id	sid	tid	token	lemma	pos
ejpam-2196	1	1	compile	compile	NOUN
ejpam-2196	1	2	/	/	SYM
ejpam-2196	1	3	output.dvi	output.dvi	NOUN
ejpam-2196	1	4	european	european	ADJ
ejpam-2196	1	5	journal	journal	NOUN
ejpam-2196	1	6	of	of	ADP
ejpam-2196	1	7	pure	pure	ADJ
ejpam-2196	1	8	and	and	CCONJ
ejpam-2196	1	9	applied	apply	VERB
ejpam-2196	1	10	mathematics	mathematic	NOUN
ejpam-2196	1	11	vol	vol	NOUN
ejpam-2196	1	12	.	.	PROPN
ejpam-2196	1	13	8	8	NUM
ejpam-2196	1	14	,	,	PUNCT
ejpam-2196	1	15	no	no	INTJ
ejpam-2196	1	16	.	.	NOUN
ejpam-2196	1	17	2	2	NUM
ejpam-2196	1	18	,	,	PUNCT
ejpam-2196	1	19	2015	2015	NUM
ejpam-2196	1	20	,	,	PUNCT
ejpam-2196	1	21	232	232	NUM
ejpam-2196	1	22	-	-	SYM
ejpam-2196	1	23	238	238	NUM
ejpam-2196	1	24	issn	issn	PROPN
ejpam-2196	1	25	1307	1307	NUM
ejpam-2196	1	26	-	-	SYM
ejpam-2196	1	27	5543	5543	NUM
ejpam-2196	1	28	–	–	PUNCT
ejpam-2196	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2196	1	30	on	on	ADP
ejpam-2196	1	31	a	a	DET
ejpam-2196	1	32	proper	proper	ADJ
ejpam-2196	1	33	subclass	subclass	NOUN
ejpam-2196	1	34	of	of	ADP
ejpam-2196	1	35	primeful	primeful	ADJ
ejpam-2196	1	36	modules	module	NOUN
ejpam-2196	1	37	which	which	PRON
ejpam-2196	1	38	contains	contain	VERB
ejpam-2196	1	39	the	the	DET
ejpam-2196	1	40	class	class	NOUN
ejpam-2196	1	41	of	of	ADP
ejpam-2196	1	42	finitely	finitely	ADV
ejpam-2196	1	43	generated	generate	VERB
ejpam-2196	1	44	modules	module	NOUN
ejpam-2196	1	45	properly	properly	ADV
ejpam-2196	1	46	hosein	hosein	PROPN
ejpam-2196	1	47	fazaeli	fazaeli	PROPN
ejpam-2196	1	48	moghimi∗	moghimi∗	PROPN
ejpam-2196	1	49	,	,	PUNCT
ejpam-2196	1	50	fatemeh	fatemeh	VERB
ejpam-2196	1	51	rashedi	rashedi	PROPN
ejpam-2196	1	52	1,2	1,2	NUM
ejpam-2196	1	53	department	department	NOUN
ejpam-2196	1	54	of	of	ADP
ejpam-2196	1	55	mathematics	mathematic	NOUN
ejpam-2196	1	56	,	,	PUNCT
ejpam-2196	1	57	university	university	NOUN
ejpam-2196	1	58	of	of	ADP
ejpam-2196	1	59	birjand	birjand	NOUN
ejpam-2196	1	60	,	,	PUNCT
ejpam-2196	1	61	p.o	p.o	PROPN
ejpam-2196	1	62	.	.	PROPN
ejpam-2196	1	63	box	box	PROPN
ejpam-2196	1	64	97175	97175	NUM
ejpam-2196	1	65	-	-	SYM
ejpam-2196	1	66	615	615	NUM
ejpam-2196	1	67	,	,	PUNCT
ejpam-2196	1	68	birjand	birjand	NOUN
ejpam-2196	1	69	,	,	PUNCT
ejpam-2196	1	70	iran	iran	PROPN
ejpam-2196	1	71	abstract	abstract	ADJ
ejpam-2196	1	72	.	.	PUNCT
ejpam-2196	2	1	let	let	VERB
ejpam-2196	2	2	r	r	PRON
ejpam-2196	2	3	be	be	AUX
ejpam-2196	2	4	a	a	DET
ejpam-2196	2	5	commutative	commutative	ADJ
ejpam-2196	2	6	ring	ring	NOUN
ejpam-2196	2	7	with	with	ADP
ejpam-2196	2	8	identity	identity	NOUN
ejpam-2196	2	9	and	and	CCONJ
ejpam-2196	2	10	m	m	VERB
ejpam-2196	2	11	a	a	DET
ejpam-2196	2	12	unital	unital	ADJ
ejpam-2196	2	13	r	r	NOUN
ejpam-2196	2	14	-	-	PUNCT
ejpam-2196	2	15	module	module	NOUN
ejpam-2196	2	16	.	.	PUNCT
ejpam-2196	3	1	moreover	moreover	ADV
ejpam-2196	3	2	,	,	PUNCT
ejpam-2196	3	3	let	let	AUX
ejpam-2196	3	4	pspec(m	pspec(m	NOUN
ejpam-2196	3	5	)	)	PUNCT
ejpam-2196	3	6	denote	denote	VERB
ejpam-2196	3	7	the	the	DET
ejpam-2196	3	8	primary	primary	ADJ
ejpam-2196	3	9	-	-	PUNCT
ejpam-2196	3	10	like	like	ADJ
ejpam-2196	3	11	spectrum	spectrum	NOUN
ejpam-2196	3	12	of	of	ADP
ejpam-2196	3	13	m	m	PROPN
ejpam-2196	3	14	and	and	CCONJ
ejpam-2196	3	15	spec(r	spec(r	PROPN
ejpam-2196	3	16	/	/	SYM
ejpam-2196	3	17	ann(m	ann(m	PROPN
ejpam-2196	3	18	)	)	PUNCT
ejpam-2196	3	19	)	)	PUNCT
ejpam-2196	4	1	the	the	DET
ejpam-2196	4	2	prime	prime	ADJ
ejpam-2196	4	3	spectrum	spectrum	NOUN
ejpam-2196	4	4	of	of	ADP
ejpam-2196	4	5	r	r	PROPN
ejpam-2196	4	6	/	/	SYM
ejpam-2196	4	7	ann(m	ann(m	NOUN
ejpam-2196	4	8	)	)	PUNCT
ejpam-2196	4	9	.	.	PUNCT
ejpam-2196	5	1	we	we	PRON
ejpam-2196	5	2	define	define	VERB
ejpam-2196	5	3	an	an	DET
ejpam-2196	5	4	r	r	NOUN
ejpam-2196	5	5	-	-	PUNCT
ejpam-2196	5	6	module	module	NOUN
ejpam-2196	5	7	m	m	NOUN
ejpam-2196	5	8	to	to	PART
ejpam-2196	5	9	be	be	AUX
ejpam-2196	5	10	a	a	DET
ejpam-2196	5	11	φ	φ	NOUN
ejpam-2196	5	12	-	-	NOUN
ejpam-2196	5	13	module	module	NOUN
ejpam-2196	5	14	,	,	PUNCT
ejpam-2196	5	15	if	if	SCONJ
ejpam-2196	5	16	φ	φ	NOUN
ejpam-2196	5	17	:	:	PUNCT
ejpam-2196	5	18	pspec(m)→	pspec(m)→	VERB
ejpam-2196	5	19	spec(r	spec(r	PROPN
ejpam-2196	5	20	/	/	SYM
ejpam-2196	5	21	ann(m	ann(m	PROPN
ejpam-2196	5	22	)	)	PUNCT
ejpam-2196	5	23	)	)	PUNCT
ejpam-2196	5	24	given	give	VERB
ejpam-2196	5	25	by	by	ADP
ejpam-2196	5	26	φ(q	φ(q	NOUN
ejpam-2196	5	27	)	)	PUNCT
ejpam-2196	5	28	=	=	SYM
ejpam-2196	6	1	p	p	X
ejpam-2196	6	2	(	(	PUNCT
ejpam-2196	6	3	q	q	NOUN
ejpam-2196	6	4	:	:	PUNCT
ejpam-2196	6	5	m)/ann(m	m)/ann(m	NOUN
ejpam-2196	6	6	)	)	PUNCT
ejpam-2196	6	7	is	be	AUX
ejpam-2196	6	8	a	a	DET
ejpam-2196	6	9	surjective	surjective	ADJ
ejpam-2196	6	10	map	map	NOUN
ejpam-2196	6	11	.	.	PUNCT
ejpam-2196	7	1	the	the	DET
ejpam-2196	7	2	class	class	NOUN
ejpam-2196	7	3	of	of	ADP
ejpam-2196	7	4	φ	φ	PROPN
ejpam-2196	7	5	-	-	PUNCT
ejpam-2196	7	6	modules	module	NOUN
ejpam-2196	7	7	is	be	AUX
ejpam-2196	7	8	a	a	DET
ejpam-2196	7	9	proper	proper	ADJ
ejpam-2196	7	10	subclass	subclass	NOUN
ejpam-2196	7	11	of	of	ADP
ejpam-2196	7	12	primeful	primeful	ADJ
ejpam-2196	7	13	modules	module	NOUN
ejpam-2196	7	14	,	,	PUNCT
ejpam-2196	7	15	calledψ	calledψ	NOUN
ejpam-2196	7	16	-	-	PUNCT
ejpam-2196	7	17	modules	module	NOUN
ejpam-2196	7	18	here	here	ADV
ejpam-2196	7	19	,	,	PUNCT
ejpam-2196	7	20	and	and	CCONJ
ejpam-2196	7	21	contains	contain	VERB
ejpam-2196	7	22	the	the	DET
ejpam-2196	7	23	class	class	NOUN
ejpam-2196	7	24	of	of	ADP
ejpam-2196	7	25	finitely	finitely	ADV
ejpam-2196	7	26	generated	generate	VERB
ejpam-2196	7	27	modules	module	NOUN
ejpam-2196	7	28	properly	properly	ADV
ejpam-2196	7	29	.	.	PUNCT
ejpam-2196	8	1	indeed	indeed	ADV
ejpam-2196	8	2	,	,	PUNCT
ejpam-2196	8	3	φ	φ	PROPN
ejpam-2196	8	4	and	and	CCONJ
ejpam-2196	8	5	ψ	ψ	PROPN
ejpam-2196	8	6	are	be	AUX
ejpam-2196	8	7	two	two	NUM
ejpam-2196	8	8	sides	side	NOUN
ejpam-2196	8	9	of	of	ADP
ejpam-2196	8	10	a	a	DET
ejpam-2196	8	11	commutative	commutative	ADJ
ejpam-2196	8	12	triangle	triangle	NOUN
ejpam-2196	8	13	of	of	ADP
ejpam-2196	8	14	maps	map	NOUN
ejpam-2196	8	15	between	between	ADP
ejpam-2196	8	16	spectrums	spectrum	NOUN
ejpam-2196	8	17	.	.	PUNCT
ejpam-2196	9	1	we	we	PRON
ejpam-2196	9	2	show	show	VERB
ejpam-2196	9	3	that	that	SCONJ
ejpam-2196	9	4	if	if	SCONJ
ejpam-2196	9	5	r	r	NOUN
ejpam-2196	9	6	is	be	AUX
ejpam-2196	9	7	an	an	DET
ejpam-2196	9	8	artinian	artinian	ADJ
ejpam-2196	9	9	ring	ring	NOUN
ejpam-2196	9	10	,	,	PUNCT
ejpam-2196	9	11	then	then	ADV
ejpam-2196	9	12	all	all	DET
ejpam-2196	9	13	r	r	NOUN
ejpam-2196	9	14	-	-	PUNCT
ejpam-2196	9	15	modules	module	NOUN
ejpam-2196	9	16	are	be	AUX
ejpam-2196	9	17	φ	φ	NOUN
ejpam-2196	9	18	-	-	PUNCT
ejpam-2196	9	19	modules	module	NOUN
ejpam-2196	9	20	and	and	CCONJ
ejpam-2196	9	21	the	the	DET
ejpam-2196	9	22	converse	converse	NOUN
ejpam-2196	9	23	is	be	AUX
ejpam-2196	9	24	true	true	ADJ
ejpam-2196	9	25	when	when	SCONJ
ejpam-2196	9	26	r	r	NOUN
ejpam-2196	9	27	is	be	AUX
ejpam-2196	9	28	a	a	DET
ejpam-2196	9	29	noetherian	noetherian	ADJ
ejpam-2196	9	30	ring	ring	NOUN
ejpam-2196	9	31	.	.	PUNCT
ejpam-2196	10	1	2010	2010	NUM
ejpam-2196	10	2	mathematics	mathematic	NOUN
ejpam-2196	10	3	subject	subject	NOUN
ejpam-2196	10	4	classifications	classification	NOUN
ejpam-2196	10	5	:	:	PUNCT
ejpam-2196	10	6	13c13	13c13	NUM
ejpam-2196	10	7	,	,	PUNCT
ejpam-2196	10	8	13c99	13c99	NUM
ejpam-2196	10	9	key	key	ADJ
ejpam-2196	10	10	words	word	NOUN
ejpam-2196	10	11	and	and	CCONJ
ejpam-2196	10	12	phrases	phrase	NOUN
ejpam-2196	10	13	:	:	PUNCT
ejpam-2196	10	14	primary	primary	ADJ
ejpam-2196	10	15	-	-	PUNCT
ejpam-2196	10	16	like	like	ADJ
ejpam-2196	10	17	submodule	submodule	NOUN
ejpam-2196	10	18	,	,	PUNCT
ejpam-2196	10	19	φ	φ	NOUN
ejpam-2196	10	20	-	-	NOUN
ejpam-2196	10	21	module	module	NOUN
ejpam-2196	10	22	,	,	PUNCT
ejpam-2196	10	23	prime	prime	ADJ
ejpam-2196	10	24	submodule	submodule	NOUN
ejpam-2196	10	25	,	,	PUNCT
ejpam-2196	10	26	ψ	ψ	NOUN
ejpam-2196	10	27	-	-	NOUN
ejpam-2196	10	28	module	module	ADJ
ejpam-2196	10	29	1	1	NUM
ejpam-2196	10	30	.	.	PUNCT
ejpam-2196	10	31	introduction	introduction	NOUN
ejpam-2196	10	32	throughout	throughout	ADP
ejpam-2196	10	33	this	this	DET
ejpam-2196	10	34	paper	paper	NOUN
ejpam-2196	10	35	,	,	PUNCT
ejpam-2196	10	36	all	all	DET
ejpam-2196	10	37	rings	ring	NOUN
ejpam-2196	10	38	are	be	AUX
ejpam-2196	10	39	commutative	commutative	ADJ
ejpam-2196	10	40	with	with	ADP
ejpam-2196	10	41	identity	identity	NOUN
ejpam-2196	10	42	and	and	CCONJ
ejpam-2196	10	43	all	all	DET
ejpam-2196	10	44	modules	module	NOUN
ejpam-2196	10	45	are	be	AUX
ejpam-2196	10	46	unital	unital	ADJ
ejpam-2196	10	47	.	.	PUNCT
ejpam-2196	11	1	for	for	ADP
ejpam-2196	11	2	a	a	DET
ejpam-2196	11	3	submodule	submodule	NOUN
ejpam-2196	11	4	n	n	PROPN
ejpam-2196	11	5	of	of	ADP
ejpam-2196	11	6	an	an	DET
ejpam-2196	11	7	r	r	NOUN
ejpam-2196	11	8	-	-	PUNCT
ejpam-2196	11	9	module	module	NOUN
ejpam-2196	11	10	m	m	NOUN
ejpam-2196	11	11	,	,	PUNCT
ejpam-2196	11	12	(	(	PUNCT
ejpam-2196	11	13	n	n	X
ejpam-2196	11	14	:	:	PUNCT
ejpam-2196	11	15	m	m	X
ejpam-2196	11	16	)	)	PUNCT
ejpam-2196	11	17	denotes	denote	VERB
ejpam-2196	11	18	the	the	DET
ejpam-2196	11	19	ideal	ideal	NOUN
ejpam-2196	11	20	{	{	PUNCT
ejpam-2196	11	21	r	r	NOUN
ejpam-2196	11	22	∈	∈	NOUN
ejpam-2196	11	23	r	r	NOUN
ejpam-2196	11	24	|	|	NOUN
ejpam-2196	11	25	rm	rm	PROPN
ejpam-2196	11	26	⊆	⊆	NUM
ejpam-2196	11	27	n	n	CCONJ
ejpam-2196	11	28	}	}	PUNCT
ejpam-2196	11	29	and	and	CCONJ
ejpam-2196	11	30	annihilator	annihilator	NOUN
ejpam-2196	11	31	of	of	ADP
ejpam-2196	11	32	m	m	PROPN
ejpam-2196	11	33	,	,	PUNCT
ejpam-2196	11	34	denoted	denote	VERB
ejpam-2196	11	35	by	by	ADP
ejpam-2196	11	36	ann(m	ann(m	PROPN
ejpam-2196	11	37	)	)	PUNCT
ejpam-2196	11	38	,	,	PUNCT
ejpam-2196	11	39	is	be	AUX
ejpam-2196	11	40	the	the	DET
ejpam-2196	11	41	ideal	ideal	ADJ
ejpam-2196	11	42	(	(	PUNCT
ejpam-2196	11	43	0	0	NUM
ejpam-2196	11	44	:	:	PUNCT
ejpam-2196	11	45	m	m	X
ejpam-2196	11	46	)	)	PUNCT
ejpam-2196	11	47	.	.	PUNCT
ejpam-2196	12	1	a	a	DET
ejpam-2196	12	2	submodule	submodule	NOUN
ejpam-2196	12	3	p	p	NOUN
ejpam-2196	12	4	of	of	ADP
ejpam-2196	12	5	an	an	DET
ejpam-2196	12	6	r	r	NOUN
ejpam-2196	12	7	-	-	PUNCT
ejpam-2196	12	8	module	module	NOUN
ejpam-2196	12	9	m	m	NOUN
ejpam-2196	12	10	is	be	AUX
ejpam-2196	12	11	said	say	VERB
ejpam-2196	12	12	to	to	PART
ejpam-2196	12	13	be	be	AUX
ejpam-2196	12	14	prime	prime	ADJ
ejpam-2196	12	15	(	(	PUNCT
ejpam-2196	12	16	or	or	CCONJ
ejpam-2196	12	17	p	p	NOUN
ejpam-2196	12	18	-	-	PUNCT
ejpam-2196	12	19	prime	prime	NOUN
ejpam-2196	12	20	)	)	PUNCT
ejpam-2196	12	21	if	if	SCONJ
ejpam-2196	12	22	p	p	PROPN
ejpam-2196	12	23	6=	6=	NOUN
ejpam-2196	12	24	m	m	PRON
ejpam-2196	12	25	and	and	CCONJ
ejpam-2196	12	26	for	for	ADP
ejpam-2196	12	27	p	p	NOUN
ejpam-2196	12	28	=	=	X
ejpam-2196	12	29	(	(	PUNCT
ejpam-2196	12	30	p	p	X
ejpam-2196	12	31	:	:	PUNCT
ejpam-2196	12	32	m	m	PROPN
ejpam-2196	12	33	)	)	PUNCT
ejpam-2196	12	34	,	,	PUNCT
ejpam-2196	12	35	whenever	whenever	SCONJ
ejpam-2196	12	36	rm	rm	PROPN
ejpam-2196	12	37	∈	∈	PROPN
ejpam-2196	12	38	p	p	X
ejpam-2196	12	39	(	(	PUNCT
ejpam-2196	12	40	where	where	SCONJ
ejpam-2196	12	41	r	r	NOUN
ejpam-2196	12	42	∈	∈	NOUN
ejpam-2196	12	43	r	r	NOUN
ejpam-2196	12	44	and	and	CCONJ
ejpam-2196	12	45	m	m	PROPN
ejpam-2196	12	46	∈	∈	PROPN
ejpam-2196	12	47	m	m	PROPN
ejpam-2196	12	48	)	)	PUNCT
ejpam-2196	12	49	then	then	ADV
ejpam-2196	12	50	m	m	VERB
ejpam-2196	12	51	∈	∈	PROPN
ejpam-2196	12	52	p	p	NOUN
ejpam-2196	12	53	or	or	CCONJ
ejpam-2196	12	54	r	r	NOUN
ejpam-2196	12	55	∈	∈	PROPN
ejpam-2196	12	56	p	p	X
ejpam-2196	13	1	[	[	X
ejpam-2196	13	2	5	5	NUM
ejpam-2196	13	3	,	,	PUNCT
ejpam-2196	13	4	11	11	NUM
ejpam-2196	13	5	,	,	PUNCT
ejpam-2196	13	6	12	12	NUM
ejpam-2196	13	7	]	]	PUNCT
ejpam-2196	13	8	.	.	PUNCT
ejpam-2196	14	1	the	the	DET
ejpam-2196	14	2	collection	collection	NOUN
ejpam-2196	14	3	of	of	ADP
ejpam-2196	14	4	all	all	DET
ejpam-2196	14	5	prime	prime	NOUN
ejpam-2196	14	6	(	(	PUNCT
ejpam-2196	14	7	resp	resp	NOUN
ejpam-2196	14	8	.	.	PUNCT
ejpam-2196	15	1	pprime	pprime	ADJ
ejpam-2196	15	2	)	)	PUNCT
ejpam-2196	15	3	submodules	submodule	NOUN
ejpam-2196	15	4	of	of	ADP
ejpam-2196	15	5	m	m	PRON
ejpam-2196	15	6	,	,	PUNCT
ejpam-2196	15	7	denoted	denote	VERB
ejpam-2196	15	8	by	by	ADP
ejpam-2196	15	9	spec(m	spec(m	PROPN
ejpam-2196	15	10	)	)	PUNCT
ejpam-2196	15	11	(	(	PUNCT
ejpam-2196	15	12	resp	resp	NOUN
ejpam-2196	15	13	.	.	PUNCT
ejpam-2196	16	1	specp(m	specp(m	NOUN
ejpam-2196	16	2	)	)	PUNCT
ejpam-2196	16	3	)	)	PUNCT
ejpam-2196	16	4	,	,	PUNCT
ejpam-2196	16	5	is	be	AUX
ejpam-2196	16	6	called	call	VERB
ejpam-2196	16	7	the	the	DET
ejpam-2196	16	8	prime	prime	NOUN
ejpam-2196	16	9	(	(	PUNCT
ejpam-2196	16	10	resp	resp	NOUN
ejpam-2196	16	11	.	.	PUNCT
ejpam-2196	17	1	p	p	X
ejpam-2196	17	2	-	-	PUNCT
ejpam-2196	17	3	prime	prime	NOUN
ejpam-2196	17	4	)	)	PUNCT
ejpam-2196	17	5	spectrum	spectrum	NOUN
ejpam-2196	17	6	of	of	ADP
ejpam-2196	17	7	m	m	PROPN
ejpam-2196	17	8	.	.	PUNCT
ejpam-2196	18	1	also	also	ADV
ejpam-2196	18	2	the	the	DET
ejpam-2196	18	3	intersection	intersection	NOUN
ejpam-2196	18	4	of	of	ADP
ejpam-2196	18	5	all	all	DET
ejpam-2196	18	6	prime	prime	ADJ
ejpam-2196	18	7	submodules	submodule	NOUN
ejpam-2196	18	8	of	of	ADP
ejpam-2196	18	9	m	m	AUX
ejpam-2196	18	10	containing	contain	VERB
ejpam-2196	18	11	a	a	DET
ejpam-2196	18	12	submodule	submodule	NOUN
ejpam-2196	18	13	n	n	NUM
ejpam-2196	18	14	is	be	AUX
ejpam-2196	18	15	called	call	VERB
ejpam-2196	18	16	the	the	DET
ejpam-2196	18	17	radical	radical	NOUN
ejpam-2196	18	18	of	of	ADP
ejpam-2196	18	19	n	n	NUM
ejpam-2196	18	20	and	and	CCONJ
ejpam-2196	18	21	is	be	AUX
ejpam-2196	18	22	denoted	denote	VERB
ejpam-2196	18	23	by	by	ADP
ejpam-2196	18	24	rad	rad	PROPN
ejpam-2196	18	25	n	n	PROPN
ejpam-2196	18	26	.	.	PUNCT
ejpam-2196	19	1	in	in	ADP
ejpam-2196	19	2	the	the	DET
ejpam-2196	19	3	ideal	ideal	ADJ
ejpam-2196	19	4	case	case	NOUN
ejpam-2196	19	5	,	,	PUNCT
ejpam-2196	19	6	we	we	PRON
ejpam-2196	19	7	denote	denote	VERB
ejpam-2196	19	8	the	the	DET
ejpam-2196	19	9	radical	radical	NOUN
ejpam-2196	19	10	of	of	ADP
ejpam-2196	19	11	an	an	DET
ejpam-2196	19	12	ideal	ideal	NOUN
ejpam-2196	19	13	i	i	PRON
ejpam-2196	19	14	of	of	ADP
ejpam-2196	19	15	r	r	NOUN
ejpam-2196	19	16	by	by	ADP
ejpam-2196	19	17	p	p	PROPN
ejpam-2196	19	18	i	i	PRON
ejpam-2196	19	19	.	.	PUNCT
ejpam-2196	20	1	an	an	DET
ejpam-2196	20	2	r	r	NOUN
ejpam-2196	20	3	-	-	PUNCT
ejpam-2196	20	4	module	module	NOUN
ejpam-2196	20	5	m	m	NOUN
ejpam-2196	20	6	is	be	AUX
ejpam-2196	20	7	said	say	VERB
ejpam-2196	20	8	to	to	PART
ejpam-2196	20	9	be	be	AUX
ejpam-2196	20	10	a	a	DET
ejpam-2196	20	11	primeful	primeful	ADJ
ejpam-2196	20	12	module	module	NOUN
ejpam-2196	20	13	or	or	CCONJ
ejpam-2196	20	14	a	a	DET
ejpam-2196	20	15	ψ	ψ	NOUN
ejpam-2196	20	16	-	-	NOUN
ejpam-2196	20	17	module	module	NOUN
ejpam-2196	20	18	if	if	SCONJ
ejpam-2196	20	19	either	either	CCONJ
ejpam-2196	20	20	m	m	VERB
ejpam-2196	20	21	=	=	SYM
ejpam-2196	20	22	(	(	PUNCT
ejpam-2196	20	23	0	0	NUM
ejpam-2196	20	24	)	)	PUNCT
ejpam-2196	20	25	or	or	CCONJ
ejpam-2196	20	26	m	m	PROPN
ejpam-2196	20	27	6=	6=	NUM
ejpam-2196	20	28	(	(	PUNCT
ejpam-2196	20	29	0	0	NUM
ejpam-2196	20	30	)	)	PUNCT
ejpam-2196	20	31	and	and	CCONJ
ejpam-2196	20	32	the	the	DET
ejpam-2196	20	33	map	map	NOUN
ejpam-2196	20	34	ψ	ψ	X
ejpam-2196	20	35	:	:	PUNCT
ejpam-2196	20	36	spec(m	spec(m	PROPN
ejpam-2196	20	37	)	)	PUNCT
ejpam-2196	20	38	→	→	SYM
ejpam-2196	20	39	spec(r	spec(r	PROPN
ejpam-2196	20	40	/	/	SYM
ejpam-2196	20	41	ann(m	ann(m	PROPN
ejpam-2196	20	42	)	)	PUNCT
ejpam-2196	20	43	)	)	PUNCT
ejpam-2196	20	44	,	,	PUNCT
ejpam-2196	20	45	defined	define	VERB
ejpam-2196	20	46	by	by	ADP
ejpam-2196	20	47	ψ(p	ψ(p	NOUN
ejpam-2196	20	48	)	)	PUNCT
ejpam-2196	20	49	=	=	PUNCT
ejpam-2196	21	1	(	(	PUNCT
ejpam-2196	21	2	p	p	X
ejpam-2196	21	3	:	:	PUNCT
ejpam-2196	21	4	m)/ann(m	m)/ann(m	PROPN
ejpam-2196	21	5	)	)	PUNCT
ejpam-2196	21	6	,	,	PUNCT
ejpam-2196	21	7	is	be	AUX
ejpam-2196	21	8	surjective	surjective	ADJ
ejpam-2196	21	9	[	[	X
ejpam-2196	21	10	9	9	NUM
ejpam-2196	21	11	]	]	PUNCT
ejpam-2196	21	12	.	.	PUNCT
ejpam-2196	22	1	if	if	SCONJ
ejpam-2196	22	2	m	m	NOUN
ejpam-2196	22	3	/	/	SYM
ejpam-2196	22	4	n	n	PROPN
ejpam-2196	22	5	is	be	AUX
ejpam-2196	22	6	a	a	DET
