id	sid	tid	token	lemma	pos
ejpam-2383	1	1	compile	compile	NOUN
ejpam-2383	1	2	/	/	SYM
ejpam-2383	1	3	output.dvi	output.dvi	NOUN
ejpam-2383	1	4	european	european	ADJ
ejpam-2383	1	5	journal	journal	NOUN
ejpam-2383	1	6	of	of	ADP
ejpam-2383	1	7	pure	pure	ADJ
ejpam-2383	1	8	and	and	CCONJ
ejpam-2383	1	9	applied	apply	VERB
ejpam-2383	1	10	mathematics	mathematic	NOUN
ejpam-2383	1	11	vol	vol	NOUN
ejpam-2383	1	12	.	.	PROPN
ejpam-2383	1	13	8	8	NUM
ejpam-2383	1	14	,	,	PUNCT
ejpam-2383	1	15	no	no	INTJ
ejpam-2383	1	16	.	.	NOUN
ejpam-2383	1	17	4	4	NUM
ejpam-2383	1	18	,	,	PUNCT
ejpam-2383	1	19	2015	2015	NUM
ejpam-2383	1	20	,	,	PUNCT
ejpam-2383	1	21	462	462	NUM
ejpam-2383	1	22	-	-	SYM
ejpam-2383	1	23	468	468	NUM
ejpam-2383	1	24	issn	issn	PROPN
ejpam-2383	1	25	1307	1307	NUM
ejpam-2383	1	26	-	-	SYM
ejpam-2383	1	27	5543	5543	NUM
ejpam-2383	1	28	–	–	PUNCT
ejpam-2383	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2383	1	30	ore	ore	NOUN
ejpam-2383	1	31	extensions	extension	NOUN
ejpam-2383	1	32	over	over	ADP
ejpam-2383	1	33	(	(	PUNCT
ejpam-2383	1	34	σ	σ	NOUN
ejpam-2383	1	35	,	,	PUNCT
ejpam-2383	1	36	δ)-rings	δ)-ring	NOUN
ejpam-2383	1	37	m.	m.	NOUN
ejpam-2383	1	38	abrol	abrol	NOUN
ejpam-2383	1	39	,	,	PUNCT
ejpam-2383	1	40	v.	v.	PROPN
ejpam-2383	1	41	k.	k.	PROPN
ejpam-2383	2	1	bhat∗	bhat∗	PROPN
ejpam-2383	2	2	1	1	NUM
ejpam-2383	2	3	school	school	NOUN
ejpam-2383	2	4	of	of	ADP
ejpam-2383	2	5	mathematics	mathematic	NOUN
ejpam-2383	2	6	,	,	PUNCT
ejpam-2383	2	7	smvd	smvd	PROPN
ejpam-2383	2	8	university	university	PROPN
ejpam-2383	2	9	,	,	PUNCT
ejpam-2383	2	10	p	p	X
ejpam-2383	2	11	/	/	SYM
ejpam-2383	2	12	o	o	PROPN
ejpam-2383	2	13	smvd	smvd	PROPN
ejpam-2383	2	14	university	university	PROPN
ejpam-2383	2	15	,	,	PUNCT
ejpam-2383	2	16	katra	katra	PROPN
ejpam-2383	2	17	,	,	PUNCT
ejpam-2383	2	18	j	j	PROPN
ejpam-2383	2	19	and	and	CCONJ
ejpam-2383	2	20	k	k	PROPN
ejpam-2383	2	21	,	,	PUNCT
ejpam-2383	2	22	india182320	india182320	PROPN
ejpam-2383	2	23	abstract	abstract	NOUN
ejpam-2383	2	24	.	.	PUNCT
ejpam-2383	3	1	let	let	VERB
ejpam-2383	3	2	r	r	PRON
ejpam-2383	3	3	be	be	AUX
ejpam-2383	3	4	a	a	DET
ejpam-2383	3	5	noetherian	noetherian	ADJ
ejpam-2383	3	6	,	,	PUNCT
ejpam-2383	3	7	integral	integral	ADJ
ejpam-2383	3	8	domain	domain	NOUN
ejpam-2383	3	9	which	which	PRON
ejpam-2383	3	10	is	be	AUX
ejpam-2383	3	11	also	also	ADV
ejpam-2383	3	12	an	an	DET
ejpam-2383	3	13	algebra	algebra	NOUN
ejpam-2383	3	14	over	over	ADP
ejpam-2383	3	15	q	q	PROPN
ejpam-2383	3	16	(	(	PUNCT
ejpam-2383	3	17	q	q	NOUN
ejpam-2383	3	18	is	be	AUX
ejpam-2383	3	19	the	the	DET
ejpam-2383	3	20	field	field	NOUN
ejpam-2383	3	21	of	of	ADP
ejpam-2383	3	22	rational	rational	ADJ
ejpam-2383	3	23	numbers	number	NOUN
ejpam-2383	3	24	)	)	PUNCT
ejpam-2383	3	25	.	.	PUNCT
ejpam-2383	4	1	let	let	VERB
ejpam-2383	4	2	σ	σ	NOUN
ejpam-2383	4	3	be	be	AUX
ejpam-2383	4	4	an	an	DET
ejpam-2383	4	5	automorphism	automorphism	NOUN
ejpam-2383	4	6	of	of	ADP
ejpam-2383	4	7	r	r	NOUN
ejpam-2383	4	8	and	and	CCONJ
ejpam-2383	4	9	δ	δ	PROPN
ejpam-2383	4	10	a	a	DET
ejpam-2383	4	11	σ	σ	NOUN
ejpam-2383	4	12	-	-	PUNCT
ejpam-2383	4	13	derivation	derivation	NOUN
ejpam-2383	4	14	of	of	ADP
ejpam-2383	4	15	r.	r.	PROPN
ejpam-2383	4	16	a	a	DET
ejpam-2383	4	17	ring	ring	NOUN
ejpam-2383	4	18	r	r	NOUN
ejpam-2383	4	19	is	be	AUX
ejpam-2383	4	20	called	call	VERB
ejpam-2383	4	21	a	a	DET
ejpam-2383	4	22	(	(	PUNCT
ejpam-2383	4	23	σ	σ	NOUN
ejpam-2383	4	24	,	,	PUNCT
ejpam-2383	4	25	δ)-ring	δ)-re	VERB
ejpam-2383	4	26	if	if	SCONJ
ejpam-2383	4	27	a(σ(a)+δ(a	a(σ(a)+δ(a	NOUN
ejpam-2383	4	28	)	)	PUNCT
ejpam-2383	4	29	)	)	PUNCT
ejpam-2383	5	1	∈	∈	PROPN
ejpam-2383	5	2	p(r	p(r	PROPN
ejpam-2383	5	3	)	)	PUNCT
ejpam-2383	5	4	implies	imply	VERB
ejpam-2383	5	5	that	that	SCONJ
ejpam-2383	5	6	a	a	DET
ejpam-2383	5	7	∈	∈	PROPN
ejpam-2383	5	8	p(r	p(r	PROPN
ejpam-2383	5	9	)	)	PUNCT
ejpam-2383	5	10	for	for	ADP
ejpam-2383	5	11	a	a	DET
ejpam-2383	5	12	∈	∈	PROPN
ejpam-2383	5	13	r	r	NOUN
ejpam-2383	5	14	,	,	PUNCT
ejpam-2383	5	15	where	where	SCONJ
ejpam-2383	5	16	p(r	p(r	NOUN
ejpam-2383	5	17	)	)	PUNCT
ejpam-2383	5	18	is	be	AUX
ejpam-2383	5	19	the	the	DET
ejpam-2383	5	20	prime	prime	ADJ
ejpam-2383	5	21	radical	radical	NOUN
ejpam-2383	5	22	of	of	ADP
ejpam-2383	5	23	r.	r.	PROPN
ejpam-2383	5	24	we	we	PRON
ejpam-2383	5	25	prove	prove	VERB
ejpam-2383	5	26	that	that	SCONJ
ejpam-2383	5	27	r	r	NOUN
ejpam-2383	5	28	is	be	AUX
ejpam-2383	5	29	2	2	NUM
ejpam-2383	5	30	-	-	PUNCT
ejpam-2383	5	31	primal	primal	ADJ
ejpam-2383	5	32	if	if	SCONJ
ejpam-2383	5	33	δ(p(r	δ(p(r	PROPN
ejpam-2383	5	34	)	)	PUNCT
ejpam-2383	5	35	)	)	PUNCT
ejpam-2383	6	1	⊆	⊆	NUM
ejpam-2383	6	2	p(r	p(r	PROPN
ejpam-2383	6	3	)	)	PUNCT
ejpam-2383	6	4	.	.	PUNCT
ejpam-2383	7	1	we	we	PRON
ejpam-2383	7	2	also	also	ADV
ejpam-2383	7	3	study	study	VERB
ejpam-2383	7	4	the	the	DET
ejpam-2383	7	5	property	property	NOUN
ejpam-2383	7	6	of	of	ADP
ejpam-2383	7	7	minimal	minimal	ADJ
ejpam-2383	7	8	prime	prime	ADJ
ejpam-2383	7	9	ideals	ideal	NOUN
ejpam-2383	7	10	of	of	ADP
ejpam-2383	7	11	r	r	NOUN
ejpam-2383	7	12	and	and	CCONJ
ejpam-2383	7	13	prove	prove	VERB
ejpam-2383	7	14	the	the	DET
ejpam-2383	7	15	following	following	NOUN
ejpam-2383	7	16	in	in	ADP
ejpam-2383	7	17	this	this	DET
ejpam-2383	7	18	direction	direction	NOUN
ejpam-2383	7	19	:	:	PUNCT
ejpam-2383	7	20	let	let	VERB
ejpam-2383	7	21	r	r	PRON
ejpam-2383	7	22	be	be	AUX
ejpam-2383	7	23	a	a	DET
ejpam-2383	7	24	noetherian	noetherian	ADJ
ejpam-2383	7	25	,	,	PUNCT
ejpam-2383	7	26	integral	integral	ADJ
ejpam-2383	7	27	domain	domain	NOUN
ejpam-2383	7	28	which	which	PRON
ejpam-2383	7	29	is	be	AUX
ejpam-2383	7	30	also	also	ADV
ejpam-2383	7	31	an	an	DET
ejpam-2383	7	32	algebra	algebra	NOUN
ejpam-2383	7	33	over	over	ADP
ejpam-2383	7	34	q.	q.	PROPN
ejpam-2383	7	35	let	let	VERB
ejpam-2383	7	36	σ	σ	NOUN
ejpam-2383	7	37	be	be	AUX
ejpam-2383	7	38	an	an	DET
ejpam-2383	7	39	automorphism	automorphism	NOUN
ejpam-2383	7	40	of	of	ADP
ejpam-2383	7	41	r	r	NOUN
ejpam-2383	7	42	and	and	CCONJ
ejpam-2383	7	43	δ	δ	PROPN
ejpam-2383	7	44	a	a	DET
ejpam-2383	7	45	σ	σ	NOUN
ejpam-2383	7	46	-	-	PUNCT
ejpam-2383	7	47	derivation	derivation	NOUN
ejpam-2383	7	48	of	of	ADP
ejpam-2383	7	49	r	r	NOUN
ejpam-2383	7	50	such	such	ADJ
ejpam-2383	7	51	that	that	SCONJ
ejpam-2383	7	52	r	r	NOUN
ejpam-2383	7	53	is	be	AUX
ejpam-2383	7	54	a	a	DET
ejpam-2383	7	55	(	(	PUNCT
ejpam-2383	7	56	σ	σ	NOUN
ejpam-2383	7	57	,	,	PUNCT
ejpam-2383	7	58	δ)-ring	δ)-ring	ADJ
ejpam-2383	7	59	.	.	PUNCT
ejpam-2383	8	1	if	if	SCONJ
ejpam-2383	8	2	p	p	PROPN
ejpam-2383	8	3	∈	∈	PROPN
ejpam-2383	8	4	min.spec(r	min.spec(r	NOUN
ejpam-2383	8	5	)	)	PUNCT
ejpam-2383	8	6	is	be	AUX
ejpam-2383	8	7	such	such	ADJ
ejpam-2383	8	8	that	that	SCONJ
ejpam-2383	8	9	σ(p	σ(p	PROPN
ejpam-2383	8	10	)	)	PUNCT
ejpam-2383	9	1	=	=	SYM
ejpam-2383	10	1	p	p	X
ejpam-2383	10	2	,	,	PUNCT
ejpam-2383	10	3	then	then	ADV
ejpam-2383	10	4	δ(p	δ(p	PROPN
ejpam-2383	10	5	)	)	PUNCT
ejpam-2383	10	6	⊆	⊆	NUM
ejpam-2383	10	7	p.	p.	NOUN
ejpam-2383	10	8	further	far	ADV
ejpam-2383	10	9	if	if	SCONJ
ejpam-2383	10	10	δ(p(r	δ(p(r	PROPN
ejpam-2383	10	11	)	)	PUNCT
ejpam-2383	10	12	)	)	PUNCT
ejpam-2383	11	1	⊆	⊆	NUM
ejpam-2383	11	2	p(r	p(r	PROPN
ejpam-2383	11	3	)	)	PUNCT
ejpam-2383	11	4	,	,	PUNCT
ejpam-2383	11	5	then	then	ADV
ejpam-2383	11	6	p[x;σ	p[x;σ	PROPN
ejpam-2383	11	7	,	,	PUNCT
ejpam-2383	11	8	δ	δ	PROPN
ejpam-2383	11	9	]	]	PUNCT
ejpam-2383	11	10	is	be	AUX
ejpam-2383	11	11	a	a	DET
ejpam-2383	11	12	completely	completely	ADV
ejpam-2383	11	13	prime	prime	ADJ
ejpam-2383	11	14	ideal	ideal	NOUN
ejpam-2383	11	15	of	of	ADP
ejpam-2383	11	16	r[x;σ	r[x;σ	NOUN
ejpam-2383	11	17	,	,	PUNCT
ejpam-2383	11	18	δ	δ	PROPN
ejpam-2383	11	19	]	]	PUNCT
ejpam-2383	11	20	.	.	PUNCT
ejpam-2383	12	1	2010	2010	NUM
ejpam-2383	12	2	mathematics	mathematic	NOUN
ejpam-2383	12	3	subject	subject	NOUN
ejpam-2383	12	4	classifications	classification	NOUN
ejpam-2383	12	5	:	:	PUNCT
ejpam-2383	12	6	16	16	NUM
ejpam-2383	12	7	-	-	SYM
ejpam-2383	12	8	xx	xx	NUM
ejpam-2383	12	9	,	,	PUNCT
ejpam-2383	12	10	16w20	16w20	NUM
ejpam-2383	12	11	,	,	PUNCT
ejpam-2383	12	12	16p40	16p40	NUM
ejpam-2383	12	13	,	,	PUNCT
ejpam-2383	12	14	16s50	16s50	NUM
ejpam-2383	12	15	key	key	ADJ
ejpam-2383	12	16	words	word	NOUN
ejpam-2383	12	17	and	and	CCONJ
ejpam-2383	12	18	phrases	phrase	NOUN
ejpam-2383	12	19	:	:	PUNCT
ejpam-2383	12	20	noetherian	noetherian	ADJ
ejpam-2383	12	21	ring	ring	NOUN
ejpam-2383	12	22	,	,	PUNCT
ejpam-2383	12	23	ore	ore	NOUN
ejpam-2383	12	24	extension	extension	NOUN
ejpam-2383	12	25	,	,	PUNCT
ejpam-2383	12	26	endomorphism	endomorphism	NOUN
ejpam-2383	12	27	,	,	PUNCT
ejpam-2383	12	28	automorphism	automorphism	NOUN
ejpam-2383	12	29	,	,	PUNCT
ejpam-2383	12	30	minimal	minimal	ADJ
ejpam-2383	12	31	prime	prime	ADJ
ejpam-2383	12	32	ideals	ideal	NOUN
ejpam-2383	12	33	,	,	PUNCT
ejpam-2383	12	34	(	(	PUNCT
ejpam-2383	12	35	σ	σ	NOUN
ejpam-2383	12	36	,	,	PUNCT
ejpam-2383	12	37	δ)-rings	δ)-ring	NOUN
ejpam-2383	12	38	and	and	CCONJ
ejpam-2383	12	39	2	2	NUM
ejpam-2383	12	40	-	-	PUNCT
ejpam-2383	12	41	primal	primal	ADJ
ejpam-2383	12	42	.	.	PUNCT
ejpam-2383	13	1	1	1	X
ejpam-2383	13	2	.	.	X
ejpam-2383	13	3	introduction	introduction	NOUN
ejpam-2383	13	4	and	and	CCONJ
ejpam-2383	13	5	preliminaries	preliminary	NOUN
ejpam-2383	13	6	all	all	DET
ejpam-2383	13	7	rings	ring	NOUN
ejpam-2383	13	8	are	be	AUX
ejpam-2383	13	9	associative	associative	ADJ
ejpam-2383	13	10	with	with	ADP
ejpam-2383	13	11	identity	identity	NOUN
ejpam-2383	13	12	1	1	NUM
ejpam-2383	13	13	6=	6=	ADP
ejpam-2383	13	14	0	0	NUM
ejpam-2383	13	15	,	,	PUNCT
ejpam-2383	13	16	unless	unless	SCONJ
ejpam-2383	13	17	otherwise	otherwise	ADV
ejpam-2383	13	18	stated	state	VERB
ejpam-2383	13	19	.	.	PUNCT
ejpam-2383	14	1	the	the	DET
ejpam-2383	14	2	prime	prime	ADJ
ejpam-2383	14	3	radical	radical	ADJ
ejpam-2383	14	4	and	and	CCONJ
ejpam-2383	14	5	the	the	DET
ejpam-2383	14	6	set	set	NOUN
ejpam-2383	14	7	of	of	ADP
ejpam-2383	14	8	nilpotent	nilpotent	ADJ
ejpam-2383	14	9	elements	element	NOUN
ejpam-2383	14	10	of	of	ADP
ejpam-2383	14	11	r	r	NOUN
ejpam-2383	14	12	are	be	AUX
ejpam-2383	14	13	denoted	denote	VERB
ejpam-2383	14	14	by	by	ADP
ejpam-2383	14	15	p(r	p(r	PROPN
ejpam-2383	14	16	)	)	PUNCT
ejpam-2383	14	17	and	and	CCONJ
ejpam-2383	14	18	n(r	n(r	NOUN
ejpam-2383	14	19	)	)	PUNCT
ejpam-2383	14	20	respectively	respectively	ADV
ejpam-2383	14	21	.	.	PUNCT
ejpam-2383	15	1	the	the	DET
ejpam-2383	15	2	ring	ring	NOUN
ejpam-2383	15	3	of	of	ADP
ejpam-2383	15	4	integers	integer	NOUN
ejpam-2383	15	5	is	be	AUX
ejpam-2383	15	6	denoted	denote	VERB
ejpam-2383	15	7	by	by	ADP
ejpam-2383	15	8	z	z	PROPN
ejpam-2383	15	9	and	and	CCONJ
ejpam-2383	15	10	the	the	DET
ejpam-2383	15	11	field	field	NOUN
ejpam-2383	15	12	of	of	ADP
ejpam-2383	15	13	rational	rational	ADJ
ejpam-2383	15	14	numbers	number	NOUN
ejpam-2383	15	15	by	by	ADP
ejpam-2383	15	16	q	q	NOUN
ejpam-2383	15	17	,	,	PUNCT
ejpam-2383	15	18	unless	unless	SCONJ
ejpam-2383	15	19	otherwise	otherwise	ADV
ejpam-2383	15	20	stated	state	VERB
ejpam-2383	15	21	.	.	PUNCT
ejpam-2383	16	1	the	the	DET
ejpam-2383	16	2	set	set	NOUN
ejpam-2383	16	3	of	of	ADP
ejpam-2383	16	4	minimal	minimal	ADJ
ejpam-2383	16	5	prime	prime	ADJ
ejpam-2383	16	6	ideals	ideal	NOUN
ejpam-2383	16	7	of	of	ADP
ejpam-2383	16	8	r	r	NOUN
ejpam-2383	16	9	is	be	AUX
ejpam-2383	16	10	denoted	denote	VERB
ejpam-2383	16	11	by	by	ADP
ejpam-2383	16	12	min.spec(r	min.spec(r	PROPN
ejpam-2383	16	13	)	)	PUNCT
ejpam-2383	16	14	.	.	PUNCT
ejpam-2383	17	1	we	we	PRON
ejpam-2383	17	2	begin	begin	VERB
ejpam-2383	17	3	with	with	ADP
ejpam-2383	17	4	the	the	DET
ejpam-2383	17	5	following	following	NOUN
ejpam-2383	17	6	:	:	PUNCT
ejpam-2383	17	7	definition	definition	NOUN
ejpam-2383	17	8	1	1	NUM
ejpam-2383	17	9	.	.	PUNCT
ejpam-2383	18	1	let	let	VERB
ejpam-2383	18	2	r	r	PRON
ejpam-2383	18	3	be	be	AUX
ejpam-2383	18	4	a	a	DET
ejpam-2383	18	5	ring	ring	NOUN
ejpam-2383	18	6	,	,	PUNCT
ejpam-2383	18	7	σ	σ	PROPN
ejpam-2383	18	8	an	an	DET
ejpam-2383	18	9	endomorphism	endomorphism	NOUN
ejpam-2383	18	10	of	of	ADP
ejpam-2383	18	11	r	r	NOUN
ejpam-2383	18	12	and	and	CCONJ
ejpam-2383	18	13	δ	δ	PROPN
ejpam-2383	18	14	a	a	DET
ejpam-2383	18	15	σ	σ	NOUN
ejpam-2383	18	16	-	-	PUNCT
ejpam-2383	18	17	derivation	derivation	NOUN
ejpam-2383	18	18	of	of	ADP
ejpam-2383	18	19	r	r	NOUN
ejpam-2383	18	20	,	,	PUNCT
ejpam-2383	18	21	which	which	PRON
ejpam-2383	18	22	is	be	AUX
ejpam-2383	18	23	defined	define	VERB
ejpam-2383	18	24	as	as	ADP
ejpam-2383	18	25	an	an	DET
ejpam-2383	18	26	additive	additive	ADJ
ejpam-2383	18	27	map	map	NOUN
ejpam-2383	18	28	from	from	ADP
ejpam-2383	18	29	r	r	NOUN
ejpam-2383	18	30	to	to	ADP
ejpam-2383	18	31	r	r	NOUN
ejpam-2383	18	32	such	such	ADJ
ejpam-2383	18	33	that	that	SCONJ
ejpam-2383	18	34	[	[	X
ejpam-2383	18	35	12	12	NUM
ejpam-2383	18	36	]	]	PUNCT
ejpam-2383	18	37	δ(ab	δ(ab	NOUN
ejpam-2383	18	38	)	)	PUNCT
ejpam-2383	18	39	=	=	SYM
ejpam-2383	18	40	δ(a)σ(b	δ(a)σ(b	NOUN
ejpam-2383	18	41	)	)	PUNCT
ejpam-2383	18	42	+	+	NUM
ejpam-2383	18	43	aδ(b	aδ(b	NOUN
ejpam-2383	18	44	)	)	PUNCT
ejpam-2383	18	45	,	,	PUNCT
ejpam-2383	18	46	for	for	ADP
ejpam-2383	18	47	all	all	DET
ejpam-2383	18	48	a	a	DET
ejpam-2383	18	49	,	,	PUNCT
ejpam-2383	18	50	b	b	PROPN
ejpam-2383	18	51	∈	∈	PROPN
ejpam-2383	18	52	r.	r.	PROPN
ejpam-2383	18	53	example	example	NOUN
ejpam-2383	19	1	1	1	X
ejpam-2383	19	2	.	.	PUNCT
ejpam-2383	20	1	let	let	VERB
ejpam-2383	20	2	r=	r=	PROPN
ejpam-2383	20	3	z	z	NOUN
ejpam-2383	20	4	[	[	X
ejpam-2383	20	5	p	p	NOUN
ejpam-2383	20	6	2	2	NUM
