id	sid	tid	token	lemma	pos
ejpam-753	1	1	7_753_behboodi.dvi	7_753_behboodi.dvi	NUM
ejpam-753	1	2	european	european	ADJ
ejpam-753	1	3	journal	journal	NOUN
ejpam-753	1	4	of	of	ADP
ejpam-753	1	5	pure	pure	ADJ
ejpam-753	1	6	and	and	CCONJ
ejpam-753	1	7	applied	apply	VERB
ejpam-753	1	8	mathematics	mathematic	NOUN
ejpam-753	1	9	vol	vol	NOUN
ejpam-753	1	10	.	.	PUNCT
ejpam-753	2	1	3	3	NUM
ejpam-753	2	2	,	,	PUNCT
ejpam-753	2	3	no	no	INTJ
ejpam-753	2	4	.	.	NOUN
ejpam-753	2	5	4	4	NUM
ejpam-753	2	6	,	,	PUNCT
ejpam-753	2	7	2010	2010	NUM
ejpam-753	2	8	,	,	PUNCT
ejpam-753	2	9	686	686	NUM
ejpam-753	2	10	-	-	SYM
ejpam-753	2	11	694	694	NUM
ejpam-753	2	12	issn	issn	PROPN
ejpam-753	2	13	1307	1307	NUM
ejpam-753	2	14	-	-	SYM
ejpam-753	2	15	5543	5543	NUM
ejpam-753	2	16	–	–	PUNCT
ejpam-753	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-753	2	18	on	on	ADP
ejpam-753	2	19	the	the	DET
ejpam-753	2	20	structure	structure	NOUN
ejpam-753	2	21	of	of	ADP
ejpam-753	2	22	commutative	commutative	ADJ
ejpam-753	2	23	rings	ring	NOUN
ejpam-753	2	24	with	with	ADP
ejpam-753	2	25	p1	p1	PROPN
ejpam-753	2	26	k1	k1	X
ejpam-753	2	27	·	·	PUNCT
ejpam-753	2	28	·	·	PUNCT
ejpam-753	3	1	·	·	PUNCT
ejpam-753	3	2	pn	pn	PROPN
ejpam-753	3	3	kn	kn	PROPN
ejpam-753	3	4	(	(	PUNCT
ejpam-753	3	5	1≤	1≤	INTJ
ejpam-753	3	6	ki	ki	PROPN
ejpam-753	3	7	≤	≤	PROPN
ejpam-753	3	8	7	7	NUM
ejpam-753	3	9	)	)	PUNCT
ejpam-753	3	10	zero	zero	NUM
ejpam-753	3	11	-	-	PUNCT
ejpam-753	3	12	divisors	divisors	PROPN
ejpam-753	3	13	ii	ii	NOUN
ejpam-753	3	14	m.	m.	NOUN
ejpam-753	3	15	behboodi1,2,∗and	behboodi1,2,∗and	PROPN
ejpam-753	3	16	r.	r.	PROPN
ejpam-753	3	17	beyranvand	beyranvand	PROPN
ejpam-753	3	18	3	3	NUM
ejpam-753	3	19	1	1	NUM
ejpam-753	3	20	department	department	NOUN
ejpam-753	3	21	of	of	ADP
ejpam-753	3	22	mathematical	mathematical	ADJ
ejpam-753	3	23	science	science	NOUN
ejpam-753	3	24	,	,	PUNCT
ejpam-753	3	25	isfahan	isfahan	PROPN
ejpam-753	3	26	university	university	PROPN
ejpam-753	3	27	of	of	ADP
ejpam-753	3	28	technology	technology	PROPN
ejpam-753	3	29	,	,	PUNCT
ejpam-753	3	30	isfahan	isfahan	PROPN
ejpam-753	3	31	,	,	PUNCT
ejpam-753	3	32	iran	iran	PROPN
ejpam-753	3	33	2	2	NUM
ejpam-753	3	34	school	school	NOUN
ejpam-753	3	35	of	of	ADP
ejpam-753	3	36	mathematics	mathematic	NOUN
ejpam-753	3	37	,	,	PUNCT
ejpam-753	3	38	institute	institute	NOUN
ejpam-753	3	39	for	for	ADP
ejpam-753	3	40	research	research	NOUN
ejpam-753	3	41	in	in	ADP
ejpam-753	3	42	fundamental	fundamental	ADJ
ejpam-753	3	43	sciences	science	NOUN
ejpam-753	3	44	(	(	PUNCT
ejpam-753	3	45	ipm	ipm	NOUN
ejpam-753	3	46	)	)	PUNCT
ejpam-753	3	47	,	,	PUNCT
ejpam-753	3	48	tehran	tehran	PROPN
ejpam-753	3	49	,	,	PUNCT
ejpam-753	3	50	iran	iran	PROPN
ejpam-753	3	51	3	3	NUM
ejpam-753	3	52	faculty	faculty	NOUN
ejpam-753	3	53	of	of	ADP
ejpam-753	3	54	science	science	NOUN
ejpam-753	3	55	,	,	PUNCT
ejpam-753	3	56	department	department	NOUN
ejpam-753	3	57	of	of	ADP
ejpam-753	3	58	mathematics	mathematics	PROPN
ejpam-753	3	59	,	,	PUNCT
ejpam-753	3	60	lorestan	lorestan	PROPN
ejpam-753	3	61	university	university	NOUN
ejpam-753	3	62	,	,	PUNCT
ejpam-753	3	63	khorramabad	khorramabad	PROPN
ejpam-753	3	64	,	,	PUNCT
ejpam-753	3	65	iran	iran	PROPN
ejpam-753	3	66	abstract	abstract	NOUN
ejpam-753	3	67	.	.	PUNCT
ejpam-753	4	1	in	in	ADP
ejpam-753	4	2	this	this	DET
ejpam-753	4	3	paper	paper	NOUN
ejpam-753	4	4	,	,	PUNCT
ejpam-753	4	5	we	we	PRON
ejpam-753	4	6	determine	determine	VERB
ejpam-753	4	7	the	the	DET
ejpam-753	4	8	structure	structure	NOUN
ejpam-753	4	9	of	of	ADP
ejpam-753	4	10	nonlocal	nonlocal	ADJ
ejpam-753	4	11	commutative	commutative	ADJ
ejpam-753	4	12	rings	ring	NOUN
ejpam-753	4	13	with	with	ADP
ejpam-753	4	14	p6	p6	PROPN
ejpam-753	4	15	zerodivisors	zerodivisor	NOUN
ejpam-753	4	16	and	and	CCONJ
ejpam-753	4	17	characterize	characterize	VERB
ejpam-753	4	18	the	the	DET
ejpam-753	4	19	structure	structure	NOUN
ejpam-753	4	20	of	of	ADP
ejpam-753	4	21	nonlocal	nonlocal	ADJ
ejpam-753	4	22	commutative	commutative	ADJ
ejpam-753	4	23	rings	ring	NOUN
ejpam-753	4	24	with	with	ADP
ejpam-753	4	25	p7	p7	ADJ
ejpam-753	4	26	zero	zero	NUM
ejpam-753	4	27	-	-	PUNCT
ejpam-753	4	28	divisors	divisor	NOUN
ejpam-753	4	29	.	.	PUNCT
ejpam-753	5	1	also	also	ADV
ejpam-753	5	2	,	,	PUNCT
ejpam-753	5	3	the	the	DET
ejpam-753	5	4	structure	structure	NOUN
ejpam-753	5	5	and	and	CCONJ
ejpam-753	5	6	classification	classification	NOUN
ejpam-753	5	7	up	up	ADP
ejpam-753	5	8	to	to	PART
ejpam-753	5	9	isomorphism	isomorphism	VERB
ejpam-753	5	10	all	all	DET
ejpam-753	5	11	commutative	commutative	ADJ
ejpam-753	5	12	rings	ring	NOUN
ejpam-753	5	13	with	with	ADP
ejpam-753	5	14	p1	p1	PROPN
ejpam-753	5	15	k1	k1	NOUN
ejpam-753	5	16	.	.	PUNCT
ejpam-753	5	17	.	.	PUNCT
ejpam-753	5	18	.	.	PUNCT
ejpam-753	6	1	pn	pn	PROPN
ejpam-753	6	2	kn	kn	PROPN
ejpam-753	6	3	zero	zero	NUM
ejpam-753	6	4	-	-	PUNCT
ejpam-753	6	5	divisors	divisor	NOUN
ejpam-753	6	6	,	,	PUNCT
ejpam-753	6	7	where	where	SCONJ
ejpam-753	6	8	n	n	PRON
ejpam-753	6	9	is	be	AUX
ejpam-753	6	10	a	a	DET
ejpam-753	6	11	positive	positive	ADJ
ejpam-753	6	12	integer	integer	NOUN
ejpam-753	6	13	,	,	PUNCT
ejpam-753	6	14	pi	pi	NOUN
ejpam-753	6	15	,	,	PUNCT
ejpam-753	6	16	s	s	PART
ejpam-753	6	17	are	be	AUX
ejpam-753	6	18	distinct	distinct	ADJ
ejpam-753	6	19	prime	prime	ADJ
ejpam-753	6	20	number	number	NOUN
ejpam-753	6	21	and	and	CCONJ
ejpam-753	6	22	1≤	1≤	NOUN
ejpam-753	6	23	ki	ki	PROPN
ejpam-753	6	24	≤	≤	ADV
ejpam-753	6	25	4	4	NUM
ejpam-753	6	26	,	,	PUNCT
ejpam-753	6	27	are	be	AUX
ejpam-753	6	28	determined	determine	VERB
ejpam-753	6	29	.	.	PUNCT
ejpam-753	7	1	2000	2000	NUM
ejpam-753	7	2	mathematics	mathematic	NOUN
ejpam-753	7	3	subject	subject	NOUN
ejpam-753	7	4	classifications	classification	NOUN
ejpam-753	7	5	:	:	PUNCT
ejpam-753	7	6	16b99	16b99	NUM
ejpam-753	7	7	;	;	PUNCT
ejpam-753	7	8	13a99	13a99	NUM
ejpam-753	7	9	;	;	PUNCT
ejpam-753	7	10	68r10	68r10	NUM
ejpam-753	7	11	key	key	ADJ
ejpam-753	7	12	words	word	NOUN
ejpam-753	7	13	and	and	CCONJ
ejpam-753	7	14	phrases	phrase	NOUN
ejpam-753	7	15	:	:	PUNCT
ejpam-753	7	16	finite	finite	PROPN
ejpam-753	7	17	ring	ring	NOUN
ejpam-753	7	18	,	,	PUNCT
ejpam-753	7	19	zero	zero	NUM
ejpam-753	7	20	-	-	PUNCT
ejpam-753	7	21	divisor	divisor	NOUN
ejpam-753	7	22	,	,	PUNCT
ejpam-753	7	23	local	local	ADJ
ejpam-753	7	24	ring	ring	NOUN
ejpam-753	7	25	1	1	NUM
ejpam-753	7	26	.	.	PUNCT
ejpam-753	8	1	introduction	introduction	NOUN
ejpam-753	8	2	the	the	DET
ejpam-753	8	3	present	present	ADJ
ejpam-753	8	4	paper	paper	NOUN
ejpam-753	8	5	is	be	AUX
ejpam-753	8	6	a	a	DET
ejpam-753	8	7	sequel	sequel	NOUN
ejpam-753	8	8	to	to	ADP
ejpam-753	8	9	[	[	X
ejpam-753	8	10	2	2	NUM
ejpam-753	8	11	]	]	PUNCT
ejpam-753	8	12	and	and	CCONJ
ejpam-753	8	13	so	so	ADV
ejpam-753	8	14	the	the	DET
ejpam-753	8	15	notations	notation	NOUN
ejpam-753	8	16	introduced	introduce	VERB
ejpam-753	8	17	in	in	ADP
ejpam-753	8	18	introduction	introduction	NOUN
ejpam-753	8	19	of	of	ADP
ejpam-753	8	20	[	[	X
ejpam-753	8	21	2	2	NUM
ejpam-753	8	22	]	]	PUNCT
ejpam-753	8	23	will	will	AUX
ejpam-753	8	24	remain	remain	VERB
ejpam-753	8	25	in	in	ADP
ejpam-753	8	26	force	force	NOUN
ejpam-753	8	27	.	.	PUNCT
ejpam-753	9	1	in	in	ADP
ejpam-753	9	2	particular	particular	ADJ
ejpam-753	9	3	,	,	PUNCT
ejpam-753	9	4	all	all	DET
ejpam-753	9	5	rings	ring	NOUN
ejpam-753	9	6	are	be	AUX
ejpam-753	9	7	associative	associative	ADJ
ejpam-753	9	8	rings	ring	NOUN
ejpam-753	9	9	with	with	ADP
ejpam-753	9	10	identity	identity	NOUN
ejpam-753	9	11	elements	element	NOUN
ejpam-753	9	12	,	,	PUNCT
ejpam-753	9	13	j(r	j(r	PROPN
ejpam-753	9	14	)	)	PUNCT
ejpam-753	9	15	denotes	denote	VERB
ejpam-753	9	16	the	the	DET
ejpam-753	9	17	jacobson	jacobson	PROPN
ejpam-753	9	18	radical	radical	PROPN
ejpam-753	9	19	of	of	ADP
ejpam-753	9	20	r	r	PROPN
ejpam-753	9	21	,	,	PUNCT
ejpam-753	9	22	z(r	z(r	PROPN
ejpam-753	9	23	)	)	PUNCT
ejpam-753	9	24	denotes	denote	VERB
ejpam-753	9	25	the	the	DET
ejpam-753	9	26	set	set	NOUN
ejpam-753	9	27	of	of	ADP
ejpam-753	9	28	all	all	DET
ejpam-753	9	29	zero	zero	NUM
ejpam-753	9	30	-	-	PUNCT
ejpam-753	9	31	divisors	divisor	NOUN
ejpam-753	9	32	of	of	ADP
ejpam-753	9	33	r	r	NOUN
ejpam-753	9	34	and	and	CCONJ
ejpam-753	9	35	for	for	ADP
ejpam-753	9	36	any	any	DET
ejpam-753	9	37	finite	finite	NOUN
ejpam-753	9	38	subset	subset	VERB
ejpam-753	9	39	y	y	PROPN
ejpam-753	9	40	of	of	ADP
ejpam-753	9	41	r	r	PROPN
ejpam-753	9	42	,	,	PUNCT
ejpam-753	9	43	we	we	PRON
ejpam-753	9	44	denote	denote	VERB
ejpam-753	9	45	|y	|y	NOUN
ejpam-753	9	46	|	|	ADV
ejpam-753	9	47	for	for	ADP
ejpam-753	9	48	the	the	DET
ejpam-753	9	49	cardinality	cardinality	NOUN
ejpam-753	9	50	of	of	ADP
ejpam-753	9	51	y	y	PROPN
ejpam-753	9	52	.	.	PUNCT
ejpam-753	10	1	also	also	ADV
ejpam-753	10	2	,	,	PUNCT
ejpam-753	10	3	fq	fq	PROPN
ejpam-753	10	4	is	be	AUX
ejpam-753	10	5	the	the	DET
ejpam-753	10	6	finite	finite	ADJ
ejpam-753	10	7	field	field	NOUN
ejpam-753	10	8	of	of	ADP
ejpam-753	10	9	order	order	NOUN
ejpam-753	10	10	q	q	X
ejpam-753	10	11	,	,	PUNCT
ejpam-753	10	12	fq	fq	PROPN
ejpam-753	10	13	∗	∗	PROPN
ejpam-753	10	14	is	be	AUX
ejpam-753	10	15	the	the	DET
ejpam-753	10	16	group	group	NOUN
ejpam-753	10	17	of	of	ADP
ejpam-753	10	18	nonzero	nonzero	PROPN
ejpam-753	10	19	elements	element	NOUN
ejpam-753	10	20	of	of	ADP
ejpam-753	10	21	fq	fq	PROPN
ejpam-753	10	22	and	and	CCONJ
ejpam-753	10	23	for	for	ADP
ejpam-753	10	24	a	a	DET
ejpam-753	10	25	prime	prime	ADJ
ejpam-753	10	26	number	number	NOUN
ejpam-753	10	27	p	p	NOUN
ejpam-753	10	28	,	,	PUNCT
ejpam-753	10	29	σm	σm	X
ejpam-753	10	30	is	be	AUX
ejpam-753	10	31	a	a	DET
ejpam-753	10	32	set	set	NOUN
ejpam-753	10	33	of	of	ADP
ejpam-753	10	34	coset	coset	NOUN
ejpam-753	10	35	representation	representation	NOUN
ejpam-753	10	36	of	of	ADP
ejpam-753	10	37	(	(	PUNCT
ejpam-753	10	38	fp	fp	INTJ
ejpam-753	10	39	∗)m	∗)m	PROPN
ejpam-753	10	40	in	in	ADP
ejpam-753	10	41	fp	fp	ADP
ejpam-753	10	42	∗	∗	NOUN
ejpam-753	10	43	,	,	PUNCT
ejpam-753	10	44	σ0	σ0	PROPN
ejpam-753	10	45	m	m	NOUN
ejpam-753	10	46	=	=	ADJ
ejpam-753	10	47	σm∪{0	σm∪{0	NOUN
ejpam-753	10	48	}	}	PUNCT
ejpam-753	10	49	and	and	CCONJ
ejpam-753	10	50	gr(pnr	gr(pnr	NOUN
ejpam-753	10	51	,	,	PUNCT
ejpam-753	10	52	pr	pr	NOUN
ejpam-753	10	53	)	)	PUNCT
ejpam-753	10	54	is	be	AUX
ejpam-753	10	55	the	the	DET
ejpam-753	10	56	galois	galois	PROPN
ejpam-753	10	57	ring	ring	NOUN
ejpam-753	10	58	of	of	ADP
ejpam-753	10	59	order	order	NOUN
ejpam-753	10	60	pnr	pnr	NOUN
ejpam-753	10	61	and	and	CCONJ
ejpam-753	10	62	characteristic	characteristic	ADJ
ejpam-753	10	63	pr	pr	NOUN
ejpam-753	10	64	.	.	PUNCT
ejpam-753	11	1	in	in	ADP
ejpam-753	11	2	[	[	X
ejpam-753	11	3	2	2	X
ejpam-753	11	4	]	]	PUNCT
ejpam-753	11	5	the	the	DET
ejpam-753	11	6	structure	structure	NOUN
ejpam-753	11	7	and	and	CCONJ
ejpam-753	11	8	classification	classification	NOUN
ejpam-753	11	9	up	up	ADP
ejpam-753	11	10	to	to	PART
ejpam-753	11	11	isomorphism	isomorphism	VERB
ejpam-753	11	12	all	all	DET
ejpam-753	11	13	rings	ring	NOUN
ejpam-753	11	14	with	with	ADP
ejpam-753	11	15	p1	p1	PROPN
ejpam-753	11	16	k1	k1	NOUN
ejpam-753	11	17	.	.	PUNCT
ejpam-753	11	18	.	.	PUNCT
ejpam-753	11	19	.	.	PUNCT
ejpam-753	12	1	ps	ps	NOUN
ejpam-753	12	2	ks	ks	PROPN
ejpam-753	12	3	zerodivisors	zerodivisors	PROPN
ejpam-753	12	4	,	,	PUNCT
ejpam-753	12	5	where	where	SCONJ
ejpam-753	12	6	s	s	NOUN
ejpam-753	12	7	is	be	AUX
ejpam-753	12	8	a	a	DET
ejpam-753	12	9	positive	positive	ADJ
ejpam-753	12	10	integer	integer	NOUN
ejpam-753	12	11	,	,	PUNCT
ejpam-753	12	12	pi	pi	NOUN
ejpam-753	12	13	,	,	PUNCT
ejpam-753	12	14	s	s	PART
ejpam-753	12	15	are	be	AUX
ejpam-753	12	16	distinct	distinct	ADJ
ejpam-753	12	17	prime	prime	ADJ
ejpam-753	12	18	number	number	NOUN
ejpam-753	12	19	and	and	CCONJ
ejpam-753	12	20	1	1	NUM
ejpam-753	12	21	≤	≤	NUM
ejpam-753	12	22	ki	ki	PROPN
ejpam-753	12	23	≤	≤	ADJ
ejpam-753	12	24	3	3	NUM
ejpam-753	12	25	were	be	AUX
ejpam-753	12	26	determined	determine	VERB
ejpam-753	12	27	.	.	PUNCT
ejpam-753	13	1	also	also	ADV
ejpam-753	13	2	we	we	PRON
ejpam-753	13	3	determined	determine	VERB
ejpam-753	13	4	the	the	DET
ejpam-753	13	5	structure	structure	NOUN
ejpam-753	13	6	of	of	ADP
ejpam-753	13	7	nonlocal	nonlocal	ADJ
ejpam-753	13	8	rings	ring	NOUN
ejpam-753	13	9	with	with	ADP
ejpam-753	13	10	pk	pk	NOUN
ejpam-753	13	11	zero	zero	NUM
ejpam-753	13	12	-	-	PUNCT
ejpam-753	13	13	divisors	divisor	NOUN
ejpam-753	13	14	where	where	SCONJ
ejpam-753	13	15	k	k	PROPN
ejpam-753	13	16	=	=	PUNCT
ejpam-753	13	17	4	4	NUM
ejpam-753	13	18	or	or	CCONJ
ejpam-753	13	19	5	5	NUM
ejpam-753	13	20	.	.	PUNCT
ejpam-753	14	1	in	in	ADP
ejpam-753	14	2	the	the	DET
ejpam-753	14	3	paper	paper	NOUN
ejpam-753	14	4	we	we	PRON
ejpam-753	14	5	develop	develop	VERB
ejpam-753	14	6	these	these	DET
ejpam-753	14	7	results	result	NOUN
ejpam-753	14	8	.	.	PUNCT
ejpam-753	15	1	in	in	ADP
ejpam-753	15	2	fact	fact	NOUN
ejpam-753	15	3	the	the	DET
ejpam-753	15	4	structure	structure	NOUN
ejpam-753	15	5	and	and	CCONJ
ejpam-753	15	6	classification	classification	NOUN
ejpam-753	15	7	up	up	ADP
ejpam-753	15	8	to	to	PART
ejpam-753	15	9	isomorphism	isomorphism	VERB
ejpam-753	15	10	all	all	DET
ejpam-753	15	11	rings	ring	NOUN
ejpam-753	15	12	with	with	ADP
ejpam-753	15	13	p1	p1	PROPN
ejpam-753	15	14	k1	k1	NOUN
ejpam-753	15	15	p2	p2	PROPN
ejpam-753	15	16	k2	k2	PROPN
ejpam-753	15	17	.	.	PUNCT
ejpam-753	15	18	.	.	PUNCT
ejpam-753	16	1	.	.	PUNCT
ejpam-753	17	1	ps	ps	NOUN
ejpam-753	17	2	ks	ks	PROPN
ejpam-753	17	3	zero	zero	NUM
ejpam-753	17	4	-	-	PUNCT
ejpam-753	17	5	divisors	divisor	NOUN
ejpam-753	17	6	,	,	PUNCT
ejpam-753	17	7	where	where	SCONJ
ejpam-753	17	8	s	s	NOUN
ejpam-753	17	9	is	be	AUX
ejpam-753	17	10	a	a	DET
ejpam-753	17	11	positive	positive	ADJ
ejpam-753	17	12	integer	integer	NOUN
ejpam-753	17	13	,	,	PUNCT
ejpam-753	17	14	pi	pi	NOUN
ejpam-753	17	15	,	,	PUNCT
ejpam-753	17	16	s	s	PART
ejpam-753	17	17	are	be	AUX
ejpam-753	17	18	distinct	distinct	ADJ
ejpam-753	17	19	prime	prime	ADJ
ejpam-753	17	20	number	number	NOUN
ejpam-753	17	21	and	and	CCONJ
ejpam-753	17	22	1≤	1≤	NUM
ejpam-753	17	23	ki	ki	PROPN
ejpam-753	17	24	≤	≤	ADV
ejpam-753	17	25	4	4	NUM
ejpam-753	17	26	are	be	AUX
ejpam-753	17	27	determined	determine	VERB
ejpam-753	17	28	.	.	PUNCT
ejpam-753	18	1	also	also	ADV
ejpam-753	18	2	we	we	PRON
ejpam-753	18	3	determine	determine	VERB
ejpam-753	18	4	the	the	DET
ejpam-753	18	5	structure	structure	NOUN
ejpam-753	18	6	of	of	ADP
ejpam-753	18	7	nonlocal	nonlocal	ADJ
ejpam-753	18	8	rings	ring	NOUN
ejpam-753	18	9	with	with	ADP
ejpam-753	18	10	p6	p6	ADJ
ejpam-753	18	11	zero	zero	NUM
ejpam-753	18	12	-	-	PUNCT
ejpam-753	18	13	divisors	divisor	NOUN
ejpam-753	18	14	and	and	CCONJ
ejpam-753	18	15	characterize	characterize	VERB
ejpam-753	18	16	the	the	DET
ejpam-753	18	17	structure	structure	NOUN
ejpam-753	18	18	of	of	ADP
ejpam-753	18	19	nonlocal	nonlocal	ADJ
ejpam-753	18	20	rings	ring	NOUN
ejpam-753	18	21	with	with	ADP
ejpam-753	18	22	p7	p7	ADJ
ejpam-753	18	23	zero	zero	NUM
ejpam-753	18	24	-	-	PUNCT
ejpam-753	18	25	divisors	divisor	NOUN
ejpam-753	18	26	.	.	PUNCT
ejpam-753	19	1	∗corresponding	∗corresponde	VERB
ejpam-753	19	2	author	author	NOUN
ejpam-753	19	3	.	.	PUNCT
ejpam-753	20	1	email	email	NOUN
ejpam-753	20	2	addresses	address	NOUN
ejpam-753	20	3	:	:	PUNCT
ejpam-753	20	4	mbehbood	mbehbood	PROPN
ejpam-753	20	5	�	�	PROPN
ejpam-753	20	6	.iut.a	.iut.a	PROPN
ejpam-753	20	7	.ir	.ir	PUNCT
ejpam-753	21	1	(	(	PUNCT
ejpam-753	21	2	m.	m.	NOUN
ejpam-753	21	3	behboodi	behboodi	PROPN
ejpam-753	21	4	)	)	PUNCT
ejpam-753	21	5	,	,	PUNCT
ejpam-753	21	6	beyranvand.r	beyranvand.r	SYM
ejpam-753	21	7	�	�	PROPN
ejpam-753	21	8	lu.a	lu.a	PROPN
ejpam-753	21	9	.ir	.ir	PUNCT
ejpam-753	22	1	(	(	PUNCT
ejpam-753	22	2	r.	r.	PROPN
ejpam-753	22	3	beyranvand	beyranvand	PROPN
ejpam-753	22	4	)	)	PUNCT
ejpam-753	22	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-753	23	1	686	686	NUM
ejpam-753	23	2	c	c	NOUN
ejpam-753	23	3	©	©	VERB
ejpam-753	23	4	2010	2010	NUM
ejpam-753	23	5	ejpam	ejpam	NOUN
ejpam-753	23	6	all	all	DET
ejpam-753	23	7	rights	right	NOUN
ejpam-753	23	8	reserved	reserve	VERB
ejpam-753	23	9	.	.	PUNCT
ejpam-753	24	1	m.	m.	NOUN
ejpam-753	24	2	behboodi	behboodi	PROPN
ejpam-753	24	3	,	,	PUNCT
ejpam-753	24	4	r.	r.	PROPN
ejpam-753	24	5	beyranvand	beyranvand	PROPN
ejpam-753	24	6	/	/	SYM
ejpam-753	24	7	eur	eur	PROPN
ejpam-753	24	8	.	.	PUNCT
ejpam-753	25	1	j.	j.	PROPN
ejpam-753	25	2	pure	pure	PROPN
ejpam-753	25	3	appl	appl	PROPN
ejpam-753	25	4	.	.	PROPN
ejpam-753	25	5	math	math	PROPN
ejpam-753	25	6	,	,	PUNCT
ejpam-753	25	7	3	3	NUM
ejpam-753	25	8	(	(	PUNCT
ejpam-753	25	9	2010	2010	NUM
ejpam-753	25	10	)	)	PUNCT
ejpam-753	25	11	,	,	PUNCT
ejpam-753	25	12	686	686	NUM
ejpam-753	25	13	-	-	SYM
ejpam-753	25	14	694	694	NUM
ejpam-753	25	15	687	687	NUM
ejpam-753	25	16	2	2	NUM
ejpam-753	25	17	.	.	PUNCT
ejpam-753	25	18	on	on	ADP
ejpam-753	25	19	rings	ring	NOUN
ejpam-753	25	20	with	with	ADP
ejpam-753	25	21	pk	pk	NOUN
ejpam-753	25	22	zero	zero	NUM
ejpam-753	25	23	-	-	PUNCT
ejpam-753	25	24	divisors	divisor	NOUN
ejpam-753	26	1	we	we	PRON
ejpam-753	26	2	recall	recall	VERB
ejpam-753	26	3	the	the	DET
ejpam-753	26	4	following	follow	VERB
ejpam-753	26	5	facts	fact	NOUN
ejpam-753	26	6	that	that	SCONJ
ejpam-753	26	7	we	we	PRON
ejpam-753	26	8	will	will	AUX
ejpam-753	26	9	use	use	VERB
ejpam-753	26	10	them	they	PRON
ejpam-753	26	11	in	in	ADP
ejpam-753	26	12	the	the	DET
ejpam-753	26	13	paper	paper	NOUN
ejpam-753	26	14	:	:	PUNCT
ejpam-753	26	15	(	(	PUNCT
ejpam-753	26	16	i	i	NOUN
ejpam-753	26	17	)	)	PUNCT
ejpam-753	26	18	an	an	DET
ejpam-753	26	19	artinian	artinian	ADJ
ejpam-753	26	20	commutative	commutative	ADJ
ejpam-753	26	21	ring	ring	NOUN
ejpam-753	26	22	r	r	NOUN
ejpam-753	26	23	is	be	AUX
ejpam-753	26	24	called	call	VERB
ejpam-753	26	25	completely	completely	ADV
ejpam-753	26	26	primary	primary	ADJ
ejpam-753	26	27	if	if	SCONJ
ejpam-753	26	28	r	r	NOUN
ejpam-753	26	29	/	/	SYM
ejpam-753	26	30	j(r	j(r	PROPN
ejpam-753	26	31	)	)	PUNCT
ejpam-753	26	32	is	be	AUX
ejpam-753	26	33	a	a	DET
ejpam-753	26	34	field	field	NOUN
ejpam-753	26	35	.	.	PUNCT
ejpam-753	27	1	one	one	PRON
ejpam-753	27	2	can	can	AUX
ejpam-753	27	3	easily	easily	ADV
ejpam-753	27	4	see	see	VERB
ejpam-753	27	5	that	that	SCONJ
ejpam-753	27	6	an	an	DET
ejpam-753	27	7	artinian	artinian	ADJ
ejpam-753	27	8	commutative	commutative	ADJ
ejpam-753	27	9	ring	ring	NOUN
ejpam-753	27	10	r	r	NOUN
ejpam-753	27	11	is	be	AUX
ejpam-753	27	12	completely	completely	ADV
ejpam-753	27	13	primary	primary	ADJ
ejpam-753	27	14	if	if	SCONJ
ejpam-753	27	15	and	and	CCONJ
ejpam-753	27	16	only	only	ADV
ejpam-753	27	17	if	if	SCONJ
ejpam-753	27	18	z(r	z(r	NOUN
ejpam-753	27	19	)	)	PUNCT
ejpam-753	27	20	is	be	AUX
ejpam-753	27	21	an	an	DET
ejpam-753	27	22	ideal	ideal	NOUN
ejpam-753	27	23	of	of	ADP
ejpam-753	27	24	r	r	NOUN
ejpam-753	27	25	,	,	PUNCT
ejpam-753	27	26	if	if	SCONJ
ejpam-753	27	27	and	and	CCONJ
ejpam-753	27	28	only	only	ADV
ejpam-753	27	29	if	if	SCONJ
ejpam-753	27	30	r	r	NOUN
ejpam-753	27	31	is	be	AUX
ejpam-753	27	32	a	a	DET
ejpam-753	27	33	local	local	ADJ
ejpam-753	27	34	ring	ring	NOUN
ejpam-753	27	35	.	.	PUNCT
ejpam-753	28	1	(	(	PUNCT
ejpam-753	28	2	ii	ii	NOUN
ejpam-753	28	3	)	)	PUNCT
ejpam-753	28	4	let	let	VERB
ejpam-753	28	5	ri	ri	PROPN
ejpam-753	28	6	(	(	PUNCT
ejpam-753	28	7	1	1	NUM
ejpam-753	28	8	≤	≤	NUM
ejpam-753	28	9	i	i	NOUN
ejpam-753	28	10	≤	≤	PROPN
ejpam-753	28	11	t	t	PROPN
ejpam-753	28	12	)	)	PUNCT
ejpam-753	28	13	be	be	AUX
ejpam-753	28	14	a	a	DET
ejpam-753	28	15	nonzero	nonzero	ADJ
ejpam-753	28	16	finite	finite	PROPN
ejpam-753	28	17	commutative	commutative	ADJ
ejpam-753	28	18	ring	ring	NOUN
ejpam-753	28	19	with	with	ADP
ejpam-753	28	20	mi	mi	NOUN
ejpam-753	28	21	elements	element	NOUN
ejpam-753	28	22	and	and	CCONJ
ejpam-753	28	23	ni	ni	PROPN
ejpam-753	28	24	zerodivisors	zerodivisors	PROPN
ejpam-753	28	25	.	.	PUNCT
ejpam-753	29	1	then	then	ADV
ejpam-753	29	2	by	by	ADP
ejpam-753	29	3	[	[	X
ejpam-753	29	4	6	6	NUM
ejpam-753	29	5	,	,	PUNCT
ejpam-753	29	6	theorem	theorem	VERB
ejpam-753	29	7	2	2	NUM
ejpam-753	29	8	]	]	PUNCT
ejpam-753	29	9	,	,	PUNCT
ejpam-753	29	10	the	the	DET
ejpam-753	29	11	ring	ring	NOUN
ejpam-753	29	12	r1×.	r1×.	NOUN
ejpam-753	29	13	.	.	PUNCT
ejpam-753	30	1	.×r	.×r	PROPN
ejpam-753	30	2	t	t	PROPN
ejpam-753	30	3	has	have	VERB
ejpam-753	30	4	m1m2	m1m2	PROPN
ejpam-753	30	5	.	.	PUNCT
ejpam-753	30	6	.	.	PUNCT
ejpam-753	30	7	.	.	PUNCT
ejpam-753	31	1	mt−(m1−n1)(m2−	mt−(m1−n1)(m2−	PROPN
ejpam-753	31	2	n2	n2	PROPN
ejpam-753	31	3	)	)	PUNCT
ejpam-753	31	4	.	.	PUNCT
ejpam-753	31	5	.	.	PUNCT
ejpam-753	31	6	.	.	PUNCT
ejpam-753	32	1	(	(	PUNCT
ejpam-753	32	2	mt	mt	PROPN
ejpam-753	32	3	−	−	PROPN
ejpam-753	32	4	nt	not	PART
ejpam-753	32	5	)	)	PUNCT
ejpam-753	32	6	zero	zero	NUM
ejpam-753	32	7	-	-	PUNCT
ejpam-753	32	8	divisors	divisor	NOUN
ejpam-753	32	9	.	.	PUNCT
ejpam-753	33	1	(	(	PUNCT
ejpam-753	33	2	iii	iii	X
ejpam-753	33	3	)	)	PUNCT
ejpam-753	33	4	every	every	DET
ejpam-753	33	5	finite	finite	PROPN
ejpam-753	33	6	commutative	commutative	ADJ
ejpam-753	33	7	ring	ring	NOUN
ejpam-753	33	8	is	be	AUX
ejpam-753	33	9	uniquely	uniquely	ADV
ejpam-753	33	10	expressible	expressible	ADJ
ejpam-753	33	11	as	as	ADP
ejpam-753	33	12	a	a	DET
ejpam-753	33	13	direct	direct	ADJ
ejpam-753	33	14	sum	sum	NOUN
ejpam-753	33	15	of	of	ADP
ejpam-753	33	16	completely	completely	ADV
ejpam-753	33	17	primary	primary	ADJ
ejpam-753	33	18	(	(	PUNCT
ejpam-753	33	19	local	local	ADJ
ejpam-753	33	20	)	)	PUNCT
ejpam-753	33	21	rings	ring	NOUN
ejpam-753	33	22	(	(	PUNCT
ejpam-753	33	23	see	see	VERB
ejpam-753	33	24	for	for	ADP
ejpam-753	33	25	example	example	NOUN
ejpam-753	33	26	[	[	X
ejpam-753	33	27	7	7	NUM
ejpam-753	33	28	,	,	PUNCT
ejpam-753	33	29	p.95	p.95	NOUN
ejpam-753	33	30	]	]	PUNCT
ejpam-753	33	31	)	)	PUNCT
ejpam-753	33	32	.	.	PUNCT
ejpam-753	34	1	we	we	PRON
ejpam-753	34	2	need	need	VERB
ejpam-753	34	3	the	the	DET
ejpam-753	34	4	following	follow	VERB
ejpam-753	34	5	two	two	NUM
ejpam-753	34	6	lemmas	lemma	NOUN
ejpam-753	34	7	which	which	PRON
ejpam-753	34	8	are	be	AUX
ejpam-753	34	9	crucial	crucial	ADJ
ejpam-753	34	10	in	in	ADP
ejpam-753	34	11	our	our	PRON
ejpam-753	34	12	investigation	investigation	NOUN
ejpam-753	34	13	.	.	PUNCT
ejpam-753	35	1	lemma	lemma	PROPN
ejpam-753	35	2	1	1	NUM
ejpam-753	35	3	.	.	PUNCT
ejpam-753	36	1	[	[	X
ejpam-753	36	2	8	8	NUM
ejpam-753	36	3	,	,	PUNCT
ejpam-753	36	4	theorem	theorem	VERB
ejpam-753	36	5	2	2	NUM
ejpam-753	36	6	]	]	PUNCT
ejpam-753	36	7	let	let	VERB
ejpam-753	36	8	r	r	PRON
ejpam-753	36	9	be	be	AUX
ejpam-753	36	10	a	a	DET
ejpam-753	36	11	finite	finite	NOUN
ejpam-753	36	12	completely	completely	ADV
ejpam-753	36	13	primary	primary	ADJ
ejpam-753	36	14	ring	ring	NOUN
ejpam-753	36	15	.	.	PUNCT
ejpam-753	37	1	then	then	ADV
ejpam-753	37	2	1	1	X
ejpam-753	37	3	.	.	X
ejpam-753	37	4	z(r	z(r	NOUN
ejpam-753	37	5	)	)	PUNCT
ejpam-753	37	6	=	=	SYM
ejpam-753	37	7	j(r	j(r	PROPN
ejpam-753	37	8	)	)	PUNCT
ejpam-753	37	9	;	;	PUNCT
ejpam-753	37	10	2	2	X
ejpam-753	37	11	.	.	PUNCT
ejpam-753	37	12	|z(r)|=	|z(r)|=	VERB
ejpam-753	37	13	p(n−1)r	p(n−1)r	NOUN
ejpam-753	37	14	and	and	CCONJ
ejpam-753	37	15	|r|=	|r|=	NOUN
ejpam-753	37	16	pnr	pnr	NOUN
ejpam-753	37	17	for	for	ADP
ejpam-753	37	18	some	some	DET
ejpam-753	37	19	prime	prime	ADJ
ejpam-753	37	20	number	number	NOUN
ejpam-753	37	21	p	p	NOUN
ejpam-753	37	22	,	,	PUNCT
ejpam-753	37	23	and	and	CCONJ
ejpam-753	37	24	some	some	DET
ejpam-753	37	25	positive	positive	ADJ
ejpam-753	37	26	integers	integer	NOUN
ejpam-753	37	27	n	n	CCONJ
ejpam-753	37	28	,	,	PUNCT
ejpam-753	37	29	r	r	NOUN
ejpam-753	37	30	;	;	PUNCT
ejpam-753	37	31	3	3	NUM
ejpam-753	37	32	.	.	X
ejpam-753	37	33	z(r)n	z(r)n	NOUN
ejpam-753	37	34	=	=	SYM
ejpam-753	37	35	0	0	NUM
ejpam-753	37	36	;	;	PUNCT
ejpam-753	37	37	4	4	NUM
ejpam-753	37	38	.	.	X
ejpam-753	37	39	char(r	char(r	NOUN
ejpam-753	37	40	)	)	PUNCT
ejpam-753	37	41	=	=	SYM
ejpam-753	37	42	pk	pk	NOUN
ejpam-753	37	43	for	for	ADP
ejpam-753	37	44	some	some	DET
ejpam-753	37	45	integer	integer	NOUN
ejpam-753	37	46	k	k	PROPN
ejpam-753	37	47	with	with	ADP
ejpam-753	37	48	1≤	1≤	PROPN
ejpam-753	37	49	k	k	PROPN
ejpam-753	37	50	≤	≤	PROPN
ejpam-753	37	51	n	n	CCONJ
ejpam-753	37	52	;	;	PUNCT
ejpam-753	37	53	5	5	NUM
ejpam-753	37	54	.	.	X
ejpam-753	37	55	r	r	NOUN
ejpam-753	37	56	/	/	SYM
ejpam-753	37	57	j(r)∼=	j(r)∼=	NOUN
ejpam-753	37	58	fq	fq	NOUN
ejpam-753	37	59	,	,	PUNCT
ejpam-753	37	60	where	where	SCONJ
ejpam-753	37	61	q	q	NOUN
ejpam-753	37	62	=	=	NOUN
ejpam-753	37	63	pr	pr	X
ejpam-753	37	64	.	.	PUNCT
ejpam-753	38	1	lemma	lemma	PROPN
ejpam-753	38	2	2	2	NUM
ejpam-753	38	3	.	.	PUNCT
ejpam-753	39	1	[	[	X
ejpam-753	39	2	2	2	NUM
ejpam-753	39	3	,	,	PUNCT
ejpam-753	39	4	theorem	theorem	VERB
ejpam-753	39	5	2	2	NUM
ejpam-753	39	6	]	]	PUNCT
ejpam-753	39	7	let	let	VERB
ejpam-753	39	8	r	r	PRON
ejpam-753	39	9	be	be	AUX
ejpam-753	39	10	a	a	DET
ejpam-753	39	11	commutative	commutative	ADJ
ejpam-753	39	12	ring	ring	NOUN
ejpam-753	39	13	such	such	ADJ
ejpam-753	39	14	that	that	DET
ejpam-753	39	15	|z(r)|	|z(r)|	PROPN
ejpam-753	39	16	=	=	SYM
ejpam-753	39	17	pk	pk	NOUN
ejpam-753	39	18	for	for	ADP
ejpam-753	39	19	some	some	DET
ejpam-753	39	20	prime	prime	ADJ
ejpam-753	39	21	number	number	NOUN
ejpam-753	39	22	p	p	NOUN
ejpam-753	39	23	and	and	CCONJ
ejpam-753	39	24	a	a	DET
ejpam-753	39	25	positive	positive	ADJ
ejpam-753	39	26	number	number	NOUN
ejpam-753	39	27	k.	k.	PROPN
ejpam-753	40	1	then	then	ADV
ejpam-753	40	2	either	either	CCONJ
ejpam-753	40	3	(	(	PUNCT
ejpam-753	40	4	i	i	NOUN
ejpam-753	40	5	)	)	PUNCT
ejpam-753	40	6	r	r	NOUN
ejpam-753	40	7	is	be	AUX
ejpam-753	40	8	local	local	ADJ
ejpam-753	40	9	,	,	PUNCT
ejpam-753	40	10	(	(	PUNCT
ejpam-753	40	11	ii	ii	NOUN
ejpam-753	40	12	)	)	PUNCT
ejpam-753	40	13	r	r	NOUN
ejpam-753	40	14	is	be	AUX
ejpam-753	40	15	reduced	reduce	VERB
ejpam-753	40	16	or	or	CCONJ
ejpam-753	40	17	(	(	PUNCT
ejpam-753	40	18	iii	iii	X
ejpam-753	40	19	)	)	PUNCT
ejpam-753	40	20	k	k	PROPN
ejpam-753	40	21	≥	≥	NUM
ejpam-753	40	22	3	3	NUM
ejpam-753	40	23	and	and	CCONJ
ejpam-753	40	24	r∼=	r∼=	NUM
ejpam-753	40	25	r1×	r1×	NOUN
ejpam-753	40	26	.	.	PUNCT
ejpam-753	40	27	.	.	PUNCT
ejpam-753	41	1	.×rs×	.×rs×	PUNCT
ejpam-753	42	1	fq1	fq1	ADV
ejpam-753	42	2	×	×	NOUN
ejpam-753	42	3	.	.	PUNCT
