57	4	q1	q1	PROPN
ejpam-5085	57	5	//	//	PROPN
ejpam-5085	57	6	q0	q0	PROPN
ejpam-5085	57	7	//m	//m	PROPN
ejpam-5085	57	8	//	//	NOUN
ejpam-5085	57	9	0	0	NUM
ejpam-5085	58	1	the	the	DET
ejpam-5085	58	2	projective	projective	ADJ
ejpam-5085	58	3	resolution	resolution	NOUN
ejpam-5085	58	4	ofm	ofm	PROPN
ejpam-5085	58	5	and	and	CCONJ
ejpam-5085	58	6	by	by	ADP
ejpam-5085	58	7	spiling	spile	VERB
ejpam-5085	58	8	the	the	DET
ejpam-5085	58	9	two	two	NUM
ejpam-5085	58	10	resolutions	resolution	NOUN
ejpam-5085	58	11	,	,	PUNCT
ejpam-5085	58	12	we	we	PRON
ejpam-5085	58	13	get	get	VERB
ejpam-5085	58	14	an	an	DET
ejpam-5085	58	15	acyclic	acyclic	ADJ
ejpam-5085	58	16	complex	complex	NOUN
ejpam-5085	58	17	p	p	NOUN
ejpam-5085	58	18	such	such	ADJ
ejpam-5085	58	19	that	that	SCONJ
ejpam-5085	58	20	m	m	VERB
ejpam-5085	58	21	≃	≃	ADJ
ejpam-5085	58	22	z0(p⋆	z0(p⋆	PROPN
ejpam-5085	58	23	)	)	PUNCT
ejpam-5085	58	24	.	.	PUNCT
ejpam-5085	59	1	1.9	1.9	NUM
ejpam-5085	59	2	proposition	proposition	NOUN
ejpam-5085	59	3	.	.	PUNCT
ejpam-5085	60	1	let	let	VERB
ejpam-5085	60	2	ε	ε	PROPN
ejpam-5085	60	3	:	:	PUNCT
ejpam-5085	60	4	0	0	NUM
ejpam-5085	60	5	//	//	PUNCT
ejpam-5085	60	6	x	x	X
ejpam-5085	60	7	//	//	PUNCT
ejpam-5085	60	8	y	y	PROPN
ejpam-5085	60	9	//	//	PROPN
ejpam-5085	60	10	z	z	PROPN
ejpam-5085	60	11	//	//	PROPN
ejpam-5085	60	12	0	0	NUM
ejpam-5085	60	13	be	be	AUX
ejpam-5085	60	14	a	a	DET
ejpam-5085	60	15	short	short	ADJ
ejpam-5085	60	16	exact	exact	ADJ
ejpam-5085	60	17	sequence	sequence	NOUN
ejpam-5085	60	18	of	of	ADP
ejpam-5085	60	19	a	a	DET
ejpam-5085	60	20	-	-	PUNCT
ejpam-5085	60	21	modules	module	NOUN
ejpam-5085	60	22	.	.	PUNCT
ejpam-5085	61	1	then	then	ADV
ejpam-5085	61	2	we	we	PRON
ejpam-5085	61	3	have	have	VERB
ejpam-5085	61	4	the	the	DET
ejpam-5085	61	5	following	following	ADJ
ejpam-5085	61	6	statements	statement	NOUN
ejpam-5085	61	7	:	:	PUNCT
ejpam-5085	61	8	(	(	PUNCT
ejpam-5085	61	9	1	1	X
ejpam-5085	61	10	)	)	PUNCT
ejpam-5085	61	11	if	if	SCONJ
ejpam-5085	61	12	x	x	NOUN
ejpam-5085	61	13	,	,	PUNCT
ejpam-5085	61	14	z	z	PROPN
ejpam-5085	61	15	are	be	AUX
ejpam-5085	61	16	gorenstein	gorenstein	ADJ
ejpam-5085	61	17	-	-	PUNCT
ejpam-5085	61	18	projective	projective	ADJ
ejpam-5085	61	19	,	,	PUNCT
ejpam-5085	61	20	then	then	ADV
ejpam-5085	61	21	so	so	ADV
ejpam-5085	61	22	is	be	AUX
ejpam-5085	61	23	y	y	PROPN
ejpam-5085	61	24	.	.	PUNCT
ejpam-5085	62	1	(	(	PUNCT
ejpam-5085	62	2	2	2	X
ejpam-5085	62	3	)	)	PUNCT
ejpam-5085	62	4	if	if	SCONJ
ejpam-5085	62	5	y	y	PROPN
ejpam-5085	62	6	,	,	PUNCT
ejpam-5085	62	7	z	z	PROPN
ejpam-5085	62	8	are	be	AUX
ejpam-5085	62	9	gorenstein	gorenstein	ADJ
ejpam-5085	62	10	-	-	PUNCT
ejpam-5085	62	11	projective	projective	ADJ
ejpam-5085	62	12	,	,	PUNCT
ejpam-5085	62	13	then	then	ADV
ejpam-5085	62	14	so	so	ADV
ejpam-5085	62	15	is	be	AUX
ejpam-5085	62	16	x.	x.	NOUN
ejpam-5085	62	17	proof	proof	NOUN
ejpam-5085	62	18	.	.	PUNCT
ejpam-5085	63	1	since	since	SCONJ
ejpam-5085	63	2	x	x	PRON
ejpam-5085	63	3	and	and	CCONJ
ejpam-5085	63	4	z	z	NOUN
ejpam-5085	63	5	are	be	AUX
ejpam-5085	63	6	gorenstein	gorenstein	ADJ
ejpam-5085	63	7	-	-	PUNCT
ejpam-5085	63	8	projective	projective	NOUN
ejpam-5085	63	9	modules	module	NOUN
ejpam-5085	63	10	,	,	PUNCT
ejpam-5085	63	11	then	then	ADV
ejpam-5085	63	12	by	by	ADP
ejpam-5085	63	13	proposition	proposition	NOUN
ejpam-5085	63	14	1.8	1.8	NUM
ejpam-5085	63	15	,	,	PUNCT
ejpam-5085	63	16	we	we	PRON
ejpam-5085	63	17	have	have	VERB
ejpam-5085	63	18	two	two	NUM
ejpam-5085	63	19	monomorphisms	monomorphism	NOUN
ejpam-5085	63	20	:	:	PUNCT
ejpam-5085	63	21	0	0	NUM
ejpam-5085	63	22	//	//	PUNCT
ejpam-5085	63	23	x	x	X
ejpam-5085	64	1	ix	ix	PROPN
ejpam-5085	64	2	//	//	NOUN
ejpam-5085	64	3	x	x	SYM
ejpam-5085	65	1	′	′	NUM
ejpam-5085	65	2	and	and	CCONJ
ejpam-5085	65	3	0	0	NUM
ejpam-5085	66	1	//	//	NUM
ejpam-5085	66	2	z	z	NOUN
ejpam-5085	67	1	iz	iz	INTJ
ejpam-5085	68	1	//	//	NOUN
ejpam-5085	68	2	z	z	NOUN
ejpam-5085	69	1	′	′	NUM
ejpam-5085	69	2	such	such	ADJ
ejpam-5085	69	3	that	that	PRON
ejpam-5085	69	4	x	x	SYM
ejpam-5085	70	1	′	′	NUM
ejpam-5085	70	2	and	and	CCONJ
ejpam-5085	70	3	z	z	NOUN
ejpam-5085	70	4	′	′	NUM
ejpam-5085	70	5	are	be	AUX
ejpam-5085	70	6	projective	projective	ADJ
ejpam-5085	70	7	modules	module	NOUN
ejpam-5085	70	8	and	and	CCONJ
ejpam-5085	70	9	the	the	DET
ejpam-5085	70	10	cokernels	cokernel	NOUN
ejpam-5085	70	11	x1	x1	PROPN
ejpam-5085	70	12	and	and	CCONJ
ejpam-5085	70	13	z1	z1	PROPN
ejpam-5085	70	14	of	of	ADP
ejpam-5085	70	15	ix	ix	PROPN
ejpam-5085	70	16	and	and	CCONJ
ejpam-5085	70	17	iz	iz	INTJ
ejpam-5085	70	18	respectively	respectively	ADV
ejpam-5085	70	19	are	be	AUX
ejpam-5085	70	20	gorenstein	gorenstein	NOUN
ejpam-5085	70	21	-	-	PUNCT
ejpam-5085	70	22	projective	projective	ADJ
ejpam-5085	70	23	.	.	PUNCT
ejpam-5085	71	1	since	since	SCONJ
ejpam-5085	71	2	by	by	ADP
ejpam-5085	71	3	corollary	corollary	ADJ
ejpam-5085	71	4	1.7	1.7	NUM
ejpam-5085	71	5	,	,	PUNCT
ejpam-5085	71	6	ext1a(z	ext1a(z	NOUN
ejpam-5085	71	7	,	,	PUNCT
ejpam-5085	71	8	x	x	NOUN
ejpam-5085	71	9	′	′	NUM
ejpam-5085	71	10	)	)	PUNCT
ejpam-5085	71	11	=	=	SYM
ejpam-5085	71	12	0	0	PUNCT
ejpam-5085	71	13	and	and	CCONJ
ejpam-5085	71	14	by	by	ADP
ejpam-5085	71	15	applying	apply	VERB
ejpam-5085	71	16	the	the	DET
ejpam-5085	71	17	functor	functor	PROPN
ejpam-5085	71	18	hom(−	hom(−	PROPN
ejpam-5085	71	19	,	,	PUNCT
ejpam-5085	71	20	x	x	NOUN
ejpam-5085	71	21	′	′	NUM
ejpam-5085	71	22	)	)	PUNCT
ejpam-5085	71	23	to	to	PART
ejpam-5085	71	24	ε	ε	PROPN
ejpam-5085	71	25	,	,	PUNCT
ejpam-5085	71	26	we	we	PRON
ejpam-5085	71	27	infer	infer	VERB
ejpam-5085	71	28	that	that	SCONJ
ejpam-5085	71	29	the	the	DET
ejpam-5085	71	30	induced	induced	ADJ
ejpam-5085	71	31	map	map	NOUN
ejpam-5085	71	32	:	:	PUNCT
ejpam-5085	71	33	homa(y	homa(y	NOUN
ejpam-5085	71	34	,	,	PUNCT
ejpam-5085	71	35	x	x	NOUN
ejpam-5085	71	36	′	′	NUM
ejpam-5085	71	37	)	)	PUNCT
ejpam-5085	71	38	homa(f	homa(f	NOUN
ejpam-5085	71	39	,	,	PUNCT
ejpam-5085	71	40	x′)//	x′)//	PROPN
ejpam-5085	71	41	homa(x	homa(x	PROPN
ejpam-5085	71	42	,	,	PUNCT
ejpam-5085	71	43	x	x	NOUN
ejpam-5085	71	44	′	′	NUM
ejpam-5085	71	45	)	)	PUNCT
ejpam-5085	71	46	is	be	AUX
ejpam-5085	71	47	epimorphism	epimorphism	NOUN
ejpam-5085	71	48	,	,	PUNCT
ejpam-5085	71	49	then	then	ADV
ejpam-5085	71	50	there	there	PRON
ejpam-5085	71	51	exists	exist	VERB
ejpam-5085	71	52	a	a	DET
ejpam-5085	71	53	morphism	morphism	NOUN
ejpam-5085	71	54	a	a	PRON
ejpam-5085	71	55	:	:	PUNCT
ejpam-5085	71	56	y	y	PROPN
ejpam-5085	71	57	−→	−→	NOUN
ejpam-5085	71	58	x	x	PUNCT
ejpam-5085	71	59	′	′	NUM
ejpam-5085	71	60	such	such	ADJ
ejpam-5085	71	61	that	that	SCONJ
ejpam-5085	71	62	:	:	PUNCT
ejpam-5085	71	63	a	a	DET
ejpam-5085	71	64	◦	◦	NOUN
ejpam-5085	71	65	f	f	X
ejpam-5085	72	1	=	=	NOUN
ejpam-5085	72	2	idx	idx	NOUN
ejpam-5085	72	3	therefore	therefore	ADV
ejpam-5085	72	4	we	we	PRON
ejpam-5085	72	5	have	have	VERB
ejpam-5085	72	6	the	the	DET
ejpam-5085	72	7	following	following	ADJ
ejpam-5085	72	8	exact	exact	ADJ
ejpam-5085	72	9	diagram	diagram	NOUN
ejpam-5085	72	10	:	:	PUNCT
ejpam-5085	72	11	0	0	NUM
ejpam-5085	72	12	//	//	PUNCT
ejpam-5085	72	13	x	x	X
ejpam-5085	73	1	f	f	PROPN
ejpam-5085	73	2	//	//	PROPN
ejpam-5085	73	3	ix	ix	PROPN
ejpam-5085	73	4	�	�	PROPN
ejpam-5085	73	5	�	�	PROPN
ejpam-5085	73	6	y	y	PROPN
ejpam-5085	73	7	g	g	PROPN
ejpam-5085	73	8	//	//	PROPN
ejpam-5085	74	1	a	a	DET
ejpam-5085	74	2	iz	iz	INTJ
ejpam-5085	74	3	◦	◦	NOUN
ejpam-5085	74	4	g	g	PROPN
ejpam-5085	74	5			PROPN
ejpam-5085	74	6	�	�	PROPN
ejpam-5085	74	7	�	�	PROPN
ejpam-5085	74	8	z	z	PROPN
ejpam-5085	74	9	//	//	PROPN
ejpam-5085	74	10	iz	iz	PROPN
ejpam-5085	74	11	�	�	PROPN
ejpam-5085	74	12	�	�	PROPN
ejpam-5085	74	13	0	0	NUM
ejpam-5085	74	14	0	0	NUM
ejpam-5085	74	15	//	//	NOUN
ejpam-5085	74	16	x	x	SYM
ejpam-5085	75	1	′	′	NUM
ejpam-5085	75	2	1	1	NUM
ejpam-5085	75	3	0	0	NUM
ejpam-5085	76	1			PROPN
ejpam-5085	76	2	//	//	PUNCT
ejpam-5085	76	3	x	x	SYM
ejpam-5085	76	4	′⊕z	′⊕z	PROPN
ejpam-5085	76	5	′	′	PROPN
ejpam-5085	76	6	(	(	PUNCT
ejpam-5085	76	7	0	0	NUM
ejpam-5085	76	8	1	1	NUM
ejpam-5085	76	9	)	)	PUNCT
ejpam-5085	76	10	//	//	NOUN
ejpam-5085	77	1	z	z	NOUN
ejpam-5085	77	2	′	′	NUM
ejpam-5085	77	3	//	//	NOUN
ejpam-5085	77	4	0	0	NUM
ejpam-5085	77	5	by	by	ADP
ejpam-5085	77	6	the	the	DET
ejpam-5085	77	7	snake	snake	NOUN
ejpam-5085	77	8	lemma	lemma	PROPN
ejpam-5085	77	9	,	,	PUNCT
ejpam-5085	77	10	we	we	PRON
ejpam-5085	77	11	have	have	VERB
ejpam-5085	77	12	a	a	DET
ejpam-5085	77	13	short	short	ADJ
ejpam-5085	77	14	exact	exact	ADJ
ejpam-5085	77	15	sequence	sequence	NOUN
ejpam-5085	77	16	:	:	PUNCT
ejpam-5085	77	17	0	0	NUM
ejpam-5085	77	18	//	//	NUM
ejpam-5085	77	19	coker(ix	coker(ix	PROPN
ejpam-5085	77	20	)	)	PUNCT
ejpam-5085	77	21	//	//	NOUN
ejpam-5085	77	22	y1	y1	NOUN
ejpam-5085	77	23	//	//	SYM
ejpam-5085	77	24	coker(iz	coker(iz	PROPN
ejpam-5085	77	25	)	)	PUNCT
ejpam-5085	77	26	//	//	NOUN
ejpam-5085	77	27	0	0	PUNCT
ejpam-5085	78	1	therefore	therefore	ADV
ejpam-5085	78	2	0	0	NUM
ejpam-5085	78	3	//	//	NUM
ejpam-5085	78	4	x1	x1	PROPN
ejpam-5085	78	5	//	//	PUNCT
ejpam-5085	78	6	y1	y1	X
ejpam-5085	78	7	//	//	X
ejpam-5085	78	8	z1	z1	PROPN
ejpam-5085	78	9	//	//	X
ejpam-5085	78	10	0	0	NUM
ejpam-5085	78	11	where	where	SCONJ
ejpam-5085	78	12	y1	y1	NOUN
ejpam-5085	78	13	=	=	PUNCT
ejpam-5085	78	14	(	(	PUNCT
ejpam-5085	78	15	a	a	DET
ejpam-5085	78	16	iz	iz	INTJ
ejpam-5085	78	17	◦	◦	NOUN
ejpam-5085	78	18	g	g	PROPN
ejpam-5085	78	19	)	)	PUNCT
ejpam-5085	78	20	and	and	CCONJ
ejpam-5085	78	21	since	since	SCONJ
ejpam-5085	78	22	x1	x1	PROPN
ejpam-5085	78	23	and	and	CCONJ
ejpam-5085	78	24	z1	z1	NOUN
ejpam-5085	78	25	are	be	AUX
ejpam-5085	78	26	in	in	ADP
ejpam-5085	78	27	⊥a	⊥a	PROPN
ejpam-5085	78	28	we	we	PRON
ejpam-5085	78	29	infer	infer	VERB
ejpam-5085	78	30	that	that	SCONJ
ejpam-5085	78	31	y1	y1	NOUN
ejpam-5085	78	32	in	in	ADP
ejpam-5085	78	33	⊥a	⊥a	PROPN
ejpam-5085	78	34	and	and	CCONJ
ejpam-5085	78	35	by	by	ADP
ejpam-5085	78	36	iterating	iterate	VERB
ejpam-5085	78	37	this	this	DET
ejpam-5085	78	38	process	process	NOUN
ejpam-5085	78	39	and	and	CCONJ