ejpam-2383	20	7	]	]	PUNCT
ejpam-2383	20	8	.	.	PUNCT
ejpam-2383	21	1	then	then	ADV
ejpam-2383	21	2	σ	σ	X
ejpam-2383	21	3	:	:	PUNCT
ejpam-2383	21	4	r→	r→	PROPN
ejpam-2383	21	5	r	r	NOUN
ejpam-2383	21	6	defined	define	VERB
ejpam-2383	21	7	as	as	ADP
ejpam-2383	21	8	σ(a+	σ(a+	PROPN
ejpam-2383	21	9	b	b	PROPN
ejpam-2383	21	10	p	p	NOUN
ejpam-2383	21	11	2	2	NUM
ejpam-2383	21	12	)	)	PUNCT
ejpam-2383	21	13	=	=	SYM
ejpam-2383	22	1	a−	a−	PROPN
ejpam-2383	22	2	b	b	PROPN
ejpam-2383	22	3	p	p	X
ejpam-2383	22	4	2	2	NUM
ejpam-2383	22	5	for	for	ADP
ejpam-2383	22	6	a+	a+	PRON
ejpam-2383	22	7	b	b	PROPN
ejpam-2383	22	8	p	p	X
ejpam-2383	22	9	2	2	NUM
ejpam-2383	22	10	∈	∈	NOUN
ejpam-2383	22	11	r	r	NOUN
ejpam-2383	22	12	∗corresponding	∗corresponde	VERB
ejpam-2383	22	13	author	author	NOUN
ejpam-2383	22	14	.	.	PUNCT
ejpam-2383	23	1	email	email	NOUN
ejpam-2383	23	2	address	address	PROPN
ejpam-2383	23	3	:	:	PUNCT
ejpam-2383	23	4	vijaykumarbhat2000@yahoo.com	vijaykumarbhat2000@yahoo.com	X
ejpam-2383	23	5	(	(	PUNCT
ejpam-2383	23	6	v.	v.	ADP
ejpam-2383	23	7	bhat	bhat	PROPN
ejpam-2383	23	8	)	)	PUNCT
ejpam-2383	23	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2383	24	1	462	462	NUM
ejpam-2383	25	1	c	c	X
ejpam-2383	25	2	©	©	PROPN
ejpam-2383	25	3	2015	2015	NUM
ejpam-2383	25	4	ejpam	ejpam	NOUN
ejpam-2383	25	5	all	all	DET
ejpam-2383	25	6	rights	right	NOUN
ejpam-2383	25	7	reserved	reserve	VERB
ejpam-2383	25	8	.	.	PUNCT
ejpam-2383	26	1	m.	m.	NOUN
ejpam-2383	26	2	abrol	abrol	PROPN
ejpam-2383	26	3	,	,	PUNCT
ejpam-2383	26	4	v.	v.	ADP
ejpam-2383	26	5	bhat	bhat	PROPN
ejpam-2383	26	6	/	/	SYM
ejpam-2383	26	7	eur	eur	PROPN
ejpam-2383	26	8	.	.	PUNCT
ejpam-2383	27	1	j.	j.	PROPN
ejpam-2383	27	2	pure	pure	PROPN
ejpam-2383	27	3	appl	appl	PROPN
ejpam-2383	27	4	.	.	PROPN
ejpam-2383	27	5	math	math	PROPN
ejpam-2383	27	6	,	,	PUNCT
ejpam-2383	27	7	8	8	NUM
ejpam-2383	27	8	(	(	PUNCT
ejpam-2383	27	9	2015	2015	NUM
ejpam-2383	27	10	)	)	PUNCT
ejpam-2383	27	11	,	,	PUNCT
ejpam-2383	27	12	462	462	NUM
ejpam-2383	27	13	-	-	SYM
ejpam-2383	27	14	468	468	NUM
ejpam-2383	27	15	463	463	NUM
ejpam-2383	27	16	is	be	AUX
ejpam-2383	27	17	an	an	DET
ejpam-2383	27	18	endomorphism	endomorphism	NOUN
ejpam-2383	27	19	of	of	ADP
ejpam-2383	27	20	r.	r.	PROPN
ejpam-2383	27	21	for	for	ADP
ejpam-2383	27	22	any	any	DET
ejpam-2383	27	23	s	s	X
ejpam-2383	27	24	∈	∈	PROPN
ejpam-2383	27	25	r	r	NOUN
ejpam-2383	27	26	,	,	PUNCT
ejpam-2383	27	27	define	define	VERB
ejpam-2383	27	28	δs	δs	NOUN
ejpam-2383	27	29	:	:	PUNCT
ejpam-2383	27	30	r→	r→	VERB
ejpam-2383	27	31	r	r	NOUN
ejpam-2383	27	32	by	by	ADP
ejpam-2383	27	33	δs(a+	δs(a+	PROPN
ejpam-2383	28	1	b	b	PROPN
ejpam-2383	28	2	p	p	NOUN
ejpam-2383	28	3	2	2	NUM
ejpam-2383	28	4	)	)	PUNCT
ejpam-2383	28	5	=	=	SYM
ejpam-2383	28	6	(	(	PUNCT
ejpam-2383	28	7	a+	a+	NOUN
ejpam-2383	28	8	b	b	PROPN
ejpam-2383	28	9	p	p	X
ejpam-2383	28	10	2)s−	2)s−	NUM
ejpam-2383	28	11	sσ(a+	sσ(a+	PROPN
ejpam-2383	28	12	b	b	PROPN
ejpam-2383	28	13	p	p	NOUN
ejpam-2383	28	14	2	2	NUM
ejpam-2383	28	15	)	)	PUNCT
ejpam-2383	28	16	for	for	ADP
ejpam-2383	28	17	a+	a+	PRON
ejpam-2383	28	18	b	b	PROPN
ejpam-2383	28	19	p	p	X
ejpam-2383	28	20	2	2	NUM
ejpam-2383	28	21	∈	∈	PROPN
ejpam-2383	28	22	r.	r.	NOUN
ejpam-2383	28	23	then	then	ADV
ejpam-2383	28	24	δs	δs	PROPN
ejpam-2383	28	25	is	be	AUX
ejpam-2383	28	26	a	a	DET
ejpam-2383	28	27	σ	σ	NOUN
ejpam-2383	28	28	-	-	PUNCT
ejpam-2383	28	29	derivation	derivation	NOUN
ejpam-2383	28	30	of	of	ADP
ejpam-2383	28	31	r.	r.	PROPN
ejpam-2383	28	32	recall	recall	PROPN
ejpam-2383	28	33	that	that	SCONJ
ejpam-2383	28	34	r[x;σ	r[x;σ	NOUN
ejpam-2383	28	35	,	,	PUNCT
ejpam-2383	28	36	δ	δ	PROPN
ejpam-2383	28	37	]	]	PUNCT
ejpam-2383	28	38	is	be	AUX
ejpam-2383	28	39	the	the	DET
ejpam-2383	28	40	usual	usual	ADJ
ejpam-2383	28	41	polynomial	polynomial	ADJ
ejpam-2383	28	42	ring	ring	NOUN
ejpam-2383	28	43	with	with	ADP
ejpam-2383	28	44	coefficients	coefficient	NOUN
ejpam-2383	28	45	in	in	ADP
ejpam-2383	28	46	r	r	NOUN
ejpam-2383	28	47	where	where	SCONJ
ejpam-2383	28	48	multiplication	multiplication	NOUN
ejpam-2383	28	49	is	be	AUX
ejpam-2383	28	50	subject	subject	ADJ
ejpam-2383	28	51	to	to	ADP
ejpam-2383	28	52	the	the	DET
ejpam-2383	28	53	relation	relation	NOUN
ejpam-2383	28	54	ax	ax	NOUN
ejpam-2383	28	55	=	=	PUNCT
ejpam-2383	28	56	xσ(a	xσ(a	PUNCT
ejpam-2383	28	57	)	)	PUNCT
ejpam-2383	29	1	+	+	CCONJ
ejpam-2383	29	2	δ(a	δ(a	X
ejpam-2383	29	3	)	)	PUNCT
ejpam-2383	29	4	,	,	PUNCT
ejpam-2383	29	5	for	for	ADP
ejpam-2383	29	6	all	all	DET
ejpam-2383	29	7	a	a	DET
ejpam-2383	29	8	∈	∈	PROPN
ejpam-2383	29	9	r.	r.	NOUN
ejpam-2383	29	10	we	we	PRON
ejpam-2383	29	11	take	take	VERB
ejpam-2383	29	12	any	any	DET
ejpam-2383	29	13	f	f	NOUN
ejpam-2383	29	14	(	(	PUNCT
ejpam-2383	29	15	x	x	X
ejpam-2383	29	16	)	)	PUNCT
ejpam-2383	29	17	∈	∈	PROPN
ejpam-2383	29	18	r[x;σ	r[x;σ	NOUN
ejpam-2383	29	19	,	,	PUNCT
ejpam-2383	29	20	δ	δ	PROPN
ejpam-2383	29	21	]	]	PUNCT
ejpam-2383	29	22	to	to	PART
ejpam-2383	29	23	be	be	AUX
ejpam-2383	29	24	of	of	ADP
ejpam-2383	29	25	the	the	DET
ejpam-2383	29	26	form	form	NOUN
ejpam-2383	29	27	f	f	X
ejpam-2383	29	28	(	(	PUNCT
ejpam-2383	29	29	x	x	X
ejpam-2383	29	30	)	)	PUNCT
ejpam-2383	29	31	=	=	SYM
ejpam-2383	30	1	∑n	∑n	NUM
ejpam-2383	30	2	i=0	i=0	PROPN
ejpam-2383	30	3	x	x	PUNCT
ejpam-2383	30	4	iai	iai	NOUN
ejpam-2383	30	5	.	.	PUNCT
ejpam-2383	31	1	we	we	PRON
ejpam-2383	31	2	denote	denote	VERB
ejpam-2383	31	3	the	the	DET
ejpam-2383	31	4	ore	ore	NOUN
ejpam-2383	31	5	extension	extension	NOUN
ejpam-2383	31	6	r[x;σ	r[x;σ	NOUN
ejpam-2383	31	7	,	,	PUNCT
ejpam-2383	31	8	δ	δ	PROPN
ejpam-2383	31	9	]	]	PUNCT
ejpam-2383	31	10	by	by	ADP
ejpam-2383	31	11	o(r	o(r	NOUN
ejpam-2383	31	12	)	)	PUNCT
ejpam-2383	31	13	.	.	PUNCT
ejpam-2383	32	1	an	an	DET
ejpam-2383	32	2	ideal	ideal	ADJ
ejpam-2383	32	3	i	i	PRON
ejpam-2383	32	4	of	of	ADP
ejpam-2383	32	5	a	a	DET
ejpam-2383	32	6	ring	ring	NOUN
ejpam-2383	32	7	r	r	NOUN
ejpam-2383	32	8	is	be	AUX
ejpam-2383	32	9	called	call	VERB
ejpam-2383	32	10	σ	σ	NOUN
ejpam-2383	32	11	-	-	NOUN
ejpam-2383	32	12	stable	stable	ADJ
ejpam-2383	32	13	if	if	SCONJ
ejpam-2383	32	14	σ(i	σ(i	NOUN
ejpam-2383	32	15	)	)	PUNCT
ejpam-2383	33	1	=	=	SYM
ejpam-2383	34	1	i	i	PRON
ejpam-2383	34	2	and	and	CCONJ
ejpam-2383	34	3	is	be	AUX
ejpam-2383	34	4	called	call	VERB
ejpam-2383	34	5	δ	δ	NOUN
ejpam-2383	34	6	-	-	PUNCT
ejpam-2383	34	7	invariant	invariant	ADJ
ejpam-2383	34	8	if	if	SCONJ
ejpam-2383	34	9	δ(i	δ(i	NOUN
ejpam-2383	34	10	)	)	PUNCT
ejpam-2383	34	11	⊆	⊆	NUM
ejpam-2383	34	12	i	i	PRON
ejpam-2383	34	13	.	.	PUNCT
ejpam-2383	35	1	if	if	SCONJ
ejpam-2383	35	2	an	an	DET
ejpam-2383	35	3	ideal	ideal	NOUN
ejpam-2383	35	4	i	i	PRON
ejpam-2383	35	5	of	of	ADP
ejpam-2383	35	6	r	r	NOUN
ejpam-2383	35	7	is	be	AUX
ejpam-2383	35	8	σ	σ	NOUN
ejpam-2383	35	9	-	-	ADJ
ejpam-2383	35	10	stable	stable	ADJ
ejpam-2383	35	11	and	and	CCONJ
ejpam-2383	35	12	δ	δ	NOUN
ejpam-2383	35	13	-	-	PUNCT
ejpam-2383	35	14	invariant	invariant	ADJ
ejpam-2383	35	15	,	,	PUNCT
ejpam-2383	35	16	then	then	ADV
ejpam-2383	35	17	i[x;σ	i[x;σ	NUM
ejpam-2383	35	18	,	,	PUNCT
ejpam-2383	35	19	δ	δ	PROPN
ejpam-2383	35	20	]	]	X
ejpam-2383	35	21	is	be	AUX
ejpam-2383	35	22	an	an	DET
ejpam-2383	35	23	ideal	ideal	NOUN
ejpam-2383	35	24	of	of	ADP
ejpam-2383	35	25	o(r	o(r	PROPN
ejpam-2383	35	26	)	)	PUNCT
ejpam-2383	35	27	and	and	CCONJ
ejpam-2383	35	28	as	as	ADP
ejpam-2383	35	29	usual	usual	ADJ
ejpam-2383	35	30	we	we	PRON
ejpam-2383	35	31	denote	denote	VERB
ejpam-2383	35	32	it	it	PRON
ejpam-2383	35	33	by	by	ADP
ejpam-2383	35	34	o(i	o(i	PROPN
ejpam-2383	35	35	)	)	PUNCT
ejpam-2383	35	36	.	.	PUNCT
ejpam-2383	36	1	definition	definition	NOUN
ejpam-2383	36	2	2	2	NUM
ejpam-2383	36	3	.	.	PUNCT
ejpam-2383	36	4	a	a	DET
ejpam-2383	36	5	completely	completely	ADV
ejpam-2383	36	6	prime	prime	ADJ
ejpam-2383	36	7	ideal	ideal	NOUN
ejpam-2383	36	8	in	in	ADP
ejpam-2383	36	9	a	a	DET
ejpam-2383	36	10	ring	ring	NOUN
ejpam-2383	36	11	r	r	NOUN
ejpam-2383	36	12	is	be	AUX
ejpam-2383	36	13	any	any	DET
ejpam-2383	36	14	ideal	ideal	NOUN
ejpam-2383	36	15	such	such	ADJ
ejpam-2383	36	16	that	that	PRON
ejpam-2383	36	17	r	r	NOUN
ejpam-2383	36	18	/	/	SYM
ejpam-2383	36	19	p	p	NOUN
ejpam-2383	36	20	is	be	AUX
ejpam-2383	36	21	a	a	DET
ejpam-2383	36	22	domain	domain	NOUN
ejpam-2383	36	23	[	[	X
ejpam-2383	36	24	7	7	NUM
ejpam-2383	36	25	]	]	PUNCT
ejpam-2383	36	26	.	.	PUNCT
ejpam-2383	37	1	also	also	ADV
ejpam-2383	37	2	an	an	DET
ejpam-2383	37	3	ideal	ideal	ADJ
ejpam-2383	37	4	p	p	NOUN
ejpam-2383	37	5	of	of	ADP
ejpam-2383	37	6	a	a	DET
ejpam-2383	37	7	ring	ring	NOUN
ejpam-2383	37	8	r	r	NOUN
ejpam-2383	37	9	is	be	AUX
ejpam-2383	37	10	said	say	VERB
ejpam-2383	37	11	to	to	PART
ejpam-2383	37	12	be	be	AUX
ejpam-2383	37	13	completely	completely	ADV
ejpam-2383	37	14	prime	prime	ADJ
ejpam-2383	37	15	if	if	SCONJ
ejpam-2383	37	16	ab	ab	PROPN
ejpam-2383	37	17	∈	∈	PROPN
ejpam-2383	37	18	p	p	PROPN
ejpam-2383	37	19	implies	imply	VERB
ejpam-2383	37	20	that	that	SCONJ
ejpam-2383	37	21	a	a	DET
ejpam-2383	37	22	∈	∈	PROPN
ejpam-2383	37	23	p	p	NOUN
ejpam-2383	37	24	or	or	CCONJ
ejpam-2383	37	25	b	b	NOUN
ejpam-2383	37	26	∈	∈	PROPN
ejpam-2383	37	27	p	p	NOUN
ejpam-2383	37	28	for	for	ADP
ejpam-2383	37	29	a	a	DET
ejpam-2383	37	30	,	,	PUNCT
ejpam-2383	37	31	b	b	PROPN
ejpam-2383	37	32	∈	∈	PROPN
ejpam-2383	37	33	r.	r.	PROPN
ejpam-2383	37	34	in	in	ADP
ejpam-2383	37	35	commutative	commutative	ADJ
ejpam-2383	37	36	sense	sense	NOUN
ejpam-2383	37	37	completely	completely	ADV
ejpam-2383	37	38	prime	prime	ADJ
ejpam-2383	37	39	and	and	CCONJ
ejpam-2383	37	40	prime	prime	NOUN
ejpam-2383	37	41	have	have	VERB
ejpam-2383	37	42	the	the	DET
ejpam-2383	37	43	same	same	ADJ
ejpam-2383	37	44	meaning	meaning	NOUN
ejpam-2383	37	45	.	.	PUNCT
ejpam-2383	38	1	we	we	PRON
ejpam-2383	38	2	also	also	ADV
ejpam-2383	38	3	note	note	VERB
ejpam-2383	38	4	that	that	SCONJ
ejpam-2383	38	5	a	a	DET
ejpam-2383	38	6	completely	completely	ADV
ejpam-2383	38	7	prime	prime	ADJ
ejpam-2383	38	8	ideal	ideal	NOUN
ejpam-2383	38	9	of	of	ADP
ejpam-2383	38	10	a	a	DET
ejpam-2383	38	11	ring	ring	NOUN
ejpam-2383	38	12	r	r	NOUN
ejpam-2383	38	13	is	be	AUX
ejpam-2383	38	14	a	a	DET
ejpam-2383	38	15	prime	prime	ADJ
ejpam-2383	38	16	ideal	ideal	NOUN
ejpam-2383	38	17	,	,	PUNCT
ejpam-2383	38	18	but	but	CCONJ
ejpam-2383	38	19	the	the	DET
ejpam-2383	38	20	converse	converse	NOUN
ejpam-2383	38	21	need	need	AUX
ejpam-2383	38	22	not	not	PART
ejpam-2383	38	23	be	be	AUX
ejpam-2383	38	24	true	true	ADJ
ejpam-2383	38	25	.	.	PUNCT
ejpam-2383	39	1	the	the	DET
ejpam-2383	39	2	following	follow	VERB
ejpam-2383	39	3	example	example	NOUN
ejpam-2383	39	4	shows	show	VERB
ejpam-2383	39	5	that	that	SCONJ
ejpam-2383	39	6	a	a	DET
ejpam-2383	39	7	prime	prime	ADJ
ejpam-2383	39	8	ideal	ideal	NOUN
ejpam-2383	39	9	need	need	AUX
ejpam-2383	39	10	not	not	PART
ejpam-2383	39	11	be	be	AUX
ejpam-2383	39	12	a	a	DET
ejpam-2383	39	13	completely	completely	ADV
ejpam-2383	39	14	prime	prime	ADJ
ejpam-2383	39	15	ideal	ideal	NOUN
ejpam-2383	39	16	.	.	PUNCT
ejpam-2383	40	1	example	example	NOUN
ejpam-2383	40	2	2	2	NUM
ejpam-2383	40	3	(	(	PUNCT
ejpam-2383	40	4	example	example	NOUN
ejpam-2383	40	5	1.1	1.1	NUM
ejpam-2383	40	6	of	of	ADP
ejpam-2383	40	7	[	[	X
ejpam-2383	40	8	2	2	NUM
ejpam-2383	40	9	]	]	PUNCT
ejpam-2383	40	10	)	)	PUNCT
ejpam-2383	40	11	.	.	PUNCT
ejpam-2383	41	1	let	let	VERB
ejpam-2383	41	2	r=	r=	PROPN
ejpam-2383	41	3	�	�	PROPN
ejpam-2383	41	4	z	z	NOUN
ejpam-2383	41	5	z	z	PROPN
ejpam-2383	41	6	z	z	NOUN
ejpam-2383	41	7	z	z	NOUN
ejpam-2383	41	8	�	�	PROPN
ejpam-2383	41	9	=	=	SYM
ejpam-2383	41	10	m2(z	m2(z	PROPN
ejpam-2383	41	11	)	)	PUNCT
ejpam-2383	41	12	.	.	PUNCT
ejpam-2383	42	1	if	if	SCONJ
ejpam-2383	42	2	p	p	NOUN
ejpam-2383	42	3	is	be	AUX
ejpam-2383	42	4	a	a	DET
ejpam-2383	42	5	prime	prime	ADJ
ejpam-2383	42	6	number	number	NOUN
ejpam-2383	42	7	,	,	PUNCT
ejpam-2383	42	8	then	then	ADV
ejpam-2383	42	9	the	the	DET
ejpam-2383	42	10	ideal	ideal	NOUN
ejpam-2383	42	11	p	p	X
ejpam-2383	42	12	=	=	SYM
ejpam-2383	42	13	m2(pz	m2(pz	PROPN
ejpam-2383	42	14	)	)	PUNCT
ejpam-2383	42	15	is	be	AUX
ejpam-2383	42	16	a	a	DET
ejpam-2383	42	17	prime	prime	ADJ
ejpam-2383	42	18	ideal	ideal	NOUN
ejpam-2383	42	19	of	of	ADP
ejpam-2383	42	20	r.	r.	PROPN
ejpam-2383	42	21	but	but	CCONJ
ejpam-2383	42	22	is	be	AUX
ejpam-2383	42	23	not	not	PART
ejpam-2383	42	24	completely	completely	ADV
ejpam-2383	42	25	prime	prime	ADJ
ejpam-2383	42	26	,	,	PUNCT
ejpam-2383	42	27	since	since	SCONJ
ejpam-2383	42	28	for	for	ADP
ejpam-2383	42	29	a	a	DET
ejpam-2383	42	30	=	=	SYM
ejpam-2383	42	31	�	�	PROPN
ejpam-2383	42	32	1	1	NUM
ejpam-2383	42	33	0	0	NUM
ejpam-2383	42	34	0	0	NUM
ejpam-2383	42	35	0	0	NUM
ejpam-2383	42	36	�	�	PROPN
ejpam-2383	42	37	and	and	CCONJ
ejpam-2383	42	38	b	b	NOUN
ejpam-2383	42	39	=	=	SYM
ejpam-2383	42	40	�	�	PROPN
ejpam-2383	42	41	0	0	NUM
ejpam-2383	42	42	0	0	NUM
ejpam-2383	42	43	0	0	NUM
ejpam-2383	42	44	1	1	NUM
ejpam-2383	42	45	�	�	NOUN
ejpam-2383	42	46	we	we	PRON
ejpam-2383	42	47	have	have	VERB
ejpam-2383	42	48	ab	ab	PROPN
ejpam-2383	42	49	∈	∈	PROPN
ejpam-2383	42	50	p	p	NOUN
ejpam-2383	42	51	,	,	PUNCT
ejpam-2383	42	52	even	even	ADV
ejpam-2383	42	53	though	though	SCONJ
ejpam-2383	42	54	a	a	DET
ejpam-2383	42	55	/∈	/∈	SYM
ejpam-2383	42	56	p	p	NOUN
ejpam-2383	42	57	and	and	CCONJ
ejpam-2383	42	58	b	b	PROPN
ejpam-2383	42	59	/∈	/∈	PUNCT
ejpam-2383	43	1	p.	p.	NOUN
ejpam-2383	43	2	there	there	PRON
ejpam-2383	43	3	are	be	VERB
ejpam-2383	43	4	examples	example	NOUN
ejpam-2383	43	5	of	of	ADP
ejpam-2383	43	6	rings	ring	NOUN
