id	sid	tid	token	lemma	pos
ejpam-3291	1	1	european	european	PROPN
ejpam-3291	1	2	journal	journal	PROPN
ejpam-3291	1	3	of	of	ADP
ejpam-3291	1	4	pure	pure	ADJ
ejpam-3291	1	5	and	and	CCONJ
ejpam-3291	1	6	applied	apply	VERB
ejpam-3291	1	7	mathematics	mathematic	NOUN
ejpam-3291	1	8	vol	vol	NOUN
ejpam-3291	1	9	.	.	PUNCT
ejpam-3291	2	1	11	11	NUM
ejpam-3291	2	2	,	,	PUNCT
ejpam-3291	2	3	no	no	INTJ
ejpam-3291	2	4	.	.	NOUN
ejpam-3291	2	5	3	3	NUM
ejpam-3291	2	6	,	,	PUNCT
ejpam-3291	2	7	2018	2018	NUM
ejpam-3291	2	8	,	,	PUNCT
ejpam-3291	2	9	815	815	NUM
ejpam-3291	2	10	-	-	SYM
ejpam-3291	2	11	822	822	NUM
ejpam-3291	2	12	issn	issn	PROPN
ejpam-3291	2	13	1307	1307	NUM
ejpam-3291	2	14	-	-	SYM
ejpam-3291	2	15	5543	5543	NUM
ejpam-3291	2	16	–	–	PUNCT
ejpam-3291	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3291	2	18	published	publish	VERB
ejpam-3291	2	19	by	by	ADP
ejpam-3291	2	20	new	new	PROPN
ejpam-3291	2	21	york	york	PROPN
ejpam-3291	2	22	business	business	PROPN
ejpam-3291	2	23	global	global	ADJ
ejpam-3291	2	24	on	on	ADP
ejpam-3291	2	25	slightly	slightly	ADV
ejpam-3291	2	26	compressible	compressible	ADJ
ejpam-3291	2	27	-	-	PUNCT
ejpam-3291	2	28	injective	injective	ADJ
ejpam-3291	2	29	modules	module	NOUN
ejpam-3291	2	30	nguyen	nguyen	NOUN
ejpam-3291	2	31	dang	dang	PROPN
ejpam-3291	2	32	hoa	hoa	PROPN
ejpam-3291	2	33	nghiem1	nghiem1	PROPN
ejpam-3291	2	34	,	,	PUNCT
ejpam-3291	2	35	phatsarapa	phatsarapa	VERB
ejpam-3291	2	36	janmuang1	janmuang1	PROPN
ejpam-3291	2	37	,	,	PUNCT
ejpam-3291	2	38	samruam	samruam	PROPN
ejpam-3291	2	39	baupradist1,3,∗	baupradist1,3,∗	PROPN
ejpam-3291	2	40	,	,	PUNCT
ejpam-3291	2	41	ronnason	ronnason	NOUN
ejpam-3291	2	42	chinram2	chinram2	NOUN
ejpam-3291	2	43	1	1	NUM
ejpam-3291	2	44	department	department	NOUN
ejpam-3291	2	45	of	of	ADP
ejpam-3291	2	46	mathematics	mathematic	NOUN
ejpam-3291	2	47	and	and	CCONJ
ejpam-3291	2	48	computer	computer	NOUN
ejpam-3291	2	49	science	science	NOUN
ejpam-3291	2	50	,	,	PUNCT
ejpam-3291	2	51	faculty	faculty	NOUN
ejpam-3291	2	52	of	of	ADP
ejpam-3291	2	53	science	science	NOUN
ejpam-3291	2	54	,	,	PUNCT
ejpam-3291	2	55	chulalongkorn	chulalongkorn	NOUN
ejpam-3291	2	56	university	university	NOUN
ejpam-3291	2	57	,	,	PUNCT
ejpam-3291	2	58	bangkok	bangkok	PROPN
ejpam-3291	2	59	,	,	PUNCT
ejpam-3291	2	60	10330	10330	NUM
ejpam-3291	2	61	,	,	PUNCT
ejpam-3291	2	62	thailand	thailand	PROPN
ejpam-3291	2	63	2	2	NUM
ejpam-3291	2	64	algebra	algebra	NOUN
ejpam-3291	2	65	and	and	CCONJ
ejpam-3291	2	66	applications	application	NOUN
ejpam-3291	2	67	research	research	NOUN
ejpam-3291	2	68	unit	unit	NOUN
ejpam-3291	2	69	,	,	PUNCT
ejpam-3291	2	70	department	department	NOUN
ejpam-3291	2	71	of	of	ADP
ejpam-3291	2	72	mathematics	mathematics	PROPN
ejpam-3291	2	73	and	and	CCONJ
ejpam-3291	2	74	statistics	statistic	NOUN
ejpam-3291	2	75	,	,	PUNCT
ejpam-3291	2	76	faculty	faculty	NOUN
ejpam-3291	2	77	of	of	ADP
ejpam-3291	2	78	science	science	NOUN
ejpam-3291	2	79	,	,	PUNCT
ejpam-3291	2	80	prince	prince	NOUN
ejpam-3291	2	81	of	of	ADP
ejpam-3291	2	82	songkla	songkla	PROPN
ejpam-3291	2	83	university	university	PROPN
ejpam-3291	2	84	,	,	PUNCT
ejpam-3291	2	85	hat	hat	PROPN
ejpam-3291	2	86	yai	yai	PROPN
ejpam-3291	2	87	,	,	PUNCT
ejpam-3291	2	88	songkhla	songkhla	ADJ
ejpam-3291	2	89	,	,	PUNCT
ejpam-3291	2	90	90110	90110	NUM
ejpam-3291	2	91	,	,	PUNCT
ejpam-3291	2	92	thailand	thailand	PROPN
ejpam-3291	2	93	3	3	NUM
ejpam-3291	2	94	centre	centre	NOUN
ejpam-3291	2	95	of	of	ADP
ejpam-3291	2	96	excellence	excellence	NOUN
ejpam-3291	2	97	in	in	ADP
ejpam-3291	2	98	mathematics	mathematics	PROPN
ejpam-3291	2	99	,	,	PUNCT
ejpam-3291	2	100	che	che	PROPN
ejpam-3291	2	101	,	,	PUNCT
ejpam-3291	2	102	si	si	PROPN
ejpam-3291	2	103	ayuthaya	ayuthaya	PROPN
ejpam-3291	2	104	road	road	PROPN
ejpam-3291	2	105	,	,	PUNCT
ejpam-3291	2	106	bangkok	bangkok	PROPN
ejpam-3291	2	107	10400	10400	NUM
ejpam-3291	2	108	,	,	PUNCT
ejpam-3291	2	109	thailand	thailand	PROPN
ejpam-3291	2	110	abstract	abstract	NOUN
ejpam-3291	2	111	.	.	PUNCT
ejpam-3291	3	1	in	in	ADP
ejpam-3291	3	2	this	this	DET
ejpam-3291	3	3	paper	paper	NOUN
ejpam-3291	3	4	,	,	PUNCT
ejpam-3291	3	5	we	we	PRON
ejpam-3291	3	6	introduce	introduce	VERB
ejpam-3291	3	7	the	the	DET
ejpam-3291	3	8	concept	concept	NOUN
ejpam-3291	3	9	of	of	ADP
ejpam-3291	3	10	slightly	slightly	ADV
ejpam-3291	3	11	compressible	compressible	ADJ
ejpam-3291	3	12	-	-	PUNCT
ejpam-3291	3	13	injective	injective	ADJ
ejpam-3291	3	14	modules	module	NOUN
ejpam-3291	3	15	,	,	PUNCT
ejpam-3291	3	16	following	follow	VERB
ejpam-3291	3	17	this	this	PRON
ejpam-3291	3	18	,	,	PUNCT
ejpam-3291	3	19	a	a	DET
ejpam-3291	3	20	right	right	ADJ
ejpam-3291	3	21	r	r	NOUN
ejpam-3291	3	22	-	-	PUNCT
ejpam-3291	3	23	module	module	NOUN
ejpam-3291	3	24	n	n	NOUN
ejpam-3291	3	25	is	be	AUX
ejpam-3291	3	26	called	call	VERB
ejpam-3291	3	27	an	an	DET
ejpam-3291	3	28	m	m	NOUN
ejpam-3291	3	29	-slightly	-slightly	ADV
ejpam-3291	3	30	compressible	compressible	ADJ
ejpam-3291	3	31	-	-	PUNCT
ejpam-3291	3	32	injective	injective	ADJ
ejpam-3291	3	33	module	module	NOUN
ejpam-3291	3	34	,	,	PUNCT
ejpam-3291	3	35	if	if	SCONJ
ejpam-3291	3	36	every	every	DET
ejpam-3291	3	37	r	r	NOUN
ejpam-3291	3	38	-	-	PUNCT
ejpam-3291	3	39	homomorphism	homomorphism	NOUN
ejpam-3291	3	40	from	from	ADP
ejpam-3291	3	41	a	a	DET
ejpam-3291	3	42	non	non	ADJ
ejpam-3291	3	43	-	-	ADJ
ejpam-3291	3	44	zero	zero	NUM
ejpam-3291	3	45	m	m	VERB
ejpam-3291	3	46	-slightly	-slightly	ADV
ejpam-3291	3	47	compressible	compressible	ADJ
ejpam-3291	3	48	submodule	submodule	NOUN
ejpam-3291	3	49	of	of	ADP
ejpam-3291	3	50	m	m	PROPN
ejpam-3291	3	51	to	to	ADP
ejpam-3291	3	52	n	n	PROPN
ejpam-3291	3	53	can	can	AUX
ejpam-3291	3	54	be	be	AUX
ejpam-3291	3	55	extended	extend	VERB
ejpam-3291	3	56	to	to	ADP
ejpam-3291	3	57	m	m	PROPN
ejpam-3291	3	58	.	.	PUNCT
ejpam-3291	4	1	we	we	PRON
ejpam-3291	4	2	give	give	VERB
ejpam-3291	4	3	some	some	DET
ejpam-3291	4	4	characterizations	characterization	NOUN
ejpam-3291	4	5	and	and	CCONJ
ejpam-3291	4	6	properties	property	NOUN
ejpam-3291	4	7	of	of	ADP
ejpam-3291	4	8	slightly	slightly	ADV
ejpam-3291	4	9	compressible	compressible	ADJ
ejpam-3291	4	10	-	-	PUNCT
ejpam-3291	4	11	injective	injective	ADJ
ejpam-3291	4	12	modules	module	NOUN
ejpam-3291	4	13	.	.	PUNCT
ejpam-3291	5	1	2010	2010	NUM
ejpam-3291	5	2	mathematics	mathematic	NOUN
ejpam-3291	5	3	subject	subject	NOUN
ejpam-3291	5	4	classifications	classification	NOUN
ejpam-3291	5	5	:	:	PUNCT
ejpam-3291	5	6	16d50	16d50	NUM
ejpam-3291	5	7	,	,	PUNCT
ejpam-3291	5	8	16d70	16d70	NUM
ejpam-3291	5	9	,	,	PUNCT
ejpam-3291	5	10	16d80	16d80	NUM
ejpam-3291	5	11	key	key	ADJ
ejpam-3291	5	12	words	word	NOUN
ejpam-3291	5	13	and	and	CCONJ
ejpam-3291	5	14	phrases	phrase	NOUN
ejpam-3291	5	15	:	:	PUNCT
ejpam-3291	5	16	m	m	VERB
ejpam-3291	5	17	-slightly	-slightly	ADV
ejpam-3291	5	18	compressible	compressible	ADJ
ejpam-3291	5	19	modules	module	NOUN
ejpam-3291	5	20	;	;	PUNCT
ejpam-3291	5	21	m	m	VERB
ejpam-3291	5	22	-slightly	-slightly	ADV
ejpam-3291	5	23	compressible	compressible	ADJ
ejpam-3291	5	24	-	-	PUNCT
ejpam-3291	5	25	injective	injective	ADJ
ejpam-3291	5	26	modules	module	NOUN
ejpam-3291	5	27	;	;	PUNCT
ejpam-3291	5	28	quasi	quasi	ADJ
ejpam-3291	5	29	-	-	ADJ
ejpam-3291	5	30	slightly	slightly	ADV
ejpam-3291	5	31	compressible	compressible	ADJ
ejpam-3291	5	32	-	-	PUNCT
ejpam-3291	5	33	injective	injective	ADJ
ejpam-3291	5	34	modules	module	NOUN
ejpam-3291	5	35	.	.	PUNCT
ejpam-3291	6	1	1	1	X
ejpam-3291	6	2	.	.	X
ejpam-3291	6	3	introduction	introduction	NOUN
ejpam-3291	6	4	throughout	throughout	ADP
ejpam-3291	6	5	all	all	DET
ejpam-3291	6	6	rings	ring	NOUN
ejpam-3291	6	7	are	be	AUX
ejpam-3291	6	8	associative	associative	ADJ
ejpam-3291	6	9	with	with	ADP
ejpam-3291	6	10	identity	identity	NOUN
ejpam-3291	6	11	and	and	CCONJ
ejpam-3291	6	12	modules	module	NOUN
ejpam-3291	6	13	are	be	AUX
ejpam-3291	6	14	unitary	unitary	ADJ
ejpam-3291	6	15	right	right	ADJ
ejpam-3291	6	16	rmodules	rmodule	NOUN
ejpam-3291	6	17	.	.	PUNCT
ejpam-3291	7	1	let	let	VERB
ejpam-3291	7	2	m	m	PRON
ejpam-3291	7	3	be	be	AUX
ejpam-3291	7	4	a	a	DET
ejpam-3291	7	5	right	right	ADJ
ejpam-3291	7	6	r	r	NOUN
ejpam-3291	7	7	-	-	PUNCT
ejpam-3291	7	8	module	module	NOUN
ejpam-3291	7	9	and	and	CCONJ
ejpam-3291	7	10	s	s	NOUN
ejpam-3291	7	11	=	=	ADJ
ejpam-3291	7	12	endr(m	endr(m	PROPN
ejpam-3291	7	13	)	)	PUNCT
ejpam-3291	7	14	,	,	PUNCT
ejpam-3291	7	15	its	its	PRON
ejpam-3291	7	16	endomorphism	endomorphism	NOUN
ejpam-3291	7	17	ring	ring	NOUN
ejpam-3291	7	18	.	.	PUNCT
ejpam-3291	8	1	we	we	PRON
ejpam-3291	8	2	denote	denote	VERB
ejpam-3291	8	3	σ[m	σ[m	ADV
ejpam-3291	8	4	]	]	PUNCT
ejpam-3291	8	5	the	the	DET
ejpam-3291	8	6	full	full	ADJ
ejpam-3291	8	7	subcategory	subcategory	NOUN
ejpam-3291	8	8	of	of	ADP
ejpam-3291	8	9	mod	mod	PROPN
ejpam-3291	8	10	-	-	PUNCT
ejpam-3291	8	11	r	r	NOUN
ejpam-3291	8	12	whose	whose	DET
ejpam-3291	8	13	objects	object	NOUN
ejpam-3291	8	14	are	be	AUX
ejpam-3291	8	15	submodules	submodule	NOUN
ejpam-3291	8	16	of	of	ADP
ejpam-3291	8	17	m	m	PUNCT
ejpam-3291	8	18	-generated	-generate	VERB
ejpam-3291	8	19	modules	module	NOUN
ejpam-3291	8	20	.	.	PUNCT
ejpam-3291	9	1	a	a	DET
ejpam-3291	9	2	right	right	ADJ
ejpam-3291	9	3	r	r	NOUN
ejpam-3291	9	4	-	-	PUNCT
ejpam-3291	9	5	module	module	NOUN
ejpam-3291	9	6	m	m	NOUN
ejpam-3291	9	7	is	be	AUX
ejpam-3291	9	8	called	call	VERB
ejpam-3291	9	9	a	a	DET
ejpam-3291	9	10	subgenerator	subgenerator	NOUN
ejpam-3291	9	11	,	,	PUNCT
ejpam-3291	9	12	if	if	SCONJ
ejpam-3291	9	13	it	it	PRON
ejpam-3291	9	14	generates	generate	VERB
ejpam-3291	9	15	σ[m	σ[m	ADJ
ejpam-3291	9	16	]	]	PUNCT
ejpam-3291	9	17	and	and	CCONJ
ejpam-3291	9	18	a	a	DET
ejpam-3291	9	19	selfgenerator	selfgenerator	NOUN
ejpam-3291	9	20	,	,	PUNCT
ejpam-3291	9	21	if	if	SCONJ
ejpam-3291	9	22	it	it	PRON
ejpam-3291	9	23	generates	generate	VERB
ejpam-3291	9	24	all	all	DET
ejpam-3291	9	25	its	its	PRON
ejpam-3291	9	26	submodules	submodule	NOUN
ejpam-3291	9	27	.	.	PUNCT
ejpam-3291	10	1	we	we	PRON
ejpam-3291	10	2	denote	denote	VERB
ejpam-3291	10	3	the	the	DET
ejpam-3291	10	4	socle	socle	NOUN
ejpam-3291	10	5	and	and	CCONJ
ejpam-3291	10	6	radical	radical	NOUN
ejpam-3291	10	7	of	of	ADP
ejpam-3291	10	8	the	the	DET
ejpam-3291	10	9	right	right	ADJ
ejpam-3291	10	10	r	r	NOUN
ejpam-3291	10	11	-	-	PUNCT
ejpam-3291	10	12	module	module	NOUN
ejpam-3291	10	13	m	m	NOUN
ejpam-3291	10	14	by	by	ADP
ejpam-3291	10	15	soc(m	soc(m	PROPN
ejpam-3291	10	16	)	)	PUNCT
ejpam-3291	10	17	and	and	CCONJ
ejpam-3291	10	18	rad(m	rad(m	NUM
ejpam-3291	10	19	)	)	PUNCT
ejpam-3291	10	20	,	,	PUNCT
ejpam-3291	10	21	respectively	respectively	ADV
ejpam-3291	10	22	.	.	PUNCT
ejpam-3291	11	1	the	the	DET
ejpam-3291	11	2	jacobson	jacobson	PROPN
ejpam-3291	11	3	radical	radical	PROPN
ejpam-3291	11	4	of	of	ADP
ejpam-3291	11	5	a	a	DET
ejpam-3291	11	6	ring	ring	NOUN
ejpam-3291	11	7	r	r	NOUN
ejpam-3291	11	8	is	be	AUX
ejpam-3291	11	9	denoted	denote	VERB
ejpam-3291	11	10	by	by	ADP
ejpam-3291	11	11	j(r	j(r	PROPN
ejpam-3291	11	12	)	)	PUNCT
ejpam-3291	11	13	.	.	PUNCT
ejpam-3291	12	1	we	we	PRON
ejpam-3291	12	2	use	use	VERB
ejpam-3291	12	3	the	the	DET
ejpam-3291	12	4	notations	notation	NOUN
ejpam-3291	12	5	l	l	NOUN
ejpam-3291	12	6	and	and	CCONJ
ejpam-3291	12	7	r	r	NOUN
ejpam-3291	12	8	to	to	PART
ejpam-3291	12	9	denote	denote	VERB
ejpam-3291	12	10	left	left	ADJ
ejpam-3291	12	11	and	and	CCONJ
ejpam-3291	12	12	right	right	ADJ
ejpam-3291	12	13	annihilator	annihilator	NOUN
ejpam-3291	12	14	,	,	PUNCT
ejpam-3291	12	15	respectively	respectively	ADV
ejpam-3291	12	16	.	.	PUNCT
ejpam-3291	13	1	the	the	DET
ejpam-3291	13	2	baer	baer	PROPN
ejpam-3291	13	3	criterion	criterion	NOUN
ejpam-3291	13	4	has	have	AUX
ejpam-3291	13	5	been	be	AUX
ejpam-3291	13	6	generalized	generalize	VERB
ejpam-3291	13	7	by	by	ADP
ejpam-3291	13	8	many	many	ADJ
ejpam-3291	13	9	authors	author	NOUN
ejpam-3291	13	10	.	.	PUNCT
ejpam-3291	14	1	for	for	ADP
ejpam-3291	14	2	example	example	NOUN
ejpam-3291	14	3	,	,	PUNCT
ejpam-3291	14	4	in	in	ADP
ejpam-3291	14	5	1989	1989	NUM
ejpam-3291	14	6	,	,	PUNCT
ejpam-3291	14	7	camillo	camillo	PROPN
ejpam-3291	14	8	introduced	introduce	VERB
ejpam-3291	14	9	the	the	DET
ejpam-3291	14	10	notion	notion	NOUN
ejpam-3291	14	11	of	of	ADP
ejpam-3291	14	12	principally	principally	ADV
ejpam-3291	14	13	injective	injective	ADJ
ejpam-3291	14	14	modules	module	NOUN
ejpam-3291	14	15	for	for	ADP
ejpam-3291	14	16	commutative	commutative	ADJ
ejpam-3291	14	17	rings	ring	NOUN
ejpam-3291	14	18	in	in	ADP
ejpam-3291	14	19	[	[	X
ejpam-3291	14	20	3	3	NUM
ejpam-3291	14	21	]	]	PUNCT
ejpam-3291	14	22	.	.	PUNCT
ejpam-3291	15	1	a	a	DET
ejpam-3291	15	2	right	right	ADJ
ejpam-3291	15	3	r	r	NOUN
ejpam-3291	15	4	-	-	PUNCT
ejpam-3291	15	5	module	module	NOUN
ejpam-3291	15	6	m	m	NOUN
ejpam-3291	15	7	is	be	AUX
ejpam-3291	15	8	called	call	VERB
ejpam-3291	15	9	principally	principally	ADV
ejpam-3291	15	10	injective	injective	ADJ
ejpam-3291	15	11	(	(	PUNCT
ejpam-3291	15	12	or	or	CCONJ
ejpam-3291	15	13	p	p	NOUN
ejpam-3291	15	14	-	-	PUNCT
ejpam-3291	15	15	injective	injective	ADJ
ejpam-3291	15	16	)	)	PUNCT
ejpam-3291	15	17	,	,	PUNCT
ejpam-3291	15	18	if	if	SCONJ
ejpam-3291	15	19	every	every	DET
ejpam-3291	15	20	rhomomorphism	rhomomorphism	NOUN
ejpam-3291	15	21	from	from	ADP
ejpam-3291	15	22	a	a	DET
ejpam-3291	15	23	principal	principal	ADJ
ejpam-3291	15	24	right	right	ADJ
ejpam-3291	15	25	ideal	ideal	NOUN
ejpam-3291	15	26	of	of	ADP
ejpam-3291	15	27	r	r	NOUN
ejpam-3291	15	28	to	to	ADP
ejpam-3291	15	29	m	m	PROPN
ejpam-3291	15	30	can	can	AUX
ejpam-3291	15	31	be	be	AUX
ejpam-3291	15	32	extended	extend	VERB
ejpam-3291	15	33	to	to	ADP
ejpam-3291	15	34	one	one	NUM
ejpam-3291	15	35	from	from	ADP
ejpam-3291	15	36	r	r	NOUN
ejpam-3291	15	37	∗corresponding	∗corresponde	VERB
ejpam-3291	15	38	author	author	NOUN
ejpam-3291	15	39	.	.	PUNCT
ejpam-3291	16	1	doi	doi	NOUN
ejpam-3291	16	2	:	:	PUNCT
ejpam-3291	16	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3291	https://doi.org/10.29020/nybg.ejpam.v11i3.3291	ADJ
ejpam-3291	16	4	email	email	NOUN
ejpam-3291	16	5	addresses	address	NOUN
ejpam-3291	16	6	:	:	PUNCT
ejpam-3291	16	7	nghiemndh@gmail.com	nghiemndh@gmail.com	X
ejpam-3291	16	8	(	(	PUNCT
ejpam-3291	16	9	n.	n.	PROPN
ejpam-3291	16	10	d.	d.	PROPN
ejpam-3291	16	11	h.	h.	PROPN
ejpam-3291	16	12	nghiem	nghiem	PROPN
ejpam-3291	16	13	)	)	PUNCT
ejpam-3291	16	14	,	,	PUNCT
ejpam-3291	16	15	phatsarapa@gmail.com	phatsarapa@gmail.com	X
ejpam-3291	17	1	(	(	PUNCT
ejpam-3291	17	2	p.	p.	PROPN
ejpam-3291	17	3	janmuang	janmuang	PROPN
ejpam-3291	17	4	)	)	PUNCT
ejpam-3291	17	5	,	,	PUNCT
ejpam-3291	17	6	samruam.b@chula.ac.th	samruam.b@chula.ac.th	PROPN
ejpam-3291	17	7	(	(	PUNCT
ejpam-3291	17	8	s.	s.	PROPN
ejpam-3291	17	9	baupradist	baupradist	PROPN
ejpam-3291	17	10	)	)	PUNCT
ejpam-3291	17	11	,	,	PUNCT
ejpam-3291	17	12	ronnason.c@psu.ac.th	ronnason.c@psu.ac.th	PROPN
ejpam-3291	17	13	(	(	PUNCT
ejpam-3291	17	14	r.	r.	PROPN
ejpam-3291	17	15	chinram	chinram	PROPN
ejpam-3291	17	16	)	)	PUNCT
ejpam-3291	17	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3291	18	1	815	815	NUM
ejpam-3291	18	2	c	c	X
ejpam-3291	18	3	©	©	PROPN
ejpam-3291	18	4	2018	2018	NUM
ejpam-3291	18	5	ejpam	ejpam	VERB
ejpam-3291	18	6	all	all	DET
ejpam-3291	18	7	rights	right	NOUN
ejpam-3291	18	8	reserved	reserve	VERB
ejpam-3291	18	9	.	.	PUNCT
ejpam-3291	19	1	n.	n.	PROPN
ejpam-3291	19	2	d.	d.	PROPN
ejpam-3291	19	3	h.	h.	PROPN
ejpam-3291	19	4	nghiem	nghiem	PROPN
ejpam-3291	19	5	et	et	PROPN
ejpam-3291	19	6	al	al	PROPN
ejpam-3291	19	7	.	.	PUNCT
ejpam-3291	19	8	/	/	SYM
ejpam-3291	19	9	eur	eur	PROPN
ejpam-3291	19	10	.	.	PUNCT
ejpam-3291	20	1	j.	j.	PROPN
ejpam-3291	20	2	pure	pure	PROPN
ejpam-3291	20	3	appl	appl	PROPN
ejpam-3291	20	4	.	.	PROPN
ejpam-3291	20	5	math	math	PROPN
ejpam-3291	20	6	,	,	PUNCT
ejpam-3291	20	7	11	11	NUM
ejpam-3291	20	8	(	(	PUNCT
ejpam-3291	20	9	3	3	NUM
ejpam-3291	20	10	)	)	PUNCT
ejpam-3291	20	11	(	(	PUNCT
ejpam-3291	20	12	2018	2018	NUM
ejpam-3291	20	13	)	)	PUNCT
ejpam-3291	20	14	,	,	PUNCT
ejpam-3291	20	15	815	815	NUM
ejpam-3291	20	16	-	-	SYM
ejpam-3291	20	17	822	822	NUM
ejpam-3291	20	18	816	816	NUM
ejpam-3291	20	19	to	to	ADP
ejpam-3291	20	20	m	m	PRON
ejpam-3291	20	21	.	.	PUNCT
ejpam-3291	21	1	next	next	ADJ
ejpam-3291	21	2	in	in	ADP
ejpam-3291	21	3	1999	1999	NUM
ejpam-3291	21	4	,	,	PUNCT
ejpam-3291	21	5	sanh	sanh	NOUN
ejpam-3291	21	6	and	and	CCONJ
ejpam-3291	21	7	his	his	PRON
ejpam-3291	21	8	group	group	NOUN
ejpam-3291	21	9	introduced	introduce	VERB
ejpam-3291	21	10	m	m	VERB
ejpam-3291	21	11	-principal	-principal	ADJ
ejpam-3291	21	12	injectivity	injectivity	NOUN
ejpam-3291	21	13	for	for	ADP
ejpam-3291	21	14	a	a	DET
ejpam-3291	21	15	given	give	VERB
ejpam-3291	21	16	right	right	ADJ
ejpam-3291	21	17	r	r	NOUN
ejpam-3291	21	18	-	-	PUNCT
ejpam-3291	21	19	module	module	NOUN
ejpam-3291	21	20	m	m	NOUN
ejpam-3291	21	21	in	in	ADP
ejpam-3291	21	22	[	[	X
ejpam-3291	21	23	7	7	NUM
ejpam-3291	21	24	]	]	PUNCT
ejpam-3291	21	25	.	.	PUNCT
ejpam-3291	22	1	let	let	VERB
ejpam-3291	22	2	m	m	PRON
ejpam-3291	22	3	be	be	AUX
ejpam-3291	22	4	a	a	DET
ejpam-3291	22	5	right	right	ADJ
ejpam-3291	22	6	r	r	NOUN
ejpam-3291	22	7	-	-	NOUN
ejpam-3291	22	8	module	module	NOUN
ejpam-3291	22	9	.	.	PUNCT
ejpam-3291	23	1	a	a	DET
ejpam-3291	23	2	right	right	ADJ
ejpam-3291	23	3	r	r	NOUN
ejpam-3291	23	4	-	-	PUNCT
ejpam-3291	23	5	module	module	NOUN
ejpam-3291	23	6	n	n	NOUN
ejpam-3291	23	7	is	be	AUX
ejpam-3291	23	8	called	call	VERB
ejpam-3291	23	9	m	m	NOUN
ejpam-3291	23	10	-principally	-principally	NOUN
ejpam-3291	23	11	injective	injective	ADJ
ejpam-3291	23	12	,	,	PUNCT
ejpam-3291	23	13	if	if	SCONJ
ejpam-3291	23	14	every	every	DET
ejpam-3291	23	15	r	r	NOUN
ejpam-3291	23	16	-	-	PUNCT
ejpam-3291	23	17	homomorphism	homomorphism	NOUN
ejpam-3291	23	18	from	from	ADP
ejpam-3291	23	19	an	an	DET
ejpam-3291	23	20	m	m	PROPN
ejpam-3291	23	21	-cyclic	-cyclic	ADJ
ejpam-3291	23	22	submodule	submodule	NOUN
ejpam-3291	23	23	of	of	ADP
ejpam-3291	23	24	m	m	PROPN
ejpam-3291	23	25	to	to	ADP
ejpam-3291	23	26	n	n	PROPN
ejpam-3291	23	27	can	can	AUX
ejpam-3291	23	28	be	be	AUX
ejpam-3291	23	29	extended	extend	VERB
ejpam-3291	23	30	to	to	ADP
ejpam-3291	23	31	one	one	NUM
ejpam-3291	23	32	from	from	ADP
ejpam-3291	23	33	m	m	PROPN
ejpam-3291	23	34	to	to	ADP
ejpam-3291	23	35	n	n	PROPN
ejpam-3291	23	36	.	.	PUNCT
ejpam-3291	24	1	slightly	slightly	ADV
ejpam-3291	24	2	compressible	compressible	ADJ
ejpam-3291	24	3	modules	module	NOUN
ejpam-3291	24	4	were	be	AUX
ejpam-3291	24	5	studied	study	VERB
ejpam-3291	24	6	by	by	ADP
ejpam-3291	24	7	smith	smith	PROPN
ejpam-3291	24	8	in	in	ADP
ejpam-3291	24	9	[	[	X
ejpam-3291	24	10	9	9	NUM
ejpam-3291	24	11	]	]	PUNCT
ejpam-3291	24	12	.	.	PUNCT
ejpam-3291	25	1	in	in	ADP
ejpam-3291	25	2	2006	2006	NUM
ejpam-3291	25	3	,	,	PUNCT
ejpam-3291	25	4	essentially	essentially	ADV
ejpam-3291	25	5	compressible	compressible	ADJ
ejpam-3291	25	6	modules	module	NOUN
ejpam-3291	25	7	and	and	CCONJ
ejpam-3291	25	8	rings	ring	NOUN
ejpam-3291	25	9	were	be	AUX
ejpam-3291	25	10	introduced	introduce	VERB
ejpam-3291	25	11	and	and	CCONJ
ejpam-3291	25	12	studied	study	VERB
ejpam-3291	25	13	by	by	ADP
ejpam-3291	25	14	smith	smith	NOUN
ejpam-3291	25	15	and	and	CCONJ
ejpam-3291	25	16	vedadi	vedadi	NOUN
ejpam-3291	25	17	in	in	ADP
ejpam-3291	25	18	[	[	X
ejpam-3291	25	19	10	10	NUM
ejpam-3291	25	20	]	]	PUNCT
ejpam-3291	25	21	.	.	PUNCT
ejpam-3291	26	1	essentially	essentially	ADV
ejpam-3291	26	2	compressible	compressible	ADJ
ejpam-3291	26	3	modules	module	NOUN
ejpam-3291	26	4	is	be	AUX
ejpam-3291	26	5	a	a	DET
ejpam-3291	26	6	one	one	NUM
ejpam-3291	26	7	of	of	ADP
ejpam-3291	26	8	generalization	generalization	NOUN
ejpam-3291	26	9	of	of	ADP
ejpam-3291	26	10	compressible	compressible	ADJ
ejpam-3291	26	11	modules	module	NOUN
ejpam-3291	26	12	.	.	PUNCT
ejpam-3291	27	1	next	next	ADV
ejpam-3291	27	2	,	,	PUNCT
ejpam-3291	27	3	the	the	DET
ejpam-3291	27	4	concepts	concept	NOUN
ejpam-3291	27	5	of	of	ADP
ejpam-3291	27	6	essentially	essentially	ADV
ejpam-3291	27	7	slightly	slightly	ADV
ejpam-3291	27	8	compressible	compressible	ADJ
ejpam-3291	27	9	modules	module	NOUN
