id	sid	tid	token	lemma	pos
ejpam-5224	1	1	european	european	PROPN
ejpam-5224	1	2	journal	journal	PROPN
ejpam-5224	1	3	of	of	ADP
ejpam-5224	1	4	pure	pure	ADJ
ejpam-5224	1	5	and	and	CCONJ
ejpam-5224	1	6	applied	apply	VERB
ejpam-5224	1	7	mathematics	mathematic	NOUN
ejpam-5224	1	8	vol	vol	NOUN
ejpam-5224	1	9	.	.	PROPN
ejpam-5224	2	1	17	17	NUM
ejpam-5224	2	2	,	,	PUNCT
ejpam-5224	2	3	no	no	INTJ
ejpam-5224	2	4	.	.	NOUN
ejpam-5224	2	5	3	3	NUM
ejpam-5224	2	6	,	,	PUNCT
ejpam-5224	2	7	2024	2024	NUM
ejpam-5224	2	8	,	,	PUNCT
ejpam-5224	2	9	1855	1855	NUM
ejpam-5224	2	10	-	-	SYM
ejpam-5224	2	11	1868	1868	NUM
ejpam-5224	2	12	issn	issn	PROPN
ejpam-5224	2	13	1307	1307	NUM
ejpam-5224	2	14	-	-	SYM
ejpam-5224	2	15	5543	5543	NUM
ejpam-5224	2	16	–	–	PUNCT
ejpam-5224	2	17	ejpam.com	ejpam.com	X
ejpam-5224	2	18	published	publish	VERB
ejpam-5224	2	19	by	by	ADP
ejpam-5224	2	20	new	new	PROPN
ejpam-5224	2	21	york	york	PROPN
ejpam-5224	2	22	business	business	PROPN
ejpam-5224	2	23	global	global	ADJ
ejpam-5224	2	24	one	one	NUM
ejpam-5224	2	25	resolution	resolution	NOUN
ejpam-5224	2	26	of	of	ADP
ejpam-5224	2	27	the	the	DET
ejpam-5224	2	28	conjecture	conjecture	NOUN
ejpam-5224	2	29	between	between	ADP
ejpam-5224	2	30	the	the	DET
ejpam-5224	2	31	projective	projective	ADJ
ejpam-5224	2	32	dimension	dimension	NOUN
ejpam-5224	2	33	of	of	ADP
ejpam-5224	2	34	a	a	DET
ejpam-5224	2	35	simple	simple	ADJ
ejpam-5224	2	36	module	module	NOUN
ejpam-5224	2	37	s	s	NOUN
ejpam-5224	2	38	of	of	ADP
ejpam-5224	2	39	an	an	DET
ejpam-5224	2	40	artinian	artinian	ADJ
ejpam-5224	2	41	ring	ring	NOUN
ejpam-5224	2	42	on	on	ADP
ejpam-5224	2	43	zero	zero	NUM
ejpam-5224	2	44	radical	radical	ADJ
ejpam-5224	2	45	’s	’s	PART
ejpam-5224	2	46	cube	cube	NOUN
ejpam-5224	2	47	and	and	CCONJ
ejpam-5224	2	48	the	the	DET
ejpam-5224	2	49	first	first	ADJ
ejpam-5224	2	50	bifunctor	bifunctor	NOUN
ejpam-5224	2	51	extension	extension	NOUN
ejpam-5224	2	52	on	on	ADP
ejpam-5224	2	53	s	s	PROPN
ejpam-5224	2	54	mounir	mounir	PROPN
ejpam-5224	2	55	laaraj1	laaraj1	PROPN
ejpam-5224	2	56	,	,	PUNCT
ejpam-5224	2	57	,	,	PUNCT
ejpam-5224	2	58	seddik	seddik	ADJ
ejpam-5224	2	59	abdelalim1	abdelalim1	PROPN
ejpam-5224	2	60	,	,	PUNCT
ejpam-5224	2	61	ilias	ilias	PROPN
ejpam-5224	2	62	elmouki1,∗	elmouki1,∗	NOUN
ejpam-5224	2	63	1	1	NUM
ejpam-5224	2	64	laboratory	laboratory	NOUN
ejpam-5224	2	65	of	of	ADP
ejpam-5224	2	66	fundamental	fundamental	ADJ
ejpam-5224	2	67	and	and	CCONJ
ejpam-5224	2	68	applied	applied	ADJ
ejpam-5224	2	69	mathematics	mathematic	NOUN
ejpam-5224	2	70	(	(	PUNCT
ejpam-5224	2	71	lmfa	lmfa	NOUN
ejpam-5224	2	72	)	)	PUNCT
ejpam-5224	2	73	,	,	PUNCT
ejpam-5224	2	74	faculty	faculty	NOUN
ejpam-5224	2	75	of	of	ADP
ejpam-5224	2	76	sciences	science	NOUN
ejpam-5224	2	77	ain	ain	PROPN
ejpam-5224	2	78	chock	chock	PROPN
ejpam-5224	2	79	(	(	PUNCT
ejpam-5224	2	80	fsac	fsac	NOUN
ejpam-5224	2	81	)	)	PUNCT
ejpam-5224	2	82	,	,	PUNCT
ejpam-5224	2	83	university	university	PROPN
ejpam-5224	2	84	hassan	hassan	PROPN
ejpam-5224	2	85	ii	ii	PROPN
ejpam-5224	2	86	of	of	ADP
ejpam-5224	2	87	casablanca	casablanca	PROPN
ejpam-5224	2	88	(	(	PUNCT
ejpam-5224	2	89	univh2c	univh2c	PROPN
ejpam-5224	2	90	)	)	PUNCT
ejpam-5224	2	91	,	,	PUNCT
ejpam-5224	2	92	morocco	morocco	PROPN
ejpam-5224	2	93	.	.	PUNCT
ejpam-5224	3	1	abstract	abstract	ADJ
ejpam-5224	3	2	.	.	PUNCT
ejpam-5224	4	1	through	through	ADP
ejpam-5224	4	2	concepts	concept	NOUN
ejpam-5224	4	3	from	from	ADP
ejpam-5224	4	4	non	non	ADJ
ejpam-5224	4	5	-	-	ADJ
ejpam-5224	4	6	commutative	commutative	ADJ
ejpam-5224	4	7	algebra	algebra	NOUN
ejpam-5224	4	8	and	and	CCONJ
ejpam-5224	4	9	homology	homology	NOUN
ejpam-5224	4	10	,	,	PUNCT
ejpam-5224	4	11	this	this	DET
ejpam-5224	4	12	paper	paper	NOUN
ejpam-5224	4	13	resolves	resolve	VERB
ejpam-5224	4	14	the	the	DET
ejpam-5224	4	15	conjecture	conjecture	NOUN
ejpam-5224	4	16	that	that	PRON
ejpam-5224	4	17	lets	let	VERB
ejpam-5224	4	18	the	the	DET
ejpam-5224	4	19	first	first	ADJ
ejpam-5224	4	20	bifunctor	bifunctor	NOUN
ejpam-5224	4	21	extension	extension	NOUN
ejpam-5224	4	22	to	to	PART
ejpam-5224	4	23	be	be	AUX
ejpam-5224	4	24	zero	zero	NUM
ejpam-5224	4	25	when	when	SCONJ
ejpam-5224	4	26	the	the	DET
ejpam-5224	4	27	projective	projective	ADJ
ejpam-5224	4	28	dimension	dimension	NOUN
ejpam-5224	4	29	is	be	AUX
ejpam-5224	4	30	finite	finite	ADJ
ejpam-5224	4	31	,	,	PUNCT
ejpam-5224	4	32	for	for	ADP
ejpam-5224	4	33	a	a	DET
ejpam-5224	4	34	simple	simple	ADJ
ejpam-5224	4	35	module	module	NOUN
ejpam-5224	4	36	s	s	NOUN
ejpam-5224	4	37	of	of	ADP
ejpam-5224	4	38	an	an	DET
ejpam-5224	4	39	artinian	artinian	ADJ
ejpam-5224	4	40	ring	ring	NOUN
ejpam-5224	4	41	whose	whose	DET
ejpam-5224	4	42	cube	cube	NOUN
ejpam-5224	4	43	of	of	ADP
ejpam-5224	4	44	its	its	PRON
ejpam-5224	4	45	jacobson	jacobson	PROPN
ejpam-5224	4	46	radical	radical	PROPN
ejpam-5224	4	47	is	be	AUX
ejpam-5224	4	48	zero	zero	NUM
ejpam-5224	4	49	and	and	CCONJ
ejpam-5224	4	50	under	under	ADP
ejpam-5224	4	51	the	the	DET
ejpam-5224	4	52	condition	condition	NOUN
ejpam-5224	4	53	that	that	SCONJ
ejpam-5224	4	54	any	any	DET
ejpam-5224	4	55	simple	simple	ADJ
ejpam-5224	4	56	module	module	NOUN
ejpam-5224	4	57	over	over	ADP
ejpam-5224	4	58	this	this	DET
ejpam-5224	4	59	ring	ring	NOUN
ejpam-5224	4	60	of	of	ADP
ejpam-5224	4	61	finite	finite	PROPN
ejpam-5224	4	62	projective	projective	PROPN
ejpam-5224	4	63	dimension	dimension	NOUN
ejpam-5224	4	64	has	have	VERB
ejpam-5224	4	65	a	a	DET
ejpam-5224	4	66	radical	radical	ADJ
ejpam-5224	4	67	square	square	NOUN
ejpam-5224	4	68	zero	zero	NUM
ejpam-5224	4	69	of	of	ADP
ejpam-5224	4	70	the	the	DET
ejpam-5224	4	71	cover	cover	NOUN
ejpam-5224	4	72	projective	projective	NOUN
ejpam-5224	4	73	of	of	ADP
ejpam-5224	4	74	its	its	PRON
ejpam-5224	4	75	first	first	ADJ
ejpam-5224	4	76	syzygy	syzygy	NOUN
ejpam-5224	4	77	.	.	PUNCT
ejpam-5224	5	1	for	for	ADP
ejpam-5224	5	2	that	that	PRON
ejpam-5224	5	3	,	,	PUNCT
ejpam-5224	5	4	we	we	PRON
ejpam-5224	5	5	use	use	VERB
ejpam-5224	5	6	a	a	DET
ejpam-5224	5	7	property	property	NOUN
ejpam-5224	5	8	of	of	ADP
ejpam-5224	5	9	the	the	DET
ejpam-5224	5	10	simple	simple	ADJ
ejpam-5224	5	11	module	module	NOUN
ejpam-5224	5	12	which	which	PRON
ejpam-5224	5	13	realizes	realize	VERB
ejpam-5224	5	14	the	the	DET
ejpam-5224	5	15	minimum	minimum	NOUN
ejpam-5224	5	16	of	of	ADP
ejpam-5224	5	17	the	the	DET
ejpam-5224	5	18	finite	finite	PROPN
ejpam-5224	5	19	projective	projective	ADJ
ejpam-5224	5	20	dimensions	dimension	NOUN
ejpam-5224	5	21	of	of	ADP
ejpam-5224	5	22	simple	simple	ADJ
ejpam-5224	5	23	modules	module	NOUN
ejpam-5224	5	24	.	.	PUNCT
ejpam-5224	6	1	our	our	PRON
ejpam-5224	6	2	main	main	ADJ
ejpam-5224	6	3	result	result	NOUN
ejpam-5224	6	4	is	be	AUX
ejpam-5224	6	5	presented	present	VERB
ejpam-5224	6	6	in	in	ADP
ejpam-5224	6	7	the	the	DET
ejpam-5224	6	8	form	form	NOUN
ejpam-5224	6	9	of	of	ADP
ejpam-5224	6	10	a	a	DET
ejpam-5224	6	11	corollary	corollary	NOUN
ejpam-5224	6	12	in	in	ADP
ejpam-5224	6	13	the	the	DET
ejpam-5224	6	14	case	case	NOUN
ejpam-5224	6	15	of	of	ADP
ejpam-5224	6	16	an	an	DET
ejpam-5224	6	17	artinian	artinian	ADJ
ejpam-5224	6	18	ring	ring	NOUN
ejpam-5224	6	19	with	with	ADP
ejpam-5224	6	20	radical	radical	ADJ
ejpam-5224	6	21	cubed	cubed	NOUN
ejpam-5224	6	22	zero	zero	NUM
ejpam-5224	6	23	such	such	ADJ
ejpam-5224	6	24	that	that	SCONJ
ejpam-5224	6	25	the	the	DET
ejpam-5224	6	26	projective	projective	ADJ
ejpam-5224	6	27	cover	cover	NOUN
ejpam-5224	6	28	of	of	ADP
ejpam-5224	6	29	its	its	PRON
ejpam-5224	6	30	radical	radical	ADJ
ejpam-5224	6	31	is	be	AUX
ejpam-5224	6	32	of	of	ADP
ejpam-5224	6	33	loewy	loewy	ADJ
ejpam-5224	6	34	length	length	NOUN
ejpam-5224	6	35	two	two	NUM
ejpam-5224	6	36	and	and	CCONJ
ejpam-5224	6	37	its	its	PRON
ejpam-5224	6	38	supremum	supremum	ADJ
ejpam-5224	6	39	being	be	AUX
ejpam-5224	6	40	finite	finite	ADJ
ejpam-5224	6	41	.	.	PUNCT
ejpam-5224	7	1	in	in	ADP
ejpam-5224	7	2	the	the	DET
ejpam-5224	7	3	part	part	NOUN
ejpam-5224	7	4	of	of	ADP
ejpam-5224	7	5	discussions	discussion	NOUN
ejpam-5224	7	6	,	,	PUNCT
ejpam-5224	7	7	we	we	PRON
ejpam-5224	7	8	succeed	succeed	VERB
ejpam-5224	7	9	to	to	PART
ejpam-5224	7	10	show	show	VERB
ejpam-5224	7	11	the	the	DET
ejpam-5224	7	12	no	no	DET
ejpam-5224	7	13	loop	loop	NOUN
ejpam-5224	7	14	conjecture	conjecture	NOUN
ejpam-5224	7	15	through	through	ADP
ejpam-5224	7	16	two	two	NUM
ejpam-5224	7	17	examples	example	NOUN
ejpam-5224	7	18	.	.	PUNCT
ejpam-5224	8	1	the	the	DET
ejpam-5224	8	2	first	first	ADJ
ejpam-5224	8	3	one	one	NOUN
ejpam-5224	8	4	is	be	AUX
ejpam-5224	8	5	about	about	ADP
ejpam-5224	8	6	its	its	PRON
ejpam-5224	8	7	weak	weak	ADJ
ejpam-5224	8	8	version	version	NOUN
ejpam-5224	8	9	by	by	ADP
ejpam-5224	8	10	taking	take	VERB
ejpam-5224	8	11	a	a	DET
ejpam-5224	8	12	quiver	quiver	NOUN
ejpam-5224	8	13	algebra	algebra	NOUN
ejpam-5224	8	14	a	a	DET
ejpam-5224	8	15	verifying	verifying	NOUN
ejpam-5224	8	16	j3	j3	PROPN
ejpam-5224	8	17	=	=	SYM
ejpam-5224	8	18	0	0	PROPN
ejpam-5224	8	19	and	and	CCONJ
ejpam-5224	8	20	without	without	ADP
ejpam-5224	8	21	considering	consider	VERB
ejpam-5224	8	22	that	that	SCONJ
ejpam-5224	8	23	rad2(p	rad2(p	NOUN
ejpam-5224	8	24	(	(	PUNCT
ejpam-5224	8	25	ω(s	ω(s	NOUN
ejpam-5224	8	26	)	)	PUNCT
ejpam-5224	8	27	)	)	PUNCT
ejpam-5224	8	28	)	)	PUNCT
ejpam-5224	9	1	=	=	SYM
ejpam-5224	9	2	0	0	NUM
ejpam-5224	9	3	for	for	ADP
ejpam-5224	9	4	every	every	DET
ejpam-5224	9	5	simple	simple	ADJ
ejpam-5224	9	6	module	module	NOUN
ejpam-5224	9	7	,	,	PUNCT
ejpam-5224	9	8	while	while	SCONJ
ejpam-5224	9	9	the	the	DET
ejpam-5224	9	10	second	second	ADJ
ejpam-5224	9	11	one	one	NUM
ejpam-5224	9	12	shows	show	VERB
ejpam-5224	9	13	that	that	SCONJ
ejpam-5224	9	14	if	if	SCONJ
ejpam-5224	9	15	the	the	DET
ejpam-5224	9	16	extension	extension	NOUN
ejpam-5224	9	17	quiver	quiver	NOUN
ejpam-5224	9	18	has	have	VERB
ejpam-5224	9	19	a	a	DET
ejpam-5224	9	20	loop	loop	NOUN
ejpam-5224	9	21	in	in	ADP
ejpam-5224	9	22	a	a	DET
ejpam-5224	9	23	simple	simple	ADJ
ejpam-5224	9	24	module	module	NOUN
ejpam-5224	9	25	then	then	ADV
ejpam-5224	9	26	its	its	PRON
ejpam-5224	9	27	projective	projective	ADJ
ejpam-5224	9	28	dimension	dimension	NOUN
ejpam-5224	9	29	is	be	AUX
ejpam-5224	9	30	infinite	infinite	ADJ
ejpam-5224	9	31	for	for	ADP
ejpam-5224	9	32	every	every	DET
ejpam-5224	9	33	nilpotence	nilpotence	NOUN
ejpam-5224	9	34	index	index	NOUN
ejpam-5224	9	35	of	of	ADP
ejpam-5224	9	36	the	the	DET
ejpam-5224	9	37	jacobson	jacobson	PROPN
ejpam-5224	9	38	radical	radical	PROPN
ejpam-5224	9	39	.	.	PUNCT
ejpam-5224	10	1	more	more	ADV
ejpam-5224	10	2	importantly	importantly	ADV
ejpam-5224	10	3	,	,	PUNCT
ejpam-5224	10	4	we	we	PRON
ejpam-5224	10	5	finally	finally	ADV
ejpam-5224	10	6	provide	provide	VERB
ejpam-5224	10	7	a	a	DET
ejpam-5224	10	8	practical	practical	ADJ
ejpam-5224	10	9	third	third	ADJ
ejpam-5224	10	10	example	example	NOUN
ejpam-5224	10	11	for	for	ADP
ejpam-5224	10	12	our	our	PRON
ejpam-5224	10	13	special	special	ADJ
ejpam-5224	10	14	case	case	NOUN
ejpam-5224	10	15	.	.	PUNCT
ejpam-5224	11	1	2020	2020	NUM
ejpam-5224	11	2	mathematics	mathematic	NOUN
ejpam-5224	11	3	subject	subject	NOUN
ejpam-5224	11	4	classifications	classification	NOUN
ejpam-5224	11	5	:	:	PUNCT
ejpam-5224	11	6	16d10	16d10	NUM
ejpam-5224	11	7	,	,	PUNCT
ejpam-5224	11	8	16d20	16d20	NUM
ejpam-5224	11	9	,	,	PUNCT
ejpam-5224	11	10	16d25	16d25	NUM
ejpam-5224	11	11	,	,	PUNCT
ejpam-5224	11	12	16d60	16d60	NUM
ejpam-5224	11	13	,	,	PUNCT
ejpam-5224	11	14	16d70	16d70	NUM
ejpam-5224	11	15	,	,	PUNCT
ejpam-5224	11	16	16e05	16e05	NUM
ejpam-5224	11	17	,	,	PUNCT
ejpam-5224	11	18	16e10	16e10	NUM
ejpam-5224	11	19	,	,	PUNCT
ejpam-5224	11	20	16e30	16e30	NUM
ejpam-5224	11	21	,	,	PUNCT
ejpam-5224	11	22	16g10	16g10	NUM
ejpam-5224	11	23	,	,	PUNCT
ejpam-5224	11	24	16g20	16g20	NUM
ejpam-5224	11	25	key	key	ADJ
ejpam-5224	11	26	words	word	NOUN
ejpam-5224	11	27	and	and	CCONJ
ejpam-5224	11	28	phrases	phrase	NOUN
ejpam-5224	11	29	:	:	PUNCT
ejpam-5224	11	30	artin	artin	PROPN
ejpam-5224	11	31	algebras	algebra	NOUN
ejpam-5224	11	32	,	,	PUNCT
ejpam-5224	11	33	representation	representation	NOUN
ejpam-5224	11	34	-	-	PUNCT
ejpam-5224	11	35	finite	finite	ADJ
ejpam-5224	11	36	algebras	algebra	NOUN
ejpam-5224	11	37	,	,	PUNCT
ejpam-5224	11	38	projective	projective	ADJ
ejpam-5224	11	39	dimension	dimension	NOUN
ejpam-5224	11	40	,	,	PUNCT
ejpam-5224	11	41	global	global	ADJ
ejpam-5224	11	42	dimension	dimension	NOUN
ejpam-5224	11	43	,	,	PUNCT
ejpam-5224	11	44	injective	injective	ADJ
ejpam-5224	11	45	dimension	dimension	NOUN
ejpam-5224	11	46	,	,	PUNCT
ejpam-5224	11	47	jacobson	jacobson	PROPN
ejpam-5224	11	48	radical	radical	PROPN
ejpam-5224	11	49	.	.	PUNCT
ejpam-5224	12	1	1	1	X
ejpam-5224	12	2	.	.	X
ejpam-5224	12	3	introduction	introduction	NOUN
ejpam-5224	12	4	1.1	1.1	NUM
ejpam-5224	12	5	.	.	PUNCT
ejpam-5224	13	1	background	background	NOUN
ejpam-5224	13	2	from	from	ADP
ejpam-5224	13	3	non	non	ADJ
ejpam-5224	13	4	-	-	ADJ
ejpam-5224	13	5	commutative	commutative	ADJ
ejpam-5224	13	6	algebra	algebra	NOUN
ejpam-5224	13	7	and	and	CCONJ
ejpam-5224	13	8	homology	homology	NOUN
ejpam-5224	13	9	among	among	ADP
ejpam-5224	13	10	the	the	DET
ejpam-5224	13	11	main	main	ADJ
ejpam-5224	13	12	branches	branch	NOUN
ejpam-5224	13	13	of	of	ADP
ejpam-5224	13	14	abstract	abstract	ADJ
ejpam-5224	13	15	algebra	algebra	NOUN
ejpam-5224	13	16	that	that	PRON
ejpam-5224	13	17	deal	deal	VERB
ejpam-5224	13	18	with	with	ADP
ejpam-5224	13	19	algebraic	algebraic	ADJ
ejpam-5224	13	20	structures	structure	NOUN
ejpam-5224	13	21	and	and	CCONJ
ejpam-5224	13	22	operations	operation	NOUN
ejpam-5224	13	23	are	be	AUX
ejpam-5224	13	24	the	the	DET
ejpam-5224	13	25	commutative	commutative	ADJ
ejpam-5224	13	26	and	and	CCONJ
ejpam-5224	13	27	non	non	ADJ
ejpam-5224	13	28	-	-	ADJ
ejpam-5224	13	29	commutative	commutative	ADJ
ejpam-5224	13	30	algebra	algebra	NOUN
ejpam-5224	13	31	.	.	PUNCT
ejpam-5224	14	1	both	both	PRON
ejpam-5224	14	2	represent	represent	VERB
ejpam-5224	14	3	active	active	ADJ
ejpam-5224	14	4	research	research	NOUN
ejpam-5224	14	5	areas	area	NOUN
ejpam-5224	14	6	with	with	ADP
ejpam-5224	14	7	many	many	ADJ
ejpam-5224	14	8	open	open	ADJ
ejpam-5224	14	9	problems	problem	NOUN
ejpam-5224	14	10	and	and	CCONJ
ejpam-5224	14	11	ongoing	ongoing	ADJ
ejpam-5224	14	12	developments	development	NOUN
ejpam-5224	14	13	[	[	X
ejpam-5224	14	14	1–3	1–3	NOUN
ejpam-5224	14	15	,	,	PUNCT
ejpam-5224	14	16	7	7	NUM
ejpam-5224	14	17	,	,	PUNCT
ejpam-5224	14	18	8	8	NUM
ejpam-5224	14	19	,	,	PUNCT
ejpam-5224	14	20	12	12	NUM
ejpam-5224	14	21	,	,	PUNCT
ejpam-5224	14	22	16	16	NUM
ejpam-5224	14	23	]	]	PUNCT
ejpam-5224	14	24	.	.	PUNCT
ejpam-5224	15	1	the	the	DET
ejpam-5224	15	2	∗corresponding	∗corresponde	VERB
ejpam-5224	15	3	author	author	NOUN
ejpam-5224	15	4	.	.	PUNCT
ejpam-5224	16	1	doi	doi	NOUN
ejpam-5224	16	2	:	:	PUNCT
ejpam-5224	16	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5224	https://doi.org/10.29020/nybg.ejpam.v17i3.5224	X
ejpam-5224	16	4	email	email	NOUN
ejpam-5224	16	5	addresses	address	NOUN
ejpam-5224	16	6	:	:	PUNCT
ejpam-5224	16	7	mounirlaaraj2@gmail.com	mounirlaaraj2@gmail.com	X
ejpam-5224	16	8	(	(	PUNCT
ejpam-5224	16	9	m.	m.	NOUN
ejpam-5224	16	10	laaraj	laaraj	PROPN
ejpam-5224	16	11	)	)	PUNCT
ejpam-5224	16	12	,	,	PUNCT
ejpam-5224	16	13	seddikabd@hotmail.com	seddikabd@hotmail.com	X
ejpam-5224	16	14	(	(	PUNCT
ejpam-5224	16	15	s.	s.	PROPN
ejpam-5224	16	16	abdelalim	abdelalim	PROPN
ejpam-5224	16	17	)	)	PUNCT
ejpam-5224	16	18	,	,	PUNCT
ejpam-5224	16	19	i.elmouki@gmail.com	i.elmouki@gmail.com	X
ejpam-5224	16	20	(	(	PUNCT
ejpam-5224	16	21	i.	i.	PROPN
ejpam-5224	16	22	elmouki	elmouki	PROPN
ejpam-5224	16	23	)	)	PUNCT
ejpam-5224	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5224	16	25	1855	1855	NUM
ejpam-5224	17	1	©	©	ADP
ejpam-5224	17	2	2024	2024	NUM
ejpam-5224	17	3	ejpam	ejpam	NOUN
ejpam-5224	17	4	all	all	DET
ejpam-5224	17	5	rights	right	NOUN
ejpam-5224	17	6	reserved	reserve	VERB
ejpam-5224	17	7	.	.	PUNCT
ejpam-5224	18	1	m.	m.	NOUN
ejpam-5224	18	2	laaraj	laaraj	PROPN
ejpam-5224	18	3	,	,	PUNCT
ejpam-5224	18	4	s.	s.	PROPN
ejpam-5224	18	5	abdelalim	abdelalim	PROPN
ejpam-5224	18	6	,	,	PUNCT
ejpam-5224	18	7	i.elmouki	i.elmouki	CCONJ
ejpam-5224	18	8	/	/	SYM
ejpam-5224	18	9	eur	eur	NOUN
ejpam-5224	18	10	.	.	PUNCT
ejpam-5224	19	1	j.	j.	PROPN
ejpam-5224	19	2	pure	pure	PROPN
ejpam-5224	19	3	appl	appl	PROPN
ejpam-5224	19	4	.	.	PROPN
ejpam-5224	19	5	math	math	PROPN
ejpam-5224	19	6	,	,	PUNCT
ejpam-5224	19	7	17	17	NUM
ejpam-5224	19	8	(	(	PUNCT
ejpam-5224	19	9	3	3	NUM
ejpam-5224	19	10	)	)	PUNCT
ejpam-5224	19	11	(	(	PUNCT
ejpam-5224	19	12	2024	2024	NUM
ejpam-5224	19	13	)	)	PUNCT
ejpam-5224	19	14	,	,	PUNCT
ejpam-5224	19	15	1855	1855	NUM
ejpam-5224	19	16	-	-	SYM
ejpam-5224	19	17	1868	1868	NUM
ejpam-5224	19	18	1856	1856	NUM
ejpam-5224	19	19	primary	primary	ADJ
ejpam-5224	19	20	distinction	distinction	NOUN
ejpam-5224	19	21	between	between	ADP
ejpam-5224	19	22	them	they	PRON
ejpam-5224	19	23	is	be	AUX
ejpam-5224	19	24	that	that	SCONJ
ejpam-5224	19	25	,	,	PUNCT
ejpam-5224	19	26	in	in	ADP
ejpam-5224	19	27	commutative	commutative	ADJ
ejpam-5224	19	28	algebra	algebra	NOUN
ejpam-5224	19	29	,	,	PUNCT
ejpam-5224	19	30	the	the	DET
ejpam-5224	19	31	order	order	NOUN
ejpam-5224	19	32	of	of	ADP
ejpam-5224	19	33	operations	operation	NOUN
ejpam-5224	19	34	is	be	AUX
ejpam-5224	19	35	irrelevant	irrelevant	ADJ
ejpam-5224	19	36	,	,	PUNCT
ejpam-5224	19	37	and	and	CCONJ
ejpam-5224	19	38	ideals	ideal	NOUN
ejpam-5224	19	39	on	on	ADP
ejpam-5224	19	40	left	left	ADJ
ejpam-5224	19	41	and	and	CCONJ
ejpam-5224	19	42	right	right	ADJ
ejpam-5224	19	43	are	be	AUX
ejpam-5224	19	44	identical	identical	ADJ
ejpam-5224	19	45	.	.	PUNCT
ejpam-5224	20	1	as	as	ADP
ejpam-5224	20	2	for	for	ADP
ejpam-5224	20	3	non	non	ADJ
ejpam-5224	20	4	-	-	ADJ
ejpam-5224	20	5	commutative	commutative	ADJ
ejpam-5224	20	6	rings	ring	NOUN
ejpam-5224	20	7	,	,	PUNCT
ejpam-5224	20	8	they	they	PRON
ejpam-5224	20	9	are	be	AUX
ejpam-5224	20	10	distinguished	distinguish	VERB
ejpam-5224	20	11	by	by	ADP
ejpam-5224	20	12	the	the	DET
ejpam-5224	20	13	need	need	NOUN
ejpam-5224	20	14	to	to	PART
ejpam-5224	20	15	consider	consider	VERB
ejpam-5224	20	16	ideals	ideal	NOUN
ejpam-5224	20	17	on	on	ADP
ejpam-5224	20	18	the	the	DET
ejpam-5224	20	19	right	right	NOUN
ejpam-5224	20	20	and	and	CCONJ
ejpam-5224	20	21	left	leave	VERB
ejpam-5224	20	22	separately	separately	ADV
ejpam-5224	20	23	.	.	PUNCT
ejpam-5224	21	1	it	it	PRON
ejpam-5224	21	2	is	be	AUX
ejpam-5224	21	3	common	common	ADJ
ejpam-5224	21	4	for	for	SCONJ
ejpam-5224	21	5	the	the	DET
ejpam-5224	21	6	study	study	NOUN
ejpam-5224	21	7	of	of	ADP
ejpam-5224	21	8	non	non	ADJ
ejpam-5224	21	9	-	-	ADJ
ejpam-5224	21	10	commutative	commutative	ADJ
ejpam-5224	21	11	rings	ring	NOUN
ejpam-5224	21	12	to	to	PART
ejpam-5224	21	13	impose	impose	VERB
ejpam-5224	21	14	a	a	DET
ejpam-5224	21	15	condition	condition	NOUN
ejpam-5224	21	16	on	on	ADP
ejpam-5224	21	17	one	one	NUM
ejpam-5224	21	18	of	of	ADP
ejpam-5224	21	19	these	these	DET
ejpam-5224	21	20	types	type	NOUN
ejpam-5224	21	21	of	of	ADP
ejpam-5224	21	22	ideals	ideal	NOUN
ejpam-5224	21	23	without	without	ADP
ejpam-5224	21	24	requiring	require	VERB
ejpam-5224	21	25	that	that	SCONJ
ejpam-5224	21	26	it	it	PRON
ejpam-5224	21	27	has	have	VERB
ejpam-5224	21	28	to	to	PART
ejpam-5224	21	29	be	be	AUX
ejpam-5224	21	30	valid	valid	ADJ
ejpam-5224	21	31	for	for	ADP
ejpam-5224	21	32	its	its	PRON
ejpam-5224	21	33	opposite	opposite	ADJ
ejpam-5224	21	34	side	side	NOUN
ejpam-5224	21	35	,	,	PUNCT
ejpam-5224	21	36	whereas	whereas	SCONJ
ejpam-5224	21	37	moving	move	VERB
ejpam-5224	21	38	to	to	ADP
ejpam-5224	21	39	the	the	DET
ejpam-5224	21	40	quotient	quotient	NOUN
ejpam-5224	21	41	of	of	ADP
ejpam-5224	21	42	the	the	DET
ejpam-5224	21	43	non	non	ADJ
ejpam-5224	21	44	-	-	ADJ
ejpam-5224	21	45	commutative	commutative	ADJ
ejpam-5224	21	46	ring	ring	NOUN
ejpam-5224	21	47	by	by	ADP
ejpam-5224	21	48	an	an	DET
ejpam-5224	21	49	ideal	ideal	NOUN
ejpam-5224	21	50	imposes	impose	VERB
ejpam-5224	21	51	that	that	SCONJ
ejpam-5224	21	52	it	it	PRON
ejpam-5224	21	53	must	must	AUX
ejpam-5224	21	54	be	be	AUX
ejpam-5224	21	55	bilateral	bilateral	ADJ
ejpam-5224	21	56	,	,	PUNCT
ejpam-5224	21	57	a	a	DET
ejpam-5224	21	58	case	case	NOUN
ejpam-5224	21	59	which	which	PRON
ejpam-5224	21	60	is	be	AUX
ejpam-5224	21	61	verified	verify	VERB
ejpam-5224	21	62	by	by	ADP
ejpam-5224	21	63	the	the	DET
ejpam-5224	21	64	jacobson	jacobson	PROPN
ejpam-5224	21	65	radical	radical	PROPN
ejpam-5224	21	66	in	in	ADP
ejpam-5224	21	67	an	an	DET
ejpam-5224	21	68	artinian	artinian	ADJ
ejpam-5224	21	69	ring	ring	NOUN
ejpam-5224	21	70	and	and	CCONJ
ejpam-5224	21	71	which	which	PRON
ejpam-5224	21	72	has	have	VERB
ejpam-5224	21	73	several	several	ADJ
ejpam-5224	21	74	properties	property	NOUN
ejpam-5224	21	75	including	include	VERB
ejpam-5224	21	76	that	that	PRON
ejpam-5224	21	77	of	of	ADP
ejpam-5224	21	78	its	its	PRON
ejpam-5224	21	79	nilpotence	nilpotence	NOUN
ejpam-5224	21	80	.	.	PUNCT
ejpam-5224	22	1	thus	thus	ADV
ejpam-5224	22	2	,	,	PUNCT
ejpam-5224	22	3	the	the	DET
ejpam-5224	22	4	study	study	NOUN
ejpam-5224	22	5	of	of	ADP
ejpam-5224	22	6	simple	simple	ADJ
ejpam-5224	22	7	,	,	PUNCT
ejpam-5224	22	8	projective	projective	ADJ
ejpam-5224	22	9	and	and	CCONJ
ejpam-5224	22	10	injective	injective	ADJ
ejpam-5224	22	11	modules	module	NOUN
ejpam-5224	22	12	of	of	ADP
ejpam-5224	22	13	finite	finite	ADJ
ejpam-5224	22	14	type	type	NOUN
ejpam-5224	22	15	on	on	ADP
ejpam-5224	22	16	this	this	DET
ejpam-5224	22	17	ring	ring	NOUN
ejpam-5224	22	18	is	be	AUX
ejpam-5224	22	19	described	describe	VERB
ejpam-5224	22	20	by	by	ADP
ejpam-5224	22	21	idempotent	idempotent	ADJ
ejpam-5224	22	22	primitives	primitive	NOUN
ejpam-5224	22	23	[	[	X
ejpam-5224	22	24	10	10	NUM
ejpam-5224	22	25	]	]	PUNCT
ejpam-5224	22	26	.	.	PUNCT
ejpam-5224	23	1	in	in	ADP
ejpam-5224	23	2	parallel	parallel	ADJ
ejpam-5224	23	3	,	,	PUNCT
ejpam-5224	23	4	homological	homological	ADJ
ejpam-5224	23	5	algebra	algebra	NOUN
ejpam-5224	23	6	has	have	AUX
ejpam-5224	23	7	been	be	AUX
ejpam-5224	23	8	categorically	categorically	ADV
ejpam-5224	23	9	interested	interested	ADJ
ejpam-5224	23	10	in	in	ADP
ejpam-5224	23	11	the	the	DET
ejpam-5224	23	12	study	study	NOUN
ejpam-5224	23	13	of	of	ADP
ejpam-5224	23	14	the	the	DET
ejpam-5224	23	15	properties	property	NOUN
ejpam-5224	23	16	of	of	ADP
ejpam-5224	23	17	the	the	DET
ejpam-5224	23	18	special	special	ADJ
ejpam-5224	23	19	functor	functor	PROPN
ejpam-5224	23	20	hom(m,−	hom(m,−	PROPN
ejpam-5224	23	21	)	)	PUNCT
ejpam-5224	23	22	and	and	CCONJ
ejpam-5224	23	23	its	its	PRON
ejpam-5224	23	24	precision	precision	NOUN
ejpam-5224	23	25	,	,	PUNCT
ejpam-5224	23	26	the	the	DET
ejpam-5224	23	27	functor	functor	PROPN
ejpam-5224	23	28	hom	hom	PROPN
ejpam-5224	23	29	is	be	AUX
ejpam-5224	23	30	only	only	ADV
ejpam-5224	23	31	exact	exact	ADJ
ejpam-5224	23	32	on	on	ADP
ejpam-5224	23	33	the	the	DET
ejpam-5224	23	34	left	left	NOUN
ejpam-5224	23	35	,	,	PUNCT
ejpam-5224	23	36	while	while	SCONJ
ejpam-5224	23	37	the	the	DET
ejpam-5224	23	38	tensor	tensor	NOUN
ejpam-5224	23	39	product	product	NOUN
ejpam-5224	23	40	functor	functor	NOUN
ejpam-5224	23	41	is	be	AUX
ejpam-5224	23	42	only	only	ADV
ejpam-5224	23	43	exact	exact	ADJ
ejpam-5224	23	44	on	on	ADP
ejpam-5224	23	45	the	the	DET
ejpam-5224	23	46	right	right	NOUN
ejpam-5224	23	47	.	.	PUNCT
ejpam-5224	24	1	to	to	PART
ejpam-5224	24	2	obtain	obtain	VERB
ejpam-5224	24	3	an	an	DET
ejpam-5224	24	4	exact	exact	ADJ
ejpam-5224	24	5	sequence	sequence	NOUN
ejpam-5224	24	6	from	from	ADP
ejpam-5224	24	7	a	a	DET
ejpam-5224	24	8	functor	functor	NOUN
ejpam-5224	24	9	of	of	ADP
ejpam-5224	24	10	the	the	DET
ejpam-5224	24	11	form	form	NOUN
ejpam-5224	24	12	hom(m,−	hom(m,−	NOUN
ejpam-5224	24	13	)	)	PUNCT
ejpam-5224	24	14	(	(	PUNCT
ejpam-5224	24	15	with	with	ADP
ejpam-5224	24	16	m	m	DET
ejpam-5224	24	17	a	a	DET
ejpam-5224	24	18	module	module	NOUN
ejpam-5224	24	19	)	)	PUNCT
ejpam-5224	24	20	,	,	PUNCT
ejpam-5224	24	21	it	it	PRON
ejpam-5224	24	22	is	be	AUX
ejpam-5224	24	23	possible	possible	ADJ
ejpam-5224	24	24	to	to	PART
ejpam-5224	24	25	use	use	VERB
ejpam-5224	24	26	an	an	DET
ejpam-5224	24	27	approximation	approximation	NOUN
ejpam-5224	24	28	of	of	ADP
ejpam-5224	24	29	m	m	PRON
ejpam-5224	24	30	by	by	ADP
ejpam-5224	24	31	projective	projective	ADJ
ejpam-5224	24	32	modules	module	NOUN
ejpam-5224	24	33	.	.	PUNCT
ejpam-5224	25	1	such	such	DET
ejpam-5224	25	2	an	an	DET
ejpam-5224	25	3	approximation	approximation	NOUN
ejpam-5224	25	4	is	be	AUX
ejpam-5224	25	5	called	call	VERB
ejpam-5224	25	6	the	the	DET
ejpam-5224	25	7	projective	projective	ADJ
ejpam-5224	25	8	resolution	resolution	NOUN
ejpam-5224	25	9	of	of	ADP
ejpam-5224	25	10	m	m	PROPN
ejpam-5224	25	11	,	,	PUNCT
ejpam-5224	25	12	and	and	CCONJ
ejpam-5224	25	13	if	if	SCONJ
ejpam-5224	25	14	we	we	PRON
ejpam-5224	25	15	apply	apply	VERB
ejpam-5224	25	16	the	the	DET
ejpam-5224	25	17	functor	functor	PROPN
ejpam-5224	25	18	hom	hom	NOUN
ejpam-5224	25	19	to	to	ADP
ejpam-5224	25	20	a	a	DET
ejpam-5224	25	21	projective	projective	ADJ
ejpam-5224	25	22	resolution	resolution	NOUN
ejpam-5224	25	23	of	of	ADP
ejpam-5224	25	24	m	m	PROPN
ejpam-5224	25	25	,	,	PUNCT
ejpam-5224	25	26	we	we	PRON
ejpam-5224	25	27	therefore	therefore	ADV
ejpam-5224	25	28	obtain	obtain	VERB
ejpam-5224	25	29	a	a	DET
ejpam-5224	25	30	sequence	sequence	NOUN
