id	sid	tid	token	lemma	pos
ejpam-2102	1	1	compile	compile	NOUN
ejpam-2102	1	2	/	/	SYM
ejpam-2102	1	3	output.dvi	output.dvi	NOUN
ejpam-2102	1	4	european	european	ADJ
ejpam-2102	1	5	journal	journal	NOUN
ejpam-2102	1	6	of	of	ADP
ejpam-2102	1	7	pure	pure	ADJ
ejpam-2102	1	8	and	and	CCONJ
ejpam-2102	1	9	applied	apply	VERB
ejpam-2102	1	10	mathematics	mathematic	NOUN
ejpam-2102	1	11	vol	vol	NOUN
ejpam-2102	1	12	.	.	PROPN
ejpam-2102	1	13	8	8	NUM
ejpam-2102	1	14	,	,	PUNCT
ejpam-2102	1	15	no	no	INTJ
ejpam-2102	1	16	.	.	NOUN
ejpam-2102	1	17	1	1	NUM
ejpam-2102	1	18	,	,	PUNCT
ejpam-2102	1	19	2015	2015	NUM
ejpam-2102	1	20	,	,	PUNCT
ejpam-2102	1	21	111	111	NUM
ejpam-2102	1	22	-	-	SYM
ejpam-2102	1	23	117	117	NUM
ejpam-2102	1	24	issn	issn	PROPN
ejpam-2102	1	25	1307	1307	NUM
ejpam-2102	1	26	-	-	SYM
ejpam-2102	1	27	5543	5543	NUM
ejpam-2102	1	28	–	–	PUNCT
ejpam-2102	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2102	1	30	transparency	transparency	NOUN
ejpam-2102	1	31	of	of	ADP
ejpam-2102	1	32	skew	skew	ADJ
ejpam-2102	1	33	polynomial	polynomial	ADJ
ejpam-2102	1	34	ring	ring	NOUN
ejpam-2102	1	35	over	over	ADP
ejpam-2102	1	36	a	a	DET
ejpam-2102	1	37	commutative	commutative	ADJ
ejpam-2102	1	38	noetherian	noetherian	ADJ
ejpam-2102	1	39	ring	ring	NOUN
ejpam-2102	1	40	v.	v.	PROPN
ejpam-2102	1	41	k.	k.	PROPN
ejpam-2102	1	42	bhat∗and	bhat∗and	PROPN
ejpam-2102	1	43	kiran	kiran	PROPN
ejpam-2102	1	44	chib	chib	VERB
ejpam-2102	1	45	school	school	PROPN
ejpam-2102	1	46	of	of	ADP
ejpam-2102	1	47	mathematics	mathematics	PROPN
ejpam-2102	1	48	,	,	PUNCT
ejpam-2102	1	49	smvd	smvd	PROPN
ejpam-2102	1	50	university	university	PROPN
ejpam-2102	1	51	,	,	PUNCT
ejpam-2102	1	52	p	p	X
ejpam-2102	1	53	/	/	SYM
ejpam-2102	1	54	o	o	PROPN
ejpam-2102	1	55	smvd	smvd	PROPN
ejpam-2102	1	56	university	university	PROPN
ejpam-2102	1	57	,	,	PUNCT
ejpam-2102	1	58	katra	katra	PROPN
ejpam-2102	1	59	,	,	PUNCT
ejpam-2102	1	60	j	j	PROPN
ejpam-2102	1	61	and	and	CCONJ
ejpam-2102	1	62	k	k	PROPN
ejpam-2102	1	63	,	,	PUNCT
ejpam-2102	1	64	india182320	india182320	PROPN
ejpam-2102	1	65	abstract	abstract	NOUN
ejpam-2102	1	66	.	.	PUNCT
ejpam-2102	2	1	in	in	ADP
ejpam-2102	2	2	this	this	DET
ejpam-2102	2	3	paper	paper	NOUN
ejpam-2102	2	4	,	,	PUNCT
ejpam-2102	2	5	we	we	PRON
ejpam-2102	2	6	discuss	discuss	VERB
ejpam-2102	2	7	a	a	DET
ejpam-2102	2	8	stronger	strong	ADJ
ejpam-2102	2	9	type	type	NOUN
ejpam-2102	2	10	of	of	ADP
ejpam-2102	2	11	primary	primary	ADJ
ejpam-2102	2	12	decomposition	decomposition	NOUN
ejpam-2102	2	13	(	(	PUNCT
ejpam-2102	2	14	known	know	VERB
ejpam-2102	2	15	as	as	ADP
ejpam-2102	2	16	transparency	transparency	NOUN
ejpam-2102	2	17	)	)	PUNCT
ejpam-2102	2	18	in	in	ADP
ejpam-2102	2	19	noncommutative	noncommutative	ADJ
ejpam-2102	2	20	set	set	VERB
ejpam-2102	2	21	up	up	ADP
ejpam-2102	2	22	.	.	PUNCT
ejpam-2102	3	1	one	one	NUM
ejpam-2102	3	2	of	of	ADP
ejpam-2102	3	3	the	the	DET
ejpam-2102	3	4	class	class	NOUN
ejpam-2102	3	5	of	of	ADP
ejpam-2102	3	6	noncommutative	noncommutative	ADJ
ejpam-2102	3	7	rings	ring	NOUN
ejpam-2102	3	8	are	be	AUX
ejpam-2102	3	9	the	the	DET
ejpam-2102	3	10	skew	skew	ADJ
ejpam-2102	3	11	polynomial	polynomial	ADJ
ejpam-2102	3	12	rings	ring	NOUN
ejpam-2102	3	13	.	.	PUNCT
ejpam-2102	4	1	we	we	PRON
ejpam-2102	4	2	show	show	VERB
ejpam-2102	4	3	that	that	SCONJ
ejpam-2102	4	4	certain	certain	ADJ
ejpam-2102	4	5	skew	skew	ADJ
ejpam-2102	4	6	polynomial	polynomial	ADJ
ejpam-2102	4	7	rings	ring	NOUN
ejpam-2102	4	8	satisfy	satisfy	VERB
ejpam-2102	4	9	this	this	DET
ejpam-2102	4	10	type	type	NOUN
ejpam-2102	4	11	of	of	ADP
ejpam-2102	4	12	primary	primary	ADJ
ejpam-2102	4	13	decomposition	decomposition	NOUN
ejpam-2102	4	14	.	.	PUNCT
ejpam-2102	5	1	recall	recall	VERB
ejpam-2102	5	2	that	that	SCONJ
ejpam-2102	5	3	a	a	DET
ejpam-2102	5	4	right	right	ADJ
ejpam-2102	5	5	noetherian	noetherian	ADJ
ejpam-2102	5	6	ring	ring	NOUN
ejpam-2102	5	7	r	r	NOUN
ejpam-2102	5	8	is	be	AUX
ejpam-2102	5	9	said	say	VERB
ejpam-2102	5	10	to	to	PART
ejpam-2102	5	11	be	be	AUX
ejpam-2102	5	12	transparent	transparent	ADJ
ejpam-2102	5	13	ring	ring	NOUN
ejpam-2102	5	14	if	if	SCONJ
ejpam-2102	5	15	there	there	PRON
ejpam-2102	5	16	exist	exist	VERB
ejpam-2102	5	17	irreducible	irreducible	ADJ
ejpam-2102	5	18	ideals	ideal	NOUN
ejpam-2102	5	19	i	i	PRON
ejpam-2102	5	20	j	j	NOUN
ejpam-2102	5	21	,	,	PUNCT
ejpam-2102	5	22	1	1	NUM
ejpam-2102	5	23	≤	≤	NUM
ejpam-2102	5	24	j	j	PROPN
ejpam-2102	5	25	≤	≤	PROPN
ejpam-2102	5	26	n	n	CCONJ
ejpam-2102	5	27	such	such	ADJ
ejpam-2102	5	28	that	that	SCONJ
ejpam-2102	5	29	∩n	∩n	NOUN
ejpam-2102	6	1	j=1	j=1	NOUN
ejpam-2102	7	1	i	i	PRON
ejpam-2102	7	2	j	j	NOUN
ejpam-2102	8	1	=	=	PUNCT
ejpam-2102	8	2	0	0	PROPN
ejpam-2102	8	3	and	and	CCONJ
ejpam-2102	8	4	each	each	DET
ejpam-2102	8	5	r	r	NOUN
ejpam-2102	8	6	/	/	SYM
ejpam-2102	9	1	i	i	PRON
ejpam-2102	9	2	j	j	PROPN
ejpam-2102	9	3	has	have	VERB
ejpam-2102	9	4	a	a	DET
ejpam-2102	9	5	right	right	ADJ
ejpam-2102	9	6	artinian	artinian	ADJ
ejpam-2102	9	7	quotient	quotient	NOUN
ejpam-2102	9	8	ring	ring	NOUN
ejpam-2102	9	9	.	.	PUNCT
ejpam-2102	10	1	let	let	VERB
ejpam-2102	10	2	r	r	PRON
ejpam-2102	10	3	be	be	AUX
ejpam-2102	10	4	a	a	DET
ejpam-2102	10	5	commutative	commutative	ADJ
ejpam-2102	10	6	noetherian	noetherian	ADJ
ejpam-2102	10	7	ring	ring	NOUN
ejpam-2102	10	8	,	,	PUNCT
ejpam-2102	10	9	which	which	PRON
ejpam-2102	10	10	is	be	AUX
ejpam-2102	10	11	also	also	ADV
ejpam-2102	10	12	an	an	DET
ejpam-2102	10	13	algebra	algebra	NOUN
ejpam-2102	10	14	over	over	ADP
ejpam-2102	10	15	q	q	PROPN
ejpam-2102	10	16	(	(	PUNCT
ejpam-2102	10	17	q	q	NOUN
ejpam-2102	10	18	is	be	AUX
ejpam-2102	10	19	the	the	DET
ejpam-2102	10	20	field	field	NOUN
ejpam-2102	10	21	of	of	ADP
ejpam-2102	10	22	rational	rational	ADJ
ejpam-2102	10	23	numbers	number	NOUN
ejpam-2102	10	24	)	)	PUNCT
ejpam-2102	10	25	.	.	PUNCT
ejpam-2102	11	1	let	let	VERB
ejpam-2102	11	2	σ	σ	NOUN
ejpam-2102	11	3	be	be	AUX
ejpam-2102	11	4	an	an	DET
ejpam-2102	11	5	automorphism	automorphism	NOUN
ejpam-2102	11	6	of	of	ADP
ejpam-2102	11	7	r	r	NOUN
ejpam-2102	11	8	and	and	CCONJ
ejpam-2102	11	9	δ	δ	PROPN
ejpam-2102	11	10	a	a	DET
ejpam-2102	11	11	σ	σ	NOUN
ejpam-2102	11	12	-	-	PUNCT
ejpam-2102	11	13	derivation	derivation	NOUN
ejpam-2102	11	14	of	of	ADP
ejpam-2102	11	15	r.	r.	PROPN
ejpam-2102	11	16	then	then	ADV
ejpam-2102	11	17	we	we	PRON
ejpam-2102	11	18	show	show	VERB
ejpam-2102	11	19	that	that	SCONJ
ejpam-2102	11	20	the	the	DET
ejpam-2102	11	21	skew	skew	ADJ
ejpam-2102	11	22	polynomial	polynomial	ADJ
ejpam-2102	11	23	ring	ring	NOUN
ejpam-2102	11	24	r[x;σ	r[x;σ	NOUN
ejpam-2102	11	25	,	,	PUNCT
ejpam-2102	11	26	δ	δ	PROPN
ejpam-2102	11	27	]	]	PUNCT
ejpam-2102	11	28	is	be	AUX
ejpam-2102	11	29	a	a	DET
ejpam-2102	11	30	transparent	transparent	ADJ
ejpam-2102	11	31	ring	ring	NOUN
ejpam-2102	11	32	.	.	PUNCT
ejpam-2102	12	1	2010	2010	NUM
ejpam-2102	12	2	mathematics	mathematic	NOUN
ejpam-2102	12	3	subject	subject	NOUN
ejpam-2102	12	4	classifications	classification	NOUN
ejpam-2102	12	5	:	:	PUNCT
ejpam-2102	12	6	16	16	NUM
ejpam-2102	12	7	-	-	SYM
ejpam-2102	12	8	xx	xx	NUM
ejpam-2102	12	9	,	,	PUNCT
ejpam-2102	12	10	16n40	16n40	NUM
ejpam-2102	12	11	,	,	PUNCT
ejpam-2102	12	12	16p40	16p40	NUM
ejpam-2102	12	13	,	,	PUNCT
ejpam-2102	12	14	16s36	16s36	NUM
ejpam-2102	12	15	.	.	PUNCT
ejpam-2102	13	1	key	key	ADJ
ejpam-2102	13	2	words	word	NOUN
ejpam-2102	13	3	and	and	CCONJ
ejpam-2102	13	4	phrases	phrase	NOUN
ejpam-2102	13	5	:	:	PUNCT
ejpam-2102	13	6	automorphism	automorphism	NOUN
ejpam-2102	13	7	,	,	PUNCT
ejpam-2102	13	8	σ	σ	NOUN
ejpam-2102	13	9	-	-	PUNCT
ejpam-2102	13	10	derivation	derivation	NOUN
ejpam-2102	13	11	,	,	PUNCT
ejpam-2102	13	12	quotient	quotient	NOUN
ejpam-2102	13	13	ring	ring	NOUN
ejpam-2102	13	14	,	,	PUNCT
ejpam-2102	13	15	transparent	transparent	ADJ
ejpam-2102	13	16	rings	ring	NOUN
ejpam-2102	13	17	1	1	NUM
ejpam-2102	13	18	.	.	PUNCT
ejpam-2102	13	19	introduction	introduction	NOUN
ejpam-2102	13	20	a	a	DET
ejpam-2102	13	21	ring	ring	NOUN
ejpam-2102	13	22	r	r	NOUN
ejpam-2102	13	23	always	always	ADV
ejpam-2102	13	24	means	mean	VERB
ejpam-2102	13	25	an	an	DET
ejpam-2102	13	26	associative	associative	ADJ
ejpam-2102	13	27	ring	ring	NOUN
ejpam-2102	13	28	with	with	ADP
ejpam-2102	13	29	identity	identity	NOUN
ejpam-2102	13	30	1	1	NUM
ejpam-2102	13	31	6=	6=	ADP
ejpam-2102	13	32	0	0	NUM
ejpam-2102	13	33	.	.	PUNCT
ejpam-2102	14	1	the	the	DET
ejpam-2102	14	2	set	set	NOUN
ejpam-2102	14	3	of	of	ADP
ejpam-2102	14	4	minimal	minimal	ADJ
ejpam-2102	14	5	prime	prime	ADJ
ejpam-2102	14	6	ideals	ideal	NOUN
ejpam-2102	14	7	of	of	ADP
ejpam-2102	14	8	r	r	NOUN
ejpam-2102	14	9	is	be	AUX
ejpam-2102	14	10	denoted	denote	VERB
ejpam-2102	14	11	by	by	ADP
ejpam-2102	14	12	min.spec(r	min.spec(r	PROPN
ejpam-2102	14	13	)	)	PUNCT
ejpam-2102	14	14	.	.	PUNCT
ejpam-2102	15	1	prime	prime	PROPN
ejpam-2102	15	2	radical	radical	ADJ
ejpam-2102	15	3	and	and	CCONJ
ejpam-2102	15	4	the	the	DET
ejpam-2102	15	5	set	set	NOUN
ejpam-2102	15	6	of	of	ADP
ejpam-2102	15	7	nilpotent	nilpotent	ADJ
ejpam-2102	15	8	elements	element	NOUN
ejpam-2102	15	9	of	of	ADP
ejpam-2102	15	10	r	r	NOUN
ejpam-2102	15	11	are	be	AUX
ejpam-2102	15	12	denoted	denote	VERB
ejpam-2102	15	13	by	by	ADP
ejpam-2102	15	14	p(r	p(r	PROPN
ejpam-2102	15	15	)	)	PUNCT
ejpam-2102	15	16	and	and	CCONJ
ejpam-2102	15	17	n(r	n(r	NOUN
ejpam-2102	15	18	)	)	PUNCT
ejpam-2102	15	19	respectively	respectively	ADV
ejpam-2102	15	20	.	.	PUNCT
ejpam-2102	16	1	the	the	DET
ejpam-2102	16	2	set	set	NOUN
ejpam-2102	16	3	of	of	ADP
ejpam-2102	16	4	associated	associate	VERB
ejpam-2102	16	5	prime	prime	ADJ
ejpam-2102	16	6	ideals	ideal	NOUN
ejpam-2102	16	7	of	of	ADP
ejpam-2102	16	8	r	r	NOUN
ejpam-2102	16	9	(	(	PUNCT
ejpam-2102	16	10	viewed	view	VERB
ejpam-2102	16	11	as	as	ADP
ejpam-2102	16	12	a	a	DET
ejpam-2102	16	13	right	right	ADJ
ejpam-2102	16	14	module	module	NOUN
ejpam-2102	16	15	over	over	ADP
ejpam-2102	16	16	itself	itself	PRON
ejpam-2102	16	17	)	)	PUNCT
ejpam-2102	16	18	is	be	AUX
ejpam-2102	16	19	denoted	denote	VERB
ejpam-2102	16	20	by	by	ADP
ejpam-2102	16	21	ass(rr	ass(rr	NOUN
ejpam-2102	16	22	)	)	PUNCT
ejpam-2102	16	23	.	.	PUNCT
ejpam-2102	17	1	the	the	DET
ejpam-2102	17	2	set	set	NOUN
ejpam-2102	17	3	of	of	ADP
ejpam-2102	17	4	positive	positive	ADJ
ejpam-2102	17	5	integers	integer	NOUN
ejpam-2102	17	6	,	,	PUNCT
ejpam-2102	17	7	the	the	DET
ejpam-2102	17	8	set	set	NOUN
ejpam-2102	17	9	of	of	ADP
ejpam-2102	17	10	integers	integer	NOUN
ejpam-2102	17	11	,	,	PUNCT
ejpam-2102	17	12	the	the	DET
ejpam-2102	17	13	field	field	NOUN
ejpam-2102	17	14	of	of	ADP
ejpam-2102	17	15	rational	rational	ADJ
ejpam-2102	17	16	numbers	number	NOUN
ejpam-2102	17	17	,	,	PUNCT
ejpam-2102	17	18	the	the	DET
ejpam-2102	17	19	field	field	NOUN
ejpam-2102	17	20	of	of	ADP
ejpam-2102	17	21	real	real	ADJ
ejpam-2102	17	22	numbers	number	NOUN
ejpam-2102	17	23	and	and	CCONJ
ejpam-2102	17	24	the	the	DET
ejpam-2102	17	25	field	field	NOUN
ejpam-2102	17	26	of	of	ADP
ejpam-2102	17	27	complex	complex	ADJ
ejpam-2102	17	28	numbers	number	NOUN
ejpam-2102	17	29	are	be	AUX
ejpam-2102	17	30	denoted	denote	VERB
ejpam-2102	17	31	by	by	ADP
ejpam-2102	17	32	n	n	CCONJ
ejpam-2102	17	33	,	,	PUNCT
ejpam-2102	17	34	z	z	NOUN
ejpam-2102	17	35	,	,	PUNCT
ejpam-2102	17	36	q	q	NOUN
ejpam-2102	17	37	,	,	PUNCT
ejpam-2102	17	38	r	r	NOUN
ejpam-2102	17	39	and	and	CCONJ
ejpam-2102	17	40	c	c	NOUN
ejpam-2102	17	41	respectively	respectively	ADV
ejpam-2102	17	42	unless	unless	SCONJ
ejpam-2102	17	43	otherwise	otherwise	ADV
ejpam-2102	17	44	stated	state	VERB
ejpam-2102	17	45	.	.	PUNCT
ejpam-2102	18	1	let	let	VERB
ejpam-2102	18	2	r	r	PRON
ejpam-2102	18	3	be	be	AUX
ejpam-2102	18	4	a	a	DET
ejpam-2102	18	5	ring	ring	NOUN
ejpam-2102	18	6	,	,	PUNCT
ejpam-2102	18	7	σ	σ	VERB
ejpam-2102	18	8	an	an	DET
ejpam-2102	18	9	automorphism	automorphism	NOUN
ejpam-2102	18	10	of	of	ADP
ejpam-2102	18	11	r	r	NOUN
ejpam-2102	18	12	and	and	CCONJ
ejpam-2102	18	13	δ	δ	PROPN
ejpam-2102	18	14	a	a	DET
ejpam-2102	18	15	σ	σ	NOUN
ejpam-2102	18	16	-	-	PUNCT
ejpam-2102	18	17	derivation	derivation	NOUN
ejpam-2102	18	18	of	of	ADP
ejpam-2102	18	19	r	r	NOUN
ejpam-2102	18	20	;	;	PUNCT
ejpam-2102	18	21	i.e.	i.e.	X
ejpam-2102	18	22	δ	δ	NOUN
ejpam-2102	18	23	:	:	PUNCT
ejpam-2102	18	24	r→	r→	PROPN
ejpam-2102	18	25	r	r	NOUN
ejpam-2102	18	26	is	be	AUX
ejpam-2102	18	27	an	an	DET
ejpam-2102	18	28	additive	additive	ADJ
ejpam-2102	18	29	mapping	mapping	NOUN
ejpam-2102	18	30	satisfying	satisfy	VERB
ejpam-2102	18	31	δ(ab	δ(ab	NOUN
ejpam-2102	18	32	)	)	PUNCT
ejpam-2102	18	33	=	=	SYM
ejpam-2102	18	34	δ(a)σ(b	δ(a)σ(b	NOUN
ejpam-2102	18	35	)	)	PUNCT
ejpam-2102	18	36	+	+	NUM
ejpam-2102	18	37	aδ(b	aδ(b	NOUN
ejpam-2102	18	38	)	)	PUNCT
ejpam-2102	18	39	.	.	PUNCT
ejpam-2102	19	1	for	for	ADP
ejpam-2102	19	2	example	example	NOUN
ejpam-2102	19	3	let	let	VERB
ejpam-2102	19	4	δ	δ	PRON
ejpam-2102	19	5	:	:	PUNCT
ejpam-2102	19	6	r→	r→	AUX
ejpam-2102	19	7	r	r	VERB
ejpam-2102	19	8	any	any	DET
ejpam-2102	19	9	map	map	NOUN
ejpam-2102	19	10	.	.	PUNCT
ejpam-2102	20	1	let	let	VERB
ejpam-2102	20	2	φ	φ	NOUN
ejpam-2102	20	3	:	:	PUNCT
ejpam-2102	20	4	r→	r→	PROPN
ejpam-2102	20	5	m2(r	m2(r	PROPN
ejpam-2102	20	6	)	)	PUNCT
ejpam-2102	20	7	be	be	VERB
ejpam-2102	20	8	a	a	DET
ejpam-2102	20	9	map	map	NOUN
ejpam-2102	20	10	defined	define	VERB
ejpam-2102	20	11	by	by	ADP
ejpam-2102	20	12	φ(r	φ(r	ADJ
ejpam-2102	20	13	)	)	PUNCT
ejpam-2102	20	14	=	=	SYM
ejpam-2102	20	15	�	�	PROPN
ejpam-2102	20	16	σ(r	σ(r	PROPN
ejpam-2102	20	17	)	)	PUNCT
ejpam-2102	20	18	0	0	PUNCT
ejpam-2102	21	1	δ(r	δ(r	NOUN
ejpam-2102	21	2	)	)	PUNCT
ejpam-2102	21	3	r	r	NOUN
ejpam-2102	21	4	�	�	PROPN
ejpam-2102	21	5	,	,	PUNCT
ejpam-2102	21	6	for	for	ADP
ejpam-2102	21	7	all	all	DET
ejpam-2102	21	8	r	r	PROPN
ejpam-2102	21	9	∈	∈	PROPN
ejpam-2102	21	10	r.	r.	NOUN
ejpam-2102	21	11	then	then	ADV
ejpam-2102	21	12	φ	φ	PROPN
ejpam-2102	21	13	is	be	AUX
ejpam-2102	21	14	a	a	DET
ejpam-2102	21	15	ring	ring	NOUN
ejpam-2102	21	16	homomorphism	homomorphism	NOUN
ejpam-2102	21	17	if	if	SCONJ
ejpam-2102	21	18	and	and	CCONJ
ejpam-2102	21	19	only	only	ADV
ejpam-2102	21	20	if	if	SCONJ
ejpam-2102	21	21	δ	δ	PROPN
ejpam-2102	21	22	is	be	AUX
ejpam-2102	21	23	a	a	DET
ejpam-2102	21	24	σ	σ	NOUN
ejpam-2102	21	25	-	-	PUNCT
ejpam-2102	21	26	derivation	derivation	NOUN
ejpam-2102	21	27	of	of	ADP
ejpam-2102	21	28	r.	r.	PROPN
ejpam-2102	21	29	∗corresponding	∗corresponde	VERB
ejpam-2102	21	30	author	author	NOUN
ejpam-2102	21	31	.	.	PUNCT
ejpam-2102	22	1	email	email	NOUN
ejpam-2102	22	2	address	address	PROPN
ejpam-2102	22	3	:	:	PUNCT
ejpam-2102	22	4	vijaykumarbhat2000@yahoo.com	vijaykumarbhat2000@yahoo.com	X
ejpam-2102	22	5	(	(	PUNCT
ejpam-2102	22	6	v.	v.	ADP
ejpam-2102	22	7	bhat	bhat	PROPN
ejpam-2102	22	8	)	)	PUNCT
ejpam-2102	22	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2102	23	1	111	111	NUM
ejpam-2102	23	2	c	c	NOUN
ejpam-2102	23	3	©	©	PROPN
ejpam-2102	23	4	2015	2015	NUM
ejpam-2102	23	5	ejpam	ejpam	VERB
ejpam-2102	23	6	all	all	DET
ejpam-2102	23	7	rights	right	NOUN
ejpam-2102	23	8	reserved	reserve	VERB
ejpam-2102	23	9	.	.	PUNCT
ejpam-2102	24	1	v.	v.	ADP
ejpam-2102	24	2	bhat	bhat	PROPN
ejpam-2102	24	3	and	and	CCONJ
ejpam-2102	24	4	k.	k.	PROPN
ejpam-2102	24	5	chib	chib	PROPN
ejpam-2102	24	6	/	/	SYM
ejpam-2102	24	7	eur	eur	PROPN
ejpam-2102	24	8	.	.	PUNCT
ejpam-2102	25	1	j.	j.	PROPN
ejpam-2102	25	2	pure	pure	PROPN
ejpam-2102	25	3	appl	appl	PROPN
ejpam-2102	25	4	.	.	PROPN
ejpam-2102	25	5	math	math	PROPN
ejpam-2102	25	6	,	,	PUNCT
ejpam-2102	25	7	8	8	NUM
ejpam-2102	25	8	(	(	PUNCT
ejpam-2102	25	9	2015	2015	NUM
ejpam-2102	25	10	)	)	PUNCT
ejpam-2102	25	11	,	,	PUNCT
ejpam-2102	25	12	111	111	NUM
ejpam-2102	25	13	-	-	SYM
ejpam-2102	25	14	117	117	NUM
ejpam-2102	25	15	112	112	NUM
ejpam-2102	25	16	this	this	DET
ejpam-2102	25	17	article	article	NOUN
ejpam-2102	25	18	concerns	concern	VERB
ejpam-2102	25	19	the	the	DET
ejpam-2102	25	20	study	study	NOUN
ejpam-2102	25	21	of	of	ADP
ejpam-2102	25	22	transparency	transparency	NOUN
ejpam-2102	25	23	of	of	ADP
ejpam-2102	25	24	skew	skew	ADJ
ejpam-2102	25	25	polynomial	polynomial	ADJ
ejpam-2102	25	26	ring	ring	NOUN
ejpam-2102	25	27	r[x;σ	r[x;σ	NOUN
ejpam-2102	25	28	,	,	PUNCT
ejpam-2102	25	29	δ	δ	PROPN
ejpam-2102	25	30	]	]	X
ejpam-2102	25	31	(	(	PUNCT
ejpam-2102	25	32	also	also	ADV
ejpam-2102	25	33	known	know	VERB
ejpam-2102	25	34	as	as	ADP
ejpam-2102	25	35	ore	ore	NOUN
ejpam-2102	25	36	extension	extension	NOUN
ejpam-2102	25	37	)	)	PUNCT
ejpam-2102	25	38	.	.	PUNCT
ejpam-2102	26	1	we	we	PRON
ejpam-2102	26	2	recall	recall	VERB
ejpam-2102	26	3	that	that	SCONJ
ejpam-2102	26	4	the	the	DET