ejpam-3291	27	10	and	and	CCONJ
ejpam-3291	27	11	rings	ring	NOUN
ejpam-3291	27	12	were	be	AUX
ejpam-3291	27	13	introduced	introduce	VERB
ejpam-3291	27	14	,	,	PUNCT
ejpam-3291	27	15	and	and	CCONJ
ejpam-3291	27	16	related	related	ADJ
ejpam-3291	27	17	properties	property	NOUN
ejpam-3291	27	18	were	be	AUX
ejpam-3291	27	19	investigated	investigate	VERB
ejpam-3291	27	20	by	by	ADP
ejpam-3291	27	21	singh	singh	PROPN
ejpam-3291	27	22	in	in	ADP
ejpam-3291	27	23	[	[	X
ejpam-3291	27	24	8	8	NUM
ejpam-3291	27	25	]	]	PUNCT
ejpam-3291	27	26	.	.	PUNCT
ejpam-3291	28	1	essentially	essentially	ADV
ejpam-3291	28	2	slightly	slightly	ADV
ejpam-3291	28	3	compressible	compressible	ADJ
ejpam-3291	28	4	modules	module	NOUN
ejpam-3291	28	5	and	and	CCONJ
ejpam-3291	28	6	rings	ring	NOUN
ejpam-3291	28	7	are	be	AUX
ejpam-3291	28	8	a	a	DET
ejpam-3291	28	9	generalization	generalization	NOUN
ejpam-3291	28	10	of	of	ADP
ejpam-3291	28	11	essentially	essentially	ADV
ejpam-3291	28	12	compressible	compressible	ADJ
ejpam-3291	28	13	modules	module	NOUN
ejpam-3291	28	14	and	and	CCONJ
ejpam-3291	28	15	rings	ring	NOUN
ejpam-3291	28	16	.	.	PUNCT
ejpam-3291	29	1	celik	celik	AUX
ejpam-3291	29	2	introduced	introduce	VERB
ejpam-3291	29	3	and	and	CCONJ
ejpam-3291	29	4	investigated	investigate	VERB
ejpam-3291	29	5	completely	completely	ADV
ejpam-3291	29	6	slightly	slightly	ADV
ejpam-3291	29	7	compressible	compressible	ADJ
ejpam-3291	29	8	modules	module	NOUN
ejpam-3291	29	9	as	as	ADP
ejpam-3291	29	10	a	a	DET
ejpam-3291	29	11	one	one	NUM
ejpam-3291	29	12	of	of	ADP
ejpam-3291	29	13	generalization	generalization	NOUN
ejpam-3291	29	14	of	of	ADP
ejpam-3291	29	15	compressible	compressible	ADJ
ejpam-3291	29	16	modules	module	NOUN
ejpam-3291	29	17	.	.	PUNCT
ejpam-3291	30	1	recently	recently	ADV
ejpam-3291	30	2	,	,	PUNCT
ejpam-3291	30	3	baupradist	baupradist	PROPN
ejpam-3291	30	4	et	et	PROPN
ejpam-3291	30	5	al	al	PROPN
ejpam-3291	30	6	.	.	PROPN
ejpam-3291	30	7	studied	study	VERB
ejpam-3291	30	8	a	a	DET
ejpam-3291	30	9	general	general	ADJ
ejpam-3291	30	10	form	form	NOUN
ejpam-3291	30	11	of	of	ADP
ejpam-3291	30	12	slightly	slightly	ADV
ejpam-3291	30	13	compressible	compressible	ADJ
ejpam-3291	30	14	modules	module	NOUN
ejpam-3291	30	15	in	in	ADP
ejpam-3291	30	16	[	[	X
ejpam-3291	30	17	2	2	NUM
ejpam-3291	30	18	]	]	PUNCT
ejpam-3291	30	19	.	.	PUNCT
ejpam-3291	31	1	that	that	PRON
ejpam-3291	31	2	is	be	AUX
ejpam-3291	31	3	,	,	PUNCT
ejpam-3291	31	4	for	for	ADP
ejpam-3291	31	5	a	a	DET
ejpam-3291	31	6	right	right	ADJ
ejpam-3291	31	7	r	r	NOUN
ejpam-3291	31	8	-	-	PUNCT
ejpam-3291	31	9	module	module	NOUN
ejpam-3291	31	10	m	m	NOUN
ejpam-3291	31	11	and	and	CCONJ
ejpam-3291	31	12	n	n	CCONJ
ejpam-3291	31	13	,	,	PUNCT
ejpam-3291	31	14	n	n	X
ejpam-3291	31	15	is	be	AUX
ejpam-3291	31	16	called	call	VERB
ejpam-3291	31	17	an	an	DET
ejpam-3291	31	18	m	m	NOUN
ejpam-3291	31	19	-slightly	-slightly	ADV
ejpam-3291	31	20	compressible	compressible	ADJ
ejpam-3291	31	21	module	module	NOUN
ejpam-3291	31	22	,	,	PUNCT
ejpam-3291	31	23	if	if	SCONJ
ejpam-3291	31	24	every	every	DET
ejpam-3291	31	25	non	non	ADJ
ejpam-3291	31	26	-	-	ADJ
ejpam-3291	31	27	zero	zero	NUM
ejpam-3291	31	28	submodule	submodule	NOUN
ejpam-3291	31	29	a	a	PRON
ejpam-3291	31	30	of	of	ADP
ejpam-3291	31	31	n	n	NOUN
ejpam-3291	31	32	,	,	PUNCT
ejpam-3291	31	33	there	there	PRON
ejpam-3291	31	34	exists	exist	VERB
ejpam-3291	31	35	a	a	DET
ejpam-3291	31	36	non	non	ADJ
ejpam-3291	31	37	-	-	ADJ
ejpam-3291	31	38	zero	zero	ADJ
ejpam-3291	31	39	r	r	NOUN
ejpam-3291	31	40	-	-	PUNCT
ejpam-3291	31	41	homomorphism	homomorphism	NOUN
ejpam-3291	31	42	from	from	ADP
ejpam-3291	31	43	m	m	PRON
ejpam-3291	31	44	to	to	ADP
ejpam-3291	31	45	a.	a.	VERB
ejpam-3291	31	46	in	in	ADP
ejpam-3291	31	47	that	that	DET
ejpam-3291	31	48	paper	paper	NOUN
ejpam-3291	31	49	,	,	PUNCT
ejpam-3291	31	50	they	they	PRON
ejpam-3291	31	51	provided	provide	VERB
ejpam-3291	31	52	conditions	condition	NOUN
ejpam-3291	31	53	for	for	ADP
ejpam-3291	31	54	right	right	ADJ
ejpam-3291	31	55	r	r	NOUN
ejpam-3291	31	56	-	-	PUNCT
ejpam-3291	31	57	module	module	NOUN
ejpam-3291	31	58	to	to	PART
ejpam-3291	31	59	be	be	AUX
ejpam-3291	31	60	an	an	DET
ejpam-3291	31	61	m	m	ADV
ejpam-3291	31	62	-slightly	-slightly	ADV
ejpam-3291	31	63	compressible	compressible	ADJ
ejpam-3291	31	64	module	module	NOUN
ejpam-3291	31	65	and	and	CCONJ
ejpam-3291	31	66	examples	example	NOUN
ejpam-3291	31	67	of	of	ADP
ejpam-3291	31	68	m	m	PRON
ejpam-3291	31	69	-slightly	-slightly	ADV
ejpam-3291	31	70	compressible	compressible	ADJ
ejpam-3291	31	71	modules	module	NOUN
ejpam-3291	31	72	.	.	PUNCT
ejpam-3291	32	1	in	in	ADP
ejpam-3291	32	2	this	this	DET
ejpam-3291	32	3	paper	paper	NOUN
ejpam-3291	32	4	,	,	PUNCT
ejpam-3291	32	5	we	we	PRON
ejpam-3291	32	6	introduce	introduce	VERB
ejpam-3291	32	7	the	the	DET
ejpam-3291	32	8	concept	concept	NOUN
ejpam-3291	32	9	of	of	ADP
ejpam-3291	32	10	m	m	NOUN
ejpam-3291	32	11	-slightly	-slightly	ADV
ejpam-3291	32	12	compressible	compressible	ADJ
ejpam-3291	32	13	-	-	PUNCT
ejpam-3291	32	14	injective	injective	ADJ
ejpam-3291	32	15	modules	module	NOUN
ejpam-3291	32	16	,	,	PUNCT
ejpam-3291	32	17	which	which	PRON
ejpam-3291	32	18	extended	extend	VERB
ejpam-3291	32	19	from	from	ADP
ejpam-3291	32	20	the	the	DET
ejpam-3291	32	21	baer	baer	PROPN
ejpam-3291	32	22	criterion	criterion	NOUN
ejpam-3291	32	23	.	.	PUNCT
ejpam-3291	33	1	moreover	moreover	ADV
ejpam-3291	33	2	,	,	PUNCT
ejpam-3291	33	3	we	we	PRON
ejpam-3291	33	4	study	study	VERB
ejpam-3291	33	5	some	some	DET
ejpam-3291	33	6	properties	property	NOUN
ejpam-3291	33	7	of	of	ADP
ejpam-3291	33	8	m	m	PRON
ejpam-3291	33	9	slightly	slightly	ADV
ejpam-3291	33	10	compressible	compressible	ADJ
ejpam-3291	33	11	-	-	PUNCT
ejpam-3291	33	12	injective	injective	ADJ
ejpam-3291	33	13	modules	module	NOUN
ejpam-3291	33	14	and	and	CCONJ
ejpam-3291	33	15	relationship	relationship	NOUN
ejpam-3291	33	16	between	between	ADP
ejpam-3291	33	17	m	m	NOUN
ejpam-3291	33	18	-principally	-principally	ADV
ejpam-3291	33	19	injective	injective	ADJ
ejpam-3291	33	20	modules	module	NOUN
ejpam-3291	33	21	and	and	CCONJ
ejpam-3291	33	22	m	m	NOUN
ejpam-3291	33	23	-slightly	-slightly	ADV
ejpam-3291	33	24	compressible	compressible	ADJ
ejpam-3291	33	25	-	-	PUNCT
ejpam-3291	33	26	injective	injective	ADJ
ejpam-3291	33	27	modules	module	NOUN
ejpam-3291	33	28	.	.	PUNCT
ejpam-3291	34	1	for	for	ADP
ejpam-3291	34	2	the	the	DET
ejpam-3291	34	3	some	some	DET
ejpam-3291	34	4	examples	example	NOUN
ejpam-3291	34	5	of	of	ADP
ejpam-3291	34	6	m	m	PRON
ejpam-3291	34	7	slightly	slightly	ADV
ejpam-3291	34	8	compressible	compressible	ADJ
ejpam-3291	34	9	-	-	PUNCT
ejpam-3291	34	10	injective	injective	ADJ
ejpam-3291	34	11	modules	module	NOUN
ejpam-3291	34	12	are	be	AUX
ejpam-3291	34	13	provided	provide	VERB
ejpam-3291	34	14	.	.	PUNCT
ejpam-3291	35	1	for	for	ADP
ejpam-3291	35	2	definitions	definition	NOUN
ejpam-3291	35	3	and	and	CCONJ
ejpam-3291	35	4	terminologies	terminology	NOUN
ejpam-3291	35	5	not	not	PART
ejpam-3291	35	6	given	give	VERB
ejpam-3291	35	7	in	in	ADP
ejpam-3291	35	8	this	this	DET
ejpam-3291	35	9	paper	paper	NOUN
ejpam-3291	35	10	,	,	PUNCT
ejpam-3291	35	11	the	the	DET
ejpam-3291	35	12	reader	reader	NOUN
ejpam-3291	35	13	is	be	AUX
ejpam-3291	35	14	refereed	refereed	ADJ
ejpam-3291	35	15	to	to	ADP
ejpam-3291	35	16	[	[	X
ejpam-3291	35	17	1	1	NUM
ejpam-3291	35	18	,	,	PUNCT
ejpam-3291	35	19	5	5	NUM
ejpam-3291	35	20	,	,	PUNCT
ejpam-3291	35	21	6	6	NUM
ejpam-3291	35	22	]	]	PUNCT
ejpam-3291	35	23	.	.	PUNCT
ejpam-3291	36	1	2	2	X
ejpam-3291	36	2	.	.	X
ejpam-3291	36	3	slightly	slightly	ADV
ejpam-3291	36	4	compressible	compressible	ADJ
ejpam-3291	36	5	injectivity	injectivity	NOUN
ejpam-3291	36	6	for	for	ADP
ejpam-3291	36	7	a	a	DET
ejpam-3291	36	8	ring	ring	NOUN
ejpam-3291	36	9	r	r	NOUN
ejpam-3291	36	10	,	,	PUNCT
ejpam-3291	36	11	we	we	PRON
ejpam-3291	36	12	see	see	VERB
ejpam-3291	36	13	that	that	SCONJ
ejpam-3291	36	14	every	every	DET
ejpam-3291	36	15	right	right	ADJ
ejpam-3291	36	16	ideal	ideal	NOUN
ejpam-3291	36	17	of	of	ADP
ejpam-3291	36	18	r	r	NOUN
ejpam-3291	36	19	is	be	AUX
ejpam-3291	36	20	an	an	DET
ejpam-3291	36	21	rr	rr	ADJ
ejpam-3291	36	22	-	-	ADJ
ejpam-3291	36	23	slightly	slightly	ADV
ejpam-3291	36	24	compressible	compressible	ADJ
ejpam-3291	36	25	submodule	submodule	NOUN
ejpam-3291	36	26	of	of	ADP
ejpam-3291	36	27	rr	rr	PROPN
ejpam-3291	36	28	and	and	CCONJ
ejpam-3291	36	29	every	every	DET
ejpam-3291	36	30	rr	rr	ADJ
ejpam-3291	36	31	-	-	ADJ
ejpam-3291	36	32	slightly	slightly	ADV
ejpam-3291	36	33	compressible	compressible	ADJ
ejpam-3291	36	34	submodule	submodule	NOUN
ejpam-3291	36	35	of	of	ADP
ejpam-3291	36	36	rr	rr	PROPN
ejpam-3291	36	37	is	be	AUX
ejpam-3291	36	38	a	a	DET
ejpam-3291	36	39	right	right	ADJ
ejpam-3291	36	40	ideal	ideal	NOUN
ejpam-3291	36	41	of	of	ADP
ejpam-3291	36	42	r	r	NOUN
ejpam-3291	36	43	because	because	SCONJ
ejpam-3291	36	44	every	every	DET
ejpam-3291	36	45	submodule	submodule	NOUN
ejpam-3291	36	46	of	of	ADP
ejpam-3291	36	47	rr	rr	PROPN
ejpam-3291	36	48	is	be	AUX
ejpam-3291	36	49	a	a	DET
ejpam-3291	36	50	right	right	ADJ
ejpam-3291	36	51	ideal	ideal	NOUN
ejpam-3291	36	52	of	of	ADP
ejpam-3291	36	53	r.	r.	PROPN
ejpam-3291	36	54	we	we	PRON
ejpam-3291	36	55	use	use	VERB
ejpam-3291	36	56	this	this	DET
ejpam-3291	36	57	fact	fact	NOUN
ejpam-3291	36	58	to	to	PART
ejpam-3291	36	59	generalize	generalize	VERB
ejpam-3291	36	60	the	the	DET
ejpam-3291	36	61	notion	notion	NOUN
ejpam-3291	36	62	of	of	ADP
ejpam-3291	36	63	injectivity	injectivity	NOUN
ejpam-3291	36	64	to	to	ADP
ejpam-3291	36	65	an	an	DET
ejpam-3291	36	66	m	m	ADV
ejpam-3291	36	67	-slightly	-slightly	ADV
ejpam-3291	36	68	compressible	compressible	ADJ
ejpam-3291	36	69	-	-	PUNCT
ejpam-3291	36	70	injective	injective	ADJ
ejpam-3291	36	71	module	module	NOUN
ejpam-3291	36	72	for	for	ADP
ejpam-3291	36	73	a	a	DET
ejpam-3291	36	74	given	give	VERB
ejpam-3291	36	75	right	right	ADJ
ejpam-3291	36	76	r	r	NOUN
ejpam-3291	36	77	-	-	PUNCT
ejpam-3291	36	78	module	module	NOUN
ejpam-3291	36	79	m	m	NOUN
ejpam-3291	36	80	.	.	PUNCT
ejpam-3291	37	1	by	by	ADP
ejpam-3291	37	2	an	an	DET
ejpam-3291	37	3	m	m	PROPN
ejpam-3291	37	4	-cyclic	-cyclic	PROPN
ejpam-3291	37	5	submodule	submodule	NOUN
ejpam-3291	37	6	,	,	PUNCT
ejpam-3291	37	7	we	we	PRON
ejpam-3291	37	8	mean	mean	VERB
ejpam-3291	37	9	the	the	DET
ejpam-3291	37	10	submodule	submodule	NOUN
ejpam-3291	37	11	of	of	ADP
ejpam-3291	37	12	m	m	PROPN
ejpam-3291	37	13	of	of	ADP
ejpam-3291	37	14	the	the	DET
ejpam-3291	37	15	form	form	NOUN
ejpam-3291	37	16	s(m	s(m	PROPN
ejpam-3291	37	17	)	)	PUNCT
ejpam-3291	37	18	with	with	ADP
ejpam-3291	37	19	s	s	X
ejpam-3291	37	20	∈	∈	PROPN
ejpam-3291	37	21	s	s	PART
ejpam-3291	37	22	=	=	X
ejpam-3291	37	23	endr(m	endr(m	PROPN
ejpam-3291	37	24	)	)	PUNCT
ejpam-3291	37	25	.	.	PUNCT
ejpam-3291	38	1	definition	definition	NOUN
ejpam-3291	38	2	1	1	NUM
ejpam-3291	38	3	.	.	PUNCT
ejpam-3291	39	1	(	(	PUNCT
ejpam-3291	39	2	[	[	X
ejpam-3291	39	3	2	2	NUM
ejpam-3291	39	4	]	]	PUNCT
ejpam-3291	39	5	)	)	PUNCT
ejpam-3291	39	6	let	let	VERB
ejpam-3291	39	7	m	m	PRON
ejpam-3291	39	8	be	be	AUX
ejpam-3291	39	9	a	a	DET
ejpam-3291	39	10	right	right	ADJ
ejpam-3291	39	11	r	r	NOUN
ejpam-3291	39	12	-	-	NOUN
ejpam-3291	39	13	module	module	NOUN
ejpam-3291	39	14	.	.	PUNCT
ejpam-3291	40	1	a	a	DET
ejpam-3291	40	2	submodule	submodule	NOUN
ejpam-3291	40	3	a	a	PRON
ejpam-3291	40	4	of	of	ADP
ejpam-3291	40	5	m	m	PROPN
ejpam-3291	40	6	is	be	AUX
ejpam-3291	40	7	called	call	VERB
ejpam-3291	40	8	an	an	DET
ejpam-3291	40	9	m	m	VERB
ejpam-3291	40	10	slightly	slightly	ADV
ejpam-3291	40	11	compressible	compressible	ADJ
ejpam-3291	40	12	submodule	submodule	NOUN
ejpam-3291	40	13	of	of	ADP
ejpam-3291	40	14	m	m	PRON
ejpam-3291	40	15	,	,	PUNCT
ejpam-3291	40	16	if	if	SCONJ
ejpam-3291	40	17	every	every	DET
ejpam-3291	40	18	non	non	ADJ
ejpam-3291	40	19	-	-	ADJ
ejpam-3291	40	20	zero	zero	NUM
ejpam-3291	40	21	submodule	submodule	NOUN
ejpam-3291	40	22	a	a	PRON
ejpam-3291	40	23	of	of	ADP
ejpam-3291	40	24	n	n	NOUN
ejpam-3291	40	25	,	,	PUNCT
ejpam-3291	40	26	there	there	PRON
ejpam-3291	40	27	exists	exist	VERB
ejpam-3291	40	28	a	a	DET
ejpam-3291	40	29	non	non	ADJ
ejpam-3291	40	30	-	-	ADJ
ejpam-3291	40	31	zero	zero	ADJ
ejpam-3291	40	32	r	r	NOUN
ejpam-3291	40	33	-	-	PUNCT
ejpam-3291	40	34	homomorphism	homomorphism	NOUN
ejpam-3291	40	35	s	s	VERB
ejpam-3291	40	36	from	from	ADP
ejpam-3291	40	37	m	m	PROPN
ejpam-3291	40	38	to	to	ADP
ejpam-3291	40	39	n	n	CCONJ
ejpam-3291	40	40	such	such	ADJ
ejpam-3291	40	41	that	that	DET
ejpam-3291	40	42	s(m	s(m	NOUN
ejpam-3291	40	43	)	)	PUNCT
ejpam-3291	40	44	↪	↪	PROPN
ejpam-3291	40	45	→	→	SYM
ejpam-3291	40	46	a.	a.	NOUN
ejpam-3291	40	47	a	a	DET
ejpam-3291	40	48	right	right	ADJ
ejpam-3291	40	49	r	r	NOUN
ejpam-3291	40	50	-	-	PUNCT
ejpam-3291	40	51	module	module	NOUN
ejpam-3291	40	52	n	n	NOUN
ejpam-3291	40	53	is	be	AUX
ejpam-3291	40	54	called	call	VERB
ejpam-3291	40	55	quasi	quasi	ADJ
ejpam-3291	40	56	-	-	ADJ
ejpam-3291	40	57	slightly	slightly	ADV
ejpam-3291	40	58	compressible	compressible	ADJ
ejpam-3291	40	59	,	,	PUNCT
ejpam-3291	40	60	if	if	SCONJ
ejpam-3291	40	61	n	n	PRON
ejpam-3291	40	62	is	be	AUX
ejpam-3291	40	63	an	an	DET
ejpam-3291	40	64	n	n	CCONJ
ejpam-3291	40	65	-slight	-slight	ADJ
ejpam-3291	40	66	compressible	compressible	ADJ
ejpam-3291	40	67	module	module	NOUN
ejpam-3291	40	68	.	.	PUNCT
ejpam-3291	41	1	definition	definition	NOUN
ejpam-3291	41	2	2	2	NUM
ejpam-3291	41	3	.	.	PUNCT
ejpam-3291	42	1	let	let	VERB
ejpam-3291	42	2	m	m	PRON
ejpam-3291	42	3	be	be	AUX
ejpam-3291	42	4	a	a	DET
ejpam-3291	42	5	right	right	ADJ
ejpam-3291	42	6	r	r	NOUN
ejpam-3291	42	7	-	-	NOUN
ejpam-3291	42	8	module	module	NOUN
ejpam-3291	42	9	.	.	PUNCT
ejpam-3291	43	1	a	a	DET
ejpam-3291	43	2	right	right	ADJ
ejpam-3291	43	3	r	r	NOUN
ejpam-3291	43	4	-	-	PUNCT
ejpam-3291	43	5	module	module	NOUN
ejpam-3291	43	6	n	n	NOUN
ejpam-3291	43	7	is	be	AUX
ejpam-3291	43	8	called	call	VERB
ejpam-3291	43	9	an	an	DET
ejpam-3291	43	10	m	m	NOUN
ejpam-3291	43	11	slightly	slightly	ADV
ejpam-3291	43	12	compressible	compressible	ADJ
ejpam-3291	43	13	-	-	PUNCT
ejpam-3291	43	14	injective	injective	ADJ
ejpam-3291	43	15	module	module	NOUN
ejpam-3291	43	16	(	(	PUNCT
ejpam-3291	43	17	or	or	CCONJ
ejpam-3291	43	18	m	m	PRON
ejpam-3291	43	19	-sc	-sc	ADJ
ejpam-3291	43	20	-	-	PUNCT
ejpam-3291	43	21	injective	injective	ADJ
ejpam-3291	43	22	module	module	NOUN
ejpam-3291	43	23	for	for	ADP
ejpam-3291	43	24	short	short	ADJ
ejpam-3291	43	25	)	)	PUNCT
ejpam-3291	43	26	,	,	PUNCT
ejpam-3291	43	27	if	if	SCONJ
ejpam-3291	43	28	every	every	DET
ejpam-3291	43	29	rhomomorphism	rhomomorphism	NOUN
ejpam-3291	43	30	from	from	ADP
ejpam-3291	43	31	an	an	DET
ejpam-3291	43	32	m	m	ADV
ejpam-3291	43	33	-slightly	-slightly	ADV
ejpam-3291	43	34	compressible	compressible	ADJ
ejpam-3291	43	35	submodule	submodule	NOUN
ejpam-3291	43	36	of	of	ADP
ejpam-3291	43	37	m	m	PROPN
ejpam-3291	43	38	to	to	ADP
ejpam-3291	43	39	n	n	PROPN
ejpam-3291	43	40	can	can	AUX
ejpam-3291	43	41	be	be	AUX
ejpam-3291	43	42	extended	extend	VERB
ejpam-3291	43	43	to	to	ADP
ejpam-3291	43	44	an	an	DET
ejpam-3291	43	45	r	r	NOUN
ejpam-3291	43	46	-	-	PUNCT
ejpam-3291	43	47	homomorphism	homomorphism	NOUN
ejpam-3291	43	48	from	from	ADP
ejpam-3291	43	49	m	m	PROPN
ejpam-3291	43	50	to	to	ADP
ejpam-3291	43	51	n	n	PROPN
ejpam-3291	43	52	.	.	PUNCT
ejpam-3291	44	1	a	a	DET
ejpam-3291	44	2	right	right	ADJ
ejpam-3291	44	3	r	r	NOUN
ejpam-3291	44	4	-	-	PUNCT
ejpam-3291	44	5	module	module	NOUN
ejpam-3291	44	6	n	n	NOUN
ejpam-3291	44	7	is	be	AUX
ejpam-3291	44	8	called	call	VERB
ejpam-3291	44	9	quasi	quasi	ADJ
ejpam-3291	44	10	-	-	ADJ
ejpam-3291	44	11	slightly	slightly	ADV
ejpam-3291	44	12	compressible	compressible	ADJ
ejpam-3291	44	13	-	-	PUNCT
ejpam-3291	44	14	injective	injective	ADJ
ejpam-3291	44	15	(	(	PUNCT
ejpam-3291	44	16	or	or	CCONJ
ejpam-3291	44	17	quasi	quasi	ADJ
ejpam-3291	44	18	-	-	ADJ
ejpam-3291	44	19	sc	sc	ADJ
ejpam-3291	44	20	-	-	PUNCT
ejpam-3291	44	21	injective	injective	ADJ
ejpam-3291	44	22	for	for	ADP
ejpam-3291	44	23	short	short	ADJ
ejpam-3291	44	24	)	)	PUNCT
ejpam-3291	44	25	,	,	PUNCT
ejpam-3291	44	26	if	if	SCONJ
ejpam-3291	44	27	n	n	PRON
ejpam-3291	44	28	is	be	AUX
ejpam-3291	44	29	an	an	DET
ejpam-3291	44	30	n	n	ADV
ejpam-3291	44	31	-slightly	-slightly	ADV
ejpam-3291	44	32	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	44	33	module	module	NOUN
ejpam-3291	44	34	.	.	PUNCT
ejpam-3291	45	1	n.	n.	PROPN
ejpam-3291	45	2	d.	d.	PROPN
ejpam-3291	45	3	h.	h.	PROPN
ejpam-3291	45	4	nghiem	nghiem	PROPN
ejpam-3291	45	5	et	et	PROPN
ejpam-3291	45	6	al	al	PROPN
ejpam-3291	45	7	.	.	PUNCT
ejpam-3291	45	8	/	/	SYM
ejpam-3291	45	9	eur	eur	PROPN
ejpam-3291	45	10	.	.	PUNCT
ejpam-3291	46	1	j.	j.	PROPN
ejpam-3291	46	2	pure	pure	PROPN
ejpam-3291	46	3	appl	appl	PROPN
ejpam-3291	46	4	.	.	PROPN
ejpam-3291	46	5	math	math	PROPN
ejpam-3291	46	6	,	,	PUNCT
ejpam-3291	46	7	11	11	NUM
ejpam-3291	46	8	(	(	PUNCT
ejpam-3291	46	9	3	3	NUM
ejpam-3291	46	10	)	)	PUNCT
ejpam-3291	46	11	(	(	PUNCT
ejpam-3291	46	12	2018	2018	NUM
ejpam-3291	46	13	)	)	PUNCT
ejpam-3291	46	14	,	,	PUNCT
ejpam-3291	46	15	815	815	NUM
ejpam-3291	46	16	-	-	SYM
ejpam-3291	46	17	822	822	NUM
ejpam-3291	46	18	817	817	NUM
ejpam-3291	46	19	example	example	NOUN
ejpam-3291	46	20	1	1	NUM
ejpam-3291	46	21	.	.	PUNCT
ejpam-3291	47	1	(	(	PUNCT
ejpam-3291	47	2	1	1	X
ejpam-3291	47	3	)	)	PUNCT
ejpam-3291	47	4	every	every	DET
ejpam-3291	47	5	simple	simple	ADJ
ejpam-3291	47	6	right	right	ADJ
ejpam-3291	47	7	r	r	NOUN
ejpam-3291	47	8	-	-	PUNCT
ejpam-3291	47	9	module	module	NOUN
ejpam-3291	47	10	is	be	AUX
ejpam-3291	47	11	a	a	DET
ejpam-3291	47	12	quasi	quasi	ADJ
ejpam-3291	47	13	-	-	ADJ
ejpam-3291	47	14	slightly	slightly	ADV
ejpam-3291	47	15	compressible	compressible	ADJ
ejpam-3291	47	16	-	-	PUNCT
ejpam-3291	47	17	injective	injective	ADJ
ejpam-3291	47	18	module	module	NOUN
ejpam-3291	47	19	.	.	PUNCT
ejpam-3291	48	1	(	(	PUNCT
ejpam-3291	48	2	2	2	X
ejpam-3291	48	3	)	)	PUNCT
ejpam-3291	48	4	the	the	DET
ejpam-3291	48	5	following	follow	VERB
ejpam-3291	48	6	example	example	NOUN
ejpam-3291	48	7	[	[	X
ejpam-3291	48	8	see	see	VERB
ejpam-3291	48	9	[	[	X
ejpam-3291	48	10	5	5	NUM
ejpam-3291	48	11	]	]	PUNCT
ejpam-3291	48	12	,	,	PUNCT
ejpam-3291	48	13	exercise(2	exercise(2	PROPN
ejpam-3291	48	14	)	)	PUNCT
ejpam-3291	48	15	,	,	PUNCT
ejpam-3291	48	16	p.361	p.361	VERB
ejpam-3291	48	17	]	]	PUNCT
ejpam-3291	48	18	,	,	PUNCT
ejpam-3291	48	19	let	let	VERB
ejpam-3291	48	20	f	f	PRON
ejpam-3291	48	21	be	be	AUX
ejpam-3291	48	22	a	a	DET
ejpam-3291	48	23	field	field	NOUN
ejpam-3291	48	24	andr=	andr=	NUM
ejpam-3291	48	25	(	(	PUNCT
ejpam-3291	48	26	f	f	PROPN
ejpam-3291	48	27	f	f	PROPN
ejpam-3291	48	28	0	0	PROPN
ejpam-3291	48	29	f	f	PROPN
ejpam-3291	48	30	)	)	PUNCT
ejpam-3291	48	31	be	be	AUX
ejpam-3291	48	32	the	the	DET
ejpam-3291	48	33	ring	ring	NOUN
ejpam-3291	48	34	of	of	ADP
ejpam-3291	48	35	all	all	DET
ejpam-3291	48	36	matrices	matrix	NOUN
ejpam-3291	48	37	of	of	ADP
ejpam-3291	48	38	the	the	DET
ejpam-3291	48	39	form	form	NOUN
ejpam-3291	48	40	(	(	PUNCT
ejpam-3291	48	41	a	a	DET
ejpam-3291	48	42	b	b	NOUN
ejpam-3291	48	43	0	0	NUM
ejpam-3291	48	44	c	c	NOUN
ejpam-3291	48	45	)	)	PUNCT
ejpam-3291	48	46	with	with	ADP
ejpam-3291	48	47	a	a	DET
ejpam-3291	48	48	,	,	PUNCT
ejpam-3291	48	49	b	b	NOUN
ejpam-3291	48	50	,	,	PUNCT
ejpam-3291	49	1	c	c	PROPN
ejpam-3291	49	2	∈	∈	PROPN
ejpam-3291	49	3	f	f	X
ejpam-3291	49	4	.	.	PUNCT
ejpam-3291	50	1	let	let	VERB
ejpam-3291	50	2	m	m	VERB
ejpam-3291	50	3	=	=	PUNCT
ejpam-3291	51	1	(	(	PUNCT
ejpam-3291	51	2	f	f	NOUN
ejpam-3291	51	3	f	f	PROPN
ejpam-3291	51	4	0	0	PROPN
ejpam-3291	51	5	0	0	NUM
ejpam-3291	51	6	)	)	PUNCT
ejpam-3291	51	7	be	be	AUX
ejpam-3291	51	8	a	a	DET
ejpam-3291	51	9	right	right	ADJ
ejpam-3291	51	10	r	r	NOUN
ejpam-3291	51	11	-	-	PUNCT
ejpam-3291	51	12	module	module	NOUN
ejpam-3291	51	13	of	of	ADP
ejpam-3291	51	14	all	all	DET
ejpam-3291	51	15	matrices	matrix	NOUN
ejpam-3291	51	16	of	of	ADP
ejpam-3291	51	17	the	the	DET
ejpam-3291	51	18	form	form	NOUN
ejpam-3291	51	19	(	(	PUNCT