ejpam-2196	22	7	ψ	ψ	NOUN
ejpam-2196	22	8	-	-	NOUN
ejpam-2196	22	9	module	module	NOUN
ejpam-2196	22	10	over	over	ADP
ejpam-2196	22	11	r	r	NOUN
ejpam-2196	22	12	,	,	PUNCT
ejpam-2196	22	13	then	then	ADV
ejpam-2196	22	14	p	p	X
ejpam-2196	22	15	(	(	PUNCT
ejpam-2196	22	16	n	n	NUM
ejpam-2196	22	17	:	:	PUNCT
ejpam-2196	22	18	m	m	X
ejpam-2196	22	19	)	)	PUNCT
ejpam-2196	23	1	=	=	SYM
ejpam-2196	23	2	(	(	PUNCT
ejpam-2196	23	3	rad	rad	NOUN
ejpam-2196	23	4	n	n	NUM
ejpam-2196	23	5	:	:	PUNCT
ejpam-2196	23	6	m	m	X
ejpam-2196	23	7	)	)	PUNCT
ejpam-2196	24	1	[	[	X
ejpam-2196	24	2	9	9	NUM
ejpam-2196	24	3	,	,	PUNCT
ejpam-2196	24	4	proposition	proposition	NOUN
ejpam-2196	24	5	5.3	5.3	NUM
ejpam-2196	24	6	]	]	PUNCT
ejpam-2196	24	7	.	.	PUNCT
ejpam-2196	25	1	a	a	DET
ejpam-2196	25	2	submodule	submodule	NOUN
ejpam-2196	25	3	q	q	PROPN
ejpam-2196	25	4	of	of	ADP
ejpam-2196	25	5	m	m	PROPN
ejpam-2196	25	6	is	be	AUX
ejpam-2196	25	7	said	say	VERB
ejpam-2196	25	8	to	to	PART
ejpam-2196	25	9	be	be	AUX
ejpam-2196	25	10	primarylike	primarylike	ADJ
ejpam-2196	25	11	if	if	SCONJ
ejpam-2196	25	12	q	q	PROPN
ejpam-2196	25	13	6=	6=	NUM
ejpam-2196	25	14	m	m	ADJ
ejpam-2196	25	15	and	and	CCONJ
ejpam-2196	25	16	whenever	whenever	SCONJ
ejpam-2196	25	17	rm	rm	PROPN
ejpam-2196	25	18	∈	∈	PROPN
ejpam-2196	25	19	q	q	PROPN
ejpam-2196	26	1	(	(	PUNCT
ejpam-2196	26	2	where	where	SCONJ
ejpam-2196	26	3	r	r	NOUN
ejpam-2196	26	4	∈	∈	NOUN
ejpam-2196	26	5	r	r	NOUN
ejpam-2196	26	6	and	and	CCONJ
ejpam-2196	26	7	m	m	PROPN
ejpam-2196	26	8	∈	∈	PROPN
ejpam-2196	26	9	m	m	PROPN
ejpam-2196	26	10	)	)	PUNCT
ejpam-2196	26	11	implies	imply	VERB
ejpam-2196	26	12	r	r	NOUN
ejpam-2196	26	13	∈	∈	PROPN
ejpam-2196	26	14	(	(	PUNCT
ejpam-2196	26	15	q	q	NOUN
ejpam-2196	26	16	:	:	PUNCT
ejpam-2196	26	17	m	m	X
ejpam-2196	26	18	)	)	PUNCT
ejpam-2196	26	19	or	or	CCONJ
ejpam-2196	26	20	∗corresponding	∗corresponde	VERB
ejpam-2196	26	21	author	author	NOUN
ejpam-2196	26	22	.	.	PUNCT
ejpam-2196	27	1	email	email	NOUN
ejpam-2196	27	2	addresses	address	NOUN
ejpam-2196	27	3	:	:	PUNCT
ejpam-2196	27	4	hfazaeli@birjand.ac.ir	hfazaeli@birjand.ac.ir	ADJ
ejpam-2196	27	5	(	(	PUNCT
ejpam-2196	27	6	hf	hf	PROPN
ejpam-2196	27	7	.	.	PUNCT
ejpam-2196	27	8	moghimi	moghimi	PROPN
ejpam-2196	27	9	)	)	PUNCT
ejpam-2196	27	10	,	,	PUNCT
ejpam-2196	27	11	fatemehrashedi@birjand.ac.ir	fatemehrashedi@birjand.ac.ir	PROPN
ejpam-2196	27	12	(	(	PUNCT
ejpam-2196	27	13	f.	f.	PROPN
ejpam-2196	27	14	rashedi	rashedi	PROPN
ejpam-2196	27	15	)	)	PUNCT
ejpam-2196	27	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2196	28	1	232	232	NUM
ejpam-2196	29	1	c	c	X
ejpam-2196	29	2	©	©	PROPN
ejpam-2196	29	3	2015	2015	NUM
ejpam-2196	29	4	ejpam	ejpam	NOUN
ejpam-2196	29	5	all	all	DET
ejpam-2196	29	6	rights	right	NOUN
ejpam-2196	29	7	reserved	reserve	VERB
ejpam-2196	29	8	.	.	PUNCT
ejpam-2196	30	1	h.	h.	PROPN
ejpam-2196	30	2	moghimi	moghimi	PROPN
ejpam-2196	30	3	,	,	PUNCT
ejpam-2196	30	4	f.	f.	PROPN
ejpam-2196	30	5	rashedi	rashedi	PROPN
ejpam-2196	30	6	/	/	SYM
ejpam-2196	30	7	eur	eur	PROPN
ejpam-2196	30	8	.	.	PUNCT
ejpam-2196	31	1	j.	j.	PROPN
ejpam-2196	31	2	pure	pure	PROPN
ejpam-2196	31	3	appl	appl	PROPN
ejpam-2196	31	4	.	.	PROPN
ejpam-2196	31	5	math	math	PROPN
ejpam-2196	31	6	,	,	PUNCT
ejpam-2196	31	7	8	8	NUM
ejpam-2196	31	8	(	(	PUNCT
ejpam-2196	31	9	2015	2015	NUM
ejpam-2196	31	10	)	)	PUNCT
ejpam-2196	31	11	,	,	PUNCT
ejpam-2196	31	12	232	232	NUM
ejpam-2196	31	13	-	-	SYM
ejpam-2196	31	14	238	238	NUM
ejpam-2196	31	15	233	233	NUM
ejpam-2196	31	16	m	m	NOUN
ejpam-2196	31	17	∈	∈	NOUN
ejpam-2196	31	18	radq	radq	NOUN
ejpam-2196	32	1	[	[	X
ejpam-2196	32	2	7	7	NUM
ejpam-2196	32	3	]	]	PUNCT
ejpam-2196	32	4	.	.	PUNCT
ejpam-2196	33	1	the	the	DET
ejpam-2196	33	2	primary	primary	ADJ
ejpam-2196	33	3	-	-	PUNCT
ejpam-2196	33	4	like	like	ADJ
ejpam-2196	33	5	spectrum	spectrum	NOUN
ejpam-2196	33	6	pspec(m	pspec(m	NOUN
ejpam-2196	33	7	)	)	PUNCT
ejpam-2196	33	8	is	be	AUX
ejpam-2196	33	9	defined	define	VERB
ejpam-2196	33	10	to	to	PART
ejpam-2196	33	11	be	be	AUX
ejpam-2196	33	12	the	the	DET
ejpam-2196	33	13	set	set	NOUN
ejpam-2196	33	14	of	of	ADP
ejpam-2196	33	15	all	all	DET
ejpam-2196	33	16	primary	primary	ADJ
ejpam-2196	33	17	-	-	PUNCT
ejpam-2196	33	18	like	like	ADJ
ejpam-2196	33	19	submodules	submodule	NOUN
ejpam-2196	33	20	n	n	PROPN
ejpam-2196	33	21	of	of	ADP
ejpam-2196	33	22	m	m	PRON
ejpam-2196	33	23	such	such	ADJ
ejpam-2196	33	24	that	that	SCONJ
ejpam-2196	33	25	m	m	NOUN
ejpam-2196	33	26	/	/	SYM
ejpam-2196	33	27	n	n	PROPN
ejpam-2196	33	28	is	be	AUX
ejpam-2196	33	29	a	a	DET
ejpam-2196	33	30	ψ	ψ	NOUN
ejpam-2196	33	31	-	-	NOUN
ejpam-2196	33	32	module	module	NOUN
ejpam-2196	33	33	over	over	ADP
ejpam-2196	33	34	r.	r.	PROPN
ejpam-2196	33	35	in	in	ADP
ejpam-2196	33	36	[	[	X
ejpam-2196	33	37	7	7	NUM
ejpam-2196	33	38	,	,	PUNCT
ejpam-2196	33	39	lemma	lemma	PROPN
ejpam-2196	33	40	2.1	2.1	NUM
ejpam-2196	33	41	]	]	PUNCT
ejpam-2196	33	42	it	it	PRON
ejpam-2196	33	43	is	be	AUX
ejpam-2196	33	44	shown	show	VERB
ejpam-2196	33	45	that	that	SCONJ
ejpam-2196	33	46	,	,	PUNCT
ejpam-2196	33	47	if	if	SCONJ
ejpam-2196	33	48	q	q	X
ejpam-2196	33	49	∈	∈	PROPN
ejpam-2196	33	50	pspec(m	pspec(m	NOUN
ejpam-2196	33	51	)	)	PUNCT
ejpam-2196	33	52	,	,	PUNCT
ejpam-2196	33	53	then	then	ADV
ejpam-2196	33	54	(	(	PUNCT
ejpam-2196	33	55	q	q	NOUN
ejpam-2196	33	56	:	:	PUNCT
ejpam-2196	33	57	m	m	X
ejpam-2196	33	58	)	)	PUNCT
ejpam-2196	33	59	is	be	AUX
ejpam-2196	33	60	a	a	DET
ejpam-2196	33	61	primary	primary	ADJ
ejpam-2196	33	62	ideal	ideal	NOUN
ejpam-2196	33	63	of	of	ADP
ejpam-2196	33	64	r	r	NOUN
ejpam-2196	33	65	and	and	CCONJ
ejpam-2196	33	66	so	so	ADV
ejpam-2196	33	67	p	p	NOUN
ejpam-2196	33	68	=	=	PUNCT
ejpam-2196	33	69	p	p	X
ejpam-2196	33	70	(	(	PUNCT
ejpam-2196	33	71	q	q	NOUN
ejpam-2196	33	72	:	:	PUNCT
ejpam-2196	33	73	m	m	X
ejpam-2196	33	74	)	)	PUNCT
ejpam-2196	33	75	is	be	AUX
ejpam-2196	33	76	a	a	DET
ejpam-2196	33	77	prime	prime	ADJ
ejpam-2196	33	78	ideal	ideal	NOUN
ejpam-2196	33	79	of	of	ADP
ejpam-2196	33	80	r.	r.	PROPN
ejpam-2196	33	81	in	in	ADP
ejpam-2196	33	82	this	this	DET
ejpam-2196	33	83	case	case	NOUN
ejpam-2196	33	84	,	,	PUNCT
ejpam-2196	33	85	the	the	DET
ejpam-2196	33	86	primary	primary	ADJ
ejpam-2196	33	87	-	-	PUNCT
ejpam-2196	33	88	like	like	ADJ
ejpam-2196	33	89	submodule	submodule	NOUN
ejpam-2196	33	90	q	q	PROPN
ejpam-2196	33	91	is	be	AUX
ejpam-2196	33	92	also	also	ADV
ejpam-2196	33	93	called	call	VERB
ejpam-2196	33	94	a	a	DET
ejpam-2196	33	95	p	p	NOUN
ejpam-2196	33	96	-	-	PUNCT
ejpam-2196	33	97	primary	primary	ADJ
ejpam-2196	33	98	-	-	PUNCT
ejpam-2196	33	99	like	like	ADJ
ejpam-2196	33	100	submodule	submodule	NOUN
ejpam-2196	33	101	of	of	ADP
ejpam-2196	33	102	m	m	PROPN
ejpam-2196	33	103	.	.	PUNCT
ejpam-2196	34	1	definition	definition	NOUN
ejpam-2196	34	2	1	1	NUM
ejpam-2196	34	3	.	.	PUNCT
ejpam-2196	35	1	we	we	PRON
ejpam-2196	35	2	say	say	VERB
ejpam-2196	35	3	that	that	SCONJ
ejpam-2196	35	4	an	an	DET
ejpam-2196	35	5	r	r	NOUN
ejpam-2196	35	6	-	-	PUNCT
ejpam-2196	35	7	module	module	NOUN
ejpam-2196	35	8	m	m	NOUN
ejpam-2196	35	9	is	be	AUX
ejpam-2196	35	10	a	a	DET
ejpam-2196	35	11	φ	φ	NOUN
ejpam-2196	35	12	-	-	PUNCT
ejpam-2196	35	13	module	module	NOUN
ejpam-2196	35	14	if	if	SCONJ
ejpam-2196	35	15	either	either	PRON
ejpam-2196	35	16	m	m	VERB
ejpam-2196	35	17	=	=	SYM
ejpam-2196	35	18	(	(	PUNCT
ejpam-2196	35	19	0	0	NUM
ejpam-2196	35	20	)	)	PUNCT
ejpam-2196	35	21	or	or	CCONJ
ejpam-2196	35	22	m	m	PROPN
ejpam-2196	35	23	6=	6=	NUM
ejpam-2196	35	24	(	(	PUNCT
ejpam-2196	35	25	0	0	NUM
ejpam-2196	35	26	)	)	PUNCT
ejpam-2196	35	27	and	and	CCONJ
ejpam-2196	35	28	the	the	DET
ejpam-2196	35	29	map	map	NOUN
ejpam-2196	35	30	φ	φ	X
ejpam-2196	35	31	:	:	PUNCT
ejpam-2196	35	32	pspec(m)→	pspec(m)→	VERB
ejpam-2196	35	33	spec(r	spec(r	PROPN
ejpam-2196	35	34	/	/	SYM
ejpam-2196	35	35	ann(m	ann(m	PROPN
ejpam-2196	35	36	)	)	PUNCT
ejpam-2196	35	37	)	)	PUNCT
ejpam-2196	35	38	defined	define	VERB
ejpam-2196	35	39	by	by	ADP
ejpam-2196	35	40	φ(q	φ(q	NOUN
ejpam-2196	35	41	)	)	PUNCT
ejpam-2196	35	42	=	=	SYM
ejpam-2196	36	1	p	p	X
ejpam-2196	36	2	(	(	PUNCT
ejpam-2196	36	3	q	q	NOUN
ejpam-2196	36	4	:	:	PUNCT
ejpam-2196	36	5	m)/ann(m	m)/ann(m	NOUN
ejpam-2196	36	6	)	)	PUNCT
ejpam-2196	36	7	is	be	AUX
ejpam-2196	36	8	surjective	surjective	ADJ
ejpam-2196	36	9	.	.	PUNCT
ejpam-2196	37	1	the	the	DET
ejpam-2196	37	2	saturation	saturation	NOUN
ejpam-2196	37	3	of	of	ADP
ejpam-2196	37	4	a	a	DET
ejpam-2196	37	5	submodule	submodule	NOUN
ejpam-2196	37	6	n	n	PROPN
ejpam-2196	37	7	of	of	ADP
ejpam-2196	37	8	an	an	DET
ejpam-2196	37	9	r	r	NOUN
ejpam-2196	37	10	-	-	PUNCT
ejpam-2196	37	11	module	module	NOUN
ejpam-2196	37	12	m	m	NOUN
ejpam-2196	37	13	with	with	ADP
ejpam-2196	37	14	respect	respect	NOUN
ejpam-2196	37	15	to	to	ADP
ejpam-2196	37	16	a	a	DET
ejpam-2196	37	17	prime	prime	ADJ
ejpam-2196	37	18	ideal	ideal	NOUN
ejpam-2196	37	19	p	p	NOUN
ejpam-2196	37	20	of	of	ADP
ejpam-2196	37	21	r	r	NOUN
ejpam-2196	37	22	is	be	AUX
ejpam-2196	37	23	the	the	DET
ejpam-2196	37	24	contraction	contraction	NOUN
ejpam-2196	37	25	of	of	ADP
ejpam-2196	37	26	np	np	INTJ
ejpam-2196	37	27	in	in	ADP
ejpam-2196	37	28	m	m	PROPN
ejpam-2196	37	29	and	and	CCONJ
ejpam-2196	37	30	designated	designate	VERB
ejpam-2196	37	31	by	by	ADP
ejpam-2196	37	32	sp(n	sp(n	PROPN
ejpam-2196	37	33	)	)	PUNCT
ejpam-2196	37	34	.	.	PUNCT
ejpam-2196	38	1	it	it	PRON
ejpam-2196	38	2	is	be	AUX
ejpam-2196	38	3	known	know	VERB
ejpam-2196	38	4	that	that	SCONJ
ejpam-2196	38	5	[	[	X
ejpam-2196	38	6	4	4	NUM
ejpam-2196	38	7	,	,	PUNCT
ejpam-2196	38	8	10	10	NUM
ejpam-2196	38	9	]	]	SYM
ejpam-2196	38	10	sp(n	sp(n	ADJ
ejpam-2196	38	11	)	)	PUNCT
ejpam-2196	38	12	=	=	PRON
ejpam-2196	38	13	{	{	PUNCT
ejpam-2196	38	14	m	m	VERB
ejpam-2196	38	15	∈	∈	NOUN
ejpam-2196	38	16	m	m	VERB
ejpam-2196	38	17	|	|	ADV
ejpam-2196	38	18	rm	rm	PROPN
ejpam-2196	38	19	∈	∈	PROPN
ejpam-2196	38	20	n	n	PROPN
ejpam-2196	38	21	for	for	ADP
ejpam-2196	38	22	some	some	DET
ejpam-2196	38	23	r	r	NOUN
ejpam-2196	38	24	∈	∈	NOUN
ejpam-2196	38	25	r\p	r\p	NOUN
ejpam-2196	38	26	}	}	PUNCT
ejpam-2196	38	27	.	.	PUNCT
ejpam-2196	39	1	if	if	SCONJ
ejpam-2196	39	2	p	p	PROPN
ejpam-2196	39	3	∈	∈	PROPN
ejpam-2196	39	4	spec(r	spec(r	PROPN
ejpam-2196	39	5	)	)	PUNCT
ejpam-2196	39	6	and	and	CCONJ
ejpam-2196	39	7	n	n	PROPN
ejpam-2196	39	8	is	be	AUX
ejpam-2196	39	9	a	a	DET
ejpam-2196	39	10	submodule	submodule	NOUN
ejpam-2196	39	11	of	of	ADP
ejpam-2196	39	12	an	an	DET
ejpam-2196	39	13	r	r	NOUN
ejpam-2196	39	14	-	-	PUNCT
ejpam-2196	39	15	module	module	NOUN
ejpam-2196	39	16	m	m	NOUN
ejpam-2196	39	17	such	such	ADJ
ejpam-2196	39	18	that	that	SCONJ
ejpam-2196	39	19	(	(	PUNCT
ejpam-2196	39	20	n	n	NUM
ejpam-2196	39	21	:	:	PUNCT
ejpam-2196	39	22	m	m	X
ejpam-2196	39	23	)	)	PUNCT
ejpam-2196	40	1	⊆	⊆	NUM
ejpam-2196	40	2	p	p	NOUN
ejpam-2196	40	3	and	and	CCONJ
ejpam-2196	40	4	m	m	PROPN
ejpam-2196	40	5	/	/	SYM
ejpam-2196	40	6	n	n	PROPN
ejpam-2196	40	7	is	be	AUX
ejpam-2196	40	8	a	a	DET
ejpam-2196	40	9	ψ	ψ	NOUN
ejpam-2196	40	10	-	-	NOUN
ejpam-2196	40	11	module	module	NOUN
ejpam-2196	40	12	over	over	ADP
ejpam-2196	40	13	r	r	NOUN
ejpam-2196	40	14	,	,	PUNCT
ejpam-2196	40	15	then	then	ADV
ejpam-2196	40	16	sp(n	sp(n	PUNCT
ejpam-2196	41	1	+	+	CCONJ
ejpam-2196	41	2	pm	pm	NOUN
ejpam-2196	41	3	)	)	PUNCT
ejpam-2196	41	4	is	be	AUX
ejpam-2196	41	5	a	a	DET
ejpam-2196	41	6	p	p	ADJ
ejpam-2196	41	7	-	-	PUNCT
ejpam-2196	41	8	prime	prime	NOUN
ejpam-2196	41	9	submodule	submodule	NOUN
ejpam-2196	41	10	of	of	ADP
ejpam-2196	41	11	m	m	PROPN
ejpam-2196	42	1	[	[	X
ejpam-2196	42	2	9	9	NUM
ejpam-2196	42	3	,	,	PUNCT
ejpam-2196	42	4	proposition	proposition	NOUN
ejpam-2196	42	5	4.4	4.4	NUM
ejpam-2196	42	6	]	]	PUNCT
ejpam-2196	42	7	.	.	PUNCT
ejpam-2196	43	1	therefore	therefore	ADV
ejpam-2196	43	2	ρ	ρ	X
ejpam-2196	43	3	:	:	PUNCT
ejpam-2196	43	4	pspec(m	pspec(m	NOUN
ejpam-2196	43	5	)	)	PUNCT
ejpam-2196	43	6	→	→	SYM
ejpam-2196	43	7	spec(m	spec(m	PROPN
ejpam-2196	43	8	)	)	PUNCT
ejpam-2196	43	9	defined	define	VERB
ejpam-2196	43	10	by	by	ADP
ejpam-2196	43	11	ρ(q	ρ(q	NOUN
ejpam-2196	43	12	)	)	PUNCT
ejpam-2196	43	13	=	=	PUNCT
ejpam-2196	43	14	sp(q	sp(q	NOUN
ejpam-2196	43	15	+	+	CCONJ
ejpam-2196	43	16	pm	pm	NOUN
ejpam-2196	43	17	)	)	PUNCT
ejpam-2196	43	18	is	be	AUX
ejpam-2196	43	19	a	a	DET
ejpam-2196	43	20	well	well	ADV
ejpam-2196	43	21	-	-	PUNCT
ejpam-2196	43	22	defined	define	VERB
ejpam-2196	43	23	map	map	NOUN
ejpam-2196	43	24	,	,	PUNCT
ejpam-2196	43	25	where	where	SCONJ
ejpam-2196	43	26	p	p	NOUN
ejpam-2196	43	27	=	=	X
ejpam-2196	43	28	p	p	X
ejpam-2196	43	29	(	(	PUNCT
ejpam-2196	43	30	q	q	NOUN
ejpam-2196	43	31	:	:	PUNCT
ejpam-2196	43	32	m	m	NUM
ejpam-2196	43	33	)	)	PUNCT
ejpam-2196	43	34	.	.	PUNCT
ejpam-2196	44	1	it	it	PRON
ejpam-2196	44	2	is	be	AUX
ejpam-2196	44	3	easy	easy	ADJ
ejpam-2196	44	4	to	to	PART
ejpam-2196	44	5	see	see	VERB
ejpam-2196	44	6	that	that	SCONJ
ejpam-2196	44	7	φ	φ	PROPN
ejpam-2196	44	8	=	=	SYM
ejpam-2196	44	9	ψ	ψ	PROPN
ejpam-2196	44	10	◦	◦	NOUN
ejpam-2196	44	11	ρ	ρ	PROPN
ejpam-2196	44	12	,	,	PUNCT
ejpam-2196	44	13	ψ	ψ	X
ejpam-2196	44	14	composed	compose	VERB
ejpam-2196	44	15	with	with	ADP
ejpam-2196	44	16	ρ	ρ	PROPN
ejpam-2196	44	17	.	.	PUNCT
ejpam-2196	45	1	thus	thus	ADV
ejpam-2196	45	2	,	,	PUNCT
ejpam-2196	45	3	if	if	SCONJ
ejpam-2196	45	4	φ	φ	PROPN
ejpam-2196	45	5	is	be	AUX
ejpam-2196	45	6	a	a	DET
ejpam-2196	45	7	surjective	surjective	ADJ
ejpam-2196	45	8	map	map	NOUN
ejpam-2196	45	9	,	,	PUNCT
ejpam-2196	45	10	so	so	ADV
ejpam-2196	45	11	is	be	AUX
ejpam-2196	45	12	ψ	ψ	X
ejpam-2196	45	13	.	.	PUNCT
ejpam-2196	46	1	this	this	PRON
ejpam-2196	46	2	means	mean	VERB
ejpam-2196	46	3	that	that	SCONJ
ejpam-2196	46	4	every	every	DET
ejpam-2196	46	5	φ	φ	NOUN
ejpam-2196	46	6	-	-	PUNCT
ejpam-2196	46	7	module	module	NOUN
ejpam-2196	46	8	is	be	AUX
ejpam-2196	46	9	a	a	DET
ejpam-2196	46	10	ψ	ψ	NOUN
ejpam-2196	46	11	-	-	NOUN
ejpam-2196	46	12	module	module	NOUN
ejpam-2196	46	13	.	.	PUNCT
ejpam-2196	47	1	we	we	PRON
ejpam-2196	47	2	give	give	VERB
ejpam-2196	47	3	an	an	DET
ejpam-2196	47	4	example	example	NOUN
ejpam-2196	47	5	of	of	ADP
ejpam-2196	47	6	a	a	DET
ejpam-2196	47	7	ψ	ψ	NOUN
ejpam-2196	47	8	-	-	NOUN
ejpam-2196	47	9	module	module	NOUN
ejpam-2196	47	10	module	module	NOUN
ejpam-2196	47	11	which	which	PRON
ejpam-2196	47	12	is	be	AUX
ejpam-2196	47	13	not	not	PART
ejpam-2196	47	14	a	a	DET
ejpam-2196	47	15	φ	φ	NOUN
ejpam-2196	47	16	-	-	PUNCT
ejpam-2196	47	17	module	module	NOUN
ejpam-2196	47	18	(	(	PUNCT
ejpam-2196	47	19	example	example	NOUN
ejpam-2196	47	20	1	1	NUM
ejpam-2196	47	21	)	)	PUNCT
ejpam-2196	47	22	.	.	PUNCT
ejpam-2196	48	1	an	an	DET
ejpam-2196	48	2	r	r	NOUN
ejpam-2196	48	3	-	-	PUNCT
ejpam-2196	48	4	module	module	NOUN
ejpam-2196	48	5	m	m	NOUN
ejpam-2196	48	6	is	be	AUX
ejpam-2196	48	7	said	say	VERB
ejpam-2196	48	8	to	to	PART
ejpam-2196	48	9	be	be	AUX
ejpam-2196	48	10	multiplication	multiplication	NOUN
ejpam-2196	48	11	module	module	NOUN
ejpam-2196	48	12	if	if	SCONJ
ejpam-2196	48	13	every	every	DET
ejpam-2196	48	14	submodule	submodule	NOUN
ejpam-2196	48	15	n	n	PROPN
ejpam-2196	48	16	of	of	ADP
ejpam-2196	48	17	m	m	PROPN
ejpam-2196	48	18	is	be	AUX
ejpam-2196	48	19	of	of	ADP
ejpam-2196	48	20	the	the	DET
ejpam-2196	48	21	form	form	NOUN
ejpam-2196	48	22	i	i	PRON
ejpam-2196	48	23	m	m	VERB
ejpam-2196	48	24	for	for	ADP
ejpam-2196	48	25	some	some	DET
ejpam-2196	48	26	ideal	ideal	ADJ
ejpam-2196	49	1	i	i	PRON
ejpam-2196	49	2	of	of	ADP
ejpam-2196	49	3	r	r	NOUN
ejpam-2196	49	4	[	[	X
ejpam-2196	49	5	6	6	NUM
ejpam-2196	49	6	]	]	PUNCT
ejpam-2196	49	7	.	.	PUNCT
ejpam-2196	50	1	we	we	PRON
ejpam-2196	50	2	show	show	VERB
ejpam-2196	50	3	that	that	SCONJ
ejpam-2196	50	4	the	the	DET
ejpam-2196	50	5	multiplicationψ	multiplicationψ	NOUN
ejpam-2196	50	6	-	-	PUNCT
ejpam-2196	50	7	modules	module	NOUN
ejpam-2196	50	8	,	,	PUNCT
ejpam-2196	50	9	finitely	finitely	ADV
ejpam-2196	50	10	generated	generate	VERB
ejpam-2196	50	11	modules	module	NOUN
ejpam-2196	50	12	,	,	PUNCT
ejpam-2196	50	13	free	free	ADJ
ejpam-2196	50	14	modules	module	NOUN
ejpam-2196	50	15	(	(	PUNCT
ejpam-2196	50	16	of	of	ADP
ejpam-2196	50	17	finite	finite	NOUN
ejpam-2196	50	18	or	or	CCONJ
ejpam-2196	50	19	infinite	infinite	ADJ
ejpam-2196	50	20	rank	rank	NOUN
ejpam-2196	50	21	)	)	PUNCT
ejpam-2196	50	22	,	,	PUNCT
ejpam-2196	50	23	faithful	faithful	ADJ
