id	sid	tid	token	lemma	pos
ejpam-1829	1	1	european	european	PROPN
ejpam-1829	1	2	journal	journal	PROPN
ejpam-1829	1	3	of	of	ADP
ejpam-1829	1	4	pure	pure	ADJ
ejpam-1829	1	5	and	and	CCONJ
ejpam-1829	1	6	applied	apply	VERB
ejpam-1829	1	7	mathematics	mathematic	NOUN
ejpam-1829	1	8	vol	vol	NOUN
ejpam-1829	1	9	.	.	PUNCT
ejpam-1829	2	1	7	7	NUM
ejpam-1829	2	2	,	,	PUNCT
ejpam-1829	2	3	no	no	INTJ
ejpam-1829	2	4	.	.	NOUN
ejpam-1829	2	5	4	4	NUM
ejpam-1829	2	6	,	,	PUNCT
ejpam-1829	2	7	2014	2014	NUM
ejpam-1829	2	8	,	,	PUNCT
ejpam-1829	2	9	387	387	NUM
ejpam-1829	2	10	-	-	SYM
ejpam-1829	2	11	394	394	NUM
ejpam-1829	2	12	issn	issn	PROPN
ejpam-1829	2	13	1307	1307	NUM
ejpam-1829	2	14	-	-	SYM
ejpam-1829	2	15	5543	5543	NUM
ejpam-1829	2	16	–	–	PUNCT
ejpam-1829	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1829	2	18	skew	skew	NOUN
ejpam-1829	2	19	-	-	PUNCT
ejpam-1829	2	20	laurent	laurent	NOUN
ejpam-1829	2	21	rings	ring	NOUN
ejpam-1829	2	22	over	over	ADP
ejpam-1829	2	23	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	2	24	v.	v.	ADP
ejpam-1829	2	25	k.	k.	PROPN
ejpam-1829	2	26	bhat	bhat	PROPN
ejpam-1829	2	27	school	school	NOUN
ejpam-1829	2	28	of	of	ADP
ejpam-1829	2	29	mathematics	mathematics	PROPN
ejpam-1829	2	30	,	,	PUNCT
ejpam-1829	2	31	smvd	smvd	PROPN
ejpam-1829	2	32	university	university	PROPN
ejpam-1829	2	33	,	,	PUNCT
ejpam-1829	2	34	p	p	X
ejpam-1829	2	35	/	/	SYM
ejpam-1829	2	36	o	o	PROPN
ejpam-1829	2	37	smvd	smvd	PROPN
ejpam-1829	2	38	university	university	PROPN
ejpam-1829	2	39	,	,	PUNCT
ejpam-1829	2	40	katra	katra	PROPN
ejpam-1829	2	41	,	,	PUNCT
ejpam-1829	2	42	j	j	PROPN
ejpam-1829	2	43	and	and	CCONJ
ejpam-1829	2	44	k	k	PROPN
ejpam-1829	2	45	,	,	PUNCT
ejpam-1829	2	46	india182320	india182320	PROPN
ejpam-1829	2	47	abstract	abstract	NOUN
ejpam-1829	2	48	.	.	PUNCT
ejpam-1829	3	1	let	let	VERB
ejpam-1829	3	2	r	r	PRON
ejpam-1829	3	3	be	be	AUX
ejpam-1829	3	4	an	an	DET
ejpam-1829	3	5	associative	associative	ADJ
ejpam-1829	3	6	ring	ring	NOUN
ejpam-1829	3	7	with	with	ADP
ejpam-1829	3	8	identity	identity	NOUN
ejpam-1829	3	9	1	1	NUM
ejpam-1829	3	10	6=	6=	ADP
ejpam-1829	3	11	0	0	NUM
ejpam-1829	3	12	,	,	PUNCT
ejpam-1829	3	13	and	and	CCONJ
ejpam-1829	3	14	σ	σ	VERB
ejpam-1829	3	15	an	an	DET
ejpam-1829	3	16	endomorphism	endomorphism	NOUN
ejpam-1829	3	17	of	of	ADP
ejpam-1829	3	18	r.	r.	PROPN
ejpam-1829	3	19	we	we	PRON
ejpam-1829	3	20	recall	recall	VERB
ejpam-1829	3	21	σ(∗	σ(∗	PROPN
ejpam-1829	3	22	)	)	PUNCT
ejpam-1829	3	23	property	property	NOUN
ejpam-1829	3	24	on	on	ADP
ejpam-1829	3	25	r	r	NOUN
ejpam-1829	3	26	(	(	PUNCT
ejpam-1829	3	27	i.e.	i.e.	X
ejpam-1829	3	28	aσ(a	aσ(a	X
ejpam-1829	3	29	)	)	PUNCT
ejpam-1829	3	30	∈	∈	PROPN
ejpam-1829	3	31	p(r	p(r	PROPN
ejpam-1829	3	32	)	)	PUNCT
ejpam-1829	3	33	implies	imply	VERB
ejpam-1829	3	34	a	a	DET
ejpam-1829	3	35	∈	∈	PROPN
ejpam-1829	3	36	p(r	p(r	PROPN
ejpam-1829	3	37	)	)	PUNCT
ejpam-1829	3	38	for	for	ADP
ejpam-1829	3	39	a	a	DET
ejpam-1829	3	40	∈	∈	PROPN
ejpam-1829	3	41	r	r	NOUN
ejpam-1829	3	42	,	,	PUNCT
ejpam-1829	3	43	where	where	SCONJ
ejpam-1829	3	44	p(r	p(r	NOUN
ejpam-1829	3	45	)	)	PUNCT
ejpam-1829	3	46	is	be	AUX
ejpam-1829	3	47	the	the	DET
ejpam-1829	3	48	prime	prime	ADJ
ejpam-1829	3	49	radical	radical	NOUN
ejpam-1829	3	50	of	of	ADP
ejpam-1829	3	51	r	r	NOUN
ejpam-1829	3	52	)	)	PUNCT
ejpam-1829	3	53	.	.	PUNCT
ejpam-1829	4	1	also	also	ADV
ejpam-1829	4	2	recall	recall	VERB
ejpam-1829	4	3	that	that	SCONJ
ejpam-1829	4	4	a	a	DET
ejpam-1829	4	5	ring	ring	NOUN
ejpam-1829	4	6	r	r	NOUN
ejpam-1829	4	7	is	be	AUX
ejpam-1829	4	8	said	say	VERB
ejpam-1829	4	9	to	to	PART
ejpam-1829	4	10	be	be	AUX
ejpam-1829	4	11	2	2	NUM
ejpam-1829	4	12	-	-	PUNCT
ejpam-1829	4	13	primal	primal	ADJ
ejpam-1829	4	14	if	if	SCONJ
ejpam-1829	4	15	and	and	CCONJ
ejpam-1829	4	16	only	only	ADV
ejpam-1829	4	17	if	if	SCONJ
ejpam-1829	4	18	p(r	p(r	PROPN
ejpam-1829	4	19	)	)	PUNCT
ejpam-1829	4	20	and	and	CCONJ
ejpam-1829	4	21	the	the	DET
ejpam-1829	4	22	set	set	NOUN
ejpam-1829	4	23	of	of	ADP
ejpam-1829	4	24	nilpotent	nilpotent	ADJ
ejpam-1829	4	25	elements	element	NOUN
ejpam-1829	4	26	of	of	ADP
ejpam-1829	4	27	r	r	NOUN
ejpam-1829	4	28	coincide	coincide	NOUN
ejpam-1829	4	29	,	,	PUNCT
ejpam-1829	4	30	if	if	SCONJ
ejpam-1829	4	31	and	and	CCONJ
ejpam-1829	4	32	only	only	ADV
ejpam-1829	4	33	if	if	SCONJ
ejpam-1829	4	34	the	the	DET
ejpam-1829	4	35	prime	prime	ADJ
ejpam-1829	4	36	radical	radical	NOUN
ejpam-1829	4	37	is	be	AUX
ejpam-1829	4	38	a	a	DET
ejpam-1829	4	39	completely	completely	ADV
ejpam-1829	4	40	semiprime	semiprime	NOUN
ejpam-1829	4	41	ideal	ideal	NOUN
ejpam-1829	4	42	.	.	PUNCT
ejpam-1829	5	1	it	it	PRON
ejpam-1829	5	2	can	can	AUX
ejpam-1829	5	3	be	be	AUX
ejpam-1829	5	4	seen	see	VERB
ejpam-1829	5	5	that	that	SCONJ
ejpam-1829	5	6	a	a	DET
ejpam-1829	5	7	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	5	8	is	be	AUX
ejpam-1829	5	9	a	a	DET
ejpam-1829	5	10	2	2	NUM
ejpam-1829	5	11	-	-	PUNCT
ejpam-1829	5	12	primal	primal	ADJ
ejpam-1829	5	13	ring	ring	NOUN
ejpam-1829	5	14	.	.	PUNCT
ejpam-1829	6	1	let	let	VERB
ejpam-1829	6	2	r	r	PRON
ejpam-1829	6	3	be	be	AUX
ejpam-1829	6	4	a	a	DET
ejpam-1829	6	5	ring	ring	NOUN
ejpam-1829	6	6	andσ	andσ	NOUN
ejpam-1829	6	7	an	an	DET
ejpam-1829	6	8	automorphism	automorphism	NOUN
ejpam-1829	6	9	of	of	ADP
ejpam-1829	6	10	r.	r.	PROPN
ejpam-1829	6	11	then	then	ADV
ejpam-1829	6	12	we	we	PRON
ejpam-1829	6	13	know	know	VERB
ejpam-1829	6	14	thatσ	thatσ	NOUN
ejpam-1829	6	15	can	can	AUX
ejpam-1829	6	16	be	be	AUX
ejpam-1829	6	17	extended	extend	VERB
ejpam-1829	6	18	to	to	ADP
ejpam-1829	6	19	an	an	DET
ejpam-1829	6	20	automorphism	automorphism	NOUN
ejpam-1829	6	21	(	(	PUNCT
ejpam-1829	6	22	say	say	INTJ
ejpam-1829	6	23	σ	σ	NOUN
ejpam-1829	6	24	)	)	PUNCT
ejpam-1829	6	25	of	of	ADP
ejpam-1829	6	26	the	the	DET
ejpam-1829	6	27	skew	skew	ADJ
ejpam-1829	6	28	-	-	PUNCT
ejpam-1829	6	29	laurent	laurent	ADJ
ejpam-1829	6	30	ring	ring	NOUN
ejpam-1829	6	31	r[x	r[x	PROPN
ejpam-1829	6	32	,	,	PUNCT
ejpam-1829	6	33	x−1;σ	x−1;σ	PROPN
ejpam-1829	6	34	]	]	PUNCT
ejpam-1829	6	35	.	.	PUNCT
ejpam-1829	7	1	in	in	ADP
ejpam-1829	7	2	this	this	DET
ejpam-1829	7	3	paper	paper	NOUN
ejpam-1829	7	4	we	we	PRON
ejpam-1829	7	5	show	show	VERB
ejpam-1829	7	6	that	that	SCONJ
ejpam-1829	7	7	if	if	SCONJ
ejpam-1829	7	8	r	r	NOUN
ejpam-1829	7	9	is	be	AUX
ejpam-1829	7	10	a	a	DET
ejpam-1829	7	11	noetherian	noetherian	ADJ
ejpam-1829	7	12	ring	ring	NOUN
ejpam-1829	7	13	and	and	CCONJ
ejpam-1829	7	14	σ	σ	PROPN
ejpam-1829	7	15	is	be	AUX
ejpam-1829	7	16	an	an	DET
ejpam-1829	7	17	automorphism	automorphism	NOUN
ejpam-1829	7	18	of	of	ADP
ejpam-1829	7	19	r	r	NOUN
ejpam-1829	7	20	such	such	ADJ
ejpam-1829	7	21	that	that	SCONJ
ejpam-1829	7	22	r	r	NOUN
ejpam-1829	7	23	is	be	AUX
ejpam-1829	7	24	a	a	DET
ejpam-1829	7	25	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	7	26	,	,	PUNCT
ejpam-1829	7	27	then	then	ADV
ejpam-1829	7	28	r[x	r[x	NOUN
ejpam-1829	7	29	,	,	PUNCT
ejpam-1829	7	30	x−1;σ	x−1;σ	PROPN
ejpam-1829	7	31	]	]	PUNCT
ejpam-1829	7	32	is	be	AUX
ejpam-1829	7	33	a	a	DET
ejpam-1829	7	34	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	7	35	.	.	PUNCT
ejpam-1829	8	1	we	we	PRON
ejpam-1829	8	2	also	also	ADV
ejpam-1829	8	3	prove	prove	VERB
ejpam-1829	8	4	a	a	DET
ejpam-1829	8	5	similar	similar	ADJ
ejpam-1829	8	6	result	result	NOUN
ejpam-1829	8	7	for	for	ADP
ejpam-1829	8	8	the	the	DET
ejpam-1829	8	9	general	general	ADJ
ejpam-1829	8	10	ore	ore	NOUN
ejpam-1829	8	11	extension	extension	NOUN
ejpam-1829	8	12	r[x;σ	r[x;σ	NOUN
ejpam-1829	8	13	,	,	PUNCT
ejpam-1829	8	14	δ	δ	PROPN
ejpam-1829	8	15	]	]	X
ejpam-1829	8	16	,	,	PUNCT
ejpam-1829	8	17	where	where	SCONJ
ejpam-1829	8	18	σ	σ	PROPN
ejpam-1829	8	19	is	be	AUX
ejpam-1829	8	20	an	an	DET
ejpam-1829	8	21	automorphism	automorphism	NOUN
ejpam-1829	8	22	of	of	ADP
ejpam-1829	8	23	r	r	NOUN
ejpam-1829	8	24	and	and	CCONJ
ejpam-1829	8	25	δ	δ	PROPN
ejpam-1829	8	26	a	a	DET
ejpam-1829	8	27	σ	σ	NOUN
ejpam-1829	8	28	-	-	PUNCT
ejpam-1829	8	29	derivation	derivation	NOUN
ejpam-1829	8	30	of	of	ADP
ejpam-1829	8	31	r.	r.	PROPN
ejpam-1829	8	32	2010	2010	NUM
ejpam-1829	8	33	mathematics	mathematics	PROPN
ejpam-1829	8	34	subject	subject	NOUN
ejpam-1829	8	35	classifications	classification	NOUN
ejpam-1829	8	36	:	:	PUNCT
ejpam-1829	8	37	16	16	NUM
ejpam-1829	8	38	-	-	SYM
ejpam-1829	8	39	xx	xx	NUM
ejpam-1829	8	40	;	;	PUNCT
ejpam-1829	8	41	16n40	16n40	NUM
ejpam-1829	8	42	,	,	PUNCT
ejpam-1829	8	43	16p40	16p40	NUM
ejpam-1829	8	44	,	,	PUNCT
ejpam-1829	8	45	16s36	16s36	NUM
ejpam-1829	8	46	.	.	PUNCT
ejpam-1829	9	1	key	key	ADJ
ejpam-1829	9	2	words	word	NOUN
ejpam-1829	9	3	and	and	CCONJ
ejpam-1829	9	4	phrases	phrase	NOUN
ejpam-1829	9	5	:	:	PUNCT
ejpam-1829	9	6	minimal	minimal	ADJ
ejpam-1829	9	7	prime	prime	ADJ
ejpam-1829	9	8	,	,	PUNCT
ejpam-1829	9	9	prime	prime	ADJ
ejpam-1829	9	10	radical	radical	ADJ
ejpam-1829	9	11	,	,	PUNCT
ejpam-1829	9	12	automorphism	automorphism	NOUN
ejpam-1829	9	13	,	,	PUNCT
ejpam-1829	9	14	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	9	15	1	1	NUM
ejpam-1829	9	16	.	.	PUNCT
ejpam-1829	9	17	introduction	introduction	NOUN
ejpam-1829	9	18	a	a	DET
ejpam-1829	9	19	ring	ring	NOUN
ejpam-1829	9	20	r	r	NOUN
ejpam-1829	9	21	always	always	ADV
ejpam-1829	9	22	means	mean	VERB
ejpam-1829	9	23	an	an	DET
ejpam-1829	9	24	associative	associative	ADJ
ejpam-1829	9	25	ring	ring	NOUN
ejpam-1829	9	26	with	with	ADP
ejpam-1829	9	27	identity	identity	NOUN
ejpam-1829	9	28	1	1	NUM
ejpam-1829	9	29	6=	6=	ADP
ejpam-1829	9	30	0	0	NUM
ejpam-1829	9	31	.	.	PUNCT
ejpam-1829	10	1	the	the	DET
ejpam-1829	10	2	set	set	NOUN
ejpam-1829	10	3	of	of	ADP
ejpam-1829	10	4	prime	prime	ADJ
ejpam-1829	10	5	ideals	ideal	NOUN
ejpam-1829	10	6	of	of	ADP
ejpam-1829	10	7	r	r	NOUN
ejpam-1829	10	8	is	be	AUX
ejpam-1829	10	9	denoted	denote	VERB
ejpam-1829	10	10	by	by	ADP
ejpam-1829	10	11	spec(r	spec(r	PROPN
ejpam-1829	10	12	)	)	PUNCT
ejpam-1829	10	13	.	.	PUNCT
ejpam-1829	11	1	the	the	DET
ejpam-1829	11	2	sets	set	NOUN
ejpam-1829	11	3	of	of	ADP
ejpam-1829	11	4	minimal	minimal	ADJ
ejpam-1829	11	5	prime	prime	ADJ
ejpam-1829	11	6	ideals	ideal	NOUN
ejpam-1829	11	7	of	of	ADP
ejpam-1829	11	8	r	r	NOUN
ejpam-1829	11	9	is	be	AUX
ejpam-1829	11	10	denoted	denote	VERB
ejpam-1829	11	11	by	by	ADP
ejpam-1829	11	12	min.spec(r	min.spec(r	PROPN
ejpam-1829	11	13	)	)	PUNCT
ejpam-1829	11	14	.	.	PUNCT
ejpam-1829	12	1	prime	prime	PROPN
ejpam-1829	12	2	radical	radical	ADJ
ejpam-1829	12	3	and	and	CCONJ
ejpam-1829	12	4	the	the	DET
ejpam-1829	12	5	set	set	NOUN
ejpam-1829	12	6	of	of	ADP
ejpam-1829	12	7	nilpotent	nilpotent	ADJ
ejpam-1829	12	8	elements	element	NOUN
ejpam-1829	12	9	of	of	ADP
ejpam-1829	12	10	r	r	NOUN
ejpam-1829	12	11	are	be	AUX
ejpam-1829	12	12	denoted	denote	VERB
ejpam-1829	12	13	by	by	ADP
ejpam-1829	12	14	p(r	p(r	PROPN
ejpam-1829	12	15	)	)	PUNCT
ejpam-1829	12	16	and	and	CCONJ
ejpam-1829	12	17	n(r	n(r	NOUN
ejpam-1829	12	18	)	)	PUNCT
ejpam-1829	12	19	respectively	respectively	ADV
ejpam-1829	12	20	.	.	PUNCT
ejpam-1829	13	1	let	let	VERB
ejpam-1829	13	2	r	r	PRON
ejpam-1829	13	3	be	be	AUX
ejpam-1829	13	4	a	a	DET
ejpam-1829	13	5	ring	ring	NOUN
ejpam-1829	13	6	and	and	CCONJ
ejpam-1829	13	7	σ	σ	NOUN
ejpam-1829	13	8	an	an	DET
ejpam-1829	13	9	automorphism	automorphism	NOUN
ejpam-1829	13	10	of	of	ADP
ejpam-1829	13	11	r.	r.	PROPN
ejpam-1829	13	12	let	let	VERB
ejpam-1829	13	13	i	i	PRON
ejpam-1829	13	14	be	be	AUX
ejpam-1829	13	15	an	an	DET
ejpam-1829	13	16	ideal	ideal	NOUN
ejpam-1829	13	17	of	of	ADP
ejpam-1829	13	18	r	r	NOUN
ejpam-1829	13	19	such	such	ADJ
ejpam-1829	13	20	that	that	PRON
ejpam-1829	13	21	σm(i	σm(i	PUNCT
ejpam-1829	13	22	)	)	PUNCT
ejpam-1829	14	1	=	=	SYM
ejpam-1829	14	2	i	i	PRON
ejpam-1829	14	3	for	for	ADP
ejpam-1829	14	4	some	some	DET
ejpam-1829	14	5	m	m	NOUN
ejpam-1829	14	6	∈	∈	NOUN
ejpam-1829	14	7	n	n	CCONJ
ejpam-1829	14	8	(	(	PUNCT
ejpam-1829	14	9	where	where	SCONJ
ejpam-1829	14	10	n	n	PRON
ejpam-1829	14	11	is	be	AUX
ejpam-1829	14	12	the	the	DET
ejpam-1829	14	13	set	set	NOUN
ejpam-1829	14	14	of	of	ADP
ejpam-1829	14	15	positive	positive	ADJ
ejpam-1829	14	16	integers	integer	NOUN
ejpam-1829	14	17	)	)	PUNCT
ejpam-1829	14	18	.	.	PUNCT
ejpam-1829	15	1	we	we	PRON
ejpam-1829	15	2	denote	denote	VERB
ejpam-1829	15	3	∩m	∩m	PROPN
ejpam-1829	15	4	i=1σ	i=1σ	NOUN
ejpam-1829	15	5	i(i	i(i	PROPN
ejpam-1829	15	6	)	)	PUNCT
ejpam-1829	15	7	by	by	ADP
ejpam-1829	15	8	i0	i0	PROPN
ejpam-1829	15	9	.	.	PUNCT
ejpam-1829	16	1	the	the	DET
ejpam-1829	16	2	field	field	NOUN
ejpam-1829	16	3	of	of	ADP
ejpam-1829	16	4	rational	rational	ADJ
ejpam-1829	16	5	numbers	number	NOUN
ejpam-1829	16	6	is	be	AUX
ejpam-1829	16	7	denoted	denote	VERB
ejpam-1829	16	8	by	by	ADP
ejpam-1829	16	9	q	q	PROPN
ejpam-1829	16	10	and	and	CCONJ
ejpam-1829	16	11	the	the	DET
ejpam-1829	16	12	field	field	NOUN
ejpam-1829	16	13	of	of	ADP
ejpam-1829	16	14	real	real	ADJ
ejpam-1829	16	15	numbers	number	NOUN
ejpam-1829	16	16	is	be	AUX
ejpam-1829	16	17	denoted	denote	VERB
ejpam-1829	16	18	by	by	ADP
ejpam-1829	16	19	r	r	NOUN
ejpam-1829	16	20	unless	unless	SCONJ
ejpam-1829	16	21	otherwise	otherwise	ADV
ejpam-1829	16	22	stated	state	VERB
ejpam-1829	16	23	.	.	PUNCT
ejpam-1829	17	1	this	this	DET
ejpam-1829	17	2	article	article	NOUN
ejpam-1829	17	3	concerns	concern	VERB
ejpam-1829	17	4	the	the	DET
ejpam-1829	17	5	study	study	NOUN
ejpam-1829	17	6	of	of	ADP
ejpam-1829	17	7	skew	skew	ADJ
ejpam-1829	17	8	-	-	PUNCT
ejpam-1829	17	9	laurent	laurent	NOUN
ejpam-1829	17	10	rings	ring	NOUN
ejpam-1829	17	11	over	over	ADP
ejpam-1829	17	12	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	17	13	,	,	PUNCT
ejpam-1829	17	14	where	where	SCONJ
ejpam-1829	17	15	σ	σ	PROPN
ejpam-1829	17	16	is	be	AUX
ejpam-1829	17	17	an	an	DET
ejpam-1829	17	18	automorphism	automorphism	NOUN
ejpam-1829	17	19	of	of	ADP
ejpam-1829	17	20	r.	r.	PROPN
ejpam-1829	17	21	email	email	PROPN
ejpam-1829	17	22	address	address	NOUN
ejpam-1829	17	23	:	:	PUNCT
ejpam-1829	17	24	vijaykumarbhat2000@yahoo.com	vijaykumarbhat2000@yahoo.com	X
ejpam-1829	17	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1829	18	1	387	387	NUM
ejpam-1829	18	2	c	c	X
ejpam-1829	18	3	©	©	PROPN
ejpam-1829	18	4	2014	2014	NUM
ejpam-1829	18	5	ejpam	ejpam	NOUN
ejpam-1829	18	6	all	all	DET
ejpam-1829	18	7	rights	right	NOUN
ejpam-1829	18	8	reserved	reserve	VERB
ejpam-1829	18	9	.	.	PUNCT
ejpam-1829	19	1	v.	v.	ADP
ejpam-1829	19	2	bhat	bhat	PROPN
ejpam-1829	19	3	/	/	SYM
ejpam-1829	19	4	eur	eur	PROPN
ejpam-1829	19	5	.	.	PUNCT
ejpam-1829	20	1	j.	j.	PROPN
ejpam-1829	20	2	pure	pure	PROPN
ejpam-1829	20	3	appl	appl	PROPN
ejpam-1829	20	4	.	.	PROPN
ejpam-1829	20	5	math	math	PROPN
ejpam-1829	20	6	,	,	PUNCT
ejpam-1829	20	7	7	7	NUM
ejpam-1829	20	8	(	(	PUNCT
ejpam-1829	20	9	2014	2014	NUM
ejpam-1829	20	10	)	)	PUNCT
ejpam-1829	20	11	,	,	PUNCT
ejpam-1829	20	12	387	387	NUM
ejpam-1829	20	13	-	-	SYM
ejpam-1829	20	14	394	394	NUM
ejpam-1829	20	15	388	388	NUM
ejpam-1829	20	16	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	20	17	recall	recall	VERB
ejpam-1829	20	18	that	that	SCONJ
ejpam-1829	20	19	in	in	ADP
ejpam-1829	20	20	krempa	krempa	NOUN
ejpam-1829	20	21	[	[	X
ejpam-1829	20	22	8	8	NUM
ejpam-1829	20	23	]	]	PUNCT
ejpam-1829	20	24	,	,	PUNCT
ejpam-1829	20	25	a	a	DET
ejpam-1829	20	26	ring	ring	NOUN
ejpam-1829	20	27	r	r	NOUN
ejpam-1829	20	28	is	be	AUX
ejpam-1829	20	29	called	call	VERB
ejpam-1829	20	30	σ	σ	NOUN
ejpam-1829	20	31	-	-	PROPN
ejpam-1829	20	32	rigid	rigid	ADJ
ejpam-1829	20	33	if	if	SCONJ
ejpam-1829	20	34	there	there	PRON
ejpam-1829	20	35	exists	exist	VERB
ejpam-1829	20	36	an	an	DET
ejpam-1829	20	37	endomorphism	endomorphism	PROPN
ejpam-1829	20	38	σ	σ	NOUN
ejpam-1829	20	39	of	of	ADP
ejpam-1829	20	40	r	r	NOUN
ejpam-1829	20	41	with	with	ADP
ejpam-1829	20	42	the	the	DET
ejpam-1829	20	43	property	property	NOUN
ejpam-1829	20	44	that	that	PRON
ejpam-1829	20	45	aσ(a	aσ(a	ADV
ejpam-1829	20	46	)	)	PUNCT
ejpam-1829	21	1	=	=	SYM
ejpam-1829	21	2	0	0	NUM
ejpam-1829	21	3	implies	imply	VERB
ejpam-1829	21	4	a	a	DET
ejpam-1829	21	5	=	=	SYM
ejpam-1829	21	6	0	0	NUM
ejpam-1829	21	7	for	for	ADP
ejpam-1829	21	8	a	a	DET
ejpam-1829	21	9	∈	∈	PROPN
ejpam-1829	21	10	r.	r.	NOUN
ejpam-1829	21	11	in	in	ADP
ejpam-1829	21	12	[	[	X
ejpam-1829	21	13	9	9	NUM
ejpam-1829	21	14	]	]	PUNCT
ejpam-1829	21	15	,	,	PUNCT
ejpam-1829	21	16	kwak	kwak	PROPN
ejpam-1829	21	17	defines	define	VERB
ejpam-1829	21	18	a	a	DET
ejpam-1829	21	19	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	21	20	r	r	NOUN
ejpam-1829	21	21	to	to	PART
ejpam-1829	21	22	be	be	AUX
ejpam-1829	21	23	a	a	DET
ejpam-1829	21	24	ring	ring	NOUN
ejpam-1829	21	25	in	in	ADP
ejpam-1829	21	26	which	which	PRON
ejpam-1829	21	27	aσ(a	aσ(a	NOUN
ejpam-1829	21	28	)	)	PUNCT
ejpam-1829	21	29	∈	∈	PROPN
ejpam-1829	21	30	p(r	p(r	PROPN
ejpam-1829	21	31	)	)	PUNCT
ejpam-1829	21	32	implies	imply	VERB
ejpam-1829	21	33	a	a	DET
ejpam-1829	21	34	∈	∈	PROPN
ejpam-1829	21	35	p(r	p(r	PROPN
ejpam-1829	21	36	)	)	PUNCT
ejpam-1829	21	37	for	for	ADP
ejpam-1829	21	38	a	a	DET
ejpam-1829	21	39	∈	∈	PROPN
ejpam-1829	21	40	r.	r.	PROPN
ejpam-1829	21	41	example	example	NOUN
ejpam-1829	22	1	1	1	NUM
ejpam-1829	22	2	.	.	PUNCT
ejpam-1829	23	1	let	let	VERB
ejpam-1829	23	2	r	r	NOUN
ejpam-1829	23	3	=	=	SYM
ejpam-1829	23	4	�	�	PROPN
ejpam-1829	23	5	f	f	PROPN
ejpam-1829	23	6	f	f	PROPN
ejpam-1829	23	7	0	0	PROPN
ejpam-1829	23	8	f	f	PROPN
ejpam-1829	23	9	�	�	PROPN
ejpam-1829	23	10	,	,	PUNCT
ejpam-1829	23	11	where	where	SCONJ
ejpam-1829	23	12	f	f	PROPN
ejpam-1829	23	13	is	be	AUX
ejpam-1829	23	14	a	a	DET
ejpam-1829	23	15	field	field	NOUN
ejpam-1829	23	16	.	.	PUNCT
ejpam-1829	24	1	then	then	ADV
ejpam-1829	24	2	p(r	p(r	PROPN