ejpam-3291	51	20	a	a	DET
ejpam-3291	51	21	b	b	NOUN
ejpam-3291	51	22	0	0	NUM
ejpam-3291	51	23	0	0	NUM
ejpam-3291	51	24	)	)	PUNCT
ejpam-3291	51	25	with	with	ADP
ejpam-3291	51	26	a	a	DET
ejpam-3291	51	27	,	,	PUNCT
ejpam-3291	51	28	b	b	PROPN
ejpam-3291	51	29	∈	∈	PROPN
ejpam-3291	51	30	f	f	PROPN
ejpam-3291	51	31	and	and	CCONJ
ejpam-3291	51	32	n	n	CCONJ
ejpam-3291	51	33	=	=	PUNCT
ejpam-3291	51	34	(	(	PUNCT
ejpam-3291	51	35	0	0	NUM
ejpam-3291	51	36	0	0	NUM
ejpam-3291	51	37	0	0	NUM
ejpam-3291	51	38	f	f	X
ejpam-3291	51	39	)	)	PUNCT
ejpam-3291	51	40	be	be	AUX
ejpam-3291	51	41	a	a	DET
ejpam-3291	51	42	right	right	ADJ
ejpam-3291	51	43	r	r	NOUN
ejpam-3291	51	44	-	-	PUNCT
ejpam-3291	51	45	module	module	NOUN
ejpam-3291	51	46	of	of	ADP
ejpam-3291	51	47	all	all	DET
ejpam-3291	51	48	matrices	matrix	NOUN
ejpam-3291	51	49	of	of	ADP
ejpam-3291	51	50	the	the	DET
ejpam-3291	51	51	form	form	NOUN
ejpam-3291	51	52	(	(	PUNCT
ejpam-3291	51	53	0	0	NUM
ejpam-3291	51	54	0	0	NUM
ejpam-3291	51	55	0	0	NUM
ejpam-3291	51	56	c	c	NOUN
ejpam-3291	51	57	)	)	PUNCT
ejpam-3291	51	58	with	with	ADP
ejpam-3291	51	59	c	c	PROPN
ejpam-3291	51	60	∈	∈	PROPN
ejpam-3291	51	61	f	f	PROPN
ejpam-3291	51	62	.	.	PUNCT
ejpam-3291	52	1	then	then	ADV
ejpam-3291	52	2	n	n	PRON
ejpam-3291	52	3	is	be	AUX
ejpam-3291	52	4	an	an	DET
ejpam-3291	52	5	m	m	ADV
ejpam-3291	52	6	-slightly	-slightly	ADV
ejpam-3291	52	7	compressible	compressible	ADJ
ejpam-3291	52	8	-	-	PUNCT
ejpam-3291	52	9	injective	injective	ADJ
ejpam-3291	52	10	module	module	NOUN
ejpam-3291	52	11	.	.	PUNCT
ejpam-3291	53	1	proof	proof	NOUN
ejpam-3291	53	2	.	.	PUNCT
ejpam-3291	54	1	let	let	VERB
ejpam-3291	54	2	a	a	PRON
ejpam-3291	54	3	be	be	AUX
ejpam-3291	54	4	a	a	DET
ejpam-3291	54	5	non	non	ADJ
ejpam-3291	54	6	-	-	ADJ
ejpam-3291	54	7	zero	zero	NUM
ejpam-3291	54	8	m	m	VERB
ejpam-3291	54	9	-slightly	-slightly	ADV
ejpam-3291	54	10	compressible	compressible	ADJ
ejpam-3291	54	11	submodule	submodule	NOUN
ejpam-3291	54	12	of	of	ADP
ejpam-3291	54	13	m	m	PROPN
ejpam-3291	54	14	and	and	CCONJ
ejpam-3291	54	15	α	α	PRON
ejpam-3291	54	16	an	an	DET
ejpam-3291	54	17	rhomomorphism	rhomomorphism	NOUN
ejpam-3291	54	18	from	from	ADP
ejpam-3291	54	19	a	a	PRON
ejpam-3291	54	20	to	to	ADP
ejpam-3291	54	21	n	n	PROPN
ejpam-3291	54	22	.	.	PUNCT
ejpam-3291	55	1	then	then	ADV
ejpam-3291	55	2	a	a	PRON
ejpam-3291	55	3	has	have	VERB
ejpam-3291	55	4	the	the	DET
ejpam-3291	55	5	form	form	NOUN
ejpam-3291	55	6	(	(	PUNCT
ejpam-3291	55	7	0	0	NUM
ejpam-3291	55	8	f1	f1	NOUN
ejpam-3291	55	9	0	0	NUM
ejpam-3291	55	10	0	0	NUM
ejpam-3291	55	11	)	)	PUNCT
ejpam-3291	55	12	,	,	PUNCT
ejpam-3291	55	13	(	(	PUNCT
ejpam-3291	55	14	f2	f2	X
ejpam-3291	55	15	0	0	NUM
ejpam-3291	55	16	0	0	NUM
ejpam-3291	55	17	0	0	NUM
ejpam-3291	55	18	)	)	PUNCT
ejpam-3291	55	19	or	or	CCONJ
ejpam-3291	55	20	(	(	PUNCT
ejpam-3291	55	21	f3	f3	VERB
ejpam-3291	55	22	f4	f4	ADJ
ejpam-3291	55	23	0	0	NUM
ejpam-3291	55	24	0	0	NUM
ejpam-3291	55	25	)	)	PUNCT
ejpam-3291	55	26	where	where	SCONJ
ejpam-3291	55	27	f1	f1	NOUN
ejpam-3291	55	28	,	,	PUNCT
ejpam-3291	55	29	f2	f2	PROPN
ejpam-3291	55	30	,	,	PUNCT
ejpam-3291	55	31	f3	f3	PROPN
ejpam-3291	55	32	and	and	CCONJ
ejpam-3291	55	33	f4	f4	NOUN
ejpam-3291	55	34	are	be	AUX
ejpam-3291	55	35	subfields	subfield	NOUN
ejpam-3291	55	36	of	of	ADP
ejpam-3291	55	37	f	f	PROPN
ejpam-3291	55	38	.	.	PUNCT
ejpam-3291	56	1	let	let	VERB
ejpam-3291	56	2	α	α	PRON
ejpam-3291	56	3	∈	∈	PROPN
ejpam-3291	56	4	homr(a	homr(a	NOUN
ejpam-3291	56	5	,	,	PUNCT
ejpam-3291	56	6	n	n	CCONJ
ejpam-3291	56	7	)	)	PUNCT
ejpam-3291	56	8	such	such	ADJ
ejpam-3291	56	9	that	that	SCONJ
ejpam-3291	56	10	any	any	DET
ejpam-3291	56	11	element	element	NOUN
ejpam-3291	56	12	x	x	SYM
ejpam-3291	56	13	∈	∈	PROPN
ejpam-3291	56	14	a	a	DET
ejpam-3291	56	15	,	,	PUNCT
ejpam-3291	56	16	α(x	α(x	NOUN
ejpam-3291	56	17	)	)	PUNCT
ejpam-3291	56	18	=	=	PUNCT
ejpam-3291	57	1	(	(	PUNCT
ejpam-3291	57	2	0	0	NUM
ejpam-3291	57	3	0	0	NUM
ejpam-3291	57	4	0	0	NUM
ejpam-3291	57	5	αx	αx	ADV
ejpam-3291	57	6	)	)	PUNCT
ejpam-3291	57	7	∈	∈	PROPN
ejpam-3291	57	8	n.	n.	NOUN
ejpam-3291	57	9	it	it	PRON
ejpam-3291	57	10	is	be	AUX
ejpam-3291	57	11	easy	easy	ADJ
ejpam-3291	57	12	to	to	PART
ejpam-3291	57	13	define	define	VERB
ejpam-3291	57	14	α	α	NOUN
ejpam-3291	57	15	from	from	ADP
ejpam-3291	57	16	m	m	PROPN
ejpam-3291	57	17	to	to	ADP
ejpam-3291	57	18	n	n	PROPN
ejpam-3291	57	19	by	by	ADP
ejpam-3291	57	20	α	α	X
ejpam-3291	57	21	(	(	PUNCT
ejpam-3291	57	22	(	(	PUNCT
ejpam-3291	57	23	a	a	DET
ejpam-3291	57	24	b	b	NOUN
ejpam-3291	57	25	0	0	NUM
ejpam-3291	57	26	0	0	NUM
ejpam-3291	57	27	)	)	PUNCT
ejpam-3291	57	28	)	)	PUNCT
ejpam-3291	58	1	=	=	PUNCT
ejpam-3291	58	2	(	(	PUNCT
ejpam-3291	58	3	0	0	NUM
ejpam-3291	58	4	0	0	NUM
ejpam-3291	58	5	0	0	NUM
ejpam-3291	59	1	αx	αx	PROPN
ejpam-3291	59	2	)	)	PUNCT
ejpam-3291	59	3	.	.	PUNCT
ejpam-3291	60	1	it	it	PRON
ejpam-3291	60	2	is	be	AUX
ejpam-3291	60	3	clear	clear	ADJ
ejpam-3291	60	4	that	that	SCONJ
ejpam-3291	60	5	ᾱ|a	ᾱ|a	NOUN
ejpam-3291	60	6	=	=	SYM
ejpam-3291	60	7	α	α	X
ejpam-3291	60	8	.	.	PUNCT
ejpam-3291	61	1	therefore	therefore	ADV
ejpam-3291	61	2	n	n	PROPN
ejpam-3291	61	3	is	be	AUX
ejpam-3291	61	4	an	an	DET
ejpam-3291	61	5	m	m	ADV
ejpam-3291	61	6	-slightly	-slightly	ADV
ejpam-3291	61	7	compressible	compressible	ADJ
ejpam-3291	61	8	-	-	PUNCT
ejpam-3291	61	9	injective	injective	ADJ
ejpam-3291	61	10	module	module	NOUN
ejpam-3291	61	11	.	.	PUNCT
ejpam-3291	62	1	proposition	proposition	NOUN
ejpam-3291	62	2	1	1	NUM
ejpam-3291	62	3	.	.	PUNCT
ejpam-3291	63	1	let	let	VERB
ejpam-3291	63	2	m	m	PRON
ejpam-3291	63	3	be	be	AUX
ejpam-3291	63	4	a	a	DET
ejpam-3291	63	5	right	right	ADJ
ejpam-3291	63	6	r	r	NOUN
ejpam-3291	63	7	-	-	PUNCT
ejpam-3291	63	8	module	module	NOUN
ejpam-3291	63	9	and	and	CCONJ
ejpam-3291	63	10	a	a	DET
ejpam-3291	63	11	be	be	AUX
ejpam-3291	63	12	a	a	DET
ejpam-3291	63	13	non	non	ADJ
ejpam-3291	63	14	-	-	ADJ
ejpam-3291	63	15	zero	zero	NUM
ejpam-3291	63	16	submodule	submodule	NOUN
ejpam-3291	63	17	of	of	ADP
ejpam-3291	63	18	m	m	PROPN
ejpam-3291	63	19	.	.	PUNCT
ejpam-3291	64	1	if	if	SCONJ
ejpam-3291	64	2	a	a	PRON
ejpam-3291	64	3	is	be	AUX
ejpam-3291	64	4	an	an	DET
ejpam-3291	64	5	m	m	NOUN
ejpam-3291	64	6	-slightly	-slightly	ADV
ejpam-3291	64	7	compressible	compressible	ADJ
ejpam-3291	64	8	-	-	PUNCT
ejpam-3291	64	9	injective	injective	ADJ
ejpam-3291	64	10	module	module	NOUN
ejpam-3291	64	11	,	,	PUNCT
ejpam-3291	64	12	then	then	ADV
ejpam-3291	64	13	a	a	PRON
ejpam-3291	64	14	is	be	AUX
ejpam-3291	64	15	a	a	DET
ejpam-3291	64	16	direct	direct	ADJ
ejpam-3291	64	17	summand	summand	NOUN
ejpam-3291	64	18	of	of	ADP
ejpam-3291	64	19	m	m	PROPN
ejpam-3291	64	20	.	.	PUNCT
ejpam-3291	65	1	proof	proof	NOUN
ejpam-3291	65	2	.	.	PUNCT
ejpam-3291	66	1	assume	assume	VERB
ejpam-3291	66	2	that	that	SCONJ
ejpam-3291	66	3	a	a	PRON
ejpam-3291	66	4	is	be	AUX
ejpam-3291	66	5	an	an	DET
ejpam-3291	66	6	m	m	ADV
ejpam-3291	66	7	-slightly	-slightly	ADV
ejpam-3291	66	8	compressible	compressible	ADJ
ejpam-3291	66	9	-	-	PUNCT
ejpam-3291	66	10	injective	injective	ADJ
ejpam-3291	66	11	module	module	NOUN
ejpam-3291	66	12	.	.	PUNCT
ejpam-3291	67	1	then	then	ADV
ejpam-3291	67	2	there	there	PRON
ejpam-3291	67	3	exists	exist	VERB
ejpam-3291	67	4	α	α	NOUN
ejpam-3291	67	5	:	:	PUNCT
ejpam-3291	67	6	m	m	VERB
ejpam-3291	67	7	→	→	SYM
ejpam-3291	67	8	a	a	DET
ejpam-3291	67	9	such	such	ADJ
ejpam-3291	67	10	that	that	DET
ejpam-3291	67	11	αia	αia	NOUN
ejpam-3291	67	12	=	=	SYM
ejpam-3291	67	13	ia	ia	PROPN
ejpam-3291	67	14	where	where	SCONJ
ejpam-3291	67	15	ia	ia	PROPN
ejpam-3291	67	16	is	be	AUX
ejpam-3291	67	17	the	the	DET
ejpam-3291	67	18	inclusion	inclusion	NOUN
ejpam-3291	67	19	map	map	NOUN
ejpam-3291	67	20	from	from	ADP
ejpam-3291	67	21	a	a	PRON
ejpam-3291	67	22	to	to	ADP
ejpam-3291	67	23	m	m	PROPN
ejpam-3291	67	24	and	and	CCONJ
ejpam-3291	67	25	ia	ia	PROPN
ejpam-3291	67	26	is	be	AUX
ejpam-3291	67	27	the	the	DET
ejpam-3291	67	28	identity	identity	NOUN
ejpam-3291	67	29	map	map	NOUN
ejpam-3291	67	30	on	on	ADP
ejpam-3291	67	31	a.	a.	NOUN
ejpam-3291	68	1	so	so	ADV
ejpam-3291	68	2	a	a	PRON
ejpam-3291	68	3	is	be	AUX
ejpam-3291	68	4	a	a	DET
ejpam-3291	68	5	direct	direct	ADJ
ejpam-3291	68	6	summand	summand	NOUN
ejpam-3291	68	7	of	of	ADP
ejpam-3291	68	8	m	m	PROPN
ejpam-3291	68	9	.	.	PUNCT
ejpam-3291	69	1	proposition	proposition	NOUN
ejpam-3291	69	2	2	2	NUM
ejpam-3291	69	3	.	.	PUNCT
ejpam-3291	70	1	let	let	VERB
ejpam-3291	70	2	m	m	PRON
ejpam-3291	70	3	be	be	AUX
ejpam-3291	70	4	a	a	DET
ejpam-3291	70	5	quasi	quasi	ADJ
ejpam-3291	70	6	-	-	ADJ
ejpam-3291	70	7	slightly	slightly	ADV
ejpam-3291	70	8	compressible	compressible	ADJ
ejpam-3291	70	9	-	-	PUNCT
ejpam-3291	70	10	injective	injective	ADJ
ejpam-3291	70	11	module	module	NOUN
ejpam-3291	70	12	and	and	CCONJ
ejpam-3291	70	13	f	f	NOUN
ejpam-3291	70	14	,	,	PUNCT
ejpam-3291	70	15	g	g	PROPN
ejpam-3291	70	16	∈	∈	PROPN
ejpam-3291	70	17	s	s	PART
ejpam-3291	70	18	=	=	X
ejpam-3291	70	19	endr(m	endr(m	PROPN
ejpam-3291	70	20	)	)	PUNCT
ejpam-3291	70	21	.	.	PUNCT
ejpam-3291	71	1	then	then	ADV
ejpam-3291	71	2	f	f	PROPN
ejpam-3291	71	3	∈	∈	PROPN
ejpam-3291	71	4	sg	sg	ADP
ejpam-3291	71	5	if	if	SCONJ
ejpam-3291	71	6	and	and	CCONJ
ejpam-3291	71	7	only	only	ADV
ejpam-3291	71	8	if	if	SCONJ
ejpam-3291	71	9	ker(g	ker(g	PROPN
ejpam-3291	71	10	)	)	PUNCT
ejpam-3291	71	11	⊆	⊆	NUM
ejpam-3291	71	12	ker(f	ker(f	PROPN
ejpam-3291	71	13	)	)	PUNCT
ejpam-3291	71	14	.	.	PUNCT
ejpam-3291	72	1	proof	proof	NOUN
ejpam-3291	72	2	.	.	PUNCT
ejpam-3291	73	1	(	(	PUNCT
ejpam-3291	73	2	⇒	⇒	NOUN
ejpam-3291	73	3	)	)	PUNCT
ejpam-3291	73	4	obviously	obviously	ADV
ejpam-3291	73	5	.	.	PUNCT
ejpam-3291	74	1	(	(	PUNCT
ejpam-3291	74	2	⇐	⇐	NOUN
ejpam-3291	74	3	)	)	PUNCT
ejpam-3291	74	4	assume	assume	VERB
ejpam-3291	74	5	that	that	SCONJ
ejpam-3291	74	6	ker(g	ker(g	PROPN
ejpam-3291	74	7	)	)	PUNCT
ejpam-3291	74	8	⊆	⊆	NUM
ejpam-3291	74	9	ker(f	ker(f	PROPN
ejpam-3291	74	10	)	)	PUNCT
ejpam-3291	74	11	.	.	PUNCT
ejpam-3291	75	1	by	by	ADP
ejpam-3291	75	2	the	the	DET
ejpam-3291	75	3	factor	factor	NOUN
ejpam-3291	75	4	’s	’s	PART
ejpam-3291	75	5	theorem	theorem	NOUN
ejpam-3291	75	6	,	,	PUNCT
ejpam-3291	75	7	there	there	PRON
ejpam-3291	75	8	exists	exist	VERB
ejpam-3291	75	9	g′	g′	NOUN
ejpam-3291	75	10	:	:	PUNCT
ejpam-3291	75	11	g(m)→m	g(m)→m	PROPN
ejpam-3291	75	12	such	such	ADJ
ejpam-3291	75	13	that	that	DET
ejpam-3291	75	14	g′g	g′g	NOUN
ejpam-3291	75	15	=	=	SYM
ejpam-3291	75	16	f	f	PROPN
ejpam-3291	75	17	.	.	PUNCT
ejpam-3291	76	1	since	since	SCONJ
ejpam-3291	76	2	m	m	PROPN
ejpam-3291	76	3	is	be	AUX
ejpam-3291	76	4	a	a	DET
ejpam-3291	76	5	quasi	quasi	ADJ
ejpam-3291	76	6	-	-	ADJ
ejpam-3291	76	7	slightly	slightly	ADV
ejpam-3291	76	8	compressible	compressible	ADJ
ejpam-3291	76	9	-	-	PUNCT
ejpam-3291	76	10	injective	injective	ADJ
ejpam-3291	76	11	module	module	NOUN
ejpam-3291	76	12	,	,	PUNCT
ejpam-3291	76	13	there	there	PRON
ejpam-3291	76	14	exists	exist	VERB
ejpam-3291	76	15	h	h	NOUN
ejpam-3291	76	16	∈	∈	PROPN
ejpam-3291	76	17	s	s	VERB
ejpam-3291	76	18	such	such	ADJ
ejpam-3291	76	19	that	that	PRON
ejpam-3291	76	20	hig(m	hig(m	ADJ
ejpam-3291	76	21	)	)	PUNCT
ejpam-3291	76	22	=	=	SYM
ejpam-3291	76	23	g′	g′	NOUN
ejpam-3291	76	24	where	where	SCONJ
ejpam-3291	76	25	ig(m	ig(m	NUM
ejpam-3291	76	26	)	)	PUNCT
ejpam-3291	76	27	:	:	PUNCT
ejpam-3291	76	28	g(m	g(m	VERB
ejpam-3291	76	29	)	)	PUNCT
ejpam-3291	76	30	→	→	PUNCT
ejpam-3291	76	31	m	m	NOUN
ejpam-3291	76	32	is	be	AUX
ejpam-3291	76	33	an	an	DET
ejpam-3291	76	34	embedding	embedding	NOUN
ejpam-3291	76	35	.	.	PUNCT
ejpam-3291	77	1	so	so	ADV
ejpam-3291	77	2	hg	hg	X
ejpam-3291	77	3	=	=	PUNCT
ejpam-3291	77	4	hig(m)g	hig(m)g	NOUN
ejpam-3291	77	5	=	=	SYM
ejpam-3291	77	6	g′g	g′g	NOUN
ejpam-3291	77	7	=	=	SYM
ejpam-3291	77	8	f	f	PROPN
ejpam-3291	77	9	.	.	PUNCT
ejpam-3291	78	1	therefore	therefore	ADV
ejpam-3291	78	2	f	f	PROPN
ejpam-3291	78	3	∈	∈	PROPN
ejpam-3291	78	4	sg	sg	PROPN
ejpam-3291	78	5	.	.	PUNCT
ejpam-3291	78	6	proposition	proposition	NOUN
ejpam-3291	78	7	3	3	NUM
ejpam-3291	78	8	.	.	PUNCT
ejpam-3291	79	1	let	let	VERB
ejpam-3291	79	2	m	m	PRON
ejpam-3291	79	3	and	and	CCONJ
ejpam-3291	79	4	n	n	ADV
ejpam-3291	79	5	be	be	AUX
ejpam-3291	79	6	right	right	ADJ
ejpam-3291	79	7	r	r	NOUN
ejpam-3291	79	8	-	-	PUNCT
ejpam-3291	79	9	modules	module	NOUN
ejpam-3291	79	10	.	.	PUNCT
ejpam-3291	80	1	if	if	SCONJ
ejpam-3291	80	2	n	n	PRON
ejpam-3291	80	3	is	be	AUX
ejpam-3291	80	4	an	an	DET
ejpam-3291	80	5	m	m	ADV
ejpam-3291	80	6	-slightly	-slightly	ADV
ejpam-3291	80	7	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	80	8	module	module	NOUN
ejpam-3291	80	9	,	,	PUNCT
ejpam-3291	80	10	then	then	ADV
ejpam-3291	80	11	any	any	DET
ejpam-3291	80	12	r	r	NOUN
ejpam-3291	80	13	-	-	NOUN
ejpam-3291	80	14	monomorphism	monomorphism	NOUN
ejpam-3291	80	15	from	from	ADP
ejpam-3291	80	16	n	n	NOUN
ejpam-3291	80	17	to	to	PART
ejpam-3291	80	18	m	m	VERB
ejpam-3291	80	19	splits	split	NOUN
ejpam-3291	80	20	.	.	PUNCT
ejpam-3291	81	1	proof	proof	NOUN
ejpam-3291	81	2	.	.	PUNCT
ejpam-3291	82	1	assume	assume	VERB
ejpam-3291	82	2	that	that	SCONJ
ejpam-3291	82	3	n	n	PRON
ejpam-3291	82	4	is	be	AUX
ejpam-3291	82	5	an	an	DET
ejpam-3291	82	6	m	m	ADV
ejpam-3291	82	7	-slightly	-slightly	ADV
ejpam-3291	82	8	compressible	compressible	ADJ
ejpam-3291	82	9	-	-	PUNCT
ejpam-3291	82	10	injective	injective	ADJ
ejpam-3291	82	11	module	module	NOUN
ejpam-3291	82	12	.	.	PUNCT
ejpam-3291	83	1	let	let	VERB
ejpam-3291	83	2	f	f	NOUN
ejpam-3291	83	3	:	:	PUNCT
ejpam-3291	83	4	n	n	X
ejpam-3291	83	5	→	→	PUNCT
ejpam-3291	83	6	m	m	AUX
ejpam-3291	83	7	be	be	AUX
ejpam-3291	83	8	an	an	DET
ejpam-3291	83	9	r	r	NOUN
ejpam-3291	83	10	-	-	PUNCT
ejpam-3291	83	11	monomorphism	monomorphism	NOUN
ejpam-3291	83	12	.	.	PUNCT
ejpam-3291	84	1	thus	thus	ADV
ejpam-3291	84	2	f−1	f−1	PROPN
ejpam-3291	84	3	:	:	PUNCT
ejpam-3291	84	4	f(n	f(n	PROPN
ejpam-3291	84	5	)	)	PUNCT
ejpam-3291	85	1	→	→	PUNCT
ejpam-3291	85	2	m	m	NOUN
ejpam-3291	85	3	is	be	AUX
ejpam-3291	85	4	well	well	ADV
ejpam-3291	85	5	defined	define	VERB
ejpam-3291	85	6	and	and	CCONJ
ejpam-3291	85	7	is	be	AUX
ejpam-3291	86	1	n.	n.	PROPN
ejpam-3291	86	2	d.	d.	PROPN
ejpam-3291	86	3	h.	h.	PROPN
ejpam-3291	86	4	nghiem	nghiem	PROPN
ejpam-3291	86	5	et	et	PROPN
ejpam-3291	86	6	al	al	PROPN
ejpam-3291	86	7	.	.	PUNCT
ejpam-3291	86	8	/	/	SYM
ejpam-3291	86	9	eur	eur	PROPN
ejpam-3291	86	10	.	.	PUNCT
ejpam-3291	87	1	j.	j.	PROPN
ejpam-3291	87	2	pure	pure	PROPN
ejpam-3291	87	3	appl	appl	PROPN
ejpam-3291	87	4	.	.	PROPN
ejpam-3291	87	5	math	math	PROPN
ejpam-3291	87	6	,	,	PUNCT
ejpam-3291	87	7	11	11	NUM
ejpam-3291	87	8	(	(	PUNCT
ejpam-3291	87	9	3	3	NUM
ejpam-3291	87	10	)	)	PUNCT
ejpam-3291	87	11	(	(	PUNCT
ejpam-3291	87	12	2018	2018	NUM
ejpam-3291	87	13	)	)	PUNCT
ejpam-3291	87	14	,	,	PUNCT
ejpam-3291	87	15	815	815	NUM
ejpam-3291	87	16	-	-	SYM
ejpam-3291	87	17	822	822	NUM
ejpam-3291	87	18	818	818	NUM
ejpam-3291	87	19	an	an	DET
ejpam-3291	87	20	r	r	NOUN
ejpam-3291	87	21	-	-	PUNCT
ejpam-3291	87	22	homomorphism	homomorphism	NOUN
ejpam-3291	87	23	.	.	PUNCT
ejpam-3291	88	1	since	since	SCONJ
ejpam-3291	88	2	f(n	f(n	PROPN
ejpam-3291	88	3	)	)	PUNCT
ejpam-3291	88	4	is	be	AUX
ejpam-3291	88	5	an	an	DET
ejpam-3291	88	6	m	m	ADV
ejpam-3291	88	7	-slightly	-slightly	ADV
ejpam-3291	88	8	compressible	compressible	ADJ
ejpam-3291	88	9	submodule	submodule	NOUN
ejpam-3291	88	10	of	of	ADP
ejpam-3291	88	11	m	m	PROPN
ejpam-3291	88	12	,	,	PUNCT
ejpam-3291	88	13	f−1	f−1	PROPN
ejpam-3291	88	14	can	can	AUX
ejpam-3291	88	15	be	be	AUX
ejpam-3291	88	16	extended	extend	VERB
ejpam-3291	88	17	to	to	ADP
ejpam-3291	88	18	an	an	DET
ejpam-3291	88	19	r	r	NOUN
ejpam-3291	88	20	-	-	PUNCT
ejpam-3291	88	21	homomorphism	homomorphism	NOUN
ejpam-3291	88	22	α	α	NOUN
ejpam-3291	88	23	:	:	PUNCT
ejpam-3291	88	24	m	m	VERB
ejpam-3291	88	25	→	→	SYM
ejpam-3291	88	26	n	n	CCONJ
ejpam-3291	88	27	such	such	ADJ
ejpam-3291	88	28	that	that	DET
ejpam-3291	88	29	αif(n	αif(n	NOUN
ejpam-3291	88	30	)	)	PUNCT
ejpam-3291	89	1	=	=	SYM
ejpam-3291	89	2	f−1	f−1	PROPN
ejpam-3291	89	3	where	where	SCONJ
ejpam-3291	89	4	if(n	if(n	NOUN
ejpam-3291	89	5	)	)	PUNCT
ejpam-3291	89	6	:	:	PUNCT
ejpam-3291	89	7	f(n	f(n	PROPN
ejpam-3291	89	8	)	)	PUNCT
ejpam-3291	90	1	→	→	PUNCT
ejpam-3291	90	2	m	m	NOUN
ejpam-3291	90	3	is	be	AUX
ejpam-3291	90	4	an	an	DET
ejpam-3291	90	5	embedding	embedding	NOUN
ejpam-3291	90	6	.	.	PUNCT
ejpam-3291	91	1	therefore	therefore	ADV
ejpam-3291	91	2	αf	αf	VERB
ejpam-3291	91	3	=	=	PUNCT
ejpam-3291	91	4	in	in	ADP
ejpam-3291	91	5	where	where	SCONJ
ejpam-3291	91	6	in	in	ADP
ejpam-3291	91	7	is	be	AUX
ejpam-3291	91	8	an	an	DET
ejpam-3291	91	9	identity	identity	NOUN
ejpam-3291	91	10	map	map	NOUN
ejpam-3291	91	11	on	on	ADP
ejpam-3291	91	12	n	n	PRON
ejpam-3291	91	13	and	and	CCONJ
ejpam-3291	91	14	hence	hence	ADV
ejpam-3291	91	15	f	f	PROPN
ejpam-3291	91	16	splits	split	VERB
ejpam-3291	91	17	.	.	PUNCT
ejpam-3291	92	1	proposition	proposition	NOUN
ejpam-3291	92	2	4	4	NUM
ejpam-3291	92	3	.	.	PUNCT
ejpam-3291	93	1	let	let	VERB
ejpam-3291	93	2	m	m	PRON
ejpam-3291	93	3	and	and	CCONJ
ejpam-3291	93	4	n	n	ADV
ejpam-3291	93	5	be	be	AUX
ejpam-3291	93	6	right	right	ADJ
ejpam-3291	93	7	r	r	NOUN
ejpam-3291	93	8	-	-	PUNCT
ejpam-3291	93	9	modules	module	NOUN
ejpam-3291	93	10	.	.	PUNCT
ejpam-3291	94	1	if	if	SCONJ
ejpam-3291	94	2	n	n	PRON
ejpam-3291	94	3	is	be	AUX
ejpam-3291	94	4	an	an	DET
ejpam-3291	94	5	m	m	ADV
ejpam-3291	94	6	-slightly	-slightly	ADV
ejpam-3291	94	7	compressible	compressible	ADJ
ejpam-3291	94	8	injective	injective	ADJ
ejpam-3291	94	9	module	module	NOUN
ejpam-3291	94	10	and	and	CCONJ
ejpam-3291	94	11	a	a	DET
ejpam-3291	94	12	⊂⊕	⊂⊕	PROPN
ejpam-3291	94	13	>	>	X
ejpam-3291	94	14	n	n	PROPN
ejpam-3291	94	15	,	,	PUNCT
ejpam-3291	94	16	then	then	ADV
ejpam-3291	94	17	a	a	PRON
ejpam-3291	94	18	is	be	AUX
ejpam-3291	94	19	an	an	DET
ejpam-3291	94	20	m	m	ADV
ejpam-3291	94	21	-slightly	-slightly	ADV
ejpam-3291	94	22	compressible	compressible	ADJ
ejpam-3291	94	23	injective	injective	ADJ
ejpam-3291	94	24	module	module	NOUN
ejpam-3291	94	25	.	.	PUNCT
ejpam-3291	95	1	proof	proof	NOUN
ejpam-3291	95	2	.	.	PUNCT
ejpam-3291	96	1	assume	assume	VERB
ejpam-3291	96	2	that	that	SCONJ
ejpam-3291	96	3	n	n	PRON
ejpam-3291	96	4	is	be	AUX
ejpam-3291	96	5	an	an	DET
ejpam-3291	96	6	m	m	ADV
ejpam-3291	96	7	-slightly	-slightly	ADV
ejpam-3291	96	8	compressible	compressible	ADJ
ejpam-3291	96	9	injective	injective	ADJ
ejpam-3291	96	10	module	module	NOUN
ejpam-3291	96	11	and	and	CCONJ
ejpam-3291	96	12	a	a	DET
ejpam-3291	96	13	⊂⊕	⊂⊕	PROPN
ejpam-3291	96	14	>	>	X
ejpam-3291	96	15	n	n	PROPN
ejpam-3291	96	16	.	.	PUNCT
ejpam-3291	97	1	let	let	VERB
ejpam-3291	97	2	b	b	X
ejpam-3291	97	3	be	be	AUX
ejpam-3291	97	4	a	a	DET
ejpam-3291	97	5	non	non	ADJ
ejpam-3291	97	6	-	-	ADJ
ejpam-3291	97	7	zero	zero	NUM
ejpam-3291	97	8	m	m	VERB
ejpam-3291	97	9	-slightly	-slightly	ADV
ejpam-3291	97	10	compressible	compressible	ADJ
ejpam-3291	97	11	submodule	submodule	NOUN
ejpam-3291	97	12	of	of	ADP
ejpam-3291	97	13	m	m	PROPN
ejpam-3291	97	14	and	and	CCONJ
ejpam-3291	97	15	α	α	PRON
ejpam-3291	97	16	:	:	PUNCT
ejpam-3291	97	17	b	b	X
ejpam-3291	97	18	→	→	X
ejpam-3291	97	19	a	a	DET
ejpam-3291	97	20	be	be	AUX
ejpam-3291	97	21	an	an	DET
ejpam-3291	97	22	r	r	NOUN
ejpam-3291	97	23	-	-	PUNCT
ejpam-3291	97	24	homomorphism	homomorphism	NOUN
ejpam-3291	97	25	.	.	PUNCT
ejpam-3291	98	1	since	since	SCONJ
ejpam-3291	98	2	a	a	DET
ejpam-3291	98	3	⊂⊕	⊂⊕	PROPN
ejpam-3291	98	4	>	>	X
ejpam-3291	98	5	n	n	PROPN
ejpam-3291	98	6	,	,	PUNCT
ejpam-3291	98	7	there	there	PRON
ejpam-3291	98	8	exists	exist	VERB
ejpam-3291	98	9	a′	a′	PROPN
ejpam-3291	98	10	↪	↪	PROPN
ejpam-3291	98	11	→	→	SYM
ejpam-3291	98	12	n	n	CCONJ
ejpam-3291	98	13	such	such	ADJ
ejpam-3291	98	14	that	that	SCONJ
ejpam-3291	98	15	n	n	NOUN
ejpam-3291	98	16	=	=	SYM
ejpam-3291	98	17	a	a	DET
ejpam-3291	98	18	⊕	⊕	PROPN
ejpam-3291	98	19	a′.	a′.	NOUN
ejpam-3291	98	20	let	let	VERB
ejpam-3291	98	21	ia	ia	PROPN
ejpam-3291	98	22	:	:	PUNCT
ejpam-3291	98	23	a	a	DET
ejpam-3291	98	24	→	→	PUNCT
ejpam-3291	98	25	n	n	CCONJ
ejpam-3291	98	26	be	be	AUX
ejpam-3291	98	27	the	the	DET