ejpam-2383	43	7	(	(	PUNCT
ejpam-2383	43	8	non	non	ADJ
ejpam-2383	43	9	-	-	ADJ
ejpam-2383	43	10	commutative	commutative	ADJ
ejpam-2383	43	11	)	)	PUNCT
ejpam-2383	43	12	in	in	ADP
ejpam-2383	43	13	which	which	PRON
ejpam-2383	43	14	prime	prime	ADJ
ejpam-2383	43	15	ideals	ideal	NOUN
ejpam-2383	43	16	are	be	AUX
ejpam-2383	43	17	completely	completely	ADV
ejpam-2383	43	18	prime	prime	ADJ
ejpam-2383	43	19	.	.	PUNCT
ejpam-2383	44	1	example	example	NOUN
ejpam-2383	44	2	3	3	NUM
ejpam-2383	44	3	(	(	PUNCT
ejpam-2383	44	4	example	example	NOUN
ejpam-2383	44	5	1.2	1.2	NUM
ejpam-2383	44	6	of	of	ADP
ejpam-2383	44	7	[	[	X
ejpam-2383	44	8	2	2	NUM
ejpam-2383	44	9	]	]	PUNCT
ejpam-2383	44	10	)	)	PUNCT
ejpam-2383	44	11	.	.	PUNCT
ejpam-2383	45	1	let	let	VERB
ejpam-2383	45	2	r	r	NOUN
ejpam-2383	45	3	=	=	SYM
ejpam-2383	45	4	�	�	PROPN
ejpam-2383	46	1	z	z	PROPN
ejpam-2383	46	2	z	z	NOUN
ejpam-2383	46	3	0	0	NUM
ejpam-2383	46	4	z	z	PROPN
ejpam-2383	46	5	�	�	PROPN
ejpam-2383	46	6	.	.	PUNCT
ejpam-2383	47	1	then	then	ADV
ejpam-2383	47	2	p1	p1	PROPN
ejpam-2383	47	3	=	=	SYM
ejpam-2383	47	4	�	�	PROPN
ejpam-2383	47	5	z	z	PROPN
ejpam-2383	47	6	z	z	NOUN
ejpam-2383	47	7	0	0	NUM
ejpam-2383	47	8	0	0	NUM
ejpam-2383	47	9	�	�	PROPN
ejpam-2383	47	10	,	,	PUNCT
ejpam-2383	47	11	p2	p2	PROPN
ejpam-2383	47	12	=	=	SYM
ejpam-2383	47	13	�	�	PROPN
ejpam-2383	47	14	0	0	NUM
ejpam-2383	47	15	z	z	NOUN
ejpam-2383	47	16	0	0	PUNCT
ejpam-2383	47	17	z	z	PROPN
ejpam-2383	47	18	�	�	PROPN
ejpam-2383	47	19	and	and	CCONJ
ejpam-2383	47	20	p3	p3	PROPN
ejpam-2383	47	21	=	=	SYM
ejpam-2383	47	22	�	�	PROPN
ejpam-2383	47	23	0	0	PUNCT
ejpam-2383	47	24	z	z	NOUN
ejpam-2383	47	25	0	0	NUM
ejpam-2383	47	26	0	0	NUM
ejpam-2383	47	27	�	�	PROPN
ejpam-2383	47	28	are	be	AUX
ejpam-2383	47	29	prime	prime	ADJ
ejpam-2383	47	30	ideals	ideal	NOUN
ejpam-2383	47	31	of	of	ADP
ejpam-2383	47	32	r.	r.	PROPN
ejpam-2383	47	33	now	now	ADV
ejpam-2383	47	34	all	all	DET
ejpam-2383	47	35	these	these	PRON
ejpam-2383	47	36	are	be	AUX
ejpam-2383	47	37	completely	completely	ADV
ejpam-2383	47	38	prime	prime	ADJ
ejpam-2383	47	39	also	also	ADV
ejpam-2383	47	40	.	.	PUNCT
ejpam-2383	48	1	definition	definition	NOUN
ejpam-2383	48	2	3	3	NUM
ejpam-2383	48	3	.	.	PUNCT
ejpam-2383	49	1	a	a	DET
ejpam-2383	49	2	minimal	minimal	ADJ
ejpam-2383	49	3	prime	prime	ADJ
ejpam-2383	49	4	ideal	ideal	NOUN
ejpam-2383	49	5	in	in	ADP
ejpam-2383	49	6	a	a	DET
ejpam-2383	49	7	ring	ring	NOUN
ejpam-2383	49	8	r	r	NOUN
ejpam-2383	49	9	is	be	AUX
ejpam-2383	49	10	any	any	DET
ejpam-2383	49	11	prime	prime	ADJ
ejpam-2383	49	12	ideal	ideal	NOUN
ejpam-2383	49	13	of	of	ADP
ejpam-2383	49	14	r	r	NOUN
ejpam-2383	49	15	that	that	PRON
ejpam-2383	49	16	does	do	AUX
ejpam-2383	49	17	not	not	PART
ejpam-2383	49	18	properly	properly	ADV
ejpam-2383	49	19	contain	contain	VERB
ejpam-2383	49	20	any	any	DET
ejpam-2383	49	21	other	other	ADJ
ejpam-2383	49	22	prime	prime	ADJ
ejpam-2383	49	23	ideal	ideal	NOUN
ejpam-2383	49	24	[	[	X
ejpam-2383	49	25	3	3	NUM
ejpam-2383	49	26	]	]	PUNCT
ejpam-2383	49	27	.	.	PUNCT
ejpam-2383	50	1	example	example	NOUN
ejpam-2383	51	1	4	4	NUM
ejpam-2383	51	2	.	.	X
ejpam-2383	52	1	in	in	ADP
ejpam-2383	52	2	example	example	NOUN
ejpam-2383	52	3	1.2	1.2	NUM
ejpam-2383	52	4	of	of	ADP
ejpam-2383	52	5	[	[	X
ejpam-2383	52	6	2	2	NUM
ejpam-2383	52	7	]	]	PUNCT
ejpam-2383	52	8	(	(	PUNCT
ejpam-2383	52	9	discussed	discuss	VERB
ejpam-2383	52	10	above	above	ADV
ejpam-2383	52	11	)	)	PUNCT
ejpam-2383	52	12	,	,	PUNCT
ejpam-2383	52	13	p3	p3	PROPN
ejpam-2383	52	14	=	=	SYM
ejpam-2383	52	15	�	�	PROPN
ejpam-2383	52	16	0	0	PUNCT
ejpam-2383	52	17	z	z	NOUN
ejpam-2383	52	18	0	0	NUM
ejpam-2383	52	19	0	0	NUM
ejpam-2383	52	20	�	�	PROPN
ejpam-2383	52	21	is	be	AUX
ejpam-2383	52	22	minimal	minimal	ADJ
ejpam-2383	52	23	prime	prime	ADJ
ejpam-2383	52	24	ideal	ideal	NOUN
ejpam-2383	52	25	.	.	PUNCT
ejpam-2383	53	1	further	far	ADV
ejpam-2383	53	2	more	more	ADV
ejpam-2383	53	3	there	there	PRON
ejpam-2383	53	4	are	be	VERB
ejpam-2383	53	5	examples	example	NOUN
ejpam-2383	53	6	of	of	ADP
ejpam-2383	53	7	rings	ring	NOUN
ejpam-2383	53	8	in	in	ADP
ejpam-2383	53	9	which	which	PRON
ejpam-2383	53	10	minimal	minimal	ADJ
ejpam-2383	53	11	prime	prime	ADJ
ejpam-2383	53	12	ideals	ideal	NOUN
ejpam-2383	53	13	are	be	AUX
ejpam-2383	53	14	completely	completely	ADV
ejpam-2383	53	15	prime	prime	ADJ
ejpam-2383	53	16	.	.	PUNCT
ejpam-2383	54	1	for	for	ADP
ejpam-2383	54	2	example	example	NOUN
ejpam-2383	54	3	a	a	DET
ejpam-2383	54	4	reduced	reduced	ADJ
ejpam-2383	54	5	ring	ring	NOUN
ejpam-2383	54	6	.	.	PUNCT
ejpam-2383	55	1	if	if	SCONJ
ejpam-2383	55	2	r	r	NOUN
ejpam-2383	55	3	is	be	AUX
ejpam-2383	55	4	a	a	DET
ejpam-2383	55	5	prime	prime	ADJ
ejpam-2383	55	6	ring	ring	NOUN
ejpam-2383	55	7	,	,	PUNCT
ejpam-2383	55	8	then	then	ADV
ejpam-2383	55	9	0	0	NUM
ejpam-2383	55	10	is	be	AUX
ejpam-2383	55	11	a	a	DET
ejpam-2383	55	12	minimal	minimal	ADJ
ejpam-2383	55	13	prime	prime	ADJ
ejpam-2383	55	14	ideal	ideal	NOUN
ejpam-2383	55	15	of	of	ADP
ejpam-2383	55	16	r	r	NOUN
ejpam-2383	55	17	and	and	CCONJ
ejpam-2383	55	18	it	it	PRON
ejpam-2383	55	19	is	be	AUX
ejpam-2383	55	20	the	the	DET
ejpam-2383	55	21	only	only	ADJ
ejpam-2383	55	22	one	one	NUM
ejpam-2383	55	23	.	.	PUNCT
ejpam-2383	56	1	in	in	ADP
ejpam-2383	56	2	proposition	proposition	NOUN
ejpam-2383	56	3	(	(	PUNCT
ejpam-2383	56	4	3.3	3.3	NUM
ejpam-2383	56	5	)	)	PUNCT
ejpam-2383	56	6	of	of	ADP
ejpam-2383	56	7	[	[	X
ejpam-2383	56	8	6	6	NUM
ejpam-2383	56	9	]	]	PUNCT
ejpam-2383	56	10	,	,	PUNCT
ejpam-2383	56	11	it	it	PRON
ejpam-2383	56	12	has	have	AUX
ejpam-2383	56	13	been	be	AUX
ejpam-2383	56	14	shown	show	VERB
ejpam-2383	56	15	that	that	SCONJ
ejpam-2383	56	16	any	any	DET
ejpam-2383	56	17	prime	prime	ADJ
ejpam-2383	56	18	ideal	ideal	NOUN
ejpam-2383	56	19	u	u	NOUN
ejpam-2383	56	20	in	in	ADP
ejpam-2383	56	21	a	a	DET
ejpam-2383	56	22	ring	ring	NOUN
ejpam-2383	56	23	r	r	NOUN
ejpam-2383	56	24	contains	contain	VERB
ejpam-2383	56	25	a	a	DET
ejpam-2383	56	26	minimal	minimal	ADJ
ejpam-2383	56	27	prime	prime	ADJ
ejpam-2383	56	28	ideal	ideal	NOUN
ejpam-2383	56	29	.	.	PUNCT
ejpam-2383	57	1	further	far	ADV
ejpam-2383	57	2	it	it	PRON
ejpam-2383	57	3	has	have	AUX
ejpam-2383	57	4	been	be	AUX
ejpam-2383	57	5	proved	prove	VERB
ejpam-2383	57	6	that	that	SCONJ
ejpam-2383	57	7	there	there	PRON
ejpam-2383	57	8	exists	exist	VERB
ejpam-2383	57	9	m.	m.	NOUN
ejpam-2383	57	10	abrol	abrol	NOUN
ejpam-2383	57	11	,	,	PUNCT
ejpam-2383	57	12	v.	v.	ADP
ejpam-2383	57	13	bhat	bhat	PROPN
ejpam-2383	57	14	/	/	SYM
ejpam-2383	57	15	eur	eur	PROPN
ejpam-2383	57	16	.	.	PUNCT
ejpam-2383	58	1	j.	j.	PROPN
ejpam-2383	58	2	pure	pure	PROPN
ejpam-2383	58	3	appl	appl	PROPN
ejpam-2383	58	4	.	.	PROPN
ejpam-2383	58	5	math	math	PROPN
ejpam-2383	58	6	,	,	PUNCT
ejpam-2383	58	7	8	8	NUM
ejpam-2383	58	8	(	(	PUNCT
ejpam-2383	58	9	2015	2015	NUM
ejpam-2383	58	10	)	)	PUNCT
ejpam-2383	58	11	,	,	PUNCT
ejpam-2383	58	12	462	462	NUM
ejpam-2383	58	13	-	-	SYM
ejpam-2383	58	14	468	468	NUM
ejpam-2383	58	15	464	464	NUM
ejpam-2383	58	16	only	only	ADV
ejpam-2383	58	17	finitely	finitely	ADV
ejpam-2383	58	18	many	many	ADJ
ejpam-2383	58	19	minimal	minimal	ADJ
ejpam-2383	58	20	prime	prime	ADJ
ejpam-2383	58	21	ideals	ideal	NOUN
ejpam-2383	58	22	in	in	ADP
ejpam-2383	58	23	a	a	DET
ejpam-2383	58	24	noetherian	noetherian	ADJ
ejpam-2383	58	25	ring	ring	NOUN
ejpam-2383	58	26	r	r	NOUN
ejpam-2383	58	27	and	and	CCONJ
ejpam-2383	58	28	there	there	PRON
ejpam-2383	58	29	is	be	VERB
ejpam-2383	58	30	a	a	DET
ejpam-2383	58	31	finite	finite	ADJ
ejpam-2383	58	32	product	product	NOUN
ejpam-2383	58	33	of	of	ADP
ejpam-2383	58	34	minimal	minimal	ADJ
ejpam-2383	58	35	prime	prime	ADJ
ejpam-2383	58	36	ideals	ideal	NOUN
ejpam-2383	58	37	(	(	PUNCT
ejpam-2383	58	38	repetition	repetition	NOUN
ejpam-2383	58	39	allowed	allow	VERB
ejpam-2383	58	40	)	)	PUNCT
ejpam-2383	58	41	that	that	PRON
ejpam-2383	58	42	equals	equal	VERB
ejpam-2383	58	43	zero	zero	NUM
ejpam-2383	58	44	.	.	PUNCT
ejpam-2383	59	1	an	an	DET
ejpam-2383	59	2	example	example	NOUN
ejpam-2383	59	3	of	of	ADP
ejpam-2383	59	4	a	a	DET
ejpam-2383	59	5	ring	ring	NOUN
ejpam-2383	59	6	which	which	PRON
ejpam-2383	59	7	has	have	VERB
ejpam-2383	59	8	infinitely	infinitely	ADV
ejpam-2383	59	9	many	many	ADJ
ejpam-2383	59	10	minimal	minimal	ADJ
ejpam-2383	59	11	prime	prime	ADJ
ejpam-2383	59	12	ideals	ideal	NOUN
ejpam-2383	59	13	is	be	AUX
ejpam-2383	59	14	:	:	PUNCT
ejpam-2383	59	15	example	example	NOUN
ejpam-2383	59	16	5	5	NUM
ejpam-2383	59	17	(	(	PUNCT
ejpam-2383	59	18	exercise	exercise	VERB
ejpam-2383	59	19	3c	3c	NUM
ejpam-2383	59	20	of	of	ADP
ejpam-2383	59	21	[	[	X
ejpam-2383	59	22	7	7	NUM
ejpam-2383	59	23	]	]	NUM
ejpam-2383	59	24	)	)	PUNCT
ejpam-2383	59	25	.	.	PUNCT
ejpam-2383	60	1	let	let	VERB
ejpam-2383	60	2	x	x	PRON
ejpam-2383	60	3	be	be	AUX
ejpam-2383	60	4	an	an	DET
ejpam-2383	60	5	infinite	infinite	ADJ
ejpam-2383	60	6	set	set	NOUN
ejpam-2383	60	7	,	,	PUNCT
ejpam-2383	60	8	k	k	PROPN
ejpam-2383	60	9	a	a	DET
ejpam-2383	60	10	field	field	NOUN
ejpam-2383	60	11	,	,	PUNCT
ejpam-2383	60	12	and	and	CCONJ
ejpam-2383	60	13	r	r	X
ejpam-2383	60	14	the	the	DET
ejpam-2383	60	15	ring	ring	NOUN
ejpam-2383	60	16	of	of	ADP
ejpam-2383	60	17	all	all	DET
ejpam-2383	60	18	functions	function	NOUN
ejpam-2383	60	19	from	from	ADP
ejpam-2383	60	20	x	x	PUNCT
ejpam-2383	60	21	to	to	ADP
ejpam-2383	60	22	k.	k.	NOUN
ejpam-2383	60	23	for	for	SCONJ
ejpam-2383	60	24	x	x	PROPN
ejpam-2383	60	25	∈	∈	PROPN
ejpam-2383	60	26	x	x	PUNCT
ejpam-2383	60	27	,	,	PUNCT
ejpam-2383	60	28	let	let	VERB
ejpam-2383	60	29	px	px	PART
ejpam-2383	60	30	be	be	AUX
ejpam-2383	60	31	the	the	DET
ejpam-2383	60	32	set	set	NOUN
ejpam-2383	60	33	of	of	ADP
ejpam-2383	60	34	those	those	DET
ejpam-2383	60	35	functions	function	NOUN
ejpam-2383	60	36	in	in	ADP
ejpam-2383	60	37	r	r	NOUN
ejpam-2383	60	38	which	which	PRON
ejpam-2383	60	39	vanish	vanish	VERB
ejpam-2383	60	40	at	at	ADP
ejpam-2383	60	41	x.	x.	NOUN
ejpam-2383	60	42	then	then	ADV
ejpam-2383	60	43	each	each	DET
ejpam-2383	60	44	px	px	PROPN
ejpam-2383	60	45	is	be	AUX
ejpam-2383	60	46	a	a	DET
ejpam-2383	60	47	minimal	minimal	ADJ
ejpam-2383	60	48	prime	prime	ADJ
ejpam-2383	60	49	ideal	ideal	NOUN
ejpam-2383	60	50	of	of	ADP
ejpam-2383	60	51	r.	r.	PROPN
ejpam-2383	60	52	it	it	PRON
ejpam-2383	60	53	is	be	AUX
ejpam-2383	60	54	also	also	ADV
ejpam-2383	60	55	known	know	VERB
ejpam-2383	60	56	that	that	SCONJ
ejpam-2383	60	57	[	[	X
ejpam-2383	60	58	6	6	NUM
ejpam-2383	60	59	]	]	PUNCT
ejpam-2383	60	60	in	in	ADP
ejpam-2383	60	61	a	a	DET
ejpam-2383	60	62	right	right	ADJ
ejpam-2383	60	63	noetherian	noetherian	ADJ
ejpam-2383	60	64	ring	ring	NOUN
ejpam-2383	60	65	which	which	PRON
ejpam-2383	60	66	is	be	AUX
ejpam-2383	60	67	also	also	ADV
ejpam-2383	60	68	an	an	DET
ejpam-2383	60	69	algebra	algebra	NOUN
ejpam-2383	60	70	over	over	ADP
ejpam-2383	60	71	q	q	PROPN
ejpam-2383	60	72	,	,	PUNCT
ejpam-2383	60	73	δ	δ	PROPN
ejpam-2383	60	74	a	a	DET
ejpam-2383	60	75	σ	σ	NOUN
ejpam-2383	60	76	-	-	PUNCT
ejpam-2383	60	77	derivation	derivation	NOUN
ejpam-2383	60	78	of	of	ADP
ejpam-2383	60	79	r	r	NOUN
ejpam-2383	60	80	and	and	CCONJ
ejpam-2383	60	81	u	u	PRON
ejpam-2383	60	82	a	a	DET
ejpam-2383	60	83	minimal	minimal	ADJ
ejpam-2383	60	84	prime	prime	ADJ
ejpam-2383	60	85	ideal	ideal	NOUN
ejpam-2383	60	86	of	of	ADP
ejpam-2383	60	87	r	r	NOUN
ejpam-2383	60	88	,	,	PUNCT
ejpam-2383	60	89	δ(u	δ(u	PROPN
ejpam-2383	60	90	)	)	PUNCT
ejpam-2383	60	91	⊆	⊆	NUM
ejpam-2383	60	92	u	u	NOUN
ejpam-2383	60	93	.	.	PUNCT
ejpam-2383	61	1	definition	definition	NOUN
ejpam-2383	61	2	4	4	NUM
ejpam-2383	61	3	.	.	PUNCT
ejpam-2383	62	1	a	a	DET
ejpam-2383	62	2	ring	ring	NOUN
ejpam-2383	62	3	r	r	NOUN
ejpam-2383	62	4	is	be	AUX
ejpam-2383	62	5	said	say	VERB
ejpam-2383	62	6	to	to	PART
ejpam-2383	62	7	be	be	AUX
ejpam-2383	62	8	2	2	NUM
ejpam-2383	62	9	-	-	PUNCT
ejpam-2383	62	10	primal	primal	ADJ
ejpam-2383	62	11	if	if	SCONJ
ejpam-2383	62	12	and	and	CCONJ
ejpam-2383	62	13	only	only	ADV
ejpam-2383	62	14	if	if	SCONJ
ejpam-2383	62	15	p(r	p(r	PROPN
ejpam-2383	62	16	)	)	PUNCT
ejpam-2383	62	17	=	=	SYM
ejpam-2383	62	18	n(r	n(r	NOUN
ejpam-2383	62	19	)	)	PUNCT
ejpam-2383	63	1	[	[	X
ejpam-2383	63	2	4	4	NUM
ejpam-2383	63	3	]	]	PUNCT
ejpam-2383	63	4	.	.	PUNCT
ejpam-2383	63	5	example	example	NOUN
ejpam-2383	64	1	6	6	NUM
ejpam-2383	64	2	.	.	PUNCT
ejpam-2383	65	1	let	let	VERB
ejpam-2383	65	2	r=	r=	ADJ
ejpam-2383	65	3	(	(	PUNCT
ejpam-2383	65	4	z/8z⊕z/8z	z/8z⊕z/8z	NOUN
ejpam-2383	65	5	)	)	PUNCT
ejpam-2383	65	6	.	.	PUNCT
ejpam-2383	66	1	then	then	ADV
ejpam-2383	66	2	r	r	NOUN
ejpam-2383	66	3	is	be	AUX
ejpam-2383	66	4	a	a	DET
ejpam-2383	66	5	commutative	commutative	ADJ
ejpam-2383	66	6	ring	ring	NOUN
ejpam-2383	66	7	and	and	CCONJ
ejpam-2383	66	8	hence	hence	ADV
ejpam-2383	66	9	2	2	NUM
ejpam-2383	66	10	-	-	PUNCT
ejpam-2383	66	11	primal	primal	ADJ
ejpam-2383	66	12	.	.	PUNCT
ejpam-2383	67	1	also	also	ADV
ejpam-2383	67	2	a	a	DET
ejpam-2383	67	3	reduced	reduce	VERB
ejpam-2383	67	4	ring	ring	NOUN
ejpam-2383	67	5	is	be	AUX
ejpam-2383	67	6	2	2	NUM
ejpam-2383	67	7	-	-	PUNCT
ejpam-2383	67	8	primal	primal	ADJ
ejpam-2383	67	9	and	and	CCONJ
ejpam-2383	67	10	so	so	ADV
ejpam-2383	67	11	is	be	AUX
ejpam-2383	67	12	a	a	DET
ejpam-2383	67	13	commutative	commutative	ADJ
ejpam-2383	67	14	noetherian	noetherian	ADJ
ejpam-2383	67	15	ring	ring	NOUN
ejpam-2383	67	16	.	.	PUNCT
ejpam-2383	68	1	part	part	NOUN
ejpam-2383	68	2	of	of	ADP
ejpam-2383	68	3	the	the	DET
ejpam-2383	68	4	attraction	attraction	NOUN
ejpam-2383	68	5	of	of	ADP