ejpam-1829	24	3	)	)	PUNCT
ejpam-1829	24	4	=	=	SYM
ejpam-1829	24	5	�	�	PROPN
ejpam-1829	24	6	0	0	NUM
ejpam-1829	24	7	f	f	PROPN
ejpam-1829	24	8	0	0	SYM
ejpam-1829	24	9	0	0	NUM
ejpam-1829	24	10	�	�	PROPN
ejpam-1829	24	11	.	.	PUNCT
ejpam-1829	25	1	let	let	VERB
ejpam-1829	25	2	σ	σ	NOUN
ejpam-1829	25	3	:	:	PUNCT
ejpam-1829	25	4	r→	r→	PROPN
ejpam-1829	25	5	r	r	NOUN
ejpam-1829	25	6	be	be	AUX
ejpam-1829	25	7	defined	define	VERB
ejpam-1829	25	8	by	by	ADP
ejpam-1829	25	9	σ	σ	PROPN
ejpam-1829	25	10	�	�	PROPN
ejpam-1829	25	11	�	�	PROPN
ejpam-1829	25	12	a	a	DET
ejpam-1829	25	13	b	b	PROPN
ejpam-1829	25	14	0	0	NUM
ejpam-1829	25	15	c	c	PROPN
ejpam-1829	25	16	�	�	PROPN
ejpam-1829	25	17	�	�	PROPN
ejpam-1829	25	18	=	=	SYM
ejpam-1829	25	19	�	�	PROPN
ejpam-1829	26	1	a	a	DET
ejpam-1829	26	2	0	0	NUM
ejpam-1829	26	3	0	0	NUM
ejpam-1829	26	4	c	c	PROPN
ejpam-1829	26	5	�	�	PROPN
ejpam-1829	26	6	.	.	PUNCT
ejpam-1829	27	1	then	then	ADV
ejpam-1829	27	2	it	it	PRON
ejpam-1829	27	3	can	can	AUX
ejpam-1829	27	4	be	be	AUX
ejpam-1829	27	5	seen	see	VERB
ejpam-1829	27	6	that	that	SCONJ
ejpam-1829	27	7	σ	σ	PROPN
ejpam-1829	27	8	is	be	AUX
ejpam-1829	27	9	an	an	DET
ejpam-1829	27	10	endomorphism	endomorphism	NOUN
ejpam-1829	27	11	of	of	ADP
ejpam-1829	27	12	r	r	NOUN
ejpam-1829	27	13	and	and	CCONJ
ejpam-1829	27	14	r	r	NOUN
ejpam-1829	27	15	is	be	AUX
ejpam-1829	27	16	a	a	DET
ejpam-1829	27	17	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	27	18	.	.	NOUN
ejpam-1829	27	19	2	2	NUM
ejpam-1829	27	20	-	-	PUNCT
ejpam-1829	27	21	primal	primal	ADJ
ejpam-1829	27	22	rings	ring	NOUN
ejpam-1829	27	23	we	we	PRON
ejpam-1829	27	24	do	do	AUX
ejpam-1829	27	25	not	not	PART
ejpam-1829	27	26	want	want	VERB
ejpam-1829	27	27	to	to	PART
ejpam-1829	27	28	talk	talk	VERB
ejpam-1829	27	29	about	about	ADP
ejpam-1829	27	30	2	2	NUM
ejpam-1829	27	31	-	-	PUNCT
ejpam-1829	27	32	primal	primal	ADJ
ejpam-1829	27	33	rings	ring	NOUN
ejpam-1829	27	34	,	,	PUNCT
ejpam-1829	27	35	but	but	CCONJ
ejpam-1829	27	36	because	because	SCONJ
ejpam-1829	27	37	of	of	ADP
ejpam-1829	27	38	a	a	DET
ejpam-1829	27	39	close	close	ADJ
ejpam-1829	27	40	relation	relation	NOUN
ejpam-1829	27	41	between	between	ADP
ejpam-1829	27	42	a	a	DET
ejpam-1829	27	43	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	27	44	and	and	CCONJ
ejpam-1829	27	45	a	a	DET
ejpam-1829	27	46	2	2	NUM
ejpam-1829	27	47	-	-	PUNCT
ejpam-1829	27	48	primal	primal	ADJ
ejpam-1829	27	49	ring	ring	NOUN
ejpam-1829	27	50	,	,	PUNCT
ejpam-1829	27	51	we	we	PRON
ejpam-1829	27	52	have	have	VERB
ejpam-1829	27	53	the	the	DET
ejpam-1829	27	54	following	following	NOUN
ejpam-1829	27	55	:	:	PUNCT
ejpam-1829	27	56	recall	recall	VERB
ejpam-1829	27	57	that	that	SCONJ
ejpam-1829	27	58	a	a	DET
ejpam-1829	27	59	ring	ring	NOUN
ejpam-1829	27	60	r	r	NOUN
ejpam-1829	27	61	is	be	AUX
ejpam-1829	27	62	2	2	NUM
ejpam-1829	27	63	-	-	PUNCT
ejpam-1829	27	64	primal	primal	ADJ
ejpam-1829	27	65	if	if	SCONJ
ejpam-1829	27	66	and	and	CCONJ
ejpam-1829	27	67	only	only	ADV
ejpam-1829	27	68	if	if	SCONJ
ejpam-1829	27	69	n(r	n(r	NUM
ejpam-1829	27	70	)	)	PUNCT
ejpam-1829	27	71	=	=	SYM
ejpam-1829	27	72	p(r	p(r	PROPN
ejpam-1829	27	73	)	)	PUNCT
ejpam-1829	27	74	,	,	PUNCT
ejpam-1829	27	75	i.e.	i.e.	X
ejpam-1829	27	76	if	if	SCONJ
ejpam-1829	27	77	the	the	DET
ejpam-1829	27	78	prime	prime	ADJ
ejpam-1829	27	79	radical	radical	NOUN
ejpam-1829	27	80	is	be	AUX
ejpam-1829	27	81	a	a	DET
ejpam-1829	27	82	completely	completely	ADV
ejpam-1829	27	83	semiprime	semiprime	NOUN
ejpam-1829	27	84	ideal	ideal	NOUN
ejpam-1829	27	85	.	.	PUNCT
ejpam-1829	28	1	an	an	DET
ejpam-1829	28	2	ideal	ideal	ADJ
ejpam-1829	28	3	i	i	PRON
ejpam-1829	28	4	of	of	ADP
ejpam-1829	28	5	a	a	DET
ejpam-1829	28	6	ring	ring	NOUN
ejpam-1829	28	7	r	r	NOUN
ejpam-1829	28	8	is	be	AUX
ejpam-1829	28	9	called	call	VERB
ejpam-1829	28	10	completely	completely	ADV
ejpam-1829	28	11	semiprime	semiprime	NOUN
ejpam-1829	28	12	if	if	SCONJ
ejpam-1829	28	13	a2	a2	PROPN
ejpam-1829	28	14	∈	∈	PROPN
ejpam-1829	28	15	i	i	PRON
ejpam-1829	28	16	implies	imply	VERB
ejpam-1829	28	17	a	a	DET
ejpam-1829	28	18	∈	∈	NOUN
ejpam-1829	28	19	i	i	PRON
ejpam-1829	28	20	for	for	ADP
ejpam-1829	28	21	a	a	DET
ejpam-1829	28	22	∈	∈	PROPN
ejpam-1829	28	23	r.	r.	NOUN
ejpam-1829	28	24	we	we	PRON
ejpam-1829	28	25	note	note	VERB
ejpam-1829	28	26	that	that	SCONJ
ejpam-1829	28	27	a	a	DET
ejpam-1829	28	28	commutative	commutative	ADJ
ejpam-1829	28	29	ring	ring	NOUN
ejpam-1829	28	30	is	be	AUX
ejpam-1829	28	31	2	2	NUM
ejpam-1829	28	32	-	-	PUNCT
ejpam-1829	28	33	primal	primal	ADJ
ejpam-1829	28	34	and	and	CCONJ
ejpam-1829	28	35	so	so	ADV
ejpam-1829	28	36	is	be	AUX
ejpam-1829	28	37	a	a	DET
ejpam-1829	28	38	reduced	reduce	VERB
ejpam-1829	28	39	ring	ring	NOUN
ejpam-1829	28	40	.	.	PUNCT
ejpam-1829	29	1	2	2	NUM
ejpam-1829	29	2	-	-	PUNCT
ejpam-1829	29	3	primal	primal	ADJ
ejpam-1829	29	4	rings	ring	NOUN
ejpam-1829	29	5	have	have	AUX
ejpam-1829	29	6	been	be	AUX
ejpam-1829	29	7	studied	study	VERB
ejpam-1829	29	8	in	in	ADP
ejpam-1829	29	9	recent	recent	ADJ
ejpam-1829	29	10	years	year	NOUN
ejpam-1829	29	11	and	and	CCONJ
ejpam-1829	29	12	the	the	DET
ejpam-1829	29	13	2	2	NUM
ejpam-1829	29	14	-	-	PUNCT
ejpam-1829	29	15	primal	primal	ADJ
ejpam-1829	29	16	property	property	NOUN
ejpam-1829	29	17	is	be	AUX
ejpam-1829	29	18	being	be	AUX
ejpam-1829	29	19	studied	study	VERB
ejpam-1829	29	20	for	for	ADP
ejpam-1829	29	21	various	various	ADJ
ejpam-1829	29	22	types	type	NOUN
ejpam-1829	29	23	of	of	ADP
ejpam-1829	29	24	rings	ring	NOUN
ejpam-1829	29	25	.	.	PUNCT
ejpam-1829	30	1	in	in	ADP
ejpam-1829	30	2	[	[	X
ejpam-1829	30	3	10	10	NUM
ejpam-1829	30	4	]	]	PUNCT
ejpam-1829	30	5	,	,	PUNCT
ejpam-1829	30	6	greg	greg	PROPN
ejpam-1829	30	7	marks	marks	PROPN
ejpam-1829	30	8	discusses	discuss	VERB
ejpam-1829	30	9	the	the	DET
ejpam-1829	30	10	2	2	NUM
ejpam-1829	30	11	-	-	PUNCT
ejpam-1829	30	12	primal	primal	ADJ
ejpam-1829	30	13	property	property	NOUN
ejpam-1829	30	14	of	of	ADP
ejpam-1829	30	15	r[x;σ	r[x;σ	NOUN
ejpam-1829	30	16	,	,	PUNCT
ejpam-1829	30	17	δ	δ	PROPN
ejpam-1829	30	18	]	]	X
ejpam-1829	30	19	,	,	PUNCT
ejpam-1829	30	20	where	where	SCONJ
ejpam-1829	30	21	r	r	NOUN
ejpam-1829	30	22	is	be	AUX
ejpam-1829	30	23	a	a	DET
ejpam-1829	30	24	local	local	ADJ
ejpam-1829	30	25	ring	ring	NOUN
ejpam-1829	30	26	,	,	PUNCT
ejpam-1829	30	27	σ	σ	PROPN
ejpam-1829	30	28	is	be	AUX
ejpam-1829	30	29	an	an	DET
ejpam-1829	30	30	automorphism	automorphism	NOUN
ejpam-1829	30	31	of	of	ADP
ejpam-1829	30	32	r	r	NOUN
ejpam-1829	30	33	and	and	CCONJ
ejpam-1829	30	34	δ	δ	PROPN
ejpam-1829	30	35	is	be	AUX
ejpam-1829	30	36	a	a	DET
ejpam-1829	30	37	σ	σ	NOUN
ejpam-1829	30	38	-	-	PUNCT
ejpam-1829	30	39	derivation	derivation	NOUN
ejpam-1829	30	40	of	of	ADP
ejpam-1829	30	41	r.	r.	PROPN
ejpam-1829	30	42	he	he	PRON
ejpam-1829	30	43	has	have	AUX
ejpam-1829	30	44	proved	prove	VERB
ejpam-1829	30	45	that	that	SCONJ
ejpam-1829	30	46	when	when	SCONJ
ejpam-1829	30	47	r	r	NOUN
ejpam-1829	30	48	is	be	AUX
ejpam-1829	30	49	a	a	DET
ejpam-1829	30	50	local	local	ADJ
ejpam-1829	30	51	ring	ring	NOUN
ejpam-1829	30	52	with	with	ADP
ejpam-1829	30	53	a	a	DET
ejpam-1829	30	54	nilpotent	nilpotent	ADJ
ejpam-1829	30	55	maximal	maximal	ADJ
ejpam-1829	30	56	ideal	ideal	NOUN
ejpam-1829	30	57	,	,	PUNCT
ejpam-1829	30	58	the	the	DET
ejpam-1829	30	59	ore	ore	NOUN
ejpam-1829	30	60	extension	extension	NOUN
ejpam-1829	30	61	r[x;σ	r[x;σ	NOUN
ejpam-1829	30	62	,	,	PUNCT
ejpam-1829	30	63	δ	δ	PROPN
ejpam-1829	30	64	]	]	PUNCT
ejpam-1829	30	65	will	will	AUX
ejpam-1829	30	66	or	or	CCONJ
ejpam-1829	30	67	will	will	AUX
ejpam-1829	30	68	not	not	PART
ejpam-1829	30	69	be	be	AUX
ejpam-1829	30	70	2	2	NUM
ejpam-1829	30	71	-	-	NOUN
ejpam-1829	30	72	primal	primal	ADJ
ejpam-1829	30	73	depending	depend	VERB
ejpam-1829	30	74	on	on	ADP
ejpam-1829	30	75	the	the	DET
ejpam-1829	30	76	δ	δ	NOUN
ejpam-1829	30	77	-	-	NOUN
ejpam-1829	30	78	stability	stability	NOUN
ejpam-1829	30	79	of	of	ADP
ejpam-1829	30	80	the	the	DET
ejpam-1829	30	81	maximal	maximal	ADJ
ejpam-1829	30	82	ideal	ideal	NOUN
ejpam-1829	30	83	of	of	ADP
ejpam-1829	30	84	r.	r.	PROPN
ejpam-1829	30	85	in	in	ADP
ejpam-1829	30	86	[	[	X
ejpam-1829	30	87	9	9	NUM
ejpam-1829	30	88	]	]	PUNCT
ejpam-1829	30	89	,	,	PUNCT
ejpam-1829	30	90	kwak	kwak	PROPN
ejpam-1829	30	91	establishes	establish	VERB
ejpam-1829	30	92	a	a	DET
ejpam-1829	30	93	relation	relation	NOUN
ejpam-1829	30	94	between	between	ADP
ejpam-1829	30	95	a	a	DET
ejpam-1829	30	96	2	2	NUM
ejpam-1829	30	97	-	-	PUNCT
ejpam-1829	30	98	primal	primal	ADJ
ejpam-1829	30	99	ring	ring	NOUN
ejpam-1829	30	100	and	and	CCONJ
ejpam-1829	30	101	a	a	DET
ejpam-1829	30	102	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	30	103	.	.	PUNCT
ejpam-1829	31	1	it	it	PRON
ejpam-1829	31	2	has	have	AUX
ejpam-1829	31	3	been	be	AUX
ejpam-1829	31	4	proved	prove	VERB
ejpam-1829	31	5	that	that	SCONJ
ejpam-1829	31	6	if	if	SCONJ
ejpam-1829	31	7	r	r	NOUN
ejpam-1829	31	8	is	be	AUX
ejpam-1829	31	9	a	a	DET
ejpam-1829	31	10	ring	ring	NOUN
ejpam-1829	31	11	and	and	CCONJ
ejpam-1829	31	12	σ	σ	NOUN
ejpam-1829	31	13	an	an	DET
ejpam-1829	31	14	endomorphism	endomorphism	NOUN
ejpam-1829	31	15	of	of	ADP
ejpam-1829	31	16	r	r	NOUN
ejpam-1829	31	17	such	such	ADJ
ejpam-1829	31	18	that	that	DET
ejpam-1829	31	19	σ(p(r	σ(p(r	PROPN
ejpam-1829	31	20	)	)	PUNCT
ejpam-1829	31	21	)	)	PUNCT
ejpam-1829	32	1	⊆	⊆	NUM
ejpam-1829	32	2	p(r	p(r	PROPN
ejpam-1829	32	3	)	)	PUNCT
ejpam-1829	32	4	,	,	PUNCT
ejpam-1829	32	5	then	then	ADV
ejpam-1829	32	6	r	r	NOUN
ejpam-1829	32	7	is	be	AUX
ejpam-1829	32	8	a	a	DET
ejpam-1829	32	9	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	32	10	implies	implie	NOUN
ejpam-1829	32	11	that	that	SCONJ
ejpam-1829	32	12	r	r	NOUN
ejpam-1829	32	13	is	be	AUX
ejpam-1829	32	14	2	2	NUM
ejpam-1829	32	15	-	-	PUNCT
ejpam-1829	32	16	primal	primal	ADJ
ejpam-1829	32	17	.	.	PUNCT
ejpam-1829	33	1	therefore	therefore	ADV
ejpam-1829	33	2	,	,	PUNCT
ejpam-1829	33	3	we	we	PRON
ejpam-1829	33	4	see	see	VERB
ejpam-1829	33	5	that	that	SCONJ
ejpam-1829	33	6	if	if	SCONJ
ejpam-1829	33	7	r	r	NOUN
ejpam-1829	33	8	is	be	AUX
ejpam-1829	33	9	a	a	DET
ejpam-1829	33	10	noetherian	noetherian	ADJ
ejpam-1829	33	11	ring	ring	NOUN
ejpam-1829	33	12	and	and	CCONJ
ejpam-1829	33	13	σ	σ	NOUN
ejpam-1829	33	14	an	an	DET
ejpam-1829	33	15	automorphism	automorphism	NOUN
ejpam-1829	33	16	of	of	ADP
ejpam-1829	33	17	r	r	NOUN
ejpam-1829	33	18	,	,	PUNCT
ejpam-1829	33	19	then	then	ADV
ejpam-1829	33	20	r	r	NOUN
ejpam-1829	33	21	is	be	AUX
ejpam-1829	33	22	a	a	DET
ejpam-1829	33	23	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	33	24	implies	implie	NOUN
ejpam-1829	33	25	that	that	SCONJ
ejpam-1829	33	26	r	r	NOUN
ejpam-1829	33	27	is	be	AUX
ejpam-1829	33	28	2	2	NUM
ejpam-1829	33	29	-	-	PUNCT
ejpam-1829	33	30	primal	primal	ADJ
ejpam-1829	33	31	.	.	PUNCT
ejpam-1829	34	1	the	the	DET
ejpam-1829	34	2	following	follow	VERB
ejpam-1829	34	3	example	example	NOUN
ejpam-1829	34	4	shows	show	VERB
ejpam-1829	34	5	that	that	SCONJ
ejpam-1829	34	6	if	if	SCONJ
ejpam-1829	34	7	r	r	NOUN
ejpam-1829	34	8	is	be	AUX
ejpam-1829	34	9	a	a	DET
ejpam-1829	34	10	noetherian	noetherian	ADJ
ejpam-1829	34	11	ring	ring	NOUN
ejpam-1829	34	12	,	,	PUNCT
ejpam-1829	34	13	then	then	ADV
ejpam-1829	34	14	even	even	ADV
ejpam-1829	34	15	r[x	r[x	NOUN
ejpam-1829	34	16	]	]	PUNCT
ejpam-1829	34	17	need	need	AUX
ejpam-1829	34	18	not	not	PART
ejpam-1829	34	19	be	be	AUX
ejpam-1829	34	20	2	2	NUM
ejpam-1829	34	21	-	-	PUNCT
ejpam-1829	34	22	primal	primal	ADJ
ejpam-1829	34	23	.	.	PUNCT
ejpam-1829	35	1	example	example	NOUN
ejpam-1829	36	1	2	2	NUM
ejpam-1829	36	2	.	.	PUNCT
ejpam-1829	36	3	let	let	VERB
ejpam-1829	36	4	r	r	NOUN
ejpam-1829	36	5	=	=	SYM
ejpam-1829	36	6	m2(q	m2(q	NOUN
ejpam-1829	36	7	)	)	PUNCT
ejpam-1829	36	8	,	,	PUNCT
ejpam-1829	36	9	the	the	DET
ejpam-1829	36	10	set	set	NOUN
ejpam-1829	36	11	of	of	ADP
ejpam-1829	36	12	2	2	NUM
ejpam-1829	36	13	×	×	NOUN
ejpam-1829	36	14	2	2	NUM
ejpam-1829	36	15	matrices	matrix	NOUN
ejpam-1829	36	16	over	over	ADP
ejpam-1829	36	17	q.	q.	PROPN
ejpam-1829	36	18	then	then	ADV
ejpam-1829	36	19	r[x	r[x	PROPN
ejpam-1829	36	20	]	]	PUNCT
ejpam-1829	36	21	is	be	AUX
ejpam-1829	36	22	a	a	DET
ejpam-1829	36	23	prime	prime	ADJ
ejpam-1829	36	24	ring	ring	NOUN
ejpam-1829	36	25	with	with	ADP
ejpam-1829	36	26	non	non	ADJ
ejpam-1829	36	27	-	-	ADJ
ejpam-1829	36	28	zero	zero	ADJ
ejpam-1829	36	29	nilpotent	nilpotent	ADJ
ejpam-1829	36	30	elements	element	NOUN
ejpam-1829	36	31	and	and	CCONJ
ejpam-1829	36	32	,	,	PUNCT
ejpam-1829	36	33	so	so	ADV
ejpam-1829	36	34	can	can	AUX
ejpam-1829	36	35	not	not	PART
ejpam-1829	36	36	be	be	AUX
ejpam-1829	36	37	2	2	NUM
ejpam-1829	36	38	-	-	PUNCT
ejpam-1829	36	39	primal	primal	ADJ
ejpam-1829	36	40	.	.	PUNCT
ejpam-1829	37	1	skew	skew	ADJ
ejpam-1829	37	2	polynomial	polynomial	ADJ
ejpam-1829	37	3	rings	ring	NOUN
ejpam-1829	37	4	let	let	VERB
ejpam-1829	37	5	r	r	PRON
ejpam-1829	37	6	be	be	AUX
ejpam-1829	37	7	a	a	DET
ejpam-1829	37	8	ring	ring	NOUN
ejpam-1829	37	9	,	,	PUNCT
ejpam-1829	37	10	σ	σ	X
ejpam-1829	37	11	be	be	VERB
ejpam-1829	37	12	an	an	DET
ejpam-1829	37	13	endomorphism	endomorphism	NOUN
ejpam-1829	37	14	of	of	ADP
ejpam-1829	37	15	r	r	NOUN
ejpam-1829	37	16	and	and	CCONJ
ejpam-1829	37	17	δ	δ	PROPN
ejpam-1829	37	18	a	a	DET
ejpam-1829	37	19	σ	σ	NOUN
ejpam-1829	37	20	-	-	PUNCT
ejpam-1829	37	21	derivation	derivation	NOUN
ejpam-1829	37	22	of	of	ADP
ejpam-1829	37	23	r.	r.	PROPN
ejpam-1829	37	24	recall	recall	PROPN
ejpam-1829	37	25	that	that	SCONJ
ejpam-1829	37	26	δ	δ	PROPN
ejpam-1829	37	27	is	be	AUX
ejpam-1829	37	28	an	an	DET
ejpam-1829	37	29	additive	additive	ADJ
ejpam-1829	37	30	map	map	NOUN
ejpam-1829	37	31	δ	δ	NOUN
ejpam-1829	37	32	:	:	PUNCT
ejpam-1829	37	33	r→	r→	AUX
ejpam-1829	37	34	r	r	NOUN
ejpam-1829	37	35	such	such	ADJ
ejpam-1829	37	36	that	that	DET
ejpam-1829	37	37	δ(ab	δ(ab	NOUN
ejpam-1829	37	38	)	)	PUNCT
ejpam-1829	37	39	=	=	SYM
ejpam-1829	37	40	δ(a)σ(b	δ(a)σ(b	NOUN
ejpam-1829	37	41	)	)	PUNCT
ejpam-1829	37	42	+	+	NUM
ejpam-1829	37	43	aδ(b	aδ(b	NOUN
ejpam-1829	37	44	)	)	PUNCT
ejpam-1829	37	45	,	,	PUNCT
ejpam-1829	37	46	for	for	ADP
ejpam-1829	37	47	all	all	DET
ejpam-1829	37	48	a	a	PRON
ejpam-1829	37	49	,	,	PUNCT
ejpam-1829	37	50	b	b	PROPN
ejpam-1829	37	51	∈	∈	PROPN
ejpam-1829	37	52	r.	r.	PROPN
ejpam-1829	37	53	example	example	NOUN
ejpam-1829	38	1	3	3	X
ejpam-1829	38	2	.	.	PUNCT
ejpam-1829	38	3	let	let	VERB
ejpam-1829	38	4	σ	σ	NOUN
ejpam-1829	38	5	be	be	AUX
ejpam-1829	38	6	an	an	DET
ejpam-1829	38	7	automorphism	automorphism	NOUN
ejpam-1829	38	8	of	of	ADP
ejpam-1829	38	9	a	a	DET
ejpam-1829	38	10	ring	ring	NOUN
ejpam-1829	38	11	r	r	NOUN
ejpam-1829	38	12	and	and	CCONJ
ejpam-1829	38	13	δ	δ	NOUN
ejpam-1829	38	14	:	:	PUNCT
ejpam-1829	39	1	r→	r→	VERB
ejpam-1829	39	2	r	r	VERB
ejpam-1829	39	3	any	any	DET
ejpam-1829	39	4	map	map	NOUN
ejpam-1829	39	5	.	.	PUNCT
ejpam-1829	40	1	let	let	VERB
ejpam-1829	40	2	φ	φ	NOUN
ejpam-1829	40	3	:	:	PUNCT
ejpam-1829	41	1	r→	r→	PROPN
ejpam-1829	41	2	m2(r	m2(r	X
ejpam-1829	41	3	)	)	PUNCT
ejpam-1829	41	4	defined	define	VERB
ejpam-1829	41	5	by	by	ADP
ejpam-1829	41	6	φ(r	φ(r	ADJ
ejpam-1829	41	7	)	)	PUNCT
ejpam-1829	41	8	=	=	SYM
ejpam-1829	41	9	�	�	PROPN
ejpam-1829	41	10	σ(r	σ(r	PROPN
ejpam-1829	41	11	)	)	PUNCT
ejpam-1829	41	12	0	0	PUNCT
ejpam-1829	42	1	δ(r	δ(r	NOUN
ejpam-1829	42	2	)	)	PUNCT
ejpam-1829	42	3	r	r	NOUN
ejpam-1829	42	4	�	�	PROPN
ejpam-1829	42	5	,	,	PUNCT
ejpam-1829	42	6	for	for	ADP
ejpam-1829	42	7	all	all	DET
ejpam-1829	42	8	r	r	NOUN
ejpam-1829	42	9	∈	∈	NOUN
ejpam-1829	42	10	r	r	NOUN
ejpam-1829	42	11	be	be	VERB
ejpam-1829	42	12	a	a	DET
ejpam-1829	42	13	homomorphism	homomorphism	NOUN
ejpam-1829	42	14	.	.	PUNCT
ejpam-1829	43	1	then	then	ADV
ejpam-1829	43	2	δ	δ	PROPN
ejpam-1829	43	3	is	be	AUX
ejpam-1829	43	4	a	a	DET
ejpam-1829	43	5	σ	σ	NOUN
ejpam-1829	43	6	-	-	PUNCT
ejpam-1829	43	7	derivation	derivation	NOUN
ejpam-1829	43	8	of	of	ADP
ejpam-1829	43	9	r.	r.	PROPN
ejpam-1829	43	10	v.	v.	PROPN
ejpam-1829	43	11	bhat	bhat	PROPN
ejpam-1829	43	12	/	/	SYM
ejpam-1829	43	13	eur	eur	PROPN
ejpam-1829	43	14	.	.	PUNCT
ejpam-1829	44	1	j.	j.	PROPN
ejpam-1829	44	2	pure	pure	PROPN
ejpam-1829	44	3	appl	appl	PROPN
ejpam-1829	44	4	.	.	PROPN
ejpam-1829	44	5	math	math	PROPN
ejpam-1829	44	6	,	,	PUNCT
ejpam-1829	44	7	7	7	NUM
ejpam-1829	44	8	(	(	PUNCT
ejpam-1829	44	9	2014	2014	NUM
ejpam-1829	44	10	)	)	PUNCT
ejpam-1829	44	11	,	,	PUNCT
ejpam-1829	44	12	387	387	NUM
ejpam-1829	44	13	-	-	SYM
ejpam-1829	44	14	394	394	NUM
ejpam-1829	44	15	389	389	NUM
ejpam-1829	44	16	recall	recall	NOUN
ejpam-1829	44	17	that	that	SCONJ
ejpam-1829	44	18	the	the	DET
ejpam-1829	44	19	skew	skew	ADJ
ejpam-1829	44	20	polynomial	polynomial	ADJ
ejpam-1829	44	21	ring	ring	NOUN
ejpam-1829	44	22	(	(	PUNCT
ejpam-1829	44	23	ore	ore	NOUN
ejpam-1829	44	24	extension	extension	NOUN
ejpam-1829	44	25	)	)	PUNCT
ejpam-1829	44	26	r[x;σ	r[x;σ	NOUN
ejpam-1829	44	27	,	,	PUNCT
ejpam-1829	44	28	δ	δ	PROPN
ejpam-1829	44	29	]	]	PUNCT
ejpam-1829	44	30	is	be	AUX
ejpam-1829	44	31	the	the	DET
ejpam-1829	44	32	usual	usual	ADJ
ejpam-1829	44	33	ring	ring	NOUN
ejpam-1829	44	34	of	of	ADP
ejpam-1829	44	35	polynomials	polynomial	NOUN
ejpam-1829	44	36	with	with	ADP
ejpam-1829	44	37	coefficients	coefficient	NOUN
ejpam-1829	44	38	in	in	ADP
ejpam-1829	44	39	r	r	NOUN
ejpam-1829	44	40	,	,	PUNCT
ejpam-1829	44	41	in	in	SCONJ
ejpam-1829	44	42	which	which	DET
ejpam-1829	44	43	multiplication	multiplication	NOUN
ejpam-1829	44	44	is	be	AUX
ejpam-1829	44	45	subject	subject	ADJ
ejpam-1829	44	46	to	to	ADP
ejpam-1829	44	47	the	the	DET
ejpam-1829	44	48	relation	relation	NOUN
ejpam-1829	44	49	ax	ax	NOUN