ejpam-753	42	4	.	.	PUNCT
ejpam-753	43	1	.×	.×	PROPN
ejpam-753	43	2	fqt	fqt	PROPN
ejpam-753	43	3	where	where	SCONJ
ejpam-753	43	4	s	s	PRON
ejpam-753	43	5	and	and	CCONJ
ejpam-753	43	6	t	t	PROPN
ejpam-753	43	7	are	be	AUX
ejpam-753	43	8	positive	positive	ADJ
ejpam-753	43	9	integers	integer	NOUN
ejpam-753	43	10	,	,	PUNCT
ejpam-753	43	11	each	each	DET
ejpam-753	43	12	fqi	fqi	VERB
ejpam-753	43	13	is	be	AUX
ejpam-753	43	14	a	a	DET
ejpam-753	43	15	field	field	NOUN
ejpam-753	43	16	,	,	PUNCT
ejpam-753	43	17	and	and	CCONJ
ejpam-753	43	18	where	where	SCONJ
ejpam-753	43	19	each	each	DET
ejpam-753	43	20	ri	ri	PROPN
ejpam-753	43	21	is	be	AUX
ejpam-753	43	22	a	a	DET
ejpam-753	43	23	commutative	commutative	ADJ
ejpam-753	43	24	finite	finite	ADJ
ejpam-753	43	25	local	local	ADJ
ejpam-753	43	26	ring	ring	NOUN
ejpam-753	43	27	with	with	ADP
ejpam-753	43	28	|z(ri)|	|z(ri)|	NOUN
ejpam-753	43	29	=	=	SYM
ejpam-753	43	30	pti	pti	PROPN
ejpam-753	43	31	,	,	PUNCT
ejpam-753	43	32	|ri|	|ri|	NOUN
ejpam-753	43	33	=	=	SYM
ejpam-753	43	34	pki	pki	NOUN
ejpam-753	43	35	for	for	ADP
ejpam-753	43	36	some	some	DET
ejpam-753	43	37	positive	positive	ADJ
ejpam-753	43	38	integers	integer	NOUN
ejpam-753	43	39	ki	ki	PROPN
ejpam-753	43	40	and	and	CCONJ
ejpam-753	43	41	t	t	PROPN
ejpam-753	43	42	i	i	PRON
ejpam-753	43	43	with	with	ADP
ejpam-753	43	44	1≤	1≤	NUM
ejpam-753	44	1	∑s	∑s	PROPN
ejpam-753	44	2	i=1	i=1	PROPN
ejpam-753	44	3	t	t	PROPN
ejpam-753	44	4	i	i	NOUN
ejpam-753	44	5	≤	≤	NUM
ejpam-753	45	1	∑s	∑s	PROPN
ejpam-753	46	1	i=1	i=1	PROPN
ejpam-753	47	1	ki	ki	PROPN
ejpam-753	48	1	−	−	PROPN
ejpam-753	48	2	s	s	PART
ejpam-753	48	3	≤	≤	PROPN
ejpam-753	48	4	k−	k−	NOUN
ejpam-753	48	5	s−	s−	PROPN
ejpam-753	48	6	1	1	NUM
ejpam-753	48	7	such	such	ADJ
ejpam-753	48	8	that	that	SCONJ
ejpam-753	48	9	pk−σs	pk−σs	PROPN
ejpam-753	48	10	i=1	i=1	PROPN
ejpam-753	48	11	ti	ti	PROPN
ejpam-753	48	12	=	=	PROPN
ejpam-753	48	13	q1	q1	PROPN
ejpam-753	48	14	.	.	PUNCT
ejpam-753	48	15	.	.	PUNCT
ejpam-753	48	16	.	.	PUNCT
ejpam-753	49	1	qt	qt	ADP
ejpam-753	49	2	p	p	NOUN
ejpam-753	49	3	σs	σs	ADP
ejpam-753	49	4	i=1(ki−ti	i=1(ki−ti	NOUN
ejpam-753	49	5	)	)	PUNCT
ejpam-753	49	6	−	−	PROPN
ejpam-753	50	1	(	(	PUNCT
ejpam-753	50	2	q1−	q1−	NOUN
ejpam-753	50	3	1	1	NUM
ejpam-753	50	4	)	)	PUNCT
ejpam-753	50	5	.	.	PUNCT
ejpam-753	50	6	.	.	PUNCT
ejpam-753	50	7	.	.	PUNCT
ejpam-753	51	1	(	(	PUNCT
ejpam-753	51	2	qt	qt	INTJ
ejpam-753	51	3	−	−	PROPN
ejpam-753	52	1	1)πs	1)πs	NUM
ejpam-753	53	1	i=1(p	i=1(p	NOUN
ejpam-753	53	2	ki−ti	ki−ti	X
ejpam-753	53	3	−	−	NOUN
ejpam-753	53	4	1	1	NUM
ejpam-753	53	5	)	)	PUNCT
ejpam-753	53	6	.	.	PUNCT
ejpam-753	54	1	(	(	PUNCT
ejpam-753	54	2	1	1	X
ejpam-753	54	3	)	)	PUNCT
ejpam-753	54	4	consequently	consequently	ADV
ejpam-753	54	5	,	,	PUNCT
ejpam-753	54	6	in	in	ADP
ejpam-753	54	7	the	the	DET
ejpam-753	54	8	latter	latter	ADJ
ejpam-753	54	9	case	case	NOUN
ejpam-753	54	10	,	,	PUNCT
ejpam-753	54	11	qi	qi	PROPN
ejpam-753	54	12	≡	≡	PROPN
ejpam-753	54	13	1	1	NUM
ejpam-753	54	14	(	(	PUNCT
ejpam-753	54	15	p	p	NOUN
ejpam-753	54	16	)	)	PUNCT
ejpam-753	54	17	and	and	CCONJ
ejpam-753	54	18	for	for	ADP
ejpam-753	54	19	each	each	DET
ejpam-753	54	20	i	i	NOUN
ejpam-753	54	21	=	=	NOUN
ejpam-753	54	22	1	1	NUM
ejpam-753	54	23	,	,	PUNCT
ejpam-753	54	24	.	.	PUNCT
ejpam-753	54	25	.	.	PUNCT
ejpam-753	55	1	.	.	PUNCT
ejpam-753	56	1	,	,	PUNCT
ejpam-753	56	2	s	s	X
ejpam-753	56	3	,	,	PUNCT
ejpam-753	56	4	t	t	PROPN
ejpam-753	57	1	i	i	NOUN
ejpam-753	57	2	≤	≤	NUM
ejpam-753	58	1	k	k	PRON
ejpam-753	59	1	−	−	NOUN
ejpam-753	59	2	2	2	X
ejpam-753	59	3	.	.	PUNCT
ejpam-753	60	1	moreover	moreover	ADV
ejpam-753	60	2	,	,	PUNCT
ejpam-753	60	3	if	if	SCONJ
ejpam-753	60	4	t	t	PROPN
ejpam-753	60	5	j	j	PROPN
ejpam-753	60	6	=	=	SYM
ejpam-753	60	7	k−	k−	PROPN
ejpam-753	60	8	2	2	NUM
ejpam-753	60	9	for	for	ADP
ejpam-753	60	10	some	some	DET
ejpam-753	60	11	j	j	PROPN
ejpam-753	60	12	∈	∈	PROPN
ejpam-753	60	13	{	{	PUNCT
ejpam-753	60	14	1	1	NUM
ejpam-753	60	15	,	,	PUNCT
ejpam-753	60	16	.	.	PUNCT
ejpam-753	60	17	.	.	PUNCT
ejpam-753	61	1	.	.	PUNCT
ejpam-753	62	1	,	,	PUNCT
ejpam-753	62	2	s	s	X
ejpam-753	62	3	}	}	PUNCT
ejpam-753	62	4	,	,	PUNCT
ejpam-753	62	5	then	then	ADV
ejpam-753	62	6	s	s	VERB
ejpam-753	62	7	=	=	X
ejpam-753	62	8	t	t	X
ejpam-753	62	9	=	=	SYM
ejpam-753	62	10	1	1	NUM
ejpam-753	62	11	,	,	PUNCT
ejpam-753	62	12	i.e.	i.e.	X
ejpam-753	62	13	,	,	PUNCT
ejpam-753	62	14	r∼=	r∼=	NUM
ejpam-753	62	15	r1×	r1×	VERB
ejpam-753	62	16	fq	fq	PROPN
ejpam-753	62	17	where	where	SCONJ
ejpam-753	62	18	|z(r1)|=	|z(r1)|=	AUX
ejpam-753	62	19	pk−2	pk−2	ADJ
ejpam-753	62	20	and	and	CCONJ
ejpam-753	62	21	so	so	ADV
ejpam-753	62	22	p2	p2	PROPN
ejpam-753	62	23	=	=	SYM
ejpam-753	62	24	p+	p+	PROPN
ejpam-753	62	25	q−	q−	PROPN
ejpam-753	62	26	1	1	NUM
ejpam-753	62	27	.	.	PUNCT
ejpam-753	62	28	m.	m.	NOUN
ejpam-753	62	29	behboodi	behboodi	PROPN
ejpam-753	62	30	,	,	PUNCT
ejpam-753	62	31	r.	r.	PROPN
ejpam-753	62	32	beyranvand	beyranvand	PROPN
ejpam-753	62	33	/	/	SYM
ejpam-753	62	34	eur	eur	PROPN
ejpam-753	62	35	.	.	PUNCT
ejpam-753	63	1	j.	j.	PROPN
ejpam-753	63	2	pure	pure	PROPN
ejpam-753	63	3	appl	appl	PROPN
ejpam-753	63	4	.	.	PROPN
ejpam-753	63	5	math	math	PROPN
ejpam-753	63	6	,	,	PUNCT
ejpam-753	63	7	3	3	NUM
ejpam-753	63	8	(	(	PUNCT
ejpam-753	63	9	2010	2010	NUM
ejpam-753	63	10	)	)	PUNCT
ejpam-753	63	11	,	,	PUNCT
ejpam-753	63	12	686	686	NUM
ejpam-753	63	13	-	-	SYM
ejpam-753	63	14	694	694	NUM
ejpam-753	63	15	688	688	NUM
ejpam-753	63	16	also	also	ADV
ejpam-753	63	17	we	we	PRON
ejpam-753	63	18	need	need	VERB
ejpam-753	63	19	the	the	DET
ejpam-753	63	20	following	follow	VERB
ejpam-753	63	21	construction	construction	NOUN
ejpam-753	63	22	[	[	X
ejpam-753	63	23	3	3	NUM
ejpam-753	63	24	,	,	PUNCT
ejpam-753	63	25	p.5071	p.5071	NOUN
ejpam-753	63	26	]	]	PUNCT
ejpam-753	63	27	.	.	PUNCT
ejpam-753	64	1	construction	construction	NOUN
ejpam-753	64	2	a.	a.	NOUN
ejpam-753	64	3	let	let	VERB
ejpam-753	64	4	r0	r0	NOUN
ejpam-753	64	5	be	be	AUX
ejpam-753	64	6	the	the	DET
ejpam-753	64	7	galois	galois	PROPN
ejpam-753	64	8	ring	ring	NOUN
ejpam-753	64	9	gr(p2r	gr(p2r	NUM
ejpam-753	64	10	,	,	PUNCT
ejpam-753	64	11	p2	p2	PROPN
ejpam-753	64	12	)	)	PUNCT
ejpam-753	64	13	or	or	CCONJ
ejpam-753	64	14	gr(p3r	gr(p3r	PROPN
ejpam-753	64	15	,	,	PUNCT
ejpam-753	64	16	p3	p3	PROPN
ejpam-753	64	17	)	)	PUNCT
ejpam-753	64	18	.	.	PUNCT
ejpam-753	65	1	let	let	VERB
ejpam-753	65	2	s	s	X
ejpam-753	65	3	,	,	PUNCT
ejpam-753	65	4	d	d	PROPN
ejpam-753	65	5	,	,	PUNCT
ejpam-753	65	6	t	t	PROPN
ejpam-753	65	7	,	,	PUNCT
ejpam-753	65	8	λ	λ	X
ejpam-753	65	9	be	be	AUX
ejpam-753	65	10	integers	integer	NOUN
ejpam-753	65	11	with	with	ADP
ejpam-753	65	12	either	either	CCONJ
ejpam-753	65	13	1≤	1≤	NUM
ejpam-753	65	14	t	t	PROPN
ejpam-753	65	15	≤	≤	PROPN
ejpam-753	65	16	s2	s2	PROPN
ejpam-753	65	17	,	,	PUNCT
ejpam-753	65	18	1≤	1≤	NUM
ejpam-753	65	19	1	1	NUM
ejpam-753	65	20	+	+	NUM
ejpam-753	65	21	t	t	NOUN
ejpam-753	65	22	≤	≤	NOUN
ejpam-753	65	23	s2	s2	NOUN
ejpam-753	65	24	or	or	CCONJ
ejpam-753	65	25	1≤	1≤	NUM
ejpam-753	65	26	d+	d+	NOUN
ejpam-753	65	27	t	t	PROPN
ejpam-753	65	28	≤	≤	NOUN
ejpam-753	65	29	s2	s2	PROPN
ejpam-753	65	30	if	if	SCONJ
ejpam-753	65	31	char(r0	char(r0	ADV
ejpam-753	65	32	)	)	PUNCT
ejpam-753	65	33	=	=	SYM
ejpam-753	65	34	p2	p2	PROPN
ejpam-753	65	35	or	or	CCONJ
ejpam-753	65	36	1≤	1≤	NUM
ejpam-753	65	37	1+d+	1+d+	NUM
ejpam-753	65	38	t	t	PROPN
ejpam-753	65	39	≤	≤	NOUN
ejpam-753	65	40	1+s2	1+s2	NUM
ejpam-753	65	41	if	if	SCONJ
ejpam-753	65	42	char(r0	char(r0	ADJ
ejpam-753	65	43	)	)	PUNCT
ejpam-753	65	44	=	=	SYM
ejpam-753	65	45	p3	p3	PROPN
ejpam-753	65	46	,	,	PUNCT
ejpam-753	65	47	and	and	CCONJ
ejpam-753	65	48	λ≥	λ≥	X
ejpam-753	65	49	0	0	NUM
ejpam-753	65	50	.	.	PUNCT
ejpam-753	66	1	let	let	VERB
ejpam-753	66	2	v	v	NOUN
ejpam-753	66	3	,	,	PUNCT
ejpam-753	66	4	w	w	NOUN
ejpam-753	66	5	be	be	AUX
ejpam-753	66	6	r0	r0	NOUN
ejpam-753	66	7	/	/	SYM
ejpam-753	66	8	pr0	pr0	NOUN
ejpam-753	66	9	-	-	PUNCT
ejpam-753	66	10	spaces	space	NOUN
ejpam-753	66	11	which	which	PRON
ejpam-753	66	12	when	when	SCONJ
ejpam-753	66	13	considered	consider	VERB
ejpam-753	66	14	as	as	ADP
ejpam-753	66	15	r0	r0	NOUN
ejpam-753	66	16	-	-	PUNCT
ejpam-753	66	17	modules	module	NOUN
ejpam-753	66	18	have	have	AUX
ejpam-753	66	19	generating	generate	VERB
ejpam-753	66	20	sets	set	NOUN
ejpam-753	66	21	{	{	PUNCT
ejpam-753	66	22	v1	v1	NOUN
ejpam-753	66	23	,	,	PUNCT
ejpam-753	66	24	.	.	PUNCT
ejpam-753	66	25	.	.	PUNCT
ejpam-753	67	1	.	.	PUNCT
ejpam-753	68	1	,	,	PUNCT
ejpam-753	68	2	vλ	vλ	X
ejpam-753	68	3	}	}	PUNCT
ejpam-753	68	4	and	and	CCONJ
ejpam-753	68	5	{	{	PUNCT
ejpam-753	68	6	w1	w1	NOUN
ejpam-753	68	7	,	,	PUNCT
ejpam-753	68	8	.	.	PUNCT
ejpam-753	68	9	.	.	PUNCT
ejpam-753	69	1	.	.	PUNCT
ejpam-753	70	1	,	,	PUNCT
ejpam-753	70	2	wt	wt	NOUN
ejpam-753	70	3	}	}	PUNCT
ejpam-753	70	4	respectively	respectively	ADV
ejpam-753	70	5	.	.	PUNCT
ejpam-753	71	1	let	let	VERB
ejpam-753	71	2	u	u	PRON
ejpam-753	71	3	be	be	AUX
ejpam-753	71	4	an	an	DET
ejpam-753	71	5	r0	r0	NOUN
ejpam-753	71	6	-	-	PUNCT
ejpam-753	71	7	module	module	NOUN
ejpam-753	71	8	with	with	ADP
ejpam-753	71	9	an	an	DET
ejpam-753	71	10	r0	r0	NOUN
ejpam-753	71	11	-	-	PUNCT
ejpam-753	71	12	modules	module	NOUN
ejpam-753	71	13	generating	generate	VERB
ejpam-753	71	14	set	set	NOUN
ejpam-753	71	15	{	{	PUNCT
ejpam-753	71	16	u1	u1	NOUN
ejpam-753	71	17	,	,	PUNCT
ejpam-753	71	18	.	.	PUNCT
ejpam-753	71	19	.	.	PUNCT
ejpam-753	72	1	.	.	PUNCT
ejpam-753	73	1	,	,	PUNCT
ejpam-753	73	2	us	we	PRON
ejpam-753	73	3	}	}	PUNCT
ejpam-753	73	4	;	;	PUNCT
ejpam-753	73	5	and	and	CCONJ
ejpam-753	73	6	suppose	suppose	VERB
ejpam-753	73	7	that	that	SCONJ
ejpam-753	73	8	d	d	PROPN
ejpam-753	73	9	≥	≥	NUM
ejpam-753	73	10	0	0	NUM
ejpam-753	73	11	of	of	ADP
ejpam-753	73	12	the	the	DET
ejpam-753	73	13	ui	ui	PROPN
ejpam-753	73	14	are	be	AUX
ejpam-753	73	15	such	such	ADJ
ejpam-753	73	16	that	that	SCONJ
ejpam-753	73	17	pui	pui	PROPN
ejpam-753	73	18	6=	6=	ADP
ejpam-753	73	19	0	0	NUM
ejpam-753	73	20	.	.	PUNCT
ejpam-753	74	1	since	since	SCONJ
ejpam-753	74	2	r0	r0	NOUN
ejpam-753	74	3	is	be	AUX
ejpam-753	74	4	commutative	commutative	ADJ
ejpam-753	74	5	,	,	PUNCT
ejpam-753	74	6	we	we	PRON
ejpam-753	74	7	can	can	AUX
ejpam-753	74	8	think	think	VERB
ejpam-753	74	9	of	of	ADP
ejpam-753	74	10	them	they	PRON
ejpam-753	74	11	as	as	SCONJ
ejpam-753	74	12	left	left	ADJ
ejpam-753	74	13	and	and	CCONJ
ejpam-753	74	14	right	right	ADJ
ejpam-753	74	15	r0	r0	NOUN
ejpam-753	74	16	-	-	PUNCT
ejpam-753	74	17	module	module	NOUN
ejpam-753	74	18	.	.	PUNCT
ejpam-753	75	1	let	let	VERB
ejpam-753	75	2	(	(	PUNCT
ejpam-753	75	3	al	al	PROPN
ejpam-753	75	4	i	i	PROPN
ejpam-753	75	5	j	j	PROPN
ejpam-753	75	6	)	)	PUNCT
ejpam-753	75	7	,	,	PUNCT
ejpam-753	75	8	for	for	ADP
ejpam-753	75	9	l	l	NOUN
ejpam-753	75	10	=	=	SYM
ejpam-753	75	11	0,1	0,1	NUM
ejpam-753	75	12	,	,	PUNCT
ejpam-753	75	13	.	.	PUNCT
ejpam-753	75	14	.	.	PUNCT
ejpam-753	76	1	.	.	PUNCT
ejpam-753	77	1	,	,	PUNCT
ejpam-753	77	2	t	t	PROPN
ejpam-753	77	3	,	,	PUNCT
ejpam-753	77	4	t	t	PROPN
ejpam-753	78	1	+	+	CCONJ
ejpam-753	78	2	1	1	NUM
ejpam-753	78	3	or	or	CCONJ
ejpam-753	78	4	d	d	PROPN
ejpam-753	78	5	+	+	PROPN
ejpam-753	78	6	t	t	PROPN
ejpam-753	78	7	,	,	PUNCT
ejpam-753	78	8	be	be	AUX
ejpam-753	78	9	s	s	PROPN
ejpam-753	78	10	×	×	NOUN
ejpam-753	78	11	s	s	NOUN
ejpam-753	78	12	matrices	matrix	NOUN
ejpam-753	78	13	with	with	ADP
ejpam-753	78	14	entries	entry	NOUN
ejpam-753	78	15	in	in	ADP
ejpam-753	78	16	r0	r0	NOUN
ejpam-753	78	17	/	/	SYM
ejpam-753	78	18	pr0	pr0	PROPN
ejpam-753	78	19	if	if	SCONJ
ejpam-753	78	20	char(r0	char(r0	ADV
ejpam-753	78	21	)	)	PUNCT
ejpam-753	78	22	=	=	SYM
ejpam-753	78	23	p2	p2	PROPN
ejpam-753	78	24	or	or	CCONJ
ejpam-753	78	25	l	l	NOUN
ejpam-753	78	26	=	=	SYM
ejpam-753	78	27	0,1	0,1	NUM
ejpam-753	78	28	,	,	PUNCT
ejpam-753	78	29	.	.	PUNCT
ejpam-753	78	30	.	.	PUNCT
ejpam-753	79	1	.	.	PUNCT
ejpam-753	80	1	,	,	PUNCT
ejpam-753	81	1	d	d	X
ejpam-753	81	2	+	+	NUM
ejpam-753	81	3	t	t	PROPN
ejpam-753	81	4	be	be	AUX
ejpam-753	81	5	(	(	PUNCT
ejpam-753	81	6	1	1	NUM
ejpam-753	81	7	+	+	NUM
ejpam-753	81	8	s	s	NOUN
ejpam-753	81	9	)	)	PUNCT
ejpam-753	81	10	×	×	NOUN
ejpam-753	81	11	(	(	PUNCT
ejpam-753	81	12	1	1	NUM
ejpam-753	81	13	+	+	NUM
ejpam-753	81	14	s	s	NOUN
ejpam-753	81	15	)	)	PUNCT
ejpam-753	81	16	matrices	matrix	NOUN
ejpam-753	81	17	with	with	ADP
ejpam-753	81	18	entries	entry	NOUN
ejpam-753	81	19	in	in	ADP
ejpam-753	81	20	r0	r0	NOUN
ejpam-753	81	21	/	/	SYM
ejpam-753	81	22	pr0	pr0	PROPN
ejpam-753	81	23	if	if	SCONJ
ejpam-753	81	24	char(r0	char(r0	ADV
ejpam-753	81	25	)	)	PUNCT
ejpam-753	81	26	=	=	SYM
ejpam-753	81	27	p3	p3	PROPN
ejpam-753	81	28	.	.	PUNCT
ejpam-753	82	1	consider	consider	VERB
ejpam-753	82	2	the	the	DET
ejpam-753	82	3	additive	additive	ADJ
ejpam-753	82	4	group	group	NOUN
ejpam-753	82	5	direct	direct	ADJ
ejpam-753	82	6	sum	sum	NOUN
ejpam-753	82	7	r=	r=	PROPN
ejpam-753	82	8	r0	r0	NOUN
ejpam-753	82	9	⊕	⊕	PROPN
ejpam-753	82	10	u	u	PROPN
ejpam-753	82	11	⊕	⊕	PROPN
ejpam-753	82	12	v	v	ADP
ejpam-753	82	13	⊕w	⊕w	NOUN
ejpam-753	82	14	and	and	CCONJ
ejpam-753	82	15	define	define	VERB
ejpam-753	82	16	a	a	DET
ejpam-753	82	17	multiplication	multiplication	NOUN
ejpam-753	82	18	on	on	ADP
ejpam-753	82	19	r	r	NOUN
ejpam-753	82	20	by	by	ADP
ejpam-753	82	21	(	(	PUNCT
ejpam-753	82	22	α0	α0	ADJ
ejpam-753	82	23	,	,	PUNCT
ejpam-753	82	24	∑s	∑s	ADJ
ejpam-753	82	25	i=1αiui	i=1αiui	NOUN
ejpam-753	82	26	,	,	PUNCT
ejpam-753	82	27	∑λ	∑λ	PROPN
ejpam-753	82	28	j=1	j=1	PROPN
ejpam-753	82	29	β	β	PROPN
ejpam-753	82	30	j	j	PROPN
ejpam-753	82	31	v	v	NUM
ejpam-753	82	32	j	j	PROPN
ejpam-753	82	33	,	,	PUNCT
ejpam-753	82	34	∑t	∑t	PROPN
ejpam-753	82	35	k=1	k=1	PUNCT
ejpam-753	83	1	γkwk).(α	γkwk).(α	ADV
ejpam-753	83	2	′	′	NUM
ejpam-753	83	3	0	0	NUM
ejpam-753	83	4	,	,	PUNCT
ejpam-753	83	5	∑s	∑s	PROPN
ejpam-753	83	6	i=1α	i=1α	PROPN
ejpam-753	83	7	′	′	NUM
ejpam-753	83	8	iui	iui	NOUN
ejpam-753	83	9	,	,	PUNCT
ejpam-753	84	1	∑λ	∑λ	ADP
ejpam-753	84	2	j=1	j=1	NOUN
ejpam-753	84	3	β	β	X
ejpam-753	84	4	′	′	NUM
ejpam-753	85	1	j	j	PROPN
ejpam-753	85	2	v	v	NUM
ejpam-753	85	3	j	j	PROPN
ejpam-753	85	4	,	,	PUNCT
ejpam-753	85	5	∑t	∑t	PROPN
ejpam-753	85	6	k=1γ	k=1γ	PROPN
ejpam-753	86	1	′	′	NUM
ejpam-753	86	2	k	k	PROPN
ejpam-753	87	1	wk	wk	PROPN
ejpam-753	87	2	)	)	PUNCT
ejpam-753	87	3	=	=	SYM
ejpam-753	87	4	(	(	PUNCT
ejpam-753	87	5	α0α	α0α	NUM
ejpam-753	87	6	′	′	NUM
ejpam-753	87	7	0+p	0+p	NUM
ejpam-753	88	1	f	f	NOUN
ejpam-753	88	2	∑s	∑s	PROPN
ejpam-753	88	3	i	i	PRON
ejpam-753	88	4	,	,	PUNCT
ejpam-753	88	5	j=1	j=1	PROPN
ejpam-753	88	6	a0	a0	PROPN
ejpam-753	89	1	i	i	PRON
ejpam-753	89	2	j	j	PROPN
ejpam-753	90	1	[	[	X
ejpam-753	90	2	αiα	αiα	NOUN
ejpam-753	90	3	′	′	NUM
ejpam-753	90	4	j	j	PROPN
ejpam-753	91	1	+	+	NOUN
ejpam-753	91	2	pr0	pr0	PROPN
ejpam-753	91	3	]	]	X
ejpam-753	91	4	,	,	PUNCT
ejpam-753	91	5	∑s	∑s	PROPN
ejpam-753	91	6	i=1[α0α	i=1[α0α	VERB
ejpam-753	92	1	′	′	NUM
ejpam-753	92	2	i	i	PRON
ejpam-753	93	1	+	+	NOUN
ejpam-753	93	2	αiα	αiα	VERB
ejpam-753	94	1	′	′	NOUN
ejpam-753	94	2	0+p	0+p	NUM
ejpam-753	95	1	∑s	∑s	PROPN
ejpam-753	95	2	i	i	PRON
ejpam-753	95	3	,	,	PUNCT
ejpam-753	95	4	j=1	j=1	PROPN
ejpam-753	95	5	ai	ai	VERB
ejpam-753	95	6	i	i	PRON
ejpam-753	95	7	j	j	PROPN
ejpam-753	96	1	[	[	X
ejpam-753	96	2	αiα	αiα	NOUN
ejpam-753	96	3	′	′	NUM
ejpam-753	96	4	j	j	NOUN
ejpam-753	97	1	+	+	PUNCT
ejpam-753	97	2	pr0]]ui	pr0]]ui	NOUN
ejpam-753	97	3	,	,	PUNCT
ejpam-753	97	4	∑λ	∑λ	PROPN
ejpam-753	97	5	j=1[(α0	j=1[(α0	PROPN
ejpam-753	97	6	+	+	PUNCT
ejpam-753	97	7	pr0)β	pr0)β	NUM
ejpam-753	97	8	′	′	NUM
ejpam-753	97	9	j	j	PROPN
ejpam-753	98	1	+	+	NOUN
ejpam-753	98	2	β	β	X
ejpam-753	98	3	j(α	j(α	PROPN
ejpam-753	98	4	′	′	NOUN
ejpam-753	98	5	0	0	NUM
ejpam-753	99	1	+	+	NUM
ejpam-753	99	2	pr0)]v	pr0)]v	NOUN
ejpam-753	99	3	j	j	PROPN
ejpam-753	99	4	,	,	PUNCT
ejpam-753	99	5	∑t	∑t	PROPN
ejpam-753	99	6	k=1[(α0	k=1[(α0	PROPN
ejpam-753	99	7	+	+	PROPN
ejpam-753	99	8	pr0)γ	pr0)γ	PROPN
ejpam-753	99	9	′	′	NUM
ejpam-753	100	1	k	k	PUNCT
ejpam-753	101	1	+	+	NOUN
ejpam-753	101	2	γk(α	γk(α	NUM
ejpam-753	101	3	′	′	NUM
ejpam-753	101	4	0	0	PUNCT
ejpam-753	102	1	+	+	CCONJ
ejpam-753	102	2	pr0)+	pr0)+	NOUN
ejpam-753	102	3	∑s	∑s	PROPN
ejpam-753	103	1	i	i	PRON
ejpam-753	103	2	,	,	PUNCT
ejpam-753	103	3	j=1	j=1	PROPN
ejpam-753	103	4	ad+k	ad+k	VERB
ejpam-753	104	1	i	i	PRON
ejpam-753	104	2	j	j	X
ejpam-753	105	1	[	[	X
ejpam-753	105	2	αiα	αiα	NOUN
ejpam-753	105	3	′	′	NUM
ejpam-753	105	4	j	j	PROPN
ejpam-753	105	5	+	+	CCONJ
ejpam-753	105	6	pr0]]wk	pr0]]wk	NOUN
ejpam-753	105	7	)	)	PUNCT
ejpam-753	106	1	where	where	SCONJ
ejpam-753	106	2	f	f	PROPN
ejpam-753	106	3	=	=	SYM
ejpam-753	106	4	1	1	NUM
ejpam-753	106	5	or	or	CCONJ
ejpam-753	106	6	2	2	NUM
ejpam-753	106	7	,	,	PUNCT
ejpam-753	106	8	depending	depend	VERB
ejpam-753	106	9	on	on	ADP
ejpam-753	106	10	whether	whether	SCONJ
ejpam-753	106	11	char(r	char(r	NOUN
ejpam-753	106	12	)	)	PUNCT
ejpam-753	106	13	=	=	NOUN
ejpam-753	106	14	p2	p2	PROPN
ejpam-753	106	15	or	or	CCONJ
ejpam-753	106	16	p3	p3	PROPN
ejpam-753	106	17	.	.	PUNCT
ejpam-753	106	18	then	then	ADV
ejpam-753	106	19	by	by	ADP
ejpam-753	106	20	[	[	X
ejpam-753	106	21	3	3	NUM
ejpam-753	106	22	,	,	PUNCT
ejpam-753	106	23	theorem	theorem	VERB
ejpam-753	106	24	6.1	6.1	NUM
ejpam-753	106	25	]	]	PUNCT
ejpam-753	106	26	,	,	PUNCT
ejpam-753	106	27	this	this	DET
ejpam-753	106	28	multiplication	multiplication	NOUN
ejpam-753	106	29	turns	turn	VERB
ejpam-753	106	30	r	r	NOUN
ejpam-753	106	31	into	into	ADP
ejpam-753	106	32	a	a	DET
ejpam-753	106	33	ring	ring	NOUN
ejpam-753	106	34	and	and	CCONJ
ejpam-753	106	35	any	any	DET
ejpam-753	106	36	local	local	ADJ
ejpam-753	106	37	ring	ring	NOUN
ejpam-753	106	38	with	with	ADP
ejpam-753	106	39	z(r)3	z(r)3	PROPN
ejpam-753	106	40	=	=	SYM
ejpam-753	106	41	0	0	NUM
ejpam-753	106	42	,	,	PUNCT
ejpam-753	106	43	z(r)2	z(r)2	X
ejpam-753	107	1	6=	6=	PRON
ejpam-753	107	2	0	0	NUM
ejpam-753	107	3	of	of	ADP
ejpam-753	107	4	characteristic	characteristic	ADJ
ejpam-753	107	5	p2	p2	NOUN
ejpam-753	107	6	or	or	CCONJ
ejpam-753	107	7	p3	p3	NOUN
ejpam-753	107	8	,	,	PUNCT
ejpam-753	107	9	is	be	AUX
ejpam-753	107	10	isomorphic	isomorphic	ADJ
ejpam-753	107	11	to	to	ADP
ejpam-753	107	12	one	one	NUM
ejpam-753	107	13	given	give	VERB
ejpam-753	107	14	by	by	ADP
ejpam-753	107	15	construction	construction	NOUN
ejpam-753	107	16	a.	a.	NOUN
ejpam-753	107	17	proposition	proposition	NOUN
ejpam-753	107	18	1	1	NUM
ejpam-753	107	19	.	.	PUNCT
ejpam-753	108	1	let	let	VERB
ejpam-753	108	2	r	r	PRON
ejpam-753	108	3	be	be	AUX
ejpam-753	108	4	a	a	DET
ejpam-753	108	5	commutative	commutative	ADJ
ejpam-753	108	6	ring	ring	NOUN
ejpam-753	108	7	with	with	ADP
ejpam-753	108	8	|z(r)|	|z(r)|	PROPN
ejpam-753	108	9	=	=	PUNCT
ejpam-753	108	10	p4	p4	ADJ
ejpam-753	108	11	and	and	CCONJ
ejpam-753	108	12	|r|	|r|	NOUN
ejpam-753	109	1	=	=	NOUN
ejpam-753	109	2	p6	p6	ADJ
ejpam-753	109	3	where	where	SCONJ
ejpam-753	109	4	p	p	NOUN
ejpam-753	109	5	is	be	AUX
ejpam-753	109	6	a	a	DET
ejpam-753	109	7	prime	prime	ADJ
ejpam-753	109	8	number	number	NOUN
ejpam-753	109	9	.	.	PUNCT
ejpam-753	110	1	then	then	ADV
ejpam-753	110	2	r	r	NOUN
ejpam-753	110	3	is	be	AUX
ejpam-753	110	4	isomorphic	isomorphic	ADJ
ejpam-753	110	5	to	to	ADP
ejpam-753	110	6	one	one	NUM
ejpam-753	110	7	of	of	ADP
ejpam-753	110	8	the	the	DET
ejpam-753	110	9	rings	ring	NOUN
ejpam-753	110	10	gr(p6	gr(p6	NOUN
ejpam-753	110	11	,	,	PUNCT
ejpam-753	110	12	p3	p3	PROPN
ejpam-753	110	13	)	)	PUNCT
ejpam-753	110	14	,	,	PUNCT
ejpam-753	110	15	fp2	fp2	PROPN
ejpam-753	110	16	⊕	⊕	PROPN
ejpam-753	110	17	fp2	fp2	PROPN
ejpam-753	110	18	⊕	⊕	PROPN
ejpam-753	110	19	fp2	fp2	PROPN
ejpam-753	110	20	with	with	ADP
ejpam-753	110	21	multiplication	multiplication	NOUN
ejpam-753	110	22	(	(	PUNCT
ejpam-753	110	23	r0	r0	NOUN
ejpam-753	110	24	,	,	PUNCT
ejpam-753	110	25	r1	r1	PROPN
ejpam-753	110	26	,	,	PUNCT
ejpam-753	110	27	r2)(s0	r2)(s0	PROPN
ejpam-753	110	28	,	,	PUNCT
ejpam-753	110	29	s1	s1	PROPN
ejpam-753	110	30	,	,	PUNCT
ejpam-753	110	31	s2	s2	PROPN
ejpam-753	110	32	)	)	PUNCT
ejpam-753	110	33	=	=	PRON
ejpam-753	111	1	(	(	PUNCT
ejpam-753	111	2	r0s0	r0s0	ADJ
ejpam-753	111	3	,	,	PUNCT
ejpam-753	111	4	r0s1	r0s1	X
ejpam-753	111	5	+	+	CCONJ
ejpam-753	111	6	r1s0	r1s0	ADJ
ejpam-753	111	7	,	,	PUNCT
ejpam-753	111	8	r0s2	r0s2	VERB
ejpam-753	111	9	+	+	CCONJ
ejpam-753	111	10	r2s0),s	r2s0),s	PUNCT
ejpam-753	111	11	⊕	⊕	PROPN
ejpam-753	111	12	f	f	PROPN
ejpam-753	111	13	with	with	ADP
ejpam-753	111	14	multiplication	multiplication	NOUN
ejpam-753	111	15	(	(	PUNCT
ejpam-753	111	16	r0	r0	NOUN
ejpam-753	111	17	,	,	PUNCT
ejpam-753	111	18	r1)(s0	r1)(s0	PROPN
ejpam-753	111	19	,	,	PUNCT
ejpam-753	111	20	s1	s1	NOUN
ejpam-753	111	21	)	)	PUNCT
ejpam-753	112	1	=	=	SYM
ejpam-753	112	2	(	(	PUNCT
ejpam-753	112	3	r0s0	r0s0	ADJ
ejpam-753	112	4	,	,	PUNCT
ejpam-753	112	5	r0s1	r0s1	X
ejpam-753	112	6	+	+	CCONJ
ejpam-753	112	7	r1s0	r1s0	X
ejpam-753	112	8	)	)	PUNCT
ejpam-753	112	9	,	,	PUNCT
ejpam-753	112	10	where	where	SCONJ
ejpam-753	112	11	s	s	NOUN
ejpam-753	112	12	=	=	NOUN
ejpam-753	112	13	gr(p4	gr(p4	NOUN
ejpam-753	112	14	,	,	PUNCT
ejpam-753	112	15	p2	p2	PROPN
ejpam-753	112	16	)	)	PUNCT
ejpam-753	112	17	and	and	CCONJ
ejpam-753	112	18	f	f	X
ejpam-753	112	19	=	=	SYM
ejpam-753	112	20	s	s	PROPN
ejpam-753	112	21	/	/	SYM
ejpam-753	112	22	ps	ps	PROPN
ejpam-753	112	23	,	,	PUNCT
ejpam-753	112	24	fp2	fp2	PROPN
ejpam-753	112	25	⊕	⊕	PROPN
ejpam-753	112	26	fp2	fp2	PROPN
ejpam-753	112	27	⊕	⊕	PROPN
ejpam-753	112	28	fp2	fp2	PROPN
ejpam-753	112	29	with	with	ADP
ejpam-753	112	30	multiplication	multiplication	NOUN
ejpam-753	112	31	(	(	PUNCT
ejpam-753	112	32	α0,α	α0,α	PROPN
ejpam-753	112	33	,	,	PUNCT
ejpam-753	112	34	γ)(α′0,α′,γ′	γ)(α′0,α′,γ′	NOUN
ejpam-753	112	35	)	)	PUNCT
ejpam-753	112	36	=	=	PUNCT
ejpam-753	112	37	(	(	PUNCT
ejpam-753	112	38	α0α	α0α	NUM
ejpam-753	112	39	′	′	NUM
ejpam-753	112	40	0,α0α	0,α0α	NUM
ejpam-753	112	41	′+αα′0,α0γ	′+αα′0,α0γ	PROPN
ejpam-753	112	42	′+γα′0+αα	′+γα′0+αα	PROPN
ejpam-753	112	43	′	′	NOUN
ejpam-753	112	44	)	)	PUNCT
ejpam-753	112	45	or	or	CCONJ
ejpam-753	112	46	r0⊕r0	r0⊕r0	NOUN
ejpam-753	112	47	/	/	SYM
ejpam-753	112	48	pr0	pr0	NOUN
ejpam-753	112	49	with	with	ADP
ejpam-753	112	50	multiplication	multiplication	NOUN
ejpam-753	112	51	(	(	PUNCT
ejpam-753	112	52	α0,α+	α0,α+	NOUN
ejpam-753	112	53	pr0)(α	pr0)(α	NOUN
ejpam-753	112	54	′	′	NOUN
ejpam-753	112	55	0,α′	0,α′	NOUN
ejpam-753	113	1	+	+	CCONJ
ejpam-753	113	2	pr0	pr0	NOUN
ejpam-753	113	3	)	)	PUNCT
ejpam-753	113	4	=	=	PUNCT
ejpam-753	113	5	(	(	PUNCT
ejpam-753	113	6	α0α	α0α	NUM
ejpam-753	113	7	′	′	NUM
ejpam-753	113	8	0	0	PUNCT
ejpam-753	114	1	+	+	ADV
ejpam-753	114	2	αα	αα	ADP
ejpam-753	114	3	′p	′p	ADJ
ejpam-753	114	4	,	,	PUNCT
ejpam-753	114	5	α0α	α0α	NUM
ejpam-753	114	6	′	′	NUM
ejpam-753	115	1	+	+	NUM
ejpam-753	115	2	αα′0	αα′0	NOUN
ejpam-753	115	3	+	+	CCONJ
ejpam-753	115	4	pr0	pr0	PROPN
ejpam-753	115	5	)	)	PUNCT
ejpam-753	115	6	where	where	SCONJ
ejpam-753	115	7	r0	r0	NOUN
ejpam-753	115	8	=	=	NOUN
ejpam-753	115	9	gr(p4	gr(p4	NOUN
ejpam-753	115	10	,	,	PUNCT
ejpam-753	115	11	p2	p2	PROPN
ejpam-753	115	12	)	)	PUNCT
ejpam-753	115	13	.	.	PUNCT
ejpam-753	116	1	proof	proof	NOUN
ejpam-753	116	2	.	.	PUNCT
ejpam-753	117	1	since	since	SCONJ
ejpam-753	117	2	r	r	NOUN
ejpam-753	117	3	is	be	AUX
ejpam-753	117	4	a	a	DET
ejpam-753	117	5	ring	ring	NOUN
ejpam-753	117	6	with	with	ADP
ejpam-753	117	7	|z(r)|	|z(r)|	PROPN
ejpam-753	117	8	=	=	PUNCT
ejpam-753	117	9	p4	p4	ADJ
ejpam-753	117	10	and	and	CCONJ
ejpam-753	117	11	|r|	|r|	NOUN
ejpam-753	117	12	=	=	PUNCT
ejpam-753	117	13	p6	p6	PROPN
ejpam-753	117	14	,	,	PUNCT
ejpam-753	117	15	by	by	ADP
ejpam-753	117	16	lemma	lemma	PROPN
ejpam-753	117	17	1	1	NUM
ejpam-753	117	18	,	,	PUNCT
ejpam-753	117	19	z(r)3	z(r)3	NOUN
ejpam-753	117	20	=	=	SYM
ejpam-753	117	21	0	0	X
ejpam-753	117	22	.	.	PUNCT
ejpam-753	118	1	thus	thus	ADV
ejpam-753	118	2	we	we	PRON
ejpam-753	118	3	consider	consider	VERB
ejpam-753	118	4	the	the	DET
ejpam-753	118	5	following	follow	VERB
ejpam-753	118	6	cases	case	NOUN
ejpam-753	118	7	.	.	PUNCT
ejpam-753	119	1	case	case	NOUN
ejpam-753	119	2	1	1	NUM
ejpam-753	119	3	:	:	PUNCT
ejpam-753	119	4	z(r)2	z(r)2	NOUN
ejpam-753	120	1	=	=	SYM
ejpam-753	120	2	0	0	PUNCT
ejpam-753	120	3	i.e.	i.e.	X
ejpam-753	120	4	,	,	PUNCT
ejpam-753	120	5	r	r	NOUN
ejpam-753	120	6	is	be	AUX
ejpam-753	120	7	a	a	DET
ejpam-753	120	8	ring	ring	NOUN
ejpam-753	120	9	in	in	ADP
ejpam-753	120	10	which	which	PRON
ejpam-753	120	11	the	the	DET
ejpam-753	120	12	multiplication	multiplication	NOUN
ejpam-753	120	13	of	of	ADP
ejpam-753	120	14	any	any	DET
ejpam-753	120	15	two	two	NUM
ejpam-753	120	16	zero	zero	NUM
ejpam-753	120	17	-	-	PUNCT
ejpam-753	120	18	divisors	divisor	NOUN
ejpam-753	120	19	is	be	AUX
ejpam-753	120	20	zero	zero	NUM
ejpam-753	120	21	.	.	PUNCT
ejpam-753	121	1	then	then	ADV
ejpam-753	121	2	by	by	ADP
ejpam-753	121	3	[	[	X
ejpam-753	121	4	1	1	NUM
ejpam-753	121	5	,	,	PUNCT
ejpam-753	121	6	theorem	theorem	VERB
ejpam-753	121	7	1	1	NUM
ejpam-753	121	8	]	]	PUNCT
ejpam-753	121	9	,	,	PUNCT
ejpam-753	121	10	r	r	NOUN
ejpam-753	121	11	is	be	AUX
ejpam-753	121	12	isomorphic	isomorphic	ADJ
ejpam-753	121	13	to	to	ADP
ejpam-753	121	14	one	one	NUM
ejpam-753	121	15	of	of	ADP
ejpam-753	121	16	the	the	DET
ejpam-753	121	17	rings	ring	NOUN
ejpam-753	121	18	s⊕f	s⊕f	PROPN
ejpam-753	122	1	k	k	NOUN
ejpam-753	122	2	,	,	PUNCT
ejpam-753	122	3	where	where	SCONJ
ejpam-753	122	4	s	s	NOUN
ejpam-753	122	5	is	be	AUX
ejpam-753	122	6	either	either	CCONJ
ejpam-753	122	7	the	the	DET
ejpam-753	122	8	field	field	NOUN
ejpam-753	122	9	of	of	ADP
ejpam-753	122	10	pr	pr	NOUN
ejpam-753	122	11	elements	element	NOUN
ejpam-753	122	12	or	or	CCONJ
ejpam-753	122	13	the	the	DET
ejpam-753	122	14	galois	galois	PROPN
ejpam-753	122	15	ring	ring	NOUN
ejpam-753	122	16	gr(p2r	gr(p2r	NUM
ejpam-753	122	17	,	,	PUNCT
ejpam-753	122	18	p2	p2	PROPN
ejpam-753	122	19	)	)	PUNCT
ejpam-753	122	20	and	and	CCONJ
ejpam-753	122	21	f	f	X
ejpam-753	122	22	=	=	SYM
ejpam-753	122	23	s	s	X
ejpam-753	122	24	/	/	SYM
ejpam-753	122	25	ps	ps	NOUN
ejpam-753	122	26	with	with	ADP
ejpam-753	122	27	the	the	DET
ejpam-753	122	28	multiplication	multiplication	NOUN
ejpam-753	122	29	(	(	PUNCT
ejpam-753	122	30	r0	r0	NOUN
ejpam-753	122	31	,	,	PUNCT