ejpam-3291	98	28	canonical	canonical	ADJ
ejpam-3291	98	29	injection	injection	NOUN
ejpam-3291	98	30	map	map	NOUN
ejpam-3291	98	31	.	.	PUNCT
ejpam-3291	99	1	since	since	SCONJ
ejpam-3291	99	2	n	n	NUM
ejpam-3291	99	3	is	be	AUX
ejpam-3291	99	4	an	an	DET
ejpam-3291	99	5	m	m	ADV
ejpam-3291	99	6	-slightly	-slightly	ADV
ejpam-3291	99	7	compressible	compressible	ADJ
ejpam-3291	99	8	injective	injective	ADJ
ejpam-3291	99	9	module	module	NOUN
ejpam-3291	99	10	,	,	PUNCT
ejpam-3291	99	11	there	there	PRON
ejpam-3291	99	12	exists	exist	VERB
ejpam-3291	99	13	f	f	X
ejpam-3291	99	14	:	:	PUNCT
ejpam-3291	99	15	m	m	VERB
ejpam-3291	99	16	→	→	SYM
ejpam-3291	99	17	n	n	CCONJ
ejpam-3291	99	18	such	such	ADJ
ejpam-3291	99	19	that	that	DET
ejpam-3291	99	20	fib	fib	NOUN
ejpam-3291	99	21	=	=	NOUN
ejpam-3291	99	22	iaα	iaα	NOUN
ejpam-3291	99	23	where	where	SCONJ
ejpam-3291	99	24	ib	ib	INTJ
ejpam-3291	99	25	:	:	PUNCT
ejpam-3291	99	26	b	b	X
ejpam-3291	99	27	→	→	PUNCT
ejpam-3291	99	28	m	m	PROPN
ejpam-3291	99	29	is	be	AUX
ejpam-3291	99	30	an	an	DET
ejpam-3291	99	31	embedding	embedding	NOUN
ejpam-3291	99	32	.	.	PUNCT
ejpam-3291	100	1	let	let	AUX
ejpam-3291	100	2	πa	πa	VERB
ejpam-3291	100	3	:	:	PUNCT
ejpam-3291	100	4	n	n	X
ejpam-3291	100	5	→	→	X
ejpam-3291	100	6	a	a	DET
ejpam-3291	100	7	be	be	AUX
ejpam-3291	100	8	the	the	DET
ejpam-3291	100	9	canonical	canonical	ADJ
ejpam-3291	100	10	projection	projection	NOUN
ejpam-3291	100	11	map	map	NOUN
ejpam-3291	100	12	.	.	PUNCT
ejpam-3291	101	1	we	we	PRON
ejpam-3291	101	2	can	can	AUX
ejpam-3291	101	3	choose	choose	VERB
ejpam-3291	101	4	ᾱ	ᾱ	NOUN
ejpam-3291	101	5	=	=	SYM
ejpam-3291	101	6	πaf	πaf	NOUN
ejpam-3291	101	7	.	.	PUNCT
ejpam-3291	102	1	then	then	ADV
ejpam-3291	102	2	ᾱib	ᾱib	PROPN
ejpam-3291	102	3	=	=	PUNCT
ejpam-3291	103	1	πafib	πafib	ADJ
ejpam-3291	103	2	=	=	SYM
ejpam-3291	103	3	πaiaα	πaiaα	NOUN
ejpam-3291	103	4	=	=	PUNCT
ejpam-3291	104	1	iaα	iaα	NOUN
ejpam-3291	104	2	=	=	SYM
ejpam-3291	104	3	α	α	PROPN
ejpam-3291	104	4	where	where	SCONJ
ejpam-3291	104	5	ia	ia	PROPN
ejpam-3291	104	6	is	be	AUX
ejpam-3291	104	7	the	the	DET
ejpam-3291	104	8	identity	identity	NOUN
ejpam-3291	104	9	on	on	ADP
ejpam-3291	104	10	a.	a.	NOUN
ejpam-3291	104	11	hence	hence	ADV
ejpam-3291	104	12	a	a	PRON
ejpam-3291	104	13	is	be	AUX
ejpam-3291	104	14	an	an	DET
ejpam-3291	104	15	m	m	ADV
ejpam-3291	104	16	-slightly	-slightly	ADV
ejpam-3291	104	17	compressible	compressible	ADJ
ejpam-3291	104	18	-	-	PUNCT
ejpam-3291	104	19	injective	injective	ADJ
ejpam-3291	104	20	module	module	NOUN
ejpam-3291	104	21	.	.	PUNCT
ejpam-3291	105	1	proposition	proposition	NOUN
ejpam-3291	105	2	5	5	NUM
ejpam-3291	105	3	.	.	PUNCT
ejpam-3291	105	4	letm	letm	PROPN
ejpam-3291	105	5	be	be	AUX
ejpam-3291	105	6	a	a	DET
ejpam-3291	105	7	right	right	ADJ
ejpam-3291	105	8	r	r	NOUN
ejpam-3291	105	9	-	-	NOUN
ejpam-3291	105	10	module	module	NOUN
ejpam-3291	105	11	.	.	PUNCT
ejpam-3291	106	1	ifm	ifm	PROPN
ejpam-3291	106	2	is	be	AUX
ejpam-3291	106	3	a	a	DET
ejpam-3291	106	4	quasi	quasi	ADJ
ejpam-3291	106	5	-	-	ADJ
ejpam-3291	106	6	slightly	slightly	ADV
ejpam-3291	106	7	compressible	compressible	ADJ
ejpam-3291	106	8	-	-	PUNCT
ejpam-3291	106	9	injective	injective	ADJ
ejpam-3291	106	10	module	module	NOUN
ejpam-3291	106	11	,	,	PUNCT
ejpam-3291	106	12	then	then	ADV
ejpam-3291	106	13	every	every	DET
ejpam-3291	106	14	submodule	submodule	NOUN
ejpam-3291	106	15	of	of	ADP
ejpam-3291	106	16	m	m	PRON
ejpam-3291	106	17	which	which	PRON
ejpam-3291	106	18	is	be	AUX
ejpam-3291	106	19	isomorphic	isomorphic	ADJ
ejpam-3291	106	20	to	to	ADP
ejpam-3291	106	21	a	a	DET
ejpam-3291	106	22	direct	direct	ADJ
ejpam-3291	106	23	summand	summand	NOUN
ejpam-3291	106	24	of	of	ADP
ejpam-3291	106	25	m	m	PROPN
ejpam-3291	106	26	is	be	AUX
ejpam-3291	106	27	a	a	DET
ejpam-3291	106	28	direct	direct	ADJ
ejpam-3291	106	29	summand	summand	NOUN
ejpam-3291	106	30	of	of	ADP
ejpam-3291	106	31	m.	m.	NOUN
ejpam-3291	106	32	proof	proof	NOUN
ejpam-3291	106	33	.	.	PUNCT
ejpam-3291	107	1	let	let	VERB
ejpam-3291	107	2	m	m	PRON
ejpam-3291	107	3	be	be	AUX
ejpam-3291	107	4	a	a	DET
ejpam-3291	107	5	quasi	quasi	ADJ
ejpam-3291	107	6	-	-	ADJ
ejpam-3291	107	7	slightly	slightly	ADV
ejpam-3291	107	8	compressible	compressible	ADJ
ejpam-3291	107	9	-	-	PUNCT
ejpam-3291	107	10	injective	injective	ADJ
ejpam-3291	107	11	module	module	NOUN
ejpam-3291	107	12	,	,	PUNCT
ejpam-3291	107	13	a	a	DET
ejpam-3291	107	14	⊂⊕	⊂⊕	PROPN
ejpam-3291	107	15	>	>	X
ejpam-3291	107	16	m	m	PROPN
ejpam-3291	107	17	and	and	CCONJ
ejpam-3291	107	18	b	b	X
ejpam-3291	107	19	↪	↪	PROPN
ejpam-3291	107	20	→m	→m	PROPN
ejpam-3291	107	21	such	such	ADJ
ejpam-3291	107	22	that	that	SCONJ
ejpam-3291	107	23	a	a	DET
ejpam-3291	107	24	∼=	∼=	PROPN
ejpam-3291	107	25	b.	b.	NOUN
ejpam-3291	107	26	by	by	ADP
ejpam-3291	107	27	proposition	proposition	NOUN
ejpam-3291	107	28	4	4	NUM
ejpam-3291	107	29	,	,	PUNCT
ejpam-3291	107	30	a	a	PRON
ejpam-3291	107	31	is	be	AUX
ejpam-3291	107	32	an	an	DET
ejpam-3291	107	33	m	m	ADV
ejpam-3291	107	34	-slightly	-slightly	ADV
ejpam-3291	107	35	compressible	compressible	ADJ
ejpam-3291	107	36	-	-	PUNCT
ejpam-3291	107	37	injective	injective	ADJ
ejpam-3291	107	38	module	module	NOUN
ejpam-3291	107	39	.	.	PUNCT
ejpam-3291	108	1	since	since	SCONJ
ejpam-3291	108	2	a	a	DET
ejpam-3291	108	3	∼=	∼=	PROPN
ejpam-3291	108	4	b	b	NOUN
ejpam-3291	108	5	,	,	PUNCT
ejpam-3291	108	6	b	b	PROPN
ejpam-3291	108	7	is	be	AUX
ejpam-3291	108	8	an	an	DET
ejpam-3291	108	9	m	m	ADV
ejpam-3291	108	10	-slightly	-slightly	ADV
ejpam-3291	108	11	compressible	compressible	ADJ
ejpam-3291	108	12	-	-	PUNCT
ejpam-3291	108	13	injective	injective	ADJ
ejpam-3291	108	14	module	module	NOUN
ejpam-3291	108	15	.	.	PUNCT
ejpam-3291	109	1	by	by	ADP
ejpam-3291	109	2	proposition	proposition	NOUN
ejpam-3291	109	3	3	3	NUM
ejpam-3291	109	4	,	,	PUNCT
ejpam-3291	109	5	we	we	PRON
ejpam-3291	109	6	have	have	VERB
ejpam-3291	109	7	ib	ib	NOUN
ejpam-3291	109	8	:	:	PUNCT
ejpam-3291	109	9	b	b	X
ejpam-3291	109	10	→	→	PUNCT
ejpam-3291	109	11	m	m	VERB
ejpam-3291	109	12	splits	split	NOUN
ejpam-3291	109	13	where	where	SCONJ
ejpam-3291	109	14	ib	ib	PROPN
ejpam-3291	109	15	is	be	AUX
ejpam-3291	109	16	a	a	DET
ejpam-3291	109	17	monomorphism	monomorphism	NOUN
ejpam-3291	109	18	from	from	ADP
ejpam-3291	109	19	b	b	PROPN
ejpam-3291	109	20	to	to	ADP
ejpam-3291	109	21	m	m	PROPN
ejpam-3291	109	22	.	.	PUNCT
ejpam-3291	110	1	therefore	therefore	ADV
ejpam-3291	110	2	b	b	PROPN
ejpam-3291	110	3	is	be	AUX
ejpam-3291	110	4	a	a	DET
ejpam-3291	110	5	direct	direct	ADJ
ejpam-3291	110	6	summand	summand	NOUN
ejpam-3291	110	7	of	of	ADP
ejpam-3291	110	8	m	m	PROPN
ejpam-3291	110	9	.	.	PUNCT
ejpam-3291	111	1	proposition	proposition	NOUN
ejpam-3291	111	2	6	6	NUM
ejpam-3291	111	3	.	.	PUNCT
ejpam-3291	112	1	let	let	VERB
ejpam-3291	112	2	m	m	PRON
ejpam-3291	112	3	,	,	PUNCT
ejpam-3291	112	4	n	n	PRON
ejpam-3291	112	5	be	be	AUX
ejpam-3291	112	6	right	right	ADJ
ejpam-3291	112	7	r	r	NOUN
ejpam-3291	112	8	-	-	PUNCT
ejpam-3291	112	9	modules	module	NOUN
ejpam-3291	112	10	and	and	CCONJ
ejpam-3291	112	11	n	n	CCONJ
ejpam-3291	112	12	be	be	VERB
ejpam-3291	112	13	an	an	DET
ejpam-3291	112	14	m	m	ADV
ejpam-3291	112	15	-slightly	-slightly	ADV
ejpam-3291	112	16	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	112	17	module	module	NOUN
ejpam-3291	112	18	.	.	PUNCT
ejpam-3291	113	1	then	then	ADV
ejpam-3291	113	2	(	(	PUNCT
ejpam-3291	113	3	1	1	X
ejpam-3291	113	4	)	)	PUNCT
ejpam-3291	113	5	n	n	PRON
ejpam-3291	113	6	is	be	AUX
ejpam-3291	113	7	a	a	DET
ejpam-3291	113	8	k	k	ADV
ejpam-3291	113	9	-	-	ADJ
ejpam-3291	113	10	slightly	slightly	ADV
ejpam-3291	113	11	compressible	compressible	ADJ
ejpam-3291	113	12	-	-	PUNCT
ejpam-3291	113	13	injective	injective	ADJ
ejpam-3291	113	14	module	module	NOUN
ejpam-3291	113	15	for	for	ADP
ejpam-3291	113	16	all	all	DET
ejpam-3291	113	17	k	k	PROPN
ejpam-3291	113	18	⊂⊕	⊂⊕	PROPN
ejpam-3291	113	19	>	>	X
ejpam-3291	113	20	m	m	VERB
ejpam-3291	113	21	.	.	PUNCT
ejpam-3291	114	1	(	(	PUNCT
ejpam-3291	114	2	2	2	X
ejpam-3291	114	3	)	)	PUNCT
ejpam-3291	114	4	h	h	NOUN
ejpam-3291	114	5	is	be	AUX
ejpam-3291	114	6	a	a	DET
ejpam-3291	114	7	k	k	ADV
ejpam-3291	114	8	-	-	ADJ
ejpam-3291	114	9	slightly	slightly	ADV
ejpam-3291	114	10	compressible	compressible	ADJ
ejpam-3291	114	11	-	-	PUNCT
ejpam-3291	114	12	injective	injective	ADJ
ejpam-3291	114	13	module	module	NOUN
ejpam-3291	114	14	for	for	ADP
ejpam-3291	114	15	all	all	DET
ejpam-3291	114	16	h	h	NOUN
ejpam-3291	114	17	⊂⊕	⊂⊕	PROPN
ejpam-3291	114	18	>	>	X
ejpam-3291	114	19	n	n	PROPN
ejpam-3291	114	20	and	and	CCONJ
ejpam-3291	114	21	k	k	PROPN
ejpam-3291	114	22	⊂⊕	⊂⊕	PROPN
ejpam-3291	114	23	>	>	X
ejpam-3291	114	24	m	m	VERB
ejpam-3291	114	25	.	.	PUNCT
ejpam-3291	115	1	proof	proof	NOUN
ejpam-3291	115	2	.	.	PUNCT
ejpam-3291	116	1	(	(	PUNCT
ejpam-3291	116	2	1	1	X
ejpam-3291	116	3	)	)	PUNCT
ejpam-3291	116	4	let	let	VERB
ejpam-3291	116	5	k	k	PROPN
ejpam-3291	116	6	⊂⊕	⊂⊕	PROPN
ejpam-3291	116	7	>	>	X
ejpam-3291	116	8	m	m	PROPN
ejpam-3291	116	9	and	and	CCONJ
ejpam-3291	116	10	0	0	NUM
ejpam-3291	116	11	6=	6=	ADP
ejpam-3291	116	12	a	a	DET
ejpam-3291	116	13	be	be	AUX
ejpam-3291	116	14	an	an	DET
ejpam-3291	116	15	k	k	ADV
ejpam-3291	116	16	-	-	ADJ
ejpam-3291	116	17	slightly	slightly	ADV
ejpam-3291	116	18	compressible	compressible	ADJ
ejpam-3291	116	19	submodule	submodule	NOUN
ejpam-3291	116	20	and	and	CCONJ
ejpam-3291	116	21	α	α	NOUN
ejpam-3291	116	22	be	be	VERB
ejpam-3291	116	23	an	an	DET
ejpam-3291	116	24	r	r	NOUN
ejpam-3291	116	25	-	-	PUNCT
ejpam-3291	116	26	homomorphism	homomorphism	NOUN
ejpam-3291	116	27	from	from	ADP
ejpam-3291	116	28	a	a	PRON
ejpam-3291	116	29	to	to	ADP
ejpam-3291	116	30	n	n	PROPN
ejpam-3291	116	31	.	.	PUNCT
ejpam-3291	117	1	then	then	ADV
ejpam-3291	117	2	there	there	PRON
ejpam-3291	117	3	exists	exist	VERB
ejpam-3291	117	4	0	0	NUM
ejpam-3291	118	1	6=	6=	NUM
ejpam-3291	118	2	s	s	NOUN
ejpam-3291	118	3	∈	∈	PROPN
ejpam-3291	118	4	endr(k	endr(k	NOUN
ejpam-3291	118	5	)	)	PUNCT
ejpam-3291	118	6	such	such	ADJ
ejpam-3291	118	7	that	that	DET
ejpam-3291	118	8	s(m	s(m	NOUN
ejpam-3291	118	9	)	)	PUNCT
ejpam-3291	118	10	↪	↪	PROPN
ejpam-3291	118	11	→	→	SYM
ejpam-3291	118	12	a	a	PRON
ejpam-3291	118	13	,	,	PUNCT
ejpam-3291	118	14	so	so	ADV
ejpam-3291	118	15	sπk	sπk	PROPN
ejpam-3291	118	16	∈	∈	PROPN
ejpam-3291	118	17	endr(m	endr(m	PROPN
ejpam-3291	118	18	)	)	PUNCT
ejpam-3291	118	19	and	and	CCONJ
ejpam-3291	118	20	sπk(m	sπk(m	PROPN
ejpam-3291	118	21	)	)	PUNCT
ejpam-3291	118	22	↪	↪	PROPN
ejpam-3291	118	23	→	→	SYM
ejpam-3291	118	24	a	a	PRON
ejpam-3291	118	25	where	where	SCONJ
ejpam-3291	118	26	πk	πk	X
ejpam-3291	118	27	:	:	PUNCT
ejpam-3291	118	28	m	m	VERB
ejpam-3291	118	29	→	→	SYM
ejpam-3291	118	30	k	k	X
ejpam-3291	118	31	is	be	AUX
ejpam-3291	118	32	the	the	DET
ejpam-3291	118	33	canonical	canonical	ADJ
ejpam-3291	118	34	map	map	NOUN
ejpam-3291	118	35	.	.	PUNCT
ejpam-3291	119	1	since	since	SCONJ
ejpam-3291	119	2	n	n	NUM
ejpam-3291	119	3	is	be	AUX
ejpam-3291	119	4	an	an	DET
ejpam-3291	119	5	m	m	ADV
ejpam-3291	119	6	-slightly	-slightly	ADV
ejpam-3291	119	7	compressible	compressible	ADJ
ejpam-3291	119	8	-	-	PUNCT
ejpam-3291	119	9	injective	injective	ADJ
ejpam-3291	119	10	module	module	NOUN
ejpam-3291	119	11	,	,	PUNCT
ejpam-3291	119	12	α	α	PROPN
ejpam-3291	119	13	extends	extend	VERB
ejpam-3291	119	14	to	to	ADP
ejpam-3291	119	15	an	an	DET
ejpam-3291	119	16	r	r	NOUN
ejpam-3291	119	17	-	-	PUNCT
ejpam-3291	119	18	homomorphism	homomorphism	NOUN
ejpam-3291	119	19	ᾱ	ᾱ	NOUN
ejpam-3291	119	20	from	from	ADP
ejpam-3291	119	21	m	m	PRON
ejpam-3291	119	22	to	to	ADP
ejpam-3291	119	23	n	n	CCONJ
ejpam-3291	119	24	such	such	ADJ
ejpam-3291	119	25	that	that	DET
ejpam-3291	119	26	ᾱia	ᾱia	NOUN
ejpam-3291	119	27	=	=	PUNCT
ejpam-3291	120	1	α	α	PROPN
ejpam-3291	120	2	where	where	SCONJ
ejpam-3291	120	3	ia	ia	PROPN
ejpam-3291	120	4	:	:	PUNCT
ejpam-3291	120	5	a→m	a→m	PRON
ejpam-3291	120	6	is	be	AUX
ejpam-3291	120	7	an	an	DET
ejpam-3291	120	8	embedding	embedding	NOUN
ejpam-3291	120	9	.	.	PUNCT
ejpam-3291	121	1	thus	thus	ADV
ejpam-3291	121	2	ᾱ|k	ᾱ|k	VERB
ejpam-3291	121	3	:	:	PUNCT
ejpam-3291	122	1	k	k	PROPN
ejpam-3291	122	2	→	→	SYM
ejpam-3291	122	3	n	n	NOUN
ejpam-3291	122	4	and	and	CCONJ
ejpam-3291	122	5	ᾱ|kia	ᾱ|kia	NOUN
ejpam-3291	122	6	=	=	SYM
ejpam-3291	122	7	α	α	X
ejpam-3291	122	8	.	.	PUNCT
ejpam-3291	123	1	therefore	therefore	ADV
ejpam-3291	123	2	n	n	PROPN
ejpam-3291	123	3	is	be	AUX
ejpam-3291	123	4	an	an	DET
ejpam-3291	123	5	k	k	ADV
ejpam-3291	123	6	-	-	ADJ
ejpam-3291	123	7	slightly	slightly	ADV
ejpam-3291	123	8	compressible	compressible	ADJ
ejpam-3291	123	9	-	-	PUNCT
ejpam-3291	123	10	injective	injective	ADJ
ejpam-3291	123	11	module	module	NOUN
ejpam-3291	123	12	.	.	PUNCT
ejpam-3291	124	1	(	(	PUNCT
ejpam-3291	124	2	2	2	X
ejpam-3291	124	3	)	)	PUNCT
ejpam-3291	124	4	let	let	VERB
ejpam-3291	124	5	h	h	NOUN
ejpam-3291	124	6	⊂⊕	⊂⊕	VERB
ejpam-3291	124	7	>	>	X
ejpam-3291	124	8	n	n	PROPN
ejpam-3291	124	9	and	and	CCONJ
ejpam-3291	124	10	k	k	PROPN
ejpam-3291	124	11	⊂⊕	⊂⊕	PROPN
ejpam-3291	124	12	>	>	X
ejpam-3291	124	13	m	m	VERB
ejpam-3291	124	14	.	.	PUNCT
ejpam-3291	125	1	from	from	ADP
ejpam-3291	125	2	(	(	PUNCT
ejpam-3291	125	3	1	1	NUM
ejpam-3291	125	4	)	)	PUNCT
ejpam-3291	125	5	,	,	PUNCT
ejpam-3291	125	6	n	n	PRON
ejpam-3291	125	7	is	be	AUX
ejpam-3291	125	8	k	k	ADJ
ejpam-3291	125	9	-	-	ADJ
ejpam-3291	125	10	slightly	slightly	ADV
ejpam-3291	125	11	compressible	compressible	ADJ
ejpam-3291	125	12	injective	injective	NOUN
ejpam-3291	125	13	.	.	PUNCT
ejpam-3291	126	1	by	by	ADP
ejpam-3291	126	2	proposition	proposition	NOUN
ejpam-3291	126	3	4	4	NUM
ejpam-3291	126	4	,	,	PUNCT
ejpam-3291	126	5	h	h	NOUN
ejpam-3291	126	6	is	be	AUX
ejpam-3291	126	7	an	an	DET
ejpam-3291	126	8	k	k	ADV
ejpam-3291	126	9	-	-	ADJ
ejpam-3291	126	10	slightly	slightly	ADV
ejpam-3291	126	11	compressible	compressible	ADJ
ejpam-3291	126	12	injective	injective	ADJ
ejpam-3291	126	13	module	module	NOUN
ejpam-3291	126	14	.	.	PUNCT
ejpam-3291	127	1	recall	recall	VERB
ejpam-3291	127	2	that	that	SCONJ
ejpam-3291	127	3	a	a	DET
ejpam-3291	127	4	right	right	ADJ
ejpam-3291	127	5	r	r	NOUN
ejpam-3291	127	6	-	-	PUNCT
ejpam-3291	127	7	module	module	NOUN
ejpam-3291	127	8	m	m	NOUN
ejpam-3291	127	9	is	be	AUX
ejpam-3291	127	10	said	say	VERB
ejpam-3291	127	11	to	to	PART
ejpam-3291	127	12	be	be	AUX
ejpam-3291	127	13	direct	direct	ADJ
ejpam-3291	127	14	-	-	PUNCT
ejpam-3291	127	15	projective	projective	ADJ
ejpam-3291	127	16	,	,	PUNCT
ejpam-3291	127	17	if	if	SCONJ
ejpam-3291	127	18	given	give	VERB
ejpam-3291	127	19	any	any	DET
ejpam-3291	127	20	summand	summand	NOUN
ejpam-3291	127	21	n	n	PROPN
ejpam-3291	127	22	of	of	ADP
ejpam-3291	127	23	m	m	PROPN
ejpam-3291	127	24	with	with	ADP
ejpam-3291	127	25	projection	projection	NOUN
ejpam-3291	127	26	map	map	NOUN
ejpam-3291	127	27	p	p	X
ejpam-3291	127	28	:	:	PUNCT
ejpam-3291	127	29	m	m	PROPN
ejpam-3291	127	30	→	→	SYM
ejpam-3291	127	31	n	n	CCONJ
ejpam-3291	127	32	and	and	CCONJ
ejpam-3291	127	33	any	any	DET
ejpam-3291	127	34	epimorphism	epimorphism	NOUN
ejpam-3291	128	1	f	f	NOUN
ejpam-3291	128	2	:	:	PUNCT
ejpam-3291	128	3	m	m	VERB
ejpam-3291	128	4	→	→	SYM
ejpam-3291	128	5	n	n	CCONJ
ejpam-3291	128	6	,	,	PUNCT
ejpam-3291	128	7	there	there	PRON
ejpam-3291	128	8	exists	exist	VERB
ejpam-3291	128	9	n.	n.	PROPN
ejpam-3291	128	10	d.	d.	PROPN
ejpam-3291	128	11	h.	h.	PROPN
ejpam-3291	128	12	nghiem	nghiem	PROPN
ejpam-3291	128	13	et	et	PROPN
ejpam-3291	128	14	al	al	PROPN
ejpam-3291	128	15	.	.	PUNCT
ejpam-3291	128	16	/	/	SYM
ejpam-3291	128	17	eur	eur	PROPN
ejpam-3291	128	18	.	.	PUNCT
ejpam-3291	129	1	j.	j.	PROPN
ejpam-3291	129	2	pure	pure	PROPN
ejpam-3291	129	3	appl	appl	PROPN
ejpam-3291	129	4	.	.	PROPN
ejpam-3291	129	5	math	math	PROPN
ejpam-3291	129	6	,	,	PUNCT
ejpam-3291	129	7	11	11	NUM
ejpam-3291	129	8	(	(	PUNCT
ejpam-3291	129	9	3	3	NUM
ejpam-3291	129	10	)	)	PUNCT
ejpam-3291	129	11	(	(	PUNCT
ejpam-3291	129	12	2018	2018	NUM
ejpam-3291	129	13	)	)	PUNCT
ejpam-3291	129	14	,	,	PUNCT
ejpam-3291	129	15	815	815	NUM
ejpam-3291	129	16	-	-	SYM
ejpam-3291	129	17	822	822	NUM
ejpam-3291	129	18	819	819	NUM
ejpam-3291	129	19	g	g	NOUN
ejpam-3291	129	20	∈	∈	PROPN
ejpam-3291	129	21	s	s	PART
ejpam-3291	129	22	=	=	X
ejpam-3291	129	23	endr(m	endr(m	PROPN
ejpam-3291	129	24	)	)	PUNCT
ejpam-3291	129	25	such	such	ADJ
ejpam-3291	129	26	that	that	SCONJ
ejpam-3291	129	27	fg	fg	PROPN
ejpam-3291	129	28	=	=	PROPN
ejpam-3291	129	29	p.	p.	NOUN
ejpam-3291	130	1	for	for	ADP
ejpam-3291	130	2	more	more	ADJ
ejpam-3291	130	3	details	detail	NOUN
ejpam-3291	130	4	of	of	ADP
ejpam-3291	130	5	direct	direct	ADJ
ejpam-3291	130	6	-	-	PUNCT
ejpam-3291	130	7	projective	projective	NOUN
ejpam-3291	130	8	,	,	PUNCT
ejpam-3291	130	9	we	we	PRON
ejpam-3291	130	10	refer	refer	VERB
ejpam-3291	130	11	to	to	ADP
ejpam-3291	130	12	[	[	X
ejpam-3291	130	13	12	12	NUM
ejpam-3291	130	14	]	]	PUNCT
ejpam-3291	130	15	.	.	PUNCT
ejpam-3291	131	1	theorem	theorem	NOUN
ejpam-3291	131	2	1	1	X
ejpam-3291	131	3	.	.	PUNCT
ejpam-3291	132	1	let	let	VERB
ejpam-3291	132	2	m	m	PRON
ejpam-3291	132	3	be	be	AUX
ejpam-3291	132	4	a	a	DET
ejpam-3291	132	5	right	right	ADJ
ejpam-3291	132	6	r	r	NOUN
ejpam-3291	132	7	-	-	PUNCT
ejpam-3291	132	8	module	module	NOUN
ejpam-3291	132	9	and	and	CCONJ
ejpam-3291	132	10	s	s	NOUN
ejpam-3291	132	11	=	=	ADJ
ejpam-3291	132	12	endr(m	endr(m	PROPN
ejpam-3291	132	13	)	)	PUNCT
ejpam-3291	132	14	be	be	VERB
ejpam-3291	132	15	the	the	DET
ejpam-3291	132	16	endomorphism	endomorphism	NOUN
ejpam-3291	132	17	ring	ring	NOUN
ejpam-3291	132	18	of	of	ADP
ejpam-3291	132	19	m	m	PROPN
ejpam-3291	132	20	.	.	PUNCT
ejpam-3291	133	1	if	if	SCONJ
ejpam-3291	133	2	m	m	NOUN
ejpam-3291	133	3	is	be	AUX
ejpam-3291	133	4	a	a	DET
ejpam-3291	133	5	direct	direct	ADJ
ejpam-3291	133	6	-	-	PUNCT
ejpam-3291	133	7	projective	projective	NOUN
ejpam-3291	133	8	and	and	CCONJ
ejpam-3291	133	9	every	every	DET
ejpam-3291	133	10	submodule	submodule	NOUN
ejpam-3291	133	11	of	of	ADP
ejpam-3291	133	12	m	m	PROPN
ejpam-3291	133	13	is	be	AUX
ejpam-3291	133	14	an	an	DET
ejpam-3291	133	15	m	m	ADV
ejpam-3291	133	16	-slightly	-slightly	ADV
ejpam-3291	133	17	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	133	18	module	module	NOUN
ejpam-3291	133	19	,	,	PUNCT
ejpam-3291	133	20	then	then	ADV
ejpam-3291	133	21	s	s	VERB
ejpam-3291	133	22	is	be	AUX
ejpam-3291	133	23	a	a	DET
ejpam-3291	133	24	von	von	PROPN
ejpam-3291	133	25	neumann	neumann	PROPN
ejpam-3291	133	26	regular	regular	PROPN
ejpam-3291	133	27	.	.	PUNCT
ejpam-3291	134	1	proof	proof	NOUN
ejpam-3291	134	2	.	.	PUNCT
ejpam-3291	135	1	assume	assume	VERB
ejpam-3291	135	2	that	that	SCONJ
ejpam-3291	135	3	m	m	PROPN
ejpam-3291	135	4	is	be	AUX
ejpam-3291	135	5	a	a	DET
ejpam-3291	135	6	direct	direct	ADJ
ejpam-3291	135	7	-	-	PUNCT
ejpam-3291	135	8	projective	projective	NOUN
ejpam-3291	135	9	and	and	CCONJ
ejpam-3291	135	10	every	every	DET
ejpam-3291	135	11	submodule	submodule	NOUN
ejpam-3291	135	12	of	of	ADP
ejpam-3291	135	13	m	m	PROPN
ejpam-3291	135	14	is	be	AUX
ejpam-3291	135	15	an	an	DET
ejpam-3291	135	16	m	m	PRON
ejpam-3291	135	17	slightly	slightly	ADV
ejpam-3291	135	18	compressible	compressible	ADJ
ejpam-3291	135	19	injective	injective	ADJ
ejpam-3291	135	20	module	module	NOUN
ejpam-3291	135	21	.	.	PUNCT
ejpam-3291	136	1	let	let	VERB
ejpam-3291	136	2	s	s	PRON
ejpam-3291	136	3	∈	∈	VERB
ejpam-3291	136	4	s.	s.	PROPN
ejpam-3291	136	5	by	by	ADP
ejpam-3291	136	6	assumption	assumption	NOUN
ejpam-3291	136	7	,	,	PUNCT
ejpam-3291	136	8	s(m	s(m	PROPN
ejpam-3291	136	9	)	)	PUNCT
ejpam-3291	136	10	is	be	AUX
ejpam-3291	136	11	an	an	DET
ejpam-3291	136	12	m	m	ADV
ejpam-3291	136	13	-slightly	-slightly	ADV
ejpam-3291	136	14	compressible	compressible	ADJ
ejpam-3291	136	15	injective	injective	ADJ
ejpam-3291	136	16	module	module	NOUN
ejpam-3291	136	17	.	.	PUNCT
ejpam-3291	137	1	let	let	VERB
ejpam-3291	137	2	is(m	is(m	PUNCT
ejpam-3291	137	3	)	)	PUNCT
ejpam-3291	137	4	:	:	PUNCT
ejpam-3291	137	5	s(m	s(m	X
ejpam-3291	137	6	)	)	PUNCT
ejpam-3291	137	7	→	→	PUNCT
ejpam-3291	137	8	m	m	AUX
ejpam-3291	137	9	be	be	AUX
ejpam-3291	137	10	an	an	DET
