id	sid	tid	token	lemma	pos
ejpam-3206	1	1	european	european	PROPN
ejpam-3206	1	2	journal	journal	PROPN
ejpam-3206	1	3	of	of	ADP
ejpam-3206	1	4	pure	pure	ADJ
ejpam-3206	1	5	and	and	CCONJ
ejpam-3206	1	6	applied	apply	VERB
ejpam-3206	1	7	mathematics	mathematic	NOUN
ejpam-3206	1	8	vol	vol	NOUN
ejpam-3206	1	9	.	.	PUNCT
ejpam-3206	2	1	11	11	NUM
ejpam-3206	2	2	,	,	PUNCT
ejpam-3206	2	3	no	no	INTJ
ejpam-3206	2	4	.	.	NOUN
ejpam-3206	2	5	1	1	NUM
ejpam-3206	2	6	,	,	PUNCT
ejpam-3206	2	7	2018	2018	NUM
ejpam-3206	2	8	,	,	PUNCT
ejpam-3206	2	9	244	244	NUM
ejpam-3206	2	10	-	-	SYM
ejpam-3206	2	11	259	259	NUM
ejpam-3206	2	12	issn	issn	PROPN
ejpam-3206	2	13	1307	1307	NUM
ejpam-3206	2	14	-	-	SYM
ejpam-3206	2	15	5543	5543	NUM
ejpam-3206	2	16	–	–	PUNCT
ejpam-3206	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3206	2	18	published	publish	VERB
ejpam-3206	2	19	by	by	ADP
ejpam-3206	2	20	new	new	PROPN
ejpam-3206	2	21	york	york	PROPN
ejpam-3206	2	22	business	business	PROPN
ejpam-3206	2	23	global	global	ADJ
ejpam-3206	2	24	weak	weak	ADJ
ejpam-3206	2	25	ps	ps	NOUN
ejpam-3206	2	26	-	-	PUNCT
ejpam-3206	2	27	rings	ring	NOUN
ejpam-3206	2	28	over	over	ADP
ejpam-3206	2	29	skew	skew	NOUN
ejpam-3206	2	30	hurwitz	hurwitz	PROPN
ejpam-3206	2	31	series	series	PROPN
ejpam-3206	2	32	mohamed	mohamed	PROPN
ejpam-3206	2	33	a.	a.	PROPN
ejpam-3206	2	34	farahat1,2,∗	farahat1,2,∗	PROPN
ejpam-3206	2	35	,	,	PUNCT
ejpam-3206	2	36	salha	salha	NOUN
ejpam-3206	2	37	t.	t.	PROPN
ejpam-3206	2	38	al	al	PROPN
ejpam-3206	2	39	-	-	PUNCT
ejpam-3206	2	40	bogamy1	bogamy1	VERB
ejpam-3206	2	41	1	1	NUM
ejpam-3206	2	42	department	department	NOUN
ejpam-3206	2	43	of	of	ADP
ejpam-3206	2	44	mathematics	mathematic	NOUN
ejpam-3206	2	45	and	and	CCONJ
ejpam-3206	2	46	statistics	statistic	NOUN
ejpam-3206	2	47	,	,	PUNCT
ejpam-3206	2	48	faculty	faculty	NOUN
ejpam-3206	2	49	of	of	ADP
ejpam-3206	2	50	science	science	NOUN
ejpam-3206	2	51	,	,	PUNCT
ejpam-3206	2	52	taif	taif	PROPN
ejpam-3206	2	53	university	university	PROPN
ejpam-3206	2	54	,	,	PUNCT
ejpam-3206	2	55	taif	taif	PROPN
ejpam-3206	2	56	,	,	PUNCT
ejpam-3206	2	57	el	el	PROPN
ejpam-3206	2	58	-	-	PUNCT
ejpam-3206	2	59	haweiah	haweiah	NOUN
ejpam-3206	2	60	,	,	PUNCT
ejpam-3206	2	61	kingdom	kingdom	NOUN
ejpam-3206	2	62	of	of	ADP
ejpam-3206	2	63	saudi	saudi	PROPN
ejpam-3206	2	64	arabia	arabia	PROPN
ejpam-3206	2	65	2	2	NUM
ejpam-3206	2	66	mathematics	mathematics	PROPN
ejpam-3206	2	67	department	department	NOUN
ejpam-3206	2	68	,	,	PUNCT
ejpam-3206	2	69	faculty	faculty	NOUN
ejpam-3206	2	70	of	of	ADP
ejpam-3206	2	71	science	science	NOUN
ejpam-3206	2	72	,	,	PUNCT
ejpam-3206	2	73	al	al	PROPN
ejpam-3206	2	74	-	-	PUNCT
ejpam-3206	2	75	azhar	azhar	PROPN
ejpam-3206	2	76	university	university	PROPN
ejpam-3206	2	77	,	,	PUNCT
ejpam-3206	2	78	cairo	cairo	PROPN
ejpam-3206	2	79	,	,	PUNCT
ejpam-3206	2	80	egypt	egypt	PROPN
ejpam-3206	2	81	abstract	abstract	PROPN
ejpam-3206	2	82	.	.	PUNCT
ejpam-3206	3	1	the	the	DET
ejpam-3206	3	2	notion	notion	NOUN
ejpam-3206	3	3	of	of	ADP
ejpam-3206	3	4	ps	ps	NOUN
ejpam-3206	3	5	-	-	PUNCT
ejpam-3206	3	6	rings	ring	NOUN
ejpam-3206	3	7	is	be	AUX
ejpam-3206	3	8	extended	extend	VERB
ejpam-3206	3	9	to	to	ADP
ejpam-3206	3	10	the	the	DET
ejpam-3206	3	11	class	class	NOUN
ejpam-3206	3	12	of	of	ADP
ejpam-3206	3	13	weak	weak	ADJ
ejpam-3206	3	14	ps	ps	NOUN
ejpam-3206	3	15	-	-	PUNCT
ejpam-3206	3	16	rings	ring	NOUN
ejpam-3206	3	17	.	.	PUNCT
ejpam-3206	4	1	we	we	PRON
ejpam-3206	4	2	explore	explore	VERB
ejpam-3206	4	3	the	the	DET
ejpam-3206	4	4	algebraic	algebraic	ADJ
ejpam-3206	4	5	properties	property	NOUN
ejpam-3206	4	6	of	of	ADP
ejpam-3206	4	7	such	such	ADJ
ejpam-3206	4	8	class	class	NOUN
ejpam-3206	4	9	and	and	CCONJ
ejpam-3206	4	10	study	study	VERB
ejpam-3206	4	11	its	its	PRON
ejpam-3206	4	12	relation	relation	NOUN
ejpam-3206	4	13	with	with	ADP
ejpam-3206	4	14	some	some	DET
ejpam-3206	4	15	other	other	ADJ
ejpam-3206	4	16	rings	ring	NOUN
ejpam-3206	4	17	such	such	ADJ
ejpam-3206	4	18	as	as	ADP
ejpam-3206	4	19	a	a	DET
ejpam-3206	4	20	local	local	ADJ
ejpam-3206	4	21	ring	ring	NOUN
ejpam-3206	4	22	and	and	CCONJ
ejpam-3206	4	23	a	a	DET
ejpam-3206	4	24	semisimple	semisimple	ADJ
ejpam-3206	4	25	ni	ni	NOUN
ejpam-3206	4	26	-	-	NOUN
ejpam-3206	4	27	ring	ring	NOUN
ejpam-3206	4	28	.	.	PUNCT
ejpam-3206	5	1	also	also	ADV
ejpam-3206	5	2	,	,	PUNCT
ejpam-3206	5	3	we	we	PRON
ejpam-3206	5	4	show	show	VERB
ejpam-3206	5	5	the	the	DET
ejpam-3206	5	6	following	following	ADJ
ejpam-3206	5	7	result	result	NOUN
ejpam-3206	5	8	concerning	concern	VERB
ejpam-3206	5	9	,	,	PUNCT
ejpam-3206	5	10	the	the	DET
ejpam-3206	5	11	ring	ring	NOUN
ejpam-3206	5	12	of	of	ADP
ejpam-3206	5	13	skew	skew	ADJ
ejpam-3206	5	14	hurwitz	hurwitz	PROPN
ejpam-3206	5	15	series	series	PROPN
ejpam-3206	5	16	,	,	PUNCT
ejpam-3206	5	17	a	a	DET
ejpam-3206	5	18	=	=	X
ejpam-3206	5	19	(	(	PUNCT
ejpam-3206	5	20	hr	hr	PROPN
ejpam-3206	5	21	,	,	PUNCT
ejpam-3206	5	22	σ	σ	PROPN
ejpam-3206	5	23	):	):	PUNCT
ejpam-3206	5	24	let	let	VERB
ejpam-3206	5	25	r	r	PRON
ejpam-3206	5	26	be	be	AUX
ejpam-3206	5	27	a	a	DET
ejpam-3206	5	28	σ	σ	NOUN
ejpam-3206	5	29	-	-	PUNCT
ejpam-3206	5	30	compatible	compatible	ADJ
ejpam-3206	5	31	ni	ni	NOUN
ejpam-3206	5	32	-	-	NOUN
ejpam-3206	5	33	ring	ring	NOUN
ejpam-3206	5	34	with	with	ADP
ejpam-3206	5	35	nil(r	nil(r	NOUN
ejpam-3206	5	36	)	)	PUNCT
ejpam-3206	5	37	nilpotent	nilpotent	NOUN
ejpam-3206	5	38	,	,	PUNCT
ejpam-3206	5	39	σ(e	σ(e	PROPN
ejpam-3206	5	40	)	)	PUNCT
ejpam-3206	5	41	=	=	PUNCT
ejpam-3206	5	42	e	e	NOUN
ejpam-3206	5	43	for	for	ADP
ejpam-3206	5	44	every	every	DET
ejpam-3206	5	45	idempotent	idempotent	ADJ
ejpam-3206	5	46	e	e	NOUN
ejpam-3206	5	47	∈	∈	NOUN
ejpam-3206	5	48	r	r	NOUN
ejpam-3206	5	49	and	and	CCONJ
ejpam-3206	5	50	r	r	NOUN
ejpam-3206	5	51	a	a	DET
ejpam-3206	5	52	torsion	torsion	NOUN
ejpam-3206	5	53	free	free	ADJ
ejpam-3206	5	54	as	as	ADP
ejpam-3206	5	55	a	a	DET
ejpam-3206	5	56	z	z	NOUN
ejpam-3206	5	57	-	-	PUNCT
ejpam-3206	5	58	module	module	NOUN
ejpam-3206	5	59	.	.	PUNCT
ejpam-3206	6	1	if	if	SCONJ
ejpam-3206	6	2	r	r	NOUN
ejpam-3206	6	3	is	be	AUX
ejpam-3206	6	4	a	a	DET
ejpam-3206	6	5	weak	weak	ADJ
ejpam-3206	6	6	right	right	ADJ
ejpam-3206	6	7	ps	ps	NOUN
ejpam-3206	6	8	-	-	NOUN
ejpam-3206	6	9	ring	ring	NOUN
ejpam-3206	6	10	,	,	PUNCT
ejpam-3206	6	11	then	then	ADV
ejpam-3206	6	12	a	a	PRON
ejpam-3206	6	13	=	=	SYM
ejpam-3206	6	14	(	(	PUNCT
ejpam-3206	6	15	hr	hr	PROPN
ejpam-3206	6	16	,	,	PUNCT
ejpam-3206	6	17	σ	σ	PROPN
ejpam-3206	6	18	)	)	PUNCT
ejpam-3206	6	19	is	be	AUX
ejpam-3206	6	20	a	a	DET
ejpam-3206	6	21	weak	weak	ADJ
ejpam-3206	6	22	right	right	ADJ
ejpam-3206	6	23	ps	ps	NOUN
ejpam-3206	6	24	-	-	NOUN
ejpam-3206	6	25	ring	ring	NOUN
ejpam-3206	6	26	.	.	PUNCT
ejpam-3206	7	1	2010	2010	NUM
ejpam-3206	7	2	mathematics	mathematic	NOUN
ejpam-3206	7	3	subject	subject	NOUN
ejpam-3206	7	4	classifications	classification	NOUN
ejpam-3206	7	5	:	:	PUNCT
ejpam-3206	7	6	06f05	06f05	NUM
ejpam-3206	7	7	,	,	PUNCT
ejpam-3206	7	8	16w60	16w60	NUM
ejpam-3206	7	9	,	,	PUNCT
ejpam-3206	7	10	16d25	16d25	NUM
ejpam-3206	7	11	,	,	PUNCT
ejpam-3206	7	12	16p60	16p60	NUM
ejpam-3206	7	13	key	key	ADJ
ejpam-3206	7	14	words	word	NOUN
ejpam-3206	7	15	and	and	CCONJ
ejpam-3206	7	16	phrases	phrase	NOUN
ejpam-3206	7	17	:	:	PUNCT
ejpam-3206	7	18	ps	ps	NOUN
ejpam-3206	7	19	-	-	PUNCT
ejpam-3206	7	20	modules	module	NOUN
ejpam-3206	7	21	,	,	PUNCT
ejpam-3206	7	22	ps	ps	NOUN
ejpam-3206	7	23	-	-	PUNCT
ejpam-3206	7	24	rings	ring	NOUN
ejpam-3206	7	25	,	,	PUNCT
ejpam-3206	7	26	skew	skew	ADJ
ejpam-3206	7	27	hurwitz	hurwitz	PROPN
ejpam-3206	7	28	series	series	PROPN
ejpam-3206	7	29	rings	ring	NOUN
ejpam-3206	7	30	1	1	NUM
ejpam-3206	7	31	.	.	PUNCT
