id	sid	tid	token	lemma	pos
american_scientific_journal-1367	1	1	american	american	PROPN
american_scientific_journal-1367	1	2	scientific	scientific	ADJ
american_scientific_journal-1367	1	3	research	research	NOUN
american_scientific_journal-1367	1	4	journal	journal	NOUN
american_scientific_journal-1367	1	5	for	for	ADP
american_scientific_journal-1367	1	6	engineering	engineering	NOUN
american_scientific_journal-1367	1	7	,	,	PUNCT
american_scientific_journal-1367	1	8	technology	technology	NOUN
american_scientific_journal-1367	1	9	,	,	PUNCT
american_scientific_journal-1367	1	10	and	and	CCONJ
american_scientific_journal-1367	1	11	sciences	science	NOUN
american_scientific_journal-1367	1	12	(	(	PUNCT
american_scientific_journal-1367	1	13	asrjets	asrjet	NOUN
american_scientific_journal-1367	1	14	)	)	PUNCT
american_scientific_journal-1367	1	15	issn	issn	PROPN
american_scientific_journal-1367	1	16	(	(	PUNCT
american_scientific_journal-1367	1	17	print	print	NOUN
american_scientific_journal-1367	1	18	)	)	PUNCT
american_scientific_journal-1367	1	19	2313	2313	NUM
american_scientific_journal-1367	1	20	-	-	SYM
american_scientific_journal-1367	1	21	4410	4410	NUM
american_scientific_journal-1367	1	22	,	,	PUNCT
american_scientific_journal-1367	1	23	issn	issn	PROPN
american_scientific_journal-1367	1	24	(	(	PUNCT
american_scientific_journal-1367	1	25	online	online	ADJ
american_scientific_journal-1367	1	26	)	)	PUNCT
american_scientific_journal-1367	1	27	2313	2313	NUM
american_scientific_journal-1367	1	28	-	-	SYM
american_scientific_journal-1367	1	29	4402	4402	NUM
american_scientific_journal-1367	1	30	©	©	PROPN
american_scientific_journal-1367	1	31	global	global	ADJ
american_scientific_journal-1367	1	32	society	society	NOUN
american_scientific_journal-1367	1	33	of	of	ADP
american_scientific_journal-1367	1	34	scientific	scientific	ADJ
american_scientific_journal-1367	1	35	research	research	NOUN
american_scientific_journal-1367	1	36	and	and	CCONJ
american_scientific_journal-1367	1	37	researchers	researcher	NOUN
american_scientific_journal-1367	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-1367	1	39	fp	fp	PROPN
american_scientific_journal-1367	1	40	-	-	PUNCT
american_scientific_journal-1367	1	41	projective	projective	ADJ
american_scientific_journal-1367	1	42	and	and	CCONJ
american_scientific_journal-1367	1	43	fp	fp	ADJ
american_scientific_journal-1367	1	44	-	-	PUNCT
american_scientific_journal-1367	1	45	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	1	46	modules	module	NOUN
american_scientific_journal-1367	1	47	shhaied	shhaie	VERB
american_scientific_journal-1367	1	48	riad	riad	PROPN
american_scientific_journal-1367	1	49	*	*	PUNCT
american_scientific_journal-1367	1	50	department	department	PROPN
american_scientific_journal-1367	1	51	of	of	ADP
american_scientific_journal-1367	1	52	university	university	NOUN
american_scientific_journal-1367	1	53	requirements	requirement	NOUN
american_scientific_journal-1367	1	54	-	-	PUNCT
american_scientific_journal-1367	1	55	faculty	faculty	NOUN
american_scientific_journal-1367	1	56	of	of	ADP
american_scientific_journal-1367	1	57	science	science	NOUN
american_scientific_journal-1367	1	58	and	and	CCONJ
american_scientific_journal-1367	1	59	arts	art	NOUN
american_scientific_journal-1367	1	60	,	,	PUNCT
american_scientific_journal-1367	1	61	international	international	ADJ
american_scientific_journal-1367	1	62	university	university	NOUN
american_scientific_journal-1367	1	63	for	for	ADP
american_scientific_journal-1367	1	64	science	science	NOUN
american_scientific_journal-1367	1	65	and	and	CCONJ
american_scientific_journal-1367	1	66	technology	technology	NOUN
american_scientific_journal-1367	1	67	,	,	PUNCT
american_scientific_journal-1367	1	68	damascus	damascus	PROPN
american_scientific_journal-1367	1	69	,	,	PUNCT
american_scientific_journal-1367	1	70	syria	syria	PROPN
american_scientific_journal-1367	1	71	e	e	PROPN
american_scientific_journal-1367	1	72	-	-	NOUN
american_scientific_journal-1367	1	73	mail	mail	NOUN
american_scientific_journal-1367	1	74	:	:	PUNCT
american_scientific_journal-1367	1	75	rshhaied@yahoo.com	rshhaied@yahoo.com	X
american_scientific_journal-1367	2	1	abstract	abstract	ADV
american_scientific_journal-1367	2	2	let	let	VERB
american_scientific_journal-1367	2	3	r	r	PRON
american_scientific_journal-1367	2	4	be	be	AUX
american_scientific_journal-1367	2	5	a	a	DET
american_scientific_journal-1367	2	6	ring	ring	NOUN
american_scientific_journal-1367	2	7	.	.	PUNCT
american_scientific_journal-1367	3	1	the	the	DET
american_scientific_journal-1367	3	2	concepts	concept	NOUN
american_scientific_journal-1367	3	3	of	of	ADP
american_scientific_journal-1367	3	4	fp	fp	X
american_scientific_journal-1367	3	5	-	-	PUNCT
american_scientific_journal-1367	3	6	projective	projective	ADJ
american_scientific_journal-1367	3	7	and	and	CCONJ
american_scientific_journal-1367	3	8	fp	fp	ADJ
american_scientific_journal-1367	3	9	-	-	PUNCT
american_scientific_journal-1367	3	10	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	3	11	r	r	NOUN
american_scientific_journal-1367	3	12	-	-	PUNCT
american_scientific_journal-1367	3	13	modules	module	NOUN
american_scientific_journal-1367	3	14	are	be	AUX
american_scientific_journal-1367	3	15	defined	define	VERB
american_scientific_journal-1367	3	16	.	.	PUNCT
american_scientific_journal-1367	4	1	these	these	DET
american_scientific_journal-1367	4	2	modules	module	NOUN
american_scientific_journal-1367	4	3	together	together	ADV
american_scientific_journal-1367	4	4	with	with	ADP
american_scientific_journal-1367	4	5	the	the	DET
american_scientific_journal-1367	4	6	concept	concept	NOUN
american_scientific_journal-1367	4	7	of	of	ADP
american_scientific_journal-1367	4	8	the	the	DET
american_scientific_journal-1367	4	9	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	4	10	theory	theory	NOUN
american_scientific_journal-1367	4	11	are	be	AUX
american_scientific_journal-1367	4	12	used	use	VERB
american_scientific_journal-1367	4	13	to	to	PART
american_scientific_journal-1367	4	14	characterize	characterize	VERB
american_scientific_journal-1367	4	15	left	left	ADJ
american_scientific_journal-1367	4	16	noetherian	noetherian	ADJ
american_scientific_journal-1367	4	17	rings	ring	NOUN
american_scientific_journal-1367	4	18	,	,	PUNCT
american_scientific_journal-1367	4	19	left	leave	VERB
american_scientific_journal-1367	4	20	perfect	perfect	ADJ
american_scientific_journal-1367	4	21	and	and	CCONJ
american_scientific_journal-1367	4	22	right	right	ADJ
american_scientific_journal-1367	4	23	coherent	coherent	ADJ
american_scientific_journal-1367	4	24	rings	ring	NOUN
american_scientific_journal-1367	4	25	,	,	PUNCT
american_scientific_journal-1367	4	26	left	leave	VERB
american_scientific_journal-1367	4	27	coherent	coherent	ADJ
american_scientific_journal-1367	4	28	rings	ring	NOUN
american_scientific_journal-1367	4	29	and	and	CCONJ
american_scientific_journal-1367	4	30	left	leave	VERB
american_scientific_journal-1367	4	31	fp	fp	NOUN
american_scientific_journal-1367	4	32	-	-	PUNCT
american_scientific_journal-1367	4	33	regular	regular	ADJ
american_scientific_journal-1367	4	34	rings	ring	NOUN
american_scientific_journal-1367	4	35	.	.	PUNCT
american_scientific_journal-1367	5	1	moreover	moreover	ADV
american_scientific_journal-1367	5	2	,	,	PUNCT
american_scientific_journal-1367	5	3	some	some	DET
american_scientific_journal-1367	5	4	known	know	VERB
american_scientific_journal-1367	5	5	characterizations	characterization	NOUN
american_scientific_journal-1367	5	6	of	of	ADP
american_scientific_journal-1367	5	7	von	von	PROPN
american_scientific_journal-1367	5	8	neumann	neumann	PROPN
american_scientific_journal-1367	5	9	regular	regular	PROPN
american_scientific_journal-1367	5	10	rings	ring	NOUN
american_scientific_journal-1367	5	11	are	be	AUX
american_scientific_journal-1367	5	12	found	find	VERB
american_scientific_journal-1367	5	13	.	.	PUNCT
american_scientific_journal-1367	6	1	keywords	keyword	NOUN
american_scientific_journal-1367	6	2	:	:	PUNCT
american_scientific_journal-1367	6	3	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	6	4	theory	theory	NOUN
american_scientific_journal-1367	6	5	;	;	PUNCT
american_scientific_journal-1367	6	6	fp	fp	ADJ
american_scientific_journal-1367	6	7	-	-	PUNCT
american_scientific_journal-1367	6	8	projective	projective	ADJ
american_scientific_journal-1367	6	9	modules	module	NOUN
american_scientific_journal-1367	6	10	;	;	PUNCT
american_scientific_journal-1367	6	11	fp	fp	X
american_scientific_journal-1367	6	12	-	-	PUNCT
american_scientific_journal-1367	6	13	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	6	14	modules	module	NOUN
american_scientific_journal-1367	6	15	;	;	PUNCT
american_scientific_journal-1367	6	16	noetherian	noetherian	ADJ
american_scientific_journal-1367	6	17	rings	ring	NOUN
american_scientific_journal-1367	6	18	;	;	PUNCT
american_scientific_journal-1367	6	19	perfect	perfect	ADJ
american_scientific_journal-1367	6	20	rings	ring	NOUN
american_scientific_journal-1367	6	21	;	;	PUNCT
american_scientific_journal-1367	6	22	coherent	coherent	ADJ
american_scientific_journal-1367	6	23	rings	ring	NOUN
american_scientific_journal-1367	6	24	;	;	PUNCT
american_scientific_journal-1367	6	25	fp	fp	X
american_scientific_journal-1367	6	26	-	-	PUNCT
american_scientific_journal-1367	6	27	regular	regular	ADJ
american_scientific_journal-1367	6	28	rings	ring	NOUN
american_scientific_journal-1367	6	29	.	.	PUNCT
american_scientific_journal-1367	7	1	1	1	X
american_scientific_journal-1367	7	2	.	.	X
american_scientific_journal-1367	7	3	introduction	introduction	NOUN
american_scientific_journal-1367	7	4	throughout	throughout	ADP
american_scientific_journal-1367	7	5	this	this	DET
american_scientific_journal-1367	7	6	paper	paper	NOUN
american_scientific_journal-1367	7	7	,	,	PUNCT
american_scientific_journal-1367	7	8	r	r	NOUN
american_scientific_journal-1367	7	9	is	be	AUX
american_scientific_journal-1367	7	10	an	an	DET
american_scientific_journal-1367	7	11	associative	associative	ADJ
american_scientific_journal-1367	7	12	ring	ring	NOUN
american_scientific_journal-1367	7	13	with	with	ADP
american_scientific_journal-1367	7	14	identity	identity	NOUN
american_scientific_journal-1367	7	15	and	and	CCONJ
american_scientific_journal-1367	7	16	all	all	DET
american_scientific_journal-1367	7	17	modules	module	NOUN
american_scientific_journal-1367	7	18	considered	consider	VERB
american_scientific_journal-1367	7	19	are	be	AUX
american_scientific_journal-1367	7	20	unitary	unitary	ADJ
american_scientific_journal-1367	7	21	.	.	PUNCT
american_scientific_journal-1367	8	1	for	for	ADP
american_scientific_journal-1367	8	2	any	any	DET
american_scientific_journal-1367	8	3	rmodule	rmodule	NOUN
american_scientific_journal-1367	8	4	m	m	PROPN
american_scientific_journal-1367	8	5	,	,	PUNCT
american_scientific_journal-1367	8	6	e(m	e(m	PROPN
american_scientific_journal-1367	8	7	)	)	PUNCT
american_scientific_journal-1367	8	8	is	be	AUX
american_scientific_journal-1367	8	9	the	the	DET
american_scientific_journal-1367	8	10	injective	injective	ADJ
american_scientific_journal-1367	8	11	envelope	envelope	NOUN
american_scientific_journal-1367	8	12	of	of	ADP
american_scientific_journal-1367	8	13	m	m	PROPN
american_scientific_journal-1367	8	14	,	,	PUNCT
american_scientific_journal-1367	8	15	the	the	DET
american_scientific_journal-1367	8	16	character	character	NOUN
american_scientific_journal-1367	8	17	module	module	NOUN
american_scientific_journal-1367	8	18	homℤ(m	homℤ(m	NOUN
american_scientific_journal-1367	8	19	,	,	PUNCT
american_scientific_journal-1367	8	20	ℚ/ℤ	ℚ/ℤ	NOUN
american_scientific_journal-1367	8	21	)	)	PUNCT
american_scientific_journal-1367	8	22	is	be	AUX
american_scientific_journal-1367	8	23	denoted	denote	VERB
american_scientific_journal-1367	8	24	by	by	ADP
american_scientific_journal-1367	8	25	m	m	PROPN
american_scientific_journal-1367	8	26	+	+	PROPN
american_scientific_journal-1367	8	27	.	.	PUNCT
american_scientific_journal-1367	9	1	r	r	X
american_scientific_journal-1367	9	2	-	-	PUNCT
american_scientific_journal-1367	9	3	mod	mod	ADJ
american_scientific_journal-1367	9	4	(	(	PUNCT
american_scientific_journal-1367	9	5	mod	mod	ADJ
american_scientific_journal-1367	9	6	-	-	PUNCT
american_scientific_journal-1367	9	7	r	r	NOUN
american_scientific_journal-1367	9	8	)	)	PUNCT
american_scientific_journal-1367	9	9	denotes	denote	NOUN
american_scientific_journal-1367	9	10	the	the	DET
american_scientific_journal-1367	9	11	category	category	NOUN
american_scientific_journal-1367	9	12	of	of	ADP
american_scientific_journal-1367	9	13	all	all	DET
american_scientific_journal-1367	9	14	left	left	ADJ
american_scientific_journal-1367	9	15	(	(	PUNCT
american_scientific_journal-1367	9	16	right	right	ADJ
american_scientific_journal-1367	9	17	)	)	PUNCT
american_scientific_journal-1367	9	18	r	r	NOUN
american_scientific_journal-1367	9	19	-	-	PUNCT
american_scientific_journal-1367	9	20	modules	module	NOUN
american_scientific_journal-1367	9	21	.	.	PUNCT
american_scientific_journal-1367	10	1	hom(m	hom(m	PROPN
american_scientific_journal-1367	10	2	,	,	PUNCT
american_scientific_journal-1367	10	3	n	n	CCONJ
american_scientific_journal-1367	10	4	)	)	PUNCT
american_scientific_journal-1367	10	5	(	(	PUNCT
american_scientific_journal-1367	10	6	resp	resp	NOUN
american_scientific_journal-1367	10	7	.	.	PROPN
american_scientific_journal-1367	10	8	,	,	PUNCT
american_scientific_journal-1367	10	9	ext1(m	ext1(m	NUM
american_scientific_journal-1367	10	10	,	,	PUNCT
american_scientific_journal-1367	10	11	n	n	CCONJ
american_scientific_journal-1367	10	12	)	)	PUNCT
american_scientific_journal-1367	10	13	,	,	PUNCT
american_scientific_journal-1367	10	14	tor1(m	tor1(m	NUM
american_scientific_journal-1367	10	15	,	,	PUNCT
american_scientific_journal-1367	10	16	n	n	CCONJ
american_scientific_journal-1367	10	17	)	)	PUNCT
american_scientific_journal-1367	10	18	)	)	PUNCT
american_scientific_journal-1367	10	19	means	mean	VERB
american_scientific_journal-1367	10	20	homr(m	homr(m	PROPN
american_scientific_journal-1367	10	21	,	,	PUNCT
american_scientific_journal-1367	10	22	n	n	CCONJ
american_scientific_journal-1367	10	23	)	)	PUNCT
american_scientific_journal-1367	10	24	(	(	PUNCT
american_scientific_journal-1367	10	25	resp	resp	NOUN
american_scientific_journal-1367	10	26	.	.	PROPN
american_scientific_journal-1367	10	27	,	,	PUNCT
american_scientific_journal-1367	10	28	extr1	extr1	PROPN
american_scientific_journal-1367	10	29	(	(	PUNCT
american_scientific_journal-1367	10	30	m	m	PROPN
american_scientific_journal-1367	10	31	,	,	PUNCT
american_scientific_journal-1367	10	32	n	n	CCONJ
american_scientific_journal-1367	10	33	)	)	PUNCT
american_scientific_journal-1367	10	34	,	,	PUNCT
american_scientific_journal-1367	10	35	tor1r(m	tor1r(m	PROPN
american_scientific_journal-1367	10	36	,	,	PUNCT
american_scientific_journal-1367	10	37	n	n	CCONJ
american_scientific_journal-1367	10	38	)	)	PUNCT
american_scientific_journal-1367	10	39	)	)	PUNCT
american_scientific_journal-1367	10	40	.	.	PUNCT
american_scientific_journal-1367	11	1	recall	recall	VERB
american_scientific_journal-1367	11	2	that	that	SCONJ
american_scientific_journal-1367	11	3	a	a	DET
american_scientific_journal-1367	11	4	left	left	ADJ
american_scientific_journal-1367	11	5	r	r	NOUN
american_scientific_journal-1367	11	6	-	-	PUNCT
american_scientific_journal-1367	11	7	module	module	NOUN
american_scientific_journal-1367	11	8	m	m	NOUN
american_scientific_journal-1367	11	9	is	be	AUX
american_scientific_journal-1367	11	10	fp	fp	ADJ
american_scientific_journal-1367	11	11	-	-	ADJ
american_scientific_journal-1367	11	12	injective	injective	ADJ
american_scientific_journal-1367	12	1	[	[	X
american_scientific_journal-1367	12	2	1	1	NUM
american_scientific_journal-1367	12	3	]	]	PUNCT
american_scientific_journal-1367	12	4	,	,	PUNCT
american_scientific_journal-1367	12	5	if	if	SCONJ
american_scientific_journal-1367	12	6	ext1(a	ext1(a	PROPN
american_scientific_journal-1367	12	7	,	,	PUNCT
american_scientific_journal-1367	12	8	m	m	NOUN
american_scientific_journal-1367	12	9	)	)	PUNCT
american_scientific_journal-1367	12	10	=	=	SYM
american_scientific_journal-1367	12	11	0	0	NUM
american_scientific_journal-1367	12	12	for	for	ADP
american_scientific_journal-1367	12	13	every	every	DET
american_scientific_journal-1367	12	14	finitely	finitely	ADV
american_scientific_journal-1367	12	15	presented	present	VERB
american_scientific_journal-1367	12	16	left	leave	VERB
american_scientific_journal-1367	12	17	r	r	NOUN
american_scientific_journal-1367	12	18	-	-	PUNCT
american_scientific_journal-1367	12	19	module	module	NOUN
american_scientific_journal-1367	12	20	a	a	NOUN
american_scientific_journal-1367	12	21	,	,	PUNCT
american_scientific_journal-1367	12	22	m	m	VERB
american_scientific_journal-1367	12	23	is	be	AUX
american_scientific_journal-1367	12	24	f	f	X
american_scientific_journal-1367	12	25	-	-	PUNCT
american_scientific_journal-1367	12	26	injective	injective	ADJ
american_scientific_journal-1367	13	1	[	[	X
american_scientific_journal-1367	13	2	2	2	NUM
american_scientific_journal-1367	13	3	]	]	PUNCT
american_scientific_journal-1367	13	4	if	if	SCONJ
american_scientific_journal-1367	13	5	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	13	6	/	/	SYM
american_scientific_journal-1367	13	7	i	i	PROPN
american_scientific_journal-1367	13	8	,	,	PUNCT
american_scientific_journal-1367	13	9	m	m	PROPN
american_scientific_journal-1367	13	10	)	)	PUNCT
american_scientific_journal-1367	13	11	=	=	SYM
american_scientific_journal-1367	13	12	0	0	NUM
american_scientific_journal-1367	13	13	for	for	ADP
american_scientific_journal-1367	13	14	every	every	DET
american_scientific_journal-1367	13	15	finitely	finitely	ADV
american_scientific_journal-1367	13	16	generated	generate	VERB
american_scientific_journal-1367	13	17	left	leave	VERB
american_scientific_journal-1367	13	18	ideal	ideal	NOUN
american_scientific_journal-1367	14	1	i	i	PRON
american_scientific_journal-1367	14	2	,	,	PUNCT
american_scientific_journal-1367	14	3	m	m	VERB
american_scientific_journal-1367	14	4	is	be	AUX
american_scientific_journal-1367	14	5	fp	fp	ADJ
american_scientific_journal-1367	14	6	-	-	PUNCT
american_scientific_journal-1367	14	7	injective	injective	ADJ
american_scientific_journal-1367	14	8	if	if	SCONJ
american_scientific_journal-1367	14	9	ext1(r	ext1(r	NOUN
american_scientific_journal-1367	14	10	/	/	SYM
american_scientific_journal-1367	14	11	i	i	PROPN
american_scientific_journal-1367	14	12	,	,	PUNCT
american_scientific_journal-1367	14	13	m	m	PROPN
american_scientific_journal-1367	14	14	)	)	PUNCT
american_scientific_journal-1367	14	15	=	=	SYM
american_scientific_journal-1367	14	16	0	0	NUM
american_scientific_journal-1367	14	17	for	for	ADP
american_scientific_journal-1367	14	18	every	every	DET
american_scientific_journal-1367	14	19	finitely	finitely	ADV
american_scientific_journal-1367	14	20	presented	present	VERB
american_scientific_journal-1367	14	21	left	leave	VERB
american_scientific_journal-1367	14	22	ideal	ideal	PROPN
american_scientific_journal-1367	14	23	i.	i.	PROPN
american_scientific_journal-1367	14	24	a	a	DET
american_scientific_journal-1367	14	25	right	right	ADJ
american_scientific_journal-1367	14	26	r	r	NOUN
american_scientific_journal-1367	14	27	-	-	PUNCT
american_scientific_journal-1367	14	28	module	module	NOUN
american_scientific_journal-1367	14	29	m	m	NOUN
american_scientific_journal-1367	14	30	is	be	AUX
american_scientific_journal-1367	14	31	fp	fp	ADJ
american_scientific_journal-1367	14	32	-	-	PUNCT
american_scientific_journal-1367	14	33	flat	flat	ADJ
american_scientific_journal-1367	14	34	,	,	PUNCT
american_scientific_journal-1367	14	35	if	if	SCONJ
american_scientific_journal-1367	14	36	tor1(m	tor1(m	NUM
american_scientific_journal-1367	14	37	,	,	PUNCT
american_scientific_journal-1367	14	38	r	r	NOUN
american_scientific_journal-1367	14	39	/	/	SYM
american_scientific_journal-1367	14	40	i	i	NOUN
american_scientific_journal-1367	14	41	)	)	PUNCT
american_scientific_journal-1367	15	1	=	=	SYM
american_scientific_journal-1367	15	2	0	0	NUM
american_scientific_journal-1367	15	3	for	for	ADP
american_scientific_journal-1367	15	4	every	every	DET
american_scientific_journal-1367	15	5	finitely	finitely	ADV
american_scientific_journal-1367	15	6	presented	present	VERB
american_scientific_journal-1367	15	7	left	leave	VERB
american_scientific_journal-1367	15	8	ideal	ideal	PROPN
american_scientific_journal-1367	15	9	i.	i.	PROPN
american_scientific_journal-1367	15	10	fp	fp	PROPN
american_scientific_journal-1367	15	11	-	-	PUNCT
american_scientific_journal-1367	15	12	injective	injective	ADJ
american_scientific_journal-1367	15	13	(	(	PUNCT
american_scientific_journal-1367	15	14	or	or	CCONJ
american_scientific_journal-1367	15	15	almost	almost	ADV
american_scientific_journal-1367	15	16	f	f	NOUN
american_scientific_journal-1367	15	17	-	-	PUNCT
american_scientific_journal-1367	15	18	injective	injective	ADJ
american_scientific_journal-1367	15	19	)	)	PUNCT
american_scientific_journal-1367	15	20	and	and	CCONJ
american_scientific_journal-1367	15	21	fp	fp	NOUN
american_scientific_journal-1367	15	22	-	-	PUNCT
american_scientific_journal-1367	15	23	flat	flat	ADJ
american_scientific_journal-1367	15	24	(	(	PUNCT
american_scientific_journal-1367	15	25	or	or	CCONJ
american_scientific_journal-1367	15	26	almost	almost	ADV
american_scientific_journal-1367	15	27	f	f	NOUN
american_scientific_journal-1367	15	28	-	-	PUNCT
american_scientific_journal-1367	15	29	flat	flat	ADJ
american_scientific_journal-1367	15	30	)	)	PUNCT
american_scientific_journal-1367	15	31	modules	module	NOUN
american_scientific_journal-1367	15	32	have	have	AUX
american_scientific_journal-1367	15	33	been	be	AUX
american_scientific_journal-1367	15	34	introduced	introduce	VERB
american_scientific_journal-1367	15	35	and	and	CCONJ
american_scientific_journal-1367	15	36	studded	stud	VERB
american_scientific_journal-1367	15	37	in	in	ADP
american_scientific_journal-1367	15	38	[	[	X
american_scientific_journal-1367	15	39	3	3	NUM
american_scientific_journal-1367	15	40	]	]	PUNCT
american_scientific_journal-1367	15	41	.	.	PUNCT
american_scientific_journal-1367	16	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-1367	17	1	*	*	PUNCT
american_scientific_journal-1367	17	2	corresponding	correspond	VERB
american_scientific_journal-1367	17	3	author	author	NOUN
american_scientific_journal-1367	17	4	.	.	PUNCT
american_scientific_journal-1367	18	1	132	132	NUM
american_scientific_journal-1367	18	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-1367	18	3	american	american	ADJ
american_scientific_journal-1367	18	4	scientific	scientific	ADJ
american_scientific_journal-1367	18	5	research	research	NOUN
american_scientific_journal-1367	18	6	journal	journal	NOUN
american_scientific_journal-1367	18	7	for	for	ADP
american_scientific_journal-1367	18	8	engineering	engineering	NOUN
american_scientific_journal-1367	18	9	,	,	PUNCT
american_scientific_journal-1367	18	10	technology	technology	NOUN
american_scientific_journal-1367	18	11	,	,	PUNCT
american_scientific_journal-1367	18	12	and	and	CCONJ
american_scientific_journal-1367	18	13	sciences	science	NOUN
american_scientific_journal-1367	18	14	(	(	PUNCT
american_scientific_journal-1367	18	15	asrjets	asrjet	NOUN
american_scientific_journal-1367	18	16	)	)	PUNCT
american_scientific_journal-1367	18	17	(	(	PUNCT
american_scientific_journal-1367	18	18	2016	2016	NUM
american_scientific_journal-1367	18	19	)	)	PUNCT
american_scientific_journal-1367	18	20	volume	volume	NOUN
american_scientific_journal-1367	18	21	17	17	NUM
american_scientific_journal-1367	18	22	,	,	PUNCT
american_scientific_journal-1367	18	23	no	no	DET
american_scientific_journal-1367	18	24	1	1	NUM
american_scientific_journal-1367	18	25	,	,	PUNCT
american_scientific_journal-1367	18	26	pp	pp	ADV
american_scientific_journal-1367	18	27	132	132	NUM
american_scientific_journal-1367	18	28	-	-	SYM
american_scientific_journal-1367	18	29	143	143	NUM
american_scientific_journal-1367	18	30	let	let	VERB
american_scientific_journal-1367	18	31	m	m	PRON
american_scientific_journal-1367	18	32	be	be	AUX
american_scientific_journal-1367	18	33	a	a	DET
american_scientific_journal-1367	18	34	left	left	ADJ
american_scientific_journal-1367	18	35	r	r	NOUN
american_scientific_journal-1367	18	36	-	-	PUNCT
american_scientific_journal-1367	18	37	module	module	NOUN
american_scientific_journal-1367	18	38	.	.	PUNCT
american_scientific_journal-1367	19	1	then	then	ADV
american_scientific_journal-1367	19	2	m	m	PROPN
american_scientific_journal-1367	19	3	is	be	AUX
american_scientific_journal-1367	19	4	fp	fp	ADJ
american_scientific_journal-1367	19	5	-	-	PUNCT
american_scientific_journal-1367	19	6	projective	projective	ADJ
american_scientific_journal-1367	19	7	(	(	PUNCT
american_scientific_journal-1367	19	8	f	f	NOUN
american_scientific_journal-1367	19	9	-	-	PUNCT
american_scientific_journal-1367	19	10	projective	projective	NOUN
american_scientific_journal-1367	19	11	)	)	PUNCT
american_scientific_journal-1367	19	12	,	,	PUNCT
american_scientific_journal-1367	19	13	if	if	SCONJ
american_scientific_journal-1367	19	14	ext1(m	ext1(m	NUM
american_scientific_journal-1367	19	15	,	,	PUNCT
american_scientific_journal-1367	19	16	n	n	CCONJ
american_scientific_journal-1367	19	17	)	)	PUNCT
american_scientific_journal-1367	20	1	=	=	SYM
american_scientific_journal-1367	20	2	0	0	NUM
american_scientific_journal-1367	20	3	for	for	ADP
american_scientific_journal-1367	20	4	any	any	DET
american_scientific_journal-1367	20	5	fp	fp	ADJ
american_scientific_journal-1367	20	6	-	-	PUNCT
american_scientific_journal-1367	20	7	injective	injective	ADJ
american_scientific_journal-1367	20	8	(	(	PUNCT
american_scientific_journal-1367	20	9	finjective	finjective	ADJ
american_scientific_journal-1367	20	10	)	)	PUNCT
american_scientific_journal-1367	20	11	left	leave	VERB
american_scientific_journal-1367	20	12	r	r	NOUN
american_scientific_journal-1367	20	13	-	-	PUNCT
american_scientific_journal-1367	20	14	module	module	NOUN
american_scientific_journal-1367	20	15	n	n	NOUN
american_scientific_journal-1367	20	16	,	,	PUNCT
american_scientific_journal-1367	20	17	m	m	VERB
american_scientific_journal-1367	20	18	is	be	AUX
american_scientific_journal-1367	20	19	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	20	20	if	if	SCONJ
american_scientific_journal-1367	20	21	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	20	22	,	,	PUNCT
american_scientific_journal-1367	20	23	m	m	NOUN
american_scientific_journal-1367	20	24	)	)	PUNCT
american_scientific_journal-1367	20	25	=	=	SYM
american_scientific_journal-1367	20	26	0	0	NUM
american_scientific_journal-1367	20	27	for	for	ADP
american_scientific_journal-1367	20	28	any	any	DET
american_scientific_journal-1367	20	29	flat	flat	ADJ
american_scientific_journal-1367	20	30	left	leave	VERB
american_scientific_journal-1367	20	31	r	r	NOUN
american_scientific_journal-1367	20	32	-	-	PUNCT
american_scientific_journal-1367	20	33	module	module	NOUN
american_scientific_journal-1367	20	34	n.	n.	NOUN
american_scientific_journal-1367	20	35	more	more	ADJ
american_scientific_journal-1367	20	36	information	information	NOUN
american_scientific_journal-1367	20	37	for	for	ADP
american_scientific_journal-1367	20	38	the	the	DET
american_scientific_journal-1367	20	39	concepts	concept	NOUN
american_scientific_journal-1367	20	40	of	of	ADP
american_scientific_journal-1367	20	41	fp	fp	PROPN
american_scientific_journal-1367	20	42	-	-	PUNCT
american_scientific_journal-1367	20	43	projective	projective	ADJ
american_scientific_journal-1367	20	44	,	,	PUNCT
american_scientific_journal-1367	20	45	f	f	NOUN
american_scientific_journal-1367	20	46	-	-	PUNCT
american_scientific_journal-1367	20	47	projective	projective	ADJ
american_scientific_journal-1367	20	48	and	and	CCONJ
american_scientific_journal-1367	20	49	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	20	50	modules	module	NOUN
american_scientific_journal-1367	20	51	can	can	AUX
american_scientific_journal-1367	20	52	be	be	AUX
american_scientific_journal-1367	20	53	found	find	VERB
american_scientific_journal-1367	20	54	in	in	ADP
american_scientific_journal-1367	20	55	[	[	X
american_scientific_journal-1367	20	56	4	4	NUM
american_scientific_journal-1367	20	57	]	]	PUNCT
american_scientific_journal-1367	20	58	,	,	PUNCT
american_scientific_journal-1367	21	1	[	[	X
american_scientific_journal-1367	21	2	5	5	NUM
american_scientific_journal-1367	21	3	]	]	PUNCT
american_scientific_journal-1367	21	4	and	and	CCONJ
american_scientific_journal-1367	21	5	[	[	X
american_scientific_journal-1367	21	6	6	6	NUM
american_scientific_journal-1367	21	7	]	]	PUNCT
american_scientific_journal-1367	21	8	.	.	PUNCT
american_scientific_journal-1367	22	1	given	give	VERB
american_scientific_journal-1367	22	2	a	a	DET
american_scientific_journal-1367	22	3	class	class	NOUN
american_scientific_journal-1367	22	4	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	22	5	⊆	⊆	NUM
american_scientific_journal-1367	22	6	mod	mod	PROPN
american_scientific_journal-1367	22	7	-	-	PUNCT
american_scientific_journal-1367	22	8	r	r	NOUN
american_scientific_journal-1367	22	9	,	,	PUNCT
american_scientific_journal-1367	22	10	then	then	ADV
american_scientific_journal-1367	22	11	𝒞𝒞⊥	𝒞𝒞⊥	PUNCT
american_scientific_journal-1367	22	12	=	=	PRON
american_scientific_journal-1367	22	13	{	{	PUNCT
american_scientific_journal-1367	22	14	n	n	CCONJ
american_scientific_journal-1367	22	15	∈	∈	PROPN
american_scientific_journal-1367	22	16	mod	mod	PROPN
american_scientific_journal-1367	22	17	-	-	PUNCT
american_scientific_journal-1367	22	18	r	r	NOUN
american_scientific_journal-1367	22	19	|	|	NOUN
american_scientific_journal-1367	22	20	ext1(c	ext1(c	NUM
american_scientific_journal-1367	22	21	,	,	PUNCT
american_scientific_journal-1367	22	22	n	n	CCONJ
american_scientific_journal-1367	22	23	)	)	PUNCT
american_scientific_journal-1367	22	24	=	=	SYM
american_scientific_journal-1367	22	25	0	0	NUM
american_scientific_journal-1367	22	26	for	for	ADP
american_scientific_journal-1367	22	27	all	all	DET
american_scientific_journal-1367	22	28	c	c	NOUN
american_scientific_journal-1367	22	29	∈	∈	NOUN
american_scientific_journal-1367	22	30	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	22	31	}	}	PUNCT
american_scientific_journal-1367	22	32	,	,	PUNCT
american_scientific_journal-1367	22	33	⊥𝒞𝒞	⊥𝒞𝒞	PROPN
american_scientific_journal-1367	22	34	=	=	SYM
american_scientific_journal-1367	22	35	{	{	PUNCT
american_scientific_journal-1367	22	36	n	n	CCONJ
american_scientific_journal-1367	22	37	∈	∈	PROPN
american_scientific_journal-1367	22	38	mod	mod	PROPN
american_scientific_journal-1367	22	39	-	-	PUNCT
american_scientific_journal-1367	22	40	r	r	NOUN
american_scientific_journal-1367	22	41	|	|	ADV
american_scientific_journal-1367	22	42	ext1	ext1	PROPN
american_scientific_journal-1367	22	43	(	(	PUNCT
american_scientific_journal-1367	22	44	n	n	CCONJ
american_scientific_journal-1367	22	45	,	,	PUNCT
american_scientific_journal-1367	22	46	c	c	NOUN
american_scientific_journal-1367	22	47	)	)	PUNCT
american_scientific_journal-1367	22	48	=	=	SYM
american_scientific_journal-1367	22	49	0	0	NUM
american_scientific_journal-1367	22	50	for	for	ADP
american_scientific_journal-1367	22	51	all	all	DET
american_scientific_journal-1367	22	52	c	c	NOUN
american_scientific_journal-1367	22	53	∈	∈	NOUN
american_scientific_journal-1367	22	54	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	22	55	}	}	PUNCT
american_scientific_journal-1367	22	56	.	.	PUNCT
american_scientific_journal-1367	23	1	when	when	SCONJ
american_scientific_journal-1367	23	2	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	23	3	⊆	⊆	NUM
american_scientific_journal-1367	23	4	r	r	NOUN
american_scientific_journal-1367	23	5	-	-	PUNCT
american_scientific_journal-1367	23	6	mod	mod	ADJ
american_scientific_journal-1367	23	7	,	,	PUNCT
american_scientific_journal-1367	23	8	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	23	9	and	and	CCONJ
american_scientific_journal-1367	23	10	⊥𝒞𝒞	⊥𝒞𝒞	PROPN
american_scientific_journal-1367	23	11	can	can	AUX
american_scientific_journal-1367	23	12	be	be	AUX
american_scientific_journal-1367	23	13	defined	define	VERB
american_scientific_journal-1367	23	14	similarly	similarly	ADV
american_scientific_journal-1367	23	15	.	.	PUNCT
american_scientific_journal-1367	24	1	let	let	VERB
american_scientific_journal-1367	24	2	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	24	3	be	be	AUX
american_scientific_journal-1367	24	4	a	a	DET
american_scientific_journal-1367	24	5	class	class	NOUN
american_scientific_journal-1367	24	6	of	of	ADP
american_scientific_journal-1367	24	7	left	left	ADJ
american_scientific_journal-1367	24	8	(	(	PUNCT
american_scientific_journal-1367	24	9	right	right	ADJ
american_scientific_journal-1367	24	10	)	)	PUNCT
american_scientific_journal-1367	24	11	r	r	NOUN
american_scientific_journal-1367	24	12	-	-	PUNCT
american_scientific_journal-1367	24	13	modules	module	NOUN
american_scientific_journal-1367	24	14	and	and	CCONJ
american_scientific_journal-1367	24	15	m	m	AUX
american_scientific_journal-1367	24	16	be	be	AUX
american_scientific_journal-1367	24	17	a	a	DET
american_scientific_journal-1367	24	18	left	left	ADJ
american_scientific_journal-1367	24	19	(	(	PUNCT
american_scientific_journal-1367	24	20	right	right	ADJ
american_scientific_journal-1367	24	21	)	)	PUNCT
american_scientific_journal-1367	24	22	r	r	NOUN
american_scientific_journal-1367	24	23	-	-	PUNCT
american_scientific_journal-1367	24	24	module	module	NOUN
american_scientific_journal-1367	24	25	.	.	PUNCT
american_scientific_journal-1367	25	1	a	a	DET
american_scientific_journal-1367	25	2	homomorphism	homomorphism	NOUN
american_scientific_journal-1367	25	3	φ	φ	NOUN
american_scientific_journal-1367	25	4	:	:	PUNCT
american_scientific_journal-1367	25	5	m	m	PROPN
american_scientific_journal-1367	25	6	→	→	SYM
american_scientific_journal-1367	25	7	f	f	X
american_scientific_journal-1367	25	8	where	where	SCONJ
american_scientific_journal-1367	25	9	f	f	PROPN
american_scientific_journal-1367	25	10	∈	∈	PROPN
american_scientific_journal-1367	25	11	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	25	12	is	be	AUX
american_scientific_journal-1367	25	13	called	call	VERB
american_scientific_journal-1367	25	14	a	a	DET
american_scientific_journal-1367	25	15	𝒞𝒞-preenvelope	𝒞𝒞-preenvelope	NOUN
american_scientific_journal-1367	25	16	[	[	X
american_scientific_journal-1367	25	17	7	7	NUM
american_scientific_journal-1367	25	18	]	]	PUNCT
american_scientific_journal-1367	25	19	of	of	ADP
american_scientific_journal-1367	25	20	m	m	PRON
american_scientific_journal-1367	25	21	if	if	SCONJ
american_scientific_journal-1367	25	22	for	for	ADP
american_scientific_journal-1367	25	23	any	any	DET
american_scientific_journal-1367	25	24	homomorphism	homomorphism	NOUN
american_scientific_journal-1367	26	1	f	f	X
american_scientific_journal-1367	26	2	:	:	PUNCT
american_scientific_journal-1367	26	3	m	m	VERB
american_scientific_journal-1367	26	4	→	→	PUNCT
american_scientific_journal-1367	26	5	f′	f′	ADJ
american_scientific_journal-1367	26	6	with	with	ADP
american_scientific_journal-1367	26	7	f′	f′	NOUN
american_scientific_journal-1367	26	8	∈	∈	PROPN
american_scientific_journal-1367	26	9	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	26	10	,	,	PUNCT
american_scientific_journal-1367	26	11	there	there	PRON
american_scientific_journal-1367	26	12	is	be	VERB
american_scientific_journal-1367	26	13	a	a	DET
american_scientific_journal-1367	26	14	homomorphism	homomorphism	NOUN
american_scientific_journal-1367	26	15	g	g	NOUN
american_scientific_journal-1367	26	16	:	:	PUNCT
american_scientific_journal-1367	26	17	f	f	PROPN
american_scientific_journal-1367	26	18	→	→	PUNCT
american_scientific_journal-1367	26	19	f′	f′	PROPN
american_scientific_journal-1367	26	20	such	such	ADJ
american_scientific_journal-1367	26	21	that	that	SCONJ
american_scientific_journal-1367	26	22	g	g	PROPN
american_scientific_journal-1367	26	23	φ	φ	PROPN
american_scientific_journal-1367	26	24	=	=	PROPN
american_scientific_journal-1367	26	25	f.	f.	PROPN
american_scientific_journal-1367	26	26	if	if	SCONJ
american_scientific_journal-1367	26	27	the	the	DET
american_scientific_journal-1367	26	28	only	only	ADJ
american_scientific_journal-1367	26	29	such	such	ADJ
american_scientific_journal-1367	26	30	g	g	NOUN
american_scientific_journal-1367	26	31	are	be	AUX
american_scientific_journal-1367	26	32	automorphisms	automorphism	NOUN
american_scientific_journal-1367	26	33	of	of	ADP
american_scientific_journal-1367	26	34	f	f	PROPN
american_scientific_journal-1367	26	35	when	when	SCONJ
american_scientific_journal-1367	26	36	f′	f′	PROPN
american_scientific_journal-1367	26	37	=	=	SYM
american_scientific_journal-1367	26	38	f	f	PROPN
american_scientific_journal-1367	26	39	and	and	CCONJ
american_scientific_journal-1367	26	40	f	f	PROPN
american_scientific_journal-1367	26	41	=	=	SYM
american_scientific_journal-1367	26	42	φ	φ	PROPN
american_scientific_journal-1367	26	43	,	,	PUNCT
american_scientific_journal-1367	26	44	then	then	ADV
american_scientific_journal-1367	26	45	the	the	DET
american_scientific_journal-1367	26	46	𝒞𝒞-preenvelope	𝒞𝒞-preenvelope	PROPN
american_scientific_journal-1367	26	47	φ	φ	PROPN
american_scientific_journal-1367	26	48	is	be	AUX
american_scientific_journal-1367	26	49	called	call	VERB
american_scientific_journal-1367	26	50	a	a	DET
american_scientific_journal-1367	26	51	𝒞𝒞-envelope	𝒞𝒞-envelope	NOUN
american_scientific_journal-1367	26	52	of	of	ADP
american_scientific_journal-1367	26	53	m.	m.	NOUN
american_scientific_journal-1367	26	54	following	follow	VERB
american_scientific_journal-1367	26	55	[	[	X
american_scientific_journal-1367	26	56	7	7	NUM
american_scientific_journal-1367	26	57	,	,	PUNCT
american_scientific_journal-1367	26	58	definition	definition	NOUN
american_scientific_journal-1367	26	59	7.1.6	7.1.6	NOUN
american_scientific_journal-1367	26	60	]	]	PUNCT
american_scientific_journal-1367	26	61	,	,	PUNCT
american_scientific_journal-1367	26	62	a	a	DET
american_scientific_journal-1367	26	63	monomorphism	monomorphism	NOUN
american_scientific_journal-1367	26	64	α	α	NOUN
american_scientific_journal-1367	26	65	:	:	PUNCT
american_scientific_journal-1367	26	66	m	m	PROPN
american_scientific_journal-1367	26	67	→	→	SYM
american_scientific_journal-1367	26	68	c	c	NOUN
american_scientific_journal-1367	26	69	with	with	ADP
american_scientific_journal-1367	26	70	c	c	PROPN
american_scientific_journal-1367	26	71	∈	∈	PROPN
american_scientific_journal-1367	26	72	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	26	73	is	be	AUX
american_scientific_journal-1367	26	74	said	say	VERB
american_scientific_journal-1367	26	75	to	to	PART
american_scientific_journal-1367	26	76	be	be	AUX
american_scientific_journal-1367	26	77	a	a	DET
american_scientific_journal-1367	26	78	special	special	ADJ
american_scientific_journal-1367	26	79	𝒞𝒞-preenvelope	𝒞𝒞-preenvelope	NOUN
american_scientific_journal-1367	26	80	of	of	ADP
american_scientific_journal-1367	26	81	m	m	PROPN
american_scientific_journal-1367	26	82	if	if	SCONJ
american_scientific_journal-1367	26	83	coker	coker	NOUN
american_scientific_journal-1367	26	84	(	(	PUNCT
american_scientific_journal-1367	26	85	α	α	NOUN
american_scientific_journal-1367	26	86	)	)	PUNCT
american_scientific_journal-1367	26	87	∈	∈	PROPN
american_scientific_journal-1367	27	1	⊥𝒞𝒞.	⊥𝒞𝒞.	ADP
american_scientific_journal-1367	27	2	dually	dually	ADV
american_scientific_journal-1367	27	3	we	we	PRON
american_scientific_journal-1367	27	4	have	have	VERB
american_scientific_journal-1367	27	5	the	the	DET
american_scientific_journal-1367	27	6	definitions	definition	NOUN
american_scientific_journal-1367	27	7	of	of	ADP
american_scientific_journal-1367	27	8	𝒞𝒞-precover	𝒞𝒞-precover	PROPN
american_scientific_journal-1367	27	9	,	,	PUNCT
american_scientific_journal-1367	27	10	special	special	ADJ
american_scientific_journal-1367	27	11	𝒞𝒞-precover	𝒞𝒞-precover	PROPN
american_scientific_journal-1367	27	12	and	and	CCONJ
american_scientific_journal-1367	27	13	-cover	-cover	PROPN
american_scientific_journal-1367	27	14	.	.	PUNCT
american_scientific_journal-1367	28	1	𝒞𝒞-envelopes	𝒞𝒞-envelope	NOUN
american_scientific_journal-1367	28	2	(	(	PUNCT
american_scientific_journal-1367	28	3	𝒞𝒞-covers	𝒞𝒞-covers	PROPN
american_scientific_journal-1367	28	4	)	)	PUNCT
american_scientific_journal-1367	28	5	may	may	AUX
american_scientific_journal-1367	28	6	not	not	PART
american_scientific_journal-1367	28	7	exist	exist	VERB
american_scientific_journal-1367	28	8	in	in	ADP
american_scientific_journal-1367	28	9	general	general	ADJ
american_scientific_journal-1367	28	10	,	,	PUNCT
american_scientific_journal-1367	28	11	but	but	CCONJ
american_scientific_journal-1367	28	12	if	if	SCONJ
american_scientific_journal-1367	28	13	they	they	PRON
american_scientific_journal-1367	28	14	exist	exist	VERB
american_scientific_journal-1367	28	15	,	,	PUNCT
american_scientific_journal-1367	28	16	they	they	PRON
american_scientific_journal-1367	28	17	are	be	AUX
american_scientific_journal-1367	28	18	unique	unique	ADJ
american_scientific_journal-1367	28	19	up	up	ADP
american_scientific_journal-1367	28	20	to	to	ADP
american_scientific_journal-1367	28	21	isomorphism	isomorphism	NOUN
american_scientific_journal-1367	28	22	.	.	PUNCT
american_scientific_journal-1367	29	1	let	let	VERB
american_scientific_journal-1367	29	2	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	29	3	,	,	PUNCT
american_scientific_journal-1367	29	4	ℬ	ℬ	PROPN
american_scientific_journal-1367	29	5	⊆	⊆	NUM
american_scientific_journal-1367	29	6	mod	mod	PROPN
american_scientific_journal-1367	29	7	-	-	PUNCT
american_scientific_journal-1367	29	8	r.	r.	VERB
american_scientific_journal-1367	29	9	the	the	DET
american_scientific_journal-1367	29	10	pair	pair	NOUN
american_scientific_journal-1367	29	11	(	(	PUNCT
american_scientific_journal-1367	29	12	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	29	13	,	,	PUNCT
american_scientific_journal-1367	29	14	ℬ	ℬ	NOUN
american_scientific_journal-1367	29	15	)	)	PUNCT
american_scientific_journal-1367	29	16	is	be	AUX
american_scientific_journal-1367	29	17	called	call	VERB
american_scientific_journal-1367	29	18	a	a	DET
american_scientific_journal-1367	29	19	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	29	20	theory	theory	NOUN
american_scientific_journal-1367	29	21	[	[	X
american_scientific_journal-1367	29	22	7	7	NUM
american_scientific_journal-1367	29	23	]	]	PUNCT
american_scientific_journal-1367	29	24	,	,	PUNCT
american_scientific_journal-1367	29	25	if	if	SCONJ
american_scientific_journal-1367	29	26	𝒜𝒜⊥=	𝒜𝒜⊥=	DET
american_scientific_journal-1367	29	27	ℬ	ℬ	NOUN
american_scientific_journal-1367	29	28	and	and	CCONJ
american_scientific_journal-1367	29	29	⊥ℬ	⊥ℬ	PROPN
american_scientific_journal-1367	29	30	=	=	SYM
american_scientific_journal-1367	29	31	𝒜𝒜.	𝒜𝒜.	X
american_scientific_journal-1367	30	1	the	the	DET
american_scientific_journal-1367	30	2	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	30	3	theory	theory	NOUN
american_scientific_journal-1367	30	4	(	(	PUNCT
american_scientific_journal-1367	30	5	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	30	6	,	,	PUNCT
american_scientific_journal-1367	30	7	ℬ	ℬ	NOUN
american_scientific_journal-1367	30	8	)	)	PUNCT
american_scientific_journal-1367	30	9	,	,	PUNCT
american_scientific_journal-1367	30	10	when	when	SCONJ
american_scientific_journal-1367	30	11	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	30	12	,	,	PUNCT
american_scientific_journal-1367	30	13	ℬ	ℬ	PROPN
american_scientific_journal-1367	30	14	⊆	⊆	NUM
american_scientific_journal-1367	30	15	r	r	NOUN
american_scientific_journal-1367	30	16	-	-	PUNCT
american_scientific_journal-1367	30	17	mod	mod	NOUN
american_scientific_journal-1367	30	18	can	can	AUX
american_scientific_journal-1367	30	19	be	be	AUX
american_scientific_journal-1367	30	20	defined	define	VERB
american_scientific_journal-1367	30	21	similarly	similarly	ADV
american_scientific_journal-1367	30	22	.	.	PUNCT
american_scientific_journal-1367	31	1	a	a	DET
american_scientific_journal-1367	31	2	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	31	3	theory	theory	NOUN
american_scientific_journal-1367	31	4	(	(	PUNCT
american_scientific_journal-1367	31	5	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	31	6	,	,	PUNCT
american_scientific_journal-1367	31	7	ℬ	ℬ	NOUN
american_scientific_journal-1367	31	8	)	)	PUNCT
american_scientific_journal-1367	31	9	is	be	AUX
american_scientific_journal-1367	31	10	generated	generate	VERB
american_scientific_journal-1367	31	11	(	(	PUNCT
american_scientific_journal-1367	31	12	cogenerated	cogenerate	VERB
american_scientific_journal-1367	31	13	)	)	PUNCT
american_scientific_journal-1367	31	14	by	by	ADP
american_scientific_journal-1367	31	15	a	a	DET
american_scientific_journal-1367	31	16	class	class	NOUN
american_scientific_journal-1367	31	17	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	31	18	⊆	⊆	NUM
american_scientific_journal-1367	31	19	mod	mod	PROPN
american_scientific_journal-1367	31	20	-	-	PUNCT
american_scientific_journal-1367	31	21	r	r	NOUN
american_scientific_journal-1367	31	22	,	,	PUNCT
american_scientific_journal-1367	31	23	if	if	SCONJ
american_scientific_journal-1367	31	24	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	31	25	=	=	PUNCT
american_scientific_journal-1367	31	26	⊥𝒞𝒞	⊥𝒞𝒞	PROPN
american_scientific_journal-1367	31	27	(	(	PUNCT
american_scientific_journal-1367	31	28	ℬ	ℬ	NOUN
american_scientific_journal-1367	31	29	=	=	ADJ
american_scientific_journal-1367	31	30	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	31	31	)	)	PUNCT
american_scientific_journal-1367	31	32	.	.	PUNCT
american_scientific_journal-1367	32	1	a	a	DET
american_scientific_journal-1367	32	2	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	32	3	theory	theory	NOUN
american_scientific_journal-1367	32	4	(	(	PUNCT
american_scientific_journal-1367	32	5	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	32	6	,	,	PUNCT
american_scientific_journal-1367	32	7	ℬ	ℬ	NOUN
american_scientific_journal-1367	32	8	)	)	PUNCT
american_scientific_journal-1367	32	9	is	be	AUX
american_scientific_journal-1367	32	10	said	say	VERB
american_scientific_journal-1367	32	11	to	to	PART
american_scientific_journal-1367	32	12	be	be	AUX
american_scientific_journal-1367	32	13	perfect	perfect	ADJ
