id	sid	tid	token	lemma	pos
ejpam-1767	1	1	european	european	PROPN
ejpam-1767	1	2	journal	journal	PROPN
ejpam-1767	1	3	of	of	ADP
ejpam-1767	1	4	pure	pure	ADJ
ejpam-1767	1	5	and	and	CCONJ
ejpam-1767	1	6	applied	apply	VERB
ejpam-1767	1	7	mathematics	mathematic	NOUN
ejpam-1767	1	8	vol	vol	NOUN
ejpam-1767	1	9	.	.	PROPN
ejpam-1767	2	1	6	6	NUM
ejpam-1767	2	2	,	,	PUNCT
ejpam-1767	2	3	no	no	INTJ
ejpam-1767	2	4	.	.	NOUN
ejpam-1767	2	5	2	2	NUM
ejpam-1767	2	6	,	,	PUNCT
ejpam-1767	2	7	2013	2013	NUM
ejpam-1767	2	8	,	,	PUNCT
ejpam-1767	2	9	119	119	NUM
ejpam-1767	2	10	-	-	SYM
ejpam-1767	2	11	125	125	NUM
ejpam-1767	2	12	issn	issn	PROPN
ejpam-1767	2	13	1307	1307	NUM
ejpam-1767	2	14	-	-	SYM
ejpam-1767	2	15	5543	5543	NUM
ejpam-1767	2	16	–	–	PUNCT
ejpam-1767	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1767	3	1	some	some	DET
ejpam-1767	3	2	remarks	remark	VERB
ejpam-1767	3	3	on	on	ADP
ejpam-1767	3	4	finitely	finitely	ADV
ejpam-1767	3	5	quasi	quasi	ADJ
ejpam-1767	3	6	-	-	ADJ
ejpam-1767	3	7	injective	injective	ADJ
ejpam-1767	3	8	modules	module	NOUN
ejpam-1767	3	9	zhu	zhu	PROPN
ejpam-1767	3	10	zhanmin	zhanmin	PROPN
ejpam-1767	3	11	department	department	PROPN
ejpam-1767	3	12	of	of	ADP
ejpam-1767	3	13	mathematics	mathematics	PROPN
ejpam-1767	3	14	,	,	PUNCT
ejpam-1767	3	15	jiaxing	jiaxing	PROPN
ejpam-1767	3	16	university	university	PROPN
ejpam-1767	3	17	,	,	PUNCT
ejpam-1767	3	18	jiaxing	jiaxing	PROPN
ejpam-1767	3	19	,	,	PUNCT
ejpam-1767	3	20	zhejiang	zhejiang	PROPN
ejpam-1767	3	21	province	province	PROPN
ejpam-1767	3	22	,	,	PUNCT
ejpam-1767	3	23	314001	314001	NUM
ejpam-1767	3	24	,	,	PUNCT
ejpam-1767	3	25	p.r.china	p.r.china	ADJ
ejpam-1767	3	26	abstract	abstract	NOUN
ejpam-1767	3	27	.	.	PUNCT
ejpam-1767	4	1	let	let	VERB
ejpam-1767	4	2	r	r	PRON
ejpam-1767	4	3	be	be	AUX
ejpam-1767	4	4	a	a	DET
ejpam-1767	4	5	ring	ring	NOUN
ejpam-1767	4	6	.	.	PUNCT
ejpam-1767	5	1	a	a	DET
ejpam-1767	5	2	right	right	ADJ
ejpam-1767	5	3	r	r	NOUN
ejpam-1767	5	4	-	-	PUNCT
ejpam-1767	5	5	module	module	NOUN
ejpam-1767	5	6	m	m	NOUN
ejpam-1767	5	7	is	be	AUX
ejpam-1767	5	8	called	call	VERB
ejpam-1767	5	9	finitely	finitely	ADV
ejpam-1767	5	10	quasi	quasi	ADJ
ejpam-1767	5	11	-	-	ADJ
ejpam-1767	5	12	injective	injective	ADJ
ejpam-1767	5	13	if	if	SCONJ
ejpam-1767	5	14	each	each	DET
ejpam-1767	5	15	r	r	NOUN
ejpam-1767	5	16	-	-	PUNCT
ejpam-1767	5	17	homomorphism	homomorphism	NOUN
ejpam-1767	5	18	from	from	ADP
ejpam-1767	5	19	a	a	DET
ejpam-1767	5	20	finitely	finitely	ADV
ejpam-1767	5	21	generated	generate	VERB
ejpam-1767	5	22	submodule	submodule	NOUN
ejpam-1767	5	23	of	of	ADP
ejpam-1767	5	24	m	m	PROPN
ejpam-1767	5	25	to	to	ADP
ejpam-1767	5	26	m	m	PROPN
ejpam-1767	5	27	can	can	AUX
ejpam-1767	5	28	be	be	AUX
ejpam-1767	5	29	extended	extend	VERB
ejpam-1767	5	30	to	to	ADP
ejpam-1767	5	31	an	an	DET
ejpam-1767	5	32	endomorphism	endomorphism	NOUN
ejpam-1767	5	33	of	of	ADP
ejpam-1767	5	34	m	m	PROPN
ejpam-1767	5	35	.	.	PUNCT
ejpam-1767	6	1	some	some	DET
ejpam-1767	6	2	conditions	condition	NOUN
ejpam-1767	6	3	under	under	ADP
ejpam-1767	6	4	which	which	PRON
ejpam-1767	6	5	finitely	finitely	ADV
ejpam-1767	6	6	generated	generate	VERB
ejpam-1767	6	7	finitely	finitely	ADV
ejpam-1767	6	8	quasi	quasi	ADJ
ejpam-1767	6	9	-	-	ADJ
ejpam-1767	6	10	injective	injective	ADJ
ejpam-1767	6	11	modules	module	NOUN
ejpam-1767	6	12	are	be	AUX
ejpam-1767	6	13	of	of	ADP
ejpam-1767	6	14	finite	finite	PROPN
ejpam-1767	6	15	goldie	goldie	PROPN
ejpam-1767	6	16	dimensions	dimension	NOUN
ejpam-1767	6	17	are	be	AUX
ejpam-1767	6	18	given	give	VERB
ejpam-1767	6	19	,	,	PUNCT
ejpam-1767	6	20	and	and	CCONJ
ejpam-1767	6	21	finitely	finitely	ADV
ejpam-1767	6	22	generated	generate	VERB
ejpam-1767	6	23	finitely	finitely	ADV
ejpam-1767	6	24	quasi	quasi	ADJ
ejpam-1767	6	25	-	-	ADJ
ejpam-1767	6	26	injective	injective	ADJ
ejpam-1767	6	27	kasch	kasch	ADJ
ejpam-1767	6	28	modules	module	NOUN
ejpam-1767	6	29	are	be	AUX
ejpam-1767	6	30	studied	study	VERB
ejpam-1767	6	31	.	.	PUNCT
ejpam-1767	7	1	2010	2010	NUM
ejpam-1767	7	2	mathematics	mathematic	NOUN
ejpam-1767	7	3	subject	subject	NOUN
ejpam-1767	7	4	classifications	classification	NOUN
ejpam-1767	7	5	:	:	PUNCT
ejpam-1767	7	6	16d50	16d50	NUM
ejpam-1767	7	7	,	,	PUNCT
ejpam-1767	7	8	16l30	16l30	NUM
ejpam-1767	7	9	key	key	ADJ
ejpam-1767	7	10	words	word	NOUN
ejpam-1767	7	11	and	and	CCONJ
ejpam-1767	7	12	phrases	phrase	NOUN
ejpam-1767	7	13	:	:	PUNCT
ejpam-1767	7	14	finitely	finitely	ADV
ejpam-1767	7	15	quasi	quasi	ADJ
ejpam-1767	7	16	-	-	ADJ
ejpam-1767	7	17	injective	injective	ADJ
ejpam-1767	7	18	modules	module	NOUN
ejpam-1767	7	19	,	,	PUNCT
ejpam-1767	7	20	kasch	kasch	PROPN
ejpam-1767	7	21	modules	module	NOUN
ejpam-1767	7	22	,	,	PUNCT
ejpam-1767	7	23	endomorphism	endomorphism	PROPN
ejpam-1767	7	24	rings	ring	NOUN
ejpam-1767	7	25	,	,	PUNCT
ejpam-1767	7	26	semiperfect	semiperfect	ADJ
ejpam-1767	7	27	rings	ring	NOUN
ejpam-1767	7	28	,	,	PUNCT
ejpam-1767	7	29	semilocal	semilocal	ADJ
ejpam-1767	7	30	rings	ring	NOUN
ejpam-1767	7	31	1	1	NUM
ejpam-1767	7	32	.	.	PUNCT
ejpam-1767	7	33	introduction	introduction	NOUN
ejpam-1767	7	34	throughout	throughout	ADP
ejpam-1767	7	35	the	the	DET
ejpam-1767	7	36	paper	paper	NOUN
ejpam-1767	7	37	,	,	PUNCT
ejpam-1767	7	38	r	r	NOUN
ejpam-1767	7	39	is	be	AUX
ejpam-1767	7	40	an	an	DET
ejpam-1767	7	41	associative	associative	ADJ
ejpam-1767	7	42	ring	ring	NOUN
ejpam-1767	7	43	with	with	ADP
ejpam-1767	7	44	identity	identity	NOUN
ejpam-1767	7	45	and	and	CCONJ
ejpam-1767	7	46	all	all	DET
ejpam-1767	7	47	modules	module	NOUN
ejpam-1767	7	48	are	be	AUX
ejpam-1767	7	49	unitary	unitary	ADJ
ejpam-1767	7	50	.	.	PUNCT
ejpam-1767	8	1	if	if	SCONJ
ejpam-1767	8	2	mr	mr	PROPN
ejpam-1767	8	3	is	be	AUX
ejpam-1767	8	4	a	a	DET
ejpam-1767	8	5	right	right	ADJ
ejpam-1767	8	6	r	r	NOUN
ejpam-1767	8	7	-	-	NOUN
ejpam-1767	8	8	module	module	NOUN
ejpam-1767	8	9	with	with	ADP
ejpam-1767	8	10	s	s	NOUN
ejpam-1767	8	11	=	=	SYM
ejpam-1767	8	12	end(mr	end(mr	NUM
ejpam-1767	8	13	)	)	PUNCT
ejpam-1767	8	14	,	,	PUNCT
ejpam-1767	8	15	and	and	CCONJ
ejpam-1767	8	16	a	a	DET
ejpam-1767	8	17	⊆	⊆	NUM
ejpam-1767	8	18	s	s	NOUN
ejpam-1767	8	19	,	,	PUNCT
ejpam-1767	8	20	x	x	PROPN
ejpam-1767	8	21	⊆	⊆	NUM
ejpam-1767	8	22	m	m	NOUN
ejpam-1767	8	23	,	,	PUNCT
ejpam-1767	8	24	b	b	X
ejpam-1767	8	25	⊆	⊆	NUM
ejpam-1767	8	26	r	r	NOUN
ejpam-1767	8	27	,	,	PUNCT
ejpam-1767	8	28	then	then	ADV
ejpam-1767	8	29	we	we	PRON
ejpam-1767	8	30	denote	denote	VERB
ejpam-1767	8	31	the	the	DET
ejpam-1767	8	32	jacobson	jacobson	PROPN
ejpam-1767	8	33	radical	radical	PROPN
ejpam-1767	8	34	of	of	ADP
ejpam-1767	8	35	s	s	PROPN
ejpam-1767	8	36	by	by	ADP
ejpam-1767	8	37	j(s	j(s	PROPN
ejpam-1767	8	38	)	)	PUNCT
ejpam-1767	8	39	,	,	PUNCT
ejpam-1767	8	40	and	and	CCONJ
ejpam-1767	8	41	we	we	PRON
ejpam-1767	8	42	write	write	VERB
ejpam-1767	8	43	ls(x	ls(x	PUNCT
ejpam-1767	8	44	)	)	PUNCT
ejpam-1767	9	1	=	=	PUNCT
ejpam-1767	9	2	{	{	PUNCT
ejpam-1767	9	3	s	s	NOUN
ejpam-1767	9	4	∈	∈	NOUN
ejpam-1767	9	5	s	s	X
ejpam-1767	9	6	|	|	ADV
ejpam-1767	9	7	sx	sx	NOUN
ejpam-1767	9	8	=	=	NOUN
ejpam-1767	9	9	0,∀x	0,∀x	NUM
ejpam-1767	9	10	∈	∈	PROPN
ejpam-1767	9	11	x	x	X
ejpam-1767	9	12	}	}	PUNCT
ejpam-1767	9	13	,	,	PUNCT
ejpam-1767	9	14	rm	rm	PROPN
ejpam-1767	9	15	(	(	PUNCT
ejpam-1767	9	16	a	a	NOUN
ejpam-1767	9	17	)	)	PUNCT
ejpam-1767	9	18	=	=	PRON
ejpam-1767	9	19	{	{	PUNCT
ejpam-1767	9	20	m	m	VERB
ejpam-1767	9	21	∈	∈	NOUN
ejpam-1767	9	22	m	m	VERB
ejpam-1767	9	23	|	|	ADV
ejpam-1767	9	24	am	be	AUX
ejpam-1767	9	25	=	=	NOUN
ejpam-1767	9	26	0,∀a	0,∀a	NUM
ejpam-1767	9	27	∈	∈	PROPN
ejpam-1767	9	28	a	a	PRON
ejpam-1767	9	29	}	}	PUNCT
ejpam-1767	9	30	,	,	PUNCT
ejpam-1767	9	31	lm	lm	INTJ
ejpam-1767	9	32	(	(	PUNCT
ejpam-1767	9	33	b	b	NOUN
ejpam-1767	9	34	)	)	PUNCT
ejpam-1767	9	35	=	=	PRON
ejpam-1767	9	36	{	{	PUNCT
ejpam-1767	9	37	m	m	VERB
ejpam-1767	9	38	∈	∈	NOUN
ejpam-1767	9	39	m	m	VERB
ejpam-1767	9	40	|	|	ADV
ejpam-1767	9	41	mb	mb	ADJ
ejpam-1767	9	42	=	=	NOUN
ejpam-1767	9	43	0,∀b	0,∀b	NUM
ejpam-1767	9	44	∈	∈	PROPN
ejpam-1767	9	45	b	b	NOUN
ejpam-1767	9	46	}	}	PUNCT
ejpam-1767	9	47	.	.	PUNCT
ejpam-1767	10	1	following	follow	VERB
ejpam-1767	10	2	[	[	X
ejpam-1767	10	3	5	5	NUM
ejpam-1767	10	4	]	]	PUNCT
ejpam-1767	10	5	,	,	PUNCT
ejpam-1767	10	6	we	we	PRON
ejpam-1767	10	7	write	write	VERB
ejpam-1767	10	8	w	w	PROPN
ejpam-1767	10	9	(	(	PUNCT
ejpam-1767	10	10	s	s	X
ejpam-1767	10	11	)	)	PUNCT
ejpam-1767	10	12	=	=	PUNCT
ejpam-1767	10	13	{	{	PUNCT
ejpam-1767	10	14	s	s	NOUN
ejpam-1767	10	15	∈	∈	NOUN
ejpam-1767	10	16	s	s	VERB
ejpam-1767	10	17	|	|	ADV
ejpam-1767	10	18	ker(s)⊆ess	ker(s)⊆ess	PROPN
ejpam-1767	10	19	m	m	PROPN
ejpam-1767	10	20	}	}	PUNCT
ejpam-1767	10	21	.	.	PUNCT
ejpam-1767	11	1	at	at	ADP
ejpam-1767	11	2	first	first	ADV
ejpam-1767	11	3	let	let	VERB
ejpam-1767	11	4	we	we	PRON
ejpam-1767	11	5	recall	recall	VERB
ejpam-1767	11	6	some	some	DET
ejpam-1767	11	7	concepts	concept	NOUN
ejpam-1767	11	8	.	.	PUNCT
ejpam-1767	12	1	a	a	DET
ejpam-1767	12	2	module	module	NOUN
ejpam-1767	12	3	mr	mr	PROPN
ejpam-1767	12	4	is	be	AUX
ejpam-1767	12	5	called	call	VERB
ejpam-1767	12	6	finitely	finitely	ADV
ejpam-1767	12	7	quasi	quasi	ADJ
ejpam-1767	12	8	-	-	ADJ
ejpam-1767	12	9	injective	injective	ADJ
ejpam-1767	12	10	(	(	PUNCT
ejpam-1767	12	11	or	or	CCONJ
ejpam-1767	12	12	fq	fq	NOUN
ejpam-1767	12	13	-	-	NOUN
ejpam-1767	12	14	injective	injective	ADJ
ejpam-1767	12	15	for	for	ADP
ejpam-1767	12	16	short	short	ADJ
ejpam-1767	12	17	)	)	PUNCT
ejpam-1767	13	1	[	[	X
ejpam-1767	13	2	7	7	X
ejpam-1767	13	3	]	]	X
ejpam-1767	13	4	if	if	SCONJ
ejpam-1767	13	5	each	each	DET
ejpam-1767	13	6	r	r	NOUN
ejpam-1767	13	7	-	-	PUNCT
ejpam-1767	13	8	homomorphism	homomorphism	NOUN
ejpam-1767	13	9	from	from	ADP
ejpam-1767	13	10	a	a	DET
ejpam-1767	13	11	finitely	finitely	ADV
ejpam-1767	13	12	generated	generate	VERB
ejpam-1767	13	13	submodule	submodule	NOUN
ejpam-1767	13	14	of	of	ADP
ejpam-1767	13	15	m	m	PROPN
ejpam-1767	13	16	to	to	ADP
ejpam-1767	13	17	m	m	PROPN
ejpam-1767	13	18	can	can	AUX
ejpam-1767	13	19	be	be	AUX
ejpam-1767	13	20	extended	extend	VERB
ejpam-1767	13	21	to	to	ADP
ejpam-1767	13	22	an	an	DET
ejpam-1767	13	23	endomorphism	endomorphism	NOUN
ejpam-1767	13	24	of	of	ADP
ejpam-1767	13	25	m	m	PROPN
ejpam-1767	13	26	;	;	PUNCT
ejpam-1767	13	27	a	a	DET
ejpam-1767	13	28	ring	ring	NOUN
ejpam-1767	13	29	r	r	NOUN
ejpam-1767	13	30	is	be	AUX
ejpam-1767	13	31	said	say	VERB
ejpam-1767	13	32	to	to	PART
ejpam-1767	13	33	be	be	AUX
ejpam-1767	13	34	right	right	ADJ
ejpam-1767	13	35	f	f	NOUN
ejpam-1767	13	36	-	-	PUNCT
ejpam-1767	13	37	injective	injective	ADJ
ejpam-1767	13	38	if	if	SCONJ
ejpam-1767	13	39	rr	rr	PROPN
ejpam-1767	13	40	is	be	AUX
ejpam-1767	13	41	finitely	finitely	ADV
ejpam-1767	13	42	quasi	quasi	ADJ
ejpam-1767	13	43	-	-	ADJ
ejpam-1767	13	44	injective	injective	ADJ
ejpam-1767	13	45	.	.	PUNCT
ejpam-1767	14	1	f	f	X
ejpam-1767	14	2	-	-	PUNCT
ejpam-1767	14	3	injective	injective	ADJ
ejpam-1767	14	4	rings	ring	NOUN
ejpam-1767	14	5	have	have	AUX
ejpam-1767	14	6	been	be	AUX
ejpam-1767	14	7	studied	study	VERB
ejpam-1767	14	8	by	by	ADP
ejpam-1767	14	9	many	many	ADJ
ejpam-1767	14	10	authors	author	NOUN
ejpam-1767	14	11	such	such	ADJ
ejpam-1767	14	12	as	as	ADP
ejpam-1767	14	13	[	[	X
ejpam-1767	14	14	2	2	NUM
ejpam-1767	14	15	,	,	PUNCT
ejpam-1767	14	16	3	3	NUM
ejpam-1767	14	17	,	,	PUNCT
ejpam-1767	14	18	8	8	NUM
ejpam-1767	14	19	]	]	PUNCT
ejpam-1767	14	20	.	.	PUNCT
ejpam-1767	15	1	a	a	DET
ejpam-1767	15	2	module	module	NOUN
ejpam-1767	15	3	mr	mr	PROPN
ejpam-1767	15	4	is	be	AUX
ejpam-1767	15	5	called	call	VERB
ejpam-1767	15	6	a	a	DET
ejpam-1767	15	7	c1	c1	NOUN
ejpam-1767	15	8	module	module	NOUN
ejpam-1767	15	9	if	if	SCONJ
ejpam-1767	15	10	every	every	DET
ejpam-1767	15	11	submodule	submodule	NOUN
ejpam-1767	15	12	of	of	ADP
ejpam-1767	15	13	m	m	PROPN
ejpam-1767	15	14	is	be	AUX
ejpam-1767	15	15	essential	essential	ADJ
ejpam-1767	15	16	in	in	ADP
ejpam-1767	15	17	a	a	DET
ejpam-1767	15	18	direct	direct	ADJ
ejpam-1767	15	19	summand	summand	NOUN
ejpam-1767	15	20	of	of	ADP
ejpam-1767	15	21	m	m	PROPN
ejpam-1767	15	22	,	,	PUNCT
ejpam-1767	15	23	c1	c1	PROPN
ejpam-1767	15	24	modules	module	NOUN
ejpam-1767	15	25	are	be	AUX
ejpam-1767	15	26	also	also	ADV
ejpam-1767	15	27	called	call	VERB
ejpam-1767	15	28	cs	cs	ADJ
ejpam-1767	15	29	modules	module	NOUN
ejpam-1767	15	30	.	.	PUNCT
ejpam-1767	16	1	a	a	DET
ejpam-1767	16	2	module	module	NOUN
ejpam-1767	16	3	mr	mr	PROPN
ejpam-1767	16	4	is	be	AUX
ejpam-1767	16	5	called	call	VERB
ejpam-1767	16	6	a	a	DET
ejpam-1767	16	7	c2	c2	PROPN
ejpam-1767	16	8	module	module	NOUN
ejpam-1767	16	9	if	if	SCONJ
ejpam-1767	16	10	every	every	DET
ejpam-1767	16	11	submodule	submodule	NOUN
ejpam-1767	16	12	of	of	ADP
ejpam-1767	16	13	m	m	PRON
ejpam-1767	16	14	that	that	PRON
ejpam-1767	16	15	is	be	AUX
ejpam-1767	16	16	isomorphic	isomorphic	ADJ
ejpam-1767	16	17	to	to	ADP
ejpam-1767	16	18	a	a	DET
ejpam-1767	16	19	direct	direct	ADJ
ejpam-1767	16	20	summand	summand	NOUN
ejpam-1767	16	21	of	of	ADP
ejpam-1767	16	22	m	m	PROPN
ejpam-1767	16	23	is	be	AUX
ejpam-1767	16	24	itself	itself	PRON
ejpam-1767	16	25	a	a	DET
ejpam-1767	16	26	direct	direct	ADJ
ejpam-1767	16	27	summand	summand	NOUN
ejpam-1767	16	28	of	of	ADP
ejpam-1767	16	29	m	m	PROPN
ejpam-1767	16	30	.	.	PUNCT
ejpam-1767	17	1	a	a	DET
ejpam-1767	17	2	module	module	NOUN
ejpam-1767	17	3	mr	mr	PROPN
ejpam-1767	17	4	is	be	AUX
ejpam-1767	17	5	called	call	VERB
ejpam-1767	17	6	a	a	DET
ejpam-1767	17	7	c3	c3	NOUN
ejpam-1767	17	8	module	module	NOUN
ejpam-1767	17	9	if	if	SCONJ
ejpam-1767	17	10	,	,	PUNCT
ejpam-1767	17	11	whenever	whenever	SCONJ
ejpam-1767	17	12	n	n	PRON
ejpam-1767	17	13	and	and	CCONJ
ejpam-1767	17	14	k	k	PROPN
ejpam-1767	17	15	are	be	AUX
ejpam-1767	17	16	submodules	submodule	NOUN
ejpam-1767	17	17	of	of	ADP
ejpam-1767	17	18	m	m	PROPN
ejpam-1767	17	19	with	with	ADP
ejpam-1767	17	20	n	n	PRON
ejpam-1767	17	21	⊆⊕	⊆⊕	NUM
ejpam-1767	17	22	m	m	NOUN
ejpam-1767	17	23	,	,	PUNCT
ejpam-1767	17	24	k	k	PROPN
ejpam-1767	17	25	⊆⊕	⊆⊕	NUM
ejpam-1767	17	26	m	m	PROPN
ejpam-1767	17	27	,	,	PUNCT
ejpam-1767	17	28	and	and	CCONJ
ejpam-1767	17	29	n	n	X
ejpam-1767	17	30	∩	∩	X
ejpam-1767	17	31	k	k	NOUN
ejpam-1767	17	32	=	=	SYM
ejpam-1767	17	33	0	0	PROPN
ejpam-1767	17	34	,	,	PUNCT
ejpam-1767	17	35	then	then	ADV
ejpam-1767	17	36	n	n	PROPN
ejpam-1767	17	37	⊕	⊕	PROPN
ejpam-1767	17	38	k	k	PROPN
ejpam-1767	17	39	⊆⊕	⊆⊕	PROPN
ejpam-1767	17	40	m	m	PROPN
ejpam-1767	17	41	.	.	PUNCT
ejpam-1767	18	1	a	a	DET
ejpam-1767	18	2	module	module	NOUN
ejpam-1767	18	3	mr	mr	PROPN
ejpam-1767	18	4	is	be	AUX
ejpam-1767	18	5	called	call	VERB
ejpam-1767	18	6	continuous	continuous	ADJ
ejpam-1767	18	7	if	if	SCONJ
ejpam-1767	18	8	it	it	PRON
ejpam-1767	18	9	is	be	AUX
ejpam-1767	18	10	both	both	PRON
ejpam-1767	18	11	c1	c1	PROPN
ejpam-1767	18	12	and	and	CCONJ
ejpam-1767	18	13	c2	c2	PROPN
ejpam-1767	18	14	.	.	PUNCT
ejpam-1767	19	1	a	a	DET
ejpam-1767	19	2	module	module	NOUN
ejpam-1767	19	3	mr	mr	PROPN
ejpam-1767	19	4	is	be	AUX
ejpam-1767	19	5	called	call	VERB
ejpam-1767	19	6	quasi	quasi	ADJ
ejpam-1767	19	7	-	-	ADJ
ejpam-1767	19	8	continuous	continuous	ADJ
ejpam-1767	19	9	if	if	SCONJ
ejpam-1767	19	10	it	it	PRON
ejpam-1767	19	11	is	be	AUX
ejpam-1767	19	12	both	both	DET
ejpam-1767	19	13	c1	c1	PROPN
ejpam-1767	19	14	and	and	CCONJ
ejpam-1767	19	15	c3	c3	PROPN
ejpam-1767	19	16	.	.	PUNCT
ejpam-1767	20	1	it	it	PRON
ejpam-1767	20	2	is	be	AUX
ejpam-1767	20	3	well	well	ADV
ejpam-1767	20	4	-	-	PUNCT
ejpam-1767	20	5	known	know	VERB
ejpam-1767	20	6	that	that	SCONJ
ejpam-1767	20	7	c2	c2	PROPN