ejpam-5224	25	31	which	which	PRON
ejpam-5224	25	32	is	be	AUX
ejpam-5224	25	33	generally	generally	ADV
ejpam-5224	25	34	not	not	PART
ejpam-5224	25	35	exact	exact	ADJ
ejpam-5224	25	36	,	,	PUNCT
ejpam-5224	25	37	but	but	CCONJ
ejpam-5224	25	38	that	that	PRON
ejpam-5224	25	39	is	be	AUX
ejpam-5224	25	40	complex	complex	ADJ
ejpam-5224	25	41	.	.	PUNCT
ejpam-5224	26	1	the	the	DET
ejpam-5224	26	2	notion	notion	NOUN
ejpam-5224	26	3	of	of	ADP
ejpam-5224	26	4	homology	homology	NOUN
ejpam-5224	26	5	corrects	correct	VERB
ejpam-5224	26	6	the	the	DET
ejpam-5224	26	7	lack	lack	NOUN
ejpam-5224	26	8	of	of	ADP
ejpam-5224	26	9	inexactness	inexactness	NOUN
ejpam-5224	26	10	of	of	ADP
ejpam-5224	26	11	this	this	DET
ejpam-5224	26	12	complex	complex	NOUN
ejpam-5224	26	13	by	by	ADP
ejpam-5224	26	14	associating	associate	VERB
ejpam-5224	26	15	it	it	PRON
ejpam-5224	26	16	with	with	ADP
ejpam-5224	26	17	a	a	DET
ejpam-5224	26	18	long	long	ADJ
ejpam-5224	26	19	exact	exact	ADJ
ejpam-5224	26	20	sequence	sequence	NOUN
ejpam-5224	26	21	,	,	PUNCT
ejpam-5224	26	22	called	call	VERB
ejpam-5224	26	23	a	a	DET
ejpam-5224	26	24	homology	homology	NOUN
ejpam-5224	26	25	sequence	sequence	NOUN
ejpam-5224	26	26	[	[	X
ejpam-5224	26	27	10	10	NUM
ejpam-5224	26	28	]	]	PUNCT
ejpam-5224	26	29	.	.	PUNCT
ejpam-5224	26	30	.	.	PUNCT
ejpam-5224	27	1	this	this	PRON
ejpam-5224	27	2	makes	make	VERB
ejpam-5224	27	3	it	it	PRON
ejpam-5224	27	4	possible	possible	ADJ
ejpam-5224	27	5	to	to	PART
ejpam-5224	27	6	associate	associate	VERB
ejpam-5224	27	7	new	new	ADJ
ejpam-5224	27	8	functors	functor	NOUN
ejpam-5224	27	9	with	with	ADP
ejpam-5224	27	10	the	the	DET
ejpam-5224	27	11	functor	functor	PROPN
ejpam-5224	27	12	hom	hom	PROPN
ejpam-5224	27	13	,	,	PUNCT
ejpam-5224	27	14	called	call	VERB
ejpam-5224	27	15	extension	extension	NOUN
ejpam-5224	27	16	functors	functor	NOUN
ejpam-5224	27	17	and	and	CCONJ
ejpam-5224	27	18	denoted	denote	VERB
ejpam-5224	27	19	extn(m,−	extn(m,−	NOUN
ejpam-5224	27	20	)	)	PUNCT
ejpam-5224	27	21	see	see	VERB
ejpam-5224	27	22	[	[	X
ejpam-5224	27	23	13	13	NUM
ejpam-5224	27	24	]	]	PUNCT
ejpam-5224	27	25	.	.	PUNCT
ejpam-5224	28	1	let	let	VERB
ejpam-5224	28	2	a	a	DET
ejpam-5224	28	3	be	be	AUX
ejpam-5224	28	4	an	an	DET
ejpam-5224	28	5	artinian	artinian	ADJ
ejpam-5224	28	6	ring	ring	NOUN
ejpam-5224	28	7	with	with	ADP
ejpam-5224	28	8	j	j	PROPN
ejpam-5224	28	9	as	as	ADP
ejpam-5224	28	10	its	its	PRON
ejpam-5224	28	11	jacobson	jacobson	PROPN
ejpam-5224	28	12	radical	radical	NOUN
ejpam-5224	28	13	,	,	PUNCT
ejpam-5224	28	14	and	and	CCONJ
ejpam-5224	28	15	let	let	VERB
ejpam-5224	28	16	mod(a	mod(a	PROPN
ejpam-5224	28	17	)	)	PUNCT
ejpam-5224	28	18	be	be	AUX
ejpam-5224	28	19	the	the	DET
ejpam-5224	28	20	category	category	NOUN
ejpam-5224	28	21	of	of	ADP
ejpam-5224	28	22	left	leave	VERB
ejpam-5224	28	23	a	a	DET
ejpam-5224	28	24	-	-	PUNCT
ejpam-5224	28	25	modules	module	NOUN
ejpam-5224	28	26	of	of	ADP
ejpam-5224	28	27	finite	finite	ADJ
ejpam-5224	28	28	type	type	NOUN
ejpam-5224	28	29	.	.	PUNCT
ejpam-5224	29	1	an	an	DET
ejpam-5224	29	2	invariant	invariant	ADJ
ejpam-5224	29	3	important	important	ADJ
ejpam-5224	29	4	of	of	ADP
ejpam-5224	29	5	a	a	PRON
ejpam-5224	29	6	is	be	AUX
ejpam-5224	29	7	its	its	PRON
ejpam-5224	29	8	global	global	ADJ
ejpam-5224	29	9	dimension	dimension	NOUN
ejpam-5224	29	10	denoted	denote	VERB
ejpam-5224	29	11	gdim(a	gdim(a	NOUN
ejpam-5224	29	12	)	)	PUNCT
ejpam-5224	29	13	and	and	CCONJ
ejpam-5224	29	14	which	which	PRON
ejpam-5224	29	15	is	be	AUX
ejpam-5224	29	16	the	the	DET
ejpam-5224	29	17	supremum	supremum	NOUN
ejpam-5224	29	18	of	of	ADP
ejpam-5224	29	19	projective	projective	ADJ
ejpam-5224	29	20	dimensions	dimension	NOUN
ejpam-5224	29	21	of	of	ADP
ejpam-5224	29	22	left	leave	VERB
ejpam-5224	29	23	a	a	DET
ejpam-5224	29	24	-	-	PUNCT
ejpam-5224	29	25	modules	module	NOUN
ejpam-5224	29	26	of	of	ADP
ejpam-5224	29	27	finite	finite	ADJ
ejpam-5224	29	28	type	type	NOUN
ejpam-5224	29	29	,	,	PUNCT
ejpam-5224	29	30	see	see	VERB
ejpam-5224	29	31	page	page	NOUN
ejpam-5224	29	32	92-[13	92-[13	NOUN
ejpam-5224	29	33	]	]	X
ejpam-5224	29	34	.	.	PUNCT
ejpam-5224	30	1	it	it	PRON
ejpam-5224	30	2	is	be	AUX
ejpam-5224	30	3	known	know	VERB
ejpam-5224	30	4	that	that	SCONJ
ejpam-5224	30	5	gdim(a	gdim(a	NOUN
ejpam-5224	30	6	)	)	PUNCT
ejpam-5224	30	7	is	be	AUX
ejpam-5224	30	8	the	the	DET
ejpam-5224	30	9	supremum	supremum	NOUN
ejpam-5224	30	10	of	of	ADP
ejpam-5224	30	11	the	the	DET
ejpam-5224	30	12	projective	projective	ADJ
ejpam-5224	30	13	dimensions	dimension	NOUN
ejpam-5224	30	14	of	of	ADP
ejpam-5224	30	15	simple	simple	ADJ
ejpam-5224	30	16	a	a	PRON
ejpam-5224	30	17	-	-	PUNCT
ejpam-5224	30	18	modules	module	NOUN
ejpam-5224	30	19	and	and	CCONJ
ejpam-5224	30	20	the	the	DET
ejpam-5224	30	21	number	number	NOUN
ejpam-5224	30	22	of	of	ADP
ejpam-5224	30	23	non	non	ADJ
ejpam-5224	30	24	-	-	ADJ
ejpam-5224	30	25	isomorphic	isomorphic	ADJ
ejpam-5224	30	26	simple	simple	ADJ
ejpam-5224	30	27	a	a	PRON
ejpam-5224	30	28	-	-	PUNCT
ejpam-5224	30	29	modules	module	NOUN
ejpam-5224	30	30	is	be	AUX
ejpam-5224	30	31	finite	finite	ADJ
ejpam-5224	30	32	and	and	CCONJ
ejpam-5224	30	33	also	also	ADV
ejpam-5224	30	34	j	j	PROPN
ejpam-5224	30	35	is	be	AUX
ejpam-5224	30	36	nilpotent	nilpotent	ADJ
ejpam-5224	31	1	[	[	X
ejpam-5224	31	2	10	10	NUM
ejpam-5224	31	3	]	]	PUNCT
ejpam-5224	31	4	.	.	PUNCT
ejpam-5224	32	1	we	we	PRON
ejpam-5224	32	2	define	define	VERB
ejpam-5224	32	3	therafter	therafter	NOUN
ejpam-5224	32	4	the	the	DET
ejpam-5224	32	5	quiver	quiver	NOUN
ejpam-5224	32	6	(	(	PUNCT
ejpam-5224	32	7	that	that	PRON
ejpam-5224	32	8	is	be	AUX
ejpam-5224	32	9	to	to	PART
ejpam-5224	32	10	say	say	VERB
ejpam-5224	32	11	a	a	DET
ejpam-5224	32	12	directed	direct	VERB
ejpam-5224	32	13	graph	graph	NOUN
ejpam-5224	32	14	)	)	PUNCT
ejpam-5224	32	15	of	of	ADP
ejpam-5224	32	16	extensions	extension	NOUN
ejpam-5224	32	17	of	of	ADP
ejpam-5224	32	18	a	a	PRON
ejpam-5224	32	19	,	,	PUNCT
ejpam-5224	32	20	whose	whose	DET
ejpam-5224	32	21	set	set	NOUN
ejpam-5224	32	22	of	of	ADP
ejpam-5224	32	23	vertices	vertex	NOUN
ejpam-5224	32	24	is	be	AUX
ejpam-5224	32	25	a	a	DET
ejpam-5224	32	26	complete	complete	ADJ
ejpam-5224	32	27	set	set	NOUN
ejpam-5224	32	28	of	of	ADP
ejpam-5224	32	29	representatives	representative	NOUN
ejpam-5224	32	30	of	of	ADP
ejpam-5224	32	31	isomorphism	isomorphism	PROPN
ejpam-5224	32	32	classes	class	NOUN
ejpam-5224	32	33	of	of	ADP
ejpam-5224	32	34	simple	simple	ADJ
ejpam-5224	32	35	a	a	PRON
ejpam-5224	32	36	-	-	PUNCT
ejpam-5224	32	37	modules	module	NOUN
ejpam-5224	32	38	,	,	PUNCT
ejpam-5224	32	39	and	and	CCONJ
ejpam-5224	32	40	given	give	VERB
ejpam-5224	32	41	two	two	NUM
ejpam-5224	32	42	vertices	vertex	NOUN
ejpam-5224	32	43	s	s	PART
ejpam-5224	32	44	and	and	CCONJ
ejpam-5224	32	45	t	t	PROPN
ejpam-5224	32	46	,	,	PUNCT
ejpam-5224	32	47	there	there	PRON
ejpam-5224	32	48	is	be	VERB
ejpam-5224	32	49	an	an	DET
ejpam-5224	32	50	arrow	arrow	NOUN
ejpam-5224	32	51	from	from	ADP
ejpam-5224	32	52	s	s	PRON
ejpam-5224	32	53	to	to	ADP
ejpam-5224	32	54	t	t	NOUN
ejpam-5224	32	55	if	if	SCONJ
ejpam-5224	32	56	the	the	DET
ejpam-5224	32	57	extension	extension	NOUN
ejpam-5224	32	58	group	group	NOUN
ejpam-5224	32	59	ext1a(s	ext1a(s	PROPN
ejpam-5224	32	60	,	,	PUNCT
ejpam-5224	32	61	t	t	PROPN
ejpam-5224	32	62	)	)	PUNCT
ejpam-5224	32	63	is	be	AUX
ejpam-5224	32	64	not	not	PART
ejpam-5224	32	65	zero	zero	NUM
ejpam-5224	32	66	.	.	PUNCT
ejpam-5224	33	1	1.2	1.2	NUM
ejpam-5224	33	2	.	.	PUNCT
ejpam-5224	33	3	history	history	NOUN
ejpam-5224	33	4	of	of	ADP
ejpam-5224	33	5	the	the	DET
ejpam-5224	33	6	conjecture	conjecture	NOUN
ejpam-5224	33	7	until	until	SCONJ
ejpam-5224	33	8	our	our	PRON
ejpam-5224	33	9	contribution	contribution	NOUN
ejpam-5224	33	10	the	the	DET
ejpam-5224	33	11	first	first	ADJ
ejpam-5224	33	12	version	version	NOUN
ejpam-5224	33	13	of	of	ADP
ejpam-5224	33	14	the	the	DET
ejpam-5224	33	15	conjecture	conjecture	NOUN
ejpam-5224	33	16	that	that	SCONJ
ejpam-5224	33	17	we	we	PRON
ejpam-5224	33	18	are	be	AUX
ejpam-5224	33	19	dealing	deal	VERB
ejpam-5224	33	20	with	with	ADP
ejpam-5224	33	21	here	here	ADV
ejpam-5224	33	22	,	,	PUNCT
ejpam-5224	33	23	was	be	AUX
ejpam-5224	33	24	stating	state	VERB
ejpam-5224	33	25	that	that	SCONJ
ejpam-5224	33	26	if	if	SCONJ
ejpam-5224	33	27	gdim(a	gdim(a	NOUN
ejpam-5224	33	28	)	)	PUNCT
ejpam-5224	33	29	is	be	AUX
ejpam-5224	33	30	finite	finite	ADJ
ejpam-5224	33	31	,	,	PUNCT
ejpam-5224	33	32	then	then	ADV
ejpam-5224	33	33	the	the	DET
ejpam-5224	33	34	quiver	quiver	NOUN
ejpam-5224	33	35	of	of	ADP
ejpam-5224	33	36	extensions	extension	NOUN
ejpam-5224	33	37	of	of	ADP
ejpam-5224	33	38	a	a	PRON
ejpam-5224	33	39	,	,	PUNCT
ejpam-5224	33	40	is	be	AUX
ejpam-5224	33	41	characterized	characterize	VERB
ejpam-5224	33	42	by	by	ADP
ejpam-5224	33	43	the	the	DET
ejpam-5224	33	44	ext1a(s	ext1a(s	PROPN
ejpam-5224	33	45	,	,	PUNCT
ejpam-5224	33	46	s	s	NOUN
ejpam-5224	33	47	)	)	PUNCT
ejpam-5224	33	48	null	null	NOUN
ejpam-5224	33	49	for	for	SCONJ
ejpam-5224	33	50	every	every	DET
ejpam-5224	33	51	simple	simple	ADJ
ejpam-5224	33	52	a	a	DET
ejpam-5224	33	53	-	-	PUNCT
ejpam-5224	33	54	module	module	NOUN
ejpam-5224	33	55	s	s	NOUN
ejpam-5224	33	56	,	,	PUNCT
ejpam-5224	33	57	then	then	ADV
ejpam-5224	33	58	the	the	DET
ejpam-5224	33	59	second	second	ADJ
ejpam-5224	33	60	version	version	NOUN
ejpam-5224	33	61	of	of	ADP
ejpam-5224	33	62	the	the	DET
ejpam-5224	33	63	conjecture	conjecture	NOUN
ejpam-5224	33	64	,	,	PUNCT
ejpam-5224	33	65	let	let	VERB
ejpam-5224	33	66	us	we	PRON
ejpam-5224	33	67	say	say	VERB
ejpam-5224	33	68	the	the	DET
ejpam-5224	33	69	more	more	ADV
ejpam-5224	33	70	localized	localized	ADJ
ejpam-5224	33	71	and	and	CCONJ
ejpam-5224	33	72	complicated	complicated	ADJ
ejpam-5224	33	73	,	,	PUNCT
ejpam-5224	33	74	and	and	CCONJ
ejpam-5224	33	75	that	that	SCONJ
ejpam-5224	33	76	interests	interest	VERB
ejpam-5224	33	77	us	we	PRON
ejpam-5224	33	78	more	more	ADV
ejpam-5224	33	79	since	since	SCONJ
ejpam-5224	33	80	the	the	DET
ejpam-5224	33	81	first	first	ADJ
ejpam-5224	33	82	one	one	NOUN
ejpam-5224	33	83	was	be	AUX
ejpam-5224	33	84	resolved	resolve	VERB
ejpam-5224	33	85	in	in	ADP
ejpam-5224	33	86	the	the	DET
ejpam-5224	33	87	case	case	NOUN
ejpam-5224	33	88	of	of	ADP
ejpam-5224	33	89	the	the	DET
ejpam-5224	33	90	supremum	supremum	NOUN
ejpam-5224	33	91	by	by	ADP
ejpam-5224	33	92	green	green	PROPN
ejpam-5224	33	93	et	et	PROPN
ejpam-5224	33	94	al	al	PROPN
ejpam-5224	33	95	.	.	PROPN
ejpam-5224	34	1	in	in	ADP
ejpam-5224	34	2	1985	1985	NUM
ejpam-5224	34	3	[	[	X
ejpam-5224	34	4	14	14	NUM
ejpam-5224	34	5	]	]	PUNCT
ejpam-5224	34	6	.	.	PUNCT
ejpam-5224	35	1	in	in	ADP
ejpam-5224	35	2	fact	fact	NOUN
ejpam-5224	35	3	,	,	PUNCT
ejpam-5224	35	4	this	this	DET
ejpam-5224	35	5	one	one	NOUN
ejpam-5224	35	6	was	be	AUX
ejpam-5224	35	7	presented	present	VERB
ejpam-5224	35	8	as	as	ADP
ejpam-5224	35	9	the	the	DET
ejpam-5224	35	10	seventh	seventh	ADJ
ejpam-5224	35	11	conjecture	conjecture	NOUN
ejpam-5224	35	12	in	in	ADP
ejpam-5224	35	13	the	the	DET
ejpam-5224	35	14	book	book	NOUN
ejpam-5224	35	15	of	of	ADP
ejpam-5224	35	16	representation	representation	NOUN
ejpam-5224	35	17	theory	theory	NOUN
ejpam-5224	35	18	of	of	ADP
ejpam-5224	35	19	artin	artin	PROPN
ejpam-5224	35	20	algebras	algebras	X
ejpam-5224	36	1	[	[	X
ejpam-5224	36	2	10	10	NUM
ejpam-5224	36	3	]	]	PUNCT
ejpam-5224	36	4	,	,	PUNCT
ejpam-5224	36	5	by	by	ADP
ejpam-5224	36	6	the	the	DET
ejpam-5224	36	7	implication	implication	NOUN
ejpam-5224	36	8	ext1a(s	ext1a(s	PROPN
ejpam-5224	36	9	,	,	PUNCT
ejpam-5224	36	10	s	s	PART
ejpam-5224	36	11	)	)	PUNCT
ejpam-5224	36	12	̸=	̸=	NOUN
ejpam-5224	36	13	0	0	NUM
ejpam-5224	36	14	⇒	⇒	PROPN
ejpam-5224	36	15	pda(s	pda(s	PROPN
ejpam-5224	36	16	)	)	PUNCT
ejpam-5224	36	17	=	=	SYM
ejpam-5224	36	18	∞	∞	NOUN
ejpam-5224	36	19	which	which	PRON
ejpam-5224	36	20	is	be	AUX
ejpam-5224	36	21	the	the	DET
ejpam-5224	36	22	same	same	ADJ
ejpam-5224	36	23	as	as	ADP
ejpam-5224	36	24	saying	say	VERB
ejpam-5224	36	25	that	that	SCONJ
ejpam-5224	36	26	if	if	SCONJ
ejpam-5224	36	27	the	the	DET
ejpam-5224	36	28	projective	projective	ADJ
ejpam-5224	36	29	dimension	dimension	NOUN
ejpam-5224	36	30	of	of	ADP
ejpam-5224	36	31	each	each	DET
ejpam-5224	36	32	simple	simple	ADJ
ejpam-5224	36	33	a	a	DET
ejpam-5224	36	34	-	-	PUNCT
ejpam-5224	36	35	module	module	NOUN
ejpam-5224	36	36	s	s	NOUN
ejpam-5224	36	37	is	be	AUX
ejpam-5224	36	38	finite	finite	ADJ
ejpam-5224	36	39	,	,	PUNCT
ejpam-5224	36	40	there	there	PRON
ejpam-5224	36	41	is	be	VERB
ejpam-5224	36	42	no	no	DET
ejpam-5224	36	43	arrow	arrow	NOUN
ejpam-5224	36	44	from	from	ADP
ejpam-5224	36	45	s	s	PRON
ejpam-5224	36	46	to	to	ADP
ejpam-5224	36	47	s.	s.	PROPN
ejpam-5224	36	48	historically	historically	ADV
ejpam-5224	36	49	,	,	PUNCT
ejpam-5224	36	50	this	this	DET
ejpam-5224	36	51	conjecture	conjecture	NOUN
ejpam-5224	36	52	was	be	AUX
ejpam-5224	36	53	demonstrated	demonstrate	VERB
ejpam-5224	36	54	in	in	ADP
ejpam-5224	36	55	several	several	ADJ
ejpam-5224	36	56	cases	case	NOUN
ejpam-5224	36	57	long	long	ADV
ejpam-5224	36	58	before	before	SCONJ
ejpam-5224	36	59	it	it	PRON
ejpam-5224	36	60	was	be	AUX
ejpam-5224	36	61	formally	formally	ADV
ejpam-5224	36	62	stated	state	VERB
ejpam-5224	36	63	.	.	PUNCT
ejpam-5224	37	1	at	at	ADP
ejpam-5224	37	2	the	the	DET
ejpam-5224	37	3	end	end	NOUN
ejpam-5224	37	4	of	of	ADP
ejpam-5224	37	5	1960	1960	NUM
ejpam-5224	37	6	,	,	PUNCT
ejpam-5224	37	7	helmut	helmut	PROPN
ejpam-5224	37	8	lenzing	lenze	VERB
ejpam-5224	37	9	proved	prove	VERB
ejpam-5224	37	10	this	this	DET
ejpam-5224	37	11	conjecture	conjecture	NOUN
ejpam-5224	37	12	in	in	ADP
ejpam-5224	37	13	the	the	DET
ejpam-5224	37	14	case	case	NOUN
ejpam-5224	37	15	m.	m.	NOUN
ejpam-5224	37	16	laaraj	laaraj	PROPN
ejpam-5224	37	17	,	,	PUNCT
ejpam-5224	37	18	s.	s.	PROPN
ejpam-5224	37	19	abdelalim	abdelalim	PROPN
ejpam-5224	37	20	,	,	PUNCT
ejpam-5224	37	21	i.elmouki	i.elmouki	CCONJ
ejpam-5224	37	22	/	/	SYM
ejpam-5224	37	23	eur	eur	NOUN
ejpam-5224	37	24	.	.	PUNCT
ejpam-5224	38	1	j.	j.	PROPN
ejpam-5224	38	2	pure	pure	PROPN
ejpam-5224	38	3	appl	appl	PROPN
ejpam-5224	38	4	.	.	PROPN
ejpam-5224	38	5	math	math	PROPN
ejpam-5224	38	6	,	,	PUNCT
ejpam-5224	38	7	17	17	NUM
ejpam-5224	38	8	(	(	PUNCT
ejpam-5224	38	9	3	3	NUM
ejpam-5224	38	10	)	)	PUNCT
ejpam-5224	38	11	(	(	PUNCT
ejpam-5224	38	12	2024	2024	NUM
ejpam-5224	38	13	)	)	PUNCT
ejpam-5224	38	14	,	,	PUNCT
ejpam-5224	38	15	1855	1855	NUM
ejpam-5224	38	16	-	-	SYM
ejpam-5224	38	17	1868	1868	NUM
ejpam-5224	38	18	1857	1857	NUM
ejpam-5224	38	19	where	where	SCONJ
ejpam-5224	38	20	a	a	PRON
ejpam-5224	38	21	is	be	AUX
ejpam-5224	38	22	an	an	DET
ejpam-5224	38	23	algebra	algebra	NOUN
ejpam-5224	38	24	over	over	ADP
ejpam-5224	38	25	an	an	DET
ejpam-5224	38	26	algebraically	algebraically	ADV
ejpam-5224	38	27	closed	close	VERB
ejpam-5224	38	28	field	field	NOUN
ejpam-5224	39	1	[	[	X
ejpam-5224	39	2	6	6	NUM
ejpam-5224	39	3	]	]	PUNCT
ejpam-5224	39	4	as	as	SCONJ
ejpam-5224	39	5	it	it	PRON
ejpam-5224	39	6	took	take	VERB
ejpam-5224	39	7	back	back	ADV
ejpam-5224	39	8	up	up	ADP
ejpam-5224	39	9	the	the	DET
ejpam-5224	39	10	idea	idea	NOUN
ejpam-5224	39	11	of	of	ADP
ejpam-5224	39	12	hattori	hattori	PROPN
ejpam-5224	39	13	-	-	PUNCT
ejpam-5224	39	14	stallings	stallings	PROPN
ejpam-5224	40	1	[	[	X
ejpam-5224	40	2	4	4	NUM
ejpam-5224	40	3	,	,	PUNCT
ejpam-5224	40	4	11	11	NUM
ejpam-5224	40	5	]	]	PUNCT
ejpam-5224	40	6	on	on	ADP
ejpam-5224	40	7	the	the	DET
ejpam-5224	40	8	notion	notion	NOUN
ejpam-5224	40	9	of	of	ADP
ejpam-5224	40	10	(	(	PUNCT
ejpam-5224	40	11	the	the	DET
ejpam-5224	40	12	trace	trace	NOUN
ejpam-5224	40	13	of	of	ADP
ejpam-5224	40	14	the	the	DET
ejpam-5224	40	15	endomorphism	endomorphism	NOUN
ejpam-5224	40	16	of	of	ADP
ejpam-5224	40	17	a	a	DET
ejpam-5224	40	18	projective	projective	ADJ
ejpam-5224	40	19	module	module	NOUN
ejpam-5224	40	20	)	)	PUNCT
ejpam-5224	40	21	.	.	PUNCT
ejpam-5224	41	1	in	in	ADP
ejpam-5224	41	2	chronological	chronological	ADJ
ejpam-5224	41	3	order	order	NOUN
ejpam-5224	41	4	,	,	PUNCT
ejpam-5224	41	5	the	the	DET
ejpam-5224	41	6	next	next	ADJ
ejpam-5224	41	7	result	result	NOUN
ejpam-5224	41	8	in	in	ADP
ejpam-5224	41	9	favor	favor	NOUN
ejpam-5224	41	10	of	of	ADP
ejpam-5224	41	11	the	the	DET
ejpam-5224	41	12	conjecture	conjecture	NOUN
ejpam-5224	41	13	goes	go	VERB
ejpam-5224	41	14	back	back	ADV
ejpam-5224	41	15	to	to	ADP
ejpam-5224	41	16	1983	1983	NUM
ejpam-5224	41	17	when	when	SCONJ
ejpam-5224	41	18	green	green	PROPN
ejpam-5224	41	19	et	et	PROPN
ejpam-5224	41	20	al	al	PROPN
ejpam-5224	41	21	.	.	PROPN
ejpam-5224	41	22	showed	show	VERB
ejpam-5224	41	23	that	that	SCONJ
ejpam-5224	41	24	conjecture	conjecture	NOUN
ejpam-5224	41	25	is	be	AUX
ejpam-5224	41	26	true	true	ADJ
ejpam-5224	41	27	when	when	SCONJ
ejpam-5224	41	28	the	the	DET
ejpam-5224	41	29	global	global	ADJ
ejpam-5224	41	30	dimension	dimension	NOUN
ejpam-5224	41	31	of	of	ADP
ejpam-5224	41	32	algebra	algebra	PROPN
ejpam-5224	41	33	is	be	AUX
ejpam-5224	41	34	bounded	bound	VERB
ejpam-5224	41	35	by	by	ADP
ejpam-5224	41	36	two	two	NUM
ejpam-5224	41	37	[	[	X
ejpam-5224	41	38	14	14	NUM
ejpam-5224	41	39	]	]	PUNCT
ejpam-5224	41	40	.	.	PUNCT
ejpam-5224	42	1	their	their	PRON
ejpam-5224	42	2	proof	proof	NOUN
ejpam-5224	42	3	consists	consist	VERB
ejpam-5224	42	4	of	of	ADP
ejpam-5224	42	5	a	a	DET
ejpam-5224	42	6	recurrence	recurrence	NOUN
ejpam-5224	42	7	of	of	ADP
ejpam-5224	42	8	the	the	DET
ejpam-5224	42	9	number	number	NOUN
ejpam-5224	42	10	of	of	ADP
ejpam-5224	42	11	isomorphic	isomorphic	ADJ
ejpam-5224	42	12	classes	class	NOUN
ejpam-5224	42	13	of	of	ADP
ejpam-5224	42	14	simple	simple	ADJ
ejpam-5224	42	15	modules	module	NOUN
ejpam-5224	42	16	.	.	PUNCT
ejpam-5224	43	1	subsequently	subsequently	ADV
ejpam-5224	43	2	,	,	PUNCT
ejpam-5224	43	3	in	in	ADP
ejpam-5224	43	4	1986	1986	NUM
ejpam-5224	43	5	,	,	PUNCT
ejpam-5224	43	6	fuller	full	ADJ
ejpam-5224	43	7	and	and	CCONJ
ejpam-5224	43	8	zimmermannhuisgen	zimmermannhuisgen	PROPN
ejpam-5224	43	9	demonstrated	demonstrate	VERB
ejpam-5224	43	10	in	in	ADP
ejpam-5224	43	11	[	[	X
ejpam-5224	43	12	17	17	NUM
ejpam-5224	43	13	]	]	PUNCT
ejpam-5224	43	14	,	,	PUNCT
ejpam-5224	43	15	the	the	DET
ejpam-5224	43	16	conjecture	conjecture	NOUN
ejpam-5224	43	17	when	when	SCONJ
ejpam-5224	43	18	(	(	PUNCT
ejpam-5224	43	19	rad(a))3	rad(a))3	NOUN
ejpam-5224	43	20	=	=	SYM
ejpam-5224	43	21	0	0	PUNCT
ejpam-5224	44	1	and	and	CCONJ
ejpam-5224	44	2	when	when	SCONJ
ejpam-5224	44	3	a	a	PRON
ejpam-5224	44	4	is	be	AUX
ejpam-5224	44	5	a	a	DET
ejpam-5224	44	6	left	left	ADJ
ejpam-5224	44	7	serial	serial	ADJ
ejpam-5224	44	8	algebra	algebra	NOUN
ejpam-5224	44	9	.	.	PUNCT
ejpam-5224	45	1	their	their	PRON
ejpam-5224	45	2	approach	approach	NOUN
ejpam-5224	45	3	uses	use	VERB
ejpam-5224	45	4	the	the	DET
ejpam-5224	45	5	matrix	matrix	NOUN
ejpam-5224	45	6	cartan	cartan	NOUN
ejpam-5224	45	7	filtered	filter	VERB
ejpam-5224	45	8	by	by	ADP
ejpam-5224	45	9	radical	radical	ADJ
ejpam-5224	45	10	algebra	algebra	NOUN
ejpam-5224	45	11	to	to	PART
ejpam-5224	45	12	prove	prove	VERB
ejpam-5224	45	13	that	that	SCONJ
ejpam-5224	45	14	the	the	DET
ejpam-5224	45	15	determinant	determinant	NOUN
ejpam-5224	45	16	of	of	ADP
ejpam-5224	45	17	the	the	DET
ejpam-5224	45	18	cartan	cartan	ADJ
ejpam-5224	45	19	matrix	matrix	NOUN
ejpam-5224	45	20	is	be	AUX
ejpam-5224	45	21	one	one	NUM
ejpam-5224	45	22	.	.	PUNCT
ejpam-5224	46	1	1.1	1.1	NUM
ejpam-5224	46	2	remark	remark	NOUN
ejpam-5224	46	3	.	.	PUNCT
ejpam-5224	47	1	we	we	PRON
ejpam-5224	47	2	note	note	VERB
ejpam-5224	47	3	that	that	SCONJ
ejpam-5224	47	4	fuller	full	ADJ
ejpam-5224	47	5	and	and	CCONJ
ejpam-5224	47	6	zimmermann	zimmermann	PROPN
ejpam-5224	47	7	-	-	PUNCT
ejpam-5224	47	8	huisgen	huisgen	PROPN
ejpam-5224	47	9	have	have	AUX
ejpam-5224	47	10	demonstrated	demonstrate	VERB
ejpam-5224	47	11	that	that	DET
ejpam-5224	47	12	conjecture	conjecture	NOUN
ejpam-5224	47	13	using	use	VERB
ejpam-5224	47	14	a	a	DET
ejpam-5224	47	15	strong	strong	ADJ
ejpam-5224	47	16	condition	condition	NOUN
ejpam-5224	47	17	and	and	CCONJ
ejpam-5224	47	18	which	which	PRON
ejpam-5224	47	19	is	be	AUX
ejpam-5224	47	20	about	about	ADP
ejpam-5224	47	21	working	work	VERB
ejpam-5224	47	22	with	with	ADP
ejpam-5224	47	23	the	the	DET
ejpam-5224	47	24	global	global	ADJ
ejpam-5224	47	25	dimension	dimension	NOUN
ejpam-5224	47	26	.	.	PUNCT
ejpam-5224	48	1	our	our	PRON
ejpam-5224	48	2	approach	approach	NOUN
ejpam-5224	48	3	is	be	AUX
ejpam-5224	48	4	interesting	interesting	ADJ
ejpam-5224	48	5	in	in	ADP
ejpam-5224	48	6	the	the	DET
ejpam-5224	48	7	sense	sense	NOUN
ejpam-5224	48	8	that	that	SCONJ
ejpam-5224	48	9	we	we	PRON
ejpam-5224	48	10	succeed	succeed	VERB
ejpam-5224	48	11	to	to	PART
ejpam-5224	48	12	weaken	weaken	VERB
ejpam-5224	48	13	that	that	DET
ejpam-5224	48	14	condition	condition	NOUN
ejpam-5224	48	15	by	by	ADP
ejpam-5224	48	16	proving	prove	VERB
ejpam-5224	48	17	that	that	SCONJ
ejpam-5224	48	18	we	we	PRON
ejpam-5224	48	19	can	can	AUX
ejpam-5224	48	20	just	just	ADV
ejpam-5224	48	21	take	take	VERB
ejpam-5224	48	22	the	the	DET
ejpam-5224	48	23	projective	projective	ADJ
ejpam-5224	48	24	dimension	dimension	NOUN
ejpam-5224	48	25	in	in	ADP
ejpam-5224	48	26	every	every	DET
ejpam-5224	48	27	simple	simple	ADJ
ejpam-5224	48	28	module	module	NOUN
ejpam-5224	48	29	.	.	PUNCT
ejpam-5224	49	1	later	later	ADV
ejpam-5224	49	2	,	,	PUNCT
ejpam-5224	49	3	k.	k.	PROPN
ejpam-5224	49	4	igusa	igusa	PROPN
ejpam-5224	49	5	proved	prove	VERB
ejpam-5224	49	6	in	in	ADP
ejpam-5224	49	7	1990	1990	NUM
ejpam-5224	49	8	[	[	X
ejpam-5224	49	9	5	5	NUM
ejpam-5224	49	10	]	]	PUNCT
ejpam-5224	49	11	the	the	DET
ejpam-5224	49	12	conjecture	conjecture	NOUN
ejpam-5224	49	13	in	in	ADP
ejpam-5224	49	14	a	a	DET
ejpam-5224	49	15	case	case	NOUN
ejpam-5224	49	16	that	that	SCONJ
ejpam-5224	49	17	all	all	DET
ejpam-5224	49	18	algebras	algebra	NOUN
ejpam-5224	49	19	of	of	ADP
ejpam-5224	49	20	endomorphism	endomorphism	NOUN
ejpam-5224	49	21	of	of	ADP
ejpam-5224	49	22	simple	simple	ADJ
ejpam-5224	49	23	modules	module	NOUN
ejpam-5224	49	24	are	be	AUX
ejpam-5224	49	25	separable	separable	ADJ
ejpam-5224	49	26	.	.	PUNCT
ejpam-5224	50	1	the	the	DET
ejpam-5224	50	2	author	author	NOUN
ejpam-5224	50	3	used	use	VERB
ejpam-5224	50	4	concepts	concept	NOUN
ejpam-5224	50	5	from	from	ADP
ejpam-5224	50	6	the	the	DET
ejpam-5224	50	7	k	k	NOUN
ejpam-5224	50	8	-	-	NOUN
ejpam-5224	50	9	theory	theory	NOUN
ejpam-5224	50	10	in	in	ADP
ejpam-5224	50	11	his	his	PRON
ejpam-5224	50	12	proof	proof	NOUN
ejpam-5224	50	13	to	to	PART
ejpam-5224	50	14	point	point	VERB
ejpam-5224	50	15	out	out	ADP
ejpam-5224	50	16	his	his	PRON
ejpam-5224	50	17	result	result	NOUN
ejpam-5224	50	18	included	include	VERB
ejpam-5224	50	19	that	that	PRON
ejpam-5224	50	20	of	of	ADP
ejpam-5224	50	21	h.	h.	PROPN
ejpam-5224	50	22	lenzing	lenze	VERB
ejpam-5224	50	23	since	since	SCONJ
ejpam-5224	50	24	all	all	DET
ejpam-5224	50	25	fields	field	NOUN
ejpam-5224	50	26	are	be	AUX
ejpam-5224	50	27	separable	separable	ADJ
ejpam-5224	50	28	algebras	algebra	NOUN
ejpam-5224	50	29	.	.	PUNCT
ejpam-5224	51	1	then	then	ADV
ejpam-5224	51	2	,	,	PUNCT
ejpam-5224	51	3	the	the	DET
ejpam-5224	51	4	lenzing	lenze	VERB
ejpam-5224	51	5	trace	trace	NOUN
ejpam-5224	51	6	function	function	NOUN
ejpam-5224	51	7	has	have	AUX
ejpam-5224	51	8	been	be	AUX
ejpam-5224	51	9	localized	localize	VERB
ejpam-5224	51	10	to	to	ADP
ejpam-5224	51	11	endomorphisms	endomorphism	NOUN
ejpam-5224	51	12	of	of	ADP
ejpam-5224	51	13	modules	module	NOUN
ejpam-5224	51	14	in	in	ADP
ejpam-5224	51	15	mod(a	mod(a	PROPN
ejpam-5224	51	16	)	)	PUNCT
ejpam-5224	51	17	with	with	ADP
ejpam-5224	51	18	the	the	DET
ejpam-5224	51	19	e	e	NOUN
ejpam-5224	51	20	-	-	ADJ
ejpam-5224	51	21	bounded	bound	VERB
ejpam-5224	51	22	projective	projective	ADJ
ejpam-5224	51	23	resolution	resolution	NOUN
ejpam-5224	51	24	,	,	PUNCT
ejpam-5224	51	25	where	where	SCONJ
ejpam-5224	51	26	e	e	NOUN
ejpam-5224	51	27	is	be	AUX
ejpam-5224	51	28	an	an	DET
ejpam-5224	51	29	idempotent	idempotent	NOUN
ejpam-5224	51	30	in	in	ADP
ejpam-5224	51	31	a	a	PRON
ejpam-5224	51	32	and	and	CCONJ
ejpam-5224	51	33	they	they	PRON
ejpam-5224	51	34	have	have	AUX
ejpam-5224	51	35	proved	prove	VERB
ejpam-5224	51	36	the	the	DET
ejpam-5224	51	37	conjecture	conjecture	NOUN
ejpam-5224	51	38	for	for	ADP
ejpam-5224	51	39	artinian	artinian	ADJ
ejpam-5224	51	40	rings	ring	NOUN
ejpam-5224	51	41	a	a	PRON
ejpam-5224	51	42	with	with	ADP
ejpam-5224	51	43	j2	j2	PROPN
ejpam-5224	51	44	=	=	SYM
ejpam-5224	51	45	0	0	PROPN
ejpam-5224	51	46	for	for	ADP
ejpam-5224	51	47	finite	finite	ADJ
ejpam-5224	51	48	dimensional	dimensional	ADJ
ejpam-5224	51	49	algebras	algebra	NOUN
ejpam-5224	51	50	over	over	ADP
ejpam-5224	51	51	an	an	DET
ejpam-5224	51	52	algebraically	algebraically	ADV
ejpam-5224	51	53	closed	close	VERB
ejpam-5224	51	54	field	field	NOUN
ejpam-5224	51	55	.	.	PUNCT
ejpam-5224	52	1	in	in	ADP
ejpam-5224	52	2	short	short	ADJ
ejpam-5224	52	3	,	,	PUNCT
ejpam-5224	52	4	our	our	PRON
ejpam-5224	52	5	research	research	NOUN
ejpam-5224	52	6	work	work	NOUN
ejpam-5224	52	7	aims	aim	VERB
ejpam-5224	52	8	to	to	PART
ejpam-5224	52	9	establish	establish	VERB
ejpam-5224	52	10	that	that	SCONJ
ejpam-5224	52	11	last	last	ADJ
ejpam-5224	52	12	conjecture	conjecture	NOUN
ejpam-5224	52	13	for	for	ADP
ejpam-5224	52	14	artinian	artinian	ADJ
ejpam-5224	52	15	rings	ring	NOUN