ejpam-3206	8	1	introduction	introduction	NOUN
ejpam-3206	8	2	all	all	DET
ejpam-3206	8	3	rings	ring	NOUN
ejpam-3206	8	4	are	be	AUX
ejpam-3206	8	5	assumed	assume	VERB
ejpam-3206	8	6	to	to	PART
ejpam-3206	8	7	be	be	AUX
ejpam-3206	8	8	an	an	DET
ejpam-3206	8	9	associative	associative	ADJ
ejpam-3206	8	10	ring	ring	NOUN
ejpam-3206	8	11	with	with	ADP
ejpam-3206	8	12	identity	identity	NOUN
ejpam-3206	8	13	and	and	CCONJ
ejpam-3206	8	14	modules	module	NOUN
ejpam-3206	8	15	are	be	AUX
ejpam-3206	8	16	nonzero	nonzero	ADJ
ejpam-3206	8	17	unitary	unitary	ADJ
ejpam-3206	8	18	right	right	ADJ
ejpam-3206	8	19	modules	module	NOUN
ejpam-3206	8	20	,	,	PUNCT
ejpam-3206	8	21	unless	unless	SCONJ
ejpam-3206	8	22	otherwise	otherwise	ADV
ejpam-3206	8	23	stated	state	VERB
ejpam-3206	8	24	.	.	PUNCT
ejpam-3206	9	1	for	for	ADP
ejpam-3206	9	2	a	a	DET
ejpam-3206	9	3	nonempty	nonempty	NOUN
ejpam-3206	9	4	subset	subset	NOUN
ejpam-3206	9	5	x	x	PUNCT
ejpam-3206	9	6	of	of	ADP
ejpam-3206	9	7	r	r	NOUN
ejpam-3206	9	8	,	,	PUNCT
ejpam-3206	9	9	rr(x	rr(x	NUM
ejpam-3206	9	10	)	)	PUNCT
ejpam-3206	9	11	(	(	PUNCT
ejpam-3206	9	12	or	or	CCONJ
ejpam-3206	9	13	`	`	PUNCT
ejpam-3206	9	14	r(x	r(x	PROPN
ejpam-3206	9	15	)	)	PUNCT
ejpam-3206	9	16	)	)	PUNCT
ejpam-3206	9	17	denote	denote	VERB
ejpam-3206	9	18	the	the	DET
ejpam-3206	9	19	right	right	NOUN
ejpam-3206	9	20	(	(	PUNCT
ejpam-3206	9	21	or	or	CCONJ
ejpam-3206	9	22	left	leave	VERB
ejpam-3206	9	23	)	)	PUNCT
ejpam-3206	9	24	annihilator	annihilator	NOUN
ejpam-3206	9	25	of	of	ADP
ejpam-3206	9	26	x	x	PUNCT
ejpam-3206	9	27	over	over	ADP
ejpam-3206	9	28	r.	r.	PROPN
ejpam-3206	9	29	also	also	ADV
ejpam-3206	9	30	,	,	PUNCT
ejpam-3206	9	31	for	for	ADP
ejpam-3206	9	32	a	a	DET
ejpam-3206	9	33	ring	ring	NOUN
ejpam-3206	9	34	r	r	NOUN
ejpam-3206	9	35	,	,	PUNCT
ejpam-3206	9	36	nil	nil	NOUN
ejpam-3206	9	37	(	(	PUNCT
ejpam-3206	9	38	r	r	NOUN
ejpam-3206	9	39	)	)	PUNCT
ejpam-3206	9	40	denotes	denote	VERB
ejpam-3206	9	41	the	the	DET
ejpam-3206	9	42	set	set	NOUN
ejpam-3206	9	43	of	of	ADP
ejpam-3206	9	44	all	all	DET
ejpam-3206	9	45	nilpotent	nilpotent	ADJ
ejpam-3206	9	46	elements	element	NOUN
ejpam-3206	9	47	of	of	ADP
ejpam-3206	9	48	r	r	NOUN
ejpam-3206	9	49	and	and	CCONJ
ejpam-3206	9	50	i	i	PROPN
ejpam-3206	9	51	d	d	PROPN
ejpam-3206	9	52	(	(	PUNCT
ejpam-3206	9	53	r	r	NOUN
ejpam-3206	9	54	)	)	PUNCT
ejpam-3206	9	55	denotes	denote	VERB
ejpam-3206	9	56	the	the	DET
ejpam-3206	9	57	set	set	NOUN
ejpam-3206	9	58	of	of	ADP
ejpam-3206	9	59	all	all	DET
ejpam-3206	9	60	idempotent	idempotent	ADJ
ejpam-3206	9	61	elements	element	NOUN
ejpam-3206	9	62	of	of	ADP
ejpam-3206	9	63	r.	r.	PROPN
ejpam-3206	9	64	furthermore	furthermore	ADV
ejpam-3206	9	65	,	,	PUNCT
ejpam-3206	9	66	we	we	PRON
ejpam-3206	9	67	use	use	VERB
ejpam-3206	9	68	j(r	j(r	PROPN
ejpam-3206	9	69	)	)	PUNCT
ejpam-3206	9	70	for	for	ADP
ejpam-3206	9	71	the	the	DET
ejpam-3206	9	72	jacobson	jacobson	PROPN
ejpam-3206	9	73	radicals	radical	NOUN
ejpam-3206	9	74	of	of	ADP
ejpam-3206	9	75	a	a	DET
ejpam-3206	9	76	ring	ring	PROPN
ejpam-3206	9	77	r.	r.	PROPN
ejpam-3206	9	78	recall	recall	VERB
ejpam-3206	9	79	that	that	SCONJ
ejpam-3206	9	80	:	:	PUNCT
ejpam-3206	9	81	a	a	DET
ejpam-3206	9	82	ring	ring	NOUN
ejpam-3206	9	83	r	r	NOUN
ejpam-3206	9	84	is	be	AUX
ejpam-3206	9	85	called	call	VERB
ejpam-3206	9	86	an	an	DET
ejpam-3206	9	87	ni	ni	NOUN
ejpam-3206	9	88	-	-	PUNCT
ejpam-3206	9	89	ring	ring	NOUN
ejpam-3206	9	90	if	if	SCONJ
ejpam-3206	9	91	nil	nil	NOUN
ejpam-3206	9	92	(	(	PUNCT
ejpam-3206	9	93	r	r	NOUN
ejpam-3206	9	94	)	)	PUNCT
ejpam-3206	9	95	is	be	AUX
ejpam-3206	9	96	a	a	DET
ejpam-3206	9	97	two	two	NUM
ejpam-3206	9	98	sided	sided	ADJ
ejpam-3206	9	99	ideal	ideal	NOUN
ejpam-3206	9	100	in	in	ADP
ejpam-3206	9	101	r	r	NOUN
ejpam-3206	9	102	and	and	CCONJ
ejpam-3206	9	103	r	r	NOUN
ejpam-3206	9	104	is	be	AUX
ejpam-3206	9	105	called	call	VERB
ejpam-3206	9	106	a	a	DET
ejpam-3206	9	107	reduced	reduce	VERB
ejpam-3206	9	108	ring	ring	NOUN
ejpam-3206	9	109	if	if	SCONJ
ejpam-3206	9	110	nil	nil	NOUN
ejpam-3206	9	111	(	(	PUNCT
ejpam-3206	10	1	r	r	NOUN
ejpam-3206	10	2	)	)	PUNCT
ejpam-3206	10	3	=	=	SYM
ejpam-3206	10	4	(	(	PUNCT
ejpam-3206	10	5	0	0	NUM
ejpam-3206	10	6	)	)	PUNCT
ejpam-3206	10	7	.	.	PUNCT
ejpam-3206	11	1	according	accord	VERB
ejpam-3206	11	2	to	to	ADP
ejpam-3206	11	3	nicholson	nicholson	PROPN
ejpam-3206	11	4	and	and	CCONJ
ejpam-3206	11	5	watters	watter	NOUN
ejpam-3206	11	6	,	,	PUNCT
ejpam-3206	11	7	in	in	ADP
ejpam-3206	11	8	(	(	PUNCT
ejpam-3206	11	9	[	[	X
ejpam-3206	11	10	15	15	NUM
ejpam-3206	11	11	]	]	NOUN
ejpam-3206	11	12	,	,	PUNCT
ejpam-3206	11	13	1988	1988	NUM
ejpam-3206	11	14	)	)	PUNCT
ejpam-3206	11	15	,	,	PUNCT
ejpam-3206	11	16	a	a	DET
ejpam-3206	11	17	right	right	ADJ
ejpam-3206	11	18	r	r	NOUN
ejpam-3206	11	19	-	-	PUNCT
ejpam-3206	11	20	module	module	NOUN
ejpam-3206	11	21	mr	mr	PROPN
ejpam-3206	11	22	is	be	AUX
ejpam-3206	11	23	called	call	VERB
ejpam-3206	11	24	a	a	DET
ejpam-3206	11	25	right	right	ADJ
ejpam-3206	11	26	ps	ps	NOUN
ejpam-3206	11	27	-	-	PUNCT
ejpam-3206	11	28	module	module	NOUN
ejpam-3206	11	29	if	if	SCONJ
ejpam-3206	11	30	every	every	DET
ejpam-3206	11	31	simple	simple	ADJ
ejpam-3206	11	32	submodule	submodule	NOUN
ejpam-3206	11	33	is	be	AUX
ejpam-3206	11	34	projective	projective	ADJ
ejpam-3206	11	35	,	,	PUNCT
ejpam-3206	11	36	equivalently	equivalently	ADV
ejpam-3206	11	37	if	if	SCONJ
ejpam-3206	11	38	its	its	PRON
ejpam-3206	11	39	right	right	ADJ
ejpam-3206	11	40	socle	socle	NOUN
ejpam-3206	11	41	,	,	PUNCT
ejpam-3206	11	42	soc(mr	soc(mr	NOUN
ejpam-3206	11	43	)	)	PUNCT
ejpam-3206	11	44	=	=	PUNCT
ejpam-3206	12	1	∑	∑	PUNCT
ejpam-3206	12	2	{	{	PUNCT
ejpam-3206	12	3	b	b	NOUN
ejpam-3206	12	4	:	:	PUNCT
ejpam-3206	12	5	b	b	NOUN
ejpam-3206	12	6	is	be	AUX
ejpam-3206	12	7	a	a	DET
ejpam-3206	12	8	simple	simple	ADJ
ejpam-3206	12	9	submodule	submodule	NOUN
ejpam-3206	12	10	of	of	ADP
ejpam-3206	12	11	mr	mr	PROPN
ejpam-3206	12	12	}	}	PUNCT
ejpam-3206	12	13	.	.	PUNCT
ejpam-3206	13	1	is	be	AUX
ejpam-3206	13	2	projective	projective	ADJ
ejpam-3206	13	3	.	.	PUNCT
ejpam-3206	14	1	the	the	DET
ejpam-3206	14	2	class	class	NOUN
ejpam-3206	14	3	of	of	ADP
ejpam-3206	14	4	ps	ps	NOUN
ejpam-3206	14	5	-	-	PUNCT
ejpam-3206	14	6	modules	module	NOUN
ejpam-3206	14	7	is	be	AUX
ejpam-3206	14	8	closed	close	VERB
ejpam-3206	14	9	under	under	ADP
ejpam-3206	14	10	direct	direct	ADJ
ejpam-3206	14	11	sums	sum	NOUN
ejpam-3206	14	12	and	and	CCONJ
ejpam-3206	14	13	submodules	submodule	NOUN
ejpam-3206	14	14	.	.	PUNCT
ejpam-3206	15	1	a	a	DET
ejpam-3206	15	2	left	left	ADJ
ejpam-3206	15	3	ps	ps	NOUN
ejpam-3206	15	4	-	-	PUNCT
ejpam-3206	15	5	module	module	NOUN
ejpam-3206	15	6	rm	rm	NOUN
ejpam-3206	15	7	is	be	AUX
ejpam-3206	15	8	defined	define	VERB
ejpam-3206	15	9	similarly	similarly	ADV
ejpam-3206	15	10	.	.	PUNCT
ejpam-3206	16	1	the	the	DET
ejpam-3206	16	2	study	study	NOUN
ejpam-3206	16	3	of	of	ADP
ejpam-3206	16	4	ps	ps	NOUN
ejpam-3206	16	5	-	-	PUNCT
ejpam-3206	16	6	modules	module	NOUN
ejpam-3206	16	7	was	be	AUX
ejpam-3206	16	8	initiated	initiate	VERB
ejpam-3206	16	9	by	by	ADP
ejpam-3206	16	10	gordon	gordon	PROPN
ejpam-3206	16	11	,	,	PUNCT
ejpam-3206	16	12	in	in	ADP
ejpam-3206	16	13	(	(	PUNCT
ejpam-3206	16	14	[	[	X
ejpam-3206	16	15	6	6	NUM
ejpam-3206	16	16	]	]	PUNCT
ejpam-3206	16	17	,	,	PUNCT
ejpam-3206	16	18	1969	1969	NUM
ejpam-3206	16	19	)	)	PUNCT
ejpam-3206	16	20	.	.	PUNCT
ejpam-3206	17	1	a	a	DET
ejpam-3206	17	2	ring	ring	NOUN
ejpam-3206	17	3	r	r	NOUN
ejpam-3206	17	4	is	be	AUX
ejpam-3206	17	5	said	say	VERB
ejpam-3206	17	6	to	to	PART
ejpam-3206	17	7	be	be	AUX
ejpam-3206	17	8	a	a	DET
ejpam-3206	17	9	right	right	NOUN
ejpam-3206	17	10	(	(	PUNCT
ejpam-3206	17	11	left	left	ADJ
ejpam-3206	17	12	)	)	PUNCT
