id	sid	tid	token	lemma	pos
ejpam-1594	1	1	7_bhat.dvi	7_bhat.dvi	NUM
ejpam-1594	1	2	european	european	ADJ
ejpam-1594	1	3	journal	journal	NOUN
ejpam-1594	1	4	of	of	ADP
ejpam-1594	1	5	pure	pure	ADJ
ejpam-1594	1	6	and	and	CCONJ
ejpam-1594	1	7	applied	apply	VERB
ejpam-1594	1	8	mathematics	mathematic	NOUN
ejpam-1594	1	9	vol	vol	NOUN
ejpam-1594	1	10	.	.	PROPN
ejpam-1594	2	1	6	6	NUM
ejpam-1594	2	2	,	,	PUNCT
ejpam-1594	2	3	no	no	INTJ
ejpam-1594	2	4	.	.	NOUN
ejpam-1594	2	5	1	1	NUM
ejpam-1594	2	6	,	,	PUNCT
ejpam-1594	2	7	2013	2013	NUM
ejpam-1594	2	8	,	,	PUNCT
ejpam-1594	2	9	59	59	NUM
ejpam-1594	2	10	-	-	SYM
ejpam-1594	2	11	65	65	NUM
ejpam-1594	2	12	issn	issn	PROPN
ejpam-1594	2	13	1307	1307	NUM
ejpam-1594	2	14	-	-	SYM
ejpam-1594	2	15	5543	5543	NUM
ejpam-1594	2	16	–	–	PUNCT
ejpam-1594	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1594	2	18	skew	skew	VERB
ejpam-1594	2	19	polynomial	polynomial	ADJ
ejpam-1594	2	20	rings	ring	NOUN
ejpam-1594	2	21	over	over	ADP
ejpam-1594	2	22	weak	weak	ADJ
ejpam-1594	2	23	σ	σ	ADJ
ejpam-1594	2	24	-	-	ADJ
ejpam-1594	2	25	rigid	rigid	ADJ
ejpam-1594	2	26	rings	ring	NOUN
ejpam-1594	2	27	and	and	CCONJ
ejpam-1594	2	28	σ(∗)-rings	σ(∗)-rings	PROPN
ejpam-1594	2	29	neetu	neetu	NOUN
ejpam-1594	2	30	kumari	kumari	PROPN
ejpam-1594	2	31	,	,	PUNCT
ejpam-1594	2	32	smarti	smarti	PROPN
ejpam-1594	2	33	gosani	gosani	PROPN
ejpam-1594	2	34	,	,	PUNCT
ejpam-1594	2	35	v.	v.	PROPN
ejpam-1594	2	36	k.	k.	PROPN
ejpam-1594	2	37	bhat∗	bhat∗	PROPN
ejpam-1594	2	38	school	school	NOUN
ejpam-1594	2	39	of	of	ADP
ejpam-1594	2	40	mathematics	mathematic	NOUN
ejpam-1594	2	41	,	,	PUNCT
ejpam-1594	2	42	smvd	smvd	PROPN
ejpam-1594	2	43	university	university	PROPN
ejpam-1594	2	44	,	,	PUNCT
ejpam-1594	2	45	p	p	X
ejpam-1594	2	46	/	/	SYM
ejpam-1594	2	47	o	o	PROPN
ejpam-1594	2	48	smvd	smvd	PROPN
ejpam-1594	2	49	university	university	PROPN
ejpam-1594	2	50	,	,	PUNCT
ejpam-1594	2	51	katra	katra	PROPN
ejpam-1594	2	52	,	,	PUNCT
ejpam-1594	2	53	j	j	PROPN
ejpam-1594	2	54	and	and	CCONJ
ejpam-1594	2	55	k	k	PROPN
ejpam-1594	2	56	,	,	PUNCT
ejpam-1594	2	57	india182320	india182320	PROPN
ejpam-1594	2	58	abstract	abstract	NOUN
ejpam-1594	2	59	.	.	PUNCT
ejpam-1594	3	1	let	let	VERB
ejpam-1594	3	2	r	r	PRON
ejpam-1594	3	3	be	be	AUX
ejpam-1594	3	4	a	a	DET
ejpam-1594	3	5	ring	ring	NOUN
ejpam-1594	3	6	and	and	CCONJ
ejpam-1594	3	7	σ	σ	NOUN
ejpam-1594	3	8	an	an	DET
ejpam-1594	3	9	endomorphism	endomorphism	NOUN
ejpam-1594	3	10	of	of	ADP
ejpam-1594	3	11	r.	r.	PROPN
ejpam-1594	3	12	recall	recall	PROPN
ejpam-1594	3	13	that	that	SCONJ
ejpam-1594	3	14	r	r	NOUN
ejpam-1594	3	15	is	be	AUX
ejpam-1594	3	16	said	say	VERB
ejpam-1594	3	17	to	to	PART
ejpam-1594	3	18	be	be	AUX
ejpam-1594	3	19	a	a	DET
ejpam-1594	3	20	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	3	21	if	if	SCONJ
ejpam-1594	3	22	aσ(a	aσ(a	NUM
ejpam-1594	3	23	)	)	PUNCT
ejpam-1594	3	24	∈	∈	PROPN
ejpam-1594	3	25	p(r	p(r	PROPN
ejpam-1594	3	26	)	)	PUNCT
ejpam-1594	3	27	implies	imply	VERB
ejpam-1594	3	28	a	a	DET
ejpam-1594	3	29	∈	∈	PROPN
ejpam-1594	3	30	p(r	p(r	PROPN
ejpam-1594	3	31	)	)	PUNCT
ejpam-1594	3	32	for	for	ADP
ejpam-1594	3	33	a	a	DET
ejpam-1594	3	34	∈	∈	PROPN
ejpam-1594	3	35	r	r	NOUN
ejpam-1594	3	36	,	,	PUNCT
ejpam-1594	3	37	where	where	SCONJ
ejpam-1594	3	38	p(r	p(r	NOUN
ejpam-1594	3	39	)	)	PUNCT
ejpam-1594	3	40	is	be	AUX
ejpam-1594	3	41	the	the	DET
ejpam-1594	3	42	prime	prime	ADJ
ejpam-1594	3	43	radical	radical	NOUN
ejpam-1594	3	44	of	of	ADP
ejpam-1594	3	45	r.	r.	PROPN
ejpam-1594	3	46	we	we	PRON
ejpam-1594	3	47	also	also	ADV
ejpam-1594	3	48	recall	recall	VERB
ejpam-1594	3	49	that	that	SCONJ
ejpam-1594	3	50	r	r	NOUN
ejpam-1594	3	51	is	be	AUX
ejpam-1594	3	52	said	say	VERB
ejpam-1594	3	53	to	to	PART
ejpam-1594	3	54	be	be	AUX
ejpam-1594	3	55	a	a	DET
ejpam-1594	3	56	weak	weak	ADJ
ejpam-1594	3	57	σ	σ	ADJ
ejpam-1594	3	58	-	-	ADJ
ejpam-1594	3	59	rigid	rigid	ADJ
ejpam-1594	3	60	ring	ring	NOUN
ejpam-1594	3	61	if	if	SCONJ
ejpam-1594	3	62	aσ(a	aσ(a	NUM
ejpam-1594	3	63	)	)	PUNCT
ejpam-1594	3	64	∈	∈	PROPN
ejpam-1594	3	65	n(r	n(r	NOUN
ejpam-1594	3	66	)	)	PUNCT
ejpam-1594	4	1	if	if	SCONJ
ejpam-1594	4	2	and	and	CCONJ
ejpam-1594	4	3	only	only	ADV
ejpam-1594	4	4	if	if	SCONJ
ejpam-1594	4	5	a	a	DET
ejpam-1594	4	6	∈	∈	PROPN
ejpam-1594	4	7	n(r	n(r	NOUN
ejpam-1594	4	8	)	)	PUNCT
ejpam-1594	4	9	for	for	ADP
ejpam-1594	4	10	a	a	DET
ejpam-1594	4	11	∈	∈	PROPN
ejpam-1594	4	12	r	r	NOUN
ejpam-1594	4	13	,	,	PUNCT
ejpam-1594	4	14	where	where	SCONJ
ejpam-1594	4	15	n(r	n(r	NOUN
ejpam-1594	4	16	)	)	PUNCT
ejpam-1594	4	17	is	be	AUX
ejpam-1594	4	18	the	the	DET
ejpam-1594	4	19	set	set	NOUN
ejpam-1594	4	20	of	of	ADP
ejpam-1594	4	21	nilpotent	nilpotent	ADJ
ejpam-1594	4	22	elements	element	NOUN
ejpam-1594	4	23	of	of	ADP
ejpam-1594	4	24	r.	r.	PROPN
ejpam-1594	4	25	in	in	ADP
ejpam-1594	4	26	this	this	DET
ejpam-1594	4	27	paper	paper	NOUN
ejpam-1594	4	28	we	we	PRON
ejpam-1594	4	29	give	give	VERB
ejpam-1594	4	30	a	a	DET
ejpam-1594	4	31	relation	relation	NOUN
ejpam-1594	4	32	between	between	ADP
ejpam-1594	4	33	a	a	DET
ejpam-1594	4	34	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	4	35	and	and	CCONJ
ejpam-1594	4	36	a	a	DET
ejpam-1594	4	37	weak	weak	ADJ
ejpam-1594	4	38	σ	σ	ADJ
ejpam-1594	4	39	-	-	ADJ
ejpam-1594	4	40	rigid	rigid	ADJ
ejpam-1594	4	41	ring	ring	NOUN
ejpam-1594	4	42	.	.	PUNCT
ejpam-1594	5	1	we	we	PRON
ejpam-1594	5	2	also	also	ADV
ejpam-1594	5	3	give	give	VERB
ejpam-1594	5	4	a	a	DET
ejpam-1594	5	5	necessary	necessary	ADJ
ejpam-1594	5	6	and	and	CCONJ
ejpam-1594	5	7	sufficient	sufficient	ADJ
ejpam-1594	5	8	condition	condition	NOUN
ejpam-1594	5	9	for	for	ADP
ejpam-1594	5	10	a	a	DET
ejpam-1594	5	11	noetherian	noetherian	ADJ
ejpam-1594	5	12	ring	ring	NOUN
ejpam-1594	5	13	to	to	PART
ejpam-1594	5	14	be	be	AUX
ejpam-1594	5	15	a	a	DET
ejpam-1594	5	16	weak	weak	ADJ
ejpam-1594	5	17	σ	σ	ADJ
ejpam-1594	5	18	-	-	ADJ
ejpam-1594	5	19	rigid	rigid	ADJ
ejpam-1594	5	20	ring	ring	NOUN
ejpam-1594	5	21	.	.	PUNCT
ejpam-1594	6	1	let	let	VERB
ejpam-1594	6	2	σ	σ	NOUN
ejpam-1594	6	3	be	be	AUX
ejpam-1594	6	4	an	an	DET
ejpam-1594	6	5	endomorphism	endomorphism	NOUN
ejpam-1594	6	6	of	of	ADP
ejpam-1594	6	7	a	a	DET
ejpam-1594	6	8	ring	ring	NOUN
ejpam-1594	6	9	r.	r.	PROPN
ejpam-1594	6	10	then	then	ADV
ejpam-1594	6	11	σ	σ	PROPN
ejpam-1594	6	12	can	can	AUX
ejpam-1594	6	13	be	be	AUX
ejpam-1594	6	14	extended	extend	VERB
ejpam-1594	6	15	to	to	ADP
ejpam-1594	6	16	an	an	DET
ejpam-1594	6	17	endomorphism	endomorphism	NOUN
ejpam-1594	6	18	(	(	PUNCT
ejpam-1594	6	19	say	say	INTJ
ejpam-1594	6	20	σ	σ	NOUN
ejpam-1594	6	21	)	)	PUNCT
ejpam-1594	6	22	of	of	ADP
ejpam-1594	6	23	r[x;σ	r[x;σ	NOUN
ejpam-1594	6	24	]	]	PUNCT
ejpam-1594	6	25	.	.	PUNCT
ejpam-1594	7	1	with	with	ADP
ejpam-1594	7	2	this	this	PRON
ejpam-1594	7	3	we	we	PRON
ejpam-1594	7	4	show	show	VERB
ejpam-1594	7	5	that	that	SCONJ
ejpam-1594	7	6	if	if	SCONJ
ejpam-1594	7	7	r	r	NOUN
ejpam-1594	7	8	is	be	AUX
ejpam-1594	7	9	a	a	DET
ejpam-1594	7	10	noetherian	noetherian	ADJ
ejpam-1594	7	11	ring	ring	NOUN
ejpam-1594	7	12	and	and	CCONJ
ejpam-1594	7	13	σ	σ	NOUN
ejpam-1594	7	14	an	an	DET
ejpam-1594	7	15	automorphism	automorphism	NOUN
ejpam-1594	7	16	of	of	ADP
ejpam-1594	7	17	r	r	NOUN
ejpam-1594	7	18	,	,	PUNCT
ejpam-1594	7	19	then	then	ADV
ejpam-1594	7	20	r	r	NOUN
ejpam-1594	7	21	is	be	AUX
ejpam-1594	7	22	a	a	DET
ejpam-1594	7	23	weak	weak	ADJ
ejpam-1594	7	24	σ	σ	ADJ
ejpam-1594	7	25	-	-	ADJ
ejpam-1594	7	26	rigid	rigid	ADJ
ejpam-1594	7	27	ring	ring	NOUN
ejpam-1594	7	28	if	if	SCONJ
ejpam-1594	7	29	and	and	CCONJ
ejpam-1594	7	30	only	only	ADV
ejpam-1594	7	31	if	if	SCONJ
ejpam-1594	7	32	r[x;σ	r[x;σ	NOUN
ejpam-1594	7	33	]	]	X
ejpam-1594	7	34	is	be	AUX
ejpam-1594	7	35	a	a	DET
ejpam-1594	7	36	weak	weak	ADJ
ejpam-1594	7	37	σ	σ	ADJ
ejpam-1594	7	38	-	-	ADJ
ejpam-1594	7	39	rigid	rigid	ADJ
ejpam-1594	7	40	ring	ring	NOUN
ejpam-1594	7	41	.	.	PUNCT
ejpam-1594	8	1	2010	2010	NUM
ejpam-1594	8	2	mathematics	mathematic	NOUN
ejpam-1594	8	3	subject	subject	NOUN
ejpam-1594	8	4	classifications	classification	NOUN
ejpam-1594	8	5	:	:	PUNCT
ejpam-1594	8	6	16	16	NUM
ejpam-1594	8	7	-	-	SYM
ejpam-1594	8	8	xx	xx	NUM
ejpam-1594	8	9	;	;	PUNCT
ejpam-1594	8	10	16s36	16s36	NUM
ejpam-1594	8	11	,	,	PUNCT
ejpam-1594	8	12	16p40	16p40	NUM
ejpam-1594	8	13	,	,	PUNCT
ejpam-1594	8	14	16p50	16p50	NUM
ejpam-1594	8	15	,	,	PUNCT
ejpam-1594	8	16	16u20	16u20	NUM
ejpam-1594	8	17	.	.	PUNCT
ejpam-1594	9	1	key	key	ADJ
ejpam-1594	9	2	words	word	NOUN
ejpam-1594	9	3	and	and	CCONJ
ejpam-1594	9	4	phrases	phrase	NOUN
ejpam-1594	9	5	:	:	PUNCT
ejpam-1594	9	6	automorphism	automorphism	NOUN
ejpam-1594	9	7	,	,	PUNCT
ejpam-1594	9	8	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	9	9	,	,	PUNCT
ejpam-1594	9	10	weak	weak	ADJ
ejpam-1594	9	11	σ	σ	VERB
ejpam-1594	9	12	-	-	ADJ
ejpam-1594	9	13	rigid	rigid	ADJ
ejpam-1594	9	14	ring	ring	NOUN
ejpam-1594	9	15	,	,	PUNCT
ejpam-1594	9	16	2	2	NUM
ejpam-1594	9	17	-	-	PUNCT
ejpam-1594	9	18	primal	primal	ADJ
ejpam-1594	9	19	ring	ring	NOUN
ejpam-1594	9	20	1	1	NUM
ejpam-1594	9	21	.	.	PUNCT
ejpam-1594	9	22	introduction	introduction	NOUN
ejpam-1594	9	23	a	a	DET
ejpam-1594	9	24	ring	ring	NOUN
ejpam-1594	9	25	r	r	NOUN
ejpam-1594	9	26	always	always	ADV
ejpam-1594	9	27	means	mean	VERB
ejpam-1594	9	28	an	an	DET
ejpam-1594	9	29	associative	associative	ADJ
ejpam-1594	9	30	ring	ring	NOUN
ejpam-1594	9	31	with	with	ADP
ejpam-1594	9	32	identity	identity	NOUN
ejpam-1594	9	33	1	1	NUM
ejpam-1594	9	34	6=	6=	ADP
ejpam-1594	9	35	0	0	NUM
ejpam-1594	9	36	.	.	PUNCT
ejpam-1594	10	1	the	the	DET
ejpam-1594	10	2	ring	ring	NOUN
ejpam-1594	10	3	of	of	ADP
ejpam-1594	10	4	integers	integer	NOUN
ejpam-1594	10	5	is	be	AUX
ejpam-1594	10	6	denoted	denote	VERB
ejpam-1594	10	7	by	by	ADP
ejpam-1594	10	8	z	z	PROPN
ejpam-1594	10	9	,	,	PUNCT
ejpam-1594	10	10	and	and	CCONJ
ejpam-1594	10	11	the	the	DET
ejpam-1594	10	12	set	set	NOUN
ejpam-1594	10	13	of	of	ADP
ejpam-1594	10	14	positive	positive	ADJ
ejpam-1594	10	15	integers	integer	NOUN
ejpam-1594	10	16	is	be	AUX
ejpam-1594	10	17	denoted	denote	VERB
ejpam-1594	10	18	by	by	ADP
ejpam-1594	10	19	n.	n.	NOUN
ejpam-1594	10	20	the	the	DET
ejpam-1594	10	21	set	set	NOUN
ejpam-1594	10	22	of	of	ADP
ejpam-1594	10	23	prime	prime	ADJ
ejpam-1594	10	24	ideals	ideal	NOUN
ejpam-1594	10	25	of	of	ADP
ejpam-1594	10	26	r	r	NOUN
ejpam-1594	10	27	is	be	AUX
ejpam-1594	10	28	denoted	denote	VERB
ejpam-1594	10	29	by	by	ADP
ejpam-1594	10	30	spec(r	spec(r	PROPN
ejpam-1594	10	31	)	)	PUNCT
ejpam-1594	10	32	.	.	PUNCT
ejpam-1594	11	1	the	the	DET
ejpam-1594	11	2	sets	set	NOUN
ejpam-1594	11	3	of	of	ADP
ejpam-1594	11	4	minimal	minimal	ADJ
ejpam-1594	11	5	prime	prime	ADJ
ejpam-1594	11	6	ideals	ideal	NOUN
ejpam-1594	11	7	of	of	ADP
ejpam-1594	11	8	r	r	NOUN
ejpam-1594	11	9	is	be	AUX
ejpam-1594	11	10	denoted	denote	VERB
ejpam-1594	11	11	by	by	ADP
ejpam-1594	11	12	min.spec(r	min.spec(r	PROPN
ejpam-1594	11	13	)	)	PUNCT
ejpam-1594	11	14	.	.	PUNCT
ejpam-1594	12	1	the	the	DET
ejpam-1594	12	2	prime	prime	ADJ
ejpam-1594	12	3	radical	radical	ADJ
ejpam-1594	12	4	and	and	CCONJ
ejpam-1594	12	5	the	the	DET
ejpam-1594	12	6	nil	nil	ADJ
ejpam-1594	12	7	radical	radical	ADJ
ejpam-1594	12	8	of	of	ADP
ejpam-1594	12	9	r	r	NOUN
ejpam-1594	12	10	are	be	AUX
ejpam-1594	12	11	denoted	denote	VERB
ejpam-1594	12	12	by	by	ADP
ejpam-1594	12	13	p(r	p(r	PROPN
ejpam-1594	12	14	)	)	PUNCT
ejpam-1594	12	15	and	and	CCONJ
ejpam-1594	12	16	n(r	n(r	NOUN
ejpam-1594	12	17	)	)	PUNCT
ejpam-1594	12	18	respectively	respectively	ADV
ejpam-1594	12	19	.	.	PUNCT
ejpam-1594	13	1	now	now	ADV
ejpam-1594	13	2	let	let	VERB
ejpam-1594	13	3	r	r	NOUN
ejpam-1594	13	4	be	be	AUX
ejpam-1594	13	5	a	a	DET
ejpam-1594	13	6	ring	ring	NOUN
ejpam-1594	13	7	and	and	CCONJ
ejpam-1594	13	8	σ	σ	NOUN
ejpam-1594	13	9	an	an	DET
ejpam-1594	13	10	endomorphism	endomorphism	NOUN
ejpam-1594	13	11	of	of	ADP
ejpam-1594	13	12	r.	r.	PROPN
ejpam-1594	13	13	recall	recall	PROPN
ejpam-1594	13	14	that	that	SCONJ
ejpam-1594	13	15	the	the	DET
ejpam-1594	13	16	skew	skew	ADJ
ejpam-1594	13	17	polynomial	polynomial	ADJ
ejpam-1594	13	18	ring	ring	NOUN
ejpam-1594	13	19	r[x	r[x	NOUN
ejpam-1594	13	20	;	;	PUNCT
ejpam-1594	13	21	σ	σ	PROPN
ejpam-1594	13	22	]	]	X
ejpam-1594	13	23	is	be	AUX
ejpam-1594	13	24	the	the	DET
ejpam-1594	13	25	set	set	NOUN
ejpam-1594	13	26	of	of	ADP
ejpam-1594	13	27	polynomials	polynomial	NOUN
ejpam-1594	13	28	{	{	PUNCT
ejpam-1594	13	29	n	n	CCONJ
ejpam-1594	13	30	∑	∑	ADP
ejpam-1594	13	31	i=0	i=0	PROPN
ejpam-1594	13	32	x	x	SYM
ejpam-1594	13	33	iai	iai	PROPN
ejpam-1594	13	34	,	,	PUNCT
ejpam-1594	13	35	ai	ai	VERB
ejpam-1594	13	36	∈	∈	PROPN
ejpam-1594	13	37	r	r	NOUN
ejpam-1594	13	38	,	,	PUNCT
ejpam-1594	13	39	n	n	PRON
ejpam-1594	13	40	∈	∈	PROPN
ejpam-1594	13	41	n	n	CCONJ
ejpam-1594	13	42	}	}	PUNCT
ejpam-1594	13	43	with	with	ADP
ejpam-1594	13	44	usual	usual	ADJ
ejpam-1594	13	45	addition	addition	NOUN
ejpam-1594	13	46	of	of	ADP
ejpam-1594	13	47	polynomials	polynomial	NOUN
ejpam-1594	13	48	and	and	CCONJ
ejpam-1594	13	49	multiplication	multiplication	NOUN
ejpam-1594	13	50	subject	subject	ADJ
ejpam-1594	13	51	to	to	ADP
ejpam-1594	13	52	the	the	DET
ejpam-1594	13	53	relation	relation	NOUN
ejpam-1594	13	54	ax	ax	NOUN
ejpam-1594	13	55	=	=	PUNCT
ejpam-1594	13	56	xσ(a	xσ(a	NUM
ejpam-1594	13	57	)	)	PUNCT
ejpam-1594	13	58	for	for	ADP
ejpam-1594	13	59	all	all	DET
ejpam-1594	13	60	a	a	DET
ejpam-1594	13	61	∈	∈	PROPN
ejpam-1594	13	62	r.	r.	NOUN
ejpam-1594	13	63	we	we	PRON
ejpam-1594	13	64	take	take	VERB
ejpam-1594	13	65	any	any	DET
ejpam-1594	13	66	f	f	NOUN
ejpam-1594	13	67	(	(	PUNCT
ejpam-1594	13	68	x	x	X
ejpam-1594	13	69	)	)	PUNCT
ejpam-1594	13	70	∈	∈	PROPN
ejpam-1594	13	71	r[x	r[x	NOUN
ejpam-1594	13	72	;	;	PUNCT
ejpam-1594	13	73	σ	σ	PROPN
ejpam-1594	13	74	]	]	PUNCT
ejpam-1594	13	75	to	to	PART
ejpam-1594	13	76	be	be	AUX
ejpam-1594	13	77	of	of	ADP
ejpam-1594	13	78	the	the	DET
ejpam-1594	13	79	form	form	NOUN
ejpam-1594	13	80	f	f	X
ejpam-1594	13	81	(	(	PUNCT
ejpam-1594	13	82	x	x	X
ejpam-1594	13	83	)	)	PUNCT
ejpam-1594	13	84	=	=	SYM
ejpam-1594	14	1	∑n	∑n	PROPN
ejpam-1594	14	2	i=0	i=0	PROPN
ejpam-1594	14	3	x	x	SYM
ejpam-1594	14	4	iai	iai	PROPN
ejpam-1594	14	5	,	,	PUNCT
ejpam-1594	14	6	n	n	NOUN
ejpam-1594	14	7	∈	∈	PROPN
ejpam-1594	14	8	n	n	CCONJ
ejpam-1594	14	9	as	as	SCONJ
ejpam-1594	14	10	followed	follow	VERB
ejpam-1594	14	11	in	in	ADP
ejpam-1594	14	12	mcconnell	mcconnell	PROPN
ejpam-1594	14	13	and	and	CCONJ
ejpam-1594	14	14	robson	robson	NOUN
ejpam-1594	15	1	[	[	X
ejpam-1594	15	2	12	12	NUM
ejpam-1594	15	3	]	]	PUNCT
ejpam-1594	15	4	.	.	PUNCT
ejpam-1594	16	1	we	we	PRON
ejpam-1594	16	2	denote	denote	VERB
ejpam-1594	16	3	r[x	r[x	NOUN
ejpam-1594	16	4	;	;	PUNCT
ejpam-1594	16	5	σ	σ	X
ejpam-1594	16	6	]	]	PUNCT
ejpam-1594	16	7	by	by	ADP
ejpam-1594	16	8	s(r	s(r	PROPN
ejpam-1594	16	9	)	)	PUNCT
ejpam-1594	16	10	.	.	PUNCT
ejpam-1594	17	1	∗corresponding	∗corresponde	VERB
ejpam-1594	17	2	author	author	NOUN
ejpam-1594	17	3	.	.	PUNCT
ejpam-1594	18	1	email	email	NOUN
ejpam-1594	18	2	address	address	NOUN
ejpam-1594	18	3	:	:	PUNCT
ejpam-1594	18	4	vijaykumarbhat2000	vijaykumarbhat2000	PROPN
ejpam-1594	18	5	�	�	NOUN
ejpam-1594	18	6	yahoo	yahoo	PROPN
ejpam-1594	18	7	.	.	PUNCT
ejpam-1594	19	1	om	om	PROPN
ejpam-1594	19	2	(	(	PUNCT
ejpam-1594	19	3	v.	v.	ADP
