id	sid	tid	token	lemma	pos
ejpam-4973	1	1	european	european	PROPN
ejpam-4973	1	2	journal	journal	PROPN
ejpam-4973	1	3	of	of	ADP
ejpam-4973	1	4	pure	pure	ADJ
ejpam-4973	1	5	and	and	CCONJ
ejpam-4973	1	6	applied	apply	VERB
ejpam-4973	1	7	mathematics	mathematic	NOUN
ejpam-4973	1	8	vol	vol	NOUN
ejpam-4973	1	9	.	.	PROPN
ejpam-4973	2	1	17	17	NUM
ejpam-4973	2	2	,	,	PUNCT
ejpam-4973	2	3	no	no	INTJ
ejpam-4973	2	4	.	.	NOUN
ejpam-4973	2	5	1	1	NUM
ejpam-4973	2	6	,	,	PUNCT
ejpam-4973	2	7	2024	2024	NUM
ejpam-4973	2	8	,	,	PUNCT
ejpam-4973	2	9	410	410	NUM
ejpam-4973	2	10	-	-	SYM
ejpam-4973	2	11	415	415	NUM
ejpam-4973	2	12	issn	issn	PROPN
ejpam-4973	2	13	1307	1307	NUM
ejpam-4973	2	14	-	-	SYM
ejpam-4973	2	15	5543	5543	NUM
ejpam-4973	2	16	–	–	PUNCT
ejpam-4973	3	1	ejpam.com	ejpam.com	X
ejpam-4973	3	2	published	publish	VERB
ejpam-4973	3	3	by	by	ADP
ejpam-4973	3	4	new	new	PROPN
ejpam-4973	3	5	york	york	PROPN
ejpam-4973	3	6	business	business	PROPN
ejpam-4973	3	7	global	global	ADJ
ejpam-4973	3	8	direct	direct	ADJ
ejpam-4973	3	9	summand	summand	NOUN
ejpam-4973	3	10	of	of	ADP
ejpam-4973	3	11	serial	serial	ADJ
ejpam-4973	3	12	modules	module	NOUN
ejpam-4973	3	13	al	al	PROPN
ejpam-4973	3	14	-	-	PUNCT
ejpam-4973	3	15	housseynou	housseynou	PROPN
ejpam-4973	3	16	ba1,∗	ba1,∗	NOUN
ejpam-4973	3	17	,	,	PUNCT
ejpam-4973	3	18	mankagna	mankagna	PROPN
ejpam-4973	3	19	albert	albert	PROPN
ejpam-4973	3	20	diompy1	diompy1	PROPN
ejpam-4973	3	21	,	,	PUNCT
ejpam-4973	3	22	andré	andré	ADJ
ejpam-4973	3	23	souleye	souleye	NOUN
ejpam-4973	3	24	diabang2	diabang2	NOUN
ejpam-4973	3	25	1	1	NUM
ejpam-4973	3	26	département	département	PROPN
ejpam-4973	3	27	de	de	X
ejpam-4973	3	28	mathématiques	mathématiques	X
ejpam-4973	3	29	et	et	PROPN
ejpam-4973	3	30	informatique	informatique	PROPN
ejpam-4973	3	31	,	,	PUNCT
ejpam-4973	3	32	faculté	faculté	NOUN
ejpam-4973	3	33	des	des	PROPN
ejpam-4973	3	34	sciences	sciences	PROPN
ejpam-4973	3	35	et	et	PROPN
ejpam-4973	3	36	techniques	technique	NOUN
ejpam-4973	3	37	,	,	PUNCT
ejpam-4973	3	38	université	université	NOUN
ejpam-4973	3	39	cheikh	cheikh	PROPN
ejpam-4973	3	40	anta	anta	PROPN
ejpam-4973	3	41	diop	diop	PROPN
ejpam-4973	3	42	,	,	PUNCT
ejpam-4973	3	43	dakar	dakar	NOUN
ejpam-4973	3	44	,	,	PUNCT
ejpam-4973	3	45	sénégal	sénégal	ADJ
ejpam-4973	3	46	2	2	NUM
ejpam-4973	3	47	département	département	PROPN
ejpam-4973	3	48	de	de	X
ejpam-4973	3	49	mathématiques	mathématiques	X
ejpam-4973	3	50	,	,	PUNCT
ejpam-4973	3	51	ufr	ufr	PROPN
ejpam-4973	3	52	sciences	sciences	PROPN
ejpam-4973	3	53	et	et	PROPN
ejpam-4973	3	54	technologies	technology	NOUN
ejpam-4973	3	55	,	,	PUNCT
ejpam-4973	3	56	université	université	NOUN
ejpam-4973	3	57	de	de	ADP
ejpam-4973	3	58	thiès	thiès	PROPN
ejpam-4973	3	59	,	,	PUNCT
ejpam-4973	3	60	thiès	thiès	NOUN
ejpam-4973	3	61	,	,	PUNCT
ejpam-4973	3	62	sénégal	sénégal	ADJ
ejpam-4973	3	63	abstract	abstract	NOUN
ejpam-4973	3	64	.	.	PUNCT
ejpam-4973	4	1	let	let	VERB
ejpam-4973	4	2	r	r	PRON
ejpam-4973	4	3	be	be	AUX
ejpam-4973	4	4	an	an	DET
ejpam-4973	4	5	associative	associative	ADJ
ejpam-4973	4	6	ring	ring	NOUN
ejpam-4973	4	7	and	and	CCONJ
ejpam-4973	4	8	m	m	VERB
ejpam-4973	4	9	a	a	DET
ejpam-4973	4	10	unitary	unitary	ADJ
ejpam-4973	4	11	left	left	ADJ
ejpam-4973	4	12	r	r	NOUN
ejpam-4973	4	13	-	-	PUNCT
ejpam-4973	4	14	module	module	NOUN
ejpam-4973	4	15	.	.	PUNCT
ejpam-4973	5	1	an	an	DET
ejpam-4973	5	2	r	r	NOUN
ejpam-4973	5	3	-	-	PUNCT
ejpam-4973	5	4	module	module	NOUN
ejpam-4973	5	5	m	m	NOUN
ejpam-4973	5	6	is	be	AUX
ejpam-4973	5	7	said	say	VERB
ejpam-4973	5	8	to	to	PART
ejpam-4973	5	9	be	be	AUX
ejpam-4973	5	10	uniserial	uniserial	ADJ
ejpam-4973	5	11	if	if	SCONJ
ejpam-4973	5	12	its	its	PRON
ejpam-4973	5	13	submodules	submodule	NOUN
ejpam-4973	5	14	are	be	AUX
ejpam-4973	5	15	linearly	linearly	ADV
ejpam-4973	5	16	ordered	order	VERB
ejpam-4973	5	17	by	by	ADP
ejpam-4973	5	18	inclusion	inclusion	NOUN
ejpam-4973	5	19	.	.	PUNCT
ejpam-4973	6	1	a	a	DET
ejpam-4973	6	2	serial	serial	ADJ
ejpam-4973	6	3	module	module	NOUN
ejpam-4973	6	4	is	be	AUX
ejpam-4973	6	5	a	a	DET
ejpam-4973	6	6	direct	direct	ADJ
ejpam-4973	6	7	sum	sum	NOUN
ejpam-4973	6	8	of	of	ADP
ejpam-4973	6	9	uniserial	uniserial	ADJ
ejpam-4973	6	10	modules	module	NOUN
ejpam-4973	6	11	.	.	PUNCT
ejpam-4973	7	1	in	in	ADP
ejpam-4973	7	2	this	this	DET
ejpam-4973	7	3	paper	paper	NOUN
ejpam-4973	7	4	,	,	PUNCT
ejpam-4973	7	5	we	we	PRON
ejpam-4973	7	6	bring	bring	VERB
ejpam-4973	7	7	our	our	PRON
ejpam-4973	7	8	modest	modest	ADJ
ejpam-4973	7	9	contribution	contribution	NOUN
ejpam-4973	7	10	to	to	ADP
ejpam-4973	7	11	the	the	DET
ejpam-4973	7	12	open	open	ADJ
ejpam-4973	7	13	problem	problem	NOUN
ejpam-4973	7	14	listed	list	VERB
ejpam-4973	7	15	in	in	ADP
ejpam-4973	7	16	the	the	DET
ejpam-4973	7	17	book	book	NOUN
ejpam-4973	7	18	of	of	ADP
ejpam-4973	7	19	alberto	alberto	PROPN
ejpam-4973	7	20	facchini	facchini	PROPN
ejpam-4973	7	21	”	"	PUNCT
ejpam-4973	7	22	module	module	NOUN
ejpam-4973	7	23	theory	theory	NOUN
ejpam-4973	7	24	”	"	PUNCT
ejpam-4973	7	25	which	which	PRON
ejpam-4973	7	26	states	state	VERB
ejpam-4973	7	27	that	that	SCONJ
ejpam-4973	7	28	:	:	PUNCT
ejpam-4973	7	29	is	be	AUX
ejpam-4973	7	30	any	any	DET
ejpam-4973	7	31	direct	direct	ADJ
ejpam-4973	7	32	summand	summand	NOUN
ejpam-4973	7	33	of	of	ADP
ejpam-4973	7	34	a	a	DET
ejpam-4973	7	35	serial	serial	ADJ
ejpam-4973	7	36	module	module	NOUN
ejpam-4973	7	37	serial	serial	NOUN
ejpam-4973	7	38	?	?	PUNCT
ejpam-4973	8	1	the	the	DET
ejpam-4973	8	2	answer	answer	NOUN
ejpam-4973	8	3	is	be	AUX
ejpam-4973	8	4	yes	yes	INTJ
ejpam-4973	8	5	for	for	ADP
ejpam-4973	8	6	particular	particular	ADJ
ejpam-4973	8	7	rings	ring	NOUN
ejpam-4973	8	8	and	and	CCONJ
ejpam-4973	8	9	r	r	NOUN
ejpam-4973	8	10	-	-	PUNCT
ejpam-4973	8	11	modules	module	NOUN
ejpam-4973	8	12	.	.	PUNCT
ejpam-4973	9	1	2020	2020	NUM
ejpam-4973	9	2	mathematics	mathematic	NOUN
ejpam-4973	9	3	subject	subject	NOUN
ejpam-4973	9	4	classifications	classification	NOUN
ejpam-4973	9	5	:	:	PUNCT
ejpam-4973	9	6	13c60	13c60	NUM
ejpam-4973	9	7	,	,	PUNCT
ejpam-4973	9	8	13c05	13c05	NUM
ejpam-4973	9	9	,	,	PUNCT
ejpam-4973	9	10	13c13	13c13	NUM
ejpam-4973	9	11	key	key	ADJ
ejpam-4973	9	12	words	word	NOUN
ejpam-4973	9	13	and	and	CCONJ
ejpam-4973	9	14	phrases	phrase	NOUN
ejpam-4973	9	15	:	:	PUNCT
ejpam-4973	9	16	uniserial	uniserial	ADJ
ejpam-4973	9	17	,	,	PUNCT
ejpam-4973	9	18	serial	serial	ADJ
ejpam-4973	9	19	,	,	PUNCT
ejpam-4973	9	20	local	local	ADJ
ejpam-4973	9	21	,	,	PUNCT
ejpam-4973	9	22	direct	direct	ADJ
ejpam-4973	9	23	summand	summand	NOUN
ejpam-4973	9	24	1	1	NUM
ejpam-4973	9	25	.	.	PUNCT
ejpam-4973	10	1	introduction	introduction	NOUN
ejpam-4973	10	2	let	let	VERB
ejpam-4973	10	3	r	r	PRON
ejpam-4973	10	4	be	be	AUX
ejpam-4973	10	5	an	an	DET
ejpam-4973	10	6	associative	associative	ADJ
ejpam-4973	10	7	ring	ring	NOUN
ejpam-4973	10	8	and	and	CCONJ
ejpam-4973	10	9	m	m	VERB
ejpam-4973	10	10	a	a	DET
ejpam-4973	10	11	unitary	unitary	ADJ
ejpam-4973	10	12	left	left	ADJ
ejpam-4973	10	13	r	r	NOUN
ejpam-4973	10	14	-	-	PUNCT
ejpam-4973	10	15	module	module	NOUN
ejpam-4973	10	16	.	.	PUNCT
ejpam-4973	11	1	an	an	DET
ejpam-4973	11	2	r	r	NOUN
ejpam-4973	11	3	-	-	PUNCT
ejpam-4973	11	4	module	module	NOUN
ejpam-4973	11	5	m	m	NOUN
ejpam-4973	11	6	is	be	AUX
ejpam-4973	11	7	said	say	VERB
ejpam-4973	11	8	to	to	PART
ejpam-4973	11	9	be	be	AUX
ejpam-4973	11	10	uniserial	uniserial	ADJ
ejpam-4973	11	11	if	if	SCONJ
ejpam-4973	11	12	its	its	PRON
ejpam-4973	11	13	submodules	submodule	NOUN
ejpam-4973	11	14	are	be	AUX
ejpam-4973	11	15	linearly	linearly	ADV
ejpam-4973	11	16	ordered	order	VERB
ejpam-4973	11	17	by	by	ADP
ejpam-4973	11	18	inclusion	inclusion	NOUN
ejpam-4973	11	19	.	.	PUNCT
ejpam-4973	12	1	a	a	DET
ejpam-4973	12	2	serial	serial	ADJ
ejpam-4973	12	3	module	module	NOUN
ejpam-4973	12	4	is	be	AUX
ejpam-4973	12	5	a	a	DET
ejpam-4973	12	6	direct	direct	ADJ
ejpam-4973	12	7	sum	sum	NOUN
ejpam-4973	12	8	of	of	ADP
ejpam-4973	12	9	uniserial	uniserial	ADJ
ejpam-4973	12	10	modules	module	NOUN
ejpam-4973	12	11	.	.	PUNCT
ejpam-4973	13	1	the	the	DET
ejpam-4973	13	2	target	target	NOUN
ejpam-4973	13	3	of	of	ADP
ejpam-4973	13	4	this	this	DET
ejpam-4973	13	5	paper	paper	NOUN
ejpam-4973	13	6	comes	come	VERB
ejpam-4973	13	7	from	from	ADP
ejpam-4973	13	8	the	the	DET
ejpam-4973	13	9	following	follow	VERB
ejpam-4973	13	10	statement	statement	NOUN
ejpam-4973	13	11	.	.	PUNCT
ejpam-4973	14	1	is	be	AUX
ejpam-4973	14	2	any	any	DET
ejpam-4973	14	3	direct	direct	ADJ
ejpam-4973	14	4	summand	summand	NOUN
ejpam-4973	14	5	of	of	ADP
ejpam-4973	14	6	serial	serial	ADJ
ejpam-4973	14	7	module	module	NOUN
ejpam-4973	14	8	serial	serial	NOUN
ejpam-4973	14	9	?	?	PUNCT
ejpam-4973	15	1	this	this	PRON
ejpam-4973	15	2	is	be	AUX
ejpam-4973	15	3	an	an	DET
ejpam-4973	15	4	open	open	ADJ
ejpam-4973	15	5	problem	problem	NOUN
ejpam-4973	15	6	listed	list	VERB
ejpam-4973	15	7	in	in	ADP
ejpam-4973	15	8	the	the	DET
ejpam-4973	15	9	module	module	NOUN
ejpam-4973	15	10	theory	theory	NOUN
ejpam-4973	15	11	book	book	NOUN
ejpam-4973	15	12	of	of	ADP
ejpam-4973	15	13	alberto	alberto	PROPN
ejpam-4973	15	14	facchini	facchini	PROPN
ejpam-4973	15	15	.	.	PUNCT
ejpam-4973	16	1	some	some	DET
ejpam-4973	16	2	results	result	NOUN