ejpam-2196	50	24	projective	projective	ADJ
ejpam-2196	50	25	modules	module	NOUN
ejpam-2196	50	26	over	over	ADP
ejpam-2196	50	27	domains	domain	NOUN
ejpam-2196	50	28	and	and	CCONJ
ejpam-2196	50	29	modules	module	NOUN
ejpam-2196	50	30	over	over	ADP
ejpam-2196	50	31	artinian	artinian	ADJ
ejpam-2196	50	32	rings	ring	NOUN
ejpam-2196	50	33	are	be	AUX
ejpam-2196	50	34	φ	φ	NOUN
ejpam-2196	50	35	-	-	PUNCT
ejpam-2196	50	36	modules	module	NOUN
ejpam-2196	50	37	(	(	PUNCT
ejpam-2196	50	38	theorem	theorem	NOUN
ejpam-2196	50	39	1	1	NUM
ejpam-2196	50	40	,	,	PUNCT
ejpam-2196	50	41	corollary	corollary	ADJ
ejpam-2196	50	42	1	1	NUM
ejpam-2196	50	43	,	,	PUNCT
ejpam-2196	50	44	theorem	theorem	ADJ
ejpam-2196	50	45	2	2	NUM
ejpam-2196	50	46	,	,	PUNCT
ejpam-2196	50	47	theorem	theorem	VERB
ejpam-2196	50	48	3	3	NUM
ejpam-2196	50	49	and	and	CCONJ
ejpam-2196	50	50	theorem	theorem	VERB
ejpam-2196	50	51	4	4	NUM
ejpam-2196	50	52	)	)	PUNCT
ejpam-2196	50	53	.	.	PUNCT
ejpam-2196	51	1	2	2	X
ejpam-2196	51	2	.	.	X
ejpam-2196	51	3	φ	φ	NOUN
ejpam-2196	51	4	-	-	NOUN
ejpam-2196	51	5	modules	module	NOUN
ejpam-2196	51	6	we	we	PRON
ejpam-2196	51	7	will	will	AUX
ejpam-2196	51	8	use	use	VERB
ejpam-2196	51	9	x	x	PUNCT
ejpam-2196	51	10	,	,	PUNCT
ejpam-2196	51	11	xp	xp	ADV
ejpam-2196	51	12	and	and	CCONJ
ejpam-2196	51	13	xp	xp	INTJ
ejpam-2196	51	14	to	to	PART
ejpam-2196	51	15	represent	represent	VERB
ejpam-2196	51	16	pspec(m	pspec(m	NOUN
ejpam-2196	51	17	)	)	PUNCT
ejpam-2196	51	18	,	,	PUNCT
ejpam-2196	51	19	specp(m	specp(m	NOUN
ejpam-2196	51	20	)	)	PUNCT
ejpam-2196	51	21	and	and	CCONJ
ejpam-2196	51	22	{	{	PUNCT
ejpam-2196	51	23	q	q	NOUN
ejpam-2196	51	24	∈	∈	PROPN
ejpam-2196	51	25	pspec(m	pspec(m	NOUN
ejpam-2196	51	26	)	)	PUNCT
ejpam-2196	52	1	|	|	ADV
ejpam-2196	52	2	p(q	p(q	PROPN
ejpam-2196	52	3	:	:	PUNCT
ejpam-2196	52	4	m	m	X
ejpam-2196	52	5	)	)	PUNCT
ejpam-2196	53	1	=	=	SYM
ejpam-2196	53	2	p	p	X
ejpam-2196	53	3	}	}	PUNCT
ejpam-2196	53	4	respectively	respectively	ADV
ejpam-2196	53	5	.	.	PUNCT
ejpam-2196	54	1	also	also	ADV
ejpam-2196	54	2	v	v	X
ejpam-2196	54	3	(	(	PUNCT
ejpam-2196	54	4	ann(m	ann(m	NOUN
ejpam-2196	54	5	)	)	PUNCT
ejpam-2196	54	6	)	)	PUNCT
ejpam-2196	54	7	will	will	AUX
ejpam-2196	54	8	be	be	AUX
ejpam-2196	54	9	the	the	DET
ejpam-2196	54	10	set	set	NOUN
ejpam-2196	54	11	of	of	ADP
ejpam-2196	54	12	all	all	DET
ejpam-2196	54	13	prime	prime	ADJ
ejpam-2196	54	14	ideals	ideal	NOUN
ejpam-2196	54	15	containing	contain	VERB
ejpam-2196	54	16	ann(m	ann(m	PROPN
ejpam-2196	54	17	)	)	PUNCT
ejpam-2196	54	18	.	.	PUNCT
ejpam-2196	55	1	we	we	PRON
ejpam-2196	55	2	begin	begin	VERB
ejpam-2196	55	3	with	with	ADP
ejpam-2196	55	4	a	a	DET
ejpam-2196	55	5	lemma	lemma	PROPN
ejpam-2196	55	6	which	which	PRON
ejpam-2196	55	7	will	will	AUX
ejpam-2196	55	8	be	be	AUX
ejpam-2196	55	9	referred	refer	VERB
ejpam-2196	55	10	to	to	ADP
ejpam-2196	55	11	in	in	ADP
ejpam-2196	55	12	the	the	DET
ejpam-2196	55	13	rest	rest	NOUN
ejpam-2196	55	14	of	of	ADP
ejpam-2196	55	15	this	this	DET
ejpam-2196	55	16	section	section	NOUN
ejpam-2196	55	17	.	.	PUNCT
ejpam-2196	56	1	lemma	lemma	PROPN
ejpam-2196	56	2	1	1	NUM
ejpam-2196	56	3	(	(	PUNCT
ejpam-2196	56	4	cf	cf	NOUN
ejpam-2196	56	5	.	.	PUNCT
ejpam-2196	57	1	[	[	X
ejpam-2196	57	2	9	9	NUM
ejpam-2196	57	3	,	,	PUNCT
ejpam-2196	57	4	theorem	theorem	VERB
ejpam-2196	57	5	2.1	2.1	NUM
ejpam-2196	57	6	]	]	PUNCT
ejpam-2196	57	7	)	)	PUNCT
ejpam-2196	57	8	.	.	PUNCT
ejpam-2196	58	1	let	let	VERB
ejpam-2196	58	2	m	m	PRON
ejpam-2196	58	3	be	be	AUX
ejpam-2196	58	4	a	a	DET
ejpam-2196	58	5	non	non	ADJ
ejpam-2196	58	6	-	-	ADJ
ejpam-2196	58	7	zero	zero	ADJ
ejpam-2196	58	8	r	r	NOUN
ejpam-2196	58	9	-	-	PUNCT
ejpam-2196	58	10	module	module	NOUN
ejpam-2196	58	11	.	.	PUNCT
ejpam-2196	59	1	then	then	ADV
ejpam-2196	59	2	the	the	DET
ejpam-2196	59	3	following	follow	VERB
ejpam-2196	59	4	statements	statement	NOUN
ejpam-2196	59	5	are	be	AUX
ejpam-2196	59	6	equivalent	equivalent	ADJ
ejpam-2196	59	7	.	.	PUNCT
ejpam-2196	60	1	(	(	PUNCT
ejpam-2196	60	2	1	1	X
ejpam-2196	60	3	)	)	PUNCT
ejpam-2196	60	4	m	m	VERB
ejpam-2196	60	5	is	be	AUX
ejpam-2196	60	6	a	a	DET
ejpam-2196	60	7	ψ	ψ	NOUN
ejpam-2196	60	8	-	-	NOUN
ejpam-2196	60	9	module	module	NOUN
ejpam-2196	60	10	;	;	PUNCT
ejpam-2196	60	11	(	(	PUNCT
ejpam-2196	60	12	2	2	X
ejpam-2196	60	13	)	)	PUNCT
ejpam-2196	60	14	xp	xp	NOUN
ejpam-2196	60	15	6=	6=	NUM
ejpam-2196	60	16	;	;	PUNCT
ejpam-2196	60	17	for	for	ADP
ejpam-2196	60	18	every	every	DET
ejpam-2196	60	19	p	p	PROPN
ejpam-2196	60	20	∈	∈	PROPN
ejpam-2196	60	21	v	v	NOUN
ejpam-2196	60	22	(	(	PUNCT
ejpam-2196	60	23	ann(m	ann(m	NOUN
ejpam-2196	60	24	)	)	PUNCT
ejpam-2196	60	25	)	)	PUNCT
ejpam-2196	60	26	;	;	PUNCT
ejpam-2196	60	27	(	(	PUNCT
ejpam-2196	60	28	3	3	X
ejpam-2196	60	29	)	)	PUNCT
ejpam-2196	60	30	pmp	pmp	PROPN
ejpam-2196	60	31	6=	6=	PROPN
ejpam-2196	60	32	mp	mp	PROPN
ejpam-2196	60	33	for	for	ADP
ejpam-2196	60	34	every	every	DET
ejpam-2196	60	35	p	p	PROPN
ejpam-2196	60	36	∈	∈	PROPN
ejpam-2196	60	37	v	v	NOUN
ejpam-2196	60	38	(	(	PUNCT
ejpam-2196	60	39	ann(m	ann(m	NOUN
ejpam-2196	60	40	)	)	PUNCT
ejpam-2196	60	41	)	)	PUNCT
ejpam-2196	60	42	;	;	PUNCT
ejpam-2196	60	43	(	(	PUNCT
ejpam-2196	60	44	4	4	X
ejpam-2196	60	45	)	)	PUNCT
ejpam-2196	60	46	sp(pm	sp(pm	NOUN
ejpam-2196	60	47	)	)	PUNCT
ejpam-2196	60	48	is	be	AUX
ejpam-2196	60	49	a	a	DET
ejpam-2196	60	50	p	p	ADJ
ejpam-2196	60	51	-	-	PUNCT
ejpam-2196	60	52	prime	prime	NOUN
ejpam-2196	60	53	submodule	submodule	NOUN
ejpam-2196	60	54	for	for	ADP
ejpam-2196	60	55	every	every	DET
ejpam-2196	60	56	p	p	PROPN
ejpam-2196	60	57	∈	∈	PROPN
ejpam-2196	60	58	v	v	NOUN
ejpam-2196	60	59	(	(	PUNCT
ejpam-2196	60	60	ann(m	ann(m	NOUN
ejpam-2196	60	61	)	)	PUNCT
ejpam-2196	60	62	)	)	PUNCT
ejpam-2196	60	63	.	.	PUNCT
ejpam-2196	61	1	theorem	theorem	NOUN
ejpam-2196	61	2	1	1	NUM
ejpam-2196	61	3	.	.	PUNCT
ejpam-2196	62	1	every	every	DET
ejpam-2196	62	2	φ	φ	NOUN
ejpam-2196	62	3	-	-	PUNCT
ejpam-2196	62	4	module	module	NOUN
ejpam-2196	62	5	m	m	NOUN
ejpam-2196	62	6	over	over	ADP
ejpam-2196	62	7	a	a	DET
ejpam-2196	62	8	ring	ring	NOUN
ejpam-2196	62	9	r	r	NOUN
ejpam-2196	62	10	is	be	AUX
ejpam-2196	62	11	a	a	DET
ejpam-2196	62	12	ψ	ψ	NOUN
ejpam-2196	62	13	-	-	NOUN
ejpam-2196	62	14	module	module	NOUN
ejpam-2196	62	15	,	,	PUNCT
ejpam-2196	62	16	and	and	CCONJ
ejpam-2196	62	17	the	the	DET
ejpam-2196	62	18	converse	converse	NOUN
ejpam-2196	62	19	is	be	AUX
ejpam-2196	62	20	true	true	ADJ
ejpam-2196	62	21	in	in	ADP
ejpam-2196	62	22	each	each	PRON
ejpam-2196	62	23	of	of	ADP
ejpam-2196	62	24	the	the	DET
ejpam-2196	62	25	following	follow	VERB
ejpam-2196	62	26	cases	case	NOUN
ejpam-2196	62	27	.	.	PUNCT
ejpam-2196	63	1	(	(	PUNCT
ejpam-2196	63	2	1	1	X
ejpam-2196	63	3	)	)	PUNCT
ejpam-2196	63	4	m	m	VERB
ejpam-2196	63	5	is	be	AUX
ejpam-2196	63	6	a	a	DET
ejpam-2196	63	7	multiplication	multiplication	NOUN
ejpam-2196	63	8	r	r	NOUN
ejpam-2196	63	9	-	-	PUNCT
ejpam-2196	63	10	module	module	NOUN
ejpam-2196	63	11	.	.	PUNCT
ejpam-2196	64	1	h.	h.	PROPN
ejpam-2196	64	2	moghimi	moghimi	PROPN
ejpam-2196	64	3	,	,	PUNCT
ejpam-2196	64	4	f.	f.	PROPN
ejpam-2196	64	5	rashedi	rashedi	PROPN
ejpam-2196	64	6	/	/	SYM
ejpam-2196	64	7	eur	eur	PROPN
ejpam-2196	64	8	.	.	PUNCT
ejpam-2196	65	1	j.	j.	PROPN
ejpam-2196	65	2	pure	pure	PROPN
ejpam-2196	65	3	appl	appl	PROPN
ejpam-2196	65	4	.	.	PROPN
ejpam-2196	65	5	math	math	PROPN
ejpam-2196	65	6	,	,	PUNCT
ejpam-2196	65	7	8	8	NUM
ejpam-2196	65	8	(	(	PUNCT
ejpam-2196	65	9	2015	2015	NUM
ejpam-2196	65	10	)	)	PUNCT
ejpam-2196	65	11	,	,	PUNCT
ejpam-2196	65	12	232	232	NUM
ejpam-2196	65	13	-	-	SYM
ejpam-2196	65	14	238	238	NUM
ejpam-2196	65	15	234	234	NUM
ejpam-2196	65	16	(	(	PUNCT
ejpam-2196	65	17	2	2	NUM
ejpam-2196	65	18	)	)	PUNCT
ejpam-2196	65	19	m	m	VERB
ejpam-2196	65	20	is	be	AUX
ejpam-2196	65	21	a	a	DET
ejpam-2196	65	22	non	non	ADJ
ejpam-2196	65	23	-	-	ADJ
ejpam-2196	65	24	zero	zero	ADJ
ejpam-2196	65	25	faithfully	faithfully	ADV
ejpam-2196	65	26	flat	flat	ADJ
ejpam-2196	65	27	(	(	PUNCT
ejpam-2196	65	28	or	or	CCONJ
ejpam-2196	65	29	in	in	ADP
ejpam-2196	65	30	particular	particular	ADJ
ejpam-2196	65	31	a	a	DET
ejpam-2196	65	32	projective	projective	NOUN
ejpam-2196	65	33	)	)	PUNCT
ejpam-2196	65	34	r	r	NOUN
ejpam-2196	65	35	-	-	PUNCT
ejpam-2196	65	36	module	module	NOUN
ejpam-2196	65	37	.	.	PUNCT
ejpam-2196	66	1	(	(	PUNCT
ejpam-2196	66	2	3	3	X
ejpam-2196	66	3	)	)	PUNCT
ejpam-2196	66	4	m	m	PROPN
ejpam-2196	66	5	/	/	SYM
ejpam-2196	66	6	sp(pm	sp(pm	NOUN
ejpam-2196	66	7	)	)	PUNCT
ejpam-2196	66	8	is	be	AUX
ejpam-2196	66	9	a	a	DET
ejpam-2196	66	10	ψ	ψ	NOUN
ejpam-2196	66	11	-	-	NOUN
ejpam-2196	66	12	module	module	NOUN
ejpam-2196	66	13	over	over	ADP
ejpam-2196	66	14	r	r	NOUN
ejpam-2196	66	15	for	for	ADP
ejpam-2196	66	16	every	every	DET
ejpam-2196	66	17	p	p	PROPN
ejpam-2196	66	18	∈	∈	PROPN
ejpam-2196	66	19	v	v	NOUN
ejpam-2196	66	20	(	(	PUNCT
ejpam-2196	66	21	ann(m	ann(m	NOUN
ejpam-2196	66	22	)	)	PUNCT
ejpam-2196	66	23	)	)	PUNCT
ejpam-2196	66	24	.	.	PUNCT
ejpam-2196	67	1	proof	proof	NOUN
ejpam-2196	67	2	.	.	PUNCT
ejpam-2196	68	1	since	since	SCONJ
ejpam-2196	68	2	φ	φ	PROPN
ejpam-2196	68	3	=	=	SYM
ejpam-2196	68	4	ψ	ψ	PROPN
ejpam-2196	68	5	◦	◦	NOUN
ejpam-2196	68	6	ρ	ρ	PROPN
ejpam-2196	68	7	,	,	PUNCT
ejpam-2196	68	8	every	every	DET
ejpam-2196	68	9	φ	φ	NOUN
ejpam-2196	68	10	-	-	PUNCT
ejpam-2196	68	11	module	module	NOUN
ejpam-2196	68	12	is	be	AUX
ejpam-2196	68	13	a	a	DET
ejpam-2196	68	14	ψ	ψ	NOUN
ejpam-2196	68	15	-	-	NOUN
ejpam-2196	68	16	module	module	NOUN
ejpam-2196	68	17	.	.	PUNCT
ejpam-2196	69	1	(	(	PUNCT
ejpam-2196	69	2	1	1	X
ejpam-2196	69	3	)	)	PUNCT
ejpam-2196	69	4	let	let	VERB
ejpam-2196	69	5	p	p	PRON
ejpam-2196	69	6	∈	∈	PROPN
ejpam-2196	69	7	v	v	X
ejpam-2196	69	8	(	(	PUNCT
ejpam-2196	69	9	ann(m	ann(m	NOUN
ejpam-2196	69	10	)	)	PUNCT
ejpam-2196	69	11	)	)	PUNCT
ejpam-2196	69	12	.	.	PUNCT
ejpam-2196	70	1	then	then	ADV
ejpam-2196	70	2	there	there	PRON
ejpam-2196	70	3	exists	exist	VERB
ejpam-2196	70	4	a	a	DET
ejpam-2196	70	5	prime	prime	ADJ
ejpam-2196	70	6	submodule	submodule	NOUN
ejpam-2196	70	7	p	p	NOUN
ejpam-2196	70	8	such	such	ADJ
ejpam-2196	70	9	that	that	PRON
ejpam-2196	70	10	(	(	PUNCT
ejpam-2196	70	11	p	p	X
ejpam-2196	70	12	:	:	PUNCT
ejpam-2196	70	13	m	m	X
ejpam-2196	70	14	)	)	PUNCT
ejpam-2196	71	1	=	=	SYM
ejpam-2196	72	1	p.	p.	NOUN
ejpam-2196	72	2	since	since	SCONJ
ejpam-2196	72	3	m	m	PROPN
ejpam-2196	72	4	is	be	AUX
ejpam-2196	72	5	a	a	DET
ejpam-2196	72	6	multiplication	multiplication	NOUN
ejpam-2196	72	7	module	module	NOUN
ejpam-2196	72	8	p	p	NOUN
ejpam-2196	72	9	=	=	NOUN
ejpam-2196	72	10	pm	pm	NOUN
ejpam-2196	72	11	.	.	PUNCT
ejpam-2196	73	1	suppose	suppose	VERB
ejpam-2196	73	2	q	q	PROPN
ejpam-2196	73	3	∈	∈	PROPN
ejpam-2196	73	4	spec(r	spec(r	PROPN
ejpam-2196	73	5	)	)	PUNCT
ejpam-2196	73	6	and	and	CCONJ
ejpam-2196	73	7	p	p	X
ejpam-2196	73	8	⊆	⊆	NUM
ejpam-2196	73	9	q.	q.	NOUN
ejpam-2196	73	10	by	by	ADP
ejpam-2196	73	11	lemma	lemma	PROPN
ejpam-2196	73	12	1	1	NUM
ejpam-2196	73	13	,	,	PUNCT
ejpam-2196	73	14	there	there	PRON
ejpam-2196	73	15	exists	exist	VERB
ejpam-2196	73	16	a	a	DET
ejpam-2196	73	17	prime	prime	ADJ
ejpam-2196	73	18	submodule	submodule	NOUN
ejpam-2196	73	19	p	p	NOUN
ejpam-2196	73	20	′	′	NUM
ejpam-2196	73	21	such	such	ADJ
ejpam-2196	73	22	that	that	PRON
ejpam-2196	73	23	(	(	PUNCT
ejpam-2196	73	24	p	p	NOUN
ejpam-2196	73	25	′	′	NUM
ejpam-2196	73	26	:	:	PUNCT
ejpam-2196	73	27	m	m	X
ejpam-2196	73	28	)	)	PUNCT
ejpam-2196	74	1	=	=	PUNCT
ejpam-2196	74	2	q.	q.	NOUN
ejpam-2196	74	3	it	it	PRON
ejpam-2196	74	4	follows	follow	VERB
ejpam-2196	74	5	that	that	SCONJ
ejpam-2196	74	6	p	p	PRON
ejpam-2196	74	7	=	=	PUNCT
ejpam-2196	74	8	pm	pm	NOUN
ejpam-2196	74	9	⊆	⊆	NUM
ejpam-2196	74	10	qm	qm	PROPN
ejpam-2196	74	11	=	=	PROPN
ejpam-2196	74	12	p	p	PROPN
ejpam-2196	74	13	′.	′.	NOUN
ejpam-2196	74	14	hence	hence	ADV
ejpam-2196	74	15	m	m	PROPN
ejpam-2196	74	16	/	/	SYM
ejpam-2196	74	17	p	p	X
ejpam-2196	74	18	is	be	AUX
ejpam-2196	74	19	a	a	DET
ejpam-2196	74	20	ψ	ψ	NOUN
ejpam-2196	74	21	-	-	NOUN
ejpam-2196	74	22	module	module	NOUN
ejpam-2196	74	23	and	and	CCONJ
ejpam-2196	74	24	so	so	ADV
ejpam-2196	74	25	p	p	X
ejpam-2196	74	26	∈	∈	PROPN
ejpam-2196	74	27	pspec(m	pspec(m	NOUN
ejpam-2196	74	28	)	)	PUNCT
ejpam-2196	74	29	.	.	PUNCT
ejpam-2196	75	1	now	now	ADV
ejpam-2196	75	2	from	from	ADP
ejpam-2196	75	3	φ(p	φ(p	NOUN
ejpam-2196	75	4	)	)	PUNCT
ejpam-2196	75	5	=	=	SYM
ejpam-2196	75	6	p	p	X
ejpam-2196	75	7	/	/	SYM
ejpam-2196	75	8	ann(m	ann(m	PROPN
ejpam-2196	75	9	)	)	PUNCT
ejpam-2196	75	10	,	,	PUNCT
ejpam-2196	75	11	we	we	PRON
ejpam-2196	75	12	conclude	conclude	VERB
ejpam-2196	75	13	that	that	SCONJ
ejpam-2196	75	14	φ	φ	PROPN
ejpam-2196	75	15	is	be	AUX
ejpam-2196	75	16	surjective	surjective	ADJ
ejpam-2196	75	17	,	,	PUNCT
ejpam-2196	75	18	i.e.	i.e.	X
ejpam-2196	75	19	,	,	PUNCT
ejpam-2196	75	20	m	m	VERB
ejpam-2196	75	21	is	be	AUX
ejpam-2196	75	22	a	a	DET
ejpam-2196	75	23	φ	φ	NOUN
ejpam-2196	75	24	-	-	PUNCT
ejpam-2196	75	25	module	module	NOUN
ejpam-2196	75	26	.	.	PUNCT
ejpam-2196	76	1	(	(	PUNCT
ejpam-2196	76	2	2	2	X
ejpam-2196	76	3	)	)	PUNCT
ejpam-2196	76	4	let	let	VERB
ejpam-2196	76	5	p	p	PRON
ejpam-2196	76	6	∈	∈	PROPN
ejpam-2196	76	7	v	v	NOUN
ejpam-2196	76	8	(	(	PUNCT
ejpam-2196	76	9	ann(m	ann(m	NOUN
ejpam-2196	76	10	)	)	PUNCT
ejpam-2196	76	11	)	)	PUNCT
ejpam-2196	77	1	and	and	CCONJ
ejpam-2196	77	2	(	(	PUNCT
ejpam-2196	77	3	p	p	X
ejpam-2196	77	4	:	:	PUNCT
ejpam-2196	77	5	m	m	X
ejpam-2196	77	6	)	)	PUNCT
ejpam-2196	78	1	=	=	SYM
ejpam-2196	79	1	p.	p.	NOUN
ejpam-2196	79	2	if	if	SCONJ
ejpam-2196	79	3	m	m	NOUN
ejpam-2196	79	4	is	be	AUX
ejpam-2196	79	5	a	a	DET
ejpam-2196	79	6	projective	projective	ADJ
ejpam-2196	79	7	module	module	NOUN
ejpam-2196	79	8	,	,	PUNCT
ejpam-2196	79	9	then	then	ADV
ejpam-2196	79	10	pm	pm	NOUN
ejpam-2196	79	11	is	be	AUX
ejpam-2196	79	12	a	a	DET
ejpam-2196	79	13	prime	prime	ADJ
ejpam-2196	79	14	submodule	submodule	NOUN
ejpam-2196	79	15	of	of	ADP
ejpam-2196	79	16	m	m	PRON
ejpam-2196	79	17	by	by	ADP
ejpam-2196	79	18	[	[	X
ejpam-2196	79	19	1	1	NUM
ejpam-2196	79	20	,	,	PUNCT
ejpam-2196	79	21	corollary	corollary	ADJ
ejpam-2196	79	22	2.3	2.3	NUM
ejpam-2196	79	23	]	]	PUNCT
ejpam-2196	79	24	.	.	PUNCT
ejpam-2196	80	1	also	also	ADV
ejpam-2196	80	2	if	if	SCONJ
ejpam-2196	80	3	m	m	NOUN
ejpam-2196	80	4	is	be	AUX
ejpam-2196	80	5	a	a	DET
ejpam-2196	80	6	faithfully	faithfully	ADV
ejpam-2196	80	7	flat	flat	ADJ
ejpam-2196	80	8	module	module	NOUN
ejpam-2196	80	9	,	,	PUNCT
ejpam-2196	80	10	then	then	ADV
ejpam-2196	80	11	pm	pm	NOUN
ejpam-2196	80	12	is	be	AUX
ejpam-2196	80	13	a	a	DET
ejpam-2196	80	14	prime	prime	ADJ
ejpam-2196	80	15	submodule	submodule	NOUN
ejpam-2196	80	16	by	by	ADP
ejpam-2196	80	17	[	[	X
ejpam-2196	80	18	3	3	NUM
ejpam-2196	80	19	,	,	PUNCT
ejpam-2196	80	20	corollary	corollary	ADJ
ejpam-2196	80	21	2.6	2.6	NUM
ejpam-2196	80	22	]	]	PUNCT
ejpam-2196	80	23	.	.	PUNCT
ejpam-2196	81	1	on	on	ADP
ejpam-2196	81	2	the	the	DET
ejpam-2196	81	3	other	other	ADJ
ejpam-2196	81	4	hand	hand	NOUN
ejpam-2196	81	5	m	m	NOUN
ejpam-2196	81	6	/	/	SYM
ejpam-2196	81	7	pm	pm	NOUN
ejpam-2196	81	8	is	be	AUX
ejpam-2196	81	9	a	a	DET
ejpam-2196	81	10	ψ	ψ	NOUN
ejpam-2196	81	11	-	-	NOUN
ejpam-2196	81	12	module	module	NOUN
ejpam-2196	81	13	and	and	CCONJ
ejpam-2196	81	14	(	(	PUNCT
ejpam-2196	81	15	pm	pm	NOUN
ejpam-2196	81	16	:	:	PUNCT
ejpam-2196	81	17	m	m	X
ejpam-2196	81	18	)	)	PUNCT
ejpam-2196	82	1	=	=	SYM
ejpam-2196	82	2	p	p	NOUN
ejpam-2196	82	3	by	by	ADP
ejpam-2196	82	4	[	[	PUNCT
ejpam-2196	82	5	9	9	NUM
ejpam-2196	82	6	,	,	PUNCT
ejpam-2196	82	7	corollary	corollary	ADJ
ejpam-2196	82	8	4.3	4.3	NUM
ejpam-2196	82	9	and	and	CCONJ
ejpam-2196	82	10	proposition	proposition	NOUN
ejpam-2196	82	11	4.5	4.5	NUM
ejpam-2196	82	12	]	]	PUNCT
ejpam-2196	82	13	.	.	PUNCT
ejpam-2196	83	1	consequently	consequently	ADV
ejpam-2196	83	2	pm	pm	VERB
ejpam-2196	83	3	∈	∈	PROPN
ejpam-2196	83	4	xp	xp	NOUN
ejpam-2196	83	5	.	.	PUNCT
ejpam-2196	84	1	thus	thus	ADV
ejpam-2196	84	2	m	m	PROPN
ejpam-2196	84	3	is	be	AUX
ejpam-2196	84	4	a	a	DET
ejpam-2196	84	5	φ	φ	NOUN
ejpam-2196	84	6	-	-	PUNCT
ejpam-2196	84	7	module	module	NOUN
ejpam-2196	84	8	.	.	PUNCT
ejpam-2196	85	1	(	(	PUNCT
ejpam-2196	85	2	3	3	X
ejpam-2196	85	3	)	)	PUNCT
ejpam-2196	85	4	since	since	SCONJ
ejpam-2196	85	5	m	m	PROPN