ejpam-2102	26	5	skew	skew	ADJ
ejpam-2102	26	6	polynomial	polynomial	ADJ
ejpam-2102	26	7	ring	ring	NOUN
ejpam-2102	26	8	r[x;σ	r[x;σ	NOUN
ejpam-2102	26	9	,	,	PUNCT
ejpam-2102	26	10	δ	δ	PROPN
ejpam-2102	26	11	]	]	PUNCT
ejpam-2102	26	12	is	be	AUX
ejpam-2102	26	13	the	the	DET
ejpam-2102	26	14	usual	usual	ADJ
ejpam-2102	26	15	set	set	NOUN
ejpam-2102	26	16	of	of	ADP
ejpam-2102	26	17	polynomials	polynomial	NOUN
ejpam-2102	26	18	over	over	ADP
ejpam-2102	26	19	r	r	NOUN
ejpam-2102	26	20	with	with	ADP
ejpam-2102	26	21	coefficients	coefficient	NOUN
ejpam-2102	26	22	in	in	ADP
ejpam-2102	26	23	r	r	NOUN
ejpam-2102	26	24	with	with	ADP
ejpam-2102	26	25	respect	respect	NOUN
ejpam-2102	26	26	to	to	ADP
ejpam-2102	26	27	usual	usual	ADJ
ejpam-2102	26	28	addition	addition	NOUN
ejpam-2102	26	29	of	of	ADP
ejpam-2102	26	30	polynomials	polynomial	NOUN
ejpam-2102	26	31	and	and	CCONJ
ejpam-2102	26	32	multiplication	multiplication	NOUN
ejpam-2102	26	33	subject	subject	ADJ
ejpam-2102	26	34	to	to	ADP
ejpam-2102	26	35	the	the	DET
ejpam-2102	26	36	relation	relation	NOUN
ejpam-2102	26	37	ax	ax	NOUN
ejpam-2102	26	38	=	=	PUNCT
ejpam-2102	26	39	xσ(a	xσ(a	PUNCT
ejpam-2102	26	40	)	)	PUNCT
ejpam-2102	27	1	+	+	CCONJ
ejpam-2102	27	2	δ(a	δ(a	PROPN
ejpam-2102	27	3	)	)	PUNCT
ejpam-2102	27	4	for	for	ADP
ejpam-2102	27	5	all	all	DET
ejpam-2102	27	6	a	a	DET
ejpam-2102	27	7	∈	∈	PROPN
ejpam-2102	27	8	r.	r.	NOUN
ejpam-2102	27	9	we	we	PRON
ejpam-2102	27	10	take	take	VERB
ejpam-2102	27	11	any	any	DET
ejpam-2102	27	12	f	f	NOUN
ejpam-2102	27	13	(	(	PUNCT
ejpam-2102	27	14	x	x	X
ejpam-2102	27	15	)	)	PUNCT
ejpam-2102	27	16	∈	∈	PROPN
ejpam-2102	27	17	r[x;σ	r[x;σ	NOUN
ejpam-2102	27	18	,	,	PUNCT
ejpam-2102	27	19	δ	δ	PROPN
ejpam-2102	27	20	]	]	PUNCT
ejpam-2102	27	21	to	to	PART
ejpam-2102	27	22	be	be	AUX
ejpam-2102	27	23	of	of	ADP
ejpam-2102	27	24	the	the	DET
ejpam-2102	27	25	form	form	NOUN
ejpam-2102	27	26	f	f	X
ejpam-2102	27	27	(	(	PUNCT
ejpam-2102	27	28	x	x	X
ejpam-2102	27	29	)	)	PUNCT
ejpam-2102	27	30	=	=	SYM
ejpam-2102	28	1	∑n	∑n	PROPN
ejpam-2102	28	2	i=0	i=0	PROPN
ejpam-2102	28	3	x	x	PUNCT
ejpam-2102	28	4	iai	iai	NOUN
ejpam-2102	28	5	as	as	ADP
ejpam-2102	28	6	in	in	ADP
ejpam-2102	28	7	mcconnell	mcconnell	PROPN
ejpam-2102	28	8	and	and	CCONJ
ejpam-2102	28	9	robson	robson	NOUN
ejpam-2102	28	10	[	[	X
ejpam-2102	28	11	15	15	NUM
ejpam-2102	28	12	]	]	PUNCT
ejpam-2102	28	13	.	.	PUNCT
ejpam-2102	29	1	we	we	PRON
ejpam-2102	29	2	denote	denote	VERB
ejpam-2102	29	3	r[x;σ	r[x;σ	NOUN
ejpam-2102	29	4	,	,	PUNCT
ejpam-2102	29	5	δ	δ	PROPN
ejpam-2102	29	6	]	]	PUNCT
ejpam-2102	29	7	by	by	ADP
ejpam-2102	29	8	o(r	o(r	NOUN
ejpam-2102	29	9	)	)	PUNCT
ejpam-2102	29	10	.	.	PUNCT
ejpam-2102	30	1	if	if	SCONJ
ejpam-2102	30	2	i	i	PRON
ejpam-2102	30	3	is	be	AUX
ejpam-2102	30	4	an	an	DET
ejpam-2102	30	5	ideal	ideal	NOUN
ejpam-2102	30	6	of	of	ADP
ejpam-2102	30	7	r	r	NOUN
ejpam-2102	30	8	such	such	ADJ
ejpam-2102	30	9	that	that	SCONJ
ejpam-2102	30	10	i	i	PRON
ejpam-2102	30	11	is	be	AUX
ejpam-2102	30	12	σ	σ	NOUN
ejpam-2102	30	13	-	-	ADJ
ejpam-2102	30	14	stable	stable	ADJ
ejpam-2102	30	15	(	(	PUNCT
ejpam-2102	30	16	i.e.	i.e.	X
ejpam-2102	30	17	σ(i	σ(i	NOUN
ejpam-2102	30	18	)	)	PUNCT
ejpam-2102	30	19	=	=	SYM
ejpam-2102	30	20	i	i	PROPN
ejpam-2102	30	21	)	)	PUNCT
ejpam-2102	30	22	and	and	CCONJ
ejpam-2102	30	23	is	be	AUX
ejpam-2102	30	24	also	also	ADV
ejpam-2102	30	25	δ	δ	NOUN
ejpam-2102	30	26	-	-	PUNCT
ejpam-2102	30	27	invariant	invariant	ADJ
ejpam-2102	30	28	(	(	PUNCT
ejpam-2102	30	29	i.e.	i.e.	X
ejpam-2102	30	30	δ(i	δ(i	NOUN
ejpam-2102	30	31	)	)	PUNCT
ejpam-2102	30	32	⊆	⊆	NUM
ejpam-2102	30	33	i	i	PROPN
ejpam-2102	30	34	)	)	PUNCT
ejpam-2102	30	35	,	,	PUNCT
ejpam-2102	30	36	then	then	ADV
ejpam-2102	30	37	clearly	clearly	ADV
ejpam-2102	30	38	i[x;σ	i[x;σ	NUM
ejpam-2102	30	39	,	,	PUNCT
ejpam-2102	30	40	δ	δ	PROPN
ejpam-2102	30	41	]	]	X
ejpam-2102	30	42	is	be	AUX
ejpam-2102	30	43	an	an	DET
ejpam-2102	30	44	ideal	ideal	NOUN
ejpam-2102	30	45	of	of	ADP
ejpam-2102	30	46	o(r	o(r	PROPN
ejpam-2102	30	47	)	)	PUNCT
ejpam-2102	30	48	,	,	PUNCT
ejpam-2102	30	49	and	and	CCONJ
ejpam-2102	30	50	we	we	PRON
ejpam-2102	30	51	denote	denote	VERB
ejpam-2102	30	52	it	it	PRON
ejpam-2102	30	53	by	by	ADP
ejpam-2102	30	54	o(i	o(i	PROPN
ejpam-2102	30	55	)	)	PUNCT
ejpam-2102	30	56	.	.	PUNCT
ejpam-2102	31	1	in	in	ADP
ejpam-2102	31	2	case	case	NOUN
ejpam-2102	31	3	σ	σ	PROPN
ejpam-2102	31	4	is	be	AUX
ejpam-2102	31	5	the	the	DET
ejpam-2102	31	6	identity	identity	NOUN
ejpam-2102	31	7	map	map	NOUN
ejpam-2102	31	8	,	,	PUNCT
ejpam-2102	31	9	we	we	PRON
ejpam-2102	31	10	denote	denote	VERB
ejpam-2102	31	11	the	the	DET
ejpam-2102	31	12	differential	differential	ADJ
ejpam-2102	31	13	operator	operator	NOUN
ejpam-2102	31	14	ring	ring	NOUN
ejpam-2102	31	15	r[x;δ	r[x;δ	NOUN
ejpam-2102	31	16	]	]	PUNCT
ejpam-2102	31	17	by	by	ADP
ejpam-2102	31	18	d(r	d(r	NOUN
ejpam-2102	31	19	)	)	PUNCT
ejpam-2102	31	20	.	.	PUNCT
ejpam-2102	32	1	if	if	SCONJ
ejpam-2102	32	2	j	j	PROPN
ejpam-2102	32	3	is	be	AUX
ejpam-2102	32	4	an	an	DET
ejpam-2102	32	5	ideal	ideal	NOUN
ejpam-2102	32	6	of	of	ADP
ejpam-2102	32	7	r	r	NOUN
ejpam-2102	32	8	such	such	ADJ
ejpam-2102	32	9	that	that	SCONJ
ejpam-2102	32	10	j	j	PROPN
ejpam-2102	32	11	is	be	AUX
ejpam-2102	32	12	δ	δ	PROPN
ejpam-2102	32	13	-	-	PUNCT
ejpam-2102	32	14	invariant	invariant	ADJ
ejpam-2102	32	15	(	(	PUNCT
ejpam-2102	32	16	i.e.	i.e.	X
ejpam-2102	32	17	δ(j	δ(j	PROPN
ejpam-2102	32	18	)	)	PUNCT
ejpam-2102	32	19	⊆	⊆	NUM
ejpam-2102	32	20	j	j	PROPN
ejpam-2102	32	21	)	)	PUNCT
ejpam-2102	32	22	,	,	PUNCT
ejpam-2102	32	23	then	then	ADV
ejpam-2102	32	24	clearly	clearly	ADV
ejpam-2102	32	25	j[x;δ	j[x;δ	PROPN
ejpam-2102	32	26	]	]	PUNCT
ejpam-2102	32	27	is	be	AUX
ejpam-2102	32	28	an	an	DET
ejpam-2102	32	29	ideal	ideal	NOUN
ejpam-2102	32	30	of	of	ADP
ejpam-2102	32	31	d(r	d(r	PROPN
ejpam-2102	32	32	)	)	PUNCT
ejpam-2102	32	33	,	,	PUNCT
ejpam-2102	32	34	and	and	CCONJ
ejpam-2102	32	35	we	we	PRON
ejpam-2102	32	36	denote	denote	VERB
ejpam-2102	32	37	it	it	PRON
ejpam-2102	32	38	by	by	ADP
ejpam-2102	32	39	d(j	d(j	NOUN
ejpam-2102	32	40	)	)	PUNCT
ejpam-2102	32	41	.	.	PUNCT
ejpam-2102	33	1	in	in	ADP
ejpam-2102	33	2	case	case	NOUN
ejpam-2102	33	3	δ	δ	PROPN
ejpam-2102	33	4	is	be	AUX
ejpam-2102	33	5	the	the	DET
ejpam-2102	33	6	zero	zero	NUM
ejpam-2102	33	7	map	map	NOUN
ejpam-2102	33	8	,	,	PUNCT
ejpam-2102	33	9	we	we	PRON
ejpam-2102	33	10	denote	denote	VERB
ejpam-2102	33	11	r[x;σ	r[x;σ	NOUN
ejpam-2102	33	12	]	]	PUNCT
ejpam-2102	33	13	by	by	ADP
ejpam-2102	33	14	s(r	s(r	PROPN
ejpam-2102	33	15	)	)	PUNCT
ejpam-2102	33	16	.	.	PUNCT
ejpam-2102	34	1	if	if	SCONJ
ejpam-2102	34	2	k	k	PROPN
ejpam-2102	34	3	is	be	AUX
ejpam-2102	34	4	an	an	DET
ejpam-2102	34	5	ideal	ideal	NOUN
ejpam-2102	34	6	of	of	ADP
ejpam-2102	34	7	r	r	NOUN
ejpam-2102	34	8	such	such	ADJ
ejpam-2102	34	9	that	that	SCONJ
ejpam-2102	34	10	k	k	PROPN
ejpam-2102	34	11	is	be	AUX
ejpam-2102	34	12	σ	σ	NOUN
ejpam-2102	34	13	-	-	ADJ
ejpam-2102	34	14	stable	stable	ADJ
ejpam-2102	34	15	(	(	PUNCT
ejpam-2102	34	16	i.e.	i.e.	X
ejpam-2102	34	17	σ(k	σ(k	NOUN
ejpam-2102	34	18	)	)	PUNCT
ejpam-2102	34	19	=	=	SYM
ejpam-2102	34	20	k	k	X
ejpam-2102	34	21	)	)	PUNCT
ejpam-2102	34	22	,	,	PUNCT
ejpam-2102	34	23	then	then	ADV
ejpam-2102	34	24	clearly	clearly	ADV
ejpam-2102	34	25	k[x;σ	k[x;σ	VERB
ejpam-2102	34	26	]	]	PUNCT
ejpam-2102	34	27	is	be	AUX
ejpam-2102	34	28	an	an	DET
ejpam-2102	34	29	ideal	ideal	NOUN
ejpam-2102	34	30	of	of	ADP
ejpam-2102	34	31	s(r	s(r	PROPN
ejpam-2102	34	32	)	)	PUNCT
ejpam-2102	34	33	,	,	PUNCT
ejpam-2102	34	34	and	and	CCONJ
ejpam-2102	34	35	we	we	PRON
ejpam-2102	34	36	denote	denote	VERB
ejpam-2102	34	37	it	it	PRON
ejpam-2102	34	38	by	by	ADP
ejpam-2102	34	39	s(k	s(k	NOUN
ejpam-2102	34	40	)	)	PUNCT
ejpam-2102	34	41	.	.	PUNCT
ejpam-2102	35	1	the	the	DET
ejpam-2102	35	2	study	study	NOUN
ejpam-2102	35	3	of	of	ADP
ejpam-2102	35	4	skew	skew	ADJ
ejpam-2102	35	5	polynomial	polynomial	ADJ
ejpam-2102	35	6	rings	ring	NOUN
ejpam-2102	35	7	have	have	AUX
ejpam-2102	35	8	been	be	AUX
ejpam-2102	35	9	of	of	ADP
ejpam-2102	35	10	interest	interest	NOUN
ejpam-2102	35	11	to	to	ADP
ejpam-2102	35	12	many	many	ADJ
ejpam-2102	35	13	authors	author	NOUN
ejpam-2102	35	14	.	.	PUNCT
ejpam-2102	36	1	for	for	ADP
ejpam-2102	36	2	example	example	NOUN
ejpam-2102	36	3	[	[	X
ejpam-2102	36	4	2–4	2–4	NUM
ejpam-2102	36	5	,	,	PUNCT
ejpam-2102	36	6	6	6	NUM
ejpam-2102	36	7	,	,	PUNCT
ejpam-2102	36	8	8	8	NUM
ejpam-2102	36	9	,	,	PUNCT
ejpam-2102	36	10	11	11	NUM
ejpam-2102	36	11	,	,	PUNCT
ejpam-2102	36	12	12	12	NUM
ejpam-2102	36	13	,	,	PUNCT
ejpam-2102	36	14	14	14	NUM
ejpam-2102	36	15	,	,	PUNCT
ejpam-2102	36	16	15	15	NUM
ejpam-2102	36	17	]	]	PUNCT
ejpam-2102	36	18	.	.	PUNCT
ejpam-2102	37	1	the	the	DET
ejpam-2102	37	2	notion	notion	NOUN
ejpam-2102	37	3	of	of	ADP
ejpam-2102	37	4	the	the	DET
ejpam-2102	37	5	quotient	quotient	NOUN
ejpam-2102	37	6	ring	ring	NOUN
ejpam-2102	37	7	of	of	ADP
ejpam-2102	37	8	a	a	DET
ejpam-2102	37	9	ring	ring	NOUN
ejpam-2102	37	10	appears	appear	VERB
ejpam-2102	37	11	in	in	ADP
ejpam-2102	37	12	chapter	chapter	NOUN
ejpam-2102	37	13	9	9	NUM
ejpam-2102	37	14	of	of	ADP
ejpam-2102	37	15	goodearl	goodearl	PROPN
ejpam-2102	37	16	and	and	CCONJ
ejpam-2102	37	17	warfield	warfield	VERB
ejpam-2102	38	1	[	[	X
ejpam-2102	38	2	12	12	NUM
ejpam-2102	38	3	]	]	PUNCT
ejpam-2102	38	4	.	.	PUNCT
ejpam-2102	39	1	it	it	PRON
ejpam-2102	39	2	is	be	AUX
ejpam-2102	39	3	shown	show	VERB
ejpam-2102	39	4	in	in	ADP
ejpam-2102	39	5	blair	blair	PROPN
ejpam-2102	39	6	and	and	CCONJ
ejpam-2102	40	1	small	small	ADJ
ejpam-2102	40	2	[	[	X
ejpam-2102	40	3	11	11	NUM
ejpam-2102	40	4	]	]	PUNCT
ejpam-2102	40	5	that	that	SCONJ
ejpam-2102	40	6	if	if	SCONJ
ejpam-2102	40	7	r	r	NOUN
ejpam-2102	40	8	is	be	AUX
ejpam-2102	40	9	embeddable	embeddable	ADJ
ejpam-2102	40	10	in	in	ADP
ejpam-2102	40	11	a	a	DET
ejpam-2102	40	12	right	right	ADJ
ejpam-2102	40	13	artinian	artinian	ADJ
ejpam-2102	40	14	ring	ring	NOUN
ejpam-2102	40	15	and	and	CCONJ
ejpam-2102	40	16	has	have	VERB
ejpam-2102	40	17	characteristic	characteristic	ADJ
ejpam-2102	40	18	zero	zero	NUM
ejpam-2102	40	19	,	,	PUNCT
ejpam-2102	40	20	then	then	ADV
ejpam-2102	40	21	the	the	DET
ejpam-2102	40	22	differential	differential	ADJ
ejpam-2102	40	23	operator	operator	NOUN
ejpam-2102	40	24	ring	ring	NOUN
ejpam-2102	40	25	r[x;δ	r[x;δ	NOUN
ejpam-2102	40	26	]	]	PUNCT
ejpam-2102	40	27	embeds	embed	VERB
ejpam-2102	40	28	in	in	ADP
ejpam-2102	40	29	a	a	DET
ejpam-2102	40	30	right	right	ADJ
ejpam-2102	40	31	artinian	artinian	ADJ
ejpam-2102	40	32	ring	ring	NOUN
ejpam-2102	40	33	.	.	PUNCT
ejpam-2102	41	1	it	it	PRON
ejpam-2102	41	2	is	be	AUX
ejpam-2102	41	3	also	also	ADV
ejpam-2102	41	4	shown	show	VERB
ejpam-2102	41	5	in	in	ADP
ejpam-2102	41	6	blair	blair	PROPN
ejpam-2102	41	7	and	and	CCONJ
ejpam-2102	42	1	small	small	ADJ
ejpam-2102	42	2	[	[	X
ejpam-2102	42	3	11	11	NUM
ejpam-2102	42	4	]	]	PUNCT
ejpam-2102	42	5	that	that	SCONJ
ejpam-2102	42	6	if	if	SCONJ
ejpam-2102	42	7	r	r	NOUN
ejpam-2102	42	8	is	be	AUX
ejpam-2102	42	9	a	a	DET
ejpam-2102	42	10	commutative	commutative	ADJ
ejpam-2102	42	11	noetherian	noetherian	ADJ
ejpam-2102	42	12	ring	ring	NOUN
ejpam-2102	42	13	and	and	CCONJ
ejpam-2102	42	14	σ	σ	PROPN
ejpam-2102	42	15	is	be	AUX
ejpam-2102	42	16	an	an	DET
ejpam-2102	42	17	automorphism	automorphism	NOUN
ejpam-2102	42	18	of	of	ADP
ejpam-2102	42	19	r	r	NOUN
ejpam-2102	42	20	,	,	PUNCT
ejpam-2102	42	21	then	then	ADV
ejpam-2102	42	22	the	the	DET
ejpam-2102	42	23	skew	skew	ADJ
ejpam-2102	42	24	polynomial	polynomial	ADJ
ejpam-2102	42	25	ring	ring	NOUN
ejpam-2102	42	26	r[x;σ	r[x;σ	NOUN
ejpam-2102	42	27	]	]	PUNCT
ejpam-2102	42	28	embeds	embed	VERB
ejpam-2102	42	29	in	in	ADP
ejpam-2102	42	30	an	an	DET
ejpam-2102	42	31	artinian	artinian	ADJ
ejpam-2102	42	32	ring	ring	NOUN
ejpam-2102	42	33	.	.	PUNCT
ejpam-2102	43	1	for	for	ADP
ejpam-2102	43	2	more	more	ADJ
ejpam-2102	43	3	results	result	NOUN
ejpam-2102	43	4	on	on	ADP
ejpam-2102	43	5	the	the	DET
ejpam-2102	43	6	existence	existence	NOUN
ejpam-2102	43	7	of	of	ADP
ejpam-2102	43	8	the	the	DET
ejpam-2102	43	9	artinian	artinian	ADJ
ejpam-2102	43	10	quotient	quotient	NOUN
ejpam-2102	43	11	rings	ring	NOUN
ejpam-2102	43	12	,	,	PUNCT
ejpam-2102	43	13	the	the	DET
ejpam-2102	43	14	reader	reader	NOUN
ejpam-2102	43	15	is	be	AUX
ejpam-2102	43	16	referred	refer	VERB
ejpam-2102	43	17	to	to	ADP
ejpam-2102	43	18	robson	robson	NOUN
ejpam-2102	43	19	[	[	X
ejpam-2102	43	20	15	15	NUM
ejpam-2102	43	21	]	]	PUNCT
ejpam-2102	43	22	.	.	PUNCT
ejpam-2102	44	1	in	in	ADP
ejpam-2102	44	2	theorem	theorem	NOUN
ejpam-2102	44	3	(	(	PUNCT
ejpam-2102	44	4	2.11	2.11	NUM
ejpam-2102	44	5	)	)	PUNCT
ejpam-2102	44	6	of	of	ADP
ejpam-2102	44	7	bhat	bhat	PROPN
ejpam-2102	44	8	[	[	X
ejpam-2102	44	9	4	4	NUM
ejpam-2102	44	10	]	]	PUNCT
ejpam-2102	44	11	,	,	PUNCT
ejpam-2102	44	12	it	it	PRON
ejpam-2102	44	13	is	be	AUX
ejpam-2102	44	14	proved	prove	VERB
ejpam-2102	44	15	that	that	SCONJ
ejpam-2102	44	16	if	if	SCONJ
ejpam-2102	44	17	r	r	NOUN
ejpam-2102	44	18	is	be	AUX
ejpam-2102	44	19	a	a	DET
ejpam-2102	44	20	ring	ring	NOUN
ejpam-2102	44	21	which	which	PRON
ejpam-2102	44	22	is	be	AUX
ejpam-2102	44	23	an	an	DET
ejpam-2102	44	24	order	order	NOUN
ejpam-2102	44	25	in	in	ADP
ejpam-2102	44	26	a	a	DET
ejpam-2102	44	27	right	right	ADJ
ejpam-2102	44	28	artinian	artinian	ADJ
ejpam-2102	44	29	ring	ring	NOUN
ejpam-2102	44	30	.	.	PUNCT
ejpam-2102	45	1	then	then	ADV
ejpam-2102	45	2	o(r	o(r	PROPN
ejpam-2102	45	3	)	)	PUNCT
ejpam-2102	45	4	is	be	AUX
ejpam-2102	45	5	an	an	DET
ejpam-2102	45	6	order	order	NOUN
ejpam-2102	45	7	in	in	ADP
ejpam-2102	45	8	a	a	DET
ejpam-2102	45	9	right	right	ADJ
ejpam-2102	45	10	artinian	artinian	ADJ
ejpam-2102	45	11	ring	ring	NOUN
ejpam-2102	45	12	.	.	PUNCT
ejpam-2102	46	1	in	in	ADP
ejpam-2102	46	2	this	this	DET
ejpam-2102	46	3	paper	paper	NOUN
ejpam-2102	46	4	the	the	DET
ejpam-2102	46	5	above	above	ADV
ejpam-2102	46	6	mentioned	mention	VERB
ejpam-2102	46	7	properties	property	NOUN
ejpam-2102	46	8	have	have	AUX
ejpam-2102	46	9	been	be	AUX
ejpam-2102	46	10	studied	study	VERB
ejpam-2102	46	11	with	with	ADP
ejpam-2102	46	12	emphasis	emphasis	NOUN
ejpam-2102	46	13	on	on	ADP
ejpam-2102	46	14	primary	primary	ADJ
ejpam-2102	46	15	decomposition	decomposition	NOUN
ejpam-2102	46	16	of	of	ADP
ejpam-2102	46	17	o(r	o(r	PROPN
ejpam-2102	46	18	)	)	PUNCT
ejpam-2102	46	19	,	,	PUNCT
ejpam-2102	46	20	where	where	SCONJ
ejpam-2102	46	21	r	r	NOUN
ejpam-2102	46	22	is	be	AUX
ejpam-2102	46	23	a	a	DET
ejpam-2102	46	24	commutative	commutative	ADJ
ejpam-2102	46	25	noetherian	noetherian	ADJ
ejpam-2102	46	26	q	q	NOUN
ejpam-2102	46	27	-	-	PUNCT
ejpam-2102	46	28	algebra	algebra	NOUN
ejpam-2102	46	29	.	.	PUNCT
ejpam-2102	47	1	we	we	PRON
ejpam-2102	47	2	actually	actually	ADV
ejpam-2102	47	3	discuss	discuss	VERB
ejpam-2102	47	4	a	a	DET
ejpam-2102	47	5	stronger	strong	ADJ
ejpam-2102	47	6	type	type	NOUN
ejpam-2102	47	7	of	of	ADP
ejpam-2102	47	8	primary	primary	ADJ
ejpam-2102	47	9	decomposition	decomposition	NOUN
ejpam-2102	47	10	of	of	ADP
ejpam-2102	47	11	a	a	DET
ejpam-2102	47	12	right	right	ADJ
ejpam-2102	47	13	noetherian	noetherian	ADJ
ejpam-2102	47	14	ring	ring	NOUN
ejpam-2102	47	15	.	.	PUNCT
ejpam-2102	48	1	we	we	PRON
ejpam-2102	48	2	recall	recall	VERB
ejpam-2102	48	3	the	the	DET
ejpam-2102	48	4	following	following	NOUN
ejpam-2102	48	5	:	:	PUNCT
ejpam-2102	48	6	definition	definition	NOUN
ejpam-2102	48	7	1	1	NUM
ejpam-2102	48	8	.	.	PUNCT
ejpam-2102	49	1	a	a	DET
ejpam-2102	49	2	ring	ring	NOUN
ejpam-2102	49	3	r	r	NOUN
ejpam-2102	49	4	is	be	AUX
ejpam-2102	49	5	said	say	VERB
ejpam-2102	49	6	to	to	PART
ejpam-2102	49	7	be	be	AUX
ejpam-2102	49	8	an	an	DET
ejpam-2102	49	9	irreducible	irreducible	ADJ
ejpam-2102	49	10	ring	ring	NOUN
ejpam-2102	49	11	if	if	SCONJ
ejpam-2102	49	12	the	the	DET
ejpam-2102	49	13	intersection	intersection	NOUN
ejpam-2102	49	14	of	of	ADP
ejpam-2102	49	15	any	any	DET
ejpam-2102	49	16	two	two	NUM
ejpam-2102	49	17	non	non	ADJ
ejpam-2102	49	18	-	-	ADJ
ejpam-2102	49	19	zero	zero	NUM
ejpam-2102	49	20	ideals	ideal	NOUN
ejpam-2102	49	21	of	of	ADP
ejpam-2102	49	22	r	r	NOUN
ejpam-2102	49	23	is	be	AUX
ejpam-2102	49	24	non	non	ADJ
ejpam-2102	49	25	-	-	ADJ
ejpam-2102	49	26	zero	zero	NUM
ejpam-2102	49	27	.	.	PUNCT
ejpam-2102	50	1	an	an	DET
ejpam-2102	50	2	ideal	ideal	ADJ
ejpam-2102	50	3	i	i	PRON
ejpam-2102	50	4	of	of	ADP
ejpam-2102	50	5	r	r	NOUN
ejpam-2102	50	6	is	be	AUX
ejpam-2102	50	7	called	call	VERB
ejpam-2102	50	8	irreducible	irreducible	ADJ
ejpam-2102	50	9	if	if	SCONJ
ejpam-2102	50	10	i	i	PRON
ejpam-2102	50	11	=	=	SYM
ejpam-2102	50	12	j	j	PROPN