ejpam-5085	78	40	using	use	VERB
ejpam-5085	78	41	proposition	proposition	NOUN
ejpam-5085	78	42	1.8	1.8	NUM
ejpam-5085	78	43	,	,	PUNCT
ejpam-5085	78	44	we	we	PRON
ejpam-5085	78	45	show	show	VERB
ejpam-5085	78	46	that	that	SCONJ
ejpam-5085	78	47	y	y	PROPN
ejpam-5085	78	48	is	be	AUX
ejpam-5085	78	49	gorenstein	gorenstein	ADV
ejpam-5085	78	50	-	-	PUNCT
ejpam-5085	78	51	projective	projective	ADJ
ejpam-5085	78	52	.	.	PUNCT
ejpam-5085	79	1	for	for	ADP
ejpam-5085	79	2	a	a	DET
ejpam-5085	79	3	second	second	ADJ
ejpam-5085	79	4	statement	statement	NOUN
ejpam-5085	79	5	,	,	PUNCT
ejpam-5085	79	6	we	we	PRON
ejpam-5085	79	7	take	take	VERB
ejpam-5085	79	8	the	the	DET
ejpam-5085	79	9	exact	exact	ADJ
ejpam-5085	79	10	sequence	sequence	NOUN
ejpam-5085	79	11	:	:	PUNCT
ejpam-5085	79	12	0	0	NUM
ejpam-5085	79	13	//	//	PUNCT
ejpam-5085	79	14	z	z	NOUN
ejpam-5085	80	1	′	′	NUM
ejpam-5085	81	1	//	//	PUNCT
ejpam-5085	82	1	p	p	X
ejpam-5085	82	2	//	//	PROPN
ejpam-5085	82	3	z	z	PROPN
ejpam-5085	82	4	//	//	SYM
ejpam-5085	82	5	0	0	NUM
ejpam-5085	82	6	m.	m.	NOUN
ejpam-5085	82	7	laaraj	laaraj	PROPN
ejpam-5085	82	8	,	,	PUNCT
ejpam-5085	82	9	s.	s.	PROPN
ejpam-5085	82	10	abdelalim	abdelalim	PROPN
ejpam-5085	82	11	/	/	SYM
ejpam-5085	82	12	eur	eur	PROPN
ejpam-5085	82	13	.	.	PUNCT
ejpam-5085	83	1	j.	j.	PROPN
ejpam-5085	83	2	pure	pure	PROPN
ejpam-5085	83	3	appl	appl	PROPN
ejpam-5085	83	4	.	.	PROPN
ejpam-5085	83	5	math	math	PROPN
ejpam-5085	83	6	,	,	PUNCT
ejpam-5085	83	7	17	17	NUM
ejpam-5085	83	8	(	(	PUNCT
ejpam-5085	83	9	2	2	NUM
ejpam-5085	83	10	)	)	PUNCT
ejpam-5085	83	11	(	(	PUNCT
ejpam-5085	83	12	2024	2024	NUM
ejpam-5085	83	13	)	)	PUNCT
ejpam-5085	83	14	,	,	PUNCT
ejpam-5085	83	15	1197	1197	NUM
ejpam-5085	83	16	-	-	SYM
ejpam-5085	83	17	1205	1205	NUM
ejpam-5085	83	18	1201	1201	NUM
ejpam-5085	83	19	such	such	ADJ
ejpam-5085	83	20	that	that	SCONJ
ejpam-5085	83	21	p	p	NOUN
ejpam-5085	83	22	is	be	AUX
ejpam-5085	83	23	projective	projective	ADJ
ejpam-5085	83	24	and	and	CCONJ
ejpam-5085	83	25	z	z	NOUN
ejpam-5085	83	26	′	′	NOUN
ejpam-5085	83	27	is	be	AUX
ejpam-5085	83	28	gorenstein	gorenstein	NOUN
ejpam-5085	83	29	-	-	PUNCT
ejpam-5085	83	30	projective	projective	ADJ
ejpam-5085	83	31	,	,	PUNCT
ejpam-5085	83	32	and	and	CCONJ
ejpam-5085	83	33	by	by	ADP
ejpam-5085	83	34	the	the	DET
ejpam-5085	83	35	following	follow	VERB
ejpam-5085	83	36	pullback	pullback	NOUN
ejpam-5085	83	37	diagram	diagram	NOUN
ejpam-5085	83	38	:	:	PUNCT
ejpam-5085	83	39	0	0	NUM
ejpam-5085	83	40	�	�	PROPN
ejpam-5085	83	41	�	�	PROPN
ejpam-5085	83	42	0	0	NUM
ejpam-5085	83	43	�	�	PROPN
ejpam-5085	83	44	�	�	PROPN
ejpam-5085	83	45	z	z	PROPN
ejpam-5085	83	46	′	′	NUM
ejpam-5085	83	47	�	�	PROPN
ejpam-5085	83	48	�	�	PROPN
ejpam-5085	83	49	z	z	PROPN
ejpam-5085	83	50	′	′	NUM
ejpam-5085	83	51	�	�	PROPN
ejpam-5085	83	52	�	�	PROPN
ejpam-5085	83	53	0	0	NUM
ejpam-5085	84	1	//	//	PUNCT
ejpam-5085	84	2	x	x	X
ejpam-5085	84	3	//	//	SYM
ejpam-5085	84	4	�	�	PROPN
ejpam-5085	84	5	�	�	PROPN
ejpam-5085	84	6	u	u	PROPN
ejpam-5085	84	7	//	//	PROPN
ejpam-5085	84	8	�	�	PROPN
ejpam-5085	84	9	�	�	PROPN
ejpam-5085	84	10	p	p	PROPN
ejpam-5085	84	11	//	//	PROPN
ejpam-5085	84	12	�	�	PROPN
ejpam-5085	84	13	�	�	PROPN
ejpam-5085	84	14	0	0	NUM
ejpam-5085	84	15	0	0	NUM
ejpam-5085	84	16	//	//	NUM
ejpam-5085	84	17	x	x	X
ejpam-5085	84	18	//	//	PUNCT
ejpam-5085	84	19	y	y	PROPN
ejpam-5085	84	20	//	//	SYM
ejpam-5085	84	21	�	�	PROPN
ejpam-5085	84	22	�	�	PROPN
ejpam-5085	84	23	z	z	PROPN
ejpam-5085	84	24	//	//	SYM
ejpam-5085	84	25	�	�	PROPN
ejpam-5085	84	26	�	�	PROPN
ejpam-5085	84	27	0	0	NUM
ejpam-5085	84	28	0	0	NUM
ejpam-5085	84	29	0	0	NUM
ejpam-5085	84	30	we	we	PRON
ejpam-5085	84	31	have	have	VERB
ejpam-5085	84	32	u	u	PRON
ejpam-5085	84	33	a	a	DET
ejpam-5085	84	34	gorenstein	gorenstein	ADJ
ejpam-5085	84	35	projective	projective	NOUN
ejpam-5085	84	36	module	module	NOUN
ejpam-5085	84	37	by	by	ADP
ejpam-5085	84	38	using	use	VERB
ejpam-5085	84	39	(	(	PUNCT
ejpam-5085	84	40	1	1	NUM
ejpam-5085	84	41	)	)	PUNCT
ejpam-5085	84	42	in	in	ADP
ejpam-5085	84	43	a	a	DET
ejpam-5085	84	44	middle	middle	ADJ
ejpam-5085	84	45	column	column	NOUN
ejpam-5085	84	46	and	and	CCONJ
ejpam-5085	84	47	by	by	ADP
ejpam-5085	84	48	the	the	DET
ejpam-5085	84	49	first	first	ADJ
ejpam-5085	84	50	row	row	NOUN
ejpam-5085	84	51	,	,	PUNCT
ejpam-5085	84	52	u	u	NOUN
ejpam-5085	84	53	≃	≃	NOUN
ejpam-5085	84	54	x	x	PUNCT
ejpam-5085	84	55	⊕	⊕	PROPN
ejpam-5085	84	56	p	p	NOUN
ejpam-5085	84	57	since	since	SCONJ
ejpam-5085	84	58	p	p	NOUN
ejpam-5085	84	59	is	be	AUX
ejpam-5085	84	60	projective	projective	ADJ
ejpam-5085	84	61	we	we	PRON
ejpam-5085	84	62	infer	infer	VERB
ejpam-5085	84	63	that	that	SCONJ
ejpam-5085	84	64	x	x	PRON
ejpam-5085	84	65	is	be	AUX
ejpam-5085	84	66	gorenstein	gorenstein	ADJ
ejpam-5085	84	67	projective	projective	ADJ
ejpam-5085	84	68	.	.	PUNCT
ejpam-5085	85	1	recall	recall	VERB
ejpam-5085	85	2	for	for	ADP
ejpam-5085	85	3	a	a	DET
ejpam-5085	85	4	left	left	ADJ
ejpam-5085	85	5	a	a	DET
ejpam-5085	85	6	-	-	PUNCT
ejpam-5085	85	7	module	module	NOUN
ejpam-5085	85	8	am	be	AUX
ejpam-5085	85	9	over	over	ADP
ejpam-5085	85	10	an	an	DET
ejpam-5085	85	11	artin	artin	PROPN
ejpam-5085	85	12	algebra	algebra	NOUN
ejpam-5085	85	13	,	,	PUNCT
ejpam-5085	85	14	there	there	PRON
ejpam-5085	85	15	exists	exist	VERB
ejpam-5085	85	16	a	a	DET
ejpam-5085	85	17	projective	projective	ADJ
ejpam-5085	85	18	module	module	NOUN
ejpam-5085	85	19	denoted	denote	VERB
ejpam-5085	85	20	p	p	PROPN
ejpam-5085	85	21	(	(	PUNCT
ejpam-5085	85	22	m	m	NOUN
ejpam-5085	85	23	)	)	PUNCT
ejpam-5085	85	24	such	such	ADJ
ejpam-5085	85	25	that	that	SCONJ
ejpam-5085	85	26	the	the	DET
ejpam-5085	85	27	kernel	kernel	NOUN
ejpam-5085	85	28	of	of	ADP
ejpam-5085	85	29	the	the	DET
ejpam-5085	85	30	epimorphism	epimorphism	NOUN
ejpam-5085	86	1	f	f	NOUN
ejpam-5085	86	2	:	:	PUNCT
ejpam-5085	86	3	p	p	X
ejpam-5085	86	4	(	(	PUNCT
ejpam-5085	86	5	m	m	NOUN
ejpam-5085	86	6	)	)	PUNCT
ejpam-5085	86	7	−→	−→	NOUN
ejpam-5085	87	1	m	m	NOUN
ejpam-5085	87	2	is	be	AUX
ejpam-5085	87	3	superfluous	superfluous	ADJ
ejpam-5085	87	4	in	in	ADP
ejpam-5085	87	5	p	p	PROPN
ejpam-5085	87	6	(	(	PUNCT
ejpam-5085	87	7	m	m	NOUN
ejpam-5085	87	8	)	)	PUNCT
ejpam-5085	88	1	that	that	PRON
ejpam-5085	88	2	to	to	PART
ejpam-5085	88	3	say	say	VERB
ejpam-5085	88	4	ker(f	ker(f	PROPN
ejpam-5085	88	5	)	)	PUNCT
ejpam-5085	88	6	⊆	⊆	NUM
ejpam-5085	88	7	rad(p	rad(p	PROPN
ejpam-5085	88	8	(	(	PUNCT
ejpam-5085	88	9	m	m	NOUN
ejpam-5085	88	10	)	)	PUNCT
ejpam-5085	88	11	)	)	PUNCT
ejpam-5085	89	1	.	.	PUNCT
ejpam-5085	90	1	also	also	ADV
ejpam-5085	90	2	,	,	PUNCT
ejpam-5085	90	3	this	this	DET
ejpam-5085	90	4	epimorphism	epimorphism	NOUN
ejpam-5085	90	5	is	be	AUX
ejpam-5085	90	6	called	call	VERB
ejpam-5085	90	7	the	the	DET
ejpam-5085	90	8	projective	projective	ADJ
ejpam-5085	90	9	cover	cover	NOUN
ejpam-5085	90	10	of	of	ADP
ejpam-5085	90	11	m	m	PRON
ejpam-5085	90	12	and	and	CCONJ
ejpam-5085	90	13	we	we	PRON
ejpam-5085	90	14	have	have	VERB
ejpam-5085	90	15	a	a	DET
ejpam-5085	90	16	short	short	ADJ
ejpam-5085	90	17	exact	exact	ADJ
ejpam-5085	90	18	sequence	sequence	NOUN
ejpam-5085	90	19	:	:	PUNCT
ejpam-5085	90	20	0	0	NUM
ejpam-5085	90	21	//	//	NUM
ejpam-5085	90	22	ω(m	ω(m	NOUN
ejpam-5085	90	23	)	)	PUNCT
ejpam-5085	91	1	//	//	NOUN
ejpam-5085	91	2	p	p	X
ejpam-5085	91	3	(	(	PUNCT
ejpam-5085	91	4	m	m	PROPN
ejpam-5085	91	5	)	)	PUNCT
ejpam-5085	91	6	//m	//m	PUNCT
ejpam-5085	91	7	//	//	NOUN
ejpam-5085	91	8	0	0	NUM
ejpam-5085	91	9	1.10	1.10	NUM
ejpam-5085	91	10	corollary	corollary	NOUN
ejpam-5085	91	11	.	.	PUNCT
ejpam-5085	92	1	let	let	VERB
ejpam-5085	92	2	m	m	PRON
ejpam-5085	92	3	be	be	AUX
ejpam-5085	92	4	an	an	DET
ejpam-5085	92	5	a	a	DET
ejpam-5085	92	6	-	-	PUNCT
ejpam-5085	92	7	module	module	NOUN
ejpam-5085	92	8	.	.	PUNCT
ejpam-5085	93	1	if	if	SCONJ
ejpam-5085	93	2	m	m	NOUN
ejpam-5085	93	3	is	be	AUX
ejpam-5085	93	4	gorenstein	gorenstein	ADJ
ejpam-5085	93	5	-	-	PUNCT
ejpam-5085	93	6	projective	projective	ADJ
ejpam-5085	93	7	,	,	PUNCT
ejpam-5085	93	8	then	then	ADV
ejpam-5085	93	9	so	so	ADV
ejpam-5085	93	10	are	be	AUX
ejpam-5085	93	11	ω	ω	NUM
ejpam-5085	93	12	i(m	i(m	NOUN
ejpam-5085	93	13	)	)	PUNCT
ejpam-5085	93	14	for	for	SCONJ
ejpam-5085	93	15	i	i	PRON
ejpam-5085	93	16	≥	≥	NOUN
ejpam-5085	93	17	1	1	NUM
ejpam-5085	93	18	.	.	PUNCT
ejpam-5085	94	1	proof	proof	NOUN
ejpam-5085	94	2	.	.	PUNCT
ejpam-5085	95	1	take	take	VERB
ejpam-5085	95	2	a	a	DET
ejpam-5085	95	3	short	short	ADJ
ejpam-5085	95	4	exact	exact	ADJ
ejpam-5085	95	5	sequence	sequence	NOUN
ejpam-5085	95	6	:	:	PUNCT
ejpam-5085	95	7	0	0	NUM
ejpam-5085	95	8	//	//	NUM
ejpam-5085	95	9	ω(m	ω(m	NOUN
ejpam-5085	95	10	)	)	PUNCT
ejpam-5085	95	11	//	//	NOUN
ejpam-5085	95	12	p	p	X
ejpam-5085	95	13	(	(	PUNCT
ejpam-5085	95	14	m	m	PROPN
ejpam-5085	95	15	)	)	PUNCT
ejpam-5085	95	16	//m	//m	PUNCT
ejpam-5085	95	17	//	//	NOUN
ejpam-5085	95	18	0	0	NUM
ejpam-5085	95	19	by	by	ADP
ejpam-5085	95	20	applying	apply	VERB
ejpam-5085	95	21	proposition	proposition	NOUN
ejpam-5085	95	22	1.9	1.9	NUM
ejpam-5085	95	23	and	and	CCONJ
ejpam-5085	95	24	since	since	SCONJ
ejpam-5085	95	25	p	p	PROPN
ejpam-5085	95	26	(	(	PUNCT
ejpam-5085	95	27	m	m	NOUN
ejpam-5085	95	28	)	)	PUNCT
ejpam-5085	95	29	is	be	AUX
ejpam-5085	95	30	projective	projective	ADJ
ejpam-5085	95	31	,	,	PUNCT
ejpam-5085	95	32	then	then	ADV
ejpam-5085	95	33	ω(m	ω(m	NOUN
ejpam-5085	95	34	)	)	PUNCT
ejpam-5085	95	35	are	be	AUX
ejpam-5085	95	36	likewise	likewise	ADV
ejpam-5085	95	37	,	,	PUNCT
ejpam-5085	95	38	and	and	CCONJ
ejpam-5085	95	39	by	by	ADP
ejpam-5085	95	40	iterating	iterate	VERB
ejpam-5085	95	41	this	this	DET
ejpam-5085	95	42	process	process	NOUN
ejpam-5085	95	43	in	in	ADP
ejpam-5085	95	44	the	the	DET
ejpam-5085	95	45	short	short	ADJ
ejpam-5085	95	46	exact	exact	ADJ
ejpam-5085	95	47	sequence	sequence	NOUN
ejpam-5085	95	48	:	:	PUNCT
ejpam-5085	96	1	0	0	NUM
ejpam-5085	96	2	//	//	SYM
ejpam-5085	96	3	ω	ω	NUM
ejpam-5085	96	4	i+1(m	i+1(m	PROPN
ejpam-5085	96	5	)	)	PUNCT
ejpam-5085	97	1	//	//	PROPN
ejpam-5085	97	2	p	p	X
ejpam-5085	97	3	(	(	PUNCT