ejpam-2196	85	6	is	be	AUX
ejpam-2196	85	7	a	a	DET
ejpam-2196	85	8	ψ	ψ	NOUN
ejpam-2196	85	9	-	-	NOUN
ejpam-2196	85	10	module	module	NOUN
ejpam-2196	85	11	,	,	PUNCT
ejpam-2196	85	12	sp(pm	sp(pm	NOUN
ejpam-2196	85	13	)	)	PUNCT
ejpam-2196	85	14	is	be	AUX
ejpam-2196	85	15	a	a	DET
ejpam-2196	85	16	p	p	ADJ
ejpam-2196	85	17	-	-	PUNCT
ejpam-2196	85	18	prime	prime	NOUN
ejpam-2196	85	19	submodule	submodule	NOUN
ejpam-2196	85	20	of	of	ADP
ejpam-2196	85	21	m	m	PRON
ejpam-2196	85	22	by	by	ADP
ejpam-2196	85	23	lemma	lemma	PROPN
ejpam-2196	85	24	1	1	NUM
ejpam-2196	85	25	.	.	PUNCT
ejpam-2196	85	26	hence	hence	ADV
ejpam-2196	85	27	sp(pm	sp(pm	NOUN
ejpam-2196	85	28	)	)	PUNCT
ejpam-2196	85	29	∈	∈	PROPN
ejpam-2196	85	30	xp	xp	PROPN
ejpam-2196	85	31	.	.	PUNCT
ejpam-2196	86	1	thus	thus	ADV
ejpam-2196	86	2	m	m	PROPN
ejpam-2196	86	3	is	be	AUX
ejpam-2196	86	4	a	a	DET
ejpam-2196	86	5	φ	φ	NOUN
ejpam-2196	86	6	-	-	PUNCT
ejpam-2196	86	7	module	module	NOUN
ejpam-2196	86	8	.	.	PUNCT
ejpam-2196	87	1	the	the	DET
ejpam-2196	87	2	following	follow	VERB
ejpam-2196	87	3	example	example	NOUN
ejpam-2196	87	4	shows	show	VERB
ejpam-2196	87	5	that	that	SCONJ
ejpam-2196	87	6	a	a	DET
ejpam-2196	87	7	ψ	ψ	NOUN
ejpam-2196	87	8	-	-	NOUN
ejpam-2196	87	9	module	module	NOUN
ejpam-2196	87	10	is	be	AUX
ejpam-2196	87	11	not	not	PART
ejpam-2196	87	12	necessarily	necessarily	ADV
ejpam-2196	87	13	a	a	DET
ejpam-2196	87	14	φ	φ	NOUN
ejpam-2196	87	15	-	-	PUNCT
ejpam-2196	87	16	module	module	NOUN
ejpam-2196	87	17	.	.	PUNCT
ejpam-2196	87	18	example	example	NOUN
ejpam-2196	87	19	1	1	NUM
ejpam-2196	87	20	(	(	PUNCT
ejpam-2196	87	21	cf	cf	NOUN
ejpam-2196	87	22	.	.	PUNCT
ejpam-2196	88	1	[	[	X
ejpam-2196	88	2	9	9	NUM
ejpam-2196	88	3	,	,	PUNCT
ejpam-2196	88	4	example	example	NOUN
ejpam-2196	88	5	1	1	NUM
ejpam-2196	88	6	]	]	PUNCT
ejpam-2196	88	7	)	)	PUNCT
ejpam-2196	88	8	.	.	PUNCT
ejpam-2196	89	1	let	let	VERB
ejpam-2196	89	2	ω	ω	NUM
ejpam-2196	89	3	be	be	AUX
ejpam-2196	89	4	the	the	DET
ejpam-2196	89	5	set	set	NOUN
ejpam-2196	89	6	of	of	ADP
ejpam-2196	89	7	all	all	DET
ejpam-2196	89	8	prime	prime	ADJ
ejpam-2196	89	9	integers	integer	NOUN
ejpam-2196	89	10	,	,	PUNCT
ejpam-2196	89	11	m	m	VERB
ejpam-2196	89	12	=	=	SYM
ejpam-2196	89	13	∏	∏	PROPN
ejpam-2196	89	14	p∈ω	p∈ω	NOUN
ejpam-2196	89	15	z	z	PROPN
ejpam-2196	89	16	pz	pz	PROPN
ejpam-2196	89	17	and	and	CCONJ
ejpam-2196	89	18	m	m	PROPN
ejpam-2196	89	19	′	′	NUM
ejpam-2196	89	20	=	=	PUNCT
ejpam-2196	89	21	⊕	⊕	PROPN
ejpam-2196	89	22	p∈ω	p∈ω	NOUN
ejpam-2196	89	23	z	z	PROPN
ejpam-2196	89	24	pz	pz	PROPN
ejpam-2196	89	25	,	,	PUNCT
ejpam-2196	89	26	where	where	SCONJ
ejpam-2196	89	27	p	p	NOUN
ejpam-2196	89	28	runs	run	VERB
ejpam-2196	89	29	through	through	ADP
ejpam-2196	89	30	ω	ω	PROPN
ejpam-2196	89	31	.	.	PUNCT
ejpam-2196	90	1	hence	hence	ADV
ejpam-2196	90	2	m	m	PROPN
ejpam-2196	90	3	is	be	AUX
ejpam-2196	90	4	a	a	DET
ejpam-2196	90	5	faithful	faithful	ADJ
ejpam-2196	90	6	ψ	ψ	NOUN
ejpam-2196	90	7	-	-	NOUN
ejpam-2196	90	8	module	module	NOUN
ejpam-2196	90	9	over	over	ADP
ejpam-2196	90	10	z	z	PROPN
ejpam-2196	90	11	and	and	CCONJ
ejpam-2196	90	12	spec(m	spec(m	PROPN
ejpam-2196	90	13	)	)	PUNCT
ejpam-2196	91	1	=	=	PRON
ejpam-2196	91	2	{	{	PUNCT
ejpam-2196	91	3	m	m	VERB
ejpam-2196	91	4	′	′	NUM
ejpam-2196	91	5	=	=	SYM
ejpam-2196	91	6	s0(0	s0(0	NOUN
ejpam-2196	91	7	)	)	PUNCT
ejpam-2196	91	8	}	}	PUNCT
ejpam-2196	91	9	∪	∪	VERB
ejpam-2196	91	10	{	{	PUNCT
ejpam-2196	91	11	pm	pm	NOUN
ejpam-2196	91	12	:	:	PUNCT
ejpam-2196	91	13	p	p	X
ejpam-2196	91	14	∈	∈	PROPN
ejpam-2196	91	15	ω	ω	PROPN
ejpam-2196	91	16	}	}	PUNCT
ejpam-2196	91	17	.	.	PUNCT
ejpam-2196	92	1	now	now	ADV
ejpam-2196	92	2	if	if	SCONJ
ejpam-2196	92	3	φ	φ	PROPN
ejpam-2196	92	4	is	be	AUX
ejpam-2196	92	5	surjective	surjective	ADJ
ejpam-2196	92	6	,	,	PUNCT
ejpam-2196	92	7	then	then	ADV
ejpam-2196	92	8	there	there	PRON
ejpam-2196	92	9	exists	exist	VERB
ejpam-2196	92	10	n	n	PRON
ejpam-2196	92	11	∈	∈	PROPN
ejpam-2196	92	12	x	x	PUNCT
ejpam-2196	92	13	such	such	ADJ
ejpam-2196	92	14	that	that	SCONJ
ejpam-2196	92	15	φ(n	φ(n	NOUN
ejpam-2196	92	16	)	)	PUNCT
ejpam-2196	92	17	=	=	SYM
ejpam-2196	92	18	p	p	X
ejpam-2196	92	19	(	(	PUNCT
ejpam-2196	92	20	n	n	NOUN
ejpam-2196	92	21	:	:	PUNCT
ejpam-2196	92	22	m	m	X
ejpam-2196	92	23	)	)	PUNCT
ejpam-2196	93	1	=	=	SYM
ejpam-2196	93	2	0	0	X
ejpam-2196	93	3	.	.	PUNCT
ejpam-2196	94	1	it	it	PRON
ejpam-2196	94	2	follows	follow	VERB
ejpam-2196	94	3	that	that	PRON
ejpam-2196	94	4	(	(	PUNCT
ejpam-2196	94	5	n	n	X
ejpam-2196	94	6	:	:	PUNCT
ejpam-2196	94	7	m	m	X
ejpam-2196	94	8	)	)	PUNCT
ejpam-2196	94	9	=	=	SYM
ejpam-2196	95	1	0	0	X
ejpam-2196	95	2	.	.	PUNCT
ejpam-2196	96	1	since	since	SCONJ
ejpam-2196	96	2	m	m	PROPN
ejpam-2196	96	3	/	/	SYM
ejpam-2196	96	4	n	n	PROPN
ejpam-2196	96	5	is	be	AUX
ejpam-2196	96	6	a	a	DET
ejpam-2196	96	7	ψ	ψ	NOUN
ejpam-2196	96	8	-	-	NOUN
ejpam-2196	96	9	module	module	NOUN
ejpam-2196	96	10	,	,	PUNCT
ejpam-2196	96	11	we	we	PRON
ejpam-2196	96	12	have	have	VERB
ejpam-2196	96	13	n	n	ADV
ejpam-2196	96	14	⊆	⊆	NUM
ejpam-2196	96	15	∩p∈ωpm	∩p∈ωpm	NOUN
ejpam-2196	96	16	=	=	NOUN
ejpam-2196	96	17	0	0	PROPN
ejpam-2196	96	18	.	.	PUNCT
ejpam-2196	97	1	but	but	CCONJ
ejpam-2196	97	2	0	0	NUM
ejpam-2196	97	3	is	be	AUX
ejpam-2196	97	4	not	not	PART
ejpam-2196	97	5	prime	prime	ADJ
ejpam-2196	97	6	and	and	CCONJ
ejpam-2196	97	7	so	so	ADV
ejpam-2196	97	8	is	be	AUX
ejpam-2196	97	9	not	not	PART
ejpam-2196	97	10	primary	primary	ADJ
ejpam-2196	97	11	-	-	PUNCT
ejpam-2196	97	12	like	like	ADJ
ejpam-2196	97	13	because	because	SCONJ
ejpam-2196	97	14	rad0	rad0	NOUN
ejpam-2196	97	15	=	=	NOUN
ejpam-2196	98	1	0	0	X
ejpam-2196	98	2	.	.	PUNCT
ejpam-2196	99	1	hence	hence	ADV
ejpam-2196	99	2	n	n	ADV
ejpam-2196	99	3	/∈	/∈	PUNCT
ejpam-2196	100	1	x	x	X
ejpam-2196	100	2	,	,	PUNCT
ejpam-2196	100	3	a	a	DET
ejpam-2196	100	4	contradiction	contradiction	NOUN
ejpam-2196	100	5	.	.	PUNCT
ejpam-2196	101	1	thus	thus	ADV
ejpam-2196	101	2	m	m	NOUN
ejpam-2196	101	3	is	be	AUX
ejpam-2196	101	4	not	not	PART
ejpam-2196	101	5	a	a	DET
ejpam-2196	101	6	φ	φ	NOUN
ejpam-2196	101	7	-	-	PUNCT
ejpam-2196	101	8	module	module	NOUN
ejpam-2196	101	9	.	.	PUNCT
ejpam-2196	102	1	corollary	corollary	ADJ
ejpam-2196	102	2	1	1	NUM
ejpam-2196	102	3	.	.	PUNCT
ejpam-2196	103	1	every	every	DET
ejpam-2196	103	2	finitely	finitely	ADV
ejpam-2196	103	3	generated	generate	VERB
ejpam-2196	103	4	r	r	NOUN
ejpam-2196	103	5	-	-	PUNCT
ejpam-2196	103	6	module	module	NOUN
ejpam-2196	103	7	m	m	NOUN
ejpam-2196	103	8	is	be	AUX
ejpam-2196	103	9	a	a	DET
ejpam-2196	103	10	φ	φ	NOUN
ejpam-2196	103	11	-	-	PUNCT
ejpam-2196	103	12	module	module	NOUN
ejpam-2196	103	13	,	,	PUNCT
ejpam-2196	103	14	hence	hence	ADV
ejpam-2196	103	15	so	so	ADV
ejpam-2196	103	16	is	be	AUX
ejpam-2196	103	17	the	the	DET
ejpam-2196	103	18	factor	factor	NOUN
ejpam-2196	103	19	module	module	NOUN
ejpam-2196	103	20	m	m	PROPN
ejpam-2196	103	21	/	/	SYM
ejpam-2196	103	22	n	n	PROPN
ejpam-2196	103	23	of	of	ADP
ejpam-2196	103	24	m	m	PRON
ejpam-2196	103	25	by	by	ADP
ejpam-2196	103	26	any	any	DET
ejpam-2196	103	27	submodule	submodule	NOUN
ejpam-2196	103	28	n	n	PROPN
ejpam-2196	103	29	of	of	ADP
ejpam-2196	103	30	m.	m.	NOUN
ejpam-2196	103	31	proof	proof	NOUN
ejpam-2196	103	32	.	.	PUNCT
ejpam-2196	104	1	follows	follow	VERB
ejpam-2196	104	2	from	from	ADP
ejpam-2196	104	3	lemma	lemma	PROPN
ejpam-2196	104	4	1	1	NUM
ejpam-2196	104	5	and	and	CCONJ
ejpam-2196	104	6	theorem	theorem	VERB
ejpam-2196	104	7	1	1	NUM
ejpam-2196	104	8	.	.	PUNCT
ejpam-2196	104	9	corollary	corollary	ADJ
ejpam-2196	104	10	2	2	NUM
ejpam-2196	104	11	.	.	PUNCT
ejpam-2196	105	1	let	let	VERB
ejpam-2196	105	2	r	r	PRON
ejpam-2196	105	3	be	be	AUX
ejpam-2196	105	4	a	a	DET
ejpam-2196	105	5	ring	ring	NOUN
ejpam-2196	105	6	of	of	ADP
ejpam-2196	105	7	(	(	PUNCT
ejpam-2196	105	8	krull	krull	PROPN
ejpam-2196	105	9	)	)	PUNCT
ejpam-2196	105	10	dimension	dimension	NOUN
ejpam-2196	105	11	0	0	NUM
ejpam-2196	106	1	and	and	CCONJ
ejpam-2196	106	2	m	m	AUX
ejpam-2196	106	3	be	be	AUX
ejpam-2196	106	4	a	a	DET
ejpam-2196	106	5	non	non	ADJ
ejpam-2196	106	6	-	-	ADJ
ejpam-2196	106	7	zero	zero	ADJ
ejpam-2196	106	8	r	r	NOUN
ejpam-2196	106	9	-	-	PUNCT
ejpam-2196	106	10	module	module	NOUN
ejpam-2196	106	11	.	.	PUNCT
ejpam-2196	107	1	then	then	ADV
ejpam-2196	107	2	the	the	DET
ejpam-2196	107	3	following	follow	VERB
ejpam-2196	107	4	statements	statement	NOUN
ejpam-2196	107	5	are	be	AUX
ejpam-2196	107	6	equivalent	equivalent	ADJ
ejpam-2196	107	7	.	.	PUNCT
ejpam-2196	108	1	(	(	PUNCT
ejpam-2196	108	2	1	1	X
ejpam-2196	108	3	)	)	PUNCT
ejpam-2196	108	4	mm	mm	PROPN
ejpam-2196	109	1	6=	6=	NUM
ejpam-2196	109	2	m	m	VERB
ejpam-2196	109	3	for	for	ADP
ejpam-2196	109	4	every	every	DET
ejpam-2196	109	5	m	m	NOUN
ejpam-2196	109	6	∈	∈	PROPN
ejpam-2196	109	7	v	v	NOUN
ejpam-2196	109	8	(	(	PUNCT
ejpam-2196	109	9	ann(m))∩max(r	ann(m))∩max(r	NUM
ejpam-2196	109	10	)	)	PUNCT
ejpam-2196	109	11	;	;	PUNCT
ejpam-2196	109	12	(	(	PUNCT
ejpam-2196	109	13	2	2	X
ejpam-2196	109	14	)	)	PUNCT
ejpam-2196	109	15	m	m	VERB
ejpam-2196	109	16	is	be	AUX
ejpam-2196	109	17	a	a	DET
ejpam-2196	109	18	ψ	ψ	NOUN
ejpam-2196	109	19	-	-	NOUN
ejpam-2196	109	20	module	module	NOUN
ejpam-2196	109	21	;	;	PUNCT
ejpam-2196	109	22	(	(	PUNCT
ejpam-2196	109	23	3	3	X
ejpam-2196	109	24	)	)	PUNCT
ejpam-2196	109	25	m	m	VERB
ejpam-2196	109	26	is	be	AUX
ejpam-2196	109	27	a	a	DET
ejpam-2196	109	28	φ	φ	NOUN
ejpam-2196	109	29	-	-	PUNCT
ejpam-2196	109	30	module	module	NOUN
ejpam-2196	109	31	.	.	PUNCT
ejpam-2196	110	1	proof	proof	NOUN
ejpam-2196	110	2	.	.	PUNCT
ejpam-2196	111	1	(	(	PUNCT
ejpam-2196	111	2	1)⇔	1)⇔	NUM
ejpam-2196	111	3	(	(	PUNCT
ejpam-2196	111	4	2	2	NUM
ejpam-2196	111	5	)	)	PUNCT
ejpam-2196	111	6	follows	follow	VERB
ejpam-2196	111	7	from	from	ADP
ejpam-2196	111	8	[	[	X
ejpam-2196	111	9	9	9	NUM
ejpam-2196	111	10	,	,	PUNCT
ejpam-2196	111	11	result	result	VERB
ejpam-2196	111	12	3	3	NUM
ejpam-2196	111	13	]	]	PUNCT
ejpam-2196	111	14	.	.	PUNCT
ejpam-2196	112	1	(	(	PUNCT
ejpam-2196	112	2	2	2	X
ejpam-2196	112	3	)	)	PUNCT
ejpam-2196	112	4	⇒	⇒	NOUN
ejpam-2196	112	5	(	(	PUNCT
ejpam-2196	112	6	3	3	X
ejpam-2196	112	7	)	)	PUNCT
ejpam-2196	112	8	suppose	suppose	VERB
ejpam-2196	112	9	m	m	PRON
ejpam-2196	112	10	is	be	AUX
ejpam-2196	112	11	a	a	DET
ejpam-2196	112	12	ψ	ψ	NOUN
ejpam-2196	112	13	-	-	NOUN
ejpam-2196	112	14	module	module	NOUN
ejpam-2196	112	15	.	.	PUNCT
ejpam-2196	113	1	we	we	PRON
ejpam-2196	113	2	show	show	VERB
ejpam-2196	113	3	that	that	SCONJ
ejpam-2196	113	4	m	m	NOUN
ejpam-2196	113	5	/	/	SYM
ejpam-2196	113	6	sp(pm	sp(pm	NOUN
ejpam-2196	113	7	)	)	PUNCT
ejpam-2196	113	8	is	be	AUX
ejpam-2196	113	9	a	a	DET
ejpam-2196	113	10	ψ	ψ	NOUN
ejpam-2196	113	11	-	-	NOUN
ejpam-2196	113	12	module	module	NOUN
ejpam-2196	113	13	for	for	ADP
ejpam-2196	113	14	every	every	DET
ejpam-2196	113	15	p	p	PROPN
ejpam-2196	113	16	∈	∈	PROPN
ejpam-2196	113	17	v	v	NOUN
ejpam-2196	113	18	(	(	PUNCT
ejpam-2196	113	19	ann(m	ann(m	NOUN
ejpam-2196	113	20	)	)	PUNCT
ejpam-2196	113	21	)	)	PUNCT
ejpam-2196	113	22	.	.	PUNCT
ejpam-2196	114	1	assume	assume	VERB
ejpam-2196	114	2	(	(	PUNCT
ejpam-2196	114	3	sp(pm	sp(pm	PROPN
ejpam-2196	114	4	)	)	PUNCT
ejpam-2196	114	5	:	:	PUNCT
ejpam-2196	114	6	m	m	X
ejpam-2196	114	7	)	)	PUNCT
ejpam-2196	115	1	⊆	⊆	NUM
ejpam-2196	115	2	q	q	NOUN
ejpam-2196	115	3	for	for	ADP
ejpam-2196	115	4	a	a	DET
ejpam-2196	115	5	prime	prime	ADJ
ejpam-2196	115	6	ideal	ideal	NOUN
ejpam-2196	115	7	q	q	PROPN
ejpam-2196	115	8	of	of	ADP
ejpam-2196	115	9	r.	r.	PROPN
ejpam-2196	115	10	hence	hence	ADV
ejpam-2196	115	11	p	p	PROPN
ejpam-2196	115	12	⊆	⊆	NUM
ejpam-2196	115	13	q.	q.	NOUN
ejpam-2196	115	14	since	since	SCONJ
ejpam-2196	115	15	dim(r	dim(r	PROPN
ejpam-2196	115	16	)	)	PUNCT
ejpam-2196	115	17	=	=	SYM
ejpam-2196	115	18	0	0	NUM
ejpam-2196	115	19	,	,	PUNCT
ejpam-2196	115	20	then	then	ADV
ejpam-2196	115	21	p	p	PROPN
ejpam-2196	115	22	=	=	NOUN
ejpam-2196	115	23	q.	q.	NOUN
ejpam-2196	115	24	hence	hence	ADV
ejpam-2196	115	25	sq(qm	sq(qm	NOUN
ejpam-2196	115	26	)	)	PUNCT
ejpam-2196	115	27	is	be	AUX
ejpam-2196	115	28	a	a	DET
ejpam-2196	115	29	q	q	ADJ
ejpam-2196	115	30	-	-	PUNCT
ejpam-2196	115	31	prime	prime	ADJ
ejpam-2196	115	32	submodule	submodule	NOUN
ejpam-2196	115	33	containing	contain	VERB
ejpam-2196	115	34	sp(pm	sp(pm	NOUN
ejpam-2196	115	35	)	)	PUNCT
ejpam-2196	115	36	.	.	PUNCT
ejpam-2196	116	1	thus	thus	ADV
ejpam-2196	116	2	m	m	PROPN
ejpam-2196	116	3	is	be	AUX
ejpam-2196	116	4	a	a	DET
ejpam-2196	116	5	φ	φ	NOUN
ejpam-2196	116	6	-	-	PUNCT
ejpam-2196	116	7	module	module	NOUN
ejpam-2196	116	8	by	by	ADP
ejpam-2196	116	9	theorem	theorem	NOUN
ejpam-2196	116	10	1	1	NUM
ejpam-2196	116	11	.	.	PUNCT
ejpam-2196	117	1	(	(	PUNCT
ejpam-2196	117	2	3)⇒	3)⇒	NUM
ejpam-2196	117	3	(	(	PUNCT
ejpam-2196	117	4	2	2	NUM
ejpam-2196	117	5	)	)	PUNCT
ejpam-2196	117	6	follows	follow	VERB
ejpam-2196	117	7	from	from	ADP
ejpam-2196	117	8	theorem	theorem	ADJ
ejpam-2196	117	9	1	1	NUM
ejpam-2196	117	10	.	.	PUNCT
ejpam-2196	117	11	h.	h.	PROPN
ejpam-2196	117	12	moghimi	moghimi	PROPN
ejpam-2196	117	13	,	,	PUNCT
ejpam-2196	117	14	f.	f.	PROPN
ejpam-2196	117	15	rashedi	rashedi	PROPN
ejpam-2196	117	16	/	/	SYM
ejpam-2196	117	17	eur	eur	PROPN
ejpam-2196	117	18	.	.	PUNCT
ejpam-2196	118	1	j.	j.	PROPN
ejpam-2196	118	2	pure	pure	PROPN
ejpam-2196	118	3	appl	appl	PROPN
ejpam-2196	118	4	.	.	PROPN
ejpam-2196	118	5	math	math	PROPN
ejpam-2196	118	6	,	,	PUNCT
ejpam-2196	118	7	8	8	NUM
ejpam-2196	118	8	(	(	PUNCT
ejpam-2196	118	9	2015	2015	NUM
ejpam-2196	118	10	)	)	PUNCT
ejpam-2196	118	11	,	,	PUNCT
ejpam-2196	118	12	232	232	NUM
ejpam-2196	118	13	-	-	SYM
ejpam-2196	118	14	238	238	NUM
ejpam-2196	118	15	235	235	NUM
ejpam-2196	118	16	corollary	corollary	ADJ
ejpam-2196	118	17	3	3	NUM
ejpam-2196	118	18	.	.	PUNCT
ejpam-2196	119	1	let	let	VERB
ejpam-2196	119	2	r	r	PRON
ejpam-2196	119	3	be	be	AUX
ejpam-2196	119	4	a	a	DET
ejpam-2196	119	5	domain	domain	NOUN
ejpam-2196	119	6	which	which	PRON
ejpam-2196	119	7	is	be	AUX
ejpam-2196	119	8	not	not	PART
ejpam-2196	119	9	a	a	DET
ejpam-2196	119	10	field	field	NOUN
ejpam-2196	119	11	.	.	PUNCT
ejpam-2196	120	1	if	if	SCONJ
ejpam-2196	120	2	a	a	DET
ejpam-2196	120	3	non	non	ADJ
ejpam-2196	120	4	-	-	ADJ
ejpam-2196	120	5	zero	zero	ADJ
ejpam-2196	120	6	r	r	NOUN
ejpam-2196	120	7	-	-	PUNCT
ejpam-2196	120	8	module	module	NOUN
ejpam-2196	120	9	m	m	NOUN
ejpam-2196	120	10	is	be	AUX
ejpam-2196	120	11	either	either	CCONJ
ejpam-2196	120	12	a	a	DET
ejpam-2196	120	13	divisible	divisible	ADJ
ejpam-2196	120	14	module	module	NOUN
ejpam-2196	120	15	or	or	CCONJ
ejpam-2196	120	16	a	a	DET
ejpam-2196	120	17	faithful	faithful	ADJ
ejpam-2196	120	18	torsion	torsion	NOUN
ejpam-2196	120	19	module	module	NOUN
ejpam-2196	120	20	,	,	PUNCT
ejpam-2196	120	21	then	then	ADV
ejpam-2196	120	22	m	m	NOUN
ejpam-2196	120	23	is	be	AUX
ejpam-2196	120	24	not	not	PART
ejpam-2196	120	25	a	a	DET
ejpam-2196	120	26	φ	φ	NOUN
ejpam-2196	120	27	-	-	PUNCT
ejpam-2196	120	28	module	module	NOUN
ejpam-2196	120	29	.	.	PUNCT
ejpam-2196	121	1	proof	proof	NOUN
ejpam-2196	121	2	.	.	PUNCT
ejpam-2196	122	1	use	use	NOUN
ejpam-2196	122	2	theorem	theorem	NOUN
ejpam-2196	122	3	1	1	NUM
ejpam-2196	122	4	and	and	CCONJ
ejpam-2196	122	5	[	[	X
ejpam-2196	122	6	9	9	NUM
ejpam-2196	122	7	,	,	PUNCT
ejpam-2196	122	8	proposition	proposition	NOUN
ejpam-2196	122	9	2.6	2.6	NUM
ejpam-2196	122	10	]	]	PUNCT
ejpam-2196	122	11	.	.	PUNCT
ejpam-2196	123	1	theorem	theorem	NOUN
ejpam-2196	123	2	2	2	NUM
ejpam-2196	123	3	.	.	PUNCT
ejpam-2196	124	1	every	every	DET
ejpam-2196	124	2	free	free	ADJ
ejpam-2196	124	3	module	module	NOUN
ejpam-2196	124	4	is	be	AUX
ejpam-2196	124	5	a	a	DET
ejpam-2196	124	6	φ	φ	NOUN
ejpam-2196	124	7	-	-	PUNCT
ejpam-2196	124	8	module	module	NOUN
ejpam-2196	124	9	.	.	PUNCT
ejpam-2196	125	1	proof	proof	NOUN
ejpam-2196	125	2	.	.	PUNCT
ejpam-2196	126	1	suppose	suppose	VERB
ejpam-2196	126	2	f	f	PROPN
ejpam-2196	126	3	is	be	AUX
ejpam-2196	126	4	a	a	DET
ejpam-2196	126	5	free	free	ADJ
ejpam-2196	126	6	r	r	NOUN
ejpam-2196	126	7	-	-	PUNCT
ejpam-2196	126	8	module	module	NOUN
ejpam-2196	126	9	and	and	CCONJ
ejpam-2196	126	10	p	p	NOUN
ejpam-2196	126	11	∈	∈	PROPN
ejpam-2196	126	12	spec(r	spec(r	PROPN
ejpam-2196	126	13	/	/	SYM
ejpam-2196	126	14	ann(f	ann(f	PROPN
ejpam-2196	126	15	)	)	PUNCT
ejpam-2196	126	16	)	)	PUNCT