ejpam-1767	20	8	modules	module	NOUN
ejpam-1767	20	9	are	be	AUX
ejpam-1767	20	10	c3	c3	NOUN
ejpam-1767	20	11	modules	module	NOUN
ejpam-1767	20	12	,	,	PUNCT
ejpam-1767	20	13	and	and	CCONJ
ejpam-1767	20	14	so	so	ADV
ejpam-1767	20	15	continuous	continuous	ADJ
ejpam-1767	20	16	modules	module	NOUN
ejpam-1767	20	17	are	be	AUX
ejpam-1767	20	18	quasi	quasi	ADJ
ejpam-1767	20	19	-	-	ADJ
ejpam-1767	20	20	continuous	continuous	ADJ
ejpam-1767	20	21	.	.	PUNCT
ejpam-1767	21	1	email	email	NOUN
ejpam-1767	21	2	address	address	NOUN
ejpam-1767	21	3	:	:	PUNCT
ejpam-1767	21	4	zhanmin_zhu@hotmail.com	zhanmin_zhu@hotmail.com	X
ejpam-1767	21	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1767	22	1	119	119	NUM
ejpam-1767	22	2	c	c	X
ejpam-1767	22	3	©	©	PROPN
ejpam-1767	22	4	2013	2013	NUM
ejpam-1767	22	5	ejpam	ejpam	NOUN
ejpam-1767	22	6	all	all	DET
ejpam-1767	22	7	rights	right	NOUN
ejpam-1767	22	8	reserved	reserve	VERB
ejpam-1767	22	9	.	.	PUNCT
ejpam-1767	23	1	z.	z.	PROPN
ejpam-1767	23	2	zhanmin	zhanmin	PROPN
ejpam-1767	23	3	/	/	SYM
ejpam-1767	23	4	eur	eur	PROPN
ejpam-1767	23	5	.	.	PUNCT
ejpam-1767	24	1	j.	j.	PROPN
ejpam-1767	24	2	pure	pure	PROPN
ejpam-1767	24	3	appl	appl	PROPN
ejpam-1767	24	4	.	.	PROPN
ejpam-1767	24	5	math	math	PROPN
ejpam-1767	24	6	,	,	PUNCT
ejpam-1767	24	7	6	6	NUM
ejpam-1767	24	8	(	(	PUNCT
ejpam-1767	24	9	2013	2013	NUM
ejpam-1767	24	10	)	)	PUNCT
ejpam-1767	24	11	,	,	PUNCT
ejpam-1767	24	12	119	119	NUM
ejpam-1767	24	13	-	-	SYM
ejpam-1767	24	14	125	125	NUM
ejpam-1767	24	15	120	120	NUM
ejpam-1767	24	16	a	a	DET
ejpam-1767	24	17	module	module	NOUN
ejpam-1767	24	18	mr	mr	PROPN
ejpam-1767	24	19	is	be	AUX
ejpam-1767	24	20	said	say	VERB
ejpam-1767	24	21	to	to	PART
ejpam-1767	24	22	be	be	AUX
ejpam-1767	24	23	kasch	kasch	VERB
ejpam-1767	25	1	[	[	X
ejpam-1767	25	2	1	1	NUM
ejpam-1767	25	3	]	]	PUNCT
ejpam-1767	25	4	provided	provide	VERB
ejpam-1767	25	5	that	that	SCONJ
ejpam-1767	25	6	every	every	DET
ejpam-1767	25	7	simple	simple	ADJ
ejpam-1767	25	8	module	module	NOUN
ejpam-1767	25	9	in	in	ADP
ejpam-1767	25	10	σ[m	σ[m	ADJ
ejpam-1767	25	11	]	]	PUNCT
ejpam-1767	25	12	embeds	embed	VERB
ejpam-1767	25	13	in	in	ADP
ejpam-1767	25	14	m	m	PROPN
ejpam-1767	25	15	,	,	PUNCT
ejpam-1767	25	16	where	where	SCONJ
ejpam-1767	25	17	σ[m	σ[m	NOUN
ejpam-1767	25	18	]	]	PUNCT
ejpam-1767	25	19	is	be	AUX
ejpam-1767	25	20	the	the	DET
ejpam-1767	25	21	category	category	NOUN
ejpam-1767	25	22	consisting	consist	VERB
ejpam-1767	25	23	of	of	ADP
ejpam-1767	25	24	all	all	PRON
ejpam-1767	25	25	m	m	NOUN
ejpam-1767	25	26	-subgenerated	-subgenerate	VERB
ejpam-1767	25	27	right	right	ADJ
ejpam-1767	25	28	r	r	NOUN
ejpam-1767	25	29	-	-	PUNCT
ejpam-1767	25	30	modules	module	NOUN
ejpam-1767	25	31	.	.	PUNCT
ejpam-1767	26	1	in	in	ADP
ejpam-1767	26	2	this	this	DET
ejpam-1767	26	3	note	note	NOUN
ejpam-1767	26	4	we	we	PRON
ejpam-1767	26	5	shall	shall	AUX
ejpam-1767	26	6	mainly	mainly	ADV
ejpam-1767	26	7	study	study	AUX
ejpam-1767	26	8	finitely	finitely	ADV
ejpam-1767	26	9	generated	generate	VERB
ejpam-1767	26	10	finitely	finitely	ADV
ejpam-1767	26	11	quasi	quasi	ADJ
ejpam-1767	26	12	-	-	ADJ
ejpam-1767	26	13	injective	injective	ADJ
ejpam-1767	26	14	modules	module	NOUN
ejpam-1767	26	15	with	with	ADP
ejpam-1767	26	16	finite	finite	PROPN
ejpam-1767	26	17	goldie	goldie	PROPN
ejpam-1767	26	18	dimensions	dimensions	PROPN
ejpam-1767	26	19	,	,	PUNCT
ejpam-1767	26	20	and	and	CCONJ
ejpam-1767	26	21	finitely	finitely	ADV
ejpam-1767	26	22	generated	generate	VERB
ejpam-1767	26	23	finitely	finitely	ADV
ejpam-1767	26	24	quasi	quasi	ADJ
ejpam-1767	26	25	-	-	ADJ
ejpam-1767	26	26	injective	injective	ADJ
ejpam-1767	26	27	kasch	kasch	ADJ
ejpam-1767	26	28	modules	module	NOUN
ejpam-1767	26	29	,	,	PUNCT
ejpam-1767	26	30	respectively	respectively	ADV
ejpam-1767	26	31	.	.	PUNCT
ejpam-1767	27	1	2	2	X
ejpam-1767	27	2	.	.	X
ejpam-1767	27	3	main	main	ADJ
ejpam-1767	27	4	results	result	NOUN
ejpam-1767	27	5	we	we	PRON
ejpam-1767	27	6	begin	begin	VERB
ejpam-1767	27	7	with	with	ADP
ejpam-1767	27	8	some	some	DET
ejpam-1767	27	9	lemmas	lemma	NOUN
ejpam-1767	27	10	.	.	PUNCT
ejpam-1767	28	1	lemma	lemma	PROPN
ejpam-1767	28	2	1	1	NUM
ejpam-1767	28	3	(	(	PUNCT
ejpam-1767	28	4	[	[	X
ejpam-1767	28	5	10	10	NUM
ejpam-1767	28	6	,	,	PUNCT
ejpam-1767	28	7	theorem	theorem	VERB
ejpam-1767	28	8	1.2	1.2	NUM
ejpam-1767	28	9	]	]	PUNCT
ejpam-1767	28	10	)	)	PUNCT
ejpam-1767	28	11	.	.	PUNCT
ejpam-1767	29	1	for	for	ADP
ejpam-1767	29	2	a	a	DET
ejpam-1767	29	3	module	module	NOUN
ejpam-1767	29	4	mr	mr	PROPN
ejpam-1767	29	5	with	with	ADP
ejpam-1767	29	6	s	s	NOUN
ejpam-1767	29	7	=	=	SYM
ejpam-1767	29	8	end(mr	end(mr	PROPN
ejpam-1767	29	9	)	)	PUNCT
ejpam-1767	29	10	,	,	PUNCT
ejpam-1767	29	11	the	the	DET
ejpam-1767	29	12	following	follow	VERB
ejpam-1767	29	13	statements	statement	NOUN
ejpam-1767	29	14	are	be	AUX
ejpam-1767	29	15	equivalent	equivalent	ADJ
ejpam-1767	29	16	:	:	PUNCT
ejpam-1767	29	17	(	(	PUNCT
ejpam-1767	29	18	1	1	X
ejpam-1767	29	19	)	)	PUNCT
ejpam-1767	29	20	mr	mr	PROPN
ejpam-1767	29	21	is	be	AUX
ejpam-1767	29	22	fq	fq	NOUN
ejpam-1767	29	23	-	-	NOUN
ejpam-1767	29	24	injective	injective	ADJ
ejpam-1767	29	25	;	;	PUNCT
ejpam-1767	29	26	(	(	PUNCT
ejpam-1767	29	27	2	2	X
ejpam-1767	29	28	)	)	PUNCT
ejpam-1767	29	29	(	(	PUNCT
ejpam-1767	29	30	a	a	X
ejpam-1767	29	31	)	)	PUNCT
ejpam-1767	29	32	ls(a	ls(a	ADV
ejpam-1767	29	33	⋂	⋂	PROPN
ejpam-1767	29	34	b	b	X
ejpam-1767	29	35	)	)	PUNCT
ejpam-1767	29	36	=	=	PUNCT
ejpam-1767	30	1	ls(a	ls(a	ADV
ejpam-1767	30	2	)	)	PUNCT
ejpam-1767	31	1	+	+	CCONJ
ejpam-1767	31	2	ls(b	ls(b	X
ejpam-1767	31	3	)	)	PUNCT
ejpam-1767	31	4	for	for	ADP
ejpam-1767	31	5	any	any	DET
ejpam-1767	31	6	finitely	finitely	ADV
ejpam-1767	31	7	generated	generate	VERB
ejpam-1767	31	8	submodules	submodule	NOUN
ejpam-1767	31	9	a	a	PRON
ejpam-1767	31	10	,	,	PUNCT
ejpam-1767	31	11	b	b	PROPN
ejpam-1767	31	12	of	of	ADP
ejpam-1767	31	13	m	m	PROPN
ejpam-1767	31	14	,	,	PUNCT
ejpam-1767	31	15	and	and	CCONJ
ejpam-1767	31	16	(	(	PUNCT
ejpam-1767	31	17	b	b	NOUN
ejpam-1767	31	18	)	)	PUNCT
ejpam-1767	31	19	lm	lm	ADJ
ejpam-1767	31	20	rr(m	rr(m	NOUN
ejpam-1767	31	21	)	)	PUNCT
ejpam-1767	31	22	=	=	VERB
ejpam-1767	31	23	sm	sm	NOUN
ejpam-1767	31	24	for	for	ADP
ejpam-1767	31	25	any	any	DET
ejpam-1767	31	26	m	m	PROPN
ejpam-1767	31	27	∈	∈	NOUN
ejpam-1767	31	28	m.	m.	NOUN
ejpam-1767	31	29	where	where	SCONJ
ejpam-1767	31	30	lm	lm	X
ejpam-1767	31	31	rr(m	rr(m	NOUN
ejpam-1767	31	32	)	)	PUNCT
ejpam-1767	31	33	consists	consist	VERB
ejpam-1767	31	34	of	of	ADP
ejpam-1767	31	35	all	all	DET
ejpam-1767	31	36	elements	element	NOUN
ejpam-1767	31	37	z	z	NOUN
ejpam-1767	31	38	∈	∈	PROPN
ejpam-1767	31	39	m	m	VERB
ejpam-1767	31	40	such	such	ADJ
ejpam-1767	31	41	that	that	DET
ejpam-1767	31	42	mx	mx	PROPN
ejpam-1767	31	43	=	=	SYM
ejpam-1767	31	44	0	0	NUM
ejpam-1767	31	45	implies	imply	VERB
ejpam-1767	31	46	zx	zx	PROPN
ejpam-1767	31	47	=	=	SYM
ejpam-1767	31	48	0	0	NUM
ejpam-1767	31	49	for	for	SCONJ
ejpam-1767	31	50	any	any	DET
ejpam-1767	31	51	x	x	SYM
ejpam-1767	31	52	∈	∈	PROPN
ejpam-1767	31	53	r.	r.	PROPN
ejpam-1767	31	54	lemma	lemma	PROPN
ejpam-1767	31	55	2	2	NUM
ejpam-1767	31	56	(	(	PUNCT
ejpam-1767	31	57	[	[	X
ejpam-1767	31	58	10	10	NUM
ejpam-1767	31	59	,	,	PUNCT
ejpam-1767	31	60	theorem	theorem	VERB
ejpam-1767	31	61	2.1	2.1	NUM
ejpam-1767	31	62	,	,	PUNCT
ejpam-1767	31	63	theorem	theorem	VERB
ejpam-1767	31	64	2.2	2.2	NUM
ejpam-1767	31	65	]	]	PUNCT
ejpam-1767	31	66	)	)	PUNCT
ejpam-1767	31	67	.	.	PUNCT
ejpam-1767	32	1	let	let	VERB
ejpam-1767	32	2	mr	mr	PROPN
ejpam-1767	32	3	be	be	AUX
ejpam-1767	32	4	a	a	DET
ejpam-1767	32	5	finitely	finitely	ADV
ejpam-1767	32	6	generated	generate	VERB
ejpam-1767	32	7	fq	fq	PROPN
ejpam-1767	32	8	-	-	ADJ
ejpam-1767	32	9	injective	injective	ADJ
ejpam-1767	32	10	module	module	NOUN
ejpam-1767	32	11	with	with	ADP
ejpam-1767	32	12	s	s	NOUN
ejpam-1767	32	13	=	=	SYM
ejpam-1767	32	14	end(mr	end(mr	NUM
ejpam-1767	32	15	)	)	PUNCT
ejpam-1767	32	16	.	.	PUNCT
ejpam-1767	33	1	then	then	ADV
ejpam-1767	33	2	(	(	PUNCT
ejpam-1767	33	3	1	1	X
ejpam-1767	33	4	)	)	PUNCT
ejpam-1767	33	5	ls(kerα	ls(kerα	PROPN
ejpam-1767	33	6	)	)	PUNCT
ejpam-1767	34	1	=	=	VERB
ejpam-1767	34	2	sα	sα	ADJ
ejpam-1767	34	3	for	for	ADP
ejpam-1767	34	4	any	any	DET
ejpam-1767	34	5	α	α	PROPN
ejpam-1767	34	6	∈	∈	PROPN
ejpam-1767	34	7	s.	s.	PROPN
ejpam-1767	34	8	(	(	PUNCT
ejpam-1767	34	9	2	2	NUM
ejpam-1767	34	10	)	)	PUNCT
ejpam-1767	34	11	w	w	NOUN
ejpam-1767	34	12	(	(	PUNCT
ejpam-1767	34	13	s	s	NOUN
ejpam-1767	34	14	)	)	PUNCT
ejpam-1767	34	15	=	=	SYM
ejpam-1767	34	16	j(s	j(s	NOUN
ejpam-1767	34	17	)	)	PUNCT
ejpam-1767	34	18	.	.	PUNCT
ejpam-1767	35	1	lemma	lemma	PROPN
ejpam-1767	35	2	3	3	NUM
ejpam-1767	35	3	(	(	PUNCT
ejpam-1767	35	4	[	[	X
ejpam-1767	35	5	10	10	NUM
ejpam-1767	35	6	,	,	PUNCT
ejpam-1767	35	7	theorem	theorem	VERB
ejpam-1767	35	8	2.3	2.3	NUM
ejpam-1767	35	9	]	]	PUNCT
ejpam-1767	35	10	)	)	PUNCT
ejpam-1767	35	11	.	.	PUNCT
ejpam-1767	36	1	let	let	VERB
ejpam-1767	36	2	mr	mr	PROPN
ejpam-1767	36	3	be	be	AUX
ejpam-1767	36	4	a	a	DET
ejpam-1767	36	5	finitely	finitely	ADV
ejpam-1767	36	6	generated	generate	VERB
ejpam-1767	36	7	finite	finite	ADJ
ejpam-1767	36	8	dimensional	dimensional	ADJ
ejpam-1767	36	9	fq	fq	PROPN
ejpam-1767	36	10	-	-	ADJ
ejpam-1767	36	11	injective	injective	ADJ
ejpam-1767	36	12	module	module	NOUN
ejpam-1767	36	13	with	with	ADP
ejpam-1767	36	14	s	s	NOUN
ejpam-1767	36	15	=	=	SYM
ejpam-1767	36	16	end(mr	end(mr	NUM
ejpam-1767	36	17	)	)	PUNCT
ejpam-1767	36	18	.	.	PUNCT
ejpam-1767	37	1	then	then	ADV
ejpam-1767	37	2	s	s	VERB
ejpam-1767	37	3	is	be	AUX
ejpam-1767	37	4	semilocal	semilocal	ADJ
ejpam-1767	37	5	.	.	PUNCT
ejpam-1767	38	1	lemma	lemma	PROPN
ejpam-1767	38	2	4	4	X
ejpam-1767	38	3	.	.	PUNCT
ejpam-1767	39	1	let	let	VERB
ejpam-1767	39	2	mr	mr	PROPN
ejpam-1767	39	3	be	be	AUX
ejpam-1767	39	4	a	a	DET
ejpam-1767	39	5	finitely	finitely	ADV
ejpam-1767	39	6	generated	generate	VERB
ejpam-1767	39	7	fq	fq	PROPN
ejpam-1767	39	8	-	-	ADJ
ejpam-1767	39	9	injective	injective	ADJ
ejpam-1767	39	10	module	module	NOUN
ejpam-1767	39	11	.	.	PUNCT
ejpam-1767	40	1	then	then	ADV
ejpam-1767	40	2	it	it	PRON
ejpam-1767	40	3	is	be	AUX
ejpam-1767	40	4	a	a	DET
ejpam-1767	40	5	c2	c2	PROPN
ejpam-1767	40	6	module	module	NOUN
ejpam-1767	40	7	.	.	PUNCT
ejpam-1767	41	1	proof	proof	NOUN
ejpam-1767	41	2	.	.	PUNCT
ejpam-1767	42	1	write	write	VERB
ejpam-1767	42	2	s	s	PART
ejpam-1767	42	3	=	=	NOUN
ejpam-1767	42	4	end(mr	end(mr	NUM
ejpam-1767	42	5	)	)	PUNCT
ejpam-1767	42	6	.	.	PUNCT
ejpam-1767	43	1	let	let	VERB
ejpam-1767	43	2	n	n	PRON
ejpam-1767	43	3	be	be	AUX
ejpam-1767	43	4	a	a	DET
ejpam-1767	43	5	submodule	submodule	NOUN
ejpam-1767	43	6	of	of	ADP
ejpam-1767	43	7	m	m	PROPN
ejpam-1767	43	8	and	and	CCONJ
ejpam-1767	43	9	n	n	PRON
ejpam-1767	43	10	∼=	∼=	VERB
ejpam-1767	43	11	em	em	PRON
ejpam-1767	43	12	for	for	ADP
ejpam-1767	43	13	some	some	DET
ejpam-1767	43	14	e2	e2	NOUN
ejpam-1767	43	15	=	=	PUNCT
ejpam-1767	43	16	e	e	PROPN
ejpam-1767	43	17	∈	∈	PROPN
ejpam-1767	43	18	s.	s.	PROPN
ejpam-1767	43	19	then	then	ADV
ejpam-1767	43	20	there	there	PRON
ejpam-1767	43	21	exists	exist	VERB
ejpam-1767	43	22	some	some	DET
ejpam-1767	43	23	s	s	VERB
ejpam-1767	43	24	∈	∈	NOUN
ejpam-1767	43	25	s	s	VERB
ejpam-1767	43	26	such	such	ADJ
ejpam-1767	43	27	that	that	SCONJ
ejpam-1767	43	28	n	n	NOUN
ejpam-1767	43	29	=	=	SYM
ejpam-1767	43	30	sem	sem	NOUN
ejpam-1767	43	31	and	and	CCONJ
ejpam-1767	43	32	ker(se	ker(se	NOUN
ejpam-1767	43	33	)	)	PUNCT
ejpam-1767	43	34	=	=	SYM
ejpam-1767	43	35	ker(e	ker(e	PROPN
ejpam-1767	43	36	)	)	PUNCT
ejpam-1767	43	37	.	.	PUNCT
ejpam-1767	44	1	by	by	ADP
ejpam-1767	44	2	lemma	lemma	PROPN
ejpam-1767	44	3	2(1	2(1	NUM
ejpam-1767	44	4	)	)	PUNCT
ejpam-1767	44	5	,	,	PUNCT
ejpam-1767	44	6	we	we	PRON
ejpam-1767	44	7	have	have	VERB
ejpam-1767	44	8	sse	sse	NOUN
ejpam-1767	44	9	=	=	SYM
ejpam-1767	44	10	se	se	X
ejpam-1767	44	11	,	,	PUNCT
ejpam-1767	44	12	and	and	CCONJ
ejpam-1767	44	13	hence	hence	ADV
ejpam-1767	44	14	e	e	X
ejpam-1767	44	15	=	=	SYM
ejpam-1767	44	16	tse	tse	PROPN
ejpam-1767	44	17	for	for	ADP
ejpam-1767	44	18	some	some	DET
ejpam-1767	44	19	t	t	NOUN
ejpam-1767	44	20	∈	∈	NOUN
ejpam-1767	44	21	s	s	PART
ejpam-1767	44	22	with	with	ADP
ejpam-1767	44	23	t	t	PROPN
ejpam-1767	44	24	=	=	SYM
ejpam-1767	44	25	et	et	PROPN
ejpam-1767	44	26	.	.	PUNCT
ejpam-1767	45	1	thus	thus	ADV
ejpam-1767	45	2	(	(	PUNCT
ejpam-1767	45	3	set)2	set)2	PROPN
ejpam-1767	45	4	=	=	SYM
ejpam-1767	45	5	set	set	NOUN
ejpam-1767	45	6	and	and	CCONJ
ejpam-1767	45	7	n	n	NOUN
ejpam-1767	45	8	=	=	SYM
ejpam-1767	45	9	(	(	PUNCT
ejpam-1767	45	10	se)m	se)m	PROPN
ejpam-1767	45	11	=	=	SYM
ejpam-1767	45	12	(	(	PUNCT
ejpam-1767	45	13	set)m	set)m	PROPN
ejpam-1767	45	14	.	.	PUNCT
ejpam-1767	46	1	therefore	therefore	ADV
ejpam-1767	46	2	n	n	PRON
ejpam-1767	46	3	is	be	AUX
ejpam-1767	46	4	a	a	DET
ejpam-1767	46	5	direct	direct	ADJ
ejpam-1767	46	6	summand	summand	NOUN
ejpam-1767	46	7	of	of	ADP
ejpam-1767	46	8	m	m	PROPN
ejpam-1767	46	9	.	.	PUNCT
ejpam-1767	47	1	lemma	lemma	PROPN
ejpam-1767	47	2	5	5	X
ejpam-1767	47	3	.	.	PUNCT
ejpam-1767	48	1	let	let	VERB
ejpam-1767	48	2	mr	mr	PROPN
ejpam-1767	48	3	be	be	AUX
ejpam-1767	48	4	a	a	DET
ejpam-1767	48	5	quasi	quasi	ADJ
ejpam-1767	48	6	-	-	ADJ
ejpam-1767	48	7	continuous	continuous	ADJ
ejpam-1767	48	8	module	module	NOUN
ejpam-1767	48	9	with	with	ADP
ejpam-1767	48	10	s	s	NOUN
ejpam-1767	48	11	=	=	SYM
ejpam-1767	48	12	end(mr	end(mr	NUM
ejpam-1767	48	13	)	)	PUNCT
ejpam-1767	48	14	.	.	PUNCT
ejpam-1767	49	1	then	then	ADV
ejpam-1767	49	2	idempotents	idempotent	NOUN
ejpam-1767	49	3	of	of	ADP
ejpam-1767	49	4	s	s	PROPN
ejpam-1767	49	5	/	/	SYM
ejpam-1767	49	6	w	w	PROPN
ejpam-1767	49	7	(	(	PUNCT
ejpam-1767	49	8	s	s	X
ejpam-1767	49	9	)	)	PUNCT
ejpam-1767	49	10	can	can	AUX
ejpam-1767	49	11	be	be	AUX
ejpam-1767	49	12	lifted	lift	VERB
ejpam-1767	49	13	.	.	PUNCT
ejpam-1767	50	1	proof	proof	NOUN
ejpam-1767	50	2	.	.	PUNCT
ejpam-1767	51	1	let	let	VERB
ejpam-1767	51	2	s2−	s2−	PROPN
ejpam-1767	51	3	s	s	PART
ejpam-1767	51	4	∈w	∈w	NOUN
ejpam-1767	51	5	(	(	PUNCT
ejpam-1767	51	6	s	s	NOUN
ejpam-1767	51	7	)	)	PUNCT
ejpam-1767	51	8	,	,	PUNCT
ejpam-1767	51	9	then	then	ADV
ejpam-1767	51	10	ker(s2−	ker(s2−	PROPN
ejpam-1767	51	11	s)ã	s)ã	VERB
ejpam-1767	51	12	m	m	VERB
ejpam-1767	51	13	.	.	PUNCT
ejpam-1767	52	1	if	if	SCONJ
ejpam-1767	52	2	x	x	PROPN
ejpam-1767	52	3	∈	∈	PROPN
ejpam-1767	52	4	ker(s2−	ker(s2−	NOUN
ejpam-1767	52	5	s	s	PROPN
ejpam-1767	52	6	)	)	PUNCT
ejpam-1767	52	7	,	,	PUNCT
ejpam-1767	52	8	then	then	ADV
ejpam-1767	52	9	(	(	PUNCT
ejpam-1767	52	10	1−	1−	NUM
ejpam-1767	52	11	s)x	s)x	X
ejpam-1767	52	12	∈	∈	PROPN
ejpam-1767	52	13	ker(s	ker(s	PROPN
ejpam-1767	52	14	)	)	PUNCT
ejpam-1767	52	15	,	,	PUNCT
ejpam-1767	52	16	sx	sx	PROPN
ejpam-1767	52	17	∈	∈	PROPN
ejpam-1767	52	18	ker(1−	ker(1−	PROPN
ejpam-1767	52	19	s	s	NOUN
ejpam-1767	52	20	)	)	PUNCT
ejpam-1767	52	21	,	,	PUNCT
ejpam-1767	52	22	and	and	CCONJ
ejpam-1767	52	23	hence	hence	ADV
ejpam-1767	52	24	x	x	X
ejpam-1767	53	1	=	=	SYM
ejpam-1767	53	2	(	(	PUNCT
ejpam-1767	53	3	1−	1−	NUM
ejpam-1767	53	4	s)x	s)x	X
ejpam-1767	54	1	+	+	CCONJ
ejpam-1767	54	2	sx	sx	PROPN
ejpam-1767	54	3	∈	∈	PROPN
ejpam-1767	54	4	ker(s)⊕	ker(s)⊕	ADV
ejpam-1767	54	5	ker(1−	ker(1−	PROPN
ejpam-1767	54	6	s	s	NOUN
ejpam-1767	54	7	)	)	PUNCT
ejpam-1767	54	8	.	.	PUNCT
ejpam-1767	55	1	it	it	PRON
ejpam-1767	55	2	shows	show	VERB
ejpam-1767	55	3	that	that	SCONJ
ejpam-1767	55	4	ker(s2	ker(s2	PROPN
ejpam-1767	55	5	−	−	PROPN
ejpam-1767	55	6	s	s	PART