ejpam-5224	52	16	a	a	PRON
ejpam-5224	52	17	with	with	ADP
ejpam-5224	52	18	j3	j3	PROPN
ejpam-5224	52	19	=	=	PROPN
ejpam-5224	52	20	0	0	NUM
ejpam-5224	52	21	in	in	ADP
ejpam-5224	52	22	the	the	DET
ejpam-5224	52	23	particular	particular	ADJ
ejpam-5224	52	24	case	case	NOUN
ejpam-5224	52	25	where	where	SCONJ
ejpam-5224	52	26	each	each	DET
ejpam-5224	52	27	simple	simple	ADJ
ejpam-5224	52	28	module	module	NOUN
ejpam-5224	52	29	having	have	VERB
ejpam-5224	52	30	the	the	DET
ejpam-5224	52	31	finite	finite	PROPN
ejpam-5224	52	32	projective	projective	PROPN
ejpam-5224	52	33	dimension	dimension	NOUN
ejpam-5224	52	34	whose	whose	DET
ejpam-5224	52	35	the	the	DET
ejpam-5224	52	36	projective	projective	ADJ
ejpam-5224	52	37	cover	cover	NOUN
ejpam-5224	52	38	of	of	ADP
ejpam-5224	52	39	its	its	PRON
ejpam-5224	52	40	first	first	ADJ
ejpam-5224	52	41	syzygy	syzygy	NOUN
ejpam-5224	52	42	is	be	AUX
ejpam-5224	52	43	canceled	cancel	VERB
ejpam-5224	52	44	by	by	ADP
ejpam-5224	52	45	j2	j2	PROPN
ejpam-5224	52	46	,	,	PUNCT
ejpam-5224	52	47	and	and	CCONJ
ejpam-5224	52	48	this	this	PRON
ejpam-5224	52	49	is	be	AUX
ejpam-5224	52	50	by	by	ADP
ejpam-5224	52	51	taking	take	VERB
ejpam-5224	52	52	inspiration	inspiration	NOUN
ejpam-5224	52	53	from	from	ADP
ejpam-5224	52	54	the	the	DET
ejpam-5224	52	55	algebra	algebra	NOUN
ejpam-5224	52	56	of	of	ADP
ejpam-5224	52	57	endomorphisms	endomorphism	NOUN
ejpam-5224	52	58	of	of	ADP
ejpam-5224	52	59	a	a	DET
ejpam-5224	52	60	projective	projective	ADJ
ejpam-5224	52	61	a	a	DET
ejpam-5224	52	62	-	-	PUNCT
ejpam-5224	52	63	module	module	NOUN
ejpam-5224	52	64	as	as	ADV
ejpam-5224	52	65	well	well	ADV
ejpam-5224	52	66	as	as	ADP
ejpam-5224	52	67	the	the	DET
ejpam-5224	52	68	jacobson	jacobson	PROPN
ejpam-5224	52	69	radical	radical	PROPN
ejpam-5224	52	70	of	of	ADP
ejpam-5224	52	71	this	this	DET
ejpam-5224	52	72	one	one	NOUN
ejpam-5224	52	73	and	and	CCONJ
ejpam-5224	52	74	the	the	DET
ejpam-5224	52	75	characterization	characterization	NOUN
ejpam-5224	52	76	of	of	ADP
ejpam-5224	52	77	simple	simple	ADJ
ejpam-5224	52	78	and	and	CCONJ
ejpam-5224	52	79	projective	projective	ADJ
ejpam-5224	52	80	end(p	end(p	PROPN
ejpam-5224	52	81	)	)	PUNCT
ejpam-5224	52	82	-modules	-module	NOUN
ejpam-5224	52	83	with	with	ADP
ejpam-5224	52	84	p	p	PROPN
ejpam-5224	52	85	is	be	AUX
ejpam-5224	52	86	a	a	DET
ejpam-5224	52	87	projective	projective	ADJ
ejpam-5224	52	88	amodule	amodule	NOUN
ejpam-5224	52	89	.	.	PUNCT
ejpam-5224	53	1	2	2	X
ejpam-5224	53	2	.	.	X
ejpam-5224	53	3	main	main	ADJ
ejpam-5224	53	4	theorem	theorem	NOUN
ejpam-5224	53	5	given	give	VERB
ejpam-5224	53	6	a	a	DET
ejpam-5224	53	7	module	module	NOUN
ejpam-5224	53	8	m	m	NOUN
ejpam-5224	53	9	in	in	ADP
ejpam-5224	53	10	mod(a	mod(a	PROPN
ejpam-5224	53	11	)	)	PUNCT
ejpam-5224	53	12	,	,	PUNCT
ejpam-5224	53	13	we	we	PRON
ejpam-5224	53	14	denote	denote	VERB
ejpam-5224	53	15	by	by	ADP
ejpam-5224	53	16	,	,	PUNCT
ejpam-5224	53	17	•	•	NUM
ejpam-5224	53	18	ω(m	ω(m	NOUN
ejpam-5224	53	19	)	)	PUNCT
ejpam-5224	53	20	the	the	DET
ejpam-5224	53	21	first	first	PROPN
ejpam-5224	53	22	syzygy	syzygy	NOUN
ejpam-5224	53	23	,	,	PUNCT
ejpam-5224	53	24	•	•	NUM
ejpam-5224	53	25	pdm	pdm	VERB
ejpam-5224	53	26	the	the	DET
ejpam-5224	53	27	projective	projective	ADJ
ejpam-5224	53	28	dimension	dimension	NOUN
ejpam-5224	53	29	of	of	ADP
ejpam-5224	53	30	m	m	PROPN
ejpam-5224	53	31	,	,	PUNCT
ejpam-5224	53	32	•	•	PRON
ejpam-5224	53	33	ω2(m	ω2(m	PRON
ejpam-5224	53	34	)	)	PUNCT
ejpam-5224	53	35	=	=	SYM
ejpam-5224	53	36	ω(ω(m	ω(ω(m	NOUN
ejpam-5224	53	37	)	)	PUNCT
ejpam-5224	53	38	)	)	PUNCT
ejpam-5224	53	39	,	,	PUNCT
ejpam-5224	53	40	•	•	NUM
ejpam-5224	53	41	pd(ω(m	pd(ω(m	NOUN
ejpam-5224	53	42	)	)	PUNCT
ejpam-5224	53	43	)	)	PUNCT
ejpam-5224	54	1	the	the	DET
ejpam-5224	54	2	projective	projective	ADJ
ejpam-5224	54	3	dimension	dimension	NOUN
ejpam-5224	54	4	of	of	ADP
ejpam-5224	54	5	the	the	DET
ejpam-5224	54	6	projective	projective	ADJ
ejpam-5224	54	7	cover	cover	NOUN
ejpam-5224	54	8	of	of	ADP
ejpam-5224	54	9	the	the	DET
ejpam-5224	54	10	first	first	ADJ
ejpam-5224	54	11	syzygy	syzygy	NOUN
ejpam-5224	54	12	of	of	ADP
ejpam-5224	54	13	m	m	PROPN
ejpam-5224	54	14	.	.	PUNCT
ejpam-5224	55	1	the	the	DET
ejpam-5224	55	2	following	follow	VERB
ejpam-5224	55	3	theorem	theorem	NOUN
ejpam-5224	55	4	represents	represent	VERB
ejpam-5224	55	5	the	the	DET
ejpam-5224	55	6	main	main	ADJ
ejpam-5224	55	7	result	result	NOUN
ejpam-5224	55	8	of	of	ADP
ejpam-5224	55	9	this	this	DET
ejpam-5224	55	10	paper	paper	NOUN
ejpam-5224	55	11	,	,	PUNCT
ejpam-5224	55	12	and	and	CCONJ
ejpam-5224	55	13	in	in	ADP
ejpam-5224	55	14	order	order	NOUN
ejpam-5224	55	15	to	to	PART
ejpam-5224	55	16	prove	prove	VERB
ejpam-5224	55	17	it	it	PRON
ejpam-5224	55	18	,	,	PUNCT
ejpam-5224	55	19	we	we	PRON
ejpam-5224	55	20	will	will	AUX
ejpam-5224	55	21	need	need	VERB
ejpam-5224	55	22	the	the	DET
ejpam-5224	55	23	results	result	NOUN
ejpam-5224	55	24	that	that	PRON
ejpam-5224	55	25	we	we	PRON
ejpam-5224	55	26	have	have	AUX
ejpam-5224	55	27	developed	develop	VERB
ejpam-5224	55	28	in	in	ADP
ejpam-5224	55	29	theorem	theorem	ADJ
ejpam-5224	55	30	4.3	4.3	NUM
ejpam-5224	55	31	.	.	PUNCT
ejpam-5224	56	1	thereafter	thereafter	ADV
ejpam-5224	56	2	.	.	PUNCT
ejpam-5224	57	1	2.1	2.1	NUM
ejpam-5224	57	2	theorem	theorem	VERB
ejpam-5224	57	3	.	.	PUNCT
ejpam-5224	58	1	let	let	VERB
ejpam-5224	58	2	a	a	DET
ejpam-5224	58	3	be	be	AUX
ejpam-5224	58	4	an	an	DET
ejpam-5224	58	5	artinian	artinian	ADJ
ejpam-5224	58	6	ring	ring	NOUN
ejpam-5224	58	7	with	with	ADP
ejpam-5224	58	8	j3	j3	PROPN
ejpam-5224	58	9	=	=	PROPN
ejpam-5224	58	10	0	0	PROPN
ejpam-5224	58	11	.	.	PUNCT
ejpam-5224	59	1	if	if	SCONJ
ejpam-5224	59	2	rad2(p	rad2(p	NOUN
ejpam-5224	59	3	(	(	PUNCT
ejpam-5224	59	4	ω(s	ω(s	NOUN
ejpam-5224	59	5	)	)	PUNCT
ejpam-5224	59	6	)	)	PUNCT
ejpam-5224	59	7	)	)	PUNCT
ejpam-5224	60	1	=	=	SYM
ejpam-5224	60	2	0	0	NUM
ejpam-5224	60	3	for	for	ADP
ejpam-5224	60	4	every	every	DET
ejpam-5224	60	5	simple	simple	ADJ
ejpam-5224	60	6	module	module	NOUN
ejpam-5224	60	7	s	s	PROPN
ejpam-5224	60	8	,	,	PUNCT
ejpam-5224	60	9	then	then	ADV
ejpam-5224	60	10	ext1a(s	ext1a(s	PROPN
ejpam-5224	60	11	,	,	PUNCT
ejpam-5224	60	12	s	s	PART
ejpam-5224	60	13	)	)	PUNCT
ejpam-5224	60	14	=	=	SYM
ejpam-5224	60	15	0	0	X
ejpam-5224	60	16	.	.	PUNCT
ejpam-5224	60	17	m.	m.	NOUN
ejpam-5224	60	18	laaraj	laaraj	PROPN
ejpam-5224	60	19	,	,	PUNCT
ejpam-5224	60	20	s.	s.	PROPN
ejpam-5224	60	21	abdelalim	abdelalim	PROPN
ejpam-5224	60	22	,	,	PUNCT
ejpam-5224	60	23	i.elmouki	i.elmouki	CCONJ
ejpam-5224	60	24	/	/	SYM
ejpam-5224	60	25	eur	eur	NOUN
ejpam-5224	60	26	.	.	PUNCT
ejpam-5224	61	1	j.	j.	PROPN
ejpam-5224	61	2	pure	pure	PROPN
ejpam-5224	61	3	appl	appl	PROPN
ejpam-5224	61	4	.	.	PROPN
ejpam-5224	61	5	math	math	PROPN
ejpam-5224	61	6	,	,	PUNCT
ejpam-5224	61	7	17	17	NUM
ejpam-5224	61	8	(	(	PUNCT
ejpam-5224	61	9	3	3	NUM
ejpam-5224	61	10	)	)	PUNCT
ejpam-5224	61	11	(	(	PUNCT
ejpam-5224	61	12	2024	2024	NUM
ejpam-5224	61	13	)	)	PUNCT
ejpam-5224	61	14	,	,	PUNCT
ejpam-5224	61	15	1855	1855	NUM
ejpam-5224	61	16	-	-	SYM
ejpam-5224	61	17	1868	1868	NUM
ejpam-5224	61	18	1858	1858	NUM
ejpam-5224	61	19	we	we	PRON
ejpam-5224	61	20	also	also	ADV
ejpam-5224	61	21	fix	fix	VERB
ejpam-5224	61	22	a	a	DET
ejpam-5224	61	23	complete	complete	ADJ
ejpam-5224	61	24	set	set	NOUN
ejpam-5224	61	25	{	{	PUNCT
ejpam-5224	61	26	e1	e1	NOUN
ejpam-5224	61	27	,	,	PUNCT
ejpam-5224	61	28	.	.	PUNCT
ejpam-5224	61	29	.	.	PUNCT
ejpam-5224	61	30	.	.	PUNCT
ejpam-5224	62	1	,	,	PUNCT
ejpam-5224	62	2	en	en	ADP
ejpam-5224	62	3	}	}	PUNCT
ejpam-5224	62	4	of	of	ADP
ejpam-5224	62	5	orthogonal	orthogonal	ADJ
ejpam-5224	62	6	primitive	primitive	ADJ
ejpam-5224	62	7	idempotents	idempotent	NOUN
ejpam-5224	62	8	in	in	ADP
ejpam-5224	62	9	a	a	PRON
ejpam-5224	62	10	and	and	CCONJ
ejpam-5224	62	11	let	let	VERB
ejpam-5224	62	12	si	si	X
ejpam-5224	62	13	=	=	PUNCT
ejpam-5224	62	14	aei	aei	PROPN
ejpam-5224	62	15	/	/	SYM
ejpam-5224	62	16	jei	jei	NOUN
ejpam-5224	62	17	the	the	DET
ejpam-5224	62	18	simple	simple	ADJ
ejpam-5224	62	19	a	a	DET
ejpam-5224	62	20	-	-	PUNCT
ejpam-5224	62	21	module	module	NOUN
ejpam-5224	62	22	associated	associate	VERB
ejpam-5224	62	23	with	with	ADP
ejpam-5224	62	24	ei	ei	PROPN
ejpam-5224	62	25	.	.	PROPN
ejpam-5224	63	1	for	for	ADP
ejpam-5224	63	2	convenience	convenience	NOUN
ejpam-5224	63	3	,	,	PUNCT
ejpam-5224	63	4	we	we	PRON
ejpam-5224	63	5	quote	quote	VERB
ejpam-5224	63	6	the	the	DET
ejpam-5224	63	7	following	follow	VERB
ejpam-5224	63	8	well	well	ADV
ejpam-5224	63	9	-	-	PUNCT
ejpam-5224	63	10	known	know	VERB
ejpam-5224	63	11	result	result	NOUN
ejpam-5224	63	12	.	.	PUNCT
ejpam-5224	64	1	2.2	2.2	NUM
ejpam-5224	64	2	lemma	lemma	PROPN
ejpam-5224	64	3	.	.	PUNCT
ejpam-5224	65	1	let	let	VERB
ejpam-5224	65	2	a	a	DET
ejpam-5224	65	3	be	be	AUX
ejpam-5224	65	4	an	an	DET
ejpam-5224	65	5	artinian	artinian	ADJ
ejpam-5224	65	6	ring	ring	NOUN
ejpam-5224	65	7	with	with	ADP
ejpam-5224	65	8	a	a	DET
ejpam-5224	65	9	short	short	ADJ
ejpam-5224	65	10	exact	exact	ADJ
ejpam-5224	65	11	sequence	sequence	NOUN
ejpam-5224	65	12	0	0	NUM
ejpam-5224	65	13	//	//	SYM
ejpam-5224	65	14	l	l	NOUN
ejpam-5224	65	15	//m	//m	PUNCT
ejpam-5224	65	16	//	//	SYM
ejpam-5224	65	17	n	n	NOUN
ejpam-5224	65	18	//	//	X
ejpam-5224	65	19	0	0	NUM
ejpam-5224	65	20	in	in	ADP
ejpam-5224	65	21	moda	moda	PROPN
ejpam-5224	65	22	.	.	PUNCT
ejpam-5224	66	1	the	the	DET
ejpam-5224	66	2	following	follow	VERB
ejpam-5224	66	3	statement	statement	NOUN
ejpam-5224	66	4	holds	hold	VERB
ejpam-5224	66	5	.	.	PUNCT
ejpam-5224	67	1	(	(	PUNCT
ejpam-5224	67	2	1	1	X
ejpam-5224	67	3	)	)	PUNCT
ejpam-5224	67	4	pdn	pdn	NOUN
ejpam-5224	67	5	≤	≤	NOUN
ejpam-5224	67	6	max{pdm	max{pdm	NOUN
ejpam-5224	67	7	,	,	PUNCT
ejpam-5224	67	8	pdl+	pdl+	X
ejpam-5224	67	9	1	1	NUM
ejpam-5224	67	10	}	}	PUNCT
ejpam-5224	67	11	,	,	PUNCT
ejpam-5224	67	12	and	and	CCONJ
ejpam-5224	67	13	the	the	DET
ejpam-5224	67	14	equality	equality	NOUN
ejpam-5224	67	15	occurs	occur	VERB
ejpam-5224	67	16	in	in	ADP
ejpam-5224	67	17	case	case	NOUN
ejpam-5224	67	18	pdm	pdm	PROPN
ejpam-5224	67	19	̸=	̸=	PROPN
ejpam-5224	67	20	pdl	pdl	PROPN
ejpam-5224	67	21	.	.	PUNCT
ejpam-5224	68	1	(	(	PUNCT
ejpam-5224	68	2	2	2	X
ejpam-5224	68	3	)	)	PUNCT
ejpam-5224	68	4	pdl	pdl	NOUN
ejpam-5224	68	5	≤	≤	NUM
ejpam-5224	68	6	max{pdm	max{pdm	NOUN
ejpam-5224	68	7	,	,	PUNCT
ejpam-5224	68	8	pdn	pdn	NOUN
ejpam-5224	68	9	−	−	NOUN
ejpam-5224	68	10	1	1	NUM
ejpam-5224	68	11	}	}	PUNCT
ejpam-5224	68	12	,	,	PUNCT
ejpam-5224	68	13	and	and	CCONJ
ejpam-5224	68	14	the	the	DET
ejpam-5224	68	15	equality	equality	NOUN
ejpam-5224	68	16	occurs	occur	VERB
ejpam-5224	68	17	in	in	ADP
ejpam-5224	68	18	case	case	NOUN
ejpam-5224	68	19	pdm	pdm	PROPN
ejpam-5224	68	20	̸=	̸=	PROPN
ejpam-5224	68	21	pdn	pdn	NOUN
ejpam-5224	68	22	.	.	PUNCT
ejpam-5224	69	1	(	(	PUNCT
ejpam-5224	69	2	3	3	X
ejpam-5224	69	3	)	)	PUNCT
ejpam-5224	69	4	pdm	pdm	NOUN
ejpam-5224	69	5	≤	≤	NUM
ejpam-5224	69	6	max{pdl	max{pdl	NOUN
ejpam-5224	69	7	,	,	PUNCT
ejpam-5224	69	8	pdn	pdn	NOUN
ejpam-5224	69	9	}	}	PUNCT
ejpam-5224	69	10	,	,	PUNCT
ejpam-5224	69	11	and	and	CCONJ
ejpam-5224	69	12	the	the	DET
ejpam-5224	69	13	equality	equality	NOUN
ejpam-5224	69	14	occurs	occur	VERB
ejpam-5224	69	15	in	in	ADP
ejpam-5224	69	16	case	case	NOUN
ejpam-5224	69	17	pdn	pdn	NOUN
ejpam-5224	69	18	̸=	̸=	PROPN
ejpam-5224	69	19	pdl+	pdl+	PROPN
ejpam-5224	69	20	1	1	NUM
ejpam-5224	69	21	.	.	NOUN
ejpam-5224	69	22	3	3	NUM
ejpam-5224	69	23	.	.	NOUN
ejpam-5224	69	24	minimal	minimal	ADJ
ejpam-5224	69	25	projective	projective	ADJ
ejpam-5224	69	26	dimension	dimension	NOUN
ejpam-5224	69	27	3.1	3.1	NUM
ejpam-5224	69	28	lemma	lemma	PROPN
ejpam-5224	69	29	.	.	PUNCT
ejpam-5224	70	1	let	let	VERB
ejpam-5224	70	2	a	a	DET
ejpam-5224	70	3	be	be	AUX
ejpam-5224	70	4	an	an	DET
ejpam-5224	70	5	artinian	artinian	ADJ
ejpam-5224	70	6	ring	ring	NOUN
ejpam-5224	70	7	with	with	ADP
ejpam-5224	70	8	a	a	DET
ejpam-5224	70	9	radical	radical	ADJ
ejpam-5224	70	10	cubed	cubed	NOUN
ejpam-5224	70	11	zero	zero	NUM
ejpam-5224	70	12	.	.	PUNCT
ejpam-5224	71	1	let	let	VERB
ejpam-5224	71	2	m	m	PRON
ejpam-5224	71	3	be	be	AUX
ejpam-5224	71	4	a	a	DET
ejpam-5224	71	5	module	module	NOUN
ejpam-5224	71	6	in	in	ADP
ejpam-5224	71	7	moda	moda	PROPN
ejpam-5224	71	8	of	of	ADP
ejpam-5224	71	9	finite	finite	PROPN
ejpam-5224	71	10	projective	projective	PROPN
ejpam-5224	71	11	dimension	dimension	NOUN
ejpam-5224	71	12	with	with	ADP
ejpam-5224	71	13	pdm	pdm	NOUN
ejpam-5224	71	14	≤	≤	NOUN
ejpam-5224	71	15	min{pd(s1	min{pd(s1	NOUN
ejpam-5224	71	16	)	)	PUNCT
ejpam-5224	71	17	,	,	PUNCT
ejpam-5224	71	18	.	.	PUNCT
ejpam-5224	71	19	.	.	PUNCT
ejpam-5224	72	1	.	.	PUNCT
ejpam-5224	73	1	,	,	PUNCT
ejpam-5224	73	2	pd(sn	pd(sn	ADJ
ejpam-5224	73	3	)	)	PUNCT
ejpam-5224	73	4	}	}	PUNCT
ejpam-5224	73	5	and	and	CCONJ
ejpam-5224	73	6	rad2(m	rad2(m	NOUN
ejpam-5224	73	7	)	)	PUNCT
ejpam-5224	73	8	=	=	SYM
ejpam-5224	74	1	0	0	X
ejpam-5224	74	2	.	.	PUNCT
ejpam-5224	75	1	if	if	SCONJ
ejpam-5224	75	2	f	f	PROPN
ejpam-5224	75	3	:	:	PUNCT
ejpam-5224	75	4	p	p	X
ejpam-5224	75	5	→	→	PUNCT
ejpam-5224	75	6	m	m	NOUN
ejpam-5224	75	7	is	be	AUX
ejpam-5224	75	8	a	a	DET
ejpam-5224	75	9	projective	projective	ADJ
ejpam-5224	75	10	cover	cover	NOUN
ejpam-5224	75	11	of	of	ADP
ejpam-5224	75	12	m	m	PRON
ejpam-5224	75	13	,	,	PUNCT
ejpam-5224	75	14	then	then	ADV
ejpam-5224	75	15	rad(ωm	rad(ωm	NOUN
ejpam-5224	75	16	)	)	PUNCT
ejpam-5224	75	17	=	=	PUNCT
ejpam-5224	75	18	rad2(p	rad2(p	NOUN
ejpam-5224	75	19	)	)	PUNCT
ejpam-5224	75	20	.	.	PUNCT
ejpam-5224	76	1	proof	proof	NOUN
ejpam-5224	76	2	.	.	PUNCT
ejpam-5224	77	1	let	let	VERB
ejpam-5224	77	2	f	f	NOUN
ejpam-5224	77	3	:	:	PUNCT
ejpam-5224	77	4	p	p	X
ejpam-5224	77	5	→	→	PUNCT
ejpam-5224	77	6	m	m	AUX
ejpam-5224	77	7	be	be	AUX
ejpam-5224	77	8	a	a	DET
ejpam-5224	77	9	projective	projective	ADJ
ejpam-5224	77	10	cover	cover	NOUN
ejpam-5224	77	11	of	of	ADP
ejpam-5224	77	12	m	m	PROPN
ejpam-5224	77	13	.	.	PUNCT
ejpam-5224	78	1	then	then	ADV
ejpam-5224	78	2	,	,	PUNCT
ejpam-5224	78	3	ωm	ωm	PUNCT
ejpam-5224	78	4	⊆	⊆	NUM
ejpam-5224	78	5	rad(p	rad(p	PROPN
ejpam-5224	78	6	)	)	PUNCT
ejpam-5224	78	7	,	,	PUNCT
ejpam-5224	78	8	and	and	CCONJ
ejpam-5224	78	9	hence	hence	ADV
ejpam-5224	78	10	,	,	PUNCT
ejpam-5224	78	11	rad(ωm	rad(ωm	NOUN
ejpam-5224	78	12	)	)	PUNCT
ejpam-5224	78	13	⊆	⊆	NUM
ejpam-5224	78	14	rad2(p	rad2(p	NOUN
ejpam-5224	78	15	)	)	PUNCT
ejpam-5224	78	16	.	.	PUNCT
ejpam-5224	79	1	since	since	SCONJ
ejpam-5224	79	2	rad2(m	rad2(m	NOUN
ejpam-5224	79	3	)	)	PUNCT
ejpam-5224	79	4	=	=	SYM
ejpam-5224	79	5	0	0	NUM
ejpam-5224	79	6	,	,	PUNCT
ejpam-5224	79	7	rad2(p	rad2(p	NOUN
ejpam-5224	79	8	)	)	PUNCT
ejpam-5224	79	9	⊆	⊆	NUM
ejpam-5224	79	10	ωm	ωm	SCONJ
ejpam-5224	79	11	.	.	PUNCT
ejpam-5224	79	12	suppose	suppose	VERB
ejpam-5224	79	13	that	that	SCONJ
ejpam-5224	79	14	rad2(p	rad2(p	NOUN
ejpam-5224	79	15	)	)	PUNCT
ejpam-5224	79	16	⊈	⊈	PROPN
ejpam-5224	79	17	rad(ωm	rad(ωm	NOUN
ejpam-5224	79	18	)	)	PUNCT
ejpam-5224	79	19	.	.	PUNCT
ejpam-5224	80	1	then	then	ADV
ejpam-5224	80	2	there	there	PRON
ejpam-5224	80	3	exists	exist	VERB
ejpam-5224	80	4	a	a	DET
ejpam-5224	80	5	maximal	maximal	ADJ
ejpam-5224	80	6	submodule	submodule	NOUN
ejpam-5224	80	7	l	l	NOUN
ejpam-5224	80	8	of	of	ADP
ejpam-5224	80	9	ωm	ωm	PUNCT
ejpam-5224	80	10	such	such	ADJ
ejpam-5224	80	11	that	that	SCONJ
ejpam-5224	80	12	rad2(p	rad2(p	NOUN
ejpam-5224	80	13	)	)	PUNCT
ejpam-5224	80	14	⊈	⊈	PROPN
ejpam-5224	80	15	l.	l.	NOUN
ejpam-5224	80	16	since	since	SCONJ
ejpam-5224	80	17	rad3(a	rad3(a	NUM
ejpam-5224	80	18	)	)	PUNCT
ejpam-5224	80	19	=	=	SYM
ejpam-5224	80	20	0	0	NUM
ejpam-5224	80	21	,	,	PUNCT
ejpam-5224	80	22	rad2(p	rad2(p	NOUN
ejpam-5224	80	23	)	)	PUNCT
ejpam-5224	80	24	is	be	AUX
ejpam-5224	80	25	semi	semi	ADJ
ejpam-5224	80	26	-	-	ADJ
ejpam-5224	80	27	simple	simple	ADJ
ejpam-5224	80	28	.	.	PUNCT
ejpam-5224	81	1	thus	thus	ADV
ejpam-5224	81	2	,	,	PUNCT
ejpam-5224	81	3	s	s	VERB
ejpam-5224	81	4	⊈	⊈	NOUN
ejpam-5224	81	5	l	l	NOUN
ejpam-5224	81	6	where	where	SCONJ
ejpam-5224	81	7	s	s	VERB
ejpam-5224	81	8	is	be	AUX
ejpam-5224	81	9	some	some	DET
ejpam-5224	81	10	simple	simple	ADJ
ejpam-5224	81	11	submodule	submodule	NOUN
ejpam-5224	81	12	of	of	ADP
ejpam-5224	81	13	rad2(p	rad2(p	NOUN
ejpam-5224	81	14	)	)	PUNCT
ejpam-5224	81	15	,	,	PUNCT
ejpam-5224	81	16	and	and	CCONJ
ejpam-5224	81	17	consequently	consequently	ADV
ejpam-5224	81	18	,	,	PUNCT
ejpam-5224	81	19	ωm	ωm	PROPN
ejpam-5224	81	20	=	=	SYM
ejpam-5224	81	21	s	s	PROPN
ejpam-5224	81	22	⊕	⊕	PROPN
ejpam-5224	81	23	l.	l.	PROPN
ejpam-5224	81	24	this	this	DET
ejpam-5224	81	25	yields	yield	NOUN
ejpam-5224	81	26	that	that	PRON
ejpam-5224	81	27	pd(s	pd(s	X
ejpam-5224	81	28	)	)	PUNCT
ejpam-5224	81	29	≤	≤	NUM
ejpam-5224	81	30	pd(ωm	pd(ωm	NOUN
ejpam-5224	81	31	)	)	PUNCT
ejpam-5224	81	32	<	<	X
ejpam-5224	81	33	pdm	pdm	NOUN
ejpam-5224	81	34	≤	≤	NOUN
ejpam-5224	81	35	pd(s	pd(s	NUM
ejpam-5224	81	36	)	)	PUNCT
ejpam-5224	81	37	,	,	PUNCT
ejpam-5224	81	38	a	a	DET
ejpam-5224	81	39	contradiction	contradiction	NOUN
ejpam-5224	81	40	.	.	PUNCT
ejpam-5224	82	1	the	the	DET
ejpam-5224	82	2	proof	proof	NOUN
ejpam-5224	82	3	is	be	AUX
ejpam-5224	82	4	completed	complete	VERB
ejpam-5224	82	5	.	.	PUNCT
ejpam-5224	83	1	3.2	3.2	NUM
ejpam-5224	83	2	lemma	lemma	PROPN
ejpam-5224	83	3	.	.	PUNCT
ejpam-5224	84	1	let	let	VERB
ejpam-5224	84	2	a	a	DET
ejpam-5224	84	3	be	be	AUX
ejpam-5224	84	4	an	an	DET
ejpam-5224	84	5	artinian	artinian	ADJ
ejpam-5224	84	6	ring	ring	NOUN
ejpam-5224	84	7	with	with	ADP
ejpam-5224	84	8	radical	radical	ADJ
ejpam-5224	84	9	cubed	cubed	NOUN
ejpam-5224	84	10	zero	zero	NUM
ejpam-5224	84	11	,	,	PUNCT
ejpam-5224	84	12	and	and	CCONJ
ejpam-5224	84	13	let	let	VERB
ejpam-5224	84	14	s	s	PRON
ejpam-5224	84	15	be	be	AUX
ejpam-5224	84	16	the	the	DET
ejpam-5224	84	17	simple	simple	ADJ
ejpam-5224	84	18	module	module	NOUN
ejpam-5224	84	19	of	of	ADP
ejpam-5224	84	20	minimal	minimal	ADJ
ejpam-5224	84	21	projective	projective	ADJ
ejpam-5224	84	22	dimension	dimension	NOUN
ejpam-5224	84	23	among	among	ADP
ejpam-5224	84	24	the	the	DET
ejpam-5224	84	25	simple	simple	ADJ
ejpam-5224	84	26	modules	module	NOUN
ejpam-5224	84	27	in	in	ADP
ejpam-5224	84	28	moda	moda	PROPN
ejpam-5224	84	29	.	.	PUNCT
ejpam-5224	85	1	if	if	SCONJ
ejpam-5224	85	2	pds	pds	NOUN
ejpam-5224	85	3	<	<	X
ejpam-5224	85	4	∞	∞	PROPN
ejpam-5224	85	5	and	and	CCONJ
ejpam-5224	85	6	rad2(p1	rad2(p1	PROPN
ejpam-5224	85	7	)	)	PUNCT
ejpam-5224	86	1	=	=	SYM
ejpam-5224	86	2	0	0	NUM
ejpam-5224	86	3	with	with	ADP
ejpam-5224	86	4	p1	p1	PROPN
ejpam-5224	86	5	is	be	AUX
ejpam-5224	86	6	the	the	DET
ejpam-5224	86	7	projective	projective	ADJ
ejpam-5224	86	8	cover	cover	NOUN
ejpam-5224	86	9	of	of	ADP
ejpam-5224	86	10	ω(s	ω(s	PROPN
ejpam-5224	86	11	)	)	PUNCT
ejpam-5224	86	12	,	,	PUNCT
ejpam-5224	86	13	then	then	ADV
ejpam-5224	86	14	pds	pds	VERB
ejpam-5224	86	15	≤	≤	NUM
ejpam-5224	86	16	1	1	NUM
ejpam-5224	86	17	.	.	PUNCT
ejpam-5224	87	1	proof	proof	NOUN
ejpam-5224	87	2	.	.	PUNCT
ejpam-5224	88	1	suppose	suppose	VERB
ejpam-5224	88	2	that	that	SCONJ
ejpam-5224	88	3	s	s	VERB
ejpam-5224	88	4	admits	admit	VERB
ejpam-5224	88	5	a	a	DET
ejpam-5224	88	6	minimal	minimal	ADJ
ejpam-5224	88	7	projective	projective	ADJ
ejpam-5224	88	8	resolution	resolution	NOUN
ejpam-5224	88	9	0	0	NUM
ejpam-5224	88	10	//	//	SYM
ejpam-5224	88	11	pm	pm	PROPN
ejpam-5224	88	12	//	//	X
ejpam-5224	88	13	·	·	PUNCT
ejpam-5224	88	14	·	·	PUNCT
ejpam-5224	88	15	·	·	PUNCT
ejpam-5224	89	1	//	//	NUM
ejpam-5224	89	2	p2	p2	PROPN
ejpam-5224	89	3	//	//	PROPN
ejpam-5224	89	4	p1	p1	PROPN
ejpam-5224	89	5	//	//	PROPN
ejpam-5224	89	6	p0	p0	PROPN
ejpam-5224	89	7	//	//	SYM
ejpam-5224	89	8	s	s	PART
ejpam-5224	89	9	//	//	X
ejpam-5224	89	10	0	0	NUM
ejpam-5224	89	11	,	,	PUNCT
ejpam-5224	89	12	where	where	SCONJ
ejpam-5224	89	13	m	m	VERB
ejpam-5224	89	14	>	>	X
ejpam-5224	89	15	1	1	NUM
ejpam-5224	89	16	then	then	ADV
ejpam-5224	89	17	,	,	PUNCT
ejpam-5224	89	18	ω2(s	ω2(s	X
ejpam-5224	89	19	)	)	PUNCT
ejpam-5224	89	20	̸=	̸=	NOUN
ejpam-5224	89	21	0	0	NUM
ejpam-5224	89	22	and	and	CCONJ
ejpam-5224	89	23	since	since	SCONJ
ejpam-5224	89	24	pd(ω(s	pd(ω(	NOUN
ejpam-5224	89	25	)	)	PUNCT
ejpam-5224	89	26	)	)	PUNCT
ejpam-5224	89	27	<	<	X
ejpam-5224	89	28	pd(s	pd(s	PUNCT
ejpam-5224	89	29	)	)	PUNCT
ejpam-5224	89	30	and	and	CCONJ
ejpam-5224	89	31	like	like	ADP
ejpam-5224	89	32	a	a	PRON
ejpam-5224	89	33	has	have	VERB
ejpam-5224	89	34	radical	radical	ADJ
ejpam-5224	89	35	cubed	cube	VERB
ejpam-5224	89	36	zero	zero	NUM
ejpam-5224	89	37	we	we	PRON
ejpam-5224	89	38	have	have	VERB
ejpam-5224	89	39	,	,	PUNCT
ejpam-5224	89	40	rad2(ω(s	rad2(ω(s	NOUN
ejpam-5224	89	41	)	)	PUNCT
ejpam-5224	89	42	)	)	PUNCT
ejpam-5224	90	1	=	=	PUNCT
ejpam-5224	90	2	rad2(je	rad2(je	PROPN
ejpam-5224	90	3	)	)	PUNCT
ejpam-5224	90	4	=	=	SYM
ejpam-5224	90	5	j3e	j3e	X
ejpam-5224	91	1	=	=	PUNCT
ejpam-5224	91	2	0	0	NUM
ejpam-5224	91	3	where	where	SCONJ
ejpam-5224	91	4	e	e	NOUN
ejpam-5224	91	5	is	be	AUX
ejpam-5224	91	6	the	the	DET
ejpam-5224	91	7	idempotent	idempotent	NOUN
ejpam-5224	91	8	associated	associate	VERB
ejpam-5224	91	9	with	with	ADP
ejpam-5224	91	10	s	s	PROPN
ejpam-5224	91	11	,	,	PUNCT
ejpam-5224	91	12	then	then	ADV
ejpam-5224	91	13	by	by	ADP
ejpam-5224	91	14	lemma	lemma	PROPN
ejpam-5224	91	15	1.1	1.1	NUM
ejpam-5224	91	16	and	and	CCONJ
ejpam-5224	91	17	according	accord	VERB
ejpam-5224	91	18	to	to	ADP
ejpam-5224	91	19	the	the	DET
ejpam-5224	91	20	hypothesis	hypothesis	NOUN
ejpam-5224	91	21	of	of	ADP
ejpam-5224	91	22	our	our	PRON
ejpam-5224	91	23	present	present	ADJ
ejpam-5224	91	24	lemma	lemma	PROPN
ejpam-5224	91	25	,	,	PUNCT
ejpam-5224	91	26	rad(ω2(s	rad(ω2(s	NOUN
ejpam-5224	91	27	)	)	PUNCT
ejpam-5224	91	28	)	)	PUNCT
ejpam-5224	92	1	=	=	SYM
ejpam-5224	92	2	rad2(p1	rad2(p1	NOUN
ejpam-5224	92	3	)	)	PUNCT
ejpam-5224	92	4	=	=	SYM
ejpam-5224	92	5	0	0	NUM
ejpam-5224	92	6	,	,	PUNCT
ejpam-5224	92	7	and	and	CCONJ
ejpam-5224	92	8	therefore	therefore	ADV
ejpam-5224	92	9	ω2(s	ω2(s	NUM
ejpam-5224	92	10	)	)	PUNCT
ejpam-5224	92	11	is	be	AUX
ejpam-5224	92	12	a	a	DET
ejpam-5224	92	13	semi	semi	ADJ
ejpam-5224	92	14	-	-	ADJ
ejpam-5224	92	15	simple	simple	ADJ
ejpam-5224	92	16	module	module	NOUN
ejpam-5224	92	17	,	,	PUNCT
ejpam-5224	92	18	then	then	ADV
ejpam-5224	92	19	pd(s	pd(s	NUM
ejpam-5224	92	20	)	)	PUNCT
ejpam-5224	92	21	≤	≤	NUM
ejpam-5224	92	22	pd(ω2(s	pd(ω2(s	NOUN
ejpam-5224	92	23	)	)	PUNCT
ejpam-5224	92	24	)	)	PUNCT
ejpam-5224	92	25	which	which	PRON
ejpam-5224	92	26	is	be	AUX
ejpam-5224	92	27	absurd	absurd	ADJ
ejpam-5224	92	28	because	because	SCONJ
ejpam-5224	92	29	pd(ω2(s	pd(ω2(s	NOUN
ejpam-5224	92	30	)	)	PUNCT
ejpam-5224	92	31	)	)	PUNCT
ejpam-5224	93	1	=	=	PUNCT
ejpam-5224	93	2	pd(s)−	pd(s)−	ADJ
ejpam-5224	93	3	2	2	NUM
ejpam-5224	93	4	.	.	X
ejpam-5224	93	5	recall	recall	VERB
ejpam-5224	93	6	that	that	SCONJ
ejpam-5224	93	7	if	if	SCONJ
ejpam-5224	93	8	m	m	VERB
ejpam-5224	93	9	and	and	CCONJ
ejpam-5224	93	10	n	n	PRON
ejpam-5224	93	11	are	be	AUX
ejpam-5224	93	12	two	two	NUM
ejpam-5224	93	13	modules	module	NOUN
ejpam-5224	93	14	,	,	PUNCT
ejpam-5224	93	15	by	by	ADP
ejpam-5224	93	16	choosing	choose	VERB
ejpam-5224	93	17	a	a	DET
ejpam-5224	93	18	projective	projective	ADJ
ejpam-5224	93	19	resolution	resolution	NOUN
ejpam-5224	93	20	p∗	p∗	NOUN
ejpam-5224	93	21	of	of	ADP
ejpam-5224	93	22	m	m	PROPN
ejpam-5224	93	23	,	,	PUNCT
ejpam-5224	93	24	then	then	ADV
ejpam-5224	93	25	extna(m	extna(m	PROPN
ejpam-5224	93	26	,	,	PUNCT
ejpam-5224	93	27	n	n	CCONJ
ejpam-5224	93	28	)	)	PUNCT
ejpam-5224	93	29	=	=	SYM
ejpam-5224	93	30	hn(homa(p∗	hn(homa(p∗	PROPN
ejpam-5224	93	31	,	,	PUNCT
ejpam-5224	93	32	n	n	CCONJ
ejpam-5224	93	33	)	)	PUNCT
ejpam-5224	93	34	)	)	PUNCT
ejpam-5224	93	35	is	be	AUX
ejpam-5224	93	36	the	the	DET
ejpam-5224	93	37	nth	nth	NOUN
ejpam-5224	93	38	co	co	NOUN
ejpam-5224	93	39	-	-	NOUN
ejpam-5224	93	40	homology	homology	NOUN
ejpam-5224	93	41	of	of	ADP
ejpam-5224	93	42	the	the	DET
ejpam-5224	93	43	cochain	cochain	NOUN
ejpam-5224	93	44	complex	complex	NOUN
ejpam-5224	93	45	of	of	ADP
ejpam-5224	93	46	m.	m.	NOUN
ejpam-5224	93	47	laaraj	laaraj	PROPN
ejpam-5224	93	48	,	,	PUNCT
ejpam-5224	93	49	s.	s.	PROPN
ejpam-5224	93	50	abdelalim	abdelalim	PROPN
ejpam-5224	93	51	,	,	PUNCT
ejpam-5224	93	52	i.elmouki	i.elmouki	CCONJ
ejpam-5224	93	53	/	/	SYM
ejpam-5224	93	54	eur	eur	NOUN
ejpam-5224	93	55	.	.	PUNCT
ejpam-5224	94	1	j.	j.	PROPN
ejpam-5224	94	2	pure	pure	PROPN
ejpam-5224	94	3	appl	appl	PROPN
ejpam-5224	94	4	.	.	PROPN
ejpam-5224	94	5	math	math	PROPN
ejpam-5224	94	6	,	,	PUNCT
ejpam-5224	94	7	17	17	NUM
ejpam-5224	94	8	(	(	PUNCT
ejpam-5224	94	9	3	3	NUM
ejpam-5224	94	10	)	)	PUNCT
ejpam-5224	94	11	(	(	PUNCT
ejpam-5224	94	12	2024	2024	NUM
ejpam-5224	94	13	)	)	PUNCT
ejpam-5224	94	14	,	,	PUNCT
ejpam-5224	94	15	1855	1855	NUM
ejpam-5224	94	16	-	-	SYM
ejpam-5224	94	17	1868	1868	NUM
ejpam-5224	94	18	1859	1859	NUM
ejpam-5224	94	19	k	k	X
ejpam-5224	94	20	-	-	PUNCT
ejpam-5224	94	21	modules	module	NOUN
ejpam-5224	94	22	homa(p∗	homa(p∗	NOUN
ejpam-5224	94	23	,	,	PUNCT
ejpam-5224	94	24	n	n	CCONJ
ejpam-5224	94	25	)	)	PUNCT
ejpam-5224	94	26	which	which	PRON
ejpam-5224	94	27	is	be	AUX
ejpam-5224	94	28	...	...	PUNCT
ejpam-5224	94	29	−→	−→	NOUN
ejpam-5224	94	30	0	0	NUM
ejpam-5224	94	31	−→	−→	NOUN
ejpam-5224	94	32	0	0	NUM
ejpam-5224	94	33	−→	−→	NOUN
ejpam-5224	94	34	homa(p0	homa(p0	PROPN
ejpam-5224	94	35	,	,	PUNCT
ejpam-5224	94	36	n	n	CCONJ
ejpam-5224	94	37	)	)	PUNCT