ejpam-1829	44	50	=	=	PUNCT
ejpam-1829	44	51	xσ(a)+δ(a	xσ(a)+δ(a	NUM
ejpam-1829	44	52	)	)	PUNCT
ejpam-1829	44	53	for	for	ADP
ejpam-1829	44	54	all	all	DET
ejpam-1829	44	55	a	a	DET
ejpam-1829	44	56	∈	∈	PROPN
ejpam-1829	44	57	r.	r.	NOUN
ejpam-1829	44	58	we	we	PRON
ejpam-1829	44	59	take	take	VERB
ejpam-1829	44	60	any	any	DET
ejpam-1829	44	61	f	f	NOUN
ejpam-1829	44	62	(	(	PUNCT
ejpam-1829	44	63	x	x	X
ejpam-1829	44	64	)	)	PUNCT
ejpam-1829	44	65	∈	∈	PROPN
ejpam-1829	44	66	r[x;σ	r[x;σ	NOUN
ejpam-1829	44	67	,	,	PUNCT
ejpam-1829	44	68	δ	δ	PROPN
ejpam-1829	44	69	]	]	PUNCT
ejpam-1829	44	70	to	to	PART
ejpam-1829	44	71	be	be	AUX
ejpam-1829	44	72	of	of	ADP
ejpam-1829	44	73	the	the	DET
ejpam-1829	44	74	form	form	NOUN
ejpam-1829	44	75	f	f	X
ejpam-1829	44	76	(	(	PUNCT
ejpam-1829	44	77	x	x	X
ejpam-1829	44	78	)	)	PUNCT
ejpam-1829	44	79	=	=	SYM
ejpam-1829	45	1	∑n	∑n	NUM
ejpam-1829	45	2	i=0	i=0	PROPN
ejpam-1829	45	3	x	x	PUNCT
ejpam-1829	45	4	iai	iai	NOUN
ejpam-1829	45	5	.	.	PUNCT
ejpam-1829	46	1	we	we	PRON
ejpam-1829	46	2	denote	denote	VERB
ejpam-1829	46	3	r[x;σ	r[x;σ	NOUN
ejpam-1829	46	4	,	,	PUNCT
ejpam-1829	46	5	δ	δ	PROPN
ejpam-1829	46	6	]	]	PUNCT
ejpam-1829	46	7	by	by	ADP
ejpam-1829	46	8	o(r	o(r	NOUN
ejpam-1829	46	9	)	)	PUNCT
ejpam-1829	46	10	.	.	PUNCT
ejpam-1829	47	1	if	if	SCONJ
ejpam-1829	47	2	i	i	PRON
ejpam-1829	47	3	is	be	AUX
ejpam-1829	47	4	an	an	DET
ejpam-1829	47	5	ideal	ideal	NOUN
ejpam-1829	47	6	of	of	ADP
ejpam-1829	47	7	r	r	NOUN
ejpam-1829	47	8	such	such	ADJ
ejpam-1829	47	9	that	that	PRON
ejpam-1829	47	10	σ(i	σ(i	NOUN
ejpam-1829	47	11	)	)	PUNCT
ejpam-1829	48	1	=	=	SYM
ejpam-1829	48	2	i	i	PROPN
ejpam-1829	48	3	and	and	CCONJ
ejpam-1829	48	4	δ(i	δ(i	PROPN
ejpam-1829	48	5	)	)	PUNCT
ejpam-1829	49	1	⊆	⊆	NUM
ejpam-1829	49	2	i	i	PRON
ejpam-1829	49	3	,	,	PUNCT
ejpam-1829	49	4	then	then	ADV
ejpam-1829	49	5	o(i	o(i	PROPN
ejpam-1829	49	6	)	)	PUNCT
ejpam-1829	49	7	denotes	denote	NOUN
ejpam-1829	49	8	i[x;σ	i[x;σ	NUM
ejpam-1829	49	9	,	,	PUNCT
ejpam-1829	49	10	δ	δ	PROPN
ejpam-1829	49	11	]	]	X
ejpam-1829	49	12	,	,	PUNCT
ejpam-1829	49	13	which	which	PRON
ejpam-1829	49	14	is	be	AUX
ejpam-1829	49	15	an	an	DET
ejpam-1829	49	16	ideal	ideal	NOUN
ejpam-1829	49	17	of	of	ADP
ejpam-1829	49	18	o(r	o(r	PROPN
ejpam-1829	49	19	)	)	PUNCT
ejpam-1829	49	20	.	.	PUNCT
ejpam-1829	50	1	skew	skew	ADJ
ejpam-1829	50	2	-	-	PUNCT
ejpam-1829	50	3	laurent	laurent	NOUN
ejpam-1829	50	4	rings	ring	NOUN
ejpam-1829	50	5	recall	recall	VERB
ejpam-1829	50	6	that	that	DET
ejpam-1829	50	7	r[x	r[x	NOUN
ejpam-1829	50	8	,	,	PUNCT
ejpam-1829	50	9	x−1;σ	x−1;σ	PROPN
ejpam-1829	50	10	]	]	PUNCT
ejpam-1829	50	11	is	be	AUX
ejpam-1829	50	12	the	the	DET
ejpam-1829	50	13	usual	usual	ADJ
ejpam-1829	50	14	ring	ring	NOUN
ejpam-1829	50	15	of	of	ADP
ejpam-1829	50	16	laurent	laurent	NOUN
ejpam-1829	50	17	polynomials	polynomial	NOUN
ejpam-1829	50	18	with	with	ADP
ejpam-1829	50	19	coefficients	coefficient	NOUN
ejpam-1829	50	20	in	in	ADP
ejpam-1829	50	21	r	r	NOUN
ejpam-1829	50	22	,	,	PUNCT
ejpam-1829	50	23	in	in	SCONJ
ejpam-1829	50	24	which	which	DET
ejpam-1829	50	25	multiplication	multiplication	NOUN
ejpam-1829	50	26	is	be	AUX
ejpam-1829	50	27	subject	subject	ADJ
ejpam-1829	50	28	to	to	ADP
ejpam-1829	50	29	the	the	DET
ejpam-1829	50	30	relation	relation	NOUN
ejpam-1829	50	31	ax	ax	NOUN
ejpam-1829	50	32	=	=	PUNCT
ejpam-1829	50	33	xσ(a	xσ(a	NUM
ejpam-1829	50	34	)	)	PUNCT
ejpam-1829	50	35	for	for	ADP
ejpam-1829	50	36	all	all	DET
ejpam-1829	50	37	a	a	DET
ejpam-1829	50	38	∈	∈	PROPN
ejpam-1829	50	39	r.	r.	NOUN
ejpam-1829	50	40	we	we	PRON
ejpam-1829	50	41	take	take	VERB
ejpam-1829	50	42	any	any	DET
ejpam-1829	50	43	f	f	NOUN
ejpam-1829	50	44	(	(	PUNCT
ejpam-1829	50	45	x	x	X
ejpam-1829	50	46	)	)	PUNCT
ejpam-1829	50	47	∈	∈	PROPN
ejpam-1829	50	48	r[x	r[x	NOUN
ejpam-1829	50	49	,	,	PUNCT
ejpam-1829	50	50	x−1;σ	x−1;σ	PROPN
ejpam-1829	50	51	]	]	PUNCT
ejpam-1829	50	52	to	to	PART
ejpam-1829	50	53	be	be	AUX
ejpam-1829	50	54	of	of	ADP
ejpam-1829	50	55	the	the	DET
ejpam-1829	50	56	form	form	NOUN
ejpam-1829	50	57	f	f	X
ejpam-1829	50	58	(	(	PUNCT
ejpam-1829	50	59	x	x	NOUN
ejpam-1829	50	60	)	)	PUNCT
ejpam-1829	50	61	=	=	SYM
ejpam-1829	51	1	∑n	∑n	PROPN
ejpam-1829	51	2	i=−m	i=−m	PROPN
ejpam-1829	51	3	x	x	SYM
ejpam-1829	51	4	iai	iai	ADJ
ejpam-1829	51	5	.	.	PUNCT
ejpam-1829	52	1	we	we	PRON
ejpam-1829	52	2	denote	denote	VERB
ejpam-1829	52	3	r[x	r[x	NOUN
ejpam-1829	52	4	,	,	PUNCT
ejpam-1829	52	5	x−1;σ	x−1;σ	PROPN
ejpam-1829	52	6	]	]	PUNCT
ejpam-1829	52	7	by	by	ADP
ejpam-1829	52	8	l(r	l(r	PROPN
ejpam-1829	52	9	)	)	PUNCT
ejpam-1829	52	10	.	.	PUNCT
ejpam-1829	53	1	if	if	SCONJ
ejpam-1829	53	2	an	an	DET
ejpam-1829	53	3	ideal	ideal	ADJ
ejpam-1829	53	4	i	i	PRON
ejpam-1829	53	5	of	of	ADP
ejpam-1829	53	6	a	a	DET
ejpam-1829	53	7	ring	ring	NOUN
ejpam-1829	53	8	r	r	NOUN
ejpam-1829	53	9	is	be	AUX
ejpam-1829	53	10	σ	σ	NOUN
ejpam-1829	53	11	-	-	ADJ
ejpam-1829	53	12	stable	stable	ADJ
ejpam-1829	53	13	(	(	PUNCT
ejpam-1829	53	14	i.e.	i.e.	X
ejpam-1829	53	15	σ(i	σ(i	NOUN
ejpam-1829	53	16	)	)	PUNCT
ejpam-1829	54	1	=	=	SYM
ejpam-1829	54	2	i	i	PROPN
ejpam-1829	54	3	)	)	PUNCT
ejpam-1829	54	4	,	,	PUNCT
ejpam-1829	54	5	then	then	ADV
ejpam-1829	54	6	we	we	PRON
ejpam-1829	54	7	denote	denote	VERB
ejpam-1829	54	8	as	as	ADP
ejpam-1829	54	9	usual	usual	ADJ
ejpam-1829	54	10	i[x	i[x	PROPN
ejpam-1829	54	11	,	,	PUNCT
ejpam-1829	54	12	x−1;σ	x−1;σ	PROPN
ejpam-1829	54	13	]	]	PUNCT
ejpam-1829	54	14	by	by	ADP
ejpam-1829	54	15	l(i	l(i	NOUN
ejpam-1829	54	16	)	)	PUNCT
ejpam-1829	54	17	.	.	PUNCT
ejpam-1829	55	1	we	we	PRON
ejpam-1829	55	2	also	also	ADV
ejpam-1829	55	3	note	note	VERB
ejpam-1829	55	4	that	that	SCONJ
ejpam-1829	55	5	ifσ	ifσ	PRON
ejpam-1829	55	6	is	be	AUX
ejpam-1829	55	7	an	an	DET
ejpam-1829	55	8	automorphism	automorphism	NOUN
ejpam-1829	55	9	of	of	ADP
ejpam-1829	55	10	r	r	NOUN
ejpam-1829	55	11	,	,	PUNCT
ejpam-1829	55	12	then	then	ADV
ejpam-1829	55	13	it	it	PRON
ejpam-1829	55	14	can	can	AUX
ejpam-1829	55	15	be	be	AUX
ejpam-1829	55	16	extended	extend	VERB
ejpam-1829	55	17	to	to	ADP
ejpam-1829	55	18	an	an	DET
ejpam-1829	55	19	automorphism	automorphism	NOUN
ejpam-1829	55	20	(	(	PUNCT
ejpam-1829	55	21	say	say	INTJ
ejpam-1829	55	22	σ	σ	NOUN
ejpam-1829	55	23	)	)	PUNCT
ejpam-1829	55	24	of	of	ADP
ejpam-1829	55	25	r[x	r[x	NOUN
ejpam-1829	55	26	,	,	PUNCT
ejpam-1829	55	27	x−1;σ	x−1;σ	PROPN
ejpam-1829	55	28	]	]	PUNCT
ejpam-1829	55	29	such	such	ADJ
ejpam-1829	55	30	that	that	SCONJ
ejpam-1829	55	31	σ(x	σ(x	NOUN
ejpam-1829	55	32	)	)	PUNCT
ejpam-1829	55	33	=	=	SYM
ejpam-1829	56	1	x	x	NOUN
ejpam-1829	56	2	;	;	PUNCT
ejpam-1829	56	3	i.e.	i.e.	X
ejpam-1829	56	4	σ(σn	σ(σn	PROPN
ejpam-1829	56	5	i=−m	i=−m	PROPN
ejpam-1829	56	6	x	x	PROPN
ejpam-1829	56	7	iai	iai	PROPN
ejpam-1829	56	8	)	)	PUNCT
ejpam-1829	56	9	=	=	PUNCT
ejpam-1829	56	10	σn	σn	PROPN
ejpam-1829	56	11	i=−m	i=−m	PROPN
ejpam-1829	56	12	x	x	SYM
ejpam-1829	56	13	iσ(ai	iσ(ai	PROPN
ejpam-1829	56	14	)	)	PUNCT
ejpam-1829	56	15	.	.	PUNCT
ejpam-1829	57	1	the	the	DET
ejpam-1829	57	2	study	study	NOUN
ejpam-1829	57	3	of	of	ADP
ejpam-1829	57	4	skew	skew	ADJ
ejpam-1829	57	5	polynomial	polynomial	ADJ
ejpam-1829	57	6	rings	ring	NOUN
ejpam-1829	57	7	and	and	CCONJ
ejpam-1829	57	8	skew	skew	NOUN
ejpam-1829	57	9	-	-	PUNCT
ejpam-1829	57	10	laurent	laurent	NOUN
ejpam-1829	57	11	rings	ring	NOUN
ejpam-1829	57	12	has	have	AUX
ejpam-1829	57	13	been	be	AUX
ejpam-1829	57	14	of	of	ADP
ejpam-1829	57	15	interest	interest	NOUN
ejpam-1829	57	16	to	to	ADP
ejpam-1829	57	17	many	many	ADJ
ejpam-1829	57	18	authors	author	NOUN
ejpam-1829	57	19	.	.	PUNCT
ejpam-1829	58	1	for	for	ADP
ejpam-1829	58	2	example	example	NOUN
ejpam-1829	58	3	[	[	X
ejpam-1829	58	4	1	1	NUM
ejpam-1829	58	5	,	,	PUNCT
ejpam-1829	58	6	6	6	NUM
ejpam-1829	58	7	,	,	PUNCT
ejpam-1829	58	8	7	7	NUM
ejpam-1829	58	9	,	,	PUNCT
ejpam-1829	58	10	9	9	NUM
ejpam-1829	58	11	]	]	PUNCT
ejpam-1829	58	12	.	.	PUNCT
ejpam-1829	59	1	in	in	ADP
ejpam-1829	59	2	this	this	DET
ejpam-1829	59	3	paper	paper	NOUN
ejpam-1829	59	4	we	we	PRON
ejpam-1829	59	5	prove	prove	VERB
ejpam-1829	59	6	the	the	DET
ejpam-1829	59	7	following	follow	VERB
ejpam-1829	59	8	results	result	NOUN
ejpam-1829	59	9	:	:	PUNCT
ejpam-1829	59	10	theorem	theorem	NOUN
ejpam-1829	59	11	2	2	NUM
ejpam-1829	59	12	:	:	PUNCT
ejpam-1829	59	13	let	let	VERB
ejpam-1829	59	14	r	r	PRON
ejpam-1829	59	15	be	be	AUX
ejpam-1829	59	16	a	a	DET
ejpam-1829	59	17	noetherian	noetherian	ADJ
ejpam-1829	59	18	ring	ring	NOUN
ejpam-1829	59	19	and	and	CCONJ
ejpam-1829	59	20	σ	σ	NOUN
ejpam-1829	59	21	an	an	DET
ejpam-1829	59	22	automorphism	automorphism	NOUN
ejpam-1829	59	23	of	of	ADP
ejpam-1829	59	24	r.	r.	PROPN
ejpam-1829	59	25	then	then	ADV
ejpam-1829	59	26	r	r	NOUN
ejpam-1829	59	27	is	be	AUX
ejpam-1829	59	28	a	a	DET
ejpam-1829	59	29	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	59	30	if	if	SCONJ
ejpam-1829	59	31	and	and	CCONJ
ejpam-1829	59	32	only	only	ADV
ejpam-1829	59	33	if	if	SCONJ
ejpam-1829	59	34	r[x	r[x	NOUN
ejpam-1829	59	35	,	,	PUNCT
ejpam-1829	59	36	x−1;σ	x−1;σ	PROPN
ejpam-1829	59	37	]	]	PUNCT
ejpam-1829	59	38	is	be	AUX
ejpam-1829	59	39	a	a	DET
ejpam-1829	59	40	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	59	41	.	.	PUNCT
ejpam-1829	60	1	theorem	theorem	NOUN
ejpam-1829	60	2	3	3	NUM
ejpam-1829	60	3	:	:	PUNCT
ejpam-1829	60	4	let	let	VERB
ejpam-1829	60	5	r	r	PRON
ejpam-1829	60	6	be	be	AUX
ejpam-1829	60	7	a	a	DET
ejpam-1829	60	8	noetherian	noetherian	ADJ
ejpam-1829	60	9	ring	ring	NOUN
ejpam-1829	60	10	which	which	PRON
ejpam-1829	60	11	is	be	AUX
ejpam-1829	60	12	also	also	ADV
ejpam-1829	60	13	an	an	DET
ejpam-1829	60	14	algebra	algebra	NOUN
ejpam-1829	60	15	over	over	ADP
ejpam-1829	60	16	q.	q.	PROPN
ejpam-1829	60	17	let	let	VERB
ejpam-1829	60	18	σ	σ	NOUN
ejpam-1829	60	19	be	be	AUX
ejpam-1829	60	20	an	an	DET
ejpam-1829	60	21	automorphism	automorphism	NOUN
ejpam-1829	60	22	of	of	ADP
ejpam-1829	60	23	r	r	NOUN
ejpam-1829	60	24	such	such	ADJ
ejpam-1829	60	25	that	that	SCONJ
ejpam-1829	60	26	r	r	NOUN
ejpam-1829	60	27	is	be	AUX
ejpam-1829	60	28	a	a	DET
ejpam-1829	60	29	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	60	30	and	and	CCONJ
ejpam-1829	60	31	δ	δ	PROPN
ejpam-1829	60	32	a	a	DET
ejpam-1829	60	33	σ	σ	NOUN
ejpam-1829	60	34	-	-	PUNCT
ejpam-1829	60	35	derivation	derivation	NOUN
ejpam-1829	60	36	of	of	ADP
ejpam-1829	60	37	r	r	NOUN
ejpam-1829	60	38	such	such	ADJ
ejpam-1829	60	39	that	that	DET
ejpam-1829	60	40	σ(δ(a	σ(δ(a	NOUN
ejpam-1829	60	41	)	)	PUNCT
ejpam-1829	60	42	)	)	PUNCT
ejpam-1829	61	1	=	=	PUNCT
ejpam-1829	61	2	δ(σ(a	δ(σ(a	NOUN
ejpam-1829	61	3	)	)	PUNCT
ejpam-1829	61	4	)	)	PUNCT
ejpam-1829	61	5	for	for	ADP
ejpam-1829	61	6	all	all	DET
ejpam-1829	61	7	a	a	DET
ejpam-1829	61	8	∈	∈	PROPN
ejpam-1829	61	9	r.	r.	NOUN
ejpam-1829	61	10	then	then	ADV
ejpam-1829	61	11	r[x;σ	r[x;σ	NOUN
ejpam-1829	61	12	,	,	PUNCT
ejpam-1829	61	13	δ	δ	PROPN
ejpam-1829	61	14	]	]	PUNCT
ejpam-1829	61	15	is	be	AUX
ejpam-1829	61	16	a	a	DET
ejpam-1829	61	17	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	61	18	.	.	NOUN
ejpam-1829	61	19	2	2	NUM
ejpam-1829	61	20	.	.	X
ejpam-1829	61	21	preliminaries	preliminary	NOUN
ejpam-1829	61	22	we	we	PRON
ejpam-1829	61	23	begin	begin	VERB
ejpam-1829	61	24	this	this	DET
ejpam-1829	61	25	section	section	NOUN
ejpam-1829	61	26	with	with	ADP
ejpam-1829	61	27	the	the	DET
ejpam-1829	61	28	following	follow	VERB
ejpam-1829	61	29	proposition	proposition	NOUN
ejpam-1829	61	30	:	:	PUNCT
ejpam-1829	61	31	proposition	proposition	NOUN
ejpam-1829	61	32	1	1	NUM
ejpam-1829	61	33	.	.	PUNCT
ejpam-1829	62	1	let	let	VERB
ejpam-1829	62	2	r	r	PRON
ejpam-1829	62	3	be	be	AUX
ejpam-1829	62	4	a	a	DET
ejpam-1829	62	5	ring	ring	NOUN
ejpam-1829	62	6	and	and	CCONJ
ejpam-1829	62	7	σ	σ	NOUN
ejpam-1829	62	8	an	an	DET
ejpam-1829	62	9	automorphism	automorphism	NOUN
ejpam-1829	62	10	of	of	ADP
ejpam-1829	62	11	r.	r.	PROPN
ejpam-1829	62	12	then	then	ADV
ejpam-1829	62	13	r	r	NOUN
ejpam-1829	62	14	is	be	AUX
ejpam-1829	62	15	a	a	DET
ejpam-1829	62	16	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	62	17	implies	implie	NOUN
ejpam-1829	62	18	r	r	NOUN
ejpam-1829	62	19	is	be	AUX
ejpam-1829	62	20	2	2	NUM
ejpam-1829	62	21	-	-	PUNCT
ejpam-1829	62	22	primal	primal	ADJ
ejpam-1829	62	23	.	.	PUNCT
ejpam-1829	63	1	proof	proof	NOUN
ejpam-1829	63	2	.	.	PUNCT
ejpam-1829	64	1	let	let	VERB
ejpam-1829	64	2	a	a	DET
ejpam-1829	64	3	∈	∈	NOUN
ejpam-1829	64	4	r	r	NOUN
ejpam-1829	64	5	be	be	VERB
ejpam-1829	64	6	such	such	ADJ
ejpam-1829	64	7	that	that	SCONJ
ejpam-1829	64	8	a2	a2	PROPN
ejpam-1829	64	9	∈	∈	PROPN
ejpam-1829	64	10	p(r	p(r	PROPN
ejpam-1829	64	11	)	)	PUNCT
ejpam-1829	64	12	.	.	PUNCT
ejpam-1829	65	1	then	then	ADV
ejpam-1829	65	2	aσ(a)σ(aσ(a	aσ(a)σ(aσ(a	X
ejpam-1829	65	3	)	)	PUNCT
ejpam-1829	65	4	)	)	PUNCT
ejpam-1829	66	1	=	=	SYM
ejpam-1829	66	2	aσ(a)σ(a)σ2(a	aσ(a)σ(a)σ2(a	NOUN
ejpam-1829	66	3	)	)	PUNCT
ejpam-1829	66	4	∈	∈	PROPN
ejpam-1829	66	5	σ(p(r	σ(p(r	PROPN
ejpam-1829	66	6	)	)	PUNCT
ejpam-1829	66	7	)	)	PUNCT
ejpam-1829	67	1	=	=	SYM
ejpam-1829	67	2	p(r	p(r	PROPN
ejpam-1829	67	3	)	)	PUNCT
ejpam-1829	67	4	.	.	PUNCT
ejpam-1829	68	1	therefore	therefore	ADV
ejpam-1829	68	2	aσ(a	aσ(a	ADV
ejpam-1829	68	3	)	)	PUNCT
ejpam-1829	68	4	∈	∈	PROPN
ejpam-1829	68	5	p(r	p(r	PROPN
ejpam-1829	68	6	)	)	PUNCT
ejpam-1829	68	7	and	and	CCONJ
ejpam-1829	68	8	hence	hence	ADV
ejpam-1829	68	9	a	a	DET
ejpam-1829	68	10	∈	∈	PROPN
ejpam-1829	68	11	p(r	p(r	NOUN
ejpam-1829	68	12	)	)	PUNCT
ejpam-1829	68	13	.	.	PUNCT
ejpam-1829	69	1	the	the	DET
ejpam-1829	69	2	following	follow	VERB
ejpam-1829	69	3	example	example	NOUN
ejpam-1829	69	4	shows	show	VERB
ejpam-1829	69	5	that	that	SCONJ
ejpam-1829	69	6	there	there	PRON
ejpam-1829	69	7	exists	exist	VERB
ejpam-1829	69	8	an	an	DET
ejpam-1829	69	9	endomorphism	endomorphism	PROPN
ejpam-1829	69	10	σ	σ	NOUN
ejpam-1829	69	11	of	of	ADP
ejpam-1829	69	12	a	a	DET
ejpam-1829	69	13	ring	ring	NOUN
ejpam-1829	69	14	r	r	NOUN
ejpam-1829	69	15	such	such	ADJ
ejpam-1829	69	16	that	that	SCONJ
ejpam-1829	69	17	the	the	DET
ejpam-1829	69	18	converse	converse	NOUN
ejpam-1829	69	19	of	of	ADP
ejpam-1829	69	20	the	the	DET
ejpam-1829	69	21	above	above	ADJ
ejpam-1829	69	22	proposition	proposition	NOUN
ejpam-1829	69	23	does	do	AUX
ejpam-1829	69	24	not	not	PART
ejpam-1829	69	25	hold	hold	VERB
ejpam-1829	69	26	.	.	PUNCT
ejpam-1829	70	1	example	example	NOUN
ejpam-1829	70	2	4	4	NUM
ejpam-1829	70	3	.	.	PUNCT
ejpam-1829	71	1	let	let	VERB
ejpam-1829	71	2	r=	r=	PROPN
ejpam-1829	71	3	f[x	f[x	PROPN
ejpam-1829	71	4	]	]	PUNCT
ejpam-1829	71	5	,	,	PUNCT
ejpam-1829	71	6	f	f	PROPN
ejpam-1829	71	7	a	a	DET
ejpam-1829	71	8	field	field	NOUN
ejpam-1829	71	9	.	.	PUNCT
ejpam-1829	72	1	then	then	ADV
ejpam-1829	72	2	r	r	NOUN
ejpam-1829	72	3	is	be	AUX
ejpam-1829	72	4	a	a	DET
ejpam-1829	72	5	commutative	commutative	ADJ
ejpam-1829	72	6	domain	domain	NOUN
ejpam-1829	72	7	,	,	PUNCT
ejpam-1829	72	8	and	and	CCONJ
ejpam-1829	72	9	therefore	therefore	ADV
ejpam-1829	72	10	is	be	AUX
ejpam-1829	72	11	2	2	NUM
ejpam-1829	72	12	-	-	NOUN
ejpam-1829	72	13	primal	primal	ADJ
ejpam-1829	72	14	with	with	ADP
ejpam-1829	72	15	p(r	p(r	NOUN
ejpam-1829	72	16	)	)	PUNCT
ejpam-1829	72	17	=	=	SYM
ejpam-1829	73	1	0	0	X
ejpam-1829	73	2	.	.	PUNCT
ejpam-1829	74	1	let	let	VERB
ejpam-1829	74	2	σ	σ	NOUN
ejpam-1829	74	3	:	:	PUNCT
ejpam-1829	74	4	r→	r→	PROPN
ejpam-1829	74	5	r	r	NOUN
ejpam-1829	74	6	be	be	AUX
ejpam-1829	74	7	defined	define	VERB
ejpam-1829	74	8	by	by	ADP
ejpam-1829	74	9	σ	σ	PROPN
ejpam-1829	74	10	(	(	PUNCT
ejpam-1829	74	11	f	f	PROPN
ejpam-1829	74	12	(	(	PUNCT
ejpam-1829	74	13	x	x	NOUN
ejpam-1829	74	14	)	)	PUNCT
ejpam-1829	74	15	)	)	PUNCT
ejpam-1829	75	1	=	=	SYM
ejpam-1829	75	2	f	f	PROPN
ejpam-1829	75	3	(	(	PUNCT
ejpam-1829	75	4	0	0	NUM
ejpam-1829	75	5	)	)	PUNCT
ejpam-1829	75	6	.	.	PUNCT
ejpam-1829	76	1	let	let	VERB
ejpam-1829	76	2	f	f	PROPN
ejpam-1829	76	3	(	(	PUNCT
ejpam-1829	76	4	x	x	X
ejpam-1829	76	5	)	)	PUNCT
ejpam-1829	76	6	=	=	SYM
ejpam-1829	76	7	xa	xa	PROPN
ejpam-1829	76	8	,	,	PUNCT
ejpam-1829	76	9	0	0	NUM
ejpam-1829	76	10	6=	6=	ADP
ejpam-1829	76	11	a	a	DET
ejpam-1829	76	12	∈	∈	PROPN
ejpam-1829	76	13	f.	f.	NOUN
ejpam-1829	77	1	then	then	ADV
ejpam-1829	77	2	f	f	X
ejpam-1829	77	3	(	(	PUNCT
ejpam-1829	77	4	x)σ	x)σ	X
ejpam-1829	77	5	(	(	PUNCT
ejpam-1829	77	6	f	f	PROPN
ejpam-1829	77	7	(	(	PUNCT
ejpam-1829	77	8	x	x	NOUN
ejpam-1829	77	9	)	)	PUNCT
ejpam-1829	77	10	)	)	PUNCT
ejpam-1829	78	1	∈	∈	PROPN
ejpam-1829	78	2	p(r	p(r	PROPN
ejpam-1829	78	3	)	)	PUNCT
ejpam-1829	78	4	,	,	PUNCT
ejpam-1829	78	5	but	but	CCONJ
ejpam-1829	78	6	f	f	X
ejpam-1829	78	7	(	(	PUNCT
ejpam-1829	78	8	x	x	NOUN
ejpam-1829	78	9	)	)	PUNCT
ejpam-1829	78	10	/∈	/∈	PUNCT
ejpam-1829	78	11	p(r	p(r	PROPN
ejpam-1829	78	12	)	)	PUNCT
ejpam-1829	78	13	.	.	PUNCT
ejpam-1829	79	1	therefore	therefore	ADV
ejpam-1829	79	2	r	r	NOUN
ejpam-1829	79	3	is	be	AUX
ejpam-1829	79	4	not	not	PART
ejpam-1829	79	5	a	a	DET
ejpam-1829	79	6	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	79	7	.	.	PUNCT
ejpam-1829	80	1	v.	v.	ADP
ejpam-1829	80	2	bhat	bhat	PROPN
ejpam-1829	80	3	/	/	SYM
ejpam-1829	80	4	eur	eur	PROPN
ejpam-1829	80	5	.	.	PUNCT
ejpam-1829	81	1	j.	j.	PROPN
ejpam-1829	81	2	pure	pure	PROPN
ejpam-1829	81	3	appl	appl	PROPN
ejpam-1829	81	4	.	.	PROPN
ejpam-1829	81	5	math	math	PROPN
ejpam-1829	81	6	,	,	PUNCT
ejpam-1829	81	7	7	7	NUM
ejpam-1829	81	8	(	(	PUNCT
ejpam-1829	81	9	2014	2014	NUM
ejpam-1829	81	10	)	)	PUNCT
ejpam-1829	81	11	,	,	PUNCT
ejpam-1829	81	12	387	387	NUM
ejpam-1829	81	13	-	-	SYM
ejpam-1829	81	14	394	394	NUM
ejpam-1829	81	15	390	390	NUM
ejpam-1829	81	16	before	before	SCONJ
ejpam-1829	81	17	we	we	PRON
ejpam-1829	81	18	give	give	VERB