ejpam-1767	55	7	)	)	PUNCT
ejpam-1767	55	8	⊆	⊆	NUM
ejpam-1767	55	9	ker(s)⊕	ker(s)⊕	ADV
ejpam-1767	55	10	ker(1−	ker(1−	PROPN
ejpam-1767	55	11	s	s	NOUN
ejpam-1767	55	12	)	)	PUNCT
ejpam-1767	55	13	,	,	PUNCT
ejpam-1767	55	14	and	and	CCONJ
ejpam-1767	55	15	thus	thus	ADV
ejpam-1767	55	16	ker(s)⊕	ker(s)⊕	ADV
ejpam-1767	55	17	ker(1−	ker(1−	PROPN
ejpam-1767	55	18	s	s	PART
ejpam-1767	55	19	)	)	PUNCT
ejpam-1767	55	20	ã	ã	X
ejpam-1767	55	21	m	m	NOUN
ejpam-1767	55	22	.	.	PUNCT
ejpam-1767	56	1	now	now	ADV
ejpam-1767	56	2	let	let	VERB
ejpam-1767	56	3	n1	n1	NOUN
ejpam-1767	56	4	and	and	CCONJ
ejpam-1767	56	5	n2	n2	ADJ
ejpam-1767	56	6	be	be	AUX
ejpam-1767	56	7	maximal	maximal	ADJ
ejpam-1767	56	8	essential	essential	ADJ
ejpam-1767	56	9	extensions	extension	NOUN
ejpam-1767	56	10	of	of	ADP
ejpam-1767	56	11	ker(s	ker(s	NOUN
ejpam-1767	56	12	)	)	PUNCT
ejpam-1767	56	13	and	and	CCONJ
ejpam-1767	56	14	ker(1−	ker(1−	PROPN
ejpam-1767	56	15	s	s	NOUN
ejpam-1767	56	16	)	)	PUNCT
ejpam-1767	56	17	in	in	ADP
ejpam-1767	56	18	m	m	PROPN
ejpam-1767	56	19	,	,	PUNCT
ejpam-1767	56	20	respectively	respectively	ADV
ejpam-1767	56	21	.	.	PUNCT
ejpam-1767	57	1	then	then	ADV
ejpam-1767	57	2	it	it	PRON
ejpam-1767	57	3	is	be	AUX
ejpam-1767	57	4	clear	clear	ADJ
ejpam-1767	57	5	that	that	SCONJ
ejpam-1767	57	6	n1∩n2	n1∩n2	AUX
ejpam-1767	57	7	=	=	SYM
ejpam-1767	57	8	0	0	NUM
ejpam-1767	58	1	and	and	CCONJ
ejpam-1767	58	2	n1⊕n2	n1⊕n2	ADJ
ejpam-1767	58	3	ã	ã	X
ejpam-1767	58	4	m	m	NOUN
ejpam-1767	58	5	.	.	PUNCT
ejpam-1767	59	1	since	since	SCONJ
ejpam-1767	59	2	m	m	PROPN
ejpam-1767	59	3	is	be	AUX
ejpam-1767	59	4	a	a	DET
ejpam-1767	59	5	c1	c1	NOUN
ejpam-1767	59	6	module	module	NOUN
ejpam-1767	59	7	and	and	CCONJ
ejpam-1767	59	8	n1	n1	PROPN
ejpam-1767	59	9	and	and	CCONJ
ejpam-1767	59	10	n2	n2	NOUN
ejpam-1767	59	11	are	be	AUX
ejpam-1767	59	12	closed	close	VERB
ejpam-1767	59	13	submodules	submodule	NOUN
ejpam-1767	59	14	of	of	ADP
ejpam-1767	59	15	m	m	PROPN
ejpam-1767	59	16	,	,	PUNCT
ejpam-1767	59	17	n1	n1	PROPN
ejpam-1767	59	18	and	and	CCONJ
ejpam-1767	59	19	n2	n2	NOUN
ejpam-1767	59	20	are	be	AUX
ejpam-1767	59	21	direct	direct	ADJ
ejpam-1767	59	22	summand	summand	NOUN
ejpam-1767	59	23	of	of	ADP
ejpam-1767	59	24	m	m	PROPN
ejpam-1767	59	25	.	.	PUNCT
ejpam-1767	60	1	but	but	CCONJ
ejpam-1767	60	2	m	m	PROPN
ejpam-1767	60	3	is	be	AUX
ejpam-1767	60	4	a	a	DET
ejpam-1767	60	5	c3	c3	NOUN
ejpam-1767	60	6	module	module	NOUN
ejpam-1767	60	7	,	,	PUNCT
ejpam-1767	60	8	n1⊕n2	n1⊕n2	PROPN
ejpam-1767	60	9	is	be	AUX
ejpam-1767	60	10	a	a	DET
ejpam-1767	60	11	direct	direct	ADJ
ejpam-1767	60	12	summand	summand	NOUN
ejpam-1767	60	13	of	of	ADP
ejpam-1767	60	14	m	m	PROPN
ejpam-1767	60	15	,	,	PUNCT
ejpam-1767	60	16	so	so	SCONJ
ejpam-1767	60	17	that	that	SCONJ
ejpam-1767	60	18	n1⊕n2	n1⊕n2	PROPN
ejpam-1767	60	19	=	=	NOUN
ejpam-1767	60	20	m	m	PROPN
ejpam-1767	60	21	.	.	PUNCT
ejpam-1767	61	1	this	this	PRON
ejpam-1767	61	2	implies	imply	VERB
ejpam-1767	61	3	that	that	SCONJ
ejpam-1767	61	4	there	there	PRON
ejpam-1767	61	5	exists	exist	VERB
ejpam-1767	61	6	an	an	DET
ejpam-1767	61	7	e2	e2	PROPN
ejpam-1767	61	8	=	=	PUNCT
ejpam-1767	61	9	e	e	PROPN
ejpam-1767	61	10	∈	∈	PROPN
ejpam-1767	61	11	s	s	VERB
ejpam-1767	61	12	such	such	ADJ
ejpam-1767	61	13	that	that	DET
ejpam-1767	61	14	n1	n1	NOUN
ejpam-1767	61	15	=	=	SYM
ejpam-1767	61	16	(	(	PUNCT
ejpam-1767	61	17	1−e)m	1−e)m	NUM
ejpam-1767	61	18	and	and	CCONJ
ejpam-1767	61	19	n2	n2	NOUN
ejpam-1767	61	20	=	=	PUNCT
ejpam-1767	61	21	em	em	PRON
ejpam-1767	61	22	.	.	PUNCT
ejpam-1767	62	1	let	let	VERB
ejpam-1767	62	2	y	y	PROPN
ejpam-1767	62	3	∈	∈	PROPN
ejpam-1767	62	4	ker(s	ker(s	PROPN
ejpam-1767	62	5	)	)	PUNCT
ejpam-1767	62	6	,	,	PUNCT
ejpam-1767	62	7	z	z	PROPN
ejpam-1767	62	8	∈	∈	PROPN
ejpam-1767	62	9	ker(1−	ker(1−	PROPN
ejpam-1767	62	10	s	s	PART
ejpam-1767	62	11	)	)	PUNCT
ejpam-1767	62	12	,	,	PUNCT
ejpam-1767	62	13	then	then	ADV
ejpam-1767	62	14	noting	note	VERB
ejpam-1767	62	15	that	that	SCONJ
ejpam-1767	62	16	y	y	PROPN
ejpam-1767	62	17	∈	∈	PROPN
ejpam-1767	62	18	(	(	PUNCT
ejpam-1767	62	19	1−	1−	NUM
ejpam-1767	62	20	e)m	e)m	X
ejpam-1767	62	21	and	and	CCONJ
ejpam-1767	62	22	z	z	NOUN
ejpam-1767	62	23	∈	∈	PROPN
ejpam-1767	62	24	em	em	PRON
ejpam-1767	62	25	,	,	PUNCT
ejpam-1767	62	26	we	we	PRON
ejpam-1767	62	27	have	have	VERB
ejpam-1767	62	28	(	(	PUNCT
ejpam-1767	62	29	e	e	X
ejpam-1767	62	30	−	−	PROPN
ejpam-1767	62	31	s)(y	s)(y	ADJ
ejpam-1767	63	1	+	+	X
ejpam-1767	63	2	z	z	X
ejpam-1767	63	3	)	)	PUNCT
ejpam-1767	63	4	=	=	PUNCT
ejpam-1767	63	5	z	z	X
ejpam-1767	63	6	−	−	PROPN
ejpam-1767	63	7	sz	sz	NOUN
ejpam-1767	63	8	=	=	SYM
ejpam-1767	63	9	(	(	PUNCT
ejpam-1767	63	10	1−	1−	NUM
ejpam-1767	63	11	s)z	s)z	X
ejpam-1767	63	12	=	=	SYM
ejpam-1767	63	13	0	0	NUM
ejpam-1767	63	14	,	,	PUNCT
ejpam-1767	63	15	so	so	SCONJ
ejpam-1767	63	16	that	that	SCONJ
ejpam-1767	63	17	ker(s)⊕	ker(s)⊕	ADV
ejpam-1767	63	18	ker(1−	ker(1−	PROPN
ejpam-1767	63	19	s	s	PART
ejpam-1767	63	20	)	)	PUNCT
ejpam-1767	63	21	⊆	⊆	NUM
ejpam-1767	63	22	ker(e	ker(e	PROPN
ejpam-1767	63	23	−	−	PROPN
ejpam-1767	63	24	s	s	NOUN
ejpam-1767	63	25	)	)	PUNCT
ejpam-1767	63	26	.	.	PUNCT
ejpam-1767	64	1	and	and	CCONJ
ejpam-1767	64	2	hence	hence	ADV
ejpam-1767	64	3	e−	e−	PROPN
ejpam-1767	64	4	s	s	PART
ejpam-1767	64	5	∈w	∈w	NOUN
ejpam-1767	64	6	(	(	PUNCT
ejpam-1767	64	7	s	s	NOUN
ejpam-1767	64	8	)	)	PUNCT
ejpam-1767	64	9	,	,	PUNCT
ejpam-1767	64	10	that	that	ADV
ejpam-1767	64	11	is	is	ADV
ejpam-1767	64	12	,	,	PUNCT
ejpam-1767	64	13	idempotents	idempotents	PROPN
ejpam-1767	64	14	modulo	modulo	PROPN
ejpam-1767	64	15	w	w	PROPN
ejpam-1767	64	16	(	(	PUNCT
ejpam-1767	64	17	s	s	NOUN
ejpam-1767	64	18	)	)	PUNCT
ejpam-1767	64	19	lift	lift	NOUN
ejpam-1767	64	20	.	.	PUNCT
ejpam-1767	65	1	z.	z.	PROPN
ejpam-1767	65	2	zhanmin	zhanmin	PROPN
ejpam-1767	65	3	/	/	SYM
ejpam-1767	65	4	eur	eur	PROPN
ejpam-1767	65	5	.	.	PUNCT
ejpam-1767	66	1	j.	j.	PROPN
ejpam-1767	66	2	pure	pure	PROPN
ejpam-1767	66	3	appl	appl	PROPN
ejpam-1767	66	4	.	.	PROPN
ejpam-1767	66	5	math	math	PROPN
ejpam-1767	66	6	,	,	PUNCT
ejpam-1767	66	7	6	6	NUM
ejpam-1767	66	8	(	(	PUNCT
ejpam-1767	66	9	2013	2013	NUM
ejpam-1767	66	10	)	)	PUNCT
ejpam-1767	66	11	,	,	PUNCT
ejpam-1767	66	12	119	119	NUM
ejpam-1767	66	13	-	-	SYM
ejpam-1767	66	14	125	125	NUM
ejpam-1767	66	15	121	121	NUM
ejpam-1767	66	16	corollary	corollary	NOUN
ejpam-1767	66	17	1	1	NUM
ejpam-1767	66	18	.	.	PUNCT
ejpam-1767	67	1	let	let	VERB
ejpam-1767	67	2	mr	mr	PROPN
ejpam-1767	67	3	be	be	AUX
ejpam-1767	67	4	a	a	DET
ejpam-1767	67	5	finitely	finitely	ADV
ejpam-1767	67	6	generated	generate	VERB
ejpam-1767	67	7	fq	fq	PROPN
ejpam-1767	67	8	-	-	ADJ
ejpam-1767	67	9	injective	injective	ADJ
ejpam-1767	67	10	c1	c1	NOUN
ejpam-1767	67	11	module	module	NOUN
ejpam-1767	67	12	with	with	ADP
ejpam-1767	67	13	s	s	NOUN
ejpam-1767	67	14	=	=	SYM
ejpam-1767	67	15	end(mr	end(mr	NUM
ejpam-1767	67	16	)	)	PUNCT
ejpam-1767	67	17	.	.	PUNCT
ejpam-1767	68	1	then	then	ADV
ejpam-1767	68	2	s	s	VERB
ejpam-1767	68	3	is	be	AUX
ejpam-1767	68	4	semiperfect	semiperfect	ADJ
ejpam-1767	68	5	if	if	SCONJ
ejpam-1767	68	6	and	and	CCONJ
ejpam-1767	68	7	only	only	ADV
ejpam-1767	68	8	if	if	SCONJ
ejpam-1767	68	9	s	s	NOUN
ejpam-1767	68	10	is	be	AUX
ejpam-1767	68	11	semilocal	semilocal	ADJ
ejpam-1767	68	12	.	.	PUNCT
ejpam-1767	69	1	proof	proof	NOUN
ejpam-1767	69	2	.	.	PUNCT
ejpam-1767	70	1	since	since	SCONJ
ejpam-1767	70	2	mr	mr	PROPN
ejpam-1767	70	3	is	be	AUX
ejpam-1767	70	4	a	a	DET
ejpam-1767	70	5	finitely	finitely	ADV
ejpam-1767	70	6	generated	generate	VERB
ejpam-1767	70	7	fq	fq	PROPN
ejpam-1767	70	8	-	-	ADJ
ejpam-1767	70	9	injective	injective	ADJ
ejpam-1767	70	10	module	module	NOUN
ejpam-1767	70	11	,	,	PUNCT
ejpam-1767	70	12	by	by	ADP
ejpam-1767	70	13	lemma	lemma	PROPN
ejpam-1767	70	14	4	4	NUM
ejpam-1767	70	15	,	,	PUNCT
ejpam-1767	70	16	it	it	PRON
ejpam-1767	70	17	is	be	AUX
ejpam-1767	70	18	a	a	DET
ejpam-1767	70	19	c2	c2	PROPN
ejpam-1767	70	20	module	module	NOUN
ejpam-1767	70	21	and	and	CCONJ
ejpam-1767	70	22	hence	hence	ADV
ejpam-1767	70	23	a	a	DET
ejpam-1767	70	24	c3	c3	NOUN
ejpam-1767	70	25	module	module	NOUN
ejpam-1767	70	26	.	.	PUNCT
ejpam-1767	71	1	thus	thus	ADV
ejpam-1767	71	2	mr	mr	PROPN
ejpam-1767	71	3	is	be	AUX
ejpam-1767	71	4	quasi	quasi	ADJ
ejpam-1767	71	5	-	-	ADJ
ejpam-1767	71	6	continuous	continuous	ADJ
ejpam-1767	71	7	by	by	ADP
ejpam-1767	71	8	the	the	DET
ejpam-1767	71	9	condition	condition	NOUN
ejpam-1767	71	10	that	that	SCONJ
ejpam-1767	71	11	mr	mr	PROPN
ejpam-1767	71	12	is	be	AUX
ejpam-1767	71	13	a	a	DET
ejpam-1767	71	14	c1	c1	NOUN
ejpam-1767	71	15	module	module	NOUN
ejpam-1767	71	16	.	.	PUNCT
ejpam-1767	72	1	and	and	CCONJ
ejpam-1767	72	2	so	so	ADV
ejpam-1767	72	3	the	the	DET
ejpam-1767	72	4	result	result	NOUN
ejpam-1767	72	5	follows	follow	VERB
ejpam-1767	72	6	from	from	ADP
ejpam-1767	72	7	lemma	lemma	PROPN
ejpam-1767	72	8	5	5	NUM
ejpam-1767	72	9	and	and	CCONJ
ejpam-1767	72	10	lemma	lemma	PROPN
ejpam-1767	72	11	2(2	2(2	NUM
ejpam-1767	72	12	)	)	PUNCT
ejpam-1767	72	13	.	.	PUNCT
ejpam-1767	73	1	recall	recall	VERB
ejpam-1767	73	2	that	that	SCONJ
ejpam-1767	73	3	a	a	DET
ejpam-1767	73	4	ring	ring	NOUN
ejpam-1767	73	5	r	r	NOUN
ejpam-1767	73	6	is	be	AUX
ejpam-1767	73	7	called	call	VERB
ejpam-1767	73	8	right	right	ADJ
ejpam-1767	73	9	mp	mp	NOUN
ejpam-1767	73	10	-	-	PUNCT
ejpam-1767	73	11	injective	injective	ADJ
ejpam-1767	73	12	[	[	X
ejpam-1767	73	13	11	11	NUM
ejpam-1767	73	14	]	]	PUNCT
ejpam-1767	73	15	if	if	SCONJ
ejpam-1767	73	16	every	every	DET
ejpam-1767	73	17	monomorphism	monomorphism	NOUN
ejpam-1767	73	18	from	from	ADP
ejpam-1767	73	19	a	a	DET
ejpam-1767	73	20	principal	principal	ADJ
ejpam-1767	73	21	right	right	ADJ
ejpam-1767	73	22	ideal	ideal	NOUN
ejpam-1767	73	23	of	of	ADP
ejpam-1767	73	24	r	r	NOUN
ejpam-1767	73	25	to	to	ADP
ejpam-1767	73	26	r	r	NOUN
ejpam-1767	73	27	extends	extend	VERB
ejpam-1767	73	28	to	to	ADP
ejpam-1767	73	29	an	an	DET
ejpam-1767	73	30	endomorphism	endomorphism	NOUN
ejpam-1767	73	31	of	of	ADP
ejpam-1767	73	32	r	r	NOUN
ejpam-1767	73	33	;	;	PUNCT
ejpam-1767	73	34	a	a	DET
ejpam-1767	73	35	ring	ring	NOUN
ejpam-1767	73	36	r	r	NOUN
ejpam-1767	73	37	is	be	AUX
ejpam-1767	73	38	called	call	VERB
ejpam-1767	73	39	right	right	ADJ
ejpam-1767	73	40	mgpinjective	mgpinjective	NOUN
ejpam-1767	74	1	[	[	X
ejpam-1767	74	2	11	11	NUM
ejpam-1767	74	3	]	]	PUNCT
ejpam-1767	74	4	if	if	SCONJ
ejpam-1767	74	5	,	,	PUNCT
ejpam-1767	74	6	for	for	ADP
ejpam-1767	74	7	any	any	DET
ejpam-1767	74	8	0	0	NUM
ejpam-1767	74	9	6=	6=	ADP
ejpam-1767	74	10	a	a	DET
ejpam-1767	74	11	∈	∈	PROPN
ejpam-1767	74	12	r	r	NOUN
ejpam-1767	74	13	,	,	PUNCT
ejpam-1767	74	14	there	there	PRON
ejpam-1767	74	15	exists	exist	VERB
ejpam-1767	74	16	a	a	DET
ejpam-1767	74	17	positive	positive	ADJ
ejpam-1767	74	18	integer	integer	NOUN
ejpam-1767	74	19	n	n	CCONJ
ejpam-1767	74	20	such	such	ADJ
ejpam-1767	74	21	that	that	SCONJ
ejpam-1767	74	22	an	an	DET
ejpam-1767	74	23	6=	6=	NUM
ejpam-1767	74	24	0	0	NUM
ejpam-1767	74	25	and	and	CCONJ
ejpam-1767	74	26	any	any	DET
ejpam-1767	74	27	r	r	NOUN
ejpam-1767	74	28	-	-	NOUN
ejpam-1767	74	29	monomorphism	monomorphism	NOUN
ejpam-1767	74	30	from	from	ADP
ejpam-1767	74	31	anr	anr	PROPN
ejpam-1767	74	32	to	to	ADP
ejpam-1767	74	33	r	r	NOUN
ejpam-1767	74	34	extends	extend	VERB
ejpam-1767	74	35	to	to	ADP
ejpam-1767	74	36	an	an	DET
ejpam-1767	74	37	endomorphism	endomorphism	NOUN
ejpam-1767	74	38	of	of	ADP
ejpam-1767	74	39	r	r	NOUN
ejpam-1767	74	40	;	;	PUNCT
ejpam-1767	74	41	a	a	DET
ejpam-1767	74	42	ring	ring	NOUN
ejpam-1767	74	43	r	r	NOUN
ejpam-1767	74	44	is	be	AUX
ejpam-1767	74	45	said	say	VERB
ejpam-1767	74	46	to	to	PART
ejpam-1767	74	47	be	be	AUX
ejpam-1767	74	48	right	right	ADJ
ejpam-1767	74	49	ap	ap	ADJ
ejpam-1767	74	50	-	-	NOUN
ejpam-1767	74	51	injective	injective	ADJ
ejpam-1767	74	52	[	[	X
ejpam-1767	74	53	6	6	NUM
ejpam-1767	74	54	]	]	PUNCT
ejpam-1767	74	55	if	if	SCONJ
ejpam-1767	74	56	,	,	PUNCT
ejpam-1767	74	57	for	for	ADP
ejpam-1767	74	58	any	any	DET
ejpam-1767	74	59	a	a	DET
ejpam-1767	74	60	∈	∈	NOUN
ejpam-1767	74	61	r	r	NOUN
ejpam-1767	74	62	,	,	PUNCT
ejpam-1767	74	63	there	there	PRON
ejpam-1767	74	64	exists	exist	VERB
ejpam-1767	74	65	a	a	DET
ejpam-1767	74	66	left	left	ADJ
ejpam-1767	74	67	ideal	ideal	NOUN
ejpam-1767	75	1	xa	xa	PROPN
ejpam-1767	75	2	such	such	ADJ
ejpam-1767	75	3	that	that	SCONJ
ejpam-1767	75	4	l	l	NOUN
ejpam-1767	75	5	r(a	r(a	X
ejpam-1767	75	6	)	)	PUNCT
ejpam-1767	75	7	=	=	SYM
ejpam-1767	75	8	ra⊕	ra⊕	PUNCT
ejpam-1767	75	9	xa	xa	PROPN
ejpam-1767	75	10	;	;	PUNCT
ejpam-1767	75	11	a	a	DET
ejpam-1767	75	12	ring	ring	NOUN
ejpam-1767	75	13	r	r	NOUN
ejpam-1767	75	14	is	be	AUX
ejpam-1767	75	15	called	call	VERB
ejpam-1767	75	16	right	right	ADJ
ejpam-1767	75	17	agp	agp	NOUN
ejpam-1767	75	18	-	-	PUNCT
ejpam-1767	75	19	injective	injective	ADJ
ejpam-1767	75	20	if	if	SCONJ
ejpam-1767	75	21	,	,	PUNCT
ejpam-1767	75	22	for	for	ADP
ejpam-1767	75	23	any	any	DET
ejpam-1767	75	24	0	0	NUM
ejpam-1767	75	25	6=	6=	ADP
ejpam-1767	75	26	a	a	DET
ejpam-1767	75	27	∈	∈	PROPN
ejpam-1767	75	28	r	r	NOUN
ejpam-1767	75	29	,	,	PUNCT
ejpam-1767	75	30	there	there	PRON
ejpam-1767	75	31	exists	exist	VERB
ejpam-1767	75	32	a	a	DET
ejpam-1767	75	33	positive	positive	ADJ
ejpam-1767	75	34	integer	integer	NOUN
ejpam-1767	75	35	n	n	NOUN
ejpam-1767	75	36	and	and	CCONJ
ejpam-1767	75	37	a	a	DET
ejpam-1767	75	38	left	left	ADJ
ejpam-1767	75	39	ideal	ideal	NOUN
ejpam-1767	75	40	xan	xan	PROPN
ejpam-1767	75	41	such	such	ADJ
ejpam-1767	75	42	that	that	SCONJ
ejpam-1767	75	43	an	an	DET
ejpam-1767	75	44	6=	6=	NUM
ejpam-1767	75	45	0	0	NUM
ejpam-1767	75	46	and	and	CCONJ
ejpam-1767	75	47	l	l	PROPN
ejpam-1767	75	48	r(an	r(an	PROPN
ejpam-1767	75	49	)	)	PUNCT
ejpam-1767	76	1	=	=	PRON
ejpam-1767	76	2	ran	run	VERB
ejpam-1767	76	3	⊕	⊕	PROPN
ejpam-1767	76	4	xan	xan	PROPN
ejpam-1767	76	5	.	.	PUNCT
ejpam-1767	77	1	clearly	clearly	ADV
ejpam-1767	77	2	,	,	PUNCT
ejpam-1767	77	3	right	right	ADJ
ejpam-1767	77	4	mp	mp	NOUN
ejpam-1767	77	5	-	-	PUNCT
ejpam-1767	77	6	injective	injective	ADJ
ejpam-1767	77	7	rings	ring	NOUN
ejpam-1767	77	8	are	be	AUX
ejpam-1767	77	9	right	right	ADJ
ejpam-1767	77	10	mgp	mgp	NOUN
ejpam-1767	77	11	-	-	PUNCT
ejpam-1767	77	12	injective	injective	ADJ
ejpam-1767	77	13	,	,	PUNCT
ejpam-1767	77	14	and	and	CCONJ
ejpam-1767	77	15	right	right	ADJ
ejpam-1767	77	16	ap	ap	ADJ
ejpam-1767	77	17	-	-	PUNCT
ejpam-1767	77	18	injective	injective	ADJ
ejpam-1767	77	19	rings	ring	NOUN
ejpam-1767	77	20	are	be	AUX
ejpam-1767	77	21	right	right	ADJ
ejpam-1767	77	22	agp	agp	NOUN
ejpam-1767	77	23	-	-	PUNCT
ejpam-1767	77	24	injective	injective	ADJ
ejpam-1767	77	25	.	.	PUNCT
ejpam-1767	78	1	if	if	SCONJ
ejpam-1767	78	2	r	r	NOUN
ejpam-1767	78	3	is	be	AUX
ejpam-1767	78	4	a	a	DET
ejpam-1767	78	5	right	right	ADJ
ejpam-1767	78	6	mp	mp	NOUN
ejpam-1767	78	7	-	-	PUNCT
ejpam-1767	78	8	injective	injective	ADJ
ejpam-1767	78	9	rings	ring	NOUN
ejpam-1767	78	10	,	,	PUNCT
ejpam-1767	78	11	then	then	ADV
ejpam-1767	78	12	r	r	NOUN
ejpam-1767	78	13	is	be	AUX
ejpam-1767	78	14	right	right	ADJ
ejpam-1767	78	15	c2	c2	PROPN
ejpam-1767	78	16	by	by	ADP
ejpam-1767	78	17	[	[	X
ejpam-1767	78	18	11	11	NUM
ejpam-1767	78	19	,	,	PUNCT
ejpam-1767	78	20	theorem	theorem	VERB
ejpam-1767	78	21	2.7	2.7	NUM
ejpam-1767	78	22	]	]	PUNCT
ejpam-1767	78	23	and	and	CCONJ
ejpam-1767	78	24	j(r	j(r	PROPN
ejpam-1767	78	25	)	)	PUNCT
ejpam-1767	79	1	=	=	PUNCT
ejpam-1767	79	2	z(rr	z(rr	NUM
ejpam-1767	79	3	)	)	PUNCT
ejpam-1767	79	4	by	by	ADP
ejpam-1767	79	5	[	[	X
ejpam-1767	79	6	11	11	NUM