ejpam-4973	16	3	has	have	AUX
ejpam-4973	16	4	been	be	AUX
ejpam-4973	16	5	obtained	obtain	VERB
ejpam-4973	16	6	if	if	SCONJ
ejpam-4973	16	7	the	the	DET
ejpam-4973	16	8	base	base	NOUN
ejpam-4973	16	9	ring	ring	NOUN
ejpam-4973	16	10	is	be	AUX
ejpam-4973	16	11	commutative	commutative	ADJ
ejpam-4973	16	12	or	or	CCONJ
ejpam-4973	16	13	noetherian	noetherian	ADJ
ejpam-4973	16	14	...	...	PUNCT
ejpam-4973	16	15	other	other	ADJ
ejpam-4973	16	16	results	result	NOUN
ejpam-4973	16	17	are	be	AUX
ejpam-4973	16	18	obtained	obtain	VERB
ejpam-4973	16	19	in	in	ADP
ejpam-4973	16	20	this	this	DET
ejpam-4973	16	21	paper	paper	NOUN
ejpam-4973	16	22	for	for	ADP
ejpam-4973	16	23	particular	particular	ADJ
ejpam-4973	16	24	rings	ring	NOUN
ejpam-4973	16	25	and	and	CCONJ
ejpam-4973	16	26	modules	module	NOUN
ejpam-4973	16	27	.	.	PUNCT
ejpam-4973	17	1	a	a	DET
ejpam-4973	17	2	module	module	NOUN
ejpam-4973	17	3	m	m	NOUN
ejpam-4973	17	4	is	be	AUX
ejpam-4973	17	5	said	say	VERB
ejpam-4973	17	6	to	to	PART
ejpam-4973	17	7	be	be	AUX
ejpam-4973	17	8	a	a	DET
ejpam-4973	17	9	prime	prime	ADJ
ejpam-4973	17	10	module	module	NOUN
ejpam-4973	17	11	if	if	SCONJ
ejpam-4973	17	12	for	for	ADP
ejpam-4973	17	13	every	every	DET
ejpam-4973	17	14	submodule	submodule	NOUN
ejpam-4973	17	15	n	n	PROPN
ejpam-4973	17	16	of	of	ADP
ejpam-4973	17	17	m	m	PROPN
ejpam-4973	17	18	,	,	PUNCT
ejpam-4973	17	19	ann(m	ann(m	PROPN
ejpam-4973	17	20	)	)	PUNCT
ejpam-4973	17	21	=	=	SYM
ejpam-4973	17	22	ann(n	ann(n	PROPN
ejpam-4973	17	23	)	)	PUNCT
ejpam-4973	17	24	.	.	PUNCT
ejpam-4973	18	1	a	a	DET
ejpam-4973	18	2	module	module	NOUN
ejpam-4973	18	3	is	be	AUX
ejpam-4973	18	4	m	m	VERB
ejpam-4973	18	5	is	be	AUX
ejpam-4973	18	6	said	say	VERB
ejpam-4973	18	7	to	to	PART
ejpam-4973	18	8	be	be	AUX
ejpam-4973	18	9	faithful	faithful	ADJ
ejpam-4973	18	10	if	if	SCONJ
ejpam-4973	18	11	ann(m	ann(m	PROPN
ejpam-4973	18	12	)	)	PUNCT
ejpam-4973	18	13	=	=	SYM
ejpam-4973	19	1	0	0	X
ejpam-4973	19	2	.	.	PUNCT
ejpam-4973	20	1	a	a	DET
ejpam-4973	20	2	module	module	NOUN
ejpam-4973	20	3	m	m	NOUN
ejpam-4973	20	4	is	be	AUX
ejpam-4973	20	5	said	say	VERB
ejpam-4973	20	6	to	to	PART
ejpam-4973	20	7	be	be	AUX
ejpam-4973	20	8	finitely	finitely	ADV
ejpam-4973	20	9	cogenerated	cogenerate	VERB
ejpam-4973	20	10	if	if	SCONJ
ejpam-4973	20	11	its	its	PRON
ejpam-4973	20	12	socle	socle	NOUN
ejpam-4973	20	13	is	be	AUX
ejpam-4973	20	14	essential	essential	ADJ
ejpam-4973	20	15	in	in	ADP
ejpam-4973	20	16	n	n	ADV
ejpam-4973	20	17	and	and	CCONJ
ejpam-4973	20	18	finitely	finitely	ADV
ejpam-4973	20	19	generated	generate	VERB
ejpam-4973	20	20	lemma	lemma	PROPN
ejpam-4973	20	21	1	1	NUM
ejpam-4973	20	22	:	:	PUNCT
ejpam-4973	20	23	let	let	VERB
ejpam-4973	20	24	m	m	PRON
ejpam-4973	20	25	be	be	AUX
ejpam-4973	20	26	an	an	DET
ejpam-4973	20	27	uniserial	uniserial	ADJ
ejpam-4973	20	28	module	module	NOUN
ejpam-4973	20	29	over	over	ADP
ejpam-4973	20	30	a	a	DET
ejpam-4973	20	31	ring	ring	NOUN
ejpam-4973	20	32	r.	r.	PROPN
ejpam-4973	20	33	m	m	PROPN
ejpam-4973	20	34	is	be	AUX
ejpam-4973	20	35	said	say	VERB
ejpam-4973	20	36	to	to	PART
ejpam-4973	20	37	be	be	AUX
ejpam-4973	20	38	of	of	ADP
ejpam-4973	20	39	type	type	NOUN
ejpam-4973	20	40	1	1	NUM
ejpam-4973	20	41	if	if	SCONJ
ejpam-4973	20	42	at	at	ADV
ejpam-4973	20	43	least	least	ADJ
ejpam-4973	20	44	one	one	NUM
ejpam-4973	20	45	of	of	ADP
ejpam-4973	20	46	the	the	DET
ejpam-4973	20	47	following	follow	VERB
ejpam-4973	20	48	hold	hold	NOUN
ejpam-4973	20	49	.	.	PUNCT
ejpam-4973	21	1	(	(	PUNCT
ejpam-4973	21	2	1	1	X
ejpam-4973	21	3	)	)	PUNCT
ejpam-4973	21	4	m	m	VERB
ejpam-4973	21	5	is	be	AUX
ejpam-4973	21	6	projective	projective	ADJ
ejpam-4973	21	7	;	;	PUNCT
ejpam-4973	21	8	(	(	PUNCT
ejpam-4973	21	9	2	2	X
ejpam-4973	21	10	)	)	PUNCT
ejpam-4973	21	11	m	m	VERB
ejpam-4973	21	12	is	be	AUX
ejpam-4973	21	13	injective	injective	ADJ
ejpam-4973	21	14	;	;	PUNCT
ejpam-4973	21	15	(	(	PUNCT
ejpam-4973	21	16	3	3	X
ejpam-4973	21	17	)	)	PUNCT
ejpam-4973	21	18	m	m	VERB
ejpam-4973	21	19	is	be	AUX
ejpam-4973	21	20	artinian	artinian	ADJ
ejpam-4973	21	21	;	;	PUNCT
ejpam-4973	21	22	∗corresponding	∗corresponde	VERB
ejpam-4973	21	23	author	author	NOUN
ejpam-4973	21	24	.	.	PUNCT
ejpam-4973	22	1	doi	doi	NOUN
ejpam-4973	22	2	:	:	PUNCT
ejpam-4973	22	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4973	https://doi.org/10.29020/nybg.ejpam.v17i1.4973	VERB
ejpam-4973	22	4	email	email	NOUN
ejpam-4973	22	5	addresses	address	NOUN
ejpam-4973	22	6	:	:	PUNCT
ejpam-4973	22	7	alhousseynou.ba@ucad.edu.sn	alhousseynou.ba@ucad.edu.sn	X
ejpam-4973	22	8	(	(	PUNCT
ejpam-4973	22	9	al	al	PROPN
ejpam-4973	22	10	-	-	PUNCT
ejpam-4973	22	11	h	h	PROPN
ejpam-4973	22	12	ba	ba	PROPN
ejpam-4973	22	13	)	)	PUNCT
ejpam-4973	22	14	,	,	PUNCT
ejpam-4973	22	15	albertdiompy@yahoo.fr	albertdiompy@yahoo.fr	PROPN
ejpam-4973	22	16	(	(	PUNCT
ejpam-4973	22	17	m.	m.	NOUN
ejpam-4973	22	18	a.	a.	NOUN
ejpam-4973	22	19	diompy	diompy	PROPN
ejpam-4973	22	20	)	)	PUNCT
ejpam-4973	22	21	,	,	PUNCT
ejpam-4973	22	22	andrediabang@yahoo.fr	andrediabang@yahoo.fr	PROPN
ejpam-4973	22	23	(	(	PUNCT
ejpam-4973	22	24	a.	a.	PROPN
ejpam-4973	22	25	s.	s.	PROPN
ejpam-4973	22	26	diabang	diabang	PROPN
ejpam-4973	22	27	)	)	PUNCT
ejpam-4973	22	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4973	23	1	410	410	NUM
ejpam-4973	23	2	©	©	PROPN
ejpam-4973	23	3	2024	2024	NUM
ejpam-4973	23	4	ejpam	ejpam	NOUN
ejpam-4973	23	5	all	all	DET
ejpam-4973	23	6	rights	right	NOUN
ejpam-4973	23	7	reserved	reserve	VERB
ejpam-4973	23	8	.	.	PUNCT
ejpam-4973	24	1	al	al	PROPN
ejpam-4973	24	2	-	-	PUNCT
ejpam-4973	24	3	h.	h.	PROPN
ejpam-4973	24	4	ba	ba	PROPN
ejpam-4973	24	5	,	,	PUNCT
ejpam-4973	24	6	m.	m.	NOUN
ejpam-4973	24	7	a.	a.	NOUN
ejpam-4973	24	8	diompy	diompy	PROPN
ejpam-4973	24	9	,	,	PUNCT
ejpam-4973	24	10	a.	a.	PROPN
ejpam-4973	24	11	s.	s.	PROPN
ejpam-4973	24	12	diabang	diabang	PROPN
ejpam-4973	24	13	/	/	SYM
ejpam-4973	24	14	eur	eur	PROPN
ejpam-4973	24	15	.	.	PUNCT
ejpam-4973	25	1	j.	j.	PROPN
ejpam-4973	25	2	pure	pure	PROPN
ejpam-4973	25	3	appl	appl	PROPN
ejpam-4973	25	4	.	.	PROPN
ejpam-4973	25	5	math	math	PROPN
ejpam-4973	25	6	,	,	PUNCT
ejpam-4973	25	7	17	17	NUM
ejpam-4973	25	8	(	(	PUNCT
ejpam-4973	25	9	1	1	NUM
ejpam-4973	25	10	)	)	PUNCT
ejpam-4973	25	11	(	(	PUNCT
ejpam-4973	25	12	2024	2024	NUM
ejpam-4973	25	13	)	)	PUNCT
ejpam-4973	25	14	,	,	PUNCT
ejpam-4973	25	15	410	410	NUM
ejpam-4973	25	16	-	-	SYM
ejpam-4973	25	17	415	415	NUM
ejpam-4973	25	18	411	411	NUM
ejpam-4973	25	19	(	(	PUNCT
ejpam-4973	25	20	4	4	NUM
ejpam-4973	25	21	)	)	PUNCT
ejpam-4973	25	22	m	m	VERB
ejpam-4973	25	23	is	be	AUX
ejpam-4973	25	24	noetherian	noetherian	ADJ
ejpam-4973	25	25	;	;	PUNCT
ejpam-4973	25	26	(	(	PUNCT
ejpam-4973	25	27	5	5	X
ejpam-4973	25	28	)	)	PUNCT
ejpam-4973	25	29	r	r	NOUN
ejpam-4973	25	30	is	be	AUX
ejpam-4973	25	31	commutative	commutative	ADJ
ejpam-4973	25	32	;	;	PUNCT
ejpam-4973	25	33	(	(	PUNCT
ejpam-4973	25	34	6	6	X
ejpam-4973	25	35	)	)	PUNCT
ejpam-4973	25	36	r	r	NOUN
ejpam-4973	25	37	is	be	AUX
ejpam-4973	25	38	a	a	DET
ejpam-4973	25	39	right	right	ADJ
ejpam-4973	25	40	noetherian	noetherian	NOUN
ejpam-4973	25	41	.	.	PUNCT
ejpam-4973	26	1	proof	proof	NOUN
ejpam-4973	26	2	:	:	PUNCT
ejpam-4973	26	3	to	to	PART
ejpam-4973	26	4	see	see	VERB
ejpam-4973	26	5	the	the	DET
ejpam-4973	26	6	proof	proof	NOUN
ejpam-4973	26	7	refer	refer	VERB
ejpam-4973	26	8	from	from	ADP
ejpam-4973	26	9	example	example	NOUN
ejpam-4973	26	10	2.3	2.3	NUM
ejpam-4973	26	11	of	of	ADP
ejpam-4973	26	12	[	[	X
ejpam-4973	26	13	1	1	NUM
ejpam-4973	26	14	]	]	PUNCT
ejpam-4973	26	15	.	.	PUNCT
ejpam-4973	27	1	proposition	proposition	NOUN
ejpam-4973	27	2	1	1	NUM
ejpam-4973	27	3	:	:	PUNCT
ejpam-4973	27	4	let	let	VERB
ejpam-4973	27	5	r	r	NOUN
ejpam-4973	27	6	be	be	AUX
ejpam-4973	27	7	ring	ring	NOUN
ejpam-4973	27	8	and	and	CCONJ
ejpam-4973	27	9	m	m	AUX
ejpam-4973	27	10	be	be	AUX
ejpam-4973	27	11	a	a	DET
ejpam-4973	27	12	left	left	ADJ
ejpam-4973	27	13	local	local	ADJ
ejpam-4973	27	14	module	module	NOUN
ejpam-4973	27	15	over	over	ADP
ejpam-4973	27	16	r	r	NOUN
ejpam-4973	27	17	,	,	PUNCT
ejpam-4973	27	18	then	then	ADV
ejpam-4973	27	19	end(m	end(m	PROPN
ejpam-4973	27	20	)	)	PUNCT
ejpam-4973	27	21	is	be	AUX
ejpam-4973	27	22	local	local	ADJ
ejpam-4973	27	23	.	.	PUNCT
ejpam-4973	28	1	proof	proof	NOUN
ejpam-4973	28	2	.	.	PUNCT
ejpam-4973	29	1	let	let	VERB
ejpam-4973	29	2	m	m	PRON
ejpam-4973	29	3	be	be	AUX
ejpam-4973	29	4	an	an	DET
ejpam-4973	29	5	hollow	hollow	ADJ
ejpam-4973	29	6	module	module	NOUN
ejpam-4973	29	7	.	.	PUNCT
ejpam-4973	30	1	hence	hence	ADV
ejpam-4973	30	2	m	m	VERB
ejpam-4973	30	3	is	be	AUX
ejpam-4973	30	4	finitely	finitely	ADV
ejpam-4973	30	5	generated	generate	VERB
ejpam-4973	30	6	.	.	PUNCT
ejpam-4973	31	1	let	let	VERB
ejpam-4973	31	2	f	f	NOUN
ejpam-4973	31	3	:	:	PUNCT
ejpam-4973	31	4	r	r	AUX
ejpam-4973	31	5	−→	−→	NOUN
ejpam-4973	31	6	m	m	VERB
ejpam-4973	31	7	an	an	DET
ejpam-4973	31	8	homomorphism	homomorphism	NOUN
ejpam-4973	31	9	which	which	PRON
ejpam-4973	31	10	is	be	AUX
ejpam-4973	31	11	an	an	DET
ejpam-4973	31	12	epimorphism	epimorphism	NOUN
ejpam-4973	31	13	.	.	PUNCT
ejpam-4973	32	1	therefore	therefore	ADV
ejpam-4973	32	2	r	r	NOUN
ejpam-4973	32	3	/	/	SYM
ejpam-4973	32	4	ann(m	ann(m	NOUN