american_scientific_journal-1367	32	14	(	(	PUNCT
american_scientific_journal-1367	32	15	complete	complete	ADJ
american_scientific_journal-1367	32	16	)	)	PUNCT
american_scientific_journal-1367	32	17	if	if	SCONJ
american_scientific_journal-1367	32	18	every	every	DET
american_scientific_journal-1367	32	19	right	right	ADJ
american_scientific_journal-1367	32	20	r	r	NOUN
american_scientific_journal-1367	32	21	-	-	PUNCT
american_scientific_journal-1367	32	22	module	module	NOUN
american_scientific_journal-1367	32	23	has	have	VERB
american_scientific_journal-1367	32	24	a	a	DET
american_scientific_journal-1367	32	25	ℬ-envelope	ℬ-envelope	PROPN
american_scientific_journal-1367	32	26	and	and	CCONJ
american_scientific_journal-1367	32	27	an	an	DET
american_scientific_journal-1367	32	28	𝒜𝒜-cover	𝒜𝒜-cover	PROPN
american_scientific_journal-1367	32	29	(	(	PUNCT
american_scientific_journal-1367	32	30	a	a	DET
american_scientific_journal-1367	32	31	special	special	ADJ
american_scientific_journal-1367	32	32	ℬ-preenvelope	ℬ-preenvelope	PROPN
american_scientific_journal-1367	32	33	and	and	CCONJ
american_scientific_journal-1367	32	34	a	a	DET
american_scientific_journal-1367	32	35	special	special	ADJ
american_scientific_journal-1367	32	36	𝒜𝒜-precover	𝒜𝒜-precover	NOUN
american_scientific_journal-1367	32	37	)	)	PUNCT
american_scientific_journal-1367	32	38	(	(	PUNCT
american_scientific_journal-1367	32	39	see	see	VERB
american_scientific_journal-1367	32	40	[	[	X
american_scientific_journal-1367	32	41	8	8	NUM
american_scientific_journal-1367	32	42	]	]	PUNCT
american_scientific_journal-1367	32	43	and	and	CCONJ
american_scientific_journal-1367	32	44	[	[	X
american_scientific_journal-1367	32	45	9	9	NUM
american_scientific_journal-1367	32	46	]	]	NUM
american_scientific_journal-1367	32	47	)	)	PUNCT
american_scientific_journal-1367	32	48	.	.	PUNCT
american_scientific_journal-1367	33	1	a	a	DET
american_scientific_journal-1367	33	2	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	33	3	theory	theory	NOUN
american_scientific_journal-1367	33	4	(	(	PUNCT
american_scientific_journal-1367	33	5	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	33	6	,	,	PUNCT
american_scientific_journal-1367	33	7	ℬ	ℬ	NOUN
american_scientific_journal-1367	33	8	)	)	PUNCT
american_scientific_journal-1367	33	9	is	be	AUX
american_scientific_journal-1367	33	10	said	say	VERB
american_scientific_journal-1367	33	11	to	to	PART
american_scientific_journal-1367	33	12	be	be	AUX
american_scientific_journal-1367	33	13	hereditary	hereditary	ADJ
american_scientific_journal-1367	33	14	[	[	X
american_scientific_journal-1367	33	15	8	8	NUM
american_scientific_journal-1367	33	16	]	]	X
american_scientific_journal-1367	33	17	if	if	SCONJ
american_scientific_journal-1367	33	18	whenever	whenever	SCONJ
american_scientific_journal-1367	33	19	0	0	NUM
american_scientific_journal-1367	33	20	→	→	SYM
american_scientific_journal-1367	33	21	k→	k→	NOUN
american_scientific_journal-1367	33	22	p	p	X
american_scientific_journal-1367	33	23	→	→	SYM
american_scientific_journal-1367	33	24	f	f	PROPN
american_scientific_journal-1367	33	25	→	→	SYM
american_scientific_journal-1367	33	26	0	0	NUM
american_scientific_journal-1367	33	27	is	be	AUX
american_scientific_journal-1367	33	28	exact	exact	ADJ
american_scientific_journal-1367	33	29	with	with	ADP
american_scientific_journal-1367	33	30	p	p	PROPN
american_scientific_journal-1367	33	31	,	,	PUNCT
american_scientific_journal-1367	33	32	f	f	PROPN
american_scientific_journal-1367	33	33	∈	∈	PROPN
american_scientific_journal-1367	33	34	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	33	35	,	,	PUNCT
american_scientific_journal-1367	33	36	then	then	ADV
american_scientific_journal-1367	33	37	k	k	PROPN
american_scientific_journal-1367	33	38	is	be	AUX
american_scientific_journal-1367	33	39	also	also	ADV
american_scientific_journal-1367	33	40	in	in	ADP
american_scientific_journal-1367	33	41	𝒜𝒜.	𝒜𝒜.	X
american_scientific_journal-1367	33	42	by	by	ADP
american_scientific_journal-1367	33	43	[	[	X
american_scientific_journal-1367	33	44	8	8	NUM
american_scientific_journal-1367	33	45	,	,	PUNCT
american_scientific_journal-1367	33	46	proposition	proposition	NOUN
american_scientific_journal-1367	33	47	1.2	1.2	NUM
american_scientific_journal-1367	33	48	]	]	PUNCT
american_scientific_journal-1367	33	49	,	,	PUNCT
american_scientific_journal-1367	33	50	(	(	PUNCT
american_scientific_journal-1367	33	51	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	33	52	,	,	PUNCT
american_scientific_journal-1367	33	53	ℬ	ℬ	NOUN
american_scientific_journal-1367	33	54	)	)	PUNCT
american_scientific_journal-1367	33	55	is	be	AUX
american_scientific_journal-1367	33	56	hereditary	hereditary	ADJ
american_scientific_journal-1367	33	57	if	if	SCONJ
american_scientific_journal-1367	33	58	and	and	CCONJ
american_scientific_journal-1367	33	59	only	only	ADV
american_scientific_journal-1367	33	60	if	if	SCONJ
american_scientific_journal-1367	33	61	0	0	NUM
american_scientific_journal-1367	33	62	→	→	SYM
american_scientific_journal-1367	33	63	a→	a→	ADP
american_scientific_journal-1367	33	64	b	b	X
american_scientific_journal-1367	33	65	→c	→c	PUNCT
american_scientific_journal-1367	33	66	→	→	SYM
american_scientific_journal-1367	33	67	0	0	NUM
american_scientific_journal-1367	33	68	is	be	AUX
american_scientific_journal-1367	33	69	exact	exact	ADJ
american_scientific_journal-1367	33	70	with	with	ADP
american_scientific_journal-1367	33	71	a	a	DET
american_scientific_journal-1367	33	72	,	,	PUNCT
american_scientific_journal-1367	33	73	b	b	PROPN
american_scientific_journal-1367	33	74	∈	∈	PROPN
american_scientific_journal-1367	33	75	ℬ	ℬ	NOUN
american_scientific_journal-1367	33	76	,	,	PUNCT
american_scientific_journal-1367	33	77	then	then	ADV
american_scientific_journal-1367	33	78	c	c	PROPN
american_scientific_journal-1367	33	79	is	be	AUX
american_scientific_journal-1367	33	80	also	also	ADV
american_scientific_journal-1367	33	81	in	in	ADP
american_scientific_journal-1367	33	82	ℬ.	ℬ.	PROPN
american_scientific_journal-1367	33	83	in	in	ADP
american_scientific_journal-1367	33	84	section	section	NOUN
american_scientific_journal-1367	33	85	two	two	NUM
american_scientific_journal-1367	33	86	of	of	ADP
american_scientific_journal-1367	33	87	this	this	DET
american_scientific_journal-1367	33	88	note	note	NOUN
american_scientific_journal-1367	33	89	,	,	PUNCT
american_scientific_journal-1367	33	90	we	we	PRON
american_scientific_journal-1367	33	91	first	first	ADV
american_scientific_journal-1367	33	92	extend	extend	VERB
american_scientific_journal-1367	33	93	the	the	DET
american_scientific_journal-1367	33	94	concepts	concept	NOUN
american_scientific_journal-1367	33	95	of	of	ADP
american_scientific_journal-1367	33	96	f	f	NOUN
american_scientific_journal-1367	33	97	-	-	PUNCT
american_scientific_journal-1367	33	98	projective	projective	ADJ
american_scientific_journal-1367	33	99	modules	module	NOUN
american_scientific_journal-1367	33	100	and	and	CCONJ
american_scientific_journal-1367	33	101	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	33	102	modules	module	NOUN
american_scientific_journal-1367	33	103	to	to	ADP
american_scientific_journal-1367	33	104	fpprojective	fpprojective	ADJ
american_scientific_journal-1367	33	105	modules	module	NOUN
american_scientific_journal-1367	33	106	and	and	CCONJ
american_scientific_journal-1367	33	107	fp	fp	ADJ
american_scientific_journal-1367	33	108	-	-	PUNCT
american_scientific_journal-1367	33	109	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	33	110	modules	module	NOUN
american_scientific_journal-1367	33	111	respectively	respectively	ADV
american_scientific_journal-1367	33	112	,	,	PUNCT
american_scientific_journal-1367	33	113	and	and	CCONJ
american_scientific_journal-1367	33	114	then	then	ADV
american_scientific_journal-1367	33	115	give	give	VERB
american_scientific_journal-1367	33	116	some	some	DET
american_scientific_journal-1367	33	117	characterizations	characterization	NOUN
american_scientific_journal-1367	33	118	and	and	CCONJ
american_scientific_journal-1367	33	119	properties	property	NOUN
american_scientific_journal-1367	33	120	of	of	ADP
american_scientific_journal-1367	33	121	fp	fp	ADJ
american_scientific_journal-1367	33	122	-	-	PUNCT
american_scientific_journal-1367	33	123	injective	injective	ADJ
american_scientific_journal-1367	33	124	modules	module	NOUN
american_scientific_journal-1367	33	125	and	and	CCONJ
american_scientific_journal-1367	33	126	fp	fp	ADJ
american_scientific_journal-1367	33	127	-	-	PUNCT
american_scientific_journal-1367	33	128	projective	projective	ADJ
american_scientific_journal-1367	33	129	modules	module	NOUN
american_scientific_journal-1367	33	130	.	.	PUNCT
american_scientific_journal-1367	34	1	we	we	PRON
american_scientific_journal-1367	34	2	also	also	ADV
american_scientific_journal-1367	34	3	prove	prove	VERB
american_scientific_journal-1367	34	4	that	that	SCONJ
american_scientific_journal-1367	34	5	(	(	PUNCT
american_scientific_journal-1367	34	6	fp	fp	NOUN
american_scientific_journal-1367	34	7	-	-	PUNCT
american_scientific_journal-1367	34	8	proj	proj	NOUN
american_scientific_journal-1367	34	9	,	,	PUNCT
american_scientific_journal-1367	34	10	fp	fp	PROPN
american_scientific_journal-1367	34	11	-	-	PUNCT
american_scientific_journal-1367	34	12	inj	inj	NOUN
american_scientific_journal-1367	34	13	)	)	PUNCT
american_scientific_journal-1367	34	14	is	be	AUX
american_scientific_journal-1367	34	15	a	a	DET
american_scientific_journal-1367	34	16	complete	complete	ADJ
american_scientific_journal-1367	34	17	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	34	18	theory	theory	NOUN
american_scientific_journal-1367	34	19	,	,	PUNCT
american_scientific_journal-1367	34	20	and	and	CCONJ
american_scientific_journal-1367	34	21	(	(	PUNCT
american_scientific_journal-1367	34	22	fp	fp	INTJ
american_scientific_journal-1367	34	23	-	-	PUNCT
american_scientific_journal-1367	34	24	fl	fl	PROPN
american_scientific_journal-1367	34	25	,	,	PUNCT
american_scientific_journal-1367	34	26	fp	fp	ADJ
american_scientific_journal-1367	34	27	-	-	PUNCT
american_scientific_journal-1367	34	28	cot	cot	NOUN
american_scientific_journal-1367	34	29	)	)	PUNCT
american_scientific_journal-1367	34	30	is	be	AUX
american_scientific_journal-1367	34	31	a	a	DET
american_scientific_journal-1367	34	32	perfect	perfect	ADJ
american_scientific_journal-1367	34	33	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	34	34	theory	theory	NOUN
american_scientific_journal-1367	34	35	,	,	PUNCT
american_scientific_journal-1367	34	36	where	where	SCONJ
american_scientific_journal-1367	34	37	fp	fp	X
american_scientific_journal-1367	34	38	-	-	PUNCT
american_scientific_journal-1367	34	39	proj	proj	PROPN
american_scientific_journal-1367	34	40	(	(	PUNCT
american_scientific_journal-1367	34	41	fp	fp	ADJ
american_scientific_journal-1367	34	42	-	-	PUNCT
american_scientific_journal-1367	34	43	inj	inj	NOUN
american_scientific_journal-1367	34	44	)	)	PUNCT
american_scientific_journal-1367	34	45	denotes	denote	VERB
american_scientific_journal-1367	34	46	the	the	DET
american_scientific_journal-1367	34	47	class	class	NOUN
american_scientific_journal-1367	34	48	of	of	ADP
american_scientific_journal-1367	34	49	all	all	DET
american_scientific_journal-1367	34	50	fpprojective	fpprojective	ADJ
american_scientific_journal-1367	34	51	(	(	PUNCT
american_scientific_journal-1367	34	52	fp	fp	ADJ
american_scientific_journal-1367	34	53	-	-	PUNCT
american_scientific_journal-1367	34	54	injective	injective	ADJ
american_scientific_journal-1367	34	55	)	)	PUNCT
american_scientific_journal-1367	34	56	modules	module	NOUN
american_scientific_journal-1367	34	57	,	,	PUNCT
american_scientific_journal-1367	34	58	and	and	CCONJ
american_scientific_journal-1367	34	59	fp	fp	X
american_scientific_journal-1367	34	60	-	-	PUNCT
american_scientific_journal-1367	34	61	fl	fl	PROPN
american_scientific_journal-1367	34	62	(	(	PUNCT
american_scientific_journal-1367	34	63	fp	fp	INTJ
american_scientific_journal-1367	34	64	-	-	PUNCT
american_scientific_journal-1367	34	65	cot	cot	NOUN
american_scientific_journal-1367	34	66	)	)	PUNCT
american_scientific_journal-1367	34	67	the	the	DET
american_scientific_journal-1367	34	68	class	class	NOUN
american_scientific_journal-1367	34	69	of	of	ADP
american_scientific_journal-1367	34	70	all	all	DET
american_scientific_journal-1367	34	71	fp	fp	ADJ
american_scientific_journal-1367	34	72	-	-	PUNCT
american_scientific_journal-1367	34	73	flat	flat	ADJ
american_scientific_journal-1367	34	74	(	(	PUNCT
american_scientific_journal-1367	34	75	fp	fp	ADJ
american_scientific_journal-1367	34	76	-	-	PUNCT
american_scientific_journal-1367	34	77	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	34	78	)	)	PUNCT
american_scientific_journal-1367	34	79	modules	module	NOUN
american_scientific_journal-1367	34	80	.	.	PUNCT
american_scientific_journal-1367	35	1	the	the	DET
american_scientific_journal-1367	35	2	activity	activity	NOUN
american_scientific_journal-1367	35	3	of	of	ADP
american_scientific_journal-1367	35	4	section	section	NOUN
american_scientific_journal-1367	35	5	two	two	NUM
american_scientific_journal-1367	35	6	will	will	AUX
american_scientific_journal-1367	35	7	be	be	AUX
american_scientific_journal-1367	35	8	appeared	appear	VERB
american_scientific_journal-1367	35	9	in	in	ADP
american_scientific_journal-1367	35	10	section	section	NOUN
american_scientific_journal-1367	35	11	three	three	NUM
american_scientific_journal-1367	35	12	,	,	PUNCT
american_scientific_journal-1367	35	13	where	where	SCONJ
american_scientific_journal-1367	35	14	we	we	PRON
american_scientific_journal-1367	35	15	present	present	VERB
american_scientific_journal-1367	35	16	some	some	DET
american_scientific_journal-1367	35	17	characterizations	characterization	NOUN
american_scientific_journal-1367	35	18	of	of	ADP
american_scientific_journal-1367	35	19	left	left	ADJ
american_scientific_journal-1367	35	20	noetherian	noetherian	ADJ
american_scientific_journal-1367	35	21	rings	ring	NOUN
american_scientific_journal-1367	35	22	,	,	PUNCT
american_scientific_journal-1367	35	23	left	leave	VERB
american_scientific_journal-1367	35	24	coherent	coherent	ADJ
american_scientific_journal-1367	35	25	and	and	CCONJ
american_scientific_journal-1367	35	26	right	right	ADJ
american_scientific_journal-1367	35	27	perfect	perfect	ADJ
american_scientific_journal-1367	35	28	rings	ring	NOUN
american_scientific_journal-1367	35	29	,	,	PUNCT
american_scientific_journal-1367	35	30	left	leave	VERB
american_scientific_journal-1367	35	31	coherent	coherent	ADJ
american_scientific_journal-1367	35	32	rings	ring	NOUN
american_scientific_journal-1367	35	33	,	,	PUNCT
american_scientific_journal-1367	35	34	left	leave	VERB
american_scientific_journal-1367	35	35	fp	fp	NOUN
american_scientific_journal-1367	35	36	-	-	ADJ
american_scientific_journal-1367	35	37	regular	regular	ADJ
american_scientific_journal-1367	35	38	[	[	X
american_scientific_journal-1367	35	39	3	3	NUM
american_scientific_journal-1367	35	40	]	]	PUNCT
american_scientific_journal-1367	35	41	rings	ring	NOUN
american_scientific_journal-1367	35	42	by	by	ADP
american_scientific_journal-1367	35	43	fpprojective	fpprojective	ADJ
american_scientific_journal-1367	35	44	and	and	CCONJ
american_scientific_journal-1367	35	45	fp	fp	ADJ
american_scientific_journal-1367	35	46	-	-	PUNCT
american_scientific_journal-1367	35	47	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	35	48	r	r	NOUN
american_scientific_journal-1367	35	49	-	-	PUNCT
american_scientific_journal-1367	35	50	modules	module	NOUN
american_scientific_journal-1367	35	51	.	.	PUNCT
american_scientific_journal-1367	36	1	moreover	moreover	ADV
american_scientific_journal-1367	36	2	,	,	PUNCT
american_scientific_journal-1367	36	3	some	some	DET
american_scientific_journal-1367	36	4	known	know	VERB
american_scientific_journal-1367	36	5	characterizations	characterization	NOUN
american_scientific_journal-1367	36	6	of	of	ADP
american_scientific_journal-1367	36	7	von	von	PROPN
american_scientific_journal-1367	36	8	neumann	neumann	PROPN
american_scientific_journal-1367	36	9	regular	regular	PROPN
american_scientific_journal-1367	36	10	rings	ring	NOUN
american_scientific_journal-1367	36	11	are	be	AUX
american_scientific_journal-1367	36	12	found	find	VERB
american_scientific_journal-1367	36	13	.	.	PUNCT
american_scientific_journal-1367	37	1	2	2	X
american_scientific_journal-1367	37	2	.	.	X
american_scientific_journal-1367	37	3	definitions	definition	NOUN
american_scientific_journal-1367	37	4	and	and	CCONJ
american_scientific_journal-1367	37	5	first	first	ADJ
american_scientific_journal-1367	37	6	results	result	NOUN
american_scientific_journal-1367	37	7	we	we	PRON
american_scientific_journal-1367	37	8	first	first	ADV
american_scientific_journal-1367	37	9	introduce	introduce	VERB
american_scientific_journal-1367	37	10	the	the	DET
american_scientific_journal-1367	37	11	concepts	concept	NOUN
american_scientific_journal-1367	37	12	of	of	ADP
american_scientific_journal-1367	37	13	fp	fp	X
american_scientific_journal-1367	37	14	-	-	PUNCT
american_scientific_journal-1367	37	15	projective	projective	ADJ
american_scientific_journal-1367	37	16	and	and	CCONJ
american_scientific_journal-1367	37	17	fp	fp	ADJ
american_scientific_journal-1367	37	18	-	-	PUNCT
american_scientific_journal-1367	37	19	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	37	20	modules	module	NOUN
american_scientific_journal-1367	37	21	.	.	PUNCT
american_scientific_journal-1367	38	1	133	133	NUM
american_scientific_journal-1367	38	2	american	american	ADJ
american_scientific_journal-1367	38	3	scientific	scientific	ADJ
american_scientific_journal-1367	38	4	research	research	NOUN
american_scientific_journal-1367	38	5	journal	journal	NOUN
american_scientific_journal-1367	38	6	for	for	ADP
american_scientific_journal-1367	38	7	engineering	engineering	NOUN
american_scientific_journal-1367	38	8	,	,	PUNCT
american_scientific_journal-1367	38	9	technology	technology	NOUN
american_scientific_journal-1367	38	10	,	,	PUNCT
american_scientific_journal-1367	38	11	and	and	CCONJ
american_scientific_journal-1367	38	12	sciences	science	NOUN
american_scientific_journal-1367	38	13	(	(	PUNCT
american_scientific_journal-1367	38	14	asrjets	asrjet	NOUN
american_scientific_journal-1367	38	15	)	)	PUNCT
american_scientific_journal-1367	38	16	(	(	PUNCT
american_scientific_journal-1367	38	17	2016	2016	NUM
american_scientific_journal-1367	38	18	)	)	PUNCT
american_scientific_journal-1367	38	19	volume	volume	NOUN
american_scientific_journal-1367	38	20	17	17	NUM
american_scientific_journal-1367	38	21	,	,	PUNCT
american_scientific_journal-1367	38	22	no	no	DET
american_scientific_journal-1367	38	23	1	1	NUM
american_scientific_journal-1367	38	24	,	,	PUNCT
american_scientific_journal-1367	38	25	pp	pp	ADV
american_scientific_journal-1367	38	26	132	132	NUM
american_scientific_journal-1367	38	27	-	-	SYM
american_scientific_journal-1367	38	28	143	143	NUM
american_scientific_journal-1367	38	29	2.1	2.1	NUM
american_scientific_journal-1367	38	30	definition	definition	NOUN
american_scientific_journal-1367	38	31	let	let	VERB
american_scientific_journal-1367	38	32	m	m	PRON
american_scientific_journal-1367	38	33	be	be	AUX
american_scientific_journal-1367	38	34	a	a	DET
american_scientific_journal-1367	38	35	left	left	ADJ
american_scientific_journal-1367	38	36	r	r	NOUN
american_scientific_journal-1367	38	37	-	-	PUNCT
american_scientific_journal-1367	38	38	module	module	NOUN
american_scientific_journal-1367	38	39	.	.	PUNCT
american_scientific_journal-1367	39	1	then	then	ADV
american_scientific_journal-1367	39	2	we	we	PRON
american_scientific_journal-1367	39	3	call	call	VERB
american_scientific_journal-1367	39	4	(	(	PUNCT
american_scientific_journal-1367	39	5	1	1	X
american_scientific_journal-1367	39	6	)	)	PUNCT
american_scientific_journal-1367	39	7	m	m	VERB
american_scientific_journal-1367	39	8	is	be	AUX
american_scientific_journal-1367	39	9	fp	fp	ADJ
american_scientific_journal-1367	39	10	-	-	PUNCT
american_scientific_journal-1367	39	11	projective	projective	ADJ
american_scientific_journal-1367	39	12	if	if	SCONJ
american_scientific_journal-1367	39	13	ext1(m	ext1(m	NUM
american_scientific_journal-1367	39	14	,	,	PUNCT
american_scientific_journal-1367	39	15	n	n	CCONJ
american_scientific_journal-1367	39	16	)	)	PUNCT
american_scientific_journal-1367	39	17	=	=	SYM
american_scientific_journal-1367	39	18	0	0	NUM
american_scientific_journal-1367	39	19	for	for	ADP
american_scientific_journal-1367	39	20	any	any	DET
american_scientific_journal-1367	39	21	fp	fp	ADJ
american_scientific_journal-1367	39	22	-	-	PUNCT
american_scientific_journal-1367	39	23	injective	injective	ADJ
american_scientific_journal-1367	39	24	left	leave	VERB
american_scientific_journal-1367	39	25	r	r	NOUN
american_scientific_journal-1367	39	26	-	-	PUNCT
american_scientific_journal-1367	39	27	module	module	NOUN
american_scientific_journal-1367	39	28	n.	n.	NOUN
american_scientific_journal-1367	39	29	(	(	PUNCT
american_scientific_journal-1367	39	30	2	2	NUM
american_scientific_journal-1367	39	31	)	)	PUNCT
american_scientific_journal-1367	40	1	m	m	VERB
american_scientific_journal-1367	40	2	is	be	AUX
american_scientific_journal-1367	40	3	fp	fp	ADJ
american_scientific_journal-1367	40	4	-	-	PUNCT
american_scientific_journal-1367	40	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	40	6	if	if	SCONJ
american_scientific_journal-1367	40	7	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	40	8	,	,	PUNCT
american_scientific_journal-1367	40	9	m	m	NOUN
american_scientific_journal-1367	40	10	)	)	PUNCT
american_scientific_journal-1367	40	11	=	=	SYM
american_scientific_journal-1367	40	12	0	0	NUM
american_scientific_journal-1367	41	1	for	for	ADP
american_scientific_journal-1367	41	2	any	any	DET
american_scientific_journal-1367	41	3	fp	fp	ADJ
american_scientific_journal-1367	41	4	-	-	PUNCT
american_scientific_journal-1367	41	5	flat	flat	ADJ
american_scientific_journal-1367	41	6	left	leave	VERB
american_scientific_journal-1367	41	7	r	r	NOUN
american_scientific_journal-1367	41	8	-	-	PUNCT
american_scientific_journal-1367	41	9	module	module	NOUN
american_scientific_journal-1367	41	10	n.	n.	NOUN
american_scientific_journal-1367	41	11	the	the	DET
american_scientific_journal-1367	41	12	right	right	ADJ
american_scientific_journal-1367	41	13	version	version	NOUN
american_scientific_journal-1367	41	14	can	can	AUX
american_scientific_journal-1367	41	15	be	be	AUX
american_scientific_journal-1367	41	16	defined	define	VERB
american_scientific_journal-1367	41	17	similarly	similarly	ADV
american_scientific_journal-1367	41	18	.	.	PUNCT
american_scientific_journal-1367	42	1	for	for	ADP
american_scientific_journal-1367	42	2	any	any	DET
american_scientific_journal-1367	42	3	ring	ring	NOUN
american_scientific_journal-1367	42	4	r	r	NOUN
american_scientific_journal-1367	42	5	,	,	PUNCT
american_scientific_journal-1367	42	6	it	it	PRON
american_scientific_journal-1367	42	7	is	be	AUX
american_scientific_journal-1367	42	8	clear	clear	ADJ
american_scientific_journal-1367	42	9	that	that	SCONJ
american_scientific_journal-1367	42	10	every	every	DET
american_scientific_journal-1367	42	11	projective	projective	NOUN
american_scientific_journal-1367	42	12	left	leave	VERB
american_scientific_journal-1367	42	13	r	r	NOUN
american_scientific_journal-1367	42	14	-	-	PUNCT
american_scientific_journal-1367	42	15	module	module	NOUN
american_scientific_journal-1367	42	16	is	be	AUX
american_scientific_journal-1367	42	17	fp	fp	NOUN
american_scientific_journal-1367	42	18	-	-	PUNCT
american_scientific_journal-1367	42	19	projective	projective	ADJ
american_scientific_journal-1367	42	20	,	,	PUNCT
american_scientific_journal-1367	42	21	r	r	X
american_scientific_journal-1367	42	22	/	/	SYM
american_scientific_journal-1367	42	23	i	i	PRON
american_scientific_journal-1367	42	24	is	be	AUX
american_scientific_journal-1367	42	25	fp	fp	ADJ
american_scientific_journal-1367	42	26	-	-	PUNCT
american_scientific_journal-1367	42	27	projective	projective	NOUN
american_scientific_journal-1367	42	28	left	leave	VERB
american_scientific_journal-1367	42	29	r	r	NOUN
american_scientific_journal-1367	42	30	-	-	PUNCT
american_scientific_journal-1367	42	31	module	module	NOUN
american_scientific_journal-1367	42	32	for	for	ADP
american_scientific_journal-1367	42	33	every	every	DET
american_scientific_journal-1367	42	34	finitely	finitely	ADV
american_scientific_journal-1367	42	35	presented	present	VERB
american_scientific_journal-1367	42	36	left	leave	VERB
american_scientific_journal-1367	42	37	ideal	ideal	PROPN
american_scientific_journal-1367	43	1	i	i	PRON
american_scientific_journal-1367	43	2	,	,	PUNCT
american_scientific_journal-1367	43	3	every	every	DET
american_scientific_journal-1367	43	4	fp	fp	PROPN
american_scientific_journal-1367	43	5	-	-	PUNCT
american_scientific_journal-1367	43	6	projective	projective	NOUN
american_scientific_journal-1367	43	7	left	leave	VERB
american_scientific_journal-1367	43	8	r	r	NOUN
american_scientific_journal-1367	43	9	-	-	PUNCT
american_scientific_journal-1367	43	10	module	module	NOUN
american_scientific_journal-1367	43	11	is	be	AUX
american_scientific_journal-1367	43	12	f	f	X
american_scientific_journal-1367	43	13	-	-	PUNCT
american_scientific_journal-1367	43	14	projective	projective	ADJ
american_scientific_journal-1367	43	15	and	and	CCONJ
american_scientific_journal-1367	43	16	fp	fp	NOUN
american_scientific_journal-1367	43	17	-	-	PUNCT
american_scientific_journal-1367	43	18	projective	projective	ADJ
american_scientific_journal-1367	43	19	,	,	PUNCT
american_scientific_journal-1367	43	20	every	every	DET
american_scientific_journal-1367	43	21	injective	injective	ADJ
american_scientific_journal-1367	43	22	left	leave	VERB
american_scientific_journal-1367	43	23	r	r	NOUN
american_scientific_journal-1367	43	24	-	-	PUNCT
american_scientific_journal-1367	43	25	module	module	NOUN
american_scientific_journal-1367	43	26	is	be	AUX
american_scientific_journal-1367	43	27	fp	fp	ADJ
american_scientific_journal-1367	43	28	-	-	PUNCT
american_scientific_journal-1367	43	29	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	43	30	and	and	CCONJ
american_scientific_journal-1367	43	31	every	every	DET
american_scientific_journal-1367	43	32	fp	fp	ADJ
american_scientific_journal-1367	43	33	-	-	PUNCT
american_scientific_journal-1367	43	34	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	43	35	left	leave	VERB
american_scientific_journal-1367	43	36	r	r	NOUN
american_scientific_journal-1367	43	37	-	-	PUNCT
american_scientific_journal-1367	43	38	module	module	NOUN
american_scientific_journal-1367	43	39	is	be	AUX
american_scientific_journal-1367	43	40	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	43	41	.	.	PUNCT
american_scientific_journal-1367	44	1	next	next	ADV
american_scientific_journal-1367	44	2	,	,	PUNCT
american_scientific_journal-1367	44	3	we	we	PRON
american_scientific_journal-1367	44	4	give	give	VERB
american_scientific_journal-1367	44	5	some	some	DET
american_scientific_journal-1367	44	6	characterizations	characterization	NOUN
american_scientific_journal-1367	44	7	of	of	ADP
american_scientific_journal-1367	44	8	fp	fp	ADJ
american_scientific_journal-1367	44	9	-	-	PUNCT
american_scientific_journal-1367	44	10	injective	injective	ADJ
american_scientific_journal-1367	44	11	r	r	NOUN
american_scientific_journal-1367	44	12	-	-	PUNCT
american_scientific_journal-1367	44	13	modules	module	NOUN
american_scientific_journal-1367	44	14	by	by	ADP
american_scientific_journal-1367	44	15	fp	fp	NOUN
american_scientific_journal-1367	44	16	-	-	PUNCT
american_scientific_journal-1367	44	17	projective	projective	ADJ
american_scientific_journal-1367	44	18	r	r	NOUN
american_scientific_journal-1367	44	19	-	-	PUNCT
american_scientific_journal-1367	44	20	modules	module	NOUN
american_scientific_journal-1367	44	21	.	.	PUNCT
american_scientific_journal-1367	45	1	2.2	2.2	NUM
american_scientific_journal-1367	45	2	theorem	theorem	NOUN
american_scientific_journal-1367	45	3	let	let	VERB
american_scientific_journal-1367	45	4	m	m	PRON
american_scientific_journal-1367	45	5	be	be	AUX
american_scientific_journal-1367	45	6	a	a	DET
american_scientific_journal-1367	45	7	left	left	ADJ
american_scientific_journal-1367	45	8	r	r	NOUN
american_scientific_journal-1367	45	9	-	-	PUNCT
american_scientific_journal-1367	45	10	module	module	NOUN
american_scientific_journal-1367	45	11	.	.	PUNCT
american_scientific_journal-1367	46	1	the	the	DET
american_scientific_journal-1367	46	2	following	follow	VERB
american_scientific_journal-1367	46	3	statements	statement	NOUN
american_scientific_journal-1367	46	4	are	be	AUX
american_scientific_journal-1367	46	5	equivalent	equivalent	ADJ
american_scientific_journal-1367	46	6	.	.	PUNCT
american_scientific_journal-1367	47	1	(	(	PUNCT
american_scientific_journal-1367	47	2	1	1	X
american_scientific_journal-1367	47	3	)	)	PUNCT
american_scientific_journal-1367	47	4	m	m	VERB
american_scientific_journal-1367	47	5	is	be	AUX
american_scientific_journal-1367	47	6	fp	fp	ADJ
american_scientific_journal-1367	47	7	-	-	ADJ
american_scientific_journal-1367	47	8	injective	injective	ADJ
american_scientific_journal-1367	47	9	left	leave	VERB
american_scientific_journal-1367	47	10	r	r	NOUN
american_scientific_journal-1367	47	11	-	-	PUNCT
american_scientific_journal-1367	47	12	module	module	NOUN
american_scientific_journal-1367	47	13	.	.	PUNCT
american_scientific_journal-1367	48	1	(	(	PUNCT
american_scientific_journal-1367	48	2	2	2	X
american_scientific_journal-1367	48	3	)	)	PUNCT
american_scientific_journal-1367	48	4	m	m	VERB
american_scientific_journal-1367	48	5	is	be	AUX
american_scientific_journal-1367	48	6	injective	injective	ADJ
american_scientific_journal-1367	48	7	with	with	ADP
american_scientific_journal-1367	48	8	respect	respect	NOUN
american_scientific_journal-1367	48	9	to	to	ADP
american_scientific_journal-1367	48	10	every	every	DET
american_scientific_journal-1367	48	11	exact	exact	ADJ
american_scientific_journal-1367	48	12	sequence	sequence	NOUN
american_scientific_journal-1367	48	13	0	0	NUM
american_scientific_journal-1367	49	1	→	→	SYM
american_scientific_journal-1367	49	2	c	c	X
american_scientific_journal-1367	49	3	→	→	SYM
american_scientific_journal-1367	49	4	b	b	X
american_scientific_journal-1367	49	5	→a	→a	PUNCT
american_scientific_journal-1367	49	6	→	→	SYM
american_scientific_journal-1367	49	7	0	0	NUM
american_scientific_journal-1367	49	8	of	of	ADP
american_scientific_journal-1367	49	9	left	left	ADJ
american_scientific_journal-1367	49	10	r	r	NOUN
american_scientific_journal-1367	49	11	-	-	PUNCT
american_scientific_journal-1367	49	12	modules	module	NOUN
american_scientific_journal-1367	49	13	with	with	ADP
american_scientific_journal-1367	49	14	a	a	DET
american_scientific_journal-1367	49	15	fpprojective	fpprojective	NOUN
american_scientific_journal-1367	49	16	.	.	PUNCT
american_scientific_journal-1367	50	1	(	(	PUNCT
american_scientific_journal-1367	50	2	3	3	X
american_scientific_journal-1367	50	3	)	)	PUNCT
american_scientific_journal-1367	50	4	m	m	VERB
american_scientific_journal-1367	50	5	is	be	AUX
american_scientific_journal-1367	50	6	injective	injective	ADJ
american_scientific_journal-1367	50	7	with	with	ADP
american_scientific_journal-1367	50	8	respect	respect	NOUN
american_scientific_journal-1367	50	9	to	to	ADP
american_scientific_journal-1367	50	10	every	every	DET
american_scientific_journal-1367	50	11	exact	exact	ADJ
american_scientific_journal-1367	50	12	sequence	sequence	NOUN
american_scientific_journal-1367	50	13	0	0	NUM
american_scientific_journal-1367	51	1	→	→	SYM
american_scientific_journal-1367	51	2	k	k	X
american_scientific_journal-1367	51	3	→	→	PUNCT
american_scientific_journal-1367	51	4	p	p	X
american_scientific_journal-1367	51	5	→a	→a	PROPN
american_scientific_journal-1367	51	6	→	→	SYM
american_scientific_journal-1367	51	7	0	0	NUM
american_scientific_journal-1367	51	8	of	of	ADP
american_scientific_journal-1367	51	9	left	left	ADJ
american_scientific_journal-1367	51	10	r	r	NOUN
american_scientific_journal-1367	51	11	-	-	PUNCT
american_scientific_journal-1367	51	12	modules	module	NOUN
american_scientific_journal-1367	51	13	with	with	ADP
american_scientific_journal-1367	51	14	p	p	NOUN
american_scientific_journal-1367	51	15	projective	projective	NOUN
american_scientific_journal-1367	51	16	and	and	CCONJ
american_scientific_journal-1367	51	17	a	a	DET
american_scientific_journal-1367	51	18	fp	fp	ADV
american_scientific_journal-1367	51	19	-	-	PUNCT
american_scientific_journal-1367	51	20	projective	projective	ADJ
american_scientific_journal-1367	51	21	.	.	PUNCT
american_scientific_journal-1367	52	1	(	(	PUNCT
american_scientific_journal-1367	52	2	4	4	X
american_scientific_journal-1367	52	3	)	)	PUNCT
american_scientific_journal-1367	52	4	every	every	DET
american_scientific_journal-1367	52	5	fp	fp	PROPN
american_scientific_journal-1367	52	6	-	-	PUNCT
american_scientific_journal-1367	52	7	projective	projective	ADJ
american_scientific_journal-1367	52	8	r	r	NOUN
american_scientific_journal-1367	52	9	-	-	PUNCT
american_scientific_journal-1367	52	10	module	module	NOUN
american_scientific_journal-1367	52	11	is	be	AUX
american_scientific_journal-1367	52	12	projective	projective	ADJ
american_scientific_journal-1367	52	13	with	with	ADP
american_scientific_journal-1367	52	14	respect	respect	NOUN
american_scientific_journal-1367	52	15	to	to	ADP
american_scientific_journal-1367	52	16	every	every	DET
american_scientific_journal-1367	52	17	exact	exact	ADJ
american_scientific_journal-1367	52	18	sequence	sequence	NOUN
american_scientific_journal-1367	52	19	of	of	ADP
american_scientific_journal-1367	52	20	left	left	ADJ
american_scientific_journal-1367	52	21	r	r	NOUN
american_scientific_journal-1367	52	22	-	-	PUNCT
american_scientific_journal-1367	52	23	modules	module	NOUN
american_scientific_journal-1367	52	24	0	0	PUNCT
american_scientific_journal-1367	52	25	→	→	SYM
american_scientific_journal-1367	52	26	m	m	PROPN
american_scientific_journal-1367	52	27	→	→	SYM
american_scientific_journal-1367	52	28	m	m	NOUN
american_scientific_journal-1367	52	29	'	'	PUNCT
american_scientific_journal-1367	52	30	→	→	SYM
american_scientific_journal-1367	52	31	m	m	NOUN
american_scientific_journal-1367	52	32	"	"	PUNCT
american_scientific_journal-1367	52	33	→	→	SYM
american_scientific_journal-1367	52	34	0	0	NUM
american_scientific_journal-1367	52	35	.	.	PUNCT
american_scientific_journal-1367	53	1	(	(	PUNCT
american_scientific_journal-1367	53	2	5	5	X
american_scientific_journal-1367	53	3	)	)	PUNCT
american_scientific_journal-1367	53	4	every	every	DET
american_scientific_journal-1367	53	5	fp	fp	PROPN
american_scientific_journal-1367	53	6	-	-	PUNCT
american_scientific_journal-1367	53	7	projective	projective	NOUN
american_scientific_journal-1367	53	8	left	leave	VERB
american_scientific_journal-1367	53	9	r	r	NOUN
american_scientific_journal-1367	53	10	-	-	PUNCT
american_scientific_journal-1367	53	11	module	module	NOUN
american_scientific_journal-1367	53	12	is	be	AUX
american_scientific_journal-1367	53	13	projective	projective	ADJ
american_scientific_journal-1367	53	14	with	with	ADP
american_scientific_journal-1367	53	15	respect	respect	NOUN
american_scientific_journal-1367	53	16	to	to	ADP
american_scientific_journal-1367	53	17	the	the	DET
american_scientific_journal-1367	53	18	canonical	canonical	ADJ
american_scientific_journal-1367	53	19	exact	exact	ADJ
american_scientific_journal-1367	53	20	sequence	sequence	NOUN
american_scientific_journal-1367	53	21	0	0	NUM
american_scientific_journal-1367	54	1	→	→	SYM
american_scientific_journal-1367	54	2	m	m	NOUN
american_scientific_journal-1367	54	3	→	→	SYM
american_scientific_journal-1367	54	4	e(m	e(m	ADJ
american_scientific_journal-1367	55	1	)	)	PUNCT
american_scientific_journal-1367	55	2	→	→	SYM
american_scientific_journal-1367	55	3	e(m)∕m	e(m)∕m	PROPN
american_scientific_journal-1367	55	4	→	→	SYM
american_scientific_journal-1367	55	5	0	0	NUM
american_scientific_journal-1367	55	6	.	.	PUNCT
american_scientific_journal-1367	56	1	(	(	PUNCT
american_scientific_journal-1367	56	2	6	6	X
american_scientific_journal-1367	56	3	)	)	PUNCT
american_scientific_journal-1367	56	4	there	there	PRON
american_scientific_journal-1367	56	5	exists	exist	VERB
american_scientific_journal-1367	56	6	an	an	DET
american_scientific_journal-1367	56	7	exact	exact	ADJ
american_scientific_journal-1367	56	8	sequence	sequence	NOUN
american_scientific_journal-1367	56	9	0	0	NUM
american_scientific_journal-1367	56	10	→	→	SYM
american_scientific_journal-1367	56	11	m	m	PROPN
american_scientific_journal-1367	56	12	→	→	SYM
american_scientific_journal-1367	56	13	m	m	NOUN
american_scientific_journal-1367	56	14	'	'	PUNCT
american_scientific_journal-1367	56	15	→	→	SYM
american_scientific_journal-1367	56	16	m	m	NOUN
american_scientific_journal-1367	56	17	"	"	PUNCT
american_scientific_journal-1367	56	18	→	→	SYM
american_scientific_journal-1367	56	19	0	0	NUM
american_scientific_journal-1367	56	20	of	of	ADP
american_scientific_journal-1367	56	21	left	left	ADJ
american_scientific_journal-1367	56	22	r	r	NOUN
american_scientific_journal-1367	56	23	-	-	PUNCT
american_scientific_journal-1367	56	24	modules	module	NOUN
american_scientific_journal-1367	56	25	with	with	ADP
american_scientific_journal-1367	56	26	m	m	NOUN
american_scientific_journal-1367	56	27	'	'	PART
american_scientific_journal-1367	56	28	injective	injective	ADJ
american_scientific_journal-1367	56	29	,	,	PUNCT
american_scientific_journal-1367	56	30	such	such	ADJ
american_scientific_journal-1367	56	31	that	that	SCONJ
american_scientific_journal-1367	56	32	every	every	DET
american_scientific_journal-1367	56	33	fp	fp	PROPN
american_scientific_journal-1367	56	34	-	-	PUNCT
american_scientific_journal-1367	56	35	projective	projective	NOUN
american_scientific_journal-1367	56	36	left	leave	VERB
american_scientific_journal-1367	56	37	r	r	NOUN
american_scientific_journal-1367	56	38	-	-	PUNCT
american_scientific_journal-1367	56	39	module	module	NOUN
american_scientific_journal-1367	56	40	is	be	AUX
american_scientific_journal-1367	56	41	projective	projective	ADJ
american_scientific_journal-1367	56	42	with	with	ADP
american_scientific_journal-1367	56	43	respect	respect	NOUN
american_scientific_journal-1367	56	44	to	to	ADP
american_scientific_journal-1367	56	45	this	this	DET
american_scientific_journal-1367	56	46	sequence	sequence	NOUN
american_scientific_journal-1367	56	47	.	.	PUNCT
american_scientific_journal-1367	57	1	(	(	PUNCT
american_scientific_journal-1367	57	2	7	7	X
american_scientific_journal-1367	57	3	)	)	PUNCT
american_scientific_journal-1367	57	4	there	there	PRON
american_scientific_journal-1367	57	5	exists	exist	VERB
american_scientific_journal-1367	57	6	an	an	DET
american_scientific_journal-1367	57	7	exact	exact	ADJ
american_scientific_journal-1367	57	8	sequence	sequence	NOUN
american_scientific_journal-1367	57	9	0	0	NUM
american_scientific_journal-1367	57	10	→	→	SYM
american_scientific_journal-1367	57	11	m	m	PROPN
american_scientific_journal-1367	57	12	→	→	SYM
american_scientific_journal-1367	57	13	m	m	NOUN
american_scientific_journal-1367	57	14	'	'	PUNCT
american_scientific_journal-1367	57	15	→	→	SYM
american_scientific_journal-1367	57	16	m	m	NOUN
american_scientific_journal-1367	57	17	"	"	PUNCT
american_scientific_journal-1367	57	18	→	→	SYM
american_scientific_journal-1367	57	19	0	0	NUM
american_scientific_journal-1367	57	20	of	of	ADP
american_scientific_journal-1367	57	21	left	left	ADJ
american_scientific_journal-1367	57	22	r	r	NOUN
american_scientific_journal-1367	57	23	-	-	PUNCT
american_scientific_journal-1367	57	24	modules	module	NOUN
american_scientific_journal-1367	57	25	with	with	ADP
american_scientific_journal-1367	57	26	m	m	PROPN
american_scientific_journal-1367	57	27	'	'	PART
american_scientific_journal-1367	57	28	fp	fp	ADJ
american_scientific_journal-1367	57	29	-	-	PUNCT
american_scientific_journal-1367	57	30	injective	injective	ADJ
american_scientific_journal-1367	57	31	,	,	PUNCT
american_scientific_journal-1367	57	32	such	such	ADJ
american_scientific_journal-1367	57	33	that	that	SCONJ
american_scientific_journal-1367	57	34	every	every	DET
american_scientific_journal-1367	57	35	fp	fp	PROPN
american_scientific_journal-1367	57	36	-	-	PUNCT
american_scientific_journal-1367	57	37	projective	projective	NOUN
american_scientific_journal-1367	57	38	left	leave	VERB
american_scientific_journal-1367	57	39	r	r	NOUN
american_scientific_journal-1367	57	40	-	-	PUNCT
american_scientific_journal-1367	57	41	module	module	NOUN
american_scientific_journal-1367	57	42	is	be	AUX
american_scientific_journal-1367	57	43	projective	projective	ADJ
american_scientific_journal-1367	57	44	with	with	ADP
american_scientific_journal-1367	57	45	respect	respect	NOUN
american_scientific_journal-1367	57	46	to	to	ADP
american_scientific_journal-1367	57	47	this	this	DET
american_scientific_journal-1367	57	48	sequence	sequence	NOUN
american_scientific_journal-1367	57	49	.	.	PUNCT
american_scientific_journal-1367	58	1	proof	proof	NOUN
american_scientific_journal-1367	58	2	.	.	PUNCT
american_scientific_journal-1367	59	1	(	(	PUNCT
american_scientific_journal-1367	59	2	1	1	X
american_scientific_journal-1367	59	3	)	)	PUNCT
american_scientific_journal-1367	59	4	⇒	⇒	NOUN
american_scientific_journal-1367	59	5	(	(	PUNCT
american_scientific_journal-1367	59	6	2	2	NUM
american_scientific_journal-1367	59	7	)	)	PUNCT
american_scientific_journal-1367	59	8	⇒	⇒	NOUN
american_scientific_journal-1367	59	9	(	(	PUNCT
american_scientific_journal-1367	59	10	3	3	X
american_scientific_journal-1367	59	11	)	)	PUNCT
american_scientific_journal-1367	59	12	are	be	AUX
american_scientific_journal-1367	59	13	clear	clear	ADJ
american_scientific_journal-1367	59	14	.	.	PUNCT
american_scientific_journal-1367	60	1	(	(	PUNCT
american_scientific_journal-1367	60	2	3	3	X
american_scientific_journal-1367	60	3	)	)	PUNCT
american_scientific_journal-1367	60	4	⇒	⇒	NOUN
american_scientific_journal-1367	60	5	(	(	PUNCT
american_scientific_journal-1367	60	6	1	1	NUM
american_scientific_journal-1367	60	7	)	)	PUNCT
american_scientific_journal-1367	60	8	.	.	PUNCT
american_scientific_journal-1367	61	1	let	let	VERB
american_scientific_journal-1367	61	2	i	i	PRON
american_scientific_journal-1367	61	3	be	be	AUX
american_scientific_journal-1367	61	4	a	a	DET
american_scientific_journal-1367	61	5	finitely	finitely	ADV
american_scientific_journal-1367	61	6	presented	present	VERB
american_scientific_journal-1367	61	7	left	leave	VERB
american_scientific_journal-1367	61	8	ideal	ideal	NOUN
american_scientific_journal-1367	61	9	of	of	ADP
american_scientific_journal-1367	61	10	r.	r.	PROPN
american_scientific_journal-1367	61	11	we	we	PRON
american_scientific_journal-1367	61	12	have	have	VERB
american_scientific_journal-1367	61	13	the	the	DET
american_scientific_journal-1367	61	14	exact	exact	ADJ
american_scientific_journal-1367	61	15	sequence	sequence	NOUN
american_scientific_journal-1367	61	16	0	0	NUM
american_scientific_journal-1367	62	1	→	→	SYM
american_scientific_journal-1367	62	2	i	i	PRON
american_scientific_journal-1367	62	3	→	→	SYM
american_scientific_journal-1367	62	4	r	r	NOUN
american_scientific_journal-1367	62	5	→	→	SYM
american_scientific_journal-1367	62	6	r	r	NOUN
american_scientific_journal-1367	62	7	/	/	SYM
american_scientific_journal-1367	62	8	i	i	PROPN
american_scientific_journal-1367	62	9	→	→	SYM
american_scientific_journal-1367	62	10	0	0	NUM
american_scientific_journal-1367	62	11	,	,	PUNCT
american_scientific_journal-1367	62	12	which	which	PRON
american_scientific_journal-1367	62	13	induces	induce	VERB
american_scientific_journal-1367	62	14	the	the	DET
american_scientific_journal-1367	62	15	exact	exact	ADJ
american_scientific_journal-1367	62	16	sequence	sequence	NOUN
american_scientific_journal-1367	62	17	hom(r	hom(r	PROPN
american_scientific_journal-1367	62	18	,	,	PUNCT
american_scientific_journal-1367	62	19	m	m	NOUN
american_scientific_journal-1367	62	20	)	)	PUNCT
american_scientific_journal-1367	62	21	→	→	SYM
american_scientific_journal-1367	62	22	hom(i	hom(i	PROPN
american_scientific_journal-1367	62	23	,	,	PUNCT
american_scientific_journal-1367	62	24	m	m	PROPN
american_scientific_journal-1367	62	25	)	)	PUNCT
american_scientific_journal-1367	62	26	→	→	SYM
american_scientific_journal-1367	62	27	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	62	28	/	/	SYM
american_scientific_journal-1367	62	29	i	i	PROPN
american_scientific_journal-1367	62	30	,	,	PUNCT
american_scientific_journal-1367	62	31	m	m	PROPN
american_scientific_journal-1367	62	32	)	)	PUNCT
american_scientific_journal-1367	62	33	→	→	SYM
american_scientific_journal-1367	62	34	0	0	X
american_scientific_journal-1367	62	35	.	.	PUNCT
american_scientific_journal-1367	63	1	since	since	SCONJ
american_scientific_journal-1367	63	2	r	r	NOUN
american_scientific_journal-1367	63	3	/	/	SYM
american_scientific_journal-1367	63	4	i	i	PRON
american_scientific_journal-1367	63	5	is	be	AUX
american_scientific_journal-1367	63	6	fp	fp	ADJ
american_scientific_journal-1367	63	7	-	-	PUNCT
american_scientific_journal-1367	63	8	projective	projective	ADJ
american_scientific_journal-1367	63	9	,	,	PUNCT
american_scientific_journal-1367	63	10	hom(r	hom(r	PROPN
american_scientific_journal-1367	63	11	,	,	PUNCT
american_scientific_journal-1367	63	12	m	m	NOUN
american_scientific_journal-1367	63	13	)	)	PUNCT
american_scientific_journal-1367	63	14	→	→	SYM
american_scientific_journal-1367	63	15	hom(i	hom(i	PROPN
american_scientific_journal-1367	63	16	,	,	PUNCT
american_scientific_journal-1367	63	17	m	m	PROPN
american_scientific_journal-1367	63	18	)	)	PUNCT
american_scientific_journal-1367	63	19	→0	→0	PUNCT
american_scientific_journal-1367	63	20	is	be	AUX
american_scientific_journal-1367	63	21	exact	exact	ADJ
american_scientific_journal-1367	63	22	by	by	ADP
american_scientific_journal-1367	63	23	(	(	PUNCT
american_scientific_journal-1367	63	24	3	3	NUM
american_scientific_journal-1367	63	25	)	)	PUNCT
american_scientific_journal-1367	63	26	.	.	PUNCT
american_scientific_journal-1367	64	1	so	so	ADV
american_scientific_journal-1367	64	2	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	64	3	/	/	SYM
american_scientific_journal-1367	64	4	i	i	PROPN
american_scientific_journal-1367	64	5	,	,	PUNCT
american_scientific_journal-1367	64	6	m	m	PROPN
american_scientific_journal-1367	64	7	)	)	PUNCT