ejpam-1594	19	4	bhat	bhat	PROPN
ejpam-1594	19	5	)	)	PUNCT
ejpam-1594	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1594	19	7	59	59	NUM
ejpam-1594	20	1	c	c	X
ejpam-1594	20	2	©	©	PROPN
ejpam-1594	20	3	2013	2013	NUM
ejpam-1594	20	4	ejpam	ejpam	NOUN
ejpam-1594	20	5	all	all	DET
ejpam-1594	20	6	rights	right	NOUN
ejpam-1594	20	7	reserved	reserve	VERB
ejpam-1594	20	8	.	.	PUNCT
ejpam-1594	21	1	n.	n.	PROPN
ejpam-1594	21	2	kumari	kumari	PROPN
ejpam-1594	21	3	,	,	PUNCT
ejpam-1594	21	4	s.	s.	PROPN
ejpam-1594	21	5	gosani	gosani	PROPN
ejpam-1594	21	6	,	,	PUNCT
ejpam-1594	21	7	v.	v.	ADP
ejpam-1594	21	8	bhat	bhat	PROPN
ejpam-1594	21	9	/	/	SYM
ejpam-1594	21	10	eur	eur	PROPN
ejpam-1594	21	11	.	.	PUNCT
ejpam-1594	22	1	j.	j.	PROPN
ejpam-1594	22	2	pure	pure	PROPN
ejpam-1594	22	3	appl	appl	PROPN
ejpam-1594	22	4	.	.	PROPN
ejpam-1594	22	5	math	math	PROPN
ejpam-1594	22	6	,	,	PUNCT
ejpam-1594	22	7	6	6	NUM
ejpam-1594	22	8	(	(	PUNCT
ejpam-1594	22	9	2013	2013	NUM
ejpam-1594	22	10	)	)	PUNCT
ejpam-1594	22	11	,	,	PUNCT
ejpam-1594	22	12	59	59	NUM
ejpam-1594	22	13	-	-	SYM
ejpam-1594	22	14	65	65	NUM
ejpam-1594	22	15	60	60	NUM
ejpam-1594	22	16	skew	skew	ADJ
ejpam-1594	22	17	-	-	PUNCT
ejpam-1594	22	18	polynomial	polynomial	ADJ
ejpam-1594	22	19	rings	ring	NOUN
ejpam-1594	22	20	have	have	AUX
ejpam-1594	22	21	been	be	AUX
ejpam-1594	22	22	of	of	ADP
ejpam-1594	22	23	interest	interest	NOUN
ejpam-1594	22	24	to	to	ADP
ejpam-1594	22	25	many	many	ADJ
ejpam-1594	22	26	authors	author	NOUN
ejpam-1594	22	27	.	.	PUNCT
ejpam-1594	23	1	for	for	ADP
ejpam-1594	23	2	example	example	NOUN
ejpam-1594	23	3	[	[	X
ejpam-1594	23	4	1	1	NUM
ejpam-1594	23	5	,	,	PUNCT
ejpam-1594	23	6	2	2	NUM
ejpam-1594	23	7	,	,	PUNCT
ejpam-1594	23	8	5	5	NUM
ejpam-1594	23	9	,	,	PUNCT
ejpam-1594	23	10	7	7	NUM
ejpam-1594	23	11	,	,	PUNCT
ejpam-1594	23	12	10	10	NUM
ejpam-1594	23	13	,	,	PUNCT
ejpam-1594	23	14	11	11	NUM
ejpam-1594	23	15	,	,	PUNCT
ejpam-1594	23	16	13	13	NUM
ejpam-1594	23	17	]	]	PUNCT
ejpam-1594	23	18	.	.	PUNCT
ejpam-1594	24	1	the	the	DET
ejpam-1594	24	2	classical	classical	ADJ
ejpam-1594	24	3	study	study	NOUN
ejpam-1594	24	4	of	of	ADP
ejpam-1594	24	5	any	any	DET
ejpam-1594	24	6	commutative	commutative	ADJ
ejpam-1594	24	7	noetherian	noetherian	ADJ
ejpam-1594	24	8	ring	ring	NOUN
ejpam-1594	24	9	is	be	AUX
ejpam-1594	24	10	done	do	VERB
ejpam-1594	24	11	by	by	ADP
ejpam-1594	24	12	studying	study	VERB
ejpam-1594	24	13	its	its	PRON
ejpam-1594	24	14	primary	primary	ADJ
ejpam-1594	24	15	decomposition	decomposition	NOUN
ejpam-1594	24	16	and	and	CCONJ
ejpam-1594	24	17	this	this	PRON
ejpam-1594	24	18	forms	form	VERB
ejpam-1594	24	19	the	the	DET
ejpam-1594	24	20	fundamental	fundamental	ADJ
ejpam-1594	24	21	edifice	edifice	NOUN
ejpam-1594	24	22	on	on	ADP
ejpam-1594	24	23	which	which	PRON
ejpam-1594	24	24	any	any	DET
ejpam-1594	24	25	such	such	ADJ
ejpam-1594	24	26	ring	ring	NOUN
ejpam-1594	24	27	is	be	AUX
ejpam-1594	24	28	studied	study	VERB
ejpam-1594	24	29	.	.	PUNCT
ejpam-1594	25	1	further	far	ADV
ejpam-1594	25	2	there	there	PRON
ejpam-1594	25	3	are	be	VERB
ejpam-1594	25	4	other	other	ADJ
ejpam-1594	25	5	structural	structural	ADJ
ejpam-1594	25	6	properties	property	NOUN
ejpam-1594	25	7	of	of	ADP
ejpam-1594	25	8	rings	ring	NOUN
ejpam-1594	25	9	,	,	PUNCT
ejpam-1594	25	10	for	for	ADP
ejpam-1594	25	11	example	example	NOUN
ejpam-1594	25	12	the	the	DET
ejpam-1594	25	13	existence	existence	NOUN
ejpam-1594	25	14	of	of	ADP
ejpam-1594	25	15	quotient	quotient	NOUN
ejpam-1594	25	16	rings	ring	NOUN
ejpam-1594	25	17	or	or	CCONJ
ejpam-1594	25	18	more	more	ADJ
ejpam-1594	25	19	particularly	particularly	ADV
ejpam-1594	25	20	the	the	DET
ejpam-1594	25	21	existence	existence	NOUN
ejpam-1594	25	22	of	of	ADP
ejpam-1594	25	23	artinian	artinian	ADJ
ejpam-1594	25	24	quotient	quotient	NOUN
ejpam-1594	25	25	rings	ring	NOUN
ejpam-1594	25	26	etc	etc	X
ejpam-1594	25	27	.	.	X
ejpam-1594	25	28	which	which	PRON
ejpam-1594	25	29	can	can	AUX
ejpam-1594	25	30	be	be	AUX
ejpam-1594	25	31	nicely	nicely	ADV
ejpam-1594	25	32	tied	tie	VERB
ejpam-1594	25	33	to	to	ADP
ejpam-1594	25	34	primary	primary	ADJ
ejpam-1594	25	35	decomposition	decomposition	NOUN
ejpam-1594	25	36	of	of	ADP
ejpam-1594	25	37	a	a	DET
ejpam-1594	25	38	noetherian	noetherian	ADJ
ejpam-1594	25	39	ring	ring	NOUN
ejpam-1594	25	40	.	.	PUNCT
ejpam-1594	26	1	the	the	DET
ejpam-1594	26	2	notion	notion	NOUN
ejpam-1594	26	3	of	of	ADP
ejpam-1594	26	4	the	the	DET
ejpam-1594	26	5	quotient	quotient	NOUN
ejpam-1594	26	6	ring	ring	NOUN
ejpam-1594	26	7	of	of	ADP
ejpam-1594	26	8	a	a	DET
ejpam-1594	26	9	ring	ring	NOUN
ejpam-1594	26	10	,	,	PUNCT
ejpam-1594	26	11	the	the	DET
ejpam-1594	26	12	contractions	contraction	NOUN
ejpam-1594	26	13	and	and	CCONJ
ejpam-1594	26	14	extensions	extension	NOUN
ejpam-1594	26	15	of	of	ADP
ejpam-1594	26	16	ideals	ideal	NOUN
ejpam-1594	26	17	arising	arise	VERB
ejpam-1594	26	18	thereby	thereby	ADV
ejpam-1594	26	19	appear	appear	VERB
ejpam-1594	26	20	in	in	ADP
ejpam-1594	26	21	chapter	chapter	NOUN
ejpam-1594	26	22	9	9	NUM
ejpam-1594	26	23	of	of	ADP
ejpam-1594	26	24	[	[	X
ejpam-1594	26	25	7	7	NUM
ejpam-1594	26	26	]	]	PUNCT
ejpam-1594	26	27	.	.	PUNCT
ejpam-1594	27	1	the	the	DET
ejpam-1594	27	2	first	first	ADJ
ejpam-1594	27	3	important	important	ADJ
ejpam-1594	27	4	result	result	NOUN
ejpam-1594	27	5	in	in	ADP
ejpam-1594	27	6	the	the	DET
ejpam-1594	27	7	theory	theory	NOUN
ejpam-1594	27	8	of	of	ADP
ejpam-1594	27	9	non	non	PROPN
ejpam-1594	27	10	commutative	commutative	ADJ
ejpam-1594	27	11	noetherian	noetherian	ADJ
ejpam-1594	27	12	rings	ring	NOUN
ejpam-1594	27	13	was	be	AUX
ejpam-1594	27	14	proved	prove	VERB
ejpam-1594	27	15	in	in	ADP
ejpam-1594	27	16	1958	1958	NUM
ejpam-1594	27	17	(	(	PUNCT
ejpam-1594	27	18	goldie	goldie	PROPN
ejpam-1594	27	19	’s	’s	PART
ejpam-1594	27	20	theorem	theorem	PROPN
ejpam-1594	27	21	)	)	PUNCT
ejpam-1594	27	22	which	which	PRON
ejpam-1594	27	23	gives	give	VERB
ejpam-1594	27	24	an	an	DET
ejpam-1594	27	25	analogue	analogue	NOUN
ejpam-1594	27	26	of	of	ADP
ejpam-1594	27	27	field	field	NOUN
ejpam-1594	27	28	of	of	ADP
ejpam-1594	27	29	fractions	fraction	NOUN
ejpam-1594	27	30	for	for	ADP
ejpam-1594	27	31	factor	factor	NOUN
ejpam-1594	27	32	rings	ring	NOUN
ejpam-1594	27	33	r	r	NOUN
ejpam-1594	27	34	/	/	SYM
ejpam-1594	27	35	p	p	NOUN
ejpam-1594	27	36	,	,	PUNCT
ejpam-1594	27	37	where	where	SCONJ
ejpam-1594	27	38	r	r	NOUN
ejpam-1594	27	39	is	be	AUX
ejpam-1594	27	40	a	a	DET
ejpam-1594	27	41	noetherian	noetherian	ADJ
ejpam-1594	27	42	ring	ring	NOUN
ejpam-1594	27	43	and	and	CCONJ
ejpam-1594	27	44	p	p	NOUN
ejpam-1594	27	45	is	be	AUX
ejpam-1594	27	46	a	a	DET
ejpam-1594	27	47	prime	prime	ADJ
ejpam-1594	27	48	ideal	ideal	NOUN
ejpam-1594	27	49	of	of	ADP
ejpam-1594	27	50	r.	r.	PROPN
ejpam-1594	27	51	in	in	ADP
ejpam-1594	27	52	1959	1959	NUM
ejpam-1594	27	53	the	the	DET
ejpam-1594	27	54	one	one	NUM
ejpam-1594	27	55	sided	sided	ADJ
ejpam-1594	27	56	version	version	NOUN
ejpam-1594	27	57	was	be	AUX
ejpam-1594	27	58	proved	prove	VERB
ejpam-1594	27	59	by	by	ADP
ejpam-1594	27	60	lesieur	lesieur	NOUN
ejpam-1594	27	61	and	and	CCONJ
ejpam-1594	27	62	croisot	croisot	NOUN
ejpam-1594	27	63	[	[	X
ejpam-1594	27	64	theorem	theorem	VERB
ejpam-1594	27	65	5.12	5.12	NUM
ejpam-1594	27	66	of	of	ADP
ejpam-1594	27	67	7	7	NUM
ejpam-1594	27	68	]	]	PUNCT
ejpam-1594	27	69	and	and	CCONJ
ejpam-1594	27	70	in	in	ADP
ejpam-1594	27	71	1960	1960	NUM
ejpam-1594	27	72	goldie	goldie	PROPN
ejpam-1594	27	73	generalized	generalize	VERB
ejpam-1594	27	74	the	the	DET
ejpam-1594	27	75	result	result	NOUN
ejpam-1594	27	76	for	for	ADP
ejpam-1594	27	77	semiprime	semiprime	NOUN
ejpam-1594	27	78	rings	ring	NOUN
ejpam-1594	28	1	[	[	X
ejpam-1594	28	2	theorem	theorem	VERB
ejpam-1594	28	3	5.10	5.10	NUM
ejpam-1594	28	4	of	of	ADP
ejpam-1594	28	5	7	7	NUM
ejpam-1594	28	6	]	]	PUNCT
ejpam-1594	28	7	.	.	PUNCT
ejpam-1594	29	1	in	in	ADP
ejpam-1594	29	2	[	[	X
ejpam-1594	29	3	5	5	X
ejpam-1594	29	4	]	]	PUNCT
ejpam-1594	29	5	it	it	PRON
ejpam-1594	29	6	is	be	AUX
ejpam-1594	29	7	shown	show	VERB
ejpam-1594	29	8	that	that	SCONJ
ejpam-1594	29	9	if	if	SCONJ
ejpam-1594	29	10	r	r	NOUN
ejpam-1594	29	11	is	be	AUX
ejpam-1594	29	12	embeddable	embeddable	ADJ
ejpam-1594	29	13	in	in	ADP
ejpam-1594	29	14	a	a	DET
ejpam-1594	29	15	right	right	ADJ
ejpam-1594	29	16	artinian	artinian	ADJ
ejpam-1594	29	17	ring	ring	NOUN
ejpam-1594	29	18	and	and	CCONJ
ejpam-1594	29	19	if	if	SCONJ
ejpam-1594	29	20	characteristic	characteristic	ADJ
ejpam-1594	29	21	of	of	ADP
ejpam-1594	29	22	r	r	NOUN
ejpam-1594	29	23	is	be	AUX
ejpam-1594	29	24	zero	zero	NUM
ejpam-1594	29	25	,	,	PUNCT
ejpam-1594	29	26	then	then	ADV
ejpam-1594	29	27	the	the	DET
ejpam-1594	29	28	differential	differential	ADJ
ejpam-1594	29	29	operator	operator	NOUN
ejpam-1594	29	30	ring	ring	NOUN
ejpam-1594	29	31	r[x	r[x	NOUN
ejpam-1594	29	32	;	;	PUNCT
ejpam-1594	29	33	δ	δ	PROPN
ejpam-1594	29	34	]	]	PUNCT
ejpam-1594	29	35	embeds	embed	VERB
ejpam-1594	29	36	in	in	ADP
ejpam-1594	29	37	a	a	DET
ejpam-1594	29	38	right	right	ADJ
ejpam-1594	29	39	artinian	artinian	ADJ
ejpam-1594	29	40	ring	ring	NOUN
ejpam-1594	29	41	.	.	PUNCT
ejpam-1594	30	1	it	it	PRON
ejpam-1594	30	2	is	be	AUX
ejpam-1594	30	3	also	also	ADV
ejpam-1594	30	4	shown	show	VERB
ejpam-1594	30	5	in	in	ADP
ejpam-1594	30	6	[	[	X
ejpam-1594	30	7	5	5	NUM
ejpam-1594	30	8	]	]	PUNCT
ejpam-1594	30	9	that	that	SCONJ
ejpam-1594	30	10	if	if	SCONJ
ejpam-1594	30	11	r	r	NOUN
ejpam-1594	30	12	is	be	AUX
ejpam-1594	30	13	a	a	DET
ejpam-1594	30	14	commutative	commutative	ADJ
ejpam-1594	30	15	noetherian	noetherian	ADJ
ejpam-1594	30	16	ring	ring	NOUN
ejpam-1594	30	17	and	and	CCONJ
ejpam-1594	30	18	σ	σ	PROPN
ejpam-1594	30	19	is	be	AUX
ejpam-1594	30	20	an	an	DET
ejpam-1594	30	21	automorphism	automorphism	NOUN
ejpam-1594	30	22	of	of	ADP
ejpam-1594	30	23	r	r	NOUN
ejpam-1594	30	24	,	,	PUNCT
ejpam-1594	30	25	then	then	ADV
ejpam-1594	30	26	the	the	DET
ejpam-1594	30	27	skew	skew	ADJ
ejpam-1594	30	28	-	-	PUNCT
ejpam-1594	30	29	polynomial	polynomial	ADJ
ejpam-1594	30	30	ring	ring	NOUN
ejpam-1594	30	31	r[x	r[x	NOUN
ejpam-1594	30	32	;	;	PUNCT
ejpam-1594	30	33	σ	σ	PROPN
ejpam-1594	30	34	]	]	PUNCT
ejpam-1594	30	35	embeds	embed	VERB
ejpam-1594	30	36	in	in	ADP
ejpam-1594	30	37	an	an	DET
ejpam-1594	30	38	artinian	artinian	ADJ
ejpam-1594	30	39	ring	ring	NOUN
ejpam-1594	30	40	.	.	PUNCT
ejpam-1594	31	1	a	a	DET
ejpam-1594	31	2	non	non	X
ejpam-1594	31	3	commutative	commutative	ADJ
ejpam-1594	31	4	analogue	analogue	NOUN
ejpam-1594	31	5	of	of	ADP
ejpam-1594	31	6	associated	associate	VERB
ejpam-1594	31	7	prime	prime	ADJ
ejpam-1594	31	8	ideals	ideal	NOUN
ejpam-1594	31	9	of	of	ADP
ejpam-1594	31	10	a	a	DET
ejpam-1594	31	11	noetherian	noetherian	ADJ
ejpam-1594	31	12	ring	ring	NOUN
ejpam-1594	31	13	has	have	AUX
ejpam-1594	31	14	also	also	ADV
ejpam-1594	31	15	been	be	AUX
ejpam-1594	31	16	discussed	discuss	VERB
ejpam-1594	31	17	.	.	PUNCT
ejpam-1594	32	1	we	we	PRON
ejpam-1594	32	2	would	would	AUX
ejpam-1594	32	3	like	like	VERB
ejpam-1594	32	4	to	to	PART
ejpam-1594	32	5	note	note	VERB
ejpam-1594	32	6	that	that	SCONJ
ejpam-1594	32	7	a	a	DET
ejpam-1594	32	8	considerable	considerable	ADJ
ejpam-1594	32	9	work	work	NOUN
ejpam-1594	32	10	has	have	AUX
ejpam-1594	32	11	been	be	AUX
ejpam-1594	32	12	done	do	VERB
ejpam-1594	32	13	in	in	ADP
ejpam-1594	32	14	the	the	DET
ejpam-1594	32	15	investigation	investigation	NOUN
ejpam-1594	32	16	of	of	ADP
ejpam-1594	32	17	prime	prime	ADJ
ejpam-1594	32	18	ideals	ideal	NOUN
ejpam-1594	32	19	(	(	PUNCT
ejpam-1594	32	20	in	in	ADP
ejpam-1594	32	21	particular	particular	ADJ
ejpam-1594	32	22	minimal	minimal	ADJ
ejpam-1594	32	23	prime	prime	ADJ
ejpam-1594	32	24	ideals	ideal	NOUN
ejpam-1594	32	25	and	and	CCONJ
ejpam-1594	32	26	associated	associate	VERB
ejpam-1594	32	27	prime	prime	ADJ
ejpam-1594	32	28	ideals	ideal	NOUN
ejpam-1594	32	29	)	)	PUNCT
ejpam-1594	32	30	of	of	ADP
ejpam-1594	32	31	skew	skew	ADJ
ejpam-1594	32	32	polynomial	polynomial	ADJ
ejpam-1594	32	33	rings	ring	NOUN
ejpam-1594	32	34	(	(	PUNCT
ejpam-1594	32	35	k.	k.	PROPN
ejpam-1594	32	36	r.	r.	PROPN
ejpam-1594	32	37	goodearl	goodearl	PROPN
ejpam-1594	32	38	and	and	CCONJ
ejpam-1594	32	39	e.	e.	PROPN
ejpam-1594	32	40	s.	s.	PROPN
ejpam-1594	32	41	letzter	letzter	PROPN
ejpam-1594	33	1	[	[	X
ejpam-1594	33	2	8	8	NUM
ejpam-1594	33	3	]	]	PUNCT
ejpam-1594	33	4	,	,	PUNCT
ejpam-1594	33	5	c.	c.	PROPN
ejpam-1594	33	6	faith	faith	NOUN
ejpam-1594	34	1	[	[	X
ejpam-1594	34	2	6	6	NUM
ejpam-1594	34	3	]	]	PUNCT
ejpam-1594	34	4	,	,	PUNCT
ejpam-1594	34	5	s.	s.	PROPN
ejpam-1594	34	6	annin	annin	PROPN
ejpam-1594	35	1	[	[	X
ejpam-1594	35	2	1	1	NUM
ejpam-1594	35	3	]	]	PUNCT
ejpam-1594	35	4	,	,	PUNCT
ejpam-1594	35	5	leroy	leroy	PROPN
ejpam-1594	35	6	and	and	CCONJ
ejpam-1594	35	7	matczuk	matczuk	ADJ
ejpam-1594	36	1	[	[	X
ejpam-1594	36	2	11	11	NUM
ejpam-1594	36	3	]	]	PUNCT
ejpam-1594	36	4	,	,	PUNCT
ejpam-1594	36	5	nordstrom	nordstrom	NOUN
ejpam-1594	37	1	[	[	X
ejpam-1594	37	2	13	13	NUM
ejpam-1594	37	3	]	]	PUNCT
ejpam-1594	37	4	)	)	PUNCT
ejpam-1594	37	5	and	and	CCONJ
ejpam-1594	37	6	bhat	bhat	X
ejpam-1594	38	1	[	[	X
ejpam-1594	38	2	2	2	NUM
ejpam-1594	38	3	]	]	PUNCT
ejpam-1594	38	4	.	.	PUNCT
ejpam-1594	39	1	another	another	DET
ejpam-1594	39	2	related	related	ADJ
ejpam-1594	39	3	area	area	NOUN
ejpam-1594	39	4	of	of	ADP
ejpam-1594	39	5	interest	interest	NOUN
ejpam-1594	39	6	since	since	SCONJ
ejpam-1594	39	7	recent	recent	ADJ
ejpam-1594	39	8	past	past	NOUN
ejpam-1594	39	9	has	have	AUX
ejpam-1594	39	10	been	be	AUX
ejpam-1594	39	11	the	the	DET
ejpam-1594	39	12	study	study	NOUN
ejpam-1594	39	13	of	of	ADP
ejpam-1594	39	14	2	2	NUM
ejpam-1594	39	15	-	-	PUNCT
ejpam-1594	39	16	primal	primal	ADJ
ejpam-1594	39	17	rings	ring	NOUN
ejpam-1594	39	18	.	.	PUNCT
ejpam-1594	40	1	this	this	PRON
ejpam-1594	40	2	involves	involve	VERB
ejpam-1594	40	3	the	the	DET
ejpam-1594	40	4	notions	notion	NOUN
ejpam-1594	40	5	of	of	ADP
ejpam-1594	40	6	prime	prime	ADJ
ejpam-1594	40	7	radical	radical	ADJ
ejpam-1594	40	8	and	and	CCONJ
ejpam-1594	40	9	the	the	DET
ejpam-1594	40	10	set	set	NOUN
ejpam-1594	40	11	of	of	ADP
ejpam-1594	40	12	nilpotent	nilpotent	ADJ
ejpam-1594	40	13	elements	element	NOUN
ejpam-1594	40	14	of	of	ADP
ejpam-1594	40	15	a	a	DET
ejpam-1594	40	16	ring	ring	NOUN
ejpam-1594	40	17	.	.	PUNCT
ejpam-1594	41	1	furthermore	furthermore	ADV
ejpam-1594	41	2	the	the	DET
ejpam-1594	41	3	concept	concept	NOUN
ejpam-1594	41	4	of	of	ADP
ejpam-1594	41	5	completely	completely	ADV
ejpam-1594	41	6	prime	prime	ADJ
ejpam-1594	41	7	ideals	ideal	NOUN
ejpam-1594	41	8	and	and	CCONJ
ejpam-1594	41	9	the	the	DET
ejpam-1594	41	10	completely	completely	ADV
ejpam-1594	41	11	semiprime	semiprime	NOUN
ejpam-1594	41	12	ideals	ideal	NOUN
ejpam-1594	41	13	are	be	AUX
ejpam-1594	41	14	also	also	ADV
ejpam-1594	41	15	studied	study	VERB
ejpam-1594	41	16	in	in	ADP
ejpam-1594	41	17	this	this	DET
ejpam-1594	41	18	area	area	NOUN
ejpam-1594	41	19	.	.	PUNCT
ejpam-1594	42	1	krempa	krempa	NOUN
ejpam-1594	42	2	in	in	ADP
ejpam-1594	42	3	[	[	X
ejpam-1594	42	4	9	9	NUM
ejpam-1594	42	5	]	]	PUNCT
ejpam-1594	42	6	introduced	introduce	VERB
ejpam-1594	42	7	σ	σ	PROPN
ejpam-1594	42	8	-	-	ADJ
ejpam-1594	42	9	rigid	rigid	ADJ
ejpam-1594	42	10	rings	ring	NOUN
ejpam-1594	42	11	;	;	PUNCT