ejpam-3291	137	11	embedding	embedding	NOUN
ejpam-3291	137	12	.	.	PUNCT
ejpam-3291	138	1	by	by	ADP
ejpam-3291	138	2	proposition	proposition	NOUN
ejpam-3291	138	3	3	3	NUM
ejpam-3291	138	4	,	,	PUNCT
ejpam-3291	138	5	is(m	is(m	NOUN
ejpam-3291	138	6	)	)	PUNCT
ejpam-3291	138	7	:	:	PUNCT
ejpam-3291	138	8	s(m	s(m	X
ejpam-3291	138	9	)	)	PUNCT
ejpam-3291	138	10	→	→	PUNCT
ejpam-3291	138	11	m	m	NOUN
ejpam-3291	138	12	splits	split	VERB
ejpam-3291	138	13	.	.	PUNCT
ejpam-3291	139	1	then	then	ADV
ejpam-3291	139	2	s(m	s(m	PROPN
ejpam-3291	139	3	)	)	PUNCT
ejpam-3291	139	4	is	be	AUX
ejpam-3291	139	5	a	a	DET
ejpam-3291	139	6	direct	direct	ADJ
ejpam-3291	139	7	summand	summand	NOUN
ejpam-3291	139	8	of	of	ADP
ejpam-3291	139	9	m	m	PROPN
ejpam-3291	139	10	.	.	PUNCT
ejpam-3291	140	1	we	we	PRON
ejpam-3291	140	2	can	can	AUX
ejpam-3291	140	3	construct	construct	VERB
ejpam-3291	140	4	epimorphism	epimorphism	NOUN
ejpam-3291	140	5	s′	s′	ADJ
ejpam-3291	140	6	:	:	PUNCT
ejpam-3291	140	7	m	m	PROPN
ejpam-3291	140	8	→	→	SYM
ejpam-3291	140	9	im(s	im(s	ADJ
ejpam-3291	140	10	)	)	PUNCT
ejpam-3291	140	11	by	by	ADP
ejpam-3291	140	12	s′(m	s′(m	NOUN
ejpam-3291	140	13	)	)	PUNCT
ejpam-3291	140	14	=	=	SYM
ejpam-3291	140	15	s(m	s(m	PROPN
ejpam-3291	140	16	)	)	PUNCT
ejpam-3291	140	17	for	for	ADP
ejpam-3291	140	18	all	all	DET
ejpam-3291	140	19	m	m	NOUN
ejpam-3291	140	20	∈	∈	NOUN
ejpam-3291	140	21	m	m	NOUN
ejpam-3291	140	22	.	.	PUNCT
ejpam-3291	141	1	since	since	SCONJ
ejpam-3291	141	2	m	m	PROPN
ejpam-3291	141	3	is	be	AUX
ejpam-3291	141	4	a	a	DET
ejpam-3291	141	5	directprojective	directprojective	NOUN
ejpam-3291	141	6	,	,	PUNCT
ejpam-3291	141	7	then	then	ADV
ejpam-3291	141	8	the	the	DET
ejpam-3291	141	9	short	short	ADJ
ejpam-3291	141	10	exact	exact	ADJ
ejpam-3291	141	11	sequence	sequence	NOUN
ejpam-3291	141	12	0	0	NUM
ejpam-3291	141	13	→	→	SYM
ejpam-3291	141	14	ker(s′	ker(s′	PROPN
ejpam-3291	141	15	)	)	PUNCT
ejpam-3291	141	16	↪	↪	PROPN
ejpam-3291	141	17	→	→	SYM
ejpam-3291	141	18	m	m	PROPN
ejpam-3291	141	19	s′→	s′→	ADJ
ejpam-3291	141	20	s(m	s(m	NOUN
ejpam-3291	141	21	)	)	PUNCT
ejpam-3291	141	22	→	→	SYM
ejpam-3291	141	23	0	0	NUM
ejpam-3291	141	24	split	split	NOUN
ejpam-3291	141	25	and	and	CCONJ
ejpam-3291	141	26	we	we	PRON
ejpam-3291	141	27	have	have	AUX
ejpam-3291	141	28	ker(s′	ker(s′	VERB
ejpam-3291	141	29	)	)	PUNCT
ejpam-3291	141	30	is	be	AUX
ejpam-3291	141	31	a	a	DET
ejpam-3291	141	32	direct	direct	ADJ
ejpam-3291	141	33	summand	summand	NOUN
ejpam-3291	141	34	m.	m.	NOUN
ejpam-3291	141	35	but	but	CCONJ
ejpam-3291	141	36	ker(s′	ker(s′	PROPN
ejpam-3291	141	37	)	)	PUNCT
ejpam-3291	141	38	=	=	PUNCT
ejpam-3291	141	39	ker(s	ker(s	PROPN
ejpam-3291	141	40	)	)	PUNCT
ejpam-3291	141	41	.	.	PUNCT
ejpam-3291	142	1	so	so	ADV
ejpam-3291	142	2	ker(s	ker(s	PROPN
ejpam-3291	142	3	)	)	PUNCT
ejpam-3291	142	4	is	be	AUX
ejpam-3291	142	5	a	a	DET
ejpam-3291	142	6	direct	direct	ADJ
ejpam-3291	142	7	summand	summand	NOUN
ejpam-3291	142	8	of	of	ADP
ejpam-3291	142	9	m	m	PROPN
ejpam-3291	142	10	.	.	PUNCT
ejpam-3291	143	1	from	from	ADP
ejpam-3291	143	2	proposition	proposition	NOUN
ejpam-3291	143	3	37.7(1	37.7(1	NUM
ejpam-3291	143	4	)	)	PUNCT
ejpam-3291	143	5	in	in	ADP
ejpam-3291	143	6	[	[	X
ejpam-3291	143	7	11	11	NUM
ejpam-3291	143	8	]	]	PUNCT
ejpam-3291	143	9	,	,	PUNCT
ejpam-3291	143	10	there	there	PRON
ejpam-3291	143	11	exists	exist	VERB
ejpam-3291	143	12	g	g	PROPN
ejpam-3291	143	13	∈	∈	PROPN
ejpam-3291	143	14	s	s	VERB
ejpam-3291	143	15	such	such	ADJ
ejpam-3291	143	16	that	that	DET
ejpam-3291	143	17	s	s	PROPN
ejpam-3291	143	18	=	=	SYM
ejpam-3291	143	19	sgs	sgs	PROPN
ejpam-3291	143	20	.	.	PUNCT
ejpam-3291	144	1	therefore	therefore	ADV
ejpam-3291	144	2	s	s	VERB
ejpam-3291	144	3	is	be	AUX
ejpam-3291	144	4	a	a	DET
ejpam-3291	144	5	von	von	PROPN
ejpam-3291	144	6	neumann	neumann	PROPN
ejpam-3291	144	7	regular	regular	PROPN
ejpam-3291	144	8	.	.	PUNCT
ejpam-3291	145	1	theorem	theorem	NOUN
ejpam-3291	145	2	2	2	NUM
ejpam-3291	145	3	.	.	PUNCT
ejpam-3291	146	1	let	let	VERB
ejpam-3291	146	2	m	m	PRON
ejpam-3291	146	3	be	be	AUX
ejpam-3291	146	4	a	a	DET
ejpam-3291	146	5	right	right	ADJ
ejpam-3291	146	6	r	r	NOUN
ejpam-3291	146	7	-	-	PUNCT
ejpam-3291	146	8	module	module	NOUN
ejpam-3291	146	9	and	and	CCONJ
ejpam-3291	146	10	s	s	NOUN
ejpam-3291	146	11	=	=	ADJ
ejpam-3291	146	12	endr(m	endr(m	PROPN
ejpam-3291	146	13	)	)	PUNCT
ejpam-3291	146	14	be	be	VERB
ejpam-3291	146	15	the	the	DET
ejpam-3291	146	16	endomorphism	endomorphism	NOUN
ejpam-3291	146	17	ring	ring	NOUN
ejpam-3291	146	18	of	of	ADP
ejpam-3291	146	19	m	m	PROPN
ejpam-3291	146	20	.	.	PUNCT
ejpam-3291	147	1	(	(	PUNCT
ejpam-3291	147	2	1	1	X
ejpam-3291	147	3	)	)	PUNCT
ejpam-3291	147	4	if	if	SCONJ
ejpam-3291	147	5	m	m	NOUN
ejpam-3291	147	6	is	be	AUX
ejpam-3291	147	7	a	a	DET
ejpam-3291	147	8	quasi	quasi	ADJ
ejpam-3291	147	9	-	-	ADJ
ejpam-3291	147	10	slightly	slightly	ADV
ejpam-3291	147	11	compressible	compressible	ADJ
ejpam-3291	147	12	-	-	PUNCT
ejpam-3291	147	13	injective	injective	ADJ
ejpam-3291	147	14	module	module	NOUN
ejpam-3291	147	15	,	,	PUNCT
ejpam-3291	147	16	then	then	ADV
ejpam-3291	147	17	ls(ker(s	ls(ker(s	NOUN
ejpam-3291	147	18	)	)	PUNCT
ejpam-3291	147	19	)	)	PUNCT
ejpam-3291	148	1	=	=	SYM
ejpam-3291	148	2	ss	ss	PROPN
ejpam-3291	148	3	for	for	ADP
ejpam-3291	148	4	all	all	PRON
ejpam-3291	148	5	s	s	PROPN
ejpam-3291	148	6	∈	∈	PROPN
ejpam-3291	148	7	s.	s.	PROPN
ejpam-3291	148	8	(	(	PUNCT
ejpam-3291	148	9	2	2	X
ejpam-3291	148	10	)	)	PUNCT
ejpam-3291	148	11	if	if	SCONJ
ejpam-3291	148	12	m	m	NOUN
ejpam-3291	148	13	is	be	AUX
ejpam-3291	148	14	a	a	DET
ejpam-3291	148	15	quasi	quasi	ADJ
ejpam-3291	148	16	-	-	ADJ
ejpam-3291	148	17	slightly	slightly	ADV
ejpam-3291	148	18	compressible	compressible	ADJ
ejpam-3291	148	19	-	-	PUNCT
ejpam-3291	148	20	injective	injective	ADJ
ejpam-3291	148	21	module	module	NOUN
ejpam-3291	148	22	,	,	PUNCT
ejpam-3291	148	23	then	then	ADV
ejpam-3291	148	24	ker(t	ker(t	PROPN
ejpam-3291	148	25	)	)	PUNCT
ejpam-3291	148	26	⊆	⊆	NUM
ejpam-3291	148	27	ker(s	ker(s	NOUN
ejpam-3291	148	28	)	)	PUNCT
ejpam-3291	148	29	implies	imply	VERB
ejpam-3291	148	30	ss	ss	PROPN
ejpam-3291	148	31	⊆	⊆	NUM
ejpam-3291	148	32	st	st	NOUN
ejpam-3291	148	33	for	for	ADP
ejpam-3291	148	34	any	any	DET
ejpam-3291	148	35	s	s	NOUN
ejpam-3291	148	36	,	,	PUNCT
ejpam-3291	148	37	t	t	PROPN
ejpam-3291	148	38	∈	∈	PROPN
ejpam-3291	148	39	s.	s.	PROPN
ejpam-3291	148	40	(	(	PUNCT
ejpam-3291	148	41	3	3	X
ejpam-3291	148	42	)	)	PUNCT
ejpam-3291	148	43	if	if	SCONJ
ejpam-3291	148	44	m	m	NOUN
ejpam-3291	148	45	is	be	AUX
ejpam-3291	148	46	a	a	DET
ejpam-3291	148	47	quasi	quasi	ADJ
ejpam-3291	148	48	-	-	ADJ
ejpam-3291	148	49	slightly	slightly	ADV
ejpam-3291	148	50	compressible	compressible	ADJ
ejpam-3291	148	51	-	-	PUNCT
ejpam-3291	148	52	injective	injective	ADJ
ejpam-3291	148	53	module	module	NOUN
ejpam-3291	148	54	,	,	PUNCT
ejpam-3291	148	55	then	then	ADV
ejpam-3291	148	56	ls(im(t	ls(im(t	NOUN
ejpam-3291	148	57	)	)	PUNCT
ejpam-3291	148	58	∩	∩	NOUN
ejpam-3291	148	59	ker(s	ker(s	NOUN
ejpam-3291	148	60	)	)	PUNCT
ejpam-3291	148	61	)	)	PUNCT
ejpam-3291	148	62	=	=	SYM
ejpam-3291	148	63	ls(im(t	ls(im(t	NOUN
ejpam-3291	148	64	)	)	PUNCT
ejpam-3291	148	65	)	)	PUNCT
ejpam-3291	149	1	+	+	CCONJ
ejpam-3291	149	2	ss	ss	NOUN
ejpam-3291	149	3	for	for	ADP
ejpam-3291	149	4	all	all	DET
ejpam-3291	149	5	s	s	PROPN
ejpam-3291	149	6	,	,	PUNCT
ejpam-3291	149	7	t	t	PROPN
ejpam-3291	149	8	∈	∈	PROPN
ejpam-3291	149	9	s.	s.	PROPN
ejpam-3291	149	10	proof	proof	PROPN
ejpam-3291	149	11	.	.	PUNCT
ejpam-3291	150	1	(	(	PUNCT
ejpam-3291	150	2	1	1	X
ejpam-3291	150	3	)	)	PUNCT
ejpam-3291	150	4	assume	assume	VERB
ejpam-3291	150	5	that	that	SCONJ
ejpam-3291	150	6	m	m	PROPN
ejpam-3291	150	7	is	be	AUX
ejpam-3291	150	8	a	a	DET
ejpam-3291	150	9	quasi	quasi	ADJ
ejpam-3291	150	10	-	-	ADJ
ejpam-3291	150	11	slightly	slightly	ADV
ejpam-3291	150	12	compressible	compressible	ADJ
ejpam-3291	150	13	-	-	PUNCT
ejpam-3291	150	14	injective	injective	ADJ
ejpam-3291	150	15	module	module	NOUN
ejpam-3291	150	16	.	.	PUNCT
ejpam-3291	151	1	it	it	PRON
ejpam-3291	151	2	is	be	AUX
ejpam-3291	151	3	easy	easy	ADJ
ejpam-3291	151	4	to	to	PART
ejpam-3291	151	5	show	show	VERB
ejpam-3291	151	6	that	that	SCONJ
ejpam-3291	151	7	ss	ss	ADP
ejpam-3291	151	8	⊆	⊆	NUM
ejpam-3291	151	9	ls(ker(s	ls(ker(s	NOUN
ejpam-3291	151	10	)	)	PUNCT
ejpam-3291	151	11	)	)	PUNCT
ejpam-3291	151	12	.	.	PUNCT
ejpam-3291	152	1	let	let	VERB
ejpam-3291	152	2	s	s	PRON
ejpam-3291	152	3	∈	∈	NOUN
ejpam-3291	152	4	s	s	PART
ejpam-3291	152	5	and	and	CCONJ
ejpam-3291	152	6	u	u	NOUN
ejpam-3291	152	7	∈	∈	NOUN
ejpam-3291	152	8	ls(ker(s	ls(ker(s	NOUN
ejpam-3291	152	9	)	)	PUNCT
ejpam-3291	152	10	)	)	PUNCT
ejpam-3291	152	11	.	.	PUNCT
ejpam-3291	153	1	we	we	PRON
ejpam-3291	153	2	have	have	VERB
ejpam-3291	153	3	u(ker(s	u(ker(s	NOUN
ejpam-3291	153	4	)	)	PUNCT
ejpam-3291	153	5	)	)	PUNCT
ejpam-3291	154	1	=	=	PUNCT
ejpam-3291	154	2	0	0	X
ejpam-3291	154	3	.	.	PUNCT
ejpam-3291	154	4	then	then	ADV
ejpam-3291	154	5	ker(s	ker(s	PROPN
ejpam-3291	154	6	)	)	PUNCT
ejpam-3291	154	7	⊆	⊆	NUM
ejpam-3291	154	8	ker(u	ker(u	PROPN
ejpam-3291	154	9	)	)	PUNCT
ejpam-3291	154	10	.	.	PUNCT
ejpam-3291	155	1	by	by	ADP
ejpam-3291	155	2	the	the	DET
ejpam-3291	155	3	factor	factor	NOUN
ejpam-3291	155	4	’s	’s	PART
ejpam-3291	155	5	theorem	theorem	NOUN
ejpam-3291	155	6	,	,	PUNCT
ejpam-3291	155	7	there	there	PRON
ejpam-3291	155	8	exists	exist	VERB
ejpam-3291	155	9	an	an	DET
ejpam-3291	155	10	r	r	NOUN
ejpam-3291	155	11	-	-	PUNCT
ejpam-3291	155	12	homomorphism	homomorphism	ADJ
ejpam-3291	155	13	α	α	NOUN
ejpam-3291	155	14	:	:	PUNCT
ejpam-3291	155	15	s(m	s(m	NOUN
ejpam-3291	155	16	)	)	PUNCT
ejpam-3291	155	17	→	→	PUNCT
ejpam-3291	155	18	m	m	VERB
ejpam-3291	155	19	such	such	ADJ
ejpam-3291	155	20	that	that	SCONJ
ejpam-3291	155	21	αs	αs	PROPN
ejpam-3291	155	22	=	=	NOUN
ejpam-3291	155	23	u.	u.	PROPN
ejpam-3291	155	24	since	since	SCONJ
ejpam-3291	155	25	m	m	PROPN
ejpam-3291	155	26	is	be	AUX
ejpam-3291	155	27	a	a	DET
ejpam-3291	155	28	quasi	quasi	ADJ
ejpam-3291	155	29	-	-	ADJ
ejpam-3291	155	30	slightly	slightly	ADV
ejpam-3291	155	31	compressible	compressible	ADJ
ejpam-3291	155	32	-	-	PUNCT
ejpam-3291	155	33	injective	injective	ADJ
ejpam-3291	155	34	module	module	NOUN
ejpam-3291	155	35	,	,	PUNCT
ejpam-3291	155	36	there	there	PRON
ejpam-3291	155	37	exists	exist	VERB
ejpam-3291	155	38	an	an	DET
ejpam-3291	155	39	r	r	NOUN
ejpam-3291	155	40	-	-	PUNCT
ejpam-3291	155	41	homomorphism	homomorphism	NOUN
ejpam-3291	155	42	ᾱ	ᾱ	NOUN
ejpam-3291	155	43	:	:	PUNCT
ejpam-3291	155	44	m	m	VERB
ejpam-3291	155	45	→	→	NOUN
ejpam-3291	155	46	m	m	VERB
ejpam-3291	155	47	such	such	ADJ
ejpam-3291	155	48	that	that	PRON
ejpam-3291	155	49	ᾱ|s(m	ᾱ|s(m	NOUN
ejpam-3291	155	50	)	)	PUNCT
ejpam-3291	155	51	=	=	SYM
ejpam-3291	156	1	α	α	X
ejpam-3291	156	2	.	.	PUNCT
ejpam-3291	157	1	then	then	ADV
ejpam-3291	157	2	u	u	X
ejpam-3291	157	3	=	=	PUNCT
ejpam-3291	157	4	αs	αs	PROPN
ejpam-3291	157	5	=	=	PUNCT
ejpam-3291	157	6	ᾱs	ᾱs	PROPN
ejpam-3291	157	7	∈	∈	PROPN
ejpam-3291	157	8	ss	ss	PROPN
ejpam-3291	157	9	.	.	PUNCT
ejpam-3291	158	1	hence	hence	ADV
ejpam-3291	158	2	ls(ker(s	ls(ker(s	NOUN
ejpam-3291	158	3	)	)	PUNCT
ejpam-3291	158	4	)	)	PUNCT
ejpam-3291	159	1	⊆	⊆	NUM
ejpam-3291	159	2	ss	ss	NOUN
ejpam-3291	159	3	.	.	PUNCT
ejpam-3291	159	4	therefore	therefore	ADV
ejpam-3291	159	5	ls(ker(s	ls(ker(s	NOUN
ejpam-3291	159	6	)	)	PUNCT
ejpam-3291	159	7	)	)	PUNCT
ejpam-3291	160	1	=	=	SYM
ejpam-3291	161	1	ss	ss	PROPN
ejpam-3291	161	2	.	.	PUNCT
ejpam-3291	162	1	(	(	PUNCT
ejpam-3291	162	2	2	2	X
ejpam-3291	162	3	)	)	PUNCT
ejpam-3291	162	4	assume	assume	VERB
ejpam-3291	162	5	that	that	SCONJ
ejpam-3291	162	6	m	m	PROPN
ejpam-3291	162	7	is	be	AUX
ejpam-3291	162	8	a	a	DET
ejpam-3291	162	9	quasi	quasi	ADJ
ejpam-3291	162	10	-	-	ADJ
ejpam-3291	162	11	slightly	slightly	ADV
ejpam-3291	162	12	compressible	compressible	ADJ
ejpam-3291	162	13	-	-	PUNCT
ejpam-3291	162	14	injective	injective	ADJ
ejpam-3291	162	15	module	module	NOUN
ejpam-3291	162	16	.	.	PUNCT
ejpam-3291	163	1	let	let	VERB
ejpam-3291	163	2	s	s	NOUN
ejpam-3291	163	3	,	,	PUNCT
ejpam-3291	163	4	t	t	PROPN
ejpam-3291	163	5	∈	∈	PROPN
ejpam-3291	163	6	s.	s.	PROPN
ejpam-3291	163	7	suppose	suppose	VERB
ejpam-3291	163	8	ker(t	ker(t	NOUN
ejpam-3291	163	9	)	)	PUNCT
ejpam-3291	163	10	⊆	⊆	NUM
ejpam-3291	163	11	ker(s	ker(s	NOUN
ejpam-3291	163	12	)	)	PUNCT
ejpam-3291	163	13	.	.	PUNCT
ejpam-3291	164	1	by	by	ADP
ejpam-3291	164	2	proposition	proposition	NOUN
ejpam-3291	164	3	2	2	NUM
ejpam-3291	164	4	,	,	PUNCT
ejpam-3291	164	5	s	s	PROPN
ejpam-3291	164	6	∈	∈	PROPN
ejpam-3291	164	7	st	st	PROPN
ejpam-3291	164	8	.	.	PROPN
ejpam-3291	164	9	therefore	therefore	ADV
ejpam-3291	164	10	ss	ss	PROPN
ejpam-3291	164	11	⊆	⊆	NUM
ejpam-3291	164	12	st	st	PROPN
ejpam-3291	164	13	.	.	PROPN
ejpam-3291	165	1	(	(	PUNCT
ejpam-3291	165	2	3	3	X
ejpam-3291	165	3	)	)	PUNCT
ejpam-3291	165	4	assume	assume	VERB
ejpam-3291	165	5	that	that	SCONJ
ejpam-3291	165	6	m	m	PROPN
ejpam-3291	165	7	is	be	AUX
ejpam-3291	165	8	a	a	DET
ejpam-3291	165	9	quasi	quasi	ADJ
ejpam-3291	165	10	-	-	ADJ
ejpam-3291	165	11	slightly	slightly	ADV
ejpam-3291	165	12	compressible	compressible	ADJ
ejpam-3291	165	13	-	-	PUNCT
ejpam-3291	165	14	injective	injective	ADJ
ejpam-3291	165	15	module	module	NOUN
ejpam-3291	165	16	.	.	PUNCT
ejpam-3291	166	1	let	let	VERB
ejpam-3291	166	2	s	s	NOUN
ejpam-3291	166	3	,	,	PUNCT
ejpam-3291	166	4	t	t	PROPN
ejpam-3291	166	5	∈	∈	PROPN
ejpam-3291	166	6	s.	s.	PROPN
ejpam-3291	166	7	suppose	suppose	VERB
ejpam-3291	166	8	u	u	PRON
ejpam-3291	166	9	∈	∈	PROPN
ejpam-3291	166	10	ls(im(t	ls(im(t	NOUN
ejpam-3291	166	11	)	)	PUNCT
ejpam-3291	166	12	∩ker(s	∩ker(s	NOUN
ejpam-3291	166	13	)	)	PUNCT
ejpam-3291	166	14	)	)	PUNCT
ejpam-3291	166	15	.	.	PUNCT
ejpam-3291	167	1	then	then	ADV
ejpam-3291	167	2	u(im(t	u(im(t	NOUN
ejpam-3291	167	3	)	)	PUNCT
ejpam-3291	167	4	∩ker(s	∩ker(s	NOUN
ejpam-3291	167	5	)	)	PUNCT
ejpam-3291	167	6	)	)	PUNCT
ejpam-3291	167	7	)	)	PUNCT
ejpam-3291	168	1	=	=	SYM
ejpam-3291	168	2	0	0	PUNCT
ejpam-3291	169	1	and	and	CCONJ
ejpam-3291	169	2	we	we	PRON
ejpam-3291	169	3	have	have	VERB
ejpam-3291	169	4	ker(st	ker(st	NOUN
ejpam-3291	169	5	)	)	PUNCT
ejpam-3291	169	6	⊆	⊆	NUM
ejpam-3291	169	7	ker(ut	ker(ut	NOUN
ejpam-3291	169	8	)	)	PUNCT
ejpam-3291	169	9	.	.	PUNCT
ejpam-3291	170	1	by	by	ADP
ejpam-3291	170	2	factor	factor	NOUN
ejpam-3291	170	3	’s	’s	PART
ejpam-3291	170	4	theorem	theorem	NOUN
ejpam-3291	170	5	,	,	PUNCT
ejpam-3291	170	6	there	there	PRON
ejpam-3291	170	7	exists	exist	VERB
ejpam-3291	170	8	a	a	DET
ejpam-3291	170	9	map	map	NOUN
ejpam-3291	170	10	g′	g′	NOUN
ejpam-3291	170	11	:	:	PUNCT
ejpam-3291	170	12	st(m	st(m	NUM
ejpam-3291	170	13	)	)	PUNCT
ejpam-3291	170	14	→	→	PUNCT
ejpam-3291	170	15	m	m	VERB
ejpam-3291	170	16	such	such	ADJ
ejpam-3291	170	17	that	that	PRON
ejpam-3291	170	18	g′st	g′st	NOUN
ejpam-3291	170	19	=	=	SYM
ejpam-3291	170	20	ut	ut	PROPN
ejpam-3291	170	21	.	.	PROPN
ejpam-3291	170	22	sincem	sincem	PROPN
ejpam-3291	170	23	is	be	AUX
ejpam-3291	170	24	a	a	DET
ejpam-3291	170	25	quasi	quasi	ADJ
ejpam-3291	170	26	-	-	ADJ
ejpam-3291	170	27	slightly	slightly	ADV
ejpam-3291	170	28	compressible	compressible	ADJ
ejpam-3291	170	29	-	-	PUNCT
ejpam-3291	170	30	injective	injective	ADJ
ejpam-3291	170	31	module	module	NOUN
ejpam-3291	170	32	,	,	PUNCT
ejpam-3291	170	33	there	there	PRON
ejpam-3291	170	34	exists	exist	VERB
ejpam-3291	170	35	anr	anr	NOUN
ejpam-3291	170	36	-	-	NOUN
ejpam-3291	170	37	homomorphism	homomorphism	NOUN
ejpam-3291	170	38	g	g	NOUN
ejpam-3291	170	39	:	:	PUNCT
ejpam-3291	170	40	m	m	VERB
ejpam-3291	170	41	→	→	NOUN
ejpam-3291	170	42	m	m	VERB
ejpam-3291	170	43	such	such	ADJ
ejpam-3291	170	44	that	that	SCONJ
ejpam-3291	170	45	g|st(m	g|st(m	NOUN
ejpam-3291	170	46	)	)	PUNCT
ejpam-3291	171	1	=	=	SYM
ejpam-3291	171	2	g′.	g′.	X
ejpam-3291	171	3	thus	thus	ADV
ejpam-3291	171	4	ut	ut	PROPN
ejpam-3291	171	5	=	=	PROPN
ejpam-3291	171	6	gst	gst	PROPN
ejpam-3291	171	7	.	.	PUNCT
ejpam-3291	172	1	it	it	PRON
ejpam-3291	172	2	follows	follow	VERB
ejpam-3291	172	3	that	that	SCONJ
ejpam-3291	172	4	(	(	PUNCT
ejpam-3291	172	5	u	u	NOUN
ejpam-3291	172	6	−	−	PROPN
ejpam-3291	172	7	gs)t	gs)t	PROPN
ejpam-3291	172	8	=	=	SYM
ejpam-3291	172	9	0	0	NUM
ejpam-3291	172	10	and	and	CCONJ
ejpam-3291	172	11	hence	hence	ADV
ejpam-3291	172	12	u	u	NOUN
ejpam-3291	172	13	−	−	PROPN
ejpam-3291	172	14	gs	gs	PROPN
ejpam-3291	172	15	∈	∈	PROPN
ejpam-3291	172	16	ls(im(t	ls(im(t	NOUN
ejpam-3291	172	17	)	)	PUNCT
ejpam-3291	172	18	)	)	PUNCT
ejpam-3291	172	19	.	.	PUNCT
ejpam-3291	173	1	thus	thus	ADV
ejpam-3291	173	2	u	u	X
ejpam-3291	173	3	∈	∈	PROPN
ejpam-3291	173	4	ls(im(t	ls(im(t	NOUN
ejpam-3291	173	5	)	)	PUNCT
ejpam-3291	173	6	)	)	PUNCT
ejpam-3291	174	1	+	+	CCONJ
ejpam-3291	174	2	ss	ss	INTJ
ejpam-3291	174	3	.	.	PUNCT
ejpam-3291	175	1	we	we	PRON
ejpam-3291	175	2	have	have	VERB
ejpam-3291	175	3	ls(im(t	ls(im(t	NOUN
ejpam-3291	175	4	)	)	PUNCT
ejpam-3291	175	5	∩	∩	ADJ
ejpam-3291	175	6	ker(s	ker(s	NOUN
ejpam-3291	175	7	)	)	PUNCT
ejpam-3291	175	8	)	)	PUNCT
ejpam-3291	175	9	⊆	⊆	NUM
ejpam-3291	175	10	ls(im(t	ls(im(t	NOUN
ejpam-3291	175	11	)	)	PUNCT
ejpam-3291	175	12	)	)	PUNCT
ejpam-3291	176	1	+	+	CCONJ
ejpam-3291	176	2	ss	ss	NOUN
ejpam-3291	176	3	.	.	PUNCT
ejpam-3291	177	1	but	but	CCONJ
ejpam-3291	177	2	it	it	PRON
ejpam-3291	177	3	is	be	AUX
ejpam-3291	177	4	clear	clear	ADJ
ejpam-3291	177	5	that	that	SCONJ
ejpam-3291	177	6	ls(im(t	ls(im(t	NOUN
ejpam-3291	177	7	)	)	PUNCT
ejpam-3291	177	8	)	)	PUNCT
ejpam-3291	178	1	+	+	CCONJ
ejpam-3291	178	2	ss	ss	NOUN
ejpam-3291	178	3	↪	↪	PROPN
ejpam-3291	178	4	→	→	SYM
ejpam-3291	178	5	ls(im(t	ls(im(t	NOUN
ejpam-3291	178	6	)	)	PUNCT
ejpam-3291	178	7	∩	∩	ADJ
ejpam-3291	178	8	ker(s	ker(s	PROPN
ejpam-3291	178	9	)	)	PUNCT
ejpam-3291	178	10	)	)	PUNCT
ejpam-3291	178	11	.	.	PUNCT
ejpam-3291	179	1	therefore	therefore	ADV
ejpam-3291	179	2	ls(im(t	ls(im(t	NOUN
ejpam-3291	179	3	)	)	PUNCT
ejpam-3291	179	4	∩ker(s	∩ker(s	NOUN
ejpam-3291	179	5	)	)	PUNCT
ejpam-3291	179	6	)	)	PUNCT
ejpam-3291	180	1	=	=	SYM
ejpam-3291	180	2	ls(im(t	ls(im(t	NOUN
ejpam-3291	180	3	)	)	PUNCT
ejpam-3291	180	4	)	)	PUNCT
ejpam-3291	181	1	+	+	CCONJ
ejpam-3291	181	2	ss	ss	NOUN
ejpam-3291	181	3	for	for	ADP
ejpam-3291	181	4	all	all	DET
ejpam-3291	181	5	s	s	PROPN
ejpam-3291	181	6	,	,	PUNCT
ejpam-3291	181	7	t	t	PROPN
ejpam-3291	181	8	∈	∈	PROPN
ejpam-3291	181	9	s.	s.	PROPN
ejpam-3291	181	10	n.	n.	PROPN
ejpam-3291	181	11	d.	d.	PROPN
ejpam-3291	181	12	h.	h.	PROPN
ejpam-3291	181	13	nghiem	nghiem	PROPN
ejpam-3291	181	14	et	et	PROPN
ejpam-3291	181	15	al	al	PROPN
ejpam-3291	181	16	.	.	PUNCT
ejpam-3291	181	17	/	/	SYM
ejpam-3291	181	18	eur	eur	PROPN
ejpam-3291	181	19	.	.	PUNCT
ejpam-3291	182	1	j.	j.	PROPN
ejpam-3291	182	2	pure	pure	PROPN
ejpam-3291	182	3	appl	appl	PROPN
ejpam-3291	182	4	.	.	PROPN
ejpam-3291	182	5	math	math	PROPN
ejpam-3291	182	6	,	,	PUNCT
ejpam-3291	182	7	11	11	NUM
ejpam-3291	182	8	(	(	PUNCT
ejpam-3291	182	9	3	3	NUM
ejpam-3291	182	10	)	)	PUNCT
ejpam-3291	182	11	(	(	PUNCT
ejpam-3291	182	12	2018	2018	NUM
ejpam-3291	182	13	)	)	PUNCT
ejpam-3291	182	14	,	,	PUNCT
ejpam-3291	182	15	815	815	NUM
ejpam-3291	182	16	-	-	SYM
ejpam-3291	182	17	822	822	NUM
ejpam-3291	182	18	820	820	NUM
ejpam-3291	182	19	theorem	theorem	NOUN
ejpam-3291	182	20	3	3	X
ejpam-3291	182	21	.	.	PUNCT
ejpam-3291	183	1	let	let	VERB
ejpam-3291	183	2	m	m	PRON
ejpam-3291	183	3	be	be	AUX
ejpam-3291	183	4	a	a	DET
ejpam-3291	183	5	quasi	quasi	ADJ
ejpam-3291	183	6	-	-	ADJ
ejpam-3291	183	7	slightly	slightly	ADV
ejpam-3291	183	8	compressible	compressible	ADJ
ejpam-3291	183	9	module	module	NOUN
ejpam-3291	183	10	,	,	PUNCT
ejpam-3291	183	11	s	s	PART
ejpam-3291	183	12	=	=	X
ejpam-3291	183	13	endr(m	endr(m	PROPN
ejpam-3291	183	14	)	)	PUNCT
ejpam-3291	183	15	,	,	PUNCT
ejpam-3291	183	16	∆	∆	PROPN
ejpam-3291	183	17	be	be	VERB
ejpam-3291	183	18	the	the	DET
ejpam-3291	183	19	set	set	NOUN
ejpam-3291	183	20	of	of	ADP
ejpam-3291	183	21	all	all	DET
ejpam-3291	183	22	s	s	PART
ejpam-3291	183	23	∈	∈	NOUN
ejpam-3291	183	24	s	s	VERB
ejpam-3291	183	25	such	such	ADJ
ejpam-3291	183	26	that	that	DET