ejpam-1767	79	7	,	,	PUNCT
ejpam-1767	79	8	theorem	theorem	VERB
ejpam-1767	79	9	3.4	3.4	NUM
ejpam-1767	79	10	]	]	PUNCT
ejpam-1767	79	11	.	.	PUNCT
ejpam-1767	80	1	if	if	SCONJ
ejpam-1767	80	2	r	r	NOUN
ejpam-1767	80	3	is	be	AUX
ejpam-1767	80	4	a	a	DET
ejpam-1767	80	5	right	right	ADJ
ejpam-1767	80	6	ap	ap	ADJ
ejpam-1767	80	7	-	-	PUNCT
ejpam-1767	80	8	injective	injective	ADJ
ejpam-1767	80	9	rings	ring	NOUN
ejpam-1767	80	10	,	,	PUNCT
ejpam-1767	80	11	then	then	ADV
ejpam-1767	80	12	r	r	NOUN
ejpam-1767	80	13	is	be	AUX
ejpam-1767	80	14	right	right	ADJ
ejpam-1767	80	15	c2	c2	PROPN
ejpam-1767	80	16	by	by	ADP
ejpam-1767	80	17	[	[	X
ejpam-1767	80	18	9	9	NUM
ejpam-1767	80	19	,	,	PUNCT
ejpam-1767	80	20	corollary	corollary	ADJ
ejpam-1767	80	21	3.4	3.4	NUM
ejpam-1767	80	22	]	]	PUNCT
ejpam-1767	80	23	and	and	CCONJ
ejpam-1767	80	24	j(r	j(r	PROPN
ejpam-1767	80	25	)	)	PUNCT
ejpam-1767	81	1	=	=	PUNCT
ejpam-1767	81	2	z(rr	z(rr	NUM
ejpam-1767	81	3	)	)	PUNCT
ejpam-1767	81	4	by	by	ADP
ejpam-1767	81	5	[	[	X
ejpam-1767	81	6	6	6	NUM
ejpam-1767	81	7	,	,	PUNCT
ejpam-1767	81	8	corollary	corollary	ADJ
ejpam-1767	81	9	2.3	2.3	NUM
ejpam-1767	81	10	]	]	PUNCT
ejpam-1767	81	11	.	.	PUNCT
ejpam-1767	82	1	so	so	ADV
ejpam-1767	82	2	by	by	ADP
ejpam-1767	82	3	lemma	lemma	PROPN
ejpam-1767	82	4	5	5	NUM
ejpam-1767	82	5	,	,	PUNCT
ejpam-1767	82	6	we	we	PRON
ejpam-1767	82	7	have	have	VERB
ejpam-1767	82	8	immediately	immediately	ADV
ejpam-1767	82	9	the	the	DET
ejpam-1767	82	10	following	follow	VERB
ejpam-1767	82	11	corollary	corollary	NOUN
ejpam-1767	82	12	.	.	PUNCT
ejpam-1767	83	1	corollary	corollary	ADJ
ejpam-1767	83	2	2	2	NUM
ejpam-1767	83	3	.	.	PUNCT
ejpam-1767	84	1	let	let	VERB
ejpam-1767	84	2	r	r	PRON
ejpam-1767	84	3	be	be	AUX
ejpam-1767	84	4	a	a	DET
ejpam-1767	84	5	right	right	ADJ
ejpam-1767	84	6	cs	cs	PROPN
ejpam-1767	84	7	ring	ring	NOUN
ejpam-1767	84	8	.	.	PUNCT
ejpam-1767	85	1	if	if	SCONJ
ejpam-1767	85	2	r	r	NOUN
ejpam-1767	85	3	is	be	AUX
ejpam-1767	85	4	right	right	ADJ
ejpam-1767	85	5	mp	mp	NOUN
ejpam-1767	85	6	-	-	PUNCT
ejpam-1767	85	7	injective	injective	ADJ
ejpam-1767	85	8	or	or	CCONJ
ejpam-1767	85	9	right	right	ADJ
ejpam-1767	85	10	ap	ap	ADJ
ejpam-1767	85	11	-	-	PUNCT
ejpam-1767	85	12	injective	injective	ADJ
ejpam-1767	85	13	,	,	PUNCT
ejpam-1767	85	14	then	then	ADV
ejpam-1767	85	15	r	r	NOUN
ejpam-1767	85	16	is	be	AUX
ejpam-1767	85	17	semiperfect	semiperfect	ADJ
ejpam-1767	85	18	if	if	SCONJ
ejpam-1767	85	19	and	and	CCONJ
ejpam-1767	85	20	only	only	ADV
ejpam-1767	85	21	if	if	SCONJ
ejpam-1767	85	22	r	r	NOUN
ejpam-1767	85	23	is	be	AUX
ejpam-1767	85	24	semilocal	semilocal	ADJ
ejpam-1767	85	25	.	.	PUNCT
ejpam-1767	86	1	let	let	VERB
ejpam-1767	86	2	m	m	PRON
ejpam-1767	86	3	be	be	AUX
ejpam-1767	86	4	a	a	DET
ejpam-1767	86	5	right	right	ADJ
ejpam-1767	86	6	r	r	NOUN
ejpam-1767	86	7	-	-	NOUN
ejpam-1767	86	8	module	module	NOUN
ejpam-1767	86	9	.	.	PUNCT
ejpam-1767	87	1	a	a	DET
ejpam-1767	87	2	finite	finite	ADJ
ejpam-1767	87	3	set	set	VERB
ejpam-1767	87	4	a1	a1	NOUN
ejpam-1767	87	5	,	,	PUNCT
ejpam-1767	87	6	.	.	PUNCT
ejpam-1767	87	7	.	.	PUNCT
ejpam-1767	88	1	.	.	PUNCT
ejpam-1767	89	1	,	,	PUNCT
ejpam-1767	89	2	an	an	PRON
ejpam-1767	89	3	of	of	ADP
ejpam-1767	89	4	proper	proper	ADJ
ejpam-1767	89	5	submodules	submodule	NOUN
ejpam-1767	89	6	of	of	ADP
ejpam-1767	89	7	m	m	PROPN
ejpam-1767	89	8	is	be	AUX
ejpam-1767	89	9	said	say	VERB
ejpam-1767	89	10	to	to	PART
ejpam-1767	89	11	be	be	AUX
ejpam-1767	89	12	coindependent	coindependent	ADJ
ejpam-1767	89	13	if	if	SCONJ
ejpam-1767	89	14	for	for	ADP
ejpam-1767	89	15	each	each	DET
ejpam-1767	89	16	i	i	PRON
ejpam-1767	89	17	,	,	PUNCT
ejpam-1767	89	18	1	1	NUM
ejpam-1767	89	19	≤	≤	NUM
ejpam-1767	89	20	i	i	PRON
ejpam-1767	89	21	≤	≤	PROPN
ejpam-1767	89	22	n	n	CCONJ
ejpam-1767	89	23	,	,	PUNCT
ejpam-1767	89	24	ai	ai	VERB
ejpam-1767	89	25	+	+	PROPN
ejpam-1767	89	26	∩	∩	ADJ
ejpam-1767	89	27	j	j	ADJ
ejpam-1767	89	28	6	6	NUM
ejpam-1767	89	29	=	=	PROPN
ejpam-1767	89	30	ia	ia	PROPN
ejpam-1767	89	31	j	j	PROPN
ejpam-1767	89	32	=	=	PROPN
ejpam-1767	89	33	m	m	PROPN
ejpam-1767	89	34	,	,	PUNCT
ejpam-1767	89	35	and	and	CCONJ
ejpam-1767	89	36	a	a	DET
ejpam-1767	89	37	family	family	NOUN
ejpam-1767	89	38	of	of	ADP
ejpam-1767	89	39	submodules	submodule	NOUN
ejpam-1767	89	40	of	of	ADP
ejpam-1767	89	41	m	m	PROPN
ejpam-1767	89	42	is	be	AUX
ejpam-1767	89	43	said	say	VERB
ejpam-1767	89	44	to	to	PART
ejpam-1767	89	45	be	be	AUX
ejpam-1767	89	46	coindependent	coindependent	ADJ
ejpam-1767	89	47	if	if	SCONJ
ejpam-1767	89	48	each	each	PRON
ejpam-1767	89	49	of	of	ADP
ejpam-1767	89	50	its	its	PRON
ejpam-1767	89	51	finite	finite	NOUN
ejpam-1767	89	52	subfamily	subfamily	ADV
ejpam-1767	89	53	is	be	AUX
ejpam-1767	89	54	coindependent	coindependent	ADJ
ejpam-1767	89	55	.	.	PUNCT
ejpam-1767	90	1	the	the	DET
ejpam-1767	90	2	module	module	NOUN
ejpam-1767	90	3	m	m	VERB
ejpam-1767	90	4	is	be	AUX
ejpam-1767	90	5	said	say	VERB
ejpam-1767	90	6	to	to	PART
ejpam-1767	90	7	have	have	VERB
ejpam-1767	90	8	finite	finite	VERB
ejpam-1767	90	9	dual	dual	PROPN
ejpam-1767	90	10	goldie	goldie	PROPN
ejpam-1767	90	11	dimension	dimension	NOUN
ejpam-1767	90	12	if	if	SCONJ
ejpam-1767	90	13	every	every	DET
ejpam-1767	90	14	coindependent	coindependent	NOUN
ejpam-1767	90	15	family	family	NOUN
ejpam-1767	90	16	of	of	ADP
ejpam-1767	90	17	submodules	submodule	NOUN
ejpam-1767	90	18	of	of	ADP
ejpam-1767	90	19	m	m	PROPN
ejpam-1767	90	20	is	be	AUX
ejpam-1767	90	21	finite	finite	ADJ
ejpam-1767	90	22	.	.	PUNCT
ejpam-1767	91	1	refer	refer	VERB
ejpam-1767	91	2	to	to	ADP
ejpam-1767	91	3	[	[	X
ejpam-1767	91	4	4	4	X
ejpam-1767	91	5	]	]	PUNCT
ejpam-1767	91	6	for	for	ADP
ejpam-1767	91	7	details	detail	NOUN
ejpam-1767	91	8	concerning	concern	VERB
ejpam-1767	91	9	the	the	DET
ejpam-1767	91	10	dual	dual	ADJ
ejpam-1767	91	11	goldie	goldie	PROPN
ejpam-1767	91	12	dimension	dimension	PROPN
ejpam-1767	91	13	.	.	PUNCT
ejpam-1767	92	1	lemma	lemma	PROPN
ejpam-1767	92	2	6	6	NUM
ejpam-1767	92	3	(	(	PUNCT
ejpam-1767	92	4	[	[	X
ejpam-1767	92	5	4	4	NUM
ejpam-1767	92	6	,	,	PUNCT
ejpam-1767	92	7	propositions	proposition	VERB
ejpam-1767	92	8	2.43	2.43	NUM
ejpam-1767	92	9	]	]	PUNCT
ejpam-1767	92	10	)	)	PUNCT
ejpam-1767	92	11	.	.	PUNCT
ejpam-1767	93	1	a	a	DET
ejpam-1767	93	2	ring	ring	NOUN
ejpam-1767	93	3	r	r	NOUN
ejpam-1767	93	4	is	be	AUX
ejpam-1767	93	5	semilocal	semilocal	ADJ
ejpam-1767	93	6	if	if	SCONJ
ejpam-1767	93	7	and	and	CCONJ
ejpam-1767	93	8	only	only	ADV
ejpam-1767	93	9	if	if	SCONJ
ejpam-1767	93	10	rr	rr	PROPN
ejpam-1767	93	11	has	have	AUX
ejpam-1767	93	12	finite	finite	VERB
ejpam-1767	93	13	dual	dual	PROPN
ejpam-1767	93	14	goldie	goldie	PROPN
ejpam-1767	93	15	dimension	dimension	PROPN
ejpam-1767	93	16	,	,	PUNCT
ejpam-1767	93	17	if	if	SCONJ
ejpam-1767	93	18	and	and	CCONJ
ejpam-1767	93	19	only	only	ADV
ejpam-1767	93	20	if	if	SCONJ
ejpam-1767	93	21	rr	rr	PROPN
ejpam-1767	93	22	has	have	AUX
ejpam-1767	93	23	finite	finite	VERB
ejpam-1767	93	24	dual	dual	PROPN
ejpam-1767	93	25	goldie	goldie	PROPN
ejpam-1767	93	26	dimension	dimension	PROPN
ejpam-1767	93	27	.	.	PUNCT
ejpam-1767	94	1	theorem	theorem	NOUN
ejpam-1767	94	2	1	1	NUM
ejpam-1767	94	3	.	.	PUNCT
ejpam-1767	95	1	let	let	VERB
ejpam-1767	95	2	mr	mr	PROPN
ejpam-1767	95	3	be	be	AUX
ejpam-1767	95	4	a	a	DET
ejpam-1767	95	5	finitely	finitely	ADV
ejpam-1767	95	6	generated	generate	VERB
ejpam-1767	95	7	fq	fq	PROPN
ejpam-1767	95	8	-	-	ADJ
ejpam-1767	95	9	injective	injective	ADJ
ejpam-1767	95	10	module	module	NOUN
ejpam-1767	95	11	with	with	ADP
ejpam-1767	95	12	s	s	NOUN
ejpam-1767	95	13	=	=	SYM
ejpam-1767	95	14	end(mr	end(mr	NUM
ejpam-1767	95	15	)	)	PUNCT
ejpam-1767	95	16	.	.	PUNCT
ejpam-1767	96	1	then	then	ADV
ejpam-1767	96	2	the	the	DET
ejpam-1767	96	3	following	follow	VERB
ejpam-1767	96	4	conditions	condition	NOUN
ejpam-1767	96	5	are	be	AUX
ejpam-1767	96	6	equivalent	equivalent	ADJ
ejpam-1767	96	7	:	:	PUNCT
ejpam-1767	96	8	(	(	PUNCT
ejpam-1767	96	9	1	1	X
ejpam-1767	96	10	)	)	PUNCT
ejpam-1767	96	11	s	s	VERB
ejpam-1767	96	12	is	be	AUX
ejpam-1767	96	13	semilocal	semilocal	ADJ
ejpam-1767	96	14	.	.	PUNCT
ejpam-1767	97	1	(	(	PUNCT
ejpam-1767	97	2	2	2	X
ejpam-1767	97	3	)	)	PUNCT
ejpam-1767	97	4	mr	mr	PROPN
ejpam-1767	97	5	is	be	AUX
ejpam-1767	97	6	finite	finite	ADJ
ejpam-1767	97	7	dimensional	dimensional	ADJ
ejpam-1767	97	8	.	.	PUNCT
ejpam-1767	98	1	furthermore	furthermore	ADV
ejpam-1767	98	2	,	,	PUNCT
ejpam-1767	98	3	if	if	SCONJ
ejpam-1767	98	4	m	m	NOUN
ejpam-1767	98	5	is	be	AUX
ejpam-1767	98	6	a	a	DET
ejpam-1767	98	7	c1	c1	NOUN
ejpam-1767	98	8	module	module	NOUN
ejpam-1767	98	9	,	,	PUNCT
ejpam-1767	98	10	then	then	ADV
ejpam-1767	98	11	these	these	DET
ejpam-1767	98	12	conditions	condition	NOUN
ejpam-1767	98	13	are	be	AUX
ejpam-1767	98	14	equivalent	equivalent	ADJ
ejpam-1767	98	15	to	to	ADP
ejpam-1767	98	16	:	:	PUNCT
ejpam-1767	98	17	(	(	PUNCT
ejpam-1767	98	18	3	3	X
ejpam-1767	98	19	)	)	PUNCT
ejpam-1767	98	20	s	s	VERB
ejpam-1767	98	21	is	be	AUX
ejpam-1767	98	22	semiperfect	semiperfect	ADJ
ejpam-1767	98	23	.	.	PUNCT
ejpam-1767	99	1	proof	proof	NOUN
ejpam-1767	99	2	.	.	PUNCT
ejpam-1767	100	1	(	(	PUNCT
ejpam-1767	100	2	1	1	X
ejpam-1767	100	3	)	)	PUNCT
ejpam-1767	100	4	⇒	⇒	NOUN
ejpam-1767	100	5	(	(	PUNCT
ejpam-1767	100	6	2	2	NUM
ejpam-1767	100	7	)	)	PUNCT
ejpam-1767	100	8	.	.	PUNCT
ejpam-1767	101	1	if	if	SCONJ
ejpam-1767	101	2	mr	mr	PROPN
ejpam-1767	101	3	is	be	AUX
ejpam-1767	101	4	not	not	PART
ejpam-1767	101	5	finite	finite	ADJ
ejpam-1767	101	6	dimensional	dimensional	ADJ
ejpam-1767	101	7	,	,	PUNCT
ejpam-1767	101	8	then	then	ADV
ejpam-1767	101	9	there	there	PRON
ejpam-1767	101	10	exists	exist	VERB
ejpam-1767	101	11	0	0	PUNCT
ejpam-1767	102	1	6=	6=	NUM
ejpam-1767	102	2	x	x	SYM
ejpam-1767	103	1	i	i	PRON
ejpam-1767	103	2	∈	∈	PROPN
ejpam-1767	103	3	m	m	VERB
ejpam-1767	103	4	,	,	PUNCT
ejpam-1767	103	5	i	i	PRON
ejpam-1767	103	6	=	=	SYM
ejpam-1767	103	7	1,2	1,2	NUM
ejpam-1767	103	8	,	,	PUNCT
ejpam-1767	103	9	3	3	NUM
ejpam-1767	103	10	,	,	PUNCT
ejpam-1767	103	11	·	·	PUNCT
ejpam-1767	103	12	·	·	PUNCT
ejpam-1767	103	13	·	·	PUNCT
ejpam-1767	103	14	,	,	PUNCT
ejpam-1767	103	15	such	such	ADJ
ejpam-1767	103	16	that	that	DET
ejpam-1767	103	17	∑∞	∑∞	NOUN
ejpam-1767	103	18	i=1	i=1	X
ejpam-1767	103	19	x	x	VERB
ejpam-1767	103	20	ir	ir	PROPN
ejpam-1767	103	21	is	be	AUX
ejpam-1767	103	22	a	a	DET
ejpam-1767	103	23	direct	direct	ADJ
ejpam-1767	103	24	sum	sum	NOUN
ejpam-1767	103	25	.	.	PUNCT
ejpam-1767	104	1	since	since	SCONJ
ejpam-1767	104	2	mr	mr	PROPN
ejpam-1767	104	3	is	be	AUX
ejpam-1767	104	4	fq	fq	NOUN
ejpam-1767	104	5	-	-	ADJ
ejpam-1767	104	6	injective	injective	ADJ
ejpam-1767	104	7	,	,	PUNCT
ejpam-1767	104	8	by	by	ADP
ejpam-1767	104	9	lemma	lemma	PROPN
ejpam-1767	104	10	1	1	NUM
ejpam-1767	104	11	,	,	PUNCT
ejpam-1767	104	12	for	for	ADP
ejpam-1767	104	13	any	any	DET
ejpam-1767	104	14	positive	positive	ADJ
ejpam-1767	104	15	integer	integer	NOUN
ejpam-1767	104	16	m	m	NOUN
ejpam-1767	104	17	and	and	CCONJ
ejpam-1767	104	18	any	any	DET
ejpam-1767	104	19	finite	finite	NOUN
ejpam-1767	104	20	subset	subset	VERB
ejpam-1767	104	21	i	i	PRON
ejpam-1767	104	22	⊂	⊂	PROPN
ejpam-1767	104	23	n	n	PRON
ejpam-1767	104	24	\m	\m	NOUN
ejpam-1767	104	25	,	,	PUNCT
ejpam-1767	104	26	s	s	PART
ejpam-1767	104	27	=	=	SYM
ejpam-1767	104	28	ls(0	ls(0	PROPN
ejpam-1767	104	29	)	)	PUNCT
ejpam-1767	104	30	=	=	SYM
ejpam-1767	104	31	ls(xmr∩	ls(xmr∩	ADJ
ejpam-1767	104	32	∑	∑	PUNCT
ejpam-1767	104	33	i∈i	i∈i	ADJ
ejpam-1767	104	34	x	x	SYM
ejpam-1767	104	35	ir	ir	ADJ
ejpam-1767	104	36	)	)	PUNCT
ejpam-1767	104	37	=	=	SYM
ejpam-1767	104	38	ls(xm	ls(xm	PROPN
ejpam-1767	104	39	)	)	PUNCT
ejpam-1767	105	1	+	+	CCONJ
ejpam-1767	105	2	ls	ls	ADJ
ejpam-1767	105	3	(	(	PUNCT
ejpam-1767	105	4	∑	∑	ADP
ejpam-1767	105	5	i∈i	i∈i	ADJ
ejpam-1767	105	6	x	x	SYM
ejpam-1767	105	7	ir	ir	ADJ
ejpam-1767	105	8	)	)	PUNCT
ejpam-1767	105	9	=	=	SYM
ejpam-1767	105	10	ls(xm	ls(xm	PROPN
ejpam-1767	105	11	)	)	PUNCT
ejpam-1767	106	1	+	+	ADP
ejpam-1767	106	2	∩i∈i	∩i∈i	ADJ
ejpam-1767	106	3	ls(x	ls(x	X
ejpam-1767	106	4	i	i	NOUN
ejpam-1767	106	5	)	)	PUNCT
ejpam-1767	106	6	.	.	PUNCT
ejpam-1767	107	1	z.	z.	PROPN
ejpam-1767	107	2	zhanmin	zhanmin	PROPN
ejpam-1767	107	3	/	/	SYM
ejpam-1767	107	4	eur	eur	PROPN
ejpam-1767	107	5	.	.	PUNCT
ejpam-1767	108	1	j.	j.	PROPN
ejpam-1767	108	2	pure	pure	PROPN
ejpam-1767	108	3	appl	appl	PROPN
ejpam-1767	108	4	.	.	PROPN
ejpam-1767	108	5	math	math	PROPN
ejpam-1767	108	6	,	,	PUNCT
ejpam-1767	108	7	6	6	NUM
ejpam-1767	108	8	(	(	PUNCT
ejpam-1767	108	9	2013	2013	NUM
ejpam-1767	108	10	)	)	PUNCT
ejpam-1767	108	11	,	,	PUNCT
ejpam-1767	108	12	119	119	NUM
ejpam-1767	108	13	-	-	SYM
ejpam-1767	108	14	125	125	NUM
ejpam-1767	108	15	122	122	NUM
ejpam-1767	108	16	thus	thus	ADV
ejpam-1767	108	17	ls(x	ls(x	X
ejpam-1767	108	18	i	i	NOUN
ejpam-1767	108	19	)	)	PUNCT
ejpam-1767	108	20	,	,	PUNCT
ejpam-1767	108	21	i	i	PRON
ejpam-1767	108	22	=	=	NOUN
ejpam-1767	108	23	1	1	NUM
ejpam-1767	108	24	,	,	PUNCT
ejpam-1767	108	25	2,3	2,3	NUM
ejpam-1767	108	26	,	,	PUNCT
ejpam-1767	108	27	·	·	PUNCT
ejpam-1767	108	28	·	·	PUNCT
ejpam-1767	108	29	·	·	PUNCT
ejpam-1767	108	30	is	be	AUX
ejpam-1767	108	31	an	an	DET
ejpam-1767	108	32	infinite	infinite	ADJ
ejpam-1767	108	33	coindependent	coindependent	NOUN
ejpam-1767	108	34	family	family	NOUN
ejpam-1767	108	35	of	of	ADP
ejpam-1767	108	36	submodules	submodule	NOUN
ejpam-1767	108	37	of	of	ADP
ejpam-1767	108	38	ss	ss	PROPN
ejpam-1767	108	39	.	.	PUNCT
ejpam-1767	109	1	by	by	ADP
ejpam-1767	109	2	lemma	lemma	PROPN
ejpam-1767	109	3	6	6	NUM
ejpam-1767	109	4	,	,	PUNCT
ejpam-1767	109	5	s	s	VERB
ejpam-1767	109	6	is	be	AUX
ejpam-1767	109	7	not	not	PART
ejpam-1767	109	8	semilocal	semilocal	ADJ
ejpam-1767	109	9	,	,	PUNCT
ejpam-1767	109	10	a	a	DET
ejpam-1767	109	11	contradiction	contradiction	NOUN
ejpam-1767	109	12	.	.	PUNCT
ejpam-1767	110	1	(	(	PUNCT
ejpam-1767	110	2	2)⇒	2)⇒	NUM
ejpam-1767	110	3	(	(	PUNCT
ejpam-1767	110	4	1	1	NUM
ejpam-1767	110	5	)	)	PUNCT
ejpam-1767	110	6	.	.	PUNCT
ejpam-1767	111	1	by	by	ADP
ejpam-1767	111	2	lemma	lemma	PROPN
ejpam-1767	111	3	3	3	NUM
ejpam-1767	111	4	.	.	PUNCT
ejpam-1767	112	1	furthermore	furthermore	ADV
ejpam-1767	112	2	,	,	PUNCT
ejpam-1767	112	3	if	if	SCONJ
ejpam-1767	112	4	m	m	NOUN
ejpam-1767	112	5	is	be	AUX
ejpam-1767	112	6	a	a	DET
ejpam-1767	112	7	c1	c1	NOUN
ejpam-1767	112	8	module	module	NOUN
ejpam-1767	112	9	,	,	PUNCT
ejpam-1767	112	10	then	then	ADV
ejpam-1767	112	11	since	since	SCONJ
ejpam-1767	112	12	it	it	PRON
ejpam-1767	112	13	is	be	AUX
ejpam-1767	112	14	a	a	DET
ejpam-1767	112	15	c2	c2	PROPN
ejpam-1767	112	16	module	module	NOUN
ejpam-1767	112	17	by	by	ADP
ejpam-1767	112	18	lemma	lemma	PROPN
ejpam-1767	112	19	4	4	NUM
ejpam-1767	112	20	and	and	CCONJ
ejpam-1767	112	21	w	w	PROPN
ejpam-1767	112	22	(	(	PUNCT
ejpam-1767	112	23	s	s	X
ejpam-1767	112	24	)	)	PUNCT
ejpam-1767	112	25	=	=	SYM
ejpam-1767	112	26	j(s	j(s	NOUN
ejpam-1767	112	27	)	)	PUNCT
ejpam-1767	112	28	by	by	ADP
ejpam-1767	112	29	lemma	lemma	PROPN
ejpam-1767	112	30	2(2	2(2	NUM
ejpam-1767	112	31	)	)	PUNCT
ejpam-1767	112	32	,	,	PUNCT
ejpam-1767	112	33	we	we	PRON
ejpam-1767	112	34	have	have	VERB
ejpam-1767	112	35	(	(	PUNCT
ejpam-1767	112	36	1)⇔	1)⇔	NUM
ejpam-1767	112	37	(	(	PUNCT
ejpam-1767	112	38	3	3	NUM
ejpam-1767	112	39	)	)	PUNCT
ejpam-1767	112	40	by	by	ADP
ejpam-1767	112	41	lemma	lemma	PROPN
ejpam-1767	112	42	5	5	NUM
ejpam-1767	112	43	.	.	PUNCT
ejpam-1767	113	1	the	the	DET
ejpam-1767	113	2	equivalence	equivalence	NOUN
ejpam-1767	113	3	of	of	ADP
ejpam-1767	113	4	(	(	PUNCT