ejpam-2383	68	6	2	2	NUM
ejpam-2383	68	7	-	-	PUNCT
ejpam-2383	68	8	primal	primal	ADJ
ejpam-2383	68	9	rings	ring	NOUN
ejpam-2383	68	10	in	in	ADP
ejpam-2383	68	11	addition	addition	NOUN
ejpam-2383	68	12	to	to	ADP
ejpam-2383	68	13	their	their	PRON
ejpam-2383	68	14	being	be	AUX
ejpam-2383	68	15	a	a	DET
ejpam-2383	68	16	common	common	ADJ
ejpam-2383	68	17	generalization	generalization	NOUN
ejpam-2383	68	18	of	of	ADP
ejpam-2383	68	19	commutative	commutative	ADJ
ejpam-2383	68	20	rings	ring	NOUN
ejpam-2383	68	21	and	and	CCONJ
ejpam-2383	68	22	rings	ring	NOUN
ejpam-2383	68	23	without	without	ADP
ejpam-2383	68	24	nilpotent	nilpotent	ADJ
ejpam-2383	68	25	elements	element	NOUN
ejpam-2383	68	26	lies	lie	VERB
ejpam-2383	68	27	in	in	ADP
ejpam-2383	68	28	the	the	DET
ejpam-2383	68	29	structure	structure	NOUN
ejpam-2383	68	30	of	of	ADP
ejpam-2383	68	31	their	their	PRON
ejpam-2383	68	32	prime	prime	ADJ
ejpam-2383	68	33	ideals	ideal	NOUN
ejpam-2383	68	34	.	.	PUNCT
ejpam-2383	69	1	we	we	PRON
ejpam-2383	69	2	refer	refer	VERB
ejpam-2383	69	3	to	to	ADP
ejpam-2383	69	4	[	[	X
ejpam-2383	69	5	4	4	NUM
ejpam-2383	69	6	,	,	PUNCT
ejpam-2383	69	7	5	5	NUM
ejpam-2383	69	8	,	,	PUNCT
ejpam-2383	69	9	8	8	NUM
ejpam-2383	69	10	,	,	PUNCT
ejpam-2383	69	11	9	9	NUM
ejpam-2383	69	12	,	,	PUNCT
ejpam-2383	69	13	11	11	NUM
ejpam-2383	69	14	,	,	PUNCT
ejpam-2383	69	15	13	13	NUM
ejpam-2383	69	16	,	,	PUNCT
ejpam-2383	69	17	14	14	NUM
ejpam-2383	69	18	]	]	PUNCT
ejpam-2383	69	19	for	for	ADP
ejpam-2383	69	20	more	more	ADJ
ejpam-2383	69	21	details	detail	NOUN
ejpam-2383	69	22	on	on	ADP
ejpam-2383	69	23	2	2	NUM
ejpam-2383	69	24	-	-	PUNCT
ejpam-2383	69	25	primal	primal	ADJ
ejpam-2383	69	26	rings	ring	NOUN
ejpam-2383	69	27	.	.	PUNCT
ejpam-2383	70	1	definition	definition	NOUN
ejpam-2383	70	2	5	5	NUM
ejpam-2383	70	3	.	.	PUNCT
ejpam-2383	71	1	let	let	VERB
ejpam-2383	71	2	r	r	PRON
ejpam-2383	71	3	be	be	AUX
ejpam-2383	71	4	a	a	DET
ejpam-2383	71	5	ring	ring	NOUN
ejpam-2383	71	6	and	and	CCONJ
ejpam-2383	71	7	σ	σ	NOUN
ejpam-2383	71	8	an	an	DET
ejpam-2383	71	9	endomorphism	endomorphism	NOUN
ejpam-2383	71	10	of	of	ADP
ejpam-2383	71	11	r.	r.	PROPN
ejpam-2383	71	12	then	then	ADV
ejpam-2383	71	13	r	r	NOUN
ejpam-2383	71	14	is	be	AUX
ejpam-2383	71	15	said	say	VERB
ejpam-2383	71	16	to	to	PART
ejpam-2383	71	17	be	be	AUX
ejpam-2383	71	18	σ(∗)-ring	σ(∗)-re	VERB
ejpam-2383	71	19	if	if	SCONJ
ejpam-2383	71	20	aσ(a	aσ(a	NOUN
ejpam-2383	71	21	)	)	PUNCT
ejpam-2383	71	22	∈	∈	PROPN
ejpam-2383	71	23	p(r	p(r	PROPN
ejpam-2383	71	24	)	)	PUNCT
ejpam-2383	71	25	implies	imply	VERB
ejpam-2383	71	26	that	that	SCONJ
ejpam-2383	71	27	a	a	DET
ejpam-2383	71	28	∈	∈	PROPN
ejpam-2383	71	29	p(r	p(r	PROPN
ejpam-2383	71	30	)	)	PUNCT
ejpam-2383	71	31	for	for	ADP
ejpam-2383	71	32	a	a	DET
ejpam-2383	71	33	∈	∈	PROPN
ejpam-2383	71	34	r	r	NOUN
ejpam-2383	72	1	[	[	X
ejpam-2383	72	2	3	3	NUM
ejpam-2383	72	3	]	]	PUNCT
ejpam-2383	72	4	.	.	PUNCT
ejpam-2383	73	1	we	we	PRON
ejpam-2383	73	2	note	note	VERB
ejpam-2383	73	3	that	that	SCONJ
ejpam-2383	73	4	if	if	SCONJ
ejpam-2383	73	5	r	r	NOUN
ejpam-2383	73	6	is	be	AUX
ejpam-2383	73	7	a	a	DET
ejpam-2383	73	8	noetherian	noetherian	ADJ
ejpam-2383	73	9	ring	ring	NOUN
ejpam-2383	73	10	and	and	CCONJ
ejpam-2383	73	11	σ	σ	NOUN
ejpam-2383	73	12	an	an	DET
ejpam-2383	73	13	automorphism	automorphism	NOUN
ejpam-2383	73	14	of	of	ADP
ejpam-2383	73	15	r	r	NOUN
ejpam-2383	73	16	,	,	PUNCT
ejpam-2383	73	17	then	then	ADV
ejpam-2383	73	18	r	r	NOUN
ejpam-2383	73	19	is	be	AUX
ejpam-2383	73	20	a	a	DET
ejpam-2383	73	21	σ(∗)-ring	σ(∗)-re	VERB
ejpam-2383	73	22	if	if	SCONJ
ejpam-2383	73	23	and	and	CCONJ
ejpam-2383	73	24	only	only	ADV
ejpam-2383	73	25	if	if	SCONJ
ejpam-2383	73	26	for	for	ADP
ejpam-2383	73	27	each	each	DET
ejpam-2383	73	28	minimal	minimal	ADJ
ejpam-2383	73	29	prime	prime	ADJ
ejpam-2383	73	30	u	u	NOUN
ejpam-2383	73	31	of	of	ADP
ejpam-2383	73	32	r	r	NOUN
ejpam-2383	73	33	,	,	PUNCT
ejpam-2383	73	34	σ(u	σ(u	NOUN
ejpam-2383	73	35	)	)	PUNCT
ejpam-2383	73	36	=	=	SYM
ejpam-2383	73	37	u	u	NOUN
ejpam-2383	73	38	and	and	CCONJ
ejpam-2383	73	39	u	u	NOUN
ejpam-2383	73	40	is	be	AUX
ejpam-2383	73	41	a	a	DET
ejpam-2383	73	42	completely	completely	ADV
ejpam-2383	73	43	prime	prime	ADJ
ejpam-2383	73	44	ideal	ideal	NOUN
ejpam-2383	73	45	of	of	ADP
ejpam-2383	73	46	r	r	NOUN
ejpam-2383	73	47	[	[	X
ejpam-2383	73	48	theorem	theorem	NOUN
ejpam-2383	73	49	(	(	PUNCT
ejpam-2383	73	50	2.3	2.3	NUM
ejpam-2383	73	51	)	)	PUNCT
ejpam-2383	73	52	of	of	ADP
ejpam-2383	73	53	3	3	NUM
ejpam-2383	73	54	]	]	PUNCT
ejpam-2383	73	55	.	.	PUNCT
ejpam-2383	74	1	definition	definition	NOUN
ejpam-2383	74	2	6	6	NUM
ejpam-2383	74	3	.	.	PUNCT
ejpam-2383	75	1	let	let	VERB
ejpam-2383	75	2	r	r	PRON
ejpam-2383	75	3	be	be	AUX
ejpam-2383	75	4	a	a	DET
ejpam-2383	75	5	ring	ring	NOUN
ejpam-2383	75	6	.	.	PUNCT
ejpam-2383	76	1	let	let	VERB
ejpam-2383	76	2	σ	σ	NOUN
ejpam-2383	76	3	be	be	AUX
ejpam-2383	76	4	an	an	DET
ejpam-2383	76	5	automorphism	automorphism	NOUN
ejpam-2383	76	6	of	of	ADP
ejpam-2383	76	7	r	r	NOUN
ejpam-2383	76	8	and	and	CCONJ
ejpam-2383	76	9	δ	δ	PROPN
ejpam-2383	76	10	a	a	DET
ejpam-2383	76	11	σ	σ	NOUN
ejpam-2383	76	12	-	-	PUNCT
ejpam-2383	76	13	derivation	derivation	NOUN
ejpam-2383	76	14	of	of	ADP
ejpam-2383	76	15	r.	r.	PROPN
ejpam-2383	76	16	then	then	ADV
ejpam-2383	76	17	r	r	NOUN
ejpam-2383	76	18	is	be	AUX
ejpam-2383	76	19	a	a	DET
ejpam-2383	76	20	δ	δ	NOUN
ejpam-2383	76	21	-	-	PUNCT
ejpam-2383	76	22	ring	ring	NOUN
ejpam-2383	76	23	if	if	SCONJ
ejpam-2383	76	24	aδ(a	aδ(a	NOUN
ejpam-2383	76	25	)	)	PUNCT
ejpam-2383	76	26	∈	∈	PROPN
ejpam-2383	76	27	p(r	p(r	PROPN
ejpam-2383	76	28	)	)	PUNCT
ejpam-2383	76	29	implies	imply	VERB
ejpam-2383	76	30	that	that	SCONJ
ejpam-2383	76	31	a	a	DET
ejpam-2383	76	32	∈	∈	PROPN
ejpam-2383	76	33	p(r	p(r	PROPN
ejpam-2383	76	34	)	)	PUNCT
ejpam-2383	76	35	for	for	ADP
ejpam-2383	76	36	a	a	DET
ejpam-2383	76	37	∈	∈	PROPN
ejpam-2383	76	38	p(r	p(r	PROPN
ejpam-2383	76	39	)	)	PUNCT
ejpam-2383	77	1	[	[	X
ejpam-2383	77	2	1	1	NUM
ejpam-2383	77	3	]	]	PUNCT
ejpam-2383	77	4	.	.	PUNCT
ejpam-2383	78	1	note	note	VERB
ejpam-2383	78	2	that	that	SCONJ
ejpam-2383	78	3	a	a	DET
ejpam-2383	78	4	ring	ring	NOUN
ejpam-2383	78	5	with	with	ADP
ejpam-2383	78	6	identity	identity	NOUN
ejpam-2383	78	7	is	be	AUX
ejpam-2383	78	8	not	not	PART
ejpam-2383	78	9	a	a	DET
ejpam-2383	78	10	δ	δ	NOUN
ejpam-2383	78	11	-	-	PUNCT
ejpam-2383	78	12	ring	ring	NOUN
ejpam-2383	78	13	as	as	ADP
ejpam-2383	78	14	1δ(1	1δ(1	NUM
ejpam-2383	78	15	)	)	PUNCT
ejpam-2383	78	16	=	=	SYM
ejpam-2383	78	17	0	0	NUM
ejpam-2383	78	18	,	,	PUNCT
ejpam-2383	78	19	but	but	CCONJ
ejpam-2383	78	20	1	1	NUM
ejpam-2383	78	21	6=	6=	NUM
ejpam-2383	78	22	0	0	NUM
ejpam-2383	78	23	.	.	PUNCT
ejpam-2383	79	1	also	also	ADV
ejpam-2383	79	2	from	from	ADP
ejpam-2383	79	3	[	[	X
ejpam-2383	79	4	1	1	X
ejpam-2383	79	5	]	]	PUNCT
ejpam-2383	79	6	we	we	PRON
ejpam-2383	79	7	know	know	VERB
ejpam-2383	79	8	that	that	SCONJ
ejpam-2383	79	9	if	if	SCONJ
ejpam-2383	79	10	r	r	NOUN
ejpam-2383	79	11	is	be	AUX
ejpam-2383	79	12	a	a	DET
ejpam-2383	79	13	δ	δ	NOUN
ejpam-2383	79	14	-	-	PUNCT
ejpam-2383	79	15	noetherian	noetherian	ADJ
ejpam-2383	79	16	q	q	NOUN
ejpam-2383	79	17	-	-	PUNCT
ejpam-2383	79	18	algebra	algebra	NOUN
ejpam-2383	79	19	such	such	ADJ
ejpam-2383	79	20	that	that	SCONJ
ejpam-2383	79	21	σ(δ(a	σ(δ(a	NOUN
ejpam-2383	79	22	)	)	PUNCT
ejpam-2383	79	23	)	)	PUNCT
ejpam-2383	80	1	=	=	PUNCT
ejpam-2383	80	2	δ(σ(a	δ(σ(a	NOUN
ejpam-2383	80	3	)	)	PUNCT
ejpam-2383	80	4	)	)	PUNCT
ejpam-2383	80	5	,	,	PUNCT
ejpam-2383	80	6	for	for	ADP
ejpam-2383	80	7	all	all	DET
ejpam-2383	80	8	a	a	DET
ejpam-2383	80	9	∈	∈	NOUN
ejpam-2383	80	10	r	r	NOUN
ejpam-2383	80	11	;	;	PUNCT
ejpam-2383	80	12	σ(p	σ(p	X
ejpam-2383	80	13	)	)	PUNCT
ejpam-2383	80	14	=	=	SYM
ejpam-2383	81	1	p	p	NOUN
ejpam-2383	81	2	,	,	PUNCT
ejpam-2383	81	3	for	for	ADP
ejpam-2383	81	4	all	all	DET
ejpam-2383	81	5	p	p	PROPN
ejpam-2383	81	6	∈	∈	PROPN
ejpam-2383	81	7	min.spec(r	min.spec(r	NOUN
ejpam-2383	81	8	)	)	PUNCT
ejpam-2383	81	9	and	and	CCONJ
ejpam-2383	81	10	δ(p(r	δ(p(r	PROPN
ejpam-2383	81	11	)	)	PUNCT
ejpam-2383	81	12	)	)	PUNCT
ejpam-2383	82	1	⊆	⊆	NUM
ejpam-2383	82	2	p(r	p(r	PROPN
ejpam-2383	82	3	)	)	PUNCT
ejpam-2383	82	4	,	,	PUNCT
ejpam-2383	82	5	then	then	ADV
ejpam-2383	82	6	r[x;σ	r[x;σ	NOUN
ejpam-2383	82	7	,	,	PUNCT
ejpam-2383	82	8	δ	δ	PROPN
ejpam-2383	82	9	]	]	PUNCT
ejpam-2383	82	10	is	be	AUX
ejpam-2383	82	11	2	2	NUM
ejpam-2383	82	12	-	-	PUNCT
ejpam-2383	82	13	primal	primal	ADJ
ejpam-2383	82	14	.	.	PUNCT
ejpam-2383	83	1	we	we	PRON
ejpam-2383	83	2	now	now	ADV
ejpam-2383	83	3	generalize	generalize	VERB
ejpam-2383	83	4	these	these	DET
ejpam-2383	83	5	notions	notion	NOUN
ejpam-2383	83	6	as	as	SCONJ
ejpam-2383	83	7	follows	follow	VERB
ejpam-2383	83	8	:	:	PUNCT
ejpam-2383	83	9	definition	definition	NOUN
ejpam-2383	83	10	7	7	NUM
ejpam-2383	83	11	.	.	PUNCT
ejpam-2383	84	1	let	let	VERB
ejpam-2383	84	2	r	r	PRON
ejpam-2383	84	3	be	be	AUX
ejpam-2383	84	4	a	a	DET
ejpam-2383	84	5	ring	ring	NOUN
ejpam-2383	84	6	.	.	PUNCT
ejpam-2383	85	1	let	let	VERB
ejpam-2383	85	2	σ	σ	NOUN
ejpam-2383	85	3	be	be	AUX
ejpam-2383	85	4	an	an	DET
ejpam-2383	85	5	endomorphism	endomorphism	NOUN
ejpam-2383	85	6	of	of	ADP
ejpam-2383	85	7	r	r	NOUN
ejpam-2383	85	8	and	and	CCONJ
ejpam-2383	85	9	δ	δ	PROPN
ejpam-2383	85	10	a	a	DET
ejpam-2383	85	11	σ	σ	NOUN
ejpam-2383	85	12	-	-	PUNCT
ejpam-2383	85	13	derivation	derivation	NOUN
ejpam-2383	85	14	of	of	ADP
ejpam-2383	85	15	r.	r.	PROPN
ejpam-2383	85	16	then	then	ADV
ejpam-2383	85	17	r	r	NOUN
ejpam-2383	85	18	is	be	AUX
ejpam-2383	85	19	said	say	VERB
ejpam-2383	85	20	to	to	PART
ejpam-2383	85	21	be	be	AUX
ejpam-2383	85	22	a	a	DET
ejpam-2383	85	23	(	(	PUNCT
ejpam-2383	85	24	σ	σ	NOUN
ejpam-2383	85	25	,	,	PUNCT
ejpam-2383	85	26	δ)-ring	δ)-re	VERB
ejpam-2383	85	27	if	if	SCONJ
ejpam-2383	85	28	a(σ(a	a(σ(a	PROPN
ejpam-2383	85	29	)	)	PUNCT
ejpam-2383	86	1	+	+	PRON
ejpam-2383	86	2	δ(a	δ(a	X
ejpam-2383	86	3	)	)	PUNCT
ejpam-2383	86	4	)	)	PUNCT
ejpam-2383	87	1	∈	∈	PROPN
ejpam-2383	87	2	p(r	p(r	PROPN
ejpam-2383	87	3	)	)	PUNCT
ejpam-2383	87	4	implies	imply	VERB
ejpam-2383	87	5	that	that	SCONJ
ejpam-2383	87	6	a	a	DET
ejpam-2383	87	7	∈	∈	PROPN
ejpam-2383	87	8	p(r	p(r	PROPN
ejpam-2383	87	9	)	)	PUNCT
ejpam-2383	87	10	for	for	ADP
ejpam-2383	87	11	a	a	DET
ejpam-2383	87	12	∈	∈	PROPN
ejpam-2383	87	13	r.	r.	PROPN
ejpam-2383	87	14	example	example	NOUN
ejpam-2383	87	15	7	7	NUM
ejpam-2383	87	16	.	.	PUNCT
ejpam-2383	88	1	let	let	VERB
ejpam-2383	88	2	r=	r=	PROPN
ejpam-2383	88	3	�	�	PROPN
ejpam-2383	88	4	z	z	PROPN
ejpam-2383	88	5	z	z	NOUN
ejpam-2383	88	6	0	0	NUM
ejpam-2383	88	7	z	z	PROPN
ejpam-2383	88	8	�	�	PROPN
ejpam-2383	88	9	.	.	PUNCT
ejpam-2383	89	1	then	then	ADV
ejpam-2383	89	2	p(r	p(r	PROPN
ejpam-2383	89	3	)	)	PUNCT
ejpam-2383	89	4	=	=	SYM
ejpam-2383	89	5	�	�	PROPN
ejpam-2383	89	6	0	0	PUNCT
ejpam-2383	89	7	z	z	NOUN
ejpam-2383	89	8	0	0	NUM
ejpam-2383	89	9	0	0	NUM
ejpam-2383	89	10	�	�	PROPN
ejpam-2383	89	11	.	.	PUNCT
ejpam-2383	90	1	let	let	VERB
ejpam-2383	90	2	σ	σ	NOUN
ejpam-2383	90	3	:	:	PUNCT
ejpam-2383	90	4	r→	r→	PROPN
ejpam-2383	90	5	r	r	NOUN
ejpam-2383	90	6	be	be	AUX
ejpam-2383	90	7	defined	define	VERB
ejpam-2383	90	8	by	by	ADP
ejpam-2383	90	9	σ	σ	PROPN
ejpam-2383	90	10	�	�	PROPN
ejpam-2383	90	11	�	�	PROPN
ejpam-2383	90	12	a	a	DET
ejpam-2383	90	13	b	b	PROPN
ejpam-2383	90	14	0	0	NUM
ejpam-2383	90	15	c	c	PROPN
ejpam-2383	90	16	�	�	PROPN
ejpam-2383	90	17	�	�	PROPN
ejpam-2383	90	18	=	=	SYM
ejpam-2383	90	19	�	�	PROPN
ejpam-2383	90	20	a	a	DET
ejpam-2383	90	21	−b	−b	NOUN
ejpam-2383	90	22	0	0	PUNCT
ejpam-2383	90	23	c	c	PROPN
ejpam-2383	90	24	�	�	PROPN
ejpam-2383	90	25	,	,	PUNCT
ejpam-2383	90	26	for	for	ADP
ejpam-2383	90	27	all	all	DET
ejpam-2383	90	28	a	a	DET
ejpam-2383	90	29	,	,	PUNCT
ejpam-2383	90	30	b	b	NOUN
ejpam-2383	90	31	,	,	PUNCT
ejpam-2383	91	1	c	c	PROPN
ejpam-2383	91	2	∈	∈	PROPN
ejpam-2383	91	3	z.	z.	PROPN
ejpam-2383	91	4	then	then	ADV
ejpam-2383	91	5	it	it	PRON
ejpam-2383	91	6	can	can	AUX
ejpam-2383	91	7	be	be	AUX
ejpam-2383	91	8	seen	see	VERB
ejpam-2383	91	9	that	that	SCONJ
ejpam-2383	91	10	σ	σ	PROPN
ejpam-2383	91	11	is	be	AUX
ejpam-2383	91	12	an	an	DET
ejpam-2383	91	13	endomorphism	endomorphism	NOUN
ejpam-2383	91	14	of	of	ADP
ejpam-2383	91	15	r.	r.	PROPN
ejpam-2383	91	16	define	define	VERB
ejpam-2383	91	17	δ	δ	PROPN
ejpam-2383	91	18	:	:	PUNCT
ejpam-2383	91	19	r→	r→	VERB
ejpam-2383	91	20	r	r	NOUN
ejpam-2383	91	21	by	by	ADP
ejpam-2383	91	22	δ(a	δ(a	NOUN
ejpam-2383	91	23	)	)	PUNCT
ejpam-2383	91	24	=	=	SYM
ejpam-2383	91	25	a−σ(a	a−σ(a	ADJ
ejpam-2383	91	26	)	)	PUNCT
ejpam-2383	91	27	,	,	PUNCT
ejpam-2383	91	28	for	for	ADP
ejpam-2383	91	29	alla	alla	NOUN
ejpam-2383	91	30	∈	∈	PROPN
ejpam-2383	91	31	r.	r.	PROPN
ejpam-2383	91	32	m.	m.	PROPN
ejpam-2383	91	33	abrol	abrol	PROPN
ejpam-2383	91	34	,	,	PUNCT
ejpam-2383	91	35	v.	v.	ADP
ejpam-2383	91	36	bhat	bhat	PROPN
ejpam-2383	91	37	/	/	SYM
ejpam-2383	91	38	eur	eur	PROPN
ejpam-2383	91	39	.	.	PUNCT
ejpam-2383	92	1	j.	j.	PROPN
ejpam-2383	92	2	pure	pure	PROPN
ejpam-2383	92	3	appl	appl	PROPN
ejpam-2383	92	4	.	.	PROPN
ejpam-2383	92	5	math	math	PROPN
ejpam-2383	92	6	,	,	PUNCT
ejpam-2383	92	7	8	8	NUM
ejpam-2383	92	8	(	(	PUNCT
ejpam-2383	92	9	2015	2015	NUM
ejpam-2383	92	10	)	)	PUNCT
ejpam-2383	92	11	,	,	PUNCT
ejpam-2383	92	12	462	462	NUM
ejpam-2383	92	13	-	-	SYM
ejpam-2383	92	14	468	468	NUM
ejpam-2383	92	15	465	465	NUM
ejpam-2383	92	16	clearly	clearly	ADV
ejpam-2383	92	17	,	,	PUNCT
