id	sid	tid	token	lemma	pos
iajs-1013	1	1	ibn	ibn	PROPN
iajs-1013	1	2	alhaitham	alhaitham	NOUN
iajs-1013	1	3	j.	j.	PROPN
iajs-1013	1	4	for	for	ADP
iajs-1013	1	5	pure	pure	ADJ
iajs-1013	1	6	&	&	CCONJ
iajs-1013	1	7	appl	appl	PROPN
iajs-1013	1	8	.	.	PUNCT
iajs-1013	2	1	sci	sci	PROPN
iajs-1013	2	2	.	.	PUNCT
iajs-1013	3	1	vol.23	vol.23	PROPN
iajs-1013	3	2	(	(	PUNCT
iajs-1013	3	3	1	1	NUM
iajs-1013	3	4	)	)	PUNCT
iajs-1013	3	5	2010	2010	NUM
iajs-1013	3	6	weakly	weakly	ADJ
iajs-1013	3	7	relative	relative	ADJ
iajs-1013	3	8	quasi	quasi	ADJ
iajs-1013	3	9	-	-	ADJ
iajs-1013	3	10	injective	injective	ADJ
iajs-1013	3	11	modules	module	NOUN
iajs-1013	3	12	l.	l.	PROPN
iajs-1013	3	13	s	s	PART
iajs-1013	3	14	mahmood	mahmood	PROPN
iajs-1013	3	15	,	,	PUNCT
iajs-1013	3	16	a.	a.	PROPN
iajs-1013	3	17	s.	s.	PROPN
iajs-1013	3	18	mijbass	mijbass	PROPN
iajs-1013	3	19	,	,	PUNCT
iajs-1013	3	20	k.	k.	PROPN
iajs-1013	3	21	s.	s.	PROPN
iajs-1013	3	22	kalaf	kalaf	PROPN
iajs-1013	3	23	department	department	PROPN
iajs-1013	3	24	of	of	ADP
iajs-1013	3	25	mathematics	mathematics	PROPN
iajs-1013	3	26	,	,	PUNCT
iajs-1013	3	27	ibn	ibn	PROPN
iajs-1013	3	28	al	al	PROPN
iajs-1013	3	29	-	-	PUNCT
iajs-1013	3	30	haitham	haitham	PROPN
iajs-1013	3	31	college	college	PROPN
iajs-1013	3	32	of	of	ADP
iajs-1013	3	33	education	education	NOUN
iajs-1013	3	34	,	,	PUNCT
iajs-1013	3	35	university	university	NOUN
iajs-1013	3	36	of	of	ADP
iajs-1013	3	37	baghdad	baghdad	PROPN
iajs-1013	3	38	.	.	PUNCT
iajs-1013	4	1	department	department	NOUN
iajs-1013	4	2	of	of	ADP
iajs-1013	4	3	mathematics	mathematics	PROPN
iajs-1013	4	4	,	,	PUNCT
iajs-1013	4	5	college	college	NOUN
iajs-1013	4	6	of	of	ADP
iajs-1013	4	7	computer	computer	NOUN
iajs-1013	4	8	science	science	NOUN
iajs-1013	4	9	and	and	CCONJ
iajs-1013	4	10	mathematics	mathematic	NOUN
iajs-1013	4	11	,	,	PUNCT
iajs-1013	4	12	tikrit	tikrit	NOUN
iajs-1013	4	13	university	university	NOUN
iajs-1013	4	14	.	.	PUNCT
iajs-1013	5	1	department	department	PROPN
iajs-1013	5	2	of	of	ADP
iajs-1013	5	3	physics	physics	PROPN
iajs-1013	5	4	,	,	PUNCT
iajs-1013	5	5	college	college	NOUN
iajs-1013	5	6	of	of	ADP
iajs-1013	5	7	science	science	NOUN
iajs-1013	5	8	,	,	PUNCT
iajs-1013	5	9	university	university	NOUN
iajs-1013	5	10	of	of	ADP
iajs-1013	5	11	al	al	PROPN
iajs-1013	5	12	-	-	PUNCT
iajs-1013	5	13	anbar	anbar	NOUN
iajs-1013	5	14	.	.	PUNCT
iajs-1013	6	1	abstract	abstract	ADJ
iajs-1013	6	2	:	:	PUNCT
iajs-1013	6	3	let	let	VERB
iajs-1013	6	4	r	r	PRON
iajs-1013	6	5	be	be	AUX
iajs-1013	6	6	a	a	DET
iajs-1013	6	7	commutative	commutative	ADJ
iajs-1013	6	8	ring	ring	NOUN
iajs-1013	6	9	with	with	ADP
iajs-1013	6	10	unity	unity	NOUN
iajs-1013	6	11	and	and	CCONJ
iajs-1013	6	12	let	let	VERB
iajs-1013	6	13	m	m	PRON
iajs-1013	6	14	,	,	PUNCT
iajs-1013	6	15	n	n	X
iajs-1013	6	16	be	be	AUX
iajs-1013	6	17	unitary	unitary	ADJ
iajs-1013	6	18	r	r	NOUN
iajs-1013	6	19	-	-	PUNCT
iajs-1013	6	20	modules	module	NOUN
iajs-1013	6	21	.	.	PUNCT
iajs-1013	7	1	in	in	ADP
iajs-1013	7	2	this	this	DET
iajs-1013	7	3	research	research	NOUN
iajs-1013	7	4	,	,	PUNCT
iajs-1013	7	5	we	we	PRON
iajs-1013	7	6	give	give	VERB
iajs-1013	7	7	generalizations	generalization	NOUN
iajs-1013	7	8	for	for	ADP
iajs-1013	7	9	the	the	DET
iajs-1013	7	10	concepts	concept	NOUN
iajs-1013	7	11	:	:	PUNCT
iajs-1013	7	12	weakly	weakly	ADJ
iajs-1013	7	13	relative	relative	ADJ
iajs-1013	7	14	injectivity	injectivity	NOUN
iajs-1013	7	15	,	,	PUNCT
iajs-1013	7	16	relative	relative	ADJ
iajs-1013	7	17	tightness	tightness	NOUN
iajs-1013	7	18	and	and	CCONJ
iajs-1013	7	19	weakly	weakly	ADJ
iajs-1013	7	20	injectivity	injectivity	NOUN
iajs-1013	7	21	of	of	ADP
iajs-1013	7	22	modules	module	NOUN
iajs-1013	7	23	.	.	PUNCT
iajs-1013	8	1	we	we	PRON
iajs-1013	8	2	call	call	VERB
iajs-1013	8	3	m	m	VERB
iajs-1013	8	4	weakly	weakly	ADJ
iajs-1013	8	5	n	n	CCONJ
iajs-1013	8	6	-	-	PUNCT
iajs-1013	8	7	quasi	quasi	NOUN
iajs-1013	8	8	-	-	ADJ
iajs-1013	8	9	injective	injective	ADJ
iajs-1013	8	10	,	,	PUNCT
iajs-1013	8	11	if	if	SCONJ
iajs-1013	8	12	for	for	ADP
iajs-1013	8	13	each	each	DET
iajs-1013	8	14	f	f	PROPN
iajs-1013	8	15			PROPN
iajs-1013	8	16	hom(n,	hom(n,	NOUN
iajs-1013	8	17	)	)	PUNCT
iajs-1013	8	18	there	there	PRON
iajs-1013	8	19	exists	exist	VERB
iajs-1013	8	20	a	a	DET
iajs-1013	8	21	submodule	submodule	NOUN
iajs-1013	8	22	x	x	PUNCT
iajs-1013	8	23	of	of	ADP
iajs-1013	8	24			NUM
iajs-1013	9	1	such	such	ADJ
iajs-1013	9	2	that	that	SCONJ
iajs-1013	9	3	f	f	PROPN
iajs-1013	9	4	(	(	PUNCT
iajs-1013	9	5	n	n	CCONJ
iajs-1013	9	6	)	)	PUNCT
iajs-1013	9	7			PROPN
iajs-1013	9	8	x	x	X
iajs-1013	10	1	≈	≈	PROPN
iajs-1013	10	2	m	m	PROPN
iajs-1013	10	3	,	,	PUNCT
iajs-1013	10	4	where	where	SCONJ
iajs-1013	10	5			PROPN
iajs-1013	10	6	is	be	AUX
iajs-1013	10	7	the	the	DET
iajs-1013	10	8	quasi	quasi	ADJ
iajs-1013	10	9	-	-	ADJ
iajs-1013	10	10	injective	injective	ADJ
iajs-1013	10	11	hull	hull	NOUN
iajs-1013	10	12	of	of	ADP
iajs-1013	10	13	m.	m.	NOUN
iajs-1013	11	1	and	and	CCONJ
iajs-1013	11	2	we	we	PRON
iajs-1013	11	3	call	call	VERB
iajs-1013	11	4	m	m	VERB
iajs-1013	11	5	n	n	CCONJ
iajs-1013	11	6	-	-	PUNCT
iajs-1013	11	7	quasi	quasi	NOUN
iajs-1013	11	8	-	-	ADJ
iajs-1013	11	9	tight	tight	ADJ
iajs-1013	11	10	,	,	PUNCT
iajs-1013	11	11	if	if	SCONJ
iajs-1013	11	12	every	every	DET
iajs-1013	11	13	quotient	quotient	NOUN
iajs-1013	11	14	n	n	INTJ
iajs-1013	11	15	/	/	SYM
iajs-1013	11	16	k	k	PROPN
iajs-1013	11	17	of	of	ADP
iajs-1013	11	18	n	n	PRON
iajs-1013	11	19	which	which	PRON
iajs-1013	11	20	embeds	embed	VERB
iajs-1013	11	21	in	in	ADP
iajs-1013	11	22			PROPN
iajs-1013	11	23	embeds	embed	NOUN
iajs-1013	11	24	in	in	ADP
iajs-1013	11	25	m.	m.	NOUN
iajs-1013	11	26	while	while	SCONJ
iajs-1013	11	27	we	we	PRON
iajs-1013	11	28	call	call	VERB
iajs-1013	11	29	m	m	VERB
iajs-1013	11	30	weakly	weakly	ADJ
iajs-1013	11	31	quasi	quasi	ADJ
iajs-1013	11	32	-	-	ADJ
iajs-1013	11	33	injective	injective	ADJ
iajs-1013	11	34	if	if	SCONJ
iajs-1013	11	35	m	m	NOUN
iajs-1013	11	36	is	be	AUX
iajs-1013	11	37	weakly	weakly	ADJ
iajs-1013	11	38	n	n	CCONJ
iajs-1013	11	39	-	-	PUNCT
iajs-1013	11	40	quasiinjective	quasiinjective	NOUN
iajs-1013	11	41	for	for	ADP
iajs-1013	11	42	every	every	DET
iajs-1013	11	43	finitely	finitely	ADV
iajs-1013	11	44	generated	generate	VERB
iajs-1013	11	45	r	r	NOUN
iajs-1013	11	46	-	-	PUNCT
iajs-1013	11	47	module	module	NOUN
iajs-1013	11	48	n.	n.	NOUN
iajs-1013	11	49	moreover	moreover	ADV
iajs-1013	11	50	,	,	PUNCT
iajs-1013	11	51	we	we	PRON
iajs-1013	11	52	generalize	generalize	VERB
iajs-1013	11	53	some	some	DET
iajs-1013	11	54	properties	property	NOUN
iajs-1013	11	55	of	of	ADP
iajs-1013	11	56	weakly	weakly	ADJ
iajs-1013	11	57	n	n	CCONJ
iajs-1013	11	58	-	-	PUNCT
iajs-1013	11	59	injective	injective	ADJ
iajs-1013	11	60	,	,	PUNCT
iajs-1013	11	61	n	n	CCONJ
iajs-1013	11	62	-	-	PUNCT
iajs-1013	11	63	tight	tight	ADJ
iajs-1013	11	64	and	and	CCONJ
iajs-1013	11	65	weakly	weakly	ADJ
iajs-1013	11	66	injective	injective	ADJ
iajs-1013	11	67	modules	module	NOUN
iajs-1013	11	68	to	to	ADP
iajs-1013	11	69	weakly	weakly	ADJ
iajs-1013	11	70	n	n	CCONJ
iajs-1013	11	71	-	-	PUNCT
iajs-1013	11	72	quasi	quasi	NOUN
iajs-1013	11	73	-	-	ADJ
iajs-1013	11	74	injective	injective	ADJ
iajs-1013	11	75	,	,	PUNCT
iajs-1013	11	76	n	n	CCONJ
iajs-1013	11	77	-	-	PUNCT
iajs-1013	11	78	quasi	quasi	NOUN
iajs-1013	11	79	-	-	ADJ
iajs-1013	11	80	tight	tight	ADJ
iajs-1013	11	81	and	and	CCONJ
iajs-1013	11	82	weakly	weakly	ADJ
iajs-1013	11	83	quasi	quasi	ADJ
iajs-1013	11	84	-	-	ADJ
iajs-1013	11	85	injective	injective	ADJ
iajs-1013	11	86	modules	module	NOUN
iajs-1013	11	87	respectively	respectively	ADV
iajs-1013	11	88	.	.	PUNCT
iajs-1013	12	1	the	the	DET
iajs-1013	12	2	relations	relation	NOUN
iajs-1013	12	3	among	among	ADP
iajs-1013	12	4	these	these	DET
iajs-1013	12	5	concepts	concept	NOUN
iajs-1013	12	6	are	be	AUX
iajs-1013	12	7	also	also	ADV
iajs-1013	12	8	studied	study	VERB
iajs-1013	12	9	.	.	PUNCT
iajs-1013	13	1	introduction	introduction	NOUN
iajs-1013	13	2	the	the	DET
iajs-1013	13	3	concept	concept	NOUN
iajs-1013	13	4	of	of	ADP
iajs-1013	13	5	weak	weak	ADJ
iajs-1013	13	6	relative	relative	ADJ
iajs-1013	13	7	injectivity	injectivity	NOUN
iajs-1013	13	8	of	of	ADP
iajs-1013	13	9	modules	module	NOUN
iajs-1013	13	10	was	be	AUX
iajs-1013	13	11	introduced	introduce	VERB
iajs-1013	13	12	originally	originally	ADV
iajs-1013	13	13	in	in	ADP
iajs-1013	13	14	[	[	X
iajs-1013	13	15	1	1	NUM
iajs-1013	13	16	]	]	PUNCT
iajs-1013	13	17	.	.	PUNCT
iajs-1013	14	1	since	since	SCONJ
iajs-1013	14	2	then	then	ADV
iajs-1013	14	3	,	,	PUNCT
iajs-1013	14	4	the	the	DET
iajs-1013	14	5	study	study	NOUN
iajs-1013	14	6	of	of	ADP
iajs-1013	14	7	this	this	DET
iajs-1013	14	8	concept	concept	NOUN
iajs-1013	14	9	has	have	AUX
iajs-1013	14	10	been	be	AUX
iajs-1013	14	11	illustrated	illustrate	VERB
iajs-1013	14	12	extensively	extensively	ADV
iajs-1013	14	13	.	.	PUNCT
iajs-1013	15	1	we	we	PRON
iajs-1013	15	2	introduced	introduce	VERB
iajs-1013	15	3	in	in	ADP
iajs-1013	15	4	this	this	DET
iajs-1013	15	5	research	research	NOUN
iajs-1013	15	6	the	the	DET
iajs-1013	15	7	concept	concept	NOUN
iajs-1013	15	8	of	of	ADP
iajs-1013	15	9	weak	weak	ADJ
iajs-1013	15	10	relative	relative	ADJ
iajs-1013	15	11	quasi	quasi	NOUN
iajs-1013	15	12	-	-	NOUN
iajs-1013	15	13	injectivity	injectivity	NOUN
iajs-1013	15	14	of	of	ADP
iajs-1013	15	15	modules	module	NOUN
iajs-1013	15	16	as	as	ADP
iajs-1013	15	17	a	a	DET
iajs-1013	15	18	generalization	generalization	NOUN
iajs-1013	15	19	of	of	ADP
iajs-1013	15	20	the	the	DET
iajs-1013	15	21	concept	concept	NOUN
iajs-1013	15	22	of	of	ADP
iajs-1013	15	23	weak	weak	ADJ
iajs-1013	15	24	relative	relative	ADJ
iajs-1013	15	25	injectivity	injectivity	NOUN
iajs-1013	15	26	which	which	PRON
iajs-1013	15	27	motivates	motivate	VERB
iajs-1013	15	28	our	our	PRON
iajs-1013	15	29	principle	principle	ADJ
iajs-1013	15	30	subject	subject	NOUN
iajs-1013	15	31	of	of	ADP
iajs-1013	15	32	this	this	DET
iajs-1013	15	33	research	research	NOUN
iajs-1013	15	34	.	.	PUNCT
iajs-1013	16	1	this	this	DET
iajs-1013	16	2	paper	paper	NOUN
iajs-1013	16	3	contains	contain	VERB
iajs-1013	16	4	five	five	NUM
iajs-1013	16	5	sections	section	NOUN
iajs-1013	16	6	.	.	PUNCT
iajs-1013	17	1	in	in	ADP
iajs-1013	17	2	the	the	DET
iajs-1013	17	3	first	first	ADJ
iajs-1013	17	4	section	section	NOUN
iajs-1013	17	5	,	,	PUNCT
iajs-1013	17	6	we	we	PRON
iajs-1013	17	7	introduced	introduce	VERB
iajs-1013	17	8	the	the	DET
iajs-1013	17	9	concept	concept	NOUN
iajs-1013	17	10	of	of	ADP
iajs-1013	17	11	weakly	weakly	ADJ
iajs-1013	17	12	relative	relative	ADJ
iajs-1013	17	13	quasi	quasi	NOUN
iajs-1013	17	14	-	-	NOUN
iajs-1013	17	15	injectivity	injectivity	NOUN
iajs-1013	17	16	of	of	ADP
iajs-1013	17	17	modules	module	NOUN
iajs-1013	17	18	,	,	PUNCT
iajs-1013	17	19	where	where	SCONJ
iajs-1013	17	20	we	we	PRON
iajs-1013	17	21	call	call	VERB
iajs-1013	17	22	an	an	DET
iajs-1013	17	23	r	r	NOUN
iajs-1013	17	24	-	-	PUNCT
iajs-1013	17	25	module	module	NOUN
iajs-1013	17	26	m	m	PRON
iajs-1013	17	27	weakly	weakly	ADJ
iajs-1013	17	28	nquasiinjective	nquasiinjective	NOUN
iajs-1013	17	29	(	(	PUNCT
iajs-1013	17	30	n	n	X
iajs-1013	17	31	is	be	AUX
iajs-1013	17	32	any	any	DET
iajs-1013	17	33	r	r	NOUN
iajs-1013	17	34	-	-	PUNCT
iajs-1013	17	35	module	module	NOUN
iajs-1013	17	36	)	)	PUNCT
iajs-1013	17	37	if	if	SCONJ
iajs-1013	17	38	for	for	ADP
iajs-1013	17	39	each	each	DET
iajs-1013	17	40	f	f	PROPN
iajs-1013	17	41			PROPN
iajs-1013	17	42	hom(n	hom(n	PROPN
iajs-1013	17	43	,	,	PUNCT
iajs-1013	17	44			NUM
iajs-1013	17	45	)	)	PUNCT
iajs-1013	17	46	implies	imply	VERB
iajs-1013	17	47	that	that	SCONJ
iajs-1013	17	48	f	f	PROPN
iajs-1013	17	49	(	(	PUNCT
iajs-1013	17	50	n	n	CCONJ
iajs-1013	17	51	)	)	PUNCT
iajs-1013	17	52	is	be	AUX
iajs-1013	17	53	contained	contain	VERB
iajs-1013	17	54	in	in	ADP
iajs-1013	17	55	this	this	DET
iajs-1013	17	56	paper	paper	NOUN
iajs-1013	17	57	represents	represent	VERB
iajs-1013	17	58	a	a	DET
iajs-1013	17	59	part	part	NOUN
iajs-1013	17	60	of	of	ADP
iajs-1013	17	61	ph.d	ph.d	PROPN
iajs-1013	17	62	thesis	thesis	NOUN
iajs-1013	17	63	written	write	VERB
iajs-1013	17	64	by	by	ADP
iajs-1013	17	65	the	the	DET
iajs-1013	17	66	third	third	ADJ
iajs-1013	17	67	author	author	NOUN
iajs-1013	17	68	under	under	ADP
iajs-1013	17	69	the	the	DET
iajs-1013	17	70	supervision	supervision	NOUN
iajs-1013	17	71	of	of	ADP
iajs-1013	17	72	the	the	DET
iajs-1013	17	73	first	first	ADJ
iajs-1013	17	74	and	and	CCONJ
iajs-1013	17	75	the	the	DET
iajs-1013	17	76	second	second	ADJ
iajs-1013	17	77	authors	author	NOUN
iajs-1013	17	78	and	and	CCONJ
iajs-1013	17	79	was	be	AUX
iajs-1013	17	80	submitted	submit	VERB
iajs-1013	17	81	to	to	ADP
iajs-1013	17	82	the	the	DET
iajs-1013	17	83	college	college	NOUN
iajs-1013	17	84	of	of	ADP
iajs-1013	17	85	education	education	PROPN
iajs-1013	17	86	ibn	ibn	PROPN
iajs-1013	17	87	-	-	PUNCT
iajs-1013	17	88	al	al	PROPN
iajs-1013	17	89	-	-	PUNCT
iajs-1013	17	90	haitham	haitham	PROPN
iajs-1013	17	91	university	university	PROPN
iajs-1013	17	92	of	of	ADP
iajs-1013	17	93	baghdad	baghdad	PROPN
iajs-1013	17	94	.	.	PUNCT
iajs-1013	18	1	ibn	ibn	PROPN
iajs-1013	18	2	alhaitham	alhaitham	PROPN
iajs-1013	18	3	j.	j.	PROPN
iajs-1013	18	4	for	for	ADP
iajs-1013	18	5	pure	pure	ADJ
iajs-1013	18	6	&	&	CCONJ
iajs-1013	18	7	appl	appl	PROPN
iajs-1013	18	8	.	.	PUNCT
iajs-1013	19	1	sci	sci	PROPN
iajs-1013	19	2	.	.	PUNCT
iajs-1013	20	1	vol.23	vol.23	PROPN
iajs-1013	20	2	(	(	PUNCT
iajs-1013	20	3	1	1	NUM
iajs-1013	20	4	)	)	PUNCT
iajs-1013	20	5	2010	2010	NUM
iajs-1013	20	6	some	some	DET
iajs-1013	20	7	submodule	submodule	NOUN
iajs-1013	20	8	of	of	ADP
iajs-1013	20	9			PROPN
iajs-1013	20	10	which	which	PRON
iajs-1013	20	11	is	be	AUX
iajs-1013	20	12	isomorphic	isomorphic	ADJ
iajs-1013	20	13	to	to	ADP
iajs-1013	20	14	m	m	PRON
iajs-1013	20	15	,	,	PUNCT
iajs-1013	20	16	see	see	VERB
iajs-1013	20	17	definition	definition	NOUN
iajs-1013	20	18	1.1	1.1	NUM
iajs-1013	20	19	.	.	PUNCT
iajs-1013	21	1	we	we	PRON
iajs-1013	21	2	established	establish	VERB
iajs-1013	21	3	some	some	DET
iajs-1013	21	4	properties	property	NOUN
iajs-1013	21	5	of	of	ADP
iajs-1013	21	6	such	such	ADJ
iajs-1013	21	7	modules	module	NOUN
iajs-1013	21	8	.	.	PUNCT
iajs-1013	22	1	we	we	PRON
iajs-1013	22	2	showed	show	VERB
iajs-1013	22	3	that	that	SCONJ
iajs-1013	22	4	the	the	DET
iajs-1013	22	5	class	class	NOUN
iajs-1013	22	6	of	of	ADP
iajs-1013	22	7	such	such	ADJ
iajs-1013	22	8	modules	module	NOUN
iajs-1013	22	9	is	be	AUX
iajs-1013	22	10	not	not	PART
iajs-1013	22	11	closed	close	VERB
iajs-1013	22	12	under	under	ADP
iajs-1013	22	13	direct	direct	ADJ
iajs-1013	22	14	summand	summand	NOUN
iajs-1013	22	15	,	,	PUNCT
iajs-1013	22	16	see	see	VERB
iajs-1013	22	17	ex	ex	NOUN
iajs-1013	22	18	.	.	PROPN
iajs-1013	22	19	1.6	1.6	NUM
iajs-1013	22	20	.	.	PUNCT
iajs-1013	23	1	while	while	SCONJ
iajs-1013	23	2	we	we	PRON
iajs-1013	23	3	could	could	AUX
iajs-1013	23	4	not	not	PART
iajs-1013	23	5	prove	prove	VERB
iajs-1013	23	6	or	or	CCONJ
iajs-1013	23	7	disprove	disprove	VERB
iajs-1013	23	8	that	that	SCONJ
iajs-1013	23	9	this	this	DET
iajs-1013	23	10	class	class	NOUN
iajs-1013	23	11	of	of	ADP
iajs-1013	23	12	modules	module	NOUN
iajs-1013	23	13	is	be	AUX
iajs-1013	23	14	closed	close	VERB
iajs-1013	23	15	under	under	ADP
iajs-1013	23	16	direct	direct	ADJ
iajs-1013	23	17	sum	sum	NOUN
iajs-1013	23	18	.	.	PUNCT
iajs-1013	24	1	but	but	CCONJ
iajs-1013	24	2	we	we	PRON
iajs-1013	24	3	proved	prove	VERB
iajs-1013	24	4	a	a	DET
iajs-1013	24	5	special	special	ADJ
iajs-1013	24	6	case	case	NOUN
iajs-1013	24	7	of	of	ADP
iajs-1013	24	8	this	this	PRON
iajs-1013	24	9	,	,	PUNCT
iajs-1013	24	10	see	see	VERB
iajs-1013	24	11	proposition	proposition	NOUN
iajs-1013	24	12	1.7	1.7	NUM
iajs-1013	24	13	.	.	PUNCT
iajs-1013	25	1	next	next	ADV
iajs-1013	25	2	we	we	PRON
iajs-1013	25	3	proved	prove	VERB
iajs-1013	25	4	that	that	SCONJ
iajs-1013	25	5	this	this	DET
iajs-1013	25	6	class	class	NOUN
iajs-1013	25	7	of	of	ADP
iajs-1013	25	8	modules	module	NOUN
iajs-1013	25	9	is	be	AUX
iajs-1013	25	10	closed	close	VERB
iajs-1013	25	11	under	under	ADP
iajs-1013	25	12	essential	essential	ADJ
iajs-1013	25	13	extension	extension	NOUN
iajs-1013	25	14	,	,	PUNCT
iajs-1013	25	15	see	see	VERB
iajs-1013	25	16	proposition	proposition	NOUN
iajs-1013	25	17	1.15	1.15	NUM
iajs-1013	25	18	.	.	PUNCT
iajs-1013	26	1	the	the	DET
iajs-1013	26	2	second	second	ADJ
iajs-1013	26	3	section	section	NOUN
iajs-1013	26	4	is	be	AUX
iajs-1013	26	5	devoted	devote	VERB
iajs-1013	26	6	to	to	PART
iajs-1013	26	7	give	give	VERB
iajs-1013	26	8	some	some	DET
iajs-1013	26	9	characterizations	characterization	NOUN
iajs-1013	26	10	of	of	ADP
iajs-1013	26	11	weakly	weakly	ADJ
iajs-1013	26	12	relative	relative	ADJ
iajs-1013	26	13	quasiinjective	quasiinjective	ADJ
iajs-1013	26	14	modules	module	NOUN
iajs-1013	26	15	which	which	PRON
iajs-1013	26	16	are	be	AUX
iajs-1013	26	17	very	very	ADV
iajs-1013	26	18	useful	useful	ADJ
iajs-1013	26	19	in	in	ADP
iajs-1013	26	20	the	the	DET
iajs-1013	26	21	next	next	ADJ
iajs-1013	26	22	sections	section	NOUN
iajs-1013	26	23	,	,	PUNCT
iajs-1013	26	24	see	see	VERB
iajs-1013	26	25	theorem	theorem	VERB
iajs-1013	26	26	2.1	2.1	NUM
iajs-1013	26	27	,	,	PUNCT
iajs-1013	26	28	theorem	theorem	VERB
iajs-1013	26	29	2.2	2.2	NUM
iajs-1013	26	30	,	,	PUNCT
iajs-1013	26	31	theorem	theorem	VERB
iajs-1013	26	32	2.3	2.3	NUM
iajs-1013	26	33	,	,	PUNCT
iajs-1013	26	34	theorem	theorem	VERB
iajs-1013	26	35	2.8	2.8	NUM
iajs-1013	26	36	,	,	PUNCT
iajs-1013	26	37	theorem	theorem	VERB
iajs-1013	26	38	2.9	2.9	NUM
iajs-1013	26	39	,	,	PUNCT
iajs-1013	26	40	and	and	CCONJ
iajs-1013	26	41	theorem	theorem	VERB
iajs-1013	26	42	2.10	2.10	NUM
iajs-1013	26	43	.	.	PUNCT
iajs-1013	27	1	in	in	ADP
iajs-1013	27	2	section	section	NOUN
iajs-1013	27	3	three	three	NUM
iajs-1013	27	4	,	,	PUNCT
iajs-1013	27	5	we	we	PRON
iajs-1013	27	6	generalized	generalize	VERB
iajs-1013	27	7	the	the	DET
iajs-1013	27	8	concept	concept	NOUN
iajs-1013	27	9	of	of	ADP
iajs-1013	27	10	relative	relative	ADJ
iajs-1013	27	11	tightness	tightness	NOUN
iajs-1013	27	12	of	of	ADP
iajs-1013	27	13	modules	module	NOUN
iajs-1013	27	14	which	which	PRON
iajs-1013	27	15	appeared	appear	VERB
iajs-1013	27	16	in	in	ADP
iajs-1013	27	17	[	[	X
iajs-1013	27	18	2	2	NUM
iajs-1013	27	19	]	]	PUNCT
iajs-1013	27	20	into	into	ADP
iajs-1013	27	21	the	the	DET
iajs-1013	27	22	concept	concept	NOUN
iajs-1013	27	23	of	of	ADP
iajs-1013	27	24	relative	relative	ADJ
iajs-1013	27	25	quasi	quasi	NOUN
iajs-1013	27	26	-	-	NOUN
iajs-1013	27	27	tightness	tightness	NOUN
iajs-1013	27	28	of	of	ADP
iajs-1013	27	29	modules	module	NOUN
iajs-1013	27	30	,	,	PUNCT
iajs-1013	27	31	where	where	SCONJ
iajs-1013	27	32	we	we	PRON
iajs-1013	27	33	called	call	VERB
iajs-1013	27	34	an	an	DET
iajs-1013	27	35	rmodule	rmodule	NOUN
iajs-1013	27	36	m	m	NOUN
iajs-1013	27	37	to	to	PART
iajs-1013	27	38	be	be	AUX
iajs-1013	27	39	n	n	X
iajs-1013	27	40	-	-	PUNCT
iajs-1013	27	41	quasi	quasi	ADJ
iajs-1013	27	42	–	–	PUNCT
iajs-1013	27	43	tight	tight	ADJ
iajs-1013	27	44	(	(	PUNCT
iajs-1013	27	45	n	n	X
iajs-1013	27	46	is	be	AUX
iajs-1013	27	47	any	any	DET
iajs-1013	27	48	r	r	NOUN
iajs-1013	27	49	-	-	PUNCT
iajs-1013	27	50	module	module	NOUN
iajs-1013	27	51	)	)	PUNCT
iajs-1013	27	52	if	if	SCONJ
iajs-1013	27	53	and	and	CCONJ
iajs-1013	27	54	only	only	ADV
iajs-1013	27	55	if	if	SCONJ
iajs-1013	27	56	every	every	DET
iajs-1013	27	57	quotient	quotient	NOUN
iajs-1013	27	58	n	n	INTJ
iajs-1013	27	59	/	/	SYM
iajs-1013	27	60	k	k	PROPN
iajs-1013	27	61	of	of	ADP
iajs-1013	27	62	n	n	PRON
iajs-1013	27	63	which	which	PRON
iajs-1013	27	64	embeds	embed	VERB
iajs-1013	27	65	in	in	ADP
iajs-1013	27	66			PROPN
iajs-1013	27	67	embeds	embed	NOUN
iajs-1013	27	68	in	in	ADP
iajs-1013	27	69	m	m	PROPN
iajs-1013	27	70	,	,	PUNCT
iajs-1013	27	71	see	see	VERB
iajs-1013	27	72	definition	definition	NOUN
iajs-1013	27	73	3.2	3.2	NUM
iajs-1013	27	74	,	,	PUNCT
iajs-1013	27	75	we	we	PRON
iajs-1013	27	76	related	relate	VERB
iajs-1013	27	77	this	this	DET
iajs-1013	27	78	concept	concept	NOUN
iajs-1013	27	79	with	with	ADP
iajs-1013	27	80	the	the	DET
iajs-1013	27	81	concept	concept	NOUN
iajs-1013	27	82	of	of	ADP
iajs-1013	27	83	relative	relative	ADJ
iajs-1013	27	84	quasi	quasi	NOUN
iajs-1013	27	85	-	-	NOUN
iajs-1013	27	86	injectivity	injectivity	NOUN
iajs-1013	27	87	of	of	ADP
iajs-1013	27	88	modules	module	NOUN
iajs-1013	27	89	.	.	PUNCT
iajs-1013	28	1	it	it	PRON
iajs-1013	28	2	truns	trun	VERB
iajs-1013	28	3	out	out	ADP
iajs-1013	28	4	that	that	DET
iajs-1013	28	5	relative	relative	ADJ
iajs-1013	28	6	quasi	quasi	NOUN
iajs-1013	28	7	-	-	NOUN
iajs-1013	28	8	lightness	lightness	NOUN
iajs-1013	28	9	of	of	ADP
iajs-1013	28	10	modules	module	NOUN
iajs-1013	28	11	is	be	AUX
iajs-1013	28	12	a	a	DET
iajs-1013	28	13	necessary	necessary	ADJ
iajs-1013	28	14	condition	condition	NOUN
iajs-1013	28	15	for	for	ADP
iajs-1013	28	16	relative	relative	ADJ
iajs-1013	28	17	quasi	quasi	NOUN
iajs-1013	28	18	-	-	NOUN
iajs-1013	28	19	injectivity	injectivity	NOUN
iajs-1013	28	20	of	of	ADP
iajs-1013	28	21	modules	module	NOUN
iajs-1013	28	22	,	,	PUNCT
iajs-1013	28	23	see	see	VERB
iajs-1013	28	24	proposition	proposition	NOUN
iajs-1013	28	25	3.4	3.4	NUM
iajs-1013	28	26	,	,	PUNCT
iajs-1013	28	27	while	while	SCONJ
iajs-1013	28	28	the	the	DET
iajs-1013	28	29	two	two	NUM
iajs-1013	28	30	concepts	concept	NOUN
iajs-1013	28	31	are	be	AUX
iajs-1013	28	32	equivalent	equivalent	ADJ
iajs-1013	28	33	in	in	ADP
iajs-1013	28	34	the	the	DET
iajs-1013	28	35	class	class	NOUN
iajs-1013	28	36	of	of	ADP
iajs-1013	28	37	uniform	uniform	ADJ
iajs-1013	28	38	modules	module	NOUN
iajs-1013	28	39	,	,	PUNCT
iajs-1013	28	40	see	see	VERB
iajs-1013	28	41	corollary	corollary	ADJ
iajs-1013	28	42	3.7	3.7	NUM
iajs-1013	28	43	and	and	CCONJ
iajs-1013	28	44	corollary	corollary	ADJ
iajs-1013	28	45	3.8	3.8	NUM
iajs-1013	28	46	.	.	PUNCT
iajs-1013	29	1	we	we	PRON
iajs-1013	29	2	established	establish	VERB
iajs-1013	29	3	in	in	ADP
iajs-1013	29	4	section	section	NOUN
iajs-1013	29	5	four	four	NUM
iajs-1013	29	6	certain	certain	ADJ
iajs-1013	29	7	relations	relation	NOUN
iajs-1013	29	8	between	between	ADP
iajs-1013	29	9	quasi	quasi	ADJ
iajs-1013	29	10	-	-	ADJ
iajs-1013	29	11	tight	tight	ADJ
iajs-1013	29	12	modules	module	NOUN
iajs-1013	29	13	and	and	CCONJ
iajs-1013	29	14	compressible	compressible	ADJ
iajs-1013	29	15	modules	module	NOUN
iajs-1013	29	16	in	in	ADP
iajs-1013	29	17	order	order	NOUN
iajs-1013	29	18	to	to	PART
iajs-1013	29	19	relate	relate	VERB
iajs-1013	29	20	weak	weak	ADJ
iajs-1013	29	21	relative	relative	ADJ
iajs-1013	29	22	quasi	quasi	NOUN
iajs-1013	29	23	-	-	NOUN
iajs-1013	29	24	injectivity	injectivity	NOUN
iajs-1013	29	25	and	and	CCONJ
iajs-1013	29	26	compressibility	compressibility	NOUN
iajs-1013	29	27	of	of	ADP
iajs-1013	29	28	modules	module	NOUN
iajs-1013	29	29	,	,	PUNCT
iajs-1013	29	30	where	where	SCONJ
iajs-1013	29	31	an	an	DET
iajs-1013	29	32	r	r	NOUN
iajs-1013	29	33	-	-	PUNCT
iajs-1013	29	34	module	module	NOUN
iajs-1013	29	35	m	m	NOUN
iajs-1013	29	36	is	be	AUX
iajs-1013	29	37	called	call	VERB
iajs-1013	29	38	compressible	compressible	ADJ
iajs-1013	29	39	,	,	PUNCT
iajs-1013	29	40	if	if	SCONJ
iajs-1013	29	41	for	for	ADP
iajs-1013	29	42	every	every	DET
iajs-1013	29	43	essential	essential	ADJ
iajs-1013	29	44	submodule	submodule	NOUN
iajs-1013	29	45	n	n	PROPN
iajs-1013	29	46	of	of	ADP
iajs-1013	29	47	m	m	PROPN
iajs-1013	29	48	,	,	PUNCT
iajs-1013	29	49	m	m	VERB
iajs-1013	29	50	embeds	embed	VERB
iajs-1013	29	51	in	in	ADP
iajs-1013	29	52	n	n	CCONJ
iajs-1013	29	53	,	,	PUNCT
iajs-1013	29	54	see	see	VERB
iajs-1013	29	55	[	[	X
iajs-1013	29	56	3	3	NUM
iajs-1013	29	57	]	]	PUNCT
iajs-1013	29	58	.	.	PUNCT
iajs-1013	30	1	some	some	PRON
iajs-1013	30	2	of	of	ADP
iajs-1013	30	3	the	the	DET
iajs-1013	30	4	results	result	NOUN
iajs-1013	30	5	of	of	ADP
iajs-1013	30	6	this	this	DET
iajs-1013	30	7	section	section	NOUN
iajs-1013	30	8	were	be	AUX
iajs-1013	30	9	given	give	VERB
iajs-1013	30	10	in	in	ADP
iajs-1013	30	11	:	:	PUNCT
iajs-1013	30	12	theorem	theorem	ADJ
iajs-1013	30	13	4.2	4.2	NUM
iajs-1013	30	14	,	,	PUNCT
iajs-1013	30	15	corollary	corollary	ADJ
iajs-1013	30	16	4.3	4.3	NUM
iajs-1013	30	17	,	,	PUNCT
iajs-1013	30	18	corollary	corollary	ADJ
iajs-1013	30	19	4.4	4.4	NUM
iajs-1013	30	20	and	and	CCONJ
iajs-1013	30	21	corollary	corollary	ADJ
iajs-1013	30	22	4.5	4.5	NUM
iajs-1013	30	23	.	.	PUNCT
iajs-1013	31	1	in	in	ADP
iajs-1013	31	2	the	the	DET
iajs-1013	31	3	last	last	ADJ
iajs-1013	31	4	section	section	NOUN
iajs-1013	31	5	of	of	ADP
iajs-1013	31	6	this	this	DET
iajs-1013	31	7	paper	paper	NOUN
iajs-1013	31	8	,	,	PUNCT
iajs-1013	31	9	we	we	PRON
iajs-1013	31	10	considered	consider	VERB
iajs-1013	31	11	those	those	DET
iajs-1013	31	12	modules	module	NOUN
iajs-1013	31	13	which	which	PRON
iajs-1013	31	14	are	be	AUX
iajs-1013	31	15	weakly	weakly	ADV
iajs-1013	31	16	quasiinjective	quasiinjective	ADJ
iajs-1013	31	17	relative	relative	NOUN
iajs-1013	31	18	to	to	ADP
iajs-1013	31	19	each	each	DET
iajs-1013	31	20	finitely	finitely	ADV
iajs-1013	31	21	generated	generate	VERB
iajs-1013	31	22	module	module	NOUN
iajs-1013	31	23	we	we	PRON
iajs-1013	31	24	would	would	AUX
iajs-1013	31	25	refer	refer	VERB
iajs-1013	31	26	to	to	ADP
iajs-1013	31	27	any	any	DET
iajs-1013	31	28	such	such	ADJ
iajs-1013	31	29	module	module	NOUN
iajs-1013	31	30	as	as	ADP
iajs-1013	31	31	being	be	AUX
iajs-1013	31	32	weakly	weakly	ADV
iajs-1013	31	33	-	-	PUNCT
iajs-1013	31	34	injective	injective	ADJ
iajs-1013	31	35	module	module	NOUN
iajs-1013	31	36	.	.	PUNCT
iajs-1013	32	1	we	we	PRON
iajs-1013	32	2	would	would	AUX
iajs-1013	32	3	establish	establish	VERB
iajs-1013	32	4	that	that	SCONJ
iajs-1013	32	5	:	:	PUNCT
iajs-1013	32	6	1	1	X
iajs-1013	32	7	.	.	X
iajs-1013	32	8	an	an	DET
iajs-1013	32	9	r	r	NOUN
iajs-1013	32	10	-	-	PUNCT
iajs-1013	32	11	module	module	NOUN
iajs-1013	32	12	m	m	NOUN
iajs-1013	32	13	is	be	AUX
iajs-1013	32	14	weakly	weakly	ADJ
iajs-1013	32	15	quasi	quasi	ADJ
iajs-1013	32	16	-	-	ADJ
iajs-1013	32	17	injective	injective	ADJ
iajs-1013	32	18	;	;	PUNCT
iajs-1013	33	1	i.	i.	NOUN
iajs-1013	33	2	if	if	SCONJ
iajs-1013	33	3	and	and	CCONJ
iajs-1013	33	4	only	only	ADV
iajs-1013	33	5	if	if	SCONJ
iajs-1013	33	6	m	m	NOUN
iajs-1013	33	7	is	be	AUX
iajs-1013	33	8	weakly	weakly	ADJ
iajs-1013	33	9	r	r	NOUN
iajs-1013	33	10	n	n	NUM
iajs-1013	33	11	–	–	PUNCT
iajs-1013	33	12	quasi	quasi	X
iajs-1013	33	13	–	–	PUNCT
iajs-1013	33	14	injective	injective	ADJ
iajs-1013	33	15	for	for	ADP
iajs-1013	33	16	all	all	DET
iajs-1013	33	17	positive	positive	ADJ
iajs-1013	33	18	integer	integer	NOUN
iajs-1013	33	19	n	n	CCONJ
iajs-1013	33	20	,	,	PUNCT
iajs-1013	33	21	see	see	VERB
iajs-1013	33	22	theorem	theorem	VERB
iajs-1013	33	23	5.3	5.3	NUM
iajs-1013	33	24	.	.	PUNCT
iajs-1013	33	25	ii	ii	PROPN
iajs-1013	33	26	.	.	PUNCT
iajs-1013	34	1	if	if	SCONJ
iajs-1013	34	2	and	and	CCONJ
iajs-1013	34	3	only	only	ADV
iajs-1013	34	4	if	if	SCONJ
iajs-1013	34	5	for	for	ADP
iajs-1013	34	6	all	all	DET
iajs-1013	34	7	x1	x1	PROPN
iajs-1013	34	8	,	,	PUNCT
iajs-1013	34	9	x2	x2	PROPN
iajs-1013	34	10	,	,	PUNCT
iajs-1013	34	11			PROPN
iajs-1013	34	12	,	,	PUNCT
iajs-1013	34	13	xn	xn	PROPN
iajs-1013	34	14			PROPN
iajs-1013	34	15			NUM
iajs-1013	34	16	,	,	PUNCT
iajs-1013	34	17	there	there	PRON
iajs-1013	34	18	exists	exist	VERB
iajs-1013	34	19	a	a	DET
iajs-1013	34	20	submodule	submodule	NOUN
iajs-1013	34	21	x	x	PUNCT
iajs-1013	34	22	of	of	ADP
iajs-1013	34	23			NUM
iajs-1013	34	24	such	such	ADJ
iajs-1013	34	25	that	that	PRON
iajs-1013	34	26	xi	xi	ADP
iajs-1013	34	27			PROPN
iajs-1013	34	28	x	x	PROPN
iajs-1013	35	1	≈	≈	PROPN
iajs-1013	35	2	m	m	PROPN
iajs-1013	35	3	for	for	ADP
iajs-1013	35	4	all	all	PRON
iajs-1013	35	5	i	i	PRON
iajs-1013	35	6	=	=	NOUN
iajs-1013	35	7	1	1	NUM
iajs-1013	35	8	,	,	PUNCT
iajs-1013	35	9	2	2	NUM
iajs-1013	35	10	,	,	PUNCT
iajs-1013	35	11			PROPN
iajs-1013	35	12	,	,	PUNCT
iajs-1013	35	13	n	n	CCONJ
iajs-1013	35	14	,	,	PUNCT
iajs-1013	35	15	see	see	VERB
iajs-1013	35	16	corollary	corollary	ADJ
iajs-1013	35	17	5.5	5.5	NUM
iajs-1013	35	18	.	.	PUNCT
iajs-1013	36	1	2	2	NUM
iajs-1013	36	2	.	.	X
iajs-1013	36	3	a	a	DET
iajs-1013	36	4	ring	ring	NOUN
iajs-1013	36	5	r	r	NOUN
iajs-1013	36	6	is	be	AUX
iajs-1013	36	7	weakly	weakly	ADJ
iajs-1013	36	8	r	r	NOUN
iajs-1013	36	9	n	n	NUM
iajs-1013	36	10	–	–	PUNCT
iajs-1013	36	11	quasi	quasi	X
iajs-1013	36	12	–	–	PUNCT
iajs-1013	36	13	injective	injective	ADJ
iajs-1013	36	14	if	if	SCONJ
iajs-1013	36	15	and	and	CCONJ
iajs-1013	36	16	only	only	ADV
iajs-1013	36	17	if	if	SCONJ
iajs-1013	36	18	for	for	ADP
iajs-1013	36	19	all	all	PRON
iajs-1013	36	20	x1	x1	PROPN
iajs-1013	36	21	,	,	PUNCT
iajs-1013	36	22	x2	x2	PROPN
iajs-1013	36	23	,	,	PUNCT
iajs-1013	36	24			PROPN
iajs-1013	36	25	,	,	PUNCT
iajs-1013	37	1	xn	xn	PROPN
iajs-1013	37	2	r	r	NOUN
iajs-1013	37	3	,	,	PUNCT
iajs-1013	37	4	there	there	PRON
iajs-1013	37	5	exists	exist	VERB
iajs-1013	37	6	an	an	DET
iajs-1013	37	7	element	element	NOUN
iajs-1013	37	8	b	b	PROPN
iajs-1013	37	9			PROPN
iajs-1013	37	10	r	r	NOUN
iajs-1013	38	1	such	such	ADJ
iajs-1013	38	2	that	that	PRON
iajs-1013	38	3	annr(b	annr(b	PROPN
iajs-1013	38	4	)	)	PUNCT
iajs-1013	38	5	=	=	SYM
iajs-1013	38	6	0	0	NUM
iajs-1013	38	7	and	and	CCONJ
iajs-1013	38	8	xi	xi	ADP
iajs-1013	38	9			PROPN
iajs-1013	38	10	r	r	NOUN
iajs-1013	38	11	b	b	PROPN
iajs-1013	38	12	for	for	ADP
iajs-1013	38	13	all	all	DET
iajs-1013	38	14	i	i	PRON
iajs-1013	38	15	=	=	NOUN
iajs-1013	38	16	1	1	NUM
iajs-1013	38	17	,	,	PUNCT
iajs-1013	38	18	2	2	NUM
iajs-1013	38	19	,	,	PUNCT
iajs-1013	38	20			PROPN
iajs-1013	38	21	,	,	PUNCT
iajs-1013	38	22	n	n	CCONJ
iajs-1013	38	23	,	,	PUNCT
iajs-1013	38	24	see	see	VERB
iajs-1013	38	25	proposition	proposition	NOUN
iajs-1013	38	26	5.6	5.6	NUM
iajs-1013	38	27	.	.	PUNCT
iajs-1013	39	1	3	3	X
iajs-1013	39	2	.	.	X
iajs-1013	39	3	a	a	DET
iajs-1013	39	4	cyclic	cyclic	ADJ
iajs-1013	39	5	r	r	NOUN
iajs-1013	39	6	-	-	PUNCT
iajs-1013	39	7	module	module	NOUN
iajs-1013	39	8	is	be	AUX
iajs-1013	39	9	weakly	weakly	ADJ
iajs-1013	39	10	quasi	quasi	ADJ
iajs-1013	39	11	-	-	ADJ
iajs-1013	39	12	injective	injective	ADJ
iajs-1013	39	13	if	if	SCONJ
iajs-1013	40	1	and	and	CCONJ
iajs-1013	40	2	only	only	ADV
iajs-1013	40	3	if	if	SCONJ
iajs-1013	40	4	it	it	PRON
iajs-1013	40	5	is	be	AUX
iajs-1013	40	6	weakly	weakly	ADJ
iajs-1013	40	7	r	r	NOUN
iajs-1013	40	8	2	2	NUM
iajs-1013	40	9	-quasiinjective	-quasiinjective	NOUN
iajs-1013	40	10	,	,	PUNCT
iajs-1013	40	11	see	see	VERB
iajs-1013	40	12	proposition	proposition	NOUN
iajs-1013	40	13	5.8	5.8	NUM
iajs-1013	40	14	.	.	PUNCT
iajs-1013	41	1	section	section	NOUN
iajs-1013	41	2	one	one	NUM
iajs-1013	41	3	:	:	PUNCT
iajs-1013	41	4	weakly	weakly	ADJ
iajs-1013	41	5	relative	relative	ADJ
iajs-1013	41	6	quasi	quasi	ADJ
iajs-1013	41	7	-	-	ADJ
iajs-1013	41	8	injective	injective	ADJ
iajs-1013	41	9	modules	module	NOUN
iajs-1013	41	10	we	we	PRON
iajs-1013	41	11	shall	shall	AUX
iajs-1013	41	12	introduce	introduce	VERB
iajs-1013	41	13	in	in	ADP
iajs-1013	41	14	this	this	DET
iajs-1013	41	15	section	section	NOUN
iajs-1013	41	16	the	the	DET
iajs-1013	41	17	concept	concept	NOUN
iajs-1013	41	18	of	of	ADP
iajs-1013	41	19	weakly	weakly	ADJ
iajs-1013	41	20	relative	relative	ADJ
iajs-1013	41	21	qusi	qusi	NOUN
iajs-1013	41	22	-	-	PUNCT
iajs-1013	41	23	injectivity	injectivity	NOUN
iajs-1013	41	24	of	of	ADP
iajs-1013	41	25	modules	module	NOUN
iajs-1013	41	26	.	.	PUNCT
iajs-1013	42	1	the	the	DET
iajs-1013	42	2	relation	relation	NOUN
iajs-1013	42	3	between	between	ADP
iajs-1013	42	4	weakly	weakly	ADJ
iajs-1013	42	5	relative	relative	ADJ
iajs-1013	42	6	quasi	quasi	ADJ
iajs-1013	42	7	-	-	ADJ
iajs-1013	42	8	injective	injective	ADJ
iajs-1013	42	9	modules	module	NOUN
iajs-1013	42	10	and	and	CCONJ
iajs-1013	42	11	certain	certain	ADJ
iajs-1013	42	12	types	type	NOUN
iajs-1013	42	13	of	of	ADP
iajs-1013	42	14	modules	module	NOUN
iajs-1013	42	15	are	be	AUX
iajs-1013	42	16	studied	study	VERB
iajs-1013	42	17	.	.	PUNCT
iajs-1013	43	1	some	some	DET
iajs-1013	43	2	properties	property	NOUN
iajs-1013	43	3	of	of	ADP
iajs-1013	43	4	weakly	weakly	ADJ
iajs-1013	43	5	relative	relative	ADJ
iajs-1013	43	6	quasi	quasi	ADJ
iajs-1013	43	7	-	-	ADJ
iajs-1013	43	8	injective	injective	ADJ
iajs-1013	43	9	modules	module	NOUN
iajs-1013	43	10	are	be	AUX
iajs-1013	43	11	established	establish	VERB
iajs-1013	43	12	.	.	PUNCT
iajs-1013	44	1	1.1	1.1	NUM
iajs-1013	44	2	definition	definition	NOUN
iajs-1013	44	3	let	let	VERB
iajs-1013	44	4	m	m	PRON
iajs-1013	44	5	and	and	CCONJ
iajs-1013	44	6	n	n	CCONJ
iajs-1013	44	7	be	be	VERB
iajs-1013	44	8	two	two	NUM
iajs-1013	44	9	r	r	NOUN
iajs-1013	44	10	-	-	PUNCT
iajs-1013	44	11	modules	module	NOUN
iajs-1013	44	12	.	.	PUNCT
iajs-1013	45	1	m	m	PROPN
iajs-1013	45	2	is	be	AUX
iajs-1013	45	3	called	call	VERB
iajs-1013	45	4	weakly	weakly	ADJ
iajs-1013	45	5	n	n	CCONJ
iajs-1013	45	6	-	-	PUNCT
iajs-1013	45	7	quasi	quasi	NOUN
iajs-1013	45	8	-	-	ADJ
iajs-1013	45	9	injective	injective	ADJ
iajs-1013	45	10	,	,	PUNCT
iajs-1013	45	11	if	if	SCONJ
iajs-1013	45	12	for	for	ADP
iajs-1013	45	13	each	each	DET
iajs-1013	45	14	f	f	PROPN
iajs-1013	45	15			PROPN
iajs-1013	45	16	hom(n,	hom(n,	NOUN
iajs-1013	45	17	)	)	PUNCT
iajs-1013	45	18	,	,	PUNCT
iajs-1013	45	19	there	there	PRON
iajs-1013	45	20	exists	exist	VERB
iajs-1013	45	21	a	a	DET
iajs-1013	45	22	submodule	submodule	NOUN
iajs-1013	45	23	x	x	PUNCT
iajs-1013	45	24	of	of	ADP
iajs-1013	45	25			NUM
iajs-1013	46	1	such	such	ADJ
iajs-1013	46	2	that	that	SCONJ
iajs-1013	46	3	f	f	PROPN
iajs-1013	46	4	(	(	PUNCT
iajs-1013	46	5	n	n	CCONJ
iajs-1013	46	6	)	)	PUNCT
iajs-1013	46	7			PROPN
iajs-1013	46	8	x	x	PUNCT
iajs-1013	46	9	≈	≈	PROPN
iajs-1013	46	10	m	m	PROPN
iajs-1013	46	11	,	,	PUNCT
iajs-1013	46	12	where	where	SCONJ
iajs-1013	46	13			PROPN
iajs-1013	46	14	is	be	AUX
iajs-1013	46	15	the	the	DET
iajs-1013	46	16	quasi	quasi	ADJ
iajs-1013	46	17	-	-	ADJ
iajs-1013	46	18	injective	injective	ADJ
iajs-1013	46	19	hull	hull	NOUN
iajs-1013	46	20	of	of	ADP
iajs-1013	46	21	m.	m.	NOUN
iajs-1013	46	22	ibn	ibn	PROPN
iajs-1013	46	23	alhaitham	alhaitham	PROPN
iajs-1013	46	24	j.	j.	PROPN
iajs-1013	46	25	for	for	ADP
iajs-1013	46	26	pure	pure	ADJ
iajs-1013	46	27	&	&	CCONJ
iajs-1013	46	28	appl	appl	PROPN
iajs-1013	46	29	.	.	PUNCT
iajs-1013	47	1	sci	sci	PROPN
iajs-1013	47	2	.	.	PUNCT
iajs-1013	48	1	vol.23	vol.23	PROPN
iajs-1013	48	2	(	(	PUNCT
iajs-1013	48	3	1	1	NUM
iajs-1013	48	4	)	)	PUNCT
iajs-1013	48	5	2010	2010	NUM
iajs-1013	48	6	1.2	1.2	NUM
iajs-1013	48	7	remark	remark	NOUN
iajs-1013	48	8	let	let	VERB
iajs-1013	48	9	m	m	PRON
iajs-1013	48	10	and	and	CCONJ
iajs-1013	48	11	n	n	CCONJ
iajs-1013	48	12	be	be	VERB
iajs-1013	48	13	two	two	NUM
iajs-1013	48	14	r	r	NOUN
iajs-1013	48	15	-	-	PUNCT
iajs-1013	48	16	modules	module	NOUN
iajs-1013	48	17	.	.	PUNCT
iajs-1013	49	1	then	then	ADV
iajs-1013	49	2	i.	i.	PROPN
iajs-1013	49	3	if	if	SCONJ
iajs-1013	49	4	m	m	NOUN
iajs-1013	49	5	is	be	AUX
iajs-1013	49	6	weakly	weakly	ADJ
iajs-1013	49	7	n	n	CCONJ
iajs-1013	49	8	-	-	PUNCT
iajs-1013	49	9	injective	injective	ADJ
iajs-1013	49	10	,	,	PUNCT
iajs-1013	49	11	then	then	ADV
iajs-1013	49	12	m	m	NOUN
iajs-1013	49	13	is	be	AUX
iajs-1013	49	14	weakly	weakly	ADJ
iajs-1013	49	15	n	n	CCONJ
iajs-1013	49	16	-	-	PUNCT
iajs-1013	49	17	quasi	quasi	NOUN
iajs-1013	49	18	-	-	ADJ
iajs-1013	49	19	injective	injective	ADJ
iajs-1013	49	20	and	and	CCONJ
iajs-1013	49	21	the	the	DET
iajs-1013	49	22	converse	converse	NOUN
iajs-1013	49	23	is	be	AUX
iajs-1013	49	24	not	not	PART
iajs-1013	49	25	true	true	ADJ
iajs-1013	49	26	in	in	ADP
iajs-1013	49	27	general	general	ADJ
iajs-1013	49	28	.	.	PUNCT
iajs-1013	50	1	ii	ii	PROPN
iajs-1013	50	2	.	.	PUNCT
iajs-1013	51	1	if	if	SCONJ
iajs-1013	51	2	m	m	PROPN
iajs-1013	51	3	is	be	AUX
iajs-1013	51	4	n	n	CCONJ
iajs-1013	51	5	-	-	PUNCT
iajs-1013	51	6	quasi	quasi	NOUN
iajs-1013	51	7	-	-	ADJ
iajs-1013	51	8	injective	injective	ADJ
iajs-1013	51	9	,	,	PUNCT
iajs-1013	51	10	then	then	ADV
iajs-1013	51	11	m	m	NOUN
iajs-1013	51	12	is	be	AUX
iajs-1013	51	13	weakly	weakly	ADJ
iajs-1013	51	14	n	n	CCONJ
iajs-1013	51	15	-	-	PUNCT
iajs-1013	51	16	quasi	quasi	NOUN
iajs-1013	51	17	-	-	ADJ
iajs-1013	51	18	injective	injective	ADJ
iajs-1013	51	19	and	and	CCONJ
iajs-1013	51	20	the	the	DET
iajs-1013	51	21	converse	converse	NOUN
iajs-1013	51	22	is	be	AUX
iajs-1013	51	23	not	not	PART
iajs-1013	51	24	true	true	ADJ
iajs-1013	51	25	in	in	ADP
iajs-1013	51	26	general	general	ADJ
iajs-1013	51	27	.	.	PUNCT
iajs-1013	52	1	iii	iii	X
iajs-1013	52	2	.	.	PUNCT
iajs-1013	53	1	if	if	SCONJ
iajs-1013	53	2	m	m	NOUN
iajs-1013	53	3	is	be	AUX
iajs-1013	53	4	quasi	quasi	ADJ
iajs-1013	53	5	-	-	ADJ
iajs-1013	53	6	injective	injective	ADJ
iajs-1013	53	7	,	,	PUNCT
iajs-1013	53	8	then	then	ADV
iajs-1013	53	9	m	m	NOUN
iajs-1013	53	10	is	be	AUX
iajs-1013	53	11	weakly	weakly	ADJ
iajs-1013	53	12	n	n	CCONJ
iajs-1013	53	13	-	-	PUNCT
iajs-1013	53	14	quasi	quasi	NOUN
iajs-1013	53	15	-	-	ADJ
iajs-1013	53	16	injective	injective	ADJ
iajs-1013	53	17	and	and	CCONJ
iajs-1013	53	18	the	the	DET
iajs-1013	53	19	converse	converse	NOUN
iajs-1013	53	20	is	be	AUX
iajs-1013	53	21	not	not	PART
iajs-1013	53	22	true	true	ADJ
iajs-1013	53	23	in	in	ADP
iajs-1013	53	24	general	general	ADJ
iajs-1013	53	25	.	.	PUNCT
iajs-1013	54	1	to	to	PART
iajs-1013	54	2	disprove	disprove	VERB
iajs-1013	54	3	the	the	DET
iajs-1013	54	4	validity	validity	NOUN
iajs-1013	54	5	of	of	ADP
iajs-1013	54	6	the	the	DET
iajs-1013	54	7	converse	converse	NOUN
iajs-1013	54	8	of	of	ADP
iajs-1013	54	9	the	the	DET
iajs-1013	54	10	above	above	ADJ
iajs-1013	54	11	remarks	remark	NOUN
iajs-1013	54	12	consider	consider	VERB
iajs-1013	54	13	the	the	DET
iajs-1013	54	14	following	follow	VERB
iajs-1013	54	15	examples	example	NOUN
iajs-1013	54	16	respectively	respectively	ADV
iajs-1013	54	17	:	:	PUNCT
iajs-1013	54	18	1.3	1.3	NUM
iajs-1013	54	19	example	example	NOUN
iajs-1013	54	20	i.	i.	NOUN
iajs-1013	54	21	let	let	VERB
iajs-1013	54	22	m	m	VERB
iajs-1013	54	23	=	=	SYM
iajs-1013	54	24	z2	z2	PROPN
iajs-1013	54	25	,	,	PUNCT
iajs-1013	54	26	n	n	NOUN
iajs-1013	54	27	=	=	SYM
iajs-1013	54	28	z	z	PROPN
iajs-1013	54	29	and	and	CCONJ
iajs-1013	54	30	r	r	PROPN
iajs-1013	54	31	=	=	SYM
iajs-1013	54	32	z.	z.	PROPN
iajs-1013	54	33	since	since	SCONJ
iajs-1013	54	34	z2	z2	PROPN
iajs-1013	54	35	is	be	AUX
iajs-1013	54	36	a	a	DET
iajs-1013	54	37	quasi	quasi	ADJ
iajs-1013	54	38	-	-	ADJ
iajs-1013	54	39	injective	injective	ADJ
iajs-1013	54	40	z	z	NOUN
iajs-1013	54	41	-	-	PUNCT
iajs-1013	54	42	module	module	NOUN
iajs-1013	54	43	,	,	PUNCT
iajs-1013	54	44	then	then	ADV
iajs-1013	54	45	z2	z2	PROPN
iajs-1013	54	46	is	be	AUX
iajs-1013	54	47	z	z	NOUN
iajs-1013	54	48	-	-	PUNCT
iajs-1013	54	49	quasiinjective	quasiinjective	NOUN
iajs-1013	54	50	and	and	CCONJ
iajs-1013	54	51	hence	hence	ADV
iajs-1013	54	52	weakly	weakly	ADJ
iajs-1013	54	53	z	z	NOUN
iajs-1013	54	54	-	-	PUNCT
iajs-1013	54	55	quasi	quasi	ADJ
iajs-1013	54	56	-	-	ADJ
iajs-1013	54	57	injective	injective	ADJ
iajs-1013	54	58	.	.	PUNCT
iajs-1013	55	1	however	however	ADV
iajs-1013	55	2	,	,	PUNCT
iajs-1013	55	3	z2	z2	PROPN
iajs-1013	55	4	is	be	AUX
iajs-1013	55	5	not	not	PART
iajs-1013	55	6	weakly	weakly	ADJ
iajs-1013	55	7	z	z	NOUN
iajs-1013	55	8	-	-	PUNCT
iajs-1013	55	9	injective	injective	ADJ
iajs-1013	55	10	,	,	PUNCT
iajs-1013	55	11	for	for	ADP
iajs-1013	55	12	if	if	SCONJ
iajs-1013	55	13	,	,	PUNCT
iajs-1013	55	14	f	f	X
iajs-1013	55	15	:	:	PUNCT
iajs-1013	55	16	z	z	PROPN
iajs-1013	55	17			NOUN