ejpam-4973	32	5	)	)	PUNCT
ejpam-4973	32	6	is	be	AUX
ejpam-4973	32	7	isomorphic	isomorphic	ADJ
ejpam-4973	32	8	to	to	ADP
ejpam-4973	32	9	m	m	PRON
ejpam-4973	32	10	.	.	PUNCT
ejpam-4973	33	1	hence	hence	ADV
ejpam-4973	33	2	r	r	NOUN
ejpam-4973	33	3	/	/	SYM
ejpam-4973	33	4	ann(m	ann(m	NOUN
ejpam-4973	33	5	)	)	PUNCT
ejpam-4973	33	6	is	be	AUX
ejpam-4973	33	7	hollow	hollow	ADJ
ejpam-4973	33	8	.	.	PUNCT
ejpam-4973	34	1	it	it	PRON
ejpam-4973	34	2	follows	follow	VERB
ejpam-4973	34	3	from	from	ADP
ejpam-4973	34	4	theorem	theorem	ADJ
ejpam-4973	34	5	4.1	4.1	NUM
ejpam-4973	34	6	of	of	ADP
ejpam-4973	34	7	[	[	X
ejpam-4973	34	8	5	5	NUM
ejpam-4973	34	9	]	]	PUNCT
ejpam-4973	34	10	that	that	SCONJ
ejpam-4973	34	11	end(r	end(r	PROPN
ejpam-4973	34	12	/	/	SYM
ejpam-4973	34	13	ann(m	ann(m	PROPN
ejpam-4973	34	14	)	)	PUNCT
ejpam-4973	34	15	)	)	PUNCT
ejpam-4973	35	1	is	be	AUX
ejpam-4973	35	2	local	local	ADJ
ejpam-4973	35	3	.	.	PUNCT
ejpam-4973	36	1	thus	thus	ADV
ejpam-4973	36	2	end(m	end(m	VERB
ejpam-4973	36	3	)	)	PUNCT
ejpam-4973	36	4	is	be	AUX
ejpam-4973	36	5	local	local	ADJ
ejpam-4973	36	6	.	.	PUNCT
ejpam-4973	37	1	theorem	theorem	ADJ
ejpam-4973	37	2	1	1	NUM
ejpam-4973	37	3	:	:	PUNCT
ejpam-4973	37	4	let	let	VERB
ejpam-4973	37	5	m1	m1	PROPN
ejpam-4973	37	6	,	,	PUNCT
ejpam-4973	37	7	...	...	PUNCT
ejpam-4973	37	8	,	,	PUNCT
ejpam-4973	37	9	mn	mn	PROPN
ejpam-4973	37	10	be	be	VERB
ejpam-4973	37	11	uniserial	uniserial	ADJ
ejpam-4973	37	12	local	local	ADJ
ejpam-4973	37	13	modules	module	NOUN
ejpam-4973	37	14	.	.	PUNCT
ejpam-4973	38	1	let	let	VERB
ejpam-4973	38	2	m	m	NOUN
ejpam-4973	38	3	=	=	PROPN
ejpam-4973	38	4	⊕	⊕	PROPN
ejpam-4973	38	5	i∈i	i∈i	ADJ
ejpam-4973	38	6	mi	mi	PROPN
ejpam-4973	38	7	a	a	DET
ejpam-4973	38	8	serial	serial	ADJ
ejpam-4973	38	9	module	module	NOUN
ejpam-4973	38	10	.	.	PUNCT
ejpam-4973	39	1	then	then	ADV
ejpam-4973	39	2	every	every	DET
ejpam-4973	39	3	summand	summand	NOUN
ejpam-4973	39	4	of	of	ADP
ejpam-4973	39	5	m	m	PROPN
ejpam-4973	39	6	is	be	AUX
ejpam-4973	39	7	serial	serial	ADJ
ejpam-4973	39	8	.	.	PUNCT
ejpam-4973	40	1	proof	proof	NOUN
ejpam-4973	40	2	.	.	PUNCT
ejpam-4973	41	1	it	it	PRON
ejpam-4973	41	2	results	result	VERB
ejpam-4973	41	3	from	from	ADP
ejpam-4973	41	4	proposition	proposition	NOUN
ejpam-4973	41	5	1	1	NUM
ejpam-4973	41	6	that	that	PRON
ejpam-4973	41	7	end(mi	end(mi	VERB
ejpam-4973	41	8	)	)	PUNCT
ejpam-4973	41	9	is	be	AUX
ejpam-4973	41	10	local	local	ADJ
ejpam-4973	41	11	.	.	PUNCT
ejpam-4973	42	1	therefore	therefore	ADV
ejpam-4973	42	2	every	every	DET
ejpam-4973	42	3	direct	direct	ADJ
ejpam-4973	42	4	summand	summand	NOUN
ejpam-4973	42	5	of	of	ADP
ejpam-4973	42	6	m	m	PROPN
ejpam-4973	42	7	is	be	AUX
ejpam-4973	42	8	serial	serial	ADJ
ejpam-4973	42	9	.	.	PUNCT
ejpam-4973	43	1	proposition	proposition	NOUN
ejpam-4973	43	2	2	2	NUM
ejpam-4973	43	3	:	:	PUNCT
ejpam-4973	43	4	let	let	VERB
ejpam-4973	43	5	r	r	NOUN
ejpam-4973	43	6	be	be	AUX
ejpam-4973	43	7	ring	ring	NOUN
ejpam-4973	43	8	and	and	CCONJ
ejpam-4973	43	9	m	m	VERB
ejpam-4973	43	10	a	a	DET
ejpam-4973	43	11	finitely	finitely	ADV
ejpam-4973	43	12	cogenerated	cogenerate	VERB
ejpam-4973	43	13	,	,	PUNCT
ejpam-4973	43	14	prime	prime	ADJ
ejpam-4973	43	15	and	and	CCONJ
ejpam-4973	43	16	faithful	faithful	ADJ
ejpam-4973	43	17	rmodule	rmodule	NOUN
ejpam-4973	43	18	.	.	PUNCT
ejpam-4973	44	1	then	then	ADV
ejpam-4973	44	2	r	r	NOUN
ejpam-4973	44	3	as	as	ADP
ejpam-4973	44	4	a	a	DET
ejpam-4973	44	5	left	left	ADJ
ejpam-4973	44	6	r	r	NOUN
ejpam-4973	44	7	-	-	PUNCT
ejpam-4973	44	8	module	module	NOUN
ejpam-4973	44	9	is	be	AUX
ejpam-4973	44	10	uniserial	uniserial	ADJ
ejpam-4973	44	11	.	.	PUNCT
ejpam-4973	45	1	moreover	moreover	ADV
ejpam-4973	45	2	end(r	end(r	NOUN
ejpam-4973	45	3	)	)	PUNCT
ejpam-4973	45	4	is	be	AUX
ejpam-4973	45	5	a	a	DET
ejpam-4973	45	6	local	local	ADJ
ejpam-4973	45	7	ring	ring	NOUN
ejpam-4973	45	8	.	.	PUNCT
ejpam-4973	46	1	proof	proof	NOUN
ejpam-4973	46	2	.	.	PUNCT
ejpam-4973	47	1	let	let	VERB
ejpam-4973	47	2	m	m	PRON
ejpam-4973	47	3	be	be	AUX
ejpam-4973	47	4	a	a	DET
ejpam-4973	47	5	finitely	finitely	ADV
ejpam-4973	47	6	cogenerated	cogenerate	VERB
ejpam-4973	47	7	module	module	NOUN
ejpam-4973	47	8	over	over	ADP
ejpam-4973	47	9	r.	r.	PROPN
ejpam-4973	47	10	it	it	PRON
ejpam-4973	47	11	is	be	AUX
ejpam-4973	47	12	well	well	ADV
ejpam-4973	47	13	known	know	VERB
ejpam-4973	47	14	that	that	SCONJ
ejpam-4973	47	15	any	any	DET
ejpam-4973	47	16	finitely	finitely	ADV
ejpam-4973	47	17	cogenerated	cogenerate	VERB
ejpam-4973	47	18	module	module	NOUN
ejpam-4973	47	19	has	have	VERB
ejpam-4973	47	20	a	a	DET
ejpam-4973	47	21	small	small	ADJ
ejpam-4973	47	22	submodule	submodule	NOUN
ejpam-4973	47	23	.	.	PUNCT
ejpam-4973	48	1	let	let	VERB
ejpam-4973	48	2	k	k	PRON
ejpam-4973	48	3	be	be	AUX
ejpam-4973	48	4	its	its	PRON
ejpam-4973	48	5	small	small	ADJ
ejpam-4973	48	6	submodule	submodule	NOUN
ejpam-4973	48	7	.	.	PUNCT
ejpam-4973	49	1	then	then	ADV
ejpam-4973	49	2	f	f	X
ejpam-4973	49	3	:	:	PUNCT
ejpam-4973	50	1	r	r	NOUN
ejpam-4973	50	2	−→	−→	NOUN
ejpam-4973	50	3	k	k	PROPN
ejpam-4973	50	4	is	be	AUX
ejpam-4973	50	5	an	an	DET
ejpam-4973	50	6	epimorphism	epimorphism	NOUN
ejpam-4973	50	7	.	.	PUNCT
ejpam-4973	51	1	f	f	X
ejpam-4973	51	2	:	:	PUNCT
ejpam-4973	52	1	r	r	VERB
ejpam-4973	52	2	−→	−→	NOUN
ejpam-4973	52	3	k	k	PROPN
ejpam-4973	52	4	↓	↓	PROPN
ejpam-4973	52	5	↙	↙	PROPN
ejpam-4973	52	6	r	r	X
ejpam-4973	52	7	/	/	SYM
ejpam-4973	52	8	ann(k	ann(k	PROPN
ejpam-4973	52	9	)	)	PUNCT
ejpam-4973	52	10	by	by	ADP
ejpam-4973	52	11	the	the	DET
ejpam-4973	52	12	first	first	ADJ
ejpam-4973	52	13	isomorphism	isomorphism	NOUN
ejpam-4973	52	14	theorem	theorem	NOUN
ejpam-4973	52	15	,	,	PUNCT
ejpam-4973	52	16	r	r	NOUN
ejpam-4973	52	17	/	/	SYM
ejpam-4973	52	18	ann(k	ann(k	PROPN
ejpam-4973	52	19	)	)	PUNCT
ejpam-4973	52	20	is	be	AUX
ejpam-4973	52	21	isomorphic	isomorphic	ADJ
ejpam-4973	52	22	to	to	ADP
ejpam-4973	52	23	k.	k.	PROPN
ejpam-4973	52	24	as	as	SCONJ
ejpam-4973	52	25	m	m	PROPN
ejpam-4973	52	26	is	be	AUX
ejpam-4973	52	27	a	a	DET
ejpam-4973	52	28	prime	prime	ADJ
ejpam-4973	52	29	and	and	CCONJ
ejpam-4973	52	30	faithful	faithful	ADJ
ejpam-4973	52	31	module	module	NOUN
ejpam-4973	52	32	then	then	ADV
ejpam-4973	52	33	ann(k	ann(k	PROPN
ejpam-4973	52	34	)	)	PUNCT
ejpam-4973	52	35	=	=	SYM
ejpam-4973	52	36	ann(m	ann(m	PROPN
ejpam-4973	52	37	)	)	PUNCT
ejpam-4973	52	38	=	=	SYM
ejpam-4973	53	1	0	0	X
ejpam-4973	53	2	.	.	PUNCT
ejpam-4973	54	1	therefore	therefore	ADV
ejpam-4973	54	2	r	r	NOUN
ejpam-4973	54	3	is	be	AUX
ejpam-4973	54	4	simple	simple	ADJ
ejpam-4973	54	5	as	as	ADP
ejpam-4973	54	6	a	a	DET
ejpam-4973	54	7	left	left	ADJ
ejpam-4973	54	8	r	r	NOUN
ejpam-4973	54	9	-	-	PUNCT
ejpam-4973	54	10	module	module	NOUN
ejpam-4973	54	11	.	.	PUNCT
ejpam-4973	55	1	hence	hence	ADV
ejpam-4973	55	2	r	r	NOUN
ejpam-4973	55	3	is	be	AUX
ejpam-4973	55	4	uniserial	uniserial	ADJ
ejpam-4973	55	5	because	because	SCONJ
ejpam-4973	55	6	{	{	PUNCT
ejpam-4973	55	7	0	0	NUM
ejpam-4973	55	8	}	}	PUNCT
ejpam-4973	55	9	⊂	⊂	PROPN
ejpam-4973	55	10	r.	r.	PROPN
ejpam-4973	55	11	since	since	SCONJ
ejpam-4973	55	12	r	r	NOUN
ejpam-4973	55	13	is	be	AUX
ejpam-4973	55	14	simple	simple	ADJ
ejpam-4973	55	15	then	then	ADV
ejpam-4973	55	16	for	for	ADP
ejpam-4973	55	17	ever	ever	ADV
ejpam-4973	55	18	endomorphism	endomorphism	NOUN
ejpam-4973	55	19	of	of	ADP
ejpam-4973	55	20	r	r	NOUN
ejpam-4973	55	21	is	be	AUX
ejpam-4973	55	22	an	an	DET
ejpam-4973	55	23	automorphism	automorphism	NOUN
ejpam-4973	55	24	.	.	PUNCT
ejpam-4973	56	1	hence	hence	ADV
ejpam-4973	56	2	for	for	ADP
ejpam-4973	56	3	every	every	DET
ejpam-4973	56	4	endomorphism	endomorphism	NOUN
ejpam-4973	56	5	g	g	NOUN
ejpam-4973	56	6	:	:	PUNCT
ejpam-4973	56	7	r	r	NOUN
ejpam-4973	56	8	−→	−→	NOUN
ejpam-4973	56	9	r	r	NOUN
ejpam-4973	56	10	there	there	PRON
ejpam-4973	56	11	exists	exist	VERB
ejpam-4973	56	12	always	always	ADV
ejpam-4973	56	13	a	a	DET
ejpam-4973	56	14	endomorphism	endomorphism	NOUN
ejpam-4973	56	15	g	g	NOUN
ejpam-4973	56	16	:	:	PUNCT
ejpam-4973	56	17	r	r	AUX
ejpam-4973	56	18	−→	−→	NOUN
ejpam-4973	56	19	r	r	NOUN
ejpam-4973	56	20	such	such	DET
ejpam-4973	56	21	that	that	DET
ejpam-4973	56	22	g	g	PROPN
ejpam-4973	56	23	◦	◦	NOUN
ejpam-4973	56	24	h	h	NOUN
ejpam-4973	57	1	=	=	PUNCT
ejpam-4973	57	2	i	i	PROPN
ejpam-4973	57	3	d	d	PROPN
ejpam-4973	57	4	and	and	CCONJ
ejpam-4973	57	5	h	h	PROPN
ejpam-4973	57	6	◦	◦	NOUN
ejpam-4973	57	7	g	g	PROPN
ejpam-4973	58	1	=	=	SYM
ejpam-4973	58	2	i	i	PROPN
ejpam-4973	58	3	d.	d.	PROPN
ejpam-4973	58	4	that	that	PRON
ejpam-4973	58	5	implies	imply	VERB
ejpam-4973	58	6	end(r	end(r	NOUN
ejpam-4973	58	7	)	)	PUNCT
ejpam-4973	58	8	is	be	AUX
ejpam-4973	58	9	a	a	DET
ejpam-4973	58	10	division	division	NOUN
ejpam-4973	58	11	ring	ring	NOUN
ejpam-4973	58	12	.	.	PUNCT
ejpam-4973	59	1	it	it	PRON
ejpam-4973	59	2	is	be	AUX
ejpam-4973	59	3	well	well	ADV
ejpam-4973	59	4	know	know	VERB
ejpam-4973	59	5	that	that	SCONJ
ejpam-4973	59	6	any	any	DET
ejpam-4973	59	7	division	division	NOUN
ejpam-4973	59	8	ring	ring	NOUN
ejpam-4973	59	9	is	be	AUX
ejpam-4973	59	10	a	a	DET
ejpam-4973	59	11	local	local	ADJ
ejpam-4973	59	12	ring	ring	NOUN
ejpam-4973	59	13	.	.	PUNCT
ejpam-4973	60	1	corollary	corollary	ADJ