ejpam-1829	81	19	a	a	DET
ejpam-1829	81	20	characterization	characterization	NOUN
ejpam-1829	81	21	of	of	ADP
ejpam-1829	81	22	a	a	DET
ejpam-1829	81	23	noetherian	noetherian	ADJ
ejpam-1829	81	24	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	81	25	,	,	PUNCT
ejpam-1829	81	26	we	we	PRON
ejpam-1829	81	27	require	require	VERB
ejpam-1829	81	28	the	the	DET
ejpam-1829	81	29	following	following	NOUN
ejpam-1829	81	30	:	:	PUNCT
ejpam-1829	81	31	recall	recall	VERB
ejpam-1829	81	32	that	that	SCONJ
ejpam-1829	81	33	an	an	DET
ejpam-1829	81	34	ideal	ideal	ADJ
ejpam-1829	81	35	p	p	NOUN
ejpam-1829	81	36	of	of	ADP
ejpam-1829	81	37	a	a	DET
ejpam-1829	81	38	ring	ring	NOUN
ejpam-1829	81	39	r	r	NOUN
ejpam-1829	81	40	is	be	AUX
ejpam-1829	81	41	completely	completely	ADV
ejpam-1829	81	42	prime	prime	ADJ
ejpam-1829	81	43	if	if	SCONJ
ejpam-1829	81	44	r	r	NOUN
ejpam-1829	81	45	/	/	SYM
ejpam-1829	81	46	p	p	NOUN
ejpam-1829	81	47	is	be	AUX
ejpam-1829	81	48	a	a	DET
ejpam-1829	81	49	domain	domain	NOUN
ejpam-1829	81	50	,	,	PUNCT
ejpam-1829	81	51	i.e.	i.e.	X
ejpam-1829	81	52	ab	ab	PROPN
ejpam-1829	81	53	∈	∈	PROPN
ejpam-1829	81	54	p	p	PROPN
ejpam-1829	81	55	implies	imply	VERB
ejpam-1829	81	56	a	a	DET
ejpam-1829	81	57	∈	∈	PROPN
ejpam-1829	81	58	p	p	NOUN
ejpam-1829	81	59	or	or	CCONJ
ejpam-1829	81	60	b	b	NOUN
ejpam-1829	81	61	∈	∈	PROPN
ejpam-1829	81	62	p	p	NOUN
ejpam-1829	81	63	for	for	ADP
ejpam-1829	81	64	a	a	DET
ejpam-1829	81	65	,	,	PUNCT
ejpam-1829	81	66	b	b	X
ejpam-1829	81	67	∈	∈	PROPN
ejpam-1829	81	68	r	r	NOUN
ejpam-1829	81	69	(	(	PUNCT
ejpam-1829	81	70	mccoy	mccoy	PROPN
ejpam-1829	82	1	[	[	X
ejpam-1829	82	2	11	11	NUM
ejpam-1829	82	3	]	]	NUM
ejpam-1829	82	4	)	)	PUNCT
ejpam-1829	82	5	.	.	PUNCT
ejpam-1829	83	1	note	note	VERB
ejpam-1829	83	2	that	that	SCONJ
ejpam-1829	83	3	a	a	DET
ejpam-1829	83	4	completely	completely	ADV
ejpam-1829	83	5	prime	prime	ADJ
ejpam-1829	83	6	ideal	ideal	NOUN
ejpam-1829	83	7	is	be	AUX
ejpam-1829	83	8	a	a	DET
ejpam-1829	83	9	prime	prime	ADJ
ejpam-1829	83	10	ideal	ideal	NOUN
ejpam-1829	83	11	,	,	PUNCT
ejpam-1829	83	12	but	but	CCONJ
ejpam-1829	83	13	the	the	DET
ejpam-1829	83	14	converse	converse	NOUN
ejpam-1829	83	15	need	need	AUX
ejpam-1829	83	16	not	not	PART
ejpam-1829	83	17	be	be	AUX
ejpam-1829	83	18	true	true	ADJ
ejpam-1829	83	19	.	.	PUNCT
ejpam-1829	84	1	for	for	ADP
ejpam-1829	84	2	example	example	NOUN
ejpam-1829	84	3	,	,	PUNCT
ejpam-1829	84	4	let	let	VERB
ejpam-1829	84	5	r=	r=	PROPN
ejpam-1829	84	6	�	�	PROPN
ejpam-1829	84	7	z	z	NOUN
ejpam-1829	84	8	z	z	PROPN
ejpam-1829	84	9	z	z	NOUN
ejpam-1829	84	10	z	z	NOUN
ejpam-1829	84	11	�	�	PROPN
ejpam-1829	84	12	=	=	SYM
ejpam-1829	84	13	m2(z	m2(z	PROPN
ejpam-1829	84	14	)	)	PUNCT
ejpam-1829	84	15	.	.	PUNCT
ejpam-1829	85	1	if	if	SCONJ
ejpam-1829	85	2	p	p	NOUN
ejpam-1829	85	3	is	be	AUX
ejpam-1829	85	4	a	a	DET
ejpam-1829	85	5	prime	prime	ADJ
ejpam-1829	85	6	number	number	NOUN
ejpam-1829	85	7	,	,	PUNCT
ejpam-1829	85	8	then	then	ADV
ejpam-1829	85	9	the	the	DET
ejpam-1829	85	10	ideal	ideal	NOUN
ejpam-1829	85	11	p	p	X
ejpam-1829	85	12	=	=	SYM
ejpam-1829	85	13	m2(pz	m2(pz	PROPN
ejpam-1829	85	14	)	)	PUNCT
ejpam-1829	85	15	is	be	AUX
ejpam-1829	85	16	a	a	DET
ejpam-1829	85	17	prime	prime	ADJ
ejpam-1829	85	18	ideal	ideal	NOUN
ejpam-1829	85	19	of	of	ADP
ejpam-1829	85	20	r	r	NOUN
ejpam-1829	85	21	,	,	PUNCT
ejpam-1829	85	22	but	but	CCONJ
ejpam-1829	85	23	is	be	AUX
ejpam-1829	85	24	not	not	PART
ejpam-1829	85	25	strongly	strongly	ADV
ejpam-1829	85	26	prime	prime	ADJ
ejpam-1829	85	27	,	,	PUNCT
ejpam-1829	85	28	since	since	SCONJ
ejpam-1829	85	29	for	for	ADP
ejpam-1829	85	30	a	a	DET
ejpam-1829	85	31	=	=	SYM
ejpam-1829	85	32	�	�	PROPN
ejpam-1829	85	33	1	1	NUM
ejpam-1829	85	34	0	0	NUM
ejpam-1829	85	35	0	0	NUM
ejpam-1829	85	36	0	0	NUM
ejpam-1829	85	37	�	�	PROPN
ejpam-1829	85	38	and	and	CCONJ
ejpam-1829	85	39	b	b	NOUN
ejpam-1829	85	40	=	=	SYM
ejpam-1829	85	41	�	�	PROPN
ejpam-1829	85	42	0	0	NUM
ejpam-1829	85	43	0	0	NUM
ejpam-1829	85	44	0	0	NUM
ejpam-1829	85	45	1	1	NUM
ejpam-1829	85	46	�	�	NOUN
ejpam-1829	85	47	we	we	PRON
ejpam-1829	85	48	have	have	VERB
ejpam-1829	85	49	ab	ab	PROPN
ejpam-1829	85	50	∈	∈	PROPN
ejpam-1829	85	51	p	p	NOUN
ejpam-1829	85	52	,	,	PUNCT
ejpam-1829	85	53	even	even	ADV
ejpam-1829	85	54	though	though	SCONJ
ejpam-1829	85	55	a	a	DET
ejpam-1829	85	56	/∈	/∈	SYM
ejpam-1829	85	57	p	p	NOUN
ejpam-1829	85	58	and	and	CCONJ
ejpam-1829	85	59	b	b	PROPN
ejpam-1829	85	60	/∈	/∈	PUNCT
ejpam-1829	86	1	p.	p.	NOUN
ejpam-1829	86	2	proposition	proposition	NOUN
ejpam-1829	86	3	2	2	NUM
ejpam-1829	86	4	(	(	PUNCT
ejpam-1829	86	5	proposition	proposition	NOUN
ejpam-1829	86	6	2.1	2.1	NUM
ejpam-1829	86	7	of	of	ADP
ejpam-1829	86	8	bhat	bhat	PROPN
ejpam-1829	87	1	[	[	X
ejpam-1829	87	2	6	6	NUM
ejpam-1829	87	3	]	]	PUNCT
ejpam-1829	87	4	)	)	PUNCT
ejpam-1829	87	5	.	.	PUNCT
ejpam-1829	88	1	let	let	VERB
ejpam-1829	88	2	r	r	PRON
ejpam-1829	88	3	be	be	AUX
ejpam-1829	88	4	a	a	DET
ejpam-1829	88	5	noetherian	noetherian	ADJ
ejpam-1829	88	6	ring	ring	NOUN
ejpam-1829	88	7	,	,	PUNCT
ejpam-1829	88	8	andσ	andσ	VERB
ejpam-1829	88	9	an	an	DET
ejpam-1829	88	10	automorphism	automorphism	NOUN
ejpam-1829	88	11	of	of	ADP
ejpam-1829	88	12	r.	r.	PROPN
ejpam-1829	88	13	then	then	ADV
ejpam-1829	88	14	r	r	NOUN
ejpam-1829	88	15	is	be	AUX
ejpam-1829	88	16	a	a	DET
ejpam-1829	88	17	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	88	18	if	if	SCONJ
ejpam-1829	88	19	and	and	CCONJ
ejpam-1829	88	20	only	only	ADV
ejpam-1829	88	21	if	if	SCONJ
ejpam-1829	88	22	for	for	ADP
ejpam-1829	88	23	each	each	DET
ejpam-1829	88	24	minimal	minimal	ADJ
ejpam-1829	88	25	prime	prime	ADJ
ejpam-1829	88	26	u	u	NOUN
ejpam-1829	88	27	of	of	ADP
ejpam-1829	88	28	r	r	NOUN
ejpam-1829	88	29	,	,	PUNCT
ejpam-1829	88	30	σ(u	σ(u	NOUN
ejpam-1829	88	31	)	)	PUNCT
ejpam-1829	88	32	=	=	SYM
ejpam-1829	88	33	u	u	NOUN
ejpam-1829	88	34	and	and	CCONJ
ejpam-1829	88	35	u	u	NOUN
ejpam-1829	88	36	is	be	AUX
ejpam-1829	88	37	a	a	DET
ejpam-1829	88	38	completely	completely	ADV
ejpam-1829	88	39	prime	prime	ADJ
ejpam-1829	88	40	ideal	ideal	NOUN
ejpam-1829	88	41	of	of	ADP
ejpam-1829	88	42	r.	r.	PROPN
ejpam-1829	88	43	proof	proof	NOUN
ejpam-1829	88	44	.	.	PUNCT
ejpam-1829	89	1	to	to	PART
ejpam-1829	89	2	make	make	VERB
ejpam-1829	89	3	the	the	DET
ejpam-1829	89	4	article	article	NOUN
ejpam-1829	89	5	self	self	NOUN
ejpam-1829	89	6	contained	contain	VERB
ejpam-1829	89	7	,	,	PUNCT
ejpam-1829	89	8	we	we	PRON
ejpam-1829	89	9	give	give	VERB
ejpam-1829	89	10	a	a	DET
ejpam-1829	89	11	proof	proof	NOUN
ejpam-1829	89	12	(	(	PUNCT
ejpam-1829	89	13	a	a	DET
ejpam-1829	89	14	modified	modified	ADJ
ejpam-1829	89	15	one	one	NUM
ejpam-1829	89	16	):	):	PUNCT
ejpam-1829	89	17	let	let	VERB
ejpam-1829	89	18	r	r	PRON
ejpam-1829	89	19	be	be	AUX
ejpam-1829	89	20	a	a	DET
ejpam-1829	89	21	noetherian	noetherian	ADJ
ejpam-1829	89	22	ring	ring	NOUN
ejpam-1829	89	23	such	such	ADJ
ejpam-1829	89	24	that	that	PRON
ejpam-1829	89	25	for	for	ADP
ejpam-1829	89	26	each	each	DET
ejpam-1829	89	27	minimal	minimal	ADJ
ejpam-1829	89	28	prime	prime	ADJ
ejpam-1829	89	29	u	u	NOUN
ejpam-1829	89	30	of	of	ADP
ejpam-1829	89	31	r	r	NOUN
ejpam-1829	89	32	,	,	PUNCT
ejpam-1829	89	33	σ(u	σ(u	NOUN
ejpam-1829	89	34	)	)	PUNCT
ejpam-1829	89	35	=	=	SYM
ejpam-1829	89	36	u	u	NOUN
ejpam-1829	89	37	and	and	CCONJ
ejpam-1829	89	38	u	u	NOUN
ejpam-1829	89	39	is	be	AUX
ejpam-1829	89	40	completely	completely	ADV
ejpam-1829	89	41	prime	prime	ADJ
ejpam-1829	89	42	ideal	ideal	NOUN
ejpam-1829	89	43	of	of	ADP
ejpam-1829	89	44	r.	r.	PROPN
ejpam-1829	89	45	let	let	VERB
ejpam-1829	89	46	a	a	DET
ejpam-1829	89	47	∈	∈	NOUN
ejpam-1829	89	48	r	r	NOUN
ejpam-1829	89	49	be	be	VERB
ejpam-1829	89	50	such	such	ADJ
ejpam-1829	89	51	that	that	PRON
ejpam-1829	89	52	aσ(a	aσ(a	NOUN
ejpam-1829	89	53	)	)	PUNCT
ejpam-1829	89	54	∈	∈	PROPN
ejpam-1829	89	55	p(r	p(r	PROPN
ejpam-1829	89	56	)	)	PUNCT
ejpam-1829	90	1	=	=	SYM
ejpam-1829	90	2	∩n	∩n	NOUN
ejpam-1829	90	3	i=1ui	i=1ui	X
ejpam-1829	90	4	,	,	PUNCT
ejpam-1829	90	5	where	where	SCONJ
ejpam-1829	90	6	ui	ui	PROPN
ejpam-1829	90	7	are	be	AUX
ejpam-1829	90	8	the	the	DET
ejpam-1829	90	9	minimal	minimal	ADJ
ejpam-1829	90	10	primes	prime	NOUN
ejpam-1829	90	11	of	of	ADP
ejpam-1829	90	12	r.	r.	PROPN
ejpam-1829	90	13	now	now	ADV
ejpam-1829	90	14	for	for	SCONJ
ejpam-1829	90	15	each	each	DET
ejpam-1829	90	16	i	i	NOUN
ejpam-1829	90	17	,	,	PUNCT
ejpam-1829	90	18	a	a	DET
ejpam-1829	90	19	∈	∈	PROPN
ejpam-1829	90	20	ui	ui	NOUN
ejpam-1829	90	21	or	or	CCONJ
ejpam-1829	90	22	σ(a	σ(a	PROPN
ejpam-1829	90	23	)	)	PUNCT
ejpam-1829	90	24	∈	∈	PROPN
ejpam-1829	90	25	ui	ui	NOUN
ejpam-1829	90	26	as	as	SCONJ
ejpam-1829	90	27	ui	ui	PROPN
ejpam-1829	90	28	are	be	AUX
ejpam-1829	90	29	completely	completely	ADV
ejpam-1829	90	30	prime	prime	ADJ
ejpam-1829	90	31	.	.	PUNCT
ejpam-1829	91	1	now	now	ADV
ejpam-1829	91	2	σ(a	σ(a	PROPN
ejpam-1829	91	3	)	)	PUNCT
ejpam-1829	91	4	∈	∈	PROPN
ejpam-1829	91	5	ui	ui	NOUN
ejpam-1829	92	1	=	=	SYM
ejpam-1829	92	2	σ(ui	σ(ui	X
ejpam-1829	92	3	)	)	PUNCT
ejpam-1829	92	4	implies	imply	VERB
ejpam-1829	92	5	that	that	SCONJ
ejpam-1829	92	6	a	a	DET
ejpam-1829	92	7	∈	∈	PROPN
ejpam-1829	92	8	ui	ui	NOUN
ejpam-1829	92	9	.	.	PUNCT
ejpam-1829	93	1	therefore	therefore	ADV
ejpam-1829	93	2	a	a	DET
ejpam-1829	93	3	∈	∈	PROPN
ejpam-1829	93	4	p(r	p(r	PROPN
ejpam-1829	93	5	)	)	PUNCT
ejpam-1829	93	6	.	.	PUNCT
ejpam-1829	94	1	hence	hence	ADV
ejpam-1829	94	2	r	r	NOUN
ejpam-1829	94	3	is	be	AUX
ejpam-1829	94	4	a	a	DET
ejpam-1829	94	5	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	94	6	.	.	PUNCT
ejpam-1829	95	1	conversely	conversely	ADV
ejpam-1829	95	2	,	,	PUNCT
ejpam-1829	95	3	suppose	suppose	VERB
ejpam-1829	95	4	that	that	SCONJ
ejpam-1829	95	5	r	r	NOUN
ejpam-1829	95	6	is	be	AUX
ejpam-1829	95	7	aσ(∗)-ring	aσ(∗)-re	VERB
ejpam-1829	95	8	and	and	CCONJ
ejpam-1829	95	9	let	let	VERB
ejpam-1829	95	10	u	u	PRON
ejpam-1829	95	11	=	=	NOUN
ejpam-1829	95	12	u1	u1	NOUN
ejpam-1829	95	13	be	be	AUX
ejpam-1829	95	14	a	a	DET
ejpam-1829	95	15	minimal	minimal	ADJ
ejpam-1829	95	16	prime	prime	ADJ
ejpam-1829	95	17	ideal	ideal	NOUN
ejpam-1829	95	18	of	of	ADP
ejpam-1829	95	19	r.	r.	PROPN
ejpam-1829	95	20	now	now	ADV
ejpam-1829	95	21	by	by	ADP
ejpam-1829	95	22	proposition	proposition	NOUN
ejpam-1829	95	23	1	1	NUM
ejpam-1829	95	24	,	,	PUNCT
ejpam-1829	95	25	p(r	p(r	NOUN
ejpam-1829	95	26	)	)	PUNCT
ejpam-1829	95	27	is	be	AUX
ejpam-1829	95	28	completely	completely	ADV
ejpam-1829	95	29	semiprime	semiprime	NOUN
ejpam-1829	95	30	.	.	PUNCT
ejpam-1829	96	1	now	now	ADV
ejpam-1829	96	2	min.spec(r	min.spec(r	X
ejpam-1829	96	3	)	)	PUNCT
ejpam-1829	96	4	is	be	AUX
ejpam-1829	96	5	finite	finite	VERB
ejpam-1829	96	6	by	by	ADP
ejpam-1829	96	7	theorem	theorem	NOUN
ejpam-1829	96	8	(	(	PUNCT
ejpam-1829	96	9	2.4	2.4	NUM
ejpam-1829	96	10	)	)	PUNCT
ejpam-1829	96	11	of	of	ADP
ejpam-1829	96	12	goodearl	goodearl	PROPN
ejpam-1829	96	13	and	and	CCONJ
ejpam-1829	96	14	warfield	warfield	VERB
ejpam-1829	96	15	[	[	X
ejpam-1829	96	16	7	7	NUM
ejpam-1829	96	17	]	]	PUNCT
ejpam-1829	96	18	.	.	PUNCT
ejpam-1829	97	1	let	let	VERB
ejpam-1829	97	2	u2	u2	NOUN
ejpam-1829	97	3	,	,	PUNCT
ejpam-1829	97	4	u3	u3	NOUN
ejpam-1829	97	5	,	,	PUNCT
ejpam-1829	97	6	.	.	PUNCT
ejpam-1829	97	7	.	.	PUNCT
ejpam-1829	98	1	.	.	PUNCT
ejpam-1829	99	1	,	,	PUNCT
ejpam-1829	99	2	un	un	PROPN
ejpam-1829	99	3	be	be	VERB
ejpam-1829	99	4	the	the	DET
ejpam-1829	99	5	other	other	ADJ
ejpam-1829	99	6	minimal	minimal	ADJ
ejpam-1829	99	7	primes	prime	NOUN
ejpam-1829	99	8	of	of	ADP
ejpam-1829	99	9	r.	r.	PROPN
ejpam-1829	99	10	suppose	suppose	VERB
ejpam-1829	99	11	that	that	SCONJ
ejpam-1829	99	12	σ(u	σ(u	NOUN
ejpam-1829	99	13	)	)	PUNCT
ejpam-1829	100	1	6=	6=	NUM
ejpam-1829	100	2	u	u	NOUN
ejpam-1829	100	3	.	.	PUNCT
ejpam-1829	101	1	then	then	ADV
ejpam-1829	101	2	σ(u	σ(u	NOUN
ejpam-1829	101	3	)	)	PUNCT
ejpam-1829	101	4	is	be	AUX
ejpam-1829	101	5	also	also	ADV
ejpam-1829	101	6	a	a	DET
ejpam-1829	101	7	minimal	minimal	ADJ
ejpam-1829	101	8	prime	prime	ADJ
ejpam-1829	101	9	ideal	ideal	NOUN
ejpam-1829	101	10	of	of	ADP
ejpam-1829	101	11	r.	r.	PROPN
ejpam-1829	101	12	renumber	renumber	PROPN
ejpam-1829	101	13	so	so	SCONJ
ejpam-1829	101	14	that	that	SCONJ
ejpam-1829	101	15	σ(u	σ(u	NOUN
ejpam-1829	101	16	)	)	PUNCT
ejpam-1829	101	17	=	=	SYM
ejpam-1829	101	18	un	un	PROPN
ejpam-1829	101	19	.	.	PROPN
ejpam-1829	102	1	let	let	VERB
ejpam-1829	102	2	a	a	DET
ejpam-1829	102	3	∈	∈	NOUN
ejpam-1829	102	4	∩n−1	∩n−1	PROPN
ejpam-1829	102	5	i=1	i=1	PROPN
ejpam-1829	103	1	ui	ui	PROPN
ejpam-1829	103	2	.	.	PUNCT
ejpam-1829	104	1	then	then	ADV
ejpam-1829	104	2	σ(a	σ(a	PROPN
ejpam-1829	104	3	)	)	PUNCT
ejpam-1829	104	4	∈	∈	PROPN
ejpam-1829	104	5	un	un	PROPN
ejpam-1829	104	6	,	,	PUNCT
ejpam-1829	104	7	and	and	CCONJ
ejpam-1829	104	8	so	so	ADV
ejpam-1829	104	9	aσ(a	aσ(a	PUNCT
ejpam-1829	104	10	)	)	PUNCT
ejpam-1829	104	11	∈	∈	PROPN
ejpam-1829	104	12	∩n	∩n	NOUN
ejpam-1829	104	13	i=1ui	i=1ui	X
ejpam-1829	105	1	=	=	PUNCT
ejpam-1829	105	2	p(r	p(r	PROPN
ejpam-1829	105	3	)	)	PUNCT
ejpam-1829	105	4	.	.	PUNCT
ejpam-1829	106	1	therefore	therefore	ADV
ejpam-1829	106	2	a	a	DET
ejpam-1829	106	3	∈	∈	PROPN
ejpam-1829	106	4	p(r	p(r	PROPN
ejpam-1829	106	5	)	)	PUNCT
ejpam-1829	106	6	,	,	PUNCT
ejpam-1829	106	7	and	and	CCONJ
ejpam-1829	106	8	thus	thus	ADV
ejpam-1829	106	9	∩n−1	∩n−1	PROPN
ejpam-1829	106	10	i=1	i=1	PROPN
ejpam-1829	106	11	ui	ui	PROPN
ejpam-1829	106	12	⊆	⊆	NUM
ejpam-1829	106	13	un	un	NOUN
ejpam-1829	106	14	,	,	PUNCT
ejpam-1829	106	15	which	which	PRON
ejpam-1829	106	16	implies	imply	VERB
ejpam-1829	106	17	that	that	SCONJ
ejpam-1829	106	18	ui	ui	PROPN
ejpam-1829	106	19	⊆	⊆	NUM
ejpam-1829	106	20	un	un	NOUN
ejpam-1829	106	21	for	for	ADP
ejpam-1829	106	22	some	some	DET
ejpam-1829	106	23	i	i	PROPN
ejpam-1829	106	24	6=	6=	PROPN
ejpam-1829	106	25	n	n	CCONJ
ejpam-1829	106	26	,	,	PUNCT
ejpam-1829	106	27	which	which	PRON
ejpam-1829	106	28	is	be	AUX
ejpam-1829	106	29	impossible	impossible	ADJ
ejpam-1829	106	30	.	.	PUNCT
ejpam-1829	107	1	hence	hence	ADV
ejpam-1829	107	2	σ(u	σ(u	NOUN
ejpam-1829	107	3	)	)	PUNCT
ejpam-1829	108	1	=	=	SYM
ejpam-1829	108	2	u	u	NOUN
ejpam-1829	108	3	.	.	PUNCT
ejpam-1829	109	1	now	now	ADV
ejpam-1829	109	2	since	since	SCONJ
ejpam-1829	109	3	a	a	DET
ejpam-1829	109	4	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	109	5	is	be	AUX
ejpam-1829	109	6	2	2	NUM
ejpam-1829	109	7	-	-	PUNCT
ejpam-1829	109	8	primal	primal	ADJ
ejpam-1829	109	9	,	,	PUNCT
ejpam-1829	109	10	minimal	minimal	ADJ
ejpam-1829	109	11	prime	prime	ADJ
ejpam-1829	109	12	ideals	ideal	NOUN
ejpam-1829	109	13	are	be	AUX
ejpam-1829	109	14	completely	completely	ADV
ejpam-1829	109	15	prime	prime	ADJ
ejpam-1829	109	16	.	.	PUNCT
ejpam-1829	110	1	hence	hence	ADV
ejpam-1829	110	2	u	u	NOUN
ejpam-1829	110	3	is	be	AUX
ejpam-1829	110	4	completely	completely	ADV
ejpam-1829	110	5	prime	prime	ADJ
ejpam-1829	110	6	.	.	PUNCT
ejpam-1829	111	1	note	note	VERB
ejpam-1829	111	2	that	that	SCONJ
ejpam-1829	111	3	in	in	ADP
ejpam-1829	111	4	above	above	ADV
ejpam-1829	111	5	theorem	theorem	VERB
ejpam-1829	111	6	the	the	DET
ejpam-1829	111	7	condition	condition	NOUN
ejpam-1829	111	8	of	of	ADP
ejpam-1829	111	9	completely	completely	ADV
ejpam-1829	111	10	primeness	primeness	NOUN
ejpam-1829	111	11	of	of	ADP
ejpam-1829	111	12	minimal	minimal	ADJ
ejpam-1829	111	13	prime	prime	ADJ
ejpam-1829	111	14	ideals	ideal	NOUN
ejpam-1829	111	15	can	can	AUX
ejpam-1829	111	16	not	not	PART
ejpam-1829	111	17	be	be	AUX
ejpam-1829	111	18	deleted	delete	VERB
ejpam-1829	111	19	.	.	PUNCT
ejpam-1829	112	1	towards	towards	ADP
ejpam-1829	112	2	this	this	PRON
ejpam-1829	112	3	we	we	PRON
ejpam-1829	112	4	have	have	VERB
ejpam-1829	112	5	the	the	DET
ejpam-1829	112	6	following	following	NOUN
ejpam-1829	112	7	:	:	PUNCT
ejpam-1829	112	8	remark	remark	NOUN
ejpam-1829	112	9	1	1	NUM
ejpam-1829	112	10	.	.	PUNCT
ejpam-1829	113	1	let	let	VERB
ejpam-1829	113	2	r	r	PRON
ejpam-1829	113	3	be	be	AUX
ejpam-1829	113	4	a	a	DET
ejpam-1829	113	5	noetherian	noetherian	ADJ
ejpam-1829	113	6	ring	ring	NOUN
ejpam-1829	113	7	and	and	CCONJ
ejpam-1829	113	8	σ	σ	NOUN
ejpam-1829	113	9	an	an	DET
ejpam-1829	113	10	automorphism	automorphism	NOUN
ejpam-1829	113	11	of	of	ADP
ejpam-1829	113	12	r	r	NOUN
ejpam-1829	113	13	such	such	ADJ
ejpam-1829	113	14	that	that	SCONJ
ejpam-1829	113	15	σ(u	σ(u	NOUN
ejpam-1829	113	16	)	)	PUNCT
ejpam-1829	113	17	=	=	SYM
ejpam-1829	113	18	u	u	NOUN
ejpam-1829	113	19	for	for	ADP
ejpam-1829	113	20	each	each	DET
ejpam-1829	113	21	minimal	minimal	ADJ
ejpam-1829	113	22	prime	prime	ADJ
ejpam-1829	113	23	ideal	ideal	NOUN
ejpam-1829	113	24	u	u	PROPN
ejpam-1829	113	25	of	of	ADP
ejpam-1829	113	26	r.	r.	PROPN
ejpam-1829	113	27	then	then	ADV
ejpam-1829	113	28	r	r	NOUN
ejpam-1829	113	29	need	need	AUX
ejpam-1829	113	30	not	not	PART
ejpam-1829	113	31	be	be	AUX
ejpam-1829	113	32	a	a	DET
ejpam-1829	113	33	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	113	34	(	(	PUNCT
ejpam-1829	113	35	example	example	NOUN
ejpam-1829	113	36	4	4	NUM
ejpam-1829	113	37	)	)	PUNCT
ejpam-1829	113	38	.	.	PUNCT
ejpam-1829	114	1	3	3	X
ejpam-1829	114	2	.	.	X
ejpam-1829	114	3	skew	skew	ADJ
ejpam-1829	114	4	-	-	PUNCT
ejpam-1829	114	5	laurent	laurent	NOUN
ejpam-1829	114	6	rings	ring	NOUN
ejpam-1829	114	7	over	over	ADP
ejpam-1829	114	8	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	114	9	goodearl	goodearl	PROPN
ejpam-1829	114	10	and	and	CCONJ
ejpam-1829	114	11	warfield	warfield	PROPN
ejpam-1829	114	12	proved	prove	VERB
ejpam-1829	114	13	in	in	ADP
ejpam-1829	114	14	(	(	PUNCT
ejpam-1829	114	15	2za	2za	NOUN
ejpam-1829	114	16	)	)	PUNCT