ejpam-2383	92	18	δ	δ	PROPN
ejpam-2383	92	19	is	be	AUX
ejpam-2383	92	20	a	a	DET
ejpam-2383	92	21	σ	σ	NOUN
ejpam-2383	92	22	-	-	PUNCT
ejpam-2383	92	23	derivation	derivation	NOUN
ejpam-2383	92	24	of	of	ADP
ejpam-2383	92	25	r.	r.	PROPN
ejpam-2383	92	26	now	now	ADV
ejpam-2383	92	27	let	let	VERB
ejpam-2383	92	28	a=	a=	VERB
ejpam-2383	92	29	�	�	PROPN
ejpam-2383	92	30	a	a	DET
ejpam-2383	92	31	b	b	PROPN
ejpam-2383	92	32	0	0	NUM
ejpam-2383	92	33	c	c	PROPN
ejpam-2383	92	34	�	�	PROPN
ejpam-2383	92	35	.	.	PUNCT
ejpam-2383	93	1	a[σ(a	a[σ(a	X
ejpam-2383	93	2	)	)	PUNCT
ejpam-2383	94	1	+	+	CCONJ
ejpam-2383	94	2	δ(a	δ(a	X
ejpam-2383	94	3	)	)	PUNCT
ejpam-2383	94	4	]	]	PUNCT
ejpam-2383	95	1	∈	∈	PROPN
ejpam-2383	95	2	p(r	p(r	PROPN
ejpam-2383	95	3	)	)	PUNCT
ejpam-2383	95	4	implies	imply	VERB
ejpam-2383	95	5	that	that	SCONJ
ejpam-2383	95	6	�	�	PROPN
ejpam-2383	95	7	a	a	DET
ejpam-2383	95	8	b	b	PROPN
ejpam-2383	95	9	0	0	NUM
ejpam-2383	95	10	c	c	PROPN
ejpam-2383	95	11	�	�	PROPN
ejpam-2383	95	12	¦	¦	PROPN
ejpam-2383	95	13	σ	σ	PROPN
ejpam-2383	95	14	�	�	PROPN
ejpam-2383	95	15	�	�	PROPN
ejpam-2383	95	16	a	a	DET
ejpam-2383	95	17	b	b	PROPN
ejpam-2383	95	18	0	0	NUM
ejpam-2383	95	19	c	c	PROPN
ejpam-2383	95	20	�	�	PROPN
ejpam-2383	95	21	�	�	PROPN
ejpam-2383	95	22	+	+	CCONJ
ejpam-2383	95	23	�	�	PROPN
ejpam-2383	95	24	a	a	DET
ejpam-2383	95	25	b	b	PROPN
ejpam-2383	95	26	0	0	NUM
ejpam-2383	95	27	c	c	PROPN
ejpam-2383	95	28	�	�	PROPN
ejpam-2383	95	29	−σ	−σ	PROPN
ejpam-2383	95	30	�	�	PROPN
ejpam-2383	95	31	�	�	PROPN
ejpam-2383	95	32	a	a	DET
ejpam-2383	95	33	b	b	PROPN
ejpam-2383	95	34	0	0	NUM
ejpam-2383	95	35	c	c	PROPN
ejpam-2383	95	36	�	�	PROPN
ejpam-2383	95	37	�	�	PROPN
ejpam-2383	95	38	©	©	PROPN
ejpam-2383	95	39	∈	∈	PROPN
ejpam-2383	95	40	p(r	p(r	PROPN
ejpam-2383	95	41	)	)	PUNCT
ejpam-2383	95	42	or	or	CCONJ
ejpam-2383	95	43	�	�	PROPN
ejpam-2383	95	44	a	a	DET
ejpam-2383	95	45	b	b	PROPN
ejpam-2383	95	46	0	0	NUM
ejpam-2383	95	47	c	c	PROPN
ejpam-2383	95	48	�	�	PROPN
ejpam-2383	95	49	¦	¦	PROPN
ejpam-2383	95	50	�	�	PROPN
ejpam-2383	95	51	a	a	DET
ejpam-2383	95	52	−b	−b	NOUN
ejpam-2383	95	53	0	0	PUNCT
ejpam-2383	95	54	c	c	PROPN
ejpam-2383	95	55	�	�	PROPN
ejpam-2383	95	56	+	+	CCONJ
ejpam-2383	95	57	�	�	PROPN
ejpam-2383	95	58	a	a	DET
ejpam-2383	95	59	b	b	PROPN
ejpam-2383	95	60	0	0	NUM
ejpam-2383	95	61	c	c	PROPN
ejpam-2383	95	62	�	�	PROPN
ejpam-2383	95	63	−σ	−σ	PROPN
ejpam-2383	95	64	�	�	PROPN
ejpam-2383	95	65	�	�	PROPN
ejpam-2383	95	66	a	a	DET
ejpam-2383	95	67	b	b	PROPN
ejpam-2383	95	68	0	0	NUM
ejpam-2383	95	69	c	c	PROPN
ejpam-2383	95	70	�	�	PROPN
ejpam-2383	95	71	�	�	PROPN
ejpam-2383	95	72	©	©	PROPN
ejpam-2383	95	73	∈	∈	PROPN
ejpam-2383	95	74	p(r	p(r	PROPN
ejpam-2383	95	75	)	)	PUNCT
ejpam-2383	95	76	which	which	PRON
ejpam-2383	95	77	gives	give	VERB
ejpam-2383	95	78	on	on	ADP
ejpam-2383	95	79	simplification	simplification	NOUN
ejpam-2383	95	80	,	,	PUNCT
ejpam-2383	95	81	�	�	PROPN
ejpam-2383	95	82	a2	a2	PROPN
ejpam-2383	95	83	ab+	ab+	PROPN
ejpam-2383	95	84	bc	bc	PROPN
ejpam-2383	95	85	0	0	PROPN
ejpam-2383	95	86	c2	c2	PROPN
ejpam-2383	95	87	�	�	PROPN
ejpam-2383	95	88	∈	∈	PROPN
ejpam-2383	95	89	p(r	p(r	PROPN
ejpam-2383	95	90	)	)	PUNCT
ejpam-2383	95	91	=	=	SYM
ejpam-2383	95	92	�	�	PROPN
ejpam-2383	95	93	0	0	PUNCT
ejpam-2383	95	94	z	z	NOUN
ejpam-2383	95	95	0	0	NUM
ejpam-2383	95	96	0	0	NUM
ejpam-2383	95	97	�	�	PROPN
ejpam-2383	95	98	which	which	PRON
ejpam-2383	95	99	implies	imply	VERB
ejpam-2383	95	100	that	that	DET
ejpam-2383	95	101	a2	a2	PROPN
ejpam-2383	95	102	=	=	SYM
ejpam-2383	95	103	0	0	PROPN
ejpam-2383	95	104	,	,	PUNCT
ejpam-2383	95	105	c2	c2	PROPN
ejpam-2383	95	106	=	=	SYM
ejpam-2383	95	107	0	0	NUM
ejpam-2383	95	108	,	,	PUNCT
ejpam-2383	95	109	i.e.	i.e.	X
ejpam-2383	95	110	a	a	PRON
ejpam-2383	95	111	=	=	SYM
ejpam-2383	95	112	0	0	NUM
ejpam-2383	95	113	,	,	PUNCT
ejpam-2383	95	114	c	c	NOUN
ejpam-2383	95	115	=	=	SYM
ejpam-2383	95	116	0	0	PROPN
ejpam-2383	95	117	.	.	PUNCT
ejpam-2383	96	1	therefore	therefore	ADV
ejpam-2383	96	2	,	,	PUNCT
ejpam-2383	96	3	a=	a=	PROPN
ejpam-2383	96	4	�	�	PROPN
ejpam-2383	96	5	a	a	DET
ejpam-2383	96	6	b	b	PROPN
ejpam-2383	96	7	0	0	NUM
ejpam-2383	96	8	c	c	PROPN
ejpam-2383	96	9	�	�	PROPN
ejpam-2383	96	10	=	=	SYM
ejpam-2383	96	11	�	�	PROPN
ejpam-2383	96	12	0	0	NUM
ejpam-2383	96	13	b	b	NOUN
ejpam-2383	96	14	0	0	NUM
ejpam-2383	96	15	0	0	NUM
ejpam-2383	96	16	�	�	PROPN
ejpam-2383	96	17	∈	∈	PROPN
ejpam-2383	96	18	p(r	p(r	PROPN
ejpam-2383	96	19	)	)	PUNCT
ejpam-2383	96	20	.	.	PUNCT
ejpam-2383	97	1	hence	hence	ADV
ejpam-2383	97	2	r	r	NOUN
ejpam-2383	97	3	is	be	AUX
ejpam-2383	97	4	a	a	DET
ejpam-2383	97	5	(	(	PUNCT
ejpam-2383	97	6	σ	σ	NOUN
ejpam-2383	97	7	,	,	PUNCT
ejpam-2383	97	8	δ)-ring	δ)-ring	PROPN
ejpam-2383	97	9	.	.	PUNCT
ejpam-2383	97	10	example	example	NOUN
ejpam-2383	98	1	8	8	NUM
ejpam-2383	98	2	.	.	PUNCT
ejpam-2383	99	1	let	let	VERB
ejpam-2383	99	2	r	r	NOUN
ejpam-2383	99	3	=	=	SYM
ejpam-2383	99	4	z2	z2	PROPN
ejpam-2383	99	5	⊕	⊕	PROPN
ejpam-2383	99	6	z2	z2	PROPN
ejpam-2383	99	7	.	.	PUNCT
ejpam-2383	100	1	then	then	ADV
ejpam-2383	100	2	r	r	NOUN
ejpam-2383	100	3	is	be	AUX
ejpam-2383	100	4	a	a	DET
ejpam-2383	100	5	commutative	commutative	ADJ
ejpam-2383	100	6	reduced	reduce	VERB
ejpam-2383	100	7	ring	ring	NOUN
ejpam-2383	100	8	.	.	PUNCT
ejpam-2383	101	1	define	define	VERB
ejpam-2383	101	2	an	an	DET
ejpam-2383	101	3	automorphism	automorphism	NOUN
ejpam-2383	101	4	σ	σ	NOUN
ejpam-2383	101	5	:	:	PUNCT
ejpam-2383	101	6	r→	r→	PROPN
ejpam-2383	101	7	r	r	NOUN
ejpam-2383	101	8	by	by	ADP
ejpam-2383	101	9	σ((a	σ((a	PROPN
ejpam-2383	101	10	,	,	PUNCT
ejpam-2383	101	11	b	b	NOUN
ejpam-2383	101	12	)	)	PUNCT
ejpam-2383	101	13	)	)	PUNCT
ejpam-2383	102	1	=	=	PUNCT
ejpam-2383	102	2	(	(	PUNCT
ejpam-2383	102	3	b	b	NOUN
ejpam-2383	102	4	,	,	PUNCT
ejpam-2383	102	5	a	a	PRON
ejpam-2383	102	6	)	)	PUNCT
ejpam-2383	102	7	for	for	ADP
ejpam-2383	102	8	a	a	DET
ejpam-2383	102	9	,	,	PUNCT
ejpam-2383	102	10	b	b	PROPN
ejpam-2383	102	11	∈	∈	PROPN
ejpam-2383	102	12	z2	z2	PROPN
ejpam-2383	102	13	.	.	PUNCT
ejpam-2383	103	1	also	also	ADV
ejpam-2383	103	2	δ	δ	NOUN
ejpam-2383	103	3	:	:	PUNCT
ejpam-2383	104	1	r→	r→	PROPN
ejpam-2383	104	2	r	r	NOUN
ejpam-2383	104	3	defined	define	VERB
ejpam-2383	104	4	by	by	ADP
ejpam-2383	104	5	δ((a	δ((a	PROPN
ejpam-2383	104	6	,	,	PUNCT
ejpam-2383	104	7	b	b	NOUN
ejpam-2383	104	8	)	)	PUNCT
ejpam-2383	104	9	)	)	PUNCT
ejpam-2383	105	1	=	=	PRON
ejpam-2383	105	2	(	(	PUNCT
ejpam-2383	105	3	a	a	DET
ejpam-2383	105	4	−	−	PROPN
ejpam-2383	105	5	b	b	PROPN
ejpam-2383	105	6	,	,	PUNCT
ejpam-2383	105	7	0	0	NUM
ejpam-2383	105	8	)	)	PUNCT
ejpam-2383	105	9	for	for	ADP
ejpam-2383	105	10	a	a	DET
ejpam-2383	105	11	,	,	PUNCT
ejpam-2383	105	12	b	b	PROPN
ejpam-2383	105	13	∈	∈	PROPN
ejpam-2383	105	14	z2	z2	PROPN
ejpam-2383	105	15	is	be	AUX
ejpam-2383	105	16	a	a	DET
ejpam-2383	105	17	σ	σ	NOUN
ejpam-2383	105	18	-	-	PUNCT
ejpam-2383	105	19	derivation	derivation	NOUN
ejpam-2383	105	20	of	of	ADP
ejpam-2383	105	21	r.	r.	PROPN
ejpam-2383	105	22	here	here	ADV
ejpam-2383	105	23	p(r	p(r	PROPN
ejpam-2383	105	24	)	)	PUNCT
ejpam-2383	105	25	=	=	PRON
ejpam-2383	105	26	{	{	PUNCT
ejpam-2383	105	27	0	0	NUM
ejpam-2383	105	28	}	}	PUNCT
ejpam-2383	105	29	.	.	PUNCT
ejpam-2383	106	1	but	but	CCONJ
ejpam-2383	106	2	r	r	NOUN
ejpam-2383	106	3	is	be	AUX
ejpam-2383	106	4	not	not	PART
ejpam-2383	106	5	a	a	DET
ejpam-2383	106	6	(	(	PUNCT
ejpam-2383	106	7	σ	σ	NOUN
ejpam-2383	106	8	,	,	PUNCT
ejpam-2383	106	9	δ)-ring	δ)-ring	NOUN
ejpam-2383	106	10	,	,	PUNCT
ejpam-2383	106	11	for	for	ADP
ejpam-2383	106	12	take	take	NOUN
ejpam-2383	106	13	(	(	PUNCT
ejpam-2383	106	14	a	a	DET
ejpam-2383	106	15	,	,	PUNCT
ejpam-2383	106	16	b	b	NOUN
ejpam-2383	106	17	)	)	PUNCT
ejpam-2383	106	18	=	=	SYM
ejpam-2383	106	19	(	(	PUNCT
ejpam-2383	106	20	0,1	0,1	NUM
ejpam-2383	106	21	)	)	PUNCT
ejpam-2383	106	22	.	.	PUNCT
ejpam-2383	107	1	with	with	ADP
ejpam-2383	107	2	this	this	PRON
ejpam-2383	107	3	we	we	PRON
ejpam-2383	107	4	prove	prove	VERB
ejpam-2383	107	5	the	the	DET
ejpam-2383	107	6	following	following	NOUN
ejpam-2383	107	7	:	:	PUNCT
ejpam-2383	107	8	theorem	theorem	NOUN
ejpam-2383	107	9	1	1	NUM
ejpam-2383	107	10	:	:	PUNCT
ejpam-2383	107	11	let	let	VERB
ejpam-2383	107	12	r	r	PRON
ejpam-2383	107	13	be	be	AUX
ejpam-2383	107	14	a	a	DET
ejpam-2383	107	15	noetherian	noetherian	ADJ
ejpam-2383	107	16	,	,	PUNCT
ejpam-2383	107	17	integral	integral	ADJ
ejpam-2383	107	18	domain	domain	NOUN
ejpam-2383	107	19	which	which	PRON
ejpam-2383	107	20	is	be	AUX
ejpam-2383	107	21	also	also	ADV
ejpam-2383	107	22	an	an	DET
ejpam-2383	107	23	algebra	algebra	NOUN
ejpam-2383	107	24	over	over	ADP
ejpam-2383	107	25	q.	q.	PROPN
ejpam-2383	107	26	let	let	VERB
ejpam-2383	107	27	σ	σ	NOUN
ejpam-2383	107	28	be	be	AUX
ejpam-2383	107	29	an	an	DET
ejpam-2383	107	30	automorphism	automorphism	NOUN
ejpam-2383	107	31	of	of	ADP
ejpam-2383	107	32	r	r	NOUN
ejpam-2383	107	33	and	and	CCONJ
ejpam-2383	107	34	δ	δ	PROPN
ejpam-2383	107	35	a	a	DET
ejpam-2383	107	36	σ	σ	NOUN
ejpam-2383	107	37	-	-	PUNCT
ejpam-2383	107	38	derivation	derivation	NOUN
ejpam-2383	107	39	of	of	ADP
ejpam-2383	107	40	r	r	NOUN
ejpam-2383	107	41	such	such	ADJ
ejpam-2383	107	42	that	that	SCONJ
ejpam-2383	107	43	r	r	NOUN
ejpam-2383	107	44	is	be	AUX
ejpam-2383	107	45	a	a	DET
ejpam-2383	107	46	(	(	PUNCT
ejpam-2383	107	47	σ	σ	NOUN
ejpam-2383	107	48	,	,	PUNCT
ejpam-2383	107	49	δ)-ring	δ)-ring	PROPN
ejpam-2383	107	50	and	and	CCONJ
ejpam-2383	107	51	δ(p(r	δ(p(r	PROPN
ejpam-2383	107	52	)	)	PUNCT
ejpam-2383	107	53	)	)	PUNCT
ejpam-2383	108	1	⊆	⊆	NUM
ejpam-2383	108	2	p(r	p(r	PROPN
ejpam-2383	108	3	)	)	PUNCT
ejpam-2383	108	4	.	.	PUNCT
ejpam-2383	109	1	then	then	ADV
ejpam-2383	109	2	r	r	NOUN
ejpam-2383	109	3	is	be	AUX
ejpam-2383	109	4	2	2	NUM
ejpam-2383	109	5	-	-	PUNCT
ejpam-2383	109	6	primal	primal	ADJ
ejpam-2383	109	7	.	.	PUNCT
ejpam-2383	110	1	theorem	theorem	NOUN
ejpam-2383	110	2	2	2	NUM
ejpam-2383	110	3	:	:	PUNCT
ejpam-2383	110	4	let	let	VERB
ejpam-2383	110	5	r	r	PRON
ejpam-2383	110	6	be	be	AUX
ejpam-2383	110	7	a	a	DET
ejpam-2383	110	8	noetherian	noetherian	ADJ
ejpam-2383	110	9	,	,	PUNCT
ejpam-2383	110	10	integral	integral	ADJ
ejpam-2383	110	11	domain	domain	NOUN
ejpam-2383	110	12	which	which	PRON
ejpam-2383	110	13	is	be	AUX
ejpam-2383	110	14	also	also	ADV
ejpam-2383	110	15	an	an	DET
ejpam-2383	110	16	algebra	algebra	NOUN
ejpam-2383	110	17	over	over	ADP
ejpam-2383	110	18	q.	q.	PROPN
ejpam-2383	110	19	let	let	VERB
ejpam-2383	110	20	σ	σ	NOUN
ejpam-2383	110	21	be	be	AUX
ejpam-2383	110	22	an	an	DET
ejpam-2383	110	23	automorphism	automorphism	NOUN
ejpam-2383	110	24	of	of	ADP
ejpam-2383	110	25	r	r	NOUN
ejpam-2383	110	26	and	and	CCONJ
ejpam-2383	110	27	δ	δ	PROPN
ejpam-2383	110	28	a	a	DET
ejpam-2383	110	29	σ	σ	NOUN
ejpam-2383	110	30	-	-	PUNCT
ejpam-2383	110	31	derivation	derivation	NOUN
ejpam-2383	110	32	of	of	ADP
ejpam-2383	110	33	r	r	NOUN
ejpam-2383	110	34	such	such	ADJ
ejpam-2383	110	35	that	that	SCONJ
ejpam-2383	110	36	r	r	NOUN
ejpam-2383	110	37	is	be	AUX
ejpam-2383	110	38	a	a	DET
ejpam-2383	110	39	(	(	PUNCT
ejpam-2383	110	40	σ	σ	NOUN
ejpam-2383	110	41	,	,	PUNCT
ejpam-2383	110	42	δ)-ring	δ)-ring	ADJ
ejpam-2383	110	43	.	.	PUNCT
ejpam-2383	111	1	if	if	SCONJ
ejpam-2383	111	2	p	p	PROPN
ejpam-2383	111	3	∈	∈	PROPN
ejpam-2383	111	4	min.spec(r	min.spec(r	NOUN
ejpam-2383	111	5	)	)	PUNCT
ejpam-2383	111	6	is	be	AUX
ejpam-2383	111	7	such	such	ADJ
ejpam-2383	111	8	that	that	SCONJ
ejpam-2383	111	9	σ(p	σ(p	PROPN
ejpam-2383	111	10	)	)	PUNCT
ejpam-2383	112	1	=	=	SYM
ejpam-2383	113	1	p	p	X
ejpam-2383	113	2	,	,	PUNCT
ejpam-2383	113	3	then	then	ADV
ejpam-2383	113	4	δ(p	δ(p	PROPN
ejpam-2383	113	5	)	)	PUNCT
ejpam-2383	113	6	⊆	⊆	NUM
ejpam-2383	113	7	p.	p.	NOUN
ejpam-2383	113	8	theorem	theorem	VERB
ejpam-2383	113	9	4	4	NUM
ejpam-2383	113	10	:	:	PUNCT
ejpam-2383	113	11	let	let	VERB
ejpam-2383	113	12	r	r	PRON
ejpam-2383	113	13	be	be	AUX
ejpam-2383	113	14	a	a	DET
ejpam-2383	113	15	noetherian	noetherian	ADJ
ejpam-2383	113	16	,	,	PUNCT
ejpam-2383	113	17	integral	integral	ADJ
ejpam-2383	113	18	domain	domain	NOUN
ejpam-2383	113	19	which	which	PRON
ejpam-2383	113	20	is	be	AUX
ejpam-2383	113	21	also	also	ADV
ejpam-2383	113	22	an	an	DET
ejpam-2383	113	23	algebra	algebra	NOUN
ejpam-2383	113	24	over	over	ADP
ejpam-2383	113	25	q.	q.	PROPN
ejpam-2383	113	26	let	let	VERB
ejpam-2383	113	27	σ	σ	NOUN
ejpam-2383	113	28	be	be	AUX
ejpam-2383	113	29	an	an	DET
ejpam-2383	113	30	automorphism	automorphism	NOUN
ejpam-2383	113	31	of	of	ADP
ejpam-2383	113	32	r	r	NOUN
ejpam-2383	113	33	and	and	CCONJ
ejpam-2383	113	34	δ	δ	PROPN
ejpam-2383	113	35	a	a	DET
ejpam-2383	113	36	σ	σ	NOUN
ejpam-2383	113	37	-	-	PUNCT
ejpam-2383	113	38	derivation	derivation	NOUN
ejpam-2383	113	39	of	of	ADP
ejpam-2383	113	40	r	r	NOUN
ejpam-2383	113	41	such	such	ADJ
ejpam-2383	113	42	that	that	SCONJ
ejpam-2383	113	43	r	r	NOUN
ejpam-2383	113	44	is	be	AUX
ejpam-2383	113	45	a	a	DET
ejpam-2383	113	46	(	(	PUNCT
ejpam-2383	113	47	σ	σ	NOUN
ejpam-2383	113	48	,	,	PUNCT
ejpam-2383	113	49	δ)-ring	δ)-ring	PROPN
ejpam-2383	113	50	and	and	CCONJ
ejpam-2383	113	51	δ(p(r	δ(p(r	PROPN
ejpam-2383	113	52	)	)	PUNCT
ejpam-2383	113	53	)	)	PUNCT
ejpam-2383	114	1	⊆	⊆	NUM
ejpam-2383	114	2	p(r	p(r	PROPN
ejpam-2383	114	3	)	)	PUNCT
ejpam-2383	114	4	.	.	PUNCT
ejpam-2383	115	1	let	let	VERB
ejpam-2383	115	2	p	p	PRON
ejpam-2383	115	3	∈	∈	PROPN
ejpam-2383	115	4	min.spec(r	min.spec(r	PROPN
ejpam-2383	115	5	)	)	PUNCT
ejpam-2383	115	6	be	be	AUX
ejpam-2383	115	7	such	such	ADJ
ejpam-2383	115	8	that	that	SCONJ