iajs-1013	55	18	2	2	NUM
iajs-1013	55	19			PROPN
iajs-1013	55	20	=	=	SYM
iajs-1013	55	21	e(z2	e(z2	NOUN
iajs-1013	55	22	)	)	PUNCT
iajs-1013	55	23	(	(	PUNCT
iajs-1013	55	24	the	the	DET
iajs-1013	55	25	injective	injective	ADJ
iajs-1013	55	26	hull	hull	NOUN
iajs-1013	55	27	of	of	ADP
iajs-1013	55	28	z2	z2	PROPN
iajs-1013	55	29	)	)	PUNCT
iajs-1013	55	30	,	,	PUNCT
iajs-1013	55	31	is	be	AUX
iajs-1013	55	32	such	such	ADJ
iajs-1013	55	33	that	that	SCONJ
iajs-1013	55	34	f	f	PROPN
iajs-1013	55	35	(	(	PUNCT
iajs-1013	55	36	a	a	X
iajs-1013	55	37	)	)	PUNCT
iajs-1013	55	38	=	=	SYM
iajs-1013	55	39	32	32	NUM
iajs-1013	55	40	a	a	DET
iajs-1013	55	41	+	+	X
iajs-1013	55	42	z	z	NOUN
iajs-1013	55	43	for	for	ADP
iajs-1013	55	44	all	all	DET
iajs-1013	55	45	a	a	DET
iajs-1013	55	46			PROPN
iajs-1013	55	47	z	z	PROPN
iajs-1013	55	48	,	,	PUNCT
iajs-1013	55	49	then	then	ADV
iajs-1013	55	50	f	f	PROPN
iajs-1013	55	51			PROPN
iajs-1013	55	52	hom(z	hom(z	PROPN
iajs-1013	55	53	,	,	PUNCT
iajs-1013	55	54	2	2	NUM
iajs-1013	55	55			PROPN
iajs-1013	55	56	)	)	PUNCT
iajs-1013	55	57	and	and	CCONJ
iajs-1013	55	58	f	f	PROPN
iajs-1013	55	59	(	(	PUNCT
iajs-1013	55	60	z	z	NOUN
iajs-1013	55	61	)	)	PUNCT
iajs-1013	56	1	≈	≈	PROPN
iajs-1013	56	2	z8	z8	NOUN
iajs-1013	56	3	which	which	PRON
iajs-1013	56	4	is	be	AUX
iajs-1013	56	5	not	not	PART
iajs-1013	56	6	embed	embe	VERB
iajs-1013	56	7	in	in	ADP
iajs-1013	56	8	z2	z2	PROPN
iajs-1013	56	9	.	.	PUNCT
iajs-1013	57	1	ii	ii	PROPN
iajs-1013	57	2	.	.	PUNCT
iajs-1013	58	1	let	let	VERB
iajs-1013	58	2	m	m	VERB
iajs-1013	58	3	=	=	PROPN
iajs-1013	58	4	z	z	PROPN
iajs-1013	58	5	,	,	PUNCT
iajs-1013	58	6	n	n	NOUN
iajs-1013	58	7	=	=	NUM
iajs-1013	58	8	2z	2z	NOUN
iajs-1013	58	9	,	,	PUNCT
iajs-1013	58	10	r	r	NOUN
iajs-1013	58	11	=	=	SYM
iajs-1013	58	12	z	z	PROPN
iajs-1013	58	13	and	and	CCONJ
iajs-1013	58	14	f	f	PROPN
iajs-1013	58	15	:	:	PUNCT
iajs-1013	59	1	2z	2z	NUM
iajs-1013	59	2			X
iajs-1013	59	3	q	q	X
iajs-1013	59	4	is	be	AUX
iajs-1013	59	5	such	such	ADJ
iajs-1013	59	6	that	that	SCONJ
iajs-1013	59	7	f	f	PROPN
iajs-1013	59	8	(	(	PUNCT
iajs-1013	59	9	2a	2a	NUM
iajs-1013	59	10	)	)	PUNCT
iajs-1013	59	11	=	=	SYM
iajs-1013	59	12	2	2	NUM
iajs-1013	59	13	5	5	NUM
iajs-1013	59	14	a	a	DET
iajs-1013	59	15	+	+	X
iajs-1013	59	16	z	z	NOUN
iajs-1013	59	17	for	for	ADP
iajs-1013	59	18	all	all	DET
iajs-1013	59	19	a	a	DET
iajs-1013	59	20			PROPN
iajs-1013	59	21	z	z	PROPN
iajs-1013	59	22	,	,	PUNCT
iajs-1013	59	23	then	then	ADV
iajs-1013	59	24	f	f	PROPN
iajs-1013	59	25			PROPN
iajs-1013	59	26	hom(2z	hom(2z	PROPN
iajs-1013	59	27	,	,	PUNCT
iajs-1013	59	28	q	q	NOUN
iajs-1013	59	29	)	)	PUNCT
iajs-1013	59	30	.	.	PUNCT
iajs-1013	60	1	we	we	PRON
iajs-1013	60	2	take	take	VERB
iajs-1013	60	3	x	x	SYM
iajs-1013	60	4	=	=	SYM
iajs-1013	60	5	2	2	NUM
iajs-1013	60	6	(	(	PUNCT
iajs-1013	60	7	)	)	PUNCT
iajs-1013	60	8	5	5	NUM
iajs-1013	60	9	the	the	DET
iajs-1013	60	10	submodule	submodule	NOUN
iajs-1013	60	11	of	of	ADP
iajs-1013	60	12	q	q	PROPN
iajs-1013	60	13	generated	generate	VERB
iajs-1013	60	14	by	by	ADP
iajs-1013	60	15	2	2	NUM
iajs-1013	60	16	5	5	NUM
iajs-1013	60	17	and	and	CCONJ
iajs-1013	60	18	consequently	consequently	ADV
iajs-1013	60	19	f	f	X
iajs-1013	60	20	(	(	PUNCT
iajs-1013	60	21	2z	2z	NUM
iajs-1013	60	22	)	)	PUNCT
iajs-1013	60	23			PROPN
iajs-1013	60	24	2	2	NUM
iajs-1013	60	25	(	(	PUNCT
iajs-1013	60	26	)	)	PUNCT
iajs-1013	60	27	5	5	NUM
iajs-1013	60	28	.	.	PUNCT
iajs-1013	61	1	hence	hence	ADV
iajs-1013	61	2	z	z	PROPN
iajs-1013	61	3	is	be	AUX
iajs-1013	61	4	weakly	weakly	ADJ
iajs-1013	61	5	2z	2z	NUM
iajs-1013	61	6	-	-	PUNCT
iajs-1013	61	7	quasi	quasi	NOUN
iajs-1013	61	8	-	-	ADJ
iajs-1013	61	9	injective	injective	ADJ
iajs-1013	61	10	.	.	PUNCT
iajs-1013	62	1	however	however	ADV
iajs-1013	62	2	,	,	PUNCT
iajs-1013	62	3	z	z	PROPN
iajs-1013	62	4	is	be	AUX
iajs-1013	62	5	not	not	PART
iajs-1013	62	6	2z	2z	NUM
iajs-1013	62	7	-	-	PUNCT
iajs-1013	62	8	quasi	quasi	NOUN
iajs-1013	62	9	-	-	ADJ
iajs-1013	62	10	injective	injective	ADJ
iajs-1013	62	11	,	,	PUNCT
iajs-1013	62	12	since	since	SCONJ
iajs-1013	62	13	f	f	PROPN
iajs-1013	62	14	(	(	PUNCT
iajs-1013	62	15	2z	2z	NUM
iajs-1013	62	16	)	)	PUNCT
iajs-1013	62	17			PROPN
iajs-1013	62	18	z.	z.	PROPN
iajs-1013	62	19	iii	iii	PROPN
iajs-1013	62	20	.	.	PUNCT
iajs-1013	63	1	let	let	VERB
iajs-1013	63	2	m	m	PROPN
iajs-1013	63	3	=	=	SYM
iajs-1013	64	1	z	z	NOUN
iajs-1013	64	2	,	,	PUNCT
iajs-1013	64	3	n	n	NOUN
iajs-1013	64	4	=	=	NOUN
iajs-1013	64	5	2z	2z	NUM
iajs-1013	64	6	and	and	CCONJ
iajs-1013	64	7	r	r	NOUN
iajs-1013	64	8	=	=	PUNCT
iajs-1013	64	9	z.	z.	PROPN
iajs-1013	64	10	then	then	ADV
iajs-1013	64	11	z	z	PROPN
iajs-1013	64	12	is	be	AUX
iajs-1013	64	13	weakly	weakly	ADJ
iajs-1013	64	14	2z	2z	NUM
iajs-1013	64	15	-	-	PUNCT
iajs-1013	64	16	quasi	quasi	NOUN
iajs-1013	64	17	-	-	ADJ
iajs-1013	64	18	injective	injective	ADJ
iajs-1013	64	19	,	,	PUNCT
iajs-1013	64	20	but	but	CCONJ
iajs-1013	64	21	z	z	NOUN
iajs-1013	64	22	is	be	AUX
iajs-1013	64	23	not	not	PART
iajs-1013	64	24	quasiinjective	quasiinjective	ADJ
iajs-1013	64	25	.	.	PUNCT
iajs-1013	65	1	1.4	1.4	NUM
iajs-1013	65	2	proposition	proposition	NOUN
iajs-1013	65	3	let	let	VERB
iajs-1013	65	4	m	m	PRON
iajs-1013	65	5	and	and	CCONJ
iajs-1013	65	6	n	n	CCONJ
iajs-1013	65	7	be	be	VERB
iajs-1013	65	8	two	two	NUM
iajs-1013	65	9	r	r	NOUN
iajs-1013	65	10	-	-	PUNCT
iajs-1013	65	11	modules	module	NOUN
iajs-1013	65	12	and	and	CCONJ
iajs-1013	65	13	let	let	VERB
iajs-1013	65	14	i	i	PRON
iajs-1013	65	15	be	be	AUX
iajs-1013	65	16	an	an	DET
iajs-1013	65	17	ideal	ideal	NOUN
iajs-1013	65	18	of	of	ADP
iajs-1013	65	19	r	r	NOUN
iajs-1013	65	20	such	such	ADJ
iajs-1013	65	21	that	that	SCONJ
iajs-1013	65	22	i	i	PRON
iajs-1013	65	23			PROPN
iajs-1013	65	24	annr(	annr(	PROPN
iajs-1013	65	25	)	)	PUNCT
iajs-1013	65	26			X
iajs-1013	65	27	annr(n	annr(n	PROPN
iajs-1013	65	28	)	)	PUNCT
iajs-1013	65	29	.	.	PUNCT
iajs-1013	66	1	then	then	ADV
iajs-1013	66	2	m	m	PROPN
iajs-1013	66	3	is	be	AUX
iajs-1013	66	4	weakly	weakly	ADJ
iajs-1013	66	5	n	n	CCONJ
iajs-1013	66	6	-	-	PUNCT
iajs-1013	66	7	quasi	quasi	ADJ
iajs-1013	66	8	-	-	ADJ
iajs-1013	66	9	injective	injective	ADJ
iajs-1013	66	10	r	r	NOUN
iajs-1013	66	11	-	-	PUNCT
iajs-1013	66	12	module	module	NOUN
iajs-1013	66	13	if	if	SCONJ
iajs-1013	66	14	and	and	CCONJ
iajs-1013	66	15	only	only	ADV
iajs-1013	66	16	if	if	SCONJ
iajs-1013	66	17	m	m	NOUN
iajs-1013	66	18	is	be	AUX
iajs-1013	66	19	weakly	weakly	ADJ
iajs-1013	66	20	n	n	CCONJ
iajs-1013	66	21	-	-	PUNCT
iajs-1013	66	22	quasiinjective	quasiinjective	NOUN
iajs-1013	66	23	r	r	NOUN
iajs-1013	66	24	/	/	SYM
iajs-1013	66	25	i	i	NOUN
iajs-1013	66	26	-	-	PUNCT
iajs-1013	66	27	module	module	NOUN
iajs-1013	66	28	.	.	PUNCT
iajs-1013	67	1	proof	proof	NOUN
iajs-1013	67	2	:	:	PUNCT
iajs-1013	68	1	i	i	PRON
iajs-1013	68	2			PROPN
iajs-1013	68	3	annr(	annr(	PROPN
iajs-1013	68	4	)	)	PUNCT
iajs-1013	68	5			X
iajs-1013	68	6	annr(n	annr(n	NOUN
iajs-1013	68	7	)	)	PUNCT
iajs-1013	68	8	,	,	PUNCT
iajs-1013	68	9	implies	imply	VERB
iajs-1013	68	10	that	that	SCONJ
iajs-1013	68	11	m	m	VERB
iajs-1013	68	12	and	and	CCONJ
iajs-1013	68	13	n	n	PROPN
iajs-1013	68	14	are	be	AUX
iajs-1013	68	15	r	r	NOUN
iajs-1013	68	16	/	/	SYM
iajs-1013	68	17	i	i	NOUN
iajs-1013	68	18	-	-	PUNCT
iajs-1013	68	19	modules	module	NOUN
iajs-1013	68	20	.	.	PUNCT
iajs-1013	69	1	moreover	moreover	ADV
iajs-1013	69	2	,	,	PUNCT
iajs-1013	69	3	f	f	X
iajs-1013	69	4	:	:	PUNCT
iajs-1013	69	5	n	n	CCONJ
iajs-1013	69	6			PROPN
iajs-1013	69	7			PROPN
iajs-1013	69	8	is	be	AUX
iajs-1013	69	9	an	an	DET
iajs-1013	69	10	r	r	NOUN
iajs-1013	69	11	-	-	PUNCT
iajs-1013	69	12	homomorphism	homomorphism	NOUN
iajs-1013	69	13	if	if	SCONJ
iajs-1013	69	14	and	and	CCONJ
iajs-1013	69	15	only	only	ADV
iajs-1013	69	16	if	if	SCONJ
iajs-1013	69	17	f	f	PROPN
iajs-1013	69	18	is	be	AUX
iajs-1013	69	19	an	an	DET
iajs-1013	69	20	r	r	NOUN
iajs-1013	69	21	/	/	SYM
iajs-1013	69	22	i	i	NOUN
iajs-1013	69	23	–	–	PUNCT
iajs-1013	69	24	homomorphism	homomorphism	NOUN
iajs-1013	69	25	,	,	PUNCT
iajs-1013	69	26	and	and	CCONJ
iajs-1013	69	27	x	x	X
iajs-1013	69	28	is	be	AUX
iajs-1013	69	29	an	an	DET
iajs-1013	69	30	rsubmodule	rsubmodule	NOUN
iajs-1013	69	31	of	of	ADP
iajs-1013	69	32			PROPN
iajs-1013	69	33	if	if	SCONJ
iajs-1013	69	34	and	and	CCONJ
iajs-1013	69	35	only	only	ADV
iajs-1013	69	36	if	if	SCONJ
iajs-1013	69	37	x	x	PRON
iajs-1013	69	38	is	be	AUX
iajs-1013	69	39	an	an	DET
iajs-1013	69	40	r	r	NOUN
iajs-1013	69	41	/	/	SYM
iajs-1013	69	42	i	i	PROPN
iajs-1013	69	43	–	–	PUNCT
iajs-1013	69	44	submodule	submodule	NOUN
iajs-1013	69	45	of	of	ADP
iajs-1013	69	46			PROPN
iajs-1013	69	47	.	.	PUNCT
iajs-1013	70	1	hence	hence	ADV
iajs-1013	70	2	the	the	DET
iajs-1013	70	3	details	detail	NOUN
iajs-1013	70	4	of	of	ADP
iajs-1013	70	5	the	the	DET
iajs-1013	70	6	proof	proof	NOUN
iajs-1013	70	7	are	be	AUX
iajs-1013	70	8	followed	follow	VERB
iajs-1013	70	9	directly	directly	ADV
iajs-1013	70	10	by	by	ADP
iajs-1013	70	11	using	use	VERB
iajs-1013	70	12	the	the	DET
iajs-1013	70	13	definition	definition	NOUN
iajs-1013	70	14	1.1	1.1	NUM
iajs-1013	70	15	.	.	PUNCT
iajs-1013	71	1	1.5	1.5	NUM
iajs-1013	71	2	remark	remark	VERB
iajs-1013	71	3	a	a	DET
iajs-1013	71	4	direct	direct	ADJ
iajs-1013	71	5	summand	summand	NOUN
iajs-1013	71	6	of	of	ADP
iajs-1013	71	7	weakly	weakly	ADJ
iajs-1013	71	8	relative	relative	ADJ
iajs-1013	71	9	quasi	quasi	ADJ
iajs-1013	71	10	-	-	ADJ
iajs-1013	71	11	injective	injective	ADJ
iajs-1013	71	12	module	module	NOUN
iajs-1013	71	13	is	be	AUX
iajs-1013	71	14	not	not	PART
iajs-1013	71	15	weakly	weakly	ADJ
iajs-1013	71	16	relative	relative	ADJ
iajs-1013	71	17	quasiinjective	quasiinjective	NOUN
iajs-1013	71	18	in	in	ADP
iajs-1013	71	19	general	general	ADJ
iajs-1013	71	20	,	,	PUNCT
iajs-1013	71	21	as	as	SCONJ
iajs-1013	71	22	it	it	PRON
iajs-1013	71	23	is	be	AUX
iajs-1013	71	24	shown	show	VERB
iajs-1013	71	25	in	in	ADP
iajs-1013	71	26	the	the	DET
iajs-1013	71	27	following	follow	VERB
iajs-1013	71	28	example	example	NOUN
iajs-1013	71	29	.	.	PUNCT
iajs-1013	72	1	1.6	1.6	NUM
iajs-1013	72	2	example	example	NOUN
iajs-1013	72	3	let	let	VERB
iajs-1013	72	4	m	m	VERB
iajs-1013	72	5	=	=	X
iajs-1013	72	6	z	z	X
iajs-1013	72	7			PROPN
iajs-1013	72	8	q	q	NOUN
iajs-1013	72	9	,	,	PUNCT
iajs-1013	72	10	n	n	NOUN
iajs-1013	72	11	=	=	PUNCT
iajs-1013	72	12	q	q	NOUN
iajs-1013	72	13	and	and	CCONJ
iajs-1013	72	14	r	r	NOUN
iajs-1013	72	15	=	=	PUNCT
iajs-1013	72	16	z.	z.	PROPN
iajs-1013	72	17	let	let	VERB
iajs-1013	72	18	f	f	PROPN
iajs-1013	72	19			PROPN
iajs-1013	72	20	hom(q	hom(q	PROPN
iajs-1013	72	21	,	,	PUNCT
iajs-1013	72	22	q	q	NUM
iajs-1013	72	23	)	)	PUNCT
iajs-1013	73	1	=	=	SYM
iajs-1013	73	2	hom(q	hom(q	PROPN
iajs-1013	73	3	,	,	PUNCT
iajs-1013	73	4	q	q	PROPN
iajs-1013	73	5			PROPN
iajs-1013	73	6	q	q	NOUN
iajs-1013	73	7	)	)	PUNCT
iajs-1013	73	8	.	.	PUNCT
iajs-1013	74	1	if	if	SCONJ
iajs-1013	74	2	f	f	PROPN
iajs-1013	74	3	=	=	SYM
iajs-1013	74	4	0	0	PROPN
iajs-1013	74	5	,	,	PUNCT
iajs-1013	74	6	the	the	DET
iajs-1013	74	7	proof	proof	NOUN
iajs-1013	74	8	is	be	AUX
iajs-1013	74	9	obvious	obvious	ADJ
iajs-1013	74	10	.	.	PUNCT
iajs-1013	75	1	ibn	ibn	PROPN
iajs-1013	75	2	alhaitham	alhaitham	PROPN
iajs-1013	75	3	j.	j.	PROPN
iajs-1013	75	4	for	for	ADP
iajs-1013	75	5	pure	pure	ADJ
iajs-1013	75	6	&	&	CCONJ
iajs-1013	75	7	appl	appl	PROPN
iajs-1013	75	8	.	.	PUNCT
iajs-1013	76	1	sci	sci	PROPN
iajs-1013	76	2	.	.	PUNCT
iajs-1013	77	1	vol.23	vol.23	PROPN
iajs-1013	77	2	(	(	PUNCT
iajs-1013	77	3	1	1	NUM
iajs-1013	77	4	)	)	PUNCT
iajs-1013	77	5	2010	2010	NUM
iajs-1013	77	6	if	if	SCONJ
iajs-1013	77	7	f	f	PROPN
iajs-1013	77	8			PROPN
iajs-1013	77	9	0	0	NUM
iajs-1013	77	10	,	,	PUNCT
iajs-1013	77	11	then	then	ADV
iajs-1013	77	12	f	f	PROPN
iajs-1013	77	13	is	be	AUX
iajs-1013	77	14	a	a	DET
iajs-1013	77	15	monomorphism	monomorphism	NOUN
iajs-1013	77	16	,	,	PUNCT
iajs-1013	77	17	for	for	ADP
iajs-1013	77	18	if	if	SCONJ
iajs-1013	77	19	x	x	SYM
iajs-1013	77	20			NOUN
iajs-1013	77	21	q	q	X
iajs-1013	77	22	and	and	CCONJ
iajs-1013	77	23	f	f	PROPN
iajs-1013	77	24	(	(	PUNCT
iajs-1013	77	25	x	x	X
iajs-1013	77	26	)	)	PUNCT
iajs-1013	77	27	=	=	SYM
iajs-1013	77	28	0	0	NUM
iajs-1013	77	29	with	with	ADP
iajs-1013	77	30	a	a	DET
iajs-1013	77	31	x	x	X
iajs-1013	77	32	b	b	PROPN
iajs-1013	77	33			NOUN
iajs-1013	77	34	and	and	CCONJ
iajs-1013	77	35	a	a	PRON
iajs-1013	77	36	,	,	PUNCT
iajs-1013	77	37	b	b	NOUN
iajs-1013	77	38			PROPN
iajs-1013	77	39	z	z	PROPN
iajs-1013	77	40	,	,	PUNCT
iajs-1013	77	41	a	a	DET
iajs-1013	77	42			PROPN
iajs-1013	77	43	0	0	NUM
iajs-1013	77	44	,	,	PUNCT
iajs-1013	77	45	b	b	PROPN
iajs-1013	77	46			PROPN
iajs-1013	77	47	0	0	NUM
iajs-1013	77	48	,	,	PUNCT
iajs-1013	77	49	then	then	ADV
iajs-1013	77	50	0	0	X
iajs-1013	78	1	=	=	SYM
iajs-1013	78	2	f	f	PROPN
iajs-1013	78	3	(	(	PUNCT
iajs-1013	78	4	)	)	PUNCT
iajs-1013	78	5	a	a	DET
iajs-1013	78	6	b	b	X
iajs-1013	78	7	=	=	PUNCT
iajs-1013	78	8	a	a	DET
iajs-1013	78	9	f	f	PROPN
iajs-1013	78	10	1	1	NUM
iajs-1013	78	11	(	(	PUNCT
iajs-1013	78	12	)	)	PUNCT
iajs-1013	78	13	b	b	NOUN
iajs-1013	78	14	implies	imply	VERB
iajs-1013	78	15	that	that	SCONJ
iajs-1013	78	16	f	f	PROPN
iajs-1013	78	17	1	1	NUM
iajs-1013	78	18	(	(	PUNCT
iajs-1013	78	19	)	)	PUNCT
iajs-1013	78	20	b	b	X
iajs-1013	78	21	=	=	SYM
iajs-1013	78	22	0	0	PROPN
iajs-1013	78	23	.	.	PUNCT
iajs-1013	79	1	now	now	ADV
iajs-1013	79	2	,	,	PUNCT
iajs-1013	79	3	f	f	PROPN
iajs-1013	79	4	(	(	PUNCT
iajs-1013	79	5	1	1	NUM
iajs-1013	79	6	)	)	PUNCT
iajs-1013	79	7	=	=	SYM
iajs-1013	79	8	f	f	PROPN
iajs-1013	79	9	(	(	PUNCT
iajs-1013	79	10	)	)	PUNCT
iajs-1013	79	11	b	b	PROPN
iajs-1013	79	12	b	b	X
iajs-1013	79	13	=	=	SYM
iajs-1013	79	14	b	b	PROPN
iajs-1013	79	15	f	f	PROPN
iajs-1013	79	16	1	1	NUM
iajs-1013	79	17	(	(	PUNCT
iajs-1013	79	18	)	)	PUNCT
iajs-1013	79	19	b	b	X
iajs-1013	79	20	=	=	SYM
iajs-1013	79	21	0	0	PROPN
iajs-1013	79	22	.	.	PUNCT
iajs-1013	80	1	hence	hence	ADV
iajs-1013	80	2	f	f	PROPN
iajs-1013	80	3	(	(	PUNCT
iajs-1013	80	4	q	q	X
iajs-1013	80	5	)	)	PUNCT
iajs-1013	80	6	=	=	SYM
iajs-1013	80	7	0	0	NUM
iajs-1013	80	8	,	,	PUNCT
iajs-1013	80	9	which	which	PRON
iajs-1013	80	10	is	be	AUX
iajs-1013	80	11	a	a	DET
iajs-1013	80	12	contradiction	contradiction	NOUN
iajs-1013	80	13	.	.	PUNCT
iajs-1013	81	1	so	so	ADV
iajs-1013	81	2	f	f	PROPN
iajs-1013	81	3	is	be	AUX
iajs-1013	81	4	a	a	DET
iajs-1013	81	5	monomorphism	monomorphism	NOUN
iajs-1013	81	6	.	.	PUNCT
iajs-1013	82	1	therefore	therefore	ADV
iajs-1013	82	2	f	f	X
iajs-1013	82	3	(	(	PUNCT
iajs-1013	82	4	q	q	X
iajs-1013	82	5	)	)	PUNCT
iajs-1013	82	6	=	=	SYM
iajs-1013	82	7	0	0	PUNCT
iajs-1013	82	8			ADJ
iajs-1013	82	9	a	a	PRON
iajs-1013	82	10	or	or	CCONJ
iajs-1013	82	11	f	f	X
iajs-1013	82	12	(	(	PUNCT
iajs-1013	82	13	q	q	X
iajs-1013	82	14	)	)	PUNCT
iajs-1013	82	15	=	=	SYM
iajs-1013	83	1	b	b	X
iajs-1013	83	2			ADJ
iajs-1013	83	3	0	0	PUNCT
iajs-1013	84	1	or	or	CCONJ
iajs-1013	84	2	f	f	X
iajs-1013	84	3	(	(	PUNCT
iajs-1013	84	4	q)={(x	q)={(x	NOUN
iajs-1013	84	5	,	,	PUNCT
iajs-1013	84	6	x	x	X
iajs-1013	84	7	):	):	PUNCT
iajs-1013	84	8	xq	xq	NUM
iajs-1013	84	9	}	}	PUNCT
iajs-1013	84	10	,	,	PUNCT
iajs-1013	84	11	where	where	SCONJ
iajs-1013	84	12	a	a	PRON
iajs-1013	84	13	and	and	CCONJ
iajs-1013	84	14	b	b	NOUN
iajs-1013	84	15	are	be	AUX
iajs-1013	84	16	submodules	submodule	NOUN
iajs-1013	84	17	of	of	ADP
iajs-1013	84	18	q.	q.	PROPN
iajs-1013	84	19	if	if	SCONJ
iajs-1013	84	20	f	f	PROPN
iajs-1013	84	21	(	(	PUNCT
iajs-1013	84	22	q	q	X
iajs-1013	84	23	)	)	PUNCT
iajs-1013	84	24	=	=	SYM
iajs-1013	84	25	0	0	PUNCT
iajs-1013	84	26			ADJ
iajs-1013	84	27	a	a	PRON
iajs-1013	84	28	,	,	PUNCT
iajs-1013	84	29	then	then	ADV
iajs-1013	84	30	f	f	X
iajs-1013	84	31	(	(	PUNCT
iajs-1013	84	32	q	q	NOUN
iajs-1013	84	33	)	)	PUNCT
iajs-1013	84	34			PROPN
iajs-1013	84	35	0	0	NUM
iajs-1013	85	1			ADJ
iajs-1013	85	2	q	q	PROPN
iajs-1013	85	3			PROPN
iajs-1013	85	4	z	z	PROPN
iajs-1013	85	5			PROPN
iajs-1013	85	6	q	q	PROPN
iajs-1013	85	7			PROPN
iajs-1013	85	8	q	q	PROPN
iajs-1013	85	9			PROPN
iajs-1013	85	10	q.	q.	PROPN
iajs-1013	85	11	take	take	VERB
iajs-1013	85	12	x	x	PUNCT
iajs-1013	86	1	=	=	VERB
iajs-1013	86	2	m	m	PUNCT
iajs-1013	86	3	=	=	SYM
iajs-1013	86	4	z	z	X
iajs-1013	86	5			PROPN
iajs-1013	86	6	q	q	NOUN
iajs-1013	86	7	,	,	PUNCT
iajs-1013	86	8	then	then	ADV
iajs-1013	86	9	f	f	X
iajs-1013	86	10	(	(	PUNCT
iajs-1013	86	11	q	q	NOUN
iajs-1013	86	12	)	)	PUNCT
iajs-1013	86	13			PROPN
iajs-1013	87	1	x	x	X
iajs-1013	87	2	≈	≈	NOUN
iajs-1013	87	3	m	m	NOUN
iajs-1013	87	4	=	=	NOUN
iajs-1013	87	5	z	z	PROPN
iajs-1013	87	6			PROPN
iajs-1013	87	7	q.	q.	PROPN
iajs-1013	87	8	similarly	similarly	ADV
iajs-1013	87	9	,	,	PUNCT
iajs-1013	87	10	if	if	SCONJ
iajs-1013	87	11	f	f	PROPN
iajs-1013	87	12	(	(	PUNCT
iajs-1013	87	13	q	q	X
iajs-1013	87	14	)	)	PUNCT
iajs-1013	88	1	=	=	SYM
iajs-1013	88	2	b	b	X
iajs-1013	88	3			ADJ
iajs-1013	88	4	0	0	PUNCT
iajs-1013	88	5	.	.	PUNCT
iajs-1013	89	1	if	if	SCONJ
iajs-1013	89	2	f	f	PROPN
iajs-1013	89	3	(	(	PUNCT
iajs-1013	89	4	q)={(x	q)={(x	NOUN
iajs-1013	89	5	,	,	PUNCT
iajs-1013	89	6	x	x	X
iajs-1013	89	7	):	):	PUNCT
iajs-1013	89	8	xq	xq	ADJ
iajs-1013	89	9	}	}	PUNCT
iajs-1013	89	10	≈	≈	PROPN
iajs-1013	90	1	q	q	X
iajs-1013	90	2	,	,	PUNCT
iajs-1013	90	3	take	take	VERB
iajs-1013	90	4	y	y	NOUN
iajs-1013	90	5	=	=	PRON
iajs-1013	90	6	{	{	PUNCT
iajs-1013	90	7	(	(	PUNCT
iajs-1013	90	8	x	x	NOUN
iajs-1013	90	9	,	,	PUNCT
iajs-1013	90	10	x	x	X
iajs-1013	90	11	):	):	PUNCT
iajs-1013	90	12	xq	xq	ADJ
iajs-1013	90	13	}	}	PUNCT
iajs-1013	90	14			PROPN
iajs-1013	90	15	q	q	PROPN
iajs-1013	90	16			PROPN
iajs-1013	90	17	q.	q.	NOUN
iajs-1013	90	18	it	it	PRON
iajs-1013	90	19	is	be	AUX
iajs-1013	90	20	easy	easy	ADJ
iajs-1013	90	21	to	to	PART
iajs-1013	90	22	prove	prove	VERB
iajs-1013	90	23	that	that	SCONJ
iajs-1013	90	24	z	z	PROPN
iajs-1013	90	25			VERB
iajs-1013	90	26	y	y	PROPN
iajs-1013	90	27	≈	≈	PROPN
iajs-1013	90	28	z	z	PROPN
iajs-1013	90	29			PROPN
iajs-1013	90	30	q.	q.	PROPN
iajs-1013	91	1	therefore	therefore	ADV
iajs-1013	91	2	f	f	PROPN
iajs-1013	91	3	(	(	PUNCT
iajs-1013	91	4	q	q	NOUN
iajs-1013	91	5	)	)	PUNCT
iajs-1013	91	6			PROPN
iajs-1013	92	1	y	y	PROPN
iajs-1013	92	2			PROPN
iajs-1013	92	3	z	z	PROPN
iajs-1013	92	4			PROPN
iajs-1013	92	5	y	y	PROPN
iajs-1013	92	6	≈	≈	PROPN
iajs-1013	92	7	z	z	PROPN
iajs-1013	92	8			PROPN
iajs-1013	92	9	q.	q.	PROPN
iajs-1013	93	1	hence	hence	ADV
iajs-1013	93	2	z	z	PROPN
iajs-1013	93	3			PROPN
iajs-1013	93	4	q	q	PROPN
iajs-1013	93	5	is	be	AUX
iajs-1013	93	6	weakly	weakly	ADJ
iajs-1013	93	7	q	q	ADJ
iajs-1013	93	8	-	-	PUNCT
iajs-1013	93	9	quasi	quasi	NOUN
iajs-1013	93	10	-	-	NOUN
iajs-1013	93	11	injective	injective	ADJ
iajs-1013	93	12	.	.	PUNCT
iajs-1013	94	1	but	but	CCONJ
iajs-1013	94	2	it	it	PRON
iajs-1013	94	3	is	be	AUX
iajs-1013	94	4	clear	clear	ADJ
iajs-1013	94	5	that	that	SCONJ
iajs-1013	94	6	z	z	NOUN
iajs-1013	94	7	is	be	AUX
iajs-1013	94	8	not	not	PART
iajs-1013	94	9	weakly	weakly	ADJ
iajs-1013	94	10	q	q	ADJ
iajs-1013	94	11	-	-	PUNCT
iajs-1013	94	12	quasi	quasi	NOUN
iajs-1013	94	13	-	-	ADJ
iajs-1013	94	14	injective	injective	ADJ
iajs-1013	94	15	.	.	PUNCT
iajs-1013	95	1	1.6	1.6	NUM
iajs-1013	95	2	remark	remark	NOUN
iajs-1013	95	3	we	we	PRON
iajs-1013	95	4	can	can	AUX
iajs-1013	95	5	not	not	PART
iajs-1013	95	6	prove	prove	VERB
iajs-1013	95	7	and	and	CCONJ
iajs-1013	95	8	we	we	PRON
iajs-1013	95	9	can	can	AUX
iajs-1013	95	10	not	not	PART
iajs-1013	95	11	disprove	disprove	VERB
iajs-1013	95	12	that	that	SCONJ
iajs-1013	95	13	the	the	DET
iajs-1013	95	14	class	class	NOUN
iajs-1013	95	15	of	of	ADP
iajs-1013	95	16	weakly	weakly	ADJ
iajs-1013	95	17	relative	relative	ADJ
iajs-1013	95	18	quasiinjective	quasiinjective	ADJ
iajs-1013	95	19	modules	module	NOUN
iajs-1013	95	20	is	be	AUX
iajs-1013	95	21	closed	close	VERB
iajs-1013	95	22	under	under	ADP
iajs-1013	95	23	direct	direct	ADJ
iajs-1013	95	24	sum	sum	NOUN
iajs-1013	95	25	.	.	PUNCT
iajs-1013	96	1	however	however	ADV
iajs-1013	96	2	,	,	PUNCT
iajs-1013	96	3	we	we	PRON
iajs-1013	96	4	give	give	VERB
iajs-1013	96	5	a	a	DET
iajs-1013	96	6	special	special	ADJ
iajs-1013	96	7	case	case	NOUN
iajs-1013	96	8	of	of	ADP
iajs-1013	96	9	this	this	PRON
iajs-1013	96	10	.	.	PUNCT
iajs-1013	97	1	1.7	1.7	NUM
iajs-1013	97	2	proposition	proposition	NOUN
iajs-1013	97	3	let	let	VERB
iajs-1013	97	4	m	m	PRON
iajs-1013	97	5	and	and	CCONJ
iajs-1013	97	6	n	n	CCONJ
iajs-1013	97	7	be	be	VERB
iajs-1013	97	8	two	two	NUM
iajs-1013	97	9	r	r	NOUN
iajs-1013	97	10	-	-	PUNCT
iajs-1013	97	11	modules	module	NOUN
iajs-1013	97	12	,	,	PUNCT
iajs-1013	97	13	such	such	ADJ
iajs-1013	97	14	that	that	SCONJ
iajs-1013	97	15	l	l	PROPN
iajs-1013	97	16	m	m	X
iajs-1013	97	17	=	=	PUNCT
iajs-1013	97	18	l	l	NOUN
iajs-1013	97	19	m	m	PROPN
iajs-1013	97	20	.	.	PUNCT
iajs-1013	98	1	if	if	SCONJ
iajs-1013	98	2	l	l	PROPN
iajs-1013	98	3	and	and	CCONJ
iajs-1013	98	4	m	m	PROPN
iajs-1013	98	5	are	be	AUX
iajs-1013	98	6	weakly	weakly	ADJ
iajs-1013	98	7	nquasi	nquasi	NOUN
iajs-1013	98	8	-	-	PUNCT
iajs-1013	98	9	injective	injective	ADJ
iajs-1013	98	10	,	,	PUNCT
iajs-1013	98	11	then	then	ADV
iajs-1013	98	12	l	l	PROPN
iajs-1013	98	13			PROPN
iajs-1013	98	14	m	m	VERB
iajs-1013	98	15	is	be	AUX
iajs-1013	98	16	also	also	ADV
iajs-1013	98	17	weakly	weakly	ADJ
iajs-1013	98	18	n	n	CCONJ
iajs-1013	98	19	-	-	PUNCT
iajs-1013	98	20	quasi	quasi	NOUN
iajs-1013	98	21	-	-	ADJ
iajs-1013	98	22	injective	injective	ADJ
iajs-1013	98	23	.	.	PUNCT
iajs-1013	99	1	proof	proof	NOUN
iajs-1013	99	2	:	:	PUNCT
iajs-1013	99	3	let	let	VERB
iajs-1013	99	4	f	f	PROPN
iajs-1013	99	5			PROPN
iajs-1013	99	6	hom(n	hom(n	PROPN
iajs-1013	99	7	,	,	PUNCT
iajs-1013	99	8	l	l	NOUN
iajs-1013	99	9	m	m	PROPN
iajs-1013	99	10	)	)	PUNCT
iajs-1013	99	11	.	.	PUNCT
iajs-1013	100	1	then	then	ADV
iajs-1013	100	2	f	f	PROPN
iajs-1013	100	3			PROPN
iajs-1013	100	4	hom(n	hom(n	PROPN
iajs-1013	100	5	,	,	PUNCT
iajs-1013	100	6	l	l	NOUN
iajs-1013	100	7	m	m	PROPN
iajs-1013	100	8	)	)	PUNCT
iajs-1013	100	9	.	.	PUNCT
iajs-1013	101	1	but	but	CCONJ
iajs-1013	101	2	hom(n	hom(n	PROPN
iajs-1013	101	3	,	,	PUNCT
iajs-1013	101	4	l	l	PROPN
iajs-1013	101	5	m	m	PROPN
iajs-1013	101	6	)	)	PUNCT
iajs-1013	102	1	≈	≈	PROPN
iajs-1013	102	2	hom(n	hom(n	PROPN
iajs-1013	102	3	,	,	PUNCT
iajs-1013	102	4	l	l	NOUN
iajs-1013	102	5	)	)	PUNCT
iajs-1013	102	6			PROPN
iajs-1013	102	7	hom(n	hom(n	PROPN
iajs-1013	102	8	,	,	PUNCT
iajs-1013	102	9	m	m	VERB
iajs-1013	102	10	)	)	PUNCT
iajs-1013	102	11	by	by	ADP
iajs-1013	102	12	[	[	X
iajs-1013	102	13	4	4	NUM
iajs-1013	102	14	]	]	PUNCT
iajs-1013	102	15	.	.	PUNCT
iajs-1013	103	1	hence	hence	ADV
iajs-1013	103	2	f	f	PROPN
iajs-1013	103	3	=	=	SYM
iajs-1013	103	4	(	(	PUNCT
iajs-1013	103	5	,	,	PROPN
iajs-1013	103	6	)	)	PUNCT
iajs-1013	103	7	with	with	ADP
iajs-1013	103	8			NUM
iajs-1013	103	9	hom(n	hom(n	PROPN
iajs-1013	103	10	,	,	PUNCT
iajs-1013	103	11	l	l	NOUN
iajs-1013	103	12	)	)	PUNCT
iajs-1013	103	13	and	and	CCONJ
iajs-1013	103	14			PROPN
iajs-1013	103	15	hom(n	hom(n	PROPN
iajs-1013	103	16	,	,	PUNCT
iajs-1013	103	17	m	m	PROPN
iajs-1013	103	18	)	)	PUNCT
iajs-1013	103	19	.	.	PUNCT
iajs-1013	104	1	therefore	therefore	ADV
iajs-1013	104	2	there	there	PRON
iajs-1013	104	3	exists	exist	VERB
iajs-1013	104	4	submodules	submodule	NOUN
iajs-1013	104	5	x	x	PUNCT
iajs-1013	104	6	and	and	CCONJ
iajs-1013	104	7	y	y	PROPN
iajs-1013	104	8	of	of	ADP
iajs-1013	104	9	l	l	PROPN
iajs-1013	104	10	and	and	CCONJ
iajs-1013	104	11	m	m	VERB
iajs-1013	104	12	respectively	respectively	ADV
iajs-1013	104	13	,	,	PUNCT
iajs-1013	104	14	such	such	ADJ
iajs-1013	104	15	that	that	SCONJ
iajs-1013	104	16	(n	(n	NOUN
iajs-1013	104	17	)	)	PUNCT
iajs-1013	104	18			PROPN
iajs-1013	104	19	x	x	PUNCT
iajs-1013	104	20	≈	≈	PROPN
iajs-1013	104	21	l	l	NOUN
iajs-1013	104	22	and	and	CCONJ
iajs-1013	104	23	(n	(n	NUM
iajs-1013	104	24	)	)	PUNCT
iajs-1013	105	1			PROPN
iajs-1013	106	1	y	y	PROPN
iajs-1013	107	1	≈	≈	PROPN
iajs-1013	107	2	m	m	PROPN
iajs-1013	107	3	.	.	PUNCT
iajs-1013	108	1	on	on	ADP
iajs-1013	108	2	the	the	DET
iajs-1013	108	3	other	other	ADJ
iajs-1013	108	4	hand	hand	NOUN
iajs-1013	108	5	,	,	PUNCT
iajs-1013	108	6	(n	(n	NUM
iajs-1013	108	7	)	)	PUNCT
iajs-1013	108	8	≈	≈	PROPN
iajs-1013	108	9	(n	(n	PROPN
iajs-1013	108	10	)	)	PUNCT
iajs-1013	108	11			PROPN
iajs-1013	108	12	0	0	NUM
iajs-1013	108	13			PROPN
iajs-1013	108	14	x	x	X
iajs-1013	108	15			PROPN
iajs-1013	108	16	y	y	PROPN
iajs-1013	108	17	≈	≈	PROPN
iajs-1013	108	18	l	l	PROPN
iajs-1013	108	19			PROPN
iajs-1013	108	20	m	m	PROPN
iajs-1013	108	21	,	,	PUNCT
iajs-1013	108	22	and	and	CCONJ
iajs-1013	108	23	(n	(n	NUM
iajs-1013	108	24	)	)	PUNCT
iajs-1013	109	1	≈	≈	PROPN
iajs-1013	109	2	0	0	NUM
iajs-1013	109	3			PROPN
iajs-1013	109	4	(n	(n	NUM
iajs-1013	109	5	)	)	PUNCT
iajs-1013	110	1			PROPN
iajs-1013	110	2	x	x	PUNCT
iajs-1013	110	3			PROPN
iajs-1013	110	4	y	y	PROPN
iajs-1013	110	5	≈	≈	PROPN
iajs-1013	110	6	l	l	PROPN
iajs-1013	110	7			ADJ
iajs-1013	110	8	m.	m.	NOUN
iajs-1013	110	9	now	now	ADV
iajs-1013	110	10	,	,	PUNCT
iajs-1013	110	11	f	f	PROPN
iajs-1013	110	12	(	(	PUNCT
iajs-1013	110	13	n	n	CCONJ
iajs-1013	110	14	)	)	PUNCT
iajs-1013	110	15	=	=	SYM
iajs-1013	110	16	(	(	PUNCT
iajs-1013	110	17	,)(n	,)(n	PROPN
iajs-1013	110	18	)	)	PUNCT
iajs-1013	110	19	=	=	SYM
iajs-1013	110	20	(	(	PUNCT
iajs-1013	110	21	(n),(n	(n),(n	NOUN
iajs-1013	110	22	)	)	PUNCT
iajs-1013	110	23	)	)	PUNCT
iajs-1013	111	1			PROPN
iajs-1013	112	1	x	x	PUNCT
iajs-1013	112	2			PROPN
iajs-1013	112	3	y	y	PROPN
iajs-1013	112	4	≈	≈	PROPN
iajs-1013	112	5	l	l	PROPN
iajs-1013	112	6			PROPN
iajs-1013	112	7	m	m	PROPN
iajs-1013	112	8	,	,	PUNCT
iajs-1013	112	9	which	which	PRON
iajs-1013	112	10	completes	complete	VERB
iajs-1013	112	11	the	the	DET
iajs-1013	112	12	proof	proof	NOUN
iajs-1013	112	13	.	.	PUNCT
iajs-1013	113	1	1.8	1.8	NUM
iajs-1013	113	2	remark	remark	NOUN
iajs-1013	113	3	if	if	SCONJ
iajs-1013	113	4	l	l	NOUN
iajs-1013	113	5	,	,	PUNCT
iajs-1013	113	6	m	m	VERB
iajs-1013	113	7	and	and	CCONJ
iajs-1013	113	8	n	n	PROPN
iajs-1013	113	9	are	be	AUX
iajs-1013	113	10	r	r	NOUN
iajs-1013	113	11	-	-	PUNCT
iajs-1013	113	12	modules	module	NOUN
iajs-1013	113	13	,	,	PUNCT
iajs-1013	113	14	such	such	ADJ
iajs-1013	113	15	that	that	SCONJ
iajs-1013	113	16	m	m	PROPN
iajs-1013	113	17	is	be	AUX
iajs-1013	113	18	weakly	weakly	ADJ
iajs-1013	113	19	n	n	CCONJ
iajs-1013	113	20	-	-	PUNCT
iajs-1013	113	21	quasi	quasi	NOUN
iajs-1013	113	22	-	-	ADJ
iajs-1013	113	23	injective	injective	ADJ
iajs-1013	113	24	and	and	CCONJ
iajs-1013	113	25	m	m	VERB
iajs-1013	113	26	is	be	AUX
iajs-1013	113	27	weakly	weakly	ADJ
iajs-1013	113	28	l	l	NOUN
iajs-1013	113	29	-	-	ADJ
iajs-1013	113	30	quasi	quasi	ADJ
iajs-1013	113	31	-	-	ADJ
iajs-1013	113	32	injective	injective	ADJ
iajs-1013	113	33	,	,	PUNCT
iajs-1013	113	34	then	then	ADV
iajs-1013	113	35	it	it	PRON
iajs-1013	113	36	is	be	AUX
iajs-1013	113	37	not	not	PART
iajs-1013	113	38	true	true	ADJ
iajs-1013	113	39	in	in	ADP
iajs-1013	113	40	general	general	ADJ
iajs-1013	113	41	that	that	SCONJ
iajs-1013	113	42	:	:	PUNCT
iajs-1013	113	43	i.	i.	PROPN
iajs-1013	113	44	m	m	PROPN
iajs-1013	113	45	is	be	AUX
iajs-1013	113	46	weakly	weakly	ADJ
iajs-1013	113	47	n	n	CCONJ
iajs-1013	113	48			ADJ
iajs-1013	113	49	l	l	NOUN
iajs-1013	113	50	quasi	quasi	NOUN
iajs-1013	113	51	-	-	ADJ
iajs-1013	113	52	injective	injective	ADJ
iajs-1013	113	53	.	.	PUNCT
iajs-1013	113	54	ii	ii	PROPN
iajs-1013	113	55	.	.	PUNCT
iajs-1013	114	1	m	m	PROPN
iajs-1013	114	2	is	be	AUX
iajs-1013	114	3	weakly	weakly	ADJ
iajs-1013	114	4	n	n	NOUN
iajs-1013	114	5	+	+	CCONJ
iajs-1013	114	6	l	l	NOUN
iajs-1013	114	7	quasi	quasi	ADJ
iajs-1013	114	8	-	-	ADJ
iajs-1013	114	9	injective	injective	ADJ
iajs-1013	114	10	.	.	PUNCT
iajs-1013	115	1	consider	consider	VERB
iajs-1013	115	2	the	the	DET
iajs-1013	115	3	following	follow	VERB
iajs-1013	115	4	examples	example	NOUN
iajs-1013	115	5	:	:	PUNCT
iajs-1013	115	6	i.	i.	NOUN
iajs-1013	115	7	let	let	VERB
iajs-1013	115	8	m	m	NOUN
iajs-1013	115	9	=	=	PUNCT
iajs-1013	115	10	l	l	NOUN
iajs-1013	115	11	=	=	SYM
iajs-1013	116	1	n	n	PROPN
iajs-1013	116	2	=	=	SYM
iajs-1013	116	3	z	z	PROPN
iajs-1013	116	4	and	and	CCONJ
iajs-1013	116	5	r	r	NOUN
iajs-1013	116	6	=	=	PUNCT
iajs-1013	116	7	z.	z.	PROPN
iajs-1013	116	8	then	then	ADV
iajs-1013	116	9	z	z	PROPN
iajs-1013	116	10	as	as	ADP
iajs-1013	116	11	a	a	DET
iajs-1013	116	12	z	z	NOUN
iajs-1013	116	13	-	-	PUNCT
iajs-1013	116	14	module	module	NOUN
iajs-1013	116	15	is	be	AUX
iajs-1013	116	16	weakly	weakly	ADV
iajs-1013	116	17	quasi	quasi	ADJ
iajs-1013	116	18	injective	injective	NOUN
iajs-1013	116	19	.	.	PUNCT
iajs-1013	117	1	but	but	CCONJ
iajs-1013	117	2	z	z	NOUN
iajs-1013	117	3	is	be	AUX
iajs-1013	117	4	not	not	PART
iajs-1013	117	5	weakly	weakly	ADJ
iajs-1013	117	6	z	z	NOUN
iajs-1013	117	7			PROPN
iajs-1013	117	8	z	z	PROPN
iajs-1013	117	9	quasiinjective	quasiinjective	NOUN
iajs-1013	117	10	.	.	PUNCT
iajs-1013	118	1	in	in	ADP
iajs-1013	118	2	fact	fact	NOUN
iajs-1013	118	3	,	,	PUNCT
iajs-1013	118	4	if	if	SCONJ
iajs-1013	118	5	we	we	PRON
iajs-1013	118	6	define	define	VERB
iajs-1013	118	7	f	f	X
iajs-1013	118	8	:	:	PUNCT
iajs-1013	118	9	z	z	PROPN
iajs-1013	118	10			PROPN
iajs-1013	118	11	z	z	PROPN
iajs-1013	118	12			PROPN
iajs-1013	118	13	q	q	PUNCT
iajs-1013	118	14	by	by	ADP
iajs-1013	118	15	f	f	PROPN
iajs-1013	118	16	(	(	PUNCT
iajs-1013	118	17	a	a	DET
iajs-1013	118	18	,	,	PUNCT
iajs-1013	118	19	b	b	NOUN
iajs-1013	118	20	)	)	PUNCT
iajs-1013	118	21	=	=	SYM
iajs-1013	118	22	2	2	NUM
iajs-1013	118	23	a	a	DET
iajs-1013	118	24	+	+	NUM
iajs-1013	118	25	3	3	NUM
iajs-1013	118	26	b	b	NOUN
iajs-1013	118	27	where	where	SCONJ
iajs-1013	118	28	a	a	PRON
iajs-1013	118	29	,	,	PUNCT
iajs-1013	118	30	b	b	NOUN
iajs-1013	118	31			PROPN
iajs-1013	118	32	z	z	PROPN
iajs-1013	118	33	,	,	PUNCT
iajs-1013	118	34	then	then	ADV
iajs-1013	118	35	it	it	PRON
iajs-1013	118	36	can	can	AUX
iajs-1013	118	37	be	be	AUX
iajs-1013	118	38	easily	easily	ADV
iajs-1013	118	39	seen	see	VERB
iajs-1013	118	40	that	that	SCONJ
iajs-1013	118	41	f	f	PROPN
iajs-1013	118	42			NOUN
iajs-1013	118	43	hom(z	hom(z	PROPN
iajs-1013	118	44			VERB
iajs-1013	118	45	z	z	PROPN
iajs-1013	118	46	,	,	PUNCT
iajs-1013	118	47	q	q	NOUN
iajs-1013	118	48	)	)	PUNCT
iajs-1013	118	49	and	and	CCONJ
iajs-1013	118	50	f	f	PROPN
iajs-1013	118	51	(	(	PUNCT
iajs-1013	118	52	z	z	PROPN
iajs-1013	118	53			PROPN
iajs-1013	118	54	z	z	PROPN
iajs-1013	118	55	)	)	PUNCT
iajs-1013	118	56	=	=	SYM
iajs-1013	118	57	(	(	PUNCT
iajs-1013	118	58	(	(	PUNCT
iajs-1013	118	59	1	1	NUM
iajs-1013	118	60	2	2	NUM
iajs-1013	118	61	,	,	PUNCT
iajs-1013	118	62	1	1	NUM
iajs-1013	118	63	3	3	NUM
iajs-1013	118	64	)	)	PUNCT
iajs-1013	118	65	)	)	PUNCT
iajs-1013	119	1	≈	≈	PROPN
iajs-1013	119	2	z.	z.	PROPN
iajs-1013	119	3	ibn	ibn	PROPN
iajs-1013	119	4	alhaitham	alhaitham	PROPN
iajs-1013	119	5	j.	j.	PROPN
iajs-1013	119	6	for	for	ADP
iajs-1013	119	7	pure	pure	ADJ
iajs-1013	119	8	&	&	CCONJ
iajs-1013	119	9	appl	appl	PROPN
iajs-1013	119	10	.	.	PUNCT
iajs-1013	120	1	sci	sci	PROPN
iajs-1013	120	2	.	.	PUNCT
iajs-1013	121	1	vol.23	vol.23	PROPN
iajs-1013	121	2	(	(	PUNCT
iajs-1013	121	3	1	1	NUM
iajs-1013	121	4	)	)	PUNCT
iajs-1013	121	5	2010	2010	NUM
iajs-1013	121	6	ii	ii	NOUN
iajs-1013	121	7	.	.	PUNCT
iajs-1013	122	1	let	let	VERB
iajs-1013	122	2	m	m	VERB
iajs-1013	122	3	=	=	SYM
iajs-1013	122	4	z	z	PROPN
iajs-1013	122	5	,	,	PUNCT
iajs-1013	122	6	n	n	NOUN
iajs-1013	122	7	=	=	SYM
iajs-1013	122	8	(	(	PUNCT
iajs-1013	122	9	1	1	NUM
iajs-1013	122	10	2	2	NUM
iajs-1013	122	11	)	)	PUNCT
iajs-1013	122	12	,	,	PUNCT
iajs-1013	122	13	l	l	NOUN
iajs-1013	122	14	=	=	PUNCT
iajs-1013	122	15	(	(	PUNCT
iajs-1013	122	16	1	1	NUM
iajs-1013	122	17	3	3	NUM
iajs-1013	122	18	)	)	PUNCT
iajs-1013	122	19	and	and	CCONJ
iajs-1013	122	20	r	r	NOUN
iajs-1013	122	21	=	=	PUNCT
iajs-1013	122	22	z.	z.	PROPN
iajs-1013	123	1	then	then	ADV
iajs-1013	123	2	z	z	PROPN
iajs-1013	123	3	as	as	ADP
iajs-1013	123	4	a	a	DET
iajs-1013	123	5	z	z	NOUN
iajs-1013	123	6	-	-	PUNCT
iajs-1013	123	7	module	module	NOUN
iajs-1013	123	8	is	be	AUX
iajs-1013	123	9	weakly	weakly	ADJ
iajs-1013	123	10	(	(	PUNCT
iajs-1013	123	11	1	1	NUM
iajs-1013	123	12	2	2	NUM
iajs-1013	123	13	)	)	PUNCT
iajs-1013	123	14	-quasiinjective	-quasiinjective	NOUN
iajs-1013	123	15	and	and	CCONJ
iajs-1013	123	16	z	z	NOUN
iajs-1013	123	17	is	be	AUX
iajs-1013	123	18	weakly	weakly	ADJ
iajs-1013	123	19	(	(	PUNCT
iajs-1013	123	20	1	1	NUM
iajs-1013	123	21	3	3	NUM
iajs-1013	123	22	)	)	PUNCT
iajs-1013	123	23	-quasi	-quasi	NOUN
iajs-1013	123	24	-	-	PUNCT
iajs-1013	123	25	injective	injective	ADJ
iajs-1013	123	26	.	.	PUNCT
iajs-1013	124	1	but	but	CCONJ
iajs-1013	124	2	z	z	NOUN
iajs-1013	124	3	is	be	AUX
iajs-1013	124	4	not	not	PART
iajs-1013	124	5	weakly	weakly	ADJ
iajs-1013	124	6	(	(	PUNCT
iajs-1013	124	7	1	1	NUM
iajs-1013	124	8	2	2	NUM
iajs-1013	124	9	)	)	PUNCT
iajs-1013	125	1	+	+	CCONJ
iajs-1013	125	2	(	(	PUNCT
iajs-1013	125	3	1	1	NUM
iajs-1013	125	4	3	3	NUM
iajs-1013	125	5	)	)	PUNCT
iajs-1013	125	6	-quasiinjective	-quasiinjective	NOUN
iajs-1013	125	7	.	.	PUNCT
iajs-1013	126	1	for	for	ADP
iajs-1013	126	2	if	if	SCONJ
iajs-1013	126	3	,	,	PUNCT
iajs-1013	126	4	we	we	PRON
iajs-1013	126	5	define	define	VERB
iajs-1013	126	6	f	f	X
iajs-1013	126	7	:	:	PUNCT
iajs-1013	126	8	(	(	PUNCT
iajs-1013	126	9	1	1	NUM
iajs-1013	126	10	2	2	NUM
iajs-1013	126	11	)	)	PUNCT
iajs-1013	127	1	+	+	CCONJ
iajs-1013	127	2	(	(	PUNCT
iajs-1013	127	3	1	1	NUM
iajs-1013	127	4	3	3	NUM
iajs-1013	127	5	)	)	PUNCT
iajs-1013	127	6			PROPN
iajs-1013	127	7	q	q	NOUN
iajs-1013	127	8	by	by	ADP
iajs-1013	127	9	f	f	PROPN
iajs-1013	127	10	(	(	PUNCT
iajs-1013	127	11	2	2	NUM
iajs-1013	127	12	a	a	DET
iajs-1013	127	13	+	+	NUM
iajs-1013	127	14	3	3	NUM
iajs-1013	127	15	b	b	NOUN
iajs-1013	127	16	)	)	PUNCT
iajs-1013	127	17	=	=	SYM
iajs-1013	128	1	2	2	NUM
iajs-1013	128	2	a	a	DET
iajs-1013	128	3	+	+	NUM
iajs-1013	128	4	3	3	NUM
iajs-1013	128	5	b	b	NOUN
iajs-1013	128	6	where	where	SCONJ
iajs-1013	128	7	a	a	PRON
iajs-1013	128	8	,	,	PUNCT
iajs-1013	128	9	b	b	NOUN
iajs-1013	128	10			PROPN
iajs-1013	128	11	z	z	PROPN
iajs-1013	128	12	,	,	PUNCT
iajs-1013	128	13	then	then	ADV
iajs-1013	128	14	it	it	PRON
iajs-1013	128	15	can	can	AUX
iajs-1013	128	16	be	be	AUX
iajs-1013	128	17	easily	easily	ADV
iajs-1013	128	18	shown	show	VERB
iajs-1013	128	19	that	that	SCONJ
iajs-1013	128	20	f	f	PROPN
iajs-1013	128	21			PROPN
iajs-1013	128	22	hom	hom	PROPN
iajs-1013	128	23	(	(	PUNCT
iajs-1013	128	24	(	(	PUNCT
iajs-1013	128	25	1	1	NUM
iajs-1013	128	26	2	2	NUM
iajs-1013	128	27	)	)	PUNCT
iajs-1013	128	28	+	+	CCONJ
iajs-1013	128	29	(	(	PUNCT
iajs-1013	128	30	1	1	NUM
iajs-1013	128	31	3	3	NUM
iajs-1013	128	32	)	)	PUNCT
iajs-1013	128	33	,	,	PUNCT
iajs-1013	128	34	q	q	X
iajs-1013	128	35	)	)	PUNCT
iajs-1013	128	36	and	and	CCONJ
iajs-1013	128	37	f	f	X
iajs-1013	128	38	(	(	PUNCT
iajs-1013	128	39	(	(	PUNCT
iajs-1013	128	40	1	1	NUM
iajs-1013	128	41	2	2	NUM
iajs-1013	128	42	)	)	PUNCT
iajs-1013	129	1	+	+	CCONJ
iajs-1013	129	2	(	(	PUNCT
iajs-1013	129	3	1	1	NUM
iajs-1013	129	4	3	3	NUM
iajs-1013	129	5	)	)	PUNCT
iajs-1013	129	6	)	)	PUNCT
iajs-1013	130	1	=	=	PUNCT
iajs-1013	130	2	(	(	PUNCT
iajs-1013	130	3	(	(	PUNCT
iajs-1013	130	4	1	1	NUM
iajs-1013	130	5	2	2	NUM
iajs-1013	130	6	,	,	PUNCT
iajs-1013	130	7	1	1	NUM
iajs-1013	130	8	3	3	NUM
iajs-1013	130	9	)	)	PUNCT
iajs-1013	130	10	)	)	PUNCT
iajs-1013	131	1	≈	≈	PROPN
iajs-1013	131	2	q.	q.	PROPN
iajs-1013	131	3	1.9	1.9	NUM
iajs-1013	131	4	proposition	proposition	NOUN
iajs-1013	131	5	let	let	VERB
iajs-1013	131	6	m	m	PRON
iajs-1013	131	7	be	be	AUX
iajs-1013	131	8	an	an	DET
iajs-1013	131	9	r	r	NOUN
iajs-1013	131	10	-	-	PUNCT
iajs-1013	131	11	module	module	NOUN
iajs-1013	131	12	and	and	CCONJ
iajs-1013	131	13	n	n	CCONJ
iajs-1013	131	14	be	be	VERB
iajs-1013	131	15	a	a	DET
iajs-1013	131	16	submodule	submodule	NOUN
iajs-1013	131	17	of	of	ADP
iajs-1013	131	18	m	m	PROPN
iajs-1013	131	19	.	.	PUNCT
iajs-1013	132	1	if	if	SCONJ
iajs-1013	132	2	m	m	NOUN
iajs-1013	132	3	is	be	AUX
iajs-1013	132	4	weakly	weakly	ADJ
iajs-1013	132	5	n	n	CCONJ
iajs-1013	132	6	-	-	PUNCT
iajs-1013	132	7	quasi	quasi	NOUN
iajs-1013	132	8	-	-	ADJ
iajs-1013	132	9	injective	injective	ADJ
iajs-1013	132	10	,	,	PUNCT
iajs-1013	132	11	then	then	ADV
iajs-1013	132	12	m	m	NOUN
iajs-1013	132	13	is	be	AUX
iajs-1013	132	14	weakly	weakly	ADJ
iajs-1013	132	15	l	l	NOUN
iajs-1013	132	16	-	-	ADJ
iajs-1013	132	17	quasi	quasi	ADJ
iajs-1013	132	18	-	-	ADJ
iajs-1013	132	19	injective	injective	ADJ
iajs-1013	132	20	for	for	ADP
iajs-1013	132	21	each	each	DET
iajs-1013	132	22	submodule	submodule	NOUN
iajs-1013	132	23	l	l	NOUN
iajs-1013	132	24	of	of	ADP
iajs-1013	132	25	n.	n.	PROPN
iajs-1013	132	26	proof	proof	NOUN
iajs-1013	132	27	:	:	PUNCT
iajs-1013	132	28	let	let	VERB
iajs-1013	132	29	f	f	PROPN
iajs-1013	132	30			PROPN
iajs-1013	132	31	hom(l	hom(l	PROPN
iajs-1013	132	32	,	,	PUNCT
iajs-1013	132	33	m	m	PROPN
iajs-1013	132	34	)	)	PUNCT
iajs-1013	132	35	.	.	PUNCT
iajs-1013	133	1	consider	consider	VERB
iajs-1013	133	2	the	the	DET
iajs-1013	133	3	following	follow	VERB
iajs-1013	133	4	diagram	diagram	NOUN
iajs-1013	133	5	:	:	PUNCT
iajs-1013	133	6	l	l	NOUN
iajs-1013	134	1	i	i	PRON
iajs-1013	134	2	j	j	PROPN
iajs-1013	134	3			PROPN
iajs-1013	134	4			PROPN
iajs-1013	134	5	f	f	PROPN
iajs-1013	134	6			PROPN
iajs-1013	134	7			PROPN
iajs-1013	134	8			X
iajs-1013	134	9			VERB
iajs-1013	134	10			NOUN
iajs-1013	134	11	m	m	VERB
iajs-1013	134	12	where	where	SCONJ
iajs-1013	134	13	i	i	PRON
iajs-1013	134	14	and	and	CCONJ
iajs-1013	134	15	j	j	PROPN
iajs-1013	134	16	are	be	AUX
iajs-1013	134	17	the	the	DET
iajs-1013	134	18	inclusion	inclusion	NOUN
iajs-1013	134	19	homomorphisms	homomorphism	NOUN
iajs-1013	134	20	and	and	CCONJ
iajs-1013	134	21	the	the	DET
iajs-1013	134	22	homomorphism	homomorphism	NOUN
iajs-1013	134	23			NOUN
iajs-1013	134	24	which	which	PRON
iajs-1013	134	25	makes	make	VERB
iajs-1013	134	26	the	the	DET
iajs-1013	134	27	diagram	diagram	NOUN
iajs-1013	134	28	commutative	commutative	ADJ
iajs-1013	134	29	exists	exist	VERB
iajs-1013	134	30	because	because	SCONJ
iajs-1013	134	31	m	m	NOUN
iajs-1013	134	32	is	be	AUX
iajs-1013	134	33	quasi	quasi	ADJ
iajs-1013	134	34	-	-	ADJ
iajs-1013	134	35	injective	injective	ADJ
iajs-1013	134	36	.	.	PUNCT
iajs-1013	135	1	therefore	therefore	ADV
iajs-1013	135	2			VERB
iajs-1013	135	3	i	i	PRON
iajs-1013	135	4	j	j	PROPN
iajs-1013	135	5	=	=	SYM
iajs-1013	135	6	f	f	PROPN
iajs-1013	135	7	.	.	PUNCT
iajs-1013	136	1	let	let	VERB
iajs-1013	136	2			NOUN
iajs-1013	136	3	=	=	PUNCT
iajs-1013	136	4	n	n	PRON
iajs-1013	136	5	:	:	PUNCT
iajs-1013	137	1	n	n	PRON
iajs-1013	137	2			NOUN
iajs-1013	137	3	m	m	VERB
iajs-1013	137	4	.	.	PUNCT
iajs-1013	138	1	so	so	ADV
iajs-1013	138	2	there	there	PRON
iajs-1013	138	3	exists	exist	VERB
iajs-1013	138	4	a	a	DET
iajs-1013	138	5	submodule	submodule	NOUN
iajs-1013	138	6	x	x	PUNCT
iajs-1013	138	7	of	of	ADP
iajs-1013	138	8	m	m	PRON
iajs-1013	138	9	such	such	ADJ
iajs-1013	138	10	that	that	PRON
iajs-1013	138	11	(n	(n	ADJ
iajs-1013	138	12	)	)	PUNCT
iajs-1013	139	1			PROPN
iajs-1013	140	1	x	x	PUNCT
iajs-1013	140	2	≈	≈	NUM
iajs-1013	140	3	m.	m.	NOUN
iajs-1013	140	4	but	but	CCONJ
iajs-1013	140	5	f	f	PROPN
iajs-1013	140	6	(	(	PUNCT
iajs-1013	140	7	l	l	NOUN
iajs-1013	140	8	)	)	PUNCT
iajs-1013	140	9			PROPN
iajs-1013	140	10	(n	(n	NUM
iajs-1013	140	11	)	)	PUNCT
iajs-1013	140	12	,	,	PUNCT
iajs-1013	140	13	thus	thus	ADV
iajs-1013	140	14	f	f	X
iajs-1013	140	15	(	(	PUNCT
iajs-1013	140	16	l	l	NOUN
iajs-1013	140	17	)	)	PUNCT
iajs-1013	140	18			PROPN
iajs-1013	140	19	x	x	PUNCT