ejpam-3206	17	13	ps	ps	NOUN
ejpam-3206	17	14	-	-	PUNCT
ejpam-3206	17	15	ring	ring	NOUN
ejpam-3206	17	16	if	if	SCONJ
ejpam-3206	17	17	rr	rr	PROPN
ejpam-3206	17	18	(	(	PUNCT
ejpam-3206	17	19	rr	rr	NOUN
ejpam-3206	17	20	)	)	PUNCT
ejpam-3206	17	21	is	be	AUX
ejpam-3206	17	22	a	a	DET
ejpam-3206	17	23	right	right	NOUN
ejpam-3206	17	24	(	(	PUNCT
ejpam-3206	17	25	left	left	ADJ
ejpam-3206	17	26	)	)	PUNCT
ejpam-3206	17	27	ps	ps	NOUN
ejpam-3206	17	28	-	-	PUNCT
ejpam-3206	17	29	module	module	NOUN
ejpam-3206	17	30	.	.	PUNCT
ejpam-3206	18	1	the	the	DET
ejpam-3206	18	2	notion	notion	NOUN
ejpam-3206	18	3	of	of	ADP
ejpam-3206	18	4	ps	ps	NOUN
ejpam-3206	18	5	-	-	PUNCT
ejpam-3206	18	6	rings	ring	NOUN
ejpam-3206	18	7	is	be	AUX
ejpam-3206	18	8	not	not	PART
ejpam-3206	18	9	left	leave	VERB
ejpam-3206	18	10	-	-	PUNCT
ejpam-3206	18	11	right	right	NOUN
ejpam-3206	18	12	symmetric	symmetric	NOUN
ejpam-3206	18	13	(	(	PUNCT
ejpam-3206	18	14	see	see	VERB
ejpam-3206	18	15	example	example	NOUN
ejpam-3206	18	16	11	11	NUM
ejpam-3206	18	17	)	)	PUNCT
ejpam-3206	18	18	.	.	PUNCT
ejpam-3206	19	1	∗corresponding	∗corresponde	VERB
ejpam-3206	19	2	author	author	NOUN
ejpam-3206	19	3	.	.	PUNCT
ejpam-3206	20	1	email	email	NOUN
ejpam-3206	20	2	addresses	address	NOUN
ejpam-3206	20	3	:	:	PUNCT
ejpam-3206	20	4	m	m	VERB
ejpam-3206	20	5	farahat79@yahoo.com	farahat79@yahoo.com	PROPN
ejpam-3206	20	6	(	(	PUNCT
ejpam-3206	20	7	mohamed	mohamed	PROPN
ejpam-3206	20	8	a.	a.	PROPN
ejpam-3206	20	9	farahat	farahat	PROPN
ejpam-3206	20	10	)	)	PUNCT
ejpam-3206	20	11	,	,	PUNCT
ejpam-3206	20	12	salhaalbogamy@hotmail.com	salhaalbogamy@hotmail.com	X
ejpam-3206	20	13	(	(	PUNCT
ejpam-3206	20	14	s.	s.	PROPN
ejpam-3206	20	15	t.	t.	PROPN
ejpam-3206	20	16	al	al	PROPN
ejpam-3206	20	17	-	-	PUNCT
ejpam-3206	20	18	bogamy	bogamy	NOUN
ejpam-3206	20	19	)	)	PUNCT
ejpam-3206	20	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3206	21	1	244	244	NUM
ejpam-3206	22	1	c	c	X
ejpam-3206	22	2	©	©	PROPN
ejpam-3206	22	3	2018	2018	NUM
ejpam-3206	22	4	ejpam	ejpam	VERB
ejpam-3206	22	5	all	all	DET
ejpam-3206	22	6	rights	right	NOUN
ejpam-3206	22	7	reserved	reserve	VERB
ejpam-3206	22	8	.	.	PUNCT
ejpam-3206	23	1	m.	m.	NOUN
ejpam-3206	23	2	a.	a.	PROPN
ejpam-3206	23	3	farahat	farahat	PROPN
ejpam-3206	23	4	,	,	PUNCT
ejpam-3206	23	5	s.	s.	PROPN
ejpam-3206	23	6	t.	t.	PROPN
ejpam-3206	23	7	al	al	PROPN
ejpam-3206	23	8	-	-	PUNCT
ejpam-3206	23	9	bogamy	bogamy	PROPN
ejpam-3206	23	10	/	/	SYM
ejpam-3206	23	11	eur	eur	PROPN
ejpam-3206	23	12	.	.	PUNCT
ejpam-3206	24	1	j.	j.	PROPN
ejpam-3206	24	2	pure	pure	PROPN
ejpam-3206	24	3	appl	appl	PROPN
ejpam-3206	24	4	.	.	PROPN
ejpam-3206	24	5	math	math	PROPN
ejpam-3206	24	6	,	,	PUNCT
ejpam-3206	24	7	11	11	NUM
ejpam-3206	24	8	(	(	PUNCT
ejpam-3206	24	9	1	1	NUM
ejpam-3206	24	10	)	)	PUNCT
ejpam-3206	24	11	(	(	PUNCT
ejpam-3206	24	12	2018	2018	NUM
ejpam-3206	24	13	)	)	PUNCT
ejpam-3206	24	14	,	,	PUNCT
ejpam-3206	24	15	244	244	NUM
ejpam-3206	24	16	-	-	SYM
ejpam-3206	24	17	259	259	NUM
ejpam-3206	24	18	245	245	NUM
ejpam-3206	24	19	example	example	NOUN
ejpam-3206	24	20	1	1	NUM
ejpam-3206	24	21	(	(	PUNCT
ejpam-3206	24	22	[	[	X
ejpam-3206	24	23	15	15	NUM
ejpam-3206	24	24	]	]	NUM
ejpam-3206	24	25	)	)	PUNCT
ejpam-3206	24	26	.	.	PUNCT
ejpam-3206	25	1	(	(	PUNCT
ejpam-3206	25	2	a	a	X
ejpam-3206	25	3	)	)	PUNCT
ejpam-3206	25	4	if	if	SCONJ
ejpam-3206	25	5	soc(mr	soc(mr	NOUN
ejpam-3206	25	6	)	)	PUNCT
ejpam-3206	25	7	=	=	SYM
ejpam-3206	26	1	0	0	NUM
ejpam-3206	26	2	,	,	PUNCT
ejpam-3206	26	3	then	then	ADV
ejpam-3206	26	4	mr	mr	PROPN
ejpam-3206	26	5	is	be	AUX
ejpam-3206	26	6	a	a	DET
ejpam-3206	26	7	right	right	ADJ
ejpam-3206	26	8	ps	ps	NOUN
ejpam-3206	26	9	-	-	NOUN
ejpam-3206	26	10	module	module	NOUN
ejpam-3206	26	11	.	.	PUNCT
ejpam-3206	27	1	(	(	PUNCT
ejpam-3206	27	2	b	b	X
ejpam-3206	27	3	)	)	PUNCT
ejpam-3206	27	4	any	any	DET
ejpam-3206	27	5	projective	projective	ADJ
ejpam-3206	27	6	semisimple	semisimple	NOUN
ejpam-3206	27	7	module	module	NOUN
ejpam-3206	27	8	is	be	AUX
ejpam-3206	27	9	a	a	DET
ejpam-3206	27	10	ps	ps	NOUN
ejpam-3206	27	11	-	-	PUNCT
ejpam-3206	27	12	module	module	NOUN
ejpam-3206	27	13	.	.	PUNCT
ejpam-3206	28	1	(	(	PUNCT
ejpam-3206	28	2	c	c	X
ejpam-3206	28	3	)	)	PUNCT
ejpam-3206	28	4	every	every	DET
ejpam-3206	28	5	regular	regular	ADJ
ejpam-3206	28	6	module	module	NOUN
ejpam-3206	28	7	is	be	AUX
ejpam-3206	28	8	a	a	DET
ejpam-3206	28	9	ps	ps	NOUN
ejpam-3206	28	10	-	-	PUNCT
ejpam-3206	28	11	module	module	NOUN
ejpam-3206	28	12	.	.	PUNCT
ejpam-3206	29	1	(	(	PUNCT
ejpam-3206	29	2	d	d	X
ejpam-3206	29	3	)	)	PUNCT
ejpam-3206	29	4	every	every	DET
ejpam-3206	29	5	nonsingular	nonsingular	ADJ
ejpam-3206	29	6	right	right	ADJ
ejpam-3206	29	7	r	r	NOUN
ejpam-3206	29	8	-	-	PUNCT
ejpam-3206	29	9	module	module	NOUN
ejpam-3206	29	10	is	be	AUX
ejpam-3206	29	11	a	a	DET
ejpam-3206	29	12	ps	ps	NOUN
ejpam-3206	29	13	-	-	PUNCT
ejpam-3206	29	14	module	module	NOUN
ejpam-3206	29	15	.	.	PUNCT
ejpam-3206	30	1	for	for	ADP
ejpam-3206	30	2	any	any	DET
ejpam-3206	30	3	subset	subset	NOUN
ejpam-3206	30	4	x	x	PUNCT
ejpam-3206	30	5	of	of	ADP
ejpam-3206	30	6	r	r	NOUN
ejpam-3206	30	7	,	,	PUNCT
ejpam-3206	30	8	the	the	DET
ejpam-3206	30	9	left	left	ADJ
ejpam-3206	30	10	annihilator	annihilator	NOUN
ejpam-3206	30	11	of	of	ADP
ejpam-3206	30	12	x	x	PROPN
ejpam-3206	30	13	in	in	ADP
ejpam-3206	30	14	a	a	DET
ejpam-3206	30	15	right	right	ADJ
ejpam-3206	30	16	r	r	NOUN
ejpam-3206	30	17	-	-	PUNCT
ejpam-3206	30	18	module	module	NOUN
ejpam-3206	30	19	mr	mr	PROPN
ejpam-3206	30	20	is	be	AUX
ejpam-3206	30	21	denoted	denote	VERB
ejpam-3206	30	22	by	by	ADP
ejpam-3206	30	23	`	`	PUNCT
ejpam-3206	30	24	m	m	VERB
ejpam-3206	30	25	(	(	PUNCT
ejpam-3206	30	26	x	x	NOUN
ejpam-3206	30	27	)	)	PUNCT
ejpam-3206	30	28	=	=	SYM
ejpam-3206	30	29	{	{	PUNCT
ejpam-3206	30	30	m	m	NOUN
ejpam-3206	30	31	∈m	∈m	NOUN
ejpam-3206	30	32	|	|	ADV
ejpam-3206	30	33	mx	mx	PROPN
ejpam-3206	30	34	=	=	NOUN
ejpam-3206	30	35	0	0	NUM
ejpam-3206	30	36	}	}	PUNCT
ejpam-3206	30	37	.	.	PUNCT
ejpam-3206	31	1	similarly	similarly	ADV
ejpam-3206	31	2	,	,	PUNCT
ejpam-3206	31	3	one	one	PRON
ejpam-3206	31	4	can	can	AUX
ejpam-3206	31	5	consider	consider	VERB
ejpam-3206	31	6	the	the	DET
ejpam-3206	31	7	right	right	ADJ
ejpam-3206	31	8	annihilator	annihilator	NOUN
ejpam-3206	31	9	of	of	ADP
ejpam-3206	31	10	x	x	PROPN
ejpam-3206	31	11	in	in	ADP
ejpam-3206	31	12	a	a	DET
ejpam-3206	31	13	left	left	ADJ
ejpam-3206	31	14	r	r	NOUN
ejpam-3206	31	15	-	-	PUNCT
ejpam-3206	31	16	module	module	NOUN
ejpam-3206	31	17	rm	rm	NOUN
ejpam-3206	31	18	,	,	PUNCT
ejpam-3206	31	19	where	where	SCONJ
ejpam-3206	31	20	x	x	PRON
ejpam-3206	31	21	is	be	AUX
ejpam-3206	31	22	any	any	DET
ejpam-3206	31	23	subset	subset	NOUN
ejpam-3206	31	24	of	of	ADP
ejpam-3206	31	25	r.	r.	PROPN
ejpam-3206	31	26	the	the	DET
ejpam-3206	31	27	following	following	ADJ
ejpam-3206	31	28	result	result	NOUN
ejpam-3206	31	29	is	be	AUX
ejpam-3206	31	30	due	due	ADJ
ejpam-3206	31	31	to	to	PART
ejpam-3206	31	32	weimin	weimin	VERB
ejpam-3206	31	33	in	in	ADP
ejpam-3206	31	34	(	(	PUNCT
ejpam-3206	31	35	[	[	X
ejpam-3206	31	36	22	22	NUM
ejpam-3206	31	37	]	]	PUNCT
ejpam-3206	31	38	,	,	PUNCT
ejpam-3206	31	39	1992	1992	NUM
ejpam-3206	31	40	)	)	PUNCT
ejpam-3206	31	41	,	,	PUNCT
ejpam-3206	31	42	which	which	PRON
ejpam-3206	31	43	gives	give	VERB
ejpam-3206	31	44	an	an	DET
ejpam-3206	31	45	equivalent	equivalent	ADJ
ejpam-3206	31	46	condition	condition	NOUN
ejpam-3206	31	47	for	for	SCONJ
ejpam-3206	31	48	a	a	DET
ejpam-3206	31	49	right	right	ADJ
ejpam-3206	31	50	r	r	NOUN
ejpam-3206	31	51	-	-	PUNCT
ejpam-3206	31	52	module	module	NOUN
ejpam-3206	31	53	mr	mr	PROPN
ejpam-3206	31	54	to	to	PART
ejpam-3206	31	55	be	be	AUX
ejpam-3206	31	56	a	a	DET