ejpam-1767	113	5	1	1	NUM
ejpam-1767	113	6	)	)	PUNCT
ejpam-1767	113	7	and	and	CCONJ
ejpam-1767	113	8	(	(	PUNCT
ejpam-1767	113	9	2	2	X
ejpam-1767	113	10	)	)	PUNCT
ejpam-1767	113	11	in	in	ADP
ejpam-1767	113	12	the	the	DET
ejpam-1767	113	13	next	next	ADJ
ejpam-1767	113	14	corollary	corollary	NOUN
ejpam-1767	113	15	3	3	NUM
ejpam-1767	113	16	appeared	appear	VERB
ejpam-1767	113	17	in	in	ADP
ejpam-1767	113	18	[	[	X
ejpam-1767	113	19	8	8	NUM
ejpam-1767	113	20	,	,	PUNCT
ejpam-1767	113	21	corollary	corollary	ADJ
ejpam-1767	113	22	4.5	4.5	NUM
ejpam-1767	113	23	]	]	PUNCT
ejpam-1767	113	24	.	.	PUNCT
ejpam-1767	114	1	corollary	corollary	ADJ
ejpam-1767	114	2	3	3	X
ejpam-1767	114	3	.	.	PUNCT
ejpam-1767	115	1	let	let	VERB
ejpam-1767	115	2	r	r	PRON
ejpam-1767	115	3	be	be	AUX
ejpam-1767	115	4	a	a	DET
ejpam-1767	115	5	right	right	ADJ
ejpam-1767	115	6	f	f	NOUN
ejpam-1767	115	7	-	-	PUNCT
ejpam-1767	115	8	injective	injective	ADJ
ejpam-1767	115	9	ring	ring	NOUN
ejpam-1767	115	10	.	.	PUNCT
ejpam-1767	116	1	then	then	ADV
ejpam-1767	116	2	the	the	DET
ejpam-1767	116	3	following	follow	VERB
ejpam-1767	116	4	conditions	condition	NOUN
ejpam-1767	116	5	are	be	AUX
ejpam-1767	116	6	equivalent	equivalent	ADJ
ejpam-1767	116	7	:	:	PUNCT
ejpam-1767	116	8	(	(	PUNCT
ejpam-1767	116	9	1	1	X
ejpam-1767	116	10	)	)	PUNCT
ejpam-1767	116	11	r	r	NOUN
ejpam-1767	116	12	is	be	AUX
ejpam-1767	116	13	semilocal	semilocal	ADJ
ejpam-1767	116	14	.	.	PUNCT
ejpam-1767	117	1	(	(	PUNCT
ejpam-1767	117	2	2	2	X
ejpam-1767	117	3	)	)	PUNCT
ejpam-1767	117	4	r	r	NOUN
ejpam-1767	117	5	is	be	AUX
ejpam-1767	117	6	right	right	ADJ
ejpam-1767	117	7	finite	finite	NOUN
ejpam-1767	117	8	dimensional	dimensional	ADJ
ejpam-1767	117	9	.	.	PUNCT
ejpam-1767	118	1	furthermore	furthermore	ADV
ejpam-1767	118	2	,	,	PUNCT
ejpam-1767	118	3	if	if	SCONJ
ejpam-1767	118	4	r	r	NOUN
ejpam-1767	118	5	is	be	AUX
ejpam-1767	118	6	a	a	DET
ejpam-1767	118	7	right	right	ADJ
ejpam-1767	118	8	cs	cs	PROPN
ejpam-1767	118	9	ring	ring	NOUN
ejpam-1767	118	10	,	,	PUNCT
ejpam-1767	118	11	then	then	ADV
ejpam-1767	118	12	these	these	DET
ejpam-1767	118	13	conditions	condition	NOUN
ejpam-1767	118	14	are	be	AUX
ejpam-1767	118	15	equivalent	equivalent	ADJ
ejpam-1767	118	16	to	to	ADP
ejpam-1767	118	17	:	:	PUNCT
ejpam-1767	118	18	(	(	PUNCT
ejpam-1767	118	19	3	3	X
ejpam-1767	118	20	)	)	PUNCT
ejpam-1767	118	21	r	r	NOUN
ejpam-1767	118	22	is	be	AUX
ejpam-1767	118	23	semiperfect	semiperfect	ADJ
ejpam-1767	118	24	.	.	PUNCT
ejpam-1767	119	1	theorem	theorem	NOUN
ejpam-1767	119	2	2	2	NUM
ejpam-1767	119	3	.	.	PUNCT
ejpam-1767	120	1	let	let	VERB
ejpam-1767	120	2	mr	mr	PROPN
ejpam-1767	120	3	be	be	AUX
ejpam-1767	120	4	a	a	DET
ejpam-1767	120	5	fq	fq	ADJ
ejpam-1767	120	6	-	-	ADJ
ejpam-1767	120	7	injective	injective	ADJ
ejpam-1767	120	8	kasch	kasch	ADJ
ejpam-1767	120	9	module	module	NOUN
ejpam-1767	120	10	with	with	ADP
ejpam-1767	120	11	s	s	NOUN
ejpam-1767	120	12	=	=	SYM
ejpam-1767	120	13	end(mr	end(mr	PROPN
ejpam-1767	120	14	)	)	PUNCT
ejpam-1767	120	15	,	,	PUNCT
ejpam-1767	120	16	then	then	ADV
ejpam-1767	120	17	(	(	PUNCT
ejpam-1767	120	18	1	1	X
ejpam-1767	120	19	)	)	PUNCT
ejpam-1767	120	20	rm	rm	NOUN
ejpam-1767	120	21	ls(k	ls(k	PUNCT
ejpam-1767	120	22	)	)	PUNCT
ejpam-1767	121	1	=	=	SYM
ejpam-1767	121	2	k	k	PROPN
ejpam-1767	121	3	for	for	ADP
ejpam-1767	121	4	every	every	DET
ejpam-1767	121	5	finitely	finitely	ADV
ejpam-1767	121	6	generarated	generarate	VERB
ejpam-1767	121	7	submodule	submodule	NOUN
ejpam-1767	121	8	kr	kr	PROPN
ejpam-1767	121	9	of	of	ADP
ejpam-1767	121	10	mr	mr	PROPN
ejpam-1767	121	11	.	.	PROPN
ejpam-1767	121	12	(	(	PUNCT
ejpam-1767	121	13	2	2	X
ejpam-1767	121	14	)	)	PUNCT
ejpam-1767	121	15	sm	sm	PROPN
ejpam-1767	121	16	is	be	AUX
ejpam-1767	121	17	simple	simple	ADJ
ejpam-1767	121	18	if	if	SCONJ
ejpam-1767	121	19	and	and	CCONJ
ejpam-1767	121	20	only	only	ADV
ejpam-1767	121	21	if	if	SCONJ
ejpam-1767	121	22	mr	mr	PROPN
ejpam-1767	121	23	is	be	AUX
ejpam-1767	121	24	simple	simple	ADJ
ejpam-1767	121	25	.	.	PUNCT
ejpam-1767	122	1	in	in	ADP
ejpam-1767	122	2	particular	particular	ADJ
ejpam-1767	122	3	,	,	PUNCT
ejpam-1767	122	4	soc(mr	soc(mr	NOUN
ejpam-1767	122	5	)	)	PUNCT
ejpam-1767	122	6	=	=	SYM
ejpam-1767	123	1	soc(s	soc(s	X
ejpam-1767	123	2	m	m	NOUN
ejpam-1767	123	3	)	)	PUNCT
ejpam-1767	123	4	.	.	PUNCT
ejpam-1767	124	1	(	(	PUNCT
ejpam-1767	124	2	3	3	X
ejpam-1767	124	3	)	)	PUNCT
ejpam-1767	124	4	lm	lm	NOUN
ejpam-1767	124	5	(	(	PUNCT
ejpam-1767	124	6	j(r))ãs	j(r))ãs	PROPN
ejpam-1767	124	7	m.	m.	PROPN
ejpam-1767	124	8	moreover	moreover	ADV
ejpam-1767	124	9	,	,	PUNCT
ejpam-1767	124	10	if	if	SCONJ
ejpam-1767	124	11	mr	mr	PROPN
ejpam-1767	124	12	is	be	AUX
ejpam-1767	124	13	finitely	finitely	ADV
ejpam-1767	124	14	generated	generate	VERB
ejpam-1767	124	15	,	,	PUNCT
ejpam-1767	124	16	then	then	ADV
ejpam-1767	124	17	(	(	PUNCT
ejpam-1767	124	18	4	4	NUM
ejpam-1767	124	19	)	)	PUNCT
ejpam-1767	124	20	ls(t	ls(t	PUNCT
ejpam-1767	124	21	)	)	PUNCT
ejpam-1767	124	22	is	be	AUX
ejpam-1767	124	23	a	a	DET
ejpam-1767	124	24	minimal	minimal	ADJ
ejpam-1767	124	25	left	leave	VERB
ejpam-1767	124	26	ideal	ideal	NOUN
ejpam-1767	124	27	of	of	ADP
ejpam-1767	124	28	s	s	PRON
ejpam-1767	124	29	for	for	ADP
ejpam-1767	124	30	any	any	DET
ejpam-1767	124	31	maximal	maximal	ADJ
ejpam-1767	124	32	submodule	submodule	NOUN
ejpam-1767	124	33	t	t	PROPN
ejpam-1767	124	34	of	of	ADP
ejpam-1767	124	35	m.	m.	NOUN
ejpam-1767	124	36	(	(	PUNCT
ejpam-1767	124	37	5	5	NUM
ejpam-1767	124	38	)	)	PUNCT
ejpam-1767	124	39	ls(rad(m))ãs	ls(rad(m))ãs	ADP
ejpam-1767	124	40	s.	s.	PROPN
ejpam-1767	124	41	proof	proof	PROPN
ejpam-1767	124	42	.	.	PUNCT
ejpam-1767	125	1	(	(	PUNCT
ejpam-1767	125	2	1	1	NUM
ejpam-1767	125	3	)	)	PUNCT
ejpam-1767	125	4	.	.	PUNCT
ejpam-1767	126	1	always	always	ADV
ejpam-1767	126	2	k	k	PROPN
ejpam-1767	126	3	⊆	⊆	NUM
ejpam-1767	126	4	rm	rm	PROPN
ejpam-1767	126	5	ls(k	ls(k	X
ejpam-1767	126	6	)	)	PUNCT
ejpam-1767	126	7	.	.	PUNCT
ejpam-1767	127	1	if	if	SCONJ
ejpam-1767	127	2	m	m	PROPN
ejpam-1767	127	3	∈	∈	PROPN
ejpam-1767	127	4	rm	rm	NOUN
ejpam-1767	127	5	ls(k	ls(k	X
ejpam-1767	127	6	)	)	PUNCT
ejpam-1767	128	1	−	−	PROPN
ejpam-1767	128	2	k	k	NOUN
ejpam-1767	128	3	,	,	PUNCT
ejpam-1767	128	4	let	let	VERB
ejpam-1767	129	1	k	k	PROPN
ejpam-1767	129	2	⊆	⊆	NUM
ejpam-1767	129	3	t	t	NOUN
ejpam-1767	129	4	⊆max	⊆max	ADV
ejpam-1767	129	5	(	(	PUNCT
ejpam-1767	129	6	mr	mr	PROPN
ejpam-1767	129	7	+	+	PROPN
ejpam-1767	129	8	k	k	NOUN
ejpam-1767	129	9	)	)	PUNCT
ejpam-1767	129	10	.	.	PUNCT
ejpam-1767	130	1	by	by	ADP
ejpam-1767	130	2	the	the	DET
ejpam-1767	130	3	kasch	kasch	PROPN
ejpam-1767	130	4	hypothesis	hypothesis	NOUN
ejpam-1767	130	5	,	,	PUNCT
ejpam-1767	130	6	let	let	VERB
ejpam-1767	130	7	σ	σ	PRON
ejpam-1767	130	8	:	:	PUNCT
ejpam-1767	130	9	(	(	PUNCT
ejpam-1767	130	10	mr+	mr+	PROPN
ejpam-1767	130	11	k)/t	k)/t	PROPN
ejpam-1767	130	12	→	→	PUNCT
ejpam-1767	130	13	m	m	AUX
ejpam-1767	130	14	be	be	AUX
ejpam-1767	130	15	monic	monic	ADJ
ejpam-1767	130	16	,	,	PUNCT
ejpam-1767	130	17	and	and	CCONJ
ejpam-1767	130	18	define	define	VERB
ejpam-1767	130	19	γ	γ	X
ejpam-1767	130	20	:	:	PUNCT
ejpam-1767	130	21	mr+	mr+	PROPN
ejpam-1767	130	22	k	k	PROPN
ejpam-1767	130	23	→	→	PUNCT
ejpam-1767	130	24	m	m	VERB
ejpam-1767	130	25	by	by	ADP
ejpam-1767	130	26	γ(x	γ(x	NOUN
ejpam-1767	130	27	)	)	PUNCT
ejpam-1767	130	28	=	=	SYM
ejpam-1767	130	29	σ(x+t	σ(x+t	PROPN
ejpam-1767	130	30	)	)	PUNCT
ejpam-1767	130	31	.	.	PUNCT
ejpam-1767	131	1	since	since	SCONJ
ejpam-1767	131	2	mr	mr	PROPN
ejpam-1767	131	3	is	be	AUX
ejpam-1767	131	4	fq	fq	NOUN
ejpam-1767	131	5	-	-	ADJ
ejpam-1767	131	6	injective	injective	ADJ
ejpam-1767	131	7	,	,	PUNCT
ejpam-1767	131	8	γ=	γ=	PROPN
ejpam-1767	131	9	s	s	PART
ejpam-1767	131	10	·	·	PUNCT
ejpam-1767	131	11	for	for	ADP
ejpam-1767	131	12	some	some	DET
ejpam-1767	131	13	s	s	PART
ejpam-1767	131	14	∈	∈	PROPN
ejpam-1767	131	15	s	s	NOUN
ejpam-1767	131	16	,	,	PUNCT
ejpam-1767	131	17	so	so	ADV
ejpam-1767	131	18	sk	sk	PROPN
ejpam-1767	131	19	=	=	SYM
ejpam-1767	131	20	γ(k	γ(k	PROPN
ejpam-1767	131	21	)	)	PUNCT
ejpam-1767	132	1	=	=	PUNCT
ejpam-1767	133	1	0	0	X
ejpam-1767	133	2	.	.	PUNCT
ejpam-1767	134	1	this	this	PRON
ejpam-1767	134	2	gives	give	VERB
ejpam-1767	134	3	sm	sm	PROPN
ejpam-1767	134	4	=	=	SYM
ejpam-1767	134	5	0	0	PUNCT
ejpam-1767	134	6	as	as	ADP
ejpam-1767	134	7	m	m	PROPN
ejpam-1767	134	8	∈	∈	PROPN
ejpam-1767	134	9	rm	rm	NOUN
ejpam-1767	134	10	ls(k	ls(k	X
ejpam-1767	134	11	)	)	PUNCT
ejpam-1767	134	12	.	.	PUNCT
ejpam-1767	135	1	but	but	CCONJ
ejpam-1767	135	2	sm	sm	PROPN
ejpam-1767	135	3	=	=	PUNCT
ejpam-1767	135	4	σ(m+	σ(m+	X
ejpam-1767	135	5	t	t	NOUN
ejpam-1767	135	6	)	)	PUNCT
ejpam-1767	135	7	6=	6=	ADP
ejpam-1767	135	8	0	0	PUNCT
ejpam-1767	136	1	because	because	SCONJ
ejpam-1767	136	2	m	m	PROPN
ejpam-1767	136	3	/∈	/∈	PROPN
ejpam-1767	136	4	t	t	PROPN
ejpam-1767	136	5	,	,	PUNCT
ejpam-1767	136	6	a	a	DET
ejpam-1767	136	7	contradiction	contradiction	NOUN
ejpam-1767	136	8	.	.	PUNCT
ejpam-1767	137	1	therefore	therefore	ADV
ejpam-1767	137	2	,	,	PUNCT
ejpam-1767	137	3	rm	rm	PROPN
ejpam-1767	137	4	ls(k	ls(k	X
ejpam-1767	137	5	)	)	PUNCT
ejpam-1767	138	1	=	=	SYM
ejpam-1767	138	2	k	k	PROPN
ejpam-1767	138	3	.	.	PUNCT
ejpam-1767	139	1	(	(	PUNCT
ejpam-1767	139	2	2	2	NUM
ejpam-1767	139	3	)	)	PUNCT
ejpam-1767	139	4	.	.	PUNCT
ejpam-1767	140	1	if	if	SCONJ
ejpam-1767	140	2	mr	mr	PROPN
ejpam-1767	140	3	is	be	AUX
ejpam-1767	140	4	simple	simple	ADJ
ejpam-1767	140	5	.	.	PUNCT
ejpam-1767	141	1	then	then	ADV
ejpam-1767	141	2	if	if	SCONJ
ejpam-1767	141	3	0	0	NUM
ejpam-1767	141	4	6=	6=	NUM
ejpam-1767	141	5	sm	sm	PROPN
ejpam-1767	141	6	∈	∈	PROPN
ejpam-1767	141	7	sm	sm	PROPN
ejpam-1767	141	8	,	,	PUNCT
ejpam-1767	141	9	define	define	VERB
ejpam-1767	141	10	γ	γ	X
ejpam-1767	141	11	:	:	PUNCT
ejpam-1767	141	12	mr→	mr→	NOUN
ejpam-1767	141	13	smr	smr	NOUN
ejpam-1767	141	14	by	by	ADP
ejpam-1767	141	15	γ(x	γ(x	NOUN
ejpam-1767	141	16	)	)	PUNCT
ejpam-1767	141	17	=	=	SYM
ejpam-1767	141	18	sx	sx	PROPN
ejpam-1767	141	19	.	.	PUNCT
ejpam-1767	142	1	then	then	ADV
ejpam-1767	142	2	γ	γ	PROPN
ejpam-1767	142	3	is	be	AUX
ejpam-1767	142	4	a	a	DET
ejpam-1767	142	5	right	right	ADJ
ejpam-1767	142	6	r	r	NOUN
ejpam-1767	142	7	-	-	PUNCT
ejpam-1767	142	8	isomorphism	isomorphism	NOUN
ejpam-1767	142	9	,	,	PUNCT
ejpam-1767	142	10	and	and	CCONJ
ejpam-1767	142	11	hence	hence	ADV
ejpam-1767	142	12	γ−1	γ−1	PROPN
ejpam-1767	142	13	extends	extend	VERB
ejpam-1767	142	14	to	to	ADP
ejpam-1767	142	15	an	an	DET
ejpam-1767	142	16	endomorphism	endomorphism	NOUN
ejpam-1767	142	17	of	of	ADP
ejpam-1767	142	18	m	m	PROPN
ejpam-1767	142	19	.	.	PUNCT
ejpam-1767	143	1	thus	thus	ADV
ejpam-1767	143	2	,	,	PUNCT
ejpam-1767	143	3	m=	m=	X
ejpam-1767	143	4	γ−1(sm	γ−1(sm	NOUN
ejpam-1767	143	5	)	)	PUNCT
ejpam-1767	143	6	=	=	SYM
ejpam-1767	143	7	α(sm	α(sm	PROPN
ejpam-1767	143	8	)	)	PUNCT
ejpam-1767	143	9	for	for	ADP
ejpam-1767	143	10	some	some	DET
ejpam-1767	143	11	α	α	NOUN
ejpam-1767	143	12	∈	∈	NOUN
ejpam-1767	143	13	s	s	NOUN
ejpam-1767	143	14	,	,	PUNCT
ejpam-1767	143	15	and	and	CCONJ
ejpam-1767	143	16	so	so	ADV
ejpam-1767	143	17	sm	sm	PROPN
ejpam-1767	143	18	is	be	AUX
ejpam-1767	143	19	simple	simple	ADJ
ejpam-1767	143	20	.	.	PUNCT
ejpam-1767	144	1	conversely	conversely	ADV
ejpam-1767	144	2	,	,	PUNCT
ejpam-1767	144	3	if	if	SCONJ
ejpam-1767	144	4	sm	sm	PROPN
ejpam-1767	144	5	is	be	AUX
ejpam-1767	144	6	simple	simple	ADJ
ejpam-1767	144	7	.	.	PUNCT
ejpam-1767	145	1	by	by	ADP
ejpam-1767	145	2	(	(	PUNCT
ejpam-1767	145	3	1	1	NUM
ejpam-1767	145	4	)	)	PUNCT
ejpam-1767	145	5	,	,	PUNCT
ejpam-1767	145	6	rm	rm	PROPN
ejpam-1767	145	7	ls(m	ls(m	X
ejpam-1767	145	8	)	)	PUNCT
ejpam-1767	145	9	=	=	SYM
ejpam-1767	145	10	mr	mr	PROPN
ejpam-1767	145	11	for	for	ADP
ejpam-1767	145	12	each	each	DET
ejpam-1767	145	13	m	m	PROPN
ejpam-1767	145	14	∈	∈	PROPN
ejpam-1767	145	15	m	m	NOUN
ejpam-1767	145	16	,	,	PUNCT
ejpam-1767	145	17	which	which	PRON
ejpam-1767	145	18	implies	imply	VERB
ejpam-1767	145	19	that	that	SCONJ
ejpam-1767	145	20	for	for	ADP
ejpam-1767	145	21	any	any	DET
ejpam-1767	145	22	m	m	NOUN
ejpam-1767	145	23	∈	∈	NOUN
ejpam-1767	145	24	m	m	NOUN
ejpam-1767	145	25	,	,	PUNCT
ejpam-1767	145	26	every	every	DET
ejpam-1767	145	27	s	s	NOUN
ejpam-1767	145	28	-	-	PUNCT
ejpam-1767	145	29	homomorphism	homomorphism	NOUN
ejpam-1767	145	30	from	from	ADP
ejpam-1767	145	31	sm	sm	PROPN
ejpam-1767	145	32	to	to	ADP
ejpam-1767	145	33	m	m	PROPN
ejpam-1767	145	34	is	be	AUX
ejpam-1767	145	35	right	right	ADJ
ejpam-1767	145	36	multiplication	multiplication	NOUN
ejpam-1767	145	37	by	by	ADP
ejpam-1767	145	38	an	an	DET
ejpam-1767	145	39	element	element	NOUN
ejpam-1767	145	40	of	of	ADP
ejpam-1767	145	41	r.	r.	PROPN
ejpam-1767	145	42	now	now	ADV
ejpam-1767	145	43	for	for	ADP
ejpam-1767	145	44	any	any	DET
ejpam-1767	145	45	0	0	NUM
ejpam-1767	145	46	6=	6=	NUM
ejpam-1767	145	47	ma	ma	PROPN
ejpam-1767	145	48	∈	∈	PROPN
ejpam-1767	145	49	mr	mr	PROPN
ejpam-1767	145	50	,	,	PUNCT
ejpam-1767	145	51	the	the	DET
ejpam-1767	145	52	right	right	ADJ
ejpam-1767	145	53	multiplication	multiplication	NOUN
ejpam-1767	145	54	·	·	PUNCT
ejpam-1767	145	55	a	a	PRON
ejpam-1767	145	56	:	:	PUNCT
ejpam-1767	145	57	sm	sm	PROPN
ejpam-1767	145	58	→	→	SYM
ejpam-1767	145	59	sma	sma	NOUN
ejpam-1767	145	60	is	be	AUX
ejpam-1767	145	61	a	a	DET
ejpam-1767	145	62	left	left	ADJ
ejpam-1767	145	63	s	s	NOUN
ejpam-1767	145	64	-	-	NOUN
ejpam-1767	145	65	isomorphism	isomorphism	NOUN
ejpam-1767	145	66	.	.	PUNCT
ejpam-1767	146	1	so	so	ADV
ejpam-1767	146	2	let	let	VERB
ejpam-1767	146	3	θ	θ	NOUN
ejpam-1767	146	4	:	:	PUNCT
ejpam-1767	146	5	sma	sma	PROPN
ejpam-1767	146	6	→	→	SYM
ejpam-1767	146	7	sm	sm	PROPN
ejpam-1767	146	8	be	be	AUX
ejpam-1767	146	9	its	its	PRON
ejpam-1767	146	10	inverse	inverse	NOUN
ejpam-1767	146	11	,	,	PUNCT
ejpam-1767	146	12	then	then	ADV
ejpam-1767	146	13	θ	θ	PROPN
ejpam-1767	146	14	is	be	AUX
ejpam-1767	146	15	a	a	DET
ejpam-1767	146	16	right	right	ADJ
ejpam-1767	146	17	multiplication	multiplication	NOUN
ejpam-1767	146	18	by	by	ADP
ejpam-1767	146	19	an	an	DET
ejpam-1767	146	20	element	element	NOUN
ejpam-1767	146	21	b	b	PROPN
ejpam-1767	146	22	of	of	ADP
ejpam-1767	146	23	r.	r.	PROPN
ejpam-1767	146	24	thus	thus	ADV
ejpam-1767	146	25	,	,	PUNCT
ejpam-1767	146	26	m	m	VERB
ejpam-1767	146	27	=	=	ADJ
ejpam-1767	146	28	θ(ma	θ(ma	ADJ
ejpam-1767	146	29	)	)	PUNCT
ejpam-1767	146	30	=	=	PUNCT
ejpam-1767	146	31	mab	mab	NOUN
ejpam-1767	146	32	∈	∈	PROPN
ejpam-1767	146	33	(	(	PUNCT
ejpam-1767	146	34	ma)r	ma)r	PROPN
ejpam-1767	146	35	.	.	PUNCT
ejpam-1767	147	1	hence	hence	ADV
ejpam-1767	147	2	mr	mr	PROPN
ejpam-1767	147	3	is	be	AUX
ejpam-1767	147	4	simple	simple	ADJ
ejpam-1767	147	5	.	.	PUNCT
ejpam-1767	148	1	(	(	PUNCT
ejpam-1767	148	2	3	3	NUM
ejpam-1767	148	3	)	)	PUNCT
ejpam-1767	148	4	.	.	PUNCT
ejpam-1767	149	1	let	let	VERB
ejpam-1767	149	2	0	0	NUM
ejpam-1767	150	1	6=	6=	ADP
ejpam-1767	150	2	m	m	PROPN
ejpam-1767	150	3	∈	∈	NOUN
ejpam-1767	150	4	m	m	VERB
ejpam-1767	150	5	.	.	PUNCT
ejpam-1767	151	1	suppose	suppose	VERB
ejpam-1767	151	2	that	that	SCONJ
ejpam-1767	151	3	t	t	PROPN
ejpam-1767	151	4	is	be	AUX
ejpam-1767	151	5	a	a	DET
ejpam-1767	151	6	maximal	maximal	ADJ
ejpam-1767	151	7	submodule	submodule	NOUN
ejpam-1767	151	8	of	of	ADP
ejpam-1767	151	9	mr	mr	PROPN
ejpam-1767	151	10	.	.	PROPN
ejpam-1767	151	11	by	by	ADP
ejpam-1767	151	12	the	the	DET
ejpam-1767	151	13	kasch	kasch	PROPN
ejpam-1767	151	14	hypothesis	hypothesis	NOUN
ejpam-1767	151	15	,	,	PUNCT
ejpam-1767	151	16	let	let	VERB
ejpam-1767	151	17	σ	σ	NOUN