ejpam-4973	60	2	1	1	NUM
ejpam-4973	60	3	:	:	PUNCT
ejpam-4973	60	4	let	let	VERB
ejpam-4973	60	5	r	r	NOUN
ejpam-4973	60	6	=	=	SYM
ejpam-4973	60	7	⊕	⊕	PROPN
ejpam-4973	60	8	i∈i	i∈i	ADJ
ejpam-4973	60	9	ri	ri	INTJ
ejpam-4973	61	1	where	where	SCONJ
ejpam-4973	61	2	(	(	PUNCT
ejpam-4973	61	3	ri)i∈i	ri)i∈i	NUM
ejpam-4973	61	4	is	be	AUX
ejpam-4973	61	5	family	family	NOUN
ejpam-4973	61	6	of	of	ADP
ejpam-4973	61	7	rings	ring	NOUN
ejpam-4973	61	8	such	such	ADJ
ejpam-4973	61	9	that	that	SCONJ
ejpam-4973	61	10	there	there	PRON
ejpam-4973	61	11	exists	exist	VERB
ejpam-4973	61	12	a	a	DET
ejpam-4973	61	13	finitely	finitely	ADV
ejpam-4973	61	14	cogenerated	cogenerate	VERB
ejpam-4973	61	15	,	,	PUNCT
ejpam-4973	61	16	prime	prime	ADJ
ejpam-4973	61	17	and	and	CCONJ
ejpam-4973	61	18	faithful	faithful	ADJ
ejpam-4973	61	19	ri0	ri0	NOUN
ejpam-4973	61	20	-	-	PUNCT
ejpam-4973	61	21	module	module	NOUN
ejpam-4973	61	22	with	with	ADP
ejpam-4973	61	23	i0	i0	PROPN
ejpam-4973	61	24	∈	∈	PROPN
ejpam-4973	61	25	i.	i.	NOUN
ejpam-4973	61	26	then	then	ADV
ejpam-4973	61	27	the	the	DET
ejpam-4973	61	28	following	follow	VERB
ejpam-4973	61	29	conditions	condition	NOUN
ejpam-4973	61	30	are	be	AUX
ejpam-4973	61	31	verified	verify	VERB
ejpam-4973	61	32	:	:	PUNCT
ejpam-4973	61	33	al	al	PROPN
ejpam-4973	61	34	-	-	PUNCT
ejpam-4973	61	35	h.	h.	PROPN
ejpam-4973	61	36	ba	ba	PROPN
ejpam-4973	61	37	,	,	PUNCT
ejpam-4973	61	38	m.	m.	NOUN
ejpam-4973	61	39	a.	a.	NOUN
ejpam-4973	61	40	diompy	diompy	PROPN
ejpam-4973	61	41	,	,	PUNCT
ejpam-4973	61	42	a.	a.	PROPN
ejpam-4973	61	43	s.	s.	PROPN
ejpam-4973	61	44	diabang	diabang	PROPN
ejpam-4973	61	45	/	/	SYM
ejpam-4973	61	46	eur	eur	PROPN
ejpam-4973	61	47	.	.	PUNCT
ejpam-4973	62	1	j.	j.	PROPN
ejpam-4973	62	2	pure	pure	PROPN
ejpam-4973	62	3	appl	appl	PROPN
ejpam-4973	62	4	.	.	PROPN
ejpam-4973	62	5	math	math	PROPN
ejpam-4973	62	6	,	,	PUNCT
ejpam-4973	62	7	17	17	NUM
ejpam-4973	62	8	(	(	PUNCT
ejpam-4973	62	9	1	1	NUM
ejpam-4973	62	10	)	)	PUNCT
ejpam-4973	62	11	(	(	PUNCT
ejpam-4973	62	12	2024	2024	NUM
ejpam-4973	62	13	)	)	PUNCT
ejpam-4973	62	14	,	,	PUNCT
ejpam-4973	62	15	410	410	NUM
ejpam-4973	62	16	-	-	SYM
ejpam-4973	62	17	415	415	NUM
ejpam-4973	62	18	412	412	NUM
ejpam-4973	62	19	(	(	PUNCT
ejpam-4973	62	20	1	1	NUM
ejpam-4973	62	21	)	)	PUNCT
ejpam-4973	62	22	each	each	DET
ejpam-4973	62	23	ri	ri	PROPN
ejpam-4973	62	24	is	be	AUX
ejpam-4973	62	25	uniserial	uniserial	ADJ
ejpam-4973	62	26	as	as	ADP
ejpam-4973	62	27	a	a	DET
ejpam-4973	62	28	left	left	ADJ
ejpam-4973	62	29	ri	ri	NOUN
ejpam-4973	62	30	-	-	PUNCT
ejpam-4973	62	31	module	module	NOUN
ejpam-4973	62	32	for	for	ADP
ejpam-4973	62	33	every	every	DET
ejpam-4973	62	34	i	i	PROPN
ejpam-4973	62	35	∈	∈	PROPN
ejpam-4973	62	36	i.	i.	NOUN
ejpam-4973	62	37	(	(	PUNCT
ejpam-4973	62	38	2	2	NUM
ejpam-4973	62	39	)	)	PUNCT
ejpam-4973	62	40	every	every	DET
ejpam-4973	62	41	summand	summand	NOUN
ejpam-4973	62	42	of	of	ADP
ejpam-4973	62	43	r	r	NOUN
ejpam-4973	62	44	is	be	AUX
ejpam-4973	62	45	serial	serial	ADJ
ejpam-4973	62	46	.	.	PUNCT
ejpam-4973	63	1	proof	proof	NOUN
ejpam-4973	63	2	.	.	PUNCT
ejpam-4973	64	1	(	(	PUNCT
ejpam-4973	64	2	1	1	X
ejpam-4973	64	3	)	)	PUNCT
ejpam-4973	64	4	let	let	VERB
ejpam-4973	64	5	m	m	PRON
ejpam-4973	64	6	be	be	AUX
ejpam-4973	64	7	a	a	DET
ejpam-4973	64	8	left	left	ADJ
ejpam-4973	64	9	finitely	finitely	ADV
ejpam-4973	64	10	cogenerated	cogenerate	VERB
ejpam-4973	64	11	prime	prime	ADJ
ejpam-4973	64	12	and	and	CCONJ
ejpam-4973	64	13	faithful	faithful	ADJ
ejpam-4973	64	14	ri0	ri0	NOUN
ejpam-4973	64	15	-	-	PUNCT
ejpam-4973	64	16	module	module	NOUN
ejpam-4973	64	17	.	.	PUNCT
ejpam-4973	65	1	then	then	ADV
ejpam-4973	65	2	m	m	PROPN
ejpam-4973	65	3	is	be	AUX
ejpam-4973	65	4	a	a	DET
ejpam-4973	65	5	module	module	NOUN
ejpam-4973	65	6	over	over	ADP
ejpam-4973	65	7	every	every	DET
ejpam-4973	65	8	ri	ri	NOUN
ejpam-4973	65	9	with	with	ADP
ejpam-4973	65	10	i	i	PRON
ejpam-4973	65	11	∈	∈	PROPN
ejpam-4973	65	12	i	i	PRON
ejpam-4973	65	13	by	by	ADP
ejpam-4973	65	14	the	the	DET
ejpam-4973	65	15	following	following	ADJ
ejpam-4973	65	16	homomorphism	homomorphism	PROPN
ejpam-4973	65	17	:	:	PUNCT
ejpam-4973	65	18	f	f	X
ejpam-4973	65	19	:	:	PUNCT
ejpam-4973	66	1	ri	ri	VERB
ejpam-4973	66	2	−→	−→	NOUN
ejpam-4973	66	3	ri0	ri0	PROPN
ejpam-4973	66	4	×m	×m	NOUN
ejpam-4973	66	5	−→	−→	NOUN
ejpam-4973	66	6	m	m	NOUN
ejpam-4973	66	7	r	r	NOUN
ejpam-4973	66	8	7−→	7−→	NOUN
ejpam-4973	66	9	(	(	PUNCT
ejpam-4973	66	10	f(r),m	f(r),m	ADJ
ejpam-4973	66	11	)	)	PUNCT
ejpam-4973	66	12	7−→	7−→	NOUN
ejpam-4973	66	13	f(r)m	f(r)m	NOUN
ejpam-4973	66	14	it	it	PRON
ejpam-4973	66	15	follows	follow	VERB
ejpam-4973	66	16	from	from	ADP
ejpam-4973	66	17	proposition	proposition	NOUN
ejpam-4973	66	18	2	2	NUM
ejpam-4973	66	19	that	that	PRON
ejpam-4973	66	20	ri	ri	PROPN
ejpam-4973	66	21	is	be	AUX
ejpam-4973	66	22	simple	simple	ADJ
ejpam-4973	66	23	hence	hence	ADV
ejpam-4973	66	24	uniserial	uniserial	ADJ
ejpam-4973	66	25	for	for	ADP
ejpam-4973	66	26	every	every	DET
ejpam-4973	66	27	i	i	PROPN
ejpam-4973	66	28	∈	∈	PROPN
ejpam-4973	66	29	i.	i.	NOUN
ejpam-4973	66	30	(	(	PUNCT
ejpam-4973	66	31	2	2	X
ejpam-4973	66	32	)	)	PUNCT
ejpam-4973	66	33	it	it	PRON
ejpam-4973	66	34	results	result	VERB
ejpam-4973	66	35	from	from	ADP
ejpam-4973	66	36	proposition	proposition	NOUN
ejpam-4973	66	37	2	2	NUM
ejpam-4973	66	38	that	that	PRON
ejpam-4973	66	39	end(ri	end(ri	NUM
ejpam-4973	66	40	)	)	PUNCT
ejpam-4973	66	41	is	be	AUX
ejpam-4973	66	42	a	a	DET
ejpam-4973	66	43	local	local	ADJ
ejpam-4973	66	44	ring	ring	NOUN
ejpam-4973	66	45	for	for	ADP
ejpam-4973	66	46	every	every	DET
ejpam-4973	66	47	i	i	PROPN
ejpam-4973	66	48	∈	∈	PROPN
ejpam-4973	66	49	i.	i.	NOUN
ejpam-4973	66	50	thus	thus	ADV
ejpam-4973	66	51	every	every	DET
ejpam-4973	66	52	summand	summand	NOUN
ejpam-4973	66	53	of	of	ADP
ejpam-4973	66	54	r	r	NOUN
ejpam-4973	66	55	is	be	AUX
ejpam-4973	66	56	serial	serial	ADJ
ejpam-4973	66	57	.	.	PUNCT
ejpam-4973	67	1	in	in	ADP
ejpam-4973	67	2	the	the	DET
ejpam-4973	67	3	following	follow	VERB
ejpam-4973	67	4	corollary	corollary	NOUN
ejpam-4973	67	5	we	we	PRON
ejpam-4973	67	6	show	show	VERB
ejpam-4973	67	7	that	that	SCONJ
ejpam-4973	67	8	a	a	DET
ejpam-4973	67	9	finitely	finitely	ADV
ejpam-4973	67	10	generated	generate	VERB
ejpam-4973	67	11	module	module	NOUN
ejpam-4973	67	12	m	m	NOUN
ejpam-4973	67	13	is	be	AUX
ejpam-4973	67	14	serial	serial	ADJ
ejpam-4973	67	15	under	under	ADP
ejpam-4973	67	16	certain	certain	ADJ
ejpam-4973	67	17	conditions	condition	NOUN
ejpam-4973	67	18	and	and	CCONJ
ejpam-4973	67	19	every	every	DET
ejpam-4973	67	20	summand	summand	NOUN
ejpam-4973	67	21	of	of	ADP
ejpam-4973	67	22	m	m	PROPN
ejpam-4973	67	23	is	be	AUX
ejpam-4973	67	24	serial	serial	ADJ
ejpam-4973	67	25	.	.	PUNCT
ejpam-4973	68	1	corollary	corollary	ADJ
ejpam-4973	68	2	2	2	NUM
ejpam-4973	68	3	:	:	PUNCT
ejpam-4973	68	4	let	let	VERB
ejpam-4973	68	5	r	r	PRON
ejpam-4973	68	6	be	be	AUX
ejpam-4973	68	7	a	a	DET
ejpam-4973	68	8	ring	ring	NOUN
ejpam-4973	68	9	and	and	CCONJ
ejpam-4973	68	10	m	m	NOUN
ejpam-4973	68	11	=	=	ADJ
ejpam-4973	68	12	⊕n	⊕n	NOUN
ejpam-4973	68	13	i=1mi	i=1mi	VERB
ejpam-4973	68	14	a	a	DET
ejpam-4973	68	15	finitely	finitely	ADV
ejpam-4973	68	16	generated	generate	VERB
ejpam-4973	68	17	and	and	CCONJ
ejpam-4973	68	18	prime	prime	ADJ
ejpam-4973	68	19	module	module	NOUN
ejpam-4973	68	20	such	such	ADJ
ejpam-4973	68	21	that	that	SCONJ
ejpam-4973	68	22	m	m	PROPN
ejpam-4973	68	23	has	have	VERB
ejpam-4973	68	24	a	a	DET
ejpam-4973	68	25	small	small	ADJ
ejpam-4973	68	26	submodule	submodule	NOUN
ejpam-4973	68	27	.	.	PUNCT
ejpam-4973	69	1	then	then	ADV
ejpam-4973	69	2	m	m	PROPN
ejpam-4973	69	3	is	be	AUX
ejpam-4973	69	4	serial	serial	ADJ
ejpam-4973	69	5	and	and	CCONJ
ejpam-4973	69	6	so	so	ADV
ejpam-4973	69	7	is	be	AUX
ejpam-4973	69	8	every	every	DET
ejpam-4973	69	9	summand	summand	NOUN
ejpam-4973	69	10	of	of	ADP
ejpam-4973	69	11	m	m	PROPN
ejpam-4973	69	12	.	.	PUNCT
ejpam-4973	70	1	proof	proof	NOUN
ejpam-4973	70	2	.	.	PUNCT
ejpam-4973	71	1	let	let	VERB
ejpam-4973	71	2	m	m	PRON
ejpam-4973	71	3	a	a	DET
ejpam-4973	71	4	finitely	finitely	ADV
ejpam-4973	71	5	generated	generate	VERB
ejpam-4973	71	6	prime	prime	ADJ
ejpam-4973	71	7	module	module	NOUN
ejpam-4973	71	8	.	.	PUNCT
ejpam-4973	72	1	let	let	VERB
ejpam-4973	72	2	f	f	NOUN
ejpam-4973	72	3	:	:	PUNCT
ejpam-4973	73	1	r	r	VERB
ejpam-4973	73	2	−→	−→	NOUN
ejpam-4973	73	3	k	k	PROPN
ejpam-4973	73	4	be	be	AUX
ejpam-4973	73	5	an	an	DET
ejpam-4973	73	6	epimorphism	epimorphism	NOUN
ejpam-4973	73	7	where	where	SCONJ
ejpam-4973	73	8	k	k	PROPN
ejpam-4973	73	9	is	be	AUX
ejpam-4973	73	10	a	a	DET
ejpam-4973	73	11	small	small	ADJ
ejpam-4973	73	12	submodule	submodule	NOUN
ejpam-4973	73	13	.	.	PUNCT
ejpam-4973	74	1	f	f	X
ejpam-4973	75	1	:	:	PUNCT
ejpam-4973	75	2	r	r	AUX
ejpam-4973	75	3	−→	−→	NOUN
ejpam-4973	75	4	k	k	PROPN
ejpam-4973	75	5	↓	↓	PROPN
ejpam-4973	75	6	↙	↙	PROPN
ejpam-4973	75	7	r	r	X
ejpam-4973	75	8	/	/	SYM
ejpam-4973	75	9	ann(k	ann(k	PROPN
ejpam-4973	75	10	)	)	PUNCT
ejpam-4973	75	11	by	by	ADP
ejpam-4973	75	12	the	the	DET
ejpam-4973	75	13	first	first	ADJ
ejpam-4973	75	14	isomorphic	isomorphic	ADJ
ejpam-4973	75	15	theorem	theorem	NOUN
ejpam-4973	75	16	r	r	NOUN
ejpam-4973	75	17	/	/	SYM