ejpam-2102	50	13	∩	∩	NOUN
ejpam-2102	50	14	k	k	PROPN
ejpam-2102	50	15	implies	imply	VERB
ejpam-2102	50	16	that	that	SCONJ
ejpam-2102	50	17	either	either	CCONJ
ejpam-2102	50	18	j	j	PROPN
ejpam-2102	50	19	=	=	PUNCT
ejpam-2102	50	20	i	i	PROPN
ejpam-2102	50	21	or	or	CCONJ
ejpam-2102	50	22	k	k	NOUN
ejpam-2102	50	23	=	=	SYM
ejpam-2102	50	24	i	i	PROPN
ejpam-2102	50	25	.	.	PUNCT
ejpam-2102	51	1	note	note	VERB
ejpam-2102	51	2	that	that	SCONJ
ejpam-2102	51	3	if	if	SCONJ
ejpam-2102	51	4	i	i	PRON
ejpam-2102	51	5	is	be	AUX
ejpam-2102	51	6	an	an	DET
ejpam-2102	51	7	irreducible	irreducible	ADJ
ejpam-2102	51	8	ideal	ideal	NOUN
ejpam-2102	51	9	of	of	ADP
ejpam-2102	51	10	r	r	NOUN
ejpam-2102	51	11	,	,	PUNCT
ejpam-2102	51	12	then	then	ADV
ejpam-2102	51	13	r	r	X
ejpam-2102	51	14	/	/	SYM
ejpam-2102	51	15	i	i	PRON
ejpam-2102	51	16	is	be	AUX
ejpam-2102	51	17	an	an	DET
ejpam-2102	51	18	irreducible	irreducible	ADJ
ejpam-2102	51	19	ring	ring	NOUN
ejpam-2102	51	20	.	.	PUNCT
ejpam-2102	52	1	proposition	proposition	NOUN
ejpam-2102	52	2	1	1	NUM
ejpam-2102	52	3	.	.	PUNCT
ejpam-2102	53	1	let	let	VERB
ejpam-2102	53	2	r	r	PRON
ejpam-2102	53	3	be	be	AUX
ejpam-2102	53	4	a	a	DET
ejpam-2102	53	5	noetherian	noetherian	ADJ
ejpam-2102	53	6	ring	ring	NOUN
ejpam-2102	53	7	.	.	PUNCT
ejpam-2102	54	1	then	then	ADV
ejpam-2102	54	2	there	there	PRON
ejpam-2102	54	3	exist	exist	VERB
ejpam-2102	54	4	irreducible	irreducible	ADJ
ejpam-2102	54	5	ideals	ideal	NOUN
ejpam-2102	54	6	i	i	PRON
ejpam-2102	54	7	j	j	NOUN
ejpam-2102	54	8	,	,	PUNCT
ejpam-2102	54	9	1	1	NUM
ejpam-2102	54	10	≤	≤	NUM
ejpam-2102	54	11	j	j	PROPN
ejpam-2102	54	12	≤	≤	NOUN
ejpam-2102	54	13	n	n	PROPN
ejpam-2102	54	14	of	of	ADP
ejpam-2102	54	15	r	r	NOUN
ejpam-2102	55	1	such	such	ADJ
ejpam-2102	55	2	that	that	DET
ejpam-2102	55	3	∩n	∩n	NOUN
ejpam-2102	55	4	j=1	j=1	NOUN
ejpam-2102	56	1	i	i	PRON
ejpam-2102	56	2	j	j	NOUN
ejpam-2102	57	1	=	=	NOUN
ejpam-2102	57	2	0	0	X
ejpam-2102	57	3	.	.	PUNCT
ejpam-2102	58	1	proof	proof	NOUN
ejpam-2102	58	2	.	.	PUNCT
ejpam-2102	59	1	the	the	DET
ejpam-2102	59	2	proof	proof	NOUN
ejpam-2102	59	3	is	be	AUX
ejpam-2102	59	4	obvious	obvious	ADJ
ejpam-2102	59	5	and	and	CCONJ
ejpam-2102	59	6	we	we	PRON
ejpam-2102	59	7	leave	leave	VERB
ejpam-2102	59	8	the	the	DET
ejpam-2102	59	9	details	detail	NOUN
ejpam-2102	59	10	to	to	ADP
ejpam-2102	59	11	the	the	DET
ejpam-2102	59	12	reader	reader	NOUN
ejpam-2102	59	13	.	.	PUNCT
ejpam-2102	60	1	definition	definition	NOUN
ejpam-2102	60	2	2	2	NUM
ejpam-2102	60	3	.	.	PUNCT
ejpam-2102	61	1	[	[	X
ejpam-2102	61	2	definition	definition	NOUN
ejpam-2102	61	3	1.2	1.2	NUM
ejpam-2102	61	4	of	of	ADP
ejpam-2102	61	5	[	[	X
ejpam-2102	61	6	8	8	NUM
ejpam-2102	61	7	]	]	X
ejpam-2102	61	8	]	]	X
ejpam-2102	61	9	a	a	DET
ejpam-2102	61	10	noetherian	noetherian	ADJ
ejpam-2102	61	11	ring	ring	NOUN
ejpam-2102	61	12	r	r	NOUN
ejpam-2102	61	13	is	be	AUX
ejpam-2102	61	14	said	say	VERB
ejpam-2102	61	15	to	to	PART
ejpam-2102	61	16	be	be	AUX
ejpam-2102	61	17	transparent	transparent	ADJ
ejpam-2102	61	18	ring	ring	NOUN
ejpam-2102	61	19	if	if	SCONJ
ejpam-2102	61	20	there	there	PRON
ejpam-2102	61	21	exist	exist	VERB
ejpam-2102	61	22	irreducible	irreducible	ADJ
ejpam-2102	61	23	ideals	ideal	NOUN
ejpam-2102	61	24	i	i	PRON
ejpam-2102	61	25	j	j	NOUN
ejpam-2102	61	26	,	,	PUNCT
ejpam-2102	61	27	1	1	NUM
ejpam-2102	61	28	≤	≤	NUM
ejpam-2102	61	29	j	j	PROPN
ejpam-2102	61	30	≤	≤	PROPN
ejpam-2102	61	31	n	n	CCONJ
ejpam-2102	61	32	such	such	ADJ
ejpam-2102	61	33	that	that	SCONJ
ejpam-2102	61	34	∩n	∩n	NOUN
ejpam-2102	61	35	j=1	j=1	NOUN
ejpam-2102	62	1	i	i	PRON
ejpam-2102	62	2	j	j	NOUN
ejpam-2102	63	1	=	=	PUNCT
ejpam-2102	63	2	0	0	PROPN
ejpam-2102	63	3	and	and	CCONJ
ejpam-2102	63	4	each	each	DET
ejpam-2102	63	5	r	r	NOUN
ejpam-2102	63	6	/	/	SYM
ejpam-2102	64	1	i	i	PRON
ejpam-2102	64	2	j	j	PROPN
ejpam-2102	64	3	has	have	VERB
ejpam-2102	64	4	a	a	DET
ejpam-2102	64	5	right	right	ADJ
ejpam-2102	64	6	artinian	artinian	ADJ
ejpam-2102	64	7	quotient	quotient	NOUN
ejpam-2102	64	8	ring	ring	NOUN
ejpam-2102	64	9	.	.	PUNCT
ejpam-2102	65	1	it	it	PRON
ejpam-2102	65	2	can	can	AUX
ejpam-2102	65	3	be	be	AUX
ejpam-2102	65	4	easily	easily	ADV
ejpam-2102	65	5	seen	see	VERB
ejpam-2102	65	6	that	that	SCONJ
ejpam-2102	65	7	a	a	DET
ejpam-2102	65	8	noetherian	noetherian	ADJ
ejpam-2102	65	9	integral	integral	ADJ
ejpam-2102	65	10	domain	domain	NOUN
ejpam-2102	65	11	is	be	AUX
ejpam-2102	65	12	a	a	DET
ejpam-2102	65	13	transparent	transparent	ADJ
ejpam-2102	65	14	ring	ring	NOUN
ejpam-2102	65	15	,	,	PUNCT
ejpam-2102	65	16	a	a	DET
ejpam-2102	65	17	commutative	commutative	ADJ
ejpam-2102	65	18	noetherian	noetherian	ADJ
ejpam-2102	65	19	ring	ring	NOUN
ejpam-2102	65	20	is	be	AUX
ejpam-2102	65	21	a	a	DET
ejpam-2102	65	22	transparent	transparent	ADJ
ejpam-2102	65	23	ring	ring	NOUN
ejpam-2102	65	24	and	and	CCONJ
ejpam-2102	65	25	so	so	ADV
ejpam-2102	65	26	is	be	AUX
ejpam-2102	65	27	a	a	DET
ejpam-2102	65	28	noetherian	noetherian	ADJ
ejpam-2102	65	29	ring	ring	NOUN
ejpam-2102	65	30	having	have	VERB
ejpam-2102	65	31	an	an	DET
ejpam-2102	65	32	artinian	artinian	ADJ
ejpam-2102	65	33	quotient	quotient	NOUN
ejpam-2102	65	34	ring	ring	NOUN
ejpam-2102	65	35	.	.	PUNCT
ejpam-2102	66	1	a	a	DET
ejpam-2102	66	2	fully	fully	ADV
ejpam-2102	66	3	bounded	bound	VERB
ejpam-2102	66	4	noetherian	noetherian	ADJ
ejpam-2102	66	5	ring	ring	NOUN
ejpam-2102	66	6	is	be	AUX
ejpam-2102	66	7	also	also	ADV
ejpam-2102	66	8	a	a	DET
ejpam-2102	66	9	transparent	transparent	ADJ
ejpam-2102	66	10	ring	ring	NOUN
ejpam-2102	66	11	.	.	PUNCT
ejpam-2102	67	1	the	the	DET
ejpam-2102	67	2	following	following	ADJ
ejpam-2102	67	3	result	result	NOUN
ejpam-2102	67	4	has	have	AUX
ejpam-2102	67	5	been	be	AUX
ejpam-2102	67	6	proved	prove	VERB
ejpam-2102	67	7	in	in	ADP
ejpam-2102	67	8	bhat	bhat	PROPN
ejpam-2102	67	9	[	[	X
ejpam-2102	67	10	2	2	NUM
ejpam-2102	67	11	]	]	PUNCT
ejpam-2102	67	12	towards	towards	ADP
ejpam-2102	67	13	the	the	DET
ejpam-2102	67	14	transparency	transparency	NOUN
ejpam-2102	67	15	of	of	ADP
ejpam-2102	67	16	skew	skew	ADJ
ejpam-2102	67	17	polynomial	polynomial	ADJ
ejpam-2102	67	18	rings	ring	NOUN
ejpam-2102	67	19	.	.	PUNCT
ejpam-2102	68	1	v.	v.	ADP
ejpam-2102	68	2	bhat	bhat	PROPN
ejpam-2102	68	3	and	and	CCONJ
ejpam-2102	68	4	k.	k.	PROPN
ejpam-2102	68	5	chib	chib	PROPN
ejpam-2102	68	6	/	/	SYM
ejpam-2102	68	7	eur	eur	PROPN
ejpam-2102	68	8	.	.	PUNCT
ejpam-2102	69	1	j.	j.	PROPN
ejpam-2102	69	2	pure	pure	PROPN
ejpam-2102	69	3	appl	appl	PROPN
ejpam-2102	69	4	.	.	PROPN
ejpam-2102	69	5	math	math	PROPN
ejpam-2102	69	6	,	,	PUNCT
ejpam-2102	69	7	8	8	NUM
ejpam-2102	69	8	(	(	PUNCT
ejpam-2102	69	9	2015	2015	NUM
ejpam-2102	69	10	)	)	PUNCT
ejpam-2102	69	11	,	,	PUNCT
ejpam-2102	69	12	111	111	NUM
ejpam-2102	69	13	-	-	SYM
ejpam-2102	69	14	117	117	NUM
ejpam-2102	69	15	113	113	NUM
ejpam-2102	69	16	result	result	NOUN
ejpam-2102	69	17	1	1	NUM
ejpam-2102	69	18	.	.	PUNCT
ejpam-2102	70	1	let	let	VERB
ejpam-2102	70	2	r	r	PRON
ejpam-2102	70	3	be	be	AUX
ejpam-2102	70	4	a	a	DET
ejpam-2102	70	5	commutative	commutative	ADJ
ejpam-2102	70	6	noetherian	noetherian	ADJ
ejpam-2102	70	7	ring	ring	NOUN
ejpam-2102	70	8	and	and	CCONJ
ejpam-2102	70	9	σ	σ	NOUN
ejpam-2102	70	10	an	an	DET
ejpam-2102	70	11	automorphism	automorphism	NOUN
ejpam-2102	70	12	of	of	ADP
ejpam-2102	70	13	r	r	NOUN
ejpam-2102	70	14	and	and	CCONJ
ejpam-2102	70	15	δ	δ	PROPN
ejpam-2102	70	16	a	a	DET
ejpam-2102	70	17	σderivation	σderivation	NOUN
ejpam-2102	70	18	of	of	ADP
ejpam-2102	70	19	r.	r.	PROPN
ejpam-2102	70	20	then	then	ADV
ejpam-2102	70	21	it	it	PRON
ejpam-2102	70	22	is	be	AUX
ejpam-2102	70	23	known	know	VERB
ejpam-2102	70	24	that	that	SCONJ
ejpam-2102	70	25	s(r	s(r	ADV
ejpam-2102	70	26	)	)	PUNCT
ejpam-2102	70	27	and	and	CCONJ
ejpam-2102	70	28	d(r	d(r	NOUN
ejpam-2102	70	29	)	)	PUNCT
ejpam-2102	70	30	are	be	AUX
ejpam-2102	70	31	transparent	transparent	ADJ
ejpam-2102	70	32	(	(	PUNCT
ejpam-2102	70	33	bhat	bhat	PROPN
ejpam-2102	71	1	[	[	X
ejpam-2102	71	2	2	2	NUM
ejpam-2102	71	3	]	]	PUNCT
ejpam-2102	71	4	)	)	PUNCT
ejpam-2102	71	5	.	.	PUNCT
ejpam-2102	72	1	the	the	DET
ejpam-2102	72	2	following	follow	VERB
ejpam-2102	72	3	result	result	NOUN
ejpam-2102	72	4	has	have	AUX
ejpam-2102	72	5	been	be	AUX
ejpam-2102	72	6	proved	prove	VERB
ejpam-2102	72	7	in	in	ADP
ejpam-2102	72	8	bhat	bhat	PROPN
ejpam-2102	72	9	[	[	X
ejpam-2102	72	10	8	8	NUM
ejpam-2102	72	11	]	]	PUNCT
ejpam-2102	72	12	.	.	PUNCT
ejpam-2102	73	1	theorem	theorem	NOUN
ejpam-2102	73	2	1	1	NUM
ejpam-2102	73	3	.	.	PUNCT
ejpam-2102	74	1	[	[	X
ejpam-2102	74	2	theorem	theorem	X
ejpam-2102	74	3	(	(	PUNCT
ejpam-2102	74	4	3.4	3.4	NUM
ejpam-2102	74	5	)	)	PUNCT
ejpam-2102	74	6	of	of	ADP
ejpam-2102	74	7	[	[	X
ejpam-2102	74	8	8	8	NUM
ejpam-2102	74	9	]	]	X
ejpam-2102	74	10	]	]	PUNCT
ejpam-2102	74	11	let	let	VERB
ejpam-2102	74	12	r	r	PRON
ejpam-2102	74	13	be	be	AUX
ejpam-2102	74	14	a	a	DET
ejpam-2102	74	15	commutative	commutative	ADJ
ejpam-2102	74	16	noetherian	noetherian	ADJ
ejpam-2102	74	17	q	q	NOUN
ejpam-2102	74	18	-	-	PUNCT
ejpam-2102	74	19	algebra	algebra	NOUN
ejpam-2102	74	20	,	,	PUNCT
ejpam-2102	74	21	σ	σ	NOUN
ejpam-2102	74	22	an	an	DET
ejpam-2102	74	23	automorphism	automorphism	NOUN
ejpam-2102	74	24	of	of	ADP
ejpam-2102	74	25	r.	r.	PROPN
ejpam-2102	74	26	then	then	ADV
ejpam-2102	74	27	there	there	PRON
ejpam-2102	74	28	exists	exist	VERB
ejpam-2102	74	29	an	an	DET
ejpam-2102	74	30	integer	integer	NOUN
ejpam-2102	74	31	m	m	NOUN
ejpam-2102	74	32	≥	≥	NOUN
ejpam-2102	74	33	1	1	NUM
ejpam-2102	74	34	such	such	ADJ
ejpam-2102	74	35	that	that	SCONJ
ejpam-2102	74	36	the	the	DET
ejpam-2102	74	37	skew	skew	ADJ
ejpam-2102	74	38	-	-	PUNCT
ejpam-2102	74	39	polynomial	polynomial	ADJ
ejpam-2102	74	40	ring	ring	NOUN
ejpam-2102	74	41	r[x;α	r[x;α	PROPN
ejpam-2102	74	42	,	,	PUNCT
ejpam-2102	74	43	δ	δ	PROPN
ejpam-2102	74	44	]	]	PUNCT
ejpam-2102	74	45	is	be	AUX
ejpam-2102	74	46	a	a	DET
ejpam-2102	74	47	transparent	transparent	ADJ
ejpam-2102	74	48	ring	ring	NOUN
ejpam-2102	74	49	,	,	PUNCT
ejpam-2102	74	50	where	where	SCONJ
ejpam-2102	74	51	σm	σm	NOUN
ejpam-2102	74	52	=	=	SYM
ejpam-2102	74	53	α	α	PROPN
ejpam-2102	74	54	and	and	CCONJ
ejpam-2102	74	55	δ	δ	PROPN
ejpam-2102	74	56	is	be	AUX
ejpam-2102	74	57	an	an	DET
ejpam-2102	74	58	α	α	NOUN
ejpam-2102	74	59	-	-	NOUN
ejpam-2102	74	60	derivation	derivation	NOUN
ejpam-2102	74	61	of	of	ADP
ejpam-2102	74	62	r	r	NOUN
ejpam-2102	74	63	such	such	ADJ
ejpam-2102	74	64	that	that	DET
ejpam-2102	74	65	α(δ(a	α(δ(a	NOUN
ejpam-2102	74	66	)	)	PUNCT
ejpam-2102	74	67	)	)	PUNCT
ejpam-2102	75	1	=	=	PUNCT
ejpam-2102	75	2	δ(α(a	δ(α(a	NOUN
ejpam-2102	75	3	)	)	PUNCT
ejpam-2102	75	4	)	)	PUNCT
ejpam-2102	75	5	,	,	PUNCT
ejpam-2102	75	6	for	for	ADP
ejpam-2102	75	7	all	all	DET
ejpam-2102	75	8	a	a	DET
ejpam-2102	75	9	∈	∈	PROPN
ejpam-2102	75	10	r.	r.	NOUN
ejpam-2102	75	11	in	in	ADP
ejpam-2102	75	12	this	this	DET
ejpam-2102	75	13	paper	paper	NOUN
ejpam-2102	75	14	,	,	PUNCT
ejpam-2102	75	15	we	we	PRON
ejpam-2102	75	16	generalize	generalize	VERB
ejpam-2102	75	17	theorem	theorem	ADJ
ejpam-2102	75	18	(	(	PUNCT
ejpam-2102	75	19	3.4	3.4	NUM
ejpam-2102	75	20	)	)	PUNCT
ejpam-2102	75	21	of	of	ADP
ejpam-2102	75	22	[	[	X
ejpam-2102	75	23	8	8	NUM
ejpam-2102	75	24	]	]	PUNCT
ejpam-2102	75	25	.	.	PUNCT
ejpam-2102	76	1	but	but	CCONJ
ejpam-2102	76	2	before	before	SCONJ
ejpam-2102	76	3	we	we	PRON
ejpam-2102	76	4	state	state	VERB
ejpam-2102	76	5	the	the	DET
ejpam-2102	76	6	main	main	ADJ
ejpam-2102	76	7	result	result	NOUN
ejpam-2102	76	8	,	,	PUNCT
ejpam-2102	76	9	we	we	PRON
ejpam-2102	76	10	need	need	VERB
ejpam-2102	76	11	the	the	DET
ejpam-2102	76	12	following	following	NOUN
ejpam-2102	76	13	:	:	PUNCT
ejpam-2102	77	1	1.1	1.1	NUM
ejpam-2102	77	2	.	.	X
ejpam-2102	77	3	2	2	NUM
ejpam-2102	77	4	-	-	PUNCT
ejpam-2102	77	5	primal	primal	ADJ
ejpam-2102	77	6	rings	ring	NOUN
ejpam-2102	77	7	a	a	DET
ejpam-2102	77	8	ring	ring	NOUN
ejpam-2102	77	9	r	r	NOUN
ejpam-2102	77	10	is	be	AUX
ejpam-2102	77	11	called	call	VERB
ejpam-2102	77	12	a	a	DET
ejpam-2102	77	13	2	2	NUM
ejpam-2102	77	14	-	-	PUNCT
ejpam-2102	77	15	primal	primal	ADJ
ejpam-2102	77	16	if	if	SCONJ
ejpam-2102	77	17	p(r	p(r	NOUN
ejpam-2102	77	18	)	)	PUNCT
ejpam-2102	77	19	=	=	SYM
ejpam-2102	77	20	n(r	n(r	NOUN
ejpam-2102	77	21	)	)	PUNCT
ejpam-2102	77	22	,	,	PUNCT
ejpam-2102	77	23	i.e.	i.e.	X
ejpam-2102	77	24	if	if	SCONJ
ejpam-2102	77	25	the	the	DET
ejpam-2102	77	26	prime	prime	ADJ
ejpam-2102	77	27	radical	radical	NOUN
ejpam-2102	77	28	is	be	AUX
ejpam-2102	77	29	a	a	DET
ejpam-2102	77	30	completely	completely	ADV
ejpam-2102	77	31	semiprime	semiprime	NOUN
ejpam-2102	77	32	ideal	ideal	NOUN
ejpam-2102	77	33	.	.	PUNCT
ejpam-2102	78	1	an	an	DET
ejpam-2102	78	2	ideal	ideal	ADJ
ejpam-2102	78	3	i	i	PRON
ejpam-2102	78	4	of	of	ADP
ejpam-2102	78	5	a	a	DET
ejpam-2102	78	6	ring	ring	NOUN
ejpam-2102	78	7	r	r	NOUN
ejpam-2102	78	8	is	be	AUX
ejpam-2102	78	9	called	call	VERB
ejpam-2102	78	10	completely	completely	ADV
ejpam-2102	78	11	semiprime	semiprime	NOUN
ejpam-2102	78	12	if	if	SCONJ
ejpam-2102	78	13	a2	a2	PROPN
ejpam-2102	78	14	∈	∈	PROPN
ejpam-2102	78	15	i	i	PRON
ejpam-2102	78	16	for	for	ADP
ejpam-2102	78	17	a	a	DET
ejpam-2102	78	18	∈	∈	PROPN
ejpam-2102	78	19	r.	r.	PROPN
ejpam-2102	78	20	minimal	minimal	ADJ
ejpam-2102	78	21	prime	prime	ADJ
ejpam-2102	78	22	ideals	ideal	NOUN
ejpam-2102	78	23	of	of	ADP
ejpam-2102	78	24	2	2	NUM
ejpam-2102	78	25	-	-	PUNCT
ejpam-2102	78	26	primal	primal	ADJ
ejpam-2102	78	27	rings	ring	NOUN
ejpam-2102	78	28	have	have	AUX
ejpam-2102	78	29	been	be	AUX
ejpam-2102	78	30	discussed	discuss	VERB
ejpam-2102	78	31	by	by	ADP
ejpam-2102	78	32	kim	kim	PROPN
ejpam-2102	78	33	and	and	CCONJ
ejpam-2102	78	34	kwak	kwak	PROPN
ejpam-2102	78	35	in	in	ADP
ejpam-2102	78	36	[	[	X
ejpam-2102	78	37	14	14	NUM
ejpam-2102	78	38	]	]	PUNCT
ejpam-2102	78	39	.	.	PUNCT
ejpam-2102	79	1	2primal	2primal	NUM
ejpam-2102	79	2	near	near	ADJ
ejpam-2102	79	3	rings	ring	NOUN
ejpam-2102	79	4	have	have	AUX
ejpam-2102	79	5	been	be	AUX
ejpam-2102	79	6	discussed	discuss	VERB
ejpam-2102	79	7	by	by	ADP
ejpam-2102	79	8	argac	argac	PROPN
ejpam-2102	79	9	and	and	CCONJ
ejpam-2102	79	10	groenewald	groenewald	NOUN
ejpam-2102	79	11	in	in	ADP
ejpam-2102	79	12	[	[	X
ejpam-2102	79	13	1	1	NUM
ejpam-2102	79	14	]	]	PUNCT
ejpam-2102	79	15	.	.	PUNCT
ejpam-2102	80	1	2	2	NUM
ejpam-2102	80	2	-	-	PUNCT
ejpam-2102	80	3	primal	primal	ADJ
ejpam-2102	80	4	rings	ring	NOUN
ejpam-2102	80	5	have	have	AUX
ejpam-2102	80	6	been	be	AUX
ejpam-2102	80	7	studied	study	VERB
ejpam-2102	80	8	in	in	ADP
ejpam-2102	80	9	recent	recent	ADJ
ejpam-2102	80	10	years	year	NOUN
ejpam-2102	80	11	and	and	CCONJ
ejpam-2102	80	12	are	be	AUX
ejpam-2102	80	13	being	be	AUX
ejpam-2102	80	14	treated	treat	VERB
ejpam-2102	80	15	by	by	ADP
ejpam-2102	80	16	authors	author	NOUN
ejpam-2102	80	17	for	for	ADP
ejpam-2102	80	18	different	different	ADJ
ejpam-2102	80	19	structures	structure	NOUN
ejpam-2102	80	20	.	.	PUNCT
ejpam-2102	81	1	in	in	ADP
ejpam-2102	81	2	[	[	X
ejpam-2102	81	3	14	14	NUM
ejpam-2102	81	4	]	]	PUNCT
ejpam-2102	81	5	,	,	PUNCT
ejpam-2102	81	6	greg	greg	PROPN
ejpam-2102	81	7	marks	marks	PROPN
ejpam-2102	81	8	discusses	discuss	VERB
ejpam-2102	81	9	the	the	DET
ejpam-2102	81	10	2	2	NUM
ejpam-2102	81	11	-	-	PUNCT
ejpam-2102	81	12	primal	primal	ADJ
ejpam-2102	81	13	property	property	NOUN
ejpam-2102	81	14	of	of	ADP
ejpam-2102	81	15	r[x;σ	r[x;σ	NOUN
ejpam-2102	81	16	,	,	PUNCT
ejpam-2102	81	17	δ	δ	PROPN
ejpam-2102	81	18	]	]	X
ejpam-2102	81	19	,	,	PUNCT
ejpam-2102	81	20	where	where	SCONJ
ejpam-2102	81	21	r	r	NOUN
ejpam-2102	81	22	is	be	AUX
ejpam-2102	81	23	a	a	DET
ejpam-2102	81	24	local	local	ADJ
ejpam-2102	81	25	ring	ring	NOUN
ejpam-2102	81	26	,	,	PUNCT
ejpam-2102	81	27	σ	σ	VERB
ejpam-2102	81	28	an	an	DET
ejpam-2102	81	29	automorphism	automorphism	NOUN
ejpam-2102	81	30	of	of	ADP
ejpam-2102	81	31	r	r	NOUN
ejpam-2102	81	32	and	and	CCONJ
ejpam-2102	81	33	δ	δ	PROPN
ejpam-2102	81	34	a	a	DET
ejpam-2102	81	35	σ	σ	NOUN
ejpam-2102	81	36	-	-	PUNCT
ejpam-2102	81	37	derivation	derivation	NOUN
ejpam-2102	81	38	of	of	ADP
ejpam-2102	81	39	r.	r.	PROPN
ejpam-2102	81	40	in	in	ADP
ejpam-2102	81	41	greg	greg	PROPN
ejpam-2102	81	42	marks	marks	PROPN
ejpam-2102	82	1	[	[	X
ejpam-2102	82	2	14	14	NUM
ejpam-2102	82	3	]	]	PUNCT
ejpam-2102	82	4	,	,	PUNCT
ejpam-2102	82	5	it	it	PRON
ejpam-2102	82	6	has	have	AUX
ejpam-2102	82	7	been	be	AUX
ejpam-2102	82	8	shown	show	VERB
ejpam-2102	82	9	that	that	SCONJ
ejpam-2102	82	10	for	for	ADP
ejpam-2102	82	11	a	a	DET
ejpam-2102	82	12	local	local	ADJ
ejpam-2102	82	13	ring	ring	NOUN
ejpam-2102	82	14	r	r	NOUN