ejpam-1767	151	18	:	:	PUNCT
ejpam-1767	151	19	mr	mr	PROPN
ejpam-1767	151	20	/	/	SYM
ejpam-1767	151	21	t	t	PROPN
ejpam-1767	151	22	→	→	SYM
ejpam-1767	151	23	m	m	AUX
ejpam-1767	151	24	be	be	AUX
ejpam-1767	151	25	monic	monic	ADJ
ejpam-1767	151	26	,	,	PUNCT
ejpam-1767	151	27	and	and	CCONJ
ejpam-1767	151	28	define	define	VERB
ejpam-1767	151	29	f	f	X
ejpam-1767	151	30	:	:	PUNCT
ejpam-1767	151	31	mr→	mr→	NOUN
ejpam-1767	151	32	m	m	VERB
ejpam-1767	151	33	by	by	ADP
ejpam-1767	151	34	f	f	PROPN
ejpam-1767	151	35	(	(	PUNCT
ejpam-1767	151	36	x	x	NOUN
ejpam-1767	151	37	)	)	PUNCT
ejpam-1767	151	38	=	=	SYM
ejpam-1767	152	1	σ(x	σ(x	PROPN
ejpam-1767	152	2	+	+	NUM
ejpam-1767	152	3	t	t	NOUN
ejpam-1767	152	4	)	)	PUNCT
ejpam-1767	152	5	.	.	PUNCT
ejpam-1767	153	1	since	since	SCONJ
ejpam-1767	153	2	mr	mr	PROPN
ejpam-1767	153	3	is	be	AUX
ejpam-1767	153	4	fq	fq	NOUN
ejpam-1767	153	5	-	-	ADJ
ejpam-1767	153	6	injective	injective	ADJ
ejpam-1767	153	7	,	,	PUNCT
ejpam-1767	153	8	f	f	PROPN
ejpam-1767	153	9	=	=	SYM
ejpam-1767	153	10	s	s	PROPN
ejpam-1767	153	11	·	·	PUNCT
ejpam-1767	153	12	for	for	ADP
ejpam-1767	153	13	some	some	DET
ejpam-1767	153	14	s	s	PART
ejpam-1767	153	15	∈	∈	PROPN
ejpam-1767	153	16	s	s	NOUN
ejpam-1767	153	17	,	,	PUNCT
ejpam-1767	153	18	and	and	CCONJ
ejpam-1767	153	19	then	then	ADV
ejpam-1767	153	20	sm=	sm=	PROPN
ejpam-1767	153	21	f	f	X
ejpam-1767	153	22	(	(	PUNCT
ejpam-1767	153	23	m	m	PROPN
ejpam-1767	153	24	)	)	PUNCT
ejpam-1767	153	25	=	=	PUNCT
ejpam-1767	153	26	σ(m+	σ(m+	NUM
ejpam-1767	153	27	t	t	NOUN
ejpam-1767	153	28	)	)	PUNCT
ejpam-1767	153	29	6=	6=	ADP
ejpam-1767	153	30	0	0	X
ejpam-1767	153	31	.	.	PUNCT
ejpam-1767	154	1	but	but	CCONJ
ejpam-1767	154	2	z.	z.	PROPN
ejpam-1767	154	3	zhanmin	zhanmin	PROPN
ejpam-1767	154	4	/	/	SYM
ejpam-1767	154	5	eur	eur	PROPN
ejpam-1767	154	6	.	.	PUNCT
ejpam-1767	155	1	j.	j.	PROPN
ejpam-1767	155	2	pure	pure	PROPN
ejpam-1767	155	3	appl	appl	PROPN
ejpam-1767	155	4	.	.	PROPN
ejpam-1767	155	5	math	math	PROPN
ejpam-1767	155	6	,	,	PUNCT
ejpam-1767	155	7	6	6	NUM
ejpam-1767	155	8	(	(	PUNCT
ejpam-1767	155	9	2013	2013	NUM
ejpam-1767	155	10	)	)	PUNCT
ejpam-1767	155	11	,	,	PUNCT
ejpam-1767	155	12	119	119	NUM
ejpam-1767	155	13	-	-	SYM
ejpam-1767	155	14	125	125	NUM
ejpam-1767	155	15	123	123	NUM
ejpam-1767	155	16	smj(r	smj(r	PROPN
ejpam-1767	155	17	)	)	PUNCT
ejpam-1767	155	18	=	=	SYM
ejpam-1767	156	1	f	f	PROPN
ejpam-1767	156	2	(	(	PUNCT
ejpam-1767	156	3	m)j(r	m)j(r	PROPN
ejpam-1767	156	4	)	)	PUNCT
ejpam-1767	156	5	=	=	PUNCT
ejpam-1767	156	6	σ(m+	σ(m+	NUM
ejpam-1767	156	7	t	t	NOUN
ejpam-1767	156	8	)	)	PUNCT
ejpam-1767	156	9	j(r	j(r	PROPN
ejpam-1767	156	10	)	)	PUNCT
ejpam-1767	157	1	=	=	SYM
ejpam-1767	158	1	0	0	NUM
ejpam-1767	158	2	,	,	PUNCT
ejpam-1767	158	3	so	so	ADV
ejpam-1767	158	4	0	0	NUM
ejpam-1767	158	5	6=	6=	NUM
ejpam-1767	158	6	sm	sm	PROPN
ejpam-1767	158	7	∈	∈	PROPN
ejpam-1767	158	8	sm∩	sm∩	PROPN
ejpam-1767	158	9	lm	lm	PROPN
ejpam-1767	158	10	(	(	PUNCT
ejpam-1767	158	11	j(r	j(r	PROPN
ejpam-1767	158	12	)	)	PUNCT
ejpam-1767	158	13	)	)	PUNCT
ejpam-1767	158	14	.	.	PUNCT
ejpam-1767	159	1	therefore	therefore	ADV
ejpam-1767	159	2	,	,	PUNCT
ejpam-1767	159	3	lm	lm	INTJ
ejpam-1767	159	4	(	(	PUNCT
ejpam-1767	159	5	j(r))ã	j(r))ã	NOUN
ejpam-1767	159	6	s	s	NOUN
ejpam-1767	159	7	m	m	NOUN
ejpam-1767	159	8	.	.	PUNCT
ejpam-1767	160	1	(	(	PUNCT
ejpam-1767	160	2	4	4	NUM
ejpam-1767	160	3	)	)	PUNCT
ejpam-1767	160	4	.	.	PUNCT
ejpam-1767	161	1	let	let	VERB
ejpam-1767	161	2	t	t	NOUN
ejpam-1767	161	3	be	be	AUX
ejpam-1767	161	4	any	any	DET
ejpam-1767	161	5	maximal	maximal	ADJ
ejpam-1767	161	6	submodule	submodule	NOUN
ejpam-1767	161	7	of	of	ADP
ejpam-1767	161	8	m.	m.	NOUN
ejpam-1767	161	9	since	since	SCONJ
ejpam-1767	161	10	mr	mr	PROPN
ejpam-1767	161	11	is	be	AUX
ejpam-1767	161	12	kasch	kasch	PROPN
ejpam-1767	161	13	,	,	PUNCT
ejpam-1767	161	14	there	there	PRON
ejpam-1767	161	15	exists	exist	VERB
ejpam-1767	161	16	a	a	DET
ejpam-1767	161	17	monomorphism	monomorphism	NOUN
ejpam-1767	161	18	ϕ	ϕ	X
ejpam-1767	161	19	:	:	PUNCT
ejpam-1767	161	20	m	m	PROPN
ejpam-1767	161	21	/	/	SYM
ejpam-1767	161	22	t	t	PROPN
ejpam-1767	161	23	→	→	SYM
ejpam-1767	161	24	m	m	VERB
ejpam-1767	161	25	.	.	PUNCT
ejpam-1767	162	1	define	define	VERB
ejpam-1767	162	2	α	α	NOUN
ejpam-1767	162	3	:	:	PUNCT
ejpam-1767	162	4	m	m	VERB
ejpam-1767	162	5	→	→	SYM
ejpam-1767	162	6	m	m	VERB
ejpam-1767	162	7	by	by	ADP
ejpam-1767	162	8	x	x	PROPN
ejpam-1767	162	9	7→	7→	PROPN
ejpam-1767	162	10	ϕ(x	ϕ(x	PROPN
ejpam-1767	162	11	+	+	X
ejpam-1767	162	12	t	t	NOUN
ejpam-1767	162	13	)	)	PUNCT
ejpam-1767	162	14	.	.	PUNCT
ejpam-1767	163	1	then	then	ADV
ejpam-1767	163	2	0	0	NUM
ejpam-1767	163	3	6=	6=	NUM
ejpam-1767	163	4	α	α	PROPN
ejpam-1767	163	5	∈	∈	PROPN
ejpam-1767	163	6	s	s	NOUN
ejpam-1767	163	7	,	,	PUNCT
ejpam-1767	163	8	αt	αt	PROPN
ejpam-1767	163	9	=	=	SYM
ejpam-1767	163	10	ϕ(0	ϕ(0	PROPN
ejpam-1767	163	11	)	)	PUNCT
ejpam-1767	163	12	=	=	PUNCT
ejpam-1767	163	13	0	0	NUM
ejpam-1767	163	14	,	,	PUNCT
ejpam-1767	163	15	and	and	CCONJ
ejpam-1767	163	16	so	so	ADV
ejpam-1767	163	17	ls(t	ls(t	PUNCT
ejpam-1767	163	18	)	)	PUNCT
ejpam-1767	164	1	6=	6=	ADP
ejpam-1767	164	2	0	0	X
ejpam-1767	164	3	.	.	PUNCT
ejpam-1767	165	1	for	for	ADP
ejpam-1767	165	2	any	any	DET
ejpam-1767	165	3	0	0	NUM
ejpam-1767	165	4	6=	6=	NUM
ejpam-1767	165	5	s	s	X
ejpam-1767	165	6	∈	∈	PROPN
ejpam-1767	165	7	ls(t	ls(t	PUNCT
ejpam-1767	165	8	)	)	PUNCT
ejpam-1767	165	9	,	,	PUNCT
ejpam-1767	165	10	we	we	PRON
ejpam-1767	165	11	have	have	VERB
ejpam-1767	165	12	t	t	PROPN
ejpam-1767	165	13	⊆	⊆	NUM
ejpam-1767	165	14	ker(s	ker(s	PROPN
ejpam-1767	165	15	)	)	PUNCT
ejpam-1767	165	16	6=	6=	ADP
ejpam-1767	165	17	m	m	PROPN
ejpam-1767	165	18	,	,	PUNCT
ejpam-1767	165	19	and	and	CCONJ
ejpam-1767	165	20	so	so	ADV
ejpam-1767	165	21	ker(s	ker(s	PROPN
ejpam-1767	165	22	)	)	PUNCT
ejpam-1767	165	23	=	=	SYM
ejpam-1767	165	24	t	t	NOUN
ejpam-1767	165	25	by	by	ADP
ejpam-1767	165	26	the	the	DET
ejpam-1767	165	27	maximality	maximality	NOUN
ejpam-1767	165	28	of	of	ADP
ejpam-1767	165	29	t	t	PROPN
ejpam-1767	165	30	.	.	PUNCT
ejpam-1767	166	1	it	it	PRON
ejpam-1767	166	2	follows	follow	VERB
ejpam-1767	166	3	that	that	PRON
ejpam-1767	166	4	ls(t	ls(t	PUNCT
ejpam-1767	166	5	)	)	PUNCT
ejpam-1767	167	1	=	=	SYM
ejpam-1767	167	2	ls(ker(s	ls(ker(s	NOUN
ejpam-1767	167	3	)	)	PUNCT
ejpam-1767	167	4	)	)	PUNCT
ejpam-1767	168	1	=	=	PUNCT
ejpam-1767	168	2	ss	ss	PROPN
ejpam-1767	168	3	by	by	ADP
ejpam-1767	168	4	lemma	lemma	PROPN
ejpam-1767	168	5	2(1	2(1	NUM
ejpam-1767	168	6	)	)	PUNCT
ejpam-1767	168	7	.	.	PUNCT
ejpam-1767	169	1	therefore	therefore	ADV
ejpam-1767	169	2	,	,	PUNCT
ejpam-1767	169	3	ls(t	ls(t	PUNCT
ejpam-1767	169	4	)	)	PUNCT
ejpam-1767	169	5	is	be	AUX
ejpam-1767	169	6	a	a	DET
ejpam-1767	169	7	minimal	minimal	ADJ
ejpam-1767	169	8	left	leave	VERB
ejpam-1767	169	9	ideal	ideal	NOUN
ejpam-1767	169	10	of	of	ADP
ejpam-1767	169	11	s.	s.	PROPN
ejpam-1767	169	12	(	(	PUNCT
ejpam-1767	169	13	5	5	NUM
ejpam-1767	169	14	)	)	PUNCT
ejpam-1767	169	15	.	.	PUNCT
ejpam-1767	170	1	if	if	SCONJ
ejpam-1767	170	2	0	0	NUM
ejpam-1767	170	3	6=	6=	ADP
ejpam-1767	170	4	a	a	DET
ejpam-1767	170	5	∈	∈	PROPN
ejpam-1767	170	6	s	s	NOUN
ejpam-1767	170	7	,	,	PUNCT
ejpam-1767	170	8	choose	choose	VERB
ejpam-1767	170	9	a	a	DET
ejpam-1767	170	10	maximal	maximal	ADJ
ejpam-1767	170	11	submodule	submodule	NOUN
ejpam-1767	170	12	t	t	PROPN
ejpam-1767	170	13	of	of	ADP
ejpam-1767	170	14	the	the	DET
ejpam-1767	170	15	right	right	ADJ
ejpam-1767	170	16	r	r	NOUN
ejpam-1767	170	17	-	-	PUNCT
ejpam-1767	170	18	module	module	NOUN
ejpam-1767	170	19	am	am	NOUN
ejpam-1767	170	20	.	.	PUNCT
ejpam-1767	171	1	since	since	SCONJ
ejpam-1767	171	2	m	m	PROPN
ejpam-1767	171	3	is	be	AUX
ejpam-1767	171	4	kasch	kasch	ADJ
ejpam-1767	171	5	,	,	PUNCT
ejpam-1767	171	6	there	there	PRON
ejpam-1767	171	7	exists	exist	VERB
ejpam-1767	171	8	a	a	DET
ejpam-1767	171	9	monomorphism	monomorphism	NOUN
ejpam-1767	171	10	f	f	X
ejpam-1767	171	11	:	:	PUNCT
ejpam-1767	171	12	am	be	AUX
ejpam-1767	171	13	/	/	SYM
ejpam-1767	171	14	t	t	PROPN
ejpam-1767	171	15	→	→	SYM
ejpam-1767	171	16	m	m	VERB
ejpam-1767	171	17	.	.	PUNCT
ejpam-1767	172	1	define	define	VERB
ejpam-1767	172	2	g	g	NOUN
ejpam-1767	172	3	:	:	PUNCT
ejpam-1767	172	4	am	am	VERB
ejpam-1767	172	5	→	→	SYM
ejpam-1767	172	6	m	m	NOUN
ejpam-1767	172	7	by	by	ADP
ejpam-1767	172	8	g(x	g(x	NOUN
ejpam-1767	172	9	)	)	PUNCT
ejpam-1767	173	1	=	=	SYM
ejpam-1767	173	2	f	f	PROPN
ejpam-1767	173	3	(	(	PUNCT
ejpam-1767	173	4	x+t	x+t	NUM
ejpam-1767	173	5	)	)	PUNCT
ejpam-1767	173	6	.	.	PUNCT
ejpam-1767	174	1	since	since	SCONJ
ejpam-1767	174	2	m	m	PROPN
ejpam-1767	174	3	is	be	AUX
ejpam-1767	174	4	fq	fq	NOUN
ejpam-1767	174	5	-	-	ADJ
ejpam-1767	174	6	injective	injective	ADJ
ejpam-1767	174	7	and	and	CCONJ
ejpam-1767	174	8	finitely	finitely	ADV
ejpam-1767	174	9	generated	generate	VERB
ejpam-1767	174	10	,	,	PUNCT
ejpam-1767	174	11	g	g	PROPN
ejpam-1767	174	12	=	=	SYM
ejpam-1767	174	13	s	s	PROPN
ejpam-1767	174	14	·	·	PUNCT
ejpam-1767	174	15	for	for	ADP
ejpam-1767	174	16	some	some	DET
ejpam-1767	174	17	s	s	NOUN
ejpam-1767	174	18	∈	∈	PROPN
ejpam-1767	174	19	s.	s.	PROPN
ejpam-1767	174	20	take	take	VERB
ejpam-1767	174	21	y	y	PROPN
ejpam-1767	174	22	∈	∈	PROPN
ejpam-1767	174	23	m	m	VERB
ejpam-1767	174	24	such	such	ADJ
ejpam-1767	174	25	that	that	SCONJ
ejpam-1767	174	26	a	a	DET
ejpam-1767	174	27	y	y	PROPN
ejpam-1767	174	28	/∈	/∈	PROPN
ejpam-1767	175	1	t	t	PROPN
ejpam-1767	175	2	,	,	PUNCT
ejpam-1767	175	3	then	then	ADV
ejpam-1767	175	4	sa	sa	PROPN
ejpam-1767	175	5	y	y	PROPN
ejpam-1767	175	6	=	=	PROPN
ejpam-1767	175	7	g(a	g(a	PROPN
ejpam-1767	175	8	y	y	PROPN
ejpam-1767	175	9	)	)	PUNCT
ejpam-1767	176	1	=	=	SYM
ejpam-1767	176	2	f	f	PROPN
ejpam-1767	176	3	(	(	PUNCT
ejpam-1767	176	4	a	a	DET
ejpam-1767	176	5	y	y	PROPN
ejpam-1767	176	6	+	+	PROPN
ejpam-1767	176	7	t	t	PROPN
ejpam-1767	176	8	)	)	PUNCT
ejpam-1767	176	9	6=	6=	ADP
ejpam-1767	176	10	0	0	NUM
ejpam-1767	176	11	,	,	PUNCT
ejpam-1767	176	12	and	and	CCONJ
ejpam-1767	176	13	hence	hence	ADV
ejpam-1767	176	14	sa	sa	VERB
ejpam-1767	176	15	6=	6=	ADP
ejpam-1767	176	16	0	0	X
ejpam-1767	176	17	.	.	PUNCT
ejpam-1767	177	1	if	if	SCONJ
ejpam-1767	177	2	a(rad(m	a(rad(m	NOUN
ejpam-1767	177	3	)	)	PUNCT
ejpam-1767	177	4	)	)	PUNCT
ejpam-1767	178	1	*	*	PUNCT
ejpam-1767	178	2	t	t	INTJ
ejpam-1767	178	3	,	,	PUNCT
ejpam-1767	178	4	then	then	ADV
ejpam-1767	178	5	a(rad(m	a(rad(m	ADJ
ejpam-1767	178	6	)	)	PUNCT
ejpam-1767	178	7	)	)	PUNCT
ejpam-1767	179	1	+	+	CCONJ
ejpam-1767	179	2	t	t	X
ejpam-1767	179	3	=	=	PUNCT
ejpam-1767	179	4	am	be	AUX
ejpam-1767	179	5	.	.	PUNCT
ejpam-1767	180	1	but	but	CCONJ
ejpam-1767	180	2	a(rad(m	a(rad(m	ADJ
ejpam-1767	180	3	)	)	PUNCT
ejpam-1767	180	4	)	)	PUNCT
ejpam-1767	181	1	<	<	X
ejpam-1767	181	2	<	<	X
ejpam-1767	181	3	am	be	AUX
ejpam-1767	181	4	because	because	SCONJ
ejpam-1767	181	5	m	m	NOUN
ejpam-1767	181	6	is	be	AUX
ejpam-1767	181	7	finitely	finitely	ADV
ejpam-1767	181	8	generated	generate	VERB
ejpam-1767	181	9	,	,	PUNCT
ejpam-1767	181	10	so	so	SCONJ
ejpam-1767	181	11	t	t	PROPN
ejpam-1767	181	12	=	=	SYM
ejpam-1767	181	13	am	be	AUX
ejpam-1767	181	14	,	,	PUNCT
ejpam-1767	181	15	a	a	DET
ejpam-1767	181	16	contradiction	contradiction	NOUN
ejpam-1767	181	17	.	.	PUNCT
ejpam-1767	182	1	thus	thus	ADV
ejpam-1767	182	2	a(rad(m	a(rad(m	ADJ
ejpam-1767	182	3	)	)	PUNCT
ejpam-1767	182	4	)	)	PUNCT
ejpam-1767	183	1	⊆	⊆	NUM
ejpam-1767	183	2	t	t	NOUN
ejpam-1767	183	3	,	,	PUNCT
ejpam-1767	183	4	and	and	CCONJ
ejpam-1767	183	5	then	then	ADV
ejpam-1767	183	6	(	(	PUNCT
ejpam-1767	183	7	sa)(rad(m	sa)(rad(m	NOUN
ejpam-1767	183	8	)	)	PUNCT
ejpam-1767	183	9	)	)	PUNCT
ejpam-1767	183	10	=	=	SYM
ejpam-1767	183	11	g(a(rad(m	g(a(rad(m	NOUN
ejpam-1767	183	12	)	)	PUNCT
ejpam-1767	183	13	)	)	PUNCT
ejpam-1767	183	14	)	)	PUNCT
ejpam-1767	184	1	=	=	SYM
ejpam-1767	184	2	f	f	PROPN
ejpam-1767	184	3	(	(	PUNCT
ejpam-1767	184	4	0	0	NUM
ejpam-1767	184	5	)	)	PUNCT
ejpam-1767	184	6	=	=	SYM
ejpam-1767	184	7	0	0	NUM
ejpam-1767	184	8	,	,	PUNCT
ejpam-1767	184	9	whence	whence	NOUN
ejpam-1767	184	10	0	0	NUM
ejpam-1767	184	11	6=	6=	NUM
ejpam-1767	184	12	sa	sa	PROPN
ejpam-1767	184	13	∈	∈	PROPN
ejpam-1767	184	14	sa	sa	PROPN
ejpam-1767	184	15	∩	∩	PROPN
ejpam-1767	184	16	ls(rad(m	ls(rad(m	PROPN
ejpam-1767	184	17	)	)	PUNCT
ejpam-1767	184	18	)	)	PUNCT
ejpam-1767	184	19	.	.	PUNCT
ejpam-1767	185	1	this	this	PRON
ejpam-1767	185	2	shows	show	VERB
ejpam-1767	185	3	that	that	SCONJ
ejpam-1767	185	4	ls(rad(m))ãs	ls(rad(m))ãs	ADV
ejpam-1767	185	5	s.	s.	PROPN
ejpam-1767	185	6	lemma	lemma	PROPN
ejpam-1767	185	7	7	7	X
ejpam-1767	185	8	.	.	PUNCT
ejpam-1767	185	9	let	let	VERB
ejpam-1767	185	10	mr	mr	PROPN
ejpam-1767	185	11	be	be	AUX
ejpam-1767	185	12	a	a	DET
ejpam-1767	185	13	finitely	finitely	ADV
ejpam-1767	185	14	generated	generate	VERB
ejpam-1767	185	15	kasch	kasch	ADJ
ejpam-1767	185	16	module	module	NOUN
ejpam-1767	185	17	with	with	ADP
ejpam-1767	185	18	s	s	NOUN
ejpam-1767	185	19	=	=	SYM
ejpam-1767	185	20	end(mr	end(mr	NUM
ejpam-1767	185	21	)	)	PUNCT
ejpam-1767	185	22	.	.	PUNCT
ejpam-1767	186	1	if	if	SCONJ
ejpam-1767	186	2	s	s	NOUN
ejpam-1767	186	3	is	be	AUX
ejpam-1767	186	4	left	leave	VERB
ejpam-1767	186	5	finite	finite	ADJ
ejpam-1767	186	6	dimensional	dimensional	ADJ
ejpam-1767	186	7	,	,	PUNCT
ejpam-1767	186	8	then	then	ADV
ejpam-1767	186	9	m	m	PROPN
ejpam-1767	186	10	/	/	SYM
ejpam-1767	186	11	radm	radm	PROPN
ejpam-1767	186	12	is	be	AUX
ejpam-1767	186	13	semisimple	semisimple	ADJ
ejpam-1767	186	14	.	.	PUNCT
ejpam-1767	187	1	proof	proof	NOUN
ejpam-1767	187	2	.	.	PUNCT
ejpam-1767	188	1	let	let	VERB
ejpam-1767	188	2	t	t	NOUN
ejpam-1767	188	3	be	be	AUX
ejpam-1767	188	4	any	any	DET
ejpam-1767	188	5	maximal	maximal	ADJ
ejpam-1767	188	6	submodule	submodule	NOUN
ejpam-1767	188	7	of	of	ADP
ejpam-1767	188	8	m	m	PROPN
ejpam-1767	188	9	.	.	PUNCT
ejpam-1767	189	1	since	since	SCONJ
ejpam-1767	189	2	mr	mr	PROPN
ejpam-1767	189	3	is	be	AUX
ejpam-1767	189	4	kasch	kasch	PROPN
ejpam-1767	189	5	,	,	PUNCT
ejpam-1767	189	6	there	there	PRON
ejpam-1767	189	7	exists	exist	VERB
ejpam-1767	189	8	a	a	DET
ejpam-1767	189	9	monomorphism	monomorphism	NOUN
ejpam-1767	189	10	ϕ	ϕ	X
ejpam-1767	189	11	:	:	PUNCT
ejpam-1767	189	12	m	m	PROPN
ejpam-1767	189	13	/	/	SYM
ejpam-1767	189	14	t	t	PROPN
ejpam-1767	189	15	→	→	SYM
ejpam-1767	189	16	m	m	VERB
ejpam-1767	189	17	.	.	PUNCT
ejpam-1767	190	1	define	define	VERB
ejpam-1767	190	2	α	α	NOUN
ejpam-1767	190	3	:	:	PUNCT
ejpam-1767	190	4	m	m	VERB
ejpam-1767	190	5	→	→	SYM
ejpam-1767	190	6	m	m	VERB
ejpam-1767	190	7	by	by	ADP
ejpam-1767	190	8	x	x	PROPN
ejpam-1767	190	9	7→	7→	PROPN
ejpam-1767	190	10	ϕ(x	ϕ(x	PROPN
ejpam-1767	190	11	+	+	X
ejpam-1767	190	12	t	t	NOUN
ejpam-1767	190	13	)	)	PUNCT
ejpam-1767	190	14	.	.	PUNCT
ejpam-1767	191	1	then	then	ADV
ejpam-1767	191	2	0	0	NUM
ejpam-1767	191	3	6=	6=	NUM
ejpam-1767	191	4	α	α	PROPN
ejpam-1767	191	5	∈	∈	PROPN
ejpam-1767	191	6	s	s	NOUN
ejpam-1767	191	7	,	,	PUNCT
ejpam-1767	191	8	αt	αt	PROPN
ejpam-1767	191	9	=	=	SYM
ejpam-1767	191	10	ϕ(0	ϕ(0	PROPN
ejpam-1767	191	11	)	)	PUNCT
ejpam-1767	191	12	=	=	PUNCT
ejpam-1767	191	13	0	0	NUM
ejpam-1767	191	14	,	,	PUNCT
ejpam-1767	191	15	and	and	CCONJ
ejpam-1767	191	16	so	so	ADV
ejpam-1767	191	17	ls(t	ls(t	PUNCT
ejpam-1767	191	18	)	)	PUNCT
ejpam-1767	191	19	6=	6=	ADP
ejpam-1767	191	20	0	0	X
ejpam-1767	191	21	.	.	PUNCT
ejpam-1767	192	1	let	let	VERB
ejpam-1767	192	2	ω	ω	NOUN
ejpam-1767	192	3	=	=	PRON
ejpam-1767	192	4	{	{	PUNCT
ejpam-1767	192	5	k	k	NOUN
ejpam-1767	193	1	|	|	NOUN