ejpam-5085	97	4	ω	ω	NOUN
ejpam-5085	97	5	i(m	i(m	NOUN
ejpam-5085	97	6	)	)	PUNCT
ejpam-5085	97	7	)	)	PUNCT
ejpam-5085	98	1	//	//	PUNCT
ejpam-5085	98	2	ω	ω	NUM
ejpam-5085	98	3	i(m	i(m	NOUN
ejpam-5085	98	4	)	)	PUNCT
ejpam-5085	98	5	//	//	NOUN
ejpam-5085	98	6	0	0	NUM
ejpam-5085	99	1	we	we	PRON
ejpam-5085	99	2	have	have	VERB
ejpam-5085	99	3	the	the	DET
ejpam-5085	99	4	result	result	NOUN
ejpam-5085	99	5	.	.	PUNCT
ejpam-5085	100	1	for	for	ADP
ejpam-5085	100	2	the	the	DET
ejpam-5085	100	3	following	follow	VERB
ejpam-5085	100	4	work	work	NOUN
ejpam-5085	100	5	,	,	PUNCT
ejpam-5085	100	6	we	we	PRON
ejpam-5085	100	7	need	need	VERB
ejpam-5085	100	8	the	the	DET
ejpam-5085	100	9	following	follow	VERB
ejpam-5085	100	10	lemma	lemma	PROPN
ejpam-5085	100	11	,	,	PUNCT
ejpam-5085	100	12	see	see	VERB
ejpam-5085	100	13	[	[	X
ejpam-5085	100	14	1	1	NUM
ejpam-5085	100	15	,	,	PUNCT
ejpam-5085	100	16	2	2	NUM
ejpam-5085	100	17	,	,	PUNCT
ejpam-5085	100	18	6	6	NUM
ejpam-5085	100	19	]	]	PUNCT
ejpam-5085	100	20	.	.	PUNCT
ejpam-5085	101	1	1.11	1.11	NUM
ejpam-5085	101	2	lemma	lemma	PROPN
ejpam-5085	101	3	.	.	PUNCT
ejpam-5085	102	1	let	let	VERB
ejpam-5085	102	2	m	m	PRON
ejpam-5085	102	3	be	be	AUX
ejpam-5085	102	4	a	a	DET
ejpam-5085	102	5	non	non	ADJ
ejpam-5085	102	6	-	-	ADJ
ejpam-5085	102	7	projective	projective	ADJ
ejpam-5085	102	8	and	and	CCONJ
ejpam-5085	102	9	indecomposable	indecomposable	ADJ
ejpam-5085	102	10	gorenstein	gorenstein	NOUN
ejpam-5085	102	11	-	-	PUNCT
ejpam-5085	102	12	projective	projective	NOUN
ejpam-5085	102	13	amodule	amodule	NOUN
ejpam-5085	102	14	,	,	PUNCT
ejpam-5085	102	15	the	the	DET
ejpam-5085	102	16	a	a	DET
ejpam-5085	102	17	-	-	PUNCT
ejpam-5085	102	18	module	module	NOUN
ejpam-5085	102	19	ω(m	ω(m	NOUN
ejpam-5085	102	20	)	)	PUNCT
ejpam-5085	102	21	is	be	AUX
ejpam-5085	102	22	also	also	ADV
ejpam-5085	102	23	non	non	ADJ
ejpam-5085	102	24	-	-	ADJ
ejpam-5085	102	25	projective	projective	ADJ
ejpam-5085	102	26	indecomposable	indecomposable	ADJ
ejpam-5085	102	27	,	,	PUNCT
ejpam-5085	102	28	and	and	CCONJ
ejpam-5085	102	29	gorenstein	gorenstein	NOUN
ejpam-5085	102	30	-	-	PUNCT
ejpam-5085	102	31	projective	projective	NOUN
ejpam-5085	102	32	.	.	PUNCT
ejpam-5085	103	1	2	2	X
ejpam-5085	103	2	.	.	X
ejpam-5085	103	3	radical	radical	ADJ
ejpam-5085	103	4	of	of	ADP
ejpam-5085	103	5	syzygy	syzygy	NOUN
ejpam-5085	103	6	of	of	ADP
ejpam-5085	103	7	an	an	DET
ejpam-5085	103	8	a	a	DET
ejpam-5085	103	9	-	-	PUNCT
ejpam-5085	103	10	module	module	NOUN
ejpam-5085	103	11	in	in	ADP
ejpam-5085	103	12	what	what	PRON
ejpam-5085	103	13	follows	follow	VERB
ejpam-5085	103	14	,	,	PUNCT
ejpam-5085	103	15	a	a	PRON
ejpam-5085	103	16	is	be	AUX
ejpam-5085	103	17	an	an	DET
ejpam-5085	103	18	artin	artin	PROPN
ejpam-5085	103	19	algebra	algebra	NOUN
ejpam-5085	103	20	whose	whose	DET
ejpam-5085	103	21	jacobson	jacobson	PROPN
ejpam-5085	103	22	cubic	cubic	PROPN
ejpam-5085	103	23	radical	radical	PROPN
ejpam-5085	103	24	is	be	AUX
ejpam-5085	103	25	zero	zero	NUM
ejpam-5085	103	26	.	.	PUNCT
ejpam-5085	104	1	m.	m.	NOUN
ejpam-5085	104	2	laaraj	laaraj	PROPN
ejpam-5085	104	3	,	,	PUNCT
ejpam-5085	104	4	s.	s.	PROPN
ejpam-5085	104	5	abdelalim	abdelalim	PROPN
ejpam-5085	104	6	/	/	SYM
ejpam-5085	104	7	eur	eur	PROPN
ejpam-5085	104	8	.	.	PUNCT
ejpam-5085	105	1	j.	j.	PROPN
ejpam-5085	105	2	pure	pure	PROPN
ejpam-5085	105	3	appl	appl	PROPN
ejpam-5085	105	4	.	.	PROPN
ejpam-5085	105	5	math	math	PROPN
ejpam-5085	105	6	,	,	PUNCT
ejpam-5085	105	7	17	17	NUM
ejpam-5085	105	8	(	(	PUNCT
ejpam-5085	105	9	2	2	NUM
ejpam-5085	105	10	)	)	PUNCT
ejpam-5085	105	11	(	(	PUNCT
ejpam-5085	105	12	2024	2024	NUM
ejpam-5085	105	13	)	)	PUNCT
ejpam-5085	105	14	,	,	PUNCT
ejpam-5085	105	15	1197	1197	NUM
ejpam-5085	105	16	-	-	SYM
ejpam-5085	105	17	1205	1205	NUM
ejpam-5085	105	18	1202	1202	NUM
ejpam-5085	105	19	2.1	2.1	NUM
ejpam-5085	105	20	lemma	lemma	PROPN
ejpam-5085	105	21	.	.	PUNCT
ejpam-5085	106	1	let	let	VERB
ejpam-5085	106	2	m	m	PRON
ejpam-5085	106	3	be	be	AUX
ejpam-5085	106	4	a	a	DET
ejpam-5085	106	5	non	non	ADJ
ejpam-5085	106	6	-	-	ADJ
ejpam-5085	106	7	projective	projective	ADJ
ejpam-5085	106	8	module	module	NOUN
ejpam-5085	106	9	in	in	ADP
ejpam-5085	106	10	moda	moda	PROPN
ejpam-5085	106	11	with	with	ADP
ejpam-5085	106	12	rad2(m	rad2(m	NOUN
ejpam-5085	106	13	)	)	PUNCT
ejpam-5085	106	14	=	=	SYM
ejpam-5085	106	15	0	0	NUM
ejpam-5085	106	16	and	and	CCONJ
ejpam-5085	106	17	ωm	ωm	NOUN
ejpam-5085	106	18	indecompasable	indecompasable	ADJ
ejpam-5085	106	19	.	.	PUNCT
ejpam-5085	107	1	if	if	SCONJ
ejpam-5085	107	2	f	f	PROPN
ejpam-5085	107	3	:	:	PUNCT
ejpam-5085	107	4	p	p	X
ejpam-5085	107	5	(	(	PUNCT
ejpam-5085	107	6	m	m	PROPN
ejpam-5085	107	7	)	)	PUNCT
ejpam-5085	107	8	→	→	PUNCT
ejpam-5085	107	9	m	m	NOUN
ejpam-5085	107	10	is	be	AUX
ejpam-5085	107	11	a	a	DET
ejpam-5085	107	12	projective	projective	ADJ
ejpam-5085	107	13	cover	cover	NOUN
ejpam-5085	107	14	of	of	ADP
ejpam-5085	107	15	m	m	PRON
ejpam-5085	107	16	,	,	PUNCT
ejpam-5085	107	17	then	then	ADV
ejpam-5085	107	18	:	:	PUNCT
ejpam-5085	107	19	rad(ωm	rad(ωm	X
ejpam-5085	107	20	)	)	PUNCT
ejpam-5085	107	21	=	=	PUNCT
ejpam-5085	107	22	rad2(p	rad2(p	NOUN
ejpam-5085	107	23	(	(	PUNCT
ejpam-5085	107	24	m	m	NOUN
ejpam-5085	107	25	)	)	PUNCT
ejpam-5085	107	26	)	)	PUNCT
ejpam-5085	107	27	.	.	PUNCT
ejpam-5085	108	1	proof	proof	NOUN
ejpam-5085	108	2	.	.	PUNCT
ejpam-5085	109	1	let	let	VERB
ejpam-5085	109	2	f	f	NOUN
ejpam-5085	109	3	:	:	PUNCT
ejpam-5085	109	4	p	p	X
ejpam-5085	109	5	→	→	PUNCT
ejpam-5085	109	6	m	m	AUX
ejpam-5085	109	7	be	be	AUX
ejpam-5085	109	8	a	a	DET
ejpam-5085	109	9	projective	projective	ADJ
ejpam-5085	109	10	cover	cover	NOUN
ejpam-5085	109	11	of	of	ADP
ejpam-5085	109	12	m	m	PROPN
ejpam-5085	109	13	.	.	PUNCT
ejpam-5085	110	1	then	then	ADV
ejpam-5085	110	2	,	,	PUNCT
ejpam-5085	110	3	ωm	ωm	PUNCT
ejpam-5085	110	4	⊆	⊆	NUM
ejpam-5085	110	5	rad(p	rad(p	PROPN
ejpam-5085	110	6	)	)	PUNCT
ejpam-5085	110	7	,	,	PUNCT
ejpam-5085	110	8	and	and	CCONJ
ejpam-5085	110	9	hence	hence	ADV
ejpam-5085	110	10	,	,	PUNCT
ejpam-5085	110	11	rad(ωm	rad(ωm	NOUN
ejpam-5085	110	12	)	)	PUNCT
ejpam-5085	110	13	⊆	⊆	NUM
ejpam-5085	110	14	rad2(p	rad2(p	NOUN
ejpam-5085	110	15	)	)	PUNCT
ejpam-5085	110	16	.	.	PUNCT
ejpam-5085	111	1	since	since	SCONJ
ejpam-5085	111	2	rad2(m	rad2(m	NOUN
ejpam-5085	111	3	)	)	PUNCT
ejpam-5085	111	4	=	=	SYM
ejpam-5085	111	5	0	0	NUM
ejpam-5085	111	6	,	,	PUNCT
ejpam-5085	111	7	rad2(p	rad2(p	NOUN
ejpam-5085	111	8	)	)	PUNCT
ejpam-5085	111	9	⊆	⊆	NUM
ejpam-5085	111	10	ωm	ωm	SCONJ
ejpam-5085	111	11	.	.	PUNCT
ejpam-5085	111	12	suppose	suppose	VERB
ejpam-5085	111	13	that	that	SCONJ
ejpam-5085	111	14	rad2(p	rad2(p	NOUN
ejpam-5085	111	15	)	)	PUNCT
ejpam-5085	111	16	⊈	⊈	PROPN
ejpam-5085	111	17	rad(ωm	rad(ωm	NOUN
ejpam-5085	111	18	)	)	PUNCT
ejpam-5085	111	19	.	.	PUNCT
ejpam-5085	112	1	then	then	ADV
ejpam-5085	112	2	;	;	PUNCT
ejpam-5085	112	3	there	there	PRON
ejpam-5085	112	4	exists	exist	VERB
ejpam-5085	112	5	a	a	DET
ejpam-5085	112	6	maximal	maximal	ADJ
ejpam-5085	112	7	submodule	submodule	NOUN
ejpam-5085	112	8	l	l	NOUN
ejpam-5085	112	9	of	of	ADP
ejpam-5085	112	10	ωm	ωm	PUNCT
ejpam-5085	112	11	such	such	ADJ
ejpam-5085	112	12	that	that	SCONJ
ejpam-5085	112	13	rad2(p	rad2(p	NOUN
ejpam-5085	112	14	)	)	PUNCT
ejpam-5085	112	15	⊈	⊈	PROPN
ejpam-5085	112	16	l.	l.	NOUN
ejpam-5085	112	17	since	since	SCONJ
ejpam-5085	112	18	rad3(a	rad3(a	NUM
ejpam-5085	112	19	)	)	PUNCT
ejpam-5085	112	20	=	=	SYM
ejpam-5085	112	21	0	0	NUM
ejpam-5085	112	22	,	,	PUNCT
ejpam-5085	112	23	rad2(p	rad2(p	NOUN
ejpam-5085	112	24	)	)	PUNCT
ejpam-5085	112	25	is	be	AUX
ejpam-5085	112	26	semi	semi	ADJ
ejpam-5085	112	27	-	-	ADJ
ejpam-5085	112	28	simple	simple	ADJ
ejpam-5085	112	29	.	.	PUNCT
ejpam-5085	113	1	thus	thus	ADV
ejpam-5085	113	2	,	,	PUNCT
ejpam-5085	113	3	s	s	VERB
ejpam-5085	113	4	⊈	⊈	NOUN
ejpam-5085	113	5	l	l	NOUN
ejpam-5085	113	6	where	where	SCONJ
ejpam-5085	113	7	s	s	VERB
ejpam-5085	113	8	is	be	AUX
ejpam-5085	113	9	some	some	DET
ejpam-5085	113	10	simple	simple	ADJ
ejpam-5085	113	11	submodule	submodule	NOUN
ejpam-5085	113	12	of	of	ADP
ejpam-5085	113	13	rad2(p	rad2(p	NOUN
ejpam-5085	113	14	)	)	PUNCT
ejpam-5085	113	15	,	,	PUNCT
ejpam-5085	113	16	and	and	CCONJ
ejpam-5085	113	17	consequently	consequently	ADV
ejpam-5085	113	18	,	,	PUNCT
ejpam-5085	113	19	ωm	ωm	PROPN
ejpam-5085	114	1	=	=	SYM
ejpam-5085	114	2	s	s	PROPN
ejpam-5085	114	3	⊕	⊕	PROPN
ejpam-5085	114	4	l.	l.	NOUN
ejpam-5085	114	5	since	since	SCONJ
ejpam-5085	114	6	now	now	ADV
ejpam-5085	114	7	ωm	ωm	X
ejpam-5085	114	8	is	be	AUX
ejpam-5085	114	9	indecomposable	indecomposable	ADJ
ejpam-5085	114	10	,	,	PUNCT
ejpam-5085	114	11	there	there	PRON
ejpam-5085	114	12	is	be	VERB
ejpam-5085	114	13	a	a	DET
ejpam-5085	114	14	contradiction	contradiction	NOUN
ejpam-5085	114	15	and	and	CCONJ
ejpam-5085	114	16	the	the	DET
ejpam-5085	114	17	proof	proof	NOUN
ejpam-5085	114	18	of	of	ADP
ejpam-5085	114	19	the	the	DET
ejpam-5085	114	20	lemma	lemma	PROPN
ejpam-5085	114	21	is	be	AUX
ejpam-5085	114	22	complete	complete	ADJ
ejpam-5085	114	23	.	.	PUNCT
ejpam-5085	115	1	2.2	2.2	NUM
ejpam-5085	115	2	corollary	corollary	NOUN
ejpam-5085	115	3	.	.	PUNCT
ejpam-5085	116	1	let	let	VERB
ejpam-5085	116	2	m	m	PRON
ejpam-5085	116	3	be	be	AUX
ejpam-5085	116	4	a	a	DET
ejpam-5085	116	5	non	non	ADJ
ejpam-5085	116	6	-	-	ADJ
ejpam-5085	116	7	projective	projective	ADJ
ejpam-5085	116	8	and	and	CCONJ
ejpam-5085	116	9	indecomposable	indecomposable	ADJ
ejpam-5085	116	10	gorenstein	gorenstein	NOUN
ejpam-5085	116	11	-	-	PUNCT
ejpam-5085	116	12	projective	projective	NOUN
ejpam-5085	116	13	a	a	NOUN
ejpam-5085	116	14	-	-	PUNCT
ejpam-5085	116	15	module	module	NOUN
ejpam-5085	116	16	in	in	ADP
ejpam-5085	116	17	moda	moda	PROPN
ejpam-5085	116	18	with	with	ADP
ejpam-5085	116	19	rad2(m	rad2(m	NOUN
ejpam-5085	116	20	)	)	PUNCT
ejpam-5085	116	21	=	=	SYM
ejpam-5085	117	1	0	0	NUM
ejpam-5085	117	2	,	,	PUNCT
ejpam-5085	117	3	then	then	ADV
ejpam-5085	117	4	:	:	PUNCT
ejpam-5085	117	5	rad(ωm	rad(ωm	X
ejpam-5085	117	6	)	)	PUNCT
ejpam-5085	117	7	=	=	PUNCT