ejpam-1829	114	17	of	of	ADP
ejpam-1829	114	18	[	[	X
ejpam-1829	114	19	7	7	X
ejpam-1829	114	20	]	]	PUNCT
ejpam-1829	114	21	that	that	SCONJ
ejpam-1829	114	22	if	if	SCONJ
ejpam-1829	114	23	r	r	NOUN
ejpam-1829	114	24	is	be	AUX
ejpam-1829	114	25	a	a	DET
ejpam-1829	114	26	commutative	commutative	ADJ
ejpam-1829	114	27	noetherian	noetherian	ADJ
ejpam-1829	114	28	ring	ring	NOUN
ejpam-1829	114	29	,	,	PUNCT
ejpam-1829	114	30	and	and	CCONJ
ejpam-1829	114	31	if	if	SCONJ
ejpam-1829	114	32	σ	σ	PROPN
ejpam-1829	114	33	is	be	AUX
ejpam-1829	114	34	an	an	DET
ejpam-1829	114	35	automorphism	automorphism	NOUN
ejpam-1829	114	36	of	of	ADP
ejpam-1829	114	37	r	r	NOUN
ejpam-1829	114	38	,	,	PUNCT
ejpam-1829	114	39	then	then	ADV
ejpam-1829	114	40	an	an	DET
ejpam-1829	114	41	ideal	ideal	NOUN
ejpam-1829	114	42	i	i	PRON
ejpam-1829	114	43	of	of	ADP
ejpam-1829	114	44	r	r	NOUN
ejpam-1829	114	45	is	be	AUX
ejpam-1829	114	46	of	of	ADP
ejpam-1829	114	47	the	the	DET
ejpam-1829	114	48	form	form	NOUN
ejpam-1829	114	49	p	p	NOUN
ejpam-1829	114	50	∩	∩	ADJ
ejpam-1829	114	51	r	r	NOUN
ejpam-1829	114	52	for	for	ADP
ejpam-1829	114	53	some	some	DET
ejpam-1829	114	54	prime	prime	ADJ
ejpam-1829	114	55	ideal	ideal	NOUN
ejpam-1829	114	56	p	p	PROPN
ejpam-1829	114	57	of	of	ADP
ejpam-1829	114	58	r[x	r[x	NOUN
ejpam-1829	114	59	,	,	PUNCT
ejpam-1829	114	60	x−1;σ	x−1;σ	PROPN
ejpam-1829	114	61	]	]	PUNCT
ejpam-1829	114	62	if	if	SCONJ
ejpam-1829	114	63	and	and	CCONJ
ejpam-1829	114	64	only	only	ADV
ejpam-1829	114	65	if	if	SCONJ
ejpam-1829	114	66	there	there	PRON
ejpam-1829	114	67	is	be	VERB
ejpam-1829	114	68	a	a	DET
ejpam-1829	114	69	prime	prime	ADJ
ejpam-1829	114	70	ideal	ideal	NOUN
ejpam-1829	114	71	s	s	PROPN
ejpam-1829	114	72	of	of	ADP
ejpam-1829	114	73	r	r	NOUN
ejpam-1829	114	74	and	and	CCONJ
ejpam-1829	114	75	a	a	DET
ejpam-1829	114	76	positive	positive	ADJ
ejpam-1829	114	77	integer	integer	NOUN
ejpam-1829	114	78	m	m	VERB
ejpam-1829	114	79	with	with	ADP
ejpam-1829	114	80	σm(s	σm(s	NOUN
ejpam-1829	114	81	)	)	PUNCT
ejpam-1829	115	1	=	=	SYM
ejpam-1829	115	2	s	s	NOUN
ejpam-1829	115	3	,	,	PUNCT
ejpam-1829	115	4	such	such	ADJ
ejpam-1829	115	5	that	that	SCONJ
ejpam-1829	115	6	i	i	PRON
ejpam-1829	115	7	=	=	PUNCT
ejpam-1829	115	8	∩σi(s	∩σi(s	PROPN
ejpam-1829	115	9	)	)	PUNCT
ejpam-1829	115	10	,	,	PUNCT
ejpam-1829	115	11	i	i	PRON
ejpam-1829	115	12	=	=	NOUN
ejpam-1829	115	13	1	1	NUM
ejpam-1829	115	14	,	,	PUNCT
ejpam-1829	115	15	2	2	NUM
ejpam-1829	115	16	,	,	PUNCT
ejpam-1829	115	17	.	.	PUNCT
ejpam-1829	115	18	.	.	PUNCT
ejpam-1829	115	19	.	.	PUNCT
ejpam-1829	116	1	,	,	PUNCT
ejpam-1829	116	2	m.	m.	NOUN
ejpam-1829	116	3	we	we	PRON
ejpam-1829	116	4	note	note	VERB
ejpam-1829	116	5	that	that	SCONJ
ejpam-1829	116	6	if	if	SCONJ
ejpam-1829	116	7	r	r	NOUN
ejpam-1829	116	8	is	be	AUX
ejpam-1829	116	9	a	a	DET
ejpam-1829	116	10	noetherian	noetherian	ADJ
ejpam-1829	116	11	ring	ring	NOUN
ejpam-1829	116	12	,	,	PUNCT
ejpam-1829	116	13	then	then	ADV
ejpam-1829	116	14	as	as	SCONJ
ejpam-1829	116	15	mentioned	mention	VERB
ejpam-1829	116	16	above	above	ADV
ejpam-1829	116	17	,	,	PUNCT
ejpam-1829	116	18	min.spec(r	min.spec(r	INTJ
ejpam-1829	116	19	)	)	PUNCT
ejpam-1829	116	20	is	be	AUX
ejpam-1829	116	21	finite	finite	ADJ
ejpam-1829	116	22	.	.	PUNCT
ejpam-1829	117	1	now	now	ADV
ejpam-1829	117	2	if	if	SCONJ
ejpam-1829	117	3	σ	σ	PROPN
ejpam-1829	117	4	is	be	AUX
ejpam-1829	117	5	an	an	DET
ejpam-1829	117	6	automorphism	automorphism	NOUN
ejpam-1829	117	7	of	of	ADP
ejpam-1829	117	8	r	r	NOUN
ejpam-1829	117	9	,	,	PUNCT
ejpam-1829	117	10	then	then	ADV
ejpam-1829	117	11	σ	σ	PROPN
ejpam-1829	117	12	j(u	j(u	PROPN
ejpam-1829	117	13	)	)	PUNCT
ejpam-1829	117	14	∈	∈	PROPN
ejpam-1829	117	15	min.spec(r	min.spec(r	PROPN
ejpam-1829	117	16	)	)	PUNCT
ejpam-1829	117	17	for	for	ADP
ejpam-1829	117	18	any	any	DET
ejpam-1829	117	19	u	u	PROPN
ejpam-1829	117	20	∈	∈	PROPN
ejpam-1829	117	21	min.spec(r	min.spec(r	NOUN
ejpam-1829	117	22	)	)	PUNCT
ejpam-1829	117	23	for	for	ADP
ejpam-1829	117	24	v.	v.	ADP
ejpam-1829	117	25	bhat	bhat	PROPN
ejpam-1829	117	26	/	/	SYM
ejpam-1829	117	27	eur	eur	PROPN
ejpam-1829	117	28	.	.	PUNCT
ejpam-1829	118	1	j.	j.	PROPN
ejpam-1829	118	2	pure	pure	PROPN
ejpam-1829	118	3	appl	appl	PROPN
ejpam-1829	118	4	.	.	PROPN
ejpam-1829	118	5	math	math	PROPN
ejpam-1829	118	6	,	,	PUNCT
ejpam-1829	118	7	7	7	NUM
ejpam-1829	118	8	(	(	PUNCT
ejpam-1829	118	9	2014	2014	NUM
ejpam-1829	118	10	)	)	PUNCT
ejpam-1829	118	11	,	,	PUNCT
ejpam-1829	118	12	387	387	NUM
ejpam-1829	118	13	-	-	SYM
ejpam-1829	118	14	394	394	NUM
ejpam-1829	118	15	391	391	NUM
ejpam-1829	118	16	all	all	DET
ejpam-1829	118	17	j	j	PROPN
ejpam-1829	118	18	∈	∈	PROPN
ejpam-1829	118	19	n.	n.	PROPN
ejpam-1829	118	20	therefore	therefore	ADV
ejpam-1829	118	21	,	,	PUNCT
ejpam-1829	118	22	there	there	PRON
ejpam-1829	118	23	exists	exist	VERB
ejpam-1829	118	24	some	some	DET
ejpam-1829	118	25	m	m	VERB
ejpam-1829	118	26	∈	∈	NOUN
ejpam-1829	118	27	n	n	PRON
ejpam-1829	118	28	such	such	ADJ
ejpam-1829	118	29	that	that	PRON
ejpam-1829	118	30	σm(u	σm(u	PUNCT
ejpam-1829	118	31	)	)	PUNCT
ejpam-1829	118	32	=	=	SYM
ejpam-1829	118	33	u	u	NOUN
ejpam-1829	118	34	for	for	ADP
ejpam-1829	118	35	all	all	DET
ejpam-1829	118	36	u	u	PROPN
ejpam-1829	118	37	∈	∈	PROPN
ejpam-1829	118	38	min.spec(r	min.spec(r	PROPN
ejpam-1829	118	39	)	)	PUNCT
ejpam-1829	118	40	.	.	PUNCT
ejpam-1829	119	1	we	we	PRON
ejpam-1829	119	2	denote	denote	VERB
ejpam-1829	119	3	∩m	∩m	PROPN
ejpam-1829	119	4	i=1σ	i=1σ	NOUN
ejpam-1829	119	5	i(u	i(u	PROPN
ejpam-1829	119	6	)	)	PUNCT
ejpam-1829	119	7	by	by	ADP
ejpam-1829	119	8	u0	u0	PROPN
ejpam-1829	119	9	.	.	PUNCT
ejpam-1829	120	1	we	we	PRON
ejpam-1829	120	2	now	now	ADV
ejpam-1829	120	3	have	have	VERB
ejpam-1829	120	4	the	the	DET
ejpam-1829	120	5	following	following	NOUN
ejpam-1829	120	6	:	:	PUNCT
ejpam-1829	120	7	theorem	theorem	NOUN
ejpam-1829	120	8	1	1	X
ejpam-1829	120	9	.	.	PUNCT
ejpam-1829	121	1	let	let	VERB
ejpam-1829	121	2	r	r	PRON
ejpam-1829	121	3	be	be	AUX
ejpam-1829	121	4	a	a	DET
ejpam-1829	121	5	noetherian	noetherian	ADJ
ejpam-1829	121	6	ring	ring	NOUN
ejpam-1829	121	7	andσ	andσ	VERB
ejpam-1829	121	8	an	an	DET
ejpam-1829	121	9	automorphism	automorphism	NOUN
ejpam-1829	121	10	of	of	ADP
ejpam-1829	121	11	r.	r.	PROPN
ejpam-1829	121	12	then	then	ADV
ejpam-1829	121	13	p	p	PROPN
ejpam-1829	121	14	∈	∈	PROPN
ejpam-1829	121	15	min.spec(l(r	min.spec(l(r	NOUN
ejpam-1829	121	16	)	)	PUNCT
ejpam-1829	121	17	)	)	PUNCT
ejpam-1829	122	1	if	if	SCONJ
ejpam-1829	122	2	and	and	CCONJ
ejpam-1829	122	3	only	only	ADV
ejpam-1829	122	4	if	if	SCONJ
ejpam-1829	122	5	there	there	PRON
ejpam-1829	122	6	exists	exist	VERB
ejpam-1829	122	7	u	u	PROPN
ejpam-1829	122	8	∈	∈	PROPN
ejpam-1829	122	9	min.spec(r	min.spec(r	PROPN
ejpam-1829	122	10	)	)	PUNCT
ejpam-1829	122	11	such	such	ADJ
ejpam-1829	122	12	that	that	DET
ejpam-1829	122	13	l(p	l(p	NOUN
ejpam-1829	122	14	∩	∩	ADJ
ejpam-1829	122	15	r	r	NOUN
ejpam-1829	122	16	)	)	PUNCT
ejpam-1829	122	17	=	=	SYM
ejpam-1829	122	18	(	(	PUNCT
ejpam-1829	122	19	p	p	X
ejpam-1829	122	20	∩	∩	ADJ
ejpam-1829	122	21	r)[x	r)[x	PROPN
ejpam-1829	122	22	,	,	PUNCT
ejpam-1829	122	23	x−1;σ	x−1;σ	ADV
ejpam-1829	122	24	]	]	PUNCT
ejpam-1829	123	1	=	=	SYM
ejpam-1829	123	2	p	p	NOUN
ejpam-1829	123	3	and	and	CCONJ
ejpam-1829	123	4	p	p	PROPN
ejpam-1829	123	5	∩	∩	ADJ
ejpam-1829	123	6	r=	r=	ADJ
ejpam-1829	123	7	u0	u0	ADJ
ejpam-1829	123	8	.	.	PUNCT
ejpam-1829	124	1	proof	proof	NOUN
ejpam-1829	124	2	.	.	PUNCT
ejpam-1829	125	1	see	see	VERB
ejpam-1829	125	2	theorem	theorem	NOUN
ejpam-1829	125	3	(	(	PUNCT
ejpam-1829	125	4	2.4	2.4	NUM
ejpam-1829	125	5	)	)	PUNCT
ejpam-1829	125	6	of	of	ADP
ejpam-1829	125	7	bhat	bhat	PROPN
ejpam-1829	126	1	[	[	X
ejpam-1829	126	2	1	1	NUM
ejpam-1829	126	3	]	]	PUNCT
ejpam-1829	126	4	.	.	PUNCT
ejpam-1829	127	1	as	as	SCONJ
ejpam-1829	127	2	mentioned	mention	VERB
ejpam-1829	127	3	in	in	ADP
ejpam-1829	127	4	the	the	DET
ejpam-1829	127	5	introduction	introduction	NOUN
ejpam-1829	127	6	,	,	PUNCT
ejpam-1829	127	7	we	we	PRON
ejpam-1829	127	8	note	note	VERB
ejpam-1829	127	9	that	that	SCONJ
ejpam-1829	127	10	if	if	SCONJ
ejpam-1829	127	11	σ	σ	PROPN
ejpam-1829	127	12	is	be	AUX
ejpam-1829	127	13	an	an	DET
ejpam-1829	127	14	automorphism	automorphism	NOUN
ejpam-1829	127	15	of	of	ADP
ejpam-1829	127	16	r	r	NOUN
ejpam-1829	127	17	,	,	PUNCT
ejpam-1829	127	18	then	then	ADV
ejpam-1829	127	19	it	it	PRON
ejpam-1829	127	20	can	can	AUX
ejpam-1829	127	21	be	be	AUX
ejpam-1829	127	22	extended	extend	VERB
ejpam-1829	127	23	to	to	ADP
ejpam-1829	127	24	an	an	DET
ejpam-1829	127	25	automorphism	automorphism	NOUN
ejpam-1829	127	26	(	(	PUNCT
ejpam-1829	127	27	say	say	INTJ
ejpam-1829	127	28	σ	σ	NOUN
ejpam-1829	127	29	)	)	PUNCT
ejpam-1829	127	30	of	of	ADP
ejpam-1829	127	31	r[x	r[x	NOUN
ejpam-1829	127	32	,	,	PUNCT
ejpam-1829	127	33	x−1;σ	x−1;σ	PROPN
ejpam-1829	127	34	]	]	PUNCT
ejpam-1829	127	35	such	such	ADJ
ejpam-1829	127	36	that	that	SCONJ
ejpam-1829	127	37	σ(x	σ(x	NOUN
ejpam-1829	127	38	)	)	PUNCT
ejpam-1829	127	39	=	=	SYM
ejpam-1829	128	1	x	x	NOUN
ejpam-1829	128	2	;	;	PUNCT
ejpam-1829	128	3	i.e.	i.e.	X
ejpam-1829	128	4	σ(σn	σ(σn	PROPN
ejpam-1829	128	5	i=−m	i=−m	PROPN
ejpam-1829	128	6	x	x	PROPN
ejpam-1829	128	7	iai	iai	PROPN
ejpam-1829	128	8	)	)	PUNCT
ejpam-1829	128	9	=	=	PUNCT
ejpam-1829	128	10	σn	σn	PROPN
ejpam-1829	128	11	i=−m	i=−m	PROPN
ejpam-1829	128	12	x	x	SYM
ejpam-1829	128	13	iσ(ai	iσ(ai	PROPN
ejpam-1829	128	14	)	)	PUNCT
ejpam-1829	128	15	.	.	PUNCT
ejpam-1829	129	1	with	with	ADP
ejpam-1829	129	2	this	this	PRON
ejpam-1829	129	3	we	we	PRON
ejpam-1829	129	4	are	be	AUX
ejpam-1829	129	5	now	now	ADV
ejpam-1829	129	6	in	in	ADP
ejpam-1829	129	7	a	a	DET
ejpam-1829	129	8	position	position	NOUN
ejpam-1829	129	9	to	to	PART
ejpam-1829	129	10	prove	prove	VERB
ejpam-1829	129	11	the	the	DET
ejpam-1829	129	12	following	follow	VERB
ejpam-1829	129	13	theorem	theorem	NOUN
ejpam-1829	129	14	:	:	PUNCT
ejpam-1829	129	15	theorem	theorem	NOUN
ejpam-1829	129	16	2	2	NUM
ejpam-1829	129	17	.	.	PUNCT
ejpam-1829	130	1	let	let	VERB
ejpam-1829	130	2	r	r	PRON
ejpam-1829	130	3	be	be	AUX
ejpam-1829	130	4	a	a	DET
ejpam-1829	130	5	noetherian	noetherian	ADJ
ejpam-1829	130	6	ring	ring	NOUN
ejpam-1829	130	7	and	and	CCONJ
ejpam-1829	130	8	σ	σ	NOUN
ejpam-1829	130	9	an	an	DET
ejpam-1829	130	10	automorphism	automorphism	NOUN
ejpam-1829	130	11	of	of	ADP
ejpam-1829	130	12	r.	r.	PROPN
ejpam-1829	130	13	then	then	ADV
ejpam-1829	130	14	r	r	NOUN
ejpam-1829	130	15	is	be	AUX
ejpam-1829	130	16	a	a	DET
ejpam-1829	130	17	σ(∗)-ring	σ(∗)-re	VERB
ejpam-1829	130	18	if	if	SCONJ
ejpam-1829	130	19	and	and	CCONJ
ejpam-1829	130	20	only	only	ADV
ejpam-1829	130	21	if	if	SCONJ
ejpam-1829	130	22	l(r	l(r	PROPN
ejpam-1829	130	23	)	)	PUNCT
ejpam-1829	130	24	=	=	SYM
ejpam-1829	130	25	r[x	r[x	NOUN
ejpam-1829	130	26	,	,	PUNCT
ejpam-1829	130	27	x−1;σ	x−1;σ	PROPN
ejpam-1829	130	28	]	]	PUNCT
ejpam-1829	130	29	is	be	AUX
ejpam-1829	130	30	a	a	DET
ejpam-1829	130	31	noetherian	noetherian	ADJ
ejpam-1829	130	32	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	130	33	.	.	PUNCT
ejpam-1829	130	34	proof	proof	NOUN
ejpam-1829	130	35	.	.	PUNCT
ejpam-1829	131	1	let	let	VERB
ejpam-1829	131	2	r	r	PRON
ejpam-1829	131	3	be	be	AUX
ejpam-1829	131	4	a	a	DET
ejpam-1829	131	5	noetherian	noetherian	ADJ
ejpam-1829	131	6	ring	ring	NOUN
ejpam-1829	131	7	,	,	PUNCT
ejpam-1829	131	8	σ	σ	VERB
ejpam-1829	131	9	an	an	DET
ejpam-1829	131	10	automorphism	automorphism	NOUN
ejpam-1829	131	11	of	of	ADP
ejpam-1829	131	12	r	r	NOUN
ejpam-1829	131	13	such	such	ADJ
ejpam-1829	131	14	that	that	SCONJ
ejpam-1829	131	15	r	r	NOUN
ejpam-1829	131	16	is	be	AUX
ejpam-1829	131	17	a	a	DET
ejpam-1829	131	18	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	131	19	and	and	CCONJ
ejpam-1829	131	20	δ	δ	PROPN
ejpam-1829	131	21	a	a	DET
ejpam-1829	131	22	σ	σ	NOUN
ejpam-1829	131	23	-	-	PUNCT
ejpam-1829	131	24	derivation	derivation	NOUN
ejpam-1829	131	25	of	of	ADP
ejpam-1829	131	26	r.	r.	PROPN
ejpam-1829	131	27	we	we	PRON
ejpam-1829	131	28	shall	shall	AUX
ejpam-1829	131	29	prove	prove	VERB
ejpam-1829	131	30	that	that	SCONJ
ejpam-1829	131	31	o(r	o(r	NOUN
ejpam-1829	131	32	)	)	PUNCT
ejpam-1829	131	33	=	=	SYM
ejpam-1829	132	1	r[x;σ	r[x;σ	NOUN
ejpam-1829	132	2	,	,	PUNCT
ejpam-1829	132	3	δ	δ	PROPN
ejpam-1829	132	4	]	]	PUNCT
ejpam-1829	132	5	is	be	AUX
ejpam-1829	132	6	a	a	DET
ejpam-1829	132	7	noetherian	noetherian	ADJ
ejpam-1829	132	8	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	132	9	.	.	PUNCT
ejpam-1829	133	1	for	for	ADP
ejpam-1829	133	2	this	this	PRON
ejpam-1829	133	3	we	we	PRON
ejpam-1829	133	4	will	will	AUX
ejpam-1829	133	5	show	show	VERB
ejpam-1829	133	6	that	that	SCONJ
ejpam-1829	133	7	any	any	DET
ejpam-1829	133	8	minimal	minimal	ADJ
ejpam-1829	133	9	p	p	X
ejpam-1829	133	10	∈	∈	PROPN
ejpam-1829	133	11	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	133	12	)	)	PUNCT
ejpam-1829	133	13	)	)	PUNCT
ejpam-1829	133	14	is	be	AUX
ejpam-1829	133	15	completely	completely	ADV
ejpam-1829	133	16	prime	prime	ADJ
ejpam-1829	133	17	and	and	CCONJ
ejpam-1829	133	18	σ(p	σ(p	PRON
ejpam-1829	133	19	)	)	PUNCT
ejpam-1829	133	20	=	=	PUNCT
ejpam-1829	134	1	p.	p.	NOUN
ejpam-1829	134	2	let	let	VERB
ejpam-1829	134	3	p	p	PROPN
ejpam-1829	134	4	∈	∈	PROPN
ejpam-1829	134	5	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	134	6	)	)	PUNCT
ejpam-1829	134	7	)	)	PUNCT
ejpam-1829	134	8	.	.	PUNCT
ejpam-1829	135	1	then	then	ADV
ejpam-1829	135	2	by	by	ADP
ejpam-1829	135	3	theorem	theorem	NOUN
ejpam-1829	135	4	1	1	NUM
ejpam-1829	135	5	,	,	PUNCT
ejpam-1829	135	6	there	there	PRON
ejpam-1829	135	7	exists	exist	VERB
ejpam-1829	135	8	u	u	PROPN
ejpam-1829	135	9	∈	∈	PROPN
ejpam-1829	135	10	min.spec(r	min.spec(r	PROPN
ejpam-1829	135	11	)	)	PUNCT
ejpam-1829	135	12	such	such	ADJ
ejpam-1829	135	13	that	that	SCONJ
ejpam-1829	135	14	p	p	X
ejpam-1829	135	15	=	=	ADJ
ejpam-1829	135	16	u0[x	u0[x	NOUN
ejpam-1829	135	17	,	,	PUNCT
ejpam-1829	135	18	x−1;σ	x−1;σ	PROPN
ejpam-1829	135	19	]	]	PUNCT
ejpam-1829	135	20	.	.	PUNCT
ejpam-1829	136	1	now	now	ADV
ejpam-1829	136	2	r	r	NOUN
ejpam-1829	136	3	is	be	AUX
ejpam-1829	136	4	aσ(∗)-ring	aσ(∗)-re	VERB
ejpam-1829	136	5	implies	imply	VERB
ejpam-1829	136	6	thatσ(u	thatσ(u	PROPN
ejpam-1829	136	7	)	)	PUNCT
ejpam-1829	136	8	=	=	SYM
ejpam-1829	136	9	u	u	NOUN
ejpam-1829	136	10	by	by	ADP
ejpam-1829	136	11	proposition	proposition	NOUN
ejpam-1829	136	12	2	2	NUM
ejpam-1829	136	13	,	,	PUNCT
ejpam-1829	136	14	and	and	CCONJ
ejpam-1829	136	15	therefore	therefore	ADV
ejpam-1829	136	16	u0	u0	ADJ
ejpam-1829	136	17	=	=	PROPN
ejpam-1829	136	18	u	u	PROPN
ejpam-1829	136	19	.	.	PUNCT
ejpam-1829	137	1	so	so	ADV
ejpam-1829	137	2	p	p	NOUN
ejpam-1829	137	3	=	=	SYM
ejpam-1829	137	4	u[x	u[x	X
ejpam-1829	137	5	,	,	PUNCT
ejpam-1829	137	6	x−1;σ	x−1;σ	X
ejpam-1829	137	7	]	]	PUNCT
ejpam-1829	137	8	and	and	CCONJ
ejpam-1829	137	9	thus	thus	ADV
ejpam-1829	137	10	σ(p	σ(p	PRON
ejpam-1829	137	11	)	)	PUNCT
ejpam-1829	138	1	=	=	PUNCT
ejpam-1829	139	1	p.	p.	NOUN
ejpam-1829	139	2	we	we	PRON
ejpam-1829	139	3	now	now	ADV
ejpam-1829	139	4	show	show	VERB
ejpam-1829	139	5	that	that	SCONJ
ejpam-1829	139	6	p	p	NOUN
ejpam-1829	139	7	=	=	X
ejpam-1829	139	8	u[x	u[x	X
ejpam-1829	139	9	,	,	PUNCT
ejpam-1829	139	10	x−1;σ	x−1;σ	PROPN
ejpam-1829	139	11	]	]	PUNCT
ejpam-1829	139	12	is	be	AUX
ejpam-1829	139	13	completely	completely	ADV
ejpam-1829	139	14	prime	prime	ADJ
ejpam-1829	139	15	.	.	PUNCT
ejpam-1829	140	1	now	now	ADV
ejpam-1829	140	2	σ	σ	NOUN
ejpam-1829	140	3	can	can	AUX
ejpam-1829	140	4	be	be	AUX
ejpam-1829	140	5	extended	extend	VERB
ejpam-1829	140	6	to	to	ADP
ejpam-1829	140	7	an	an	DET
ejpam-1829	140	8	automorphism	automorphism	NOUN
ejpam-1829	140	9	of	of	ADP
ejpam-1829	140	10	r	r	NOUN
ejpam-1829	140	11	/	/	SYM
ejpam-1829	140	12	u	u	NOUN
ejpam-1829	140	13	in	in	ADP
ejpam-1829	140	14	a	a	DET
ejpam-1829	140	15	natural	natural	ADJ
ejpam-1829	140	16	way	way	NOUN
ejpam-1829	140	17	.	.	PUNCT
ejpam-1829	141	1	we	we	PRON
ejpam-1829	141	2	note	note	VERB
ejpam-1829	141	3	that	that	SCONJ
ejpam-1829	141	4	o(r)/p	o(r)/p	PROPN
ejpam-1829	141	5	∼=	∼=	PROPN
ejpam-1829	141	6	(	(	PUNCT
ejpam-1829	141	7	r	r	X
ejpam-1829	141	8	/	/	SYM
ejpam-1829	141	9	u)[x	u)[x	PROPN
ejpam-1829	141	10	,	,	PUNCT
ejpam-1829	141	11	x−1;σ	x−1;σ	PROPN
ejpam-1829	141	12	]	]	PUNCT
ejpam-1829	141	13	,	,	PUNCT
ejpam-1829	141	14	and	and	CCONJ
ejpam-1829	141	15	since	since	SCONJ
ejpam-1829	141	16	u	u	NOUN
ejpam-1829	141	17	is	be	AUX
ejpam-1829	141	18	completely	completely	ADV
ejpam-1829	141	19	prime	prime	ADJ
ejpam-1829	141	20	,	,	PUNCT
ejpam-1829	141	21	r	r	NOUN
ejpam-1829	141	22	/	/	SYM
ejpam-1829	141	23	u	u	NOUN
ejpam-1829	141	24	is	be	AUX
ejpam-1829	141	25	a	a	DET
ejpam-1829	141	26	domain	domain	NOUN
ejpam-1829	141	27	and	and	CCONJ
ejpam-1829	141	28	so	so	ADV
ejpam-1829	141	29	(	(	PUNCT
ejpam-1829	141	30	r	r	X
ejpam-1829	141	31	/	/	SYM
ejpam-1829	141	32	u)[x	u)[x	PROPN
ejpam-1829	141	33	,	,	PUNCT
ejpam-1829	141	34	x−1;σ	x−1;σ	PROPN
ejpam-1829	141	35	]	]	PUNCT
ejpam-1829	141	36	is	be	AUX
ejpam-1829	141	37	also	also	ADV
ejpam-1829	141	38	a	a	DET
ejpam-1829	141	39	domain	domain	NOUN
ejpam-1829	141	40	.	.	PUNCT
ejpam-1829	142	1	hence	hence	ADV
ejpam-1829	142	2	p	p	NOUN
ejpam-1829	142	3	=	=	SYM
ejpam-1829	142	4	u[x	u[x	X
ejpam-1829	142	5	,	,	PUNCT
ejpam-1829	142	6	x−1;σ	x−1;σ	PROPN
ejpam-1829	142	7	]	]	PUNCT
ejpam-1829	142	8	is	be	AUX
ejpam-1829	142	9	completely	completely	ADV
ejpam-1829	142	10	prime	prime	ADJ
ejpam-1829	142	11	.	.	PUNCT
ejpam-1829	143	1	thus	thus	ADV
ejpam-1829	143	2	σ(p	σ(p	PRON
ejpam-1829	143	3	)	)	PUNCT
ejpam-1829	143	4	=	=	SYM