ejpam-5224	94	38	−→	−→	ADJ
ejpam-5224	94	39	homa(p1	homa(p1	NOUN
ejpam-5224	94	40	,	,	PUNCT
ejpam-5224	94	41	n	n	CCONJ
ejpam-5224	94	42	)	)	PUNCT
ejpam-5224	95	1	−→	−→	NOUN
ejpam-5224	95	2	homa(p2	homa(p2	ADJ
ejpam-5224	95	3	,	,	PUNCT
ejpam-5224	95	4	n	n	CCONJ
ejpam-5224	95	5	)	)	PUNCT
ejpam-5224	95	6	−→	−→	NOUN
ejpam-5224	95	7	...	...	PUNCT
ejpam-5224	95	8	where	where	SCONJ
ejpam-5224	95	9	homa(pn	homa(pn	NOUN
ejpam-5224	95	10	,	,	PUNCT
ejpam-5224	95	11	n	n	CCONJ
ejpam-5224	95	12	)	)	PUNCT
ejpam-5224	95	13	is	be	AUX
ejpam-5224	95	14	in	in	ADP
ejpam-5224	95	15	degree	degree	NOUN
ejpam-5224	95	16	n	n	NOUN
ejpam-5224	95	17	and	and	CCONJ
ejpam-5224	95	18	p∗	p∗	VERB
ejpam-5224	95	19	the	the	DET
ejpam-5224	95	20	complex	complex	NOUN
ejpam-5224	95	21	deduced	deduce	VERB
ejpam-5224	95	22	from	from	ADP
ejpam-5224	95	23	the	the	DET
ejpam-5224	95	24	projective	projective	ADJ
ejpam-5224	95	25	resolution	resolution	NOUN
ejpam-5224	95	26	of	of	ADP
ejpam-5224	95	27	m	m	PRON
ejpam-5224	95	28	,	,	PUNCT
ejpam-5224	95	29	see	see	VERB
ejpam-5224	95	30	[	[	X
ejpam-5224	95	31	10	10	NUM
ejpam-5224	95	32	]	]	PUNCT
ejpam-5224	95	33	.	.	PUNCT
ejpam-5224	96	1	3.3	3.3	NUM
ejpam-5224	96	2	theorem	theorem	VERB
ejpam-5224	96	3	.	.	PUNCT
ejpam-5224	97	1	let	let	VERB
ejpam-5224	97	2	a	a	PRON
ejpam-5224	97	3	be	be	AUX
ejpam-5224	97	4	an	an	DET
ejpam-5224	97	5	artinian	artinian	ADJ
ejpam-5224	97	6	ring	ring	NOUN
ejpam-5224	97	7	and	and	CCONJ
ejpam-5224	97	8	s	s	PART
ejpam-5224	97	9	=	=	PROPN
ejpam-5224	97	10	ae	ae	PROPN
ejpam-5224	97	11	/	/	SYM
ejpam-5224	97	12	je	je	PROPN
ejpam-5224	97	13	be	be	AUX
ejpam-5224	97	14	a	a	DET
ejpam-5224	97	15	simple	simple	ADJ
ejpam-5224	97	16	a	a	DET
ejpam-5224	97	17	-	-	PUNCT
ejpam-5224	97	18	module	module	NOUN
ejpam-5224	97	19	with	with	ADP
ejpam-5224	97	20	e	e	NOUN
ejpam-5224	97	21	primitive	primitive	ADJ
ejpam-5224	97	22	idempotent	idempotent	NOUN
ejpam-5224	97	23	such	such	ADJ
ejpam-5224	97	24	that	that	SCONJ
ejpam-5224	97	25	pd(s	pd(s	NUM
ejpam-5224	97	26	)	)	PUNCT
ejpam-5224	97	27	≤	≤	NUM
ejpam-5224	97	28	1	1	NUM
ejpam-5224	97	29	,	,	PUNCT
ejpam-5224	97	30	then	then	ADV
ejpam-5224	97	31	ext1a(s	ext1a(s	PROPN
ejpam-5224	97	32	,	,	PUNCT
ejpam-5224	97	33	s	s	PART
ejpam-5224	97	34	)	)	PUNCT
ejpam-5224	97	35	=	=	SYM
ejpam-5224	98	1	0	0	X
ejpam-5224	98	2	.	.	PUNCT
ejpam-5224	99	1	proof	proof	NOUN
ejpam-5224	99	2	.	.	PUNCT
ejpam-5224	100	1	if	if	SCONJ
ejpam-5224	100	2	s	s	NOUN
ejpam-5224	100	3	is	be	AUX
ejpam-5224	100	4	projective	projective	ADJ
ejpam-5224	100	5	ie	ie	X
ejpam-5224	100	6	pd(s	pd(s	X
ejpam-5224	100	7	)	)	PUNCT
ejpam-5224	101	1	=	=	SYM
ejpam-5224	101	2	0	0	NUM
ejpam-5224	101	3	,	,	PUNCT
ejpam-5224	101	4	then	then	ADV
ejpam-5224	101	5	the	the	DET
ejpam-5224	101	6	result	result	NOUN
ejpam-5224	101	7	holds	hold	VERB
ejpam-5224	101	8	.	.	PUNCT
ejpam-5224	102	1	if	if	SCONJ
ejpam-5224	102	2	pd(s	pd(s	NUM
ejpam-5224	102	3	)	)	PUNCT
ejpam-5224	103	1	=	=	SYM
ejpam-5224	103	2	1	1	NUM
ejpam-5224	103	3	and	and	CCONJ
ejpam-5224	103	4	ext1a(s	ext1a(s	PROPN
ejpam-5224	103	5	,	,	PUNCT
ejpam-5224	103	6	s	s	PART
ejpam-5224	103	7	)	)	PUNCT
ejpam-5224	103	8	̸=	̸=	PROPN
ejpam-5224	103	9	0	0	NUM
ejpam-5224	103	10	,	,	PUNCT
ejpam-5224	103	11	then	then	ADV
ejpam-5224	103	12	hom(je	hom(je	NOUN
ejpam-5224	103	13	,	,	PUNCT
ejpam-5224	103	14	s	s	PART
ejpam-5224	103	15	)	)	PUNCT
ejpam-5224	103	16	̸=	̸=	PROPN
ejpam-5224	103	17	0	0	NUM
ejpam-5224	103	18	,	,	PUNCT
ejpam-5224	103	19	therefore	therefore	ADV
ejpam-5224	103	20	je	je	PROPN
ejpam-5224	103	21	is	be	AUX
ejpam-5224	103	22	projective	projective	ADJ
ejpam-5224	103	23	then	then	ADV
ejpam-5224	103	24	ae	ae	PROPN
ejpam-5224	103	25	is	be	AUX
ejpam-5224	103	26	isomorphic	isomorphic	ADJ
ejpam-5224	103	27	to	to	ADP
ejpam-5224	103	28	a	a	DET
ejpam-5224	103	29	summand	summand	NOUN
ejpam-5224	103	30	of	of	ADP
ejpam-5224	103	31	je	je	PROPN
ejpam-5224	103	32	since	since	SCONJ
ejpam-5224	103	33	ae	ae	PROPN
ejpam-5224	103	34	is	be	AUX
ejpam-5224	103	35	a	a	DET
ejpam-5224	103	36	projective	projective	ADJ
ejpam-5224	103	37	cover	cover	NOUN
ejpam-5224	103	38	of	of	ADP
ejpam-5224	103	39	s	s	PROPN
ejpam-5224	103	40	,	,	PUNCT
ejpam-5224	103	41	therefore	therefore	ADV
ejpam-5224	103	42	l(ae	l(ae	NOUN
ejpam-5224	103	43	)	)	PUNCT
ejpam-5224	103	44	⩽	⩽	ADJ
ejpam-5224	103	45	l(je	l(je	NOUN
ejpam-5224	103	46	)	)	PUNCT
ejpam-5224	103	47	and	and	CCONJ
ejpam-5224	103	48	since	since	SCONJ
ejpam-5224	103	49	l(je	l(je	NOUN
ejpam-5224	103	50	)	)	PUNCT
ejpam-5224	103	51	⩽	⩽	ADJ
ejpam-5224	103	52	l(ae	l(ae	NOUN
ejpam-5224	103	53	)	)	PUNCT
ejpam-5224	103	54	,	,	PUNCT
ejpam-5224	103	55	then	then	ADV
ejpam-5224	103	56	l(s	l(s	PROPN
ejpam-5224	103	57	)	)	PUNCT
ejpam-5224	104	1	=	=	SYM
ejpam-5224	104	2	0	0	NUM
ejpam-5224	104	3	and	and	CCONJ
ejpam-5224	104	4	s	s	NOUN
ejpam-5224	104	5	=	=	SYM
ejpam-5224	104	6	0	0	NUM
ejpam-5224	104	7	contradiction	contradiction	NOUN
ejpam-5224	104	8	.	.	PUNCT
ejpam-5224	105	1	4	4	X
ejpam-5224	105	2	.	.	X
ejpam-5224	105	3	jacobson	jacobson	PROPN
ejpam-5224	105	4	radical	radical	PROPN
ejpam-5224	105	5	of	of	ADP
ejpam-5224	105	6	end(p	end(p	PROPN
ejpam-5224	105	7	)	)	PUNCT
ejpam-5224	105	8	with	with	ADP
ejpam-5224	105	9	p	p	PRON
ejpam-5224	105	10	an	an	DET
ejpam-5224	105	11	a	a	PRON
ejpam-5224	105	12	-	-	PUNCT
ejpam-5224	105	13	projective	projective	NOUN
ejpam-5224	105	14	module	module	NOUN
ejpam-5224	105	15	.	.	PUNCT
ejpam-5224	106	1	let	let	VERB
ejpam-5224	106	2	p	p	PRON
ejpam-5224	106	3	be	be	AUX
ejpam-5224	106	4	an	an	DET
ejpam-5224	106	5	a	a	PRON
ejpam-5224	106	6	-	-	PUNCT
ejpam-5224	106	7	projective	projective	ADJ
ejpam-5224	106	8	module	module	NOUN
ejpam-5224	106	9	in	in	ADP
ejpam-5224	106	10	moda	moda	PROPN
ejpam-5224	106	11	,	,	PUNCT
ejpam-5224	106	12	we	we	PRON
ejpam-5224	106	13	consider	consider	VERB
ejpam-5224	106	14	the	the	DET
ejpam-5224	106	15	algebra	algebra	NOUN
ejpam-5224	106	16	e	e	NOUN
ejpam-5224	106	17	=	=	PUNCT
ejpam-5224	106	18	enda(p	enda(p	PROPN
ejpam-5224	106	19	)	)	PUNCT
ejpam-5224	106	20	and	and	CCONJ
ejpam-5224	106	21	we	we	PRON
ejpam-5224	106	22	denote	denote	VERB
ejpam-5224	106	23	j(e	j(e	PROPN
ejpam-5224	106	24	)	)	PUNCT
ejpam-5224	106	25	the	the	DET
ejpam-5224	106	26	jacobson	jacobson	PROPN
ejpam-5224	106	27	radical	radical	PROPN
ejpam-5224	106	28	of	of	ADP
ejpam-5224	106	29	the	the	DET
ejpam-5224	106	30	algebra	algebra	NOUN
ejpam-5224	106	31	enda(p	enda(p	PROPN
ejpam-5224	106	32	)	)	PUNCT
ejpam-5224	106	33	or	or	CCONJ
ejpam-5224	106	34	otherwise	otherwise	ADV
ejpam-5224	106	35	j(e	j(e	VERB
ejpam-5224	106	36	)	)	PUNCT
ejpam-5224	107	1	=	=	PUNCT
ejpam-5224	107	2	radenda(p	radenda(p	PROPN
ejpam-5224	107	3	)	)	PUNCT
ejpam-5224	107	4	(	(	PUNCT
ejpam-5224	107	5	enda(p	enda(p	NOUN
ejpam-5224	107	6	)	)	PUNCT
ejpam-5224	107	7	)	)	PUNCT
ejpam-5224	107	8	and	and	CCONJ
ejpam-5224	107	9	according	accord	VERB
ejpam-5224	107	10	to	to	ADP
ejpam-5224	107	11	lemma	lemma	PROPN
ejpam-5224	107	12	1	1	NUM
ejpam-5224	107	13	in	in	ADP
ejpam-5224	107	14	[	[	X
ejpam-5224	107	15	15	15	NUM
ejpam-5224	107	16	]	]	PUNCT
ejpam-5224	107	17	,	,	PUNCT
ejpam-5224	107	18	we	we	PRON
ejpam-5224	107	19	have	have	VERB
ejpam-5224	107	20	,	,	PUNCT
ejpam-5224	107	21	j(e	j(e	PROPN
ejpam-5224	107	22	)	)	PUNCT
ejpam-5224	107	23	=	=	PRON
ejpam-5224	107	24	{	{	PUNCT
ejpam-5224	107	25	φ	φ	PROPN
ejpam-5224	107	26	∈	∈	PROPN
ejpam-5224	107	27	e	e	X
ejpam-5224	107	28	/	/	SYM
ejpam-5224	107	29	φ(p	φ(p	PROPN
ejpam-5224	107	30	)	)	PUNCT
ejpam-5224	107	31	is	be	AUX
ejpam-5224	107	32	a	a	DET
ejpam-5224	107	33	small	small	ADJ
ejpam-5224	107	34	submodule	submodule	NOUN
ejpam-5224	107	35	of	of	ADP
ejpam-5224	107	36	p	p	X
ejpam-5224	107	37	}	}	PUNCT
ejpam-5224	107	38	4.1	4.1	NUM
ejpam-5224	107	39	proposition	proposition	NOUN
ejpam-5224	107	40	.	.	PUNCT
ejpam-5224	108	1	for	for	ADP
ejpam-5224	108	2	n	n	PRON
ejpam-5224	108	3	≥	≥	NOUN
ejpam-5224	108	4	0	0	NUM
ejpam-5224	108	5	and	and	CCONJ
ejpam-5224	108	6	p	p	X
ejpam-5224	108	7	an	an	DET
ejpam-5224	108	8	a	a	PRON
ejpam-5224	108	9	-	-	PUNCT
ejpam-5224	108	10	projective	projective	ADJ
ejpam-5224	108	11	module	module	NOUN
ejpam-5224	108	12	in	in	ADP
ejpam-5224	108	13	moda	moda	PROPN
ejpam-5224	108	14	we	we	PRON
ejpam-5224	108	15	have	have	VERB
ejpam-5224	108	16	:	:	PUNCT
ejpam-5224	108	17	(	(	PUNCT
ejpam-5224	108	18	1	1	X
ejpam-5224	108	19	)	)	PUNCT
ejpam-5224	108	20	jn(e	jn(e	PUNCT
ejpam-5224	108	21	)	)	PUNCT
ejpam-5224	109	1	⊆	⊆	NUM
ejpam-5224	109	2	hom(p	hom(p	PROPN
ejpam-5224	109	3	,	,	PUNCT
ejpam-5224	109	4	radn	radn	NOUN
ejpam-5224	109	5	a(p	a(p	NOUN
ejpam-5224	109	6	)	)	PUNCT
ejpam-5224	109	7	)	)	PUNCT
ejpam-5224	109	8	(	(	PUNCT
ejpam-5224	109	9	2	2	X
ejpam-5224	109	10	)	)	PUNCT
ejpam-5224	109	11	radn	radn	NOUN
ejpam-5224	109	12	end(p	end(p	PROPN
ejpam-5224	109	13	)	)	PUNCT
ejpam-5224	109	14	(	(	PUNCT
ejpam-5224	109	15	hom(p	hom(p	PROPN
ejpam-5224	109	16	,	,	PUNCT
ejpam-5224	109	17	m	m	NOUN
ejpam-5224	109	18	)	)	PUNCT
ejpam-5224	109	19	)	)	PUNCT
ejpam-5224	110	1	⊆	⊆	NUM
ejpam-5224	110	2	hom(p	hom(p	PROPN
ejpam-5224	110	3	,	,	PUNCT
ejpam-5224	110	4	radn	radn	NOUN
ejpam-5224	110	5	a(m	a(m	NOUN
ejpam-5224	110	6	)	)	PUNCT
ejpam-5224	110	7	)	)	PUNCT
ejpam-5224	110	8	proof	proof	NOUN
ejpam-5224	110	9	.	.	PUNCT
ejpam-5224	111	1	for	for	ADP
ejpam-5224	111	2	the	the	DET
ejpam-5224	111	3	first	first	ADJ
ejpam-5224	111	4	assertion	assertion	NOUN
ejpam-5224	111	5	,	,	PUNCT
ejpam-5224	111	6	if	if	SCONJ
ejpam-5224	111	7	n	n	ADJ
ejpam-5224	111	8	=	=	SYM
ejpam-5224	111	9	0	0	NUM
ejpam-5224	111	10	is	be	AUX
ejpam-5224	111	11	obvious	obvious	ADJ
ejpam-5224	111	12	,	,	PUNCT
ejpam-5224	111	13	we	we	PRON
ejpam-5224	111	14	have	have	VERB
ejpam-5224	111	15	equality	equality	NOUN
ejpam-5224	111	16	.	.	PUNCT
ejpam-5224	112	1	if	if	SCONJ
ejpam-5224	112	2	φ	φ	PROPN
ejpam-5224	112	3	∈	∈	PROPN
ejpam-5224	112	4	j(e	j(e	PROPN
ejpam-5224	112	5	)	)	PUNCT
ejpam-5224	112	6	,	,	PUNCT
ejpam-5224	112	7	we	we	PRON
ejpam-5224	112	8	still	still	ADV
ejpam-5224	112	9	have	have	VERB
ejpam-5224	112	10	by	by	ADP
ejpam-5224	112	11	lemma	lemma	PROPN
ejpam-5224	112	12	1-[15	1-[15	PROPN
ejpam-5224	112	13	]	]	X
ejpam-5224	112	14	,	,	PUNCT
ejpam-5224	112	15	φ(p	φ(p	PROPN
ejpam-5224	112	16	)	)	PUNCT
ejpam-5224	113	1	⊆	⊆	NUM
ejpam-5224	113	2	rada(p	rada(p	NOUN
ejpam-5224	113	3	)	)	PUNCT
ejpam-5224	113	4	,	,	PUNCT
ejpam-5224	113	5	because	because	SCONJ
ejpam-5224	113	6	otherwise	otherwise	ADV
ejpam-5224	113	7	,	,	PUNCT
ejpam-5224	113	8	there	there	PRON
ejpam-5224	113	9	exists	exist	VERB
ejpam-5224	113	10	a	a	DET
ejpam-5224	113	11	maximal	maximal	ADJ
ejpam-5224	113	12	submodule	submodule	NOUN
ejpam-5224	113	13	m	m	NOUN
ejpam-5224	113	14	of	of	ADP
ejpam-5224	113	15	p	p	PRON
ejpam-5224	113	16	such	such	ADJ
ejpam-5224	113	17	that	that	SCONJ
ejpam-5224	113	18	φ(p	φ(p	PROPN
ejpam-5224	113	19	)	)	PUNCT
ejpam-5224	114	1	+	+	VERB
ejpam-5224	114	2	m	m	NOUN
ejpam-5224	114	3	=	=	ADJ
ejpam-5224	114	4	p	p	X
ejpam-5224	114	5	but	but	CCONJ
ejpam-5224	114	6	m	m	PROPN
ejpam-5224	114	7	̸=	̸=	PROPN
ejpam-5224	114	8	p	p	NOUN
ejpam-5224	114	9	and	and	CCONJ
ejpam-5224	114	10	this	this	PRON
ejpam-5224	114	11	contradicts	contradict	VERB
ejpam-5224	114	12	that	that	SCONJ
ejpam-5224	114	13	φ(p	φ(p	PROPN
ejpam-5224	114	14	)	)	PUNCT
ejpam-5224	114	15	is	be	AUX
ejpam-5224	114	16	small	small	ADJ
ejpam-5224	114	17	in	in	ADP
ejpam-5224	114	18	p	p	NOUN
ejpam-5224	114	19	,	,	PUNCT
ejpam-5224	114	20	and	and	CCONJ
ejpam-5224	114	21	then	then	ADV
ejpam-5224	114	22	consequently	consequently	ADV
ejpam-5224	114	23	φ	φ	PROPN
ejpam-5224	114	24	∈	∈	PROPN
ejpam-5224	114	25	hom(p	hom(p	PROPN
ejpam-5224	114	26	,	,	PUNCT
ejpam-5224	114	27	rada(p	rada(p	NOUN
ejpam-5224	114	28	)	)	PUNCT
ejpam-5224	114	29	)	)	PUNCT
ejpam-5224	114	30	and	and	CCONJ
ejpam-5224	114	31	the	the	DET
ejpam-5224	114	32	inclusion	inclusion	NOUN
ejpam-5224	114	33	is	be	AUX
ejpam-5224	114	34	true	true	ADJ
ejpam-5224	114	35	for	for	ADP
ejpam-5224	114	36	n	n	NOUN
ejpam-5224	114	37	=	=	SYM
ejpam-5224	114	38	1	1	NUM
ejpam-5224	114	39	.	.	PUNCT
ejpam-5224	114	40	similarly	similarly	ADV
ejpam-5224	114	41	,	,	PUNCT
ejpam-5224	114	42	we	we	PRON
ejpam-5224	114	43	have	have	VERB
ejpam-5224	114	44	,	,	PUNCT
ejpam-5224	114	45	j2(e	j2(e	NUM
ejpam-5224	114	46	)	)	PUNCT
ejpam-5224	114	47	=	=	NOUN
ejpam-5224	114	48	{	{	PUNCT
ejpam-5224	114	49	∑	∑	PART
ejpam-5224	114	50	g	g	NOUN
ejpam-5224	114	51	◦	◦	NOUN
ejpam-5224	114	52	f	f	X
ejpam-5224	114	53	/	/	SYM
ejpam-5224	114	54	f	f	PROPN
ejpam-5224	114	55	∈	∈	PROPN
ejpam-5224	114	56	j(e	j(e	PROPN
ejpam-5224	114	57	)	)	PUNCT
ejpam-5224	114	58	et	et	PROPN
ejpam-5224	114	59	g	g	PROPN
ejpam-5224	114	60	∈	∈	PROPN
ejpam-5224	114	61	j(e	j(e	PROPN
ejpam-5224	114	62	)	)	PUNCT
ejpam-5224	114	63	}	}	PUNCT
ejpam-5224	114	64	,	,	PUNCT
ejpam-5224	114	65	then	then	ADV
ejpam-5224	114	66	f(p	f(p	PROPN
ejpam-5224	114	67	)	)	PUNCT
ejpam-5224	115	1	⊆	⊆	NUM
ejpam-5224	115	2	rada(p	rada(p	NOUN
ejpam-5224	115	3	)	)	PUNCT
ejpam-5224	115	4	,	,	PUNCT
ejpam-5224	115	5	and	and	CCONJ
ejpam-5224	115	6	g(f(p	g(f(p	PROPN
ejpam-5224	115	7	)	)	PUNCT
ejpam-5224	115	8	)	)	PUNCT
ejpam-5224	116	1	⊆	⊆	NUM
ejpam-5224	116	2	g(rada(p	g(rada(p	NOUN
ejpam-5224	116	3	)	)	PUNCT
ejpam-5224	116	4	)	)	PUNCT
ejpam-5224	116	5	,	,	PUNCT
ejpam-5224	116	6	that	that	PRON
ejpam-5224	116	7	is	be	AUX
ejpam-5224	116	8	to	to	PART
ejpam-5224	116	9	say	say	VERB
ejpam-5224	116	10	g	g	PROPN
ejpam-5224	116	11	◦	◦	PROPN
ejpam-5224	116	12	f(p	f(p	PROPN
ejpam-5224	116	13	)	)	PUNCT
ejpam-5224	117	1	⊆	⊆	NUM
ejpam-5224	117	2	g(rada(a)p	g(rada(a)p	NOUN
ejpam-5224	117	3	)	)	PUNCT
ejpam-5224	117	4	,	,	PUNCT
ejpam-5224	117	5	and	and	CCONJ
ejpam-5224	117	6	thus	thus	ADV
ejpam-5224	117	7	g	g	PROPN
ejpam-5224	117	8	◦	◦	PROPN
ejpam-5224	117	9	f(p	f(p	PROPN
ejpam-5224	117	10	)	)	PUNCT
ejpam-5224	118	1	⊆	⊆	NUM
ejpam-5224	118	2	rada(a)g(p	rada(a)g(p	NOUN
ejpam-5224	118	3	)	)	PUNCT
ejpam-5224	118	4	and	and	CCONJ
ejpam-5224	118	5	g	g	PROPN
ejpam-5224	118	6	◦	◦	PROPN
ejpam-5224	118	7	f(p	f(p	PROPN
ejpam-5224	118	8	)	)	PUNCT
ejpam-5224	119	1	⊆	⊆	NUM
ejpam-5224	119	2	rad2	rad2	PROPN
ejpam-5224	119	3	a(a)p	a(a)p	PROPN
ejpam-5224	119	4	because	because	SCONJ
ejpam-5224	119	5	g(p	g(p	PROPN
ejpam-5224	119	6	)	)	PUNCT
ejpam-5224	120	1	⊆	⊆	NUM
ejpam-5224	120	2	rada(p	rada(p	NOUN
ejpam-5224	120	3	)	)	PUNCT
ejpam-5224	120	4	,	,	PUNCT
ejpam-5224	120	5	hence	hence	ADV
ejpam-5224	120	6	j2(e	j2(e	NUM
ejpam-5224	120	7	)	)	PUNCT
ejpam-5224	120	8	⊆	⊆	NUM
ejpam-5224	120	9	hom(p	hom(p	PROPN
ejpam-5224	120	10	,	,	PUNCT
ejpam-5224	120	11	rad2	rad2	PROPN
ejpam-5224	120	12	a(p	a(p	PROPN
ejpam-5224	120	13	)	)	PUNCT
ejpam-5224	120	14	)	)	PUNCT
ejpam-5224	120	15	,	,	PUNCT
ejpam-5224	120	16	so	so	CCONJ
ejpam-5224	120	17	the	the	DET
ejpam-5224	120	18	proposition	proposition	NOUN
ejpam-5224	120	19	is	be	AUX
ejpam-5224	120	20	true	true	ADJ
ejpam-5224	120	21	by	by	ADP
ejpam-5224	120	22	induction	induction	NOUN
ejpam-5224	120	23	,	,	PUNCT
ejpam-5224	120	24	while	while	SCONJ
ejpam-5224	120	25	the	the	DET
ejpam-5224	120	26	second	second	ADJ
ejpam-5224	120	27	inclusion	inclusion	NOUN
ejpam-5224	120	28	comes	come	VERB
ejpam-5224	120	29	from	from	ADP
ejpam-5224	120	30	the	the	DET
ejpam-5224	120	31	fact	fact	NOUN
ejpam-5224	120	32	that	that	SCONJ
ejpam-5224	120	33	hom(p	hom(p	PROPN
ejpam-5224	120	34	,	,	PUNCT
ejpam-5224	120	35	m	m	PRON
ejpam-5224	120	36	)	)	PUNCT
ejpam-5224	120	37	is	be	AUX
ejpam-5224	120	38	end(p	end(p	PROPN
ejpam-5224	120	39	)	)	PUNCT
ejpam-5224	120	40	-module	-module	PROPN
ejpam-5224	120	41	on	on	ADP
ejpam-5224	120	42	the	the	DET
ejpam-5224	120	43	right	right	NOUN
ejpam-5224	120	44	and	and	CCONJ
ejpam-5224	120	45	radend(p	radend(p	NOUN
ejpam-5224	120	46	)	)	PUNCT
ejpam-5224	120	47	(	(	PUNCT
ejpam-5224	120	48	hom(p	hom(p	PROPN
ejpam-5224	120	49	,	,	PUNCT
ejpam-5224	120	50	m	m	NOUN
ejpam-5224	120	51	)	)	PUNCT
ejpam-5224	120	52	)	)	PUNCT
ejpam-5224	121	1	=	=	PUNCT
ejpam-5224	121	2	hom(p	hom(p	PROPN
ejpam-5224	121	3	,	,	PUNCT
ejpam-5224	121	4	m).j(e	m).j(e	NUM
ejpam-5224	121	5	)	)	PUNCT
ejpam-5224	121	6	5	5	NUM
ejpam-5224	121	7	.	.	X
ejpam-5224	121	8	conjecture	conjecture	NOUN
ejpam-5224	121	9	for	for	ADP
ejpam-5224	121	10	artinian	artinian	ADJ
ejpam-5224	121	11	ring	ring	NOUN
ejpam-5224	121	12	with	with	ADP
ejpam-5224	121	13	j3	j3	PROPN
ejpam-5224	121	14	=	=	SYM
ejpam-5224	121	15	0	0	PUNCT
ejpam-5224	121	16	let	let	VERB
ejpam-5224	121	17	a	a	PRON
ejpam-5224	121	18	be	be	AUX
ejpam-5224	121	19	an	an	DET
ejpam-5224	121	20	artinian	artinian	ADJ
ejpam-5224	121	21	ring	ring	NOUN
ejpam-5224	121	22	whose	whose	DET
ejpam-5224	121	23	j3	j3	PROPN
ejpam-5224	121	24	=	=	PUNCT
ejpam-5224	121	25	0	0	PUNCT
ejpam-5224	121	26	and	and	CCONJ
ejpam-5224	121	27	let	let	VERB
ejpam-5224	121	28	{	{	PUNCT
ejpam-5224	121	29	pi	pi	NOUN
ejpam-5224	121	30	=	=	PUNCT
ejpam-5224	121	31	aei}1≤i≤n	aei}1≤i≤n	NOUN
ejpam-5224	121	32	the	the	DET
ejpam-5224	121	33	complete	complete	ADJ
ejpam-5224	121	34	set	set	NOUN
ejpam-5224	121	35	of	of	ADP
ejpam-5224	121	36	non	non	ADJ
ejpam-5224	121	37	-	-	ADJ
ejpam-5224	121	38	isomorphic	isomorphic	ADJ
ejpam-5224	121	39	indecomposable	indecomposable	ADJ
ejpam-5224	121	40	projective	projective	NOUN
ejpam-5224	121	41	a	a	DET
ejpam-5224	121	42	-	-	PUNCT
ejpam-5224	121	43	modules	module	NOUN
ejpam-5224	121	44	,	,	PUNCT
ejpam-5224	121	45	for	for	ADP
ejpam-5224	121	46	any	any	DET
ejpam-5224	121	47	simple	simple	ADJ
ejpam-5224	121	48	a	a	DET
ejpam-5224	121	49	-	-	PUNCT
ejpam-5224	121	50	module	module	NOUN
ejpam-5224	121	51	s	s	NOUN
ejpam-5224	121	52	we	we	PRON
ejpam-5224	121	53	assume	assume	VERB
ejpam-5224	121	54	that	that	SCONJ
ejpam-5224	121	55	rad2(p	rad2(p	NOUN
ejpam-5224	121	56	(	(	PUNCT
ejpam-5224	121	57	ω(s	ω(s	NOUN
ejpam-5224	121	58	)	)	PUNCT
ejpam-5224	121	59	)	)	PUNCT
ejpam-5224	121	60	)	)	PUNCT
ejpam-5224	122	1	=	=	SYM
ejpam-5224	122	2	0	0	PUNCT
ejpam-5224	123	1	with	with	ADP
ejpam-5224	123	2	p	p	X
ejpam-5224	123	3	(	(	PUNCT
ejpam-5224	123	4	ω(s	ω(s	PROPN
ejpam-5224	123	5	)	)	PUNCT
ejpam-5224	123	6	)	)	PUNCT
ejpam-5224	123	7	being	be	AUX
ejpam-5224	123	8	the	the	DET
ejpam-5224	123	9	projective	projective	ADJ
ejpam-5224	123	10	cover	cover	NOUN
ejpam-5224	123	11	of	of	ADP
ejpam-5224	123	12	the	the	DET
ejpam-5224	123	13	first	first	ADJ
ejpam-5224	123	14	syzygy	syzygy	NOUN
ejpam-5224	123	15	m.	m.	NOUN
ejpam-5224	123	16	laaraj	laaraj	PROPN
ejpam-5224	123	17	,	,	PUNCT
ejpam-5224	123	18	s.	s.	PROPN
ejpam-5224	123	19	abdelalim	abdelalim	PROPN
ejpam-5224	123	20	,	,	PUNCT
ejpam-5224	123	21	i.elmouki	i.elmouki	CCONJ
ejpam-5224	123	22	/	/	SYM
ejpam-5224	123	23	eur	eur	NOUN
ejpam-5224	123	24	.	.	PUNCT
ejpam-5224	124	1	j.	j.	PROPN
ejpam-5224	124	2	pure	pure	PROPN
ejpam-5224	124	3	appl	appl	PROPN
ejpam-5224	124	4	.	.	PROPN
ejpam-5224	124	5	math	math	PROPN
ejpam-5224	124	6	,	,	PUNCT
ejpam-5224	124	7	17	17	NUM
ejpam-5224	124	8	(	(	PUNCT
ejpam-5224	124	9	3	3	NUM
ejpam-5224	124	10	)	)	PUNCT
ejpam-5224	124	11	(	(	PUNCT
ejpam-5224	124	12	2024	2024	NUM
ejpam-5224	124	13	)	)	PUNCT
ejpam-5224	124	14	,	,	PUNCT
ejpam-5224	124	15	1855	1855	NUM
ejpam-5224	124	16	-	-	SYM
ejpam-5224	124	17	1868	1868	NUM
ejpam-5224	124	18	1860	1860	NUM
ejpam-5224	124	19	ω(s	ω(s	NOUN
ejpam-5224	124	20	)	)	PUNCT
ejpam-5224	124	21	,	,	PUNCT
ejpam-5224	124	22	let	let	VERB
ejpam-5224	124	23	i	i	PRON
ejpam-5224	124	24	be	be	AUX
ejpam-5224	124	25	the	the	DET
ejpam-5224	124	26	set	set	NOUN
ejpam-5224	124	27	such	such	ADJ
ejpam-5224	124	28	that	that	SCONJ
ejpam-5224	124	29	any	any	DET
ejpam-5224	124	30	simple	simple	ADJ
ejpam-5224	124	31	module	module	NOUN
ejpam-5224	124	32	si	si	NOUN
ejpam-5224	124	33	for	for	ADP
ejpam-5224	124	34	i	i	PRON
ejpam-5224	124	35	∈	∈	PROPN
ejpam-5224	125	1	i	i	PRON
ejpam-5224	125	2	has	have	VERB
ejpam-5224	125	3	a	a	DET
ejpam-5224	125	4	finite	finite	ADJ
ejpam-5224	125	5	projective	projective	ADJ
ejpam-5224	125	6	dimension	dimension	NOUN
ejpam-5224	125	7	,	,	PUNCT
ejpam-5224	125	8	let	let	VERB
ejpam-5224	125	9	i1	i1	PROPN
ejpam-5224	125	10	⊆	⊆	NUM
ejpam-5224	125	11	i	i	PRON
ejpam-5224	125	12	such	such	ADJ
ejpam-5224	125	13	that	that	SCONJ
ejpam-5224	125	14	top(pj	top(pj	NOUN
ejpam-5224	125	15	)	)	PUNCT
ejpam-5224	125	16	≃	≃	NOUN
ejpam-5224	125	17	si1	si1	VERB
ejpam-5224	125	18	for	for	ADP
ejpam-5224	125	19	j	j	PROPN
ejpam-5224	125	20	∈	∈	PROPN
ejpam-5224	125	21	i1	i1	PROPN
ejpam-5224	125	22	where	where	SCONJ
ejpam-5224	125	23	si1	si1	PROPN
ejpam-5224	125	24	is	be	AUX
ejpam-5224	125	25	the	the	DET
ejpam-5224	125	26	simple	simple	ADJ
ejpam-5224	125	27	a	a	DET
ejpam-5224	125	28	-	-	PUNCT
ejpam-5224	125	29	module	module	NOUN
ejpam-5224	125	30	of	of	ADP
ejpam-5224	125	31	minimal	minimal	ADJ
ejpam-5224	125	32	projective	projective	ADJ
ejpam-5224	125	33	dimension	dimension	NOUN
ejpam-5224	125	34	among	among	ADP
ejpam-5224	125	35	the	the	DET
ejpam-5224	125	36	simple	simple	ADJ
ejpam-5224	125	37	modules	module	NOUN
ejpam-5224	125	38	in	in	ADP
ejpam-5224	125	39	moda	moda	PROPN
ejpam-5224	125	40	for	for	ADP
ejpam-5224	125	41	all	all	PRON
ejpam-5224	125	42	i	i	PRON
ejpam-5224	125	43	∈	∈	PROPN
ejpam-5224	125	44	i1	i1	PROPN
ejpam-5224	125	45	.	.	PUNCT
ejpam-5224	126	1	we	we	PRON
ejpam-5224	126	2	consider	consider	VERB
ejpam-5224	126	3	the	the	DET
ejpam-5224	126	4	algebra	algebra	NOUN
ejpam-5224	126	5	γ1	γ1	NOUN
ejpam-5224	126	6	=	=	SYM
ejpam-5224	126	7	end	end	NOUN
ejpam-5224	126	8	(	(	PUNCT
ejpam-5224	126	9	⊕	⊕	PROPN
ejpam-5224	126	10	i∈i−i1	i∈i−i1	PRON
ejpam-5224	126	11	pi	pi	NOUN
ejpam-5224	126	12	)	)	PUNCT
ejpam-5224	126	13	op	op	NOUN
ejpam-5224	126	14	and	and	CCONJ
ejpam-5224	126	15	we	we	PRON
ejpam-5224	126	16	denote	denote	VERB
ejpam-5224	126	17	hom	hom	PROPN
ejpam-5224	126	18	(	(	PUNCT
ejpam-5224	126	19	⊕	⊕	PROPN
ejpam-5224	126	20	i∈i−i1	i∈i−i1	PRON
ejpam-5224	126	21	pi	pi	PROPN
ejpam-5224	126	22	,	,	PUNCT
ejpam-5224	126	23	s	s	AUX
ejpam-5224	126	24	)	)	PUNCT
ejpam-5224	126	25	by	by	ADP
ejpam-5224	126	26	s̃	s̃	PROPN
ejpam-5224	126	27	for	for	ADP
ejpam-5224	126	28	every	every	DET
ejpam-5224	126	29	simple	simple	ADJ
ejpam-5224	126	30	a	a	DET
ejpam-5224	126	31	-	-	PUNCT
ejpam-5224	126	32	module	module	NOUN
ejpam-5224	126	33	s	s	NOUN
ejpam-5224	126	34	,	,	PUNCT
ejpam-5224	126	35	then	then	ADV
ejpam-5224	126	36	we	we	PRON
ejpam-5224	126	37	have	have	VERB
ejpam-5224	126	38	the	the	DET
ejpam-5224	126	39	following	follow	VERB
ejpam-5224	126	40	proposition	proposition	NOUN
ejpam-5224	126	41	.	.	PUNCT
ejpam-5224	127	1	5.1	5.1	NUM
ejpam-5224	127	2	proposition	proposition	NOUN
ejpam-5224	127	3	.	.	PUNCT
ejpam-5224	128	1	the	the	DET
ejpam-5224	128	2	ring	ring	NOUN
ejpam-5224	128	3	γ1	γ1	NOUN
ejpam-5224	128	4	is	be	AUX
ejpam-5224	128	5	artinian	artinian	ADJ
ejpam-5224	128	6	with	with	ADP
ejpam-5224	128	7	:	:	PUNCT
ejpam-5224	128	8	(	(	PUNCT
ejpam-5224	128	9	1	1	X
ejpam-5224	128	10	)	)	PUNCT
ejpam-5224	128	11	rad3	rad3	NOUN
ejpam-5224	128	12	γ1	γ1	PROPN
ejpam-5224	128	13	(	(	PUNCT
ejpam-5224	128	14	γ1	γ1	PROPN
ejpam-5224	128	15	)	)	PUNCT
ejpam-5224	128	16	=	=	SYM
ejpam-5224	129	1	0	0	X
ejpam-5224	129	2	.	.	PUNCT
ejpam-5224	130	1	(	(	PUNCT
ejpam-5224	130	2	2	2	X
ejpam-5224	130	3	)	)	PUNCT
ejpam-5224	130	4	pd(hom	pd(hom	PROPN
ejpam-5224	130	5	(	(	PUNCT
ejpam-5224	130	6	⊕	⊕	PROPN
ejpam-5224	130	7	i∈i−i1	i∈i−i1	PRON
ejpam-5224	130	8	pi	pi	PROPN
ejpam-5224	130	9	,	,	PUNCT
ejpam-5224	130	10	s	s	NOUN
ejpam-5224	130	11	)	)	PUNCT
ejpam-5224	130	12	)	)	PUNCT
ejpam-5224	131	1	<	<	X
ejpam-5224	131	2	∞	∞	PROPN
ejpam-5224	131	3	for	for	ADP
ejpam-5224	131	4	every	every	DET
ejpam-5224	131	5	simple	simple	ADJ
ejpam-5224	131	6	a	a	DET
ejpam-5224	131	7	-	-	PUNCT
ejpam-5224	131	8	module	module	NOUN
ejpam-5224	131	9	s	s	NOUN
ejpam-5224	131	10	such	such	ADJ
ejpam-5224	131	11	that	that	SCONJ
ejpam-5224	131	12	pd(s	pd(s	NUM
ejpam-5224	131	13	)	)	PUNCT
ejpam-5224	131	14	<	<	X
ejpam-5224	131	15	∞.	∞.	PROPN
ejpam-5224	131	16	(	(	PUNCT
ejpam-5224	131	17	3	3	NUM
ejpam-5224	131	18	)	)	PUNCT
ejpam-5224	131	19	rad2p	rad2p	NOUN
ejpam-5224	131	20	(	(	PUNCT
ejpam-5224	131	21	ω(s̃	ω(s̃	NOUN
ejpam-5224	131	22	)	)	PUNCT
ejpam-5224	131	23	)	)	PUNCT
ejpam-5224	132	1	=	=	SYM
ejpam-5224	132	2	0	0	PUNCT
ejpam-5224	133	1	with	with	ADP
ejpam-5224	133	2	p	p	X
ejpam-5224	133	3	(	(	PUNCT
ejpam-5224	133	4	ω(s̃	ω(s̃	NOUN
ejpam-5224	133	5	)	)	PUNCT
ejpam-5224	133	6	)	)	PUNCT
ejpam-5224	134	1	the	the	DET
ejpam-5224	134	2	projective	projective	ADJ
ejpam-5224	134	3	cover	cover	NOUN
ejpam-5224	134	4	of	of	ADP
ejpam-5224	134	5	the	the	DET
ejpam-5224	134	6	first	first	ADJ
ejpam-5224	134	7	syzygy	syzygy	NOUN
ejpam-5224	134	8	ω(s̃	ω(s̃	NOUN
ejpam-5224	134	9	)	)	PUNCT
ejpam-5224	134	10	.	.	PUNCT
ejpam-5224	135	1	proof	proof	NOUN
ejpam-5224	135	2	.	.	PUNCT
ejpam-5224	136	1	it	it	PRON
ejpam-5224	136	2	is	be	AUX
ejpam-5224	136	3	easy	easy	ADJ
ejpam-5224	136	4	to	to	PART
ejpam-5224	136	5	verify	verify	VERB
ejpam-5224	136	6	that	that	PRON
ejpam-5224	136	7	γ1	γ1	NOUN
ejpam-5224	136	8	is	be	AUX
ejpam-5224	136	9	an	an	DET
ejpam-5224	136	10	artinian	artinian	ADJ
ejpam-5224	136	11	ring	ring	NOUN
ejpam-5224	136	12	,	,	PUNCT
ejpam-5224	136	13	we	we	PRON
ejpam-5224	136	14	have	have	VERB
ejpam-5224	136	15	by	by	ADP
ejpam-5224	136	16	proposition	proposition	NOUN
ejpam-5224	136	17	2.1	2.1	NUM
ejpam-5224	136	18	,	,	PUNCT
ejpam-5224	136	19	j3(γ1	j3(γ1	NOUN
ejpam-5224	136	20	)	)	PUNCT
ejpam-5224	136	21	⊆	⊆	NUM
ejpam-5224	136	22	hom(γ1	hom(γ1	NOUN