ejpam-1594	42	12	kwak	kwak	PROPN
ejpam-1594	42	13	in	in	ADP
ejpam-1594	42	14	[	[	X
ejpam-1594	42	15	10	10	NUM
ejpam-1594	42	16	]	]	PUNCT
ejpam-1594	42	17	introduced	introduce	VERB
ejpam-1594	42	18	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1594	42	19	and	and	CCONJ
ejpam-1594	42	20	ouyang	ouyang	NOUN
ejpam-1594	42	21	in	in	ADP
ejpam-1594	42	22	[	[	X
ejpam-1594	42	23	14	14	NUM
ejpam-1594	42	24	]	]	PUNCT
ejpam-1594	42	25	introduced	introduce	VERB
ejpam-1594	42	26	weak	weak	ADJ
ejpam-1594	42	27	σ	σ	ADJ
ejpam-1594	42	28	-	-	ADJ
ejpam-1594	42	29	rigid	rigid	ADJ
ejpam-1594	42	30	rings	ring	NOUN
ejpam-1594	42	31	,	,	PUNCT
ejpam-1594	42	32	where	where	SCONJ
ejpam-1594	42	33	σ	σ	PROPN
ejpam-1594	42	34	is	be	AUX
ejpam-1594	42	35	an	an	DET
ejpam-1594	42	36	endomorphism	endomorphism	NOUN
ejpam-1594	42	37	of	of	ADP
ejpam-1594	42	38	ring	ring	PROPN
ejpam-1594	42	39	r.	r.	PROPN
ejpam-1594	42	40	these	these	DET
ejpam-1594	42	41	rings	ring	NOUN
ejpam-1594	42	42	are	be	AUX
ejpam-1594	42	43	related	relate	VERB
ejpam-1594	42	44	to	to	ADP
ejpam-1594	42	45	2	2	NUM
ejpam-1594	42	46	-	-	PUNCT
ejpam-1594	42	47	primal	primal	ADJ
ejpam-1594	42	48	rings	ring	NOUN
ejpam-1594	42	49	.	.	PUNCT
ejpam-1594	43	1	in	in	ADP
ejpam-1594	43	2	this	this	DET
ejpam-1594	43	3	paper	paper	NOUN
ejpam-1594	43	4	we	we	PRON
ejpam-1594	43	5	study	study	VERB
ejpam-1594	43	6	these	these	DET
ejpam-1594	43	7	rings	ring	NOUN
ejpam-1594	43	8	and	and	CCONJ
ejpam-1594	43	9	find	find	VERB
ejpam-1594	43	10	a	a	DET
ejpam-1594	43	11	relation	relation	NOUN
ejpam-1594	43	12	between	between	ADP
ejpam-1594	43	13	them	they	PRON
ejpam-1594	43	14	.	.	PUNCT
ejpam-1594	44	1	towards	towards	ADP
ejpam-1594	44	2	this	this	PRON
ejpam-1594	44	3	we	we	PRON
ejpam-1594	44	4	prove	prove	VERB
ejpam-1594	44	5	the	the	DET
ejpam-1594	44	6	following	follow	VERB
ejpam-1594	44	7	theorem	theorem	NOUN
ejpam-1594	44	8	:	:	PUNCT
ejpam-1594	44	9	let	let	VERB
ejpam-1594	44	10	r	r	PRON
ejpam-1594	44	11	be	be	AUX
ejpam-1594	44	12	a	a	DET
ejpam-1594	44	13	ring	ring	NOUN
ejpam-1594	44	14	.	.	PUNCT
ejpam-1594	45	1	let	let	VERB
ejpam-1594	45	2	σ	σ	NOUN
ejpam-1594	45	3	be	be	AUX
ejpam-1594	45	4	an	an	DET
ejpam-1594	45	5	endomorphism	endomorphism	NOUN
ejpam-1594	45	6	of	of	ADP
ejpam-1594	45	7	r	r	NOUN
ejpam-1594	45	8	such	such	ADJ
ejpam-1594	45	9	that	that	SCONJ
ejpam-1594	45	10	r	r	NOUN
ejpam-1594	45	11	is	be	AUX
ejpam-1594	45	12	a	a	DET
ejpam-1594	45	13	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	45	14	.	.	PUNCT
ejpam-1594	46	1	then	then	ADV
ejpam-1594	46	2	r	r	NOUN
ejpam-1594	46	3	is	be	AUX
ejpam-1594	46	4	a	a	DET
ejpam-1594	46	5	weak	weak	ADJ
ejpam-1594	46	6	σ	σ	ADJ
ejpam-1594	46	7	-	-	ADJ
ejpam-1594	46	8	rigid	rigid	ADJ
ejpam-1594	46	9	ring	ring	NOUN
ejpam-1594	46	10	.	.	PUNCT
ejpam-1594	47	1	conversely	conversely	ADV
ejpam-1594	47	2	a	a	DET
ejpam-1594	47	3	2	2	NUM
ejpam-1594	47	4	-	-	PUNCT
ejpam-1594	47	5	primal	primal	ADJ
ejpam-1594	47	6	weak	weak	ADJ
ejpam-1594	47	7	σ	σ	ADJ
ejpam-1594	47	8	-	-	ADJ
ejpam-1594	47	9	rigid	rigid	ADJ
ejpam-1594	47	10	ring	ring	NOUN
ejpam-1594	47	11	is	be	AUX
ejpam-1594	47	12	a	a	DET
ejpam-1594	47	13	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	47	14	.	.	PUNCT
ejpam-1594	48	1	(	(	PUNCT
ejpam-1594	48	2	this	this	PRON
ejpam-1594	48	3	is	be	AUX
ejpam-1594	48	4	proved	prove	VERB
ejpam-1594	48	5	in	in	ADP
ejpam-1594	48	6	theorem	theorem	NOUN
ejpam-1594	48	7	2	2	NUM
ejpam-1594	48	8	)	)	PUNCT
ejpam-1594	48	9	.	.	PUNCT
ejpam-1594	49	1	we	we	PRON
ejpam-1594	49	2	also	also	ADV
ejpam-1594	49	3	discuss	discuss	VERB
ejpam-1594	49	4	skew	skew	ADJ
ejpam-1594	49	5	polynomial	polynomial	ADJ
ejpam-1594	49	6	rings	ring	NOUN
ejpam-1594	49	7	over	over	ADP
ejpam-1594	49	8	weak	weak	ADJ
ejpam-1594	49	9	σ	σ	ADJ
ejpam-1594	49	10	-	-	ADJ
ejpam-1594	49	11	rigid	rigid	ADJ
ejpam-1594	49	12	rings	ring	NOUN
ejpam-1594	49	13	.	.	PUNCT
ejpam-1594	50	1	we	we	PRON
ejpam-1594	50	2	note	note	VERB
ejpam-1594	50	3	that	that	SCONJ
ejpam-1594	50	4	if	if	SCONJ
ejpam-1594	50	5	σ	σ	PROPN
ejpam-1594	50	6	is	be	AUX
ejpam-1594	50	7	an	an	DET
ejpam-1594	50	8	endomorphism	endomorphism	NOUN
ejpam-1594	50	9	of	of	ADP
ejpam-1594	50	10	a	a	DET
ejpam-1594	50	11	ring	ring	NOUN
ejpam-1594	50	12	r	r	NOUN
ejpam-1594	50	13	,	,	PUNCT
ejpam-1594	50	14	then	then	ADV
ejpam-1594	50	15	it	it	PRON
ejpam-1594	50	16	can	can	AUX
ejpam-1594	50	17	be	be	AUX
ejpam-1594	50	18	extended	extend	VERB
ejpam-1594	50	19	to	to	ADP
ejpam-1594	50	20	an	an	DET
ejpam-1594	50	21	endomorphism	endomorphism	PROPN
ejpam-1594	50	22	σ	σ	PROPN
ejpam-1594	50	23	of	of	ADP
ejpam-1594	50	24	s(r	s(r	PROPN
ejpam-1594	50	25	)	)	PUNCT
ejpam-1594	50	26	=	=	SYM
ejpam-1594	50	27	r[x	r[x	NOUN
ejpam-1594	50	28	;	;	PUNCT
ejpam-1594	50	29	σ	σ	PROPN
ejpam-1594	50	30	]	]	PUNCT
ejpam-1594	50	31	by	by	ADP
ejpam-1594	50	32	σ	σ	PROPN
ejpam-1594	50	33	(	(	PUNCT
ejpam-1594	50	34	∑m	∑m	PROPN
ejpam-1594	50	35	i=0	i=0	PROPN
ejpam-1594	50	36	x	x	X
ejpam-1594	50	37	iai	iai	ADJ
ejpam-1594	50	38	)	)	PUNCT
ejpam-1594	50	39	=	=	VERB
ejpam-1594	50	40	∑m	∑m	PROPN
ejpam-1594	50	41	i=0	i=0	PROPN
ejpam-1594	50	42	x	x	SYM
ejpam-1594	50	43	iσ(ai	iσ(ai	PROPN
ejpam-1594	50	44	)	)	PUNCT
ejpam-1594	50	45	.	.	PUNCT
ejpam-1594	51	1	with	with	ADP
ejpam-1594	51	2	this	this	PRON
ejpam-1594	51	3	we	we	PRON
ejpam-1594	51	4	prove	prove	VERB
ejpam-1594	51	5	the	the	DET
ejpam-1594	51	6	following	follow	VERB
ejpam-1594	51	7	theorem	theorem	NOUN
ejpam-1594	51	8	:	:	PUNCT
ejpam-1594	51	9	let	let	VERB
ejpam-1594	51	10	r	r	PRON
ejpam-1594	51	11	be	be	AUX
ejpam-1594	51	12	a	a	DET
ejpam-1594	51	13	noetherian	noetherian	ADJ
ejpam-1594	51	14	ring	ring	NOUN
ejpam-1594	51	15	.	.	PUNCT
ejpam-1594	52	1	let	let	VERB
ejpam-1594	52	2	σ	σ	NOUN
ejpam-1594	52	3	be	be	AUX
ejpam-1594	52	4	an	an	DET
ejpam-1594	52	5	automorphism	automorphism	NOUN
ejpam-1594	52	6	of	of	ADP
ejpam-1594	52	7	r.	r.	PROPN
ejpam-1594	52	8	then	then	ADV
ejpam-1594	52	9	r	r	NOUN
ejpam-1594	52	10	is	be	AUX
ejpam-1594	52	11	a	a	DET
ejpam-1594	52	12	weak	weak	ADJ
ejpam-1594	52	13	σ	σ	ADJ
ejpam-1594	52	14	-	-	ADJ
ejpam-1594	52	15	rigid	rigid	ADJ
ejpam-1594	52	16	ring	ring	NOUN
ejpam-1594	52	17	if	if	SCONJ
ejpam-1594	52	18	and	and	CCONJ
ejpam-1594	52	19	only	only	ADV
ejpam-1594	52	20	if	if	SCONJ
ejpam-1594	52	21	s(r	s(r	VERB
ejpam-1594	52	22	)	)	PUNCT
ejpam-1594	52	23	=	=	SYM
ejpam-1594	52	24	r[x	r[x	NOUN
ejpam-1594	52	25	;	;	PUNCT
ejpam-1594	53	1	σ	σ	PROPN
ejpam-1594	53	2	]	]	X
ejpam-1594	53	3	is	be	AUX
ejpam-1594	53	4	a	a	DET
ejpam-1594	53	5	weak	weak	ADJ
ejpam-1594	53	6	σ	σ	ADJ
ejpam-1594	53	7	-	-	ADJ
ejpam-1594	53	8	rigid	rigid	ADJ
ejpam-1594	53	9	ring	ring	NOUN
ejpam-1594	53	10	.	.	PUNCT
ejpam-1594	54	1	(	(	PUNCT
ejpam-1594	54	2	this	this	PRON
ejpam-1594	54	3	is	be	AUX
ejpam-1594	54	4	proved	prove	VERB
ejpam-1594	54	5	in	in	ADP
ejpam-1594	54	6	theorem	theorem	NOUN
ejpam-1594	54	7	3	3	NUM
ejpam-1594	54	8	)	)	PUNCT
ejpam-1594	54	9	.	.	PUNCT
ejpam-1594	55	1	n.	n.	PROPN
ejpam-1594	55	2	kumari	kumari	PROPN
ejpam-1594	55	3	,	,	PUNCT
ejpam-1594	55	4	s.	s.	PROPN
ejpam-1594	55	5	gosani	gosani	PROPN
ejpam-1594	55	6	,	,	PUNCT
ejpam-1594	55	7	v.	v.	ADP
ejpam-1594	55	8	bhat	bhat	PROPN
ejpam-1594	55	9	/	/	SYM
ejpam-1594	55	10	eur	eur	PROPN
ejpam-1594	55	11	.	.	PUNCT
ejpam-1594	56	1	j.	j.	PROPN
ejpam-1594	56	2	pure	pure	PROPN
ejpam-1594	56	3	appl	appl	PROPN
ejpam-1594	56	4	.	.	PROPN
ejpam-1594	56	5	math	math	PROPN
ejpam-1594	56	6	,	,	PUNCT
ejpam-1594	56	7	6	6	NUM
ejpam-1594	56	8	(	(	PUNCT
ejpam-1594	56	9	2013	2013	NUM
ejpam-1594	56	10	)	)	PUNCT
ejpam-1594	56	11	,	,	PUNCT
ejpam-1594	56	12	59	59	NUM
ejpam-1594	56	13	-	-	SYM
ejpam-1594	56	14	65	65	NUM
ejpam-1594	56	15	61	61	NUM
ejpam-1594	56	16	2	2	NUM
ejpam-1594	56	17	.	.	PUNCT
ejpam-1594	56	18	preliminaries	preliminary	NOUN
ejpam-1594	56	19	we	we	PRON
ejpam-1594	56	20	begin	begin	VERB
ejpam-1594	56	21	with	with	ADP
ejpam-1594	56	22	the	the	DET
ejpam-1594	56	23	following	follow	VERB
ejpam-1594	56	24	definitions	definition	NOUN
ejpam-1594	56	25	:	:	PUNCT
ejpam-1594	56	26	definition	definition	NOUN
ejpam-1594	56	27	1	1	NUM
ejpam-1594	56	28	(	(	PUNCT
ejpam-1594	56	29	krempa	krempa	NOUN
ejpam-1594	56	30	[	[	X
ejpam-1594	56	31	9	9	NUM
ejpam-1594	56	32	]	]	NUM
ejpam-1594	56	33	)	)	PUNCT
ejpam-1594	56	34	.	.	PUNCT
ejpam-1594	57	1	an	an	DET
ejpam-1594	57	2	endomorphism	endomorphism	PROPN
ejpam-1594	57	3	σ	σ	PROPN
ejpam-1594	57	4	of	of	ADP
ejpam-1594	57	5	a	a	DET
ejpam-1594	57	6	ring	ring	NOUN
ejpam-1594	57	7	r	r	NOUN
ejpam-1594	57	8	is	be	AUX
ejpam-1594	57	9	said	say	VERB
ejpam-1594	57	10	to	to	PART
ejpam-1594	57	11	be	be	AUX
ejpam-1594	57	12	rigid	rigid	ADJ
ejpam-1594	57	13	if	if	SCONJ
ejpam-1594	57	14	aσ(a	aσ(a	VERB
ejpam-1594	57	15	)	)	PUNCT
ejpam-1594	57	16	=	=	SYM
ejpam-1594	57	17	0	0	NUM
ejpam-1594	57	18	implies	imply	VERB
ejpam-1594	57	19	a	a	DET
ejpam-1594	57	20	=	=	SYM
ejpam-1594	57	21	0	0	NUM
ejpam-1594	57	22	for	for	ADP
ejpam-1594	57	23	a	a	DET
ejpam-1594	57	24	∈	∈	PROPN
ejpam-1594	57	25	r.	r.	NOUN
ejpam-1594	57	26	a	a	DET
ejpam-1594	57	27	ring	ring	NOUN
ejpam-1594	57	28	r	r	NOUN
ejpam-1594	57	29	is	be	AUX
ejpam-1594	57	30	said	say	VERB
ejpam-1594	57	31	to	to	PART
ejpam-1594	57	32	be	be	AUX
ejpam-1594	57	33	σ	σ	NOUN
ejpam-1594	57	34	-	-	ADJ
ejpam-1594	57	35	rigid	rigid	ADJ
ejpam-1594	57	36	if	if	SCONJ
ejpam-1594	57	37	there	there	PRON
ejpam-1594	57	38	exists	exist	VERB
ejpam-1594	57	39	a	a	DET
ejpam-1594	57	40	rigid	rigid	ADJ
ejpam-1594	57	41	endomorphism	endomorphism	NOUN
ejpam-1594	57	42	σ	σ	PROPN
ejpam-1594	57	43	of	of	ADP
ejpam-1594	57	44	r.	r.	PROPN
ejpam-1594	57	45	definition	definition	NOUN
ejpam-1594	57	46	2	2	NUM
ejpam-1594	57	47	(	(	PUNCT
ejpam-1594	57	48	kwak	kwak	PROPN
ejpam-1594	58	1	[	[	X
ejpam-1594	58	2	10	10	NUM
ejpam-1594	58	3	]	]	PUNCT
ejpam-1594	58	4	)	)	PUNCT
ejpam-1594	58	5	.	.	PUNCT
ejpam-1594	59	1	let	let	VERB
ejpam-1594	59	2	r	r	PRON
ejpam-1594	59	3	be	be	AUX
ejpam-1594	59	4	a	a	DET
ejpam-1594	59	5	ring	ring	NOUN
ejpam-1594	59	6	and	and	CCONJ
ejpam-1594	59	7	σ	σ	NOUN
ejpam-1594	59	8	an	an	DET
ejpam-1594	59	9	endomorphism	endomorphism	NOUN
ejpam-1594	59	10	of	of	ADP
ejpam-1594	59	11	r.	r.	PROPN
ejpam-1594	59	12	then	then	ADV
ejpam-1594	59	13	r	r	NOUN
ejpam-1594	59	14	is	be	AUX
ejpam-1594	59	15	said	say	VERB
ejpam-1594	59	16	to	to	PART
ejpam-1594	59	17	be	be	AUX
ejpam-1594	59	18	a	a	DET
ejpam-1594	59	19	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	59	20	if	if	SCONJ
ejpam-1594	59	21	aσ(a	aσ(a	NUM
ejpam-1594	59	22	)	)	PUNCT
ejpam-1594	59	23	∈	∈	PROPN
ejpam-1594	59	24	p(r	p(r	PROPN
ejpam-1594	59	25	)	)	PUNCT
ejpam-1594	59	26	implies	imply	VERB
ejpam-1594	59	27	a	a	DET
ejpam-1594	59	28	∈	∈	PROPN
ejpam-1594	59	29	p(r	p(r	PROPN
ejpam-1594	59	30	)	)	PUNCT
ejpam-1594	59	31	for	for	ADP
ejpam-1594	59	32	a	a	DET
ejpam-1594	59	33	∈	∈	PROPN
ejpam-1594	59	34	r.	r.	PROPN
ejpam-1594	59	35	example	example	NOUN
ejpam-1594	59	36	1	1	NUM
ejpam-1594	59	37	(	(	PUNCT
ejpam-1594	59	38	kwak	kwak	PROPN
ejpam-1594	60	1	[	[	X
ejpam-1594	60	2	10	10	NUM
ejpam-1594	60	3	]	]	PUNCT
ejpam-1594	60	4	)	)	PUNCT
ejpam-1594	60	5	.	.	PUNCT
ejpam-1594	61	1	let	let	VERB
ejpam-1594	61	2	r	r	NOUN
ejpam-1594	61	3	=	=	SYM
ejpam-1594	61	4	�	�	PROPN
ejpam-1594	61	5	f	f	PROPN
ejpam-1594	61	6	f	f	PROPN
ejpam-1594	61	7	0	0	PROPN
ejpam-1594	61	8	f	f	PROPN
ejpam-1594	61	9	�	�	PROPN
ejpam-1594	61	10	,	,	PUNCT
ejpam-1594	61	11	where	where	SCONJ
ejpam-1594	61	12	f	f	PROPN
ejpam-1594	61	13	is	be	AUX
ejpam-1594	61	14	a	a	DET
ejpam-1594	61	15	field	field	NOUN
ejpam-1594	61	16	.	.	PUNCT
ejpam-1594	62	1	then	then	ADV
ejpam-1594	62	2	p(r	p(r	PROPN
ejpam-1594	62	3	)	)	PUNCT
ejpam-1594	62	4	=	=	SYM
ejpam-1594	62	5	�	�	PROPN
ejpam-1594	62	6	0	0	NUM
ejpam-1594	62	7	f	f	PROPN
ejpam-1594	62	8	0	0	SYM
ejpam-1594	62	9	0	0	NUM
ejpam-1594	62	10	�	�	PROPN
ejpam-1594	62	11	.	.	PUNCT
ejpam-1594	63	1	let	let	VERB
ejpam-1594	63	2	σ	σ	NOUN
ejpam-1594	63	3	:	:	PUNCT
ejpam-1594	63	4	r	r	NOUN
ejpam-1594	63	5	→	→	SYM
ejpam-1594	63	6	r	r	NOUN
ejpam-1594	63	7	be	be	AUX
ejpam-1594	63	8	defined	define	VERB
ejpam-1594	63	9	by	by	ADP
ejpam-1594	63	10	σ	σ	PROPN
ejpam-1594	63	11	�	�	PROPN
ejpam-1594	63	12	�	�	PROPN
ejpam-1594	63	13	a	a	DET
ejpam-1594	63	14	b	b	PROPN
ejpam-1594	63	15	0	0	NUM
ejpam-1594	63	16	c	c	PROPN
ejpam-1594	63	17	�	�	PROPN
ejpam-1594	63	18	�	�	PROPN
ejpam-1594	63	19	=	=	SYM
ejpam-1594	63	20	�	�	PROPN
ejpam-1594	63	21	a	a	DET
ejpam-1594	63	22	0	0	NUM
ejpam-1594	63	23	0	0	NUM
ejpam-1594	63	24	c	c	PROPN
ejpam-1594	63	25	�	�	PROPN
ejpam-1594	63	26	.	.	PUNCT
ejpam-1594	64	1	then	then	ADV
ejpam-1594	64	2	it	it	PRON
ejpam-1594	64	3	can	can	AUX
ejpam-1594	64	4	be	be	AUX
ejpam-1594	64	5	seen	see	VERB
ejpam-1594	64	6	that	that	SCONJ
ejpam-1594	64	7	σ	σ	PROPN
ejpam-1594	64	8	is	be	AUX
ejpam-1594	64	9	an	an	DET
ejpam-1594	64	10	endomorphism	endomorphism	NOUN
ejpam-1594	64	11	of	of	ADP
ejpam-1594	64	12	r	r	NOUN
ejpam-1594	64	13	and	and	CCONJ
ejpam-1594	64	14	r	r	NOUN
ejpam-1594	64	15	is	be	AUX
ejpam-1594	64	16	a	a	DET
ejpam-1594	64	17	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	64	18	.	.	PUNCT
ejpam-1594	65	1	we	we	PRON
ejpam-1594	65	2	note	note	VERB
ejpam-1594	65	3	that	that	SCONJ
ejpam-1594	65	4	the	the	DET
ejpam-1594	65	5	above	above	ADJ
ejpam-1594	65	6	ring	ring	NOUN
ejpam-1594	65	7	is	be	AUX
ejpam-1594	65	8	not	not	PART
ejpam-1594	65	9	σ	σ	NOUN
ejpam-1594	65	10	-	-	NOUN
ejpam-1594	65	11	rigid	rigid	ADJ
ejpam-1594	65	12	.	.	PUNCT
ejpam-1594	66	1	let	let	VERB
ejpam-1594	66	2	0	0	NUM
ejpam-1594	66	3	6=	6=	ADP
ejpam-1594	66	4	a	a	DET
ejpam-1594	66	5	∈	∈	PROPN
ejpam-1594	66	6	f	f	X
ejpam-1594	66	7	.	.	PUNCT
ejpam-1594	67	1	then	then	ADV
ejpam-1594	67	2	�	�	PROPN
ejpam-1594	67	3	0	0	NUM
ejpam-1594	67	4	a	a	DET
ejpam-1594	67	5	0	0	NUM
ejpam-1594	67	6	0	0	NUM
ejpam-1594	67	7	�	�	PROPN
ejpam-1594	67	8	σ	σ	X
ejpam-1594	67	9	�	�	PROPN
ejpam-1594	67	10	0	0	NUM
ejpam-1594	67	11	a	a	DET
ejpam-1594	67	12	0	0	NUM
ejpam-1594	67	13	0	0	NUM
ejpam-1594	67	14	�	�	PROPN
ejpam-1594	67	15	=	=	SYM
ejpam-1594	67	16	�	�	PROPN
ejpam-1594	67	17	0	0	NUM
ejpam-1594	67	18	0	0	NUM
ejpam-1594	67	19	0	0	SYM
ejpam-1594	67	20	0	0	NUM
ejpam-1594	67	21	�	�	PROPN
ejpam-1594	67	22	,	,	PUNCT
ejpam-1594	67	23	but	but	CCONJ
ejpam-1594	67	24	�	�	PROPN
ejpam-1594	67	25	0	0	NUM
ejpam-1594	67	26	a	a	DET
ejpam-1594	67	27	0	0	NUM
ejpam-1594	67	28	0	0	NUM
ejpam-1594	67	29	�	�	PROPN
ejpam-1594	67	30	6=	6=	SYM
ejpam-1594	67	31	�	�	PROPN
ejpam-1594	67	32	0	0	NUM
ejpam-1594	67	33	0	0	NUM
ejpam-1594	67	34	0	0	SYM
ejpam-1594	67	35	0	0	NUM
ejpam-1594	67	36	�	�	PROPN
ejpam-1594	67	37	.	.	PUNCT
ejpam-1594	68	1	in	in	ADP
ejpam-1594	68	2	[	[	X
ejpam-1594	68	3	10	10	NUM
ejpam-1594	68	4	]	]	PUNCT
ejpam-1594	68	5	,	,	PUNCT
ejpam-1594	68	6	kwak	kwak	PROPN
ejpam-1594	68	7	also	also	ADV
ejpam-1594	68	8	establishes	establish	VERB
ejpam-1594	68	9	a	a	DET
ejpam-1594	68	10	relation	relation	NOUN
ejpam-1594	68	11	between	between	ADP
ejpam-1594	68	12	a	a	DET
ejpam-1594	68	13	2	2	NUM
ejpam-1594	68	14	-	-	PUNCT
ejpam-1594	68	15	primal	primal	ADJ
ejpam-1594	68	16	ring	ring	NOUN
ejpam-1594	68	17	and	and	CCONJ
ejpam-1594	68	18	a	a	DET
ejpam-1594	68	19	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	68	20	.	.	PUNCT
ejpam-1594	68	21	recall	recall	VERB