ejpam-753	122	32	r1	r1	NOUN
ejpam-753	122	33	,	,	PUNCT
ejpam-753	122	34	.	.	PUNCT
ejpam-753	122	35	.	.	PUNCT
ejpam-753	122	36	.	.	PUNCT
ejpam-753	123	1	,	,	PUNCT
ejpam-753	123	2	rk)(s0	rk)(s0	VERB
ejpam-753	123	3	,	,	PUNCT
ejpam-753	123	4	s1	s1	NOUN
ejpam-753	123	5	,	,	PUNCT
ejpam-753	123	6	.	.	PUNCT
ejpam-753	123	7	.	.	PUNCT
ejpam-753	124	1	.	.	PUNCT
ejpam-753	125	1	,	,	PUNCT
ejpam-753	125	2	sk	sk	PROPN
ejpam-753	125	3	)	)	PUNCT
ejpam-753	125	4	=	=	SYM
ejpam-753	125	5	(	(	PUNCT
ejpam-753	125	6	r0s0	r0s0	ADJ
ejpam-753	125	7	,	,	PUNCT
ejpam-753	125	8	r0s1	r0s1	X
ejpam-753	125	9	+	+	CCONJ
ejpam-753	125	10	r1s0	r1s0	X
ejpam-753	125	11	,	,	PUNCT
ejpam-753	125	12	.	.	PUNCT
ejpam-753	125	13	.	.	PUNCT
ejpam-753	126	1	.	.	PUNCT
ejpam-753	127	1	,	,	PUNCT
ejpam-753	127	2	r0sk	r0sk	NOUN
ejpam-753	127	3	+	+	CCONJ
ejpam-753	127	4	rks0	rks0	NOUN
ejpam-753	127	5	)	)	PUNCT
ejpam-753	127	6	for	for	ADP
ejpam-753	127	7	some	some	DET
ejpam-753	127	8	positive	positive	ADJ
ejpam-753	127	9	integers	integer	NOUN
ejpam-753	127	10	r	r	NOUN
ejpam-753	127	11	and	and	CCONJ
ejpam-753	127	12	k.	k.	PROPN
ejpam-753	128	1	now	now	ADV
ejpam-753	128	2	since	since	SCONJ
ejpam-753	128	3	|z(r)|	|z(r)|	PROPN
ejpam-753	128	4	=	=	PUNCT
ejpam-753	128	5	p4	p4	ADJ
ejpam-753	128	6	and	and	CCONJ
ejpam-753	128	7	|r|	|r|	NOUN
ejpam-753	128	8	=	=	PUNCT
ejpam-753	128	9	p6	p6	PROPN
ejpam-753	128	10	,	,	PUNCT
ejpam-753	128	11	we	we	PRON
ejpam-753	128	12	can	can	AUX
ejpam-753	128	13	conclude	conclude	VERB
ejpam-753	128	14	that	that	DET
ejpam-753	128	15	s	s	VERB
ejpam-753	128	16	=	=	SYM
ejpam-753	128	17	fp2	fp2	PROPN
ejpam-753	128	18	and	and	CCONJ
ejpam-753	128	19	k	k	PROPN
ejpam-753	128	20	=	=	SYM
ejpam-753	128	21	2	2	NUM
ejpam-753	128	22	or	or	CCONJ
ejpam-753	128	23	s	s	NOUN
ejpam-753	128	24	=	=	NOUN
ejpam-753	128	25	gr(p4	gr(p4	NOUN
ejpam-753	128	26	,	,	PUNCT
ejpam-753	128	27	p2	p2	PROPN
ejpam-753	128	28	)	)	PUNCT
ejpam-753	128	29	and	and	CCONJ
ejpam-753	128	30	k	k	NOUN
ejpam-753	128	31	=	=	SYM
ejpam-753	128	32	1	1	X
ejpam-753	128	33	.	.	PUNCT
ejpam-753	129	1	thus	thus	ADV
ejpam-753	129	2	r	r	NOUN
ejpam-753	129	3	is	be	AUX
ejpam-753	129	4	isomorphic	isomorphic	ADJ
ejpam-753	129	5	to	to	ADP
ejpam-753	129	6	one	one	NUM
ejpam-753	129	7	of	of	ADP
ejpam-753	129	8	the	the	DET
ejpam-753	129	9	rings	ring	NOUN
ejpam-753	129	10	fp2	fp2	PROPN
ejpam-753	129	11	⊕	⊕	PROPN
ejpam-753	129	12	fp2	fp2	PROPN
ejpam-753	129	13	⊕	⊕	PROPN
ejpam-753	129	14	fp2	fp2	PROPN
ejpam-753	129	15	with	with	ADP
ejpam-753	129	16	(	(	PUNCT
ejpam-753	129	17	r0	r0	NOUN
ejpam-753	129	18	,	,	PUNCT
ejpam-753	129	19	r1	r1	PROPN
ejpam-753	129	20	,	,	PUNCT
ejpam-753	129	21	r2)(s0	r2)(s0	PROPN
ejpam-753	129	22	,	,	PUNCT
ejpam-753	129	23	s1	s1	PROPN
ejpam-753	129	24	,	,	PUNCT
ejpam-753	129	25	s2	s2	PROPN
ejpam-753	129	26	)	)	PUNCT
ejpam-753	129	27	=	=	PRON
ejpam-753	129	28	(	(	PUNCT
ejpam-753	129	29	r0s0	r0s0	ADJ
ejpam-753	129	30	,	,	PUNCT
ejpam-753	129	31	r0s1	r0s1	X
ejpam-753	129	32	+	+	CCONJ
ejpam-753	129	33	r1s0	r1s0	ADJ
ejpam-753	129	34	,	,	PUNCT
ejpam-753	129	35	r0s2	r0s2	VERB
ejpam-753	129	36	+	+	CCONJ
ejpam-753	129	37	r2s0	r2s0	NOUN
ejpam-753	129	38	)	)	PUNCT
ejpam-753	129	39	or	or	CCONJ
ejpam-753	129	40	s	s	PROPN
ejpam-753	129	41	⊕	⊕	PROPN
ejpam-753	129	42	f	f	PROPN
ejpam-753	129	43	with	with	ADP
ejpam-753	129	44	(	(	PUNCT
ejpam-753	129	45	r0	r0	NOUN
ejpam-753	129	46	,	,	PUNCT
ejpam-753	129	47	r1)(s0	r1)(s0	PROPN
ejpam-753	129	48	,	,	PUNCT
ejpam-753	129	49	s1	s1	NOUN
ejpam-753	129	50	)	)	PUNCT
ejpam-753	129	51	=	=	SYM
ejpam-753	129	52	(	(	PUNCT
ejpam-753	129	53	r0s0	r0s0	ADJ
ejpam-753	129	54	,	,	PUNCT
ejpam-753	129	55	r0s1	r0s1	X
ejpam-753	129	56	+	+	CCONJ
ejpam-753	129	57	r1s0	r1s0	X
ejpam-753	129	58	)	)	PUNCT
ejpam-753	129	59	,	,	PUNCT
ejpam-753	129	60	where	where	SCONJ
ejpam-753	129	61	s	s	NOUN
ejpam-753	129	62	=	=	NOUN
ejpam-753	129	63	gr(p4	gr(p4	NOUN
ejpam-753	129	64	,	,	PUNCT
ejpam-753	129	65	p2	p2	PROPN
ejpam-753	129	66	)	)	PUNCT
ejpam-753	129	67	and	and	CCONJ
ejpam-753	129	68	f	f	X
ejpam-753	129	69	=	=	SYM
ejpam-753	129	70	s	s	PROPN
ejpam-753	129	71	/	/	SYM
ejpam-753	129	72	ps	ps	NOUN
ejpam-753	129	73	.	.	NOUN
ejpam-753	129	74	case	case	NOUN
ejpam-753	129	75	2	2	NUM
ejpam-753	129	76	:	:	PUNCT
ejpam-753	129	77	z(r)2	z(r)2	NOUN
ejpam-753	129	78	6=	6=	PRON
ejpam-753	129	79	0	0	X
ejpam-753	129	80	.	.	PUNCT
ejpam-753	130	1	if	if	SCONJ
ejpam-753	130	2	char(r	char(r	NOUN
ejpam-753	130	3	)	)	PUNCT
ejpam-753	131	1	=	=	SYM
ejpam-753	131	2	p	p	NOUN
ejpam-753	131	3	,	,	PUNCT
ejpam-753	131	4	then	then	ADV
ejpam-753	131	5	by	by	ADP
ejpam-753	131	6	[	[	PUNCT
ejpam-753	131	7	3	3	NUM
ejpam-753	131	8	,	,	PUNCT
ejpam-753	131	9	theorem	theorem	VERB
ejpam-753	131	10	4.1	4.1	NUM
ejpam-753	131	11	]	]	PUNCT
ejpam-753	131	12	,	,	PUNCT
ejpam-753	131	13	any	any	DET
ejpam-753	131	14	commutative	commutative	ADJ
ejpam-753	131	15	local	local	ADJ
ejpam-753	131	16	ring	ring	NOUN
ejpam-753	131	17	of	of	ADP
ejpam-753	131	18	characteristic	characteristic	ADJ
ejpam-753	131	19	p	p	NOUN
ejpam-753	131	20	in	in	ADP
ejpam-753	131	21	which	which	PRON
ejpam-753	131	22	the	the	DET
ejpam-753	131	23	multiplication	multiplication	NOUN
ejpam-753	131	24	of	of	ADP
ejpam-753	131	25	any	any	DET
ejpam-753	131	26	two	two	NUM
ejpam-753	131	27	zero	zero	NUM
ejpam-753	131	28	-	-	PUNCT
ejpam-753	131	29	divisors	divisor	NOUN
ejpam-753	131	30	is	be	AUX
ejpam-753	131	31	zero	zero	NUM
ejpam-753	131	32	,	,	PUNCT
ejpam-753	131	33	is	be	AUX
ejpam-753	131	34	isomorm	isomorm	NOUN
ejpam-753	131	35	.	.	PUNCT
ejpam-753	132	1	behboodi	behboodi	PROPN
ejpam-753	132	2	,	,	PUNCT
ejpam-753	132	3	r.	r.	PROPN
ejpam-753	132	4	beyranvand	beyranvand	PROPN
ejpam-753	132	5	/	/	SYM
ejpam-753	132	6	eur	eur	PROPN
ejpam-753	132	7	.	.	PUNCT
ejpam-753	133	1	j.	j.	PROPN
ejpam-753	133	2	pure	pure	PROPN
ejpam-753	133	3	appl	appl	PROPN
ejpam-753	133	4	.	.	PROPN
ejpam-753	133	5	math	math	PROPN
ejpam-753	133	6	,	,	PUNCT
ejpam-753	133	7	3	3	NUM
ejpam-753	133	8	(	(	PUNCT
ejpam-753	133	9	2010	2010	NUM
ejpam-753	133	10	)	)	PUNCT
ejpam-753	133	11	,	,	PUNCT
ejpam-753	133	12	686	686	NUM
ejpam-753	133	13	-	-	SYM
ejpam-753	133	14	694	694	NUM
ejpam-753	133	15	689	689	NUM
ejpam-753	133	16	phic	phic	NOUN
ejpam-753	133	17	to	to	ADP
ejpam-753	133	18	one	one	NUM
ejpam-753	133	19	of	of	ADP
ejpam-753	133	20	the	the	DET
ejpam-753	133	21	rings	ring	NOUN
ejpam-753	133	22	f	f	PROPN
ejpam-753	133	23	⊕	⊕	PROPN
ejpam-753	133	24	u	u	PROPN
ejpam-753	133	25	⊕	⊕	PROPN
ejpam-753	133	26	v	v	ADP
ejpam-753	133	27	⊕w	⊕w	NOUN
ejpam-753	133	28	with	with	ADP
ejpam-753	133	29	multiplication	multiplication	NOUN
ejpam-753	133	30	(	(	PUNCT
ejpam-753	133	31	α0	α0	ADJ
ejpam-753	133	32	,	,	PUNCT
ejpam-753	133	33	s∑	s∑	PROPN
ejpam-753	133	34	i=1	i=1	PROPN
ejpam-753	133	35	αiui	αiui	VERB
ejpam-753	133	36	,	,	PUNCT
ejpam-753	133	37	λ∑	λ∑	X
ejpam-753	133	38	j=1	j=1	NOUN
ejpam-753	133	39	β	β	PROPN
ejpam-753	133	40	j	j	PROPN
ejpam-753	133	41	v	v	NUM
ejpam-753	133	42	j	j	PROPN
ejpam-753	133	43	,	,	PUNCT
ejpam-753	133	44	t∑	t∑	PUNCT
ejpam-753	133	45	k=1	k=1	PROPN
ejpam-753	133	46	γkwk)(α	γkwk)(α	NOUN
ejpam-753	134	1	′	′	NUM
ejpam-753	134	2	0	0	NUM
ejpam-753	134	3	,	,	PUNCT
ejpam-753	134	4	s∑	s∑	PROPN
ejpam-753	134	5	i=1	i=1	PROPN
ejpam-753	134	6	α′iui	α′iui	PROPN
ejpam-753	134	7	,	,	PUNCT
ejpam-753	135	1	λ∑	λ∑	PROPN
ejpam-753	136	1	j=1	j=1	NOUN
ejpam-753	136	2	β	β	X
ejpam-753	136	3	′j	′j	NOUN
ejpam-753	136	4	v	v	ADP
ejpam-753	136	5	j	j	PROPN
ejpam-753	136	6	,	,	PUNCT
ejpam-753	136	7	t∑	t∑	X
ejpam-753	136	8	k=1	k=1	X
ejpam-753	136	9	γ′kwk	γ′kwk	PROPN
ejpam-753	136	10	)	)	PUNCT
ejpam-753	137	1	=	=	PUNCT
ejpam-753	137	2	(	(	PUNCT
ejpam-753	137	3	α0α	α0α	NUM
ejpam-753	137	4	′	′	NUM
ejpam-753	137	5	0	0	NUM
ejpam-753	137	6	,	,	PUNCT
ejpam-753	137	7	s∑	s∑	PROPN
ejpam-753	137	8	i=1	i=1	PUNCT
ejpam-753	138	1	[	[	X
ejpam-753	138	2	α0α	α0α	NUM
ejpam-753	138	3	′	′	NUM
ejpam-753	138	4	i	i	PRON
ejpam-753	139	1	+	+	NOUN
ejpam-753	139	2	αiα	αiα	VERB
ejpam-753	139	3	′	′	NUM
ejpam-753	139	4	0]ui	0]ui	NUM
ejpam-753	139	5	,	,	PUNCT
ejpam-753	139	6	λ∑	λ∑	X
ejpam-753	139	7	j=1	j=1	X
ejpam-753	140	1	[	[	X
ejpam-753	140	2	α0β	α0β	NUM
ejpam-753	140	3	′	′	NUM
ejpam-753	140	4	j	j	PROPN
ejpam-753	141	1	+	+	CCONJ
ejpam-753	141	2	β	β	X
ejpam-753	141	3	jα	jα	NOUN
ejpam-753	141	4	′	′	NUM
ejpam-753	141	5	0]v	0]v	NOUN
ejpam-753	141	6	j	j	NOUN
ejpam-753	141	7	,	,	PUNCT
ejpam-753	141	8	t∑	t∑	X
ejpam-753	141	9	k=1	k=1	PUNCT
ejpam-753	142	1	[	[	X
ejpam-753	142	2	α0γ	α0γ	NOUN
ejpam-753	142	3	′	′	NUM
ejpam-753	142	4	k	k	NOUN
ejpam-753	143	1	+	+	CCONJ
ejpam-753	143	2	γkα	γkα	NOUN
ejpam-753	144	1	′	′	NOUN
ejpam-753	144	2	0	0	NUM
ejpam-753	145	1	+	+	CCONJ
ejpam-753	145	2	s∑	s∑	PROPN
ejpam-753	145	3	i	i	PRON
ejpam-753	145	4	,	,	PUNCT
ejpam-753	145	5	j=1	j=1	PROPN
ejpam-753	145	6	ak	ak	PROPN
ejpam-753	145	7	i	i	PROPN
ejpam-753	145	8	,	,	PUNCT
ejpam-753	145	9	jαiα	jαiα	PROPN
ejpam-753	145	10	′	′	NUM
ejpam-753	145	11	j]wk	j]wk	PROPN
ejpam-753	145	12	)	)	PUNCT
ejpam-753	145	13	where	where	SCONJ
ejpam-753	145	14	f	f	PROPN
ejpam-753	145	15	is	be	AUX
ejpam-753	145	16	the	the	DET
ejpam-753	145	17	field	field	NOUN
ejpam-753	145	18	of	of	ADP
ejpam-753	145	19	order	order	NOUN
ejpam-753	145	20	r	r	NOUN
ejpam-753	145	21	and	and	CCONJ
ejpam-753	145	22	u	u	NOUN
ejpam-753	145	23	,	,	PUNCT
ejpam-753	145	24	v	v	ADP
ejpam-753	145	25	,	,	PUNCT
ejpam-753	145	26	w	w	NOUN
ejpam-753	145	27	are	be	AUX
ejpam-753	145	28	s	s	PROPN
ejpam-753	145	29	,	,	PUNCT
ejpam-753	145	30	λ	λ	PROPN
ejpam-753	145	31	,	,	PUNCT
ejpam-753	145	32	t	t	PROPN
ejpam-753	145	33	-dimensional	-dimensional	ADJ
ejpam-753	145	34	f	f	PROPN
ejpam-753	145	35	-spaces	-space	NOUN
ejpam-753	145	36	respectively	respectively	ADV
ejpam-753	145	37	,	,	PUNCT
ejpam-753	145	38	for	for	ADP
ejpam-753	145	39	some	some	DET
ejpam-753	145	40	integers	integer	NOUN
ejpam-753	145	41	s	s	PART
ejpam-753	145	42	,	,	PUNCT
ejpam-753	145	43	λ	λ	PROPN
ejpam-753	145	44	,	,	PUNCT
ejpam-753	145	45	t	t	PROPN
ejpam-753	145	46	with	with	ADP
ejpam-753	145	47	λ	λ	PROPN
ejpam-753	145	48	≥	≥	X
ejpam-753	145	49	0	0	NUM
ejpam-753	145	50	and	and	CCONJ
ejpam-753	145	51	1	1	NUM
ejpam-753	145	52	≤	≤	NOUN
ejpam-753	145	53	t	t	PROPN
ejpam-753	145	54	≤	≤	NUM
ejpam-753	145	55	s2	s2	PROPN
ejpam-753	145	56	,	,	PUNCT
ejpam-753	145	57	where	where	SCONJ
ejpam-753	145	58	{	{	PUNCT
ejpam-753	145	59	ui	ui	NOUN
ejpam-753	145	60	}	}	PUNCT
ejpam-753	145	61	,	,	PUNCT
ejpam-753	145	62	{	{	PUNCT
ejpam-753	145	63	vi	vi	NOUN
ejpam-753	145	64	}	}	PUNCT
ejpam-753	145	65	and	and	CCONJ
ejpam-753	145	66	{	{	PUNCT
ejpam-753	145	67	wi	wi	PROPN
ejpam-753	145	68	}	}	PUNCT
ejpam-753	145	69	are	be	AUX
ejpam-753	145	70	bases	basis	NOUN
ejpam-753	145	71	for	for	ADP
ejpam-753	145	72	u	u	PROPN
ejpam-753	145	73	,	,	PUNCT
ejpam-753	145	74	v	v	NOUN
ejpam-753	145	75	and	and	CCONJ
ejpam-753	145	76	w	w	NOUN
ejpam-753	145	77	respectively	respectively	ADV
ejpam-753	145	78	,	,	PUNCT
ejpam-753	145	79	and	and	CCONJ
ejpam-753	145	80	(	(	PUNCT
ejpam-753	145	81	ak	ak	PROPN
ejpam-753	145	82	i	i	PROPN
ejpam-753	145	83	,	,	PUNCT
ejpam-753	145	84	j	j	PROPN
ejpam-753	145	85	)	)	PUNCT
ejpam-753	145	86	1≤	1≤	PROPN
ejpam-753	146	1	k	k	PROPN
ejpam-753	146	2	≤	≤	PROPN
ejpam-753	146	3	t	t	PROPN
ejpam-753	146	4	are	be	AUX
ejpam-753	146	5	t	t	NOUN
ejpam-753	146	6	matrices	matrix	NOUN
ejpam-753	146	7	of	of	ADP
ejpam-753	146	8	size	size	NOUN
ejpam-753	146	9	s×	s×	NOUN
ejpam-753	146	10	s	s	PART
ejpam-753	146	11	with	with	ADP
ejpam-753	146	12	entries	entry	NOUN
ejpam-753	146	13	in	in	ADP
ejpam-753	146	14	f	f	PROPN
ejpam-753	146	15	.	.	PUNCT
ejpam-753	147	1	since	since	SCONJ
ejpam-753	147	2	|r|	|r|	NOUN
ejpam-753	147	3	=	=	PUNCT
ejpam-753	147	4	p6	p6	PROPN
ejpam-753	147	5	,	,	PUNCT
ejpam-753	147	6	we	we	PRON
ejpam-753	147	7	can	can	AUX
ejpam-753	147	8	conclude	conclude	VERB
ejpam-753	147	9	that	that	PRON
ejpam-753	147	10	t	t	PROPN
ejpam-753	147	11	=	=	SYM
ejpam-753	147	12	s	s	PART
ejpam-753	147	13	=	=	SYM
ejpam-753	147	14	1	1	NUM
ejpam-753	147	15	and	and	CCONJ
ejpam-753	147	16	λ	λ	X
ejpam-753	147	17	=	=	NOUN
ejpam-753	147	18	0	0	PROPN
ejpam-753	147	19	.	.	PUNCT
ejpam-753	148	1	on	on	ADP
ejpam-753	148	2	the	the	DET
ejpam-753	148	3	other	other	ADJ
ejpam-753	148	4	hand	hand	NOUN
ejpam-753	148	5	by	by	ADP
ejpam-753	148	6	[	[	X
ejpam-753	148	7	3	3	NUM
ejpam-753	148	8	,	,	PUNCT
ejpam-753	148	9	corollary	corollary	ADJ
ejpam-753	148	10	5.2	5.2	NUM
ejpam-753	148	11	]	]	PUNCT
ejpam-753	148	12	,	,	PUNCT
ejpam-753	148	13	we	we	PRON
ejpam-753	148	14	can	can	AUX
ejpam-753	148	15	put	put	VERB
ejpam-753	148	16	a1	a1	NOUN
ejpam-753	148	17	11	11	NUM
ejpam-753	148	18	=	=	SYM
ejpam-753	148	19	1	1	NUM
ejpam-753	148	20	.	.	PUNCT
ejpam-753	148	21	thus	thus	ADV
ejpam-753	148	22	r	r	X
ejpam-753	148	23	∼=	∼=	PROPN
ejpam-753	148	24	fp2	fp2	PROPN
ejpam-753	148	25	⊕	⊕	PROPN
ejpam-753	148	26	fp2	fp2	PROPN
ejpam-753	148	27	⊕	⊕	PROPN
ejpam-753	148	28	fp2	fp2	PROPN
ejpam-753	148	29	with	with	ADP
ejpam-753	148	30	multiplication	multiplication	NOUN
ejpam-753	148	31	(	(	PUNCT
ejpam-753	148	32	α0,α	α0,α	PROPN
ejpam-753	148	33	,	,	PUNCT
ejpam-753	148	34	γ)(α′0,α′,γ′	γ)(α′0,α′,γ′	NOUN
ejpam-753	148	35	)	)	PUNCT
ejpam-753	148	36	=	=	PUNCT
ejpam-753	149	1	(	(	PUNCT
ejpam-753	149	2	α0α	α0α	NUM
ejpam-753	149	3	′	′	NUM
ejpam-753	149	4	0,α0α	0,α0α	NOUN
ejpam-753	150	1	′	′	NUM
ejpam-753	151	1	+	+	NUM
ejpam-753	151	2	αα′0,α0γ	αα′0,α0γ	NOUN
ejpam-753	151	3	′	′	NOUN
ejpam-753	152	1	+	+	CCONJ
ejpam-753	152	2	γα′0	γα′0	X
ejpam-753	152	3	+	+	ADJ
ejpam-753	152	4	αα	αα	NOUN
ejpam-753	152	5	′	′	NUM
ejpam-753	152	6	)	)	PUNCT
ejpam-753	152	7	.	.	PUNCT
ejpam-753	153	1	now	now	ADV
ejpam-753	153	2	suppose	suppose	VERB
ejpam-753	153	3	that	that	SCONJ
ejpam-753	153	4	char(r	char(r	NOUN
ejpam-753	153	5	)	)	PUNCT
ejpam-753	153	6	=	=	NOUN
ejpam-753	153	7	p2	p2	PROPN
ejpam-753	153	8	or	or	CCONJ
ejpam-753	153	9	p3	p3	PROPN
ejpam-753	153	10	.	.	PUNCT
ejpam-753	154	1	since	since	SCONJ
ejpam-753	154	2	|r|=	|r|=	NOUN
ejpam-753	154	3	p6	p6	VERB
ejpam-753	154	4	and	and	CCONJ
ejpam-753	154	5	|r	|r	PROPN
ejpam-753	154	6	/	/	SYM
ejpam-753	154	7	j(r)|=	j(r)|=	PROPN
ejpam-753	154	8	p2	p2	NOUN
ejpam-753	154	9	,	,	PUNCT
ejpam-753	154	10	by	by	ADP
ejpam-753	154	11	construction	construction	NOUN
ejpam-753	154	12	a	a	PRON
ejpam-753	154	13	we	we	PRON
ejpam-753	154	14	conclude	conclude	VERB
ejpam-753	154	15	that	that	PRON
ejpam-753	154	16	s	s	VERB
ejpam-753	154	17	=	=	SYM
ejpam-753	154	18	1	1	NUM
ejpam-753	154	19	and	and	CCONJ
ejpam-753	154	20	t	t	NOUN
ejpam-753	155	1	=	=	SYM
ejpam-753	155	2	λ	λ	X
ejpam-753	155	3	=	=	SYM
ejpam-753	155	4	0	0	PUNCT
ejpam-753	155	5	if	if	SCONJ
ejpam-753	155	6	char(r	char(r	NOUN
ejpam-753	155	7	)	)	PUNCT
ejpam-753	155	8	=	=	NOUN
ejpam-753	155	9	p2	p2	PROPN
ejpam-753	155	10	and	and	CCONJ
ejpam-753	155	11	s	s	NOUN
ejpam-753	155	12	=	=	PROPN
ejpam-753	155	13	t	t	PROPN
ejpam-753	155	14	=	=	SYM
ejpam-753	155	15	λ	λ	SYM
ejpam-753	155	16	=	=	SYM
ejpam-753	155	17	0	0	PUNCT
ejpam-753	156	1	if	if	SCONJ
ejpam-753	156	2	char(r	char(r	NOUN
ejpam-753	156	3	)	)	PUNCT
ejpam-753	156	4	=	=	SYM
ejpam-753	156	5	p3	p3	PROPN
ejpam-753	156	6	.	.	PUNCT
ejpam-753	157	1	also	also	ADV
ejpam-753	157	2	by	by	ADP
ejpam-753	157	3	[	[	X
ejpam-753	157	4	3	3	NUM
ejpam-753	157	5	,	,	PUNCT
ejpam-753	157	6	lemma	lemma	PROPN
ejpam-753	157	7	7.1	7.1	NUM
ejpam-753	157	8	]	]	PUNCT
ejpam-753	157	9	,	,	PUNCT
ejpam-753	157	10	we	we	PRON
ejpam-753	157	11	can	can	AUX
ejpam-753	157	12	put	put	VERB
ejpam-753	157	13	a0	a0	PROPN
ejpam-753	157	14	11	11	NUM
ejpam-753	157	15	=	=	SYM
ejpam-753	157	16	1	1	NUM
ejpam-753	157	17	and	and	CCONJ
ejpam-753	157	18	so	so	ADV
ejpam-753	157	19	the	the	DET
ejpam-753	157	20	following	follow	VERB
ejpam-753	157	21	rings	ring	NOUN
ejpam-753	157	22	is	be	AUX
ejpam-753	157	23	obtained	obtain	VERB
ejpam-753	157	24	.	.	PUNCT
ejpam-753	158	1	if	if	SCONJ
ejpam-753	158	2	char(r	char(r	NOUN
ejpam-753	158	3	)	)	PUNCT
ejpam-753	158	4	=	=	NOUN
ejpam-753	158	5	p2	p2	NOUN
ejpam-753	158	6	,	,	PUNCT
ejpam-753	158	7	then	then	ADV
ejpam-753	158	8	r∼=	r∼=	ADV
ejpam-753	158	9	r0⊕r0	r0⊕r0	NOUN
ejpam-753	158	10	/	/	SYM
ejpam-753	158	11	pr0	pr0	NOUN
ejpam-753	158	12	with	with	ADP
ejpam-753	158	13	multiplication	multiplication	NOUN
ejpam-753	158	14	(	(	PUNCT
ejpam-753	158	15	α0,α+pr0).(α	α0,α+pr0).(α	NOUN
ejpam-753	158	16	′	′	NUM
ejpam-753	158	17	0,α′+pr0	0,α′+pr0	NOUN
ejpam-753	158	18	)	)	PUNCT
ejpam-753	159	1	=	=	PUNCT
ejpam-753	160	1	(	(	PUNCT
ejpam-753	160	2	α0α	α0α	NUM
ejpam-753	160	3	′	′	NUM
ejpam-753	160	4	0	0	NUM
ejpam-753	161	1	+	+	CCONJ
ejpam-753	161	2	αα	αα	X
ejpam-753	161	3	′p	′p	ADJ
ejpam-753	161	4	,	,	PUNCT
ejpam-753	161	5	α0α	α0α	NUM
ejpam-753	161	6	′	′	NUM
ejpam-753	162	1	+	+	NUM
ejpam-753	162	2	αα′0	αα′0	NOUN
ejpam-753	162	3	+	+	CCONJ
ejpam-753	162	4	pr0	pr0	PROPN
ejpam-753	162	5	)	)	PUNCT
ejpam-753	162	6	,	,	PUNCT
ejpam-753	162	7	where	where	SCONJ
ejpam-753	162	8	r0	r0	NOUN
ejpam-753	162	9	=	=	NOUN
ejpam-753	162	10	gr(p4	gr(p4	NOUN
ejpam-753	162	11	,	,	PUNCT
ejpam-753	162	12	p2	p2	PROPN
ejpam-753	162	13	)	)	PUNCT
ejpam-753	162	14	and	and	CCONJ
ejpam-753	162	15	if	if	SCONJ
ejpam-753	162	16	char(r	char(r	NOUN
ejpam-753	162	17	)	)	PUNCT
ejpam-753	162	18	=	=	SYM
ejpam-753	162	19	p3	p3	PROPN
ejpam-753	162	20	,	,	PUNCT
ejpam-753	162	21	then	then	ADV
ejpam-753	162	22	r∼=	r∼=	ADV
ejpam-753	162	23	gr(p6	gr(p6	NOUN
ejpam-753	162	24	,	,	PUNCT
ejpam-753	162	25	p3	p3	PROPN
ejpam-753	162	26	)	)	PUNCT
ejpam-753	162	27	.	.	PUNCT
ejpam-753	163	1	proposition	proposition	NOUN
ejpam-753	163	2	2	2	X
ejpam-753	163	3	.	.	PUNCT
ejpam-753	164	1	let	let	VERB
ejpam-753	164	2	r	r	PRON
ejpam-753	164	3	be	be	AUX
ejpam-753	164	4	a	a	DET
ejpam-753	164	5	commutative	commutative	ADJ
ejpam-753	164	6	ring	ring	NOUN
ejpam-753	164	7	with	with	ADP
ejpam-753	164	8	|z(r)|	|z(r)|	PROPN
ejpam-753	164	9	=	=	PUNCT
ejpam-753	164	10	p4	p4	ADJ
ejpam-753	164	11	and	and	CCONJ
ejpam-753	164	12	|r|	|r|	NOUN
ejpam-753	164	13	=	=	NOUN
ejpam-753	164	14	p5	p5	ADJ
ejpam-753	164	15	where	where	SCONJ
ejpam-753	164	16	p	p	NOUN
ejpam-753	164	17	is	be	AUX
ejpam-753	164	18	a	a	DET
ejpam-753	164	19	prime	prime	ADJ
ejpam-753	164	20	number	number	NOUN
ejpam-753	164	21	.	.	PUNCT
ejpam-753	165	1	then	then	ADV
ejpam-753	165	2	r	r	NOUN
ejpam-753	165	3	is	be	AUX
ejpam-753	165	4	isomorphic	isomorphic	ADJ
ejpam-753	165	5	to	to	ADP
ejpam-753	165	6	one	one	NUM
ejpam-753	165	7	of	of	ADP
ejpam-753	165	8	the	the	DET
ejpam-753	165	9	rings	ring	NOUN
ejpam-753	165	10	zp5	zp5	PROPN
ejpam-753	165	11	,	,	PUNCT
ejpam-753	165	12	fp[x]/(x	fp[x]/(x	PROPN
ejpam-753	165	13	5	5	NUM
ejpam-753	165	14	)	)	PUNCT
ejpam-753	165	15	,	,	PUNCT
ejpam-753	165	16	fp[x	fp[x	PROPN
ejpam-753	165	17	,	,	PUNCT
ejpam-753	165	18	y]/(x4	y]/(x4	PROPN
ejpam-753	165	19	,	,	PUNCT
ejpam-753	165	20	x	x	PROPN
ejpam-753	165	21	y	y	PROPN
ejpam-753	165	22	,	,	PUNCT
ejpam-753	165	23	y2	y2	PROPN
ejpam-753	165	24	)	)	PUNCT
ejpam-753	165	25	,	,	PUNCT
ejpam-753	165	26	fp[x	fp[x	PROPN
ejpam-753	165	27	,	,	PUNCT
ejpam-753	165	28	y]/(x4	y]/(x4	PROPN
ejpam-753	165	29	,	,	PUNCT
ejpam-753	165	30	x	x	PROPN
ejpam-753	165	31	y	y	PROPN
ejpam-753	165	32	,	,	PUNCT
ejpam-753	165	33	y2	y2	PROPN
ejpam-753	165	34	−	−	NOUN
ejpam-753	165	35	x3	x3	ADJ
ejpam-753	165	36	)	)	PUNCT
ejpam-753	165	37	,	,	PUNCT
ejpam-753	165	38	zp[x	zp[x	PROPN
ejpam-753	165	39	,	,	PUNCT
ejpam-753	165	40	y	y	PROPN
ejpam-753	165	41	,	,	PUNCT
ejpam-753	165	42	z	z	PROPN
ejpam-753	165	43	,	,	PUNCT
ejpam-753	165	44	t]/(x	t]/(x	PROPN
ejpam-753	165	45	,	,	PUNCT
ejpam-753	165	46	y	y	PROPN
ejpam-753	165	47	,	,	PUNCT
ejpam-753	165	48	z	z	PROPN
ejpam-753	165	49	,	,	PUNCT
ejpam-753	165	50	t)2	t)2	PROPN
ejpam-753	165	51	,	,	PUNCT
ejpam-753	165	52	zp2[x]/(px	zp2[x]/(px	PROPN
ejpam-753	165	53	,	,	PUNCT
ejpam-753	165	54	x4	x4	PROPN
ejpam-753	165	55	−	−	PROPN
ejpam-753	165	56	ap	ap	PROPN
ejpam-753	165	57	)	)	PUNCT
ejpam-753	165	58	where	where	SCONJ
ejpam-753	165	59	a	a	DET
ejpam-753	165	60	∈	∈	PROPN
ejpam-753	165	61	σ0	σ0	NOUN
ejpam-753	165	62	4	4	NUM
ejpam-753	165	63	,	,	PUNCT
ejpam-753	165	64	zp2[x]/(px2	zp2[x]/(px2	PROPN
ejpam-753	165	65	,	,	PUNCT
ejpam-753	165	66	x3	x3	ADJ
ejpam-753	165	67	−	−	PROPN
ejpam-753	165	68	bp	bp	PROPN
ejpam-753	165	69	)	)	PUNCT
ejpam-753	165	70	where	where	SCONJ
ejpam-753	165	71	b	b	X
ejpam-753	165	72	∈	∈	PROPN
ejpam-753	165	73	σ3	σ3	NOUN
ejpam-753	165	74	and	and	CCONJ
ejpam-753	165	75	p	p	NOUN
ejpam-753	165	76	6=	6=	PROPN
ejpam-753	165	77	3	3	NUM
ejpam-753	165	78	,	,	PUNCT
ejpam-753	165	79	z9[x]/(3x2	z9[x]/(3x2	PROPN
ejpam-753	165	80	,	,	PUNCT
ejpam-753	165	81	x3	x3	ADJ
ejpam-753	165	82	−	−	PROPN
ejpam-753	165	83	3	3	NUM
ejpam-753	165	84	−	−	PROPN
ejpam-753	165	85	3bx	3bx	NOUN
ejpam-753	165	86	)	)	PUNCT
ejpam-753	165	87	where	where	SCONJ
ejpam-753	165	88	b	b	X
ejpam-753	165	89	∈	∈	PROPN
ejpam-753	165	90	{	{	PUNCT
ejpam-753	165	91	−1,0,1	−1,0,1	NOUN
ejpam-753	165	92	}	}	PUNCT
ejpam-753	165	93	,	,	PUNCT
ejpam-753	165	94	zp2[x]/(px2	zp2[x]/(px2	PROPN
ejpam-753	165	95	,	,	PUNCT
ejpam-753	165	96	x3−	x3−	PROPN
ejpam-753	165	97	apx	apx	PROPN
ejpam-753	165	98	)	)	PUNCT
ejpam-753	165	99	where	where	SCONJ
ejpam-753	165	100	a	a	DET
ejpam-753	165	101	∈	∈	PROPN
ejpam-753	165	102	σ0	σ0	NOUN
ejpam-753	165	103	2	2	NUM
ejpam-753	165	104	,	,	PUNCT
ejpam-753	165	105	zp2[x	zp2[x	PROPN
ejpam-753	165	106	,	,	PUNCT
ejpam-753	165	107	y	y	PROPN
ejpam-753	165	108	,	,	PUNCT
ejpam-753	165	109	z]/(p	z]/(p	PROPN
ejpam-753	165	110	,	,	PUNCT
ejpam-753	165	111	x	x	INTJ
ejpam-753	165	112	,	,	PUNCT
ejpam-753	165	113	y	y	PROPN
ejpam-753	165	114	,	,	PUNCT
ejpam-753	165	115	z)2	z)2	PROPN
ejpam-753	165	116	,	,	PUNCT
ejpam-753	165	117	zp3[x]/(p2	zp3[x]/(p2	PROPN
ejpam-753	165	118	x	x	SYM
ejpam-753	165	119	,	,	PUNCT
ejpam-753	165	120	x2−	x2−	PROPN
ejpam-753	165	121	ap	ap	PROPN
ejpam-753	165	122	)	)	PUNCT
ejpam-753	165	123	where	where	SCONJ
ejpam-753	165	124	a	a	DET
ejpam-753	165	125	∈	∈	PROPN
ejpam-753	165	126	σ2	σ2	NOUN
ejpam-753	165	127	and	and	CCONJ
ejpam-753	165	128	p	p	NOUN
ejpam-753	165	129	6=	6=	PROPN
ejpam-753	165	130	2	2	NUM
ejpam-753	165	131	,	,	PUNCT
ejpam-753	165	132	z8[x]/(4x	z8[x]/(4x	NOUN
ejpam-753	165	133	,	,	PUNCT
ejpam-753	165	134	x2−2a−2bx	x2−2a−2bx	PROPN
ejpam-753	165	135	)	)	PUNCT
ejpam-753	165	136	where	where	SCONJ
ejpam-753	165	137	(	(	PUNCT
ejpam-753	165	138	a	a	PRON
ejpam-753	165	139	,	,	PUNCT
ejpam-753	165	140	b	b	NOUN
ejpam-753	165	141	)	)	PUNCT
ejpam-753	165	142	∈	∈	NOUN
ejpam-753	165	143	{	{	PUNCT
ejpam-753	165	144	(	(	PUNCT
ejpam-753	165	145	1,0	1,0	NUM
ejpam-753	165	146	)	)	PUNCT
ejpam-753	165	147	,	,	PUNCT
ejpam-753	165	148	(	(	PUNCT
ejpam-753	165	149	1,1	1,1	NUM
ejpam-753	165	150	)	)	PUNCT
ejpam-753	165	151	,	,	PUNCT
ejpam-753	165	152	(	(	PUNCT
ejpam-753	165	153	−1,1	−1,1	NOUN
ejpam-753	165	154	)	)	PUNCT
ejpam-753	165	155	}	}	PUNCT
ejpam-753	165	156	,	,	PUNCT
ejpam-753	165	157	zp3[x]/(px	zp3[x]/(px	NUM
ejpam-753	165	158	,	,	PUNCT
ejpam-753	165	159	x3	x3	PROPN
ejpam-753	165	160	−	−	PROPN
ejpam-753	165	161	ap2	ap2	PROPN
ejpam-753	165	162	)	)	PUNCT
ejpam-753	165	163	where	where	SCONJ
ejpam-753	165	164	a	a	DET
ejpam-753	165	165	∈	∈	PROPN
ejpam-753	165	166	σ0	σ0	NOUN
ejpam-753	165	167	3	3	NUM
ejpam-753	165	168	,	,	PUNCT
ejpam-753	165	169	zp3[x]/(p2	zp3[x]/(p2	ADJ
ejpam-753	165	170	x	x	SYM
ejpam-753	165	171	,	,	PUNCT
ejpam-753	165	172	x2	x2	PROPN
ejpam-753	165	173	−	−	PROPN
ejpam-753	165	174	ap2	ap2	PROPN
ejpam-753	165	175	)	)	PUNCT
ejpam-753	165	176	where	where	SCONJ
ejpam-753	165	177	a	a	DET
ejpam-753	165	178	∈	∈	PROPN
ejpam-753	165	179	σ0	σ0	NOUN
ejpam-753	165	180	2	2	NUM
ejpam-753	165	181	and	and	CCONJ
ejpam-753	165	182	p	p	NOUN
ejpam-753	165	183	6=	6=	PROPN
ejpam-753	165	184	2	2	NUM
ejpam-753	165	185	,	,	PUNCT
ejpam-753	165	186	z8[x]/(4x	z8[x]/(4x	NOUN
ejpam-753	165	187	,	,	PUNCT
ejpam-753	165	188	x2−	x2−	PROPN
ejpam-753	165	189	4a−	4a−	NUM
ejpam-753	165	190	2bx	2bx	NOUN
ejpam-753	165	191	)	)	PUNCT
ejpam-753	165	192	where	where	SCONJ
ejpam-753	165	193	(	(	PUNCT
ejpam-753	165	194	a	a	PRON
ejpam-753	165	195	,	,	PUNCT
ejpam-753	165	196	b	b	NOUN
ejpam-753	165	197	)	)	PUNCT
ejpam-753	165	198	∈	∈	NOUN
ejpam-753	165	199	{	{	PUNCT
ejpam-753	165	200	(	(	PUNCT
ejpam-753	165	201	0,0	0,0	NOUN
ejpam-753	165	202	)	)	PUNCT
ejpam-753	165	203	,	,	PUNCT
ejpam-753	165	204	(	(	PUNCT
ejpam-753	165	205	0,1	0,1	NOUN
ejpam-753	165	206	)	)	PUNCT
ejpam-753	165	207	,	,	PUNCT
ejpam-753	165	208	(	(	PUNCT
ejpam-753	165	209	1,1	1,1	NUM
ejpam-753	165	210	)	)	PUNCT
ejpam-753	165	211	}	}	PUNCT
ejpam-753	165	212	,	,	PUNCT
ejpam-753	165	213	zp4[x]/(px	zp4[x]/(px	X
ejpam-753	165	214	,	,	PUNCT
ejpam-753	165	215	x2−	x2−	PROPN
ejpam-753	165	216	ap3	ap3	NOUN
ejpam-753	165	217	)	)	PUNCT
ejpam-753	165	218	where	where	SCONJ
ejpam-753	165	219	a	a	DET
ejpam-753	165	220	∈	∈	PROPN
ejpam-753	165	221	σ0	σ0	NOUN
ejpam-753	165	222	2	2	NUM
ejpam-753	165	223	,	,	PUNCT
ejpam-753	165	224	〈	〈	NOUN
ejpam-753	165	225	1	1	NUM
ejpam-753	165	226	,	,	PUNCT
ejpam-753	165	227	x1	x1	PROPN
ejpam-753	165	228	,	,	PUNCT
ejpam-753	165	229	x2	x2	PROPN
ejpam-753	165	230	,	,	PUNCT
ejpam-753	165	231	y1	y1	NOUN
ejpam-753	165	232	,	,	PUNCT
ejpam-753	165	233	y2	y2	PROPN
ejpam-753	165	234	;	;	PUNCT
ejpam-753	165	235	p1	p1	PROPN
ejpam-753	165	236	=	=	SYM
ejpam-753	165	237	0	0	PROPN
ejpam-753	165	238	,	,	PUNCT
ejpam-753	165	239	x1	x1	PROPN
ejpam-753	165	240	2	2	NUM
ejpam-753	165	241	=	=	SYM
ejpam-753	165	242	y1	y1	PROPN
ejpam-753	165	243	,	,	PUNCT
ejpam-753	165	244	x2	x2	PROPN
ejpam-753	165	245	2	2	NUM
ejpam-753	165	246	=	=	SYM
ejpam-753	165	247	0	0	NUM
ejpam-753	165	248	,	,	PUNCT
ejpam-753	165	249	x1	x1	PROPN
ejpam-753	165	250	x2	x2	PROPN
ejpam-753	166	1	=	=	PUNCT
ejpam-753	167	1	y2	y2	PROPN
ejpam-753	167	2	,	,	PUNCT
ejpam-753	167	3	x	x	PROPN
ejpam-753	168	1	i	i	PRON
ejpam-753	168	2	yi	yi	NOUN
ejpam-753	169	1	=	=	SYM
ejpam-753	169	2	yi	yi	PROPN
ejpam-753	169	3	y	y	PROPN
ejpam-753	169	4	j	j	PROPN
ejpam-753	169	5	=	=	SYM
ejpam-753	169	6	0	0	NUM
ejpam-753	169	7	〉	〉	NOUN
ejpam-753	169	8	,	,	PUNCT
ejpam-753	169	9	〈	〈	PROPN
ejpam-753	169	10	1	1	NUM
ejpam-753	169	11	,	,	PUNCT
ejpam-753	169	12	x1	x1	PROPN
ejpam-753	169	13	,	,	PUNCT
ejpam-753	169	14	x2	x2	PROPN