ejpam-3206	31	57	right	right	ADJ
ejpam-3206	31	58	ps	ps	NOUN
ejpam-3206	31	59	-	-	PUNCT
ejpam-3206	31	60	module	module	NOUN
ejpam-3206	31	61	.	.	PUNCT
ejpam-3206	32	1	theorem	theorem	ADJ
ejpam-3206	32	2	1	1	NUM
ejpam-3206	32	3	(	(	PUNCT
ejpam-3206	32	4	[	[	X
ejpam-3206	32	5	22	22	NUM
ejpam-3206	32	6	]	]	PUNCT
ejpam-3206	32	7	)	)	PUNCT
ejpam-3206	32	8	.	.	PUNCT
ejpam-3206	33	1	the	the	DET
ejpam-3206	33	2	following	follow	VERB
ejpam-3206	33	3	statements	statement	NOUN
ejpam-3206	33	4	are	be	AUX
ejpam-3206	33	5	equivalent	equivalent	ADJ
ejpam-3206	33	6	for	for	ADP
ejpam-3206	33	7	a	a	DET
ejpam-3206	33	8	right	right	ADJ
ejpam-3206	33	9	r	r	NOUN
ejpam-3206	33	10	-	-	PUNCT
ejpam-3206	33	11	module	module	NOUN
ejpam-3206	33	12	mr	mr	NOUN
ejpam-3206	33	13	:	:	PUNCT
ejpam-3206	33	14	(	(	PUNCT
ejpam-3206	33	15	1	1	X
ejpam-3206	33	16	)	)	PUNCT
ejpam-3206	33	17	mr	mr	PROPN
ejpam-3206	33	18	(	(	PUNCT
ejpam-3206	33	19	rm	rm	PROPN
ejpam-3206	33	20	)	)	PUNCT
ejpam-3206	33	21	is	be	AUX
ejpam-3206	33	22	a	a	DET
ejpam-3206	33	23	right	right	NOUN
ejpam-3206	33	24	(	(	PUNCT
ejpam-3206	33	25	left	left	ADJ
ejpam-3206	33	26	)	)	PUNCT
ejpam-3206	33	27	ps	ps	NOUN
ejpam-3206	33	28	-	-	PUNCT
ejpam-3206	33	29	module	module	NOUN
ejpam-3206	33	30	.	.	PUNCT
ejpam-3206	34	1	(	(	PUNCT
ejpam-3206	34	2	2	2	X
ejpam-3206	34	3	)	)	PUNCT
ejpam-3206	34	4	if	if	SCONJ
ejpam-3206	34	5	l	l	NOUN
ejpam-3206	34	6	is	be	AUX
ejpam-3206	34	7	a	a	DET
ejpam-3206	34	8	maximal	maximal	ADJ
ejpam-3206	34	9	right	right	NOUN
ejpam-3206	34	10	(	(	PUNCT
ejpam-3206	34	11	left	left	ADJ
ejpam-3206	34	12	)	)	PUNCT
ejpam-3206	34	13	ideal	ideal	NOUN
ejpam-3206	34	14	of	of	ADP
ejpam-3206	34	15	r	r	NOUN
ejpam-3206	34	16	,	,	PUNCT
ejpam-3206	34	17	then	then	ADV
ejpam-3206	34	18	`	`	PUNCT
ejpam-3206	34	19	m	m	VERB
ejpam-3206	34	20	(	(	PUNCT
ejpam-3206	34	21	l	l	NOUN
ejpam-3206	34	22	)	)	PUNCT
ejpam-3206	34	23	=	=	SYM
ejpam-3206	34	24	re	re	X
ejpam-3206	34	25	(	(	PUNCT
ejpam-3206	34	26	rm	rm	PROPN
ejpam-3206	34	27	(	(	PUNCT
ejpam-3206	34	28	l	l	NOUN
ejpam-3206	34	29	)	)	PUNCT
ejpam-3206	34	30	=	=	SYM
ejpam-3206	34	31	er	er	INTJ
ejpam-3206	34	32	)	)	PUNCT
ejpam-3206	34	33	,	,	PUNCT
ejpam-3206	34	34	where	where	SCONJ
ejpam-3206	34	35	e	e	PROPN
ejpam-3206	34	36	∈	∈	PROPN
ejpam-3206	34	37	i	i	PROPN
ejpam-3206	34	38	d	d	PROPN
ejpam-3206	34	39	(	(	PUNCT
ejpam-3206	34	40	r	r	NOUN
ejpam-3206	34	41	)	)	PUNCT
ejpam-3206	34	42	.	.	PUNCT
ejpam-3206	35	1	(	(	PUNCT
ejpam-3206	35	2	3	3	X
ejpam-3206	35	3	)	)	PUNCT
ejpam-3206	35	4	if	if	SCONJ
ejpam-3206	35	5	l	l	NOUN
ejpam-3206	35	6	is	be	AUX
ejpam-3206	35	7	a	a	DET
ejpam-3206	35	8	maximal	maximal	ADJ
ejpam-3206	35	9	right	right	NOUN
ejpam-3206	35	10	(	(	PUNCT
ejpam-3206	35	11	left	left	ADJ
ejpam-3206	35	12	)	)	PUNCT
ejpam-3206	35	13	ideal	ideal	NOUN
ejpam-3206	35	14	of	of	ADP
ejpam-3206	35	15	r	r	NOUN
ejpam-3206	35	16	,	,	PUNCT
ejpam-3206	35	17	then	then	ADV
ejpam-3206	35	18	either	either	CCONJ
ejpam-3206	35	19	l	l	NOUN
ejpam-3206	35	20	=	=	SYM
ejpam-3206	35	21	re	re	X
ejpam-3206	35	22	(	(	PUNCT
ejpam-3206	35	23	l	l	NOUN
ejpam-3206	35	24	=	=	SYM
ejpam-3206	35	25	er	er	INTJ
ejpam-3206	35	26	)	)	PUNCT
ejpam-3206	35	27	,	,	PUNCT
ejpam-3206	35	28	or	or	CCONJ
ejpam-3206	35	29	`	`	PUNCT
ejpam-3206	35	30	m	m	VERB
ejpam-3206	35	31	(	(	PUNCT
ejpam-3206	35	32	l	l	NOUN
ejpam-3206	35	33	)	)	PUNCT
ejpam-3206	35	34	=	=	SYM
ejpam-3206	35	35	(	(	PUNCT
ejpam-3206	35	36	0	0	NUM
ejpam-3206	35	37	)	)	PUNCT
ejpam-3206	35	38	(	(	PUNCT
ejpam-3206	35	39	rm	rm	NOUN
ejpam-3206	35	40	(	(	PUNCT
ejpam-3206	35	41	l	l	NOUN
ejpam-3206	35	42	)	)	PUNCT
ejpam-3206	35	43	=	=	SYM
ejpam-3206	35	44	(	(	PUNCT
ejpam-3206	35	45	0	0	NUM
ejpam-3206	35	46	)	)	PUNCT
ejpam-3206	35	47	)	)	PUNCT
ejpam-3206	35	48	,	,	PUNCT
ejpam-3206	35	49	where	where	SCONJ
ejpam-3206	35	50	e	e	PROPN
ejpam-3206	35	51	∈	∈	PROPN
ejpam-3206	35	52	i	i	PROPN
ejpam-3206	35	53	d	d	PROPN
ejpam-3206	35	54	(	(	PUNCT
ejpam-3206	35	55	r	r	NOUN
ejpam-3206	35	56	)	)	PUNCT
ejpam-3206	35	57	.	.	PUNCT
ejpam-3206	35	58	example	example	NOUN
ejpam-3206	36	1	2	2	NUM
ejpam-3206	36	2	(	(	PUNCT
ejpam-3206	36	3	[	[	X
ejpam-3206	36	4	15	15	NUM
ejpam-3206	36	5	]	]	NUM
ejpam-3206	36	6	)	)	PUNCT
ejpam-3206	36	7	.	.	PUNCT
ejpam-3206	37	1	(	(	PUNCT
ejpam-3206	37	2	a	a	X
ejpam-3206	37	3	)	)	PUNCT
ejpam-3206	37	4	every	every	PRON
ejpam-3206	37	5	right	right	NOUN
ejpam-3206	37	6	(	(	PUNCT
ejpam-3206	37	7	left	left	ADJ
ejpam-3206	37	8	)	)	PUNCT
ejpam-3206	37	9	pp	pp	ADP
ejpam-3206	37	10	-	-	PUNCT
ejpam-3206	37	11	ring	ring	NOUN
ejpam-3206	37	12	is	be	AUX
ejpam-3206	37	13	a	a	DET
ejpam-3206	37	14	right	right	NOUN
ejpam-3206	37	15	(	(	PUNCT
ejpam-3206	37	16	left	left	ADJ
ejpam-3206	37	17	)	)	PUNCT
ejpam-3206	37	18	ps	ps	NOUN
ejpam-3206	37	19	-	-	PUNCT
ejpam-3206	37	20	ring	ring	NOUN
ejpam-3206	37	21	.	.	PUNCT
ejpam-3206	38	1	in	in	ADP
ejpam-3206	38	2	particular	particular	ADJ
ejpam-3206	38	3	,	,	PUNCT
ejpam-3206	38	4	every	every	DET
ejpam-3206	38	5	right	right	NOUN
ejpam-3206	38	6	(	(	PUNCT
ejpam-3206	38	7	left	left	ADJ
ejpam-3206	38	8	)	)	PUNCT
ejpam-3206	38	9	baer	baer	PROPN
ejpam-3206	38	10	ring	ring	NOUN
ejpam-3206	38	11	is	be	AUX
ejpam-3206	38	12	a	a	DET
ejpam-3206	38	13	right	right	NOUN
ejpam-3206	38	14	(	(	PUNCT
ejpam-3206	38	15	left	left	ADJ
ejpam-3206	38	16	)	)	PUNCT
ejpam-3206	38	17	ps	ps	NOUN
ejpam-3206	38	18	-	-	PUNCT
ejpam-3206	38	19	ring	ring	NOUN
ejpam-3206	38	20	.	.	PUNCT
ejpam-3206	39	1	(	(	PUNCT
ejpam-3206	39	2	b	b	X
ejpam-3206	39	3	)	)	PUNCT
ejpam-3206	39	4	every	every	DET
ejpam-3206	39	5	semiprime	semiprime	NOUN
ejpam-3206	39	6	ring	ring	NOUN
ejpam-3206	39	7	is	be	AUX
ejpam-3206	39	8	a	a	DET
ejpam-3206	39	9	right	right	NOUN
ejpam-3206	39	10	(	(	PUNCT
ejpam-3206	39	11	left	left	ADJ
ejpam-3206	39	12	)	)	PUNCT
ejpam-3206	39	13	ps	ps	NOUN
ejpam-3206	39	14	-	-	PUNCT
ejpam-3206	39	15	ring	ring	NOUN
ejpam-3206	39	16	.	.	PUNCT
ejpam-3206	40	1	but	but	CCONJ
ejpam-3206	40	2	the	the	DET
ejpam-3206	40	3	converse	converse	NOUN
ejpam-3206	40	4	is	be	AUX
ejpam-3206	40	5	not	not	PART
ejpam-3206	40	6	true	true	ADJ
ejpam-3206	40	7	.	.	PUNCT
ejpam-3206	41	1	(	(	PUNCT
ejpam-3206	41	2	c	c	X
ejpam-3206	41	3	)	)	PUNCT
ejpam-3206	41	4	if	if	SCONJ
ejpam-3206	41	5	`	`	PUNCT
ejpam-3206	41	6	r(j(r	r(j(r	PROPN
ejpam-3206	41	7	)	)	PUNCT
ejpam-3206	41	8	)	)	PUNCT
ejpam-3206	42	1	=	=	PUNCT
ejpam-3206	42	2	0	0	NUM
ejpam-3206	42	3	,	,	PUNCT
ejpam-3206	42	4	then	then	ADV
ejpam-3206	42	5	r	r	NOUN
ejpam-3206	42	6	is	be	AUX
ejpam-3206	42	7	a	a	DET
ejpam-3206	42	8	ps	ps	NOUN
ejpam-3206	42	9	-	-	PUNCT
ejpam-3206	42	10	ring	ring	NOUN
ejpam-3206	42	11	,	,	PUNCT
ejpam-3206	42	12	since	since	SCONJ
ejpam-3206	42	13	we	we	PRON
ejpam-3206	42	14	have	have	VERB
ejpam-3206	42	15	j(r	j(r	NOUN
ejpam-3206	42	16	)	)	PUNCT
ejpam-3206	42	17	⊆	⊆	NUM
ejpam-3206	42	18	l	l	NOUN
ejpam-3206	42	19	for	for	ADP
ejpam-3206	42	20	every	every	DET
ejpam-3206	42	21	maximal	maximal	ADJ
ejpam-3206	42	22	right	right	NOUN
ejpam-3206	42	23	(	(	PUNCT
ejpam-3206	42	24	left	left	ADJ
ejpam-3206	42	25	)	)	PUNCT
ejpam-3206	42	26	ideal	ideal	ADJ
ejpam-3206	42	27	l	l	NOUN
ejpam-3206	42	28	in	in	ADP
ejpam-3206	42	29	r	r	NOUN
ejpam-3206	42	30	and	and	CCONJ
ejpam-3206	42	31	hence	hence	ADV
ejpam-3206	42	32	`	`	PUNCT
ejpam-3206	42	33	r(l	r(l	NOUN
ejpam-3206	42	34	)	)	PUNCT
ejpam-3206	42	35	⊆	⊆	NUM
ejpam-3206	42	36	`	`	PUNCT
ejpam-3206	42	37	r(j(r	r(j(r	PROPN
ejpam-3206	42	38	)	)	PUNCT
ejpam-3206	42	39	)	)	PUNCT
ejpam-3206	43	1	=	=	SYM
ejpam-3206	43	2	0	0	NUM
ejpam-3206	43	3	implies	imply	VERB
ejpam-3206	43	4	that	that	SCONJ
ejpam-3206	43	5	for	for	SCONJ
ejpam-3206	43	6	every	every	DET
ejpam-3206	43	7	maximal	maximal	ADJ
ejpam-3206	43	8	right	right	NOUN