ejpam-5085	117	8	rad2(p	rad2(p	NOUN
ejpam-5085	117	9	(	(	PUNCT
ejpam-5085	117	10	m	m	NOUN
ejpam-5085	117	11	)	)	PUNCT
ejpam-5085	117	12	)	)	PUNCT
ejpam-5085	118	1	3	3	X
ejpam-5085	118	2	.	.	PUNCT
ejpam-5085	119	1	the	the	DET
ejpam-5085	119	2	self	self	NOUN
ejpam-5085	119	3	-	-	PUNCT
ejpam-5085	119	4	injectivity	injectivity	NOUN
ejpam-5085	119	5	and	and	CCONJ
ejpam-5085	119	6	cm	cm	NOUN
ejpam-5085	119	7	-	-	PUNCT
ejpam-5085	119	8	free	free	ADJ
ejpam-5085	119	9	algebras	algebra	NOUN
ejpam-5085	119	10	recall	recall	VERB
ejpam-5085	119	11	that	that	SCONJ
ejpam-5085	119	12	an	an	DET
ejpam-5085	119	13	artin	artin	PROPN
ejpam-5085	119	14	algebra	algebra	NOUN
ejpam-5085	119	15	a	a	PRON
ejpam-5085	119	16	is	be	AUX
ejpam-5085	119	17	said	say	VERB
ejpam-5085	119	18	to	to	PART
ejpam-5085	119	19	be	be	AUX
ejpam-5085	119	20	cm	cm	NOUN
ejpam-5085	119	21	-	-	NOUN
ejpam-5085	119	22	finite	finite	NOUN
ejpam-5085	119	23	if	if	SCONJ
ejpam-5085	119	24	,	,	PUNCT
ejpam-5085	119	25	up	up	ADP
ejpam-5085	119	26	to	to	ADP
ejpam-5085	119	27	isomorphism	isomorphism	NOUN
ejpam-5085	119	28	,	,	PUNCT
ejpam-5085	119	29	there	there	PRON
ejpam-5085	119	30	are	be	VERB
ejpam-5085	119	31	only	only	ADV
ejpam-5085	119	32	a	a	DET
ejpam-5085	119	33	finite	finite	ADJ
ejpam-5085	119	34	number	number	NOUN
ejpam-5085	119	35	of	of	ADP
ejpam-5085	119	36	indecomposable	indecomposable	ADJ
ejpam-5085	119	37	modules	module	NOUN
ejpam-5085	119	38	in	in	ADP
ejpam-5085	119	39	a	a	DET
ejpam-5085	119	40	-	-	PUNCT
ejpam-5085	119	41	gproj	gproj	NOUN
ejpam-5085	119	42	,	,	PUNCT
ejpam-5085	119	43	and	and	CCONJ
ejpam-5085	119	44	this	this	DET
ejpam-5085	119	45	algebra	algebra	NOUN
ejpam-5085	119	46	is	be	AUX
ejpam-5085	119	47	said	say	VERB
ejpam-5085	119	48	to	to	PART
ejpam-5085	119	49	be	be	AUX
ejpam-5085	119	50	cm	cm	NOUN
ejpam-5085	119	51	-	-	PUNCT
ejpam-5085	119	52	free	free	ADJ
ejpam-5085	119	53	if	if	SCONJ
ejpam-5085	119	54	each	each	DET
ejpam-5085	119	55	indecomposable	indecomposable	ADJ
ejpam-5085	119	56	gorenstein	gorenstein	ADJ
ejpam-5085	119	57	-	-	PUNCT
ejpam-5085	119	58	projective	projective	NOUN
ejpam-5085	119	59	module	module	NOUN
ejpam-5085	119	60	is	be	AUX
ejpam-5085	119	61	projective	projective	ADJ
ejpam-5085	119	62	.	.	PUNCT
ejpam-5085	120	1	the	the	DET
ejpam-5085	120	2	following	follow	VERB
ejpam-5085	120	3	theorem	theorem	NOUN
ejpam-5085	120	4	is	be	AUX
ejpam-5085	120	5	the	the	DET
ejpam-5085	120	6	extension	extension	NOUN
ejpam-5085	120	7	of	of	ADP
ejpam-5085	120	8	theorem	theorem	ADJ
ejpam-5085	120	9	2.3.9	2.3.9	NUM
ejpam-5085	120	10	quoted	quote	VERB
ejpam-5085	120	11	by	by	ADP
ejpam-5085	120	12	[	[	X
ejpam-5085	120	13	2	2	NUM
ejpam-5085	120	14	]	]	PUNCT
ejpam-5085	120	15	in	in	ADP
ejpam-5085	120	16	the	the	DET
ejpam-5085	120	17	case	case	NOUN
ejpam-5085	120	18	rad3(a	rad3(a	NUM
ejpam-5085	120	19	)	)	PUNCT
ejpam-5085	120	20	=	=	SYM
ejpam-5085	120	21	0	0	PUNCT
ejpam-5085	121	1	under	under	ADP
ejpam-5085	121	2	some	some	DET
ejpam-5085	121	3	condition	condition	NOUN
ejpam-5085	121	4	and	and	CCONJ
ejpam-5085	121	5	the	the	DET
ejpam-5085	121	6	generalization	generalization	NOUN
ejpam-5085	121	7	is	be	AUX
ejpam-5085	121	8	false	false	ADJ
ejpam-5085	121	9	as	as	SCONJ
ejpam-5085	121	10	the	the	DET
ejpam-5085	121	11	author	author	NOUN
ejpam-5085	121	12	has	have	AUX
ejpam-5085	121	13	given	give	VERB
ejpam-5085	121	14	this	this	DET
ejpam-5085	121	15	counterexample	counterexample	NOUN
ejpam-5085	121	16	:	:	PUNCT
ejpam-5085	121	17	leta	leta	PROPN
ejpam-5085	121	18	=	=	X
ejpam-5085	121	19	[	[	PUNCT
ejpam-5085	121	20	k[x]/(x2	k[x]/(x2	NOUN
ejpam-5085	121	21	)	)	PUNCT
ejpam-5085	121	22	k[x]/(x2	k[x]/(x2	NOUN
ejpam-5085	121	23	)	)	PUNCT
ejpam-5085	121	24	0	0	NUM
ejpam-5085	122	1	k[x]/(x2	k[x]/(x2	NOUN
ejpam-5085	122	2	)	)	PUNCT
ejpam-5085	123	1	]	]	PUNCT
ejpam-5085	123	2	be	be	AUX
ejpam-5085	123	3	the	the	DET
ejpam-5085	123	4	artin	artin	PROPN
ejpam-5085	123	5	algebra	algebra	PROPN
ejpam-5085	123	6	,	,	PUNCT
ejpam-5085	123	7	it	it	PRON
ejpam-5085	123	8	is	be	AUX
ejpam-5085	123	9	easy	easy	ADJ
ejpam-5085	123	10	to	to	PART
ejpam-5085	123	11	show	show	VERB
ejpam-5085	123	12	that	that	SCONJ
ejpam-5085	123	13	rad3(a	rad3(a	NOUN
ejpam-5085	123	14	)	)	PUNCT
ejpam-5085	123	15	=	=	SYM
ejpam-5085	123	16	0	0	NUM
ejpam-5085	123	17	and	and	CCONJ
ejpam-5085	123	18	rad2(a	rad2(a	NOUN
ejpam-5085	123	19	)	)	PUNCT
ejpam-5085	123	20	̸=	̸=	PROPN
ejpam-5085	123	21	0	0	NUM
ejpam-5085	123	22	.	.	PUNCT
ejpam-5085	124	1	also	also	ADV
ejpam-5085	124	2	,	,	PUNCT
ejpam-5085	124	3	it	it	PRON
ejpam-5085	124	4	is	be	AUX
ejpam-5085	124	5	not	not	PART
ejpam-5085	124	6	self	self	NOUN
ejpam-5085	124	7	-	-	PUNCT
ejpam-5085	124	8	injective	injective	ADJ
ejpam-5085	124	9	.	.	PUNCT
ejpam-5085	125	1	our	our	PRON
ejpam-5085	125	2	work	work	NOUN
ejpam-5085	125	3	shows	show	VERB
ejpam-5085	125	4	that	that	SCONJ
ejpam-5085	125	5	the	the	DET
ejpam-5085	125	6	result	result	NOUN
ejpam-5085	125	7	is	be	AUX
ejpam-5085	125	8	true	true	ADJ
ejpam-5085	125	9	in	in	ADP
ejpam-5085	125	10	a	a	DET
ejpam-5085	125	11	particular	particular	ADJ
ejpam-5085	125	12	case	case	NOUN
ejpam-5085	125	13	for	for	ADP
ejpam-5085	125	14	a	a	DET
ejpam-5085	125	15	specific	specific	ADJ
ejpam-5085	125	16	algebra	algebra	NOUN
ejpam-5085	125	17	that	that	PRON
ejpam-5085	125	18	we	we	PRON
ejpam-5085	125	19	will	will	AUX
ejpam-5085	125	20	introduce	introduce	VERB
ejpam-5085	125	21	its	its	PRON
ejpam-5085	125	22	definition	definition	NOUN
ejpam-5085	125	23	,	,	PUNCT
ejpam-5085	125	24	3.1	3.1	NUM
ejpam-5085	125	25	definition	definition	NOUN
ejpam-5085	125	26	.	.	PUNCT
ejpam-5085	126	1	let	let	VERB
ejpam-5085	126	2	a	a	DET
ejpam-5085	126	3	be	be	AUX
ejpam-5085	126	4	an	an	DET
ejpam-5085	126	5	artin	artin	PROPN
ejpam-5085	126	6	algebra	algebra	NOUN
ejpam-5085	126	7	,	,	PUNCT
ejpam-5085	126	8	we	we	PRON
ejpam-5085	126	9	say	say	VERB
ejpam-5085	126	10	that	that	SCONJ
ejpam-5085	126	11	a	a	DET
ejpam-5085	126	12	verifies	verifie	NOUN
ejpam-5085	126	13	the	the	DET
ejpam-5085	126	14	coincidence	coincidence	NOUN
ejpam-5085	126	15	covers	cover	VERB
ejpam-5085	126	16	if	if	SCONJ
ejpam-5085	126	17	,	,	PUNCT
ejpam-5085	126	18	p	p	X
ejpam-5085	126	19	(	(	PUNCT
ejpam-5085	126	20	ω(s	ω(s	NOUN
ejpam-5085	126	21	)	)	PUNCT
ejpam-5085	126	22	)	)	PUNCT
ejpam-5085	126	23	≃	≃	NOUN
ejpam-5085	126	24	p	p	NOUN
ejpam-5085	126	25	(	(	PUNCT
ejpam-5085	126	26	ω(t	ω(t	NOUN
ejpam-5085	126	27	)	)	PUNCT
ejpam-5085	126	28	)	)	PUNCT
ejpam-5085	126	29	implies	imply	VERB
ejpam-5085	126	30	s	s	NOUN
ejpam-5085	126	31	≃	≃	PROPN
ejpam-5085	126	32	t	t	NOUN
ejpam-5085	126	33	for	for	ADP
ejpam-5085	126	34	all	all	DET
ejpam-5085	126	35	s	s	PART
ejpam-5085	126	36	and	and	CCONJ
ejpam-5085	126	37	t	t	PROPN
ejpam-5085	126	38	simples	simple	NOUN
ejpam-5085	126	39	modules	module	NOUN
ejpam-5085	126	40	.	.	PUNCT
ejpam-5085	127	1	3.2	3.2	NUM
ejpam-5085	127	2	theorem	theorem	VERB
ejpam-5085	127	3	.	.	PUNCT
ejpam-5085	128	1	let	let	VERB
ejpam-5085	128	2	a	a	DET
ejpam-5085	128	3	be	be	AUX
ejpam-5085	128	4	a	a	DET
ejpam-5085	128	5	connected	connected	ADJ
ejpam-5085	128	6	artin	artin	NOUN
ejpam-5085	128	7	algebra	algebra	PROPN
ejpam-5085	128	8	with	with	ADP
ejpam-5085	128	9	radical	radical	ADJ
ejpam-5085	128	10	cubed	cubed	NOUN
ejpam-5085	128	11	zero	zero	NUM
ejpam-5085	128	12	,	,	PUNCT
ejpam-5085	128	13	and	and	CCONJ
ejpam-5085	128	14	rad2(p	rad2(p	NOUN
ejpam-5085	128	15	(	(	PUNCT
ejpam-5085	128	16	ωm	ωm	NOUN
ejpam-5085	128	17	)	)	PUNCT
ejpam-5085	128	18	)	)	PUNCT
ejpam-5085	129	1	=	=	SYM
ejpam-5085	129	2	0	0	NUM
ejpam-5085	129	3	for	for	ADP
ejpam-5085	129	4	any	any	DET
ejpam-5085	129	5	a	a	DET
ejpam-5085	129	6	-	-	PUNCT
ejpam-5085	129	7	module	module	NOUN
ejpam-5085	129	8	m	m	NOUN
ejpam-5085	129	9	either	either	CCONJ
ejpam-5085	129	10	simple	simple	ADJ
ejpam-5085	129	11	or	or	CCONJ
ejpam-5085	129	12	gorenstein	gorenstein	ADV
ejpam-5085	129	13	-	-	PUNCT
ejpam-5085	129	14	projective	projective	NOUN
ejpam-5085	129	15	and	and	CCONJ
ejpam-5085	129	16	verifying	verify	VERB
ejpam-5085	129	17	the	the	DET
ejpam-5085	129	18	coincidence	coincidence	NOUN
ejpam-5085	129	19	covers	cover	VERB
ejpam-5085	129	20	,	,	PUNCT
ejpam-5085	129	21	then	then	ADV
ejpam-5085	129	22	a	a	PRON
ejpam-5085	129	23	is	be	AUX
ejpam-5085	129	24	self	self	NOUN
ejpam-5085	129	25	-	-	PUNCT
ejpam-5085	129	26	injective	injective	ADJ
ejpam-5085	129	27	or	or	CCONJ
ejpam-5085	129	28	cm	cm	NOUN
ejpam-5085	129	29	-	-	PUNCT
ejpam-5085	129	30	free	free	ADJ
ejpam-5085	129	31	.	.	PUNCT
ejpam-5085	130	1	proof	proof	NOUN
ejpam-5085	130	2	.	.	PUNCT
ejpam-5085	131	1	suppose	suppose	VERB
ejpam-5085	131	2	that	that	SCONJ
ejpam-5085	131	3	a	a	PRON
ejpam-5085	131	4	is	be	AUX
ejpam-5085	131	5	not	not	PART
ejpam-5085	131	6	cm	cm	NOUN
ejpam-5085	131	7	-	-	PUNCT
ejpam-5085	131	8	free	free	ADJ
ejpam-5085	131	9	,	,	PUNCT
ejpam-5085	131	10	then	then	ADV
ejpam-5085	131	11	there	there	PRON
ejpam-5085	131	12	exists	exist	VERB
ejpam-5085	131	13	a	a	DET
ejpam-5085	131	14	non	non	ADJ
ejpam-5085	131	15	-	-	ADJ
ejpam-5085	131	16	projective	projective	ADJ
ejpam-5085	131	17	indecomposable	indecomposable	ADJ
ejpam-5085	131	18	a	a	DET
ejpam-5085	131	19	-	-	PUNCT
ejpam-5085	131	20	module	module	NOUN
ejpam-5085	131	21	m	m	NOUN
ejpam-5085	131	22	and	and	CCONJ
ejpam-5085	131	23	gorenstein	gorenstein	NOUN
ejpam-5085	131	24	-	-	PUNCT
ejpam-5085	131	25	projective	projective	NOUN
ejpam-5085	131	26	,	,	PUNCT
ejpam-5085	131	27	and	and	CCONJ
ejpam-5085	131	28	we	we	PRON
ejpam-5085	131	29	have	have	VERB
ejpam-5085	131	30	a	a	DET
ejpam-5085	131	31	short	short	ADJ
ejpam-5085	131	32	exact	exact	NOUN
ejpam-5085	131	33	not	not	PART
ejpam-5085	131	34	-	-	PUNCT
ejpam-5085	131	35	split	split	ADJ
ejpam-5085	131	36	sequence	sequence	NOUN
ejpam-5085	131	37	:	:	PUNCT
ejpam-5085	131	38	0	0	NUM
ejpam-5085	131	39	//m	//m	PUNCT
ejpam-5085	131	40	f	f	PROPN
ejpam-5085	131	41	//	//	X
ejpam-5085	131	42	p	p	X
ejpam-5085	131	43	(	(	PUNCT
ejpam-5085	131	44	m	m	NOUN
ejpam-5085	131	45	)	)	PUNCT
ejpam-5085	131	46	p	p	NOUN