ejpam-753	169	15	,	,	PUNCT
ejpam-753	169	16	y1	y1	NOUN
ejpam-753	169	17	,	,	PUNCT
ejpam-753	169	18	y2	y2	PROPN
ejpam-753	169	19	;	;	PUNCT
ejpam-753	169	20	p1	p1	PROPN
ejpam-753	169	21	=	=	SYM
ejpam-753	169	22	0	0	PROPN
ejpam-753	169	23	,	,	PUNCT
ejpam-753	169	24	x1	x1	PROPN
ejpam-753	169	25	2	2	X
ejpam-753	169	26	=	=	SYM
ejpam-753	169	27	x2	x2	PROPN
ejpam-753	169	28	2	2	X
ejpam-753	169	29	=	=	SYM
ejpam-753	169	30	y1	y1	PROPN
ejpam-753	169	31	,	,	PUNCT
ejpam-753	169	32	x1	x1	PROPN
ejpam-753	169	33	x2	x2	PROPN
ejpam-753	169	34	=	=	PUNCT
ejpam-753	169	35	y2	y2	PROPN
ejpam-753	169	36	,	,	PUNCT
ejpam-753	169	37	x	x	PROPN
ejpam-753	169	38	i	i	PRON
ejpam-753	169	39	yi	yi	NOUN
ejpam-753	170	1	=	=	SYM
ejpam-753	170	2	yi	yi	PROPN
ejpam-753	171	1	y	y	PROPN
ejpam-753	171	2	j	j	PROPN
ejpam-753	171	3	=	=	SYM
ejpam-753	171	4	0	0	NUM
ejpam-753	171	5	〉	〉	NOUN
ejpam-753	171	6	where	where	SCONJ
ejpam-753	171	7	p	p	PROPN
ejpam-753	171	8	6=	6=	PROPN
ejpam-753	171	9	2	2	NUM
ejpam-753	171	10	,	,	PUNCT
ejpam-753	171	11	〈	〈	PROPN
ejpam-753	171	12	1	1	NUM
ejpam-753	171	13	,	,	PUNCT
ejpam-753	171	14	x1	x1	PROPN
ejpam-753	171	15	,	,	PUNCT
ejpam-753	171	16	x2	x2	PROPN
ejpam-753	171	17	,	,	PUNCT
ejpam-753	171	18	y1	y1	NOUN
ejpam-753	171	19	,	,	PUNCT
ejpam-753	171	20	y2	y2	PROPN
ejpam-753	171	21	;	;	PUNCT
ejpam-753	171	22	p1=	p1=	PROPN
ejpam-753	171	23	0	0	NUM
ejpam-753	171	24	,	,	PUNCT
ejpam-753	171	25	x1	x1	PROPN
ejpam-753	171	26	2	2	NUM
ejpam-753	171	27	=	=	SYM
ejpam-753	171	28	y1	y1	PROPN
ejpam-753	171	29	,	,	PUNCT
ejpam-753	171	30	x2	x2	PROPN
ejpam-753	171	31	2	2	X
ejpam-753	171	32	=	=	SYM
ejpam-753	171	33	ξy1	ξy1	NOUN
ejpam-753	171	34	,	,	PUNCT
ejpam-753	171	35	x1	x1	PROPN
ejpam-753	171	36	x2	x2	PROPN
ejpam-753	171	37	=	=	PUNCT
ejpam-753	171	38	y2	y2	PROPN
ejpam-753	171	39	,	,	PUNCT
ejpam-753	171	40	x	x	PROPN
ejpam-753	172	1	i	i	PRON
ejpam-753	172	2	yi	yi	NOUN
ejpam-753	173	1	=	=	SYM
ejpam-753	173	2	yi	yi	PROPN
ejpam-753	174	1	y	y	PROPN
ejpam-753	174	2	j	j	PROPN
ejpam-753	174	3	=	=	SYM
ejpam-753	174	4	0	0	NUM
ejpam-753	174	5	〉	〉	NOUN
ejpam-753	174	6	where	where	SCONJ
ejpam-753	174	7	p	p	PROPN
ejpam-753	174	8	6=	6=	PROPN
ejpam-753	174	9	2	2	NUM
ejpam-753	174	10	and	and	CCONJ
ejpam-753	174	11	ξ	ξ	PROPN
ejpam-753	174	12	is	be	AUX
ejpam-753	174	13	a	a	DET
ejpam-753	174	14	non	non	ADJ
ejpam-753	174	15	-	-	ADJ
ejpam-753	174	16	square	square	ADJ
ejpam-753	174	17	in	in	ADP
ejpam-753	174	18	fp	fp	PROPN
ejpam-753	174	19	,	,	PUNCT
ejpam-753	174	20	〈	〈	PROPN
ejpam-753	174	21	1	1	NUM
ejpam-753	174	22	,	,	PUNCT
ejpam-753	174	23	x1	x1	PROPN
ejpam-753	174	24	,	,	PUNCT
ejpam-753	174	25	x2	x2	PROPN
ejpam-753	174	26	,	,	PUNCT
ejpam-753	174	27	y1	y1	NOUN
ejpam-753	174	28	,	,	PUNCT
ejpam-753	174	29	y2	y2	PROPN
ejpam-753	174	30	;	;	PUNCT
ejpam-753	174	31	2.1=	2.1=	PROPN
ejpam-753	174	32	0	0	NUM
ejpam-753	174	33	,	,	PUNCT
ejpam-753	174	34	x1	x1	PROPN
ejpam-753	174	35	2	2	NUM
ejpam-753	174	36	=	=	SYM
ejpam-753	174	37	y1	y1	PROPN
ejpam-753	174	38	,	,	PUNCT
ejpam-753	174	39	x2	x2	PROPN
ejpam-753	174	40	2	2	X
ejpam-753	174	41	=	=	SYM
ejpam-753	174	42	y2	y2	PROPN
ejpam-753	174	43	,	,	PUNCT
ejpam-753	175	1	x1	x1	PROPN
ejpam-753	175	2	x2	x2	PROPN
ejpam-753	176	1	=	=	PUNCT
ejpam-753	176	2	y2	y2	PROPN
ejpam-753	176	3	,	,	PUNCT
ejpam-753	176	4	x	x	PROPN
ejpam-753	177	1	i	i	PRON
ejpam-753	177	2	yi	yi	NOUN
ejpam-753	178	1	=	=	SYM
ejpam-753	178	2	yi	yi	PROPN
ejpam-753	178	3	y	y	PROPN
ejpam-753	178	4	j	j	PROPN
ejpam-753	178	5	=	=	SYM
ejpam-753	178	6	0	0	NUM
ejpam-753	178	7	〉	〉	NOUN
ejpam-753	178	8	,	,	PUNCT
ejpam-753	178	9	〈	〈	PROPN
ejpam-753	178	10	1	1	NUM
ejpam-753	178	11	,	,	PUNCT
ejpam-753	178	12	x1	x1	PROPN
ejpam-753	178	13	,	,	PUNCT
ejpam-753	178	14	x2	x2	PROPN
ejpam-753	178	15	,	,	PUNCT
ejpam-753	178	16	y1	y1	NOUN
ejpam-753	178	17	,	,	PUNCT
ejpam-753	178	18	y2	y2	PROPN
ejpam-753	178	19	;	;	PUNCT
ejpam-753	178	20	2.1=	2.1=	PROPN
ejpam-753	178	21	0	0	NUM
ejpam-753	178	22	,	,	PUNCT
ejpam-753	178	23	x1	x1	PROPN
ejpam-753	178	24	2	2	NUM
ejpam-753	178	25	=	=	SYM
ejpam-753	178	26	y1	y1	PROPN
ejpam-753	178	27	,	,	PUNCT
ejpam-753	178	28	x2	x2	PROPN
ejpam-753	178	29	2	2	NUM
ejpam-753	178	30	=	=	SYM
ejpam-753	178	31	y1	y1	NOUN
ejpam-753	178	32	+	+	CCONJ
ejpam-753	178	33	y2	y2	NOUN
ejpam-753	178	34	,	,	PUNCT
ejpam-753	178	35	x1	x1	PROPN
ejpam-753	178	36	x2	x2	PROPN
ejpam-753	178	37	=	=	PUNCT
ejpam-753	178	38	y2	y2	PROPN
ejpam-753	178	39	,	,	PUNCT
ejpam-753	178	40	x	x	PROPN
ejpam-753	178	41	i	i	PRON
ejpam-753	178	42	yi	yi	NOUN
ejpam-753	179	1	=	=	SYM
ejpam-753	179	2	yi	yi	PROPN
ejpam-753	179	3	y	y	PROPN
ejpam-753	179	4	j	j	PROPN
ejpam-753	179	5	=	=	SYM
ejpam-753	179	6	0	0	NUM
ejpam-753	179	7	〉	〉	NOUN
ejpam-753	179	8	,	,	PUNCT
ejpam-753	179	9	〈	〈	PROPN
ejpam-753	179	10	1	1	NUM
ejpam-753	179	11	,	,	PUNCT
ejpam-753	179	12	x1	x1	PROPN
ejpam-753	179	13	,	,	PUNCT
ejpam-753	179	14	x2	x2	PROPN
ejpam-753	179	15	,	,	PUNCT
ejpam-753	179	16	x3	x3	ADJ
ejpam-753	179	17	,	,	PUNCT
ejpam-753	179	18	y	y	PRON
ejpam-753	179	19	;	;	PUNCT
ejpam-753	179	20	p1=	p1=	PROPN
ejpam-753	179	21	0	0	NUM
ejpam-753	179	22	,	,	PUNCT
ejpam-753	179	23	x1	x1	PROPN
ejpam-753	179	24	2	2	NUM
ejpam-753	179	25	=	=	SYM
ejpam-753	179	26	y	y	PROPN
ejpam-753	179	27	,	,	PUNCT
ejpam-753	179	28	x2	x2	PROPN
ejpam-753	179	29	2	2	X
ejpam-753	180	1	=	=	SYM
ejpam-753	180	2	x3	x3	NOUN
ejpam-753	180	3	2	2	X
ejpam-753	181	1	=	=	NOUN
ejpam-753	181	2	x	x	PUNCT
ejpam-753	181	3	i	i	NOUN
ejpam-753	181	4	x	x	X
ejpam-753	181	5	j	j	NOUN
ejpam-753	182	1	=	=	PUNCT
ejpam-753	182	2	x	x	PROPN
ejpam-753	182	3	i	i	NOUN
ejpam-753	182	4	y	y	NOUN
ejpam-753	182	5	=	=	PUNCT
ejpam-753	182	6	y2	y2	PROPN
ejpam-753	182	7	=	=	SYM
ejpam-753	182	8	0	0	NUM
ejpam-753	182	9	,	,	PUNCT
ejpam-753	182	10	for	for	ADP
ejpam-753	182	11	i	i	PROPN
ejpam-753	182	12	6=	6=	PROPN
ejpam-753	182	13	j	j	PROPN
ejpam-753	182	14	〉	〉	PROPN
ejpam-753	182	15	,	,	PUNCT
ejpam-753	182	16	〈	〈	PROPN
ejpam-753	182	17	1	1	NUM
ejpam-753	182	18	,	,	PUNCT
ejpam-753	182	19	x1	x1	PROPN
ejpam-753	182	20	,	,	PUNCT
ejpam-753	182	21	x2	x2	PROPN
ejpam-753	182	22	,	,	PUNCT
ejpam-753	182	23	x3	x3	ADJ
ejpam-753	182	24	,	,	PUNCT
ejpam-753	182	25	y	y	PRON
ejpam-753	182	26	;	;	PUNCT
ejpam-753	182	27	p1=	p1=	PROPN
ejpam-753	182	28	0	0	NUM
ejpam-753	182	29	,	,	PUNCT
ejpam-753	182	30	x1	x1	PROPN
ejpam-753	182	31	2	2	X
ejpam-753	182	32	=	=	SYM
ejpam-753	182	33	x2	x2	NOUN
ejpam-753	182	34	2	2	NUM
ejpam-753	182	35	=	=	SYM
ejpam-753	182	36	y	y	NOUN
ejpam-753	182	37	,	,	PUNCT
ejpam-753	182	38	x3	x3	NOUN
ejpam-753	182	39	2	2	NUM
ejpam-753	182	40	=	=	SYM
ejpam-753	182	41	x	x	PUNCT
ejpam-753	182	42	i	i	NOUN
ejpam-753	182	43	x	x	X
ejpam-753	182	44	j	j	NOUN
ejpam-753	182	45	=	=	PUNCT
ejpam-753	182	46	x	x	PROPN
ejpam-753	183	1	i	i	NOUN
ejpam-753	183	2	y	y	NOUN
ejpam-753	183	3	=	=	PUNCT
ejpam-753	183	4	y2	y2	PROPN
ejpam-753	184	1	=	=	SYM
ejpam-753	184	2	0	0	NUM
ejpam-753	184	3	,	,	PUNCT
ejpam-753	184	4	for	for	ADP
ejpam-753	184	5	i	i	PROPN
ejpam-753	184	6	6=	6=	PROPN
ejpam-753	184	7	j	j	PROPN
ejpam-753	184	8	〉	〉	PROPN
ejpam-753	184	9	,	,	PUNCT
ejpam-753	184	10	〈	〈	PROPN
ejpam-753	184	11	1	1	NUM
ejpam-753	184	12	,	,	PUNCT
ejpam-753	184	13	x1	x1	PROPN
ejpam-753	184	14	,	,	PUNCT
ejpam-753	184	15	x2	x2	PROPN
ejpam-753	184	16	,	,	PUNCT
ejpam-753	184	17	x3	x3	ADJ
ejpam-753	184	18	,	,	PUNCT
ejpam-753	184	19	y	y	PRON
ejpam-753	184	20	;	;	PUNCT
ejpam-753	184	21	p1=	p1=	PROPN
ejpam-753	184	22	0	0	NUM
ejpam-753	184	23	,	,	PUNCT
ejpam-753	184	24	x	x	PUNCT
ejpam-753	184	25	i	i	NOUN
ejpam-753	184	26	2	2	NUM
ejpam-753	184	27	=	=	SYM
ejpam-753	184	28	y	y	PROPN
ejpam-753	184	29	,	,	PUNCT
ejpam-753	184	30	x	x	VERB
ejpam-753	185	1	i	i	NOUN
ejpam-753	185	2	x	x	X
ejpam-753	185	3	j	j	NOUN
ejpam-753	186	1	=	=	PUNCT
ejpam-753	186	2	x	x	PROPN
ejpam-753	186	3	i	i	NOUN
ejpam-753	186	4	y	y	NOUN
ejpam-753	186	5	=	=	PUNCT
ejpam-753	186	6	y2	y2	PROPN
ejpam-753	186	7	=	=	SYM
ejpam-753	186	8	0	0	NUM
ejpam-753	186	9	,	,	PUNCT
ejpam-753	186	10	for	for	ADP
ejpam-753	186	11	i	i	PROPN
ejpam-753	186	12	6=	6=	PROPN
ejpam-753	186	13	j	j	PROPN
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ejpam-753	186	16	〈	〈	PROPN
ejpam-753	186	17	1	1	NUM
ejpam-753	186	18	,	,	PUNCT
ejpam-753	186	19	x1	x1	PROPN
ejpam-753	186	20	,	,	PUNCT
ejpam-753	186	21	x2	x2	PROPN
ejpam-753	186	22	,	,	PUNCT
ejpam-753	186	23	x3	x3	ADJ
ejpam-753	186	24	,	,	PUNCT
ejpam-753	186	25	y	y	PROPN
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ejpam-753	186	27	p1	p1	PROPN
ejpam-753	186	28	=	=	SYM
ejpam-753	186	29	0	0	PROPN
ejpam-753	186	30	,	,	PUNCT
ejpam-753	186	31	x1	x1	PROPN
ejpam-753	186	32	2	2	NUM
ejpam-753	186	33	=	=	SYM
ejpam-753	186	34	y	y	PROPN
ejpam-753	186	35	,	,	PUNCT
ejpam-753	186	36	x2	x2	PROPN
ejpam-753	186	37	2	2	NUM
ejpam-753	186	38	=	=	SYM
ejpam-753	186	39	εy	εy	NOUN
ejpam-753	186	40	,	,	PUNCT
ejpam-753	186	41	x3	x3	NOUN
ejpam-753	186	42	2	2	NUM
ejpam-753	186	43	=	=	SYM
ejpam-753	186	44	x	x	PUNCT
ejpam-753	186	45	i	i	NOUN
ejpam-753	186	46	x	x	X
ejpam-753	186	47	j	j	NOUN
ejpam-753	186	48	=	=	PUNCT
ejpam-753	186	49	x	x	PROPN
ejpam-753	187	1	i	i	NOUN
ejpam-753	187	2	y	y	NOUN
ejpam-753	187	3	=	=	PUNCT
ejpam-753	187	4	y2	y2	PROPN
ejpam-753	188	1	=	=	SYM
ejpam-753	188	2	0	0	NUM
ejpam-753	188	3	,	,	PUNCT
ejpam-753	188	4	for	for	ADP
ejpam-753	188	5	i	i	PRON
ejpam-753	188	6	6=	6=	PROPN
ejpam-753	188	7	j	j	X
ejpam-753	188	8	〉	〉	NOUN
ejpam-753	188	9	where	where	SCONJ
ejpam-753	188	10	p	p	PROPN
ejpam-753	188	11	6=	6=	PROPN
ejpam-753	188	12	2	2	NUM
ejpam-753	188	13	and	and	CCONJ
ejpam-753	188	14	ε	ε	PROPN
ejpam-753	188	15	is	be	AUX
ejpam-753	188	16	a	a	DET
ejpam-753	188	17	non	non	ADJ
ejpam-753	188	18	-	-	ADJ
ejpam-753	188	19	square	square	ADJ
ejpam-753	188	20	in	in	ADP
ejpam-753	188	21	fp	fp	PROPN
ejpam-753	188	22	,	,	PUNCT
ejpam-753	188	23	m.	m.	NOUN
ejpam-753	188	24	behboodi	behboodi	PROPN
ejpam-753	188	25	,	,	PUNCT
ejpam-753	188	26	r.	r.	PROPN
ejpam-753	188	27	beyranvand	beyranvand	PROPN
ejpam-753	188	28	/	/	SYM
ejpam-753	188	29	eur	eur	PROPN
ejpam-753	188	30	.	.	PUNCT
ejpam-753	189	1	j.	j.	PROPN
ejpam-753	189	2	pure	pure	PROPN
ejpam-753	189	3	appl	appl	PROPN
ejpam-753	189	4	.	.	PROPN
ejpam-753	189	5	math	math	PROPN
ejpam-753	189	6	,	,	PUNCT
ejpam-753	189	7	3	3	NUM
ejpam-753	189	8	(	(	PUNCT
ejpam-753	189	9	2010	2010	NUM
ejpam-753	189	10	)	)	PUNCT
ejpam-753	189	11	,	,	PUNCT
ejpam-753	189	12	686	686	NUM
ejpam-753	189	13	-	-	SYM
ejpam-753	189	14	694	694	NUM
ejpam-753	189	15	690	690	NUM
ejpam-753	189	16	〈	〈	NOUN
ejpam-753	189	17	1	1	NUM
ejpam-753	189	18	,	,	PUNCT
ejpam-753	189	19	x1	x1	PROPN
ejpam-753	189	20	,	,	PUNCT
ejpam-753	189	21	x2	x2	PROPN
ejpam-753	189	22	,	,	PUNCT
ejpam-753	189	23	x3	x3	ADJ
ejpam-753	189	24	,	,	PUNCT
ejpam-753	189	25	y	y	PROPN
ejpam-753	189	26	;	;	PUNCT
ejpam-753	189	27	2.1=	2.1=	PROPN
ejpam-753	189	28	0	0	NUM
ejpam-753	189	29	,	,	PUNCT
ejpam-753	189	30	x	x	PUNCT
ejpam-753	189	31	i	i	NOUN
ejpam-753	189	32	2	2	NUM
ejpam-753	190	1	=	=	SYM
ejpam-753	190	2	x1	x1	NUM
ejpam-753	190	3	x2	x2	NOUN
ejpam-753	191	1	=	=	PUNCT
ejpam-753	191	2	x1	x1	NUM
ejpam-753	191	3	x3	x3	NOUN
ejpam-753	191	4	=	=	PUNCT
ejpam-753	192	1	x	x	PUNCT
ejpam-753	192	2	i	i	NOUN
ejpam-753	192	3	y	y	NOUN
ejpam-753	192	4	=	=	PUNCT
ejpam-753	192	5	y2	y2	PROPN
ejpam-753	192	6	=	=	SYM
ejpam-753	193	1	0	0	NUM
ejpam-753	193	2	,	,	PUNCT
ejpam-753	193	3	x2	x2	NOUN
ejpam-753	193	4	x3	x3	NOUN
ejpam-753	193	5	=	=	SYM
ejpam-753	193	6	y	y	SYM
ejpam-753	193	7	〉	〉	NOUN
ejpam-753	193	8	,	,	PUNCT
ejpam-753	193	9	〈	〈	PROPN
ejpam-753	193	10	1	1	NUM
ejpam-753	193	11	,	,	PUNCT
ejpam-753	193	12	x	x	INTJ
ejpam-753	193	13	,	,	PUNCT
ejpam-753	193	14	y	y	PROPN
ejpam-753	193	15	,	,	PUNCT
ejpam-753	193	16	z	z	PROPN
ejpam-753	193	17	,	,	PUNCT
ejpam-753	193	18	p	p	X
ejpam-753	193	19	;	;	PUNCT
ejpam-753	193	20	p21	p21	NOUN
ejpam-753	193	21	=	=	SYM
ejpam-753	193	22	0	0	PROPN
ejpam-753	193	23	,	,	PUNCT
ejpam-753	193	24	x2	x2	NOUN
ejpam-753	193	25	=	=	SYM
ejpam-753	193	26	αz	αz	PROPN
ejpam-753	193	27	,	,	PUNCT
ejpam-753	193	28	xz	xz	PROPN
ejpam-753	194	1	=	=	SYM
ejpam-753	194	2	p	p	PROPN
ejpam-753	194	3	,	,	PUNCT
ejpam-753	194	4	y2	y2	PROPN
ejpam-753	194	5	=	=	SYM
ejpam-753	194	6	δp	δp	PROPN
ejpam-753	194	7	,	,	PUNCT
ejpam-753	194	8	z2	z2	NOUN
ejpam-753	194	9	=	=	PUNCT
ejpam-753	194	10	x	x	PUNCT
ejpam-753	194	11	y	y	NOUN
ejpam-753	194	12	=	=	PUNCT
ejpam-753	194	13	yz	yz	PROPN
ejpam-753	194	14	=	=	SYM
ejpam-753	194	15	0	0	NUM
ejpam-753	194	16	〉	〉	NOUN
ejpam-753	195	1	where	where	SCONJ
ejpam-753	195	2	α	α	PROPN
ejpam-753	195	3	∈	∈	PROPN
ejpam-753	195	4	σ3	σ3	PROPN
ejpam-753	195	5	and	and	CCONJ
ejpam-753	195	6	δ	δ	PROPN
ejpam-753	195	7	∈	∈	PROPN
ejpam-753	195	8	σ0	σ0	NOUN
ejpam-753	195	9	2	2	NUM
ejpam-753	195	10	,	,	PUNCT
ejpam-753	195	11	〈	〈	NOUN
ejpam-753	195	12	1	1	NUM
ejpam-753	195	13	,	,	PUNCT
ejpam-753	195	14	x	x	INTJ
ejpam-753	195	15	,	,	PUNCT
ejpam-753	195	16	y	y	PROPN
ejpam-753	195	17	;	;	PUNCT
ejpam-753	195	18	p21	p21	NOUN
ejpam-753	195	19	=	=	SYM
ejpam-753	195	20	p2	p2	NOUN
ejpam-753	195	21	x	x	X
ejpam-753	196	1	=	=	PUNCT
ejpam-753	196	2	p	p	X
ejpam-753	196	3	y	y	PROPN
ejpam-753	196	4	=	=	SYM
ejpam-753	196	5	0	0	PROPN
ejpam-753	196	6	,	,	PUNCT
ejpam-753	196	7	x2	x2	NOUN
ejpam-753	197	1	=	=	PUNCT
ejpam-753	197	2	αp	αp	NOUN
ejpam-753	197	3	,	,	PUNCT
ejpam-753	197	4	y2	y2	PROPN
ejpam-753	197	5	=	=	SYM
ejpam-753	197	6	δpx	δpx	PROPN
ejpam-753	197	7	,	,	PUNCT
ejpam-753	197	8	x	x	PUNCT
ejpam-753	197	9	y	y	NOUN
ejpam-753	197	10	=	=	SYM
ejpam-753	197	11	0	0	NUM
ejpam-753	197	12	〉	〉	NOUN
ejpam-753	197	13	where	where	SCONJ
ejpam-753	197	14	p	p	PROPN
ejpam-753	197	15	6=	6=	PROPN
ejpam-753	197	16	2	2	NUM
ejpam-753	197	17	,	,	PUNCT
ejpam-753	197	18	α	α	PROPN
ejpam-753	197	19	∈	∈	PROPN
ejpam-753	197	20	σ2	σ2	PROPN
ejpam-753	197	21	and	and	CCONJ
ejpam-753	197	22	δ	δ	PROPN
ejpam-753	197	23	=	=	SYM
ejpam-753	197	24	0	0	NUM
ejpam-753	197	25	or	or	CCONJ
ejpam-753	197	26	α	α	PRON
ejpam-753	197	27	∈	∈	PROPN
ejpam-753	197	28	σ4	σ4	NOUN
ejpam-753	197	29	and	and	CCONJ
ejpam-753	197	30	δ	δ	NOUN
ejpam-753	197	31	=	=	SYM
ejpam-753	197	32	1	1	NUM
ejpam-753	197	33	,	,	PUNCT
ejpam-753	197	34	〈	〈	PROPN
ejpam-753	197	35	1	1	NUM
ejpam-753	197	36	,	,	PUNCT
ejpam-753	197	37	x	x	INTJ
ejpam-753	197	38	,	,	PUNCT
ejpam-753	197	39	y	y	PROPN
ejpam-753	197	40	;	;	PUNCT
ejpam-753	197	41	4.1=	4.1=	PROPN
ejpam-753	197	42	4x	4x	NOUN
ejpam-753	197	43	=	=	SYM
ejpam-753	197	44	2y	2y	PROPN
ejpam-753	197	45	=	=	SYM
ejpam-753	197	46	0	0	NUM
ejpam-753	197	47	,	,	PUNCT
ejpam-753	197	48	x2	x2	NOUN
ejpam-753	197	49	=	=	SYM
ejpam-753	197	50	2	2	NUM
ejpam-753	197	51	,	,	PUNCT
ejpam-753	197	52	y2	y2	NOUN
ejpam-753	197	53	=	=	PUNCT
ejpam-753	198	1	x	x	PUNCT
ejpam-753	198	2	y	y	PROPN
ejpam-753	198	3	=	=	SYM
ejpam-753	198	4	0	0	NUM
ejpam-753	198	5	〉	〉	NOUN
ejpam-753	198	6	,	,	PUNCT
ejpam-753	198	7	〈	〈	PROPN
ejpam-753	198	8	1	1	NUM
ejpam-753	198	9	,	,	PUNCT
ejpam-753	198	10	x	x	INTJ
ejpam-753	198	11	,	,	PUNCT
ejpam-753	198	12	y	y	PROPN
ejpam-753	198	13	;	;	PUNCT
ejpam-753	198	14	4.1=	4.1=	PROPN
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ejpam-753	198	16	=	=	SYM
ejpam-753	198	17	2y	2y	PROPN
ejpam-753	198	18	=	=	SYM
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ejpam-753	198	20	,	,	PUNCT
ejpam-753	198	21	x2	x2	NOUN
ejpam-753	198	22	=	=	VERB
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ejpam-753	198	25	2x	2x	NUM
ejpam-753	198	26	,	,	PUNCT
ejpam-753	198	27	y2	y2	X
ejpam-753	198	28	=	=	PUNCT
ejpam-753	199	1	x	x	PUNCT
ejpam-753	199	2	y	y	PROPN
ejpam-753	199	3	=	=	SYM
ejpam-753	199	4	0	0	NUM
ejpam-753	199	5	〉	〉	NOUN
ejpam-753	199	6	,	,	PUNCT
ejpam-753	199	7	〈	〈	PROPN
ejpam-753	199	8	1	1	NUM
ejpam-753	199	9	,	,	PUNCT
ejpam-753	199	10	x	x	INTJ
ejpam-753	199	11	,	,	PUNCT
ejpam-753	199	12	y	y	PROPN
ejpam-753	199	13	;	;	PUNCT
ejpam-753	199	14	4.1=	4.1=	PROPN
ejpam-753	199	15	4x	4x	NOUN
ejpam-753	199	16	=	=	SYM
ejpam-753	199	17	2y	2y	PROPN
ejpam-753	199	18	=	=	SYM
ejpam-753	199	19	0	0	NUM
ejpam-753	199	20	,	,	PUNCT
ejpam-753	199	21	x2	x2	NOUN
ejpam-753	199	22	=	=	SYM
ejpam-753	199	23	2	2	NUM
ejpam-753	199	24	,	,	PUNCT
ejpam-753	199	25	y2	y2	NOUN
ejpam-753	199	26	=	=	SYM
ejpam-753	199	27	2x	2x	NOUN
ejpam-753	199	28	,	,	PUNCT
ejpam-753	199	29	x	x	X
ejpam-753	199	30	y	y	NOUN
ejpam-753	199	31	=	=	SYM
ejpam-753	199	32	0	0	NUM
ejpam-753	199	33	〉	〉	NOUN
ejpam-753	199	34	,	,	PUNCT
ejpam-753	199	35	〈	〈	PROPN
ejpam-753	199	36	1	1	NUM
ejpam-753	199	37	,	,	PUNCT
ejpam-753	199	38	x1	x1	PROPN
ejpam-753	199	39	,	,	PUNCT
ejpam-753	199	40	x2	x2	PROPN
ejpam-753	199	41	,	,	PUNCT
ejpam-753	199	42	x3	x3	ADJ
ejpam-753	199	43	,	,	PUNCT
ejpam-753	199	44	p	p	X
ejpam-753	199	45	;	;	PUNCT
ejpam-753	199	46	p21	p21	NOUN
ejpam-753	199	47	=	=	PUNCT
ejpam-753	199	48	px	px	PROPN
ejpam-753	200	1	i	i	NOUN
ejpam-753	200	2	=	=	PROPN
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ejpam-753	200	4	,	,	PUNCT
ejpam-753	200	5	x1	x1	PROPN
ejpam-753	200	6	2	2	NUM
ejpam-753	200	7	=	=	SYM
ejpam-753	200	8	νp	νp	NOUN
ejpam-753	200	9	,	,	PUNCT
ejpam-753	200	10	x2	x2	PROPN
ejpam-753	200	11	2	2	X
ejpam-753	200	12	=	=	SYM
ejpam-753	200	13	x3	x3	NOUN
ejpam-753	200	14	2	2	NUM
ejpam-753	200	15	=	=	SYM
ejpam-753	200	16	0	0	NUM
ejpam-753	200	17	,	,	PUNCT
ejpam-753	200	18	x	x	X
ejpam-753	200	19	i	i	NOUN
ejpam-753	200	20	x	x	X
ejpam-753	200	21	j	j	PROPN
ejpam-753	200	22	=	=	NOUN
ejpam-753	200	23	0	0	PROPN
ejpam-753	201	1	for	for	ADP
ejpam-753	201	2	i	i	PRON
ejpam-753	201	3	6=	6=	PROPN
ejpam-753	201	4	j	j	X
ejpam-753	201	5	〉	〉	NOUN
ejpam-753	201	6	where	where	SCONJ
ejpam-753	201	7	p	p	PROPN
ejpam-753	201	8	6=	6=	PROPN
ejpam-753	201	9	2	2	NUM
ejpam-753	201	10	,	,	PUNCT
ejpam-753	201	11	ε	ε	PROPN
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ejpam-753	201	15	-	-	ADJ
ejpam-753	201	16	square	square	ADJ
ejpam-753	201	17	in	in	ADP
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ejpam-753	201	19	and	and	CCONJ
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ejpam-753	201	22	{	{	PUNCT
ejpam-753	201	23	1,ε	1,ε	NUM
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ejpam-753	201	25	,	,	PUNCT
ejpam-753	201	26	〈	〈	PROPN
ejpam-753	201	27	1	1	NUM
ejpam-753	201	28	,	,	PUNCT
ejpam-753	201	29	x1	x1	PROPN
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ejpam-753	201	31	x2	x2	PROPN
ejpam-753	201	32	,	,	PUNCT
ejpam-753	201	33	x3	x3	ADJ
ejpam-753	201	34	,	,	PUNCT
ejpam-753	201	35	p	p	X
ejpam-753	201	36	;	;	PUNCT
ejpam-753	201	37	p21	p21	NOUN
ejpam-753	201	38	=	=	PUNCT
ejpam-753	201	39	px	px	PROPN
ejpam-753	201	40	i	i	NOUN
ejpam-753	201	41	=	=	PROPN
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ejpam-753	201	43	,	,	PUNCT
ejpam-753	201	44	x1	x1	PROPN
ejpam-753	201	45	2	2	NUM
ejpam-753	201	46	=	=	SYM
ejpam-753	201	47	1	1	NUM
ejpam-753	201	48	,	,	PUNCT
ejpam-753	201	49	x2	x2	PROPN
ejpam-753	201	50	2	2	X
ejpam-753	201	51	=	=	SYM
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ejpam-753	201	53	,	,	PUNCT
ejpam-753	201	54	x3	x3	NOUN
ejpam-753	201	55	2	2	NUM
ejpam-753	201	56	=	=	SYM
ejpam-753	201	57	0	0	NUM
ejpam-753	201	58	,	,	PUNCT
ejpam-753	201	59	x	x	X
ejpam-753	201	60	i	i	NOUN
ejpam-753	201	61	x	x	X
ejpam-753	201	62	j	j	PROPN
ejpam-753	201	63	=	=	NOUN
ejpam-753	201	64	0	0	PROPN
ejpam-753	201	65	for	for	ADP
ejpam-753	201	66	i	i	PRON
ejpam-753	201	67	6=	6=	PROPN
ejpam-753	201	68	j	j	X
ejpam-753	201	69	〉	〉	NOUN
ejpam-753	201	70	where	where	SCONJ
ejpam-753	201	71	p	p	PROPN
ejpam-753	201	72	6=	6=	PROPN
ejpam-753	201	73	2	2	NUM
ejpam-753	201	74	,	,	PUNCT
ejpam-753	201	75	ε	ε	PROPN
ejpam-753	201	76	is	be	AUX
ejpam-753	201	77	a	a	DET
ejpam-753	201	78	non	non	ADJ
ejpam-753	201	79	-	-	ADJ
ejpam-753	201	80	square	square	ADJ
ejpam-753	201	81	in	in	ADP
ejpam-753	201	82	fp	fp	PROPN
ejpam-753	201	83	and	and	CCONJ
ejpam-753	201	84	ν	ν	X
ejpam-753	201	85	∈	∈	PROPN
ejpam-753	201	86	{	{	PUNCT
ejpam-753	201	87	1,ε	1,ε	NUM
ejpam-753	201	88	}	}	PUNCT
ejpam-753	201	89	,	,	PUNCT
ejpam-753	201	90	〈	〈	PROPN
ejpam-753	201	91	1	1	NUM
ejpam-753	201	92	,	,	PUNCT
ejpam-753	201	93	x1	x1	PROPN
ejpam-753	201	94	,	,	PUNCT
ejpam-753	201	95	x2	x2	PROPN
ejpam-753	201	96	,	,	PUNCT
ejpam-753	201	97	x3	x3	ADJ
ejpam-753	201	98	,	,	PUNCT
ejpam-753	201	99	p	p	X
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ejpam-753	201	101	p21	p21	NOUN
ejpam-753	201	102	=	=	PUNCT
ejpam-753	201	103	px	px	PROPN
ejpam-753	201	104	i	i	NOUN
ejpam-753	201	105	=	=	PROPN
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ejpam-753	201	107	,	,	PUNCT
ejpam-753	201	108	x1	x1	PROPN
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ejpam-753	202	2	x2	x2	NOUN
ejpam-753	202	3	2	2	NUM
ejpam-753	202	4	=	=	SYM
ejpam-753	202	5	1	1	NUM
ejpam-753	202	6	,	,	PUNCT
ejpam-753	202	7	x3	x3	NOUN
ejpam-753	202	8	2	2	NUM
ejpam-753	202	9	=	=	SYM
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ejpam-753	202	11	,	,	PUNCT
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ejpam-753	202	13	i	i	NOUN
ejpam-753	202	14	x	x	X
ejpam-753	202	15	j	j	PROPN
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ejpam-753	202	17	0	0	PROPN
ejpam-753	203	1	for	for	ADP
ejpam-753	203	2	i	i	PRON
ejpam-753	203	3	6=	6=	PROPN
ejpam-753	203	4	j	j	X
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ejpam-753	203	7	p	p	PROPN
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ejpam-753	203	9	2	2	NUM
ejpam-753	203	10	,	,	PUNCT
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ejpam-753	203	17	in	in	ADP
ejpam-753	203	18	fp	fp	PROPN
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ejpam-753	203	20	ν	ν	X
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ejpam-753	203	23	1,ε	1,ε	NUM
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ejpam-753	203	25	,	,	PUNCT
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ejpam-753	203	28	,	,	PUNCT
ejpam-753	203	29	x1	x1	PROPN
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ejpam-753	203	31	x2	x2	PROPN
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ejpam-753	203	33	x3	x3	ADJ
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ejpam-753	203	35	4.1=	4.1=	PROPN
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ejpam-753	203	37	i	i	NOUN
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ejpam-753	203	39	0	0	PROPN
ejpam-753	203	40	,	,	PUNCT
ejpam-753	203	41	x1	x1	PROPN
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ejpam-753	203	43	=	=	SYM
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ejpam-753	203	45	,	,	PUNCT
ejpam-753	203	46	x2	x2	NOUN
ejpam-753	203	47	2	2	X
ejpam-753	203	48	=	=	SYM
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ejpam-753	203	50	2	2	NUM
ejpam-753	203	51	=	=	SYM
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ejpam-753	203	53	,	,	PUNCT
ejpam-753	203	54	x	x	X
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ejpam-753	204	2	x	x	X
ejpam-753	204	3	j	j	PROPN
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ejpam-753	204	5	0	0	PROPN
ejpam-753	204	6	for	for	ADP
ejpam-753	204	7	i	i	PROPN
ejpam-753	204	8	6=	6=	PROPN
ejpam-753	204	9	j	j	PROPN
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ejpam-753	204	11	,	,	PUNCT
ejpam-753	204	12	〈	〈	PROPN
ejpam-753	204	13	1	1	NUM
ejpam-753	204	14	,	,	PUNCT
ejpam-753	204	15	x1	x1	PROPN
ejpam-753	204	16	,	,	PUNCT
ejpam-753	204	17	x2	x2	PROPN
ejpam-753	204	18	,	,	PUNCT
ejpam-753	204	19	x3	x3	ADJ
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ejpam-753	204	21	4.1=	4.1=	PROPN
ejpam-753	204	22	2x	2x	NUM
ejpam-753	205	1	i	i	NOUN
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ejpam-753	205	3	0	0	PROPN
ejpam-753	205	4	,	,	PUNCT
ejpam-753	205	5	x1	x1	PROPN
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ejpam-753	205	7	=	=	SYM
ejpam-753	205	8	1	1	NUM
ejpam-753	205	9	,	,	PUNCT
ejpam-753	205	10	x2	x2	PROPN
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ejpam-753	205	12	=	=	SYM
ejpam-753	205	13	2	2	NUM
ejpam-753	205	14	,	,	PUNCT
ejpam-753	205	15	x3	x3	NOUN
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ejpam-753	205	17	=	=	SYM
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ejpam-753	205	19	,	,	PUNCT
ejpam-753	205	20	x	x	X
ejpam-753	205	21	i	i	NOUN
ejpam-753	205	22	x	x	X
ejpam-753	205	23	j	j	PROPN
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ejpam-753	205	25	0	0	PROPN
ejpam-753	206	1	for	for	ADP
ejpam-753	206	2	i	i	PROPN
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ejpam-753	206	4	j	j	PROPN
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ejpam-753	206	6	,	,	PUNCT
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ejpam-753	206	9	,	,	PUNCT
ejpam-753	206	10	x1	x1	PROPN
ejpam-753	206	11	,	,	PUNCT
ejpam-753	206	12	x2	x2	PROPN
ejpam-753	206	13	,	,	PUNCT
ejpam-753	206	14	x3	x3	ADJ
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ejpam-753	206	16	4.1=	4.1=	PROPN
ejpam-753	206	17	2x	2x	NUM
ejpam-753	206	18	i	i	NOUN
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ejpam-753	206	20	0	0	PROPN
ejpam-753	206	21	,	,	PUNCT
ejpam-753	206	22	x1	x1	PROPN
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ejpam-753	206	24	=	=	SYM
ejpam-753	206	25	x2	x2	NOUN
ejpam-753	206	26	2	2	NUM
ejpam-753	206	27	=	=	SYM
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ejpam-753	206	29	,	,	PUNCT
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ejpam-753	206	31	2	2	NUM
ejpam-753	206	32	=	=	SYM
ejpam-753	206	33	2	2	NUM
ejpam-753	206	34	,	,	PUNCT
ejpam-753	206	35	x	x	PROPN
ejpam-753	206	36	i	i	NOUN
ejpam-753	206	37	x	x	X
ejpam-753	206	38	j	j	PROPN
ejpam-753	206	39	=	=	NOUN
ejpam-753	206	40	0	0	PROPN
ejpam-753	206	41	for	for	ADP
ejpam-753	206	42	i	i	PROPN
ejpam-753	206	43	6=	6=	PROPN
ejpam-753	206	44	j	j	PROPN
ejpam-753	206	45	〉	〉	PROPN
ejpam-753	206	46	,	,	PUNCT
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ejpam-753	206	49	,	,	PUNCT
ejpam-753	206	50	x1	x1	PROPN
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ejpam-753	206	52	x2	x2	PROPN
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ejpam-753	206	54	y	y	PROPN
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ejpam-753	206	56	p21=	p21=	X
ejpam-753	206	57	px	px	X
ejpam-753	207	1	i	i	NOUN
ejpam-753	207	2	=	=	PROPN
ejpam-753	208	1	p	p	X