ejpam-1829	144	1	p	p	NOUN
ejpam-1829	144	2	and	and	CCONJ
ejpam-1829	144	3	p	p	NOUN
ejpam-1829	144	4	is	be	AUX
ejpam-1829	144	5	completely	completely	ADV
ejpam-1829	144	6	prime	prime	ADJ
ejpam-1829	144	7	for	for	ADP
ejpam-1829	144	8	all	all	DET
ejpam-1829	144	9	p	p	PROPN
ejpam-1829	144	10	∈	∈	PROPN
ejpam-1829	144	11	min.spec(l(r	min.spec(l(r	NOUN
ejpam-1829	144	12	)	)	PUNCT
ejpam-1829	144	13	)	)	PUNCT
ejpam-1829	144	14	.	.	PUNCT
ejpam-1829	145	1	moreover	moreover	ADV
ejpam-1829	145	2	l(r	l(r	PROPN
ejpam-1829	145	3	)	)	PUNCT
ejpam-1829	145	4	=	=	SYM
ejpam-1829	145	5	r[x	r[x	NOUN
ejpam-1829	145	6	,	,	PUNCT
ejpam-1829	145	7	x−1;σ	x−1;σ	PROPN
ejpam-1829	145	8	]	]	PUNCT
ejpam-1829	145	9	is	be	AUX
ejpam-1829	145	10	noetherian	noetherian	ADJ
ejpam-1829	145	11	by	by	ADP
ejpam-1829	145	12	theorem	theorem	NOUN
ejpam-1829	145	13	(	(	PUNCT
ejpam-1829	145	14	1.17	1.17	NUM
ejpam-1829	145	15	)	)	PUNCT
ejpam-1829	145	16	of	of	ADP
ejpam-1829	145	17	goodearl	goodearl	PROPN
ejpam-1829	145	18	and	and	CCONJ
ejpam-1829	145	19	warfield	warfield	VERB
ejpam-1829	145	20	[	[	X
ejpam-1829	145	21	7	7	NUM
ejpam-1829	145	22	]	]	PUNCT
ejpam-1829	145	23	.	.	PUNCT
ejpam-1829	146	1	hence	hence	ADV
ejpam-1829	146	2	by	by	ADP
ejpam-1829	146	3	proposition	proposition	NOUN
ejpam-1829	146	4	2	2	NUM
ejpam-1829	146	5	r[x	r[x	NOUN
ejpam-1829	146	6	,	,	PUNCT
ejpam-1829	146	7	x−1;σ	x−1;σ	PROPN
ejpam-1829	146	8	]	]	PUNCT
ejpam-1829	146	9	is	be	AUX
ejpam-1829	146	10	a	a	DET
ejpam-1829	146	11	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	146	12	.	.	PUNCT
ejpam-1829	147	1	conversely	conversely	ADV
ejpam-1829	147	2	let	let	VERB
ejpam-1829	147	3	l(r	l(r	PROPN
ejpam-1829	147	4	)	)	PUNCT
ejpam-1829	147	5	=	=	SYM
ejpam-1829	147	6	r[x	r[x	NOUN
ejpam-1829	147	7	,	,	PUNCT
ejpam-1829	147	8	x−1;σ	x−1;σ	PROPN
ejpam-1829	147	9	]	]	PUNCT
ejpam-1829	147	10	be	be	AUX
ejpam-1829	147	11	a	a	DET
ejpam-1829	147	12	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	147	13	.	.	PUNCT
ejpam-1829	148	1	let	let	VERB
ejpam-1829	148	2	u	u	PRON
ejpam-1829	148	3	∈	∈	PROPN
ejpam-1829	148	4	min.spec(r	min.spec(r	PROPN
ejpam-1829	148	5	)	)	PUNCT
ejpam-1829	148	6	.	.	PUNCT
ejpam-1829	149	1	then	then	ADV
ejpam-1829	149	2	theorem	theorem	VERB
ejpam-1829	149	3	1	1	NUM
ejpam-1829	149	4	implies	imply	VERB
ejpam-1829	149	5	that	that	SCONJ
ejpam-1829	149	6	l(u0	l(u0	NOUN
ejpam-1829	149	7	)	)	PUNCT
ejpam-1829	149	8	∈	∈	PROPN
ejpam-1829	149	9	min.spec(l(r	min.spec(l(r	NOUN
ejpam-1829	149	10	)	)	PUNCT
ejpam-1829	149	11	)	)	PUNCT
ejpam-1829	149	12	.	.	PUNCT
ejpam-1829	150	1	now	now	ADV
ejpam-1829	150	2	l(r	l(r	PROPN
ejpam-1829	150	3	)	)	PUNCT
ejpam-1829	150	4	be	be	VERB
ejpam-1829	150	5	a	a	DET
ejpam-1829	150	6	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	150	7	implies	imply	VERB
ejpam-1829	150	8	that	that	SCONJ
ejpam-1829	150	9	σ(l(u0	σ(l(u0	NOUN
ejpam-1829	150	10	)	)	PUNCT
ejpam-1829	150	11	)	)	PUNCT
ejpam-1829	151	1	=	=	PUNCT
ejpam-1829	151	2	l(u0	l(u0	NOUN
ejpam-1829	151	3	)	)	PUNCT
ejpam-1829	151	4	and	and	CCONJ
ejpam-1829	151	5	l(u0	l(u0	NOUN
ejpam-1829	151	6	)	)	PUNCT
ejpam-1829	151	7	is	be	AUX
ejpam-1829	151	8	completely	completely	ADV
ejpam-1829	151	9	prime	prime	ADJ
ejpam-1829	151	10	ideal	ideal	NOUN
ejpam-1829	151	11	of	of	ADP
ejpam-1829	151	12	l(r	l(r	PROPN
ejpam-1829	151	13	)	)	PUNCT
ejpam-1829	151	14	.	.	PUNCT
ejpam-1829	152	1	now	now	ADV
ejpam-1829	152	2	there	there	PRON
ejpam-1829	152	3	is	be	VERB
ejpam-1829	152	4	an	an	DET
ejpam-1829	152	5	embedding	embed	VERB
ejpam-1829	152	6	r/(l(u0	r/(l(u0	NOUN
ejpam-1829	152	7	)	)	PUNCT
ejpam-1829	152	8	∩	∩	NOUN
ejpam-1829	152	9	r)→	r)→	NOUN
ejpam-1829	152	10	l(r)/l(u0	l(r)/l(u0	NUM
ejpam-1829	152	11	)	)	PUNCT
ejpam-1829	152	12	.	.	PUNCT
ejpam-1829	153	1	since	since	SCONJ
ejpam-1829	153	2	l(r)/l(u0	l(r)/l(u0	NUM
ejpam-1829	153	3	)	)	PUNCT
ejpam-1829	153	4	is	be	AUX
ejpam-1829	153	5	an	an	DET
ejpam-1829	153	6	integral	integral	ADJ
ejpam-1829	153	7	domain	domain	NOUN
ejpam-1829	153	8	,	,	PUNCT
ejpam-1829	153	9	so	so	ADV
ejpam-1829	153	10	is	be	AUX
ejpam-1829	153	11	r/(l(u0	r/(l(u0	NOUN
ejpam-1829	153	12	)	)	PUNCT
ejpam-1829	153	13	∩	∩	ADJ
ejpam-1829	153	14	r	r	NOUN
ejpam-1829	153	15	)	)	PUNCT
ejpam-1829	153	16	.	.	PUNCT
ejpam-1829	154	1	therefore	therefore	ADV
ejpam-1829	154	2	,	,	PUNCT
ejpam-1829	154	3	u0	u0	ADJ
ejpam-1829	154	4	=	=	PUNCT
ejpam-1829	154	5	l(u0	l(u0	NOUN
ejpam-1829	154	6	)	)	PUNCT
ejpam-1829	154	7	∩	∩	NOUN
ejpam-1829	154	8	r	r	X
ejpam-1829	154	9	)	)	PUNCT
ejpam-1829	154	10	is	be	AUX
ejpam-1829	154	11	a	a	DET
ejpam-1829	154	12	completely	completely	ADV
ejpam-1829	154	13	prime	prime	ADJ
ejpam-1829	154	14	ideal	ideal	NOUN
ejpam-1829	154	15	of	of	ADP
ejpam-1829	154	16	r.	r.	PROPN
ejpam-1829	154	17	now	now	ADV
ejpam-1829	154	18	u0	u0	VERB
ejpam-1829	154	19	⊆	⊆	NUM
ejpam-1829	154	20	u	u	NOUN
ejpam-1829	154	21	implies	imply	VERB
ejpam-1829	154	22	that	that	SCONJ
ejpam-1829	154	23	u0	u0	ADJ
ejpam-1829	154	24	=	=	PROPN
ejpam-1829	154	25	u	u	PROPN
ejpam-1829	154	26	.	.	PUNCT
ejpam-1829	155	1	so	so	ADV
ejpam-1829	155	2	σ(u	σ(u	NOUN
ejpam-1829	155	3	)	)	PUNCT
ejpam-1829	155	4	=	=	SYM
ejpam-1829	155	5	u	u	NOUN
ejpam-1829	155	6	and	and	CCONJ
ejpam-1829	155	7	u	u	NOUN
ejpam-1829	155	8	is	be	AUX
ejpam-1829	155	9	a	a	DET
ejpam-1829	155	10	completely	completely	ADV
ejpam-1829	155	11	prime	prime	ADJ
ejpam-1829	155	12	ideal	ideal	NOUN
ejpam-1829	155	13	of	of	ADP
ejpam-1829	155	14	r.	r.	PROPN
ejpam-1829	155	15	hence	hence	ADV
ejpam-1829	155	16	by	by	ADP
ejpam-1829	155	17	proposition	proposition	NOUN
ejpam-1829	155	18	2	2	NUM
ejpam-1829	155	19	r	r	NOUN
ejpam-1829	155	20	is	be	AUX
ejpam-1829	155	21	a	a	DET
ejpam-1829	155	22	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	155	23	.	.	PUNCT
ejpam-1829	155	24	remark	remark	PROPN
ejpam-1829	155	25	2	2	NUM
ejpam-1829	155	26	.	.	PUNCT
ejpam-1829	156	1	i	i	PRON
ejpam-1829	156	2	)	)	PUNCT
ejpam-1829	156	3	let	let	VERB
ejpam-1829	156	4	r	r	PRON
ejpam-1829	156	5	be	be	AUX
ejpam-1829	156	6	a	a	DET
ejpam-1829	156	7	noetherian	noetherian	ADJ
ejpam-1829	156	8	ring	ring	NOUN
ejpam-1829	156	9	and	and	CCONJ
ejpam-1829	156	10	σ	σ	NOUN
ejpam-1829	156	11	an	an	DET
ejpam-1829	156	12	automorphism	automorphism	NOUN
ejpam-1829	156	13	of	of	ADP
ejpam-1829	156	14	r	r	NOUN
ejpam-1829	156	15	such	such	ADJ
ejpam-1829	156	16	that	that	SCONJ
ejpam-1829	156	17	r	r	NOUN
ejpam-1829	156	18	is	be	AUX
ejpam-1829	156	19	a	a	DET
ejpam-1829	156	20	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	156	21	.	.	PUNCT
ejpam-1829	157	1	then	then	ADV
ejpam-1829	157	2	r[x	r[x	NOUN
ejpam-1829	157	3	,	,	PUNCT
ejpam-1829	157	4	x−1;σ	x−1;σ	PROPN
ejpam-1829	157	5	]	]	PUNCT
ejpam-1829	157	6	is	be	AUX
ejpam-1829	157	7	a	a	DET
ejpam-1829	157	8	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	157	9	.	.	PUNCT
ejpam-1829	158	1	therefore	therefore	ADV
ejpam-1829	158	2	,	,	PUNCT
ejpam-1829	158	3	proposition	proposition	NOUN
ejpam-1829	158	4	1	1	NUM
ejpam-1829	158	5	implies	imply	VERB
ejpam-1829	158	6	that	that	DET
ejpam-1829	158	7	r[x	r[x	NOUN
ejpam-1829	158	8	,	,	PUNCT
ejpam-1829	158	9	x−1;σ	x−1;σ	PROPN
ejpam-1829	158	10	]	]	PUNCT
ejpam-1829	158	11	is	be	AUX
ejpam-1829	158	12	2	2	NUM
ejpam-1829	158	13	-	-	PUNCT
ejpam-1829	158	14	primal	primal	ADJ
ejpam-1829	158	15	.	.	PUNCT
ejpam-1829	159	1	v.	v.	ADP
ejpam-1829	159	2	bhat	bhat	PROPN
ejpam-1829	159	3	/	/	SYM
ejpam-1829	159	4	eur	eur	PROPN
ejpam-1829	159	5	.	.	PUNCT
ejpam-1829	160	1	j.	j.	PROPN
ejpam-1829	160	2	pure	pure	PROPN
ejpam-1829	160	3	appl	appl	PROPN
ejpam-1829	160	4	.	.	PROPN
ejpam-1829	160	5	math	math	PROPN
ejpam-1829	160	6	,	,	PUNCT
ejpam-1829	160	7	7	7	NUM
ejpam-1829	160	8	(	(	PUNCT
ejpam-1829	160	9	2014	2014	NUM
ejpam-1829	160	10	)	)	PUNCT
ejpam-1829	160	11	,	,	PUNCT
ejpam-1829	160	12	387	387	NUM
ejpam-1829	160	13	-	-	SYM
ejpam-1829	160	14	394	394	NUM
ejpam-1829	160	15	392	392	NUM
ejpam-1829	160	16	ii	ii	NOUN
ejpam-1829	160	17	)	)	PUNCT
ejpam-1829	160	18	if	if	SCONJ
ejpam-1829	160	19	r	r	NOUN
ejpam-1829	160	20	is	be	AUX
ejpam-1829	160	21	2	2	NUM
ejpam-1829	160	22	-	-	PUNCT
ejpam-1829	160	23	primal	primal	ADJ
ejpam-1829	160	24	noetherian	noetherian	ADJ
ejpam-1829	160	25	ring	ring	NOUN
ejpam-1829	160	26	,	,	PUNCT
ejpam-1829	160	27	then	then	ADV
ejpam-1829	160	28	r[x	r[x	NOUN
ejpam-1829	160	29	,	,	PUNCT
ejpam-1829	160	30	x−1;σ	x−1;σ	PROPN
ejpam-1829	160	31	]	]	PUNCT
ejpam-1829	160	32	need	need	AUX
ejpam-1829	160	33	not	not	PART
ejpam-1829	160	34	be	be	AUX
ejpam-1829	160	35	2	2	NUM
ejpam-1829	160	36	-	-	NOUN
ejpam-1829	160	37	primal	primal	ADJ
ejpam-1829	160	38	.	.	PUNCT
ejpam-1829	161	1	for	for	ADP
ejpam-1829	161	2	example	example	NOUN
ejpam-1829	161	3	consider	consider	VERB
ejpam-1829	161	4	z2	z2	NOUN
ejpam-1829	161	5	and	and	CCONJ
ejpam-1829	161	6	let	let	VERB
ejpam-1829	161	7	r=	r=	PROPN
ejpam-1829	161	8	z2⊕z2	z2⊕z2	PROPN
ejpam-1829	161	9	.	.	PUNCT
ejpam-1829	162	1	then	then	ADV
ejpam-1829	162	2	r	r	NOUN
ejpam-1829	162	3	is	be	AUX
ejpam-1829	162	4	a	a	DET
ejpam-1829	162	5	commutative	commutative	ADJ
ejpam-1829	162	6	reduced	reduce	VERB
ejpam-1829	162	7	ring	ring	NOUN
ejpam-1829	162	8	with	with	ADP
ejpam-1829	162	9	p(r	p(r	NOUN
ejpam-1829	162	10	)	)	PUNCT
ejpam-1829	162	11	=	=	PUNCT
ejpam-1829	162	12	0	0	NUM
ejpam-1829	162	13	,	,	PUNCT
ejpam-1829	162	14	and	and	CCONJ
ejpam-1829	162	15	therefore	therefore	ADV
ejpam-1829	162	16	r	r	NOUN
ejpam-1829	162	17	is	be	AUX
ejpam-1829	162	18	2	2	NUM
ejpam-1829	162	19	-	-	PUNCT
ejpam-1829	162	20	primal	primal	ADJ
ejpam-1829	162	21	.	.	PUNCT
ejpam-1829	163	1	define	define	VERB
ejpam-1829	163	2	σ	σ	NOUN
ejpam-1829	163	3	:	:	PUNCT
ejpam-1829	163	4	r→	r→	PROPN
ejpam-1829	163	5	r	r	NOUN
ejpam-1829	163	6	by	by	ADP
ejpam-1829	163	7	σ(a	σ(a	PROPN
ejpam-1829	163	8	,	,	PUNCT
ejpam-1829	163	9	b	b	NOUN
ejpam-1829	163	10	)	)	PUNCT
ejpam-1829	163	11	=	=	SYM
ejpam-1829	163	12	(	(	PUNCT
ejpam-1829	163	13	b	b	NOUN
ejpam-1829	163	14	,	,	PUNCT
ejpam-1829	163	15	a	a	PRON
ejpam-1829	163	16	)	)	PUNCT
ejpam-1829	163	17	.	.	PUNCT
ejpam-1829	164	1	then	then	ADV
ejpam-1829	164	2	it	it	PRON
ejpam-1829	164	3	can	can	AUX
ejpam-1829	164	4	be	be	AUX
ejpam-1829	164	5	seen	see	VERB
ejpam-1829	164	6	that	that	SCONJ
ejpam-1829	164	7	p(r[x	p(r[x	NOUN
ejpam-1829	164	8	,	,	PUNCT
ejpam-1829	164	9	x−1;σ	x−1;σ	PROPN
ejpam-1829	164	10	]	]	PUNCT
ejpam-1829	164	11	)	)	PUNCT
ejpam-1829	164	12	=	=	SYM
ejpam-1829	164	13	0	0	NUM
ejpam-1829	164	14	,	,	PUNCT
ejpam-1829	164	15	but	but	CCONJ
ejpam-1829	164	16	p(r[x	p(r[x	NOUN
ejpam-1829	164	17	,	,	PUNCT
ejpam-1829	164	18	x−1;σ	x−1;σ	PROPN
ejpam-1829	164	19	]	]	PUNCT
ejpam-1829	164	20	)	)	PUNCT
ejpam-1829	164	21	is	be	AUX
ejpam-1829	164	22	not	not	PART
ejpam-1829	164	23	completely	completely	ADV
ejpam-1829	164	24	semiprime	semiprime	ADJ
ejpam-1829	164	25	as	as	ADP
ejpam-1829	164	26	(	(	PUNCT
ejpam-1829	164	27	(	(	PUNCT
ejpam-1829	164	28	1	1	NUM
ejpam-1829	164	29	,	,	PUNCT
ejpam-1829	164	30	0)x)2	0)x)2	NOUN
ejpam-1829	165	1	=	=	SYM
ejpam-1829	165	2	0=	0=	NUM
ejpam-1829	165	3	p(r[x	p(r[x	NOUN
ejpam-1829	165	4	,	,	PUNCT
ejpam-1829	165	5	x−1;σ	x−1;σ	PROPN
ejpam-1829	165	6	]	]	PUNCT
ejpam-1829	165	7	)	)	PUNCT
ejpam-1829	165	8	,	,	PUNCT
ejpam-1829	165	9	but	but	CCONJ
ejpam-1829	165	10	(	(	PUNCT
ejpam-1829	165	11	1,0)x	1,0)x	NUM
ejpam-1829	165	12	/∈	/∈	NOUN
ejpam-1829	165	13	p(r[x	p(r[x	NOUN
ejpam-1829	165	14	,	,	PUNCT
ejpam-1829	165	15	x−1;σ	x−1;σ	PROPN
ejpam-1829	165	16	]	]	PUNCT
ejpam-1829	165	17	)	)	PUNCT
ejpam-1829	165	18	.	.	PUNCT
ejpam-1829	166	1	thus	thus	ADV
ejpam-1829	166	2	r[x	r[x	NOUN
ejpam-1829	166	3	,	,	PUNCT
ejpam-1829	166	4	x−1;σ	x−1;σ	PROPN
ejpam-1829	166	5	]	]	PUNCT
ejpam-1829	166	6	is	be	AUX
ejpam-1829	166	7	not	not	PART
ejpam-1829	166	8	2	2	NUM
ejpam-1829	166	9	-	-	PUNCT
ejpam-1829	166	10	primal	primal	ADJ
ejpam-1829	166	11	.	.	PUNCT
ejpam-1829	167	1	4	4	X
ejpam-1829	167	2	.	.	X
ejpam-1829	167	3	skew	skew	ADJ
ejpam-1829	167	4	polynomial	polynomial	ADJ
ejpam-1829	167	5	rings	ring	NOUN
ejpam-1829	167	6	over	over	ADP
ejpam-1829	167	7	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	167	8	let	let	VERB
ejpam-1829	167	9	σ	σ	NOUN
ejpam-1829	167	10	be	be	AUX
ejpam-1829	167	11	an	an	DET
ejpam-1829	167	12	endomorphism	endomorphism	NOUN
ejpam-1829	167	13	of	of	ADP
ejpam-1829	167	14	a	a	DET
ejpam-1829	167	15	ring	ring	NOUN
ejpam-1829	167	16	r	r	NOUN
ejpam-1829	167	17	and	and	CCONJ
ejpam-1829	167	18	δ	δ	PROPN
ejpam-1829	167	19	a	a	DET
ejpam-1829	167	20	σ	σ	NOUN
ejpam-1829	167	21	-	-	PUNCT
ejpam-1829	167	22	derivation	derivation	NOUN
ejpam-1829	167	23	of	of	ADP
ejpam-1829	167	24	r	r	NOUN
ejpam-1829	167	25	such	such	ADJ
ejpam-1829	167	26	that	that	DET
ejpam-1829	167	27	σ(δ(a	σ(δ(a	NOUN
ejpam-1829	167	28	)	)	PUNCT
ejpam-1829	167	29	)	)	PUNCT
ejpam-1829	168	1	=	=	PUNCT
ejpam-1829	168	2	δ(σ(a	δ(σ(a	NOUN
ejpam-1829	168	3	)	)	PUNCT
ejpam-1829	168	4	)	)	PUNCT
ejpam-1829	168	5	for	for	ADP
ejpam-1829	168	6	all	all	DET
ejpam-1829	168	7	a	a	DET
ejpam-1829	168	8	∈	∈	PROPN
ejpam-1829	168	9	r.	r.	NOUN
ejpam-1829	168	10	then	then	ADV
ejpam-1829	168	11	σ	σ	PROPN
ejpam-1829	168	12	can	can	AUX
ejpam-1829	168	13	be	be	AUX
ejpam-1829	168	14	extended	extend	VERB
ejpam-1829	168	15	to	to	ADP
ejpam-1829	168	16	an	an	DET
ejpam-1829	168	17	endomorphism	endomorphism	NOUN
ejpam-1829	168	18	(	(	PUNCT
ejpam-1829	168	19	say	say	INTJ
ejpam-1829	168	20	σ	σ	NOUN
ejpam-1829	168	21	)	)	PUNCT
ejpam-1829	168	22	of	of	ADP
ejpam-1829	168	23	r[x;σ	r[x;σ	NOUN
ejpam-1829	168	24	,	,	PUNCT
ejpam-1829	168	25	δ	δ	PROPN
ejpam-1829	168	26	]	]	PUNCT
ejpam-1829	168	27	by	by	ADP
ejpam-1829	168	28	σ	σ	PROPN
ejpam-1829	168	29	(	(	PUNCT
ejpam-1829	168	30	∑m	∑m	PROPN
ejpam-1829	168	31	i=0	i=0	PROPN
ejpam-1829	168	32	x	x	X
ejpam-1829	168	33	iai	iai	ADJ
ejpam-1829	168	34	)	)	PUNCT
ejpam-1829	168	35	=	=	VERB
ejpam-1829	168	36	∑m	∑m	PROPN
ejpam-1829	168	37	i=0	i=0	PROPN
ejpam-1829	168	38	x	x	SYM
ejpam-1829	168	39	iσ(ai	iσ(ai	PROPN
ejpam-1829	168	40	)	)	PUNCT
ejpam-1829	168	41	.	.	PUNCT
ejpam-1829	169	1	also	also	ADV
ejpam-1829	169	2	δ	δ	PROPN
ejpam-1829	169	3	can	can	AUX
ejpam-1829	169	4	be	be	AUX
ejpam-1829	169	5	extended	extend	VERB
ejpam-1829	169	6	to	to	ADP
ejpam-1829	169	7	a	a	DET
ejpam-1829	169	8	σ	σ	NOUN
ejpam-1829	169	9	-	-	PUNCT
ejpam-1829	169	10	derivation	derivation	NOUN
ejpam-1829	169	11	(	(	PUNCT
ejpam-1829	169	12	say	say	VERB
ejpam-1829	169	13	δ	δ	PROPN
ejpam-1829	169	14	)	)	PUNCT
ejpam-1829	169	15	of	of	ADP
ejpam-1829	169	16	r[x;σ	r[x;σ	NOUN
ejpam-1829	169	17	,	,	PUNCT
ejpam-1829	169	18	δ	δ	PROPN
ejpam-1829	169	19	]	]	PUNCT
ejpam-1829	169	20	by	by	ADP
ejpam-1829	169	21	δ	δ	PROPN
ejpam-1829	169	22	(	(	PUNCT
ejpam-1829	169	23	∑m	∑m	PROPN
ejpam-1829	169	24	i=0	i=0	PROPN
ejpam-1829	169	25	x	x	X
ejpam-1829	169	26	iai	iai	ADJ
ejpam-1829	169	27	)	)	PUNCT
ejpam-1829	170	1	=	=	PUNCT
ejpam-1829	170	2	∑m	∑m	PROPN
ejpam-1829	170	3	i=0	i=0	PROPN
ejpam-1829	170	4	x	x	SYM
ejpam-1829	170	5	iδ(ai	iδ(ai	PROPN
ejpam-1829	170	6	)	)	PUNCT
ejpam-1829	170	7	.	.	PUNCT
ejpam-1829	171	1	example	example	NOUN
ejpam-1829	171	2	5	5	NUM
ejpam-1829	171	3	(	(	PUNCT
ejpam-1829	171	4	example	example	NOUN
ejpam-1829	171	5	2.13	2.13	NUM
ejpam-1829	171	6	of	of	ADP
ejpam-1829	171	7	bhat	bhat	PROPN
ejpam-1829	171	8	[	[	X
ejpam-1829	171	9	5	5	NUM
ejpam-1829	171	10	]	]	PUNCT
ejpam-1829	171	11	)	)	PUNCT
ejpam-1829	171	12	.	.	PUNCT
ejpam-1829	172	1	let	let	VERB
ejpam-1829	172	2	r=	r=	PROPN
ejpam-1829	172	3	r×r	r×r	PROPN
ejpam-1829	172	4	,	,	PUNCT
ejpam-1829	172	5	σ	σ	NOUN
ejpam-1829	172	6	:	:	PUNCT
ejpam-1829	172	7	r→	r→	PROPN
ejpam-1829	172	8	r	r	NOUN
ejpam-1829	172	9	defined	define	VERB
ejpam-1829	172	10	by	by	ADP
ejpam-1829	172	11	σ((a	σ((a	PROPN
ejpam-1829	172	12	,	,	PUNCT
ejpam-1829	172	13	b	b	NOUN
ejpam-1829	172	14	)	)	PUNCT
ejpam-1829	172	15	)	)	PUNCT
ejpam-1829	173	1	=	=	PUNCT
ejpam-1829	173	2	(	(	PUNCT
ejpam-1829	173	3	b	b	NOUN
ejpam-1829	173	4	,	,	PUNCT
ejpam-1829	173	5	a	a	PRON
ejpam-1829	173	6	)	)	PUNCT
ejpam-1829	173	7	for	for	ADP
ejpam-1829	173	8	a	a	DET
ejpam-1829	173	9	,	,	PUNCT
ejpam-1829	173	10	b	b	PROPN
ejpam-1829	173	11	∈	∈	PROPN
ejpam-1829	173	12	r.	r.	PROPN
ejpam-1829	173	13	then	then	ADV
ejpam-1829	173	14	σ	σ	PROPN
ejpam-1829	173	15	is	be	AUX
ejpam-1829	173	16	an	an	DET
ejpam-1829	173	17	automorphism	automorphism	NOUN
ejpam-1829	173	18	of	of	ADP
ejpam-1829	173	19	r.	r.	PROPN
ejpam-1829	173	20	let	let	VERB
ejpam-1829	173	21	now	now	ADV
ejpam-1829	173	22	r	r	PROPN
ejpam-1829	173	23	∈	∈	PROPN
ejpam-1829	173	24	r.	r.	NOUN
ejpam-1829	173	25	define	define	VERB
ejpam-1829	173	26	δr	δr	NOUN
ejpam-1829	173	27	:	:	PUNCT
ejpam-1829	173	28	r→	r→	PROPN
ejpam-1829	173	29	r	r	NOUN
ejpam-1829	173	30	by	by	ADP
ejpam-1829	173	31	δr((a	δr((a	NOUN
ejpam-1829	173	32	,	,	PUNCT
ejpam-1829	173	33	b	b	NOUN
ejpam-1829	173	34	)	)	PUNCT
ejpam-1829	173	35	)	)	PUNCT
ejpam-1829	174	1	=	=	PRON
ejpam-1829	174	2	(	(	PUNCT
ejpam-1829	174	3	a	a	PRON
ejpam-1829	174	4	,	,	PUNCT
ejpam-1829	174	5	b)r	b)r	NOUN
ejpam-1829	174	6	−	−	PROPN
ejpam-1829	174	7	rσ((a	rσ((a	PROPN
ejpam-1829	174	8	,	,	PUNCT
ejpam-1829	174	9	b	b	NOUN
ejpam-1829	174	10	)	)	PUNCT
ejpam-1829	174	11	)	)	PUNCT
ejpam-1829	174	12	for	for	ADP
ejpam-1829	174	13	a	a	DET
ejpam-1829	174	14	,	,	PUNCT
ejpam-1829	174	15	b	b	PROPN
ejpam-1829	174	16	∈	∈	PROPN
ejpam-1829	174	17	r.	r.	PROPN
ejpam-1829	174	18	then	then	ADV
ejpam-1829	174	19	δ	δ	PROPN
ejpam-1829	174	20	is	be	AUX
ejpam-1829	174	21	a	a	DET
ejpam-1829	174	22	σ	σ	NOUN
ejpam-1829	174	23	-	-	PUNCT
ejpam-1829	174	24	derivation	derivation	NOUN
ejpam-1829	174	25	.	.	PUNCT
ejpam-1829	175	1	now	now	ADV
ejpam-1829	175	2	for	for	ADP