ejpam-3291	183	27	ker(s	ker(s	NOUN
ejpam-3291	183	28	)	)	PUNCT
ejpam-3291	183	29	is	be	AUX
ejpam-3291	183	30	an	an	DET
ejpam-3291	183	31	essential	essential	ADJ
ejpam-3291	183	32	in	in	ADP
ejpam-3291	183	33	m	m	PROPN
ejpam-3291	183	34	and	and	CCONJ
ejpam-3291	183	35	j(s	j(s	NOUN
ejpam-3291	183	36	)	)	PUNCT
ejpam-3291	183	37	be	be	VERB
ejpam-3291	183	38	the	the	DET
ejpam-3291	183	39	jacobson	jacobson	PROPN
ejpam-3291	183	40	radical	radical	PROPN
ejpam-3291	183	41	of	of	ADP
ejpam-3291	183	42	s.	s.	PROPN
ejpam-3291	183	43	if	if	SCONJ
ejpam-3291	183	44	m	m	PROPN
ejpam-3291	183	45	is	be	AUX
ejpam-3291	183	46	a	a	DET
ejpam-3291	183	47	quasi	quasi	ADJ
ejpam-3291	183	48	-	-	ADJ
ejpam-3291	183	49	slightly	slightly	ADV
ejpam-3291	183	50	compressible	compressible	ADJ
ejpam-3291	183	51	-	-	PUNCT
ejpam-3291	183	52	injective	injective	ADJ
ejpam-3291	183	53	module	module	NOUN
ejpam-3291	183	54	and	and	CCONJ
ejpam-3291	183	55	every	every	DET
ejpam-3291	183	56	m	m	NOUN
ejpam-3291	183	57	-cyclic	-cyclic	ADJ
ejpam-3291	183	58	submodule	submodule	NOUN
ejpam-3291	183	59	of	of	ADP
ejpam-3291	183	60	m	m	PROPN
ejpam-3291	183	61	is	be	AUX
ejpam-3291	183	62	an	an	DET
ejpam-3291	183	63	injective	injective	ADJ
ejpam-3291	183	64	,	,	PUNCT
ejpam-3291	183	65	then	then	ADV
ejpam-3291	183	66	j(s	j(s	NOUN
ejpam-3291	183	67	)	)	PUNCT
ejpam-3291	184	1	=	=	PUNCT
ejpam-3291	185	1	∆.	∆.	NOUN
ejpam-3291	185	2	proof	proof	NOUN
ejpam-3291	185	3	.	.	PUNCT
ejpam-3291	186	1	assume	assume	VERB
ejpam-3291	186	2	that	that	SCONJ
ejpam-3291	186	3	m	m	PROPN
ejpam-3291	186	4	is	be	AUX
ejpam-3291	186	5	a	a	DET
ejpam-3291	186	6	quasi	quasi	ADJ
ejpam-3291	186	7	-	-	ADJ
ejpam-3291	186	8	slightly	slightly	ADV
ejpam-3291	186	9	compressible	compressible	ADJ
ejpam-3291	186	10	-	-	PUNCT
ejpam-3291	186	11	injective	injective	ADJ
ejpam-3291	186	12	module	module	NOUN
ejpam-3291	186	13	and	and	CCONJ
ejpam-3291	186	14	every	every	DET
ejpam-3291	186	15	m	m	NOUN
ejpam-3291	186	16	-cyclic	-cyclic	ADJ
ejpam-3291	186	17	submodule	submodule	NOUN
ejpam-3291	186	18	of	of	ADP
ejpam-3291	186	19	m	m	PROPN
ejpam-3291	186	20	is	be	AUX
ejpam-3291	186	21	an	an	DET
ejpam-3291	186	22	injective	injective	ADJ
ejpam-3291	186	23	.	.	PUNCT
ejpam-3291	187	1	let	let	VERB
ejpam-3291	187	2	s	s	PRON
ejpam-3291	187	3	∈	∈	VERB
ejpam-3291	187	4	∆.	∆.	X
ejpam-3291	187	5	then	then	ADV
ejpam-3291	187	6	ker(s	ker(s	PROPN
ejpam-3291	187	7	)	)	PUNCT
ejpam-3291	187	8	is	be	AUX
ejpam-3291	187	9	an	an	DET
ejpam-3291	187	10	essential	essential	ADJ
ejpam-3291	187	11	in	in	ADP
ejpam-3291	187	12	m	m	PROPN
ejpam-3291	187	13	.	.	PUNCT
ejpam-3291	188	1	since	since	SCONJ
ejpam-3291	188	2	ker(s	ker(s	PROPN
ejpam-3291	188	3	)	)	PUNCT
ejpam-3291	188	4	∩ker(1	∩ker(1	PUNCT
ejpam-3291	189	1	−	−	PROPN
ejpam-3291	189	2	s	s	X
ejpam-3291	189	3	)	)	PUNCT
ejpam-3291	189	4	=	=	SYM
ejpam-3291	189	5	0	0	NUM
ejpam-3291	189	6	,	,	PUNCT
ejpam-3291	189	7	ker(1	ker(1	PUNCT
ejpam-3291	189	8	−	−	PROPN
ejpam-3291	190	1	s	s	X
ejpam-3291	190	2	)	)	PUNCT
ejpam-3291	190	3	=	=	SYM
ejpam-3291	190	4	0	0	NUM
ejpam-3291	190	5	,	,	PUNCT
ejpam-3291	190	6	ls(ker(1	ls(ker(1	PROPN
ejpam-3291	190	7	−	−	PUNCT
ejpam-3291	190	8	s	s	X
ejpam-3291	190	9	)	)	PUNCT
ejpam-3291	190	10	)	)	PUNCT
ejpam-3291	191	1	=	=	VERB
ejpam-3291	191	2	s.	s.	PROPN
ejpam-3291	191	3	by	by	ADP
ejpam-3291	191	4	theorem	theorem	NOUN
ejpam-3291	191	5	2(2	2(2	NUM
ejpam-3291	191	6	)	)	PUNCT
ejpam-3291	191	7	,	,	PUNCT
ejpam-3291	191	8	ls(ker(1	ls(ker(1	PROPN
ejpam-3291	191	9	−	−	PROPN
ejpam-3291	191	10	s	s	X
ejpam-3291	191	11	)	)	PUNCT
ejpam-3291	191	12	)	)	PUNCT
ejpam-3291	192	1	=	=	PUNCT
ejpam-3291	192	2	s(1	s(1	PROPN
ejpam-3291	192	3	−	−	PROPN
ejpam-3291	192	4	s	s	NOUN
ejpam-3291	192	5	)	)	PUNCT
ejpam-3291	192	6	.	.	PUNCT
ejpam-3291	193	1	then	then	ADV
ejpam-3291	193	2	s(1	s(1	PROPN
ejpam-3291	193	3	−	−	PROPN
ejpam-3291	193	4	s	s	PART
ejpam-3291	193	5	)	)	PUNCT
ejpam-3291	193	6	=	=	VERB
ejpam-3291	194	1	s.	s.	PROPN
ejpam-3291	194	2	hence	hence	ADV
ejpam-3291	194	3	1	1	NUM
ejpam-3291	194	4	−	−	NOUN
ejpam-3291	194	5	s	s	NOUN
ejpam-3291	194	6	has	have	AUX
ejpam-3291	194	7	left	leave	VERB
ejpam-3291	194	8	inverse	inverse	NOUN
ejpam-3291	194	9	in	in	ADP
ejpam-3291	194	10	s.	s.	PROPN
ejpam-3291	194	11	by	by	ADP
ejpam-3291	194	12	theorem	theorem	NOUN
ejpam-3291	194	13	9.3.1	9.3.1	NUM
ejpam-3291	194	14	in	in	ADP
ejpam-3291	194	15	[	[	X
ejpam-3291	194	16	5	5	NUM
ejpam-3291	194	17	]	]	PUNCT
ejpam-3291	194	18	,	,	PUNCT
ejpam-3291	194	19	∆	∆	PROPN
ejpam-3291	194	20	⊆	⊆	NUM
ejpam-3291	194	21	j(s	j(s	NOUN
ejpam-3291	194	22	)	)	PUNCT
ejpam-3291	194	23	.	.	PUNCT
ejpam-3291	195	1	next	next	ADV
ejpam-3291	195	2	,	,	PUNCT
ejpam-3291	195	3	let	let	VERB
ejpam-3291	195	4	s	s	PRON
ejpam-3291	195	5	∈	∈	PROPN
ejpam-3291	195	6	j(s	j(s	NOUN
ejpam-3291	195	7	)	)	PUNCT
ejpam-3291	195	8	.	.	PUNCT
ejpam-3291	196	1	we	we	PRON
ejpam-3291	196	2	want	want	VERB
ejpam-3291	196	3	to	to	PART
ejpam-3291	196	4	show	show	VERB
ejpam-3291	196	5	that	that	SCONJ
ejpam-3291	196	6	ker(s	ker(s	PROPN
ejpam-3291	196	7	)	)	PUNCT
ejpam-3291	196	8	is	be	AUX
ejpam-3291	196	9	an	an	DET
ejpam-3291	196	10	essential	essential	ADJ
ejpam-3291	196	11	in	in	ADP
ejpam-3291	196	12	m	m	PROPN
ejpam-3291	196	13	.	.	PUNCT
ejpam-3291	197	1	first	first	ADV
ejpam-3291	197	2	,	,	PUNCT
ejpam-3291	197	3	we	we	PRON
ejpam-3291	197	4	claim	claim	VERB
ejpam-3291	197	5	that	that	SCONJ
ejpam-3291	197	6	if	if	SCONJ
ejpam-3291	197	7	im(t	im(t	VERB
ejpam-3291	197	8	)	)	PUNCT
ejpam-3291	197	9	∩ker(s	∩ker(s	NUM
ejpam-3291	197	10	)	)	PUNCT
ejpam-3291	197	11	=	=	SYM
ejpam-3291	197	12	0	0	NUM
ejpam-3291	198	1	for	for	ADP
ejpam-3291	198	2	all	all	DET
ejpam-3291	198	3	t	t	NOUN
ejpam-3291	198	4	∈	∈	PROPN
ejpam-3291	198	5	s	s	NOUN
ejpam-3291	198	6	,	,	PUNCT
ejpam-3291	198	7	then	then	ADV
ejpam-3291	198	8	t	t	PROPN
ejpam-3291	198	9	=	=	SYM
ejpam-3291	198	10	0	0	X
ejpam-3291	198	11	.	.	PUNCT
ejpam-3291	199	1	let	let	VERB
ejpam-3291	199	2	t	t	PROPN
ejpam-3291	199	3	∈	∈	PROPN
ejpam-3291	199	4	s	s	VERB
ejpam-3291	199	5	such	such	ADJ
ejpam-3291	199	6	that	that	SCONJ
ejpam-3291	199	7	im(t)∩ker(s	im(t)∩ker(s	NOUN
ejpam-3291	199	8	)	)	PUNCT
ejpam-3291	199	9	=	=	SYM
ejpam-3291	200	1	0	0	X
ejpam-3291	200	2	.	.	PUNCT
ejpam-3291	200	3	by	by	ADP
ejpam-3291	200	4	theorem	theorem	ADJ
ejpam-3291	200	5	2(3	2(3	NUM
ejpam-3291	200	6	)	)	PUNCT
ejpam-3291	200	7	,	,	PUNCT
ejpam-3291	200	8	ls(im(t)∩ker(s	ls(im(t)∩ker(s	NOUN
ejpam-3291	200	9	)	)	PUNCT
ejpam-3291	200	10	)	)	PUNCT
ejpam-3291	201	1	=	=	SYM
ejpam-3291	201	2	ls(im(t))+ss	ls(im(t))+ss	NOUN
ejpam-3291	201	3	but	but	CCONJ
ejpam-3291	201	4	ls(im(t)∩ker(s	ls(im(t)∩ker(s	NOUN
ejpam-3291	201	5	)	)	PUNCT
ejpam-3291	201	6	)	)	PUNCT
ejpam-3291	202	1	=	=	PUNCT
ejpam-3291	202	2	s.	s.	PROPN
ejpam-3291	202	3	then	then	ADV
ejpam-3291	202	4	ls(im(t))+ss	ls(im(t))+ss	PROPN
ejpam-3291	202	5	=	=	PUNCT
ejpam-3291	202	6	s.	s.	PROPN
ejpam-3291	202	7	since	since	SCONJ
ejpam-3291	202	8	s	s	PROPN
ejpam-3291	202	9	∈	∈	PROPN
ejpam-3291	202	10	j(s	j(s	NOUN
ejpam-3291	202	11	)	)	PUNCT
ejpam-3291	202	12	,	,	PUNCT
ejpam-3291	202	13	ss	ss	PROPN
ejpam-3291	202	14	is	be	AUX
ejpam-3291	202	15	a	a	DET
ejpam-3291	202	16	small	small	ADJ
ejpam-3291	202	17	in	in	ADP
ejpam-3291	202	18	s	s	PROPN
ejpam-3291	202	19	,	,	PUNCT
ejpam-3291	202	20	ls(im(t	ls(im(t	NOUN
ejpam-3291	202	21	)	)	PUNCT
ejpam-3291	202	22	)	)	PUNCT
ejpam-3291	203	1	=	=	SYM
ejpam-3291	203	2	s	s	NOUN
ejpam-3291	203	3	,	,	PUNCT
ejpam-3291	203	4	im(t	im(t	VERB
ejpam-3291	203	5	)	)	PUNCT
ejpam-3291	203	6	=	=	SYM
ejpam-3291	204	1	0	0	X
ejpam-3291	204	2	.	.	PUNCT
ejpam-3291	205	1	then	then	ADV
ejpam-3291	205	2	t	t	PROPN
ejpam-3291	205	3	=	=	SYM
ejpam-3291	205	4	0	0	X
ejpam-3291	205	5	.	.	PUNCT
ejpam-3291	206	1	let	let	VERB
ejpam-3291	206	2	a	a	DET
ejpam-3291	206	3	↪	↪	PROPN
ejpam-3291	206	4	→m	→m	NOUN
ejpam-3291	206	5	such	such	ADJ
ejpam-3291	206	6	that	that	DET
ejpam-3291	206	7	ker(s)∩a	ker(s)∩a	NOUN
ejpam-3291	206	8	=	=	NOUN
ejpam-3291	207	1	0	0	X
ejpam-3291	207	2	.	.	PUNCT
ejpam-3291	208	1	since	since	SCONJ
ejpam-3291	208	2	m	m	PROPN
ejpam-3291	208	3	is	be	AUX
ejpam-3291	208	4	a	a	DET
ejpam-3291	208	5	quasi	quasi	ADJ
ejpam-3291	208	6	-	-	ADJ
ejpam-3291	208	7	slightly	slightly	ADV
ejpam-3291	208	8	compressible	compressible	ADJ
ejpam-3291	208	9	module	module	NOUN
ejpam-3291	208	10	and	and	CCONJ
ejpam-3291	208	11	every	every	DET
ejpam-3291	208	12	m	m	PROPN
ejpam-3291	208	13	-cyclic	-cyclic	PROPN
ejpam-3291	208	14	submodule	submodule	NOUN
ejpam-3291	208	15	is	be	AUX
ejpam-3291	208	16	an	an	DET
ejpam-3291	208	17	injective	injective	ADJ
ejpam-3291	208	18	,	,	PUNCT
ejpam-3291	208	19	from	from	ADP
ejpam-3291	208	20	corollary	corollary	ADJ
ejpam-3291	208	21	2.14	2.14	NUM
ejpam-3291	208	22	in	in	ADP
ejpam-3291	208	23	[	[	X
ejpam-3291	208	24	2	2	NUM
ejpam-3291	208	25	]	]	PUNCT
ejpam-3291	208	26	,	,	PUNCT
ejpam-3291	208	27	m	m	PROPN
ejpam-3291	208	28	is	be	AUX
ejpam-3291	208	29	a	a	DET
ejpam-3291	208	30	self	self	NOUN
ejpam-3291	208	31	-	-	PUNCT
ejpam-3291	208	32	generator	generator	NOUN
ejpam-3291	208	33	,	,	PUNCT
ejpam-3291	208	34	a	a	PRON
ejpam-3291	208	35	=	=	X
ejpam-3291	208	36	∑	∑	NOUN
ejpam-3291	208	37	t∈i	t∈i	NOUN
ejpam-3291	208	38	t(m	t(m	PROPN
ejpam-3291	208	39	)	)	PUNCT
ejpam-3291	208	40	where	where	SCONJ
ejpam-3291	208	41	i	i	PRON
ejpam-3291	208	42	⊆	⊆	NUM
ejpam-3291	208	43	s	s	NOUN
ejpam-3291	208	44	=	=	NOUN
ejpam-3291	208	45	endr(m),∑	endr(m),∑	PROPN
ejpam-3291	208	46	t∈i	t∈i	NOUN
ejpam-3291	208	47	t(m	t(m	PROPN
ejpam-3291	208	48	)	)	PUNCT
ejpam-3291	208	49	∩ker(s	∩ker(s	NUM
ejpam-3291	208	50	)	)	PUNCT
ejpam-3291	209	1	=	=	SYM
ejpam-3291	209	2	0	0	NUM
ejpam-3291	209	3	,	,	PUNCT
ejpam-3291	209	4	t(m	t(m	PROPN
ejpam-3291	209	5	)	)	PUNCT
ejpam-3291	209	6	∩ker(s	∩ker(s	NUM
ejpam-3291	209	7	)	)	PUNCT
ejpam-3291	210	1	=	=	SYM
ejpam-3291	210	2	0	0	NUM
ejpam-3291	210	3	for	for	ADP
ejpam-3291	210	4	all	all	DET
ejpam-3291	210	5	t	t	PROPN
ejpam-3291	210	6	∈	∈	PROPN
ejpam-3291	210	7	i.	i.	NOUN
ejpam-3291	210	8	we	we	PRON
ejpam-3291	210	9	have	have	VERB
ejpam-3291	210	10	t	t	NOUN
ejpam-3291	210	11	=	=	SYM
ejpam-3291	210	12	0	0	NUM
ejpam-3291	210	13	for	for	ADP
ejpam-3291	210	14	all	all	DET
ejpam-3291	210	15	t	t	PROPN
ejpam-3291	210	16	∈	∈	PROPN
ejpam-3291	210	17	i.	i.	NOUN
ejpam-3291	210	18	then	then	ADV
ejpam-3291	210	19	a	a	DET
ejpam-3291	210	20	=	=	PUNCT
ejpam-3291	210	21	∑	∑	ADP
ejpam-3291	210	22	t∈i	t∈i	NOUN
ejpam-3291	210	23	t(m	t(m	PROPN
ejpam-3291	210	24	)	)	PUNCT
ejpam-3291	211	1	=	=	PUNCT
ejpam-3291	211	2	0	0	NUM
ejpam-3291	211	3	,	,	PUNCT
ejpam-3291	211	4	so	so	ADV
ejpam-3291	211	5	ker(s	ker(s	PROPN
ejpam-3291	211	6	)	)	PUNCT
ejpam-3291	211	7	is	be	AUX
ejpam-3291	211	8	an	an	DET
ejpam-3291	211	9	essential	essential	ADJ
ejpam-3291	211	10	in	in	ADP
ejpam-3291	211	11	m	m	PRON
ejpam-3291	211	12	.	.	PUNCT
ejpam-3291	212	1	hence	hence	ADV
ejpam-3291	212	2	s	s	X
ejpam-3291	212	3	∈	∈	NOUN
ejpam-3291	212	4	∆	∆	X
ejpam-3291	212	5	,	,	PUNCT
ejpam-3291	212	6	j(s	j(s	NOUN
ejpam-3291	212	7	)	)	PUNCT
ejpam-3291	213	1	⊆	⊆	NUM
ejpam-3291	213	2	∆.	∆.	X
ejpam-3291	213	3	therefore	therefore	ADV
ejpam-3291	213	4	j(s	j(s	NOUN
ejpam-3291	213	5	)	)	PUNCT
ejpam-3291	214	1	=	=	PUNCT
ejpam-3291	215	1	∆.	∆.	NOUN
ejpam-3291	215	2	theorem	theorem	NOUN
ejpam-3291	215	3	4	4	X
ejpam-3291	215	4	.	.	PUNCT
ejpam-3291	216	1	let	let	VERB
ejpam-3291	216	2	m	m	PRON
ejpam-3291	216	3	be	be	AUX
ejpam-3291	216	4	a	a	DET
ejpam-3291	216	5	quasi	quasi	ADJ
ejpam-3291	216	6	-	-	ADJ
ejpam-3291	216	7	slightly	slightly	ADV
ejpam-3291	216	8	compressible	compressible	ADJ
ejpam-3291	216	9	-	-	PUNCT
ejpam-3291	216	10	injective	injective	ADJ
ejpam-3291	216	11	module	module	NOUN
ejpam-3291	216	12	and	and	CCONJ
ejpam-3291	216	13	s	s	NOUN
ejpam-3291	216	14	,	,	PUNCT
ejpam-3291	216	15	t	t	PROPN
ejpam-3291	216	16	∈	∈	PROPN
ejpam-3291	216	17	s	s	PART
ejpam-3291	216	18	=	=	X
ejpam-3291	216	19	endr(m	endr(m	PROPN
ejpam-3291	216	20	)	)	PUNCT
ejpam-3291	216	21	.	.	PUNCT
ejpam-3291	217	1	if	if	SCONJ
ejpam-3291	217	2	s(m	s(m	NOUN
ejpam-3291	217	3	)	)	PUNCT
ejpam-3291	217	4	∼=	∼=	PROPN
ejpam-3291	217	5	t(m	t(m	PROPN
ejpam-3291	217	6	)	)	PUNCT
ejpam-3291	217	7	,	,	PUNCT
ejpam-3291	217	8	then	then	ADV
ejpam-3291	217	9	ss	ss	PROPN
ejpam-3291	217	10	∼=	∼=	PROPN
ejpam-3291	217	11	st	st	PROPN
ejpam-3291	217	12	.	.	PROPN
ejpam-3291	217	13	proof	proof	PROPN
ejpam-3291	217	14	.	.	PUNCT
ejpam-3291	218	1	assume	assume	VERB
ejpam-3291	218	2	that	that	SCONJ
ejpam-3291	218	3	s(m	s(m	NOUN
ejpam-3291	218	4	)	)	PUNCT
ejpam-3291	218	5	∼=	∼=	PROPN
ejpam-3291	218	6	t(m	t(m	PROPN
ejpam-3291	218	7	)	)	PUNCT
ejpam-3291	218	8	.	.	PUNCT
ejpam-3291	219	1	then	then	ADV
ejpam-3291	219	2	there	there	PRON
ejpam-3291	219	3	exists	exist	VERB
ejpam-3291	219	4	an	an	DET
ejpam-3291	219	5	isomorphism	isomorphism	NOUN
ejpam-3291	219	6	f	f	PROPN
ejpam-3291	219	7	from	from	ADP
ejpam-3291	219	8	s(m	s(m	PROPN
ejpam-3291	219	9	)	)	PUNCT
ejpam-3291	219	10	to	to	ADP
ejpam-3291	219	11	t(m	t(m	PROPN
ejpam-3291	219	12	)	)	PUNCT
ejpam-3291	219	13	.	.	PUNCT
ejpam-3291	220	1	since	since	SCONJ
ejpam-3291	220	2	m	m	PROPN
ejpam-3291	220	3	is	be	AUX
ejpam-3291	220	4	a	a	DET
ejpam-3291	220	5	quasi	quasi	ADJ
ejpam-3291	220	6	-	-	ADJ
ejpam-3291	220	7	slightly	slightly	ADV
ejpam-3291	220	8	compressible	compressible	ADJ
ejpam-3291	220	9	-	-	PUNCT
ejpam-3291	220	10	injective	injective	ADJ
ejpam-3291	220	11	module	module	NOUN
ejpam-3291	220	12	,	,	PUNCT
ejpam-3291	220	13	s(m	s(m	PROPN
ejpam-3291	220	14	)	)	PUNCT
ejpam-3291	220	15	is	be	AUX
ejpam-3291	220	16	an	an	DET
ejpam-3291	220	17	m	m	ADV
ejpam-3291	220	18	-slightly	-slightly	ADV
ejpam-3291	220	19	compressible	compressible	ADJ
ejpam-3291	220	20	submodule	submodule	NOUN
ejpam-3291	220	21	,	,	PUNCT
ejpam-3291	220	22	it(m)f	it(m)f	NUM
ejpam-3291	220	23	:	:	PUNCT
ejpam-3291	220	24	s(m	s(m	PROPN
ejpam-3291	220	25	)	)	PUNCT
ejpam-3291	220	26	→	→	PUNCT
ejpam-3291	220	27	m	m	NOUN
ejpam-3291	220	28	is	be	AUX
ejpam-3291	220	29	an	an	DET
ejpam-3291	220	30	r	r	NOUN
ejpam-3291	220	31	-	-	PUNCT
ejpam-3291	220	32	homomorphism	homomorphism	NOUN
ejpam-3291	220	33	,	,	PUNCT
ejpam-3291	220	34	so	so	ADV
ejpam-3291	220	35	it(m)f	it(m)f	PROPN
ejpam-3291	220	36	can	can	AUX
ejpam-3291	220	37	be	be	AUX
ejpam-3291	220	38	extended	extend	VERB
ejpam-3291	220	39	to	to	ADP
ejpam-3291	220	40	f̄	f̄	NOUN
ejpam-3291	220	41	:	:	PUNCT
ejpam-3291	220	42	m	m	VERB
ejpam-3291	220	43	→	→	NOUN
ejpam-3291	220	44	m	m	VERB
ejpam-3291	220	45	such	such	ADJ
ejpam-3291	220	46	that	that	SCONJ
ejpam-3291	220	47	f̄	f̄	PROPN
ejpam-3291	220	48	is(m	is(m	NOUN
ejpam-3291	220	49	)	)	PUNCT
ejpam-3291	221	1	=	=	PUNCT
ejpam-3291	222	1	it(m)f	it(m)f	ADP
ejpam-3291	222	2	where	where	SCONJ
ejpam-3291	222	3	is(m	is(m	NOUN
ejpam-3291	222	4	)	)	PUNCT
ejpam-3291	222	5	:	:	PUNCT
ejpam-3291	222	6	s(m	s(m	X
ejpam-3291	222	7	)	)	PUNCT
ejpam-3291	222	8	→	→	SYM
ejpam-3291	222	9	m	m	NOUN
ejpam-3291	222	10	and	and	CCONJ
ejpam-3291	222	11	it(m	it(m	NOUN
ejpam-3291	222	12	)	)	PUNCT
ejpam-3291	222	13	:	:	PUNCT
ejpam-3291	223	1	t(m	t(m	PROPN
ejpam-3291	223	2	)	)	PUNCT
ejpam-3291	223	3	→	→	PUNCT
ejpam-3291	223	4	m	m	NOUN
ejpam-3291	223	5	are	be	AUX
ejpam-3291	223	6	embedding	embed	VERB
ejpam-3291	223	7	.	.	PUNCT
ejpam-3291	224	1	define	define	VERB
ejpam-3291	224	2	β	β	X
ejpam-3291	224	3	:	:	PUNCT
ejpam-3291	224	4	st	st	PROPN
ejpam-3291	224	5	→	→	SYM
ejpam-3291	224	6	ss	ss	NOUN
ejpam-3291	224	7	by	by	ADP
ejpam-3291	224	8	β(ut	β(ut	PROPN
ejpam-3291	224	9	)	)	PUNCT
ejpam-3291	225	1	=	=	SYM
ejpam-3291	225	2	uf̄s	uf̄s	NOUN
ejpam-3291	225	3	for	for	ADP
ejpam-3291	225	4	all	all	DET
ejpam-3291	225	5	u	u	PROPN
ejpam-3291	225	6	∈	∈	PROPN
ejpam-3291	225	7	s.	s.	PROPN
ejpam-3291	225	8	since	since	SCONJ
ejpam-3291	225	9	im(f̄	im(f̄	PROPN
ejpam-3291	225	10	s	s	PART
ejpam-3291	225	11	)	)	PUNCT
ejpam-3291	225	12	=	=	SYM
ejpam-3291	225	13	im(t	im(t	X
ejpam-3291	225	14	)	)	PUNCT
ejpam-3291	225	15	,	,	PUNCT
ejpam-3291	225	16	we	we	PRON
ejpam-3291	225	17	can	can	AUX
ejpam-3291	225	18	show	show	VERB
ejpam-3291	225	19	that	that	SCONJ
ejpam-3291	225	20	β	β	NOUN
ejpam-3291	225	21	is	be	AUX
ejpam-3291	225	22	an	an	DET
ejpam-3291	225	23	well	well	ADV
ejpam-3291	225	24	-	-	PUNCT
ejpam-3291	225	25	defined	define	VERB
ejpam-3291	225	26	.	.	PUNCT
ejpam-3291	226	1	moreover	moreover	ADV
ejpam-3291	226	2	,	,	PUNCT
ejpam-3291	226	3	β	β	X
ejpam-3291	226	4	is	be	AUX
ejpam-3291	226	5	a	a	DET
ejpam-3291	226	6	left	left	ADJ
ejpam-3291	226	7	s	s	NOUN
ejpam-3291	226	8	-	-	NOUN
ejpam-3291	226	9	homomorphism	homomorphism	NOUN
ejpam-3291	226	10	.	.	PUNCT
ejpam-3291	227	1	for	for	ADP
ejpam-3291	227	2	any	any	DET
ejpam-3291	227	3	v	v	NUM
ejpam-3291	227	4	∈	∈	PROPN
ejpam-3291	227	5	s	s	NOUN
ejpam-3291	227	6	,	,	PUNCT
ejpam-3291	227	7	vis(m	vis(m	PROPN
ejpam-3291	227	8	)	)	PUNCT
ejpam-3291	227	9	:	:	PUNCT
ejpam-3291	227	10	s(m	s(m	X
ejpam-3291	227	11	)	)	PUNCT
ejpam-3291	227	12	→	→	PUNCT
ejpam-3291	227	13	m	m	NOUN
ejpam-3291	227	14	can	can	AUX
ejpam-3291	227	15	be	be	AUX
ejpam-3291	227	16	extended	extend	VERB
ejpam-3291	227	17	to	to	ADP
ejpam-3291	227	18	an	an	DET
ejpam-3291	227	19	r	r	NOUN
ejpam-3291	227	20	-	-	PUNCT
ejpam-3291	227	21	homomorphism	homomorphism	NOUN
ejpam-3291	227	22	ϕ	ϕ	NOUN
ejpam-3291	227	23	:	:	PUNCT
ejpam-3291	227	24	m	m	VERB
ejpam-3291	227	25	→	→	NOUN
ejpam-3291	227	26	m	m	VERB
ejpam-3291	227	27	such	such	ADJ
ejpam-3291	227	28	that	that	SCONJ
ejpam-3291	227	29	ϕit(m)f	ϕit(m)f	ADJ
ejpam-3291	227	30	=	=	SYM
ejpam-3291	227	31	vis(m	vis(m	PROPN
ejpam-3291	227	32	)	)	PUNCT
ejpam-3291	227	33	and	and	CCONJ
ejpam-3291	227	34	we	we	PRON
ejpam-3291	227	35	can	can	AUX
ejpam-3291	227	36	construct	construct	VERB
ejpam-3291	227	37	the	the	DET
ejpam-3291	227	38	map	map	NOUN
ejpam-3291	227	39	s′	s′	ADJ
ejpam-3291	227	40	:	:	PUNCT
ejpam-3291	227	41	m	m	PROPN
ejpam-3291	227	42	→	→	SYM
ejpam-3291	227	43	s(m	s(m	PROPN
ejpam-3291	227	44	)	)	PUNCT
ejpam-3291	227	45	such	such	ADJ
ejpam-3291	227	46	that	that	SCONJ
ejpam-3291	227	47	s′(m	s′(m	NOUN
ejpam-3291	227	48	)	)	PUNCT
ejpam-3291	227	49	=	=	SYM
ejpam-3291	227	50	s(m	s(m	PROPN
ejpam-3291	227	51	)	)	PUNCT
ejpam-3291	227	52	for	for	ADP
ejpam-3291	227	53	all	all	DET
ejpam-3291	227	54	m	m	NOUN
ejpam-3291	227	55	∈	∈	ADJ
ejpam-3291	227	56	m	m	NOUN
ejpam-3291	227	57	,	,	PUNCT
ejpam-3291	227	58	so	so	ADV
ejpam-3291	227	59	is(m)s	is(m)s	PROPN
ejpam-3291	227	60	′	′	NUM
ejpam-3291	228	1	=	=	PUNCT
ejpam-3291	228	2	s	s	VERB
ejpam-3291	228	3	where	where	SCONJ
ejpam-3291	228	4	is(m	is(m	NOUN
ejpam-3291	228	5	)	)	PUNCT
ejpam-3291	228	6	:	:	PUNCT
ejpam-3291	228	7	s(m	s(m	X
ejpam-3291	228	8	)	)	PUNCT
ejpam-3291	228	9	→	→	SYM
ejpam-3291	228	10	m	m	NOUN
ejpam-3291	228	11	and	and	CCONJ
ejpam-3291	228	12	it(m	it(m	NOUN
ejpam-3291	228	13	)	)	PUNCT
ejpam-3291	228	14	:	:	PUNCT
ejpam-3291	229	1	t(m	t(m	PROPN
ejpam-3291	229	2	)	)	PUNCT
ejpam-3291	229	3	→	→	PUNCT
ejpam-3291	229	4	m	m	NOUN
ejpam-3291	229	5	are	be	AUX
ejpam-3291	229	6	embedding	embed	VERB
ejpam-3291	229	7	.	.	PUNCT
ejpam-3291	230	1	we	we	PRON
ejpam-3291	230	2	have	have	VERB
ejpam-3291	230	3	β(ϕt	β(ϕt	NOUN
ejpam-3291	230	4	)	)	PUNCT
ejpam-3291	230	5	=	=	SYM
ejpam-3291	230	6	ϕf̄s	ϕf̄s	NOUN
ejpam-3291	231	1	=	=	SYM
ejpam-3291	231	2	ϕf̄is(m)s	ϕf̄is(m)s	ADJ
ejpam-3291	231	3	′	′	NUM
ejpam-3291	232	1	=	=	PUNCT
ejpam-3291	232	2	ϕit(m)fs	ϕit(m)fs	NOUN
ejpam-3291	233	1	′	′	NUM
ejpam-3291	233	2	=	=	PUNCT
ejpam-3291	233	3	vis(m)s	vis(m)s	ADJ
ejpam-3291	233	4	′	′	NUM
ejpam-3291	234	1	=	=	PUNCT
ejpam-3291	234	2	vs.	vs.	X
ejpam-3291	234	3	this	this	PRON
ejpam-3291	234	4	shows	show	VERB
ejpam-3291	234	5	that	that	SCONJ
ejpam-3291	234	6	β	β	PROPN
ejpam-3291	234	7	is	be	AUX
ejpam-3291	234	8	an	an	DET
ejpam-3291	234	9	epimorphism	epimorphism	NOUN
ejpam-3291	234	10	.	.	PUNCT
ejpam-3291	235	1	it	it	PRON
ejpam-3291	235	2	is	be	AUX
ejpam-3291	235	3	clear	clear	ADJ
ejpam-3291	235	4	that	that	SCONJ
ejpam-3291	235	5	β	β	NOUN
ejpam-3291	235	6	is	be	AUX
ejpam-3291	235	7	a	a	DET
ejpam-3291	235	8	left	left	ADJ
ejpam-3291	235	9	s	s	NOUN
ejpam-3291	235	10	-	-	NOUN
ejpam-3291	235	11	monomorphism	monomorphism	NOUN