ejpam-2383	115	9	σ(p	σ(p	PROPN
ejpam-2383	115	10	)	)	PUNCT
ejpam-2383	116	1	=	=	SYM
ejpam-2383	116	2	p	p	NOUN
ejpam-2383	116	3	,	,	PUNCT
ejpam-2383	116	4	then	then	ADV
ejpam-2383	116	5	o(p	o(p	PROPN
ejpam-2383	116	6	)	)	PUNCT
ejpam-2383	116	7	is	be	AUX
ejpam-2383	116	8	a	a	DET
ejpam-2383	116	9	completely	completely	ADV
ejpam-2383	116	10	prime	prime	ADJ
ejpam-2383	116	11	ideal	ideal	NOUN
ejpam-2383	116	12	of	of	ADP
ejpam-2383	116	13	o(r	o(r	PROPN
ejpam-2383	116	14	)	)	PUNCT
ejpam-2383	116	15	.	.	PUNCT
ejpam-2383	117	1	2	2	X
ejpam-2383	117	2	.	.	X
ejpam-2383	117	3	proof	proof	NOUN
ejpam-2383	117	4	of	of	ADP
ejpam-2383	117	5	main	main	ADJ
ejpam-2383	117	6	results	result	NOUN
ejpam-2383	117	7	we	we	PRON
ejpam-2383	117	8	now	now	ADV
ejpam-2383	117	9	prove	prove	VERB
ejpam-2383	117	10	theorems	theorem	NOUN
ejpam-2383	117	11	1	1	NUM
ejpam-2383	117	12	,	,	PUNCT
ejpam-2383	117	13	2	2	NUM
ejpam-2383	117	14	and	and	CCONJ
ejpam-2383	117	15	3	3	NUM
ejpam-2383	117	16	as	as	SCONJ
ejpam-2383	117	17	follows	follow	VERB
ejpam-2383	117	18	:	:	PUNCT
ejpam-2383	117	19	theorem	theorem	NOUN
ejpam-2383	117	20	1	1	NUM
ejpam-2383	117	21	.	.	PUNCT
ejpam-2383	118	1	let	let	VERB
ejpam-2383	118	2	r	r	PRON
ejpam-2383	118	3	be	be	AUX
ejpam-2383	118	4	a	a	DET
ejpam-2383	118	5	noetherian	noetherian	ADJ
ejpam-2383	118	6	,	,	PUNCT
ejpam-2383	118	7	integral	integral	ADJ
ejpam-2383	118	8	domain	domain	NOUN
ejpam-2383	118	9	which	which	PRON
ejpam-2383	118	10	is	be	AUX
ejpam-2383	118	11	also	also	ADV
ejpam-2383	118	12	an	an	DET
ejpam-2383	118	13	algebra	algebra	NOUN
ejpam-2383	118	14	over	over	ADP
ejpam-2383	118	15	q.	q.	PROPN
ejpam-2383	118	16	let	let	VERB
ejpam-2383	118	17	σ	σ	NOUN
ejpam-2383	118	18	be	be	AUX
ejpam-2383	118	19	an	an	DET
ejpam-2383	118	20	automorphism	automorphism	NOUN
ejpam-2383	118	21	of	of	ADP
ejpam-2383	118	22	r	r	NOUN
ejpam-2383	118	23	and	and	CCONJ
ejpam-2383	118	24	δ	δ	PROPN
ejpam-2383	119	1	a	a	DET
ejpam-2383	119	2	σ	σ	NOUN
ejpam-2383	119	3	-	-	PUNCT
ejpam-2383	119	4	derivation	derivation	NOUN
ejpam-2383	119	5	of	of	ADP
ejpam-2383	119	6	r	r	NOUN
ejpam-2383	119	7	such	such	ADJ
ejpam-2383	119	8	that	that	SCONJ
ejpam-2383	119	9	r	r	NOUN
ejpam-2383	119	10	is	be	AUX
ejpam-2383	119	11	a	a	DET
ejpam-2383	119	12	(	(	PUNCT
ejpam-2383	119	13	σ	σ	NOUN
ejpam-2383	119	14	,	,	PUNCT
ejpam-2383	119	15	δ)-ring	δ)-ring	PROPN
ejpam-2383	119	16	and	and	CCONJ
ejpam-2383	119	17	δ(p(r	δ(p(r	PROPN
ejpam-2383	119	18	)	)	PUNCT
ejpam-2383	119	19	)	)	PUNCT
ejpam-2383	120	1	⊆	⊆	NUM
ejpam-2383	120	2	p(r	p(r	PROPN
ejpam-2383	120	3	)	)	PUNCT
ejpam-2383	120	4	.	.	PUNCT
ejpam-2383	121	1	then	then	ADV
ejpam-2383	121	2	r	r	NOUN
ejpam-2383	121	3	is	be	AUX
ejpam-2383	121	4	2	2	NUM
ejpam-2383	121	5	-	-	PUNCT
ejpam-2383	121	6	primal	primal	ADJ
ejpam-2383	121	7	.	.	PUNCT
ejpam-2383	122	1	m.	m.	NOUN
ejpam-2383	122	2	abrol	abrol	NOUN
ejpam-2383	122	3	,	,	PUNCT
ejpam-2383	122	4	v.	v.	ADP
ejpam-2383	122	5	bhat	bhat	PROPN
ejpam-2383	122	6	/	/	SYM
ejpam-2383	122	7	eur	eur	PROPN
ejpam-2383	122	8	.	.	PUNCT
ejpam-2383	123	1	j.	j.	PROPN
ejpam-2383	123	2	pure	pure	PROPN
ejpam-2383	123	3	appl	appl	PROPN
ejpam-2383	123	4	.	.	PROPN
ejpam-2383	123	5	math	math	PROPN
ejpam-2383	123	6	,	,	PUNCT
ejpam-2383	123	7	8	8	NUM
ejpam-2383	123	8	(	(	PUNCT
ejpam-2383	123	9	2015	2015	NUM
ejpam-2383	123	10	)	)	PUNCT
ejpam-2383	123	11	,	,	PUNCT
ejpam-2383	123	12	462	462	NUM
ejpam-2383	123	13	-	-	SYM
ejpam-2383	123	14	468	468	NUM
ejpam-2383	123	15	466	466	NUM
ejpam-2383	123	16	proof	proof	NOUN
ejpam-2383	123	17	.	.	PUNCT
ejpam-2383	124	1	define	define	VERB
ejpam-2383	124	2	a	a	DET
ejpam-2383	124	3	map	map	NOUN
ejpam-2383	124	4	ρ	ρ	NOUN
ejpam-2383	124	5	:	:	PUNCT
ejpam-2383	124	6	r	r	X
ejpam-2383	124	7	/	/	SYM
ejpam-2383	124	8	p(r)→	p(r)→	PROPN
ejpam-2383	124	9	r	r	NOUN
ejpam-2383	124	10	/	/	SYM
ejpam-2383	124	11	p(r	p(r	PROPN
ejpam-2383	124	12	)	)	PUNCT
ejpam-2383	124	13	by	by	ADP
ejpam-2383	124	14	ρ(a+	ρ(a+	NOUN
ejpam-2383	124	15	p(r	p(r	NOUN
ejpam-2383	124	16	)	)	PUNCT
ejpam-2383	124	17	)	)	PUNCT
ejpam-2383	125	1	=	=	SYM
ejpam-2383	125	2	δ(a	δ(a	PROPN
ejpam-2383	125	3	)	)	PUNCT
ejpam-2383	126	1	+	+	CCONJ
ejpam-2383	126	2	p(r	p(r	NOUN
ejpam-2383	126	3	)	)	PUNCT
ejpam-2383	126	4	for	for	ADP
ejpam-2383	126	5	a	a	DET
ejpam-2383	126	6	∈	∈	NOUN
ejpam-2383	126	7	r	r	NOUN
ejpam-2383	126	8	also	also	ADV
ejpam-2383	126	9	define	define	VERB
ejpam-2383	126	10	τ	τ	X
ejpam-2383	126	11	:	:	PUNCT
ejpam-2383	126	12	r	r	X
ejpam-2383	126	13	/	/	SYM
ejpam-2383	126	14	p(r)→	p(r)→	PROPN
ejpam-2383	126	15	r	r	NOUN
ejpam-2383	126	16	/	/	SYM
ejpam-2383	126	17	p(r	p(r	PROPN
ejpam-2383	126	18	)	)	PUNCT
ejpam-2383	126	19	by	by	ADP
ejpam-2383	126	20	τ(a+	τ(a+	NOUN
ejpam-2383	126	21	p(r	p(r	NOUN
ejpam-2383	126	22	)	)	PUNCT
ejpam-2383	126	23	)	)	PUNCT
ejpam-2383	127	1	=	=	SYM
ejpam-2383	127	2	σ(a	σ(a	PROPN
ejpam-2383	127	3	)	)	PUNCT
ejpam-2383	127	4	+	+	CCONJ
ejpam-2383	127	5	p(r	p(r	NOUN
ejpam-2383	127	6	)	)	PUNCT
ejpam-2383	127	7	for	for	ADP
ejpam-2383	127	8	a	a	DET
ejpam-2383	127	9	∈	∈	PROPN
ejpam-2383	127	10	r.	r.	NOUN
ejpam-2383	127	11	then	then	ADV
ejpam-2383	127	12	τ	τ	PROPN
ejpam-2383	127	13	is	be	AUX
ejpam-2383	127	14	an	an	DET
ejpam-2383	127	15	automorphism	automorphism	NOUN
ejpam-2383	127	16	of	of	ADP
ejpam-2383	127	17	r	r	NOUN
ejpam-2383	127	18	/	/	SYM
ejpam-2383	127	19	p(r	p(r	PROPN
ejpam-2383	127	20	)	)	PUNCT
ejpam-2383	127	21	and	and	CCONJ
ejpam-2383	127	22	ρ	ρ	PROPN
ejpam-2383	127	23	is	be	AUX
ejpam-2383	127	24	a	a	DET
ejpam-2383	127	25	τ	τ	NOUN
ejpam-2383	127	26	-	-	NOUN
ejpam-2383	127	27	derivation	derivation	NOUN
ejpam-2383	127	28	of	of	ADP
ejpam-2383	127	29	r	r	NOUN
ejpam-2383	127	30	/	/	SYM
ejpam-2383	127	31	p(r	p(r	PROPN
ejpam-2383	127	32	)	)	PUNCT
ejpam-2383	127	33	.	.	PUNCT
ejpam-2383	128	1	also	also	ADV
ejpam-2383	128	2	a(σ(a	a(σ(a	PROPN
ejpam-2383	128	3	)	)	PUNCT
ejpam-2383	129	1	+	+	PRON
ejpam-2383	129	2	δ(a	δ(a	X
ejpam-2383	129	3	)	)	PUNCT
ejpam-2383	129	4	)	)	PUNCT
ejpam-2383	130	1	∈	∈	PROPN
ejpam-2383	130	2	p(r	p(r	PROPN
ejpam-2383	130	3	)	)	PUNCT
ejpam-2383	130	4	if	if	SCONJ
ejpam-2383	130	5	and	and	CCONJ
ejpam-2383	130	6	only	only	ADV
ejpam-2383	130	7	if	if	SCONJ
ejpam-2383	130	8	(	(	PUNCT
ejpam-2383	130	9	a+	a+	PUNCT
ejpam-2383	130	10	p(r))ρ(a+	p(r))ρ(a+	PROPN
ejpam-2383	130	11	p(r	p(r	PROPN
ejpam-2383	130	12	)	)	PUNCT
ejpam-2383	130	13	)	)	PUNCT
ejpam-2383	131	1	+	+	CCONJ
ejpam-2383	131	2	(	(	PUNCT
ejpam-2383	131	3	a+	a+	PUNCT
ejpam-2383	131	4	p(r))τ(a+	p(r))τ(a+	NOUN
ejpam-2383	131	5	p(r	p(r	PROPN
ejpam-2383	131	6	)	)	PUNCT
ejpam-2383	131	7	)	)	PUNCT
ejpam-2383	132	1	=	=	PUNCT
ejpam-2383	132	2	p(r)inr	p(r)inr	X
ejpam-2383	132	3	/	/	SYM
ejpam-2383	132	4	p(r	p(r	PROPN
ejpam-2383	132	5	)	)	PUNCT
ejpam-2383	132	6	.	.	PUNCT
ejpam-2383	133	1	then	then	ADV
ejpam-2383	133	2	as	as	ADP
ejpam-2383	133	3	in	in	ADP
ejpam-2383	133	4	proposition	proposition	NOUN
ejpam-2383	133	5	(	(	PUNCT
ejpam-2383	133	6	5	5	NUM
ejpam-2383	133	7	)	)	PUNCT
ejpam-2383	133	8	of	of	ADP
ejpam-2383	133	9	[	[	X
ejpam-2383	133	10	10	10	NUM
ejpam-2383	133	11	]	]	PUNCT
ejpam-2383	133	12	,	,	PUNCT
ejpam-2383	133	13	r	r	NOUN
ejpam-2383	133	14	is	be	AUX
ejpam-2383	133	15	a	a	DET
ejpam-2383	133	16	reduced	reduce	VERB
ejpam-2383	133	17	ring	ring	NOUN
ejpam-2383	133	18	.	.	PUNCT
ejpam-2383	134	1	hence	hence	ADV
ejpam-2383	134	2	it	it	PRON
ejpam-2383	134	3	is	be	AUX
ejpam-2383	134	4	2	2	NUM
ejpam-2383	134	5	-	-	PUNCT
ejpam-2383	134	6	primal	primal	ADJ
ejpam-2383	134	7	.	.	PUNCT
ejpam-2383	135	1	for	for	ADP
ejpam-2383	135	2	the	the	DET
ejpam-2383	135	3	proof	proof	NOUN
ejpam-2383	135	4	of	of	ADP
ejpam-2383	135	5	theorem	theorem	NOUN
ejpam-2383	135	6	2	2	NUM
ejpam-2383	135	7	,	,	PUNCT
ejpam-2383	135	8	we	we	PRON
ejpam-2383	135	9	need	need	VERB
ejpam-2383	135	10	the	the	DET
ejpam-2383	135	11	following	following	NOUN
ejpam-2383	135	12	:	:	PUNCT
ejpam-2383	135	13	proposition	proposition	NOUN
ejpam-2383	135	14	1	1	NUM
ejpam-2383	135	15	.	.	PUNCT
ejpam-2383	136	1	let	let	VERB
ejpam-2383	136	2	r	r	PRON
ejpam-2383	136	3	be	be	AUX
ejpam-2383	136	4	a	a	DET
ejpam-2383	136	5	noetherian	noetherian	ADJ
ejpam-2383	136	6	ring	ring	NOUN
ejpam-2383	136	7	which	which	PRON
ejpam-2383	136	8	is	be	AUX
ejpam-2383	136	9	also	also	ADV
ejpam-2383	136	10	an	an	DET
ejpam-2383	136	11	algebra	algebra	NOUN
ejpam-2383	136	12	over	over	ADP
ejpam-2383	136	13	q.	q.	PROPN
ejpam-2383	136	14	let	let	VERB
ejpam-2383	136	15	δ	δ	PRON
ejpam-2383	136	16	be	be	AUX
ejpam-2383	136	17	a	a	DET
ejpam-2383	136	18	derivation	derivation	NOUN
ejpam-2383	136	19	of	of	ADP
ejpam-2383	136	20	r.	r.	PROPN
ejpam-2383	136	21	then	then	ADV
ejpam-2383	136	22	δ(p(r	δ(p(r	PROPN
ejpam-2383	136	23	)	)	PUNCT
ejpam-2383	136	24	)	)	PUNCT
ejpam-2383	137	1	⊆	⊆	NUM
ejpam-2383	137	2	p(r	p(r	PROPN
ejpam-2383	137	3	)	)	PUNCT
ejpam-2383	137	4	.	.	PUNCT
ejpam-2383	138	1	proof	proof	NOUN
ejpam-2383	138	2	.	.	PUNCT
ejpam-2383	139	1	see	see	VERB
ejpam-2383	139	2	proposition	proposition	NOUN
ejpam-2383	139	3	(	(	PUNCT
ejpam-2383	139	4	1.1	1.1	NUM
ejpam-2383	139	5	)	)	PUNCT
ejpam-2383	139	6	of	of	ADP
ejpam-2383	139	7	[	[	X
ejpam-2383	139	8	1	1	NUM
ejpam-2383	139	9	]	]	PUNCT
ejpam-2383	139	10	.	.	PUNCT
ejpam-2383	140	1	proposition	proposition	NOUN
ejpam-2383	140	2	2	2	NUM
ejpam-2383	140	3	.	.	PUNCT
ejpam-2383	141	1	let	let	VERB
ejpam-2383	141	2	r	r	PRON
ejpam-2383	141	3	be	be	AUX
ejpam-2383	141	4	a	a	DET
ejpam-2383	141	5	2	2	NUM
ejpam-2383	141	6	-	-	PUNCT
ejpam-2383	141	7	primal	primal	ADJ
ejpam-2383	141	8	ring	ring	NOUN
ejpam-2383	141	9	.	.	PUNCT
ejpam-2383	142	1	let	let	VERB
ejpam-2383	142	2	σ	σ	NOUN
ejpam-2383	142	3	be	be	AUX
ejpam-2383	142	4	an	an	DET
ejpam-2383	142	5	automorphism	automorphism	NOUN
ejpam-2383	142	6	of	of	ADP
ejpam-2383	142	7	r	r	NOUN
ejpam-2383	142	8	and	and	CCONJ
ejpam-2383	142	9	δ	δ	PROPN
ejpam-2383	142	10	a	a	DET
ejpam-2383	142	11	σ	σ	NOUN
ejpam-2383	142	12	-	-	PUNCT
ejpam-2383	142	13	derivation	derivation	NOUN
ejpam-2383	142	14	of	of	ADP
ejpam-2383	142	15	r	r	NOUN
ejpam-2383	142	16	such	such	ADJ
ejpam-2383	142	17	that	that	SCONJ
ejpam-2383	142	18	δ(p(r	δ(p(r	PROPN
ejpam-2383	142	19	)	)	PUNCT
ejpam-2383	142	20	)	)	PUNCT
ejpam-2383	143	1	⊆	⊆	NUM
ejpam-2383	143	2	p(r	p(r	PROPN
ejpam-2383	143	3	)	)	PUNCT
ejpam-2383	143	4	.	.	PUNCT
ejpam-2383	144	1	if	if	SCONJ
ejpam-2383	144	2	p	p	PROPN
ejpam-2383	144	3	∈	∈	PROPN
ejpam-2383	144	4	min.spec(r	min.spec(r	NOUN
ejpam-2383	144	5	)	)	PUNCT
ejpam-2383	144	6	is	be	AUX
ejpam-2383	144	7	such	such	ADJ
ejpam-2383	144	8	that	that	SCONJ
ejpam-2383	144	9	σ(p	σ(p	PROPN
ejpam-2383	144	10	)	)	PUNCT
ejpam-2383	145	1	=	=	SYM
ejpam-2383	146	1	p	p	X
ejpam-2383	146	2	,	,	PUNCT
ejpam-2383	146	3	then	then	ADV
ejpam-2383	146	4	δ(p	δ(p	PROPN
ejpam-2383	146	5	)	)	PUNCT
ejpam-2383	146	6	⊆	⊆	NUM
ejpam-2383	146	7	p.	p.	NOUN
ejpam-2383	146	8	proof	proof	NOUN
ejpam-2383	146	9	.	.	PUNCT
ejpam-2383	147	1	let	let	VERB
ejpam-2383	147	2	p	p	PRON
ejpam-2383	147	3	∈	∈	PROPN
ejpam-2383	147	4	min.spec(r	min.spec(r	PROPN
ejpam-2383	147	5	)	)	PUNCT
ejpam-2383	147	6	.	.	PUNCT
ejpam-2383	148	1	now	now	ADV
ejpam-2383	148	2	p	p	X
ejpam-2383	148	3	is	be	AUX
ejpam-2383	148	4	a	a	DET
ejpam-2383	148	5	completely	completely	ADV
ejpam-2383	148	6	prime	prime	ADJ
ejpam-2383	148	7	ideal	ideal	NOUN
ejpam-2383	148	8	,	,	PUNCT
ejpam-2383	148	9	therefore	therefore	ADV
ejpam-2383	148	10	,	,	PUNCT
ejpam-2383	148	11	for	for	ADP
ejpam-2383	148	12	any	any	DET
ejpam-2383	148	13	a	a	DET
ejpam-2383	148	14	∈	∈	PROPN
ejpam-2383	148	15	p	p	NOUN
ejpam-2383	148	16	there	there	PRON
ejpam-2383	148	17	exists	exist	VERB
ejpam-2383	148	18	b	b	NOUN
ejpam-2383	148	19	/∈	/∈	PUNCT
ejpam-2383	148	20	p	p	X
ejpam-2383	149	1	such	such	ADJ
ejpam-2383	149	2	that	that	SCONJ
ejpam-2383	149	3	ab	ab	PROPN
ejpam-2383	149	4	∈	∈	PROPN
ejpam-2383	149	5	p(r	p(r	PROPN
ejpam-2383	149	6	)	)	PUNCT
ejpam-2383	149	7	by	by	ADP
ejpam-2383	149	8	corollary	corollary	ADJ
ejpam-2383	149	9	(	(	PUNCT
ejpam-2383	149	10	1.10	1.10	NUM
ejpam-2383	149	11	)	)	PUNCT
ejpam-2383	149	12	of	of	ADP
ejpam-2383	149	13	shin	shin	NOUN
ejpam-2383	149	14	[	[	X
ejpam-2383	149	15	13	13	NUM
ejpam-2383	149	16	]	]	PUNCT
ejpam-2383	149	17	.	.	PUNCT
ejpam-2383	150	1	now	now	ADV
ejpam-2383	150	2	δ(p(r	δ(p(r	PROPN
ejpam-2383	150	3	)	)	PUNCT
ejpam-2383	150	4	)	)	PUNCT
ejpam-2383	151	1	⊆	⊆	NUM
ejpam-2383	151	2	p(r	p(r	PROPN
ejpam-2383	151	3	)	)	PUNCT
ejpam-2383	151	4	,	,	PUNCT
ejpam-2383	151	5	and	and	CCONJ
ejpam-2383	151	6	therefore	therefore	ADV
ejpam-2383	151	7	δ(ab	δ(ab	NOUN
ejpam-2383	151	8	)	)	PUNCT
ejpam-2383	151	9	⊆	⊆	NUM
ejpam-2383	151	10	p(r	p(r	PROPN
ejpam-2383	151	11	)	)	PUNCT
ejpam-2383	151	12	;	;	PUNCT
ejpam-2383	151	13	i.e.	i.e.	X
ejpam-2383	151	14	,	,	PUNCT
ejpam-2383	151	15	δ(a)σ(b	δ(a)σ(b	NOUN
ejpam-2383	151	16	)	)	PUNCT
ejpam-2383	151	17	+	+	NUM
ejpam-2383	151	18	aδ(b	aδ(b	NOUN
ejpam-2383	151	19	)	)	PUNCT
ejpam-2383	151	20	∈	∈	PROPN
ejpam-2383	151	21	p(r	p(r	PROPN
ejpam-2383	151	22	)	)	PUNCT
ejpam-2383	151	23	⊆	⊆	NUM
ejpam-2383	151	24	p.	p.	NOUN
ejpam-2383	151	25	now	now	ADV
ejpam-2383	151	26	aδ(b	aδ(b	VERB
ejpam-2383	151	27	)	)	PUNCT
ejpam-2383	151	28	∈	∈	PROPN
ejpam-2383	152	1	p	p	NOUN
ejpam-2383	152	2	implies	imply	VERB
ejpam-2383	152	3	that	that	SCONJ
ejpam-2383	152	4	δ(a)σ(b	δ(a)σ(b	NOUN
ejpam-2383	152	5	)	)	PUNCT
ejpam-2383	152	6	∈	∈	PROPN
ejpam-2383	152	7	p.	p.	NOUN
ejpam-2383	152	8	now	now	ADV
ejpam-2383	152	9	σ(p	σ(p	X
ejpam-2383	152	10	)	)	PUNCT
ejpam-2383	153	1	=	=	SYM