ejpam-2196	126	17	.	.	PUNCT
ejpam-2196	127	1	it	it	PRON
ejpam-2196	127	2	is	be	AUX
ejpam-2196	127	3	easy	easy	ADJ
ejpam-2196	127	4	to	to	PART
ejpam-2196	127	5	see	see	VERB
ejpam-2196	127	6	that	that	SCONJ
ejpam-2196	127	7	pf	pf	PROPN
ejpam-2196	127	8	is	be	AUX
ejpam-2196	127	9	a	a	DET
ejpam-2196	127	10	prime	prime	NOUN
ejpam-2196	127	11	,	,	PUNCT
ejpam-2196	127	12	and	and	CCONJ
ejpam-2196	127	13	hence	hence	ADV
ejpam-2196	127	14	a	a	DET
ejpam-2196	127	15	primary	primary	ADJ
ejpam-2196	127	16	-	-	PUNCT
ejpam-2196	127	17	like	like	ADJ
ejpam-2196	127	18	submodule	submodule	NOUN
ejpam-2196	127	19	,	,	PUNCT
ejpam-2196	127	20	of	of	ADP
ejpam-2196	127	21	f	f	PROPN
ejpam-2196	127	22	.	.	PUNCT
ejpam-2196	128	1	now	now	ADV
ejpam-2196	128	2	we	we	PRON
ejpam-2196	128	3	show	show	VERB
ejpam-2196	128	4	that	that	SCONJ
ejpam-2196	128	5	f	f	X
ejpam-2196	128	6	/	/	SYM
ejpam-2196	128	7	pf	pf	PROPN
ejpam-2196	128	8	is	be	AUX
ejpam-2196	128	9	a	a	DET
ejpam-2196	128	10	ψ	ψ	NOUN
ejpam-2196	128	11	-	-	NOUN
ejpam-2196	128	12	module	module	NOUN
ejpam-2196	128	13	.	.	PUNCT
ejpam-2196	129	1	assume	assume	VERB
ejpam-2196	129	2	q	q	PROPN
ejpam-2196	129	3	is	be	AUX
ejpam-2196	129	4	a	a	DET
ejpam-2196	129	5	prime	prime	ADJ
ejpam-2196	129	6	ideal	ideal	NOUN
ejpam-2196	129	7	of	of	ADP
ejpam-2196	129	8	r	r	NOUN
ejpam-2196	129	9	containing	contain	VERB
ejpam-2196	129	10	(	(	PUNCT
ejpam-2196	129	11	pf	pf	NOUN
ejpam-2196	129	12	:	:	PUNCT
ejpam-2196	129	13	f	f	X
ejpam-2196	129	14	)	)	PUNCT
ejpam-2196	129	15	.	.	PUNCT
ejpam-2196	130	1	it	it	PRON
ejpam-2196	130	2	follows	follow	VERB
ejpam-2196	130	3	from	from	ADP
ejpam-2196	130	4	[	[	X
ejpam-2196	130	5	13	13	NUM
ejpam-2196	130	6	,	,	PUNCT
ejpam-2196	130	7	proposition	proposition	NOUN
ejpam-2196	130	8	2.2	2.2	NUM
ejpam-2196	130	9	]	]	PUNCT
ejpam-2196	131	1	that	that	SCONJ
ejpam-2196	131	2	(	(	PUNCT
ejpam-2196	131	3	qf	qf	INTJ
ejpam-2196	131	4	:	:	PUNCT
ejpam-2196	131	5	f	f	X
ejpam-2196	131	6	)	)	PUNCT
ejpam-2196	131	7	=	=	SYM
ejpam-2196	131	8	q	q	NOUN
ejpam-2196	131	9	and	and	CCONJ
ejpam-2196	131	10	hence	hence	ADV
ejpam-2196	131	11	qf	qf	PROPN
ejpam-2196	131	12	6=	6=	PROPN
ejpam-2196	131	13	f	f	PROPN
ejpam-2196	131	14	.	.	PUNCT
ejpam-2196	132	1	thus	thus	ADV
ejpam-2196	132	2	qf	qf	PROPN
ejpam-2196	132	3	is	be	AUX
ejpam-2196	132	4	a	a	DET
ejpam-2196	132	5	q	q	ADJ
ejpam-2196	132	6	-	-	PUNCT
ejpam-2196	132	7	prime	prime	ADJ
ejpam-2196	132	8	submodule	submodule	NOUN
ejpam-2196	132	9	of	of	ADP
ejpam-2196	132	10	f	f	PROPN
ejpam-2196	132	11	containing	contain	VERB
ejpam-2196	132	12	pf	pf	PROPN
ejpam-2196	132	13	[	[	X
ejpam-2196	132	14	11	11	NUM
ejpam-2196	132	15	,	,	PUNCT
ejpam-2196	132	16	theorem	theorem	VERB
ejpam-2196	132	17	3	3	NUM
ejpam-2196	132	18	]	]	PUNCT
ejpam-2196	132	19	.	.	PUNCT
ejpam-2196	133	1	it	it	PRON
ejpam-2196	133	2	implies	imply	VERB
ejpam-2196	133	3	that	that	SCONJ
ejpam-2196	133	4	f	f	X
ejpam-2196	133	5	/	/	SYM
ejpam-2196	133	6	pf	pf	PROPN
ejpam-2196	133	7	is	be	AUX
ejpam-2196	133	8	a	a	DET
ejpam-2196	133	9	ψ	ψ	NOUN
ejpam-2196	133	10	-	-	NOUN
ejpam-2196	133	11	module	module	NOUN
ejpam-2196	133	12	.	.	PUNCT
ejpam-2196	134	1	theorem	theorem	NOUN
ejpam-2196	134	2	3	3	X
ejpam-2196	134	3	.	.	PUNCT
ejpam-2196	135	1	let	let	VERB
ejpam-2196	135	2	r	r	PRON
ejpam-2196	135	3	be	be	AUX
ejpam-2196	135	4	a	a	DET
ejpam-2196	135	5	domain	domain	NOUN
ejpam-2196	135	6	and	and	CCONJ
ejpam-2196	135	7	m	m	AUX
ejpam-2196	135	8	be	be	AUX
ejpam-2196	135	9	a	a	DET
ejpam-2196	135	10	faithful	faithful	ADJ
ejpam-2196	135	11	projective	projective	ADJ
ejpam-2196	135	12	r	r	NOUN
ejpam-2196	135	13	-	-	PUNCT
ejpam-2196	135	14	module	module	NOUN
ejpam-2196	135	15	.	.	PUNCT
ejpam-2196	136	1	then	then	ADV
ejpam-2196	136	2	m	m	PROPN
ejpam-2196	136	3	is	be	AUX
ejpam-2196	136	4	a	a	DET
ejpam-2196	136	5	φ	φ	NOUN
ejpam-2196	136	6	-	-	PUNCT
ejpam-2196	136	7	module	module	NOUN
ejpam-2196	136	8	.	.	PUNCT
ejpam-2196	137	1	proof	proof	NOUN
ejpam-2196	137	2	.	.	PUNCT
ejpam-2196	138	1	assume	assume	VERB
ejpam-2196	138	2	m	m	PRON
ejpam-2196	138	3	6=	6=	NUM
ejpam-2196	138	4	(	(	PUNCT
ejpam-2196	138	5	0	0	NUM
ejpam-2196	138	6	)	)	PUNCT
ejpam-2196	138	7	and	and	CCONJ
ejpam-2196	138	8	p	p	PROPN
ejpam-2196	138	9	∈	∈	PROPN
ejpam-2196	138	10	spec(r	spec(r	PROPN
ejpam-2196	138	11	)	)	PUNCT
ejpam-2196	138	12	.	.	PUNCT
ejpam-2196	139	1	we	we	PRON
ejpam-2196	139	2	show	show	VERB
ejpam-2196	139	3	that	that	SCONJ
ejpam-2196	139	4	pm	pm	NOUN
ejpam-2196	139	5	∈	∈	PROPN
ejpam-2196	139	6	x	x	INTJ
ejpam-2196	139	7	.	.	PUNCT
ejpam-2196	140	1	by	by	ADP
ejpam-2196	140	2	[	[	X
ejpam-2196	140	3	9	9	NUM
ejpam-2196	140	4	,	,	PUNCT
ejpam-2196	140	5	corollary	corollary	NOUN
ejpam-2196	140	6	3.4	3.4	NUM
ejpam-2196	140	7	]	]	PUNCT
ejpam-2196	140	8	,	,	PUNCT
ejpam-2196	140	9	m	m	VERB
ejpam-2196	140	10	is	be	AUX
ejpam-2196	140	11	a	a	DET
ejpam-2196	140	12	ψ	ψ	NOUN
ejpam-2196	140	13	-	-	NOUN
ejpam-2196	140	14	module	module	NOUN
ejpam-2196	140	15	and	and	CCONJ
ejpam-2196	140	16	hence	hence	ADV
ejpam-2196	140	17	pm	pm	VERB
ejpam-2196	140	18	6=	6=	NUM
ejpam-2196	140	19	m	m	VERB
ejpam-2196	140	20	by	by	ADP
ejpam-2196	140	21	[	[	X
ejpam-2196	140	22	9	9	NUM
ejpam-2196	140	23	,	,	PUNCT
ejpam-2196	140	24	result	result	VERB
ejpam-2196	140	25	2	2	NUM
ejpam-2196	140	26	]	]	PUNCT
ejpam-2196	140	27	.	.	PUNCT
ejpam-2196	141	1	it	it	PRON
ejpam-2196	141	2	follows	follow	VERB
ejpam-2196	141	3	from	from	ADP
ejpam-2196	141	4	[	[	X
ejpam-2196	141	5	11	11	NUM
ejpam-2196	141	6	,	,	PUNCT
ejpam-2196	141	7	theorem	theorem	VERB
ejpam-2196	141	8	3	3	NUM
ejpam-2196	141	9	]	]	PUNCT
ejpam-2196	141	10	that	that	PRON
ejpam-2196	141	11	pm	pm	NOUN
ejpam-2196	141	12	is	be	AUX
ejpam-2196	141	13	a	a	DET
ejpam-2196	141	14	p	p	NOUN
ejpam-2196	141	15	-	-	PUNCT
ejpam-2196	141	16	prime	prime	NOUN
ejpam-2196	141	17	,	,	PUNCT
ejpam-2196	141	18	and	and	CCONJ
ejpam-2196	141	19	hence	hence	ADV
ejpam-2196	141	20	a	a	DET
ejpam-2196	141	21	p	p	NOUN
ejpam-2196	141	22	-	-	PUNCT
ejpam-2196	141	23	primary	primary	ADJ
ejpam-2196	141	24	-	-	PUNCT
ejpam-2196	141	25	like	like	ADJ
ejpam-2196	141	26	,	,	PUNCT
ejpam-2196	141	27	submodule	submodule	NOUN
ejpam-2196	141	28	of	of	ADP
ejpam-2196	141	29	m	m	PROPN
ejpam-2196	141	30	.	.	PUNCT
ejpam-2196	142	1	it	it	PRON
ejpam-2196	142	2	remains	remain	VERB
ejpam-2196	142	3	to	to	PART
ejpam-2196	142	4	show	show	VERB
ejpam-2196	142	5	that	that	SCONJ
ejpam-2196	142	6	m	m	NOUN
ejpam-2196	142	7	/	/	SYM
ejpam-2196	142	8	pm	pm	NOUN
ejpam-2196	142	9	is	be	AUX
ejpam-2196	142	10	a	a	DET
ejpam-2196	142	11	ψ	ψ	NOUN
ejpam-2196	142	12	-	-	NOUN
ejpam-2196	142	13	module	module	NOUN
ejpam-2196	142	14	.	.	PUNCT
ejpam-2196	143	1	suppose	suppose	VERB
ejpam-2196	143	2	q	q	NOUN
ejpam-2196	143	3	is	be	AUX
ejpam-2196	143	4	a	a	DET
ejpam-2196	143	5	prime	prime	ADJ
ejpam-2196	143	6	ideal	ideal	NOUN
ejpam-2196	143	7	of	of	ADP
ejpam-2196	143	8	r	r	NOUN
ejpam-2196	143	9	containing	contain	VERB
ejpam-2196	143	10	p	p	NOUN
ejpam-2196	143	11	=	=	PUNCT
ejpam-2196	143	12	(	(	PUNCT
ejpam-2196	143	13	pm	pm	NOUN
ejpam-2196	143	14	:	:	PUNCT
ejpam-2196	143	15	m	m	NOUN
ejpam-2196	143	16	)	)	PUNCT
ejpam-2196	143	17	.	.	PUNCT
ejpam-2196	144	1	therefore	therefore	ADV
ejpam-2196	144	2	pm	pm	VERB
ejpam-2196	144	3	⊆	⊆	NUM
ejpam-2196	144	4	qm	qm	PROPN
ejpam-2196	144	5	and	and	CCONJ
ejpam-2196	144	6	qm	qm	PROPN
ejpam-2196	144	7	∈	∈	PROPN
ejpam-2196	144	8	xq	xq	PROPN
ejpam-2196	144	9	.	.	PUNCT
ejpam-2196	145	1	thus	thus	ADV
ejpam-2196	145	2	m	m	X
ejpam-2196	145	3	/	/	SYM
ejpam-2196	145	4	pm	pm	NOUN
ejpam-2196	145	5	is	be	AUX
ejpam-2196	145	6	a	a	DET
ejpam-2196	145	7	ψ	ψ	NOUN
ejpam-2196	145	8	-	-	NOUN
ejpam-2196	145	9	module	module	NOUN
ejpam-2196	145	10	and	and	CCONJ
ejpam-2196	145	11	so	so	ADV
ejpam-2196	145	12	m	m	VERB
ejpam-2196	145	13	is	be	AUX
ejpam-2196	145	14	a	a	DET
ejpam-2196	145	15	φ	φ	NOUN
ejpam-2196	145	16	-	-	PUNCT
ejpam-2196	145	17	module	module	NOUN
ejpam-2196	145	18	.	.	PUNCT
ejpam-2196	146	1	proposition	proposition	NOUN
ejpam-2196	146	2	1	1	NUM
ejpam-2196	146	3	.	.	PUNCT
ejpam-2196	147	1	let	let	VERB
ejpam-2196	147	2	m	m	PRON
ejpam-2196	147	3	be	be	AUX
ejpam-2196	147	4	a	a	DET
ejpam-2196	147	5	non	non	ADJ
ejpam-2196	147	6	-	-	ADJ
ejpam-2196	147	7	zero	zero	NUM
ejpam-2196	147	8	φ	φ	NOUN
ejpam-2196	147	9	-	-	NOUN
ejpam-2196	147	10	module	module	NOUN
ejpam-2196	147	11	over	over	ADP
ejpam-2196	147	12	a	a	DET
ejpam-2196	147	13	ring	ring	NOUN
ejpam-2196	147	14	r.	r.	PROPN
ejpam-2196	147	15	then	then	ADV
ejpam-2196	147	16	the	the	DET
ejpam-2196	147	17	following	follow	VERB
ejpam-2196	147	18	statements	statement	NOUN
ejpam-2196	147	19	hold	hold	VERB
ejpam-2196	147	20	.	.	PUNCT
ejpam-2196	148	1	(	(	PUNCT
ejpam-2196	148	2	1	1	X
ejpam-2196	148	3	)	)	PUNCT
ejpam-2196	148	4	let	let	VERB
ejpam-2196	148	5	i	i	PRON
ejpam-2196	148	6	be	be	AUX
ejpam-2196	148	7	a	a	DET
ejpam-2196	148	8	radical	radical	ADJ
ejpam-2196	148	9	ideal	ideal	NOUN
ejpam-2196	148	10	of	of	ADP
ejpam-2196	148	11	r.	r.	PROPN
ejpam-2196	148	12	then	then	ADV
ejpam-2196	148	13	(	(	PUNCT
ejpam-2196	148	14	i	i	PRON
ejpam-2196	148	15	m	m	VERB
ejpam-2196	148	16	:	:	PUNCT
ejpam-2196	148	17	m	m	VERB
ejpam-2196	148	18	)	)	PUNCT
ejpam-2196	149	1	=	=	SYM
ejpam-2196	150	1	i	i	PRON
ejpam-2196	150	2	if	if	SCONJ
ejpam-2196	151	1	and	and	CCONJ
ejpam-2196	151	2	only	only	ADV
ejpam-2196	151	3	if	if	SCONJ
ejpam-2196	151	4	i	i	PRON
ejpam-2196	151	5	⊇	⊇	PROPN
ejpam-2196	151	6	ann(m	ann(m	PROPN
ejpam-2196	151	7	)	)	PUNCT
ejpam-2196	151	8	.	.	PUNCT
ejpam-2196	152	1	(	(	PUNCT
ejpam-2196	152	2	2	2	X
ejpam-2196	152	3	)	)	PUNCT
ejpam-2196	152	4	mm	mm	NOUN
ejpam-2196	152	5	∈	∈	PROPN
ejpam-2196	152	6	x	x	PUNCT
ejpam-2196	152	7	for	for	ADP
ejpam-2196	152	8	every	every	DET
ejpam-2196	152	9	m	m	NOUN
ejpam-2196	152	10	∈	∈	PROPN
ejpam-2196	152	11	v	v	NOUN
ejpam-2196	152	12	(	(	PUNCT
ejpam-2196	152	13	ann(m))∩max(r	ann(m))∩max(r	NUM
ejpam-2196	152	14	)	)	PUNCT
ejpam-2196	152	15	.	.	PUNCT
ejpam-2196	153	1	(	(	PUNCT
ejpam-2196	153	2	3	3	X
ejpam-2196	153	3	)	)	PUNCT
ejpam-2196	153	4	if	if	SCONJ
ejpam-2196	153	5	m	m	NOUN
ejpam-2196	153	6	is	be	AUX
ejpam-2196	153	7	faithful	faithful	ADJ
ejpam-2196	153	8	,	,	PUNCT
ejpam-2196	153	9	then	then	ADV
ejpam-2196	153	10	m	m	VERB
ejpam-2196	153	11	is	be	AUX
ejpam-2196	153	12	flat	flat	ADJ
ejpam-2196	153	13	if	if	SCONJ
ejpam-2196	153	14	and	and	CCONJ
ejpam-2196	153	15	only	only	ADV
ejpam-2196	153	16	if	if	SCONJ
ejpam-2196	153	17	m	m	NOUN
ejpam-2196	153	18	is	be	AUX
ejpam-2196	153	19	faithfully	faithfully	ADV
ejpam-2196	153	20	flat	flat	ADJ
ejpam-2196	153	21	.	.	PUNCT
ejpam-2196	154	1	proof	proof	NOUN
ejpam-2196	154	2	.	.	PUNCT
ejpam-2196	155	1	(	(	PUNCT
ejpam-2196	155	2	1	1	X
ejpam-2196	155	3	)	)	PUNCT
ejpam-2196	155	4	follows	follow	VERB
ejpam-2196	155	5	from	from	ADP
ejpam-2196	155	6	[	[	X
ejpam-2196	155	7	9	9	NUM
ejpam-2196	155	8	,	,	PUNCT
ejpam-2196	155	9	proposition	proposition	NOUN
ejpam-2196	155	10	3.1	3.1	NUM
ejpam-2196	155	11	]	]	PUNCT
ejpam-2196	155	12	and	and	CCONJ
ejpam-2196	155	13	theorem	theorem	VERB
ejpam-2196	155	14	1	1	NUM
ejpam-2196	155	15	.	.	PUNCT
ejpam-2196	156	1	(	(	PUNCT
ejpam-2196	156	2	2	2	NUM
ejpam-2196	156	3	)	)	PUNCT
ejpam-2196	156	4	by	by	ADP
ejpam-2196	156	5	theorem	theorem	NOUN
ejpam-2196	156	6	1	1	NUM
ejpam-2196	156	7	,	,	PUNCT
ejpam-2196	156	8	m	m	VERB
ejpam-2196	156	9	is	be	AUX
ejpam-2196	156	10	aψ	aψ	NOUN
ejpam-2196	156	11	-	-	NOUN
ejpam-2196	156	12	module	module	NOUN
ejpam-2196	156	13	.	.	PUNCT
ejpam-2196	157	1	hence	hence	ADV
ejpam-2196	157	2	by	by	ADP
ejpam-2196	157	3	[	[	X
ejpam-2196	157	4	9	9	NUM
ejpam-2196	157	5	,	,	PUNCT
ejpam-2196	157	6	result	result	VERB
ejpam-2196	157	7	2	2	NUM
ejpam-2196	157	8	]	]	PUNCT
ejpam-2196	157	9	,	,	PUNCT
ejpam-2196	157	10	mm	mm	PROPN
ejpam-2196	157	11	6=	6=	NUM
ejpam-2196	157	12	m	m	PROPN
ejpam-2196	157	13	.	.	PUNCT
ejpam-2196	158	1	thus	thus	ADV
ejpam-2196	158	2	mm	mm	PROPN
ejpam-2196	158	3	is	be	AUX
ejpam-2196	158	4	a	a	DET
ejpam-2196	158	5	m	m	NOUN
ejpam-2196	158	6	-	-	NOUN
ejpam-2196	158	7	prime	prime	ADJ
ejpam-2196	158	8	,	,	PUNCT
ejpam-2196	158	9	and	and	CCONJ
ejpam-2196	158	10	hence	hence	ADV
ejpam-2196	158	11	m	m	NOUN
ejpam-2196	158	12	-	-	ADJ
ejpam-2196	158	13	primary	primary	ADJ
ejpam-2196	158	14	-	-	PUNCT
ejpam-2196	158	15	like	like	ADJ
ejpam-2196	158	16	,	,	PUNCT
ejpam-2196	158	17	submodule	submodule	NOUN
ejpam-2196	158	18	of	of	ADP
ejpam-2196	158	19	m	m	PROPN
ejpam-2196	158	20	.	.	PUNCT
ejpam-2196	159	1	it	it	PRON
ejpam-2196	159	2	remains	remain	VERB
ejpam-2196	159	3	to	to	PART
ejpam-2196	159	4	show	show	VERB
ejpam-2196	159	5	that	that	SCONJ
ejpam-2196	159	6	m	m	PROPN
ejpam-2196	159	7	/	/	SYM
ejpam-2196	159	8	mm	mm	PROPN
ejpam-2196	159	9	is	be	AUX
ejpam-2196	159	10	a	a	DET
ejpam-2196	159	11	ψ	ψ	NOUN
ejpam-2196	159	12	-	-	NOUN
ejpam-2196	159	13	module	module	NOUN
ejpam-2196	159	14	.	.	PUNCT
ejpam-2196	160	1	assume	assume	VERB
ejpam-2196	160	2	p	p	NOUN
ejpam-2196	160	3	is	be	AUX
ejpam-2196	160	4	a	a	DET
ejpam-2196	160	5	prime	prime	ADJ
ejpam-2196	160	6	ideal	ideal	NOUN
ejpam-2196	160	7	of	of	ADP
ejpam-2196	160	8	r	r	NOUN
ejpam-2196	160	9	containing	contain	VERB
ejpam-2196	160	10	(	(	PUNCT
ejpam-2196	160	11	mm	mm	INTJ
ejpam-2196	160	12	:	:	PUNCT
ejpam-2196	160	13	m	m	PROPN
ejpam-2196	160	14	)	)	PUNCT
ejpam-2196	160	15	.	.	PUNCT
ejpam-2196	161	1	since	since	SCONJ
ejpam-2196	161	2	m	m	PROPN
ejpam-2196	161	3	∈	∈	PROPN
ejpam-2196	161	4	max(r	max(r	PROPN
ejpam-2196	161	5	)	)	PUNCT
ejpam-2196	161	6	,	,	PUNCT
ejpam-2196	161	7	then	then	ADV
ejpam-2196	161	8	m	m	VERB
ejpam-2196	161	9	=	=	ADJ
ejpam-2196	161	10	p	p	PROPN
ejpam-2196	161	11	and	and	CCONJ
ejpam-2196	161	12	so	so	ADV
ejpam-2196	161	13	m	m	ADJ
ejpam-2196	161	14	/	/	SYM
ejpam-2196	161	15	mm	mm	PROPN
ejpam-2196	161	16	is	be	AUX
ejpam-2196	161	17	a	a	DET
ejpam-2196	161	18	ψ	ψ	NOUN
ejpam-2196	161	19	-	-	NOUN
ejpam-2196	161	20	module	module	NOUN
ejpam-2196	161	21	.	.	PUNCT
ejpam-2196	162	1	thus	thus	ADV
ejpam-2196	162	2	mm	mm	PROPN
ejpam-2196	162	3	∈	∈	PROPN
ejpam-2196	162	4	x	x	X
ejpam-2196	162	5	.	.	PUNCT
ejpam-2196	163	1	(	(	PUNCT
ejpam-2196	163	2	3	3	X
ejpam-2196	163	3	)	)	PUNCT
ejpam-2196	163	4	the	the	DET
ejpam-2196	163	5	sufficiency	sufficiency	NOUN
ejpam-2196	163	6	is	be	AUX
ejpam-2196	163	7	clear	clear	ADJ
ejpam-2196	163	8	.	.	PUNCT
ejpam-2196	164	1	suppose	suppose	VERB
ejpam-2196	164	2	that	that	SCONJ
ejpam-2196	164	3	m	m	PROPN
ejpam-2196	164	4	is	be	AUX
ejpam-2196	164	5	flat	flat	ADJ
ejpam-2196	164	6	.	.	PUNCT
ejpam-2196	165	1	hence	hence	ADV
ejpam-2196	165	2	by	by	ADP
ejpam-2196	165	3	part	part	NOUN
ejpam-2196	165	4	(	(	PUNCT
ejpam-2196	165	5	2	2	NUM
ejpam-2196	165	6	)	)	PUNCT
ejpam-2196	165	7	,	,	PUNCT
ejpam-2196	165	8	we	we	PRON
ejpam-2196	165	9	have	have	VERB
ejpam-2196	165	10	mm	mm	PROPN
ejpam-2196	165	11	6=	6=	NUM
ejpam-2196	165	12	m	m	PRON
ejpam-2196	165	13	for	for	ADP
ejpam-2196	165	14	every	every	DET
ejpam-2196	165	15	m	m	PROPN
ejpam-2196	165	16	∈	∈	PROPN
ejpam-2196	165	17	max(r	max(r	PROPN
ejpam-2196	165	18	)	)	PUNCT
ejpam-2196	165	19	.	.	PUNCT
ejpam-2196	166	1	this	this	PRON
ejpam-2196	166	2	implies	imply	VERB
ejpam-2196	166	3	that	that	SCONJ
ejpam-2196	166	4	m	m	NOUN
ejpam-2196	166	5	is	be	AUX
ejpam-2196	166	6	faithfully	faithfully	ADV
ejpam-2196	166	7	flat	flat	ADJ
ejpam-2196	166	8	.	.	PUNCT
ejpam-2196	167	1	we	we	PRON
ejpam-2196	167	2	give	give	VERB
ejpam-2196	167	3	an	an	DET
ejpam-2196	167	4	elementary	elementary	ADJ
ejpam-2196	167	5	example	example	NOUN
ejpam-2196	167	6	of	of	ADP
ejpam-2196	167	7	a	a	DET
ejpam-2196	167	8	module	module	NOUN
ejpam-2196	167	9	which	which	PRON
ejpam-2196	167	10	is	be	AUX
ejpam-2196	167	11	not	not	PART
ejpam-2196	167	12	a	a	DET
ejpam-2196	167	13	φ	φ	NOUN
ejpam-2196	167	14	-	-	PUNCT
ejpam-2196	167	15	module	module	NOUN
ejpam-2196	167	16	.	.	PUNCT
ejpam-2196	167	17	example	example	NOUN
ejpam-2196	168	1	2	2	NUM
ejpam-2196	168	2	.	.	PUNCT
ejpam-2196	169	1	the	the	DET
ejpam-2196	169	2	z	z	NOUN
ejpam-2196	169	3	-	-	PUNCT
ejpam-2196	169	4	module	module	NOUN
ejpam-2196	169	5	q	q	NOUN
ejpam-2196	169	6	is	be	AUX
ejpam-2196	169	7	flat	flat	ADJ
ejpam-2196	169	8	and	and	CCONJ
ejpam-2196	169	9	faithful	faithful	ADJ
ejpam-2196	169	10	,	,	PUNCT
ejpam-2196	169	11	but	but	CCONJ
ejpam-2196	169	12	not	not	PART