ejpam-4973	75	18	ann(k	ann(k	PROPN
ejpam-4973	75	19	)	)	PUNCT
ejpam-4973	75	20	≃	≃	PROPN
ejpam-4973	75	21	k.	k.	PROPN
ejpam-4973	75	22	let	let	VERB
ejpam-4973	75	23	g	g	NOUN
ejpam-4973	75	24	:	:	PUNCT
ejpam-4973	75	25	r	r	VERB
ejpam-4973	75	26	−→	−→	NOUN
ejpam-4973	75	27	mi	mi	PROPN
ejpam-4973	75	28	another	another	DET
ejpam-4973	75	29	epimorphism	epimorphism	NOUN
ejpam-4973	75	30	for	for	ADP
ejpam-4973	75	31	every	every	DET
ejpam-4973	75	32	1	1	NUM
ejpam-4973	75	33	≤	≤	NUM
ejpam-4973	75	34	i	i	NOUN
ejpam-4973	75	35	≤	≤	NOUN
ejpam-4973	76	1	n	n	DET
ejpam-4973	76	2	f	f	NOUN
ejpam-4973	76	3	:	:	PUNCT
ejpam-4973	76	4	r	r	NOUN
ejpam-4973	76	5	−→	−→	NOUN
ejpam-4973	76	6	mi	mi	PROPN
ejpam-4973	76	7	↓	↓	PROPN
ejpam-4973	76	8	↙	↙	PROPN
ejpam-4973	76	9	r	r	X
ejpam-4973	76	10	/	/	SYM
ejpam-4973	76	11	ann(mi	ann(mi	NOUN
ejpam-4973	76	12	)	)	PUNCT
ejpam-4973	76	13	we	we	PRON
ejpam-4973	76	14	have	have	VERB
ejpam-4973	76	15	also	also	ADV
ejpam-4973	76	16	r	r	NOUN
ejpam-4973	76	17	/	/	SYM
ejpam-4973	76	18	ann(mi	ann(mi	NOUN
ejpam-4973	76	19	)	)	PUNCT
ejpam-4973	76	20	≃	≃	PROPN
ejpam-4973	76	21	mi	mi	PROPN
ejpam-4973	76	22	.	.	PROPN
ejpam-4973	77	1	since	since	SCONJ
ejpam-4973	77	2	m	m	PROPN
ejpam-4973	77	3	is	be	AUX
ejpam-4973	77	4	a	a	DET
ejpam-4973	77	5	prime	prime	ADJ
ejpam-4973	77	6	module	module	NOUN
ejpam-4973	77	7	ann(k	ann(k	PROPN
ejpam-4973	77	8	)	)	PUNCT
ejpam-4973	77	9	=	=	SYM
ejpam-4973	77	10	ann(mi	ann(mi	NOUN
ejpam-4973	77	11	)	)	PUNCT
ejpam-4973	77	12	,	,	PUNCT
ejpam-4973	77	13	therefore	therefore	ADV
ejpam-4973	77	14	r	r	X
ejpam-4973	77	15	/	/	SYM
ejpam-4973	77	16	ann(k	ann(k	PROPN
ejpam-4973	77	17	)	)	PUNCT
ejpam-4973	77	18	=	=	SYM
ejpam-4973	78	1	r	r	X
ejpam-4973	78	2	/	/	SYM
ejpam-4973	78	3	ann(mi	ann(mi	NOUN
ejpam-4973	78	4	)	)	PUNCT
ejpam-4973	78	5	≃	≃	NOUN
ejpam-4973	78	6	mi	mi	PROPN
ejpam-4973	78	7	is	be	AUX
ejpam-4973	78	8	simple	simple	ADJ
ejpam-4973	78	9	for	for	ADP
ejpam-4973	78	10	1	1	NUM
ejpam-4973	78	11	≤	≤	NUM
ejpam-4973	78	12	i	i	PRON
ejpam-4973	78	13	≤	≤	ADJ
ejpam-4973	79	1	n.	n.	NOUN
ejpam-4973	79	2	therefore	therefore	ADV
ejpam-4973	79	3	m	m	VERB
ejpam-4973	79	4	=	=	ADJ
ejpam-4973	79	5	⊕n	⊕n	NOUN
ejpam-4973	79	6	i=1mi	i=1mi	X
ejpam-4973	79	7	is	be	AUX
ejpam-4973	79	8	semisimple	semisimple	ADJ
ejpam-4973	79	9	.	.	PUNCT
ejpam-4973	80	1	proposition	proposition	NOUN
ejpam-4973	80	2	3	3	NUM
ejpam-4973	80	3	:	:	PUNCT
ejpam-4973	80	4	let	let	VERB
ejpam-4973	80	5	r	r	PRON
ejpam-4973	80	6	be	be	AUX
ejpam-4973	80	7	a	a	DET
ejpam-4973	80	8	ring	ring	NOUN
ejpam-4973	80	9	and	and	CCONJ
ejpam-4973	80	10	m	m	VERB
ejpam-4973	80	11	an	an	DET
ejpam-4973	80	12	uniserial	uniserial	ADJ
ejpam-4973	80	13	r	r	NOUN
ejpam-4973	80	14	-	-	PUNCT
ejpam-4973	80	15	module	module	NOUN
ejpam-4973	80	16	,	,	PUNCT
ejpam-4973	80	17	then	then	ADV
ejpam-4973	80	18	end(m	end(m	PROPN
ejpam-4973	80	19	)	)	PUNCT
ejpam-4973	80	20	is	be	AUX
ejpam-4973	80	21	local	local	ADJ
ejpam-4973	80	22	if	if	SCONJ
ejpam-4973	80	23	,	,	PUNCT
ejpam-4973	80	24	(	(	PUNCT
ejpam-4973	80	25	1	1	X
ejpam-4973	80	26	)	)	PUNCT
ejpam-4973	80	27	m	m	VERB
ejpam-4973	80	28	is	be	AUX
ejpam-4973	80	29	self	self	NOUN
ejpam-4973	80	30	-	-	PUNCT
ejpam-4973	80	31	projective	projective	ADJ
ejpam-4973	80	32	;	;	PUNCT
ejpam-4973	80	33	(	(	PUNCT
ejpam-4973	80	34	2	2	X
ejpam-4973	80	35	)	)	PUNCT
ejpam-4973	80	36	m	m	VERB
ejpam-4973	80	37	is	be	AUX
ejpam-4973	80	38	self	self	NOUN
ejpam-4973	80	39	-	-	PUNCT
ejpam-4973	80	40	injective	injective	ADJ
ejpam-4973	80	41	;	;	PUNCT
ejpam-4973	80	42	(	(	PUNCT
ejpam-4973	80	43	3	3	X
ejpam-4973	80	44	)	)	PUNCT
ejpam-4973	80	45	m	m	VERB
ejpam-4973	80	46	is	be	AUX
ejpam-4973	80	47	a	a	DET
ejpam-4973	80	48	free	free	ADJ
ejpam-4973	80	49	module	module	NOUN
ejpam-4973	80	50	.	.	PUNCT
ejpam-4973	81	1	proof	proof	NOUN
ejpam-4973	81	2	:	:	PUNCT
ejpam-4973	81	3	(	(	PUNCT
ejpam-4973	81	4	1	1	X
ejpam-4973	81	5	)	)	PUNCT
ejpam-4973	81	6	as	as	SCONJ
ejpam-4973	81	7	m	m	PROPN
ejpam-4973	81	8	is	be	AUX
ejpam-4973	81	9	uniserial	uniserial	ADJ
ejpam-4973	81	10	,	,	PUNCT
ejpam-4973	81	11	hence	hence	ADV
ejpam-4973	81	12	it	it	PRON
ejpam-4973	81	13	is	be	AUX
ejpam-4973	81	14	uniform	uniform	ADJ
ejpam-4973	81	15	and	and	CCONJ
ejpam-4973	81	16	indecomposable	indecomposable	ADJ
ejpam-4973	81	17	.	.	PUNCT
ejpam-4973	82	1	let	let	VERB
ejpam-4973	82	2	f	f	PROPN
ejpam-4973	82	3	∈	∈	PROPN
ejpam-4973	82	4	end(m	end(m	PROPN
ejpam-4973	82	5	)	)	PUNCT
ejpam-4973	82	6	therefore	therefore	ADV
ejpam-4973	82	7	ker	ker	PROPN
ejpam-4973	82	8	f	f	PROPN
ejpam-4973	82	9	∩	∩	PROPN
ejpam-4973	82	10	ker(1	ker(1	PROPN
ejpam-4973	82	11	−	−	PROPN
ejpam-4973	83	1	f	f	X
ejpam-4973	83	2	)	)	PUNCT
ejpam-4973	83	3	=	=	NOUN
ejpam-4973	83	4	0	0	X
ejpam-4973	83	5	.	.	PUNCT
ejpam-4973	84	1	since	since	SCONJ
ejpam-4973	84	2	m	m	PROPN
ejpam-4973	84	3	is	be	AUX
ejpam-4973	84	4	uniform	uniform	ADJ
ejpam-4973	84	5	,	,	PUNCT
ejpam-4973	84	6	then	then	ADV
ejpam-4973	84	7	f	f	PROPN
ejpam-4973	84	8	or	or	CCONJ
ejpam-4973	84	9	1	1	NUM
ejpam-4973	84	10	−	−	PROPN
ejpam-4973	84	11	f	f	PROPN
ejpam-4973	84	12	is	be	AUX
ejpam-4973	84	13	a	a	DET
ejpam-4973	84	14	monomorphism	monomorphism	NOUN
ejpam-4973	84	15	.	.	PUNCT
ejpam-4973	85	1	if	if	SCONJ
ejpam-4973	85	2	m	m	PROPN
ejpam-4973	85	3	al	al	PROPN
ejpam-4973	85	4	-	-	PUNCT
ejpam-4973	85	5	h.	h.	PROPN
ejpam-4973	85	6	ba	ba	PROPN
ejpam-4973	85	7	,	,	PUNCT
ejpam-4973	85	8	m.	m.	NOUN
ejpam-4973	85	9	a.	a.	NOUN
ejpam-4973	85	10	diompy	diompy	PROPN
ejpam-4973	85	11	,	,	PUNCT
ejpam-4973	85	12	a.	a.	PROPN
ejpam-4973	85	13	s.	s.	PROPN
ejpam-4973	85	14	diabang	diabang	PROPN
ejpam-4973	85	15	/	/	SYM
ejpam-4973	85	16	eur	eur	PROPN
ejpam-4973	85	17	.	.	PUNCT
ejpam-4973	86	1	j.	j.	PROPN
ejpam-4973	86	2	pure	pure	PROPN
ejpam-4973	86	3	appl	appl	PROPN
ejpam-4973	86	4	.	.	PROPN
ejpam-4973	86	5	math	math	PROPN
ejpam-4973	86	6	,	,	PUNCT
ejpam-4973	86	7	17	17	NUM
ejpam-4973	86	8	(	(	PUNCT
ejpam-4973	86	9	1	1	NUM
ejpam-4973	86	10	)	)	PUNCT
ejpam-4973	86	11	(	(	PUNCT
ejpam-4973	86	12	2024	2024	NUM
ejpam-4973	86	13	)	)	PUNCT
ejpam-4973	86	14	,	,	PUNCT
ejpam-4973	86	15	410	410	NUM
ejpam-4973	86	16	-	-	SYM
ejpam-4973	86	17	415	415	NUM
ejpam-4973	86	18	413	413	NUM
ejpam-4973	86	19	is	be	AUX
ejpam-4973	86	20	self	self	NOUN
ejpam-4973	86	21	-	-	PUNCT
ejpam-4973	86	22	projective	projective	NOUN
ejpam-4973	86	23	then	then	ADV
ejpam-4973	86	24	any	any	DET
ejpam-4973	86	25	sequence	sequence	NOUN
ejpam-4973	86	26	0	0	NUM
ejpam-4973	87	1	−→	−→	NOUN
ejpam-4973	87	2	n	n	CCONJ
ejpam-4973	87	3	−→	−→	NOUN
ejpam-4973	87	4	m	m	VERB
ejpam-4973	87	5	−→	−→	ADJ
ejpam-4973	88	1	m	m	VERB
ejpam-4973	88	2	−→	−→	ADJ
ejpam-4973	88	3	0	0	NUM
ejpam-4973	88	4	is	be	AUX
ejpam-4973	88	5	split	split	VERB
ejpam-4973	88	6	.	.	PUNCT
ejpam-4973	89	1	hence	hence	ADV
ejpam-4973	89	2	an	an	DET
ejpam-4973	89	3	endomorphism	endomorphism	NOUN
ejpam-4973	89	4	of	of	ADP
ejpam-4973	89	5	m	m	PROPN
ejpam-4973	89	6	is	be	AUX
ejpam-4973	89	7	surjective	surjective	ADJ
ejpam-4973	89	8	.	.	PUNCT
ejpam-4973	90	1	therefore	therefore	ADV
ejpam-4973	90	2	end(m	end(m	PROPN
ejpam-4973	90	3	)	)	PUNCT
ejpam-4973	90	4	is	be	AUX
ejpam-4973	90	5	local	local	ADJ
ejpam-4973	90	6	.	.	PUNCT
ejpam-4973	91	1	(	(	PUNCT
ejpam-4973	91	2	2	2	X
ejpam-4973	91	3	)	)	PUNCT
ejpam-4973	91	4	let	let	VERB
ejpam-4973	91	5	f	f	PROPN
ejpam-4973	91	6	∈	∈	PROPN
ejpam-4973	91	7	end(m	end(m	PROPN
ejpam-4973	91	8	)	)	PUNCT
ejpam-4973	91	9	therefore	therefore	ADV
ejpam-4973	91	10	ker	ker	PROPN
ejpam-4973	91	11	f	f	PROPN
ejpam-4973	91	12	∩	∩	PROPN
ejpam-4973	91	13	ker(1	ker(1	PROPN
ejpam-4973	91	14	−	−	PROPN
ejpam-4973	92	1	f	f	X
ejpam-4973	92	2	)	)	PUNCT
ejpam-4973	92	3	=	=	SYM
ejpam-4973	92	4	0	0	X
ejpam-4973	92	5	.	.	PUNCT
ejpam-4973	93	1	then	then	ADV
ejpam-4973	93	2	f	f	PROPN
ejpam-4973	93	3	is	be	AUX
ejpam-4973	93	4	injective	injective	ADJ
ejpam-4973	93	5	.	.	PUNCT
ejpam-4973	94	1	since	since	SCONJ
ejpam-4973	94	2	m	m	PROPN
ejpam-4973	94	3	is	be	AUX
ejpam-4973	94	4	self	self	NOUN
ejpam-4973	94	5	-	-	PUNCT
ejpam-4973	94	6	injective	injective	ADJ
ejpam-4973	94	7	,	,	PUNCT
ejpam-4973	94	8	then	then	ADV
ejpam-4973	94	9	f(m	f(m	PROPN
ejpam-4973	94	10	)	)	PUNCT
ejpam-4973	94	11	is	be	AUX
ejpam-4973	94	12	a	a	DET
ejpam-4973	94	13	direct	direct	ADJ
ejpam-4973	94	14	summand	summand	NOUN
ejpam-4973	94	15	of	of	ADP
ejpam-4973	94	16	m	m	PROPN
ejpam-4973	94	17	that	that	PRON
ejpam-4973	94	18	is	be	AUX
ejpam-4973	94	19	m	m	NOUN
ejpam-4973	94	20	=	=	SYM
ejpam-4973	94	21	f(m	f(m	PROPN
ejpam-4973	94	22	)	)	PUNCT
ejpam-4973	94	23	⊕	⊕	PROPN
ejpam-4973	94	24	n	n	PROPN
ejpam-4973	94	25	.	.	PUNCT
ejpam-4973	95	1	but	but	CCONJ
ejpam-4973	95	2	m	m	PROPN
ejpam-4973	95	3	is	be	AUX
ejpam-4973	95	4	uniserial	uniserial	ADJ
ejpam-4973	95	5	,	,	PUNCT
ejpam-4973	95	6	hence	hence	ADV
ejpam-4973	95	7	m	m	VERB
ejpam-4973	95	8	is	be	AUX
ejpam-4973	95	9	indecomposable	indecomposable	ADJ
ejpam-4973	95	10	.	.	PUNCT
ejpam-4973	96	1	therefore	therefore	ADV
ejpam-4973	96	2	f(m	f(m	PROPN
ejpam-4973	96	3	)	)	PUNCT
ejpam-4973	96	4	=	=	PUNCT
ejpam-4973	97	1	m	m	VERB
ejpam-4973	97	2	which	which	PRON
ejpam-4973	97	3	states	state	VERB
ejpam-4973	97	4	that	that	SCONJ
ejpam-4973	97	5	f	f	PROPN