american_scientific_journal-1367	64	8	=	=	SYM
american_scientific_journal-1367	64	9	0	0	NUM
american_scientific_journal-1367	65	1	and	and	CCONJ
american_scientific_journal-1367	65	2	so	so	ADV
american_scientific_journal-1367	65	3	(	(	PUNCT
american_scientific_journal-1367	65	4	1	1	X
american_scientific_journal-1367	65	5	)	)	PUNCT
american_scientific_journal-1367	65	6	follows	follow	VERB
american_scientific_journal-1367	65	7	.	.	PUNCT
american_scientific_journal-1367	66	1	(	(	PUNCT
american_scientific_journal-1367	66	2	1	1	X
american_scientific_journal-1367	66	3	)	)	PUNCT
american_scientific_journal-1367	66	4	⇒	⇒	NOUN
american_scientific_journal-1367	66	5	(	(	PUNCT
american_scientific_journal-1367	66	6	4	4	NUM
american_scientific_journal-1367	66	7	)	)	PUNCT
american_scientific_journal-1367	66	8	.	.	PUNCT
american_scientific_journal-1367	67	1	let	let	VERB
american_scientific_journal-1367	67	2	m	m	PRON
american_scientific_journal-1367	67	3	be	be	AUX
american_scientific_journal-1367	67	4	an	an	DET
american_scientific_journal-1367	67	5	fp	fp	ADJ
american_scientific_journal-1367	67	6	-	-	PUNCT
american_scientific_journal-1367	67	7	injective	injective	ADJ
american_scientific_journal-1367	67	8	left	leave	VERB
american_scientific_journal-1367	67	9	r	r	NOUN
american_scientific_journal-1367	67	10	-	-	PUNCT
american_scientific_journal-1367	67	11	module	module	NOUN
american_scientific_journal-1367	67	12	.	.	PUNCT
american_scientific_journal-1367	68	1	then	then	ADV
american_scientific_journal-1367	68	2	the	the	DET
american_scientific_journal-1367	68	3	sequence	sequence	NOUN
american_scientific_journal-1367	68	4	hom(p	hom(p	PROPN
american_scientific_journal-1367	68	5	,	,	PUNCT
american_scientific_journal-1367	68	6	m	m	NOUN
american_scientific_journal-1367	68	7	'	'	PUNCT
american_scientific_journal-1367	68	8	)	)	PUNCT
american_scientific_journal-1367	68	9	→	→	PUNCT
american_scientific_journal-1367	68	10	hom(p	hom(p	PROPN
american_scientific_journal-1367	68	11	,	,	PUNCT
american_scientific_journal-1367	68	12	m")→	m")→	NOUN
american_scientific_journal-1367	68	13	ext1(p	ext1(p	NUM
american_scientific_journal-1367	68	14	,	,	PUNCT
american_scientific_journal-1367	68	15	m	m	NOUN
american_scientific_journal-1367	68	16	)	)	PUNCT
american_scientific_journal-1367	68	17	=	=	SYM
american_scientific_journal-1367	68	18	0	0	NUM
american_scientific_journal-1367	68	19	is	be	AUX
american_scientific_journal-1367	68	20	exact	exact	ADJ
american_scientific_journal-1367	68	21	for	for	SCONJ
american_scientific_journal-1367	68	22	every	every	DET
american_scientific_journal-1367	68	23	fp	fp	ADJ
american_scientific_journal-1367	68	24	-	-	PUNCT
american_scientific_journal-1367	68	25	projective	projective	NOUN
american_scientific_journal-1367	68	26	left	leave	VERB
american_scientific_journal-1367	68	27	r	r	NOUN
american_scientific_journal-1367	68	28	-	-	PUNCT
american_scientific_journal-1367	68	29	module	module	NOUN
american_scientific_journal-1367	68	30	p	p	NOUN
american_scientific_journal-1367	68	31	,	,	PUNCT
american_scientific_journal-1367	68	32	and	and	CCONJ
american_scientific_journal-1367	68	33	so	so	ADV
american_scientific_journal-1367	68	34	(	(	PUNCT
american_scientific_journal-1367	68	35	4	4	X
american_scientific_journal-1367	68	36	)	)	PUNCT
american_scientific_journal-1367	68	37	follows	follow	VERB
american_scientific_journal-1367	68	38	.	.	PUNCT
american_scientific_journal-1367	69	1	134	134	NUM
american_scientific_journal-1367	69	2	american	american	ADJ
american_scientific_journal-1367	69	3	scientific	scientific	ADJ
american_scientific_journal-1367	69	4	research	research	NOUN
american_scientific_journal-1367	69	5	journal	journal	NOUN
american_scientific_journal-1367	69	6	for	for	ADP
american_scientific_journal-1367	69	7	engineering	engineering	NOUN
american_scientific_journal-1367	69	8	,	,	PUNCT
american_scientific_journal-1367	69	9	technology	technology	NOUN
american_scientific_journal-1367	69	10	,	,	PUNCT
american_scientific_journal-1367	69	11	and	and	CCONJ
american_scientific_journal-1367	69	12	sciences	science	NOUN
american_scientific_journal-1367	69	13	(	(	PUNCT
american_scientific_journal-1367	69	14	asrjets	asrjet	NOUN
american_scientific_journal-1367	69	15	)	)	PUNCT
american_scientific_journal-1367	69	16	(	(	PUNCT
american_scientific_journal-1367	69	17	2016	2016	NUM
american_scientific_journal-1367	69	18	)	)	PUNCT
american_scientific_journal-1367	69	19	volume	volume	NOUN
american_scientific_journal-1367	69	20	17	17	NUM
american_scientific_journal-1367	69	21	,	,	PUNCT
american_scientific_journal-1367	69	22	no	no	DET
american_scientific_journal-1367	69	23	1	1	NUM
american_scientific_journal-1367	69	24	,	,	PUNCT
american_scientific_journal-1367	69	25	pp	pp	ADV
american_scientific_journal-1367	69	26	132	132	NUM
american_scientific_journal-1367	69	27	-	-	SYM
american_scientific_journal-1367	69	28	143	143	NUM
american_scientific_journal-1367	69	29	(	(	PUNCT
american_scientific_journal-1367	69	30	4	4	NUM
american_scientific_journal-1367	69	31	)	)	PUNCT
american_scientific_journal-1367	69	32	⇒	⇒	NOUN
american_scientific_journal-1367	69	33	(	(	PUNCT
american_scientific_journal-1367	69	34	5	5	NUM
american_scientific_journal-1367	69	35	)	)	PUNCT
american_scientific_journal-1367	69	36	⇒	⇒	NOUN
american_scientific_journal-1367	69	37	(	(	PUNCT
american_scientific_journal-1367	69	38	6	6	NUM
american_scientific_journal-1367	69	39	)	)	PUNCT
american_scientific_journal-1367	69	40	⇒	⇒	NOUN
american_scientific_journal-1367	69	41	(	(	PUNCT
american_scientific_journal-1367	69	42	7	7	X
american_scientific_journal-1367	69	43	)	)	PUNCT
american_scientific_journal-1367	69	44	are	be	AUX
american_scientific_journal-1367	69	45	obvious	obvious	ADJ
american_scientific_journal-1367	69	46	.	.	PUNCT
american_scientific_journal-1367	70	1	(	(	PUNCT
american_scientific_journal-1367	70	2	7	7	X
american_scientific_journal-1367	70	3	)	)	PUNCT
american_scientific_journal-1367	70	4	⇒	⇒	NOUN
american_scientific_journal-1367	70	5	(	(	PUNCT
american_scientific_journal-1367	70	6	1	1	NUM
american_scientific_journal-1367	70	7	)	)	PUNCT
american_scientific_journal-1367	70	8	.	.	PUNCT
american_scientific_journal-1367	71	1	assume	assume	VERB
american_scientific_journal-1367	71	2	that	that	SCONJ
american_scientific_journal-1367	71	3	0	0	NUM
american_scientific_journal-1367	71	4	→	→	SYM
american_scientific_journal-1367	71	5	m	m	PROPN
american_scientific_journal-1367	71	6	→	→	SYM
american_scientific_journal-1367	71	7	m	m	NOUN
american_scientific_journal-1367	71	8	'	'	PUNCT
american_scientific_journal-1367	71	9	→	→	SYM
american_scientific_journal-1367	71	10	m	m	NOUN
american_scientific_journal-1367	71	11	"	"	PUNCT
american_scientific_journal-1367	71	12	→	→	SYM
american_scientific_journal-1367	71	13	0	0	NUM
american_scientific_journal-1367	71	14	is	be	AUX
american_scientific_journal-1367	71	15	exact	exact	ADJ
american_scientific_journal-1367	71	16	sequence	sequence	NOUN
american_scientific_journal-1367	71	17	of	of	ADP
american_scientific_journal-1367	71	18	left	left	ADJ
american_scientific_journal-1367	71	19	r	r	NOUN
american_scientific_journal-1367	71	20	-	-	PUNCT
american_scientific_journal-1367	71	21	modules	module	NOUN
american_scientific_journal-1367	71	22	with	with	ADP
american_scientific_journal-1367	71	23	m	m	PROPN
american_scientific_journal-1367	71	24	'	'	PART
american_scientific_journal-1367	71	25	fp	fp	ADJ
american_scientific_journal-1367	71	26	-	-	PUNCT
american_scientific_journal-1367	71	27	injective	injective	ADJ
american_scientific_journal-1367	71	28	and	and	CCONJ
american_scientific_journal-1367	71	29	,	,	PUNCT
american_scientific_journal-1367	71	30	i	i	PRON
american_scientific_journal-1367	71	31	is	be	AUX
american_scientific_journal-1367	71	32	any	any	DET
american_scientific_journal-1367	71	33	finitely	finitely	ADV
american_scientific_journal-1367	71	34	presented	present	VERB
american_scientific_journal-1367	71	35	left	leave	VERB
american_scientific_journal-1367	71	36	ideal	ideal	NOUN
american_scientific_journal-1367	71	37	of	of	ADP
american_scientific_journal-1367	71	38	r.	r.	PROPN
american_scientific_journal-1367	71	39	since	since	SCONJ
american_scientific_journal-1367	71	40	r	r	PROPN
american_scientific_journal-1367	71	41	/	/	SYM
american_scientific_journal-1367	71	42	i	i	PRON
american_scientific_journal-1367	71	43	is	be	AUX
american_scientific_journal-1367	71	44	fp	fp	ADJ
american_scientific_journal-1367	71	45	-	-	PUNCT
american_scientific_journal-1367	71	46	projective	projective	NOUN
american_scientific_journal-1367	71	47	left	leave	VERB
american_scientific_journal-1367	71	48	r	r	NOUN
american_scientific_journal-1367	71	49	-	-	PUNCT
american_scientific_journal-1367	71	50	module	module	NOUN
american_scientific_journal-1367	71	51	,	,	PUNCT
american_scientific_journal-1367	71	52	then	then	ADV
american_scientific_journal-1367	71	53	by	by	ADP
american_scientific_journal-1367	71	54	(	(	PUNCT
american_scientific_journal-1367	71	55	7	7	NUM
american_scientific_journal-1367	71	56	)	)	PUNCT
american_scientific_journal-1367	71	57	,	,	PUNCT
american_scientific_journal-1367	71	58	the	the	DET
american_scientific_journal-1367	71	59	sequences	sequence	NOUN
american_scientific_journal-1367	71	60	hom(r	hom(r	PROPN
american_scientific_journal-1367	71	61	/	/	SYM
american_scientific_journal-1367	71	62	i	i	PROPN
american_scientific_journal-1367	71	63	,	,	PUNCT
american_scientific_journal-1367	71	64	m	m	VERB
american_scientific_journal-1367	71	65	'	'	PUNCT
american_scientific_journal-1367	71	66	)	)	PUNCT
american_scientific_journal-1367	71	67	→	→	PUNCT
american_scientific_journal-1367	71	68	hom(r	hom(r	PROPN
american_scientific_journal-1367	71	69	/	/	SYM
american_scientific_journal-1367	71	70	i	i	PROPN
american_scientific_journal-1367	71	71	,	,	PUNCT
american_scientific_journal-1367	71	72	m	m	VERB
american_scientific_journal-1367	71	73	"	"	PUNCT
american_scientific_journal-1367	71	74	)	)	PUNCT
american_scientific_journal-1367	71	75	→	→	SYM
american_scientific_journal-1367	71	76	ext1(r	ext1(r	X
american_scientific_journal-1367	71	77	/	/	SYM
american_scientific_journal-1367	71	78	i	i	PROPN
american_scientific_journal-1367	71	79	,	,	PUNCT
american_scientific_journal-1367	71	80	m	m	PROPN
american_scientific_journal-1367	71	81	)	)	PUNCT
american_scientific_journal-1367	71	82	→	→	SYM
american_scientific_journal-1367	71	83	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	71	84	/	/	SYM
american_scientific_journal-1367	71	85	i	i	PROPN
american_scientific_journal-1367	71	86	,	,	PUNCT
american_scientific_journal-1367	71	87	m	m	NOUN
american_scientific_journal-1367	71	88	'	'	PUNCT
american_scientific_journal-1367	71	89	)	)	PUNCT
american_scientific_journal-1367	72	1	=	=	SYM
american_scientific_journal-1367	72	2	0	0	NUM
american_scientific_journal-1367	72	3	and	and	CCONJ
american_scientific_journal-1367	72	4	hom(r	hom(r	PROPN
american_scientific_journal-1367	72	5	/	/	SYM
american_scientific_journal-1367	72	6	i	i	PROPN
american_scientific_journal-1367	72	7	,	,	PUNCT
american_scientific_journal-1367	72	8	m	m	VERB
american_scientific_journal-1367	72	9	'	'	PUNCT
american_scientific_journal-1367	72	10	)	)	PUNCT
american_scientific_journal-1367	72	11	→	→	PUNCT
american_scientific_journal-1367	72	12	hom(r	hom(r	PROPN
american_scientific_journal-1367	72	13	/	/	SYM
american_scientific_journal-1367	72	14	i	i	PROPN
american_scientific_journal-1367	72	15	,	,	PUNCT
american_scientific_journal-1367	72	16	m	m	VERB
american_scientific_journal-1367	72	17	"	"	PUNCT
american_scientific_journal-1367	72	18	)	)	PUNCT
american_scientific_journal-1367	72	19	→	→	SYM
american_scientific_journal-1367	72	20	0	0	NUM
american_scientific_journal-1367	72	21	are	be	AUX
american_scientific_journal-1367	72	22	exact	exact	ADJ
american_scientific_journal-1367	72	23	.	.	PUNCT
american_scientific_journal-1367	73	1	this	this	PRON
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american_scientific_journal-1367	73	3	that	that	SCONJ
american_scientific_journal-1367	73	4	ext1(r	ext1(r	NOUN
american_scientific_journal-1367	73	5	/	/	SYM
american_scientific_journal-1367	73	6	i	i	PROPN
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american_scientific_journal-1367	73	8	m	m	PROPN
american_scientific_journal-1367	73	9	)	)	PUNCT
american_scientific_journal-1367	73	10	=	=	SYM
american_scientific_journal-1367	73	11	0	0	NUM
american_scientific_journal-1367	73	12	,	,	PUNCT
american_scientific_journal-1367	73	13	and	and	CCONJ
american_scientific_journal-1367	73	14	(	(	PUNCT
american_scientific_journal-1367	73	15	1	1	X
american_scientific_journal-1367	73	16	)	)	PUNCT
american_scientific_journal-1367	73	17	follows	follow	VERB
american_scientific_journal-1367	73	18	.	.	PUNCT
american_scientific_journal-1367	74	1	□	□	PUNCT
american_scientific_journal-1367	74	2	now	now	ADV
american_scientific_journal-1367	74	3	,	,	PUNCT
american_scientific_journal-1367	74	4	we	we	PRON
american_scientific_journal-1367	74	5	give	give	VERB
american_scientific_journal-1367	74	6	some	some	DET
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american_scientific_journal-1367	74	8	of	of	ADP
american_scientific_journal-1367	74	9	fp	fp	ADJ
american_scientific_journal-1367	74	10	-	-	PUNCT
american_scientific_journal-1367	74	11	projective	projective	ADJ
american_scientific_journal-1367	74	12	r	r	NOUN
american_scientific_journal-1367	74	13	-	-	PUNCT
american_scientific_journal-1367	74	14	modules	module	NOUN
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american_scientific_journal-1367	74	16	fp	fp	ADJ
american_scientific_journal-1367	74	17	-	-	PUNCT
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american_scientific_journal-1367	74	20	-	-	PUNCT
american_scientific_journal-1367	74	21	modules	module	NOUN
american_scientific_journal-1367	74	22	.	.	PUNCT
american_scientific_journal-1367	75	1	2.3	2.3	NUM
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american_scientific_journal-1367	75	3	let	let	VERB
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american_scientific_journal-1367	75	5	be	be	AUX
american_scientific_journal-1367	75	6	a	a	DET
american_scientific_journal-1367	75	7	left	left	ADJ
american_scientific_journal-1367	75	8	r	r	NOUN
american_scientific_journal-1367	75	9	-	-	PUNCT
american_scientific_journal-1367	75	10	module	module	NOUN
american_scientific_journal-1367	75	11	.	.	PUNCT
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american_scientific_journal-1367	76	2	following	follow	VERB
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american_scientific_journal-1367	76	4	are	be	AUX
american_scientific_journal-1367	76	5	equivalent	equivalent	ADJ
american_scientific_journal-1367	76	6	.	.	PUNCT
american_scientific_journal-1367	77	1	(	(	PUNCT
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american_scientific_journal-1367	77	3	)	)	PUNCT
american_scientific_journal-1367	77	4	m	m	VERB
american_scientific_journal-1367	77	5	is	be	AUX
american_scientific_journal-1367	77	6	left	leave	VERB
american_scientific_journal-1367	77	7	fp	fp	NOUN
american_scientific_journal-1367	77	8	-	-	PUNCT
american_scientific_journal-1367	77	9	projective	projective	ADJ
american_scientific_journal-1367	77	10	.	.	PUNCT
american_scientific_journal-1367	78	1	(	(	PUNCT
american_scientific_journal-1367	78	2	2	2	X
american_scientific_journal-1367	78	3	)	)	PUNCT
american_scientific_journal-1367	78	4	m	m	VERB
american_scientific_journal-1367	78	5	is	be	AUX
american_scientific_journal-1367	78	6	projective	projective	ADJ
american_scientific_journal-1367	78	7	with	with	ADP
american_scientific_journal-1367	78	8	respect	respect	NOUN
american_scientific_journal-1367	78	9	to	to	ADP
american_scientific_journal-1367	78	10	every	every	DET
american_scientific_journal-1367	78	11	exact	exact	ADJ
american_scientific_journal-1367	78	12	sequence	sequence	NOUN
american_scientific_journal-1367	78	13	0	0	NUM
american_scientific_journal-1367	79	1	→	→	SYM
american_scientific_journal-1367	79	2	a	a	DET
american_scientific_journal-1367	79	3	→	→	SYM
american_scientific_journal-1367	79	4	b	b	PROPN
american_scientific_journal-1367	79	5	→	→	SYM
american_scientific_journal-1367	79	6	c	c	PROPN
american_scientific_journal-1367	79	7	→	→	SYM
american_scientific_journal-1367	79	8	0	0	NUM
american_scientific_journal-1367	79	9	of	of	ADP
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american_scientific_journal-1367	79	11	r	r	NOUN
american_scientific_journal-1367	79	12	-	-	PUNCT
american_scientific_journal-1367	79	13	modules	module	NOUN
american_scientific_journal-1367	79	14	with	with	ADP
american_scientific_journal-1367	79	15	a	a	DET
american_scientific_journal-1367	79	16	fp	fp	ADJ
american_scientific_journal-1367	79	17	-	-	PUNCT
american_scientific_journal-1367	79	18	injective	injective	ADJ
american_scientific_journal-1367	79	19	.	.	PUNCT
american_scientific_journal-1367	80	1	(	(	PUNCT
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american_scientific_journal-1367	80	3	)	)	PUNCT
american_scientific_journal-1367	80	4	m	m	VERB
american_scientific_journal-1367	80	5	is	be	AUX
american_scientific_journal-1367	80	6	projective	projective	ADJ
american_scientific_journal-1367	80	7	with	with	ADP
american_scientific_journal-1367	80	8	respect	respect	NOUN
american_scientific_journal-1367	80	9	to	to	ADP
american_scientific_journal-1367	80	10	every	every	DET
american_scientific_journal-1367	80	11	exact	exact	ADJ
american_scientific_journal-1367	80	12	sequence	sequence	NOUN
american_scientific_journal-1367	80	13	0	0	NUM
american_scientific_journal-1367	81	1	→	→	SYM
american_scientific_journal-1367	81	2	a	a	DET
american_scientific_journal-1367	81	3	→	→	SYM
american_scientific_journal-1367	81	4	f	f	X
american_scientific_journal-1367	81	5	→	→	SYM
american_scientific_journal-1367	81	6	k	k	X
american_scientific_journal-1367	81	7	→	→	SYM
american_scientific_journal-1367	81	8	0	0	NUM
american_scientific_journal-1367	81	9	of	of	ADP
american_scientific_journal-1367	81	10	r	r	NOUN
american_scientific_journal-1367	81	11	-	-	PUNCT
american_scientific_journal-1367	81	12	modules	module	NOUN
american_scientific_journal-1367	81	13	with	with	ADP
american_scientific_journal-1367	81	14	f	f	PROPN
american_scientific_journal-1367	81	15	injective	injective	PROPN
american_scientific_journal-1367	81	16	and	and	CCONJ
american_scientific_journal-1367	81	17	a	a	DET
american_scientific_journal-1367	81	18	fp	fp	ADJ
american_scientific_journal-1367	81	19	-	-	PUNCT
american_scientific_journal-1367	81	20	injective	injective	ADJ
american_scientific_journal-1367	81	21	.	.	PUNCT
american_scientific_journal-1367	82	1	(	(	PUNCT
american_scientific_journal-1367	82	2	4	4	X
american_scientific_journal-1367	82	3	)	)	PUNCT
american_scientific_journal-1367	82	4	every	every	DET
american_scientific_journal-1367	82	5	fp	fp	ADJ
american_scientific_journal-1367	82	6	-	-	PUNCT
american_scientific_journal-1367	82	7	injective	injective	ADJ
american_scientific_journal-1367	82	8	r	r	NOUN
american_scientific_journal-1367	82	9	-	-	PUNCT
american_scientific_journal-1367	82	10	module	module	NOUN
american_scientific_journal-1367	82	11	is	be	AUX
american_scientific_journal-1367	82	12	injective	injective	ADJ
american_scientific_journal-1367	82	13	with	with	ADP
american_scientific_journal-1367	82	14	respect	respect	NOUN
american_scientific_journal-1367	82	15	to	to	ADP
american_scientific_journal-1367	82	16	every	every	DET
american_scientific_journal-1367	82	17	exact	exact	ADJ
american_scientific_journal-1367	82	18	sequence	sequence	NOUN
american_scientific_journal-1367	82	19	of	of	ADP
american_scientific_journal-1367	82	20	left	left	ADJ
american_scientific_journal-1367	82	21	r	r	NOUN
american_scientific_journal-1367	82	22	-	-	PUNCT
american_scientific_journal-1367	82	23	modules	module	NOUN
american_scientific_journal-1367	82	24	0	0	NUM
american_scientific_journal-1367	82	25	→	→	SYM
american_scientific_journal-1367	82	26	m	m	NOUN
american_scientific_journal-1367	82	27	"	"	PUNCT
american_scientific_journal-1367	82	28	→	→	SYM
american_scientific_journal-1367	82	29	m	m	NOUN
american_scientific_journal-1367	82	30	'	'	PUNCT
american_scientific_journal-1367	82	31	→	→	SYM
american_scientific_journal-1367	82	32	m	m	PROPN
american_scientific_journal-1367	82	33	→	→	SYM
american_scientific_journal-1367	82	34	0	0	NUM
american_scientific_journal-1367	82	35	.	.	PUNCT
american_scientific_journal-1367	83	1	(	(	PUNCT
american_scientific_journal-1367	83	2	5	5	X
american_scientific_journal-1367	83	3	)	)	PUNCT
american_scientific_journal-1367	83	4	there	there	PRON
american_scientific_journal-1367	83	5	exists	exist	VERB
american_scientific_journal-1367	83	6	an	an	DET
american_scientific_journal-1367	83	7	exact	exact	ADJ
american_scientific_journal-1367	83	8	sequence	sequence	NOUN
american_scientific_journal-1367	83	9	0	0	NUM
american_scientific_journal-1367	83	10	→	→	SYM
american_scientific_journal-1367	83	11	m	m	NOUN
american_scientific_journal-1367	83	12	"	"	PUNCT
american_scientific_journal-1367	83	13	→	→	SYM
american_scientific_journal-1367	83	14	m	m	NOUN
american_scientific_journal-1367	83	15	'	'	PUNCT
american_scientific_journal-1367	83	16	→	→	SYM
american_scientific_journal-1367	83	17	m	m	PROPN
american_scientific_journal-1367	83	18	→	→	SYM
american_scientific_journal-1367	83	19	0	0	NUM
american_scientific_journal-1367	83	20	of	of	ADP
american_scientific_journal-1367	83	21	left	left	ADJ
american_scientific_journal-1367	83	22	r	r	NOUN
american_scientific_journal-1367	83	23	-	-	PUNCT
american_scientific_journal-1367	83	24	modules	module	NOUN
american_scientific_journal-1367	83	25	with	with	ADP
american_scientific_journal-1367	83	26	m	m	NOUN
american_scientific_journal-1367	83	27	'	'	PART
american_scientific_journal-1367	83	28	projective	projective	NOUN
american_scientific_journal-1367	83	29	,	,	PUNCT
american_scientific_journal-1367	83	30	such	such	ADJ
american_scientific_journal-1367	83	31	that	that	SCONJ
american_scientific_journal-1367	83	32	every	every	DET
american_scientific_journal-1367	83	33	fp	fp	ADJ
american_scientific_journal-1367	83	34	-	-	PUNCT
american_scientific_journal-1367	83	35	injective	injective	ADJ
american_scientific_journal-1367	83	36	left	leave	VERB
american_scientific_journal-1367	83	37	r	r	NOUN
american_scientific_journal-1367	83	38	-	-	PUNCT
american_scientific_journal-1367	83	39	module	module	NOUN
american_scientific_journal-1367	83	40	is	be	AUX
american_scientific_journal-1367	83	41	injective	injective	ADJ
american_scientific_journal-1367	83	42	with	with	ADP
american_scientific_journal-1367	83	43	respect	respect	NOUN
american_scientific_journal-1367	83	44	to	to	ADP
american_scientific_journal-1367	83	45	this	this	DET
american_scientific_journal-1367	83	46	sequence	sequence	NOUN
american_scientific_journal-1367	83	47	.	.	PUNCT
american_scientific_journal-1367	84	1	(	(	PUNCT
american_scientific_journal-1367	84	2	6	6	X
american_scientific_journal-1367	84	3	)	)	PUNCT
american_scientific_journal-1367	84	4	there	there	PRON
american_scientific_journal-1367	84	5	exists	exist	VERB
american_scientific_journal-1367	84	6	an	an	DET
american_scientific_journal-1367	84	7	exact	exact	ADJ
american_scientific_journal-1367	84	8	sequence	sequence	NOUN
american_scientific_journal-1367	84	9	0	0	NUM
american_scientific_journal-1367	84	10	→	→	SYM
american_scientific_journal-1367	84	11	m	m	NOUN
american_scientific_journal-1367	84	12	"	"	PUNCT
american_scientific_journal-1367	84	13	→	→	SYM
american_scientific_journal-1367	84	14	m	m	NOUN
american_scientific_journal-1367	84	15	'	'	PUNCT
american_scientific_journal-1367	84	16	→	→	SYM
american_scientific_journal-1367	84	17	m	m	PROPN
american_scientific_journal-1367	84	18	→	→	SYM
american_scientific_journal-1367	84	19	0	0	NUM
american_scientific_journal-1367	84	20	of	of	ADP
american_scientific_journal-1367	84	21	left	left	ADJ
american_scientific_journal-1367	84	22	r	r	NOUN
american_scientific_journal-1367	84	23	-	-	PUNCT
american_scientific_journal-1367	84	24	modules	module	NOUN
american_scientific_journal-1367	84	25	with	with	ADP
american_scientific_journal-1367	84	26	m	m	PROPN
american_scientific_journal-1367	84	27	'	'	PART
american_scientific_journal-1367	84	28	fp	fp	PROPN
american_scientific_journal-1367	84	29	-	-	PUNCT
american_scientific_journal-1367	84	30	projective	projective	ADJ
american_scientific_journal-1367	84	31	,	,	PUNCT
american_scientific_journal-1367	84	32	such	such	ADJ
american_scientific_journal-1367	84	33	that	that	SCONJ
american_scientific_journal-1367	84	34	every	every	DET
american_scientific_journal-1367	84	35	fp	fp	ADJ
american_scientific_journal-1367	84	36	-	-	PUNCT
american_scientific_journal-1367	84	37	injective	injective	ADJ
american_scientific_journal-1367	84	38	left	leave	VERB
american_scientific_journal-1367	84	39	r	r	NOUN
american_scientific_journal-1367	84	40	-	-	PUNCT
american_scientific_journal-1367	84	41	module	module	NOUN
american_scientific_journal-1367	84	42	is	be	AUX
american_scientific_journal-1367	84	43	injective	injective	ADJ
american_scientific_journal-1367	84	44	with	with	ADP
american_scientific_journal-1367	84	45	respect	respect	NOUN
american_scientific_journal-1367	84	46	to	to	ADP
american_scientific_journal-1367	84	47	this	this	DET
american_scientific_journal-1367	84	48	sequence	sequence	NOUN
american_scientific_journal-1367	84	49	.	.	PUNCT
american_scientific_journal-1367	85	1	proof	proof	NOUN
american_scientific_journal-1367	85	2	.	.	PUNCT
american_scientific_journal-1367	86	1	(	(	PUNCT
american_scientific_journal-1367	86	2	1	1	X
american_scientific_journal-1367	86	3	)	)	PUNCT
american_scientific_journal-1367	86	4	⇒	⇒	NOUN
american_scientific_journal-1367	86	5	(	(	PUNCT
american_scientific_journal-1367	86	6	2	2	NUM
american_scientific_journal-1367	86	7	)	)	PUNCT
american_scientific_journal-1367	86	8	.	.	PUNCT
american_scientific_journal-1367	87	1	let	let	VERB
american_scientific_journal-1367	87	2	m	m	PRON
american_scientific_journal-1367	87	3	be	be	AUX
american_scientific_journal-1367	87	4	an	an	DET
american_scientific_journal-1367	87	5	fp	fp	ADJ
american_scientific_journal-1367	87	6	-	-	PUNCT
american_scientific_journal-1367	87	7	projective	projective	NOUN
american_scientific_journal-1367	87	8	left	leave	VERB
american_scientific_journal-1367	87	9	r	r	NOUN
american_scientific_journal-1367	87	10	-	-	PUNCT
american_scientific_journal-1367	87	11	module	module	NOUN
american_scientific_journal-1367	87	12	.	.	PUNCT
american_scientific_journal-1367	88	1	then	then	ADV
american_scientific_journal-1367	88	2	the	the	DET
american_scientific_journal-1367	88	3	sequence	sequence	NOUN
american_scientific_journal-1367	88	4	hom(m	hom(m	PROPN
american_scientific_journal-1367	88	5	,	,	PUNCT
american_scientific_journal-1367	88	6	b	b	NOUN
american_scientific_journal-1367	88	7	)	)	PUNCT
american_scientific_journal-1367	88	8	→	→	SYM
american_scientific_journal-1367	88	9	hom(m	hom(m	PROPN
american_scientific_journal-1367	88	10	,	,	PUNCT
american_scientific_journal-1367	88	11	c	c	NOUN
american_scientific_journal-1367	88	12	)	)	PUNCT
american_scientific_journal-1367	88	13	→	→	SYM
american_scientific_journal-1367	88	14	ext1(m	ext1(m	NUM
american_scientific_journal-1367	88	15	,	,	PUNCT
american_scientific_journal-1367	88	16	a	a	PRON
american_scientific_journal-1367	88	17	)	)	PUNCT
american_scientific_journal-1367	88	18	=	=	SYM
american_scientific_journal-1367	88	19	0	0	NUM
american_scientific_journal-1367	88	20	is	be	AUX
american_scientific_journal-1367	88	21	exact	exact	ADJ
american_scientific_journal-1367	88	22	for	for	SCONJ
american_scientific_journal-1367	88	23	every	every	DET
american_scientific_journal-1367	88	24	fp	fp	ADJ
american_scientific_journal-1367	88	25	-	-	PUNCT
american_scientific_journal-1367	88	26	injective	injective	ADJ
american_scientific_journal-1367	88	27	r	r	NOUN
american_scientific_journal-1367	88	28	-	-	PUNCT
american_scientific_journal-1367	88	29	module	module	NOUN
american_scientific_journal-1367	88	30	a.	a.	NOUN
american_scientific_journal-1367	88	31	hence	hence	ADV
american_scientific_journal-1367	88	32	(	(	PUNCT
american_scientific_journal-1367	88	33	2	2	X
american_scientific_journal-1367	88	34	)	)	PUNCT
american_scientific_journal-1367	88	35	holds	hold	VERB
american_scientific_journal-1367	88	36	.	.	PUNCT
american_scientific_journal-1367	89	1	(	(	PUNCT
american_scientific_journal-1367	89	2	2	2	X
american_scientific_journal-1367	89	3	)	)	PUNCT
american_scientific_journal-1367	89	4	⇒	⇒	NOUN
american_scientific_journal-1367	89	5	(	(	PUNCT
american_scientific_journal-1367	89	6	3	3	X
american_scientific_journal-1367	89	7	)	)	PUNCT
american_scientific_journal-1367	89	8	is	be	AUX
american_scientific_journal-1367	89	9	clear	clear	ADJ
american_scientific_journal-1367	89	10	.	.	PUNCT
american_scientific_journal-1367	90	1	(	(	PUNCT
american_scientific_journal-1367	90	2	3	3	X
american_scientific_journal-1367	90	3	)	)	PUNCT
american_scientific_journal-1367	90	4	⇒	⇒	NOUN
american_scientific_journal-1367	90	5	(	(	PUNCT
american_scientific_journal-1367	90	6	1	1	NUM
american_scientific_journal-1367	90	7	)	)	PUNCT
american_scientific_journal-1367	90	8	.	.	PUNCT
american_scientific_journal-1367	91	1	let	let	VERB
american_scientific_journal-1367	91	2	0	0	NUM
american_scientific_journal-1367	92	1	→	→	SYM
american_scientific_journal-1367	92	2	a	a	DET
american_scientific_journal-1367	92	3	→	→	SYM
american_scientific_journal-1367	92	4	f	f	X
american_scientific_journal-1367	92	5	→	→	SYM
american_scientific_journal-1367	92	6	k	k	X
american_scientific_journal-1367	92	7	→	→	SYM
american_scientific_journal-1367	92	8	0	0	NUM
american_scientific_journal-1367	92	9	be	be	AUX
american_scientific_journal-1367	92	10	an	an	DET
american_scientific_journal-1367	92	11	exact	exact	ADJ
american_scientific_journal-1367	92	12	sequence	sequence	NOUN
american_scientific_journal-1367	92	13	of	of	ADP
american_scientific_journal-1367	92	14	left	left	ADJ
american_scientific_journal-1367	92	15	r	r	NOUN
american_scientific_journal-1367	92	16	-	-	PUNCT
american_scientific_journal-1367	92	17	modules	module	NOUN
american_scientific_journal-1367	92	18	with	with	ADP
american_scientific_journal-1367	92	19	f	f	PROPN
american_scientific_journal-1367	92	20	injective	injective	ADJ
american_scientific_journal-1367	92	21	and	and	CCONJ
american_scientific_journal-1367	92	22	a	a	DET
american_scientific_journal-1367	92	23	fpinjective	fpinjective	NOUN
american_scientific_journal-1367	92	24	.	.	PUNCT
american_scientific_journal-1367	93	1	then	then	ADV
american_scientific_journal-1367	93	2	the	the	DET
american_scientific_journal-1367	93	3	sequence	sequence	NOUN
american_scientific_journal-1367	93	4	hom(m	hom(m	PROPN
american_scientific_journal-1367	93	5	,	,	PUNCT
american_scientific_journal-1367	93	6	f	f	NOUN
american_scientific_journal-1367	93	7	)	)	PUNCT
american_scientific_journal-1367	93	8	→	→	SYM
american_scientific_journal-1367	93	9	hom(m	hom(m	PROPN
american_scientific_journal-1367	93	10	,	,	PUNCT
american_scientific_journal-1367	93	11	k	k	NOUN
american_scientific_journal-1367	93	12	)	)	PUNCT
american_scientific_journal-1367	93	13	→	→	SYM
american_scientific_journal-1367	93	14	0	0	NUM
american_scientific_journal-1367	93	15	is	be	AUX
american_scientific_journal-1367	93	16	exact	exact	ADJ
american_scientific_journal-1367	93	17	by	by	ADP
american_scientific_journal-1367	93	18	(	(	PUNCT
american_scientific_journal-1367	93	19	3	3	NUM
american_scientific_journal-1367	93	20	)	)	PUNCT
american_scientific_journal-1367	93	21	.	.	PUNCT
american_scientific_journal-1367	94	1	so	so	ADV
american_scientific_journal-1367	94	2	ext1(m	ext1(m	NUM
american_scientific_journal-1367	94	3	,	,	PUNCT
american_scientific_journal-1367	94	4	a	a	PRON
american_scientific_journal-1367	94	5	)	)	PUNCT
american_scientific_journal-1367	94	6	=	=	SYM
american_scientific_journal-1367	94	7	0	0	NUM
american_scientific_journal-1367	94	8	for	for	ADP
american_scientific_journal-1367	94	9	any	any	DET
american_scientific_journal-1367	94	10	fpinjective	fpinjective	ADJ
american_scientific_journal-1367	94	11	left	leave	VERB
american_scientific_journal-1367	94	12	r	r	NOUN
american_scientific_journal-1367	94	13	-	-	PUNCT
american_scientific_journal-1367	94	14	module	module	NOUN
american_scientific_journal-1367	94	15	a.	a.	NOUN
american_scientific_journal-1367	94	16	hence	hence	ADV
american_scientific_journal-1367	94	17	m	m	VERB
american_scientific_journal-1367	94	18	is	be	AUX
american_scientific_journal-1367	94	19	fp	fp	ADJ
american_scientific_journal-1367	94	20	-	-	PUNCT
american_scientific_journal-1367	94	21	projective	projective	NOUN
american_scientific_journal-1367	94	22	left	leave	VERB
american_scientific_journal-1367	94	23	r	r	NOUN
american_scientific_journal-1367	94	24	-	-	PUNCT
american_scientific_journal-1367	94	25	module	module	NOUN
american_scientific_journal-1367	94	26	.	.	PUNCT
american_scientific_journal-1367	95	1	(	(	PUNCT
american_scientific_journal-1367	95	2	1	1	X
american_scientific_journal-1367	95	3	)	)	PUNCT
american_scientific_journal-1367	95	4	⇒	⇒	NOUN
american_scientific_journal-1367	95	5	(	(	PUNCT
american_scientific_journal-1367	95	6	4	4	NUM
american_scientific_journal-1367	95	7	)	)	PUNCT
american_scientific_journal-1367	95	8	.	.	PUNCT
american_scientific_journal-1367	96	1	let	let	VERB
american_scientific_journal-1367	96	2	m	m	PRON
american_scientific_journal-1367	96	3	be	be	AUX
american_scientific_journal-1367	96	4	an	an	DET
american_scientific_journal-1367	96	5	fp	fp	ADJ
american_scientific_journal-1367	96	6	-	-	PUNCT
american_scientific_journal-1367	96	7	projective	projective	NOUN
american_scientific_journal-1367	96	8	left	leave	VERB
american_scientific_journal-1367	96	9	r	r	NOUN
american_scientific_journal-1367	96	10	-	-	PUNCT
american_scientific_journal-1367	96	11	module	module	NOUN
american_scientific_journal-1367	96	12	,	,	PUNCT
american_scientific_journal-1367	96	13	f	f	PROPN
american_scientific_journal-1367	96	14	be	be	AUX
american_scientific_journal-1367	96	15	an	an	DET
american_scientific_journal-1367	96	16	fp	fp	ADJ
american_scientific_journal-1367	96	17	-	-	PUNCT
american_scientific_journal-1367	96	18	injective	injective	ADJ
american_scientific_journal-1367	96	19	left	leave	VERB
american_scientific_journal-1367	96	20	r	r	NOUN
american_scientific_journal-1367	96	21	-	-	PUNCT
american_scientific_journal-1367	96	22	module	module	NOUN
american_scientific_journal-1367	96	23	.	.	PUNCT
american_scientific_journal-1367	97	1	then	then	ADV
american_scientific_journal-1367	97	2	the	the	DET
american_scientific_journal-1367	97	3	sequence	sequence	NOUN
american_scientific_journal-1367	97	4	hom(m	hom(m	PROPN
american_scientific_journal-1367	97	5	'	'	PUNCT
american_scientific_journal-1367	97	6	,	,	PUNCT
american_scientific_journal-1367	97	7	f	f	X
american_scientific_journal-1367	97	8	)	)	PUNCT
american_scientific_journal-1367	97	9	→	→	SYM
american_scientific_journal-1367	97	10	hom(m	hom(m	PROPN
american_scientific_journal-1367	97	11	"	"	PUNCT
american_scientific_journal-1367	97	12	,	,	PUNCT
american_scientific_journal-1367	97	13	f)→	f)→	PROPN
american_scientific_journal-1367	97	14	ext1(m	ext1(m	NUM
american_scientific_journal-1367	97	15	,	,	PUNCT
american_scientific_journal-1367	97	16	f	f	X
american_scientific_journal-1367	97	17	)	)	PUNCT
american_scientific_journal-1367	97	18	=	=	SYM
american_scientific_journal-1367	97	19	0	0	NUM
american_scientific_journal-1367	97	20	is	be	AUX
american_scientific_journal-1367	97	21	exact	exact	ADJ
american_scientific_journal-1367	97	22	.	.	PUNCT
american_scientific_journal-1367	98	1	so	so	ADV
american_scientific_journal-1367	98	2	(	(	PUNCT
american_scientific_journal-1367	98	3	4	4	X
american_scientific_journal-1367	98	4	)	)	PUNCT
american_scientific_journal-1367	98	5	holds	hold	VERB
american_scientific_journal-1367	98	6	.	.	PUNCT
american_scientific_journal-1367	99	1	(	(	PUNCT
american_scientific_journal-1367	99	2	4	4	X
american_scientific_journal-1367	99	3	)	)	PUNCT
american_scientific_journal-1367	99	4	⇒	⇒	NOUN
american_scientific_journal-1367	99	5	(	(	PUNCT
american_scientific_journal-1367	99	6	5	5	NUM
american_scientific_journal-1367	99	7	)	)	PUNCT
american_scientific_journal-1367	99	8	⇒	⇒	NOUN
american_scientific_journal-1367	99	9	(	(	PUNCT
american_scientific_journal-1367	99	10	6	6	NUM
american_scientific_journal-1367	99	11	)	)	PUNCT
american_scientific_journal-1367	99	12	are	be	AUX
american_scientific_journal-1367	99	13	obvious	obvious	ADJ
american_scientific_journal-1367	99	14	.	.	PUNCT
american_scientific_journal-1367	100	1	(	(	PUNCT
american_scientific_journal-1367	100	2	6	6	NUM
american_scientific_journal-1367	100	3	)	)	PUNCT
american_scientific_journal-1367	100	4	⇒	⇒	NOUN
american_scientific_journal-1367	100	5	(	(	PUNCT
american_scientific_journal-1367	100	6	1	1	NUM
american_scientific_journal-1367	100	7	)	)	PUNCT
american_scientific_journal-1367	100	8	.	.	PUNCT
american_scientific_journal-1367	101	1	let	let	VERB
american_scientific_journal-1367	101	2	0	0	NUM
american_scientific_journal-1367	101	3	→	→	SYM
american_scientific_journal-1367	101	4	m	m	NOUN
american_scientific_journal-1367	101	5	"	"	PUNCT
american_scientific_journal-1367	101	6	→	→	SYM
american_scientific_journal-1367	101	7	m	m	NOUN
american_scientific_journal-1367	101	8	'	'	PUNCT
american_scientific_journal-1367	101	9	→	→	SYM
american_scientific_journal-1367	101	10	m	m	PROPN
american_scientific_journal-1367	101	11	→	→	SYM
american_scientific_journal-1367	101	12	0	0	NUM
american_scientific_journal-1367	101	13	be	be	AUX
american_scientific_journal-1367	101	14	an	an	DET
american_scientific_journal-1367	101	15	exact	exact	ADJ
american_scientific_journal-1367	101	16	sequence	sequence	NOUN
american_scientific_journal-1367	101	17	of	of	ADP
american_scientific_journal-1367	101	18	left	left	ADJ
american_scientific_journal-1367	101	19	r	r	NOUN
american_scientific_journal-1367	101	20	-	-	PUNCT
american_scientific_journal-1367	101	21	modules	module	NOUN
american_scientific_journal-1367	101	22	with	with	ADP
american_scientific_journal-1367	101	23	m	m	PROPN
american_scientific_journal-1367	101	24	'	'	PART
american_scientific_journal-1367	101	25	fp	fp	PROPN
american_scientific_journal-1367	101	26	-	-	PUNCT
american_scientific_journal-1367	101	27	projective	projective	NOUN
american_scientific_journal-1367	101	28	.	.	PUNCT
american_scientific_journal-1367	102	1	then	then	ADV
american_scientific_journal-1367	102	2	for	for	ADP
american_scientific_journal-1367	102	3	any	any	DET
american_scientific_journal-1367	102	4	fp	fp	ADJ
american_scientific_journal-1367	102	5	-	-	PUNCT
american_scientific_journal-1367	102	6	injective	injective	ADJ
american_scientific_journal-1367	102	7	left	leave	VERB
american_scientific_journal-1367	102	8	r	r	NOUN
american_scientific_journal-1367	102	9	-	-	PUNCT
american_scientific_journal-1367	102	10	module	module	NOUN
american_scientific_journal-1367	102	11	n	n	CCONJ
american_scientific_journal-1367	102	12	,	,	PUNCT
american_scientific_journal-1367	102	13	the	the	DET
american_scientific_journal-1367	102	14	sequence	sequence	NOUN
american_scientific_journal-1367	102	15	hom(m	hom(m	PROPN
american_scientific_journal-1367	102	16	'	'	PUNCT
american_scientific_journal-1367	102	17	,	,	PUNCT
american_scientific_journal-1367	102	18	n	n	CCONJ
american_scientific_journal-1367	102	19	)	)	PUNCT
american_scientific_journal-1367	102	20	→	→	SYM
american_scientific_journal-1367	102	21	hom(m	hom(m	PROPN
american_scientific_journal-1367	102	22	"	"	PUNCT
american_scientific_journal-1367	102	23	,	,	PUNCT
american_scientific_journal-1367	102	24	n	n	CCONJ
american_scientific_journal-1367	102	25	)	)	PUNCT
american_scientific_journal-1367	102	26	→	→	SYM
american_scientific_journal-1367	102	27	ext1(m	ext1(m	NUM
american_scientific_journal-1367	102	28	,	,	PUNCT
american_scientific_journal-1367	102	29	n	n	CCONJ
american_scientific_journal-1367	102	30	)	)	PUNCT
american_scientific_journal-1367	102	31	→	→	SYM
american_scientific_journal-1367	102	32	ext1(m	ext1(m	NUM
american_scientific_journal-1367	102	33	'	'	NUM
american_scientific_journal-1367	102	34	,	,	PUNCT
american_scientific_journal-1367	102	35	n	n	CCONJ
american_scientific_journal-1367	102	36	)	)	PUNCT
american_scientific_journal-1367	103	1	=	=	SYM
american_scientific_journal-1367	103	2	0	0	NUM
american_scientific_journal-1367	103	3	is	be	AUX
american_scientific_journal-1367	103	4	exact	exact	ADJ
american_scientific_journal-1367	103	5	,	,	PUNCT
american_scientific_journal-1367	103	6	and	and	CCONJ
american_scientific_journal-1367	103	7	the	the	DET
american_scientific_journal-1367	103	8	sequence	sequence	NOUN
american_scientific_journal-1367	103	9	(	(	PUNCT
american_scientific_journal-1367	103	10	m	m	NOUN
american_scientific_journal-1367	103	11	'	'	NUM
american_scientific_journal-1367	103	12	,	,	PUNCT
american_scientific_journal-1367	103	13	n	n	CCONJ
american_scientific_journal-1367	103	14	)	)	PUNCT
american_scientific_journal-1367	103	15	→	→	SYM
american_scientific_journal-1367	103	16	hom(m	hom(m	PROPN
american_scientific_journal-1367	103	17	"	"	PUNCT
american_scientific_journal-1367	103	18	,	,	PUNCT
american_scientific_journal-1367	103	19	n	n	CCONJ
american_scientific_journal-1367	103	20	)	)	PUNCT
american_scientific_journal-1367	103	21	→	→	SYM
american_scientific_journal-1367	103	22	0	0	NUM
american_scientific_journal-1367	103	23	is	be	AUX
american_scientific_journal-1367	103	24	exact	exact	ADJ
american_scientific_journal-1367	103	25	by	by	ADP
american_scientific_journal-1367	103	26	(	(	PUNCT
american_scientific_journal-1367	103	27	6).this	6).this	NUM
american_scientific_journal-1367	103	28	implies	imply	VERB
american_scientific_journal-1367	103	29	that	that	SCONJ
american_scientific_journal-1367	103	30	ext1(m	ext1(m	NUM
american_scientific_journal-1367	103	31	,	,	PUNCT
american_scientific_journal-1367	103	32	n	n	CCONJ
american_scientific_journal-1367	103	33	)	)	PUNCT
american_scientific_journal-1367	103	34	=	=	SYM
american_scientific_journal-1367	103	35	0	0	NUM
american_scientific_journal-1367	103	36	,	,	PUNCT
american_scientific_journal-1367	103	37	and	and	CCONJ
american_scientific_journal-1367	103	38	(	(	PUNCT
american_scientific_journal-1367	103	39	1	1	X
american_scientific_journal-1367	103	40	)	)	PUNCT
american_scientific_journal-1367	103	41	135	135	NUM
american_scientific_journal-1367	103	42	american	american	ADJ
american_scientific_journal-1367	103	43	scientific	scientific	ADJ
american_scientific_journal-1367	103	44	research	research	NOUN
american_scientific_journal-1367	103	45	journal	journal	NOUN
american_scientific_journal-1367	103	46	for	for	ADP
american_scientific_journal-1367	103	47	engineering	engineering	NOUN
american_scientific_journal-1367	103	48	,	,	PUNCT
american_scientific_journal-1367	103	49	technology	technology	NOUN
american_scientific_journal-1367	103	50	,	,	PUNCT
american_scientific_journal-1367	103	51	and	and	CCONJ
american_scientific_journal-1367	103	52	sciences	science	NOUN
american_scientific_journal-1367	103	53	(	(	PUNCT
american_scientific_journal-1367	103	54	asrjets	asrjet	NOUN
american_scientific_journal-1367	103	55	)	)	PUNCT
american_scientific_journal-1367	103	56	(	(	PUNCT
american_scientific_journal-1367	103	57	2016	2016	NUM
american_scientific_journal-1367	103	58	)	)	PUNCT
american_scientific_journal-1367	103	59	volume	volume	NOUN
american_scientific_journal-1367	103	60	17	17	NUM
american_scientific_journal-1367	103	61	,	,	PUNCT
american_scientific_journal-1367	103	62	no	no	DET
american_scientific_journal-1367	103	63	1	1	NUM
american_scientific_journal-1367	103	64	,	,	PUNCT
american_scientific_journal-1367	103	65	pp	pp	ADV
american_scientific_journal-1367	103	66	132	132	NUM
american_scientific_journal-1367	103	67	-	-	SYM
american_scientific_journal-1367	103	68	143	143	NUM
american_scientific_journal-1367	103	69	follows	follow	VERB
american_scientific_journal-1367	103	70	.	.	PUNCT
american_scientific_journal-1367	104	1	□	□	PUNCT
american_scientific_journal-1367	104	2	a	a	DET
american_scientific_journal-1367	104	3	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	104	4	theory	theory	NOUN
american_scientific_journal-1367	104	5	(	(	PUNCT
american_scientific_journal-1367	104	6	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	104	7	,	,	PUNCT
american_scientific_journal-1367	104	8	ℬ	ℬ	NOUN
american_scientific_journal-1367	104	9	)	)	PUNCT
american_scientific_journal-1367	104	10	is	be	AUX
american_scientific_journal-1367	104	11	said	say	VERB
american_scientific_journal-1367	104	12	to	to	PART
american_scientific_journal-1367	104	13	have	have	VERB
american_scientific_journal-1367	104	14	enough	enough	ADJ
american_scientific_journal-1367	104	15	injectives	injective	NOUN
american_scientific_journal-1367	104	16	(	(	PUNCT
american_scientific_journal-1367	104	17	resp	resp	NOUN
american_scientific_journal-1367	104	18	.	.	PUNCT
american_scientific_journal-1367	104	19	,	,	PUNCT
american_scientific_journal-1367	104	20	enough	enough	ADJ
american_scientific_journal-1367	104	21	projectives	projective	NOUN
american_scientific_journal-1367	104	22	)	)	PUNCT
american_scientific_journal-1367	104	23	(	(	PUNCT
american_scientific_journal-1367	104	24	see	see	VERB
american_scientific_journal-1367	104	25	.	.	PUNCT
american_scientific_journal-1367	105	1	[	[	X
american_scientific_journal-1367	105	2	10	10	NUM
american_scientific_journal-1367	105	3	,	,	PUNCT
american_scientific_journal-1367	105	4	p.	p.	NOUN
american_scientific_journal-1367	105	5	5	5	NUM
american_scientific_journal-1367	105	6	]	]	SYM
american_scientific_journal-1367	105	7	)	)	PUNCT
american_scientific_journal-1367	105	8	if	if	SCONJ
american_scientific_journal-1367	105	9	for	for	ADP
american_scientific_journal-1367	105	10	every	every	DET
american_scientific_journal-1367	105	11	module	module	NOUN
american_scientific_journal-1367	105	12	l	l	NOUN
american_scientific_journal-1367	105	13	there	there	PRON
american_scientific_journal-1367	105	14	is	be	VERB
american_scientific_journal-1367	105	15	a	a	DET
american_scientific_journal-1367	105	16	short	short	ADJ
american_scientific_journal-1367	105	17	exact	exact	ADJ
american_scientific_journal-1367	105	18	sequence	sequence	NOUN
american_scientific_journal-1367	105	19	0	0	NUM
american_scientific_journal-1367	105	20	→	→	SYM
american_scientific_journal-1367	105	21	l	l	NOUN
american_scientific_journal-1367	105	22	→b	→b	NUM
american_scientific_journal-1367	105	23	→	→	SYM