ejpam-1829	175	3	any	any	DET
ejpam-1829	175	4	(	(	PUNCT
ejpam-1829	175	5	u	u	NOUN
ejpam-1829	175	6	,	,	PUNCT
ejpam-1829	175	7	v	v	NOUN
ejpam-1829	175	8	)	)	PUNCT
ejpam-1829	175	9	∈	∈	PROPN
ejpam-1829	175	10	r	r	NOUN
ejpam-1829	175	11	,	,	PUNCT
ejpam-1829	175	12	σ(δr((u	σ(δr((u	NOUN
ejpam-1829	175	13	,	,	PUNCT
ejpam-1829	175	14	v	v	NOUN
ejpam-1829	175	15	)	)	PUNCT
ejpam-1829	175	16	)	)	PUNCT
ejpam-1829	175	17	)	)	PUNCT
ejpam-1829	176	1	=	=	NOUN
ejpam-1829	176	2	σ((u	σ((u	NOUN
ejpam-1829	176	3	,	,	PUNCT
ejpam-1829	176	4	v)r	v)r	PUNCT
ejpam-1829	176	5	−	−	NOUN
ejpam-1829	176	6	rσ((u	rσ((u	NOUN
ejpam-1829	176	7	,	,	PUNCT
ejpam-1829	176	8	v	v	NOUN
ejpam-1829	176	9	)	)	PUNCT
ejpam-1829	176	10	)	)	PUNCT
ejpam-1829	176	11	)	)	PUNCT
ejpam-1829	177	1	=	=	NOUN
ejpam-1829	177	2	σ((u	σ((u	NOUN
ejpam-1829	177	3	,	,	PUNCT
ejpam-1829	177	4	v)r	v)r	PUNCT
ejpam-1829	177	5	−	−	ADP
ejpam-1829	177	6	r(v	r(v	PROPN
ejpam-1829	177	7	,	,	PUNCT
ejpam-1829	177	8	u	u	NOUN
ejpam-1829	177	9	)	)	PUNCT
ejpam-1829	177	10	)	)	PUNCT
ejpam-1829	177	11	=	=	SYM
ejpam-1829	177	12	σ((ur	σ((ur	X
ejpam-1829	177	13	,	,	PUNCT
ejpam-1829	177	14	vr)−σ(vr	vr)−σ(vr	PROPN
ejpam-1829	177	15	,	,	PUNCT
ejpam-1829	177	16	ur	ur	NOUN
ejpam-1829	177	17	)	)	PUNCT
ejpam-1829	177	18	)	)	PUNCT
ejpam-1829	177	19	=(	=(	PROPN
ejpam-1829	177	20	vr	vr	PROPN
ejpam-1829	177	21	,	,	PUNCT
ejpam-1829	177	22	ur)−	ur)−	PUNCT
ejpam-1829	177	23	(	(	PUNCT
ejpam-1829	177	24	ur	ur	INTJ
ejpam-1829	177	25	,	,	PUNCT
ejpam-1829	177	26	vr	vr	NOUN
ejpam-1829	177	27	)	)	PUNCT
ejpam-1829	177	28	)	)	PUNCT
ejpam-1829	177	29	.	.	PUNCT
ejpam-1829	178	1	also	also	ADV
ejpam-1829	178	2	δr(σ((u	δr(σ((u	PROPN
ejpam-1829	178	3	,	,	PUNCT
ejpam-1829	178	4	v	v	NOUN
ejpam-1829	178	5	)	)	PUNCT
ejpam-1829	178	6	)	)	PUNCT
ejpam-1829	178	7	)	)	PUNCT
ejpam-1829	179	1	=	=	NOUN
ejpam-1829	179	2	δr(v	δr(v	X
ejpam-1829	179	3	,	,	PUNCT
ejpam-1829	179	4	u	u	NOUN
ejpam-1829	179	5	)	)	PUNCT
ejpam-1829	179	6	=(	=(	PROPN
ejpam-1829	179	7	v	v	NOUN
ejpam-1829	179	8	,	,	PUNCT
ejpam-1829	179	9	u)r	u)r	PUNCT
ejpam-1829	179	10	−	−	PROPN
ejpam-1829	179	11	rσ((v	rσ((v	NOUN
ejpam-1829	179	12	,	,	PUNCT
ejpam-1829	179	13	u	u	NOUN
ejpam-1829	179	14	)	)	PUNCT
ejpam-1829	179	15	)	)	PUNCT
ejpam-1829	179	16	=(	=(	PROPN
ejpam-1829	179	17	v	v	NOUN
ejpam-1829	179	18	,	,	PUNCT
ejpam-1829	179	19	u)r	u)r	VERB
ejpam-1829	179	20	−	−	PROPN
ejpam-1829	179	21	r(u	r(u	PROPN
ejpam-1829	179	22	,	,	PUNCT
ejpam-1829	179	23	v	v	NOUN
ejpam-1829	179	24	)	)	PUNCT
ejpam-1829	179	25	=(	=(	NOUN
ejpam-1829	179	26	vr	vr	PROPN
ejpam-1829	179	27	,	,	PUNCT
ejpam-1829	179	28	ur)−	ur)−	PUNCT
ejpam-1829	179	29	(	(	PUNCT
ejpam-1829	179	30	ur	ur	INTJ
ejpam-1829	179	31	,	,	PUNCT
ejpam-1829	179	32	vr	vr	NOUN
ejpam-1829	179	33	)	)	PUNCT
ejpam-1829	179	34	)	)	PUNCT
ejpam-1829	179	35	.	.	PUNCT
ejpam-1829	180	1	therefore	therefore	ADV
ejpam-1829	180	2	σ(δ((u	σ(δ((u	NOUN
ejpam-1829	180	3	,	,	PUNCT
ejpam-1829	180	4	v	v	NOUN
ejpam-1829	180	5	)	)	PUNCT
ejpam-1829	180	6	)	)	PUNCT
ejpam-1829	180	7	)	)	PUNCT
ejpam-1829	181	1	=	=	PUNCT
ejpam-1829	181	2	δ(σ((u	δ(σ((u	NOUN
ejpam-1829	181	3	,	,	PUNCT
ejpam-1829	181	4	v	v	NOUN
ejpam-1829	181	5	)	)	PUNCT
ejpam-1829	181	6	)	)	PUNCT
ejpam-1829	181	7	)	)	PUNCT
ejpam-1829	182	1	for	for	ADP
ejpam-1829	182	2	all	all	DET
ejpam-1829	182	3	(	(	PUNCT
ejpam-1829	182	4	u	u	NOUN
ejpam-1829	182	5	,	,	PUNCT
ejpam-1829	182	6	v	v	NOUN
ejpam-1829	182	7	)	)	PUNCT
ejpam-1829	182	8	∈	∈	PROPN
ejpam-1829	182	9	r.	r.	PROPN
ejpam-1829	182	10	remark	remark	NOUN
ejpam-1829	182	11	3	3	NUM
ejpam-1829	182	12	.	.	PUNCT
ejpam-1829	183	1	we	we	PRON
ejpam-1829	183	2	note	note	VERB
ejpam-1829	183	3	that	that	SCONJ
ejpam-1829	183	4	if	if	SCONJ
ejpam-1829	183	5	σ(δ(a	σ(δ(a	PROPN
ejpam-1829	183	6	)	)	PUNCT
ejpam-1829	183	7	)	)	PUNCT
ejpam-1829	183	8	6=	6=	X
ejpam-1829	184	1	δ(σ(a	δ(σ(a	NOUN
ejpam-1829	184	2	)	)	PUNCT
ejpam-1829	184	3	)	)	PUNCT
ejpam-1829	184	4	for	for	ADP
ejpam-1829	184	5	all	all	DET
ejpam-1829	184	6	a	a	DET
ejpam-1829	184	7	∈	∈	NOUN
ejpam-1829	184	8	r	r	NOUN
ejpam-1829	184	9	,	,	PUNCT
ejpam-1829	184	10	then	then	ADV
ejpam-1829	184	11	the	the	DET
ejpam-1829	184	12	above	above	ADJ
ejpam-1829	184	13	does	do	AUX
ejpam-1829	184	14	not	not	PART
ejpam-1829	184	15	hold	hold	VERB
ejpam-1829	184	16	.	.	PUNCT
ejpam-1829	185	1	for	for	ADP
ejpam-1829	185	2	example	example	NOUN
ejpam-1829	185	3	let	let	VERB
ejpam-1829	185	4	f	f	PROPN
ejpam-1829	185	5	(	(	PUNCT
ejpam-1829	185	6	x	x	X
ejpam-1829	185	7	)	)	PUNCT
ejpam-1829	185	8	=	=	SYM
ejpam-1829	185	9	x	x	SYM
ejpam-1829	185	10	l	l	NOUN
ejpam-1829	185	11	and	and	CCONJ
ejpam-1829	185	12	g(x	g(x	NOUN
ejpam-1829	185	13	)	)	PUNCT
ejpam-1829	186	1	=	=	PUNCT
ejpam-1829	186	2	x	x	PUNCT
ejpam-1829	187	1	p	p	X
ejpam-1829	187	2	,	,	PUNCT
ejpam-1829	187	3	a	a	PRON
ejpam-1829	187	4	,	,	PUNCT
ejpam-1829	187	5	b	b	PROPN
ejpam-1829	187	6	∈	∈	PROPN
ejpam-1829	187	7	r.	r.	PROPN
ejpam-1829	187	8	then	then	ADV
ejpam-1829	187	9	δ	δ	PROPN
ejpam-1829	187	10	(	(	PUNCT
ejpam-1829	187	11	f	f	PROPN
ejpam-1829	187	12	(	(	PUNCT
ejpam-1829	187	13	x)g(x	x)g(x	ADJ
ejpam-1829	187	14	)	)	PUNCT
ejpam-1829	187	15	)	)	PUNCT
ejpam-1829	188	1	=	=	PUNCT
ejpam-1829	188	2	x2{δ(σ(l))σ(p	x2{δ(σ(l))σ(p	NUM
ejpam-1829	188	3	)	)	PUNCT
ejpam-1829	189	1	+	+	NOUN
ejpam-1829	189	2	σ(l)δ(p)}+	σ(l)δ(p)}+	NOUN
ejpam-1829	189	3	x{δ2(l)σ(p	x{δ2(l)σ(p	NUM
ejpam-1829	189	4	)	)	PUNCT
ejpam-1829	189	5	+	+	NOUN
ejpam-1829	189	6	δ(l)σ(p	δ(l)σ(p	NOUN
ejpam-1829	189	7	)	)	PUNCT
ejpam-1829	189	8	}	}	PUNCT
ejpam-1829	189	9	,	,	PUNCT
ejpam-1829	189	10	but	but	CCONJ
ejpam-1829	189	11	δ	δ	PROPN
ejpam-1829	189	12	(	(	PUNCT
ejpam-1829	189	13	f	f	PROPN
ejpam-1829	189	14	(	(	PUNCT
ejpam-1829	189	15	x))σ(g(x	x))σ(g(x	NOUN
ejpam-1829	189	16	)	)	PUNCT
ejpam-1829	189	17	)	)	PUNCT
ejpam-1829	190	1	+	+	CCONJ
ejpam-1829	190	2	f	f	X
ejpam-1829	190	3	(	(	PUNCT
ejpam-1829	190	4	x)δ(g(x	x)δ(g(x	NUM
ejpam-1829	190	5	)	)	PUNCT
ejpam-1829	190	6	)	)	PUNCT
ejpam-1829	191	1	=	=	PUNCT
ejpam-1829	192	1	x2{σ(δ(l))σ(p	x2{σ(δ(l))σ(p	NUM
ejpam-1829	192	2	)	)	PUNCT
ejpam-1829	193	1	+	+	NOUN
ejpam-1829	193	2	σ(l)δ(p)}+	σ(l)δ(p)}+	NOUN
ejpam-1829	193	3	x{δ2(l)σ(p	x{δ2(l)σ(p	NUM
ejpam-1829	193	4	)	)	PUNCT
ejpam-1829	193	5	+	+	NOUN
ejpam-1829	193	6	δ(l)σ(p	δ(l)σ(p	NOUN
ejpam-1829	193	7	)	)	PUNCT
ejpam-1829	193	8	}	}	PUNCT
ejpam-1829	193	9	.	.	PUNCT
ejpam-1829	194	1	so	so	ADV
ejpam-1829	194	2	,	,	PUNCT
ejpam-1829	194	3	δ	δ	PROPN
ejpam-1829	194	4	(	(	PUNCT
ejpam-1829	194	5	f	f	PROPN
ejpam-1829	194	6	(	(	PUNCT
ejpam-1829	194	7	x)g(x	x)g(x	PROPN
ejpam-1829	194	8	)	)	PUNCT
ejpam-1829	194	9	)	)	PUNCT
ejpam-1829	194	10	6=	6=	X
ejpam-1829	195	1	δ	δ	PROPN
ejpam-1829	195	2	(	(	PUNCT
ejpam-1829	195	3	f	f	PROPN
ejpam-1829	195	4	(	(	PUNCT
ejpam-1829	195	5	x))σ(g(x	x))σ(g(x	NOUN
ejpam-1829	195	6	)	)	PUNCT
ejpam-1829	195	7	)	)	PUNCT
ejpam-1829	196	1	+	+	CCONJ
ejpam-1829	196	2	f	f	X
ejpam-1829	196	3	(	(	PUNCT
ejpam-1829	196	4	x)δ(g(x	x)δ(g(x	NUM
ejpam-1829	196	5	)	)	PUNCT
ejpam-1829	196	6	)	)	PUNCT
ejpam-1829	196	7	,	,	PUNCT
ejpam-1829	196	8	i.e.	i.e.	X
ejpam-1829	196	9	δ	δ	PROPN
ejpam-1829	196	10	is	be	AUX
ejpam-1829	196	11	not	not	PART
ejpam-1829	196	12	a	a	DET
ejpam-1829	196	13	δ	δ	NOUN
ejpam-1829	196	14	-	-	NOUN
ejpam-1829	196	15	derivation	derivation	NOUN
ejpam-1829	196	16	.	.	PUNCT
ejpam-1829	197	1	references	reference	NOUN
ejpam-1829	197	2	393	393	NUM
ejpam-1829	197	3	with	with	ADP
ejpam-1829	197	4	this	this	PRON
ejpam-1829	197	5	we	we	PRON
ejpam-1829	197	6	now	now	ADV
ejpam-1829	197	7	prove	prove	VERB
ejpam-1829	197	8	the	the	DET
ejpam-1829	197	9	following	following	NOUN
ejpam-1829	197	10	:	:	PUNCT
ejpam-1829	197	11	theorem	theorem	NOUN
ejpam-1829	197	12	3	3	X
ejpam-1829	197	13	.	.	PUNCT
ejpam-1829	198	1	let	let	VERB
ejpam-1829	198	2	r	r	PRON
ejpam-1829	198	3	be	be	AUX
ejpam-1829	198	4	a	a	DET
ejpam-1829	198	5	noetherian	noetherian	ADJ
ejpam-1829	198	6	ring	ring	NOUN
ejpam-1829	198	7	which	which	PRON
ejpam-1829	198	8	is	be	AUX
ejpam-1829	198	9	also	also	ADV
ejpam-1829	198	10	an	an	DET
ejpam-1829	198	11	algebra	algebra	NOUN
ejpam-1829	198	12	over	over	ADP
ejpam-1829	198	13	q.	q.	PROPN
ejpam-1829	198	14	let	let	VERB
ejpam-1829	198	15	σ	σ	NOUN
ejpam-1829	198	16	be	be	AUX
ejpam-1829	198	17	an	an	DET
ejpam-1829	198	18	automorphism	automorphism	NOUN
ejpam-1829	198	19	of	of	ADP
ejpam-1829	198	20	r	r	NOUN
ejpam-1829	198	21	and	and	CCONJ
ejpam-1829	198	22	δ	δ	PROPN
ejpam-1829	199	1	a	a	DET
ejpam-1829	199	2	σ	σ	NOUN
ejpam-1829	199	3	-	-	PUNCT
ejpam-1829	199	4	derivation	derivation	NOUN
ejpam-1829	199	5	of	of	ADP
ejpam-1829	199	6	r	r	NOUN
ejpam-1829	199	7	such	such	ADJ
ejpam-1829	199	8	that	that	DET
ejpam-1829	199	9	σ(δ(a	σ(δ(a	NOUN
ejpam-1829	199	10	)	)	PUNCT
ejpam-1829	199	11	)	)	PUNCT
ejpam-1829	200	1	=	=	PUNCT
ejpam-1829	200	2	δ(σ(a	δ(σ(a	NOUN
ejpam-1829	200	3	)	)	PUNCT
ejpam-1829	200	4	)	)	PUNCT
ejpam-1829	201	1	for	for	ADP
ejpam-1829	201	2	all	all	DET
ejpam-1829	201	3	a	a	DET
ejpam-1829	201	4	∈	∈	PROPN
ejpam-1829	201	5	r.	r.	NOUN
ejpam-1829	201	6	further	far	ADV
ejpam-1829	201	7	let	let	VERB
ejpam-1829	201	8	p	p	PROPN
ejpam-1829	201	9	∈	∈	PROPN
ejpam-1829	201	10	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	201	11	)	)	PUNCT
ejpam-1829	201	12	)	)	PUNCT
ejpam-1829	201	13	implies	imply	VERB
ejpam-1829	201	14	that	that	SCONJ
ejpam-1829	201	15	p	p	NOUN
ejpam-1829	201	16	∩	∩	NOUN
ejpam-1829	201	17	r	r	NOUN
ejpam-1829	201	18	∈	∈	PROPN
ejpam-1829	201	19	min.spec(r	min.spec(r	PROPN
ejpam-1829	201	20	)	)	PUNCT
ejpam-1829	201	21	.	.	PUNCT
ejpam-1829	202	1	then	then	ADV
ejpam-1829	202	2	r	r	NOUN
ejpam-1829	202	3	is	be	AUX
ejpam-1829	202	4	a	a	DET
ejpam-1829	202	5	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	202	6	implies	imply	VERB
ejpam-1829	202	7	that	that	SCONJ
ejpam-1829	202	8	o(r	o(r	NOUN
ejpam-1829	202	9	)	)	PUNCT
ejpam-1829	202	10	=	=	SYM
ejpam-1829	202	11	r[x;σ	r[x;σ	NOUN
ejpam-1829	202	12	,	,	PUNCT
ejpam-1829	202	13	δ	δ	PROPN
ejpam-1829	202	14	]	]	PUNCT
ejpam-1829	202	15	is	be	AUX
ejpam-1829	202	16	a	a	DET
ejpam-1829	202	17	noetherian	noetherian	ADJ
ejpam-1829	202	18	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	202	19	.	.	PUNCT
ejpam-1829	203	1	proof	proof	NOUN
ejpam-1829	203	2	.	.	PUNCT
ejpam-1829	204	1	let	let	VERB
ejpam-1829	204	2	r	r	PRON
ejpam-1829	204	3	be	be	AUX
ejpam-1829	204	4	a	a	DET
ejpam-1829	204	5	noetherian	noetherian	ADJ
ejpam-1829	204	6	ring	ring	NOUN
ejpam-1829	204	7	and	and	CCONJ
ejpam-1829	204	8	σ	σ	NOUN
ejpam-1829	204	9	an	an	DET
ejpam-1829	204	10	automorphism	automorphism	NOUN
ejpam-1829	204	11	of	of	ADP
ejpam-1829	204	12	r	r	NOUN
ejpam-1829	204	13	such	such	ADJ
ejpam-1829	204	14	that	that	SCONJ
ejpam-1829	204	15	r	r	NOUN
ejpam-1829	204	16	is	be	AUX
ejpam-1829	204	17	a	a	DET
ejpam-1829	204	18	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	204	19	.	.	PUNCT
ejpam-1829	205	1	we	we	PRON
ejpam-1829	205	2	shall	shall	AUX
ejpam-1829	205	3	prove	prove	VERB
ejpam-1829	205	4	that	that	SCONJ
ejpam-1829	205	5	o(r	o(r	NOUN
ejpam-1829	205	6	)	)	PUNCT
ejpam-1829	205	7	=	=	SYM
ejpam-1829	205	8	r[x;σ	r[x;σ	NOUN
ejpam-1829	205	9	,	,	PUNCT
ejpam-1829	205	10	δ	δ	PROPN
ejpam-1829	205	11	]	]	PUNCT
ejpam-1829	205	12	is	be	AUX
ejpam-1829	205	13	a	a	DET
ejpam-1829	205	14	noetherian	noetherian	ADJ
ejpam-1829	205	15	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	205	16	.	.	PUNCT
ejpam-1829	206	1	for	for	ADP
ejpam-1829	206	2	this	this	PRON
ejpam-1829	206	3	we	we	PRON
ejpam-1829	206	4	will	will	AUX
ejpam-1829	206	5	show	show	VERB
ejpam-1829	206	6	that	that	SCONJ
ejpam-1829	206	7	any	any	DET
ejpam-1829	206	8	minimal	minimal	ADJ
ejpam-1829	206	9	p	p	X
ejpam-1829	206	10	∈	∈	PROPN
ejpam-1829	206	11	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	206	12	)	)	PUNCT
ejpam-1829	206	13	)	)	PUNCT
ejpam-1829	206	14	is	be	AUX
ejpam-1829	206	15	completely	completely	ADV
ejpam-1829	206	16	prime	prime	ADJ
ejpam-1829	206	17	and	and	CCONJ
ejpam-1829	206	18	σ(p	σ(p	PRON
ejpam-1829	206	19	)	)	PUNCT
ejpam-1829	206	20	=	=	PUNCT
ejpam-1829	207	1	p.	p.	NOUN
ejpam-1829	207	2	let	let	VERB
ejpam-1829	207	3	p	p	PROPN
ejpam-1829	207	4	∈	∈	PROPN
ejpam-1829	207	5	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	207	6	)	)	PUNCT
ejpam-1829	207	7	)	)	PUNCT
ejpam-1829	207	8	.	.	PUNCT
ejpam-1829	208	1	now	now	ADV
ejpam-1829	208	2	p	p	X
ejpam-1829	208	3	∩	∩	NOUN
ejpam-1829	208	4	r	r	NOUN
ejpam-1829	208	5	∈	∈	PROPN
ejpam-1829	208	6	min.spec(r	min.spec(r	NOUN
ejpam-1829	208	7	)	)	PUNCT
ejpam-1829	208	8	and	and	CCONJ
ejpam-1829	208	9	r	r	NOUN
ejpam-1829	208	10	is	be	AUX
ejpam-1829	208	11	a	a	DET
ejpam-1829	208	12	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	208	13	implies	implie	NOUN
ejpam-1829	209	1	that	that	SCONJ
ejpam-1829	209	2	σ(p	σ(p	PROPN
ejpam-1829	209	3	∩	∩	NOUN
ejpam-1829	209	4	r	r	NOUN
ejpam-1829	209	5	)	)	PUNCT
ejpam-1829	209	6	=	=	SYM
ejpam-1829	209	7	p	p	NOUN
ejpam-1829	209	8	∩	∩	ADJ
ejpam-1829	209	9	r	r	NOUN
ejpam-1829	209	10	and	and	CCONJ
ejpam-1829	209	11	p	p	NOUN
ejpam-1829	209	12	∩	∩	NOUN
ejpam-1829	209	13	r	r	NOUN
ejpam-1829	209	14	is	be	AUX
ejpam-1829	209	15	a	a	DET
ejpam-1829	209	16	completely	completely	ADV
ejpam-1829	209	17	prime	prime	ADJ
ejpam-1829	209	18	ideal	ideal	NOUN
ejpam-1829	209	19	of	of	ADP
ejpam-1829	209	20	r.	r.	PROPN
ejpam-1829	209	21	now	now	ADV
ejpam-1829	209	22	proposition	proposition	NOUN
ejpam-1829	209	23	(	(	PUNCT
ejpam-1829	209	24	2.1	2.1	NUM
ejpam-1829	209	25	)	)	PUNCT
ejpam-1829	209	26	of	of	ADP
ejpam-1829	209	27	bhat	bhat	PROPN
ejpam-1829	209	28	[	[	X
ejpam-1829	209	29	2	2	NUM
ejpam-1829	209	30	]	]	PUNCT
ejpam-1829	209	31	implies	imply	VERB
ejpam-1829	209	32	that	that	SCONJ
ejpam-1829	209	33	δ(p	δ(p	PROPN
ejpam-1829	209	34	∩	∩	ADJ
ejpam-1829	209	35	r	r	NOUN
ejpam-1829	209	36	)	)	PUNCT
ejpam-1829	209	37	⊆	⊆	NUM
ejpam-1829	209	38	p	p	NOUN
ejpam-1829	209	39	∩	∩	PROPN
ejpam-1829	209	40	r.	r.	PROPN
ejpam-1829	209	41	now	now	ADV
ejpam-1829	209	42	theorem	theorem	VERB
ejpam-1829	209	43	(	(	PUNCT
ejpam-1829	209	44	2.4	2.4	NUM
ejpam-1829	209	45	)	)	PUNCT
ejpam-1829	209	46	of	of	ADP
ejpam-1829	209	47	bhat	bhat	PROPN
ejpam-1829	210	1	[	[	X
ejpam-1829	210	2	4	4	NUM
ejpam-1829	210	3	]	]	PUNCT
ejpam-1829	210	4	implies	imply	VERB
ejpam-1829	210	5	that	that	SCONJ
ejpam-1829	210	6	o(p	o(p	PROPN
ejpam-1829	210	7	∩	∩	ADJ
ejpam-1829	210	8	r	r	NOUN
ejpam-1829	210	9	)	)	PUNCT
ejpam-1829	210	10	is	be	AUX
ejpam-1829	210	11	a	a	DET
ejpam-1829	210	12	completely	completely	ADV
ejpam-1829	210	13	prime	prime	ADJ
ejpam-1829	210	14	ideal	ideal	NOUN
ejpam-1829	210	15	of	of	ADP
ejpam-1829	210	16	o(r	o(r	PROPN
ejpam-1829	210	17	)	)	PUNCT
ejpam-1829	210	18	.	.	PUNCT
ejpam-1829	211	1	now	now	ADV
ejpam-1829	211	2	o(p	o(p	PROPN
ejpam-1829	211	3	∩r	∩r	PROPN
ejpam-1829	211	4	)	)	PUNCT
ejpam-1829	212	1	⊆	⊆	NUM
ejpam-1829	212	2	p	p	NOUN
ejpam-1829	212	3	implies	imply	VERB
ejpam-1829	212	4	that	that	SCONJ
ejpam-1829	212	5	o(p	o(p	PROPN
ejpam-1829	212	6	∩r	∩r	PROPN
ejpam-1829	212	7	)	)	PUNCT
ejpam-1829	213	1	=	=	PUNCT
ejpam-1829	213	2	p	p	NOUN
ejpam-1829	213	3	as	as	SCONJ
ejpam-1829	213	4	p	p	PROPN
ejpam-1829	213	5	is	be	AUX
ejpam-1829	213	6	minimal	minimal	ADJ
ejpam-1829	213	7	.	.	PUNCT
ejpam-1829	214	1	now	now	ADV
ejpam-1829	214	2	σ(p	σ(p	PRON
ejpam-1829	214	3	∩	∩	ADJ
ejpam-1829	214	4	r	r	NOUN
ejpam-1829	214	5	)	)	PUNCT
ejpam-1829	214	6	=	=	SYM
ejpam-1829	214	7	p	p	NOUN
ejpam-1829	214	8	∩	∩	NOUN
ejpam-1829	214	9	r	r	NOUN
ejpam-1829	214	10	implies	imply	VERB
ejpam-1829	214	11	that	that	SCONJ
ejpam-1829	214	12	σ(p	σ(p	PROPN
ejpam-1829	214	13	)	)	PUNCT
ejpam-1829	214	14	=	=	PUNCT
ejpam-1829	215	1	p.	p.	NOUN
ejpam-1829	215	2	thus	thus	ADV
ejpam-1829	215	3	σ(p	σ(p	X
ejpam-1829	215	4	)	)	PUNCT
ejpam-1829	216	1	=	=	SYM
ejpam-1829	217	1	p	p	NOUN
ejpam-1829	217	2	and	and	CCONJ
ejpam-1829	217	3	p	p	NOUN
ejpam-1829	217	4	is	be	AUX
ejpam-1829	217	5	completely	completely	ADV
ejpam-1829	217	6	prime	prime	ADJ
ejpam-1829	217	7	for	for	ADP
ejpam-1829	217	8	all	all	PRON
ejpam-1829	217	9	p	p	PROPN
ejpam-1829	217	10	∈	∈	PROPN
ejpam-1829	217	11	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	217	12	)	)	PUNCT
ejpam-1829	217	13	)	)	PUNCT
ejpam-1829	217	14	.	.	PUNCT
ejpam-1829	218	1	moreover	moreover	ADV
ejpam-1829	218	2	o(r	o(r	PROPN
ejpam-1829	218	3	)	)	PUNCT
ejpam-1829	218	4	=	=	SYM
ejpam-1829	218	5	r[x;σ	r[x;σ	NOUN
ejpam-1829	218	6	,	,	PUNCT
ejpam-1829	218	7	δ	δ	PROPN
ejpam-1829	218	8	]	]	PUNCT
ejpam-1829	218	9	is	be	AUX
ejpam-1829	218	10	noetherian	noetherian	ADJ
ejpam-1829	218	11	by	by	ADP
ejpam-1829	218	12	theorem	theorem	NOUN
ejpam-1829	218	13	(	(	PUNCT
ejpam-1829	218	14	1.12	1.12	NUM
ejpam-1829	218	15	)	)	PUNCT
ejpam-1829	218	16	of	of	ADP
ejpam-1829	218	17	goodearl	goodearl	PROPN
ejpam-1829	218	18	and	and	CCONJ
ejpam-1829	218	19	warfield	warfield	VERB
ejpam-1829	219	1	[	[	X
ejpam-1829	219	2	7	7	NUM
ejpam-1829	219	3	]	]	PUNCT
ejpam-1829	219	4	.	.	PUNCT
ejpam-1829	220	1	hence	hence	ADV
ejpam-1829	220	2	by	by	ADP
ejpam-1829	220	3	proposition	proposition	NOUN
ejpam-1829	220	4	2	2	NUM
ejpam-1829	220	5	r[x;σ	r[x;σ	NOUN
ejpam-1829	220	6	,	,	PUNCT
ejpam-1829	220	7	δ	δ	PROPN
ejpam-1829	220	8	]	]	PUNCT
ejpam-1829	220	9	is	be	AUX
ejpam-1829	220	10	a	a	DET
ejpam-1829	220	11	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	220	12	.	.	PUNCT
ejpam-1829	221	1	we	we	PRON
ejpam-1829	221	2	note	note	VERB
ejpam-1829	221	3	that	that	SCONJ
ejpam-1829	221	4	the	the	DET
ejpam-1829	221	5	condition	condition	NOUN
ejpam-1829	221	6	that	that	SCONJ
ejpam-1829	221	7	p	p	PROPN
ejpam-1829	221	8	∈	∈	PROPN
ejpam-1829	221	9	min.spec(o(r	min.spec(o(r	NOUN