ejpam-5224	136	23	,	,	PUNCT
ejpam-5224	136	24	rad	rad	NOUN
ejpam-5224	136	25	3	3	NUM
ejpam-5224	136	26	a	a	PRON
ejpam-5224	136	27	(	(	PUNCT
ejpam-5224	136	28	⊕	⊕	PROPN
ejpam-5224	136	29	i∈i−i1	i∈i−i1	PRON
ejpam-5224	136	30	pi	pi	NOUN
ejpam-5224	136	31	)	)	PUNCT
ejpam-5224	136	32	)	)	PUNCT
ejpam-5224	136	33	,	,	PUNCT
ejpam-5224	136	34	as	as	ADP
ejpam-5224	136	35	j3	j3	PROPN
ejpam-5224	136	36	=	=	SYM
ejpam-5224	136	37	0	0	PROPN
ejpam-5224	136	38	,	,	PUNCT
ejpam-5224	136	39	then	then	ADV
ejpam-5224	136	40	rad3	rad3	PROPN
ejpam-5224	136	41	γ1	γ1	PROPN
ejpam-5224	136	42	(	(	PUNCT
ejpam-5224	136	43	γ1	γ1	PROPN
ejpam-5224	136	44	)	)	PUNCT
ejpam-5224	136	45	=	=	SYM
ejpam-5224	136	46	0	0	NUM
ejpam-5224	136	47	,	,	PUNCT
ejpam-5224	136	48	and	and	CCONJ
ejpam-5224	136	49	since	since	SCONJ
ejpam-5224	136	50	there	there	PRON
ejpam-5224	136	51	is	be	VERB
ejpam-5224	136	52	an	an	DET
ejpam-5224	136	53	equivalence	equivalence	NOUN
ejpam-5224	136	54	between	between	ADP
ejpam-5224	136	55	the	the	DET
ejpam-5224	136	56	two	two	NUM
ejpam-5224	136	57	categories	category	NOUN
ejpam-5224	136	58	mod(a	mod(a	PROPN
ejpam-5224	136	59	)	)	PUNCT
ejpam-5224	136	60	and	and	CCONJ
ejpam-5224	136	61	mod(γ1	mod(γ1	NOUN
ejpam-5224	136	62	)	)	PUNCT
ejpam-5224	136	63	see	see	VERB
ejpam-5224	136	64	proposition	proposition	NOUN
ejpam-5224	136	65	2.5	2.5	NUM
ejpam-5224	136	66	in	in	ADP
ejpam-5224	136	67	[	[	X
ejpam-5224	136	68	10	10	NUM
ejpam-5224	136	69	]	]	PUNCT
ejpam-5224	136	70	,	,	PUNCT
ejpam-5224	136	71	then	then	ADV
ejpam-5224	136	72	the	the	DET
ejpam-5224	136	73	projective	projective	ADJ
ejpam-5224	136	74	γ1	γ1	NOUN
ejpam-5224	136	75	-	-	PUNCT
ejpam-5224	136	76	modules	module	NOUN
ejpam-5224	136	77	are	be	AUX
ejpam-5224	136	78	of	of	ADP
ejpam-5224	136	79	the	the	DET
ejpam-5224	136	80	form	form	NOUN
ejpam-5224	136	81	hom	hom	INTJ
ejpam-5224	136	82	(	(	PUNCT
ejpam-5224	136	83	⊕	⊕	PROPN
ejpam-5224	136	84	i∈i−i1	i∈i−i1	PRON
ejpam-5224	136	85	pi	pi	PROPN
ejpam-5224	136	86	,	,	PUNCT
ejpam-5224	136	87	q	q	NOUN
ejpam-5224	136	88	)	)	PUNCT
ejpam-5224	136	89	denoted	denote	VERB
ejpam-5224	136	90	by	by	ADP
ejpam-5224	136	91	q̃	q̃	PROPN
ejpam-5224	136	92	with	with	ADP
ejpam-5224	136	93	q	q	NOUN
ejpam-5224	136	94	is	be	AUX
ejpam-5224	136	95	a	a	DET
ejpam-5224	136	96	projective	projective	ADJ
ejpam-5224	136	97	a	a	DET
ejpam-5224	136	98	-	-	PUNCT
ejpam-5224	136	99	module	module	NOUN
ejpam-5224	136	100	and	and	CCONJ
ejpam-5224	136	101	the	the	DET
ejpam-5224	136	102	simple	simple	ADJ
ejpam-5224	136	103	γ1	γ1	NOUN
ejpam-5224	136	104	-	-	PUNCT
ejpam-5224	136	105	modules	module	NOUN
ejpam-5224	136	106	are	be	AUX
ejpam-5224	136	107	of	of	ADP
ejpam-5224	136	108	the	the	DET
ejpam-5224	136	109	form	form	NOUN
ejpam-5224	136	110	hom	hom	INTJ
ejpam-5224	136	111	(	(	PUNCT
ejpam-5224	136	112	⊕	⊕	PROPN
ejpam-5224	136	113	i∈i−i1	i∈i−i1	PRON
ejpam-5224	136	114	pi	pi	PROPN
ejpam-5224	136	115	,	,	PUNCT
ejpam-5224	136	116	s	s	AUX
ejpam-5224	136	117	)	)	PUNCT
ejpam-5224	136	118	with	with	ADP
ejpam-5224	136	119	s	s	PRON
ejpam-5224	136	120	a	a	DET
ejpam-5224	136	121	simple	simple	ADJ
ejpam-5224	136	122	a	a	DET
ejpam-5224	136	123	-	-	PUNCT
ejpam-5224	136	124	module	module	NOUN
ejpam-5224	136	125	,	,	PUNCT
ejpam-5224	136	126	the	the	DET
ejpam-5224	136	127	same	same	ADJ
ejpam-5224	136	128	if	if	SCONJ
ejpam-5224	136	129	pd(s	pd(s	NUM
ejpam-5224	136	130	)	)	PUNCT
ejpam-5224	137	1	=	=	PUNCT
ejpam-5224	137	2	m	m	VERB
ejpam-5224	137	3	for	for	ADP
ejpam-5224	137	4	a	a	DET
ejpam-5224	137	5	simple	simple	ADJ
ejpam-5224	137	6	a	a	DET
ejpam-5224	137	7	-	-	PUNCT
ejpam-5224	137	8	module	module	NOUN
ejpam-5224	137	9	s	s	NOUN
ejpam-5224	137	10	,	,	PUNCT
ejpam-5224	137	11	then	then	ADV
ejpam-5224	137	12	by	by	ADP
ejpam-5224	137	13	application	application	NOUN
ejpam-5224	137	14	of	of	ADP
ejpam-5224	137	15	the	the	DET
ejpam-5224	137	16	functor	functor	PROPN
ejpam-5224	137	17	hom	hom	PROPN
ejpam-5224	137	18	(	(	PUNCT
ejpam-5224	137	19	⊕	⊕	PROPN
ejpam-5224	137	20	i∈i−i1	i∈i−i1	PRON
ejpam-5224	137	21	pi,−	pi,−	NOUN
ejpam-5224	137	22	)	)	PUNCT
ejpam-5224	137	23	in	in	ADP
ejpam-5224	137	24	the	the	DET
ejpam-5224	137	25	projective	projective	ADJ
ejpam-5224	137	26	resolution	resolution	NOUN
ejpam-5224	137	27	0	0	NUM
ejpam-5224	137	28	//	//	SYM
ejpam-5224	137	29	pm	pm	PROPN
ejpam-5224	137	30	//	//	X
ejpam-5224	137	31	·	·	PUNCT
ejpam-5224	137	32	·	·	PUNCT
ejpam-5224	137	33	·	·	PUNCT
ejpam-5224	138	1	//	//	NUM
ejpam-5224	138	2	p2	p2	PROPN
ejpam-5224	138	3	//	//	PROPN
ejpam-5224	138	4	p1	p1	PROPN
ejpam-5224	138	5	//	//	PROPN
ejpam-5224	138	6	p0	p0	PROPN
ejpam-5224	138	7	//	//	SYM
ejpam-5224	138	8	s	s	PART
ejpam-5224	138	9	//	//	X
ejpam-5224	138	10	0	0	NUM
ejpam-5224	138	11	we	we	PRON
ejpam-5224	138	12	will	will	AUX
ejpam-5224	138	13	have	have	VERB
ejpam-5224	138	14	,	,	PUNCT
ejpam-5224	138	15	0	0	NUM
ejpam-5224	138	16	//	//	NUM
ejpam-5224	138	17	p̃m	p̃m	PROPN
ejpam-5224	138	18	//	//	X
ejpam-5224	138	19	·	·	PUNCT
ejpam-5224	138	20	·	·	PUNCT
ejpam-5224	138	21	·	·	PUNCT
ejpam-5224	138	22	//	//	PUNCT
ejpam-5224	139	1	p̃2	p̃2	PROPN
ejpam-5224	139	2	//	//	PROPN
ejpam-5224	140	1	p̃1	p̃1	PROPN
ejpam-5224	140	2	//	//	NUM
ejpam-5224	140	3	p̃0	p̃0	PROPN
ejpam-5224	140	4	//	//	PROPN
ejpam-5224	140	5	s̃	s̃	PROPN
ejpam-5224	140	6	//	//	PUNCT
ejpam-5224	140	7	0	0	NUM
ejpam-5224	141	1	so	so	CCONJ
ejpam-5224	141	2	pdγ1(s̃	pdγ1(s̃	PROPN
ejpam-5224	141	3	)	)	PUNCT
ejpam-5224	141	4	≤	≤	NUM
ejpam-5224	141	5	m	m	VERB
ejpam-5224	141	6	because	because	SCONJ
ejpam-5224	141	7	rad2	rad2	PROPN
ejpam-5224	141	8	a(p	a(p	PROPN
ejpam-5224	141	9	(	(	PUNCT
ejpam-5224	141	10	ω(s	ω(s	PROPN
ejpam-5224	141	11	)	)	PUNCT
ejpam-5224	141	12	)	)	PUNCT
ejpam-5224	141	13	)	)	PUNCT
ejpam-5224	142	1	=	=	SYM
ejpam-5224	142	2	0	0	NUM
ejpam-5224	143	1	and	and	CCONJ
ejpam-5224	143	2	p	p	X
ejpam-5224	143	3	(	(	PUNCT
ejpam-5224	143	4	ω(s̃	ω(s̃	NOUN
ejpam-5224	143	5	)	)	PUNCT
ejpam-5224	143	6	)	)	PUNCT
ejpam-5224	144	1	=	=	SYM
ejpam-5224	144	2	p	p	X
ejpam-5224	144	3	(	(	PUNCT
ejpam-5224	144	4	˜ω(s	˜ω(s	PROPN
ejpam-5224	144	5	)	)	PUNCT
ejpam-5224	144	6	)	)	PUNCT
ejpam-5224	145	1	=	=	SYM
ejpam-5224	145	2	p	p	X
ejpam-5224	145	3	(	(	PUNCT
ejpam-5224	145	4	ω(s	ω(s	PROPN
ejpam-5224	145	5	)	)	PUNCT
ejpam-5224	145	6	)	)	PUNCT
ejpam-5224	146	1	and	and	CCONJ
ejpam-5224	146	2	according	accord	VERB
ejpam-5224	146	3	to	to	ADP
ejpam-5224	146	4	proposition	proposition	NOUN
ejpam-5224	146	5	2.1	2.1	NUM
ejpam-5224	146	6	,	,	PUNCT
ejpam-5224	146	7	rad2	rad2	ADJ
ejpam-5224	146	8	γ1	γ1	PROPN
ejpam-5224	146	9	(	(	PUNCT
ejpam-5224	146	10	hom	hom	INTJ
ejpam-5224	146	11	(	(	PUNCT
ejpam-5224	146	12	⊕	⊕	PROPN
ejpam-5224	146	13	i∈i−i1	i∈i−i1	PRON
ejpam-5224	146	14	pi	pi	NOUN
ejpam-5224	146	15	,	,	PUNCT
ejpam-5224	146	16	p	p	X
ejpam-5224	146	17	(	(	PUNCT
ejpam-5224	146	18	ω(s	ω(s	PROPN
ejpam-5224	146	19	)	)	PUNCT
ejpam-5224	146	20	)	)	PUNCT
ejpam-5224	146	21	)	)	PUNCT
ejpam-5224	146	22	)	)	PUNCT
ejpam-5224	147	1	⊆	⊆	NUM
ejpam-5224	147	2	hom	hom	NUM
ejpam-5224	147	3	(	(	PUNCT
ejpam-5224	147	4	⊕	⊕	PROPN
ejpam-5224	147	5	i∈i−i1	i∈i−i1	PRON
ejpam-5224	147	6	pi	pi	PROPN
ejpam-5224	147	7	,	,	PUNCT
ejpam-5224	147	8	rad	rad	PROPN
ejpam-5224	147	9	2	2	NUM
ejpam-5224	147	10	a(p	a(p	NOUN
ejpam-5224	147	11	(	(	PUNCT
ejpam-5224	147	12	ω(s	ω(s	PROPN
ejpam-5224	147	13	)	)	PUNCT
ejpam-5224	147	14	)	)	PUNCT
ejpam-5224	147	15	)	)	PUNCT
ejpam-5224	147	16	)	)	PUNCT
ejpam-5224	147	17	and	and	CCONJ
ejpam-5224	147	18	the	the	DET
ejpam-5224	147	19	third	third	ADJ
ejpam-5224	147	20	assertion	assertion	NOUN
ejpam-5224	147	21	is	be	AUX
ejpam-5224	147	22	verified	verify	VERB
ejpam-5224	147	23	.	.	PUNCT
ejpam-5224	148	1	5.2	5.2	NUM
ejpam-5224	148	2	remark	remark	NOUN
ejpam-5224	148	3	.	.	PUNCT
ejpam-5224	149	1	the	the	DET
ejpam-5224	149	2	simple	simple	ADJ
ejpam-5224	149	3	a	a	NOUN
ejpam-5224	149	4	-	-	PUNCT
ejpam-5224	149	5	modules	module	NOUN
ejpam-5224	149	6	(	(	PUNCT
ejpam-5224	149	7	si)i∈i−i1	si)i∈i−i1	NOUN
ejpam-5224	149	8	have	have	AUX
ejpam-5224	149	9	finite	finite	PROPN
ejpam-5224	149	10	projective	projective	ADJ
ejpam-5224	149	11	dimensions	dimension	NOUN
ejpam-5224	149	12	so	so	SCONJ
ejpam-5224	149	13	the	the	DET
ejpam-5224	149	14	γ1	γ1	NOUN
ejpam-5224	149	15	-	-	PUNCT
ejpam-5224	149	16	simple	simple	ADJ
ejpam-5224	149	17	modules	module	NOUN
ejpam-5224	149	18	are	be	AUX
ejpam-5224	149	19	also	also	ADV
ejpam-5224	149	20	simple	simple	ADJ
ejpam-5224	149	21	,	,	PUNCT
ejpam-5224	149	22	and	and	CCONJ
ejpam-5224	149	23	by	by	ADP
ejpam-5224	149	24	the	the	DET
ejpam-5224	149	25	third	third	ADJ
ejpam-5224	149	26	assertion	assertion	NOUN
ejpam-5224	149	27	in	in	ADP
ejpam-5224	149	28	proposition	proposition	NOUN
ejpam-5224	149	29	3.1	3.1	NUM
ejpam-5224	149	30	and	and	CCONJ
ejpam-5224	149	31	by	by	ADP
ejpam-5224	149	32	lemma	lemma	PROPN
ejpam-5224	149	33	1.2	1.2	NUM
ejpam-5224	149	34	,	,	PUNCT
ejpam-5224	149	35	the	the	DET
ejpam-5224	149	36	γ1	γ1	NOUN
ejpam-5224	149	37	-	-	PUNCT
ejpam-5224	149	38	simple	simple	ADJ
ejpam-5224	149	39	module	module	NOUN
ejpam-5224	149	40	s̃i2	s̃i2	NOUN
ejpam-5224	149	41	of	of	ADP
ejpam-5224	149	42	minimal	minimal	ADJ
ejpam-5224	149	43	projective	projective	ADJ
ejpam-5224	149	44	dimension	dimension	NOUN
ejpam-5224	149	45	among	among	ADP
ejpam-5224	149	46	the	the	DET
ejpam-5224	149	47	simple	simple	ADJ
ejpam-5224	149	48	modules	module	NOUN
ejpam-5224	149	49	in	in	ADP
ejpam-5224	149	50	modγ1	modγ1	PROPN
ejpam-5224	149	51	checks	check	NOUN
ejpam-5224	149	52	pdγ1(s̃i2	pdγ1(s̃i2	NOUN
ejpam-5224	149	53	)	)	PUNCT
ejpam-5224	149	54	≤	≤	NUM
ejpam-5224	149	55	1	1	NUM
ejpam-5224	149	56	and	and	CCONJ
ejpam-5224	149	57	ext1γ1	ext1γ1	NOUN
ejpam-5224	149	58	(	(	PUNCT
ejpam-5224	149	59	s̃i2	s̃i2	PROPN
ejpam-5224	149	60	,	,	PUNCT
ejpam-5224	149	61	s̃i2	s̃i2	PROPN
ejpam-5224	149	62	)	)	PUNCT
ejpam-5224	150	1	=	=	SYM
ejpam-5224	150	2	0	0	PUNCT
ejpam-5224	150	3	by	by	ADP
ejpam-5224	150	4	theorem	theorem	NOUN
ejpam-5224	150	5	1.3	1.3	NUM
ejpam-5224	150	6	.	.	PUNCT
ejpam-5224	151	1	5.3	5.3	NUM
ejpam-5224	151	2	theorem	theorem	VERB
ejpam-5224	151	3	.	.	PUNCT
ejpam-5224	152	1	if	if	SCONJ
ejpam-5224	152	2	s̃i2	s̃i2	PROPN
ejpam-5224	152	3	is	be	AUX
ejpam-5224	152	4	the	the	DET
ejpam-5224	152	5	γ1	γ1	NOUN
ejpam-5224	152	6	-	-	PUNCT
ejpam-5224	152	7	simple	simple	ADJ
ejpam-5224	152	8	module	module	NOUN
ejpam-5224	152	9	of	of	ADP
ejpam-5224	152	10	minimal	minimal	ADJ
ejpam-5224	152	11	projective	projective	ADJ
ejpam-5224	152	12	dimension	dimension	NOUN
ejpam-5224	152	13	among	among	ADP
ejpam-5224	152	14	the	the	DET
ejpam-5224	152	15	simple	simple	ADJ
ejpam-5224	152	16	modules	module	NOUN
ejpam-5224	152	17	of	of	ADP
ejpam-5224	152	18	modγ1	modγ1	PROPN
ejpam-5224	152	19	,	,	PUNCT
ejpam-5224	152	20	then	then	ADV
ejpam-5224	152	21	ext1a(si2	ext1a(si2	NOUN
ejpam-5224	152	22	,	,	PUNCT
ejpam-5224	152	23	si2	si2	NOUN
ejpam-5224	152	24	)	)	PUNCT
ejpam-5224	152	25	=	=	SYM
ejpam-5224	152	26	0	0	NUM
ejpam-5224	152	27	proof	proof	NOUN
ejpam-5224	152	28	.	.	PUNCT
ejpam-5224	153	1	s̃i2	s̃i2	NOUN
ejpam-5224	153	2	is	be	AUX
ejpam-5224	153	3	a	a	DET
ejpam-5224	153	4	simple	simple	ADJ
ejpam-5224	153	5	γ1	γ1	NOUN
ejpam-5224	153	6	-	-	PUNCT
ejpam-5224	153	7	module	module	NOUN
ejpam-5224	153	8	and	and	CCONJ
ejpam-5224	153	9	s̃i2	s̃i2	PROPN
ejpam-5224	153	10	=	=	SYM
ejpam-5224	153	11	hom	hom	PROPN
ejpam-5224	153	12	(	(	PUNCT
ejpam-5224	153	13	⊕	⊕	PROPN
ejpam-5224	153	14	i∈i−i1	i∈i−i1	PRON
ejpam-5224	153	15	pi	pi	NOUN
ejpam-5224	153	16	,	,	PUNCT
ejpam-5224	153	17	si2	si2	NOUN
ejpam-5224	153	18	)	)	PUNCT
ejpam-5224	153	19	with	with	ADP
ejpam-5224	153	20	si2	si2	NOUN
ejpam-5224	153	21	=	=	SYM
ejpam-5224	153	22	aei2	aei2	PROPN
ejpam-5224	153	23	/	/	SYM
ejpam-5224	153	24	jei2	jei2	NOUN
ejpam-5224	153	25	where	where	SCONJ
ejpam-5224	153	26	ei2	ei2	NOUN
ejpam-5224	153	27	is	be	AUX
ejpam-5224	153	28	a	a	DET
ejpam-5224	153	29	primitive	primitive	ADJ
ejpam-5224	153	30	idempotent	idempotent	NOUN
ejpam-5224	153	31	a	a	DET
ejpam-5224	153	32	simple	simple	ADJ
ejpam-5224	153	33	a	a	DET
ejpam-5224	153	34	-module	-module	NOUN
ejpam-5224	153	35	not	not	PART
ejpam-5224	153	36	isomorphic	isomorphic	ADJ
ejpam-5224	153	37	to	to	ADP
ejpam-5224	153	38	si1	si1	PROPN
ejpam-5224	153	39	,	,	PUNCT
ejpam-5224	153	40	then	then	ADV
ejpam-5224	153	41	ext1a(s̃i2	ext1a(s̃i2	PROPN
ejpam-5224	153	42	,	,	PUNCT
ejpam-5224	153	43	s̃i2	s̃i2	PROPN
ejpam-5224	153	44	)	)	PUNCT
ejpam-5224	154	1	=	=	SYM
ejpam-5224	154	2	0	0	PUNCT
ejpam-5224	154	3	with	with	ADP
ejpam-5224	154	4	pdγ1(s̃i2	pdγ1(s̃i2	NOUN
ejpam-5224	154	5	)	)	PUNCT
ejpam-5224	154	6	=	=	SYM
ejpam-5224	154	7	0	0	NUM
ejpam-5224	154	8	or	or	CCONJ
ejpam-5224	154	9	1	1	NUM
ejpam-5224	154	10	.	.	PUNCT
ejpam-5224	154	11	m.	m.	NOUN
ejpam-5224	154	12	laaraj	laaraj	PROPN
ejpam-5224	154	13	,	,	PUNCT
ejpam-5224	154	14	s.	s.	PROPN
ejpam-5224	154	15	abdelalim	abdelalim	PROPN
ejpam-5224	154	16	,	,	PUNCT
ejpam-5224	154	17	i.elmouki	i.elmouki	CCONJ
ejpam-5224	154	18	/	/	SYM
ejpam-5224	154	19	eur	eur	NOUN
ejpam-5224	154	20	.	.	PUNCT
ejpam-5224	155	1	j.	j.	PROPN
ejpam-5224	155	2	pure	pure	PROPN
ejpam-5224	155	3	appl	appl	PROPN
ejpam-5224	155	4	.	.	PROPN
ejpam-5224	155	5	math	math	PROPN
ejpam-5224	155	6	,	,	PUNCT
ejpam-5224	155	7	17	17	NUM
ejpam-5224	155	8	(	(	PUNCT
ejpam-5224	155	9	3	3	NUM
ejpam-5224	155	10	)	)	PUNCT
ejpam-5224	155	11	(	(	PUNCT
ejpam-5224	155	12	2024	2024	NUM
ejpam-5224	155	13	)	)	PUNCT
ejpam-5224	155	14	,	,	PUNCT
ejpam-5224	155	15	1855	1855	NUM
ejpam-5224	155	16	-	-	SYM
ejpam-5224	155	17	1868	1868	NUM
ejpam-5224	155	18	1861	1861	NUM
ejpam-5224	155	19	thus	thus	ADV
ejpam-5224	155	20	,	,	PUNCT
ejpam-5224	155	21	•	•	SCONJ
ejpam-5224	155	22	if	if	SCONJ
ejpam-5224	155	23	s̃i2	s̃i2	NOUN
ejpam-5224	155	24	is	be	AUX
ejpam-5224	155	25	projective	projective	ADJ
ejpam-5224	155	26	,	,	PUNCT
ejpam-5224	155	27	then	then	ADV
ejpam-5224	155	28	si2	si2	NOUN
ejpam-5224	155	29	is	be	AUX
ejpam-5224	155	30	projective	projective	ADJ
ejpam-5224	155	31	and	and	CCONJ
ejpam-5224	155	32	ext1a(si2	ext1a(si2	NOUN
ejpam-5224	155	33	,	,	PUNCT
ejpam-5224	155	34	si2	si2	NOUN
ejpam-5224	155	35	)	)	PUNCT
ejpam-5224	155	36	=	=	SYM
ejpam-5224	156	1	0	0	X
ejpam-5224	156	2	.	.	NOUN
ejpam-5224	156	3	•	•	NOUN
ejpam-5224	156	4	if	if	SCONJ
ejpam-5224	156	5	s̃i2	s̃i2	PROPN
ejpam-5224	156	6	is	be	AUX
ejpam-5224	156	7	not	not	PART
ejpam-5224	156	8	projective	projective	ADJ
ejpam-5224	156	9	,	,	PUNCT
ejpam-5224	156	10	then	then	ADV
ejpam-5224	156	11	ext1a(si2	ext1a(si2	NOUN
ejpam-5224	156	12	,	,	PUNCT
ejpam-5224	156	13	si2	si2	NOUN
ejpam-5224	156	14	)	)	PUNCT
ejpam-5224	156	15	̸=	̸=	PROPN
ejpam-5224	156	16	0	0	NUM
ejpam-5224	156	17	,	,	PUNCT
ejpam-5224	156	18	therefore	therefore	ADV
ejpam-5224	156	19	hom(jei2	hom(jei2	NOUN
ejpam-5224	156	20	,	,	PUNCT
ejpam-5224	156	21	si2	si2	NOUN
ejpam-5224	156	22	)	)	PUNCT
ejpam-5224	156	23	̸=	̸=	NOUN
ejpam-5224	156	24	0	0	NUM
ejpam-5224	156	25	and	and	CCONJ
ejpam-5224	156	26	the	the	DET
ejpam-5224	156	27	exact	exact	ADJ
ejpam-5224	156	28	sequence	sequence	NOUN
ejpam-5224	156	29	,	,	PUNCT
ejpam-5224	156	30	0	0	NUM
ejpam-5224	156	31	−→	−→	NOUN
ejpam-5224	156	32	jei2	jei2	NOUN
ejpam-5224	156	33	−→	−→	ADJ
ejpam-5224	156	34	pi2	pi2	NOUN
ejpam-5224	156	35	−→	−→	NOUN
ejpam-5224	156	36	si2	si2	NOUN
ejpam-5224	156	37	−→	−→	ADJ
ejpam-5224	156	38	0	0	NUM
ejpam-5224	156	39	will	will	AUX
ejpam-5224	156	40	not	not	PART
ejpam-5224	156	41	be	be	AUX
ejpam-5224	156	42	split	split	VERB
ejpam-5224	156	43	,	,	PUNCT
ejpam-5224	156	44	by	by	ADP
ejpam-5224	156	45	the	the	DET
ejpam-5224	156	46	same	same	ADJ
ejpam-5224	156	47	pda(si2	pda(si2	PROPN
ejpam-5224	156	48	)	)	PUNCT
ejpam-5224	156	49	≥	≥	NOUN
ejpam-5224	156	50	2	2	NUM
ejpam-5224	156	51	because	because	SCONJ
ejpam-5224	156	52	i2	i2	PROPN
ejpam-5224	156	53	/∈	/∈	PROPN
ejpam-5224	156	54	i1	i1	PROPN
ejpam-5224	156	55	and	and	CCONJ
ejpam-5224	156	56	by	by	ADP
ejpam-5224	156	57	application	application	NOUN
ejpam-5224	156	58	of	of	ADP
ejpam-5224	156	59	the	the	DET
ejpam-5224	156	60	functor	functor	PROPN
ejpam-5224	156	61	hom	hom	PROPN
ejpam-5224	156	62	(	(	PUNCT
ejpam-5224	156	63	⊕	⊕	PROPN
ejpam-5224	156	64	i∈i−i1	i∈i−i1	PRON
ejpam-5224	156	65	pi,−	pi,−	NOUN
ejpam-5224	156	66	)	)	PUNCT
ejpam-5224	156	67	,	,	PUNCT
ejpam-5224	156	68	we	we	PRON
ejpam-5224	156	69	will	will	AUX
ejpam-5224	156	70	have	have	VERB
ejpam-5224	156	71	the	the	DET
ejpam-5224	156	72	exact	exact	ADJ
ejpam-5224	156	73	sequence	sequence	NOUN
ejpam-5224	156	74	,	,	PUNCT
ejpam-5224	156	75	0	0	NUM
ejpam-5224	156	76	−→	−→	NOUN
ejpam-5224	156	77	hom	hom	PROPN
ejpam-5224	156	78	(	(	PUNCT
ejpam-5224	156	79	⊕	⊕	PROPN
ejpam-5224	156	80	i∈i−i1	i∈i−i1	PRON
ejpam-5224	156	81	pi	pi	PROPN
ejpam-5224	156	82	,	,	PUNCT
ejpam-5224	156	83	jei2	jei2	NOUN
ejpam-5224	156	84	)	)	PUNCT
ejpam-5224	157	1	−→	−→	ADV
ejpam-5224	157	2	hom	hom	PROPN
ejpam-5224	157	3	(	(	PUNCT
ejpam-5224	157	4	⊕	⊕	PROPN
ejpam-5224	157	5	i∈i−i1	i∈i−i1	PRON
ejpam-5224	157	6	pi	pi	PROPN
ejpam-5224	157	7	,	,	PUNCT
ejpam-5224	157	8	pi2	pi2	PROPN
ejpam-5224	157	9	)	)	PUNCT
ejpam-5224	157	10	−→	−→	NOUN
ejpam-5224	157	11	hom	hom	PROPN
ejpam-5224	157	12	(	(	PUNCT
ejpam-5224	157	13	⊕	⊕	PROPN
ejpam-5224	157	14	i∈i−i1	i∈i−i1	PRON
ejpam-5224	157	15	pi	pi	NOUN
ejpam-5224	157	16	,	,	PUNCT
ejpam-5224	157	17	si2	si2	NOUN
ejpam-5224	157	18	)	)	PUNCT
ejpam-5224	157	19	−→	−→	NOUN
ejpam-5224	157	20	0	0	NUM
ejpam-5224	157	21	and	and	CCONJ
ejpam-5224	157	22	since	since	SCONJ
ejpam-5224	157	23	hom	hom	ADV
ejpam-5224	157	24	(	(	PUNCT
ejpam-5224	157	25	⊕	⊕	PROPN
ejpam-5224	157	26	i∈i−i1	i∈i−i1	PRON
ejpam-5224	157	27	pi	pi	PROPN
ejpam-5224	157	28	,	,	PUNCT
ejpam-5224	157	29	jei2	jei2	PROPN
ejpam-5224	157	30	)	)	PUNCT
ejpam-5224	157	31	is	be	AUX
ejpam-5224	157	32	not	not	PART
ejpam-5224	157	33	projective	projective	ADJ
ejpam-5224	157	34	,	,	PUNCT
ejpam-5224	157	35	then	then	ADV
ejpam-5224	157	36	pdγ1(hom	pdγ1(hom	X
ejpam-5224	157	37	(	(	PUNCT
ejpam-5224	157	38	⊕	⊕	PROPN
ejpam-5224	157	39	i∈i−i1	i∈i−i1	PRON
ejpam-5224	157	40	pi	pi	NOUN
ejpam-5224	157	41	,	,	PUNCT
ejpam-5224	157	42	si2	si2	NOUN
ejpam-5224	157	43	)	)	PUNCT
ejpam-5224	157	44	>	>	X
ejpam-5224	157	45	1	1	NUM
ejpam-5224	157	46	i.e.	i.e.	X
ejpam-5224	157	47	pdγ1(s̃i2	pdγ1(s̃i2	NOUN
ejpam-5224	157	48	)	)	PUNCT
ejpam-5224	157	49	>	>	X
ejpam-5224	157	50	1	1	NUM
ejpam-5224	157	51	which	which	PRON
ejpam-5224	157	52	is	be	AUX
ejpam-5224	157	53	absurd	absurd	ADJ
ejpam-5224	157	54	,	,	PUNCT
ejpam-5224	157	55	thus	thus	ADV
ejpam-5224	157	56	ext1a(si2	ext1a(si2	NOUN
ejpam-5224	157	57	,	,	PUNCT
ejpam-5224	157	58	si2	si2	NOUN
ejpam-5224	157	59	)	)	PUNCT
ejpam-5224	157	60	=	=	SYM
ejpam-5224	157	61	0	0	PUNCT
ejpam-5224	158	1	now	now	ADV
ejpam-5224	158	2	,	,	PUNCT
ejpam-5224	158	3	to	to	PART
ejpam-5224	158	4	deduce	deduce	VERB
ejpam-5224	158	5	the	the	DET
ejpam-5224	158	6	proof	proof	NOUN
ejpam-5224	158	7	of	of	ADP
ejpam-5224	158	8	our	our	PRON
ejpam-5224	158	9	main	main	ADJ
ejpam-5224	158	10	contribution	contribution	NOUN
ejpam-5224	158	11	,	,	PUNCT
ejpam-5224	158	12	namely	namely	ADV
ejpam-5224	158	13	theorem	theorem	VERB
ejpam-5224	158	14	1.1	1.1	NUM
ejpam-5224	158	15	.	.	PUNCT
ejpam-5224	159	1	in	in	ADP
ejpam-5224	159	2	fact	fact	NOUN
ejpam-5224	159	3	,	,	PUNCT
ejpam-5224	159	4	by	by	ADP
ejpam-5224	159	5	induction	induction	NOUN
ejpam-5224	159	6	and	and	CCONJ
ejpam-5224	159	7	in	in	ADP
ejpam-5224	159	8	the	the	DET
ejpam-5224	159	9	same	same	ADJ
ejpam-5224	159	10	way	way	NOUN
ejpam-5224	159	11	,	,	PUNCT
ejpam-5224	159	12	we	we	PRON
ejpam-5224	159	13	consider	consider	VERB
ejpam-5224	159	14	the	the	DET
ejpam-5224	159	15	artin	artin	PROPN
ejpam-5224	159	16	algebras	algebra	NOUN
ejpam-5224	159	17	,	,	PUNCT
ejpam-5224	159	18	γk	γk	PROPN
ejpam-5224	159	19	=	=	PUNCT
ejpam-5224	159	20	end	end	NOUN
ejpam-5224	159	21	(	(	PUNCT
ejpam-5224	159	22	⊕	⊕	PROPN
ejpam-5224	159	23	i∈i−i1∪i2∪i3	i∈i−i1∪i2∪i3	NOUN
ejpam-5224	159	24	...	...	PUNCT
ejpam-5224	159	25	∪ik	∪ik	PROPN
ejpam-5224	159	26	pi	pi	NOUN
ejpam-5224	159	27	)	)	PUNCT
ejpam-5224	159	28	op	op	NOUN
ejpam-5224	159	29	where	where	SCONJ
ejpam-5224	159	30	ik	ik	PROPN
ejpam-5224	159	31	⊆	⊆	NUM
ejpam-5224	159	32	i	i	PRON
ejpam-5224	159	33	such	such	ADJ
ejpam-5224	159	34	as	as	ADP
ejpam-5224	159	35	top(pi	top(pi	NOUN
ejpam-5224	159	36	)	)	PUNCT
ejpam-5224	159	37	≃	≃	VERB
ejpam-5224	159	38	sik+1	sik+1	NOUN
ejpam-5224	159	39	for	for	ADP
ejpam-5224	159	40	all	all	DET
ejpam-5224	159	41	index	index	NOUN
ejpam-5224	159	42	i	i	PRON
ejpam-5224	159	43	∈	∈	PROPN
ejpam-5224	159	44	i−i1∪i2∪i3	i−i1∪i2∪i3	VERB
ejpam-5224	159	45	...	...	PUNCT
ejpam-5224	159	46	∪ik	∪ik	NOUN
ejpam-5224	159	47	and	and	CCONJ
ejpam-5224	159	48	sik+1	sik+1	NOUN
ejpam-5224	159	49	be	be	VERB
ejpam-5224	159	50	a	a	DET
ejpam-5224	159	51	simple	simple	ADJ
ejpam-5224	159	52	module	module	NOUN
ejpam-5224	159	53	of	of	ADP
ejpam-5224	159	54	minimal	minimal	ADJ
ejpam-5224	159	55	projective	projective	ADJ
ejpam-5224	159	56	dimension	dimension	NOUN
ejpam-5224	159	57	among	among	ADP
ejpam-5224	159	58	the	the	DET
ejpam-5224	159	59	simple	simple	ADJ
ejpam-5224	159	60	modules	module	NOUN
ejpam-5224	159	61	in	in	ADP
ejpam-5224	159	62	modγk	modγk	NOUN
ejpam-5224	159	63	for	for	ADP
ejpam-5224	159	64	all	all	DET
ejpam-5224	159	65	i	i	PRON
ejpam-5224	159	66	∈	∈	PROPN
ejpam-5224	160	1	i	i	PRON
ejpam-5224	160	2	−	−	PROPN
ejpam-5224	160	3	i1	i1	PROPN
ejpam-5224	160	4	∪	∪	PROPN
ejpam-5224	160	5	i2	i2	PROPN
ejpam-5224	160	6	∪	∪	PROPN
ejpam-5224	160	7	i3	i3	NOUN
ejpam-5224	160	8	...	...	PUNCT
ejpam-5224	160	9	∪	∪	ADP
ejpam-5224	160	10	ik	ik	NOUN
ejpam-5224	160	11	,	,	PUNCT
ejpam-5224	160	12	and	and	CCONJ
ejpam-5224	160	13	ext1a(sik	ext1a(sik	NOUN
ejpam-5224	160	14	,	,	PUNCT
ejpam-5224	160	15	sik	sik	ADJ
ejpam-5224	160	16	)	)	PUNCT
ejpam-5224	160	17	=	=	SYM
ejpam-5224	160	18	0	0	NUM
ejpam-5224	160	19	,	,	PUNCT
ejpam-5224	160	20	then	then	ADV
ejpam-5224	160	21	we	we	PRON
ejpam-5224	160	22	get	get	VERB
ejpam-5224	160	23	the	the	DET
ejpam-5224	160	24	result	result	NOUN
ejpam-5224	160	25	.	.	PUNCT
ejpam-5224	161	1	6	6	X
ejpam-5224	161	2	.	.	X
ejpam-5224	161	3	theoretical	theoretical	ADJ
ejpam-5224	161	4	application	application	NOUN
ejpam-5224	161	5	as	as	ADP
ejpam-5224	161	6	a	a	DET
ejpam-5224	161	7	corollary	corollary	ADJ
ejpam-5224	161	8	6.1	6.1	NUM
ejpam-5224	161	9	corollary	corollary	NOUN
ejpam-5224	161	10	.	.	PUNCT
ejpam-5224	162	1	let	let	VERB
ejpam-5224	162	2	a	a	DET
ejpam-5224	162	3	be	be	AUX
ejpam-5224	162	4	an	an	DET
ejpam-5224	162	5	artinian	artinian	ADJ
ejpam-5224	162	6	ring	ring	NOUN
ejpam-5224	162	7	with	with	ADP
ejpam-5224	162	8	radical	radical	ADJ
ejpam-5224	162	9	cubed	cubed	NOUN
ejpam-5224	162	10	zero	zero	NUM
ejpam-5224	162	11	such	such	ADJ
ejpam-5224	162	12	that	that	SCONJ
ejpam-5224	162	13	the	the	DET
ejpam-5224	162	14	projective	projective	ADJ
ejpam-5224	162	15	cover	cover	NOUN
ejpam-5224	162	16	of	of	ADP
ejpam-5224	162	17	rad(a	rad(a	PROPN
ejpam-5224	162	18	)	)	PUNCT
ejpam-5224	162	19	is	be	AUX
ejpam-5224	162	20	of	of	ADP
ejpam-5224	162	21	loewy	loewy	ADJ
ejpam-5224	162	22	length	length	NOUN
ejpam-5224	162	23	two	two	NUM
ejpam-5224	162	24	.	.	PUNCT
ejpam-5224	163	1	if	if	SCONJ
ejpam-5224	163	2	gdim(a	gdim(a	NOUN
ejpam-5224	163	3	)	)	PUNCT
ejpam-5224	163	4	is	be	AUX
ejpam-5224	163	5	finite	finite	ADJ
ejpam-5224	163	6	,	,	PUNCT
ejpam-5224	163	7	then	then	ADV
ejpam-5224	163	8	ext1a(s	ext1a(s	PROPN
ejpam-5224	163	9	,	,	PUNCT
ejpam-5224	163	10	s	s	PART
ejpam-5224	163	11	)	)	PUNCT
ejpam-5224	163	12	=	=	SYM
ejpam-5224	163	13	0	0	NUM
ejpam-5224	163	14	for	for	ADP
ejpam-5224	163	15	every	every	DET
ejpam-5224	163	16	simple	simple	ADJ
ejpam-5224	163	17	module	module	NOUN
ejpam-5224	163	18	s.	s.	PROPN
ejpam-5224	163	19	proof	proof	NOUN
ejpam-5224	163	20	.	.	PUNCT
ejpam-5224	164	1	if	if	SCONJ
ejpam-5224	164	2	rad2(p	rad2(p	NOUN
ejpam-5224	164	3	(	(	PUNCT
ejpam-5224	164	4	rad(a	rad(a	PROPN
ejpam-5224	164	5	)	)	PUNCT
ejpam-5224	164	6	)	)	PUNCT
ejpam-5224	165	1	=	=	SYM
ejpam-5224	165	2	0	0	NUM
ejpam-5224	165	3	,	,	PUNCT
ejpam-5224	165	4	then	then	ADV
ejpam-5224	165	5	rad2(p	rad2(p	NOUN
ejpam-5224	165	6	(	(	PUNCT
ejpam-5224	165	7	ω(s	ω(s	NOUN
ejpam-5224	165	8	)	)	PUNCT
ejpam-5224	165	9	)	)	PUNCT
ejpam-5224	165	10	)	)	PUNCT
ejpam-5224	166	1	=	=	SYM
ejpam-5224	166	2	0	0	NUM
ejpam-5224	166	3	for	for	ADP
ejpam-5224	166	4	all	all	DET
ejpam-5224	166	5	simple	simple	ADJ
ejpam-5224	166	6	a	a	PRON
ejpam-5224	166	7	-	-	PUNCT
ejpam-5224	166	8	modules	module	NOUN
ejpam-5224	166	9	indeed	indeed	ADV
ejpam-5224	166	10	a	a	DET
ejpam-5224	166	11	/	/	SYM
ejpam-5224	166	12	rad(a	rad(a	NOUN
ejpam-5224	166	13	)	)	PUNCT
ejpam-5224	166	14	=	=	SYM
ejpam-5224	166	15	⊕	⊕	PROPN
ejpam-5224	166	16	i∈j	i∈j	NOUN
ejpam-5224	166	17	sai	sai	PROPN
ejpam-5224	167	1	i	i	PRON
ejpam-5224	167	2	where	where	SCONJ
ejpam-5224	167	3	the	the	DET
ejpam-5224	167	4	(	(	PUNCT
ejpam-5224	167	5	si)i∈j	si)i∈j	NUM
ejpam-5224	167	6	are	be	AUX
ejpam-5224	167	7	all	all	DET
ejpam-5224	167	8	the	the	DET
ejpam-5224	167	9	a	a	DET
ejpam-5224	167	10	non	non	ADJ
ejpam-5224	167	11	-	-	ADJ
ejpam-5224	167	12	isomorphic	isomorphic	ADJ
ejpam-5224	167	13	simple	simple	ADJ
ejpam-5224	167	14	modules	module	NOUN
ejpam-5224	167	15	and	and	CCONJ
ejpam-5224	167	16	as	as	SCONJ
ejpam-5224	167	17	we	we	PRON
ejpam-5224	167	18	have	have	VERB
ejpam-5224	167	19	the	the	DET
ejpam-5224	167	20	exact	exact	ADJ