american_scientific_journal-1367	105	24	a	a	DET
american_scientific_journal-1367	105	25	→	→	SYM
american_scientific_journal-1367	105	26	0	0	NUM
american_scientific_journal-1367	105	27	(	(	PUNCT
american_scientific_journal-1367	105	28	resp	resp	NOUN
american_scientific_journal-1367	105	29	.	.	PUNCT
american_scientific_journal-1367	105	30	,	,	PUNCT
american_scientific_journal-1367	105	31	0	0	NUM
american_scientific_journal-1367	105	32	→	→	SYM
american_scientific_journal-1367	105	33	b	b	X
american_scientific_journal-1367	105	34	→	→	SYM
american_scientific_journal-1367	105	35	a	a	DET
american_scientific_journal-1367	105	36	→	→	SYM
american_scientific_journal-1367	105	37	l	l	NOUN
american_scientific_journal-1367	105	38	→	→	SYM
american_scientific_journal-1367	105	39	0	0	NUM
american_scientific_journal-1367	105	40	)	)	PUNCT
american_scientific_journal-1367	105	41	such	such	ADJ
american_scientific_journal-1367	105	42	that	that	DET
american_scientific_journal-1367	105	43	b	b	X
american_scientific_journal-1367	105	44	∈	∈	PROPN
american_scientific_journal-1367	105	45	ℬ	ℬ	NOUN
american_scientific_journal-1367	105	46	and	and	CCONJ
american_scientific_journal-1367	105	47	a	a	DET
american_scientific_journal-1367	105	48	∈	∈	NOUN
american_scientific_journal-1367	105	49	𝒜𝒜.	𝒜𝒜.	X
american_scientific_journal-1367	105	50	2.4	2.4	NUM
american_scientific_journal-1367	105	51	lemma	lemma	PROPN
american_scientific_journal-1367	106	1	[	[	X
american_scientific_journal-1367	106	2	10	10	NUM
american_scientific_journal-1367	106	3	,	,	PUNCT
american_scientific_journal-1367	106	4	theorem	theorem	VERB
american_scientific_journal-1367	106	5	10	10	NUM
american_scientific_journal-1367	106	6	]	]	PUNCT
american_scientific_journal-1367	106	7	.	.	PUNCT
american_scientific_journal-1367	107	1	every	every	DET
american_scientific_journal-1367	107	2	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	107	3	theory	theory	NOUN
american_scientific_journal-1367	107	4	which	which	PRON
american_scientific_journal-1367	107	5	is	be	AUX
american_scientific_journal-1367	107	6	cogenerated	cogenerate	VERB
american_scientific_journal-1367	107	7	by	by	ADP
american_scientific_journal-1367	107	8	a	a	DET
american_scientific_journal-1367	107	9	set	set	NOUN
american_scientific_journal-1367	107	10	of	of	ADP
american_scientific_journal-1367	107	11	modules	module	NOUN
american_scientific_journal-1367	107	12	has	have	VERB
american_scientific_journal-1367	107	13	enough	enough	ADJ
american_scientific_journal-1367	107	14	projectives	projective	NOUN
american_scientific_journal-1367	107	15	and	and	CCONJ
american_scientific_journal-1367	107	16	enough	enough	ADJ
american_scientific_journal-1367	107	17	injectives	injective	NOUN
american_scientific_journal-1367	107	18	.	.	PUNCT
american_scientific_journal-1367	108	1	□	□	PUNCT
american_scientific_journal-1367	108	2	2.5	2.5	NUM
american_scientific_journal-1367	108	3	lemma	lemma	X
american_scientific_journal-1367	108	4	(	(	PUNCT
american_scientific_journal-1367	108	5	see	see	VERB
american_scientific_journal-1367	108	6	[	[	X
american_scientific_journal-1367	108	7	7	7	NUM
american_scientific_journal-1367	108	8	,	,	PUNCT
american_scientific_journal-1367	108	9	p.159	p.159	X
american_scientific_journal-1367	108	10	]	]	PUNCT
american_scientific_journal-1367	108	11	)	)	PUNCT
american_scientific_journal-1367	108	12	.	.	PUNCT
american_scientific_journal-1367	109	1	if	if	SCONJ
american_scientific_journal-1367	109	2	a	a	DET
american_scientific_journal-1367	109	3	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	109	4	theory	theory	NOUN
american_scientific_journal-1367	109	5	(	(	PUNCT
american_scientific_journal-1367	109	6	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	109	7	,	,	PUNCT
american_scientific_journal-1367	109	8	ℬ	ℬ	NOUN
american_scientific_journal-1367	109	9	)	)	PUNCT
american_scientific_journal-1367	109	10	has	have	VERB
american_scientific_journal-1367	109	11	enough	enough	ADJ
american_scientific_journal-1367	109	12	projectives	projective	NOUN
american_scientific_journal-1367	109	13	and	and	CCONJ
american_scientific_journal-1367	109	14	enough	enough	ADJ
american_scientific_journal-1367	109	15	injectives	injective	NOUN
american_scientific_journal-1367	109	16	,	,	PUNCT
american_scientific_journal-1367	109	17	then	then	ADV
american_scientific_journal-1367	109	18	every	every	DET
american_scientific_journal-1367	109	19	module	module	NOUN
american_scientific_journal-1367	109	20	has	have	VERB
american_scientific_journal-1367	109	21	a	a	DET
american_scientific_journal-1367	109	22	special	special	ADJ
american_scientific_journal-1367	109	23	ℬ-preenvelope	ℬ-preenvelope	PROPN
american_scientific_journal-1367	109	24	and	and	CCONJ
american_scientific_journal-1367	109	25	a	a	DET
american_scientific_journal-1367	109	26	special	special	ADJ
american_scientific_journal-1367	109	27	𝒜𝒜-precover	𝒜𝒜-precover	NOUN
american_scientific_journal-1367	109	28	.	.	PUNCT
american_scientific_journal-1367	110	1	□	□	PUNCT
american_scientific_journal-1367	110	2	in	in	ADP
american_scientific_journal-1367	110	3	what	what	PRON
american_scientific_journal-1367	110	4	follows	follow	VERB
american_scientific_journal-1367	110	5	,	,	PUNCT
american_scientific_journal-1367	110	6	we	we	PRON
american_scientific_journal-1367	110	7	assume	assume	VERB
american_scientific_journal-1367	110	8	that	that	SCONJ
american_scientific_journal-1367	110	9	fp	fp	PROPN
american_scientific_journal-1367	110	10	-	-	PUNCT
american_scientific_journal-1367	110	11	proj	proj	PROPN
american_scientific_journal-1367	110	12	(	(	PUNCT
american_scientific_journal-1367	110	13	fp	fp	ADJ
american_scientific_journal-1367	110	14	-	-	PUNCT
american_scientific_journal-1367	110	15	inj	inj	NOUN
american_scientific_journal-1367	110	16	)	)	PUNCT
american_scientific_journal-1367	110	17	denotes	denote	VERB
american_scientific_journal-1367	110	18	the	the	DET
american_scientific_journal-1367	110	19	class	class	NOUN
american_scientific_journal-1367	110	20	of	of	ADP
american_scientific_journal-1367	110	21	all	all	DET
american_scientific_journal-1367	110	22	fp	fp	ADJ
american_scientific_journal-1367	110	23	-	-	PUNCT
american_scientific_journal-1367	110	24	projective	projective	ADJ
american_scientific_journal-1367	110	25	(	(	PUNCT
american_scientific_journal-1367	110	26	fp	fp	ADJ
american_scientific_journal-1367	110	27	-	-	PUNCT
american_scientific_journal-1367	110	28	injective	injective	ADJ
american_scientific_journal-1367	110	29	)	)	PUNCT
american_scientific_journal-1367	110	30	left	leave	VERB
american_scientific_journal-1367	110	31	rmodules	rmodule	NOUN
american_scientific_journal-1367	110	32	,	,	PUNCT
american_scientific_journal-1367	110	33	and	and	CCONJ
american_scientific_journal-1367	110	34	fp	fp	X
american_scientific_journal-1367	110	35	-	-	PUNCT
american_scientific_journal-1367	110	36	fl	fl	PROPN
american_scientific_journal-1367	110	37	(	(	PUNCT
american_scientific_journal-1367	110	38	fp	fp	ADJ
american_scientific_journal-1367	110	39	-	-	PUNCT
american_scientific_journal-1367	110	40	cot	cot	NOUN
american_scientific_journal-1367	110	41	)	)	PUNCT
american_scientific_journal-1367	110	42	denotes	denote	VERB
american_scientific_journal-1367	110	43	the	the	DET
american_scientific_journal-1367	110	44	class	class	NOUN
american_scientific_journal-1367	110	45	of	of	ADP
american_scientific_journal-1367	110	46	all	all	DET
american_scientific_journal-1367	110	47	fp	fp	ADJ
american_scientific_journal-1367	110	48	-	-	PUNCT
american_scientific_journal-1367	110	49	flat	flat	ADJ
american_scientific_journal-1367	110	50	(	(	PUNCT
american_scientific_journal-1367	110	51	fp	fp	ADJ
american_scientific_journal-1367	110	52	-	-	PUNCT
american_scientific_journal-1367	110	53	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	110	54	)	)	PUNCT
american_scientific_journal-1367	110	55	right	right	ADJ
american_scientific_journal-1367	110	56	r	r	NOUN
american_scientific_journal-1367	110	57	-	-	PUNCT
american_scientific_journal-1367	110	58	modules	module	NOUN
american_scientific_journal-1367	110	59	.	.	PUNCT
american_scientific_journal-1367	111	1	2.6	2.6	NUM
american_scientific_journal-1367	111	2	theorem	theorem	NOUN
american_scientific_journal-1367	111	3	let	let	VERB
american_scientific_journal-1367	111	4	r	r	PRON
american_scientific_journal-1367	111	5	be	be	AUX
american_scientific_journal-1367	111	6	a	a	DET
american_scientific_journal-1367	111	7	ring	ring	NOUN
american_scientific_journal-1367	111	8	.	.	PUNCT
american_scientific_journal-1367	112	1	then	then	ADV
american_scientific_journal-1367	112	2	(	(	PUNCT
american_scientific_journal-1367	112	3	fp	fp	X
american_scientific_journal-1367	112	4	-	-	PUNCT
american_scientific_journal-1367	112	5	proj	proj	NOUN
american_scientific_journal-1367	112	6	,	,	PUNCT
american_scientific_journal-1367	112	7	fp	fp	PROPN
american_scientific_journal-1367	112	8	-	-	PUNCT
american_scientific_journal-1367	112	9	inj	inj	NOUN
american_scientific_journal-1367	112	10	)	)	PUNCT
american_scientific_journal-1367	112	11	is	be	AUX
american_scientific_journal-1367	112	12	a	a	DET
american_scientific_journal-1367	112	13	complete	complete	ADJ
american_scientific_journal-1367	112	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	112	15	theory	theory	NOUN
american_scientific_journal-1367	112	16	.	.	PUNCT
american_scientific_journal-1367	113	1	proof	proof	NOUN
american_scientific_journal-1367	113	2	.	.	PUNCT
american_scientific_journal-1367	114	1	let	let	VERB
american_scientific_journal-1367	114	2	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	114	3	=	=	NOUN
american_scientific_journal-1367	114	4	{	{	PUNCT
american_scientific_journal-1367	115	1	r	r	NOUN
american_scientific_journal-1367	115	2	/	/	SYM
american_scientific_journal-1367	115	3	i	i	PRON
american_scientific_journal-1367	115	4	|	|	ADV
american_scientific_journal-1367	115	5	i	i	PRON
american_scientific_journal-1367	115	6	is	be	AUX
american_scientific_journal-1367	115	7	finitely	finitely	ADV
american_scientific_journal-1367	115	8	presented	present	VERB
american_scientific_journal-1367	115	9	left	leave	VERB
american_scientific_journal-1367	115	10	ideal	ideal	NOUN
american_scientific_journal-1367	115	11	i	i	PRON
american_scientific_journal-1367	115	12	of	of	ADP
american_scientific_journal-1367	115	13	r	r	NOUN
american_scientific_journal-1367	115	14	}	}	PUNCT
american_scientific_journal-1367	115	15	.	.	PUNCT
american_scientific_journal-1367	116	1	then	then	ADV
american_scientific_journal-1367	116	2	𝒞𝒞⊥={n	𝒞𝒞⊥={n	VERB
american_scientific_journal-1367	116	3	∈	∈	PROPN
american_scientific_journal-1367	116	4	r	r	NOUN
american_scientific_journal-1367	116	5	-	-	PUNCT
american_scientific_journal-1367	116	6	mod	mod	NOUN
american_scientific_journal-1367	117	1	|	|	NOUN
american_scientific_journal-1367	117	2	ext1(r	ext1(r	NOUN
american_scientific_journal-1367	117	3	/	/	SYM
american_scientific_journal-1367	117	4	i	i	PROPN
american_scientific_journal-1367	117	5	,	,	PUNCT
american_scientific_journal-1367	117	6	n	n	CCONJ
american_scientific_journal-1367	117	7	)	)	PUNCT
american_scientific_journal-1367	117	8	}	}	PUNCT
american_scientific_journal-1367	117	9	=	=	SYM
american_scientific_journal-1367	117	10	0	0	NUM
american_scientific_journal-1367	117	11	for	for	ADP
american_scientific_journal-1367	117	12	any	any	DET
american_scientific_journal-1367	117	13	finitely	finitely	ADV
american_scientific_journal-1367	117	14	presented	present	VERB
american_scientific_journal-1367	117	15	left	leave	VERB
american_scientific_journal-1367	117	16	ideal	ideal	NOUN
american_scientific_journal-1367	117	17	i	i	PRON
american_scientific_journal-1367	117	18	of	of	ADP
american_scientific_journal-1367	117	19	r	r	NOUN
american_scientific_journal-1367	117	20	}	}	PUNCT
american_scientific_journal-1367	117	21	,	,	PUNCT
american_scientific_journal-1367	117	22	so	so	SCONJ
american_scientific_journal-1367	117	23	𝒞𝒞⊥	𝒞𝒞⊥	PROPN
american_scientific_journal-1367	117	24	=	=	SYM
american_scientific_journal-1367	118	1	fp	fp	PROPN
american_scientific_journal-1367	118	2	-	-	PUNCT
american_scientific_journal-1367	118	3	inj	inj	NOUN
american_scientific_journal-1367	118	4	.	.	PUNCT
american_scientific_journal-1367	119	1	on	on	ADP
american_scientific_journal-1367	119	2	the	the	DET
american_scientific_journal-1367	119	3	other	other	ADJ
american_scientific_journal-1367	119	4	hand	hand	NOUN
american_scientific_journal-1367	119	5	,	,	PUNCT
american_scientific_journal-1367	119	6	we	we	PRON
american_scientific_journal-1367	119	7	have	have	VERB
american_scientific_journal-1367	119	8	⊥	⊥	NOUN
american_scientific_journal-1367	119	9	(	(	PUNCT
american_scientific_journal-1367	119	10	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	119	11	)	)	PUNCT
american_scientific_journal-1367	119	12	=	=	PUNCT
american_scientific_journal-1367	119	13	{	{	PUNCT
american_scientific_journal-1367	119	14	n	n	CCONJ
american_scientific_journal-1367	119	15	∈	∈	PROPN
american_scientific_journal-1367	119	16	r	r	NOUN
american_scientific_journal-1367	119	17	-	-	PUNCT
american_scientific_journal-1367	119	18	mod	mod	NOUN
american_scientific_journal-1367	119	19	|	|	NOUN
american_scientific_journal-1367	119	20	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	119	21	,	,	PUNCT
american_scientific_journal-1367	119	22	c	c	NOUN
american_scientific_journal-1367	119	23	)	)	PUNCT
american_scientific_journal-1367	119	24	=	=	SYM
american_scientific_journal-1367	119	25	0	0	NUM
american_scientific_journal-1367	120	1	for	for	ADP
american_scientific_journal-1367	120	2	all	all	DET
american_scientific_journal-1367	120	3	c	c	PROPN
american_scientific_journal-1367	120	4	∈	∈	PROPN
american_scientific_journal-1367	120	5	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	120	6	}	}	PUNCT
american_scientific_journal-1367	120	7	,	,	PUNCT
american_scientific_journal-1367	120	8	so	so	ADV
american_scientific_journal-1367	120	9	⊥	⊥	PROPN
american_scientific_journal-1367	120	10	(	(	PUNCT
american_scientific_journal-1367	120	11	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	120	12	)	)	PUNCT
american_scientific_journal-1367	120	13	=	=	SYM
american_scientific_journal-1367	120	14	fp	fp	NOUN
american_scientific_journal-1367	120	15	-	-	PUNCT
american_scientific_journal-1367	120	16	proj	proj	NOUN
american_scientific_journal-1367	120	17	.	.	PUNCT
american_scientific_journal-1367	121	1	now	now	ADV
american_scientific_journal-1367	121	2	we	we	PRON
american_scientific_journal-1367	121	3	have	have	VERB
american_scientific_journal-1367	121	4	𝒞𝒞⊥	𝒞𝒞⊥	NOUN
american_scientific_journal-1367	121	5	=	=	SYM
american_scientific_journal-1367	121	6	(	(	PUNCT
american_scientific_journal-1367	121	7	⊥	⊥	X
american_scientific_journal-1367	121	8	(	(	PUNCT
american_scientific_journal-1367	121	9	𝒞𝒞⊥))⊥.	𝒞𝒞⊥))⊥.	NOUN
american_scientific_journal-1367	121	10	it	it	PRON
american_scientific_journal-1367	121	11	follows	follow	VERB
american_scientific_journal-1367	121	12	that	that	SCONJ
american_scientific_journal-1367	121	13	the	the	DET
american_scientific_journal-1367	121	14	pair	pair	NOUN
american_scientific_journal-1367	121	15	(	(	PUNCT
american_scientific_journal-1367	121	16	fp	fp	NOUN
american_scientific_journal-1367	121	17	-	-	PUNCT
american_scientific_journal-1367	121	18	proj	proj	NOUN
american_scientific_journal-1367	121	19	,	,	PUNCT
american_scientific_journal-1367	121	20	fpinj	fpinj	NOUN
american_scientific_journal-1367	121	21	)	)	PUNCT
american_scientific_journal-1367	121	22	is	be	AUX
american_scientific_journal-1367	121	23	a	a	DET
american_scientific_journal-1367	121	24	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	121	25	theory	theory	NOUN
american_scientific_journal-1367	121	26	that	that	PRON
american_scientific_journal-1367	121	27	is	be	AUX
american_scientific_journal-1367	121	28	cogenerated	cogenerate	VERB
american_scientific_journal-1367	121	29	by	by	ADP
american_scientific_journal-1367	121	30	the	the	DET
american_scientific_journal-1367	121	31	class	class	NOUN
american_scientific_journal-1367	122	1	𝒞𝒞.	𝒞𝒞.	INTJ
american_scientific_journal-1367	123	1	so	so	ADV
american_scientific_journal-1367	123	2	the	the	DET
american_scientific_journal-1367	123	3	result	result	NOUN
american_scientific_journal-1367	123	4	follows	follow	VERB
american_scientific_journal-1367	123	5	from	from	ADP
american_scientific_journal-1367	123	6	lemma	lemma	PROPN
american_scientific_journal-1367	123	7	2.4	2.4	NUM
american_scientific_journal-1367	123	8	and	and	CCONJ
american_scientific_journal-1367	123	9	lemma	lemma	PROPN
american_scientific_journal-1367	123	10	2.5	2.5	NUM
american_scientific_journal-1367	123	11	□	□	PUNCT
american_scientific_journal-1367	123	12	following	follow	VERB
american_scientific_journal-1367	123	13	[	[	X
american_scientific_journal-1367	123	14	9	9	NUM
american_scientific_journal-1367	123	15	]	]	PUNCT
american_scientific_journal-1367	123	16	,	,	PUNCT
american_scientific_journal-1367	123	17	for	for	ADP
american_scientific_journal-1367	123	18	a	a	DET
american_scientific_journal-1367	123	19	class	class	NOUN
american_scientific_journal-1367	123	20	of	of	ADP
american_scientific_journal-1367	123	21	(	(	PUNCT
american_scientific_journal-1367	123	22	right	right	ADJ
american_scientific_journal-1367	123	23	,	,	PUNCT
american_scientific_journal-1367	123	24	resp	resp	NOUN
american_scientific_journal-1367	123	25	.	.	PUNCT
american_scientific_journal-1367	124	1	left	leave	VERB
american_scientific_journal-1367	124	2	)	)	PUNCT
american_scientific_journal-1367	125	1	r	r	NOUN
american_scientific_journal-1367	125	2	-	-	PUNCT
american_scientific_journal-1367	125	3	modules	module	NOUN
american_scientific_journal-1367	125	4	𝒞𝒞,we	𝒞𝒞,we	VERB
american_scientific_journal-1367	125	5	put	put	VERB
american_scientific_journal-1367	125	6	𝒞𝒞т	𝒞𝒞т	NOUN
american_scientific_journal-1367	125	7	=	=	PUNCT
american_scientific_journal-1367	125	8	{	{	PUNCT
american_scientific_journal-1367	125	9	n	n	CCONJ
american_scientific_journal-1367	125	10	∈	∈	PROPN
american_scientific_journal-1367	125	11	r	r	NOUN
american_scientific_journal-1367	125	12	-	-	PUNCT
american_scientific_journal-1367	125	13	mod	mod	NOUN
american_scientific_journal-1367	125	14	|	|	NOUN
american_scientific_journal-1367	125	15	tor1(c	tor1(c	NOUN
american_scientific_journal-1367	125	16	,	,	PUNCT
american_scientific_journal-1367	125	17	n	n	CCONJ
american_scientific_journal-1367	125	18	)	)	PUNCT
american_scientific_journal-1367	125	19	=	=	SYM
american_scientific_journal-1367	125	20	0	0	NUM
american_scientific_journal-1367	125	21	for	for	ADP
american_scientific_journal-1367	125	22	all	all	DET
american_scientific_journal-1367	125	23	c	c	NOUN
american_scientific_journal-1367	125	24	∈	∈	NOUN
american_scientific_journal-1367	125	25	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	125	26	}	}	PUNCT
american_scientific_journal-1367	125	27	,	,	PUNCT
american_scientific_journal-1367	125	28	resp	resp	NOUN
american_scientific_journal-1367	125	29	.	.	PUNCT
american_scientific_journal-1367	126	1	т𝒞𝒞	т𝒞𝒞	X
american_scientific_journal-1367	126	2	=	=	SYM
american_scientific_journal-1367	126	3	{	{	PUNCT
american_scientific_journal-1367	126	4	n	n	CCONJ
american_scientific_journal-1367	126	5	∈	∈	PROPN
american_scientific_journal-1367	126	6	mod	mod	PROPN
american_scientific_journal-1367	126	7	-	-	PUNCT
american_scientific_journal-1367	126	8	r	r	NOUN
american_scientific_journal-1367	126	9	|	|	NOUN
american_scientific_journal-1367	126	10	tor1(n	tor1(n	NUM
american_scientific_journal-1367	126	11	,	,	PUNCT
american_scientific_journal-1367	126	12	c	c	NOUN
american_scientific_journal-1367	126	13	)	)	PUNCT
american_scientific_journal-1367	126	14	=	=	SYM
american_scientific_journal-1367	126	15	0	0	NUM
american_scientific_journal-1367	126	16	for	for	ADP
american_scientific_journal-1367	126	17	all	all	DET
american_scientific_journal-1367	126	18	c	c	NOUN
american_scientific_journal-1367	126	19	∈	∈	NOUN
american_scientific_journal-1367	126	20	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	126	21	}	}	PUNCT
american_scientific_journal-1367	126	22	.	.	PUNCT
american_scientific_journal-1367	127	1	let	let	VERB
american_scientific_journal-1367	127	2	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	127	3	⊆	⊆	NUM
american_scientific_journal-1367	127	4	mod	mod	PROPN
american_scientific_journal-1367	127	5	-	-	PUNCT
american_scientific_journal-1367	127	6	r	r	NOUN
american_scientific_journal-1367	127	7	,	,	PUNCT
american_scientific_journal-1367	127	8	ℬ	ℬ	NOUN
american_scientific_journal-1367	127	9	⊆	⊆	NUM
american_scientific_journal-1367	127	10	r	r	NOUN
american_scientific_journal-1367	127	11	-	-	PUNCT
american_scientific_journal-1367	127	12	mod	mod	NOUN
american_scientific_journal-1367	127	13	.	.	PUNCT
american_scientific_journal-1367	128	1	the	the	DET
american_scientific_journal-1367	128	2	pair	pair	NOUN
american_scientific_journal-1367	128	3	(	(	PUNCT
american_scientific_journal-1367	128	4	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	128	5	,	,	PUNCT
american_scientific_journal-1367	128	6	ℬ	ℬ	NOUN
american_scientific_journal-1367	128	7	)	)	PUNCT
american_scientific_journal-1367	128	8	is	be	AUX
american_scientific_journal-1367	128	9	called	call	VERB
american_scientific_journal-1367	128	10	a	a	DET
american_scientific_journal-1367	128	11	tor	tor	NOUN
american_scientific_journal-1367	128	12	-	-	PUNCT
american_scientific_journal-1367	128	13	torsion	torsion	NOUN
american_scientific_journal-1367	128	14	theory	theory	NOUN
american_scientific_journal-1367	128	15	if	if	SCONJ
american_scientific_journal-1367	128	16	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	128	17	=	=	SYM
american_scientific_journal-1367	128	18	тℬ	тℬ	PROPN
american_scientific_journal-1367	128	19	and	and	CCONJ
american_scientific_journal-1367	128	20	ℬ	ℬ	NOUN
american_scientific_journal-1367	128	21	=	=	NOUN
american_scientific_journal-1367	128	22	𝒜𝒜т	𝒜𝒜т	NOUN
american_scientific_journal-1367	128	23	.	.	PUNCT
american_scientific_journal-1367	129	1	in	in	ADP
american_scientific_journal-1367	129	2	what	what	PRON
american_scientific_journal-1367	129	3	follows	follow	VERB
american_scientific_journal-1367	129	4	,	,	PUNCT
american_scientific_journal-1367	129	5	by	by	ADP
american_scientific_journal-1367	129	6	𝒫𝒫ℐ	𝒫𝒫ℐ	NOUN
american_scientific_journal-1367	129	7	we	we	PRON
american_scientific_journal-1367	129	8	denote	denote	VERB
american_scientific_journal-1367	129	9	the	the	DET
american_scientific_journal-1367	129	10	class	class	NOUN
american_scientific_journal-1367	129	11	of	of	ADP
american_scientific_journal-1367	129	12	all	all	DET
american_scientific_journal-1367	129	13	pure	pure	ADJ
american_scientific_journal-1367	129	14	injective	injective	ADJ
american_scientific_journal-1367	129	15	right	right	ADJ
american_scientific_journal-1367	129	16	r	r	NOUN
american_scientific_journal-1367	129	17	-	-	PUNCT
american_scientific_journal-1367	129	18	modules	module	NOUN
american_scientific_journal-1367	129	19	.	.	PUNCT
american_scientific_journal-1367	130	1	2.7	2.7	NUM
american_scientific_journal-1367	130	2	lemma	lemma	PROPN
american_scientific_journal-1367	130	3	[	[	AUX
american_scientific_journal-1367	130	4	see	see	VERB
american_scientific_journal-1367	130	5	.	.	PUNCT
american_scientific_journal-1367	131	1	9	9	NUM
american_scientific_journal-1367	131	2	,	,	PUNCT
american_scientific_journal-1367	131	3	lemma	lemma	PROPN
american_scientific_journal-1367	131	4	1.11	1.11	NUM
american_scientific_journal-1367	131	5	]	]	PUNCT
american_scientific_journal-1367	131	6	.	.	PUNCT
american_scientific_journal-1367	132	1	let	let	VERB
american_scientific_journal-1367	132	2	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	132	3	⊆	⊆	NUM
american_scientific_journal-1367	132	4	mod	mod	PROPN
american_scientific_journal-1367	132	5	-	-	PUNCT
american_scientific_journal-1367	132	6	r	r	NOUN
american_scientific_journal-1367	132	7	,	,	PUNCT
american_scientific_journal-1367	132	8	ℬ	ℬ	NOUN
american_scientific_journal-1367	132	9	⊆	⊆	NUM
american_scientific_journal-1367	132	10	r	r	NOUN
american_scientific_journal-1367	132	11	-	-	PUNCT
american_scientific_journal-1367	132	12	mod	mod	NOUN
american_scientific_journal-1367	132	13	and	and	CCONJ
american_scientific_journal-1367	132	14	(	(	PUNCT
american_scientific_journal-1367	132	15	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	132	16	,	,	PUNCT
american_scientific_journal-1367	132	17	ℬ	ℬ	NOUN
american_scientific_journal-1367	132	18	)	)	PUNCT
american_scientific_journal-1367	132	19	be	be	VERB
american_scientific_journal-1367	132	20	a	a	DET
american_scientific_journal-1367	132	21	tor	tor	NOUN
american_scientific_journal-1367	132	22	-	-	PUNCT
american_scientific_journal-1367	132	23	torsion	torsion	NOUN
american_scientific_journal-1367	132	24	theory	theory	NOUN
american_scientific_journal-1367	132	25	.	.	PUNCT
american_scientific_journal-1367	133	1	then	then	ADV
american_scientific_journal-1367	133	2	(	(	PUNCT
american_scientific_journal-1367	133	3	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	133	4	,	,	PUNCT
american_scientific_journal-1367	133	5	𝒜𝒜⊥	𝒜𝒜⊥	NOUN
american_scientific_journal-1367	133	6	)	)	PUNCT
american_scientific_journal-1367	133	7	is	be	AUX
american_scientific_journal-1367	133	8	a	a	DET
american_scientific_journal-1367	133	9	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	133	10	theory	theory	NOUN
american_scientific_journal-1367	133	11	generated	generate	VERB
american_scientific_journal-1367	133	12	by	by	ADP
american_scientific_journal-1367	133	13	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	133	14	=	=	PUNCT
american_scientific_journal-1367	133	15	{	{	PUNCT
american_scientific_journal-1367	134	1	m	m	VERB
american_scientific_journal-1367	134	2	+	+	X
american_scientific_journal-1367	135	1	|	|	ADV
american_scientific_journal-1367	135	2	m	m	NOUN
american_scientific_journal-1367	135	3	∈	∈	NOUN
american_scientific_journal-1367	135	4	ℬ	ℬ	NOUN
american_scientific_journal-1367	135	5	}	}	PUNCT
american_scientific_journal-1367	135	6	⊆	⊆	NUM
american_scientific_journal-1367	135	7	𝒫𝒫ℐ.	𝒫𝒫ℐ.	X
american_scientific_journal-1367	135	8	□	□	SYM
american_scientific_journal-1367	135	9	136	136	NUM
american_scientific_journal-1367	135	10	american	american	ADJ
american_scientific_journal-1367	135	11	scientific	scientific	ADJ
american_scientific_journal-1367	135	12	research	research	NOUN
american_scientific_journal-1367	135	13	journal	journal	NOUN
american_scientific_journal-1367	135	14	for	for	ADP
american_scientific_journal-1367	135	15	engineering	engineering	NOUN
american_scientific_journal-1367	135	16	,	,	PUNCT
american_scientific_journal-1367	135	17	technology	technology	NOUN
american_scientific_journal-1367	135	18	,	,	PUNCT
american_scientific_journal-1367	135	19	and	and	CCONJ
american_scientific_journal-1367	135	20	sciences	science	NOUN
american_scientific_journal-1367	135	21	(	(	PUNCT
american_scientific_journal-1367	135	22	asrjets	asrjet	NOUN
american_scientific_journal-1367	135	23	)	)	PUNCT
american_scientific_journal-1367	135	24	(	(	PUNCT
american_scientific_journal-1367	135	25	2016	2016	NUM
american_scientific_journal-1367	135	26	)	)	PUNCT
american_scientific_journal-1367	135	27	volume	volume	NOUN
american_scientific_journal-1367	135	28	17	17	NUM
american_scientific_journal-1367	135	29	,	,	PUNCT
american_scientific_journal-1367	135	30	no	no	DET
american_scientific_journal-1367	135	31	1	1	NUM
american_scientific_journal-1367	135	32	,	,	PUNCT
american_scientific_journal-1367	135	33	pp	pp	ADV
american_scientific_journal-1367	135	34	132	132	NUM
american_scientific_journal-1367	135	35	-	-	SYM
american_scientific_journal-1367	135	36	143	143	NUM
american_scientific_journal-1367	135	37	2.8	2.8	NUM
american_scientific_journal-1367	135	38	lemma	lemma	PROPN
american_scientific_journal-1367	135	39	[	[	X
american_scientific_journal-1367	135	40	see.9	see.9	PROPN
american_scientific_journal-1367	135	41	,	,	PUNCT
american_scientific_journal-1367	135	42	theorem	theorem	VERB
american_scientific_journal-1367	135	43	2.8	2.8	NUM
american_scientific_journal-1367	135	44	]	]	PUNCT
american_scientific_journal-1367	135	45	.	.	PUNCT
american_scientific_journal-1367	136	1	let	let	VERB
american_scientific_journal-1367	136	2	r	r	PRON
american_scientific_journal-1367	136	3	be	be	AUX
american_scientific_journal-1367	136	4	a	a	DET
american_scientific_journal-1367	136	5	ring	ring	NOUN
american_scientific_journal-1367	136	6	and	and	CCONJ
american_scientific_journal-1367	136	7	(	(	PUNCT
american_scientific_journal-1367	136	8	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	136	9	,	,	PUNCT
american_scientific_journal-1367	136	10	ℬ	ℬ	NOUN
american_scientific_journal-1367	136	11	)	)	PUNCT
american_scientific_journal-1367	136	12	be	be	VERB
american_scientific_journal-1367	136	13	a	a	DET
american_scientific_journal-1367	136	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	136	15	theory	theory	NOUN
american_scientific_journal-1367	136	16	generated	generate	VERB
american_scientific_journal-1367	136	17	by	by	ADP
american_scientific_journal-1367	136	18	a	a	DET
american_scientific_journal-1367	136	19	class	class	NOUN
american_scientific_journal-1367	136	20	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	136	21	⊆	⊆	NUM
american_scientific_journal-1367	136	22	𝒫𝒫ℐ.	𝒫𝒫ℐ.	NUM
american_scientific_journal-1367	136	23	then	then	ADV
american_scientific_journal-1367	136	24	(	(	PUNCT
american_scientific_journal-1367	136	25	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	136	26	,	,	PUNCT
american_scientific_journal-1367	136	27	ℬ	ℬ	NOUN
american_scientific_journal-1367	136	28	)	)	PUNCT
american_scientific_journal-1367	136	29	is	be	AUX
american_scientific_journal-1367	136	30	complete	complete	ADJ
american_scientific_journal-1367	136	31	.	.	PUNCT
american_scientific_journal-1367	137	1	moreover	moreover	ADV
american_scientific_journal-1367	137	2	,	,	PUNCT
american_scientific_journal-1367	137	3	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	137	4	is	be	AUX
american_scientific_journal-1367	137	5	a	a	DET
american_scientific_journal-1367	137	6	cover	cover	NOUN
american_scientific_journal-1367	137	7	class	class	NOUN
american_scientific_journal-1367	137	8	and	and	CCONJ
american_scientific_journal-1367	137	9	ℬ	ℬ	NOUN
american_scientific_journal-1367	137	10	is	be	AUX
american_scientific_journal-1367	137	11	an	an	DET
american_scientific_journal-1367	137	12	envelope	envelope	NOUN
american_scientific_journal-1367	137	13	class	class	NOUN
american_scientific_journal-1367	137	14	.	.	PUNCT
american_scientific_journal-1367	138	1	□	□	PUNCT
american_scientific_journal-1367	138	2	2.9	2.9	NUM
american_scientific_journal-1367	138	3	theorem	theorem	NOUN
american_scientific_journal-1367	138	4	let	let	VERB
american_scientific_journal-1367	138	5	r	r	PRON
american_scientific_journal-1367	138	6	be	be	AUX
american_scientific_journal-1367	138	7	a	a	DET
american_scientific_journal-1367	138	8	ring	ring	NOUN
american_scientific_journal-1367	138	9	.	.	PUNCT
american_scientific_journal-1367	139	1	then	then	ADV
american_scientific_journal-1367	139	2	(	(	PUNCT
american_scientific_journal-1367	139	3	fp	fp	PROPN
american_scientific_journal-1367	139	4	-	-	PUNCT
american_scientific_journal-1367	139	5	fl	fl	PROPN
american_scientific_journal-1367	139	6	,	,	PUNCT
american_scientific_journal-1367	139	7	fp	fp	ADJ
american_scientific_journal-1367	139	8	-	-	PUNCT
american_scientific_journal-1367	139	9	cot	cot	NOUN
american_scientific_journal-1367	139	10	)	)	PUNCT
american_scientific_journal-1367	139	11	is	be	AUX
american_scientific_journal-1367	139	12	a	a	DET
american_scientific_journal-1367	139	13	perfect	perfect	ADJ
american_scientific_journal-1367	139	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	139	15	theory	theory	NOUN
american_scientific_journal-1367	139	16	.	.	PUNCT
american_scientific_journal-1367	140	1	proof	proof	NOUN
american_scientific_journal-1367	140	2	.	.	PUNCT
american_scientific_journal-1367	141	1	let	let	VERB
american_scientific_journal-1367	141	2	ℬ	ℬ	PRON
american_scientific_journal-1367	141	3	=	=	NOUN
american_scientific_journal-1367	141	4	{	{	PUNCT
american_scientific_journal-1367	141	5	r	r	NOUN
american_scientific_journal-1367	141	6	/	/	SYM
american_scientific_journal-1367	141	7	i	i	PRON
american_scientific_journal-1367	142	1	|	|	ADV
american_scientific_journal-1367	142	2	i	i	PRON
american_scientific_journal-1367	142	3	is	be	AUX
american_scientific_journal-1367	142	4	finitely	finitely	ADV
american_scientific_journal-1367	142	5	presented	present	VERB
american_scientific_journal-1367	142	6	left	leave	VERB
american_scientific_journal-1367	142	7	ideal	ideal	NOUN
american_scientific_journal-1367	142	8	i	i	PRON
american_scientific_journal-1367	142	9	of	of	ADP
american_scientific_journal-1367	142	10	r	r	NOUN
american_scientific_journal-1367	142	11	}	}	PUNCT
american_scientific_journal-1367	142	12	,	,	PUNCT
american_scientific_journal-1367	142	13	тℬ	тℬ	PROPN
american_scientific_journal-1367	142	14	=	=	SYM
american_scientific_journal-1367	142	15	{	{	PUNCT
american_scientific_journal-1367	142	16	n	n	CCONJ
american_scientific_journal-1367	142	17	∈	∈	PROPN
american_scientific_journal-1367	142	18	mod	mod	PROPN
american_scientific_journal-1367	142	19	-	-	PUNCT
american_scientific_journal-1367	142	20	r	r	NOUN
american_scientific_journal-1367	142	21	|	|	NOUN
american_scientific_journal-1367	142	22	tor1(n	tor1(n	NUM
american_scientific_journal-1367	142	23	,	,	PUNCT
american_scientific_journal-1367	142	24	r	r	X
american_scientific_journal-1367	142	25	/	/	SYM
american_scientific_journal-1367	142	26	i	i	NOUN
american_scientific_journal-1367	142	27	)	)	PUNCT
american_scientific_journal-1367	143	1	=	=	SYM
american_scientific_journal-1367	143	2	0	0	NUM
american_scientific_journal-1367	143	3	for	for	ADP
american_scientific_journal-1367	143	4	any	any	DET
american_scientific_journal-1367	143	5	finitely	finitely	ADV
american_scientific_journal-1367	143	6	presented	present	VERB
american_scientific_journal-1367	143	7	left	leave	VERB
american_scientific_journal-1367	143	8	ideal	ideal	NOUN
american_scientific_journal-1367	143	9	i	i	PRON
american_scientific_journal-1367	143	10	of	of	ADP
american_scientific_journal-1367	143	11	r	r	NOUN
american_scientific_journal-1367	143	12	}	}	PUNCT
american_scientific_journal-1367	143	13	.	.	PUNCT
american_scientific_journal-1367	144	1	let	let	VERB
american_scientific_journal-1367	144	2	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	144	3	=	=	SYM
american_scientific_journal-1367	144	4	fp	fp	PROPN
american_scientific_journal-1367	144	5	-	-	PUNCT
american_scientific_journal-1367	144	6	fl	fl	PROPN
american_scientific_journal-1367	144	7	.	.	PUNCT
american_scientific_journal-1367	145	1	then	then	ADV
american_scientific_journal-1367	145	2	we	we	PRON
american_scientific_journal-1367	145	3	have	have	VERB
american_scientific_journal-1367	145	4	𝒜𝒜т	𝒜𝒜т	NOUN
american_scientific_journal-1367	145	5	=	=	PUNCT
american_scientific_journal-1367	145	6	{	{	PUNCT
american_scientific_journal-1367	145	7	n	n	CCONJ
american_scientific_journal-1367	145	8	∈	∈	PROPN
american_scientific_journal-1367	145	9	r	r	NOUN
american_scientific_journal-1367	145	10	-	-	PUNCT
american_scientific_journal-1367	145	11	mod	mod	NOUN
american_scientific_journal-1367	146	1	|	|	ADV
american_scientific_journal-1367	146	2	tor1(m	tor1(m	NUM
american_scientific_journal-1367	146	3	,	,	PUNCT
american_scientific_journal-1367	146	4	n	n	CCONJ
american_scientific_journal-1367	146	5	)	)	PUNCT
american_scientific_journal-1367	147	1	=	=	SYM
american_scientific_journal-1367	147	2	0	0	NUM
american_scientific_journal-1367	147	3	for	for	ADP
american_scientific_journal-1367	147	4	any	any	DET
american_scientific_journal-1367	147	5	fp	fp	ADJ
american_scientific_journal-1367	147	6	-	-	PUNCT
american_scientific_journal-1367	147	7	flat	flat	ADJ
american_scientific_journal-1367	147	8	right	right	ADJ
american_scientific_journal-1367	147	9	r	r	NOUN
american_scientific_journal-1367	147	10	-	-	PUNCT
american_scientific_journal-1367	147	11	module	module	NOUN
american_scientific_journal-1367	147	12	m	m	NOUN
american_scientific_journal-1367	147	13	}	}	PUNCT
american_scientific_journal-1367	147	14	.	.	PUNCT
american_scientific_journal-1367	148	1	since	since	SCONJ
american_scientific_journal-1367	148	2	m	m	PROPN
american_scientific_journal-1367	148	3	is	be	AUX
american_scientific_journal-1367	148	4	a	a	DET
american_scientific_journal-1367	148	5	fp	fp	ADJ
american_scientific_journal-1367	148	6	-	-	PUNCT
american_scientific_journal-1367	148	7	flat	flat	ADJ
american_scientific_journal-1367	148	8	right	right	ADJ
american_scientific_journal-1367	148	9	r	r	NOUN
american_scientific_journal-1367	148	10	-	-	PUNCT
american_scientific_journal-1367	148	11	module	module	NOUN
american_scientific_journal-1367	148	12	if	if	SCONJ
american_scientific_journal-1367	148	13	and	and	CCONJ
american_scientific_journal-1367	148	14	only	only	ADV
american_scientific_journal-1367	148	15	if	if	SCONJ
american_scientific_journal-1367	148	16	tor1(m	tor1(m	NUM
american_scientific_journal-1367	148	17	,	,	PUNCT
american_scientific_journal-1367	148	18	r	r	NOUN
american_scientific_journal-1367	148	19	/	/	SYM
american_scientific_journal-1367	148	20	i	i	NOUN
american_scientific_journal-1367	148	21	)	)	PUNCT
american_scientific_journal-1367	149	1	=	=	SYM
american_scientific_journal-1367	149	2	0	0	NUM
american_scientific_journal-1367	149	3	for	for	ADP
american_scientific_journal-1367	149	4	every	every	DET
american_scientific_journal-1367	149	5	finitely	finitely	ADV
american_scientific_journal-1367	149	6	presented	present	VERB
american_scientific_journal-1367	149	7	left	leave	VERB
american_scientific_journal-1367	149	8	ideal	ideal	PROPN
american_scientific_journal-1367	149	9	i	i	PRON
american_scientific_journal-1367	149	10	,	,	PUNCT
american_scientific_journal-1367	149	11	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	149	12	=	=	SYM
american_scientific_journal-1367	149	13	тℬ	тℬ	PROPN
american_scientific_journal-1367	149	14	and	and	CCONJ
american_scientific_journal-1367	149	15	ℬ	ℬ	NOUN
american_scientific_journal-1367	149	16	=	=	SYM
american_scientific_journal-1367	149	17	𝒜𝒜т	𝒜𝒜т	NOUN
american_scientific_journal-1367	149	18	.	.	PUNCT
american_scientific_journal-1367	150	1	so	so	ADV
american_scientific_journal-1367	150	2	(	(	PUNCT
american_scientific_journal-1367	150	3	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	150	4	,	,	PUNCT
american_scientific_journal-1367	150	5	ℬ	ℬ	NOUN
american_scientific_journal-1367	150	6	)	)	PUNCT
american_scientific_journal-1367	150	7	is	be	AUX
american_scientific_journal-1367	150	8	a	a	DET
american_scientific_journal-1367	150	9	tor	tor	NOUN
american_scientific_journal-1367	150	10	-	-	PUNCT
american_scientific_journal-1367	150	11	torsion	torsion	NOUN
american_scientific_journal-1367	150	12	theory	theory	NOUN
american_scientific_journal-1367	150	13	.	.	PUNCT
american_scientific_journal-1367	151	1	by	by	ADP
american_scientific_journal-1367	151	2	lemma	lemma	PROPN
american_scientific_journal-1367	151	3	2.7	2.7	NUM
american_scientific_journal-1367	151	4	,	,	PUNCT
american_scientific_journal-1367	151	5	(	(	PUNCT
american_scientific_journal-1367	151	6	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	151	7	,	,	PUNCT
american_scientific_journal-1367	151	8	𝒜𝒜⊥	𝒜𝒜⊥	NOUN
american_scientific_journal-1367	151	9	)	)	PUNCT
american_scientific_journal-1367	151	10	is	be	AUX
american_scientific_journal-1367	151	11	a	a	DET
american_scientific_journal-1367	151	12	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	151	13	theory	theory	NOUN
american_scientific_journal-1367	151	14	generated	generate	VERB
american_scientific_journal-1367	151	15	by	by	ADP
american_scientific_journal-1367	151	16	𝒞𝒞	𝒞𝒞	PROPN
american_scientific_journal-1367	151	17	=	=	PUNCT
american_scientific_journal-1367	151	18	{	{	PUNCT
american_scientific_journal-1367	152	1	m	m	VERB
american_scientific_journal-1367	152	2	+	+	X
american_scientific_journal-1367	153	1	|	|	ADV
american_scientific_journal-1367	153	2	m	m	NOUN
american_scientific_journal-1367	153	3	∈	∈	NOUN
american_scientific_journal-1367	153	4	ℬ	ℬ	NOUN
american_scientific_journal-1367	153	5	}	}	PUNCT
american_scientific_journal-1367	153	6	⊆	⊆	NUM
american_scientific_journal-1367	153	7	𝒫𝒫ℐ.	𝒫𝒫ℐ.	NUM
american_scientific_journal-1367	153	8	by	by	ADP
american_scientific_journal-1367	153	9	lemma	lemma	PROPN
american_scientific_journal-1367	153	10	2.8	2.8	NUM
american_scientific_journal-1367	153	11	,	,	PUNCT
american_scientific_journal-1367	153	12	(	(	PUNCT
american_scientific_journal-1367	153	13	𝒜𝒜	𝒜𝒜	PROPN
american_scientific_journal-1367	153	14	,	,	PUNCT
american_scientific_journal-1367	153	15	𝒜𝒜⊥	𝒜𝒜⊥	NOUN
american_scientific_journal-1367	153	16	)	)	PUNCT
american_scientific_journal-1367	153	17	is	be	AUX
american_scientific_journal-1367	153	18	a	a	DET
american_scientific_journal-1367	153	19	perfect	perfect	ADJ
american_scientific_journal-1367	153	20	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	153	21	theory	theory	NOUN
american_scientific_journal-1367	153	22	.	.	PUNCT
american_scientific_journal-1367	154	1	finally	finally	ADV
american_scientific_journal-1367	154	2	we	we	PRON
american_scientific_journal-1367	154	3	note	note	VERB
american_scientific_journal-1367	154	4	that	that	SCONJ
american_scientific_journal-1367	154	5	𝒜𝒜⊥	𝒜𝒜⊥	PRON
american_scientific_journal-1367	154	6	=	=	PRON
american_scientific_journal-1367	154	7	{	{	PUNCT
american_scientific_journal-1367	154	8	n	n	CCONJ
american_scientific_journal-1367	154	9	∈	∈	PROPN
american_scientific_journal-1367	154	10	mod	mod	PROPN
american_scientific_journal-1367	154	11	-	-	PUNCT
american_scientific_journal-1367	154	12	r	r	NOUN
american_scientific_journal-1367	154	13	|	|	NOUN
american_scientific_journal-1367	154	14	ext1(m	ext1(m	NUM
american_scientific_journal-1367	154	15	,	,	PUNCT
american_scientific_journal-1367	154	16	n	n	CCONJ
american_scientific_journal-1367	154	17	)	)	PUNCT
american_scientific_journal-1367	154	18	=	=	SYM
american_scientific_journal-1367	154	19	0	0	NUM
american_scientific_journal-1367	154	20	,	,	PUNCT
american_scientific_journal-1367	154	21	for	for	ADP
american_scientific_journal-1367	154	22	any	any	DET
american_scientific_journal-1367	154	23	fp	fp	ADJ
american_scientific_journal-1367	154	24	-	-	PUNCT
american_scientific_journal-1367	154	25	flat	flat	ADJ
american_scientific_journal-1367	154	26	right	right	ADJ
american_scientific_journal-1367	154	27	r	r	NOUN
american_scientific_journal-1367	154	28	-	-	PUNCT
american_scientific_journal-1367	154	29	module	module	NOUN
american_scientific_journal-1367	154	30	m	m	NOUN
american_scientific_journal-1367	154	31	}	}	PUNCT
american_scientific_journal-1367	154	32	=	=	SYM
american_scientific_journal-1367	154	33	fp	fp	ADJ
american_scientific_journal-1367	154	34	-	-	PUNCT
american_scientific_journal-1367	154	35	cot	cot	NOUN
american_scientific_journal-1367	154	36	.	.	PUNCT
american_scientific_journal-1367	155	1	thus	thus	ADV
american_scientific_journal-1367	155	2	(	(	PUNCT
american_scientific_journal-1367	155	3	fpfl	fpfl	NOUN
american_scientific_journal-1367	155	4	,	,	PUNCT
american_scientific_journal-1367	155	5	fp	fp	ADJ
american_scientific_journal-1367	155	6	-	-	PUNCT
american_scientific_journal-1367	155	7	cot	cot	NOUN
american_scientific_journal-1367	155	8	)	)	PUNCT
american_scientific_journal-1367	155	9	is	be	AUX
american_scientific_journal-1367	155	10	a	a	DET
american_scientific_journal-1367	155	11	perfect	perfect	ADJ
american_scientific_journal-1367	155	12	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	155	13	theory	theory	NOUN
american_scientific_journal-1367	155	14	,	,	PUNCT
american_scientific_journal-1367	155	15	as	as	SCONJ
american_scientific_journal-1367	155	16	desired	desire	VERB
american_scientific_journal-1367	155	17	.	.	PUNCT
american_scientific_journal-1367	156	1	□	□	PUNCT
american_scientific_journal-1367	156	2	3	3	X
american_scientific_journal-1367	156	3	.	.	PUNCT
american_scientific_journal-1367	156	4	characterizations	characterization	NOUN
american_scientific_journal-1367	156	5	of	of	ADP
american_scientific_journal-1367	156	6	some	some	DET
american_scientific_journal-1367	156	7	classes	class	NOUN
american_scientific_journal-1367	156	8	of	of	ADP
american_scientific_journal-1367	156	9	rings	ring	NOUN
american_scientific_journal-1367	156	10	it	it	PRON
american_scientific_journal-1367	156	11	is	be	AUX
american_scientific_journal-1367	156	12	well	well	ADV
american_scientific_journal-1367	156	13	known	know	VERB
american_scientific_journal-1367	156	14	that	that	SCONJ
american_scientific_journal-1367	156	15	a	a	DET
american_scientific_journal-1367	156	16	ring	ring	NOUN
american_scientific_journal-1367	156	17	r	r	NOUN
american_scientific_journal-1367	156	18	is	be	AUX
american_scientific_journal-1367	156	19	left	leave	VERB
american_scientific_journal-1367	156	20	noetherian	noetherian	ADJ
american_scientific_journal-1367	157	1	if	if	SCONJ
american_scientific_journal-1367	158	1	and	and	CCONJ
american_scientific_journal-1367	158	2	only	only	ADV
american_scientific_journal-1367	158	3	if	if	SCONJ
american_scientific_journal-1367	158	4	every	every	DET
american_scientific_journal-1367	158	5	f	f	NOUN
american_scientific_journal-1367	158	6	-	-	PUNCT
american_scientific_journal-1367	158	7	injective	injective	ADJ
american_scientific_journal-1367	158	8	left	leave	VERB
american_scientific_journal-1367	158	9	r	r	NOUN
american_scientific_journal-1367	158	10	-	-	PUNCT
american_scientific_journal-1367	158	11	module	module	NOUN
american_scientific_journal-1367	158	12	is	be	AUX
american_scientific_journal-1367	158	13	injective	injective	ADJ
american_scientific_journal-1367	158	14	[	[	X
american_scientific_journal-1367	158	15	11	11	NUM
american_scientific_journal-1367	158	16	,	,	PUNCT
american_scientific_journal-1367	158	17	corollarly1.10	corollarly1.10	NOUN
american_scientific_journal-1367	158	18	]	]	X
american_scientific_journal-1367	158	19	.	.	PUNCT
american_scientific_journal-1367	159	1	next	next	ADV
american_scientific_journal-1367	159	2	,	,	PUNCT
american_scientific_journal-1367	159	3	we	we	PRON
american_scientific_journal-1367	159	4	characterize	characterize	VERB
american_scientific_journal-1367	159	5	left	leave	VERB
american_scientific_journal-1367	159	6	noetherian	noetherian	ADJ
american_scientific_journal-1367	159	7	rings	ring	NOUN
american_scientific_journal-1367	159	8	by	by	ADP
american_scientific_journal-1367	159	9	fp	fp	ADJ
american_scientific_journal-1367	159	10	-	-	PUNCT