ejpam-5085	131	47	//m	//m	PROPN
ejpam-5085	131	48	′	′	NUM
ejpam-5085	131	49	//	//	NOUN
ejpam-5085	131	50	0	0	NUM
ejpam-5085	131	51	m.	m.	NOUN
ejpam-5085	131	52	laaraj	laaraj	PROPN
ejpam-5085	131	53	,	,	PUNCT
ejpam-5085	131	54	s.	s.	PROPN
ejpam-5085	131	55	abdelalim	abdelalim	PROPN
ejpam-5085	131	56	/	/	SYM
ejpam-5085	131	57	eur	eur	PROPN
ejpam-5085	131	58	.	.	PUNCT
ejpam-5085	132	1	j.	j.	PROPN
ejpam-5085	132	2	pure	pure	PROPN
ejpam-5085	132	3	appl	appl	PROPN
ejpam-5085	132	4	.	.	PROPN
ejpam-5085	132	5	math	math	PROPN
ejpam-5085	132	6	,	,	PUNCT
ejpam-5085	132	7	17	17	NUM
ejpam-5085	132	8	(	(	PUNCT
ejpam-5085	132	9	2	2	NUM
ejpam-5085	132	10	)	)	PUNCT
ejpam-5085	132	11	(	(	PUNCT
ejpam-5085	132	12	2024	2024	NUM
ejpam-5085	132	13	)	)	PUNCT
ejpam-5085	132	14	,	,	PUNCT
ejpam-5085	132	15	1197	1197	NUM
ejpam-5085	132	16	-	-	SYM
ejpam-5085	132	17	1205	1205	NUM
ejpam-5085	132	18	1203	1203	NUM
ejpam-5085	132	19	and	and	CCONJ
ejpam-5085	132	20	we	we	PRON
ejpam-5085	132	21	have	have	VERB
ejpam-5085	132	22	m	m	VERB
ejpam-5085	132	23	′	′	NUM
ejpam-5085	132	24	=	=	SYM
ejpam-5085	132	25	coker(f	coker(f	NOUN
ejpam-5085	132	26	)	)	PUNCT
ejpam-5085	132	27	is	be	AUX
ejpam-5085	132	28	a	a	DET
ejpam-5085	132	29	gorenstein	gorenstein	NOUN
ejpam-5085	132	30	-	-	PUNCT
ejpam-5085	132	31	projective	projective	NOUN
ejpam-5085	132	32	a	a	NOUN
ejpam-5085	132	33	-	-	PUNCT
ejpam-5085	132	34	module	module	NOUN
ejpam-5085	132	35	and	and	CCONJ
ejpam-5085	132	36	p	p	NOUN
ejpam-5085	132	37	is	be	AUX
ejpam-5085	132	38	the	the	DET
ejpam-5085	132	39	projective	projective	ADJ
ejpam-5085	132	40	cover	cover	NOUN
ejpam-5085	132	41	of	of	ADP
ejpam-5085	132	42	m	m	PROPN
ejpam-5085	132	43	′	′	NOUN
ejpam-5085	132	44	,	,	PUNCT
ejpam-5085	132	45	then	then	ADV
ejpam-5085	132	46	ω(m	ω(m	NOUN
ejpam-5085	132	47	′	′	NUM
ejpam-5085	132	48	)	)	PUNCT
ejpam-5085	133	1	=	=	SYM
ejpam-5085	134	1	m	m	ADJ
ejpam-5085	134	2	and	and	CCONJ
ejpam-5085	134	3	since	since	SCONJ
ejpam-5085	134	4	ω(m	ω(m	NOUN
ejpam-5085	134	5	′	′	NUM
ejpam-5085	134	6	)	)	PUNCT
ejpam-5085	135	1	⊆	⊆	NUM
ejpam-5085	135	2	rad(p	rad(p	PROPN
ejpam-5085	135	3	(	(	PUNCT
ejpam-5085	135	4	m	m	NOUN
ejpam-5085	135	5	)	)	PUNCT
ejpam-5085	135	6	)	)	PUNCT
ejpam-5085	135	7	,	,	PUNCT
ejpam-5085	135	8	then	then	ADV
ejpam-5085	135	9	rad2(ω(m	rad2(ω(m	VERB
ejpam-5085	135	10	′	′	NUM
ejpam-5085	135	11	)	)	PUNCT
ejpam-5085	135	12	)	)	PUNCT
ejpam-5085	136	1	=	=	SYM
ejpam-5085	136	2	0	0	NUM
ejpam-5085	136	3	,	,	PUNCT
ejpam-5085	136	4	i.e.	i.e.	X
ejpam-5085	136	5	rad2(m	rad2(m	NOUN
ejpam-5085	136	6	)	)	PUNCT
ejpam-5085	136	7	=	=	SYM
ejpam-5085	136	8	0	0	PUNCT
ejpam-5085	136	9	and	and	CCONJ
ejpam-5085	136	10	since	since	SCONJ
ejpam-5085	136	11	m	m	PROPN
ejpam-5085	136	12	is	be	AUX
ejpam-5085	136	13	non	non	ADJ
ejpam-5085	136	14	-	-	ADJ
ejpam-5085	136	15	projective	projective	ADJ
ejpam-5085	136	16	and	and	CCONJ
ejpam-5085	136	17	indecomposable	indecomposable	ADJ
ejpam-5085	136	18	,	,	PUNCT
ejpam-5085	136	19	then	then	ADV
ejpam-5085	136	20	by	by	ADP
ejpam-5085	136	21	corollary	corollary	ADJ
ejpam-5085	136	22	2	2	NUM
ejpam-5085	136	23	,	,	PUNCT
ejpam-5085	136	24	we	we	PRON
ejpam-5085	136	25	have	have	VERB
ejpam-5085	136	26	rad(ω(m	rad(ω(m	NOUN
ejpam-5085	136	27	)	)	PUNCT
ejpam-5085	136	28	)	)	PUNCT
ejpam-5085	137	1	=	=	PUNCT
ejpam-5085	137	2	rad2(p	rad2(p	NOUN
ejpam-5085	137	3	(	(	PUNCT
ejpam-5085	137	4	m	m	NOUN
ejpam-5085	137	5	)	)	PUNCT
ejpam-5085	137	6	)	)	PUNCT
ejpam-5085	138	1	=	=	PUNCT
ejpam-5085	138	2	rad2(p	rad2(p	NOUN
ejpam-5085	138	3	(	(	PUNCT
ejpam-5085	138	4	ω(m	ω(m	NOUN
ejpam-5085	138	5	′	′	NUM
ejpam-5085	138	6	)	)	PUNCT
ejpam-5085	138	7	)	)	PUNCT
ejpam-5085	138	8	)	)	PUNCT
ejpam-5085	139	1	=	=	SYM
ejpam-5085	139	2	0	0	NUM
ejpam-5085	139	3	,	,	PUNCT
ejpam-5085	139	4	then	then	ADV
ejpam-5085	139	5	ω(m	ω(m	NOUN
ejpam-5085	139	6	)	)	PUNCT
ejpam-5085	139	7	is	be	AUX
ejpam-5085	139	8	semisimple	semisimple	ADJ
ejpam-5085	139	9	and	and	CCONJ
ejpam-5085	139	10	since	since	SCONJ
ejpam-5085	139	11	ω(m	ω(m	NOUN
ejpam-5085	139	12	)	)	PUNCT
ejpam-5085	139	13	is	be	AUX
ejpam-5085	139	14	indecomposable	indecomposable	ADJ
ejpam-5085	139	15	,	,	PUNCT
ejpam-5085	139	16	the	the	DET
ejpam-5085	139	17	a	a	NOUN
ejpam-5085	139	18	-	-	PUNCT
ejpam-5085	139	19	module	module	NOUN
ejpam-5085	139	20	ω(m	ω(m	NOUN
ejpam-5085	139	21	)	)	PUNCT
ejpam-5085	139	22	is	be	AUX
ejpam-5085	139	23	simple	simple	ADJ
ejpam-5085	139	24	.	.	PUNCT
ejpam-5085	140	1	let	let	VERB
ejpam-5085	140	2	s1	s1	PROPN
ejpam-5085	140	3	=	=	SYM
ejpam-5085	140	4	ω(m	ω(m	NOUN
ejpam-5085	140	5	)	)	PUNCT
ejpam-5085	140	6	and	and	CCONJ
ejpam-5085	140	7	take	take	VERB
ejpam-5085	140	8	the	the	DET
ejpam-5085	140	9	short	short	ADJ
ejpam-5085	140	10	not	not	PART
ejpam-5085	140	11	-	-	PUNCT
ejpam-5085	140	12	split	split	VERB
ejpam-5085	140	13	exact	exact	ADJ
ejpam-5085	140	14	sequence	sequence	NOUN
ejpam-5085	140	15	:	:	PUNCT
ejpam-5085	140	16	0	0	NUM
ejpam-5085	140	17	//	//	NUM
ejpam-5085	140	18	ω(s1	ω(s1	X
ejpam-5085	140	19	)	)	PUNCT
ejpam-5085	140	20	i2	i2	PROPN
ejpam-5085	140	21	//	//	PROPN
ejpam-5085	140	22	p0	p0	PROPN
ejpam-5085	140	23	p	p	PROPN
ejpam-5085	140	24	//	//	PROPN
ejpam-5085	140	25	s1	s1	PROPN
ejpam-5085	140	26	//	//	X
ejpam-5085	140	27	0	0	NUM
ejpam-5085	141	1	we	we	PRON
ejpam-5085	141	2	consider	consider	VERB
ejpam-5085	141	3	s2	s2	NOUN
ejpam-5085	141	4	=	=	SYM
ejpam-5085	141	5	ω(s1	ω(s1	X
ejpam-5085	141	6	)	)	PUNCT
ejpam-5085	141	7	,	,	PUNCT
ejpam-5085	141	8	then	then	ADV
ejpam-5085	141	9	ext1a(s1	ext1a(s1	NOUN
ejpam-5085	141	10	,	,	PUNCT
ejpam-5085	141	11	s2	s2	PROPN
ejpam-5085	141	12	)	)	PUNCT
ejpam-5085	141	13	̸=	̸=	PROPN
ejpam-5085	141	14	0	0	NUM
ejpam-5085	142	1	and	and	CCONJ
ejpam-5085	142	2	we	we	PRON
ejpam-5085	142	3	are	be	AUX
ejpam-5085	142	4	finding	find	VERB
ejpam-5085	142	5	an	an	DET
ejpam-5085	142	6	arrow	arrow	NOUN
ejpam-5085	142	7	in	in	ADP
ejpam-5085	142	8	s1	s1	NOUN
ejpam-5085	142	9	to	to	PART
ejpam-5085	142	10	s2	s2	VERB
ejpam-5085	142	11	because	because	SCONJ
ejpam-5085	142	12	s2	s2	PROPN
ejpam-5085	142	13	is	be	AUX
ejpam-5085	142	14	non	non	ADJ
ejpam-5085	142	15	-	-	ADJ
ejpam-5085	142	16	projective	projective	ADJ
ejpam-5085	142	17	and	and	CCONJ
ejpam-5085	142	18	indecomposable	indecomposable	ADJ
ejpam-5085	142	19	,	,	PUNCT
ejpam-5085	142	20	i.e.	i.e.	X
ejpam-5085	142	21	s2	s2	PROPN
ejpam-5085	142	22	is	be	AUX
ejpam-5085	142	23	a	a	DET
ejpam-5085	142	24	simple	simple	ADJ
ejpam-5085	142	25	module	module	NOUN
ejpam-5085	142	26	.	.	PUNCT
ejpam-5085	143	1	in	in	ADP
ejpam-5085	143	2	fact	fact	NOUN
ejpam-5085	143	3	,	,	PUNCT
ejpam-5085	143	4	we	we	PRON
ejpam-5085	143	5	show	show	VERB
ejpam-5085	143	6	that	that	SCONJ
ejpam-5085	143	7	the	the	DET
ejpam-5085	143	8	only	only	ADJ
ejpam-5085	143	9	arrow	arrow	NOUN
ejpam-5085	143	10	having	have	VERB
ejpam-5085	143	11	the	the	DET
ejpam-5085	143	12	target	target	NOUN
ejpam-5085	143	13	s2	s2	NOUN
ejpam-5085	143	14	has	have	VERB
ejpam-5085	143	15	s1	s1	NOUN
ejpam-5085	143	16	for	for	ADP
ejpam-5085	143	17	vertices	vertex	NOUN
ejpam-5085	143	18	in	in	ADP
ejpam-5085	143	19	the	the	DET
ejpam-5085	143	20	contrast	contrast	NOUN
ejpam-5085	143	21	case	case	NOUN
ejpam-5085	143	22	,	,	PUNCT
ejpam-5085	143	23	assume	assume	VERB
ejpam-5085	143	24	that	that	SCONJ
ejpam-5085	143	25	there	there	PRON
ejpam-5085	143	26	exists	exist	VERB
ejpam-5085	143	27	a	a	DET
ejpam-5085	143	28	simple	simple	ADJ
ejpam-5085	143	29	module	module	NOUN
ejpam-5085	143	30	s	s	PRON
ejpam-5085	143	31	such	such	ADJ
ejpam-5085	143	32	that	that	DET
ejpam-5085	143	33	ext1a(s	ext1a(s	PROPN
ejpam-5085	143	34	,	,	PUNCT
ejpam-5085	143	35	s2	s2	PROPN
ejpam-5085	143	36	)	)	PUNCT
ejpam-5085	143	37	̸=	̸=	PROPN
ejpam-5085	143	38	0	0	NUM
ejpam-5085	143	39	and	and	CCONJ
ejpam-5085	143	40	consider	consider	VERB
ejpam-5085	143	41	the	the	DET
ejpam-5085	143	42	projective	projective	ADJ
ejpam-5085	143	43	resolution	resolution	NOUN
ejpam-5085	143	44	of	of	ADP
ejpam-5085	143	45	s	s	NOUN
ejpam-5085	143	46	is	be	AUX
ejpam-5085	143	47	as	as	SCONJ
ejpam-5085	143	48	follows	follow	VERB
ejpam-5085	143	49	:	:	PUNCT
ejpam-5085	143	50	0	0	NUM
ejpam-5085	143	51	//	//	NUM
ejpam-5085	143	52	ω2(s	ω2(s	NUM
ejpam-5085	143	53	)	)	PUNCT
ejpam-5085	143	54	//	//	X
ejpam-5085	144	1	p1(s	p1(s	NOUN
ejpam-5085	144	2	)	)	PUNCT
ejpam-5085	144	3	//	//	NOUN
ejpam-5085	144	4	p0(s	p0(s	X
ejpam-5085	144	5	)	)	PUNCT
ejpam-5085	144	6	//	//	PROPN
ejpam-5085	144	7	s	s	PART
ejpam-5085	145	1	//	//	NOUN
ejpam-5085	145	2	0	0	NUM
ejpam-5085	146	1	we	we	PRON
ejpam-5085	146	2	know	know	VERB
ejpam-5085	146	3	that	that	SCONJ
ejpam-5085	146	4	,	,	PUNCT
ejpam-5085	146	5	0	0	NUM
ejpam-5085	146	6	//	//	SYM
ejpam-5085	147	1	ω(s	ω(s	PROPN
ejpam-5085	147	2	)	)	PUNCT
ejpam-5085	148	1	i0	i0	PROPN
ejpam-5085	148	2	//	//	NUM
ejpam-5085	148	3	p0(s	p0(s	PROPN
ejpam-5085	148	4	)	)	PUNCT
ejpam-5085	148	5	//	//	PROPN
ejpam-5085	148	6	s	s	PART
ejpam-5085	148	7	//	//	X
ejpam-5085	148	8	0	0	NUM
ejpam-5085	148	9	and	and	CCONJ
ejpam-5085	148	10	0	0	NUM
ejpam-5085	148	11	//	//	NUM
ejpam-5085	148	12	ω2(s	ω2(s	NUM
ejpam-5085	148	13	)	)	PUNCT
ejpam-5085	148	14	//	//	PUNCT
ejpam-5085	148	15	p1(s	p1(s	NOUN
ejpam-5085	148	16	)	)	PUNCT
ejpam-5085	148	17	//	//	NOUN
ejpam-5085	148	18	ω(s	ω(s	PROPN
ejpam-5085	148	19	)	)	PUNCT
ejpam-5085	148	20	//	//	NOUN
ejpam-5085	148	21	0	0	NUM
ejpam-5085	148	22	are	be	AUX
ejpam-5085	148	23	the	the	DET
ejpam-5085	148	24	short	short	ADJ
ejpam-5085	148	25	exact	exact	ADJ
ejpam-5085	148	26	sequences	sequence	NOUN
ejpam-5085	148	27	characterezing	charactereze	VERB
ejpam-5085	148	28	the	the	DET
ejpam-5085	148	29	first	first	ADJ
ejpam-5085	148	30	and	and	CCONJ
ejpam-5085	148	31	second	second	ADJ
ejpam-5085	148	32	syzygy	syzygy	NOUN
ejpam-5085	148	33	of	of	ADP
ejpam-5085	148	34	s	s	PROPN
ejpam-5085	148	35	,	,	PUNCT
ejpam-5085	148	36	then	then	ADV
ejpam-5085	148	37	ω2(s	ω2(s	NUM
ejpam-5085	148	38	)	)	PUNCT
ejpam-5085	148	39	⊆	⊆	NUM
ejpam-5085	148	40	rad(p1(s	rad(p1(	NOUN
ejpam-5085	148	41	)	)	PUNCT
ejpam-5085	148	42	)	)	PUNCT