ejpam-5224	167	21	sequence	sequence	NOUN
ejpam-5224	167	22	,	,	PUNCT
ejpam-5224	167	23	0	0	NUM
ejpam-5224	167	24	//	//	SYM
ejpam-5224	167	25	rad(a	rad(a	PROPN
ejpam-5224	167	26	)	)	PUNCT
ejpam-5224	167	27	//	//	NOUN
ejpam-5224	167	28	a	a	DET
ejpam-5224	167	29	//	//	PUNCT
ejpam-5224	167	30	a	a	X
ejpam-5224	167	31	/	/	SYM
ejpam-5224	167	32	rad(a	rad(a	PROPN
ejpam-5224	167	33	)	)	PUNCT
ejpam-5224	167	34	//	//	NOUN
ejpam-5224	167	35	0	0	PUNCT
ejpam-5224	168	1	then	then	ADV
ejpam-5224	168	2	,	,	PUNCT
ejpam-5224	168	3	ω(a	ω(a	PROPN
ejpam-5224	168	4	/	/	SYM
ejpam-5224	168	5	rad(a	rad(a	PROPN
ejpam-5224	168	6	)	)	PUNCT
ejpam-5224	168	7	)	)	PUNCT
ejpam-5224	169	1	=	=	SYM
ejpam-5224	169	2	rad(a	rad(a	X
ejpam-5224	169	3	)	)	PUNCT
ejpam-5224	169	4	and	and	CCONJ
ejpam-5224	169	5	if	if	SCONJ
ejpam-5224	169	6	rad2(p	rad2(p	NOUN
ejpam-5224	169	7	(	(	PUNCT
ejpam-5224	169	8	rad(a	rad(a	PROPN
ejpam-5224	169	9	)	)	PUNCT
ejpam-5224	169	10	)	)	PUNCT
ejpam-5224	169	11	)	)	PUNCT
ejpam-5224	170	1	=	=	SYM
ejpam-5224	170	2	0	0	NUM
ejpam-5224	170	3	,	,	PUNCT
ejpam-5224	170	4	then	then	ADV
ejpam-5224	170	5	,	,	PUNCT
ejpam-5224	170	6	rad2(p	rad2(p	NOUN
ejpam-5224	170	7	(	(	PUNCT
ejpam-5224	170	8	ω(a	ω(a	PROPN
ejpam-5224	170	9	/	/	SYM
ejpam-5224	170	10	rad(a	rad(a	PROPN
ejpam-5224	170	11	)	)	PUNCT
ejpam-5224	170	12	)	)	PUNCT
ejpam-5224	170	13	)	)	PUNCT
ejpam-5224	170	14	)	)	PUNCT
ejpam-5224	171	1	=	=	PUNCT
ejpam-5224	171	2	0	0	NUM
ejpam-5224	171	3	,	,	PUNCT
ejpam-5224	171	4	then	then	ADV
ejpam-5224	171	5	we	we	PRON
ejpam-5224	171	6	have	have	VERB
ejpam-5224	171	7	rad2(p	rad2(p	NOUN
ejpam-5224	171	8	(	(	PUNCT
ejpam-5224	171	9	ω(si	ω(si	PROPN
ejpam-5224	171	10	)	)	PUNCT
ejpam-5224	171	11	)	)	PUNCT
ejpam-5224	171	12	)	)	PUNCT
ejpam-5224	172	1	=	=	SYM
ejpam-5224	172	2	0	0	PUNCT
ejpam-5224	173	1	and	and	CCONJ
ejpam-5224	173	2	according	accord	VERB
ejpam-5224	173	3	to	to	ADP
ejpam-5224	173	4	the	the	DET
ejpam-5224	173	5	theorem	theorem	NOUN
ejpam-5224	173	6	3.4	3.4	NUM
ejpam-5224	173	7	,	,	PUNCT
ejpam-5224	173	8	we	we	PRON
ejpam-5224	173	9	obtain	obtain	VERB
ejpam-5224	173	10	ext1a(s	ext1a(s	PROPN
ejpam-5224	173	11	,	,	PUNCT
ejpam-5224	173	12	s	s	PART
ejpam-5224	173	13	)	)	PUNCT
ejpam-5224	173	14	=	=	SYM
ejpam-5224	173	15	0	0	X
ejpam-5224	173	16	.	.	PUNCT
ejpam-5224	173	17	m.	m.	NOUN
ejpam-5224	173	18	laaraj	laaraj	PROPN
ejpam-5224	173	19	,	,	PUNCT
ejpam-5224	173	20	s.	s.	PROPN
ejpam-5224	173	21	abdelalim	abdelalim	PROPN
ejpam-5224	173	22	,	,	PUNCT
ejpam-5224	173	23	i.elmouki	i.elmouki	CCONJ
ejpam-5224	173	24	/	/	SYM
ejpam-5224	173	25	eur	eur	NOUN
ejpam-5224	173	26	.	.	PUNCT
ejpam-5224	174	1	j.	j.	PROPN
ejpam-5224	174	2	pure	pure	PROPN
ejpam-5224	174	3	appl	appl	PROPN
ejpam-5224	174	4	.	.	PROPN
ejpam-5224	174	5	math	math	PROPN
ejpam-5224	174	6	,	,	PUNCT
ejpam-5224	174	7	17	17	NUM
ejpam-5224	174	8	(	(	PUNCT
ejpam-5224	174	9	3	3	NUM
ejpam-5224	174	10	)	)	PUNCT
ejpam-5224	174	11	(	(	PUNCT
ejpam-5224	174	12	2024	2024	NUM
ejpam-5224	174	13	)	)	PUNCT
ejpam-5224	174	14	,	,	PUNCT
ejpam-5224	174	15	1855	1855	NUM
ejpam-5224	174	16	-	-	SYM
ejpam-5224	174	17	1868	1868	NUM
ejpam-5224	174	18	1862	1862	NUM
ejpam-5224	174	19	7	7	NUM
ejpam-5224	174	20	.	.	PUNCT
ejpam-5224	175	1	discussions	discussion	NOUN
ejpam-5224	175	2	by	by	ADP
ejpam-5224	175	3	practical	practical	ADJ
ejpam-5224	175	4	examples	example	NOUN
ejpam-5224	175	5	7.1	7.1	NUM
ejpam-5224	175	6	.	.	PUNCT
ejpam-5224	176	1	couterexample	couterexample	NOUN
ejpam-5224	176	2	to	to	PART
ejpam-5224	176	3	theorem	theorem	VERB
ejpam-5224	176	4	2.3	2.3	NUM
ejpam-5224	176	5	the	the	DET
ejpam-5224	176	6	condition	condition	NOUN
ejpam-5224	176	7	pd(s	pd(s	NUM
ejpam-5224	176	8	)	)	PUNCT
ejpam-5224	176	9	≤	≤	NUM
ejpam-5224	176	10	1	1	NUM
ejpam-5224	176	11	is	be	AUX
ejpam-5224	176	12	not	not	PART
ejpam-5224	176	13	necessary	necessary	ADJ
ejpam-5224	176	14	but	but	CCONJ
ejpam-5224	176	15	its	its	PRON
ejpam-5224	176	16	consideration	consideration	NOUN
ejpam-5224	176	17	let	let	VERB
ejpam-5224	176	18	us	we	PRON
ejpam-5224	176	19	be	be	AUX
ejpam-5224	176	20	sure	sure	ADJ
ejpam-5224	176	21	to	to	PART
ejpam-5224	176	22	get	get	VERB
ejpam-5224	176	23	ext1a(s	ext1a(s	PROPN
ejpam-5224	176	24	,	,	PUNCT
ejpam-5224	176	25	s	s	PART
ejpam-5224	176	26	)	)	PUNCT
ejpam-5224	176	27	=	=	SYM
ejpam-5224	176	28	0	0	NUM
ejpam-5224	177	1	which	which	PRON
ejpam-5224	177	2	is	be	AUX
ejpam-5224	177	3	the	the	DET
ejpam-5224	177	4	more	more	ADV
ejpam-5224	177	5	practical	practical	ADJ
ejpam-5224	177	6	result	result	NOUN
ejpam-5224	177	7	as	as	SCONJ
ejpam-5224	177	8	it	it	PRON
ejpam-5224	177	9	leads	lead	VERB
ejpam-5224	177	10	to	to	ADP
ejpam-5224	177	11	the	the	DET
ejpam-5224	177	12	existence	existence	NOUN
ejpam-5224	177	13	of	of	ADP
ejpam-5224	177	14	the	the	DET
ejpam-5224	177	15	arrows	arrow	NOUN
ejpam-5224	177	16	in	in	ADP
ejpam-5224	177	17	the	the	DET
ejpam-5224	177	18	extension	extension	NOUN
ejpam-5224	177	19	quiver	quiver	NOUN
ejpam-5224	177	20	.	.	PUNCT
ejpam-5224	178	1	this	this	PRON
ejpam-5224	178	2	is	be	AUX
ejpam-5224	178	3	just	just	ADV
ejpam-5224	178	4	to	to	PART
ejpam-5224	178	5	say	say	VERB
ejpam-5224	178	6	that	that	SCONJ
ejpam-5224	178	7	we	we	PRON
ejpam-5224	178	8	should	should	AUX
ejpam-5224	178	9	not	not	PART
ejpam-5224	178	10	deny	deny	VERB
ejpam-5224	178	11	that	that	SCONJ
ejpam-5224	178	12	there	there	PRON
ejpam-5224	178	13	may	may	AUX
ejpam-5224	178	14	be	be	AUX
ejpam-5224	178	15	some	some	DET
ejpam-5224	178	16	particular	particular	ADJ
ejpam-5224	178	17	cases	case	NOUN
ejpam-5224	178	18	where	where	SCONJ
ejpam-5224	178	19	we	we	PRON
ejpam-5224	178	20	may	may	AUX
ejpam-5224	178	21	have	have	VERB
ejpam-5224	178	22	ext1a(s	ext1a(s	PROPN
ejpam-5224	178	23	,	,	PUNCT
ejpam-5224	178	24	s	s	PART
ejpam-5224	178	25	)	)	PUNCT
ejpam-5224	178	26	=	=	SYM
ejpam-5224	178	27	0	0	PUNCT
ejpam-5224	179	1	even	even	ADV
ejpam-5224	179	2	if	if	SCONJ
ejpam-5224	179	3	pd(s	pd(s	NUM
ejpam-5224	179	4	)	)	PUNCT
ejpam-5224	179	5	>	>	X
ejpam-5224	179	6	1	1	NUM
ejpam-5224	179	7	as	as	SCONJ
ejpam-5224	179	8	we	we	PRON
ejpam-5224	179	9	can	can	AUX
ejpam-5224	179	10	illustrate	illustrate	VERB
ejpam-5224	179	11	in	in	ADP
ejpam-5224	179	12	the	the	DET
ejpam-5224	179	13	following	follow	VERB
ejpam-5224	179	14	example	example	NOUN
ejpam-5224	179	15	.	.	PUNCT
ejpam-5224	180	1	7.1	7.1	NUM
ejpam-5224	180	2	example	example	NOUN
ejpam-5224	180	3	.	.	PUNCT
ejpam-5224	181	1	consider	consider	VERB
ejpam-5224	181	2	the	the	DET
ejpam-5224	181	3	quiver	quiver	NOUN
ejpam-5224	181	4	1	1	NUM
ejpam-5224	181	5	2	2	NUM
ejpam-5224	181	6	3	3	NUM
ejpam-5224	181	7	4	4	NUM
ejpam-5224	181	8	5a	5a	NUM
ejpam-5224	181	9	b	b	NOUN
ejpam-5224	181	10	c	c	NOUN
ejpam-5224	181	11	d	d	NOUN
ejpam-5224	181	12	and	and	CCONJ
ejpam-5224	181	13	let	let	VERB
ejpam-5224	181	14	a	a	DET
ejpam-5224	181	15	=	=	SYM
ejpam-5224	181	16	kq	kq	PROPN
ejpam-5224	181	17	/	/	SYM
ejpam-5224	181	18	i	i	PRON
ejpam-5224	181	19	be	be	VERB
ejpam-5224	181	20	its	its	PRON
ejpam-5224	181	21	quiver	quiver	NOUN
ejpam-5224	181	22	algebra	algebra	NOUN
ejpam-5224	181	23	bounded	bound	VERB
ejpam-5224	181	24	by	by	ADP
ejpam-5224	181	25	i	i	PROPN
ejpam-5224	181	26	=	=	NOUN
ejpam-5224	181	27	<	<	X
ejpam-5224	181	28	abc	abc	PROPN
ejpam-5224	181	29	,	,	PUNCT
ejpam-5224	181	30	cd	cd	PROPN
ejpam-5224	181	31	>	>	PUNCT
ejpam-5224	181	32	.	.	PUNCT
ejpam-5224	182	1	we	we	PRON
ejpam-5224	182	2	have	have	VERB
ejpam-5224	182	3	the	the	DET
ejpam-5224	182	4	list	list	NOUN
ejpam-5224	182	5	of	of	ADP
ejpam-5224	182	6	all	all	DET
ejpam-5224	182	7	projective	projective	ADJ
ejpam-5224	182	8	and	and	CCONJ
ejpam-5224	182	9	indecomposable	indecomposable	ADJ
ejpam-5224	182	10	modules	module	NOUN
ejpam-5224	182	11	,	,	PUNCT
ejpam-5224	182	12	p	p	X
ejpam-5224	182	13	(	(	PUNCT
ejpam-5224	182	14	1	1	NUM
ejpam-5224	182	15	)	)	PUNCT
ejpam-5224	182	16	:	:	PUNCT
ejpam-5224	183	1	k	k	X
ejpam-5224	183	2	−→	−→	NOUN
ejpam-5224	183	3	k	k	INTJ
ejpam-5224	183	4	−→	−→	NOUN
ejpam-5224	184	1	k	k	INTJ
ejpam-5224	184	2	−→	−→	NOUN
ejpam-5224	184	3	0	0	NUM
ejpam-5224	185	1	−→	−→	NOUN
ejpam-5224	185	2	0	0	NUM
ejpam-5224	186	1	p	p	NOUN
ejpam-5224	186	2	(	(	PUNCT
ejpam-5224	186	3	2	2	NUM
ejpam-5224	186	4	)	)	PUNCT
ejpam-5224	186	5	:	:	PUNCT
ejpam-5224	186	6	0	0	NUM
ejpam-5224	187	1	−→	−→	NOUN
ejpam-5224	187	2	k	k	INTJ
ejpam-5224	187	3	−→	−→	NOUN
ejpam-5224	188	1	k	k	INTJ
ejpam-5224	188	2	−→	−→	NOUN
ejpam-5224	189	1	k	k	INTJ
ejpam-5224	189	2	−→	−→	NOUN
ejpam-5224	189	3	0	0	PUNCT
ejpam-5224	190	1	p	p	NOUN
ejpam-5224	190	2	(	(	PUNCT
ejpam-5224	190	3	3	3	NUM
ejpam-5224	190	4	)	)	PUNCT
ejpam-5224	190	5	:	:	PUNCT
ejpam-5224	190	6	0	0	NUM
ejpam-5224	191	1	−→	−→	NOUN
ejpam-5224	191	2	0	0	NUM
ejpam-5224	191	3	−→	−→	NOUN
ejpam-5224	191	4	k	k	INTJ
ejpam-5224	191	5	−→	−→	NOUN
ejpam-5224	192	1	k	k	INTJ
ejpam-5224	192	2	−→	−→	NOUN
ejpam-5224	192	3	0	0	PUNCT
ejpam-5224	193	1	p	p	NOUN
ejpam-5224	193	2	(	(	PUNCT
ejpam-5224	193	3	4	4	NUM
ejpam-5224	193	4	)	)	PUNCT
ejpam-5224	193	5	:	:	PUNCT
ejpam-5224	193	6	0	0	NUM
ejpam-5224	194	1	−→	−→	NOUN
ejpam-5224	194	2	0	0	NUM
ejpam-5224	194	3	−→	−→	NOUN
ejpam-5224	194	4	0	0	NUM
ejpam-5224	194	5	−→	−→	NOUN
ejpam-5224	194	6	k	k	INTJ
ejpam-5224	194	7	−→	−→	NOUN
ejpam-5224	195	1	k	k	PROPN
ejpam-5224	195	2	p	p	X
ejpam-5224	195	3	(	(	PUNCT
ejpam-5224	195	4	5	5	NUM
ejpam-5224	195	5	)	)	PUNCT
ejpam-5224	195	6	:	:	PUNCT
ejpam-5224	195	7	0	0	NUM
ejpam-5224	196	1	−→	−→	NOUN
ejpam-5224	196	2	0	0	NUM
ejpam-5224	196	3	−→	−→	NOUN
ejpam-5224	196	4	0	0	NUM
ejpam-5224	196	5	−→	−→	NOUN
ejpam-5224	196	6	0	0	NUM
ejpam-5224	196	7	−→	−→	NOUN
ejpam-5224	196	8	k	k	PROPN
ejpam-5224	196	9	and	and	CCONJ
ejpam-5224	196	10	also	also	ADV
ejpam-5224	196	11	,	,	PUNCT
ejpam-5224	196	12	s(1	s(1	PROPN
ejpam-5224	196	13	)	)	PUNCT
ejpam-5224	196	14	:	:	PUNCT
ejpam-5224	197	1	k	k	X
ejpam-5224	197	2	−→	−→	NOUN
ejpam-5224	197	3	0	0	NUM
ejpam-5224	197	4	−→	−→	NOUN
ejpam-5224	197	5	0	0	NUM
ejpam-5224	197	6	−→	−→	NOUN
ejpam-5224	197	7	0	0	NUM
ejpam-5224	197	8	−→	−→	NOUN
ejpam-5224	197	9	0	0	NUM
ejpam-5224	197	10	is	be	AUX
ejpam-5224	197	11	the	the	DET
ejpam-5224	197	12	simple	simple	ADJ
ejpam-5224	197	13	module	module	NOUN
ejpam-5224	197	14	corresponding	correspond	VERB
ejpam-5224	197	15	to	to	ADP
ejpam-5224	197	16	vertices	vertex	NOUN
ejpam-5224	197	17	1	1	NUM
ejpam-5224	197	18	which	which	PRON
ejpam-5224	197	19	is	be	AUX
ejpam-5224	197	20	injective	injective	ADJ
ejpam-5224	197	21	and	and	CCONJ
ejpam-5224	197	22	coincides	coincide	VERB
ejpam-5224	197	23	by	by	ADP
ejpam-5224	197	24	i(1	i(1	PROPN
ejpam-5224	197	25	)	)	PUNCT
ejpam-5224	197	26	.	.	PUNCT
ejpam-5224	198	1	then	then	ADV
ejpam-5224	198	2	,	,	PUNCT
ejpam-5224	198	3	ext1a(s(1	ext1a(s(1	PROPN
ejpam-5224	198	4	)	)	PUNCT
ejpam-5224	198	5	,	,	PUNCT
ejpam-5224	198	6	s(1	s(1	PROPN
ejpam-5224	198	7	)	)	PUNCT
ejpam-5224	198	8	)	)	PUNCT
ejpam-5224	198	9	=	=	PUNCT
ejpam-5224	198	10	0	0	PUNCT
ejpam-5224	198	11	because	because	SCONJ
ejpam-5224	198	12	s(1	s(1	PROPN
ejpam-5224	198	13	)	)	PUNCT
ejpam-5224	198	14	is	be	AUX
ejpam-5224	198	15	an	an	DET
ejpam-5224	198	16	injective	injective	ADJ
ejpam-5224	198	17	module	module	NOUN
ejpam-5224	198	18	and	and	CCONJ
ejpam-5224	198	19	we	we	PRON
ejpam-5224	198	20	have	have	VERB
ejpam-5224	198	21	,	,	PUNCT
ejpam-5224	199	1	0	0	NUM
ejpam-5224	199	2	−→	−→	NOUN
ejpam-5224	199	3	p	p	X
ejpam-5224	199	4	(	(	PUNCT
ejpam-5224	199	5	5	5	NUM
ejpam-5224	199	6	)	)	PUNCT
ejpam-5224	199	7	−→	−→	NOUN
ejpam-5224	199	8	p	p	X
ejpam-5224	199	9	(	(	PUNCT
ejpam-5224	199	10	4	4	NUM
ejpam-5224	199	11	)	)	PUNCT
ejpam-5224	199	12	−→	−→	NOUN
ejpam-5224	199	13	p	p	X
ejpam-5224	199	14	(	(	PUNCT
ejpam-5224	199	15	2	2	NUM
ejpam-5224	199	16	)	)	PUNCT
ejpam-5224	199	17	−→	−→	NOUN
ejpam-5224	199	18	p	p	X
ejpam-5224	199	19	(	(	PUNCT
ejpam-5224	199	20	1	1	NUM
ejpam-5224	199	21	)	)	PUNCT
ejpam-5224	199	22	−→	−→	PROPN
ejpam-5224	199	23	s(1	s(1	PROPN
ejpam-5224	199	24	)	)	PUNCT
ejpam-5224	199	25	−→	−→	NOUN
ejpam-5224	199	26	0	0	NUM
ejpam-5224	199	27	which	which	PRON
ejpam-5224	199	28	implies	imply	VERB
ejpam-5224	199	29	that	that	SCONJ
ejpam-5224	199	30	pd(s	pd(s	PUNCT
ejpam-5224	199	31	)	)	PUNCT
ejpam-5224	199	32	=	=	PUNCT
ejpam-5224	199	33	3	3	NUM
ejpam-5224	199	34	7.2	7.2	NUM
ejpam-5224	199	35	.	.	PUNCT
ejpam-5224	200	1	weak	weak	ADJ
ejpam-5224	200	2	no	no	DET
ejpam-5224	200	3	loop	loop	NOUN
ejpam-5224	200	4	conjecture	conjecture	NOUN
ejpam-5224	200	5	in	in	ADP
ejpam-5224	200	6	what	what	PRON
ejpam-5224	200	7	follows	follow	VERB
ejpam-5224	200	8	,	,	PUNCT
ejpam-5224	200	9	we	we	PRON
ejpam-5224	200	10	provide	provide	VERB
ejpam-5224	200	11	an	an	DET
ejpam-5224	200	12	example	example	NOUN
ejpam-5224	200	13	for	for	ADP
ejpam-5224	200	14	the	the	DET
ejpam-5224	200	15	resolution	resolution	NOUN
ejpam-5224	200	16	of	of	ADP
ejpam-5224	200	17	the	the	DET
ejpam-5224	200	18	weak	weak	ADJ
ejpam-5224	200	19	no	no	DET
ejpam-5224	200	20	loop	loop	NOUN
ejpam-5224	200	21	conjecture	conjecture	NOUN
ejpam-5224	200	22	,	,	PUNCT
ejpam-5224	200	23	by	by	ADP
ejpam-5224	200	24	taking	take	VERB
ejpam-5224	200	25	a	a	DET
ejpam-5224	200	26	quiver	quiver	NOUN
ejpam-5224	200	27	algebra	algebra	NOUN
ejpam-5224	200	28	a	a	DET
ejpam-5224	200	29	verifying	verifying	NOUN
ejpam-5224	200	30	j3	j3	PROPN
ejpam-5224	200	31	=	=	SYM
ejpam-5224	200	32	0	0	PROPN
ejpam-5224	200	33	and	and	CCONJ
ejpam-5224	200	34	without	without	ADP
ejpam-5224	200	35	considering	consider	VERB
ejpam-5224	200	36	that	that	SCONJ
ejpam-5224	200	37	rad2(p	rad2(p	NOUN
ejpam-5224	200	38	(	(	PUNCT
ejpam-5224	200	39	ω(s	ω(s	NOUN
ejpam-5224	200	40	)	)	PUNCT
ejpam-5224	200	41	)	)	PUNCT
ejpam-5224	200	42	)	)	PUNCT
ejpam-5224	201	1	=	=	SYM
ejpam-5224	201	2	0	0	NUM
ejpam-5224	201	3	for	for	ADP
ejpam-5224	201	4	every	every	DET
ejpam-5224	201	5	simple	simple	ADJ
ejpam-5224	201	6	module	module	NOUN
ejpam-5224	201	7	and	and	CCONJ
ejpam-5224	201	8	that	that	PRON
ejpam-5224	201	9	is	be	AUX
ejpam-5224	201	10	to	to	PART
ejpam-5224	201	11	say	say	VERB
ejpam-5224	201	12	that	that	SCONJ
ejpam-5224	201	13	we	we	PRON
ejpam-5224	201	14	may	may	AUX
ejpam-5224	201	15	have	have	VERB
ejpam-5224	201	16	some	some	PRON
ejpam-5224	201	17	of	of	ADP
ejpam-5224	201	18	these	these	DET
ejpam-5224	201	19	modules	module	NOUN
ejpam-5224	201	20	checking	check	VERB
ejpam-5224	201	21	this	this	DET
ejpam-5224	201	22	condition	condition	NOUN
ejpam-5224	201	23	.	.	PUNCT
ejpam-5224	202	1	this	this	PRON
ejpam-5224	202	2	is	be	AUX
ejpam-5224	202	3	introduced	introduce	VERB
ejpam-5224	202	4	just	just	ADV
ejpam-5224	202	5	to	to	PART
ejpam-5224	202	6	help	help	VERB
ejpam-5224	202	7	the	the	DET
ejpam-5224	202	8	reader	reader	NOUN
ejpam-5224	202	9	to	to	PART
ejpam-5224	202	10	get	get	AUX
ejpam-5224	202	11	used	use	VERB
ejpam-5224	202	12	and	and	CCONJ
ejpam-5224	202	13	understand	understand	VERB
ejpam-5224	202	14	the	the	DET
ejpam-5224	202	15	steps	step	NOUN
ejpam-5224	202	16	followed	follow	VERB
ejpam-5224	202	17	in	in	ADP
ejpam-5224	202	18	our	our	PRON
ejpam-5224	202	19	main	main	ADJ
ejpam-5224	202	20	final	final	ADJ
ejpam-5224	202	21	example	example	NOUN
ejpam-5224	202	22	and	and	CCONJ
ejpam-5224	202	23	which	which	PRON
ejpam-5224	202	24	the	the	DET
ejpam-5224	202	25	strong	strong	ADJ
ejpam-5224	202	26	no	no	DET
ejpam-5224	202	27	loop	loop	NOUN
ejpam-5224	202	28	conjecture	conjecture	NOUN
ejpam-5224	202	29	.	.	PUNCT
ejpam-5224	203	1	7.2	7.2	NUM
ejpam-5224	203	2	example	example	NOUN
ejpam-5224	203	3	.	.	PUNCT
ejpam-5224	204	1	consider	consider	VERB
ejpam-5224	204	2	the	the	DET
ejpam-5224	204	3	quiver	quiver	NOUN
ejpam-5224	204	4	defined	define	VERB
ejpam-5224	204	5	by	by	ADP
ejpam-5224	204	6	:	:	PUNCT
ejpam-5224	204	7	m.	m.	NOUN
ejpam-5224	204	8	laaraj	laaraj	PROPN
ejpam-5224	204	9	,	,	PUNCT
ejpam-5224	204	10	s.	s.	PROPN
ejpam-5224	204	11	abdelalim	abdelalim	PROPN
ejpam-5224	204	12	,	,	PUNCT
ejpam-5224	204	13	i.elmouki	i.elmouki	CCONJ
ejpam-5224	204	14	/	/	SYM
ejpam-5224	204	15	eur	eur	NOUN
ejpam-5224	204	16	.	.	PUNCT
ejpam-5224	205	1	j.	j.	PROPN
ejpam-5224	205	2	pure	pure	PROPN
ejpam-5224	205	3	appl	appl	PROPN
ejpam-5224	205	4	.	.	PROPN
ejpam-5224	205	5	math	math	PROPN
ejpam-5224	205	6	,	,	PUNCT
ejpam-5224	205	7	17	17	NUM
ejpam-5224	205	8	(	(	PUNCT
ejpam-5224	205	9	3	3	NUM
ejpam-5224	205	10	)	)	PUNCT
ejpam-5224	205	11	(	(	PUNCT
ejpam-5224	205	12	2024	2024	NUM
ejpam-5224	205	13	)	)	PUNCT
ejpam-5224	205	14	,	,	PUNCT
ejpam-5224	205	15	1855	1855	NUM
ejpam-5224	205	16	-	-	SYM
ejpam-5224	205	17	1868	1868	NUM
ejpam-5224	205	18	1863	1863	NUM
ejpam-5224	205	19	4	4	NUM
ejpam-5224	205	20	1	1	NUM
ejpam-5224	205	21	2	2	NUM
ejpam-5224	205	22	3	3	NUM
ejpam-5224	205	23	5	5	NUM
ejpam-5224	205	24	a	a	DET
ejpam-5224	205	25	b	b	NOUN
ejpam-5224	205	26	c	c	NOUN
ejpam-5224	205	27	e	e	NOUN
ejpam-5224	205	28	d	d	PROPN
ejpam-5224	205	29	and	and	CCONJ
ejpam-5224	205	30	let	let	VERB
ejpam-5224	205	31	a	a	DET
ejpam-5224	205	32	=	=	SYM
ejpam-5224	205	33	kq	kq	PROPN
ejpam-5224	205	34	/	/	SYM
ejpam-5224	205	35	i	i	PRON
ejpam-5224	205	36	its	its	PRON
ejpam-5224	205	37	quiver	quiver	NOUN
ejpam-5224	205	38	algebra	algebra	NOUN
ejpam-5224	205	39	bounded	bound	VERB
ejpam-5224	205	40	by	by	ADP
ejpam-5224	205	41	i	i	PROPN
ejpam-5224	205	42	=	=	PROPN
ejpam-5224	205	43	<	<	X
ejpam-5224	205	44	ab	ab	PROPN
ejpam-5224	205	45	,	,	PUNCT
ejpam-5224	205	46	ac	ac	PROPN
ejpam-5224	205	47	>	>	X
ejpam-5224	206	1	it	it	PRON
ejpam-5224	206	2	’s	’	VERB
ejpam-5224	206	3	clear	clear	ADJ
ejpam-5224	206	4	that	that	SCONJ
ejpam-5224	206	5	any	any	DET
ejpam-5224	206	6	path	path	NOUN
ejpam-5224	206	7	of	of	ADP
ejpam-5224	206	8	length	length	NOUN
ejpam-5224	206	9	3	3	NUM
ejpam-5224	206	10	is	be	AUX
ejpam-5224	206	11	null	null	ADJ
ejpam-5224	206	12	therefore	therefore	ADV
ejpam-5224	206	13	rad3(a	rad3(a	NUM
ejpam-5224	206	14	)	)	PUNCT
ejpam-5224	206	15	=	=	SYM
ejpam-5224	206	16	0	0	PUNCT
ejpam-5224	207	1	and	and	CCONJ
ejpam-5224	207	2	we	we	PRON
ejpam-5224	207	3	listed	list	VERB
ejpam-5224	207	4	the	the	DET
ejpam-5224	207	5	way	way	NOUN
ejpam-5224	207	6	how	how	SCONJ
ejpam-5224	207	7	to	to	PART
ejpam-5224	207	8	find	find	VERB
ejpam-5224	207	9	the	the	DET
ejpam-5224	207	10	resolution	resolution	NOUN
ejpam-5224	207	11	projectives	projective	NOUN
ejpam-5224	207	12	of	of	ADP
ejpam-5224	207	13	any	any	DET
ejpam-5224	207	14	simple	simple	ADJ
ejpam-5224	207	15	a	a	PRON
ejpam-5224	207	16	-	-	PUNCT
ejpam-5224	207	17	module	module	NOUN
ejpam-5224	207	18	in	in	ADP
ejpam-5224	207	19	our	our	PRON
ejpam-5224	207	20	example	example	NOUN
ejpam-5224	207	21	:	:	PUNCT
ejpam-5224	207	22	we	we	PRON
ejpam-5224	207	23	have	have	VERB
ejpam-5224	207	24	0	0	NUM
ejpam-5224	207	25	p	p	NOUN
ejpam-5224	207	26	(	(	PUNCT
ejpam-5224	207	27	1	1	NUM
ejpam-5224	207	28	)	)	PUNCT
ejpam-5224	207	29	:	:	PUNCT
ejpam-5224	208	1	k	k	PROPN
ejpam-5224	208	2	k	k	PROPN
ejpam-5224	208	3	0	0	PUNCT
ejpam-5224	208	4	0	0	NUM
ejpam-5224	208	5	k2	k2	PROPN
ejpam-5224	208	6	p	p	PROPN
ejpam-5224	208	7	(	(	PUNCT
ejpam-5224	208	8	2	2	NUM
ejpam-5224	208	9	)	)	PUNCT
ejpam-5224	208	10	:	:	PUNCT
ejpam-5224	208	11	0	0	NUM
ejpam-5224	209	1	k	k	PROPN
ejpam-5224	209	2	k2	k2	PROPN
ejpam-5224	209	3	k2	k2	PROPN
ejpam-5224	209	4	k	k	PROPN
ejpam-5224	209	5	p	p	X
ejpam-5224	209	6	(	(	PUNCT
ejpam-5224	209	7	3	3	NUM
ejpam-5224	209	8	)	)	PUNCT
ejpam-5224	209	9	:	:	PUNCT
ejpam-5224	209	10	0	0	NUM
ejpam-5224	209	11	0	0	NUM
ejpam-5224	210	1	k	k	X
ejpam-5224	210	2	k	k	PROPN
ejpam-5224	211	1	k	k	PROPN
ejpam-5224	211	2	p	p	X
ejpam-5224	211	3	(	(	PUNCT
ejpam-5224	211	4	4	4	NUM
ejpam-5224	211	5	)	)	PUNCT
ejpam-5224	211	6	:	:	PUNCT
ejpam-5224	211	7	0	0	NUM
ejpam-5224	211	8	0	0	NUM
ejpam-5224	211	9	0	0	NUM
ejpam-5224	211	10	0	0	NUM
ejpam-5224	211	11	0	0	NUM
ejpam-5224	212	1	p	p	NOUN
ejpam-5224	212	2	(	(	PUNCT
ejpam-5224	212	3	5	5	NUM
ejpam-5224	212	4	)	)	PUNCT
ejpam-5224	212	5	:	:	PUNCT
ejpam-5224	212	6	0	0	NUM
ejpam-5224	212	7	0	0	NUM
ejpam-5224	212	8	0	0	NUM
ejpam-5224	213	1	k	k	PROPN
ejpam-5224	213	2	m.	m.	NOUN
ejpam-5224	213	3	laaraj	laaraj	PROPN
ejpam-5224	213	4	,	,	PUNCT
ejpam-5224	213	5	s.	s.	PROPN
ejpam-5224	213	6	abdelalim	abdelalim	PROPN
ejpam-5224	213	7	,	,	PUNCT
ejpam-5224	213	8	i.elmouki	i.elmouki	CCONJ
ejpam-5224	213	9	/	/	SYM
ejpam-5224	213	10	eur	eur	NOUN
ejpam-5224	213	11	.	.	PUNCT
ejpam-5224	214	1	j.	j.	PROPN
ejpam-5224	214	2	pure	pure	PROPN
ejpam-5224	214	3	appl	appl	PROPN
ejpam-5224	214	4	.	.	PROPN
ejpam-5224	214	5	math	math	PROPN
ejpam-5224	214	6	,	,	PUNCT
ejpam-5224	214	7	17	17	NUM
ejpam-5224	214	8	(	(	PUNCT
ejpam-5224	214	9	3	3	NUM
ejpam-5224	214	10	)	)	PUNCT
ejpam-5224	214	11	(	(	PUNCT
ejpam-5224	214	12	2024	2024	NUM
ejpam-5224	214	13	)	)	PUNCT
ejpam-5224	214	14	,	,	PUNCT
ejpam-5224	214	15	1855	1855	NUM
ejpam-5224	214	16	-	-	SYM
ejpam-5224	214	17	1868	1868	NUM
ejpam-5224	214	18	1864	1864	NUM
ejpam-5224	214	19	and	and	CCONJ
ejpam-5224	214	20	we	we	PRON
ejpam-5224	214	21	also	also	ADV
ejpam-5224	214	22	have	have	VERB
ejpam-5224	214	23	,	,	PUNCT
ejpam-5224	214	24	0	0	NUM
ejpam-5224	214	25	−→	−→	NOUN
ejpam-5224	214	26	ω(s(1	ω(s(1	PROPN
ejpam-5224	214	27	)	)	PUNCT
ejpam-5224	214	28	)	)	PUNCT
ejpam-5224	215	1	−→	−→	NOUN
ejpam-5224	215	2	p	p	X
ejpam-5224	215	3	(	(	PUNCT
ejpam-5224	215	4	1	1	NUM
ejpam-5224	215	5	)	)	PUNCT
ejpam-5224	215	6	−→	−→	PROPN
ejpam-5224	215	7	s(1	s(1	PROPN
ejpam-5224	215	8	)	)	PUNCT
ejpam-5224	215	9	−→	−→	NOUN
ejpam-5224	215	10	0	0	NUM
ejpam-5224	215	11	with	with	ADP
ejpam-5224	215	12	,	,	PUNCT
ejpam-5224	215	13	0	0	NUM
ejpam-5224	215	14	ω(s(1	ω(s(1	PROPN
ejpam-5224	215	15	)	)	PUNCT
ejpam-5224	215	16	)	)	PUNCT
ejpam-5224	216	1	=	=	SYM
ejpam-5224	216	2	s(2	s(2	PROPN
ejpam-5224	216	3	)	)	PUNCT
ejpam-5224	216	4	:	:	PUNCT
ejpam-5224	216	5	0	0	PUNCT
ejpam-5224	217	1	k	k	NOUN
ejpam-5224	217	2	0	0	NUM
ejpam-5224	217	3	0	0	NUM
ejpam-5224	218	1	and	and	CCONJ
ejpam-5224	218	2	we	we	PRON
ejpam-5224	218	3	can	can	AUX
ejpam-5224	218	4	check	check	VERB
ejpam-5224	218	5	that	that	PRON
ejpam-5224	218	6	rad2(p	rad2(p	NOUN
ejpam-5224	218	7	(	(	PUNCT
ejpam-5224	218	8	ω(s(1	ω(s(1	PROPN
ejpam-5224	218	9	)	)	PUNCT
ejpam-5224	218	10	)	)	PUNCT
ejpam-5224	218	11	)	)	PUNCT
ejpam-5224	219	1	̸=	̸=	PROPN
ejpam-5224	219	2	0	0	NUM
ejpam-5224	219	3	.	.	PUNCT
ejpam-5224	220	1	then	then	ADV
ejpam-5224	220	2	,	,	PUNCT
ejpam-5224	220	3	we	we	PRON
ejpam-5224	220	4	have	have	VERB
ejpam-5224	220	5	the	the	DET
ejpam-5224	220	6	exact	exact	ADJ
ejpam-5224	220	7	sequence	sequence	NOUN
ejpam-5224	220	8	,	,	PUNCT
ejpam-5224	220	9	0	0	NUM
ejpam-5224	220	10	−→	−→	NOUN
ejpam-5224	220	11	ω(s(2	ω(s(2	NOUN
ejpam-5224	220	12	)	)	PUNCT
ejpam-5224	220	13	)	)	PUNCT
ejpam-5224	221	1	−→	−→	NOUN
ejpam-5224	221	2	p	p	X
ejpam-5224	221	3	(	(	PUNCT
ejpam-5224	221	4	2	2	NUM
ejpam-5224	221	5	)	)	PUNCT
ejpam-5224	221	6	−→	−→	NOUN
ejpam-5224	221	7	ω(s(1	ω(s(1	PROPN
ejpam-5224	221	8	)	)	PUNCT
ejpam-5224	221	9	)	)	PUNCT
ejpam-5224	222	1	−→	−→	NOUN
ejpam-5224	222	2	0	0	NUM
ejpam-5224	222	3	with	with	ADP
ejpam-5224	222	4	,	,	PUNCT
ejpam-5224	222	5	k2	k2	ADJ
ejpam-5224	222	6	ω(s(2	ω(s(2	NOUN
ejpam-5224	222	7	)	)	PUNCT
ejpam-5224	222	8	)	)	PUNCT
ejpam-5224	222	9	:	:	PUNCT
ejpam-5224	222	10	0	0	NUM
ejpam-5224	222	11	0	0	NUM
ejpam-5224	222	12	k2	k2	PROPN
ejpam-5224	222	13	k2	k2	PROPN
ejpam-5224	222	14	and	and	CCONJ
ejpam-5224	222	15	k2	k2	ADJ
ejpam-5224	222	16	rad(ω(s(2	rad(ω(s(2	NOUN
ejpam-5224	222	17	)	)	PUNCT
ejpam-5224	222	18	)	)	PUNCT
ejpam-5224	222	19	)	)	PUNCT
ejpam-5224	222	20	:	:	PUNCT
ejpam-5224	222	21	0	0	NUM
ejpam-5224	222	22	0	0	NUM
ejpam-5224	222	23	0	0	NUM
ejpam-5224	222	24	k2	k2	PROPN
ejpam-5224	222	25	then	then	ADV
ejpam-5224	222	26	,	,	PUNCT
ejpam-5224	222	27	ω(s(2))/rad(ω(s(2	ω(s(2))/rad(ω(s(2	ADV
ejpam-5224	222	28	)	)	PUNCT
ejpam-5224	222	29	)	)	PUNCT
ejpam-5224	222	30	)	)	PUNCT
ejpam-5224	223	1	=	=	SYM
ejpam-5224	223	2	s(3)2	s(3)2	PROPN
ejpam-5224	223	3	,	,	PUNCT
ejpam-5224	223	4	and	and	CCONJ
ejpam-5224	223	5	we	we	PRON
ejpam-5224	223	6	have	have	VERB
ejpam-5224	223	7	the	the	DET
ejpam-5224	223	8	exact	exact	ADJ
ejpam-5224	223	9	sequence	sequence	NOUN
ejpam-5224	223	10	:	:	PUNCT
ejpam-5224	223	11	0	0	NUM
ejpam-5224	223	12	−→	−→	NOUN
ejpam-5224	223	13	ω2(s(2	ω2(s(2	NOUN
ejpam-5224	223	14	)	)	PUNCT
ejpam-5224	223	15	)	)	PUNCT
ejpam-5224	224	1	−→	−→	NOUN
ejpam-5224	224	2	p	p	X
ejpam-5224	224	3	(	(	PUNCT
ejpam-5224	224	4	3)2	3)2	NUM
ejpam-5224	224	5	−→	−→	NOUN
ejpam-5224	224	6	(	(	PUNCT
ejpam-5224	224	7	s(3))2	s(3))2	NOUN
ejpam-5224	224	8	−→	−→	NOUN
ejpam-5224	224	9	0	0	NUM
ejpam-5224	224	10	with	with	ADP
ejpam-5224	224	11	k2	k2	PROPN
ejpam-5224	224	12	ω2(s(2	ω2(s(2	NOUN
ejpam-5224	224	13	)	)	PUNCT
ejpam-5224	224	14	)	)	PUNCT
ejpam-5224	224	15	:	:	PUNCT
ejpam-5224	224	16	0	0	NUM
ejpam-5224	224	17	0	0	NUM
ejpam-5224	224	18	0	0	NUM
ejpam-5224	224	19	k2	k2	ADJ
ejpam-5224	224	20	m.	m.	NOUN
ejpam-5224	224	21	laaraj	laaraj	PROPN
ejpam-5224	224	22	,	,	PUNCT
ejpam-5224	224	23	s.	s.	PROPN
ejpam-5224	224	24	abdelalim	abdelalim	PROPN
ejpam-5224	224	25	,	,	PUNCT
ejpam-5224	224	26	i.elmouki	i.elmouki	CCONJ
ejpam-5224	224	27	/	/	SYM
ejpam-5224	224	28	eur	eur	NOUN
ejpam-5224	224	29	.	.	PUNCT
ejpam-5224	225	1	j.	j.	PROPN
ejpam-5224	225	2	pure	pure	PROPN
ejpam-5224	225	3	appl	appl	PROPN
ejpam-5224	225	4	.	.	PROPN
ejpam-5224	225	5	math	math	PROPN
ejpam-5224	225	6	,	,	PUNCT
ejpam-5224	225	7	17	17	NUM
ejpam-5224	225	8	(	(	PUNCT
ejpam-5224	225	9	3	3	NUM
ejpam-5224	225	10	)	)	PUNCT
ejpam-5224	225	11	(	(	PUNCT