ejpam-3206	43	9	(	(	PUNCT
ejpam-3206	43	10	left	left	ADJ
ejpam-3206	43	11	)	)	PUNCT
ejpam-3206	43	12	ideal	ideal	ADJ
ejpam-3206	43	13	l	l	NOUN
ejpam-3206	43	14	in	in	ADP
ejpam-3206	43	15	r	r	NOUN
ejpam-3206	43	16	,	,	PUNCT
ejpam-3206	43	17	hence	hence	ADV
ejpam-3206	43	18	`	`	PUNCT
ejpam-3206	43	19	r(l	r(l	NOUN
ejpam-3206	43	20	)	)	PUNCT
ejpam-3206	43	21	=	=	SYM
ejpam-3206	43	22	0	0	X
ejpam-3206	43	23	.	.	PUNCT
ejpam-3206	44	1	in	in	ADP
ejpam-3206	44	2	[	[	X
ejpam-3206	44	3	15	15	NUM
ejpam-3206	44	4	]	]	PUNCT
ejpam-3206	44	5	,	,	PUNCT
ejpam-3206	44	6	the	the	DET
ejpam-3206	44	7	class	class	NOUN
ejpam-3206	44	8	of	of	ADP
ejpam-3206	44	9	ps	ps	NOUN
ejpam-3206	44	10	-	-	PUNCT
ejpam-3206	44	11	rings	ring	NOUN
ejpam-3206	44	12	is	be	AUX
ejpam-3206	44	13	closed	close	VERB
ejpam-3206	44	14	under	under	ADP
ejpam-3206	44	15	the	the	DET
ejpam-3206	44	16	formulation	formulation	NOUN
ejpam-3206	44	17	of	of	ADP
ejpam-3206	44	18	polynomials	polynomial	NOUN
ejpam-3206	44	19	and	and	CCONJ
ejpam-3206	44	20	power	power	NOUN
ejpam-3206	44	21	series	series	NOUN
ejpam-3206	44	22	extensions	extension	NOUN
ejpam-3206	44	23	,	,	PUNCT
ejpam-3206	44	24	by	by	ADP
ejpam-3206	44	25	other	other	ADJ
ejpam-3206	44	26	words	word	NOUN
ejpam-3206	44	27	,	,	PUNCT
ejpam-3206	44	28	if	if	SCONJ
ejpam-3206	44	29	a	a	DET
ejpam-3206	44	30	ring	ring	NOUN
ejpam-3206	44	31	r	r	NOUN
ejpam-3206	44	32	is	be	AUX
ejpam-3206	44	33	a	a	DET
ejpam-3206	44	34	right	right	ADJ
ejpam-3206	44	35	ps	ps	NOUN
ejpam-3206	44	36	-	-	NOUN
ejpam-3206	44	37	ring	ring	NOUN
ejpam-3206	44	38	,	,	PUNCT
ejpam-3206	44	39	then	then	ADV
ejpam-3206	44	40	so	so	ADV
ejpam-3206	44	41	is	be	AUX
ejpam-3206	44	42	r	r	NOUN
ejpam-3206	44	43	[	[	X
ejpam-3206	44	44	x	x	X
ejpam-3206	44	45	]	]	X
ejpam-3206	44	46	and	and	CCONJ
ejpam-3206	44	47	r	r	X
ejpam-3206	45	1	[	[	X
ejpam-3206	45	2	[	[	X
ejpam-3206	45	3	x	x	X
ejpam-3206	45	4	]	]	X
ejpam-3206	45	5	]	]	PUNCT
ejpam-3206	45	6	.	.	PUNCT
ejpam-3206	46	1	the	the	DET
ejpam-3206	46	2	converse	converse	NOUN
ejpam-3206	46	3	of	of	ADP
ejpam-3206	46	4	this	this	DET
ejpam-3206	46	5	result	result	NOUN
ejpam-3206	46	6	is	be	AUX
ejpam-3206	46	7	false	false	ADJ
ejpam-3206	46	8	by	by	ADP
ejpam-3206	46	9	the	the	DET
ejpam-3206	46	10	following	follow	VERB
ejpam-3206	46	11	example	example	NOUN
ejpam-3206	46	12	:	:	PUNCT
ejpam-3206	46	13	example	example	NOUN
ejpam-3206	46	14	3	3	NUM
ejpam-3206	46	15	(	(	PUNCT
ejpam-3206	46	16	[	[	X
ejpam-3206	46	17	15	15	NUM
ejpam-3206	46	18	]	]	PUNCT
ejpam-3206	46	19	,	,	PUNCT
ejpam-3206	46	20	example	example	NOUN
ejpam-3206	46	21	3.2	3.2	NUM
ejpam-3206	46	22	)	)	PUNCT
ejpam-3206	46	23	.	.	PUNCT
ejpam-3206	47	1	if	if	SCONJ
ejpam-3206	47	2	r	r	NOUN
ejpam-3206	47	3	=	=	SYM
ejpam-3206	47	4	z4	z4	X
ejpam-3206	47	5	,	,	PUNCT
ejpam-3206	47	6	then	then	ADV
ejpam-3206	47	7	r[x	r[x	NOUN
ejpam-3206	47	8	]	]	PUNCT
ejpam-3206	47	9	and	and	CCONJ
ejpam-3206	47	10	r[[x	r[[x	PROPN
ejpam-3206	47	11	]	]	X
ejpam-3206	47	12	]	]	X
ejpam-3206	47	13	are	be	AUX
ejpam-3206	47	14	ps	ps	NOUN
ejpam-3206	47	15	-	-	PUNCT
ejpam-3206	47	16	rings	ring	NOUN
ejpam-3206	47	17	,	,	PUNCT
ejpam-3206	47	18	but	but	CCONJ
ejpam-3206	47	19	r	r	NOUN
ejpam-3206	47	20	is	be	AUX
ejpam-3206	47	21	not	not	PART
ejpam-3206	47	22	a	a	DET
ejpam-3206	47	23	ps	ps	NOUN
ejpam-3206	47	24	-	-	PUNCT
ejpam-3206	47	25	ring	ring	NOUN
ejpam-3206	47	26	.	.	PUNCT
ejpam-3206	48	1	nicholson	nicholson	PROPN
ejpam-3206	48	2	and	and	CCONJ
ejpam-3206	48	3	watters	watter	NOUN
ejpam-3206	48	4	,	,	PUNCT
ejpam-3206	48	5	in	in	ADP
ejpam-3206	48	6	[	[	X
ejpam-3206	48	7	15	15	NUM
ejpam-3206	48	8	]	]	PUNCT
ejpam-3206	48	9	,	,	PUNCT
ejpam-3206	48	10	proved	prove	VERB
ejpam-3206	48	11	that	that	SCONJ
ejpam-3206	48	12	:	:	PUNCT
ejpam-3206	48	13	a	a	DET
ejpam-3206	48	14	ring	ring	NOUN
ejpam-3206	48	15	r	r	NOUN
ejpam-3206	48	16	is	be	AUX
ejpam-3206	48	17	a	a	DET
ejpam-3206	48	18	right	right	ADJ
ejpam-3206	48	19	ps	ps	NOUN
ejpam-3206	48	20	-	-	NOUN
ejpam-3206	48	21	ring	ring	NOUN
ejpam-3206	48	22	if	if	SCONJ
ejpam-3206	48	23	and	and	CCONJ
ejpam-3206	48	24	only	only	ADV
ejpam-3206	48	25	if	if	SCONJ
ejpam-3206	48	26	the	the	DET
ejpam-3206	48	27	full	full	ADJ
ejpam-3206	48	28	matrix	matrix	NOUN
ejpam-3206	48	29	ring	ring	NOUN
ejpam-3206	48	30	mn(r	mn(r	NOUN
ejpam-3206	48	31	)	)	PUNCT
ejpam-3206	48	32	,	,	PUNCT
ejpam-3206	48	33	where	where	SCONJ
ejpam-3206	48	34	n	n	PRON
ejpam-3206	48	35	is	be	AUX
ejpam-3206	48	36	a	a	DET
ejpam-3206	48	37	positive	positive	ADJ
ejpam-3206	48	38	integer	integer	NOUN
ejpam-3206	48	39	,	,	PUNCT
ejpam-3206	48	40	is	be	AUX
ejpam-3206	48	41	a	a	DET
ejpam-3206	48	42	right	right	ADJ
ejpam-3206	48	43	ps	ps	NOUN
ejpam-3206	48	44	-	-	NOUN
ejpam-3206	48	45	ring	ring	NOUN
ejpam-3206	48	46	.	.	PUNCT
ejpam-3206	49	1	the	the	DET
ejpam-3206	49	2	authors	author	NOUN
ejpam-3206	49	3	in	in	ADP
ejpam-3206	49	4	(	(	PUNCT
ejpam-3206	49	5	[	[	X
ejpam-3206	49	6	14	14	NUM
ejpam-3206	49	7	]	]	SYM
ejpam-3206	49	8	,	,	PUNCT
ejpam-3206	49	9	1998	1998	NUM
ejpam-3206	49	10	)	)	PUNCT
ejpam-3206	49	11	,	,	PUNCT
ejpam-3206	49	12	showed	show	VERB
ejpam-3206	49	13	that	that	SCONJ
ejpam-3206	49	14	the	the	DET
ejpam-3206	49	15	commutative	commutative	ADJ
ejpam-3206	49	16	ps	ps	NOUN
ejpam-3206	49	17	-	-	PUNCT
ejpam-3206	49	18	ring	ring	NOUN
ejpam-3206	49	19	condition	condition	NOUN
ejpam-3206	49	20	is	be	AUX
ejpam-3206	49	21	preserved	preserve	VERB
ejpam-3206	49	22	by	by	ADP
ejpam-3206	49	23	the	the	DET
ejpam-3206	49	24	generalized	generalize	VERB
ejpam-3206	49	25	power	power	NOUN
ejpam-3206	49	26	series	series	PROPN
ejpam-3206	49	27	rings	ring	NOUN
ejpam-3206	49	28	under	under	ADP
ejpam-3206	49	29	certain	certain	ADJ
ejpam-3206	49	30	conditions	condition	NOUN
ejpam-3206	49	31	.	.	PUNCT
ejpam-3206	50	1	recently	recently	ADV
ejpam-3206	50	2	,	,	PUNCT
ejpam-3206	50	3	salem	salem	NOUN
ejpam-3206	50	4	,	,	PUNCT
ejpam-3206	50	5	farahat	farahat	NOUN
ejpam-3206	50	6	and	and	CCONJ
ejpam-3206	50	7	abdelmalk	abdelmalk	NOUN
ejpam-3206	50	8	,	,	PUNCT
ejpam-3206	50	9	in	in	ADP
ejpam-3206	50	10	(	(	PUNCT
ejpam-3206	50	11	[	[	X
ejpam-3206	50	12	20	20	NUM
ejpam-3206	50	13	]	]	PUNCT
ejpam-3206	50	14	,	,	PUNCT
ejpam-3206	50	15	2015	2015	NUM
ejpam-3206	50	16	)	)	PUNCT
ejpam-3206	50	17	,	,	PUNCT
ejpam-3206	50	18	investigated	investigate	VERB
ejpam-3206	50	19	ps	ps	NOUN
ejpam-3206	50	20	-	-	PUNCT
ejpam-3206	50	21	modules	module	NOUN
ejpam-3206	50	22	over	over	ADP
ejpam-3206	50	23	ore	ore	NOUN
ejpam-3206	50	24	extensions	extension	NOUN
ejpam-3206	50	25	and	and	CCONJ
ejpam-3206	50	26	skew	skew	VERB
ejpam-3206	50	27	generalized	generalized	ADJ
ejpam-3206	50	28	power	power	NOUN
ejpam-3206	50	29	series	series	NOUN
ejpam-3206	50	30	extensions	extension	NOUN
ejpam-3206	50	31	.	.	PUNCT
ejpam-3206	51	1	also	also	ADV
ejpam-3206	51	2	,	,	PUNCT
ejpam-3206	51	3	farahat	farahat	NOUN
ejpam-3206	51	4	and	and	CCONJ
ejpam-3206	51	5	al	al	PROPN
ejpam-3206	51	6	-	-	PUNCT
ejpam-3206	51	7	harthy	harthy	ADJ
ejpam-3206	51	8	,	,	PUNCT
ejpam-3206	51	9	in	in	ADP
ejpam-3206	51	10	(	(	PUNCT
ejpam-3206	51	11	[	[	X
ejpam-3206	51	12	3	3	NUM
ejpam-3206	51	13	]	]	PUNCT
ejpam-3206	51	14	,	,	PUNCT
ejpam-3206	51	15	2017	2017	NUM
ejpam-3206	51	16	)	)	PUNCT
ejpam-3206	51	17	,	,	PUNCT
ejpam-3206	51	18	investigated	investigate	VERB
ejpam-3206	51	19	psmodules	psmodule	NOUN
ejpam-3206	51	20	over	over	ADP
ejpam-3206	51	21	generalized	generalized	ADJ
ejpam-3206	51	22	mal’cev	mal’cev	PROPN
ejpam-3206	51	23	-	-	PUNCT
ejpam-3206	51	24	neumann	neumann	PROPN
ejpam-3206	51	25	series	series	PROPN
ejpam-3206	51	26	rings	ring	NOUN
ejpam-3206	51	27	.	.	PUNCT
ejpam-3206	52	1	in	in	ADP
ejpam-3206	52	2	(	(	PUNCT
ejpam-3206	52	3	[	[	X
ejpam-3206	52	4	18	18	NUM