ejpam-1767	193	2	0	0	NUM
ejpam-1767	193	3	6=	6=	NUM
ejpam-1767	193	4	k	k	NOUN
ejpam-1767	193	5	=	=	X
ejpam-1767	193	6	ls(x	ls(x	X
ejpam-1767	193	7	)	)	PUNCT
ejpam-1767	193	8	for	for	ADP
ejpam-1767	193	9	some	some	DET
ejpam-1767	193	10	x	x	SYM
ejpam-1767	193	11	⊆	⊆	NUM
ejpam-1767	193	12	m	m	PRON
ejpam-1767	193	13	}	}	PUNCT
ejpam-1767	193	14	,	,	PUNCT
ejpam-1767	193	15	then	then	ADV
ejpam-1767	193	16	ls(t	ls(t	PUNCT
ejpam-1767	193	17	)	)	PUNCT
ejpam-1767	193	18	is	be	AUX
ejpam-1767	193	19	minimal	minimal	ADJ
ejpam-1767	193	20	in	in	ADP
ejpam-1767	193	21	ω	ω	NUM
ejpam-1767	193	22	for	for	ADP
ejpam-1767	193	23	any	any	DET
ejpam-1767	193	24	maximal	maximal	ADJ
ejpam-1767	193	25	submodule	submodule	NOUN
ejpam-1767	193	26	t	t	PROPN
ejpam-1767	193	27	of	of	ADP
ejpam-1767	193	28	m	m	PROPN
ejpam-1767	193	29	.	.	PUNCT
ejpam-1767	194	1	in	in	ADP
ejpam-1767	194	2	fact	fact	NOUN
ejpam-1767	194	3	,	,	PUNCT
ejpam-1767	194	4	if	if	SCONJ
ejpam-1767	194	5	ls(t	ls(t	PUNCT
ejpam-1767	194	6	)	)	PUNCT
ejpam-1767	194	7	⊇	⊇	NOUN
ejpam-1767	194	8	ls(x	ls(x	X
ejpam-1767	194	9	)	)	PUNCT
ejpam-1767	194	10	6=	6=	ADP
ejpam-1767	194	11	0	0	NUM
ejpam-1767	194	12	,	,	PUNCT
ejpam-1767	194	13	where	where	SCONJ
ejpam-1767	194	14	x	x	PUNCT
ejpam-1767	194	15	⊆	⊆	NUM
ejpam-1767	194	16	m	m	NOUN
ejpam-1767	194	17	,	,	PUNCT
ejpam-1767	194	18	then	then	ADV
ejpam-1767	194	19	t	t	PROPN
ejpam-1767	194	20	⊆	⊆	NUM
ejpam-1767	194	21	rm	rm	X
ejpam-1767	194	22	ls(x	ls(x	X
ejpam-1767	194	23	)	)	PUNCT
ejpam-1767	194	24	6=	6=	ADP
ejpam-1767	194	25	m	m	PROPN
ejpam-1767	194	26	.	.	PUNCT
ejpam-1767	195	1	so	so	ADV
ejpam-1767	195	2	t	t	PROPN
ejpam-1767	195	3	=	=	SYM
ejpam-1767	195	4	rm	rm	PROPN
ejpam-1767	195	5	ls(x	ls(x	X
ejpam-1767	195	6	)	)	PUNCT
ejpam-1767	195	7	,	,	PUNCT
ejpam-1767	195	8	and	and	CCONJ
ejpam-1767	195	9	hence	hence	ADV
ejpam-1767	195	10	ls(t	ls(t	PUNCT
ejpam-1767	195	11	)	)	PUNCT
ejpam-1767	196	1	=	=	SYM
ejpam-1767	196	2	ls(x	ls(x	NOUN
ejpam-1767	196	3	)	)	PUNCT
ejpam-1767	196	4	.	.	PUNCT
ejpam-1767	197	1	since	since	SCONJ
ejpam-1767	197	2	s	s	NOUN
ejpam-1767	197	3	is	be	AUX
ejpam-1767	197	4	left	leave	VERB
ejpam-1767	197	5	finite	finite	ADJ
ejpam-1767	197	6	dimensional	dimensional	ADJ
ejpam-1767	197	7	,	,	PUNCT
ejpam-1767	197	8	there	there	PRON
ejpam-1767	197	9	exist	exist	VERB
ejpam-1767	197	10	some	some	DET
ejpam-1767	197	11	minimal	minimal	ADJ
ejpam-1767	197	12	members	member	NOUN
ejpam-1767	197	13	i1	i1	PROPN
ejpam-1767	197	14	,	,	PUNCT
ejpam-1767	197	15	i2	i2	PROPN
ejpam-1767	197	16	,	,	PUNCT
ejpam-1767	197	17	·	·	PUNCT
ejpam-1767	197	18	·	·	PUNCT
ejpam-1767	197	19	·	·	PUNCT
ejpam-1767	197	20	,	,	PUNCT
ejpam-1767	197	21	in	in	ADP
ejpam-1767	197	22	in	in	ADP
ejpam-1767	197	23	ω	ω	NUM
ejpam-1767	197	24	such	such	ADJ
ejpam-1767	197	25	that	that	SCONJ
ejpam-1767	197	26	i	i	PRON
ejpam-1767	197	27	=	=	NOUN
ejpam-1767	197	28	⊕n	⊕n	NOUN
ejpam-1767	197	29	i=1	i=1	PROPN
ejpam-1767	197	30	ii	ii	PROPN
ejpam-1767	197	31	is	be	AUX
ejpam-1767	197	32	a	a	DET
ejpam-1767	197	33	maximal	maximal	ADJ
ejpam-1767	197	34	direct	direct	ADJ
ejpam-1767	197	35	sum	sum	NOUN
ejpam-1767	197	36	of	of	ADP
ejpam-1767	197	37	minimal	minimal	ADJ
ejpam-1767	197	38	members	member	NOUN
ejpam-1767	197	39	in	in	ADP
ejpam-1767	197	40	ω	ω	PROPN
ejpam-1767	197	41	.	.	PUNCT
ejpam-1767	198	1	now	now	ADV
ejpam-1767	198	2	we	we	PRON
ejpam-1767	198	3	establish	establish	VERB
ejpam-1767	198	4	the	the	DET
ejpam-1767	198	5	following	follow	VERB
ejpam-1767	198	6	claims	claim	NOUN
ejpam-1767	198	7	:	:	PUNCT
ejpam-1767	198	8	claim	claim	NOUN
ejpam-1767	198	9	1	1	X
ejpam-1767	198	10	.	.	X
ejpam-1767	198	11	rm	rm	PROPN
ejpam-1767	198	12	(	(	PUNCT
ejpam-1767	198	13	ii	ii	PROPN
ejpam-1767	198	14	)	)	PUNCT
ejpam-1767	198	15	is	be	AUX
ejpam-1767	198	16	a	a	DET
ejpam-1767	198	17	maximal	maximal	ADJ
ejpam-1767	198	18	submodule	submodule	NOUN
ejpam-1767	198	19	of	of	ADP
ejpam-1767	198	20	m	m	PROPN
ejpam-1767	198	21	for	for	ADP
ejpam-1767	198	22	each	each	DET
ejpam-1767	198	23	i.	i.	NOUN
ejpam-1767	198	24	since	since	SCONJ
ejpam-1767	198	25	m	m	PROPN
ejpam-1767	198	26	is	be	AUX
ejpam-1767	198	27	finitely	finitely	ADV
ejpam-1767	198	28	generated	generate	VERB
ejpam-1767	198	29	and	and	CCONJ
ejpam-1767	198	30	kasch	kasch	PROPN
ejpam-1767	198	31	,	,	PUNCT
ejpam-1767	198	32	rm	rm	PROPN
ejpam-1767	198	33	(	(	PUNCT
ejpam-1767	198	34	ii	ii	PROPN
ejpam-1767	198	35	)	)	PUNCT
ejpam-1767	198	36	⊆	⊆	NUM
ejpam-1767	198	37	ti	ti	NOUN
ejpam-1767	198	38	=	=	PROPN
ejpam-1767	198	39	rm	rm	PROPN
ejpam-1767	198	40	ls(ti	ls(ti	PROPN
ejpam-1767	198	41	)	)	PUNCT
ejpam-1767	198	42	for	for	ADP
ejpam-1767	198	43	some	some	DET
ejpam-1767	198	44	maximal	maximal	ADJ
ejpam-1767	198	45	submodule	submodule	NOUN
ejpam-1767	198	46	ti	ti	NOUN
ejpam-1767	198	47	.	.	PUNCT
ejpam-1767	199	1	thus	thus	ADV
ejpam-1767	199	2	ii	ii	PROPN
ejpam-1767	199	3	⊇	⊇	PROPN
ejpam-1767	199	4	ls	ls	PROPN
ejpam-1767	199	5	rm	rm	PROPN
ejpam-1767	199	6	ls(ti	ls(ti	PROPN
ejpam-1767	199	7	)	)	PUNCT
ejpam-1767	200	1	=	=	SYM
ejpam-1767	200	2	ls(ti	ls(ti	NOUN
ejpam-1767	200	3	)	)	PUNCT
ejpam-1767	201	1	6=	6=	ADP
ejpam-1767	201	2	0	0	NUM
ejpam-1767	201	3	,	,	PUNCT
ejpam-1767	201	4	and	and	CCONJ
ejpam-1767	201	5	so	so	ADV
ejpam-1767	201	6	ii	ii	NOUN
ejpam-1767	201	7	=	=	SYM
ejpam-1767	201	8	ls(ti	ls(ti	PROPN
ejpam-1767	201	9	)	)	PUNCT
ejpam-1767	201	10	by	by	ADP
ejpam-1767	201	11	the	the	DET
ejpam-1767	201	12	minimality	minimality	NOUN
ejpam-1767	201	13	of	of	ADP
ejpam-1767	201	14	ii	ii	PROPN
ejpam-1767	201	15	in	in	ADP
ejpam-1767	201	16	ω	ω	PROPN
ejpam-1767	201	17	.	.	PUNCT
ejpam-1767	202	1	now	now	ADV
ejpam-1767	202	2	we	we	PRON
ejpam-1767	202	3	choose	choose	VERB
ejpam-1767	202	4	0	0	NUM
ejpam-1767	202	5	6=	6=	NUM
ejpam-1767	202	6	ai	ai	PROPN
ejpam-1767	202	7	∈	∈	PROPN
ejpam-1767	202	8	ls(ti	ls(ti	NOUN
ejpam-1767	202	9	)	)	PUNCT
ejpam-1767	202	10	.	.	PUNCT
ejpam-1767	203	1	then	then	ADV
ejpam-1767	203	2	ti	ti	X
ejpam-1767	203	3	=	=	PROPN
ejpam-1767	203	4	rm	rm	PROPN
ejpam-1767	203	5	(	(	PUNCT
ejpam-1767	203	6	ai	ai	PROPN
ejpam-1767	203	7	)	)	PUNCT
ejpam-1767	203	8	,	,	PUNCT
ejpam-1767	203	9	and	and	CCONJ
ejpam-1767	203	10	hence	hence	ADV
ejpam-1767	203	11	rm	rm	PROPN
ejpam-1767	203	12	(	(	PUNCT
ejpam-1767	203	13	ii	ii	PROPN
ejpam-1767	203	14	)	)	PUNCT
ejpam-1767	203	15	=	=	SYM
ejpam-1767	203	16	rm	rm	PROPN
ejpam-1767	203	17	ls(ti	ls(ti	PROPN
ejpam-1767	203	18	)	)	PUNCT
ejpam-1767	204	1	=	=	SYM
ejpam-1767	204	2	rm	rm	PROPN
ejpam-1767	204	3	ls	ls	PROPN
ejpam-1767	204	4	rm	rm	PROPN
ejpam-1767	204	5	(	(	PUNCT
ejpam-1767	204	6	ai	ai	PROPN
ejpam-1767	204	7	)	)	PUNCT
ejpam-1767	204	8	=	=	SYM
ejpam-1767	204	9	rm	rm	PROPN
ejpam-1767	204	10	(	(	PUNCT
ejpam-1767	204	11	ai	ai	PROPN
ejpam-1767	204	12	)	)	PUNCT
ejpam-1767	204	13	=	=	SYM
ejpam-1767	204	14	ti	ti	NOUN
ejpam-1767	204	15	.	.	PUNCT
ejpam-1767	205	1	claim	claim	NOUN
ejpam-1767	205	2	2	2	NUM
ejpam-1767	205	3	.	.	PUNCT
ejpam-1767	206	1	radm	radm	NOUN
ejpam-1767	206	2	=	=	SYM
ejpam-1767	206	3	∩n	∩n	PROPN
ejpam-1767	206	4	i=1rm	i=1rm	X
ejpam-1767	206	5	(	(	PUNCT
ejpam-1767	206	6	ii	ii	NOUN
ejpam-1767	206	7	)	)	PUNCT
ejpam-1767	206	8	.	.	PUNCT
ejpam-1767	207	1	clearly	clearly	ADV
ejpam-1767	207	2	,	,	PUNCT
ejpam-1767	207	3	radm	radm	NOUN
ejpam-1767	207	4	⊆	⊆	NUM
ejpam-1767	207	5	∩n	∩n	PROPN
ejpam-1767	207	6	i=1rm	i=1rm	X
ejpam-1767	207	7	(	(	PUNCT
ejpam-1767	207	8	ii	ii	NOUN
ejpam-1767	207	9	)	)	PUNCT
ejpam-1767	207	10	.	.	PUNCT
ejpam-1767	208	1	if	if	SCONJ
ejpam-1767	208	2	t	t	PROPN
ejpam-1767	208	3	is	be	AUX
ejpam-1767	208	4	a	a	DET
ejpam-1767	208	5	maximal	maximal	ADJ
ejpam-1767	208	6	submodule	submodule	NOUN
ejpam-1767	208	7	of	of	ADP
ejpam-1767	208	8	m	m	PROPN
ejpam-1767	208	9	,	,	PUNCT
ejpam-1767	208	10	then	then	ADV
ejpam-1767	208	11	ls(t	ls(t	PUNCT
ejpam-1767	208	12	)	)	PUNCT
ejpam-1767	208	13	∩	∩	NOUN
ejpam-1767	208	14	i	i	PRON
ejpam-1767	208	15	6=	6=	PROPN
ejpam-1767	208	16	0	0	NUM
ejpam-1767	208	17	.	.	PUNCT
ejpam-1767	209	1	taking	take	VERB
ejpam-1767	209	2	some	some	DET
ejpam-1767	209	3	0	0	NUM
ejpam-1767	210	1	6=	6=	SYM
ejpam-1767	210	2	b	b	PROPN
ejpam-1767	210	3	∈	∈	PROPN
ejpam-1767	210	4	ls(t	ls(t	NUM
ejpam-1767	210	5	)	)	PUNCT
ejpam-1767	210	6	∩	∩	NOUN
ejpam-1767	210	7	i	i	PRON
ejpam-1767	210	8	,	,	PUNCT
ejpam-1767	210	9	we	we	PRON
ejpam-1767	210	10	have	have	VERB
ejpam-1767	210	11	t	t	PROPN
ejpam-1767	210	12	=	=	SYM
ejpam-1767	210	13	rm	rm	PROPN
ejpam-1767	210	14	(	(	PUNCT
ejpam-1767	210	15	b)⊇	b)⊇	NOUN
ejpam-1767	210	16	∩n	∩n	NOUN
ejpam-1767	210	17	i=1rm	i=1rm	X
ejpam-1767	210	18	(	(	PUNCT
ejpam-1767	210	19	ii	ii	NOUN
ejpam-1767	210	20	)	)	PUNCT
ejpam-1767	210	21	.	.	PUNCT
ejpam-1767	211	1	this	this	PRON
ejpam-1767	211	2	gives	give	VERB
ejpam-1767	211	3	that	that	DET
ejpam-1767	211	4	∩n	∩n	PROPN
ejpam-1767	211	5	i=1rm	i=1rm	NOUN
ejpam-1767	211	6	(	(	PUNCT
ejpam-1767	211	7	ii)⊆	ii)⊆	PROPN
ejpam-1767	211	8	radm	radm	NOUN
ejpam-1767	211	9	,	,	PUNCT
ejpam-1767	211	10	and	and	CCONJ
ejpam-1767	211	11	the	the	DET
ejpam-1767	211	12	claim	claim	NOUN
ejpam-1767	211	13	follows	follow	VERB
ejpam-1767	211	14	.	.	PUNCT
ejpam-1767	212	1	finally	finally	ADV
ejpam-1767	212	2	,	,	PUNCT
ejpam-1767	212	3	observing	observe	VERB
ejpam-1767	212	4	that	that	SCONJ
ejpam-1767	212	5	each	each	DET
ejpam-1767	212	6	m	m	PROPN
ejpam-1767	212	7	/	/	SYM
ejpam-1767	212	8	rm	rm	PROPN
ejpam-1767	212	9	(	(	PUNCT
ejpam-1767	212	10	ii	ii	PROPN
ejpam-1767	212	11	)	)	PUNCT
ejpam-1767	212	12	is	be	AUX
ejpam-1767	212	13	simple	simple	ADJ
ejpam-1767	212	14	by	by	ADP
ejpam-1767	212	15	claim	claim	NOUN
ejpam-1767	212	16	1	1	NUM
ejpam-1767	212	17	,	,	PUNCT
ejpam-1767	212	18	and	and	CCONJ
ejpam-1767	213	1	the	the	DET
ejpam-1767	213	2	mapping	mapping	NOUN
ejpam-1767	213	3	f	f	X
ejpam-1767	213	4	:	:	PUNCT
ejpam-1767	213	5	m	m	X
ejpam-1767	213	6	/	/	SYM
ejpam-1767	213	7	radm	radm	NOUN
ejpam-1767	213	8	→⊕n	→⊕n	NOUN
ejpam-1767	213	9	i=1m	i=1m	PROPN
ejpam-1767	213	10	/	/	SYM
ejpam-1767	213	11	rm	rm	PROPN
ejpam-1767	213	12	(	(	PUNCT
ejpam-1767	213	13	ii	ii	PROPN
ejpam-1767	213	14	)	)	PUNCT
ejpam-1767	213	15	;	;	PUNCT
ejpam-1767	213	16	m+	m+	NUM
ejpam-1767	213	17	radm	radm	NOUN
ejpam-1767	213	18	7→	7→	PROPN
ejpam-1767	214	1	(	(	PUNCT
ejpam-1767	214	2	m+	m+	NUM
ejpam-1767	214	3	rm	rm	PROPN
ejpam-1767	214	4	(	(	PUNCT
ejpam-1767	214	5	i1	i1	PROPN
ejpam-1767	214	6	)	)	PUNCT
ejpam-1767	214	7	,	,	PUNCT
ejpam-1767	214	8	·	·	PUNCT
ejpam-1767	214	9	·	·	PUNCT
ejpam-1767	214	10	·	·	PUNCT
ejpam-1767	214	11	,	,	PUNCT
ejpam-1767	214	12	m+	m+	NUM
ejpam-1767	214	13	rm	rm	NOUN
ejpam-1767	214	14	(	(	PUNCT
ejpam-1767	214	15	in	in	ADP
ejpam-1767	214	16	)	)	PUNCT
ejpam-1767	214	17	)	)	PUNCT
ejpam-1767	214	18	is	be	AUX
ejpam-1767	214	19	a	a	DET
ejpam-1767	214	20	monomorphism	monomorphism	NOUN
ejpam-1767	214	21	by	by	ADP
ejpam-1767	214	22	claim	claim	NOUN
ejpam-1767	214	23	2	2	NUM
ejpam-1767	214	24	,	,	PUNCT
ejpam-1767	214	25	we	we	PRON
ejpam-1767	214	26	have	have	VERB
ejpam-1767	214	27	that	that	PRON
ejpam-1767	214	28	m	m	PROPN
ejpam-1767	214	29	/	/	SYM
ejpam-1767	214	30	radm	radm	NOUN
ejpam-1767	214	31	is	be	AUX
ejpam-1767	214	32	semisimple	semisimple	ADJ
ejpam-1767	214	33	.	.	PUNCT
ejpam-1767	215	1	theorem	theorem	NOUN
ejpam-1767	215	2	3	3	X
ejpam-1767	215	3	.	.	PUNCT
ejpam-1767	216	1	let	let	VERB
ejpam-1767	216	2	mr	mr	PROPN
ejpam-1767	216	3	be	be	AUX
ejpam-1767	216	4	a	a	DET
ejpam-1767	216	5	finitely	finitely	ADV
ejpam-1767	216	6	generated	generate	VERB
ejpam-1767	216	7	and	and	CCONJ
ejpam-1767	216	8	fq	fq	PROPN
ejpam-1767	216	9	-	-	ADJ
ejpam-1767	216	10	injective	injective	ADJ
ejpam-1767	216	11	kasch	kasch	ADJ
ejpam-1767	216	12	module	module	NOUN
ejpam-1767	216	13	with	with	ADP
ejpam-1767	216	14	s	s	NOUN
ejpam-1767	216	15	=	=	SYM
ejpam-1767	216	16	end(mr	end(mr	NUM
ejpam-1767	216	17	)	)	PUNCT
ejpam-1767	216	18	.	.	PUNCT
ejpam-1767	217	1	then	then	ADV
ejpam-1767	217	2	the	the	DET
ejpam-1767	217	3	following	follow	VERB
ejpam-1767	217	4	conditions	condition	NOUN
ejpam-1767	217	5	are	be	AUX
ejpam-1767	217	6	equivalent	equivalent	ADJ
ejpam-1767	217	7	:	:	PUNCT
ejpam-1767	217	8	references	reference	NOUN
ejpam-1767	217	9	124	124	NUM
ejpam-1767	217	10	(	(	PUNCT
ejpam-1767	217	11	1	1	NUM
ejpam-1767	217	12	)	)	PUNCT
ejpam-1767	217	13	m	m	PROPN
ejpam-1767	217	14	/	/	SYM
ejpam-1767	217	15	rad(m	rad(m	NOUN
ejpam-1767	217	16	)	)	PUNCT
ejpam-1767	217	17	is	be	AUX
ejpam-1767	217	18	semisimple	semisimple	ADJ
ejpam-1767	217	19	.	.	PUNCT
ejpam-1767	218	1	(	(	PUNCT
ejpam-1767	218	2	2	2	X
ejpam-1767	218	3	)	)	PUNCT
ejpam-1767	218	4	s	s	VERB
ejpam-1767	218	5	is	be	AUX
ejpam-1767	218	6	left	leave	VERB
ejpam-1767	218	7	finitely	finitely	ADV
ejpam-1767	218	8	cogenerated	cogenerate	VERB
ejpam-1767	218	9	.	.	PUNCT
ejpam-1767	219	1	(	(	PUNCT
ejpam-1767	219	2	3	3	X
ejpam-1767	219	3	)	)	PUNCT
ejpam-1767	219	4	s	s	VERB
ejpam-1767	219	5	is	be	AUX
ejpam-1767	219	6	left	leave	VERB
ejpam-1767	219	7	finite	finite	ADJ
ejpam-1767	219	8	dimensional	dimensional	ADJ
ejpam-1767	219	9	.	.	PUNCT
ejpam-1767	220	1	in	in	ADP
ejpam-1767	220	2	this	this	DET
ejpam-1767	220	3	case	case	NOUN
ejpam-1767	220	4	,	,	PUNCT
ejpam-1767	220	5	soc(ss	soc(s	NOUN
ejpam-1767	220	6	)	)	PUNCT
ejpam-1767	220	7	=	=	SYM
ejpam-1767	220	8	ls(rad(m	ls(rad(m	NOUN
ejpam-1767	220	9	)	)	PUNCT
ejpam-1767	220	10	)	)	PUNCT
ejpam-1767	220	11	,	,	PUNCT
ejpam-1767	220	12	and	and	CCONJ
ejpam-1767	220	13	g(ss	g(ss	NUM
ejpam-1767	220	14	)	)	PUNCT
ejpam-1767	220	15	=	=	SYM
ejpam-1767	220	16	c(ssoc(ss	c(ssoc(ss	NOUN
ejpam-1767	220	17	)	)	PUNCT
ejpam-1767	220	18	)	)	PUNCT
ejpam-1767	221	1	=	=	SYM
ejpam-1767	221	2	c(m	c(m	PROPN
ejpam-1767	221	3	/	/	SYM
ejpam-1767	221	4	rad(m	rad(m	PROPN
ejpam-1767	221	5	)	)	PUNCT
ejpam-1767	221	6	)	)	PUNCT
ejpam-1767	221	7	.	.	PUNCT
ejpam-1767	222	1	proof	proof	NOUN
ejpam-1767	222	2	.	.	PUNCT
ejpam-1767	223	1	(	(	PUNCT
ejpam-1767	223	2	1	1	X
ejpam-1767	223	3	)	)	PUNCT
ejpam-1767	223	4	⇒	⇒	NOUN
ejpam-1767	223	5	(	(	PUNCT
ejpam-1767	223	6	2	2	NUM
ejpam-1767	223	7	)	)	PUNCT
ejpam-1767	223	8	.	.	PUNCT
ejpam-1767	224	1	it	it	PRON
ejpam-1767	224	2	is	be	AUX
ejpam-1767	224	3	trival	trival	NOUN
ejpam-1767	224	4	in	in	ADP
ejpam-1767	224	5	case	case	NOUN
ejpam-1767	224	6	m	m	ADJ
ejpam-1767	224	7	=	=	NOUN
ejpam-1767	224	8	0	0	X
ejpam-1767	224	9	.	.	PUNCT
ejpam-1767	225	1	if	if	SCONJ
ejpam-1767	225	2	m	m	PROPN
ejpam-1767	225	3	6=	6=	NUM
ejpam-1767	225	4	0	0	NUM
ejpam-1767	225	5	,	,	PUNCT
ejpam-1767	225	6	then	then	ADV
ejpam-1767	225	7	m	m	PROPN
ejpam-1767	225	8	/	/	SYM
ejpam-1767	225	9	radm	radm	NOUN
ejpam-1767	225	10	6=	6=	ADP
ejpam-1767	225	11	0	0	PUNCT
ejpam-1767	226	1	because	because	SCONJ
ejpam-1767	226	2	m	m	PROPN
ejpam-1767	226	3	is	be	AUX
ejpam-1767	226	4	finitely	finitely	ADV
ejpam-1767	226	5	generated	generate	VERB
ejpam-1767	226	6	.	.	PUNCT
ejpam-1767	227	1	as	as	SCONJ
ejpam-1767	227	2	m	m	NOUN
ejpam-1767	227	3	/	/	SYM
ejpam-1767	227	4	radm	radm	NOUN
ejpam-1767	227	5	is	be	AUX
ejpam-1767	227	6	semisimple	semisimple	ADJ
ejpam-1767	227	7	,	,	PUNCT
ejpam-1767	227	8	there	there	PRON
ejpam-1767	227	9	exist	exist	VERB
ejpam-1767	227	10	maximal	maximal	ADJ
ejpam-1767	227	11	submodules	submodule	NOUN
ejpam-1767	227	12	t1	t1	NOUN
ejpam-1767	227	13	,	,	PUNCT
ejpam-1767	227	14	t2	t2	NOUN
ejpam-1767	227	15	,	,	PUNCT
ejpam-1767	227	16	·	·	PUNCT
ejpam-1767	227	17	·	·	PUNCT
ejpam-1767	227	18	·	·	PUNCT
ejpam-1767	227	19	,	,	PUNCT
ejpam-1767	227	20	tn	tn	ADP
ejpam-1767	227	21	such	such	ADJ
ejpam-1767	227	22	that	that	SCONJ
ejpam-1767	227	23	m	m	PROPN