ejpam-5085	148	43	and	and	CCONJ
ejpam-5085	148	44	since	since	SCONJ
ejpam-5085	148	45	rad2(p1(s	rad2(p1(	NOUN
ejpam-5085	148	46	)	)	PUNCT
ejpam-5085	148	47	)	)	PUNCT
ejpam-5085	149	1	=	=	SYM
ejpam-5085	149	2	0	0	NUM
ejpam-5085	149	3	,	,	PUNCT
ejpam-5085	149	4	then	then	ADV
ejpam-5085	149	5	rad(ω2(s	rad(ω2(s	NOUN
ejpam-5085	149	6	)	)	PUNCT
ejpam-5085	149	7	)	)	PUNCT
ejpam-5085	150	1	=	=	PUNCT
ejpam-5085	150	2	0	0	NUM
ejpam-5085	150	3	,	,	PUNCT
ejpam-5085	150	4	then	then	ADV
ejpam-5085	150	5	ω2(s	ω2(s	NUM
ejpam-5085	150	6	)	)	PUNCT
ejpam-5085	150	7	is	be	AUX
ejpam-5085	150	8	a	a	DET
ejpam-5085	150	9	semisimple	semisimple	NOUN
ejpam-5085	150	10	module	module	NOUN
ejpam-5085	150	11	.	.	PUNCT
ejpam-5085	151	1	since	since	SCONJ
ejpam-5085	151	2	ext1a(s	ext1a(s	PROPN
ejpam-5085	151	3	,	,	PUNCT
ejpam-5085	151	4	s2	s2	PROPN
ejpam-5085	151	5	)	)	PUNCT
ejpam-5085	151	6	̸=	̸=	PROPN
ejpam-5085	151	7	0	0	NUM
ejpam-5085	151	8	and	and	CCONJ
ejpam-5085	151	9	hom(ω(s	hom(ω(s	PROPN
ejpam-5085	151	10	)	)	PUNCT
ejpam-5085	151	11	,	,	PUNCT
ejpam-5085	151	12	s2	s2	PROPN
ejpam-5085	151	13	)	)	PUNCT
ejpam-5085	151	14	̸=	̸=	PROPN
ejpam-5085	151	15	0	0	NUM
ejpam-5085	152	1	so	so	CCONJ
ejpam-5085	152	2	,	,	PUNCT
ejpam-5085	152	3	there	there	PRON
ejpam-5085	152	4	exists	exist	VERB
ejpam-5085	152	5	an	an	DET
ejpam-5085	152	6	epimorphism	epimorphism	NOUN
ejpam-5085	152	7	f	f	PROPN
ejpam-5085	152	8	̸=	̸=	PROPN
ejpam-5085	152	9	0	0	NUM
ejpam-5085	152	10	in	in	ADP
ejpam-5085	152	11	hom(ω(s),ω(s1	hom(ω(s),ω(s1	NOUN
ejpam-5085	152	12	)	)	PUNCT
ejpam-5085	152	13	)	)	PUNCT
ejpam-5085	152	14	and	and	CCONJ
ejpam-5085	152	15	we	we	PRON
ejpam-5085	152	16	get	get	VERB
ejpam-5085	152	17	the	the	DET
ejpam-5085	152	18	diagram	diagram	NOUN
ejpam-5085	152	19	:	:	PUNCT
ejpam-5085	152	20	0	0	NUM
ejpam-5085	152	21	//	//	SYM
ejpam-5085	152	22	ω2(s	ω2(s	NUM
ejpam-5085	152	23	)	)	PUNCT
ejpam-5085	153	1	i	i	PRON
ejpam-5085	153	2	//	//	VERB
ejpam-5085	153	3	g	g	PROPN
ejpam-5085	153	4	�	�	PROPN
ejpam-5085	153	5	�	�	PROPN
ejpam-5085	153	6	p	p	PROPN
ejpam-5085	153	7	π	π	PROPN
ejpam-5085	153	8	//	//	PROPN
ejpam-5085	153	9	h	h	PROPN
ejpam-5085	153	10	�	�	PROPN
ejpam-5085	153	11	�	�	PROPN
ejpam-5085	153	12	ω(s	ω(s	PROPN
ejpam-5085	153	13	)	)	PUNCT
ejpam-5085	153	14	//	//	NOUN
ejpam-5085	153	15	f	f	PROPN
ejpam-5085	153	16	�	�	PROPN
ejpam-5085	153	17	�	�	PROPN
ejpam-5085	153	18	0	0	NUM
ejpam-5085	153	19	0	0	NUM
ejpam-5085	153	20	//	//	SYM
ejpam-5085	153	21	ω2(s1	ω2(s1	PROPN
ejpam-5085	153	22	)	)	PUNCT
ejpam-5085	153	23	i1	i1	PROPN
ejpam-5085	153	24	//	//	SYM
ejpam-5085	153	25	p1	p1	PROPN
ejpam-5085	153	26	π1	π1	PROPN
ejpam-5085	153	27	//	//	X
ejpam-5085	154	1	k	k	X
ejpam-5085	154	2	<	<	X
ejpam-5085	154	3	<	<	X
ejpam-5085	154	4	ω(s1	ω(s1	X
ejpam-5085	154	5	)	)	PUNCT
ejpam-5085	154	6	//	//	X
ejpam-5085	154	7	0	0	NUM
ejpam-5085	154	8	,	,	PUNCT
ejpam-5085	154	9	then	then	ADV
ejpam-5085	154	10	f	f	PROPN
ejpam-5085	154	11	̸=	̸=	PROPN
ejpam-5085	154	12	0	0	NUM
ejpam-5085	154	13	implies	imply	VERB
ejpam-5085	154	14	h	h	NOUN
ejpam-5085	154	15	̸=	̸=	PROPN
ejpam-5085	154	16	0	0	PUNCT
ejpam-5085	154	17	if	if	SCONJ
ejpam-5085	154	18	not	not	PART
ejpam-5085	154	19	we	we	PRON
ejpam-5085	154	20	get	get	VERB
ejpam-5085	154	21	f	f	NOUN
ejpam-5085	154	22	◦	◦	NOUN
ejpam-5085	154	23	π	π	NOUN
ejpam-5085	154	24	=	=	SYM
ejpam-5085	154	25	π1	π1	PROPN
ejpam-5085	154	26	◦	◦	NOUN
ejpam-5085	154	27	h	h	NOUN
ejpam-5085	155	1	=	=	NOUN
ejpam-5085	155	2	0	0	NUM
ejpam-5085	155	3	absurd	absurd	ADJ
ejpam-5085	155	4	,	,	PUNCT
ejpam-5085	155	5	so	so	CCONJ
ejpam-5085	155	6	because	because	SCONJ
ejpam-5085	155	7	f	f	PROPN
ejpam-5085	155	8	̸=	̸=	PROPN
ejpam-5085	155	9	0	0	NUM
ejpam-5085	155	10	and	and	CCONJ
ejpam-5085	155	11	ω(s1	ω(s1	NOUN
ejpam-5085	155	12	)	)	PUNCT
ejpam-5085	155	13	is	be	AUX
ejpam-5085	155	14	a	a	DET
ejpam-5085	155	15	simple	simple	ADJ
ejpam-5085	155	16	module	module	NOUN
ejpam-5085	155	17	,	,	PUNCT
ejpam-5085	155	18	then	then	ADV
ejpam-5085	155	19	f	f	PROPN
ejpam-5085	155	20	is	be	AUX
ejpam-5085	155	21	an	an	DET
ejpam-5085	155	22	epimorphism	epimorphism	NOUN
ejpam-5085	155	23	,	,	PUNCT
ejpam-5085	155	24	and	and	CCONJ
ejpam-5085	155	25	since	since	SCONJ
ejpam-5085	155	26	p1	p1	PROPN
ejpam-5085	155	27	is	be	AUX
ejpam-5085	155	28	a	a	DET
ejpam-5085	155	29	projective	projective	ADJ
ejpam-5085	155	30	module	module	NOUN
ejpam-5085	155	31	,	,	PUNCT
ejpam-5085	155	32	then	then	ADV
ejpam-5085	155	33	there	there	PRON
ejpam-5085	155	34	exists	exist	VERB
ejpam-5085	155	35	a	a	DET
ejpam-5085	155	36	non	non	ADJ
ejpam-5085	155	37	-	-	ADJ
ejpam-5085	155	38	zero	zero	NUM
ejpam-5085	155	39	morphism	morphism	NOUN
ejpam-5085	155	40	k	k	PROPN
ejpam-5085	155	41	:	:	PUNCT
ejpam-5085	155	42	p1	p1	VERB
ejpam-5085	155	43	−→	−→	NOUN
ejpam-5085	155	44	ω(s	ω(s	PROPN
ejpam-5085	155	45	)	)	PUNCT
ejpam-5085	155	46	such	such	ADJ
ejpam-5085	155	47	that	that	SCONJ
ejpam-5085	155	48	f	f	PROPN
ejpam-5085	155	49	◦	◦	NOUN
ejpam-5085	155	50	k	k	X
ejpam-5085	155	51	=	=	SYM
ejpam-5085	155	52	π1	π1	NOUN
ejpam-5085	155	53	,	,	PUNCT
ejpam-5085	155	54	if	if	SCONJ
ejpam-5085	155	55	one	one	PRON
ejpam-5085	155	56	could	could	AUX
ejpam-5085	155	57	prove	prove	VERB
ejpam-5085	155	58	that	that	SCONJ
ejpam-5085	155	59	i0	i0	PROPN
ejpam-5085	155	60	◦	◦	PROPN
ejpam-5085	156	1	k	k	PROPN
ejpam-5085	156	2	is	be	AUX
ejpam-5085	156	3	an	an	DET
ejpam-5085	156	4	epimorphism	epimorphism	NOUN
ejpam-5085	156	5	,	,	PUNCT
ejpam-5085	156	6	that	that	PRON
ejpam-5085	156	7	would	would	AUX
ejpam-5085	156	8	be	be	AUX
ejpam-5085	156	9	a	a	DET
ejpam-5085	156	10	great	great	ADJ
ejpam-5085	156	11	proof	proof	NOUN
ejpam-5085	156	12	,	,	PUNCT
ejpam-5085	156	13	however	however	ADV
ejpam-5085	156	14	,	,	PUNCT
ejpam-5085	156	15	this	this	PRON
ejpam-5085	156	16	is	be	AUX
ejpam-5085	156	17	not	not	PART
ejpam-5085	156	18	that	that	ADV
ejpam-5085	156	19	easy	easy	ADJ
ejpam-5085	156	20	since	since	SCONJ
ejpam-5085	156	21	the	the	DET
ejpam-5085	156	22	only	only	ADJ
ejpam-5085	156	23	information	information	NOUN
ejpam-5085	156	24	that	that	PRON
ejpam-5085	156	25	we	we	PRON
ejpam-5085	156	26	have	have	VERB
ejpam-5085	156	27	,	,	PUNCT
ejpam-5085	156	28	is	be	AUX
ejpam-5085	156	29	that	that	SCONJ
ejpam-5085	156	30	i0	i0	PROPN
ejpam-5085	156	31	is	be	AUX
ejpam-5085	156	32	injective	injective	ADJ
ejpam-5085	156	33	.	.	PUNCT
ejpam-5085	157	1	this	this	DET
ejpam-5085	157	2	point	point	NOUN
ejpam-5085	157	3	will	will	AUX
ejpam-5085	157	4	be	be	AUX
ejpam-5085	157	5	true	true	ADJ
ejpam-5085	157	6	through	through	ADP
ejpam-5085	157	7	the	the	DET
ejpam-5085	157	8	gorenstein	gorenstein	NOUN
ejpam-5085	157	9	projective	projective	NOUN
ejpam-5085	157	10	,	,	PUNCT
ejpam-5085	157	11	but	but	CCONJ
ejpam-5085	157	12	this	this	PRON
ejpam-5085	157	13	is	be	AUX
ejpam-5085	157	14	very	very	ADV
ejpam-5085	157	15	difficult	difficult	ADJ
ejpam-5085	157	16	to	to	PART
ejpam-5085	157	17	prove	prove	VERB
ejpam-5085	157	18	even	even	ADV
ejpam-5085	157	19	if	if	SCONJ
ejpam-5085	157	20	the	the	DET
ejpam-5085	157	21	existence	existence	NOUN
ejpam-5085	157	22	of	of	ADP
ejpam-5085	157	23	such	such	ADJ
ejpam-5085	157	24	epimorphism	epimorphism	NOUN
ejpam-5085	157	25	looks	look	VERB
ejpam-5085	157	26	right	right	ADJ
ejpam-5085	157	27	by	by	ADP
ejpam-5085	157	28	using	use	VERB
ejpam-5085	157	29	this	this	DET
ejpam-5085	157	30	property	property	NOUN
ejpam-5085	157	31	,	,	PUNCT
ejpam-5085	157	32	as	as	ADP
ejpam-5085	157	33	in	in	ADP
ejpam-5085	157	34	the	the	DET
ejpam-5085	157	35	end	end	NOUN
ejpam-5085	157	36	i0	i0	PROPN
ejpam-5085	157	37	◦	◦	NOUN
ejpam-5085	158	1	k	k	VERB
ejpam-5085	158	2	being	be	AUX
ejpam-5085	158	3	an	an	DET
ejpam-5085	158	4	epimorphism	epimorphism	NOUN
ejpam-5085	158	5	will	will	AUX
ejpam-5085	158	6	imply	imply	VERB
ejpam-5085	158	7	a	a	DET
ejpam-5085	158	8	contradiction	contradiction	NOUN
ejpam-5085	158	9	that	that	PRON
ejpam-5085	158	10	s	s	VERB
ejpam-5085	158	11	=	=	NOUN
ejpam-5085	158	12	0	0	PUNCT
ejpam-5085	159	1	thus	thus	ADV
ejpam-5085	159	2	,	,	PUNCT
ejpam-5085	159	3	we	we	PRON
ejpam-5085	159	4	choose	choose	VERB
ejpam-5085	159	5	to	to	PART
ejpam-5085	159	6	proceed	proceed	VERB
ejpam-5085	159	7	as	as	SCONJ
ejpam-5085	159	8	follows	follow	VERB
ejpam-5085	159	9	.	.	PUNCT
ejpam-5085	160	1	references	reference	NOUN
ejpam-5085	160	2	1204	1204	NUM
ejpam-5085	160	3	as	as	ADP
ejpam-5085	160	4	ω2(s	ω2(s	PROPN
ejpam-5085	160	5	)	)	PUNCT
ejpam-5085	160	6	is	be	AUX
ejpam-5085	160	7	semisimple	semisimple	NOUN
ejpam-5085	160	8	and	and	CCONJ
ejpam-5085	160	9	ω2(s1	ω2(s1	NOUN
ejpam-5085	160	10	)	)	PUNCT
ejpam-5085	160	11	is	be	AUX
ejpam-5085	160	12	simple	simple	ADJ
ejpam-5085	160	13	and	and	CCONJ
ejpam-5085	160	14	g	g	PROPN
ejpam-5085	160	15	̸=	̸=	PROPN
ejpam-5085	160	16	0	0	NUM
ejpam-5085	160	17	,	,	PUNCT
ejpam-5085	160	18	then	then	ADV
ejpam-5085	160	19	ω2(s1	ω2(s1	NUM
ejpam-5085	160	20	)	)	PUNCT
ejpam-5085	160	21	is	be	AUX
ejpam-5085	160	22	a	a	DET
ejpam-5085	160	23	direct	direct	ADJ
ejpam-5085	160	24	summand	summand	NOUN
ejpam-5085	160	25	of	of	ADP
ejpam-5085	160	26	ω2(s	ω2(s	PROPN
ejpam-5085	160	27	)	)	PUNCT
ejpam-5085	160	28	,	,	PUNCT
ejpam-5085	160	29	so	so	SCONJ
ejpam-5085	160	30	we	we	PRON
ejpam-5085	160	31	can	can	AUX
ejpam-5085	160	32	inject	inject	VERB
ejpam-5085	160	33	ω2(s1	ω2(s1	NOUN
ejpam-5085	160	34	)	)	PUNCT
ejpam-5085	160	35	into	into	ADP
ejpam-5085	160	36	ω2(s	ω2(s	PROPN
ejpam-5085	160	37	)	)	PUNCT
ejpam-5085	160	38	which	which	PRON
ejpam-5085	160	39	in	in	ADP
ejpam-5085	160	40	turn	turn	NOUN
ejpam-5085	160	41	is	be	AUX
ejpam-5085	160	42	injected	inject	VERB
ejpam-5085	160	43	into	into	ADP
ejpam-5085	160	44	p	p	NOUN
ejpam-5085	160	45	,	,	PUNCT
ejpam-5085	160	46	let	let	VERB
ejpam-5085	160	47	l	l	NOUN
ejpam-5085	160	48	:	:	PUNCT
ejpam-5085	160	49	ω2(s1	ω2(s1	ADJ
ejpam-5085	160	50	)	)	PUNCT
ejpam-5085	160	51	↪	↪	PROPN
ejpam-5085	160	52	→	→	SYM
ejpam-5085	160	53	p	p	X
ejpam-5085	160	54	be	be	VERB
ejpam-5085	160	55	the	the	DET
ejpam-5085	160	56	injection	injection	NOUN
ejpam-5085	160	57	composed	compose	VERB