ejpam-2102	82	15	with	with	ADP
ejpam-2102	82	16	a	a	DET
ejpam-2102	82	17	nilpotent	nilpotent	ADJ
ejpam-2102	82	18	maximal	maximal	ADJ
ejpam-2102	82	19	ideal	ideal	NOUN
ejpam-2102	82	20	,	,	PUNCT
ejpam-2102	82	21	the	the	DET
ejpam-2102	82	22	ore	ore	NOUN
ejpam-2102	82	23	extension	extension	NOUN
ejpam-2102	82	24	r[x;σ	r[x;σ	NOUN
ejpam-2102	82	25	,	,	PUNCT
ejpam-2102	82	26	δ	δ	PROPN
ejpam-2102	82	27	]	]	PUNCT
ejpam-2102	82	28	will	will	AUX
ejpam-2102	82	29	or	or	CCONJ
ejpam-2102	82	30	will	will	AUX
ejpam-2102	82	31	not	not	PART
ejpam-2102	82	32	be	be	AUX
ejpam-2102	82	33	2	2	NUM
ejpam-2102	82	34	-	-	NOUN
ejpam-2102	82	35	primal	primal	ADJ
ejpam-2102	82	36	depending	depend	VERB
ejpam-2102	82	37	on	on	ADP
ejpam-2102	82	38	the	the	DET
ejpam-2102	82	39	δ	δ	NOUN
ejpam-2102	82	40	-	-	NOUN
ejpam-2102	82	41	stability	stability	NOUN
ejpam-2102	82	42	of	of	ADP
ejpam-2102	82	43	the	the	DET
ejpam-2102	82	44	maximal	maximal	ADJ
ejpam-2102	82	45	ideal	ideal	NOUN
ejpam-2102	82	46	of	of	ADP
ejpam-2102	82	47	r.	r.	PROPN
ejpam-2102	82	48	in	in	ADP
ejpam-2102	82	49	the	the	DET
ejpam-2102	82	50	case	case	NOUN
ejpam-2102	82	51	where	where	SCONJ
ejpam-2102	82	52	r[x;σ	r[x;σ	NOUN
ejpam-2102	82	53	,	,	PUNCT
ejpam-2102	82	54	δ	δ	PROPN
ejpam-2102	82	55	]	]	PUNCT
ejpam-2102	82	56	is	be	AUX
ejpam-2102	82	57	2	2	NUM
ejpam-2102	82	58	-	-	PUNCT
ejpam-2102	82	59	primal	primal	ADJ
ejpam-2102	82	60	,	,	PUNCT
ejpam-2102	82	61	it	it	PRON
ejpam-2102	82	62	will	will	AUX
ejpam-2102	82	63	satisfy	satisfy	VERB
ejpam-2102	82	64	an	an	DET
ejpam-2102	82	65	even	even	ADV
ejpam-2102	82	66	stronger	strong	ADJ
ejpam-2102	82	67	condition	condition	NOUN
ejpam-2102	82	68	;	;	PUNCT
ejpam-2102	82	69	in	in	ADP
ejpam-2102	82	70	the	the	DET
ejpam-2102	82	71	case	case	NOUN
ejpam-2102	82	72	where	where	SCONJ
ejpam-2102	82	73	r[x;σ	r[x;σ	NOUN
ejpam-2102	82	74	,	,	PUNCT
ejpam-2102	82	75	δ	δ	PROPN
ejpam-2102	82	76	]	]	PUNCT
ejpam-2102	82	77	is	be	AUX
ejpam-2102	82	78	not	not	PART
ejpam-2102	82	79	2	2	NUM
ejpam-2102	82	80	-	-	PUNCT
ejpam-2102	82	81	primal	primal	ADJ
ejpam-2102	82	82	,	,	PUNCT
ejpam-2102	82	83	it	it	PRON
ejpam-2102	82	84	will	will	AUX
ejpam-2102	82	85	fail	fail	VERB
ejpam-2102	82	86	to	to	PART
ejpam-2102	82	87	satisfy	satisfy	VERB
ejpam-2102	82	88	an	an	DET
ejpam-2102	82	89	even	even	ADV
ejpam-2102	82	90	weaker	weak	ADJ
ejpam-2102	82	91	condition	condition	NOUN
ejpam-2102	82	92	.	.	PUNCT
ejpam-2102	83	1	we	we	PRON
ejpam-2102	83	2	note	note	VERB
ejpam-2102	83	3	that	that	SCONJ
ejpam-2102	83	4	a	a	DET
ejpam-2102	83	5	reduced	reduce	VERB
ejpam-2102	83	6	ring	ring	NOUN
ejpam-2102	83	7	(	(	PUNCT
ejpam-2102	83	8	i.e.	i.e.	X
ejpam-2102	83	9	a	a	DET
ejpam-2102	83	10	ring	ring	NOUN
ejpam-2102	83	11	with	with	ADP
ejpam-2102	83	12	no	no	DET
ejpam-2102	83	13	non	non	ADJ
ejpam-2102	83	14	-	-	ADJ
ejpam-2102	83	15	zero	zero	ADJ
ejpam-2102	83	16	nilpotent	nilpotent	ADJ
ejpam-2102	83	17	elements	element	NOUN
ejpam-2102	83	18	)	)	PUNCT
ejpam-2102	83	19	is	be	AUX
ejpam-2102	83	20	2	2	NUM
ejpam-2102	83	21	-	-	PUNCT
ejpam-2102	83	22	primal	primal	ADJ
ejpam-2102	83	23	and	and	CCONJ
ejpam-2102	83	24	a	a	DET
ejpam-2102	83	25	commutative	commutative	ADJ
ejpam-2102	83	26	ring	ring	NOUN
ejpam-2102	83	27	is	be	AUX
ejpam-2102	83	28	also	also	ADV
ejpam-2102	83	29	2	2	NUM
ejpam-2102	83	30	-	-	PUNCT
ejpam-2102	83	31	primal	primal	ADJ
ejpam-2102	83	32	.	.	PUNCT
ejpam-2102	84	1	for	for	ADP
ejpam-2102	84	2	further	further	ADJ
ejpam-2102	84	3	details	detail	NOUN
ejpam-2102	84	4	on	on	ADP
ejpam-2102	84	5	2	2	NUM
ejpam-2102	84	6	-	-	PUNCT
ejpam-2102	84	7	primal	primal	ADJ
ejpam-2102	84	8	rings	ring	NOUN
ejpam-2102	84	9	,	,	PUNCT
ejpam-2102	84	10	we	we	PRON
ejpam-2102	84	11	refer	refer	VERB
ejpam-2102	84	12	the	the	DET
ejpam-2102	84	13	reader	reader	NOUN
ejpam-2102	84	14	to	to	ADP
ejpam-2102	84	15	[	[	X
ejpam-2102	84	16	1	1	NUM
ejpam-2102	84	17	,	,	PUNCT
ejpam-2102	84	18	5	5	NUM
ejpam-2102	84	19	,	,	PUNCT
ejpam-2102	84	20	7	7	NUM
ejpam-2102	84	21	,	,	PUNCT
ejpam-2102	84	22	13	13	NUM
ejpam-2102	84	23	,	,	PUNCT
ejpam-2102	84	24	14	14	NUM
ejpam-2102	84	25	]	]	PUNCT
ejpam-2102	84	26	.	.	PUNCT
ejpam-2102	85	1	we	we	PRON
ejpam-2102	85	2	note	note	VERB
ejpam-2102	85	3	that	that	SCONJ
ejpam-2102	85	4	a	a	DET
ejpam-2102	85	5	noetherian	noetherian	ADJ
ejpam-2102	85	6	ring	ring	NOUN
ejpam-2102	85	7	need	need	AUX
ejpam-2102	85	8	not	not	PART
ejpam-2102	85	9	be	be	AUX
ejpam-2102	85	10	2	2	NUM
ejpam-2102	85	11	-	-	NOUN
ejpam-2102	85	12	primal	primal	ADJ
ejpam-2102	85	13	.	.	PUNCT
ejpam-2102	86	1	for	for	ADP
ejpam-2102	86	2	this	this	PRON
ejpam-2102	86	3	we	we	PRON
ejpam-2102	86	4	have	have	VERB
ejpam-2102	86	5	the	the	DET
ejpam-2102	86	6	following	following	NOUN
ejpam-2102	86	7	:	:	PUNCT
ejpam-2102	86	8	example	example	NOUN
ejpam-2102	87	1	1	1	NUM
ejpam-2102	87	2	.	.	PUNCT
ejpam-2102	88	1	[	[	X
ejpam-2102	88	2	example	example	NOUN
ejpam-2102	88	3	(	(	PUNCT
ejpam-2102	88	4	4	4	NUM
ejpam-2102	88	5	)	)	PUNCT
ejpam-2102	88	6	of	of	ADP
ejpam-2102	88	7	bhat	bhat	PROPN
ejpam-2102	88	8	[	[	X
ejpam-2102	88	9	10	10	NUM
ejpam-2102	88	10	]	]	X
ejpam-2102	88	11	]	]	X
ejpam-2102	88	12	let	let	VERB
ejpam-2102	88	13	r	r	NOUN
ejpam-2102	88	14	=	=	PUNCT
ejpam-2102	88	15	q	q	NOUN
ejpam-2102	88	16	⊕q	⊕q	NOUN
ejpam-2102	88	17	with	with	ADP
ejpam-2102	88	18	σ(a	σ(a	PROPN
ejpam-2102	88	19	,	,	PUNCT
ejpam-2102	88	20	b	b	NOUN
ejpam-2102	88	21	)	)	PUNCT
ejpam-2102	88	22	=	=	SYM
ejpam-2102	88	23	(	(	PUNCT
ejpam-2102	88	24	b	b	NOUN
ejpam-2102	88	25	,	,	PUNCT
ejpam-2102	88	26	a	a	PRON
ejpam-2102	88	27	)	)	PUNCT
ejpam-2102	88	28	.	.	PUNCT
ejpam-2102	89	1	then	then	ADV
ejpam-2102	89	2	the	the	DET
ejpam-2102	89	3	only	only	ADJ
ejpam-2102	89	4	σ	σ	PROPN
ejpam-2102	89	5	-	-	PUNCT
ejpam-2102	89	6	invariant	invariant	ADJ
ejpam-2102	89	7	ideals	ideal	NOUN
ejpam-2102	89	8	of	of	ADP
ejpam-2102	89	9	r	r	NOUN
ejpam-2102	89	10	are	be	AUX
ejpam-2102	89	11	0	0	NUM
ejpam-2102	89	12	and	and	CCONJ
ejpam-2102	89	13	r	r	NOUN
ejpam-2102	89	14	,	,	PUNCT
ejpam-2102	89	15	and	and	CCONJ
ejpam-2102	89	16	so	so	ADV
ejpam-2102	89	17	r	r	NOUN
ejpam-2102	89	18	is	be	AUX
ejpam-2102	89	19	σ	σ	NOUN
ejpam-2102	89	20	-	-	NOUN
ejpam-2102	89	21	prime	prime	NOUN
ejpam-2102	89	22	.	.	PUNCT
ejpam-2102	90	1	let	let	VERB
ejpam-2102	90	2	δ	δ	NOUN
ejpam-2102	90	3	:	:	PUNCT
ejpam-2102	91	1	r→	r→	PROPN
ejpam-2102	91	2	r	r	NOUN
ejpam-2102	91	3	be	be	AUX
ejpam-2102	91	4	defined	define	VERB
ejpam-2102	91	5	by	by	ADP
ejpam-2102	91	6	δ(r	δ(r	NOUN
ejpam-2102	91	7	)	)	PUNCT
ejpam-2102	92	1	=	=	SYM
ejpam-2102	92	2	ra−	ra−	PROPN
ejpam-2102	92	3	aσ(r	aσ(r	NOUN
ejpam-2102	92	4	)	)	PUNCT
ejpam-2102	92	5	,	,	PUNCT
ejpam-2102	92	6	where	where	SCONJ
ejpam-2102	92	7	a	a	DET
ejpam-2102	92	8	=	=	SYM
ejpam-2102	92	9	(	(	PUNCT
ejpam-2102	92	10	0,α	0,α	PROPN
ejpam-2102	92	11	)	)	PUNCT
ejpam-2102	92	12	∈	∈	PROPN
ejpam-2102	92	13	r.	r.	PROPN
ejpam-2102	92	14	then	then	ADV
ejpam-2102	92	15	δ	δ	PROPN
ejpam-2102	92	16	is	be	AUX
ejpam-2102	92	17	a	a	DET
ejpam-2102	92	18	σ	σ	NOUN
ejpam-2102	92	19	-	-	PUNCT
ejpam-2102	92	20	derivation	derivation	NOUN
ejpam-2102	92	21	of	of	ADP
ejpam-2102	92	22	r	r	NOUN
ejpam-2102	92	23	and	and	CCONJ
ejpam-2102	92	24	r[x;σ	r[x;σ	NOUN
ejpam-2102	92	25	,	,	PUNCT
ejpam-2102	92	26	δ	δ	PROPN
ejpam-2102	92	27	]	]	PUNCT
ejpam-2102	92	28	is	be	AUX
ejpam-2102	92	29	prime	prime	ADJ
ejpam-2102	92	30	and	and	CCONJ
ejpam-2102	92	31	p(r[x;σ	p(r[x;σ	VERB
ejpam-2102	92	32	,	,	PUNCT
ejpam-2102	92	33	δ	δ	NOUN
ejpam-2102	92	34	]	]	X
ejpam-2102	92	35	)	)	PUNCT
ejpam-2102	93	1	=	=	SYM
ejpam-2102	93	2	0	0	X
ejpam-2102	93	3	.	.	PUNCT
ejpam-2102	94	1	but	but	CCONJ
ejpam-2102	94	2	(	(	PUNCT
ejpam-2102	94	3	x(1,0))2	x(1,0))2	NOUN
ejpam-2102	94	4	=	=	SYM
ejpam-2102	94	5	0	0	NUM
ejpam-2102	94	6	as	as	ADP
ejpam-2102	94	7	δ(1,0	δ(1,0	NOUN
ejpam-2102	94	8	)	)	PUNCT
ejpam-2102	94	9	=	=	SYM
ejpam-2102	94	10	−(0,α	−(0,α	PROPN
ejpam-2102	94	11	)	)	PUNCT
ejpam-2102	94	12	.	.	PUNCT
ejpam-2102	95	1	therefore	therefore	ADV
ejpam-2102	95	2	r[x;σ	r[x;σ	NOUN
ejpam-2102	95	3	,	,	PUNCT
ejpam-2102	95	4	δ	δ	PROPN
ejpam-2102	95	5	]	]	PUNCT
ejpam-2102	95	6	is	be	AUX
ejpam-2102	95	7	not	not	PART
ejpam-2102	95	8	2	2	NUM
ejpam-2102	95	9	-	-	PUNCT
ejpam-2102	95	10	primal	primal	ADJ
ejpam-2102	95	11	.	.	PUNCT
ejpam-2102	96	1	if	if	SCONJ
ejpam-2102	96	2	δ	δ	PROPN
ejpam-2102	96	3	is	be	AUX
ejpam-2102	96	4	taken	take	VERB
ejpam-2102	96	5	to	to	PART
ejpam-2102	96	6	be	be	AUX
ejpam-2102	96	7	the	the	DET
ejpam-2102	96	8	zero	zero	NUM
ejpam-2102	96	9	map	map	NOUN
ejpam-2102	96	10	,	,	PUNCT
ejpam-2102	96	11	then	then	ADV
ejpam-2102	96	12	even	even	ADV
ejpam-2102	96	13	r[x;σ	r[x;σ	NOUN
ejpam-2102	96	14	]	]	PUNCT
ejpam-2102	96	15	is	be	AUX
ejpam-2102	96	16	not	not	PART
ejpam-2102	96	17	2	2	NUM
ejpam-2102	96	18	-	-	PUNCT
ejpam-2102	96	19	primal	primal	ADJ
ejpam-2102	96	20	.	.	PUNCT
ejpam-2102	96	21	example	example	NOUN
ejpam-2102	97	1	2	2	NUM
ejpam-2102	97	2	.	.	PUNCT
ejpam-2102	98	1	[	[	X
ejpam-2102	98	2	example	example	NOUN
ejpam-2102	98	3	(	(	PUNCT
ejpam-2102	98	4	5	5	NUM
ejpam-2102	98	5	)	)	PUNCT
ejpam-2102	98	6	of	of	ADP
ejpam-2102	98	7	bhat	bhat	PROPN
ejpam-2102	98	8	[	[	X
ejpam-2102	98	9	10	10	NUM
ejpam-2102	98	10	]	]	PUNCT
ejpam-2102	98	11	]	]	X
ejpam-2102	98	12	let	let	VERB
ejpam-2102	98	13	r	r	NOUN
ejpam-2102	98	14	=	=	SYM
ejpam-2102	98	15	m2(q	m2(q	NOUN
ejpam-2102	98	16	)	)	PUNCT
ejpam-2102	98	17	,	,	PUNCT
ejpam-2102	98	18	the	the	DET
ejpam-2102	98	19	set	set	NOUN
ejpam-2102	98	20	of	of	ADP
ejpam-2102	98	21	2×	2×	NUM
ejpam-2102	98	22	2	2	NUM
ejpam-2102	98	23	matrices	matrix	NOUN
ejpam-2102	98	24	over	over	ADP
ejpam-2102	98	25	q.	q.	PROPN
ejpam-2102	98	26	then	then	ADV
ejpam-2102	98	27	r[x	r[x	PROPN
ejpam-2102	98	28	]	]	PUNCT
ejpam-2102	98	29	is	be	AUX
ejpam-2102	98	30	a	a	DET
ejpam-2102	98	31	prime	prime	ADJ
ejpam-2102	98	32	ring	ring	NOUN
ejpam-2102	98	33	with	with	ADP
ejpam-2102	98	34	non	non	ADJ
ejpam-2102	98	35	-	-	ADJ
ejpam-2102	98	36	zero	zero	ADJ
ejpam-2102	98	37	nilpotent	nilpotent	ADJ
ejpam-2102	98	38	elements	element	NOUN
ejpam-2102	98	39	and	and	CCONJ
ejpam-2102	98	40	so	so	ADV
ejpam-2102	98	41	can	can	AUX
ejpam-2102	98	42	not	not	PART
ejpam-2102	98	43	be	be	AUX
ejpam-2102	98	44	2	2	NUM
ejpam-2102	98	45	-	-	NOUN
ejpam-2102	98	46	primal	primal	ADJ
ejpam-2102	98	47	.	.	PUNCT
ejpam-2102	99	1	from	from	ADP
ejpam-2102	99	2	these	these	DET
ejpam-2102	99	3	examples	example	NOUN
ejpam-2102	99	4	we	we	PRON
ejpam-2102	99	5	conclude	conclude	VERB
ejpam-2102	99	6	that	that	SCONJ
ejpam-2102	99	7	if	if	SCONJ
ejpam-2102	99	8	r	r	NOUN
ejpam-2102	99	9	is	be	AUX
ejpam-2102	99	10	a	a	DET
ejpam-2102	99	11	noetherian	noetherian	ADJ
ejpam-2102	99	12	ring	ring	NOUN
ejpam-2102	99	13	,	,	PUNCT
ejpam-2102	99	14	then	then	ADV
ejpam-2102	99	15	r[x;σ	r[x;σ	NOUN
ejpam-2102	99	16	,	,	PUNCT
ejpam-2102	99	17	δ	δ	PROPN
ejpam-2102	99	18	]	]	PUNCT
ejpam-2102	99	19	and	and	CCONJ
ejpam-2102	99	20	r[x	r[x	NOUN
ejpam-2102	99	21	]	]	PUNCT
ejpam-2102	99	22	need	need	AUX
ejpam-2102	99	23	not	not	PART
ejpam-2102	99	24	be	be	AUX
ejpam-2102	99	25	2	2	NUM
ejpam-2102	99	26	-	-	PUNCT
ejpam-2102	99	27	primal	primal	ADJ
ejpam-2102	99	28	.	.	PUNCT
ejpam-2102	100	1	but	but	CCONJ
ejpam-2102	100	2	it	it	PRON
ejpam-2102	100	3	is	be	AUX
ejpam-2102	100	4	known	know	VERB
ejpam-2102	100	5	that	that	SCONJ
ejpam-2102	100	6	if	if	SCONJ
ejpam-2102	100	7	r	r	NOUN
ejpam-2102	100	8	is	be	AUX
ejpam-2102	100	9	a	a	DET
ejpam-2102	100	10	2	2	NUM
ejpam-2102	100	11	-	-	PUNCT
ejpam-2102	100	12	primal	primal	ADJ
ejpam-2102	100	13	noetherian	noetherian	ADJ
ejpam-2102	100	14	q	q	NOUN
ejpam-2102	100	15	-	-	PUNCT
ejpam-2102	100	16	algebra	algebra	NOUN
ejpam-2102	100	17	and	and	CCONJ
ejpam-2102	100	18	δ	δ	PROPN
ejpam-2102	100	19	is	be	AUX
ejpam-2102	100	20	a	a	DET
ejpam-2102	100	21	derivation	derivation	NOUN
ejpam-2102	100	22	of	of	ADP
ejpam-2102	100	23	r	r	NOUN
ejpam-2102	100	24	,	,	PUNCT
ejpam-2102	100	25	then	then	ADV
ejpam-2102	100	26	r[x;δ	r[x;δ	NOUN
ejpam-2102	100	27	]	]	PUNCT
ejpam-2102	100	28	is	be	AUX
ejpam-2102	100	29	2	2	NUM
ejpam-2102	100	30	-	-	PUNCT
ejpam-2102	100	31	primal	primal	ADJ
ejpam-2102	100	32	noetherian	noetherian	NOUN
ejpam-2102	100	33	(	(	PUNCT
ejpam-2102	100	34	theorem	theorem	NOUN
ejpam-2102	100	35	(	(	PUNCT
ejpam-2102	100	36	1.2	1.2	NUM
ejpam-2102	100	37	)	)	PUNCT
ejpam-2102	100	38	of	of	ADP
ejpam-2102	100	39	bhat	bhat	PROPN
ejpam-2102	101	1	[	[	X
ejpam-2102	101	2	7	7	NUM
ejpam-2102	101	3	]	]	NUM
ejpam-2102	101	4	)	)	PUNCT
ejpam-2102	101	5	.	.	PUNCT
ejpam-2102	102	1	v.	v.	CCONJ
ejpam-2102	102	2	bhat	bhat	PROPN
ejpam-2102	102	3	and	and	CCONJ
ejpam-2102	102	4	k.	k.	PROPN
ejpam-2102	102	5	chib	chib	PROPN
ejpam-2102	102	6	/	/	SYM
ejpam-2102	102	7	eur	eur	PROPN
ejpam-2102	102	8	.	.	PUNCT
ejpam-2102	103	1	j.	j.	PROPN
ejpam-2102	103	2	pure	pure	PROPN
ejpam-2102	103	3	appl	appl	PROPN
ejpam-2102	103	4	.	.	PROPN
ejpam-2102	103	5	math	math	PROPN
ejpam-2102	103	6	,	,	PUNCT
ejpam-2102	103	7	8	8	NUM
ejpam-2102	103	8	(	(	PUNCT
ejpam-2102	103	9	2015	2015	NUM
ejpam-2102	103	10	)	)	PUNCT
ejpam-2102	103	11	,	,	PUNCT
ejpam-2102	103	12	111	111	NUM
ejpam-2102	103	13	-	-	SYM
ejpam-2102	103	14	117	117	NUM
ejpam-2102	103	15	114	114	NUM
ejpam-2102	103	16	1.2	1.2	NUM
ejpam-2102	103	17	.	.	PUNCT
ejpam-2102	104	1	weak	weak	ADJ
ejpam-2102	104	2	σ	σ	ADJ
ejpam-2102	104	3	-	-	ADJ
ejpam-2102	104	4	rigid	rigid	ADJ
ejpam-2102	104	5	ring	ring	NOUN
ejpam-2102	104	6	let	let	VERB
ejpam-2102	104	7	r	r	PRON
ejpam-2102	104	8	be	be	AUX
ejpam-2102	104	9	a	a	DET
ejpam-2102	104	10	ring	ring	NOUN
ejpam-2102	104	11	and	and	CCONJ
ejpam-2102	104	12	σ	σ	PROPN
ejpam-2102	104	13	be	be	VERB
ejpam-2102	104	14	an	an	DET
ejpam-2102	104	15	endomorphism	endomorphism	NOUN
ejpam-2102	104	16	of	of	ADP
ejpam-2102	104	17	r.	r.	PROPN
ejpam-2102	104	18	recall	recall	VERB
ejpam-2102	104	19	that	that	SCONJ
ejpam-2102	104	20	in	in	ADP
ejpam-2102	104	21	[	[	X
ejpam-2102	104	22	8	8	NUM
ejpam-2102	104	23	]	]	PUNCT
ejpam-2102	104	24	,	,	PUNCT
ejpam-2102	104	25	σ	σ	PROPN
ejpam-2102	104	26	is	be	AUX
ejpam-2102	104	27	called	call	VERB
ejpam-2102	104	28	a	a	DET
ejpam-2102	104	29	rigid	rigid	ADJ
ejpam-2102	104	30	endomorphism	endomorphism	NOUN
ejpam-2102	104	31	if	if	SCONJ
ejpam-2102	104	32	aσ(a	aσ(a	VERB
ejpam-2102	104	33	)	)	PUNCT
ejpam-2102	104	34	=	=	SYM
ejpam-2102	104	35	0	0	NUM
ejpam-2102	104	36	implies	imply	VERB
ejpam-2102	104	37	a	a	DET
ejpam-2102	104	38	=	=	SYM
ejpam-2102	104	39	0	0	NUM
ejpam-2102	104	40	for	for	ADP
ejpam-2102	104	41	a	a	DET
ejpam-2102	104	42	∈	∈	PROPN
ejpam-2102	104	43	r	r	NOUN
ejpam-2102	104	44	,	,	PUNCT
ejpam-2102	104	45	and	and	CCONJ
ejpam-2102	104	46	r	r	NOUN
ejpam-2102	104	47	is	be	AUX
ejpam-2102	104	48	called	call	VERB
ejpam-2102	104	49	a	a	DET
ejpam-2102	104	50	σ	σ	PROPN
ejpam-2102	104	51	-	-	ADJ
ejpam-2102	104	52	rigid	rigid	ADJ
ejpam-2102	104	53	ring	ring	NOUN
ejpam-2102	104	54	.	.	PUNCT
ejpam-2102	104	55	example	example	NOUN
ejpam-2102	105	1	3	3	X
ejpam-2102	105	2	.	.	PUNCT
ejpam-2102	105	3	let	let	VERB
ejpam-2102	105	4	r=	r=	PRON
ejpam-2102	105	5	c	c	NOUN
ejpam-2102	105	6	,	,	PUNCT
ejpam-2102	105	7	and	and	CCONJ
ejpam-2102	105	8	σ	σ	NOUN
ejpam-2102	105	9	:	:	PUNCT
ejpam-2102	105	10	r→	r→	PROPN
ejpam-2102	105	11	r	r	NOUN
ejpam-2102	105	12	be	be	VERB
ejpam-2102	105	13	the	the	DET
ejpam-2102	105	14	map	map	NOUN
ejpam-2102	105	15	defined	define	VERB
ejpam-2102	105	16	by	by	ADP
ejpam-2102	105	17	σ(a+	σ(a+	PROPN
ejpam-2102	105	18	i	i	PROPN
ejpam-2102	105	19	b	b	NOUN
ejpam-2102	105	20	)	)	PUNCT
ejpam-2102	105	21	=	=	SYM
ejpam-2102	105	22	a−	a−	PROPN
ejpam-2102	105	23	i	i	NOUN
ejpam-2102	105	24	b	b	PROPN
ejpam-2102	105	25	,	,	PUNCT
ejpam-2102	105	26	a	a	PRON
ejpam-2102	105	27	,	,	PUNCT
ejpam-2102	105	28	b	b	PROPN
ejpam-2102	105	29	∈	∈	PROPN
ejpam-2102	105	30	r.	r.	NOUN
ejpam-2102	105	31	then	then	ADV
ejpam-2102	105	32	it	it	PRON
ejpam-2102	105	33	can	can	AUX
ejpam-2102	105	34	be	be	AUX
ejpam-2102	105	35	seen	see	VERB
ejpam-2102	105	36	that	that	SCONJ
ejpam-2102	105	37	r	r	NOUN
ejpam-2102	105	38	is	be	AUX
ejpam-2102	105	39	a	a	DET
ejpam-2102	105	40	σ	σ	PROPN
ejpam-2102	105	41	-	-	ADJ
ejpam-2102	105	42	rigid	rigid	ADJ
ejpam-2102	105	43	ring	ring	NOUN
ejpam-2102	105	44	.	.	PUNCT
ejpam-2102	106	1	definition	definition	NOUN
ejpam-2102	106	2	3	3	NUM
ejpam-2102	106	3	.	.	PUNCT
ejpam-2102	107	1	[	[	X
ejpam-2102	107	2	ouyang	ouyang	X
ejpam-2102	107	3	[	[	X
ejpam-2102	107	4	16	16	NUM
ejpam-2102	107	5	]	]	X
ejpam-2102	107	6	]	]	X
ejpam-2102	107	7	let	let	VERB
ejpam-2102	107	8	r	r	PRON
ejpam-2102	107	9	be	be	AUX
ejpam-2102	107	10	a	a	DET
ejpam-2102	107	11	ring	ring	NOUN