iajs-1013	141	1	≈	≈	NOUN
iajs-1013	141	2	m	m	NOUN
iajs-1013	141	3	and	and	CCONJ
iajs-1013	141	4	hence	hence	ADV
iajs-1013	141	5	m	m	VERB
iajs-1013	141	6	is	be	AUX
iajs-1013	141	7	weakly	weakly	ADJ
iajs-1013	141	8	l	l	NOUN
iajs-1013	141	9	-	-	ADJ
iajs-1013	141	10	quasi	quasi	ADJ
iajs-1013	141	11	-	-	ADJ
iajs-1013	141	12	injective	injective	ADJ
iajs-1013	141	13	.	.	PUNCT
iajs-1013	142	1	1.10	1.10	NUM
iajs-1013	142	2	corollary	corollary	NOUN
iajs-1013	142	3	let	let	VERB
iajs-1013	142	4	l	l	NOUN
iajs-1013	142	5	and	and	CCONJ
iajs-1013	142	6	n	n	CCONJ
iajs-1013	142	7	be	be	AUX
iajs-1013	142	8	two	two	NUM
iajs-1013	142	9	submodules	submodule	NOUN
iajs-1013	142	10	of	of	ADP
iajs-1013	142	11	an	an	DET
iajs-1013	142	12	r	r	NOUN
iajs-1013	142	13	-	-	PUNCT
iajs-1013	142	14	module	module	NOUN
iajs-1013	142	15	m	m	NOUN
iajs-1013	142	16	such	such	ADJ
iajs-1013	142	17	that	that	SCONJ
iajs-1013	142	18	l	l	NOUN
iajs-1013	142	19			PROPN
iajs-1013	142	20	n.	n.	NOUN
iajs-1013	142	21	if	if	SCONJ
iajs-1013	142	22	m	m	NOUN
iajs-1013	142	23	is	be	AUX
iajs-1013	142	24	weakly	weakly	ADJ
iajs-1013	142	25	nquasi	nquasi	NOUN
iajs-1013	142	26	–	–	PUNCT
iajs-1013	142	27	injective	injective	ADJ
iajs-1013	142	28	,	,	PUNCT
iajs-1013	142	29	then	then	ADV
iajs-1013	142	30	m	m	NOUN
iajs-1013	142	31	is	be	AUX
iajs-1013	142	32	weakly	weakly	ADJ
iajs-1013	142	33	l	l	NOUN
iajs-1013	142	34	-	-	ADJ
iajs-1013	142	35	quasi	quasi	ADJ
iajs-1013	142	36	-	-	ADJ
iajs-1013	142	37	injective	injective	ADJ
iajs-1013	142	38	.	.	PUNCT
iajs-1013	143	1	1.11	1.11	NUM
iajs-1013	143	2	corollary	corollary	NOUN
iajs-1013	143	3	let	let	VERB
iajs-1013	143	4	m	m	PRON
iajs-1013	143	5	be	be	AUX
iajs-1013	143	6	an	an	DET
iajs-1013	143	7	r	r	NOUN
iajs-1013	143	8	-	-	PUNCT
iajs-1013	143	9	module	module	NOUN
iajs-1013	143	10	and	and	CCONJ
iajs-1013	143	11	n	n	CCONJ
iajs-1013	143	12	be	be	VERB
iajs-1013	143	13	a	a	DET
iajs-1013	143	14	submodule	submodule	NOUN
iajs-1013	143	15	of	of	ADP
iajs-1013	143	16	m	m	PROPN
iajs-1013	143	17	.	.	PUNCT
iajs-1013	144	1	if	if	SCONJ
iajs-1013	144	2	l	l	NOUN
iajs-1013	144	3	is	be	AUX
iajs-1013	144	4	a	a	DET
iajs-1013	144	5	submodule	submodule	NOUN
iajs-1013	144	6	of	of	ADP
iajs-1013	144	7	m	m	PROPN
iajs-1013	144	8	and	and	CCONJ
iajs-1013	144	9	m	m	PROPN
iajs-1013	144	10	is	be	AUX
iajs-1013	144	11	weakly	weakly	ADJ
iajs-1013	144	12	n	n	CCONJ
iajs-1013	144	13	-	-	PUNCT
iajs-1013	144	14	quasi	quasi	NOUN
iajs-1013	144	15	-	-	ADJ
iajs-1013	144	16	injective	injective	ADJ
iajs-1013	144	17	,	,	PUNCT
iajs-1013	144	18	then	then	ADV
iajs-1013	144	19	m	m	VERB
iajs-1013	144	20	is	be	AUX
iajs-1013	144	21	weakly	weakly	ADJ
iajs-1013	144	22	n	n	CCONJ
iajs-1013	144	23			PUNCT
iajs-1013	144	24	l	l	NOUN
iajs-1013	144	25	quasi	quasi	NOUN
iajs-1013	144	26	-	-	ADJ
iajs-1013	144	27	injective	injective	ADJ
iajs-1013	144	28	.	.	PUNCT
iajs-1013	145	1	in	in	ADP
iajs-1013	145	2	the	the	DET
iajs-1013	145	3	following	follow	VERB
iajs-1013	145	4	two	two	NUM
iajs-1013	145	5	results	result	NOUN
iajs-1013	145	6	,	,	PUNCT
iajs-1013	145	7	we	we	PRON
iajs-1013	145	8	explain	explain	VERB
iajs-1013	145	9	the	the	DET
iajs-1013	145	10	behavior	behavior	NOUN
iajs-1013	145	11	of	of	ADP
iajs-1013	145	12	weakly	weakly	ADJ
iajs-1013	145	13	-	-	PUNCT
iajs-1013	145	14	quasi	quasi	NOUN
iajs-1013	145	15	-	-	NOUN
iajs-1013	145	16	injectivity	injectivity	NOUN
iajs-1013	145	17	under	under	ADP
iajs-1013	145	18	homomorphism	homomorphism	NOUN
iajs-1013	145	19	.	.	PUNCT
iajs-1013	146	1	1.12	1.12	NUM
iajs-1013	146	2	proposition	proposition	NOUN
iajs-1013	146	3	let	let	VERB
iajs-1013	146	4	h	h	NOUN
iajs-1013	146	5	,	,	PUNCT
iajs-1013	146	6	n	n	PROPN
iajs-1013	146	7	and	and	CCONJ
iajs-1013	146	8	m	m	AUX
iajs-1013	146	9	be	be	VERB
iajs-1013	146	10	r	r	NOUN
iajs-1013	146	11	-	-	PUNCT
iajs-1013	146	12	modules	module	NOUN
iajs-1013	146	13	and	and	CCONJ
iajs-1013	146	14	let	let	VERB
iajs-1013	146	15	g	g	NOUN
iajs-1013	146	16	:	:	PUNCT
iajs-1013	146	17	n	n	PRON
iajs-1013	146	18			PROPN
iajs-1013	146	19	h	h	NOUN
iajs-1013	146	20	be	be	VERB
iajs-1013	146	21	an	an	DET
iajs-1013	146	22	epimorphism	epimorphism	NOUN
iajs-1013	146	23	.	.	PUNCT
iajs-1013	147	1	if	if	SCONJ
iajs-1013	147	2	m	m	NOUN
iajs-1013	147	3	is	be	AUX
iajs-1013	147	4	weakly	weakly	ADJ
iajs-1013	147	5	n	n	CCONJ
iajs-1013	147	6	-	-	PUNCT
iajs-1013	147	7	quasi	quasi	NOUN
iajs-1013	147	8	-	-	ADJ
iajs-1013	147	9	injective	injective	ADJ
iajs-1013	147	10	,	,	PUNCT
iajs-1013	147	11	then	then	ADV
iajs-1013	147	12	m	m	NOUN
iajs-1013	147	13	is	be	AUX
iajs-1013	147	14	weakly	weakly	ADJ
iajs-1013	147	15	h	h	NOUN
iajs-1013	147	16	-	-	PUNCT
iajs-1013	147	17	quasi	quasi	NOUN
iajs-1013	147	18	-	-	ADJ
iajs-1013	147	19	injective	injective	ADJ
iajs-1013	147	20	.	.	PUNCT
iajs-1013	148	1	proof	proof	NOUN
iajs-1013	148	2	:	:	PUNCT
iajs-1013	148	3	let	let	VERB
iajs-1013	148	4	f	f	PRON
iajs-1013	148	5			PROPN
iajs-1013	148	6	hom(h	hom(h	PROPN
iajs-1013	148	7	,	,	PUNCT
iajs-1013	148	8	m	m	PROPN
iajs-1013	148	9	)	)	PUNCT
iajs-1013	148	10	.	.	PUNCT
iajs-1013	149	1	then	then	ADV
iajs-1013	149	2	f	f	PROPN
iajs-1013	149	3			PROPN
iajs-1013	149	4	g	g	PROPN
iajs-1013	149	5			PROPN
iajs-1013	149	6	hom(n	hom(n	PROPN
iajs-1013	149	7	,	,	PUNCT
iajs-1013	149	8	m	m	PROPN
iajs-1013	149	9	)	)	PUNCT
iajs-1013	149	10	.	.	PUNCT
iajs-1013	150	1	so	so	ADV
iajs-1013	150	2	there	there	PRON
iajs-1013	150	3	exists	exist	VERB
iajs-1013	150	4	a	a	DET
iajs-1013	150	5	submodule	submodule	NOUN
iajs-1013	150	6	x	x	PUNCT
iajs-1013	150	7	of	of	ADP
iajs-1013	150	8	m	m	PRON
iajs-1013	150	9	such	such	ADJ
iajs-1013	150	10	that	that	SCONJ
iajs-1013	150	11	f	f	PROPN
iajs-1013	150	12	(	(	PUNCT
iajs-1013	150	13	g(n	g(n	PROPN
iajs-1013	150	14	)	)	PUNCT
iajs-1013	150	15	)	)	PUNCT
iajs-1013	151	1			PROPN
iajs-1013	151	2	x	x	PUNCT
iajs-1013	152	1	≈	≈	NOUN
iajs-1013	152	2	m	m	VERB
iajs-1013	152	3	which	which	PRON
iajs-1013	152	4	means	mean	VERB
iajs-1013	152	5	that	that	SCONJ
iajs-1013	152	6	m	m	NOUN
iajs-1013	152	7	is	be	AUX
iajs-1013	152	8	weakly	weakly	ADJ
iajs-1013	152	9	h	h	NOUN
iajs-1013	152	10	-	-	PUNCT
iajs-1013	152	11	quasi	quasi	NOUN
iajs-1013	152	12	-	-	ADJ
iajs-1013	152	13	injective	injective	ADJ
iajs-1013	152	14	.	.	PUNCT
iajs-1013	153	1	1.13	1.13	NUM
iajs-1013	153	2	corollary	corollary	NOUN
iajs-1013	153	3	let	let	VERB
iajs-1013	153	4	n	n	PRON
iajs-1013	153	5	be	be	AUX
iajs-1013	153	6	a	a	DET
iajs-1013	153	7	submodule	submodule	NOUN
iajs-1013	153	8	of	of	ADP
iajs-1013	153	9	an	an	DET
iajs-1013	153	10	r	r	NOUN
iajs-1013	153	11	-	-	PUNCT
iajs-1013	153	12	module	module	NOUN
iajs-1013	153	13	m	m	NOUN
iajs-1013	153	14	and	and	CCONJ
iajs-1013	153	15	let	let	VERB
iajs-1013	153	16	g	g	NOUN
iajs-1013	153	17	:	:	PUNCT
iajs-1013	153	18	m	m	PROPN
iajs-1013	153	19			PROPN
iajs-1013	153	20	m	m	AUX
iajs-1013	153	21	be	be	VERB
iajs-1013	153	22	an	an	DET
iajs-1013	153	23	epimorphism	epimorphism	NOUN
iajs-1013	153	24	.	.	PUNCT
iajs-1013	154	1	if	if	SCONJ
iajs-1013	154	2	m	m	NOUN
iajs-1013	154	3	is	be	AUX
iajs-1013	154	4	weakly	weakly	ADJ
iajs-1013	154	5	n	n	CCONJ
iajs-1013	154	6	-	-	PUNCT
iajs-1013	154	7	quasi	quasi	NOUN
iajs-1013	154	8	-	-	ADJ
iajs-1013	154	9	injective	injective	ADJ
iajs-1013	154	10	,	,	PUNCT
iajs-1013	154	11	then	then	ADV
iajs-1013	154	12	m	m	NOUN
iajs-1013	154	13	is	be	AUX
iajs-1013	154	14	weakly	weakly	ADJ
iajs-1013	154	15	g(n)-quasi	g(n)-quasi	NOUN
iajs-1013	154	16	-	-	PUNCT
iajs-1013	154	17	injective	injective	ADJ
iajs-1013	154	18	.	.	PUNCT
iajs-1013	155	1	ibn	ibn	PROPN
iajs-1013	155	2	alhaitham	alhaitham	PROPN
iajs-1013	155	3	j.	j.	PROPN
iajs-1013	155	4	for	for	ADP
iajs-1013	155	5	pure	pure	ADJ
iajs-1013	155	6	&	&	CCONJ
iajs-1013	155	7	appl	appl	PROPN
iajs-1013	155	8	.	.	PUNCT
iajs-1013	156	1	sci	sci	PROPN
iajs-1013	156	2	.	.	PUNCT
iajs-1013	157	1	vol.23	vol.23	PROPN
iajs-1013	157	2	(	(	PUNCT
iajs-1013	157	3	1	1	NUM
iajs-1013	157	4	)	)	PUNCT
iajs-1013	157	5	2010	2010	NUM
iajs-1013	157	6	recall	recall	VERB
iajs-1013	157	7	that	that	SCONJ
iajs-1013	157	8	,	,	PUNCT
iajs-1013	157	9	a	a	DET
iajs-1013	157	10	submodule	submodule	NOUN
iajs-1013	157	11	n	n	PROPN
iajs-1013	157	12	of	of	ADP
iajs-1013	157	13	an	an	DET
iajs-1013	157	14	r	r	NOUN
iajs-1013	157	15	-	-	PUNCT
iajs-1013	157	16	module	module	NOUN
iajs-1013	157	17	m	m	NOUN
iajs-1013	157	18	is	be	AUX
iajs-1013	157	19	called	call	VERB
iajs-1013	157	20	quasi	quasi	ADJ
iajs-1013	157	21	-	-	ADJ
iajs-1013	157	22	invertible	invertible	ADJ
iajs-1013	157	23	if	if	SCONJ
iajs-1013	157	24	hom(m	hom(m	PROPN
iajs-1013	157	25	/	/	SYM
iajs-1013	157	26	n	n	CCONJ
iajs-1013	157	27	,	,	PUNCT
iajs-1013	157	28	m	m	NOUN
iajs-1013	157	29	)	)	PUNCT
iajs-1013	157	30	=	=	SYM
iajs-1013	158	1	0	0	NUM
iajs-1013	158	2	,	,	PUNCT
iajs-1013	158	3	[	[	X
iajs-1013	158	4	5	5	NUM
iajs-1013	158	5	]	]	PUNCT
iajs-1013	158	6	.	.	PUNCT
iajs-1013	159	1	1.14	1.14	NUM
iajs-1013	159	2	proposition	proposition	NOUN
iajs-1013	159	3	let	let	VERB
iajs-1013	159	4	m	m	PRON
iajs-1013	159	5	be	be	AUX
iajs-1013	159	6	a	a	DET
iajs-1013	159	7	torsion	torsion	NOUN
iajs-1013	159	8	-	-	PUNCT
iajs-1013	159	9	free	free	ADJ
iajs-1013	159	10	r	r	NOUN
iajs-1013	159	11	-	-	PUNCT
iajs-1013	159	12	module	module	NOUN
iajs-1013	159	13	and	and	CCONJ
iajs-1013	159	14	let	let	VERB
iajs-1013	159	15	n	n	PRON
iajs-1013	159	16	be	be	AUX
iajs-1013	159	17	a	a	DET
iajs-1013	159	18	quasi	quasi	ADJ
iajs-1013	159	19	-	-	ADJ
iajs-1013	159	20	invertible	invertible	ADJ
iajs-1013	159	21	submodule	submodule	NOUN
iajs-1013	159	22	of	of	ADP
iajs-1013	159	23	m.	m.	NOUN
iajs-1013	159	24	if	if	SCONJ
iajs-1013	159	25	m	m	NOUN
iajs-1013	159	26	is	be	AUX
iajs-1013	159	27	weakly	weakly	ADJ
iajs-1013	159	28	m	m	PROPN
iajs-1013	159	29	/	/	SYM
iajs-1013	159	30	n	n	CCONJ
iajs-1013	159	31	-	-	PUNCT
iajs-1013	159	32	quasi	quasi	NOUN
iajs-1013	159	33	-	-	ADJ
iajs-1013	159	34	injective	injective	ADJ
iajs-1013	159	35	,	,	PUNCT
iajs-1013	159	36	then	then	ADV
iajs-1013	159	37	n	n	PRON
iajs-1013	159	38	is	be	AUX
iajs-1013	159	39	a	a	DET
iajs-1013	159	40	quasi	quasi	ADJ
iajs-1013	159	41	-	-	ADJ
iajs-1013	159	42	invertible	invertible	ADJ
iajs-1013	159	43	submodule	submodule	NOUN
iajs-1013	159	44	of	of	ADP
iajs-1013	159	45	m	m	PROPN
iajs-1013	159	46	.	.	PUNCT
iajs-1013	160	1	proof	proof	NOUN
iajs-1013	160	2	:	:	PUNCT
iajs-1013	160	3	assume	assume	VERB
iajs-1013	160	4	that	that	SCONJ
iajs-1013	160	5	n	n	PRON
iajs-1013	160	6	is	be	AUX
iajs-1013	160	7	not	not	PART
iajs-1013	160	8	quasi	quasi	ADJ
iajs-1013	160	9	-	-	ADJ
iajs-1013	160	10	invertible	invertible	ADJ
iajs-1013	160	11	in	in	ADP
iajs-1013	160	12	m	m	PROPN
iajs-1013	160	13	.	.	PUNCT
iajs-1013	161	1	then	then	ADV
iajs-1013	161	2	hom	hom	INTJ
iajs-1013	161	3	(	(	PUNCT
iajs-1013	161	4	m	m	VERB
iajs-1013	161	5	/n	/n	PRON
iajs-1013	161	6	,	,	PUNCT
iajs-1013	161	7	m	m	VERB
iajs-1013	161	8	)	)	PUNCT
iajs-1013	161	9			NOUN
iajs-1013	161	10	0	0	NUM
iajs-1013	161	11	.	.	PUNCT
iajs-1013	162	1	let	let	VERB
iajs-1013	162	2	f	f	NOUN
iajs-1013	162	3	:	:	PUNCT
iajs-1013	162	4	m	m	VERB
iajs-1013	162	5	/	/	SYM
iajs-1013	162	6	n	n	CCONJ
iajs-1013	162	7			PROPN
iajs-1013	162	8	m	m	VERB
iajs-1013	162	9	be	be	VERB
iajs-1013	162	10	a	a	DET
iajs-1013	162	11	non	non	ADJ
iajs-1013	162	12	-	-	ADJ
iajs-1013	162	13	zero	zero	NUM
iajs-1013	162	14	homomorphism	homomorphism	NOUN
iajs-1013	162	15	.	.	PUNCT
iajs-1013	163	1	therefore	therefore	ADV
iajs-1013	163	2	there	there	PRON
iajs-1013	163	3	exists	exist	VERB
iajs-1013	163	4	m	m	VERB
iajs-1013	163	5	+	+	ADJ
iajs-1013	163	6	n	n	CCONJ
iajs-1013	163	7			NOUN
iajs-1013	163	8	m	m	PROPN
iajs-1013	163	9	/	/	SYM
iajs-1013	163	10	n	n	PROPN
iajs-1013	163	11	with	with	ADP
iajs-1013	163	12	m	m	PROPN
iajs-1013	163	13			NOUN
iajs-1013	163	14	m	m	VERB
iajs-1013	163	15	and	and	CCONJ
iajs-1013	163	16	m	m	PROPN
iajs-1013	163	17			NOUN
iajs-1013	163	18	n	n	CCONJ
iajs-1013	163	19	such	such	ADJ
iajs-1013	163	20	that	that	SCONJ
iajs-1013	163	21	0	0	NUM
iajs-1013	163	22			NOUN
iajs-1013	163	23	f	f	X
iajs-1013	163	24	(	(	PUNCT
iajs-1013	163	25	m	m	PROPN
iajs-1013	163	26	+	+	NOUN
iajs-1013	163	27	n	n	CCONJ
iajs-1013	163	28	)	)	PUNCT
iajs-1013	163	29	=	=	SYM
iajs-1013	164	1	x	x	PUNCT
iajs-1013	164	2	for	for	ADP
iajs-1013	164	3	some	some	PRON
iajs-1013	164	4	x	x	SYM
iajs-1013	164	5			NOUN
iajs-1013	164	6	m	m	VERB
iajs-1013	164	7	.	.	PUNCT
iajs-1013	165	1	let	let	VERB
iajs-1013	166	1	i	i	PRON
iajs-1013	166	2	:	:	PUNCT
iajs-1013	166	3	m	m	VERB
iajs-1013	166	4	/	/	SYM
iajs-1013	166	5	n	n	PROPN
iajs-1013	166	6			PROPN
iajs-1013	166	7	m	m	PROPN
iajs-1013	166	8	/	/	SYM
iajs-1013	166	9	n	n	PROPN
iajs-1013	166	10	be	be	VERB
iajs-1013	166	11	the	the	DET
iajs-1013	166	12	inclusion	inclusion	NOUN
iajs-1013	166	13	homomorphism	homomorphism	NOUN
iajs-1013	166	14	.	.	PUNCT
iajs-1013	167	1	then	then	ADV
iajs-1013	167	2	f	f	PROPN
iajs-1013	167	3			PROPN
iajs-1013	167	4	i	i	PRON
iajs-1013	167	5			PROPN
iajs-1013	167	6	hom(m	hom(m	PROPN
iajs-1013	167	7	/	/	SYM
iajs-1013	167	8	n	n	CCONJ
iajs-1013	167	9	,	,	PUNCT
iajs-1013	167	10	m	m	PROPN
iajs-1013	167	11	)	)	PUNCT
iajs-1013	167	12	.	.	PUNCT
iajs-1013	168	1	so	so	ADV
iajs-1013	168	2	there	there	PRON
iajs-1013	168	3	exists	exist	VERB
iajs-1013	168	4	a	a	DET
iajs-1013	168	5	submodule	submodule	NOUN
iajs-1013	168	6	x	x	PUNCT
iajs-1013	168	7	of	of	ADP
iajs-1013	168	8	m	m	PRON
iajs-1013	168	9	such	such	ADJ
iajs-1013	168	10	that	that	SCONJ
iajs-1013	168	11	f	f	PROPN
iajs-1013	169	1			INTJ
iajs-1013	169	2	i	i	PRON
iajs-1013	169	3	(	(	PUNCT
iajs-1013	169	4	m	m	PROPN
iajs-1013	169	5	/	/	SYM
iajs-1013	169	6	n	n	PROPN
iajs-1013	169	7	)	)	PUNCT
iajs-1013	169	8			PROPN
iajs-1013	169	9	x	x	SYM
iajs-1013	169	10	≈	≈	NUM
iajs-1013	169	11	m.	m.	NOUN
iajs-1013	169	12	let	let	VERB
iajs-1013	169	13	g	g	NOUN
iajs-1013	169	14	:	:	PUNCT
iajs-1013	169	15	x	x	SYM
iajs-1013	169	16			PROPN
iajs-1013	169	17	m	m	AUX
iajs-1013	169	18	be	be	VERB
iajs-1013	169	19	an	an	DET
iajs-1013	169	20	isomorphism	isomorphism	NOUN
iajs-1013	169	21	,	,	PUNCT
iajs-1013	169	22	then	then	ADV
iajs-1013	169	23	g	g	NUM
iajs-1013	169	24	f	f	NOUN
iajs-1013	170	1	i	i	PRON
iajs-1013	170	2			PROPN
iajs-1013	170	3	hom(m	hom(m	PROPN
iajs-1013	170	4	/	/	SYM
iajs-1013	170	5	n	n	CCONJ
iajs-1013	170	6	,	,	PUNCT
iajs-1013	170	7	m	m	NOUN
iajs-1013	170	8	)	)	PUNCT
iajs-1013	171	1	=	=	SYM
iajs-1013	171	2	0	0	X
iajs-1013	171	3	.	.	PUNCT
iajs-1013	171	4	therefore	therefore	ADV
iajs-1013	171	5	g	g	NUM
iajs-1013	171	6	f	f	NOUN
iajs-1013	172	1	i	i	PRON
iajs-1013	172	2	=	=	NOUN
iajs-1013	172	3	0	0	NUM
iajs-1013	172	4	implies	imply	VERB
iajs-1013	172	5	that	that	SCONJ
iajs-1013	172	6	f	f	VERB
iajs-1013	173	1	i	i	PRON
iajs-1013	173	2	=	=	NOUN
iajs-1013	173	3	0	0	PUNCT
iajs-1013	173	4	and	and	CCONJ
iajs-1013	173	5	hence	hence	ADV
iajs-1013	173	6	f	f	PROPN
iajs-1013	173	7	(	(	PUNCT
iajs-1013	173	8	m	m	PROPN
iajs-1013	173	9	/	/	SYM
iajs-1013	173	10	n	n	CCONJ
iajs-1013	173	11	)	)	PUNCT
iajs-1013	173	12	=	=	SYM
iajs-1013	174	1	0	0	X
iajs-1013	174	2	.	.	PUNCT
iajs-1013	175	1	but	but	CCONJ
iajs-1013	175	2	m	m	VERB
iajs-1013	175	3			NOUN
iajs-1013	175	4	m	m	VERB
iajs-1013	175	5	and	and	CCONJ
iajs-1013	175	6	m	m	PROPN
iajs-1013	175	7			NUM
iajs-1013	175	8	n	n	NOUN
iajs-1013	175	9	and	and	CCONJ
iajs-1013	175	10	m	m	PROPN
iajs-1013	175	11	is	be	AUX
iajs-1013	175	12	essential	essential	ADJ
iajs-1013	175	13	in	in	ADP
iajs-1013	175	14	m	m	PROPN
iajs-1013	175	15	,	,	PUNCT
iajs-1013	175	16	so	so	ADV
iajs-1013	175	17	there	there	PRON
iajs-1013	175	18	exists	exist	VERB
iajs-1013	175	19	0	0	NUM
iajs-1013	175	20			NOUN
iajs-1013	175	21	r	r	NOUN
iajs-1013	175	22			NOUN
iajs-1013	175	23	r	r	NOUN
iajs-1013	175	24	such	such	ADJ
iajs-1013	175	25	that	that	SCONJ
iajs-1013	175	26	r	r	NOUN
iajs-1013	175	27	m	m	PROPN
iajs-1013	175	28			NOUN
iajs-1013	175	29	m.	m.	NOUN
iajs-1013	175	30	hence	hence	ADV
iajs-1013	175	31	r	r	NOUN
iajs-1013	175	32	m	m	NOUN
iajs-1013	175	33	+	+	NOUN
iajs-1013	175	34	n	n	CCONJ
iajs-1013	175	35			NOUN
iajs-1013	175	36	m	m	PROPN
iajs-1013	175	37	/	/	SYM
iajs-1013	175	38	n	n	PROPN
iajs-1013	175	39	and	and	CCONJ
iajs-1013	175	40	f	f	PROPN
iajs-1013	175	41	(	(	PUNCT
iajs-1013	175	42	r	r	NOUN
iajs-1013	175	43	m	m	PROPN
iajs-1013	175	44	+	+	NOUN
iajs-1013	175	45	n	n	CCONJ
iajs-1013	175	46	)	)	PUNCT
iajs-1013	175	47	=	=	SYM
iajs-1013	175	48	0	0	PUNCT
iajs-1013	176	1	=	=	SYM
iajs-1013	176	2	r	r	NOUN
iajs-1013	176	3	f	f	X
iajs-1013	176	4	(	(	PUNCT
iajs-1013	176	5	m	m	PROPN
iajs-1013	176	6	)	)	PUNCT
iajs-1013	176	7	+	+	CCONJ
iajs-1013	177	1	n	n	NOUN
iajs-1013	177	2	=	=	SYM
iajs-1013	177	3	r	r	NOUN
iajs-1013	177	4	x	x	NOUN
iajs-1013	177	5	implies	imply	VERB
iajs-1013	177	6	that	that	SCONJ
iajs-1013	177	7	r	r	NOUN
iajs-1013	177	8	=	=	SYM
iajs-1013	177	9	0	0	NUM
iajs-1013	177	10	which	which	PRON
iajs-1013	177	11	is	be	AUX
iajs-1013	177	12	a	a	DET
iajs-1013	177	13	contradiction	contradiction	NOUN
iajs-1013	177	14	.	.	PUNCT
iajs-1013	178	1	therefore	therefore	ADV
iajs-1013	178	2	n	n	PROPN
iajs-1013	178	3	is	be	AUX
iajs-1013	178	4	quasi	quasi	ADJ
iajs-1013	178	5	-	-	ADJ
iajs-1013	178	6	invertible	invertible	ADJ
iajs-1013	178	7	in	in	ADP
iajs-1013	178	8	m	m	PROPN
iajs-1013	178	9	.	.	PUNCT
iajs-1013	179	1	1.15	1.15	NUM
iajs-1013	179	2	proposition	proposition	NOUN
iajs-1013	179	3	let	let	VERB
iajs-1013	179	4	m	m	PRON
iajs-1013	179	5	and	and	CCONJ
iajs-1013	179	6	n	n	CCONJ
iajs-1013	179	7	be	be	VERB
iajs-1013	179	8	two	two	NUM
iajs-1013	179	9	r	r	NOUN
iajs-1013	179	10	-	-	PUNCT
iajs-1013	179	11	modules	module	NOUN
iajs-1013	179	12	and	and	CCONJ
iajs-1013	179	13	let	let	VERB
iajs-1013	179	14	l	l	NOUN
iajs-1013	179	15	be	be	AUX
iajs-1013	179	16	an	an	DET
iajs-1013	179	17	essential	essential	ADJ
iajs-1013	179	18	extension	extension	NOUN
iajs-1013	179	19	of	of	ADP
iajs-1013	179	20	m.	m.	NOUN
iajs-1013	179	21	if	if	SCONJ
iajs-1013	179	22	m	m	NOUN
iajs-1013	179	23	is	be	AUX
iajs-1013	179	24	weakly	weakly	ADJ
iajs-1013	179	25	n	n	CCONJ
iajs-1013	179	26	-	-	PUNCT
iajs-1013	179	27	quasi	quasi	NOUN
iajs-1013	179	28	-	-	ADJ
iajs-1013	179	29	injective	injective	ADJ
iajs-1013	179	30	,	,	PUNCT
iajs-1013	179	31	then	then	ADV
iajs-1013	179	32	l	l	NOUN
iajs-1013	179	33	is	be	AUX
iajs-1013	179	34	also	also	ADV
iajs-1013	179	35	weakly	weakly	ADJ
iajs-1013	179	36	n	n	CCONJ
iajs-1013	179	37	-	-	PUNCT
iajs-1013	179	38	quasi	quasi	NOUN
iajs-1013	179	39	-	-	ADJ
iajs-1013	179	40	injective	injective	ADJ
iajs-1013	179	41	.	.	PUNCT
iajs-1013	180	1	proof	proof	NOUN
iajs-1013	180	2	:	:	PUNCT
iajs-1013	180	3	let	let	VERB
iajs-1013	180	4	f	f	PROPN
iajs-1013	180	5			PROPN
iajs-1013	180	6	hom(n	hom(n	PROPN
iajs-1013	180	7	,	,	PUNCT
iajs-1013	180	8	l	l	NOUN
iajs-1013	180	9	)	)	PUNCT
iajs-1013	180	10	.	.	PUNCT
iajs-1013	181	1	but	but	CCONJ
iajs-1013	181	2	l	l	X
iajs-1013	181	3	=	=	PUNCT
iajs-1013	182	1	m	m	VERB
iajs-1013	183	1	[	[	X
iajs-1013	183	2	by	by	ADP
iajs-1013	183	3	cor.19.8	cor.19.8	NOUN
iajs-1013	183	4	,	,	PUNCT
iajs-1013	183	5	p.65	p.65	ADP
iajs-1013	183	6	,	,	PUNCT
iajs-1013	183	7	[	[	X
iajs-1013	183	8	6	6	NUM
iajs-1013	183	9	]	]	PUNCT
iajs-1013	183	10	]	]	PUNCT
iajs-1013	183	11	.	.	PUNCT
iajs-1013	184	1	hence	hence	ADV
iajs-1013	184	2	f	f	PROPN
iajs-1013	184	3			PROPN
iajs-1013	184	4	hom(n	hom(n	PROPN
iajs-1013	184	5	,	,	PUNCT
iajs-1013	184	6	m	m	PROPN
iajs-1013	184	7	)	)	PUNCT
iajs-1013	184	8	.	.	PUNCT
iajs-1013	185	1	so	so	ADV
iajs-1013	185	2	there	there	PRON
iajs-1013	185	3	exists	exist	VERB
iajs-1013	185	4	a	a	DET
iajs-1013	185	5	submodule	submodule	NOUN
iajs-1013	185	6	x	x	PUNCT
iajs-1013	185	7	of	of	ADP
iajs-1013	185	8	m	m	PRON
iajs-1013	185	9	such	such	ADJ
iajs-1013	185	10	that	that	SCONJ
iajs-1013	185	11	f	f	PROPN
iajs-1013	185	12	(	(	PUNCT
iajs-1013	185	13	n	n	CCONJ
iajs-1013	185	14	)	)	PUNCT
iajs-1013	185	15			PROPN
iajs-1013	185	16	x	x	SYM
iajs-1013	185	17	≈	≈	PROPN
iajs-1013	185	18	m.	m.	NOUN
iajs-1013	185	19	consider	consider	VERB
iajs-1013	185	20	the	the	DET
iajs-1013	185	21	following	follow	VERB
iajs-1013	185	22	diagram	diagram	NOUN
iajs-1013	185	23	:	:	PUNCT
iajs-1013	185	24	32	32	NUM
iajs-1013	185	25	l	l	NOUN
iajs-1013	185	26	l	l	X
iajs-1013	185	27	iig	iig	PROPN
iajs-1013	185	28			PROPN
iajs-1013	185	29			PROPN
iajs-1013	185	30			PROPN
iajs-1013	185	31			PROPN
iajs-1013	185	32			PROPN
iajs-1013	185	33	i1	i1	PROPN
iajs-1013	185	34			PROPN
iajs-1013	185	35			PROPN
iajs-1013	185	36			PROPN
iajs-1013	185	37			PROPN
iajs-1013	185	38			PROPN
iajs-1013	185	39			PROPN
iajs-1013	185	40			PROPN
iajs-1013	185	41			PROPN
iajs-1013	185	42			PROPN
iajs-1013	185	43			PROPN
iajs-1013	185	44			PROPN
iajs-1013	185	45			PROPN
iajs-1013	185	46			NOUN
iajs-1013	185	47			NOUN
iajs-1013	185	48			PROPN
iajs-1013	185	49	l	l	NOUN
iajs-1013	185	50	where	where	SCONJ
iajs-1013	185	51	g	g	NOUN
iajs-1013	185	52	:	:	PUNCT
iajs-1013	185	53	x	x	SYM
iajs-1013	186	1			PROPN
iajs-1013	186	2	m	m	AUX
iajs-1013	186	3	be	be	VERB
iajs-1013	186	4	an	an	DET
iajs-1013	186	5	isomorphism	isomorphism	NOUN
iajs-1013	186	6	and	and	CCONJ
iajs-1013	186	7	i1	i1	PROPN
iajs-1013	186	8	,	,	PUNCT
iajs-1013	186	9	i2	i2	PROPN
iajs-1013	186	10	,	,	PUNCT
iajs-1013	186	11	i3	i3	NOUN
iajs-1013	186	12	are	be	AUX
iajs-1013	186	13	inclusion	inclusion	NOUN
iajs-1013	186	14	homomorphisims	homomorphisim	NOUN
iajs-1013	186	15	.	.	PUNCT
iajs-1013	187	1	l	l	NOUN
iajs-1013	187	2	being	be	AUX
iajs-1013	187	3	quasi	quasi	ADJ
iajs-1013	187	4	-	-	ADJ
iajs-1013	187	5	injective	injective	ADJ
iajs-1013	187	6	,	,	PUNCT
iajs-1013	187	7	so	so	SCONJ
iajs-1013	187	8	there	there	PRON
iajs-1013	187	9	exists	exist	VERB
iajs-1013	187	10	a	a	DET
iajs-1013	187	11	homomorphism	homomorphism	NOUN
iajs-1013	187	12			X
iajs-1013	187	13	:	:	PUNCT
iajs-1013	187	14	l	l	NOUN
iajs-1013	187	15			X
iajs-1013	187	16	l	l	NOUN
iajs-1013	187	17	such	such	ADJ
iajs-1013	187	18	that	that	SCONJ
iajs-1013	187	19			PROPN
iajs-1013	187	20	i	i	NOUN
iajs-1013	187	21	g	g	PROPN
iajs-1013	187	22	=	=	PROPN
iajs-1013	187	23	i1	i1	PROPN
iajs-1013	187	24	with	with	ADP
iajs-1013	187	25	i	i	PROPN
iajs-1013	187	26	=	=	SYM
iajs-1013	187	27	i3	i3	NOUN
iajs-1013	187	28	i2	i2	PROPN
iajs-1013	187	29	.	.	PUNCT
iajs-1013	188	1	we	we	PRON
iajs-1013	188	2	claim	claim	VERB
iajs-1013	188	3	that	that	SCONJ
iajs-1013	188	4	ker	ker	NOUN
iajs-1013	188	5			X
iajs-1013	188	6	=	=	SYM
iajs-1013	188	7	{	{	PUNCT
iajs-1013	188	8	0	0	NUM
iajs-1013	188	9	}	}	PUNCT
iajs-1013	188	10	.	.	PUNCT
iajs-1013	189	1	let	let	VERB
iajs-1013	189	2	0	0	NUM
iajs-1013	189	3			PROPN
iajs-1013	189	4	ℓ	ℓ	PROPN
iajs-1013	189	5			NOUN
iajs-1013	189	6	l	l	NOUN
iajs-1013	189	7	and	and	CCONJ
iajs-1013	189	8	(ℓ	(ℓ	NUM
iajs-1013	189	9	)	)	PUNCT
iajs-1013	189	10	=	=	SYM
iajs-1013	190	1	0	0	X
iajs-1013	190	2	.	.	PUNCT
iajs-1013	191	1	but	but	CCONJ
iajs-1013	191	2	m	m	PROPN
iajs-1013	191	3	is	be	AUX
iajs-1013	191	4	essential	essential	ADJ
iajs-1013	191	5	in	in	ADP
iajs-1013	191	6	l	l	NOUN
iajs-1013	191	7	,	,	PUNCT
iajs-1013	191	8	so	so	SCONJ
iajs-1013	191	9	there	there	PRON
iajs-1013	191	10	exists	exist	VERB
iajs-1013	191	11	0	0	NUM
iajs-1013	191	12			NOUN
iajs-1013	191	13	r	r	NOUN
iajs-1013	191	14			NOUN
iajs-1013	191	15	r	r	NOUN
iajs-1013	191	16	such	such	ADJ
iajs-1013	191	17	that	that	DET
iajs-1013	191	18	0	0	NUM
iajs-1013	191	19			NOUN
iajs-1013	191	20	r	r	NOUN
iajs-1013	191	21	ℓ	ℓ	PROPN
iajs-1013	191	22			NOUN
iajs-1013	191	23	m.	m.	NOUN
iajs-1013	191	24	hence	hence	ADV
iajs-1013	191	25	there	there	PRON
iajs-1013	191	26	exists	exist	VERB
iajs-1013	191	27	x	x	X
iajs-1013	191	28			NOUN
iajs-1013	191	29	x	x	PUNCT
iajs-1013	191	30	such	such	ADJ
iajs-1013	191	31	that	that	SCONJ
iajs-1013	191	32	g(x	g(x	NOUN
iajs-1013	191	33	)	)	PUNCT
iajs-1013	192	1	=	=	SYM
iajs-1013	192	2	r	r	NOUN
iajs-1013	192	3	ℓ.	ℓ.	NOUN
iajs-1013	192	4	now	now	ADV
iajs-1013	192	5	,	,	PUNCT
iajs-1013	192	6	x	x	X
iajs-1013	192	7	=	=	PUNCT
iajs-1013	192	8			PROPN
iajs-1013	192	9	i	i	NOUN
iajs-1013	192	10	g	g	PROPN
iajs-1013	192	11	(	(	PUNCT
iajs-1013	192	12	x	x	NOUN
iajs-1013	192	13	)	)	PUNCT
iajs-1013	192	14	=	=	NOUN
iajs-1013	192	15			NOUN
iajs-1013	192	16	(	(	PUNCT
iajs-1013	192	17	r	r	NOUN
iajs-1013	192	18	ℓ	ℓ	PROPN
iajs-1013	192	19	)	)	PUNCT
iajs-1013	192	20	=	=	SYM
iajs-1013	192	21	r	r	NOUN
iajs-1013	192	22	(ℓ	(ℓ	NUM
iajs-1013	192	23	)	)	PUNCT
iajs-1013	192	24	=	=	SYM
iajs-1013	192	25	0	0	X
iajs-1013	192	26	.	.	PUNCT
iajs-1013	193	1	so	so	ADV
iajs-1013	193	2	,	,	PUNCT
iajs-1013	193	3	r	r	NOUN
iajs-1013	193	4	ℓ	ℓ	NOUN
iajs-1013	193	5	=	=	SYM
iajs-1013	193	6	0	0	NUM
iajs-1013	193	7	which	which	PRON
iajs-1013	193	8	is	be	AUX
iajs-1013	193	9	a	a	DET
iajs-1013	193	10	contradiction	contradiction	NOUN
iajs-1013	193	11	.	.	PUNCT
iajs-1013	194	1	therefore	therefore	ADV
iajs-1013	194	2			NOUN
iajs-1013	194	3	is	be	AUX
iajs-1013	194	4	a	a	DET
iajs-1013	194	5	monomorphism	monomorphism	NOUN
iajs-1013	194	6	.	.	PUNCT
iajs-1013	195	1	let	let	VERB
iajs-1013	195	2			NOUN
iajs-1013	195	3	=	=	PUNCT
iajs-1013	195	4	l	l	PROPN
iajs-1013	195	5	.	.	PUNCT
iajs-1013	196	1	then	then	ADV
iajs-1013	196	2			PROPN
iajs-1013	196	3	i	i	PROPN
iajs-1013	196	4	g	g	PROPN
iajs-1013	196	5	=	=	PROPN
iajs-1013	196	6	i1	i1	PROPN
iajs-1013	196	7	.	.	PUNCT
iajs-1013	197	1	hence	hence	ADV
iajs-1013	197	2	x	x	X
iajs-1013	197	3			PROPN
iajs-1013	197	4	(l	(l	X
iajs-1013	197	5	)	)	PUNCT
iajs-1013	198	1	≈	≈	PROPN
iajs-1013	198	2	l.	l.	PROPN
iajs-1013	198	3	therefore	therefore	ADV
iajs-1013	198	4	f	f	PROPN
iajs-1013	198	5	(	(	PUNCT
iajs-1013	198	6	n	n	CCONJ
iajs-1013	198	7	)	)	PUNCT
iajs-1013	198	8			PROPN
iajs-1013	198	9	x	x	X
iajs-1013	198	10			PROPN
iajs-1013	198	11	(l	(l	X
iajs-1013	198	12	)	)	PUNCT
iajs-1013	198	13	,	,	PUNCT
iajs-1013	198	14	which	which	PRON
iajs-1013	198	15	means	mean	VERB
iajs-1013	198	16	that	that	SCONJ
iajs-1013	198	17	l	l	NOUN
iajs-1013	198	18	is	be	AUX
iajs-1013	198	19	weakly	weakly	ADJ
iajs-1013	198	20	n	n	CCONJ
iajs-1013	198	21	-	-	PUNCT
iajs-1013	198	22	quasi	quasi	NOUN
iajs-1013	198	23	-	-	ADJ
iajs-1013	198	24	injective	injective	ADJ
iajs-1013	198	25	.	.	PUNCT
iajs-1013	199	1	ibn	ibn	PROPN
iajs-1013	199	2	alhaitham	alhaitham	PROPN
iajs-1013	199	3	j.	j.	PROPN
iajs-1013	199	4	for	for	ADP
iajs-1013	199	5	pure	pure	ADJ
iajs-1013	199	6	&	&	CCONJ
iajs-1013	199	7	appl	appl	PROPN
iajs-1013	199	8	.	.	PUNCT
iajs-1013	200	1	sci	sci	PROPN
iajs-1013	200	2	.	.	PUNCT
iajs-1013	201	1	vol.23	vol.23	PROPN
iajs-1013	201	2	(	(	PUNCT
iajs-1013	201	3	1	1	NUM
iajs-1013	201	4	)	)	PUNCT
iajs-1013	201	5	2010	2010	NUM
iajs-1013	201	6	section	section	NOUN
iajs-1013	201	7	two	two	NUM
iajs-1013	201	8	:	:	PUNCT
iajs-1013	201	9	characterizations	characterization	NOUN
iajs-1013	201	10	of	of	ADP
iajs-1013	201	11	weakly	weakly	ADJ
iajs-1013	201	12	relative	relative	ADJ
iajs-1013	201	13	quasi	quasi	ADJ
iajs-1013	201	14	injective	injective	ADJ
iajs-1013	201	15	modules	module	NOUN
iajs-1013	201	16	we	we	PRON
iajs-1013	201	17	give	give	VERB
iajs-1013	201	18	in	in	ADP
iajs-1013	201	19	this	this	DET
iajs-1013	201	20	section	section	NOUN
iajs-1013	201	21	many	many	ADJ
iajs-1013	201	22	interesting	interesting	ADJ
iajs-1013	201	23	characterizations	characterization	NOUN
iajs-1013	201	24	of	of	ADP
iajs-1013	201	25	weakly	weakly	ADJ
iajs-1013	201	26	relative	relative	ADJ
iajs-1013	201	27	quasiinjective	quasiinjective	ADJ
iajs-1013	201	28	modules	module	NOUN
iajs-1013	201	29	which	which	PRON
iajs-1013	201	30	are	be	AUX
iajs-1013	201	31	very	very	ADV
iajs-1013	201	32	useful	useful	ADJ
iajs-1013	201	33	in	in	ADP
iajs-1013	201	34	the	the	DET
iajs-1013	201	35	next	next	ADJ
iajs-1013	201	36	sections	section	NOUN
iajs-1013	201	37	.	.	PUNCT
iajs-1013	202	1	first	first	ADV
iajs-1013	202	2	,	,	PUNCT
iajs-1013	202	3	we	we	PRON
iajs-1013	202	4	shall	shall	AUX
iajs-1013	202	5	show	show	VERB
iajs-1013	202	6	that	that	SCONJ
iajs-1013	202	7	the	the	DET
iajs-1013	202	8	concept	concept	NOUN
iajs-1013	202	9	of	of	ADP
iajs-1013	202	10	weakly	weakly	ADJ
iajs-1013	202	11	quasi	quasi	NOUN
iajs-1013	202	12	-	-	NOUN
iajs-1013	202	13	injectivity	injectivity	NOUN
iajs-1013	202	14	can	can	AUX
iajs-1013	202	15	be	be	AUX
iajs-1013	202	16	given	give	VERB
iajs-1013	202	17	in	in	ADP
iajs-1013	202	18	terms	term	NOUN
iajs-1013	202	19	of	of	ADP
iajs-1013	202	20	commutative	commutative	ADJ
iajs-1013	202	21	diagram	diagram	NOUN
iajs-1013	202	22	.	.	PUNCT
iajs-1013	203	1	2.1	2.1	NUM
iajs-1013	203	2	theorem	theorem	NOUN
iajs-1013	203	3	let	let	VERB
iajs-1013	203	4	m	m	PRON
iajs-1013	203	5	and	and	CCONJ
iajs-1013	203	6	n	n	CCONJ
iajs-1013	203	7	be	be	VERB
iajs-1013	203	8	two	two	NUM
iajs-1013	203	9	r	r	NOUN
iajs-1013	203	10	-	-	PUNCT
iajs-1013	203	11	modules	module	NOUN
iajs-1013	203	12	.	.	PUNCT
iajs-1013	204	1	then	then	ADV
iajs-1013	204	2	m	m	PROPN
iajs-1013	204	3	is	be	AUX
iajs-1013	204	4	weakly	weakly	ADJ
iajs-1013	204	5	n	n	CCONJ
iajs-1013	204	6	-	-	PUNCT
iajs-1013	204	7	quasi	quasi	NOUN
iajs-1013	204	8	-	-	ADJ
iajs-1013	204	9	injective	injective	ADJ
iajs-1013	204	10	if	if	SCONJ
iajs-1013	204	11	and	and	CCONJ
iajs-1013	204	12	only	only	ADV
iajs-1013	204	13	if	if	SCONJ
iajs-1013	204	14	every	every	DET
iajs-1013	204	15	element	element	NOUN
iajs-1013	204	16	f	f	PROPN
iajs-1013	204	17			PROPN
iajs-1013	204	18	hom(n,	hom(n,	NOUN
iajs-1013	204	19	)	)	PUNCT
iajs-1013	204	20	can	can	AUX
iajs-1013	204	21	be	be	AUX
iajs-1013	204	22	written	write	VERB
iajs-1013	204	23	as	as	ADP
iajs-1013	204	24	a	a	DET
iajs-1013	204	25	composition	composition	NOUN
iajs-1013	204	26	g	g	NUM
iajs-1013	204	27	h	h	NOUN
iajs-1013	204	28	where	where	SCONJ
iajs-1013	204	29	h	h	NOUN
iajs-1013	204	30	:	:	PUNCT
iajs-1013	204	31	n	n	PRON
iajs-1013	204	32			PROPN
iajs-1013	204	33	m	m	VERB
iajs-1013	204	34	is	be	AUX
iajs-1013	204	35	a	a	DET
iajs-1013	204	36	homomorphism	homomorphism	NOUN
iajs-1013	204	37	and	and	CCONJ
iajs-1013	204	38	g	g	NOUN
iajs-1013	204	39	:	:	PUNCT
iajs-1013	204	40	m	m	PROPN
iajs-1013	204	41			PROPN
iajs-1013	204	42			PROPN
iajs-1013	204	43	is	be	AUX
iajs-1013	204	44	a	a	DET
iajs-1013	204	45	monomorphism	monomorphism	NOUN
iajs-1013	204	46	.	.	PUNCT
iajs-1013	205	1	that	that	PRON
iajs-1013	205	2	is	be	AUX
iajs-1013	205	3	the	the	DET
iajs-1013	205	4	following	follow	VERB
iajs-1013	205	5	diagram	diagram	NOUN
iajs-1013	205	6	is	be	AUX
iajs-1013	205	7	commutative	commutative	ADJ
iajs-1013	205	8	.	.	PUNCT
iajs-1013	206	1	hom	hom	X
iajs-1013	207	1	o.	o.	PROPN
iajs-1013	207	2	h	h	PROPN
iajs-1013	207	3			PROPN
iajs-1013	207	4			PROPN
iajs-1013	207	5			PROPN
iajs-1013	207	6	f	f	PROPN
iajs-1013	207	7			PROPN
iajs-1013	207	8			PROPN
iajs-1013	207	9	g	g	PROPN
iajs-1013	207	10			NOUN
iajs-1013	207	11			VERB
iajs-1013	207	12			ADJ
iajs-1013	207	13	proof	proof	NOUN
iajs-1013	207	14	:	:	PUNCT
iajs-1013	207	15	assume	assume	VERB
iajs-1013	207	16	that	that	SCONJ
iajs-1013	207	17	m	m	NOUN
iajs-1013	207	18	is	be	AUX
iajs-1013	207	19	weakly	weakly	ADJ
iajs-1013	207	20	n	n	CCONJ
iajs-1013	207	21	-	-	PUNCT
iajs-1013	207	22	quasi	quasi	NOUN
iajs-1013	207	23	-	-	ADJ
iajs-1013	207	24	injective	injective	ADJ
iajs-1013	207	25	.	.	PUNCT
iajs-1013	208	1	let	let	VERB
iajs-1013	208	2	f	f	PROPN
iajs-1013	208	3			PROPN
iajs-1013	208	4	hom(n,	hom(n,	NOUN
iajs-1013	208	5	)	)	PUNCT
iajs-1013	208	6	.	.	PUNCT
iajs-1013	209	1	then	then	ADV
iajs-1013	209	2	there	there	PRON
iajs-1013	209	3	exists	exist	VERB
iajs-1013	209	4	a	a	DET
iajs-1013	209	5	submodule	submodule	NOUN
iajs-1013	209	6	x	x	PUNCT
iajs-1013	209	7	of	of	ADP
iajs-1013	209	8			NUM
iajs-1013	209	9	such	such	ADJ
iajs-1013	209	10	that	that	SCONJ
iajs-1013	209	11	f	f	PROPN
iajs-1013	209	12	(	(	PUNCT
iajs-1013	209	13	n	n	CCONJ
iajs-1013	209	14	)	)	PUNCT
iajs-1013	209	15			PROPN
iajs-1013	209	16	x	x	X
iajs-1013	209	17	≈	≈	NUM
iajs-1013	209	18	m.	m.	NOUN
iajs-1013	210	1	so	so	ADV
iajs-1013	210	2	,	,	PUNCT
iajs-1013	210	3	f	f	X
iajs-1013	210	4	:	:	PUNCT
iajs-1013	210	5	n	n	PRON
iajs-1013	210	6			NUM
iajs-1013	210	7	x	x	X
iajs-1013	210	8	is	be	AUX
iajs-1013	210	9	a	a	DET
iajs-1013	210	10	homomorphism	homomorphism	NOUN
iajs-1013	210	11	.	.	PUNCT
iajs-1013	211	1	let	let	VERB
iajs-1013	211	2			NOUN
iajs-1013	211	3	:	:	PUNCT
iajs-1013	211	4	x	x	SYM
iajs-1013	211	5			PROPN
iajs-1013	211	6	m	m	AUX
iajs-1013	211	7	be	be	VERB
iajs-1013	211	8	an	an	DET
iajs-1013	211	9	isomorphism	isomorphism	NOUN
iajs-1013	211	10	.	.	PUNCT
iajs-1013	212	1	we	we	PRON
iajs-1013	212	2	take	take	VERB
iajs-1013	212	3	h	h	NOUN
iajs-1013	212	4	=	=	PUNCT
iajs-1013	212	5			PROPN
iajs-1013	212	6	f.	f.	PROPN
iajs-1013	213	1	then	then	ADV
iajs-1013	213	2	h	h	VERB
iajs-1013	213	3	:	:	PUNCT
iajs-1013	213	4	n	n	PRON
iajs-1013	213	5			PROPN
iajs-1013	213	6	m	m	VERB
iajs-1013	213	7	is	be	AUX
iajs-1013	213	8	a	a	DET
iajs-1013	213	9	homomorphism	homomorphism	NOUN
iajs-1013	213	10	.	.	PUNCT
iajs-1013	214	1	let	let	VERB
iajs-1013	214	2	g	g	NOUN
iajs-1013	214	3	=	=	PUNCT
iajs-1013	214	4	i	i	NOUN
iajs-1013	214	5			NOUN
iajs-1013	214	6	–	–	PUNCT
iajs-1013	214	7	1	1	NUM
iajs-1013	214	8	where	where	SCONJ
iajs-1013	214	9	i	i	PRON
iajs-1013	214	10	:	:	PUNCT
iajs-1013	214	11	x	x	SYM
iajs-1013	214	12			PROPN
iajs-1013	214	13			PROPN
iajs-1013	214	14	is	be	AUX
iajs-1013	214	15	the	the	DET
iajs-1013	214	16	inclusion	inclusion	NOUN
iajs-1013	214	17	homomorphism	homomorphism	NOUN
iajs-1013	214	18	.	.	PUNCT
iajs-1013	215	1	hence	hence	ADV
iajs-1013	215	2	g	g	NOUN
iajs-1013	215	3	:	:	PUNCT
iajs-1013	215	4	m	m	PROPN
iajs-1013	215	5			PROPN
iajs-1013	215	6			PROPN
iajs-1013	215	7	is	be	AUX
iajs-1013	215	8	a	a	DET
iajs-1013	215	9	monomorphism	monomorphism	NOUN
iajs-1013	215	10	.	.	PUNCT
iajs-1013	216	1	now	now	ADV
iajs-1013	216	2	,	,	PUNCT
iajs-1013	216	3	g	g	PROPN
iajs-1013	216	4			PROPN
iajs-1013	216	5	h	h	NOUN
iajs-1013	216	6	=	=	PUNCT
iajs-1013	216	7	(	(	PUNCT
iajs-1013	216	8	i	i	X
iajs-1013	216	9			NOUN
iajs-1013	216	10	–	–	PUNCT
iajs-1013	216	11	1	1	NUM
iajs-1013	216	12	)	)	PUNCT
iajs-1013	216	13			PROPN
iajs-1013	216	14	(	(	PUNCT
iajs-1013	216	15			PROPN
iajs-1013	216	16	f.	f.	PROPN
iajs-1013	216	17	)	)	PUNCT
iajs-1013	217	1	=	=	PUNCT
iajs-1013	217	2	i	i	NOUN
iajs-1013	218	1	f	f	X
iajs-1013	218	2	=	=	SYM
iajs-1013	218	3	f	f	X
iajs-1013	218	4	which	which	PRON
iajs-1013	218	5	proves	prove	VERB
iajs-1013	218	6	the	the	DET
iajs-1013	218	7	"	"	PUNCT
iajs-1013	218	8	only	only	ADV
iajs-1013	218	9	if	if	SCONJ
iajs-1013	218	10	”	"	PUNCT
iajs-1013	218	11	part	part	NOUN
iajs-1013	218	12	.	.	PUNCT
iajs-1013	219	1	to	to	PART
iajs-1013	219	2	prove	prove	VERB
iajs-1013	219	3	the	the	DET
iajs-1013	219	4	"	"	PUNCT
iajs-1013	219	5	if	if	SCONJ
iajs-1013	219	6	”	"	PUNCT
iajs-1013	219	7	part	part	NOUN
iajs-1013	219	8	:	:	PUNCT
iajs-1013	219	9	let	let	VERB
iajs-1013	219	10	f	f	PROPN
iajs-1013	219	11			PROPN
iajs-1013	219	12	hom(n,	hom(n,	NOUN
iajs-1013	219	13	)	)	PUNCT
iajs-1013	219	14	.	.	PUNCT
iajs-1013	220	1	by	by	ADP
iajs-1013	220	2	hypothesis	hypothesis	NOUN
iajs-1013	220	3	,	,	PUNCT
iajs-1013	220	4	there	there	PRON
iajs-1013	220	5	exists	exist	VERB
iajs-1013	220	6	a	a	DET
iajs-1013	220	7	homomorphism	homomorphism	ADJ
iajs-1013	220	8	h	h	NOUN
iajs-1013	220	9	:	:	PUNCT
iajs-1013	220	10	n	n	PRON
iajs-1013	220	11			PROPN
iajs-1013	220	12	m	m	VERB
iajs-1013	220	13	and	and	CCONJ
iajs-1013	220	14	a	a	DET
iajs-1013	220	15	monomorphism	monomorphism	NOUN
iajs-1013	220	16	g	g	NOUN
iajs-1013	220	17	:	:	PUNCT
iajs-1013	220	18	n	n	PRON
iajs-1013	220	19			NOUN
iajs-1013	220	20			VERB
iajs-1013	221	1	such	such	ADJ
iajs-1013	221	2	that	that	SCONJ
iajs-1013	221	3	f	f	PROPN
iajs-1013	221	4	=	=	SYM
iajs-1013	221	5	g	g	NUM
iajs-1013	221	6	h.	h.	NOUN
iajs-1013	221	7	we	we	PRON
iajs-1013	221	8	take	take	VERB
iajs-1013	221	9	x	x	NOUN
iajs-1013	221	10	=	=	SYM
iajs-1013	221	11	g(m	g(m	PROPN
iajs-1013	221	12	)	)	PUNCT
iajs-1013	221	13	.	.	PUNCT
iajs-1013	222	1	then	then	ADV
iajs-1013	222	2	x	x	PRON
iajs-1013	222	3	is	be	AUX
iajs-1013	222	4	a	a	DET
iajs-1013	222	5	submodule	submodule	NOUN
iajs-1013	222	6	of	of	ADP
iajs-1013	222	7			PROPN
iajs-1013	222	8	and	and	CCONJ
iajs-1013	222	9	x	x	SYM
iajs-1013	222	10	≈	≈	PROPN
iajs-1013	222	11	m	m	PROPN
iajs-1013	222	12	,	,	PUNCT
iajs-1013	222	13	moreover	moreover	ADV
iajs-1013	222	14	,	,	PUNCT
iajs-1013	222	15	f	f	PROPN
iajs-1013	222	16	(	(	PUNCT
iajs-1013	222	17	n	n	CCONJ
iajs-1013	222	18	)	)	PUNCT
iajs-1013	222	19	=	=	SYM
iajs-1013	222	20	g(h(n	g(h(n	NOUN
iajs-1013	222	21	)	)	PUNCT
iajs-1013	222	22	)	)	PUNCT
iajs-1013	222	23			PROPN
iajs-1013	222	24	g(m	g(m	PROPN
iajs-1013	222	25	)	)	PUNCT
iajs-1013	222	26	=	=	PUNCT
iajs-1013	222	27	x	x	X
iajs-1013	222	28	≈	≈	NUM
iajs-1013	222	29	m.	m.	NOUN
iajs-1013	222	30	therefore	therefore	ADV
iajs-1013	222	31	m	m	VERB
iajs-1013	222	32	is	be	AUX
iajs-1013	222	33	weakly	weakly	ADJ
iajs-1013	222	34	nquasi	nquasi	NOUN
iajs-1013	222	35	-	-	PUNCT
iajs-1013	222	36	injective	injective	ADJ
iajs-1013	222	37	.	.	PUNCT
iajs-1013	223	1	the	the	DET
iajs-1013	223	2	following	follow	VERB
iajs-1013	223	3	concept	concept	NOUN
iajs-1013	223	4	is	be	AUX
iajs-1013	223	5	needed	need	VERB
iajs-1013	223	6	for	for	ADP
iajs-1013	223	7	our	our	PRON
iajs-1013	223	8	next	next	ADJ
iajs-1013	223	9	result	result	NOUN
iajs-1013	223	10	.	.	PUNCT
iajs-1013	224	1	let	let	VERB
iajs-1013	224	2	m	m	PRON
iajs-1013	224	3	and	and	CCONJ
iajs-1013	224	4	n	n	CCONJ
iajs-1013	224	5	be	be	VERB
iajs-1013	224	6	two	two	NUM
iajs-1013	224	7	r	r	NOUN
iajs-1013	224	8	-	-	PUNCT
iajs-1013	224	9	modules	module	NOUN
iajs-1013	224	10	.	.	PUNCT
iajs-1013	225	1	m	m	PROPN
iajs-1013	225	2	is	be	AUX
iajs-1013	225	3	called	call	VERB
iajs-1013	225	4	n	n	CCONJ
iajs-1013	225	5	-	-	PUNCT
iajs-1013	225	6	cyclic	cyclic	NOUN
iajs-1013	225	7	,	,	PUNCT
iajs-1013	225	8	if	if	SCONJ
iajs-1013	225	9	m	m	NOUN
iajs-1013	225	10	is	be	AUX
iajs-1013	225	11	isomorphic	isomorphic	ADJ
iajs-1013	225	12	to	to	ADP
iajs-1013	225	13	n	n	PROPN
iajs-1013	225	14	/	/	SYM
iajs-1013	225	15	k	k	PROPN
iajs-1013	225	16	for	for	ADP
iajs-1013	225	17	some	some	DET
iajs-1013	225	18	submodule	submodule	NOUN
iajs-1013	225	19	k	k	PROPN
iajs-1013	225	20	of	of	ADP
iajs-1013	225	21	n	n	CCONJ
iajs-1013	225	22	,	,	PUNCT
iajs-1013	225	23	[	[	X
iajs-1013	225	24	7	7	NUM
iajs-1013	225	25	]	]	PUNCT
iajs-1013	225	26	.	.	PUNCT
iajs-1013	226	1	2.2	2.2	NUM
iajs-1013	226	2	theorem	theorem	NOUN
iajs-1013	226	3	let	let	VERB
iajs-1013	226	4	m	m	PRON
iajs-1013	226	5	and	and	CCONJ
iajs-1013	226	6	n	n	CCONJ
iajs-1013	226	7	be	be	VERB
iajs-1013	226	8	two	two	NUM
iajs-1013	226	9	r	r	NOUN
iajs-1013	226	10	-	-	PUNCT
iajs-1013	226	11	modules	module	NOUN
iajs-1013	226	12	.	.	PUNCT
iajs-1013	227	1	then	then	ADV
iajs-1013	227	2	m	m	PROPN
iajs-1013	227	3	is	be	AUX
iajs-1013	227	4	weakly	weakly	ADJ
iajs-1013	227	5	n	n	CCONJ
iajs-1013	227	6	-	-	PUNCT
iajs-1013	227	7	quasi	quasi	NOUN
iajs-1013	227	8	-	-	ADJ
iajs-1013	227	9	injective	injective	ADJ
iajs-1013	227	10	if	if	SCONJ
iajs-1013	227	11	and	and	CCONJ
iajs-1013	227	12	only	only	ADV
iajs-1013	227	13	if	if	SCONJ
iajs-1013	227	14	for	for	ADP
iajs-1013	227	15	any	any	DET
iajs-1013	227	16	n	n	CCONJ
iajs-1013	227	17	-	-	PUNCT
iajs-1013	227	18	cyclic	cyclic	NOUN
iajs-1013	227	19	submodule	submodule	NOUN
iajs-1013	227	20	x	x	PROPN
iajs-1013	227	21	of	of	ADP
iajs-1013	227	22			NOUN
iajs-1013	227	23	there	there	PRON
iajs-1013	227	24	exists	exist	VERB
iajs-1013	227	25	a	a	DET
iajs-1013	227	26	submodule	submodule	NOUN
iajs-1013	227	27	l	l	NOUN
iajs-1013	227	28	of	of	ADP
iajs-1013	227	29			NUM
iajs-1013	227	30	such	such	ADJ
iajs-1013	227	31	that	that	SCONJ
iajs-1013	227	32	x	x	PART
iajs-1013	227	33			PROPN
iajs-1013	227	34	l	l	PROPN