ejpam-3206	52	5	]	]	PUNCT
ejpam-3206	52	6	,	,	PUNCT
ejpam-3206	52	7	2017	2017	NUM
ejpam-3206	52	8	)	)	PUNCT
ejpam-3206	52	9	,	,	PUNCT
ejpam-3206	52	10	paykan	paykan	PROPN
ejpam-3206	52	11	proved	prove	VERB
ejpam-3206	52	12	that	that	SCONJ
ejpam-3206	52	13	,	,	PUNCT
ejpam-3206	52	14	under	under	ADP
ejpam-3206	52	15	suitable	suitable	ADJ
ejpam-3206	52	16	conditions	condition	NOUN
ejpam-3206	52	17	,	,	PUNCT
ejpam-3206	52	18	if	if	SCONJ
ejpam-3206	52	19	r	r	NOUN
ejpam-3206	52	20	is	be	AUX
ejpam-3206	52	21	a	a	DET
ejpam-3206	52	22	right	right	ADJ
ejpam-3206	52	23	ps	ps	NOUN
ejpam-3206	52	24	-	-	NOUN
ejpam-3206	52	25	ring	ring	NOUN
ejpam-3206	52	26	,	,	PUNCT
ejpam-3206	52	27	then	then	ADV
ejpam-3206	52	28	so	so	ADV
ejpam-3206	52	29	the	the	DET
ejpam-3206	52	30	skew	skew	ADJ
ejpam-3206	52	31	inverse	inverse	NOUN
ejpam-3206	52	32	power	power	NOUN
ejpam-3206	52	33	series	series	PROPN
ejpam-3206	52	34	rings	rings	PROPN
ejpam-3206	52	35	.	.	PUNCT
ejpam-3206	53	1	as	as	ADP
ejpam-3206	53	2	a	a	DET
ejpam-3206	53	3	generalization	generalization	NOUN
ejpam-3206	53	4	of	of	ADP
ejpam-3206	53	5	the	the	DET
ejpam-3206	53	6	annihilator	annihilator	PROPN
ejpam-3206	53	7	concept	concept	PROPN
ejpam-3206	53	8	,	,	PUNCT
ejpam-3206	53	9	ouyang	ouyang	PROPN
ejpam-3206	53	10	,	,	PUNCT
ejpam-3206	53	11	in	in	ADP
ejpam-3206	53	12	(	(	PUNCT
ejpam-3206	53	13	[	[	X
ejpam-3206	53	14	16	16	NUM
ejpam-3206	53	15	]	]	PUNCT
ejpam-3206	53	16	,	,	PUNCT
ejpam-3206	53	17	2009	2009	NUM
ejpam-3206	53	18	)	)	PUNCT
ejpam-3206	53	19	,	,	PUNCT
ejpam-3206	53	20	introduced	introduce	VERB
ejpam-3206	53	21	the	the	DET
ejpam-3206	53	22	weak	weak	ADJ
ejpam-3206	53	23	annihilator	annihilator	NOUN
ejpam-3206	53	24	(	(	PUNCT
ejpam-3206	53	25	or	or	CCONJ
ejpam-3206	53	26	nilpotent	nilpotent	ADJ
ejpam-3206	53	27	annihilator	annihilator	NOUN
ejpam-3206	53	28	)	)	PUNCT
ejpam-3206	53	29	,	,	PUNCT
ejpam-3206	53	30	for	for	ADP
ejpam-3206	53	31	a	a	DET
ejpam-3206	53	32	nonempty	nonempty	NOUN
ejpam-3206	53	33	subset	subset	NOUN
ejpam-3206	53	34	x	x	PUNCT
ejpam-3206	53	35	of	of	ADP
ejpam-3206	53	36	a	a	DET
ejpam-3206	53	37	ring	ring	NOUN
ejpam-3206	53	38	r	r	NOUN
ejpam-3206	53	39	,	,	PUNCT
ejpam-3206	53	40	the	the	DET
ejpam-3206	53	41	weak	weak	ADJ
ejpam-3206	53	42	m.	m.	NOUN
ejpam-3206	53	43	a.	a.	NOUN
ejpam-3206	53	44	farahat	farahat	PROPN
ejpam-3206	53	45	,	,	PUNCT
ejpam-3206	53	46	s.	s.	PROPN
ejpam-3206	53	47	t.	t.	PROPN
ejpam-3206	53	48	al	al	PROPN
ejpam-3206	53	49	-	-	PUNCT
ejpam-3206	53	50	bogamy	bogamy	PROPN
ejpam-3206	53	51	/	/	SYM
ejpam-3206	53	52	eur	eur	PROPN
ejpam-3206	53	53	.	.	PUNCT
ejpam-3206	54	1	j.	j.	PROPN
ejpam-3206	54	2	pure	pure	PROPN
ejpam-3206	54	3	appl	appl	PROPN
ejpam-3206	54	4	.	.	PROPN
ejpam-3206	54	5	math	math	PROPN
ejpam-3206	54	6	,	,	PUNCT
ejpam-3206	54	7	11	11	NUM
ejpam-3206	54	8	(	(	PUNCT
ejpam-3206	54	9	1	1	NUM
ejpam-3206	54	10	)	)	PUNCT
ejpam-3206	54	11	(	(	PUNCT
ejpam-3206	54	12	2018	2018	NUM
ejpam-3206	54	13	)	)	PUNCT
ejpam-3206	54	14	,	,	PUNCT
ejpam-3206	54	15	244	244	NUM
ejpam-3206	54	16	-	-	SYM
ejpam-3206	54	17	259	259	NUM
ejpam-3206	54	18	246	246	NUM
ejpam-3206	54	19	annihilator	annihilator	NOUN
ejpam-3206	54	20	of	of	ADP
ejpam-3206	54	21	x	x	PUNCT
ejpam-3206	54	22	in	in	ADP
ejpam-3206	54	23	r	r	NOUN
ejpam-3206	54	24	is	be	AUX
ejpam-3206	54	25	defined	define	VERB
ejpam-3206	54	26	as	as	SCONJ
ejpam-3206	54	27	follows	follow	VERB
ejpam-3206	54	28	:	:	PUNCT
ejpam-3206	54	29	nr	nr	PROPN
ejpam-3206	54	30	(	(	PUNCT
ejpam-3206	54	31	x	x	NOUN
ejpam-3206	54	32	)	)	PUNCT
ejpam-3206	54	33	=	=	PRON
ejpam-3206	54	34	{	{	PUNCT
ejpam-3206	54	35	a	a	DET
ejpam-3206	54	36	∈	∈	NOUN
ejpam-3206	54	37	r	r	NOUN
ejpam-3206	54	38	|xa	|xa	ADP
ejpam-3206	54	39	∈	∈	PROPN
ejpam-3206	54	40	nil	nil	NOUN
ejpam-3206	54	41	(	(	PUNCT
ejpam-3206	54	42	r	r	NOUN
ejpam-3206	54	43	)	)	PUNCT
ejpam-3206	54	44	for	for	ADP
ejpam-3206	54	45	all	all	DET
ejpam-3206	54	46	x	x	SYM
ejpam-3206	54	47	∈	∈	NOUN
ejpam-3206	54	48	x	x	PUNCT
ejpam-3206	54	49	}	}	PUNCT
ejpam-3206	54	50	.	.	PUNCT
ejpam-3206	55	1	it	it	PRON
ejpam-3206	55	2	can	can	AUX
ejpam-3206	55	3	be	be	AUX
ejpam-3206	55	4	easily	easily	ADV
ejpam-3206	55	5	shown	show	VERB
ejpam-3206	55	6	that	that	SCONJ
ejpam-3206	55	7	ab	ab	PROPN
ejpam-3206	55	8	∈	∈	PROPN
ejpam-3206	55	9	nil	nil	NOUN
ejpam-3206	55	10	(	(	PUNCT
ejpam-3206	55	11	r)⇔	r)⇔	PROPN
ejpam-3206	55	12	ba	ba	PROPN
ejpam-3206	55	13	∈	∈	PROPN
ejpam-3206	55	14	nil	nil	NOUN
ejpam-3206	55	15	(	(	PUNCT
ejpam-3206	55	16	r	r	NOUN
ejpam-3206	55	17	)	)	PUNCT
ejpam-3206	55	18	for	for	ADP
ejpam-3206	55	19	all	all	DET
ejpam-3206	55	20	a	a	PRON
ejpam-3206	55	21	,	,	PUNCT
ejpam-3206	55	22	b	b	X
ejpam-3206	55	23	∈	∈	PROPN
ejpam-3206	55	24	r.	r.	PROPN
ejpam-3206	55	25	therefore	therefore	ADV
ejpam-3206	55	26	there	there	PRON
ejpam-3206	55	27	is	be	VERB
ejpam-3206	55	28	no	no	DET
ejpam-3206	55	29	way	way	NOUN
ejpam-3206	55	30	to	to	PART
ejpam-3206	55	31	distinguish	distinguish	VERB
ejpam-3206	55	32	between	between	ADP
ejpam-3206	55	33	the	the	DET
ejpam-3206	55	34	right	right	ADJ
ejpam-3206	55	35	weak	weak	ADJ
ejpam-3206	55	36	annihilator	annihilator	NOUN
ejpam-3206	55	37	and	and	CCONJ
ejpam-3206	55	38	the	the	DET
ejpam-3206	55	39	left	left	ADJ
ejpam-3206	55	40	weak	weak	ADJ
ejpam-3206	55	41	annihilator	annihilator	NOUN
ejpam-3206	55	42	.	.	PUNCT
ejpam-3206	56	1	obviously	obviously	ADV
ejpam-3206	56	2	,	,	PUNCT
ejpam-3206	56	3	rr	rr	PROPN
ejpam-3206	56	4	(	(	PUNCT
ejpam-3206	56	5	x	x	X
ejpam-3206	56	6	)	)	PUNCT
ejpam-3206	56	7	⊆	⊆	NUM
ejpam-3206	56	8	nr	nr	PROPN
ejpam-3206	56	9	(	(	PUNCT
ejpam-3206	56	10	x	x	NOUN
ejpam-3206	56	11	)	)	PUNCT
ejpam-3206	56	12	for	for	ADP
ejpam-3206	56	13	any	any	DET
ejpam-3206	56	14	subset	subset	NOUN
ejpam-3206	56	15	x	x	PUNCT
ejpam-3206	56	16	of	of	ADP
ejpam-3206	56	17	r	r	NOUN
ejpam-3206	56	18	and	and	CCONJ
ejpam-3206	56	19	if	if	SCONJ
ejpam-3206	56	20	r	r	NOUN
ejpam-3206	56	21	is	be	AUX
ejpam-3206	56	22	reduced	reduce	VERB
ejpam-3206	56	23	,	,	PUNCT
ejpam-3206	56	24	then	then	ADV
ejpam-3206	56	25	rr	rr	VERB
ejpam-3206	56	26	(	(	PUNCT
ejpam-3206	56	27	x	x	X
ejpam-3206	56	28	)	)	PUNCT
ejpam-3206	56	29	=	=	SYM
ejpam-3206	56	30	nr	nr	PROPN
ejpam-3206	56	31	(	(	PUNCT
ejpam-3206	56	32	x	x	NOUN
ejpam-3206	56	33	)	)	PUNCT
ejpam-3206	56	34	.	.	PUNCT
ejpam-3206	57	1	for	for	ADP
ejpam-3206	57	2	example	example	NOUN
ejpam-3206	57	3	,	,	PUNCT
ejpam-3206	57	4	let	let	VERB
ejpam-3206	57	5	d	d	PRON
ejpam-3206	57	6	be	be	AUX
ejpam-3206	57	7	an	an	DET
ejpam-3206	57	8	integral	integral	ADJ
ejpam-3206	57	9	domain	domain	NOUN
ejpam-3206	57	10	and	and	CCONJ
ejpam-3206	57	11	r	r	NOUN
ejpam-3206	57	12	=	=	SYM
ejpam-3206	57	13	t2	t2	NOUN
ejpam-3206	57	14	(	(	PUNCT
ejpam-3206	57	15	d	d	NOUN
ejpam-3206	57	16	)	)	PUNCT
ejpam-3206	57	17	=	=	SYM
ejpam-3206	57	18	{	{	PUNCT
ejpam-3206	57	19	(	(	PUNCT
ejpam-3206	57	20	a	a	DET
ejpam-3206	57	21	b	b	NOUN
ejpam-3206	57	22	0	0	NUM
ejpam-3206	57	23	c	c	NOUN
ejpam-3206	57	24	)	)	PUNCT
ejpam-3206	57	25	|	|	ADV
ejpam-3206	57	26	a	a	DET
ejpam-3206	57	27	,	,	PUNCT
ejpam-3206	57	28	b	b	NOUN
ejpam-3206	57	29	,	,	PUNCT
ejpam-3206	57	30	c	c	PROPN
ejpam-3206	57	31	∈	∈	PROPN
ejpam-3206	58	1	d	d	NOUN
ejpam-3206	58	2	}	}	PUNCT
ejpam-3206	58	3	=	=	SYM
ejpam-3206	58	4	(	(	PUNCT
ejpam-3206	58	5	d	d	X
ejpam-3206	58	6	d	d	NOUN
ejpam-3206	58	7	0	0	NUM
ejpam-3206	58	8	d	d	NOUN
ejpam-3206	58	9	)	)	PUNCT
ejpam-3206	58	10	.	.	PUNCT
ejpam-3206	59	1	we	we	PRON
ejpam-3206	59	2	can	can	AUX
ejpam-3206	59	3	check	check	VERB
ejpam-3206	59	4	that	that	DET
ejpam-3206	59	5	nil	nil	NOUN
ejpam-3206	59	6	(	(	PUNCT
ejpam-3206	59	7	r	r	NOUN
ejpam-3206	59	8	)	)	PUNCT
ejpam-3206	59	9	=	=	SYM
ejpam-3206	59	10	{	{	PUNCT