ejpam-5224	225	12	2024	2024	NUM
ejpam-5224	225	13	)	)	PUNCT
ejpam-5224	225	14	,	,	PUNCT
ejpam-5224	225	15	1855	1855	NUM
ejpam-5224	225	16	-	-	SYM
ejpam-5224	225	17	1868	1868	NUM
ejpam-5224	225	18	1865	1865	NUM
ejpam-5224	225	19	then	then	ADV
ejpam-5224	225	20	we	we	PRON
ejpam-5224	225	21	have	have	VERB
ejpam-5224	225	22	,	,	PUNCT
ejpam-5224	225	23	0	0	NUM
ejpam-5224	225	24	−→	−→	NOUN
ejpam-5224	225	25	p	p	X
ejpam-5224	225	26	(	(	PUNCT
ejpam-5224	225	27	4)2	4)2	PROPN
ejpam-5224	225	28	⊕	⊕	PROPN
ejpam-5224	225	29	p	p	NOUN
ejpam-5224	225	30	(	(	PUNCT
ejpam-5224	225	31	5)2	5)2	NUM
ejpam-5224	225	32	−→	−→	NOUN
ejpam-5224	225	33	ω2(s(2	ω2(s(2	NOUN
ejpam-5224	225	34	)	)	PUNCT
ejpam-5224	225	35	)	)	PUNCT
ejpam-5224	226	1	−→	−→	NOUN
ejpam-5224	226	2	0	0	NUM
ejpam-5224	227	1	and	and	CCONJ
ejpam-5224	227	2	finally	finally	ADV
ejpam-5224	227	3	the	the	DET
ejpam-5224	227	4	projective	projective	ADJ
ejpam-5224	227	5	resolution	resolution	NOUN
ejpam-5224	227	6	of	of	ADP
ejpam-5224	227	7	s(1	s(1	PROPN
ejpam-5224	227	8	)	)	PUNCT
ejpam-5224	227	9	is	be	AUX
ejpam-5224	227	10	,	,	PUNCT
ejpam-5224	227	11	0	0	NUM
ejpam-5224	227	12	−→	−→	NOUN
ejpam-5224	227	13	p	p	X
ejpam-5224	227	14	(	(	PUNCT
ejpam-5224	227	15	4)2	4)2	PROPN
ejpam-5224	227	16	⊕	⊕	PROPN
ejpam-5224	227	17	p	p	NOUN
ejpam-5224	227	18	(	(	PUNCT
ejpam-5224	227	19	5)2	5)2	NUM
ejpam-5224	227	20	−→	−→	NOUN
ejpam-5224	227	21	(	(	PUNCT
ejpam-5224	227	22	p	p	X
ejpam-5224	227	23	(	(	PUNCT
ejpam-5224	227	24	3))2	3))2	NUM
ejpam-5224	227	25	−→	−→	NOUN
ejpam-5224	227	26	p	p	X
ejpam-5224	227	27	(	(	PUNCT
ejpam-5224	227	28	2	2	NUM
ejpam-5224	227	29	)	)	PUNCT
ejpam-5224	227	30	−→	−→	NOUN
ejpam-5224	227	31	p	p	X
ejpam-5224	227	32	(	(	PUNCT
ejpam-5224	227	33	1	1	NUM
ejpam-5224	227	34	)	)	PUNCT
ejpam-5224	227	35	−→	−→	PROPN
ejpam-5224	227	36	s(1	s(1	PROPN
ejpam-5224	227	37	)	)	PUNCT
ejpam-5224	228	1	−→	−→	NOUN
ejpam-5224	228	2	0	0	NUM
ejpam-5224	228	3	in	in	ADP
ejpam-5224	228	4	the	the	DET
ejpam-5224	228	5	same	same	ADJ
ejpam-5224	228	6	way	way	NOUN
ejpam-5224	228	7	,	,	PUNCT
ejpam-5224	228	8	we	we	PRON
ejpam-5224	228	9	get	get	VERB
ejpam-5224	228	10	,	,	PUNCT
ejpam-5224	228	11	0	0	NUM
ejpam-5224	229	1	−→	−→	NOUN
ejpam-5224	229	2	p	p	X
ejpam-5224	229	3	(	(	PUNCT
ejpam-5224	229	4	4)2	4)2	PROPN
ejpam-5224	229	5	⊕	⊕	PROPN
ejpam-5224	229	6	p	p	NOUN
ejpam-5224	229	7	(	(	PUNCT
ejpam-5224	229	8	5)2	5)2	NUM
ejpam-5224	229	9	−→	−→	NOUN
ejpam-5224	229	10	(	(	PUNCT
ejpam-5224	229	11	p	p	X
ejpam-5224	229	12	(	(	PUNCT
ejpam-5224	229	13	3))2	3))2	NUM
ejpam-5224	229	14	−→	−→	NOUN
ejpam-5224	229	15	p	p	X
ejpam-5224	229	16	(	(	PUNCT
ejpam-5224	229	17	2	2	NUM
ejpam-5224	229	18	)	)	PUNCT
ejpam-5224	229	19	−→	−→	NOUN
ejpam-5224	229	20	s(2	s(2	NOUN
ejpam-5224	229	21	)	)	PUNCT
ejpam-5224	229	22	−→	−→	NOUN
ejpam-5224	229	23	0	0	NUM
ejpam-5224	229	24	0	0	NUM
ejpam-5224	230	1	−→	−→	NOUN
ejpam-5224	230	2	p	p	X
ejpam-5224	230	3	(	(	PUNCT
ejpam-5224	230	4	4	4	NUM
ejpam-5224	230	5	)	)	PUNCT
ejpam-5224	230	6	⊕	⊕	PROPN
ejpam-5224	230	7	p	p	NOUN
ejpam-5224	230	8	(	(	PUNCT
ejpam-5224	230	9	5	5	NUM
ejpam-5224	230	10	)	)	PUNCT
ejpam-5224	230	11	−→	−→	NOUN
ejpam-5224	230	12	p	p	X
ejpam-5224	230	13	(	(	PUNCT
ejpam-5224	230	14	3	3	NUM
ejpam-5224	230	15	)	)	PUNCT
ejpam-5224	230	16	−→	−→	NOUN
ejpam-5224	230	17	s(3	s(3	NOUN
ejpam-5224	230	18	)	)	PUNCT
ejpam-5224	231	1	−→	−→	NOUN
ejpam-5224	231	2	0	0	NUM
ejpam-5224	231	3	0	0	NUM
ejpam-5224	231	4	−→	−→	NOUN
ejpam-5224	231	5	p	p	X
ejpam-5224	231	6	(	(	PUNCT
ejpam-5224	231	7	4	4	NUM
ejpam-5224	231	8	)	)	PUNCT
ejpam-5224	231	9	−→	−→	NOUN
ejpam-5224	231	10	s(4	s(4	NOUN
ejpam-5224	231	11	)	)	PUNCT
ejpam-5224	232	1	−→	−→	NOUN
ejpam-5224	232	2	0	0	NUM
ejpam-5224	232	3	0	0	NUM
ejpam-5224	233	1	−→	−→	NOUN
ejpam-5224	233	2	p	p	X
ejpam-5224	233	3	(	(	PUNCT
ejpam-5224	233	4	5	5	NUM
ejpam-5224	233	5	)	)	PUNCT
ejpam-5224	233	6	−→	−→	NOUN
ejpam-5224	233	7	s(5	s(5	PROPN
ejpam-5224	233	8	)	)	PUNCT
ejpam-5224	233	9	−→	−→	NOUN
ejpam-5224	233	10	0	0	NUM
ejpam-5224	233	11	by	by	ADP
ejpam-5224	233	12	using	use	VERB
ejpam-5224	233	13	the	the	DET
ejpam-5224	233	14	formula	formula	NOUN
ejpam-5224	233	15	,	,	PUNCT
ejpam-5224	233	16	hom(p	hom(p	PROPN
ejpam-5224	233	17	(	(	PUNCT
ejpam-5224	233	18	i	i	NOUN
ejpam-5224	233	19	)	)	PUNCT
ejpam-5224	233	20	,	,	PUNCT
ejpam-5224	233	21	s(j	s(j	PROPN
ejpam-5224	233	22	)	)	PUNCT
ejpam-5224	233	23	)	)	PUNCT
ejpam-5224	234	1	=	=	SYM
ejpam-5224	234	2	hom(aei	hom(aei	PROPN
ejpam-5224	234	3	,	,	PUNCT
ejpam-5224	234	4	s(j	s(j	PROPN
ejpam-5224	234	5	)	)	PUNCT
ejpam-5224	234	6	)	)	PUNCT
ejpam-5224	234	7	≃	≃	VERB
ejpam-5224	234	8	eis(j	eis(j	PROPN
ejpam-5224	234	9	)	)	PUNCT
ejpam-5224	234	10	=	=	PRON
ejpam-5224	234	11	{	{	PUNCT
ejpam-5224	234	12	k	k	X
ejpam-5224	234	13	if	if	SCONJ
ejpam-5224	234	14	j	j	PROPN
ejpam-5224	234	15	=	=	VERB
ejpam-5224	235	1	i	i	PRON
ejpam-5224	235	2	0	0	PUNCT
ejpam-5224	236	1	if	if	SCONJ
ejpam-5224	236	2	j	j	PROPN
ejpam-5224	236	3	̸=	̸=	PROPN
ejpam-5224	236	4	i	i	PROPN
ejpam-5224	236	5	and	and	CCONJ
ejpam-5224	236	6	by	by	ADP
ejpam-5224	236	7	application	application	NOUN
ejpam-5224	236	8	of	of	ADP
ejpam-5224	236	9	the	the	DET
ejpam-5224	236	10	functor	functor	PROPN
ejpam-5224	236	11	hom(−	hom(−	PROPN
ejpam-5224	236	12	,	,	PUNCT
ejpam-5224	236	13	s(1	s(1	PROPN
ejpam-5224	236	14	)	)	PUNCT
ejpam-5224	236	15	)	)	PUNCT
ejpam-5224	236	16	to	to	ADP
ejpam-5224	236	17	the	the	DET
ejpam-5224	236	18	resolution	resolution	NOUN
ejpam-5224	236	19	p∗(s(1	p∗(s(1	NOUN
ejpam-5224	236	20	)	)	PUNCT
ejpam-5224	236	21	)	)	PUNCT
ejpam-5224	236	22	,	,	PUNCT
ejpam-5224	236	23	i.e.	i.e.	X
ejpam-5224	236	24	the	the	DET
ejpam-5224	236	25	complex	complex	NOUN
ejpam-5224	236	26	obtained	obtain	VERB
ejpam-5224	236	27	by	by	ADP
ejpam-5224	236	28	eliminating	eliminating	NOUN
ejpam-5224	236	29	of	of	ADP
ejpam-5224	236	30	s(1	s(1	PROPN
ejpam-5224	236	31	)	)	PUNCT
ejpam-5224	236	32	in	in	ADP
ejpam-5224	236	33	the	the	DET
ejpam-5224	236	34	resolution	resolution	NOUN
ejpam-5224	236	35	projective	projective	NOUN
ejpam-5224	236	36	of	of	ADP
ejpam-5224	236	37	s(1	s(1	PROPN
ejpam-5224	236	38	)	)	PUNCT
ejpam-5224	236	39	we	we	PRON
ejpam-5224	236	40	find	find	VERB
ejpam-5224	236	41	the	the	DET
ejpam-5224	236	42	complex	complex	NOUN
ejpam-5224	236	43	:	:	PUNCT
ejpam-5224	236	44	0	0	NUM
ejpam-5224	236	45	−→	−→	NOUN
ejpam-5224	236	46	k	k	INTJ
ejpam-5224	236	47	−→	−→	NOUN
ejpam-5224	236	48	0	0	NUM
ejpam-5224	236	49	−→	−→	NOUN
ejpam-5224	236	50	0	0	NUM
ejpam-5224	236	51	−→	−→	NOUN
ejpam-5224	236	52	...	...	PUNCT
ejpam-5224	236	53	and	and	CCONJ
ejpam-5224	236	54	ext1a(s(1	ext1a(s(1	PROPN
ejpam-5224	236	55	)	)	PUNCT
ejpam-5224	236	56	,	,	PUNCT
ejpam-5224	236	57	s(1	s(1	PROPN
ejpam-5224	236	58	)	)	PUNCT
ejpam-5224	236	59	)	)	PUNCT
ejpam-5224	237	1	=	=	PUNCT
ejpam-5224	237	2	0	0	X
ejpam-5224	237	3	.	.	PUNCT
ejpam-5224	237	4	thus	thus	ADV
ejpam-5224	237	5	,	,	PUNCT
ejpam-5224	237	6	by	by	ADP
ejpam-5224	237	7	the	the	DET
ejpam-5224	237	8	same	same	ADJ
ejpam-5224	237	9	way	way	NOUN
ejpam-5224	237	10	,	,	PUNCT
ejpam-5224	237	11	ext1a(s(i	ext1a(s(i	NOUN
ejpam-5224	237	12	)	)	PUNCT
ejpam-5224	237	13	,	,	PUNCT
ejpam-5224	237	14	s(i	s(i	PROPN
ejpam-5224	237	15	)	)	PUNCT
ejpam-5224	237	16	)	)	PUNCT
ejpam-5224	237	17	=	=	SYM
ejpam-5224	237	18	0	0	NUM
ejpam-5224	237	19	for	for	ADP
ejpam-5224	237	20	every	every	DET
ejpam-5224	237	21	1	1	NUM
ejpam-5224	237	22	≤	≤	NUM
ejpam-5224	237	23	i	i	PRON
ejpam-5224	237	24	≤	≤	ADV
ejpam-5224	237	25	5	5	NUM
ejpam-5224	237	26	.	.	X
ejpam-5224	237	27	7.3	7.3	NUM
ejpam-5224	237	28	.	.	PUNCT
ejpam-5224	238	1	strong	strong	ADJ
ejpam-5224	238	2	no	no	DET
ejpam-5224	238	3	loop	loop	NOUN
ejpam-5224	238	4	conjecture	conjecture	NOUN
ejpam-5224	238	5	without	without	ADP
ejpam-5224	238	6	necessary	necessary	ADJ
ejpam-5224	238	7	specification	specification	NOUN
ejpam-5224	238	8	of	of	ADP
ejpam-5224	238	9	the	the	DET
ejpam-5224	238	10	nilpotence	nilpotence	NOUN
ejpam-5224	238	11	index	index	NOUN
ejpam-5224	238	12	of	of	ADP
ejpam-5224	238	13	the	the	DET
ejpam-5224	238	14	jacobson	jacobson	PROPN
ejpam-5224	238	15	radical	radical	PROPN
ejpam-5224	238	16	the	the	DET
ejpam-5224	238	17	following	follow	VERB
ejpam-5224	238	18	example	example	NOUN
ejpam-5224	238	19	clearly	clearly	ADV
ejpam-5224	238	20	shows	show	VERB
ejpam-5224	238	21	that	that	SCONJ
ejpam-5224	238	22	if	if	SCONJ
ejpam-5224	238	23	the	the	DET
ejpam-5224	238	24	extension	extension	NOUN
ejpam-5224	238	25	quiver	quiver	NOUN
ejpam-5224	238	26	has	have	VERB
ejpam-5224	238	27	a	a	DET
ejpam-5224	238	28	loop	loop	NOUN
ejpam-5224	238	29	in	in	ADP
ejpam-5224	238	30	a	a	DET
ejpam-5224	238	31	simple	simple	ADJ
ejpam-5224	238	32	module	module	NOUN
ejpam-5224	238	33	then	then	ADV
ejpam-5224	238	34	its	its	PRON
ejpam-5224	238	35	projective	projective	ADJ
ejpam-5224	238	36	dimension	dimension	NOUN
ejpam-5224	238	37	,	,	PUNCT
ejpam-5224	238	38	is	be	AUX
ejpam-5224	238	39	infinite	infinite	ADJ
ejpam-5224	238	40	although	although	SCONJ
ejpam-5224	238	41	it	it	PRON
ejpam-5224	238	42	is	be	AUX
ejpam-5224	238	43	the	the	DET
ejpam-5224	238	44	nilpotence	nilpotence	NOUN
ejpam-5224	238	45	index	index	NOUN
ejpam-5224	238	46	of	of	ADP
ejpam-5224	238	47	the	the	DET
ejpam-5224	238	48	jacobson	jacobson	PROPN
ejpam-5224	238	49	radical	radical	PROPN
ejpam-5224	238	50	7.3	7.3	NUM
ejpam-5224	238	51	example	example	NOUN
ejpam-5224	238	52	.	.	PUNCT
ejpam-5224	239	1	let	let	VERB
ejpam-5224	239	2	q	q	PROPN
ejpam-5224	239	3	the	the	DET
ejpam-5224	239	4	quiver	quiver	NOUN
ejpam-5224	239	5	defined	define	VERB
ejpam-5224	239	6	by	by	ADP
ejpam-5224	239	7	1	1	NUM
ejpam-5224	239	8	2	2	NUM
ejpam-5224	239	9	α	α	NOUN
ejpam-5224	239	10	β	β	NOUN
ejpam-5224	239	11	γ	γ	NOUN
ejpam-5224	239	12	and	and	CCONJ
ejpam-5224	239	13	let	let	VERB
ejpam-5224	239	14	a	a	DET
ejpam-5224	239	15	=	=	SYM
ejpam-5224	239	16	kq	kq	PROPN
ejpam-5224	239	17	/	/	SYM
ejpam-5224	239	18	i	i	PROPN
ejpam-5224	239	19	which	which	PRON
ejpam-5224	239	20	is	be	AUX
ejpam-5224	239	21	algebra	algebra	NOUN
ejpam-5224	239	22	bounded	bound	VERB
ejpam-5224	239	23	by	by	ADP
ejpam-5224	239	24	the	the	DET
ejpam-5224	239	25	relations	relation	NOUN
ejpam-5224	239	26	α2	α2	VERB
ejpam-5224	239	27	−	−	PROPN
ejpam-5224	240	1	βγ	βγ	NOUN
ejpam-5224	240	2	,	,	PUNCT
ejpam-5224	240	3	γαβ	γαβ	NOUN
ejpam-5224	240	4	and	and	CCONJ
ejpam-5224	240	5	γβ	γβ	NOUN
ejpam-5224	240	6	.	.	PUNCT
ejpam-5224	241	1	by	by	ADP
ejpam-5224	241	2	definition	definition	NOUN
ejpam-5224	241	3	,	,	PUNCT
ejpam-5224	241	4	in	in	ADP
ejpam-5224	241	5	the	the	DET
ejpam-5224	241	6	quiver	quiver	NOUN
ejpam-5224	241	7	algebra	algebra	NOUN
ejpam-5224	241	8	,	,	PUNCT
ejpam-5224	241	9	we	we	PRON
ejpam-5224	241	10	get	get	VERB
ejpam-5224	241	11	ext1a(s(1	ext1a(s(1	PROPN
ejpam-5224	241	12	)	)	PUNCT
ejpam-5224	241	13	,	,	PUNCT
ejpam-5224	241	14	s(1	s(1	PROPN
ejpam-5224	241	15	)	)	PUNCT
ejpam-5224	241	16	)	)	PUNCT
ejpam-5224	242	1	=	=	PUNCT
ejpam-5224	242	2	0	0	X
ejpam-5224	242	3	.	.	PUNCT
ejpam-5224	243	1	then	then	ADV
ejpam-5224	243	2	,	,	PUNCT
ejpam-5224	243	3	by	by	ADP
ejpam-5224	243	4	further	further	ADJ
ejpam-5224	243	5	calculations	calculation	NOUN
ejpam-5224	243	6	,	,	PUNCT
ejpam-5224	243	7	we	we	PRON
ejpam-5224	243	8	can	can	AUX
ejpam-5224	243	9	find	find	VERB
ejpam-5224	243	10	the	the	DET
ejpam-5224	243	11	infinite	infinite	ADJ
ejpam-5224	243	12	resolution	resolution	NOUN
ejpam-5224	243	13	of	of	ADP
ejpam-5224	243	14	s(1	s(1	PROPN
ejpam-5224	243	15	)	)	PUNCT
ejpam-5224	243	16	as	as	ADP
ejpam-5224	243	17	following	follow	VERB
ejpam-5224	243	18	,	,	PUNCT
ejpam-5224	243	19	...	...	PUNCT
ejpam-5224	243	20	−→	−→	NOUN
ejpam-5224	243	21	p	p	X
ejpam-5224	243	22	(	(	PUNCT
ejpam-5224	243	23	2	2	NUM
ejpam-5224	243	24	)	)	PUNCT
ejpam-5224	243	25	−→	−→	NOUN
ejpam-5224	243	26	p	p	X
ejpam-5224	243	27	(	(	PUNCT
ejpam-5224	243	28	1	1	NUM
ejpam-5224	243	29	)	)	PUNCT
ejpam-5224	243	30	−→	−→	NOUN
ejpam-5224	243	31	p	p	X
ejpam-5224	243	32	(	(	PUNCT
ejpam-5224	243	33	1	1	NUM
ejpam-5224	243	34	)	)	PUNCT
ejpam-5224	243	35	⊕	⊕	PROPN
ejpam-5224	243	36	p	p	NOUN
ejpam-5224	243	37	(	(	PUNCT
ejpam-5224	243	38	2	2	NUM
ejpam-5224	243	39	)	)	PUNCT
ejpam-5224	243	40	−→	−→	NOUN
ejpam-5224	243	41	p	p	X
ejpam-5224	243	42	(	(	PUNCT
ejpam-5224	243	43	1	1	NUM
ejpam-5224	243	44	)	)	PUNCT
ejpam-5224	243	45	−→	−→	PROPN
ejpam-5224	243	46	s(1	s(1	PROPN
ejpam-5224	243	47	)	)	PUNCT
ejpam-5224	243	48	−→	−→	NOUN
ejpam-5224	243	49	0	0	NUM
ejpam-5224	243	50	m.	m.	NOUN
ejpam-5224	243	51	laaraj	laaraj	PROPN
ejpam-5224	243	52	,	,	PUNCT
ejpam-5224	243	53	s.	s.	PROPN
ejpam-5224	243	54	abdelalim	abdelalim	PROPN
ejpam-5224	243	55	,	,	PUNCT
ejpam-5224	243	56	i.elmouki	i.elmouki	CCONJ
ejpam-5224	243	57	/	/	SYM
ejpam-5224	243	58	eur	eur	NOUN
ejpam-5224	243	59	.	.	PUNCT
ejpam-5224	244	1	j.	j.	PROPN
ejpam-5224	244	2	pure	pure	PROPN
ejpam-5224	244	3	appl	appl	PROPN
ejpam-5224	244	4	.	.	PROPN
ejpam-5224	244	5	math	math	PROPN
ejpam-5224	244	6	,	,	PUNCT
ejpam-5224	244	7	17	17	NUM
ejpam-5224	244	8	(	(	PUNCT
ejpam-5224	244	9	3	3	NUM
ejpam-5224	244	10	)	)	PUNCT
ejpam-5224	244	11	(	(	PUNCT
ejpam-5224	244	12	2024	2024	NUM
ejpam-5224	244	13	)	)	PUNCT
ejpam-5224	244	14	,	,	PUNCT
ejpam-5224	244	15	1855	1855	NUM
ejpam-5224	244	16	-	-	SYM
ejpam-5224	244	17	1868	1868	NUM
ejpam-5224	244	18	1866	1866	NUM
ejpam-5224	244	19	with	with	ADP
ejpam-5224	244	20	,	,	PUNCT
ejpam-5224	244	21	p	p	X
ejpam-5224	244	22	(	(	PUNCT
ejpam-5224	244	23	1	1	NUM
ejpam-5224	244	24	)	)	PUNCT
ejpam-5224	244	25	:	:	PUNCT
ejpam-5224	244	26	k4	k4	PROPN
ejpam-5224	244	27	k2	k2	PROPN
ejpam-5224	244	28	and	and	CCONJ
ejpam-5224	244	29	,	,	PUNCT
ejpam-5224	244	30	p	p	X
ejpam-5224	244	31	(	(	PUNCT
ejpam-5224	244	32	2	2	NUM
ejpam-5224	244	33	)	)	PUNCT
ejpam-5224	244	34	:	:	PUNCT
ejpam-5224	244	35	k2	k2	PROPN
ejpam-5224	244	36	k	k	PROPN
ejpam-5224	244	37	7.4	7.4	NUM
ejpam-5224	244	38	.	.	PUNCT
ejpam-5224	245	1	strong	strong	ADJ
ejpam-5224	245	2	no	no	DET
ejpam-5224	245	3	loop	loop	NOUN
ejpam-5224	245	4	conjecture	conjecture	NOUN
ejpam-5224	245	5	finally	finally	ADV
ejpam-5224	245	6	resolved	resolve	VERB
ejpam-5224	245	7	in	in	ADP
ejpam-5224	245	8	j3	j3	PROPN
ejpam-5224	245	9	=	=	PROPN
ejpam-5224	245	10	0	0	NUM
ejpam-5224	246	1	in	in	ADP
ejpam-5224	246	2	this	this	DET
ejpam-5224	246	3	paper	paper	NOUN
ejpam-5224	246	4	,	,	PUNCT
ejpam-5224	246	5	we	we	PRON
ejpam-5224	246	6	have	have	AUX
ejpam-5224	246	7	succeed	succeed	VERB
ejpam-5224	246	8	to	to	PART
ejpam-5224	246	9	resolve	resolve	VERB
ejpam-5224	246	10	the	the	DET
ejpam-5224	246	11	strong	strong	ADJ
ejpam-5224	246	12	no	no	DET
ejpam-5224	246	13	loop	loop	NOUN
ejpam-5224	246	14	conjecture	conjecture	NOUN
ejpam-5224	246	15	posed	pose	VERB
ejpam-5224	246	16	in	in	ADP
ejpam-5224	246	17	[	[	X
ejpam-5224	246	18	14	14	NUM
ejpam-5224	246	19	]	]	PUNCT
ejpam-5224	246	20	but	but	CCONJ
ejpam-5224	246	21	here	here	ADV
ejpam-5224	246	22	in	in	ADP
ejpam-5224	246	23	the	the	DET
ejpam-5224	246	24	special	special	ADJ
ejpam-5224	246	25	case	case	NOUN
ejpam-5224	246	26	of	of	ADP
ejpam-5224	246	27	j3	j3	PROPN
ejpam-5224	246	28	=	=	PROPN
ejpam-5224	246	29	0	0	PROPN
ejpam-5224	246	30	under	under	ADP
ejpam-5224	246	31	the	the	DET
ejpam-5224	246	32	condition	condition	NOUN
ejpam-5224	246	33	that	that	SCONJ
ejpam-5224	246	34	the	the	DET
ejpam-5224	246	35	radical	radical	PROPN
ejpam-5224	246	36	’s	’s	NOUN
ejpam-5224	246	37	square	square	NOUN
ejpam-5224	246	38	of	of	ADP
ejpam-5224	246	39	the	the	DET
ejpam-5224	246	40	cover	cover	NOUN
ejpam-5224	246	41	projective	projective	NOUN
ejpam-5224	246	42	of	of	ADP
ejpam-5224	246	43	the	the	DET
ejpam-5224	246	44	first	first	ADJ
ejpam-5224	246	45	syzygy	syzygy	NOUN
ejpam-5224	246	46	is	be	AUX
ejpam-5224	246	47	zero	zero	NUM
ejpam-5224	246	48	,	,	PUNCT
ejpam-5224	246	49	while	while	SCONJ
ejpam-5224	246	50	using	use	VERB
ejpam-5224	246	51	more	more	ADJ
ejpam-5224	246	52	tractable	tractable	ADJ
ejpam-5224	246	53	background	background	NOUN
ejpam-5224	246	54	focusing	focus	VERB
ejpam-5224	246	55	on	on	ADP
ejpam-5224	246	56	non	non	ADJ
ejpam-5224	246	57	-	-	ADJ
ejpam-5224	246	58	commutative	commutative	ADJ
ejpam-5224	246	59	algebra	algebra	NOUN
ejpam-5224	246	60	and	and	CCONJ
ejpam-5224	246	61	homology	homology	NOUN
ejpam-5224	246	62	instead	instead	ADV
ejpam-5224	246	63	of	of	ADP
ejpam-5224	246	64	some	some	DET
ejpam-5224	246	65	combination	combination	NOUN
ejpam-5224	246	66	with	with	ADP
ejpam-5224	246	67	k	k	NOUN
ejpam-5224	246	68	-	-	NOUN
ejpam-5224	246	69	theory	theory	NOUN
ejpam-5224	246	70	as	as	SCONJ
ejpam-5224	246	71	used	use	VERB
ejpam-5224	246	72	in	in	ADP
ejpam-5224	246	73	the	the	DET
ejpam-5224	246	74	past	past	ADJ
ejpam-5224	246	75	authors	author	NOUN
ejpam-5224	246	76	in	in	ADP
ejpam-5224	246	77	[	[	X
ejpam-5224	246	78	9	9	NUM
ejpam-5224	246	79	]	]	PUNCT
ejpam-5224	246	80	to	to	PART
ejpam-5224	246	81	solve	solve	VERB
ejpam-5224	246	82	this	this	DET
ejpam-5224	246	83	conjecture	conjecture	NOUN
ejpam-5224	246	84	at	at	ADP
ejpam-5224	246	85	least	least	ADJ
ejpam-5224	246	86	in	in	ADP
ejpam-5224	246	87	the	the	DET
ejpam-5224	246	88	case	case	NOUN
ejpam-5224	246	89	of	of	ADP
ejpam-5224	246	90	j2	j2	PROPN
ejpam-5224	246	91	=	=	SYM
ejpam-5224	246	92	0	0	PROPN
ejpam-5224	246	93	,	,	PUNCT
ejpam-5224	246	94	however	however	ADV
ejpam-5224	246	95	,	,	PUNCT
ejpam-5224	246	96	the	the	DET
ejpam-5224	246	97	problem	problem	NOUN
ejpam-5224	246	98	has	have	AUX
ejpam-5224	246	99	remained	remain	VERB
ejpam-5224	246	100	open	open	ADJ
ejpam-5224	246	101	since	since	SCONJ
ejpam-5224	246	102	that	that	DET
ejpam-5224	246	103	time	time	NOUN
ejpam-5224	246	104	for	for	ADP
ejpam-5224	246	105	the	the	DET
ejpam-5224	246	106	case	case	NOUN
ejpam-5224	246	107	of	of	ADP
ejpam-5224	246	108	j3	j3	PROPN
ejpam-5224	246	109	=	=	PROPN
ejpam-5224	246	110	0	0	PROPN
ejpam-5224	246	111	and	and	CCONJ
ejpam-5224	246	112	which	which	PRON
ejpam-5224	246	113	is	be	AUX
ejpam-5224	246	114	of	of	ADP
ejpam-5224	246	115	course	course	NOUN
ejpam-5224	246	116	very	very	ADV
ejpam-5224	246	117	important	important	ADJ
ejpam-5224	246	118	to	to	PART
ejpam-5224	246	119	resolve	resolve	VERB
ejpam-5224	246	120	for	for	ADP
ejpam-5224	246	121	getting	get	VERB
ejpam-5224	246	122	some	some	DET
ejpam-5224	246	123	inspiration	inspiration	NOUN
ejpam-5224	246	124	and	and	CCONJ
ejpam-5224	246	125	try	try	VERB
ejpam-5224	246	126	to	to	PART
ejpam-5224	246	127	resolve	resolve	VERB
ejpam-5224	246	128	further	further	ADJ
ejpam-5224	246	129	cases	case	NOUN
ejpam-5224	246	130	like	like	ADP
ejpam-5224	246	131	j4	j4	PROPN
ejpam-5224	246	132	=	=	SYM
ejpam-5224	246	133	0	0	NUM
ejpam-5224	246	134	or	or	CCONJ
ejpam-5224	246	135	more	more	ADV
ejpam-5224	246	136	generally	generally	ADV
ejpam-5224	246	137	jn	jn	PROPN
ejpam-5224	247	1	=	=	SYM
ejpam-5224	247	2	0	0	PROPN
ejpam-5224	247	3	,	,	PUNCT
ejpam-5224	247	4	either	either	CCONJ
ejpam-5224	247	5	by	by	ADP
ejpam-5224	247	6	introducing	introduce	VERB
ejpam-5224	247	7	one	one	NUM
ejpam-5224	247	8	condition	condition	NOUN
ejpam-5224	247	9	like	like	SCONJ
ejpam-5224	247	10	we	we	PRON
ejpam-5224	247	11	have	have	AUX
ejpam-5224	247	12	done	do	VERB
ejpam-5224	247	13	here	here	ADV
ejpam-5224	247	14	by	by	ADP
ejpam-5224	247	15	taking	take	VERB
ejpam-5224	247	16	a	a	DET
ejpam-5224	247	17	zero	zero	NUM
ejpam-5224	247	18	radical	radical	ADJ
ejpam-5224	247	19	’s	’s	NOUN
ejpam-5224	247	20	square	square	NOUN
ejpam-5224	247	21	of	of	ADP
ejpam-5224	247	22	the	the	DET
ejpam-5224	247	23	cover	cover	NOUN
ejpam-5224	247	24	projective	projective	NOUN
ejpam-5224	247	25	of	of	ADP
ejpam-5224	247	26	the	the	DET
ejpam-5224	247	27	first	first	ADJ
ejpam-5224	247	28	syzygy	syzygy	NOUN
ejpam-5224	247	29	,	,	PUNCT
ejpam-5224	247	30	or	or	CCONJ
ejpam-5224	247	31	maybe	maybe	ADV
ejpam-5224	247	32	some	some	PRON
ejpam-5224	247	33	would	would	AUX
ejpam-5224	247	34	think	think	VERB
ejpam-5224	247	35	about	about	ADP
ejpam-5224	247	36	more	more	ADV
ejpam-5224	247	37	additional	additional	ADJ
ejpam-5224	247	38	conditions	condition	NOUN
ejpam-5224	247	39	in	in	ADP
ejpam-5224	247	40	the	the	DET
ejpam-5224	247	41	future	future	NOUN
ejpam-5224	247	42	.	.	PUNCT
ejpam-5224	248	1	in	in	ADP
ejpam-5224	248	2	what	what	PRON
ejpam-5224	248	3	follows	follow	VERB
ejpam-5224	248	4	we	we	PRON
ejpam-5224	248	5	will	will	AUX
ejpam-5224	248	6	present	present	VERB
ejpam-5224	248	7	an	an	DET
ejpam-5224	248	8	example	example	NOUN
ejpam-5224	248	9	of	of	ADP
ejpam-5224	248	10	an	an	DET
ejpam-5224	248	11	artin	artin	PROPN
ejpam-5224	248	12	algebra	algebra	PROPN
ejpam-5224	248	13	with	with	ADP
ejpam-5224	248	14	jacobson	jacobson	PROPN
ejpam-5224	248	15	cube	cube	PROPN
ejpam-5224	248	16	radical	radical	PROPN
ejpam-5224	248	17	0	0	PUNCT
ejpam-5224	248	18	and	and	CCONJ
ejpam-5224	248	19	that	that	PRON
ejpam-5224	248	20	also	also	ADV
ejpam-5224	248	21	satisfies	satisfy	VERB
ejpam-5224	248	22	the	the	DET
ejpam-5224	248	23	condition	condition	NOUN
ejpam-5224	248	24	of	of	ADP
ejpam-5224	248	25	the	the	DET
ejpam-5224	248	26	first	first	ADJ
ejpam-5224	248	27	lemma	lemma	PROPN
ejpam-5224	248	28	.	.	PUNCT
ejpam-5224	249	1	7.4	7.4	NUM
ejpam-5224	249	2	example	example	NOUN
ejpam-5224	249	3	.	.	PUNCT
ejpam-5224	250	1	consider	consider	VERB
ejpam-5224	250	2	the	the	DET
ejpam-5224	250	3	algebra	algebra	NOUN
ejpam-5224	250	4	a	a	DET
ejpam-5224	250	5	=	=	SYM
ejpam-5224	250	6	kq	kq	PROPN
ejpam-5224	250	7	/	/	SYM
ejpam-5224	250	8	i	i	PRON
ejpam-5224	250	9	given	give	VERB
ejpam-5224	250	10	over	over	ADP
ejpam-5224	250	11	a	a	DET
ejpam-5224	250	12	field	field	NOUN
ejpam-5224	250	13	k	k	VERB
ejpam-5224	250	14	by	by	ADP
ejpam-5224	250	15	a	a	DET
ejpam-5224	250	16	quiver	quiver	NOUN
ejpam-5224	250	17	q	q	NOUN
ejpam-5224	250	18	and	and	CCONJ
ejpam-5224	250	19	an	an	DET
ejpam-5224	250	20	admissible	admissible	ADJ
ejpam-5224	250	21	ideal	ideal	NOUN
ejpam-5224	251	1	i	i	NOUN
ejpam-5224	251	2	=	=	X
ejpam-5224	251	3	<	<	X
ejpam-5224	251	4	bc	bc	PROPN
ejpam-5224	251	5	,	,	PUNCT
ejpam-5224	251	6	ad	ad	NOUN
ejpam-5224	251	7	>	>	X
ejpam-5224	251	8	as	as	ADP
ejpam-5224	251	9	following	follow	VERB
ejpam-5224	251	10	:	:	PUNCT
ejpam-5224	251	11	3	3	NUM
ejpam-5224	251	12	1	1	NUM
ejpam-5224	251	13	2	2	NUM
ejpam-5224	251	14	5	5	NUM
ejpam-5224	251	15	4	4	NUM
ejpam-5224	251	16	c	c	NOUN
ejpam-5224	251	17	α	α	NOUN
ejpam-5224	251	18	β	β	NOUN
ejpam-5224	251	19	a	a	PRON
ejpam-5224	251	20	b	b	X
ejpam-5224	252	1	d	d	X
ejpam-5224	252	2	clearly	clearly	ADV
ejpam-5224	252	3	,	,	PUNCT
ejpam-5224	252	4	any	any	DET
ejpam-5224	252	5	path	path	NOUN
ejpam-5224	252	6	in	in	ADP
ejpam-5224	252	7	a	a	DET
ejpam-5224	252	8	of	of	ADP
ejpam-5224	252	9	length	length	NOUN
ejpam-5224	252	10	3	3	NUM
ejpam-5224	252	11	is	be	AUX
ejpam-5224	252	12	zero	zero	NUM
ejpam-5224	252	13	,	,	PUNCT
ejpam-5224	252	14	and	and	CCONJ
ejpam-5224	252	15	therefore	therefore	ADV
ejpam-5224	252	16	rad3(kq	rad3(kq	ADV
ejpam-5224	252	17	/	/	SYM
ejpam-5224	252	18	i	i	NOUN
ejpam-5224	252	19	)	)	PUNCT
ejpam-5224	252	20	=	=	PUNCT
ejpam-5224	253	1	0	0	X
ejpam-5224	253	2	.	.	PUNCT
ejpam-5224	254	1	here	here	ADV
ejpam-5224	254	2	are	be	AUX
ejpam-5224	254	3	the	the	DET
ejpam-5224	254	4	calculations	calculation	NOUN
ejpam-5224	254	5	of	of	ADP
ejpam-5224	254	6	the	the	DET
ejpam-5224	254	7	projective	projective	ADJ
ejpam-5224	254	8	resolutions	resolution	NOUN
ejpam-5224	254	9	of	of	ADP
ejpam-5224	254	10	simple	simple	ADJ
ejpam-5224	254	11	modules	module	NOUN
ejpam-5224	254	12	(	(	PUNCT
ejpam-5224	254	13	s(i))1≤i≤5	s(i))1≤i≤5	NOUN
ejpam-5224	254	14	,	,	PUNCT
ejpam-5224	254	15	0	0	NUM
ejpam-5224	255	1	−→	−→	NOUN
ejpam-5224	255	2	p	p	X
ejpam-5224	255	3	(	(	PUNCT
ejpam-5224	255	4	3)⊕	3)⊕	NUM
ejpam-5224	255	5	p	p	X
ejpam-5224	255	6	(	(	PUNCT
ejpam-5224	255	7	4	4	NUM
ejpam-5224	255	8	)	)	PUNCT
ejpam-5224	255	9	−→	−→	NOUN
ejpam-5224	255	10	p	p	X
ejpam-5224	255	11	(	(	PUNCT
ejpam-5224	255	12	2)2	2)2	NUM
ejpam-5224	255	13	−→	−→	NOUN
ejpam-5224	255	14	p	p	X
ejpam-5224	255	15	(	(	PUNCT
ejpam-5224	255	16	1	1	NUM
ejpam-5224	255	17	)	)	PUNCT
ejpam-5224	255	18	−→	−→	PROPN
ejpam-5224	255	19	s(1	s(1	PROPN
ejpam-5224	255	20	)	)	PUNCT
ejpam-5224	255	21	−→	−→	NOUN
ejpam-5224	255	22	0	0	NUM
ejpam-5224	255	23	references	reference	NOUN
ejpam-5224	255	24	1867	1867	NUM
ejpam-5224	255	25	0	0	NUM
ejpam-5224	255	26	−→	−→	NOUN
ejpam-5224	255	27	p	p	X
ejpam-5224	255	28	(	(	PUNCT
ejpam-5224	255	29	3)⊕	3)⊕	NUM
ejpam-5224	255	30	p	p	X
ejpam-5224	255	31	(	(	PUNCT
ejpam-5224	255	32	4	4	NUM
ejpam-5224	255	33	)	)	PUNCT
ejpam-5224	255	34	−→	−→	NOUN
ejpam-5224	255	35	p	p	X
ejpam-5224	255	36	(	(	PUNCT
ejpam-5224	255	37	2	2	NUM
ejpam-5224	255	38	)	)	PUNCT
ejpam-5224	255	39	−→	−→	NOUN
ejpam-5224	255	40	s(2	s(2	NOUN
ejpam-5224	255	41	)	)	PUNCT
ejpam-5224	255	42	−→	−→	NOUN
ejpam-5224	255	43	0	0	NUM
ejpam-5224	255	44	0	0	NUM
ejpam-5224	256	1	−→	−→	NOUN
ejpam-5224	256	2	p	p	X
ejpam-5224	256	3	(	(	PUNCT
ejpam-5224	256	4	5	5	NUM
ejpam-5224	256	5	)	)	PUNCT
ejpam-5224	256	6	−→	−→	NOUN
ejpam-5224	256	7	p	p	X
ejpam-5224	256	8	(	(	PUNCT
ejpam-5224	256	9	3	3	NUM
ejpam-5224	256	10	)	)	PUNCT
ejpam-5224	256	11	−→	−→	NOUN
ejpam-5224	256	12	s(3	s(3	NOUN
ejpam-5224	256	13	)	)	PUNCT
ejpam-5224	257	1	−→	−→	NOUN
ejpam-5224	257	2	0	0	NUM
ejpam-5224	257	3	0	0	NUM
ejpam-5224	257	4	−→	−→	NOUN
ejpam-5224	257	5	p	p	X
ejpam-5224	257	6	(	(	PUNCT
ejpam-5224	257	7	5	5	NUM
ejpam-5224	257	8	)	)	PUNCT
ejpam-5224	257	9	−→	−→	NOUN