iajs-1013	227	35	≈	≈	PROPN
iajs-1013	227	36	m.	m.	NOUN
iajs-1013	227	37	proof	proof	NOUN
iajs-1013	227	38	:	:	PUNCT
iajs-1013	227	39	assume	assume	VERB
iajs-1013	227	40	that	that	SCONJ
iajs-1013	227	41	m	m	NOUN
iajs-1013	227	42	is	be	AUX
iajs-1013	227	43	weakly	weakly	ADJ
iajs-1013	227	44	n	n	CCONJ
iajs-1013	227	45	-	-	PUNCT
iajs-1013	227	46	quasi	quasi	NOUN
iajs-1013	227	47	-	-	ADJ
iajs-1013	227	48	injective	injective	ADJ
iajs-1013	227	49	.	.	PUNCT
iajs-1013	228	1	let	let	VERB
iajs-1013	228	2	x	x	PRON
iajs-1013	228	3	be	be	AUX
iajs-1013	228	4	an	an	DET
iajs-1013	228	5	n	n	CCONJ
iajs-1013	228	6	-	-	PUNCT
iajs-1013	228	7	cyclic	cyclic	NOUN
iajs-1013	228	8	submodule	submodule	NOUN
iajs-1013	228	9	of	of	PROPN
iajs-1013	228	10	.	.	PUNCT
iajs-1013	229	1	so	so	ADV
iajs-1013	229	2	,	,	PUNCT
iajs-1013	229	3	x	x	PROPN
iajs-1013	229	4	≈	≈	PROPN
iajs-1013	229	5	n	n	PROPN
iajs-1013	229	6	/	/	SYM
iajs-1013	229	7	k	k	PROPN
iajs-1013	229	8	for	for	ADP
iajs-1013	229	9	some	some	DET
iajs-1013	229	10	submodule	submodule	NOUN
iajs-1013	229	11	k	k	PROPN
iajs-1013	229	12	of	of	ADP
iajs-1013	229	13	n.	n.	PROPN
iajs-1013	229	14	then	then	ADV
iajs-1013	229	15	we	we	PRON
iajs-1013	229	16	have	have	VERB
iajs-1013	229	17	:	:	PUNCT
iajs-1013	229	18	/	/	SYM
iajs-1013	230	1	i	i	PROPN
iajs-1013	230	2			NUM
iajs-1013	230	3			NUM
iajs-1013	230	4			PROPN
iajs-1013	230	5	where	where	SCONJ
iajs-1013	230	6			PROPN
iajs-1013	230	7	is	be	AUX
iajs-1013	230	8	the	the	DET
iajs-1013	230	9	natural	natural	ADJ
iajs-1013	230	10	homomorphism	homomorphism	NOUN
iajs-1013	230	11	,	,	PUNCT
iajs-1013	230	12			PROPN
iajs-1013	230	13	is	be	AUX
iajs-1013	230	14	an	an	DET
iajs-1013	230	15	isomorphism	isomorphism	NOUN
iajs-1013	230	16	and	and	CCONJ
iajs-1013	230	17	i	i	PRON
iajs-1013	230	18	is	be	AUX
iajs-1013	230	19	the	the	DET
iajs-1013	230	20	inclusion	inclusion	NOUN
iajs-1013	230	21	homomorphism	homomorphism	NOUN
iajs-1013	230	22	.	.	PUNCT
iajs-1013	231	1	let	let	VERB
iajs-1013	231	2	f	f	NOUN
iajs-1013	231	3	=	=	PUNCT
iajs-1013	231	4	i	i	NOUN
iajs-1013	232	1			PROPN
iajs-1013	232	2			PROPN
iajs-1013	232	3	.	.	NUM
iajs-1013	232	4	then	then	ADV
iajs-1013	232	5	f	f	PROPN
iajs-1013	232	6			PROPN
iajs-1013	232	7	hom(n,	hom(n,	NOUN
iajs-1013	232	8	)	)	PUNCT
iajs-1013	232	9	,	,	PUNCT
iajs-1013	232	10	implies	imply	VERB
iajs-1013	232	11	that	that	SCONJ
iajs-1013	232	12	there	there	PRON
iajs-1013	232	13	exists	exist	VERB
iajs-1013	232	14	a	a	DET
iajs-1013	232	15	homomorphism	homomorphism	ADJ
iajs-1013	232	16	h	h	NOUN
iajs-1013	232	17	:	:	PUNCT
iajs-1013	232	18	n	n	PRON
iajs-1013	232	19			PROPN
iajs-1013	232	20	m	m	VERB
iajs-1013	232	21	and	and	CCONJ
iajs-1013	232	22	a	a	DET
iajs-1013	232	23	monomorphism	monomorphism	NOUN
iajs-1013	232	24	g	g	NOUN
iajs-1013	232	25	:	:	PUNCT
iajs-1013	232	26	n	n	PRON
iajs-1013	232	27			NOUN
iajs-1013	232	28			VERB
iajs-1013	232	29	such	such	ADJ
iajs-1013	232	30	that	that	SCONJ
iajs-1013	232	31	f	f	PROPN
iajs-1013	232	32	=	=	SYM
iajs-1013	232	33	g	g	NUM
iajs-1013	232	34	h	h	NOUN
iajs-1013	232	35	(	(	PUNCT
iajs-1013	232	36	by	by	ADP
iajs-1013	232	37	theorem	theorem	NOUN
iajs-1013	232	38	2.1	2.1	NUM
iajs-1013	232	39	)	)	PUNCT
iajs-1013	232	40	.	.	PUNCT
iajs-1013	233	1	ibn	ibn	PROPN
iajs-1013	233	2	alhaitham	alhaitham	PROPN
iajs-1013	233	3	j.	j.	PROPN
iajs-1013	233	4	for	for	ADP
iajs-1013	233	5	pure	pure	ADJ
iajs-1013	233	6	&	&	CCONJ
iajs-1013	233	7	appl	appl	PROPN
iajs-1013	233	8	.	.	PUNCT
iajs-1013	234	1	sci	sci	PROPN
iajs-1013	234	2	.	.	PUNCT
iajs-1013	235	1	vol.23	vol.23	PROPN
iajs-1013	235	2	(	(	PUNCT
iajs-1013	235	3	1	1	NUM
iajs-1013	235	4	)	)	PUNCT
iajs-1013	235	5	2010	2010	NUM
iajs-1013	235	6	now	now	ADV
iajs-1013	235	7	,	,	PUNCT
iajs-1013	235	8	g	g	PROPN
iajs-1013	235	9	h(n	h(n	PROPN
iajs-1013	235	10	)	)	PUNCT
iajs-1013	236	1	=	=	SYM
iajs-1013	236	2	f	f	X
iajs-1013	236	3	(	(	PUNCT
iajs-1013	236	4	n	n	CCONJ
iajs-1013	236	5	)	)	PUNCT
iajs-1013	236	6	=	=	SYM
iajs-1013	236	7	i	i	ADP
iajs-1013	236	8	(n	(n	NOUN
iajs-1013	236	9	)	)	PUNCT
iajs-1013	236	10	=	=	PUNCT
iajs-1013	236	11	i(n	i(n	PROPN
iajs-1013	236	12	/	/	SYM
iajs-1013	236	13	k	k	NOUN
iajs-1013	236	14	)	)	PUNCT
iajs-1013	236	15	=	=	SYM
iajs-1013	236	16	i(x	i(x	NOUN
iajs-1013	236	17	)	)	PUNCT
iajs-1013	236	18	=	=	PUNCT
iajs-1013	237	1	x.	x.	NOUN
iajs-1013	237	2	therefore	therefore	ADV
iajs-1013	237	3	g	g	PROPN
iajs-1013	237	4	h(n	h(n	PROPN
iajs-1013	237	5	)	)	PUNCT
iajs-1013	238	1	=	=	PUNCT
iajs-1013	239	1	x.	x.	NOUN
iajs-1013	239	2	we	we	PRON
iajs-1013	239	3	take	take	VERB
iajs-1013	239	4	l	l	NOUN
iajs-1013	239	5	=	=	SYM
iajs-1013	239	6	g(n	g(n	PROPN
iajs-1013	239	7	)	)	PUNCT
iajs-1013	239	8	to	to	PART
iajs-1013	239	9	obtain	obtain	VERB
iajs-1013	239	10	that	that	DET
iajs-1013	239	11	l	l	NOUN
iajs-1013	239	12	is	be	AUX
iajs-1013	239	13	a	a	DET
iajs-1013	239	14	submodule	submodule	NOUN
iajs-1013	239	15	of	of	ADP
iajs-1013	239	16			PROPN
iajs-1013	239	17	and	and	CCONJ
iajs-1013	239	18	l	l	NOUN
iajs-1013	240	1	≈	≈	PROPN
iajs-1013	240	2	m	m	PROPN
iajs-1013	240	3	.	.	PUNCT
iajs-1013	241	1	moreover	moreover	ADV
iajs-1013	241	2	x	x	X
iajs-1013	241	3	=	=	SYM
iajs-1013	241	4	g(n	g(n	PROPN
iajs-1013	241	5	)	)	PUNCT
iajs-1013	241	6			PROPN
iajs-1013	241	7	g(m	g(m	PROPN
iajs-1013	241	8	)	)	PUNCT
iajs-1013	241	9	=	=	PUNCT
iajs-1013	241	10	l.	l.	PROPN
iajs-1013	241	11	conversely	conversely	ADV
iajs-1013	241	12	,	,	PUNCT
iajs-1013	241	13	to	to	PART
iajs-1013	241	14	prove	prove	VERB
iajs-1013	241	15	m	m	NOUN
iajs-1013	241	16	is	be	AUX
iajs-1013	241	17	weakly	weakly	ADJ
iajs-1013	241	18	n	n	CCONJ
iajs-1013	241	19	-	-	PUNCT
iajs-1013	241	20	quasi	quasi	NOUN
iajs-1013	241	21	-	-	ADJ
iajs-1013	241	22	injective	injective	ADJ
iajs-1013	241	23	.	.	PUNCT
iajs-1013	242	1	let	let	VERB
iajs-1013	242	2	f	f	PROPN
iajs-1013	242	3			PROPN
iajs-1013	242	4	hom(n,	hom(n,	NOUN
iajs-1013	242	5	)	)	PUNCT
iajs-1013	242	6	.	.	PUNCT
iajs-1013	243	1	then	then	ADV
iajs-1013	243	2	f	f	PROPN
iajs-1013	243	3	(	(	PUNCT
iajs-1013	243	4	n	n	CCONJ
iajs-1013	243	5	)	)	PUNCT
iajs-1013	243	6	is	be	AUX
iajs-1013	243	7	a	a	DET
iajs-1013	243	8	submodule	submodule	NOUN
iajs-1013	243	9	of	of	ADP
iajs-1013	243	10			PROPN
iajs-1013	243	11	and	and	CCONJ
iajs-1013	243	12	f	f	PROPN
iajs-1013	243	13	(	(	PUNCT
iajs-1013	243	14	n	n	CCONJ
iajs-1013	243	15	)	)	PUNCT
iajs-1013	244	1	≈	≈	PROPN
iajs-1013	244	2	n	n	PROPN
iajs-1013	244	3	/	/	SYM
iajs-1013	244	4	ker	ker	PROPN
iajs-1013	244	5	f.	f.	PROPN
iajs-1013	244	6	that	that	PRON
iajs-1013	244	7	means	mean	VERB
iajs-1013	244	8	f	f	PROPN
iajs-1013	244	9	(	(	PUNCT
iajs-1013	244	10	n	n	CCONJ
iajs-1013	244	11	)	)	PUNCT
iajs-1013	244	12	is	be	AUX
iajs-1013	244	13	an	an	DET
iajs-1013	244	14	n	n	CCONJ
iajs-1013	244	15	-	-	PUNCT
iajs-1013	244	16	cyclic	cyclic	NOUN
iajs-1013	244	17	submodule	submodule	NOUN
iajs-1013	244	18	of	of	PROPN
iajs-1013	244	19	.	.	PUNCT
iajs-1013	245	1	therefore	therefore	ADV
iajs-1013	245	2	there	there	PRON
iajs-1013	245	3	exists	exist	VERB
iajs-1013	245	4	a	a	DET
iajs-1013	245	5	submodule	submodule	NOUN
iajs-1013	245	6	l	l	NOUN
iajs-1013	245	7	of	of	ADP
iajs-1013	245	8			NUM
iajs-1013	245	9	such	such	ADJ
iajs-1013	245	10	that	that	SCONJ
iajs-1013	245	11	f	f	PROPN
iajs-1013	245	12	(	(	PUNCT
iajs-1013	245	13	n	n	CCONJ
iajs-1013	245	14	)	)	PUNCT
iajs-1013	245	15			PROPN
iajs-1013	245	16	l	l	PROPN
iajs-1013	246	1	≈	≈	PROPN
iajs-1013	246	2	m	m	PROPN
iajs-1013	246	3	,	,	PUNCT
iajs-1013	246	4	and	and	CCONJ
iajs-1013	246	5	hence	hence	ADV
iajs-1013	246	6	the	the	DET
iajs-1013	246	7	result	result	NOUN
iajs-1013	246	8	follows	follow	VERB
iajs-1013	246	9	.	.	PUNCT
iajs-1013	247	1	2.3	2.3	NUM
iajs-1013	247	2	theorem	theorem	NOUN
iajs-1013	247	3	let	let	VERB
iajs-1013	247	4	m	m	PRON
iajs-1013	247	5	and	and	CCONJ
iajs-1013	247	6	n	n	CCONJ
iajs-1013	247	7	be	be	VERB
iajs-1013	247	8	two	two	NUM
iajs-1013	247	9	r	r	NOUN
iajs-1013	247	10	-	-	PUNCT
iajs-1013	247	11	modules	module	NOUN
iajs-1013	247	12	.	.	PUNCT
iajs-1013	248	1	then	then	ADV
iajs-1013	248	2	the	the	DET
iajs-1013	248	3	following	follow	VERB
iajs-1013	248	4	statements	statement	NOUN
iajs-1013	248	5	are	be	AUX
iajs-1013	248	6	equivalent	equivalent	ADJ
iajs-1013	248	7	:	:	PUNCT
iajs-1013	248	8	1	1	X
iajs-1013	248	9	.	.	X
iajs-1013	248	10	m	m	PROPN
iajs-1013	248	11	is	be	AUX
iajs-1013	248	12	weakly	weakly	ADJ
iajs-1013	248	13	n	n	CCONJ
iajs-1013	248	14	-	-	PUNCT
iajs-1013	248	15	quasi	quasi	NOUN
iajs-1013	248	16	-	-	ADJ
iajs-1013	248	17	injective	injective	ADJ
iajs-1013	248	18	.	.	PUNCT
iajs-1013	249	1	2	2	X
iajs-1013	249	2	.	.	X
iajs-1013	249	3	for	for	ADP
iajs-1013	249	4	any	any	DET
iajs-1013	249	5	submodule	submodule	NOUN
iajs-1013	249	6	k	k	PROPN
iajs-1013	249	7	of	of	ADP
iajs-1013	249	8	n	n	CCONJ
iajs-1013	249	9	,	,	PUNCT
iajs-1013	249	10	m	m	VERB
iajs-1013	249	11	is	be	AUX
iajs-1013	249	12	weakly	weakly	ADJ
iajs-1013	249	13	n	n	CCONJ
iajs-1013	249	14	/	/	SYM
iajs-1013	249	15	k	k	ADJ
iajs-1013	249	16	-	-	ADJ
iajs-1013	249	17	quasi	quasi	ADJ
iajs-1013	249	18	-	-	ADJ
iajs-1013	249	19	injective	injective	ADJ
iajs-1013	249	20	.	.	PUNCT
iajs-1013	250	1	3	3	X
iajs-1013	250	2	.	.	X
iajs-1013	250	3	for	for	ADP
iajs-1013	250	4	any	any	DET
iajs-1013	250	5	submodule	submodule	NOUN
iajs-1013	250	6	k	k	PROPN
iajs-1013	250	7	of	of	ADP
iajs-1013	250	8	n	n	PROPN
iajs-1013	250	9	and	and	CCONJ
iajs-1013	250	10	any	any	DET
iajs-1013	250	11	homomorphism	homomorphism	PROPN
iajs-1013	250	12	f	f	X
iajs-1013	250	13	:	:	PUNCT
iajs-1013	250	14	n	n	PROPN
iajs-1013	250	15	/	/	SYM
iajs-1013	250	16	k	k	PROPN
iajs-1013	250	17			PROPN
iajs-1013	250	18			PROPN
iajs-1013	250	19	,	,	PUNCT
iajs-1013	250	20	there	there	PRON
iajs-1013	250	21	exists	exist	VERB
iajs-1013	250	22	a	a	DET
iajs-1013	250	23	monomorphism	monomorphism	NOUN
iajs-1013	250	24	g	g	NOUN
iajs-1013	250	25	:	:	PUNCT
iajs-1013	250	26	m	m	PROPN
iajs-1013	250	27			PROPN
iajs-1013	250	28			ADJ
iajs-1013	250	29	and	and	CCONJ
iajs-1013	250	30	a	a	DET
iajs-1013	250	31	homomorphism	homomorphism	NOUN
iajs-1013	250	32	h	h	NOUN
iajs-1013	250	33	:	:	PUNCT
iajs-1013	250	34	n	n	PROPN
iajs-1013	250	35	/	/	SYM
iajs-1013	250	36	k	k	PROPN
iajs-1013	250	37			PROPN
iajs-1013	250	38	m	m	VERB
iajs-1013	250	39	such	such	ADJ
iajs-1013	250	40	that	that	DET
iajs-1013	250	41	g	g	ADJ
iajs-1013	250	42	h	h	NOUN
iajs-1013	251	1	=	=	SYM
iajs-1013	251	2	f.	f.	PROPN
iajs-1013	251	3	proof	proof	NOUN
iajs-1013	251	4	:	:	PUNCT
iajs-1013	251	5	(	(	PUNCT
iajs-1013	251	6	1	1	X
iajs-1013	251	7	)	)	PUNCT
iajs-1013	251	8			NOUN
iajs-1013	251	9	(	(	PUNCT
iajs-1013	251	10	2	2	X
iajs-1013	251	11	)	)	PUNCT
iajs-1013	251	12	let	let	VERB
iajs-1013	251	13	k	k	PRON
iajs-1013	251	14	be	be	AUX
iajs-1013	251	15	a	a	DET
iajs-1013	251	16	submodule	submodule	NOUN
iajs-1013	251	17	of	of	ADP
iajs-1013	251	18	n	n	PROPN
iajs-1013	251	19	and	and	CCONJ
iajs-1013	251	20	let	let	VERB
iajs-1013	251	21	f	f	PRON
iajs-1013	251	22			PROPN
iajs-1013	251	23	hom(n	hom(n	PROPN
iajs-1013	251	24	/	/	PUNCT
iajs-1013	251	25	k,	k,	PROPN
iajs-1013	251	26	)	)	PUNCT
iajs-1013	251	27	.	.	PUNCT
iajs-1013	252	1	let	let	VERB
iajs-1013	252	2			ADJ
iajs-1013	252	3	:	:	PUNCT
iajs-1013	252	4	n	n	PRON
iajs-1013	252	5			PROPN
iajs-1013	252	6	n	n	PROPN
iajs-1013	252	7	/	/	SYM
iajs-1013	252	8	k	k	PROPN
iajs-1013	252	9	be	be	AUX
iajs-1013	252	10	the	the	DET
iajs-1013	252	11	natural	natural	ADJ
iajs-1013	252	12	homomorphism	homomorphism	NOUN
iajs-1013	252	13	.	.	PUNCT
iajs-1013	253	1	then	then	ADV
iajs-1013	253	2	f	f	VERB
iajs-1013	253	3			ADJ
iajs-1013	253	4			NOUN
iajs-1013	253	5	hom(n,	hom(n,	NOUN
iajs-1013	253	6	)	)	PUNCT
iajs-1013	253	7	and	and	CCONJ
iajs-1013	253	8	hence	hence	ADV
iajs-1013	253	9	by	by	ADP
iajs-1013	253	10	(	(	PUNCT
iajs-1013	253	11	1	1	NUM
iajs-1013	253	12	)	)	PUNCT
iajs-1013	253	13	,	,	PUNCT
iajs-1013	253	14	there	there	PRON
iajs-1013	253	15	exists	exist	VERB
iajs-1013	253	16	a	a	DET
iajs-1013	253	17	submodule	submodule	NOUN
iajs-1013	253	18	x	x	PUNCT
iajs-1013	253	19	of	of	ADP
iajs-1013	253	20			NUM
iajs-1013	253	21	such	such	ADJ
iajs-1013	253	22	that	that	DET
iajs-1013	253	23	f	f	PROPN
iajs-1013	253	24	(n	(n	NOUN
iajs-1013	253	25	)	)	PUNCT
iajs-1013	253	26			PROPN
iajs-1013	253	27	x	x	SYM
iajs-1013	253	28	≈	≈	NUM
iajs-1013	253	29	m.	m.	NOUN
iajs-1013	254	1	therefore	therefore	ADV
iajs-1013	254	2	f	f	PROPN
iajs-1013	254	3	(	(	PUNCT
iajs-1013	254	4	n	n	PROPN
iajs-1013	254	5	/	/	SYM
iajs-1013	254	6	k	k	NOUN
iajs-1013	254	7	)	)	PUNCT
iajs-1013	254	8			PROPN
iajs-1013	254	9	x	x	PUNCT
iajs-1013	255	1	≈	≈	NOUN
iajs-1013	255	2	m	m	VERB
iajs-1013	255	3	which	which	PRON
iajs-1013	255	4	proves	prove	VERB
iajs-1013	255	5	(	(	PUNCT
iajs-1013	255	6	2	2	NUM
iajs-1013	255	7	)	)	PUNCT
iajs-1013	255	8	.	.	PUNCT
iajs-1013	256	1	(	(	PUNCT
iajs-1013	256	2	2	2	X
iajs-1013	256	3	)	)	PUNCT
iajs-1013	256	4			NOUN
iajs-1013	256	5	(	(	PUNCT
iajs-1013	256	6	3	3	X
iajs-1013	256	7	)	)	PUNCT
iajs-1013	256	8	we	we	PRON
iajs-1013	256	9	follow	follow	VERB
iajs-1013	256	10	as	as	ADP
iajs-1013	256	11	in	in	ADP
iajs-1013	256	12	the	the	DET
iajs-1013	256	13	proof	proof	NOUN
iajs-1013	256	14	of	of	ADP
iajs-1013	256	15	theorem	theorem	ADJ
iajs-1013	256	16	2.1	2.1	NUM
iajs-1013	256	17	.	.	PUNCT
iajs-1013	257	1	(	(	PUNCT
iajs-1013	257	2	3	3	X
iajs-1013	257	3	)	)	PUNCT
iajs-1013	257	4			NOUN
iajs-1013	257	5	(	(	PUNCT
iajs-1013	257	6	1	1	X
iajs-1013	257	7	)	)	PUNCT
iajs-1013	257	8	let	let	VERB
iajs-1013	257	9	f	f	PROPN
iajs-1013	257	10			PROPN
iajs-1013	257	11	hom(n,	hom(n,	NOUN
iajs-1013	257	12	)	)	PUNCT
iajs-1013	257	13	and	and	CCONJ
iajs-1013	257	14	let	let	VERB
iajs-1013	257	15	k	k	PROPN
iajs-1013	257	16	=	=	PUNCT
iajs-1013	258	1	ker	ker	PROPN
iajs-1013	259	1	f	f	X
iajs-1013	259	2	.	.	PUNCT
iajs-1013	260	1	then	then	ADV
iajs-1013	260	2	define	define	VERB
iajs-1013	260	3	f	f	X
iajs-1013	260	4	:	:	PUNCT
iajs-1013	260	5	n	n	PROPN
iajs-1013	260	6	/	/	SYM
iajs-1013	260	7	k	k	PROPN
iajs-1013	260	8			PROPN
iajs-1013	260	9			VERB
iajs-1013	260	10	by	by	ADP
iajs-1013	260	11	f	f	PROPN
iajs-1013	260	12	(	(	PUNCT
iajs-1013	260	13	a	a	DET
iajs-1013	260	14	+	+	X
iajs-1013	260	15	k	k	NOUN
iajs-1013	260	16	)	)	PUNCT
iajs-1013	261	1	=	=	SYM
iajs-1013	261	2	f	f	X
iajs-1013	261	3	(	(	PUNCT
iajs-1013	261	4	a	a	NOUN
iajs-1013	261	5	)	)	PUNCT
iajs-1013	261	6	for	for	ADP
iajs-1013	261	7	all	all	DET
iajs-1013	261	8	a	a	DET
iajs-1013	261	9			NOUN
iajs-1013	261	10	n.	n.	NOUN
iajs-1013	261	11	f	f	PROPN
iajs-1013	261	12	is	be	AUX
iajs-1013	261	13	a	a	DET
iajs-1013	261	14	homomorphism	homomorphism	NOUN
iajs-1013	261	15	.	.	PUNCT
iajs-1013	262	1	it	it	PRON
iajs-1013	262	2	can	can	AUX
iajs-1013	262	3	be	be	AUX
iajs-1013	262	4	easily	easily	ADV
iajs-1013	262	5	shown	show	VERB
iajs-1013	262	6	that	that	SCONJ
iajs-1013	262	7	f	f	PROPN
iajs-1013	262	8	is	be	AUX
iajs-1013	262	9	a	a	DET
iajs-1013	262	10	monomorphism	monomorphism	NOUN
iajs-1013	262	11	.	.	PUNCT
iajs-1013	263	1	hence	hence	ADV
iajs-1013	263	2	by	by	ADP
iajs-1013	263	3	(	(	PUNCT
iajs-1013	263	4	3	3	NUM
iajs-1013	263	5	)	)	PUNCT
iajs-1013	263	6	,	,	PUNCT
iajs-1013	263	7	there	there	PRON
iajs-1013	263	8	exists	exist	VERB
iajs-1013	263	9	a	a	DET
iajs-1013	263	10	monomorphism	monomorphism	NOUN
iajs-1013	263	11	g	g	NOUN
iajs-1013	263	12	:	:	PUNCT
iajs-1013	263	13	m	m	PROPN
iajs-1013	263	14			PROPN
iajs-1013	263	15			ADJ
iajs-1013	263	16	and	and	CCONJ
iajs-1013	263	17	a	a	DET
iajs-1013	263	18	homomorphism	homomorphism	ADJ
iajs-1013	263	19	h	h	NOUN
iajs-1013	263	20	:	:	PUNCT
iajs-1013	263	21	n	n	X
iajs-1013	263	22	/	/	SYM
iajs-1013	263	23	k	k	PROPN
iajs-1013	263	24			PROPN
iajs-1013	263	25	m	m	VERB
iajs-1013	263	26	such	such	ADJ
iajs-1013	263	27	that	that	DET
iajs-1013	263	28	g	g	ADJ
iajs-1013	263	29	h	h	NOUN
iajs-1013	264	1	=	=	SYM
iajs-1013	264	2	f	f	PROPN
iajs-1013	264	3	.	.	PUNCT
iajs-1013	265	1	now	now	ADV
iajs-1013	265	2	,	,	PUNCT
iajs-1013	265	3	f	f	PROPN
iajs-1013	265	4	(	(	PUNCT
iajs-1013	265	5	n	n	CCONJ
iajs-1013	265	6	)	)	PUNCT
iajs-1013	265	7	=	=	SYM
iajs-1013	265	8	f	f	PROPN
iajs-1013	265	9	(	(	PUNCT
iajs-1013	265	10	n	n	CCONJ
iajs-1013	265	11	/	/	SYM
iajs-1013	265	12	k	k	NOUN
iajs-1013	265	13	)	)	PUNCT
iajs-1013	265	14	=	=	PUNCT
iajs-1013	266	1	g(h(n	g(h(n	NOUN
iajs-1013	266	2	/	/	SYM
iajs-1013	266	3	k	k	NOUN
iajs-1013	266	4	)	)	PUNCT
iajs-1013	266	5	)	)	PUNCT
iajs-1013	267	1			PROPN
iajs-1013	267	2	g(m	g(m	PROPN
iajs-1013	267	3	)	)	PUNCT
iajs-1013	267	4	.	.	PUNCT
iajs-1013	268	1	we	we	PRON
iajs-1013	268	2	take	take	VERB
iajs-1013	268	3	x	x	NOUN
iajs-1013	268	4	=	=	SYM
iajs-1013	268	5	g(m	g(m	PROPN
iajs-1013	268	6	)	)	PUNCT
iajs-1013	268	7	,	,	PUNCT
iajs-1013	268	8	implies	imply	VERB
iajs-1013	268	9	that	that	SCONJ
iajs-1013	268	10	f	f	PROPN
iajs-1013	268	11	(	(	PUNCT
iajs-1013	268	12	n	n	CCONJ
iajs-1013	268	13	)	)	PUNCT
iajs-1013	268	14			PROPN
iajs-1013	268	15	x	x	X
iajs-1013	268	16	≈	≈	PROPN
iajs-1013	268	17	m	m	PROPN
iajs-1013	268	18	,	,	PUNCT
iajs-1013	268	19	which	which	PRON
iajs-1013	268	20	proves	prove	VERB
iajs-1013	268	21	(	(	PUNCT
iajs-1013	268	22	1	1	NUM
iajs-1013	268	23	)	)	PUNCT
iajs-1013	268	24	.	.	PUNCT
iajs-1013	269	1	the	the	DET
iajs-1013	269	2	following	follow	VERB
iajs-1013	269	3	lemma	lemma	PROPN
iajs-1013	269	4	is	be	AUX
iajs-1013	269	5	needed	need	VERB
iajs-1013	269	6	in	in	ADP
iajs-1013	269	7	order	order	NOUN
iajs-1013	269	8	to	to	PART
iajs-1013	269	9	give	give	VERB
iajs-1013	269	10	some	some	DET
iajs-1013	269	11	applications	application	NOUN
iajs-1013	269	12	of	of	ADP
iajs-1013	269	13	theorem	theorem	ADJ
iajs-1013	269	14	2.3	2.3	NUM
iajs-1013	269	15	.	.	PUNCT
iajs-1013	270	1	2.4	2.4	NUM
iajs-1013	270	2	lemma	lemma	PROPN
iajs-1013	270	3	let	let	VERB
iajs-1013	270	4	k	k	NOUN
iajs-1013	270	5	,	,	PUNCT
iajs-1013	270	6	m	m	VERB
iajs-1013	270	7	and	and	CCONJ
iajs-1013	270	8	n	n	ADV
iajs-1013	270	9	be	be	VERB
iajs-1013	270	10	r	r	NOUN
iajs-1013	270	11	-	-	PUNCT
iajs-1013	270	12	modules	module	NOUN
iajs-1013	270	13	with	with	ADP
iajs-1013	270	14	n	n	PROPN
iajs-1013	270	15	≈	≈	PROPN
iajs-1013	270	16	k.	k.	PROPN
iajs-1013	271	1	if	if	SCONJ
iajs-1013	271	2	m	m	NOUN
iajs-1013	271	3	is	be	AUX
iajs-1013	271	4	weakly	weakly	ADJ
iajs-1013	271	5	n	n	CCONJ
iajs-1013	271	6	-	-	PUNCT
iajs-1013	271	7	quasi	quasi	NOUN
iajs-1013	271	8	-	-	ADJ
iajs-1013	271	9	injective	injective	ADJ
iajs-1013	271	10	,	,	PUNCT
iajs-1013	271	11	then	then	ADV
iajs-1013	271	12	m	m	NOUN
iajs-1013	271	13	is	be	AUX
iajs-1013	271	14	weakly	weakly	ADJ
iajs-1013	271	15	k	k	ADJ
iajs-1013	271	16	-	-	ADJ
iajs-1013	271	17	quasi	quasi	ADJ
iajs-1013	271	18	-	-	ADJ
iajs-1013	271	19	injective	injective	ADJ
iajs-1013	271	20	.	.	PUNCT
iajs-1013	272	1	proof	proof	NOUN
iajs-1013	272	2	:	:	PUNCT
iajs-1013	272	3	is	be	AUX
iajs-1013	272	4	obvious	obvious	ADJ
iajs-1013	272	5	,	,	PUNCT
iajs-1013	272	6	so	so	CCONJ
iajs-1013	272	7	it	it	PRON
iajs-1013	272	8	is	be	AUX
iajs-1013	272	9	omitted	omit	VERB
iajs-1013	272	10	.	.	PUNCT
iajs-1013	273	1	2.5	2.5	NUM
iajs-1013	273	2	corollary	corollary	NOUN
iajs-1013	273	3	let	let	VERB
iajs-1013	273	4	k	k	NOUN
iajs-1013	273	5	,	,	PUNCT
iajs-1013	273	6	m	m	VERB
iajs-1013	273	7	and	and	CCONJ
iajs-1013	273	8	n	n	ADV
iajs-1013	273	9	be	be	VERB
iajs-1013	273	10	r	r	NOUN
iajs-1013	273	11	-	-	PUNCT
iajs-1013	273	12	modules	module	NOUN
iajs-1013	273	13	.	.	PUNCT
iajs-1013	274	1	if	if	SCONJ
iajs-1013	274	2	m	m	NOUN
iajs-1013	274	3	is	be	AUX
iajs-1013	274	4	weakly	weakly	ADJ
iajs-1013	274	5	k	k	ADJ
iajs-1013	274	6	-	-	ADJ
iajs-1013	274	7	quasi	quasi	ADJ
iajs-1013	274	8	-	-	ADJ
iajs-1013	274	9	injective	injective	ADJ
iajs-1013	274	10	and	and	CCONJ
iajs-1013	274	11	n	n	NOUN
iajs-1013	274	12	is	be	AUX
iajs-1013	274	13	k	k	NOUN
iajs-1013	274	14	-	-	NOUN
iajs-1013	274	15	cyclic	cyclic	NOUN
iajs-1013	274	16	.	.	PUNCT
iajs-1013	275	1	then	then	ADV
iajs-1013	275	2	m	m	PROPN
iajs-1013	275	3	is	be	AUX
iajs-1013	275	4	weakly	weakly	ADJ
iajs-1013	275	5	n	n	CCONJ
iajs-1013	275	6	-	-	PUNCT
iajs-1013	275	7	quasi	quasi	NOUN
iajs-1013	275	8	-	-	ADJ
iajs-1013	275	9	injective	injective	ADJ
iajs-1013	275	10	.	.	PUNCT
iajs-1013	276	1	proof	proof	NOUN
iajs-1013	276	2	:	:	PUNCT
iajs-1013	276	3	m	m	AUX
iajs-1013	276	4	being	be	AUX
iajs-1013	276	5	k	k	X
iajs-1013	276	6	-	-	ADJ
iajs-1013	276	7	quasi	quasi	ADJ
iajs-1013	276	8	-	-	ADJ
iajs-1013	276	9	injective	injective	ADJ
iajs-1013	276	10	,	,	PUNCT
iajs-1013	276	11	implies	imply	VERB
iajs-1013	276	12	that	that	SCONJ
iajs-1013	276	13	m	m	NOUN
iajs-1013	276	14	is	be	AUX
iajs-1013	276	15	weakly	weakly	ADJ
iajs-1013	276	16	k	k	PROPN
iajs-1013	276	17	/	/	SYM
iajs-1013	276	18	l	l	NOUN
iajs-1013	276	19	-	-	ADJ
iajs-1013	276	20	quasi	quasi	ADJ
iajs-1013	276	21	-	-	ADJ
iajs-1013	276	22	injective	injective	ADJ
iajs-1013	276	23	for	for	ADP
iajs-1013	276	24	every	every	DET
iajs-1013	276	25	submodule	submodule	NOUN
iajs-1013	276	26	l	l	NOUN
iajs-1013	276	27	of	of	ADP
iajs-1013	276	28	k	k	PROPN
iajs-1013	276	29	(	(	PUNCT
iajs-1013	276	30	by	by	ADP
iajs-1013	276	31	theorem	theorem	NOUN
iajs-1013	276	32	2.3	2.3	NUM
iajs-1013	276	33	)	)	PUNCT
iajs-1013	276	34	.	.	PUNCT
iajs-1013	277	1	but	but	CCONJ
iajs-1013	277	2	n	n	PRON
iajs-1013	277	3	is	be	AUX
iajs-1013	277	4	k	k	ADJ
iajs-1013	277	5	-	-	ADJ
iajs-1013	277	6	cyclic	cyclic	ADJ
iajs-1013	277	7	,	,	PUNCT
iajs-1013	278	1	so	so	ADV
iajs-1013	279	1	n	n	PROPN
iajs-1013	280	1	≈	≈	PROPN
iajs-1013	280	2	k	k	PROPN
iajs-1013	280	3	/	/	SYM
iajs-1013	280	4	l	l	NOUN
iajs-1013	280	5	for	for	ADP
iajs-1013	280	6	some	some	DET
iajs-1013	280	7	submodule	submodule	NOUN
iajs-1013	280	8	l	l	NOUN
iajs-1013	280	9	of	of	ADP
iajs-1013	280	10	k.	k.	PROPN
iajs-1013	281	1	hence	hence	ADV
iajs-1013	281	2	m	m	VERB
iajs-1013	281	3	is	be	AUX
iajs-1013	281	4	weakly	weakly	ADJ
iajs-1013	281	5	n	n	CCONJ
iajs-1013	281	6	-	-	PUNCT
iajs-1013	281	7	quasi	quasi	NOUN
iajs-1013	281	8	-	-	ADJ
iajs-1013	281	9	injective	injective	ADJ
iajs-1013	281	10	(	(	PUNCT
iajs-1013	281	11	by	by	ADP
iajs-1013	281	12	lemma	lemma	PROPN
iajs-1013	281	13	2.4	2.4	NUM
iajs-1013	281	14	)	)	PUNCT
iajs-1013	281	15	.	.	PUNCT
iajs-1013	282	1	2.6	2.6	NUM
iajs-1013	282	2	corollary	corollary	NOUN
iajs-1013	282	3	if	if	SCONJ
iajs-1013	282	4	m	m	NOUN
iajs-1013	282	5	is	be	AUX
iajs-1013	282	6	weakly	weakly	ADJ
iajs-1013	282	7	n	n	CCONJ
iajs-1013	282	8	-	-	PUNCT
iajs-1013	282	9	quasi	quasi	ADJ
iajs-1013	282	10	-	-	ADJ
iajs-1013	282	11	injective	injective	ADJ
iajs-1013	282	12	r	r	NOUN
iajs-1013	282	13	-	-	PUNCT
iajs-1013	282	14	module	module	NOUN
iajs-1013	282	15	and	and	CCONJ
iajs-1013	282	16	a	a	PRON
iajs-1013	282	17	is	be	AUX
iajs-1013	282	18	a	a	DET
iajs-1013	282	19	direct	direct	ADJ
iajs-1013	282	20	summand	summand	NOUN
iajs-1013	282	21	of	of	ADP
iajs-1013	282	22	n	n	CCONJ
iajs-1013	282	23	,	,	PUNCT
iajs-1013	282	24	then	then	ADV
iajs-1013	282	25	m	m	VERB
iajs-1013	282	26	is	be	AUX
iajs-1013	282	27	weakly	weakly	ADJ
iajs-1013	282	28	a	a	DET
iajs-1013	282	29	-	-	PUNCT
iajs-1013	282	30	quasi	quasi	NOUN
iajs-1013	282	31	-	-	ADJ
iajs-1013	282	32	injective	injective	ADJ
iajs-1013	282	33	.	.	PUNCT
iajs-1013	283	1	proof	proof	NOUN
iajs-1013	283	2	:	:	PUNCT
iajs-1013	283	3	follows	follow	VERB
iajs-1013	283	4	easily	easily	ADV
iajs-1013	283	5	by	by	ADP
iajs-1013	283	6	using	use	VERB
iajs-1013	283	7	theorem	theorem	ADJ
iajs-1013	283	8	2.3	2.3	NUM
iajs-1013	283	9	and	and	CCONJ
iajs-1013	283	10	lemma	lemma	PROPN
iajs-1013	283	11	2.4	2.4	NUM
iajs-1013	283	12	.	.	PUNCT
iajs-1013	284	1	as	as	ADP
iajs-1013	284	2	a	a	DET
iajs-1013	284	3	consequence	consequence	NOUN
iajs-1013	284	4	of	of	ADP
iajs-1013	284	5	2.6	2.6	NUM
iajs-1013	284	6	we	we	PRON
iajs-1013	284	7	have	have	VERB
iajs-1013	284	8	the	the	DET
iajs-1013	284	9	following	follow	VERB
iajs-1013	284	10	result	result	NOUN
iajs-1013	284	11	:	:	PUNCT
iajs-1013	284	12	ibn	ibn	NOUN
iajs-1013	284	13	alhaitham	alhaitham	NOUN
iajs-1013	284	14	j.	j.	PROPN
iajs-1013	284	15	for	for	ADP
iajs-1013	284	16	pure	pure	ADJ
iajs-1013	284	17	&	&	CCONJ
iajs-1013	284	18	appl	appl	PROPN
iajs-1013	284	19	.	.	PUNCT
iajs-1013	285	1	sci	sci	PROPN
iajs-1013	285	2	.	.	PUNCT
iajs-1013	286	1	vol.23	vol.23	PROPN
iajs-1013	286	2	(	(	PUNCT
iajs-1013	286	3	1	1	NUM
iajs-1013	286	4	)	)	PUNCT
iajs-1013	286	5	2010	2010	NUM
iajs-1013	286	6	2.7	2.7	NUM
iajs-1013	286	7	corollary	corollary	NOUN
iajs-1013	286	8	let	let	VERB
iajs-1013	286	9	m	m	PRON
iajs-1013	286	10	and	and	CCONJ
iajs-1013	286	11	n	n	CCONJ
iajs-1013	286	12	be	be	VERB
iajs-1013	286	13	two	two	NUM
iajs-1013	286	14	r	r	NOUN
iajs-1013	286	15	-	-	PUNCT
iajs-1013	286	16	modules	module	NOUN
iajs-1013	286	17	such	such	ADJ
iajs-1013	286	18	that	that	SCONJ
iajs-1013	286	19	n	n	NOUN
iajs-1013	286	20	is	be	AUX
iajs-1013	286	21	quasi	quasi	ADJ
iajs-1013	286	22	-	-	ADJ
iajs-1013	286	23	injective	injective	ADJ
iajs-1013	286	24	and	and	CCONJ
iajs-1013	286	25	m	m	NOUN
iajs-1013	286	26	is	be	AUX
iajs-1013	286	27	weakly	weakly	ADJ
iajs-1013	286	28	n	n	CCONJ
iajs-1013	286	29	-	-	PUNCT
iajs-1013	286	30	quasiinjective	quasiinjective	NOUN
iajs-1013	286	31	.	.	PUNCT
iajs-1013	287	1	then	then	ADV
iajs-1013	287	2	m	m	VERB
iajs-1013	287	3	is	be	AUX
iajs-1013	287	4	weakly	weakly	ADJ
iajs-1013	287	5	a	a	DET
iajs-1013	287	6	-	-	PUNCT
iajs-1013	287	7	quasi	quasi	NOUN
iajs-1013	287	8	-	-	NOUN
iajs-1013	287	9	injective	injective	ADJ
iajs-1013	287	10	for	for	ADP
iajs-1013	287	11	every	every	DET
iajs-1013	287	12	closed	closed	ADJ
iajs-1013	287	13	submodule	submodule	NOUN
iajs-1013	287	14	a	a	PRON
iajs-1013	287	15	of	of	ADP
iajs-1013	287	16	n.	n.	NOUN
iajs-1013	287	17	proof	proof	NOUN
iajs-1013	287	18	:	:	PUNCT
iajs-1013	287	19	n	n	PRON
iajs-1013	287	20	being	be	AUX
iajs-1013	287	21	quasi	quasi	ADJ
iajs-1013	287	22	-	-	ADJ
iajs-1013	287	23	injective	injective	ADJ
iajs-1013	287	24	and	and	CCONJ
iajs-1013	287	25	a	a	PRON
iajs-1013	287	26	is	be	AUX
iajs-1013	287	27	a	a	DET
iajs-1013	287	28	closed	closed	ADJ
iajs-1013	287	29	submodule	submodule	NOUN
iajs-1013	287	30	of	of	ADP
iajs-1013	287	31	n	n	PROPN
iajs-1013	287	32	implies	imply	VERB
iajs-1013	287	33	that	that	SCONJ
iajs-1013	287	34	a	a	PRON
iajs-1013	287	35	is	be	AUX
iajs-1013	287	36	a	a	DET
iajs-1013	287	37	direct	direct	ADJ
iajs-1013	287	38	summand	summand	NOUN
iajs-1013	287	39	of	of	ADP
iajs-1013	287	40	n	n	PROPN
iajs-1013	288	1	[	[	AUX
iajs-1013	288	2	see	see	VERB
iajs-1013	288	3	cor	cor	PROPN
iajs-1013	288	4	.	.	PROPN
iajs-1013	289	1	16.9	16.9	NUM
iajs-1013	289	2	,	,	PUNCT
iajs-1013	289	3	p.64	p.64	X
iajs-1013	289	4	,	,	PUNCT
iajs-1013	289	5	[	[	X
iajs-1013	289	6	6	6	NUM
iajs-1013	289	7	]	]	PUNCT
iajs-1013	289	8	]	]	PUNCT
iajs-1013	289	9	.	.	PUNCT
iajs-1013	290	1	hence	hence	ADV
iajs-1013	290	2	the	the	DET
iajs-1013	290	3	result	result	NOUN
iajs-1013	290	4	follows	follow	VERB
iajs-1013	290	5	by	by	ADP
iajs-1013	290	6	2.6	2.6	NUM
iajs-1013	290	7	.	.	PUNCT
iajs-1013	291	1	the	the	DET
iajs-1013	291	2	following	follow	VERB
iajs-1013	291	3	theorem	theorem	NOUN
iajs-1013	291	4	characterizes	characterize	VERB
iajs-1013	291	5	weakly	weakly	ADJ
iajs-1013	291	6	-	-	PUNCT
iajs-1013	291	7	quasi	quasi	NOUN
iajs-1013	291	8	-	-	NOUN
iajs-1013	291	9	injectivity	injectivity	NOUN
iajs-1013	291	10	relative	relative	ADJ
iajs-1013	291	11	to	to	ADP
iajs-1013	291	12	the	the	DET
iajs-1013	291	13	r	r	NOUN
iajs-1013	291	14	-	-	PUNCT
iajs-1013	291	15	module	module	NOUN
iajs-1013	291	16	r.	r.	NOUN
iajs-1013	291	17	2.8	2.8	NUM
iajs-1013	291	18	theorem	theorem	NOUN
iajs-1013	291	19	let	let	VERB
iajs-1013	291	20	m	m	PRON
iajs-1013	291	21	be	be	AUX
iajs-1013	291	22	an	an	DET
iajs-1013	291	23	r	r	NOUN
iajs-1013	291	24	-	-	PUNCT
iajs-1013	291	25	module	module	NOUN
iajs-1013	291	26	.	.	PUNCT
iajs-1013	292	1	then	then	ADV
iajs-1013	292	2	m	m	VERB
iajs-1013	292	3	is	be	AUX
iajs-1013	292	4	weakly	weakly	ADJ
iajs-1013	292	5	r	r	NOUN
iajs-1013	292	6	-	-	PUNCT
iajs-1013	292	7	quasi	quasi	NOUN
iajs-1013	292	8	-	-	ADJ
iajs-1013	292	9	injective	injective	ADJ
iajs-1013	292	10	if	if	SCONJ
iajs-1013	292	11	and	and	CCONJ
iajs-1013	292	12	only	only	ADV
iajs-1013	292	13	if	if	SCONJ
iajs-1013	292	14	for	for	ADP
iajs-1013	292	15	each	each	DET
iajs-1013	292	16	element	element	NOUN
iajs-1013	292	17	x	x	PROPN
iajs-1013	292	18			PROPN
iajs-1013	292	19			NUM
iajs-1013	292	20	,	,	PUNCT
iajs-1013	292	21	there	there	PRON
iajs-1013	292	22	exists	exist	VERB
iajs-1013	292	23	a	a	DET
iajs-1013	292	24	submodule	submodule	NOUN
iajs-1013	292	25	x	x	PUNCT
iajs-1013	292	26	of	of	ADP
iajs-1013	292	27			NUM
iajs-1013	293	1	such	such	ADJ
iajs-1013	293	2	that	that	SCONJ
iajs-1013	293	3	x	x	PRON
iajs-1013	293	4			NOUN
iajs-1013	293	5	x	x	X
iajs-1013	293	6	≈	≈	PROPN
iajs-1013	293	7	m.	m.	NOUN
iajs-1013	293	8	proof	proof	NOUN
iajs-1013	293	9	:	:	PUNCT
iajs-1013	293	10	assume	assume	VERB
iajs-1013	293	11	that	that	SCONJ
iajs-1013	293	12	m	m	NOUN
iajs-1013	293	13	is	be	AUX
iajs-1013	293	14	weakly	weakly	ADJ
iajs-1013	293	15	r	r	NOUN
iajs-1013	293	16	-	-	PUNCT
iajs-1013	293	17	quasi	quasi	NOUN
iajs-1013	293	18	-	-	ADJ
iajs-1013	293	19	injective	injective	ADJ
iajs-1013	293	20	.	.	PUNCT
iajs-1013	294	1	let	let	VERB
iajs-1013	294	2	x	x	SYM
iajs-1013	294	3			PROPN
iajs-1013	294	4			PROPN
iajs-1013	294	5	.	.	PUNCT
iajs-1013	295	1	define	define	VERB
iajs-1013	295	2	f	f	NOUN
iajs-1013	295	3	:	:	PUNCT
iajs-1013	295	4	r	r	NOUN
iajs-1013	295	5			NOUN
iajs-1013	295	6			VERB
iajs-1013	295	7	by	by	ADP
iajs-1013	295	8	f	f	PROPN
iajs-1013	295	9	(	(	PUNCT
iajs-1013	295	10	r	r	NOUN
iajs-1013	295	11	)	)	PUNCT
iajs-1013	295	12	=	=	SYM
iajs-1013	296	1	r	r	NOUN
iajs-1013	296	2	x	x	PUNCT
iajs-1013	296	3	for	for	ADP
iajs-1013	296	4	each	each	DET
iajs-1013	296	5	r	r	NOUN
iajs-1013	296	6			PROPN
iajs-1013	296	7	r.	r.	PROPN
iajs-1013	296	8	clearly	clearly	ADV
iajs-1013	296	9	f	f	PROPN
iajs-1013	296	10	is	be	AUX
iajs-1013	296	11	well	well	ADV
iajs-1013	296	12	-	-	PUNCT
iajs-1013	296	13	defined	define	VERB
iajs-1013	296	14	r	r	NOUN
iajs-1013	296	15	-	-	PUNCT
iajs-1013	296	16	homomorphism	homomorphism	NOUN
iajs-1013	296	17	.	.	PUNCT
iajs-1013	297	1	thus	thus	ADV
iajs-1013	297	2	there	there	PRON
iajs-1013	297	3	exists	exist	VERB
iajs-1013	297	4	a	a	DET
iajs-1013	297	5	submodule	submodule	NOUN
iajs-1013	297	6	x	x	PUNCT
iajs-1013	297	7	of	of	ADP
iajs-1013	297	8			NUM
iajs-1013	297	9	such	such	ADJ
iajs-1013	297	10	that	that	SCONJ
iajs-1013	297	11	f	f	PROPN
iajs-1013	297	12	(	(	PUNCT
iajs-1013	297	13	r	r	NOUN
iajs-1013	297	14	)	)	PUNCT
iajs-1013	297	15			NOUN
iajs-1013	297	16	x	x	PUNCT
iajs-1013	297	17	≈	≈	NUM
iajs-1013	297	18	m.	m.	NOUN
iajs-1013	297	19	but	but	CCONJ
iajs-1013	297	20	x	x	X
iajs-1013	297	21	=	=	SYM
iajs-1013	298	1	1x	1x	NUM
iajs-1013	298	2	=	=	SYM
iajs-1013	298	3	f	f	X
iajs-1013	298	4	(	(	PUNCT
iajs-1013	298	5	1	1	NUM
iajs-1013	298	6	)	)	PUNCT
iajs-1013	298	7			NOUN
iajs-1013	298	8	f	f	X
iajs-1013	298	9	(	(	PUNCT
iajs-1013	298	10	r	r	NOUN
iajs-1013	298	11	)	)	PUNCT
iajs-1013	298	12	.	.	PUNCT
iajs-1013	299	1	hence	hence	ADV
iajs-1013	299	2	x	x	X
iajs-1013	299	3			NOUN
iajs-1013	299	4	x	x	NUM
iajs-1013	299	5	which	which	PRON
iajs-1013	299	6	is	be	AUX
iajs-1013	299	7	what	what	PRON
iajs-1013	299	8	we	we	PRON
iajs-1013	299	9	wanted	want	VERB
iajs-1013	299	10	.	.	PUNCT
iajs-1013	300	1	conversely	conversely	ADV
iajs-1013	300	2	,	,	PUNCT
iajs-1013	300	3	let	let	VERB
iajs-1013	300	4	f	f	PRON
iajs-1013	300	5			PROPN
iajs-1013	300	6	hom(r,	hom(r,	PROPN
iajs-1013	300	7	)	)	PUNCT
iajs-1013	300	8	.	.	PUNCT
iajs-1013	301	1	then	then	ADV
iajs-1013	301	2	f	f	X
iajs-1013	301	3	(	(	PUNCT
iajs-1013	301	4	1	1	NUM
iajs-1013	301	5	)	)	PUNCT
iajs-1013	301	6			NOUN
iajs-1013	301	7			NUM
iajs-1013	301	8	.	.	PUNCT
iajs-1013	302	1	let	let	VERB
iajs-1013	302	2	x	x	SYM
iajs-1013	302	3	=	=	SYM
iajs-1013	302	4	f	f	X
iajs-1013	302	5	(	(	PUNCT
iajs-1013	302	6	1	1	NUM
iajs-1013	302	7	)	)	PUNCT
iajs-1013	302	8	.	.	PUNCT
iajs-1013	303	1	hence	hence	ADV
iajs-1013	303	2	there	there	PRON
iajs-1013	303	3	exists	exist	VERB
iajs-1013	303	4	a	a	DET
iajs-1013	303	5	submodule	submodule	NOUN
iajs-1013	303	6	x	x	PUNCT
iajs-1013	303	7	of	of	ADP
iajs-1013	303	8			NUM
iajs-1013	303	9	such	such	ADJ
iajs-1013	303	10	that	that	SCONJ
iajs-1013	303	11	x	x	PRON
iajs-1013	303	12			NOUN
iajs-1013	303	13	x	x	X
iajs-1013	303	14	≈	≈	PROPN
iajs-1013	303	15	m.	m.	NOUN
iajs-1013	303	16	it	it	PRON
iajs-1013	303	17	is	be	AUX
iajs-1013	303	18	left	leave	VERB
iajs-1013	303	19	to	to	PART
iajs-1013	303	20	show	show	VERB
iajs-1013	303	21	that	that	SCONJ
iajs-1013	303	22	f	f	PROPN
iajs-1013	303	23	(	(	PUNCT
iajs-1013	303	24	r	r	NOUN
iajs-1013	303	25	)	)	PUNCT
iajs-1013	303	26			PROPN
iajs-1013	303	27	x.	x.	NOUN
iajs-1013	303	28	let	let	VERB
iajs-1013	303	29	a	a	DET
iajs-1013	303	30			NOUN
iajs-1013	303	31	f	f	X
iajs-1013	303	32	(	(	PUNCT
iajs-1013	303	33	r	r	NOUN
iajs-1013	303	34	)	)	PUNCT
iajs-1013	303	35	,	,	PUNCT
iajs-1013	303	36	then	then	ADV
iajs-1013	303	37	a	a	DET
iajs-1013	303	38	=	=	SYM
iajs-1013	303	39	f	f	X
iajs-1013	303	40	(	(	PUNCT
iajs-1013	303	41	r	r	NOUN
iajs-1013	303	42	)	)	PUNCT
iajs-1013	303	43	for	for	ADP
iajs-1013	303	44	some	some	DET
iajs-1013	303	45	r	r	NOUN
iajs-1013	303	46			PROPN
iajs-1013	303	47	r.	r.	NOUN
iajs-1013	303	48	a	a	PROPN
iajs-1013	303	49	=	=	X
iajs-1013	303	50	f	f	X
iajs-1013	303	51	(	(	PUNCT
iajs-1013	303	52	r	r	NOUN
iajs-1013	303	53	)	)	PUNCT
iajs-1013	303	54	=	=	SYM
iajs-1013	304	1	r	r	NOUN
iajs-1013	304	2	f	f	X
iajs-1013	304	3	(	(	PUNCT
iajs-1013	304	4	1	1	NUM
iajs-1013	304	5	)	)	PUNCT
iajs-1013	304	6	=	=	SYM
iajs-1013	305	1	r	r	NOUN
iajs-1013	305	2	x	x	PUNCT
iajs-1013	305	3			NOUN
iajs-1013	305	4	x.	x.	NOUN
iajs-1013	306	1	therefore	therefore	ADV
iajs-1013	306	2	f	f	PROPN
iajs-1013	306	3	(	(	PUNCT
iajs-1013	306	4	r	r	NOUN
iajs-1013	306	5	)	)	PUNCT
iajs-1013	306	6			NOUN
iajs-1013	306	7	x	x	X
iajs-1013	306	8	and	and	CCONJ
iajs-1013	306	9	hence	hence	ADV
iajs-1013	306	10	m	m	VERB
iajs-1013	306	11	is	be	AUX
iajs-1013	306	12	weakly	weakly	ADJ
iajs-1013	306	13	r	r	NOUN
iajs-1013	306	14	-	-	PUNCT
iajs-1013	306	15	quasi	quasi	NOUN
iajs-1013	306	16	-	-	ADJ
iajs-1013	306	17	injective	injective	ADJ
iajs-1013	306	18	.	.	PUNCT
iajs-1013	307	1	as	as	ADP
iajs-1013	307	2	a	a	DET
iajs-1013	307	3	special	special	ADJ
iajs-1013	307	4	case	case	NOUN
iajs-1013	307	5	,	,	PUNCT
iajs-1013	307	6	we	we	PRON
iajs-1013	307	7	shall	shall	AUX
iajs-1013	307	8	characterize	characterize	VERB
iajs-1013	307	9	the	the	DET
iajs-1013	307	10	weakly	weakly	ADJ
iajs-1013	307	11	quasi	quasi	NOUN
iajs-1013	307	12	-	-	NOUN
iajs-1013	307	13	injectivity	injectivity	NOUN
iajs-1013	307	14	of	of	ADP
iajs-1013	307	15	the	the	DET
iajs-1013	307	16	r	r	NOUN
iajs-1013	307	17	-	-	PUNCT
iajs-1013	307	18	module	module	NOUN
iajs-1013	307	19	r	r	NOUN
iajs-1013	307	20	relative	relative	NOUN
iajs-1013	307	21	to	to	ADP
iajs-1013	307	22	itself	itself	PRON
iajs-1013	307	23	.	.	PUNCT
iajs-1013	308	1	2.9	2.9	NUM
iajs-1013	308	2	theorem	theorem	NOUN
iajs-1013	308	3	r	r	NOUN
iajs-1013	308	4	is	be	AUX
iajs-1013	308	5	weakly	weakly	ADJ
iajs-1013	308	6	r	r	NOUN
iajs-1013	308	7	-	-	PUNCT
iajs-1013	308	8	quasi	quasi	ADJ
iajs-1013	308	9	-	-	ADJ
iajs-1013	308	10	injective	injective	ADJ
iajs-1013	308	11	r	r	NOUN
iajs-1013	308	12	-	-	PUNCT
iajs-1013	308	13	module	module	NOUN
iajs-1013	308	14	if	if	SCONJ
iajs-1013	308	15	and	and	CCONJ
iajs-1013	308	16	only	only	ADV
iajs-1013	308	17	if	if	SCONJ
iajs-1013	308	18	for	for	ADP
iajs-1013	308	19	each	each	DET
iajs-1013	308	20	element	element	NOUN
iajs-1013	308	21	a	a	DET
iajs-1013	308	22			NOUN
iajs-1013	308	23	r	r	NOUN
iajs-1013	308	24	,	,	PUNCT
iajs-1013	308	25	there	there	PRON
iajs-1013	308	26	exists	exist	VERB
iajs-1013	308	27	an	an	DET
iajs-1013	308	28	element	element	NOUN
iajs-1013	308	29	b	b	PROPN
iajs-1013	308	30			PROPN
iajs-1013	308	31	r	r	NOUN
iajs-1013	309	1	such	such	ADJ
iajs-1013	309	2	that	that	SCONJ
iajs-1013	309	3	a	a	DET
iajs-1013	309	4			NOUN
iajs-1013	309	5	r	r	NOUN
iajs-1013	309	6	b	b	PROPN
iajs-1013	309	7	and	and	CCONJ
iajs-1013	309	8	annr(b	annr(b	ADJ
iajs-1013	309	9	)	)	PUNCT
iajs-1013	309	10	=	=	SYM
iajs-1013	309	11	0	0	X
iajs-1013	309	12	.	.	PUNCT
iajs-1013	310	1	proof	proof	NOUN
iajs-1013	310	2	:	:	PUNCT
iajs-1013	310	3	assume	assume	VERB
iajs-1013	310	4	that	that	SCONJ
iajs-1013	310	5	r	r	NOUN
iajs-1013	310	6	is	be	AUX
iajs-1013	310	7	weakly	weakly	ADJ
iajs-1013	310	8	r	r	NOUN
iajs-1013	310	9	-	-	PUNCT
iajs-1013	310	10	quasi	quasi	ADJ
iajs-1013	310	11	-	-	ADJ
iajs-1013	310	12	injective	injective	ADJ
iajs-1013	310	13	r	r	NOUN
iajs-1013	310	14	-	-	PUNCT
iajs-1013	310	15	module	module	NOUN
iajs-1013	310	16	.	.	PUNCT
iajs-1013	311	1	let	let	VERB
iajs-1013	311	2	a	a	DET
iajs-1013	311	3			NOUN
iajs-1013	311	4	r	r	NOUN
iajs-1013	311	5	.	.	PUNCT
iajs-1013	312	1	define	define	VERB
iajs-1013	312	2	f	f	NOUN
iajs-1013	312	3	:	:	PUNCT
iajs-1013	312	4	r	r	NOUN
iajs-1013	312	5			NOUN
iajs-1013	312	6	r	r	NOUN
iajs-1013	312	7	by	by	ADP
iajs-1013	312	8	f	f	PROPN
iajs-1013	312	9	(	(	PUNCT
iajs-1013	312	10	r	r	NOUN
iajs-1013	312	11	)	)	PUNCT
iajs-1013	312	12	=	=	SYM
iajs-1013	313	1	r	r	NOUN
iajs-1013	313	2	a	a	PRON
iajs-1013	313	3	for	for	ADP
iajs-1013	313	4	each	each	DET
iajs-1013	313	5	r	r	NOUN
iajs-1013	313	6			PROPN
iajs-1013	313	7	r.	r.	NOUN
iajs-1013	313	8	it	it	PRON
iajs-1013	313	9	can	can	AUX
iajs-1013	313	10	be	be	AUX
iajs-1013	313	11	easily	easily	ADV
iajs-1013	313	12	shown	show	VERB
iajs-1013	313	13	that	that	SCONJ
iajs-1013	313	14	f	f	PROPN
iajs-1013	313	15	is	be	AUX
iajs-1013	313	16	a	a	DET
iajs-1013	313	17	well	well	ADV
iajs-1013	313	18	-	-	PUNCT
iajs-1013	313	19	defined	define	VERB
iajs-1013	313	20	rhomomorphism	rhomomorphism	NOUN
iajs-1013	313	21	.	.	PUNCT
iajs-1013	314	1	hence	hence	ADV
iajs-1013	314	2	there	there	PRON
iajs-1013	314	3	exists	exist	VERB
iajs-1013	314	4	a	a	DET
iajs-1013	314	5	submodule	submodule	NOUN
iajs-1013	314	6	x	x	PUNCT
iajs-1013	314	7	of	of	ADP
iajs-1013	314	8	r	r	NOUN
iajs-1013	314	9	such	such	ADJ
iajs-1013	314	10	that	that	SCONJ
iajs-1013	314	11	f	f	PROPN
iajs-1013	314	12	(	(	PUNCT
iajs-1013	314	13	r	r	NOUN
iajs-1013	314	14	)	)	PUNCT
iajs-1013	314	15			NOUN
iajs-1013	314	16	x	x	PROPN
iajs-1013	314	17	≈	≈	PROPN
iajs-1013	314	18	r.	r.	PROPN
iajs-1013	314	19	clearly	clearly	ADV
iajs-1013	314	20	,	,	PUNCT
iajs-1013	314	21	f	f	PROPN
iajs-1013	314	22	(	(	PUNCT
iajs-1013	314	23	r	r	NOUN
iajs-1013	314	24	)	)	PUNCT
iajs-1013	314	25	=	=	SYM
iajs-1013	314	26	r	r	NOUN
iajs-1013	314	27	a.	a.	NOUN
iajs-1013	314	28	thus	thus	ADV
iajs-1013	314	29	r	r	VERB
iajs-1013	314	30	a	a	DET
iajs-1013	314	31			PROPN
iajs-1013	314	32	x	x	X
iajs-1013	314	33	,	,	PUNCT
iajs-1013	314	34	implies	imply	VERB
iajs-1013	314	35	that	that	SCONJ
iajs-1013	314	36	a	a	DET
iajs-1013	314	37	=	=	SYM
iajs-1013	314	38	1a	1a	NUM
iajs-1013	314	39			NOUN
iajs-1013	314	40	x.	x.	NOUN
iajs-1013	314	41	let	let	VERB
iajs-1013	314	42			NOUN
iajs-1013	314	43	:	:	PUNCT
iajs-1013	314	44	r	r	NOUN
iajs-1013	314	45			NUM
iajs-1013	314	46	x	x	AUX
iajs-1013	314	47	be	be	AUX
iajs-1013	314	48	an	an	DET
iajs-1013	314	49	isomorphism	isomorphism	NOUN
iajs-1013	314	50	.	.	PUNCT
iajs-1013	315	1	so	so	ADV
iajs-1013	315	2	there	there	PRON
iajs-1013	315	3	exists	exist	VERB
iajs-1013	315	4	an	an	DET
iajs-1013	315	5	element	element	NOUN
iajs-1013	315	6	c	c	NOUN
iajs-1013	315	7			PROPN
iajs-1013	315	8	r	r	NOUN
iajs-1013	315	9	such	such	ADJ
iajs-1013	315	10	that	that	SCONJ
iajs-1013	315	11	a	a	DET
iajs-1013	315	12	=	=	SYM
iajs-1013	315	13	(c	(c	NOUN
iajs-1013	315	14	)	)	PUNCT
iajs-1013	315	15	.	.	PUNCT
iajs-1013	316	1	hence	hence	ADV