ejpam-1594	68	22	that	that	SCONJ
ejpam-1594	68	23	a	a	DET
ejpam-1594	68	24	ring	ring	NOUN
ejpam-1594	68	25	r	r	NOUN
ejpam-1594	68	26	is	be	AUX
ejpam-1594	68	27	2	2	NUM
ejpam-1594	68	28	-	-	PUNCT
ejpam-1594	68	29	primal	primal	ADJ
ejpam-1594	68	30	if	if	SCONJ
ejpam-1594	68	31	n(r	n(r	NUM
ejpam-1594	68	32	)	)	PUNCT
ejpam-1594	69	1	=	=	SYM
ejpam-1594	69	2	p(r	p(r	PROPN
ejpam-1594	69	3	)	)	PUNCT
ejpam-1594	69	4	.	.	PUNCT
ejpam-1594	70	1	also	also	ADV
ejpam-1594	70	2	an	an	DET
ejpam-1594	70	3	ideal	ideal	ADJ
ejpam-1594	70	4	i	i	PRON
ejpam-1594	70	5	of	of	ADP
ejpam-1594	70	6	a	a	DET
ejpam-1594	70	7	ring	ring	NOUN
ejpam-1594	70	8	r	r	NOUN
ejpam-1594	70	9	is	be	AUX
ejpam-1594	70	10	called	call	VERB
ejpam-1594	70	11	completely	completely	ADV
ejpam-1594	70	12	semiprime	semiprime	NOUN
ejpam-1594	70	13	if	if	SCONJ
ejpam-1594	70	14	a2	a2	PROPN
ejpam-1594	70	15	∈	∈	PROPN
ejpam-1594	70	16	i	i	PRON
ejpam-1594	70	17	implies	imply	VERB
ejpam-1594	70	18	a	a	DET
ejpam-1594	70	19	∈	∈	NOUN
ejpam-1594	70	20	i	i	PRON
ejpam-1594	70	21	for	for	ADP
ejpam-1594	70	22	a	a	DET
ejpam-1594	70	23	∈	∈	PROPN
ejpam-1594	70	24	r.	r.	NOUN
ejpam-1594	70	25	clearly	clearly	ADV
ejpam-1594	70	26	r	r	NOUN
ejpam-1594	70	27	is	be	AUX
ejpam-1594	70	28	a	a	DET
ejpam-1594	70	29	i(*)-ring	i(*)-ring	NOUN
ejpam-1594	70	30	if	if	SCONJ
ejpam-1594	71	1	and	and	CCONJ
ejpam-1594	71	2	only	only	ADV
ejpam-1594	71	3	if	if	SCONJ
ejpam-1594	71	4	r	r	NOUN
ejpam-1594	71	5	is	be	AUX
ejpam-1594	71	6	a	a	DET
ejpam-1594	71	7	2	2	NUM
ejpam-1594	71	8	-	-	PUNCT
ejpam-1594	71	9	primal	primal	ADJ
ejpam-1594	71	10	ring	ring	NOUN
ejpam-1594	71	11	,	,	PUNCT
ejpam-1594	71	12	where	where	SCONJ
ejpam-1594	71	13	i	i	PRON
ejpam-1594	71	14	is	be	AUX
ejpam-1594	71	15	the	the	DET
ejpam-1594	71	16	identity	identity	NOUN
ejpam-1594	71	17	map	map	NOUN
ejpam-1594	71	18	on	on	ADP
ejpam-1594	71	19	r.	r.	PROPN
ejpam-1594	71	20	the	the	DET
ejpam-1594	71	21	ring	ring	NOUN
ejpam-1594	71	22	in	in	ADP
ejpam-1594	71	23	example	example	NOUN
ejpam-1594	72	1	1	1	NUM
ejpam-1594	72	2	is	be	AUX
ejpam-1594	72	3	2	2	NUM
ejpam-1594	72	4	-	-	PUNCT
ejpam-1594	72	5	primal	primal	ADJ
ejpam-1594	72	6	.	.	PUNCT
ejpam-1594	73	1	in	in	ADP
ejpam-1594	73	2	[	[	X
ejpam-1594	73	3	10	10	NUM
ejpam-1594	73	4	]	]	PUNCT
ejpam-1594	73	5	,	,	PUNCT
ejpam-1594	73	6	the	the	DET
ejpam-1594	73	7	2	2	NUM
ejpam-1594	73	8	-	-	PUNCT
ejpam-1594	73	9	primal	primal	ADJ
ejpam-1594	73	10	property	property	NOUN
ejpam-1594	73	11	has	have	AUX
ejpam-1594	73	12	also	also	ADV
ejpam-1594	73	13	been	be	AUX
ejpam-1594	73	14	extended	extend	VERB
ejpam-1594	73	15	to	to	ADP
ejpam-1594	73	16	the	the	DET
ejpam-1594	73	17	skew	skew	ADJ
ejpam-1594	73	18	-	-	PUNCT
ejpam-1594	73	19	polynomial	polynomial	ADJ
ejpam-1594	73	20	ring	ring	NOUN
ejpam-1594	73	21	r[x	r[x	NOUN
ejpam-1594	73	22	;	;	PUNCT
ejpam-1594	73	23	σ	σ	PROPN
ejpam-1594	73	24	]	]	X
ejpam-1594	73	25	.	.	PUNCT
ejpam-1594	74	1	we	we	PRON
ejpam-1594	74	2	now	now	ADV
ejpam-1594	74	3	give	give	VERB
ejpam-1594	74	4	an	an	DET
ejpam-1594	74	5	example	example	NOUN
ejpam-1594	74	6	of	of	ADP
ejpam-1594	74	7	a	a	DET
ejpam-1594	74	8	ring	ring	NOUN
ejpam-1594	74	9	r	r	NOUN
ejpam-1594	74	10	,	,	PUNCT
ejpam-1594	74	11	and	and	CCONJ
ejpam-1594	74	12	an	an	DET
ejpam-1594	74	13	endomorphism	endomorphism	PROPN
ejpam-1594	74	14	σ	σ	NOUN
ejpam-1594	74	15	of	of	ADP
ejpam-1594	74	16	r	r	NOUN
ejpam-1594	74	17	such	such	ADJ
ejpam-1594	74	18	that	that	SCONJ
ejpam-1594	74	19	r	r	NOUN
ejpam-1594	74	20	is	be	AUX
ejpam-1594	74	21	not	not	PART
ejpam-1594	74	22	a	a	DET
ejpam-1594	74	23	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	74	24	,	,	PUNCT
ejpam-1594	74	25	however	however	ADV
ejpam-1594	74	26	r	r	NOUN
ejpam-1594	74	27	is	be	AUX
ejpam-1594	74	28	2	2	NUM
ejpam-1594	74	29	-	-	PUNCT
ejpam-1594	74	30	primal	primal	ADJ
ejpam-1594	74	31	.	.	PUNCT
ejpam-1594	75	1	example	example	NOUN
ejpam-1594	75	2	2	2	NUM
ejpam-1594	75	3	(	(	PUNCT
ejpam-1594	75	4	kwak	kwak	PROPN
ejpam-1594	76	1	[	[	X
ejpam-1594	76	2	10	10	NUM
ejpam-1594	76	3	]	]	PUNCT
ejpam-1594	76	4	)	)	PUNCT
ejpam-1594	76	5	.	.	PUNCT
ejpam-1594	77	1	let	let	VERB
ejpam-1594	77	2	r	r	NOUN
ejpam-1594	77	3	=	=	SYM
ejpam-1594	77	4	f[x	f[x	PROPN
ejpam-1594	77	5	]	]	PUNCT
ejpam-1594	77	6	be	be	VERB
ejpam-1594	77	7	the	the	DET
ejpam-1594	77	8	polynomial	polynomial	ADJ
ejpam-1594	77	9	ring	ring	NOUN
ejpam-1594	77	10	over	over	ADP
ejpam-1594	77	11	a	a	DET
ejpam-1594	77	12	field	field	NOUN
ejpam-1594	78	1	f.	f.	NOUN
ejpam-1594	78	2	then	then	ADV
ejpam-1594	78	3	r	r	NOUN
ejpam-1594	78	4	is	be	AUX
ejpam-1594	78	5	2	2	NUM
ejpam-1594	78	6	-	-	NOUN
ejpam-1594	78	7	primal	primal	ADJ
ejpam-1594	78	8	with	with	ADP
ejpam-1594	78	9	p(r	p(r	NOUN
ejpam-1594	78	10	)	)	PUNCT
ejpam-1594	78	11	=	=	SYM
ejpam-1594	79	1	0	0	X
ejpam-1594	79	2	.	.	PUNCT
ejpam-1594	80	1	let	let	VERB
ejpam-1594	80	2	σ	σ	NOUN
ejpam-1594	80	3	:	:	PUNCT
ejpam-1594	80	4	r→	r→	PROPN
ejpam-1594	80	5	r	r	NOUN
ejpam-1594	80	6	be	be	AUX
ejpam-1594	80	7	an	an	DET
ejpam-1594	80	8	endomorphism	endomorphism	NOUN
ejpam-1594	80	9	defined	define	VERB
ejpam-1594	80	10	by	by	ADP
ejpam-1594	80	11	σ	σ	PROPN
ejpam-1594	80	12	(	(	PUNCT
ejpam-1594	80	13	f	f	PROPN
ejpam-1594	80	14	(	(	PUNCT
ejpam-1594	80	15	x	x	NOUN
ejpam-1594	80	16	)	)	PUNCT
ejpam-1594	80	17	)	)	PUNCT
ejpam-1594	81	1	=	=	SYM
ejpam-1594	81	2	f	f	PROPN
ejpam-1594	81	3	(	(	PUNCT
ejpam-1594	81	4	0	0	NUM
ejpam-1594	81	5	)	)	PUNCT
ejpam-1594	81	6	.	.	PUNCT
ejpam-1594	82	1	then	then	ADV
ejpam-1594	82	2	r	r	NOUN
ejpam-1594	82	3	is	be	AUX
ejpam-1594	82	4	not	not	PART
ejpam-1594	82	5	a	a	DET
ejpam-1594	82	6	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	82	7	.	.	PUNCT
ejpam-1594	83	1	for	for	ADP
ejpam-1594	83	2	example	example	NOUN
ejpam-1594	83	3	consider	consider	VERB
ejpam-1594	83	4	f	f	PROPN
ejpam-1594	83	5	(	(	PUNCT
ejpam-1594	83	6	x	x	NOUN
ejpam-1594	83	7	)	)	PUNCT
ejpam-1594	83	8	=	=	SYM
ejpam-1594	83	9	xa	xa	PROPN
ejpam-1594	83	10	,	,	PUNCT
ejpam-1594	83	11	a	a	PRON
ejpam-1594	83	12	6=	6=	NUM
ejpam-1594	83	13	0	0	NUM
ejpam-1594	83	14	.	.	PUNCT
ejpam-1594	84	1	let	let	VERB
ejpam-1594	84	2	r	r	PRON
ejpam-1594	84	3	be	be	AUX
ejpam-1594	84	4	a	a	DET
ejpam-1594	84	5	ring	ring	NOUN
ejpam-1594	84	6	and	and	CCONJ
ejpam-1594	84	7	σ	σ	NOUN
ejpam-1594	84	8	an	an	DET
ejpam-1594	84	9	automorphism	automorphism	NOUN
ejpam-1594	84	10	of	of	ADP
ejpam-1594	84	11	r.	r.	PROPN
ejpam-1594	84	12	we	we	PRON
ejpam-1594	84	13	now	now	ADV
ejpam-1594	84	14	give	give	VERB
ejpam-1594	84	15	a	a	DET
ejpam-1594	84	16	necessary	necessary	ADJ
ejpam-1594	84	17	and	and	CCONJ
ejpam-1594	84	18	sufficient	sufficient	ADJ
ejpam-1594	84	19	condition	condition	NOUN
ejpam-1594	84	20	for	for	SCONJ
ejpam-1594	84	21	r	r	NOUN
ejpam-1594	84	22	to	to	PART
ejpam-1594	84	23	be	be	AUX
ejpam-1594	84	24	a	a	DET
ejpam-1594	84	25	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	84	26	in	in	ADP
ejpam-1594	84	27	the	the	DET
ejpam-1594	84	28	following	follow	VERB
ejpam-1594	84	29	proposition	proposition	NOUN
ejpam-1594	84	30	:	:	PUNCT
ejpam-1594	84	31	proposition	proposition	NOUN
ejpam-1594	84	32	1	1	NUM
ejpam-1594	84	33	.	.	PUNCT
ejpam-1594	85	1	let	let	VERB
ejpam-1594	85	2	r	r	PRON
ejpam-1594	85	3	be	be	AUX
ejpam-1594	85	4	a	a	DET
ejpam-1594	85	5	noetherian	noetherian	ADJ
ejpam-1594	85	6	ring	ring	NOUN
ejpam-1594	85	7	and	and	CCONJ
ejpam-1594	85	8	σ	σ	NOUN
ejpam-1594	85	9	an	an	DET
ejpam-1594	85	10	automorphism	automorphism	NOUN
ejpam-1594	85	11	of	of	ADP
ejpam-1594	85	12	r.	r.	PROPN
ejpam-1594	85	13	then	then	ADV
ejpam-1594	85	14	r	r	NOUN
ejpam-1594	85	15	is	be	AUX
ejpam-1594	85	16	a	a	DET
ejpam-1594	85	17	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	85	18	implies	implie	NOUN
ejpam-1594	85	19	that	that	SCONJ
ejpam-1594	85	20	p(r	p(r	PROPN
ejpam-1594	85	21	)	)	PUNCT
ejpam-1594	85	22	is	be	AUX
ejpam-1594	85	23	completely	completely	ADV
ejpam-1594	85	24	semiprime	semiprime	NOUN
ejpam-1594	85	25	.	.	PUNCT
ejpam-1594	86	1	proof	proof	NOUN
ejpam-1594	86	2	.	.	PUNCT
ejpam-1594	87	1	let	let	VERB
ejpam-1594	87	2	r	r	PRON
ejpam-1594	87	3	be	be	AUX
ejpam-1594	87	4	a	a	DET
ejpam-1594	87	5	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	87	6	.	.	PUNCT
ejpam-1594	88	1	we	we	PRON
ejpam-1594	88	2	show	show	VERB
ejpam-1594	88	3	that	that	SCONJ
ejpam-1594	88	4	p(r	p(r	PROPN
ejpam-1594	88	5	)	)	PUNCT
ejpam-1594	88	6	is	be	AUX
ejpam-1594	88	7	completely	completely	ADV
ejpam-1594	88	8	semiprime	semiprime	ADJ
ejpam-1594	88	9	.	.	PUNCT
ejpam-1594	89	1	let	let	VERB
ejpam-1594	89	2	a	a	DET
ejpam-1594	89	3	∈	∈	NOUN
ejpam-1594	89	4	r	r	NOUN
ejpam-1594	89	5	be	be	VERB
ejpam-1594	89	6	such	such	ADJ
ejpam-1594	89	7	that	that	SCONJ
ejpam-1594	89	8	a2	a2	PROPN
ejpam-1594	89	9	∈	∈	PROPN
ejpam-1594	89	10	p(r	p(r	PROPN
ejpam-1594	89	11	)	)	PUNCT
ejpam-1594	89	12	.	.	PUNCT
ejpam-1594	90	1	then	then	ADV
ejpam-1594	90	2	aσ(a)σ(aσ(a	aσ(a)σ(aσ(a	X
ejpam-1594	90	3	)	)	PUNCT
ejpam-1594	90	4	)	)	PUNCT
ejpam-1594	91	1	=	=	SYM
ejpam-1594	91	2	aσ(a)σ(a)σ2(a	aσ(a)σ(a)σ2(a	NOUN
ejpam-1594	91	3	)	)	PUNCT
ejpam-1594	91	4	∈	∈	PROPN
ejpam-1594	91	5	σ(p(r	σ(p(r	PROPN
ejpam-1594	91	6	)	)	PUNCT
ejpam-1594	91	7	)	)	PUNCT
ejpam-1594	92	1	=	=	SYM
ejpam-1594	92	2	p(r	p(r	PROPN
ejpam-1594	92	3	)	)	PUNCT
ejpam-1594	92	4	.	.	PUNCT
ejpam-1594	93	1	therefore	therefore	ADV
ejpam-1594	93	2	aσ(a	aσ(a	ADV
ejpam-1594	93	3	)	)	PUNCT
ejpam-1594	93	4	∈	∈	PROPN
ejpam-1594	93	5	p(r	p(r	PROPN
ejpam-1594	93	6	)	)	PUNCT
ejpam-1594	93	7	and	and	CCONJ
ejpam-1594	93	8	hence	hence	ADV
ejpam-1594	93	9	a	a	DET
ejpam-1594	93	10	∈	∈	PROPN
ejpam-1594	93	11	p(r	p(r	NOUN
ejpam-1594	93	12	)	)	PUNCT
ejpam-1594	93	13	.	.	PUNCT
ejpam-1594	94	1	converse	converse	NOUN
ejpam-1594	94	2	of	of	ADP
ejpam-1594	94	3	the	the	DET
ejpam-1594	94	4	above	above	ADJ
ejpam-1594	94	5	need	need	AUX
ejpam-1594	94	6	not	not	PART
ejpam-1594	94	7	be	be	AUX
ejpam-1594	94	8	true	true	ADJ
ejpam-1594	94	9	.	.	PUNCT
ejpam-1594	95	1	n.	n.	PROPN
ejpam-1594	95	2	kumari	kumari	PROPN
ejpam-1594	95	3	,	,	PUNCT
ejpam-1594	95	4	s.	s.	PROPN
ejpam-1594	95	5	gosani	gosani	PROPN
ejpam-1594	95	6	,	,	PUNCT
ejpam-1594	95	7	v.	v.	ADP
ejpam-1594	95	8	bhat	bhat	PROPN
ejpam-1594	95	9	/	/	SYM
ejpam-1594	95	10	eur	eur	PROPN
ejpam-1594	95	11	.	.	PUNCT
ejpam-1594	96	1	j.	j.	PROPN
ejpam-1594	96	2	pure	pure	PROPN
ejpam-1594	96	3	appl	appl	PROPN
ejpam-1594	96	4	.	.	PROPN
ejpam-1594	96	5	math	math	PROPN
ejpam-1594	96	6	,	,	PUNCT
ejpam-1594	96	7	6	6	NUM
ejpam-1594	96	8	(	(	PUNCT
ejpam-1594	96	9	2013	2013	NUM
ejpam-1594	96	10	)	)	PUNCT
ejpam-1594	96	11	,	,	PUNCT
ejpam-1594	96	12	59	59	NUM
ejpam-1594	96	13	-	-	SYM
ejpam-1594	96	14	65	65	NUM
ejpam-1594	96	15	62	62	NUM
ejpam-1594	96	16	example	example	NOUN
ejpam-1594	96	17	3	3	NUM
ejpam-1594	96	18	(	(	PUNCT
ejpam-1594	96	19	kwak	kwak	PROPN
ejpam-1594	97	1	[	[	X
ejpam-1594	97	2	10	10	NUM
ejpam-1594	97	3	]	]	PUNCT
ejpam-1594	97	4	)	)	PUNCT
ejpam-1594	97	5	.	.	PUNCT
ejpam-1594	98	1	let	let	VERB
ejpam-1594	98	2	k	k	PRON
ejpam-1594	98	3	be	be	AUX
ejpam-1594	98	4	a	a	DET
ejpam-1594	98	5	field	field	NOUN
ejpam-1594	98	6	,	,	PUNCT
ejpam-1594	98	7	r	r	NOUN
ejpam-1594	98	8	=	=	PUNCT
ejpam-1594	98	9	k	k	PROPN
ejpam-1594	98	10	×	×	PROPN
ejpam-1594	98	11	k	k	PROPN
ejpam-1594	98	12	and	and	CCONJ
ejpam-1594	98	13	the	the	DET
ejpam-1594	98	14	automorphism	automorphism	NOUN
ejpam-1594	98	15	σ	σ	PROPN
ejpam-1594	98	16	of	of	ADP
ejpam-1594	98	17	r	r	NOUN
ejpam-1594	98	18	defined	define	VERB
ejpam-1594	98	19	by	by	ADP
ejpam-1594	98	20	σ((a	σ((a	PROPN
ejpam-1594	98	21	,	,	PUNCT
ejpam-1594	98	22	b	b	NOUN
ejpam-1594	98	23	)	)	PUNCT
ejpam-1594	98	24	)	)	PUNCT
ejpam-1594	99	1	=	=	PUNCT
ejpam-1594	99	2	(	(	PUNCT
ejpam-1594	99	3	b	b	NOUN
ejpam-1594	99	4	,	,	PUNCT
ejpam-1594	99	5	a	a	NOUN
ejpam-1594	99	6	)	)	PUNCT
ejpam-1594	99	7	,	,	PUNCT
ejpam-1594	99	8	a	a	PRON
ejpam-1594	99	9	,	,	PUNCT
ejpam-1594	99	10	b	b	PROPN
ejpam-1594	99	11	∈	∈	PROPN
ejpam-1594	99	12	k.	k.	NOUN
ejpam-1594	100	1	then	then	ADV
ejpam-1594	100	2	r	r	NOUN
ejpam-1594	100	3	is	be	AUX
ejpam-1594	100	4	a	a	DET
ejpam-1594	100	5	reduced	reduce	VERB
ejpam-1594	100	6	ring	ring	NOUN
ejpam-1594	100	7	and	and	CCONJ
ejpam-1594	100	8	so	so	ADV
ejpam-1594	100	9	p(r	p(r	PROPN
ejpam-1594	100	10	)	)	PUNCT
ejpam-1594	101	1	=	=	SYM
ejpam-1594	101	2	0	0	NUM
ejpam-1594	101	3	is	be	AUX
ejpam-1594	101	4	completely	completely	ADV
ejpam-1594	101	5	semiprime	semiprime	ADJ
ejpam-1594	101	6	.	.	PUNCT
ejpam-1594	102	1	but	but	CCONJ
ejpam-1594	102	2	the	the	DET
ejpam-1594	102	3	ring	ring	NOUN
ejpam-1594	102	4	r	r	NOUN
ejpam-1594	102	5	is	be	AUX
ejpam-1594	102	6	not	not	PART
ejpam-1594	102	7	a	a	DET
ejpam-1594	102	8	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	102	9	since	since	SCONJ
ejpam-1594	102	10	(	(	PUNCT
ejpam-1594	102	11	1,0)σ((1,0	1,0)σ((1,0	NUM
ejpam-1594	102	12	)	)	PUNCT
ejpam-1594	102	13	)	)	PUNCT
ejpam-1594	103	1	=	=	SYM
ejpam-1594	103	2	(	(	PUNCT
ejpam-1594	103	3	0,0	0,0	NOUN
ejpam-1594	103	4	)	)	PUNCT
ejpam-1594	103	5	but	but	CCONJ
ejpam-1594	103	6	(	(	PUNCT
ejpam-1594	103	7	1,0	1,0	NUM
ejpam-1594	103	8	)	)	PUNCT
ejpam-1594	103	9	/∈	/∈	PUNCT
ejpam-1594	104	1	p(r	p(r	PROPN
ejpam-1594	104	2	)	)	PUNCT
ejpam-1594	104	3	.	.	PUNCT
ejpam-1594	105	1	recall	recall	VERB
ejpam-1594	105	2	that	that	SCONJ
ejpam-1594	105	3	an	an	DET
ejpam-1594	105	4	ideal	ideal	ADJ
ejpam-1594	105	5	p	p	NOUN
ejpam-1594	105	6	of	of	ADP
ejpam-1594	105	7	a	a	DET
ejpam-1594	105	8	ring	ring	NOUN
ejpam-1594	105	9	r	r	NOUN
ejpam-1594	105	10	is	be	AUX
ejpam-1594	105	11	completely	completely	ADV
ejpam-1594	105	12	prime	prime	ADJ
ejpam-1594	105	13	if	if	SCONJ
ejpam-1594	105	14	ab	ab	PROPN
ejpam-1594	105	15	∈	∈	PROPN
ejpam-1594	105	16	p	p	PROPN
ejpam-1594	105	17	implies	imply	VERB
ejpam-1594	105	18	a	a	DET
ejpam-1594	105	19	∈	∈	PROPN
ejpam-1594	105	20	p	p	NOUN
ejpam-1594	105	21	or	or	CCONJ
ejpam-1594	105	22	b	b	NOUN
ejpam-1594	105	23	∈	∈	PROPN
ejpam-1594	105	24	p	p	NOUN
ejpam-1594	105	25	for	for	ADP
ejpam-1594	105	26	a	a	DET
ejpam-1594	105	27	,	,	PUNCT
ejpam-1594	105	28	b	b	PROPN
ejpam-1594	105	29	∈	∈	PROPN
ejpam-1594	105	30	r.	r.	PROPN
ejpam-1594	105	31	in	in	ADP
ejpam-1594	105	32	commutative	commutative	ADJ
ejpam-1594	105	33	sense	sense	NOUN
ejpam-1594	105	34	completely	completely	ADV
ejpam-1594	105	35	prime	prime	ADJ
ejpam-1594	105	36	and	and	CCONJ
ejpam-1594	105	37	prime	prime	NOUN
ejpam-1594	105	38	have	have	VERB
ejpam-1594	105	39	the	the	DET
ejpam-1594	105	40	same	same	ADJ
ejpam-1594	105	41	meaning	meaning	NOUN
ejpam-1594	105	42	.	.	PUNCT
ejpam-1594	106	1	we	we	PRON
ejpam-1594	106	2	also	also	ADV
ejpam-1594	106	3	note	note	VERB
ejpam-1594	106	4	that	that	SCONJ
ejpam-1594	106	5	every	every	DET
ejpam-1594	106	6	completely	completely	ADV
ejpam-1594	106	7	prime	prime	ADJ
ejpam-1594	106	8	ideal	ideal	NOUN
ejpam-1594	106	9	of	of	ADP
ejpam-1594	106	10	a	a	DET
ejpam-1594	106	11	ring	ring	NOUN
ejpam-1594	106	12	r	r	NOUN
ejpam-1594	106	13	is	be	AUX
ejpam-1594	106	14	a	a	DET
ejpam-1594	106	15	prime	prime	ADJ
ejpam-1594	106	16	ideal	ideal	NOUN
ejpam-1594	106	17	,	,	PUNCT
ejpam-1594	106	18	but	but	CCONJ
ejpam-1594	106	19	the	the	DET
ejpam-1594	106	20	converse	converse	NOUN
ejpam-1594	106	21	need	need	AUX
ejpam-1594	106	22	not	not	PART
ejpam-1594	106	23	be	be	AUX