ejpam-2196	169	13	faithfully	faithfully	ADV
ejpam-2196	169	14	flat	flat	ADJ
ejpam-2196	169	15	.	.	PUNCT
ejpam-2196	170	1	so	so	ADV
ejpam-2196	170	2	,	,	PUNCT
ejpam-2196	170	3	q	q	X
ejpam-2196	170	4	is	be	AUX
ejpam-2196	170	5	not	not	PART
ejpam-2196	170	6	a	a	DET
ejpam-2196	170	7	φ	φ	NOUN
ejpam-2196	170	8	-	-	NOUN
ejpam-2196	170	9	module	module	NOUN
ejpam-2196	170	10	,	,	PUNCT
ejpam-2196	170	11	by	by	ADP
ejpam-2196	170	12	proposition	proposition	NOUN
ejpam-2196	170	13	1	1	NUM
ejpam-2196	170	14	.	.	PUNCT
ejpam-2196	170	15	proposition	proposition	NOUN
ejpam-2196	170	16	2	2	NUM
ejpam-2196	170	17	.	.	PUNCT
ejpam-2196	171	1	let	let	VERB
ejpam-2196	171	2	m	m	PRON
ejpam-2196	171	3	be	be	AUX
ejpam-2196	171	4	a	a	DET
ejpam-2196	171	5	non	non	ADJ
ejpam-2196	171	6	-	-	ADJ
ejpam-2196	171	7	zero	zero	NUM
ejpam-2196	171	8	φ	φ	NOUN
ejpam-2196	171	9	-	-	NOUN
ejpam-2196	171	10	module	module	NOUN
ejpam-2196	171	11	over	over	ADP
ejpam-2196	171	12	a	a	DET
ejpam-2196	171	13	ring	ring	NOUN
ejpam-2196	171	14	r.	r.	PROPN
ejpam-2196	171	15	then	then	ADV
ejpam-2196	171	16	mp	mp	PROPN
ejpam-2196	171	17	is	be	AUX
ejpam-2196	171	18	a	a	DET
ejpam-2196	171	19	non	non	ADJ
ejpam-2196	171	20	-	-	ADJ
ejpam-2196	171	21	zero	zero	NUM
ejpam-2196	171	22	φ	φ	NOUN
ejpam-2196	171	23	-	-	NOUN
ejpam-2196	171	24	module	module	NOUN
ejpam-2196	171	25	over	over	ADP
ejpam-2196	171	26	rp	rp	NOUN
ejpam-2196	171	27	for	for	ADP
ejpam-2196	171	28	every	every	DET
ejpam-2196	171	29	p	p	PROPN
ejpam-2196	171	30	∈	∈	PROPN
ejpam-2196	171	31	v	v	NOUN
ejpam-2196	171	32	(	(	PUNCT
ejpam-2196	171	33	ann(m	ann(m	PROPN
ejpam-2196	171	34	)	)	PUNCT
ejpam-2196	171	35	)	)	PUNCT
ejpam-2196	171	36	.	.	PUNCT
ejpam-2196	172	1	h.	h.	PROPN
ejpam-2196	172	2	moghimi	moghimi	PROPN
ejpam-2196	172	3	,	,	PUNCT
ejpam-2196	172	4	f.	f.	PROPN
ejpam-2196	172	5	rashedi	rashedi	PROPN
ejpam-2196	172	6	/	/	SYM
ejpam-2196	172	7	eur	eur	PROPN
ejpam-2196	172	8	.	.	PUNCT
ejpam-2196	173	1	j.	j.	PROPN
ejpam-2196	173	2	pure	pure	PROPN
ejpam-2196	173	3	appl	appl	PROPN
ejpam-2196	173	4	.	.	PROPN
ejpam-2196	173	5	math	math	PROPN
ejpam-2196	173	6	,	,	PUNCT
ejpam-2196	173	7	8	8	NUM
ejpam-2196	173	8	(	(	PUNCT
ejpam-2196	173	9	2015	2015	NUM
ejpam-2196	173	10	)	)	PUNCT
ejpam-2196	173	11	,	,	PUNCT
ejpam-2196	173	12	232	232	NUM
ejpam-2196	173	13	-	-	SYM
ejpam-2196	173	14	238	238	NUM
ejpam-2196	173	15	236	236	NUM
ejpam-2196	173	16	proof	proof	NOUN
ejpam-2196	173	17	.	.	PUNCT
ejpam-2196	174	1	suppose	suppose	VERB
ejpam-2196	174	2	m	m	PRON
ejpam-2196	174	3	is	be	AUX
ejpam-2196	174	4	a	a	DET
ejpam-2196	174	5	non	non	ADJ
ejpam-2196	174	6	-	-	ADJ
ejpam-2196	174	7	zeroφ	zeroφ	ADJ
ejpam-2196	174	8	-	-	PUNCT
ejpam-2196	174	9	module	module	NOUN
ejpam-2196	174	10	over	over	ADP
ejpam-2196	174	11	r.	r.	PROPN
ejpam-2196	174	12	hence	hence	ADV
ejpam-2196	174	13	mp	mp	PROPN
ejpam-2196	175	1	6=	6=	PROPN
ejpam-2196	175	2	(	(	PUNCT
ejpam-2196	175	3	0	0	NUM
ejpam-2196	175	4	)	)	PUNCT
ejpam-2196	175	5	for	for	ADP
ejpam-2196	175	6	every	every	DET
ejpam-2196	175	7	p	p	PROPN
ejpam-2196	175	8	∈	∈	PROPN
ejpam-2196	175	9	v	v	NOUN
ejpam-2196	175	10	(	(	PUNCT
ejpam-2196	175	11	ann(m	ann(m	NOUN
ejpam-2196	175	12	)	)	PUNCT
ejpam-2196	175	13	)	)	PUNCT
ejpam-2196	175	14	.	.	PUNCT
ejpam-2196	176	1	assume	assume	VERB
ejpam-2196	176	2	q′	q′	X
ejpam-2196	176	3	∈	∈	PROPN
ejpam-2196	176	4	spec(rp	spec(rp	PROPN
ejpam-2196	176	5	/	/	SYM
ejpam-2196	176	6	ann(mp	ann(mp	NOUN
ejpam-2196	176	7	)	)	PUNCT
ejpam-2196	176	8	)	)	PUNCT
ejpam-2196	176	9	.	.	PUNCT
ejpam-2196	177	1	we	we	PRON
ejpam-2196	177	2	set	set	VERB
ejpam-2196	177	3	q	q	NOUN
ejpam-2196	177	4	=	=	PUNCT
ejpam-2196	177	5	(	(	PUNCT
ejpam-2196	177	6	q′)c	q′)c	PROPN
ejpam-2196	177	7	,	,	PUNCT
ejpam-2196	177	8	the	the	DET
ejpam-2196	177	9	contraction	contraction	NOUN
ejpam-2196	177	10	of	of	ADP
ejpam-2196	177	11	q′	q′	NOUN
ejpam-2196	177	12	in	in	ADP
ejpam-2196	177	13	r.	r.	PROPN
ejpam-2196	177	14	it	it	PRON
ejpam-2196	177	15	is	be	AUX
ejpam-2196	177	16	easy	easy	ADJ
ejpam-2196	177	17	to	to	PART
ejpam-2196	177	18	check	check	VERB
ejpam-2196	177	19	that	that	DET
ejpam-2196	177	20	q	q	NOUN
ejpam-2196	177	21	is	be	AUX
ejpam-2196	177	22	a	a	DET
ejpam-2196	177	23	prime	prime	ADJ
ejpam-2196	177	24	ideal	ideal	NOUN
ejpam-2196	177	25	of	of	ADP
ejpam-2196	177	26	r.	r.	PROPN
ejpam-2196	177	27	we	we	PRON
ejpam-2196	177	28	show	show	VERB
ejpam-2196	177	29	that	that	SCONJ
ejpam-2196	177	30	there	there	PRON
ejpam-2196	177	31	exists	exist	VERB
ejpam-2196	177	32	a	a	DET
ejpam-2196	177	33	q′-primary	q′-primary	NUM
ejpam-2196	177	34	-	-	PUNCT
ejpam-2196	177	35	like	like	ADJ
ejpam-2196	177	36	submodule	submodule	NOUN
ejpam-2196	177	37	qp	qp	PROPN
ejpam-2196	177	38	of	of	ADP
ejpam-2196	177	39	mp	mp	PROPN
ejpam-2196	177	40	such	such	ADJ
ejpam-2196	177	41	that	that	DET
ejpam-2196	177	42	mp	mp	PROPN
ejpam-2196	177	43	/	/	SYM
ejpam-2196	177	44	qp	qp	PROPN
ejpam-2196	177	45	is	be	AUX
ejpam-2196	177	46	a	a	DET
ejpam-2196	177	47	ψ	ψ	NOUN
ejpam-2196	177	48	-	-	NOUN
ejpam-2196	177	49	module	module	NOUN
ejpam-2196	177	50	.	.	PUNCT
ejpam-2196	178	1	since	since	SCONJ
ejpam-2196	178	2	rp	rp	NOUN
ejpam-2196	178	3	is	be	AUX
ejpam-2196	178	4	a	a	DET
ejpam-2196	178	5	local	local	ADJ
ejpam-2196	178	6	ring	ring	NOUN
ejpam-2196	178	7	,	,	PUNCT
ejpam-2196	178	8	pp	pp	ADP
ejpam-2196	178	9	⊇	⊇	PROPN
ejpam-2196	178	10	q′	q′	NOUN
ejpam-2196	178	11	⊇	⊇	PROPN
ejpam-2196	178	12	ann(mp	ann(mp	PROPN
ejpam-2196	178	13	)	)	PUNCT
ejpam-2196	178	14	⊇	⊇	NOUN
ejpam-2196	178	15	(	(	PUNCT
ejpam-2196	178	16	ann(m))p	ann(m))p	PROPN
ejpam-2196	178	17	.	.	PUNCT
ejpam-2196	179	1	taking	take	VERB
ejpam-2196	179	2	the	the	DET
ejpam-2196	179	3	contraction	contraction	NOUN
ejpam-2196	179	4	of	of	ADP
ejpam-2196	179	5	each	each	DET
ejpam-2196	179	6	term	term	NOUN
ejpam-2196	179	7	of	of	ADP
ejpam-2196	179	8	this	this	DET
ejpam-2196	179	9	sequence	sequence	NOUN
ejpam-2196	179	10	of	of	ADP
ejpam-2196	179	11	ideals	ideal	NOUN
ejpam-2196	179	12	in	in	ADP
ejpam-2196	179	13	r	r	NOUN
ejpam-2196	179	14	,	,	PUNCT
ejpam-2196	179	15	we	we	PRON
ejpam-2196	179	16	have	have	VERB
ejpam-2196	179	17	that	that	DET
ejpam-2196	179	18	p	p	PROPN
ejpam-2196	179	19	⊇	⊇	PROPN
ejpam-2196	179	20	q	q	PROPN
ejpam-2196	179	21	⊇	⊇	PROPN
ejpam-2196	179	22	ann(mp)∩	ann(mp)∩	PROPN
ejpam-2196	179	23	r	r	PROPN
ejpam-2196	179	24	⊇	⊇	PROPN
ejpam-2196	179	25	sp(ann(m	sp(ann(m	PROPN
ejpam-2196	179	26	)	)	PUNCT
ejpam-2196	179	27	)	)	PUNCT
ejpam-2196	179	28	⊇	⊇	PROPN
ejpam-2196	179	29	ann(m	ann(m	PROPN
ejpam-2196	179	30	)	)	PUNCT
ejpam-2196	179	31	.	.	PUNCT
ejpam-2196	180	1	hence	hence	ADV
ejpam-2196	180	2	q	q	PROPN
ejpam-2196	180	3	∈	∈	PROPN
ejpam-2196	180	4	spec(r	spec(r	PROPN
ejpam-2196	180	5	/	/	SYM
ejpam-2196	180	6	ann(m	ann(m	PROPN
ejpam-2196	180	7	)	)	PUNCT
ejpam-2196	180	8	)	)	PUNCT
ejpam-2196	180	9	.	.	PUNCT
ejpam-2196	181	1	since	since	SCONJ
ejpam-2196	181	2	m	m	PROPN
ejpam-2196	181	3	is	be	AUX
ejpam-2196	181	4	a	a	DET
ejpam-2196	181	5	φ	φ	NOUN
ejpam-2196	181	6	-	-	NOUN
ejpam-2196	181	7	module	module	NOUN
ejpam-2196	181	8	over	over	ADP
ejpam-2196	181	9	r	r	NOUN
ejpam-2196	181	10	,	,	PUNCT
ejpam-2196	181	11	there	there	PRON
ejpam-2196	181	12	exists	exist	VERB
ejpam-2196	181	13	q	q	PROPN
ejpam-2196	181	14	∈	∈	PROPN
ejpam-2196	181	15	x	x	PUNCT
ejpam-2196	182	1	such	such	ADJ
ejpam-2196	182	2	that	that	SCONJ
ejpam-2196	182	3	p	p	X
ejpam-2196	182	4	(	(	PUNCT
ejpam-2196	182	5	q	q	NOUN
ejpam-2196	182	6	:	:	PUNCT
ejpam-2196	182	7	m	m	X
ejpam-2196	182	8	)	)	PUNCT
ejpam-2196	182	9	=	=	VERB
ejpam-2196	182	10	q.	q.	NOUN
ejpam-2196	182	11	thus	thus	ADV
ejpam-2196	182	12	by	by	ADP
ejpam-2196	182	13	[	[	X
ejpam-2196	182	14	7	7	NUM
ejpam-2196	182	15	,	,	PUNCT
ejpam-2196	182	16	theorem	theorem	VERB
ejpam-2196	182	17	3.8	3.8	NUM
ejpam-2196	182	18	]	]	PUNCT
ejpam-2196	182	19	qp	qp	ADP
ejpam-2196	182	20	is	be	AUX
ejpam-2196	182	21	a	a	DET
ejpam-2196	182	22	q′-primary	q′-primary	NUM
ejpam-2196	182	23	-	-	PUNCT
ejpam-2196	182	24	like	like	ADJ
ejpam-2196	182	25	submodule	submodule	NOUN
ejpam-2196	182	26	in	in	ADP
ejpam-2196	182	27	mp	mp	NOUN
ejpam-2196	182	28	such	such	ADJ
ejpam-2196	182	29	that	that	DET
ejpam-2196	182	30	mp	mp	PROPN
ejpam-2196	182	31	/	/	SYM
ejpam-2196	182	32	qp	qp	PROPN
ejpam-2196	182	33	is	be	AUX
ejpam-2196	182	34	a	a	DET
ejpam-2196	182	35	ψ	ψ	NOUN
ejpam-2196	182	36	-	-	NOUN
ejpam-2196	182	37	module	module	NOUN
ejpam-2196	182	38	and	and	CCONJ
ejpam-2196	182	39	hence	hence	ADV
ejpam-2196	182	40	mp	mp	PROPN
ejpam-2196	182	41	is	be	AUX
ejpam-2196	182	42	a	a	DET
ejpam-2196	182	43	φ	φ	NOUN
ejpam-2196	182	44	-	-	PUNCT
ejpam-2196	182	45	module	module	NOUN
ejpam-2196	182	46	over	over	ADP
ejpam-2196	182	47	rp	rp	NOUN
ejpam-2196	182	48	for	for	ADP
ejpam-2196	182	49	every	every	DET
ejpam-2196	182	50	p	p	PROPN
ejpam-2196	182	51	∈	∈	PROPN
ejpam-2196	182	52	v	v	NOUN
ejpam-2196	182	53	(	(	PUNCT
ejpam-2196	182	54	ann(m	ann(m	NOUN
ejpam-2196	182	55	)	)	PUNCT
ejpam-2196	182	56	)	)	PUNCT
ejpam-2196	182	57	.	.	PUNCT
ejpam-2196	183	1	theorem	theorem	ADJ
ejpam-2196	183	2	4	4	NUM
ejpam-2196	183	3	.	.	PUNCT
ejpam-2196	184	1	let	let	VERB
ejpam-2196	184	2	r	r	PRON
ejpam-2196	184	3	be	be	AUX
ejpam-2196	184	4	a	a	DET
ejpam-2196	184	5	ring	ring	NOUN
ejpam-2196	184	6	.	.	PUNCT
ejpam-2196	185	1	consider	consider	VERB
ejpam-2196	185	2	the	the	DET
ejpam-2196	185	3	following	follow	VERB
ejpam-2196	185	4	statements	statement	NOUN
ejpam-2196	185	5	.	.	PUNCT
ejpam-2196	186	1	(	(	PUNCT
ejpam-2196	186	2	1	1	X
ejpam-2196	186	3	)	)	PUNCT
ejpam-2196	186	4	r	r	NOUN
ejpam-2196	186	5	is	be	AUX
ejpam-2196	186	6	an	an	DET
ejpam-2196	186	7	artinian	artinian	ADJ
ejpam-2196	186	8	ring	ring	NOUN
ejpam-2196	186	9	.	.	PUNCT
ejpam-2196	187	1	(	(	PUNCT
ejpam-2196	187	2	2	2	X
ejpam-2196	187	3	)	)	PUNCT
ejpam-2196	187	4	every	every	DET
ejpam-2196	187	5	r	r	NOUN
ejpam-2196	187	6	-	-	PUNCT
ejpam-2196	187	7	module	module	NOUN
ejpam-2196	187	8	is	be	AUX
ejpam-2196	187	9	a	a	DET
ejpam-2196	187	10	φ	φ	NOUN
ejpam-2196	187	11	-	-	PUNCT
ejpam-2196	187	12	module	module	NOUN
ejpam-2196	187	13	.	.	PUNCT
ejpam-2196	188	1	(	(	PUNCT
ejpam-2196	188	2	3	3	X
ejpam-2196	188	3	)	)	PUNCT
ejpam-2196	188	4	every	every	DET
ejpam-2196	188	5	r	r	NOUN
ejpam-2196	188	6	-	-	PUNCT
ejpam-2196	188	7	module	module	NOUN
ejpam-2196	188	8	is	be	AUX
ejpam-2196	188	9	a	a	DET
ejpam-2196	188	10	ψ	ψ	NOUN
ejpam-2196	188	11	-	-	NOUN
ejpam-2196	188	12	module	module	NOUN
ejpam-2196	188	13	.	.	PUNCT
ejpam-2196	189	1	(	(	PUNCT
ejpam-2196	189	2	4	4	X
ejpam-2196	189	3	)	)	PUNCT
ejpam-2196	189	4	mm	mm	PROPN
ejpam-2196	190	1	6=	6=	NUM
ejpam-2196	190	2	m	m	VERB
ejpam-2196	190	3	for	for	ADP
ejpam-2196	190	4	every	every	DET
ejpam-2196	190	5	r	r	NOUN
ejpam-2196	190	6	-	-	PUNCT
ejpam-2196	190	7	module	module	NOUN
ejpam-2196	190	8	m	m	NOUN
ejpam-2196	190	9	and	and	CCONJ
ejpam-2196	190	10	m	m	PROPN
ejpam-2196	190	11	∈	∈	PROPN
ejpam-2196	190	12	v	v	NOUN
ejpam-2196	190	13	(	(	PUNCT
ejpam-2196	190	14	ann(m))∩max(r	ann(m))∩max(r	NUM
ejpam-2196	190	15	)	)	PUNCT
ejpam-2196	190	16	.	.	PUNCT
ejpam-2196	191	1	(	(	PUNCT
ejpam-2196	191	2	5	5	X
ejpam-2196	191	3	)	)	PUNCT
ejpam-2196	191	4	dim(r	dim(r	NOUN
ejpam-2196	191	5	)	)	PUNCT
ejpam-2196	192	1	=	=	SYM
ejpam-2196	192	2	0	0	PUNCT
ejpam-2196	193	1	then	then	ADV
ejpam-2196	193	2	(	(	PUNCT
ejpam-2196	193	3	1	1	X
ejpam-2196	193	4	)	)	PUNCT
ejpam-2196	193	5	⇒	⇒	NOUN
ejpam-2196	193	6	(	(	PUNCT
ejpam-2196	193	7	2	2	NUM
ejpam-2196	193	8	)	)	PUNCT
ejpam-2196	193	9	⇒	⇒	NOUN
ejpam-2196	193	10	(	(	PUNCT
ejpam-2196	193	11	3	3	NUM
ejpam-2196	193	12	)	)	PUNCT
ejpam-2196	193	13	⇒	⇒	NOUN
ejpam-2196	193	14	(	(	PUNCT
ejpam-2196	193	15	4	4	NUM
ejpam-2196	193	16	)	)	PUNCT
ejpam-2196	193	17	⇒	⇒	NOUN
ejpam-2196	193	18	(	(	PUNCT
ejpam-2196	193	19	5	5	NUM
ejpam-2196	193	20	)	)	PUNCT
ejpam-2196	193	21	.	.	PUNCT
ejpam-2196	194	1	furthermore	furthermore	ADV
ejpam-2196	194	2	,	,	PUNCT
ejpam-2196	194	3	if	if	SCONJ
ejpam-2196	194	4	r	r	NOUN
ejpam-2196	194	5	is	be	AUX
ejpam-2196	194	6	a	a	DET
ejpam-2196	194	7	noetherian	noetherian	ADJ
ejpam-2196	194	8	ring	ring	NOUN
ejpam-2196	194	9	,	,	PUNCT
ejpam-2196	194	10	then	then	ADV
ejpam-2196	194	11	the	the	DET
ejpam-2196	194	12	above	above	ADJ
ejpam-2196	194	13	statements	statement	NOUN
ejpam-2196	194	14	are	be	AUX
ejpam-2196	194	15	equivalent	equivalent	ADJ
ejpam-2196	194	16	.	.	PUNCT
ejpam-2196	195	1	proof	proof	NOUN
ejpam-2196	195	2	.	.	PUNCT
ejpam-2196	196	1	(	(	PUNCT
ejpam-2196	196	2	1)⇒	1)⇒	NUM
ejpam-2196	196	3	(	(	PUNCT
ejpam-2196	196	4	2	2	NUM
ejpam-2196	196	5	)	)	PUNCT
ejpam-2196	196	6	let	let	VERB
ejpam-2196	196	7	m	m	PRON
ejpam-2196	196	8	be	be	AUX
ejpam-2196	196	9	a	a	DET
ejpam-2196	196	10	non	non	ADJ
ejpam-2196	196	11	-	-	ADJ
ejpam-2196	196	12	zero	zero	ADJ
ejpam-2196	196	13	r	r	NOUN
ejpam-2196	196	14	-	-	PUNCT
ejpam-2196	196	15	module	module	NOUN
ejpam-2196	196	16	.	.	PUNCT
ejpam-2196	197	1	then	then	ADV
ejpam-2196	197	2	ann(m	ann(m	PROPN
ejpam-2196	197	3	)	)	PUNCT
ejpam-2196	198	1	6=	6=	ADP
ejpam-2196	198	2	r.	r.	PROPN
ejpam-2196	198	3	since	since	SCONJ
ejpam-2196	198	4	r	r	NOUN
ejpam-2196	198	5	is	be	AUX
ejpam-2196	198	6	artinian	artinian	ADJ
ejpam-2196	198	7	,	,	PUNCT
ejpam-2196	198	8	we	we	PRON
ejpam-2196	198	9	have	have	VERB
ejpam-2196	198	10	r=	r=	ADJ
ejpam-2196	198	11	r1×	r1×	NOUN
ejpam-2196	198	12	·	·	PUNCT
ejpam-2196	198	13	·	·	PUNCT
ejpam-2196	198	14	·	·	PUNCT
ejpam-2196	198	15	×rn	×rn	NOUN
ejpam-2196	198	16	,	,	PUNCT
ejpam-2196	198	17	where	where	SCONJ
ejpam-2196	198	18	n	n	X
ejpam-2196	198	19	∈	∈	PROPN
ejpam-2196	198	20	n	n	CCONJ
ejpam-2196	198	21	and	and	CCONJ
ejpam-2196	198	22	each	each	DET
ejpam-2196	198	23	ri	ri	PROPN
ejpam-2196	198	24	is	be	AUX
ejpam-2196	198	25	an	an	DET
ejpam-2196	198	26	artinian	artinian	ADJ
ejpam-2196	198	27	local	local	ADJ
ejpam-2196	198	28	ring	ring	NOUN
ejpam-2196	198	29	.	.	PUNCT
ejpam-2196	199	1	first	first	ADV
ejpam-2196	199	2	we	we	PRON
ejpam-2196	199	3	assume	assume	VERB
ejpam-2196	199	4	that	that	SCONJ
ejpam-2196	199	5	n	n	NOUN
ejpam-2196	199	6	=	=	SYM
ejpam-2196	199	7	1	1	NUM
ejpam-2196	199	8	,	,	PUNCT
ejpam-2196	199	9	i.e.	i.e.	X
ejpam-2196	199	10	,	,	PUNCT
ejpam-2196	199	11	r	r	NOUN
ejpam-2196	199	12	is	be	AUX
ejpam-2196	199	13	an	an	DET
ejpam-2196	199	14	artinian	artinian	ADJ
ejpam-2196	199	15	local	local	ADJ
ejpam-2196	199	16	ring	ring	NOUN
ejpam-2196	199	17	with	with	ADP
ejpam-2196	199	18	maximal	maximal	ADJ
ejpam-2196	199	19	ideal	ideal	ADJ
ejpam-2196	199	20	m.	m.	NOUN
ejpam-2196	199	21	since	since	SCONJ
ejpam-2196	199	22	j(r	j(r	PROPN
ejpam-2196	199	23	)	)	PUNCT
ejpam-2196	199	24	,	,	PUNCT
ejpam-2196	199	25	the	the	DET
ejpam-2196	199	26	jacobson	jacobson	PROPN
ejpam-2196	199	27	radical	radical	PROPN
ejpam-2196	199	28	of	of	ADP
ejpam-2196	199	29	r	r	PROPN
ejpam-2196	199	30	,	,	PUNCT
ejpam-2196	199	31	equals	equal	VERB
ejpam-2196	199	32	to	to	ADP
ejpam-2196	199	33	m	m	PROPN
ejpam-2196	199	34	and	and	CCONJ
ejpam-2196	199	35	j(r	j(r	PROPN
ejpam-2196	199	36	)	)	PUNCT
ejpam-2196	199	37	is	be	AUX
ejpam-2196	199	38	t	t	NOUN
ejpam-2196	199	39	-	-	PUNCT
ejpam-2196	199	40	nilpotent	nilpotent	ADJ
ejpam-2196	199	41	,	,	PUNCT
ejpam-2196	199	42	mm	mm	PROPN
ejpam-2196	199	43	6=	6=	ADP
ejpam-2196	199	44	m	m	VERB
ejpam-2196	199	45	by	by	ADP
ejpam-2196	199	46	[	[	X
ejpam-2196	199	47	8	8	NUM
ejpam-2196	199	48	,	,	PUNCT
ejpam-2196	199	49	theorem	theorem	VERB
ejpam-2196	199	50	23.16	23.16	NUM
ejpam-2196	199	51	]	]	PUNCT
ejpam-2196	199	52	.	.	PUNCT
ejpam-2196	200	1	thus	thus	ADV
ejpam-2196	200	2	every	every	DET
ejpam-2196	200	3	r	r	NOUN
ejpam-2196	200	4	-	-	PUNCT
ejpam-2196	200	5	module	module	NOUN
ejpam-2196	200	6	is	be	AUX
ejpam-2196	200	7	aφ	aφ	NOUN
ejpam-2196	200	8	-	-	PUNCT
ejpam-2196	200	9	module	module	NOUN
ejpam-2196	200	10	,	,	PUNCT
ejpam-2196	200	11	by	by	ADP
ejpam-2196	200	12	corollary	corollary	ADJ
ejpam-2196	200	13	2	2	NUM
ejpam-2196	200	14	.	.	PUNCT
ejpam-2196	201	1	now	now	ADV
ejpam-2196	201	2	assume	assume	VERB
ejpam-2196	201	3	n≥	n≥	NOUN
ejpam-2196	201	4	2	2	NUM
ejpam-2196	201	5	and	and	CCONJ
ejpam-2196	201	6	let	let	VERB
ejpam-2196	201	7	mi	mi	PROPN
ejpam-2196	201	8	be	be	AUX
ejpam-2196	201	9	the	the	DET
ejpam-2196	201	10	maximal	maximal	ADJ
ejpam-2196	201	11	ideal	ideal	NOUN
ejpam-2196	201	12	of	of	ADP
ejpam-2196	201	13	the	the	DET