ejpam-3206	59	11	(	(	PUNCT
ejpam-3206	59	12	0	0	NUM
ejpam-3206	59	13	b	b	NOUN
ejpam-3206	59	14	0	0	NUM
ejpam-3206	59	15	0	0	NUM
ejpam-3206	59	16	)	)	PUNCT
ejpam-3206	60	1	|	|	ADV
ejpam-3206	60	2	b	b	X
ejpam-3206	60	3	∈	∈	NOUN
ejpam-3206	61	1	d	d	NOUN
ejpam-3206	61	2	}	}	PUNCT
ejpam-3206	61	3	=	=	SYM
ejpam-3206	61	4	(	(	PUNCT
ejpam-3206	61	5	0	0	NUM
ejpam-3206	61	6	d	d	NOUN
ejpam-3206	61	7	0	0	NUM
ejpam-3206	61	8	0	0	NUM
ejpam-3206	61	9	)	)	PUNCT
ejpam-3206	61	10	is	be	AUX
ejpam-3206	61	11	a	a	DET
ejpam-3206	61	12	two	two	NUM
ejpam-3206	61	13	sided	sided	ADJ
ejpam-3206	61	14	ideal	ideal	NOUN
ejpam-3206	61	15	in	in	ADP
ejpam-3206	61	16	r	r	NOUN
ejpam-3206	61	17	,	,	PUNCT
ejpam-3206	61	18	hence	hence	ADV
ejpam-3206	61	19	r	r	NOUN
ejpam-3206	61	20	is	be	AUX
ejpam-3206	61	21	an	an	DET
ejpam-3206	61	22	ni	ni	NOUN
ejpam-3206	61	23	-	-	PUNCT
ejpam-3206	61	24	ring	ring	NOUN
ejpam-3206	61	25	.	.	PUNCT
ejpam-3206	62	1	consider	consider	VERB
ejpam-3206	62	2	the	the	DET
ejpam-3206	62	3	subset	subset	NOUN
ejpam-3206	62	4	x	x	PUNCT
ejpam-3206	63	1	=	=	PUNCT
ejpam-3206	63	2	{	{	PUNCT
ejpam-3206	63	3	(	(	PUNCT
ejpam-3206	63	4	x	x	SYM
ejpam-3206	63	5	0	0	NUM
ejpam-3206	63	6	0	0	NUM
ejpam-3206	63	7	x	x	X
ejpam-3206	63	8	)	)	PUNCT
ejpam-3206	64	1	|	|	ADV
ejpam-3206	64	2	x	x	SYM
ejpam-3206	64	3	∈	∈	PROPN
ejpam-3206	64	4	d	d	X
ejpam-3206	64	5	}	}	PUNCT
ejpam-3206	64	6	of	of	ADP
ejpam-3206	64	7	r.	r.	PROPN
ejpam-3206	64	8	then	then	ADV
ejpam-3206	64	9	rr	rr	VERB
ejpam-3206	64	10	(	(	PUNCT
ejpam-3206	64	11	x	x	X
ejpam-3206	64	12	)	)	PUNCT
ejpam-3206	64	13	=	=	SYM
ejpam-3206	64	14	0	0	PUNCT
ejpam-3206	65	1	but	but	CCONJ
ejpam-3206	65	2	nr	nr	PRON
ejpam-3206	65	3	(	(	PUNCT
ejpam-3206	65	4	x	x	NOUN
ejpam-3206	65	5	)	)	PUNCT
ejpam-3206	65	6	=	=	SYM
ejpam-3206	65	7	{	{	PUNCT
ejpam-3206	65	8	(	(	PUNCT
ejpam-3206	65	9	0	0	NUM
ejpam-3206	65	10	y	y	NOUN
ejpam-3206	65	11	0	0	NUM
ejpam-3206	65	12	0	0	NUM
ejpam-3206	65	13	)	)	PUNCT
ejpam-3206	66	1	|	|	ADV
ejpam-3206	66	2	y	y	PROPN
ejpam-3206	66	3	∈	∈	PROPN
ejpam-3206	66	4	d	d	NOUN
ejpam-3206	66	5	}	}	PUNCT
ejpam-3206	66	6	=	=	SYM
ejpam-3206	66	7	(	(	PUNCT
ejpam-3206	66	8	0	0	NUM
ejpam-3206	66	9	d	d	NOUN
ejpam-3206	66	10	0	0	NUM
ejpam-3206	66	11	0	0	NUM
ejpam-3206	66	12	)	)	PUNCT
ejpam-3206	67	1	=	=	SYM
ejpam-3206	67	2	nil	nil	NOUN
ejpam-3206	67	3	(	(	PUNCT
ejpam-3206	67	4	r	r	NOUN
ejpam-3206	67	5	)	)	PUNCT
ejpam-3206	67	6	.	.	PUNCT
ejpam-3206	68	1	thus	thus	ADV
ejpam-3206	68	2	rr	rr	X
ejpam-3206	68	3	(	(	PUNCT
ejpam-3206	68	4	x	x	NOUN
ejpam-3206	68	5	)	)	PUNCT
ejpam-3206	68	6	$	$	SYM
ejpam-3206	68	7	nr	nr	PROPN
ejpam-3206	68	8	(	(	PUNCT
ejpam-3206	68	9	x	x	NOUN
ejpam-3206	68	10	)	)	PUNCT
ejpam-3206	68	11	.	.	PUNCT
ejpam-3206	69	1	hence	hence	ADV
ejpam-3206	69	2	the	the	DET
ejpam-3206	69	3	weak	weak	ADJ
ejpam-3206	69	4	annihilator	annihilator	NOUN
ejpam-3206	69	5	is	be	AUX
ejpam-3206	69	6	a	a	DET
ejpam-3206	69	7	nontrivial	nontrivial	ADJ
ejpam-3206	69	8	generalization	generalization	NOUN
ejpam-3206	69	9	of	of	ADP
ejpam-3206	69	10	the	the	DET
ejpam-3206	69	11	annihilator	annihilator	PROPN
ejpam-3206	69	12	.	.	PUNCT
ejpam-3206	70	1	proposition	proposition	NOUN
ejpam-3206	70	2	1	1	NUM
ejpam-3206	70	3	(	(	PUNCT
ejpam-3206	70	4	[	[	X
ejpam-3206	70	5	16	16	NUM
ejpam-3206	70	6	]	]	PUNCT
ejpam-3206	70	7	)	)	PUNCT
ejpam-3206	70	8	.	.	PUNCT
ejpam-3206	71	1	let	let	VERB
ejpam-3206	71	2	r	r	PRON
ejpam-3206	71	3	be	be	AUX
ejpam-3206	71	4	a	a	DET
ejpam-3206	71	5	ring	ring	NOUN
ejpam-3206	71	6	.	.	PUNCT
ejpam-3206	72	1	then	then	ADV
ejpam-3206	72	2	:	:	PUNCT
ejpam-3206	72	3	1	1	X
ejpam-3206	72	4	)	)	PUNCT
ejpam-3206	72	5	if	if	SCONJ
ejpam-3206	72	6	x	x	PROPN
ejpam-3206	72	7	⊆	⊆	NUM
ejpam-3206	72	8	y	y	PROPN
ejpam-3206	72	9	⊂	⊂	PROPN
ejpam-3206	72	10	r	r	NOUN
ejpam-3206	72	11	,	,	PUNCT
ejpam-3206	72	12	then	then	ADV
ejpam-3206	72	13	nr(y	nr(y	NUM
ejpam-3206	72	14	)	)	PUNCT
ejpam-3206	72	15	⊆	⊆	NUM
ejpam-3206	72	16	nr(x	nr(x	NUM
ejpam-3206	72	17	)	)	PUNCT
ejpam-3206	72	18	,	,	PUNCT
ejpam-3206	72	19	2	2	X
ejpam-3206	72	20	)	)	PUNCT
ejpam-3206	72	21	x	x	SYM
ejpam-3206	73	1	⊆	⊆	NUM
ejpam-3206	73	2	nr(nr(x	nr(nr(x	NOUN
ejpam-3206	73	3	)	)	PUNCT
ejpam-3206	73	4	)	)	PUNCT
ejpam-3206	73	5	,	,	PUNCT
ejpam-3206	73	6	3	3	X
ejpam-3206	73	7	)	)	PUNCT
ejpam-3206	73	8	nr(nr(nr(x	nr(nr(nr(x	NOUN
ejpam-3206	73	9	)	)	PUNCT
ejpam-3206	73	10	)	)	PUNCT
ejpam-3206	73	11	)	)	PUNCT
ejpam-3206	74	1	=	=	SYM
ejpam-3206	74	2	nr(x	nr(x	NUM
ejpam-3206	74	3	)	)	PUNCT
ejpam-3206	74	4	,	,	PUNCT
ejpam-3206	74	5	4	4	X
ejpam-3206	74	6	)	)	PUNCT
ejpam-3206	74	7	if	if	SCONJ
ejpam-3206	74	8	s	s	VERB
ejpam-3206	74	9	≤	≤	NUM
ejpam-3206	74	10	r	r	NOUN
ejpam-3206	74	11	and	and	CCONJ
ejpam-3206	74	12	x	x	SYM
ejpam-3206	74	13	⊆	⊆	NUM
ejpam-3206	74	14	s	s	NOUN
ejpam-3206	74	15	,	,	PUNCT
ejpam-3206	74	16	then	then	ADV
ejpam-3206	74	17	ns(x	ns(x	PUNCT
ejpam-3206	74	18	)	)	PUNCT
ejpam-3206	74	19	=	=	SYM
ejpam-3206	74	20	nr(x	nr(x	NUM
ejpam-3206	74	21	)	)	PUNCT
ejpam-3206	74	22	∩	∩	PROPN
ejpam-3206	74	23	s.	s.	PROPN
ejpam-3206	74	24	lemma	lemma	PROPN
ejpam-3206	75	1	1	1	X
ejpam-3206	75	2	.	.	PUNCT
ejpam-3206	76	1	let	let	VERB
ejpam-3206	76	2	r	r	PRON
ejpam-3206	76	3	be	be	AUX
ejpam-3206	76	4	an	an	DET
ejpam-3206	76	5	ni	ni	NOUN
ejpam-3206	76	6	-	-	NOUN
ejpam-3206	76	7	ring	ring	NOUN
ejpam-3206	76	8	.	.	PUNCT
ejpam-3206	77	1	if	if	SCONJ
ejpam-3206	77	2	ab	ab	PROPN
ejpam-3206	77	3	∈	∈	PROPN
ejpam-3206	77	4	nil	nil	NOUN
ejpam-3206	77	5	(	(	PUNCT
ejpam-3206	77	6	r	r	NOUN
ejpam-3206	77	7	)	)	PUNCT
ejpam-3206	77	8	,	,	PUNCT
ejpam-3206	77	9	then	then	ADV
ejpam-3206	77	10	arb	arb	PROPN
ejpam-3206	77	11	∈	∈	PROPN
ejpam-3206	77	12	nil	nil	NOUN
ejpam-3206	77	13	(	(	PUNCT
ejpam-3206	77	14	r	r	NOUN
ejpam-3206	77	15	)	)	PUNCT
ejpam-3206	77	16	for	for	ADP
ejpam-3206	77	17	all	all	DET
ejpam-3206	77	18	a	a	DET
ejpam-3206	77	19	,	,	PUNCT
ejpam-3206	77	20	b	b	NOUN
ejpam-3206	77	21	,	,	PUNCT
ejpam-3206	77	22	r	r	PROPN
ejpam-3206	77	23	∈	∈	PROPN
ejpam-3206	77	24	r.	r.	NOUN
ejpam-3206	77	25	proof	proof	NOUN
ejpam-3206	77	26	.	.	PUNCT
ejpam-3206	78	1	let	let	VERB
ejpam-3206	78	2	a	a	DET
ejpam-3206	78	3	,	,	PUNCT
ejpam-3206	78	4	b	b	X
ejpam-3206	78	5	∈	∈	NOUN
ejpam-3206	78	6	r	r	NOUN
ejpam-3206	78	7	such	such	ADJ
ejpam-3206	78	8	that	that	SCONJ
ejpam-3206	78	9	ab	ab	PROPN
ejpam-3206	78	10	∈	∈	PROPN
ejpam-3206	78	11	nil	nil	NOUN
ejpam-3206	78	12	(	(	PUNCT
ejpam-3206	78	13	r	r	NOUN
ejpam-3206	78	14	)	)	PUNCT
ejpam-3206	78	15	.	.	PUNCT
ejpam-3206	79	1	hence	hence	ADV
ejpam-3206	79	2	ba	ba	PROPN
ejpam-3206	79	3	∈	∈	PROPN
ejpam-3206	79	4	nil	nil	NOUN
ejpam-3206	79	5	(	(	PUNCT
ejpam-3206	79	6	r	r	NOUN
ejpam-3206	79	7	)	)	PUNCT
ejpam-3206	79	8	.	.	PUNCT
ejpam-3206	80	1	we	we	PRON
ejpam-3206	80	2	thus	thus	ADV
ejpam-3206	80	3	get	get	VERB
ejpam-3206	80	4	bar	bar	NOUN
ejpam-3206	80	5	∈	∈	NOUN
ejpam-3206	80	6	nil	nil	NOUN
ejpam-3206	80	7	(	(	PUNCT
ejpam-3206	80	8	r	r	NOUN
ejpam-3206	80	9	)	)	PUNCT
ejpam-3206	80	10	for	for	ADP
ejpam-3206	80	11	each	each	DET
ejpam-3206	80	12	r	r	NOUN
ejpam-3206	80	13	∈	∈	PROPN
ejpam-3206	80	14	r.	r.	NOUN
ejpam-3206	80	15	it	it	PRON
ejpam-3206	80	16	follows	follow	VERB
ejpam-3206	80	17	that	that	SCONJ
ejpam-3206	80	18	arb	arb	PROPN
ejpam-3206	80	19	∈	∈	PROPN
ejpam-3206	80	20	nil	nil	NOUN
ejpam-3206	80	21	(	(	PUNCT
ejpam-3206	80	22	r	r	NOUN
ejpam-3206	80	23	)	)	PUNCT
ejpam-3206	80	24	for	for	ADP
ejpam-3206	80	25	each	each	DET
ejpam-3206	80	26	r	r	PROPN
ejpam-3206	80	27	∈	∈	PROPN
ejpam-3206	80	28	r.	r.	NOUN
ejpam-3206	80	29	remark	remark	NOUN
ejpam-3206	80	30	1	1	NUM
ejpam-3206	80	31	.	.	PUNCT
ejpam-3206	81	1	if	if	SCONJ
ejpam-3206	81	2	r	r	NOUN
ejpam-3206	81	3	is	be	AUX
ejpam-3206	81	4	an	an	DET
ejpam-3206	81	5	ni	ni	NOUN