ejpam-1594	106	24	true	true	ADJ
ejpam-1594	106	25	.	.	PUNCT
ejpam-1594	107	1	the	the	DET
ejpam-1594	107	2	following	follow	VERB
ejpam-1594	107	3	example	example	NOUN
ejpam-1594	107	4	shows	show	VERB
ejpam-1594	107	5	that	that	SCONJ
ejpam-1594	107	6	a	a	DET
ejpam-1594	107	7	prime	prime	ADJ
ejpam-1594	107	8	ideal	ideal	NOUN
ejpam-1594	107	9	need	need	AUX
ejpam-1594	107	10	not	not	PART
ejpam-1594	107	11	be	be	AUX
ejpam-1594	107	12	a	a	DET
ejpam-1594	107	13	completely	completely	ADV
ejpam-1594	107	14	prime	prime	ADJ
ejpam-1594	107	15	ideal	ideal	NOUN
ejpam-1594	107	16	.	.	PUNCT
ejpam-1594	108	1	example	example	NOUN
ejpam-1594	109	1	4	4	X
ejpam-1594	109	2	.	.	PUNCT
ejpam-1594	109	3	let	let	VERB
ejpam-1594	109	4	r=	r=	PROPN
ejpam-1594	109	5	�	�	PROPN
ejpam-1594	109	6	z	z	NOUN
ejpam-1594	109	7	z	z	PROPN
ejpam-1594	109	8	z	z	NOUN
ejpam-1594	109	9	z	z	NOUN
ejpam-1594	109	10	�	�	PROPN
ejpam-1594	109	11	=	=	SYM
ejpam-1594	109	12	m2(z	m2(z	PROPN
ejpam-1594	109	13	)	)	PUNCT
ejpam-1594	109	14	.	.	PUNCT
ejpam-1594	110	1	if	if	SCONJ
ejpam-1594	110	2	p	p	NOUN
ejpam-1594	110	3	is	be	AUX
ejpam-1594	110	4	a	a	DET
ejpam-1594	110	5	prime	prime	ADJ
ejpam-1594	110	6	number	number	NOUN
ejpam-1594	110	7	,	,	PUNCT
ejpam-1594	110	8	then	then	ADV
ejpam-1594	110	9	the	the	DET
ejpam-1594	110	10	ideal	ideal	NOUN
ejpam-1594	110	11	p	p	X
ejpam-1594	110	12	=	=	SYM
ejpam-1594	110	13	m2(pz	m2(pz	PROPN
ejpam-1594	110	14	)	)	PUNCT
ejpam-1594	110	15	is	be	AUX
ejpam-1594	110	16	a	a	DET
ejpam-1594	110	17	prime	prime	ADJ
ejpam-1594	110	18	ideal	ideal	NOUN
ejpam-1594	110	19	of	of	ADP
ejpam-1594	110	20	r	r	NOUN
ejpam-1594	110	21	,	,	PUNCT
ejpam-1594	110	22	but	but	CCONJ
ejpam-1594	110	23	is	be	AUX
ejpam-1594	110	24	not	not	PART
ejpam-1594	110	25	completely	completely	ADV
ejpam-1594	110	26	prime	prime	ADJ
ejpam-1594	110	27	,	,	PUNCT
ejpam-1594	110	28	since	since	SCONJ
ejpam-1594	110	29	for	for	ADP
ejpam-1594	110	30	a	a	DET
ejpam-1594	110	31	=	=	SYM
ejpam-1594	110	32	�	�	PROPN
ejpam-1594	110	33	1	1	NUM
ejpam-1594	110	34	0	0	NUM
ejpam-1594	110	35	0	0	NUM
ejpam-1594	110	36	0	0	NUM
ejpam-1594	110	37	�	�	PROPN
ejpam-1594	110	38	and	and	CCONJ
ejpam-1594	110	39	b	b	NOUN
ejpam-1594	110	40	=	=	SYM
ejpam-1594	110	41	�	�	PROPN
ejpam-1594	110	42	0	0	NUM
ejpam-1594	110	43	0	0	NUM
ejpam-1594	110	44	0	0	NUM
ejpam-1594	110	45	1	1	NUM
ejpam-1594	110	46	�	�	PROPN
ejpam-1594	110	47	,	,	PUNCT
ejpam-1594	110	48	we	we	PRON
ejpam-1594	110	49	have	have	VERB
ejpam-1594	110	50	ab	ab	PROPN
ejpam-1594	110	51	∈	∈	PROPN
ejpam-1594	110	52	p	p	NOUN
ejpam-1594	110	53	,	,	PUNCT
ejpam-1594	110	54	even	even	ADV
ejpam-1594	110	55	though	though	SCONJ
ejpam-1594	110	56	a	a	DET
ejpam-1594	110	57	/∈	/∈	SYM
ejpam-1594	110	58	p	p	NOUN
ejpam-1594	110	59	and	and	CCONJ
ejpam-1594	110	60	b	b	PROPN
ejpam-1594	110	61	/∈	/∈	PUNCT
ejpam-1594	111	1	p.	p.	NOUN
ejpam-1594	111	2	there	there	PRON
ejpam-1594	111	3	are	be	VERB
ejpam-1594	111	4	examples	example	NOUN
ejpam-1594	111	5	of	of	ADP
ejpam-1594	111	6	rings	ring	NOUN
ejpam-1594	111	7	(	(	PUNCT
ejpam-1594	111	8	noncommutative	noncommutative	NOUN
ejpam-1594	111	9	)	)	PUNCT
ejpam-1594	111	10	in	in	ADP
ejpam-1594	111	11	which	which	PRON
ejpam-1594	111	12	prime	prime	ADJ
ejpam-1594	111	13	ideals	ideal	NOUN
ejpam-1594	111	14	are	be	AUX
ejpam-1594	111	15	completely	completely	ADV
ejpam-1594	111	16	prime	prime	ADJ
ejpam-1594	111	17	.	.	PUNCT
ejpam-1594	111	18	example	example	NOUN
ejpam-1594	112	1	5	5	NUM
ejpam-1594	112	2	.	.	PUNCT
ejpam-1594	113	1	let	let	VERB
ejpam-1594	113	2	r=	r=	PROPN
ejpam-1594	113	3	�	�	PROPN
ejpam-1594	113	4	z	z	PROPN
ejpam-1594	113	5	z	z	NOUN
ejpam-1594	113	6	0	0	NUM
ejpam-1594	113	7	z	z	PROPN
ejpam-1594	113	8	�	�	PROPN
ejpam-1594	113	9	.	.	PUNCT
ejpam-1594	114	1	then	then	ADV
ejpam-1594	114	2	p1	p1	PROPN
ejpam-1594	114	3	=	=	SYM
ejpam-1594	114	4	�	�	PROPN
ejpam-1594	114	5	z	z	PROPN
ejpam-1594	114	6	z	z	NOUN
ejpam-1594	114	7	0	0	NUM
ejpam-1594	114	8	0	0	NUM
ejpam-1594	114	9	�	�	PROPN
ejpam-1594	114	10	,	,	PUNCT
ejpam-1594	114	11	p2	p2	PROPN
ejpam-1594	114	12	=	=	SYM
ejpam-1594	114	13	�	�	PROPN
ejpam-1594	114	14	0	0	NUM
ejpam-1594	114	15	z	z	NOUN
ejpam-1594	114	16	0	0	PUNCT
ejpam-1594	114	17	z	z	PROPN
ejpam-1594	114	18	�	�	PROPN
ejpam-1594	114	19	and	and	CCONJ
ejpam-1594	114	20	p3	p3	PROPN
ejpam-1594	114	21	=	=	SYM
ejpam-1594	114	22	�	�	PROPN
ejpam-1594	114	23	0	0	PUNCT
ejpam-1594	114	24	z	z	NOUN
ejpam-1594	114	25	0	0	NUM
ejpam-1594	114	26	0	0	NUM
ejpam-1594	114	27	�	�	PROPN
ejpam-1594	114	28	are	be	AUX
ejpam-1594	114	29	prime	prime	ADJ
ejpam-1594	114	30	ideals	ideal	NOUN
ejpam-1594	114	31	of	of	ADP
ejpam-1594	114	32	r	r	NOUN
ejpam-1594	114	33	and	and	CCONJ
ejpam-1594	114	34	all	all	DET
ejpam-1594	114	35	these	these	PRON
ejpam-1594	114	36	are	be	AUX
ejpam-1594	114	37	completely	completely	ADV
ejpam-1594	114	38	prime	prime	ADJ
ejpam-1594	114	39	also	also	ADV
ejpam-1594	114	40	.	.	PUNCT
ejpam-1594	115	1	a	a	DET
ejpam-1594	115	2	necessary	necessary	ADJ
ejpam-1594	115	3	and	and	CCONJ
ejpam-1594	115	4	sufficient	sufficient	ADJ
ejpam-1594	115	5	condition	condition	NOUN
ejpam-1594	115	6	for	for	ADP
ejpam-1594	115	7	a	a	DET
ejpam-1594	115	8	noetherian	noetherian	ADJ
ejpam-1594	115	9	ring	ring	NOUN
ejpam-1594	115	10	r	r	NOUN
ejpam-1594	115	11	to	to	PART
ejpam-1594	115	12	be	be	AUX
ejpam-1594	115	13	a	a	DET
ejpam-1594	115	14	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	115	15	(	(	PUNCT
ejpam-1594	115	16	where	where	SCONJ
ejpam-1594	115	17	σ	σ	PROPN
ejpam-1594	115	18	is	be	AUX
ejpam-1594	115	19	an	an	DET
ejpam-1594	115	20	automorphism	automorphism	NOUN
ejpam-1594	115	21	of	of	ADP
ejpam-1594	115	22	r	r	NOUN
ejpam-1594	115	23	)	)	PUNCT
ejpam-1594	115	24	has	have	AUX
ejpam-1594	115	25	been	be	AUX
ejpam-1594	115	26	given	give	VERB
ejpam-1594	115	27	in	in	ADP
ejpam-1594	115	28	theorem	theorem	ADJ
ejpam-1594	115	29	2.4	2.4	NUM
ejpam-1594	115	30	of	of	ADP
ejpam-1594	115	31	[	[	X
ejpam-1594	115	32	3	3	NUM
ejpam-1594	115	33	]	]	NOUN
ejpam-1594	115	34	:	:	PUNCT
ejpam-1594	115	35	theorem	theorem	NOUN
ejpam-1594	115	36	1	1	X
ejpam-1594	115	37	.	.	PUNCT
ejpam-1594	116	1	let	let	VERB
ejpam-1594	116	2	r	r	PRON
ejpam-1594	116	3	be	be	AUX
ejpam-1594	116	4	a	a	DET
ejpam-1594	116	5	noetherian	noetherian	ADJ
ejpam-1594	116	6	ring	ring	NOUN
ejpam-1594	116	7	.	.	PUNCT
ejpam-1594	117	1	let	let	VERB
ejpam-1594	117	2	σ	σ	NOUN
ejpam-1594	117	3	be	be	AUX
ejpam-1594	117	4	an	an	DET
ejpam-1594	117	5	automorphism	automorphism	NOUN
ejpam-1594	117	6	of	of	ADP
ejpam-1594	117	7	r.	r.	PROPN
ejpam-1594	117	8	then	then	ADV
ejpam-1594	117	9	r	r	NOUN
ejpam-1594	117	10	is	be	AUX
ejpam-1594	117	11	a	a	DET
ejpam-1594	117	12	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	117	13	if	if	SCONJ
ejpam-1594	117	14	and	and	CCONJ
ejpam-1594	117	15	only	only	ADV
ejpam-1594	117	16	if	if	SCONJ
ejpam-1594	117	17	for	for	ADP
ejpam-1594	117	18	each	each	DET
ejpam-1594	117	19	minimal	minimal	ADJ
ejpam-1594	117	20	prime	prime	ADJ
ejpam-1594	117	21	u	u	NOUN
ejpam-1594	117	22	of	of	ADP
ejpam-1594	117	23	r	r	NOUN
ejpam-1594	117	24	,	,	PUNCT
ejpam-1594	117	25	σ(u	σ(u	NOUN
ejpam-1594	117	26	)	)	PUNCT
ejpam-1594	117	27	=	=	SYM
ejpam-1594	117	28	u	u	NOUN
ejpam-1594	117	29	and	and	CCONJ
ejpam-1594	117	30	u	u	NOUN
ejpam-1594	117	31	is	be	AUX
ejpam-1594	117	32	completely	completely	ADV
ejpam-1594	117	33	prime	prime	ADJ
ejpam-1594	117	34	ideal	ideal	NOUN
ejpam-1594	117	35	of	of	ADP
ejpam-1594	117	36	r.	r.	PROPN
ejpam-1594	117	37	proof	proof	NOUN
ejpam-1594	117	38	.	.	PUNCT
ejpam-1594	118	1	see	see	AUX
ejpam-1594	118	2	theorem	theorem	VERB
ejpam-1594	118	3	2.4	2.4	NUM
ejpam-1594	118	4	of	of	ADP
ejpam-1594	118	5	[	[	X
ejpam-1594	118	6	3	3	NUM
ejpam-1594	118	7	]	]	PUNCT
ejpam-1594	118	8	.	.	PUNCT
ejpam-1594	119	1	please	please	INTJ
ejpam-1594	119	2	note	note	VERB
ejpam-1594	119	3	that	that	SCONJ
ejpam-1594	119	4	in	in	ADP
ejpam-1594	119	5	proposition	proposition	NOUN
ejpam-1594	119	6	2.2	2.2	NUM
ejpam-1594	119	7	of	of	ADP
ejpam-1594	119	8	[	[	X
ejpam-1594	119	9	3	3	NUM
ejpam-1594	119	10	]	]	X
ejpam-1594	119	11	r	r	NOUN
ejpam-1594	119	12	should	should	AUX
ejpam-1594	119	13	be	be	AUX
ejpam-1594	119	14	noetharian	noetharian	ADJ
ejpam-1594	119	15	.	.	PUNCT
ejpam-1594	120	1	proposition	proposition	NOUN
ejpam-1594	120	2	2.2	2.2	NUM
ejpam-1594	120	3	of	of	ADP
ejpam-1594	120	4	[	[	X
ejpam-1594	120	5	3	3	X
ejpam-1594	120	6	]	]	PUNCT
ejpam-1594	120	7	has	have	AUX
ejpam-1594	120	8	been	be	AUX
ejpam-1594	120	9	used	use	VERB
ejpam-1594	120	10	to	to	PART
ejpam-1594	120	11	prove	prove	VERB
ejpam-1594	120	12	theorem	theorem	VERB
ejpam-1594	120	13	2.4	2.4	NUM
ejpam-1594	120	14	of	of	ADP
ejpam-1594	120	15	[	[	X
ejpam-1594	120	16	3	3	NUM
ejpam-1594	120	17	]	]	PUNCT
ejpam-1594	120	18	.	.	PUNCT
ejpam-1594	121	1	proposition	proposition	NOUN
ejpam-1594	121	2	2	2	NUM
ejpam-1594	121	3	.	.	PUNCT
ejpam-1594	122	1	let	let	VERB
ejpam-1594	122	2	r	r	PRON
ejpam-1594	122	3	be	be	AUX
ejpam-1594	122	4	a	a	DET
ejpam-1594	122	5	noetherian	noetherian	ADJ
ejpam-1594	122	6	ring	ring	NOUN
ejpam-1594	122	7	.	.	PUNCT
ejpam-1594	123	1	let	let	VERB
ejpam-1594	123	2	σ	σ	NOUN
ejpam-1594	123	3	be	be	AUX
ejpam-1594	123	4	an	an	DET
ejpam-1594	123	5	automorphism	automorphism	NOUN
ejpam-1594	123	6	of	of	ADP
ejpam-1594	123	7	r	r	NOUN
ejpam-1594	123	8	such	such	ADJ
ejpam-1594	123	9	that	that	SCONJ
ejpam-1594	123	10	r	r	NOUN
ejpam-1594	123	11	is	be	AUX
ejpam-1594	123	12	a	a	DET
ejpam-1594	123	13	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	123	14	.	.	PUNCT
ejpam-1594	124	1	then	then	ADV
ejpam-1594	124	2	u	u	PROPN
ejpam-1594	124	3	∈	∈	PROPN
ejpam-1594	124	4	min.spec(r	min.spec(r	PROPN
ejpam-1594	124	5	)	)	PUNCT
ejpam-1594	124	6	implies	imply	VERB
ejpam-1594	124	7	that	that	PRON
ejpam-1594	124	8	us(r	us(r	PUNCT
ejpam-1594	124	9	)	)	PUNCT
ejpam-1594	124	10	=	=	SYM
ejpam-1594	125	1	u[x	u[x	PRON
ejpam-1594	125	2	;	;	PUNCT
ejpam-1594	125	3	σ	σ	X
ejpam-1594	125	4	]	]	X
ejpam-1594	125	5	is	be	AUX
ejpam-1594	125	6	a	a	DET
ejpam-1594	125	7	completely	completely	ADV
ejpam-1594	125	8	prime	prime	ADJ
ejpam-1594	125	9	ideal	ideal	NOUN
ejpam-1594	125	10	of	of	ADP
ejpam-1594	125	11	s(r	s(r	PROPN
ejpam-1594	125	12	)	)	PUNCT
ejpam-1594	125	13	=	=	SYM
ejpam-1594	125	14	r[x	r[x	NOUN
ejpam-1594	125	15	;	;	PUNCT
ejpam-1594	125	16	σ	σ	PROPN
ejpam-1594	125	17	]	]	PUNCT
ejpam-1594	125	18	.	.	PUNCT
ejpam-1594	126	1	proof	proof	NOUN
ejpam-1594	126	2	.	.	PUNCT
ejpam-1594	127	1	proposition	proposition	NOUN
ejpam-1594	127	2	1	1	NUM
ejpam-1594	127	3	implies	imply	VERB
ejpam-1594	127	4	that	that	SCONJ
ejpam-1594	127	5	p(r	p(r	PROPN
ejpam-1594	127	6	)	)	PUNCT
ejpam-1594	127	7	is	be	AUX
ejpam-1594	127	8	completely	completely	ADV
ejpam-1594	127	9	semiprime	semiprime	NOUN
ejpam-1594	127	10	ideal	ideal	NOUN
ejpam-1594	127	11	of	of	ADP
ejpam-1594	127	12	r.	r.	PROPN
ejpam-1594	127	13	let	let	VERB
ejpam-1594	127	14	u	u	PRON
ejpam-1594	127	15	∈	∈	PROPN
ejpam-1594	127	16	min.spec(r	min.spec(r	PROPN
ejpam-1594	127	17	)	)	PUNCT
ejpam-1594	127	18	.	.	PUNCT
ejpam-1594	128	1	then	then	ADV
ejpam-1594	128	2	theorem	theorem	VERB
ejpam-1594	128	3	1	1	NUM
ejpam-1594	128	4	implies	imply	VERB
ejpam-1594	128	5	that	that	SCONJ
ejpam-1594	128	6	σ(u	σ(u	NOUN
ejpam-1594	128	7	)	)	PUNCT
ejpam-1594	128	8	=	=	SYM
ejpam-1594	128	9	u	u	NOUN
ejpam-1594	128	10	and	and	CCONJ
ejpam-1594	128	11	u	u	NOUN
ejpam-1594	128	12	is	be	AUX
ejpam-1594	128	13	completely	completely	ADV
ejpam-1594	128	14	prime	prime	ADJ
ejpam-1594	128	15	.	.	PUNCT
ejpam-1594	129	1	now	now	ADV
ejpam-1594	129	2	we	we	PRON
ejpam-1594	129	3	note	note	VERB
ejpam-1594	129	4	that	that	SCONJ
ejpam-1594	129	5	σ	σ	PROPN
ejpam-1594	129	6	can	can	AUX
ejpam-1594	129	7	be	be	AUX
ejpam-1594	129	8	extended	extend	VERB
ejpam-1594	129	9	to	to	ADP
ejpam-1594	129	10	an	an	DET
ejpam-1594	129	11	automorphism	automorphism	NOUN
ejpam-1594	129	12	σ	σ	NOUN
ejpam-1594	129	13	of	of	ADP
ejpam-1594	129	14	r	r	PROPN
ejpam-1594	129	15	/	/	SYM
ejpam-1594	129	16	u	u	NOUN
ejpam-1594	129	17	.	.	PUNCT
ejpam-1594	130	1	now	now	ADV
ejpam-1594	130	2	it	it	PRON
ejpam-1594	130	3	is	be	AUX
ejpam-1594	130	4	well	well	ADV
ejpam-1594	130	5	known	know	VERB
ejpam-1594	130	6	that	that	SCONJ
ejpam-1594	130	7	s	s	PROPN
ejpam-1594	130	8	/	/	SYM
ejpam-1594	130	9	us	us	PROPN
ejpam-1594	130	10	≃	≃	NOUN
ejpam-1594	130	11	(	(	PUNCT
ejpam-1594	130	12	r	r	X
ejpam-1594	130	13	/	/	SYM
ejpam-1594	130	14	u)[x	u)[x	NOUN
ejpam-1594	130	15	;	;	PUNCT
ejpam-1594	130	16	σ	σ	X
ejpam-1594	130	17	]	]	PUNCT
ejpam-1594	130	18	and	and	CCONJ
ejpam-1594	130	19	hence	hence	ADV
ejpam-1594	130	20	us	we	PRON
ejpam-1594	130	21	is	be	AUX
ejpam-1594	130	22	a	a	DET
ejpam-1594	130	23	completely	completely	ADV
ejpam-1594	130	24	prime	prime	ADJ
ejpam-1594	130	25	ideal	ideal	NOUN
ejpam-1594	130	26	of	of	ADP
ejpam-1594	130	27	s.	s.	PROPN
ejpam-1594	130	28	3	3	NUM
ejpam-1594	130	29	.	.	NOUN
ejpam-1594	130	30	skew	skew	ADJ
ejpam-1594	130	31	polynomial	polynomial	ADJ
ejpam-1594	130	32	rings	ring	NOUN
ejpam-1594	130	33	over	over	ADP
ejpam-1594	130	34	weak	weak	ADJ
ejpam-1594	130	35	σ	σ	ADJ
ejpam-1594	130	36	-	-	ADJ
ejpam-1594	130	37	rigid	rigid	ADJ
ejpam-1594	130	38	rings	ring	NOUN
ejpam-1594	130	39	definition	definition	NOUN
ejpam-1594	130	40	3	3	NUM
ejpam-1594	130	41	(	(	PUNCT
ejpam-1594	130	42	ouyang	ouyang	X
ejpam-1594	130	43	[	[	X
ejpam-1594	130	44	14	14	NUM
ejpam-1594	130	45	]	]	PUNCT
ejpam-1594	130	46	)	)	PUNCT
ejpam-1594	130	47	.	.	PUNCT
ejpam-1594	131	1	let	let	VERB
ejpam-1594	131	2	r	r	PRON
ejpam-1594	131	3	be	be	AUX
ejpam-1594	131	4	a	a	DET
ejpam-1594	131	5	ring	ring	NOUN
ejpam-1594	131	6	.	.	PUNCT
ejpam-1594	132	1	then	then	ADV
ejpam-1594	132	2	r	r	NOUN
ejpam-1594	132	3	is	be	AUX
ejpam-1594	132	4	said	say	VERB
ejpam-1594	132	5	to	to	PART
ejpam-1594	132	6	be	be	AUX
ejpam-1594	132	7	a	a	DET
ejpam-1594	132	8	weak	weak	ADJ
ejpam-1594	132	9	σ	σ	ADJ
ejpam-1594	132	10	-	-	ADJ
ejpam-1594	132	11	rigid	rigid	ADJ
ejpam-1594	132	12	ring	ring	NOUN
ejpam-1594	132	13	if	if	SCONJ
ejpam-1594	132	14	aσ(a	aσ(a	NUM
ejpam-1594	132	15	)	)	PUNCT
ejpam-1594	132	16	∈	∈	PROPN
ejpam-1594	132	17	n(r	n(r	NOUN
ejpam-1594	132	18	)	)	PUNCT
ejpam-1594	133	1	if	if	SCONJ
ejpam-1594	133	2	and	and	CCONJ
ejpam-1594	133	3	only	only	ADV
ejpam-1594	133	4	if	if	SCONJ
ejpam-1594	133	5	a	a	DET
ejpam-1594	133	6	∈	∈	PROPN
ejpam-1594	133	7	n(r	n(r	NOUN
ejpam-1594	133	8	)	)	PUNCT
ejpam-1594	133	9	for	for	ADP
ejpam-1594	133	10	a	a	DET
ejpam-1594	133	11	∈	∈	PROPN
ejpam-1594	133	12	r.	r.	PROPN
ejpam-1594	133	13	n.	n.	PROPN
ejpam-1594	133	14	kumari	kumari	PROPN
ejpam-1594	133	15	,	,	PUNCT
ejpam-1594	133	16	s.	s.	PROPN
ejpam-1594	133	17	gosani	gosani	PROPN
ejpam-1594	133	18	,	,	PUNCT
ejpam-1594	133	19	v.	v.	ADP
ejpam-1594	133	20	bhat	bhat	PROPN
ejpam-1594	133	21	/	/	SYM
ejpam-1594	133	22	eur	eur	PROPN
ejpam-1594	133	23	.	.	PUNCT
ejpam-1594	134	1	j.	j.	PROPN
ejpam-1594	134	2	pure	pure	PROPN
ejpam-1594	134	3	appl	appl	PROPN
ejpam-1594	134	4	.	.	PROPN
ejpam-1594	134	5	math	math	PROPN
ejpam-1594	134	6	,	,	PUNCT
ejpam-1594	134	7	6	6	NUM
ejpam-1594	134	8	(	(	PUNCT
ejpam-1594	134	9	2013	2013	NUM
ejpam-1594	134	10	)	)	PUNCT
ejpam-1594	134	11	,	,	PUNCT
ejpam-1594	134	12	59	59	NUM
ejpam-1594	134	13	-	-	SYM
ejpam-1594	134	14	65	65	NUM