ejpam-5085	160	58	of	of	ADP
ejpam-5085	160	59	these	these	DET
ejpam-5085	160	60	last	last	ADJ
ejpam-5085	160	61	injections	injection	NOUN
ejpam-5085	160	62	and	and	CCONJ
ejpam-5085	160	63	with	with	ADP
ejpam-5085	160	64	the	the	DET
ejpam-5085	160	65	previous	previous	ADJ
ejpam-5085	160	66	notations	notation	NOUN
ejpam-5085	160	67	and	and	CCONJ
ejpam-5085	160	68	in	in	ADP
ejpam-5085	160	69	short	short	ADJ
ejpam-5085	160	70	we	we	PRON
ejpam-5085	160	71	have	have	VERB
ejpam-5085	160	72	l	l	PROPN
ejpam-5085	160	73	∈	∈	PROPN
ejpam-5085	160	74	hom(s3	hom(s3	PROPN
ejpam-5085	160	75	,	,	PUNCT
ejpam-5085	160	76	p	p	NOUN
ejpam-5085	160	77	)	)	PUNCT
ejpam-5085	160	78	with	with	ADP
ejpam-5085	160	79	s3	s3	PROPN
ejpam-5085	160	80	=	=	SYM
ejpam-5085	160	81	ω2(s1	ω2(s1	NOUN
ejpam-5085	160	82	)	)	PUNCT
ejpam-5085	160	83	and	and	CCONJ
ejpam-5085	160	84	by	by	ADP
ejpam-5085	160	85	application	application	NOUN
ejpam-5085	160	86	of	of	ADP
ejpam-5085	160	87	the	the	DET
ejpam-5085	160	88	functor	functor	PROPN
ejpam-5085	160	89	hom(−	hom(−	PROPN
ejpam-5085	160	90	,	,	PUNCT
ejpam-5085	160	91	p	p	NOUN
ejpam-5085	160	92	)	)	PUNCT
ejpam-5085	160	93	to	to	ADP
ejpam-5085	160	94	the	the	DET
ejpam-5085	160	95	short	short	ADJ
ejpam-5085	160	96	exact	exact	ADJ
ejpam-5085	160	97	sequence	sequence	NOUN
ejpam-5085	160	98	,	,	PUNCT
ejpam-5085	160	99	0	0	NUM
ejpam-5085	160	100	//	//	NUM
ejpam-5085	160	101	s3	s3	PROPN
ejpam-5085	160	102	i1	i1	PROPN
ejpam-5085	160	103	//	//	PROPN
ejpam-5085	160	104	p1	p1	PROPN
ejpam-5085	160	105	π1	π1	PROPN
ejpam-5085	160	106	//	//	SYM
ejpam-5085	160	107	s2	s2	PROPN
ejpam-5085	160	108	//	//	X
ejpam-5085	160	109	0	0	NUM
ejpam-5085	161	1	we	we	PRON
ejpam-5085	161	2	will	will	AUX
ejpam-5085	161	3	have	have	VERB
ejpam-5085	161	4	,	,	PUNCT
ejpam-5085	161	5	0	0	NUM
ejpam-5085	161	6	//	//	NUM
ejpam-5085	161	7	hom(s2	hom(s2	PROPN
ejpam-5085	161	8	,	,	PUNCT
ejpam-5085	161	9	p	p	NOUN
ejpam-5085	161	10	)	)	PUNCT
ejpam-5085	161	11	//	//	X
ejpam-5085	162	1	hom(p1	hom(p1	PROPN
ejpam-5085	162	2	,	,	PUNCT
ejpam-5085	162	3	p	p	NOUN
ejpam-5085	162	4	)	)	PUNCT
ejpam-5085	162	5	hom(i1,p	hom(i1,p	PROPN
ejpam-5085	162	6	)	)	PUNCT
ejpam-5085	162	7	//	//	SYM
ejpam-5085	163	1	hom(s3	hom(s3	PROPN
ejpam-5085	163	2	,	,	PUNCT
ejpam-5085	163	3	p	p	NOUN
ejpam-5085	163	4	)	)	PUNCT
ejpam-5085	163	5	//	//	X
ejpam-5085	163	6	ext1a(s2	ext1a(s2	PROPN
ejpam-5085	163	7	,	,	PUNCT
ejpam-5085	163	8	p	p	NOUN
ejpam-5085	163	9	)	)	PUNCT
ejpam-5085	163	10	=	=	SYM
ejpam-5085	163	11	0	0	NUM
ejpam-5085	163	12	and	and	CCONJ
ejpam-5085	163	13	this	this	PRON
ejpam-5085	163	14	because	because	SCONJ
ejpam-5085	163	15	s2	s2	PROPN
ejpam-5085	163	16	is	be	AUX
ejpam-5085	163	17	a	a	DET
ejpam-5085	163	18	simple	simple	ADJ
ejpam-5085	163	19	and	and	CCONJ
ejpam-5085	163	20	gorenstein	gorenstein	NOUN
ejpam-5085	163	21	projective	projective	ADJ
ejpam-5085	163	22	a	a	DET
ejpam-5085	163	23	-	-	PUNCT
ejpam-5085	163	24	module	module	NOUN
ejpam-5085	163	25	,	,	PUNCT
ejpam-5085	163	26	so	so	SCONJ
ejpam-5085	163	27	l	l	NOUN
ejpam-5085	163	28	=	=	SYM
ejpam-5085	163	29	hom(i1	hom(i1	NOUN
ejpam-5085	163	30	,	,	PUNCT
ejpam-5085	163	31	p	p	NOUN
ejpam-5085	163	32	)	)	PUNCT
ejpam-5085	163	33	(	(	PUNCT
ejpam-5085	163	34	a	a	X
ejpam-5085	163	35	)	)	PUNCT
ejpam-5085	163	36	=	=	SYM
ejpam-5085	163	37	a	a	DET
ejpam-5085	163	38	◦	◦	NOUN
ejpam-5085	163	39	i1	i1	NOUN
ejpam-5085	163	40	with	with	ADP
ejpam-5085	163	41	a	a	DET
ejpam-5085	163	42	∈	∈	PROPN
ejpam-5085	163	43	hom(p1	hom(p1	PROPN
ejpam-5085	163	44	,	,	PUNCT
ejpam-5085	163	45	p	p	NOUN
ejpam-5085	163	46	)	)	PUNCT
ejpam-5085	163	47	and	and	CCONJ
ejpam-5085	163	48	note	note	VERB
ejpam-5085	163	49	that	that	SCONJ
ejpam-5085	163	50	s3	s3	PROPN
ejpam-5085	163	51	is	be	AUX
ejpam-5085	163	52	the	the	DET
ejpam-5085	163	53	socle	socle	NOUN
ejpam-5085	163	54	of	of	ADP
ejpam-5085	163	55	p1	p1	PROPN
ejpam-5085	163	56	on	on	ADP
ejpam-5085	163	57	which	which	PRON
ejpam-5085	163	58	a	a	PRON
ejpam-5085	163	59	is	be	AUX
ejpam-5085	163	60	non	non	ADJ
ejpam-5085	163	61	-	-	ADJ
ejpam-5085	163	62	zero	zero	NUM
ejpam-5085	163	63	so	so	SCONJ
ejpam-5085	163	64	a	a	PRON
ejpam-5085	163	65	is	be	AUX
ejpam-5085	163	66	a	a	DET
ejpam-5085	163	67	monomorphism	monomorphism	NOUN
ejpam-5085	163	68	and	and	CCONJ
ejpam-5085	163	69	length(p1	length(p1	NOUN
ejpam-5085	163	70	)	)	PUNCT
ejpam-5085	163	71	≤	≤	NUM
ejpam-5085	163	72	length(p	length(p	PROPN
ejpam-5085	163	73	)	)	PUNCT
ejpam-5085	163	74	and	and	CCONJ
ejpam-5085	163	75	as	as	SCONJ
ejpam-5085	163	76	f	f	PROPN
ejpam-5085	163	77	and	and	CCONJ
ejpam-5085	163	78	g	g	PROPN
ejpam-5085	163	79	are	be	AUX
ejpam-5085	163	80	epimorphisms	epimorphism	NOUN
ejpam-5085	163	81	,	,	PUNCT
ejpam-5085	163	82	then	then	ADV
ejpam-5085	163	83	h	h	NOUN
ejpam-5085	163	84	is	be	AUX
ejpam-5085	163	85	also	also	ADV
ejpam-5085	163	86	and	and	CCONJ
ejpam-5085	163	87	length(p	length(p	PROPN
ejpam-5085	163	88	)	)	PUNCT
ejpam-5085	163	89	≤	≤	NUM
ejpam-5085	163	90	length(p1	length(p1	NOUN
ejpam-5085	163	91	)	)	PUNCT
ejpam-5085	163	92	,	,	PUNCT
ejpam-5085	163	93	therefore	therefore	ADV
ejpam-5085	163	94	,	,	PUNCT
ejpam-5085	163	95	p	p	NOUN
ejpam-5085	163	96	≃	≃	PROPN
ejpam-5085	163	97	p1	p1	NOUN
ejpam-5085	163	98	that	that	PRON
ejpam-5085	163	99	implies	imply	VERB
ejpam-5085	163	100	that	that	SCONJ
ejpam-5085	163	101	ω(s1	ω(s1	ADV
ejpam-5085	163	102	)	)	PUNCT
ejpam-5085	163	103	≃	≃	NOUN
ejpam-5085	163	104	ω(s	ω(s	ADP
ejpam-5085	163	105	)	)	PUNCT
ejpam-5085	163	106	,	,	PUNCT
ejpam-5085	163	107	and	and	CCONJ
ejpam-5085	163	108	like	like	ADP
ejpam-5085	163	109	a	a	DET
ejpam-5085	163	110	verifying	verifying	NOUN
ejpam-5085	163	111	the	the	DET
ejpam-5085	163	112	coincidence	coincidence	NOUN
ejpam-5085	163	113	covers	cover	NOUN
ejpam-5085	163	114	see	see	VERB
ejpam-5085	163	115	definition	definition	NOUN
ejpam-5085	163	116	3.1	3.1	NUM
ejpam-5085	163	117	,	,	PUNCT
ejpam-5085	163	118	therefore	therefore	ADV
ejpam-5085	163	119	s1	s1	PROPN
ejpam-5085	163	120	≃	≃	PROPN
ejpam-5085	163	121	s.	s.	PROPN
ejpam-5085	163	122	finally	finally	ADV
ejpam-5085	163	123	,	,	PUNCT
ejpam-5085	163	124	our	our	PRON
ejpam-5085	163	125	construction	construction	NOUN
ejpam-5085	163	126	affirms	affirm	VERB
ejpam-5085	163	127	the	the	DET
ejpam-5085	163	128	existence	existence	NOUN
ejpam-5085	163	129	of	of	ADP
ejpam-5085	163	130	the	the	DET
ejpam-5085	163	131	set	set	NOUN
ejpam-5085	163	132	{	{	PUNCT
ejpam-5085	163	133	s1	s1	NOUN
ejpam-5085	163	134	,	,	PUNCT
ejpam-5085	163	135	s2	s2	PROPN
ejpam-5085	163	136	,	,	PUNCT
ejpam-5085	163	137	...	...	PUNCT
ejpam-5085	163	138	,	,	PUNCT
ejpam-5085	163	139	sn−1	sn−1	PROPN
ejpam-5085	163	140	}	}	PUNCT
ejpam-5085	163	141	of	of	ADP
ejpam-5085	163	142	pairwise	pairwise	PROPN
ejpam-5085	163	143	non	non	ADJ
ejpam-5085	163	144	-	-	ADJ
ejpam-5085	163	145	isomorphic	isomorphic	ADJ
ejpam-5085	163	146	simple	simple	ADJ
ejpam-5085	163	147	a	a	DET
ejpam-5085	163	148	-	-	PUNCT
ejpam-5085	163	149	modules	module	NOUN
ejpam-5085	163	150	;	;	PUNCT
ejpam-5085	163	151	moreover	moreover	ADV
ejpam-5085	163	152	,	,	PUNCT
ejpam-5085	163	153	each	each	DET
ejpam-5085	163	154	si	si	NOUN
ejpam-5085	163	155	satisfies	satisfy	VERB
ejpam-5085	163	156	that	that	SCONJ
ejpam-5085	163	157	any	any	DET
ejpam-5085	163	158	simple	simple	ADJ
ejpam-5085	163	159	a	a	DET
ejpam-5085	163	160	-	-	PUNCT
ejpam-5085	163	161	module	module	NOUN
ejpam-5085	163	162	s	s	NOUN
ejpam-5085	163	163	with	with	ADP
ejpam-5085	163	164	ext1a(s	ext1a(s	PROPN
ejpam-5085	163	165	,	,	PUNCT
ejpam-5085	163	166	si	si	NOUN
ejpam-5085	163	167	)	)	PUNCT
ejpam-5085	163	168	̸=	̸=	PROPN
ejpam-5085	163	169	0	0	NUM
ejpam-5085	163	170	is	be	AUX
ejpam-5085	163	171	isomorphic	isomorphic	ADJ
ejpam-5085	163	172	to	to	ADP
ejpam-5085	163	173	si−1	si−1	PROPN
ejpam-5085	163	174	and	and	CCONJ
ejpam-5085	163	175	we	we	PRON
ejpam-5085	163	176	considered	consider	VERB
ejpam-5085	163	177	si+1	si+1	PROPN
ejpam-5085	163	178	=	=	SYM
ejpam-5085	163	179	ω(si	ω(si	PROPN
ejpam-5085	163	180	)	)	PUNCT
ejpam-5085	163	181	,	,	PUNCT
ejpam-5085	163	182	then	then	ADV
ejpam-5085	163	183	we	we	PRON
ejpam-5085	163	184	have	have	VERB
ejpam-5085	163	185	any	any	DET
ejpam-5085	163	186	simple	simple	ADJ
ejpam-5085	163	187	a	a	DET
ejpam-5085	163	188	-	-	PUNCT
ejpam-5085	163	189	module	module	NOUN
ejpam-5085	163	190	s	s	NOUN
ejpam-5085	163	191	with	with	ADP
ejpam-5085	163	192	ext1a(si	ext1a(si	PROPN
ejpam-5085	163	193	,	,	PUNCT
ejpam-5085	163	194	s	s	X
ejpam-5085	163	195	)	)	PUNCT
ejpam-5085	163	196	̸=	̸=	NOUN
ejpam-5085	163	197	0	0	NUM
ejpam-5085	163	198	is	be	AUX
ejpam-5085	163	199	isomorphic	isomorphic	ADJ
ejpam-5085	163	200	to	to	PART
ejpam-5085	163	201	si+1	si+1	VERB
ejpam-5085	163	202	and	and	CCONJ
ejpam-5085	163	203	by	by	ADP
ejpam-5085	163	204	identification	identification	NOUN
ejpam-5085	163	205	s0	s0	NOUN
ejpam-5085	163	206	with	with	ADP
ejpam-5085	163	207	sn−1	sn−1	PROPN
ejpam-5085	163	208	and	and	CCONJ
ejpam-5085	163	209	sn	sn	PROPN
ejpam-5085	163	210	with	with	ADP
ejpam-5085	163	211	s1	s1	PROPN
ejpam-5085	163	212	it	it	PRON
ejpam-5085	163	213	follows	follow	VERB
ejpam-5085	163	214	that	that	SCONJ
ejpam-5085	163	215	the	the	DET
ejpam-5085	163	216	full	full	ADJ
ejpam-5085	163	217	subquiver	subquiver	NOUN
ejpam-5085	163	218	qa	qa	PROPN
ejpam-5085	163	219	with	with	ADP
ejpam-5085	163	220	vertices	vertex	NOUN
ejpam-5085	163	221	{	{	PUNCT
ejpam-5085	163	222	s1	s1	NOUN
ejpam-5085	163	223	,	,	PUNCT
ejpam-5085	163	224	s2	s2	PROPN
ejpam-5085	163	225	,	,	PUNCT
ejpam-5085	163	226	...	...	PUNCT
ejpam-5085	163	227	,	,	PUNCT
ejpam-5085	163	228	sn−1	sn−1	PROPN
ejpam-5085	163	229	}	}	PUNCT
ejpam-5085	163	230	is	be	AUX
ejpam-5085	163	231	a	a	DET
ejpam-5085	163	232	connected	connect	VERB
ejpam-5085	163	233	.	.	PUNCT
ejpam-5085	164	1	since	since	SCONJ
ejpam-5085	164	2	the	the	DET
ejpam-5085	164	3	algebra	algebra	NOUN
ejpam-5085	164	4	a	a	PRON
ejpam-5085	164	5	is	be	AUX
ejpam-5085	164	6	connected	connect	VERB
ejpam-5085	164	7	and	and	CCONJ
ejpam-5085	164	8	since	since	SCONJ