ejpam-1829	221	10	)	)	PUNCT
ejpam-1829	221	11	)	)	PUNCT
ejpam-1829	221	12	implies	imply	VERB
ejpam-1829	221	13	that	that	SCONJ
ejpam-1829	221	14	p	p	NOUN
ejpam-1829	221	15	∩	∩	NOUN
ejpam-1829	221	16	r	r	NOUN
ejpam-1829	221	17	∈	∈	PROPN
ejpam-1829	221	18	min.spec(r	min.spec(r	NOUN
ejpam-1829	221	19	)	)	PUNCT
ejpam-1829	221	20	can	can	AUX
ejpam-1829	221	21	not	not	PART
ejpam-1829	221	22	be	be	AUX
ejpam-1829	221	23	ignored	ignore	VERB
ejpam-1829	221	24	as	as	SCONJ
ejpam-1829	221	25	follows	follow	VERB
ejpam-1829	221	26	:	:	PUNCT
ejpam-1829	221	27	let	let	VERB
ejpam-1829	221	28	r	r	NOUN
ejpam-1829	221	29	=	=	SYM
ejpam-1829	221	30	q×q	q×q	PROPN
ejpam-1829	221	31	.	.	PUNCT
ejpam-1829	222	1	let	let	VERB
ejpam-1829	222	2	σ	σ	NOUN
ejpam-1829	222	3	:	:	PUNCT
ejpam-1829	222	4	r→	r→	PROPN
ejpam-1829	222	5	r	r	NOUN
ejpam-1829	222	6	be	be	AUX
ejpam-1829	222	7	defined	define	VERB
ejpam-1829	222	8	by	by	ADP
ejpam-1829	222	9	σ((a	σ((a	PROPN
ejpam-1829	222	10	,	,	PUNCT
ejpam-1829	222	11	b	b	NOUN
ejpam-1829	222	12	)	)	PUNCT
ejpam-1829	222	13	)	)	PUNCT
ejpam-1829	223	1	=	=	PUNCT
ejpam-1829	223	2	(	(	PUNCT
ejpam-1829	223	3	b	b	NOUN
ejpam-1829	223	4	,	,	PUNCT
ejpam-1829	223	5	a	a	NOUN
ejpam-1829	223	6	)	)	PUNCT
ejpam-1829	223	7	and	and	CCONJ
ejpam-1829	223	8	δ	δ	PROPN
ejpam-1829	223	9	=	=	NOUN
ejpam-1829	224	1	0	0	X
ejpam-1829	224	2	.	.	PUNCT
ejpam-1829	225	1	then	then	ADV
ejpam-1829	225	2	p	p	X
ejpam-1829	225	3	=	=	SYM
ejpam-1829	225	4	0	0	NUM
ejpam-1829	225	5	is	be	AUX
ejpam-1829	225	6	a	a	DET
ejpam-1829	225	7	prime	prime	ADJ
ejpam-1829	225	8	ideal	ideal	NOUN
ejpam-1829	225	9	of	of	ADP
ejpam-1829	225	10	o(r	o(r	PROPN
ejpam-1829	225	11	)	)	PUNCT
ejpam-1829	225	12	,	,	PUNCT
ejpam-1829	225	13	but	but	CCONJ
ejpam-1829	225	14	p	p	NOUN
ejpam-1829	225	15	∩	∩	NOUN
ejpam-1829	225	16	r	r	NOUN
ejpam-1829	225	17	is	be	AUX
ejpam-1829	225	18	not	not	PART
ejpam-1829	225	19	a	a	DET
ejpam-1829	225	20	prime	prime	ADJ
ejpam-1829	225	21	ideal	ideal	NOUN
ejpam-1829	225	22	of	of	ADP
ejpam-1829	225	23	r.	r.	PROPN
ejpam-1829	225	24	we	we	PRON
ejpam-1829	225	25	have	have	AUX
ejpam-1829	225	26	not	not	PART
ejpam-1829	225	27	been	be	AUX
ejpam-1829	225	28	able	able	ADJ
ejpam-1829	225	29	to	to	PART
ejpam-1829	225	30	prove	prove	VERB
ejpam-1829	225	31	the	the	DET
ejpam-1829	225	32	converse	converse	NOUN
ejpam-1829	225	33	part	part	NOUN
ejpam-1829	225	34	of	of	ADP
ejpam-1829	225	35	the	the	DET
ejpam-1829	225	36	above	above	ADJ
ejpam-1829	225	37	result	result	NOUN
ejpam-1829	225	38	.	.	PUNCT
ejpam-1829	226	1	the	the	DET
ejpam-1829	226	2	main	main	ADJ
ejpam-1829	226	3	reason	reason	NOUN
ejpam-1829	226	4	being	be	AUX
ejpam-1829	226	5	that	that	SCONJ
ejpam-1829	226	6	a	a	DET
ejpam-1829	226	7	generalization	generalization	NOUN
ejpam-1829	226	8	of	of	ADP
ejpam-1829	226	9	theorem	theorem	NOUN
ejpam-1829	226	10	1	1	NUM
ejpam-1829	226	11	in	in	ADP
ejpam-1829	226	12	terms	term	NOUN
ejpam-1829	226	13	of	of	ADP
ejpam-1829	226	14	o(r	o(r	PROPN
ejpam-1829	226	15	)	)	PUNCT
ejpam-1829	226	16	is	be	AUX
ejpam-1829	226	17	not	not	PART
ejpam-1829	226	18	known	know	VERB
ejpam-1829	226	19	.	.	PUNCT
ejpam-1829	227	1	the	the	DET
ejpam-1829	227	2	known	known	ADJ
ejpam-1829	227	3	towards	towards	ADP
ejpam-1829	227	4	this	this	PRON
ejpam-1829	227	5	is	be	AUX
ejpam-1829	227	6	:	:	PUNCT
ejpam-1829	227	7	let	let	VERB
ejpam-1829	227	8	r	r	PRON
ejpam-1829	227	9	be	be	AUX
ejpam-1829	227	10	a	a	DET
ejpam-1829	227	11	noetherian	noetherian	ADJ
ejpam-1829	227	12	ring	ring	NOUN
ejpam-1829	227	13	which	which	PRON
ejpam-1829	227	14	is	be	AUX
ejpam-1829	227	15	also	also	ADV
ejpam-1829	227	16	an	an	DET
ejpam-1829	227	17	algebra	algebra	NOUN
ejpam-1829	227	18	overq	overq	ADJ
ejpam-1829	227	19	.	.	PUNCT
ejpam-1829	228	1	let	let	VERB
ejpam-1829	228	2	σ	σ	NOUN
ejpam-1829	228	3	be	be	AUX
ejpam-1829	228	4	an	an	DET
ejpam-1829	228	5	automorphism	automorphism	NOUN
ejpam-1829	228	6	of	of	ADP
ejpam-1829	228	7	r	r	NOUN
ejpam-1829	228	8	and	and	CCONJ
ejpam-1829	228	9	δ	δ	PROPN
ejpam-1829	228	10	a	a	DET
ejpam-1829	228	11	σ	σ	NOUN
ejpam-1829	228	12	-	-	PUNCT
ejpam-1829	228	13	derivation	derivation	NOUN
ejpam-1829	228	14	of	of	ADP
ejpam-1829	228	15	r.	r.	PROPN
ejpam-1829	228	16	then	then	ADV
ejpam-1829	228	17	u	u	PROPN
ejpam-1829	228	18	∈	∈	PROPN
ejpam-1829	228	19	min.spec(r	min.spec(r	PROPN
ejpam-1829	228	20	)	)	PUNCT
ejpam-1829	228	21	such	such	ADJ
ejpam-1829	228	22	that	that	SCONJ
ejpam-1829	228	23	σ(u	σ(u	NOUN
ejpam-1829	228	24	)	)	PUNCT
ejpam-1829	228	25	=	=	SYM
ejpam-1829	228	26	u	u	NOUN
ejpam-1829	228	27	implies	imply	VERB
ejpam-1829	228	28	that	that	SCONJ
ejpam-1829	228	29	δ(u	δ(u	PROPN
ejpam-1829	228	30	)	)	PUNCT
ejpam-1829	228	31	⊆	⊆	NUM
ejpam-1829	228	32	u	u	NOUN
ejpam-1829	228	33	(	(	PUNCT
ejpam-1829	228	34	lemma	lemma	PROPN
ejpam-1829	228	35	2.6	2.6	NUM
ejpam-1829	228	36	of	of	ADP
ejpam-1829	228	37	bhat	bhat	PROPN
ejpam-1829	228	38	[	[	X
ejpam-1829	228	39	3	3	NUM
ejpam-1829	228	40	]	]	PUNCT
ejpam-1829	228	41	)	)	PUNCT
ejpam-1829	228	42	.	.	PUNCT
ejpam-1829	229	1	question	question	NOUN
ejpam-1829	229	2	let	let	VERB
ejpam-1829	229	3	r	r	PRON
ejpam-1829	229	4	be	be	AUX
ejpam-1829	229	5	a	a	DET
ejpam-1829	229	6	noetherian	noetherian	ADJ
ejpam-1829	229	7	ring	ring	NOUN
ejpam-1829	229	8	which	which	PRON
ejpam-1829	229	9	is	be	AUX
ejpam-1829	229	10	also	also	ADV
ejpam-1829	229	11	an	an	DET
ejpam-1829	229	12	algebra	algebra	NOUN
ejpam-1829	229	13	over	over	ADP
ejpam-1829	229	14	q.	q.	PROPN
ejpam-1829	229	15	let	let	VERB
ejpam-1829	229	16	σ	σ	NOUN
ejpam-1829	229	17	be	be	AUX
ejpam-1829	229	18	an	an	DET
ejpam-1829	229	19	automorphism	automorphism	NOUN
ejpam-1829	229	20	of	of	ADP
ejpam-1829	229	21	r	r	NOUN
ejpam-1829	229	22	and	and	CCONJ
ejpam-1829	229	23	δ	δ	PROPN
ejpam-1829	229	24	a	a	DET
ejpam-1829	229	25	σ	σ	NOUN
ejpam-1829	229	26	-	-	PUNCT
ejpam-1829	229	27	derivation	derivation	NOUN
ejpam-1829	229	28	of	of	ADP
ejpam-1829	229	29	r.	r.	PROPN
ejpam-1829	229	30	if	if	SCONJ
ejpam-1829	229	31	o(r	o(r	PRON
ejpam-1829	229	32	)	)	PUNCT
ejpam-1829	229	33	=	=	SYM
ejpam-1829	230	1	r[x;σ	r[x;σ	NOUN
ejpam-1829	230	2	,	,	PUNCT
ejpam-1829	230	3	δ	δ	PROPN
ejpam-1829	230	4	]	]	PUNCT
ejpam-1829	230	5	is	be	AUX
ejpam-1829	230	6	a	a	DET
ejpam-1829	230	7	noetherian	noetherian	ADJ
ejpam-1829	230	8	σ(∗)ring	σ(∗)ring	NOUN
ejpam-1829	230	9	.	.	PUNCT
ejpam-1829	231	1	is	be	AUX
ejpam-1829	231	2	r	r	NOUN
ejpam-1829	231	3	is	be	AUX
ejpam-1829	231	4	a	a	DET
ejpam-1829	231	5	σ(∗)-ring	σ(∗)-ring	NOUN
ejpam-1829	231	6	?	?	PUNCT
ejpam-1829	231	7	references	reference	NOUN
ejpam-1829	232	1	[	[	X
ejpam-1829	232	2	1	1	X
ejpam-1829	232	3	]	]	PUNCT
ejpam-1829	232	4	v.	v.	PROPN
ejpam-1829	232	5	k.	k.	PROPN
ejpam-1829	232	6	bhat	bhat	PROPN
ejpam-1829	232	7	.	.	PUNCT
ejpam-1829	233	1	associated	associate	VERB
ejpam-1829	233	2	prime	prime	ADJ
ejpam-1829	233	3	ideals	ideal	NOUN
ejpam-1829	233	4	of	of	ADP
ejpam-1829	233	5	skew	skew	ADJ
ejpam-1829	233	6	polynomial	polynomial	ADJ
ejpam-1829	233	7	rings	ring	NOUN
ejpam-1829	233	8	,	,	PUNCT
ejpam-1829	233	9	beitrage	beitrage	NOUN
ejpam-1829	233	10	zur	zur	NOUN
ejpam-1829	233	11	algebra	algebra	NOUN
ejpam-1829	233	12	und	und	NOUN
ejpam-1829	233	13	geometrie	geometrie	NOUN
ejpam-1829	233	14	,	,	PUNCT
ejpam-1829	233	15	vol	vol	NOUN
ejpam-1829	233	16	.	.	PUNCT
ejpam-1829	233	17	49(1	49(1	NUM
ejpam-1829	233	18	)	)	PUNCT
ejpam-1829	233	19	.	.	PUNCT
ejpam-1829	234	1	277	277	NUM
ejpam-1829	234	2	-	-	SYM
ejpam-1829	234	3	283	283	NUM
ejpam-1829	234	4	.	.	PUNCT
ejpam-1829	234	5	2008	2008	NUM
ejpam-1829	234	6	.	.	PUNCT
ejpam-1829	235	1	[	[	X
ejpam-1829	235	2	2	2	X
ejpam-1829	235	3	]	]	PUNCT
ejpam-1829	235	4	v.	v.	PROPN
ejpam-1829	235	5	k.	k.	PROPN
ejpam-1829	235	6	bhat	bhat	PROPN
ejpam-1829	235	7	.	.	PUNCT
ejpam-1829	236	1	on	on	ADP
ejpam-1829	236	2	near	near	ADP
ejpam-1829	236	3	pseudo	pseudo	NOUN
ejpam-1829	236	4	-	-	NOUN
ejpam-1829	236	5	valuation	valuation	NOUN
ejpam-1829	236	6	rings	ring	NOUN
ejpam-1829	236	7	and	and	CCONJ
ejpam-1829	236	8	their	their	PRON
ejpam-1829	236	9	extensions	extension	NOUN
ejpam-1829	236	10	,	,	PUNCT
ejpam-1829	236	11	international	international	ADJ
ejpam-1829	236	12	electronic	electronic	ADJ
ejpam-1829	236	13	journal	journal	NOUN
ejpam-1829	236	14	of	of	ADP
ejpam-1829	236	15	algebra	algebra	PROPN
ejpam-1829	236	16	,	,	PUNCT
ejpam-1829	236	17	5:70	5:70	PROPN
ejpam-1829	236	18	-	-	SYM
ejpam-1829	236	19	77	77	NUM
ejpam-1829	236	20	,	,	PUNCT
ejpam-1829	236	21	2009	2009	NUM
ejpam-1829	236	22	.	.	PUNCT
ejpam-1829	237	1	[	[	X
ejpam-1829	237	2	3	3	X
ejpam-1829	237	3	]	]	PUNCT
ejpam-1829	237	4	v.	v.	PROPN
ejpam-1829	237	5	k.	k.	PROPN
ejpam-1829	237	6	bhat	bhat	PROPN
ejpam-1829	237	7	.	.	PUNCT
ejpam-1829	238	1	transparent	transparent	ADJ
ejpam-1829	238	2	rings	ring	NOUN
ejpam-1829	238	3	and	and	CCONJ
ejpam-1829	238	4	their	their	PRON
ejpam-1829	238	5	extensions	extension	NOUN
ejpam-1829	238	6	,	,	PUNCT
ejpam-1829	238	7	new	new	PROPN
ejpam-1829	238	8	york	york	PROPN
ejpam-1829	238	9	journal	journal	PROPN
ejpam-1829	238	10	of	of	ADP
ejpam-1829	238	11	mathematics	mathematics	PROPN
ejpam-1829	238	12	,	,	PUNCT
ejpam-1829	238	13	vol	vol	NOUN
ejpam-1829	238	14	.	.	PROPN
ejpam-1829	238	15	15	15	NUM
ejpam-1829	238	16	.	.	X
ejpam-1829	238	17	291	291	NUM
ejpam-1829	238	18	-	-	SYM
ejpam-1829	238	19	299	299	NUM
ejpam-1829	238	20	.	.	PUNCT
ejpam-1829	238	21	2009	2009	NUM
ejpam-1829	238	22	.	.	PUNCT
ejpam-1829	239	1	references	reference	NOUN
ejpam-1829	239	2	394	394	NUM
ejpam-1829	239	3	[	[	X
ejpam-1829	239	4	4	4	NUM
ejpam-1829	239	5	]	]	PUNCT
ejpam-1829	239	6	v.	v.	PROPN
ejpam-1829	239	7	k.	k.	PROPN
ejpam-1829	239	8	bhat	bhat	PROPN
ejpam-1829	239	9	.	.	PUNCT
ejpam-1829	240	1	a	a	DET
ejpam-1829	240	2	note	note	NOUN
ejpam-1829	240	3	on	on	ADP
ejpam-1829	240	4	completely	completely	ADV
ejpam-1829	240	5	prime	prime	ADJ
ejpam-1829	240	6	ideals	ideal	NOUN
ejpam-1829	240	7	of	of	ADP
ejpam-1829	240	8	ore	ore	NOUN
ejpam-1829	240	9	extensions	extension	NOUN
ejpam-1829	240	10	,	,	PUNCT
ejpam-1829	240	11	international	international	ADJ
ejpam-1829	240	12	journal	journal	NOUN
ejpam-1829	240	13	of	of	ADP
ejpam-1829	240	14	algebra	algebra	NOUN
ejpam-1829	240	15	and	and	CCONJ
ejpam-1829	240	16	computation	computation	NOUN
ejpam-1829	240	17	,	,	PUNCT
ejpam-1829	240	18	vol	vol	NOUN
ejpam-1829	240	19	.	.	PUNCT
ejpam-1829	241	1	20(3	20(3	NOUN
ejpam-1829	241	2	)	)	PUNCT
ejpam-1829	241	3	.	.	PUNCT
ejpam-1829	242	1	457	457	NUM
ejpam-1829	242	2	-	-	SYM
ejpam-1829	242	3	463	463	NUM
ejpam-1829	242	4	.	.	PUNCT
ejpam-1829	243	1	2010	2010	NUM
ejpam-1829	243	2	.	.	PUNCT
ejpam-1829	244	1	[	[	X
ejpam-1829	244	2	5	5	X
ejpam-1829	244	3	]	]	PUNCT
ejpam-1829	244	4	v.	v.	PROPN
ejpam-1829	244	5	k.	k.	PROPN
ejpam-1829	244	6	bhat	bhat	PROPN
ejpam-1829	244	7	.	.	PUNCT
ejpam-1829	245	1	associated	associate	VERB
ejpam-1829	245	2	prime	prime	ADJ
ejpam-1829	245	3	ideals	ideal	NOUN
ejpam-1829	245	4	of	of	ADP
ejpam-1829	245	5	weak	weak	ADJ
ejpam-1829	245	6	σ	σ	ADJ
ejpam-1829	245	7	-	-	ADJ
ejpam-1829	245	8	rigid	rigid	ADJ
ejpam-1829	245	9	rings	ring	NOUN
ejpam-1829	245	10	and	and	CCONJ
ejpam-1829	245	11	their	their	PRON
ejpam-1829	245	12	extensions	extension	NOUN
ejpam-1829	245	13	,	,	PUNCT
ejpam-1829	245	14	algebra	algebra	NOUN
ejpam-1829	245	15	and	and	CCONJ
ejpam-1829	245	16	discrete	discrete	ADJ
ejpam-1829	245	17	mathematics	mathematic	NOUN
ejpam-1829	245	18	,	,	PUNCT
ejpam-1829	245	19	vol.10(1	vol.10(1	ADJ
ejpam-1829	245	20	)	)	PUNCT
ejpam-1829	245	21	.	.	PUNCT
ejpam-1829	246	1	8	8	NUM
ejpam-1829	246	2	-	-	SYM
ejpam-1829	246	3	17	17	NUM
ejpam-1829	246	4	.	.	PUNCT
ejpam-1829	247	1	2010	2010	NUM
ejpam-1829	247	2	.	.	PUNCT
ejpam-1829	248	1	[	[	X
ejpam-1829	248	2	6	6	NUM
ejpam-1829	248	3	]	]	PUNCT
ejpam-1829	248	4	v.	v.	PROPN
ejpam-1829	248	5	k.	k.	PROPN
ejpam-1829	248	6	bhat	bhat	PROPN
ejpam-1829	248	7	.	.	PUNCT
ejpam-1829	249	1	prime	prime	ADJ
ejpam-1829	249	2	ideals	ideal	NOUN
ejpam-1829	249	3	of	of	ADP
ejpam-1829	249	4	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-1829	249	5	and	and	CCONJ
ejpam-1829	249	6	their	their	PRON
ejpam-1829	249	7	extensions	extension	NOUN
ejpam-1829	249	8	,	,	PUNCT
ejpam-1829	249	9	lobachevskii	lobachevskii	ADJ
ejpam-1829	249	10	journal	journal	NOUN
ejpam-1829	249	11	of	of	ADP
ejpam-1829	249	12	mathematics	mathematics	PROPN
ejpam-1829	249	13	,	,	PUNCT
ejpam-1829	249	14	vol	vol	NOUN
ejpam-1829	249	15	.	.	PUNCT
ejpam-1829	249	16	32(1	32(1	NUM
ejpam-1829	249	17	)	)	PUNCT
ejpam-1829	249	18	.	.	PUNCT
ejpam-1829	250	1	102	102	NUM
ejpam-1829	250	2	-	-	SYM
ejpam-1829	250	3	106	106	NUM
ejpam-1829	250	4	.	.	PUNCT
ejpam-1829	251	1	2011	2011	NUM
ejpam-1829	251	2	.	.	PUNCT
ejpam-1829	252	1	[	[	X
ejpam-1829	252	2	7	7	X
ejpam-1829	252	3	]	]	PUNCT
ejpam-1829	252	4	k.	k.	PROPN
ejpam-1829	252	5	r.	r.	PROPN
ejpam-1829	252	6	goodearl	goodearl	PROPN
ejpam-1829	252	7	and	and	CCONJ
ejpam-1829	252	8	r.	r.	PROPN
ejpam-1829	252	9	b.	b.	PROPN
ejpam-1829	252	10	warfield	warfield	PROPN
ejpam-1829	252	11	jr	jr	PROPN
ejpam-1829	252	12	.	.	PUNCT
ejpam-1829	253	1	an	an	DET
ejpam-1829	253	2	introduction	introduction	NOUN
ejpam-1829	253	3	to	to	ADP
ejpam-1829	253	4	non	non	ADJ
ejpam-1829	253	5	-	-	ADJ
ejpam-1829	253	6	commutative	commutative	ADJ
ejpam-1829	253	7	noetherian	noetherian	ADJ
ejpam-1829	253	8	rings	ring	NOUN
ejpam-1829	253	9	,	,	PUNCT
ejpam-1829	253	10	cambridge	cambridge	PROPN
ejpam-1829	253	11	university	university	PROPN
ejpam-1829	253	12	press	press	NOUN
ejpam-1829	253	13	,	,	PUNCT
ejpam-1829	253	14	1989	1989	NUM
ejpam-1829	253	15	.	.	PUNCT
ejpam-1829	254	1	[	[	X
ejpam-1829	254	2	8	8	X
ejpam-1829	254	3	]	]	X
ejpam-1829	254	4	j.	j.	PROPN
ejpam-1829	254	5	krempa	krempa	PROPN
ejpam-1829	254	6	.	.	PUNCT
ejpam-1829	255	1	some	some	DET
ejpam-1829	255	2	examples	example	NOUN
ejpam-1829	255	3	of	of	ADP
ejpam-1829	255	4	reduced	reduce	VERB
ejpam-1829	255	5	rings	ring	NOUN
ejpam-1829	255	6	,	,	PUNCT
ejpam-1829	255	7	algebra	algebra	NOUN
ejpam-1829	255	8	colloqium	colloqium	NOUN
ejpam-1829	255	9	,	,	PUNCT
ejpam-1829	255	10	vol	vol	NOUN
ejpam-1829	255	11	.	.	PUNCT
ejpam-1829	255	12	3(4	3(4	NUM
ejpam-1829	255	13	)	)	PUNCT
ejpam-1829	255	14	.	.	PUNCT
ejpam-1829	256	1	289	289	NUM
ejpam-1829	256	2	-	-	SYM
ejpam-1829	256	3	300	300	NUM
ejpam-1829	256	4	.	.	PUNCT
ejpam-1829	256	5	1996	1996	NUM
ejpam-1829	256	6	.	.	PUNCT
ejpam-1829	257	1	[	[	X
ejpam-1829	257	2	9	9	NUM
ejpam-1829	257	3	]	]	PUNCT
ejpam-1829	257	4	t.	t.	PROPN
ejpam-1829	257	5	k.	k.	PROPN
ejpam-1829	257	6	kwak	kwak	PROPN
ejpam-1829	257	7	.	.	PUNCT
ejpam-1829	258	1	prime	prime	ADJ
ejpam-1829	258	2	radicals	radical	NOUN
ejpam-1829	258	3	of	of	ADP
ejpam-1829	258	4	skew	skew	ADJ
ejpam-1829	258	5	-	-	PUNCT
ejpam-1829	258	6	polynomial	polynomial	ADJ
ejpam-1829	258	7	rings	ring	NOUN
ejpam-1829	258	8	,	,	PUNCT
ejpam-1829	258	9	international	international	ADJ
ejpam-1829	258	10	journal	journal	NOUN
ejpam-1829	258	11	of	of	ADP
ejpam-1829	258	12	mathematical	mathematical	ADJ
ejpam-1829	258	13	sciences	sciences	PROPN
ejpam-1829	258	14	,	,	PUNCT
ejpam-1829	258	15	vol	vol	NOUN
ejpam-1829	258	16	.	.	PROPN
ejpam-1829	258	17	2(2	2(2	NUM
ejpam-1829	258	18	)	)	PUNCT
ejpam-1829	258	19	.	.	PUNCT
ejpam-1829	259	1	219	219	NUM
ejpam-1829	259	2	-	-	SYM
ejpam-1829	259	3	227	227	NUM
ejpam-1829	259	4	.	.	PUNCT
ejpam-1829	259	5	2003	2003	NUM
ejpam-1829	259	6	.	.	PUNCT
ejpam-1829	260	1	[	[	X
ejpam-1829	260	2	10	10	NUM
ejpam-1829	260	3	]	]	X
ejpam-1829	260	4	g.	g.	NOUN
ejpam-1829	260	5	marks	marks	PROPN
ejpam-1829	260	6	.	.	PUNCT
ejpam-1829	261	1	on	on	ADP
ejpam-1829	261	2	2	2	NUM
ejpam-1829	261	3	-	-	PUNCT
ejpam-1829	261	4	primal	primal	ADJ
ejpam-1829	261	5	ore	ore	NOUN
ejpam-1829	261	6	extensions	extension	NOUN
ejpam-1829	261	7	,	,	PUNCT
ejpam-1829	261	8	communications	communication	NOUN
ejpam-1829	261	9	in	in	ADP
ejpam-1829	261	10	algebra	algebra	NOUN
ejpam-1829	261	11	,	,	PUNCT
ejpam-1829	261	12	vol	vol	NOUN
ejpam-1829	261	13	.	.	PUNCT
ejpam-1829	261	14	29(5	29(5	NUM
ejpam-1829	261	15	)	)	PUNCT
ejpam-1829	261	16	.	.	PUNCT
ejpam-1829	261	17	2113	2113	NUM
ejpam-1829	261	18	-	-	SYM
ejpam-1829	261	19	2123	2123	NUM
ejpam-1829	261	20	.	.	PUNCT
ejpam-1829	261	21	2001	2001	NUM
ejpam-1829	261	22	.	.	PUNCT
ejpam-1829	262	1	[	[	X
ejpam-1829	262	2	11	11	NUM
ejpam-1829	262	3	]	]	X
ejpam-1829	262	4	n.	n.	PROPN
ejpam-1829	262	5	h.	h.	PROPN
ejpam-1829	262	6	mccoy	mccoy	PROPN
ejpam-1829	262	7	.	.	PUNCT
ejpam-1829	263	1	completely	completely	ADV
ejpam-1829	263	2	prime	prime	ADJ
ejpam-1829	263	3	and	and	CCONJ
ejpam-1829	263	4	completely	completely	ADV
ejpam-1829	263	5	semi	semi	ADJ
ejpam-1829	263	6	-	-	ADJ
ejpam-1829	263	7	prime	prime	ADJ
ejpam-1829	263	8	ideals	ideal	NOUN
ejpam-1829	263	9	,	,	PUNCT
ejpam-1829	263	10	in	in	ADP
ejpam-1829	263	11	:	:	PUNCT
ejpam-1829	263	12	“	"	PUNCT
ejpam-1829	263	13	rings	ring	NOUN
ejpam-1829	263	14	,	,	PUNCT
ejpam-1829	263	15	modules	module	NOUN
ejpam-1829	263	16	and	and	CCONJ
ejpam-1829	263	17	radicals	radical	NOUN
ejpam-1829	263	18	”	"	PUNCT
ejpam-1829	263	19	,	,	PUNCT
ejpam-1829	263	20	a.	a.	NOUN
ejpam-1829	263	21	kertész	kertész	PROPN
ejpam-1829	263	22	(	(	PUNCT
ejpam-1829	263	23	ed.),journal	ed.),journal	PROPN
ejpam-1829	263	24	of	of	ADP
ejpam-1829	263	25	bolyai	bolyai	PROPN
ejpam-1829	263	26	mathematical	mathematical	ADJ
ejpam-1829	263	27	society	society	NOUN
ejpam-1829	263	28	,	,	PUNCT
ejpam-1829	263	29	budapest	budapest	NOUN
ejpam-1829	263	30	.	.	PUNCT
ejpam-1829	264	1	147	147	NUM
ejpam-1829	264	2	-	-	SYM
ejpam-1829	264	3	152	152	NUM
ejpam-1829	264	4	.	.	PUNCT
ejpam-1829	264	5	1973	1973	NUM
ejpam-1829	264	6	.	.	PUNCT