ejpam-1594	134	15	63	63	NUM
ejpam-1594	134	16	example	example	NOUN
ejpam-1594	134	17	6	6	NUM
ejpam-1594	134	18	(	(	PUNCT
ejpam-1594	134	19	example	example	NOUN
ejpam-1594	134	20	2.1	2.1	NUM
ejpam-1594	134	21	of	of	ADP
ejpam-1594	134	22	ouyang	ouyang	PROPN
ejpam-1594	134	23	[	[	X
ejpam-1594	134	24	14	14	NUM
ejpam-1594	134	25	]	]	PUNCT
ejpam-1594	134	26	)	)	PUNCT
ejpam-1594	134	27	.	.	PUNCT
ejpam-1594	135	1	let	let	VERB
ejpam-1594	135	2	σ	σ	NOUN
ejpam-1594	135	3	be	be	AUX
ejpam-1594	135	4	an	an	DET
ejpam-1594	135	5	endomorphism	endomorphism	NOUN
ejpam-1594	135	6	of	of	ADP
ejpam-1594	135	7	a	a	DET
ejpam-1594	135	8	ring	ring	NOUN
ejpam-1594	135	9	r	r	NOUN
ejpam-1594	135	10	such	such	ADJ
ejpam-1594	135	11	that	that	SCONJ
ejpam-1594	135	12	r	r	NOUN
ejpam-1594	135	13	is	be	AUX
ejpam-1594	135	14	a	a	DET
ejpam-1594	135	15	σ	σ	PROPN
ejpam-1594	135	16	-	-	ADJ
ejpam-1594	135	17	rigid	rigid	ADJ
ejpam-1594	135	18	ring	ring	NOUN
ejpam-1594	135	19	.	.	PUNCT
ejpam-1594	136	1	let	let	VERB
ejpam-1594	136	2	a=	a=	ADV
ejpam-1594	136	3	n	n	PART
ejpam-1594	136	4			VERB
ejpam-1594	136	5			NOUN
ejpam-1594	136	6			NOUN
ejpam-1594	136	7	a	a	DET
ejpam-1594	136	8	b	b	NOUN
ejpam-1594	136	9	c	c	NOUN
ejpam-1594	136	10	0	0	PUNCT
ejpam-1594	136	11	a	a	DET
ejpam-1594	136	12	d	d	NOUN
ejpam-1594	136	13	0	0	NUM
ejpam-1594	136	14	0	0	NUM
ejpam-1594	137	1	a	a	DET
ejpam-1594	137	2			NOUN
ejpam-1594	137	3			NOUN
ejpam-1594	137	4			PUNCT
ejpam-1594	138	1	|	|	ADV
ejpam-1594	138	2	a	a	DET
ejpam-1594	138	3	,	,	PUNCT
ejpam-1594	138	4	b	b	NOUN
ejpam-1594	138	5	,	,	PUNCT
ejpam-1594	138	6	c	c	NOUN
ejpam-1594	138	7	,	,	PUNCT
ejpam-1594	138	8	d	d	PROPN
ejpam-1594	138	9	∈	∈	PROPN
ejpam-1594	138	10	r	r	NOUN
ejpam-1594	138	11	o	o	AUX
ejpam-1594	138	12	be	be	AUX
ejpam-1594	138	13	a	a	DET
ejpam-1594	138	14	subring	subring	NOUN
ejpam-1594	138	15	of	of	ADP
ejpam-1594	138	16	t3(r	t3(r	NOUN
ejpam-1594	138	17	)	)	PUNCT
ejpam-1594	138	18	,	,	PUNCT
ejpam-1594	138	19	the	the	DET
ejpam-1594	138	20	ring	ring	NOUN
ejpam-1594	138	21	of	of	ADP
ejpam-1594	138	22	upper	upper	ADJ
ejpam-1594	138	23	triangular	triangular	NOUN
ejpam-1594	138	24	matrices	matrix	NOUN
ejpam-1594	138	25	over	over	ADP
ejpam-1594	138	26	r.	r.	PROPN
ejpam-1594	138	27	now	now	ADV
ejpam-1594	138	28	σ	σ	PROPN
ejpam-1594	138	29	can	can	AUX
ejpam-1594	138	30	be	be	AUX
ejpam-1594	138	31	extended	extend	VERB
ejpam-1594	138	32	to	to	ADP
ejpam-1594	138	33	an	an	DET
ejpam-1594	138	34	endomorphism	endomorphism	PROPN
ejpam-1594	138	35	σ	σ	NOUN
ejpam-1594	138	36	of	of	ADP
ejpam-1594	138	37	a	a	PRON
ejpam-1594	138	38	by	by	ADP
ejpam-1594	138	39	σ((ai	σ((ai	PROPN
ejpam-1594	138	40	j	j	PROPN
ejpam-1594	138	41	)	)	PUNCT
ejpam-1594	138	42	)	)	PUNCT
ejpam-1594	139	1	=	=	PRON
ejpam-1594	139	2	(	(	PUNCT
ejpam-1594	139	3	σ(ai	σ(ai	PROPN
ejpam-1594	139	4	j	j	PROPN
ejpam-1594	139	5	)	)	PUNCT
ejpam-1594	139	6	)	)	PUNCT
ejpam-1594	139	7	.	.	PUNCT
ejpam-1594	140	1	then	then	ADV
ejpam-1594	140	2	it	it	PRON
ejpam-1594	140	3	can	can	AUX
ejpam-1594	140	4	be	be	AUX
ejpam-1594	140	5	seen	see	VERB
ejpam-1594	140	6	that	that	SCONJ
ejpam-1594	140	7	a	a	PRON
ejpam-1594	140	8	is	be	AUX
ejpam-1594	140	9	a	a	DET
ejpam-1594	140	10	weak	weak	ADJ
ejpam-1594	140	11	σ	σ	ADJ
ejpam-1594	140	12	-	-	ADJ
ejpam-1594	140	13	rigid	rigid	ADJ
ejpam-1594	140	14	ring	ring	NOUN
ejpam-1594	140	15	.	.	PUNCT
ejpam-1594	141	1	we	we	PRON
ejpam-1594	141	2	now	now	ADV
ejpam-1594	141	3	give	give	VERB
ejpam-1594	141	4	a	a	DET
ejpam-1594	141	5	relation	relation	NOUN
ejpam-1594	141	6	between	between	ADP
ejpam-1594	141	7	a	a	DET
ejpam-1594	141	8	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	141	9	and	and	CCONJ
ejpam-1594	141	10	a	a	DET
ejpam-1594	141	11	weak	weak	ADJ
ejpam-1594	141	12	σ	σ	ADJ
ejpam-1594	141	13	-	-	ADJ
ejpam-1594	141	14	rigid	rigid	ADJ
ejpam-1594	141	15	ring	ring	NOUN
ejpam-1594	141	16	in	in	ADP
ejpam-1594	141	17	the	the	DET
ejpam-1594	141	18	following	following	NOUN
ejpam-1594	141	19	theorem	theorem	NOUN
ejpam-1594	141	20	:	:	PUNCT
ejpam-1594	141	21	theorem	theorem	NOUN
ejpam-1594	141	22	2	2	NUM
ejpam-1594	141	23	.	.	PUNCT
ejpam-1594	142	1	let	let	VERB
ejpam-1594	142	2	r	r	PRON
ejpam-1594	142	3	be	be	AUX
ejpam-1594	142	4	a	a	DET
ejpam-1594	142	5	noetherian	noetherian	ADJ
ejpam-1594	142	6	ring	ring	NOUN
ejpam-1594	142	7	.	.	PUNCT
ejpam-1594	143	1	let	let	VERB
ejpam-1594	143	2	σ	σ	NOUN
ejpam-1594	143	3	be	be	AUX
ejpam-1594	143	4	an	an	DET
ejpam-1594	143	5	endomorphism	endomorphism	NOUN
ejpam-1594	143	6	of	of	ADP
ejpam-1594	143	7	r	r	NOUN
ejpam-1594	143	8	such	such	ADJ
ejpam-1594	143	9	that	that	SCONJ
ejpam-1594	143	10	r	r	NOUN
ejpam-1594	143	11	is	be	AUX
ejpam-1594	143	12	a	a	DET
ejpam-1594	143	13	σ(∗)ring	σ(∗)ring	NOUN
ejpam-1594	143	14	.	.	PUNCT
ejpam-1594	144	1	then	then	ADV
ejpam-1594	144	2	r	r	NOUN
ejpam-1594	144	3	is	be	AUX
ejpam-1594	144	4	a	a	DET
ejpam-1594	144	5	weak	weak	ADJ
ejpam-1594	144	6	σ	σ	ADJ
ejpam-1594	144	7	-	-	ADJ
ejpam-1594	144	8	rigid	rigid	ADJ
ejpam-1594	144	9	ring	ring	NOUN
ejpam-1594	144	10	.	.	PUNCT
ejpam-1594	145	1	conversely	conversely	ADV
ejpam-1594	145	2	a	a	DET
ejpam-1594	145	3	2	2	NUM
ejpam-1594	145	4	-	-	PUNCT
ejpam-1594	145	5	primal	primal	ADJ
ejpam-1594	145	6	weak	weak	ADJ
ejpam-1594	145	7	σ	σ	ADJ
ejpam-1594	145	8	-	-	ADJ
ejpam-1594	145	9	rigid	rigid	ADJ
ejpam-1594	145	10	ring	ring	NOUN
ejpam-1594	145	11	is	be	AUX
ejpam-1594	145	12	a	a	DET
ejpam-1594	145	13	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	145	14	.	.	PUNCT
ejpam-1594	146	1	proof	proof	NOUN
ejpam-1594	146	2	.	.	PUNCT
ejpam-1594	147	1	let	let	VERB
ejpam-1594	147	2	σ	σ	NOUN
ejpam-1594	147	3	be	be	AUX
ejpam-1594	147	4	an	an	DET
ejpam-1594	147	5	endomorphism	endomorphism	NOUN
ejpam-1594	147	6	of	of	ADP
ejpam-1594	147	7	r	r	NOUN
ejpam-1594	147	8	such	such	ADJ
ejpam-1594	147	9	that	that	SCONJ
ejpam-1594	147	10	r	r	NOUN
ejpam-1594	147	11	is	be	AUX
ejpam-1594	147	12	a	a	DET
ejpam-1594	147	13	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1594	147	14	.	.	PUNCT
ejpam-1594	148	1	now	now	ADV
ejpam-1594	148	2	r	r	NOUN
ejpam-1594	148	3	is	be	AUX
ejpam-1594	148	4	completely	completely	ADV
ejpam-1594	148	5	semiprime	semiprime	NOUN
ejpam-1594	148	6	by	by	ADP
ejpam-1594	148	7	proposition	proposition	NOUN
ejpam-1594	148	8	1	1	NUM
ejpam-1594	148	9	.	.	PUNCT
ejpam-1594	149	1	therefore	therefore	ADV
ejpam-1594	149	2	,	,	PUNCT
ejpam-1594	149	3	r	r	NOUN
ejpam-1594	149	4	is	be	AUX
ejpam-1594	149	5	2	2	NUM
ejpam-1594	149	6	-	-	PUNCT
ejpam-1594	149	7	primal	primal	ADJ
ejpam-1594	149	8	,	,	PUNCT
ejpam-1594	149	9	i.e.	i.e.	X
ejpam-1594	149	10	n(r	n(r	NOUN
ejpam-1594	149	11	)	)	PUNCT
ejpam-1594	149	12	=	=	SYM
ejpam-1594	149	13	p(r	p(r	PROPN
ejpam-1594	149	14	)	)	PUNCT
ejpam-1594	149	15	.	.	PUNCT
ejpam-1594	150	1	thus	thus	ADV
ejpam-1594	150	2	aσ(a	aσ(a	X
ejpam-1594	150	3	)	)	PUNCT
ejpam-1594	150	4	∈	∈	PROPN
ejpam-1594	150	5	n(r	n(r	NOUN
ejpam-1594	150	6	)	)	PUNCT
ejpam-1594	150	7	=	=	SYM
ejpam-1594	150	8	p(r	p(r	NOUN
ejpam-1594	150	9	)	)	PUNCT
ejpam-1594	150	10	implies	imply	VERB
ejpam-1594	150	11	that	that	SCONJ
ejpam-1594	150	12	a	a	DET
ejpam-1594	150	13	∈	∈	PROPN
ejpam-1594	150	14	p(r	p(r	NOUN
ejpam-1594	150	15	)	)	PUNCT
ejpam-1594	150	16	=	=	SYM
ejpam-1594	150	17	n(r	n(r	NOUN
ejpam-1594	150	18	)	)	PUNCT
ejpam-1594	150	19	.	.	PUNCT
ejpam-1594	151	1	hence	hence	ADV
ejpam-1594	151	2	r	r	NOUN
ejpam-1594	151	3	is	be	AUX
ejpam-1594	151	4	weak	weak	ADJ
ejpam-1594	151	5	σ	σ	ADJ
ejpam-1594	151	6	-	-	ADJ
ejpam-1594	151	7	rigid	rigid	ADJ
ejpam-1594	151	8	ring	ring	NOUN
ejpam-1594	151	9	.	.	PUNCT
ejpam-1594	152	1	conversely	conversely	ADV
ejpam-1594	152	2	let	let	VERB
ejpam-1594	152	3	r	r	NOUN
ejpam-1594	152	4	be	be	AUX
ejpam-1594	152	5	2	2	NUM
ejpam-1594	152	6	-	-	PUNCT
ejpam-1594	152	7	primal	primal	ADJ
ejpam-1594	152	8	weak	weak	ADJ
ejpam-1594	152	9	σ	σ	ADJ
ejpam-1594	152	10	-	-	ADJ
ejpam-1594	152	11	rigid	rigid	ADJ
ejpam-1594	152	12	ring	ring	NOUN
ejpam-1594	152	13	.	.	PUNCT
ejpam-1594	153	1	then	then	ADV
ejpam-1594	153	2	n(r	n(r	PRON
ejpam-1594	153	3	)	)	PUNCT
ejpam-1594	153	4	=	=	SYM
ejpam-1594	153	5	p(r	p(r	PROPN
ejpam-1594	153	6	)	)	PUNCT
ejpam-1594	153	7	and	and	CCONJ
ejpam-1594	153	8	aσ(a	aσ(a	NUM
ejpam-1594	153	9	)	)	PUNCT
ejpam-1594	153	10	∈	∈	PROPN
ejpam-1594	153	11	n(r	n(r	NOUN
ejpam-1594	153	12	)	)	PUNCT
ejpam-1594	153	13	implies	imply	VERB
ejpam-1594	153	14	that	that	SCONJ
ejpam-1594	153	15	a	a	DET
ejpam-1594	153	16	∈	∈	PROPN
ejpam-1594	153	17	n(r	n(r	NOUN
ejpam-1594	153	18	)	)	PUNCT
ejpam-1594	153	19	.	.	PUNCT
ejpam-1594	154	1	hence	hence	ADV
ejpam-1594	154	2	r	r	NOUN
ejpam-1594	154	3	is	be	AUX
ejpam-1594	154	4	a	a	DET
ejpam-1594	154	5	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1594	154	6	.	.	PUNCT
ejpam-1594	154	7	corollary	corollary	ADJ
ejpam-1594	154	8	1	1	NUM
ejpam-1594	154	9	.	.	PUNCT
ejpam-1594	155	1	let	let	VERB
ejpam-1594	155	2	r	r	PRON
ejpam-1594	155	3	be	be	AUX
ejpam-1594	155	4	a	a	DET
ejpam-1594	155	5	noetherian	noetherian	ADJ
ejpam-1594	155	6	ring	ring	NOUN
ejpam-1594	155	7	.	.	PUNCT
ejpam-1594	156	1	let	let	VERB
ejpam-1594	156	2	σ	σ	NOUN
ejpam-1594	156	3	be	be	AUX
ejpam-1594	156	4	an	an	DET
ejpam-1594	156	5	automorphism	automorphism	NOUN
ejpam-1594	156	6	of	of	ADP
ejpam-1594	156	7	r.	r.	PROPN
ejpam-1594	156	8	then	then	ADV
ejpam-1594	156	9	r	r	NOUN
ejpam-1594	156	10	is	be	AUX
ejpam-1594	156	11	a	a	DET
ejpam-1594	156	12	2	2	NUM
ejpam-1594	156	13	-	-	PUNCT
ejpam-1594	156	14	primal	primal	ADJ
ejpam-1594	156	15	weak	weak	ADJ
ejpam-1594	156	16	σ	σ	ADJ
ejpam-1594	156	17	-	-	ADJ
ejpam-1594	156	18	rigid	rigid	ADJ
ejpam-1594	156	19	ring	ring	NOUN
ejpam-1594	156	20	if	if	SCONJ
ejpam-1594	156	21	and	and	CCONJ
ejpam-1594	156	22	only	only	ADV
ejpam-1594	156	23	if	if	SCONJ
ejpam-1594	156	24	for	for	ADP
ejpam-1594	156	25	each	each	DET
ejpam-1594	156	26	minimal	minimal	ADJ
ejpam-1594	156	27	prime	prime	ADJ
ejpam-1594	156	28	u	u	NOUN
ejpam-1594	156	29	of	of	ADP
ejpam-1594	156	30	r	r	NOUN
ejpam-1594	156	31	,	,	PUNCT
ejpam-1594	156	32	σ(u	σ(u	NOUN
ejpam-1594	156	33	)	)	PUNCT
ejpam-1594	156	34	=	=	SYM
ejpam-1594	156	35	u	u	NOUN
ejpam-1594	156	36	and	and	CCONJ
ejpam-1594	156	37	u	u	NOUN
ejpam-1594	156	38	is	be	AUX
ejpam-1594	156	39	completely	completely	ADV
ejpam-1594	156	40	prime	prime	ADJ
ejpam-1594	156	41	ideal	ideal	NOUN
ejpam-1594	156	42	of	of	ADP
ejpam-1594	156	43	r.	r.	PROPN
ejpam-1594	156	44	proof	proof	PROPN
ejpam-1594	156	45	.	.	PUNCT
ejpam-1594	157	1	combine	combine	PROPN
ejpam-1594	157	2	theorem	theorem	VERB
ejpam-1594	157	3	1	1	NUM
ejpam-1594	157	4	and	and	CCONJ
ejpam-1594	157	5	theorem	theorem	VERB
ejpam-1594	157	6	2	2	NUM
ejpam-1594	157	7	.	.	PUNCT
ejpam-1594	158	1	let	let	VERB
ejpam-1594	158	2	r	r	PRON
ejpam-1594	158	3	be	be	AUX
ejpam-1594	158	4	a	a	DET
ejpam-1594	158	5	noetherian	noetherian	ADJ
ejpam-1594	158	6	ring	ring	NOUN
ejpam-1594	158	7	and	and	CCONJ
ejpam-1594	158	8	σ	σ	NOUN
ejpam-1594	158	9	an	an	DET
ejpam-1594	158	10	automorphism	automorphism	NOUN
ejpam-1594	158	11	of	of	ADP
ejpam-1594	158	12	r.	r.	PROPN
ejpam-1594	158	13	we	we	PRON
ejpam-1594	158	14	now	now	ADV
ejpam-1594	158	15	give	give	VERB
ejpam-1594	158	16	a	a	DET
ejpam-1594	158	17	characterization	characterization	NOUN
ejpam-1594	158	18	for	for	SCONJ
ejpam-1594	158	19	r	r	NOUN
ejpam-1594	158	20	to	to	PART
ejpam-1594	158	21	be	be	AUX
ejpam-1594	158	22	a	a	DET
ejpam-1594	158	23	weak	weak	ADJ
ejpam-1594	158	24	σ	σ	ADJ
ejpam-1594	158	25	-	-	ADJ
ejpam-1594	158	26	rigid	rigid	ADJ
ejpam-1594	158	27	ring	ring	NOUN
ejpam-1594	158	28	(	(	PUNCT
ejpam-1594	158	29	an	an	DET
ejpam-1594	158	30	analog	analog	NOUN
ejpam-1594	158	31	of	of	ADP
ejpam-1594	158	32	proposition	proposition	NOUN
ejpam-1594	158	33	1	1	NUM
ejpam-1594	158	34	for	for	ADP
ejpam-1594	158	35	weak	weak	ADJ
ejpam-1594	158	36	σ	σ	ADJ
ejpam-1594	158	37	-	-	ADJ
ejpam-1594	158	38	rigid	rigid	ADJ
ejpam-1594	158	39	rings	ring	NOUN
ejpam-1594	158	40	)	)	PUNCT
ejpam-1594	158	41	.	.	PUNCT
ejpam-1594	159	1	proposition	proposition	NOUN
ejpam-1594	159	2	3	3	X
ejpam-1594	159	3	.	.	PUNCT
ejpam-1594	160	1	let	let	VERB
ejpam-1594	160	2	r	r	PRON
ejpam-1594	160	3	be	be	AUX
ejpam-1594	160	4	a	a	DET
ejpam-1594	160	5	noetherian	noetherian	ADJ
ejpam-1594	160	6	ring	ring	NOUN
ejpam-1594	160	7	.	.	PUNCT
ejpam-1594	161	1	let	let	VERB
ejpam-1594	161	2	σ	σ	NOUN
ejpam-1594	161	3	be	be	AUX
ejpam-1594	161	4	an	an	DET
ejpam-1594	161	5	automorphism	automorphism	NOUN
ejpam-1594	161	6	of	of	ADP
ejpam-1594	161	7	r.	r.	PROPN
ejpam-1594	161	8	then	then	ADV
ejpam-1594	161	9	r	r	NOUN
ejpam-1594	161	10	is	be	AUX
ejpam-1594	161	11	a	a	DET
ejpam-1594	161	12	weak	weak	ADJ
ejpam-1594	161	13	σ	σ	ADJ
ejpam-1594	161	14	-	-	ADJ
ejpam-1594	161	15	rigid	rigid	ADJ
ejpam-1594	161	16	ring	ring	NOUN
ejpam-1594	161	17	implies	imply	VERB
ejpam-1594	161	18	that	that	SCONJ
ejpam-1594	161	19	n(r	n(r	NOUN
ejpam-1594	161	20	)	)	PUNCT
ejpam-1594	161	21	is	be	AUX
ejpam-1594	161	22	completely	completely	ADV
ejpam-1594	161	23	semiprime	semiprime	NOUN
ejpam-1594	161	24	.	.	PUNCT
ejpam-1594	162	1	proof	proof	NOUN
ejpam-1594	162	2	.	.	PUNCT
ejpam-1594	163	1	first	first	ADV
ejpam-1594	163	2	of	of	ADP
ejpam-1594	163	3	all	all	PRON
ejpam-1594	163	4	we	we	PRON
ejpam-1594	163	5	show	show	VERB
ejpam-1594	163	6	that	that	SCONJ
ejpam-1594	163	7	σ(n(r	σ(n(r	NOUN
ejpam-1594	163	8	)	)	PUNCT
ejpam-1594	163	9	)	)	PUNCT
ejpam-1594	164	1	=	=	SYM
ejpam-1594	164	2	n(r	n(r	NOUN
ejpam-1594	164	3	)	)	PUNCT
ejpam-1594	164	4	.	.	PUNCT
ejpam-1594	165	1	we	we	PRON
ejpam-1594	165	2	have	have	VERB
ejpam-1594	165	3	σ(n(r	σ(n(r	PROPN
ejpam-1594	165	4	)	)	PUNCT
ejpam-1594	165	5	)	)	PUNCT
ejpam-1594	166	1	⊆	⊆	NUM
ejpam-1594	166	2	n(r	n(r	NOUN
ejpam-1594	166	3	)	)	PUNCT
ejpam-1594	166	4	as	as	ADP
ejpam-1594	166	5	σ(n(r	σ(n(r	PROPN
ejpam-1594	166	6	)	)	PUNCT
ejpam-1594	166	7	)	)	PUNCT
ejpam-1594	166	8	is	be	AUX
ejpam-1594	166	9	a	a	DET
ejpam-1594	166	10	nilpotent	nilpotent	ADJ
ejpam-1594	166	11	ideal	ideal	NOUN
ejpam-1594	166	12	of	of	ADP
ejpam-1594	166	13	r.	r.	PROPN
ejpam-1594	166	14	now	now	ADV
ejpam-1594	166	15	for	for	ADP
ejpam-1594	166	16	any	any	DET
ejpam-1594	166	17	n	n	PRON
ejpam-1594	166	18	∈	∈	PROPN
ejpam-1594	166	19	n(r	n(r	NOUN
ejpam-1594	166	20	)	)	PUNCT
ejpam-1594	166	21	,	,	PUNCT
ejpam-1594	166	22	there	there	PRON
ejpam-1594	166	23	exists	exist	VERB
ejpam-1594	166	24	a	a	DET
ejpam-1594	166	25	∈	∈	NOUN
ejpam-1594	166	26	r	r	NOUN
ejpam-1594	166	27	such	such	ADJ
ejpam-1594	166	28	that	that	SCONJ
ejpam-1594	166	29	n	n	NOUN
ejpam-1594	166	30	=	=	SYM
ejpam-1594	166	31	σ(a	σ(a	PROPN
ejpam-1594	166	32	)	)	PUNCT
ejpam-1594	166	33	.	.	PUNCT
ejpam-1594	167	1	so	so	ADV
ejpam-1594	167	2	i	i	PRON
ejpam-1594	167	3	=	=	SYM
ejpam-1594	167	4	σ−1(n(r	σ−1(n(r	NOUN
ejpam-1594	167	5	)	)	PUNCT
ejpam-1594	167	6	)	)	PUNCT
ejpam-1594	168	1	=	=	PRON
ejpam-1594	168	2	{	{	PUNCT
ejpam-1594	168	3	a	a	DET
ejpam-1594	168	4	∈	∈	NOUN
ejpam-1594	168	5	r	r	NOUN
ejpam-1594	168	6	such	such	ADJ
ejpam-1594	168	7	that	that	DET
ejpam-1594	168	8	σ(a	σ(a	PROPN
ejpam-1594	168	9	)	)	PUNCT
ejpam-1594	168	10	=	=	SYM
ejpam-1594	168	11	n	n	CCONJ
ejpam-1594	168	12	∈	∈	PROPN
ejpam-1594	168	13	n(r	n(r	NOUN
ejpam-1594	168	14	)	)	PUNCT
ejpam-1594	168	15	}	}	PUNCT
ejpam-1594	168	16	is	be	AUX