ejpam-3291	235	12	.	.	PUNCT
ejpam-3291	236	1	therefore	therefore	ADV
ejpam-3291	236	2	ss	ss	ADP
ejpam-3291	236	3	∼=	∼=	PROPN
ejpam-3291	236	4	st	st	PROPN
ejpam-3291	236	5	.	.	PROPN
ejpam-3291	236	6	theorem	theorem	PROPN
ejpam-3291	236	7	5	5	NUM
ejpam-3291	236	8	.	.	PUNCT
ejpam-3291	237	1	let	let	VERB
ejpam-3291	237	2	m	m	PRON
ejpam-3291	237	3	be	be	AUX
ejpam-3291	237	4	a	a	DET
ejpam-3291	237	5	quasi	quasi	ADJ
ejpam-3291	237	6	-	-	ADJ
ejpam-3291	237	7	slightly	slightly	ADV
ejpam-3291	237	8	compressible	compressible	ADJ
ejpam-3291	237	9	-	-	PUNCT
ejpam-3291	237	10	injective	injective	ADJ
ejpam-3291	237	11	module	module	NOUN
ejpam-3291	237	12	and	and	CCONJ
ejpam-3291	237	13	s1	s1	NOUN
ejpam-3291	237	14	,	,	PUNCT
ejpam-3291	237	15	.	.	PUNCT
ejpam-3291	237	16	.	.	PUNCT
ejpam-3291	238	1	.	.	PUNCT
ejpam-3291	239	1	,	,	PUNCT
ejpam-3291	239	2	sn	sn	PROPN
ejpam-3291	239	3	∈	∈	PROPN
ejpam-3291	239	4	s	s	PART
ejpam-3291	239	5	=	=	X
ejpam-3291	239	6	endr(m	endr(m	PROPN
ejpam-3291	239	7	)	)	PUNCT
ejpam-3291	239	8	such	such	ADJ
ejpam-3291	239	9	that	that	SCONJ
ejpam-3291	239	10	the	the	DET
ejpam-3291	239	11	sum	sum	NOUN
ejpam-3291	239	12	∑n	∑n	PROPN
ejpam-3291	239	13	i=1	i=1	PROPN
ejpam-3291	239	14	ssi	ssi	PROPN
ejpam-3291	239	15	is	be	AUX
ejpam-3291	239	16	direct	direct	ADJ
ejpam-3291	239	17	.	.	PUNCT
ejpam-3291	240	1	then	then	ADV
ejpam-3291	240	2	any	any	DET
ejpam-3291	240	3	r	r	NOUN
ejpam-3291	240	4	-	-	PUNCT
ejpam-3291	240	5	homomorphism	homomorphism	NOUN
ejpam-3291	240	6	from∑n	from∑n	VERB
ejpam-3291	240	7	i=1	i=1	PROPN
ejpam-3291	240	8	si(m	si(m	NOUN
ejpam-3291	240	9	)	)	PUNCT
ejpam-3291	240	10	to	to	ADP
ejpam-3291	240	11	m	m	PROPN
ejpam-3291	240	12	can	can	AUX
ejpam-3291	240	13	be	be	AUX
ejpam-3291	240	14	extended	extend	VERB
ejpam-3291	240	15	to	to	ADP
ejpam-3291	240	16	an	an	DET
ejpam-3291	240	17	r	r	NOUN
ejpam-3291	240	18	-	-	PUNCT
ejpam-3291	240	19	homomorphism	homomorphism	NOUN
ejpam-3291	240	20	from	from	ADP
ejpam-3291	240	21	m	m	PROPN
ejpam-3291	240	22	to	to	ADP
ejpam-3291	240	23	m	m	PROPN
ejpam-3291	240	24	.	.	PUNCT
ejpam-3291	241	1	proof	proof	NOUN
ejpam-3291	241	2	.	.	PUNCT
ejpam-3291	242	1	since	since	SCONJ
ejpam-3291	242	2	(	(	PUNCT
ejpam-3291	242	3	∑n	∑n	PROPN
ejpam-3291	242	4	i=1	i=1	PROPN
ejpam-3291	242	5	si	si	PROPN
ejpam-3291	242	6	)	)	PUNCT
ejpam-3291	242	7	(	(	PUNCT
ejpam-3291	242	8	m	m	NOUN
ejpam-3291	242	9	)	)	PUNCT
ejpam-3291	242	10	⊆	⊆	PROPN
ejpam-3291	242	11	∑n	∑n	PROPN
ejpam-3291	242	12	i=1	i=1	PROPN
ejpam-3291	242	13	si(m	si(m	NOUN
ejpam-3291	242	14	)	)	PUNCT
ejpam-3291	242	15	and	and	CCONJ
ejpam-3291	242	16	m	m	PROPN
ejpam-3291	242	17	is	be	AUX
ejpam-3291	242	18	a	a	DET
ejpam-3291	242	19	quasi	quasi	ADJ
ejpam-3291	242	20	-	-	ADJ
ejpam-3291	242	21	slightly	slightly	ADV
ejpam-3291	242	22	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	242	23	module	module	NOUN
ejpam-3291	242	24	,	,	PUNCT
ejpam-3291	242	25	so	so	SCONJ
ejpam-3291	242	26	any	any	DET
ejpam-3291	242	27	r	r	NOUN
ejpam-3291	242	28	-	-	PUNCT
ejpam-3291	242	29	homomorphism	homomorphism	NOUN
ejpam-3291	242	30	from	from	ADP
ejpam-3291	242	31	∑n	∑n	PROPN
ejpam-3291	242	32	i=1	i=1	PROPN
ejpam-3291	242	33	si(m	si(m	NOUN
ejpam-3291	242	34	)	)	PUNCT
ejpam-3291	242	35	to	to	ADP
ejpam-3291	242	36	m	m	PROPN
ejpam-3291	242	37	can	can	AUX
ejpam-3291	242	38	be	be	AUX
ejpam-3291	242	39	extended	extend	VERB
ejpam-3291	242	40	to	to	ADP
ejpam-3291	242	41	an	an	DET
ejpam-3291	242	42	r	r	NOUN
ejpam-3291	242	43	-	-	PUNCT
ejpam-3291	242	44	homomorphism	homomorphism	NOUN
ejpam-3291	242	45	from	from	ADP
ejpam-3291	242	46	m	m	PROPN
ejpam-3291	242	47	to	to	ADP
ejpam-3291	242	48	m	m	PROPN
ejpam-3291	242	49	.	.	PUNCT
ejpam-3291	243	1	n.	n.	PROPN
ejpam-3291	243	2	d.	d.	PROPN
ejpam-3291	243	3	h.	h.	PROPN
ejpam-3291	243	4	nghiem	nghiem	PROPN
ejpam-3291	243	5	et	et	PROPN
ejpam-3291	243	6	al	al	PROPN
ejpam-3291	243	7	.	.	PUNCT
ejpam-3291	243	8	/	/	SYM
ejpam-3291	243	9	eur	eur	PROPN
ejpam-3291	243	10	.	.	PUNCT
ejpam-3291	244	1	j.	j.	PROPN
ejpam-3291	244	2	pure	pure	PROPN
ejpam-3291	244	3	appl	appl	PROPN
ejpam-3291	244	4	.	.	PROPN
ejpam-3291	244	5	math	math	PROPN
ejpam-3291	244	6	,	,	PUNCT
ejpam-3291	244	7	11	11	NUM
ejpam-3291	244	8	(	(	PUNCT
ejpam-3291	244	9	3	3	NUM
ejpam-3291	244	10	)	)	PUNCT
ejpam-3291	244	11	(	(	PUNCT
ejpam-3291	244	12	2018	2018	NUM
ejpam-3291	244	13	)	)	PUNCT
ejpam-3291	244	14	,	,	PUNCT
ejpam-3291	244	15	815	815	NUM
ejpam-3291	244	16	-	-	SYM
ejpam-3291	244	17	822	822	NUM
ejpam-3291	244	18	821	821	NUM
ejpam-3291	244	19	theorem	theorem	NOUN
ejpam-3291	244	20	6	6	NUM
ejpam-3291	244	21	.	.	PUNCT
ejpam-3291	245	1	let	let	VERB
ejpam-3291	245	2	m	m	PRON
ejpam-3291	245	3	be	be	AUX
ejpam-3291	245	4	a	a	DET
ejpam-3291	245	5	quasi	quasi	ADJ
ejpam-3291	245	6	-	-	ADJ
ejpam-3291	245	7	slightly	slightly	ADV
ejpam-3291	245	8	compressible	compressible	ADJ
ejpam-3291	245	9	-	-	PUNCT
ejpam-3291	245	10	injective	injective	ADJ
ejpam-3291	245	11	module	module	NOUN
ejpam-3291	245	12	,	,	PUNCT
ejpam-3291	245	13	s1	s1	NOUN
ejpam-3291	245	14	,	,	PUNCT
ejpam-3291	245	15	.	.	PUNCT
ejpam-3291	245	16	.	.	PUNCT
ejpam-3291	246	1	.	.	PUNCT
ejpam-3291	247	1	,	,	PUNCT
ejpam-3291	247	2	sn	sn	PROPN
ejpam-3291	247	3	∈	∈	PROPN
ejpam-3291	247	4	s	s	PART
ejpam-3291	247	5	=	=	X
ejpam-3291	247	6	endr(m	endr(m	PROPN
ejpam-3291	247	7	)	)	PUNCT
ejpam-3291	247	8	such	such	ADJ
ejpam-3291	247	9	that	that	SCONJ
ejpam-3291	247	10	the	the	DET
ejpam-3291	247	11	sum	sum	NOUN
ejpam-3291	247	12	∑n	∑n	PROPN
ejpam-3291	247	13	i=1	i=1	PROPN
ejpam-3291	247	14	ssi	ssi	PROPN
ejpam-3291	247	15	is	be	AUX
ejpam-3291	247	16	direct	direct	ADJ
ejpam-3291	247	17	,	,	PUNCT
ejpam-3291	247	18	a	a	DET
ejpam-3291	247	19	=	=	SYM
ejpam-3291	247	20	s1(m	s1(m	PROPN
ejpam-3291	247	21	)	)	PUNCT
ejpam-3291	247	22	+	+	CCONJ
ejpam-3291	247	23	.	.	PUNCT
ejpam-3291	247	24	.	.	PUNCT
ejpam-3291	247	25	.	.	PUNCT
ejpam-3291	248	1	+	+	CCONJ
ejpam-3291	248	2	sk(m	sk(m	NUM
ejpam-3291	248	3	)	)	PUNCT
ejpam-3291	248	4	and	and	CCONJ
ejpam-3291	248	5	b	b	X
ejpam-3291	248	6	=	=	SYM
ejpam-3291	248	7	sk+1(m	sk+1(m	PROPN
ejpam-3291	248	8	)	)	PUNCT
ejpam-3291	248	9	+	+	CCONJ
ejpam-3291	248	10	.	.	PUNCT
ejpam-3291	248	11	.	.	PUNCT
ejpam-3291	249	1	.+	.+	NOUN
ejpam-3291	249	2	sn(m	sn(m	PROPN
ejpam-3291	249	3	)	)	PUNCT
ejpam-3291	249	4	where	where	SCONJ
ejpam-3291	249	5	1	1	NUM
ejpam-3291	249	6	≤	≤	NUM
ejpam-3291	249	7	k	k	PROPN
ejpam-3291	249	8	≤	≤	PROPN
ejpam-3291	249	9	n.	n.	NOUN
ejpam-3291	249	10	then	then	ADV
ejpam-3291	249	11	ls(a	ls(a	ADV
ejpam-3291	249	12	∩b	∩b	NOUN
ejpam-3291	249	13	)	)	PUNCT
ejpam-3291	249	14	=	=	PUNCT
ejpam-3291	249	15	ls(a	ls(a	ADV
ejpam-3291	249	16	)	)	PUNCT
ejpam-3291	249	17	+	+	CCONJ
ejpam-3291	249	18	ls(b	ls(b	NOUN
ejpam-3291	249	19	)	)	PUNCT
ejpam-3291	249	20	.	.	PUNCT
ejpam-3291	250	1	proof	proof	NOUN
ejpam-3291	250	2	.	.	PUNCT
ejpam-3291	251	1	clearly	clearly	ADV
ejpam-3291	251	2	,	,	PUNCT
ejpam-3291	251	3	ls(a	ls(a	ADV
ejpam-3291	251	4	∩	∩	ADJ
ejpam-3291	251	5	b	b	X
ejpam-3291	251	6	)	)	PUNCT
ejpam-3291	251	7	⊇	⊇	NOUN
ejpam-3291	251	8	ls(a	ls(a	ADV
ejpam-3291	251	9	)	)	PUNCT
ejpam-3291	252	1	+	+	CCONJ
ejpam-3291	252	2	ls(b	ls(b	NOUN
ejpam-3291	252	3	)	)	PUNCT
ejpam-3291	252	4	.	.	PUNCT
ejpam-3291	253	1	let	let	VERB
ejpam-3291	253	2	u	u	PRON
ejpam-3291	253	3	∈	∈	PROPN
ejpam-3291	253	4	ls(a	ls(a	ADV
ejpam-3291	253	5	∩	∩	ADJ
ejpam-3291	253	6	b	b	X
ejpam-3291	253	7	)	)	PUNCT
ejpam-3291	253	8	.	.	PUNCT
ejpam-3291	254	1	consider	consider	VERB
ejpam-3291	254	2	the	the	DET
ejpam-3291	254	3	map	map	NOUN
ejpam-3291	254	4	α	α	NOUN
ejpam-3291	254	5	:	:	PUNCT
ejpam-3291	254	6	a	a	DET
ejpam-3291	254	7	+	+	NUM
ejpam-3291	254	8	b	b	NOUN
ejpam-3291	254	9	→	→	SYM
ejpam-3291	254	10	m	m	NOUN
ejpam-3291	254	11	by	by	ADP
ejpam-3291	254	12	α(a	α(a	NOUN
ejpam-3291	254	13	+	+	CCONJ
ejpam-3291	254	14	b	b	X
ejpam-3291	254	15	)	)	PUNCT
ejpam-3291	254	16	=	=	SYM
ejpam-3291	254	17	u(a	u(a	PROPN
ejpam-3291	254	18	)	)	PUNCT
ejpam-3291	254	19	for	for	ADP
ejpam-3291	254	20	all	all	DET
ejpam-3291	254	21	a	a	DET
ejpam-3291	254	22	∈	∈	PROPN
ejpam-3291	254	23	a	a	PRON
ejpam-3291	254	24	,	,	PUNCT
ejpam-3291	254	25	b	b	PROPN
ejpam-3291	254	26	∈	∈	PROPN
ejpam-3291	254	27	b.	b.	PROPN
ejpam-3291	254	28	since	since	SCONJ
ejpam-3291	254	29	u(a	u(a	PROPN
ejpam-3291	254	30	∩	∩	ADJ
ejpam-3291	254	31	b	b	NOUN
ejpam-3291	254	32	)	)	PUNCT
ejpam-3291	254	33	=	=	SYM
ejpam-3291	254	34	0	0	NUM
ejpam-3291	254	35	,	,	PUNCT
ejpam-3291	254	36	α	α	PROPN
ejpam-3291	254	37	is	be	AUX
ejpam-3291	254	38	well	well	ADV
ejpam-3291	254	39	-	-	PUNCT
ejpam-3291	254	40	defined	define	VERB
ejpam-3291	254	41	and	and	CCONJ
ejpam-3291	254	42	is	be	AUX
ejpam-3291	254	43	an	an	DET
ejpam-3291	254	44	r	r	NOUN
ejpam-3291	254	45	-	-	PUNCT
ejpam-3291	254	46	homomorphism	homomorphism	NOUN
ejpam-3291	254	47	.	.	PUNCT
ejpam-3291	255	1	by	by	ADP
ejpam-3291	255	2	theorem	theorem	NOUN
ejpam-3291	255	3	5	5	NUM
ejpam-3291	255	4	,	,	PUNCT
ejpam-3291	255	5	α	α	PRON
ejpam-3291	255	6	:	:	PUNCT
ejpam-3291	255	7	a+b	a+b	X
ejpam-3291	255	8	→m	→m	PUNCT
ejpam-3291	255	9	can	can	AUX
ejpam-3291	255	10	be	be	AUX
ejpam-3291	255	11	extended	extend	VERB
ejpam-3291	255	12	to	to	ADP
ejpam-3291	255	13	an	an	DET
ejpam-3291	255	14	r	r	NOUN
ejpam-3291	255	15	-	-	PUNCT
ejpam-3291	255	16	homomorphism	homomorphism	NOUN
ejpam-3291	255	17	ϕ	ϕ	NOUN
ejpam-3291	255	18	:	:	PUNCT
ejpam-3291	255	19	m	m	VERB
ejpam-3291	255	20	→m	→m	PROPN
ejpam-3291	255	21	.	.	PUNCT
ejpam-3291	256	1	clearly	clearly	ADV
ejpam-3291	256	2	,	,	PUNCT
ejpam-3291	256	3	ϕ(b	ϕ(b	PROPN
ejpam-3291	256	4	)	)	PUNCT
ejpam-3291	257	1	=	=	SYM
ejpam-3291	257	2	0	0	NUM
ejpam-3291	258	1	for	for	ADP
ejpam-3291	258	2	all	all	DET
ejpam-3291	258	3	b	b	PROPN
ejpam-3291	258	4	∈	∈	PROPN
ejpam-3291	258	5	b	b	NOUN
ejpam-3291	258	6	and	and	CCONJ
ejpam-3291	258	7	hence	hence	ADV
ejpam-3291	258	8	ϕ	ϕ	X
ejpam-3291	258	9	∈	∈	PROPN
ejpam-3291	258	10	ls(b	ls(b	PUNCT
ejpam-3291	258	11	)	)	PUNCT
ejpam-3291	258	12	and	and	CCONJ
ejpam-3291	258	13	u−	u−	PROPN
ejpam-3291	258	14	ϕ	ϕ	PROPN
ejpam-3291	258	15	∈	∈	PROPN
ejpam-3291	258	16	ls(a	ls(a	ADV
ejpam-3291	258	17	)	)	PUNCT
ejpam-3291	258	18	.	.	PUNCT
ejpam-3291	259	1	therefore	therefore	ADV
ejpam-3291	259	2	u	u	X
ejpam-3291	259	3	=	=	PUNCT
ejpam-3291	259	4	(	(	PUNCT
ejpam-3291	259	5	u−	u−	PROPN
ejpam-3291	259	6	ϕ	ϕ	NOUN
ejpam-3291	259	7	)	)	PUNCT
ejpam-3291	259	8	+	+	NUM
ejpam-3291	259	9	ϕ	ϕ	PROPN
ejpam-3291	259	10	∈	∈	PROPN
ejpam-3291	259	11	ls(a	ls(a	ADV
ejpam-3291	259	12	)	)	PUNCT
ejpam-3291	259	13	+	+	CCONJ
ejpam-3291	259	14	ls(b	ls(b	NOUN
ejpam-3291	259	15	)	)	PUNCT
ejpam-3291	259	16	.	.	PUNCT
ejpam-3291	260	1	theorem	theorem	VERB
ejpam-3291	260	2	7	7	NUM
ejpam-3291	260	3	.	.	PUNCT
ejpam-3291	261	1	let	let	VERB
ejpam-3291	261	2	m	m	PRON
ejpam-3291	261	3	and	and	CCONJ
ejpam-3291	261	4	mi	mi	PROPN
ejpam-3291	261	5	be	be	AUX
ejpam-3291	261	6	right	right	ADJ
ejpam-3291	261	7	r	r	NOUN
ejpam-3291	261	8	-	-	PUNCT
ejpam-3291	261	9	modules	module	NOUN
ejpam-3291	261	10	for	for	ADP
ejpam-3291	261	11	all	all	PRON
ejpam-3291	261	12	i	i	PRON
ejpam-3291	261	13	∈	∈	VERB
ejpam-3291	262	1	i	i	PRON
ejpam-3291	262	2	=	=	PUNCT
ejpam-3291	262	3	{	{	PUNCT
ejpam-3291	262	4	1	1	NUM
ejpam-3291	262	5	,	,	PUNCT
ejpam-3291	262	6	2	2	NUM
ejpam-3291	262	7	,	,	PUNCT
ejpam-3291	262	8	...	...	PUNCT
ejpam-3291	262	9	,	,	PUNCT
ejpam-3291	262	10	n	n	CCONJ
ejpam-3291	262	11	}	}	PUNCT
ejpam-3291	262	12	where	where	SCONJ
ejpam-3291	262	13	n	n	PRON
ejpam-3291	262	14	is	be	AUX
ejpam-3291	262	15	a	a	DET
ejpam-3291	262	16	positive	positive	ADJ
ejpam-3291	262	17	integer	integer	NOUN
ejpam-3291	262	18	.	.	PUNCT
ejpam-3291	263	1	then	then	ADV
ejpam-3291	263	2	mi	mi	PROPN
ejpam-3291	263	3	is	be	AUX
ejpam-3291	263	4	an	an	DET
ejpam-3291	263	5	m	m	ADV
ejpam-3291	263	6	-slightly	-slightly	ADV
ejpam-3291	263	7	compressible	compressible	ADJ
ejpam-3291	263	8	-	-	PUNCT
ejpam-3291	263	9	injective	injective	ADJ
ejpam-3291	263	10	module	module	NOUN
ejpam-3291	263	11	for	for	ADP
ejpam-3291	263	12	all	all	PRON
ejpam-3291	263	13	i	i	PRON
ejpam-3291	263	14	∈	∈	VERB
ejpam-3291	264	1	i	i	PRON
ejpam-3291	264	2	if	if	SCONJ
ejpam-3291	264	3	and	and	CCONJ
ejpam-3291	264	4	only	only	ADV
ejpam-3291	264	5	if	if	SCONJ
ejpam-3291	264	6	⊕ni=1mi	⊕ni=1mi	PROPN
ejpam-3291	264	7	is	be	AUX
ejpam-3291	264	8	an	an	DET
ejpam-3291	264	9	m	m	NOUN
ejpam-3291	264	10	-slightly	-slightly	ADV
ejpam-3291	264	11	compressible	compressible	ADJ
ejpam-3291	264	12	-	-	PUNCT
ejpam-3291	264	13	injective	injective	ADJ
ejpam-3291	264	14	module	module	NOUN
ejpam-3291	264	15	.	.	PUNCT
ejpam-3291	265	1	proof	proof	NOUN
ejpam-3291	265	2	.	.	PUNCT
ejpam-3291	266	1	(	(	PUNCT
ejpam-3291	266	2	⇒	⇒	NOUN
ejpam-3291	266	3	)	)	PUNCT
ejpam-3291	266	4	assume	assume	VERB
ejpam-3291	266	5	that	that	SCONJ
ejpam-3291	266	6	mi	mi	PROPN
ejpam-3291	266	7	is	be	AUX
ejpam-3291	266	8	an	an	DET
ejpam-3291	266	9	m	m	ADV
ejpam-3291	266	10	-slightly	-slightly	ADV
ejpam-3291	266	11	compressible	compressible	ADJ
ejpam-3291	266	12	-	-	PUNCT
ejpam-3291	266	13	injective	injective	ADJ
ejpam-3291	266	14	module	module	NOUN
ejpam-3291	266	15	for	for	ADP
ejpam-3291	266	16	all	all	PRON
ejpam-3291	266	17	i	i	PRON
ejpam-3291	266	18	∈	∈	PROPN
ejpam-3291	266	19	i.	i.	NOUN
ejpam-3291	266	20	let	let	VERB
ejpam-3291	266	21	j	j	PROPN
ejpam-3291	266	22	∈	∈	PROPN
ejpam-3291	267	1	i	i	PRON
ejpam-3291	267	2	,	,	PUNCT
ejpam-3291	267	3	p	p	PROPN
ejpam-3291	267	4	=	=	SYM
ejpam-3291	267	5	⊕ni=1mi	⊕ni=1mi	PROPN
ejpam-3291	267	6	,	,	PUNCT
ejpam-3291	267	7	a	a	DET
ejpam-3291	267	8	be	be	AUX
ejpam-3291	267	9	a	a	DET
ejpam-3291	267	10	non	non	ADJ
ejpam-3291	267	11	-	-	ADJ
ejpam-3291	267	12	zero	zero	NUM
ejpam-3291	267	13	m	m	VERB
ejpam-3291	267	14	-slightly	-slightly	ADV
ejpam-3291	267	15	compressible	compressible	ADJ
ejpam-3291	267	16	submodule	submodule	NOUN
ejpam-3291	267	17	of	of	ADP
ejpam-3291	267	18	m	m	PROPN
ejpam-3291	267	19	and	and	CCONJ
ejpam-3291	267	20	α	α	PRON
ejpam-3291	267	21	be	be	VERB
ejpam-3291	267	22	an	an	DET
ejpam-3291	267	23	r	r	NOUN
ejpam-3291	267	24	-	-	PUNCT
ejpam-3291	267	25	homomorphism	homomorphism	NOUN
ejpam-3291	267	26	from	from	ADP
ejpam-3291	267	27	a	a	PRON
ejpam-3291	267	28	to	to	ADP
ejpam-3291	267	29	p	p	PROPN
ejpam-3291	267	30	.	.	PUNCT
ejpam-3291	268	1	since	since	SCONJ
ejpam-3291	268	2	πiα	πiα	NOUN
ejpam-3291	268	3	is	be	AUX
ejpam-3291	268	4	an	an	DET
ejpam-3291	268	5	r	r	NOUN
ejpam-3291	268	6	-	-	PUNCT
ejpam-3291	268	7	homomorphism	homomorphism	NOUN
ejpam-3291	268	8	from	from	ADP
ejpam-3291	268	9	a	a	PRON
ejpam-3291	268	10	to	to	ADP
ejpam-3291	268	11	mi	mi	PROPN
ejpam-3291	268	12	where	where	SCONJ
ejpam-3291	268	13	πj	πj	VERB
ejpam-3291	268	14	the	the	DET
ejpam-3291	268	15	jth	jth	PROPN
ejpam-3291	268	16	canonical	canonical	PROPN
ejpam-3291	268	17	projection	projection	NOUN
ejpam-3291	268	18	map	map	NOUN
ejpam-3291	268	19	from	from	ADP
ejpam-3291	268	20	p	p	NOUN
ejpam-3291	268	21	to	to	ADP
ejpam-3291	268	22	mj	mj	PROPN
ejpam-3291	268	23	and	and	CCONJ
ejpam-3291	268	24	mj	mj	PROPN
ejpam-3291	268	25	is	be	AUX
ejpam-3291	268	26	an	an	DET
ejpam-3291	268	27	m	m	ADV
ejpam-3291	268	28	-slightly	-slightly	ADV
ejpam-3291	268	29	compressible	compressible	ADJ
ejpam-3291	268	30	-	-	PUNCT
ejpam-3291	268	31	injective	injective	ADJ
ejpam-3291	268	32	module	module	NOUN
ejpam-3291	268	33	,	,	PUNCT
ejpam-3291	268	34	there	there	PRON
ejpam-3291	268	35	exists	exist	VERB
ejpam-3291	268	36	ᾱj	ᾱj	NOUN
ejpam-3291	268	37	:	:	PUNCT
ejpam-3291	268	38	m	m	VERB
ejpam-3291	268	39	→	→	PUNCT
ejpam-3291	268	40	mj	mj	VERB
ejpam-3291	268	41	such	such	ADJ
ejpam-3291	268	42	that	that	SCONJ
ejpam-3291	268	43	ᾱjia	ᾱjia	NUM
ejpam-3291	268	44	=	=	SYM
ejpam-3291	268	45	πjα	πjα	ADJ
ejpam-3291	268	46	where	where	SCONJ
ejpam-3291	268	47	ia	ia	PROPN
ejpam-3291	268	48	:	:	PUNCT
ejpam-3291	268	49	a	a	DET
ejpam-3291	268	50	→	→	SYM
ejpam-3291	268	51	m	m	NOUN
ejpam-3291	268	52	is	be	AUX
ejpam-3291	268	53	an	an	DET
ejpam-3291	268	54	embedding	embedding	NOUN
ejpam-3291	268	55	.	.	PUNCT
ejpam-3291	269	1	we	we	PRON
ejpam-3291	269	2	can	can	AUX
ejpam-3291	269	3	choose	choose	VERB
ejpam-3291	269	4	ᾱ	ᾱ	NOUN
ejpam-3291	269	5	=	=	SYM
ejpam-3291	269	6	∑n	∑n	PROPN
ejpam-3291	269	7	j=1	j=1	NOUN
ejpam-3291	269	8	ijᾱj	ijᾱj	NUM
ejpam-3291	269	9	where	where	SCONJ
ejpam-3291	269	10	ij	ij	NOUN
ejpam-3291	269	11	:	:	PUNCT
ejpam-3291	269	12	mj	mj	PROPN
ejpam-3291	269	13	→	→	PUNCT
ejpam-3291	269	14	m	m	AUX
ejpam-3291	269	15	be	be	AUX
ejpam-3291	269	16	the	the	DET
ejpam-3291	269	17	canonical	canonical	ADJ
ejpam-3291	269	18	injection	injection	NOUN
ejpam-3291	269	19	map	map	NOUN
ejpam-3291	269	20	.	.	PUNCT
ejpam-3291	270	1	then	then	ADV
ejpam-3291	270	2	ᾱia	ᾱia	NOUN
ejpam-3291	270	3	=	=	PUNCT
ejpam-3291	271	1	∑n	∑n	PROPN
ejpam-3291	271	2	j=1	j=1	PROPN
ejpam-3291	271	3	ijᾱjia	ijᾱjia	PROPN
ejpam-3291	272	1	=	=	PUNCT
ejpam-3291	273	1	(	(	PUNCT
ejpam-3291	273	2	∑n	∑n	PROPN
ejpam-3291	273	3	j=1	j=1	NOUN
ejpam-3291	273	4	ijπj)α	ijπj)α	PROPN
ejpam-3291	274	1	=	=	SYM
ejpam-3291	275	1	ipα	ipα	NOUN
ejpam-3291	276	1	=	=	PUNCT
ejpam-3291	277	1	α	α	PROPN
ejpam-3291	277	2	where	where	SCONJ
ejpam-3291	277	3	ip	ip	NOUN
ejpam-3291	277	4	is	be	AUX
ejpam-3291	277	5	the	the	DET
ejpam-3291	277	6	identity	identity	NOUN
ejpam-3291	277	7	map	map	NOUN
ejpam-3291	277	8	on	on	ADP
ejpam-3291	277	9	p	p	PROPN
ejpam-3291	277	10	.	.	PUNCT
ejpam-3291	278	1	hence	hence	ADV
ejpam-3291	278	2	p	p	NOUN
ejpam-3291	278	3	=	=	PUNCT
ejpam-3291	278	4	⊕ni=1mi	⊕ni=1mi	PROPN
ejpam-3291	278	5	is	be	AUX
ejpam-3291	278	6	an	an	DET
ejpam-3291	278	7	m	m	NOUN
ejpam-3291	278	8	-sligthly	-sligthly	ADV
ejpam-3291	278	9	compressible	compressible	ADJ
ejpam-3291	278	10	-	-	PUNCT
ejpam-3291	278	11	injective	injective	ADJ
ejpam-3291	278	12	module	module	NOUN
ejpam-3291	278	13	.	.	PUNCT
ejpam-3291	279	1	(	(	PUNCT
ejpam-3291	279	2	⇐	⇐	NOUN
ejpam-3291	279	3	)	)	PUNCT
ejpam-3291	279	4	assume	assume	VERB
ejpam-3291	279	5	that	that	SCONJ
ejpam-3291	279	6	p	p	PRON
ejpam-3291	279	7	=	=	PUNCT
ejpam-3291	279	8	⊕ni=1mi	⊕ni=1mi	PROPN
ejpam-3291	279	9	is	be	AUX
ejpam-3291	279	10	an	an	DET
ejpam-3291	279	11	m	m	NOUN
ejpam-3291	279	12	-slightly	-slightly	ADV
ejpam-3291	279	13	compressible	compressible	ADJ
ejpam-3291	279	14	-	-	PUNCT
ejpam-3291	279	15	injective	injective	ADJ
ejpam-3291	279	16	module	module	NOUN
ejpam-3291	279	17	.	.	PUNCT
ejpam-3291	280	1	let	let	VERB
ejpam-3291	280	2	j	j	PROPN
ejpam-3291	280	3	∈	∈	PROPN
ejpam-3291	281	1	i	i	PRON
ejpam-3291	281	2	,	,	PUNCT
ejpam-3291	281	3	a	a	DET
ejpam-3291	281	4	be	be	AUX
ejpam-3291	281	5	a	a	DET
ejpam-3291	281	6	non	non	ADJ
ejpam-3291	281	7	-	-	ADJ
ejpam-3291	281	8	zero	zero	NUM
ejpam-3291	281	9	m	m	VERB
ejpam-3291	281	10	-slightly	-slightly	ADV
ejpam-3291	281	11	compressible	compressible	ADJ
ejpam-3291	281	12	submodule	submodule	NOUN
ejpam-3291	281	13	of	of	ADP
ejpam-3291	281	14	m	m	PROPN
ejpam-3291	281	15	and	and	CCONJ
ejpam-3291	281	16	αj	αj	PROPN
ejpam-3291	281	17	be	be	AUX
ejpam-3291	281	18	an	an	DET
ejpam-3291	281	19	rhomomorphism	rhomomorphism	NOUN
ejpam-3291	281	20	from	from	ADP
ejpam-3291	281	21	a	a	PRON
ejpam-3291	281	22	to	to	ADP
ejpam-3291	281	23	mj	mj	PROPN
ejpam-3291	281	24	.	.	PUNCT
ejpam-3291	282	1	since	since	SCONJ
ejpam-3291	282	2	ijαj	ijαj	NOUN
ejpam-3291	282	3	is	be	AUX
ejpam-3291	282	4	an	an	DET
ejpam-3291	282	5	r	r	NOUN
ejpam-3291	282	6	-	-	PUNCT
ejpam-3291	282	7	homomorphism	homomorphism	NOUN
ejpam-3291	282	8	from	from	ADP
ejpam-3291	282	9	a	a	PRON
ejpam-3291	282	10	to	to	ADP
ejpam-3291	282	11	p	p	PRON
ejpam-3291	282	12	where	where	SCONJ
ejpam-3291	282	13	ij	ij	NOUN
ejpam-3291	282	14	:	:	PUNCT
ejpam-3291	282	15	mj	mj	PROPN
ejpam-3291	282	16	→m	→m	PROPN
ejpam-3291	282	17	is	be	AUX
ejpam-3291	282	18	the	the	DET
ejpam-3291	282	19	canonical	canonical	ADJ
ejpam-3291	282	20	injection	injection	NOUN
ejpam-3291	282	21	map	map	NOUN
ejpam-3291	282	22	and	and	CCONJ
ejpam-3291	282	23	p	p	NOUN
ejpam-3291	282	24	is	be	AUX
ejpam-3291	282	25	an	an	DET
ejpam-3291	282	26	m	m	NOUN
ejpam-3291	282	27	-slightly	-slightly	ADV
ejpam-3291	282	28	compressible	compressible	ADJ