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ejpam-753	208	5	,	,	PUNCT
ejpam-753	208	6	x1	x1	PROPN
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ejpam-753	208	9	1	1	NUM
ejpam-753	208	10	,	,	PUNCT
ejpam-753	208	11	x2	x2	PROPN
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ejpam-753	208	15	,	,	PUNCT
ejpam-753	208	16	x1	x1	NOUN
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ejpam-753	210	4	x2	x2	PROPN
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ejpam-753	210	9	,	,	PUNCT
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ejpam-753	210	13	x1	x1	PROPN
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ejpam-753	210	15	x2	x2	PROPN
ejpam-753	210	16	,	,	PUNCT
ejpam-753	210	17	y	y	PROPN
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ejpam-753	210	19	p21=	p21=	X
ejpam-753	210	20	px	px	X
ejpam-753	210	21	i	i	NOUN
ejpam-753	210	22	=	=	PROPN
ejpam-753	211	1	p	p	X
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ejpam-753	211	4	0	0	PROPN
ejpam-753	211	5	,	,	PUNCT
ejpam-753	211	6	x1	x1	PROPN
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ejpam-753	211	16	x1	x1	PROPN
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ejpam-753	213	1	x1	x1	NUM
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ejpam-753	213	4	x2	x2	PROPN
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ejpam-753	213	7	0	0	NUM
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ejpam-753	213	9	,	,	PUNCT
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ejpam-753	213	11	1	1	NUM
ejpam-753	213	12	,	,	PUNCT
ejpam-753	213	13	x1	x1	PROPN
ejpam-753	213	14	,	,	PUNCT
ejpam-753	213	15	x2	x2	PROPN
ejpam-753	213	16	,	,	PUNCT
ejpam-753	213	17	y	y	PROPN
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ejpam-753	214	1	p21	p21	NOUN
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ejpam-753	214	3	px	px	PROPN
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ejpam-753	216	1	=	=	PROPN
ejpam-753	217	1	p	p	X
ejpam-753	217	2	y	y	PROPN
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ejpam-753	217	4	0	0	PROPN
ejpam-753	217	5	,	,	PUNCT
ejpam-753	217	6	x1	x1	PROPN
ejpam-753	217	7	2	2	NUM
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ejpam-753	217	9	1	1	NUM
ejpam-753	217	10	,	,	PUNCT
ejpam-753	217	11	x2	x2	PROPN
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ejpam-753	217	13	=	=	SYM
ejpam-753	217	14	ξy	ξy	PROPN
ejpam-753	217	15	,	,	PUNCT
ejpam-753	217	16	x1	x1	PROPN
ejpam-753	218	1	x2	x2	NOUN
ejpam-753	219	1	=	=	PUNCT
ejpam-753	220	1	x1	x1	NUM
ejpam-753	220	2	y	y	NOUN
ejpam-753	220	3	=	=	SYM
ejpam-753	220	4	x2	x2	PROPN
ejpam-753	220	5	y	y	PROPN
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ejpam-753	220	7	0	0	NUM
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ejpam-753	220	10	p	p	PROPN
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ejpam-753	220	13	,	,	PUNCT
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ejpam-753	220	28	x2	x2	PROPN
ejpam-753	220	29	,	,	PUNCT
ejpam-753	220	30	y	y	PROPN
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ejpam-753	220	32	4.1=	4.1=	PROPN
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ejpam-753	221	7	x1	x1	PROPN
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ejpam-753	222	1	=	=	SYM
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ejpam-753	223	1	x2	x2	PROPN
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ejpam-753	224	1	x2	x2	NOUN
ejpam-753	224	2	=	=	PUNCT
ejpam-753	224	3	y	y	SYM
ejpam-753	224	4	〉	〉	NOUN
ejpam-753	224	5	,	,	PUNCT
ejpam-753	224	6	〈	〈	PROPN
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ejpam-753	224	8	,	,	PUNCT
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ejpam-753	224	11	y	y	PROPN
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ejpam-753	224	15	p21=	p21=	X
ejpam-753	224	16	p2	p2	X
ejpam-753	224	17	x	x	X
ejpam-753	224	18	=	=	PUNCT
ejpam-753	224	19	p	p	X
ejpam-753	224	20	y	y	PROPN
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ejpam-753	224	22	0	0	PROPN
ejpam-753	224	23	,	,	PUNCT
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ejpam-753	224	31	,	,	PUNCT
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ejpam-753	224	33	y	y	NOUN
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ejpam-753	224	35	0	0	NUM
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ejpam-753	224	75	α	α	NOUN
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ejpam-753	224	82	0,0	0,0	NOUN
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ejpam-753	224	86	1,0	1,0	NUM
ejpam-753	224	87	)	)	PUNCT
ejpam-753	224	88	,	,	PUNCT
ejpam-753	224	89	(	(	PUNCT
ejpam-753	224	90	1,1	1,1	NUM
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ejpam-753	224	92	}	}	PUNCT
ejpam-753	224	93	,	,	PUNCT
ejpam-753	224	94	〈	〈	PROPN
ejpam-753	224	95	1	1	NUM
ejpam-753	224	96	,	,	PUNCT
ejpam-753	224	97	x1	x1	PROPN
ejpam-753	224	98	,	,	PUNCT
ejpam-753	224	99	x2	x2	PROPN
ejpam-753	224	100	;	;	PUNCT
ejpam-753	224	101	p31=	p31=	NUM
ejpam-753	224	102	px	px	NOUN
ejpam-753	224	103	i	i	NOUN
ejpam-753	224	104	=	=	PROPN
ejpam-753	224	105	0	0	PROPN
ejpam-753	224	106	,	,	PUNCT
ejpam-753	224	107	x1	x1	PROPN
ejpam-753	224	108	2	2	X
ejpam-753	224	109	=	=	SYM
ejpam-753	224	110	x2	x2	NOUN
ejpam-753	224	111	2	2	NUM
ejpam-753	224	112	=	=	SYM
ejpam-753	224	113	0	0	NUM
ejpam-753	224	114	,	,	PUNCT
ejpam-753	224	115	x1	x1	PROPN
ejpam-753	224	116	x2	x2	NOUN
ejpam-753	224	117	=	=	SYM
ejpam-753	224	118	0	0	NUM
ejpam-753	224	119	〉	〉	NOUN
ejpam-753	224	120	,	,	PUNCT
ejpam-753	224	121	〈	〈	PROPN
ejpam-753	224	122	1	1	NUM
ejpam-753	224	123	,	,	PUNCT
ejpam-753	224	124	x1	x1	PROPN
ejpam-753	224	125	,	,	PUNCT
ejpam-753	224	126	x2	x2	PROPN
ejpam-753	224	127	;	;	PUNCT
ejpam-753	224	128	p31=	p31=	NUM
ejpam-753	224	129	px	px	NOUN
ejpam-753	224	130	i	i	NOUN
ejpam-753	224	131	=	=	PROPN
ejpam-753	224	132	0	0	PROPN
ejpam-753	224	133	,	,	PUNCT
ejpam-753	224	134	x1	x1	PROPN
ejpam-753	224	135	2	2	NUM
ejpam-753	224	136	=	=	SYM
ejpam-753	224	137	p2	p2	NOUN
ejpam-753	224	138	,	,	PUNCT
ejpam-753	224	139	x2	x2	PROPN
ejpam-753	224	140	2	2	NUM
ejpam-753	224	141	=	=	SYM
ejpam-753	224	142	x1	x1	NOUN
ejpam-753	224	143	x2	x2	NOUN
ejpam-753	224	144	=	=	SYM
ejpam-753	224	145	0	0	NUM
ejpam-753	224	146	〉	〉	NOUN
ejpam-753	224	147	,	,	PUNCT
ejpam-753	224	148	〈	〈	PROPN
ejpam-753	224	149	1	1	NUM
ejpam-753	224	150	,	,	PUNCT
ejpam-753	224	151	x1	x1	PROPN
ejpam-753	224	152	,	,	PUNCT
ejpam-753	224	153	x2	x2	PROPN
ejpam-753	224	154	;	;	PUNCT
ejpam-753	224	155	p31=	p31=	NUM
ejpam-753	224	156	px	px	NOUN
ejpam-753	224	157	i	i	NOUN
ejpam-753	224	158	=	=	PROPN
ejpam-753	224	159	0	0	PROPN
ejpam-753	224	160	,	,	PUNCT
ejpam-753	224	161	x1	x1	PROPN
ejpam-753	224	162	2	2	X
ejpam-753	224	163	=	=	SYM
ejpam-753	224	164	εp2	εp2	PROPN
ejpam-753	224	165	,	,	PUNCT
ejpam-753	224	166	x2	x2	PROPN
ejpam-753	224	167	2	2	NUM
ejpam-753	224	168	=	=	SYM
ejpam-753	224	169	x1	x1	NOUN
ejpam-753	224	170	x2	x2	NOUN
ejpam-753	224	171	=	=	SYM
ejpam-753	224	172	0	0	NUM
ejpam-753	224	173	〉	〉	NOUN
ejpam-753	224	174	where	where	SCONJ
ejpam-753	224	175	p	p	PROPN
ejpam-753	224	176	6=	6=	PROPN
ejpam-753	224	177	2	2	NUM
ejpam-753	224	178	,	,	PUNCT
ejpam-753	224	179	〈	〈	PROPN
ejpam-753	224	180	1	1	NUM
ejpam-753	224	181	,	,	PUNCT
ejpam-753	224	182	x1	x1	PROPN
ejpam-753	224	183	,	,	PUNCT
ejpam-753	224	184	x2	x2	PROPN
ejpam-753	224	185	;	;	PUNCT
ejpam-753	224	186	p31=	p31=	NUM
ejpam-753	224	187	px	px	NOUN
ejpam-753	224	188	i	i	NOUN
ejpam-753	224	189	=	=	PROPN
ejpam-753	224	190	0	0	PROPN
ejpam-753	224	191	,	,	PUNCT
ejpam-753	224	192	x1	x1	PROPN
ejpam-753	224	193	2	2	X
ejpam-753	224	194	=	=	SYM
ejpam-753	224	195	x2	x2	NOUN
ejpam-753	224	196	2	2	NUM
ejpam-753	224	197	=	=	SYM
ejpam-753	224	198	p2	p2	NOUN
ejpam-753	224	199	,	,	PUNCT
ejpam-753	224	200	x1	x1	PROPN
ejpam-753	224	201	x2	x2	NOUN
ejpam-753	224	202	=	=	SYM
ejpam-753	224	203	0	0	NUM
ejpam-753	224	204	〉	〉	NOUN
ejpam-753	224	205	,	,	PUNCT
ejpam-753	224	206	〈	〈	PROPN
ejpam-753	224	207	1	1	NUM
ejpam-753	224	208	,	,	PUNCT
ejpam-753	224	209	x1	x1	PROPN
ejpam-753	224	210	,	,	PUNCT
ejpam-753	224	211	x2	x2	PROPN
ejpam-753	224	212	;	;	PUNCT
ejpam-753	224	213	p31	p31	NOUN
ejpam-753	224	214	=	=	PUNCT
ejpam-753	224	215	px	px	PROPN
ejpam-753	224	216	i	i	NOUN
ejpam-753	224	217	=	=	PROPN
ejpam-753	224	218	0	0	PROPN
ejpam-753	224	219	,	,	PUNCT
ejpam-753	224	220	x1	x1	PROPN
ejpam-753	224	221	2	2	NUM
ejpam-753	224	222	=	=	SYM
ejpam-753	224	223	p2	p2	NOUN
ejpam-753	224	224	,	,	PUNCT
ejpam-753	224	225	x2	x2	PROPN
ejpam-753	224	226	2	2	NUM
ejpam-753	224	227	=	=	SYM
ejpam-753	224	228	εp2	εp2	PROPN
ejpam-753	224	229	,	,	PUNCT
ejpam-753	224	230	x1	x1	PROPN
ejpam-753	224	231	x2	x2	NOUN
ejpam-753	224	232	=	=	SYM
ejpam-753	224	233	0	0	NUM
ejpam-753	224	234	〉	〉	NOUN
ejpam-753	224	235	where	where	SCONJ
ejpam-753	224	236	p	p	PROPN
ejpam-753	224	237	6=	6=	PROPN
ejpam-753	224	238	2	2	NUM
ejpam-753	224	239	and	and	CCONJ
ejpam-753	224	240	ε	ε	PROPN
ejpam-753	224	241	is	be	AUX
ejpam-753	224	242	a	a	DET
ejpam-753	224	243	non	non	ADJ
ejpam-753	224	244	-	-	ADJ
ejpam-753	224	245	square	square	ADJ
ejpam-753	224	246	in	in	ADP
ejpam-753	224	247	fp	fp	PROPN
ejpam-753	224	248	,	,	PUNCT
ejpam-753	224	249	〈	〈	PROPN
ejpam-753	224	250	1	1	NUM
ejpam-753	224	251	,	,	PUNCT
ejpam-753	224	252	x1	x1	PROPN
ejpam-753	224	253	,	,	PUNCT
ejpam-753	224	254	x2	x2	PROPN
ejpam-753	224	255	;	;	PUNCT
ejpam-753	224	256	8.1=	8.1=	PROPN
ejpam-753	224	257	2x	2x	NUM
ejpam-753	224	258	i	i	NOUN
ejpam-753	224	259	=	=	NOUN
ejpam-753	224	260	0	0	PROPN
ejpam-753	224	261	,	,	PUNCT
ejpam-753	224	262	x1	x1	PROPN
ejpam-753	224	263	2	2	X
ejpam-753	224	264	=	=	SYM
ejpam-753	224	265	x2	x2	NOUN
ejpam-753	224	266	2	2	NUM
ejpam-753	224	267	=	=	SYM
ejpam-753	224	268	0	0	NUM
ejpam-753	224	269	,	,	PUNCT
ejpam-753	224	270	x1	x1	PROPN
ejpam-753	224	271	x2	x2	NOUN
ejpam-753	224	272	=	=	NOUN
ejpam-753	224	273	4	4	NUM
ejpam-753	224	274	〉	〉	NOUN
ejpam-753	224	275	or	or	CCONJ
ejpam-753	224	276	one	one	NUM
ejpam-753	224	277	of	of	ADP
ejpam-753	224	278	the	the	DET
ejpam-753	224	279	rings	ring	NOUN
ejpam-753	224	280	given	give	VERB
ejpam-753	224	281	in	in	ADP
ejpam-753	224	282	full	full	ADJ
ejpam-753	224	283	in	in	ADP
ejpam-753	224	284	[	[	X
ejpam-753	224	285	9	9	NUM
ejpam-753	224	286	]	]	PUNCT
ejpam-753	224	287	.	.	PUNCT
ejpam-753	225	1	the	the	DET
ejpam-753	225	2	number	number	NOUN
ejpam-753	225	3	of	of	ADP
ejpam-753	225	4	these	these	DET
ejpam-753	225	5	rings	ring	NOUN
ejpam-753	225	6	is	be	AUX
ejpam-753	225	7	10	10	NUM
ejpam-753	225	8	or	or	CCONJ
ejpam-753	225	9	6	6	NUM
ejpam-753	225	10	according	accord	VERB
ejpam-753	225	11	to	to	ADP
ejpam-753	225	12	whether	whether	SCONJ
ejpam-753	225	13	p	p	NOUN
ejpam-753	225	14	6=	6=	NUM
ejpam-753	225	15	2	2	NUM
ejpam-753	225	16	or	or	CCONJ
ejpam-753	225	17	p	p	NOUN
ejpam-753	225	18	=	=	NOUN
ejpam-753	225	19	2	2	X
ejpam-753	225	20	.	.	PUNCT
ejpam-753	225	21	proof	proof	NOUN
ejpam-753	225	22	.	.	PUNCT
ejpam-753	226	1	by	by	ADP
ejpam-753	226	2	using	use	VERB
ejpam-753	226	3	[	[	X
ejpam-753	226	4	5	5	NUM
ejpam-753	226	5	]	]	PUNCT
ejpam-753	226	6	and	and	CCONJ
ejpam-753	226	7	[	[	X
ejpam-753	226	8	9	9	NUM
ejpam-753	226	9	]	]	PUNCT
ejpam-753	226	10	one	one	PRON
ejpam-753	226	11	can	can	AUX
ejpam-753	226	12	check	check	VERB
ejpam-753	226	13	that	that	PRON
ejpam-753	226	14	r	r	NOUN
ejpam-753	226	15	is	be	AUX
ejpam-753	226	16	isomorphic	isomorphic	ADJ
ejpam-753	226	17	to	to	ADP
ejpam-753	226	18	one	one	NUM
ejpam-753	226	19	of	of	ADP
ejpam-753	226	20	the	the	DET
ejpam-753	226	21	above	above	ADJ
ejpam-753	226	22	rings	ring	NOUN
ejpam-753	226	23	.	.	PUNCT
ejpam-753	227	1	theorem	theorem	NOUN
ejpam-753	227	2	1	1	NUM
ejpam-753	227	3	.	.	PUNCT
ejpam-753	228	1	let	let	VERB
ejpam-753	228	2	r	r	PRON
ejpam-753	228	3	be	be	AUX
ejpam-753	228	4	a	a	DET
ejpam-753	228	5	ring	ring	NOUN
ejpam-753	228	6	with	with	ADP
ejpam-753	228	7	|z(r)|	|z(r)|	PROPN
ejpam-753	228	8	=	=	PUNCT
ejpam-753	228	9	p4	p4	NOUN
ejpam-753	228	10	,	,	PUNCT
ejpam-753	228	11	where	where	SCONJ
ejpam-753	228	12	p	p	NOUN
ejpam-753	228	13	is	be	AUX
ejpam-753	228	14	a	a	DET
ejpam-753	228	15	prime	prime	ADJ
ejpam-753	228	16	number	number	NOUN
ejpam-753	228	17	.	.	PUNCT
ejpam-753	229	1	then	then	ADV
ejpam-753	229	2	r	r	NOUN
ejpam-753	229	3	is	be	AUX
ejpam-753	229	4	isomorphic	isomorphic	ADJ
ejpam-753	229	5	to	to	ADP
ejpam-753	229	6	one	one	NUM
ejpam-753	229	7	of	of	ADP
ejpam-753	229	8	the	the	DET
ejpam-753	229	9	rings	ring	NOUN
ejpam-753	229	10	described	describe	VERB
ejpam-753	229	11	in	in	ADP
ejpam-753	229	12	proposition	proposition	NOUN
ejpam-753	229	13	1	1	NUM
ejpam-753	229	14	,	,	PUNCT
ejpam-753	229	15	proposition	proposition	NOUN
ejpam-753	229	16	2	2	NUM
ejpam-753	229	17	,	,	PUNCT
ejpam-753	229	18	the	the	DET
ejpam-753	229	19	galois	galois	PROPN
ejpam-753	229	20	ring	ring	NOUN
ejpam-753	229	21	gr(p8	gr(p8	NOUN
ejpam-753	229	22	,	,	PUNCT
ejpam-753	229	23	p2	p2	PROPN
ejpam-753	229	24	)	)	PUNCT
ejpam-753	229	25	,	,	PUNCT
ejpam-753	229	26	fp4[x]/(x2	fp4[x]/(x2	PROPN
ejpam-753	229	27	)	)	PUNCT
ejpam-753	229	28	,	,	PUNCT
ejpam-753	229	29	zp2	zp2	INTJ
ejpam-753	229	30	×	×	NOUN
ejpam-753	229	31	fq1	fq1	INTJ
ejpam-753	229	32	×	×	NOUN
ejpam-753	229	33	.	.	PUNCT
ejpam-753	229	34	.	.	PUNCT
ejpam-753	230	1	.×	.×	PROPN
ejpam-753	230	2	fqt	fqt	PROPN
ejpam-753	230	3	,	,	PUNCT
ejpam-753	230	4	zp[x]/(x	zp[x]/(x	PROPN
ejpam-753	230	5	2)×	2)×	NUM
ejpam-753	231	1	fq1	fq1	NUM
ejpam-753	231	2	×	×	NOUN
ejpam-753	231	3	.	.	PUNCT
ejpam-753	231	4	.	.	PUNCT
ejpam-753	232	1	.×	.×	PROPN
ejpam-753	232	2	fqt	fqt	VERB
ejpam-753	232	3	where	where	SCONJ
ejpam-753	232	4	p3	p3	PROPN
ejpam-753	232	5	=	=	PUNCT
ejpam-753	233	1	p2q1	p2q1	PROPN
ejpam-753	233	2	.	.	PUNCT
ejpam-753	233	3	.	.	PUNCT
ejpam-753	233	4	.	.	PUNCT
ejpam-753	234	1	qt	qt	INTJ
ejpam-753	234	2	−	−	PROPN
ejpam-753	235	1	(	(	PUNCT
ejpam-753	235	2	p	p	NOUN
ejpam-753	235	3	2	2	NUM
ejpam-753	235	4	−	−	NOUN
ejpam-753	235	5	p)(q1	p)(q1	NOUN
ejpam-753	235	6	−	−	NOUN
ejpam-753	235	7	1	1	NUM
ejpam-753	235	8	)	)	PUNCT
ejpam-753	235	9	.	.	PUNCT
ejpam-753	235	10	.	.	PUNCT
ejpam-753	235	11	.	.	PUNCT
ejpam-753	236	1	(	(	PUNCT
ejpam-753	236	2	qt	qt	INTJ
ejpam-753	236	3	−	−	PROPN
ejpam-753	236	4	1	1	NUM
ejpam-753	236	5	)	)	PUNCT
ejpam-753	236	6	,	,	PUNCT
ejpam-753	236	7	fq1	fq1	CCONJ
ejpam-753	236	8	×	×	NOUN
ejpam-753	236	9	.	.	PUNCT
ejpam-753	236	10	.	.	PUNCT
ejpam-753	236	11	.	.	PUNCT
ejpam-753	237	1	×	×	NOUN
ejpam-753	237	2	fqt	fqt	NOUN
ejpam-753	237	3	where	where	SCONJ
ejpam-753	237	4	p4	p4	ADJ
ejpam-753	237	5	=	=	SYM
ejpam-753	237	6	q1q2	q1q2	PROPN
ejpam-753	237	7	.	.	PUNCT
ejpam-753	237	8	.	.	PUNCT
ejpam-753	237	9	.	.	PUNCT
ejpam-753	238	1	qt	qt	INTJ
ejpam-753	238	2	−	−	PROPN
ejpam-753	238	3	(	(	PUNCT
ejpam-753	238	4	q1	q1	PROPN
ejpam-753	238	5	−	−	PROPN
ejpam-753	238	6	1)(q2	1)(q2	NUM
ejpam-753	238	7	−	−	PROPN
ejpam-753	238	8	1	1	NUM
ejpam-753	238	9	)	)	PUNCT
ejpam-753	238	10	.	.	PUNCT
ejpam-753	238	11	.	.	PUNCT
ejpam-753	238	12	.	.	PUNCT
ejpam-753	239	1	(	(	PUNCT
ejpam-753	239	2	qt	qt	INTJ
ejpam-753	239	3	−	−	PROPN
ejpam-753	239	4	1	1	NUM
ejpam-753	239	5	)	)	PUNCT
ejpam-753	239	6	or	or	CCONJ
ejpam-753	239	7	r1	r1	PROPN
ejpam-753	239	8	×	×	PROPN
ejpam-753	239	9	fq	fq	PROPN
ejpam-753	239	10	with	with	ADP
ejpam-753	239	11	p2	p2	PROPN
ejpam-753	239	12	=	=	PUNCT
ejpam-753	240	1	p	p	X
ejpam-753	240	2	+	+	NOUN
ejpam-753	240	3	q−	q−	PROPN
ejpam-753	240	4	1	1	NUM
ejpam-753	240	5	where	where	SCONJ
ejpam-753	240	6	r1	r1	PROPN
ejpam-753	240	7	is	be	AUX
ejpam-753	240	8	isomorphic	isomorphic	ADJ
ejpam-753	240	9	to	to	ADP
ejpam-753	240	10	one	one	NUM
ejpam-753	240	11	of	of	ADP
ejpam-753	240	12	the	the	DET
ejpam-753	240	13	rings	ring	NOUN
ejpam-753	240	14	zp3	zp3	PROPN
ejpam-753	240	15	,	,	PUNCT
ejpam-753	240	16	fp[x	fp[x	PROPN
ejpam-753	240	17	,	,	PUNCT
ejpam-753	240	18	y]/(x	y]/(x	PROPN
ejpam-753	240	19	,	,	PUNCT
ejpam-753	240	20	y)2	y)2	NOUN
ejpam-753	240	21	,	,	PUNCT
ejpam-753	240	22	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	240	23	3	3	NUM
ejpam-753	240	24	)	)	PUNCT
ejpam-753	240	25	or	or	CCONJ
ejpam-753	240	26	zp2[x]/(px	zp2[x]/(px	X
ejpam-753	240	27	,	,	PUNCT
ejpam-753	240	28	x2−	x2−	PROPN
ejpam-753	240	29	ǫp	ǫp	NOUN
ejpam-753	240	30	)	)	PUNCT
ejpam-753	240	31	where	where	SCONJ
ejpam-753	240	32	ǫ	ǫ	PROPN
ejpam-753	240	33	∈	∈	PROPN
ejpam-753	240	34	σ0	σ0	NOUN
ejpam-753	240	35	2	2	NUM
ejpam-753	240	36	.	.	PUNCT
ejpam-753	240	37	m.	m.	NOUN
ejpam-753	240	38	behboodi	behboodi	PROPN
ejpam-753	240	39	,	,	PUNCT
ejpam-753	240	40	r.	r.	PROPN
ejpam-753	240	41	beyranvand	beyranvand	PROPN
ejpam-753	240	42	/	/	SYM
ejpam-753	240	43	eur	eur	PROPN
ejpam-753	240	44	.	.	PUNCT
ejpam-753	241	1	j.	j.	PROPN
ejpam-753	241	2	pure	pure	PROPN
ejpam-753	241	3	appl	appl	PROPN
ejpam-753	241	4	.	.	PROPN
ejpam-753	241	5	math	math	PROPN
ejpam-753	241	6	,	,	PUNCT
ejpam-753	241	7	3	3	NUM
ejpam-753	241	8	(	(	PUNCT
ejpam-753	241	9	2010	2010	NUM
ejpam-753	241	10	)	)	PUNCT
ejpam-753	241	11	,	,	PUNCT
ejpam-753	241	12	686	686	NUM
ejpam-753	241	13	-	-	SYM
ejpam-753	241	14	694	694	NUM
ejpam-753	241	15	691	691	NUM
ejpam-753	241	16	proof	proof	NOUN
ejpam-753	241	17	.	.	PUNCT
ejpam-753	241	18	suppose	suppose	VERB
ejpam-753	241	19	that	that	SCONJ
ejpam-753	241	20	r	r	NOUN
ejpam-753	241	21	is	be	AUX
ejpam-753	241	22	a	a	DET
ejpam-753	241	23	local	local	ADJ
ejpam-753	241	24	ring	ring	NOUN
ejpam-753	241	25	.	.	PUNCT
ejpam-753	242	1	then	then	ADV
ejpam-753	242	2	by	by	ADP
ejpam-753	242	3	lemma	lemma	PROPN
ejpam-753	242	4	1	1	NUM
ejpam-753	242	5	,	,	PUNCT
ejpam-753	242	6	|r|=	|r|=	NOUN
ejpam-753	242	7	p5	p5	ADJ
ejpam-753	242	8	,	,	PUNCT
ejpam-753	242	9	p6	p6	ADJ
ejpam-753	242	10	or	or	CCONJ
ejpam-753	242	11	p8	p8	ADJ
ejpam-753	242	12	.	.	PUNCT
ejpam-753	243	1	if	if	SCONJ
ejpam-753	243	2	|r|=	|r|=	NOUN
ejpam-753	243	3	p5	p5	ADJ
ejpam-753	243	4	or	or	CCONJ
ejpam-753	243	5	p6	p6	PROPN
ejpam-753	243	6	,	,	PUNCT
ejpam-753	243	7	then	then	ADV
ejpam-753	243	8	r	r	NOUN
ejpam-753	243	9	is	be	AUX
ejpam-753	243	10	isomorphic	isomorphic	ADJ
ejpam-753	243	11	to	to	ADP
ejpam-753	243	12	one	one	NUM
ejpam-753	243	13	of	of	ADP
ejpam-753	243	14	the	the	DET
ejpam-753	243	15	rings	ring	NOUN
ejpam-753	243	16	described	describe	VERB
ejpam-753	243	17	in	in	ADP
ejpam-753	243	18	proposition	proposition	NOUN
ejpam-753	243	19	1	1	NUM
ejpam-753	243	20	or	or	CCONJ
ejpam-753	243	21	proposition	proposition	NOUN
ejpam-753	243	22	2	2	NUM
ejpam-753	243	23	.	.	PUNCT
ejpam-753	244	1	if	if	SCONJ
ejpam-753	244	2	|r|=	|r|=	PRON
ejpam-753	244	3	p8	p8	VERB
ejpam-753	244	4	,	,	PUNCT
ejpam-753	244	5	then	then	ADV
ejpam-753	244	6	by	by	ADP
ejpam-753	244	7	[	[	X
ejpam-753	244	8	8	8	NUM
ejpam-753	244	9	,	,	PUNCT
ejpam-753	244	10	theorem	theorem	VERB
ejpam-753	244	11	12	12	NUM
ejpam-753	244	12	]	]	PUNCT
ejpam-753	244	13	,	,	PUNCT
ejpam-753	244	14	r	r	NOUN
ejpam-753	244	15	is	be	AUX
ejpam-753	244	16	isomorphic	isomorphic	ADJ
ejpam-753	244	17	to	to	ADP
ejpam-753	244	18	the	the	DET
ejpam-753	244	19	galois	galois	PROPN
ejpam-753	244	20	ring	ring	NOUN
ejpam-753	244	21	gr(p8	gr(p8	NOUN
ejpam-753	244	22	,	,	PUNCT
ejpam-753	244	23	p2	p2	PROPN
ejpam-753	244	24	)	)	PUNCT
ejpam-753	244	25	or	or	CCONJ
ejpam-753	244	26	fp4[x]/(x2	fp4[x]/(x2	NOUN
ejpam-753	244	27	)	)	PUNCT
ejpam-753	244	28	.	.	PUNCT
ejpam-753	245	1	now	now	ADV
ejpam-753	245	2	suppose	suppose	VERB
ejpam-753	245	3	r	r	NOUN
ejpam-753	245	4	is	be	AUX
ejpam-753	245	5	a	a	DET
ejpam-753	245	6	nonlocal	nonlocal	ADJ
ejpam-753	245	7	ring	ring	NOUN
ejpam-753	245	8	.	.	PUNCT
ejpam-753	246	1	if	if	SCONJ
ejpam-753	246	2	r	r	NOUN
ejpam-753	246	3	is	be	AUX
ejpam-753	246	4	reduced	reduce	VERB
ejpam-753	246	5	,	,	PUNCT
ejpam-753	246	6	then	then	ADV
ejpam-753	246	7	we	we	PRON
ejpam-753	246	8	are	be	AUX
ejpam-753	246	9	down	down	ADV
ejpam-753	246	10	.	.	PUNCT
ejpam-753	247	1	otherwise	otherwise	ADV
ejpam-753	247	2	by	by	ADP
ejpam-753	247	3	lemma	lemma	PROPN
ejpam-753	247	4	2	2	NUM
ejpam-753	247	5	,	,	PUNCT
ejpam-753	247	6	1≤	1≤	NUM
ejpam-753	247	7	∑s	∑s	PROPN
ejpam-753	247	8	i=1	i=1	PROPN
ejpam-753	247	9	t	t	PROPN
ejpam-753	247	10	i	i	PRON
ejpam-753	247	11	≤	≤	ADV
ejpam-753	247	12	2	2	NUM
ejpam-753	247	13	and	and	CCONJ
ejpam-753	247	14	hence	hence	ADV
ejpam-753	247	15	1≤	1≤	NUM
ejpam-753	247	16	s	s	PART
ejpam-753	247	17	≤	≤	NOUN
ejpam-753	247	18	2	2	NUM
ejpam-753	247	19	.	.	PUNCT
ejpam-753	248	1	thus	thus	ADV
ejpam-753	248	2	we	we	PRON
ejpam-753	248	3	proceed	proceed	VERB
ejpam-753	248	4	by	by	ADP
ejpam-753	248	5	cases	case	NOUN
ejpam-753	248	6	.	.	PUNCT
ejpam-753	249	1	case	case	NOUN
ejpam-753	249	2	1	1	NUM
ejpam-753	249	3	:	:	PUNCT
ejpam-753	249	4	s	s	X
ejpam-753	249	5	=	=	SYM
ejpam-753	249	6	1	1	X
ejpam-753	249	7	.	.	PUNCT
ejpam-753	250	1	then	then	ADV
ejpam-753	250	2	t1	t1	NOUN
ejpam-753	250	3	=	=	PUNCT
ejpam-753	250	4	1	1	NUM
ejpam-753	250	5	or	or	CCONJ
ejpam-753	250	6	2	2	NUM
ejpam-753	250	7	.	.	PUNCT
ejpam-753	251	1	if	if	SCONJ
ejpam-753	251	2	t1	t1	NOUN
ejpam-753	251	3	=	=	SYM
ejpam-753	251	4	1	1	NUM
ejpam-753	251	5	,	,	PUNCT
ejpam-753	251	6	then	then	ADV
ejpam-753	251	7	r∼=	r∼=	X
ejpam-753	251	8	r1	r1	PROPN
ejpam-753	251	9	×	×	NOUN
ejpam-753	251	10	fq1	fq1	CCONJ
ejpam-753	251	11	×	×	NOUN
ejpam-753	251	12	.	.	PUNCT
ejpam-753	251	13	.	.	PUNCT
ejpam-753	252	1	.×	.×	PROPN
ejpam-753	252	2	fqt	fqt	PROPN
ejpam-753	252	3	,	,	PUNCT
ejpam-753	252	4	where	where	SCONJ
ejpam-753	252	5	r1	r1	PROPN
ejpam-753	252	6	is	be	AUX
ejpam-753	252	7	a	a	DET
ejpam-753	252	8	local	local	ADJ
ejpam-753	252	9	ring	ring	NOUN
ejpam-753	252	10	of	of	ADP
ejpam-753	252	11	order	order	NOUN
ejpam-753	252	12	p2	p2	NOUN
ejpam-753	252	13	with	with	ADP
ejpam-753	252	14	p	p	NOUN
ejpam-753	252	15	zero	zero	NUM
ejpam-753	252	16	-	-	PUNCT
ejpam-753	252	17	divisors	divisor	NOUN
ejpam-753	252	18	.	.	PUNCT
ejpam-753	253	1	by	by	ADP
ejpam-753	253	2	[	[	X
ejpam-753	253	3	4	4	NUM
ejpam-753	253	4	,	,	PUNCT
ejpam-753	253	5	p.687	p.687	NOUN
ejpam-753	253	6	]	]	PUNCT
ejpam-753	253	7	,	,	PUNCT
ejpam-753	253	8	r1	r1	PROPN
ejpam-753	253	9	is	be	AUX
ejpam-753	253	10	isomorphic	isomorphic	ADJ
ejpam-753	253	11	to	to	ADP
ejpam-753	253	12	zp2	zp2	PROPN
ejpam-753	253	13	or	or	CCONJ
ejpam-753	253	14	zp[x]/(x	zp[x]/(x	PROPN
ejpam-753	253	15	2	2	NUM
ejpam-753	253	16	)	)	PUNCT
ejpam-753	253	17	.	.	PUNCT
ejpam-753	254	1	if	if	SCONJ
ejpam-753	254	2	t1	t1	NOUN
ejpam-753	254	3	=	=	SYM
ejpam-753	254	4	2	2	NUM
ejpam-753	254	5	,	,	PUNCT
ejpam-753	254	6	then	then	ADV
ejpam-753	254	7	by	by	ADP
ejpam-753	254	8	lemma	lemma	PROPN
ejpam-753	254	9	2	2	NUM
ejpam-753	254	10	,	,	PUNCT
ejpam-753	254	11	r	r	NOUN
ejpam-753	254	12	∼=	∼=	PROPN
ejpam-753	254	13	r1	r1	NOUN
ejpam-753	254	14	×	×	PROPN
ejpam-753	254	15	fq	fq	PROPN
ejpam-753	254	16	,	,	PUNCT
ejpam-753	254	17	where	where	SCONJ
ejpam-753	254	18	r1	r1	PROPN
ejpam-753	254	19	is	be	AUX
ejpam-753	254	20	a	a	DET
ejpam-753	254	21	local	local	ADJ
ejpam-753	254	22	ring	ring	NOUN
ejpam-753	254	23	of	of	ADP
ejpam-753	254	24	order	order	NOUN
ejpam-753	254	25	p3	p3	PROPN
ejpam-753	254	26	with	with	ADP
ejpam-753	254	27	p2	p2	PROPN
ejpam-753	254	28	zero	zero	NUM
ejpam-753	254	29	-	-	PUNCT
ejpam-753	254	30	divisors	divisor	NOUN
ejpam-753	254	31	and	and	CCONJ
ejpam-753	254	32	p2	p2	PROPN
ejpam-753	254	33	=	=	SYM
ejpam-753	254	34	p	p	PROPN
ejpam-753	255	1	+	+	CCONJ
ejpam-753	255	2	q−	q−	PROPN
ejpam-753	255	3	1	1	NUM
ejpam-753	255	4	.	.	PUNCT
ejpam-753	256	1	moreover	moreover	ADV
ejpam-753	256	2	by	by	ADP
ejpam-753	256	3	[	[	PUNCT
ejpam-753	256	4	4	4	NUM
ejpam-753	256	5	,	,	PUNCT
ejpam-753	256	6	p.687	p.687	NOUN
ejpam-753	256	7	]	]	PUNCT
ejpam-753	256	8	,	,	PUNCT
ejpam-753	256	9	r1	r1	PROPN
ejpam-753	256	10	is	be	AUX
ejpam-753	256	11	isomorphic	isomorphic	ADJ
ejpam-753	256	12	to	to	ADP
ejpam-753	256	13	zp3	zp3	PROPN
ejpam-753	256	14	,	,	PUNCT
ejpam-753	256	15	fp[x	fp[x	PROPN
ejpam-753	256	16	,	,	PUNCT
ejpam-753	256	17	y]/(x	y]/(x	PROPN
ejpam-753	256	18	,	,	PUNCT
ejpam-753	256	19	y)2	y)2	NOUN
ejpam-753	256	20	,	,	PUNCT
ejpam-753	256	21	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	256	22	3	3	NUM
ejpam-753	256	23	)	)	PUNCT
ejpam-753	256	24	or	or	CCONJ
ejpam-753	256	25	zp2[x]/(px	zp2[x]/(px	X
ejpam-753	256	26	,	,	PUNCT
ejpam-753	256	27	x2−	x2−	PROPN
ejpam-753	256	28	ǫp	ǫp	NOUN
ejpam-753	256	29	)	)	PUNCT
ejpam-753	256	30	where	where	SCONJ
ejpam-753	256	31	ǫ	ǫ	PROPN
ejpam-753	256	32	∈	∈	PROPN
ejpam-753	256	33	σ0	σ0	NOUN
ejpam-753	256	34	2	2	NUM
ejpam-753	256	35	.	.	PUNCT
ejpam-753	256	36	case	case	NOUN
ejpam-753	256	37	2	2	NUM
ejpam-753	256	38	:	:	PUNCT
ejpam-753	256	39	s	s	X
ejpam-753	256	40	=	=	SYM
ejpam-753	256	41	2	2	NUM
ejpam-753	256	42	,	,	PUNCT
ejpam-753	256	43	i.e.	i.e.	X
ejpam-753	256	44	,	,	PUNCT
ejpam-753	256	45	t1	t1	NOUN
ejpam-753	256	46	=	=	NOUN
ejpam-753	256	47	t2	t2	NOUN
ejpam-753	256	48	=	=	SYM
ejpam-753	257	1	1	1	X
ejpam-753	257	2	.	.	PUNCT
ejpam-753	257	3	then	then	ADV
ejpam-753	257	4	r∼=	r∼=	X
ejpam-753	257	5	r1×	r1×	NOUN
ejpam-753	257	6	r2×	r2×	NOUN
ejpam-753	257	7	fq1	fq1	CCONJ
ejpam-753	257	8	×	×	NOUN
ejpam-753	257	9	.	.	PUNCT
ejpam-753	257	10	.	.	PUNCT
ejpam-753	258	1	.×	.×	PROPN
ejpam-753	258	2	fqt	fqt	PROPN
ejpam-753	258	3	,	,	PUNCT
ejpam-753	258	4	where	where	SCONJ
ejpam-753	258	5	each	each	DET
ejpam-753	258	6	ri	ri	PROPN
ejpam-753	258	7	is	be	AUX
ejpam-753	258	8	a	a	DET
ejpam-753	258	9	local	local	ADJ
ejpam-753	258	10	ring	ring	NOUN
ejpam-753	258	11	with	with	ADP
ejpam-753	258	12	|z(ri)|	|z(ri)|	NOUN
ejpam-753	258	13	=	=	PUNCT
ejpam-753	259	1	p.	p.	NOUN
ejpam-753	259	2	now	now	ADV
ejpam-753	259	3	by	by	ADP
ejpam-753	259	4	lemma	lemma	PROPN
ejpam-753	259	5	1	1	NUM
ejpam-753	259	6	,	,	PUNCT
ejpam-753	259	7	|r1|	|r1|	NOUN
ejpam-753	259	8	=	=	SYM
ejpam-753	259	9	|r2|	|r2|	NOUN
ejpam-753	259	10	=	=	NOUN
ejpam-753	259	11	p2	p2	NOUN
ejpam-753	259	12	.	.	PUNCT
ejpam-753	260	1	if	if	SCONJ
ejpam-753	260	2	t	t	PROPN
ejpam-753	260	3	>	>	X
ejpam-753	260	4	1	1	NUM
ejpam-753	260	5	,	,	PUNCT
ejpam-753	260	6	then	then	ADV
ejpam-753	260	7	clearly	clearly	ADV
ejpam-753	260	8	|z(r)|	|z(r)|	PROPN
ejpam-753	260	9	>	>	X
ejpam-753	260	10	p4	p4	NOUN
ejpam-753	260	11	,	,	PUNCT
ejpam-753	260	12	a	a	DET
ejpam-753	260	13	contradiction	contradiction	NOUN
ejpam-753	260	14	.	.	PUNCT