american_scientific_journal-1367	159	11	injective	injective	ADJ
american_scientific_journal-1367	159	12	left	leave	VERB
american_scientific_journal-1367	159	13	r	r	NOUN
american_scientific_journal-1367	159	14	-	-	PUNCT
american_scientific_journal-1367	159	15	modules	module	NOUN
american_scientific_journal-1367	159	16	and	and	CCONJ
american_scientific_journal-1367	159	17	fp	fp	NOUN
american_scientific_journal-1367	159	18	-	-	PUNCT
american_scientific_journal-1367	159	19	projective	projective	NOUN
american_scientific_journal-1367	159	20	left	leave	VERB
american_scientific_journal-1367	159	21	r	r	NOUN
american_scientific_journal-1367	159	22	-	-	PUNCT
american_scientific_journal-1367	159	23	modules	module	NOUN
american_scientific_journal-1367	159	24	.	.	PUNCT
american_scientific_journal-1367	160	1	3.1	3.1	NUM
american_scientific_journal-1367	160	2	theorem	theorem	NOUN
american_scientific_journal-1367	160	3	for	for	ADP
american_scientific_journal-1367	160	4	any	any	DET
american_scientific_journal-1367	160	5	ring	ring	NOUN
american_scientific_journal-1367	160	6	r	r	NOUN
american_scientific_journal-1367	160	7	,	,	PUNCT
american_scientific_journal-1367	160	8	the	the	DET
american_scientific_journal-1367	160	9	following	follow	VERB
american_scientific_journal-1367	160	10	statements	statement	NOUN
american_scientific_journal-1367	160	11	are	be	AUX
american_scientific_journal-1367	160	12	equivalent	equivalent	ADJ
american_scientific_journal-1367	160	13	.	.	PUNCT
american_scientific_journal-1367	161	1	(	(	PUNCT
american_scientific_journal-1367	161	2	1	1	X
american_scientific_journal-1367	161	3	)	)	PUNCT
american_scientific_journal-1367	161	4	r	r	NOUN
american_scientific_journal-1367	161	5	is	be	AUX
american_scientific_journal-1367	161	6	left	leave	VERB
american_scientific_journal-1367	161	7	noetherian	noetherian	ADJ
american_scientific_journal-1367	161	8	.	.	PUNCT
american_scientific_journal-1367	162	1	(	(	PUNCT
american_scientific_journal-1367	162	2	2	2	X
american_scientific_journal-1367	162	3	)	)	PUNCT
american_scientific_journal-1367	162	4	every	every	DET
american_scientific_journal-1367	162	5	left	left	ADJ
american_scientific_journal-1367	162	6	r	r	NOUN
american_scientific_journal-1367	162	7	-	-	PUNCT
american_scientific_journal-1367	162	8	module	module	NOUN
american_scientific_journal-1367	162	9	is	be	AUX
american_scientific_journal-1367	162	10	fp	fp	NOUN
american_scientific_journal-1367	162	11	-	-	PUNCT
american_scientific_journal-1367	162	12	projective	projective	ADJ
american_scientific_journal-1367	162	13	.	.	PUNCT
american_scientific_journal-1367	163	1	(	(	PUNCT
american_scientific_journal-1367	163	2	3	3	X
american_scientific_journal-1367	163	3	)	)	PUNCT
american_scientific_journal-1367	163	4	every	every	PRON
american_scientific_journal-1367	163	5	finitely	finitely	ADV
american_scientific_journal-1367	163	6	generated	generate	VERB
american_scientific_journal-1367	163	7	left	leave	VERB
american_scientific_journal-1367	163	8	r	r	NOUN
american_scientific_journal-1367	163	9	-	-	PUNCT
american_scientific_journal-1367	163	10	module	module	NOUN
american_scientific_journal-1367	163	11	is	be	AUX
american_scientific_journal-1367	163	12	fp	fp	NOUN
american_scientific_journal-1367	163	13	-	-	PUNCT
american_scientific_journal-1367	163	14	projective	projective	ADJ
american_scientific_journal-1367	163	15	.	.	PUNCT
american_scientific_journal-1367	164	1	(	(	PUNCT
american_scientific_journal-1367	164	2	4	4	X
american_scientific_journal-1367	164	3	)	)	PUNCT
american_scientific_journal-1367	164	4	every	every	DET
american_scientific_journal-1367	164	5	cyclic	cyclic	NOUN
american_scientific_journal-1367	164	6	left	leave	VERB
american_scientific_journal-1367	164	7	r	r	NOUN
american_scientific_journal-1367	164	8	-	-	PUNCT
american_scientific_journal-1367	164	9	module	module	NOUN
american_scientific_journal-1367	164	10	is	be	AUX
american_scientific_journal-1367	164	11	fp	fp	NOUN
american_scientific_journal-1367	164	12	-	-	PUNCT
american_scientific_journal-1367	164	13	projective	projective	ADJ
american_scientific_journal-1367	164	14	.	.	PUNCT
american_scientific_journal-1367	165	1	(	(	PUNCT
american_scientific_journal-1367	165	2	5	5	X
american_scientific_journal-1367	165	3	)	)	PUNCT
american_scientific_journal-1367	165	4	every	every	DET
american_scientific_journal-1367	165	5	fp	fp	ADJ
american_scientific_journal-1367	165	6	-	-	PUNCT
american_scientific_journal-1367	165	7	injective	injective	ADJ
american_scientific_journal-1367	165	8	left	leave	VERB
american_scientific_journal-1367	165	9	r	r	NOUN
american_scientific_journal-1367	165	10	-	-	PUNCT
american_scientific_journal-1367	165	11	module	module	NOUN
american_scientific_journal-1367	165	12	is	be	AUX
american_scientific_journal-1367	165	13	injective	injective	ADJ
american_scientific_journal-1367	165	14	.	.	PUNCT
american_scientific_journal-1367	166	1	(	(	PUNCT
american_scientific_journal-1367	166	2	6	6	NUM
american_scientific_journal-1367	166	3	)	)	PUNCT
american_scientific_journal-1367	166	4	(	(	PUNCT
american_scientific_journal-1367	166	5	fp	fp	NOUN
american_scientific_journal-1367	166	6	-	-	PUNCT
american_scientific_journal-1367	166	7	proj	proj	NOUN
american_scientific_journal-1367	166	8	,	,	PUNCT
american_scientific_journal-1367	166	9	fp	fp	PROPN
american_scientific_journal-1367	166	10	-	-	PUNCT
american_scientific_journal-1367	166	11	inj	inj	NOUN
american_scientific_journal-1367	166	12	)	)	PUNCT
american_scientific_journal-1367	166	13	is	be	AUX
american_scientific_journal-1367	166	14	hereditary	hereditary	ADJ
american_scientific_journal-1367	166	15	,	,	PUNCT
american_scientific_journal-1367	166	16	and	and	CCONJ
american_scientific_journal-1367	166	17	every	every	DET
american_scientific_journal-1367	166	18	fp	fp	ADJ
american_scientific_journal-1367	166	19	-	-	PUNCT
american_scientific_journal-1367	166	20	injective	injective	ADJ
american_scientific_journal-1367	166	21	left	leave	VERB
american_scientific_journal-1367	166	22	r	r	NOUN
american_scientific_journal-1367	166	23	-	-	PUNCT
american_scientific_journal-1367	166	24	module	module	NOUN
american_scientific_journal-1367	166	25	is	be	AUX
american_scientific_journal-1367	166	26	fp	fp	NOUN
american_scientific_journal-1367	166	27	-	-	PUNCT
american_scientific_journal-1367	166	28	projective	projective	ADJ
american_scientific_journal-1367	166	29	.	.	PUNCT
american_scientific_journal-1367	167	1	proof	proof	NOUN
american_scientific_journal-1367	167	2	.	.	PUNCT
american_scientific_journal-1367	168	1	(	(	PUNCT
american_scientific_journal-1367	168	2	2	2	X
american_scientific_journal-1367	168	3	)	)	PUNCT
american_scientific_journal-1367	168	4	⇒	⇒	NOUN
american_scientific_journal-1367	168	5	(	(	PUNCT
american_scientific_journal-1367	168	6	3	3	NUM
american_scientific_journal-1367	168	7	)	)	PUNCT
american_scientific_journal-1367	168	8	⇒	⇒	NOUN
american_scientific_journal-1367	168	9	(	(	PUNCT
american_scientific_journal-1367	168	10	4	4	X
american_scientific_journal-1367	168	11	)	)	PUNCT
american_scientific_journal-1367	168	12	are	be	AUX
american_scientific_journal-1367	168	13	clear	clear	ADJ
american_scientific_journal-1367	168	14	.	.	PUNCT
american_scientific_journal-1367	169	1	(	(	PUNCT
american_scientific_journal-1367	169	2	4	4	X
american_scientific_journal-1367	169	3	)	)	PUNCT
american_scientific_journal-1367	169	4	⇒	⇒	NOUN
american_scientific_journal-1367	169	5	(	(	PUNCT
american_scientific_journal-1367	169	6	5	5	NUM
american_scientific_journal-1367	169	7	)	)	PUNCT
american_scientific_journal-1367	169	8	.	.	PUNCT
american_scientific_journal-1367	170	1	let	let	VERB
american_scientific_journal-1367	170	2	m	m	PRON
american_scientific_journal-1367	170	3	any	any	DET
american_scientific_journal-1367	170	4	fp	fp	ADJ
american_scientific_journal-1367	170	5	-	-	PUNCT
american_scientific_journal-1367	170	6	injective	injective	ADJ
american_scientific_journal-1367	170	7	left	leave	VERB
american_scientific_journal-1367	170	8	r	r	NOUN
american_scientific_journal-1367	170	9	-	-	PUNCT
american_scientific_journal-1367	170	10	module	module	NOUN
american_scientific_journal-1367	171	1	and	and	CCONJ
american_scientific_journal-1367	171	2	i	i	PRON
american_scientific_journal-1367	171	3	any	any	DET
american_scientific_journal-1367	171	4	left	leave	VERB
american_scientific_journal-1367	171	5	ideal	ideal	NOUN
american_scientific_journal-1367	171	6	of	of	ADP
american_scientific_journal-1367	171	7	r.	r.	PROPN
american_scientific_journal-1367	171	8	then	then	ADV
american_scientific_journal-1367	171	9	ext1(r	ext1(r	AUX
american_scientific_journal-1367	171	10	/	/	SYM
american_scientific_journal-1367	171	11	i	i	PROPN
american_scientific_journal-1367	171	12	,	,	PUNCT
american_scientific_journal-1367	171	13	m	m	PROPN
american_scientific_journal-1367	171	14	)	)	PUNCT
american_scientific_journal-1367	171	15	=	=	SYM
american_scientific_journal-1367	171	16	0	0	NUM
american_scientific_journal-1367	171	17	by	by	ADP
american_scientific_journal-1367	171	18	(	(	PUNCT
american_scientific_journal-1367	171	19	4).thus	4).thus	NUM
american_scientific_journal-1367	171	20	m	m	VERB
american_scientific_journal-1367	171	21	is	be	AUX
american_scientific_journal-1367	171	22	injective	injective	ADJ
american_scientific_journal-1367	171	23	,	,	PUNCT
american_scientific_journal-1367	171	24	as	as	SCONJ
american_scientific_journal-1367	171	25	required	require	VERB
american_scientific_journal-1367	171	26	.	.	PUNCT
american_scientific_journal-1367	172	1	(	(	PUNCT
american_scientific_journal-1367	172	2	5	5	X
american_scientific_journal-1367	172	3	)	)	PUNCT
american_scientific_journal-1367	172	4	⇒	⇒	NOUN
american_scientific_journal-1367	172	5	(	(	PUNCT
american_scientific_journal-1367	172	6	2	2	NUM
american_scientific_journal-1367	172	7	)	)	PUNCT
american_scientific_journal-1367	172	8	.	.	PUNCT
american_scientific_journal-1367	173	1	let	let	VERB
american_scientific_journal-1367	173	2	m	m	PRON
american_scientific_journal-1367	173	3	any	any	DET
american_scientific_journal-1367	173	4	left	left	ADJ
american_scientific_journal-1367	173	5	r	r	NOUN
american_scientific_journal-1367	173	6	-	-	PUNCT
american_scientific_journal-1367	173	7	module	module	NOUN
american_scientific_journal-1367	173	8	,	,	PUNCT
american_scientific_journal-1367	173	9	0	0	NUM
american_scientific_journal-1367	173	10	→	→	SYM
american_scientific_journal-1367	173	11	a	a	DET
american_scientific_journal-1367	173	12	→	→	SYM
american_scientific_journal-1367	173	13	b	b	PROPN
american_scientific_journal-1367	173	14	→	→	SYM
american_scientific_journal-1367	173	15	c	c	PROPN
american_scientific_journal-1367	173	16	→	→	SYM
american_scientific_journal-1367	173	17	0	0	NUM
american_scientific_journal-1367	173	18	be	be	AUX
american_scientific_journal-1367	173	19	an	an	DET
american_scientific_journal-1367	173	20	exact	exact	ADJ
american_scientific_journal-1367	173	21	sequence	sequence	NOUN
american_scientific_journal-1367	173	22	with	with	ADP
american_scientific_journal-1367	173	23	a	a	DET
american_scientific_journal-1367	173	24	fp	fp	ADJ
american_scientific_journal-1367	173	25	-	-	PUNCT
american_scientific_journal-1367	173	26	injective	injective	ADJ
american_scientific_journal-1367	173	27	.	.	PUNCT
american_scientific_journal-1367	174	1	since	since	SCONJ
american_scientific_journal-1367	174	2	a	a	PRON
american_scientific_journal-1367	174	3	is	be	AUX
american_scientific_journal-1367	174	4	injective	injective	ADJ
american_scientific_journal-1367	174	5	by	by	ADP
american_scientific_journal-1367	174	6	(	(	PUNCT
american_scientific_journal-1367	174	7	5	5	NUM
american_scientific_journal-1367	174	8	)	)	PUNCT
american_scientific_journal-1367	174	9	,	,	PUNCT
american_scientific_journal-1367	174	10	the	the	DET
american_scientific_journal-1367	174	11	sequence	sequence	NOUN
american_scientific_journal-1367	174	12	hom(m	hom(m	PROPN
american_scientific_journal-1367	174	13	,	,	PUNCT
american_scientific_journal-1367	174	14	b	b	NOUN
american_scientific_journal-1367	174	15	)	)	PUNCT
american_scientific_journal-1367	174	16	→	→	SYM
american_scientific_journal-1367	174	17	hom(m	hom(m	PROPN
american_scientific_journal-1367	174	18	,	,	PUNCT
american_scientific_journal-1367	174	19	c	c	NOUN
american_scientific_journal-1367	174	20	)	)	PUNCT
american_scientific_journal-1367	174	21	→	→	SYM
american_scientific_journal-1367	174	22	ext1(m	ext1(m	NUM
american_scientific_journal-1367	174	23	,	,	PUNCT
american_scientific_journal-1367	174	24	a	a	PRON
american_scientific_journal-1367	174	25	)	)	PUNCT
american_scientific_journal-1367	174	26	=	=	SYM
american_scientific_journal-1367	174	27	0	0	NUM
american_scientific_journal-1367	174	28	is	be	AUX
american_scientific_journal-1367	174	29	exact	exact	ADJ
american_scientific_journal-1367	174	30	.	.	PUNCT
american_scientific_journal-1367	175	1	so	so	ADV
american_scientific_journal-1367	175	2	m	m	PROPN
american_scientific_journal-1367	175	3	is	be	AUX
american_scientific_journal-1367	175	4	fp	fp	ADJ
american_scientific_journal-1367	175	5	-	-	PUNCT
american_scientific_journal-1367	175	6	projective	projective	ADJ
american_scientific_journal-1367	175	7	by	by	ADP
american_scientific_journal-1367	175	8	theorem	theorem	ADJ
american_scientific_journal-1367	175	9	2.3	2.3	NUM
american_scientific_journal-1367	175	10	(	(	PUNCT
american_scientific_journal-1367	175	11	2	2	NUM
american_scientific_journal-1367	175	12	)	)	PUNCT
american_scientific_journal-1367	175	13	.	.	PUNCT
american_scientific_journal-1367	176	1	137	137	NUM
american_scientific_journal-1367	176	2	american	american	ADJ
american_scientific_journal-1367	176	3	scientific	scientific	ADJ
american_scientific_journal-1367	176	4	research	research	NOUN
american_scientific_journal-1367	176	5	journal	journal	NOUN
american_scientific_journal-1367	176	6	for	for	ADP
american_scientific_journal-1367	176	7	engineering	engineering	NOUN
american_scientific_journal-1367	176	8	,	,	PUNCT
american_scientific_journal-1367	176	9	technology	technology	NOUN
american_scientific_journal-1367	176	10	,	,	PUNCT
american_scientific_journal-1367	176	11	and	and	CCONJ
american_scientific_journal-1367	176	12	sciences	science	NOUN
american_scientific_journal-1367	176	13	(	(	PUNCT
american_scientific_journal-1367	176	14	asrjets	asrjet	NOUN
american_scientific_journal-1367	176	15	)	)	PUNCT
american_scientific_journal-1367	176	16	(	(	PUNCT
american_scientific_journal-1367	176	17	2016	2016	NUM
american_scientific_journal-1367	176	18	)	)	PUNCT
american_scientific_journal-1367	176	19	volume	volume	NOUN
american_scientific_journal-1367	176	20	17	17	NUM
american_scientific_journal-1367	176	21	,	,	PUNCT
american_scientific_journal-1367	176	22	no	no	DET
american_scientific_journal-1367	176	23	1	1	NUM
american_scientific_journal-1367	176	24	,	,	PUNCT
american_scientific_journal-1367	176	25	pp	pp	ADV
american_scientific_journal-1367	176	26	132	132	NUM
american_scientific_journal-1367	176	27	-	-	SYM
american_scientific_journal-1367	176	28	143	143	NUM
american_scientific_journal-1367	176	29	(	(	PUNCT
american_scientific_journal-1367	176	30	5	5	NUM
american_scientific_journal-1367	176	31	)	)	PUNCT
american_scientific_journal-1367	176	32	⇒	⇒	NOUN
american_scientific_journal-1367	176	33	(	(	PUNCT
american_scientific_journal-1367	176	34	1	1	NUM
american_scientific_journal-1367	176	35	)	)	PUNCT
american_scientific_journal-1367	176	36	.	.	PUNCT
american_scientific_journal-1367	177	1	it	it	PRON
american_scientific_journal-1367	177	2	is	be	AUX
american_scientific_journal-1367	177	3	clear	clear	ADJ
american_scientific_journal-1367	177	4	that	that	SCONJ
american_scientific_journal-1367	177	5	every	every	DET
american_scientific_journal-1367	177	6	f	f	NOUN
american_scientific_journal-1367	177	7	-	-	PUNCT
american_scientific_journal-1367	177	8	injective	injective	ADJ
american_scientific_journal-1367	177	9	left	leave	VERB
american_scientific_journal-1367	177	10	r	r	NOUN
american_scientific_journal-1367	177	11	-	-	PUNCT
american_scientific_journal-1367	177	12	module	module	NOUN
american_scientific_journal-1367	177	13	is	be	AUX
american_scientific_journal-1367	177	14	fp	fp	ADJ
american_scientific_journal-1367	177	15	-	-	PUNCT
american_scientific_journal-1367	177	16	injective	injective	ADJ
american_scientific_journal-1367	177	17	.	.	PUNCT
american_scientific_journal-1367	178	1	so	so	ADV
american_scientific_journal-1367	178	2	by	by	ADP
american_scientific_journal-1367	178	3	(	(	PUNCT
american_scientific_journal-1367	178	4	5	5	NUM
american_scientific_journal-1367	178	5	)	)	PUNCT
american_scientific_journal-1367	178	6	and	and	CCONJ
american_scientific_journal-1367	178	7	[	[	X
american_scientific_journal-1367	178	8	11	11	NUM
american_scientific_journal-1367	178	9	,	,	PUNCT
american_scientific_journal-1367	178	10	corollary1.10	corollary1.10	NOUN
american_scientific_journal-1367	178	11	]	]	X
american_scientific_journal-1367	178	12	,	,	PUNCT
american_scientific_journal-1367	178	13	r	r	NOUN
american_scientific_journal-1367	178	14	is	be	AUX
american_scientific_journal-1367	178	15	left	leave	VERB
american_scientific_journal-1367	178	16	noetherian	noetherian	ADJ
american_scientific_journal-1367	178	17	.	.	PUNCT
american_scientific_journal-1367	179	1	(	(	PUNCT
american_scientific_journal-1367	179	2	1	1	X
american_scientific_journal-1367	179	3	)	)	PUNCT
american_scientific_journal-1367	179	4	⇒	⇒	NOUN
american_scientific_journal-1367	179	5	(	(	PUNCT
american_scientific_journal-1367	179	6	5	5	NUM
american_scientific_journal-1367	179	7	)	)	PUNCT
american_scientific_journal-1367	179	8	.	.	PUNCT
american_scientific_journal-1367	180	1	let	let	VERB
american_scientific_journal-1367	180	2	r	r	PRON
american_scientific_journal-1367	180	3	be	be	AUX
american_scientific_journal-1367	180	4	a	a	DET
american_scientific_journal-1367	180	5	left	left	ADJ
american_scientific_journal-1367	180	6	noetherian	noetherian	ADJ
american_scientific_journal-1367	180	7	ring	ring	NOUN
american_scientific_journal-1367	180	8	.	.	PUNCT
american_scientific_journal-1367	181	1	then	then	ADV
american_scientific_journal-1367	181	2	every	every	DET
american_scientific_journal-1367	181	3	left	leave	VERB
american_scientific_journal-1367	181	4	ideal	ideal	NOUN
american_scientific_journal-1367	181	5	of	of	ADP
american_scientific_journal-1367	181	6	r	r	NOUN
american_scientific_journal-1367	181	7	is	be	AUX
american_scientific_journal-1367	181	8	finitely	finitely	ADV
american_scientific_journal-1367	181	9	presented	present	VERB
american_scientific_journal-1367	181	10	.	.	PUNCT
american_scientific_journal-1367	182	1	so	so	ADV
american_scientific_journal-1367	182	2	every	every	DET
american_scientific_journal-1367	182	3	fp	fp	ADJ
american_scientific_journal-1367	182	4	-	-	PUNCT
american_scientific_journal-1367	182	5	injective	injective	ADJ
american_scientific_journal-1367	182	6	left	leave	VERB
american_scientific_journal-1367	182	7	r	r	NOUN
american_scientific_journal-1367	182	8	-	-	PUNCT
american_scientific_journal-1367	182	9	module	module	NOUN
american_scientific_journal-1367	182	10	is	be	AUX
american_scientific_journal-1367	182	11	f	f	NOUN
american_scientific_journal-1367	182	12	-	-	PUNCT
american_scientific_journal-1367	182	13	injective	injective	ADJ
american_scientific_journal-1367	182	14	.	.	PUNCT
american_scientific_journal-1367	183	1	thus	thus	ADV
american_scientific_journal-1367	183	2	(	(	PUNCT
american_scientific_journal-1367	183	3	5	5	X
american_scientific_journal-1367	183	4	)	)	PUNCT
american_scientific_journal-1367	183	5	holds	hold	VERB
american_scientific_journal-1367	183	6	by	by	ADP
american_scientific_journal-1367	183	7	[	[	PUNCT
american_scientific_journal-1367	183	8	11	11	NUM
american_scientific_journal-1367	183	9	,	,	PUNCT
american_scientific_journal-1367	183	10	corollary1.10	corollary1.10	NOUN
american_scientific_journal-1367	183	11	]	]	X
american_scientific_journal-1367	183	12	.	.	PUNCT
american_scientific_journal-1367	184	1	(	(	PUNCT
american_scientific_journal-1367	184	2	2	2	X
american_scientific_journal-1367	184	3	)	)	PUNCT
american_scientific_journal-1367	184	4	⇒	⇒	NOUN
american_scientific_journal-1367	184	5	(	(	PUNCT
american_scientific_journal-1367	184	6	6	6	NUM
american_scientific_journal-1367	184	7	)	)	PUNCT
american_scientific_journal-1367	184	8	is	be	AUX
american_scientific_journal-1367	184	9	clear	clear	ADJ
american_scientific_journal-1367	184	10	.	.	PUNCT
american_scientific_journal-1367	185	1	(	(	PUNCT
american_scientific_journal-1367	185	2	6	6	NUM
american_scientific_journal-1367	185	3	)	)	PUNCT
american_scientific_journal-1367	185	4	⇒	⇒	NOUN
american_scientific_journal-1367	185	5	(	(	PUNCT
american_scientific_journal-1367	185	6	2	2	NUM
american_scientific_journal-1367	185	7	)	)	PUNCT
american_scientific_journal-1367	185	8	.	.	PUNCT
american_scientific_journal-1367	186	1	let	let	VERB
american_scientific_journal-1367	186	2	m	m	PRON
american_scientific_journal-1367	186	3	any	any	DET
american_scientific_journal-1367	186	4	left	left	ADJ
american_scientific_journal-1367	186	5	r	r	NOUN
american_scientific_journal-1367	186	6	-	-	PUNCT
american_scientific_journal-1367	186	7	module	module	NOUN
american_scientific_journal-1367	186	8	.	.	PUNCT
american_scientific_journal-1367	187	1	since	since	SCONJ
american_scientific_journal-1367	187	2	(	(	PUNCT
american_scientific_journal-1367	187	3	fp	fp	INTJ
american_scientific_journal-1367	187	4	-	-	PUNCT
american_scientific_journal-1367	187	5	proj	proj	NOUN
american_scientific_journal-1367	187	6	,	,	PUNCT
american_scientific_journal-1367	187	7	fp	fp	PROPN
american_scientific_journal-1367	187	8	-	-	PUNCT
american_scientific_journal-1367	187	9	inj	inj	NOUN
american_scientific_journal-1367	187	10	)	)	PUNCT
american_scientific_journal-1367	187	11	is	be	AUX
american_scientific_journal-1367	187	12	a	a	DET
american_scientific_journal-1367	187	13	complete	complete	ADJ
american_scientific_journal-1367	187	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	187	15	theory	theory	NOUN
american_scientific_journal-1367	187	16	by	by	ADP
american_scientific_journal-1367	187	17	theorem	theorem	NOUN
american_scientific_journal-1367	187	18	2.6	2.6	NUM
american_scientific_journal-1367	187	19	,	,	PUNCT
american_scientific_journal-1367	187	20	m	m	VERB
american_scientific_journal-1367	187	21	has	have	VERB
american_scientific_journal-1367	187	22	a	a	DET
american_scientific_journal-1367	187	23	special	special	ADJ
american_scientific_journal-1367	187	24	fp	fp	ADJ
american_scientific_journal-1367	187	25	-	-	PUNCT
american_scientific_journal-1367	187	26	injective	injective	ADJ
american_scientific_journal-1367	187	27	preenvelope	preenvelope	NOUN
american_scientific_journal-1367	187	28	,	,	PUNCT
american_scientific_journal-1367	187	29	i.e.	i.e.	X
american_scientific_journal-1367	187	30	there	there	PRON
american_scientific_journal-1367	187	31	is	be	VERB
american_scientific_journal-1367	187	32	a	a	DET
american_scientific_journal-1367	187	33	short	short	ADJ
american_scientific_journal-1367	187	34	exact	exact	ADJ
american_scientific_journal-1367	187	35	sequence	sequence	NOUN
american_scientific_journal-1367	187	36	0	0	NUM
american_scientific_journal-1367	187	37	→	→	SYM
american_scientific_journal-1367	187	38	m	m	PROPN
american_scientific_journal-1367	187	39	→	→	SYM
american_scientific_journal-1367	187	40	f	f	PROPN
american_scientific_journal-1367	187	41	→	→	SYM
american_scientific_journal-1367	187	42	p	p	X
american_scientific_journal-1367	187	43	,	,	PUNCT
american_scientific_journal-1367	187	44	where	where	SCONJ
american_scientific_journal-1367	187	45	f	f	PROPN
american_scientific_journal-1367	187	46	is	be	AUX
american_scientific_journal-1367	187	47	fpinjective	fpinjective	ADJ
american_scientific_journal-1367	187	48	and	and	CCONJ
american_scientific_journal-1367	187	49	p	p	NOUN
american_scientific_journal-1367	187	50	is	be	AUX
american_scientific_journal-1367	187	51	fp	fp	NOUN
american_scientific_journal-1367	187	52	-	-	PUNCT
american_scientific_journal-1367	187	53	projective	projective	NOUN
american_scientific_journal-1367	187	54	.	.	PUNCT
american_scientific_journal-1367	188	1	since	since	SCONJ
american_scientific_journal-1367	188	2	p	p	NOUN
american_scientific_journal-1367	188	3	is	be	AUX
american_scientific_journal-1367	188	4	fp	fp	NOUN
american_scientific_journal-1367	188	5	-	-	PUNCT
american_scientific_journal-1367	188	6	projective	projective	ADJ
american_scientific_journal-1367	188	7	,	,	PUNCT
american_scientific_journal-1367	188	8	and	and	CCONJ
american_scientific_journal-1367	188	9	(	(	PUNCT
american_scientific_journal-1367	188	10	fp	fp	INTJ
american_scientific_journal-1367	188	11	-	-	PUNCT
american_scientific_journal-1367	188	12	proj	proj	NOUN
american_scientific_journal-1367	188	13	,	,	PUNCT
american_scientific_journal-1367	188	14	fp	fp	PROPN
american_scientific_journal-1367	188	15	-	-	PUNCT
american_scientific_journal-1367	188	16	inj	inj	NOUN
american_scientific_journal-1367	188	17	)	)	PUNCT
american_scientific_journal-1367	188	18	is	be	AUX
american_scientific_journal-1367	188	19	hereditary	hereditary	ADJ
american_scientific_journal-1367	188	20	and	and	CCONJ
american_scientific_journal-1367	188	21	f	f	PROPN
american_scientific_journal-1367	188	22	is	be	AUX
american_scientific_journal-1367	188	23	fp	fp	NOUN
american_scientific_journal-1367	188	24	-	-	PUNCT
american_scientific_journal-1367	188	25	projective	projective	NOUN
american_scientific_journal-1367	188	26	by	by	ADP
american_scientific_journal-1367	188	27	(	(	PUNCT
american_scientific_journal-1367	188	28	6	6	NUM
american_scientific_journal-1367	188	29	)	)	PUNCT
american_scientific_journal-1367	188	30	,	,	PUNCT
american_scientific_journal-1367	188	31	m	m	PROPN
american_scientific_journal-1367	188	32	must	must	AUX
american_scientific_journal-1367	188	33	be	be	AUX
american_scientific_journal-1367	188	34	fp	fp	NOUN
american_scientific_journal-1367	188	35	-	-	PUNCT
american_scientific_journal-1367	188	36	projective	projective	ADJ
american_scientific_journal-1367	188	37	.	.	PUNCT
american_scientific_journal-1367	189	1	thus	thus	ADV
american_scientific_journal-1367	189	2	(	(	PUNCT
american_scientific_journal-1367	189	3	2	2	X
american_scientific_journal-1367	189	4	)	)	PUNCT
american_scientific_journal-1367	189	5	holds	hold	NOUN
american_scientific_journal-1367	189	6	.	.	PUNCT
american_scientific_journal-1367	190	1	□	□	PUNCT
american_scientific_journal-1367	190	2	recall	recall	VERB
american_scientific_journal-1367	190	3	that	that	SCONJ
american_scientific_journal-1367	190	4	a	a	DET
american_scientific_journal-1367	190	5	ring	ring	NOUN
american_scientific_journal-1367	190	6	r	r	NOUN
american_scientific_journal-1367	190	7	is	be	AUX
american_scientific_journal-1367	190	8	called	call	VERB
american_scientific_journal-1367	190	9	left	left	ADJ
american_scientific_journal-1367	190	10	coherent	coherent	ADJ
american_scientific_journal-1367	190	11	if	if	SCONJ
american_scientific_journal-1367	190	12	every	every	PRON
american_scientific_journal-1367	190	13	finitely	finitely	ADV
american_scientific_journal-1367	190	14	generated	generate	VERB
american_scientific_journal-1367	190	15	left	leave	VERB
american_scientific_journal-1367	190	16	ideal	ideal	NOUN
american_scientific_journal-1367	190	17	of	of	ADP
american_scientific_journal-1367	190	18	r	r	NOUN
american_scientific_journal-1367	190	19	is	be	AUX
american_scientific_journal-1367	190	20	finitely	finitely	ADV
american_scientific_journal-1367	190	21	presented	present	VERB
american_scientific_journal-1367	190	22	.	.	PUNCT
american_scientific_journal-1367	191	1	coherent	coherent	ADJ
american_scientific_journal-1367	191	2	rings	ring	NOUN
american_scientific_journal-1367	191	3	and	and	CCONJ
american_scientific_journal-1367	191	4	their	their	PRON
american_scientific_journal-1367	191	5	generations	generation	NOUN
american_scientific_journal-1367	191	6	have	have	AUX
american_scientific_journal-1367	191	7	been	be	AUX
american_scientific_journal-1367	191	8	studied	study	VERB
american_scientific_journal-1367	191	9	and	and	CCONJ
american_scientific_journal-1367	191	10	characterized	characterize	VERB
american_scientific_journal-1367	191	11	by	by	ADP
american_scientific_journal-1367	191	12	many	many	ADJ
american_scientific_journal-1367	191	13	authors	author	NOUN
american_scientific_journal-1367	191	14	(	(	PUNCT
american_scientific_journal-1367	191	15	see	see	VERB
american_scientific_journal-1367	191	16	.	.	PUNCT
american_scientific_journal-1367	192	1	for	for	ADP
american_scientific_journal-1367	192	2	example	example	NOUN
american_scientific_journal-1367	192	3	[	[	X
american_scientific_journal-1367	192	4	1	1	NUM
american_scientific_journal-1367	192	5	,	,	PUNCT
american_scientific_journal-1367	192	6	3,5,6,12,13	3,5,6,12,13	NUM
american_scientific_journal-1367	192	7	]	]	PUNCT
american_scientific_journal-1367	192	8	)	)	PUNCT
american_scientific_journal-1367	192	9	.	.	PUNCT
american_scientific_journal-1367	193	1	next	next	ADV
american_scientific_journal-1367	193	2	,	,	PUNCT
american_scientific_journal-1367	193	3	we	we	PRON
american_scientific_journal-1367	193	4	give	give	VERB
american_scientific_journal-1367	193	5	some	some	DET
american_scientific_journal-1367	193	6	characterizations	characterization	NOUN
american_scientific_journal-1367	193	7	of	of	ADP
american_scientific_journal-1367	193	8	left	left	ADJ
american_scientific_journal-1367	193	9	coherent	coherent	ADJ
american_scientific_journal-1367	193	10	rings	ring	NOUN
american_scientific_journal-1367	193	11	in	in	ADP
american_scientific_journal-1367	193	12	terms	term	NOUN
american_scientific_journal-1367	193	13	of	of	ADP
american_scientific_journal-1367	193	14	fp	fp	X
american_scientific_journal-1367	193	15	-	-	PUNCT
american_scientific_journal-1367	193	16	projective	projective	ADJ
american_scientific_journal-1367	193	17	and	and	CCONJ
american_scientific_journal-1367	193	18	fp	fp	ADJ
american_scientific_journal-1367	193	19	-	-	PUNCT
american_scientific_journal-1367	193	20	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	193	21	left	leave	VERB
american_scientific_journal-1367	193	22	rmodules	rmodule	NOUN
american_scientific_journal-1367	193	23	.	.	PUNCT
american_scientific_journal-1367	194	1	3.2	3.2	NUM
american_scientific_journal-1367	194	2	theorem	theorem	VERB
american_scientific_journal-1367	194	3	the	the	DET
american_scientific_journal-1367	194	4	following	following	ADJ
american_scientific_journal-1367	194	5	statements	statement	NOUN
american_scientific_journal-1367	194	6	are	be	AUX
american_scientific_journal-1367	194	7	equivalent	equivalent	ADJ
american_scientific_journal-1367	194	8	for	for	ADP
american_scientific_journal-1367	194	9	a	a	DET
american_scientific_journal-1367	194	10	ring	ring	NOUN
american_scientific_journal-1367	194	11	r.	r.	NOUN
american_scientific_journal-1367	194	12	(	(	PUNCT
american_scientific_journal-1367	194	13	1	1	X
american_scientific_journal-1367	194	14	)	)	PUNCT
american_scientific_journal-1367	194	15	r	r	NOUN
american_scientific_journal-1367	194	16	is	be	AUX
american_scientific_journal-1367	194	17	left	leave	VERB
american_scientific_journal-1367	194	18	coherent	coherent	ADJ
american_scientific_journal-1367	194	19	.	.	PUNCT
american_scientific_journal-1367	195	1	(	(	PUNCT
american_scientific_journal-1367	195	2	2	2	X
american_scientific_journal-1367	195	3	)	)	PUNCT
american_scientific_journal-1367	195	4	every	every	DET
american_scientific_journal-1367	195	5	fp	fp	ADJ
american_scientific_journal-1367	195	6	-	-	PUNCT
american_scientific_journal-1367	195	7	injective	injective	ADJ
american_scientific_journal-1367	195	8	left	leave	VERB
american_scientific_journal-1367	195	9	r	r	NOUN
american_scientific_journal-1367	195	10	-	-	PUNCT
american_scientific_journal-1367	195	11	module	module	NOUN
american_scientific_journal-1367	195	12	is	be	AUX
american_scientific_journal-1367	195	13	fp	fp	ADJ
american_scientific_journal-1367	195	14	-	-	PUNCT
american_scientific_journal-1367	195	15	injective	injective	ADJ
american_scientific_journal-1367	195	16	.	.	PUNCT
american_scientific_journal-1367	196	1	(	(	PUNCT
american_scientific_journal-1367	196	2	3	3	X
american_scientific_journal-1367	196	3	)	)	PUNCT
american_scientific_journal-1367	196	4	every	every	DET
american_scientific_journal-1367	196	5	fp	fp	ADJ
american_scientific_journal-1367	196	6	-	-	PUNCT
american_scientific_journal-1367	196	7	injective	injective	ADJ
american_scientific_journal-1367	196	8	left	leave	VERB
american_scientific_journal-1367	196	9	r	r	NOUN
american_scientific_journal-1367	196	10	-	-	PUNCT
american_scientific_journal-1367	196	11	module	module	NOUN
american_scientific_journal-1367	196	12	is	be	AUX
american_scientific_journal-1367	196	13	f	f	NOUN
american_scientific_journal-1367	196	14	-	-	PUNCT
american_scientific_journal-1367	196	15	injective	injective	ADJ
american_scientific_journal-1367	196	16	.	.	PUNCT
american_scientific_journal-1367	197	1	(	(	PUNCT
american_scientific_journal-1367	197	2	4	4	X
american_scientific_journal-1367	197	3	)	)	PUNCT
american_scientific_journal-1367	197	4	every	every	DET
american_scientific_journal-1367	197	5	fp	fp	ADJ
american_scientific_journal-1367	197	6	-	-	PUNCT
american_scientific_journal-1367	197	7	flat	flat	ADJ
american_scientific_journal-1367	197	8	right	right	ADJ
american_scientific_journal-1367	197	9	r	r	NOUN
american_scientific_journal-1367	197	10	-	-	PUNCT
american_scientific_journal-1367	197	11	module	module	NOUN
american_scientific_journal-1367	197	12	is	be	AUX
american_scientific_journal-1367	197	13	flat	flat	ADJ
american_scientific_journal-1367	197	14	.	.	PUNCT
american_scientific_journal-1367	198	1	(	(	PUNCT
american_scientific_journal-1367	198	2	5	5	X
american_scientific_journal-1367	198	3	)	)	PUNCT
american_scientific_journal-1367	198	4	every	every	DET
american_scientific_journal-1367	198	5	fp	fp	PROPN
american_scientific_journal-1367	198	6	-	-	PUNCT
american_scientific_journal-1367	198	7	projective	projective	NOUN
american_scientific_journal-1367	198	8	left	leave	VERB
american_scientific_journal-1367	198	9	r	r	NOUN
american_scientific_journal-1367	198	10	-	-	PUNCT
american_scientific_journal-1367	198	11	module	module	NOUN
american_scientific_journal-1367	198	12	is	be	AUX
american_scientific_journal-1367	198	13	fp	fp	NOUN
american_scientific_journal-1367	198	14	-	-	PUNCT
american_scientific_journal-1367	198	15	projective	projective	ADJ
american_scientific_journal-1367	198	16	.	.	PUNCT
american_scientific_journal-1367	199	1	(	(	PUNCT
american_scientific_journal-1367	199	2	6	6	NUM
american_scientific_journal-1367	199	3	)	)	PUNCT
american_scientific_journal-1367	199	4	every	every	PRON
american_scientific_journal-1367	199	5	finitely	finitely	ADV
american_scientific_journal-1367	199	6	presented	present	VERB
american_scientific_journal-1367	199	7	left	leave	VERB
american_scientific_journal-1367	199	8	r	r	NOUN
american_scientific_journal-1367	199	9	-	-	PUNCT
american_scientific_journal-1367	199	10	module	module	NOUN
american_scientific_journal-1367	199	11	is	be	AUX
american_scientific_journal-1367	199	12	fp	fp	NOUN
american_scientific_journal-1367	199	13	-	-	PUNCT
american_scientific_journal-1367	199	14	projective	projective	ADJ
american_scientific_journal-1367	199	15	.	.	PUNCT
american_scientific_journal-1367	200	1	(	(	PUNCT
american_scientific_journal-1367	200	2	7	7	X
american_scientific_journal-1367	200	3	)	)	PUNCT
american_scientific_journal-1367	200	4	every	every	DET
american_scientific_journal-1367	200	5	f	f	PROPN
american_scientific_journal-1367	200	6	-	-	PUNCT
american_scientific_journal-1367	200	7	projective	projective	NOUN
american_scientific_journal-1367	200	8	left	leave	VERB
american_scientific_journal-1367	200	9	r	r	NOUN
american_scientific_journal-1367	200	10	-	-	PUNCT
american_scientific_journal-1367	200	11	module	module	NOUN
american_scientific_journal-1367	200	12	is	be	AUX
american_scientific_journal-1367	200	13	fp	fp	NOUN
american_scientific_journal-1367	200	14	-	-	PUNCT
american_scientific_journal-1367	200	15	projective	projective	ADJ
american_scientific_journal-1367	200	16	.	.	PUNCT
american_scientific_journal-1367	201	1	(	(	PUNCT
american_scientific_journal-1367	201	2	8)	8)	NUM
american_scientific_journal-1367	201	3	for	for	ADP
american_scientific_journal-1367	201	4	every	every	PRON
american_scientific_journal-1367	201	5	finitely	finitely	ADV
american_scientific_journal-1367	201	6	generated	generate	VERB
american_scientific_journal-1367	201	7	left	leave	VERB
american_scientific_journal-1367	201	8	ideal	ideal	NOUN
american_scientific_journal-1367	201	9	i	i	PRON
american_scientific_journal-1367	201	10	of	of	ADP
american_scientific_journal-1367	201	11	r	r	NOUN
american_scientific_journal-1367	201	12	,	,	PUNCT
american_scientific_journal-1367	201	13	r	r	NOUN
american_scientific_journal-1367	201	14	/	/	SYM
american_scientific_journal-1367	201	15	i	i	PRON
american_scientific_journal-1367	201	16	is	be	AUX
american_scientific_journal-1367	201	17	fp	fp	ADJ
american_scientific_journal-1367	201	18	-	-	PUNCT
american_scientific_journal-1367	201	19	projective	projective	ADJ
american_scientific_journal-1367	201	20	.	.	PUNCT
american_scientific_journal-1367	202	1	(	(	PUNCT
american_scientific_journal-1367	202	2	9	9	X
american_scientific_journal-1367	202	3	)	)	PUNCT
american_scientific_journal-1367	202	4	every	every	DET
american_scientific_journal-1367	202	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	202	6	right	right	ADJ
american_scientific_journal-1367	202	7	r	r	NOUN
american_scientific_journal-1367	202	8	-	-	PUNCT
american_scientific_journal-1367	202	9	module	module	NOUN
american_scientific_journal-1367	202	10	is	be	AUX
american_scientific_journal-1367	202	11	fp	fp	ADJ
american_scientific_journal-1367	202	12	-	-	PUNCT
american_scientific_journal-1367	202	13	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	202	14	.	.	PUNCT
american_scientific_journal-1367	203	1	proof	proof	NOUN
american_scientific_journal-1367	203	2	.	.	PUNCT
american_scientific_journal-1367	204	1	(	(	PUNCT
american_scientific_journal-1367	204	2	1	1	X
american_scientific_journal-1367	204	3	)	)	PUNCT
american_scientific_journal-1367	204	4	⇔	⇔	X
american_scientific_journal-1367	204	5	(	(	PUNCT
american_scientific_journal-1367	204	6	2	2	NUM
american_scientific_journal-1367	204	7	)	)	PUNCT
american_scientific_journal-1367	204	8	⇔	⇔	X
american_scientific_journal-1367	204	9	(	(	PUNCT
american_scientific_journal-1367	204	10	3	3	NUM
american_scientific_journal-1367	204	11	)	)	PUNCT
american_scientific_journal-1367	204	12	⇔	⇔	X
american_scientific_journal-1367	204	13	(	(	PUNCT
american_scientific_journal-1367	204	14	4	4	NUM
american_scientific_journal-1367	204	15	)	)	PUNCT
american_scientific_journal-1367	204	16	by	by	ADP
american_scientific_journal-1367	204	17	[	[	X
american_scientific_journal-1367	204	18	3	3	NUM
american_scientific_journal-1367	204	19	,	,	PUNCT
american_scientific_journal-1367	204	20	theorem	theorem	VERB
american_scientific_journal-1367	204	21	2.8	2.8	NUM
american_scientific_journal-1367	204	22	]	]	PUNCT
american_scientific_journal-1367	204	23	.	.	PUNCT
american_scientific_journal-1367	205	1	(	(	PUNCT
american_scientific_journal-1367	205	2	5	5	X
american_scientific_journal-1367	205	3	)	)	PUNCT
american_scientific_journal-1367	205	4	⇒	⇒	NOUN
american_scientific_journal-1367	205	5	(	(	PUNCT
american_scientific_journal-1367	205	6	6	6	NUM
american_scientific_journal-1367	205	7	)	)	PUNCT
american_scientific_journal-1367	205	8	is	be	AUX
american_scientific_journal-1367	205	9	clear	clear	ADJ
american_scientific_journal-1367	205	10	,	,	PUNCT
american_scientific_journal-1367	205	11	since	since	SCONJ
american_scientific_journal-1367	205	12	every	every	DET
american_scientific_journal-1367	205	13	finitely	finitely	ADV
american_scientific_journal-1367	205	14	presented	present	VERB
american_scientific_journal-1367	205	15	left	leave	VERB
american_scientific_journal-1367	205	16	r	r	NOUN
american_scientific_journal-1367	205	17	-	-	PUNCT
american_scientific_journal-1367	205	18	module	module	NOUN
american_scientific_journal-1367	205	19	is	be	AUX
american_scientific_journal-1367	205	20	fp	fp	NOUN
american_scientific_journal-1367	205	21	-	-	PUNCT
american_scientific_journal-1367	205	22	projective	projective	ADJ
american_scientific_journal-1367	205	23	.	.	PUNCT
american_scientific_journal-1367	206	1	(	(	PUNCT
american_scientific_journal-1367	206	2	6	6	NUM
american_scientific_journal-1367	206	3	)	)	PUNCT
american_scientific_journal-1367	206	4	⇒	⇒	NOUN
american_scientific_journal-1367	206	5	(	(	PUNCT
american_scientific_journal-1367	206	6	2	2	NUM
american_scientific_journal-1367	206	7	)	)	PUNCT
american_scientific_journal-1367	206	8	.	.	PUNCT
american_scientific_journal-1367	207	1	let	let	VERB
american_scientific_journal-1367	207	2	m	m	PRON
american_scientific_journal-1367	207	3	be	be	AUX
american_scientific_journal-1367	207	4	an	an	DET
american_scientific_journal-1367	207	5	fp	fp	ADJ
american_scientific_journal-1367	207	6	-	-	PUNCT
american_scientific_journal-1367	207	7	injective	injective	ADJ
american_scientific_journal-1367	207	8	left	leave	VERB
american_scientific_journal-1367	207	9	r	r	NOUN
american_scientific_journal-1367	207	10	-	-	PUNCT
american_scientific_journal-1367	207	11	module	module	NOUN
american_scientific_journal-1367	207	12	and	and	CCONJ
american_scientific_journal-1367	207	13	a	a	DET
american_scientific_journal-1367	207	14	any	any	PRON
american_scientific_journal-1367	207	15	finitely	finitely	ADV
american_scientific_journal-1367	207	16	presented	present	VERB
american_scientific_journal-1367	207	17	left	leave	VERB
american_scientific_journal-1367	207	18	r	r	NOUN
american_scientific_journal-1367	207	19	-	-	PUNCT
american_scientific_journal-1367	207	20	module	module	NOUN
american_scientific_journal-1367	207	21	.	.	PUNCT
american_scientific_journal-1367	208	1	then	then	ADV
american_scientific_journal-1367	208	2	ext1(a	ext1(a	PROPN
american_scientific_journal-1367	208	3	,	,	PUNCT
american_scientific_journal-1367	208	4	m	m	NOUN
american_scientific_journal-1367	208	5	)	)	PUNCT
american_scientific_journal-1367	208	6	=	=	SYM
american_scientific_journal-1367	208	7	0	0	NUM
american_scientific_journal-1367	208	8	by	by	ADP
american_scientific_journal-1367	208	9	(	(	PUNCT
american_scientific_journal-1367	208	10	6).thus	6).thus	NUM
american_scientific_journal-1367	208	11	m	m	NOUN
american_scientific_journal-1367	208	12	is	be	AUX
american_scientific_journal-1367	208	13	fp	fp	ADJ
american_scientific_journal-1367	208	14	-	-	PUNCT
american_scientific_journal-1367	208	15	injective	injective	ADJ
american_scientific_journal-1367	208	16	.	.	PUNCT
american_scientific_journal-1367	209	1	(	(	PUNCT
american_scientific_journal-1367	209	2	2	2	X
american_scientific_journal-1367	209	3	)	)	PUNCT
american_scientific_journal-1367	209	4	⇒	⇒	NOUN
american_scientific_journal-1367	209	5	(	(	PUNCT
american_scientific_journal-1367	209	6	5	5	NUM
american_scientific_journal-1367	209	7	)	)	PUNCT
american_scientific_journal-1367	209	8	.	.	PUNCT
american_scientific_journal-1367	210	1	let	let	VERB
american_scientific_journal-1367	210	2	m	m	PRON
american_scientific_journal-1367	210	3	be	be	AUX
american_scientific_journal-1367	210	4	an	an	DET
american_scientific_journal-1367	210	5	fp	fp	ADJ
american_scientific_journal-1367	210	6	-	-	PUNCT
american_scientific_journal-1367	210	7	projective	projective	NOUN
american_scientific_journal-1367	210	8	left	leave	VERB
american_scientific_journal-1367	210	9	r	r	NOUN
american_scientific_journal-1367	210	10	-	-	PUNCT
american_scientific_journal-1367	210	11	module	module	NOUN
american_scientific_journal-1367	210	12	and	and	CCONJ
american_scientific_journal-1367	210	13	n	n	DET
american_scientific_journal-1367	210	14	any	any	DET
american_scientific_journal-1367	210	15	fp	fp	ADJ
american_scientific_journal-1367	210	16	-	-	PUNCT
american_scientific_journal-1367	210	17	injective	injective	ADJ
american_scientific_journal-1367	210	18	left	leave	VERB
american_scientific_journal-1367	210	19	r	r	NOUN
american_scientific_journal-1367	210	20	-	-	PUNCT
american_scientific_journal-1367	210	21	module	module	NOUN
american_scientific_journal-1367	210	22	.	.	PUNCT
american_scientific_journal-1367	211	1	since	since	SCONJ
american_scientific_journal-1367	211	2	n	n	NUM
american_scientific_journal-1367	211	3	is	be	AUX
american_scientific_journal-1367	211	4	fp138	fp138	PROPN
american_scientific_journal-1367	211	5	american	american	PROPN
american_scientific_journal-1367	211	6	scientific	scientific	ADJ
american_scientific_journal-1367	211	7	research	research	PROPN
american_scientific_journal-1367	211	8	journal	journal	NOUN
american_scientific_journal-1367	211	9	for	for	ADP
american_scientific_journal-1367	211	10	engineering	engineering	NOUN
american_scientific_journal-1367	211	11	,	,	PUNCT
american_scientific_journal-1367	211	12	technology	technology	NOUN
american_scientific_journal-1367	211	13	,	,	PUNCT
american_scientific_journal-1367	211	14	and	and	CCONJ
american_scientific_journal-1367	211	15	sciences	science	NOUN
american_scientific_journal-1367	211	16	(	(	PUNCT
american_scientific_journal-1367	211	17	asrjets	asrjet	NOUN
american_scientific_journal-1367	211	18	)	)	PUNCT
american_scientific_journal-1367	211	19	(	(	PUNCT
american_scientific_journal-1367	211	20	2016	2016	NUM
american_scientific_journal-1367	211	21	)	)	PUNCT
american_scientific_journal-1367	211	22	volume	volume	NOUN
american_scientific_journal-1367	211	23	17	17	NUM
american_scientific_journal-1367	211	24	,	,	PUNCT
american_scientific_journal-1367	211	25	no	no	DET
american_scientific_journal-1367	211	26	1	1	NUM
american_scientific_journal-1367	211	27	,	,	PUNCT
american_scientific_journal-1367	211	28	pp	pp	ADV
american_scientific_journal-1367	211	29	132	132	NUM
american_scientific_journal-1367	211	30	-	-	SYM
american_scientific_journal-1367	211	31	143	143	NUM
american_scientific_journal-1367	211	32	injective	injective	ADJ
american_scientific_journal-1367	211	33	by	by	ADP
american_scientific_journal-1367	211	34	(	(	PUNCT
american_scientific_journal-1367	211	35	2	2	NUM
american_scientific_journal-1367	211	36	)	)	PUNCT
american_scientific_journal-1367	211	37	,	,	PUNCT
american_scientific_journal-1367	211	38	ext1(m	ext1(m	NUM
american_scientific_journal-1367	211	39	,	,	PUNCT
american_scientific_journal-1367	211	40	n	n	CCONJ
american_scientific_journal-1367	211	41	)	)	PUNCT
american_scientific_journal-1367	211	42	=	=	SYM
american_scientific_journal-1367	211	43	0	0	X