iajs-1013	316	2	a	a	DET
iajs-1013	316	3	=	=	X
iajs-1013	316	4	(c1	(c1	ADJ
iajs-1013	316	5	)	)	PUNCT
iajs-1013	316	6	=	=	PUNCT
iajs-1013	316	7	c	c	X
iajs-1013	316	8	(1	(1	NOUN
iajs-1013	316	9	)	)	PUNCT
iajs-1013	316	10	=	=	PUNCT
iajs-1013	317	1	c	c	PROPN
iajs-1013	317	2	b	b	PROPN
iajs-1013	317	3			PROPN
iajs-1013	317	4	r	r	NOUN
iajs-1013	317	5	b	b	PROPN
iajs-1013	317	6	where	where	SCONJ
iajs-1013	317	7	b	b	NOUN
iajs-1013	317	8	=	=	SYM
iajs-1013	317	9	(1	(1	PROPN
iajs-1013	317	10	)	)	PUNCT
iajs-1013	317	11	.	.	PUNCT
iajs-1013	318	1	therefore	therefore	ADV
iajs-1013	318	2	a	a	DET
iajs-1013	318	3			PROPN
iajs-1013	318	4	r	r	NOUN
iajs-1013	318	5	b.	b.	NOUN
iajs-1013	318	6	now	now	ADV
iajs-1013	318	7	,	,	PUNCT
iajs-1013	318	8	let	let	VERB
iajs-1013	318	9	r	r	NOUN
iajs-1013	318	10			PROPN
iajs-1013	318	11	annr(b	annr(b	ADP
iajs-1013	318	12	)	)	PUNCT
iajs-1013	318	13	.	.	PUNCT
iajs-1013	319	1	then	then	ADV
iajs-1013	319	2	r	r	NOUN
iajs-1013	319	3	b	b	PROPN
iajs-1013	319	4	=	=	SYM
iajs-1013	319	5	0	0	PROPN
iajs-1013	319	6	and	and	CCONJ
iajs-1013	319	7	hence	hence	ADV
iajs-1013	319	8	0	0	X
iajs-1013	320	1	=	=	SYM
iajs-1013	320	2	r	r	NOUN
iajs-1013	320	3	(1	(1	PROPN
iajs-1013	320	4	)	)	PUNCT
iajs-1013	320	5	=	=	SYM
iajs-1013	320	6	(r	(r	NOUN
iajs-1013	320	7	)	)	PUNCT
iajs-1013	320	8	implies	imply	VERB
iajs-1013	320	9	that	that	SCONJ
iajs-1013	320	10	r	r	NOUN
iajs-1013	320	11	=	=	SYM
iajs-1013	320	12	0	0	NUM
iajs-1013	320	13	.	.	PUNCT
iajs-1013	321	1	hence	hence	ADV
iajs-1013	321	2	annr(b	annr(b	ADV
iajs-1013	321	3	)	)	PUNCT
iajs-1013	321	4	=	=	SYM
iajs-1013	322	1	0	0	X
iajs-1013	322	2	.	.	PUNCT
iajs-1013	323	1	conversely	conversely	ADV
iajs-1013	323	2	,	,	PUNCT
iajs-1013	323	3	let	let	VERB
iajs-1013	323	4	f	f	PRON
iajs-1013	323	5			PROPN
iajs-1013	323	6	hom(r	hom(r	PROPN
iajs-1013	323	7	,	,	PUNCT
iajs-1013	323	8	r	r	NOUN
iajs-1013	323	9	)	)	PUNCT
iajs-1013	323	10	.	.	PUNCT
iajs-1013	324	1	then	then	ADV
iajs-1013	324	2	f	f	X
iajs-1013	324	3	(	(	PUNCT
iajs-1013	324	4	1	1	NUM
iajs-1013	324	5	)	)	PUNCT
iajs-1013	324	6			NOUN
iajs-1013	324	7	r	r	NOUN
iajs-1013	324	8	.	.	PUNCT
iajs-1013	325	1	let	let	VERB
iajs-1013	325	2	f	f	PROPN
iajs-1013	325	3	(	(	PUNCT
iajs-1013	325	4	1	1	NUM
iajs-1013	325	5	)	)	PUNCT
iajs-1013	325	6	=	=	NOUN
iajs-1013	326	1	a.	a.	NOUN
iajs-1013	327	1	so	so	ADV
iajs-1013	327	2	there	there	PRON
iajs-1013	327	3	exists	exist	VERB
iajs-1013	327	4	an	an	DET
iajs-1013	327	5	element	element	NOUN
iajs-1013	327	6	b	b	PROPN
iajs-1013	327	7			PROPN
iajs-1013	327	8	r	r	NOUN
iajs-1013	327	9	such	such	ADJ
iajs-1013	327	10	that	that	SCONJ
iajs-1013	327	11	a	a	DET
iajs-1013	327	12			NOUN
iajs-1013	327	13	r	r	NOUN
iajs-1013	327	14	b	b	PROPN
iajs-1013	327	15	and	and	CCONJ
iajs-1013	327	16	annr(b	annr(b	ADJ
iajs-1013	327	17	)	)	PUNCT
iajs-1013	327	18	=	=	SYM
iajs-1013	328	1	0	0	X
iajs-1013	328	2	.	.	PUNCT
iajs-1013	329	1	we	we	PRON
iajs-1013	329	2	take	take	VERB
iajs-1013	329	3	x	x	PUNCT
iajs-1013	329	4	=	=	SYM
iajs-1013	329	5	r	r	NOUN
iajs-1013	329	6	b	b	PROPN
iajs-1013	329	7	implies	imply	VERB
iajs-1013	329	8	that	that	SCONJ
iajs-1013	329	9	x	x	SYM
iajs-1013	329	10			PROPN
iajs-1013	329	11	r	r	NOUN
iajs-1013	329	12	.	.	PUNCT
iajs-1013	330	1	but	but	CCONJ
iajs-1013	330	2	r	r	NOUN
iajs-1013	330	3	b	b	PROPN
iajs-1013	330	4	≈	≈	PROPN
iajs-1013	330	5	r	r	PROPN
iajs-1013	330	6	/	/	SYM
iajs-1013	330	7	annr(b	annr(b	PROPN
iajs-1013	330	8	)	)	PUNCT
iajs-1013	331	1	≈	≈	PROPN
iajs-1013	331	2	r.	r.	PROPN
iajs-1013	331	3	moreover	moreover	ADV
iajs-1013	331	4	f	f	X
iajs-1013	331	5	(	(	PUNCT
iajs-1013	331	6	r	r	NOUN
iajs-1013	331	7	)	)	PUNCT
iajs-1013	331	8	=	=	SYM
iajs-1013	331	9	{	{	PUNCT
iajs-1013	331	10	f	f	X
iajs-1013	331	11	(	(	PUNCT
iajs-1013	331	12	r	r	NOUN
iajs-1013	331	13	)	)	PUNCT
iajs-1013	331	14	:	:	PUNCT
iajs-1013	331	15	r	r	NOUN
iajs-1013	331	16			NOUN
iajs-1013	331	17	r	r	NOUN
iajs-1013	331	18	}	}	PUNCT
iajs-1013	331	19	=	=	SYM
iajs-1013	331	20	{	{	PUNCT
iajs-1013	331	21	r	r	NOUN
iajs-1013	331	22	f	f	X
iajs-1013	331	23	(	(	PUNCT
iajs-1013	331	24	1	1	NUM
iajs-1013	331	25	)	)	PUNCT
iajs-1013	331	26	:	:	PUNCT
iajs-1013	331	27	r	r	NOUN
iajs-1013	331	28			NOUN
iajs-1013	331	29	r	r	NOUN
iajs-1013	331	30	}	}	PUNCT
iajs-1013	331	31	=	=	PUNCT
iajs-1013	331	32	r	r	NOUN
iajs-1013	331	33	a	a	DET
iajs-1013	331	34			PROPN
iajs-1013	331	35	r	r	PROPN
iajs-1013	331	36	b.	b.	NOUN
iajs-1013	331	37	therefore	therefore	ADV
iajs-1013	331	38	f	f	X
iajs-1013	331	39	(	(	PUNCT
iajs-1013	331	40	r	r	NOUN
iajs-1013	331	41	)	)	PUNCT
iajs-1013	331	42			NOUN
iajs-1013	331	43	x	x	X
iajs-1013	332	1	≈	≈	PROPN
iajs-1013	332	2	r.	r.	PROPN
iajs-1013	332	3	this	this	PRON
iajs-1013	332	4	completes	complete	VERB
iajs-1013	332	5	the	the	DET
iajs-1013	332	6	proof	proof	NOUN
iajs-1013	332	7	.	.	PUNCT
iajs-1013	333	1	we	we	PRON
iajs-1013	333	2	shall	shall	AUX
iajs-1013	333	3	establish	establish	VERB
iajs-1013	333	4	in	in	ADP
iajs-1013	333	5	the	the	DET
iajs-1013	333	6	following	following	NOUN
iajs-1013	333	7	theorem	theorem	VERB
iajs-1013	333	8	a	a	DET
iajs-1013	333	9	general	general	ADJ
iajs-1013	333	10	case	case	NOUN
iajs-1013	333	11	of	of	ADP
iajs-1013	333	12	theorem	theorem	ADJ
iajs-1013	333	13	2.9	2.9	NUM
iajs-1013	333	14	.	.	PUNCT
iajs-1013	334	1	2.10	2.10	NUM
iajs-1013	334	2	theorem	theorem	NOUN
iajs-1013	334	3	r	r	NOUN
iajs-1013	334	4	be	be	AUX
iajs-1013	334	5	an	an	DET
iajs-1013	334	6	integral	integral	ADJ
iajs-1013	334	7	domain	domain	NOUN
iajs-1013	334	8	.	.	PUNCT
iajs-1013	335	1	let	let	VERB
iajs-1013	335	2	m	m	PRON
iajs-1013	335	3	and	and	CCONJ
iajs-1013	335	4	n	n	CCONJ
iajs-1013	335	5	be	be	AUX
iajs-1013	335	6	two	two	NUM
iajs-1013	335	7	cyclic	cyclic	ADJ
iajs-1013	335	8	torsion	torsion	NOUN
iajs-1013	335	9	-	-	PUNCT
iajs-1013	335	10	free	free	ADJ
iajs-1013	335	11	r	r	NOUN
iajs-1013	335	12	-	-	PUNCT
iajs-1013	335	13	modules	module	NOUN
iajs-1013	335	14	.	.	PUNCT
iajs-1013	336	1	then	then	ADV
iajs-1013	336	2	m	m	PROPN
iajs-1013	336	3	is	be	AUX
iajs-1013	336	4	weakly	weakly	ADJ
iajs-1013	336	5	n	n	CCONJ
iajs-1013	336	6	-	-	PUNCT
iajs-1013	336	7	quasi	quasi	NOUN
iajs-1013	336	8	-	-	ADJ
iajs-1013	336	9	injective	injective	ADJ
iajs-1013	336	10	if	if	SCONJ
iajs-1013	336	11	and	and	CCONJ
iajs-1013	336	12	only	only	ADV
iajs-1013	336	13	if	if	SCONJ
iajs-1013	336	14	for	for	ADP
iajs-1013	336	15	each	each	DET
iajs-1013	336	16	element	element	NOUN
iajs-1013	336	17	x	x	PROPN
iajs-1013	336	18			PROPN
iajs-1013	336	19			VERB
iajs-1013	336	20	there	there	PRON
iajs-1013	336	21	exists	exist	VERB
iajs-1013	336	22	an	an	DET
iajs-1013	336	23	element	element	NOUN
iajs-1013	336	24	y	y	PROPN
iajs-1013	336	25			PROPN
iajs-1013	336	26			VERB
iajs-1013	336	27	such	such	ADJ
iajs-1013	336	28	that	that	SCONJ
iajs-1013	336	29	x	x	PRON
iajs-1013	336	30			NOUN
iajs-1013	336	31	ry	ry	NOUN
iajs-1013	336	32	and	and	CCONJ
iajs-1013	336	33	annr(y	annr(y	VERB
iajs-1013	336	34	)	)	PUNCT
iajs-1013	336	35	=	=	SYM
iajs-1013	336	36	0	0	X
iajs-1013	336	37	.	.	PUNCT
iajs-1013	337	1	proof	proof	NOUN
iajs-1013	337	2	:	:	PUNCT
iajs-1013	337	3	assume	assume	VERB
iajs-1013	337	4	that	that	SCONJ
iajs-1013	337	5	m	m	NOUN
iajs-1013	337	6	is	be	AUX
iajs-1013	337	7	weakly	weakly	ADJ
iajs-1013	337	8	n	n	CCONJ
iajs-1013	337	9	-	-	PUNCT
iajs-1013	337	10	quasi	quasi	NOUN
iajs-1013	337	11	-	-	ADJ
iajs-1013	337	12	injective	injective	ADJ
iajs-1013	337	13	.	.	PUNCT
iajs-1013	338	1	let	let	VERB
iajs-1013	338	2	x	x	SYM
iajs-1013	338	3			PROPN
iajs-1013	338	4			PROPN
iajs-1013	338	5	.	.	PUNCT
iajs-1013	339	1	suppose	suppose	VERB
iajs-1013	339	2	that	that	SCONJ
iajs-1013	339	3	m	m	VERB
iajs-1013	339	4	=	=	SYM
iajs-1013	339	5	(	(	PUNCT
iajs-1013	339	6	m	m	NOUN
iajs-1013	339	7	)	)	PUNCT
iajs-1013	339	8	and	and	CCONJ
iajs-1013	339	9	n	n	CCONJ
iajs-1013	339	10	=	=	SYM
iajs-1013	339	11	(	(	PUNCT
iajs-1013	339	12	n	n	CCONJ
iajs-1013	339	13	)	)	PUNCT
iajs-1013	339	14	for	for	ADP
iajs-1013	339	15	some	some	DET
iajs-1013	339	16	m	m	PROPN
iajs-1013	339	17			NOUN
iajs-1013	339	18	m	m	ADJ
iajs-1013	339	19	and	and	CCONJ
iajs-1013	339	20	n	n	PROPN
iajs-1013	339	21			PROPN
iajs-1013	339	22	n.	n.	NOUN
iajs-1013	339	23	define	define	VERB
iajs-1013	339	24	f	f	X
iajs-1013	339	25	:	:	PUNCT
iajs-1013	339	26	n	n	PRON
iajs-1013	339	27			PROPN
iajs-1013	339	28			VERB
iajs-1013	339	29	by	by	ADP
iajs-1013	339	30	f	f	PROPN
iajs-1013	339	31	(	(	PUNCT
iajs-1013	339	32	r	r	NOUN
iajs-1013	339	33	n	n	CCONJ
iajs-1013	339	34	)	)	PUNCT
iajs-1013	340	1	=	=	SYM
iajs-1013	340	2	r	r	NOUN
iajs-1013	340	3	x	x	X
iajs-1013	340	4	for	for	ADP
iajs-1013	340	5	all	all	DET
iajs-1013	340	6	r	r	NOUN
iajs-1013	340	7			PROPN
iajs-1013	340	8	r.	r.	PROPN
iajs-1013	340	9	f	f	PROPN
iajs-1013	340	10	is	be	AUX
iajs-1013	340	11	well	well	ADV
iajs-1013	340	12	ibn	ibn	PROPN
iajs-1013	340	13	alhaitham	alhaitham	NOUN
iajs-1013	340	14	j.	j.	PROPN
iajs-1013	340	15	for	for	ADP
iajs-1013	340	16	pure	pure	ADJ
iajs-1013	340	17	&	&	CCONJ
iajs-1013	340	18	appl	appl	PROPN
iajs-1013	340	19	.	.	PUNCT
iajs-1013	341	1	sci	sci	PROPN
iajs-1013	341	2	.	.	PUNCT
iajs-1013	342	1	vol.23	vol.23	PROPN
iajs-1013	342	2	(	(	PUNCT
iajs-1013	342	3	1	1	NUM
iajs-1013	342	4	)	)	PUNCT
iajs-1013	342	5	2010	2010	NUM
iajs-1013	342	6	defined	define	VERB
iajs-1013	342	7	homomorphism	homomorphism	NOUN
iajs-1013	342	8	.	.	PUNCT
iajs-1013	343	1	therefore	therefore	ADV
iajs-1013	343	2	there	there	PRON
iajs-1013	343	3	exists	exist	VERB
iajs-1013	343	4	a	a	DET
iajs-1013	343	5	submodule	submodule	NOUN
iajs-1013	343	6	x	x	PUNCT
iajs-1013	343	7	of	of	ADP
iajs-1013	343	8			NUM
iajs-1013	343	9	such	such	ADJ
iajs-1013	343	10	that	that	SCONJ
iajs-1013	343	11	f	f	PROPN
iajs-1013	343	12	(	(	PUNCT
iajs-1013	343	13	n	n	CCONJ
iajs-1013	343	14	)	)	PUNCT
iajs-1013	343	15			PROPN
iajs-1013	343	16	x	x	SYM
iajs-1013	343	17	≈	≈	NUM
iajs-1013	343	18	m.	m.	NOUN
iajs-1013	343	19	let	let	VERB
iajs-1013	343	20	y	y	PROPN
iajs-1013	343	21	=	=	PUNCT
iajs-1013	343	22	f	f	PROPN
iajs-1013	343	23	(	(	PUNCT
iajs-1013	343	24	n	n	CCONJ
iajs-1013	343	25	)	)	PUNCT
iajs-1013	343	26	.	.	PUNCT
iajs-1013	344	1	then	then	ADV
iajs-1013	344	2	y	y	PROPN
iajs-1013	344	3	=	=	PUNCT
iajs-1013	344	4	x	x	PROPN
iajs-1013	344	5			NOUN
iajs-1013	344	6			VERB
iajs-1013	344	7	and	and	CCONJ
iajs-1013	344	8	x	x	SYM
iajs-1013	344	9	=	=	SYM
iajs-1013	344	10	1y	1y	NUM
iajs-1013	344	11			NOUN
iajs-1013	344	12	r	r	NOUN
iajs-1013	344	13	y.	y.	NOUN
iajs-1013	344	14	now	now	ADV
iajs-1013	344	15	,	,	PUNCT
iajs-1013	344	16	if	if	SCONJ
iajs-1013	344	17	t	t	PROPN
iajs-1013	344	18			PROPN
iajs-1013	344	19	annr(y	annr(y	VERB
iajs-1013	344	20	)	)	PUNCT
iajs-1013	344	21	,	,	PUNCT
iajs-1013	344	22	then	then	ADV
iajs-1013	344	23	t	t	PROPN
iajs-1013	344	24	y	y	PROPN
iajs-1013	344	25	=	=	SYM
iajs-1013	344	26	0	0	X
iajs-1013	344	27	.	.	PUNCT
iajs-1013	345	1	let	let	VERB
iajs-1013	345	2	g	g	NOUN
iajs-1013	345	3	:	:	PUNCT
iajs-1013	345	4	x	x	SYM
iajs-1013	345	5			PROPN
iajs-1013	345	6	m	m	AUX
iajs-1013	345	7	be	be	VERB
iajs-1013	345	8	an	an	DET
iajs-1013	345	9	isomorphism	isomorphism	NOUN
iajs-1013	345	10	,	,	PUNCT
iajs-1013	345	11	implies	imply	VERB
iajs-1013	345	12	that	that	SCONJ
iajs-1013	345	13	0	0	X
iajs-1013	345	14	=	=	SYM
iajs-1013	345	15	g(ty	g(ty	X
iajs-1013	345	16	)	)	PUNCT
iajs-1013	345	17	=	=	SYM
iajs-1013	345	18	t	t	NOUN
iajs-1013	345	19	g(y	g(y	PROPN
iajs-1013	345	20	)	)	PUNCT
iajs-1013	345	21	and	and	CCONJ
iajs-1013	345	22	hence	hence	ADV
iajs-1013	345	23	t	t	NOUN
iajs-1013	345	24	=	=	SYM
iajs-1013	345	25	0	0	NUM
iajs-1013	345	26	.	.	PUNCT
iajs-1013	346	1	thus	thus	ADV
iajs-1013	346	2	annr(y	annr(y	VERB
iajs-1013	346	3	)	)	PUNCT
iajs-1013	346	4	=	=	SYM
iajs-1013	346	5	0	0	X
iajs-1013	346	6	.	.	PUNCT
iajs-1013	347	1	conversely	conversely	ADV
iajs-1013	347	2	,	,	PUNCT
iajs-1013	347	3	let	let	VERB
iajs-1013	347	4	f	f	PRON
iajs-1013	347	5			PROPN
iajs-1013	347	6	hom(n,	hom(n,	NOUN
iajs-1013	347	7	)	)	PUNCT
iajs-1013	347	8	,	,	PUNCT
iajs-1013	347	9	and	and	CCONJ
iajs-1013	347	10	let	let	VERB
iajs-1013	347	11	x	x	SYM
iajs-1013	347	12	=	=	SYM
iajs-1013	347	13	f	f	X
iajs-1013	347	14	(	(	PUNCT
iajs-1013	347	15	n	n	CCONJ
iajs-1013	347	16	)	)	PUNCT
iajs-1013	347	17	.	.	PUNCT
iajs-1013	348	1	then	then	ADV
iajs-1013	348	2	x	x	SYM
iajs-1013	348	3			NOUN
iajs-1013	348	4			VERB
iajs-1013	348	5	and	and	CCONJ
iajs-1013	348	6	hence	hence	ADV
iajs-1013	348	7	there	there	PRON
iajs-1013	348	8	exists	exist	VERB
iajs-1013	348	9	an	an	DET
iajs-1013	348	10	element	element	NOUN
iajs-1013	348	11	y	y	PROPN
iajs-1013	348	12			PROPN
iajs-1013	348	13			VERB
iajs-1013	348	14	such	such	ADJ
iajs-1013	348	15	that	that	SCONJ
iajs-1013	348	16	x	x	PRON
iajs-1013	348	17			NOUN
iajs-1013	348	18	r	r	NOUN
iajs-1013	348	19	y	y	PROPN
iajs-1013	348	20	and	and	CCONJ
iajs-1013	348	21	annr(y	annr(y	VERB
iajs-1013	348	22	)	)	PUNCT
iajs-1013	348	23	=	=	SYM
iajs-1013	349	1	0	0	X
iajs-1013	349	2	.	.	PUNCT
iajs-1013	350	1	let	let	VERB
iajs-1013	350	2	x	x	PUNCT
iajs-1013	350	3	=	=	PUNCT
iajs-1013	350	4	(	(	PUNCT
iajs-1013	350	5	x	x	NOUN
iajs-1013	350	6	)	)	PUNCT
iajs-1013	350	7	.	.	PUNCT
iajs-1013	351	1	then	then	ADV
iajs-1013	351	2	x	x	PRON
iajs-1013	351	3	is	be	AUX
iajs-1013	351	4	a	a	DET
iajs-1013	351	5	submodule	submodule	NOUN
iajs-1013	351	6	of	of	ADP
iajs-1013	351	7			PROPN
iajs-1013	351	8	and	and	CCONJ
iajs-1013	351	9	f	f	PROPN
iajs-1013	351	10	(	(	PUNCT
iajs-1013	351	11	n	n	CCONJ
iajs-1013	351	12	)	)	PUNCT
iajs-1013	351	13			PROPN
iajs-1013	351	14	x.	x.	NOUN
iajs-1013	352	1	we	we	PRON
iajs-1013	352	2	claim	claim	VERB
iajs-1013	352	3	that	that	SCONJ
iajs-1013	352	4	x	x	SYM
iajs-1013	352	5	≈	≈	NUM
iajs-1013	352	6	m.	m.	NOUN
iajs-1013	352	7	define	define	VERB
iajs-1013	352	8	h	h	NOUN
iajs-1013	352	9	:	:	PUNCT
iajs-1013	352	10	m	m	VERB
iajs-1013	352	11			X
iajs-1013	352	12	x	x	PUNCT
iajs-1013	352	13	by	by	ADP
iajs-1013	352	14	h(r	h(r	PROPN
iajs-1013	352	15	m	m	PROPN
iajs-1013	352	16	)	)	PUNCT
iajs-1013	353	1	=	=	SYM
iajs-1013	353	2	r	r	NOUN
iajs-1013	353	3	x	x	X
iajs-1013	353	4	for	for	ADP
iajs-1013	353	5	all	all	DET
iajs-1013	353	6	r	r	NOUN
iajs-1013	353	7			PROPN
iajs-1013	353	8	r.	r.	NOUN
iajs-1013	353	9	it	it	PRON
iajs-1013	353	10	is	be	AUX
iajs-1013	353	11	clear	clear	ADJ
iajs-1013	353	12	that	that	SCONJ
iajs-1013	353	13	h	h	NOUN
iajs-1013	353	14	is	be	AUX
iajs-1013	353	15	a	a	DET
iajs-1013	353	16	well	well	ADV
iajs-1013	353	17	-	-	PUNCT
iajs-1013	353	18	defined	define	VERB
iajs-1013	353	19	homomorphism	homomorphism	NOUN
iajs-1013	353	20	.	.	PUNCT
iajs-1013	354	1	moreover	moreover	ADV
iajs-1013	354	2	if	if	SCONJ
iajs-1013	354	3	r	r	NOUN
iajs-1013	354	4	x	x	NOUN
iajs-1013	354	5	=	=	SYM
iajs-1013	354	6	0	0	NUM
iajs-1013	354	7	,	,	PUNCT
iajs-1013	354	8	implies	imply	VERB
iajs-1013	354	9	that	that	SCONJ
iajs-1013	355	1	r	r	NOUN
iajs-1013	355	2	(	(	PUNCT
iajs-1013	355	3	t	t	NOUN
iajs-1013	355	4	y	y	PROPN
iajs-1013	355	5	)	)	PUNCT
iajs-1013	355	6	=	=	SYM
iajs-1013	355	7	0	0	NUM
iajs-1013	355	8	for	for	ADP
iajs-1013	355	9	some	some	DET
iajs-1013	355	10	t	t	NOUN
iajs-1013	355	11			PROPN
iajs-1013	355	12	r.	r.	PROPN
iajs-1013	355	13	thus	thus	ADV
iajs-1013	355	14	r	r	NOUN
iajs-1013	355	15	t	t	NOUN
iajs-1013	355	16	=	=	SYM
iajs-1013	355	17	0	0	X
iajs-1013	355	18	.	.	PUNCT
iajs-1013	356	1	if	if	SCONJ
iajs-1013	356	2	r	r	NOUN
iajs-1013	356	3	=	=	SYM
iajs-1013	356	4	0	0	NUM
iajs-1013	356	5	,	,	PUNCT
iajs-1013	356	6	we	we	PRON
iajs-1013	356	7	have	have	AUX
iajs-1013	356	8	done	do	VERB
iajs-1013	356	9	.	.	PUNCT
iajs-1013	357	1	if	if	SCONJ
iajs-1013	357	2	t	t	PROPN
iajs-1013	357	3	=	=	SYM
iajs-1013	357	4	0	0	NUM
iajs-1013	357	5	,	,	PUNCT
iajs-1013	357	6	then	then	ADV
iajs-1013	357	7	x	x	X
iajs-1013	357	8	=	=	SYM
iajs-1013	357	9	0	0	NUM
iajs-1013	357	10	which	which	PRON
iajs-1013	357	11	is	be	AUX
iajs-1013	357	12	a	a	DET
iajs-1013	357	13	contradiction	contradiction	NOUN
iajs-1013	357	14	.	.	PUNCT
iajs-1013	358	1	thus	thus	ADV
iajs-1013	358	2	h	h	NOUN
iajs-1013	358	3	is	be	AUX
iajs-1013	358	4	a	a	DET
iajs-1013	358	5	monomorphism	monomorphism	NOUN
iajs-1013	358	6	.	.	PUNCT
iajs-1013	359	1	clearly	clearly	ADV
iajs-1013	359	2	h	h	PROPN
iajs-1013	359	3	is	be	AUX
iajs-1013	359	4	an	an	DET
iajs-1013	359	5	epimorphism	epimorphism	NOUN
iajs-1013	359	6	.	.	PUNCT
iajs-1013	360	1	hence	hence	ADV
iajs-1013	360	2	x	x	PROPN
iajs-1013	360	3	≈	≈	PROPN
iajs-1013	360	4	m	m	ADJ
iajs-1013	360	5	and	and	CCONJ
iajs-1013	360	6	therefore	therefore	ADV
iajs-1013	360	7	m	m	VERB
iajs-1013	360	8	is	be	AUX
iajs-1013	360	9	weakly	weakly	ADJ
iajs-1013	360	10	nquasi	nquasi	NOUN
iajs-1013	360	11	-	-	PUNCT
iajs-1013	360	12	injective	injective	ADJ
iajs-1013	360	13	.	.	PUNCT
iajs-1013	361	1	when	when	SCONJ
iajs-1013	361	2	we	we	PRON
iajs-1013	361	3	weaken	weaken	VERB
iajs-1013	361	4	the	the	DET
iajs-1013	361	5	conditions	condition	NOUN
iajs-1013	361	6	in	in	ADP
iajs-1013	361	7	theorem	theorem	ADJ
iajs-1013	361	8	2.10	2.10	NUM
iajs-1013	361	9	,	,	PUNCT
iajs-1013	361	10	we	we	PRON
iajs-1013	361	11	get	get	VERB
iajs-1013	361	12	the	the	DET
iajs-1013	361	13	following	follow	VERB
iajs-1013	361	14	result	result	NOUN
iajs-1013	361	15	:	:	PUNCT
iajs-1013	361	16	2.11	2.11	NUM
iajs-1013	361	17	proposition	proposition	NOUN
iajs-1013	361	18	let	let	VERB
iajs-1013	361	19	m	m	PRON
iajs-1013	361	20	and	and	CCONJ
iajs-1013	361	21	n	n	CCONJ
iajs-1013	361	22	be	be	AUX
iajs-1013	361	23	two	two	NUM
iajs-1013	361	24	cyclic	cyclic	ADJ
iajs-1013	361	25	r	r	NOUN
iajs-1013	361	26	-	-	PUNCT
iajs-1013	361	27	modules	module	NOUN
iajs-1013	361	28	.	.	PUNCT
iajs-1013	362	1	if	if	SCONJ
iajs-1013	362	2	m	m	NOUN
iajs-1013	362	3	is	be	AUX
iajs-1013	362	4	torsion	torsion	NOUN
iajs-1013	362	5	-	-	PUNCT
iajs-1013	362	6	free	free	ADJ
iajs-1013	362	7	,	,	PUNCT
iajs-1013	362	8	then	then	ADV
iajs-1013	362	9	m	m	VERB
iajs-1013	362	10	is	be	AUX
iajs-1013	362	11	weakly	weakly	ADJ
iajs-1013	362	12	n	n	CCONJ
iajs-1013	362	13	-	-	PUNCT
iajs-1013	362	14	quasiinjective	quasiinjective	NOUN
iajs-1013	362	15	.	.	PUNCT
iajs-1013	363	1	proof	proof	NOUN
iajs-1013	363	2	:	:	PUNCT
iajs-1013	363	3	let	let	VERB
iajs-1013	363	4	m	m	VERB
iajs-1013	363	5	=	=	SYM
iajs-1013	363	6	(	(	PUNCT
iajs-1013	363	7	m	m	NOUN
iajs-1013	363	8	)	)	PUNCT
iajs-1013	363	9	and	and	CCONJ
iajs-1013	363	10	n	n	CCONJ
iajs-1013	363	11	=	=	SYM
iajs-1013	363	12	(	(	PUNCT
iajs-1013	363	13	n	n	CCONJ
iajs-1013	363	14	)	)	PUNCT
iajs-1013	363	15	for	for	ADP
iajs-1013	363	16	some	some	DET
iajs-1013	363	17	m	m	PROPN
iajs-1013	363	18			NOUN
iajs-1013	363	19	m	m	ADJ
iajs-1013	363	20	and	and	CCONJ
iajs-1013	363	21	n	n	PROPN
iajs-1013	363	22			PROPN
iajs-1013	363	23	n.	n.	PROPN
iajs-1013	363	24	let	let	VERB
iajs-1013	363	25	f	f	PROPN
iajs-1013	363	26			PROPN
iajs-1013	363	27	hom(n,	hom(n,	NOUN
iajs-1013	363	28	)	)	PUNCT
iajs-1013	363	29	and	and	CCONJ
iajs-1013	363	30	let	let	VERB
iajs-1013	363	31	x	x	SYM
iajs-1013	363	32	=	=	SYM
iajs-1013	363	33	f	f	X
iajs-1013	363	34	(	(	PUNCT
iajs-1013	363	35	n	n	CCONJ
iajs-1013	363	36	)	)	PUNCT
iajs-1013	363	37	.	.	PUNCT
iajs-1013	364	1	then	then	ADV
iajs-1013	364	2	x	x	SYM
iajs-1013	364	3			PROPN
iajs-1013	364	4			PROPN
iajs-1013	364	5	.	.	PUNCT
iajs-1013	364	6	suppose	suppose	VERB
iajs-1013	364	7	that	that	SCONJ
iajs-1013	364	8	x	x	X
iajs-1013	364	9	=	=	SYM
iajs-1013	364	10	(	(	PUNCT
iajs-1013	364	11	x	x	NOUN
iajs-1013	364	12	)	)	PUNCT
iajs-1013	364	13	.	.	PUNCT
iajs-1013	365	1	then	then	ADV
iajs-1013	365	2	x	x	PRON
iajs-1013	365	3	is	be	AUX
iajs-1013	365	4	a	a	DET
iajs-1013	365	5	submodule	submodule	NOUN
iajs-1013	365	6	of	of	ADP
iajs-1013	365	7			PROPN
iajs-1013	365	8	and	and	CCONJ
iajs-1013	365	9	f	f	PROPN
iajs-1013	365	10	(	(	PUNCT
iajs-1013	365	11	n	n	CCONJ
iajs-1013	365	12	)	)	PUNCT
iajs-1013	365	13			PROPN
iajs-1013	365	14	x.	x.	NOUN
iajs-1013	365	15	define	define	VERB
iajs-1013	365	16	g	g	NOUN
iajs-1013	365	17	:	:	PUNCT
iajs-1013	365	18	x	x	SYM
iajs-1013	365	19			X
iajs-1013	365	20	m	m	VERB
iajs-1013	365	21	by	by	ADP
iajs-1013	365	22	g(r	g(r	NOUN
iajs-1013	365	23	x	x	NOUN
iajs-1013	365	24	)	)	PUNCT
iajs-1013	366	1	=	=	SYM
iajs-1013	366	2	r	r	NOUN
iajs-1013	366	3	m	m	VERB
iajs-1013	366	4	for	for	ADP
iajs-1013	366	5	all	all	DET
iajs-1013	366	6	r	r	NOUN
iajs-1013	366	7			PROPN
iajs-1013	366	8	r.	r.	NOUN
iajs-1013	366	9	if	if	SCONJ
iajs-1013	366	10	r	r	NOUN
iajs-1013	366	11	x	x	NOUN
iajs-1013	366	12	=	=	SYM
iajs-1013	366	13	0	0	NUM
iajs-1013	366	14	,	,	PUNCT
iajs-1013	366	15	we	we	PRON
iajs-1013	366	16	claim	claim	VERB
iajs-1013	366	17	that	that	SCONJ
iajs-1013	366	18	r	r	NOUN
iajs-1013	366	19	=	=	NOUN
iajs-1013	366	20	0	0	X
iajs-1013	366	21	.	.	PUNCT
iajs-1013	367	1	we	we	PRON
iajs-1013	367	2	have	have	VERB
iajs-1013	367	3	x	x	PUNCT
iajs-1013	367	4			NOUN
iajs-1013	367	5			VERB
iajs-1013	367	6	and	and	CCONJ
iajs-1013	367	7	m	m	VERB
iajs-1013	367	8	is	be	AUX
iajs-1013	367	9	an	an	DET
iajs-1013	367	10	essential	essential	ADJ
iajs-1013	367	11	submodule	submodule	NOUN
iajs-1013	367	12	of	of	ADP
iajs-1013	367	13			PROPN
iajs-1013	367	14	,	,	PUNCT
iajs-1013	367	15	so	so	CCONJ
iajs-1013	367	16	there	there	PRON
iajs-1013	367	17	exists	exist	VERB
iajs-1013	367	18	a	a	DET
iajs-1013	367	19	non	non	ADJ
iajs-1013	367	20	-	-	ADJ
iajs-1013	367	21	zero	zero	NUM
iajs-1013	367	22	element	element	NOUN
iajs-1013	367	23	t	t	PROPN
iajs-1013	367	24			PROPN
iajs-1013	367	25	r	r	NOUN
iajs-1013	367	26	such	such	ADJ
iajs-1013	367	27	that	that	DET
iajs-1013	367	28	t	t	NOUN
iajs-1013	367	29	x	x	SYM
iajs-1013	367	30			NOUN
iajs-1013	367	31	m.	m.	NOUN
iajs-1013	367	32	hence	hence	ADV
iajs-1013	367	33	annr(t	annr(t	ADP
iajs-1013	367	34	x	x	X
iajs-1013	367	35	)	)	PUNCT
iajs-1013	367	36	=	=	SYM
iajs-1013	368	1	0	0	X
iajs-1013	368	2	.	.	PUNCT
iajs-1013	369	1	but	but	CCONJ
iajs-1013	369	2	annr(x	annr(x	NOUN
iajs-1013	369	3	)	)	PUNCT
iajs-1013	369	4			PROPN
iajs-1013	369	5	annr(t	annr(t	ADP
iajs-1013	369	6	x	x	NOUN
iajs-1013	369	7	)	)	PUNCT
iajs-1013	369	8	,	,	PUNCT
iajs-1013	369	9	so	so	ADV
iajs-1013	369	10	annr(x	annr(x	NOUN
iajs-1013	369	11	)	)	PUNCT
iajs-1013	369	12	=	=	SYM
iajs-1013	370	1	0	0	X
iajs-1013	370	2	.	.	PUNCT
iajs-1013	371	1	hence	hence	ADV
iajs-1013	371	2	r	r	NOUN
iajs-1013	371	3	=	=	SYM
iajs-1013	371	4	0	0	NUM
iajs-1013	371	5	,	,	PUNCT
iajs-1013	371	6	thus	thus	ADV
iajs-1013	371	7	g	g	PROPN
iajs-1013	371	8	is	be	AUX
iajs-1013	371	9	well	well	ADV
iajs-1013	371	10	-	-	PUNCT
iajs-1013	371	11	defined	define	VERB
iajs-1013	371	12	.	.	PUNCT
iajs-1013	372	1	it	it	PRON
iajs-1013	372	2	can	can	AUX
iajs-1013	372	3	be	be	AUX
iajs-1013	372	4	easily	easily	ADV
iajs-1013	372	5	shown	show	VERB
iajs-1013	372	6	that	that	SCONJ
iajs-1013	372	7	g	g	PROPN
iajs-1013	372	8	is	be	AUX
iajs-1013	372	9	an	an	DET
iajs-1013	372	10	isomorphism	isomorphism	NOUN
iajs-1013	372	11	.	.	PUNCT
iajs-1013	373	1	therefore	therefore	ADV
iajs-1013	373	2	x	x	X
iajs-1013	373	3	≈	≈	NOUN
iajs-1013	373	4	m	m	ADJ
iajs-1013	373	5	and	and	CCONJ
iajs-1013	373	6	hence	hence	ADV
iajs-1013	373	7	the	the	DET
iajs-1013	373	8	result	result	NOUN
iajs-1013	373	9	follows	follow	VERB
iajs-1013	373	10	.	.	PUNCT
iajs-1013	374	1	2.12	2.12	NUM
iajs-1013	374	2	remark	remark	NOUN
iajs-1013	374	3	the	the	DET
iajs-1013	374	4	converse	converse	NOUN
iajs-1013	374	5	of	of	ADP
iajs-1013	374	6	proposition	proposition	NOUN
iajs-1013	374	7	2.11	2.11	NUM
iajs-1013	374	8	,	,	PUNCT
iajs-1013	374	9	may	may	AUX
iajs-1013	374	10	not	not	PART
iajs-1013	374	11	be	be	AUX
iajs-1013	374	12	true	true	ADJ
iajs-1013	374	13	in	in	ADP
iajs-1013	374	14	general	general	ADJ
iajs-1013	374	15	,	,	PUNCT
iajs-1013	374	16	consider	consider	VERB
iajs-1013	374	17	the	the	DET
iajs-1013	374	18	following	follow	VERB
iajs-1013	374	19	example	example	NOUN
iajs-1013	374	20	:	:	PUNCT
iajs-1013	374	21	2.13	2.13	NUM
iajs-1013	374	22	example	example	NOUN
iajs-1013	374	23	let	let	VERB
iajs-1013	374	24	m	m	VERB
iajs-1013	374	25	=	=	SYM
iajs-1013	374	26	z4	z4	X
iajs-1013	374	27	,	,	PUNCT
iajs-1013	374	28	n	n	NOUN
iajs-1013	374	29	=	=	SYM
iajs-1013	374	30	z	z	PROPN
iajs-1013	374	31	and	and	CCONJ
iajs-1013	374	32	r	r	NOUN
iajs-1013	374	33	=	=	PUNCT
iajs-1013	374	34	z.	z.	PROPN
iajs-1013	374	35	then	then	ADV
iajs-1013	374	36	m	m	VERB
iajs-1013	374	37	is	be	AUX
iajs-1013	374	38	weakly	weakly	ADJ
iajs-1013	374	39	n	n	CCONJ
iajs-1013	374	40	-	-	PUNCT
iajs-1013	374	41	quasi	quasi	NOUN
iajs-1013	374	42	-	-	ADJ
iajs-1013	374	43	injective	injective	ADJ
iajs-1013	374	44	.	.	PUNCT
iajs-1013	375	1	but	but	CCONJ
iajs-1013	375	2	m	m	PROPN
iajs-1013	375	3	is	be	AUX
iajs-1013	375	4	not	not	PART
iajs-1013	375	5	torsionfree	torsionfree	ADJ
iajs-1013	375	6	r	r	NOUN
iajs-1013	375	7	-	-	PUNCT
iajs-1013	375	8	module	module	NOUN
iajs-1013	375	9	.	.	PUNCT
iajs-1013	376	1	on	on	ADP
iajs-1013	376	2	the	the	DET
iajs-1013	376	3	other	other	ADJ
iajs-1013	376	4	hand	hand	NOUN
iajs-1013	376	5	,	,	PUNCT
iajs-1013	376	6	example	example	NOUN
iajs-1013	376	7	1.6	1.6	NUM
iajs-1013	376	8	shows	show	VERB
iajs-1013	376	9	that	that	SCONJ
iajs-1013	376	10	the	the	DET
iajs-1013	376	11	condition	condition	NOUN
iajs-1013	376	12	n	n	VERB
iajs-1013	376	13	is	be	AUX
iajs-1013	376	14	cyclic	cyclic	ADJ
iajs-1013	376	15	in	in	ADP
iajs-1013	376	16	proposition	proposition	NOUN
iajs-1013	376	17	2.11	2.11	NUM
iajs-1013	376	18	,	,	PUNCT
iajs-1013	376	19	can	can	AUX
iajs-1013	376	20	not	not	PART
iajs-1013	376	21	be	be	AUX
iajs-1013	376	22	dropped	drop	VERB
iajs-1013	376	23	.	.	PUNCT
iajs-1013	377	1	section	section	NOUN
iajs-1013	377	2	three	three	NUM
iajs-1013	377	3	:	:	PUNCT
iajs-1013	377	4	weakly	weakly	ADJ
iajs-1013	377	5	relative	relative	ADJ
iajs-1013	377	6	quasi	quasi	ADJ
iajs-1013	377	7	-	-	ADJ
iajs-1013	377	8	injective	injective	ADJ
iajs-1013	377	9	modules	module	NOUN
iajs-1013	377	10	and	and	CCONJ
iajs-1013	377	11	quasitight	quasitight	ADJ
iajs-1013	377	12	modules	module	NOUN
iajs-1013	377	13	we	we	PRON
iajs-1013	377	14	introduce	introduce	VERB
iajs-1013	377	15	in	in	ADP
iajs-1013	377	16	this	this	DET
iajs-1013	377	17	section	section	NOUN
iajs-1013	377	18	the	the	DET
iajs-1013	377	19	concept	concept	NOUN
iajs-1013	377	20	of	of	ADP
iajs-1013	377	21	relative	relative	ADJ
iajs-1013	377	22	quasi	quasi	NOUN
iajs-1013	377	23	-	-	NOUN
iajs-1013	377	24	tightness	tightness	NOUN
iajs-1013	377	25	of	of	ADP
iajs-1013	377	26	modules	module	NOUN
iajs-1013	377	27	and	and	CCONJ
iajs-1013	377	28	we	we	PRON
iajs-1013	377	29	study	study	VERB
iajs-1013	377	30	the	the	DET
iajs-1013	377	31	relation	relation	NOUN
iajs-1013	377	32	of	of	ADP
iajs-1013	377	33	this	this	DET
iajs-1013	377	34	concept	concept	NOUN
iajs-1013	377	35	with	with	ADP
iajs-1013	377	36	the	the	DET
iajs-1013	377	37	concept	concept	NOUN
iajs-1013	377	38	of	of	ADP
iajs-1013	377	39	relative	relative	ADJ
iajs-1013	377	40	weakly	weakly	ADJ
iajs-1013	377	41	quasi	quasi	NOUN
iajs-1013	377	42	-	-	NOUN
iajs-1013	377	43	injectivity	injectivity	NOUN
iajs-1013	377	44	of	of	ADP
iajs-1013	377	45	modules	module	NOUN
iajs-1013	377	46	.	.	PUNCT
iajs-1013	378	1	3.1	3.1	NUM
iajs-1013	378	2	definition	definition	NOUN
iajs-1013	378	3	let	let	VERB
iajs-1013	378	4	m	m	PRON
iajs-1013	378	5	and	and	CCONJ
iajs-1013	378	6	n	n	CCONJ
iajs-1013	378	7	be	be	VERB
iajs-1013	378	8	two	two	NUM
iajs-1013	378	9	r	r	NOUN
iajs-1013	378	10	-	-	PUNCT
iajs-1013	378	11	modules	module	NOUN
iajs-1013	378	12	.	.	PUNCT
iajs-1013	379	1	we	we	PRON
iajs-1013	379	2	say	say	VERB
iajs-1013	379	3	that	that	SCONJ
iajs-1013	379	4	m	m	PROPN
iajs-1013	379	5	is	be	AUX
iajs-1013	379	6	n	n	CCONJ
iajs-1013	379	7	-	-	PUNCT
iajs-1013	379	8	quasi	quasi	NOUN
iajs-1013	379	9	-	-	NOUN
iajs-1013	379	10	tight	tight	ADJ
iajs-1013	379	11	if	if	SCONJ
iajs-1013	379	12	and	and	CCONJ
iajs-1013	379	13	only	only	ADV
iajs-1013	379	14	if	if	SCONJ
iajs-1013	379	15	every	every	DET
iajs-1013	379	16	quotient	quotient	NOUN
iajs-1013	379	17	n	n	INTJ
iajs-1013	379	18	/	/	SYM
iajs-1013	379	19	k	k	PROPN
iajs-1013	379	20	of	of	ADP
iajs-1013	379	21	n	n	PRON
iajs-1013	379	22	which	which	PRON
iajs-1013	379	23	embeds	embed	VERB
iajs-1013	379	24	in	in	ADP
iajs-1013	379	25			PROPN
iajs-1013	379	26	embeds	embed	NOUN
iajs-1013	379	27	in	in	ADP
iajs-1013	379	28	m.	m.	NOUN
iajs-1013	379	29	ibn	ibn	PROPN
iajs-1013	379	30	alhaitham	alhaitham	PROPN
iajs-1013	379	31	j.	j.	PROPN
iajs-1013	379	32	for	for	ADP
iajs-1013	379	33	pure	pure	ADJ
iajs-1013	379	34	&	&	CCONJ
iajs-1013	379	35	appl	appl	PROPN
iajs-1013	379	36	.	.	PUNCT
iajs-1013	380	1	sci	sci	PROPN
iajs-1013	380	2	.	.	PUNCT
iajs-1013	381	1	vol.23	vol.23	PROPN
iajs-1013	381	2	(	(	PUNCT
iajs-1013	381	3	1	1	NUM
iajs-1013	381	4	)	)	PUNCT
iajs-1013	381	5	2010	2010	NUM
iajs-1013	381	6	m	m	VERB
iajs-1013	381	7	is	be	AUX
iajs-1013	381	8	called	call	VERB
iajs-1013	381	9	r	r	NOUN
iajs-1013	381	10	-	-	PUNCT
iajs-1013	381	11	quasi	quasi	NOUN
iajs-1013	381	12	-	-	NOUN
iajs-1013	381	13	tight	tight	ADJ
iajs-1013	381	14	if	if	SCONJ
iajs-1013	382	1	and	and	CCONJ
iajs-1013	382	2	only	only	ADV
iajs-1013	382	3	if	if	SCONJ
iajs-1013	382	4	for	for	ADP
iajs-1013	382	5	every	every	DET
iajs-1013	382	6	ideal	ideal	NOUN
iajs-1013	382	7	i	i	PRON
iajs-1013	382	8	of	of	ADP
iajs-1013	382	9	r	r	PROPN
iajs-1013	382	10	,	,	PUNCT
iajs-1013	382	11	every	every	DET
iajs-1013	382	12	quotient	quotient	NOUN
iajs-1013	382	13	r	r	NOUN
iajs-1013	382	14	/	/	PUNCT
iajs-1013	382	15	i	i	NOUN
iajs-1013	382	16	of	of	ADP
iajs-1013	382	17	r	r	NOUN
iajs-1013	382	18	which	which	PRON
iajs-1013	382	19	embeds	embed	VERB
iajs-1013	382	20	in	in	ADP
iajs-1013	382	21			PROPN
iajs-1013	382	22	embed	embed	NOUN
iajs-1013	382	23	in	in	ADP
iajs-1013	382	24	m.	m.	NOUN
iajs-1013	382	25	3.2	3.2	NUM
iajs-1013	382	26	definition	definition	NOUN
iajs-1013	382	27	an	an	DET
iajs-1013	382	28	r	r	NOUN
iajs-1013	382	29	-	-	PUNCT
iajs-1013	382	30	module	module	NOUN
iajs-1013	382	31	m	m	NOUN
iajs-1013	382	32	is	be	AUX
iajs-1013	382	33	called	call	VERB
iajs-1013	382	34	quasi	quasi	ADJ
iajs-1013	382	35	-	-	NOUN
iajs-1013	382	36	tight	tight	ADJ
iajs-1013	382	37	if	if	SCONJ
iajs-1013	382	38	m	m	NOUN
iajs-1013	382	39	is	be	AUX
iajs-1013	382	40	n	n	CCONJ
iajs-1013	382	41	-	-	PUNCT
iajs-1013	382	42	quasi	quasi	NOUN
iajs-1013	382	43	-	-	NOUN
iajs-1013	382	44	tight	tight	ADJ
iajs-1013	382	45	for	for	ADP
iajs-1013	382	46	every	every	DET
iajs-1013	382	47	finitely	finitely	ADV
iajs-1013	382	48	generated	generate	VERB
iajs-1013	382	49	rmodule	rmodule	NOUN
iajs-1013	382	50	n.	n.	PROPN
iajs-1013	382	51	3.3	3.3	NUM
iajs-1013	382	52	remark	remark	NOUN
iajs-1013	382	53	every	every	DET
iajs-1013	382	54	n	n	ADV
iajs-1013	382	55	-	-	PUNCT
iajs-1013	382	56	tight	tight	NOUN
iajs-1013	382	57	r	r	NOUN
iajs-1013	382	58	-	-	PUNCT
iajs-1013	382	59	module	module	NOUN
iajs-1013	382	60	is	be	AUX
iajs-1013	382	61	n	n	CCONJ
iajs-1013	382	62	-	-	PUNCT
iajs-1013	382	63	quasi	quasi	NOUN
iajs-1013	382	64	-	-	NOUN
iajs-1013	382	65	tight	tight	ADJ
iajs-1013	382	66	and	and	CCONJ
iajs-1013	382	67	the	the	DET
iajs-1013	382	68	converse	converse	NOUN
iajs-1013	382	69	is	be	AUX
iajs-1013	382	70	not	not	PART
iajs-1013	382	71	true	true	ADJ
iajs-1013	382	72	in	in	ADP
iajs-1013	382	73	general	general	ADJ
iajs-1013	382	74	.	.	PUNCT
iajs-1013	383	1	consider	consider	VERB
iajs-1013	383	2	the	the	DET
iajs-1013	383	3	following	follow	VERB
iajs-1013	383	4	example	example	NOUN
iajs-1013	383	5	:	:	PUNCT
iajs-1013	383	6	let	let	VERB
iajs-1013	383	7	m	m	VERB
iajs-1013	383	8	=	=	SYM
iajs-1013	383	9	z2	z2	PROPN
iajs-1013	383	10	,	,	PUNCT
iajs-1013	383	11	n	n	NOUN
iajs-1013	383	12	=	=	SYM
iajs-1013	383	13	z	z	NOUN
iajs-1013	383	14	,	,	PUNCT
iajs-1013	383	15	and	and	CCONJ
iajs-1013	383	16	r	r	NOUN
iajs-1013	383	17	=	=	PUNCT
iajs-1013	383	18	z.	z.	PROPN
iajs-1013	383	19	let	let	VERB
iajs-1013	383	20	k	k	X
iajs-1013	383	21	be	be	AUX
iajs-1013	383	22	a	a	DET
iajs-1013	383	23	submodule	submodule	NOUN
iajs-1013	383	24	of	of	ADP
iajs-1013	383	25	n.	n.	NOUN
iajs-1013	383	26	if	if	SCONJ
iajs-1013	383	27	n	n	PROPN
iajs-1013	383	28	/	/	SYM
iajs-1013	383	29	k	k	PROPN
iajs-1013	383	30	embeds	embed	VERB
iajs-1013	383	31	in	in	ADP
iajs-1013	383	32	2	2	NUM
iajs-1013	384	1	=	=	SYM
iajs-1013	384	2	z2	z2	PROPN
iajs-1013	384	3	,	,	PUNCT
iajs-1013	384	4	so	so	ADV
iajs-1013	384	5	m	m	NOUN
iajs-1013	384	6	is	be	AUX
iajs-1013	384	7	n	n	CCONJ
iajs-1013	384	8	-	-	PUNCT
iajs-1013	384	9	quasi	quasi	NOUN
iajs-1013	384	10	-	-	ADJ
iajs-1013	384	11	tight	tight	NOUN
iajs-1013	384	12	.	.	PUNCT
iajs-1013	385	1	now	now	ADV
iajs-1013	385	2	,	,	PUNCT
iajs-1013	385	3	let	let	VERB
iajs-1013	385	4	k	k	NOUN
iajs-1013	385	5	=	=	NOUN
iajs-1013	385	6	4z	4z	X
iajs-1013	385	7	.	.	PUNCT
iajs-1013	386	1	thus	thus	ADV
iajs-1013	386	2	z	z	X
iajs-1013	386	3	/	/	SYM
iajs-1013	386	4	4z	4z	PROPN
iajs-1013	386	5	≈	≈	PROPN
iajs-1013	386	6	z4	z4	PROPN
iajs-1013	386	7	embeds	embed	VERB
iajs-1013	386	8	in	in	ADP
iajs-1013	386	9	2	2	NUM
iajs-1013	386	10			ADJ
iajs-1013	386	11	=	=	SYM
iajs-1013	386	12	e(z2	e(z2	NOUN
iajs-1013	386	13	)	)	PUNCT
iajs-1013	386	14	,	,	PUNCT
iajs-1013	386	15	but	but	CCONJ
iajs-1013	386	16	z4	z4	PROPN
iajs-1013	386	17	can	can	AUX
iajs-1013	386	18	not	not	PART
iajs-1013	386	19	embeds	embed	VERB
iajs-1013	386	20	in	in	ADP
iajs-1013	386	21	z2	z2	PROPN
iajs-1013	386	22	.	.	PUNCT
iajs-1013	387	1	whence	whence	ADP
iajs-1013	387	2	m	m	PROPN
iajs-1013	387	3	is	be	AUX
iajs-1013	387	4	not	not	PART
iajs-1013	387	5	n	n	CCONJ
iajs-1013	387	6	-	-	PUNCT
iajs-1013	387	7	tight	tight	NOUN
iajs-1013	387	8	.	.	PUNCT
iajs-1013	388	1	3.4	3.4	NUM
iajs-1013	388	2	proposition	proposition	NOUN
iajs-1013	388	3	let	let	VERB
iajs-1013	388	4	m	m	PRON
iajs-1013	388	5	and	and	CCONJ
iajs-1013	388	6	n	n	CCONJ
iajs-1013	388	7	be	be	VERB
iajs-1013	388	8	two	two	NUM
iajs-1013	388	9	r	r	NOUN
iajs-1013	388	10	-	-	PUNCT
iajs-1013	388	11	modules	module	NOUN
iajs-1013	388	12	.	.	PUNCT
iajs-1013	389	1	if	if	SCONJ
iajs-1013	389	2	m	m	NOUN
iajs-1013	389	3	is	be	AUX
iajs-1013	389	4	weakly	weakly	ADJ
iajs-1013	389	5	n	n	CCONJ
iajs-1013	389	6	-	-	PUNCT
iajs-1013	389	7	quasi	quasi	NOUN
iajs-1013	389	8	-	-	ADJ
iajs-1013	389	9	injective	injective	ADJ
iajs-1013	389	10	,	,	PUNCT
iajs-1013	389	11	then	then	ADV
iajs-1013	389	12	m	m	PROPN
iajs-1013	389	13	is	be	AUX
iajs-1013	389	14	n	n	CCONJ
iajs-1013	389	15	-	-	PUNCT
iajs-1013	389	16	quasitight	quasitight	NOUN
iajs-1013	389	17	.	.	PUNCT
iajs-1013	390	1	proof	proof	NOUN
iajs-1013	390	2	:	:	PUNCT
iajs-1013	390	3	let	let	VERB
iajs-1013	390	4	k	k	PRON
iajs-1013	390	5	be	be	AUX
iajs-1013	390	6	a	a	DET
iajs-1013	390	7	submodule	submodule	NOUN
iajs-1013	390	8	of	of	ADP
iajs-1013	390	9	n	n	PRON
iajs-1013	390	10	such	such	ADJ
iajs-1013	390	11	that	that	SCONJ
iajs-1013	390	12	n	n	PROPN
iajs-1013	390	13	/	/	SYM
iajs-1013	390	14	k	k	PROPN
iajs-1013	390	15	embeds	embed	VERB
iajs-1013	390	16	in	in	PROPN
iajs-1013	390	17	.	.	PUNCT
iajs-1013	391	1	then	then	ADV
iajs-1013	391	2	there	there	PRON
iajs-1013	391	3	exists	exist	VERB
iajs-1013	391	4	a	a	DET
iajs-1013	391	5	monomorphism	monomorphism	NOUN
iajs-1013	391	6	f	f	X
iajs-1013	391	7	:	:	PUNCT
iajs-1013	391	8	n	n	PROPN
iajs-1013	391	9	/	/	SYM
iajs-1013	391	10	k	k	PROPN
iajs-1013	391	11			PROPN
iajs-1013	391	12			PROPN
iajs-1013	391	13	.	.	PUNCT
iajs-1013	392	1	let	let	VERB
iajs-1013	392	2			VERB
iajs-1013	392	3	:	:	PUNCT
iajs-1013	392	4	n	n	CCONJ
iajs-1013	392	5			PROPN
iajs-1013	392	6	n	n	CCONJ
iajs-1013	392	7	/k	/k	VERB
iajs-1013	392	8	be	be	AUX
iajs-1013	392	9	the	the	DET
iajs-1013	392	10	natural	natural	ADJ
iajs-1013	392	11	homomorphism	homomorphism	NOUN
iajs-1013	392	12	.	.	PUNCT
iajs-1013	393	1	hence	hence	ADV
iajs-1013	393	2	f	f	VERB
iajs-1013	393	3			ADJ
iajs-1013	393	4			NOUN
iajs-1013	393	5	hom(n,	hom(n,	NOUN
iajs-1013	393	6	)	)	PUNCT
iajs-1013	393	7	,	,	PUNCT
iajs-1013	393	8	so	so	CCONJ
iajs-1013	393	9	there	there	PRON
iajs-1013	393	10	exists	exist	VERB
iajs-1013	393	11	a	a	DET
iajs-1013	393	12	submodule	submodule	NOUN
iajs-1013	393	13	x	x	PUNCT
iajs-1013	393	14	of	of	ADP
iajs-1013	393	15			NUM
iajs-1013	393	16	such	such	ADJ
iajs-1013	393	17	that	that	PRON
iajs-1013	393	18	(	(	PUNCT
iajs-1013	393	19	f	f	NUM
iajs-1013	393	20	)(n	)(n	NOUN
iajs-1013	393	21	)	)	PUNCT
iajs-1013	393	22			PROPN
iajs-1013	393	23	x	x	PUNCT
iajs-1013	393	24	≈	≈	NUM
iajs-1013	393	25	m.	m.	NOUN
iajs-1013	394	1	hence	hence	ADV
iajs-1013	394	2	f	f	PROPN
iajs-1013	394	3	(	(	PUNCT
iajs-1013	394	4	n	n	CCONJ
iajs-1013	394	5	/	/	SYM
iajs-1013	394	6	k	k	NOUN
iajs-1013	394	7	)	)	PUNCT
iajs-1013	394	8			PROPN
iajs-1013	395	1	x	x	PUNCT
iajs-1013	396	1	≈	≈	NOUN
iajs-1013	396	2	m	m	VERB
iajs-1013	396	3	which	which	PRON
iajs-1013	396	4	implies	imply	VERB
iajs-1013	396	5	that	that	SCONJ
iajs-1013	396	6	f	f	X
iajs-1013	396	7	:	:	PUNCT
iajs-1013	396	8	n	n	PROPN
iajs-1013	396	9	/	/	SYM
iajs-1013	396	10	k	k	PROPN
iajs-1013	396	11			PROPN
iajs-1013	396	12	x	x	X
iajs-1013	396	13	is	be	AUX
iajs-1013	396	14	a	a	DET
iajs-1013	396	15	homomorphism	homomorphism	NOUN
iajs-1013	396	16	.	.	PUNCT
iajs-1013	397	1	let	let	VERB
iajs-1013	397	2	g	g	NOUN
iajs-1013	397	3	:	:	PUNCT
iajs-1013	397	4	x	x	SYM
iajs-1013	397	5			PROPN
iajs-1013	397	6	m	m	AUX
iajs-1013	397	7	be	be	VERB
iajs-1013	397	8	an	an	DET
iajs-1013	397	9	isomorphism	isomorphism	NOUN
iajs-1013	397	10	.	.	PUNCT
iajs-1013	398	1	then	then	ADV
iajs-1013	398	2	g	g	NUM
iajs-1013	398	3	f	f	NOUN
iajs-1013	398	4	:	:	PUNCT
iajs-1013	399	1	n	n	PROPN
iajs-1013	399	2	/	/	SYM
iajs-1013	399	3	k	k	PROPN
iajs-1013	399	4			PROPN
iajs-1013	399	5	m	m	VERB
iajs-1013	399	6	is	be	AUX
iajs-1013	399	7	a	a	DET
iajs-1013	399	8	monomorphism	monomorphism	NOUN
iajs-1013	399	9	.	.	PUNCT
iajs-1013	400	1	which	which	PRON
iajs-1013	400	2	completes	complete	VERB
iajs-1013	400	3	the	the	DET
iajs-1013	400	4	proof	proof	NOUN
iajs-1013	400	5	.	.	PUNCT
iajs-1013	401	1	3.5	3.5	NUM
iajs-1013	401	2	corollary	corollary	NOUN
iajs-1013	401	3	let	let	VERB
iajs-1013	401	4	m	m	PRON
iajs-1013	401	5	be	be	AUX
iajs-1013	401	6	an	an	DET
iajs-1013	401	7	r	r	NOUN
iajs-1013	401	8	-	-	PUNCT
iajs-1013	401	9	module	module	NOUN
iajs-1013	401	10	.	.	PUNCT
iajs-1013	402	1	if	if	SCONJ
iajs-1013	402	2	m	m	NOUN
iajs-1013	402	3	is	be	AUX
iajs-1013	402	4	weakly	weakly	ADJ
iajs-1013	402	5	r	r	NOUN
iajs-1013	402	6	-	-	PUNCT
iajs-1013	402	7	quasi	quasi	NOUN
iajs-1013	402	8	-	-	ADJ
iajs-1013	402	9	injective	injective	ADJ
iajs-1013	402	10	,	,	PUNCT
iajs-1013	402	11	then	then	ADV
iajs-1013	402	12	m	m	PROPN
iajs-1013	402	13	is	be	AUX
iajs-1013	402	14	r	r	NOUN
iajs-1013	402	15	-	-	PUNCT
iajs-1013	402	16	quasi	quasi	NOUN
iajs-1013	402	17	-	-	ADJ
iajs-1013	402	18	tight	tight	ADJ
iajs-1013	402	19	.	.	PUNCT
iajs-1013	403	1	recall	recall	VERB
iajs-1013	403	2	that	that	SCONJ
iajs-1013	403	3	,	,	PUNCT
iajs-1013	403	4	if	if	SCONJ
iajs-1013	403	5	a	a	PRON
iajs-1013	403	6	and	and	CCONJ
iajs-1013	403	7	b	b	NOUN
iajs-1013	403	8	are	be	AUX
iajs-1013	403	9	submodules	submodule	NOUN
iajs-1013	403	10	of	of	ADP
iajs-1013	403	11	an	an	DET
iajs-1013	403	12	r	r	NOUN
iajs-1013	403	13	-	-	PUNCT
iajs-1013	403	14	module	module	NOUN
iajs-1013	403	15	c	c	NOUN
iajs-1013	403	16	,	,	PUNCT
iajs-1013	403	17	such	such	ADJ
iajs-1013	403	18	that	that	SCONJ
iajs-1013	403	19	a	a	PRON
iajs-1013	403	20	is	be	AUX
iajs-1013	403	21	a	a	DET
iajs-1013	403	22	maximal	maximal	ADJ
iajs-1013	403	23	submodule	submodule	NOUN
iajs-1013	403	24	of	of	ADP
iajs-1013	403	25	c	c	PROPN
iajs-1013	403	26	with	with	ADP
iajs-1013	403	27	the	the	DET
iajs-1013	403	28	property	property	NOUN
iajs-1013	403	29	that	that	PRON
iajs-1013	403	30	a	a	DET
iajs-1013	403	31			NOUN
iajs-1013	403	32	b	b	NOUN