ejpam-2102	107	12	and	and	CCONJ
ejpam-2102	107	13	σ	σ	NOUN
ejpam-2102	107	14	an	an	DET
ejpam-2102	107	15	endomorphism	endomorphism	NOUN
ejpam-2102	107	16	of	of	ADP
ejpam-2102	107	17	r	r	NOUN
ejpam-2102	107	18	such	such	ADJ
ejpam-2102	107	19	that	that	DET
ejpam-2102	107	20	aσ(a	aσ(a	NOUN
ejpam-2102	107	21	)	)	PUNCT
ejpam-2102	107	22	∈	∈	PROPN
ejpam-2102	107	23	n(r	n(r	NOUN
ejpam-2102	107	24	)	)	PUNCT
ejpam-2102	107	25	if	if	SCONJ
ejpam-2102	107	26	and	and	CCONJ
ejpam-2102	107	27	only	only	ADV
ejpam-2102	107	28	if	if	SCONJ
ejpam-2102	107	29	a	a	DET
ejpam-2102	107	30	∈	∈	PROPN
ejpam-2102	107	31	n(r	n(r	NOUN
ejpam-2102	107	32	)	)	PUNCT
ejpam-2102	107	33	for	for	ADP
ejpam-2102	107	34	a	a	DET
ejpam-2102	107	35	∈	∈	PROPN
ejpam-2102	107	36	r.	r.	NOUN
ejpam-2102	107	37	then	then	ADV
ejpam-2102	107	38	r	r	NOUN
ejpam-2102	107	39	is	be	AUX
ejpam-2102	107	40	called	call	VERB
ejpam-2102	107	41	a	a	DET
ejpam-2102	107	42	weak	weak	ADJ
ejpam-2102	107	43	σ	σ	ADJ
ejpam-2102	107	44	-	-	ADJ
ejpam-2102	107	45	rigid	rigid	ADJ
ejpam-2102	107	46	ring	ring	NOUN
ejpam-2102	107	47	.	.	PUNCT
ejpam-2102	108	1	example	example	NOUN
ejpam-2102	108	2	4	4	NUM
ejpam-2102	108	3	(	(	PUNCT
ejpam-2102	108	4	example	example	NOUN
ejpam-2102	108	5	(	(	PUNCT
ejpam-2102	108	6	2.1	2.1	NUM
ejpam-2102	108	7	)	)	PUNCT
ejpam-2102	108	8	of	of	ADP
ejpam-2102	108	9	ouyang	ouyang	PROPN
ejpam-2102	109	1	[	[	X
ejpam-2102	109	2	16	16	NUM
ejpam-2102	109	3	]	]	PUNCT
ejpam-2102	109	4	)	)	PUNCT
ejpam-2102	109	5	.	.	PUNCT
ejpam-2102	110	1	let	let	VERB
ejpam-2102	110	2	σ	σ	NOUN
ejpam-2102	110	3	be	be	AUX
ejpam-2102	110	4	an	an	DET
ejpam-2102	110	5	endomorphism	endomorphism	NOUN
ejpam-2102	110	6	of	of	ADP
ejpam-2102	110	7	a	a	DET
ejpam-2102	110	8	ring	ring	NOUN
ejpam-2102	110	9	r	r	NOUN
ejpam-2102	110	10	such	such	ADJ
ejpam-2102	110	11	that	that	SCONJ
ejpam-2102	110	12	r	r	NOUN
ejpam-2102	110	13	is	be	AUX
ejpam-2102	110	14	a	a	DET
ejpam-2102	110	15	σ	σ	PROPN
ejpam-2102	110	16	-	-	ADJ
ejpam-2102	110	17	rigid	rigid	ADJ
ejpam-2102	110	18	ring	ring	NOUN
ejpam-2102	110	19	.	.	PUNCT
ejpam-2102	111	1	let	let	VERB
ejpam-2102	111	2	a=	a=	ADV
ejpam-2102	111	3	¦	¦	X
ejpam-2102	111	4			PROPN
ejpam-2102	111	5			VERB
ejpam-2102	111	6	a	a	DET
ejpam-2102	111	7	b	b	NOUN
ejpam-2102	111	8	c	c	NOUN
ejpam-2102	111	9	0	0	PUNCT
ejpam-2102	111	10	a	a	DET
ejpam-2102	111	11	d	d	NOUN
ejpam-2102	111	12	0	0	NUM
ejpam-2102	111	13	0	0	NUM
ejpam-2102	112	1	a	a	DET
ejpam-2102	112	2			NOUN
ejpam-2102	112	3			PUNCT
ejpam-2102	113	1	|	|	ADV
ejpam-2102	113	2	a	a	DET
ejpam-2102	113	3	,	,	PUNCT
ejpam-2102	113	4	b	b	NOUN
ejpam-2102	113	5	,	,	PUNCT
ejpam-2102	113	6	c	c	NOUN
ejpam-2102	113	7	,	,	PUNCT
ejpam-2102	113	8	d	d	PROPN
ejpam-2102	113	9	∈	∈	NOUN
ejpam-2102	113	10	r	r	NOUN
ejpam-2102	113	11	©	©	PROPN
ejpam-2102	113	12	be	be	AUX
ejpam-2102	113	13	a	a	DET
ejpam-2102	113	14	subring	subring	NOUN
ejpam-2102	113	15	of	of	ADP
ejpam-2102	113	16	t3(r	t3(r	NOUN
ejpam-2102	113	17	)	)	PUNCT
ejpam-2102	113	18	,	,	PUNCT
ejpam-2102	113	19	the	the	DET
ejpam-2102	113	20	ring	ring	NOUN
ejpam-2102	113	21	of	of	ADP
ejpam-2102	113	22	upper	upper	ADJ
ejpam-2102	113	23	triangular	triangular	NOUN
ejpam-2102	113	24	matrices	matrix	NOUN
ejpam-2102	113	25	over	over	ADP
ejpam-2102	113	26	r.	r.	PROPN
ejpam-2102	113	27	now	now	ADV
ejpam-2102	113	28	σ	σ	PROPN
ejpam-2102	113	29	can	can	AUX
ejpam-2102	113	30	be	be	AUX
ejpam-2102	113	31	extended	extend	VERB
ejpam-2102	113	32	to	to	ADP
ejpam-2102	113	33	an	an	DET
ejpam-2102	113	34	endomorphism	endomorphism	PROPN
ejpam-2102	113	35	σ	σ	NOUN
ejpam-2102	113	36	of	of	ADP
ejpam-2102	113	37	a	a	PRON
ejpam-2102	113	38	by	by	ADP
ejpam-2102	113	39	σ((ai	σ((ai	PROPN
ejpam-2102	113	40	j	j	PROPN
ejpam-2102	113	41	)	)	PUNCT
ejpam-2102	113	42	)	)	PUNCT
ejpam-2102	114	1	=	=	PRON
ejpam-2102	114	2	(	(	PUNCT
ejpam-2102	114	3	σ(ai	σ(ai	PROPN
ejpam-2102	114	4	j	j	PROPN
ejpam-2102	114	5	)	)	PUNCT
ejpam-2102	114	6	)	)	PUNCT
ejpam-2102	114	7	.	.	PUNCT
ejpam-2102	115	1	then	then	ADV
ejpam-2102	115	2	it	it	PRON
ejpam-2102	115	3	can	can	AUX
ejpam-2102	115	4	be	be	AUX
ejpam-2102	115	5	seen	see	VERB
ejpam-2102	115	6	that	that	SCONJ
ejpam-2102	115	7	a	a	PRON
ejpam-2102	115	8	is	be	AUX
ejpam-2102	115	9	a	a	DET
ejpam-2102	115	10	weak	weak	ADJ
ejpam-2102	115	11	σ	σ	ADJ
ejpam-2102	115	12	-	-	ADJ
ejpam-2102	115	13	rigid	rigid	ADJ
ejpam-2102	115	14	ring	ring	NOUN
ejpam-2102	115	15	.	.	PUNCT
ejpam-2102	116	1	we	we	PRON
ejpam-2102	116	2	now	now	ADV
ejpam-2102	116	3	state	state	VERB
ejpam-2102	116	4	the	the	DET
ejpam-2102	116	5	main	main	ADJ
ejpam-2102	116	6	result	result	NOUN
ejpam-2102	116	7	of	of	ADP
ejpam-2102	116	8	this	this	DET
ejpam-2102	116	9	paper	paper	NOUN
ejpam-2102	116	10	in	in	ADP
ejpam-2102	116	11	the	the	DET
ejpam-2102	116	12	form	form	NOUN
ejpam-2102	116	13	of	of	ADP
ejpam-2102	116	14	the	the	DET
ejpam-2102	116	15	following	follow	VERB
ejpam-2102	116	16	statement	statement	NOUN
ejpam-2102	116	17	which	which	PRON
ejpam-2102	116	18	we	we	PRON
ejpam-2102	116	19	will	will	AUX
ejpam-2102	116	20	prove	prove	VERB
ejpam-2102	116	21	in	in	ADP
ejpam-2102	116	22	section	section	NOUN
ejpam-2102	116	23	3	3	NUM
ejpam-2102	116	24	:	:	PUNCT
ejpam-2102	116	25	“	"	PUNCT
ejpam-2102	116	26	let	let	VERB
ejpam-2102	116	27	r	r	PRON
ejpam-2102	116	28	be	be	AUX
ejpam-2102	116	29	a	a	DET
ejpam-2102	116	30	commutative	commutative	ADJ
ejpam-2102	116	31	noetherian	noetherian	ADJ
ejpam-2102	116	32	ring	ring	NOUN
ejpam-2102	116	33	,	,	PUNCT
ejpam-2102	116	34	which	which	PRON
ejpam-2102	116	35	is	be	AUX
ejpam-2102	116	36	also	also	ADV
ejpam-2102	116	37	an	an	DET
ejpam-2102	116	38	algebra	algebra	NOUN
ejpam-2102	116	39	over	over	ADP
ejpam-2102	116	40	q.	q.	PROPN
ejpam-2102	116	41	let	let	VERB
ejpam-2102	116	42	σ	σ	NOUN
ejpam-2102	116	43	be	be	AUX
ejpam-2102	116	44	an	an	DET
ejpam-2102	116	45	automorphism	automorphism	NOUN
ejpam-2102	116	46	of	of	ADP
ejpam-2102	116	47	r	r	NOUN
ejpam-2102	116	48	and	and	CCONJ
ejpam-2102	116	49	δ	δ	PROPN
ejpam-2102	116	50	a	a	DET
ejpam-2102	116	51	σ	σ	NOUN
ejpam-2102	116	52	-	-	PUNCT
ejpam-2102	116	53	derivation	derivation	NOUN
ejpam-2102	116	54	of	of	ADP
ejpam-2102	116	55	r.	r.	PROPN
ejpam-2102	116	56	then	then	ADV
ejpam-2102	116	57	o(r	o(r	PROPN
ejpam-2102	116	58	)	)	PUNCT
ejpam-2102	116	59	=	=	SYM
ejpam-2102	117	1	r[x;σ	r[x;σ	NOUN
ejpam-2102	117	2	,	,	PUNCT
ejpam-2102	117	3	δ	δ	PROPN
ejpam-2102	117	4	]	]	PUNCT
ejpam-2102	117	5	is	be	AUX
ejpam-2102	117	6	a	a	DET
ejpam-2102	117	7	transparent	transparent	ADJ
ejpam-2102	117	8	ring	ring	NOUN
ejpam-2102	117	9	.	.	PUNCT
ejpam-2102	117	10	”	"	PUNCT
ejpam-2102	118	1	2	2	NUM
ejpam-2102	118	2	.	.	PUNCT
ejpam-2102	118	3	preliminaries	preliminary	NOUN
ejpam-2102	118	4	recall	recall	VERB
ejpam-2102	118	5	that	that	SCONJ
ejpam-2102	118	6	an	an	DET
ejpam-2102	118	7	ideal	ideal	NOUN
ejpam-2102	118	8	i	i	PRON
ejpam-2102	118	9	of	of	ADP
ejpam-2102	118	10	a	a	DET
ejpam-2102	118	11	ring	ring	NOUN
ejpam-2102	118	12	r	r	NOUN
ejpam-2102	118	13	is	be	AUX
ejpam-2102	118	14	said	say	VERB
ejpam-2102	118	15	to	to	PART
ejpam-2102	118	16	be	be	AUX
ejpam-2102	118	17	completely	completely	ADV
ejpam-2102	118	18	semiprime	semiprime	ADJ
ejpam-2102	118	19	if	if	SCONJ
ejpam-2102	118	20	a2	a2	PROPN
ejpam-2102	118	21	∈	∈	PROPN
ejpam-2102	118	22	i	i	PRON
ejpam-2102	118	23	implies	imply	VERB
ejpam-2102	118	24	that	that	SCONJ
ejpam-2102	118	25	a	a	DET
ejpam-2102	118	26	∈	∈	NOUN
ejpam-2102	118	27	i	i	PRON
ejpam-2102	118	28	.	.	PUNCT
ejpam-2102	119	1	we	we	PRON
ejpam-2102	119	2	now	now	ADV
ejpam-2102	119	3	have	have	VERB
ejpam-2102	119	4	the	the	DET
ejpam-2102	119	5	following	follow	VERB
ejpam-2102	119	6	theorem	theorem	VERB
ejpam-2102	119	7	.	.	PUNCT
ejpam-2102	120	1	proposition	proposition	NOUN
ejpam-2102	120	2	2	2	NUM
ejpam-2102	120	3	.	.	PUNCT
ejpam-2102	121	1	let	let	VERB
ejpam-2102	121	2	r	r	PRON
ejpam-2102	121	3	be	be	AUX
ejpam-2102	121	4	a	a	DET
ejpam-2102	121	5	commutative	commutative	ADJ
ejpam-2102	121	6	noetherian	noetherian	ADJ
ejpam-2102	121	7	ring	ring	NOUN
ejpam-2102	121	8	.	.	PUNCT
ejpam-2102	122	1	let	let	VERB
ejpam-2102	122	2	σ	σ	NOUN
ejpam-2102	122	3	be	be	AUX
ejpam-2102	122	4	an	an	DET
ejpam-2102	122	5	automorphism	automorphism	NOUN
ejpam-2102	122	6	of	of	ADP
ejpam-2102	122	7	r.	r.	PROPN
ejpam-2102	122	8	then	then	ADV
ejpam-2102	122	9	r	r	NOUN
ejpam-2102	122	10	is	be	AUX
ejpam-2102	122	11	a	a	DET
ejpam-2102	122	12	weak	weak	ADJ
ejpam-2102	122	13	σ	σ	ADJ
ejpam-2102	122	14	-	-	ADJ
ejpam-2102	122	15	rigid	rigid	ADJ
ejpam-2102	122	16	ring	ring	NOUN
ejpam-2102	122	17	if	if	SCONJ
ejpam-2102	122	18	and	and	CCONJ
ejpam-2102	122	19	only	only	ADV
ejpam-2102	122	20	if	if	SCONJ
ejpam-2102	122	21	n(r	n(r	NOUN
ejpam-2102	122	22	)	)	PUNCT
ejpam-2102	122	23	is	be	AUX
ejpam-2102	122	24	completely	completely	ADV
ejpam-2102	122	25	semiprime	semiprime	NOUN
ejpam-2102	122	26	ideal	ideal	NOUN
ejpam-2102	122	27	of	of	ADP
ejpam-2102	122	28	r.	r.	PROPN
ejpam-2102	122	29	proof	proof	NOUN
ejpam-2102	122	30	.	.	PUNCT
ejpam-2102	123	1	r	r	NOUN
ejpam-2102	123	2	is	be	AUX
ejpam-2102	123	3	commutative	commutative	ADJ
ejpam-2102	123	4	noetherian	noetherian	NOUN
ejpam-2102	123	5	implies	imply	VERB
ejpam-2102	123	6	that	that	SCONJ
ejpam-2102	123	7	n(r	n(r	NOUN
ejpam-2102	123	8	)	)	PUNCT
ejpam-2102	123	9	is	be	AUX
ejpam-2102	123	10	an	an	DET
ejpam-2102	123	11	ideal	ideal	NOUN
ejpam-2102	123	12	of	of	ADP
ejpam-2102	123	13	r.	r.	PROPN
ejpam-2102	123	14	it	it	PRON
ejpam-2102	123	15	is	be	AUX
ejpam-2102	123	16	easy	easy	ADJ
ejpam-2102	123	17	to	to	PART
ejpam-2102	123	18	see	see	VERB
ejpam-2102	123	19	that	that	SCONJ
ejpam-2102	123	20	σ(n(r	σ(n(r	NOUN
ejpam-2102	123	21	)	)	PUNCT
ejpam-2102	123	22	)	)	PUNCT
ejpam-2102	124	1	=	=	SYM
ejpam-2102	124	2	n(r	n(r	NOUN
ejpam-2102	124	3	)	)	PUNCT
ejpam-2102	124	4	.	.	PUNCT
ejpam-2102	125	1	now	now	ADV
ejpam-2102	125	2	let	let	VERB
ejpam-2102	125	3	r	r	NOUN
ejpam-2102	125	4	be	be	AUX
ejpam-2102	125	5	a	a	DET
ejpam-2102	125	6	weak	weak	ADJ
ejpam-2102	125	7	σ	σ	ADJ
ejpam-2102	125	8	-	-	ADJ
ejpam-2102	125	9	rigid	rigid	ADJ
ejpam-2102	125	10	ring	ring	NOUN
ejpam-2102	125	11	.	.	PUNCT
ejpam-2102	126	1	we	we	PRON
ejpam-2102	126	2	will	will	AUX
ejpam-2102	126	3	show	show	VERB
ejpam-2102	126	4	that	that	SCONJ
ejpam-2102	126	5	n(r	n(r	NOUN
ejpam-2102	126	6	)	)	PUNCT
ejpam-2102	126	7	is	be	AUX
ejpam-2102	126	8	completely	completely	ADV
ejpam-2102	126	9	semiprime	semiprime	ADJ
ejpam-2102	126	10	.	.	PUNCT
ejpam-2102	127	1	let	let	VERB
ejpam-2102	127	2	a	a	DET
ejpam-2102	127	3	∈	∈	NOUN
ejpam-2102	127	4	r	r	NOUN
ejpam-2102	127	5	be	be	VERB
ejpam-2102	127	6	such	such	ADJ
ejpam-2102	127	7	that	that	SCONJ
ejpam-2102	127	8	a2	a2	PROPN
ejpam-2102	127	9	∈	∈	PROPN
ejpam-2102	127	10	n(r	n(r	NOUN
ejpam-2102	127	11	)	)	PUNCT
ejpam-2102	127	12	.	.	PUNCT
ejpam-2102	128	1	then	then	ADV
ejpam-2102	128	2	aσ(a)σ(aσ(a	aσ(a)σ(aσ(a	X
ejpam-2102	128	3	)	)	PUNCT
ejpam-2102	128	4	)	)	PUNCT
ejpam-2102	129	1	=	=	SYM
ejpam-2102	129	2	aσ(a)σ(a)σ2(a	aσ(a)σ(a)σ2(a	NOUN
ejpam-2102	129	3	)	)	PUNCT
ejpam-2102	129	4	∈	∈	PROPN
ejpam-2102	129	5	σ(n(r	σ(n(r	PROPN
ejpam-2102	129	6	)	)	PUNCT
ejpam-2102	129	7	)	)	PUNCT
ejpam-2102	130	1	=	=	SYM
ejpam-2102	130	2	n(r	n(r	NOUN
ejpam-2102	130	3	)	)	PUNCT
ejpam-2102	130	4	.	.	PUNCT
ejpam-2102	131	1	therefore	therefore	ADV
ejpam-2102	131	2	,	,	PUNCT
ejpam-2102	131	3	aσ(a	aσ(a	X
ejpam-2102	131	4	)	)	PUNCT
ejpam-2102	131	5	∈	∈	PROPN
ejpam-2102	131	6	n(r	n(r	NOUN
ejpam-2102	131	7	)	)	PUNCT
ejpam-2102	131	8	and	and	CCONJ
ejpam-2102	131	9	hence	hence	ADV
ejpam-2102	131	10	a	a	DET
ejpam-2102	131	11	∈	∈	NOUN
ejpam-2102	131	12	n(r	n(r	NOUN
ejpam-2102	131	13	)	)	PUNCT
ejpam-2102	131	14	.	.	PUNCT
ejpam-2102	132	1	so	so	ADV
ejpam-2102	132	2	n(r	n(r	NOUN
ejpam-2102	132	3	)	)	PUNCT
ejpam-2102	132	4	is	be	AUX
ejpam-2102	132	5	completely	completely	ADV
ejpam-2102	132	6	semiprime	semiprime	NOUN
ejpam-2102	132	7	.	.	PUNCT
ejpam-2102	133	1	conversely	conversely	ADV
ejpam-2102	133	2	let	let	VERB
ejpam-2102	133	3	n(r	n(r	PRON
ejpam-2102	133	4	)	)	PUNCT
ejpam-2102	133	5	be	be	AUX
ejpam-2102	133	6	completely	completely	ADV
ejpam-2102	133	7	semiprime	semiprime	ADJ
ejpam-2102	133	8	.	.	PUNCT
ejpam-2102	134	1	we	we	PRON
ejpam-2102	134	2	will	will	AUX
ejpam-2102	134	3	show	show	VERB
ejpam-2102	134	4	that	that	SCONJ
ejpam-2102	134	5	r	r	NOUN
ejpam-2102	134	6	is	be	AUX
ejpam-2102	134	7	a	a	DET
ejpam-2102	134	8	weak	weak	ADJ
ejpam-2102	134	9	σ	σ	ADJ
ejpam-2102	134	10	-	-	ADJ
ejpam-2102	134	11	rigid	rigid	ADJ
ejpam-2102	134	12	ring	ring	NOUN
ejpam-2102	134	13	.	.	PUNCT
ejpam-2102	135	1	let	let	VERB
ejpam-2102	135	2	a	a	DET
ejpam-2102	135	3	∈	∈	NOUN
ejpam-2102	135	4	r	r	NOUN
ejpam-2102	135	5	be	be	VERB
ejpam-2102	135	6	such	such	ADJ
ejpam-2102	135	7	that	that	PRON
ejpam-2102	135	8	aσ(a	aσ(a	NOUN
ejpam-2102	135	9	)	)	PUNCT
ejpam-2102	135	10	∈	∈	PROPN
ejpam-2102	135	11	n(r	n(r	NOUN
ejpam-2102	135	12	)	)	PUNCT
ejpam-2102	135	13	.	.	PUNCT
ejpam-2102	136	1	now	now	ADV
ejpam-2102	136	2	aσ(a)σ−1(aσ(a	aσ(a)σ−1(aσ(a	NOUN
ejpam-2102	136	3	)	)	PUNCT
ejpam-2102	136	4	)	)	PUNCT
ejpam-2102	137	1	∈	∈	PROPN
ejpam-2102	137	2	n(r	n(r	NOUN
ejpam-2102	137	3	)	)	PUNCT
ejpam-2102	137	4	implies	imply	VERB
ejpam-2102	137	5	that	that	SCONJ
ejpam-2102	137	6	a2	a2	PROPN
ejpam-2102	137	7	∈	∈	PROPN
ejpam-2102	137	8	n(r	n(r	NOUN
ejpam-2102	137	9	)	)	PUNCT
ejpam-2102	137	10	,	,	PUNCT
ejpam-2102	137	11	and	and	CCONJ
ejpam-2102	137	12	so	so	ADV
ejpam-2102	137	13	a	a	DET
ejpam-2102	137	14	∈	∈	PROPN
ejpam-2102	137	15	n(r	n(r	NOUN
ejpam-2102	137	16	)	)	PUNCT
ejpam-2102	137	17	.	.	PUNCT
ejpam-2102	138	1	hence	hence	ADV
ejpam-2102	138	2	r	r	NOUN
ejpam-2102	138	3	is	be	AUX
ejpam-2102	138	4	a	a	DET
ejpam-2102	138	5	weak	weak	ADJ
ejpam-2102	138	6	σ	σ	ADJ
ejpam-2102	138	7	-	-	ADJ
ejpam-2102	138	8	rigid	rigid	ADJ
ejpam-2102	138	9	ring	ring	NOUN
ejpam-2102	138	10	.	.	PUNCT
ejpam-2102	139	1	in	in	ADP
ejpam-2102	139	2	this	this	DET
ejpam-2102	139	3	paper	paper	NOUN
ejpam-2102	139	4	we	we	PRON
ejpam-2102	139	5	investigate	investigate	VERB
ejpam-2102	139	6	the	the	DET
ejpam-2102	139	7	transparency	transparency	NOUN
ejpam-2102	139	8	for	for	ADP
ejpam-2102	139	9	o(r	o(r	NOUN
ejpam-2102	139	10	)	)	PUNCT
ejpam-2102	139	11	=	=	SYM
ejpam-2102	140	1	r[x;σ	r[x;σ	NOUN
ejpam-2102	140	2	,	,	PUNCT
ejpam-2102	140	3	δ	δ	NOUN
ejpam-2102	140	4	]	]	PUNCT
ejpam-2102	140	5	.	.	PUNCT
ejpam-2102	141	1	before	before	SCONJ
ejpam-2102	141	2	we	we	PRON
ejpam-2102	141	3	prove	prove	VERB
ejpam-2102	141	4	the	the	DET
ejpam-2102	141	5	main	main	ADJ
ejpam-2102	141	6	result	result	NOUN
ejpam-2102	141	7	,	,	PUNCT
ejpam-2102	141	8	we	we	PRON
ejpam-2102	141	9	have	have	VERB
ejpam-2102	141	10	the	the	DET
ejpam-2102	141	11	following	following	NOUN
ejpam-2102	141	12	:	:	PUNCT
ejpam-2102	142	1	v.	v.	CCONJ
ejpam-2102	142	2	bhat	bhat	PROPN
ejpam-2102	142	3	and	and	CCONJ
ejpam-2102	142	4	k.	k.	PROPN
ejpam-2102	142	5	chib	chib	PROPN
ejpam-2102	142	6	/	/	SYM
ejpam-2102	142	7	eur	eur	PROPN
ejpam-2102	142	8	.	.	PUNCT
ejpam-2102	143	1	j.	j.	PROPN
ejpam-2102	143	2	pure	pure	PROPN
ejpam-2102	143	3	appl	appl	PROPN
ejpam-2102	143	4	.	.	PROPN
ejpam-2102	143	5	math	math	PROPN
ejpam-2102	143	6	,	,	PUNCT
ejpam-2102	143	7	8	8	NUM
ejpam-2102	143	8	(	(	PUNCT
ejpam-2102	143	9	2015	2015	NUM
ejpam-2102	143	10	)	)	PUNCT
ejpam-2102	143	11	,	,	PUNCT
ejpam-2102	143	12	111	111	NUM
ejpam-2102	143	13	-	-	SYM
ejpam-2102	143	14	117	117	NUM
ejpam-2102	143	15	115	115	NUM
ejpam-2102	143	16	proposition	proposition	NOUN
ejpam-2102	143	17	3	3	NUM
ejpam-2102	143	18	.	.	PUNCT
ejpam-2102	144	1	let	let	VERB
ejpam-2102	144	2	r	r	PRON
ejpam-2102	144	3	be	be	AUX
ejpam-2102	144	4	a	a	DET
ejpam-2102	144	5	commutative	commutative	ADJ
ejpam-2102	144	6	noetherian	noetherian	ADJ
ejpam-2102	144	7	ring	ring	NOUN
ejpam-2102	144	8	which	which	PRON
ejpam-2102	144	9	is	be	AUX
ejpam-2102	144	10	also	also	ADV
ejpam-2102	144	11	an	an	DET
ejpam-2102	144	12	algebra	algebra	NOUN
ejpam-2102	144	13	over	over	ADP
ejpam-2102	144	14	q.	q.	PROPN
ejpam-2102	144	15	let	let	VERB
ejpam-2102	144	16	σ	σ	NOUN
ejpam-2102	144	17	be	be	AUX
ejpam-2102	144	18	an	an	DET
ejpam-2102	144	19	automorphism	automorphism	NOUN
ejpam-2102	144	20	of	of	ADP
ejpam-2102	144	21	r.	r.	PROPN
ejpam-2102	144	22	then	then	ADV
ejpam-2102	144	23	σ(u	σ(u	NOUN
ejpam-2102	144	24	)	)	PUNCT
ejpam-2102	144	25	=	=	SYM
ejpam-2102	144	26	u	u	NOUN
ejpam-2102	144	27	for	for	ADP
ejpam-2102	144	28	all	all	DET
ejpam-2102	144	29	u	u	PROPN
ejpam-2102	144	30	∈	∈	PROPN
ejpam-2102	144	31	min.spec(r	min.spec(r	PROPN
ejpam-2102	144	32	)	)	PUNCT
ejpam-2102	144	33	.	.	PUNCT