ejpam-4973	97	6	is	be	AUX
ejpam-4973	97	7	an	an	DET
ejpam-4973	97	8	epimorphism	epimorphism	NOUN
ejpam-4973	97	9	.	.	PUNCT
ejpam-4973	98	1	thus	thus	ADV
ejpam-4973	98	2	f	f	PROPN
ejpam-4973	98	3	is	be	AUX
ejpam-4973	98	4	an	an	DET
ejpam-4973	98	5	automorphism	automorphism	NOUN
ejpam-4973	98	6	.	.	PUNCT
ejpam-4973	99	1	end(m	end(m	VERB
ejpam-4973	99	2	)	)	PUNCT
ejpam-4973	99	3	is	be	AUX
ejpam-4973	99	4	a	a	DET
ejpam-4973	99	5	division	division	NOUN
ejpam-4973	99	6	ring	ring	NOUN
ejpam-4973	99	7	(	(	PUNCT
ejpam-4973	99	8	3	3	NUM
ejpam-4973	99	9	)	)	PUNCT
ejpam-4973	99	10	since	since	SCONJ
ejpam-4973	99	11	any	any	DET
ejpam-4973	99	12	free	free	ADJ
ejpam-4973	99	13	module	module	NOUN
ejpam-4973	99	14	is	be	AUX
ejpam-4973	99	15	projective	projective	ADJ
ejpam-4973	99	16	then	then	ADV
ejpam-4973	99	17	end(m	end(m	PROPN
ejpam-4973	99	18	)	)	PUNCT
ejpam-4973	99	19	is	be	AUX
ejpam-4973	99	20	local	local	ADJ
ejpam-4973	99	21	by	by	ADP
ejpam-4973	99	22	lemma	lemma	PROPN
ejpam-4973	99	23	1	1	NUM
ejpam-4973	99	24	.	.	PUNCT
ejpam-4973	99	25	theorem	theorem	NOUN
ejpam-4973	99	26	2	2	NUM
ejpam-4973	99	27	:	:	PUNCT
ejpam-4973	99	28	let	let	VERB
ejpam-4973	99	29	r	r	PRON
ejpam-4973	99	30	be	be	AUX
ejpam-4973	99	31	a	a	DET
ejpam-4973	99	32	ring	ring	NOUN
ejpam-4973	99	33	and	and	CCONJ
ejpam-4973	99	34	m	m	NOUN
ejpam-4973	99	35	=	=	ADJ
ejpam-4973	99	36	⊕n	⊕n	NOUN
ejpam-4973	99	37	i=1mi	i=1mi	VERB
ejpam-4973	99	38	a	a	DET
ejpam-4973	99	39	serial	serial	ADJ
ejpam-4973	99	40	module	module	NOUN
ejpam-4973	99	41	with	with	ADP
ejpam-4973	99	42	mi	mi	PROPN
ejpam-4973	99	43	selfprojective(resp	selfprojective(resp	PROPN
ejpam-4973	99	44	.	.	PUNCT
ejpam-4973	100	1	self	self	NOUN
ejpam-4973	100	2	-	-	PUNCT
ejpam-4973	100	3	injective	injective	ADJ
ejpam-4973	100	4	or	or	CCONJ
ejpam-4973	100	5	free	free	ADJ
ejpam-4973	100	6	)	)	PUNCT
ejpam-4973	100	7	.	.	PUNCT
ejpam-4973	101	1	then	then	ADV
ejpam-4973	101	2	any	any	DET
ejpam-4973	101	3	direct	direct	ADJ
ejpam-4973	101	4	summand	summand	NOUN
ejpam-4973	101	5	of	of	ADP
ejpam-4973	101	6	m	m	PROPN
ejpam-4973	101	7	is	be	AUX
ejpam-4973	101	8	serial	serial	ADJ
ejpam-4973	101	9	.	.	PUNCT
ejpam-4973	102	1	proof	proof	NOUN
ejpam-4973	102	2	.	.	PUNCT
ejpam-4973	103	1	let	let	VERB
ejpam-4973	103	2	r	r	PRON
ejpam-4973	103	3	be	be	AUX
ejpam-4973	103	4	a	a	DET
ejpam-4973	103	5	ring	ring	NOUN
ejpam-4973	103	6	and	and	CCONJ
ejpam-4973	103	7	m	m	NOUN
ejpam-4973	103	8	=	=	ADJ
ejpam-4973	103	9	⊕n	⊕n	NOUN
ejpam-4973	103	10	i=1mi	i=1mi	VERB
ejpam-4973	103	11	a	a	DET
ejpam-4973	103	12	serial	serial	ADJ
ejpam-4973	103	13	module	module	NOUN
ejpam-4973	103	14	with	with	ADP
ejpam-4973	103	15	mi	mi	PROPN
ejpam-4973	103	16	self	self	NOUN
ejpam-4973	103	17	-	-	PUNCT
ejpam-4973	103	18	projective(resp	projective(resp	PROPN
ejpam-4973	103	19	.	.	PUNCT
ejpam-4973	104	1	selfinjective	selfinjective	ADJ
ejpam-4973	104	2	or	or	CCONJ
ejpam-4973	104	3	free	free	ADJ
ejpam-4973	104	4	.	.	PUNCT
ejpam-4973	105	1	it	it	PRON
ejpam-4973	105	2	results	result	VERB
ejpam-4973	105	3	from	from	ADP
ejpam-4973	105	4	proposition	proposition	NOUN
ejpam-4973	105	5	3	3	NUM
ejpam-4973	105	6	that	that	SCONJ
ejpam-4973	105	7	the	the	DET
ejpam-4973	105	8	endomorphism	endomorphism	NOUN
ejpam-4973	105	9	ring	ring	NOUN
ejpam-4973	105	10	of	of	ADP
ejpam-4973	105	11	any	any	DET
ejpam-4973	105	12	selfprojective(resp	selfprojective(resp	PROPN
ejpam-4973	105	13	.	.	PUNCT
ejpam-4973	106	1	self	self	NOUN
ejpam-4973	106	2	-	-	PUNCT
ejpam-4973	106	3	injective	injective	ADJ
ejpam-4973	106	4	or	or	CCONJ
ejpam-4973	106	5	free	free	ADJ
ejpam-4973	106	6	)	)	PUNCT
ejpam-4973	106	7	module	module	NOUN
ejpam-4973	106	8	is	be	AUX
ejpam-4973	106	9	local	local	ADJ
ejpam-4973	106	10	.	.	PUNCT
ejpam-4973	107	1	it	it	PRON
ejpam-4973	107	2	follows	follow	VERB
ejpam-4973	107	3	from	from	ADP
ejpam-4973	107	4	proposition	proposition	NOUN
ejpam-4973	107	5	2.2	2.2	NUM
ejpam-4973	107	6	of	of	ADP
ejpam-4973	107	7	[	[	X
ejpam-4973	107	8	4	4	X
ejpam-4973	107	9	]	]	PUNCT
ejpam-4973	107	10	that	that	SCONJ
ejpam-4973	107	11	the	the	DET
ejpam-4973	107	12	direct	direct	ADJ
ejpam-4973	107	13	summand	summand	NOUN
ejpam-4973	107	14	of	of	ADP
ejpam-4973	107	15	any	any	DET
ejpam-4973	107	16	direct	direct	ADJ
ejpam-4973	107	17	sum	sum	NOUN
ejpam-4973	107	18	of	of	ADP
ejpam-4973	107	19	uniserial	uniserial	ADJ
ejpam-4973	107	20	modules	module	NOUN
ejpam-4973	107	21	with	with	ADP
ejpam-4973	107	22	local	local	ADJ
ejpam-4973	107	23	endomorphism	endomorphism	NOUN
ejpam-4973	107	24	rings	ring	NOUN
ejpam-4973	107	25	is	be	AUX
ejpam-4973	107	26	serial	serial	ADJ
ejpam-4973	107	27	.	.	PUNCT
ejpam-4973	108	1	proposition	proposition	NOUN
ejpam-4973	108	2	4	4	NUM
ejpam-4973	108	3	:	:	PUNCT
ejpam-4973	108	4	let	let	VERB
ejpam-4973	108	5	r	r	PRON
ejpam-4973	108	6	be	be	AUX
ejpam-4973	108	7	a	a	DET
ejpam-4973	108	8	ring	ring	NOUN
ejpam-4973	108	9	.	.	PUNCT
ejpam-4973	109	1	(	(	PUNCT
ejpam-4973	109	2	1	1	X
ejpam-4973	109	3	)	)	PUNCT
ejpam-4973	109	4	if	if	SCONJ
ejpam-4973	109	5	r	r	NOUN
ejpam-4973	109	6	is	be	AUX
ejpam-4973	109	7	semisimple	semisimple	NOUN
ejpam-4973	109	8	ring	ring	NOUN
ejpam-4973	109	9	,	,	PUNCT
ejpam-4973	109	10	then	then	ADV
ejpam-4973	109	11	every	every	DET
ejpam-4973	109	12	a	a	DET
ejpam-4973	109	13	left	left	ADJ
ejpam-4973	109	14	module	module	NOUN
ejpam-4973	109	15	m	m	NOUN
ejpam-4973	109	16	over	over	ADP
ejpam-4973	109	17	r	r	NOUN
ejpam-4973	109	18	is	be	AUX
ejpam-4973	109	19	serial	serial	ADJ
ejpam-4973	109	20	.	.	PUNCT
ejpam-4973	110	1	moreover	moreover	ADV
ejpam-4973	110	2	,	,	PUNCT
ejpam-4973	110	3	every	every	DET
ejpam-4973	110	4	direct	direct	ADJ
ejpam-4973	110	5	summand	summand	NOUN
ejpam-4973	110	6	of	of	ADP
ejpam-4973	110	7	m	m	PROPN
ejpam-4973	110	8	is	be	AUX
ejpam-4973	110	9	serial	serial	ADJ
ejpam-4973	110	10	.	.	PUNCT
ejpam-4973	111	1	(	(	PUNCT
ejpam-4973	111	2	2	2	X
ejpam-4973	111	3	)	)	PUNCT
ejpam-4973	111	4	if	if	SCONJ
ejpam-4973	111	5	r	r	NOUN
ejpam-4973	111	6	is	be	AUX
ejpam-4973	111	7	principal	principal	ADJ
ejpam-4973	111	8	ring	ring	NOUN
ejpam-4973	111	9	and	and	CCONJ
ejpam-4973	111	10	m	m	VERB
ejpam-4973	111	11	a	a	DET
ejpam-4973	111	12	left	left	ADJ
ejpam-4973	111	13	serial	serial	ADJ
ejpam-4973	111	14	r	r	NOUN
ejpam-4973	111	15	-	-	PUNCT
ejpam-4973	111	16	module	module	NOUN
ejpam-4973	111	17	,	,	PUNCT
ejpam-4973	111	18	then	then	ADV
ejpam-4973	111	19	every	every	DET
ejpam-4973	111	20	direct	direct	ADJ
ejpam-4973	111	21	summand	summand	NOUN
ejpam-4973	111	22	of	of	ADP
ejpam-4973	111	23	m	m	PROPN
ejpam-4973	111	24	is	be	AUX
ejpam-4973	111	25	serial	serial	ADJ
ejpam-4973	111	26	.	.	PUNCT
ejpam-4973	112	1	proof	proof	NOUN
ejpam-4973	112	2	:	:	PUNCT
ejpam-4973	112	3	(	(	PUNCT
ejpam-4973	112	4	1	1	X
ejpam-4973	112	5	)	)	PUNCT
ejpam-4973	112	6	let	let	VERB
ejpam-4973	112	7	m	m	PRON
ejpam-4973	112	8	be	be	AUX
ejpam-4973	112	9	a	a	DET
ejpam-4973	112	10	left	left	ADJ
ejpam-4973	112	11	r	r	NOUN
ejpam-4973	112	12	-	-	PUNCT
ejpam-4973	112	13	module	module	NOUN
ejpam-4973	112	14	.	.	PUNCT
ejpam-4973	113	1	since	since	SCONJ
ejpam-4973	113	2	r	r	NOUN
ejpam-4973	113	3	is	be	AUX
ejpam-4973	113	4	semisimple	semisimple	NOUN
ejpam-4973	113	5	hence	hence	ADV
ejpam-4973	113	6	,	,	PUNCT
ejpam-4973	113	7	m	m	PROPN
ejpam-4973	113	8	is	be	AUX
ejpam-4973	113	9	semisimple	semisimple	ADJ
ejpam-4973	113	10	.	.	PUNCT
ejpam-4973	114	1	let	let	VERB
ejpam-4973	114	2	m	m	NOUN
ejpam-4973	114	3	=	=	PROPN
ejpam-4973	114	4	⊕	⊕	PROPN
ejpam-4973	114	5	i∈i	i∈i	ADJ
ejpam-4973	114	6	mi	mi	PROPN
ejpam-4973	114	7	with	with	ADP
ejpam-4973	114	8	mi	mi	PROPN
ejpam-4973	114	9	simple	simple	NOUN
ejpam-4973	114	10	.	.	PUNCT
ejpam-4973	115	1	it	it	PRON
ejpam-4973	115	2	is	be	AUX
ejpam-4973	115	3	well	well	ADV
ejpam-4973	115	4	know	know	VERB
ejpam-4973	115	5	that	that	SCONJ
ejpam-4973	115	6	any	any	DET
ejpam-4973	115	7	simple	simple	ADJ
ejpam-4973	115	8	module	module	NOUN
ejpam-4973	115	9	is	be	AUX
ejpam-4973	115	10	uniserial	uniserial	ADJ
ejpam-4973	115	11	.	.	PUNCT
ejpam-4973	116	1	hence	hence	ADV
ejpam-4973	116	2	,	,	PUNCT
ejpam-4973	116	3	m	m	VERB
ejpam-4973	116	4	is	be	AUX
ejpam-4973	116	5	serial	serial	ADJ
ejpam-4973	116	6	.	.	PUNCT
ejpam-4973	117	1	let	let	VERB
ejpam-4973	117	2	s	s	PRON
ejpam-4973	117	3	=	=	VERB
ejpam-4973	117	4	end(mi	end(mi	PROPN
ejpam-4973	117	5	)	)	PUNCT
ejpam-4973	117	6	an	an	DET
ejpam-4973	117	7	endomorphism	endomorphism	NOUN
ejpam-4973	117	8	ring	ring	NOUN
ejpam-4973	117	9	of	of	ADP
ejpam-4973	117	10	simple	simple	ADJ
ejpam-4973	117	11	module	module	NOUN
ejpam-4973	117	12	mi	mi	PROPN
ejpam-4973	117	13	,	,	PUNCT
ejpam-4973	117	14	by	by	ADP
ejpam-4973	117	15	schur	schur	PROPN
ejpam-4973	117	16	’s	’s	PROPN
ejpam-4973	117	17	lemma	lemma	PROPN
ejpam-4973	117	18	s	s	PROPN
ejpam-4973	117	19	is	be	AUX
ejpam-4973	117	20	a	a	DET
ejpam-4973	117	21	division	division	NOUN
ejpam-4973	117	22	ring	ring	NOUN
ejpam-4973	117	23	.	.	PUNCT
ejpam-4973	118	1	therefore	therefore	ADV
ejpam-4973	118	2	s	s	VERB
ejpam-4973	118	3	is	be	AUX
ejpam-4973	118	4	a	a	DET
ejpam-4973	118	5	local	local	ADJ
ejpam-4973	118	6	ring	ring	NOUN
ejpam-4973	118	7	.	.	PUNCT
ejpam-4973	119	1	thus	thus	ADV
ejpam-4973	119	2	every	every	DET