ejpam-3291	282	29	-	-	PUNCT
ejpam-3291	282	30	injective	injective	ADJ
ejpam-3291	282	31	module	module	NOUN
ejpam-3291	282	32	,	,	PUNCT
ejpam-3291	282	33	there	there	PRON
ejpam-3291	282	34	exists	exist	VERB
ejpam-3291	282	35	ᾱ	ᾱ	NOUN
ejpam-3291	282	36	:	:	PUNCT
ejpam-3291	282	37	m	m	VERB
ejpam-3291	282	38	→	→	X
ejpam-3291	282	39	p	p	X
ejpam-3291	282	40	such	such	ADJ
ejpam-3291	282	41	that	that	DET
ejpam-3291	282	42	ᾱia	ᾱia	NOUN
ejpam-3291	282	43	=	=	PUNCT
ejpam-3291	282	44	ijαj	ijαj	NOUN
ejpam-3291	282	45	where	where	SCONJ
ejpam-3291	282	46	ia	ia	PROPN
ejpam-3291	282	47	:	:	PUNCT
ejpam-3291	282	48	a	a	DET
ejpam-3291	282	49	→	→	SYM
ejpam-3291	282	50	m	m	NOUN
ejpam-3291	282	51	is	be	AUX
ejpam-3291	282	52	an	an	DET
ejpam-3291	282	53	embedding	embedding	NOUN
ejpam-3291	282	54	.	.	PUNCT
ejpam-3291	283	1	we	we	PRON
ejpam-3291	283	2	can	can	AUX
ejpam-3291	283	3	choose	choose	VERB
ejpam-3291	283	4	ᾱj	ᾱj	NOUN
ejpam-3291	283	5	=	=	SYM
ejpam-3291	283	6	πjᾱ	πjᾱ	NOUN
ejpam-3291	283	7	where	where	SCONJ
ejpam-3291	283	8	πj	πj	PROPN
ejpam-3291	283	9	is	be	AUX
ejpam-3291	283	10	the	the	DET
ejpam-3291	283	11	jth	jth	PROPN
ejpam-3291	283	12	canonical	canonical	PROPN
ejpam-3291	283	13	projection	projection	NOUN
ejpam-3291	283	14	map	map	NOUN
ejpam-3291	283	15	.	.	PUNCT
ejpam-3291	284	1	then	then	ADV
ejpam-3291	284	2	ᾱjia	ᾱjia	NUM
ejpam-3291	284	3	=	=	SYM
ejpam-3291	284	4	πjᾱia	πjᾱia	PROPN
ejpam-3291	284	5	=	=	PUNCT
ejpam-3291	284	6	πjijαj	πjijαj	VERB
ejpam-3291	284	7	=	=	PUNCT
ejpam-3291	284	8	imjαj	imjαj	NOUN
ejpam-3291	285	1	=	=	SYM
ejpam-3291	286	1	αj	αj	NOUN
ejpam-3291	287	1	where	where	SCONJ
ejpam-3291	287	2	imj	imj	ADJ
ejpam-3291	287	3	is	be	AUX
ejpam-3291	287	4	an	an	DET
ejpam-3291	287	5	identity	identity	NOUN
ejpam-3291	287	6	map	map	NOUN
ejpam-3291	287	7	on	on	ADP
ejpam-3291	287	8	mj	mj	PROPN
ejpam-3291	287	9	.	.	PUNCT
ejpam-3291	288	1	hence	hence	ADV
ejpam-3291	288	2	mi	mi	PROPN
ejpam-3291	288	3	is	be	AUX
ejpam-3291	288	4	an	an	DET
ejpam-3291	288	5	m	m	ADV
ejpam-3291	288	6	-slightly	-slightly	ADV
ejpam-3291	288	7	compressible	compressible	ADJ
ejpam-3291	288	8	-	-	PUNCT
ejpam-3291	288	9	injective	injective	ADJ
ejpam-3291	288	10	module	module	NOUN
ejpam-3291	288	11	for	for	ADP
ejpam-3291	288	12	all	all	PRON
ejpam-3291	288	13	i	i	PRON
ejpam-3291	288	14	∈	∈	PROPN
ejpam-3291	288	15	i.	i.	NOUN
ejpam-3291	288	16	theorem	theorem	VERB
ejpam-3291	288	17	8	8	NUM
ejpam-3291	288	18	.	.	PUNCT
ejpam-3291	289	1	let	let	VERB
ejpam-3291	289	2	m	m	PRON
ejpam-3291	289	3	be	be	AUX
ejpam-3291	289	4	a	a	DET
ejpam-3291	289	5	quasi	quasi	ADJ
ejpam-3291	289	6	-	-	ADJ
ejpam-3291	289	7	slightly	slightly	ADV
ejpam-3291	289	8	compressible	compressible	ADJ
ejpam-3291	289	9	module	module	NOUN
ejpam-3291	289	10	.	.	PUNCT
ejpam-3291	290	1	then	then	ADV
ejpam-3291	290	2	m	m	PROPN
ejpam-3291	290	3	is	be	AUX
ejpam-3291	290	4	a	a	DET
ejpam-3291	290	5	semisimple	semisimple	NOUN
ejpam-3291	290	6	module	module	NOUN
ejpam-3291	290	7	if	if	SCONJ
ejpam-3291	290	8	and	and	CCONJ
ejpam-3291	290	9	only	only	ADV
ejpam-3291	290	10	if	if	SCONJ
ejpam-3291	290	11	every	every	DET
ejpam-3291	290	12	non	non	ADJ
ejpam-3291	290	13	-	-	ADJ
ejpam-3291	290	14	zero	zero	NUM
ejpam-3291	290	15	submodule	submodule	NOUN
ejpam-3291	290	16	of	of	ADP
ejpam-3291	290	17	m	m	PROPN
ejpam-3291	290	18	is	be	AUX
ejpam-3291	290	19	m	m	VERB
ejpam-3291	290	20	-slightly	-slightly	ADV
ejpam-3291	290	21	compressible	compressible	ADJ
ejpam-3291	290	22	-	-	PUNCT
ejpam-3291	290	23	injective	injective	ADJ
ejpam-3291	290	24	.	.	PUNCT
ejpam-3291	291	1	proof	proof	NOUN
ejpam-3291	291	2	.	.	PUNCT
ejpam-3291	292	1	(	(	PUNCT
ejpam-3291	292	2	⇒	⇒	PROPN
ejpam-3291	292	3	)	)	PUNCT
ejpam-3291	292	4	it	it	PRON
ejpam-3291	292	5	is	be	AUX
ejpam-3291	292	6	easy	easy	ADJ
ejpam-3291	292	7	.	.	PUNCT
ejpam-3291	293	1	(	(	PUNCT
ejpam-3291	293	2	⇐	⇐	ADJ
ejpam-3291	293	3	)	)	PUNCT
ejpam-3291	293	4	assume	assume	VERB
ejpam-3291	293	5	that	that	SCONJ
ejpam-3291	293	6	every	every	DET
ejpam-3291	293	7	non	non	ADJ
ejpam-3291	293	8	-	-	ADJ
ejpam-3291	293	9	zero	zero	NUM
ejpam-3291	293	10	submodule	submodule	NOUN
ejpam-3291	293	11	of	of	ADP
ejpam-3291	293	12	m	m	PROPN
ejpam-3291	293	13	is	be	AUX
ejpam-3291	293	14	an	an	DET
ejpam-3291	293	15	m	m	ADV
ejpam-3291	293	16	-slightly	-slightly	ADV
ejpam-3291	293	17	compressibleinjective	compressibleinjective	ADJ
ejpam-3291	293	18	module	module	NOUN
ejpam-3291	293	19	.	.	PUNCT
ejpam-3291	294	1	let	let	VERB
ejpam-3291	294	2	a	a	PRON
ejpam-3291	294	3	be	be	AUX
ejpam-3291	294	4	a	a	DET
ejpam-3291	294	5	submodule	submodule	NOUN
ejpam-3291	294	6	of	of	ADP
ejpam-3291	294	7	m	m	PROPN
ejpam-3291	294	8	.	.	PUNCT
ejpam-3291	295	1	if	if	SCONJ
ejpam-3291	295	2	a	a	DET
ejpam-3291	295	3	=	=	SYM
ejpam-3291	295	4	0	0	NUM
ejpam-3291	295	5	,	,	PUNCT
ejpam-3291	295	6	then	then	ADV
ejpam-3291	295	7	we	we	PRON
ejpam-3291	295	8	are	be	AUX
ejpam-3291	295	9	done	do	VERB
ejpam-3291	295	10	.	.	PUNCT
ejpam-3291	296	1	suppose	suppose	VERB
ejpam-3291	296	2	that	that	SCONJ
ejpam-3291	296	3	0	0	NUM
ejpam-3291	296	4	6=	6=	ADP
ejpam-3291	296	5	a	a	DET
ejpam-3291	296	6	↪	↪	PROPN
ejpam-3291	296	7	→m	→m	X
ejpam-3291	296	8	.	.	PUNCT
ejpam-3291	297	1	by	by	ADP
ejpam-3291	297	2	assumption	assumption	NOUN
ejpam-3291	297	3	,	,	PUNCT
ejpam-3291	297	4	a	a	PRON
ejpam-3291	297	5	is	be	AUX
ejpam-3291	297	6	an	an	DET
ejpam-3291	297	7	m	m	ADV
ejpam-3291	297	8	-slightly	-slightly	ADV
ejpam-3291	297	9	compressible	compressible	ADJ
ejpam-3291	297	10	-	-	PUNCT
ejpam-3291	297	11	injective	injective	ADJ
ejpam-3291	297	12	module	module	NOUN
ejpam-3291	297	13	.	.	PUNCT
ejpam-3291	298	1	since	since	SCONJ
ejpam-3291	298	2	m	m	PROPN
ejpam-3291	298	3	is	be	AUX
ejpam-3291	298	4	a	a	DET
ejpam-3291	298	5	quasi	quasi	ADJ
ejpam-3291	298	6	-	-	ADJ
ejpam-3291	298	7	slightly	slightly	ADV
ejpam-3291	298	8	compressible	compressible	ADJ
ejpam-3291	298	9	module	module	NOUN
ejpam-3291	298	10	,	,	PUNCT
ejpam-3291	298	11	a	a	PRON
ejpam-3291	298	12	is	be	AUX
ejpam-3291	298	13	an	an	DET
ejpam-3291	298	14	m	m	ADV
ejpam-3291	298	15	-slightly	-slightly	ADV
ejpam-3291	298	16	compressible	compressible	ADJ
ejpam-3291	298	17	submodule	submodule	NOUN
ejpam-3291	298	18	of	of	ADP
ejpam-3291	298	19	m	m	PROPN
ejpam-3291	298	20	.	.	PUNCT
ejpam-3291	299	1	then	then	ADV
ejpam-3291	299	2	there	there	PRON
ejpam-3291	299	3	exists	exist	VERB
ejpam-3291	299	4	α	α	NOUN
ejpam-3291	299	5	:	:	PUNCT
ejpam-3291	299	6	m	m	VERB
ejpam-3291	299	7	→	→	SYM
ejpam-3291	299	8	a	a	DET
ejpam-3291	299	9	such	such	ADJ
ejpam-3291	299	10	that	that	DET
ejpam-3291	299	11	αia	αia	NOUN
ejpam-3291	299	12	=	=	SYM
ejpam-3291	299	13	ia	ia	PROPN
ejpam-3291	299	14	where	where	SCONJ
ejpam-3291	299	15	ia	ia	PROPN
ejpam-3291	299	16	:	:	PUNCT
ejpam-3291	299	17	a→m	a→m	PRON
ejpam-3291	299	18	is	be	AUX
ejpam-3291	299	19	the	the	DET
ejpam-3291	299	20	embedding	embedding	NOUN
ejpam-3291	299	21	and	and	CCONJ
ejpam-3291	299	22	ia	ia	PROPN
ejpam-3291	299	23	is	be	AUX
ejpam-3291	299	24	an	an	DET
ejpam-3291	299	25	identity	identity	NOUN
ejpam-3291	299	26	map	map	NOUN
ejpam-3291	299	27	of	of	ADP
ejpam-3291	299	28	a.	a.	NOUN
ejpam-3291	299	29	then	then	ADV
ejpam-3291	299	30	the	the	DET
ejpam-3291	299	31	short	short	ADJ
ejpam-3291	299	32	exact	exact	ADJ
ejpam-3291	299	33	sequence	sequence	NOUN
ejpam-3291	299	34	0	0	NUM
ejpam-3291	299	35	→	→	SYM
ejpam-3291	299	36	a	a	DET
ejpam-3291	299	37	ia−→	ia−→	NUM
ejpam-3291	299	38	m	m	NOUN
ejpam-3291	299	39	π−→	π−→	PROPN
ejpam-3291	299	40	m	m	PROPN
ejpam-3291	299	41	/	/	SYM
ejpam-3291	299	42	a	a	DET
ejpam-3291	299	43	→	→	SYM
ejpam-3291	299	44	0	0	NUM
ejpam-3291	299	45	splits	split	NOUN
ejpam-3291	299	46	.	.	PUNCT
ejpam-3291	300	1	thus	thus	ADV
ejpam-3291	300	2	a	a	PRON
ejpam-3291	300	3	is	be	AUX
ejpam-3291	300	4	a	a	DET
ejpam-3291	300	5	direct	direct	ADJ
ejpam-3291	300	6	summand	summand	NOUN
ejpam-3291	300	7	of	of	ADP
ejpam-3291	300	8	m	m	PROPN
ejpam-3291	300	9	.	.	PUNCT
ejpam-3291	301	1	therefore	therefore	ADV
ejpam-3291	301	2	m	m	PROPN
ejpam-3291	301	3	is	be	AUX
ejpam-3291	301	4	a	a	DET
ejpam-3291	301	5	semisimple	semisimple	NOUN
ejpam-3291	301	6	module	module	NOUN
ejpam-3291	301	7	.	.	PUNCT
ejpam-3291	302	1	references	reference	NOUN
ejpam-3291	302	2	822	822	NUM
ejpam-3291	302	3	acknowledgements	acknowledgement	NOUN
ejpam-3291	302	4	the	the	DET
ejpam-3291	302	5	first	first	ADJ
ejpam-3291	302	6	author	author	NOUN
ejpam-3291	302	7	was	be	AUX
ejpam-3291	302	8	supported	support	VERB
ejpam-3291	302	9	from	from	ADP
ejpam-3291	302	10	rachadapisek	rachadapisek	PROPN
ejpam-3291	302	11	sompot	sompot	NOUN
ejpam-3291	302	12	fund	fund	NOUN
ejpam-3291	302	13	for	for	ADP
ejpam-3291	302	14	postdoctoral	postdoctoral	ADJ
ejpam-3291	302	15	fellowship	fellowship	NOUN
ejpam-3291	302	16	,	,	PUNCT
ejpam-3291	302	17	chulalongkorn	chulalongkorn	NOUN
ejpam-3291	302	18	university	university	NOUN
ejpam-3291	302	19	.	.	PUNCT
ejpam-3291	303	1	we	we	PRON
ejpam-3291	303	2	would	would	AUX
ejpam-3291	303	3	like	like	VERB
ejpam-3291	303	4	to	to	PART
ejpam-3291	303	5	thank	thank	VERB
ejpam-3291	303	6	the	the	DET
ejpam-3291	303	7	reviewers	reviewer	NOUN
ejpam-3291	303	8	of	of	ADP
ejpam-3291	303	9	this	this	DET
ejpam-3291	303	10	paper	paper	NOUN
ejpam-3291	303	11	for	for	ADP
ejpam-3291	303	12	their	their	PRON
ejpam-3291	303	13	time	time	NOUN
ejpam-3291	303	14	to	to	PART
ejpam-3291	303	15	read	read	VERB
ejpam-3291	303	16	our	our	PRON
ejpam-3291	303	17	manuscript	manuscript	NOUN
ejpam-3291	303	18	carefully	carefully	ADV
ejpam-3291	303	19	and	and	CCONJ
ejpam-3291	303	20	their	their	PRON
ejpam-3291	303	21	comments	comment	NOUN
ejpam-3291	303	22	and	and	CCONJ
ejpam-3291	303	23	suggestions	suggestion	NOUN
ejpam-3291	303	24	.	.	PUNCT
ejpam-3291	304	1	references	reference	NOUN
ejpam-3291	304	2	[	[	X
ejpam-3291	304	3	1	1	NUM
ejpam-3291	304	4	]	]	X
ejpam-3291	304	5	f	f	PROPN
ejpam-3291	304	6	w	w	PROPN
ejpam-3291	304	7	anderson	anderson	PROPN
ejpam-3291	304	8	and	and	CCONJ
ejpam-3291	304	9	k	k	PROPN
ejpam-3291	304	10	r	r	NOUN
ejpam-3291	304	11	fuller	full	ADJ
ejpam-3291	304	12	,	,	PUNCT
ejpam-3291	304	13	rings	ring	NOUN
ejpam-3291	304	14	and	and	CCONJ
ejpam-3291	304	15	categories	category	NOUN
ejpam-3291	304	16	of	of	ADP
ejpam-3291	304	17	modules	module	NOUN
ejpam-3291	304	18	,	,	PUNCT
ejpam-3291	304	19	springer	springer	NOUN
ejpam-3291	304	20	,	,	PUNCT
ejpam-3291	304	21	new	new	PROPN
ejpam-3291	304	22	york	york	PROPN
ejpam-3291	304	23	/	/	SYM
ejpam-3291	304	24	heidelberg	heidelberg	PROPN
ejpam-3291	304	25	/	/	SYM
ejpam-3291	304	26	berlin	berlin	PROPN
ejpam-3291	304	27	,	,	PUNCT
ejpam-3291	304	28	1974	1974	NUM
ejpam-3291	304	29	.	.	PUNCT
ejpam-3291	305	1	[	[	X
ejpam-3291	305	2	2	2	NUM
ejpam-3291	305	3	]	]	PUNCT
ejpam-3291	305	4	s	s	PART
ejpam-3291	305	5	baupradist	baupradist	NOUN
ejpam-3291	305	6	,	,	PUNCT
ejpam-3291	305	7	p	p	PROPN
ejpam-3291	305	8	janmuang	janmuang	PROPN
ejpam-3291	305	9	and	and	CCONJ
ejpam-3291	305	10	s	s	PROPN
ejpam-3291	305	11	asawasamrit	asawasamrit	NOUN
ejpam-3291	305	12	,	,	PUNCT
ejpam-3291	305	13	generalization	generalization	NOUN
ejpam-3291	305	14	of	of	ADP
ejpam-3291	305	15	slightly	slightly	ADV
ejpam-3291	305	16	compressible	compressible	ADJ
ejpam-3291	305	17	modules	module	NOUN
ejpam-3291	305	18	,	,	PUNCT
ejpam-3291	305	19	journal	journal	NOUN
ejpam-3291	305	20	of	of	ADP
ejpam-3291	305	21	mathematical	mathematical	ADJ
ejpam-3291	305	22	and	and	CCONJ
ejpam-3291	305	23	fundamental	fundamental	ADJ
ejpam-3291	305	24	sciences	science	NOUN
ejpam-3291	305	25	,	,	PUNCT
ejpam-3291	305	26	to	to	PART
ejpam-3291	305	27	appear	appear	VERB
ejpam-3291	305	28	.	.	PUNCT
ejpam-3291	306	1	[	[	X
ejpam-3291	306	2	3	3	X
ejpam-3291	306	3	]	]	SYM
ejpam-3291	306	4	v	v	ADP
ejpam-3291	306	5	p	p	PROPN
ejpam-3291	306	6	camillo	camillo	PROPN
ejpam-3291	306	7	,	,	PUNCT
ejpam-3291	306	8	commutative	commutative	ADJ
ejpam-3291	306	9	ring	ring	NOUN
ejpam-3291	306	10	whose	whose	DET
ejpam-3291	306	11	principal	principal	ADJ
ejpam-3291	306	12	ideals	ideal	NOUN
ejpam-3291	306	13	are	be	AUX
ejpam-3291	306	14	annihilators	annihilators	PROPN
ejpam-3291	306	15	,	,	PUNCT
ejpam-3291	306	16	portugaliae	portugaliae	PROPN
ejpam-3291	306	17	mathematica	mathematica	PROPN
ejpam-3291	306	18	,	,	PUNCT
ejpam-3291	306	19	46:33	46:33	NUM
ejpam-3291	306	20	-	-	SYM
ejpam-3291	306	21	37	37	NUM
ejpam-3291	306	22	,	,	PUNCT
ejpam-3291	306	23	1989	1989	NUM
ejpam-3291	306	24	.	.	PUNCT
ejpam-3291	307	1	[	[	X
ejpam-3291	307	2	4	4	NUM
ejpam-3291	307	3	]	]	X
ejpam-3291	307	4	c	c	NOUN
ejpam-3291	307	5	celik	celik	X
ejpam-3291	307	6	,	,	PUNCT
ejpam-3291	307	7	completely	completely	ADV
ejpam-3291	307	8	slightly	slightly	ADV
ejpam-3291	307	9	compressible	compressible	ADJ
ejpam-3291	307	10	modules	module	NOUN
ejpam-3291	307	11	,	,	PUNCT
ejpam-3291	307	12	thai	thai	PROPN
ejpam-3291	307	13	journal	journal	PROPN
ejpam-3291	307	14	of	of	ADP
ejpam-3291	307	15	mathematics	mathematic	NOUN
ejpam-3291	307	16	,	,	PUNCT
ejpam-3291	307	17	10:137	10:137	NUM
ejpam-3291	307	18	-	-	SYM
ejpam-3291	307	19	145	145	NUM
ejpam-3291	307	20	,	,	PUNCT
ejpam-3291	307	21	2012	2012	NUM
ejpam-3291	307	22	.	.	PUNCT
ejpam-3291	308	1	[	[	X
ejpam-3291	308	2	5	5	NUM
ejpam-3291	308	3	]	]	X
ejpam-3291	308	4	f	f	PROPN
ejpam-3291	308	5	kasch	kasch	PROPN
ejpam-3291	308	6	,	,	PUNCT
ejpam-3291	308	7	modules	module	NOUN
ejpam-3291	308	8	and	and	CCONJ
ejpam-3291	308	9	rings	ring	NOUN
ejpam-3291	308	10	,	,	PUNCT
ejpam-3291	308	11	london	london	PROPN
ejpam-3291	308	12	mathematical	mathematical	ADJ
ejpam-3291	308	13	society	society	NOUN
ejpam-3291	308	14	monographs	monograph	VERB
ejpam-3291	308	15	17(c.u.p	17(c.u.p	PROPN
ejpam-3291	308	16	.	.	PUNCT
ejpam-3291	308	17	)	)	PUNCT
ejpam-3291	308	18	,	,	PUNCT
ejpam-3291	308	19	1982	1982	NUM
ejpam-3291	308	20	.	.	PUNCT
ejpam-3291	309	1	[	[	X
ejpam-3291	309	2	6	6	NUM
ejpam-3291	309	3	]	]	PUNCT
ejpam-3291	309	4	t	t	PROPN
ejpam-3291	309	5	y	y	PROPN
ejpam-3291	309	6	lam	lam	PROPN
ejpam-3291	309	7	,	,	PUNCT
ejpam-3291	309	8	serre	serre	PROPN
ejpam-3291	309	9	’s	’s	PART
ejpam-3291	309	10	problem	problem	NOUN
ejpam-3291	309	11	on	on	ADP
ejpam-3291	309	12	projective	projective	ADJ
ejpam-3291	309	13	modules	module	NOUN
ejpam-3291	309	14	,	,	PUNCT
ejpam-3291	309	15	springer	springer	NOUN
ejpam-3291	309	16	-	-	PUNCT
ejpam-3291	309	17	verlag	verlag	PROPN
ejpam-3291	309	18	,	,	PUNCT
ejpam-3291	309	19	berlin	berlin	PROPN
ejpam-3291	309	20	/	/	SYM
ejpam-3291	309	21	heidelberg	heidelberg	PROPN
ejpam-3291	309	22	,	,	PUNCT
ejpam-3291	309	23	2006	2006	NUM
ejpam-3291	309	24	.	.	PUNCT
ejpam-3291	310	1	[	[	X
ejpam-3291	310	2	7	7	X
ejpam-3291	310	3	]	]	SYM
ejpam-3291	310	4	n	n	PRON
ejpam-3291	310	5	v	v	X
ejpam-3291	310	6	sanh	sanh	NOUN
ejpam-3291	310	7	,	,	PUNCT
ejpam-3291	310	8	k	k	PROPN
ejpam-3291	310	9	p	p	X
ejpam-3291	310	10	shum	shum	NOUN
ejpam-3291	310	11	,	,	PUNCT
ejpam-3291	310	12	s	s	PART
ejpam-3291	310	13	dhompongsa	dhompongsa	NOUN
ejpam-3291	310	14	and	and	CCONJ
ejpam-3291	310	15	s	s	VERB
ejpam-3291	310	16	wongwai	wongwai	NOUN
ejpam-3291	310	17	,	,	PUNCT
ejpam-3291	310	18	on	on	ADP
ejpam-3291	310	19	quasi	quasi	ADJ
ejpam-3291	310	20	-	-	ADJ
ejpam-3291	310	21	principally	principally	ADV
ejpam-3291	310	22	injective	injective	ADJ
ejpam-3291	310	23	modules	module	NOUN
ejpam-3291	310	24	,	,	PUNCT
ejpam-3291	310	25	algebra	algebra	NOUN
ejpam-3291	310	26	colloquium	colloquium	NOUN
ejpam-3291	310	27	,	,	PUNCT
ejpam-3291	310	28	6:269	6:269	NUM
ejpam-3291	310	29	-	-	SYM
ejpam-3291	310	30	276	276	NUM
ejpam-3291	310	31	,	,	PUNCT
ejpam-3291	310	32	1999	1999	NUM
ejpam-3291	310	33	.	.	PUNCT
ejpam-3291	311	1	[	[	X
ejpam-3291	311	2	8	8	NUM
ejpam-3291	311	3	]	]	PUNCT
ejpam-3291	311	4	a	a	DET
ejpam-3291	311	5	k	k	PROPN
ejpam-3291	311	6	singh	singh	PROPN
ejpam-3291	311	7	,	,	PUNCT
ejpam-3291	311	8	essentially	essentially	ADV
ejpam-3291	311	9	slightly	slightly	ADV
ejpam-3291	311	10	compressible	compressible	ADJ
ejpam-3291	311	11	modules	module	NOUN
ejpam-3291	311	12	and	and	CCONJ
ejpam-3291	311	13	rings	ring	NOUN
ejpam-3291	311	14	,	,	PUNCT
ejpam-3291	311	15	asian	asian	ADJ
ejpam-3291	311	16	-	-	PUNCT
ejpam-3291	311	17	european	european	ADJ
ejpam-3291	311	18	journal	journal	NOUN
ejpam-3291	311	19	of	of	ADP
ejpam-3291	311	20	mathematics	mathematic	NOUN
ejpam-3291	311	21	,	,	PUNCT
ejpam-3291	311	22	5	5	NUM
ejpam-3291	311	23	:	:	PUNCT
ejpam-3291	311	24	article	article	NOUN
ejpam-3291	311	25	number	number	NOUN
ejpam-3291	311	26	1250028	1250028	NUM
ejpam-3291	311	27	,	,	PUNCT
ejpam-3291	311	28	2012	2012	NUM
ejpam-3291	311	29	.	.	PUNCT
ejpam-3291	312	1	[	[	X
ejpam-3291	312	2	9	9	X
ejpam-3291	312	3	]	]	X
ejpam-3291	312	4	p	p	X
ejpam-3291	312	5	f	f	PROPN
ejpam-3291	312	6	smith	smith	PROPN
ejpam-3291	312	7	,	,	PUNCT
ejpam-3291	312	8	modules	module	NOUN
ejpam-3291	312	9	with	with	ADP
ejpam-3291	312	10	many	many	ADJ
ejpam-3291	312	11	homomorphisms	homomorphism	NOUN
ejpam-3291	312	12	,	,	PUNCT
ejpam-3291	312	13	journal	journal	NOUN
ejpam-3291	312	14	of	of	ADP
ejpam-3291	312	15	pure	pure	ADJ
ejpam-3291	312	16	and	and	CCONJ
ejpam-3291	312	17	applied	applied	ADJ
ejpam-3291	312	18	algebra	algebra	NOUN
ejpam-3291	312	19	,	,	PUNCT
ejpam-3291	312	20	197:305	197:305	NUM
ejpam-3291	312	21	-	-	PUNCT
ejpam-3291	312	22	321	321	NUM
ejpam-3291	312	23	,	,	PUNCT
ejpam-3291	312	24	2005	2005	NUM
ejpam-3291	312	25	.	.	PUNCT
ejpam-3291	313	1	[	[	X
ejpam-3291	313	2	10	10	NUM
ejpam-3291	313	3	]	]	X
ejpam-3291	313	4	p	p	X
ejpam-3291	313	5	f	f	PROPN
ejpam-3291	313	6	smith	smith	PROPN
ejpam-3291	313	7	and	and	CCONJ
ejpam-3291	313	8	m	m	PROPN
ejpam-3291	313	9	r	r	NOUN
ejpam-3291	313	10	vedadi	vedadi	NOUN
ejpam-3291	313	11	,	,	PUNCT
ejpam-3291	313	12	essentially	essentially	ADV
ejpam-3291	313	13	compressible	compressible	ADJ
ejpam-3291	313	14	modules	module	NOUN
ejpam-3291	313	15	and	and	CCONJ
ejpam-3291	313	16	rings	ring	NOUN
ejpam-3291	313	17	,	,	PUNCT
ejpam-3291	313	18	journal	journal	NOUN
ejpam-3291	313	19	of	of	ADP
ejpam-3291	313	20	algebra	algebra	NOUN
ejpam-3291	313	21	,	,	PUNCT
ejpam-3291	313	22	304:812	304:812	PROPN
ejpam-3291	313	23	-	-	PUNCT
ejpam-3291	313	24	831	831	NUM
ejpam-3291	313	25	,	,	PUNCT
ejpam-3291	313	26	2006	2006	NUM
ejpam-3291	313	27	.	.	PUNCT
ejpam-3291	314	1	[	[	X
ejpam-3291	314	2	11	11	NUM
ejpam-3291	314	3	]	]	X
ejpam-3291	314	4	r	r	NOUN
ejpam-3291	314	5	wisbauer	wisbauer	NOUN
ejpam-3291	314	6	,	,	PUNCT
ejpam-3291	314	7	foundations	foundation	NOUN
ejpam-3291	314	8	of	of	ADP
ejpam-3291	314	9	module	module	NOUN
ejpam-3291	314	10	and	and	CCONJ
ejpam-3291	314	11	ring	ring	NOUN
ejpam-3291	314	12	theory	theory	NOUN
ejpam-3291	314	13	,	,	PUNCT
ejpam-3291	314	14	philadelphia	philadelphia	PROPN
ejpam-3291	314	15	,	,	PUNCT
ejpam-3291	314	16	pa	pa	PROPN
ejpam-3291	314	17	,	,	PUNCT
ejpam-3291	314	18	usa	usa	PROPN
ejpam-3291	314	19	:	:	PUNCT
ejpam-3291	314	20	gordon	gordon	PROPN
ejpam-3291	314	21	and	and	CCONJ
ejpam-3291	314	22	breach	breach	VERB
ejpam-3291	314	23	,	,	PUNCT
ejpam-3291	314	24	1991	1991	NUM
ejpam-3291	314	25	.	.	PUNCT
ejpam-3291	315	1	[	[	X
ejpam-3291	315	2	12	12	NUM
ejpam-3291	315	3	]	]	X
ejpam-3291	315	4	w	w	PROPN
ejpam-3291	315	5	xue	xue	PROPN
ejpam-3291	315	6	,	,	PUNCT
ejpam-3291	315	7	characterization	characterization	NOUN
ejpam-3291	315	8	of	of	ADP
ejpam-3291	315	9	rings	ring	NOUN
ejpam-3291	315	10	using	use	VERB
ejpam-3291	315	11	direct	direct	ADJ
ejpam-3291	315	12	-	-	PUNCT
ejpam-3291	315	13	projective	projective	ADJ
ejpam-3291	315	14	modules	module	NOUN
ejpam-3291	315	15	and	and	CCONJ
ejpam-3291	315	16	direct	direct	ADJ
ejpam-3291	315	17	-	-	PUNCT
ejpam-3291	315	18	injective	injective	ADJ
ejpam-3291	315	19	modules	module	NOUN
ejpam-3291	315	20	,	,	PUNCT
ejpam-3291	315	21	journal	journal	NOUN
ejpam-3291	315	22	of	of	ADP
ejpam-3291	315	23	pure	pure	ADJ
ejpam-3291	315	24	and	and	CCONJ
ejpam-3291	315	25	applied	applied	ADJ
ejpam-3291	315	26	algebra	algebra	NOUN
ejpam-3291	315	27	,	,	PUNCT
ejpam-3291	315	28	87:99	87:99	NUM
ejpam-3291	315	29	-	-	SYM
ejpam-3291	315	30	104	104	NUM
ejpam-3291	315	31	,	,	PUNCT
ejpam-3291	315	32	1993	1993	NUM
ejpam-3291	315	33	.	.	PUNCT