ejpam-2102	145	1	proof	proof	NOUN
ejpam-2102	145	2	.	.	PUNCT
ejpam-2102	146	1	the	the	DET
ejpam-2102	146	2	proof	proof	NOUN
ejpam-2102	146	3	is	be	AUX
ejpam-2102	146	4	on	on	ADP
ejpam-2102	146	5	the	the	DET
ejpam-2102	146	6	same	same	ADJ
ejpam-2102	146	7	lines	line	NOUN
ejpam-2102	146	8	as	as	ADP
ejpam-2102	146	9	in	in	ADP
ejpam-2102	146	10	bhat	bhat	PROPN
ejpam-2102	146	11	and	and	CCONJ
ejpam-2102	146	12	kiran	kiran	PROPN
ejpam-2102	146	13	[	[	X
ejpam-2102	146	14	9	9	NUM
ejpam-2102	146	15	]	]	X
ejpam-2102	146	16	r	r	NOUN
ejpam-2102	146	17	is	be	AUX
ejpam-2102	146	18	a	a	DET
ejpam-2102	146	19	commutative	commutative	ADJ
ejpam-2102	146	20	noetherian	noetherian	ADJ
ejpam-2102	146	21	ring	ring	NOUN
ejpam-2102	146	22	implies	imply	VERB
ejpam-2102	146	23	r	r	NOUN
ejpam-2102	146	24	is	be	AUX
ejpam-2102	146	25	2	2	NUM
ejpam-2102	146	26	-	-	PUNCT
ejpam-2102	146	27	primal	primal	ADJ
ejpam-2102	146	28	.	.	PUNCT
ejpam-2102	147	1	this	this	PRON
ejpam-2102	147	2	implies	imply	VERB
ejpam-2102	147	3	that	that	SCONJ
ejpam-2102	147	4	p(r	p(r	NOUN
ejpam-2102	147	5	)	)	PUNCT
ejpam-2102	147	6	=	=	SYM
ejpam-2102	147	7	n(r	n(r	NOUN
ejpam-2102	147	8	)	)	PUNCT
ejpam-2102	147	9	i.e.	i.e.	X
ejpam-2102	147	10	,	,	PUNCT
ejpam-2102	147	11	p(r	p(r	PROPN
ejpam-2102	147	12	)	)	PUNCT
ejpam-2102	147	13	is	be	AUX
ejpam-2102	147	14	completely	completely	ADV
ejpam-2102	147	15	semiprime	semiprime	NOUN
ejpam-2102	147	16	.	.	PUNCT
ejpam-2102	148	1	therefore	therefore	ADV
ejpam-2102	148	2	,	,	PUNCT
ejpam-2102	148	3	if	if	SCONJ
ejpam-2102	148	4	a	a	DET
ejpam-2102	148	5	∈	∈	NOUN
ejpam-2102	148	6	r	r	NOUN
ejpam-2102	148	7	is	be	AUX
ejpam-2102	148	8	such	such	ADJ
ejpam-2102	148	9	that	that	SCONJ
ejpam-2102	148	10	a2	a2	PROPN
ejpam-2102	148	11	∈	∈	PROPN
ejpam-2102	148	12	p(r	p(r	PROPN
ejpam-2102	148	13	)	)	PUNCT
ejpam-2102	148	14	,	,	PUNCT
ejpam-2102	148	15	then	then	ADV
ejpam-2102	148	16	a	a	DET
ejpam-2102	148	17	∈	∈	PROPN
ejpam-2102	148	18	p(r	p(r	PROPN
ejpam-2102	148	19	)	)	PUNCT
ejpam-2102	148	20	.	.	PUNCT
ejpam-2102	149	1	now	now	ADV
ejpam-2102	149	2	,	,	PUNCT
ejpam-2102	149	3	p(r	p(r	PROPN
ejpam-2102	149	4	)	)	PUNCT
ejpam-2102	149	5	=	=	SYM
ejpam-2102	149	6	n(r	n(r	NOUN
ejpam-2102	149	7	)	)	PUNCT
ejpam-2102	149	8	,	,	PUNCT
ejpam-2102	149	9	therefore	therefore	ADV
ejpam-2102	149	10	n(r	n(r	NOUN
ejpam-2102	149	11	)	)	PUNCT
ejpam-2102	149	12	is	be	AUX
ejpam-2102	149	13	also	also	ADV
ejpam-2102	149	14	completely	completely	ADV
ejpam-2102	149	15	semiprime	semiprime	NOUN
ejpam-2102	149	16	.	.	PUNCT
ejpam-2102	150	1	now	now	ADV
ejpam-2102	150	2	proposition	proposition	NOUN
ejpam-2102	150	3	2	2	NUM
ejpam-2102	150	4	implies	imply	VERB
ejpam-2102	150	5	that	that	SCONJ
ejpam-2102	150	6	r	r	NOUN
ejpam-2102	150	7	is	be	AUX
ejpam-2102	150	8	a	a	DET
ejpam-2102	150	9	weak	weak	ADJ
ejpam-2102	150	10	σ	σ	ADJ
ejpam-2102	150	11	-	-	ADJ
ejpam-2102	150	12	rigid	rigid	ADJ
ejpam-2102	150	13	ring	ring	NOUN
ejpam-2102	150	14	.	.	PUNCT
ejpam-2102	151	1	we	we	PRON
ejpam-2102	151	2	now	now	ADV
ejpam-2102	151	3	show	show	VERB
ejpam-2102	151	4	that	that	SCONJ
ejpam-2102	151	5	σ(u	σ(u	NOUN
ejpam-2102	151	6	)	)	PUNCT
ejpam-2102	151	7	=	=	SYM
ejpam-2102	151	8	u	u	NOUN
ejpam-2102	151	9	for	for	ADP
ejpam-2102	151	10	all	all	DET
ejpam-2102	151	11	u	u	PROPN
ejpam-2102	151	12	∈	∈	PROPN
ejpam-2102	151	13	min.spec(r	min.spec(r	PROPN
ejpam-2102	151	14	)	)	PUNCT
ejpam-2102	151	15	.	.	PUNCT
ejpam-2102	152	1	let	let	VERB
ejpam-2102	152	2	u	u	PRON
ejpam-2102	152	3	=	=	NOUN
ejpam-2102	152	4	u1	u1	NOUN
ejpam-2102	152	5	be	be	AUX
ejpam-2102	152	6	a	a	DET
ejpam-2102	152	7	minimal	minimal	ADJ
ejpam-2102	152	8	prime	prime	ADJ
ejpam-2102	152	9	ideal	ideal	NOUN
ejpam-2102	152	10	of	of	ADP
ejpam-2102	152	11	r.	r.	PROPN
ejpam-2102	152	12	now	now	ADV
ejpam-2102	152	13	theorem	theorem	ADJ
ejpam-2102	152	14	(	(	PUNCT
ejpam-2102	152	15	2.4	2.4	NUM
ejpam-2102	152	16	)	)	PUNCT
ejpam-2102	152	17	of	of	ADP
ejpam-2102	152	18	goodearl	goodearl	PROPN
ejpam-2102	152	19	and	and	CCONJ
ejpam-2102	152	20	warfield	warfield	PROPN
ejpam-2102	153	1	[	[	X
ejpam-2102	153	2	12	12	NUM
ejpam-2102	153	3	]	]	PUNCT
ejpam-2102	153	4	implies	imply	VERB
ejpam-2102	153	5	that	that	SCONJ
ejpam-2102	153	6	min.spec(r	min.spec(r	PROPN
ejpam-2102	153	7	)	)	PUNCT
ejpam-2102	153	8	is	be	AUX
ejpam-2102	153	9	finite	finite	PROPN
ejpam-2102	153	10	.	.	PUNCT
ejpam-2102	154	1	let	let	VERB
ejpam-2102	154	2	u2	u2	NOUN
ejpam-2102	154	3	,	,	PUNCT
ejpam-2102	154	4	u3	u3	NOUN
ejpam-2102	154	5	,	,	PUNCT
ejpam-2102	154	6	.	.	PUNCT
ejpam-2102	154	7	.	.	PUNCT
ejpam-2102	155	1	.	.	PUNCT
ejpam-2102	156	1	,	,	PUNCT
ejpam-2102	156	2	un	un	PROPN
ejpam-2102	156	3	be	be	VERB
ejpam-2102	156	4	the	the	DET
ejpam-2102	156	5	other	other	ADJ
ejpam-2102	156	6	minimal	minimal	ADJ
ejpam-2102	156	7	primes	prime	NOUN
ejpam-2102	156	8	of	of	ADP
ejpam-2102	156	9	r.	r.	PROPN
ejpam-2102	156	10	suppose	suppose	VERB
ejpam-2102	156	11	that	that	SCONJ
ejpam-2102	156	12	σ(u	σ(u	NOUN
ejpam-2102	156	13	)	)	PUNCT
ejpam-2102	157	1	6=	6=	NUM
ejpam-2102	157	2	u	u	NOUN
ejpam-2102	157	3	.	.	PUNCT
ejpam-2102	158	1	then	then	ADV
ejpam-2102	158	2	σ(u	σ(u	NOUN
ejpam-2102	158	3	)	)	PUNCT
ejpam-2102	158	4	is	be	AUX
ejpam-2102	158	5	also	also	ADV
ejpam-2102	158	6	a	a	DET
ejpam-2102	158	7	minimal	minimal	ADJ
ejpam-2102	158	8	prime	prime	ADJ
ejpam-2102	158	9	ideal	ideal	NOUN
ejpam-2102	158	10	of	of	ADP
ejpam-2102	158	11	r.	r.	PROPN
ejpam-2102	158	12	renumber	renumber	PROPN
ejpam-2102	158	13	so	so	SCONJ
ejpam-2102	158	14	that	that	SCONJ
ejpam-2102	158	15	σ(u	σ(u	NOUN
ejpam-2102	158	16	)	)	PUNCT
ejpam-2102	158	17	=	=	SYM
ejpam-2102	158	18	un	un	PROPN
ejpam-2102	158	19	.	.	PROPN
ejpam-2102	159	1	let	let	VERB
ejpam-2102	159	2	a	a	DET
ejpam-2102	159	3	∈	∈	NOUN
ejpam-2102	159	4	∩n−1	∩n−1	PROPN
ejpam-2102	159	5	i=1	i=1	PROPN
ejpam-2102	160	1	ui	ui	PROPN
ejpam-2102	160	2	.	.	PUNCT
ejpam-2102	161	1	then	then	ADV
ejpam-2102	161	2	σ(a	σ(a	PROPN
ejpam-2102	161	3	)	)	PUNCT
ejpam-2102	161	4	∈	∈	PROPN
ejpam-2102	161	5	un	un	PROPN
ejpam-2102	161	6	,	,	PUNCT
ejpam-2102	161	7	and	and	CCONJ
ejpam-2102	161	8	so	so	ADV
ejpam-2102	161	9	aσ(a	aσ(a	PUNCT
ejpam-2102	161	10	)	)	PUNCT
ejpam-2102	162	1	∈	∈	PROPN
ejpam-2102	162	2	∩n	∩n	NOUN
ejpam-2102	162	3	i=1	i=1	PROPN
ejpam-2102	162	4	ui	ui	PROPN
ejpam-2102	163	1	=	=	PUNCT
ejpam-2102	163	2	p(r	p(r	PROPN
ejpam-2102	163	3	)	)	PUNCT
ejpam-2102	163	4	.	.	PUNCT
ejpam-2102	164	1	now	now	ADV
ejpam-2102	164	2	p(r	p(r	PROPN
ejpam-2102	164	3	)	)	PUNCT
ejpam-2102	164	4	is	be	AUX
ejpam-2102	164	5	completely	completely	ADV
ejpam-2102	164	6	semiprime	semiprime	NOUN
ejpam-2102	164	7	implies	imply	VERB
ejpam-2102	164	8	that	that	SCONJ
ejpam-2102	164	9	a	a	DET
ejpam-2102	164	10	∈	∈	PROPN
ejpam-2102	164	11	p(r	p(r	PROPN
ejpam-2102	164	12	)	)	PUNCT
ejpam-2102	164	13	and	and	CCONJ
ejpam-2102	164	14	thus	thus	ADV
ejpam-2102	164	15	∩n−1	∩n−1	PROPN
ejpam-2102	164	16	i=1	i=1	PROPN
ejpam-2102	164	17	ui	ui	PROPN
ejpam-2102	165	1	⊆	⊆	NUM
ejpam-2102	165	2	un	un	NOUN
ejpam-2102	165	3	which	which	PRON
ejpam-2102	165	4	implies	imply	VERB
ejpam-2102	165	5	that	that	SCONJ
ejpam-2102	165	6	ui	ui	PROPN
ejpam-2102	165	7	⊆	⊆	NUM
ejpam-2102	165	8	un	un	NOUN
ejpam-2102	165	9	for	for	ADP
ejpam-2102	165	10	some	some	DET
ejpam-2102	165	11	i	i	PROPN
ejpam-2102	165	12	6=	6=	PROPN
ejpam-2102	165	13	n	n	CCONJ
ejpam-2102	165	14	,	,	PUNCT
ejpam-2102	165	15	which	which	PRON
ejpam-2102	165	16	is	be	AUX
ejpam-2102	165	17	impossible	impossible	ADJ
ejpam-2102	165	18	.	.	PUNCT
ejpam-2102	166	1	hence	hence	ADV
ejpam-2102	166	2	,	,	PUNCT
ejpam-2102	166	3	σ(u	σ(u	NOUN
ejpam-2102	166	4	)	)	PUNCT
ejpam-2102	166	5	=	=	SYM
ejpam-2102	166	6	u	u	NOUN
ejpam-2102	166	7	for	for	ADP
ejpam-2102	166	8	all	all	DET
ejpam-2102	166	9	u	u	PROPN
ejpam-2102	166	10	∈	∈	PROPN
ejpam-2102	166	11	min.spec(r	min.spec(r	PROPN
ejpam-2102	166	12	)	)	PUNCT
ejpam-2102	166	13	.	.	PUNCT
ejpam-2102	167	1	theorem	theorem	NOUN
ejpam-2102	167	2	2	2	NUM
ejpam-2102	167	3	.	.	PUNCT
ejpam-2102	168	1	[	[	X
ejpam-2102	168	2	hilbert	hilbert	NOUN
ejpam-2102	168	3	basis	basis	NOUN
ejpam-2102	168	4	theorem	theorem	VERB
ejpam-2102	168	5	]	]	X
ejpam-2102	168	6	let	let	VERB
ejpam-2102	168	7	r	r	PRON
ejpam-2102	168	8	be	be	AUX
ejpam-2102	168	9	a	a	DET
ejpam-2102	168	10	right	right	ADJ
ejpam-2102	168	11	/	/	SYM
ejpam-2102	168	12	left	left	ADJ
ejpam-2102	168	13	noetherian	noetherian	ADJ
ejpam-2102	168	14	ring	ring	NOUN
ejpam-2102	168	15	.	.	PUNCT
ejpam-2102	169	1	let	let	VERB
ejpam-2102	169	2	σ	σ	NOUN
ejpam-2102	169	3	and	and	CCONJ
ejpam-2102	169	4	δ	δ	PROPN
ejpam-2102	169	5	be	be	VERB
ejpam-2102	169	6	as	as	ADV
ejpam-2102	169	7	usual	usual	ADJ
ejpam-2102	169	8	.	.	PUNCT
ejpam-2102	170	1	then	then	ADV
ejpam-2102	170	2	o(r	o(r	PRON
ejpam-2102	170	3	)	)	PUNCT
ejpam-2102	170	4	=	=	SYM
ejpam-2102	170	5	r[x;σ	r[x;σ	NOUN
ejpam-2102	170	6	,	,	PUNCT
ejpam-2102	170	7	δ	δ	PROPN
ejpam-2102	170	8	]	]	PUNCT
ejpam-2102	170	9	is	be	AUX
ejpam-2102	170	10	a	a	DET
ejpam-2102	170	11	right	right	ADJ
ejpam-2102	170	12	/	/	SYM
ejpam-2102	170	13	left	leave	VERB
ejpam-2102	170	14	noetherian	noetherian	NOUN
ejpam-2102	170	15	.	.	PUNCT
ejpam-2102	171	1	proof	proof	NOUN
ejpam-2102	171	2	.	.	PUNCT
ejpam-2102	172	1	see	see	VERB
ejpam-2102	172	2	theorem	theorem	NOUN
ejpam-2102	172	3	(	(	PUNCT
ejpam-2102	172	4	2.6	2.6	NUM
ejpam-2102	172	5	)	)	PUNCT
ejpam-2102	172	6	of	of	ADP
ejpam-2102	172	7	goodearl	goodearl	PROPN
ejpam-2102	172	8	and	and	CCONJ
ejpam-2102	172	9	warfield	warfield	VERB
ejpam-2102	173	1	[	[	X
ejpam-2102	173	2	12	12	NUM
ejpam-2102	173	3	]	]	PUNCT
ejpam-2102	173	4	.	.	PUNCT
ejpam-2102	174	1	proposition	proposition	NOUN
ejpam-2102	174	2	4	4	NUM
ejpam-2102	174	3	.	.	PUNCT
ejpam-2102	175	1	let	let	VERB
ejpam-2102	175	2	r	r	PRON
ejpam-2102	175	3	be	be	AUX
ejpam-2102	175	4	a	a	DET
ejpam-2102	175	5	noetherian	noetherian	ADJ
ejpam-2102	175	6	ring	ring	NOUN
ejpam-2102	175	7	having	have	VERB
ejpam-2102	175	8	an	an	DET
ejpam-2102	175	9	artinian	artinian	ADJ
ejpam-2102	175	10	quotient	quotient	NOUN
ejpam-2102	175	11	ring	ring	NOUN
ejpam-2102	175	12	.	.	PUNCT
ejpam-2102	176	1	then	then	ADV
ejpam-2102	176	2	r	r	NOUN
ejpam-2102	176	3	is	be	AUX
ejpam-2102	176	4	a	a	DET
ejpam-2102	176	5	transparent	transparent	ADJ
ejpam-2102	176	6	ring	ring	NOUN
ejpam-2102	176	7	.	.	PUNCT
ejpam-2102	177	1	proof	proof	NOUN
ejpam-2102	177	2	.	.	PUNCT
ejpam-2102	178	1	see	see	VERB
ejpam-2102	178	2	lemma	lemma	PROPN
ejpam-2102	178	3	(	(	PUNCT
ejpam-2102	178	4	2.8	2.8	NUM
ejpam-2102	178	5	)	)	PUNCT
ejpam-2102	178	6	of	of	ADP
ejpam-2102	178	7	bhat	bhat	PROPN
ejpam-2102	178	8	[	[	X
ejpam-2102	178	9	8	8	NUM
ejpam-2102	178	10	]	]	PUNCT
ejpam-2102	178	11	.	.	PUNCT
ejpam-2102	179	1	definition	definition	NOUN
ejpam-2102	179	2	4	4	NUM
ejpam-2102	179	3	.	.	PUNCT
ejpam-2102	180	1	let	let	VERB
ejpam-2102	180	2	p	p	PRON
ejpam-2102	180	3	be	be	AUX
ejpam-2102	180	4	a	a	DET
ejpam-2102	180	5	prime	prime	ADJ
ejpam-2102	180	6	ideal	ideal	NOUN
ejpam-2102	180	7	of	of	ADP
ejpam-2102	180	8	a	a	DET
ejpam-2102	180	9	commutative	commutative	ADJ
ejpam-2102	180	10	ring	ring	NOUN
ejpam-2102	180	11	r.	r.	PROPN
ejpam-2102	180	12	then	then	ADV
ejpam-2102	180	13	the	the	DET
ejpam-2102	180	14	symbolic	symbolic	ADJ
ejpam-2102	180	15	power	power	NOUN
ejpam-2102	180	16	of	of	ADP
ejpam-2102	180	17	p	p	NOUN
ejpam-2102	180	18	for	for	ADP
ejpam-2102	180	19	any	any	DET
ejpam-2102	180	20	n	n	PRON
ejpam-2102	180	21	∈	∈	NOUN
ejpam-2102	180	22	n	n	PRON
ejpam-2102	180	23	is	be	AUX
ejpam-2102	180	24	denoted	denote	VERB
ejpam-2102	180	25	by	by	ADP
ejpam-2102	180	26	pn	pn	PROPN
ejpam-2102	180	27	and	and	CCONJ
ejpam-2102	180	28	is	be	AUX
ejpam-2102	180	29	defined	define	VERB
ejpam-2102	180	30	as	as	ADP
ejpam-2102	180	31	pn	pn	PROPN
ejpam-2102	180	32	=	=	VERB
ejpam-2102	180	33	{	{	PUNCT
ejpam-2102	180	34	a	a	DET
ejpam-2102	180	35	∈	∈	NOUN
ejpam-2102	180	36	r	r	NOUN
ejpam-2102	180	37	such	such	ADJ
ejpam-2102	180	38	that	that	SCONJ
ejpam-2102	180	39	there	there	PRON
ejpam-2102	180	40	exists	exist	VERB
ejpam-2102	180	41	some	some	PRON
ejpam-2102	180	42	d	d	PROPN
ejpam-2102	180	43	∈	∈	PROPN
ejpam-2102	180	44	r	r	NOUN
ejpam-2102	180	45	,	,	PUNCT
ejpam-2102	180	46	d	d	NOUN
ejpam-2102	180	47	/∈	/∈	PUNCT
ejpam-2102	181	1	p	p	X
ejpam-2102	181	2	such	such	ADJ
ejpam-2102	181	3	that	that	SCONJ
ejpam-2102	181	4	da	da	PROPN
ejpam-2102	181	5	∈	∈	PROPN
ejpam-2102	181	6	pn	pn	PROPN
ejpam-2102	181	7	}	}	PUNCT
ejpam-2102	181	8	.	.	PUNCT
ejpam-2102	182	1	also	also	ADV
ejpam-2102	182	2	if	if	SCONJ
ejpam-2102	182	3	i	i	PRON
ejpam-2102	182	4	is	be	AUX
ejpam-2102	182	5	an	an	DET
ejpam-2102	182	6	ideal	ideal	NOUN
ejpam-2102	182	7	of	of	ADP
ejpam-2102	182	8	r	r	NOUN
ejpam-2102	182	9	,	,	PUNCT
ejpam-2102	182	10	define	define	VERB
ejpam-2102	182	11	as	as	ADP
ejpam-2102	182	12	usual	usual	ADJ
ejpam-2102	182	13	p	p	NOUN
ejpam-2102	182	14	i	i	PRON
ejpam-2102	182	15	=	=	PUNCT
ejpam-2102	182	16	{	{	PUNCT
ejpam-2102	182	17	a	a	DET
ejpam-2102	182	18	∈	∈	NOUN
ejpam-2102	182	19	r	r	NOUN
ejpam-2102	182	20	such	such	ADJ
ejpam-2102	182	21	that	that	SCONJ
ejpam-2102	182	22	an	an	DET
ejpam-2102	182	23	∈	∈	PROPN
ejpam-2102	182	24	i	i	PRON
ejpam-2102	182	25	for	for	ADP
ejpam-2102	182	26	some	some	DET
ejpam-2102	182	27	n	n	PRON
ejpam-2102	182	28	∈	∈	PROPN
ejpam-2102	182	29	n	n	CCONJ
ejpam-2102	182	30	}	}	PUNCT
ejpam-2102	182	31	.	.	PUNCT
ejpam-2102	183	1	lemma	lemma	PROPN
ejpam-2102	183	2	1	1	X
ejpam-2102	183	3	.	.	PUNCT
ejpam-2102	184	1	let	let	VERB
ejpam-2102	184	2	r	r	PRON
ejpam-2102	184	3	be	be	AUX
ejpam-2102	184	4	a	a	DET
ejpam-2102	184	5	commutative	commutative	ADJ
ejpam-2102	184	6	noetherian	noetherian	ADJ
ejpam-2102	184	7	ring	ring	NOUN
ejpam-2102	184	8	,	,	PUNCT
ejpam-2102	184	9	and	and	CCONJ
ejpam-2102	184	10	σ	σ	VERB
ejpam-2102	184	11	an	an	DET
ejpam-2102	184	12	automorphism	automorphism	NOUN
ejpam-2102	184	13	of	of	ADP
ejpam-2102	184	14	r.	r.	PROPN
ejpam-2102	184	15	if	if	SCONJ
ejpam-2102	184	16	p	p	NOUN
ejpam-2102	184	17	is	be	AUX
ejpam-2102	184	18	a	a	DET
ejpam-2102	184	19	prime	prime	ADJ
ejpam-2102	184	20	ideal	ideal	NOUN
ejpam-2102	184	21	of	of	ADP
ejpam-2102	184	22	r	r	NOUN
ejpam-2102	184	23	such	such	ADJ
ejpam-2102	184	24	that	that	SCONJ
ejpam-2102	184	25	σ(p	σ(p	PROPN
ejpam-2102	184	26	)	)	PUNCT
ejpam-2102	184	27	=	=	SYM
ejpam-2102	185	1	p	p	X
ejpam-2102	185	2	,	,	PUNCT
ejpam-2102	185	3	then	then	ADV
ejpam-2102	185	4	σ(pn	σ(pn	NOUN
ejpam-2102	185	5	)	)	PUNCT
ejpam-2102	185	6	=	=	SYM
ejpam-2102	185	7	pn	pn	NOUN
ejpam-2102	185	8	for	for	ADP
ejpam-2102	185	9	all	all	DET
ejpam-2102	185	10	integers	integer	NOUN
ejpam-2102	185	11	n≥	n≥	NOUN
ejpam-2102	185	12	1	1	NUM
ejpam-2102	185	13	.	.	PUNCT
ejpam-2102	186	1	proof	proof	NOUN
ejpam-2102	186	2	.	.	PUNCT
ejpam-2102	187	1	see	see	VERB
ejpam-2102	187	2	lemma	lemma	PROPN
ejpam-2102	187	3	(	(	PUNCT
ejpam-2102	187	4	2.10	2.10	NUM
ejpam-2102	187	5	)	)	PUNCT
ejpam-2102	187	6	of	of	ADP
ejpam-2102	187	7	bhat	bhat	PROPN
ejpam-2102	188	1	[	[	X
ejpam-2102	188	2	8	8	NUM
ejpam-2102	188	3	]	]	PUNCT
ejpam-2102	188	4	.	.	PUNCT
ejpam-2102	189	1	lemma	lemma	PROPN
ejpam-2102	189	2	2	2	X
ejpam-2102	189	3	.	.	PUNCT
ejpam-2102	190	1	let	let	VERB
ejpam-2102	190	2	r	r	PRON
ejpam-2102	190	3	be	be	AUX
ejpam-2102	190	4	a	a	DET
ejpam-2102	190	5	noetherianq	noetherianq	NOUN
ejpam-2102	190	6	-	-	PUNCT
ejpam-2102	190	7	algebra	algebra	NOUN
ejpam-2102	190	8	.	.	PUNCT
ejpam-2102	191	1	letσ	letσ	PROPN
ejpam-2102	191	2	be	be	AUX
ejpam-2102	191	3	an	an	DET
ejpam-2102	191	4	automorphism	automorphism	NOUN
ejpam-2102	191	5	of	of	ADP
ejpam-2102	191	6	r	r	NOUN
ejpam-2102	191	7	and	and	CCONJ
ejpam-2102	191	8	δ	δ	NOUN
ejpam-2102	191	9	aσ	aσ	NOUN
ejpam-2102	191	10	-	-	NOUN
ejpam-2102	191	11	derivation	derivation	NOUN
ejpam-2102	191	12	of	of	ADP
ejpam-2102	191	13	r.	r.	PROPN
ejpam-2102	191	14	if	if	SCONJ
ejpam-2102	191	15	p	p	PROPN
ejpam-2102	191	16	∈	∈	PROPN
ejpam-2102	191	17	min.spec(r	min.spec(r	NOUN
ejpam-2102	191	18	)	)	PUNCT
ejpam-2102	191	19	is	be	AUX
ejpam-2102	191	20	such	such	ADJ
ejpam-2102	191	21	that	that	SCONJ
ejpam-2102	191	22	σ(p	σ(p	PROPN
ejpam-2102	191	23	)	)	PUNCT
ejpam-2102	192	1	=	=	SYM
ejpam-2102	193	1	p	p	X
ejpam-2102	193	2	,	,	PUNCT
ejpam-2102	193	3	then	then	ADV
ejpam-2102	193	4	δ(p	δ(p	PROPN
ejpam-2102	193	5	)	)	PUNCT
ejpam-2102	193	6	⊆	⊆	NUM
ejpam-2102	193	7	p.	p.	NOUN
ejpam-2102	193	8	proof	proof	NOUN
ejpam-2102	193	9	.	.	PUNCT
ejpam-2102	194	1	see	see	VERB
ejpam-2102	194	2	lemma	lemma	PROPN
ejpam-2102	194	3	(	(	PUNCT
ejpam-2102	194	4	2.6	2.6	NUM
ejpam-2102	194	5	)	)	PUNCT
ejpam-2102	194	6	of	of	ADP
ejpam-2102	194	7	bhat	bhat	PROPN