ejpam-4973	119	3	direct	direct	ADJ
ejpam-4973	119	4	summand	summand	NOUN
ejpam-4973	119	5	of	of	ADP
ejpam-4973	119	6	m	m	PROPN
ejpam-4973	119	7	is	be	AUX
ejpam-4973	119	8	serial	serial	ADJ
ejpam-4973	119	9	.	.	PUNCT
ejpam-4973	120	1	(	(	PUNCT
ejpam-4973	120	2	2	2	X
ejpam-4973	120	3	)	)	PUNCT
ejpam-4973	120	4	if	if	SCONJ
ejpam-4973	120	5	r	r	NOUN
ejpam-4973	120	6	is	be	AUX
ejpam-4973	120	7	principal	principal	ADJ
ejpam-4973	120	8	ring	ring	NOUN
ejpam-4973	120	9	,	,	PUNCT
ejpam-4973	120	10	then	then	ADV
ejpam-4973	120	11	every	every	DET
ejpam-4973	120	12	ideal	ideal	NOUN
ejpam-4973	120	13	over	over	ADP
ejpam-4973	120	14	r	r	NOUN
ejpam-4973	120	15	is	be	AUX
ejpam-4973	120	16	principal	principal	ADJ
ejpam-4973	120	17	is	be	AUX
ejpam-4973	120	18	cyclic	cyclic	ADJ
ejpam-4973	120	19	(	(	PUNCT
ejpam-4973	120	20	finitely	finitely	ADV
ejpam-4973	120	21	generated	generate	VERB
ejpam-4973	120	22	)	)	PUNCT
ejpam-4973	120	23	.	.	PUNCT
ejpam-4973	121	1	thus	thus	ADV
ejpam-4973	121	2	by	by	ADP
ejpam-4973	121	3	the	the	DET
ejpam-4973	121	4	definition	definition	NOUN
ejpam-4973	121	5	of	of	ADP
ejpam-4973	121	6	noetherian	noetherian	ADJ
ejpam-4973	121	7	ring	ring	NOUN
ejpam-4973	121	8	,	,	PUNCT
ejpam-4973	121	9	r	r	NOUN
ejpam-4973	121	10	is	be	AUX
ejpam-4973	121	11	noetherian	noetherian	ADJ
ejpam-4973	121	12	.	.	PUNCT
ejpam-4973	122	1	theorem	theorem	NOUN
ejpam-4973	122	2	3	3	NUM
ejpam-4973	122	3	:	:	PUNCT
ejpam-4973	122	4	let	let	VERB
ejpam-4973	122	5	r	r	PRON
ejpam-4973	122	6	be	be	AUX
ejpam-4973	122	7	a	a	DET
ejpam-4973	122	8	semisimple	semisimple	NOUN
ejpam-4973	122	9	or	or	CCONJ
ejpam-4973	122	10	principal	principal	ADJ
ejpam-4973	122	11	ring	ring	NOUN
ejpam-4973	122	12	and	and	CCONJ
ejpam-4973	122	13	m	m	NOUN
ejpam-4973	122	14	=	=	ADJ
ejpam-4973	122	15	⊕n	⊕n	NOUN
ejpam-4973	122	16	i=1mi	i=1mi	VERB
ejpam-4973	122	17	a	a	DET
ejpam-4973	122	18	serial	serial	ADJ
ejpam-4973	122	19	module	module	NOUN
ejpam-4973	122	20	.	.	PUNCT
ejpam-4973	123	1	then	then	ADV
ejpam-4973	123	2	every	every	DET
ejpam-4973	123	3	direct	direct	ADJ
ejpam-4973	123	4	summand	summand	NOUN
ejpam-4973	123	5	of	of	ADP
ejpam-4973	123	6	m	m	PROPN
ejpam-4973	123	7	is	be	AUX
ejpam-4973	123	8	serial	serial	ADJ
ejpam-4973	123	9	.	.	PUNCT
ejpam-4973	124	1	proof	proof	NOUN
ejpam-4973	124	2	:	:	PUNCT
ejpam-4973	124	3	let	let	VERB
ejpam-4973	124	4	r	r	PRON
ejpam-4973	124	5	be	be	AUX
ejpam-4973	124	6	a	a	DET
ejpam-4973	124	7	semisimple	semisimple	NOUN
ejpam-4973	124	8	m	m	NOUN
ejpam-4973	124	9	=	=	NOUN
ejpam-4973	124	10	⊕n	⊕n	NOUN
ejpam-4973	124	11	i=1mi	i=1mi	VERB
ejpam-4973	124	12	a	a	DET
ejpam-4973	124	13	serial	serial	ADJ
ejpam-4973	124	14	module	module	NOUN
ejpam-4973	124	15	.	.	PUNCT
ejpam-4973	125	1	it	it	PRON
ejpam-4973	125	2	results	result	VERB
ejpam-4973	125	3	from	from	ADP
ejpam-4973	125	4	proposition	proposition	NOUN
ejpam-4973	125	5	4	4	NUM
ejpam-4973	125	6	that	that	PRON
ejpam-4973	125	7	end(mi	end(mi	VERB
ejpam-4973	125	8	)	)	PUNCT
ejpam-4973	125	9	is	be	AUX
ejpam-4973	125	10	a	a	DET
ejpam-4973	125	11	local	local	ADJ
ejpam-4973	125	12	endomorphisme	endomorphisme	NOUN
ejpam-4973	125	13	ring	ring	NOUN
ejpam-4973	125	14	for	for	ADP
ejpam-4973	125	15	any	any	DET
ejpam-4973	125	16	1	1	NUM
ejpam-4973	125	17	≤	≤	NUM
ejpam-4973	125	18	i	i	PRON
ejpam-4973	125	19	≤	≤	ADJ
ejpam-4973	125	20	n.	n.	NOUN
ejpam-4973	125	21	by	by	ADP
ejpam-4973	125	22	the	the	DET
ejpam-4973	125	23	proposition	proposition	NOUN
ejpam-4973	125	24	2.2	2.2	NUM
ejpam-4973	125	25	of	of	ADP
ejpam-4973	125	26	[	[	X
ejpam-4973	125	27	4	4	X
ejpam-4973	125	28	]	]	PUNCT
ejpam-4973	125	29	that	that	SCONJ
ejpam-4973	125	30	any	any	DET
ejpam-4973	125	31	direct	direct	ADJ
ejpam-4973	125	32	summand	summand	NOUN
ejpam-4973	125	33	of	of	ADP
ejpam-4973	125	34	m	m	PROPN
ejpam-4973	125	35	is	be	AUX
ejpam-4973	125	36	a	a	DET
ejpam-4973	125	37	direct	direct	ADJ
ejpam-4973	125	38	sum	sum	NOUN
ejpam-4973	125	39	of	of	ADP
ejpam-4973	125	40	serial	serial	ADJ
ejpam-4973	125	41	module	module	NOUN
ejpam-4973	125	42	.	.	PUNCT
ejpam-4973	126	1	references	reference	NOUN
ejpam-4973	126	2	414	414	NUM
ejpam-4973	126	3	assume	assume	VERB
ejpam-4973	126	4	r	r	NOUN
ejpam-4973	126	5	is	be	AUX
ejpam-4973	126	6	a	a	DET
ejpam-4973	126	7	principal	principal	ADJ
ejpam-4973	126	8	ring	ring	NOUN
ejpam-4973	126	9	.	.	PUNCT
ejpam-4973	127	1	it	it	PRON
ejpam-4973	127	2	results	result	VERB
ejpam-4973	127	3	from	from	ADP
ejpam-4973	127	4	proposition	proposition	NOUN
ejpam-4973	127	5	4	4	NUM
ejpam-4973	127	6	that	that	PRON
ejpam-4973	127	7	r	r	NOUN
ejpam-4973	127	8	is	be	AUX
ejpam-4973	127	9	a	a	DET
ejpam-4973	127	10	noetherian	noetherian	ADJ
ejpam-4973	127	11	ring	ring	NOUN
ejpam-4973	127	12	.	.	PUNCT
ejpam-4973	128	1	it	it	PRON
ejpam-4973	128	2	follows	follow	VERB
ejpam-4973	128	3	from	from	ADP
ejpam-4973	128	4	example	example	NOUN
ejpam-4973	128	5	2.3	2.3	NUM
ejpam-4973	128	6	of	of	ADP
ejpam-4973	128	7	[	[	X
ejpam-4973	128	8	1	1	X
ejpam-4973	128	9	]	]	PUNCT
ejpam-4973	128	10	that	that	SCONJ
ejpam-4973	128	11	any	any	DET
ejpam-4973	128	12	direct	direct	ADJ
ejpam-4973	128	13	summand	summand	NOUN
ejpam-4973	128	14	of	of	ADP
ejpam-4973	128	15	m	m	PROPN
ejpam-4973	128	16	is	be	AUX
ejpam-4973	128	17	serial	serial	ADJ
ejpam-4973	128	18	.	.	PUNCT
ejpam-4973	129	1	proposition	proposition	NOUN
ejpam-4973	129	2	5	5	NUM
ejpam-4973	129	3	:	:	PUNCT
ejpam-4973	129	4	let	let	VERB
ejpam-4973	129	5	r	r	NOUN
ejpam-4973	129	6	=	=	SYM
ejpam-4973	129	7	⊕n	⊕n	NOUN
ejpam-4973	129	8	i=1ri	i=1ri	X
ejpam-4973	129	9	be	be	AUX
ejpam-4973	129	10	a	a	DET
ejpam-4973	129	11	serial	serial	ADJ
ejpam-4973	129	12	semiperfect	semiperfect	NOUN
ejpam-4973	129	13	ring	ring	NOUN
ejpam-4973	129	14	then	then	ADV
ejpam-4973	129	15	(	(	PUNCT
ejpam-4973	129	16	1	1	X
ejpam-4973	129	17	)	)	PUNCT
ejpam-4973	129	18	end(ri	end(ri	NUM
ejpam-4973	129	19	)	)	PUNCT
ejpam-4973	129	20	is	be	AUX
ejpam-4973	129	21	local	local	ADJ
ejpam-4973	129	22	,	,	PUNCT
ejpam-4973	129	23	(	(	PUNCT
ejpam-4973	129	24	2	2	X
ejpam-4973	129	25	)	)	PUNCT
ejpam-4973	129	26	every	every	DET
ejpam-4973	129	27	direct	direct	ADJ
ejpam-4973	129	28	summand	summand	NOUN
ejpam-4973	129	29	of	of	ADP
ejpam-4973	129	30	r	r	NOUN
ejpam-4973	129	31	is	be	AUX
ejpam-4973	129	32	serial	serial	ADJ
ejpam-4973	129	33	.	.	PUNCT
ejpam-4973	130	1	proof	proof	NOUN
ejpam-4973	130	2	:	:	PUNCT
ejpam-4973	130	3	as	as	SCONJ
ejpam-4973	130	4	r	r	NOUN
ejpam-4973	130	5	is	be	AUX
ejpam-4973	130	6	semiperfect	semiperfect	ADJ
ejpam-4973	130	7	then	then	ADV
ejpam-4973	130	8	r	r	NOUN
ejpam-4973	130	9	is	be	AUX
ejpam-4973	130	10	a	a	DET
ejpam-4973	130	11	sum	sum	NOUN
ejpam-4973	130	12	of	of	ADP
ejpam-4973	130	13	is	be	AUX
ejpam-4973	130	14	local	local	ADJ
ejpam-4973	130	15	ring	ring	NOUN
ejpam-4973	130	16	.	.	PUNCT
ejpam-4973	131	1	hence	hence	ADV
ejpam-4973	131	2	ri	ri	PROPN
ejpam-4973	131	3	is	be	AUX
ejpam-4973	131	4	local	local	ADJ
ejpam-4973	131	5	for	for	ADP
ejpam-4973	131	6	any	any	DET
ejpam-4973	131	7	1	1	NUM
ejpam-4973	131	8	≤	≤	NUM
ejpam-4973	131	9	i	i	PRON
ejpam-4973	131	10	≤	≤	NUM
ejpam-4973	132	1	n.	n.	NOUN
ejpam-4973	132	2	it	it	PRON
ejpam-4973	132	3	results	result	VERB
ejpam-4973	132	4	from	from	ADP
ejpam-4973	132	5	proposition	proposition	NOUN
ejpam-4973	132	6	1	1	NUM
ejpam-4973	132	7	,	,	PUNCT
ejpam-4973	133	1	that	that	SCONJ
ejpam-4973	133	2	end(ri	end(ri	NOUN
ejpam-4973	133	3	)	)	PUNCT
ejpam-4973	133	4	is	be	AUX
ejpam-4973	133	5	local	local	ADJ
ejpam-4973	133	6	.	.	PUNCT
ejpam-4973	134	1	therefore	therefore	ADV
ejpam-4973	134	2	any	any	DET
ejpam-4973	134	3	direct	direct	ADJ
ejpam-4973	134	4	summand	summand	NOUN
ejpam-4973	134	5	of	of	ADP
ejpam-4973	134	6	r	r	NOUN
ejpam-4973	134	7	is	be	AUX
ejpam-4973	134	8	serial	serial	ADJ
ejpam-4973	134	9	.	.	PUNCT
ejpam-4973	135	1	theorem	theorem	ADJ
ejpam-4973	135	2	4	4	NUM
ejpam-4973	135	3	:	:	PUNCT
ejpam-4973	135	4	let	let	VERB
ejpam-4973	135	5	r	r	PRON
ejpam-4973	135	6	be	be	AUX
ejpam-4973	135	7	a	a	DET
ejpam-4973	135	8	local	local	ADJ
ejpam-4973	135	9	ring	ring	NOUN
ejpam-4973	135	10	and	and	CCONJ
ejpam-4973	135	11	m	m	NOUN
ejpam-4973	135	12	=	=	ADJ
ejpam-4973	135	13	⊕n	⊕n	NOUN
ejpam-4973	135	14	i=1mi	i=1mi	VERB
ejpam-4973	135	15	a	a	DET
ejpam-4973	135	16	finitely	finitely	ADV
ejpam-4973	135	17	generated	generate	VERB
ejpam-4973	135	18	serial	serial	ADJ
ejpam-4973	135	19	module	module	NOUN
ejpam-4973	135	20	.	.	PUNCT
ejpam-4973	136	1	then	then	ADV
ejpam-4973	136	2	every	every	DET
ejpam-4973	136	3	direct	direct	ADJ
ejpam-4973	136	4	summand	summand	NOUN
ejpam-4973	136	5	of	of	ADP
ejpam-4973	136	6	m	m	PROPN
ejpam-4973	136	7	is	be	AUX
ejpam-4973	136	8	serial	serial	ADJ
ejpam-4973	136	9	.	.	PUNCT
ejpam-4973	137	1	proof	proof	NOUN
ejpam-4973	137	2	.	.	PUNCT
ejpam-4973	138	1	let	let	VERB
ejpam-4973	138	2	r	r	PRON
ejpam-4973	138	3	be	be	AUX
ejpam-4973	138	4	a	a	DET
ejpam-4973	138	5	local	local	ADJ
ejpam-4973	138	6	ring	ring	NOUN
ejpam-4973	138	7	and	and	CCONJ
ejpam-4973	138	8	m	m	NOUN
ejpam-4973	138	9	=	=	ADJ
ejpam-4973	138	10	⊕n	⊕n	NOUN
ejpam-4973	138	11	i=1mi	i=1mi	VERB
ejpam-4973	138	12	a	a	DET
ejpam-4973	138	13	finitely	finitely	ADV
ejpam-4973	138	14	generated	generate	VERB
ejpam-4973	138	15	serial	serial	ADJ