ejpam-2196	201	14	local	local	ADJ
ejpam-2196	201	15	ring	ring	NOUN
ejpam-2196	201	16	ri	ri	NOUN
ejpam-2196	201	17	for	for	ADP
ejpam-2196	201	18	every	every	DET
ejpam-2196	201	19	1≤	1≤	NUM
ejpam-2196	201	20	i	i	PROPN
ejpam-2196	201	21	≤	≤	PROPN
ejpam-2196	201	22	n.	n.	NOUN
ejpam-2196	201	23	let	let	VERB
ejpam-2196	201	24	m	m	PRON
ejpam-2196	201	25	be	be	AUX
ejpam-2196	201	26	a	a	DET
ejpam-2196	201	27	maximal	maximal	ADJ
ejpam-2196	201	28	ideal	ideal	NOUN
ejpam-2196	201	29	of	of	ADP
ejpam-2196	201	30	r	r	NOUN
ejpam-2196	201	31	containing	contain	VERB
ejpam-2196	201	32	ann(m	ann(m	PROPN
ejpam-2196	201	33	)	)	PUNCT
ejpam-2196	201	34	.	.	PUNCT
ejpam-2196	202	1	clearly	clearly	ADV
ejpam-2196	202	2	m	m	VERB
ejpam-2196	202	3	is	be	AUX
ejpam-2196	202	4	the	the	DET
ejpam-2196	202	5	form	form	NOUN
ejpam-2196	202	6	r1×	r1×	NOUN
ejpam-2196	202	7	·	·	PUNCT
ejpam-2196	202	8	·	·	PUNCT
ejpam-2196	202	9	·	·	PUNCT
ejpam-2196	202	10	ri−1×mi	ri−1×mi	X
ejpam-2196	202	11	×ri+1×	×ri+1×	NOUN
ejpam-2196	202	12	·	·	PUNCT
ejpam-2196	202	13	·	·	PUNCT
ejpam-2196	202	14	·	·	PUNCT
ejpam-2196	202	15	×rn	×rn	VERB
ejpam-2196	202	16	for	for	ADP
ejpam-2196	202	17	some	some	DET
ejpam-2196	202	18	i.	i.	NOUN
ejpam-2196	202	19	without	without	ADP
ejpam-2196	202	20	loss	loss	NOUN
ejpam-2196	202	21	of	of	ADP
ejpam-2196	202	22	generality	generality	NOUN
ejpam-2196	202	23	we	we	PRON
ejpam-2196	202	24	may	may	AUX
ejpam-2196	202	25	assume	assume	VERB
ejpam-2196	202	26	that	that	SCONJ
ejpam-2196	202	27	i	i	PRON
ejpam-2196	202	28	=	=	NOUN
ejpam-2196	202	29	1	1	NUM
ejpam-2196	202	30	,	,	PUNCT
ejpam-2196	202	31	i.e.	i.e.	X
ejpam-2196	202	32	,	,	PUNCT
ejpam-2196	202	33	m	m	VERB
ejpam-2196	202	34	=	=	ADJ
ejpam-2196	202	35	m1	m1	PROPN
ejpam-2196	202	36	×	×	NOUN
ejpam-2196	202	37	r2	r2	PROPN
ejpam-2196	202	38	×	×	PROPN
ejpam-2196	202	39	·	·	PUNCT
ejpam-2196	202	40	·	·	PUNCT
ejpam-2196	202	41	·	·	PUNCT
ejpam-2196	203	1	×	×	PROPN
ejpam-2196	203	2	rn	rn	PROPN
ejpam-2196	203	3	.	.	PROPN
ejpam-2196	203	4	again	again	ADV
ejpam-2196	203	5	,	,	PUNCT
ejpam-2196	203	6	by	by	ADP
ejpam-2196	203	7	corollary	corollary	ADJ
ejpam-2196	203	8	2	2	NUM
ejpam-2196	203	9	,	,	PUNCT
ejpam-2196	203	10	it	it	PRON
ejpam-2196	203	11	suffices	suffice	VERB
ejpam-2196	203	12	to	to	PART
ejpam-2196	203	13	show	show	VERB
ejpam-2196	203	14	that	that	SCONJ
ejpam-2196	203	15	mm	mm	NOUN
ejpam-2196	203	16	=	=	SYM
ejpam-2196	203	17	(	(	PUNCT
ejpam-2196	203	18	m1×r2×	m1×r2×	X
ejpam-2196	203	19	·	·	PUNCT
ejpam-2196	203	20	·	·	PUNCT
ejpam-2196	203	21	·	·	PUNCT
ejpam-2196	203	22	×rn)m	×rn)m	PROPN
ejpam-2196	204	1	6=	6=	NUM
ejpam-2196	204	2	m	m	VERB
ejpam-2196	204	3	.	.	PUNCT
ejpam-2196	205	1	on	on	ADP
ejpam-2196	205	2	the	the	DET
ejpam-2196	205	3	contrary	contrary	NOUN
ejpam-2196	205	4	,	,	PUNCT
ejpam-2196	205	5	suppose	suppose	VERB
ejpam-2196	205	6	that	that	SCONJ
ejpam-2196	205	7	(	(	PUNCT
ejpam-2196	205	8	m1×r2×	m1×r2×	X
ejpam-2196	205	9	·	·	PUNCT
ejpam-2196	205	10	·	·	PUNCT
ejpam-2196	205	11	·	·	PUNCT
ejpam-2196	205	12	×rn)m	×rn)m	NOUN
ejpam-2196	205	13	=	=	NOUN
ejpam-2196	205	14	m	m	VERB
ejpam-2196	205	15	.	.	PUNCT
ejpam-2196	206	1	take	take	VERB
ejpam-2196	206	2	m1	m1	NOUN
ejpam-2196	206	3	=	=	PUNCT
ejpam-2196	207	1	(	(	PUNCT
ejpam-2196	207	2	r1	r1	PROPN
ejpam-2196	207	3	×	×	PROPN
ejpam-2196	207	4	(	(	PUNCT
ejpam-2196	207	5	0	0	NUM
ejpam-2196	207	6	)	)	PUNCT
ejpam-2196	207	7	×	×	NOUN
ejpam-2196	207	8	·	·	PUNCT
ejpam-2196	207	9	·	·	PUNCT
ejpam-2196	207	10	·	·	PUNCT
ejpam-2196	208	1	×	×	NOUN
ejpam-2196	208	2	(	(	PUNCT
ejpam-2196	208	3	0))m	0))m	NOUN
ejpam-2196	208	4	.	.	PUNCT
ejpam-2196	209	1	it	it	PRON
ejpam-2196	209	2	is	be	AUX
ejpam-2196	209	3	easy	easy	ADJ
ejpam-2196	209	4	to	to	PART
ejpam-2196	209	5	verify	verify	VERB
ejpam-2196	209	6	that	that	SCONJ
ejpam-2196	209	7	r1	r1	NOUN
ejpam-2196	209	8	∼=	∼=	PROPN
ejpam-2196	209	9	r/(0	r/(0	NOUN
ejpam-2196	209	10	)	)	PUNCT
ejpam-2196	209	11	×	×	NOUN
ejpam-2196	209	12	r2	r2	PROPN
ejpam-2196	209	13	×	×	PROPN
ejpam-2196	209	14	·	·	PUNCT
ejpam-2196	209	15	·	·	PUNCT
ejpam-2196	209	16	·	·	PUNCT
ejpam-2196	209	17	×	×	PROPN
ejpam-2196	209	18	rn	rn	NOUN
ejpam-2196	209	19	and	and	CCONJ
ejpam-2196	209	20	hence	hence	ADV
ejpam-2196	209	21	m1	m1	PROPN
ejpam-2196	209	22	can	can	AUX
ejpam-2196	209	23	be	be	AUX
ejpam-2196	209	24	expressed	express	VERB
ejpam-2196	209	25	as	as	ADP
ejpam-2196	209	26	an	an	DET
ejpam-2196	209	27	r1	r1	NOUN
ejpam-2196	209	28	-	-	PUNCT
ejpam-2196	209	29	module	module	NOUN
ejpam-2196	209	30	by	by	ADP
ejpam-2196	209	31	defining	define	VERB
ejpam-2196	209	32	r1	r1	NOUN
ejpam-2196	210	1	x1	x1	PROPN
ejpam-2196	210	2	=	=	PUNCT
ejpam-2196	210	3	r1(1,0	r1(1,0	PROPN
ejpam-2196	210	4	,	,	PUNCT
ejpam-2196	210	5	·	·	PUNCT
ejpam-2196	210	6	·	·	PUNCT
ejpam-2196	210	7	·	·	PUNCT
ejpam-2196	210	8	,	,	PUNCT
ejpam-2196	210	9	0)x1	0)x1	NOUN
ejpam-2196	210	10	for	for	ADP
ejpam-2196	210	11	r1	r1	PROPN
ejpam-2196	210	12	∈	∈	PROPN
ejpam-2196	210	13	r1	r1	PROPN
ejpam-2196	210	14	and	and	CCONJ
ejpam-2196	210	15	x1	x1	PROPN
ejpam-2196	210	16	∈	∈	PROPN
ejpam-2196	210	17	m1	m1	NOUN
ejpam-2196	210	18	.	.	PUNCT
ejpam-2196	211	1	we	we	PRON
ejpam-2196	211	2	may	may	AUX
ejpam-2196	211	3	assume	assume	VERB
ejpam-2196	211	4	that	that	SCONJ
ejpam-2196	211	5	m1	m1	PROPN
ejpam-2196	211	6	6=	6=	ADP
ejpam-2196	211	7	0	0	NUM
ejpam-2196	211	8	,	,	PUNCT
ejpam-2196	211	9	for	for	ADP
ejpam-2196	211	10	otherwise	otherwise	ADV
ejpam-2196	211	11	we	we	PRON
ejpam-2196	211	12	have	have	VERB
ejpam-2196	211	13	r1	r1	VERB
ejpam-2196	211	14	×	×	NOUN
ejpam-2196	211	15	(	(	PUNCT
ejpam-2196	211	16	0)×	0)×	NUM
ejpam-2196	211	17	·	·	PUNCT
ejpam-2196	211	18	·	·	PUNCT
ejpam-2196	211	19	·	·	PUNCT
ejpam-2196	212	1	×	×	NOUN
ejpam-2196	212	2	(	(	PUNCT
ejpam-2196	212	3	0	0	NUM
ejpam-2196	212	4	)	)	PUNCT
ejpam-2196	212	5	⊆	⊆	NUM
ejpam-2196	212	6	ann(m	ann(m	PROPN
ejpam-2196	212	7	)	)	PUNCT
ejpam-2196	212	8	⊆	⊆	NUM
ejpam-2196	212	9	m1	m1	PROPN
ejpam-2196	212	10	×	×	NOUN
ejpam-2196	212	11	r2	r2	PROPN
ejpam-2196	212	12	×	×	PROPN
ejpam-2196	212	13	·	·	PUNCT
ejpam-2196	212	14	·	·	PUNCT
ejpam-2196	212	15	·	·	PUNCT
ejpam-2196	212	16	×	×	PROPN
ejpam-2196	212	17	rn	rn	PROPN
ejpam-2196	212	18	,	,	PUNCT
ejpam-2196	212	19	a	a	DET
ejpam-2196	212	20	contradiction	contradiction	NOUN
ejpam-2196	212	21	.	.	PUNCT
ejpam-2196	213	1	thus	thus	ADV
ejpam-2196	213	2	m1m1	m1m1	X
ejpam-2196	213	3	6=	6=	X
ejpam-2196	213	4	m1	m1	NOUN
ejpam-2196	213	5	by	by	ADP
ejpam-2196	213	6	using	use	VERB
ejpam-2196	213	7	case	case	NOUN
ejpam-2196	213	8	n=	n=	ADJ
ejpam-2196	213	9	1	1	NUM
ejpam-2196	213	10	.	.	PUNCT
ejpam-2196	214	1	on	on	ADP
ejpam-2196	214	2	the	the	DET
ejpam-2196	214	3	other	other	ADJ
ejpam-2196	214	4	hand	hand	NOUN
ejpam-2196	214	5	,	,	PUNCT
ejpam-2196	214	6	for	for	ADP
ejpam-2196	214	7	each	each	DET
ejpam-2196	214	8	x	x	SYM
ejpam-2196	214	9	∈	∈	PROPN
ejpam-2196	214	10	m	m	NOUN
ejpam-2196	214	11	,	,	PUNCT
ejpam-2196	214	12	(	(	PUNCT
ejpam-2196	214	13	1,0	1,0	NUM
ejpam-2196	214	14	,	,	PUNCT
ejpam-2196	214	15	·	·	PUNCT
ejpam-2196	214	16	·	·	PUNCT
ejpam-2196	214	17	·	·	PUNCT
ejpam-2196	214	18	,	,	PUNCT
ejpam-2196	214	19	0)x	0)x	NOUN
ejpam-2196	214	20	∈	∈	PROPN
ejpam-2196	214	21	m	m	VERB
ejpam-2196	214	22	=	=	SYM
ejpam-2196	214	23	(	(	PUNCT
ejpam-2196	214	24	m1	m1	PROPN
ejpam-2196	214	25	×	×	PROPN
ejpam-2196	214	26	r2	r2	PROPN
ejpam-2196	214	27	×	×	PROPN
ejpam-2196	214	28	·	·	PUNCT
ejpam-2196	214	29	·	·	PUNCT
ejpam-2196	214	30	·	·	PUNCT
ejpam-2196	214	31	×	×	NOUN
ejpam-2196	214	32	rn)m	rn)m	PROPN
ejpam-2196	214	33	.	.	PUNCT
ejpam-2196	215	1	thus	thus	ADV
ejpam-2196	215	2	for	for	ADP
ejpam-2196	215	3	each	each	DET
ejpam-2196	215	4	x	x	SYM
ejpam-2196	215	5	∈	∈	PROPN
ejpam-2196	215	6	m	m	NOUN
ejpam-2196	215	7	,	,	PUNCT
ejpam-2196	215	8	(	(	PUNCT
ejpam-2196	215	9	1,0	1,0	NUM
ejpam-2196	215	10	,	,	PUNCT
ejpam-2196	215	11	·	·	PUNCT
ejpam-2196	215	12	·	·	PUNCT
ejpam-2196	215	13	·	·	PUNCT
ejpam-2196	215	14	,	,	PUNCT
ejpam-2196	215	15	0)x	0)x	NOUN
ejpam-2196	216	1	=	=	PUNCT
ejpam-2196	216	2	∑sj=1(p1	∑sj=1(p1	PROPN
ejpam-2196	216	3	j	j	PROPN
ejpam-2196	216	4	,	,	PUNCT
ejpam-2196	216	5	r2	r2	PROPN
ejpam-2196	216	6	j	j	PROPN
ejpam-2196	216	7	,	,	PUNCT
ejpam-2196	216	8	·	·	PUNCT
ejpam-2196	216	9	·	·	PUNCT
ejpam-2196	216	10	·	·	PUNCT
ejpam-2196	216	11	,	,	PUNCT
ejpam-2196	216	12	rn	rn	PROPN
ejpam-2196	216	13	j)x	j)x	PROPN
ejpam-2196	216	14	j	j	PROPN
ejpam-2196	216	15	for	for	ADP
ejpam-2196	216	16	some	some	DET
ejpam-2196	216	17	s	s	PART
ejpam-2196	216	18	∈	∈	PROPN
ejpam-2196	216	19	n	n	CCONJ
ejpam-2196	216	20	,	,	PUNCT
ejpam-2196	216	21	x	x	PUNCT
ejpam-2196	216	22	j	j	PROPN
ejpam-2196	216	23	∈	∈	PROPN
ejpam-2196	216	24	m	m	PROPN
ejpam-2196	216	25	,	,	PUNCT
ejpam-2196	216	26	p1	p1	PROPN
ejpam-2196	216	27	j	j	PROPN
ejpam-2196	216	28	∈	∈	PROPN
ejpam-2196	216	29	m1	m1	PROPN
ejpam-2196	216	30	and	and	CCONJ
ejpam-2196	216	31	ri	ri	X
ejpam-2196	216	32	j	j	PROPN
ejpam-2196	216	33	∈	∈	PROPN
ejpam-2196	216	34	r	r	PROPN
ejpam-2196	216	35	,	,	PUNCT
ejpam-2196	216	36	references	reference	NOUN
ejpam-2196	216	37	237	237	NUM
ejpam-2196	216	38	where	where	SCONJ
ejpam-2196	216	39	2	2	NUM
ejpam-2196	216	40	≤	≤	NOUN
ejpam-2196	216	41	i	i	NOUN
ejpam-2196	216	42	≤	≤	ADJ
ejpam-2196	216	43	n	n	CCONJ
ejpam-2196	216	44	and	and	CCONJ
ejpam-2196	216	45	1	1	NUM
ejpam-2196	216	46	≤	≤	NUM
ejpam-2196	216	47	j	j	PROPN
ejpam-2196	216	48	≤	≤	PROPN
ejpam-2196	216	49	s.	s.	PROPN
ejpam-2196	216	50	multiplying	multiply	VERB
ejpam-2196	216	51	the	the	DET
ejpam-2196	216	52	former	former	ADJ
ejpam-2196	216	53	equation	equation	NOUN
ejpam-2196	216	54	by	by	ADP
ejpam-2196	216	55	(	(	PUNCT
ejpam-2196	216	56	1,0	1,0	NUM
ejpam-2196	216	57	,	,	PUNCT
ejpam-2196	216	58	·	·	PUNCT
ejpam-2196	216	59	·	·	PUNCT
ejpam-2196	216	60	·	·	PUNCT
ejpam-2196	216	61	,	,	PUNCT
ejpam-2196	216	62	0	0	NUM
ejpam-2196	216	63	)	)	PUNCT
ejpam-2196	216	64	,	,	PUNCT
ejpam-2196	216	65	we	we	PRON
ejpam-2196	216	66	get	get	VERB
ejpam-2196	216	67	(	(	PUNCT
ejpam-2196	216	68	1,0	1,0	NUM
ejpam-2196	216	69	,	,	PUNCT
ejpam-2196	216	70	·	·	PUNCT
ejpam-2196	216	71	·	·	PUNCT
ejpam-2196	216	72	·	·	PUNCT
ejpam-2196	216	73	,	,	PUNCT
ejpam-2196	216	74	0)x	0)x	NUM
ejpam-2196	216	75	∈	∈	PROPN
ejpam-2196	216	76	(	(	PUNCT
ejpam-2196	216	77	m1	m1	PROPN
ejpam-2196	216	78	×	×	NOUN
ejpam-2196	216	79	(	(	PUNCT
ejpam-2196	216	80	0)×	0)×	NUM
ejpam-2196	216	81	·	·	PUNCT
ejpam-2196	216	82	·	·	PUNCT
ejpam-2196	216	83	·	·	PUNCT
ejpam-2196	217	1	×	×	NOUN
ejpam-2196	217	2	(	(	PUNCT
ejpam-2196	217	3	0))m	0))m	NOUN
ejpam-2196	217	4	for	for	ADP
ejpam-2196	217	5	each	each	DET
ejpam-2196	217	6	x	x	SYM
ejpam-2196	217	7	∈	∈	PROPN
ejpam-2196	217	8	m	m	VERB
ejpam-2196	217	9	.	.	PUNCT
ejpam-2196	218	1	it	it	PRON
ejpam-2196	218	2	follows	follow	VERB
ejpam-2196	218	3	that	that	SCONJ
ejpam-2196	218	4	(	(	PUNCT
ejpam-2196	218	5	r1	r1	PROPN
ejpam-2196	218	6	×	×	PROPN
ejpam-2196	218	7	(	(	PUNCT
ejpam-2196	218	8	0)×	0)×	NUM
ejpam-2196	218	9	·	·	PUNCT
ejpam-2196	218	10	·	·	PUNCT
ejpam-2196	218	11	·	·	PUNCT
ejpam-2196	219	1	×	×	NOUN
ejpam-2196	219	2	(	(	PUNCT
ejpam-2196	219	3	0))m	0))m	NOUN
ejpam-2196	219	4	⊆	⊆	NUM
ejpam-2196	219	5	(	(	PUNCT
ejpam-2196	219	6	m1	m1	PROPN
ejpam-2196	219	7	×	×	NOUN
ejpam-2196	219	8	(	(	PUNCT
ejpam-2196	219	9	0)×	0)×	NUM
ejpam-2196	219	10	·	·	PUNCT
ejpam-2196	219	11	·	·	PUNCT
ejpam-2196	219	12	·	·	PUNCT
ejpam-2196	220	1	×	×	NOUN
ejpam-2196	220	2	(	(	PUNCT
ejpam-2196	220	3	0))m	0))m	NOUN
ejpam-2196	220	4	and	and	CCONJ
ejpam-2196	220	5	so	so	ADV
ejpam-2196	220	6	m1m1	m1m1	NOUN
ejpam-2196	220	7	=	=	SYM
ejpam-2196	220	8	m1	m1	NOUN
ejpam-2196	220	9	,	,	PUNCT
ejpam-2196	220	10	a	a	DET
ejpam-2196	220	11	contradiction	contradiction	NOUN
ejpam-2196	220	12	.	.	PUNCT
ejpam-2196	221	1	(	(	PUNCT
ejpam-2196	221	2	2)⇒	2)⇒	NUM
ejpam-2196	221	3	(	(	PUNCT
ejpam-2196	221	4	3	3	NUM
ejpam-2196	221	5	)	)	PUNCT
ejpam-2196	221	6	follows	follow	VERB
ejpam-2196	221	7	from	from	ADP
ejpam-2196	221	8	theorem	theorem	ADJ
ejpam-2196	221	9	1	1	NUM
ejpam-2196	221	10	.	.	PUNCT
ejpam-2196	222	1	(	(	PUNCT
ejpam-2196	222	2	3)⇒	3)⇒	NUM
ejpam-2196	222	3	(	(	PUNCT
ejpam-2196	222	4	4	4	NUM
ejpam-2196	222	5	)	)	PUNCT
ejpam-2196	222	6	follows	follow	VERB
ejpam-2196	222	7	from	from	ADP
ejpam-2196	222	8	[	[	X
ejpam-2196	222	9	9	9	NUM
ejpam-2196	222	10	,	,	PUNCT
ejpam-2196	222	11	result	result	VERB
ejpam-2196	222	12	2	2	NUM
ejpam-2196	222	13	]	]	PUNCT
ejpam-2196	222	14	.	.	PUNCT
ejpam-2196	223	1	(	(	PUNCT
ejpam-2196	223	2	4	4	X
ejpam-2196	223	3	)	)	PUNCT
ejpam-2196	223	4	⇒	⇒	NOUN
ejpam-2196	223	5	(	(	PUNCT
ejpam-2196	223	6	5	5	X
ejpam-2196	223	7	)	)	PUNCT
ejpam-2196	223	8	suppose	suppose	VERB
ejpam-2196	223	9	p	p	PRON
ejpam-2196	223	10	be	be	AUX
ejpam-2196	223	11	a	a	DET
ejpam-2196	223	12	prime	prime	ADJ
ejpam-2196	223	13	ideal	ideal	NOUN
ejpam-2196	223	14	of	of	ADP
ejpam-2196	223	15	r	r	NOUN
ejpam-2196	223	16	and	and	CCONJ
ejpam-2196	223	17	k	k	NOUN
ejpam-2196	223	18	the	the	DET
ejpam-2196	223	19	quotient	quotient	NOUN
ejpam-2196	223	20	field	field	NOUN
ejpam-2196	223	21	of	of	ADP
ejpam-2196	223	22	r	r	NOUN
ejpam-2196	223	23	/	/	SYM
ejpam-2196	223	24	p.	p.	NOUN
ejpam-2196	223	25	we	we	PRON
ejpam-2196	223	26	know	know	VERB
ejpam-2196	223	27	that	that	SCONJ
ejpam-2196	223	28	k	k	PROPN
ejpam-2196	223	29	is	be	AUX
ejpam-2196	223	30	a	a	DET
ejpam-2196	223	31	non	non	ADJ
ejpam-2196	223	32	-	-	ADJ
ejpam-2196	223	33	zero	zero	ADJ
ejpam-2196	223	34	divisible	divisible	ADJ
ejpam-2196	223	35	r	r	NOUN
ejpam-2196	223	36	/	/	SYM
ejpam-2196	223	37	p	p	NOUN
ejpam-2196	223	38	-	-	PUNCT
ejpam-2196	223	39	module	module	NOUN
ejpam-2196	223	40	.	.	PUNCT
ejpam-2196	224	1	let	let	VERB
ejpam-2196	224	2	0	0	NUM
ejpam-2196	225	1	6=	6=	NUM
ejpam-2196	225	2	r	r	NOUN
ejpam-2196	225	3	+	+	X
ejpam-2196	225	4	p	p	NOUN
ejpam-2196	225	5	∈	∈	NOUN
ejpam-2196	225	6	r	r	NOUN
ejpam-2196	225	7	/	/	SYM
ejpam-2196	225	8	p.	p.	NOUN
ejpam-2196	225	9	then	then	ADV
ejpam-2196	226	1	(	(	PUNCT
ejpam-2196	226	2	r	r	NOUN
ejpam-2196	226	3	+	+	NOUN
ejpam-2196	226	4	p)k	p)k	NOUN
ejpam-2196	227	1	=	=	SYM
ejpam-2196	227	2	k	k	PROPN
ejpam-2196	227	3	implies	imply	VERB
ejpam-2196	227	4	that	that	SCONJ
ejpam-2196	227	5	ann(k	ann(k	PROPN
ejpam-2196	227	6	)	)	PUNCT
ejpam-2196	228	1	+	+	X
ejpam-2196	228	2	r	r	X
ejpam-2196	228	3	/	/	SYM
ejpam-2196	228	4	p(r	p(r	NOUN
ejpam-2196	228	5	+	+	CCONJ
ejpam-2196	228	6	p	p	X
ejpam-2196	228	7	)	)	PUNCT
ejpam-2196	229	1	=	=	SYM
ejpam-2196	229	2	r	r	X
ejpam-2196	229	3	/	/	SYM
ejpam-2196	229	4	p.	p.	NOUN
ejpam-2196	229	5	otherwise	otherwise	ADV
ejpam-2196	229	6	,	,	PUNCT
ejpam-2196	229	7	if	if	SCONJ
ejpam-2196	229	8	ann(k	ann(k	PROPN
ejpam-2196	229	9	)	)	PUNCT
ejpam-2196	230	1	+	+	X
ejpam-2196	230	2	r	r	X
ejpam-2196	230	3	/	/	SYM
ejpam-2196	230	4	p(r	p(r	NOUN
ejpam-2196	230	5	+	+	CCONJ
ejpam-2196	230	6	p	p	X
ejpam-2196	230	7	)	)	PUNCT
ejpam-2196	230	8	6=	6=	ADP
ejpam-2196	230	9	r	r	X
ejpam-2196	230	10	/	/	SYM
ejpam-2196	230	11	p	p	NOUN
ejpam-2196	230	12	,	,	PUNCT
ejpam-2196	230	13	then	then	ADV
ejpam-2196	230	14	there	there	PRON
ejpam-2196	230	15	is	be	VERB
ejpam-2196	230	16	a	a	DET
ejpam-2196	230	17	maximal	maximal	ADJ
ejpam-2196	230	18	ideal	ideal	NOUN
ejpam-2196	230	19	m	m	PROPN
ejpam-2196	230	20	/	/	SYM
ejpam-2196	230	21	p	p	NOUN
ejpam-2196	230	22	of	of	ADP
ejpam-2196	230	23	r	r	NOUN
ejpam-2196	230	24	/	/	SYM
ejpam-2196	230	25	p	p	NOUN
ejpam-2196	230	26	containing	contain	VERB
ejpam-2196	230	27	ann(k	ann(k	PROPN
ejpam-2196	230	28	)	)	PUNCT
ejpam-2196	231	1	+	+	CCONJ
ejpam-2196	231	2	r	r	X
ejpam-2196	231	3	/	/	SYM
ejpam-2196	231	4	p(r	p(r	NOUN
ejpam-2196	231	5	+	+	CCONJ
ejpam-2196	231	6	p	p	X
ejpam-2196	231	7	)	)	PUNCT
ejpam-2196	231	8	.	.	PUNCT
ejpam-2196	232	1	thus	thus	ADV
ejpam-2196	232	2	k	k	X
ejpam-2196	232	3	=	=	PUNCT
ejpam-2196	232	4	(	(	PUNCT
ejpam-2196	232	5	r	r	NOUN
ejpam-2196	232	6	+	+	NOUN
ejpam-2196	232	7	p)k	p)k	NOUN
ejpam-2196	232	8	⊆	⊆	NUM
ejpam-2196	232	9	(	(	PUNCT
ejpam-2196	232	10	m	m	NOUN
ejpam-2196	232	11	/	/	SYM
ejpam-2196	232	12	p)k	p)k	NOUN
ejpam-2196	232	13	follows	follow	VERB
ejpam-2196	232	14	that	that	SCONJ
ejpam-2196	232	15	(	(	PUNCT
ejpam-2196	232	16	m	m	NOUN
ejpam-2196	232	17	/	/	SYM
ejpam-2196	232	18	p)k	p)k	NOUN
ejpam-2196	232	19	=	=	SYM
ejpam-2196	232	20	k	k	PROPN
ejpam-2196	232	21	,	,	PUNCT