ejpam-753	261	1	therefore	therefore	ADV
ejpam-753	261	2	t	t	PROPN
ejpam-753	261	3	=	=	PUNCT
ejpam-753	261	4	1	1	NUM
ejpam-753	261	5	and	and	CCONJ
ejpam-753	261	6	hence	hence	ADV
ejpam-753	261	7	by	by	ADP
ejpam-753	261	8	relation	relation	NOUN
ejpam-753	261	9	(	(	PUNCT
ejpam-753	261	10	1	1	NUM
ejpam-753	261	11	)	)	PUNCT
ejpam-753	261	12	in	in	ADP
ejpam-753	261	13	lemma	lemma	PROPN
ejpam-753	261	14	2	2	NUM
ejpam-753	261	15	,	,	PUNCT
ejpam-753	261	16	p2	p2	PROPN
ejpam-753	261	17	is	be	AUX
ejpam-753	261	18	a	a	DET
ejpam-753	261	19	divisor	divisor	NOUN
ejpam-753	261	20	of	of	ADP
ejpam-753	261	21	q1−	q1−	NOUN
ejpam-753	261	22	1	1	NUM
ejpam-753	261	23	.	.	PUNCT
ejpam-753	261	24	thus	thus	ADV
ejpam-753	261	25	q1	q1	VERB
ejpam-753	261	26	>	>	X
ejpam-753	261	27	p2	p2	PROPN
ejpam-753	261	28	and	and	CCONJ
ejpam-753	261	29	so	so	ADV
ejpam-753	261	30	|z(r)|	|z(r)|	PROPN
ejpam-753	261	31	>	>	X
ejpam-753	261	32	|z(r1)||r2||fq1	|z(r1)||r2||fq1	PROPN
ejpam-753	261	33	|	|	ADV
ejpam-753	261	34	≥	≥	NOUN
ejpam-753	261	35	p5	p5	PROPN
ejpam-753	261	36	,	,	PUNCT
ejpam-753	261	37	a	a	DET
ejpam-753	261	38	contradiction	contradiction	NOUN
ejpam-753	261	39	.	.	PUNCT
ejpam-753	262	1	corollary	corollary	ADJ
ejpam-753	262	2	1	1	NUM
ejpam-753	262	3	.	.	PUNCT
ejpam-753	263	1	let	let	VERB
ejpam-753	263	2	r	r	PRON
ejpam-753	263	3	be	be	AUX
ejpam-753	263	4	a	a	DET
ejpam-753	263	5	ring	ring	NOUN
ejpam-753	263	6	with	with	ADP
ejpam-753	263	7	|z(r)|	|z(r)|	PROPN
ejpam-753	263	8	=	=	SYM
ejpam-753	263	9	p	p	PROPN
ejpam-753	263	10	k1	k1	NOUN
ejpam-753	263	11	1	1	NUM
ejpam-753	263	12	p	p	NOUN
ejpam-753	263	13	k2	k2	PROPN
ejpam-753	263	14	2	2	NUM
ejpam-753	263	15	.	.	PUNCT
ejpam-753	263	16	.	.	PUNCT
ejpam-753	263	17	.	.	PUNCT
ejpam-753	264	1	p	p	X
ejpam-753	264	2	kn	kn	PROPN
ejpam-753	264	3	n	n	PROPN
ejpam-753	264	4	,	,	PUNCT
ejpam-753	264	5	where	where	SCONJ
ejpam-753	264	6	n	n	PRON
ejpam-753	264	7	≥	≥	NOUN
ejpam-753	264	8	1	1	NUM
ejpam-753	264	9	,	,	PUNCT
ejpam-753	264	10	1	1	NUM
ejpam-753	264	11	≤	≤	NUM
ejpam-753	264	12	ki	ki	PROPN
ejpam-753	265	1	≤	≤	ADV
ejpam-753	265	2	4	4	NUM
ejpam-753	265	3	and	and	CCONJ
ejpam-753	265	4	pi	pi	NOUN
ejpam-753	265	5	,	,	PUNCT
ejpam-753	265	6	s	s	VERB
ejpam-753	265	7	are	be	AUX
ejpam-753	265	8	distinct	distinct	ADJ
ejpam-753	265	9	prime	prime	ADJ
ejpam-753	265	10	numbers	number	NOUN
ejpam-753	265	11	.	.	PUNCT
ejpam-753	266	1	then	then	ADV
ejpam-753	266	2	there	there	PRON
ejpam-753	266	3	exist	exist	VERB
ejpam-753	266	4	0≤	0≤	NUM
ejpam-753	266	5	s	s	PART
ejpam-753	266	6	≤	≤	NUM
ejpam-753	266	7	σn	σn	NOUN
ejpam-753	266	8	i=1ki	i=1ki	PROPN
ejpam-753	266	9	and	and	CCONJ
ejpam-753	266	10	t	t	PROPN
ejpam-753	266	11	≥	≥	NUM
ejpam-753	266	12	0	0	NUM
ejpam-753	267	1	such	such	ADJ
ejpam-753	267	2	that	that	SCONJ
ejpam-753	267	3	r∼=	r∼=	ADV
ejpam-753	267	4	r1	r1	PROPN
ejpam-753	267	5	×	×	NOUN
ejpam-753	267	6	.	.	PUNCT
ejpam-753	267	7	.	.	PUNCT
ejpam-753	268	1	.×	.×	NOUN
ejpam-753	268	2	rs	r	VERB
ejpam-753	268	3	×	×	NOUN
ejpam-753	269	1	fq1	fq1	INTJ
ejpam-753	269	2	×	×	NOUN
ejpam-753	269	3	.	.	PUNCT
ejpam-753	269	4	.	.	PUNCT
ejpam-753	270	1	.×	.×	PROPN
ejpam-753	270	2	fqt	fqt	PROPN
ejpam-753	270	3	where	where	SCONJ
ejpam-753	270	4	fqi	fqi	NOUN
ejpam-753	270	5	,	,	PUNCT
ejpam-753	270	6	s	s	VERB
ejpam-753	270	7	are	be	AUX
ejpam-753	270	8	finite	finite	ADJ
ejpam-753	270	9	fields	field	NOUN
ejpam-753	270	10	and	and	CCONJ
ejpam-753	270	11	each	each	DET
ejpam-753	270	12	ri	ri	PROPN
ejpam-753	270	13	is	be	AUX
ejpam-753	270	14	local	local	ADJ
ejpam-753	270	15	ring	ring	NOUN
ejpam-753	270	16	with	with	ADP
ejpam-753	270	17	|z(ri)|	|z(ri)|	NOUN
ejpam-753	270	18	=	=	SYM
ejpam-753	270	19	p	p	PROPN
ejpam-753	270	20	t	t	PROPN
ejpam-753	270	21	j	j	PROPN
ejpam-753	270	22	j	j	PROPN
ejpam-753	270	23	for	for	ADP
ejpam-753	270	24	some	some	DET
ejpam-753	270	25	p	p	PRON
ejpam-753	270	26	j	j	PROPN
ejpam-753	270	27	(	(	PUNCT
ejpam-753	270	28	1	1	NUM
ejpam-753	270	29	≤	≤	NUM
ejpam-753	270	30	j	j	PROPN
ejpam-753	270	31	≤	≤	NUM
ejpam-753	270	32	n	n	CCONJ
ejpam-753	270	33	)	)	PUNCT
ejpam-753	270	34	and	and	CCONJ
ejpam-753	270	35	1	1	NUM
ejpam-753	270	36	≤	≤	NOUN
ejpam-753	271	1	t	t	PROPN
ejpam-753	271	2	j	j	PROPN
ejpam-753	271	3	≤	≤	PROPN
ejpam-753	272	1	k	k	PROPN
ejpam-753	272	2	j	j	PROPN
ejpam-753	272	3	.	.	PUNCT
ejpam-753	273	1	consequently	consequently	ADV
ejpam-753	273	2	,	,	PUNCT
ejpam-753	273	3	each	each	DET
ejpam-753	273	4	ri	ri	PROPN
ejpam-753	273	5	is	be	AUX
ejpam-753	273	6	isomorphic	isomorphic	ADJ
ejpam-753	273	7	to	to	ADP
ejpam-753	273	8	one	one	NUM
ejpam-753	273	9	of	of	ADP
ejpam-753	273	10	the	the	DET
ejpam-753	273	11	local	local	ADJ
ejpam-753	273	12	rings	ring	NOUN
ejpam-753	273	13	described	describe	VERB
ejpam-753	273	14	in	in	ADP
ejpam-753	273	15	[	[	X
ejpam-753	273	16	2	2	NUM
ejpam-753	273	17	,	,	PUNCT
ejpam-753	273	18	theorem	theorem	VERB
ejpam-753	273	19	5	5	NUM
ejpam-753	273	20	]	]	PUNCT
ejpam-753	273	21	or	or	CCONJ
ejpam-753	273	22	theorem	theorem	VERB
ejpam-753	273	23	1	1	NUM
ejpam-753	273	24	.	.	PUNCT
ejpam-753	273	25	proof	proof	NOUN
ejpam-753	273	26	.	.	PUNCT
ejpam-753	274	1	we	we	PRON
ejpam-753	274	2	put	put	VERB
ejpam-753	274	3	r∼=	r∼=	NUM
ejpam-753	274	4	r1×	r1×	NOUN
ejpam-753	274	5	.	.	PUNCT
ejpam-753	274	6	.	.	PUNCT
ejpam-753	275	1	.×	.×	NOUN
ejpam-753	275	2	rs	r	VERB
ejpam-753	275	3	×	×	NOUN
ejpam-753	276	1	fq1	fq1	INTJ
ejpam-753	276	2	×	×	NOUN
ejpam-753	276	3	.	.	PUNCT
ejpam-753	276	4	.	.	PUNCT
ejpam-753	277	1	.×	.×	PROPN
ejpam-753	277	2	fqt	fqt	PROPN
ejpam-753	277	3	,	,	PUNCT
ejpam-753	277	4	where	where	SCONJ
ejpam-753	277	5	fq1	fq1	ADV
ejpam-753	277	6	,	,	PUNCT
ejpam-753	277	7	.	.	PUNCT
ejpam-753	277	8	.	.	PUNCT
ejpam-753	277	9	.	.	PUNCT
ejpam-753	278	1	,	,	PUNCT
ejpam-753	278	2	fqt	fqt	PROPN
ejpam-753	278	3	are	be	AUX
ejpam-753	278	4	finite	finite	ADJ
ejpam-753	278	5	fields	field	NOUN
ejpam-753	278	6	and	and	CCONJ
ejpam-753	278	7	each	each	DET
ejpam-753	278	8	ri	ri	PROPN
ejpam-753	278	9	is	be	AUX
ejpam-753	278	10	a	a	DET
ejpam-753	278	11	commutative	commutative	ADJ
ejpam-753	278	12	finite	finite	ADJ
ejpam-753	278	13	local	local	ADJ
ejpam-753	278	14	ring	ring	NOUN
ejpam-753	278	15	with	with	ADP
ejpam-753	278	16	identity	identity	NOUN
ejpam-753	278	17	that	that	PRON
ejpam-753	278	18	is	be	AUX
ejpam-753	278	19	not	not	PART
ejpam-753	278	20	a	a	DET
ejpam-753	278	21	field	field	NOUN
ejpam-753	278	22	.	.	PUNCT
ejpam-753	279	1	by	by	ADP
ejpam-753	279	2	lemma	lemma	PROPN
ejpam-753	279	3	2	2	NUM
ejpam-753	279	4	,	,	PUNCT
ejpam-753	279	5	for	for	ADP
ejpam-753	279	6	each	each	DET
ejpam-753	279	7	i	i	PROPN
ejpam-753	279	8	,	,	PUNCT
ejpam-753	279	9	|z(ri)|	|z(ri)|	NOUN
ejpam-753	279	10	=	=	SYM
ejpam-753	279	11	pk	pk	NOUN
ejpam-753	279	12	for	for	ADP
ejpam-753	279	13	some	some	DET
ejpam-753	279	14	prime	prime	ADJ
ejpam-753	279	15	number	number	NOUN
ejpam-753	279	16	p	p	NOUN
ejpam-753	279	17	and	and	CCONJ
ejpam-753	279	18	k	k	PROPN
ejpam-753	279	19	≥	≥	NUM
ejpam-753	279	20	1	1	NUM
ejpam-753	279	21	such	such	ADJ
ejpam-753	279	22	that	that	DET
ejpam-753	279	23	pk	pk	NOUN
ejpam-753	279	24	is	be	AUX
ejpam-753	279	25	a	a	DET
ejpam-753	279	26	divisor	divisor	NOUN
ejpam-753	279	27	of	of	ADP
ejpam-753	279	28	|z(r)|	|z(r)|	PROPN
ejpam-753	279	29	and	and	CCONJ
ejpam-753	279	30	also	also	ADV
ejpam-753	279	31	0	0	NUM
ejpam-753	279	32	≤	≤	NUM
ejpam-753	279	33	s	s	PART
ejpam-753	279	34	≤	≤	NUM
ejpam-753	279	35	σn	σn	NOUN
ejpam-753	279	36	i=1	i=1	PROPN
ejpam-753	279	37	ki	ki	PROPN
ejpam-753	279	38	.	.	PUNCT
ejpam-753	280	1	thus	thus	ADV
ejpam-753	280	2	|z(ri)|	|z(ri)|	ADP
ejpam-753	280	3	=	=	SYM
ejpam-753	280	4	p	p	PROPN
ejpam-753	280	5	t	t	PROPN
ejpam-753	281	1	j	j	PROPN
ejpam-753	281	2	j	j	PROPN
ejpam-753	281	3	where	where	SCONJ
ejpam-753	281	4	1≤	1≤	PROPN
ejpam-753	281	5	t	t	PROPN
ejpam-753	281	6	j	j	PROPN
ejpam-753	281	7	≤	≤	PROPN
ejpam-753	282	1	k	k	PROPN
ejpam-753	282	2	j	j	PROPN
ejpam-753	282	3	,	,	PUNCT
ejpam-753	282	4	1	1	NUM
ejpam-753	282	5	≤	≤	NUM
ejpam-753	282	6	j	j	PROPN
ejpam-753	282	7	≤	≤	PROPN
ejpam-753	282	8	n	n	ADP
ejpam-753	282	9	and	and	CCONJ
ejpam-753	282	10	1≤	1≤	NUM
ejpam-753	283	1	i	i	PRON
ejpam-753	283	2	≤	≤	VERB
ejpam-753	283	3	s.	s.	PROPN
ejpam-753	283	4	hence	hence	ADV
ejpam-753	283	5	for	for	ADP
ejpam-753	283	6	each	each	DET
ejpam-753	283	7	1≤	1≤	NUM
ejpam-753	283	8	i	i	PRON
ejpam-753	283	9	≤	≤	PROPN
ejpam-753	283	10	s	s	X
ejpam-753	283	11	,	,	PUNCT
ejpam-753	283	12	t	t	PROPN
ejpam-753	284	1	i	i	NOUN
ejpam-753	284	2	=	=	PROPN
ejpam-753	284	3	1,2,3	1,2,3	NUM
ejpam-753	284	4	or	or	CCONJ
ejpam-753	284	5	4	4	NUM
ejpam-753	285	1	and	and	CCONJ
ejpam-753	285	2	so	so	ADV
ejpam-753	285	3	each	each	DET
ejpam-753	285	4	ri	ri	PROPN
ejpam-753	285	5	is	be	AUX
ejpam-753	285	6	isomorphic	isomorphic	ADJ
ejpam-753	285	7	to	to	ADP
ejpam-753	285	8	one	one	NUM
ejpam-753	285	9	of	of	ADP
ejpam-753	285	10	the	the	DET
ejpam-753	285	11	local	local	ADJ
ejpam-753	285	12	rings	ring	NOUN
ejpam-753	285	13	described	describe	VERB
ejpam-753	285	14	in	in	ADP
ejpam-753	285	15	[	[	X
ejpam-753	285	16	2	2	NUM
ejpam-753	285	17	,	,	PUNCT
ejpam-753	285	18	theorem	theorem	VERB
ejpam-753	285	19	5	5	NUM
ejpam-753	285	20	]	]	PUNCT
ejpam-753	285	21	or	or	CCONJ
ejpam-753	285	22	theorem	theorem	VERB
ejpam-753	285	23	1	1	NUM
ejpam-753	285	24	.	.	PUNCT
ejpam-753	285	25	theorem	theorem	NOUN
ejpam-753	285	26	2	2	NUM
ejpam-753	285	27	.	.	PUNCT
ejpam-753	286	1	let	let	VERB
ejpam-753	286	2	r	r	PRON
ejpam-753	286	3	be	be	AUX
ejpam-753	286	4	a	a	DET
ejpam-753	286	5	commutative	commutative	ADJ
ejpam-753	286	6	nonlocal	nonlocal	ADJ
ejpam-753	286	7	ring	ring	NOUN
ejpam-753	286	8	with	with	ADP
ejpam-753	286	9	|z(r)|=	|z(r)|=	VERB
ejpam-753	286	10	p6	p6	NOUN
ejpam-753	286	11	where	where	SCONJ
ejpam-753	286	12	p	p	NOUN
ejpam-753	286	13	is	be	AUX
ejpam-753	286	14	a	a	DET
ejpam-753	286	15	prime	prime	ADJ
ejpam-753	286	16	number	number	NOUN
ejpam-753	286	17	.	.	PUNCT
ejpam-753	287	1	then	then	ADV
ejpam-753	287	2	r	r	NOUN
ejpam-753	287	3	is	be	AUX
ejpam-753	287	4	isomorphic	isomorphic	ADJ
ejpam-753	287	5	to	to	ADP
ejpam-753	287	6	one	one	NUM
ejpam-753	287	7	of	of	ADP
ejpam-753	287	8	the	the	DET
ejpam-753	287	9	rings	ring	NOUN
ejpam-753	287	10	fq1	fq1	VERB
ejpam-753	287	11	×	×	NOUN
ejpam-753	287	12	.	.	PUNCT
ejpam-753	287	13	.	.	PUNCT
ejpam-753	287	14	.	.	PUNCT
ejpam-753	288	1	×	×	NOUN
ejpam-753	288	2	fqt	fqt	NOUN
ejpam-753	288	3	with	with	ADP
ejpam-753	288	4	p6	p6	PROPN
ejpam-753	288	5	=	=	PUNCT
ejpam-753	288	6	q1q2	q1q2	PROPN
ejpam-753	288	7	.	.	PUNCT
ejpam-753	288	8	.	.	PUNCT
ejpam-753	288	9	.	.	PUNCT
ejpam-753	289	1	qt	qt	INTJ
ejpam-753	289	2	−	−	PROPN
ejpam-753	289	3	(	(	PUNCT
ejpam-753	289	4	q1	q1	PROPN
ejpam-753	289	5	−	−	PROPN
ejpam-753	289	6	1)(q2	1)(q2	NUM
ejpam-753	289	7	−	−	PROPN
ejpam-753	289	8	1	1	NUM
ejpam-753	289	9	)	)	PUNCT
ejpam-753	289	10	.	.	PUNCT
ejpam-753	289	11	.	.	PUNCT
ejpam-753	289	12	.	.	PUNCT
ejpam-753	290	1	(	(	PUNCT
ejpam-753	290	2	qt	qt	INTJ
ejpam-753	290	3	−	−	PROPN
ejpam-753	290	4	1	1	NUM
ejpam-753	290	5	)	)	PUNCT
ejpam-753	290	6	,	,	PUNCT
ejpam-753	290	7	z4	z4	PROPN
ejpam-753	290	8	×	×	PROPN
ejpam-753	290	9	z4	z4	PROPN
ejpam-753	290	10	×	×	PROPN
ejpam-753	290	11	f5,z2[x]/(x	f5,z2[x]/(x	X
ejpam-753	290	12	2	2	NUM
ejpam-753	290	13	)	)	PUNCT
ejpam-753	290	14	×	×	NOUN
ejpam-753	290	15	z4	z4	PROPN
ejpam-753	290	16	×	×	NOUN
ejpam-753	290	17	f5	f5	PROPN
ejpam-753	290	18	,	,	PUNCT
ejpam-753	290	19	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	290	20	2	2	NUM
ejpam-753	290	21	)	)	PUNCT
ejpam-753	290	22	×	×	NOUN
ejpam-753	290	23	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	290	24	2	2	NUM
ejpam-753	290	25	)	)	PUNCT
ejpam-753	290	26	×	×	NOUN
ejpam-753	290	27	f5	f5	NOUN
ejpam-753	290	28	,	,	PUNCT
ejpam-753	290	29	r1	r1	NOUN
ejpam-753	290	30	×	×	NOUN
ejpam-753	290	31	fq1	fq1	CCONJ
ejpam-753	290	32	×	×	NOUN
ejpam-753	290	33	.	.	PUNCT
ejpam-753	290	34	.	.	PUNCT
ejpam-753	290	35	.	.	PUNCT
ejpam-753	291	1	×	×	NOUN
ejpam-753	291	2	fqt	fqt	NOUN
ejpam-753	291	3	,	,	PUNCT
ejpam-753	291	4	where	where	SCONJ
ejpam-753	291	5	r1	r1	PROPN
ejpam-753	291	6	is	be	AUX
ejpam-753	291	7	isomorphic	isomorphic	ADJ
ejpam-753	291	8	to	to	ADP
ejpam-753	291	9	zp2	zp2	PROPN
ejpam-753	291	10	or	or	CCONJ
ejpam-753	291	11	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	291	12	2	2	NUM
ejpam-753	291	13	)	)	PUNCT
ejpam-753	291	14	and	and	CCONJ
ejpam-753	291	15	p5	p5	NOUN
ejpam-753	291	16	=	=	SYM
ejpam-753	291	17	pq1q2	pq1q2	PROPN
ejpam-753	291	18	.	.	PUNCT
ejpam-753	291	19	.	.	PUNCT
ejpam-753	291	20	.	.	PUNCT
ejpam-753	292	1	qt	qt	INTJ
ejpam-753	292	2	−	−	PROPN
ejpam-753	293	1	(	(	PUNCT
ejpam-753	293	2	p	p	NOUN
ejpam-753	293	3	−	−	PROPN
ejpam-753	293	4	1)(q1−	1)(q1−	NUM
ejpam-753	293	5	1)(q2−	1)(q2−	NUM
ejpam-753	293	6	1	1	NUM
ejpam-753	293	7	)	)	PUNCT
ejpam-753	293	8	.	.	PUNCT
ejpam-753	293	9	.	.	PUNCT
ejpam-753	294	1	.	.	PUNCT
ejpam-753	295	1	(	(	PUNCT
ejpam-753	295	2	qt	qt	INTJ
ejpam-753	295	3	−	−	PROPN
ejpam-753	295	4	1	1	NUM
ejpam-753	295	5	)	)	PUNCT
ejpam-753	295	6	,	,	PUNCT
ejpam-753	295	7	r1	r1	PROPN
ejpam-753	295	8	×	×	NOUN
ejpam-753	295	9	fq1	fq1	CCONJ
ejpam-753	295	10	×	×	NOUN
ejpam-753	295	11	.	.	PUNCT
ejpam-753	295	12	.	.	PUNCT
ejpam-753	296	1	.×	.×	PROPN
ejpam-753	296	2	fqt	fqt	PROPN
ejpam-753	296	3	where	where	SCONJ
ejpam-753	296	4	r1	r1	PROPN
ejpam-753	296	5	is	be	AUX
ejpam-753	296	6	isomorphic	isomorphic	ADJ
ejpam-753	296	7	to	to	ADP
ejpam-753	296	8	one	one	NUM
ejpam-753	296	9	the	the	DET
ejpam-753	296	10	rings	ring	NOUN
ejpam-753	296	11	zp3	zp3	PROPN
ejpam-753	296	12	,	,	PUNCT
ejpam-753	296	13	fp[x	fp[x	PROPN
ejpam-753	296	14	,	,	PUNCT
ejpam-753	296	15	y]/(x	y]/(x	PROPN
ejpam-753	296	16	,	,	PUNCT
ejpam-753	296	17	y)2	y)2	NOUN
ejpam-753	296	18	,	,	PUNCT
ejpam-753	296	19	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	296	20	3	3	NUM
ejpam-753	296	21	)	)	PUNCT
ejpam-753	296	22	or	or	CCONJ
ejpam-753	296	23	zp2[x]/(px	zp2[x]/(px	PROPN
ejpam-753	296	24	,	,	PUNCT
ejpam-753	297	1	x2	x2	PROPN
ejpam-753	297	2	−	−	PROPN
ejpam-753	298	1	ǫp	ǫp	NOUN
ejpam-753	298	2	)	)	PUNCT
ejpam-753	298	3	where	where	SCONJ
ejpam-753	298	4	ǫ	ǫ	PRON
ejpam-753	298	5	∈	∈	PROPN
ejpam-753	298	6	σ0	σ0	NOUN
ejpam-753	298	7	2	2	NUM
ejpam-753	298	8	and	and	CCONJ
ejpam-753	298	9	p4	p4	ADJ
ejpam-753	298	10	=	=	SYM
ejpam-753	298	11	pq1q2	pq1q2	PROPN
ejpam-753	298	12	.	.	PUNCT
ejpam-753	298	13	.	.	PUNCT
ejpam-753	298	14	.	.	PUNCT
ejpam-753	299	1	qt	qt	INTJ
ejpam-753	299	2	−	−	PROPN
ejpam-753	299	3	(	(	PUNCT
ejpam-753	299	4	p−	p−	NOUN
ejpam-753	299	5	1)(q1−	1)(q1−	NUM
ejpam-753	299	6	1)(q2−	1)(q2−	NUM
ejpam-753	299	7	1	1	NUM
ejpam-753	299	8	)	)	PUNCT
ejpam-753	299	9	.	.	PUNCT
ejpam-753	299	10	.	.	PUNCT
ejpam-753	299	11	.	.	PUNCT
ejpam-753	300	1	(	(	PUNCT
ejpam-753	300	2	qt	qt	INTJ
ejpam-753	300	3	−	−	PROPN
ejpam-753	300	4	1	1	NUM
ejpam-753	300	5	)	)	PUNCT
ejpam-753	300	6	,	,	PUNCT
ejpam-753	300	7	r1×	r1×	NOUN
ejpam-753	300	8	fq1	fq1	ADV
ejpam-753	300	9	×	×	NOUN
ejpam-753	300	10	.	.	PUNCT
ejpam-753	300	11	.	.	PUNCT
ejpam-753	301	1	.×	.×	PROPN
ejpam-753	301	2	fqt	fqt	PROPN
ejpam-753	301	3	,	,	PUNCT
ejpam-753	301	4	where	where	SCONJ
ejpam-753	301	5	r1	r1	PROPN
ejpam-753	301	6	is	be	AUX
ejpam-753	301	7	isomorphic	isomorphic	ADJ
ejpam-753	301	8	to	to	ADP
ejpam-753	301	9	fp2[x]/(x2	fp2[x]/(x2	NOUN
ejpam-753	301	10	)	)	PUNCT
ejpam-753	301	11	or	or	CCONJ
ejpam-753	301	12	gr(p4	gr(p4	NOUN
ejpam-753	301	13	,	,	PUNCT
ejpam-753	301	14	p2	p2	PROPN
ejpam-753	301	15	)	)	PUNCT
ejpam-753	301	16	and	and	CCONJ
ejpam-753	301	17	p4	p4	ADJ
ejpam-753	301	18	=	=	SYM
ejpam-753	301	19	p2q1q2	p2q1q2	PROPN
ejpam-753	301	20	.	.	PUNCT
ejpam-753	301	21	.	.	PUNCT
ejpam-753	301	22	.	.	PUNCT
ejpam-753	302	1	qt	qt	INTJ
ejpam-753	302	2	−	−	PROPN
ejpam-753	303	1	(	(	PUNCT
ejpam-753	303	2	p	p	NOUN
ejpam-753	303	3	2−1)(q1−1)(q2−1	2−1)(q1−1)(q2−1	NOUN
ejpam-753	303	4	)	)	PUNCT
ejpam-753	303	5	.	.	PUNCT
ejpam-753	303	6	.	.	PUNCT
ejpam-753	304	1	.	.	PUNCT
ejpam-753	305	1	(	(	PUNCT
ejpam-753	305	2	qt	qt	NOUN
ejpam-753	305	3	−1	−1	NOUN
ejpam-753	305	4	)	)	PUNCT
ejpam-753	305	5	,	,	PUNCT
ejpam-753	305	6	r1×	r1×	NOUN
ejpam-753	305	7	fq1	fq1	ADV
ejpam-753	305	8	×	×	NOUN
ejpam-753	305	9	.	.	PUNCT
ejpam-753	305	10	.	.	PUNCT
ejpam-753	306	1	.×	.×	PROPN
ejpam-753	306	2	fqt	fqt	PROPN
ejpam-753	306	3	,	,	PUNCT
ejpam-753	306	4	m.	m.	NOUN
ejpam-753	306	5	behboodi	behboodi	PROPN
ejpam-753	306	6	,	,	PUNCT
ejpam-753	306	7	r.	r.	PROPN
ejpam-753	306	8	beyranvand	beyranvand	PROPN
ejpam-753	306	9	/	/	SYM
ejpam-753	306	10	eur	eur	PROPN
ejpam-753	306	11	.	.	PUNCT
ejpam-753	307	1	j.	j.	PROPN
ejpam-753	307	2	pure	pure	PROPN
ejpam-753	307	3	appl	appl	PROPN
ejpam-753	307	4	.	.	PROPN
ejpam-753	307	5	math	math	PROPN
ejpam-753	307	6	,	,	PUNCT
ejpam-753	307	7	3	3	NUM
ejpam-753	307	8	(	(	PUNCT
ejpam-753	307	9	2010	2010	NUM
ejpam-753	307	10	)	)	PUNCT
ejpam-753	307	11	,	,	PUNCT
ejpam-753	307	12	686	686	NUM
ejpam-753	307	13	-	-	SYM
ejpam-753	307	14	694	694	NUM
ejpam-753	307	15	692	692	NUM
ejpam-753	307	16	where	where	SCONJ
ejpam-753	307	17	r1	r1	PROPN
ejpam-753	307	18	is	be	AUX
ejpam-753	307	19	isomorphic	isomorphic	ADJ
ejpam-753	307	20	to	to	ADP
ejpam-753	307	21	one	one	NUM
ejpam-753	307	22	of	of	ADP
ejpam-753	307	23	the	the	DET
ejpam-753	307	24	local	local	ADJ
ejpam-753	307	25	rings	ring	NOUN
ejpam-753	307	26	of	of	ADP
ejpam-753	307	27	order	order	NOUN
ejpam-753	307	28	p4	p4	PROPN
ejpam-753	307	29	described	describe	VERB
ejpam-753	307	30	in	in	ADP
ejpam-753	307	31	[	[	X
ejpam-753	307	32	2	2	NUM
ejpam-753	307	33	,	,	PUNCT
ejpam-753	307	34	corollary	corollary	ADJ
ejpam-753	307	35	3	3	NUM
ejpam-753	307	36	]	]	PUNCT
ejpam-753	307	37	and	and	CCONJ
ejpam-753	307	38	p3	p3	PROPN
ejpam-753	307	39	=	=	SYM
ejpam-753	307	40	pq1q2	pq1q2	PROPN
ejpam-753	307	41	.	.	PUNCT
ejpam-753	307	42	.	.	PUNCT
ejpam-753	307	43	.	.	PUNCT
ejpam-753	308	1	qt	qt	INTJ
ejpam-753	308	2	−	−	PROPN
ejpam-753	308	3	(	(	PUNCT
ejpam-753	308	4	p−	p−	NOUN
ejpam-753	308	5	1)(q1−	1)(q1−	NUM
ejpam-753	308	6	1)(q2−	1)(q2−	NUM
ejpam-753	308	7	1	1	NUM
ejpam-753	308	8	)	)	PUNCT
ejpam-753	308	9	.	.	PUNCT
ejpam-753	308	10	.	.	PUNCT
ejpam-753	308	11	.	.	PUNCT
ejpam-753	309	1	(	(	PUNCT
ejpam-753	309	2	qt	qt	INTJ
ejpam-753	309	3	−	−	PROPN
ejpam-753	309	4	1	1	NUM
ejpam-753	309	5	)	)	PUNCT
ejpam-753	309	6	or	or	CCONJ
ejpam-753	309	7	r1×	r1×	NOUN
ejpam-753	309	8	fq	fq	PROPN
ejpam-753	309	9	where	where	SCONJ
ejpam-753	309	10	r1	r1	PROPN
ejpam-753	309	11	is	be	AUX
ejpam-753	309	12	isomorphic	isomorphic	ADJ
ejpam-753	309	13	to	to	ADP
ejpam-753	309	14	one	one	NUM
ejpam-753	309	15	of	of	ADP
ejpam-753	309	16	the	the	DET
ejpam-753	309	17	rings	ring	NOUN
ejpam-753	309	18	described	describe	VERB
ejpam-753	309	19	in	in	ADP
ejpam-753	309	20	proposition	proposition	NOUN
ejpam-753	309	21	2	2	NUM
ejpam-753	309	22	,	,	PUNCT
ejpam-753	309	23	and	and	CCONJ
ejpam-753	309	24	p2	p2	PROPN
ejpam-753	309	25	=	=	SYM
ejpam-753	309	26	p+	p+	PROPN
ejpam-753	309	27	q−	q−	PROPN
ejpam-753	309	28	1	1	NUM
ejpam-753	309	29	.	.	PUNCT
ejpam-753	310	1	proof	proof	NOUN
ejpam-753	310	2	.	.	PUNCT
ejpam-753	311	1	if	if	SCONJ
ejpam-753	311	2	r	r	NOUN
ejpam-753	311	3	is	be	AUX
ejpam-753	311	4	reduced	reduce	VERB
ejpam-753	311	5	,	,	PUNCT
ejpam-753	311	6	then	then	ADV
ejpam-753	311	7	we	we	PRON
ejpam-753	311	8	are	be	AUX
ejpam-753	311	9	down	down	ADV
ejpam-753	311	10	.	.	PUNCT
ejpam-753	312	1	now	now	ADV
ejpam-753	312	2	suppose	suppose	VERB
ejpam-753	312	3	that	that	SCONJ
ejpam-753	312	4	r	r	NOUN
ejpam-753	312	5	is	be	AUX
ejpam-753	312	6	not	not	PART
ejpam-753	312	7	reduced	reduce	VERB
ejpam-753	312	8	.	.	PUNCT
ejpam-753	313	1	then	then	ADV
ejpam-753	313	2	by	by	ADP
ejpam-753	313	3	[	[	X
ejpam-753	313	4	2	2	NUM
ejpam-753	313	5	,	,	PUNCT
ejpam-753	313	6	theorem	theorem	VERB
ejpam-753	313	7	4	4	NUM
ejpam-753	313	8	]	]	PUNCT
ejpam-753	313	9	,	,	PUNCT
ejpam-753	313	10	either	either	CCONJ
ejpam-753	313	11	r	r	NOUN
ejpam-753	313	12	is	be	AUX
ejpam-753	313	13	isomorphic	isomorphic	ADJ
ejpam-753	313	14	to	to	ADP
ejpam-753	313	15	z4	z4	PROPN
ejpam-753	313	16	×	×	PROPN
ejpam-753	313	17	z4	z4	PROPN
ejpam-753	313	18	×	×	PROPN
ejpam-753	313	19	f5	f5	PROPN
ejpam-753	313	20	,	,	PUNCT
ejpam-753	313	21	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	313	22	2)×z4	2)×z4	NUM
ejpam-753	313	23	×	×	NOUN
ejpam-753	313	24	f5	f5	NOUN
ejpam-753	313	25	,	,	PUNCT
ejpam-753	314	1	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	314	2	2)×	2)×	NUM
ejpam-753	314	3	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	314	4	2	2	NUM
ejpam-753	314	5	)	)	PUNCT
ejpam-753	314	6	×	×	NOUN
ejpam-753	314	7	f5	f5	NOUN
ejpam-753	314	8	or	or	CCONJ
ejpam-753	314	9	r	r	NOUN
ejpam-753	314	10	∼=	∼=	PROPN
ejpam-753	314	11	r1	r1	NOUN
ejpam-753	314	12	×	×	NOUN
ejpam-753	314	13	fq1	fq1	CCONJ
ejpam-753	314	14	×	×	NOUN
ejpam-753	314	15	.	.	PUNCT
ejpam-753	314	16	.	.	PUNCT
ejpam-753	314	17	.	.	PUNCT
ejpam-753	315	1	×	×	NOUN
ejpam-753	315	2	fqt	fqt	NOUN
ejpam-753	315	3	,	,	PUNCT
ejpam-753	315	4	where	where	SCONJ
ejpam-753	315	5	r1	r1	PROPN
ejpam-753	315	6	is	be	AUX
ejpam-753	315	7	a	a	DET
ejpam-753	315	8	local	local	ADJ
ejpam-753	315	9	ring	ring	NOUN
ejpam-753	315	10	with	with	ADP
ejpam-753	315	11	|z(r1)|	|z(r1)|	PROPN
ejpam-753	315	12	=	=	SYM
ejpam-753	315	13	pk	pk	PROPN
ejpam-753	315	14	(	(	PUNCT
ejpam-753	315	15	1≤	1≤	NUM
ejpam-753	315	16	k	k	PROPN
ejpam-753	315	17	≤	≤	PROPN
ejpam-753	315	18	4	4	NUM
ejpam-753	315	19	)	)	PUNCT
ejpam-753	315	20	and	and	CCONJ
ejpam-753	315	21	t	t	PROPN
ejpam-753	315	22	≥	≥	NUM
ejpam-753	315	23	1	1	NUM
ejpam-753	315	24	.	.	PUNCT
ejpam-753	316	1	thus	thus	ADV
ejpam-753	316	2	we	we	PRON
ejpam-753	316	3	proceed	proceed	VERB
ejpam-753	316	4	by	by	ADP
ejpam-753	316	5	cases	case	NOUN
ejpam-753	316	6	.	.	PUNCT
ejpam-753	317	1	case	case	NOUN
ejpam-753	317	2	1	1	NUM
ejpam-753	317	3	:	:	PUNCT
ejpam-753	317	4	|z(r1)|	|z(r1)|	X
ejpam-753	317	5	=	=	SYM
ejpam-753	318	1	p.	p.	NOUN
ejpam-753	318	2	then	then	ADV
ejpam-753	318	3	by	by	ADP
ejpam-753	318	4	[	[	X
ejpam-753	318	5	4	4	NUM
ejpam-753	318	6	,	,	PUNCT
ejpam-753	318	7	p.687	p.687	NOUN
ejpam-753	318	8	]	]	PUNCT
ejpam-753	318	9	,	,	PUNCT
ejpam-753	318	10	r1	r1	PROPN
ejpam-753	318	11	is	be	AUX
ejpam-753	318	12	isomorphic	isomorphic	ADJ
ejpam-753	318	13	to	to	ADP
ejpam-753	318	14	zp2	zp2	PROPN
ejpam-753	318	15	or	or	CCONJ
ejpam-753	318	16	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	318	17	2	2	NUM
ejpam-753	318	18	)	)	PUNCT
ejpam-753	318	19	and	and	CCONJ
ejpam-753	318	20	p5	p5	NOUN
ejpam-753	318	21	=	=	SYM
ejpam-753	318	22	pq1q2	pq1q2	PROPN
ejpam-753	318	23	.	.	PUNCT
ejpam-753	318	24	.	.	PUNCT
ejpam-753	318	25	.	.	PUNCT
ejpam-753	319	1	qt	qt	INTJ
ejpam-753	319	2	−	−	PROPN
ejpam-753	319	3	(	(	PUNCT
ejpam-753	319	4	p−	p−	NOUN
ejpam-753	319	5	1)(q1−	1)(q1−	NUM
ejpam-753	319	6	1)(q2−	1)(q2−	NUM
ejpam-753	319	7	1	1	NUM
ejpam-753	319	8	)	)	PUNCT
ejpam-753	319	9	.	.	PUNCT
ejpam-753	319	10	.	.	PUNCT
ejpam-753	319	11	.	.	PUNCT
ejpam-753	320	1	(	(	PUNCT
ejpam-753	320	2	qt	qt	INTJ
ejpam-753	320	3	−	−	NOUN
ejpam-753	320	4	1	1	NUM
ejpam-753	320	5	)	)	PUNCT
ejpam-753	320	6	.	.	PUNCT
ejpam-753	321	1	case	case	NOUN
ejpam-753	321	2	2	2	NUM
ejpam-753	321	3	:	:	PUNCT
ejpam-753	321	4	|z(r1)|	|z(r1)|	NOUN
ejpam-753	321	5	=	=	PUNCT
ejpam-753	321	6	p2	p2	PROPN
ejpam-753	321	7	.	.	PUNCT
ejpam-753	322	1	then	then	ADV
ejpam-753	322	2	by	by	ADP
ejpam-753	322	3	lemma	lemma	PROPN
ejpam-753	322	4	1	1	NUM
ejpam-753	322	5	,	,	PUNCT
ejpam-753	322	6	|r1|	|r1|	NOUN
ejpam-753	322	7	=	=	SYM
ejpam-753	322	8	p3	p3	PROPN
ejpam-753	322	9	or	or	CCONJ
ejpam-753	322	10	p4	p4	ADJ
ejpam-753	322	11	.	.	PUNCT
ejpam-753	323	1	if	if	SCONJ
ejpam-753	323	2	|r1|	|r1|	PROPN
ejpam-753	323	3	=	=	SYM
ejpam-753	323	4	p3	p3	PROPN
ejpam-753	323	5	,	,	PUNCT
ejpam-753	323	6	then	then	ADV
ejpam-753	323	7	by	by	ADP
ejpam-753	323	8	[	[	X
ejpam-753	323	9	4	4	NUM
ejpam-753	323	10	,	,	PUNCT
ejpam-753	323	11	p.687	p.687	NOUN
ejpam-753	323	12	]	]	PUNCT
ejpam-753	323	13	,	,	PUNCT
ejpam-753	323	14	r1	r1	PROPN
ejpam-753	323	15	is	be	AUX
ejpam-753	323	16	isomorphic	isomorphic	ADJ
ejpam-753	323	17	to	to	ADP
ejpam-753	323	18	one	one	NUM
ejpam-753	323	19	the	the	DET
ejpam-753	323	20	rings	ring	NOUN
ejpam-753	323	21	zp3	zp3	PROPN
ejpam-753	323	22	,	,	PUNCT
ejpam-753	323	23	fp[x	fp[x	PROPN
ejpam-753	323	24	,	,	PUNCT
ejpam-753	323	25	y]/(x	y]/(x	PROPN
ejpam-753	323	26	,	,	PUNCT
ejpam-753	323	27	y)2	y)2	NOUN
ejpam-753	323	28	,	,	PUNCT
ejpam-753	323	29	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	323	30	3	3	NUM
ejpam-753	323	31	)	)	PUNCT
ejpam-753	323	32	or	or	CCONJ
ejpam-753	323	33	zp2[x]/(px	zp2[x]/(px	X
ejpam-753	323	34	,	,	PUNCT
ejpam-753	323	35	x2−	x2−	PROPN
ejpam-753	323	36	ǫp	ǫp	NOUN
ejpam-753	323	37	)	)	PUNCT
ejpam-753	324	1	where	where	SCONJ
ejpam-753	324	2	ǫ	ǫ	PRON
ejpam-753	324	3	∈	∈	PROPN
ejpam-753	324	4	σ0	σ0	NOUN
ejpam-753	324	5	2	2	NUM
ejpam-753	324	6	and	and	CCONJ
ejpam-753	324	7	p4	p4	ADJ
ejpam-753	324	8	=	=	SYM
ejpam-753	324	9	pq1q2	pq1q2	PROPN
ejpam-753	324	10	.	.	PUNCT
ejpam-753	324	11	.	.	PUNCT
ejpam-753	324	12	.	.	PUNCT
ejpam-753	325	1	qt	qt	INTJ
ejpam-753	325	2	−	−	PROPN
ejpam-753	326	1	(	(	PUNCT
ejpam-753	326	2	p	p	X
ejpam-753	326	3	−	−	PROPN
ejpam-753	326	4	1)(q1	1)(q1	NUM
ejpam-753	327	1	−	−	PROPN
ejpam-753	327	2	1)(q2	1)(q2	NUM
ejpam-753	327	3	−	−	NOUN
ejpam-753	327	4	1	1	NUM
ejpam-753	327	5	)	)	PUNCT
ejpam-753	327	6	.	.	PUNCT
ejpam-753	327	7	.	.	PUNCT
ejpam-753	327	8	.	.	PUNCT
ejpam-753	328	1	(	(	PUNCT
ejpam-753	328	2	qt	qt	INTJ
ejpam-753	328	3	−	−	NOUN
ejpam-753	328	4	1	1	NUM
ejpam-753	328	5	)	)	PUNCT
ejpam-753	328	6	.	.	PUNCT
ejpam-753	329	1	if	if	SCONJ
ejpam-753	329	2	|r1|	|r1|	NOUN
ejpam-753	329	3	=	=	SYM
ejpam-753	329	4	p4	p4	ADJ
ejpam-753	329	5	,	,	PUNCT
ejpam-753	329	6	then	then	ADV
ejpam-753	329	7	by	by	ADP
ejpam-753	329	8	[	[	X
ejpam-753	329	9	8	8	NUM
ejpam-753	329	10	,	,	PUNCT
ejpam-753	329	11	theorem	theorem	VERB
ejpam-753	329	12	12	12	NUM
ejpam-753	329	13	]	]	PUNCT
ejpam-753	329	14	,	,	PUNCT
ejpam-753	329	15	r1	r1	PROPN
ejpam-753	329	16	is	be	AUX
ejpam-753	329	17	isomorphic	isomorphic	ADJ
ejpam-753	329	18	to	to	ADP
ejpam-753	329	19	fp2[x]/(x2	fp2[x]/(x2	NOUN