iajs-1013	403	33	=	=	SYM
iajs-1013	403	34	0	0	NUM
iajs-1013	403	35	,	,	PUNCT
iajs-1013	403	36	then	then	ADV
iajs-1013	403	37	a	a	PRON
iajs-1013	403	38	is	be	AUX
iajs-1013	403	39	called	call	VERB
iajs-1013	403	40	a	a	DET
iajs-1013	403	41	complement	complement	NOUN
iajs-1013	403	42	of	of	ADP
iajs-1013	403	43	b	b	NOUN
iajs-1013	403	44	in	in	ADP
iajs-1013	403	45	c	c	PROPN
iajs-1013	403	46	,	,	PUNCT
iajs-1013	403	47	[	[	X
iajs-1013	403	48	8	8	NUM
iajs-1013	403	49	]	]	SYM
iajs-1013	403	50	.	.	PUNCT
iajs-1013	404	1	3.6	3.6	NUM
iajs-1013	404	2	theorem	theorem	VERB
iajs-1013	404	3	let	let	VERB
iajs-1013	404	4	m	m	PRON
iajs-1013	404	5	and	and	CCONJ
iajs-1013	404	6	n	n	CCONJ
iajs-1013	404	7	be	be	VERB
iajs-1013	404	8	two	two	NUM
iajs-1013	404	9	r	r	NOUN
iajs-1013	404	10	-	-	PUNCT
iajs-1013	404	11	modules	module	NOUN
iajs-1013	404	12	.	.	PUNCT
iajs-1013	405	1	then	then	ADV
iajs-1013	405	2	m	m	PROPN
iajs-1013	405	3	is	be	AUX
iajs-1013	405	4	weakly	weakly	ADJ
iajs-1013	405	5	n	n	CCONJ
iajs-1013	405	6	-	-	PUNCT
iajs-1013	405	7	quasi	quasi	NOUN
iajs-1013	405	8	-	-	ADJ
iajs-1013	405	9	injective	injective	ADJ
iajs-1013	405	10	if	if	SCONJ
iajs-1013	405	11	and	and	CCONJ
iajs-1013	405	12	only	only	ADV
iajs-1013	405	13	if	if	SCONJ
iajs-1013	405	14	for	for	ADP
iajs-1013	405	15	each	each	DET
iajs-1013	405	16	submodule	submodule	NOUN
iajs-1013	405	17	l	l	NOUN
iajs-1013	405	18	of	of	ADP
iajs-1013	405	19	n	n	PROPN
iajs-1013	405	20	and	and	CCONJ
iajs-1013	405	21	for	for	ADP
iajs-1013	405	22	every	every	DET
iajs-1013	405	23	monomorphism	monomorphism	NOUN
iajs-1013	405	24	f	f	X
iajs-1013	405	25	:	:	PUNCT
iajs-1013	405	26	n	n	PROPN
iajs-1013	405	27	/	/	SYM
iajs-1013	405	28	l	l	NOUN
iajs-1013	405	29			PROPN
iajs-1013	405	30			NUM
iajs-1013	405	31	,	,	PUNCT
iajs-1013	405	32	we	we	PRON
iajs-1013	405	33	have	have	VERB
iajs-1013	405	34	:	:	PUNCT
iajs-1013	405	35	i.	i.	PROPN
iajs-1013	405	36	there	there	PRON
iajs-1013	405	37	exists	exist	VERB
iajs-1013	405	38	a	a	DET
iajs-1013	405	39	monomorphism	monomorphism	NOUN
iajs-1013	405	40	f	f	PROPN
iajs-1013	405	41			ADJ
iajs-1013	405	42	:	:	PUNCT
iajs-1013	405	43	n	n	PROPN
iajs-1013	405	44	/	/	SYM
iajs-1013	405	45	l	l	NOUN
iajs-1013	405	46			PROPN
iajs-1013	405	47	m	m	PROPN
iajs-1013	405	48	,	,	PUNCT
iajs-1013	405	49	and	and	CCONJ
iajs-1013	405	50	ii	ii	X
iajs-1013	405	51	.	.	PUNCT
iajs-1013	406	1	for	for	ADP
iajs-1013	406	2	every	every	DET
iajs-1013	406	3	complement	complement	NOUN
iajs-1013	406	4	k	k	PROPN
iajs-1013	406	5	of	of	ADP
iajs-1013	406	6	f	f	PROPN
iajs-1013	406	7	(n	(n	PROPN
iajs-1013	406	8	/	/	SYM
iajs-1013	406	9	l	l	NOUN
iajs-1013	406	10	)	)	PUNCT
iajs-1013	406	11	in	in	ADP
iajs-1013	406	12	m	m	PROPN
iajs-1013	406	13	,	,	PUNCT
iajs-1013	406	14	there	there	PRON
iajs-1013	406	15	exists	exist	VERB
iajs-1013	406	16	a	a	DET
iajs-1013	406	17	submodule	submodule	NOUN
iajs-1013	406	18	k	k	NOUN
iajs-1013	406	19	of	of	ADP
iajs-1013	406	20			NUM
iajs-1013	406	21	such	such	ADJ
iajs-1013	406	22	that	that	DET
iajs-1013	406	23	k	k	X
iajs-1013	406	24			NOUN
iajs-1013	406	25	f	f	X
iajs-1013	406	26	(	(	PUNCT
iajs-1013	406	27	n	n	CCONJ
iajs-1013	406	28	/	/	SYM
iajs-1013	406	29	l	l	NOUN
iajs-1013	406	30	)	)	PUNCT
iajs-1013	406	31	=	=	SYM
iajs-1013	406	32	0	0	NUM
iajs-1013	407	1	and	and	CCONJ
iajs-1013	407	2	k	k	VERB
iajs-1013	408	1	≈	≈	PROPN
iajs-1013	408	2	k.	k.	PROPN
iajs-1013	408	3	proof	proof	PROPN
iajs-1013	408	4	:	:	PUNCT
iajs-1013	408	5	assume	assume	VERB
iajs-1013	408	6	that	that	SCONJ
iajs-1013	408	7	m	m	NOUN
iajs-1013	408	8	is	be	AUX
iajs-1013	408	9	weakly	weakly	ADJ
iajs-1013	408	10	n	n	CCONJ
iajs-1013	408	11	-	-	PUNCT
iajs-1013	408	12	quasi	quasi	NOUN
iajs-1013	408	13	-	-	ADJ
iajs-1013	408	14	injective	injective	ADJ
iajs-1013	408	15	.	.	PUNCT
iajs-1013	409	1	let	let	VERB
iajs-1013	409	2	l	l	NOUN
iajs-1013	409	3	be	be	AUX
iajs-1013	409	4	a	a	DET
iajs-1013	409	5	submodule	submodule	NOUN
iajs-1013	409	6	of	of	ADP
iajs-1013	409	7	n	n	PROPN
iajs-1013	409	8	and	and	CCONJ
iajs-1013	409	9	let	let	VERB
iajs-1013	409	10	f	f	NOUN
iajs-1013	409	11	:	:	PUNCT
iajs-1013	409	12	n	n	CCONJ
iajs-1013	409	13	/	/	SYM
iajs-1013	409	14	l	l	NOUN
iajs-1013	409	15			PROPN
iajs-1013	409	16			PROPN
iajs-1013	409	17	be	be	AUX
iajs-1013	409	18	a	a	DET
iajs-1013	409	19	monomorphism	monomorphism	NOUN
iajs-1013	409	20	,	,	PUNCT
iajs-1013	409	21	m	m	VERB
iajs-1013	409	22	being	be	AUX
iajs-1013	409	23	weakly	weakly	ADJ
iajs-1013	409	24	n	n	CCONJ
iajs-1013	409	25	-	-	PUNCT
iajs-1013	409	26	quasi	quasi	ADJ
iajs-1013	409	27	-	-	ADJ
iajs-1013	409	28	injective	injective	ADJ
iajs-1013	409	29	implies	imply	VERB
iajs-1013	409	30	that	that	SCONJ
iajs-1013	409	31	m	m	NOUN
iajs-1013	409	32	is	be	AUX
iajs-1013	409	33	weakly	weakly	ADJ
iajs-1013	409	34	n	n	CCONJ
iajs-1013	409	35	/	/	SYM
iajs-1013	409	36	l	l	NOUN
iajs-1013	409	37	-	-	ADJ
iajs-1013	409	38	quasi	quasi	ADJ
iajs-1013	409	39	-	-	ADJ
iajs-1013	409	40	injective	injective	ADJ
iajs-1013	409	41	(	(	PUNCT
iajs-1013	409	42	by	by	ADP
iajs-1013	409	43	theorem	theorem	NOUN
iajs-1013	409	44	2.3	2.3	NUM
iajs-1013	409	45	)	)	PUNCT
iajs-1013	409	46	and	and	CCONJ
iajs-1013	409	47	hence	hence	ADV
iajs-1013	409	48	there	there	PRON
iajs-1013	409	49	exists	exist	VERB
iajs-1013	409	50	a	a	DET
iajs-1013	409	51	homomorphism	homomorphism	NOUN
iajs-1013	409	52	f	f	X
iajs-1013	409	53			ADJ
iajs-1013	409	54	:	:	PUNCT
iajs-1013	409	55	n	n	PROPN
iajs-1013	409	56	/	/	SYM
iajs-1013	409	57	l	l	NOUN
iajs-1013	409	58			PROPN
iajs-1013	410	1	m	m	VERB
iajs-1013	410	2	and	and	CCONJ
iajs-1013	410	3	there	there	PRON
iajs-1013	410	4	exists	exist	VERB
iajs-1013	410	5	a	a	DET
iajs-1013	410	6	monomorphism	monomorphism	NOUN
iajs-1013	410	7			X
iajs-1013	410	8	:	:	PUNCT
iajs-1013	410	9	m	m	PROPN
iajs-1013	410	10			NOUN
iajs-1013	410	11			VERB
iajs-1013	410	12	such	such	ADJ
iajs-1013	410	13	that	that	SCONJ
iajs-1013	410	14			PROPN
iajs-1013	410	15	f	f	PROPN
iajs-1013	410	16	=	=	PROPN
iajs-1013	410	17	f	f	PROPN
iajs-1013	410	18	(	(	PUNCT
iajs-1013	410	19	by	by	ADP
iajs-1013	410	20	theorem	theorem	NOUN
iajs-1013	410	21	2.1	2.1	NUM
iajs-1013	410	22	)	)	PUNCT
iajs-1013	410	23	.	.	PUNCT
iajs-1013	411	1	but	but	CCONJ
iajs-1013	411	2	f	f	PROPN
iajs-1013	411	3	is	be	AUX
iajs-1013	411	4	a	a	DET
iajs-1013	411	5	monomorphism	monomorphism	NOUN
iajs-1013	411	6	,	,	PUNCT
iajs-1013	411	7	therefore	therefore	ADV
iajs-1013	411	8	f	f	PROPN
iajs-1013	412	1			ADV
iajs-1013	412	2	is	be	AUX
iajs-1013	412	3	also	also	ADV
iajs-1013	412	4	a	a	DET
iajs-1013	412	5	monomorphism	monomorphism	NOUN
iajs-1013	412	6	.	.	PUNCT
iajs-1013	413	1	thus	thus	ADV
iajs-1013	413	2	(	(	PUNCT
iajs-1013	413	3	i	i	NOUN
iajs-1013	413	4	)	)	PUNCT
iajs-1013	413	5	follow	follow	VERB
iajs-1013	413	6	.	.	PUNCT
iajs-1013	414	1	to	to	PART
iajs-1013	414	2	verify	verify	VERB
iajs-1013	414	3	(	(	PUNCT
iajs-1013	414	4	ii	ii	NOUN
iajs-1013	414	5	)	)	PUNCT
iajs-1013	414	6	,	,	PUNCT
iajs-1013	414	7	let	let	VERB
iajs-1013	414	8	k	k	PRON
iajs-1013	414	9	be	be	AUX
iajs-1013	414	10	a	a	DET
iajs-1013	414	11	complement	complement	NOUN
iajs-1013	414	12	of	of	ADP
iajs-1013	414	13	f	f	PROPN
iajs-1013	414	14	(n	(n	PROPN
iajs-1013	414	15	/	/	SYM
iajs-1013	414	16	l	l	NOUN
iajs-1013	414	17	)	)	PUNCT
iajs-1013	414	18	in	in	ADP
iajs-1013	414	19	m.	m.	NOUN
iajs-1013	414	20	let	let	VERB
iajs-1013	414	21	k	k	NOUN
iajs-1013	414	22	=	=	SYM
iajs-1013	414	23	(k	(k	PROPN
iajs-1013	414	24	)	)	PUNCT
iajs-1013	414	25	.	.	PUNCT
iajs-1013	415	1	then	then	ADV
iajs-1013	415	2	k	k	VERB
iajs-1013	415	3	is	be	AUX
iajs-1013	415	4	a	a	DET
iajs-1013	415	5	submodule	submodule	NOUN
iajs-1013	415	6	of	of	ADP
iajs-1013	415	7			PROPN
iajs-1013	415	8	.	.	PUNCT
iajs-1013	416	1	we	we	PRON
iajs-1013	416	2	claim	claim	VERB
iajs-1013	416	3	that	that	SCONJ
iajs-1013	416	4	k	k	VERB
iajs-1013	416	5			NOUN
iajs-1013	416	6	f	f	X
iajs-1013	416	7	(	(	PUNCT
iajs-1013	416	8	n	n	CCONJ
iajs-1013	416	9	/	/	SYM
iajs-1013	416	10	l	l	NOUN
iajs-1013	416	11	)	)	PUNCT
iajs-1013	416	12	=	=	SYM
iajs-1013	417	1	0	0	X
iajs-1013	417	2	.	.	PUNCT
iajs-1013	418	1	let	let	VERB
iajs-1013	418	2	x	x	PRON
iajs-1013	418	3			NOUN
iajs-1013	418	4	k	k	VERB
iajs-1013	418	5			PROPN
iajs-1013	418	6	f	f	X
iajs-1013	418	7	(	(	PUNCT
iajs-1013	418	8	n	n	CCONJ
iajs-1013	418	9	/	/	SYM
iajs-1013	418	10	l	l	NOUN
iajs-1013	418	11	)	)	PUNCT
iajs-1013	418	12	and	and	CCONJ
iajs-1013	418	13	x	x	PUNCT
iajs-1013	418	14			NOUN
iajs-1013	418	15	0	0	NUM
iajs-1013	418	16	.	.	PUNCT
iajs-1013	419	1	hence	hence	ADV
iajs-1013	419	2	there	there	PRON
iajs-1013	419	3	exists	exist	VERB
iajs-1013	419	4	0	0	NUM
iajs-1013	419	5			PROPN
iajs-1013	419	6	y	y	PROPN
iajs-1013	419	7			PROPN
iajs-1013	419	8	k	k	PROPN
iajs-1013	419	9	such	such	ADJ
iajs-1013	419	10	that	that	SCONJ
iajs-1013	419	11	x	x	X
iajs-1013	419	12	=	=	PRON
iajs-1013	419	13	(y	(y	VERB
iajs-1013	419	14	)	)	PUNCT
iajs-1013	419	15	and	and	CCONJ
iajs-1013	419	16	there	there	PRON
iajs-1013	419	17	exists	exist	VERB
iajs-1013	419	18	0	0	NUM
iajs-1013	419	19			PROPN
iajs-1013	419	20	z	z	NOUN
iajs-1013	419	21			PROPN
iajs-1013	419	22	n	n	PROPN
iajs-1013	419	23	/	/	SYM
iajs-1013	419	24	l	l	NOUN
iajs-1013	419	25	such	such	ADJ
iajs-1013	419	26	that	that	PRON
iajs-1013	419	27	x	x	X
iajs-1013	419	28	=	=	SYM
iajs-1013	419	29	f	f	X
iajs-1013	419	30	(	(	PUNCT
iajs-1013	419	31	z	z	NOUN
iajs-1013	419	32	)	)	PUNCT
iajs-1013	419	33	.	.	PUNCT
iajs-1013	420	1	therefore	therefore	ADV
iajs-1013	420	2	(y	(y	VERB
iajs-1013	420	3	)	)	PUNCT
iajs-1013	420	4	=	=	SYM
iajs-1013	421	1	f	f	X
iajs-1013	421	2	(	(	PUNCT
iajs-1013	421	3	z	z	NOUN
iajs-1013	421	4	)	)	PUNCT
iajs-1013	421	5	and	and	CCONJ
iajs-1013	421	6	hence	hence	ADV
iajs-1013	421	7	(y	(y	VERB
iajs-1013	421	8	)	)	PUNCT
iajs-1013	421	9	=	=	SYM
iajs-1013	421	10			NOUN
iajs-1013	421	11	(	(	PUNCT
iajs-1013	421	12	f	f	NOUN
iajs-1013	421	13	(z	(z	NOUN
iajs-1013	421	14	)	)	PUNCT
iajs-1013	421	15	)	)	PUNCT
iajs-1013	421	16	,	,	PUNCT
iajs-1013	421	17	but	but	CCONJ
iajs-1013	421	18			X
iajs-1013	421	19	ibn	ibn	PROPN
iajs-1013	421	20	alhaitham	alhaitham	NOUN
iajs-1013	421	21	j.	j.	PROPN
iajs-1013	421	22	for	for	ADP
iajs-1013	421	23	pure	pure	ADJ
iajs-1013	421	24	&	&	CCONJ
iajs-1013	421	25	appl	appl	PROPN
iajs-1013	421	26	.	.	PUNCT
iajs-1013	422	1	sci	sci	PROPN
iajs-1013	422	2	.	.	PUNCT
iajs-1013	423	1	vol.23	vol.23	PROPN
iajs-1013	423	2	(	(	PUNCT
iajs-1013	423	3	1	1	NUM
iajs-1013	423	4	)	)	PUNCT
iajs-1013	423	5	2010	2010	NUM
iajs-1013	423	6	is	be	AUX
iajs-1013	423	7	a	a	DET
iajs-1013	423	8	monomorphism	monomorphism	NOUN
iajs-1013	423	9	,	,	PUNCT
iajs-1013	423	10	so	so	ADV
iajs-1013	423	11	y	y	PROPN
iajs-1013	423	12	=	=	PUNCT
iajs-1013	423	13	f	f	PROPN
iajs-1013	423	14	(z	(z	NOUN
iajs-1013	423	15	)	)	PUNCT
iajs-1013	423	16	,	,	PUNCT
iajs-1013	423	17	implies	imply	VERB
iajs-1013	423	18	that	that	SCONJ
iajs-1013	423	19	0	0	NUM
iajs-1013	423	20			PROPN
iajs-1013	423	21	y	y	PROPN
iajs-1013	423	22			PROPN
iajs-1013	423	23	k	k	PROPN
iajs-1013	423	24			PUNCT
iajs-1013	423	25	f	f	PROPN
iajs-1013	423	26	(n	(n	PROPN
iajs-1013	423	27	/	/	SYM
iajs-1013	423	28	l	l	NOUN
iajs-1013	423	29	)	)	PUNCT
iajs-1013	423	30	which	which	PRON
iajs-1013	423	31	is	be	AUX
iajs-1013	423	32	a	a	DET
iajs-1013	423	33	contradiction	contradiction	NOUN
iajs-1013	423	34	.	.	PUNCT
iajs-1013	424	1	hence	hence	ADV
iajs-1013	424	2	k	k	VERB
iajs-1013	424	3			NOUN
iajs-1013	424	4	f	f	X
iajs-1013	424	5	(	(	PUNCT
iajs-1013	424	6	n	n	CCONJ
iajs-1013	424	7	/	/	SYM
iajs-1013	424	8	l	l	NOUN
iajs-1013	424	9	)	)	PUNCT
iajs-1013	424	10	=	=	SYM
iajs-1013	424	11	0	0	NUM
iajs-1013	424	12	,	,	PUNCT
iajs-1013	424	13	so	so	CCONJ
iajs-1013	424	14	(	(	PUNCT
iajs-1013	424	15	ii	ii	NOUN
iajs-1013	424	16	)	)	PUNCT
iajs-1013	424	17	is	be	AUX
iajs-1013	424	18	also	also	ADV
iajs-1013	424	19	hold	hold	VERB
iajs-1013	424	20	.	.	PUNCT
iajs-1013	425	1	conversely	conversely	ADV
iajs-1013	425	2	,	,	PUNCT
iajs-1013	425	3	let	let	VERB
iajs-1013	425	4	us	we	PRON
iajs-1013	425	5	assume	assume	VERB
iajs-1013	425	6	that	that	SCONJ
iajs-1013	425	7	(	(	PUNCT
iajs-1013	425	8	i	i	NOUN
iajs-1013	425	9	)	)	PUNCT
iajs-1013	425	10	and	and	CCONJ
iajs-1013	425	11	(	(	PUNCT
iajs-1013	425	12	ii	ii	NOUN
iajs-1013	425	13	)	)	PUNCT
iajs-1013	425	14	are	be	AUX
iajs-1013	425	15	hold	hold	ADJ
iajs-1013	425	16	.	.	PUNCT
iajs-1013	426	1	let	let	VERB
iajs-1013	426	2	l	l	NOUN
iajs-1013	426	3	be	be	AUX
iajs-1013	426	4	a	a	DET
iajs-1013	426	5	submodule	submodule	NOUN
iajs-1013	426	6	of	of	ADP
iajs-1013	426	7	n	n	PROPN
iajs-1013	426	8	and	and	CCONJ
iajs-1013	426	9	let	let	VERB
iajs-1013	426	10	f	f	NOUN
iajs-1013	426	11	:	:	PUNCT
iajs-1013	426	12	n	n	CCONJ
iajs-1013	426	13	/	/	SYM
iajs-1013	426	14	l	l	NOUN
iajs-1013	426	15			PROPN
iajs-1013	426	16			PROPN
iajs-1013	426	17	be	be	AUX
iajs-1013	426	18	a	a	DET
iajs-1013	426	19	monomorphism	monomorphism	NOUN
iajs-1013	426	20	.	.	PUNCT
iajs-1013	427	1	by	by	ADP
iajs-1013	427	2	(	(	PUNCT
iajs-1013	427	3	i	i	NOUN
iajs-1013	427	4	)	)	PUNCT
iajs-1013	427	5	,	,	PUNCT
iajs-1013	427	6	there	there	PRON
iajs-1013	427	7	exists	exist	VERB
iajs-1013	427	8	a	a	DET
iajs-1013	427	9	monomorphism	monomorphism	NOUN
iajs-1013	427	10	f	f	PROPN
iajs-1013	427	11			ADJ
iajs-1013	427	12	:	:	PUNCT
iajs-1013	427	13	n	n	PROPN
iajs-1013	427	14	/	/	SYM
iajs-1013	427	15	l	l	NOUN
iajs-1013	427	16			PROPN
iajs-1013	428	1	m.	m.	NOUN
iajs-1013	428	2	let	let	VERB
iajs-1013	428	3	k	k	PRON
iajs-1013	428	4	be	be	AUX
iajs-1013	428	5	a	a	DET
iajs-1013	428	6	complement	complement	NOUN
iajs-1013	428	7	of	of	ADP
iajs-1013	428	8	f	f	PROPN
iajs-1013	428	9	(n	(n	PROPN
iajs-1013	428	10	/	/	SYM
iajs-1013	428	11	l	l	NOUN
iajs-1013	428	12	)	)	PUNCT
iajs-1013	428	13	in	in	ADP
iajs-1013	428	14	m.	m.	NOUN
iajs-1013	428	15	by	by	ADP
iajs-1013	428	16	(	(	PUNCT
iajs-1013	428	17	ii	ii	NOUN
iajs-1013	428	18	)	)	PUNCT
iajs-1013	428	19	,	,	PUNCT
iajs-1013	428	20	there	there	PRON
iajs-1013	428	21	exists	exist	VERB
iajs-1013	428	22	a	a	DET
iajs-1013	428	23	submodule	submodule	NOUN
iajs-1013	428	24	k	k	NOUN
iajs-1013	428	25	of	of	ADP
iajs-1013	428	26			NUM
iajs-1013	428	27	such	such	ADJ
iajs-1013	428	28	that	that	DET
iajs-1013	428	29	k	k	X
iajs-1013	429	1			NOUN
iajs-1013	429	2	f	f	X
iajs-1013	429	3	(	(	PUNCT
iajs-1013	429	4	n	n	CCONJ
iajs-1013	429	5	/	/	SYM
iajs-1013	429	6	l	l	NOUN
iajs-1013	429	7	)	)	PUNCT
iajs-1013	429	8	=	=	SYM
iajs-1013	429	9	0	0	NUM
iajs-1013	429	10	and	and	CCONJ
iajs-1013	429	11	k	k	VERB
iajs-1013	430	1	≈	≈	PROPN
iajs-1013	430	2	k.	k.	PROPN
iajs-1013	430	3	let	let	VERB
iajs-1013	430	4	h	h	NOUN
iajs-1013	430	5	:	:	PUNCT
iajs-1013	431	1	k	k	PROPN
iajs-1013	431	2	k	k	NOUN
iajs-1013	431	3	be	be	AUX
iajs-1013	431	4	an	an	DET
iajs-1013	431	5	isomorphism	isomorphism	NOUN
iajs-1013	431	6	and	and	CCONJ
iajs-1013	431	7	define	define	VERB
iajs-1013	431	8			NOUN
iajs-1013	431	9	:	:	PUNCT
iajs-1013	431	10	f	f	PROPN
iajs-1013	431	11	(n	(n	PROPN
iajs-1013	431	12	/	/	SYM
iajs-1013	431	13	l	l	NOUN
iajs-1013	431	14	)	)	PUNCT
iajs-1013	431	15			PROPN
iajs-1013	431	16	k	k	PROPN
iajs-1013	431	17			PROPN
iajs-1013	431	18			VERB
iajs-1013	431	19	by	by	ADP
iajs-1013	431	20			NOUN
iajs-1013	431	21	(	(	PUNCT
iajs-1013	431	22	f	f	PROPN
iajs-1013	431	23	(x	(x	PROPN
iajs-1013	431	24	)	)	PUNCT
iajs-1013	432	1	+	+	CCONJ
iajs-1013	432	2	k	k	X
iajs-1013	432	3	)	)	PUNCT
iajs-1013	432	4	=	=	SYM
iajs-1013	432	5	f	f	PROPN
iajs-1013	432	6	(	(	PUNCT
iajs-1013	432	7	x	x	X
iajs-1013	432	8	)	)	PUNCT
iajs-1013	432	9	+	+	CCONJ
iajs-1013	432	10	h(k	h(k	PROPN
iajs-1013	432	11	)	)	PUNCT
iajs-1013	432	12	for	for	ADP
iajs-1013	432	13	all	all	DET
iajs-1013	432	14	x	x	ADJ
iajs-1013	432	15			NOUN
iajs-1013	432	16	n	n	PROPN
iajs-1013	432	17	/	/	SYM
iajs-1013	432	18	l	l	NOUN
iajs-1013	432	19	,	,	PUNCT
iajs-1013	432	20	for	for	ADP
iajs-1013	432	21	all	all	DET
iajs-1013	432	22	k	k	PROPN
iajs-1013	432	23			PROPN
iajs-1013	432	24	k.	k.	PROPN
iajs-1013	433	1	then	then	ADV
iajs-1013	433	2			NOUN
iajs-1013	433	3	is	be	AUX
iajs-1013	433	4	well	well	ADV
iajs-1013	433	5	-	-	PUNCT
iajs-1013	433	6	defined	define	VERB
iajs-1013	433	7	homomorphism	homomorphism	NOUN
iajs-1013	433	8	,	,	PUNCT
iajs-1013	433	9	moreover	moreover	ADV
iajs-1013	433	10	,	,	PUNCT
iajs-1013	433	11	if	if	SCONJ
iajs-1013	433	12	f	f	PROPN
iajs-1013	433	13	(	(	PUNCT
iajs-1013	433	14	x	x	X
iajs-1013	433	15	)	)	PUNCT
iajs-1013	433	16	+	+	CCONJ
iajs-1013	434	1	h(k	h(k	PROPN
iajs-1013	434	2	)	)	PUNCT
iajs-1013	435	1	=	=	SYM
iajs-1013	435	2	0	0	NUM
iajs-1013	436	1	for	for	ADP
iajs-1013	436	2	some	some	PRON
iajs-1013	436	3	x	x	ADJ
iajs-1013	436	4			NOUN
iajs-1013	436	5	n	n	PROPN
iajs-1013	436	6	/	/	SYM
iajs-1013	436	7	l	l	NOUN
iajs-1013	436	8	and	and	CCONJ
iajs-1013	436	9	k	k	PROPN
iajs-1013	436	10			PROPN
iajs-1013	436	11	k	k	PROPN
iajs-1013	436	12	,	,	PUNCT
iajs-1013	436	13	implies	imply	VERB
iajs-1013	436	14	that	that	SCONJ
iajs-1013	436	15	f	f	PROPN
iajs-1013	436	16	(	(	PUNCT
iajs-1013	436	17	x	x	X
iajs-1013	436	18	)	)	PUNCT
iajs-1013	436	19	=	=	SYM
iajs-1013	436	20	–	–	PUNCT
iajs-1013	436	21	h(k	h(k	PROPN
iajs-1013	436	22	)	)	PUNCT
iajs-1013	436	23			NOUN
iajs-1013	436	24	k	k	VERB
iajs-1013	436	25			PROPN
iajs-1013	436	26	f	f	X
iajs-1013	436	27	(	(	PUNCT
iajs-1013	436	28	n	n	CCONJ
iajs-1013	436	29	/	/	SYM
iajs-1013	436	30	l	l	NOUN
iajs-1013	436	31	)	)	PUNCT
iajs-1013	436	32	=	=	SYM
iajs-1013	437	1	0	0	X
iajs-1013	437	2	.	.	PUNCT
iajs-1013	438	1	so	so	ADV
iajs-1013	438	2	,	,	PUNCT
iajs-1013	438	3	f	f	PROPN
iajs-1013	438	4	(	(	PUNCT
iajs-1013	438	5	x	x	X
iajs-1013	438	6	)	)	PUNCT
iajs-1013	438	7	=	=	SYM
iajs-1013	438	8	0	0	NUM
iajs-1013	438	9	and	and	CCONJ
iajs-1013	438	10	h(k	h(k	PROPN
iajs-1013	438	11	)	)	PUNCT
iajs-1013	439	1	=	=	SYM
iajs-1013	439	2	0	0	NUM
iajs-1013	439	3	,	,	PUNCT
iajs-1013	439	4	hence	hence	ADV
iajs-1013	439	5			NOUN
iajs-1013	439	6	is	be	AUX
iajs-1013	439	7	a	a	DET
iajs-1013	439	8	monomorphism	monomorphism	NOUN
iajs-1013	439	9	.	.	PUNCT
iajs-1013	440	1	therefore	therefore	ADV
iajs-1013	440	2			NOUN
iajs-1013	440	3	is	be	AUX
iajs-1013	440	4	extended	extend	VERB
iajs-1013	440	5	to	to	ADP
iajs-1013	440	6	a	a	DET
iajs-1013	440	7	monomorphism	monomorphism	NOUN
iajs-1013	440	8			NOUN
iajs-1013	440	9	:	:	PUNCT
iajs-1013	440	10	m	m	PROPN
iajs-1013	440	11			PROPN
iajs-1013	440	12			PROPN
iajs-1013	440	13	.	.	PUNCT
iajs-1013	441	1	we	we	PRON
iajs-1013	441	2	claim	claim	VERB
iajs-1013	441	3	that	that	SCONJ
iajs-1013	441	4			PROPN
iajs-1013	441	5	f	f	PROPN
iajs-1013	441	6	=	=	PROPN
iajs-1013	441	7	f.	f.	PROPN
iajs-1013	441	8	let	let	VERB
iajs-1013	441	9	x	x	PUNCT
iajs-1013	441	10			PROPN
iajs-1013	441	11	n	n	PROPN
iajs-1013	441	12	/	/	SYM
iajs-1013	441	13	l.	l.	PROPN
iajs-1013	441	14	then	then	ADV
iajs-1013	441	15			PROPN
iajs-1013	441	16	(	(	PUNCT
iajs-1013	441	17	f	f	PROPN
iajs-1013	441	18	(x	(x	PROPN
iajs-1013	441	19	)	)	PUNCT
iajs-1013	441	20	)	)	PUNCT
iajs-1013	442	1	=	=	SYM
iajs-1013	442	2			NOUN
iajs-1013	442	3	(	(	PUNCT
iajs-1013	442	4	f	f	PROPN
iajs-1013	442	5	(x	(x	PROPN
iajs-1013	442	6	)	)	PUNCT
iajs-1013	442	7	)	)	PUNCT
iajs-1013	443	1	=	=	SYM
iajs-1013	443	2			NOUN
iajs-1013	443	3	(	(	PUNCT
iajs-1013	443	4	f	f	PROPN
iajs-1013	443	5	(x	(x	PROPN
iajs-1013	443	6	)	)	PUNCT
iajs-1013	444	1	+	+	CCONJ
iajs-1013	444	2	0	0	X
iajs-1013	444	3	)	)	PUNCT
iajs-1013	445	1	=	=	SYM
iajs-1013	445	2	f	f	X
iajs-1013	445	3	(	(	PUNCT
iajs-1013	445	4	x	x	NOUN
iajs-1013	445	5	)	)	PUNCT
iajs-1013	445	6	.	.	PUNCT
iajs-1013	446	1	hence	hence	ADV
iajs-1013	446	2			PROPN
iajs-1013	446	3	f	f	PROPN
iajs-1013	446	4	=	=	PROPN
iajs-1013	446	5	f	f	PROPN
iajs-1013	447	1	and	and	CCONJ
iajs-1013	447	2	so	so	ADV
iajs-1013	447	3	,	,	PUNCT
iajs-1013	447	4	m	m	VERB
iajs-1013	447	5	is	be	AUX
iajs-1013	447	6	weakly	weakly	ADJ
iajs-1013	447	7	n	n	CCONJ
iajs-1013	447	8	-	-	PUNCT
iajs-1013	447	9	quasi	quasi	NOUN
iajs-1013	447	10	-	-	ADJ
iajs-1013	447	11	injective	injective	ADJ
iajs-1013	447	12	(	(	PUNCT
iajs-1013	447	13	by	by	ADP
iajs-1013	447	14	theorem	theorem	NOUN
iajs-1013	447	15	2.1	2.1	NUM
iajs-1013	447	16	)	)	PUNCT
iajs-1013	447	17	.	.	PUNCT
iajs-1013	448	1	3.7	3.7	NUM
iajs-1013	448	2	corollary	corollary	NOUN
iajs-1013	448	3	let	let	VERB
iajs-1013	448	4	m	m	PRON
iajs-1013	448	5	and	and	CCONJ
iajs-1013	448	6	n	n	CCONJ
iajs-1013	448	7	be	be	VERB
iajs-1013	448	8	two	two	NUM
iajs-1013	448	9	r	r	NOUN
iajs-1013	448	10	-	-	PUNCT
iajs-1013	448	11	modules	module	NOUN
iajs-1013	448	12	.	.	PUNCT
iajs-1013	449	1	if	if	SCONJ
iajs-1013	449	2	m	m	NOUN
iajs-1013	449	3	is	be	AUX
iajs-1013	449	4	uniform	uniform	ADJ
iajs-1013	449	5	and	and	CCONJ
iajs-1013	449	6	n	n	CCONJ
iajs-1013	449	7	-	-	PUNCT
iajs-1013	449	8	quasi	quasi	NOUN
iajs-1013	449	9	-	-	ADJ
iajs-1013	449	10	tight	tight	ADJ
iajs-1013	449	11	,	,	PUNCT
iajs-1013	449	12	then	then	ADV
iajs-1013	449	13	m	m	NOUN
iajs-1013	449	14	is	be	AUX
iajs-1013	449	15	weakly	weakly	ADJ
iajs-1013	449	16	nquasi	nquasi	NOUN
iajs-1013	449	17	-	-	PUNCT
iajs-1013	449	18	injective	injective	ADJ
iajs-1013	449	19	.	.	PUNCT
iajs-1013	450	1	proof	proof	NOUN
iajs-1013	450	2	:	:	PUNCT
iajs-1013	450	3	let	let	VERB
iajs-1013	450	4	l	l	NOUN
iajs-1013	450	5	be	be	AUX
iajs-1013	450	6	a	a	DET
iajs-1013	450	7	submodule	submodule	NOUN
iajs-1013	450	8	of	of	ADP
iajs-1013	450	9	n	n	ADV
iajs-1013	450	10	let	let	VERB
iajs-1013	450	11	f	f	PRON
iajs-1013	450	12	:	:	PUNCT
iajs-1013	450	13	n	n	CCONJ
iajs-1013	450	14	/	/	SYM
iajs-1013	450	15	l	l	NOUN
iajs-1013	450	16			PROPN
iajs-1013	450	17			PROPN
iajs-1013	450	18	be	be	AUX
iajs-1013	450	19	a	a	DET
iajs-1013	450	20	monomorphism	monomorphism	NOUN
iajs-1013	450	21	.	.	PUNCT
iajs-1013	451	1	but	but	CCONJ
iajs-1013	451	2	m	m	PROPN
iajs-1013	451	3	is	be	AUX
iajs-1013	451	4	nquasi	nquasi	NOUN
iajs-1013	451	5	-	-	PUNCT
iajs-1013	451	6	tight	tight	ADJ
iajs-1013	451	7	,	,	PUNCT
iajs-1013	451	8	therefore	therefore	ADV
iajs-1013	451	9	there	there	PRON
iajs-1013	451	10	exists	exist	VERB
iajs-1013	451	11	a	a	DET
iajs-1013	451	12	monomorphism	monomorphism	NOUN
iajs-1013	451	13	f	f	PROPN
iajs-1013	451	14			ADJ
iajs-1013	451	15	:	:	PUNCT
iajs-1013	451	16	n	n	PROPN
iajs-1013	451	17	/	/	SYM
iajs-1013	451	18	l	l	NOUN
iajs-1013	451	19			PROPN
iajs-1013	451	20	m	m	NOUN
iajs-1013	451	21	and	and	CCONJ
iajs-1013	451	22	hence	hence	ADV
iajs-1013	451	23	(	(	PUNCT
iajs-1013	451	24	i	i	NOUN
iajs-1013	451	25	)	)	PUNCT
iajs-1013	451	26	in	in	ADP
iajs-1013	451	27	theorem	theorem	ADJ
iajs-1013	451	28	3.6	3.6	NUM
iajs-1013	451	29	holds	hold	NOUN
iajs-1013	451	30	.	.	PUNCT
iajs-1013	452	1	now	now	ADV
iajs-1013	452	2	,	,	PUNCT
iajs-1013	452	3	if	if	SCONJ
iajs-1013	452	4	l	l	NOUN
iajs-1013	452	5	=	=	SYM
iajs-1013	452	6	n	n	CCONJ
iajs-1013	452	7	,	,	PUNCT
iajs-1013	452	8	then	then	ADV
iajs-1013	452	9	f	f	PROPN
iajs-1013	452	10	(n	(n	PROPN
iajs-1013	452	11	/	/	SYM
iajs-1013	452	12	l	l	NOUN
iajs-1013	452	13	)	)	PUNCT
iajs-1013	452	14	=	=	SYM
iajs-1013	452	15	0	0	PUNCT
iajs-1013	452	16	and	and	CCONJ
iajs-1013	452	17	hence	hence	ADV
iajs-1013	452	18	m	m	VERB
iajs-1013	452	19	is	be	AUX
iajs-1013	452	20	a	a	DET
iajs-1013	452	21	complement	complement	NOUN
iajs-1013	452	22	of	of	ADP
iajs-1013	452	23	f	f	PROPN
iajs-1013	452	24	(n	(n	PROPN
iajs-1013	452	25	/	/	SYM
iajs-1013	452	26	l	l	NOUN
iajs-1013	452	27	)	)	PUNCT
iajs-1013	452	28	in	in	ADP
iajs-1013	452	29	m	m	PROPN
iajs-1013	452	30	and	and	CCONJ
iajs-1013	452	31	m	m	PRON
iajs-1013	452	32			NOUN
iajs-1013	452	33	f	f	PROPN
iajs-1013	452	34	(n	(n	PROPN
iajs-1013	452	35	/	/	SYM
iajs-1013	452	36	l	l	NOUN
iajs-1013	452	37	)	)	PUNCT
iajs-1013	452	38	=	=	SYM
iajs-1013	453	1	0	0	X
iajs-1013	453	2	.	.	PUNCT
iajs-1013	454	1	if	if	SCONJ
iajs-1013	454	2	l	l	PROPN
iajs-1013	454	3			NOUN
iajs-1013	454	4	n	n	CCONJ
iajs-1013	454	5	,	,	PUNCT
iajs-1013	454	6	then	then	ADV
iajs-1013	454	7	f	f	PROPN
iajs-1013	454	8	(n	(n	PROPN
iajs-1013	454	9	/	/	SYM
iajs-1013	454	10	l	l	NOUN
iajs-1013	454	11	)	)	PUNCT
iajs-1013	454	12	is	be	AUX
iajs-1013	454	13	a	a	DET
iajs-1013	454	14	non	non	ADJ
iajs-1013	454	15	-	-	ADJ
iajs-1013	454	16	zero	zero	NUM
iajs-1013	454	17	submodule	submodule	NOUN
iajs-1013	454	18	of	of	ADP
iajs-1013	454	19	m	m	PROPN
iajs-1013	454	20	and	and	CCONJ
iajs-1013	454	21	since	since	SCONJ
iajs-1013	454	22	m	m	PROPN
iajs-1013	454	23	is	be	AUX
iajs-1013	454	24	uniform	uniform	ADJ
iajs-1013	454	25	implies	imply	VERB
iajs-1013	454	26	that	that	SCONJ
iajs-1013	454	27	0	0	NUM
iajs-1013	454	28	is	be	AUX
iajs-1013	454	29	the	the	DET
iajs-1013	454	30	only	only	ADJ
iajs-1013	454	31	complement	complement	NOUN
iajs-1013	454	32	of	of	ADP
iajs-1013	454	33	f	f	PROPN
iajs-1013	454	34	(n	(n	PROPN
iajs-1013	454	35	/	/	SYM
iajs-1013	454	36	l	l	NOUN
iajs-1013	454	37	)	)	PUNCT
iajs-1013	454	38	in	in	ADP
iajs-1013	454	39	m	m	PROPN
iajs-1013	454	40	,	,	PUNCT
iajs-1013	454	41	and	and	CCONJ
iajs-1013	454	42	hence	hence	ADV
iajs-1013	454	43	(	(	PUNCT
iajs-1013	454	44	ii	ii	NOUN
iajs-1013	454	45	)	)	PUNCT
iajs-1013	454	46	in	in	ADP
iajs-1013	454	47	theorem	theorem	ADJ
iajs-1013	454	48	3.6	3.6	NUM
iajs-1013	454	49	is	be	AUX
iajs-1013	454	50	also	also	ADV
iajs-1013	454	51	hold	hold	VERB
iajs-1013	454	52	.	.	PUNCT
iajs-1013	455	1	therefore	therefore	ADV
iajs-1013	455	2	m	m	PROPN
iajs-1013	455	3	is	be	AUX
iajs-1013	455	4	weakly	weakly	ADJ
iajs-1013	455	5	n	n	CCONJ
iajs-1013	455	6	-	-	PUNCT
iajs-1013	455	7	quasi	quasi	NOUN
iajs-1013	455	8	-	-	ADJ
iajs-1013	455	9	injective	injective	ADJ
iajs-1013	455	10	(	(	PUNCT
iajs-1013	455	11	by	by	ADP
iajs-1013	455	12	theorem	theorem	NOUN
iajs-1013	455	13	3.6	3.6	NUM
iajs-1013	455	14	)	)	PUNCT
iajs-1013	455	15	.	.	PUNCT
iajs-1013	456	1	3.8	3.8	NUM
iajs-1013	456	2	corollary	corollary	NOUN
iajs-1013	456	3	let	let	VERB
iajs-1013	456	4	m	m	PRON
iajs-1013	456	5	and	and	CCONJ
iajs-1013	456	6	n	n	CCONJ
iajs-1013	456	7	be	be	VERB
iajs-1013	456	8	two	two	NUM
iajs-1013	456	9	r	r	NOUN
iajs-1013	456	10	-	-	PUNCT
iajs-1013	456	11	modules	module	NOUN
iajs-1013	456	12	such	such	ADJ
iajs-1013	456	13	that	that	SCONJ
iajs-1013	456	14	m	m	PROPN
iajs-1013	456	15	is	be	AUX
iajs-1013	456	16	uniform	uniform	ADJ
iajs-1013	456	17	.	.	PUNCT
iajs-1013	457	1	then	then	ADV
iajs-1013	457	2	m	m	PROPN
iajs-1013	457	3	is	be	AUX
iajs-1013	457	4	n	n	CCONJ
iajs-1013	457	5	-	-	PUNCT
iajs-1013	457	6	quasi	quasi	NOUN
iajs-1013	457	7	-	-	NOUN
iajs-1013	457	8	tight	tight	ADJ
iajs-1013	457	9	if	if	SCONJ
iajs-1013	458	1	and	and	CCONJ
iajs-1013	458	2	only	only	ADV
iajs-1013	458	3	if	if	SCONJ
iajs-1013	458	4	m	m	NOUN
iajs-1013	458	5	is	be	AUX
iajs-1013	458	6	weakly	weakly	ADJ
iajs-1013	458	7	n	n	CCONJ
iajs-1013	458	8	-	-	PUNCT
iajs-1013	458	9	quasi	quasi	NOUN
iajs-1013	458	10	-	-	ADJ
iajs-1013	458	11	injective	injective	ADJ
iajs-1013	458	12	.	.	PUNCT
iajs-1013	459	1	proof	proof	NOUN
iajs-1013	459	2	:	:	PUNCT
iajs-1013	459	3	follows	follow	VERB
iajs-1013	459	4	by	by	ADP
iajs-1013	459	5	proposition	proposition	NOUN
iajs-1013	459	6	3.4	3.4	NUM
iajs-1013	459	7	and	and	CCONJ
iajs-1013	459	8	corollary	corollary	ADJ
iajs-1013	459	9	3.7	3.7	NUM
iajs-1013	459	10	.	.	PUNCT
iajs-1013	460	1	section	section	NOUN
iajs-1013	460	2	four	four	NUM
iajs-1013	460	3	:	:	PUNCT
iajs-1013	460	4	quasi	quasi	ADJ
iajs-1013	460	5	-	-	ADJ
iajs-1013	460	6	tight	tight	ADJ
iajs-1013	460	7	modules	module	NOUN
iajs-1013	460	8	and	and	CCONJ
iajs-1013	460	9	compressible	compressible	ADJ
iajs-1013	460	10	modules	module	NOUN
iajs-1013	460	11	in	in	ADP
iajs-1013	460	12	this	this	DET
iajs-1013	460	13	section	section	NOUN
iajs-1013	460	14	,	,	PUNCT
iajs-1013	460	15	we	we	PRON
iajs-1013	460	16	establish	establish	VERB
iajs-1013	460	17	some	some	DET
iajs-1013	460	18	relations	relation	NOUN
iajs-1013	460	19	between	between	ADP
iajs-1013	460	20	relative	relative	ADJ
iajs-1013	460	21	quasi	quasi	ADJ
iajs-1013	460	22	-	-	ADJ
iajs-1013	460	23	tight	tight	ADJ
iajs-1013	460	24	modules	module	NOUN
iajs-1013	460	25	and	and	CCONJ
iajs-1013	460	26	compressible	compressible	ADJ
iajs-1013	460	27	modules	module	NOUN
iajs-1013	460	28	in	in	ADP
iajs-1013	460	29	the	the	DET
iajs-1013	460	30	class	class	NOUN
iajs-1013	460	31	of	of	ADP
iajs-1013	460	32	quasi	quasi	ADJ
iajs-1013	460	33	-	-	ADJ
iajs-1013	460	34	injective	injective	ADJ
iajs-1013	460	35	modules	module	NOUN
iajs-1013	460	36	.	.	PUNCT
iajs-1013	461	1	4.1	4.1	NUM
iajs-1013	461	2	definition	definition	NOUN
iajs-1013	461	3	an	an	DET
iajs-1013	461	4	r	r	NOUN
iajs-1013	461	5	-	-	PUNCT
iajs-1013	461	6	module	module	NOUN
iajs-1013	461	7	m	m	NOUN
iajs-1013	461	8	is	be	AUX
iajs-1013	461	9	called	call	VERB
iajs-1013	461	10	compressible	compressible	ADJ
iajs-1013	461	11	if	if	SCONJ
iajs-1013	461	12	for	for	ADP
iajs-1013	461	13	all	all	DET
iajs-1013	461	14	non	non	ADJ
iajs-1013	461	15	-	-	ADJ
iajs-1013	461	16	zero	zero	NUM
iajs-1013	461	17	submodules	submodule	NOUN
iajs-1013	461	18	n	n	PROPN
iajs-1013	461	19	of	of	ADP
iajs-1013	461	20	m	m	PROPN
iajs-1013	461	21	,	,	PUNCT
iajs-1013	461	22	m	m	VERB
iajs-1013	461	23	embeds	embed	VERB
iajs-1013	461	24	in	in	ADP
iajs-1013	461	25	n	n	CCONJ
iajs-1013	461	26	,	,	PUNCT
iajs-1013	462	1	[	[	X
iajs-1013	462	2	9	9	NUM
iajs-1013	462	3	]	]	PUNCT
iajs-1013	462	4	.	.	PUNCT
iajs-1013	463	1	in	in	ADP
iajs-1013	463	2	general	general	ADJ
iajs-1013	463	3	,	,	PUNCT
iajs-1013	463	4	an	an	DET
iajs-1013	463	5	r	r	NOUN
iajs-1013	463	6	-	-	PUNCT
iajs-1013	463	7	module	module	NOUN
iajs-1013	463	8	m	m	NOUN
iajs-1013	463	9	is	be	AUX
iajs-1013	463	10	compressible	compressible	ADJ
iajs-1013	463	11	if	if	SCONJ
iajs-1013	463	12	for	for	ADP
iajs-1013	463	13	every	every	DET
iajs-1013	463	14	essential	essential	ADJ
iajs-1013	463	15	submodule	submodule	NOUN
iajs-1013	463	16	n	n	PROPN
iajs-1013	463	17	of	of	ADP
iajs-1013	463	18	m	m	PROPN
iajs-1013	463	19	,	,	PUNCT
iajs-1013	463	20	m	m	VERB
iajs-1013	463	21	embeds	embed	VERB
iajs-1013	463	22	in	in	ADP
iajs-1013	463	23	n	n	CCONJ
iajs-1013	463	24	,	,	PUNCT
iajs-1013	463	25	[	[	X
iajs-1013	463	26	4	4	NUM
iajs-1013	463	27	]	]	PUNCT
iajs-1013	463	28	.	.	PUNCT
iajs-1013	464	1	first	first	ADV
iajs-1013	464	2	,	,	PUNCT
iajs-1013	464	3	we	we	PRON
iajs-1013	464	4	establish	establish	VERB
iajs-1013	464	5	the	the	DET
iajs-1013	464	6	relationship	relationship	NOUN
iajs-1013	464	7	between	between	ADP
iajs-1013	464	8	relative	relative	ADJ
iajs-1013	464	9	quasi	quasi	ADJ
iajs-1013	464	10	-	-	ADJ
iajs-1013	464	11	tight	tight	ADJ
iajs-1013	464	12	modules	module	NOUN
iajs-1013	464	13	and	and	CCONJ
iajs-1013	464	14	compressible	compressible	ADJ
iajs-1013	464	15	modules	module	NOUN
iajs-1013	464	16	.	.	PUNCT
iajs-1013	465	1	ibn	ibn	PROPN
iajs-1013	465	2	alhaitham	alhaitham	PROPN
iajs-1013	465	3	j.	j.	PROPN
iajs-1013	465	4	for	for	ADP
iajs-1013	465	5	pure	pure	ADJ
iajs-1013	465	6	&	&	CCONJ
iajs-1013	465	7	appl	appl	PROPN
iajs-1013	465	8	.	.	PUNCT
iajs-1013	466	1	sci	sci	PROPN
iajs-1013	466	2	.	.	PUNCT
iajs-1013	467	1	vol.23	vol.23	PROPN
iajs-1013	467	2	(	(	PUNCT
iajs-1013	467	3	1	1	NUM
iajs-1013	467	4	)	)	PUNCT
iajs-1013	467	5	2010	2010	NUM
iajs-1013	467	6	4.2	4.2	NUM
iajs-1013	467	7	theorem	theorem	NOUN
iajs-1013	467	8	let	let	VERB
iajs-1013	467	9	m	m	PRON
iajs-1013	467	10	be	be	AUX
iajs-1013	467	11	a	a	DET
iajs-1013	467	12	quasi	quasi	ADJ
iajs-1013	467	13	-	-	ADJ
iajs-1013	467	14	injective	injective	ADJ
iajs-1013	467	15	r	r	NOUN
iajs-1013	467	16	-	-	PUNCT
iajs-1013	467	17	module	module	NOUN
iajs-1013	467	18	and	and	CCONJ
iajs-1013	467	19	let	let	VERB
iajs-1013	467	20	n	n	PRON
iajs-1013	467	21	be	be	AUX
iajs-1013	467	22	any	any	DET
iajs-1013	467	23	r	r	NOUN
iajs-1013	467	24	-	-	PUNCT
iajs-1013	467	25	module	module	NOUN
iajs-1013	467	26	.	.	PUNCT
iajs-1013	468	1	then	then	ADV
iajs-1013	468	2	every	every	DET
iajs-1013	468	3	submodule	submodule	NOUN
iajs-1013	468	4	of	of	ADP
iajs-1013	468	5	m	m	PROPN
iajs-1013	468	6	is	be	AUX
iajs-1013	468	7	n	n	CCONJ
iajs-1013	468	8	-	-	PUNCT
iajs-1013	468	9	quasi	quasi	NOUN
iajs-1013	468	10	-	-	NOUN
iajs-1013	468	11	tight	tight	ADJ
iajs-1013	468	12	if	if	SCONJ
iajs-1013	469	1	and	and	CCONJ
iajs-1013	469	2	only	only	ADV
iajs-1013	469	3	if	if	SCONJ
iajs-1013	469	4	every	every	DET
iajs-1013	469	5	quotient	quotient	NOUN
iajs-1013	469	6	n	n	INTJ
iajs-1013	469	7	/	/	SYM
iajs-1013	469	8	k	k	PROPN
iajs-1013	469	9	of	of	ADP
iajs-1013	469	10	n	n	PRON
iajs-1013	469	11	which	which	PRON
iajs-1013	469	12	embeds	embed	VERB
iajs-1013	469	13	in	in	ADP
iajs-1013	469	14	m	m	PROPN
iajs-1013	469	15	is	be	AUX
iajs-1013	469	16	compressible	compressible	ADJ
iajs-1013	469	17	.	.	PUNCT
iajs-1013	470	1	proof	proof	NOUN
iajs-1013	470	2	:	:	PUNCT
iajs-1013	470	3	assume	assume	VERB
iajs-1013	470	4	that	that	SCONJ
iajs-1013	470	5	every	every	DET
iajs-1013	470	6	submodule	submodule	NOUN
iajs-1013	470	7	of	of	ADP
iajs-1013	470	8	m	m	PROPN
iajs-1013	470	9	is	be	AUX
iajs-1013	470	10	n	n	CCONJ
iajs-1013	470	11	-	-	PUNCT
iajs-1013	470	12	quasi	quasi	NOUN
iajs-1013	470	13	-	-	ADJ
iajs-1013	470	14	tight	tight	ADJ
iajs-1013	470	15	.	.	PUNCT
iajs-1013	471	1	let	let	VERB
iajs-1013	471	2	n	n	PRON
iajs-1013	471	3	/	/	SYM
iajs-1013	471	4	k	k	X
iajs-1013	471	5	be	be	AUX
iajs-1013	471	6	embeds	embed	VERB
iajs-1013	471	7	in	in	ADP
iajs-1013	471	8	m.	m.	NOUN
iajs-1013	471	9	hence	hence	ADV
iajs-1013	471	10	there	there	PRON
iajs-1013	471	11	exists	exist	VERB
iajs-1013	471	12	a	a	DET
iajs-1013	471	13	monomorphism	monomorphism	NOUN
iajs-1013	471	14	f	f	NOUN
iajs-1013	471	15	:	:	PUNCT
iajs-1013	471	16	n	n	PROPN
iajs-1013	471	17	/	/	SYM
iajs-1013	471	18	k	k	PROPN
iajs-1013	471	19			PROPN
iajs-1013	471	20	m.	m.	NOUN
iajs-1013	471	21	we	we	PRON
iajs-1013	471	22	have	have	VERB
iajs-1013	471	23	to	to	PART
iajs-1013	471	24	show	show	VERB
iajs-1013	471	25	that	that	SCONJ
iajs-1013	471	26	n	n	NOUN
iajs-1013	471	27	/	/	SYM
iajs-1013	471	28	k	k	PROPN
iajs-1013	471	29	is	be	AUX
iajs-1013	471	30	compressible	compressible	ADJ
iajs-1013	471	31	.	.	PUNCT
iajs-1013	472	1	let	let	VERB
iajs-1013	472	2	l	l	NOUN
iajs-1013	472	3	be	be	AUX
iajs-1013	472	4	an	an	DET
iajs-1013	472	5	essential	essential	ADJ
iajs-1013	472	6	submodule	submodule	NOUN
iajs-1013	472	7	of	of	ADP
iajs-1013	472	8	n	n	PROPN
iajs-1013	472	9	/	/	SYM
iajs-1013	472	10	k.	k.	NOUN
iajs-1013	473	1	it	it	PRON
iajs-1013	473	2	can	can	AUX
iajs-1013	473	3	be	be	AUX
iajs-1013	473	4	easily	easily	ADV
iajs-1013	473	5	seen	see	VERB
iajs-1013	473	6	that	that	SCONJ
iajs-1013	473	7	f	f	PROPN
iajs-1013	473	8	(	(	PUNCT
iajs-1013	473	9	l	l	NOUN
iajs-1013	473	10	)	)	PUNCT
iajs-1013	473	11	is	be	AUX
iajs-1013	473	12	essential	essential	ADJ
iajs-1013	473	13	in	in	ADP
iajs-1013	473	14	f	f	PROPN
iajs-1013	473	15	(	(	PUNCT
iajs-1013	473	16	n	n	PROPN
iajs-1013	473	17	/	/	SYM
iajs-1013	473	18	k	k	NOUN
iajs-1013	473	19	)	)	PUNCT
iajs-1013	473	20	and	and	CCONJ
iajs-1013	473	21	hence	hence	ADV
iajs-1013	473	22	(	(	PUNCT
iajs-1013	473	23	l	l	NOUN
iajs-1013	473	24	)	)	PUNCT
iajs-1013	473	25	(	(	PUNCT
iajs-1013	473	26	/	/	SYM
iajs-1013	473	27	l)f	l)f	ADJ
iajs-1013	473	28	f	f	NOUN
iajs-1013	473	29			NOUN
iajs-1013	473	30	[	[	X
iajs-1013	473	31	by	by	ADP
iajs-1013	473	32	cor.19.8	cor.19.8	NOUN
iajs-1013	473	33	,	,	PUNCT
iajs-1013	473	34	p.65	p.65	ADP
iajs-1013	473	35	,	,	PUNCT
iajs-1013	473	36	[	[	X
iajs-1013	473	37	6	6	NUM
iajs-1013	473	38	]	]	PUNCT
iajs-1013	473	39	]	]	PUNCT
iajs-1013	473	40	.	.	PUNCT
iajs-1013	474	1	since	since	SCONJ
iajs-1013	474	2	n	n	PROPN
iajs-1013	474	3	/	/	SYM
iajs-1013	474	4	k	k	PROPN
iajs-1013	474	5	embeds	embed	VERB
iajs-1013	474	6	in	in	ADP
iajs-1013	474	7	(	(	PUNCT
iajs-1013	474	8	/	/	SYM
iajs-1013	474	9	l	l	NOUN
iajs-1013	474	10	)	)	PUNCT
iajs-1013	474	11	(	(	PUNCT
iajs-1013	474	12	l)f	l)f	NOUN
iajs-1013	474	13	f	f	ADV
iajs-1013	474	14			PROPN
iajs-1013	474	15	and	and	CCONJ
iajs-1013	474	16	f	f	PROPN
iajs-1013	474	17	(	(	PUNCT
iajs-1013	474	18	l	l	NOUN
iajs-1013	474	19	)	)	PUNCT
iajs-1013	474	20	is	be	AUX
iajs-1013	474	21	n	n	CCONJ
iajs-1013	474	22	-	-	PUNCT
iajs-1013	474	23	quasi	quasi	NOUN
iajs-1013	474	24	-	-	ADJ
iajs-1013	474	25	tight	tight	ADJ
iajs-1013	474	26	,	,	PUNCT
iajs-1013	474	27	we	we	PRON
iajs-1013	474	28	get	get	VERB
iajs-1013	474	29	that	that	PRON
iajs-1013	474	30	n	n	PROPN
iajs-1013	474	31	/	/	SYM
iajs-1013	474	32	k	k	PROPN
iajs-1013	474	33	embeds	embed	VERB
iajs-1013	474	34	in	in	ADP
iajs-1013	474	35	f	f	PROPN
iajs-1013	474	36	(	(	PUNCT
iajs-1013	474	37	l	l	NOUN
iajs-1013	474	38	)	)	PUNCT
iajs-1013	475	1	≈	≈	PROPN
iajs-1013	475	2	l.	l.	NOUN
iajs-1013	475	3	thus	thus	ADV
iajs-1013	475	4	n	n	PROPN
iajs-1013	475	5	/	/	SYM
iajs-1013	475	6	k	k	PROPN
iajs-1013	475	7	embeds	embed	VERB
iajs-1013	475	8	in	in	ADP
iajs-1013	475	9	l	l	NOUN
iajs-1013	475	10	which	which	PRON
iajs-1013	475	11	is	be	AUX
iajs-1013	475	12	what	what	PRON
iajs-1013	475	13	we	we	PRON
iajs-1013	475	14	wanted	want	VERB
iajs-1013	475	15	.	.	PUNCT
iajs-1013	476	1	conversely	conversely	ADV
iajs-1013	476	2	,	,	PUNCT
iajs-1013	476	3	suppose	suppose	VERB
iajs-1013	476	4	that	that	SCONJ
iajs-1013	476	5	every	every	DET
iajs-1013	476	6	quotient	quotient	NOUN
iajs-1013	476	7	of	of	ADP
iajs-1013	476	8	n	n	PRON
iajs-1013	476	9	which	which	PRON
iajs-1013	476	10	embeds	embed	VERB
iajs-1013	476	11	in	in	ADP
iajs-1013	476	12	m	m	PROPN
iajs-1013	476	13	is	be	AUX
iajs-1013	476	14	compressible	compressible	ADJ
iajs-1013	476	15	.	.	PUNCT
iajs-1013	477	1	let	let	VERB
iajs-1013	477	2	a	a	PRON
iajs-1013	477	3	be	be	AUX
iajs-1013	477	4	a	a	DET
iajs-1013	477	5	submodule	submodule	NOUN
iajs-1013	477	6	of	of	ADP
iajs-1013	477	7	m.	m.	NOUN
iajs-1013	477	8	we	we	PRON
iajs-1013	477	9	have	have	VERB
iajs-1013	477	10	to	to	PART
iajs-1013	477	11	show	show	VERB
iajs-1013	477	12	that	that	SCONJ
iajs-1013	477	13	a	a	PRON
iajs-1013	477	14	is	be	AUX
iajs-1013	477	15	n	n	PRON
iajs-1013	477	16	-	-	PUNCT
iajs-1013	477	17	quasi	quasi	NOUN
iajs-1013	477	18	-	-	ADJ
iajs-1013	477	19	tight	tight	ADJ
iajs-1013	477	20	.	.	PUNCT
iajs-1013	478	1	let	let	VERB
iajs-1013	478	2	k	k	PRON
iajs-1013	478	3	be	be	AUX
iajs-1013	478	4	a	a	DET
iajs-1013	478	5	submodule	submodule	NOUN
iajs-1013	478	6	of	of	ADP
iajs-1013	478	7	n	n	PROPN
iajs-1013	478	8	and	and	CCONJ
iajs-1013	478	9	let	let	VERB
iajs-1013	478	10	h	h	NOUN
iajs-1013	478	11	:	:	PUNCT
iajs-1013	478	12	n	n	X
iajs-1013	478	13	/	/	SYM
iajs-1013	478	14	k	k	PROPN
iajs-1013	478	15			PROPN
iajs-1013	479	1			PROPN
iajs-1013	479	2	be	be	AUX
iajs-1013	479	3	a	a	DET
iajs-1013	479	4	monomorphism	monomorphism	NOUN
iajs-1013	479	5	.	.	PUNCT
iajs-1013	480	1	but	but	CCONJ
iajs-1013	480	2			PROPN
iajs-1013	480	3			PROPN
iajs-1013	480	4			PROPN
iajs-1013	480	5	=	=	SYM
iajs-1013	480	6	m	m	NOUN
iajs-1013	480	7	,	,	PUNCT
iajs-1013	480	8	implies	imply	VERB
iajs-1013	480	9	that	that	SCONJ
iajs-1013	480	10	i	i	PROPN
iajs-1013	480	11	h	h	NOUN
iajs-1013	480	12	:	:	PUNCT
iajs-1013	480	13	n	n	X
iajs-1013	480	14	/	/	SYM
iajs-1013	480	15	k	k	PROPN
iajs-1013	480	16			PROPN
iajs-1013	480	17	m	m	VERB
iajs-1013	480	18	is	be	AUX
iajs-1013	480	19	a	a	DET
iajs-1013	480	20	monomorphism	monomorphism	NOUN
iajs-1013	480	21	where	where	SCONJ
iajs-1013	480	22	i	i	PRON
iajs-1013	480	23	:	:	PUNCT
iajs-1013	480	24			PROPN
iajs-1013	480	25			PROPN
iajs-1013	480	26			PROPN
iajs-1013	480	27	is	be	AUX
iajs-1013	480	28	the	the	DET
iajs-1013	480	29	inclusion	inclusion	NOUN
iajs-1013	480	30	homomorphism	homomorphism	NOUN
iajs-1013	480	31	.	.	PUNCT
iajs-1013	481	1	let	let	VERB
iajs-1013	481	2	b	b	NOUN
iajs-1013	481	3	=	=	SYM
iajs-1013	481	4	h(n	h(n	PROPN
iajs-1013	481	5	/	/	SYM
iajs-1013	481	6	k	k	NOUN
iajs-1013	481	7	)	)	PUNCT
iajs-1013	481	8			PUNCT
iajs-1013	481	9	a.	a.	NOUN