ejpam-2196	232	22	contradicting	contradict	VERB
ejpam-2196	232	23	the	the	DET
ejpam-2196	232	24	assumption	assumption	NOUN
ejpam-2196	232	25	in	in	ADP
ejpam-2196	232	26	(	(	PUNCT
ejpam-2196	232	27	4	4	NUM
ejpam-2196	232	28	)	)	PUNCT
ejpam-2196	232	29	.	.	PUNCT
ejpam-2196	233	1	now	now	ADV
ejpam-2196	233	2	,	,	PUNCT
ejpam-2196	233	3	let	let	VERB
ejpam-2196	233	4	ann(k	ann(k	NOUN
ejpam-2196	233	5	)	)	PUNCT
ejpam-2196	233	6	6=	6=	ADP
ejpam-2196	233	7	(	(	PUNCT
ejpam-2196	233	8	0	0	NUM
ejpam-2196	233	9	)	)	PUNCT
ejpam-2196	233	10	.	.	PUNCT
ejpam-2196	234	1	take	take	VERB
ejpam-2196	234	2	r+p	r+p	NOUN
ejpam-2196	234	3	∈	∈	PROPN
ejpam-2196	234	4	ann(k	ann(k	PROPN
ejpam-2196	234	5	)	)	PUNCT
ejpam-2196	234	6	and	and	CCONJ
ejpam-2196	234	7	hence	hence	ADV
ejpam-2196	234	8	by	by	ADP
ejpam-2196	234	9	the	the	DET
ejpam-2196	234	10	above	above	ADJ
ejpam-2196	234	11	argument	argument	NOUN
ejpam-2196	234	12	ann(k	ann(k	PROPN
ejpam-2196	234	13	)	)	PUNCT
ejpam-2196	234	14	=	=	SYM
ejpam-2196	235	1	r	r	X
ejpam-2196	235	2	/	/	SYM
ejpam-2196	235	3	p	p	X
ejpam-2196	235	4	,	,	PUNCT
ejpam-2196	235	5	i.e.	i.e.	X
ejpam-2196	235	6	,	,	PUNCT
ejpam-2196	235	7	k	k	X
ejpam-2196	235	8	=	=	SYM
ejpam-2196	235	9	(	(	PUNCT
ejpam-2196	235	10	0	0	NUM
ejpam-2196	235	11	)	)	PUNCT
ejpam-2196	235	12	,	,	PUNCT
ejpam-2196	235	13	a	a	DET
ejpam-2196	235	14	contradiction	contradiction	NOUN
ejpam-2196	235	15	.	.	PUNCT
ejpam-2196	236	1	thus	thus	ADV
ejpam-2196	236	2	ann(k	ann(k	X
ejpam-2196	236	3	)	)	PUNCT
ejpam-2196	236	4	=	=	SYM
ejpam-2196	236	5	(	(	PUNCT
ejpam-2196	236	6	0	0	NUM
ejpam-2196	236	7	)	)	PUNCT
ejpam-2196	236	8	.	.	PUNCT
ejpam-2196	237	1	hence	hence	ADV
ejpam-2196	237	2	r	r	NOUN
ejpam-2196	237	3	/	/	SYM
ejpam-2196	237	4	p(r	p(r	NOUN
ejpam-2196	237	5	+	+	CCONJ
ejpam-2196	237	6	p	p	X
ejpam-2196	237	7	)	)	PUNCT
ejpam-2196	238	1	=	=	SYM
ejpam-2196	238	2	r	r	X
ejpam-2196	238	3	/	/	SYM
ejpam-2196	238	4	p	p	NOUN
ejpam-2196	238	5	for	for	ADP
ejpam-2196	238	6	any	any	DET
ejpam-2196	238	7	0	0	NUM
ejpam-2196	238	8	6=	6=	NUM
ejpam-2196	238	9	r	r	NOUN
ejpam-2196	239	1	+	+	X
ejpam-2196	239	2	p	p	NOUN
ejpam-2196	239	3	∈	∈	NOUN
ejpam-2196	239	4	r	r	NOUN
ejpam-2196	239	5	/	/	SYM
ejpam-2196	239	6	p.	p.	NOUN
ejpam-2196	239	7	thus	thus	ADV
ejpam-2196	239	8	dim(r	dim(r	NOUN
ejpam-2196	239	9	)	)	PUNCT
ejpam-2196	240	1	=	=	SYM
ejpam-2196	241	1	0	0	X
ejpam-2196	241	2	.	.	PUNCT
ejpam-2196	242	1	(	(	PUNCT
ejpam-2196	242	2	4)⇒	4)⇒	X
ejpam-2196	242	3	(	(	PUNCT
ejpam-2196	242	4	5	5	NUM
ejpam-2196	242	5	)	)	PUNCT
ejpam-2196	242	6	follows	follow	VERB
ejpam-2196	242	7	from	from	ADP
ejpam-2196	242	8	[	[	X
ejpam-2196	242	9	2	2	NUM
ejpam-2196	242	10	,	,	PUNCT
ejpam-2196	242	11	theorem	theorem	VERB
ejpam-2196	242	12	8.5	8.5	NUM
ejpam-2196	242	13	]	]	PUNCT
ejpam-2196	242	14	.	.	PUNCT
ejpam-2196	243	1	the	the	DET
ejpam-2196	243	2	following	follow	VERB
ejpam-2196	243	3	is	be	AUX
ejpam-2196	243	4	now	now	ADV
ejpam-2196	243	5	immediate	immediate	ADJ
ejpam-2196	243	6	.	.	PUNCT
ejpam-2196	244	1	corollary	corollary	ADJ
ejpam-2196	244	2	4	4	NUM
ejpam-2196	244	3	.	.	PUNCT
ejpam-2196	245	1	let	let	VERB
ejpam-2196	245	2	r	r	PRON
ejpam-2196	245	3	be	be	AUX
ejpam-2196	245	4	a	a	DET
ejpam-2196	245	5	domain	domain	NOUN
ejpam-2196	245	6	.	.	PUNCT
ejpam-2196	246	1	then	then	ADV
ejpam-2196	246	2	the	the	DET
ejpam-2196	246	3	following	follow	VERB
ejpam-2196	246	4	statements	statement	NOUN
ejpam-2196	246	5	are	be	AUX
ejpam-2196	246	6	equivalent	equivalent	ADJ
ejpam-2196	246	7	.	.	PUNCT
ejpam-2196	247	1	(	(	PUNCT
ejpam-2196	247	2	1	1	X
ejpam-2196	247	3	)	)	PUNCT
ejpam-2196	247	4	every	every	DET
ejpam-2196	247	5	r	r	NOUN
ejpam-2196	247	6	-	-	PUNCT
ejpam-2196	247	7	module	module	NOUN
ejpam-2196	247	8	is	be	AUX
ejpam-2196	247	9	a	a	DET
ejpam-2196	247	10	φ	φ	NOUN
ejpam-2196	247	11	-	-	NOUN
ejpam-2196	247	12	module	module	NOUN
ejpam-2196	247	13	;	;	PUNCT
ejpam-2196	247	14	(	(	PUNCT
ejpam-2196	247	15	2	2	X
ejpam-2196	247	16	)	)	PUNCT
ejpam-2196	247	17	every	every	DET
ejpam-2196	247	18	r	r	NOUN
ejpam-2196	247	19	-	-	PUNCT
ejpam-2196	247	20	module	module	NOUN
ejpam-2196	247	21	is	be	AUX
ejpam-2196	247	22	a	a	DET
ejpam-2196	247	23	ψ	ψ	NOUN
ejpam-2196	247	24	-	-	NOUN
ejpam-2196	247	25	module	module	NOUN
ejpam-2196	247	26	;	;	PUNCT
ejpam-2196	247	27	(	(	PUNCT
ejpam-2196	247	28	3	3	X
ejpam-2196	247	29	)	)	PUNCT
ejpam-2196	247	30	r	r	NOUN
ejpam-2196	247	31	is	be	AUX
ejpam-2196	247	32	a	a	DET
ejpam-2196	247	33	field	field	NOUN
ejpam-2196	247	34	.	.	PUNCT
ejpam-2196	248	1	references	reference	NOUN
ejpam-2196	248	2	[	[	X
ejpam-2196	248	3	1	1	NUM
ejpam-2196	248	4	]	]	PUNCT
ejpam-2196	248	5	m.	m.	NOUN
ejpam-2196	248	6	alkan	alkan	PROPN
ejpam-2196	248	7	and	and	CCONJ
ejpam-2196	248	8	y.	y.	PROPN
ejpam-2196	248	9	tiras	tiras	PROPN
ejpam-2196	248	10	.	.	PUNCT
ejpam-2196	248	11	projective	projective	ADJ
ejpam-2196	248	12	modules	module	NOUN
ejpam-2196	248	13	and	and	CCONJ
ejpam-2196	248	14	prime	prime	ADJ
ejpam-2196	248	15	submodules	submodule	NOUN
ejpam-2196	248	16	,	,	PUNCT
ejpam-2196	248	17	czechoslovak	czechoslovak	ADJ
ejpam-2196	248	18	mathematical	mathematical	ADJ
ejpam-2196	248	19	journal	journal	NOUN
ejpam-2196	248	20	,	,	PUNCT
ejpam-2196	248	21	56(2	56(2	NUM
ejpam-2196	248	22	)	)	PUNCT
ejpam-2196	248	23	,	,	PUNCT
ejpam-2196	248	24	601	601	NUM
ejpam-2196	248	25	-	-	SYM
ejpam-2196	248	26	611	611	NUM
ejpam-2196	248	27	,	,	PUNCT
ejpam-2196	248	28	2006	2006	NUM
ejpam-2196	248	29	.	.	PUNCT
ejpam-2196	249	1	[	[	X
ejpam-2196	249	2	2	2	NUM
ejpam-2196	249	3	]	]	PUNCT
ejpam-2196	249	4	m.	m.	PROPN
ejpam-2196	249	5	f.	f.	PROPN
ejpam-2196	249	6	atiyah	atiyah	PROPN
ejpam-2196	249	7	and	and	CCONJ
ejpam-2196	249	8	i.	i.	PROPN
ejpam-2196	249	9	g.	g.	PROPN
ejpam-2196	249	10	mcdonald	mcdonald	PROPN
ejpam-2196	249	11	.	.	PUNCT
ejpam-2196	250	1	introduction	introduction	NOUN
ejpam-2196	250	2	to	to	ADP
ejpam-2196	250	3	commutative	commutative	ADJ
ejpam-2196	250	4	algebra	algebra	PROPN
ejpam-2196	250	5	,	,	PUNCT
ejpam-2196	250	6	addison	addison	PROPN
ejpam-2196	250	7	wesley	wesley	PROPN
ejpam-2196	250	8	publishing	publishing	PROPN
ejpam-2196	250	9	company	company	PROPN
ejpam-2196	250	10	,	,	PUNCT
ejpam-2196	250	11	inc	inc	PROPN
ejpam-2196	250	12	.	.	PROPN
ejpam-2196	250	13	,	,	PUNCT
ejpam-2196	250	14	1969	1969	NUM
ejpam-2196	250	15	.	.	PUNCT
ejpam-2196	251	1	[	[	X
ejpam-2196	251	2	3	3	NUM
ejpam-2196	251	3	]	]	PUNCT
ejpam-2196	251	4	a.	a.	PROPN
ejpam-2196	251	5	azizi	azizi	PROPN
ejpam-2196	251	6	.	.	PUNCT
ejpam-2196	252	1	prime	prime	ADJ
ejpam-2196	252	2	submodules	submodule	NOUN
ejpam-2196	252	3	and	and	CCONJ
ejpam-2196	252	4	flat	flat	ADJ
ejpam-2196	252	5	modules	module	NOUN
ejpam-2196	252	6	,	,	PUNCT
ejpam-2196	252	7	acta	acta	PROPN
ejpam-2196	252	8	mathematica	mathematica	PROPN
ejpam-2196	252	9	sinica	sinica	PROPN
ejpam-2196	252	10	,	,	PUNCT
ejpam-2196	252	11	english	english	ADJ
ejpam-2196	252	12	series	series	NOUN
ejpam-2196	252	13	,	,	PUNCT
ejpam-2196	252	14	23	23	NUM
ejpam-2196	252	15	,	,	PUNCT
ejpam-2196	252	16	147	147	NUM
ejpam-2196	252	17	-	-	SYM
ejpam-2196	252	18	152	152	NUM
ejpam-2196	252	19	,	,	PUNCT
ejpam-2196	252	20	2007	2007	NUM
ejpam-2196	252	21	.	.	PUNCT
ejpam-2196	253	1	[	[	X
ejpam-2196	253	2	4	4	NUM
ejpam-2196	253	3	]	]	X
ejpam-2196	253	4	n.	n.	NOUN
ejpam-2196	253	5	bourbaki	bourbaki	PROPN
ejpam-2196	253	6	.	.	PUNCT
ejpam-2196	254	1	algebre	algebre	NOUN
ejpam-2196	254	2	commutative	commutative	ADJ
ejpam-2196	254	3	,	,	PUNCT
ejpam-2196	254	4	paris	paris	PROPN
ejpam-2196	254	5	:	:	PUNCT
ejpam-2196	254	6	hermann	hermann	PROPN
ejpam-2196	254	7	,	,	PUNCT
ejpam-2196	254	8	1961	1961	NUM
ejpam-2196	254	9	.	.	PUNCT
ejpam-2196	255	1	[	[	X
ejpam-2196	255	2	5	5	X
ejpam-2196	255	3	]	]	PUNCT
ejpam-2196	255	4	f.	f.	PROPN
ejpam-2196	255	5	callialp	callialp	PROPN
ejpam-2196	255	6	and	and	CCONJ
ejpam-2196	255	7	u.	u.	PROPN
ejpam-2196	255	8	tekir	tekir	PROPN
ejpam-2196	255	9	.	.	PUNCT
ejpam-2196	256	1	on	on	ADP
ejpam-2196	256	2	unions	union	NOUN
ejpam-2196	256	3	of	of	ADP
ejpam-2196	256	4	prime	prime	ADJ
ejpam-2196	256	5	submodules	submodule	NOUN
ejpam-2196	256	6	,	,	PUNCT
ejpam-2196	256	7	the	the	DET
ejpam-2196	256	8	southeast	southeast	ADJ
ejpam-2196	256	9	asian	asian	ADJ
ejpam-2196	256	10	bulletin	bulletin	NOUN
ejpam-2196	256	11	of	of	ADP
ejpam-2196	256	12	mathematics	mathematic	NOUN
ejpam-2196	256	13	,	,	PUNCT
ejpam-2196	256	14	28	28	NUM
ejpam-2196	256	15	,	,	PUNCT
ejpam-2196	256	16	213	213	NUM
ejpam-2196	256	17	-	-	SYM
ejpam-2196	256	18	218	218	NUM
ejpam-2196	256	19	,	,	PUNCT
ejpam-2196	256	20	2004	2004	NUM
ejpam-2196	256	21	.	.	PUNCT
ejpam-2196	257	1	[	[	X
ejpam-2196	257	2	6	6	NUM
ejpam-2196	257	3	]	]	PUNCT
ejpam-2196	257	4	z.	z.	PROPN
ejpam-2196	257	5	a.	a.	PROPN
ejpam-2196	257	6	el	el	PROPN
ejpam-2196	257	7	-	-	PUNCT
ejpam-2196	257	8	bast	bast	NOUN
ejpam-2196	257	9	and	and	CCONJ
ejpam-2196	257	10	p.	p.	PROPN
ejpam-2196	257	11	f.	f.	PROPN
ejpam-2196	257	12	smith	smith	PROPN
ejpam-2196	257	13	.	.	PUNCT
ejpam-2196	258	1	multiplication	multiplication	NOUN
ejpam-2196	258	2	modules	module	NOUN
ejpam-2196	258	3	,	,	PUNCT
ejpam-2196	258	4	communications	communication	NOUN
ejpam-2196	258	5	in	in	ADP
ejpam-2196	258	6	algebra	algebra	NOUN
ejpam-2196	258	7	,	,	PUNCT
ejpam-2196	258	8	16	16	NUM
ejpam-2196	258	9	,	,	PUNCT
ejpam-2196	258	10	755	755	NUM
ejpam-2196	258	11	-	-	SYM
ejpam-2196	258	12	779	779	NUM
ejpam-2196	258	13	,	,	PUNCT
ejpam-2196	258	14	1988	1988	NUM
ejpam-2196	258	15	.	.	PUNCT
ejpam-2196	259	1	[	[	X
ejpam-2196	259	2	7	7	X
ejpam-2196	259	3	]	]	PUNCT
ejpam-2196	259	4	h.	h.	PROPN
ejpam-2196	259	5	f.	f.	PROPN
ejpam-2196	259	6	moghimi	moghimi	PROPN
ejpam-2196	259	7	and	and	CCONJ
ejpam-2196	259	8	f.	f.	PROPN
ejpam-2196	259	9	rashedi	rashedi	PROPN
ejpam-2196	259	10	.	.	PUNCT
ejpam-2196	260	1	primary	primary	ADJ
ejpam-2196	260	2	-	-	PUNCT
ejpam-2196	260	3	like	like	ADJ
ejpam-2196	260	4	submodules	submodule	NOUN
ejpam-2196	260	5	satisfying	satisfy	VERB
ejpam-2196	260	6	the	the	DET
ejpam-2196	260	7	primeful	primeful	ADJ
ejpam-2196	260	8	property	property	NOUN
ejpam-2196	260	9	,	,	PUNCT
ejpam-2196	260	10	transactions	transaction	NOUN
ejpam-2196	260	11	on	on	ADP
ejpam-2196	260	12	algebra	algebra	NOUN
ejpam-2196	260	13	and	and	CCONJ
ejpam-2196	260	14	its	its	PRON
ejpam-2196	260	15	applications	application	NOUN
ejpam-2196	260	16	,	,	PUNCT
ejpam-2196	260	17	1:43	1:43	PROPN
ejpam-2196	260	18	-	-	SYM
ejpam-2196	260	19	54	54	NUM
ejpam-2196	260	20	,	,	PUNCT
ejpam-2196	260	21	2015	2015	NUM
ejpam-2196	260	22	.	.	PUNCT
ejpam-2196	261	1	references	reference	NOUN
ejpam-2196	261	2	238	238	NUM
ejpam-2196	262	1	[	[	NOUN
ejpam-2196	262	2	8	8	NUM
ejpam-2196	262	3	]	]	PUNCT
ejpam-2196	262	4	t.	t.	PROPN
ejpam-2196	262	5	y.	y.	PROPN
ejpam-2196	262	6	lam	lam	PROPN
ejpam-2196	262	7	.	.	PUNCT
ejpam-2196	263	1	a	a	DET
ejpam-2196	263	2	first	first	ADJ
ejpam-2196	263	3	course	course	NOUN
ejpam-2196	263	4	in	in	ADP
ejpam-2196	263	5	noncommutative	noncommutative	ADJ
ejpam-2196	263	6	rings	ring	NOUN
ejpam-2196	263	7	,	,	PUNCT
ejpam-2196	263	8	graduate	graduate	NOUN
ejpam-2196	263	9	text	text	NOUN
ejpam-2196	263	10	in	in	ADP
ejpam-2196	263	11	math	math	NOUN
ejpam-2196	263	12	,	,	PUNCT
ejpam-2196	263	13	springerverlag	springerverlag	NOUN
ejpam-2196	263	14	,	,	PUNCT
ejpam-2196	263	15	berlin	berlin	PROPN
ejpam-2196	263	16	-	-	PUNCT
ejpam-2196	263	17	heidelberg	heidelberg	NOUN
ejpam-2196	263	18	-	-	PUNCT
ejpam-2196	263	19	new	new	PROPN
ejpam-2196	263	20	york	york	PROPN
ejpam-2196	263	21	,	,	PUNCT
ejpam-2196	263	22	1991	1991	NUM
ejpam-2196	263	23	.	.	PUNCT
ejpam-2196	264	1	[	[	X
ejpam-2196	264	2	9	9	NUM
ejpam-2196	264	3	]	]	PUNCT
ejpam-2196	264	4	c.	c.	PROPN
ejpam-2196	264	5	p.	p.	PROPN
ejpam-2196	264	6	lu	lu	PROPN
ejpam-2196	264	7	.	.	PUNCT
ejpam-2196	265	1	a	a	DET
ejpam-2196	265	2	module	module	NOUN
ejpam-2196	265	3	whose	whose	DET
ejpam-2196	265	4	prime	prime	ADJ
ejpam-2196	265	5	spectrum	spectrum	NOUN
ejpam-2196	265	6	has	have	VERB
ejpam-2196	265	7	the	the	DET
ejpam-2196	265	8	surjective	surjective	ADJ
ejpam-2196	265	9	natural	natural	ADJ
ejpam-2196	265	10	map	map	NOUN
ejpam-2196	265	11	,	,	PUNCT
ejpam-2196	265	12	houston	houston	PROPN
ejpam-2196	265	13	journal	journal	PROPN
ejpam-2196	265	14	of	of	ADP
ejpam-2196	265	15	mathematics	mathematic	NOUN
ejpam-2196	265	16	,	,	PUNCT
ejpam-2196	265	17	33	33	NUM
ejpam-2196	265	18	,	,	PUNCT
ejpam-2196	265	19	125	125	NUM
ejpam-2196	265	20	-	-	SYM
ejpam-2196	265	21	143	143	NUM
ejpam-2196	265	22	,	,	PUNCT
ejpam-2196	265	23	2007	2007	NUM
ejpam-2196	265	24	.	.	PUNCT
ejpam-2196	266	1	[	[	X
ejpam-2196	266	2	10	10	NUM
ejpam-2196	266	3	]	]	X
ejpam-2196	266	4	c.	c.	PROPN
ejpam-2196	266	5	p.	p.	PROPN
ejpam-2196	266	6	lu	lu	PROPN
ejpam-2196	266	7	.	.	PUNCT
ejpam-2196	267	1	saturations	saturation	NOUN
ejpam-2196	267	2	of	of	ADP
ejpam-2196	267	3	submodules	submodule	NOUN
ejpam-2196	267	4	,	,	PUNCT
ejpam-2196	267	5	communications	communication	NOUN
ejpam-2196	267	6	in	in	ADP
ejpam-2196	267	7	algebra	algebra	NOUN
ejpam-2196	267	8	,	,	PUNCT
ejpam-2196	267	9	31	31	NUM
ejpam-2196	267	10	,	,	PUNCT
ejpam-2196	267	11	2655	2655	NUM
ejpam-2196	267	12	-	-	SYM
ejpam-2196	267	13	2673	2673	NUM
ejpam-2196	267	14	,	,	PUNCT
ejpam-2196	267	15	2003	2003	NUM
ejpam-2196	267	16	.	.	PUNCT
ejpam-2196	268	1	[	[	X
ejpam-2196	268	2	11	11	NUM
ejpam-2196	268	3	]	]	PUNCT
ejpam-2196	268	4	c.	c.	PROPN
ejpam-2196	268	5	p.	p.	PROPN
ejpam-2196	268	6	lu	lu	PROPN
ejpam-2196	268	7	.	.	PUNCT
ejpam-2196	269	1	prime	prime	ADJ
ejpam-2196	269	2	submodules	submodule	NOUN
ejpam-2196	269	3	of	of	ADP
ejpam-2196	269	4	modules	module	NOUN
ejpam-2196	269	5	,	,	PUNCT
ejpam-2196	269	6	commentarii	commentarii	PROPN
ejpam-2196	269	7	mathematici	mathematici	PROPN
ejpam-2196	269	8	universitatis	universitatis	PROPN
ejpam-2196	269	9	sancti	sancti	PROPN
ejpam-2196	269	10	pauli	pauli	PROPN
ejpam-2196	269	11	,	,	PUNCT
ejpam-2196	269	12	33	33	NUM
ejpam-2196	269	13	,	,	PUNCT
ejpam-2196	269	14	61	61	NUM
ejpam-2196	269	15	-	-	SYM
ejpam-2196	269	16	69	69	NUM
ejpam-2196	269	17	,	,	PUNCT
ejpam-2196	269	18	1984	1984	NUM
ejpam-2196	269	19	.	.	PUNCT
ejpam-2196	270	1	[	[	X
ejpam-2196	270	2	12	12	NUM
ejpam-2196	270	3	]	]	PUNCT
ejpam-2196	270	4	r.	r.	PROPN
ejpam-2196	270	5	l.	l.	PROPN
ejpam-2196	270	6	mccasland	mccasland	PROPN
ejpam-2196	270	7	,	,	PUNCT
ejpam-2196	270	8	m.	m.	PROPN
ejpam-2196	270	9	e.	e.	PROPN
ejpam-2196	270	10	moore	moore	PROPN
ejpam-2196	270	11	and	and	CCONJ
ejpam-2196	270	12	p.	p.	PROPN
ejpam-2196	270	13	f.	f.	PROPN
ejpam-2196	270	14	smith	smith	PROPN
ejpam-2196	270	15	.	.	PUNCT
ejpam-2196	271	1	on	on	ADP
ejpam-2196	271	2	the	the	DET
ejpam-2196	271	3	spectrum	spectrum	NOUN
ejpam-2196	271	4	of	of	ADP
ejpam-2196	271	5	a	a	DET
ejpam-2196	271	6	module	module	NOUN
ejpam-2196	271	7	over	over	ADP
ejpam-2196	271	8	a	a	DET
ejpam-2196	271	9	commutative	commutative	ADJ
ejpam-2196	271	10	ring	ring	NOUN
ejpam-2196	271	11	,	,	PUNCT
ejpam-2196	271	12	communications	communication	NOUN
ejpam-2196	271	13	in	in	ADP
ejpam-2196	271	14	algebra	algebra	NOUN
ejpam-2196	271	15	,	,	PUNCT
ejpam-2196	271	16	25	25	NUM
ejpam-2196	271	17	,	,	PUNCT
ejpam-2196	271	18	79	79	NUM
ejpam-2196	271	19	-	-	SYM
ejpam-2196	271	20	103	103	NUM
ejpam-2196	271	21	,	,	PUNCT
ejpam-2196	271	22	1997	1997	NUM
ejpam-2196	271	23	.	.	PUNCT
ejpam-2196	272	1	[	[	X
ejpam-2196	272	2	13	13	NUM
ejpam-2196	272	3	]	]	PUNCT
ejpam-2196	272	4	d.	d.	PROPN
ejpam-2196	272	5	p.	p.	PROPN
ejpam-2196	272	6	yilmaz	yilmaz	PROPN
ejpam-2196	272	7	and	and	CCONJ
ejpam-2196	272	8	p.	p.	PROPN
ejpam-2196	272	9	f.	f.	PROPN
ejpam-2196	272	10	smith	smith	PROPN
ejpam-2196	272	11	.	.	PUNCT
ejpam-2196	273	1	radicals	radical	NOUN
ejpam-2196	273	2	of	of	ADP
ejpam-2196	273	3	submodules	submodule	NOUN
ejpam-2196	273	4	of	of	ADP
ejpam-2196	273	5	free	free	ADJ
ejpam-2196	273	6	modules	module	NOUN
ejpam-2196	273	7	,	,	PUNCT
ejpam-2196	273	8	communications	communication	NOUN
ejpam-2196	273	9	in	in	ADP
ejpam-2196	273	10	algebra	algebra	NOUN
ejpam-2196	273	11	,	,	PUNCT
ejpam-2196	273	12	27	27	NUM
ejpam-2196	273	13	,	,	PUNCT
ejpam-2196	273	14	2253	2253	NUM
ejpam-2196	273	15	-	-	SYM
ejpam-2196	273	16	2266	2266	NUM
ejpam-2196	273	17	,	,	PUNCT
ejpam-2196	273	18	1999	1999	NUM
ejpam-2196	273	19	.	.	PUNCT