ejpam-1594	168	17	an	an	DET
ejpam-1594	168	18	ideal	ideal	NOUN
ejpam-1594	168	19	of	of	ADP
ejpam-1594	168	20	r.	r.	PROPN
ejpam-1594	168	21	now	now	ADV
ejpam-1594	168	22	i	i	PRON
ejpam-1594	168	23	is	be	AUX
ejpam-1594	168	24	nilpotent	nilpotent	ADJ
ejpam-1594	168	25	,	,	PUNCT
ejpam-1594	168	26	therefore	therefore	ADV
ejpam-1594	168	27	i	i	PROPN
ejpam-1594	168	28	⊆	⊆	NUM
ejpam-1594	168	29	n(r	n(r	NUM
ejpam-1594	168	30	)	)	PUNCT
ejpam-1594	168	31	,	,	PUNCT
ejpam-1594	168	32	which	which	PRON
ejpam-1594	168	33	implies	imply	VERB
ejpam-1594	168	34	that	that	SCONJ
ejpam-1594	168	35	n(r)⊆	n(r)⊆	PROPN
ejpam-1594	168	36	σ(n(r	σ(n(r	PROPN
ejpam-1594	168	37	)	)	PUNCT
ejpam-1594	168	38	)	)	PUNCT
ejpam-1594	168	39	.	.	PUNCT
ejpam-1594	169	1	hence	hence	ADV
ejpam-1594	169	2	σ(n(r	σ(n(r	NUM
ejpam-1594	169	3	)	)	PUNCT
ejpam-1594	169	4	)	)	PUNCT
ejpam-1594	170	1	=	=	SYM
ejpam-1594	170	2	n(r	n(r	NOUN
ejpam-1594	170	3	)	)	PUNCT
ejpam-1594	170	4	.	.	PUNCT
ejpam-1594	171	1	now	now	ADV
ejpam-1594	171	2	let	let	VERB
ejpam-1594	171	3	r	r	NOUN
ejpam-1594	171	4	be	be	AUX
ejpam-1594	171	5	a	a	DET
ejpam-1594	171	6	weak	weak	ADJ
ejpam-1594	171	7	σ	σ	ADJ
ejpam-1594	171	8	-	-	ADJ
ejpam-1594	171	9	rigid	rigid	ADJ
ejpam-1594	171	10	ring	ring	NOUN
ejpam-1594	171	11	.	.	PUNCT
ejpam-1594	172	1	we	we	PRON
ejpam-1594	172	2	will	will	AUX
ejpam-1594	172	3	show	show	VERB
ejpam-1594	172	4	that	that	SCONJ
ejpam-1594	172	5	n(r	n(r	NOUN
ejpam-1594	172	6	)	)	PUNCT
ejpam-1594	172	7	is	be	AUX
ejpam-1594	172	8	completely	completely	ADV
ejpam-1594	172	9	semiprime	semiprime	ADJ
ejpam-1594	172	10	.	.	PUNCT
ejpam-1594	173	1	let	let	VERB
ejpam-1594	173	2	a	a	DET
ejpam-1594	173	3	∈	∈	NOUN
ejpam-1594	173	4	r	r	NOUN
ejpam-1594	173	5	be	be	VERB
ejpam-1594	173	6	such	such	ADJ
ejpam-1594	173	7	that	that	SCONJ
ejpam-1594	173	8	a2	a2	PROPN
ejpam-1594	173	9	∈	∈	PROPN
ejpam-1594	173	10	n(r	n(r	NOUN
ejpam-1594	173	11	)	)	PUNCT
ejpam-1594	173	12	.	.	PUNCT
ejpam-1594	174	1	then	then	ADV
ejpam-1594	174	2	aσ(a)σ(aσ(a	aσ(a)σ(aσ(a	X
ejpam-1594	174	3	)	)	PUNCT
ejpam-1594	174	4	)	)	PUNCT
ejpam-1594	175	1	=	=	SYM
ejpam-1594	175	2	aσ(a)σ(a)σ2(a	aσ(a)σ(a)σ2(a	NOUN
ejpam-1594	175	3	)	)	PUNCT
ejpam-1594	175	4	∈	∈	PROPN
ejpam-1594	175	5	σ(n(r	σ(n(r	PROPN
ejpam-1594	175	6	)	)	PUNCT
ejpam-1594	175	7	)	)	PUNCT
ejpam-1594	176	1	=	=	SYM
ejpam-1594	176	2	n(r	n(r	NOUN
ejpam-1594	176	3	)	)	PUNCT
ejpam-1594	176	4	.	.	PUNCT
ejpam-1594	177	1	therefore	therefore	ADV
ejpam-1594	177	2	aσ(a	aσ(a	X
ejpam-1594	177	3	)	)	PUNCT
ejpam-1594	177	4	∈	∈	PROPN
ejpam-1594	177	5	n(r	n(r	NOUN
ejpam-1594	177	6	)	)	PUNCT
ejpam-1594	177	7	and	and	CCONJ
ejpam-1594	177	8	hence	hence	ADV
ejpam-1594	177	9	a	a	DET
ejpam-1594	177	10	∈	∈	NOUN
ejpam-1594	177	11	n(r	n(r	NOUN
ejpam-1594	177	12	)	)	PUNCT
ejpam-1594	177	13	.	.	PUNCT
ejpam-1594	178	1	so	so	ADV
ejpam-1594	178	2	n(r	n(r	NOUN
ejpam-1594	178	3	)	)	PUNCT
ejpam-1594	178	4	is	be	AUX
ejpam-1594	178	5	completely	completely	ADV
ejpam-1594	178	6	semiprime	semiprime	NOUN
ejpam-1594	178	7	.	.	PUNCT
ejpam-1594	179	1	converse	converse	NOUN
ejpam-1594	179	2	of	of	ADP
ejpam-1594	179	3	the	the	DET
ejpam-1594	179	4	above	above	ADJ
ejpam-1594	179	5	proposition	proposition	NOUN
ejpam-1594	179	6	need	need	AUX
ejpam-1594	179	7	not	not	PART
ejpam-1594	179	8	be	be	AUX
ejpam-1594	179	9	true	true	ADJ
ejpam-1594	179	10	(	(	PUNCT
ejpam-1594	179	11	example	example	NOUN
ejpam-1594	179	12	3	3	NUM
ejpam-1594	179	13	)	)	PUNCT
ejpam-1594	179	14	.	.	PUNCT
ejpam-1594	180	1	as	as	SCONJ
ejpam-1594	180	2	mentioned	mention	VERB
ejpam-1594	180	3	earlier	early	ADV
ejpam-1594	180	4	,	,	PUNCT
ejpam-1594	180	5	we	we	PRON
ejpam-1594	180	6	note	note	VERB
ejpam-1594	180	7	that	that	SCONJ
ejpam-1594	180	8	if	if	SCONJ
ejpam-1594	180	9	σ	σ	PROPN
ejpam-1594	180	10	is	be	AUX
ejpam-1594	180	11	an	an	DET
ejpam-1594	180	12	endomorphism	endomorphism	NOUN
ejpam-1594	180	13	of	of	ADP
ejpam-1594	180	14	a	a	DET
ejpam-1594	180	15	ring	ring	NOUN
ejpam-1594	180	16	r	r	NOUN
ejpam-1594	180	17	,	,	PUNCT
ejpam-1594	180	18	then	then	ADV
ejpam-1594	180	19	it	it	PRON
ejpam-1594	180	20	can	can	AUX
ejpam-1594	180	21	be	be	AUX
ejpam-1594	180	22	extended	extend	VERB
ejpam-1594	180	23	to	to	ADP
ejpam-1594	180	24	an	an	DET
ejpam-1594	180	25	endomorphism	endomorphism	PROPN
ejpam-1594	180	26	σ	σ	PROPN
ejpam-1594	180	27	of	of	ADP
ejpam-1594	180	28	s(r	s(r	PROPN
ejpam-1594	180	29	)	)	PUNCT
ejpam-1594	180	30	=	=	SYM
ejpam-1594	180	31	r[x	r[x	NOUN
ejpam-1594	180	32	;	;	PUNCT
ejpam-1594	180	33	σ	σ	PROPN
ejpam-1594	180	34	]	]	PUNCT
ejpam-1594	180	35	by	by	ADP
ejpam-1594	180	36	σ	σ	PROPN
ejpam-1594	180	37	(	(	PUNCT
ejpam-1594	180	38	∑m	∑m	PROPN
ejpam-1594	180	39	i=0	i=0	PROPN
ejpam-1594	180	40	x	x	X
ejpam-1594	180	41	iai	iai	ADJ
ejpam-1594	180	42	)	)	PUNCT
ejpam-1594	180	43	=	=	VERB
ejpam-1594	180	44	∑m	∑m	PROPN
ejpam-1594	180	45	i=0	i=0	PROPN
ejpam-1594	180	46	x	x	SYM
ejpam-1594	180	47	iσ(ai	iσ(ai	PROPN
ejpam-1594	180	48	)	)	PUNCT
ejpam-1594	180	49	.	.	PUNCT
ejpam-1594	181	1	we	we	PRON
ejpam-1594	181	2	now	now	ADV
ejpam-1594	181	3	prove	prove	VERB
ejpam-1594	181	4	the	the	DET
ejpam-1594	181	5	following	following	NOUN
ejpam-1594	181	6	:	:	PUNCT
ejpam-1594	181	7	references	reference	NOUN
ejpam-1594	181	8	64	64	NUM
ejpam-1594	181	9	theorem	theorem	NOUN
ejpam-1594	181	10	3	3	NUM
ejpam-1594	181	11	.	.	PUNCT
ejpam-1594	182	1	let	let	VERB
ejpam-1594	182	2	r	r	PRON
ejpam-1594	182	3	be	be	AUX
ejpam-1594	182	4	a	a	DET
ejpam-1594	182	5	noetherian	noetherian	ADJ
ejpam-1594	182	6	ring	ring	NOUN
ejpam-1594	182	7	.	.	PUNCT
ejpam-1594	183	1	let	let	VERB
ejpam-1594	183	2	σ	σ	NOUN
ejpam-1594	183	3	be	be	AUX
ejpam-1594	183	4	an	an	DET
ejpam-1594	183	5	automorphism	automorphism	NOUN
ejpam-1594	183	6	of	of	ADP
ejpam-1594	183	7	r.	r.	PROPN
ejpam-1594	183	8	then	then	ADV
ejpam-1594	183	9	r	r	NOUN
ejpam-1594	183	10	is	be	AUX
ejpam-1594	183	11	a	a	DET
ejpam-1594	183	12	weak	weak	ADJ
ejpam-1594	183	13	σ	σ	ADJ
ejpam-1594	183	14	-	-	ADJ
ejpam-1594	183	15	rigid	rigid	ADJ
ejpam-1594	183	16	ring	ring	NOUN
ejpam-1594	183	17	if	if	SCONJ
ejpam-1594	183	18	and	and	CCONJ
ejpam-1594	183	19	only	only	ADV
ejpam-1594	183	20	if	if	SCONJ
ejpam-1594	183	21	s(r	s(r	VERB
ejpam-1594	183	22	)	)	PUNCT
ejpam-1594	183	23	=	=	SYM
ejpam-1594	183	24	r[x	r[x	NOUN
ejpam-1594	183	25	;	;	PUNCT
ejpam-1594	184	1	σ	σ	PROPN
ejpam-1594	184	2	]	]	X
ejpam-1594	184	3	is	be	AUX
ejpam-1594	184	4	a	a	DET
ejpam-1594	184	5	weak	weak	ADJ
ejpam-1594	184	6	σ	σ	ADJ
ejpam-1594	184	7	-	-	ADJ
ejpam-1594	184	8	rigid	rigid	ADJ
ejpam-1594	184	9	ring	ring	NOUN
ejpam-1594	184	10	.	.	PUNCT
ejpam-1594	185	1	proof	proof	NOUN
ejpam-1594	185	2	.	.	PUNCT
ejpam-1594	186	1	first	first	ADV
ejpam-1594	186	2	of	of	ADP
ejpam-1594	186	3	all	all	PRON
ejpam-1594	186	4	we	we	PRON
ejpam-1594	186	5	note	note	VERB
ejpam-1594	186	6	that	that	SCONJ
ejpam-1594	186	7	proposition	proposition	NOUN
ejpam-1594	186	8	2.2	2.2	NUM
ejpam-1594	186	9	of	of	ADP
ejpam-1594	186	10	bhat	bhat	PROPN
ejpam-1594	186	11	[	[	X
ejpam-1594	186	12	4	4	NUM
ejpam-1594	186	13	]	]	PUNCT
ejpam-1594	186	14	implies	imply	VERB
ejpam-1594	186	15	that	that	SCONJ
ejpam-1594	186	16	s(n(r	s(n(r	NOUN
ejpam-1594	186	17	)	)	PUNCT
ejpam-1594	186	18	)	)	PUNCT
ejpam-1594	187	1	=	=	PUNCT
ejpam-1594	187	2	n(s(r	n(s(r	ADJ
ejpam-1594	187	3	)	)	PUNCT
ejpam-1594	187	4	)	)	PUNCT
ejpam-1594	187	5	.	.	PUNCT
ejpam-1594	188	1	now	now	ADV
ejpam-1594	188	2	let	let	VERB
ejpam-1594	188	3	r	r	NOUN
ejpam-1594	188	4	be	be	AUX
ejpam-1594	188	5	a	a	DET
ejpam-1594	188	6	weak	weak	ADJ
ejpam-1594	188	7	σ	σ	ADJ
ejpam-1594	188	8	-	-	ADJ
ejpam-1594	188	9	rigid	rigid	ADJ
ejpam-1594	188	10	ring	ring	NOUN
ejpam-1594	188	11	.	.	PUNCT
ejpam-1594	189	1	we	we	PRON
ejpam-1594	189	2	show	show	VERB
ejpam-1594	189	3	that	that	DET
ejpam-1594	189	4	r[x	r[x	NOUN
ejpam-1594	189	5	;	;	PUNCT
ejpam-1594	189	6	σ	σ	PROPN
ejpam-1594	189	7	]	]	X
ejpam-1594	189	8	is	be	AUX
ejpam-1594	189	9	a	a	DET
ejpam-1594	189	10	weak	weak	ADJ
ejpam-1594	189	11	σ	σ	ADJ
ejpam-1594	189	12	-	-	ADJ
ejpam-1594	189	13	rigid	rigid	ADJ
ejpam-1594	189	14	ring	ring	NOUN
ejpam-1594	189	15	.	.	PUNCT
ejpam-1594	190	1	let	let	VERB
ejpam-1594	190	2	f	f	PRON
ejpam-1594	190	3	∈	∈	PROPN
ejpam-1594	190	4	s(r	s(r	PROPN
ejpam-1594	190	5	)	)	PUNCT
ejpam-1594	190	6	(	(	PUNCT
ejpam-1594	190	7	say	say	VERB
ejpam-1594	190	8	f	f	PROPN
ejpam-1594	190	9	=	=	SYM
ejpam-1594	190	10	∑m	∑m	PROPN
ejpam-1594	190	11	i=0	i=0	PROPN
ejpam-1594	190	12	x	x	SYM
ejpam-1594	190	13	iai	iai	NOUN
ejpam-1594	190	14	)	)	PUNCT
ejpam-1594	190	15	be	be	VERB
ejpam-1594	190	16	such	such	ADJ
ejpam-1594	190	17	that	that	SCONJ
ejpam-1594	190	18	f	f	PROPN
ejpam-1594	190	19	σ	σ	PROPN
ejpam-1594	190	20	(	(	PUNCT
ejpam-1594	190	21	f	f	PROPN
ejpam-1594	190	22	)	)	PUNCT
ejpam-1594	190	23	∈	∈	PROPN
ejpam-1594	190	24	n(s(r	n(s(r	PROPN
ejpam-1594	190	25	)	)	PUNCT
ejpam-1594	190	26	)	)	PUNCT
ejpam-1594	190	27	.	.	PUNCT
ejpam-1594	191	1	we	we	PRON
ejpam-1594	191	2	use	use	VERB
ejpam-1594	191	3	induction	induction	NOUN
ejpam-1594	191	4	on	on	ADP
ejpam-1594	191	5	m	m	NOUN
ejpam-1594	191	6	to	to	PART
ejpam-1594	191	7	prove	prove	VERB
ejpam-1594	191	8	the	the	DET
ejpam-1594	191	9	theorem	theorem	NOUN
ejpam-1594	191	10	.	.	PROPN
ejpam-1594	192	1	for	for	ADP
ejpam-1594	192	2	m	m	PROPN
ejpam-1594	192	3	=	=	SYM
ejpam-1594	192	4	1	1	NUM
ejpam-1594	192	5	,	,	PUNCT
ejpam-1594	192	6	f	f	PROPN
ejpam-1594	192	7	=	=	PUNCT
ejpam-1594	192	8	xa1	xa1	PROPN
ejpam-1594	193	1	+	+	NUM
ejpam-1594	193	2	a0	a0	PROPN
ejpam-1594	193	3	.	.	PUNCT
ejpam-1594	194	1	now	now	ADV
ejpam-1594	194	2	f	f	PROPN
ejpam-1594	194	3	σ	σ	PROPN
ejpam-1594	194	4	(	(	PUNCT
ejpam-1594	194	5	f	f	PROPN
ejpam-1594	194	6	)	)	PUNCT
ejpam-1594	194	7	∈	∈	PROPN
ejpam-1594	194	8	n(s(r	n(s(r	PROPN
ejpam-1594	194	9	)	)	PUNCT
ejpam-1594	194	10	)	)	PUNCT
ejpam-1594	194	11	implies	imply	VERB
ejpam-1594	194	12	that	that	SCONJ
ejpam-1594	194	13	(	(	PUNCT
ejpam-1594	194	14	xa1	xa1	PROPN
ejpam-1594	194	15	+	+	PROPN
ejpam-1594	194	16	a0)(xσ(a1	a0)(xσ(a1	X
ejpam-1594	194	17	)	)	PUNCT
ejpam-1594	195	1	+	+	NOUN
ejpam-1594	195	2	σ(a0	σ(a0	X
ejpam-1594	195	3	)	)	PUNCT
ejpam-1594	195	4	)	)	PUNCT
ejpam-1594	196	1	∈	∈	PROPN
ejpam-1594	196	2	n(s(r	n(s(r	PROPN
ejpam-1594	196	3	)	)	PUNCT
ejpam-1594	196	4	)	)	PUNCT
ejpam-1594	197	1	=	=	SYM
ejpam-1594	197	2	s(n(r	s(n(r	NOUN
ejpam-1594	197	3	)	)	PUNCT
ejpam-1594	197	4	)	)	PUNCT
ejpam-1594	197	5	,	,	PUNCT
ejpam-1594	197	6	i.e.	i.e.	X
ejpam-1594	197	7	x2σ2(a1	x2σ2(a1	X
ejpam-1594	197	8	)	)	PUNCT
ejpam-1594	198	1	+	+	CCONJ
ejpam-1594	198	2	xσ(a0)σ(a1	xσ(a0)σ(a1	X
ejpam-1594	198	3	)	)	PUNCT
ejpam-1594	198	4	+	+	CCONJ
ejpam-1594	198	5	xa1σ(a0	xa1σ(a0	X
ejpam-1594	198	6	)	)	PUNCT
ejpam-1594	198	7	+	+	CCONJ
ejpam-1594	198	8	a0σ(a0	a0σ(a0	X
ejpam-1594	198	9	)	)	PUNCT
ejpam-1594	198	10	∈	∈	PROPN
ejpam-1594	198	11	s(n(r	s(n(r	NOUN
ejpam-1594	198	12	)	)	PUNCT
ejpam-1594	198	13	)	)	PUNCT
ejpam-1594	199	1	(	(	PUNCT
ejpam-1594	199	2	1	1	X
ejpam-1594	199	3	)	)	PUNCT
ejpam-1594	199	4	therefore	therefore	ADV
ejpam-1594	199	5	,	,	PUNCT
ejpam-1594	199	6	σ2(a1	σ2(a1	ADJ
ejpam-1594	199	7	)	)	PUNCT
ejpam-1594	199	8	∈	∈	PROPN
ejpam-1594	199	9	n(r	n(r	NOUN
ejpam-1594	199	10	)	)	PUNCT
ejpam-1594	199	11	.	.	PUNCT
ejpam-1594	200	1	now	now	ADV
ejpam-1594	200	2	σ(n(r	σ(n(r	NUM
ejpam-1594	200	3	)	)	PUNCT
ejpam-1594	200	4	)	)	PUNCT
ejpam-1594	201	1	=	=	SYM
ejpam-1594	201	2	n(r	n(r	NOUN
ejpam-1594	201	3	)	)	PUNCT
ejpam-1594	201	4	implies	imply	VERB
ejpam-1594	201	5	that	that	SCONJ
ejpam-1594	201	6	a1	a1	NOUN
ejpam-1594	201	7	∈	∈	PROPN
ejpam-1594	201	8	n(r	n(r	NOUN
ejpam-1594	201	9	)	)	PUNCT
ejpam-1594	201	10	.	.	PUNCT
ejpam-1594	202	1	so	so	ADV
ejpam-1594	202	2	(	(	PUNCT
ejpam-1594	202	3	1	1	X
ejpam-1594	202	4	)	)	PUNCT
ejpam-1594	202	5	implies	imply	VERB
ejpam-1594	202	6	that	that	SCONJ
ejpam-1594	202	7	a0σ(a0	a0σ(a0	VERB
ejpam-1594	202	8	)	)	PUNCT
ejpam-1594	202	9	∈	∈	PROPN
ejpam-1594	202	10	n(r	n(r	NOUN
ejpam-1594	202	11	)	)	PUNCT
ejpam-1594	202	12	implies	imply	VERB
ejpam-1594	202	13	that	that	SCONJ
ejpam-1594	202	14	a0	a0	PROPN
ejpam-1594	202	15	∈	∈	PROPN
ejpam-1594	202	16	n(r	n(r	PROPN
ejpam-1594	202	17	)	)	PUNCT
ejpam-1594	202	18	.	.	PUNCT
ejpam-1594	203	1	therefore	therefore	ADV
ejpam-1594	203	2	,	,	PUNCT
ejpam-1594	203	3	f	f	PROPN
ejpam-1594	203	4	∈	∈	PROPN
ejpam-1594	203	5	s(n(r	s(n(r	NOUN
ejpam-1594	203	6	)	)	PUNCT
ejpam-1594	203	7	)	)	PUNCT
ejpam-1594	204	1	=	=	PUNCT
ejpam-1594	204	2	n(s(r	n(s(r	ADJ
ejpam-1594	204	3	)	)	PUNCT
ejpam-1594	204	4	)	)	PUNCT
ejpam-1594	204	5	.	.	PUNCT
ejpam-1594	205	1	suppose	suppose	VERB
ejpam-1594	205	2	the	the	DET
ejpam-1594	205	3	result	result	NOUN
ejpam-1594	205	4	is	be	AUX
ejpam-1594	205	5	true	true	ADJ
ejpam-1594	205	6	for	for	ADP
ejpam-1594	205	7	m	m	PROPN
ejpam-1594	206	1	=	=	PUNCT
ejpam-1594	206	2	k.	k.	NOUN
ejpam-1594	206	3	we	we	PRON
ejpam-1594	206	4	prove	prove	VERB
ejpam-1594	206	5	for	for	ADP
ejpam-1594	206	6	m	m	PROPN
ejpam-1594	207	1	=	=	SYM
ejpam-1594	207	2	k	k	PROPN
ejpam-1594	208	1	+	+	NOUN
ejpam-1594	208	2	1	1	X
ejpam-1594	208	3	.	.	PUNCT
ejpam-1594	208	4	now	now	ADV
ejpam-1594	208	5	f	f	PROPN
ejpam-1594	208	6	σ	σ	PROPN
ejpam-1594	208	7	(	(	PUNCT
ejpam-1594	208	8	f	f	PROPN
ejpam-1594	208	9	)	)	PUNCT
ejpam-1594	208	10	∈	∈	PROPN
ejpam-1594	208	11	n(s(r	n(s(r	PROPN
ejpam-1594	208	12	)	)	PUNCT
ejpam-1594	208	13	)	)	PUNCT
ejpam-1594	208	14	implies	imply	VERB
ejpam-1594	208	15	that	that	SCONJ
ejpam-1594	208	16	(	(	PUNCT
ejpam-1594	208	17	x	x	X
ejpam-1594	208	18	k+1ak+1	k+1ak+1	NOUN
ejpam-1594	208	19	+	+	X
ejpam-1594	208	20	.	.	PUNCT
ejpam-1594	208	21	.	.	PUNCT
ejpam-1594	209	1	.+	.+	NOUN
ejpam-1594	209	2	a0)(x	a0)(x	PROPN
ejpam-1594	209	3	k+1σ(ak+1	k+1σ(ak+1	PROPN
ejpam-1594	209	4	)	)	PUNCT
ejpam-1594	210	1	+	+	CCONJ
ejpam-1594	210	2	ldots+σ(a0	ldots+σ(a0	VERB
ejpam-1594	210	3	)	)	PUNCT
ejpam-1594	210	4	)	)	PUNCT
ejpam-1594	211	1	∈	∈	PROPN
ejpam-1594	211	2	n(s(r	n(s(r	PROPN
ejpam-1594	211	3	)	)	PUNCT
ejpam-1594	211	4	)	)	PUNCT
ejpam-1594	212	1	=	=	SYM
ejpam-1594	212	2	s(n(r	s(n(r	NOUN
ejpam-1594	212	3	)	)	PUNCT
ejpam-1594	212	4	)	)	PUNCT
ejpam-1594	212	5	,	,	PUNCT
ejpam-1594	212	6	i.e.	i.e.	X
ejpam-1594	212	7	x2k+2σk+2(ak+1	x2k+2σk+2(ak+1	X
ejpam-1594	212	8	)	)	PUNCT
ejpam-1594	212	9	+	+	CCONJ
ejpam-1594	212	10	x2k+1(σk(ak+1)σ(ak	x2k+1(σk(ak+1)σ(ak	X
ejpam-1594	212	11	)	)	PUNCT
ejpam-1594	213	1	+	+	NOUN
ejpam-1594	213	2	σ	σ	PROPN
ejpam-1594	213	3	k+1(ak)σ(ak+1	k+1(ak)σ(ak+1	NOUN
ejpam-1594	213	4	)	)	PUNCT
ejpam-1594	213	5	)	)	PUNCT
ejpam-1594	214	1	+	+	CCONJ
ejpam-1594	214	2	gσ(g	gσ(g	X
ejpam-1594	214	3	)	)	PUNCT
ejpam-1594	214	4	∈	∈	PROPN
ejpam-1594	214	5	s(n(r	s(n(r	NOUN
ejpam-1594	214	6	)	)	PUNCT
ejpam-1594	214	7	)	)	PUNCT
ejpam-1594	214	8	,	,	PUNCT
ejpam-1594	214	9	where	where	SCONJ
ejpam-1594	214	10	g	g	PROPN
ejpam-1594	214	11	=	=	PROPN
ejpam-1594	214	12	∑k	∑k	PROPN
ejpam-1594	214	13	i=0	i=0	PROPN
ejpam-1594	214	14	x	x	SYM
ejpam-1594	214	15	iai	iai	PROPN
ejpam-1594	214	16	.	.	PUNCT
ejpam-1594	215	1	therefore	therefore	ADV
ejpam-1594	215	2	,	,	PUNCT
ejpam-1594	215	3	σk+2(ak+1	σk+2(ak+1	X
ejpam-1594	215	4	)	)	PUNCT
ejpam-1594	215	5	∈	∈	PROPN
ejpam-1594	215	6	n(r	n(r	NOUN
ejpam-1594	215	7	)	)	PUNCT
ejpam-1594	215	8	implies	imply	VERB
ejpam-1594	215	9	that	that	SCONJ