ejpam-4973	138	16	module	module	NOUN
ejpam-4973	138	17	left	leave	VERB
ejpam-4973	138	18	r	r	NOUN
ejpam-4973	138	19	-	-	PUNCT
ejpam-4973	138	20	module	module	NOUN
ejpam-4973	138	21	.	.	PUNCT
ejpam-4973	139	1	assume	assume	VERB
ejpam-4973	139	2	mi	mi	PROPN
ejpam-4973	139	3	a	a	DET
ejpam-4973	139	4	cyclic	cyclic	ADJ
ejpam-4973	139	5	module	module	NOUN
ejpam-4973	139	6	.	.	PUNCT
ejpam-4973	140	1	by	by	ADP
ejpam-4973	140	2	the	the	DET
ejpam-4973	140	3	following	follow	VERB
ejpam-4973	140	4	diagram	diagram	NOUN
ejpam-4973	140	5	,	,	PUNCT
ejpam-4973	140	6	f	f	X
ejpam-4973	140	7	:	:	PUNCT
ejpam-4973	140	8	r	r	VERB
ejpam-4973	140	9	−→	−→	NOUN
ejpam-4973	140	10	mi	mi	PROPN
ejpam-4973	140	11	↓	↓	PROPN
ejpam-4973	140	12	↙	↙	PROPN
ejpam-4973	140	13	r	r	X
ejpam-4973	140	14	/	/	SYM
ejpam-4973	140	15	ann(mi	ann(mi	NOUN
ejpam-4973	140	16	)	)	PUNCT
ejpam-4973	140	17	r	r	NOUN
ejpam-4973	140	18	/	/	SYM
ejpam-4973	140	19	ann(mi	ann(mi	NOUN
ejpam-4973	140	20	)	)	PUNCT
ejpam-4973	140	21	is	be	AUX
ejpam-4973	140	22	isomorphic	isomorphic	ADJ
ejpam-4973	140	23	to	to	ADP
ejpam-4973	140	24	mi	mi	PROPN
ejpam-4973	140	25	.	.	PROPN
ejpam-4973	140	26	as	as	SCONJ
ejpam-4973	140	27	r	r	NOUN
ejpam-4973	140	28	is	be	AUX
ejpam-4973	140	29	local	local	ADJ
ejpam-4973	140	30	,	,	PUNCT
ejpam-4973	140	31	it	it	PRON
ejpam-4973	140	32	has	have	VERB
ejpam-4973	140	33	a	a	DET
ejpam-4973	140	34	unique	unique	ADJ
ejpam-4973	140	35	maximal	maximal	ADJ
ejpam-4973	140	36	ideal	ideal	NOUN
ejpam-4973	140	37	,	,	PUNCT
ejpam-4973	140	38	j	j	PROPN
ejpam-4973	140	39	.	.	PUNCT
ejpam-4973	141	1	let	let	VERB
ejpam-4973	141	2	ī	ī	NOUN
ejpam-4973	141	3	be	be	AUX
ejpam-4973	141	4	an	an	DET
ejpam-4973	141	5	ideal	ideal	NOUN
ejpam-4973	141	6	of	of	ADP
ejpam-4973	141	7	r	r	NOUN
ejpam-4973	141	8	/	/	SYM
ejpam-4973	141	9	ann(mi	ann(mi	NOUN
ejpam-4973	141	10	)	)	PUNCT
ejpam-4973	141	11	then	then	ADV
ejpam-4973	141	12	ī	ī	NOUN
ejpam-4973	141	13	=	=	PUNCT
ejpam-4973	141	14	i	i	NOUN
ejpam-4973	141	15	/	/	SYM
ejpam-4973	141	16	ann(mi	ann(mi	VERB
ejpam-4973	141	17	)	)	PUNCT
ejpam-4973	141	18	with	with	ADP
ejpam-4973	141	19	i	i	PRON
ejpam-4973	141	20	an	an	DET
ejpam-4973	141	21	ideal	ideal	NOUN
ejpam-4973	141	22	of	of	ADP
ejpam-4973	141	23	r	r	NOUN
ejpam-4973	141	24	and	and	CCONJ
ejpam-4973	141	25	ann(mi	ann(mi	NOUN
ejpam-4973	141	26	)	)	PUNCT
ejpam-4973	141	27	⊆	⊆	NUM
ejpam-4973	141	28	j	j	PROPN
ejpam-4973	141	29	.	.	PUNCT
ejpam-4973	142	1	therefore	therefore	ADV
ejpam-4973	142	2	j	j	PROPN
ejpam-4973	142	3	/	/	SYM
ejpam-4973	142	4	ann(mi	ann(mi	PROPN
ejpam-4973	142	5	)	)	PUNCT
ejpam-4973	142	6	is	be	AUX
ejpam-4973	142	7	the	the	DET
ejpam-4973	142	8	unique	unique	ADJ
ejpam-4973	142	9	maximal	maximal	ADJ
ejpam-4973	142	10	ideal	ideal	NOUN
ejpam-4973	142	11	of	of	ADP
ejpam-4973	142	12	r	r	NOUN
ejpam-4973	142	13	/	/	SYM
ejpam-4973	142	14	ann(mi	ann(mi	NOUN
ejpam-4973	142	15	)	)	PUNCT
ejpam-4973	142	16	.	.	PUNCT
ejpam-4973	143	1	hence	hence	ADV
ejpam-4973	143	2	,	,	PUNCT
ejpam-4973	143	3	r	r	NOUN
ejpam-4973	143	4	/	/	SYM
ejpam-4973	143	5	ann(mi	ann(mi	NOUN
ejpam-4973	143	6	)	)	PUNCT
ejpam-4973	143	7	is	be	AUX
ejpam-4973	143	8	a	a	DET
ejpam-4973	143	9	local	local	ADJ
ejpam-4973	143	10	ring	ring	NOUN
ejpam-4973	143	11	.	.	PUNCT
ejpam-4973	144	1	thus	thus	ADV
ejpam-4973	144	2	mi	mi	PROPN
ejpam-4973	144	3	is	be	AUX
ejpam-4973	144	4	local	local	ADJ
ejpam-4973	144	5	.	.	PUNCT
ejpam-4973	145	1	references	reference	NOUN
ejpam-4973	145	2	[	[	X
ejpam-4973	145	3	1	1	NUM
ejpam-4973	145	4	]	]	PUNCT
ejpam-4973	145	5	a.	a.	NOUN
ejpam-4973	145	6	facchini	facchini	PROPN
ejpam-4973	145	7	,	,	PUNCT
ejpam-4973	145	8	krull	krull	PROPN
ejpam-4973	145	9	-	-	PUNCT
ejpam-4973	145	10	schmidt	schmidt	PROPN
ejpam-4973	145	11	fails	fail	VERB
ejpam-4973	145	12	for	for	ADP
ejpam-4973	145	13	serial	serial	ADJ
ejpam-4973	145	14	modules	module	NOUN
ejpam-4973	145	15	,	,	PUNCT
ejpam-4973	145	16	trans	trans	PROPN
ejpam-4973	145	17	.	.	PROPN
ejpam-4973	146	1	amer	amer	PROPN
ejpam-4973	146	2	.	.	PUNCT
ejpam-4973	146	3	math	math	PROPN
ejpam-4973	146	4	.	.	PUNCT
ejpam-4973	147	1	soc	soc	PROPN
ejpam-4973	147	2	.	.	PUNCT
ejpam-4973	148	1	348	348	NUM
ejpam-4973	148	2	(	(	PUNCT
ejpam-4973	148	3	1996	1996	NUM
ejpam-4973	148	4	)	)	PUNCT
ejpam-4973	148	5	,	,	PUNCT
ejpam-4973	148	6	4561	4561	NUM
ejpam-4973	148	7	-	-	SYM
ejpam-4973	148	8	4575	4575	NUM
ejpam-4973	148	9	[	[	X
ejpam-4973	148	10	2	2	NUM
ejpam-4973	148	11	]	]	PUNCT
ejpam-4973	148	12	a.	a.	NOUN
ejpam-4973	148	13	facchini	facchini	PROPN
ejpam-4973	148	14	,	,	PUNCT
ejpam-4973	148	15	modules	module	NOUN
ejpam-4973	148	16	theory	theory	NOUN
ejpam-4973	148	17	:	:	PUNCT
ejpam-4973	148	18	endomorphism	endomorphism	PROPN
ejpam-4973	148	19	rings	ring	NOUN
ejpam-4973	148	20	and	and	CCONJ
ejpam-4973	148	21	direct	direct	ADJ
ejpam-4973	148	22	sum	sum	NOUN
ejpam-4973	148	23	decompositions	decomposition	NOUN
ejpam-4973	148	24	in	in	ADP
ejpam-4973	148	25	some	some	DET
ejpam-4973	148	26	classes	class	NOUN
ejpam-4973	148	27	of	of	ADP
ejpam-4973	148	28	modules	module	NOUN
ejpam-4973	148	29	,	,	PUNCT
ejpam-4973	148	30	reprint	reprint	NOUN
ejpam-4973	148	31	of	of	ADP
ejpam-4973	148	32	1998	1998	NUM
ejpam-4973	148	33	edition	edition	NOUN
ejpam-4973	149	1	[	[	X
ejpam-4973	149	2	3	3	NUM
ejpam-4973	149	3	]	]	X
ejpam-4973	149	4	f.w	f.w	PROPN
ejpam-4973	149	5	.	.	PROPN
ejpam-4973	149	6	anderson	anderson	PROPN
ejpam-4973	149	7	and	and	CCONJ
ejpam-4973	149	8	k.	k.	PROPN
ejpam-4973	149	9	fuller	fuller	PROPN
ejpam-4973	149	10	,	,	PUNCT
ejpam-4973	149	11	rings	ring	NOUN
ejpam-4973	149	12	and	and	CCONJ
ejpam-4973	149	13	categories	category	NOUN
ejpam-4973	149	14	of	of	ADP
ejpam-4973	149	15	modules	module	NOUN
ejpam-4973	149	16	,	,	PUNCT
ejpam-4973	149	17	springer	springer	NOUN
ejpam-4973	149	18	-	-	PUNCT
ejpam-4973	149	19	verlag	verlag	PROPN
ejpam-4973	149	20	(	(	PUNCT
ejpam-4973	149	21	1974	1974	NUM
ejpam-4973	149	22	)	)	PUNCT
ejpam-4973	150	1	[	[	X
ejpam-4973	150	2	4	4	X
ejpam-4973	150	3	]	]	X
ejpam-4973	150	4	n.	n.	NOUN
ejpam-4973	150	5	v.	v.	ADP
ejpam-4973	150	6	dung	dung	NOUN
ejpam-4973	150	7	and	and	CCONJ
ejpam-4973	150	8	a.	a.	NOUN
ejpam-4973	150	9	facchini	facchini	PROPN
ejpam-4973	150	10	,	,	PUNCT
ejpam-4973	150	11	direct	direct	ADJ
ejpam-4973	150	12	summands	summand	NOUN
ejpam-4973	150	13	of	of	ADP
ejpam-4973	150	14	serial	serial	ADJ
ejpam-4973	150	15	modules	module	NOUN
ejpam-4973	150	16	,	,	PUNCT
ejpam-4973	150	17	j.	j.	PROPN
ejpam-4973	150	18	pure	pure	PROPN
ejpam-4973	150	19	appl	appl	PROPN
ejpam-4973	150	20	.	.	PUNCT
ejpam-4973	151	1	algebra	algebra	NOUN
ejpam-4973	151	2	133	133	NUM
ejpam-4973	151	3	(	(	PUNCT
ejpam-4973	151	4	1998	1998	NUM
ejpam-4973	151	5	)	)	PUNCT
ejpam-4973	151	6	,	,	PUNCT
ejpam-4973	151	7	93	93	NUM
ejpam-4973	151	8	-	-	SYM
ejpam-4973	151	9	106	106	NUM
ejpam-4973	151	10	references	reference	NOUN
ejpam-4973	151	11	415	415	NUM
ejpam-4973	152	1	[	[	X
ejpam-4973	152	2	5	5	NUM
ejpam-4973	152	3	]	]	PUNCT
ejpam-4973	152	4	p.	p.	NOUN
ejpam-4973	152	5	fleury	fleury	PROPN
ejpam-4973	152	6	,	,	PUNCT
ejpam-4973	152	7	hollow	hollow	ADJ
ejpam-4973	152	8	modules	module	NOUN
ejpam-4973	152	9	and	and	CCONJ
ejpam-4973	152	10	local	local	ADJ
ejpam-4973	152	11	endomorphism	endomorphism	NOUN
ejpam-4973	152	12	rings	ring	NOUN
ejpam-4973	152	13	,	,	PUNCT
ejpam-4973	152	14	pac.j.math	pac.j.math	NOUN
ejpam-4973	152	15	.	.	PUNCT
ejpam-4973	153	1	53	53	NUM
ejpam-4973	153	2	,	,	PUNCT
ejpam-4973	153	3	379	379	NUM
ejpam-4973	153	4	-	-	SYM
ejpam-4973	153	5	385	385	NUM
ejpam-4973	153	6	(	(	PUNCT
ejpam-4973	153	7	1974	1974	NUM
ejpam-4973	153	8	)	)	PUNCT
ejpam-4973	154	1	[	[	X
ejpam-4973	154	2	6	6	NUM
ejpam-4973	154	3	]	]	PUNCT
ejpam-4973	154	4	a.	a.	NOUN
ejpam-4973	154	5	m.	m.	NOUN
ejpam-4973	154	6	kaidi	kaidi	PROPN
ejpam-4973	154	7	and	and	CCONJ
ejpam-4973	154	8	m.	m.	NOUN
ejpam-4973	154	9	sangharé	sangharé	PROPN
ejpam-4973	154	10	,	,	PUNCT
ejpam-4973	154	11	une	une	PROPN
ejpam-4973	154	12	caractérisation	caractérisation	NOUN
ejpam-4973	154	13	des	des	PROPN
ejpam-4973	154	14	anneaux	anneaux	PROPN
ejpam-4973	154	15	artiniens	artinien	VERB
ejpam-4973	154	16	à	à	PROPN
ejpam-4973	154	17	idéaux	idéaux	PROPN
ejpam-4973	154	18	principaux	principaux	PROPN
ejpam-4973	154	19	.	.	PUNCT
ejpam-4973	155	1	l.notes	l.notes	PROPN
ejpam-4973	155	2	in	in	ADP
ejpam-4973	155	3	math.springer	math.spring	ADJ
ejpam-4973	155	4	verlag	verlag	NOUN
ejpam-4973	155	5	(	(	PUNCT
ejpam-4973	155	6	1988	1988	NUM
ejpam-4973	155	7	)	)	PUNCT
ejpam-4973	156	1	pp.245	pp.245	NOUN
ejpam-4973	156	2	254	254	NUM
ejpam-4973	157	1	[	[	X
ejpam-4973	157	2	7	7	NUM
ejpam-4973	157	3	]	]	X
ejpam-4973	157	4	r.	r.	PROPN
ejpam-4973	157	5	wisbauer	wisbauer	NOUN
ejpam-4973	157	6	,	,	PUNCT
ejpam-4973	157	7	foundation	foundation	NOUN
ejpam-4973	157	8	of	of	ADP
ejpam-4973	157	9	modules	module	NOUN
ejpam-4973	157	10	and	and	CCONJ
ejpam-4973	157	11	ring	ring	NOUN
ejpam-4973	157	12	theory	theory	NOUN
ejpam-4973	157	13	,	,	PUNCT
ejpam-4973	157	14	gordon	gordon	PROPN
ejpam-4973	157	15	and	and	CCONJ
ejpam-4973	157	16	breach	breach	VERB
ejpam-4973	157	17	science	science	NOUN
ejpam-4973	157	18	publishers(1991	publishers(1991	NOUN
ejpam-4973	157	19	)	)	PUNCT
ejpam-4973	157	20	.	.	PUNCT