iajs-1013	481	10	then	then	ADV
iajs-1013	481	11	b	b	PROPN
iajs-1013	481	12			PROPN
iajs-1013	481	13	0	0	NUM
iajs-1013	481	14	.	.	PUNCT
iajs-1013	482	1	we	we	PRON
iajs-1013	482	2	claim	claim	VERB
iajs-1013	482	3	that	that	SCONJ
iajs-1013	482	4	b	b	NOUN
iajs-1013	482	5	is	be	AUX
iajs-1013	482	6	essential	essential	ADJ
iajs-1013	482	7	in	in	ADP
iajs-1013	482	8	h(n	h(n	PROPN
iajs-1013	482	9	/	/	SYM
iajs-1013	482	10	k	k	NOUN
iajs-1013	482	11	)	)	PUNCT
iajs-1013	482	12	.	.	PUNCT
iajs-1013	483	1	for	for	ADP
iajs-1013	483	2	if	if	SCONJ
iajs-1013	483	3	,	,	PUNCT
iajs-1013	483	4	b	b	NOUN
iajs-1013	483	5			PUNCT
iajs-1013	483	6	c	c	NOUN
iajs-1013	483	7	=	=	SYM
iajs-1013	483	8	0	0	NUM
iajs-1013	483	9	for	for	ADP
iajs-1013	483	10	some	some	DET
iajs-1013	483	11	non	non	ADJ
iajs-1013	483	12	-	-	ADJ
iajs-1013	483	13	zero	zero	NUM
iajs-1013	483	14	submodule	submodule	NOUN
iajs-1013	483	15	c	c	NOUN
iajs-1013	483	16	of	of	ADP
iajs-1013	483	17	h(n	h(n	PROPN
iajs-1013	483	18	/	/	SYM
iajs-1013	483	19	k	k	PROPN
iajs-1013	483	20	)	)	PUNCT
iajs-1013	483	21	,	,	PUNCT
iajs-1013	483	22	then	then	ADV
iajs-1013	483	23	0	0	NUM
iajs-1013	483	24	=	=	SYM
iajs-1013	483	25	(	(	PUNCT
iajs-1013	483	26	h(n	h(n	PROPN
iajs-1013	483	27	/	/	SYM
iajs-1013	483	28	k	k	PROPN
iajs-1013	483	29	)	)	PUNCT
iajs-1013	483	30			PUNCT
iajs-1013	483	31	a	a	PRON
iajs-1013	483	32	)	)	PUNCT
iajs-1013	483	33			PUNCT
iajs-1013	483	34	c	c	NOUN
iajs-1013	483	35	=	=	PUNCT
iajs-1013	483	36	a	a	DET
iajs-1013	483	37			PROPN
iajs-1013	483	38	c	c	NOUN
iajs-1013	483	39	which	which	PRON
iajs-1013	483	40	is	be	AUX
iajs-1013	483	41	a	a	DET
iajs-1013	483	42	contradiction	contradiction	NOUN
iajs-1013	483	43	.	.	PUNCT
iajs-1013	484	1	therefore	therefore	ADV
iajs-1013	484	2	0	0	NUM
iajs-1013	484	3			NOUN
iajs-1013	484	4	b	b	PROPN
iajs-1013	484	5	is	be	AUX
iajs-1013	484	6	essential	essential	ADJ
iajs-1013	484	7	in	in	ADP
iajs-1013	484	8	h(n	h(n	PROPN
iajs-1013	484	9	/	/	SYM
iajs-1013	484	10	k	k	NOUN
iajs-1013	484	11	)	)	PUNCT
iajs-1013	484	12	,	,	PUNCT
iajs-1013	484	13	which	which	PRON
iajs-1013	484	14	implies	imply	VERB
iajs-1013	484	15	that	that	SCONJ
iajs-1013	484	16	h	h	NOUN
iajs-1013	484	17	–	–	PUNCT
iajs-1013	484	18	1(b	1(b	NUM
iajs-1013	484	19	)	)	PUNCT
iajs-1013	484	20	is	be	AUX
iajs-1013	484	21	essential	essential	ADJ
iajs-1013	484	22	in	in	ADP
iajs-1013	484	23	n	n	PROPN
iajs-1013	484	24	/	/	SYM
iajs-1013	484	25	k.	k.	PROPN
iajs-1013	485	1	but	but	CCONJ
iajs-1013	485	2	n	n	PROPN
iajs-1013	485	3	/	/	SYM
iajs-1013	485	4	k	k	PROPN
iajs-1013	485	5	is	be	AUX
iajs-1013	485	6	compressible	compressible	ADJ
iajs-1013	485	7	therefore	therefore	ADV
iajs-1013	485	8	n	n	PROPN
iajs-1013	485	9	/	/	SYM
iajs-1013	485	10	k	k	PROPN
iajs-1013	485	11	embeds	embed	VERB
iajs-1013	485	12	in	in	ADP
iajs-1013	485	13	h	h	NOUN
iajs-1013	485	14	–	–	PUNCT
iajs-1013	485	15	1(b	1(b	NUM
iajs-1013	485	16	)	)	PUNCT
iajs-1013	485	17	.	.	PUNCT
iajs-1013	486	1	on	on	ADP
iajs-1013	486	2	the	the	DET
iajs-1013	486	3	other	other	ADJ
iajs-1013	486	4	hand	hand	NOUN
iajs-1013	486	5	h	h	NOUN
iajs-1013	486	6	–	–	PUNCT
iajs-1013	486	7	1(b	1(b	NUM
iajs-1013	486	8	)	)	PUNCT
iajs-1013	487	1	≈	≈	PROPN
iajs-1013	487	2	b	b	ADJ
iajs-1013	487	3	a.	a.	NOUN
iajs-1013	487	4	thus	thus	ADV
iajs-1013	487	5	n	n	PROPN
iajs-1013	487	6	/	/	SYM
iajs-1013	487	7	k	k	PROPN
iajs-1013	487	8	embed	embed	NOUN
iajs-1013	487	9	in	in	ADP
iajs-1013	487	10	a	a	PRON
iajs-1013	487	11	,	,	PUNCT
iajs-1013	487	12	as	as	SCONJ
iajs-1013	487	13	desired	desire	VERB
iajs-1013	487	14	.	.	PUNCT
iajs-1013	488	1	4.3	4.3	NUM
iajs-1013	488	2	corollary	corollary	NOUN
iajs-1013	488	3	let	let	VERB
iajs-1013	488	4	m	m	PRON
iajs-1013	488	5	be	be	AUX
iajs-1013	488	6	a	a	DET
iajs-1013	488	7	quasi	quasi	ADJ
iajs-1013	488	8	-	-	ADJ
iajs-1013	488	9	injective	injective	ADJ
iajs-1013	488	10	r	r	NOUN
iajs-1013	488	11	-	-	PUNCT
iajs-1013	488	12	module	module	NOUN
iajs-1013	488	13	.	.	PUNCT
iajs-1013	489	1	then	then	ADV
iajs-1013	489	2	every	every	DET
iajs-1013	489	3	submodule	submodule	NOUN
iajs-1013	489	4	of	of	ADP
iajs-1013	489	5	m	m	PROPN
iajs-1013	489	6	is	be	AUX
iajs-1013	489	7	quasi	quasi	ADJ
iajs-1013	489	8	-	-	ADJ
iajs-1013	489	9	tight	tight	ADJ
iajs-1013	489	10	if	if	SCONJ
iajs-1013	490	1	and	and	CCONJ
iajs-1013	490	2	only	only	ADV
iajs-1013	490	3	if	if	SCONJ
iajs-1013	490	4	every	every	DET
iajs-1013	490	5	finitely	finitely	ADV
iajs-1013	490	6	generated	generate	VERB
iajs-1013	490	7	submodule	submodule	NOUN
iajs-1013	490	8	of	of	ADP
iajs-1013	490	9	m	m	PROPN
iajs-1013	490	10	is	be	AUX
iajs-1013	490	11	compressible	compressible	ADJ
iajs-1013	490	12	.	.	PUNCT
iajs-1013	491	1	proof	proof	NOUN
iajs-1013	491	2	:	:	PUNCT
iajs-1013	491	3	assume	assume	VERB
iajs-1013	491	4	that	that	SCONJ
iajs-1013	491	5	every	every	DET
iajs-1013	491	6	submodule	submodule	NOUN
iajs-1013	491	7	of	of	ADP
iajs-1013	491	8	m	m	PROPN
iajs-1013	491	9	is	be	AUX
iajs-1013	491	10	quasi	quasi	ADJ
iajs-1013	491	11	-	-	ADJ
iajs-1013	491	12	tight	tight	ADJ
iajs-1013	491	13	.	.	PUNCT
iajs-1013	492	1	let	let	VERB
iajs-1013	492	2	a	a	DET
iajs-1013	492	3	be	be	AUX
iajs-1013	492	4	a	a	DET
iajs-1013	492	5	finitely	finitely	ADV
iajs-1013	492	6	generated	generate	VERB
iajs-1013	492	7	submodule	submodule	NOUN
iajs-1013	492	8	of	of	ADP
iajs-1013	492	9	m.	m.	NOUN
iajs-1013	492	10	then	then	ADV
iajs-1013	492	11	a	a	PRON
iajs-1013	492	12	is	be	AUX
iajs-1013	492	13	n	n	CCONJ
iajs-1013	492	14	-	-	PUNCT
iajs-1013	492	15	quasi	quasi	NOUN
iajs-1013	492	16	-	-	NOUN
iajs-1013	492	17	tight	tight	ADJ
iajs-1013	492	18	for	for	ADP
iajs-1013	492	19	every	every	DET
iajs-1013	492	20	finitely	finitely	ADV
iajs-1013	492	21	generated	generate	VERB
iajs-1013	492	22	r	r	NOUN
iajs-1013	492	23	-	-	PUNCT
iajs-1013	492	24	module	module	NOUN
iajs-1013	492	25	n.	n.	NOUN
iajs-1013	492	26	therefore	therefore	ADV
iajs-1013	492	27	m	m	VERB
iajs-1013	492	28	is	be	AUX
iajs-1013	492	29	a	a	DET
iajs-1013	492	30	-	-	PUNCT
iajs-1013	492	31	quasi	quasi	NOUN
iajs-1013	492	32	-	-	NOUN
iajs-1013	492	33	tight	tight	ADJ
iajs-1013	492	34	and	and	CCONJ
iajs-1013	492	35	according	accord	VERB
iajs-1013	492	36	to	to	ADP
iajs-1013	492	37	theorem	theorem	NOUN
iajs-1013	492	38	4.2	4.2	NUM
iajs-1013	492	39	.	.	PUNCT
iajs-1013	493	1	we	we	PRON
iajs-1013	493	2	get	get	VERB
iajs-1013	493	3	that	that	PRON
iajs-1013	493	4	for	for	ADP
iajs-1013	493	5	each	each	DET
iajs-1013	493	6	submodule	submodule	PROPN
iajs-1013	493	7	b	b	PROPN
iajs-1013	493	8	of	of	ADP
iajs-1013	493	9	a	a	DET
iajs-1013	493	10	such	such	ADJ
iajs-1013	493	11	that	that	SCONJ
iajs-1013	493	12	a	a	DET
iajs-1013	493	13	/	/	SYM
iajs-1013	493	14	b	b	NOUN
iajs-1013	493	15	embeds	embed	NOUN
iajs-1013	493	16	in	in	ADP
iajs-1013	493	17	m	m	PROPN
iajs-1013	493	18	is	be	AUX
iajs-1013	493	19	compressible	compressible	ADJ
iajs-1013	493	20	.	.	PUNCT
iajs-1013	494	1	but	but	CCONJ
iajs-1013	494	2	a	a	PRON
iajs-1013	494	3	is	be	AUX
iajs-1013	494	4	finitely	finitely	ADV
iajs-1013	494	5	generated	generate	VERB
iajs-1013	494	6	implies	imply	VERB
iajs-1013	494	7	that	that	SCONJ
iajs-1013	494	8	a	a	DET
iajs-1013	494	9	/	/	SYM
iajs-1013	494	10	b	b	NOUN
iajs-1013	494	11	is	be	AUX
iajs-1013	494	12	also	also	ADV
iajs-1013	494	13	finitely	finitely	ADV
iajs-1013	494	14	generated	generate	VERB
iajs-1013	494	15	.	.	PUNCT
iajs-1013	495	1	hence	hence	ADV
iajs-1013	495	2	every	every	DET
iajs-1013	495	3	finitely	finitely	ADV
iajs-1013	495	4	generated	generate	VERB
iajs-1013	495	5	submodule	submodule	NOUN
iajs-1013	495	6	of	of	ADP
iajs-1013	495	7	m	m	PROPN
iajs-1013	495	8	is	be	AUX
iajs-1013	495	9	compressible	compressible	ADJ
iajs-1013	495	10	.	.	PUNCT
iajs-1013	496	1	conversely	conversely	ADV
iajs-1013	496	2	,	,	PUNCT
iajs-1013	496	3	assume	assume	VERB
iajs-1013	496	4	that	that	SCONJ
iajs-1013	496	5	every	every	DET
iajs-1013	496	6	finitely	finitely	ADV
iajs-1013	496	7	generated	generate	VERB
iajs-1013	496	8	submodule	submodule	NOUN
iajs-1013	496	9	of	of	ADP
iajs-1013	496	10	m	m	PROPN
iajs-1013	496	11	is	be	AUX
iajs-1013	496	12	compressible	compressible	ADJ
iajs-1013	496	13	.	.	PUNCT
iajs-1013	497	1	to	to	PART
iajs-1013	497	2	prove	prove	VERB
iajs-1013	497	3	that	that	SCONJ
iajs-1013	497	4	every	every	DET
iajs-1013	497	5	submodule	submodule	NOUN
iajs-1013	497	6	of	of	ADP
iajs-1013	497	7	m	m	PROPN
iajs-1013	497	8	is	be	AUX
iajs-1013	497	9	quasi	quasi	ADJ
iajs-1013	497	10	-	-	ADJ
iajs-1013	497	11	tight	tight	ADJ
iajs-1013	497	12	.	.	PUNCT
iajs-1013	498	1	let	let	VERB
iajs-1013	498	2	a	a	PRON
iajs-1013	498	3	be	be	AUX
iajs-1013	498	4	a	a	DET
iajs-1013	498	5	submodule	submodule	NOUN
iajs-1013	498	6	of	of	ADP
iajs-1013	498	7	m	m	PRON
iajs-1013	498	8	and	and	CCONJ
iajs-1013	498	9	let	let	VERB
iajs-1013	498	10	n	n	PRON
iajs-1013	498	11	be	be	AUX
iajs-1013	498	12	a	a	DET
iajs-1013	498	13	finitely	finitely	ADV
iajs-1013	498	14	generated	generate	VERB
iajs-1013	498	15	r	r	NOUN
iajs-1013	498	16	-	-	PUNCT
iajs-1013	498	17	module	module	NOUN
iajs-1013	498	18	.	.	PUNCT
iajs-1013	499	1	let	let	VERB
iajs-1013	499	2	k	k	PRON
iajs-1013	499	3	be	be	AUX
iajs-1013	499	4	a	a	DET
iajs-1013	499	5	submodule	submodule	NOUN
iajs-1013	499	6	of	of	ADP
iajs-1013	499	7	n	n	PRON
iajs-1013	499	8	such	such	ADJ
iajs-1013	499	9	that	that	SCONJ
iajs-1013	499	10	n	n	PROPN
iajs-1013	499	11	/	/	SYM
iajs-1013	499	12	k	k	PROPN
iajs-1013	499	13	embeds	embed	VERB
iajs-1013	499	14	in	in	ADP
iajs-1013	499	15			PROPN
iajs-1013	499	16	.	.	PUNCT
iajs-1013	500	1	but	but	CCONJ
iajs-1013	500	2	n	n	CCONJ
iajs-1013	500	3	/	/	SYM
iajs-1013	500	4	k	k	PROPN
iajs-1013	500	5	is	be	AUX
iajs-1013	500	6	a	a	DET
iajs-1013	500	7	finitely	finitely	ADV
iajs-1013	500	8	generated	generate	VERB
iajs-1013	500	9	r	r	NOUN
iajs-1013	500	10	-	-	PUNCT
iajs-1013	500	11	module	module	NOUN
iajs-1013	500	12	which	which	PRON
iajs-1013	500	13	embeds	embed	VERB
iajs-1013	500	14	in	in	ADP
iajs-1013	500	15	m	m	PROPN
iajs-1013	500	16	,	,	PUNCT
iajs-1013	500	17	so	so	ADV
iajs-1013	500	18	by	by	ADP
iajs-1013	500	19	hypothesis	hypothesis	NOUN
iajs-1013	500	20	,	,	PUNCT
iajs-1013	500	21	n	n	PROPN
iajs-1013	500	22	/	/	SYM
iajs-1013	500	23	k	k	PROPN
iajs-1013	500	24	is	be	AUX
iajs-1013	500	25	compressible	compressible	ADJ
iajs-1013	500	26	.	.	PUNCT
iajs-1013	501	1	therefore	therefore	ADV
iajs-1013	501	2	a	a	PRON
iajs-1013	501	3	is	be	AUX
iajs-1013	501	4	n	n	CCONJ
iajs-1013	501	5	-	-	PUNCT
iajs-1013	501	6	quasi	quasi	NOUN
iajs-1013	501	7	-	-	NOUN
iajs-1013	501	8	tight	tight	ADJ
iajs-1013	501	9	for	for	ADP
iajs-1013	501	10	each	each	DET
iajs-1013	501	11	finitely	finitely	ADV
iajs-1013	501	12	generated	generate	VERB
iajs-1013	501	13	r	r	NOUN
iajs-1013	501	14	-	-	PUNCT
iajs-1013	501	15	module	module	NOUN
iajs-1013	501	16	n	n	NOUN
iajs-1013	501	17	(	(	PUNCT
iajs-1013	501	18	by	by	ADP
iajs-1013	501	19	theorem	theorem	NOUN
iajs-1013	501	20	4.2	4.2	NUM
iajs-1013	501	21	)	)	PUNCT
iajs-1013	501	22	.	.	PUNCT
iajs-1013	502	1	hence	hence	ADV
iajs-1013	502	2	a	a	PRON
iajs-1013	502	3	is	be	AUX
iajs-1013	502	4	aquasi	aquasi	NOUN
iajs-1013	502	5	-	-	PUNCT
iajs-1013	502	6	tight	tight	PROPN
iajs-1013	502	7	.	.	PUNCT
iajs-1013	503	1	4.4	4.4	NUM
iajs-1013	503	2	corollary	corollary	NOUN
iajs-1013	503	3	let	let	VERB
iajs-1013	503	4	m	m	PRON
iajs-1013	503	5	be	be	AUX
iajs-1013	503	6	a	a	DET
iajs-1013	503	7	quasi	quasi	ADJ
iajs-1013	503	8	-	-	ADJ
iajs-1013	503	9	injective	injective	ADJ
iajs-1013	503	10	r	r	NOUN
iajs-1013	503	11	-	-	PUNCT
iajs-1013	503	12	module	module	NOUN
iajs-1013	503	13	.	.	PUNCT
iajs-1013	504	1	then	then	ADV
iajs-1013	504	2	every	every	DET
iajs-1013	504	3	submodule	submodule	NOUN
iajs-1013	504	4	of	of	ADP
iajs-1013	504	5	m	m	PROPN
iajs-1013	504	6	is	be	AUX
iajs-1013	504	7	weakly	weakly	ADJ
iajs-1013	504	8	r	r	NOUN
iajs-1013	504	9	-	-	PUNCT
iajs-1013	504	10	quasiinjective	quasiinjective	NOUN
iajs-1013	504	11	if	if	SCONJ
iajs-1013	505	1	and	and	CCONJ
iajs-1013	505	2	only	only	ADV
iajs-1013	505	3	if	if	SCONJ
iajs-1013	505	4	every	every	DET
iajs-1013	505	5	cyclic	cyclic	ADJ
iajs-1013	505	6	submodule	submodule	NOUN
iajs-1013	505	7	of	of	ADP
iajs-1013	505	8	m	m	PROPN
iajs-1013	505	9	is	be	AUX
iajs-1013	505	10	compressible	compressible	ADJ
iajs-1013	505	11	.	.	PUNCT
iajs-1013	506	1	proof	proof	NOUN
iajs-1013	506	2	:	:	PUNCT
iajs-1013	506	3	assume	assume	VERB
iajs-1013	506	4	that	that	SCONJ
iajs-1013	506	5	every	every	DET
iajs-1013	506	6	submodule	submodule	NOUN
iajs-1013	506	7	of	of	ADP
iajs-1013	506	8	m	m	PROPN
iajs-1013	506	9	is	be	AUX
iajs-1013	506	10	weakly	weakly	ADJ
iajs-1013	506	11	r	r	NOUN
iajs-1013	506	12	-	-	PUNCT
iajs-1013	506	13	quasi	quasi	NOUN
iajs-1013	506	14	-	-	ADJ
iajs-1013	506	15	injective	injective	ADJ
iajs-1013	506	16	.	.	PUNCT
iajs-1013	507	1	then	then	ADV
iajs-1013	507	2	every	every	DET
iajs-1013	507	3	submodule	submodule	NOUN
iajs-1013	507	4	of	of	ADP
iajs-1013	507	5	m	m	PROPN
iajs-1013	507	6	is	be	AUX
iajs-1013	507	7	r	r	NOUN
iajs-1013	507	8	-	-	PUNCT
iajs-1013	507	9	quasi	quasi	NOUN
iajs-1013	507	10	-	-	NOUN
iajs-1013	507	11	tight	tight	ADJ
iajs-1013	507	12	(	(	PUNCT
iajs-1013	507	13	by	by	ADP
iajs-1013	507	14	corollary	corollary	ADJ
iajs-1013	507	15	3.5	3.5	NUM
iajs-1013	507	16	)	)	PUNCT
iajs-1013	507	17	and	and	CCONJ
iajs-1013	507	18	according	accord	VERB
iajs-1013	507	19	to	to	ADP
iajs-1013	507	20	theorem	theorem	ADJ
iajs-1013	507	21	4.2	4.2	NUM
iajs-1013	507	22	,	,	PUNCT
iajs-1013	507	23	we	we	PRON
iajs-1013	507	24	get	get	VERB
iajs-1013	507	25	that	that	SCONJ
iajs-1013	507	26	every	every	DET
iajs-1013	507	27	quotient	quotient	NOUN
iajs-1013	507	28	r	r	NOUN
iajs-1013	507	29	/	/	PUNCT
iajs-1013	507	30	i	i	NOUN
iajs-1013	507	31	of	of	ADP
iajs-1013	507	32	r	r	NOUN
iajs-1013	507	33	(	(	PUNCT
iajs-1013	507	34	with	with	ADP
iajs-1013	507	35	i	i	PRON
iajs-1013	507	36	is	be	AUX
iajs-1013	507	37	an	an	DET
iajs-1013	507	38	ideal	ideal	NOUN
iajs-1013	507	39	of	of	ADP
iajs-1013	507	40	r	r	NOUN
iajs-1013	507	41	)	)	PUNCT
iajs-1013	507	42	which	which	PRON
iajs-1013	507	43	embeds	embed	VERB
iajs-1013	507	44	in	in	ADP
iajs-1013	507	45	m	m	PROPN
iajs-1013	507	46	is	be	AUX
iajs-1013	507	47	compressible	compressible	ADJ
iajs-1013	507	48	.	.	PUNCT
iajs-1013	508	1	now	now	ADV
iajs-1013	508	2	,	,	PUNCT
iajs-1013	508	3	let	let	VERB
iajs-1013	508	4	a	a	PRON
iajs-1013	508	5	=	=	X
iajs-1013	508	6	(	(	PUNCT
iajs-1013	508	7	a	a	X
iajs-1013	508	8	)	)	PUNCT
iajs-1013	508	9	be	be	AUX
iajs-1013	508	10	a	a	DET
iajs-1013	508	11	cyclic	cyclic	ADJ
iajs-1013	508	12	submodule	submodule	NOUN
iajs-1013	508	13	of	of	ADP
iajs-1013	508	14	m	m	PROPN
iajs-1013	508	15	for	for	ADP
iajs-1013	508	16	some	some	DET
iajs-1013	508	17	a	a	DET
iajs-1013	508	18			NOUN
iajs-1013	508	19	m.	m.	NOUN
iajs-1013	508	20	then	then	ADV
iajs-1013	508	21	a	a	DET
iajs-1013	508	22	≈	≈	PROPN
iajs-1013	508	23	r	r	NOUN
iajs-1013	508	24	/	/	SYM
iajs-1013	508	25	annr(a	annr(a	NOUN
iajs-1013	508	26	)	)	PUNCT
iajs-1013	508	27	.	.	PUNCT
iajs-1013	509	1	so	so	ADV
iajs-1013	509	2	,	,	PUNCT
iajs-1013	509	3	r	r	NOUN
iajs-1013	509	4	/	/	SYM
iajs-1013	509	5	annr(a	annr(a	NOUN
iajs-1013	509	6	)	)	PUNCT
iajs-1013	509	7	is	be	AUX
iajs-1013	509	8	compressible	compressible	ADJ
iajs-1013	509	9	.	.	PUNCT
iajs-1013	510	1	hence	hence	ADV
iajs-1013	510	2	a	a	PRON
iajs-1013	510	3	is	be	AUX
iajs-1013	510	4	compressible	compressible	ADJ
iajs-1013	510	5	.	.	PUNCT
iajs-1013	511	1	conversely	conversely	ADV
iajs-1013	511	2	,	,	PUNCT
iajs-1013	511	3	assume	assume	VERB
iajs-1013	511	4	that	that	SCONJ
iajs-1013	511	5	every	every	DET
iajs-1013	511	6	cyclic	cyclic	ADJ
iajs-1013	511	7	submodule	submodule	NOUN
iajs-1013	511	8	of	of	ADP
iajs-1013	511	9	m	m	PROPN
iajs-1013	511	10	is	be	AUX
iajs-1013	511	11	compressible	compressible	ADJ
iajs-1013	511	12	.	.	PUNCT
iajs-1013	512	1	because	because	SCONJ
iajs-1013	512	2	of	of	ADP
iajs-1013	512	3	the	the	DET
iajs-1013	512	4	fact	fact	NOUN
iajs-1013	512	5	that	that	SCONJ
iajs-1013	512	6	every	every	DET
iajs-1013	512	7	cyclic	cyclic	ADJ
iajs-1013	512	8	submodule	submodule	NOUN
iajs-1013	512	9	of	of	ADP
iajs-1013	512	10	m	m	PROPN
iajs-1013	512	11	can	can	AUX
iajs-1013	512	12	be	be	AUX
iajs-1013	512	13	written	write	VERB
iajs-1013	512	14	as	as	ADP
iajs-1013	512	15	a	a	DET
iajs-1013	512	16	quotient	quotient	NOUN
iajs-1013	512	17	r	r	NOUN
iajs-1013	512	18	/	/	PUNCT
iajs-1013	512	19	i	i	PRON
iajs-1013	512	20	for	for	ADP
iajs-1013	512	21	some	some	DET
iajs-1013	512	22	ideal	ideal	ADJ
iajs-1013	512	23	i	i	PRON
iajs-1013	512	24	of	of	ADP
iajs-1013	512	25	r	r	NOUN
iajs-1013	512	26	,	,	PUNCT
iajs-1013	512	27	and	and	CCONJ
iajs-1013	512	28	hence	hence	ADV
iajs-1013	512	29	for	for	ADP
iajs-1013	512	30	each	each	DET
iajs-1013	512	31	ideal	ideal	ADJ
iajs-1013	512	32	i	i	PRON
iajs-1013	512	33	of	of	ADP
iajs-1013	512	34	r	r	NOUN
iajs-1013	512	35	,	,	PUNCT
iajs-1013	512	36	if	if	SCONJ
iajs-1013	512	37	r	r	NOUN
iajs-1013	512	38	/	/	SYM
iajs-1013	512	39	i	i	PRON
iajs-1013	512	40	embeds	embed	VERB
iajs-1013	512	41	in	in	ADP
iajs-1013	512	42	m	m	PROPN
iajs-1013	512	43	is	be	AUX
iajs-1013	512	44	compressible	compressible	ADJ
iajs-1013	512	45	,	,	PUNCT
iajs-1013	512	46	therefore	therefore	ADV
iajs-1013	512	47	every	every	DET
iajs-1013	512	48	cyclic	cyclic	ADJ
iajs-1013	512	49	submodule	submodule	NOUN
iajs-1013	512	50	of	of	ADP
iajs-1013	512	51	m	m	PROPN
iajs-1013	512	52	is	be	AUX
iajs-1013	512	53	r	r	NOUN
iajs-1013	512	54	-	-	PUNCT
iajs-1013	512	55	quasi	quasi	NOUN
iajs-1013	512	56	-	-	NOUN
iajs-1013	512	57	tight	tight	ADJ
iajs-1013	512	58	(	(	PUNCT
iajs-1013	512	59	by	by	ADP
iajs-1013	512	60	theorem	theorem	NOUN
iajs-1013	512	61	4.2	4.2	NUM
iajs-1013	512	62	)	)	PUNCT
iajs-1013	512	63	.	.	PUNCT
iajs-1013	513	1	to	to	PART
iajs-1013	513	2	prove	prove	VERB
iajs-1013	513	3	every	every	DET
iajs-1013	513	4	submodule	submodule	NOUN
iajs-1013	513	5	of	of	ADP
iajs-1013	513	6	m	m	PROPN
iajs-1013	513	7	is	be	AUX
iajs-1013	513	8	weakly	weakly	ADJ
iajs-1013	513	9	r	r	NOUN
iajs-1013	513	10	-	-	PUNCT
iajs-1013	513	11	quasi	quasi	ADJ
iajs-1013	513	12	ibn	ibn	PROPN
iajs-1013	513	13	alhaitham	alhaitham	PROPN
iajs-1013	513	14	j.	j.	PROPN
iajs-1013	513	15	for	for	ADP
iajs-1013	513	16	pure	pure	ADJ
iajs-1013	513	17	&	&	CCONJ
iajs-1013	513	18	appl	appl	PROPN
iajs-1013	513	19	.	.	PUNCT
iajs-1013	514	1	sci	sci	PROPN
iajs-1013	514	2	.	.	PUNCT
iajs-1013	515	1	vol.23	vol.23	PROPN
iajs-1013	515	2	(	(	PUNCT
iajs-1013	515	3	1	1	NUM
iajs-1013	515	4	)	)	PUNCT
iajs-1013	515	5	2010	2010	NUM
iajs-1013	515	6	injective	injective	NOUN
iajs-1013	515	7	.	.	PUNCT
iajs-1013	516	1	let	let	VERB
iajs-1013	516	2	a	a	PRON
iajs-1013	516	3	be	be	AUX
iajs-1013	516	4	a	a	DET
iajs-1013	516	5	submodule	submodule	NOUN
iajs-1013	516	6	of	of	ADP
iajs-1013	516	7	m	m	PRON
iajs-1013	516	8	and	and	CCONJ
iajs-1013	516	9	let	let	VERB
iajs-1013	516	10	x	x	PUNCT
iajs-1013	516	11			PROPN
iajs-1013	516	12			PROPN
iajs-1013	516	13	.	.	PUNCT
iajs-1013	517	1	then	then	ADV
iajs-1013	517	2	(	(	PUNCT
iajs-1013	517	3	x	x	X
iajs-1013	517	4	)	)	PUNCT
iajs-1013	517	5	≈	≈	NOUN
iajs-1013	517	6	r	r	NOUN
iajs-1013	517	7	/	/	SYM
iajs-1013	517	8	annr(x	annr(x	NOUN
iajs-1013	517	9	)	)	PUNCT
iajs-1013	517	10			PROPN
iajs-1013	517	11			PROPN
iajs-1013	517	12	.	.	PUNCT
iajs-1013	518	1	but	but	CCONJ
iajs-1013	518	2	every	every	DET
iajs-1013	518	3	cyclic	cyclic	ADJ
iajs-1013	518	4	submodule	submodule	NOUN
iajs-1013	518	5	of	of	ADP
iajs-1013	518	6	m	m	PROPN
iajs-1013	518	7	is	be	AUX
iajs-1013	518	8	r	r	NOUN
iajs-1013	518	9	-	-	PUNCT
iajs-1013	518	10	quasi	quasi	NOUN
iajs-1013	518	11	-	-	ADJ
iajs-1013	518	12	tight	tight	ADJ
iajs-1013	518	13	,	,	PUNCT
iajs-1013	518	14	hence	hence	ADV
iajs-1013	518	15	(	(	PUNCT
iajs-1013	518	16	x	x	X
iajs-1013	518	17	)	)	PUNCT
iajs-1013	518	18			PROPN
iajs-1013	518	19	a.	a.	NOUN
iajs-1013	518	20	we	we	PRON
iajs-1013	518	21	take	take	VERB
iajs-1013	518	22	x	x	PUNCT
iajs-1013	518	23	=	=	PRON
iajs-1013	518	24	a	a	PRON
iajs-1013	518	25	implies	imply	VERB
iajs-1013	518	26	that	that	SCONJ
iajs-1013	518	27	x	x	SYM
iajs-1013	518	28			NOUN
iajs-1013	518	29	x	x	X
iajs-1013	518	30	=	=	SYM
iajs-1013	518	31	a.	a.	NOUN
iajs-1013	518	32	thus	thus	ADV
iajs-1013	518	33	a	a	PRON
iajs-1013	518	34	is	be	AUX
iajs-1013	518	35	weakly	weakly	ADJ
iajs-1013	518	36	r	r	NOUN
iajs-1013	518	37	-	-	PUNCT
iajs-1013	518	38	quasi	quasi	NOUN
iajs-1013	518	39	-	-	ADJ
iajs-1013	518	40	injective	injective	ADJ
iajs-1013	518	41	(	(	PUNCT
iajs-1013	518	42	by	by	ADP
iajs-1013	518	43	theorem	theorem	NOUN
iajs-1013	518	44	2.8	2.8	NUM
iajs-1013	518	45	)	)	PUNCT
iajs-1013	518	46	.	.	PUNCT
iajs-1013	519	1	4.5	4.5	NUM
iajs-1013	519	2	corollary	corollary	NOUN
iajs-1013	519	3	let	let	VERB
iajs-1013	519	4	n	n	PRON
iajs-1013	519	5	be	be	AUX
iajs-1013	519	6	an	an	DET
iajs-1013	519	7	r	r	NOUN
iajs-1013	519	8	-	-	PUNCT
iajs-1013	519	9	module	module	NOUN
iajs-1013	519	10	.	.	PUNCT
iajs-1013	520	1	if	if	SCONJ
iajs-1013	520	2	every	every	DET
iajs-1013	520	3	r	r	NOUN
iajs-1013	520	4	-	-	PUNCT
iajs-1013	520	5	module	module	NOUN
iajs-1013	520	6	is	be	AUX
iajs-1013	520	7	n	n	CCONJ
iajs-1013	520	8	-	-	PUNCT
iajs-1013	520	9	quasi	quasi	NOUN
iajs-1013	520	10	-	-	ADJ
iajs-1013	520	11	tight	tight	ADJ
iajs-1013	520	12	,	,	PUNCT
iajs-1013	520	13	then	then	ADV
iajs-1013	520	14	n	n	CCONJ
iajs-1013	520	15	/	/	SYM
iajs-1013	520	16	k	k	PROPN
iajs-1013	520	17	is	be	AUX
iajs-1013	520	18	compressible	compressible	ADJ
iajs-1013	520	19	for	for	ADP
iajs-1013	520	20	every	every	DET
iajs-1013	520	21	submodule	submodule	NOUN
iajs-1013	520	22	k	k	PROPN
iajs-1013	520	23	of	of	ADP
iajs-1013	520	24	n.	n.	PROPN
iajs-1013	520	25	proof	proof	NOUN
iajs-1013	520	26	:	:	PUNCT
iajs-1013	520	27	assume	assume	VERB
iajs-1013	520	28	that	that	SCONJ
iajs-1013	520	29	every	every	DET
iajs-1013	520	30	r	r	NOUN
iajs-1013	520	31	-	-	PUNCT
iajs-1013	520	32	module	module	NOUN
iajs-1013	520	33	is	be	AUX
iajs-1013	520	34	n	n	CCONJ
iajs-1013	520	35	-	-	PUNCT
iajs-1013	520	36	quasi	quasi	NOUN
iajs-1013	520	37	-	-	ADJ
iajs-1013	520	38	tight	tight	ADJ
iajs-1013	520	39	.	.	PUNCT
iajs-1013	521	1	let	let	VERB
iajs-1013	521	2	k	k	PRON
iajs-1013	521	3	be	be	AUX
iajs-1013	521	4	a	a	DET
iajs-1013	521	5	submodule	submodule	NOUN
iajs-1013	521	6	of	of	ADP
iajs-1013	521	7	n	n	NUM
iajs-1013	521	8	and	and	CCONJ
iajs-1013	521	9	let	let	VERB
iajs-1013	521	10	a	a	DET
iajs-1013	521	11	=	=	SYM
iajs-1013	521	12	/	/	SYM
iajs-1013	521	13			PROPN
iajs-1013	521	14	.	.	PUNCT
iajs-1013	522	1	by	by	ADP
iajs-1013	522	2	hypothesis	hypothesis	NOUN
iajs-1013	522	3	,	,	PUNCT
iajs-1013	522	4	we	we	PRON
iajs-1013	522	5	get	get	VERB
iajs-1013	522	6	that	that	SCONJ
iajs-1013	522	7	every	every	DET
iajs-1013	522	8	submodule	submodule	NOUN
iajs-1013	522	9	of	of	ADP
iajs-1013	522	10	a	a	DET
iajs-1013	522	11	is	be	AUX
iajs-1013	522	12	n	n	CCONJ
iajs-1013	522	13	-	-	PUNCT
iajs-1013	522	14	quasi	quasi	NOUN
iajs-1013	522	15	-	-	ADJ
iajs-1013	522	16	tight	tight	ADJ
iajs-1013	522	17	,	,	PUNCT
iajs-1013	522	18	and	and	CCONJ
iajs-1013	522	19	since	since	SCONJ
iajs-1013	522	20	a	a	PRON
iajs-1013	522	21	is	be	AUX
iajs-1013	522	22	a	a	DET
iajs-1013	522	23	quasi	quasi	ADJ
iajs-1013	522	24	-	-	ADJ
iajs-1013	522	25	injective	injective	ADJ
iajs-1013	522	26	r	r	NOUN
iajs-1013	522	27	-	-	PUNCT
iajs-1013	522	28	module	module	NOUN
iajs-1013	522	29	,	,	PUNCT
iajs-1013	522	30	implies	imply	VERB
iajs-1013	522	31	that	that	SCONJ
iajs-1013	522	32	n	n	PROPN
iajs-1013	522	33	/	/	SYM
iajs-1013	522	34	k	k	PROPN
iajs-1013	522	35	is	be	AUX
iajs-1013	522	36	compressible	compressible	ADJ
iajs-1013	522	37	for	for	ADP
iajs-1013	522	38	every	every	DET
iajs-1013	522	39	submodule	submodule	NOUN
iajs-1013	522	40	k	k	PROPN
iajs-1013	522	41	of	of	ADP
iajs-1013	522	42	n	n	PROPN
iajs-1013	522	43	(	(	PUNCT
iajs-1013	522	44	by	by	ADP
iajs-1013	522	45	theorem	theorem	NOUN
iajs-1013	522	46	4.2	4.2	NUM
iajs-1013	522	47	)	)	PUNCT
iajs-1013	522	48	.	.	PUNCT
iajs-1013	523	1	section	section	NOUN
iajs-1013	523	2	five	five	NUM
iajs-1013	523	3	:	:	PUNCT
iajs-1013	523	4	weakly	weakly	ADJ
iajs-1013	523	5	quasi	quasi	ADJ
iajs-1013	523	6	-	-	ADJ
iajs-1013	523	7	injective	injective	ADJ
iajs-1013	523	8	modules	module	NOUN
iajs-1013	523	9	in	in	ADP
iajs-1013	523	10	this	this	DET
iajs-1013	523	11	section	section	NOUN
iajs-1013	523	12	,	,	PUNCT
iajs-1013	523	13	we	we	PRON
iajs-1013	523	14	shall	shall	AUX
iajs-1013	523	15	concentrate	concentrate	VERB
iajs-1013	523	16	on	on	ADP
iajs-1013	523	17	considering	consider	VERB
iajs-1013	523	18	those	those	DET
iajs-1013	523	19	modules	module	NOUN
iajs-1013	523	20	which	which	PRON
iajs-1013	523	21	are	be	AUX
iajs-1013	523	22	weakly	weakly	ADJ
iajs-1013	523	23	quasi	quasi	ADJ
iajs-1013	523	24	-	-	ADJ
iajs-1013	523	25	injective	injective	ADJ
iajs-1013	523	26	relative	relative	NOUN
iajs-1013	523	27	to	to	ADP
iajs-1013	523	28	each	each	DET
iajs-1013	523	29	finitely	finitely	ADV
iajs-1013	523	30	generated	generate	VERB
iajs-1013	523	31	module	module	NOUN
iajs-1013	523	32	;	;	PUNCT
iajs-1013	523	33	we	we	PRON
iajs-1013	523	34	shall	shall	AUX
iajs-1013	523	35	refer	refer	VERB
iajs-1013	523	36	to	to	ADP
iajs-1013	523	37	any	any	DET
iajs-1013	523	38	such	such	ADJ
iajs-1013	523	39	module	module	NOUN
iajs-1013	523	40	as	as	ADP
iajs-1013	523	41	being	be	AUX
iajs-1013	523	42	weakly	weakly	ADJ
iajs-1013	523	43	quasi	quasi	ADJ
iajs-1013	523	44	-	-	ADJ
iajs-1013	523	45	injective	injective	ADJ
iajs-1013	523	46	module	module	NOUN
iajs-1013	523	47	.	.	PUNCT
iajs-1013	524	1	5.1	5.1	NUM
iajs-1013	524	2	definition	definition	NOUN
iajs-1013	524	3	an	an	DET
iajs-1013	524	4	r	r	NOUN
iajs-1013	524	5	-	-	PUNCT
iajs-1013	524	6	module	module	NOUN
iajs-1013	524	7	m	m	NOUN
iajs-1013	524	8	is	be	AUX
iajs-1013	524	9	called	call	VERB
iajs-1013	524	10	weakly	weakly	ADJ
iajs-1013	524	11	quasi	quasi	ADJ
iajs-1013	524	12	-	-	ADJ
iajs-1013	524	13	injective	injective	ADJ
iajs-1013	524	14	,	,	PUNCT
iajs-1013	524	15	if	if	SCONJ
iajs-1013	524	16	m	m	NOUN
iajs-1013	524	17	is	be	AUX
iajs-1013	524	18	weakly	weakly	ADJ
iajs-1013	524	19	n	n	CCONJ
iajs-1013	524	20	-	-	PUNCT
iajs-1013	524	21	quasi	quasi	NOUN
iajs-1013	524	22	-	-	ADJ
iajs-1013	524	23	injective	injective	ADJ
iajs-1013	524	24	for	for	ADP
iajs-1013	524	25	every	every	DET
iajs-1013	524	26	finitely	finitely	ADV
iajs-1013	524	27	generated	generate	VERB
iajs-1013	524	28	r	r	NOUN
iajs-1013	524	29	-	-	PUNCT
iajs-1013	524	30	module	module	NOUN
iajs-1013	524	31	n.	n.	NOUN
iajs-1013	524	32	equivalently	equivalently	ADV
iajs-1013	524	33	,	,	PUNCT
iajs-1013	524	34	m	m	VERB
iajs-1013	524	35	is	be	AUX
iajs-1013	524	36	weakly	weakly	ADJ
iajs-1013	524	37	quasi	quasi	ADJ
iajs-1013	524	38	-	-	ADJ
iajs-1013	524	39	injective	injective	ADJ
iajs-1013	524	40	if	if	SCONJ
iajs-1013	524	41	and	and	CCONJ
iajs-1013	524	42	only	only	ADV
iajs-1013	524	43	if	if	SCONJ
iajs-1013	524	44	for	for	ADP
iajs-1013	524	45	each	each	DET
iajs-1013	524	46	finitely	finitely	ADV
iajs-1013	524	47	generated	generate	VERB
iajs-1013	524	48	r	r	NOUN
iajs-1013	524	49	-	-	PUNCT
iajs-1013	524	50	module	module	NOUN
iajs-1013	524	51	n	n	NOUN
iajs-1013	524	52	and	and	CCONJ
iajs-1013	524	53	for	for	ADP
iajs-1013	524	54	each	each	DET
iajs-1013	524	55	f	f	PROPN
iajs-1013	524	56			PROPN
iajs-1013	524	57	hom(n,	hom(n,	NOUN
iajs-1013	524	58	)	)	PUNCT
iajs-1013	524	59	,	,	PUNCT
iajs-1013	524	60	there	there	PRON
iajs-1013	524	61	exists	exist	VERB
iajs-1013	524	62	a	a	DET
iajs-1013	524	63	submodule	submodule	NOUN
iajs-1013	524	64	x	x	PUNCT
iajs-1013	524	65	of	of	ADP
iajs-1013	524	66	m	m	PRON
iajs-1013	524	67	such	such	ADJ
iajs-1013	524	68	that	that	SCONJ
iajs-1013	524	69	f	f	PROPN
iajs-1013	524	70	(	(	PUNCT
iajs-1013	524	71	n	n	CCONJ
iajs-1013	524	72	)	)	PUNCT
iajs-1013	524	73			PROPN
iajs-1013	524	74	x	x	X
iajs-1013	524	75	≈	≈	PROPN
iajs-1013	524	76	m.	m.	NOUN
iajs-1013	524	77	5.2	5.2	NUM
iajs-1013	524	78	remarks	remark	VERB
iajs-1013	524	79	1	1	NUM
iajs-1013	524	80	.	.	PUNCT
iajs-1013	525	1	a	a	DET
iajs-1013	525	2	ring	ring	NOUN
iajs-1013	525	3	r	r	NOUN
iajs-1013	525	4	is	be	AUX
iajs-1013	525	5	called	call	VERB
iajs-1013	525	6	weakly	weakly	ADJ
iajs-1013	525	7	quasi	quasi	ADJ
iajs-1013	525	8	-	-	ADJ
iajs-1013	525	9	injective	injective	ADJ
iajs-1013	525	10	if	if	SCONJ
iajs-1013	525	11	and	and	CCONJ
iajs-1013	525	12	only	only	ADV
iajs-1013	525	13	if	if	SCONJ
iajs-1013	525	14	the	the	DET
iajs-1013	525	15	r	r	NOUN
iajs-1013	525	16	-	-	PUNCT
iajs-1013	525	17	module	module	NOUN
iajs-1013	525	18	r	r	NOUN
iajs-1013	525	19	is	be	AUX
iajs-1013	525	20	weakly	weakly	ADV
iajs-1013	525	21	quasiinjective	quasiinjective	ADJ
iajs-1013	525	22	.	.	PUNCT
iajs-1013	526	1	2	2	X
iajs-1013	526	2	.	.	X
iajs-1013	526	3	every	every	DET
iajs-1013	526	4	weakly	weakly	ADJ
iajs-1013	526	5	injective	injective	ADJ
iajs-1013	526	6	r	r	NOUN
iajs-1013	526	7	-	-	PUNCT
iajs-1013	526	8	module	module	NOUN
iajs-1013	526	9	is	be	AUX
iajs-1013	526	10	weakly	weakly	ADJ
iajs-1013	526	11	quasi	quasi	ADJ
iajs-1013	526	12	-	-	ADJ
iajs-1013	526	13	injective	injective	ADJ
iajs-1013	526	14	and	and	CCONJ
iajs-1013	526	15	the	the	DET
iajs-1013	526	16	converse	converse	NOUN
iajs-1013	526	17	is	be	AUX
iajs-1013	526	18	not	not	PART
iajs-1013	526	19	true	true	ADJ
iajs-1013	526	20	in	in	ADP
iajs-1013	526	21	general	general	ADJ
iajs-1013	526	22	,	,	PUNCT
iajs-1013	526	23	see	see	VERB
iajs-1013	526	24	example	example	NOUN
iajs-1013	527	1	1.3	1.3	NUM
iajs-1013	527	2	.	.	PUNCT
iajs-1013	528	1	5.3	5.3	NUM
iajs-1013	528	2	theorem	theorem	NOUN
iajs-1013	528	3	let	let	VERB
iajs-1013	528	4	m	m	PRON
iajs-1013	528	5	be	be	AUX
iajs-1013	528	6	an	an	DET
iajs-1013	528	7	r	r	NOUN
iajs-1013	528	8	-	-	PUNCT
iajs-1013	528	9	module	module	NOUN
iajs-1013	528	10	.	.	PUNCT
iajs-1013	529	1	then	then	ADV
iajs-1013	529	2	m	m	PROPN
iajs-1013	529	3	is	be	AUX
iajs-1013	529	4	weakly	weakly	ADJ
iajs-1013	529	5	quasi	quasi	ADJ
iajs-1013	529	6	-	-	ADJ
iajs-1013	529	7	injective	injective	ADJ
iajs-1013	529	8	if	if	SCONJ
iajs-1013	529	9	and	and	CCONJ
iajs-1013	529	10	only	only	ADV
iajs-1013	529	11	if	if	SCONJ
iajs-1013	529	12	m	m	NOUN
iajs-1013	529	13	is	be	AUX
iajs-1013	529	14	weakly	weakly	ADJ
iajs-1013	529	15	r	r	NOUN
iajs-1013	529	16	nquasi	nquasi	NOUN
iajs-1013	529	17	-	-	PUNCT
iajs-1013	529	18	injective	injective	ADJ
iajs-1013	529	19	for	for	ADP
iajs-1013	529	20	all	all	DET
iajs-1013	529	21	positive	positive	ADJ
iajs-1013	529	22	integer	integer	NOUN
iajs-1013	529	23	n.	n.	NOUN
iajs-1013	529	24	proof	proof	NOUN
iajs-1013	529	25	:	:	PUNCT
iajs-1013	529	26	the	the	DET
iajs-1013	529	27	"	"	PUNCT
iajs-1013	529	28	only	only	ADV
iajs-1013	529	29	if	if	SCONJ
iajs-1013	529	30	”	"	PUNCT
iajs-1013	529	31	part	part	NOUN
iajs-1013	529	32	is	be	AUX
iajs-1013	529	33	obvious	obvious	ADJ
iajs-1013	529	34	.	.	PUNCT
iajs-1013	530	1	to	to	PART
iajs-1013	530	2	prove	prove	VERB
iajs-1013	530	3	the	the	DET
iajs-1013	530	4	"	"	PUNCT
iajs-1013	530	5	if	if	SCONJ
iajs-1013	530	6	”	"	PUNCT
iajs-1013	530	7	part	part	NOUN
iajs-1013	530	8	.	.	PUNCT
iajs-1013	531	1	let	let	VERB
iajs-1013	531	2	n	n	PRON
iajs-1013	531	3	be	be	AUX
iajs-1013	531	4	a	a	DET
iajs-1013	531	5	finitely	finitely	ADV
iajs-1013	531	6	generated	generate	VERB
iajs-1013	531	7	r	r	NOUN
iajs-1013	531	8	-	-	PUNCT
iajs-1013	531	9	module	module	NOUN
iajs-1013	531	10	.	.	PUNCT
iajs-1013	532	1	we	we	PRON
iajs-1013	532	2	have	have	VERB
iajs-1013	532	3	to	to	PART
iajs-1013	532	4	show	show	VERB
iajs-1013	532	5	that	that	SCONJ
iajs-1013	532	6	m	m	NOUN
iajs-1013	532	7	is	be	AUX
iajs-1013	532	8	weakly	weakly	ADJ
iajs-1013	532	9	n	n	CCONJ
iajs-1013	532	10	-	-	PUNCT
iajs-1013	532	11	quasi	quasi	NOUN
iajs-1013	532	12	-	-	ADJ
iajs-1013	532	13	injective	injective	ADJ
iajs-1013	532	14	.	.	PUNCT
iajs-1013	533	1	suppose	suppose	VERB
iajs-1013	533	2	that	that	SCONJ
iajs-1013	533	3	n	n	PROPN
iajs-1013	533	4	=	=	SYM
iajs-1013	533	5	ra1	ra1	PROPN
iajs-1013	533	6	+	+	CCONJ
iajs-1013	533	7	ra2	ra2	PROPN
iajs-1013	533	8	+	+	PROPN
iajs-1013	533	9			PROPN
iajs-1013	533	10	+	+	CCONJ
iajs-1013	533	11	ran	run	VERB
iajs-1013	533	12	where	where	SCONJ
iajs-1013	533	13	ai	ai	VERB
iajs-1013	533	14			PROPN
iajs-1013	533	15	n	n	CCONJ
iajs-1013	533	16	for	for	ADP
iajs-1013	533	17	all	all	DET
iajs-1013	533	18	i	i	PRON
iajs-1013	533	19	=	=	NOUN
iajs-1013	533	20	1	1	NUM
iajs-1013	533	21	,	,	PUNCT
iajs-1013	533	22	2	2	NUM
iajs-1013	533	23	,	,	PUNCT
iajs-1013	533	24			PROPN
iajs-1013	533	25	,	,	PUNCT
iajs-1013	533	26	n.	n.	NOUN
iajs-1013	533	27	define	define	VERB
iajs-1013	533	28	f	f	NOUN
iajs-1013	533	29	:	:	PUNCT
iajs-1013	533	30	r	r	NOUN
iajs-1013	533	31	n	n	PRON
iajs-1013	533	32			NOUN
iajs-1013	533	33	n	n	PRON
iajs-1013	533	34	such	such	ADJ
iajs-1013	533	35	that	that	SCONJ
iajs-1013	533	36	f	f	PROPN
iajs-1013	533	37	(	(	PUNCT
iajs-1013	533	38	r1	r1	PROPN
iajs-1013	533	39	,	,	PUNCT
iajs-1013	533	40	r2	r2	PROPN
iajs-1013	533	41	,	,	PUNCT
iajs-1013	533	42			PROPN
iajs-1013	533	43	,	,	PUNCT
iajs-1013	533	44	rn	rn	PROPN
iajs-1013	533	45	)	)	PUNCT
iajs-1013	534	1	=	=	SYM
iajs-1013	534	2	r1	r1	NOUN
iajs-1013	534	3	a1	a1	NOUN
iajs-1013	534	4	+	+	CCONJ
iajs-1013	534	5	r2	r2	PROPN
iajs-1013	534	6	a2	a2	PROPN
iajs-1013	534	7	+	+	CCONJ
iajs-1013	534	8			PROPN
iajs-1013	534	9	+	+	CCONJ
iajs-1013	534	10	rn	rn	PROPN
iajs-1013	534	11	an	an	PRON
iajs-1013	534	12	for	for	ADP
iajs-1013	534	13	all	all	DET
iajs-1013	534	14	r1	r1	NOUN
iajs-1013	534	15	,	,	PUNCT
iajs-1013	534	16	r2	r2	PROPN
iajs-1013	534	17	,	,	PUNCT
iajs-1013	534	18			PROPN
iajs-1013	534	19	,	,	PUNCT
iajs-1013	534	20	rn	rn	PROPN
iajs-1013	534	21			PROPN
iajs-1013	534	22	r.	r.	PROPN
iajs-1013	534	23	it	it	PRON
iajs-1013	534	24	can	can	AUX
iajs-1013	534	25	be	be	AUX
iajs-1013	534	26	easily	easily	ADV
iajs-1013	534	27	checked	check	VERB
iajs-1013	534	28	that	that	SCONJ
iajs-1013	534	29	f	f	PROPN
iajs-1013	534	30	is	be	AUX
iajs-1013	534	31	well	well	ADV
iajs-1013	534	32	-	-	PUNCT
iajs-1013	534	33	defined	define	VERB
iajs-1013	534	34	epimorphism	epimorphism	NOUN
iajs-1013	534	35	.	.	PUNCT
iajs-1013	535	1	therefore	therefore	ADV
iajs-1013	535	2	,	,	PUNCT
iajs-1013	535	3	r	r	NOUN
iajs-1013	535	4	n	n	PROPN
iajs-1013	535	5	/	/	SYM
iajs-1013	535	6	ker	ker	NOUN
iajs-1013	535	7	f	f	PROPN
iajs-1013	535	8	n.	n.	NOUN
iajs-1013	535	9	but	but	CCONJ
iajs-1013	535	10	m	m	PROPN
iajs-1013	535	11	is	be	AUX
iajs-1013	535	12	weakly	weakly	ADJ
iajs-1013	535	13	rn	rn	ADJ
iajs-1013	535	14	-	-	ADJ
iajs-1013	535	15	quasi	quasi	ADJ
iajs-1013	535	16	-	-	ADJ
iajs-1013	535	17	injective	injective	ADJ
iajs-1013	535	18	,	,	PUNCT
iajs-1013	535	19	implies	imply	VERB
iajs-1013	535	20	that	that	SCONJ
iajs-1013	535	21	m	m	NOUN
iajs-1013	535	22	is	be	AUX
iajs-1013	535	23	weakly	weakly	ADJ
iajs-1013	535	24	rn	rn	PROPN
iajs-1013	535	25	/	/	SYM
iajs-1013	535	26	ker	ker	NOUN
iajs-1013	536	1	f	f	X
iajs-1013	536	2	-	-	PUNCT
iajs-1013	536	3	quasi	quasi	NOUN
iajs-1013	536	4	-	-	ADJ
iajs-1013	536	5	injective	injective	ADJ
iajs-1013	536	6	(	(	PUNCT
iajs-1013	536	7	by	by	ADP
iajs-1013	536	8	theorem	theorem	NOUN
iajs-1013	536	9	2.3	2.3	NUM
iajs-1013	536	10	)	)	PUNCT
iajs-1013	536	11	.	.	PUNCT
iajs-1013	537	1	therefore	therefore	ADV
iajs-1013	537	2	m	m	PROPN
iajs-1013	537	3	is	be	AUX
iajs-1013	537	4	weakly	weakly	ADJ
iajs-1013	537	5	n	n	CCONJ
iajs-1013	537	6	-	-	PUNCT
iajs-1013	537	7	quasi	quasi	NOUN
iajs-1013	537	8	–	–	PUNCT
iajs-1013	537	9	injective	injective	ADJ
iajs-1013	537	10	.	.	PUNCT
iajs-1013	538	1	5.4	5.4	NUM
iajs-1013	538	2	proposition	proposition	NOUN
iajs-1013	538	3	an	an	DET
iajs-1013	538	4	r	r	NOUN
iajs-1013	538	5	-	-	PUNCT
iajs-1013	538	6	module	module	NOUN
iajs-1013	538	7	m	m	NOUN
iajs-1013	538	8	is	be	AUX
iajs-1013	538	9	weakly	weakly	ADJ
iajs-1013	538	10	rn	rn	ADJ
iajs-1013	538	11	-	-	ADJ
iajs-1013	538	12	quasi	quasi	ADJ
iajs-1013	538	13	-	-	ADJ
iajs-1013	538	14	injective	injective	ADJ
iajs-1013	538	15	if	if	SCONJ
iajs-1013	539	1	and	and	CCONJ
iajs-1013	539	2	only	only	ADV
iajs-1013	539	3	if	if	SCONJ
iajs-1013	539	4	for	for	ADP
iajs-1013	539	5	all	all	DET
iajs-1013	539	6	x1	x1	PROPN
iajs-1013	539	7	,	,	PUNCT
iajs-1013	539	8	x2	x2	PROPN
iajs-1013	539	9	,	,	PUNCT
iajs-1013	539	10			PROPN
iajs-1013	539	11	,	,	PUNCT
iajs-1013	539	12	xn	xn	PROPN
iajs-1013	539	13			PROPN
iajs-1013	539	14			NUM
iajs-1013	539	15	,	,	PUNCT
iajs-1013	539	16	there	there	PRON
iajs-1013	539	17	exists	exist	VERB
iajs-1013	539	18	a	a	DET
iajs-1013	539	19	submodule	submodule	NOUN
iajs-1013	539	20	x	x	PUNCT
iajs-1013	539	21	of	of	ADP
iajs-1013	539	22			NUM
iajs-1013	539	23	such	such	ADJ
iajs-1013	539	24	that	that	PRON
iajs-1013	539	25	xi	xi	ADP
iajs-1013	539	26			PROPN
iajs-1013	539	27	x	x	PROPN
iajs-1013	540	1	≈	≈	PROPN
iajs-1013	540	2	m	m	PROPN
iajs-1013	540	3	for	for	ADP
iajs-1013	540	4	all	all	PRON
iajs-1013	541	1	i	i	NOUN
iajs-1013	541	2	=	=	SYM
iajs-1013	541	3	1,2	1,2	NUM
iajs-1013	541	4	,	,	PUNCT
iajs-1013	541	5			PROPN
iajs-1013	541	6	,	,	PUNCT
iajs-1013	541	7	n.	n.	NOUN
iajs-1013	541	8	proof	proof	NOUN
iajs-1013	541	9	:	:	PUNCT
iajs-1013	541	10	assume	assume	VERB
iajs-1013	541	11	that	that	SCONJ
iajs-1013	541	12	m	m	NOUN
iajs-1013	541	13	is	be	AUX
iajs-1013	541	14	weakly	weakly	ADJ
iajs-1013	542	1	r	r	NOUN
iajs-1013	542	2	n	n	CCONJ
iajs-1013	542	3	-quasi	-quasi	NOUN
iajs-1013	542	4	-	-	PUNCT
iajs-1013	542	5	injective	injective	ADJ
iajs-1013	542	6	.	.	PUNCT
iajs-1013	543	1	let	let	VERB
iajs-1013	543	2	x1	x1	NUM
iajs-1013	543	3	,	,	PUNCT
iajs-1013	543	4	x2	x2	PROPN
iajs-1013	543	5	,	,	PUNCT
iajs-1013	543	6			PROPN
iajs-1013	543	7	,	,	PUNCT
iajs-1013	543	8	xn	xn	PROPN
iajs-1013	543	9			PROPN
iajs-1013	543	10			PROPN
iajs-1013	543	11	.	.	PUNCT
iajs-1013	544	1	let	let	VERB
iajs-1013	544	2	n	n	NOUN
iajs-1013	544	3	=	=	PUNCT
iajs-1013	544	4	rx1	rx1	PROPN
iajs-1013	544	5	+	+	CCONJ
iajs-1013	544	6	rx2	rx2	PROPN
iajs-1013	544	7	+	+	PROPN
iajs-1013	544	8			PROPN
iajs-1013	544	9	+	+	CCONJ
iajs-1013	544	10	rxn	rxn	NOUN
iajs-1013	544	11	.	.	PUNCT
iajs-1013	545	1	thus	thus	ADV
iajs-1013	545	2	n	n	PRON
iajs-1013	545	3	is	be	AUX
iajs-1013	545	4	a	a	DET
iajs-1013	545	5	finitely	finitely	ADV
iajs-1013	545	6	generated	generate	VERB
iajs-1013	545	7	r	r	NOUN
iajs-1013	545	8	-	-	PUNCT
iajs-1013	545	9	module	module	NOUN
iajs-1013	545	10	.	.	PUNCT
iajs-1013	546	1	in	in	ADP
iajs-1013	546	2	fact	fact	NOUN
iajs-1013	546	3	n	n	NOUN
iajs-1013	546	4	is	be	AUX
iajs-1013	546	5	a	a	DET
iajs-1013	546	6	submodule	submodule	NOUN
iajs-1013	546	7	of	of	ADP
iajs-1013	546	8			PROPN
iajs-1013	546	9	.	.	PUNCT
iajs-1013	547	1	let	let	VERB
iajs-1013	547	2	j	j	NOUN
iajs-1013	547	3	:	:	PUNCT
iajs-1013	547	4	n	n	PROPN
iajs-1013	547	5			PROPN
iajs-1013	547	6			PROPN
iajs-1013	547	7	be	be	AUX
iajs-1013	547	8	the	the	DET
iajs-1013	547	9	inclusion	inclusion	NOUN
iajs-1013	547	10	homomorphism	homomorphism	NOUN
iajs-1013	547	11	.	.	PUNCT
iajs-1013	548	1	by	by	ADP
iajs-1013	548	2	theorem	theorem	NOUN
iajs-1013	548	3	5.4	5.4	NUM
iajs-1013	548	4	,	,	PUNCT
iajs-1013	548	5	m	m	VERB
iajs-1013	548	6	is	be	AUX
iajs-1013	548	7	weakly	weakly	ADJ
iajs-1013	548	8	n	n	CCONJ
iajs-1013	548	9	-	-	PUNCT
iajs-1013	548	10	quasiinjective	quasiinjective	NOUN
iajs-1013	548	11	,	,	PUNCT
iajs-1013	548	12	therefore	therefore	ADV
iajs-1013	548	13	there	there	PRON
iajs-1013	548	14	exists	exist	VERB
iajs-1013	548	15	a	a	DET
iajs-1013	548	16	submodule	submodule	NOUN
iajs-1013	548	17	x	x	PUNCT
iajs-1013	548	18	of	of	ADP
iajs-1013	548	19			NUM
iajs-1013	548	20	such	such	ADJ
iajs-1013	548	21	that	that	SCONJ
iajs-1013	548	22	j(n	j(n	NOUN
iajs-1013	548	23	)	)	PUNCT
iajs-1013	548	24			PROPN