ejpam-2383	153	2	p	p	NOUN
ejpam-2383	153	3	implies	imply	VERB
ejpam-2383	153	4	that	that	SCONJ
ejpam-2383	153	5	σ(b	σ(b	PROPN
ejpam-2383	153	6	)	)	PUNCT
ejpam-2383	153	7	/∈	/∈	PUNCT
ejpam-2383	154	1	p	p	NOUN
ejpam-2383	155	1	and	and	CCONJ
ejpam-2383	155	2	since	since	SCONJ
ejpam-2383	155	3	p	p	NOUN
ejpam-2383	155	4	is	be	AUX
ejpam-2383	155	5	completely	completely	ADV
ejpam-2383	155	6	prime	prime	ADJ
ejpam-2383	155	7	in	in	ADP
ejpam-2383	155	8	r	r	NOUN
ejpam-2383	155	9	,	,	PUNCT
ejpam-2383	155	10	we	we	PRON
ejpam-2383	155	11	have	have	VERB
ejpam-2383	155	12	δ(a	δ(a	PROPN
ejpam-2383	155	13	)	)	PUNCT
ejpam-2383	155	14	∈	∈	PROPN
ejpam-2383	155	15	p.	p.	NOUN
ejpam-2383	155	16	hence	hence	ADV
ejpam-2383	155	17	δ(p	δ(p	X
ejpam-2383	155	18	)	)	PUNCT
ejpam-2383	155	19	⊆	⊆	NUM
ejpam-2383	155	20	p.	p.	NOUN
ejpam-2383	155	21	theorem	theorem	NOUN
ejpam-2383	155	22	2	2	X
ejpam-2383	155	23	.	.	PUNCT
ejpam-2383	156	1	let	let	VERB
ejpam-2383	156	2	r	r	PRON
ejpam-2383	156	3	be	be	AUX
ejpam-2383	156	4	a	a	DET
ejpam-2383	156	5	noetherian	noetherian	ADJ
ejpam-2383	156	6	,	,	PUNCT
ejpam-2383	156	7	integral	integral	ADJ
ejpam-2383	156	8	domain	domain	NOUN
ejpam-2383	156	9	which	which	PRON
ejpam-2383	156	10	is	be	AUX
ejpam-2383	156	11	also	also	ADV
ejpam-2383	156	12	an	an	DET
ejpam-2383	156	13	algebra	algebra	NOUN
ejpam-2383	156	14	over	over	ADP
ejpam-2383	156	15	q.	q.	PROPN
ejpam-2383	156	16	let	let	VERB
ejpam-2383	156	17	σ	σ	NOUN
ejpam-2383	156	18	be	be	AUX
ejpam-2383	156	19	an	an	DET
ejpam-2383	156	20	automorphism	automorphism	NOUN
ejpam-2383	156	21	of	of	ADP
ejpam-2383	156	22	r	r	NOUN
ejpam-2383	156	23	and	and	CCONJ
ejpam-2383	156	24	δ	δ	PROPN
ejpam-2383	157	1	a	a	DET
ejpam-2383	157	2	σ	σ	NOUN
ejpam-2383	157	3	-	-	PUNCT
ejpam-2383	157	4	derivation	derivation	NOUN
ejpam-2383	157	5	of	of	ADP
ejpam-2383	157	6	r	r	NOUN
ejpam-2383	157	7	such	such	ADJ
ejpam-2383	157	8	that	that	SCONJ
ejpam-2383	157	9	r	r	NOUN
ejpam-2383	157	10	is	be	AUX
ejpam-2383	157	11	a	a	DET
ejpam-2383	157	12	(	(	PUNCT
ejpam-2383	157	13	σ	σ	NOUN
ejpam-2383	157	14	,	,	PUNCT
ejpam-2383	157	15	δ)-ring	δ)-ring	ADJ
ejpam-2383	157	16	.	.	PUNCT
ejpam-2383	158	1	if	if	SCONJ
ejpam-2383	158	2	p	p	PROPN
ejpam-2383	158	3	∈	∈	PROPN
ejpam-2383	158	4	min.spec(r	min.spec(r	NOUN
ejpam-2383	158	5	)	)	PUNCT
ejpam-2383	158	6	is	be	AUX
ejpam-2383	158	7	such	such	ADJ
ejpam-2383	158	8	that	that	SCONJ
ejpam-2383	158	9	σ(p	σ(p	PROPN
ejpam-2383	158	10	)	)	PUNCT
ejpam-2383	159	1	=	=	SYM
ejpam-2383	160	1	p	p	X
ejpam-2383	160	2	,	,	PUNCT
ejpam-2383	160	3	then	then	ADV
ejpam-2383	160	4	δ(p	δ(p	PROPN
ejpam-2383	160	5	)	)	PUNCT
ejpam-2383	160	6	⊆	⊆	NUM
ejpam-2383	160	7	p.	p.	NOUN
ejpam-2383	160	8	proof	proof	NOUN
ejpam-2383	160	9	.	.	PUNCT
ejpam-2383	161	1	let	let	VERB
ejpam-2383	161	2	p	p	PRON
ejpam-2383	161	3	∈	∈	PROPN
ejpam-2383	161	4	min.spec(r	min.spec(r	PROPN
ejpam-2383	161	5	)	)	PUNCT
ejpam-2383	161	6	.	.	PUNCT
ejpam-2383	162	1	then	then	ADV
ejpam-2383	162	2	by	by	ADP
ejpam-2383	162	3	proposition	proposition	NOUN
ejpam-2383	162	4	1	1	NUM
ejpam-2383	162	5	,	,	PUNCT
ejpam-2383	162	6	δ(p(r	δ(p(r	PROPN
ejpam-2383	162	7	)	)	PUNCT
ejpam-2383	162	8	)	)	PUNCT
ejpam-2383	163	1	⊆	⊆	NUM
ejpam-2383	163	2	p(r	p(r	PROPN
ejpam-2383	163	3	)	)	PUNCT
ejpam-2383	163	4	and	and	CCONJ
ejpam-2383	163	5	by	by	ADP
ejpam-2383	163	6	theorem	theorem	NOUN
ejpam-2383	163	7	1	1	NUM
ejpam-2383	163	8	,	,	PUNCT
ejpam-2383	163	9	r	r	NOUN
ejpam-2383	163	10	is	be	AUX
ejpam-2383	163	11	2	2	NUM
ejpam-2383	163	12	-	-	PUNCT
ejpam-2383	163	13	primal	primal	ADJ
ejpam-2383	163	14	.	.	PUNCT
ejpam-2383	164	1	since	since	SCONJ
ejpam-2383	164	2	σ(p	σ(p	PROPN
ejpam-2383	164	3	)	)	PUNCT
ejpam-2383	164	4	=	=	SYM
ejpam-2383	165	1	p	p	NOUN
ejpam-2383	165	2	,	,	PUNCT
ejpam-2383	165	3	the	the	DET
ejpam-2383	165	4	result	result	NOUN
ejpam-2383	165	5	follows	follow	VERB
ejpam-2383	165	6	by	by	ADP
ejpam-2383	165	7	proposition	proposition	NOUN
ejpam-2383	165	8	2	2	NUM
ejpam-2383	165	9	.	.	X
ejpam-2383	166	1	for	for	ADP
ejpam-2383	166	2	the	the	DET
ejpam-2383	166	3	proof	proof	NOUN
ejpam-2383	166	4	of	of	ADP
ejpam-2383	166	5	theorem	theorem	ADJ
ejpam-2383	166	6	4	4	NUM
ejpam-2383	166	7	,	,	PUNCT
ejpam-2383	166	8	we	we	PRON
ejpam-2383	166	9	need	need	VERB
ejpam-2383	166	10	the	the	DET
ejpam-2383	166	11	following	following	NOUN
ejpam-2383	166	12	:	:	PUNCT
ejpam-2383	166	13	theorem	theorem	NOUN
ejpam-2383	166	14	3	3	X
ejpam-2383	166	15	.	.	PUNCT
ejpam-2383	167	1	let	let	VERB
ejpam-2383	167	2	r	r	PRON
ejpam-2383	167	3	be	be	AUX
ejpam-2383	167	4	a	a	DET
ejpam-2383	167	5	ring	ring	NOUN
ejpam-2383	167	6	.	.	PUNCT
ejpam-2383	168	1	let	let	VERB
ejpam-2383	168	2	σ	σ	NOUN
ejpam-2383	168	3	be	be	AUX
ejpam-2383	168	4	an	an	DET
ejpam-2383	168	5	automorphism	automorphism	NOUN
ejpam-2383	168	6	of	of	ADP
ejpam-2383	168	7	r	r	NOUN
ejpam-2383	168	8	and	and	CCONJ
ejpam-2383	168	9	δ	δ	PROPN
ejpam-2383	168	10	a	a	DET
ejpam-2383	168	11	σ	σ	NOUN
ejpam-2383	168	12	-	-	PUNCT
ejpam-2383	168	13	derivation	derivation	NOUN
ejpam-2383	168	14	of	of	ADP
ejpam-2383	168	15	r.	r.	PROPN
ejpam-2383	168	16	then	then	ADV
ejpam-2383	168	17	:	:	PUNCT
ejpam-2383	168	18	(	(	PUNCT
ejpam-2383	168	19	i	i	NOUN
ejpam-2383	168	20	)	)	PUNCT
ejpam-2383	168	21	for	for	ADP
ejpam-2383	168	22	any	any	DET
ejpam-2383	168	23	completely	completely	ADV
ejpam-2383	168	24	prime	prime	ADJ
ejpam-2383	168	25	ideal	ideal	NOUN
ejpam-2383	168	26	p	p	NOUN
ejpam-2383	168	27	of	of	ADP
ejpam-2383	168	28	r	r	NOUN
ejpam-2383	168	29	with	with	ADP
ejpam-2383	168	30	σ(p	σ(p	PROPN
ejpam-2383	168	31	)	)	PUNCT
ejpam-2383	168	32	=	=	SYM
ejpam-2383	168	33	p	p	NOUN
ejpam-2383	168	34	and	and	CCONJ
ejpam-2383	168	35	δ(p	δ(p	NUM
ejpam-2383	168	36	)	)	PUNCT
ejpam-2383	168	37	⊆	⊆	NUM
ejpam-2383	168	38	p	p	NOUN
ejpam-2383	168	39	,	,	PUNCT
ejpam-2383	168	40	o(p	o(p	PROPN
ejpam-2383	168	41	)	)	PUNCT
ejpam-2383	168	42	is	be	AUX
ejpam-2383	168	43	a	a	DET
ejpam-2383	168	44	completely	completely	ADV
ejpam-2383	168	45	prime	prime	ADJ
ejpam-2383	168	46	ideal	ideal	NOUN
ejpam-2383	168	47	of	of	ADP
ejpam-2383	168	48	o(r	o(r	PROPN
ejpam-2383	168	49	)	)	PUNCT
ejpam-2383	168	50	.	.	PUNCT
ejpam-2383	169	1	(	(	PUNCT
ejpam-2383	169	2	ii	ii	NOUN
ejpam-2383	169	3	)	)	PUNCT
ejpam-2383	169	4	for	for	ADP
ejpam-2383	169	5	any	any	DET
ejpam-2383	169	6	completely	completely	ADV
ejpam-2383	169	7	prime	prime	ADJ
ejpam-2383	169	8	ideal	ideal	ADJ
ejpam-2383	169	9	u	u	NOUN
ejpam-2383	169	10	of	of	ADP
ejpam-2383	169	11	o(r	o(r	PROPN
ejpam-2383	169	12	)	)	PUNCT
ejpam-2383	169	13	,	,	PUNCT
ejpam-2383	169	14	u	u	NOUN
ejpam-2383	169	15	∩	∩	NOUN
ejpam-2383	169	16	r	r	NOUN
ejpam-2383	169	17	is	be	AUX
ejpam-2383	169	18	a	a	DET
ejpam-2383	169	19	completely	completely	ADV
ejpam-2383	169	20	prime	prime	ADJ
ejpam-2383	169	21	ideal	ideal	NOUN
ejpam-2383	169	22	of	of	ADP
ejpam-2383	169	23	r.	r.	PROPN
ejpam-2383	169	24	proof	proof	NOUN
ejpam-2383	169	25	.	.	PUNCT
ejpam-2383	170	1	see	see	VERB
ejpam-2383	170	2	theorem	theorem	NOUN
ejpam-2383	170	3	(	(	PUNCT
ejpam-2383	170	4	2.4	2.4	NUM
ejpam-2383	170	5	)	)	PUNCT
ejpam-2383	170	6	of	of	ADP
ejpam-2383	170	7	[	[	X
ejpam-2383	170	8	2	2	NUM
ejpam-2383	170	9	]	]	PUNCT
ejpam-2383	170	10	.	.	PUNCT
ejpam-2383	171	1	references	reference	NOUN
ejpam-2383	171	2	467	467	NUM
ejpam-2383	171	3	theorem	theorem	VERB
ejpam-2383	171	4	4	4	NUM
ejpam-2383	171	5	.	.	PUNCT
ejpam-2383	172	1	let	let	VERB
ejpam-2383	172	2	r	r	PRON
ejpam-2383	172	3	be	be	AUX
ejpam-2383	172	4	a	a	DET
ejpam-2383	172	5	noetherian	noetherian	ADJ
ejpam-2383	172	6	,	,	PUNCT
ejpam-2383	172	7	integral	integral	ADJ
ejpam-2383	172	8	domain	domain	NOUN
ejpam-2383	172	9	which	which	PRON
ejpam-2383	172	10	is	be	AUX
ejpam-2383	172	11	also	also	ADV
ejpam-2383	172	12	an	an	DET
ejpam-2383	172	13	algebra	algebra	NOUN
ejpam-2383	172	14	over	over	ADP
ejpam-2383	172	15	q.	q.	PROPN
ejpam-2383	172	16	let	let	VERB
ejpam-2383	172	17	σ	σ	NOUN
ejpam-2383	172	18	be	be	AUX
ejpam-2383	172	19	an	an	DET
ejpam-2383	172	20	automorphism	automorphism	NOUN
ejpam-2383	172	21	of	of	ADP
ejpam-2383	172	22	r	r	NOUN
ejpam-2383	172	23	and	and	CCONJ
ejpam-2383	172	24	δ	δ	PROPN
ejpam-2383	173	1	a	a	DET
ejpam-2383	173	2	σ	σ	NOUN
ejpam-2383	173	3	-	-	PUNCT
ejpam-2383	173	4	derivation	derivation	NOUN
ejpam-2383	173	5	of	of	ADP
ejpam-2383	173	6	r	r	NOUN
ejpam-2383	173	7	such	such	ADJ
ejpam-2383	173	8	that	that	SCONJ
ejpam-2383	173	9	r	r	NOUN
ejpam-2383	173	10	is	be	AUX
ejpam-2383	173	11	a	a	DET
ejpam-2383	173	12	(	(	PUNCT
ejpam-2383	173	13	σ	σ	NOUN
ejpam-2383	173	14	,	,	PUNCT
ejpam-2383	173	15	δ)-ring	δ)-ring	PROPN
ejpam-2383	173	16	and	and	CCONJ
ejpam-2383	173	17	δ(p(r	δ(p(r	PROPN
ejpam-2383	173	18	)	)	PUNCT
ejpam-2383	173	19	)	)	PUNCT
ejpam-2383	174	1	⊆	⊆	NUM
ejpam-2383	174	2	p(r	p(r	PROPN
ejpam-2383	174	3	)	)	PUNCT
ejpam-2383	174	4	.	.	PUNCT
ejpam-2383	175	1	let	let	VERB
ejpam-2383	175	2	p	p	PRON
ejpam-2383	175	3	∈	∈	PROPN
ejpam-2383	175	4	min.spec(r	min.spec(r	PROPN
ejpam-2383	175	5	)	)	PUNCT
ejpam-2383	175	6	be	be	AUX
ejpam-2383	175	7	such	such	ADJ
ejpam-2383	175	8	that	that	SCONJ
ejpam-2383	175	9	σ(p	σ(p	PROPN
ejpam-2383	175	10	)	)	PUNCT
ejpam-2383	176	1	=	=	SYM
ejpam-2383	176	2	p	p	NOUN
ejpam-2383	176	3	,	,	PUNCT
ejpam-2383	176	4	then	then	ADV
ejpam-2383	176	5	o(p	o(p	PROPN
ejpam-2383	176	6	)	)	PUNCT
ejpam-2383	176	7	is	be	AUX
ejpam-2383	176	8	a	a	DET
ejpam-2383	176	9	completely	completely	ADV
ejpam-2383	176	10	prime	prime	ADJ
ejpam-2383	176	11	ideal	ideal	NOUN
ejpam-2383	176	12	of	of	ADP
ejpam-2383	176	13	o(r	o(r	PROPN
ejpam-2383	176	14	)	)	PUNCT
ejpam-2383	176	15	.	.	PUNCT
ejpam-2383	177	1	proof	proof	NOUN
ejpam-2383	177	2	.	.	PUNCT
ejpam-2383	178	1	r	r	NOUN
ejpam-2383	178	2	is	be	AUX
ejpam-2383	178	3	2	2	NUM
ejpam-2383	178	4	-	-	PUNCT
ejpam-2383	178	5	primal	primal	ADJ
ejpam-2383	178	6	by	by	ADP
ejpam-2383	178	7	theorem	theorem	NOUN
ejpam-2383	178	8	1	1	NUM
ejpam-2383	178	9	and	and	CCONJ
ejpam-2383	178	10	so	so	ADV
ejpam-2383	178	11	by	by	ADP
ejpam-2383	178	12	proposition	proposition	NOUN
ejpam-2383	178	13	2	2	NUM
ejpam-2383	178	14	,	,	PUNCT
ejpam-2383	178	15	δ(p	δ(p	NUM
ejpam-2383	178	16	)	)	PUNCT
ejpam-2383	178	17	⊆	⊆	NUM
ejpam-2383	178	18	p	p	NOUN
ejpam-2383	178	19	and	and	CCONJ
ejpam-2383	178	20	as	as	ADP
ejpam-2383	178	21	in	in	ADP
ejpam-2383	178	22	proof	proof	NOUN
ejpam-2383	178	23	of	of	ADP
ejpam-2383	178	24	proposition	proposition	NOUN
ejpam-2383	178	25	2	2	NUM
ejpam-2383	178	26	above	above	ADV
ejpam-2383	178	27	,	,	PUNCT
ejpam-2383	178	28	p	p	NOUN
ejpam-2383	178	29	is	be	AUX
ejpam-2383	178	30	a	a	DET
ejpam-2383	178	31	completely	completely	ADV
ejpam-2383	178	32	prime	prime	ADJ
ejpam-2383	178	33	ideal	ideal	NOUN
ejpam-2383	178	34	of	of	ADP
ejpam-2383	178	35	r.	r.	PROPN
ejpam-2383	178	36	now	now	ADV
ejpam-2383	178	37	use	use	VERB
ejpam-2383	178	38	theorem	theorem	NOUN
ejpam-2383	178	39	3	3	NUM
ejpam-2383	178	40	and	and	CCONJ
ejpam-2383	178	41	the	the	DET
ejpam-2383	178	42	proof	proof	NOUN
ejpam-2383	178	43	is	be	AUX
ejpam-2383	178	44	complete	complete	ADJ
ejpam-2383	178	45	.	.	PUNCT
ejpam-2383	179	1	references	reference	NOUN
ejpam-2383	179	2	[	[	X
ejpam-2383	179	3	1	1	X
ejpam-2383	179	4	]	]	PUNCT
ejpam-2383	179	5	v.	v.	PROPN
ejpam-2383	179	6	k.	k.	PROPN
ejpam-2383	179	7	bhat	bhat	PROPN
ejpam-2383	179	8	.	.	PUNCT
ejpam-2383	180	1	differential	differential	ADJ
ejpam-2383	180	2	operator	operator	NOUN
ejpam-2383	180	3	rings	ring	NOUN
ejpam-2383	180	4	over	over	ADP
ejpam-2383	180	5	2	2	NUM
ejpam-2383	180	6	-	-	PUNCT
ejpam-2383	180	7	primal	primal	ADJ
ejpam-2383	180	8	rings	ring	NOUN
ejpam-2383	180	9	,	,	PUNCT
ejpam-2383	180	10	ukranian	ukranian	PROPN
ejpam-2383	180	11	mathematical	mathematical	ADJ
ejpam-2383	180	12	bulletin	bulletin	NOUN
ejpam-2383	180	13	,	,	PUNCT
ejpam-2383	180	14	5(2	5(2	NUM
ejpam-2383	180	15	)	)	PUNCT
ejpam-2383	180	16	,	,	PUNCT
ejpam-2383	180	17	153	153	NUM
ejpam-2383	180	18	-	-	SYM
ejpam-2383	180	19	158	158	NUM
ejpam-2383	180	20	.	.	PUNCT
ejpam-2383	180	21	2008	2008	NUM
ejpam-2383	180	22	.	.	PUNCT
ejpam-2383	181	1	[	[	X
ejpam-2383	181	2	2	2	X
ejpam-2383	181	3	]	]	PUNCT
ejpam-2383	181	4	v.	v.	PROPN
ejpam-2383	181	5	k.	k.	PROPN
ejpam-2383	181	6	bhat	bhat	PROPN
ejpam-2383	181	7	.	.	PUNCT
ejpam-2383	182	1	a	a	DET
ejpam-2383	182	2	note	note	NOUN
ejpam-2383	182	3	on	on	ADP
ejpam-2383	182	4	completely	completely	ADV
ejpam-2383	182	5	prime	prime	ADJ
ejpam-2383	182	6	ideals	ideal	NOUN
ejpam-2383	182	7	of	of	ADP
ejpam-2383	182	8	ore	ore	NOUN
ejpam-2383	182	9	extensions	extension	NOUN
ejpam-2383	182	10	,	,	PUNCT
ejpam-2383	182	11	international	international	ADJ
ejpam-2383	182	12	journal	journal	NOUN
ejpam-2383	182	13	of	of	ADP
ejpam-2383	182	14	algebra	algebra	NOUN
ejpam-2383	182	15	and	and	CCONJ
ejpam-2383	182	16	computation	computation	NOUN
ejpam-2383	182	17	,	,	PUNCT
ejpam-2383	182	18	20(3	20(3	NOUN
ejpam-2383	182	19	)	)	PUNCT
ejpam-2383	182	20	,	,	PUNCT
ejpam-2383	182	21	457	457	NUM
ejpam-2383	182	22	-	-	SYM
ejpam-2383	182	23	463	463	NUM
ejpam-2383	182	24	.	.	PUNCT
ejpam-2383	183	1	2010	2010	NUM
ejpam-2383	183	2	.	.	PUNCT
ejpam-2383	184	1	[	[	X
ejpam-2383	184	2	3	3	X
ejpam-2383	184	3	]	]	PUNCT
ejpam-2383	184	4	v.	v.	PROPN
ejpam-2383	184	5	k.	k.	PROPN
ejpam-2383	184	6	bhat	bhat	PROPN
ejpam-2383	184	7	.	.	PUNCT
ejpam-2383	185	1	minimal	minimal	ADJ
ejpam-2383	185	2	prime	prime	ADJ
ejpam-2383	185	3	ideals	ideal	NOUN
ejpam-2383	185	4	of	of	ADP
ejpam-2383	185	5	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-2383	185	6	and	and	CCONJ