ejpam-5085	164	9	there	there	PRON
ejpam-5085	164	10	are	be	VERB
ejpam-5085	164	11	simple	simple	ADJ
ejpam-5085	164	12	a	a	PRON
ejpam-5085	164	13	-	-	PUNCT
ejpam-5085	164	14	modules	module	NOUN
ejpam-5085	164	15	associated	associate	VERB
ejpam-5085	164	16	with	with	ADP
ejpam-5085	164	17	all	all	DET
ejpam-5085	164	18	the	the	DET
ejpam-5085	164	19	indecomposable	indecomposable	ADJ
ejpam-5085	164	20	projective	projective	NOUN
ejpam-5085	164	21	a	a	DET
ejpam-5085	164	22	-	-	PUNCT
ejpam-5085	164	23	modules	module	NOUN
ejpam-5085	164	24	given	give	VERB
ejpam-5085	164	25	by	by	ADP
ejpam-5085	164	26	{	{	PUNCT
ejpam-5085	164	27	p1	p1	NOUN
ejpam-5085	164	28	,	,	PUNCT
ejpam-5085	164	29	p2	p2	NOUN
ejpam-5085	164	30	,	,	PUNCT
ejpam-5085	164	31	...	...	PUNCT
ejpam-5085	164	32	,	,	PUNCT
ejpam-5085	164	33	pn−1	pn−1	ADJ
ejpam-5085	164	34	}	}	PUNCT
ejpam-5085	164	35	it	it	PRON
ejpam-5085	164	36	follows	follow	VERB
ejpam-5085	164	37	by	by	ADP
ejpam-5085	164	38	theorem	theorem	ADJ
ejpam-5085	164	39	9.3.7	9.3.7	NOUN
ejpam-5085	164	40	[	[	X
ejpam-5085	164	41	4	4	NUM
ejpam-5085	164	42	]	]	PUNCT
ejpam-5085	164	43	that	that	SCONJ
ejpam-5085	164	44	the	the	DET
ejpam-5085	164	45	algebra	algebra	NOUN
ejpam-5085	164	46	a	a	PRON
ejpam-5085	164	47	is	be	AUX
ejpam-5085	164	48	self	self	NOUN
ejpam-5085	164	49	-	-	PUNCT
ejpam-5085	164	50	injective	injective	ADJ
ejpam-5085	164	51	.	.	PUNCT
ejpam-5085	165	1	acknowledgements	acknowledgement	NOUN
ejpam-5085	165	2	a	a	DET
ejpam-5085	165	3	special	special	ADJ
ejpam-5085	165	4	thanks	thank	NOUN
ejpam-5085	165	5	to	to	ADP
ejpam-5085	165	6	the	the	DET
ejpam-5085	165	7	editor	editor	NOUN
ejpam-5085	165	8	professor	professor	PROPN
ejpam-5085	165	9	dr	dr	PROPN
ejpam-5085	165	10	.	.	PROPN
ejpam-5085	165	11	eyup	eyup	PROPN
ejpam-5085	165	12	cetin	cetin	PROPN
ejpam-5085	165	13	and	and	CCONJ
ejpam-5085	165	14	dr	dr	PROPN
ejpam-5085	165	15	.	.	PROPN
ejpam-5085	165	16	ilias	ilias	PROPN
ejpam-5085	165	17	elmouki	elmouki	PROPN
ejpam-5085	165	18	.	.	PUNCT
ejpam-5085	166	1	we	we	PRON
ejpam-5085	166	2	would	would	AUX
ejpam-5085	166	3	also	also	ADV
ejpam-5085	166	4	like	like	VERB
ejpam-5085	166	5	to	to	PART
ejpam-5085	166	6	thank	thank	VERB
ejpam-5085	166	7	all	all	DET
ejpam-5085	166	8	the	the	DET
ejpam-5085	166	9	three	three	NUM
ejpam-5085	166	10	anonymous	anonymous	ADJ
ejpam-5085	166	11	referees	referee	NOUN
ejpam-5085	166	12	for	for	ADP
ejpam-5085	166	13	their	their	PRON
ejpam-5085	166	14	time	time	NOUN
ejpam-5085	166	15	,	,	PUNCT
ejpam-5085	166	16	effort	effort	NOUN
ejpam-5085	166	17	and	and	CCONJ
ejpam-5085	166	18	help	help	VERB
ejpam-5085	166	19	for	for	ADP
ejpam-5085	166	20	improving	improve	VERB
ejpam-5085	166	21	the	the	DET
ejpam-5085	166	22	content	content	NOUN
ejpam-5085	166	23	of	of	ADP
ejpam-5085	166	24	our	our	PRON
ejpam-5085	166	25	paper	paper	NOUN
ejpam-5085	166	26	.	.	PUNCT
ejpam-5085	167	1	references	reference	NOUN
ejpam-5085	167	2	[	[	X
ejpam-5085	167	3	1	1	NUM
ejpam-5085	167	4	]	]	X
ejpam-5085	167	5	xiao	xiao	PROPN
ejpam-5085	167	6	-	-	PUNCT
ejpam-5085	167	7	wu	wu	PROPN
ejpam-5085	167	8	chen	chen	PROPN
ejpam-5085	167	9	.	.	PUNCT
ejpam-5085	168	1	gorenstein	gorenstein	PROPN
ejpam-5085	168	2	homological	homological	PROPN
ejpam-5085	168	3	algebra	algebra	PROPN
ejpam-5085	168	4	of	of	ADP
ejpam-5085	168	5	artin	artin	PROPN
ejpam-5085	168	6	algebras	algebras	PROPN
ejpam-5085	168	7	.	.	PUNCT
ejpam-5085	169	1	departement	departement	NOUN
ejpam-5085	169	2	of	of	ADP
ejpam-5085	169	3	mathematics	mathematics	PROPN
ejpam-5085	169	4	(	(	PUNCT
ejpam-5085	169	5	university	university	NOUN
ejpam-5085	169	6	of	of	ADP
ejpam-5085	169	7	science	science	NOUN
ejpam-5085	169	8	and	and	CCONJ
ejpam-5085	169	9	technology	technology	NOUN
ejpam-5085	169	10	of	of	ADP
ejpam-5085	169	11	china	china	PROPN
ejpam-5085	169	12	,	,	PUNCT
ejpam-5085	169	13	cambridge	cambridge	PROPN
ejpam-5085	169	14	,	,	PUNCT
ejpam-5085	169	15	2010	2010	NUM
ejpam-5085	169	16	.	.	PUNCT
ejpam-5085	170	1	[	[	X
ejpam-5085	170	2	2	2	NUM
ejpam-5085	170	3	]	]	X
ejpam-5085	170	4	xiao	xiao	PROPN
ejpam-5085	170	5	-	-	PUNCT
ejpam-5085	170	6	wu	wu	PROPN
ejpam-5085	170	7	chen	chen	PROPN
ejpam-5085	170	8	.	.	PUNCT
ejpam-5085	171	1	algebras	algebras	PROPN
ejpam-5085	171	2	with	with	ADP
ejpam-5085	171	3	radical	radical	ADJ
ejpam-5085	171	4	square	square	ADJ
ejpam-5085	171	5	zero	zero	NUM
ejpam-5085	171	6	are	be	AUX
ejpam-5085	171	7	either	either	PRON
ejpam-5085	171	8	self	self	NOUN
ejpam-5085	171	9	-	-	PUNCT
ejpam-5085	171	10	injective	injective	ADJ
ejpam-5085	171	11	or	or	CCONJ
ejpam-5085	171	12	cm	cm	NOUN
ejpam-5085	171	13	-	-	PUNCT
ejpam-5085	171	14	free	free	ADJ
ejpam-5085	171	15	.	.	PUNCT
ejpam-5085	172	1	proceedings	proceeding	NOUN
ejpam-5085	172	2	of	of	ADP
ejpam-5085	172	3	the	the	DET
ejpam-5085	172	4	american	american	PROPN
ejpam-5085	172	5	mathematical	mathematical	PROPN
ejpam-5085	172	6	society	society	NOUN
ejpam-5085	172	7	,	,	PUNCT
ejpam-5085	172	8	2011	2011	NUM
ejpam-5085	172	9	.	.	PUNCT
ejpam-5085	173	1	[	[	X
ejpam-5085	173	2	3	3	X
ejpam-5085	173	3	]	]	X
ejpam-5085	173	4	d.	d.	PROPN
ejpam-5085	173	5	simson	simson	PROPN
ejpam-5085	173	6	i.	i.	PROPN
ejpam-5085	173	7	assem	assem	PROPN
ejpam-5085	173	8	and	and	CCONJ
ejpam-5085	173	9	a.	a.	NOUN
ejpam-5085	173	10	skowroński	skowroński	PROPN
ejpam-5085	173	11	.	.	PUNCT
ejpam-5085	174	1	elements	element	NOUN
ejpam-5085	174	2	of	of	ADP
ejpam-5085	174	3	the	the	DET
ejpam-5085	174	4	representation	representation	NOUN
ejpam-5085	174	5	theory	theory	NOUN
ejpam-5085	174	6	of	of	ADP
ejpam-5085	174	7	associative	associative	ADJ
ejpam-5085	174	8	algebras	algebra	NOUN
ejpam-5085	174	9	.	.	PUNCT
ejpam-5085	175	1	volume	volume	NOUN
ejpam-5085	175	2	1	1	NUM
ejpam-5085	175	3	:	:	PUNCT
ejpam-5085	175	4	techniques	technique	NOUN
ejpam-5085	175	5	of	of	ADP
ejpam-5085	175	6	representation	representation	NOUN
ejpam-5085	175	7	theory	theory	NOUN
ejpam-5085	175	8	,	,	PUNCT
ejpam-5085	175	9	london	london	PROPN
ejpam-5085	175	10	mathematical	mathematical	ADJ
ejpam-5085	175	11	society	society	NOUN
ejpam-5085	175	12	student	student	NOUN
ejpam-5085	175	13	texts	text	NOUN
ejpam-5085	175	14	65	65	NUM
ejpam-5085	175	15	(	(	PUNCT
ejpam-5085	175	16	cambridge	cambridge	PROPN
ejpam-5085	175	17	university	university	PROPN
ejpam-5085	175	18	press	press	PROPN
ejpam-5085	175	19	,	,	PUNCT
ejpam-5085	175	20	cambridge	cambridge	PROPN
ejpam-5085	175	21	,	,	PUNCT
ejpam-5085	175	22	2006	2006	NUM
ejpam-5085	175	23	.	.	PUNCT
ejpam-5085	176	1	references	reference	NOUN
ejpam-5085	176	2	1205	1205	NUM
ejpam-5085	176	3	[	[	X
ejpam-5085	176	4	4	4	NUM
ejpam-5085	176	5	]	]	X
ejpam-5085	176	6	i.	i.	NOUN
ejpam-5085	176	7	reiten	reiten	PROPN
ejpam-5085	176	8	m.	m.	NOUN
ejpam-5085	176	9	auslander	auslander	NOUN
ejpam-5085	176	10	and	and	CCONJ
ejpam-5085	176	11	s.	s.	PROPN
ejpam-5085	176	12	o.	o.	PROPN
ejpam-5085	176	13	smalø	smalø	PROPN
ejpam-5085	176	14	.	.	PUNCT
ejpam-5085	177	1	representation	representation	NOUN
ejpam-5085	177	2	theory	theory	NOUN
ejpam-5085	177	3	of	of	ADP
ejpam-5085	177	4	artin	artin	PROPN
ejpam-5085	177	5	algebras	algebras	PROPN
ejpam-5085	177	6	.	.	PUNCT
ejpam-5085	178	1	cambridge	cambridge	PROPN
ejpam-5085	178	2	studies	study	NOUN
ejpam-5085	178	3	in	in	ADP
ejpam-5085	178	4	advanced	advanced	ADJ
ejpam-5085	178	5	mathematics	mathematic	NOUN
ejpam-5085	178	6	36	36	NUM
ejpam-5085	178	7	(	(	PUNCT
ejpam-5085	178	8	cambridge	cambridge	PROPN
ejpam-5085	178	9	university	university	PROPN
ejpam-5085	178	10	press	press	PROPN
ejpam-5085	178	11	,	,	PUNCT
ejpam-5085	178	12	cambridge	cambridge	PROPN
ejpam-5085	178	13	,	,	PUNCT
ejpam-5085	178	14	1995	1995	NUM
ejpam-5085	178	15	.	.	PUNCT
ejpam-5085	179	1	[	[	X
ejpam-5085	179	2	5	5	NUM
ejpam-5085	179	3	]	]	X
ejpam-5085	179	4	luo	luo	PROPN
ejpam-5085	179	5	rong	rong	PROPN
ejpam-5085	179	6	.	.	PUNCT
ejpam-5085	180	1	local	local	ADJ
ejpam-5085	180	2	algebras	algebra	NOUN
ejpam-5085	180	3	with	with	ADP
ejpam-5085	180	4	radical	radical	ADJ
ejpam-5085	180	5	cubic	cubic	ADJ
ejpam-5085	180	6	zero	zero	NUM
ejpam-5085	180	7	are	be	AUX
ejpam-5085	180	8	pcm	pcm	ADJ
ejpam-5085	180	9	-	-	PUNCT
ejpam-5085	180	10	free	free	ADJ
ejpam-5085	180	11	.	.	PUNCT
ejpam-5085	181	1	college	college	NOUN
ejpam-5085	181	2	of	of	ADP
ejpam-5085	181	3	mathematics	mathematic	NOUN
ejpam-5085	181	4	,	,	PUNCT
ejpam-5085	181	5	southwest	southwest	PROPN
ejpam-5085	181	6	jiaotong	jiaotong	PROPN
ejpam-5085	181	7	university	university	PROPN
ejpam-5085	181	8	,	,	PUNCT
ejpam-5085	181	9	chengdu	chengdu	PROPN
ejpam-5085	181	10	610031	610031	NUM
ejpam-5085	181	11	,	,	PUNCT
ejpam-5085	181	12	p.	p.	PROPN
ejpam-5085	181	13	r.	r.	PROPN
ejpam-5085	181	14	china	china	PROPN
ejpam-5085	181	15	.	.	PROPN
ejpam-5085	181	16	,	,	PUNCT
ejpam-5085	181	17	2013	2013	NUM
ejpam-5085	181	18	.	.	PUNCT
ejpam-5085	182	1	[	[	X
ejpam-5085	182	2	6	6	NUM
ejpam-5085	182	3	]	]	X
ejpam-5085	182	4	guodong	guodong	PROPN
ejpam-5085	182	5	zhou	zhou	PROPN
ejpam-5085	182	6	xiao	xiao	PROPN
ejpam-5085	182	7	-	-	PUNCT
ejpam-5085	182	8	wu	wu	PROPN
ejpam-5085	182	9	chen	chen	PROPN
ejpam-5085	182	10	,	,	PUNCT
ejpam-5085	182	11	dawei	dawei	PROPN
ejpam-5085	182	12	shen	shen	PROPN
ejpam-5085	182	13	.	.	PUNCT
ejpam-5085	183	1	the	the	DET
ejpam-5085	183	2	gorenstein	gorenstein	ADJ
ejpam-5085	183	3	-	-	PUNCT
ejpam-5085	183	4	projective	projective	NOUN
ejpam-5085	183	5	modules	module	NOUN
ejpam-5085	183	6	over	over	ADP
ejpam-5085	183	7	a	a	DET
ejpam-5085	183	8	monomial	monomial	ADJ
ejpam-5085	183	9	algebra	algebra	NOUN
ejpam-5085	183	10	.	.	PUNCT
ejpam-5085	184	1	proceedings	proceeding	NOUN
ejpam-5085	184	2	of	of	ADP
ejpam-5085	184	3	the	the	DET
ejpam-5085	184	4	royal	royal	ADJ
ejpam-5085	184	5	society	society	NOUN
ejpam-5085	184	6	of	of	ADP
ejpam-5085	184	7	edinburgh	edinburgh	PROPN
ejpam-5085	184	8	:	:	PUNCT
ejpam-5085	184	9	section	section	VERB
ejpam-5085	184	10	a	a	DET
ejpam-5085	184	11	mathematics	mathematic	NOUN
ejpam-5085	184	12	,	,	PUNCT
ejpam-5085	184	13	2015	2015	NUM
ejpam-5085	184	14	.	.	PUNCT