ejpam-2102	194	8	[	[	X
ejpam-2102	194	9	8	8	NUM
ejpam-2102	194	10	]	]	PUNCT
ejpam-2102	194	11	.	.	PUNCT
ejpam-2102	195	1	lemma	lemma	PROPN
ejpam-2102	195	2	3	3	X
ejpam-2102	195	3	.	.	PUNCT
ejpam-2102	196	1	let	let	VERB
ejpam-2102	196	2	r	r	PRON
ejpam-2102	196	3	be	be	AUX
ejpam-2102	196	4	a	a	DET
ejpam-2102	196	5	commutative	commutative	ADJ
ejpam-2102	196	6	noetherian	noetherian	ADJ
ejpam-2102	196	7	ring	ring	NOUN
ejpam-2102	196	8	;	;	PUNCT
ejpam-2102	196	9	σ	σ	PROPN
ejpam-2102	196	10	and	and	CCONJ
ejpam-2102	196	11	δ	δ	PROPN
ejpam-2102	196	12	as	as	ADP
ejpam-2102	196	13	usual	usual	ADJ
ejpam-2102	196	14	.	.	PUNCT
ejpam-2102	197	1	let	let	VERB
ejpam-2102	197	2	p	p	PRON
ejpam-2102	197	3	be	be	AUX
ejpam-2102	197	4	a	a	DET
ejpam-2102	197	5	prime	prime	ADJ
ejpam-2102	197	6	ideal	ideal	NOUN
ejpam-2102	197	7	of	of	ADP
ejpam-2102	197	8	r	r	NOUN
ejpam-2102	197	9	such	such	ADJ
ejpam-2102	197	10	that	that	SCONJ
ejpam-2102	197	11	σ(p	σ(p	PROPN
ejpam-2102	197	12	)	)	PUNCT
ejpam-2102	197	13	=	=	SYM
ejpam-2102	197	14	p	p	NOUN
ejpam-2102	197	15	and	and	CCONJ
ejpam-2102	197	16	δ(p	δ(p	NUM
ejpam-2102	197	17	)	)	PUNCT
ejpam-2102	197	18	⊆	⊆	NUM
ejpam-2102	197	19	p.	p.	NOUN
ejpam-2102	197	20	then	then	ADV
ejpam-2102	197	21	δ(p(k	δ(p(k	NOUN
ejpam-2102	197	22	)	)	PUNCT
ejpam-2102	197	23	)	)	PUNCT
ejpam-2102	198	1	⊆	⊆	NUM
ejpam-2102	198	2	p(k	p(k	NOUN
ejpam-2102	198	3	)	)	PUNCT
ejpam-2102	198	4	for	for	ADP
ejpam-2102	198	5	all	all	DET
ejpam-2102	198	6	integers	integer	NOUN
ejpam-2102	198	7	k	k	X
ejpam-2102	198	8	≥	≥	NUM
ejpam-2102	198	9	1	1	NUM
ejpam-2102	198	10	.	.	PUNCT
ejpam-2102	199	1	proof	proof	NOUN
ejpam-2102	199	2	.	.	PUNCT
ejpam-2102	200	1	see	see	VERB
ejpam-2102	200	2	lemma	lemma	PROPN
ejpam-2102	200	3	(	(	PUNCT
ejpam-2102	200	4	2.11	2.11	NUM
ejpam-2102	200	5	)	)	PUNCT
ejpam-2102	200	6	of	of	ADP
ejpam-2102	200	7	bhat	bhat	PROPN
ejpam-2102	201	1	[	[	X
ejpam-2102	201	2	8	8	NUM
ejpam-2102	201	3	]	]	PUNCT
ejpam-2102	201	4	.	.	PUNCT
ejpam-2102	202	1	references	reference	NOUN
ejpam-2102	202	2	116	116	NUM
ejpam-2102	202	3	3	3	NUM
ejpam-2102	202	4	.	.	PUNCT
ejpam-2102	203	1	proof	proof	NOUN
ejpam-2102	203	2	of	of	ADP
ejpam-2102	203	3	the	the	DET
ejpam-2102	203	4	main	main	ADJ
ejpam-2102	203	5	theorem	theorem	NOUN
ejpam-2102	203	6	we	we	PRON
ejpam-2102	203	7	are	be	AUX
ejpam-2102	203	8	now	now	ADV
ejpam-2102	203	9	in	in	ADP
ejpam-2102	203	10	a	a	DET
ejpam-2102	203	11	position	position	NOUN
ejpam-2102	203	12	to	to	PART
ejpam-2102	203	13	prove	prove	VERB
ejpam-2102	203	14	the	the	DET
ejpam-2102	203	15	main	main	ADJ
ejpam-2102	203	16	result	result	NOUN
ejpam-2102	203	17	in	in	ADP
ejpam-2102	203	18	the	the	DET
ejpam-2102	203	19	form	form	NOUN
ejpam-2102	203	20	of	of	ADP
ejpam-2102	203	21	the	the	DET
ejpam-2102	203	22	following	follow	VERB
ejpam-2102	203	23	theorem	theorem	NOUN
ejpam-2102	203	24	:	:	PUNCT
ejpam-2102	203	25	theorem	theorem	NOUN
ejpam-2102	203	26	3	3	NUM
ejpam-2102	203	27	.	.	PUNCT
ejpam-2102	204	1	[	[	PUNCT
ejpam-2102	204	2	repeated	repeat	VERB
ejpam-2102	204	3	from	from	ADP
ejpam-2102	204	4	introduction	introduction	NOUN
ejpam-2102	204	5	]	]	PUNCT
ejpam-2102	204	6	let	let	VERB
ejpam-2102	204	7	r	r	PRON
ejpam-2102	204	8	be	be	AUX
ejpam-2102	204	9	a	a	DET
ejpam-2102	204	10	commutative	commutative	ADJ
ejpam-2102	204	11	noetherian	noetherian	ADJ
ejpam-2102	204	12	ring	ring	NOUN
ejpam-2102	204	13	,	,	PUNCT
ejpam-2102	204	14	which	which	PRON
ejpam-2102	204	15	is	be	AUX
ejpam-2102	204	16	also	also	ADV
ejpam-2102	204	17	an	an	DET
ejpam-2102	204	18	algebra	algebra	NOUN
ejpam-2102	204	19	over	over	ADP
ejpam-2102	204	20	q.	q.	PROPN
ejpam-2102	204	21	let	let	VERB
ejpam-2102	204	22	σ	σ	NOUN
ejpam-2102	204	23	be	be	AUX
ejpam-2102	204	24	an	an	DET
ejpam-2102	204	25	automorphism	automorphism	NOUN
ejpam-2102	204	26	of	of	ADP
ejpam-2102	204	27	r	r	NOUN
ejpam-2102	204	28	and	and	CCONJ
ejpam-2102	204	29	δ	δ	PROPN
ejpam-2102	204	30	a	a	DET
ejpam-2102	204	31	σ	σ	NOUN
ejpam-2102	204	32	-	-	PUNCT
ejpam-2102	204	33	derivation	derivation	NOUN
ejpam-2102	204	34	of	of	ADP
ejpam-2102	204	35	r.	r.	PROPN
ejpam-2102	204	36	then	then	ADV
ejpam-2102	204	37	o(r	o(r	PROPN
ejpam-2102	204	38	)	)	PUNCT
ejpam-2102	205	1	=	=	SYM
ejpam-2102	205	2	r[x;σ	r[x;σ	NOUN
ejpam-2102	205	3	,	,	PUNCT
ejpam-2102	205	4	δ	δ	PROPN
ejpam-2102	205	5	]	]	PUNCT
ejpam-2102	205	6	is	be	AUX
ejpam-2102	205	7	a	a	DET
ejpam-2102	205	8	transparent	transparent	ADJ
ejpam-2102	205	9	ring	ring	NOUN
ejpam-2102	205	10	.	.	PUNCT
ejpam-2102	206	1	proof	proof	NOUN
ejpam-2102	206	2	.	.	PUNCT
ejpam-2102	207	1	r[x;σ	r[x;σ	NOUN
ejpam-2102	207	2	,	,	PUNCT
ejpam-2102	207	3	δ	δ	PROPN
ejpam-2102	207	4	]	]	PUNCT
ejpam-2102	207	5	is	be	AUX
ejpam-2102	207	6	noetherian	noetherian	ADJ
ejpam-2102	207	7	ring	ring	NOUN
ejpam-2102	207	8	by	by	ADP
ejpam-2102	207	9	hilbert	hilbert	NOUN
ejpam-2102	207	10	basis	basis	NOUN
ejpam-2102	207	11	theorem	theorem	VERB
ejpam-2102	207	12	,	,	PUNCT
ejpam-2102	207	13	namely	namely	ADV
ejpam-2102	207	14	theorem	theorem	ADJ
ejpam-2102	207	15	(	(	PUNCT
ejpam-2102	207	16	1.12	1.12	NUM
ejpam-2102	207	17	)	)	PUNCT
ejpam-2102	207	18	of	of	ADP
ejpam-2102	207	19	goodearl	goodearl	PROPN
ejpam-2102	207	20	and	and	CCONJ
ejpam-2102	207	21	warfield	warfield	VERB
ejpam-2102	208	1	[	[	X
ejpam-2102	208	2	12	12	NUM
ejpam-2102	208	3	]	]	PUNCT
ejpam-2102	208	4	.	.	PUNCT
ejpam-2102	209	1	now	now	ADV
ejpam-2102	209	2	r	r	NOUN
ejpam-2102	209	3	is	be	AUX
ejpam-2102	209	4	a	a	DET
ejpam-2102	209	5	commutative	commutative	ADJ
ejpam-2102	209	6	noetherian	noetherian	ADJ
ejpam-2102	209	7	q	q	NOUN
ejpam-2102	209	8	-	-	PUNCT
ejpam-2102	209	9	algebra	algebra	NOUN
ejpam-2102	209	10	,	,	PUNCT
ejpam-2102	209	11	therefore	therefore	ADV
ejpam-2102	209	12	,	,	PUNCT
ejpam-2102	209	13	the	the	DET
ejpam-2102	209	14	ideal	ideal	ADJ
ejpam-2102	209	15	{	{	PUNCT
ejpam-2102	209	16	0	0	NUM
ejpam-2102	209	17	}	}	PUNCT
ejpam-2102	209	18	has	have	VERB
ejpam-2102	209	19	a	a	DET
ejpam-2102	209	20	reduced	reduce	VERB
ejpam-2102	209	21	primary	primary	ADJ
ejpam-2102	209	22	decomposition	decomposition	NOUN
ejpam-2102	209	23	.	.	PUNCT
ejpam-2102	210	1	let	let	VERB
ejpam-2102	210	2	i	i	PRON
ejpam-2102	210	3	j	j	PROPN
ejpam-2102	210	4	,	,	PUNCT
ejpam-2102	210	5	1≤	1≤	NUM
ejpam-2102	210	6	j	j	PROPN
ejpam-2102	210	7	≤	≤	PROPN
ejpam-2102	210	8	n	n	VERB
ejpam-2102	210	9	be	be	AUX
ejpam-2102	210	10	irreducible	irreducible	ADJ
ejpam-2102	210	11	ideals	ideal	NOUN
ejpam-2102	210	12	of	of	ADP
ejpam-2102	210	13	r	r	NOUN
ejpam-2102	211	1	such	such	ADJ
ejpam-2102	211	2	that	that	SCONJ
ejpam-2102	211	3	(	(	PUNCT
ejpam-2102	211	4	0	0	NUM
ejpam-2102	211	5	)	)	PUNCT
ejpam-2102	211	6	=	=	NOUN
ejpam-2102	212	1	∩n	∩n	NOUN
ejpam-2102	213	1	j=1	j=1	NOUN
ejpam-2102	213	2	i	i	PRON
ejpam-2102	213	3	j	j	PROPN
ejpam-2102	213	4	.	.	PUNCT
ejpam-2102	214	1	for	for	ADP
ejpam-2102	214	2	this	this	DET
ejpam-2102	214	3	see	see	NOUN
ejpam-2102	214	4	theorem	theorem	NOUN
ejpam-2102	214	5	(	(	PUNCT
ejpam-2102	214	6	4	4	NUM
ejpam-2102	214	7	)	)	PUNCT
ejpam-2102	214	8	of	of	ADP
ejpam-2102	214	9	zariski	zariski	NOUN
ejpam-2102	214	10	and	and	CCONJ
ejpam-2102	214	11	samuel	samuel	NOUN
ejpam-2102	214	12	[	[	X
ejpam-2102	214	13	17	17	NUM
ejpam-2102	214	14	]	]	PUNCT
ejpam-2102	214	15	.	.	PUNCT
ejpam-2102	215	1	let	let	VERB
ejpam-2102	215	2	æ	æ	PROPN
ejpam-2102	216	1	i	i	PRON
ejpam-2102	216	2	j	j	PROPN
ejpam-2102	216	3	=	=	SYM
ejpam-2102	216	4	pj	pj	PROPN
ejpam-2102	216	5	,	,	PUNCT
ejpam-2102	216	6	where	where	SCONJ
ejpam-2102	216	7	pj	pj	PROPN
ejpam-2102	216	8	is	be	AUX
ejpam-2102	216	9	a	a	DET
ejpam-2102	216	10	prime	prime	ADJ
ejpam-2102	216	11	ideal	ideal	NOUN
ejpam-2102	216	12	belonging	belong	VERB
ejpam-2102	216	13	to	to	ADP
ejpam-2102	216	14	i	i	PROPN
ejpam-2102	216	15	j	j	PROPN
ejpam-2102	216	16	.	.	PUNCT
ejpam-2102	217	1	now	now	ADV
ejpam-2102	217	2	pj	pj	PROPN
ejpam-2102	217	3	∈	∈	PROPN
ejpam-2102	217	4	ass(rr	ass(rr	PROPN
ejpam-2102	217	5	)	)	PUNCT
ejpam-2102	217	6	,	,	PUNCT
ejpam-2102	217	7	1	1	NUM
ejpam-2102	217	8	≤	≤	NUM
ejpam-2102	217	9	j	j	PROPN
ejpam-2102	217	10	≤	≤	NOUN
ejpam-2102	217	11	n	n	X
ejpam-2102	217	12	by	by	ADP
ejpam-2102	217	13	first	first	ADJ
ejpam-2102	217	14	uniqueness	uniqueness	NOUN
ejpam-2102	217	15	theorem	theorem	VERB
ejpam-2102	217	16	.	.	PUNCT
ejpam-2102	218	1	now	now	ADV
ejpam-2102	218	2	by	by	ADP
ejpam-2102	218	3	theorem	theorem	NOUN
ejpam-2102	218	4	(	(	PUNCT
ejpam-2102	218	5	23	23	NUM
ejpam-2102	218	6	)	)	PUNCT
ejpam-2102	218	7	of	of	ADP
ejpam-2102	218	8	zariski	zariski	NOUN
ejpam-2102	218	9	and	and	CCONJ
ejpam-2102	218	10	samuel	samuel	PROPN
ejpam-2102	219	1	[	[	X
ejpam-2102	219	2	17	17	NUM
ejpam-2102	219	3	]	]	PUNCT
ejpam-2102	219	4	,	,	PUNCT
ejpam-2102	219	5	there	there	PRON
ejpam-2102	219	6	exists	exist	VERB
ejpam-2102	219	7	a	a	DET
ejpam-2102	219	8	positive	positive	ADJ
ejpam-2102	219	9	integer	integer	NOUN
ejpam-2102	219	10	k	k	PROPN
ejpam-2102	220	1	such	such	ADJ
ejpam-2102	220	2	that	that	SCONJ
ejpam-2102	220	3	p	p	X
ejpam-2102	220	4	(	(	PUNCT
ejpam-2102	220	5	k	k	NOUN
ejpam-2102	220	6	)	)	PUNCT
ejpam-2102	220	7	j	j	PROPN
ejpam-2102	221	1	⊆	⊆	NUM
ejpam-2102	221	2	i	i	PRON
ejpam-2102	221	3	j	j	PROPN
ejpam-2102	221	4	,	,	PUNCT
ejpam-2102	221	5	1	1	NUM
ejpam-2102	221	6	≤	≤	NUM
ejpam-2102	221	7	j	j	PROPN
ejpam-2102	221	8	≤	≤	PROPN
ejpam-2102	221	9	n.	n.	NOUN
ejpam-2102	221	10	therefore	therefore	ADV
ejpam-2102	221	11	we	we	PRON
ejpam-2102	221	12	have	have	VERB
ejpam-2102	221	13	∩n	∩n	NOUN
ejpam-2102	221	14	j=1	j=1	PROPN
ejpam-2102	221	15	pk	pk	PROPN
ejpam-2102	221	16	j	j	PROPN
ejpam-2102	221	17	=	=	SYM
ejpam-2102	221	18	0	0	PROPN
ejpam-2102	221	19	.	.	PUNCT
ejpam-2102	222	1	now	now	ADV
ejpam-2102	222	2	each	each	DET
ejpam-2102	222	3	pj	pj	PROPN
ejpam-2102	222	4	contains	contain	VERB
ejpam-2102	222	5	a	a	DET
ejpam-2102	222	6	minimal	minimal	ADJ
ejpam-2102	222	7	prime	prime	ADJ
ejpam-2102	222	8	ideal	ideal	NOUN
ejpam-2102	222	9	u	u	PROPN
ejpam-2102	222	10	j	j	PROPN
ejpam-2102	222	11	by	by	ADP
ejpam-2102	222	12	proposition	proposition	NOUN
ejpam-2102	222	13	(	(	PUNCT
ejpam-2102	222	14	2.3	2.3	NUM
ejpam-2102	222	15	)	)	PUNCT
ejpam-2102	222	16	of	of	ADP
ejpam-2102	222	17	goodearl	goodearl	PROPN
ejpam-2102	222	18	and	and	CCONJ
ejpam-2102	222	19	warfield	warfield	VERB
ejpam-2102	223	1	[	[	X
ejpam-2102	223	2	12	12	NUM
ejpam-2102	223	3	]	]	PUNCT
ejpam-2102	223	4	,	,	PUNCT
ejpam-2102	223	5	therefore	therefore	ADV
ejpam-2102	223	6	∩n	∩n	PROPN
ejpam-2102	223	7	j=1	j=1	PROPN
ejpam-2102	223	8	uk	uk	PROPN
ejpam-2102	223	9	j	j	PROPN
ejpam-2102	223	10	=	=	PUNCT
ejpam-2102	223	11	0	0	PROPN
ejpam-2102	223	12	.	.	PUNCT
ejpam-2102	224	1	now	now	ADV
ejpam-2102	224	2	r	r	NOUN
ejpam-2102	224	3	is	be	AUX
ejpam-2102	224	4	commutative	commutative	ADJ
ejpam-2102	224	5	,	,	PUNCT
ejpam-2102	224	6	therefore	therefore	ADV
ejpam-2102	224	7	,	,	PUNCT
ejpam-2102	224	8	proposition	proposition	NOUN
ejpam-2102	224	9	3	3	NUM
ejpam-2102	224	10	implies	imply	VERB
ejpam-2102	224	11	that	that	SCONJ
ejpam-2102	224	12	σ(u	σ(u	PROPN
ejpam-2102	224	13	j	j	X
ejpam-2102	224	14	)	)	PUNCT
ejpam-2102	224	15	=	=	SYM
ejpam-2102	224	16	u	u	PROPN
ejpam-2102	224	17	j	j	PROPN
ejpam-2102	224	18	,	,	PUNCT
ejpam-2102	224	19	for	for	ADP
ejpam-2102	224	20	all	all	DET
ejpam-2102	224	21	j	j	PROPN
ejpam-2102	224	22	,	,	PUNCT
ejpam-2102	224	23	1	1	NUM
ejpam-2102	224	24	≤	≤	NUM
ejpam-2102	224	25	j	j	PROPN
ejpam-2102	224	26	≤	≤	PROPN
ejpam-2102	224	27	n.	n.	NOUN
ejpam-2102	224	28	also	also	ADV
ejpam-2102	224	29	,	,	PUNCT
ejpam-2102	224	30	by	by	ADP
ejpam-2102	224	31	lemma	lemma	PROPN
ejpam-2102	224	32	2	2	NUM
ejpam-2102	224	33	,	,	PUNCT
ejpam-2102	224	34	we	we	PRON
ejpam-2102	224	35	have	have	VERB
ejpam-2102	224	36	δ(u	δ(u	PROPN
ejpam-2102	224	37	j	j	PROPN
ejpam-2102	224	38	)	)	PUNCT
ejpam-2102	224	39	⊆	⊆	NUM
ejpam-2102	224	40	u	u	SYM
ejpam-2102	224	41	j	j	PROPN
ejpam-2102	224	42	,	,	PUNCT
ejpam-2102	224	43	for	for	ADP
ejpam-2102	224	44	all	all	DET
ejpam-2102	224	45	j	j	PROPN
ejpam-2102	224	46	,	,	PUNCT
ejpam-2102	224	47	1≤	1≤	PROPN
ejpam-2102	224	48	j	j	PROPN
ejpam-2102	224	49	≤	≤	PROPN
ejpam-2102	224	50	n.	n.	NOUN
ejpam-2102	224	51	now	now	ADV
ejpam-2102	224	52	lemma	lemma	PROPN
ejpam-2102	224	53	1	1	NUM
ejpam-2102	224	54	implies	imply	VERB
ejpam-2102	224	55	that	that	SCONJ
ejpam-2102	224	56	σ(u	σ(u	PROPN
ejpam-2102	224	57	j	j	X
ejpam-2102	224	58	)	)	PUNCT
ejpam-2102	224	59	(	(	PUNCT
ejpam-2102	224	60	k	k	X
ejpam-2102	224	61	)	)	PUNCT
ejpam-2102	224	62	=	=	SYM
ejpam-2102	224	63	u	u	NOUN
ejpam-2102	224	64	(	(	PUNCT
ejpam-2102	224	65	k	k	NOUN
ejpam-2102	224	66	)	)	PUNCT
ejpam-2102	224	67	j	j	PROPN
ejpam-2102	224	68	and	and	CCONJ
ejpam-2102	224	69	lemma	lemma	PROPN
ejpam-2102	224	70	3	3	NUM
ejpam-2102	224	71	implies	imply	VERB
ejpam-2102	224	72	that	that	SCONJ
ejpam-2102	224	73	δ(u	δ(u	PROPN
ejpam-2102	224	74	(	(	PUNCT
ejpam-2102	224	75	k	k	NOUN
ejpam-2102	224	76	)	)	PUNCT
ejpam-2102	224	77	j	j	PROPN
ejpam-2102	224	78	)	)	PUNCT
ejpam-2102	224	79	⊆	⊆	NUM
ejpam-2102	224	80	u	u	NOUN
ejpam-2102	224	81	(	(	PUNCT
ejpam-2102	224	82	k	k	NOUN
ejpam-2102	224	83	)	)	PUNCT
ejpam-2102	224	84	j	j	PROPN
ejpam-2102	224	85	,	,	PUNCT
ejpam-2102	224	86	for	for	ADP
ejpam-2102	224	87	all	all	DET
ejpam-2102	224	88	j	j	PROPN
ejpam-2102	224	89	,	,	PUNCT
ejpam-2102	224	90	1	1	NUM
ejpam-2102	224	91	≤	≤	NUM
ejpam-2102	224	92	j	j	PROPN
ejpam-2102	224	93	≤	≤	PROPN
ejpam-2102	224	94	n	n	CCONJ
ejpam-2102	224	95	and	and	CCONJ
ejpam-2102	224	96	for	for	ADP
ejpam-2102	224	97	all	all	DET
ejpam-2102	224	98	k	k	PROPN
ejpam-2102	224	99	≥	≥	NUM
ejpam-2102	224	100	1	1	NUM
ejpam-2102	224	101	.	.	PUNCT
ejpam-2102	225	1	therefore	therefore	ADV
ejpam-2102	225	2	,	,	PUNCT
ejpam-2102	225	3	o(u	o(u	PROPN
ejpam-2102	225	4	(	(	PUNCT
ejpam-2102	225	5	k	k	NOUN
ejpam-2102	225	6	)	)	PUNCT
ejpam-2102	225	7	j	j	PROPN
ejpam-2102	225	8	)	)	PUNCT
ejpam-2102	225	9	is	be	AUX
ejpam-2102	225	10	an	an	DET
ejpam-2102	225	11	ideal	ideal	NOUN
ejpam-2102	225	12	of	of	ADP
ejpam-2102	225	13	o(r	o(r	PROPN
ejpam-2102	225	14	)	)	PUNCT
ejpam-2102	225	15	and	and	CCONJ
ejpam-2102	225	16	∩n	∩n	PROPN
ejpam-2102	225	17	j=1	j=1	PROPN
ejpam-2102	225	18	o(u	o(u	PROPN
ejpam-2102	225	19	(	(	PUNCT
ejpam-2102	225	20	k	k	NOUN
ejpam-2102	225	21	)	)	PUNCT
ejpam-2102	225	22	j	j	NOUN
ejpam-2102	225	23	)	)	PUNCT
ejpam-2102	226	1	=	=	PUNCT
ejpam-2102	226	2	0	0	X
ejpam-2102	226	3	.	.	PUNCT
ejpam-2102	227	1	now	now	ADV
ejpam-2102	227	2	r	r	NOUN
ejpam-2102	227	3	/	/	SYM
ejpam-2102	227	4	u	u	NOUN
ejpam-2102	227	5	(	(	PUNCT
ejpam-2102	227	6	k	k	NOUN
ejpam-2102	227	7	)	)	PUNCT
ejpam-2102	227	8	j	j	PROPN
ejpam-2102	227	9	has	have	VERB
ejpam-2102	227	10	an	an	DET
ejpam-2102	227	11	artinian	artinian	ADJ
ejpam-2102	227	12	quotient	quotient	NOUN
ejpam-2102	227	13	ring	ring	NOUN
ejpam-2102	227	14	,	,	PUNCT
ejpam-2102	227	15	as	as	SCONJ
ejpam-2102	227	16	it	it	PRON
ejpam-2102	227	17	has	have	VERB
ejpam-2102	227	18	no	no	DET
ejpam-2102	227	19	embedded	embed	VERB
ejpam-2102	227	20	primes	prime	NOUN
ejpam-2102	227	21	,	,	PUNCT
ejpam-2102	227	22	therefore	therefore	ADV
ejpam-2102	227	23	o(r)/o(u	o(r)/o(u	ADJ
ejpam-2102	227	24	(	(	PUNCT
ejpam-2102	227	25	k	k	NOUN
ejpam-2102	227	26	)	)	PUNCT
ejpam-2102	227	27	j	j	PROPN
ejpam-2102	227	28	)	)	PUNCT
ejpam-2102	227	29	has	have	VERB
ejpam-2102	227	30	also	also	ADV
ejpam-2102	227	31	an	an	DET
ejpam-2102	227	32	artinian	artinian	ADJ
ejpam-2102	227	33	quotient	quotient	NOUN
ejpam-2102	227	34	ring	ring	NOUN
ejpam-2102	227	35	by	by	ADP
ejpam-2102	227	36	theorem	theorem	NOUN
ejpam-2102	227	37	(	(	PUNCT
ejpam-2102	227	38	2.11	2.11	NUM
ejpam-2102	227	39	)	)	PUNCT
ejpam-2102	227	40	of	of	ADP
ejpam-2102	227	41	bhat	bhat	PROPN
ejpam-2102	228	1	[	[	X
ejpam-2102	228	2	4	4	NUM
ejpam-2102	228	3	]	]	PUNCT
ejpam-2102	228	4	.	.	PUNCT
ejpam-2102	229	1	hence	hence	ADV
ejpam-2102	229	2	o(r	o(r	NOUN
ejpam-2102	229	3	)	)	PUNCT
ejpam-2102	229	4	=	=	SYM
ejpam-2102	229	5	r[x;σ	r[x;σ	NOUN
ejpam-2102	229	6	,	,	PUNCT
ejpam-2102	229	7	δ	δ	PROPN
ejpam-2102	229	8	]	]	PUNCT
ejpam-2102	229	9	is	be	AUX
ejpam-2102	229	10	transparent	transparent	ADJ
ejpam-2102	229	11	ring	ring	NOUN
ejpam-2102	229	12	.	.	PUNCT
ejpam-2102	230	1	acknowledgements	acknowledgement	NOUN
ejpam-2102	230	2	the	the	DET
ejpam-2102	230	3	work	work	NOUN
ejpam-2102	230	4	is	be	AUX
ejpam-2102	230	5	supported	support	VERB
ejpam-2102	230	6	by	by	ADP
ejpam-2102	230	7	natioal	natioal	ADJ
ejpam-2102	230	8	booard	booard	NOUN
ejpam-2102	230	9	for	for	ADP
ejpam-2102	230	10	higher	high	ADJ
ejpam-2102	230	11	mathematics	mathematic	NOUN
ejpam-2102	230	12	,	,	PUNCT