american_scientific_journal-1367	211	44	.	.	PUNCT
american_scientific_journal-1367	212	1	thus	thus	ADV
american_scientific_journal-1367	212	2	m	m	PROPN
american_scientific_journal-1367	212	3	is	be	AUX
american_scientific_journal-1367	212	4	fp	fp	NOUN
american_scientific_journal-1367	212	5	-	-	PUNCT
american_scientific_journal-1367	212	6	projective	projective	ADJ
american_scientific_journal-1367	212	7	.	.	PUNCT
american_scientific_journal-1367	213	1	(	(	PUNCT
american_scientific_journal-1367	213	2	3	3	X
american_scientific_journal-1367	213	3	)	)	PUNCT
american_scientific_journal-1367	213	4	⇒	⇒	NOUN
american_scientific_journal-1367	213	5	(	(	PUNCT
american_scientific_journal-1367	213	6	7	7	NUM
american_scientific_journal-1367	213	7	)	)	PUNCT
american_scientific_journal-1367	213	8	.	.	PUNCT
american_scientific_journal-1367	214	1	let	let	VERB
american_scientific_journal-1367	214	2	m	m	PRON
american_scientific_journal-1367	214	3	be	be	AUX
american_scientific_journal-1367	214	4	an	an	DET
american_scientific_journal-1367	214	5	f	f	NOUN
american_scientific_journal-1367	214	6	-	-	PUNCT
american_scientific_journal-1367	214	7	projective	projective	NOUN
american_scientific_journal-1367	214	8	left	leave	VERB
american_scientific_journal-1367	214	9	r	r	NOUN
american_scientific_journal-1367	214	10	-	-	PUNCT
american_scientific_journal-1367	214	11	module	module	NOUN
american_scientific_journal-1367	214	12	and	and	CCONJ
american_scientific_journal-1367	214	13	n	n	DET
american_scientific_journal-1367	214	14	any	any	DET
american_scientific_journal-1367	214	15	fp	fp	ADJ
american_scientific_journal-1367	214	16	-	-	PUNCT
american_scientific_journal-1367	214	17	injective	injective	ADJ
american_scientific_journal-1367	214	18	left	leave	VERB
american_scientific_journal-1367	214	19	r	r	NOUN
american_scientific_journal-1367	214	20	-	-	PUNCT
american_scientific_journal-1367	214	21	module	module	NOUN
american_scientific_journal-1367	214	22	.	.	PUNCT
american_scientific_journal-1367	215	1	since	since	SCONJ
american_scientific_journal-1367	215	2	n	n	NUM
american_scientific_journal-1367	215	3	is	be	AUX
american_scientific_journal-1367	215	4	f	f	X
american_scientific_journal-1367	215	5	-	-	PUNCT
american_scientific_journal-1367	215	6	injective	injective	ADJ
american_scientific_journal-1367	215	7	by	by	ADP
american_scientific_journal-1367	215	8	(	(	PUNCT
american_scientific_journal-1367	215	9	3	3	NUM
american_scientific_journal-1367	215	10	)	)	PUNCT
american_scientific_journal-1367	215	11	,	,	PUNCT
american_scientific_journal-1367	215	12	ext1(m	ext1(m	NUM
american_scientific_journal-1367	215	13	,	,	PUNCT
american_scientific_journal-1367	215	14	n	n	CCONJ
american_scientific_journal-1367	215	15	)	)	PUNCT
american_scientific_journal-1367	215	16	=	=	SYM
american_scientific_journal-1367	215	17	0	0	X
american_scientific_journal-1367	215	18	.	.	PUNCT
american_scientific_journal-1367	216	1	thus	thus	ADV
american_scientific_journal-1367	216	2	m	m	PROPN
american_scientific_journal-1367	216	3	is	be	AUX
american_scientific_journal-1367	216	4	fp	fp	NOUN
american_scientific_journal-1367	216	5	-	-	PUNCT
american_scientific_journal-1367	216	6	projective	projective	ADJ
american_scientific_journal-1367	216	7	.	.	PUNCT
american_scientific_journal-1367	217	1	(	(	PUNCT
american_scientific_journal-1367	217	2	7)⇒(8	7)⇒(8	NUM
american_scientific_journal-1367	217	3	)	)	PUNCT
american_scientific_journal-1367	217	4	since	since	SCONJ
american_scientific_journal-1367	217	5	r	r	NOUN
american_scientific_journal-1367	217	6	/	/	SYM
american_scientific_journal-1367	217	7	i	i	PRON
american_scientific_journal-1367	217	8	is	be	AUX
american_scientific_journal-1367	217	9	f	f	NOUN
american_scientific_journal-1367	217	10	-	-	PUNCT
american_scientific_journal-1367	217	11	projective	projective	NOUN
american_scientific_journal-1367	217	12	left	leave	VERB
american_scientific_journal-1367	217	13	r	r	NOUN
american_scientific_journal-1367	217	14	-	-	PUNCT
american_scientific_journal-1367	217	15	module	module	NOUN
american_scientific_journal-1367	217	16	for	for	ADP
american_scientific_journal-1367	217	17	any	any	DET
american_scientific_journal-1367	217	18	finitely	finitely	ADV
american_scientific_journal-1367	217	19	generated	generate	VERB
american_scientific_journal-1367	217	20	left	leave	VERB
american_scientific_journal-1367	217	21	ideal	ideal	NOUN
american_scientific_journal-1367	217	22	i	i	PRON
american_scientific_journal-1367	217	23	of	of	ADP
american_scientific_journal-1367	217	24	r.	r.	PROPN
american_scientific_journal-1367	217	25	(	(	PUNCT
american_scientific_journal-1367	217	26	8)	8)	NUM
american_scientific_journal-1367	217	27	⇒	⇒	NOUN
american_scientific_journal-1367	217	28	(	(	PUNCT
american_scientific_journal-1367	217	29	3	3	NUM
american_scientific_journal-1367	217	30	)	)	PUNCT
american_scientific_journal-1367	217	31	.	.	PUNCT
american_scientific_journal-1367	218	1	let	let	VERB
american_scientific_journal-1367	218	2	m	m	PRON
american_scientific_journal-1367	218	3	be	be	AUX
american_scientific_journal-1367	218	4	an	an	DET
american_scientific_journal-1367	218	5	fp	fp	ADJ
american_scientific_journal-1367	218	6	-	-	PUNCT
american_scientific_journal-1367	218	7	injective	injective	ADJ
american_scientific_journal-1367	218	8	left	leave	VERB
american_scientific_journal-1367	218	9	r	r	NOUN
american_scientific_journal-1367	218	10	-	-	PUNCT
american_scientific_journal-1367	218	11	module	module	NOUN
american_scientific_journal-1367	218	12	and	and	CCONJ
american_scientific_journal-1367	218	13	i	i	PRON
american_scientific_journal-1367	218	14	any	any	PRON
american_scientific_journal-1367	218	15	finitely	finitely	ADV
american_scientific_journal-1367	218	16	generated	generate	VERB
american_scientific_journal-1367	218	17	left	leave	VERB
american_scientific_journal-1367	218	18	ideal	ideal	NOUN
american_scientific_journal-1367	218	19	.	.	PUNCT
american_scientific_journal-1367	219	1	then	then	ADV
american_scientific_journal-1367	219	2	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	219	3	/	/	SYM
american_scientific_journal-1367	219	4	i	i	PROPN
american_scientific_journal-1367	219	5	,	,	PUNCT
american_scientific_journal-1367	219	6	m	m	PROPN
american_scientific_journal-1367	219	7	)	)	PUNCT
american_scientific_journal-1367	219	8	=	=	SYM
american_scientific_journal-1367	219	9	0	0	NUM
american_scientific_journal-1367	219	10	by	by	ADP
american_scientific_journal-1367	219	11	(	(	PUNCT
american_scientific_journal-1367	219	12	8)	8)	NUM
american_scientific_journal-1367	219	13	.	.	PUNCT
american_scientific_journal-1367	220	1	thus	thus	ADV
american_scientific_journal-1367	220	2	m	m	PROPN
american_scientific_journal-1367	220	3	is	be	AUX
american_scientific_journal-1367	220	4	f	f	X
american_scientific_journal-1367	220	5	-	-	PUNCT
american_scientific_journal-1367	220	6	injective	injective	ADJ
american_scientific_journal-1367	220	7	.	.	PUNCT
american_scientific_journal-1367	221	1	(	(	PUNCT
american_scientific_journal-1367	221	2	4	4	X
american_scientific_journal-1367	221	3	)	)	PUNCT
american_scientific_journal-1367	221	4	⇒	⇒	NOUN
american_scientific_journal-1367	221	5	(	(	PUNCT
american_scientific_journal-1367	221	6	9	9	NUM
american_scientific_journal-1367	221	7	)	)	PUNCT
american_scientific_journal-1367	221	8	.	.	PUNCT
american_scientific_journal-1367	222	1	let	let	VERB
american_scientific_journal-1367	222	2	m	m	PRON
american_scientific_journal-1367	222	3	be	be	AUX
american_scientific_journal-1367	222	4	a	a	DET
american_scientific_journal-1367	222	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	222	6	right	right	ADJ
american_scientific_journal-1367	222	7	r	r	NOUN
american_scientific_journal-1367	222	8	-	-	PUNCT
american_scientific_journal-1367	222	9	module	module	NOUN
american_scientific_journal-1367	222	10	and	and	CCONJ
american_scientific_journal-1367	222	11	n	n	DET
american_scientific_journal-1367	222	12	any	any	DET
american_scientific_journal-1367	222	13	fp	fp	ADJ
american_scientific_journal-1367	222	14	-	-	PUNCT
american_scientific_journal-1367	222	15	flat	flat	ADJ
american_scientific_journal-1367	222	16	right	right	ADJ
american_scientific_journal-1367	222	17	r	r	NOUN
american_scientific_journal-1367	222	18	-	-	NOUN
american_scientific_journal-1367	222	19	module	module	NOUN
american_scientific_journal-1367	222	20	.	.	PUNCT
american_scientific_journal-1367	223	1	since	since	SCONJ
american_scientific_journal-1367	223	2	n	n	NUM
american_scientific_journal-1367	223	3	is	be	AUX
american_scientific_journal-1367	223	4	flat	flat	ADJ
american_scientific_journal-1367	223	5	by	by	ADP
american_scientific_journal-1367	223	6	(	(	PUNCT
american_scientific_journal-1367	223	7	4	4	NUM
american_scientific_journal-1367	223	8	)	)	PUNCT
american_scientific_journal-1367	223	9	,	,	PUNCT
american_scientific_journal-1367	223	10	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	223	11	,	,	PUNCT
american_scientific_journal-1367	223	12	m	m	NOUN
american_scientific_journal-1367	223	13	)	)	PUNCT
american_scientific_journal-1367	223	14	=	=	SYM
american_scientific_journal-1367	224	1	0	0	X
american_scientific_journal-1367	224	2	.	.	PUNCT
american_scientific_journal-1367	225	1	so	so	ADV
american_scientific_journal-1367	225	2	m	m	PROPN
american_scientific_journal-1367	225	3	is	be	AUX
american_scientific_journal-1367	225	4	fp	fp	ADJ
american_scientific_journal-1367	225	5	-	-	PUNCT
american_scientific_journal-1367	225	6	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	225	7	.	.	PUNCT
american_scientific_journal-1367	226	1	(	(	PUNCT
american_scientific_journal-1367	226	2	9	9	X
american_scientific_journal-1367	226	3	)	)	PUNCT
american_scientific_journal-1367	226	4	⇒	⇒	NOUN
american_scientific_journal-1367	226	5	(	(	PUNCT
american_scientific_journal-1367	226	6	4	4	X
american_scientific_journal-1367	226	7	)	)	PUNCT
american_scientific_journal-1367	226	8	is	be	AUX
american_scientific_journal-1367	226	9	similar	similar	ADJ
american_scientific_journal-1367	226	10	to	to	ADP
american_scientific_journal-1367	226	11	(	(	PUNCT
american_scientific_journal-1367	226	12	4	4	NUM
american_scientific_journal-1367	226	13	)	)	PUNCT
american_scientific_journal-1367	226	14	⇒	⇒	NOUN
american_scientific_journal-1367	226	15	(	(	PUNCT
american_scientific_journal-1367	226	16	9	9	NUM
american_scientific_journal-1367	226	17	)	)	PUNCT
american_scientific_journal-1367	226	18	.	.	PUNCT
american_scientific_journal-1367	227	1	□	□	PUNCT
american_scientific_journal-1367	227	2	recall	recall	VERB
american_scientific_journal-1367	227	3	that	that	SCONJ
american_scientific_journal-1367	227	4	a	a	DET
american_scientific_journal-1367	227	5	ring	ring	NOUN
american_scientific_journal-1367	227	6	r	r	NOUN
american_scientific_journal-1367	227	7	is	be	AUX
american_scientific_journal-1367	227	8	called	call	VERB
american_scientific_journal-1367	227	9	right	right	ADV
american_scientific_journal-1367	227	10	perfect	perfect	ADJ
american_scientific_journal-1367	227	11	if	if	SCONJ
american_scientific_journal-1367	227	12	every	every	DET
american_scientific_journal-1367	227	13	left	left	ADJ
american_scientific_journal-1367	227	14	r	r	NOUN
american_scientific_journal-1367	227	15	-	-	PUNCT
american_scientific_journal-1367	227	16	module	module	NOUN
american_scientific_journal-1367	227	17	has	have	VERB
american_scientific_journal-1367	227	18	a	a	DET
american_scientific_journal-1367	227	19	projective	projective	ADJ
american_scientific_journal-1367	227	20	cover	cover	NOUN
american_scientific_journal-1367	227	21	[	[	X
american_scientific_journal-1367	227	22	14	14	NUM
american_scientific_journal-1367	227	23	]	]	PUNCT
american_scientific_journal-1367	227	24	.	.	PUNCT
american_scientific_journal-1367	228	1	a	a	DET
american_scientific_journal-1367	228	2	classical	classical	ADJ
american_scientific_journal-1367	228	3	theorem	theorem	NOUN
american_scientific_journal-1367	228	4	of	of	ADP
american_scientific_journal-1367	228	5	bass	bass	NOUN
american_scientific_journal-1367	228	6	states	state	NOUN
american_scientific_journal-1367	228	7	that	that	SCONJ
american_scientific_journal-1367	228	8	r	r	NOUN
american_scientific_journal-1367	228	9	is	be	AUX
american_scientific_journal-1367	228	10	right	right	ADV
american_scientific_journal-1367	228	11	perfect	perfect	ADJ
american_scientific_journal-1367	228	12	if	if	SCONJ
american_scientific_journal-1367	228	13	and	and	CCONJ
american_scientific_journal-1367	228	14	only	only	ADV
american_scientific_journal-1367	228	15	if	if	SCONJ
american_scientific_journal-1367	228	16	every	every	DET
american_scientific_journal-1367	228	17	flat	flat	ADJ
american_scientific_journal-1367	228	18	right	right	ADJ
american_scientific_journal-1367	228	19	r	r	NOUN
american_scientific_journal-1367	228	20	-	-	PUNCT
american_scientific_journal-1367	228	21	module	module	NOUN
american_scientific_journal-1367	228	22	is	be	AUX
american_scientific_journal-1367	228	23	projective	projective	ADJ
american_scientific_journal-1367	229	1	[	[	X
american_scientific_journal-1367	229	2	15	15	NUM
american_scientific_journal-1367	229	3	,	,	PUNCT
american_scientific_journal-1367	229	4	theorem	theorem	NOUN
american_scientific_journal-1367	229	5	and	and	CCONJ
american_scientific_journal-1367	229	6	definition	definition	NOUN
american_scientific_journal-1367	229	7	2.1	2.1	NUM
american_scientific_journal-1367	229	8	]	]	PUNCT
american_scientific_journal-1367	229	9	.	.	PUNCT
american_scientific_journal-1367	230	1	using	use	VERB
american_scientific_journal-1367	230	2	this	this	DET
american_scientific_journal-1367	230	3	fact	fact	NOUN
american_scientific_journal-1367	230	4	with	with	ADP
american_scientific_journal-1367	230	5	the	the	DET
american_scientific_journal-1367	230	6	theorem	theorem	NOUN
american_scientific_journal-1367	230	7	3.2	3.2	NUM
american_scientific_journal-1367	230	8	,	,	PUNCT
american_scientific_journal-1367	230	9	we	we	PRON
american_scientific_journal-1367	230	10	get	get	VERB
american_scientific_journal-1367	230	11	the	the	DET
american_scientific_journal-1367	230	12	following	follow	VERB
american_scientific_journal-1367	230	13	characterizations	characterization	NOUN
american_scientific_journal-1367	230	14	of	of	ADP
american_scientific_journal-1367	230	15	left	left	ADJ
american_scientific_journal-1367	230	16	coherent	coherent	ADJ
american_scientific_journal-1367	230	17	and	and	CCONJ
american_scientific_journal-1367	230	18	right	right	ADJ
american_scientific_journal-1367	230	19	perfect	perfect	ADJ
american_scientific_journal-1367	230	20	ring	ring	NOUN
american_scientific_journal-1367	230	21	in	in	ADP
american_scientific_journal-1367	230	22	terms	term	NOUN
american_scientific_journal-1367	230	23	of	of	ADP
american_scientific_journal-1367	230	24	fp	fp	ADJ
american_scientific_journal-1367	230	25	-	-	PUNCT
american_scientific_journal-1367	230	26	injective	injective	ADJ
american_scientific_journal-1367	230	27	and	and	CCONJ
american_scientific_journal-1367	230	28	fp	fp	ADJ
american_scientific_journal-1367	230	29	-	-	PUNCT
american_scientific_journal-1367	230	30	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	230	31	modules	module	NOUN
american_scientific_journal-1367	230	32	.	.	PUNCT
american_scientific_journal-1367	231	1	3.3	3.3	NUM
american_scientific_journal-1367	231	2	theorem	theorem	VERB
american_scientific_journal-1367	231	3	the	the	DET
american_scientific_journal-1367	231	4	following	following	ADJ
american_scientific_journal-1367	231	5	statements	statement	NOUN
american_scientific_journal-1367	231	6	are	be	AUX
american_scientific_journal-1367	231	7	equivalent	equivalent	ADJ
american_scientific_journal-1367	231	8	for	for	ADP
american_scientific_journal-1367	231	9	a	a	DET
american_scientific_journal-1367	231	10	ring	ring	NOUN
american_scientific_journal-1367	231	11	r.	r.	NOUN
american_scientific_journal-1367	231	12	(	(	PUNCT
american_scientific_journal-1367	231	13	1	1	X
american_scientific_journal-1367	231	14	)	)	PUNCT
american_scientific_journal-1367	231	15	r	r	NOUN
american_scientific_journal-1367	231	16	is	be	AUX
american_scientific_journal-1367	231	17	left	leave	VERB
american_scientific_journal-1367	231	18	coherent	coherent	ADJ
american_scientific_journal-1367	231	19	and	and	CCONJ
american_scientific_journal-1367	231	20	right	right	ADV
american_scientific_journal-1367	231	21	perfect	perfect	ADJ
american_scientific_journal-1367	231	22	.	.	PUNCT
american_scientific_journal-1367	232	1	(	(	PUNCT
american_scientific_journal-1367	232	2	2	2	X
american_scientific_journal-1367	232	3	)	)	PUNCT
american_scientific_journal-1367	232	4	every	every	DET
american_scientific_journal-1367	232	5	right	right	ADJ
american_scientific_journal-1367	232	6	r	r	NOUN
american_scientific_journal-1367	232	7	-	-	PUNCT
american_scientific_journal-1367	232	8	module	module	NOUN
american_scientific_journal-1367	232	9	m	m	NOUN
american_scientific_journal-1367	232	10	is	be	AUX
american_scientific_journal-1367	232	11	fp	fp	NOUN
american_scientific_journal-1367	232	12	-	-	PUNCT
american_scientific_journal-1367	232	13	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	232	14	.	.	PUNCT
american_scientific_journal-1367	233	1	(	(	PUNCT
american_scientific_journal-1367	233	2	3	3	X
american_scientific_journal-1367	233	3	)	)	PUNCT
american_scientific_journal-1367	233	4	(	(	PUNCT
american_scientific_journal-1367	233	5	fp	fp	PROPN
american_scientific_journal-1367	233	6	-	-	PUNCT
american_scientific_journal-1367	233	7	fl	fl	PROPN
american_scientific_journal-1367	233	8	,	,	PUNCT
american_scientific_journal-1367	233	9	fp	fp	ADJ
american_scientific_journal-1367	233	10	-	-	PUNCT
american_scientific_journal-1367	233	11	cot	cot	NOUN
american_scientific_journal-1367	233	12	)	)	PUNCT
american_scientific_journal-1367	233	13	is	be	AUX
american_scientific_journal-1367	233	14	hereditary	hereditary	ADJ
american_scientific_journal-1367	233	15	and	and	CCONJ
american_scientific_journal-1367	233	16	every	every	DET
american_scientific_journal-1367	233	17	fp	fp	ADJ
american_scientific_journal-1367	233	18	-	-	PUNCT
american_scientific_journal-1367	233	19	flat	flat	ADJ
american_scientific_journal-1367	233	20	right	right	ADJ
american_scientific_journal-1367	233	21	r	r	NOUN
american_scientific_journal-1367	233	22	-	-	PUNCT
american_scientific_journal-1367	233	23	module	module	NOUN
american_scientific_journal-1367	233	24	is	be	AUX
american_scientific_journal-1367	233	25	fp	fp	ADJ
american_scientific_journal-1367	233	26	-	-	PUNCT
american_scientific_journal-1367	233	27	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	233	28	.	.	PUNCT
american_scientific_journal-1367	234	1	proof	proof	NOUN
american_scientific_journal-1367	234	2	.	.	PUNCT
american_scientific_journal-1367	235	1	(	(	PUNCT
american_scientific_journal-1367	235	2	1	1	X
american_scientific_journal-1367	235	3	)	)	PUNCT
american_scientific_journal-1367	235	4	⇒	⇒	NOUN
american_scientific_journal-1367	235	5	(	(	PUNCT
american_scientific_journal-1367	235	6	2	2	NUM
american_scientific_journal-1367	235	7	)	)	PUNCT
american_scientific_journal-1367	235	8	.	.	PUNCT
american_scientific_journal-1367	236	1	let	let	VERB
american_scientific_journal-1367	236	2	m	m	PRON
american_scientific_journal-1367	236	3	be	be	AUX
american_scientific_journal-1367	236	4	a	a	DET
american_scientific_journal-1367	236	5	right	right	ADJ
american_scientific_journal-1367	236	6	r	r	NOUN
american_scientific_journal-1367	236	7	-	-	PUNCT
american_scientific_journal-1367	236	8	module	module	NOUN
american_scientific_journal-1367	236	9	and	and	CCONJ
american_scientific_journal-1367	236	10	n	n	DET
american_scientific_journal-1367	236	11	any	any	DET
american_scientific_journal-1367	236	12	fp	fp	ADJ
american_scientific_journal-1367	236	13	-	-	PUNCT
american_scientific_journal-1367	236	14	flat	flat	ADJ
american_scientific_journal-1367	236	15	right	right	ADJ
american_scientific_journal-1367	236	16	r	r	NOUN
american_scientific_journal-1367	236	17	-	-	NOUN
american_scientific_journal-1367	236	18	module	module	NOUN
american_scientific_journal-1367	236	19	.	.	PUNCT
american_scientific_journal-1367	237	1	since	since	SCONJ
american_scientific_journal-1367	237	2	r	r	NOUN
american_scientific_journal-1367	237	3	is	be	AUX
american_scientific_journal-1367	237	4	left	leave	VERB
american_scientific_journal-1367	237	5	coherent	coherent	ADJ
american_scientific_journal-1367	237	6	,	,	PUNCT
american_scientific_journal-1367	237	7	n	n	PRON
american_scientific_journal-1367	237	8	is	be	AUX
american_scientific_journal-1367	237	9	flat	flat	ADJ
american_scientific_journal-1367	237	10	right	right	ADJ
american_scientific_journal-1367	237	11	r	r	NOUN
american_scientific_journal-1367	237	12	-	-	PUNCT
american_scientific_journal-1367	237	13	module	module	NOUN
american_scientific_journal-1367	237	14	by	by	ADP
american_scientific_journal-1367	237	15	[	[	X
american_scientific_journal-1367	237	16	3	3	NUM
american_scientific_journal-1367	237	17	,	,	PUNCT
american_scientific_journal-1367	237	18	theorem	theorem	VERB
american_scientific_journal-1367	237	19	2.8	2.8	NUM
american_scientific_journal-1367	237	20	(	(	PUNCT
american_scientific_journal-1367	237	21	4	4	NUM
american_scientific_journal-1367	237	22	)	)	PUNCT
american_scientific_journal-1367	237	23	]	]	PUNCT
american_scientific_journal-1367	237	24	.	.	PUNCT
american_scientific_journal-1367	238	1	since	since	SCONJ
american_scientific_journal-1367	238	2	r	r	NOUN
american_scientific_journal-1367	238	3	is	be	AUX
american_scientific_journal-1367	238	4	right	right	ADV
american_scientific_journal-1367	238	5	perfect	perfect	ADJ
american_scientific_journal-1367	238	6	,	,	PUNCT
american_scientific_journal-1367	238	7	n	n	X
american_scientific_journal-1367	238	8	is	be	AUX
american_scientific_journal-1367	238	9	projective	projective	ADJ
american_scientific_journal-1367	238	10	right	right	ADJ
american_scientific_journal-1367	238	11	r	r	NOUN
american_scientific_journal-1367	238	12	-	-	PUNCT
american_scientific_journal-1367	238	13	module	module	NOUN
american_scientific_journal-1367	238	14	,	,	PUNCT
american_scientific_journal-1367	238	15	so	so	SCONJ
american_scientific_journal-1367	238	16	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	238	17	,	,	PUNCT
american_scientific_journal-1367	238	18	m	m	NOUN
american_scientific_journal-1367	238	19	)	)	PUNCT
american_scientific_journal-1367	239	1	=	=	SYM
american_scientific_journal-1367	239	2	0	0	X
american_scientific_journal-1367	239	3	.	.	PUNCT
american_scientific_journal-1367	240	1	hence	hence	ADV
american_scientific_journal-1367	240	2	m	m	PROPN
american_scientific_journal-1367	240	3	is	be	AUX
american_scientific_journal-1367	240	4	fp	fp	NOUN
american_scientific_journal-1367	240	5	-	-	PUNCT
american_scientific_journal-1367	240	6	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	240	7	.	.	PUNCT
american_scientific_journal-1367	241	1	(	(	PUNCT
american_scientific_journal-1367	241	2	2	2	X
american_scientific_journal-1367	241	3	)	)	PUNCT
american_scientific_journal-1367	241	4	⇒	⇒	NOUN
american_scientific_journal-1367	241	5	(	(	PUNCT
american_scientific_journal-1367	241	6	1	1	NUM
american_scientific_journal-1367	241	7	)	)	PUNCT
american_scientific_journal-1367	241	8	.	.	PUNCT
american_scientific_journal-1367	242	1	since	since	SCONJ
american_scientific_journal-1367	242	2	every	every	DET
american_scientific_journal-1367	242	3	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	242	4	right	right	ADJ
american_scientific_journal-1367	242	5	r	r	NOUN
american_scientific_journal-1367	242	6	-	-	PUNCT
american_scientific_journal-1367	242	7	module	module	NOUN
american_scientific_journal-1367	242	8	is	be	AUX
american_scientific_journal-1367	242	9	fp	fp	NOUN
american_scientific_journal-1367	242	10	-	-	PUNCT
american_scientific_journal-1367	242	11	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	242	12	by	by	ADP
american_scientific_journal-1367	242	13	(	(	PUNCT
american_scientific_journal-1367	242	14	2	2	NUM
american_scientific_journal-1367	242	15	)	)	PUNCT
american_scientific_journal-1367	242	16	,	,	PUNCT
american_scientific_journal-1367	242	17	r	r	NOUN
american_scientific_journal-1367	242	18	is	be	AUX
american_scientific_journal-1367	242	19	left	leave	VERB
american_scientific_journal-1367	242	20	coherent	coherent	ADJ
american_scientific_journal-1367	242	21	by	by	ADP
american_scientific_journal-1367	242	22	theorem	theorem	ADJ
american_scientific_journal-1367	242	23	3.2	3.2	NUM
american_scientific_journal-1367	242	24	(	(	PUNCT
american_scientific_journal-1367	242	25	9	9	NUM
american_scientific_journal-1367	242	26	)	)	PUNCT
american_scientific_journal-1367	242	27	.	.	PUNCT
american_scientific_journal-1367	243	1	on	on	ADP
american_scientific_journal-1367	243	2	the	the	DET
american_scientific_journal-1367	243	3	other	other	ADJ
american_scientific_journal-1367	243	4	hand	hand	NOUN
american_scientific_journal-1367	243	5	,	,	PUNCT
american_scientific_journal-1367	243	6	if	if	SCONJ
american_scientific_journal-1367	243	7	n	n	PRON
american_scientific_journal-1367	243	8	is	be	AUX
american_scientific_journal-1367	243	9	a	a	DET
american_scientific_journal-1367	243	10	flat	flat	ADJ
american_scientific_journal-1367	243	11	right	right	ADJ
american_scientific_journal-1367	243	12	r	r	NOUN
american_scientific_journal-1367	243	13	-	-	NOUN
american_scientific_journal-1367	243	14	module	module	NOUN
american_scientific_journal-1367	243	15	,	,	PUNCT
american_scientific_journal-1367	243	16	then	then	ADV
american_scientific_journal-1367	243	17	for	for	ADP
american_scientific_journal-1367	243	18	any	any	DET
american_scientific_journal-1367	243	19	right	right	ADJ
american_scientific_journal-1367	243	20	r	r	NOUN
american_scientific_journal-1367	243	21	-	-	PUNCT
american_scientific_journal-1367	243	22	module	module	NOUN
american_scientific_journal-1367	243	23	m	m	NOUN
american_scientific_journal-1367	243	24	,	,	PUNCT
american_scientific_journal-1367	243	25	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	243	26	,	,	PUNCT
american_scientific_journal-1367	243	27	m	m	NOUN
american_scientific_journal-1367	243	28	)	)	PUNCT
american_scientific_journal-1367	243	29	=	=	SYM
american_scientific_journal-1367	243	30	0	0	NUM
american_scientific_journal-1367	243	31	by	by	ADP
american_scientific_journal-1367	243	32	(	(	PUNCT
american_scientific_journal-1367	243	33	2	2	NUM
american_scientific_journal-1367	243	34	)	)	PUNCT
american_scientific_journal-1367	243	35	.	.	PUNCT
american_scientific_journal-1367	244	1	so	so	ADV
american_scientific_journal-1367	244	2	n	n	ADV
american_scientific_journal-1367	244	3	is	be	AUX
american_scientific_journal-1367	244	4	projective	projective	ADJ
american_scientific_journal-1367	244	5	right	right	ADJ
american_scientific_journal-1367	244	6	r	r	NOUN
american_scientific_journal-1367	244	7	-	-	PUNCT
american_scientific_journal-1367	244	8	module	module	NOUN
american_scientific_journal-1367	245	1	and	and	CCONJ
american_scientific_journal-1367	245	2	hence	hence	ADV
american_scientific_journal-1367	245	3	r	r	NOUN
american_scientific_journal-1367	245	4	is	be	AUX
american_scientific_journal-1367	245	5	right	right	ADV
american_scientific_journal-1367	245	6	perfect	perfect	ADJ
american_scientific_journal-1367	245	7	.	.	PUNCT
american_scientific_journal-1367	246	1	(	(	PUNCT
american_scientific_journal-1367	246	2	2	2	X
american_scientific_journal-1367	246	3	)	)	PUNCT
american_scientific_journal-1367	246	4	⇒	⇒	NOUN
american_scientific_journal-1367	246	5	(	(	PUNCT
american_scientific_journal-1367	246	6	3	3	X
american_scientific_journal-1367	246	7	)	)	PUNCT
american_scientific_journal-1367	246	8	is	be	AUX
american_scientific_journal-1367	246	9	clear	clear	ADJ
american_scientific_journal-1367	246	10	.	.	PUNCT
american_scientific_journal-1367	247	1	(	(	PUNCT
american_scientific_journal-1367	247	2	3	3	X
american_scientific_journal-1367	247	3	)	)	PUNCT
american_scientific_journal-1367	247	4	⇒	⇒	NOUN
american_scientific_journal-1367	247	5	(	(	PUNCT
american_scientific_journal-1367	247	6	2	2	NUM
american_scientific_journal-1367	247	7	)	)	PUNCT
american_scientific_journal-1367	247	8	.	.	PUNCT
american_scientific_journal-1367	248	1	let	let	VERB
american_scientific_journal-1367	248	2	m	m	PRON
american_scientific_journal-1367	248	3	be	be	AUX
american_scientific_journal-1367	248	4	any	any	DET
american_scientific_journal-1367	248	5	right	right	ADJ
american_scientific_journal-1367	248	6	r	r	NOUN
american_scientific_journal-1367	248	7	-	-	NOUN
american_scientific_journal-1367	248	8	module	module	NOUN
american_scientific_journal-1367	248	9	.	.	PUNCT
american_scientific_journal-1367	249	1	since	since	SCONJ
american_scientific_journal-1367	249	2	(	(	PUNCT
american_scientific_journal-1367	249	3	fp	fp	PROPN
american_scientific_journal-1367	249	4	-	-	PUNCT
american_scientific_journal-1367	249	5	fl	fl	PROPN
american_scientific_journal-1367	249	6	,	,	PUNCT
american_scientific_journal-1367	249	7	fp	fp	ADJ
american_scientific_journal-1367	249	8	-	-	PUNCT
american_scientific_journal-1367	249	9	cot	cot	NOUN
american_scientific_journal-1367	249	10	)	)	PUNCT
american_scientific_journal-1367	249	11	is	be	AUX
american_scientific_journal-1367	249	12	a	a	DET
american_scientific_journal-1367	249	13	perfect	perfect	ADJ
american_scientific_journal-1367	249	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	249	15	theory	theory	NOUN
american_scientific_journal-1367	249	16	,	,	PUNCT
american_scientific_journal-1367	249	17	m	m	PROPN
american_scientific_journal-1367	249	18	has	have	VERB
american_scientific_journal-1367	249	19	an	an	DET
american_scientific_journal-1367	249	20	fp	fp	ADJ
american_scientific_journal-1367	249	21	-	-	PUNCT
american_scientific_journal-1367	249	22	flat	flat	ADJ
american_scientific_journal-1367	249	23	cover	cover	NOUN
american_scientific_journal-1367	249	24	by	by	ADP
american_scientific_journal-1367	249	25	theorem	theorem	NOUN
american_scientific_journal-1367	249	26	2.9	2.9	NUM
american_scientific_journal-1367	249	27	,	,	PUNCT
american_scientific_journal-1367	249	28	i.e.	i.e.	X
american_scientific_journal-1367	249	29	there	there	PRON
american_scientific_journal-1367	249	30	exists	exist	VERB
american_scientific_journal-1367	249	31	an	an	DET
american_scientific_journal-1367	249	32	exact	exact	ADJ
american_scientific_journal-1367	249	33	sequence	sequence	NOUN
american_scientific_journal-1367	249	34	0	0	NUM
american_scientific_journal-1367	249	35	→	→	SYM
american_scientific_journal-1367	249	36	l	l	X
american_scientific_journal-1367	249	37	→	→	SYM
american_scientific_journal-1367	249	38	f	f	X
american_scientific_journal-1367	249	39	→	→	SYM
american_scientific_journal-1367	249	40	m	m	PROPN
american_scientific_journal-1367	249	41	→	→	SYM
american_scientific_journal-1367	249	42	0	0	NUM
american_scientific_journal-1367	249	43	with	with	ADP
american_scientific_journal-1367	249	44	f	f	PROPN
american_scientific_journal-1367	249	45	fp	fp	PROPN
american_scientific_journal-1367	249	46	-	-	PUNCT
american_scientific_journal-1367	249	47	flat	flat	ADJ
american_scientific_journal-1367	249	48	right	right	ADJ
american_scientific_journal-1367	249	49	rmodule	rmodule	NOUN
american_scientific_journal-1367	249	50	and	and	CCONJ
american_scientific_journal-1367	249	51	l	l	NOUN
american_scientific_journal-1367	249	52	fp	fp	ADJ
american_scientific_journal-1367	249	53	-	-	PUNCT
american_scientific_journal-1367	249	54	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	249	55	right	right	ADJ
american_scientific_journal-1367	249	56	r	r	NOUN
american_scientific_journal-1367	249	57	-	-	NOUN
american_scientific_journal-1367	249	58	module	module	NOUN
american_scientific_journal-1367	249	59	.	.	PUNCT
american_scientific_journal-1367	250	1	by	by	ADP
american_scientific_journal-1367	250	2	(	(	PUNCT
american_scientific_journal-1367	250	3	3	3	X
american_scientific_journal-1367	250	4	)	)	PUNCT
american_scientific_journal-1367	250	5	f	f	PROPN
american_scientific_journal-1367	250	6	is	be	AUX
american_scientific_journal-1367	250	7	fp	fp	ADJ
american_scientific_journal-1367	250	8	-	-	PUNCT
american_scientific_journal-1367	250	9	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	250	10	right	right	ADJ
american_scientific_journal-1367	250	11	r	r	NOUN
american_scientific_journal-1367	250	12	-	-	NOUN
american_scientific_journal-1367	250	13	module	module	NOUN
american_scientific_journal-1367	250	14	,	,	PUNCT
american_scientific_journal-1367	250	15	and	and	CCONJ
american_scientific_journal-1367	250	16	so	so	ADV
american_scientific_journal-1367	250	17	m	m	NOUN
american_scientific_journal-1367	250	18	must	must	AUX
american_scientific_journal-1367	250	19	be	be	AUX
american_scientific_journal-1367	250	20	fpcotorsion	fpcotorsion	NOUN
american_scientific_journal-1367	250	21	.	.	PUNCT
american_scientific_journal-1367	251	1	thus	thus	ADV
american_scientific_journal-1367	251	2	(	(	PUNCT
american_scientific_journal-1367	251	3	2	2	X
american_scientific_journal-1367	251	4	)	)	PUNCT
american_scientific_journal-1367	251	5	holds	hold	NOUN
american_scientific_journal-1367	251	6	.	.	PUNCT
american_scientific_journal-1367	252	1	□	□	SYM
american_scientific_journal-1367	252	2	139	139	NUM
american_scientific_journal-1367	252	3	american	american	ADJ
american_scientific_journal-1367	252	4	scientific	scientific	ADJ
american_scientific_journal-1367	252	5	research	research	NOUN
american_scientific_journal-1367	252	6	journal	journal	NOUN
american_scientific_journal-1367	252	7	for	for	ADP
american_scientific_journal-1367	252	8	engineering	engineering	NOUN
american_scientific_journal-1367	252	9	,	,	PUNCT
american_scientific_journal-1367	252	10	technology	technology	NOUN
american_scientific_journal-1367	252	11	,	,	PUNCT
american_scientific_journal-1367	252	12	and	and	CCONJ
american_scientific_journal-1367	252	13	sciences	science	NOUN
american_scientific_journal-1367	252	14	(	(	PUNCT
american_scientific_journal-1367	252	15	asrjets	asrjet	NOUN
american_scientific_journal-1367	252	16	)	)	PUNCT
american_scientific_journal-1367	252	17	(	(	PUNCT
american_scientific_journal-1367	252	18	2016	2016	NUM
american_scientific_journal-1367	252	19	)	)	PUNCT
american_scientific_journal-1367	252	20	volume	volume	NOUN
american_scientific_journal-1367	252	21	17	17	NUM
american_scientific_journal-1367	252	22	,	,	PUNCT
american_scientific_journal-1367	252	23	no	no	DET
american_scientific_journal-1367	252	24	1	1	NUM
american_scientific_journal-1367	252	25	,	,	PUNCT
american_scientific_journal-1367	252	26	pp	pp	ADV
american_scientific_journal-1367	252	27	132	132	NUM
american_scientific_journal-1367	252	28	-	-	SYM
american_scientific_journal-1367	252	29	143	143	NUM
american_scientific_journal-1367	252	30	it	it	PRON
american_scientific_journal-1367	252	31	is	be	AUX
american_scientific_journal-1367	252	32	well	well	ADV
american_scientific_journal-1367	252	33	known	know	VERB
american_scientific_journal-1367	252	34	that	that	SCONJ
american_scientific_journal-1367	252	35	a	a	DET
american_scientific_journal-1367	252	36	ring	ring	NOUN
american_scientific_journal-1367	252	37	r	r	NOUN
american_scientific_journal-1367	252	38	is	be	AUX
american_scientific_journal-1367	252	39	a	a	DET
american_scientific_journal-1367	252	40	von	von	PROPN
american_scientific_journal-1367	252	41	neumann	neumann	PROPN
american_scientific_journal-1367	252	42	regular	regular	ADJ
american_scientific_journal-1367	252	43	ring	ring	NOUN
american_scientific_journal-1367	252	44	if	if	SCONJ
american_scientific_journal-1367	252	45	and	and	CCONJ
american_scientific_journal-1367	252	46	only	only	ADV
american_scientific_journal-1367	252	47	if	if	SCONJ
american_scientific_journal-1367	252	48	every	every	PRON
american_scientific_journal-1367	252	49	finitely	finitely	ADV
american_scientific_journal-1367	252	50	generated	generate	VERB
american_scientific_journal-1367	252	51	left	leave	VERB
american_scientific_journal-1367	252	52	ideal	ideal	NOUN
american_scientific_journal-1367	252	53	of	of	ADP
american_scientific_journal-1367	252	54	r	r	NOUN
american_scientific_journal-1367	252	55	is	be	AUX
american_scientific_journal-1367	252	56	a	a	DET
american_scientific_journal-1367	252	57	direct	direct	ADJ
american_scientific_journal-1367	252	58	summand	summand	NOUN
american_scientific_journal-1367	252	59	of	of	ADP
american_scientific_journal-1367	252	60	r.	r.	PROPN
american_scientific_journal-1367	252	61	regular	regular	PROPN
american_scientific_journal-1367	252	62	rings	ring	NOUN
american_scientific_journal-1367	252	63	and	and	CCONJ
american_scientific_journal-1367	252	64	their	their	PRON
american_scientific_journal-1367	252	65	generations	generation	NOUN
american_scientific_journal-1367	252	66	have	have	AUX
american_scientific_journal-1367	252	67	been	be	AUX
american_scientific_journal-1367	252	68	studied	study	VERB
american_scientific_journal-1367	252	69	and	and	CCONJ
american_scientific_journal-1367	252	70	characterized	characterize	VERB
american_scientific_journal-1367	252	71	by	by	ADP
american_scientific_journal-1367	252	72	many	many	ADJ
american_scientific_journal-1367	252	73	authors	author	NOUN
american_scientific_journal-1367	252	74	(	(	PUNCT
american_scientific_journal-1367	252	75	see	see	VERB
american_scientific_journal-1367	252	76	.	.	PUNCT
american_scientific_journal-1367	253	1	for	for	ADP
american_scientific_journal-1367	253	2	example	example	NOUN
american_scientific_journal-1367	253	3	[	[	X
american_scientific_journal-1367	253	4	3,5,6,8,16	3,5,6,8,16	NUM
american_scientific_journal-1367	253	5	]	]	PUNCT
american_scientific_journal-1367	253	6	)	)	PUNCT
american_scientific_journal-1367	253	7	.	.	PUNCT
american_scientific_journal-1367	254	1	following	follow	VERB
american_scientific_journal-1367	254	2	[	[	X
american_scientific_journal-1367	254	3	3	3	NUM
american_scientific_journal-1367	254	4	,	,	PUNCT
american_scientific_journal-1367	254	5	p.	p.	NOUN
american_scientific_journal-1367	254	6	124	124	NUM
american_scientific_journal-1367	254	7	]	]	PUNCT
american_scientific_journal-1367	254	8	,	,	PUNCT
american_scientific_journal-1367	254	9	we	we	PRON
american_scientific_journal-1367	254	10	call	call	VERB
american_scientific_journal-1367	254	11	a	a	DET
american_scientific_journal-1367	254	12	ring	ring	NOUN
american_scientific_journal-1367	254	13	r	r	NOUN
american_scientific_journal-1367	254	14	,	,	PUNCT
american_scientific_journal-1367	254	15	a	a	DET
american_scientific_journal-1367	254	16	left	left	ADJ
american_scientific_journal-1367	254	17	fp	fp	NOUN
american_scientific_journal-1367	254	18	-	-	ADJ
american_scientific_journal-1367	254	19	regular	regular	ADJ
american_scientific_journal-1367	254	20	(	(	PUNCT
american_scientific_journal-1367	254	21	or	or	CCONJ
american_scientific_journal-1367	254	22	left	leave	VERB
american_scientific_journal-1367	254	23	almost	almost	ADV
american_scientific_journal-1367	254	24	regular	regular	ADJ
american_scientific_journal-1367	254	25	)	)	PUNCT
american_scientific_journal-1367	254	26	,	,	PUNCT
american_scientific_journal-1367	254	27	if	if	SCONJ
american_scientific_journal-1367	254	28	every	every	DET
american_scientific_journal-1367	254	29	finitely	finitely	ADV
american_scientific_journal-1367	254	30	presented	present	VERB
american_scientific_journal-1367	254	31	left	leave	VERB
american_scientific_journal-1367	254	32	ideal	ideal	NOUN
american_scientific_journal-1367	254	33	of	of	ADP
american_scientific_journal-1367	254	34	r	r	NOUN
american_scientific_journal-1367	254	35	is	be	AUX
american_scientific_journal-1367	254	36	a	a	DET
american_scientific_journal-1367	254	37	direct	direct	ADJ
american_scientific_journal-1367	254	38	summand	summand	NOUN
american_scientific_journal-1367	254	39	of	of	ADP
american_scientific_journal-1367	254	40	r.	r.	PROPN
american_scientific_journal-1367	254	41	the	the	DET
american_scientific_journal-1367	254	42	right	right	ADJ
american_scientific_journal-1367	254	43	fp	fp	ADJ
american_scientific_journal-1367	254	44	-	-	ADJ
american_scientific_journal-1367	254	45	regular	regular	ADJ
american_scientific_journal-1367	254	46	ring	ring	NOUN
american_scientific_journal-1367	254	47	can	can	AUX
american_scientific_journal-1367	254	48	be	be	AUX
american_scientific_journal-1367	254	49	defined	define	VERB
american_scientific_journal-1367	254	50	similarly	similarly	ADV
american_scientific_journal-1367	254	51	.	.	PUNCT
american_scientific_journal-1367	255	1	next	next	ADV
american_scientific_journal-1367	255	2	,	,	PUNCT
american_scientific_journal-1367	255	3	we	we	PRON
american_scientific_journal-1367	255	4	give	give	VERB
american_scientific_journal-1367	255	5	some	some	DET
american_scientific_journal-1367	255	6	characterizations	characterization	NOUN
american_scientific_journal-1367	255	7	of	of	ADP
american_scientific_journal-1367	255	8	left	left	ADJ
american_scientific_journal-1367	255	9	fp	fp	ADJ
american_scientific_journal-1367	255	10	-	-	PUNCT
american_scientific_journal-1367	255	11	regular	regular	ADJ
american_scientific_journal-1367	255	12	rings	ring	NOUN
american_scientific_journal-1367	255	13	in	in	ADP
american_scientific_journal-1367	255	14	terms	term	NOUN
american_scientific_journal-1367	255	15	of	of	ADP
american_scientific_journal-1367	255	16	fp	fp	X
american_scientific_journal-1367	255	17	-	-	PUNCT
american_scientific_journal-1367	255	18	projective	projective	ADJ
american_scientific_journal-1367	255	19	and	and	CCONJ
american_scientific_journal-1367	255	20	fp	fp	ADJ
american_scientific_journal-1367	255	21	-	-	PUNCT
american_scientific_journal-1367	255	22	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	255	23	r	r	NOUN
american_scientific_journal-1367	255	24	-	-	PUNCT
american_scientific_journal-1367	255	25	modules	module	NOUN
american_scientific_journal-1367	255	26	.	.	PUNCT
american_scientific_journal-1367	256	1	3.4	3.4	NUM
american_scientific_journal-1367	256	2	theorem	theorem	NOUN
american_scientific_journal-1367	256	3	for	for	ADP
american_scientific_journal-1367	256	4	any	any	DET
american_scientific_journal-1367	256	5	ring	ring	NOUN
american_scientific_journal-1367	256	6	r	r	NOUN
american_scientific_journal-1367	256	7	,	,	PUNCT
american_scientific_journal-1367	256	8	the	the	DET
american_scientific_journal-1367	256	9	following	follow	VERB
american_scientific_journal-1367	256	10	statements	statement	NOUN
american_scientific_journal-1367	256	11	are	be	AUX
american_scientific_journal-1367	256	12	equivalent	equivalent	ADJ
american_scientific_journal-1367	256	13	.	.	PUNCT
american_scientific_journal-1367	257	1	(	(	PUNCT
american_scientific_journal-1367	257	2	1	1	X
american_scientific_journal-1367	257	3	)	)	PUNCT
american_scientific_journal-1367	257	4	r	r	NOUN
american_scientific_journal-1367	257	5	is	be	AUX
american_scientific_journal-1367	257	6	a	a	DET
american_scientific_journal-1367	257	7	left	left	ADJ
american_scientific_journal-1367	257	8	fp	fp	NOUN
american_scientific_journal-1367	257	9	-	-	PUNCT
american_scientific_journal-1367	257	10	regular	regular	ADJ
american_scientific_journal-1367	257	11	.	.	PUNCT
american_scientific_journal-1367	258	1	(	(	PUNCT
american_scientific_journal-1367	258	2	2	2	X
american_scientific_journal-1367	258	3	)	)	PUNCT
american_scientific_journal-1367	258	4	for	for	ADP
american_scientific_journal-1367	258	5	any	any	DET
american_scientific_journal-1367	258	6	finitely	finitely	ADV
american_scientific_journal-1367	258	7	presented	present	VERB
american_scientific_journal-1367	258	8	left	leave	VERB
american_scientific_journal-1367	258	9	ideal	ideal	PROPN
american_scientific_journal-1367	259	1	i	i	PRON
american_scientific_journal-1367	259	2	,	,	PUNCT
american_scientific_journal-1367	259	3	r	r	X
american_scientific_journal-1367	259	4	/	/	SYM
american_scientific_journal-1367	259	5	i	i	PRON
american_scientific_journal-1367	259	6	is	be	AUX
american_scientific_journal-1367	259	7	projective	projective	ADJ
american_scientific_journal-1367	259	8	left	leave	VERB
american_scientific_journal-1367	259	9	r	r	NOUN
american_scientific_journal-1367	259	10	-	-	PUNCT
american_scientific_journal-1367	259	11	module	module	NOUN
american_scientific_journal-1367	259	12	.	.	PUNCT
american_scientific_journal-1367	260	1	(	(	PUNCT
american_scientific_journal-1367	260	2	3	3	X
american_scientific_journal-1367	260	3	)	)	PUNCT
american_scientific_journal-1367	260	4	every	every	DET
american_scientific_journal-1367	260	5	left	left	ADJ
american_scientific_journal-1367	260	6	r	r	NOUN
american_scientific_journal-1367	260	7	-	-	PUNCT
american_scientific_journal-1367	260	8	module	module	NOUN
american_scientific_journal-1367	260	9	is	be	AUX
american_scientific_journal-1367	260	10	fp	fp	ADJ
american_scientific_journal-1367	260	11	-	-	PUNCT
american_scientific_journal-1367	260	12	injective	injective	ADJ
american_scientific_journal-1367	260	13	.	.	PUNCT
american_scientific_journal-1367	261	1	(	(	PUNCT
american_scientific_journal-1367	261	2	4	4	X
american_scientific_journal-1367	261	3	)	)	PUNCT
american_scientific_journal-1367	261	4	every	every	PRON
american_scientific_journal-1367	261	5	right	right	ADJ
american_scientific_journal-1367	261	6	r	r	NOUN
american_scientific_journal-1367	261	7	-	-	PUNCT
american_scientific_journal-1367	261	8	module	module	NOUN
american_scientific_journal-1367	261	9	is	be	AUX
american_scientific_journal-1367	261	10	fp	fp	NOUN
american_scientific_journal-1367	261	11	-	-	PUNCT
american_scientific_journal-1367	261	12	flat	flat	ADJ
american_scientific_journal-1367	261	13	.	.	PUNCT
american_scientific_journal-1367	262	1	(	(	PUNCT
american_scientific_journal-1367	262	2	5	5	X
american_scientific_journal-1367	262	3	)	)	PUNCT
american_scientific_journal-1367	262	4	every	every	DET
american_scientific_journal-1367	262	5	fp	fp	PROPN
american_scientific_journal-1367	262	6	-	-	PUNCT
american_scientific_journal-1367	262	7	projective	projective	NOUN
american_scientific_journal-1367	262	8	left	leave	VERB
american_scientific_journal-1367	262	9	r	r	NOUN
american_scientific_journal-1367	262	10	-	-	PUNCT
american_scientific_journal-1367	262	11	module	module	NOUN
american_scientific_journal-1367	262	12	is	be	AUX
american_scientific_journal-1367	262	13	projective	projective	ADJ
american_scientific_journal-1367	262	14	.	.	PUNCT
american_scientific_journal-1367	263	1	(	(	PUNCT
american_scientific_journal-1367	263	2	6	6	NUM
american_scientific_journal-1367	263	3	)	)	PUNCT
american_scientific_journal-1367	263	4	every	every	DET
american_scientific_journal-1367	263	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	263	6	left	leave	VERB
american_scientific_journal-1367	263	7	r	r	NOUN
american_scientific_journal-1367	263	8	-	-	PUNCT