ejpam-753	329	20	)	)	PUNCT
ejpam-753	329	21	or	or	CCONJ
ejpam-753	329	22	gr(p4	gr(p4	NOUN
ejpam-753	329	23	,	,	PUNCT
ejpam-753	329	24	p2	p2	PROPN
ejpam-753	329	25	)	)	PUNCT
ejpam-753	329	26	and	and	CCONJ
ejpam-753	329	27	p4	p4	ADJ
ejpam-753	329	28	=	=	SYM
ejpam-753	329	29	p2q1q2	p2q1q2	PROPN
ejpam-753	329	30	.	.	PUNCT
ejpam-753	329	31	.	.	PUNCT
ejpam-753	329	32	.	.	PUNCT
ejpam-753	330	1	qt	qt	INTJ
ejpam-753	330	2	−	−	PROPN
ejpam-753	331	1	(	(	PUNCT
ejpam-753	331	2	p	p	NOUN
ejpam-753	331	3	2	2	NUM
ejpam-753	331	4	−	−	PROPN
ejpam-753	331	5	1)(q1−	1)(q1−	NUM
ejpam-753	331	6	1)(q2−	1)(q2−	NUM
ejpam-753	331	7	1	1	NUM
ejpam-753	331	8	)	)	PUNCT
ejpam-753	331	9	.	.	PUNCT
ejpam-753	331	10	.	.	PUNCT
ejpam-753	331	11	.	.	PUNCT
ejpam-753	332	1	(	(	PUNCT
ejpam-753	332	2	qt	qt	INTJ
ejpam-753	332	3	−	−	NOUN
ejpam-753	332	4	1	1	NUM
ejpam-753	332	5	)	)	PUNCT
ejpam-753	332	6	.	.	PUNCT
ejpam-753	333	1	case	case	NOUN
ejpam-753	333	2	3	3	NUM
ejpam-753	333	3	:	:	PUNCT
ejpam-753	333	4	|z(r1)|	|z(r1)|	NOUN
ejpam-753	333	5	=	=	SYM
ejpam-753	333	6	p3	p3	PROPN
ejpam-753	333	7	.	.	PUNCT
ejpam-753	334	1	then	then	ADV
ejpam-753	334	2	by	by	ADP
ejpam-753	334	3	lemma	lemma	PROPN
ejpam-753	334	4	1	1	NUM
ejpam-753	334	5	,	,	PUNCT
ejpam-753	334	6	|r1|	|r1|	NOUN
ejpam-753	334	7	=	=	SYM
ejpam-753	334	8	p4	p4	ADJ
ejpam-753	334	9	or	or	CCONJ
ejpam-753	334	10	p6	p6	ADJ
ejpam-753	334	11	.	.	PUNCT
ejpam-753	335	1	if	if	SCONJ
ejpam-753	335	2	|r1|	|r1|	PROPN
ejpam-753	335	3	=	=	SYM
ejpam-753	335	4	p6	p6	PROPN
ejpam-753	335	5	,	,	PUNCT
ejpam-753	335	6	then	then	ADV
ejpam-753	335	7	|z(r)|	|z(r)|	PROPN
ejpam-753	335	8	>	>	X
ejpam-753	335	9	|r1|	|r1|	PROPN
ejpam-753	335	10	which	which	PRON
ejpam-753	335	11	is	be	AUX
ejpam-753	335	12	impossible	impossible	ADJ
ejpam-753	336	1	.	.	PUNCT
ejpam-753	337	1	thus	thus	ADV
ejpam-753	337	2	|r1|	|r1|	ADJ
ejpam-753	337	3	=	=	SYM
ejpam-753	337	4	p4	p4	ADJ
ejpam-753	337	5	and	and	CCONJ
ejpam-753	337	6	so	so	ADV
ejpam-753	337	7	r1	r1	PROPN
ejpam-753	337	8	is	be	AUX
ejpam-753	337	9	isomorphic	isomorphic	ADJ
ejpam-753	337	10	to	to	ADP
ejpam-753	337	11	one	one	NUM
ejpam-753	337	12	of	of	ADP
ejpam-753	337	13	the	the	DET
ejpam-753	337	14	local	local	ADJ
ejpam-753	337	15	rings	ring	NOUN
ejpam-753	337	16	of	of	ADP
ejpam-753	337	17	order	order	NOUN
ejpam-753	337	18	p4	p4	PROPN
ejpam-753	337	19	described	describe	VERB
ejpam-753	337	20	in	in	ADP
ejpam-753	337	21	[	[	X
ejpam-753	337	22	2	2	NUM
ejpam-753	337	23	,	,	PUNCT
ejpam-753	337	24	corollary	corollary	ADJ
ejpam-753	337	25	3	3	NUM
ejpam-753	337	26	]	]	PUNCT
ejpam-753	337	27	and	and	CCONJ
ejpam-753	337	28	p3	p3	PROPN
ejpam-753	337	29	=	=	SYM
ejpam-753	337	30	pq1q2	pq1q2	PROPN
ejpam-753	337	31	.	.	PUNCT
ejpam-753	337	32	.	.	PUNCT
ejpam-753	337	33	.	.	PUNCT
ejpam-753	338	1	qt−(p−1)(q1−1)(q2−1	qt−(p−1)(q1−1)(q2−1	VERB
ejpam-753	338	2	)	)	PUNCT
ejpam-753	338	3	.	.	PUNCT
ejpam-753	338	4	.	.	PUNCT
ejpam-753	338	5	.	.	PUNCT
ejpam-753	339	1	(	(	PUNCT
ejpam-753	339	2	qt−1	qt−1	PROPN
ejpam-753	339	3	)	)	PUNCT
ejpam-753	339	4	.	.	PUNCT
ejpam-753	340	1	case	case	NOUN
ejpam-753	340	2	4	4	NUM
ejpam-753	340	3	:	:	PUNCT
ejpam-753	340	4	|z(r1)|=	|z(r1)|=	NOUN
ejpam-753	340	5	p4	p4	ADJ
ejpam-753	340	6	.	.	PUNCT
ejpam-753	341	1	then	then	ADV
ejpam-753	341	2	by	by	ADP
ejpam-753	341	3	lemma	lemma	PROPN
ejpam-753	341	4	1	1	NUM
ejpam-753	341	5	,	,	PUNCT
ejpam-753	341	6	|r1|	|r1|	NOUN
ejpam-753	341	7	=	=	SYM
ejpam-753	341	8	p5	p5	PROPN
ejpam-753	341	9	,	,	PUNCT
ejpam-753	341	10	p6	p6	ADJ
ejpam-753	341	11	or	or	CCONJ
ejpam-753	341	12	p8	p8	ADJ
ejpam-753	341	13	.	.	PUNCT
ejpam-753	342	1	if	if	SCONJ
ejpam-753	342	2	|r1|	|r1|	PROPN
ejpam-753	342	3	=	=	PUNCT
ejpam-753	342	4	p6	p6	PROPN
ejpam-753	342	5	or	or	CCONJ
ejpam-753	342	6	p8	p8	ADJ
ejpam-753	342	7	,	,	PUNCT
ejpam-753	342	8	then	then	ADV
ejpam-753	342	9	|z(r)|	|z(r)|	PROPN
ejpam-753	342	10	>	>	X
ejpam-753	342	11	|r1|	|r1|	PROPN
ejpam-753	342	12	which	which	PRON
ejpam-753	342	13	is	be	AUX
ejpam-753	342	14	impossible	impossible	ADJ
ejpam-753	342	15	.	.	PUNCT
ejpam-753	343	1	thus	thus	ADV
ejpam-753	343	2	|r1|	|r1|	NOUN
ejpam-753	343	3	=	=	SYM
ejpam-753	343	4	p5	p5	ADJ
ejpam-753	343	5	and	and	CCONJ
ejpam-753	343	6	so	so	ADV
ejpam-753	343	7	r1	r1	PROPN
ejpam-753	343	8	is	be	AUX
ejpam-753	343	9	isomorphic	isomorphic	ADJ
ejpam-753	343	10	to	to	ADP
ejpam-753	343	11	one	one	NUM
ejpam-753	343	12	of	of	ADP
ejpam-753	343	13	the	the	DET
ejpam-753	343	14	rings	ring	NOUN
ejpam-753	343	15	described	describe	VERB
ejpam-753	343	16	in	in	ADP
ejpam-753	343	17	proposition	proposition	NOUN
ejpam-753	343	18	2	2	NUM
ejpam-753	343	19	.	.	PUNCT
ejpam-753	343	20	also	also	ADV
ejpam-753	343	21	by	by	ADP
ejpam-753	343	22	lemma	lemma	PROPN
ejpam-753	343	23	2	2	NUM
ejpam-753	343	24	,	,	PUNCT
ejpam-753	343	25	r∼=	r∼=	NUM
ejpam-753	343	26	r1×	r1×	VERB
ejpam-753	343	27	fq	fq	PROPN
ejpam-753	343	28	and	and	CCONJ
ejpam-753	343	29	p2	p2	PROPN
ejpam-753	343	30	=	=	SYM
ejpam-753	343	31	p+	p+	PROPN
ejpam-753	343	32	q−	q−	PROPN
ejpam-753	343	33	1	1	NUM
ejpam-753	343	34	.	.	PUNCT
ejpam-753	344	1	theorem	theorem	NOUN
ejpam-753	344	2	3	3	X
ejpam-753	344	3	.	.	PUNCT
ejpam-753	345	1	let	let	VERB
ejpam-753	345	2	r	r	PRON
ejpam-753	345	3	be	be	AUX
ejpam-753	345	4	a	a	DET
ejpam-753	345	5	commutative	commutative	ADJ
ejpam-753	345	6	nonlocal	nonlocal	ADJ
ejpam-753	345	7	ring	ring	NOUN
ejpam-753	345	8	with	with	ADP
ejpam-753	345	9	|z(r)|=	|z(r)|=	VERB
ejpam-753	345	10	p7	p7	NOUN
ejpam-753	345	11	where	where	SCONJ
ejpam-753	345	12	p	p	NOUN
ejpam-753	345	13	is	be	AUX
ejpam-753	345	14	a	a	DET
ejpam-753	345	15	prime	prime	ADJ
ejpam-753	345	16	number	number	NOUN
ejpam-753	345	17	.	.	PUNCT
ejpam-753	346	1	then	then	ADV
ejpam-753	346	2	r	r	NOUN
ejpam-753	346	3	is	be	AUX
ejpam-753	346	4	isomorphic	isomorphic	ADJ
ejpam-753	346	5	to	to	ADP
ejpam-753	346	6	one	one	NUM
ejpam-753	346	7	of	of	ADP
ejpam-753	346	8	the	the	DET
ejpam-753	346	9	rings	ring	NOUN
ejpam-753	346	10	fq1	fq1	VERB
ejpam-753	346	11	×	×	NOUN
ejpam-753	346	12	.	.	PUNCT
ejpam-753	346	13	.	.	PUNCT
ejpam-753	346	14	.	.	PUNCT
ejpam-753	347	1	×	×	NOUN
ejpam-753	347	2	fqt	fqt	NOUN
ejpam-753	347	3	with	with	ADP
ejpam-753	347	4	p7	p7	ADJ
ejpam-753	347	5	=	=	SYM
ejpam-753	347	6	q1q2	q1q2	PROPN
ejpam-753	347	7	.	.	PUNCT
ejpam-753	347	8	.	.	PUNCT
ejpam-753	347	9	.	.	PUNCT
ejpam-753	348	1	qt	qt	INTJ
ejpam-753	348	2	−	−	PROPN
ejpam-753	348	3	(	(	PUNCT
ejpam-753	348	4	q1	q1	PROPN
ejpam-753	348	5	−	−	PROPN
ejpam-753	348	6	1)(q2	1)(q2	NUM
ejpam-753	348	7	−	−	PROPN
ejpam-753	348	8	1	1	NUM
ejpam-753	348	9	)	)	PUNCT
ejpam-753	348	10	.	.	PUNCT
ejpam-753	348	11	.	.	PUNCT
ejpam-753	348	12	.	.	PUNCT
ejpam-753	349	1	(	(	PUNCT
ejpam-753	349	2	qt−1	qt−1	PROPN
ejpam-753	349	3	)	)	PUNCT
ejpam-753	349	4	,	,	PUNCT
ejpam-753	349	5	z4×z4×f3×f3	z4×z4×f3×f3	PROPN
ejpam-753	349	6	,	,	PUNCT
ejpam-753	349	7	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	349	8	2)×z4×f3×f3	2)×z4×f3×f3	NUM
ejpam-753	349	9	,	,	PUNCT
ejpam-753	349	10	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	349	11	2)×z2[x]/(x	2)×z2[x]/(x	NUM
ejpam-753	349	12	2)×f3×f3	2)×f3×f3	NUM
ejpam-753	349	13	,	,	PUNCT
ejpam-753	349	14	r1	r1	NOUN
ejpam-753	349	15	×	×	PROPN
ejpam-753	349	16	r2	r2	PROPN
ejpam-753	349	17	×	×	PROPN
ejpam-753	349	18	f5	f5	NOUN
ejpam-753	349	19	where	where	SCONJ
ejpam-753	349	20	r1	r1	PROPN
ejpam-753	349	21	is	be	AUX
ejpam-753	349	22	isomorphic	isomorphic	ADJ
ejpam-753	349	23	to	to	ADP
ejpam-753	349	24	z4	z4	PROPN
ejpam-753	349	25	or	or	CCONJ
ejpam-753	349	26	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	349	27	2	2	NUM
ejpam-753	349	28	)	)	PUNCT
ejpam-753	349	29	and	and	CCONJ
ejpam-753	349	30	r2	r2	PROPN
ejpam-753	349	31	is	be	AUX
ejpam-753	349	32	isomorphic	isomorphic	ADJ
ejpam-753	349	33	to	to	ADP
ejpam-753	349	34	one	one	NUM
ejpam-753	349	35	of	of	ADP
ejpam-753	349	36	the	the	DET
ejpam-753	349	37	rings	ring	NOUN
ejpam-753	349	38	z8	z8	PROPN
ejpam-753	349	39	,	,	PUNCT
ejpam-753	349	40	z2[x	z2[x	PROPN
ejpam-753	349	41	,	,	PUNCT
ejpam-753	349	42	y]/(x	y]/(x	PROPN
ejpam-753	349	43	,	,	PUNCT
ejpam-753	349	44	y)2	y)2	NOUN
ejpam-753	349	45	,	,	PUNCT
ejpam-753	349	46	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	349	47	3	3	NUM
ejpam-753	349	48	)	)	PUNCT
ejpam-753	349	49	or	or	CCONJ
ejpam-753	349	50	z4[x]/(2x	z4[x]/(2x	VERB
ejpam-753	349	51	,	,	PUNCT
ejpam-753	349	52	x2−	x2−	PROPN
ejpam-753	349	53	2ǫ	2ǫ	NOUN
ejpam-753	349	54	)	)	PUNCT
ejpam-753	349	55	where	where	SCONJ
ejpam-753	349	56	ǫ	ǫ	PROPN
ejpam-753	349	57	∈	∈	PROPN
ejpam-753	349	58	σ0	σ0	NOUN
ejpam-753	349	59	2	2	NUM
ejpam-753	349	60	,	,	PUNCT
ejpam-753	349	61	r1	r1	NOUN
ejpam-753	349	62	×	×	PROPN
ejpam-753	349	63	r2	r2	PROPN
ejpam-753	349	64	×	×	NOUN
ejpam-753	349	65	fq1	fq1	CCONJ
ejpam-753	349	66	×	×	NOUN
ejpam-753	349	67	.	.	PUNCT
ejpam-753	349	68	.	.	PUNCT
ejpam-753	350	1	.×	.×	PROPN
ejpam-753	350	2	fqt	fqt	PROPN
ejpam-753	350	3	,	,	PUNCT
ejpam-753	350	4	where	where	SCONJ
ejpam-753	350	5	p	p	NOUN
ejpam-753	350	6	is	be	AUX
ejpam-753	350	7	an	an	DET
ejpam-753	350	8	odd	odd	ADJ
ejpam-753	350	9	prime	prime	ADJ
ejpam-753	350	10	number	number	NOUN
ejpam-753	350	11	,	,	PUNCT
ejpam-753	350	12	each	each	DET
ejpam-753	350	13	ri	ri	PROPN
ejpam-753	350	14	is	be	AUX
ejpam-753	350	15	isomorphic	isomorphic	ADJ
ejpam-753	350	16	to	to	ADP
ejpam-753	350	17	zp2	zp2	PROPN
ejpam-753	350	18	or	or	CCONJ
ejpam-753	350	19	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	350	20	2	2	NUM
ejpam-753	350	21	)	)	PUNCT
ejpam-753	350	22	and	and	CCONJ
ejpam-753	350	23	p5	p5	ADJ
ejpam-753	350	24	=	=	SYM
ejpam-753	350	25	p2q1q2	p2q1q2	PROPN
ejpam-753	350	26	.	.	PUNCT
ejpam-753	350	27	.	.	PUNCT
ejpam-753	350	28	.	.	PUNCT
ejpam-753	351	1	qt−(p−1)2(q1−1)(q2−1	qt−(p−1)2(q1−1)(q2−1	X
ejpam-753	351	2	)	)	PUNCT
ejpam-753	351	3	.	.	PUNCT
ejpam-753	351	4	.	.	PUNCT
ejpam-753	351	5	.	.	PUNCT
ejpam-753	352	1	(	(	PUNCT
ejpam-753	352	2	qt−1),r1×fq1	qt−1),r1×fq1	NOUN
ejpam-753	352	3	×.	×.	NUM
ejpam-753	352	4	.	.	PUNCT
ejpam-753	353	1	.×fqt	.×fqt	PUNCT
ejpam-753	353	2	where	where	SCONJ
ejpam-753	353	3	r1	r1	PROPN
ejpam-753	353	4	is	be	AUX
ejpam-753	353	5	isomorphic	isomorphic	ADJ
ejpam-753	353	6	to	to	ADP
ejpam-753	353	7	zp2	zp2	PROPN
ejpam-753	353	8	or	or	CCONJ
ejpam-753	353	9	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	353	10	2)with	2)with	NUM
ejpam-753	353	11	p6	p6	NOUN
ejpam-753	353	12	=	=	PUNCT
ejpam-753	353	13	pq1q2	pq1q2	PROPN
ejpam-753	353	14	.	.	PUNCT
ejpam-753	353	15	.	.	PUNCT
ejpam-753	353	16	.	.	PUNCT
ejpam-753	354	1	qt−(p−1)(q1−1)(q2−1	qt−(p−1)(q1−1)(q2−1	VERB
ejpam-753	354	2	)	)	PUNCT
ejpam-753	354	3	.	.	PUNCT
ejpam-753	354	4	.	.	PUNCT
ejpam-753	354	5	.	.	PUNCT
ejpam-753	355	1	(	(	PUNCT
ejpam-753	355	2	qt−1	qt−1	PROPN
ejpam-753	355	3	)	)	PUNCT
ejpam-753	355	4	,	,	PUNCT
ejpam-753	355	5	r1×fq1	r1×fq1	PROPN
ejpam-753	355	6	×.	×.	NUM
ejpam-753	355	7	.	.	PUNCT
ejpam-753	356	1	.×fqt	.×fqt	PUNCT
ejpam-753	356	2	where	where	SCONJ
ejpam-753	356	3	r1	r1	PROPN
ejpam-753	356	4	is	be	AUX
ejpam-753	356	5	isomorphic	isomorphic	ADJ
ejpam-753	356	6	to	to	ADP
ejpam-753	356	7	one	one	NUM
ejpam-753	356	8	the	the	DET
ejpam-753	356	9	rings	ring	NOUN
ejpam-753	356	10	zp3	zp3	PROPN
ejpam-753	356	11	,	,	PUNCT
ejpam-753	356	12	fp[x	fp[x	PROPN
ejpam-753	356	13	,	,	PUNCT
ejpam-753	356	14	y]/(x	y]/(x	PROPN
ejpam-753	356	15	,	,	PUNCT
ejpam-753	356	16	y)2	y)2	NOUN
ejpam-753	356	17	,	,	PUNCT
ejpam-753	356	18	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	356	19	3	3	NUM
ejpam-753	356	20	)	)	PUNCT
ejpam-753	356	21	or	or	CCONJ
ejpam-753	356	22	zp2[x]/(px	zp2[x]/(px	PROPN
ejpam-753	356	23	,	,	PUNCT
ejpam-753	356	24	x2	x2	PROPN
ejpam-753	356	25	−	−	PROPN
ejpam-753	357	1	ǫp	ǫp	NOUN
ejpam-753	357	2	)	)	PUNCT
ejpam-753	358	1	where	where	SCONJ
ejpam-753	358	2	ǫ	ǫ	PRON
ejpam-753	358	3	∈	∈	PROPN
ejpam-753	358	4	σ0	σ0	NOUN
ejpam-753	358	5	2	2	NUM
ejpam-753	358	6	with	with	ADP
ejpam-753	358	7	p5	p5	ADJ
ejpam-753	358	8	=	=	SYM
ejpam-753	358	9	pq1q2	pq1q2	PROPN
ejpam-753	358	10	.	.	PUNCT
ejpam-753	358	11	.	.	PUNCT
ejpam-753	358	12	.	.	PUNCT
ejpam-753	359	1	qt−(p−1)(q1−1)(q2−1	qt−(p−1)(q1−1)(q2−1	VERB
ejpam-753	359	2	)	)	PUNCT
ejpam-753	359	3	.	.	PUNCT
ejpam-753	359	4	.	.	PUNCT
ejpam-753	359	5	.	.	PUNCT
ejpam-753	360	1	(	(	PUNCT
ejpam-753	360	2	qt−1	qt−1	PROPN
ejpam-753	360	3	)	)	PUNCT
ejpam-753	360	4	,	,	PUNCT
ejpam-753	360	5	r1×fq1	r1×fq1	PROPN
ejpam-753	360	6	×.	×.	NUM
ejpam-753	360	7	.	.	PUNCT
ejpam-753	360	8	.×fqt	.×fqt	PUNCT
ejpam-753	361	1	where	where	SCONJ
ejpam-753	361	2	r1	r1	NOUN
ejpam-753	361	3	∼=	∼=	PROPN
ejpam-753	361	4	fp2[x]/(x2	fp2[x]/(x2	NOUN
ejpam-753	361	5	)	)	PUNCT
ejpam-753	361	6	or	or	CCONJ
ejpam-753	361	7	gr(p4	gr(p4	NOUN
ejpam-753	361	8	,	,	PUNCT
ejpam-753	361	9	p2	p2	PROPN
ejpam-753	361	10	)	)	PUNCT
ejpam-753	361	11	with	with	ADP
ejpam-753	361	12	p5	p5	PROPN
ejpam-753	361	13	=	=	SYM
ejpam-753	361	14	p2q1q2	p2q1q2	PROPN
ejpam-753	361	15	.	.	PUNCT
ejpam-753	361	16	.	.	PUNCT
ejpam-753	362	1	.	.	PUNCT
ejpam-753	363	1	qt	qt	INTJ
ejpam-753	363	2	−	−	PROPN
ejpam-753	364	1	(	(	PUNCT
ejpam-753	364	2	p	p	NOUN
ejpam-753	364	3	2	2	NUM
ejpam-753	364	4	−	−	PROPN
ejpam-753	364	5	1)(q1−	1)(q1−	NUM
ejpam-753	364	6	1)(q2−	1)(q2−	NUM
ejpam-753	364	7	1	1	NUM
ejpam-753	364	8	)	)	PUNCT
ejpam-753	364	9	.	.	PUNCT
ejpam-753	364	10	.	.	PUNCT
ejpam-753	364	11	.	.	PUNCT
ejpam-753	365	1	(	(	PUNCT
ejpam-753	365	2	qt	qt	INTJ
ejpam-753	365	3	−	−	PROPN
ejpam-753	365	4	1	1	NUM
ejpam-753	365	5	)	)	PUNCT
ejpam-753	365	6	,	,	PUNCT
ejpam-753	365	7	r1	r1	PROPN
ejpam-753	365	8	×	×	NOUN
ejpam-753	365	9	fq1	fq1	CCONJ
ejpam-753	365	10	×	×	NOUN
ejpam-753	365	11	.	.	PUNCT
ejpam-753	365	12	.	.	PUNCT
ejpam-753	366	1	.×	.×	PROPN
ejpam-753	366	2	fqt	fqt	PROPN
ejpam-753	366	3	where	where	SCONJ
ejpam-753	366	4	r1	r1	PROPN
ejpam-753	366	5	is	be	AUX
ejpam-753	366	6	isomorphic	isomorphic	ADJ
ejpam-753	366	7	to	to	ADP
ejpam-753	366	8	one	one	NUM
ejpam-753	366	9	of	of	ADP
ejpam-753	366	10	the	the	DET
ejpam-753	366	11	local	local	ADJ
ejpam-753	366	12	rings	ring	NOUN
ejpam-753	366	13	of	of	ADP
ejpam-753	366	14	order	order	NOUN
ejpam-753	366	15	p4	p4	PROPN
ejpam-753	366	16	described	describe	VERB
ejpam-753	366	17	in	in	ADP
ejpam-753	366	18	[	[	X
ejpam-753	366	19	2	2	NUM
ejpam-753	366	20	,	,	PUNCT
ejpam-753	366	21	corollary	corollary	ADJ
ejpam-753	366	22	3	3	NUM
ejpam-753	366	23	]	]	PUNCT
ejpam-753	366	24	and	and	CCONJ
ejpam-753	366	25	p4	p4	ADJ
ejpam-753	366	26	=	=	SYM
ejpam-753	366	27	pq1q2	pq1q2	PROPN
ejpam-753	366	28	.	.	PUNCT
ejpam-753	366	29	.	.	PUNCT
ejpam-753	366	30	.	.	PUNCT
ejpam-753	367	1	qt	qt	INTJ
ejpam-753	367	2	−	−	PROPN
ejpam-753	368	1	(	(	PUNCT
ejpam-753	368	2	p	p	X
ejpam-753	368	3	−	−	PROPN
ejpam-753	368	4	1)(q1	1)(q1	NUM
ejpam-753	369	1	−	−	PROPN
ejpam-753	369	2	1)(q2	1)(q2	NUM
ejpam-753	369	3	−	−	NOUN
ejpam-753	369	4	1	1	NUM
ejpam-753	369	5	)	)	PUNCT
ejpam-753	369	6	.	.	PUNCT
ejpam-753	369	7	.	.	PUNCT
ejpam-753	369	8	.	.	PUNCT
ejpam-753	370	1	(	(	PUNCT
ejpam-753	370	2	qt	qt	INTJ
ejpam-753	370	3	−	−	PROPN
ejpam-753	370	4	1	1	NUM
ejpam-753	370	5	)	)	PUNCT
ejpam-753	370	6	,	,	PUNCT
ejpam-753	370	7	r1	r1	PROPN
ejpam-753	370	8	×	×	PROPN
ejpam-753	370	9	fq	fq	PROPN
ejpam-753	370	10	where	where	SCONJ
ejpam-753	370	11	r1	r1	NOUN
ejpam-753	370	12	∼=	∼=	PROPN
ejpam-753	370	13	fp3[x]/(x2	fp3[x]/(x2	NOUN
ejpam-753	370	14	)	)	PUNCT
ejpam-753	370	15	or	or	CCONJ
ejpam-753	370	16	gr(p6	gr(p6	NOUN
ejpam-753	370	17	,	,	PUNCT
ejpam-753	370	18	p2	p2	PROPN
ejpam-753	370	19	)	)	PUNCT
ejpam-753	370	20	with	with	ADP
ejpam-753	370	21	p4	p4	ADJ
ejpam-753	370	22	=	=	SYM
ejpam-753	370	23	p3+p−1	p3+p−1	PROPN
ejpam-753	370	24	,	,	PUNCT
ejpam-753	370	25	r1×fq1	r1×fq1	PROPN
ejpam-753	370	26	×.	×.	NUM
ejpam-753	370	27	.	.	PUNCT
ejpam-753	370	28	.×fqt	.×fqt	PUNCT
ejpam-753	371	1	where	where	SCONJ
ejpam-753	371	2	r1	r1	PROPN
ejpam-753	371	3	is	be	AUX
ejpam-753	371	4	isomorphic	isomorphic	ADJ
ejpam-753	371	5	to	to	ADP
ejpam-753	371	6	one	one	NUM
ejpam-753	371	7	of	of	ADP
ejpam-753	371	8	the	the	DET
ejpam-753	371	9	rings	ring	NOUN
ejpam-753	371	10	described	describe	VERB
ejpam-753	371	11	in	in	ADP
ejpam-753	371	12	proposition	proposition	NOUN
ejpam-753	371	13	2	2	NUM
ejpam-753	371	14	,	,	PUNCT
ejpam-753	371	15	with	with	ADP
ejpam-753	371	16	p3	p3	PROPN
ejpam-753	371	17	=	=	SYM
ejpam-753	371	18	pq1q2	pq1q2	PROPN
ejpam-753	371	19	.	.	PUNCT
ejpam-753	371	20	.	.	PUNCT
ejpam-753	372	1	.	.	PUNCT
ejpam-753	373	1	qt−(p−1)(q1−1)(q2−1	qt−(p−1)(q1−1)(q2−1	VERB
ejpam-753	373	2	)	)	PUNCT
ejpam-753	373	3	.	.	PUNCT
ejpam-753	373	4	.	.	PUNCT
ejpam-753	373	5	.	.	PUNCT
ejpam-753	374	1	(	(	PUNCT
ejpam-753	374	2	qt−1	qt−1	PROPN
ejpam-753	374	3	)	)	PUNCT
ejpam-753	374	4	,	,	PUNCT
ejpam-753	374	5	r1×fq	r1×fq	PROPN
ejpam-753	374	6	where	where	SCONJ
ejpam-753	374	7	r1	r1	PROPN
ejpam-753	374	8	is	be	AUX
ejpam-753	374	9	isomorphic	isomorphic	ADJ
ejpam-753	374	10	to	to	ADP
ejpam-753	374	11	one	one	NUM
ejpam-753	374	12	of	of	ADP
ejpam-753	374	13	the	the	DET
ejpam-753	374	14	rings	ring	NOUN
ejpam-753	374	15	described	describe	VERB
ejpam-753	374	16	in	in	ADP
ejpam-753	374	17	proposition	proposition	NOUN
ejpam-753	374	18	1	1	NUM
ejpam-753	374	19	,	,	PUNCT
ejpam-753	374	20	with	with	ADP
ejpam-753	374	21	p3	p3	PROPN
ejpam-753	374	22	=	=	PUNCT
ejpam-753	375	1	p2+q−1	p2+q−1	PROPN
ejpam-753	375	2	or	or	CCONJ
ejpam-753	375	3	r1×	r1×	VERB
ejpam-753	375	4	fq	fq	PROPN
ejpam-753	375	5	,	,	PUNCT
ejpam-753	375	6	where	where	SCONJ
ejpam-753	375	7	r1	r1	PROPN
ejpam-753	375	8	is	be	AUX
ejpam-753	375	9	a	a	DET
ejpam-753	375	10	local	local	ADJ
ejpam-753	375	11	ring	ring	NOUN
ejpam-753	375	12	of	of	ADP
ejpam-753	375	13	order	order	NOUN
ejpam-753	375	14	p6	p6	VERB
ejpam-753	375	15	with	with	ADP
ejpam-753	375	16	p5	p5	ADJ
ejpam-753	375	17	zero	zero	NUM
ejpam-753	375	18	-	-	PUNCT
ejpam-753	375	19	divisors	divisor	NOUN
ejpam-753	375	20	and	and	CCONJ
ejpam-753	375	21	p2	p2	PROPN
ejpam-753	375	22	=	=	SYM
ejpam-753	375	23	p+	p+	PROPN
ejpam-753	375	24	q−	q−	PROPN
ejpam-753	375	25	1	1	NUM
ejpam-753	375	26	.	.	PUNCT
ejpam-753	375	27	m.	m.	NOUN
ejpam-753	375	28	behboodi	behboodi	PROPN
ejpam-753	375	29	,	,	PUNCT
ejpam-753	375	30	r.	r.	PROPN
ejpam-753	375	31	beyranvand	beyranvand	PROPN
ejpam-753	375	32	/	/	SYM
ejpam-753	375	33	eur	eur	PROPN
ejpam-753	375	34	.	.	PUNCT
ejpam-753	376	1	j.	j.	PROPN
ejpam-753	376	2	pure	pure	PROPN
ejpam-753	376	3	appl	appl	PROPN
ejpam-753	376	4	.	.	PROPN
ejpam-753	376	5	math	math	PROPN
ejpam-753	376	6	,	,	PUNCT
ejpam-753	376	7	3	3	NUM
ejpam-753	376	8	(	(	PUNCT
ejpam-753	376	9	2010	2010	NUM
ejpam-753	376	10	)	)	PUNCT
ejpam-753	376	11	,	,	PUNCT
ejpam-753	376	12	686	686	NUM
ejpam-753	376	13	-	-	SYM
ejpam-753	376	14	694	694	NUM
ejpam-753	376	15	693	693	NUM
ejpam-753	376	16	proof	proof	NOUN
ejpam-753	376	17	.	.	PUNCT
ejpam-753	377	1	if	if	SCONJ
ejpam-753	377	2	r	r	NOUN
ejpam-753	377	3	is	be	AUX
ejpam-753	377	4	reduced	reduce	VERB
ejpam-753	377	5	or	or	CCONJ
ejpam-753	377	6	r∼=	r∼=	PUNCT
ejpam-753	377	7	r1×r2×	r1×r2×	NOUN
ejpam-753	377	8	f5	f5	NOUN
ejpam-753	377	9	where	where	SCONJ
ejpam-753	377	10	r1	r1	PROPN
ejpam-753	377	11	is	be	AUX
ejpam-753	377	12	isomorphic	isomorphic	ADJ
ejpam-753	377	13	to	to	ADP
ejpam-753	377	14	z4	z4	PROPN
ejpam-753	377	15	or	or	CCONJ
ejpam-753	377	16	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	377	17	2	2	NUM
ejpam-753	377	18	)	)	PUNCT
ejpam-753	377	19	and	and	CCONJ
ejpam-753	377	20	r2	r2	PROPN
ejpam-753	377	21	is	be	AUX
ejpam-753	377	22	isomorphic	isomorphic	ADJ
ejpam-753	377	23	to	to	ADP
ejpam-753	377	24	one	one	NUM
ejpam-753	377	25	of	of	ADP
ejpam-753	377	26	the	the	DET
ejpam-753	377	27	rings	ring	NOUN
ejpam-753	377	28	z8	z8	PROPN
ejpam-753	377	29	,	,	PUNCT
ejpam-753	377	30	z2[x	z2[x	PROPN
ejpam-753	377	31	,	,	PUNCT
ejpam-753	377	32	y]/(x	y]/(x	PROPN
ejpam-753	377	33	,	,	PUNCT
ejpam-753	377	34	y)2	y)2	NOUN
ejpam-753	377	35	,	,	PUNCT
ejpam-753	377	36	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	377	37	3	3	NUM
ejpam-753	377	38	)	)	PUNCT
ejpam-753	377	39	or	or	CCONJ
ejpam-753	377	40	z4[x]/(2x	z4[x]/(2x	VERB
ejpam-753	377	41	,	,	PUNCT
ejpam-753	377	42	x2−	x2−	PROPN
ejpam-753	377	43	2ǫ	2ǫ	NOUN
ejpam-753	377	44	)	)	PUNCT
ejpam-753	377	45	where	where	SCONJ
ejpam-753	377	46	ǫ	ǫ	PROPN
ejpam-753	377	47	∈	∈	PROPN
ejpam-753	377	48	σ0	σ0	NOUN
ejpam-753	377	49	2	2	NUM
ejpam-753	377	50	,	,	PUNCT
ejpam-753	377	51	then	then	ADV
ejpam-753	377	52	we	we	PRON
ejpam-753	377	53	are	be	AUX
ejpam-753	377	54	done	do	VERB
ejpam-753	377	55	.	.	PUNCT
ejpam-753	378	1	otherwise	otherwise	ADV
ejpam-753	378	2	by	by	ADP
ejpam-753	378	3	[	[	X
ejpam-753	378	4	2	2	NUM
ejpam-753	378	5	,	,	PUNCT
ejpam-753	378	6	theorem	theorem	VERB
ejpam-753	378	7	4	4	NUM
ejpam-753	378	8	]	]	PUNCT
ejpam-753	378	9	,	,	PUNCT
ejpam-753	378	10	we	we	PRON
ejpam-753	378	11	have	have	VERB
ejpam-753	378	12	the	the	DET
ejpam-753	378	13	following	follow	VERB
ejpam-753	378	14	two	two	NUM
ejpam-753	378	15	cases	case	NOUN
ejpam-753	378	16	.	.	PUNCT
ejpam-753	379	1	case	case	NOUN
ejpam-753	379	2	1	1	NUM
ejpam-753	379	3	:	:	PUNCT
ejpam-753	379	4	r∼=	r∼=	NUM
ejpam-753	379	5	r1×	r1×	VERB
ejpam-753	379	6	fq1	fq1	ADV
ejpam-753	379	7	×	×	NOUN
ejpam-753	379	8	.	.	PUNCT
ejpam-753	379	9	.	.	PUNCT
ejpam-753	380	1	.×	.×	PROPN
ejpam-753	380	2	fqt	fqt	PROPN
ejpam-753	380	3	,	,	PUNCT
ejpam-753	380	4	where	where	SCONJ
ejpam-753	380	5	each	each	DET
ejpam-753	380	6	fqi	fqi	NOUN
ejpam-753	380	7	(	(	PUNCT
ejpam-753	380	8	1≤	1≤	INTJ
ejpam-753	380	9	i	i	PROPN
ejpam-753	380	10	≤	≤	PROPN
ejpam-753	380	11	t	t	PROPN
ejpam-753	380	12	)	)	PUNCT
ejpam-753	380	13	is	be	AUX
ejpam-753	380	14	a	a	DET
ejpam-753	380	15	finite	finite	ADJ
ejpam-753	380	16	field	field	NOUN
ejpam-753	380	17	and	and	CCONJ
ejpam-753	380	18	r1	r1	PROPN
ejpam-753	380	19	is	be	AUX
ejpam-753	380	20	a	a	DET
ejpam-753	380	21	local	local	ADJ
ejpam-753	380	22	ring	ring	NOUN
ejpam-753	380	23	with	with	ADP
ejpam-753	380	24	|z(r1)|	|z(r1)|	PROPN
ejpam-753	380	25	=	=	SYM
ejpam-753	380	26	pm	pm	NOUN
ejpam-753	380	27	,	,	PUNCT
ejpam-753	380	28	|r1|	|r1|	NOUN
ejpam-753	380	29	=	=	PUNCT
ejpam-753	380	30	pn	pn	PROPN
ejpam-753	381	1	such	such	ADJ
ejpam-753	381	2	that	that	SCONJ
ejpam-753	381	3	0	0	NUM
ejpam-753	381	4	<	<	X
ejpam-753	381	5	m	m	X
ejpam-753	381	6	<	<	X
ejpam-753	381	7	n≤	n≤	PRON
ejpam-753	381	8	6	6	NUM
ejpam-753	381	9	and	and	CCONJ
ejpam-753	381	10	p7	p7	ADJ
ejpam-753	381	11	=	=	SYM
ejpam-753	381	12	pnq1q2	pnq1q2	NOUN
ejpam-753	381	13	.	.	PUNCT
ejpam-753	381	14	.	.	PUNCT
ejpam-753	381	15	.	.	PUNCT
ejpam-753	382	1	qt	qt	INTJ
ejpam-753	382	2	−	−	PROPN
ejpam-753	383	1	(	(	PUNCT
ejpam-753	383	2	p	p	NOUN
ejpam-753	383	3	n	n	CCONJ
ejpam-753	383	4	−	−	NOUN
ejpam-753	383	5	pm)(q1−	pm)(q1−	NOUN
ejpam-753	383	6	1)(q2−	1)(q2−	NUM
ejpam-753	383	7	1	1	NUM
ejpam-753	383	8	)	)	PUNCT
ejpam-753	383	9	.	.	PUNCT
ejpam-753	383	10	.	.	PUNCT
ejpam-753	384	1	.	.	PUNCT
ejpam-753	385	1	(	(	PUNCT
ejpam-753	385	2	qt	qt	INTJ
ejpam-753	385	3	−	−	NOUN
ejpam-753	385	4	1	1	NUM
ejpam-753	385	5	)	)	PUNCT
ejpam-753	385	6	.	.	PUNCT
ejpam-753	386	1	case	case	NOUN
ejpam-753	386	2	2	2	NUM
ejpam-753	386	3	:	:	PUNCT
ejpam-753	386	4	r	r	NOUN
ejpam-753	386	5	∼=	∼=	PROPN
ejpam-753	386	6	r1	r1	NOUN
ejpam-753	386	7	×	×	NOUN
ejpam-753	386	8	r2	r2	NOUN
ejpam-753	386	9	×	×	NOUN
ejpam-753	386	10	fq1	fq1	CCONJ
ejpam-753	386	11	×	×	NOUN
ejpam-753	386	12	.	.	PUNCT
ejpam-753	386	13	.	.	PUNCT
ejpam-753	386	14	.	.	PUNCT
ejpam-753	387	1	×	×	NOUN
ejpam-753	387	2	fqt	fqt	NOUN
ejpam-753	387	3	,	,	PUNCT
ejpam-753	387	4	where	where	SCONJ
ejpam-753	387	5	each	each	DET
ejpam-753	387	6	fqi	fqi	NOUN
ejpam-753	387	7	(	(	PUNCT
ejpam-753	387	8	1	1	NUM
ejpam-753	387	9	≤	≤	NUM
ejpam-753	387	10	i	i	NOUN
ejpam-753	387	11	≤	≤	PROPN
ejpam-753	387	12	t	t	PROPN
ejpam-753	387	13	)	)	PUNCT
ejpam-753	387	14	is	be	AUX
ejpam-753	387	15	a	a	DET
ejpam-753	387	16	finite	finite	ADJ
ejpam-753	387	17	field	field	NOUN
ejpam-753	387	18	,	,	PUNCT
ejpam-753	387	19	each	each	DET
ejpam-753	387	20	ri	ri	PROPN
ejpam-753	387	21	is	be	AUX
ejpam-753	387	22	isomorphic	isomorphic	ADJ
ejpam-753	387	23	to	to	ADP
ejpam-753	387	24	zp2	zp2	PROPN
ejpam-753	387	25	or	or	CCONJ
ejpam-753	387	26	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	387	27	2	2	NUM
ejpam-753	387	28	)	)	PUNCT
ejpam-753	387	29	and	and	CCONJ
ejpam-753	387	30	p5	p5	ADJ
ejpam-753	387	31	=	=	SYM
ejpam-753	387	32	p2q1q2	p2q1q2	PROPN
ejpam-753	387	33	.	.	PUNCT
ejpam-753	387	34	.	.	PUNCT
ejpam-753	387	35	.	.	PUNCT
ejpam-753	388	1	qt	qt	INTJ
ejpam-753	388	2	−	−	PROPN
ejpam-753	388	3	(	(	PUNCT
ejpam-753	388	4	p−	p−	NOUN
ejpam-753	388	5	1)2(q1−	1)2(q1−	NUM
ejpam-753	388	6	1)(q2−	1)(q2−	NUM
ejpam-753	388	7	1	1	NUM
ejpam-753	388	8	)	)	PUNCT
ejpam-753	388	9	.	.	PUNCT
ejpam-753	388	10	.	.	PUNCT
ejpam-753	388	11	.	.	PUNCT
ejpam-753	389	1	(	(	PUNCT
ejpam-753	389	2	qt	qt	INTJ
ejpam-753	389	3	−	−	NOUN
ejpam-753	389	4	1	1	NUM
ejpam-753	389	5	)	)	PUNCT
ejpam-753	389	6	.	.	PUNCT
ejpam-753	390	1	(	(	PUNCT
ejpam-753	390	2	2	2	X
ejpam-753	390	3	)	)	PUNCT
ejpam-753	390	4	in	in	ADP
ejpam-753	390	5	case	case	NOUN
ejpam-753	390	6	1	1	NUM
ejpam-753	390	7	,	,	PUNCT
ejpam-753	390	8	as	as	ADP
ejpam-753	390	9	in	in	ADP
ejpam-753	390	10	the	the	DET
ejpam-753	390	11	proof	proof	NOUN
ejpam-753	390	12	of	of	ADP
ejpam-753	390	13	theorem	theorem	NOUN
ejpam-753	390	14	2	2	NUM
ejpam-753	390	15	,	,	PUNCT
ejpam-753	390	16	r	r	NOUN
ejpam-753	390	17	is	be	AUX
ejpam-753	390	18	isomorphic	isomorphic	ADJ
ejpam-753	390	19	to	to	ADP
ejpam-753	390	20	one	one	NUM
ejpam-753	390	21	of	of	ADP
ejpam-753	390	22	the	the	DET
ejpam-753	390	23	rings	ring	NOUN
ejpam-753	390	24	r1	r1	PROPN
ejpam-753	390	25	×	×	NOUN
ejpam-753	390	26	fq1	fq1	CCONJ
ejpam-753	390	27	×	×	NOUN
ejpam-753	390	28	.	.	PUNCT
ejpam-753	390	29	.	.	PUNCT
ejpam-753	391	1	.	.	PUNCT
ejpam-753	392	1	×	×	NOUN
ejpam-753	392	2	fqt	fqt	NOUN
ejpam-753	392	3	where	where	SCONJ
ejpam-753	392	4	r1	r1	PROPN
ejpam-753	392	5	is	be	AUX
ejpam-753	392	6	isomorphic	isomorphic	ADJ
ejpam-753	392	7	to	to	ADP
ejpam-753	392	8	zp2	zp2	PROPN
ejpam-753	392	9	or	or	CCONJ
ejpam-753	392	10	zp[x]/(x	zp[x]/(x	NUM
ejpam-753	392	11	2	2	NUM
ejpam-753	392	12	)	)	PUNCT
ejpam-753	392	13	with	with	ADP