ejpam-2102	230	13	department	department	NOUN
ejpam-2102	230	14	of	of	ADP
ejpam-2102	230	15	atomic	atomic	ADJ
ejpam-2102	230	16	energy	energy	NOUN
ejpam-2102	230	17	,	,	PUNCT
ejpam-2102	230	18	government	government	NOUN
ejpam-2102	230	19	of	of	ADP
ejpam-2102	230	20	india	india	PROPN
ejpam-2102	230	21	(	(	PUNCT
ejpam-2102	230	22	no.2/48(9)/2010	no.2/48(9)/2010	NOUN
ejpam-2102	230	23	/	/	SYM
ejpam-2102	230	24	r	r	NOUN
ejpam-2102	230	25	and	and	CCONJ
ejpam-2102	230	26	d	d	NOUN
ejpam-2102	230	27	ii/11193	ii/11193	NOUN
ejpam-2102	230	28	)	)	PUNCT
ejpam-2102	230	29	.	.	PUNCT
ejpam-2102	231	1	references	reference	NOUN
ejpam-2102	231	2	[	[	X
ejpam-2102	231	3	1	1	NUM
ejpam-2102	231	4	]	]	X
ejpam-2102	231	5	n.	n.	NOUN
ejpam-2102	231	6	argac	argac	PROPN
ejpam-2102	231	7	and	and	CCONJ
ejpam-2102	231	8	n.	n.	PROPN
ejpam-2102	231	9	j.	j.	PROPN
ejpam-2102	231	10	groenewald	groenewald	PROPN
ejpam-2102	231	11	.	.	PUNCT
ejpam-2102	232	1	a	a	DET
ejpam-2102	232	2	generalization	generalization	NOUN
ejpam-2102	232	3	of	of	ADP
ejpam-2102	232	4	2	2	NUM
ejpam-2102	232	5	-	-	PUNCT
ejpam-2102	232	6	primal	primal	ADJ
ejpam-2102	232	7	near	near	ADP
ejpam-2102	232	8	rings	ring	NOUN
ejpam-2102	232	9	,	,	PUNCT
ejpam-2102	232	10	quaestiones	quaestione	NOUN
ejpam-2102	232	11	mathematicae	mathematicae	VERB
ejpam-2102	232	12	,	,	PUNCT
ejpam-2102	232	13	27(4	27(4	PROPN
ejpam-2102	232	14	)	)	PUNCT
ejpam-2102	232	15	,	,	PUNCT
ejpam-2102	232	16	397	397	NUM
ejpam-2102	232	17	-	-	SYM
ejpam-2102	232	18	413	413	NUM
ejpam-2102	232	19	.	.	PUNCT
ejpam-2102	232	20	2004	2004	NUM
ejpam-2102	232	21	.	.	PUNCT
ejpam-2102	233	1	[	[	X
ejpam-2102	233	2	2	2	X
ejpam-2102	233	3	]	]	PUNCT
ejpam-2102	233	4	v.	v.	PROPN
ejpam-2102	233	5	k.	k.	PROPN
ejpam-2102	233	6	bhat	bhat	PROPN
ejpam-2102	233	7	.	.	PUNCT
ejpam-2102	234	1	decomposability	decomposability	NOUN
ejpam-2102	234	2	of	of	ADP
ejpam-2102	234	3	iterated	iterated	ADJ
ejpam-2102	234	4	extension	extension	NOUN
ejpam-2102	234	5	,	,	PUNCT
ejpam-2102	234	6	international	international	ADJ
ejpam-2102	234	7	journal	journal	NOUN
ejpam-2102	234	8	of	of	ADP
ejpam-2102	234	9	mathematical	mathematical	ADJ
ejpam-2102	234	10	game	game	NOUN
ejpam-2102	234	11	theory	theory	NOUN
ejpam-2102	234	12	algebra	algebra	NOUN
ejpam-2102	234	13	,	,	PUNCT
ejpam-2102	234	14	15(1	15(1	NUM
ejpam-2102	234	15	)	)	PUNCT
ejpam-2102	234	16	,	,	PUNCT
ejpam-2102	234	17	45	45	NUM
ejpam-2102	234	18	-	-	SYM
ejpam-2102	234	19	48	48	NUM
ejpam-2102	234	20	.	.	PUNCT
ejpam-2102	235	1	2006	2006	NUM
ejpam-2102	235	2	.	.	PUNCT
ejpam-2102	236	1	[	[	X
ejpam-2102	236	2	3	3	X
ejpam-2102	236	3	]	]	PUNCT
ejpam-2102	236	4	v.	v.	PROPN
ejpam-2102	236	5	k.	k.	PROPN
ejpam-2102	236	6	bhat	bhat	PROPN
ejpam-2102	236	7	.	.	PUNCT
ejpam-2102	237	1	polynomial	polynomial	ADJ
ejpam-2102	237	2	rings	ring	NOUN
ejpam-2102	237	3	over	over	ADP
ejpam-2102	237	4	pseudovaluation	pseudovaluation	NOUN
ejpam-2102	237	5	rings	ring	NOUN
ejpam-2102	237	6	,	,	PUNCT
ejpam-2102	237	7	international	international	ADJ
ejpam-2102	237	8	journal	journal	NOUN
ejpam-2102	237	9	of	of	ADP
ejpam-2102	237	10	mathematics	mathematics	PROPN
ejpam-2102	237	11	and	and	CCONJ
ejpam-2102	237	12	mathematical	mathematical	ADJ
ejpam-2102	237	13	sciences	science	NOUN
ejpam-2102	237	14	,	,	PUNCT
ejpam-2102	237	15	art	art	NOUN
ejpam-2102	237	16	.	.	PUNCT
ejpam-2102	238	1	i	i	PRON
ejpam-2102	238	2	d	d	PROPN
ejpam-2102	238	3	20138	20138	NUM
ejpam-2102	238	4	.	.	PUNCT
ejpam-2102	239	1	2007	2007	NUM
ejpam-2102	239	2	.	.	PUNCT
ejpam-2102	240	1	[	[	X
ejpam-2102	240	2	4	4	X
ejpam-2102	240	3	]	]	PUNCT
ejpam-2102	240	4	v.	v.	PROPN
ejpam-2102	240	5	k.	k.	PROPN
ejpam-2102	240	6	bhat	bhat	PROPN
ejpam-2102	240	7	.	.	PUNCT
ejpam-2102	241	1	ring	ring	NOUN
ejpam-2102	241	2	extensions	extension	NOUN
ejpam-2102	241	3	and	and	CCONJ
ejpam-2102	241	4	their	their	PRON
ejpam-2102	241	5	quotient	quotient	NOUN
ejpam-2102	241	6	rings	ring	NOUN
ejpam-2102	241	7	,	,	PUNCT
ejpam-2102	241	8	east	east	PROPN
ejpam-2102	241	9	-	-	PUNCT
ejpam-2102	241	10	west	west	PROPN
ejpam-2102	241	11	journal	journal	PROPN
ejpam-2102	241	12	of	of	ADP
ejpam-2102	241	13	mathematics	mathematic	NOUN
ejpam-2102	241	14	,	,	PUNCT
ejpam-2102	241	15	9(1	9(1	NUM
ejpam-2102	241	16	)	)	PUNCT
ejpam-2102	241	17	,	,	PUNCT
ejpam-2102	241	18	25	25	NUM
ejpam-2102	241	19	-	-	SYM
ejpam-2102	241	20	30	30	NUM
ejpam-2102	241	21	.	.	PUNCT
ejpam-2102	241	22	2007	2007	NUM
ejpam-2102	241	23	.	.	PUNCT
ejpam-2102	242	1	[	[	X
ejpam-2102	242	2	5	5	X
ejpam-2102	242	3	]	]	PUNCT
ejpam-2102	242	4	v.	v.	PROPN
ejpam-2102	242	5	k.	k.	PROPN
ejpam-2102	242	6	bhat	bhat	PROPN
ejpam-2102	242	7	.	.	PUNCT
ejpam-2102	243	1	on	on	ADP
ejpam-2102	243	2	2	2	NUM
ejpam-2102	243	3	-	-	PUNCT
ejpam-2102	243	4	primal	primal	ADJ
ejpam-2102	243	5	ore	ore	NOUN
ejpam-2102	243	6	extensions	extension	NOUN
ejpam-2102	243	7	,	,	PUNCT
ejpam-2102	243	8	ukranian	ukranian	ADJ
ejpam-2102	243	9	mathematical	mathematical	ADJ
ejpam-2102	243	10	bulletin	bulletin	NOUN
ejpam-2102	243	11	,	,	PUNCT
ejpam-2102	243	12	4(2	4(2	NUM
ejpam-2102	243	13	)	)	PUNCT
ejpam-2102	243	14	,	,	PUNCT
ejpam-2102	243	15	173	173	NUM
ejpam-2102	243	16	-	-	SYM
ejpam-2102	243	17	179	179	NUM
ejpam-2102	243	18	.	.	PUNCT
ejpam-2102	243	19	2007	2007	NUM
ejpam-2102	243	20	.	.	PUNCT
ejpam-2102	244	1	references	reference	NOUN
ejpam-2102	244	2	117	117	NUM
ejpam-2102	244	3	[	[	X
ejpam-2102	244	4	6	6	NUM
ejpam-2102	244	5	]	]	PUNCT
ejpam-2102	244	6	v.	v.	PROPN
ejpam-2102	244	7	k.	k.	PROPN
ejpam-2102	244	8	bhat	bhat	PROPN
ejpam-2102	244	9	.	.	PUNCT
ejpam-2102	245	1	associated	associate	VERB
ejpam-2102	245	2	prime	prime	ADJ
ejpam-2102	245	3	ideals	ideal	NOUN
ejpam-2102	245	4	of	of	ADP
ejpam-2102	245	5	skew	skew	ADJ
ejpam-2102	245	6	polynomial	polynomial	ADJ
ejpam-2102	245	7	rings	ring	NOUN
ejpam-2102	245	8	,	,	PUNCT
ejpam-2102	245	9	beitrage	beitrage	NOUN
ejpam-2102	245	10	algebra	algebra	NOUN
ejpam-2102	245	11	geometry	geometry	NOUN
ejpam-2102	245	12	,	,	PUNCT
ejpam-2102	245	13	49(1	49(1	NOUN
ejpam-2102	245	14	)	)	PUNCT
ejpam-2102	245	15	,	,	PUNCT
ejpam-2102	245	16	277	277	NUM
ejpam-2102	245	17	-	-	SYM
ejpam-2102	245	18	283	283	NUM
ejpam-2102	245	19	.	.	PUNCT
ejpam-2102	245	20	2008	2008	NUM
ejpam-2102	245	21	.	.	PUNCT
ejpam-2102	246	1	[	[	X
ejpam-2102	246	2	7	7	X
ejpam-2102	246	3	]	]	X
ejpam-2102	246	4	v.	v.	PROPN
ejpam-2102	246	5	k.	k.	PROPN
ejpam-2102	246	6	bhat	bhat	PROPN
ejpam-2102	246	7	.	.	PUNCT
ejpam-2102	247	1	differential	differential	ADJ
ejpam-2102	247	2	operator	operator	NOUN
ejpam-2102	247	3	rings	ring	NOUN
ejpam-2102	247	4	over	over	ADP
ejpam-2102	247	5	2	2	NUM
ejpam-2102	247	6	-	-	PUNCT
ejpam-2102	247	7	primal	primal	ADJ
ejpam-2102	247	8	rings	ring	NOUN
ejpam-2102	247	9	,	,	PUNCT
ejpam-2102	247	10	ukranian	ukranian	PROPN
ejpam-2102	247	11	mathematical	mathematical	ADJ
ejpam-2102	247	12	bulletin	bulletin	NOUN
ejpam-2102	247	13	,	,	PUNCT
ejpam-2102	247	14	5(2	5(2	NUM
ejpam-2102	247	15	)	)	PUNCT
ejpam-2102	247	16	,	,	PUNCT
ejpam-2102	247	17	153	153	NUM
ejpam-2102	247	18	-	-	SYM
ejpam-2102	247	19	158	158	NUM
ejpam-2102	247	20	.	.	PUNCT
ejpam-2102	247	21	2008	2008	NUM
ejpam-2102	247	22	.	.	PUNCT
ejpam-2102	248	1	[	[	X
ejpam-2102	248	2	8	8	NUM
ejpam-2102	248	3	]	]	X
ejpam-2102	248	4	v.	v.	PROPN
ejpam-2102	248	5	k.	k.	PROPN
ejpam-2102	248	6	bhat	bhat	PROPN
ejpam-2102	248	7	.	.	PUNCT
ejpam-2102	249	1	transparent	transparent	ADJ
ejpam-2102	249	2	rings	ring	NOUN
ejpam-2102	249	3	and	and	CCONJ
ejpam-2102	249	4	their	their	PRON
ejpam-2102	249	5	extensions	extension	NOUN
ejpam-2102	249	6	,	,	PUNCT
ejpam-2102	249	7	new	new	PROPN
ejpam-2102	249	8	york	york	PROPN
ejpam-2102	249	9	journal	journal	PROPN
ejpam-2102	249	10	of	of	ADP
ejpam-2102	249	11	mathematics	mathematic	NOUN
ejpam-2102	249	12	,	,	PUNCT
ejpam-2102	249	13	15	15	NUM
ejpam-2102	249	14	,	,	PUNCT
ejpam-2102	249	15	291	291	NUM
ejpam-2102	249	16	-	-	SYM
ejpam-2102	249	17	299	299	NUM
ejpam-2102	249	18	.	.	PUNCT
ejpam-2102	249	19	2009	2009	NUM
ejpam-2102	249	20	.	.	PUNCT
ejpam-2102	250	1	[	[	X
ejpam-2102	250	2	9	9	NUM
ejpam-2102	250	3	]	]	PUNCT
ejpam-2102	250	4	v.	v.	PROPN
ejpam-2102	250	5	k.	k.	PROPN
ejpam-2102	250	6	bhat	bhat	PROPN
ejpam-2102	250	7	and	and	CCONJ
ejpam-2102	250	8	kiran	kiran	PROPN
ejpam-2102	250	9	chib	chib	NOUN
ejpam-2102	250	10	.	.	PUNCT
ejpam-2102	251	1	transparent	transparent	ADJ
ejpam-2102	251	2	ore	ore	NOUN
ejpam-2102	251	3	extensions	extension	NOUN
ejpam-2102	251	4	over	over	ADP
ejpam-2102	251	5	weak	weak	ADJ
ejpam-2102	251	6	σ	σ	ADJ
ejpam-2102	251	7	-	-	ADJ
ejpam-2102	251	8	rigid	rigid	ADJ
ejpam-2102	251	9	rings	ring	NOUN
ejpam-2102	251	10	,	,	PUNCT
ejpam-2102	251	11	siberian	siberian	ADJ
ejpam-2102	251	12	electronic	electronic	ADJ
ejpam-2102	251	13	mathematical	mathematical	ADJ
ejpam-2102	251	14	reports	report	NOUN
ejpam-2102	251	15	,	,	PUNCT
ejpam-2102	251	16	8	8	NUM
ejpam-2102	251	17	,	,	PUNCT
ejpam-2102	251	18	116	116	NUM
ejpam-2102	251	19	-	-	SYM
ejpam-2102	251	20	122	122	NUM
ejpam-2102	251	21	.	.	PUNCT
ejpam-2102	251	22	2011	2011	NUM
ejpam-2102	251	23	.	.	PUNCT
ejpam-2102	252	1	[	[	X
ejpam-2102	252	2	10	10	NUM
ejpam-2102	252	3	]	]	X
ejpam-2102	252	4	v.	v.	PROPN
ejpam-2102	252	5	k.	k.	PROPN
ejpam-2102	252	6	bhat	bhat	PROPN
ejpam-2102	252	7	.	.	PUNCT
ejpam-2102	253	1	on	on	ADP
ejpam-2102	253	2	2	2	NUM
ejpam-2102	253	3	-	-	PUNCT
ejpam-2102	253	4	primal	primal	ADJ
ejpam-2102	253	5	ore	ore	NOUN
ejpam-2102	253	6	extensions	extension	NOUN
ejpam-2102	253	7	over	over	ADP
ejpam-2102	253	8	noetherian	noetherian	ADJ
ejpam-2102	253	9	σ(∗)-rings	σ(∗)-ring	NOUN
ejpam-2102	253	10	,	,	PUNCT
ejpam-2102	253	11	buletinul	buletinul	NOUN
ejpam-2102	253	12	academiei	academiei	PROPN
ejpam-2102	253	13	de	de	X
ejpam-2102	253	14	stiinte	stiinte	VERB
ejpam-2102	253	15	a	a	DET
ejpam-2102	253	16	republicii	republicii	PROPN
ejpam-2102	253	17	moldova	moldova	PROPN
ejpam-2102	253	18	matematica	matematica	PROPN
ejpam-2102	253	19	,	,	PUNCT
ejpam-2102	253	20	1(65	1(65	NUM
ejpam-2102	253	21	)	)	PUNCT
ejpam-2102	253	22	,	,	PUNCT
ejpam-2102	253	23	42	42	NUM
ejpam-2102	253	24	-	-	SYM
ejpam-2102	253	25	49	49	NUM
ejpam-2102	253	26	.	.	PUNCT
ejpam-2102	254	1	2011	2011	NUM
ejpam-2102	254	2	.	.	PUNCT
ejpam-2102	255	1	[	[	X
ejpam-2102	255	2	11	11	NUM
ejpam-2102	255	3	]	]	X
ejpam-2102	255	4	w.	w.	PROPN
ejpam-2102	255	5	d.	d.	PROPN
ejpam-2102	255	6	blair	blair	PROPN
ejpam-2102	255	7	and	and	CCONJ
ejpam-2102	255	8	l.	l.	PROPN
ejpam-2102	255	9	w.	w.	PROPN
ejpam-2102	255	10	small	small	PROPN
ejpam-2102	255	11	.	.	PUNCT
ejpam-2102	256	1	embedding	embed	VERB
ejpam-2102	256	2	differential	differential	NOUN
ejpam-2102	256	3	and	and	CCONJ
ejpam-2102	256	4	skew	skew	ADJ
ejpam-2102	256	5	polynomial	polynomial	ADJ
ejpam-2102	256	6	rings	ring	NOUN
ejpam-2102	256	7	into	into	ADP
ejpam-2102	256	8	artinian	artinian	ADJ
ejpam-2102	256	9	rings	ring	NOUN
ejpam-2102	256	10	,	,	PUNCT
ejpam-2102	256	11	proceedings	proceeding	NOUN
ejpam-2102	256	12	of	of	ADP
ejpam-2102	256	13	american	american	PROPN
ejpam-2102	256	14	mathematical	mathematical	PROPN
ejpam-2102	256	15	society	society	NOUN
ejpam-2102	256	16	,	,	PUNCT
ejpam-2102	256	17	109(4	109(4	NUM
ejpam-2102	256	18	)	)	PUNCT
ejpam-2102	256	19	,	,	PUNCT
ejpam-2102	256	20	881	881	NUM
ejpam-2102	256	21	-	-	SYM
ejpam-2102	256	22	886	886	NUM
ejpam-2102	256	23	.	.	PUNCT
ejpam-2102	256	24	1990	1990	NUM
ejpam-2102	256	25	.	.	PUNCT
ejpam-2102	257	1	[	[	X
ejpam-2102	257	2	12	12	NUM
ejpam-2102	257	3	]	]	PUNCT
ejpam-2102	257	4	k.	k.	PROPN
ejpam-2102	257	5	r.	r.	PROPN
ejpam-2102	257	6	goodearl	goodearl	PROPN
ejpam-2102	257	7	and	and	CCONJ
ejpam-2102	257	8	r.	r.	PROPN
ejpam-2102	257	9	b.	b.	PROPN
ejpam-2102	257	10	warfield	warfield	PROPN
ejpam-2102	257	11	.	.	PUNCT
ejpam-2102	258	1	an	an	DET
ejpam-2102	258	2	introduction	introduction	NOUN
ejpam-2102	258	3	to	to	ADP
ejpam-2102	258	4	non	non	ADJ
ejpam-2102	258	5	-	-	ADJ
ejpam-2102	258	6	commutative	commutative	ADJ
ejpam-2102	258	7	noetherian	noetherian	ADJ
ejpam-2102	258	8	rings	ring	NOUN
ejpam-2102	258	9	,	,	PUNCT
ejpam-2102	258	10	cambridge	cambridge	PROPN
ejpam-2102	258	11	university	university	PROPN
ejpam-2102	258	12	press	press	NOUN
ejpam-2102	258	13	,	,	PUNCT
ejpam-2102	258	14	1989	1989	NUM
ejpam-2102	258	15	.	.	PUNCT
ejpam-2102	259	1	[	[	X
ejpam-2102	259	2	13	13	NUM
ejpam-2102	259	3	]	]	X
ejpam-2102	259	4	n.	n.	PROPN
ejpam-2102	259	5	k.	k.	PROPN
ejpam-2102	259	6	kim	kim	PROPN
ejpam-2102	259	7	and	and	CCONJ
ejpam-2102	259	8	t.	t.	PROPN
ejpam-2102	259	9	k.	k.	PROPN
ejpam-2102	259	10	kwak	kwak	PROPN
ejpam-2102	259	11	.	.	PUNCT
ejpam-2102	260	1	minimal	minimal	ADJ
ejpam-2102	260	2	prime	prime	ADJ
ejpam-2102	260	3	ideals	ideal	NOUN
ejpam-2102	260	4	in	in	ADP
ejpam-2102	260	5	2	2	NUM
ejpam-2102	260	6	-	-	PUNCT
ejpam-2102	260	7	primal	primal	ADJ
ejpam-2102	260	8	rings	ring	NOUN
ejpam-2102	260	9	,	,	PUNCT
ejpam-2102	260	10	mathematica	mathematica	PROPN
ejpam-2102	260	11	japonica	japonica	PROPN
ejpam-2102	260	12	,	,	PUNCT
ejpam-2102	260	13	50(3	50(3	NUM
ejpam-2102	260	14	)	)	PUNCT
ejpam-2102	260	15	,	,	PUNCT
ejpam-2102	260	16	415	415	NUM
ejpam-2102	260	17	-	-	SYM
ejpam-2102	260	18	420	420	NUM
ejpam-2102	260	19	.	.	PUNCT
ejpam-2102	261	1	1999	1999	NUM
ejpam-2102	262	1	[	[	X
ejpam-2102	262	2	14	14	NUM
ejpam-2102	262	3	]	]	X
ejpam-2102	262	4	g.	g.	PROPN
ejpam-2102	262	5	marks	marks	PROPN
ejpam-2102	262	6	.	.	PUNCT
ejpam-2102	263	1	on	on	ADP
ejpam-2102	263	2	2	2	NUM
ejpam-2102	263	3	-	-	PUNCT
ejpam-2102	263	4	primal	primal	ADJ
ejpam-2102	263	5	ore	ore	NOUN
ejpam-2102	263	6	extensions	extension	NOUN
ejpam-2102	263	7	,	,	PUNCT
ejpam-2102	263	8	communications	communication	NOUN
ejpam-2102	263	9	in	in	ADP
ejpam-2102	263	10	algebra	algebra	NOUN
ejpam-2102	263	11	,	,	PUNCT
ejpam-2102	263	12	29(5	29(5	NUM
ejpam-2102	263	13	)	)	PUNCT
ejpam-2102	263	14	,	,	PUNCT
ejpam-2102	263	15	2113	2113	NUM
ejpam-2102	263	16	-	-	SYM
ejpam-2102	263	17	2123	2123	NUM
ejpam-2102	263	18	.	.	PUNCT
ejpam-2102	263	19	2001	2001	NUM
ejpam-2102	263	20	.	.	PUNCT
ejpam-2102	264	1	[	[	X
ejpam-2102	264	2	15	15	NUM
ejpam-2102	264	3	]	]	X
ejpam-2102	264	4	j.	j.	PROPN
ejpam-2102	264	5	c.	c.	PROPN
ejpam-2102	264	6	mcconnell	mcconnell	PROPN
ejpam-2102	264	7	and	and	CCONJ
ejpam-2102	264	8	j.	j.	PROPN
ejpam-2102	264	9	c.	c.	PROPN
ejpam-2102	264	10	robson	robson	PROPN
ejpam-2102	264	11	.	.	PUNCT
ejpam-2102	265	1	noncommutative	noncommutative	ADJ
ejpam-2102	265	2	noetherian	noetherian	ADJ
ejpam-2102	265	3	rings	ring	NOUN
ejpam-2102	265	4	,	,	PUNCT
ejpam-2102	265	5	wiley(1987	wiley(1987	NOUN
ejpam-2102	265	6	)	)	PUNCT
ejpam-2102	265	7	;	;	PUNCT
ejpam-2102	265	8	revised	revise	VERB
ejpam-2102	265	9	edition	edition	NOUN
ejpam-2102	265	10	:	:	PUNCT
ejpam-2102	265	11	american	american	PROPN
ejpam-2102	265	12	mathematical	mathematical	PROPN
ejpam-2102	265	13	society	society	NOUN
ejpam-2102	265	14	,	,	PUNCT
ejpam-2102	265	15	2001	2001	NUM
ejpam-2102	265	16	.	.	PUNCT
ejpam-2102	266	1	[	[	X
ejpam-2102	266	2	16	16	NUM
ejpam-2102	266	3	]	]	PUNCT
ejpam-2102	266	4	l.	l.	PROPN
ejpam-2102	266	5	ouyang	ouyang	PROPN
ejpam-2102	266	6	.	.	PUNCT
ejpam-2102	267	1	extensions	extension	NOUN
ejpam-2102	267	2	of	of	ADP
ejpam-2102	267	3	generalized	generalized	ADJ
ejpam-2102	267	4	α	α	ADJ
ejpam-2102	267	5	-	-	ADJ
ejpam-2102	267	6	rigid	rigid	ADJ
ejpam-2102	267	7	rings	ring	NOUN
ejpam-2102	267	8	,	,	PUNCT
ejpam-2102	267	9	international	international	ADJ
ejpam-2102	267	10	electronic	electronic	ADJ
ejpam-2102	267	11	journal	journal	NOUN
ejpam-2102	267	12	of	of	ADP
ejpam-2102	267	13	algebra	algebra	PROPN
ejpam-2102	267	14	,	,	PUNCT
ejpam-2102	267	15	3	3	NUM
ejpam-2102	267	16	,	,	PUNCT
ejpam-2102	267	17	103	103	NUM
ejpam-2102	267	18	-	-	SYM
ejpam-2102	267	19	116	116	NUM
ejpam-2102	267	20	.	.	PUNCT
ejpam-2102	267	21	2008	2008	NUM
ejpam-2102	267	22	.	.	PUNCT
ejpam-2102	268	1	[	[	X
ejpam-2102	268	2	17	17	NUM
ejpam-2102	268	3	]	]	X
ejpam-2102	268	4	o.	o.	PROPN
ejpam-2102	268	5	zariski	zariski	PROPN
ejpam-2102	268	6	and	and	CCONJ
ejpam-2102	268	7	p.	p.	PROPN
ejpam-2102	268	8	samuel	samuel	PROPN
ejpam-2102	268	9	.	.	PUNCT
ejpam-2102	269	1	commutative	commutative	ADJ
ejpam-2102	269	2	algebra	algebra	PROPN
ejpam-2102	269	3	,	,	PUNCT
ejpam-2102	269	4	vol	vol	NOUN
ejpam-2102	269	5	.	.	PUNCT
ejpam-2102	270	1	i	i	PRON
ejpam-2102	270	2	,	,	PUNCT
ejpam-2102	270	3	d.	d.	PROPN
ejpam-2102	270	4	van	van	PROPN
ejpam-2102	270	5	nostrand	nostrand	PROPN
ejpam-2102	270	6	company	company	PROPN
ejpam-2102	270	7	,	,	PUNCT
ejpam-2102	270	8	inc	inc	PROPN
ejpam-2102	270	9	.	.	PROPN
ejpam-2102	270	10	1967	1967	NUM
ejpam-2102	270	11	.	.	PUNCT