iajs-1013	548	25	x	x	SYM
iajs-1013	548	26	≈	≈	NUM
iajs-1013	548	27	m.	m.	NOUN
iajs-1013	548	28	hence	hence	ADV
iajs-1013	548	29	xi	xi	ADP
iajs-1013	548	30			PROPN
iajs-1013	548	31	x	x	PUNCT
iajs-1013	548	32	for	for	ADP
iajs-1013	548	33	all	all	DET
iajs-1013	548	34	i	i	PRON
iajs-1013	548	35	=	=	NOUN
iajs-1013	548	36	1	1	NUM
iajs-1013	548	37	,	,	PUNCT
iajs-1013	548	38	2	2	NUM
iajs-1013	548	39	,	,	PUNCT
iajs-1013	548	40			PROPN
iajs-1013	548	41	,	,	PUNCT
iajs-1013	548	42	n	n	CCONJ
iajs-1013	548	43	which	which	PRON
iajs-1013	548	44	completes	complete	VERB
iajs-1013	548	45	the	the	DET
iajs-1013	548	46	proof	proof	NOUN
iajs-1013	548	47	of	of	ADP
iajs-1013	548	48	the	the	DET
iajs-1013	548	49	first	first	ADJ
iajs-1013	548	50	part	part	NOUN
iajs-1013	548	51	.	.	PUNCT
iajs-1013	549	1	conversely	conversely	ADV
iajs-1013	549	2	,	,	PUNCT
iajs-1013	549	3	ibn	ibn	PROPN
iajs-1013	549	4	alhaitham	alhaitham	NOUN
iajs-1013	549	5	j.	j.	PROPN
iajs-1013	549	6	for	for	ADP
iajs-1013	549	7	pure	pure	ADJ
iajs-1013	549	8	&	&	CCONJ
iajs-1013	549	9	appl	appl	PROPN
iajs-1013	549	10	.	.	PUNCT
iajs-1013	550	1	sci	sci	PROPN
iajs-1013	550	2	.	.	PUNCT
iajs-1013	551	1	vol.23	vol.23	PROPN
iajs-1013	551	2	(	(	PUNCT
iajs-1013	551	3	1	1	NUM
iajs-1013	551	4	)	)	PUNCT
iajs-1013	551	5	2010	2010	NUM
iajs-1013	551	6	we	we	PRON
iajs-1013	551	7	have	have	VERB
iajs-1013	551	8	to	to	PART
iajs-1013	551	9	show	show	VERB
iajs-1013	551	10	that	that	SCONJ
iajs-1013	551	11	m	m	NOUN
iajs-1013	551	12	is	be	AUX
iajs-1013	551	13	weakly	weakly	ADJ
iajs-1013	551	14	rn	rn	ADJ
iajs-1013	551	15	-	-	ADJ
iajs-1013	551	16	quasi	quasi	ADJ
iajs-1013	551	17	-	-	ADJ
iajs-1013	551	18	injective	injective	ADJ
iajs-1013	551	19	.	.	PUNCT
iajs-1013	552	1	let	let	VERB
iajs-1013	552	2	f	f	PROPN
iajs-1013	552	3			PROPN
iajs-1013	552	4	hom(rn,	hom(rn,	ADV
iajs-1013	552	5	)	)	PUNCT
iajs-1013	552	6	.	.	PUNCT
iajs-1013	553	1	suppose	suppose	VERB
iajs-1013	554	1	that	that	SCONJ
iajs-1013	554	2	f	f	PROPN
iajs-1013	554	3	(	(	PUNCT
iajs-1013	554	4	1,0,0,,0	1,0,0,,0	NUM
iajs-1013	554	5	)	)	PUNCT
iajs-1013	554	6	=	=	SYM
iajs-1013	554	7	x1	x1	PROPN
iajs-1013	554	8	,	,	PUNCT
iajs-1013	554	9	f	f	PROPN
iajs-1013	554	10	(	(	PUNCT
iajs-1013	554	11	0,1,0,,0	0,1,0,,0	NUM
iajs-1013	554	12	)	)	PUNCT
iajs-1013	554	13	=	=	SYM
iajs-1013	555	1	x2	x2	PROPN
iajs-1013	555	2	,	,	PUNCT
iajs-1013	555	3			PROPN
iajs-1013	555	4	,	,	PUNCT
iajs-1013	555	5	f	f	PROPN
iajs-1013	555	6	(	(	PUNCT
iajs-1013	555	7	0,0,0,,1	0,0,0,,1	NOUN
iajs-1013	555	8	)	)	PUNCT
iajs-1013	555	9	=	=	SYM
iajs-1013	556	1	xn	xn	X
iajs-1013	556	2	.	.	PUNCT
iajs-1013	557	1	then	then	ADV
iajs-1013	557	2	x1	x1	NUM
iajs-1013	557	3	,	,	PUNCT
iajs-1013	557	4	x2	x2	PROPN
iajs-1013	557	5	,	,	PUNCT
iajs-1013	557	6			PROPN
iajs-1013	557	7	,	,	PUNCT
iajs-1013	557	8	xn	xn	PROPN
iajs-1013	557	9			PROPN
iajs-1013	557	10			VERB
iajs-1013	557	11	.	.	PUNCT
iajs-1013	558	1	so	so	ADV
iajs-1013	558	2	,	,	PUNCT
iajs-1013	558	3	by	by	ADP
iajs-1013	558	4	hypothesis	hypothesis	NOUN
iajs-1013	558	5	there	there	PRON
iajs-1013	558	6	exists	exist	VERB
iajs-1013	558	7	a	a	DET
iajs-1013	558	8	submodule	submodule	NOUN
iajs-1013	558	9	x	x	PUNCT
iajs-1013	558	10	of	of	ADP
iajs-1013	558	11			NUM
iajs-1013	558	12	such	such	ADJ
iajs-1013	558	13	that	that	PRON
iajs-1013	558	14	xi	xi	ADP
iajs-1013	558	15			PROPN
iajs-1013	558	16	x	x	PROPN
iajs-1013	559	1	≈	≈	PROPN
iajs-1013	559	2	m	m	PROPN
iajs-1013	559	3	for	for	ADP
iajs-1013	559	4	all	all	PRON
iajs-1013	559	5	i	i	PRON
iajs-1013	559	6	=	=	NOUN
iajs-1013	559	7	1	1	NUM
iajs-1013	559	8	,	,	PUNCT
iajs-1013	559	9	2	2	NUM
iajs-1013	559	10	,	,	PUNCT
iajs-1013	559	11			PROPN
iajs-1013	559	12	,	,	PUNCT
iajs-1013	559	13	n	n	CCONJ
iajs-1013	559	14	which	which	PRON
iajs-1013	559	15	implies	imply	VERB
iajs-1013	559	16	that	that	SCONJ
iajs-1013	560	1	f	f	PROPN
iajs-1013	560	2	(	(	PUNCT
iajs-1013	560	3	r	r	NOUN
iajs-1013	560	4	n	n	ADJ
iajs-1013	560	5	)	)	PUNCT
iajs-1013	560	6			PROPN
iajs-1013	560	7	x	x	X
iajs-1013	561	1	≈m	≈m	ADJ
iajs-1013	561	2	and	and	CCONJ
iajs-1013	561	3	hence	hence	ADV
iajs-1013	561	4	m	m	VERB
iajs-1013	561	5	is	be	AUX
iajs-1013	561	6	weakly	weakly	ADJ
iajs-1013	561	7	r	r	NOUN
iajs-1013	561	8	n	n	CCONJ
iajs-1013	561	9	-quasi	-quasi	NOUN
iajs-1013	561	10	-	-	PUNCT
iajs-1013	561	11	injective	injective	ADJ
iajs-1013	561	12	.	.	PUNCT
iajs-1013	562	1	5.5	5.5	NUM
iajs-1013	562	2	corollary	corollary	NOUN
iajs-1013	562	3	an	an	DET
iajs-1013	562	4	r	r	NOUN
iajs-1013	562	5	-	-	PUNCT
iajs-1013	562	6	module	module	NOUN
iajs-1013	562	7	m	m	NOUN
iajs-1013	562	8	is	be	AUX
iajs-1013	562	9	weakly	weakly	ADJ
iajs-1013	562	10	quasi	quasi	ADJ
iajs-1013	562	11	-	-	ADJ
iajs-1013	562	12	injective	injective	ADJ
iajs-1013	562	13	if	if	SCONJ
iajs-1013	562	14	and	and	CCONJ
iajs-1013	562	15	only	only	ADV
iajs-1013	562	16	if	if	SCONJ
iajs-1013	562	17	for	for	ADP
iajs-1013	562	18	all	all	DET
iajs-1013	562	19	x1,x2,,xn	x1,x2,,xn	PROPN
iajs-1013	562	20	,	,	PUNCT
iajs-1013	562	21	there	there	PRON
iajs-1013	562	22	exists	exist	VERB
iajs-1013	562	23	a	a	DET
iajs-1013	562	24	submodule	submodule	NOUN
iajs-1013	562	25	x	x	PUNCT
iajs-1013	562	26	of	of	ADP
iajs-1013	562	27			NUM
iajs-1013	562	28	such	such	ADJ
iajs-1013	562	29	that	that	PRON
iajs-1013	562	30	xi	xi	ADP
iajs-1013	562	31			PROPN
iajs-1013	562	32	x	x	PROPN
iajs-1013	563	1	≈	≈	PROPN
iajs-1013	563	2	m	m	PROPN
iajs-1013	563	3	for	for	ADP
iajs-1013	563	4	all	all	PRON
iajs-1013	563	5	i	i	PRON
iajs-1013	563	6	=	=	NOUN
iajs-1013	563	7	1	1	NUM
iajs-1013	563	8	,	,	PUNCT
iajs-1013	563	9	2	2	NUM
iajs-1013	563	10	,	,	PUNCT
iajs-1013	563	11			PROPN
iajs-1013	563	12	,	,	PUNCT
iajs-1013	563	13	n.	n.	NOUN
iajs-1013	563	14	5.6	5.6	NUM
iajs-1013	563	15	proposition	proposition	NOUN
iajs-1013	563	16	a	a	DET
iajs-1013	563	17	ring	ring	NOUN
iajs-1013	563	18	r	r	NOUN
iajs-1013	563	19	is	be	AUX
iajs-1013	563	20	weakly	weakly	ADJ
iajs-1013	563	21	r	r	NOUN
iajs-1013	563	22	n	n	CCONJ
iajs-1013	563	23	-quasi	-quasi	NOUN
iajs-1013	563	24	-	-	PUNCT
iajs-1013	563	25	injective	injective	ADJ
iajs-1013	563	26	if	if	SCONJ
iajs-1013	563	27	and	and	CCONJ
iajs-1013	563	28	only	only	ADV
iajs-1013	563	29	if	if	SCONJ
iajs-1013	563	30	for	for	ADP
iajs-1013	563	31	all	all	DET
iajs-1013	563	32	x1	x1	PROPN
iajs-1013	563	33	,	,	PUNCT
iajs-1013	563	34	x2	x2	PROPN
iajs-1013	563	35	,	,	PUNCT
iajs-1013	563	36			PROPN
iajs-1013	563	37	,	,	PUNCT
iajs-1013	563	38	xn	xn	PROPN
iajs-1013	564	1			PROPN
iajs-1013	564	2	r	r	NOUN
iajs-1013	564	3	there	there	PRON
iajs-1013	564	4	exists	exist	VERB
iajs-1013	564	5	an	an	DET
iajs-1013	564	6	element	element	NOUN
iajs-1013	564	7	b	b	PROPN
iajs-1013	564	8			PROPN
iajs-1013	564	9	r	r	NOUN
iajs-1013	565	1	such	such	ADJ
iajs-1013	565	2	that	that	PRON
iajs-1013	565	3	annr(b	annr(b	PROPN
iajs-1013	565	4	)	)	PUNCT
iajs-1013	565	5	=	=	SYM
iajs-1013	565	6	0	0	NUM
iajs-1013	565	7	and	and	CCONJ
iajs-1013	565	8	xi	xi	ADP
iajs-1013	565	9			NOUN
iajs-1013	565	10	rb	rb	VERB
iajs-1013	565	11	for	for	ADP
iajs-1013	565	12	all	all	PRON
iajs-1013	565	13	i	i	PRON
iajs-1013	565	14	=	=	NOUN
iajs-1013	565	15	1,2,,n	1,2,,n	NUM
iajs-1013	565	16	.	.	PUNCT
iajs-1013	566	1	proof	proof	NOUN
iajs-1013	566	2	:	:	PUNCT
iajs-1013	566	3	suppose	suppose	VERB
iajs-1013	566	4	that	that	SCONJ
iajs-1013	566	5	r	r	NOUN
iajs-1013	566	6	is	be	AUX
iajs-1013	566	7	weakly	weakly	ADJ
iajs-1013	566	8	r	r	NOUN
iajs-1013	566	9	n	n	CCONJ
iajs-1013	566	10	-	-	PUNCT
iajs-1013	566	11	quasi	quasi	NOUN
iajs-1013	566	12	-	-	ADJ
iajs-1013	566	13	injective	injective	ADJ
iajs-1013	566	14	.	.	PUNCT
iajs-1013	567	1	let	let	VERB
iajs-1013	567	2	x1	x1	NUM
iajs-1013	567	3	,	,	PUNCT
iajs-1013	567	4	x2	x2	PROPN
iajs-1013	567	5	,	,	PUNCT
iajs-1013	567	6			PROPN
iajs-1013	567	7	,	,	PUNCT
iajs-1013	567	8	xn	xn	PROPN
iajs-1013	568	1			PROPN
iajs-1013	568	2	r	r	NOUN
iajs-1013	568	3	.	.	PUNCT
iajs-1013	569	1	by	by	ADP
iajs-1013	569	2	proposition	proposition	NOUN
iajs-1013	569	3	5.4	5.4	NUM
iajs-1013	569	4	.	.	PUNCT
iajs-1013	569	5	,	,	PUNCT
iajs-1013	569	6	there	there	PRON
iajs-1013	569	7	exists	exist	VERB
iajs-1013	569	8	a	a	DET
iajs-1013	569	9	submodule	submodule	NOUN
iajs-1013	569	10	x	x	PUNCT
iajs-1013	569	11	of	of	ADP
iajs-1013	569	12	r	r	NOUN
iajs-1013	569	13	such	such	ADJ
iajs-1013	569	14	that	that	PRON
iajs-1013	569	15	xi	xi	ADP
iajs-1013	569	16			PROPN
iajs-1013	569	17	x	x	X
iajs-1013	570	1	≈	≈	PROPN
iajs-1013	570	2	r	r	NOUN
iajs-1013	570	3	,	,	PUNCT
iajs-1013	570	4	for	for	ADP
iajs-1013	570	5	all	all	DET
iajs-1013	570	6	i	i	PRON
iajs-1013	570	7	=	=	NOUN
iajs-1013	570	8	1	1	NUM
iajs-1013	570	9	,	,	PUNCT
iajs-1013	570	10	2	2	NUM
iajs-1013	570	11	,	,	PUNCT
iajs-1013	570	12			PROPN
iajs-1013	570	13	,	,	PUNCT
iajs-1013	570	14	n.	n.	PROPN
iajs-1013	570	15	let	let	VERB
iajs-1013	570	16			NOUN
iajs-1013	570	17	:	:	PUNCT
iajs-1013	570	18	r	r	NOUN
iajs-1013	570	19			NUM
iajs-1013	570	20	x	x	AUX
iajs-1013	570	21	be	be	AUX
iajs-1013	570	22	an	an	DET
iajs-1013	570	23	isomorphism	isomorphism	NOUN
iajs-1013	570	24	.	.	PUNCT
iajs-1013	571	1	put	put	VERB
iajs-1013	571	2	b	b	NOUN
iajs-1013	571	3	=	=	PUNCT
iajs-1013	571	4	(1	(1	NOUN
iajs-1013	571	5	)	)	PUNCT
iajs-1013	571	6	.	.	PUNCT
iajs-1013	572	1	then	then	ADV
iajs-1013	572	2	b	b	X
iajs-1013	572	3			NOUN
iajs-1013	572	4	r	r	NOUN
iajs-1013	572	5	and	and	CCONJ
iajs-1013	572	6	for	for	ADP
iajs-1013	572	7	all	all	DET
iajs-1013	572	8	i	i	PRON
iajs-1013	572	9	=	=	NOUN
iajs-1013	572	10	1	1	NUM
iajs-1013	572	11	,	,	PUNCT
iajs-1013	572	12	2	2	NUM
iajs-1013	572	13	,	,	PUNCT
iajs-1013	572	14			PROPN
iajs-1013	572	15	,	,	PUNCT
iajs-1013	572	16	n	n	CCONJ
iajs-1013	572	17	,	,	PUNCT
iajs-1013	572	18	xi	xi	X
iajs-1013	572	19	=	=	PUNCT
iajs-1013	572	20	(ri	(ri	NOUN
iajs-1013	572	21	)	)	PUNCT
iajs-1013	572	22	for	for	ADP
iajs-1013	572	23	some	some	DET
iajs-1013	572	24	ri	ri	PROPN
iajs-1013	572	25			NOUN
iajs-1013	572	26	r	r	NOUN
iajs-1013	572	27	and	and	CCONJ
iajs-1013	572	28	hence	hence	ADV
iajs-1013	572	29	xi	xi	PUNCT
iajs-1013	573	1	=	=	SYM
iajs-1013	573	2	ri	ri	PROPN
iajs-1013	573	3	(1	(1	NOUN
iajs-1013	573	4	)	)	PUNCT
iajs-1013	574	1	=	=	SYM
iajs-1013	574	2	ri	ri	PROPN
iajs-1013	574	3	b	b	PROPN
iajs-1013	574	4	for	for	ADP
iajs-1013	574	5	all	all	DET
iajs-1013	574	6	i	i	PRON
iajs-1013	574	7	=	=	NOUN
iajs-1013	574	8	1	1	NUM
iajs-1013	574	9	,	,	PUNCT
iajs-1013	574	10	2	2	NUM
iajs-1013	574	11	,	,	PUNCT
iajs-1013	574	12			PROPN
iajs-1013	574	13	,	,	PUNCT
iajs-1013	574	14	n.	n.	PROPN
iajs-1013	574	15	therefore	therefore	ADV
iajs-1013	574	16	xi	xi	VERB
iajs-1013	574	17			PROPN
iajs-1013	574	18	rb	rb	VERB
iajs-1013	574	19	for	for	ADP
iajs-1013	574	20	all	all	PRON
iajs-1013	574	21	i	i	PRON
iajs-1013	574	22	=	=	NOUN
iajs-1013	574	23	1	1	NUM
iajs-1013	574	24	,	,	PUNCT
iajs-1013	574	25	2	2	NUM
iajs-1013	574	26	,	,	PUNCT
iajs-1013	574	27			PROPN
iajs-1013	574	28	,	,	PUNCT
iajs-1013	574	29	n.	n.	PROPN
iajs-1013	574	30	moreover	moreover	ADV
iajs-1013	574	31	,	,	PUNCT
iajs-1013	574	32	if	if	SCONJ
iajs-1013	574	33	r	r	NOUN
iajs-1013	574	34	b	b	NOUN
iajs-1013	574	35	=	=	NOUN
iajs-1013	574	36	0	0	NUM
iajs-1013	574	37	for	for	ADP
iajs-1013	574	38	some	some	DET
iajs-1013	574	39	r	r	NOUN
iajs-1013	574	40			NOUN
iajs-1013	574	41	r	r	NOUN
iajs-1013	574	42	,	,	PUNCT
iajs-1013	574	43	implies	imply	VERB
iajs-1013	574	44	that	that	SCONJ
iajs-1013	574	45	r	r	NOUN
iajs-1013	574	46	=	=	SYM
iajs-1013	574	47	0	0	NUM
iajs-1013	574	48	and	and	CCONJ
iajs-1013	574	49	hence	hence	ADV
iajs-1013	574	50	annr(b	annr(b	ADV
iajs-1013	574	51	)	)	PUNCT
iajs-1013	574	52	=	=	SYM
iajs-1013	575	1	0	0	X
iajs-1013	575	2	.	.	PUNCT
iajs-1013	576	1	conversely	conversely	ADV
iajs-1013	576	2	,	,	PUNCT
iajs-1013	576	3	we	we	PRON
iajs-1013	576	4	have	have	VERB
iajs-1013	576	5	to	to	PART
iajs-1013	576	6	show	show	VERB
iajs-1013	576	7	that	that	SCONJ
iajs-1013	576	8	r	r	NOUN
iajs-1013	576	9	is	be	AUX
iajs-1013	576	10	weakly	weakly	ADJ
iajs-1013	576	11	r	r	NOUN
iajs-1013	576	12	n	n	CCONJ
iajs-1013	576	13	-	-	PUNCT
iajs-1013	576	14	quasi	quasi	NOUN
iajs-1013	576	15	-	-	ADJ
iajs-1013	576	16	injective	injective	ADJ
iajs-1013	576	17	.	.	PUNCT
iajs-1013	577	1	let	let	VERB
iajs-1013	577	2	f	f	PROPN
iajs-1013	577	3			PROPN
iajs-1013	577	4	hom(rn	hom(rn	PROPN
iajs-1013	577	5	,	,	PUNCT
iajs-1013	577	6	r	r	NOUN
iajs-1013	577	7	)	)	PUNCT
iajs-1013	577	8	.	.	PUNCT
iajs-1013	578	1	let	let	VERB
iajs-1013	578	2	f	f	PROPN
iajs-1013	578	3	(	(	PUNCT
iajs-1013	578	4	1,0,0,,0	1,0,0,,0	NUM
iajs-1013	578	5	)	)	PUNCT
iajs-1013	578	6	=	=	SYM
iajs-1013	578	7	x1	x1	PROPN
iajs-1013	578	8	,	,	PUNCT
iajs-1013	578	9	f	f	PROPN
iajs-1013	578	10	(	(	PUNCT
iajs-1013	578	11	0,1,0,,0	0,1,0,,0	NUM
iajs-1013	578	12	)	)	PUNCT
iajs-1013	579	1	=	=	SYM
iajs-1013	579	2	x2	x2	PROPN
iajs-1013	579	3	,	,	PUNCT
iajs-1013	579	4			PROPN
iajs-1013	579	5	,	,	PUNCT
iajs-1013	579	6	f	f	PROPN
iajs-1013	579	7	(	(	PUNCT
iajs-1013	579	8	0,0,0,,1	0,0,0,,1	NOUN
iajs-1013	579	9	)	)	PUNCT
iajs-1013	579	10	=	=	SYM
iajs-1013	580	1	xn	xn	X
iajs-1013	580	2	.	.	PUNCT
iajs-1013	581	1	then	then	ADV
iajs-1013	581	2	x1	x1	NUM
iajs-1013	581	3	,	,	PUNCT
iajs-1013	581	4	x2	x2	PROPN
iajs-1013	581	5	,	,	PUNCT
iajs-1013	581	6			PROPN
iajs-1013	581	7	,	,	PUNCT
iajs-1013	581	8	xn	xn	PROPN
iajs-1013	581	9			PROPN
iajs-1013	581	10	r	r	NOUN
iajs-1013	581	11	and	and	CCONJ
iajs-1013	581	12	hence	hence	ADV
iajs-1013	581	13	there	there	PRON
iajs-1013	581	14	exists	exist	VERB
iajs-1013	581	15	b	b	NUM
iajs-1013	581	16			PROPN
iajs-1013	581	17	r	r	NOUN
iajs-1013	581	18	such	such	ADJ
iajs-1013	581	19	that	that	PRON
iajs-1013	581	20	xi	xi	PROPN
iajs-1013	581	21			NOUN
iajs-1013	581	22	rb	rb	VERB
iajs-1013	581	23	for	for	ADP
iajs-1013	581	24	all	all	PRON
iajs-1013	581	25	i	i	PRON
iajs-1013	581	26	=	=	NOUN
iajs-1013	581	27	1	1	NUM
iajs-1013	581	28	,	,	PUNCT
iajs-1013	581	29	2	2	NUM
iajs-1013	581	30	,	,	PUNCT
iajs-1013	581	31			PROPN
iajs-1013	581	32	,	,	PUNCT
iajs-1013	581	33	n	n	NOUN
iajs-1013	581	34	and	and	CCONJ
iajs-1013	581	35	annr(b)=0	annr(b)=0	ADJ
iajs-1013	581	36	.	.	PUNCT
iajs-1013	582	1	let	let	VERB
iajs-1013	582	2	x	x	SYM
iajs-1013	582	3	=	=	SYM
iajs-1013	582	4	rb	rb	PROPN
iajs-1013	582	5	.	.	PUNCT
iajs-1013	583	1	then	then	ADV
iajs-1013	583	2	x	x	PRON
iajs-1013	583	3	is	be	AUX
iajs-1013	583	4	a	a	DET
iajs-1013	583	5	submodule	submodule	NOUN
iajs-1013	583	6	of	of	ADP
iajs-1013	583	7	r	r	NOUN
iajs-1013	583	8	,	,	PUNCT
iajs-1013	583	9	xi	xi	ADP
iajs-1013	583	10			PROPN
iajs-1013	583	11	x	x	PUNCT
iajs-1013	583	12	for	for	ADP
iajs-1013	583	13	all	all	DET
iajs-1013	583	14	i	i	PRON
iajs-1013	583	15	=	=	NOUN
iajs-1013	583	16	1	1	NUM
iajs-1013	583	17	,	,	PUNCT
iajs-1013	583	18	2	2	NUM
iajs-1013	583	19	,	,	PUNCT
iajs-1013	583	20			PROPN
iajs-1013	583	21	,	,	PUNCT
iajs-1013	583	22	n	n	PROPN
iajs-1013	583	23	and	and	CCONJ
iajs-1013	583	24	x	x	PROPN
iajs-1013	583	25	≈	≈	PROPN
iajs-1013	583	26	r.	r.	PROPN
iajs-1013	583	27	therefore	therefore	ADV
iajs-1013	583	28	r	r	NOUN
iajs-1013	583	29	is	be	AUX
iajs-1013	583	30	weakly	weakly	ADJ
iajs-1013	583	31	rn	rn	NOUN
iajs-1013	583	32	-	-	NOUN
iajs-1013	583	33	quasiinjective	quasiinjective	ADJ
iajs-1013	583	34	(	(	PUNCT
iajs-1013	583	35	by	by	ADP
iajs-1013	583	36	proposition	proposition	NOUN
iajs-1013	583	37	5.4	5.4	NUM
iajs-1013	583	38	)	)	PUNCT
iajs-1013	583	39	.	.	PUNCT
iajs-1013	584	1	the	the	DET
iajs-1013	584	2	following	follow	VERB
iajs-1013	584	3	corollary	corollary	NOUN
iajs-1013	584	4	is	be	AUX
iajs-1013	584	5	also	also	ADV
iajs-1013	584	6	a	a	DET
iajs-1013	584	7	consequence	consequence	NOUN
iajs-1013	584	8	of	of	ADP
iajs-1013	584	9	theorem	theorem	ADJ
iajs-1013	584	10	5.3	5.3	NUM
iajs-1013	584	11	and	and	CCONJ
iajs-1013	584	12	proposition	proposition	NOUN
iajs-1013	584	13	5.6	5.6	NUM
iajs-1013	584	14	.	.	PUNCT
iajs-1013	585	1	5.7	5.7	NUM
iajs-1013	585	2	corollary	corollary	NOUN
iajs-1013	585	3	a	a	DET
iajs-1013	585	4	ring	ring	NOUN
iajs-1013	585	5	r	r	NOUN
iajs-1013	585	6	is	be	AUX
iajs-1013	585	7	weakly	weakly	ADJ
iajs-1013	585	8	quasi	quasi	ADJ
iajs-1013	585	9	-	-	ADJ
iajs-1013	585	10	injective	injective	ADJ
iajs-1013	585	11	if	if	SCONJ
iajs-1013	585	12	and	and	CCONJ
iajs-1013	585	13	only	only	ADV
iajs-1013	585	14	if	if	SCONJ
iajs-1013	585	15	for	for	ADP
iajs-1013	585	16	all	all	DET
iajs-1013	585	17	x1	x1	PROPN
iajs-1013	585	18	,	,	PUNCT
iajs-1013	585	19	x2	x2	PROPN
iajs-1013	585	20	,	,	PUNCT
iajs-1013	585	21			PROPN
iajs-1013	585	22	,	,	PUNCT
iajs-1013	585	23	xn	xn	PROPN
iajs-1013	586	1			PROPN
iajs-1013	586	2	r	r	NOUN
iajs-1013	586	3	there	there	PRON
iajs-1013	586	4	exists	exist	VERB
iajs-1013	586	5	an	an	DET
iajs-1013	586	6	element	element	NOUN
iajs-1013	586	7	b	b	PROPN
iajs-1013	586	8			PROPN
iajs-1013	586	9	r	r	NOUN
iajs-1013	587	1	such	such	ADJ
iajs-1013	587	2	that	that	PRON
iajs-1013	587	3	annr(b	annr(b	PROPN
iajs-1013	587	4	)	)	PUNCT
iajs-1013	587	5	=	=	SYM
iajs-1013	587	6	0	0	NUM
iajs-1013	587	7	and	and	CCONJ
iajs-1013	587	8	xi	xi	ADP
iajs-1013	587	9			NOUN
iajs-1013	587	10	rb	rb	VERB
iajs-1013	587	11	for	for	ADP
iajs-1013	587	12	all	all	PRON
iajs-1013	587	13	i	i	PRON
iajs-1013	587	14	=	=	NOUN
iajs-1013	587	15	1	1	NUM
iajs-1013	587	16	,	,	PUNCT
iajs-1013	587	17	2	2	NUM
iajs-1013	587	18	,	,	PUNCT
iajs-1013	587	19			PROPN
iajs-1013	587	20	,	,	PUNCT
iajs-1013	587	21	n.	n.	PROPN
iajs-1013	587	22	finally	finally	ADV
iajs-1013	587	23	,	,	PUNCT
iajs-1013	587	24	we	we	PRON
iajs-1013	587	25	give	give	VERB
iajs-1013	587	26	the	the	DET
iajs-1013	587	27	following	follow	VERB
iajs-1013	587	28	characterization	characterization	NOUN
iajs-1013	587	29	.	.	PUNCT
iajs-1013	588	1	5.8	5.8	NUM
iajs-1013	588	2	proposition	proposition	NOUN
iajs-1013	588	3	a	a	DET
iajs-1013	588	4	cyclic	cyclic	ADJ
iajs-1013	588	5	r	r	NOUN
iajs-1013	588	6	-	-	PUNCT
iajs-1013	588	7	module	module	NOUN
iajs-1013	588	8	is	be	AUX
iajs-1013	588	9	weakly	weakly	ADJ
iajs-1013	588	10	quasi	quasi	ADJ
iajs-1013	588	11	-	-	ADJ
iajs-1013	588	12	injective	injective	ADJ
iajs-1013	588	13	if	if	SCONJ
iajs-1013	589	1	and	and	CCONJ
iajs-1013	589	2	only	only	ADV
iajs-1013	589	3	if	if	SCONJ
iajs-1013	589	4	it	it	PRON
iajs-1013	589	5	is	be	AUX
iajs-1013	589	6	weakly	weakly	ADJ
iajs-1013	589	7	r	r	NOUN
iajs-1013	589	8	2	2	NUM
iajs-1013	589	9	-quasiinjective	-quasiinjective	NOUN
iajs-1013	589	10	.	.	PUNCT
iajs-1013	590	1	proof	proof	NOUN
iajs-1013	590	2	:	:	PUNCT
iajs-1013	590	3	the	the	DET
iajs-1013	590	4	"	"	PUNCT
iajs-1013	590	5	only	only	ADV
iajs-1013	590	6	if	if	SCONJ
iajs-1013	590	7	"	"	PUNCT
iajs-1013	590	8	part	part	NOUN
iajs-1013	590	9	is	be	AUX
iajs-1013	590	10	obvious	obvious	ADJ
iajs-1013	590	11	.	.	PUNCT
iajs-1013	591	1	to	to	PART
iajs-1013	591	2	prove	prove	VERB
iajs-1013	591	3	the	the	DET
iajs-1013	591	4	"	"	PUNCT
iajs-1013	591	5	if	if	SCONJ
iajs-1013	591	6	"	"	PUNCT
iajs-1013	591	7	part	part	NOUN
iajs-1013	591	8	,	,	PUNCT
iajs-1013	591	9	let	let	VERB
iajs-1013	591	10	m	m	PRON
iajs-1013	591	11	be	be	AUX
iajs-1013	591	12	a	a	DET
iajs-1013	591	13	cyclic	cyclic	ADJ
iajs-1013	591	14	r	r	NOUN
iajs-1013	591	15	-	-	PUNCT
iajs-1013	591	16	module	module	NOUN
iajs-1013	591	17	.	.	PUNCT
iajs-1013	592	1	suppose	suppose	VERB
iajs-1013	592	2	that	that	SCONJ
iajs-1013	592	3	m	m	PROPN
iajs-1013	592	4	is	be	AUX
iajs-1013	592	5	weakly	weakly	ADJ
iajs-1013	592	6	r	r	NOUN
iajs-1013	592	7	2	2	NUM
iajs-1013	592	8	-quasi	-quasi	NOUN
iajs-1013	592	9	-	-	PUNCT
iajs-1013	592	10	injective	injective	ADJ
iajs-1013	592	11	.	.	PUNCT
iajs-1013	593	1	let	let	VERB
iajs-1013	593	2	us	we	PRON
iajs-1013	593	3	proceed	proceed	VERB
iajs-1013	593	4	by	by	ADP
iajs-1013	593	5	induction	induction	NOUN
iajs-1013	593	6	.	.	PUNCT
iajs-1013	594	1	assume	assume	VERB
iajs-1013	594	2	that	that	SCONJ
iajs-1013	594	3	m	m	NOUN
iajs-1013	594	4	is	be	AUX
iajs-1013	594	5	weakly	weakly	ADJ
iajs-1013	594	6	r	r	NOUN
iajs-1013	594	7	n	n	NUM
iajs-1013	594	8	–	–	PUNCT
iajs-1013	594	9	1	1	NUM
iajs-1013	594	10	–	–	PUNCT
iajs-1013	594	11	quasi	quasi	ADJ
iajs-1013	594	12	-	-	ADJ
iajs-1013	594	13	injective	injective	ADJ
iajs-1013	594	14	and	and	CCONJ
iajs-1013	594	15	let	let	VERB
iajs-1013	594	16	x1	x1	NUM
iajs-1013	594	17	,	,	PUNCT
iajs-1013	594	18	x2	x2	PROPN
iajs-1013	594	19	,	,	PUNCT
iajs-1013	594	20			PROPN
iajs-1013	594	21	,	,	PUNCT
iajs-1013	594	22	xn	xn	VERB
iajs-1013	594	23	.	.	PUNCT
iajs-1013	595	1	by	by	ADP
iajs-1013	595	2	proposition	proposition	NOUN
iajs-1013	595	3	5.6	5.6	NUM
iajs-1013	595	4	,	,	PUNCT
iajs-1013	595	5	there	there	PRON
iajs-1013	595	6	exists	exist	VERB
iajs-1013	595	7	a	a	DET
iajs-1013	595	8	submodule	submodule	NOUN
iajs-1013	595	9	rx	rx	ADP
iajs-1013	595	10			PROPN
iajs-1013	595	11			NUM
iajs-1013	595	12	such	such	ADJ
iajs-1013	595	13	that	that	SCONJ
iajs-1013	595	14	x1	x1	PROPN
iajs-1013	595	15	,	,	PUNCT
iajs-1013	595	16	x2	x2	PROPN
iajs-1013	595	17	,	,	PUNCT
iajs-1013	595	18			PROPN
iajs-1013	595	19	,	,	PUNCT
iajs-1013	595	20	xn	xn	PROPN
iajs-1013	595	21	–	–	PUNCT
iajs-1013	595	22	1	1	NUM
iajs-1013	595	23			NOUN
iajs-1013	595	24	rx	rx	VERB
iajs-1013	595	25	≈	≈	PROPN
iajs-1013	595	26	m	m	PROPN
iajs-1013	595	27	.	.	PUNCT
iajs-1013	596	1	but	but	CCONJ
iajs-1013	596	2	m	m	PROPN
iajs-1013	596	3	is	be	AUX
iajs-1013	596	4	weakly	weakly	ADJ
iajs-1013	596	5	r2	r2	NOUN
iajs-1013	596	6	-	-	PUNCT
iajs-1013	596	7	quasi	quasi	NOUN
iajs-1013	596	8	-	-	ADJ
iajs-1013	596	9	injective	injective	ADJ
iajs-1013	596	10	,	,	PUNCT
iajs-1013	596	11	so	so	SCONJ
iajs-1013	596	12	there	there	PRON
iajs-1013	596	13	exists	exist	VERB
iajs-1013	596	14	a	a	DET
iajs-1013	596	15	submodule	submodule	NOUN
iajs-1013	596	16	x	x	PUNCT
iajs-1013	596	17	of	of	ADP
iajs-1013	596	18			NUM
iajs-1013	596	19	such	such	ADJ
iajs-1013	596	20	that	that	SCONJ
iajs-1013	596	21	x	x	PROPN
iajs-1013	597	1	≈	≈	NOUN
iajs-1013	597	2	m	m	PROPN
iajs-1013	597	3	and	and	CCONJ
iajs-1013	597	4	x	x	SYM
iajs-1013	597	5	,	,	PUNCT
iajs-1013	597	6	xn	xn	PROPN
iajs-1013	597	7			PROPN
iajs-1013	597	8	x.	x.	NOUN
iajs-1013	597	9	hence	hence	ADV
iajs-1013	597	10	x1	x1	PROPN
iajs-1013	597	11	,	,	PUNCT
iajs-1013	597	12	x2	x2	PROPN
iajs-1013	597	13	,	,	PUNCT
iajs-1013	597	14			PROPN
iajs-1013	597	15	,	,	PUNCT
iajs-1013	597	16	xn	xn	PROPN
iajs-1013	598	1	x	x	SYM
iajs-1013	598	2	≈	≈	NUM
iajs-1013	598	3	m.	m.	NOUN
iajs-1013	598	4	therefore	therefore	ADV
iajs-1013	598	5	m	m	VERB
iajs-1013	598	6	is	be	AUX
iajs-1013	598	7	weakly	weakly	ADJ
iajs-1013	598	8	quasi	quasi	ADJ
iajs-1013	598	9	-	-	ADJ
iajs-1013	598	10	injective	injective	ADJ
iajs-1013	598	11	(	(	PUNCT
iajs-1013	598	12	by	by	ADP
iajs-1013	598	13	corollary	corollary	ADJ
iajs-1013	598	14	5.5	5.5	NUM
iajs-1013	598	15	)	)	PUNCT
iajs-1013	598	16	.	.	PUNCT
iajs-1013	599	1	5.9	5.9	NUM
iajs-1013	599	2	corollary	corollary	NOUN
iajs-1013	599	3	a	a	DET
iajs-1013	599	4	cyclic	cyclic	ADJ
iajs-1013	599	5	r	r	NOUN
iajs-1013	599	6	-	-	PUNCT
iajs-1013	599	7	module	module	NOUN
iajs-1013	599	8	is	be	AUX
iajs-1013	599	9	weakly	weakly	ADJ
iajs-1013	599	10	r	r	NOUN
iajs-1013	599	11	n	n	CCONJ
iajs-1013	599	12	-quasi	-quasi	NOUN
iajs-1013	599	13	-	-	PUNCT
iajs-1013	599	14	injective	injective	ADJ
iajs-1013	599	15	if	if	SCONJ
iajs-1013	600	1	and	and	CCONJ
iajs-1013	600	2	only	only	ADV
iajs-1013	600	3	if	if	SCONJ
iajs-1013	600	4	it	it	PRON
iajs-1013	600	5	is	be	AUX
iajs-1013	600	6	weakly	weakly	ADJ
iajs-1013	600	7	r	r	NOUN
iajs-1013	600	8	2	2	NUM
iajs-1013	600	9	-quasiinjective	-quasiinjective	NOUN
iajs-1013	600	10	.	.	PUNCT
iajs-1013	601	1	proof	proof	NOUN
iajs-1013	601	2	:	:	PUNCT
iajs-1013	601	3	follows	follow	VERB
iajs-1013	601	4	from	from	ADP
iajs-1013	601	5	theorem	theorem	ADJ
iajs-1013	601	6	5.3	5.3	NUM
iajs-1013	601	7	and	and	CCONJ
iajs-1013	601	8	proposition	proposition	NOUN
iajs-1013	601	9	5.8	5.8	NUM
iajs-1013	601	10	.	.	PUNCT
iajs-1013	602	1	ibn	ibn	PROPN
iajs-1013	602	2	alhaitham	alhaitham	PROPN
iajs-1013	602	3	j.	j.	PROPN
iajs-1013	602	4	for	for	ADP
iajs-1013	602	5	pure	pure	ADJ
iajs-1013	602	6	&	&	CCONJ
iajs-1013	602	7	appl	appl	PROPN
iajs-1013	602	8	.	.	PUNCT
iajs-1013	603	1	sci	sci	PROPN
iajs-1013	603	2	.	.	PUNCT
iajs-1013	604	1	vol.23	vol.23	PROPN
iajs-1013	604	2	(	(	PUNCT
iajs-1013	604	3	1	1	NUM
iajs-1013	604	4	)	)	PUNCT
iajs-1013	604	5	2010	2010	NUM
iajs-1013	604	6	references	reference	NOUN
iajs-1013	604	7	1	1	NUM
iajs-1013	604	8	.	.	PUNCT
iajs-1013	604	9	jain	jain	PROPN
iajs-1013	604	10	,	,	PUNCT
iajs-1013	604	11	s.	s.	PROPN
iajs-1013	604	12	k.	k.	PROPN
iajs-1013	604	13	and	and	CCONJ
iajs-1013	604	14	lopes	lopes	PROPN
iajs-1013	604	15	permonth	permonth	PROPN
iajs-1013	604	16	,	,	PUNCT
iajs-1013	604	17	s.	s.	PROPN
iajs-1013	604	18	r.	r.	PROPN
iajs-1013	604	19	,	,	PUNCT
iajs-1013	604	20	(	(	PUNCT
iajs-1013	604	21	1990	1990	NUM
iajs-1013	604	22	)	)	PUNCT
iajs-1013	604	23	,	,	PUNCT
iajs-1013	604	24	"	"	PUNCT
iajs-1013	604	25	a	a	DET
iajs-1013	604	26	survry	survry	NOUN
iajs-1013	604	27	on	on	ADP
iajs-1013	604	28	the	the	DET
iajs-1013	604	29	theory	theory	NOUN
iajs-1013	604	30	of	of	ADP
iajs-1013	604	31	weaklyinjective	weaklyinjective	ADJ
iajs-1013	604	32	modules	module	NOUN
iajs-1013	604	33	"	"	PUNCT
iajs-1013	604	34	,	,	PUNCT
iajs-1013	604	35	computational	computational	ADJ
iajs-1013	604	36	algebra	algebra	NOUN
iajs-1013	604	37	,	,	PUNCT
iajs-1013	604	38	marcel	marcel	PROPN
iajs-1013	604	39	dekker	dekker	PROPN
iajs-1013	604	40	,	,	PUNCT
iajs-1013	604	41	205	205	NUM
iajs-1013	604	42	-	-	SYM
iajs-1013	604	43	232	232	NUM
iajs-1013	604	44	.	.	NOUN
iajs-1013	605	1	2	2	NUM
iajs-1013	605	2	.	.	X
iajs-1013	605	3	salih	salih	PROPN
iajs-1013	605	4	,	,	PUNCT
iajs-1013	605	5	m.	m.	NOUN
iajs-1013	605	6	,	,	PUNCT
iajs-1013	605	7	(	(	PUNCT
iajs-1013	605	8	1999	1999	NUM
iajs-1013	605	9	)	)	PUNCT
iajs-1013	605	10	,	,	PUNCT
iajs-1013	605	11	"	"	PUNCT
iajs-1013	605	12	a	a	DET
iajs-1013	605	13	note	note	NOUN
iajs-1013	605	14	on	on	ADP
iajs-1013	605	15	tightness	tightness	NOUN
iajs-1013	605	16	"	"	PUNCT
iajs-1013	605	17	,	,	PUNCT
iajs-1013	605	18	math	math	NOUN
iajs-1013	605	19	.	.	PUNCT
iajs-1013	606	1	dep	dep	NOUN
iajs-1013	606	2	.	.	PUNCT
iajs-1013	607	1	birzeit	birzeit	PROPN
iajs-1013	607	2	university	university	PROPN
iajs-1013	607	3	,	,	PUNCT
iajs-1013	607	4	p.o.box	p.o.box	PROPN
iajs-1013	607	5	14	14	NUM
iajs-1013	607	6	,	,	PUNCT
iajs-1013	607	7	glasqow	glasqow	PROPN
iajs-1013	607	8	m	m	PROPN
iajs-1013	607	9	ath	ath	PROPN
iajs-1013	607	10	.	.	PUNCT
iajs-1013	608	1	j.	j.	PROPN
iajs-1013	608	2	,	,	PUNCT
iajs-1013	608	3	41	41	NUM
iajs-1013	608	4	:	:	SYM
iajs-1013	608	5	43	43	NUM
iajs-1013	608	6	-	-	SYM
iajs-1013	608	7	44	44	NUM
iajs-1013	608	8	.	.	PUNCT
iajs-1013	609	1	3	3	X
iajs-1013	609	2	.	.	X
iajs-1013	609	3	jain	jain	PROPN
iajs-1013	609	4	,	,	PUNCT
iajs-1013	609	5	s.	s.	PROPN
iajs-1013	609	6	k.	k.	PROPN
iajs-1013	609	7	and	and	CCONJ
iajs-1013	609	8	lopez	lopez	PROPN
iajs-1013	609	9	-	-	PUNCT
iajs-1013	609	10	p	p	PROPN
iajs-1013	609	11	,	,	PUNCT
iajs-1013	609	12	s.	s.	PROPN
iajs-1013	609	13	r.	r.	PROPN
iajs-1013	609	14	,	,	PUNCT
iajs-1013	609	15	(	(	PUNCT
iajs-1013	609	16	1990	1990	NUM
iajs-1013	609	17	)	)	PUNCT
iajs-1013	609	18	,	,	PUNCT
iajs-1013	609	19	"	"	PUNCT
iajs-1013	609	20	rings	ring	NOUN
iajs-1013	609	21	whose	whose	DET
iajs-1013	609	22	cyclics	cyclic	NOUN
iajs-1013	609	23	are	be	AUX
iajs-1013	609	24	essentially	essentially	ADV
iajs-1013	609	25	embeddable	embeddable	ADJ
iajs-1013	609	26	in	in	ADP
iajs-1013	609	27	projective	projective	ADJ
iajs-1013	609	28	modules	module	NOUN
iajs-1013	609	29	"	"	PUNCT
iajs-1013	609	30	,	,	PUNCT
iajs-1013	609	31	j.	j.	PROPN
iajs-1013	609	32	of	of	ADP
iajs-1013	609	33	algebra	algebra	PROPN
iajs-1013	609	34	,	,	PUNCT
iajs-1013	609	35	128(1	128(1	NUM
iajs-1013	609	36	):	):	PUNCT
iajs-1013	609	37	208	208	NUM
iajs-1013	609	38	-	-	SYM
iajs-1013	609	39	220	220	NUM
iajs-1013	609	40	.	.	NOUN
iajs-1013	609	41	4	4	NUM
iajs-1013	609	42	.	.	X
iajs-1013	610	1	kasch	kasch	PROPN
iajs-1013	610	2	f.	f.	PROPN
iajs-1013	610	3	,	,	PUNCT
iajs-1013	610	4	(	(	PUNCT
iajs-1013	610	5	1982	1982	NUM
iajs-1013	610	6	)	)	PUNCT
iajs-1013	610	7	,	,	PUNCT
iajs-1013	610	8	"	"	PUNCT
iajs-1013	610	9	m	m	VERB
iajs-1013	610	10	odules	odule	NOUN
iajs-1013	610	11	and	and	CCONJ
iajs-1013	610	12	rings	ring	NOUN
iajs-1013	610	13	"	"	PUNCT
iajs-1013	610	14	,	,	PUNCT
iajs-1013	610	15	academic	academic	ADJ
iajs-1013	610	16	press	press	NOUN
iajs-1013	610	17	,	,	PUNCT
iajs-1013	610	18	london	london	PROPN
iajs-1013	610	19	,	,	PUNCT
iajs-1013	610	20	newyork	newyork	NOUN
iajs-1013	610	21	.	.	PUNCT
iajs-1013	611	1	5	5	X
iajs-1013	611	2	.	.	X
iajs-1013	611	3	mijbas	mijbas	PROPN
iajs-1013	611	4	a.	a.	PROPN
iajs-1013	611	5	s.	s.	PROPN
iajs-1013	611	6	,	,	PUNCT
iajs-1013	611	7	(	(	PUNCT
iajs-1013	611	8	1997	1997	NUM
iajs-1013	611	9	)	)	PUNCT
iajs-1013	611	10	,	,	PUNCT
iajs-1013	611	11	"	"	PUNCT
iajs-1013	611	12	quasi	quasi	ADJ
iajs-1013	611	13	-	-	ADJ
iajs-1013	611	14	dedekind	dedekind	ADJ
iajs-1013	611	15	modules	module	NOUN
iajs-1013	611	16	"	"	PUNCT
iajs-1013	611	17	,	,	PUNCT
iajs-1013	611	18	ph.d	ph.d	PROPN
iajs-1013	611	19	.	.	PUNCT
iajs-1013	612	1	thesis	thesis	NOUN
iajs-1013	612	2	,	,	PUNCT
iajs-1013	612	3	university	university	NOUN
iajs-1013	612	4	of	of	ADP
iajs-1013	612	5	baghdad	baghdad	PROPN
iajs-1013	612	6	.	.	PUNCT
iajs-1013	613	1	6	6	NUM
iajs-1013	613	2	.	.	X
iajs-1013	613	3	faith	faith	PROPN
iajs-1013	613	4	ii	ii	PROPN
iajs-1013	613	5	,	,	PUNCT
iajs-1013	613	6	c.	c.	PROPN
iajs-1013	613	7	,	,	PUNCT
iajs-1013	613	8	(	(	PUNCT
iajs-1013	613	9	1976	1976	NUM
iajs-1013	613	10	)	)	PUNCT
iajs-1013	613	11	,	,	PUNCT
iajs-1013	613	12	"	"	PUNCT
iajs-1013	613	13	algebra	algebra	NOUN
iajs-1013	613	14	,	,	PUNCT
iajs-1013	613	15	rings	ring	NOUN
iajs-1013	613	16	theory	theory	NOUN
iajs-1013	613	17	"	"	PUNCT
iajs-1013	613	18	,	,	PUNCT
iajs-1013	613	19	springer	springer	NOUN
iajs-1013	613	20	-	-	PUNCT
iajs-1013	613	21	verlay	verlay	NOUN
iajs-1013	613	22	,	,	PUNCT
iajs-1013	613	23	berlin	berlin	PROPN
iajs-1013	613	24	heidelberg	heidelberg	PROPN
iajs-1013	613	25	,	,	PUNCT
iajs-1013	613	26	new	new	PROPN
iajs-1013	613	27	york	york	PROPN
iajs-1013	613	28	.	.	PUNCT
iajs-1013	614	1	7	7	X
iajs-1013	614	2	.	.	NUM
iajs-1013	614	3	somchit	somchit	PROPN
iajs-1013	614	4	chotchasithit	chotchasithit	PROPN
iajs-1013	614	5	,	,	PUNCT
iajs-1013	614	6	(	(	PUNCT
iajs-1013	614	7	2002	2002	NUM
iajs-1013	614	8	)	)	PUNCT
iajs-1013	614	9	,	,	PUNCT
iajs-1013	614	10	"	"	PUNCT
iajs-1013	614	11	when	when	SCONJ
iajs-1013	614	12	is	be	AUX
iajs-1013	614	13	quasi	quasi	ADJ
iajs-1013	614	14	-	-	ADJ
iajs-1013	614	15	p	p	ADJ
iajs-1013	614	16	-	-	PUNCT
iajs-1013	614	17	injective	injective	ADJ
iajs-1013	614	18	module	module	NOUN
iajs-1013	614	19	continuous	continuous	ADJ
iajs-1013	614	20	,	,	PUNCT
iajs-1013	614	21	south	south	PROPN
iajs-1013	614	22	east	east	ADJ
iajs-1013	614	23	asian	asian	ADJ
iajs-1013	614	24	bulletin	bulletin	NOUN
iajs-1013	614	25	of	of	ADP
iajs-1013	614	26	mathematics	mathematic	NOUN
iajs-1013	614	27	,	,	PUNCT
iajs-1013	614	28	26	26	NUM
iajs-1013	614	29	:	:	SYM
iajs-1013	614	30	391	391	NUM
iajs-1013	614	31	-	-	SYM
iajs-1013	614	32	394	394	NUM
iajs-1013	614	33	.	.	NOUN
iajs-1013	614	34	8	8	NUM
iajs-1013	614	35	.	.	X
iajs-1013	615	1	goodearl	goodearl	PROPN
iajs-1013	615	2	,	,	PUNCT
iajs-1013	615	3	k.	k.	PROPN
iajs-1013	615	4	r.	r.	PROPN
iajs-1013	615	5	,	,	PUNCT
iajs-1013	615	6	(	(	PUNCT
iajs-1013	615	7	1976	1976	NUM
iajs-1013	615	8	)	)	PUNCT
iajs-1013	615	9	,	,	PUNCT
iajs-1013	615	10	"	"	PUNCT
iajs-1013	615	11	ring	ring	NOUN
iajs-1013	615	12	theory	theory	NOUN
iajs-1013	615	13	"	"	PUNCT
iajs-1013	615	14	,	,	PUNCT
iajs-1013	615	15	marcel	marcel	PROPN
iajs-1013	615	16	dekker	dekker	PROPN
iajs-1013	615	17	,	,	PUNCT
iajs-1013	615	18	new	new	PROPN
iajs-1013	615	19	york	york	PROPN
iajs-1013	615	20	.	.	PUNCT
iajs-1013	616	1	9	9	X
iajs-1013	616	2	.	.	X
iajs-1013	616	3	nicholson	nicholson	PROPN
iajs-1013	616	4	,	,	PUNCT
iajs-1013	616	5	w.	w.	PROPN
iajs-1013	616	6	k.	k.	PROPN
iajs-1013	616	7	and	and	CCONJ
iajs-1013	616	8	desale	desale	NOUN
iajs-1013	616	9	,	,	PUNCT
iajs-1013	616	10	g.	g.	PROPN
iajs-1013	616	11	,	,	PUNCT
iajs-1013	616	12	(	(	PUNCT
iajs-1013	616	13	1981	1981	NUM
iajs-1013	616	14	)	)	PUNCT
iajs-1013	616	15	,	,	PUNCT
iajs-1013	616	16	"	"	PUNCT
iajs-1013	616	17	endoprimitive	endoprimitive	ADJ
iajs-1013	616	18	rings	ring	NOUN
iajs-1013	616	19	"	"	PUNCT
iajs-1013	616	20	,	,	PUNCT
iajs-1013	616	21	j.	j.	PROPN
iajs-1013	616	22	algebra	algebra	PROPN
iajs-1013	616	23	,	,	PUNCT
iajs-1013	616	24	70	70	NUM
iajs-1013	616	25	:	:	SYM
iajs-1013	616	26	548560	548560	NUM
iajs-1013	616	27	.	.	PUNCT
iajs-1013	617	1	2010	2010	NUM
iajs-1013	617	2	)	)	PUNCT
iajs-1013	617	3	1	1	NUM
iajs-1013	617	4	(	(	PUNCT
iajs-1013	617	5	23المجلد	23المجلد	NUM
iajs-1013	617	6	مجلة	مجلة	VERB
iajs-1013	617	7	ابن	ابن	PROPN
iajs-1013	617	8	الھیثم	الھیثم	PROPN
iajs-1013	617	9	للعلوم	للعلوم	PROPN
iajs-1013	617	10	الصرفة	الصرفة	PROPN
iajs-1013	617	11	والتطبیقیة	والتطبیقیة	PROPN
iajs-1013	617	12	اغماریة	اغماریة	PROPN
iajs-1013	617	13	نسبیة	نسبیة	PROPN
iajs-1013	617	14	ضعیفة	ضعیفة	NOUN
iajs-1013	617	15	مقاسات	مقاسات	PROPN
iajs-1013	617	16	شبه	شبه	VERB
iajs-1013	617	17	علي	علي	NOUN
iajs-1013	617	18	سبع	سبع	ADV
iajs-1013	617	19	مجباس	مجباس	VERB
iajs-1013	617	20	،	،	NOUN
iajs-1013	617	21	كریم	كریم	NOUN
iajs-1013	617	22	صبر	صبر	PROPN
iajs-1013	617	23	خلف	خلف	PROPN
iajs-1013	617	24	،	،	PROPN
iajs-1013	617	25	لیلى	لیلى	PROPN
iajs-1013	617	26	سلمان	سلمان	PROPN
iajs-1013	617	27	محمود	محمود	ADJ
iajs-1013	617	28	د	د	PROPN
iajs-1013	617	29	،	،	NOUN
iajs-1013	617	30	بن	بن	PROPN
iajs-1013	617	31	الهیثمكلیة	الهیثمكلیة	PROPN
iajs-1013	617	32	التربیة	التربیة	PROPN
iajs-1013	617	33	ا	ا	PROPN
iajs-1013	617	34	،	،	PROPN
iajs-1013	617	35	قسم	قسم	PROPN
iajs-1013	617	36	الریاضیات	الریاضیات	PROPN
iajs-1013	617	37	جامعة	جامعة	PROPN
iajs-1013	617	38	بغدا	بغدا	PROPN
iajs-1013	617	39	جامعة	جامعة	PROPN
iajs-1013	617	40	تكریت	تكریت	PROPN
iajs-1013	617	41	،	،	PROPN
iajs-1013	617	42	كلیة	كلیة	PROPN
iajs-1013	617	43	علوم	علوم	PROPN
iajs-1013	617	44	الحاسبات	الحاسبات	PROPN
iajs-1013	617	45	والریاضیات	والریاضیات	VERB
iajs-1013	617	46	،	،	PROPN
iajs-1013	617	47	قسم	قسم	PROPN
iajs-1013	617	48	الریاضیات	الریاضیات	PROPN
iajs-1013	617	49	جامعة	جامعة	VERB
iajs-1013	617	50	االنبار	االنبار	PROPN
iajs-1013	617	51	،	،	NOUN
iajs-1013	618	1	كلیة	كلیة	PROPN
iajs-1013	618	2	العلوم	العلوم	NOUN
iajs-1013	618	3	،	،	PROPN
iajs-1013	618	4	قسم	قسم	PROPN
iajs-1013	618	5	الفیزیاء	الفیزیاء	PROPN
iajs-1013	618	6	الخالصة	الخالصة	PROPN
iajs-1013	618	7	م	م	PROPN
iajs-1013	618	8	.	.	PUNCT
iajs-1013	619	1	rمقاسا	rمقاسا	NOUN
iajs-1013	619	2	احادیاً	احادیاً	PROPN
iajs-1013	619	3	على	على	NOUN
iajs-1013	619	4	nو	nو	ADP
iajs-1013	619	5	mحلقة	mحلقة	PROPN
iajs-1013	619	6	تبادلیة	تبادلیة	PROPN
iajs-1013	619	7	بمحاید	بمحاید	PROPN
iajs-1013	619	8	وكل	وكل	PROPN
iajs-1013	620	1	من	من	DET
iajs-1013	620	2	rلتكن	rلتكن	NOUN
iajs-1013	620	3	أعطینا	أعطینا	NOUN
iajs-1013	620	4	هذا	هذا	NOUN
iajs-1013	620	5	البحث	البحث	NOUN
iajs-1013	620	6	اعماماً	اعماماً	DET
iajs-1013	620	7	للمفاهی	للمفاهی	NOUN
iajs-1013	620	8	ضعیف	ضعیف	PROPN
iajs-1013	620	9	n	n	CCONJ
iajs-1013	620	10	–	–	PUNCT
iajs-1013	620	11	اغماري	اغماري	ADJ
iajs-1013	620	12	–	–	PUNCT
iajs-1013	620	13	مقاس	مقاس	NOUN
iajs-1013	620	14	شبه	شبه	NOUN
iajs-1013	620	15	mأسمینا	mأسمینا	NOUN
iajs-1013	620	16	.	.	PUNCT
iajs-1013	621	1	اغماریة	اغماریة	PROPN
iajs-1013	621	2	نسبیة	نسبیة	PROPN
iajs-1013	621	3	ضعیفة	ضعیفة	VERB
iajs-1013	621	4	واحكام	واحكام	PROPN
iajs-1013	621	5	االغالق	االغالق	NOUN
iajs-1013	621	6	النسبیة	النسبیة	PROPN
iajs-1013	621	7	واغماریة	واغماریة	VERB
iajs-1013	621	8	ضعیفة	ضعیفة	NOUN
iajs-1013	621	9	للمقاسات	للمقاسات	NOUN
iajs-1013	621	10	,	,	PUNCT
iajs-1013	621	11	f	f	PROPN
iajs-1013	621	12			PROPN
iajs-1013	621	13	hom(n	hom(n	PROPN
iajs-1013	621	14	اذا	اذا	NOUN
iajs-1013	621	15	كان	كان	PROPN
iajs-1013	621	16	لكل	لكل	PRON
iajs-1013	621	17			VERB
iajs-1013	621	18	ان	ان	PROPN
iajs-1013	621	19	،	،	PROPN
iajs-1013	621	20	إذ	إذ	PROPN
iajs-1013	621	21	من	من	PROPN
iajs-1013	621	22	xیوجد	xیوجد	PROPN
iajs-1013	621	23	مقاس	مقاس	PROPN
iajs-1013	621	24	جزئي	جزئي	NOUN
iajs-1013	621	25	،	،	PROPN
iajs-1013	621	26	mاغماري	mاغماري	PROPN
iajs-1013	621	27	للمقاس	للمقاس	PROPN
iajs-1013	621	28	–	–	PUNCT
iajs-1013	621	29	الغالف	الغالف	NOUN
iajs-1013	621	30	الشبه	الشبه	VERB
iajs-1013	621	31			PROPN
iajs-1013	621	32	،	،	NOUN
iajs-1013	621	33	إذ	إذ	PROPN
iajs-1013	621	34	(	(	PUNCT
iajs-1013	621	35	f	f	PROPN
iajs-1013	621	36	(	(	PUNCT
iajs-1013	621	37	n	n	CCONJ
iajs-1013	621	38	)	)	PUNCT
iajs-1013	621	39			PROPN
iajs-1013	621	40	x	x	X
iajs-1013	622	1	≈	≈	PROPN
iajs-1013	622	2	m	m	PROPN
iajs-1013	622	3	.	.	PUNCT
iajs-1013	622	4	.mیمكن	.mیمكن	PUNCT
iajs-1013	623	1	ان	ان	ADV
iajs-1013	623	2	یغمر	یغمر	PROPN
iajs-1013	623	3	في	في	INTJ
iajs-1013	624	1	یغمر	یغمر	PROPN
iajs-1013	624	2	في	في	VERB
iajs-1013	624	3	nمن	nمن	CCONJ
iajs-1013	624	4	n	n	CCONJ
iajs-1013	624	5	/	/	SYM
iajs-1013	624	6	kاذا	kاذا	PROPN
iajs-1013	624	7	كان	كان	PROPN
iajs-1013	624	8	كل	كل	PROPN
iajs-1013	624	9	كسر	كسر	VERB
iajs-1013	624	10	n	n	CCONJ
iajs-1013	624	11	-محكم	-محكم	PROPN
iajs-1013	624	12	االغالق	االغالق	NOUN
iajs-1013	624	13	-	-	PUNCT
iajs-1013	624	14	مقاس	مقاس	NOUN
iajs-1013	624	15	شبه	شبه	NOUN
iajs-1013	624	16	mواسمینا	mواسمینا	PROPN
iajs-1013	624	17	ة	ة	ADP
iajs-1013	624	18	nلكل	nلكل	NOUN
iajs-1013	624	19	مقاس	مقاس	VERB
iajs-1013	624	20	منته	منته	ADJ
iajs-1013	624	21	التولد	التولد	PROPN
iajs-1013	624	22	ضعیف	ضعیف	PROPN
iajs-1013	624	23	n	n	CCONJ
iajs-1013	624	24	–	–	PUNCT
iajs-1013	624	25	اغماري	اغماري	ADJ
iajs-1013	624	26	–	–	PUNCT
iajs-1013	624	27	شبه	شبه	NOUN
iajs-1013	624	28	mاغماري	mاغماري	ADJ
iajs-1013	624	29	ضعیف	ضعیف	PROPN
iajs-1013	624	30	اذا	اذا	NOUN
iajs-1013	624	31	كان	كان	PROPN
iajs-1013	624	32	-مقاس	-مقاس	PROPN
iajs-1013	624	33	شبه	شبه	NOUN
iajs-1013	624	34	mبینما	mبینما	NOUN
iajs-1013	624	35	اسمینا	اسمینا	NOUN
iajs-1013	624	36	على	على	NOUN
iajs-1013	624	37	الحلق	الحلق	PROPN
iajs-1013	624	38	r	r	NOUN
iajs-1013	624	39	.	.	PUNCT
iajs-1013	625	1	ً	ً	NOUN
iajs-1013	625	2	عن	عن	NOUN
iajs-1013	625	3	ذلك	ذلك	ADJ
iajs-1013	625	4	عممنا	عممنا	NOUN
iajs-1013	625	5	بعض	بعض	NOUN
iajs-1013	625	6	الخواص	الخواص	PROPN
iajs-1013	625	7	للمقاسات	للمقاسات	NOUN
iajs-1013	625	8	االغماریة	االغماریة	VERB
iajs-1013	625	9	فضال	فضال	NOUN
iajs-1013	625	10	–	–	PUNCT
iajs-1013	625	11	n	n	NUM
iajs-1013	625	12	االغالق	االغالق	NOUN
iajs-1013	625	13	الضعیفة	الضعیفة	VERB
iajs-1013	625	14	والمحكمة	والمحكمة	NOUN
iajs-1013	625	15	–	–	PUNCT
iajs-1013	625	16	n	n	PRON
iajs-1013	625	17	واالغماریة	واالغماریة	PROPN
iajs-1013	625	18	الضعیفة	الضعیفة	NOUN
iajs-1013	625	19	االغماریة	االغماریة	PROPN
iajs-1013	625	20	الضعیفة	الضعیفة	VERB
iajs-1013	625	21	على	على	NOUN
iajs-1013	625	22	–	–	PUNCT
iajs-1013	625	23	وشبه	وشبه	VERB
iajs-1013	625	24	،	،	NOUN
iajs-1013	625	25	n	n	CCONJ
iajs-1013	625	26	–	–	PUNCT
iajs-1013	625	27	االغالق	االغالق	NOUN
iajs-1013	625	28	المحكمة	المحكمة	NOUN
iajs-1013	625	29	–	–	PUNCT
iajs-1013	625	30	وشبه	وشبه	VERB
iajs-1013	625	31	،	،	PROPN
iajs-1013	625	32	الضعیفة	الضعیفة	VERB
iajs-1013	625	33	n	n	NUM
iajs-1013	625	34	–	–	PUNCT
iajs-1013	625	35	االغماریة	االغماریة	PROPN
iajs-1013	625	36	–	–	PUNCT
iajs-1013	625	37	الى	الى	PROPN
iajs-1013	625	38	المقاسات	المقاسات	PROPN
iajs-1013	625	39	شبه	شبه	VERB
iajs-1013	625	40	.راسة	.راسة	PROPN
iajs-1013	625	41	العالقة	العالقة	PROPN
iajs-1013	625	42	بین	بین	PROPN
iajs-1013	625	43	هذه	هذه	PROPN
iajs-1013	625	44	المفاهیموقمنا	المفاهیموقمنا	PROPN
iajs-1013	625	45	بد	بد	PROPN
iajs-1013	625	46	.	.	PUNCT
iajs-1013	625	47	التوالي	التوالي	VERB