american_scientific_journal-1367	263	9	module	module	NOUN
american_scientific_journal-1367	263	10	is	be	AUX
american_scientific_journal-1367	263	11	fp	fp	ADJ
american_scientific_journal-1367	263	12	-	-	PUNCT
american_scientific_journal-1367	263	13	injective	injective	ADJ
american_scientific_journal-1367	263	14	.	.	PUNCT
american_scientific_journal-1367	264	1	(	(	PUNCT
american_scientific_journal-1367	264	2	7	7	X
american_scientific_journal-1367	264	3	)	)	PUNCT
american_scientific_journal-1367	264	4	every	every	DET
american_scientific_journal-1367	264	5	fp	fp	ADJ
american_scientific_journal-1367	264	6	-	-	PUNCT
american_scientific_journal-1367	264	7	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	264	8	right	right	ADJ
american_scientific_journal-1367	264	9	r	r	NOUN
american_scientific_journal-1367	264	10	-	-	PUNCT
american_scientific_journal-1367	264	11	module	module	NOUN
american_scientific_journal-1367	264	12	is	be	AUX
american_scientific_journal-1367	264	13	injective	injective	ADJ
american_scientific_journal-1367	264	14	.	.	PUNCT
american_scientific_journal-1367	265	1	(	(	PUNCT
american_scientific_journal-1367	265	2	8)	8)	NUM
american_scientific_journal-1367	265	3	every	every	DET
american_scientific_journal-1367	265	4	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	265	5	right	right	ADJ
american_scientific_journal-1367	265	6	r	r	NOUN
american_scientific_journal-1367	265	7	-	-	PUNCT
american_scientific_journal-1367	265	8	module	module	NOUN
american_scientific_journal-1367	265	9	is	be	AUX
american_scientific_journal-1367	265	10	fp	fp	NOUN
american_scientific_journal-1367	265	11	-	-	PUNCT
american_scientific_journal-1367	265	12	flat	flat	ADJ
american_scientific_journal-1367	265	13	.	.	PUNCT
american_scientific_journal-1367	266	1	(	(	PUNCT
american_scientific_journal-1367	266	2	9	9	NUM
american_scientific_journal-1367	266	3	)	)	PUNCT
american_scientific_journal-1367	266	4	(	(	PUNCT
american_scientific_journal-1367	266	5	fp	fp	PROPN
american_scientific_journal-1367	266	6	-	-	PUNCT
american_scientific_journal-1367	266	7	fl	fl	PROPN
american_scientific_journal-1367	266	8	,	,	PUNCT
american_scientific_journal-1367	266	9	fp	fp	ADJ
american_scientific_journal-1367	266	10	-	-	PUNCT
american_scientific_journal-1367	266	11	cot	cot	NOUN
american_scientific_journal-1367	266	12	)	)	PUNCT
american_scientific_journal-1367	266	13	is	be	AUX
american_scientific_journal-1367	266	14	hereditary	hereditary	ADJ
american_scientific_journal-1367	266	15	and	and	CCONJ
american_scientific_journal-1367	266	16	every	every	DET
american_scientific_journal-1367	266	17	fp	fp	ADJ
american_scientific_journal-1367	266	18	-	-	PUNCT
american_scientific_journal-1367	266	19	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	266	20	right	right	ADJ
american_scientific_journal-1367	266	21	r	r	NOUN
american_scientific_journal-1367	266	22	-	-	PUNCT
american_scientific_journal-1367	266	23	module	module	NOUN
american_scientific_journal-1367	266	24	is	be	AUX
american_scientific_journal-1367	266	25	fp	fp	NOUN
american_scientific_journal-1367	266	26	-	-	PUNCT
american_scientific_journal-1367	266	27	flat	flat	ADJ
american_scientific_journal-1367	266	28	.	.	PUNCT
american_scientific_journal-1367	267	1	(	(	PUNCT
american_scientific_journal-1367	267	2	10	10	NUM
american_scientific_journal-1367	267	3	)	)	PUNCT
american_scientific_journal-1367	267	4	(	(	PUNCT
american_scientific_journal-1367	267	5	fp	fp	NOUN
american_scientific_journal-1367	267	6	-	-	PUNCT
american_scientific_journal-1367	267	7	proj	proj	NOUN
american_scientific_journal-1367	267	8	,	,	PUNCT
american_scientific_journal-1367	267	9	fp	fp	PROPN
american_scientific_journal-1367	267	10	-	-	PUNCT
american_scientific_journal-1367	267	11	inj	inj	NOUN
american_scientific_journal-1367	267	12	)	)	PUNCT
american_scientific_journal-1367	267	13	is	be	AUX
american_scientific_journal-1367	267	14	hereditary	hereditary	ADJ
american_scientific_journal-1367	267	15	and	and	CCONJ
american_scientific_journal-1367	267	16	every	every	DET
american_scientific_journal-1367	267	17	fp	fp	ADJ
american_scientific_journal-1367	267	18	-	-	PUNCT
american_scientific_journal-1367	267	19	projective	projective	NOUN
american_scientific_journal-1367	267	20	left	leave	VERB
american_scientific_journal-1367	267	21	r	r	NOUN
american_scientific_journal-1367	267	22	-	-	PUNCT
american_scientific_journal-1367	267	23	module	module	NOUN
american_scientific_journal-1367	267	24	is	be	AUX
american_scientific_journal-1367	267	25	fpinjective	fpinjective	ADJ
american_scientific_journal-1367	267	26	.	.	PUNCT
american_scientific_journal-1367	268	1	proof	proof	NOUN
american_scientific_journal-1367	268	2	.	.	PUNCT
american_scientific_journal-1367	269	1	(	(	PUNCT
american_scientific_journal-1367	269	2	1	1	X
american_scientific_journal-1367	269	3	)	)	PUNCT
american_scientific_journal-1367	269	4	⇔	⇔	X
american_scientific_journal-1367	269	5	(	(	PUNCT
american_scientific_journal-1367	269	6	2	2	NUM
american_scientific_journal-1367	269	7	)	)	PUNCT
american_scientific_journal-1367	269	8	⇔	⇔	X
american_scientific_journal-1367	269	9	(	(	PUNCT
american_scientific_journal-1367	269	10	3	3	NUM
american_scientific_journal-1367	269	11	)	)	PUNCT
american_scientific_journal-1367	269	12	⇔	⇔	X
american_scientific_journal-1367	269	13	(	(	PUNCT
american_scientific_journal-1367	269	14	4	4	NUM
american_scientific_journal-1367	269	15	)	)	PUNCT
american_scientific_journal-1367	269	16	by	by	ADP
american_scientific_journal-1367	269	17	[	[	X
american_scientific_journal-1367	269	18	3	3	NUM
american_scientific_journal-1367	269	19	,	,	PUNCT
american_scientific_journal-1367	269	20	theorem	theorem	VERB
american_scientific_journal-1367	269	21	3.5	3.5	NUM
american_scientific_journal-1367	269	22	]	]	PUNCT
american_scientific_journal-1367	269	23	.	.	PUNCT
american_scientific_journal-1367	270	1	(	(	PUNCT
american_scientific_journal-1367	270	2	3	3	X
american_scientific_journal-1367	270	3	)	)	PUNCT
american_scientific_journal-1367	270	4	⇒	⇒	NOUN
american_scientific_journal-1367	270	5	(	(	PUNCT
american_scientific_journal-1367	270	6	5	5	NUM
american_scientific_journal-1367	270	7	)	)	PUNCT
american_scientific_journal-1367	270	8	.	.	PUNCT
american_scientific_journal-1367	271	1	let	let	VERB
american_scientific_journal-1367	271	2	m	m	PRON
american_scientific_journal-1367	271	3	any	any	DET
american_scientific_journal-1367	271	4	fp	fp	ADJ
american_scientific_journal-1367	271	5	-	-	PUNCT
american_scientific_journal-1367	271	6	projective	projective	NOUN
american_scientific_journal-1367	271	7	left	leave	VERB
american_scientific_journal-1367	271	8	r	r	NOUN
american_scientific_journal-1367	271	9	-	-	PUNCT
american_scientific_journal-1367	271	10	module	module	NOUN
american_scientific_journal-1367	271	11	.	.	PUNCT
american_scientific_journal-1367	272	1	then	then	ADV
american_scientific_journal-1367	272	2	by	by	ADP
american_scientific_journal-1367	272	3	(	(	PUNCT
american_scientific_journal-1367	272	4	3	3	NUM
american_scientific_journal-1367	272	5	)	)	PUNCT
american_scientific_journal-1367	272	6	,	,	PUNCT
american_scientific_journal-1367	272	7	ext1(m	ext1(m	NUM
american_scientific_journal-1367	272	8	,	,	PUNCT
american_scientific_journal-1367	272	9	n	n	CCONJ
american_scientific_journal-1367	272	10	)	)	PUNCT
american_scientific_journal-1367	272	11	=	=	SYM
american_scientific_journal-1367	272	12	0	0	NUM
american_scientific_journal-1367	272	13	for	for	ADP
american_scientific_journal-1367	272	14	any	any	DET
american_scientific_journal-1367	272	15	left	left	ADJ
american_scientific_journal-1367	272	16	r	r	NOUN
american_scientific_journal-1367	272	17	-	-	PUNCT
american_scientific_journal-1367	272	18	module	module	NOUN
american_scientific_journal-1367	272	19	n	n	CCONJ
american_scientific_journal-1367	272	20	,	,	PUNCT
american_scientific_journal-1367	272	21	so	so	ADV
american_scientific_journal-1367	272	22	m	m	VERB
american_scientific_journal-1367	272	23	is	be	AUX
american_scientific_journal-1367	272	24	projective	projective	ADJ
american_scientific_journal-1367	272	25	.	.	PUNCT
american_scientific_journal-1367	273	1	(	(	PUNCT
american_scientific_journal-1367	273	2	5	5	X
american_scientific_journal-1367	273	3	)	)	PUNCT
american_scientific_journal-1367	273	4	⇒	⇒	NOUN
american_scientific_journal-1367	273	5	(	(	PUNCT
american_scientific_journal-1367	273	6	2	2	X
american_scientific_journal-1367	273	7	)	)	PUNCT
american_scientific_journal-1367	273	8	is	be	AUX
american_scientific_journal-1367	273	9	clear	clear	ADJ
american_scientific_journal-1367	273	10	,	,	PUNCT
american_scientific_journal-1367	273	11	since	since	SCONJ
american_scientific_journal-1367	273	12	r	r	NOUN
american_scientific_journal-1367	273	13	/	/	SYM
american_scientific_journal-1367	273	14	i	i	PRON
american_scientific_journal-1367	273	15	is	be	AUX
american_scientific_journal-1367	273	16	fp	fp	ADJ
american_scientific_journal-1367	273	17	-	-	PUNCT
american_scientific_journal-1367	273	18	projective	projective	NOUN
american_scientific_journal-1367	273	19	left	leave	VERB
american_scientific_journal-1367	273	20	r	r	NOUN
american_scientific_journal-1367	273	21	-	-	PUNCT
american_scientific_journal-1367	273	22	module	module	NOUN
american_scientific_journal-1367	273	23	for	for	ADP
american_scientific_journal-1367	273	24	every	every	DET
american_scientific_journal-1367	273	25	finitely	finitely	ADV
american_scientific_journal-1367	273	26	presented	present	VERB
american_scientific_journal-1367	273	27	left	leave	VERB
american_scientific_journal-1367	273	28	ideal	ideal	ADJ
american_scientific_journal-1367	273	29	i.	i.	NOUN
american_scientific_journal-1367	273	30	(	(	PUNCT
american_scientific_journal-1367	273	31	3	3	NUM
american_scientific_journal-1367	273	32	)	)	PUNCT
american_scientific_journal-1367	273	33	⇒	⇒	NOUN
american_scientific_journal-1367	273	34	(	(	PUNCT
american_scientific_journal-1367	273	35	6	6	NUM
american_scientific_journal-1367	273	36	)	)	PUNCT
american_scientific_journal-1367	273	37	is	be	AUX
american_scientific_journal-1367	273	38	clear	clear	ADJ
american_scientific_journal-1367	273	39	.	.	PUNCT
american_scientific_journal-1367	274	1	(	(	PUNCT
american_scientific_journal-1367	274	2	6	6	NUM
american_scientific_journal-1367	274	3	)	)	PUNCT
american_scientific_journal-1367	274	4	⇒	⇒	NOUN
american_scientific_journal-1367	274	5	(	(	PUNCT
american_scientific_journal-1367	274	6	2	2	NUM
american_scientific_journal-1367	274	7	)	)	PUNCT
american_scientific_journal-1367	274	8	.	.	PUNCT
american_scientific_journal-1367	275	1	let	let	VERB
american_scientific_journal-1367	275	2	i	i	PRON
american_scientific_journal-1367	275	3	any	any	DET
american_scientific_journal-1367	275	4	finitely	finitely	ADV
american_scientific_journal-1367	275	5	presented	present	VERB
american_scientific_journal-1367	275	6	left	leave	VERB
american_scientific_journal-1367	275	7	ideal	ideal	NOUN
american_scientific_journal-1367	275	8	of	of	ADP
american_scientific_journal-1367	275	9	r	r	NOUN
american_scientific_journal-1367	275	10	,	,	PUNCT
american_scientific_journal-1367	275	11	m	m	VERB
american_scientific_journal-1367	275	12	any	any	DET
american_scientific_journal-1367	275	13	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	275	14	left	leave	VERB
american_scientific_journal-1367	275	15	r	r	NOUN
american_scientific_journal-1367	275	16	-	-	PUNCT
american_scientific_journal-1367	275	17	module	module	NOUN
american_scientific_journal-1367	275	18	.	.	PUNCT
american_scientific_journal-1367	276	1	we	we	PRON
american_scientific_journal-1367	276	2	have	have	VERB
american_scientific_journal-1367	276	3	m	m	PROPN
american_scientific_journal-1367	276	4	is	be	AUX
american_scientific_journal-1367	276	5	fp	fp	ADJ
american_scientific_journal-1367	276	6	-	-	PUNCT
american_scientific_journal-1367	276	7	injective	injective	ADJ
american_scientific_journal-1367	276	8	by	by	ADP
american_scientific_journal-1367	276	9	(	(	PUNCT
american_scientific_journal-1367	276	10	6	6	NUM
american_scientific_journal-1367	276	11	)	)	PUNCT
american_scientific_journal-1367	276	12	,	,	PUNCT
american_scientific_journal-1367	276	13	and	and	CCONJ
american_scientific_journal-1367	276	14	r	r	X
american_scientific_journal-1367	276	15	/	/	SYM
american_scientific_journal-1367	276	16	i	i	PRON
american_scientific_journal-1367	276	17	is	be	AUX
american_scientific_journal-1367	276	18	fp	fp	ADJ
american_scientific_journal-1367	276	19	-	-	PUNCT
american_scientific_journal-1367	276	20	projective	projective	NOUN
american_scientific_journal-1367	276	21	left	leave	VERB
american_scientific_journal-1367	276	22	r	r	NOUN
american_scientific_journal-1367	276	23	-	-	PUNCT
american_scientific_journal-1367	276	24	module	module	NOUN
american_scientific_journal-1367	276	25	.	.	PUNCT
american_scientific_journal-1367	277	1	so	so	ADV
american_scientific_journal-1367	277	2	m	m	NOUN
american_scientific_journal-1367	277	3	is	be	AUX
american_scientific_journal-1367	277	4	injective	injective	ADJ
american_scientific_journal-1367	277	5	with	with	ADP
american_scientific_journal-1367	277	6	respect	respect	NOUN
american_scientific_journal-1367	277	7	to	to	ADP
american_scientific_journal-1367	277	8	the	the	DET
american_scientific_journal-1367	277	9	exact	exact	ADJ
american_scientific_journal-1367	277	10	sequence	sequence	NOUN
american_scientific_journal-1367	277	11	0	0	NUM
american_scientific_journal-1367	278	1	→	→	SYM
american_scientific_journal-1367	278	2	i	i	PRON
american_scientific_journal-1367	278	3	→	→	SYM
american_scientific_journal-1367	278	4	r	r	NOUN
american_scientific_journal-1367	278	5	→	→	SYM
american_scientific_journal-1367	278	6	r	r	NOUN
american_scientific_journal-1367	278	7	/	/	SYM
american_scientific_journal-1367	278	8	i	i	PROPN
american_scientific_journal-1367	278	9	→	→	SYM
american_scientific_journal-1367	278	10	0	0	NUM
american_scientific_journal-1367	278	11	of	of	ADP
american_scientific_journal-1367	278	12	left	left	ADJ
american_scientific_journal-1367	278	13	r	r	NOUN
american_scientific_journal-1367	278	14	-	-	PUNCT
american_scientific_journal-1367	278	15	modules	module	NOUN
american_scientific_journal-1367	278	16	by	by	ADP
american_scientific_journal-1367	278	17	theorem	theorem	ADJ
american_scientific_journal-1367	278	18	2.2	2.2	NUM
american_scientific_journal-1367	278	19	(	(	PUNCT
american_scientific_journal-1367	278	20	2	2	NUM
american_scientific_journal-1367	278	21	)	)	PUNCT
american_scientific_journal-1367	278	22	,	,	PUNCT
american_scientific_journal-1367	278	23	and	and	CCONJ
american_scientific_journal-1367	278	24	so	so	ADV
american_scientific_journal-1367	278	25	ext1(r	ext1(r	PROPN
american_scientific_journal-1367	278	26	/	/	SYM
american_scientific_journal-1367	278	27	i	i	PROPN
american_scientific_journal-1367	278	28	,	,	PUNCT
american_scientific_journal-1367	278	29	m	m	PROPN
american_scientific_journal-1367	278	30	)	)	PUNCT
american_scientific_journal-1367	279	1	=	=	SYM
american_scientific_journal-1367	279	2	0	0	X
american_scientific_journal-1367	279	3	.	.	PUNCT
american_scientific_journal-1367	280	1	by	by	ADP
american_scientific_journal-1367	280	2	the	the	DET
american_scientific_journal-1367	280	3	arbitrariness	arbitrariness	NOUN
american_scientific_journal-1367	280	4	of	of	ADP
american_scientific_journal-1367	280	5	the	the	DET
american_scientific_journal-1367	280	6	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	280	7	left	leave	VERB
american_scientific_journal-1367	280	8	r	r	NOUN
american_scientific_journal-1367	280	9	-	-	PUNCT
american_scientific_journal-1367	280	10	module	module	NOUN
american_scientific_journal-1367	280	11	m	m	NOUN
american_scientific_journal-1367	280	12	,	,	PUNCT
american_scientific_journal-1367	280	13	it	it	PRON
american_scientific_journal-1367	280	14	follows	follow	VERB
american_scientific_journal-1367	280	15	that	that	SCONJ
american_scientific_journal-1367	280	16	r	r	NOUN
american_scientific_journal-1367	280	17	/	/	SYM
american_scientific_journal-1367	280	18	i	i	PRON
american_scientific_journal-1367	280	19	is	be	AUX
american_scientific_journal-1367	280	20	flat	flat	ADJ
american_scientific_journal-1367	280	21	.	.	PUNCT
american_scientific_journal-1367	281	1	thus	thus	ADV
american_scientific_journal-1367	281	2	r	r	X
american_scientific_journal-1367	281	3	/	/	SYM
american_scientific_journal-1367	281	4	i	i	PRON
american_scientific_journal-1367	281	5	is	be	AUX
american_scientific_journal-1367	281	6	projective	projective	ADJ
american_scientific_journal-1367	281	7	since	since	SCONJ
american_scientific_journal-1367	281	8	r	r	NOUN
american_scientific_journal-1367	281	9	/	/	SYM
american_scientific_journal-1367	281	10	i	i	PRON
american_scientific_journal-1367	281	11	is	be	AUX
american_scientific_journal-1367	281	12	finitely	finitely	ADV
american_scientific_journal-1367	281	13	presented	present	VERB
american_scientific_journal-1367	281	14	.	.	PUNCT
american_scientific_journal-1367	282	1	(	(	PUNCT
american_scientific_journal-1367	282	2	4	4	X
american_scientific_journal-1367	282	3	)	)	PUNCT
american_scientific_journal-1367	282	4	⇒	⇒	NOUN
american_scientific_journal-1367	282	5	(	(	PUNCT
american_scientific_journal-1367	282	6	7	7	NUM
american_scientific_journal-1367	282	7	)	)	PUNCT
american_scientific_journal-1367	282	8	.	.	PUNCT
american_scientific_journal-1367	283	1	let	let	VERB
american_scientific_journal-1367	283	2	m	m	PRON
american_scientific_journal-1367	283	3	be	be	AUX
american_scientific_journal-1367	283	4	an	an	DET
american_scientific_journal-1367	283	5	fp	fp	ADJ
american_scientific_journal-1367	283	6	-	-	PUNCT
american_scientific_journal-1367	283	7	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	283	8	right	right	ADJ
american_scientific_journal-1367	283	9	r	r	NOUN
american_scientific_journal-1367	283	10	-	-	NOUN
american_scientific_journal-1367	283	11	module	module	NOUN
american_scientific_journal-1367	283	12	.	.	PUNCT
american_scientific_journal-1367	284	1	then	then	ADV
american_scientific_journal-1367	284	2	,	,	PUNCT
american_scientific_journal-1367	284	3	by	by	ADP
american_scientific_journal-1367	284	4	(	(	PUNCT
american_scientific_journal-1367	284	5	4	4	NUM
american_scientific_journal-1367	284	6	)	)	PUNCT
american_scientific_journal-1367	284	7	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	284	8	,	,	PUNCT
american_scientific_journal-1367	284	9	m	m	NOUN
american_scientific_journal-1367	284	10	)	)	PUNCT
american_scientific_journal-1367	284	11	=	=	SYM
american_scientific_journal-1367	284	12	0	0	NUM
american_scientific_journal-1367	284	13	for	for	ADP
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american_scientific_journal-1367	284	15	right	right	ADJ
american_scientific_journal-1367	284	16	r	r	NOUN
american_scientific_journal-1367	284	17	-	-	PUNCT
american_scientific_journal-1367	284	18	module	module	NOUN
american_scientific_journal-1367	284	19	n	n	CCONJ
american_scientific_journal-1367	284	20	,	,	PUNCT
american_scientific_journal-1367	284	21	so	so	ADV
american_scientific_journal-1367	284	22	m	m	VERB
american_scientific_journal-1367	284	23	is	be	AUX
american_scientific_journal-1367	284	24	injective	injective	ADJ
american_scientific_journal-1367	284	25	right	right	ADJ
american_scientific_journal-1367	284	26	r	r	NOUN
american_scientific_journal-1367	284	27	-	-	NOUN
american_scientific_journal-1367	284	28	module	module	NOUN
american_scientific_journal-1367	284	29	.	.	PUNCT
american_scientific_journal-1367	285	1	(	(	PUNCT
american_scientific_journal-1367	285	2	7	7	X
american_scientific_journal-1367	285	3	)	)	PUNCT
american_scientific_journal-1367	285	4	⇒	⇒	NOUN
american_scientific_journal-1367	285	5	(	(	PUNCT
american_scientific_journal-1367	285	6	4	4	NUM
american_scientific_journal-1367	285	7	)	)	PUNCT
american_scientific_journal-1367	285	8	.	.	PUNCT
american_scientific_journal-1367	286	1	let	let	VERB
american_scientific_journal-1367	286	2	n	n	PRON
american_scientific_journal-1367	286	3	be	be	AUX
american_scientific_journal-1367	286	4	a	a	DET
american_scientific_journal-1367	286	5	right	right	ADJ
american_scientific_journal-1367	286	6	r	r	NOUN
american_scientific_journal-1367	286	7	-	-	NOUN
american_scientific_journal-1367	286	8	module	module	NOUN
american_scientific_journal-1367	286	9	,	,	PUNCT
american_scientific_journal-1367	286	10	m	m	VERB
american_scientific_journal-1367	286	11	any	any	DET
american_scientific_journal-1367	286	12	fp	fp	ADJ
american_scientific_journal-1367	286	13	-	-	PUNCT
american_scientific_journal-1367	286	14	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	286	15	right	right	ADJ
american_scientific_journal-1367	286	16	r	r	NOUN
american_scientific_journal-1367	286	17	-	-	NOUN
american_scientific_journal-1367	286	18	module	module	NOUN
american_scientific_journal-1367	286	19	.	.	PUNCT
american_scientific_journal-1367	287	1	then	then	ADV
american_scientific_journal-1367	287	2	,	,	PUNCT
american_scientific_journal-1367	287	3	by	by	ADP
american_scientific_journal-1367	287	4	(	(	PUNCT
american_scientific_journal-1367	287	5	7	7	NUM
american_scientific_journal-1367	287	6	)	)	PUNCT
american_scientific_journal-1367	287	7	ext1(n	ext1(n	NOUN
american_scientific_journal-1367	287	8	,	,	PUNCT
american_scientific_journal-1367	287	9	m	m	NOUN
american_scientific_journal-1367	287	10	)	)	PUNCT
american_scientific_journal-1367	287	11	=	=	SYM
american_scientific_journal-1367	287	12	0	0	NUM
american_scientific_journal-1367	287	13	,	,	PUNCT
american_scientific_journal-1367	287	14	so	so	ADV
american_scientific_journal-1367	287	15	n	n	PROPN
american_scientific_journal-1367	287	16	is	be	AUX
american_scientific_journal-1367	287	17	fp	fp	ADJ
american_scientific_journal-1367	287	18	-	-	PUNCT
american_scientific_journal-1367	287	19	flat	flat	ADJ
american_scientific_journal-1367	287	20	right	right	ADJ
american_scientific_journal-1367	287	21	r	r	NOUN
american_scientific_journal-1367	287	22	-	-	NOUN
american_scientific_journal-1367	287	23	module	module	NOUN
american_scientific_journal-1367	287	24	.	.	PUNCT
american_scientific_journal-1367	288	1	140	140	NUM
american_scientific_journal-1367	288	2	american	american	ADJ
american_scientific_journal-1367	288	3	scientific	scientific	ADJ
american_scientific_journal-1367	288	4	research	research	NOUN
american_scientific_journal-1367	288	5	journal	journal	NOUN
american_scientific_journal-1367	288	6	for	for	ADP
american_scientific_journal-1367	288	7	engineering	engineering	NOUN
american_scientific_journal-1367	288	8	,	,	PUNCT
american_scientific_journal-1367	288	9	technology	technology	NOUN
american_scientific_journal-1367	288	10	,	,	PUNCT
american_scientific_journal-1367	288	11	and	and	CCONJ
american_scientific_journal-1367	288	12	sciences	science	NOUN
american_scientific_journal-1367	288	13	(	(	PUNCT
american_scientific_journal-1367	288	14	asrjets	asrjet	NOUN
american_scientific_journal-1367	288	15	)	)	PUNCT
american_scientific_journal-1367	288	16	(	(	PUNCT
american_scientific_journal-1367	288	17	2016	2016	NUM
american_scientific_journal-1367	288	18	)	)	PUNCT
american_scientific_journal-1367	288	19	volume	volume	NOUN
american_scientific_journal-1367	288	20	17	17	NUM
american_scientific_journal-1367	288	21	,	,	PUNCT
american_scientific_journal-1367	288	22	no	no	DET
american_scientific_journal-1367	288	23	1	1	NUM
american_scientific_journal-1367	288	24	,	,	PUNCT
american_scientific_journal-1367	288	25	pp	pp	ADV
american_scientific_journal-1367	288	26	132	132	NUM
american_scientific_journal-1367	288	27	-	-	SYM
american_scientific_journal-1367	288	28	143	143	NUM
american_scientific_journal-1367	288	29	(	(	PUNCT
american_scientific_journal-1367	288	30	4	4	NUM
american_scientific_journal-1367	288	31	)	)	PUNCT
american_scientific_journal-1367	288	32	⇒	⇒	NOUN
american_scientific_journal-1367	288	33	(	(	PUNCT
american_scientific_journal-1367	288	34	8)	8)	NUM
american_scientific_journal-1367	288	35	is	be	AUX
american_scientific_journal-1367	288	36	clear	clear	ADJ
american_scientific_journal-1367	288	37	.	.	PUNCT
american_scientific_journal-1367	289	1	(	(	PUNCT
american_scientific_journal-1367	289	2	8)	8)	NUM
american_scientific_journal-1367	289	3	⇒	⇒	NOUN
american_scientific_journal-1367	289	4	(	(	PUNCT
american_scientific_journal-1367	289	5	3	3	NUM
american_scientific_journal-1367	289	6	)	)	PUNCT
american_scientific_journal-1367	289	7	.	.	PUNCT
american_scientific_journal-1367	290	1	let	let	VERB
american_scientific_journal-1367	290	2	m	m	PRON
american_scientific_journal-1367	290	3	be	be	AUX
american_scientific_journal-1367	290	4	any	any	DET
american_scientific_journal-1367	290	5	left	left	ADJ
american_scientific_journal-1367	290	6	r	r	NOUN
american_scientific_journal-1367	290	7	-	-	PUNCT
american_scientific_journal-1367	290	8	module	module	NOUN
american_scientific_journal-1367	290	9	.	.	PUNCT
american_scientific_journal-1367	291	1	then	then	ADV
american_scientific_journal-1367	291	2	m	m	VERB
american_scientific_journal-1367	291	3	+	+	PUNCT
american_scientific_journal-1367	291	4	is	be	AUX
american_scientific_journal-1367	291	5	pure	pure	ADJ
american_scientific_journal-1367	291	6	-	-	PUNCT
american_scientific_journal-1367	291	7	injective	injective	ADJ
american_scientific_journal-1367	291	8	right	right	ADJ
american_scientific_journal-1367	291	9	r	r	NOUN
american_scientific_journal-1367	291	10	-	-	PUNCT
american_scientific_journal-1367	291	11	module	module	NOUN
american_scientific_journal-1367	291	12	and	and	CCONJ
american_scientific_journal-1367	291	13	hence	hence	ADV
american_scientific_journal-1367	291	14	m	m	VERB
american_scientific_journal-1367	291	15	+	+	PRON
american_scientific_journal-1367	291	16	is	be	AUX
american_scientific_journal-1367	291	17	a	a	DET
american_scientific_journal-1367	291	18	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	291	19	right	right	ADJ
american_scientific_journal-1367	291	20	r	r	NOUN
american_scientific_journal-1367	291	21	-	-	NOUN
american_scientific_journal-1367	291	22	module	module	NOUN
american_scientific_journal-1367	291	23	.	.	PUNCT
american_scientific_journal-1367	292	1	so	so	ADV
american_scientific_journal-1367	292	2	m	m	PROPN
american_scientific_journal-1367	292	3	+	+	PROPN
american_scientific_journal-1367	292	4	is	be	AUX
american_scientific_journal-1367	292	5	fp	fp	ADJ
american_scientific_journal-1367	292	6	-	-	PUNCT
american_scientific_journal-1367	292	7	flat	flat	ADJ
american_scientific_journal-1367	292	8	right	right	ADJ
american_scientific_journal-1367	292	9	r	r	NOUN
american_scientific_journal-1367	292	10	-	-	PUNCT
american_scientific_journal-1367	292	11	module	module	NOUN
american_scientific_journal-1367	292	12	by	by	ADP
american_scientific_journal-1367	292	13	(	(	PUNCT
american_scientific_journal-1367	292	14	8)	8)	NUM
american_scientific_journal-1367	292	15	,	,	PUNCT
american_scientific_journal-1367	292	16	and	and	CCONJ
american_scientific_journal-1367	292	17	so	so	ADV
american_scientific_journal-1367	292	18	m	m	VERB
american_scientific_journal-1367	292	19	is	be	AUX
american_scientific_journal-1367	292	20	fp	fp	ADJ
american_scientific_journal-1367	292	21	-	-	ADJ
american_scientific_journal-1367	292	22	injective	injective	ADJ
american_scientific_journal-1367	292	23	left	leave	VERB
american_scientific_journal-1367	292	24	r	r	NOUN
american_scientific_journal-1367	292	25	-	-	PUNCT
american_scientific_journal-1367	292	26	module	module	NOUN
american_scientific_journal-1367	292	27	by	by	ADP
american_scientific_journal-1367	292	28	[	[	X
american_scientific_journal-1367	292	29	3	3	NUM
american_scientific_journal-1367	292	30	,	,	PUNCT
american_scientific_journal-1367	292	31	theorem	theorem	VERB
american_scientific_journal-1367	292	32	2.7	2.7	NUM
american_scientific_journal-1367	292	33	(	(	PUNCT
american_scientific_journal-1367	292	34	1	1	NUM
american_scientific_journal-1367	292	35	)	)	PUNCT
american_scientific_journal-1367	292	36	]	]	PUNCT
american_scientific_journal-1367	292	37	.	.	PUNCT
american_scientific_journal-1367	293	1	(	(	PUNCT
american_scientific_journal-1367	293	2	4	4	X
american_scientific_journal-1367	293	3	)	)	PUNCT
american_scientific_journal-1367	293	4	⇒	⇒	NOUN
american_scientific_journal-1367	293	5	(	(	PUNCT
american_scientific_journal-1367	293	6	9	9	NUM
american_scientific_journal-1367	293	7	)	)	PUNCT
american_scientific_journal-1367	293	8	and	and	CCONJ
american_scientific_journal-1367	293	9	(	(	PUNCT
american_scientific_journal-1367	293	10	3	3	X
american_scientific_journal-1367	293	11	)	)	PUNCT
american_scientific_journal-1367	293	12	⇒	⇒	NOUN
american_scientific_journal-1367	293	13	(	(	PUNCT
american_scientific_journal-1367	293	14	10	10	NUM
american_scientific_journal-1367	293	15	)	)	PUNCT
american_scientific_journal-1367	293	16	are	be	AUX
american_scientific_journal-1367	293	17	obvious	obvious	ADJ
american_scientific_journal-1367	293	18	.	.	PUNCT
american_scientific_journal-1367	294	1	(	(	PUNCT
american_scientific_journal-1367	294	2	9	9	X
american_scientific_journal-1367	294	3	)	)	PUNCT
american_scientific_journal-1367	294	4	⇒	⇒	NOUN
american_scientific_journal-1367	294	5	(	(	PUNCT
american_scientific_journal-1367	294	6	4	4	X
american_scientific_journal-1367	294	7	)	)	PUNCT
american_scientific_journal-1367	294	8	let	let	VERB
american_scientific_journal-1367	294	9	m	m	PRON
american_scientific_journal-1367	294	10	be	be	AUX
american_scientific_journal-1367	294	11	any	any	DET
american_scientific_journal-1367	294	12	right	right	ADJ
american_scientific_journal-1367	294	13	r	r	NOUN
american_scientific_journal-1367	294	14	-	-	NOUN
american_scientific_journal-1367	294	15	module	module	NOUN
american_scientific_journal-1367	294	16	.	.	PUNCT
american_scientific_journal-1367	295	1	by	by	ADP
american_scientific_journal-1367	295	2	theorem	theorem	NOUN
american_scientific_journal-1367	295	3	2.9	2.9	NUM
american_scientific_journal-1367	295	4	there	there	PRON
american_scientific_journal-1367	295	5	exists	exist	VERB
american_scientific_journal-1367	295	6	an	an	DET
american_scientific_journal-1367	295	7	exact	exact	ADJ
american_scientific_journal-1367	295	8	sequence	sequence	NOUN
american_scientific_journal-1367	295	9	0	0	NUM
american_scientific_journal-1367	295	10	→	→	SYM
american_scientific_journal-1367	295	11	m	m	PROPN
american_scientific_journal-1367	295	12	→	→	SYM
american_scientific_journal-1367	295	13	c	c	PROPN
american_scientific_journal-1367	295	14	→	→	SYM
american_scientific_journal-1367	295	15	l	l	NOUN
american_scientific_journal-1367	295	16	→	→	SYM
american_scientific_journal-1367	295	17	0	0	NUM
american_scientific_journal-1367	295	18	with	with	ADP
american_scientific_journal-1367	295	19	c	c	PROPN
american_scientific_journal-1367	295	20	fp	fp	NOUN
american_scientific_journal-1367	295	21	-	-	PUNCT
american_scientific_journal-1367	295	22	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	295	23	right	right	ADJ
american_scientific_journal-1367	295	24	r	r	NOUN
american_scientific_journal-1367	295	25	-	-	PUNCT
american_scientific_journal-1367	295	26	module	module	NOUN
american_scientific_journal-1367	295	27	and	and	CCONJ
american_scientific_journal-1367	295	28	l	l	NOUN
american_scientific_journal-1367	295	29	fp	fp	ADJ
american_scientific_journal-1367	295	30	-	-	PUNCT
american_scientific_journal-1367	295	31	flat	flat	ADJ
american_scientific_journal-1367	295	32	right	right	ADJ
american_scientific_journal-1367	295	33	r	r	NOUN
american_scientific_journal-1367	295	34	-	-	NOUN
american_scientific_journal-1367	295	35	module	module	NOUN
american_scientific_journal-1367	295	36	.	.	PUNCT
american_scientific_journal-1367	296	1	so	so	ADV
american_scientific_journal-1367	296	2	c	c	PROPN
american_scientific_journal-1367	296	3	is	be	AUX
american_scientific_journal-1367	296	4	fp	fp	ADJ
american_scientific_journal-1367	296	5	-	-	PUNCT
american_scientific_journal-1367	296	6	flat	flat	ADJ
american_scientific_journal-1367	296	7	right	right	ADJ
american_scientific_journal-1367	296	8	r	r	NOUN
american_scientific_journal-1367	296	9	-	-	PUNCT
american_scientific_journal-1367	296	10	module	module	NOUN
american_scientific_journal-1367	296	11	by	by	ADP
american_scientific_journal-1367	296	12	(	(	PUNCT
american_scientific_journal-1367	296	13	9	9	NUM
american_scientific_journal-1367	296	14	)	)	PUNCT
american_scientific_journal-1367	296	15	.	.	PUNCT
american_scientific_journal-1367	297	1	since	since	SCONJ
american_scientific_journal-1367	297	2	(	(	PUNCT
american_scientific_journal-1367	297	3	fp	fp	PROPN
american_scientific_journal-1367	297	4	-	-	PUNCT
american_scientific_journal-1367	297	5	fl	fl	PROPN
american_scientific_journal-1367	297	6	,	,	PUNCT
american_scientific_journal-1367	297	7	fp	fp	ADJ
american_scientific_journal-1367	297	8	-	-	PUNCT
american_scientific_journal-1367	297	9	cot	cot	NOUN
american_scientific_journal-1367	297	10	)	)	PUNCT
american_scientific_journal-1367	297	11	is	be	AUX
american_scientific_journal-1367	297	12	hereditary	hereditary	ADJ
american_scientific_journal-1367	297	13	m	m	NOUN
american_scientific_journal-1367	297	14	is	be	AUX
american_scientific_journal-1367	297	15	fp	fp	ADJ
american_scientific_journal-1367	297	16	-	-	PUNCT
american_scientific_journal-1367	297	17	flat	flat	ADJ
american_scientific_journal-1367	297	18	right	right	ADJ
american_scientific_journal-1367	297	19	r	r	NOUN
american_scientific_journal-1367	297	20	-	-	NOUN
american_scientific_journal-1367	297	21	module	module	NOUN
american_scientific_journal-1367	297	22	.	.	PUNCT
american_scientific_journal-1367	298	1	(	(	PUNCT
american_scientific_journal-1367	298	2	10	10	NUM
american_scientific_journal-1367	298	3	)	)	PUNCT
american_scientific_journal-1367	298	4	⇒	⇒	NOUN
american_scientific_journal-1367	298	5	(	(	PUNCT
american_scientific_journal-1367	298	6	3	3	NUM
american_scientific_journal-1367	298	7	)	)	PUNCT
american_scientific_journal-1367	298	8	.	.	PUNCT
american_scientific_journal-1367	299	1	let	let	VERB
american_scientific_journal-1367	299	2	m	m	PRON
american_scientific_journal-1367	299	3	be	be	AUX
american_scientific_journal-1367	299	4	any	any	DET
american_scientific_journal-1367	299	5	left	left	ADJ
american_scientific_journal-1367	299	6	r	r	NOUN
american_scientific_journal-1367	299	7	-	-	PUNCT
american_scientific_journal-1367	299	8	module	module	NOUN
american_scientific_journal-1367	299	9	.	.	PUNCT
american_scientific_journal-1367	300	1	by	by	ADP
american_scientific_journal-1367	300	2	theorem	theorem	NOUN
american_scientific_journal-1367	300	3	2.6	2.6	NUM
american_scientific_journal-1367	300	4	there	there	PRON
american_scientific_journal-1367	300	5	exists	exist	VERB
american_scientific_journal-1367	300	6	an	an	DET
american_scientific_journal-1367	300	7	exact	exact	ADJ
american_scientific_journal-1367	300	8	sequence	sequence	NOUN
american_scientific_journal-1367	300	9	0	0	NUM
american_scientific_journal-1367	300	10	→	→	SYM
american_scientific_journal-1367	300	11	n	n	CCONJ
american_scientific_journal-1367	300	12	→	→	SYM
american_scientific_journal-1367	300	13	p	p	X
american_scientific_journal-1367	300	14	→	→	PROPN
american_scientific_journal-1367	300	15	m	m	PROPN
american_scientific_journal-1367	300	16	→	→	SYM
american_scientific_journal-1367	300	17	0	0	NUM
american_scientific_journal-1367	300	18	,	,	PUNCT
american_scientific_journal-1367	300	19	where	where	SCONJ
american_scientific_journal-1367	300	20	p	p	NOUN
american_scientific_journal-1367	300	21	is	be	AUX
american_scientific_journal-1367	300	22	fpprojective	fpprojective	ADJ
american_scientific_journal-1367	300	23	left	leave	VERB
american_scientific_journal-1367	300	24	r	r	NOUN
american_scientific_journal-1367	300	25	-	-	PUNCT
american_scientific_journal-1367	300	26	module	module	NOUN
american_scientific_journal-1367	300	27	and	and	CCONJ
american_scientific_journal-1367	300	28	n	n	NOUN
american_scientific_journal-1367	300	29	is	be	AUX
american_scientific_journal-1367	300	30	fp	fp	ADJ
american_scientific_journal-1367	300	31	-	-	ADJ
american_scientific_journal-1367	300	32	injective	injective	ADJ
american_scientific_journal-1367	300	33	left	leave	VERB
american_scientific_journal-1367	300	34	r	r	NOUN
american_scientific_journal-1367	300	35	-	-	PUNCT
american_scientific_journal-1367	300	36	module	module	NOUN
american_scientific_journal-1367	300	37	.	.	PUNCT
american_scientific_journal-1367	301	1	so	so	ADV
american_scientific_journal-1367	301	2	p	p	PROPN
american_scientific_journal-1367	301	3	is	be	AUX
american_scientific_journal-1367	301	4	fp	fp	NOUN
american_scientific_journal-1367	301	5	-	-	PUNCT
american_scientific_journal-1367	301	6	injective	injective	ADJ
american_scientific_journal-1367	301	7	by	by	ADP
american_scientific_journal-1367	301	8	(	(	PUNCT
american_scientific_journal-1367	301	9	10).since	10).since	NUM
american_scientific_journal-1367	301	10	(	(	PUNCT
american_scientific_journal-1367	301	11	fp	fp	NOUN
american_scientific_journal-1367	301	12	-	-	PUNCT
american_scientific_journal-1367	301	13	proj	proj	NOUN
american_scientific_journal-1367	301	14	,	,	PUNCT
american_scientific_journal-1367	301	15	fp	fp	PROPN
american_scientific_journal-1367	301	16	-	-	PUNCT
american_scientific_journal-1367	301	17	inj	inj	NOUN
american_scientific_journal-1367	301	18	)	)	PUNCT
american_scientific_journal-1367	301	19	is	be	AUX
american_scientific_journal-1367	301	20	hereditary	hereditary	ADJ
american_scientific_journal-1367	301	21	,	,	PUNCT
american_scientific_journal-1367	301	22	m	m	VERB
american_scientific_journal-1367	301	23	is	be	AUX
american_scientific_journal-1367	301	24	fp	fp	ADJ
american_scientific_journal-1367	301	25	-	-	PUNCT
american_scientific_journal-1367	301	26	injective	injective	ADJ
american_scientific_journal-1367	301	27	.	.	PUNCT
american_scientific_journal-1367	302	1	□	□	PUNCT
american_scientific_journal-1367	302	2	4	4	X
american_scientific_journal-1367	302	3	.	.	X
american_scientific_journal-1367	302	4	conclusion	conclusion	NOUN
american_scientific_journal-1367	302	5	it	it	PRON
american_scientific_journal-1367	302	6	is	be	AUX
american_scientific_journal-1367	302	7	not	not	PART
american_scientific_journal-1367	302	8	known	know	VERB
american_scientific_journal-1367	302	9	whether	whether	SCONJ
american_scientific_journal-1367	302	10	,	,	PUNCT
american_scientific_journal-1367	302	11	the	the	DET
american_scientific_journal-1367	302	12	left	left	ADJ
american_scientific_journal-1367	302	13	fp	fp	NOUN
american_scientific_journal-1367	302	14	-	-	ADJ
american_scientific_journal-1367	302	15	regular	regular	ADJ
american_scientific_journal-1367	302	16	right	right	ADJ
american_scientific_journal-1367	302	17	coherent	coherent	ADJ
american_scientific_journal-1367	302	18	ring	ring	NOUN
american_scientific_journal-1367	302	19	is	be	AUX
american_scientific_journal-1367	302	20	von	von	PROPN
american_scientific_journal-1367	302	21	neumann	neumann	PROPN
american_scientific_journal-1367	302	22	regular	regular	ADJ
american_scientific_journal-1367	302	23	ring	ring	NOUN
american_scientific_journal-1367	302	24	.	.	PUNCT
american_scientific_journal-1367	303	1	on	on	ADP
american_scientific_journal-1367	303	2	the	the	DET
american_scientific_journal-1367	303	3	other	other	ADJ
american_scientific_journal-1367	303	4	hand	hand	NOUN
american_scientific_journal-1367	303	5	,	,	PUNCT
american_scientific_journal-1367	303	6	it	it	PRON
american_scientific_journal-1367	303	7	is	be	AUX
american_scientific_journal-1367	303	8	clear	clear	ADJ
american_scientific_journal-1367	303	9	that	that	SCONJ
american_scientific_journal-1367	303	10	every	every	DET
american_scientific_journal-1367	303	11	von	von	PROPN
american_scientific_journal-1367	303	12	neumann	neumann	PROPN
american_scientific_journal-1367	303	13	regular	regular	ADJ
american_scientific_journal-1367	303	14	ring	ring	NOUN
american_scientific_journal-1367	303	15	is	be	AUX
american_scientific_journal-1367	303	16	right	right	ADJ
american_scientific_journal-1367	303	17	and	and	CCONJ
american_scientific_journal-1367	303	18	left	leave	VERB
american_scientific_journal-1367	303	19	fp	fp	NOUN
american_scientific_journal-1367	303	20	-	-	PUNCT
american_scientific_journal-1367	303	21	regular	regular	ADJ
american_scientific_journal-1367	303	22	ring	ring	NOUN
american_scientific_journal-1367	303	23	,	,	PUNCT
american_scientific_journal-1367	303	24	but	but	CCONJ
american_scientific_journal-1367	303	25	the	the	DET
american_scientific_journal-1367	303	26	converse	converse	NOUN
american_scientific_journal-1367	303	27	is	be	AUX
american_scientific_journal-1367	303	28	not	not	PART
american_scientific_journal-1367	303	29	true	true	ADJ
american_scientific_journal-1367	303	30	as	as	SCONJ
american_scientific_journal-1367	303	31	shown	show	VERB
american_scientific_journal-1367	303	32	by	by	ADP
american_scientific_journal-1367	303	33	[	[	X
american_scientific_journal-1367	303	34	3	3	NUM
american_scientific_journal-1367	303	35	,	,	PUNCT
american_scientific_journal-1367	303	36	example	example	NOUN
american_scientific_journal-1367	303	37	3.6	3.6	NUM
american_scientific_journal-1367	303	38	]	]	PUNCT
american_scientific_journal-1367	303	39	.	.	PUNCT
american_scientific_journal-1367	304	1	by	by	ADP
american_scientific_journal-1367	304	2	theorem	theorem	NOUN
american_scientific_journal-1367	304	3	3.2(4	3.2(4	NUM
american_scientific_journal-1367	304	4	)	)	PUNCT
american_scientific_journal-1367	304	5	and	and	CCONJ
american_scientific_journal-1367	304	6	theorem	theorem	VERB
american_scientific_journal-1367	304	7	3.4(4	3.4(4	NUM
american_scientific_journal-1367	304	8	)	)	PUNCT
american_scientific_journal-1367	304	9	,	,	PUNCT
american_scientific_journal-1367	304	10	it	it	PRON
american_scientific_journal-1367	304	11	is	be	AUX
american_scientific_journal-1367	304	12	obvious	obvious	ADJ
american_scientific_journal-1367	304	13	that	that	SCONJ
american_scientific_journal-1367	304	14	r	r	NOUN
american_scientific_journal-1367	304	15	is	be	AUX
american_scientific_journal-1367	304	16	a	a	DET
american_scientific_journal-1367	304	17	von	von	PROPN
american_scientific_journal-1367	304	18	neumann	neumann	PROPN
american_scientific_journal-1367	304	19	regular	regular	ADJ
american_scientific_journal-1367	304	20	ring	ring	NOUN
american_scientific_journal-1367	305	1	if	if	SCONJ
american_scientific_journal-1367	306	1	and	and	CCONJ
american_scientific_journal-1367	306	2	only	only	ADV
american_scientific_journal-1367	306	3	if	if	SCONJ
american_scientific_journal-1367	306	4	r	r	NOUN
american_scientific_journal-1367	306	5	is	be	AUX
american_scientific_journal-1367	306	6	a	a	DET
american_scientific_journal-1367	306	7	left	left	ADJ
american_scientific_journal-1367	306	8	fp	fp	ADJ
american_scientific_journal-1367	306	9	-	-	ADJ
american_scientific_journal-1367	306	10	regular	regular	ADJ
american_scientific_journal-1367	306	11	left	left	ADJ
american_scientific_journal-1367	306	12	coherent	coherent	NOUN
american_scientific_journal-1367	306	13	.	.	PUNCT
american_scientific_journal-1367	307	1	using	use	VERB
american_scientific_journal-1367	307	2	this	this	DET
american_scientific_journal-1367	307	3	fact	fact	NOUN
american_scientific_journal-1367	307	4	with	with	ADP
american_scientific_journal-1367	307	5	theorem	theorem	ADJ
american_scientific_journal-1367	307	6	3.2	3.2	NUM
american_scientific_journal-1367	307	7	and	and	CCONJ
american_scientific_journal-1367	307	8	theorem	theorem	VERB
american_scientific_journal-1367	307	9	3.4	3.4	NUM
american_scientific_journal-1367	307	10	,	,	PUNCT
american_scientific_journal-1367	307	11	we	we	PRON
american_scientific_journal-1367	307	12	can	can	AUX
american_scientific_journal-1367	307	13	get	get	VERB
american_scientific_journal-1367	307	14	the	the	DET
american_scientific_journal-1367	307	15	following	follow	VERB
american_scientific_journal-1367	307	16	known	know	VERB
american_scientific_journal-1367	307	17	characterizations	characterization	NOUN
american_scientific_journal-1367	307	18	of	of	ADP
american_scientific_journal-1367	307	19	von	von	PROPN
american_scientific_journal-1367	307	20	neumann	neumann	PROPN
american_scientific_journal-1367	307	21	regular	regular	PROPN
american_scientific_journal-1367	307	22	ring	ring	NOUN
american_scientific_journal-1367	307	23	:	:	PUNCT
american_scientific_journal-1367	307	24	(	(	PUNCT
american_scientific_journal-1367	307	25	1	1	X
american_scientific_journal-1367	307	26	)	)	PUNCT
american_scientific_journal-1367	307	27	r	r	NOUN
american_scientific_journal-1367	307	28	is	be	AUX
american_scientific_journal-1367	307	29	von	von	PROPN
american_scientific_journal-1367	307	30	neumann	neumann	PROPN
american_scientific_journal-1367	307	31	regular	regular	PROPN
american_scientific_journal-1367	307	32	ring	ring	NOUN
american_scientific_journal-1367	307	33	.	.	PUNCT
american_scientific_journal-1367	308	1	(	(	PUNCT
american_scientific_journal-1367	308	2	2	2	X
american_scientific_journal-1367	308	3	)	)	PUNCT
american_scientific_journal-1367	308	4	every	every	PRON
american_scientific_journal-1367	308	5	right	right	ADJ
american_scientific_journal-1367	308	6	r	r	NOUN
american_scientific_journal-1367	308	7	-	-	PUNCT
american_scientific_journal-1367	308	8	module	module	NOUN
american_scientific_journal-1367	308	9	is	be	AUX
american_scientific_journal-1367	308	10	flat	flat	ADJ
american_scientific_journal-1367	308	11	.	.	PUNCT
american_scientific_journal-1367	309	1	(	(	PUNCT
american_scientific_journal-1367	309	2	3	3	X
american_scientific_journal-1367	309	3	)	)	PUNCT
american_scientific_journal-1367	309	4	every	every	DET
american_scientific_journal-1367	309	5	left	left	ADJ
american_scientific_journal-1367	309	6	r	r	NOUN
american_scientific_journal-1367	309	7	-	-	PUNCT
american_scientific_journal-1367	309	8	module	module	NOUN
american_scientific_journal-1367	309	9	is	be	AUX
american_scientific_journal-1367	309	10	f	f	NOUN
american_scientific_journal-1367	309	11	-	-	PUNCT
american_scientific_journal-1367	309	12	injective	injective	ADJ
american_scientific_journal-1367	309	13	.	.	PUNCT
american_scientific_journal-1367	310	1	(	(	PUNCT
american_scientific_journal-1367	310	2	4	4	X
american_scientific_journal-1367	310	3	)	)	PUNCT
american_scientific_journal-1367	310	4	every	every	DET
american_scientific_journal-1367	310	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	310	6	left	leave	VERB
american_scientific_journal-1367	310	7	r	r	NOUN
american_scientific_journal-1367	310	8	-	-	PUNCT
american_scientific_journal-1367	310	9	module	module	NOUN
american_scientific_journal-1367	310	10	is	be	AUX
american_scientific_journal-1367	310	11	f	f	NOUN
american_scientific_journal-1367	310	12	-	-	PUNCT
american_scientific_journal-1367	310	13	injective	injective	ADJ