ejpam-753	392	14	p6	p6	PROPN
ejpam-753	392	15	=	=	PUNCT
ejpam-753	392	16	pq1q2	pq1q2	PROPN
ejpam-753	392	17	.	.	PUNCT
ejpam-753	392	18	.	.	PUNCT
ejpam-753	392	19	.	.	PUNCT
ejpam-753	393	1	qt	qt	INTJ
ejpam-753	393	2	−	−	PROPN
ejpam-753	394	1	(	(	PUNCT
ejpam-753	394	2	p	p	X
ejpam-753	394	3	−	−	PROPN
ejpam-753	394	4	1)(q1	1)(q1	NUM
ejpam-753	395	1	−	−	PROPN
ejpam-753	395	2	1)(q2	1)(q2	NUM
ejpam-753	395	3	−	−	NOUN
ejpam-753	395	4	1	1	NUM
ejpam-753	395	5	)	)	PUNCT
ejpam-753	395	6	.	.	PUNCT
ejpam-753	395	7	.	.	PUNCT
ejpam-753	395	8	.	.	PUNCT
ejpam-753	396	1	(	(	PUNCT
ejpam-753	396	2	qt	qt	INTJ
ejpam-753	396	3	−	−	PROPN
ejpam-753	396	4	1	1	NUM
ejpam-753	396	5	)	)	PUNCT
ejpam-753	396	6	,	,	PUNCT
ejpam-753	396	7	r1	r1	PROPN
ejpam-753	396	8	×	×	NOUN
ejpam-753	396	9	fq1	fq1	CCONJ
ejpam-753	396	10	×	×	NOUN
ejpam-753	396	11	.	.	PUNCT
ejpam-753	396	12	.	.	PUNCT
ejpam-753	396	13	.	.	PUNCT
ejpam-753	397	1	×	×	NOUN
ejpam-753	397	2	fqt	fqt	NOUN
ejpam-753	397	3	,	,	PUNCT
ejpam-753	397	4	where	where	SCONJ
ejpam-753	397	5	r1	r1	PROPN
ejpam-753	397	6	is	be	AUX
ejpam-753	397	7	isomorphic	isomorphic	ADJ
ejpam-753	397	8	to	to	ADP
ejpam-753	397	9	one	one	NUM
ejpam-753	397	10	the	the	DET
ejpam-753	397	11	rings	ring	NOUN
ejpam-753	397	12	zp3	zp3	PROPN
ejpam-753	397	13	,	,	PUNCT
ejpam-753	397	14	fp[x	fp[x	PROPN
ejpam-753	397	15	,	,	PUNCT
ejpam-753	397	16	y]/(x	y]/(x	PROPN
ejpam-753	397	17	,	,	PUNCT
ejpam-753	397	18	y)2	y)2	NOUN
ejpam-753	397	19	,	,	PUNCT
ejpam-753	397	20	fp[x]/(x	fp[x]/(x	NOUN
ejpam-753	397	21	3	3	NUM
ejpam-753	397	22	)	)	PUNCT
ejpam-753	397	23	or	or	CCONJ
ejpam-753	397	24	zp2[x]/(px	zp2[x]/(px	X
ejpam-753	397	25	,	,	PUNCT
ejpam-753	397	26	x2−ǫp	x2−ǫp	PROPN
ejpam-753	397	27	)	)	PUNCT
ejpam-753	397	28	where	where	SCONJ
ejpam-753	397	29	ǫ	ǫ	PROPN
ejpam-753	397	30	∈	∈	PROPN
ejpam-753	397	31	σ0	σ0	NOUN
ejpam-753	397	32	2	2	NUM
ejpam-753	397	33	with	with	ADP
ejpam-753	397	34	p5	p5	ADJ
ejpam-753	397	35	=	=	SYM
ejpam-753	397	36	pq1q2	pq1q2	PROPN
ejpam-753	397	37	.	.	PUNCT
ejpam-753	397	38	.	.	PUNCT
ejpam-753	397	39	.	.	PUNCT
ejpam-753	398	1	qt−(p−1)(q1−1)(q2−1	qt−(p−1)(q1−1)(q2−1	VERB
ejpam-753	398	2	)	)	PUNCT
ejpam-753	398	3	.	.	PUNCT
ejpam-753	398	4	.	.	PUNCT
ejpam-753	398	5	.	.	PUNCT
ejpam-753	399	1	(	(	PUNCT
ejpam-753	399	2	qt−1	qt−1	PROPN
ejpam-753	399	3	)	)	PUNCT
ejpam-753	399	4	,	,	PUNCT
ejpam-753	399	5	r1×fq1	r1×fq1	PROPN
ejpam-753	399	6	×.	×.	X
ejpam-753	399	7	.	.	PUNCT
ejpam-753	400	1	.×fqt	.×fqt	PUNCT
ejpam-753	400	2	,	,	PUNCT
ejpam-753	400	3	where	where	SCONJ
ejpam-753	400	4	r1	r1	PROPN
ejpam-753	400	5	is	be	AUX
ejpam-753	400	6	isomorphic	isomorphic	ADJ
ejpam-753	400	7	to	to	ADP
ejpam-753	400	8	fp2[x]/(x2	fp2[x]/(x2	NOUN
ejpam-753	400	9	)	)	PUNCT
ejpam-753	400	10	or	or	CCONJ
ejpam-753	400	11	gr(p4	gr(p4	NOUN
ejpam-753	400	12	,	,	PUNCT
ejpam-753	400	13	p2	p2	PROPN
ejpam-753	400	14	)	)	PUNCT
ejpam-753	400	15	with	with	ADP
ejpam-753	400	16	p5	p5	PROPN
ejpam-753	400	17	=	=	SYM
ejpam-753	400	18	p2q1q2	p2q1q2	PROPN
ejpam-753	400	19	.	.	PUNCT
ejpam-753	400	20	.	.	PUNCT
ejpam-753	400	21	.	.	PUNCT
ejpam-753	401	1	qt−(p	qt−(p	PROPN
ejpam-753	401	2	2−1)(q1−1)(q2−1	2−1)(q1−1)(q2−1	NUM
ejpam-753	401	3	)	)	PUNCT
ejpam-753	401	4	.	.	PUNCT
ejpam-753	401	5	.	.	PUNCT
ejpam-753	402	1	.	.	PUNCT
ejpam-753	403	1	(	(	PUNCT
ejpam-753	403	2	qt−1	qt−1	PROPN
ejpam-753	403	3	)	)	PUNCT
ejpam-753	403	4	,	,	PUNCT
ejpam-753	403	5	r1×fq1	r1×fq1	PROPN
ejpam-753	403	6	×	×	NOUN
ejpam-753	403	7	.	.	PUNCT
ejpam-753	403	8	.	.	PUNCT
ejpam-753	404	1	.×fqt	.×fqt	PUNCT
ejpam-753	404	2	,	,	PUNCT
ejpam-753	404	3	where	where	SCONJ
ejpam-753	404	4	r1	r1	PROPN
ejpam-753	404	5	is	be	AUX
ejpam-753	404	6	isomorphic	isomorphic	ADJ
ejpam-753	404	7	to	to	ADP
ejpam-753	404	8	one	one	NUM
ejpam-753	404	9	of	of	ADP
ejpam-753	404	10	the	the	DET
ejpam-753	404	11	local	local	ADJ
ejpam-753	404	12	rings	ring	NOUN
ejpam-753	404	13	of	of	ADP
ejpam-753	404	14	order	order	NOUN
ejpam-753	404	15	p4	p4	PROPN
ejpam-753	404	16	described	describe	VERB
ejpam-753	404	17	in	in	ADP
ejpam-753	404	18	[	[	X
ejpam-753	404	19	2	2	NUM
ejpam-753	404	20	,	,	PUNCT
ejpam-753	404	21	corollary	corollary	ADJ
ejpam-753	404	22	3	3	NUM
ejpam-753	404	23	]	]	PUNCT
ejpam-753	404	24	with	with	ADP
ejpam-753	404	25	p4	p4	ADJ
ejpam-753	404	26	=	=	SYM
ejpam-753	404	27	pq1q2	pq1q2	PROPN
ejpam-753	404	28	.	.	PUNCT
ejpam-753	404	29	.	.	PUNCT
ejpam-753	404	30	.	.	PUNCT
ejpam-753	405	1	qt	qt	INTJ
ejpam-753	405	2	−	−	PROPN
ejpam-753	405	3	(	(	PUNCT
ejpam-753	405	4	p−	p−	NOUN
ejpam-753	405	5	1)(q1	1)(q1	NUM
ejpam-753	405	6	−	−	NOUN
ejpam-753	405	7	1)(q2	1)(q2	NUM
ejpam-753	405	8	−	−	NOUN
ejpam-753	405	9	1	1	NUM
ejpam-753	405	10	)	)	PUNCT
ejpam-753	405	11	.	.	PUNCT
ejpam-753	405	12	.	.	PUNCT
ejpam-753	405	13	.	.	PUNCT
ejpam-753	406	1	(	(	PUNCT
ejpam-753	406	2	qt	qt	INTJ
ejpam-753	406	3	−	−	PROPN
ejpam-753	406	4	1	1	NUM
ejpam-753	406	5	)	)	PUNCT
ejpam-753	406	6	,	,	PUNCT
ejpam-753	406	7	r1	r1	PROPN
ejpam-753	406	8	×	×	PROPN
ejpam-753	406	9	fq	fq	PROPN
ejpam-753	406	10	where	where	SCONJ
ejpam-753	406	11	r1	r1	PROPN
ejpam-753	406	12	is	be	AUX
ejpam-753	406	13	isomorphic	isomorphic	ADJ
ejpam-753	406	14	to	to	ADP
ejpam-753	406	15	fp3[x]/(x2	fp3[x]/(x2	NOUN
ejpam-753	406	16	)	)	PUNCT
ejpam-753	406	17	or	or	CCONJ
ejpam-753	406	18	gr(p6	gr(p6	NOUN
ejpam-753	406	19	,	,	PUNCT
ejpam-753	406	20	p2	p2	PROPN
ejpam-753	406	21	)	)	PUNCT
ejpam-753	406	22	with	with	ADP
ejpam-753	406	23	p4	p4	ADJ
ejpam-753	406	24	=	=	SYM
ejpam-753	406	25	p3	p3	PROPN
ejpam-753	406	26	+	+	CCONJ
ejpam-753	406	27	p−	p−	NOUN
ejpam-753	406	28	1	1	NUM
ejpam-753	406	29	,	,	PUNCT
ejpam-753	406	30	r1	r1	NOUN
ejpam-753	406	31	×	×	NOUN
ejpam-753	406	32	fq1	fq1	CCONJ
ejpam-753	406	33	×	×	NOUN
ejpam-753	406	34	.	.	PUNCT
ejpam-753	406	35	.	.	PUNCT
ejpam-753	406	36	.	.	PUNCT
ejpam-753	407	1	×	×	NOUN
ejpam-753	407	2	fqt	fqt	NOUN
ejpam-753	407	3	where	where	SCONJ
ejpam-753	407	4	r1	r1	PROPN
ejpam-753	407	5	is	be	AUX
ejpam-753	407	6	isomorphic	isomorphic	ADJ
ejpam-753	407	7	to	to	ADP
ejpam-753	407	8	one	one	NUM
ejpam-753	407	9	of	of	ADP
ejpam-753	407	10	the	the	DET
ejpam-753	407	11	rings	ring	NOUN
ejpam-753	407	12	described	describe	VERB
ejpam-753	407	13	in	in	ADP
ejpam-753	407	14	proposition	proposition	NOUN
ejpam-753	407	15	2	2	NUM
ejpam-753	407	16	,	,	PUNCT
ejpam-753	407	17	with	with	ADP
ejpam-753	407	18	p3	p3	PROPN
ejpam-753	407	19	=	=	SYM
ejpam-753	407	20	pq1q2	pq1q2	PROPN
ejpam-753	407	21	.	.	PUNCT
ejpam-753	407	22	.	.	PUNCT
ejpam-753	407	23	.	.	PUNCT
ejpam-753	408	1	qt	qt	INTJ
ejpam-753	408	2	−	−	NOUN
ejpam-753	408	3	(	(	PUNCT
ejpam-753	408	4	p−1)(q1−1)(q2−1	p−1)(q1−1)(q2−1	NOUN
ejpam-753	408	5	)	)	PUNCT
ejpam-753	408	6	.	.	PUNCT
ejpam-753	408	7	.	.	PUNCT
ejpam-753	408	8	.	.	PUNCT
ejpam-753	409	1	(	(	PUNCT
ejpam-753	409	2	qt	qt	NOUN
ejpam-753	409	3	−1	−1	NOUN
ejpam-753	409	4	)	)	PUNCT
ejpam-753	409	5	,	,	PUNCT
ejpam-753	409	6	r1×	r1×	PROPN
ejpam-753	409	7	fq	fq	PROPN
ejpam-753	409	8	where	where	SCONJ
ejpam-753	409	9	r1	r1	PROPN
ejpam-753	409	10	is	be	AUX
ejpam-753	409	11	isomorphic	isomorphic	ADJ
ejpam-753	409	12	to	to	ADP
ejpam-753	409	13	one	one	NUM
ejpam-753	409	14	of	of	ADP
ejpam-753	409	15	the	the	DET
ejpam-753	409	16	rings	ring	NOUN
ejpam-753	409	17	described	describe	VERB
ejpam-753	409	18	in	in	ADP
ejpam-753	409	19	proposition	proposition	NOUN
ejpam-753	409	20	1	1	NUM
ejpam-753	409	21	,	,	PUNCT
ejpam-753	409	22	with	with	ADP
ejpam-753	409	23	p3	p3	NOUN
ejpam-753	409	24	=	=	PUNCT
ejpam-753	409	25	p2	p2	PROPN
ejpam-753	409	26	+	+	X
ejpam-753	409	27	q−	q−	PROPN
ejpam-753	409	28	1	1	NUM
ejpam-753	409	29	or	or	CCONJ
ejpam-753	409	30	r1×	r1×	PROPN
ejpam-753	409	31	fq	fq	PROPN
ejpam-753	409	32	,	,	PUNCT
ejpam-753	409	33	where	where	SCONJ
ejpam-753	409	34	r1	r1	PROPN
ejpam-753	409	35	is	be	AUX
ejpam-753	409	36	a	a	DET
ejpam-753	409	37	local	local	ADJ
ejpam-753	409	38	ring	ring	NOUN
ejpam-753	409	39	of	of	ADP
ejpam-753	409	40	order	order	NOUN
ejpam-753	409	41	p6	p6	VERB
ejpam-753	409	42	with	with	ADP
ejpam-753	409	43	p5	p5	ADJ
ejpam-753	409	44	zero	zero	NUM
ejpam-753	409	45	-	-	PUNCT
ejpam-753	409	46	divisors	divisor	NOUN
ejpam-753	409	47	.	.	PUNCT
ejpam-753	410	1	in	in	ADP
ejpam-753	410	2	case	case	NOUN
ejpam-753	410	3	2	2	NUM
ejpam-753	410	4	,	,	PUNCT
ejpam-753	410	5	if	if	SCONJ
ejpam-753	410	6	p	p	NOUN
ejpam-753	410	7	=	=	NOUN
ejpam-753	410	8	2	2	NUM
ejpam-753	410	9	,	,	PUNCT
ejpam-753	410	10	then	then	ADV
ejpam-753	410	11	since	since	SCONJ
ejpam-753	410	12	|z(r)|	|z(r)|	PROPN
ejpam-753	410	13	>	>	SYM
ejpam-753	410	14	|r1||r2|q1	|r1||r2|q1	NOUN
ejpam-753	410	15	.	.	PUNCT
ejpam-753	410	16	.	.	PUNCT
ejpam-753	410	17	.	.	PUNCT
ejpam-753	411	1	qt−1	qt−1	PROPN
ejpam-753	411	2	,	,	PUNCT
ejpam-753	411	3	t	t	VERB
ejpam-753	411	4	≤	≤	NUM
ejpam-753	411	5	3	3	X
ejpam-753	411	6	.	.	PUNCT
ejpam-753	412	1	we	we	PRON
ejpam-753	412	2	claim	claim	VERB
ejpam-753	412	3	that	that	SCONJ
ejpam-753	412	4	t	t	NOUN
ejpam-753	412	5	=	=	SYM
ejpam-753	412	6	2	2	X
ejpam-753	412	7	.	.	PUNCT
ejpam-753	413	1	if	if	SCONJ
ejpam-753	413	2	t	t	NOUN
ejpam-753	413	3	=	=	SYM
ejpam-753	413	4	1	1	NUM
ejpam-753	413	5	,	,	PUNCT
ejpam-753	413	6	then	then	ADV
ejpam-753	413	7	the	the	DET
ejpam-753	413	8	relation	relation	NOUN
ejpam-753	413	9	(	(	PUNCT
ejpam-753	413	10	2	2	NUM
ejpam-753	413	11	)	)	PUNCT
ejpam-753	413	12	implies	imply	VERB
ejpam-753	413	13	that	that	DET
ejpam-753	413	14	q1	q1	PROPN
ejpam-753	413	15	=	=	SYM
ejpam-753	413	16	31/3	31/3	NUM
ejpam-753	413	17	,	,	PUNCT
ejpam-753	413	18	a	a	DET
ejpam-753	413	19	contradiction	contradiction	NOUN
ejpam-753	413	20	.	.	PUNCT
ejpam-753	414	1	if	if	SCONJ
ejpam-753	414	2	t	t	NOUN
ejpam-753	414	3	=	=	SYM
ejpam-753	414	4	3	3	NUM
ejpam-753	414	5	,	,	PUNCT
ejpam-753	414	6	then	then	ADV
ejpam-753	414	7	the	the	DET
ejpam-753	414	8	relation	relation	NOUN
ejpam-753	414	9	(	(	PUNCT
ejpam-753	414	10	2	2	NUM
ejpam-753	414	11	)	)	PUNCT
ejpam-753	414	12	implies	imply	VERB
ejpam-753	414	13	that	that	SCONJ
ejpam-753	414	14	4	4	NUM
ejpam-753	414	15	is	be	AUX
ejpam-753	414	16	a	a	DET
ejpam-753	414	17	divisor	divisor	NOUN
ejpam-753	414	18	of	of	ADP
ejpam-753	414	19	(	(	PUNCT
ejpam-753	414	20	q1	q1	PROPN
ejpam-753	414	21	−	−	PROPN
ejpam-753	414	22	1)(q2	1)(q2	NUM
ejpam-753	414	23	−	−	PROPN
ejpam-753	414	24	1)(q3	1)(q3	NUM
ejpam-753	414	25	−	−	NOUN
ejpam-753	414	26	1	1	NUM
ejpam-753	414	27	)	)	PUNCT
ejpam-753	414	28	.	.	PUNCT
ejpam-753	415	1	without	without	ADP
ejpam-753	415	2	loss	loss	NOUN
ejpam-753	415	3	of	of	ADP
ejpam-753	415	4	generality	generality	NOUN
ejpam-753	415	5	we	we	PRON
ejpam-753	415	6	can	can	AUX
ejpam-753	415	7	assume	assume	VERB
ejpam-753	415	8	that	that	SCONJ
ejpam-753	415	9	either	either	DET
ejpam-753	415	10	4	4	NUM
ejpam-753	415	11	is	be	AUX
ejpam-753	415	12	a	a	DET
ejpam-753	415	13	divisor	divisor	NOUN
ejpam-753	415	14	of	of	ADP
ejpam-753	415	15	(	(	PUNCT
ejpam-753	415	16	q1	q1	NOUN
ejpam-753	415	17	−	−	NOUN
ejpam-753	415	18	1	1	NUM
ejpam-753	415	19	)	)	PUNCT
ejpam-753	415	20	or	or	CCONJ
ejpam-753	415	21	2	2	NUM
ejpam-753	415	22	is	be	AUX
ejpam-753	415	23	a	a	DET
ejpam-753	415	24	divisor	divisor	NOUN
ejpam-753	415	25	of	of	ADP
ejpam-753	415	26	both	both	PRON
ejpam-753	415	27	(	(	PUNCT
ejpam-753	415	28	q1	q1	NOUN
ejpam-753	415	29	−	−	NOUN
ejpam-753	415	30	1	1	NUM
ejpam-753	415	31	)	)	PUNCT
ejpam-753	415	32	and	and	CCONJ
ejpam-753	415	33	(	(	PUNCT
ejpam-753	415	34	q2	q2	NOUN
ejpam-753	415	35	−	−	PROPN
ejpam-753	415	36	1	1	NUM
ejpam-753	415	37	)	)	PUNCT
ejpam-753	415	38	.	.	PUNCT
ejpam-753	416	1	therefore	therefore	ADV
ejpam-753	416	2	either	either	CCONJ
ejpam-753	416	3	q1	q1	PROPN
ejpam-753	416	4	≥	≥	NUM
ejpam-753	416	5	5	5	NUM
ejpam-753	416	6	or	or	CCONJ
ejpam-753	416	7	q1	q1	PROPN
ejpam-753	416	8	≥	≥	NUM
ejpam-753	416	9	3	3	NUM
ejpam-753	416	10	and	and	CCONJ
ejpam-753	416	11	q2	q2	PROPN
ejpam-753	416	12	≥	≥	NUM
ejpam-753	416	13	3	3	NUM
ejpam-753	416	14	.	.	PUNCT
ejpam-753	417	1	this	this	PRON
ejpam-753	417	2	implies	imply	VERB
ejpam-753	417	3	that	that	SCONJ
ejpam-753	417	4	either	either	CCONJ
ejpam-753	417	5	27	27	NUM
ejpam-753	417	6	=	=	SYM
ejpam-753	417	7	|z(r)|	|z(r)|	PROPN
ejpam-753	417	8	>	>	X
ejpam-753	417	9	5|r1||r2|q2	5|r1||r2|q2	NUM
ejpam-753	417	10	=	=	SYM
ejpam-753	417	11	80q2	80q2	NUM
ejpam-753	417	12	or	or	CCONJ
ejpam-753	417	13	27	27	NUM
ejpam-753	417	14	=	=	SYM
ejpam-753	417	15	|z(r)|	|z(r)|	PROPN
ejpam-753	417	16	>	>	X
ejpam-753	417	17	9|r1||r2|	9|r1||r2|	NOUN
ejpam-753	417	18	=	=	SYM
ejpam-753	417	19	144	144	NUM
ejpam-753	417	20	.	.	PUNCT
ejpam-753	418	1	but	but	CCONJ
ejpam-753	418	2	it	it	PRON
ejpam-753	418	3	is	be	AUX
ejpam-753	418	4	impossible	impossible	ADJ
ejpam-753	418	5	in	in	ADP
ejpam-753	418	6	any	any	DET
ejpam-753	418	7	case	case	NOUN
ejpam-753	418	8	.	.	PUNCT
ejpam-753	419	1	thus	thus	ADV
ejpam-753	419	2	t	t	X
ejpam-753	419	3	=	=	SYM
ejpam-753	419	4	2	2	NUM
ejpam-753	419	5	and	and	CCONJ
ejpam-753	419	6	by	by	ADP
ejpam-753	419	7	the	the	DET
ejpam-753	419	8	relation	relation	NOUN
ejpam-753	419	9	(	(	PUNCT
ejpam-753	419	10	2	2	X
ejpam-753	419	11	)	)	PUNCT
ejpam-753	419	12	we	we	PRON
ejpam-753	419	13	have	have	VERB
ejpam-753	419	14	25	25	NUM
ejpam-753	419	15	=	=	SYM
ejpam-753	419	16	22q1q2−	22q1q2−	NUM
ejpam-753	419	17	(	(	PUNCT
ejpam-753	419	18	q1	q1	PROPN
ejpam-753	419	19	−	−	PROPN
ejpam-753	419	20	1)(q2−	1)(q2−	NUM
ejpam-753	419	21	1	1	NUM
ejpam-753	419	22	)	)	PUNCT
ejpam-753	419	23	.	.	PUNCT
ejpam-753	420	1	(	(	PUNCT
ejpam-753	420	2	3	3	X
ejpam-753	420	3	)	)	PUNCT
ejpam-753	420	4	if	if	SCONJ
ejpam-753	420	5	4	4	NUM
ejpam-753	420	6	is	be	AUX
ejpam-753	420	7	a	a	DET
ejpam-753	420	8	divisor	divisor	NOUN
ejpam-753	420	9	of	of	ADP
ejpam-753	420	10	(	(	PUNCT
ejpam-753	420	11	qi	qi	NOUN
ejpam-753	420	12	−	−	PROPN
ejpam-753	420	13	1	1	NUM
ejpam-753	420	14	)	)	PUNCT
ejpam-753	420	15	for	for	ADP
ejpam-753	420	16	some	some	DET
ejpam-753	420	17	i	i	PRON
ejpam-753	420	18	,	,	PUNCT
ejpam-753	420	19	then	then	ADV
ejpam-753	420	20	qi	qi	PROPN
ejpam-753	420	21	≥	≥	NUM
ejpam-753	420	22	5	5	NUM
ejpam-753	420	23	and	and	CCONJ
ejpam-753	420	24	hence	hence	ADV
ejpam-753	420	25	25	25	NUM
ejpam-753	420	26	=	=	SYM
ejpam-753	420	27	3q1q2	3q1q2	ADJ
ejpam-753	420	28	+	+	NUM
ejpam-753	420	29	q1	q1	PROPN
ejpam-753	420	30	+	+	CCONJ
ejpam-753	420	31	q2−	q2−	NOUN
ejpam-753	420	32	1≥	1≥	NUM
ejpam-753	420	33	30	30	NUM
ejpam-753	420	34	+	+	NOUN
ejpam-753	420	35	7−1=	7−1=	NUM
ejpam-753	420	36	36	36	NUM
ejpam-753	420	37	,	,	PUNCT
ejpam-753	420	38	a	a	DET
ejpam-753	420	39	contradiction	contradiction	NOUN
ejpam-753	420	40	.	.	PUNCT
ejpam-753	421	1	thus	thus	ADV
ejpam-753	421	2	2	2	NUM
ejpam-753	421	3	is	be	AUX
ejpam-753	421	4	a	a	DET
ejpam-753	421	5	divisor	divisor	NOUN
ejpam-753	421	6	of	of	ADP
ejpam-753	421	7	both	both	PRON
ejpam-753	421	8	(	(	PUNCT
ejpam-753	421	9	q1−1	q1−1	PROPN
ejpam-753	421	10	)	)	PUNCT
ejpam-753	421	11	and	and	CCONJ
ejpam-753	421	12	(	(	PUNCT
ejpam-753	421	13	q2−1	q2−1	NOUN
ejpam-753	421	14	)	)	PUNCT
ejpam-753	421	15	.	.	PUNCT
ejpam-753	422	1	then	then	ADV
ejpam-753	422	2	q1−1=	q1−1=	VERB
ejpam-753	422	3	2k1	2k1	NUM
ejpam-753	422	4	,	,	PUNCT
ejpam-753	422	5	q2−1=	q2−1=	NOUN
ejpam-753	422	6	2k2	2k2	NUM
ejpam-753	422	7	for	for	ADP
ejpam-753	422	8	some	some	DET
ejpam-753	422	9	positive	positive	ADJ
ejpam-753	422	10	integers	integer	NOUN
ejpam-753	422	11	k1	k1	NOUN
ejpam-753	422	12	,	,	PUNCT
ejpam-753	422	13	k2	k2	NOUN
ejpam-753	422	14	and	and	CCONJ
ejpam-753	422	15	put	put	VERB
ejpam-753	422	16	them	they	PRON
ejpam-753	422	17	into	into	ADP
ejpam-753	422	18	(	(	PUNCT
ejpam-753	422	19	3	3	NUM
ejpam-753	422	20	)	)	PUNCT
ejpam-753	422	21	.	.	PUNCT
ejpam-753	423	1	then	then	ADV
ejpam-753	423	2	we	we	PRON
ejpam-753	423	3	obtain	obtain	VERB
ejpam-753	423	4	8=	8=	NUM
ejpam-753	423	5	3k1k2	3k1k2	NUM
ejpam-753	423	6	+	+	SYM
ejpam-753	423	7	2k1	2k1	NUM
ejpam-753	423	8	+	+	NUM
ejpam-753	423	9	2k2	2k2	NUM
ejpam-753	423	10	+	+	NUM
ejpam-753	423	11	1	1	NUM
ejpam-753	423	12	.	.	PUNCT
ejpam-753	424	1	it	it	PRON
ejpam-753	424	2	yields	yield	VERB
ejpam-753	424	3	k1	k1	NOUN
ejpam-753	424	4	=	=	SYM
ejpam-753	424	5	k2	k2	PROPN
ejpam-753	424	6	=	=	SYM
ejpam-753	424	7	1	1	NUM
ejpam-753	424	8	and	and	CCONJ
ejpam-753	424	9	hence	hence	ADV
ejpam-753	424	10	q1	q1	NOUN
ejpam-753	424	11	=	=	SYM
ejpam-753	424	12	q2	q2	PROPN
ejpam-753	424	13	=	=	SYM
ejpam-753	424	14	3	3	X
ejpam-753	424	15	.	.	PUNCT
ejpam-753	424	16	thus	thus	ADV
ejpam-753	424	17	r∼=	r∼=	NUM
ejpam-753	424	18	r1	r1	PROPN
ejpam-753	424	19	×	×	PROPN
ejpam-753	424	20	r2×	r2×	NOUN
ejpam-753	424	21	f3	f3	PROPN
ejpam-753	424	22	×	×	PROPN
ejpam-753	424	23	f3	f3	PROPN
ejpam-753	424	24	where	where	SCONJ
ejpam-753	424	25	r1	r1	PROPN
ejpam-753	424	26	and	and	CCONJ
ejpam-753	424	27	r2	r2	PROPN
ejpam-753	424	28	are	be	AUX
ejpam-753	424	29	isomorphic	isomorphic	ADJ
ejpam-753	424	30	to	to	ADP
ejpam-753	424	31	z4	z4	PROPN
ejpam-753	424	32	or	or	CCONJ
ejpam-753	424	33	z2[x]/(x	z2[x]/(x	NUM
ejpam-753	424	34	2	2	NUM
ejpam-753	424	35	)	)	PUNCT
ejpam-753	424	36	.	.	PUNCT
ejpam-753	425	1	references	reference	NOUN
ejpam-753	425	2	694	694	NUM
ejpam-753	425	3	acknowledgements	acknowledgement	NOUN
ejpam-753	425	4	this	this	DET
ejpam-753	425	5	work	work	NOUN
ejpam-753	425	6	was	be	AUX
ejpam-753	425	7	partially	partially	ADV
ejpam-753	425	8	supported	support	VERB
ejpam-753	425	9	by	by	ADP
ejpam-753	425	10	iut	iut	PROPN
ejpam-753	425	11	(	(	PUNCT
ejpam-753	425	12	ceama	ceama	PROPN
ejpam-753	425	13	)	)	PUNCT
ejpam-753	425	14	.	.	PUNCT
ejpam-753	426	1	the	the	DET
ejpam-753	426	2	research	research	NOUN
ejpam-753	426	3	of	of	ADP
ejpam-753	426	4	the	the	DET
ejpam-753	426	5	first	first	ADJ
ejpam-753	426	6	author	author	NOUN
ejpam-753	426	7	was	be	AUX
ejpam-753	426	8	in	in	ADP
ejpam-753	426	9	part	part	NOUN
ejpam-753	426	10	supported	support	VERB
ejpam-753	426	11	by	by	ADP
ejpam-753	426	12	a	a	DET
ejpam-753	426	13	grant	grant	NOUN
ejpam-753	426	14	from	from	ADP
ejpam-753	426	15	ipm	ipm	NOUN
ejpam-753	426	16	(	(	PUNCT
ejpam-753	426	17	no	no	NOUN
ejpam-753	426	18	.	.	NOUN
ejpam-753	426	19	87160026	87160026	NUM
ejpam-753	426	20	)	)	PUNCT
ejpam-753	426	21	.	.	PUNCT
ejpam-753	427	1	references	reference	NOUN
ejpam-753	427	2	[	[	X
ejpam-753	427	3	1	1	X
ejpam-753	427	4	]	]	X
ejpam-753	427	5	y.	y.	PROPN
ejpam-753	427	6	al	al	PROPN
ejpam-753	427	7	-	-	PUNCT
ejpam-753	427	8	khamees	khamees	PROPN
ejpam-753	427	9	,	,	PUNCT
ejpam-753	427	10	finite	finite	PROPN
ejpam-753	427	11	rings	ring	NOUN
ejpam-753	427	12	in	in	ADP
ejpam-753	427	13	which	which	PRON
ejpam-753	427	14	the	the	DET
ejpam-753	427	15	multiplication	multiplication	NOUN
ejpam-753	427	16	of	of	ADP
ejpam-753	427	17	any	any	DET
ejpam-753	427	18	two	two	NUM
ejpam-753	427	19	zero	zero	NUM
ejpam-753	427	20	-	-	PUNCT
ejpam-753	427	21	divisors	divisor	NOUN
ejpam-753	427	22	is	be	AUX
ejpam-753	427	23	zero	zero	NUM
ejpam-753	427	24	,	,	PUNCT
ejpam-753	427	25	arch	arch	NOUN
ejpam-753	427	26	.	.	PUNCT
ejpam-753	428	1	math	math	NOUN
ejpam-753	428	2	,	,	PUNCT
ejpam-753	428	3	37	37	NUM
ejpam-753	428	4	(	(	PUNCT
ejpam-753	428	5	1981	1981	NUM
ejpam-753	428	6	)	)	PUNCT
ejpam-753	428	7	,	,	PUNCT
ejpam-753	428	8	144	144	NUM
ejpam-753	428	9	-	-	SYM
ejpam-753	428	10	149	149	NUM
ejpam-753	428	11	.	.	PUNCT
ejpam-753	428	12	1981	1981	NUM
ejpam-753	428	13	.	.	PUNCT
ejpam-753	429	1	[	[	X
ejpam-753	429	2	2	2	NUM
ejpam-753	429	3	]	]	PUNCT
ejpam-753	429	4	m.	m.	NOUN
ejpam-753	429	5	behboodi	behboodi	PROPN
ejpam-753	429	6	,	,	PUNCT
ejpam-753	429	7	r.	r.	PROPN
ejpam-753	429	8	beyranvand	beyranvand	PROPN
ejpam-753	429	9	,	,	PUNCT
ejpam-753	429	10	on	on	ADP
ejpam-753	429	11	the	the	DET
ejpam-753	429	12	structure	structure	NOUN
ejpam-753	429	13	of	of	ADP
ejpam-753	429	14	commutative	commutative	ADJ
ejpam-753	429	15	rings	ring	NOUN
ejpam-753	429	16	with	with	ADP
ejpam-753	429	17	p1	p1	PROPN
ejpam-753	429	18	k1	k1	X
ejpam-753	429	19	·	·	PUNCT
ejpam-753	429	20	·	·	PUNCT
ejpam-753	429	21	·	·	PUNCT
ejpam-753	430	1	pn	pn	PROPN
ejpam-753	430	2	kn(1	kn(1	PROPN
ejpam-753	430	3	≤	≤	PROPN
ejpam-753	430	4	ki	ki	PROPN
ejpam-753	430	5	≤	≤	ADV
ejpam-753	430	6	7	7	NUM
ejpam-753	430	7	)	)	PUNCT
ejpam-753	430	8	zero	zero	NUM
ejpam-753	430	9	-	-	PUNCT
ejpam-753	430	10	divisors	divisor	NOUN
ejpam-753	430	11	,	,	PUNCT
ejpam-753	430	12	euro	euro	PROPN
ejpam-753	430	13	.	.	PUNCT
ejpam-753	431	1	j.	j.	PROPN
ejpam-753	431	2	pure	pure	PROPN
ejpam-753	431	3	and	and	CCONJ
ejpam-753	431	4	appl	appl	PROPN
ejpam-753	431	5	.	.	PROPN
ejpam-753	431	6	math	math	NOUN
ejpam-753	431	7	.	.	PUNCT
ejpam-753	432	1	3(2	3(2	NUM
ejpam-753	432	2	)	)	PUNCT
ejpam-753	432	3	,	,	PUNCT
ejpam-753	432	4	303	303	NUM
ejpam-753	432	5	-	-	SYM
ejpam-753	432	6	316	316	NUM
ejpam-753	432	7	.	.	PUNCT
ejpam-753	432	8	2010	2010	NUM
ejpam-753	432	9	.	.	PUNCT
ejpam-753	433	1	[	[	X
ejpam-753	433	2	3	3	X
ejpam-753	433	3	]	]	X
ejpam-753	433	4	c.j	c.j	PROPN
ejpam-753	433	5	.	.	PROPN
ejpam-753	433	6	chikunji	chikunji	PROPN
ejpam-753	433	7	,	,	PUNCT
ejpam-753	433	8	on	on	ADP
ejpam-753	433	9	a	a	DET
ejpam-753	433	10	class	class	NOUN
ejpam-753	433	11	of	of	ADP
ejpam-753	433	12	finite	finite	PROPN
ejpam-753	433	13	rings	ring	NOUN
ejpam-753	433	14	,	,	PUNCT
ejpam-753	433	15	comm	comm	NOUN
ejpam-753	433	16	.	.	PUNCT
ejpam-753	434	1	algebra	algebra	PROPN
ejpam-753	434	2	27(10	27(10	PROPN
ejpam-753	434	3	)	)	PUNCT
ejpam-753	434	4	,	,	PUNCT
ejpam-753	434	5	5049	5049	NUM
ejpam-753	434	6	-	-	SYM
ejpam-753	434	7	5081	5081	NUM
ejpam-753	434	8	.	.	PUNCT
ejpam-753	435	1	1999	1999	NUM
ejpam-753	436	1	[	[	X
ejpam-753	436	2	4	4	NUM
ejpam-753	436	3	]	]	PUNCT
ejpam-753	436	4	b.	b.	PROPN
ejpam-753	436	5	corbas	corbas	PROPN
ejpam-753	436	6	and	and	CCONJ
ejpam-753	436	7	g.d	g.d	PROPN
ejpam-753	436	8	.	.	PROPN
ejpam-753	436	9	williams	williams	PROPN
ejpam-753	436	10	,	,	PUNCT
ejpam-753	436	11	rings	ring	NOUN
ejpam-753	436	12	of	of	ADP
ejpam-753	436	13	order	order	NOUN
ejpam-753	436	14	p5	p5	ADJ
ejpam-753	436	15	part	part	NOUN
ejpam-753	436	16	i.	i.	PROPN
ejpam-753	436	17	nonlocal	nonlocal	ADJ
ejpam-753	436	18	rings	ring	NOUN
ejpam-753	436	19	,	,	PUNCT
ejpam-753	436	20	j.	j.	PROPN
ejpam-753	436	21	algebra	algebra	PROPN
ejpam-753	436	22	,	,	PUNCT
ejpam-753	436	23	231	231	NUM
ejpam-753	436	24	677	677	NUM
ejpam-753	436	25	-	-	SYM
ejpam-753	436	26	690	690	NUM
ejpam-753	436	27	.	.	PUNCT
ejpam-753	436	28	2000	2000	NUM
ejpam-753	437	1	[	[	X
ejpam-753	437	2	5	5	X
ejpam-753	437	3	]	]	PUNCT
ejpam-753	437	4	b.	b.	PROPN
ejpam-753	437	5	corbas	corbas	PROPN
ejpam-753	437	6	and	and	CCONJ
ejpam-753	437	7	g.d	g.d	PROPN
ejpam-753	437	8	.	.	PROPN
ejpam-753	437	9	williams	williams	PROPN
ejpam-753	437	10	,	,	PUNCT
ejpam-753	437	11	rings	ring	NOUN
ejpam-753	437	12	of	of	ADP
ejpam-753	437	13	order	order	NOUN
ejpam-753	437	14	p5	p5	PROPN
ejpam-753	437	15	part	part	PROPN
ejpam-753	437	16	ii	ii	PROPN
ejpam-753	437	17	.	.	PUNCT
ejpam-753	438	1	local	local	ADJ
ejpam-753	438	2	rings	ring	NOUN
ejpam-753	438	3	,	,	PUNCT
ejpam-753	438	4	j.	j.	PROPN
ejpam-753	438	5	algebra	algebra	PROPN
ejpam-753	438	6	,	,	PUNCT
ejpam-753	438	7	231	231	NUM
ejpam-753	438	8	691	691	NUM
ejpam-753	438	9	-	-	SYM
ejpam-753	438	10	704	704	NUM
ejpam-753	438	11	.	.	PUNCT
ejpam-753	438	12	2000	2000	NUM
ejpam-753	438	13	.	.	PUNCT
ejpam-753	439	1	[	[	X
ejpam-753	439	2	6	6	NUM
ejpam-753	439	3	]	]	PUNCT
ejpam-753	439	4	r.	r.	PROPN
ejpam-753	439	5	gilmer	gilmer	PROPN
ejpam-753	439	6	,	,	PUNCT
ejpam-753	439	7	zero	zero	NUM
ejpam-753	439	8	-	-	PUNCT
ejpam-753	439	9	divisors	divisor	NOUN
ejpam-753	439	10	in	in	ADP
ejpam-753	439	11	commutative	commutative	ADJ
ejpam-753	439	12	rings	ring	NOUN
ejpam-753	439	13	.	.	PUNCT
ejpam-753	440	1	the	the	DET
ejpam-753	440	2	american	american	PROPN
ejpam-753	440	3	mathematical	mathematical	PROPN
ejpam-753	440	4	monthly	monthly	ADJ
ejpam-753	440	5	,	,	PUNCT
ejpam-753	440	6	93(5	93(5	NUM
ejpam-753	440	7	)	)	PUNCT
ejpam-753	440	8	,	,	PUNCT
ejpam-753	440	9	382	382	NUM
ejpam-753	440	10	-	-	SYM
ejpam-753	440	11	387	387	NUM
ejpam-753	440	12	.	.	NOUN
ejpam-753	440	13	1986	1986	NUM
ejpam-753	440	14	.	.	PUNCT
ejpam-753	441	1	[	[	X
ejpam-753	441	2	7	7	NUM
ejpam-753	441	3	]	]	X
ejpam-753	441	4	b.r	b.r	PROPN
ejpam-753	441	5	.	.	PROPN
ejpam-753	441	6	mcdonald	mcdonald	PROPN
ejpam-753	441	7	,	,	PUNCT
ejpam-753	441	8	finite	finite	PROPN
ejpam-753	441	9	rings	ring	NOUN
ejpam-753	441	10	with	with	ADP
ejpam-753	441	11	identity	identity	NOUN
ejpam-753	441	12	(	(	PUNCT
ejpam-753	441	13	marcell	marcell	PROPN
ejpam-753	441	14	dekker	dekker	PROPN
ejpam-753	441	15	,	,	PUNCT
ejpam-753	441	16	new	new	PROPN
ejpam-753	441	17	york	york	PROPN
ejpam-753	441	18	)	)	PUNCT
ejpam-753	441	19	.	.	PUNCT
ejpam-753	442	1	1974	1974	NUM
ejpam-753	442	2	.	.	PUNCT
ejpam-753	443	1	[	[	X
ejpam-753	443	2	8	8	NUM
ejpam-753	443	3	]	]	X
ejpam-753	443	4	r.	r.	PROPN
ejpam-753	443	5	raghavendran	raghavendran	PROPN
ejpam-753	443	6	,	,	PUNCT
ejpam-753	443	7	finite	finite	PROPN
ejpam-753	443	8	associative	associative	ADJ
ejpam-753	443	9	rings	ring	NOUN
ejpam-753	443	10	,	,	PUNCT
ejpam-753	443	11	compositio	compositio	NOUN
ejpam-753	443	12	math	math	NOUN
ejpam-753	443	13	.	.	PUNCT
ejpam-753	444	1	21	21	NUM
ejpam-753	444	2	,	,	PUNCT
ejpam-753	444	3	195	195	NUM
ejpam-753	444	4	-	-	SYM
ejpam-753	444	5	229	229	NUM
ejpam-753	444	6	.	.	PUNCT
ejpam-753	444	7	1969	1969	NUM
ejpam-753	444	8	.	.	PUNCT
ejpam-753	445	1	[	[	X
ejpam-753	445	2	9	9	NUM
ejpam-753	445	3	]	]	X
ejpam-753	445	4	g.d	g.d	PROPN
ejpam-753	445	5	.	.	PROPN
ejpam-753	445	6	williams	williams	PROPN
ejpam-753	445	7	,	,	PUNCT
ejpam-753	445	8	on	on	ADP
ejpam-753	445	9	a	a	DET
ejpam-753	445	10	class	class	NOUN
ejpam-753	445	11	of	of	ADP
ejpam-753	445	12	finite	finite	ADJ
ejpam-753	445	13	rings	ring	NOUN
ejpam-753	445	14	of	of	ADP
ejpam-753	445	15	characteristic	characteristic	ADJ
ejpam-753	445	16	p2	p2	NOUN
ejpam-753	445	17	,	,	PUNCT
ejpam-753	445	18	result	result	NOUN
ejpam-753	445	19	.	.	PUNCT
ejpam-753	446	1	math	math	NOUN
ejpam-753	446	2	,	,	PUNCT
ejpam-753	446	3	38	38	NUM
ejpam-753	446	4	,	,	PUNCT
ejpam-753	446	5	377	377	NUM
ejpam-753	446	6	-	-	SYM
ejpam-753	446	7	390	390	NUM
ejpam-753	446	8	.	.	PUNCT
ejpam-753	446	9	2000	2000	NUM
ejpam-753	446	10	.	.	PUNCT