ejpam-5224	257	10	p	p	X
ejpam-5224	257	11	(	(	PUNCT
ejpam-5224	257	12	4	4	NUM
ejpam-5224	257	13	)	)	PUNCT
ejpam-5224	257	14	−→	−→	NOUN
ejpam-5224	257	15	s(4	s(4	NOUN
ejpam-5224	257	16	)	)	PUNCT
ejpam-5224	258	1	−→	−→	NOUN
ejpam-5224	258	2	0	0	NUM
ejpam-5224	258	3	0	0	NUM
ejpam-5224	259	1	−→	−→	NOUN
ejpam-5224	259	2	p	p	X
ejpam-5224	259	3	(	(	PUNCT
ejpam-5224	259	4	5	5	NUM
ejpam-5224	259	5	)	)	PUNCT
ejpam-5224	259	6	−→	−→	NOUN
ejpam-5224	259	7	p	p	X
ejpam-5224	259	8	(	(	PUNCT
ejpam-5224	259	9	4	4	NUM
ejpam-5224	259	10	)	)	PUNCT
ejpam-5224	259	11	−→	−→	NOUN
ejpam-5224	259	12	s(5	s(5	PROPN
ejpam-5224	259	13	)	)	PUNCT
ejpam-5224	260	1	−→	−→	NOUN
ejpam-5224	260	2	0	0	NUM
ejpam-5224	261	1	then	then	ADV
ejpam-5224	261	2	,	,	PUNCT
ejpam-5224	261	3	we	we	PRON
ejpam-5224	261	4	have	have	VERB
ejpam-5224	261	5	inf(pd(si))1≤i≤5	inf(pd(si))1≤i≤5	NOUN
ejpam-5224	261	6	=	=	PUNCT
ejpam-5224	261	7	pd(s2	pd(s2	X
ejpam-5224	261	8	)	)	PUNCT
ejpam-5224	261	9	=	=	SYM
ejpam-5224	261	10	pd(s3	pd(s3	NOUN
ejpam-5224	261	11	)	)	PUNCT
ejpam-5224	261	12	=	=	SYM
ejpam-5224	261	13	pd(s4	pd(s4	PROPN
ejpam-5224	261	14	)	)	PUNCT
ejpam-5224	261	15	and	and	CCONJ
ejpam-5224	261	16	rad2(p	rad2(p	NOUN
ejpam-5224	261	17	(	(	PUNCT
ejpam-5224	261	18	ω(s	ω(s	NOUN
ejpam-5224	261	19	)	)	PUNCT
ejpam-5224	261	20	)	)	PUNCT
ejpam-5224	261	21	)	)	PUNCT
ejpam-5224	262	1	=	=	PUNCT
ejpam-5224	262	2	0	0	NUM
ejpam-5224	262	3	,	,	PUNCT
ejpam-5224	262	4	where	where	SCONJ
ejpam-5224	262	5	p	p	NOUN
ejpam-5224	262	6	(	(	PUNCT
ejpam-5224	262	7	ω(s	ω(s	PROPN
ejpam-5224	262	8	)	)	PUNCT
ejpam-5224	262	9	)	)	PUNCT
ejpam-5224	262	10	the	the	DET
ejpam-5224	262	11	projective	projective	ADJ
ejpam-5224	262	12	cover	cover	NOUN
ejpam-5224	262	13	for	for	ADP
ejpam-5224	262	14	ω(s	ω(	NOUN
ejpam-5224	262	15	)	)	PUNCT
ejpam-5224	262	16	for	for	ADP
ejpam-5224	262	17	every	every	DET
ejpam-5224	262	18	simple	simple	ADJ
ejpam-5224	262	19	module	module	NOUN
ejpam-5224	262	20	s.	s.	PROPN
ejpam-5224	262	21	thus	thus	ADV
ejpam-5224	262	22	,	,	PUNCT
ejpam-5224	262	23	ext1a(s(i	ext1a(s(i	PROPN
ejpam-5224	262	24	)	)	PUNCT
ejpam-5224	262	25	,	,	PUNCT
ejpam-5224	262	26	s(i	s(i	PROPN
ejpam-5224	262	27	)	)	PUNCT
ejpam-5224	262	28	)	)	PUNCT
ejpam-5224	263	1	=	=	SYM
ejpam-5224	263	2	0	0	PUNCT
ejpam-5224	264	1	for	for	ADP
ejpam-5224	264	2	i	i	PRON
ejpam-5224	264	3	=	=	NOUN
ejpam-5224	264	4	2	2	NUM
ejpam-5224	264	5	;	;	PUNCT
ejpam-5224	264	6	i	i	NOUN
ejpam-5224	264	7	=	=	NOUN
ejpam-5224	264	8	3	3	NUM
ejpam-5224	264	9	and	and	CCONJ
ejpam-5224	264	10	i	i	PRON
ejpam-5224	264	11	=	=	NOUN
ejpam-5224	264	12	4	4	NUM
ejpam-5224	264	13	.	.	NOUN
ejpam-5224	264	14	8	8	NUM
ejpam-5224	264	15	.	.	X
ejpam-5224	264	16	conclusion	conclusion	NOUN
ejpam-5224	264	17	our	our	PRON
ejpam-5224	264	18	work	work	NOUN
ejpam-5224	264	19	ultimately	ultimately	ADV
ejpam-5224	264	20	resolved	resolve	VERB
ejpam-5224	264	21	the	the	DET
ejpam-5224	264	22	conjecture	conjecture	NOUN
ejpam-5224	264	23	for	for	ADP
ejpam-5224	264	24	artinian	artinian	ADJ
ejpam-5224	264	25	rings	ring	NOUN
ejpam-5224	264	26	by	by	ADP
ejpam-5224	264	27	relying	rely	VERB
ejpam-5224	264	28	on	on	ADP
ejpam-5224	264	29	our	our	PRON
ejpam-5224	264	30	main	main	ADJ
ejpam-5224	264	31	results	result	NOUN
ejpam-5224	264	32	and	and	CCONJ
ejpam-5224	264	33	that	that	PRON
ejpam-5224	264	34	could	could	AUX
ejpam-5224	264	35	be	be	AUX
ejpam-5224	264	36	summarized	summarize	VERB
ejpam-5224	264	37	on	on	ADP
ejpam-5224	264	38	the	the	DET
ejpam-5224	264	39	statement	statement	NOUN
ejpam-5224	264	40	of	of	ADP
ejpam-5224	264	41	theorem	theorem	ADJ
ejpam-5224	264	42	2.1	2.1	NUM
ejpam-5224	264	43	and	and	CCONJ
ejpam-5224	264	44	which	which	PRON
ejpam-5224	264	45	we	we	PRON
ejpam-5224	264	46	have	have	AUX
ejpam-5224	264	47	succeeded	succeed	VERB
ejpam-5224	264	48	to	to	PART
ejpam-5224	264	49	prove	prove	VERB
ejpam-5224	264	50	along	along	ADP
ejpam-5224	264	51	this	this	DET
ejpam-5224	264	52	paper	paper	NOUN
ejpam-5224	264	53	,	,	PUNCT
ejpam-5224	264	54	as	as	ADV
ejpam-5224	264	55	well	well	ADV
ejpam-5224	264	56	as	as	ADP
ejpam-5224	264	57	the	the	DET
ejpam-5224	264	58	statement	statement	NOUN
ejpam-5224	264	59	of	of	ADP
ejpam-5224	264	60	corollary	corollary	ADJ
ejpam-5224	264	61	6.1	6.1	NUM
ejpam-5224	264	62	.	.	PUNCT
ejpam-5224	264	63	which	which	PRON
ejpam-5224	264	64	generalizes	generalize	VERB
ejpam-5224	264	65	it	it	PRON
ejpam-5224	264	66	,	,	PUNCT
ejpam-5224	264	67	and	and	CCONJ
ejpam-5224	264	68	finally	finally	ADV
ejpam-5224	264	69	without	without	ADP
ejpam-5224	264	70	forgetting	forget	VERB
ejpam-5224	264	71	our	our	PRON
ejpam-5224	264	72	other	other	ADJ
ejpam-5224	264	73	contribution	contribution	NOUN
ejpam-5224	264	74	point	point	NOUN
ejpam-5224	264	75	stated	state	VERB
ejpam-5224	264	76	in	in	ADP
ejpam-5224	264	77	remark	remark	NOUN
ejpam-5224	264	78	1.1	1.1	NUM
ejpam-5224	264	79	.	.	PUNCT
ejpam-5224	265	1	we	we	PRON
ejpam-5224	265	2	may	may	AUX
ejpam-5224	265	3	follow	follow	VERB
ejpam-5224	265	4	similar	similar	ADJ
ejpam-5224	265	5	process	process	NOUN
ejpam-5224	265	6	in	in	ADP
ejpam-5224	265	7	the	the	DET
ejpam-5224	265	8	future	future	NOUN
ejpam-5224	265	9	in	in	ADP
ejpam-5224	265	10	the	the	DET
ejpam-5224	265	11	hope	hope	NOUN
ejpam-5224	265	12	to	to	PART
ejpam-5224	265	13	demonstrate	demonstrate	VERB
ejpam-5224	265	14	the	the	DET
ejpam-5224	265	15	conjecture	conjecture	NOUN
ejpam-5224	265	16	in	in	ADP
ejpam-5224	265	17	the	the	DET
ejpam-5224	265	18	case	case	NOUN
ejpam-5224	265	19	of	of	ADP
ejpam-5224	265	20	zero	zero	NUM
ejpam-5224	265	21	radical	radical	ADJ
ejpam-5224	265	22	cube	cube	NOUN
ejpam-5224	265	23	without	without	ADP
ejpam-5224	265	24	a	a	DET
ejpam-5224	265	25	condition	condition	NOUN
ejpam-5224	265	26	on	on	ADP
ejpam-5224	265	27	the	the	DET
ejpam-5224	265	28	syzygies	syzygy	NOUN
ejpam-5224	265	29	but	but	CCONJ
ejpam-5224	265	30	also	also	ADV
ejpam-5224	265	31	extending	extend	VERB
ejpam-5224	265	32	this	this	DET
ejpam-5224	265	33	research	research	NOUN
ejpam-5224	265	34	by	by	ADP
ejpam-5224	265	35	attacking	attack	VERB
ejpam-5224	265	36	the	the	DET
ejpam-5224	265	37	conjecture	conjecture	NOUN
ejpam-5224	265	38	in	in	ADP
ejpam-5224	265	39	the	the	DET
ejpam-5224	265	40	case	case	NOUN
ejpam-5224	265	41	of	of	ADP
ejpam-5224	265	42	j4	j4	PROPN
ejpam-5224	265	43	=	=	SYM
ejpam-5224	265	44	0	0	NUM
ejpam-5224	265	45	under	under	ADP
ejpam-5224	265	46	constraints	constraint	NOUN
ejpam-5224	265	47	on	on	ADP
ejpam-5224	265	48	the	the	DET
ejpam-5224	265	49	syzygies	syzygy	NOUN
ejpam-5224	265	50	.	.	PUNCT
ejpam-5224	266	1	the	the	DET
ejpam-5224	266	2	whole	whole	ADJ
ejpam-5224	266	3	approach	approach	NOUN
ejpam-5224	266	4	may	may	AUX
ejpam-5224	266	5	lead	lead	VERB
ejpam-5224	266	6	to	to	ADP
ejpam-5224	266	7	a	a	DET
ejpam-5224	266	8	process	process	NOUN
ejpam-5224	266	9	of	of	ADP
ejpam-5224	266	10	proving	prove	VERB
ejpam-5224	266	11	the	the	DET
ejpam-5224	266	12	conjecture	conjecture	NOUN
ejpam-5224	266	13	in	in	ADP
ejpam-5224	266	14	general	general	ADJ
ejpam-5224	266	15	.	.	PUNCT
ejpam-5224	267	1	acknowledgements	acknowledgement	NOUN
ejpam-5224	267	2	a	a	DET
ejpam-5224	267	3	special	special	ADJ
ejpam-5224	267	4	thanks	thank	NOUN
ejpam-5224	267	5	to	to	ADP
ejpam-5224	267	6	the	the	DET
ejpam-5224	267	7	editor	editor	NOUN
ejpam-5224	267	8	professors	professor	NOUN
ejpam-5224	267	9	eyup	eyup	VERB
ejpam-5224	267	10	cetin	cetin	NOUN
ejpam-5224	267	11	and	and	CCONJ
ejpam-5224	267	12	baris	baris	PROPN
ejpam-5224	267	13	kiremitci	kiremitci	NOUN
ejpam-5224	267	14	.	.	PUNCT
ejpam-5224	268	1	we	we	PRON
ejpam-5224	268	2	would	would	AUX
ejpam-5224	268	3	also	also	ADV
ejpam-5224	268	4	like	like	VERB
ejpam-5224	268	5	to	to	PART
ejpam-5224	268	6	thank	thank	VERB
ejpam-5224	268	7	all	all	DET
ejpam-5224	268	8	the	the	DET
ejpam-5224	268	9	three	three	NUM
ejpam-5224	268	10	anonymous	anonymous	ADJ
ejpam-5224	268	11	referees	referee	NOUN
ejpam-5224	268	12	for	for	ADP
ejpam-5224	268	13	their	their	PRON
ejpam-5224	268	14	time	time	NOUN
ejpam-5224	268	15	,	,	PUNCT
ejpam-5224	268	16	effort	effort	NOUN
ejpam-5224	268	17	and	and	CCONJ
ejpam-5224	268	18	help	help	VERB
ejpam-5224	268	19	for	for	ADP
ejpam-5224	268	20	improving	improve	VERB
ejpam-5224	268	21	the	the	DET
ejpam-5224	268	22	content	content	NOUN
ejpam-5224	268	23	of	of	ADP
ejpam-5224	268	24	our	our	PRON
ejpam-5224	268	25	paper	paper	NOUN
ejpam-5224	268	26	.	.	PUNCT
ejpam-5224	269	1	references	reference	NOUN
ejpam-5224	269	2	[	[	X
ejpam-5224	269	3	1	1	NUM
ejpam-5224	269	4	]	]	PUNCT
ejpam-5224	269	5	i.	i.	PROPN
ejpam-5224	269	6	elmouki	elmouki	PROPN
ejpam-5224	269	7	s.	s.	PROPN
ejpam-5224	269	8	abdelalim	abdelalim	PROPN
ejpam-5224	269	9	.	.	PUNCT
ejpam-5224	270	1	a	a	DET
ejpam-5224	270	2	note	note	NOUN
ejpam-5224	270	3	on	on	ADP
ejpam-5224	270	4	wedderburn	wedderburn	NOUN
ejpam-5224	270	5	and	and	CCONJ
ejpam-5224	270	6	hasse	hasse	NOUN
ejpam-5224	270	7	theorems	theorem	NOUN
ejpam-5224	270	8	.	.	PUNCT
ejpam-5224	271	1	gulf	gulf	PROPN
ejpam-5224	271	2	journal	journal	PROPN
ejpam-5224	271	3	of	of	ADP
ejpam-5224	271	4	mathematics	mathematics	PROPN
ejpam-5224	271	5	,	,	PUNCT
ejpam-5224	271	6	16(1	16(1	NUM
ejpam-5224	271	7	)	)	PUNCT
ejpam-5224	271	8	,	,	PUNCT
ejpam-5224	271	9	68	68	NUM
ejpam-5224	271	10	-	-	SYM
ejpam-5224	271	11	78	78	NUM
ejpam-5224	271	12	,	,	PUNCT
ejpam-5224	271	13	2024	2024	NUM
ejpam-5224	271	14	.	.	PUNCT
ejpam-5224	272	1	[	[	X
ejpam-5224	272	2	2	2	X
ejpam-5224	272	3	]	]	PUNCT
ejpam-5224	272	4	s.	s.	PROPN
ejpam-5224	272	5	abdelalim	abdelalim	PROPN
ejpam-5224	272	6	.	.	PUNCT
ejpam-5224	273	1	characterization	characterization	NOUN
ejpam-5224	273	2	the	the	DET
ejpam-5224	273	3	strongly	strongly	ADV
ejpam-5224	273	4	hopfian	hopfian	ADJ
ejpam-5224	273	5	abelian	abelian	ADJ
ejpam-5224	273	6	groups	group	NOUN
ejpam-5224	273	7	in	in	ADP
ejpam-5224	273	8	the	the	DET
ejpam-5224	273	9	category	category	NOUN
ejpam-5224	273	10	of	of	ADP
ejpam-5224	273	11	abelian	abelian	ADJ
ejpam-5224	273	12	torsion	torsion	NOUN
ejpam-5224	273	13	groups	group	NOUN
ejpam-5224	273	14	.	.	PUNCT
ejpam-5224	274	1	journal	journal	PROPN
ejpam-5224	274	2	of	of	ADP
ejpam-5224	274	3	mathematical	mathematical	ADJ
ejpam-5224	274	4	analysis	analysis	NOUN
ejpam-5224	274	5	,	,	PUNCT
ejpam-5224	274	6	6(4	6(4	NUM
ejpam-5224	274	7	)	)	PUNCT
ejpam-5224	274	8	,	,	PUNCT
ejpam-5224	274	9	1	1	NUM
ejpam-5224	274	10	-	-	SYM
ejpam-5224	274	11	10	10	NUM
ejpam-5224	274	12	,	,	PUNCT
ejpam-5224	274	13	2015	2015	NUM
ejpam-5224	274	14	.	.	PUNCT
ejpam-5224	275	1	[	[	X
ejpam-5224	275	2	3	3	X
ejpam-5224	275	3	]	]	X
ejpam-5224	275	4	s.	s.	PROPN
ejpam-5224	275	5	abdelalim	abdelalim	PROPN
ejpam-5224	275	6	a.	a.	NOUN
ejpam-5224	275	7	chaichaa	chaichaa	PROPN
ejpam-5224	275	8	m.	m.	NOUN
ejpam-5224	275	9	el	el	PROPN
ejpam-5224	275	10	garn	garn	PROPN
ejpam-5224	275	11	.	.	PUNCT
ejpam-5224	276	1	the	the	DET
ejpam-5224	276	2	automorphisms	automorphism	NOUN
ejpam-5224	276	3	having	have	VERB
ejpam-5224	276	4	the	the	DET
ejpam-5224	276	5	extension	extension	NOUN
ejpam-5224	276	6	property	property	NOUN
ejpam-5224	276	7	in	in	ADP
ejpam-5224	276	8	a	a	DET
ejpam-5224	276	9	category	category	NOUN
ejpam-5224	276	10	of	of	ADP
ejpam-5224	276	11	a	a	DET
ejpam-5224	276	12	finite	finite	ADJ
ejpam-5224	276	13	direct	direct	ADJ
ejpam-5224	276	14	sum	sum	NOUN
ejpam-5224	276	15	of	of	ADP
ejpam-5224	276	16	cyclic	cyclic	ADJ
ejpam-5224	276	17	modules	module	NOUN
ejpam-5224	276	18	.	.	PUNCT
ejpam-5224	277	1	discussiones	discussione	NOUN
ejpam-5224	277	2	mathematicae	mathematicae	VERB
ejpam-5224	277	3	:	:	PUNCT
ejpam-5224	277	4	general	general	ADJ
ejpam-5224	277	5	algebra	algebra	NOUN
ejpam-5224	277	6	and	and	CCONJ
ejpam-5224	277	7	applications	application	NOUN
ejpam-5224	277	8	,	,	PUNCT
ejpam-5224	277	9	43(1	43(1	NOUN
ejpam-5224	277	10	)	)	PUNCT
ejpam-5224	277	11	,	,	PUNCT
ejpam-5224	277	12	2024	2024	NUM
ejpam-5224	277	13	.	.	PUNCT
ejpam-5224	278	1	[	[	X
ejpam-5224	278	2	4	4	NUM
ejpam-5224	278	3	]	]	PUNCT
ejpam-5224	278	4	a.	a.	PROPN
ejpam-5224	278	5	hattori	hattori	PROPN
ejpam-5224	278	6	.	.	PUNCT
ejpam-5224	278	7	rank	rank	PROPN
ejpam-5224	278	8	element	element	NOUN
ejpam-5224	278	9	of	of	ADP
ejpam-5224	278	10	a	a	DET
ejpam-5224	278	11	projective	projective	ADJ
ejpam-5224	278	12	module	module	NOUN
ejpam-5224	278	13	.	.	PUNCT
ejpam-5224	279	1	nagoya	nagoya	PROPN
ejpam-5224	279	2	mathematical	mathematical	PROPN
ejpam-5224	279	3	journal	journal	PROPN
ejpam-5224	279	4	,	,	PUNCT
ejpam-5224	279	5	25	25	NUM
ejpam-5224	279	6	,	,	PUNCT
ejpam-5224	279	7	113	113	NUM
ejpam-5224	279	8	-	-	SYM
ejpam-5224	279	9	120	120	NUM
ejpam-5224	279	10	,	,	PUNCT
ejpam-5224	279	11	1965	1965	NUM
ejpam-5224	279	12	.	.	PUNCT
ejpam-5224	280	1	[	[	X
ejpam-5224	280	2	5	5	X
ejpam-5224	280	3	]	]	PUNCT
ejpam-5224	280	4	k.	k.	PROPN
ejpam-5224	280	5	igusa	igusa	PROPN
ejpam-5224	280	6	.	.	PUNCT
ejpam-5224	281	1	notes	note	NOUN
ejpam-5224	281	2	on	on	ADP
ejpam-5224	281	3	the	the	DET
ejpam-5224	281	4	no	no	PROPN
ejpam-5224	281	5	loops	loop	NOUN
ejpam-5224	281	6	conjecture	conjecture	VERB
ejpam-5224	281	7	.	.	PUNCT
ejpam-5224	282	1	journal	journal	NOUN
ejpam-5224	282	2	of	of	ADP
ejpam-5224	282	3	pure	pure	ADJ
ejpam-5224	282	4	and	and	CCONJ
ejpam-5224	282	5	applied	applied	ADJ
ejpam-5224	282	6	algebra	algebra	NOUN
ejpam-5224	282	7	,	,	PUNCT
ejpam-5224	282	8	69(2	69(2	NOUN
ejpam-5224	282	9	)	)	PUNCT
ejpam-5224	282	10	,	,	PUNCT
ejpam-5224	282	11	161	161	NUM
ejpam-5224	282	12	-	-	SYM
ejpam-5224	282	13	176	176	NUM
ejpam-5224	282	14	,	,	PUNCT
ejpam-5224	282	15	1990	1990	NUM
ejpam-5224	282	16	.	.	PUNCT
ejpam-5224	283	1	references	reference	NOUN
ejpam-5224	283	2	1868	1868	NUM
ejpam-5224	284	1	[	[	X
ejpam-5224	284	2	6	6	NUM
ejpam-5224	284	3	]	]	X
ejpam-5224	284	4	h.	h.	NOUN
ejpam-5224	284	5	lenzing	lenzing	NOUN
ejpam-5224	284	6	.	.	PUNCT
ejpam-5224	285	1	nilpotente	nilpotente	PROPN
ejpam-5224	285	2	elemente	elemente	PROPN
ejpam-5224	285	3	in	in	ADP
ejpam-5224	285	4	ringen	ringen	PROPN
ejpam-5224	285	5	von	von	PROPN
ejpam-5224	285	6	endlicher	endlicher	PROPN
ejpam-5224	285	7	globaler	globaler	PROPN
ejpam-5224	285	8	dimension	dimension	NOUN
ejpam-5224	285	9	.	.	PUNCT
ejpam-5224	286	1	mathematische	mathematische	PROPN
ejpam-5224	286	2	zeitschrift	zeitschrift	NOUN
ejpam-5224	286	3	,	,	PUNCT
ejpam-5224	286	4	108	108	NUM
ejpam-5224	286	5	,	,	PUNCT
ejpam-5224	286	6	313	313	NUM
ejpam-5224	286	7	-	-	SYM
ejpam-5224	286	8	324	324	NUM
ejpam-5224	286	9	,	,	PUNCT
ejpam-5224	286	10	1969	1969	NUM
ejpam-5224	286	11	.	.	PUNCT
ejpam-5224	287	1	[	[	X
ejpam-5224	287	2	7	7	X
ejpam-5224	287	3	]	]	PUNCT
ejpam-5224	287	4	a.	a.	NOUN
ejpam-5224	287	5	louly	louly	PROPN
ejpam-5224	287	6	.	.	PUNCT
ejpam-5224	288	1	local	local	ADJ
ejpam-5224	288	2	derivations	derivation	NOUN
ejpam-5224	288	3	of	of	ADP
ejpam-5224	288	4	quantum	quantum	ADJ
ejpam-5224	288	5	plane	plane	NOUN
ejpam-5224	288	6	algebra	algebra	NOUN
ejpam-5224	288	7	.	.	PUNCT
ejpam-5224	289	1	communications	communication	NOUN
ejpam-5224	289	2	in	in	ADP
ejpam-5224	289	3	algebra	algebra	NOUN
ejpam-5224	289	4	,	,	PUNCT
ejpam-5224	289	5	52(2	52(2	NUM
ejpam-5224	289	6	)	)	PUNCT
ejpam-5224	289	7	,	,	PUNCT
ejpam-5224	289	8	711	711	NOUN
ejpam-5224	289	9	-	-	SYM
ejpam-5224	289	10	716	716	NUM
ejpam-5224	289	11	,	,	PUNCT
ejpam-5224	289	12	2024	2024	NUM
ejpam-5224	289	13	.	.	PUNCT
ejpam-5224	290	1	[	[	X
ejpam-5224	290	2	8	8	NUM
ejpam-5224	290	3	]	]	PUNCT
ejpam-5224	290	4	k.	k.	PROPN
ejpam-5224	290	5	charrabi	charrabi	PROPN
ejpam-5224	290	6	a.	a.	PROPN
ejpam-5224	290	7	mamouni	mamouni	PROPN
ejpam-5224	290	8	.	.	PUNCT
ejpam-5224	291	1	on	on	ADP
ejpam-5224	291	2	prime	prime	ADJ
ejpam-5224	291	3	ideals	ideal	NOUN
ejpam-5224	291	4	in	in	ADP
ejpam-5224	291	5	rings	ring	NOUN
ejpam-5224	291	6	with	with	ADP
ejpam-5224	291	7	involution	involution	NOUN
ejpam-5224	291	8	involving	involve	VERB
ejpam-5224	291	9	pair	pair	NOUN
ejpam-5224	291	10	of	of	ADP
ejpam-5224	291	11	generalized	generalized	ADJ
ejpam-5224	291	12	derivations	derivation	NOUN
ejpam-5224	291	13	.	.	PUNCT
ejpam-5224	292	1	asian	asian	ADJ
ejpam-5224	292	2	-	-	PUNCT
ejpam-5224	292	3	european	european	ADJ
ejpam-5224	292	4	journal	journal	NOUN
ejpam-5224	292	5	of	of	ADP
ejpam-5224	292	6	mathematics	mathematic	NOUN
ejpam-5224	292	7	,	,	PUNCT
ejpam-5224	292	8	2024	2024	NUM
ejpam-5224	292	9	.	.	PUNCT
ejpam-5224	293	1	[	[	X
ejpam-5224	293	2	9	9	NUM
ejpam-5224	293	3	]	]	PUNCT
ejpam-5224	293	4	k.	k.	PROPN
ejpam-5224	293	5	igusa	igusa	PROPN
ejpam-5224	293	6	s.	s.	PROPN
ejpam-5224	293	7	liu	liu	PROPN
ejpam-5224	293	8	c.	c.	PROPN
ejpam-5224	293	9	paquette	paquette	PROPN
ejpam-5224	293	10	.	.	PUNCT
ejpam-5224	294	1	a	a	DET
ejpam-5224	294	2	proof	proof	NOUN
ejpam-5224	294	3	of	of	ADP
ejpam-5224	294	4	the	the	DET
ejpam-5224	294	5	strong	strong	ADJ
ejpam-5224	294	6	no	no	DET
ejpam-5224	294	7	loop	loop	NOUN
ejpam-5224	294	8	conjecture	conjecture	NOUN
ejpam-5224	294	9	.	.	PUNCT
ejpam-5224	295	1	advances	advance	NOUN
ejpam-5224	295	2	in	in	ADP
ejpam-5224	295	3	mathematics	mathematic	NOUN
ejpam-5224	295	4	,	,	PUNCT
ejpam-5224	295	5	228(5	228(5	NUM
ejpam-5224	295	6	)	)	PUNCT
ejpam-5224	295	7	,	,	PUNCT
ejpam-5224	295	8	2731	2731	NUM
ejpam-5224	295	9	-	-	SYM
ejpam-5224	295	10	2742	2742	NUM
ejpam-5224	295	11	,	,	PUNCT
ejpam-5224	295	12	2011	2011	NUM
ejpam-5224	295	13	.	.	PUNCT
ejpam-5224	296	1	[	[	X
ejpam-5224	296	2	10	10	NUM
ejpam-5224	296	3	]	]	PUNCT
ejpam-5224	296	4	m.	m.	NOUN
ejpam-5224	296	5	auslander	auslander	PROPN
ejpam-5224	296	6	i.	i.	PROPN
ejpam-5224	296	7	reiten	reiten	PROPN
ejpam-5224	296	8	s.	s.	PROPN
ejpam-5224	296	9	o.	o.	PROPN
ejpam-5224	297	1	smalø	smalø	PROPN
ejpam-5224	297	2	.	.	PUNCT
ejpam-5224	298	1	representation	representation	NOUN
ejpam-5224	298	2	theory	theory	NOUN
ejpam-5224	298	3	of	of	ADP
ejpam-5224	298	4	artin	artin	PROPN
ejpam-5224	298	5	algebras	algebras	PROPN
ejpam-5224	298	6	.	.	PUNCT
ejpam-5224	299	1	cambridge	cambridge	PROPN
ejpam-5224	299	2	studies	study	NOUN
ejpam-5224	299	3	in	in	ADP
ejpam-5224	299	4	advanced	advanced	ADJ
ejpam-5224	299	5	mathematics	mathematic	NOUN
ejpam-5224	299	6	36	36	NUM
ejpam-5224	299	7	,	,	PUNCT
ejpam-5224	299	8	1995	1995	NUM
ejpam-5224	299	9	.	.	PUNCT
ejpam-5224	300	1	[	[	X
ejpam-5224	300	2	11	11	NUM
ejpam-5224	300	3	]	]	PUNCT
ejpam-5224	300	4	j.	j.	PROPN
ejpam-5224	300	5	stallings	stallings	PROPN
ejpam-5224	300	6	.	.	PUNCT
ejpam-5224	301	1	centerless	centerless	NOUN
ejpam-5224	301	2	groups	group	NOUN
ejpam-5224	301	3	an	an	DET
ejpam-5224	301	4	algebraic	algebraic	ADJ
ejpam-5224	301	5	formulation	formulation	NOUN
ejpam-5224	301	6	of	of	ADP
ejpam-5224	301	7	gottlieb	gottlieb	PROPN
ejpam-5224	301	8	’s	’s	PART
ejpam-5224	301	9	theorem	theorem	PROPN
ejpam-5224	301	10	.	.	PROPN
ejpam-5224	301	11	topology	topology	NOUN
ejpam-5224	301	12	,	,	PUNCT
ejpam-5224	301	13	4(2	4(2	NUM
ejpam-5224	301	14	)	)	PUNCT
ejpam-5224	301	15	,	,	PUNCT
ejpam-5224	301	16	129	129	NUM
ejpam-5224	301	17	-	-	SYM
ejpam-5224	301	18	134	134	NUM
ejpam-5224	301	19	,	,	PUNCT
ejpam-5224	301	20	1965	1965	NUM
ejpam-5224	301	21	.	.	PUNCT
ejpam-5224	302	1	[	[	X
ejpam-5224	302	2	12	12	NUM
ejpam-5224	302	3	]	]	X
ejpam-5224	302	4	o.	o.	PROPN
ejpam-5224	302	5	ajebbar	ajebbar	PROPN
ejpam-5224	302	6	e.	e.	PROPN
ejpam-5224	302	7	elqorachi	elqorachi	PROPN
ejpam-5224	302	8	h.	h.	PROPN
ejpam-5224	302	9	stetkaer	stetkaer	PROPN
ejpam-5224	302	10	.	.	PUNCT
ejpam-5224	303	1	the	the	DET
ejpam-5224	303	2	cosine	cosine	NOUN
ejpam-5224	303	3	addition	addition	NOUN
ejpam-5224	303	4	and	and	CCONJ
ejpam-5224	303	5	subtraction	subtraction	NOUN
ejpam-5224	303	6	formulas	formula	NOUN
ejpam-5224	303	7	on	on	ADP
ejpam-5224	303	8	non	non	ADJ
ejpam-5224	303	9	-	-	ADJ
ejpam-5224	303	10	abelian	abelian	ADJ
ejpam-5224	303	11	groups	group	NOUN
ejpam-5224	303	12	.	.	PUNCT
ejpam-5224	304	1	aequationes	aequatione	NOUN
ejpam-5224	304	2	mathematicae	mathematicae	PROPN
ejpam-5224	304	3	,	,	PUNCT
ejpam-5224	304	4	1	1	NUM
ejpam-5224	304	5	-	-	SYM
ejpam-5224	304	6	20	20	NUM
ejpam-5224	304	7	,	,	PUNCT
ejpam-5224	304	8	2024	2024	NUM
ejpam-5224	304	9	.	.	PUNCT
ejpam-5224	305	1	[	[	X
ejpam-5224	305	2	13	13	NUM
ejpam-5224	305	3	]	]	X
ejpam-5224	305	4	c.a	c.a	PROPN
ejpam-5224	305	5	.	.	PROPN
ejpam-5224	305	6	weibel	weibel	PROPN
ejpam-5224	305	7	.	.	PUNCT
ejpam-5224	306	1	an	an	DET
ejpam-5224	306	2	introduction	introduction	NOUN
ejpam-5224	306	3	to	to	ADP
ejpam-5224	306	4	homological	homological	ADJ
ejpam-5224	306	5	algebra	algebra	NOUN
ejpam-5224	306	6	.	.	PUNCT
ejpam-5224	307	1	cambridge	cambridge	PROPN
ejpam-5224	307	2	studies	study	NOUN
ejpam-5224	307	3	in	in	ADP
ejpam-5224	307	4	advanced	advanced	ADJ
ejpam-5224	307	5	mathematics	mathematic	NOUN
ejpam-5224	307	6	38	38	NUM
ejpam-5224	307	7	,	,	PUNCT
ejpam-5224	307	8	1994	1994	NUM
ejpam-5224	307	9	.	.	PUNCT
ejpam-5224	308	1	[	[	X
ejpam-5224	308	2	14	14	NUM
ejpam-5224	308	3	]	]	X
ejpam-5224	308	4	e.l	e.l	PROPN
ejpam-5224	308	5	.	.	PROPN
ejpam-5224	308	6	green	green	PROPN
ejpam-5224	308	7	w.	w.	PROPN
ejpam-5224	308	8	h.	h.	PROPN
ejpam-5224	308	9	gustafson	gustafson	PROPN
ejpam-5224	308	10	d.	d.	PROPN
ejpam-5224	308	11	zacharia	zacharia	PROPN
ejpam-5224	308	12	.	.	PUNCT
ejpam-5224	309	1	artin	artin	PROPN
ejpam-5224	309	2	rings	ring	NOUN
ejpam-5224	309	3	of	of	ADP
ejpam-5224	309	4	global	global	ADJ
ejpam-5224	309	5	dimension	dimension	PROPN
ejpam-5224	309	6	two	two	NUM
ejpam-5224	309	7	.	.	PUNCT
ejpam-5224	310	1	journal	journal	PROPN
ejpam-5224	310	2	of	of	ADP
ejpam-5224	310	3	algebra	algebra	PROPN
ejpam-5224	310	4	,	,	PUNCT
ejpam-5224	310	5	92(2	92(2	NUM
ejpam-5224	310	6	)	)	PUNCT
ejpam-5224	310	7	,	,	PUNCT
ejpam-5224	310	8	375	375	NUM
ejpam-5224	310	9	-	-	SYM
ejpam-5224	310	10	379	379	NUM
ejpam-5224	310	11	.	.	NUM
ejpam-5224	310	12	,	,	PUNCT
ejpam-5224	310	13	1985	1985	NUM
ejpam-5224	310	14	.	.	PUNCT
ejpam-5224	311	1	[	[	X
ejpam-5224	311	2	15	15	NUM
ejpam-5224	311	3	]	]	X
ejpam-5224	311	4	r.	r.	PROPN
ejpam-5224	311	5	ware	ware	PROPN
ejpam-5224	311	6	j.	j.	PROPN
ejpam-5224	311	7	zelmanowitz	zelmanowitz	PROPN
ejpam-5224	311	8	.	.	PUNCT
ejpam-5224	312	1	the	the	DET
ejpam-5224	312	2	jacobson	jacobson	PROPN
ejpam-5224	312	3	radical	radical	PROPN
ejpam-5224	312	4	of	of	ADP
ejpam-5224	312	5	the	the	DET
ejpam-5224	312	6	endomorphism	endomorphism	NOUN
ejpam-5224	312	7	ring	ring	NOUN
ejpam-5224	312	8	of	of	ADP
ejpam-5224	312	9	a	a	DET
ejpam-5224	312	10	projective	projective	ADJ
ejpam-5224	312	11	module	module	NOUN
ejpam-5224	312	12	.	.	PUNCT
ejpam-5224	313	1	proceedings	proceeding	NOUN
ejpam-5224	313	2	of	of	ADP
ejpam-5224	313	3	the	the	DET
ejpam-5224	313	4	american	american	PROPN
ejpam-5224	313	5	mathematical	mathematical	PROPN
ejpam-5224	313	6	society	society	NOUN
ejpam-5224	313	7	,	,	PUNCT
ejpam-5224	313	8	26(1	26(1	NUM
ejpam-5224	313	9	)	)	PUNCT
ejpam-5224	313	10	,	,	PUNCT
ejpam-5224	313	11	15	15	NUM
ejpam-5224	313	12	-	-	SYM
ejpam-5224	313	13	20	20	NUM
ejpam-5224	313	14	,	,	PUNCT
ejpam-5224	313	15	1970	1970	NUM
ejpam-5224	313	16	.	.	PUNCT
ejpam-5224	314	1	[	[	X
ejpam-5224	314	2	16	16	NUM
ejpam-5224	314	3	]	]	X
ejpam-5224	314	4	s.	s.	PROPN
ejpam-5224	314	5	abdelalim	abdelalim	PROPN
ejpam-5224	314	6	a.	a.	PROPN
ejpam-5224	314	7	chillali	chillali	PROPN
ejpam-5224	314	8	h.	h.	PROPN
ejpam-5224	314	9	essanouni	essanouni	PROPN
ejpam-5224	314	10	m.	m.	PROPN
ejpam-5224	314	11	zeriouh	zeriouh	PROPN
ejpam-5224	314	12	m.h	m.h	PROPN
ejpam-5224	314	13	.	.	PROPN
ejpam-5224	314	14	ziane	ziane	PROPN
ejpam-5224	314	15	.	.	PUNCT
ejpam-5224	315	1	construction	construction	NOUN
ejpam-5224	315	2	of	of	ADP
ejpam-5224	315	3	the	the	DET
ejpam-5224	315	4	α2−automorphism	α2−automorphism	NOUN
ejpam-5224	315	5	.	.	PUNCT
ejpam-5224	316	1	international	international	ADJ
ejpam-5224	316	2	journal	journal	PROPN
ejpam-5224	316	3	of	of	ADP
ejpam-5224	316	4	algebra	algebra	PROPN
ejpam-5224	316	5	,	,	PUNCT
ejpam-5224	316	6	8(5	8(5	NUM
ejpam-5224	316	7	)	)	PUNCT
ejpam-5224	316	8	,	,	PUNCT
ejpam-5224	316	9	247	247	NUM
ejpam-5224	316	10	-	-	SYM
ejpam-5224	316	11	251	251	NUM
ejpam-5224	316	12	,	,	PUNCT
ejpam-5224	316	13	2014	2014	NUM
ejpam-5224	316	14	.	.	PUNCT
ejpam-5224	317	1	[	[	X
ejpam-5224	317	2	17	17	NUM
ejpam-5224	317	3	]	]	X
ejpam-5224	317	4	k.r	k.r	PROPN
ejpam-5224	317	5	.	.	PROPN
ejpam-5224	317	6	fuller	full	ADJ
ejpam-5224	317	7	b.	b.	PROPN
ejpam-5224	317	8	zimmermann	zimmermann	PROPN
ejpam-5224	317	9	-	-	PUNCT
ejpam-5224	317	10	huisgen	huisgen	PROPN
ejpam-5224	317	11	.	.	PUNCT
ejpam-5224	318	1	on	on	ADP
ejpam-5224	318	2	the	the	DET
ejpam-5224	318	3	generalized	generalize	VERB
ejpam-5224	318	4	nakayama	nakayama	NOUN
ejpam-5224	318	5	conjecture	conjecture	NOUN
ejpam-5224	318	6	and	and	CCONJ
ejpam-5224	318	7	the	the	DET
ejpam-5224	318	8	cartan	cartan	ADJ
ejpam-5224	318	9	determinant	determinant	ADJ
ejpam-5224	318	10	problem	problem	NOUN
ejpam-5224	318	11	.	.	PUNCT
ejpam-5224	319	1	transactions	transaction	NOUN
ejpam-5224	319	2	of	of	ADP
ejpam-5224	319	3	the	the	DET
ejpam-5224	319	4	american	american	PROPN
ejpam-5224	319	5	mathematical	mathematical	PROPN
ejpam-5224	319	6	society	society	NOUN
ejpam-5224	319	7	,	,	PUNCT
ejpam-5224	319	8	294(2	294(2	NUM
ejpam-5224	319	9	)	)	PUNCT
ejpam-5224	319	10	,	,	PUNCT
ejpam-5224	319	11	679	679	NUM
ejpam-5224	319	12	-	-	SYM
ejpam-5224	319	13	691	691	NUM
ejpam-5224	319	14	,	,	PUNCT
ejpam-5224	319	15	1986	1986	NUM
ejpam-5224	319	16	.	.	PUNCT