american_scientific_journal-1367	310	14	.	.	PUNCT
american_scientific_journal-1367	311	1	(	(	PUNCT
american_scientific_journal-1367	311	2	5	5	X
american_scientific_journal-1367	311	3	)	)	PUNCT
american_scientific_journal-1367	311	4	every	every	DET
american_scientific_journal-1367	311	5	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	311	6	right	right	ADJ
american_scientific_journal-1367	311	7	r	r	NOUN
american_scientific_journal-1367	311	8	-	-	PUNCT
american_scientific_journal-1367	311	9	module	module	NOUN
american_scientific_journal-1367	311	10	is	be	AUX
american_scientific_journal-1367	311	11	flat	flat	ADJ
american_scientific_journal-1367	311	12	.	.	PUNCT
american_scientific_journal-1367	312	1	(	(	PUNCT
american_scientific_journal-1367	312	2	6	6	NUM
american_scientific_journal-1367	312	3	)	)	PUNCT
american_scientific_journal-1367	312	4	every	every	DET
american_scientific_journal-1367	312	5	f	f	PROPN
american_scientific_journal-1367	312	6	-	-	PUNCT
american_scientific_journal-1367	312	7	projective	projective	NOUN
american_scientific_journal-1367	312	8	left	leave	VERB
american_scientific_journal-1367	312	9	r	r	NOUN
american_scientific_journal-1367	312	10	-	-	PUNCT
american_scientific_journal-1367	312	11	module	module	NOUN
american_scientific_journal-1367	312	12	is	be	AUX
american_scientific_journal-1367	312	13	projective	projective	ADJ
american_scientific_journal-1367	312	14	.	.	PUNCT
american_scientific_journal-1367	313	1	(	(	PUNCT
american_scientific_journal-1367	313	2	7	7	NUM
american_scientific_journal-1367	313	3	)	)	PUNCT
american_scientific_journal-1367	313	4	(	(	PUNCT
american_scientific_journal-1367	313	5	f	f	X
american_scientific_journal-1367	313	6	-	-	PUNCT
american_scientific_journal-1367	313	7	proj	proj	NOUN
american_scientific_journal-1367	313	8	,	,	PUNCT
american_scientific_journal-1367	313	9	f	f	X
american_scientific_journal-1367	313	10	-	-	PUNCT
american_scientific_journal-1367	313	11	inj	inj	NOUN
american_scientific_journal-1367	313	12	)	)	PUNCT
american_scientific_journal-1367	313	13	is	be	AUX
american_scientific_journal-1367	313	14	hereditary	hereditary	ADJ
american_scientific_journal-1367	313	15	and	and	CCONJ
american_scientific_journal-1367	313	16	every	every	DET
american_scientific_journal-1367	313	17	f	f	NOUN
american_scientific_journal-1367	313	18	-	-	PUNCT
american_scientific_journal-1367	313	19	projective	projective	NOUN
american_scientific_journal-1367	313	20	left	leave	VERB
american_scientific_journal-1367	313	21	r	r	NOUN
american_scientific_journal-1367	313	22	-	-	PUNCT
american_scientific_journal-1367	313	23	module	module	NOUN
american_scientific_journal-1367	313	24	is	be	AUX
american_scientific_journal-1367	313	25	f	f	NOUN
american_scientific_journal-1367	313	26	-	-	PUNCT
american_scientific_journal-1367	313	27	injective	injective	ADJ
american_scientific_journal-1367	313	28	.	.	PUNCT
american_scientific_journal-1367	314	1	□	□	PUNCT
american_scientific_journal-1367	314	2	note	note	VERB
american_scientific_journal-1367	314	3	that	that	SCONJ
american_scientific_journal-1367	314	4	the	the	DET
american_scientific_journal-1367	314	5	equivalences	equivalence	NOUN
american_scientific_journal-1367	314	6	(	(	PUNCT
american_scientific_journal-1367	314	7	1	1	X
american_scientific_journal-1367	314	8	)	)	PUNCT
american_scientific_journal-1367	314	9	⇔	⇔	X
american_scientific_journal-1367	314	10	(	(	PUNCT
american_scientific_journal-1367	314	11	2	2	NUM
american_scientific_journal-1367	314	12	)	)	PUNCT
american_scientific_journal-1367	314	13	⇔	⇔	X
american_scientific_journal-1367	314	14	(	(	PUNCT
american_scientific_journal-1367	314	15	3	3	NUM
american_scientific_journal-1367	314	16	)	)	PUNCT
american_scientific_journal-1367	314	17	have	have	AUX
american_scientific_journal-1367	314	18	been	be	AUX
american_scientific_journal-1367	314	19	proved	prove	VERB
american_scientific_journal-1367	314	20	by	by	ADP
american_scientific_journal-1367	314	21	other	other	ADJ
american_scientific_journal-1367	314	22	ways	way	NOUN
american_scientific_journal-1367	314	23	in	in	ADP
american_scientific_journal-1367	314	24	[	[	X
american_scientific_journal-1367	314	25	11	11	NUM
american_scientific_journal-1367	314	26	,	,	PUNCT
american_scientific_journal-1367	314	27	theorem	theorem	VERB
american_scientific_journal-1367	314	28	1.11	1.11	NUM
american_scientific_journal-1367	314	29	]	]	PUNCT
american_scientific_journal-1367	314	30	,	,	PUNCT
american_scientific_journal-1367	314	31	(	(	PUNCT
american_scientific_journal-1367	314	32	1	1	X
american_scientific_journal-1367	314	33	)	)	PUNCT
american_scientific_journal-1367	314	34	⇔	⇔	X
american_scientific_journal-1367	314	35	(	(	PUNCT
american_scientific_journal-1367	314	36	4	4	NUM
american_scientific_journal-1367	314	37	)	)	PUNCT
american_scientific_journal-1367	314	38	⇔	⇔	X
american_scientific_journal-1367	314	39	(	(	PUNCT
american_scientific_journal-1367	314	40	5	5	NUM
american_scientific_journal-1367	314	41	)	)	PUNCT
american_scientific_journal-1367	314	42	in	in	ADP
american_scientific_journal-1367	314	43	[	[	X
american_scientific_journal-1367	314	44	17	17	NUM
american_scientific_journal-1367	314	45	,	,	PUNCT
american_scientific_journal-1367	314	46	theorem	theorem	VERB
american_scientific_journal-1367	314	47	3.2.2	3.2.2	NUM
american_scientific_journal-1367	314	48	]	]	PUNCT
american_scientific_journal-1367	314	49	.	.	PUNCT
american_scientific_journal-1367	315	1	and	and	CCONJ
american_scientific_journal-1367	315	2	(	(	PUNCT
american_scientific_journal-1367	315	3	1	1	X
american_scientific_journal-1367	315	4	)	)	PUNCT
american_scientific_journal-1367	315	5	⇔	⇔	X
american_scientific_journal-1367	315	6	(	(	PUNCT
american_scientific_journal-1367	315	7	6	6	NUM
american_scientific_journal-1367	315	8	)	)	PUNCT
american_scientific_journal-1367	315	9	⇔	⇔	X
american_scientific_journal-1367	315	10	(	(	PUNCT
american_scientific_journal-1367	315	11	7	7	NUM
american_scientific_journal-1367	315	12	)	)	PUNCT
american_scientific_journal-1367	315	13	in	in	ADP
american_scientific_journal-1367	315	14	[	[	X
american_scientific_journal-1367	315	15	6	6	NUM
american_scientific_journal-1367	315	16	,	,	PUNCT
american_scientific_journal-1367	315	17	theorem	theorem	VERB
american_scientific_journal-1367	315	18	3.2	3.2	NUM
american_scientific_journal-1367	315	19	]	]	PUNCT
american_scientific_journal-1367	315	20	.	.	PUNCT
american_scientific_journal-1367	316	1	5	5	X
american_scientific_journal-1367	316	2	.	.	X
american_scientific_journal-1367	316	3	recommendations	recommendation	NOUN
american_scientific_journal-1367	316	4	it	it	PRON
american_scientific_journal-1367	316	5	is	be	AUX
american_scientific_journal-1367	316	6	well	well	ADV
american_scientific_journal-1367	316	7	known	know	VERB
american_scientific_journal-1367	316	8	that	that	SCONJ
american_scientific_journal-1367	316	9	a	a	DET
american_scientific_journal-1367	316	10	ring	ring	NOUN
american_scientific_journal-1367	316	11	r	r	NOUN
american_scientific_journal-1367	316	12	is	be	AUX
american_scientific_journal-1367	316	13	quasi	quasi	ADJ
american_scientific_journal-1367	316	14	-	-	ADJ
american_scientific_journal-1367	316	15	frobenius	frobenius	ADJ
american_scientific_journal-1367	316	16	when	when	SCONJ
american_scientific_journal-1367	316	17	every	every	DET
american_scientific_journal-1367	316	18	left	left	ADJ
american_scientific_journal-1367	316	19	r	r	NOUN
american_scientific_journal-1367	316	20	-	-	PUNCT
american_scientific_journal-1367	316	21	module	module	NOUN
american_scientific_journal-1367	316	22	embeds	embed	VERB
american_scientific_journal-1367	316	23	in	in	ADP
american_scientific_journal-1367	316	24	a	a	DET
american_scientific_journal-1367	316	25	free	free	ADJ
american_scientific_journal-1367	316	26	left	left	ADJ
american_scientific_journal-1367	316	27	r	r	NOUN
american_scientific_journal-1367	316	28	-	-	PUNCT
american_scientific_journal-1367	316	29	module	module	NOUN
american_scientific_journal-1367	316	30	.	.	PUNCT
american_scientific_journal-1367	317	1	if	if	SCONJ
american_scientific_journal-1367	317	2	the	the	DET
american_scientific_journal-1367	317	3	embedding	embedding	NOUN
american_scientific_journal-1367	317	4	is	be	AUX
american_scientific_journal-1367	317	5	restricted	restrict	VERB
american_scientific_journal-1367	317	6	to	to	PART
american_scientific_journal-1367	317	7	finitely	finitely	ADV
american_scientific_journal-1367	317	8	generated	generate	VERB
american_scientific_journal-1367	317	9	left	leave	VERB
american_scientific_journal-1367	317	10	r	r	NOUN
american_scientific_journal-1367	317	11	-	-	PUNCT
american_scientific_journal-1367	317	12	modules	module	NOUN
american_scientific_journal-1367	317	13	,	,	PUNCT
american_scientific_journal-1367	317	14	then	then	ADV
american_scientific_journal-1367	317	15	r	r	NOUN
american_scientific_journal-1367	317	16	is	be	AUX
american_scientific_journal-1367	317	17	called	call	VERB
american_scientific_journal-1367	317	18	left	leave	VERB
american_scientific_journal-1367	317	19	fgf	fgf	PROPN
american_scientific_journal-1367	317	20	ring	ring	NOUN
american_scientific_journal-1367	317	21	,	,	PUNCT
american_scientific_journal-1367	317	22	and	and	CCONJ
american_scientific_journal-1367	317	23	the	the	DET
american_scientific_journal-1367	317	24	question	question	NOUN
american_scientific_journal-1367	317	25	of	of	ADP
american_scientific_journal-1367	317	26	whether	whether	SCONJ
american_scientific_journal-1367	317	27	any	any	DET
american_scientific_journal-1367	317	28	left	left	ADJ
american_scientific_journal-1367	317	29	fgf	fgf	PROPN
american_scientific_journal-1367	317	30	ring	ring	NOUN
american_scientific_journal-1367	317	31	is	be	AUX
american_scientific_journal-1367	317	32	qf	qf	PROPN
american_scientific_journal-1367	317	33	is	be	AUX
american_scientific_journal-1367	317	34	known	know	VERB
american_scientific_journal-1367	317	35	as	as	ADP
american_scientific_journal-1367	317	36	the	the	DET
american_scientific_journal-1367	317	37	fgf	fgf	PROPN
american_scientific_journal-1367	317	38	conjecture	conjecture	NOUN
american_scientific_journal-1367	317	39	(	(	PUNCT
american_scientific_journal-1367	317	40	or	or	CCONJ
american_scientific_journal-1367	317	41	faith	faith	NOUN
american_scientific_journal-1367	317	42	’s	’s	PART
american_scientific_journal-1367	317	43	problem	problem	NOUN
american_scientific_journal-1367	317	44	)	)	PUNCT
american_scientific_journal-1367	317	45	.	.	PUNCT
american_scientific_journal-1367	318	1	this	this	DET
american_scientific_journal-1367	318	2	conjecture	conjecture	NOUN
american_scientific_journal-1367	318	3	is	be	AUX
american_scientific_journal-1367	318	4	still	still	ADV
american_scientific_journal-1367	318	5	141	141	NUM
american_scientific_journal-1367	318	6	american	american	ADJ
american_scientific_journal-1367	318	7	scientific	scientific	ADJ
american_scientific_journal-1367	318	8	research	research	NOUN
american_scientific_journal-1367	318	9	journal	journal	NOUN
american_scientific_journal-1367	318	10	for	for	ADP
american_scientific_journal-1367	318	11	engineering	engineering	NOUN
american_scientific_journal-1367	318	12	,	,	PUNCT
american_scientific_journal-1367	318	13	technology	technology	NOUN
american_scientific_journal-1367	318	14	,	,	PUNCT
american_scientific_journal-1367	318	15	and	and	CCONJ
american_scientific_journal-1367	318	16	sciences	science	NOUN
american_scientific_journal-1367	318	17	(	(	PUNCT
american_scientific_journal-1367	318	18	asrjets	asrjet	NOUN
american_scientific_journal-1367	318	19	)	)	PUNCT
american_scientific_journal-1367	318	20	(	(	PUNCT
american_scientific_journal-1367	318	21	2016	2016	NUM
american_scientific_journal-1367	318	22	)	)	PUNCT
american_scientific_journal-1367	318	23	volume	volume	NOUN
american_scientific_journal-1367	318	24	17	17	NUM
american_scientific_journal-1367	318	25	,	,	PUNCT
american_scientific_journal-1367	318	26	no	no	DET
american_scientific_journal-1367	318	27	1	1	NUM
american_scientific_journal-1367	318	28	,	,	PUNCT
american_scientific_journal-1367	318	29	pp	pp	ADV
american_scientific_journal-1367	318	30	132	132	NUM
american_scientific_journal-1367	318	31	-	-	SYM
american_scientific_journal-1367	318	32	143	143	ADP
american_scientific_journal-1367	318	33	an	an	DET
american_scientific_journal-1367	318	34	open	open	ADJ
american_scientific_journal-1367	318	35	question	question	NOUN
american_scientific_journal-1367	318	36	.	.	PUNCT
american_scientific_journal-1367	319	1	but	but	CCONJ
american_scientific_journal-1367	319	2	there	there	PRON
american_scientific_journal-1367	319	3	are	be	VERB
american_scientific_journal-1367	319	4	many	many	ADJ
american_scientific_journal-1367	319	5	affirmative	affirmative	ADJ
american_scientific_journal-1367	319	6	answers	answer	NOUN
american_scientific_journal-1367	319	7	to	to	ADP
american_scientific_journal-1367	319	8	this	this	DET
american_scientific_journal-1367	319	9	question	question	NOUN
american_scientific_journal-1367	319	10	with	with	ADP
american_scientific_journal-1367	319	11	different	different	ADJ
american_scientific_journal-1367	319	12	additional	additional	ADJ
american_scientific_journal-1367	319	13	conditions	condition	NOUN
american_scientific_journal-1367	319	14	.	.	PUNCT
american_scientific_journal-1367	320	1	(	(	PUNCT
american_scientific_journal-1367	320	2	see	see	VERB
american_scientific_journal-1367	320	3	[	[	X
american_scientific_journal-1367	320	4	18]–[20	18]–[20	X
american_scientific_journal-1367	320	5	]	]	PUNCT
american_scientific_journal-1367	320	6	)	)	PUNCT
american_scientific_journal-1367	320	7	.	.	PUNCT
american_scientific_journal-1367	321	1	it	it	PRON
american_scientific_journal-1367	321	2	is	be	AUX
american_scientific_journal-1367	321	3	recommended	recommend	VERB
american_scientific_journal-1367	321	4	to	to	PART
american_scientific_journal-1367	321	5	characterize	characterize	VERB
american_scientific_journal-1367	321	6	the	the	DET
american_scientific_journal-1367	321	7	quasi	quasi	ADJ
american_scientific_journal-1367	321	8	-	-	ADJ
american_scientific_journal-1367	321	9	frobenius	frobenius	ADJ
american_scientific_journal-1367	321	10	rings	ring	NOUN
american_scientific_journal-1367	321	11	in	in	ADP
american_scientific_journal-1367	321	12	terms	term	NOUN
american_scientific_journal-1367	321	13	of	of	ADP
american_scientific_journal-1367	321	14	fp	fp	X
american_scientific_journal-1367	321	15	-	-	PUNCT
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american_scientific_journal-1367	321	17	and	and	CCONJ
american_scientific_journal-1367	321	18	fpcotorsion	fpcotorsion	NOUN
american_scientific_journal-1367	321	19	left	leave	VERB
american_scientific_journal-1367	321	20	r	r	NOUN
american_scientific_journal-1367	321	21	-	-	PUNCT
american_scientific_journal-1367	321	22	modules	module	NOUN
american_scientific_journal-1367	321	23	,	,	PUNCT
american_scientific_journal-1367	321	24	and	and	CCONJ
american_scientific_journal-1367	321	25	then	then	ADV
american_scientific_journal-1367	321	26	reach	reach	VERB
american_scientific_journal-1367	321	27	a	a	DET
american_scientific_journal-1367	321	28	new	new	ADJ
american_scientific_journal-1367	321	29	affirmative	affirmative	ADJ
american_scientific_journal-1367	321	30	answers	answer	NOUN
american_scientific_journal-1367	321	31	to	to	ADP
american_scientific_journal-1367	321	32	the	the	DET
american_scientific_journal-1367	321	33	fgf	fgf	PROPN
american_scientific_journal-1367	321	34	conjecture	conjecture	NOUN
american_scientific_journal-1367	321	35	with	with	ADP
american_scientific_journal-1367	321	36	additional	additional	ADJ
american_scientific_journal-1367	321	37	condition	condition	NOUN
american_scientific_journal-1367	321	38	.	.	PUNCT
american_scientific_journal-1367	322	1	acknowledgment	acknowledgment	NOUN
american_scientific_journal-1367	322	2	the	the	DET
american_scientific_journal-1367	322	3	author	author	NOUN
american_scientific_journal-1367	322	4	would	would	AUX
american_scientific_journal-1367	322	5	like	like	VERB
american_scientific_journal-1367	322	6	to	to	PART
american_scientific_journal-1367	322	7	thank	thank	VERB
american_scientific_journal-1367	322	8	the	the	DET
american_scientific_journal-1367	322	9	referee	referee	NOUN
american_scientific_journal-1367	322	10	for	for	ADP
american_scientific_journal-1367	322	11	the	the	DET
american_scientific_journal-1367	322	12	valuable	valuable	ADJ
american_scientific_journal-1367	322	13	comments	comment	NOUN
american_scientific_journal-1367	322	14	and	and	CCONJ
american_scientific_journal-1367	322	15	suggestions	suggestion	NOUN
american_scientific_journal-1367	322	16	.	.	PUNCT
american_scientific_journal-1367	323	1	references	reference	NOUN
american_scientific_journal-1367	323	2	[	[	X
american_scientific_journal-1367	323	3	1	1	NUM
american_scientific_journal-1367	323	4	]	]	PUNCT
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american_scientific_journal-1367	323	7	,	,	PUNCT
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american_scientific_journal-1367	323	9	rings	ring	NOUN
american_scientific_journal-1367	323	10	and	and	CCONJ
american_scientific_journal-1367	323	11	fp	fp	ADJ
american_scientific_journal-1367	323	12	-	-	PUNCT
american_scientific_journal-1367	323	13	injective	injective	ADJ
american_scientific_journal-1367	323	14	modules	module	NOUN
american_scientific_journal-1367	323	15	,	,	PUNCT
american_scientific_journal-1367	323	16	j.	j.	PROPN
american_scientific_journal-1367	323	17	london	london	PROPN
american_scientific_journal-1367	323	18	math	math	PROPN
american_scientific_journal-1367	323	19	.	.	PUNCT
american_scientific_journal-1367	324	1	soc	soc	PROPN
american_scientific_journal-1367	324	2	.	.	PUNCT
american_scientific_journal-1367	324	3	,	,	PUNCT
american_scientific_journal-1367	324	4	2	2	NUM
american_scientific_journal-1367	324	5	,	,	PUNCT
american_scientific_journal-1367	324	6	323	323	NUM
american_scientific_journal-1367	324	7	-	-	SYM
american_scientific_journal-1367	324	8	329	329	NUM
american_scientific_journal-1367	324	9	,	,	PUNCT
american_scientific_journal-1367	324	10	1970	1970	NUM
american_scientific_journal-1367	324	11	.	.	PUNCT
american_scientific_journal-1367	325	1	[	[	X
american_scientific_journal-1367	325	2	2	2	NUM
american_scientific_journal-1367	325	3	]	]	PUNCT
american_scientific_journal-1367	325	4	r.	r.	PROPN
american_scientific_journal-1367	325	5	n.	n.	PROPN
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american_scientific_journal-1367	325	7	,	,	PUNCT
american_scientific_journal-1367	325	8	on	on	ADP
american_scientific_journal-1367	325	9	f	f	ADJ
american_scientific_journal-1367	325	10	-	-	PUNCT
american_scientific_journal-1367	325	11	injective	injective	ADJ
american_scientific_journal-1367	325	12	modules	module	NOUN
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american_scientific_journal-1367	325	14	semihereditary	semihereditary	ADJ
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american_scientific_journal-1367	325	16	,	,	PUNCT
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american_scientific_journal-1367	325	18	.	.	PUNCT
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american_scientific_journal-1367	326	2	.	.	PUNCT
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american_scientific_journal-1367	326	4	.	.	PUNCT
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american_scientific_journal-1367	327	2	,	,	PUNCT
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american_scientific_journal-1367	327	5	,	,	PUNCT
american_scientific_journal-1367	327	6	35	35	NUM
american_scientific_journal-1367	327	7	,	,	PUNCT
american_scientific_journal-1367	327	8	323	323	NUM
american_scientific_journal-1367	327	9	-	-	SYM
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american_scientific_journal-1367	327	11	.	.	PUNCT
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american_scientific_journal-1367	328	4	zhu	zhu	PROPN
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american_scientific_journal-1367	328	6	,	,	PUNCT
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american_scientific_journal-1367	328	8	f	f	X
american_scientific_journal-1367	328	9	-	-	PUNCT
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american_scientific_journal-1367	328	16	,	,	PUNCT
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american_scientific_journal-1367	328	22	,	,	PUNCT
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american_scientific_journal-1367	328	25	-	-	SYM
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american_scientific_journal-1367	328	27	,	,	PUNCT
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american_scientific_journal-1367	328	29	.	.	PUNCT
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american_scientific_journal-1367	329	4	mao	mao	X
american_scientific_journal-1367	329	5	li	li	PROPN
american_scientific_journal-1367	329	6	-	-	PROPN
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american_scientific_journal-1367	329	8	,	,	PUNCT
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american_scientific_journal-1367	329	11	-	-	PUNCT
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american_scientific_journal-1367	329	16	-	-	PUNCT
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american_scientific_journal-1367	329	19	,	,	PUNCT
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american_scientific_journal-1367	329	24	,	,	PUNCT
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american_scientific_journal-1367	329	26	:	:	SYM
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american_scientific_journal-1367	329	30	.	.	PUNCT
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american_scientific_journal-1367	331	1	li	li	PROPN
american_scientific_journal-1367	331	2	-	-	PROPN
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american_scientific_journal-1367	331	4	,	,	PUNCT
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american_scientific_journal-1367	331	7	-	-	NOUN
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american_scientific_journal-1367	331	9	.	.	PUNCT
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american_scientific_journal-1367	333	4	,	,	PUNCT
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american_scientific_journal-1367	333	6	.	.	PUNCT
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american_scientific_journal-1367	334	2	,	,	PUNCT
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american_scientific_journal-1367	334	4	):	):	PUNCT
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american_scientific_journal-1367	334	6	,	,	PUNCT
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american_scientific_journal-1367	334	8	.	.	PUNCT
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american_scientific_journal-1367	335	6	-	-	PROPN
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american_scientific_journal-1367	335	8	,	,	PUNCT
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american_scientific_journal-1367	335	10	-	-	PUNCT
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american_scientific_journal-1367	335	13	f	f	X
american_scientific_journal-1367	335	14	-	-	PUNCT
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american_scientific_journal-1367	335	24	,	,	PUNCT
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american_scientific_journal-1367	335	28	,	,	PUNCT
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american_scientific_journal-1367	335	31	1	1	NUM
american_scientific_journal-1367	335	32	,	,	PUNCT
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american_scientific_journal-1367	336	1	[	[	X
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american_scientific_journal-1367	336	4	e.	e.	PROPN
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american_scientific_journal-1367	336	12	,	,	PUNCT
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american_scientific_journal-1367	336	20	,	,	PUNCT
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american_scientific_journal-1367	337	5	,	,	PUNCT
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american_scientific_journal-1367	337	8	,	,	PUNCT
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american_scientific_journal-1367	337	10	,	,	PUNCT
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american_scientific_journal-1367	337	17	,	,	PUNCT
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american_scientific_journal-1367	337	20	,	,	PUNCT
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american_scientific_journal-1367	337	28	math	math	NOUN
american_scientific_journal-1367	337	29	,	,	PUNCT
american_scientific_journal-1367	337	30	scand,94(1):46–62	scand,94(1):46–62	PROPN
american_scientific_journal-1367	337	31	,	,	PUNCT
american_scientific_journal-1367	337	32	2004	2004	NUM
american_scientific_journal-1367	337	33	.	.	PUNCT
american_scientific_journal-1367	338	1	[	[	X
american_scientific_journal-1367	338	2	9	9	NUM
american_scientific_journal-1367	338	3	]	]	SYM
american_scientific_journal-1367	338	4	trlifaj	trlifaj	NOUN
american_scientific_journal-1367	338	5	,	,	PUNCT
american_scientific_journal-1367	338	6	j.	j.	PROPN
american_scientific_journal-1367	338	7	,	,	PUNCT
american_scientific_journal-1367	338	8	covers	cover	VERB
american_scientific_journal-1367	338	9	,	,	PUNCT
american_scientific_journal-1367	338	10	envelopes	envelope	NOUN
american_scientific_journal-1367	338	11	,	,	PUNCT
american_scientific_journal-1367	338	12	and	and	CCONJ
american_scientific_journal-1367	338	13	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	338	14	theories	theory	NOUN
american_scientific_journal-1367	338	15	.	.	PUNCT
american_scientific_journal-1367	339	1	lecture	lecture	NOUN
american_scientific_journal-1367	339	2	notes	note	NOUN
american_scientific_journal-1367	339	3	for	for	ADP
american_scientific_journal-1367	339	4	the	the	DET
american_scientific_journal-1367	339	5	workshop,“homological	workshop,“homological	ADJ
american_scientific_journal-1367	339	6	methods	method	NOUN
american_scientific_journal-1367	339	7	in	in	ADP
american_scientific_journal-1367	339	8	module	module	NOUN
american_scientific_journal-1367	339	9	theory	theory	NOUN
american_scientific_journal-1367	339	10	”	"	PUNCT
american_scientific_journal-1367	339	11	cortona	cortona	PROPN
american_scientific_journal-1367	339	12	,	,	PUNCT
american_scientific_journal-1367	339	13	september	september	PROPN
american_scientific_journal-1367	339	14	10–16	10–16	NUM
american_scientific_journal-1367	339	15	,	,	PUNCT
american_scientific_journal-1367	339	16	2000	2000	NUM
american_scientific_journal-1367	339	17	.	.	PUNCT
american_scientific_journal-1367	340	1	[	[	X
american_scientific_journal-1367	340	2	10	10	NUM
american_scientific_journal-1367	340	3	]	]	PUNCT
american_scientific_journal-1367	340	4	eklof	eklof	PROPN
american_scientific_journal-1367	340	5	,	,	PUNCT
american_scientific_journal-1367	340	6	p.	p.	PROPN
american_scientific_journal-1367	340	7	c.	c.	PROPN
american_scientific_journal-1367	340	8	,	,	PUNCT
american_scientific_journal-1367	340	9	trlifaj	trlifaj	PROPN
american_scientific_journal-1367	340	10	,	,	PUNCT
american_scientific_journal-1367	340	11	j.	j.	PROPN
american_scientific_journal-1367	340	12	,	,	PUNCT
american_scientific_journal-1367	340	13	how	how	SCONJ
american_scientific_journal-1367	340	14	to	to	PART
american_scientific_journal-1367	340	15	make	make	VERB
american_scientific_journal-1367	340	16	ext	ext	NOUN
american_scientific_journal-1367	340	17	vanish	vanish	VERB
american_scientific_journal-1367	340	18	.	.	PUNCT
american_scientific_journal-1367	341	1	bull	bull	NOUN
american_scientific_journal-1367	341	2	.	.	PUNCT
american_scientific_journal-1367	342	1	london	london	PROPN
american_scientific_journal-1367	342	2	math	math	PROPN
american_scientific_journal-1367	342	3	.	.	PUNCT
american_scientific_journal-1367	343	1	soc	soc	PROPN
american_scientific_journal-1367	343	2	.	.	PUNCT
american_scientific_journal-1367	344	1	33(1):41–51	33(1):41–51	NUM
american_scientific_journal-1367	344	2	,	,	PUNCT
american_scientific_journal-1367	344	3	2001	2001	NUM
american_scientific_journal-1367	344	4	.	.	PUNCT
american_scientific_journal-1367	345	1	[	[	X
american_scientific_journal-1367	345	2	11	11	NUM
american_scientific_journal-1367	345	3	]	]	X
american_scientific_journal-1367	345	4	robert	robert	PROPN
american_scientific_journal-1367	345	5	f.	f.	PROPN
american_scientific_journal-1367	345	6	damiano	damiano	PROPN
american_scientific_journal-1367	345	7	,	,	PUNCT
american_scientific_journal-1367	345	8	coflat	coflat	NOUN
american_scientific_journal-1367	345	9	rings	ring	NOUN
american_scientific_journal-1367	345	10	and	and	CCONJ
american_scientific_journal-1367	345	11	modules	module	NOUN
american_scientific_journal-1367	345	12	,	,	PUNCT
american_scientific_journal-1367	345	13	pacific	pacific	PROPN
american_scientific_journal-1367	345	14	journal	journal	NOUN
american_scientific_journal-1367	345	15	of	of	ADP
american_scientific_journal-1367	345	16	mathematics	mathematics	PROPN
american_scientific_journal-1367	345	17	,	,	PUNCT
american_scientific_journal-1367	345	18	vol	vol	NOUN
american_scientific_journal-1367	345	19	.	.	PROPN
american_scientific_journal-1367	345	20	81	81	NUM
american_scientific_journal-1367	345	21	,	,	PUNCT
american_scientific_journal-1367	345	22	no	no	INTJ
american_scientific_journal-1367	345	23	.	.	NOUN
american_scientific_journal-1367	345	24	2	2	NUM
american_scientific_journal-1367	345	25	,	,	PUNCT
american_scientific_journal-1367	345	26	349369	349369	NUM
american_scientific_journal-1367	345	27	,	,	PUNCT
american_scientific_journal-1367	345	28	1979	1979	NUM
american_scientific_journal-1367	345	29	.	.	PUNCT
american_scientific_journal-1367	346	1	[	[	X
american_scientific_journal-1367	346	2	12	12	NUM
american_scientific_journal-1367	346	3	]	]	PUNCT
american_scientific_journal-1367	346	4	x.	x.	NOUN
american_scientific_journal-1367	346	5	x.	x.	PROPN
american_scientific_journal-1367	346	6	zhang	zhang	PROPN
american_scientific_journal-1367	346	7	,	,	PUNCT
american_scientific_journal-1367	346	8	j.	j.	PROPN
american_scientific_journal-1367	346	9	l.	l.	PROPN
american_scientific_journal-1367	346	10	chen	chen	PROPN
american_scientific_journal-1367	346	11	and	and	CCONJ
american_scientific_journal-1367	346	12	j.	j.	PROPN
american_scientific_journal-1367	346	13	zhang	zhang	PROPN
american_scientific_journal-1367	346	14	,	,	PUNCT
american_scientific_journal-1367	346	15	on	on	ADP
american_scientific_journal-1367	346	16	(	(	PUNCT
american_scientific_journal-1367	346	17	m	m	PROPN
american_scientific_journal-1367	346	18	,	,	PUNCT
american_scientific_journal-1367	346	19	n)-injective	n)-injective	ADJ
american_scientific_journal-1367	346	20	modules	module	NOUN
american_scientific_journal-1367	346	21	and	and	CCONJ
american_scientific_journal-1367	346	22	(	(	PUNCT
american_scientific_journal-1367	346	23	m	m	PROPN
american_scientific_journal-1367	346	24	,	,	PUNCT
american_scientific_journal-1367	346	25	n)-coherent	n)-coherent	NOUN
american_scientific_journal-1367	346	26	rings	ring	NOUN
american_scientific_journal-1367	346	27	,	,	PUNCT
american_scientific_journal-1367	346	28	algebra	algebra	NOUN
american_scientific_journal-1367	346	29	colloq	colloq	PROPN
american_scientific_journal-1367	346	30	.	.	PUNCT
american_scientific_journal-1367	346	31	,	,	PUNCT
american_scientific_journal-1367	346	32	12	12	NUM
american_scientific_journal-1367	346	33	,	,	PUNCT
american_scientific_journal-1367	346	34	149	149	NUM
american_scientific_journal-1367	346	35	-	-	SYM
american_scientific_journal-1367	346	36	160	160	NUM
american_scientific_journal-1367	346	37	,	,	PUNCT
american_scientific_journal-1367	346	38	2005	2005	NUM
american_scientific_journal-1367	346	39	.	.	PUNCT
american_scientific_journal-1367	347	1	[	[	X
american_scientific_journal-1367	347	2	13	13	NUM
american_scientific_journal-1367	347	3	]	]	PUNCT
american_scientific_journal-1367	347	4	j.	j.	PROPN
american_scientific_journal-1367	347	5	l.	l.	PROPN
american_scientific_journal-1367	347	6	chen	chen	PROPN
american_scientific_journal-1367	347	7	and	and	CCONJ
american_scientific_journal-1367	347	8	n.	n.	PROPN
american_scientific_journal-1367	347	9	q.	q.	PROPN
american_scientific_journal-1367	347	10	ding	ding	PROPN
american_scientific_journal-1367	347	11	,	,	PUNCT
american_scientific_journal-1367	347	12	on	on	ADP
american_scientific_journal-1367	347	13	n	n	CCONJ
american_scientific_journal-1367	347	14	-	-	PUNCT
american_scientific_journal-1367	347	15	coherent	coherent	ADJ
american_scientific_journal-1367	347	16	rings	ring	NOUN
american_scientific_journal-1367	347	17	,	,	PUNCT
american_scientific_journal-1367	347	18	comm	comm	NOUN
american_scientific_journal-1367	347	19	.	.	PUNCT
american_scientific_journal-1367	348	1	algebra	algebra	NOUN
american_scientific_journal-1367	348	2	,	,	PUNCT
american_scientific_journal-1367	348	3	24	24	NUM
american_scientific_journal-1367	348	4	,	,	PUNCT
american_scientific_journal-1367	348	5	3211	3211	NUM
american_scientific_journal-1367	348	6	-	-	SYM
american_scientific_journal-1367	348	7	3216	3216	NUM
american_scientific_journal-1367	348	8	,	,	PUNCT
american_scientific_journal-1367	348	9	1996	1996	NUM
american_scientific_journal-1367	348	10	.	.	PUNCT
american_scientific_journal-1367	349	1	[	[	X
american_scientific_journal-1367	349	2	14	14	NUM
american_scientific_journal-1367	349	3	]	]	X
american_scientific_journal-1367	349	4	h.	h.	PROPN
american_scientific_journal-1367	349	5	bass	bass	PROPN
american_scientific_journal-1367	349	6	,	,	PUNCT
american_scientific_journal-1367	349	7	“	"	PUNCT
american_scientific_journal-1367	349	8	finitistic	finitistic	ADJ
american_scientific_journal-1367	349	9	dimension	dimension	NOUN
american_scientific_journal-1367	349	10	and	and	CCONJ
american_scientific_journal-1367	349	11	a	a	DET
american_scientific_journal-1367	349	12	homological	homological	ADJ
american_scientific_journal-1367	349	13	generalization	generalization	NOUN
american_scientific_journal-1367	349	14	of	of	ADP
american_scientific_journal-1367	349	15	semiprimary	semiprimary	NOUN
american_scientific_journal-1367	349	16	,	,	PUNCT
american_scientific_journal-1367	349	17	rings	ring	NOUN
american_scientific_journal-1367	349	18	,	,	PUNCT
american_scientific_journal-1367	349	19	”	"	PUNCT
american_scientific_journal-1367	349	20	trans	tran	NOUN
american_scientific_journal-1367	349	21	.	.	PUNCT
american_scientific_journal-1367	350	1	amer	amer	PROPN
american_scientific_journal-1367	350	2	.	.	PUNCT
american_scientific_journal-1367	350	3	math	math	PROPN
american_scientific_journal-1367	350	4	.	.	PUNCT
american_scientific_journal-1367	351	1	soc	soc	PROPN
american_scientific_journal-1367	351	2	.	.	PUNCT
american_scientific_journal-1367	352	1	95	95	NUM
american_scientific_journal-1367	352	2	,	,	PUNCT
american_scientific_journal-1367	352	3	466–488	466–488	NUM
american_scientific_journal-1367	352	4	,	,	PUNCT
american_scientific_journal-1367	352	5	1960	1960	NUM
american_scientific_journal-1367	352	6	.	.	PUNCT
american_scientific_journal-1367	353	1	[	[	X
american_scientific_journal-1367	353	2	15	15	NUM
american_scientific_journal-1367	353	3	]	]	X
american_scientific_journal-1367	353	4	carl	carl	PROPN
american_scientific_journal-1367	353	5	faith	faith	PROPN
american_scientific_journal-1367	353	6	,	,	PUNCT
american_scientific_journal-1367	353	7	when	when	SCONJ
american_scientific_journal-1367	353	8	selfinjective	selfinjective	ADJ
american_scientific_journal-1367	353	9	rings	ring	NOUN
american_scientific_journal-1367	353	10	are	be	AUX
american_scientific_journal-1367	353	11	qf	qf	NOUN
american_scientific_journal-1367	353	12	:	:	PUNCT
american_scientific_journal-1367	353	13	a	a	DET
american_scientific_journal-1367	353	14	report	report	NOUN
american_scientific_journal-1367	353	15	on	on	ADP
american_scientific_journal-1367	353	16	a	a	DET
american_scientific_journal-1367	353	17	problem	problem	NOUN
american_scientific_journal-1367	353	18	,	,	PUNCT
american_scientific_journal-1367	353	19	journal	journal	NOUN
american_scientific_journal-1367	353	20	of	of	ADP
american_scientific_journal-1367	353	21	algebra	algebra	NOUN
american_scientific_journal-1367	353	22	and	and	CCONJ
american_scientific_journal-1367	353	23	its	its	PRON
american_scientific_journal-1367	353	24	applications	application	NOUN
american_scientific_journal-1367	353	25	,	,	PUNCT
american_scientific_journal-1367	353	26	vol	vol	NOUN
american_scientific_journal-1367	353	27	.	.	PROPN
american_scientific_journal-1367	353	28	1	1	NUM
american_scientific_journal-1367	353	29	,	,	PUNCT
american_scientific_journal-1367	353	30	no	no	INTJ
american_scientific_journal-1367	353	31	.	.	NOUN
american_scientific_journal-1367	353	32	1	1	NUM
american_scientific_journal-1367	353	33	,	,	PUNCT
american_scientific_journal-1367	353	34	75–105	75–105	PROPN
american_scientific_journal-1367	353	35	,	,	PUNCT
american_scientific_journal-1367	353	36	2002	2002	NUM
american_scientific_journal-1367	353	37	.	.	PUNCT
american_scientific_journal-1367	354	1	[	[	X
american_scientific_journal-1367	354	2	16	16	NUM
american_scientific_journal-1367	354	3	]	]	X
american_scientific_journal-1367	354	4	mao	mao	PROPN
american_scientific_journal-1367	355	1	li	li	PROPN
american_scientific_journal-1367	355	2	-	-	PROPN
american_scientific_journal-1367	355	3	xin	xin	PROPN
american_scientific_journal-1367	355	4	,	,	PUNCT
american_scientific_journal-1367	355	5	ding	ding	PROPN
american_scientific_journal-1367	355	6	nan	nan	PROPN
american_scientific_journal-1367	355	7	-	-	PROPN
american_scientific_journal-1367	355	8	qing	qing	PROPN
american_scientific_journal-1367	355	9	,	,	PUNCT
american_scientific_journal-1367	355	10	notes	note	NOUN
american_scientific_journal-1367	355	11	on	on	ADP
american_scientific_journal-1367	355	12	cotorsion	cotorsion	NOUN
american_scientific_journal-1367	355	13	modules	module	NOUN
american_scientific_journal-1367	356	1	[	[	X
american_scientific_journal-1367	356	2	j	j	X
american_scientific_journal-1367	356	3	]	]	X
american_scientific_journal-1367	356	4	.	.	PUNCT
american_scientific_journal-1367	357	1	comm	comm	NOUN
american_scientific_journal-1367	357	2	.	.	PUNCT
american_scientific_journal-1367	358	1	algebra	algebra	PROPN
american_scientific_journal-1367	358	2	,	,	PUNCT
american_scientific_journal-1367	358	3	33(1	33(1	NUM
american_scientific_journal-1367	358	4	):	):	PUNCT
american_scientific_journal-1367	358	5	349–360	349–360	NUM
american_scientific_journal-1367	358	6	,	,	PUNCT
american_scientific_journal-1367	358	7	2005	2005	NUM
american_scientific_journal-1367	358	8	.	.	PUNCT
american_scientific_journal-1367	359	1	[	[	X
american_scientific_journal-1367	359	2	17	17	NUM
american_scientific_journal-1367	359	3	]	]	X
american_scientific_journal-1367	359	4	xu	xu	PROPN
american_scientific_journal-1367	359	5	,	,	PUNCT
american_scientific_journal-1367	359	6	j.	j.	PROPN
american_scientific_journal-1367	359	7	(	(	PUNCT
american_scientific_journal-1367	359	8	1996	1996	NUM
american_scientific_journal-1367	359	9	)	)	PUNCT
american_scientific_journal-1367	359	10	.	.	PUNCT
american_scientific_journal-1367	360	1	flat	flat	ADJ
american_scientific_journal-1367	360	2	covers	cover	NOUN
american_scientific_journal-1367	360	3	of	of	ADP
american_scientific_journal-1367	360	4	modules	module	NOUN
american_scientific_journal-1367	360	5	.	.	PUNCT
american_scientific_journal-1367	361	1	lecture	lecture	NOUN
american_scientific_journal-1367	361	2	notes	note	NOUN
american_scientific_journal-1367	361	3	in	in	ADP
american_scientific_journal-1367	361	4	math	math	NOUN
american_scientific_journal-1367	361	5	.	.	PUNCT
american_scientific_journal-1367	362	1	vol	vol	NOUN
american_scientific_journal-1367	362	2	.	.	PROPN
american_scientific_journal-1367	362	3	1634	1634	NUM
american_scientific_journal-1367	362	4	.	.	PUNCT
american_scientific_journal-1367	363	1	berlin	berlin	PROPN
american_scientific_journal-1367	363	2	-	-	PUNCT
american_scientific_journal-1367	363	3	heidelberg	heidelberg	PROPN
american_scientific_journal-1367	363	4	-	-	PUNCT
american_scientific_journal-1367	363	5	new	new	PROPN
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american_scientific_journal-1367	363	7	:	:	PUNCT
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american_scientific_journal-1367	363	9	verlag	verlag	PROPN
american_scientific_journal-1367	363	10	.	.	PUNCT
american_scientific_journal-1367	364	1	142	142	NUM
american_scientific_journal-1367	364	2	american	american	ADJ
american_scientific_journal-1367	364	3	scientific	scientific	ADJ
american_scientific_journal-1367	364	4	research	research	NOUN
american_scientific_journal-1367	364	5	journal	journal	NOUN
american_scientific_journal-1367	364	6	for	for	ADP
american_scientific_journal-1367	364	7	engineering	engineering	NOUN
american_scientific_journal-1367	364	8	,	,	PUNCT
american_scientific_journal-1367	364	9	technology	technology	NOUN
american_scientific_journal-1367	364	10	,	,	PUNCT
american_scientific_journal-1367	364	11	and	and	CCONJ
american_scientific_journal-1367	364	12	sciences	science	NOUN
american_scientific_journal-1367	364	13	(	(	PUNCT
american_scientific_journal-1367	364	14	asrjets	asrjet	NOUN
american_scientific_journal-1367	364	15	)	)	PUNCT
american_scientific_journal-1367	364	16	(	(	PUNCT
american_scientific_journal-1367	364	17	2016	2016	NUM
american_scientific_journal-1367	364	18	)	)	PUNCT
american_scientific_journal-1367	364	19	volume	volume	NOUN
american_scientific_journal-1367	364	20	17	17	NUM
american_scientific_journal-1367	364	21	,	,	PUNCT
american_scientific_journal-1367	364	22	no	no	DET
american_scientific_journal-1367	364	23	1	1	NUM
american_scientific_journal-1367	364	24	,	,	PUNCT
american_scientific_journal-1367	364	25	pp	pp	ADV
american_scientific_journal-1367	364	26	132	132	NUM
american_scientific_journal-1367	364	27	-	-	SYM
american_scientific_journal-1367	364	28	143	143	NUM
american_scientific_journal-1367	364	29	[	[	X
american_scientific_journal-1367	364	30	18	18	NUM
american_scientific_journal-1367	364	31	]	]	PUNCT
american_scientific_journal-1367	364	32	faith	faith	NOUN
american_scientific_journal-1367	364	33	c	c	PROPN
american_scientific_journal-1367	364	34	,	,	PUNCT
american_scientific_journal-1367	364	35	huynh	huynh	PROPN
american_scientific_journal-1367	364	36	dv	dv	PROPN
american_scientific_journal-1367	364	37	,	,	PUNCT
american_scientific_journal-1367	364	38	when	when	SCONJ
american_scientific_journal-1367	364	39	self	self	NOUN
american_scientific_journal-1367	364	40	-	-	PUNCT
american_scientific_journal-1367	364	41	injective	injective	ADJ
american_scientific_journal-1367	364	42	rings	ring	NOUN
american_scientific_journal-1367	364	43	are	be	AUX
american_scientific_journal-1367	364	44	qf	qf	NOUN
american_scientific_journal-1367	364	45	:	:	PUNCT
american_scientific_journal-1367	364	46	a	a	DET
american_scientific_journal-1367	364	47	report	report	NOUN
american_scientific_journal-1367	364	48	on	on	ADP
american_scientific_journal-1367	364	49	a	a	DET
american_scientific_journal-1367	364	50	problem	problem	NOUN
american_scientific_journal-1367	364	51	.	.	PUNCT
american_scientific_journal-1367	365	1	j.	j.	PROPN
american_scientific_journal-1367	365	2	algebra	algebra	PROPN
american_scientific_journal-1367	365	3	appl	appl	PROPN
american_scientific_journal-1367	365	4	.	.	PROPN
american_scientific_journal-1367	365	5	1	1	NUM
american_scientific_journal-1367	365	6	,	,	PUNCT
american_scientific_journal-1367	365	7	75105	75105	NUM
american_scientific_journal-1367	365	8	,	,	PUNCT
american_scientific_journal-1367	365	9	2002	2002	NUM
american_scientific_journal-1367	365	10	.	.	PUNCT
american_scientific_journal-1367	366	1	[	[	X
american_scientific_journal-1367	366	2	19	19	NUM
american_scientific_journal-1367	366	3	]	]	X
american_scientific_journal-1367	366	4	nicholson	nicholson	PROPN
american_scientific_journal-1367	366	5	,	,	PUNCT
american_scientific_journal-1367	366	6	wk	wk	PROPN
american_scientific_journal-1367	366	7	,	,	PUNCT
american_scientific_journal-1367	366	8	yousif	yousif	PROPN
american_scientific_journal-1367	366	9	,	,	PUNCT
american_scientific_journal-1367	366	10	mf	mf	X
american_scientific_journal-1367	366	11	,	,	PUNCT
american_scientific_journal-1367	366	12	quasi	quasi	ADJ
american_scientific_journal-1367	366	13	-	-	ADJ
american_scientific_journal-1367	366	14	frobenius	frobenius	ADJ
american_scientific_journal-1367	366	15	rings	ring	NOUN
american_scientific_journal-1367	366	16	.	.	PUNCT
american_scientific_journal-1367	367	1	cambridge	cambridge	PROPN
american_scientific_journal-1367	367	2	university	university	PROPN
american_scientific_journal-1367	367	3	press	press	PROPN
american_scientific_journal-1367	367	4	,	,	PUNCT
american_scientific_journal-1367	367	5	cambridge	cambridge	PROPN
american_scientific_journal-1367	367	6	,	,	PUNCT
american_scientific_journal-1367	367	7	35163	35163	NUM
american_scientific_journal-1367	367	8	.	.	PUNCT
american_scientific_journal-1367	368	1	[	[	X
american_scientific_journal-1367	368	2	20	20	NUM
american_scientific_journal-1367	368	3	]	]	PUNCT
american_scientific_journal-1367	368	4	shen	shen	NOUN
american_scientific_journal-1367	368	5	,	,	PUNCT
american_scientific_journal-1367	368	6	l	l	PROPN
american_scientific_journal-1367	368	7	,	,	PUNCT
american_scientific_journal-1367	368	8	chen	chen	PROPN
american_scientific_journal-1367	368	9	,	,	PUNCT
american_scientific_journal-1367	368	10	jl	jl	NOUN
american_scientific_journal-1367	368	11	,	,	PUNCT
american_scientific_journal-1367	368	12	,	,	PUNCT
american_scientific_journal-1367	368	13	new	new	ADJ
american_scientific_journal-1367	368	14	characterizations	characterization	NOUN
american_scientific_journal-1367	368	15	of	of	ADP
american_scientific_journal-1367	368	16	quasi	quasi	ADJ
american_scientific_journal-1367	368	17	-	-	ADJ
american_scientific_journal-1367	368	18	frobenius	frobenius	ADJ
american_scientific_journal-1367	368	19	rings	ring	NOUN
american_scientific_journal-1367	368	20	.	.	PUNCT
american_scientific_journal-1367	369	1	commun	commun	PROPN
american_scientific_journal-1367	369	2	.	.	PUNCT
american_scientific_journal-1367	370	1	algebra	algebra	PROPN
american_scientific_journal-1367	370	2	34	34	NUM
american_scientific_journal-1367	370	3	,	,	PUNCT
american_scientific_journal-1367	370	4	21572165	21572165	NUM
american_scientific_journal-1367	370	5	,	,	PUNCT
american_scientific_journal-1367	370	6	2006	2006	NUM
american_scientific_journal-1367	370	7	.	.	PUNCT
american_scientific_journal-1367	371	1	143	143	NUM