ejpam-1594	215	10	ak+1	ak+1	VERB
ejpam-1594	215	11	∈	∈	PROPN
ejpam-1594	215	12	n(r	n(r	NOUN
ejpam-1594	215	13	)	)	PUNCT
ejpam-1594	215	14	.	.	PUNCT
ejpam-1594	216	1	alsoσk(ak+1)σ(ak)+	alsoσk(ak+1)σ(ak)+	PROPN
ejpam-1594	216	2	σk+1(ak)σ(ak+1	σk+1(ak)σ(ak+1	VERB
ejpam-1594	216	3	)	)	PUNCT
ejpam-1594	216	4	∈	∈	PROPN
ejpam-1594	216	5	n(r	n(r	NOUN
ejpam-1594	216	6	)	)	PUNCT
ejpam-1594	216	7	implies	imply	VERB
ejpam-1594	216	8	that	that	SCONJ
ejpam-1594	216	9	gσ(g	gσ(g	NOUN
ejpam-1594	216	10	)	)	PUNCT
ejpam-1594	216	11	∈	∈	PROPN
ejpam-1594	216	12	n(s(r	n(s(r	PROPN
ejpam-1594	216	13	)	)	PUNCT
ejpam-1594	216	14	)	)	PUNCT
ejpam-1594	216	15	,	,	PUNCT
ejpam-1594	216	16	but	but	CCONJ
ejpam-1594	216	17	the	the	DET
ejpam-1594	216	18	degree	degree	NOUN
ejpam-1594	216	19	of	of	ADP
ejpam-1594	216	20	g	g	PROPN
ejpam-1594	216	21	is	be	AUX
ejpam-1594	216	22	k	k	PROPN
ejpam-1594	216	23	,	,	PUNCT
ejpam-1594	216	24	therefore	therefore	ADV
ejpam-1594	216	25	,	,	PUNCT
ejpam-1594	216	26	by	by	ADP
ejpam-1594	216	27	induction	induction	NOUN
ejpam-1594	216	28	hypothesis	hypothesis	NOUN
ejpam-1594	216	29	,	,	PUNCT
ejpam-1594	216	30	the	the	DET
ejpam-1594	216	31	result	result	NOUN
ejpam-1594	216	32	is	be	AUX
ejpam-1594	216	33	true	true	ADJ
ejpam-1594	216	34	for	for	SCONJ
ejpam-1594	216	35	all	all	DET
ejpam-1594	216	36	m.	m.	NOUN
ejpam-1594	216	37	converse	converse	NOUN
ejpam-1594	216	38	is	be	AUX
ejpam-1594	216	39	obvious	obvious	ADJ
ejpam-1594	216	40	.	.	PUNCT
ejpam-1594	217	1	references	reference	NOUN
ejpam-1594	217	2	[	[	X
ejpam-1594	217	3	1	1	X
ejpam-1594	217	4	]	]	PUNCT
ejpam-1594	217	5	s.	s.	PROPN
ejpam-1594	217	6	annin	annin	PROPN
ejpam-1594	217	7	.	.	PUNCT
ejpam-1594	218	1	associated	associate	VERB
ejpam-1594	218	2	primes	prime	NOUN
ejpam-1594	218	3	over	over	ADP
ejpam-1594	218	4	skew	skew	ADJ
ejpam-1594	218	5	polynomial	polynomial	ADJ
ejpam-1594	218	6	rings	ring	NOUN
ejpam-1594	218	7	,	,	PUNCT
ejpam-1594	218	8	communications	communication	NOUN
ejpam-1594	218	9	in	in	ADP
ejpam-1594	218	10	algebra	algebra	NOUN
ejpam-1594	218	11	,	,	PUNCT
ejpam-1594	218	12	vol	vol	NOUN
ejpam-1594	218	13	.	.	PUNCT
ejpam-1594	218	14	30(5	30(5	NUM
ejpam-1594	218	15	)	)	PUNCT
ejpam-1594	218	16	,	,	PUNCT
ejpam-1594	218	17	2511	2511	NUM
ejpam-1594	218	18	-	-	SYM
ejpam-1594	218	19	2528	2528	NUM
ejpam-1594	218	20	.	.	PUNCT
ejpam-1594	219	1	2002	2002	NUM
ejpam-1594	219	2	.	.	PUNCT
ejpam-1594	220	1	[	[	X
ejpam-1594	220	2	2	2	X
ejpam-1594	220	3	]	]	PUNCT
ejpam-1594	220	4	v.	v.	PROPN
ejpam-1594	220	5	k.	k.	PROPN
ejpam-1594	220	6	bhat	bhat	PROPN
ejpam-1594	220	7	.	.	PUNCT
ejpam-1594	221	1	associated	associate	VERB
ejpam-1594	221	2	prime	prime	ADJ
ejpam-1594	221	3	ideals	ideal	NOUN
ejpam-1594	221	4	of	of	ADP
ejpam-1594	221	5	skew	skew	ADJ
ejpam-1594	221	6	polynomial	polynomial	ADJ
ejpam-1594	221	7	rings	ring	NOUN
ejpam-1594	221	8	,	,	PUNCT
ejpam-1594	221	9	beitrage	beitrage	NOUN
ejpam-1594	221	10	algebra	algebra	NOUN
ejpam-1594	221	11	geometry	geometry	NOUN
ejpam-1594	221	12	,	,	PUNCT
ejpam-1594	221	13	vol	vol	NOUN
ejpam-1594	221	14	.	.	PUNCT
ejpam-1594	221	15	49(1	49(1	NUM
ejpam-1594	221	16	)	)	PUNCT
ejpam-1594	221	17	,	,	PUNCT
ejpam-1594	221	18	277	277	NUM
ejpam-1594	221	19	-	-	SYM
ejpam-1594	221	20	283	283	NUM
ejpam-1594	221	21	.	.	PUNCT
ejpam-1594	221	22	2008	2008	NUM
ejpam-1594	221	23	.	.	PUNCT
ejpam-1594	222	1	[	[	X
ejpam-1594	222	2	3	3	X
ejpam-1594	222	3	]	]	PUNCT
ejpam-1594	222	4	v.	v.	PROPN
ejpam-1594	222	5	k.	k.	PROPN
ejpam-1594	222	6	bhat	bhat	PROPN
ejpam-1594	222	7	and	and	CCONJ
ejpam-1594	222	8	n.	n.	PROPN
ejpam-1594	222	9	kumari	kumari	PROPN
ejpam-1594	222	10	.	.	PUNCT
ejpam-1594	223	1	transparency	transparency	NOUN
ejpam-1594	223	2	of	of	ADP
ejpam-1594	223	3	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1594	223	4	and	and	CCONJ
ejpam-1594	223	5	their	their	PRON
ejpam-1594	223	6	extensions	extension	NOUN
ejpam-1594	223	7	,	,	PUNCT
ejpam-1594	223	8	international	international	ADJ
ejpam-1594	223	9	journal	journal	NOUN
ejpam-1594	223	10	of	of	ADP
ejpam-1594	223	11	algebra	algebra	PROPN
ejpam-1594	223	12	,	,	PUNCT
ejpam-1594	223	13	vol	vol	NOUN
ejpam-1594	223	14	.	.	PUNCT
ejpam-1594	223	15	2(19	2(19	NUM
ejpam-1594	223	16	)	)	PUNCT
ejpam-1594	223	17	,	,	PUNCT
ejpam-1594	223	18	919	919	NUM
ejpam-1594	223	19	924	924	NUM
ejpam-1594	223	20	.	.	SYM
ejpam-1594	223	21	2008	2008	NUM
ejpam-1594	223	22	.	.	PUNCT
ejpam-1594	224	1	[	[	X
ejpam-1594	224	2	4	4	X
ejpam-1594	224	3	]	]	PUNCT
ejpam-1594	224	4	v.	v.	PROPN
ejpam-1594	224	5	k.	k.	PROPN
ejpam-1594	224	6	bhat	bhat	PROPN
ejpam-1594	224	7	and	and	CCONJ
ejpam-1594	224	8	r.	r.	PROPN
ejpam-1594	224	9	raina	raina	PROPN
ejpam-1594	224	10	.	.	PUNCT
ejpam-1594	225	1	ore	ore	NOUN
ejpam-1594	225	2	extensions	extension	NOUN
ejpam-1594	225	3	over	over	ADP
ejpam-1594	225	4	2	2	NUM
ejpam-1594	225	5	-	-	PUNCT
ejpam-1594	225	6	primal	primal	ADJ
ejpam-1594	225	7	rings	ring	NOUN
ejpam-1594	225	8	,	,	PUNCT
ejpam-1594	225	9	vietnam	vietnam	PROPN
ejpam-1594	225	10	journal	journal	NOUN
ejpam-1594	225	11	of	of	ADP
ejpam-1594	225	12	mathematics	mathematics	PROPN
ejpam-1594	225	13	,	,	PUNCT
ejpam-1594	225	14	vol	vol	NOUN
ejpam-1594	225	15	.	.	PROPN
ejpam-1594	225	16	36(4	36(4	NUM
ejpam-1594	225	17	)	)	PUNCT
ejpam-1594	225	18	,	,	PUNCT
ejpam-1594	225	19	455	455	NUM
ejpam-1594	225	20	-	-	SYM
ejpam-1594	225	21	461	461	NUM
ejpam-1594	225	22	.	.	PUNCT
ejpam-1594	225	23	2008	2008	NUM
ejpam-1594	225	24	.	.	PUNCT
ejpam-1594	226	1	[	[	X
ejpam-1594	226	2	5	5	X
ejpam-1594	226	3	]	]	PUNCT
ejpam-1594	226	4	w.	w.	PROPN
ejpam-1594	226	5	d.	d.	PROPN
ejpam-1594	226	6	blair	blair	PROPN
ejpam-1594	226	7	and	and	CCONJ
ejpam-1594	226	8	l.w	l.w	PROPN
ejpam-1594	226	9	.	.	PROPN
ejpam-1594	226	10	small	small	ADJ
ejpam-1594	226	11	.	.	PUNCT
ejpam-1594	227	1	embedding	embed	VERB
ejpam-1594	227	2	differential	differential	NOUN
ejpam-1594	227	3	and	and	CCONJ
ejpam-1594	227	4	skew	skew	ADJ
ejpam-1594	227	5	polynomial	polynomial	ADJ
ejpam-1594	227	6	rings	ring	NOUN
ejpam-1594	227	7	into	into	ADP
ejpam-1594	227	8	artinian	artinian	ADJ
ejpam-1594	227	9	rings	ring	NOUN
ejpam-1594	227	10	,	,	PUNCT
ejpam-1594	227	11	proceedings	proceeding	NOUN
ejpam-1594	227	12	of	of	ADP
ejpam-1594	227	13	the	the	DET
ejpam-1594	227	14	american	american	PROPN
ejpam-1594	227	15	mathematical	mathematical	PROPN
ejpam-1594	227	16	society	society	NOUN
ejpam-1594	227	17	,	,	PUNCT
ejpam-1594	227	18	vol	vol	NOUN
ejpam-1594	227	19	.	.	PROPN
ejpam-1594	228	1	109	109	NUM
ejpam-1594	228	2	(	(	PUNCT
ejpam-1594	228	3	4	4	NUM
ejpam-1594	228	4	)	)	PUNCT
ejpam-1594	228	5	,	,	PUNCT
ejpam-1594	228	6	881886	881886	NUM
ejpam-1594	228	7	.	.	PUNCT
ejpam-1594	229	1	1990	1990	NUM
ejpam-1594	229	2	.	.	PUNCT
ejpam-1594	230	1	[	[	X
ejpam-1594	230	2	6	6	NUM
ejpam-1594	230	3	]	]	PUNCT
ejpam-1594	230	4	c.	c.	NOUN
ejpam-1594	230	5	faith	faith	NOUN
ejpam-1594	230	6	.	.	PUNCT
ejpam-1594	231	1	associated	associate	VERB
ejpam-1594	231	2	primes	prime	NOUN
ejpam-1594	231	3	in	in	ADP
ejpam-1594	231	4	commutative	commutative	ADJ
ejpam-1594	231	5	polynomial	polynomial	ADJ
ejpam-1594	231	6	rings	ring	NOUN
ejpam-1594	231	7	,	,	PUNCT
ejpam-1594	231	8	communications	communication	NOUN
ejpam-1594	231	9	in	in	ADP
ejpam-1594	231	10	algebra	algebra	NOUN
ejpam-1594	231	11	,	,	PUNCT
ejpam-1594	231	12	vol	vol	NOUN
ejpam-1594	231	13	.	.	PROPN
ejpam-1594	231	14	28	28	NUM
ejpam-1594	231	15	,	,	PUNCT
ejpam-1594	231	16	3983	3983	NUM
ejpam-1594	231	17	-	-	SYM
ejpam-1594	231	18	3986	3986	NUM
ejpam-1594	231	19	.	.	PUNCT
ejpam-1594	232	1	2000	2000	NUM
ejpam-1594	232	2	.	.	PUNCT
ejpam-1594	233	1	[	[	X
ejpam-1594	233	2	7	7	X
ejpam-1594	233	3	]	]	PUNCT
ejpam-1594	233	4	k.	k.	PROPN
ejpam-1594	233	5	r.	r.	PROPN
ejpam-1594	233	6	goodearl	goodearl	PROPN
ejpam-1594	233	7	and	and	CCONJ
ejpam-1594	233	8	r.b	r.b	PROPN
ejpam-1594	233	9	.	.	PROPN
ejpam-1594	233	10	warfield	warfield	PROPN
ejpam-1594	233	11	.	.	PUNCT
ejpam-1594	234	1	an	an	DET
ejpam-1594	234	2	introduction	introduction	NOUN
ejpam-1594	234	3	to	to	ADP
ejpam-1594	234	4	non	non	ADJ
ejpam-1594	234	5	-	-	ADJ
ejpam-1594	234	6	commutative	commutative	ADJ
ejpam-1594	234	7	noetherian	noetherian	ADJ
ejpam-1594	234	8	rings	ring	NOUN
ejpam-1594	234	9	,	,	PUNCT
ejpam-1594	234	10	camb	camb	PROPN
ejpam-1594	234	11	.	.	PUNCT
ejpam-1594	235	1	uni	uni	PROPN
ejpam-1594	235	2	.	.	PUNCT
ejpam-1594	235	3	press	press	PROPN
ejpam-1594	235	4	,	,	PUNCT
ejpam-1594	235	5	1989	1989	NUM
ejpam-1594	235	6	.	.	PUNCT
ejpam-1594	236	1	references	reference	NOUN
ejpam-1594	236	2	65	65	NUM
ejpam-1594	237	1	[	[	X
ejpam-1594	237	2	8	8	NUM
ejpam-1594	237	3	]	]	PUNCT
ejpam-1594	237	4	k.	k.	PROPN
ejpam-1594	237	5	r.	r.	PROPN
ejpam-1594	237	6	goodearl	goodearl	PROPN
ejpam-1594	237	7	and	and	CCONJ
ejpam-1594	237	8	e.	e.	PROPN
ejpam-1594	237	9	s.	s.	PROPN
ejpam-1594	237	10	letzter	letzter	PROPN
ejpam-1594	237	11	.	.	PUNCT
ejpam-1594	238	1	prime	prime	ADJ
ejpam-1594	238	2	ideals	ideal	NOUN
ejpam-1594	238	3	in	in	ADP
ejpam-1594	238	4	skew	skew	ADJ
ejpam-1594	238	5	and	and	CCONJ
ejpam-1594	238	6	q	q	ADJ
ejpam-1594	238	7	-	-	PUNCT
ejpam-1594	238	8	skew	skew	ADJ
ejpam-1594	238	9	polynomial	polynomial	ADJ
ejpam-1594	238	10	rings	ring	NOUN
ejpam-1594	238	11	,	,	PUNCT
ejpam-1594	238	12	memoirs	memoir	NOUN
ejpam-1594	238	13	of	of	ADP
ejpam-1594	238	14	the	the	DET
ejpam-1594	238	15	american	american	PROPN
ejpam-1594	238	16	mathematical	mathematical	PROPN
ejpam-1594	238	17	society	society	NOUN
ejpam-1594	238	18	,	,	PUNCT
ejpam-1594	238	19	521	521	NUM
ejpam-1594	238	20	,	,	PUNCT
ejpam-1594	238	21	1994	1994	NUM
ejpam-1594	238	22	.	.	PUNCT
ejpam-1594	239	1	[	[	X
ejpam-1594	239	2	9	9	X
ejpam-1594	239	3	]	]	PUNCT
ejpam-1594	239	4	j.	j.	PROPN
ejpam-1594	239	5	krempa	krempa	PROPN
ejpam-1594	239	6	.	.	PUNCT
ejpam-1594	240	1	some	some	DET
ejpam-1594	240	2	examples	example	NOUN
ejpam-1594	240	3	of	of	ADP
ejpam-1594	240	4	reduced	reduce	VERB
ejpam-1594	240	5	rings	ring	NOUN
ejpam-1594	240	6	,	,	PUNCT
ejpam-1594	240	7	algebra	algebra	NOUN
ejpam-1594	240	8	colloquium	colloquium	NOUN
ejpam-1594	240	9	,	,	PUNCT
ejpam-1594	240	10	vol	vol	NOUN
ejpam-1594	240	11	.	.	PUNCT
ejpam-1594	240	12	3(4	3(4	NUM
ejpam-1594	240	13	)	)	PUNCT
ejpam-1594	240	14	,	,	PUNCT
ejpam-1594	240	15	289	289	NUM
ejpam-1594	240	16	-	-	SYM
ejpam-1594	240	17	300	300	NUM
ejpam-1594	240	18	.	.	PUNCT
ejpam-1594	240	19	1996	1996	NUM
ejpam-1594	240	20	.	.	PUNCT
ejpam-1594	241	1	[	[	X
ejpam-1594	241	2	10	10	NUM
ejpam-1594	241	3	]	]	PUNCT
ejpam-1594	241	4	t.	t.	PROPN
ejpam-1594	241	5	k.	k.	PROPN
ejpam-1594	241	6	kwak	kwak	PROPN
ejpam-1594	241	7	.	.	PUNCT
ejpam-1594	242	1	prime	prime	ADJ
ejpam-1594	242	2	radicals	radical	NOUN
ejpam-1594	242	3	of	of	ADP
ejpam-1594	242	4	skew	skew	ADJ
ejpam-1594	242	5	-	-	PUNCT
ejpam-1594	242	6	polynomial	polynomial	ADJ
ejpam-1594	242	7	rings	ring	NOUN
ejpam-1594	242	8	,	,	PUNCT
ejpam-1594	242	9	international	international	ADJ
ejpam-1594	242	10	journal	journal	NOUN
ejpam-1594	242	11	of	of	ADP
ejpam-1594	242	12	mathematical	mathematical	ADJ
ejpam-1594	242	13	sciences	sciences	PROPN
ejpam-1594	242	14	,	,	PUNCT
ejpam-1594	242	15	vol	vol	NOUN
ejpam-1594	242	16	.	.	PROPN
ejpam-1594	242	17	2(2	2(2	NUM
ejpam-1594	242	18	)	)	PUNCT
ejpam-1594	242	19	,	,	PUNCT
ejpam-1594	242	20	219	219	NUM
ejpam-1594	242	21	-	-	SYM
ejpam-1594	242	22	227	227	NUM
ejpam-1594	242	23	.	.	PUNCT
ejpam-1594	242	24	2003	2003	NUM
ejpam-1594	242	25	.	.	PUNCT
ejpam-1594	243	1	[	[	X
ejpam-1594	243	2	11	11	NUM
ejpam-1594	243	3	]	]	PUNCT
ejpam-1594	243	4	a.	a.	PROPN
ejpam-1594	243	5	leroy	leroy	PROPN
ejpam-1594	243	6	and	and	CCONJ
ejpam-1594	243	7	j.	j.	PROPN
ejpam-1594	243	8	matczuk	matczuk	PROPN
ejpam-1594	243	9	.	.	PUNCT
ejpam-1594	244	1	on	on	ADP
ejpam-1594	244	2	induced	induced	ADJ
ejpam-1594	244	3	modules	module	NOUN
ejpam-1594	244	4	over	over	ADP
ejpam-1594	244	5	ore	ore	NOUN
ejpam-1594	244	6	extensions	extension	NOUN
ejpam-1594	244	7	,	,	PUNCT
ejpam-1594	244	8	communications	communication	NOUN
ejpam-1594	244	9	in	in	ADP
ejpam-1594	244	10	algebra	algebra	NOUN
ejpam-1594	244	11	,	,	PUNCT
ejpam-1594	244	12	vol	vol	NOUN
ejpam-1594	244	13	.	.	PUNCT
ejpam-1594	244	14	32(7	32(7	NOUN
ejpam-1594	244	15	)	)	PUNCT
ejpam-1594	244	16	,	,	PUNCT
ejpam-1594	244	17	2743	2743	NUM
ejpam-1594	244	18	-	-	SYM
ejpam-1594	244	19	2766	2766	NUM
ejpam-1594	244	20	.	.	PUNCT
ejpam-1594	244	21	2004	2004	NUM
ejpam-1594	244	22	.	.	PUNCT
ejpam-1594	245	1	[	[	X
ejpam-1594	245	2	12	12	NUM
ejpam-1594	245	3	]	]	PUNCT
ejpam-1594	245	4	j.	j.	PROPN
ejpam-1594	245	5	c.	c.	PROPN
ejpam-1594	245	6	mcconnell	mcconnell	PROPN
ejpam-1594	245	7	and	and	CCONJ
ejpam-1594	245	8	j.	j.	PROPN
ejpam-1594	245	9	c.	c.	PROPN
ejpam-1594	245	10	robson	robson	PROPN
ejpam-1594	245	11	.	.	PUNCT
ejpam-1594	246	1	noncommutative	noncommutative	ADJ
ejpam-1594	246	2	noetherian	noetherian	ADJ
ejpam-1594	246	3	rings	ring	NOUN
ejpam-1594	246	4	,	,	PUNCT
ejpam-1594	246	5	wiley	wiley	NOUN
ejpam-1594	246	6	(	(	PUNCT
ejpam-1594	246	7	1987	1987	NUM
ejpam-1594	246	8	)	)	PUNCT
ejpam-1594	246	9	;	;	PUNCT
ejpam-1594	246	10	revised	revise	VERB
ejpam-1594	246	11	edition	edition	NOUN
ejpam-1594	246	12	:	:	PUNCT
ejpam-1594	246	13	american	american	PROPN
ejpam-1594	246	14	mathematical	mathematical	PROPN
ejpam-1594	246	15	society	society	NOUN
ejpam-1594	246	16	(	(	PUNCT
ejpam-1594	246	17	2001	2001	NUM
ejpam-1594	246	18	)	)	PUNCT
ejpam-1594	246	19	.	.	PUNCT
ejpam-1594	247	1	[	[	X
ejpam-1594	247	2	13	13	NUM
ejpam-1594	247	3	]	]	X
ejpam-1594	247	4	h.	h.	PROPN
ejpam-1594	247	5	e.	e.	PROPN
ejpam-1594	247	6	nordstorm	nordstorm	PROPN
ejpam-1594	247	7	.	.	PUNCT
ejpam-1594	248	1	associated	associate	VERB
ejpam-1594	248	2	primes	prime	NOUN
ejpam-1594	248	3	over	over	ADP
ejpam-1594	248	4	ore	ore	NOUN
ejpam-1594	248	5	extensions	extension	NOUN
ejpam-1594	248	6	,	,	PUNCT
ejpam-1594	248	7	journal	journal	NOUN
ejpam-1594	248	8	of	of	ADP
ejpam-1594	248	9	algebra	algebra	PROPN
ejpam-1594	248	10	,	,	PUNCT
ejpam-1594	248	11	vol	vol	NOUN
ejpam-1594	248	12	.	.	PUNCT
ejpam-1594	248	13	286(1	286(1	NUM
ejpam-1594	248	14	)	)	PUNCT
ejpam-1594	248	15	,	,	PUNCT
ejpam-1594	248	16	69	69	NUM
ejpam-1594	248	17	-	-	SYM
ejpam-1594	248	18	75	75	NUM
ejpam-1594	248	19	.	.	PUNCT
ejpam-1594	248	20	2005	2005	NUM
ejpam-1594	248	21	.	.	PUNCT
ejpam-1594	249	1	[	[	X
ejpam-1594	249	2	14	14	NUM
ejpam-1594	249	3	]	]	X
ejpam-1594	249	4	l.	l.	PROPN
ejpam-1594	249	5	ouyang	ouyang	PROPN
ejpam-1594	249	6	.	.	PUNCT
ejpam-1594	250	1	extensions	extension	NOUN
ejpam-1594	250	2	of	of	ADP
ejpam-1594	250	3	generalized	generalized	ADJ
ejpam-1594	250	4	α	α	ADJ
ejpam-1594	250	5	-	-	ADJ
ejpam-1594	250	6	rigid	rigid	ADJ
ejpam-1594	250	7	rings	ring	NOUN
ejpam-1594	250	8	,	,	PUNCT
ejpam-1594	250	9	international	international	ADJ
ejpam-1594	250	10	electronic	electronic	ADJ
ejpam-1594	250	11	journal	journal	NOUN
ejpam-1594	250	12	of	of	ADP
ejpam-1594	250	13	algebra	algebra	PROPN
ejpam-1594	250	14	,	,	PUNCT
ejpam-1594	250	15	vol	vol	NOUN
ejpam-1594	250	16	.	.	PROPN
ejpam-1594	250	17	3	3	NUM
ejpam-1594	250	18	,	,	PUNCT
ejpam-1594	250	19	103	103	NUM
ejpam-1594	250	20	-	-	SYM
ejpam-1594	250	21	116	116	NUM
ejpam-1594	250	22	.	.	PUNCT
ejpam-1594	250	23	2008	2008	NUM
ejpam-1594	250	24	.	.	PUNCT