ejpam-2383	185	7	their	their	PRON
ejpam-2383	185	8	extensions	extension	NOUN
ejpam-2383	185	9	,	,	PUNCT
ejpam-2383	185	10	armenian	armenian	ADJ
ejpam-2383	185	11	journal	journal	NOUN
ejpam-2383	185	12	of	of	ADP
ejpam-2383	185	13	mathematics	mathematic	NOUN
ejpam-2383	185	14	,	,	PUNCT
ejpam-2383	185	15	5(2	5(2	NUM
ejpam-2383	185	16	)	)	PUNCT
ejpam-2383	185	17	,	,	PUNCT
ejpam-2383	185	18	98	98	NUM
ejpam-2383	185	19	-	-	SYM
ejpam-2383	185	20	104	104	NUM
ejpam-2383	185	21	.	.	PUNCT
ejpam-2383	185	22	2013	2013	NUM
ejpam-2383	185	23	.	.	PUNCT
ejpam-2383	186	1	[	[	X
ejpam-2383	186	2	4	4	X
ejpam-2383	186	3	]	]	X
ejpam-2383	186	4	g.	g.	PROPN
ejpam-2383	186	5	f.	f.	PROPN
ejpam-2383	186	6	birkenmeier	birkenmeier	PROPN
ejpam-2383	186	7	,	,	PUNCT
ejpam-2383	186	8	h.	h.	PROPN
ejpam-2383	186	9	e.	e.	PROPN
ejpam-2383	186	10	heatherly	heatherly	PROPN
ejpam-2383	186	11	,	,	PUNCT
ejpam-2383	186	12	and	and	CCONJ
ejpam-2383	186	13	e.	e.	PROPN
ejpam-2383	186	14	k.	k.	PROPN
ejpam-2383	186	15	lee	lee	PROPN
ejpam-2383	186	16	.	.	PROPN
ejpam-2383	187	1	completely	completely	ADV
ejpam-2383	187	2	prime	prime	ADJ
ejpam-2383	187	3	ideals	ideal	NOUN
ejpam-2383	187	4	and	and	CCONJ
ejpam-2383	187	5	associated	associated	ADJ
ejpam-2383	187	6	radicals	radical	NOUN
ejpam-2383	187	7	,	,	PUNCT
ejpam-2383	187	8	in	in	ADV
ejpam-2383	187	9	.	.	PUNCT
ejpam-2383	188	1	s.	s.	PROPN
ejpam-2383	188	2	k.jain	k.jain	PROPN
ejpam-2383	188	3	,	,	PUNCT
ejpam-2383	188	4	s.	s.	PROPN
ejpam-2383	188	5	t.	t.	PROPN
ejpam-2383	188	6	rizvi	rizvi	PROPN
ejpam-2383	188	7	,	,	PUNCT
ejpam-2383	188	8	eds	ed	NOUN
ejpam-2383	188	9	,	,	PUNCT
ejpam-2383	188	10	proc	proc	NOUN
ejpam-2383	188	11	.	.	PUNCT
ejpam-2383	189	1	biennal	biennal	ADJ
ejpam-2383	189	2	ohio	ohio	PROPN
ejpam-2383	189	3	state	state	PROPN
ejpam-2383	189	4	denison	denison	PROPN
ejpam-2383	189	5	conference	conference	NOUN
ejpam-2383	189	6	1992	1992	NUM
ejpam-2383	189	7	.	.	PUNCT
ejpam-2383	190	1	singapore	singapore	PROPN
ejpam-2383	190	2	-	-	PUNCT
ejpam-2383	190	3	new	new	PROPN
ejpam-2383	190	4	jersey	jersey	PROPN
ejpam-2383	190	5	-	-	PUNCT
ejpam-2383	190	6	london	london	PROPN
ejpam-2383	190	7	-	-	PUNCT
ejpam-2383	190	8	hongkong	hongkong	PROPN
ejpam-2383	190	9	:	:	PUNCT
ejpam-2383	190	10	world	world	NOUN
ejpam-2383	190	11	scientific	scientific	ADJ
ejpam-2383	190	12	(	(	PUNCT
ejpam-2383	190	13	singapore	singapore	PROPN
ejpam-2383	190	14	)	)	PUNCT
ejpam-2383	190	15	,	,	PUNCT
ejpam-2383	190	16	102	102	NUM
ejpam-2383	190	17	-	-	SYM
ejpam-2383	190	18	129	129	NUM
ejpam-2383	190	19	.	.	PUNCT
ejpam-2383	190	20	1993	1993	NUM
ejpam-2383	190	21	.	.	PUNCT
ejpam-2383	191	1	[	[	X
ejpam-2383	191	2	5	5	X
ejpam-2383	191	3	]	]	PUNCT
ejpam-2383	191	4	g.	g.	PROPN
ejpam-2383	191	5	f.	f.	PROPN
ejpam-2383	191	6	birkenmeier	birkenmeier	PROPN
ejpam-2383	191	7	,	,	PUNCT
ejpam-2383	191	8	j.	j.	PROPN
ejpam-2383	191	9	y.	y.	PROPN
ejpam-2383	191	10	kim	kim	PROPN
ejpam-2383	191	11	,	,	PUNCT
ejpam-2383	191	12	and	and	CCONJ
ejpam-2383	191	13	j.	j.	PROPN
ejpam-2383	191	14	k.	k.	PROPN
ejpam-2383	191	15	park	park	PROPN
ejpam-2383	191	16	.	.	PUNCT
ejpam-2383	192	1	polynomial	polynomial	ADJ
ejpam-2383	192	2	extensions	extension	NOUN
ejpam-2383	192	3	of	of	ADP
ejpam-2383	192	4	baer	baer	PROPN
ejpam-2383	192	5	and	and	CCONJ
ejpam-2383	192	6	quasi	quasi	PROPN
ejpam-2383	192	7	-	-	PROPN
ejpam-2383	192	8	baer	baer	PROPN
ejpam-2383	192	9	rings	rings	PROPN
ejpam-2383	192	10	,	,	PUNCT
ejpam-2383	192	11	journal	journal	NOUN
ejpam-2383	192	12	of	of	ADP
ejpam-2383	192	13	pure	pure	ADJ
ejpam-2383	192	14	and	and	CCONJ
ejpam-2383	192	15	applied	applied	ADJ
ejpam-2383	192	16	algebra	algebra	NOUN
ejpam-2383	192	17	,	,	PUNCT
ejpam-2383	192	18	159(1	159(1	NUM
ejpam-2383	192	19	)	)	PUNCT
ejpam-2383	192	20	,	,	PUNCT
ejpam-2383	192	21	25	25	NUM
ejpam-2383	192	22	-	-	SYM
ejpam-2383	192	23	41	41	NUM
ejpam-2383	192	24	.	.	PUNCT
ejpam-2383	192	25	2001	2001	NUM
ejpam-2383	192	26	.	.	PUNCT
ejpam-2383	193	1	[	[	X
ejpam-2383	193	2	6	6	NUM
ejpam-2383	193	3	]	]	PUNCT
ejpam-2383	193	4	p.	p.	PROPN
ejpam-2383	193	5	gabriel	gabriel	PROPN
ejpam-2383	193	6	.	.	PUNCT
ejpam-2383	194	1	representations	representation	NOUN
ejpam-2383	194	2	des	des	PROPN
ejpam-2383	194	3	algebres	algebres	PROPN
ejpam-2383	194	4	de	de	PROPN
ejpam-2383	194	5	lie	lie	NOUN
ejpam-2383	194	6	resoulubles	resouluble	NOUN
ejpam-2383	194	7	(	(	PUNCT
ejpam-2383	194	8	d	d	PROPN
ejpam-2383	194	9	apres	apres	PROPN
ejpam-2383	194	10	j.	j.	PROPN
ejpam-2383	194	11	dixmier	dixmier	PROPN
ejpam-2383	194	12	)	)	PUNCT
ejpam-2383	194	13	.	.	PUNCT
ejpam-2383	195	1	in	in	ADP
ejpam-2383	195	2	seminaire	seminaire	PROPN
ejpam-2383	195	3	bourbaki	bourbaki	PROPN
ejpam-2383	195	4	,	,	PUNCT
ejpam-2383	195	5	1968	1968	NUM
ejpam-2383	195	6	-	-	SYM
ejpam-2383	195	7	69	69	NUM
ejpam-2383	195	8	,	,	PUNCT
ejpam-2383	195	9	pp	pp	ADV
ejpam-2383	195	10	1	1	NUM
ejpam-2383	195	11	-	-	SYM
ejpam-2383	195	12	22	22	NUM
ejpam-2383	195	13	,	,	PUNCT
ejpam-2383	195	14	lecture	lecture	NOUN
ejpam-2383	195	15	notes	note	NOUN
ejpam-2383	195	16	in	in	ADP
ejpam-2383	195	17	math	math	NOUN
ejpam-2383	195	18	.	.	PUNCT
ejpam-2383	196	1	no	no	INTJ
ejpam-2383	196	2	.	.	NOUN
ejpam-2383	196	3	179	179	NUM
ejpam-2383	196	4	,	,	PUNCT
ejpam-2383	196	5	berlin	berlin	PROPN
ejpam-2383	196	6	1971	1971	NUM
ejpam-2383	196	7	springer	springer	NOUN
ejpam-2383	196	8	verlag	verlag	NOUN
ejpam-2383	196	9	,	,	PUNCT
ejpam-2383	196	10	1971	1971	NUM
ejpam-2383	196	11	.	.	PUNCT
ejpam-2383	197	1	[	[	X
ejpam-2383	197	2	7	7	X
ejpam-2383	197	3	]	]	PUNCT
ejpam-2383	197	4	k.	k.	PROPN
ejpam-2383	197	5	r.	r.	PROPN
ejpam-2383	197	6	goodearl	goodearl	PROPN
ejpam-2383	197	7	and	and	CCONJ
ejpam-2383	197	8	r.	r.	PROPN
ejpam-2383	197	9	b.	b.	PROPN
ejpam-2383	197	10	warfield	warfield	PROPN
ejpam-2383	197	11	.	.	PUNCT
ejpam-2383	198	1	an	an	DET
ejpam-2383	198	2	introduction	introduction	NOUN
ejpam-2383	198	3	to	to	ADP
ejpam-2383	198	4	non	non	ADJ
ejpam-2383	198	5	-	-	ADJ
ejpam-2383	198	6	commutative	commutative	ADJ
ejpam-2383	198	7	noetherian	noetherian	ADJ
ejpam-2383	198	8	rings	ring	NOUN
ejpam-2383	198	9	,	,	PUNCT
ejpam-2383	198	10	cambridge	cambridge	PROPN
ejpam-2383	198	11	university	university	PROPN
ejpam-2383	198	12	press	press	NOUN
ejpam-2383	198	13	,	,	PUNCT
ejpam-2383	198	14	2004	2004	NUM
ejpam-2383	198	15	.	.	PUNCT
ejpam-2383	199	1	[	[	X
ejpam-2383	199	2	8	8	NUM
ejpam-2383	199	3	]	]	X
ejpam-2383	199	4	y.	y.	PROPN
ejpam-2383	199	5	hirano	hirano	PROPN
ejpam-2383	199	6	some	some	DET
ejpam-2383	199	7	studies	study	NOUN
ejpam-2383	199	8	on	on	ADP
ejpam-2383	199	9	strongly	strongly	ADV
ejpam-2383	199	10	π	π	ADJ
ejpam-2383	199	11	-	-	ADJ
ejpam-2383	199	12	regular	regular	ADJ
ejpam-2383	199	13	ring	ring	NOUN
ejpam-2383	199	14	,	,	PUNCT
ejpam-2383	199	15	mathematical	mathematical	ADJ
ejpam-2383	199	16	journal	journal	NOUN
ejpam-2383	199	17	of	of	ADP
ejpam-2383	199	18	okayama	okayama	PROPN
ejpam-2383	199	19	university	university	PROPN
ejpam-2383	199	20	,	,	PUNCT
ejpam-2383	199	21	20(2	20(2	NUM
ejpam-2383	199	22	)	)	PUNCT
ejpam-2383	199	23	,	,	PUNCT
ejpam-2383	199	24	141	141	NUM
ejpam-2383	199	25	-	-	SYM
ejpam-2383	199	26	149	149	NUM
ejpam-2383	199	27	.	.	PUNCT
ejpam-2383	199	28	1978	1978	NUM
ejpam-2383	199	29	.	.	PUNCT
ejpam-2383	200	1	[	[	X
ejpam-2383	200	2	9	9	NUM
ejpam-2383	200	3	]	]	X
ejpam-2383	200	4	c.y	c.y	PROPN
ejpam-2383	200	5	.	.	PROPN
ejpam-2383	200	6	hong	hong	PROPN
ejpam-2383	200	7	and	and	CCONJ
ejpam-2383	200	8	t.k	t.k	PROPN
ejpam-2383	200	9	.	.	PROPN
ejpam-2383	200	10	kwak	kwak	PROPN
ejpam-2383	200	11	.	.	PUNCT
ejpam-2383	201	1	on	on	ADP
ejpam-2383	201	2	minimal	minimal	ADJ
ejpam-2383	201	3	strongly	strongly	ADV
ejpam-2383	201	4	prime	prime	ADJ
ejpam-2383	201	5	ideals	ideal	NOUN
ejpam-2383	201	6	,	,	PUNCT
ejpam-2383	201	7	communications	communication	NOUN
ejpam-2383	201	8	in	in	ADP
ejpam-2383	201	9	algebra	algebra	NOUN
ejpam-2383	201	10	,	,	PUNCT
ejpam-2383	201	11	28(10	28(10	NUM
ejpam-2383	201	12	)	)	PUNCT
ejpam-2383	201	13	,	,	PUNCT
ejpam-2383	201	14	4868	4868	NUM
ejpam-2383	201	15	-	-	SYM
ejpam-2383	201	16	4878	4878	NUM
ejpam-2383	201	17	.	.	PUNCT
ejpam-2383	201	18	2000	2000	NUM
ejpam-2383	201	19	.	.	PUNCT
ejpam-2383	202	1	[	[	X
ejpam-2383	202	2	10	10	NUM
ejpam-2383	202	3	]	]	X
ejpam-2383	202	4	c.y.hong	c.y.hong	NOUN
ejpam-2383	202	5	,	,	PUNCT
ejpam-2383	202	6	n.	n.	PROPN
ejpam-2383	202	7	k.	k.	PROPN
ejpam-2383	202	8	kim	kim	PROPN
ejpam-2383	202	9	,	,	PUNCT
ejpam-2383	202	10	and	and	CCONJ
ejpam-2383	202	11	t.	t.	PROPN
ejpam-2383	202	12	k.	k.	PROPN
ejpam-2383	202	13	kwak	kwak	PROPN
ejpam-2383	202	14	.	.	PUNCT
ejpam-2383	203	1	ore	ore	NOUN
ejpam-2383	203	2	extensions	extension	NOUN
ejpam-2383	203	3	of	of	ADP
ejpam-2383	203	4	baer	baer	PROPN
ejpam-2383	203	5	and	and	CCONJ
ejpam-2383	203	6	p.p	p.p	PROPN
ejpam-2383	203	7	-	-	PUNCT
ejpam-2383	203	8	rings	ring	NOUN
ejpam-2383	203	9	,	,	PUNCT
ejpam-2383	203	10	journal	journal	NOUN
ejpam-2383	203	11	of	of	ADP
ejpam-2383	203	12	pure	pure	ADJ
ejpam-2383	203	13	and	and	CCONJ
ejpam-2383	203	14	applied	applied	ADJ
ejpam-2383	203	15	algebra	algebra	NOUN
ejpam-2383	203	16	,	,	PUNCT
ejpam-2383	203	17	151(3	151(3	NUM
ejpam-2383	203	18	)	)	PUNCT
ejpam-2383	203	19	,	,	PUNCT
ejpam-2383	203	20	215	215	NUM
ejpam-2383	203	21	-	-	SYM
ejpam-2383	203	22	226	226	NUM
ejpam-2383	203	23	.	.	PUNCT
ejpam-2383	203	24	2000	2000	NUM
ejpam-2383	203	25	.	.	PUNCT
ejpam-2383	204	1	[	[	X
ejpam-2383	204	2	11	11	NUM
ejpam-2383	204	3	]	]	X
ejpam-2383	204	4	n.k	n.k	PROPN
ejpam-2383	204	5	.	.	PROPN
ejpam-2383	204	6	kim	kim	PROPN
ejpam-2383	204	7	and	and	CCONJ
ejpam-2383	204	8	t.k.kwak	t.k.kwak	NOUN
ejpam-2383	204	9	.	.	PUNCT
ejpam-2383	205	1	minimal	minimal	ADJ
ejpam-2383	205	2	prime	prime	ADJ
ejpam-2383	205	3	ideals	ideal	NOUN
ejpam-2383	205	4	in	in	ADP
ejpam-2383	205	5	2	2	NUM
ejpam-2383	205	6	-	-	PUNCT
ejpam-2383	205	7	primal	primal	ADJ
ejpam-2383	205	8	rings	ring	NOUN
ejpam-2383	205	9	,	,	PUNCT
ejpam-2383	205	10	mathematica	mathematica	PROPN
ejpam-2383	205	11	japonica	japonica	PROPN
ejpam-2383	205	12	,	,	PUNCT
ejpam-2383	205	13	50(3	50(3	NUM
ejpam-2383	205	14	)	)	PUNCT
ejpam-2383	205	15	,	,	PUNCT
ejpam-2383	205	16	415	415	NUM
ejpam-2383	205	17	-	-	SYM
ejpam-2383	205	18	420	420	NUM
ejpam-2383	205	19	.	.	PUNCT
ejpam-2383	205	20	1999	1999	NUM
ejpam-2383	205	21	.	.	PUNCT
ejpam-2383	206	1	references	reference	NOUN
ejpam-2383	206	2	468	468	NUM
ejpam-2383	207	1	[	[	X
ejpam-2383	207	2	12	12	NUM
ejpam-2383	207	3	]	]	PUNCT
ejpam-2383	207	4	j.	j.	PROPN
ejpam-2383	207	5	c.	c.	PROPN
ejpam-2383	207	6	mcconnell	mcconnell	PROPN
ejpam-2383	207	7	and	and	CCONJ
ejpam-2383	207	8	j.	j.	PROPN
ejpam-2383	207	9	c.	c.	PROPN
ejpam-2383	207	10	robson	robson	PROPN
ejpam-2383	207	11	.	.	PUNCT
ejpam-2383	208	1	noncommutative	noncommutative	ADJ
ejpam-2383	208	2	noetherian	noetherian	ADJ
ejpam-2383	208	3	rings	ring	NOUN
ejpam-2383	208	4	,	,	PUNCT
ejpam-2383	208	5	wiley,1987	wiley,1987	NOUN
ejpam-2383	208	6	;	;	PUNCT
ejpam-2383	208	7	revised	revised	ADJ
ejpam-2383	208	8	edition	edition	NOUN
ejpam-2383	208	9	:	:	PUNCT
ejpam-2383	208	10	ams	am	NOUN
ejpam-2383	208	11	,	,	PUNCT
ejpam-2383	208	12	2001	2001	NUM
ejpam-2383	208	13	.	.	PUNCT
ejpam-2383	209	1	[	[	X
ejpam-2383	209	2	13	13	NUM
ejpam-2383	209	3	]	]	X
ejpam-2383	209	4	g.	g.	PROPN
ejpam-2383	209	5	y.	y.	PROPN
ejpam-2383	209	6	shin	shin	PROPN
ejpam-2383	209	7	.	.	PUNCT
ejpam-2383	210	1	prime	prime	ADJ
ejpam-2383	210	2	ideals	ideal	NOUN
ejpam-2383	210	3	and	and	CCONJ
ejpam-2383	210	4	sheaf	sheaf	NOUN
ejpam-2383	210	5	representations	representation	NOUN
ejpam-2383	210	6	of	of	ADP
ejpam-2383	210	7	a	a	DET
ejpam-2383	210	8	pseudo	pseudo	NOUN
ejpam-2383	210	9	symmetric	symmetric	ADJ
ejpam-2383	210	10	ring	ring	NOUN
ejpam-2383	210	11	,	,	PUNCT
ejpam-2383	210	12	transactions	transaction	NOUN
ejpam-2383	210	13	of	of	ADP
ejpam-2383	210	14	american	american	PROPN
ejpam-2383	210	15	mathematical	mathematical	PROPN
ejpam-2383	210	16	society	society	NOUN
ejpam-2383	210	17	,	,	PUNCT
ejpam-2383	210	18	184	184	NUM
ejpam-2383	210	19	,	,	PUNCT
ejpam-2383	210	20	43	43	NUM
ejpam-2383	210	21	-	-	SYM
ejpam-2383	210	22	60	60	NUM
ejpam-2383	210	23	.	.	PUNCT
ejpam-2383	210	24	1973	1973	NUM
ejpam-2383	210	25	.	.	PUNCT
ejpam-2383	211	1	[	[	X
ejpam-2383	211	2	14	14	NUM
ejpam-2383	211	3	]	]	X
ejpam-2383	211	4	s.	s.	PROPN
ejpam-2383	211	5	h.	h.	PROPN
ejpam-2383	211	6	sun	sun	PROPN
ejpam-2383	211	7	.	.	PUNCT
ejpam-2383	212	1	non	non	ADJ
ejpam-2383	212	2	-	-	ADJ
ejpam-2383	212	3	commutative	commutative	ADJ
ejpam-2383	212	4	rings	ring	NOUN
ejpam-2383	212	5	in	in	ADP
ejpam-2383	212	6	which	which	PRON
ejpam-2383	212	7	every	every	DET
ejpam-2383	212	8	prime	prime	ADJ
ejpam-2383	212	9	ideal	ideal	NOUN
ejpam-2383	212	10	is	be	AUX
ejpam-2383	212	11	contained	contain	VERB
ejpam-2383	212	12	in	in	ADP
ejpam-2383	212	13	a	a	DET
ejpam-2383	212	14	unique	unique	ADJ
ejpam-2383	212	15	maximal	maximal	ADJ
ejpam-2383	212	16	ideal	ideal	NOUN
ejpam-2383	212	17	,	,	PUNCT
ejpam-2383	212	18	journal	journal	NOUN
ejpam-2383	212	19	of	of	ADP
ejpam-2383	212	20	pure	pure	ADJ
ejpam-2383	212	21	and	and	CCONJ
ejpam-2383	212	22	applied	applied	ADJ
ejpam-2383	212	23	algebra	algebra	NOUN
ejpam-2383	212	24	,	,	PUNCT
ejpam-2383	212	25	76(2	76(2	NUM
ejpam-2383	212	26	)	)	PUNCT
ejpam-2383	212	27	,	,	PUNCT
ejpam-2383	212	28	179	179	NUM
ejpam-2383	212	29	-	-	SYM
ejpam-2383	212	30	192	192	NUM
ejpam-2383	212	31	.	.	PUNCT
ejpam-2383	212	32	1991	1991	NUM
ejpam-2383	212	33	.	.	PUNCT