ejpam-1767	227	24	/	/	SYM
ejpam-1767	227	25	radm	radm	PROPN
ejpam-1767	227	26	∼=⊕n	∼=⊕n	PROPN
ejpam-1767	227	27	i=1m	i=1m	PROPN
ejpam-1767	227	28	/	/	SYM
ejpam-1767	227	29	ti	ti	NOUN
ejpam-1767	227	30	.	.	PUNCT
ejpam-1767	228	1	hence	hence	ADV
ejpam-1767	228	2	,	,	PUNCT
ejpam-1767	228	3	by	by	ADP
ejpam-1767	228	4	theorem	theorem	NOUN
ejpam-1767	228	5	2(4	2(4	NUM
ejpam-1767	228	6	)	)	PUNCT
ejpam-1767	228	7	,	,	PUNCT
ejpam-1767	228	8	ls(radm)∼=	ls(radm)∼=	ADJ
ejpam-1767	228	9	shomr(m	shomr(m	NOUN
ejpam-1767	228	10	/	/	SYM
ejpam-1767	228	11	radm	radm	NOUN
ejpam-1767	228	12	,	,	PUNCT
ejpam-1767	228	13	s	s	PART
ejpam-1767	228	14	mr)∼=	mr)∼=	NOUN
ejpam-1767	228	15	shomr(⊕n	shomr(⊕n	NOUN
ejpam-1767	228	16	i=1m	i=1m	X
ejpam-1767	228	17	/	/	SYM
ejpam-1767	228	18	ti	ti	PROPN
ejpam-1767	228	19	,	,	PUNCT
ejpam-1767	228	20	s	s	PART
ejpam-1767	228	21	mr)∼=⊕n	mr)∼=⊕n	ADJ
ejpam-1767	228	22	i=1ls(ti	i=1ls(ti	NOUN
ejpam-1767	228	23	)	)	PUNCT
ejpam-1767	228	24	is	be	AUX
ejpam-1767	228	25	an	an	DET
ejpam-1767	228	26	n	n	ADV
ejpam-1767	228	27	-	-	PUNCT
ejpam-1767	228	28	generated	generate	VERB
ejpam-1767	228	29	semisimple	semisimple	NOUN
ejpam-1767	228	30	left	leave	VERB
ejpam-1767	228	31	ideal	ideal	NOUN
ejpam-1767	228	32	of	of	ADP
ejpam-1767	228	33	s.	s.	PROPN
ejpam-1767	228	34	this	this	PRON
ejpam-1767	228	35	implies	imply	VERB
ejpam-1767	228	36	that	that	SCONJ
ejpam-1767	228	37	ls(radm	ls(radm	NOUN
ejpam-1767	228	38	)	)	PUNCT
ejpam-1767	228	39	=	=	SYM
ejpam-1767	228	40	soc(ss	soc(s	NOUN
ejpam-1767	228	41	)	)	PUNCT
ejpam-1767	229	1	ãs	ãs	PRON
ejpam-1767	229	2	s	s	VERB
ejpam-1767	229	3	by	by	ADP
ejpam-1767	229	4	theorem	theorem	ADJ
ejpam-1767	229	5	2(5	2(5	NOUN
ejpam-1767	229	6	)	)	PUNCT
ejpam-1767	229	7	,	,	PUNCT
ejpam-1767	229	8	and	and	CCONJ
ejpam-1767	229	9	therefore	therefore	ADV
ejpam-1767	229	10	s	s	VERB
ejpam-1767	229	11	is	be	AUX
ejpam-1767	229	12	left	leave	VERB
ejpam-1767	229	13	finitely	finitely	ADV
ejpam-1767	229	14	cogenerated	cogenerate	VERB
ejpam-1767	229	15	,	,	PUNCT
ejpam-1767	229	16	and	and	CCONJ
ejpam-1767	229	17	g(ss	g(ss	NUM
ejpam-1767	229	18	)	)	PUNCT
ejpam-1767	229	19	=	=	SYM
ejpam-1767	229	20	n=	n=	ADJ
ejpam-1767	229	21	c(ssoc(ss	c(ssoc(ss	NOUN
ejpam-1767	229	22	)	)	PUNCT
ejpam-1767	229	23	)	)	PUNCT
ejpam-1767	229	24	.	.	PUNCT
ejpam-1767	230	1	(	(	PUNCT
ejpam-1767	230	2	2)⇒	2)⇒	NUM
ejpam-1767	230	3	(	(	PUNCT
ejpam-1767	230	4	3	3	NUM
ejpam-1767	230	5	)	)	PUNCT
ejpam-1767	230	6	.	.	PUNCT
ejpam-1767	231	1	obvious	obvious	ADJ
ejpam-1767	231	2	.	.	PUNCT
ejpam-1767	232	1	(	(	PUNCT
ejpam-1767	232	2	3)⇒	3)⇒	NUM
ejpam-1767	232	3	(	(	PUNCT
ejpam-1767	232	4	1	1	NUM
ejpam-1767	232	5	)	)	PUNCT
ejpam-1767	232	6	.	.	PUNCT
ejpam-1767	233	1	see	see	VERB
ejpam-1767	233	2	lemma	lemma	PROPN
ejpam-1767	233	3	7	7	X
ejpam-1767	233	4	.	.	PUNCT
ejpam-1767	233	5	corollary	corollary	ADJ
ejpam-1767	233	6	4	4	NUM
ejpam-1767	233	7	.	.	PUNCT
ejpam-1767	234	1	let	let	VERB
ejpam-1767	234	2	r	r	PRON
ejpam-1767	234	3	be	be	AUX
ejpam-1767	234	4	a	a	DET
ejpam-1767	234	5	right	right	ADJ
ejpam-1767	234	6	f	f	NOUN
ejpam-1767	234	7	-	-	PUNCT
ejpam-1767	234	8	injective	injective	ADJ
ejpam-1767	234	9	right	right	ADJ
ejpam-1767	234	10	kasch	kasch	PROPN
ejpam-1767	234	11	ring	ring	NOUN
ejpam-1767	234	12	.	.	PUNCT
ejpam-1767	235	1	then	then	ADV
ejpam-1767	235	2	the	the	DET
ejpam-1767	235	3	following	follow	VERB
ejpam-1767	235	4	conditions	condition	NOUN
ejpam-1767	235	5	are	be	AUX
ejpam-1767	235	6	equivalent	equivalent	ADJ
ejpam-1767	235	7	:	:	PUNCT
ejpam-1767	235	8	(	(	PUNCT
ejpam-1767	235	9	1	1	X
ejpam-1767	235	10	)	)	PUNCT
ejpam-1767	235	11	r	r	NOUN
ejpam-1767	235	12	is	be	AUX
ejpam-1767	235	13	semilocal	semilocal	ADJ
ejpam-1767	235	14	.	.	PUNCT
ejpam-1767	236	1	(	(	PUNCT
ejpam-1767	236	2	2	2	X
ejpam-1767	236	3	)	)	PUNCT
ejpam-1767	236	4	r	r	NOUN
ejpam-1767	236	5	is	be	AUX
ejpam-1767	236	6	left	leave	VERB
ejpam-1767	236	7	finitely	finitely	ADV
ejpam-1767	236	8	cogenerated	cogenerate	VERB
ejpam-1767	236	9	.	.	PUNCT
ejpam-1767	237	1	(	(	PUNCT
ejpam-1767	237	2	3	3	X
ejpam-1767	237	3	)	)	PUNCT
ejpam-1767	237	4	r	r	NOUN
ejpam-1767	237	5	is	be	AUX
ejpam-1767	237	6	left	leave	VERB
ejpam-1767	237	7	finite	finite	ADJ
ejpam-1767	237	8	dimensional	dimensional	ADJ
ejpam-1767	237	9	.	.	PUNCT
ejpam-1767	238	1	in	in	ADP
ejpam-1767	238	2	this	this	DET
ejpam-1767	238	3	case	case	NOUN
ejpam-1767	238	4	,	,	PUNCT
ejpam-1767	238	5	soc(rr	soc(rr	PROPN
ejpam-1767	238	6	)	)	PUNCT
ejpam-1767	238	7	=	=	SYM
ejpam-1767	238	8	lr(j(r	lr(j(r	PROPN
ejpam-1767	238	9	)	)	PUNCT
ejpam-1767	238	10	)	)	PUNCT
ejpam-1767	238	11	,	,	PUNCT
ejpam-1767	238	12	and	and	CCONJ
ejpam-1767	238	13	g(rr	g(rr	X
ejpam-1767	238	14	)	)	PUNCT
ejpam-1767	238	15	=	=	SYM
ejpam-1767	238	16	c(rsoc(rr	c(rsoc(rr	PROPN
ejpam-1767	238	17	)	)	PUNCT
ejpam-1767	238	18	)	)	PUNCT
ejpam-1767	239	1	=	=	SYM
ejpam-1767	239	2	c(r	c(r	PROPN
ejpam-1767	239	3	/	/	SYM
ejpam-1767	239	4	j(r	j(r	PROPN
ejpam-1767	239	5	)	)	PUNCT
ejpam-1767	239	6	)	)	PUNCT
ejpam-1767	239	7	.	.	PUNCT
ejpam-1767	240	1	references	reference	NOUN
ejpam-1767	240	2	[	[	X
ejpam-1767	240	3	1	1	X
ejpam-1767	240	4	]	]	PUNCT
ejpam-1767	240	5	t.	t.	PROPN
ejpam-1767	240	6	albu	albu	PROPN
ejpam-1767	240	7	and	and	CCONJ
ejpam-1767	240	8	r.	r.	PROPN
ejpam-1767	240	9	wisbauer	wisbauer	PROPN
ejpam-1767	240	10	.	.	PUNCT
ejpam-1767	241	1	kasch	kasch	VERB
ejpam-1767	241	2	modules	module	NOUN
ejpam-1767	241	3	.	.	PUNCT
ejpam-1767	242	1	in	in	ADP
ejpam-1767	242	2	s.	s.	PROPN
ejpam-1767	242	3	k.	k.	PROPN
ejpam-1767	242	4	jain	jain	PROPN
ejpam-1767	242	5	and	and	CCONJ
ejpam-1767	242	6	s.	s.	PROPN
ejpam-1767	242	7	t.	t.	PROPN
ejpam-1767	242	8	rizvi	rizvi	PROPN
ejpam-1767	242	9	,	,	PUNCT
ejpam-1767	242	10	editors	editor	NOUN
ejpam-1767	242	11	,	,	PUNCT
ejpam-1767	242	12	advances	advance	NOUN
ejpam-1767	242	13	in	in	ADP
ejpam-1767	242	14	ring	ring	NOUN
ejpam-1767	242	15	theory	theory	NOUN
ejpam-1767	242	16	,	,	PUNCT
ejpam-1767	242	17	pages	page	NOUN
ejpam-1767	242	18	1–16	1–16	PROPN
ejpam-1767	242	19	,	,	PUNCT
ejpam-1767	242	20	1997	1997	NUM
ejpam-1767	242	21	.	.	PUNCT
ejpam-1767	243	1	[	[	X
ejpam-1767	243	2	2	2	X
ejpam-1767	243	3	]	]	PUNCT
ejpam-1767	243	4	j.	j.	PROPN
ejpam-1767	243	5	l.	l.	PROPN
ejpam-1767	243	6	chen	chen	PROPN
ejpam-1767	243	7	,	,	PUNCT
ejpam-1767	243	8	n.	n.	PROPN
ejpam-1767	243	9	q.	q.	PROPN
ejpam-1767	243	10	ding	ding	PROPN
ejpam-1767	243	11	,	,	PUNCT
ejpam-1767	243	12	y.	y.	PROPN
ejpam-1767	243	13	l.	l.	PROPN
ejpam-1767	243	14	li	li	PROPN
ejpam-1767	243	15	,	,	PUNCT
ejpam-1767	243	16	and	and	CCONJ
ejpam-1767	243	17	y.	y.	PROPN
ejpam-1767	243	18	q.	q.	PROPN
ejpam-1767	243	19	zhou	zhou	PROPN
ejpam-1767	243	20	.	.	PUNCT
ejpam-1767	244	1	on	on	ADP
ejpam-1767	244	2	(	(	PUNCT
ejpam-1767	244	3	m	m	PROPN
ejpam-1767	244	4	,	,	PUNCT
ejpam-1767	244	5	n)-injectivity	n)-injectivity	NOUN
ejpam-1767	244	6	of	of	ADP
ejpam-1767	244	7	modules	module	NOUN
ejpam-1767	244	8	.	.	PUNCT
ejpam-1767	245	1	communications	communication	NOUN
ejpam-1767	245	2	in	in	ADP
ejpam-1767	245	3	algebra	algebra	NOUN
ejpam-1767	245	4	,	,	PUNCT
ejpam-1767	245	5	29:5589–5603	29:5589–5603	NUM
ejpam-1767	245	6	,	,	PUNCT
ejpam-1767	245	7	2001	2001	NUM
ejpam-1767	245	8	.	.	PUNCT
ejpam-1767	246	1	[	[	X
ejpam-1767	246	2	3	3	X
ejpam-1767	246	3	]	]	X
ejpam-1767	246	4	j.	j.	PROPN
ejpam-1767	246	5	l.	l.	PROPN
ejpam-1767	246	6	chen	chen	PROPN
ejpam-1767	246	7	,	,	PUNCT
ejpam-1767	246	8	n.	n.	PROPN
ejpam-1767	246	9	q.	q.	PROPN
ejpam-1767	246	10	ding	ding	PROPN
ejpam-1767	246	11	,	,	PUNCT
ejpam-1767	246	12	and	and	CCONJ
ejpam-1767	246	13	m.	m.	PROPN
ejpam-1767	246	14	f.	f.	PROPN
ejpam-1767	246	15	yousif	yousif	PROPN
ejpam-1767	246	16	.	.	PUNCT
ejpam-1767	247	1	on	on	ADP
ejpam-1767	247	2	generalizations	generalization	NOUN
ejpam-1767	247	3	of	of	ADP
ejpam-1767	247	4	pf	pf	NOUN
ejpam-1767	247	5	-	-	PUNCT
ejpam-1767	247	6	rings	ring	NOUN
ejpam-1767	247	7	.	.	PUNCT
ejpam-1767	248	1	communications	communication	NOUN
ejpam-1767	248	2	in	in	ADP
ejpam-1767	248	3	algebra	algebra	NOUN
ejpam-1767	248	4	,	,	PUNCT
ejpam-1767	248	5	32:521–533	32:521–533	PROPN
ejpam-1767	248	6	,	,	PUNCT
ejpam-1767	248	7	2004	2004	NUM
ejpam-1767	248	8	.	.	PUNCT
ejpam-1767	249	1	[	[	X
ejpam-1767	249	2	4	4	NUM
ejpam-1767	249	3	]	]	PUNCT
ejpam-1767	249	4	a.	a.	NOUN
ejpam-1767	249	5	facchini	facchini	PROPN
ejpam-1767	249	6	.	.	PUNCT
ejpam-1767	249	7	module	module	NOUN
ejpam-1767	249	8	theory	theory	NOUN
ejpam-1767	249	9	,	,	PUNCT
ejpam-1767	249	10	endomorphism	endomorphism	PROPN
ejpam-1767	249	11	rings	ring	NOUN
ejpam-1767	249	12	and	and	CCONJ
ejpam-1767	249	13	direct	direct	ADJ
ejpam-1767	249	14	sum	sum	NOUN
ejpam-1767	249	15	decompositions	decomposition	NOUN
ejpam-1767	249	16	in	in	ADP
ejpam-1767	249	17	some	some	DET
ejpam-1767	249	18	classes	class	NOUN
ejpam-1767	249	19	of	of	ADP
ejpam-1767	249	20	modules	module	NOUN
ejpam-1767	249	21	.	.	PUNCT
ejpam-1767	250	1	birkhäuser	birkhäuser	PROPN
ejpam-1767	250	2	verlag	verlag	PROPN
ejpam-1767	250	3	,	,	PUNCT
ejpam-1767	250	4	basel	basel	PROPN
ejpam-1767	250	5	,	,	PUNCT
ejpam-1767	250	6	1998	1998	NUM
ejpam-1767	250	7	.	.	PUNCT
ejpam-1767	251	1	[	[	X
ejpam-1767	251	2	5	5	X
ejpam-1767	251	3	]	]	PUNCT
ejpam-1767	251	4	w.	w.	PROPN
ejpam-1767	251	5	k.	k.	PROPN
ejpam-1767	251	6	nicholson	nicholson	PROPN
ejpam-1767	251	7	,	,	PUNCT
ejpam-1767	251	8	j.	j.	PROPN
ejpam-1767	251	9	k.	k.	PROPN
ejpam-1767	251	10	park	park	PROPN
ejpam-1767	251	11	,	,	PUNCT
ejpam-1767	251	12	and	and	CCONJ
ejpam-1767	251	13	m.	m.	PROPN
ejpam-1767	251	14	f.	f.	PROPN
ejpam-1767	251	15	yousif	yousif	PROPN
ejpam-1767	251	16	.	.	PUNCT
ejpam-1767	252	1	principally	principally	ADV
ejpam-1767	252	2	quasi	quasi	ADJ
ejpam-1767	252	3	-	-	ADJ
ejpam-1767	252	4	injective	injective	ADJ
ejpam-1767	252	5	modules	module	NOUN
ejpam-1767	252	6	.	.	PUNCT
ejpam-1767	253	1	communications	communication	NOUN
ejpam-1767	253	2	in	in	ADP
ejpam-1767	253	3	algebra	algebra	NOUN
ejpam-1767	253	4	,	,	PUNCT
ejpam-1767	253	5	27:1683–1693	27:1683–1693	NUM
ejpam-1767	253	6	,	,	PUNCT
ejpam-1767	253	7	1999	1999	NUM
ejpam-1767	253	8	.	.	PUNCT
ejpam-1767	254	1	[	[	X
ejpam-1767	254	2	6	6	NUM
ejpam-1767	254	3	]	]	PUNCT
ejpam-1767	254	4	s.	s.	PROPN
ejpam-1767	254	5	page	page	PROPN
ejpam-1767	254	6	and	and	CCONJ
ejpam-1767	254	7	y.	y.	PROPN
ejpam-1767	254	8	q.	q.	PROPN
ejpam-1767	254	9	zhou	zhou	PROPN
ejpam-1767	254	10	.	.	PUNCT
ejpam-1767	255	1	generalization	generalization	NOUN
ejpam-1767	255	2	of	of	ADP
ejpam-1767	255	3	principally	principally	ADV
ejpam-1767	255	4	injective	injective	ADJ
ejpam-1767	255	5	rings	ring	NOUN
ejpam-1767	255	6	.	.	PUNCT
ejpam-1767	256	1	journal	journal	PROPN
ejpam-1767	256	2	of	of	ADP
ejpam-1767	256	3	algebra	algebra	PROPN
ejpam-1767	256	4	,	,	PUNCT
ejpam-1767	256	5	206:706–721	206:706–721	NUM
ejpam-1767	256	6	,	,	PUNCT
ejpam-1767	256	7	1998	1998	NUM
ejpam-1767	256	8	.	.	PUNCT
ejpam-1767	257	1	references	reference	NOUN
ejpam-1767	257	2	125	125	NUM
ejpam-1767	257	3	[	[	X
ejpam-1767	257	4	7	7	X
ejpam-1767	257	5	]	]	PUNCT
ejpam-1767	257	6	v.	v.	CCONJ
ejpam-1767	257	7	s.	s.	PROPN
ejpam-1767	257	8	ramamurthi	ramamurthi	PROPN
ejpam-1767	257	9	and	and	CCONJ
ejpam-1767	257	10	k.	k.	PROPN
ejpam-1767	257	11	m.	m.	PROPN
ejpam-1767	257	12	rangaswamy	rangaswamy	PROPN
ejpam-1767	257	13	.	.	PUNCT
ejpam-1767	258	1	on	on	ADP
ejpam-1767	258	2	finitely	finitely	ADV
ejpam-1767	258	3	injective	injective	ADJ
ejpam-1767	258	4	modules	module	NOUN
ejpam-1767	258	5	.	.	PUNCT
ejpam-1767	259	1	journal	journal	NOUN
ejpam-1767	259	2	of	of	ADP
ejpam-1767	259	3	the	the	DET
ejpam-1767	259	4	australian	australian	ADJ
ejpam-1767	259	5	mathematical	mathematical	ADJ
ejpam-1767	259	6	society	society	NOUN
ejpam-1767	259	7	,	,	PUNCT
ejpam-1767	259	8	16:239–248	16:239–248	NUM
ejpam-1767	259	9	,	,	PUNCT
ejpam-1767	259	10	1973	1973	NUM
ejpam-1767	259	11	.	.	PUNCT
ejpam-1767	260	1	[	[	X
ejpam-1767	260	2	8	8	X
ejpam-1767	260	3	]	]	PUNCT
ejpam-1767	260	4	l.	l.	PROPN
ejpam-1767	260	5	shen	shen	PROPN
ejpam-1767	260	6	and	and	CCONJ
ejpam-1767	260	7	j.	j.	PROPN
ejpam-1767	260	8	l.	l.	PROPN
ejpam-1767	260	9	chen	chen	PROPN
ejpam-1767	260	10	.	.	PUNCT
ejpam-1767	261	1	on	on	ADP
ejpam-1767	261	2	strong	strong	ADJ
ejpam-1767	261	3	goldie	goldie	PROPN
ejpam-1767	261	4	dimension	dimension	NOUN
ejpam-1767	261	5	.	.	PUNCT
ejpam-1767	262	1	communications	communication	NOUN
ejpam-1767	262	2	in	in	ADP
ejpam-1767	262	3	algebra	algebra	NOUN
ejpam-1767	262	4	,	,	PUNCT
ejpam-1767	262	5	35:3018–3025	35:3018–3025	NUM
ejpam-1767	262	6	,	,	PUNCT
ejpam-1767	262	7	2007	2007	NUM
ejpam-1767	262	8	.	.	PUNCT
ejpam-1767	263	1	[	[	X
ejpam-1767	263	2	9	9	NUM
ejpam-1767	263	3	]	]	X
ejpam-1767	263	4	g.	g.	PROPN
ejpam-1767	263	5	s.	s.	PROPN
ejpam-1767	263	6	xiao	xiao	PROPN
ejpam-1767	263	7	,	,	PUNCT
ejpam-1767	263	8	x.	x.	PROPN
ejpam-1767	263	9	b.	b.	PROPN
ejpam-1767	263	10	yin	yin	PROPN
ejpam-1767	263	11	,	,	PUNCT
ejpam-1767	263	12	and	and	CCONJ
ejpam-1767	263	13	w.	w.	PROPN
ejpam-1767	263	14	t.	t.	PROPN
ejpam-1767	263	15	tong	tong	PROPN
ejpam-1767	263	16	.	.	PUNCT
ejpam-1767	264	1	a	a	DET
ejpam-1767	264	2	note	note	NOUN
ejpam-1767	264	3	on	on	ADP
ejpam-1767	264	4	ap	ap	ADJ
ejpam-1767	264	5	-	-	PUNCT
ejpam-1767	264	6	injective	injective	ADJ
ejpam-1767	264	7	rings	ring	NOUN
ejpam-1767	264	8	.	.	PUNCT
ejpam-1767	265	1	journal	journal	PROPN
ejpam-1767	265	2	of	of	ADP
ejpam-1767	265	3	mathematical	mathematical	ADJ
ejpam-1767	265	4	research	research	NOUN
ejpam-1767	265	5	&	&	CCONJ
ejpam-1767	265	6	exposition	exposition	PROPN
ejpam-1767	265	7	,	,	PUNCT
ejpam-1767	265	8	35:211–216	35:211–216	NUM
ejpam-1767	265	9	,	,	PUNCT
ejpam-1767	265	10	2003	2003	NUM
ejpam-1767	265	11	.	.	PUNCT
ejpam-1767	266	1	[	[	X
ejpam-1767	266	2	10	10	NUM
ejpam-1767	266	3	]	]	PUNCT
ejpam-1767	267	1	z.	z.	PROPN
ejpam-1767	267	2	m.	m.	PROPN
ejpam-1767	267	3	zhu	zhu	PROPN
ejpam-1767	267	4	.	.	PUNCT
ejpam-1767	268	1	finitely	finitely	ADV
ejpam-1767	268	2	quasi	quasi	ADJ
ejpam-1767	268	3	-	-	ADJ
ejpam-1767	268	4	injective	injective	ADJ
ejpam-1767	268	5	modules	module	NOUN
ejpam-1767	268	6	.	.	PUNCT
ejpam-1767	269	1	journal	journal	PROPN
ejpam-1767	269	2	of	of	ADP
ejpam-1767	269	3	shandong	shandong	PROPN
ejpam-1767	269	4	university	university	PROPN
ejpam-1767	269	5	(	(	PUNCT
ejpam-1767	269	6	nat	nat	PROPN
ejpam-1767	269	7	.	.	PUNCT
ejpam-1767	270	1	sci	sci	PROPN
ejpam-1767	270	2	.	.	PROPN
ejpam-1767	270	3	)	)	PUNCT
ejpam-1767	270	4	,	,	PUNCT
ejpam-1767	270	5	45:20–23	45:20–23	PROPN
ejpam-1767	270	6	,	,	PUNCT
ejpam-1767	270	7	2010	2010	NUM
ejpam-1767	270	8	.	.	PUNCT
ejpam-1767	271	1	[	[	X
ejpam-1767	271	2	11	11	NUM
ejpam-1767	271	3	]	]	PUNCT
ejpam-1767	271	4	z.	z.	PROPN
ejpam-1767	271	5	m.	m.	PROPN
ejpam-1767	271	6	zhu	zhu	PROPN
ejpam-1767	271	7	.	.	PUNCT
ejpam-1767	272	1	mp	mp	NOUN
ejpam-1767	272	2	-	-	PUNCT
ejpam-1767	272	3	injective	injective	ADJ
ejpam-1767	272	4	rings	ring	NOUN
ejpam-1767	272	5	and	and	CCONJ
ejpam-1767	272	6	mgp	mgp	NOUN
ejpam-1767	272	7	-	-	PUNCT
ejpam-1767	272	8	injective	injective	ADJ
ejpam-1767	272	9	rings	ring	NOUN
ejpam-1767	272	10	.	.	PUNCT
ejpam-1767	273	1	indian	indian	PROPN
ejpam-1767	273	2	journal	journal	PROPN
ejpam-1767	273	3	of	of	ADP
ejpam-1767	273	4	pure	pure	PROPN
ejpam-1767	273	5	&	&	CCONJ
ejpam-1767	273	6	applied	applied	ADJ
ejpam-1767	273	7	mathematics	mathematic	NOUN
ejpam-1767	273	8	,	,	PUNCT
ejpam-1767	273	9	41:627–645	41:627–645	PROPN
ejpam-1767	273	10	,	,	PUNCT
ejpam-1767	273	11	2010	2010	NUM
ejpam-1767	273	12	.	.	PUNCT