ejpam-3206	81	6	-	-	NOUN
ejpam-3206	81	7	ring	ring	NOUN
ejpam-3206	81	8	,	,	PUNCT
ejpam-3206	81	9	then	then	ADV
ejpam-3206	81	10	nr	nr	PRON
ejpam-3206	81	11	(	(	PUNCT
ejpam-3206	81	12	x	x	X
ejpam-3206	81	13	)	)	PUNCT
ejpam-3206	81	14	is	be	AUX
ejpam-3206	81	15	an	an	DET
ejpam-3206	81	16	ideal	ideal	NOUN
ejpam-3206	81	17	of	of	ADP
ejpam-3206	81	18	r	r	NOUN
ejpam-3206	81	19	for	for	ADP
ejpam-3206	81	20	any	any	DET
ejpam-3206	81	21	subset	subset	NOUN
ejpam-3206	81	22	x	x	PUNCT
ejpam-3206	81	23	of	of	ADP
ejpam-3206	81	24	r.	r.	PROPN
ejpam-3206	81	25	in	in	ADP
ejpam-3206	81	26	particular	particular	ADJ
ejpam-3206	81	27	,	,	PUNCT
ejpam-3206	81	28	nr	nr	PROPN
ejpam-3206	81	29	(	(	PUNCT
ejpam-3206	81	30	a	a	PRON
ejpam-3206	81	31	)	)	PUNCT
ejpam-3206	81	32	is	be	AUX
ejpam-3206	81	33	an	an	DET
ejpam-3206	81	34	ideal	ideal	NOUN
ejpam-3206	81	35	of	of	ADP
ejpam-3206	81	36	r	r	NOUN
ejpam-3206	81	37	for	for	ADP
ejpam-3206	81	38	any	any	DET
ejpam-3206	81	39	a	a	DET
ejpam-3206	81	40	∈	∈	PROPN
ejpam-3206	81	41	r.	r.	NOUN
ejpam-3206	81	42	in	in	ADP
ejpam-3206	81	43	this	this	DET
ejpam-3206	81	44	paper	paper	NOUN
ejpam-3206	81	45	,	,	PUNCT
ejpam-3206	81	46	we	we	PRON
ejpam-3206	81	47	introduce	introduce	VERB
ejpam-3206	81	48	the	the	DET
ejpam-3206	81	49	class	class	NOUN
ejpam-3206	81	50	of	of	ADP
ejpam-3206	81	51	weak	weak	ADJ
ejpam-3206	81	52	ps	ps	NOUN
ejpam-3206	81	53	-	-	PUNCT
ejpam-3206	81	54	rings	ring	NOUN
ejpam-3206	81	55	and	and	CCONJ
ejpam-3206	81	56	investigate	investigate	VERB
ejpam-3206	81	57	some	some	PRON
ejpam-3206	81	58	of	of	ADP
ejpam-3206	81	59	its	its	PRON
ejpam-3206	81	60	characterization	characterization	NOUN
ejpam-3206	81	61	and	and	CCONJ
ejpam-3206	81	62	study	study	VERB
ejpam-3206	81	63	the	the	DET
ejpam-3206	81	64	transfer	transfer	NOUN
ejpam-3206	81	65	of	of	ADP
ejpam-3206	81	66	weak	weak	ADJ
ejpam-3206	81	67	ps	ps	NOUN
ejpam-3206	81	68	-	-	PUNCT
ejpam-3206	81	69	condition	condition	NOUN
ejpam-3206	81	70	between	between	ADP
ejpam-3206	81	71	a	a	DET
ejpam-3206	81	72	base	base	NOUN
ejpam-3206	81	73	ring	ring	NOUN
ejpam-3206	81	74	r	r	NOUN
ejpam-3206	81	75	and	and	CCONJ
ejpam-3206	81	76	the	the	DET
ejpam-3206	81	77	extension	extension	NOUN
ejpam-3206	81	78	ring	ring	NOUN
ejpam-3206	81	79	of	of	ADP
ejpam-3206	81	80	skew	skew	ADJ
ejpam-3206	81	81	hurwitz	hurwitz	PROPN
ejpam-3206	81	82	series	series	PROPN
ejpam-3206	81	83	a	a	PROPN
ejpam-3206	81	84	=	=	X
ejpam-3206	81	85	(	(	PUNCT
ejpam-3206	81	86	hr	hr	PROPN
ejpam-3206	81	87	,	,	PUNCT
ejpam-3206	81	88	σ	σ	PROPN
ejpam-3206	81	89	)	)	PUNCT
ejpam-3206	81	90	.	.	PUNCT
ejpam-3206	82	1	m.	m.	NOUN
ejpam-3206	82	2	a.	a.	PROPN
ejpam-3206	82	3	farahat	farahat	PROPN
ejpam-3206	82	4	,	,	PUNCT
ejpam-3206	82	5	s.	s.	PROPN
ejpam-3206	82	6	t.	t.	PROPN
ejpam-3206	82	7	al	al	PROPN
ejpam-3206	82	8	-	-	PUNCT
ejpam-3206	82	9	bogamy	bogamy	PROPN
ejpam-3206	82	10	/	/	SYM
ejpam-3206	82	11	eur	eur	PROPN
ejpam-3206	82	12	.	.	PUNCT
ejpam-3206	83	1	j.	j.	PROPN
ejpam-3206	83	2	pure	pure	PROPN
ejpam-3206	83	3	appl	appl	PROPN
ejpam-3206	83	4	.	.	PROPN
ejpam-3206	83	5	math	math	PROPN
ejpam-3206	83	6	,	,	PUNCT
ejpam-3206	83	7	11	11	NUM
ejpam-3206	83	8	(	(	PUNCT
ejpam-3206	83	9	1	1	NUM
ejpam-3206	83	10	)	)	PUNCT
ejpam-3206	83	11	(	(	PUNCT
ejpam-3206	83	12	2018	2018	NUM
ejpam-3206	83	13	)	)	PUNCT
ejpam-3206	83	14	,	,	PUNCT
ejpam-3206	83	15	244	244	NUM
ejpam-3206	83	16	-	-	SYM
ejpam-3206	83	17	259	259	NUM
ejpam-3206	83	18	247	247	NUM
ejpam-3206	83	19	2	2	NUM
ejpam-3206	83	20	.	.	PUNCT
ejpam-3206	83	21	rings	ring	NOUN
ejpam-3206	83	22	satisfy	satisfy	VERB
ejpam-3206	83	23	the	the	DET
ejpam-3206	83	24	weak	weak	ADJ
ejpam-3206	83	25	ps	ps	NOUN
ejpam-3206	83	26	-	-	PUNCT
ejpam-3206	83	27	condition	condition	NOUN
ejpam-3206	83	28	motivated	motivate	VERB
ejpam-3206	83	29	by	by	ADP
ejpam-3206	83	30	the	the	DET
ejpam-3206	83	31	definition	definition	NOUN
ejpam-3206	83	32	of	of	ADP
ejpam-3206	83	33	the	the	DET
ejpam-3206	83	34	ps	ps	NOUN
ejpam-3206	83	35	-	-	PUNCT
ejpam-3206	83	36	condition	condition	NOUN
ejpam-3206	83	37	and	and	CCONJ
ejpam-3206	83	38	the	the	DET
ejpam-3206	83	39	definition	definition	NOUN
ejpam-3206	83	40	of	of	ADP
ejpam-3206	83	41	the	the	DET
ejpam-3206	83	42	weak	weak	ADJ
ejpam-3206	83	43	annihilator	annihilator	NOUN
ejpam-3206	83	44	,	,	PUNCT
ejpam-3206	83	45	we	we	PRON
ejpam-3206	83	46	introduced	introduce	VERB
ejpam-3206	83	47	the	the	DET
ejpam-3206	83	48	notion	notion	NOUN
ejpam-3206	83	49	of	of	ADP
ejpam-3206	83	50	weak	weak	ADJ
ejpam-3206	83	51	ps	ps	NOUN
ejpam-3206	83	52	-	-	PUNCT
ejpam-3206	83	53	condition	condition	NOUN
ejpam-3206	83	54	as	as	SCONJ
ejpam-3206	83	55	follows	follow	VERB
ejpam-3206	83	56	:	:	PUNCT
ejpam-3206	83	57	definition	definition	NOUN
ejpam-3206	83	58	1	1	NUM
ejpam-3206	83	59	.	.	PUNCT
ejpam-3206	84	1	a	a	DET
ejpam-3206	84	2	ring	ring	NOUN
ejpam-3206	84	3	r	r	NOUN
ejpam-3206	84	4	satisfies	satisfie	NOUN
ejpam-3206	84	5	the	the	DET
ejpam-3206	84	6	right	right	ADJ
ejpam-3206	84	7	weak	weak	ADJ
ejpam-3206	84	8	ps	ps	NOUN
ejpam-3206	84	9	-	-	PUNCT
ejpam-3206	84	10	condition	condition	NOUN
ejpam-3206	84	11	if	if	SCONJ
ejpam-3206	84	12	,	,	PUNCT
ejpam-3206	84	13	for	for	ADP
ejpam-3206	84	14	every	every	DET
ejpam-3206	84	15	maximal	maximal	ADJ
ejpam-3206	84	16	right	right	ADJ
ejpam-3206	84	17	ideal	ideal	ADJ
ejpam-3206	84	18	l	l	NOUN
ejpam-3206	84	19	of	of	ADP
ejpam-3206	84	20	r	r	NOUN
ejpam-3206	84	21	,	,	PUNCT
ejpam-3206	84	22	either	either	CCONJ
ejpam-3206	84	23	nr	nr	PROPN
ejpam-3206	84	24	(	(	PUNCT
ejpam-3206	84	25	l	l	NOUN
ejpam-3206	84	26	)	)	PUNCT
ejpam-3206	84	27	⊆	⊆	NUM
ejpam-3206	84	28	nil	nil	NOUN
ejpam-3206	84	29	(	(	PUNCT
ejpam-3206	84	30	r	r	NOUN
ejpam-3206	84	31	)	)	PUNCT
ejpam-3206	84	32	or	or	CCONJ
ejpam-3206	84	33	nr	nr	PRON
ejpam-3206	84	34	(	(	PUNCT
ejpam-3206	84	35	l	l	NOUN
ejpam-3206	84	36	)	)	PUNCT
ejpam-3206	84	37	=	=	SYM
ejpam-3206	84	38	re	re	PROPN
ejpam-3206	84	39	,	,	PUNCT
ejpam-3206	84	40	(	(	PUNCT
ejpam-3206	84	41	principal	principal	NOUN
ejpam-3206	84	42	left	leave	VERB
ejpam-3206	84	43	ideal	ideal	NOUN
ejpam-3206	84	44	generated	generate	VERB
ejpam-3206	84	45	by	by	ADP
ejpam-3206	84	46	e	e	PROPN
ejpam-3206	84	47	)	)	PUNCT
ejpam-3206	84	48	,	,	PUNCT
ejpam-3206	84	49	where	where	SCONJ
ejpam-3206	84	50	e	e	PROPN
ejpam-3206	84	51	∈	∈	PROPN
ejpam-3206	84	52	id(r	id(r	NOUN
ejpam-3206	84	53	)	)	PUNCT
ejpam-3206	84	54	.	.	PUNCT
ejpam-3206	85	1	similarly	similarly	ADV
ejpam-3206	85	2	,	,	PUNCT
ejpam-3206	85	3	we	we	PRON
ejpam-3206	85	4	can	can	AUX
ejpam-3206	85	5	define	define	VERB
ejpam-3206	85	6	the	the	DET
ejpam-3206	85	7	left	left	ADJ
ejpam-3206	85	8	weak	weak	ADJ
ejpam-3206	85	9	ps	ps	NOUN
ejpam-3206	85	10	-	-	NOUN
ejpam-3206	85	11	condition	condition	NOUN
ejpam-3206	85	12	.	.	PUNCT
ejpam-3206	86	1	a	a	DET
ejpam-3206	86	2	ring	ring	NOUN
ejpam-3206	86	3	r	r	NOUN
ejpam-3206	86	4	satisfies	satisfie	NOUN
ejpam-3206	86	5	the	the	DET
ejpam-3206	86	6	weak	weak	ADJ
ejpam-3206	86	7	ps	ps	NOUN
ejpam-3206	86	8	-	-	PUNCT
ejpam-3206	86	9	condition	condition	NOUN
ejpam-3206	86	10	if	if	SCONJ
ejpam-3206	86	11	it	it	PRON
ejpam-3206	86	12	satisfies	satisfy	VERB
ejpam-3206	86	13	both	both	CCONJ
ejpam-3206	86	14	the	the	DET
ejpam-3206	86	15	right	right	NOUN
ejpam-3206	86	16	and	and	CCONJ
ejpam-3206	86	17	the	the	DET
ejpam-3206	86	18	left	left	ADJ
ejpam-3206	86	19	weak	weak	ADJ
ejpam-3206	86	20	ps	ps	NOUN
ejpam-3206	86	21	-	-	PUNCT
ejpam-3206	86	22	conditions	condition	NOUN
ejpam-3206	86	23	.	.	PUNCT
ejpam-3206	87	1	remark	remark	NOUN
ejpam-3206	87	2	2	2	NUM
ejpam-3206	87	3	.	.	NOUN
ejpam-3206	87	4	1	1	NUM
ejpam-3206	87	5	)	)	PUNCT
ejpam-3206	87	6	in	in	ADP
ejpam-3206	87	7	the	the	DET
ejpam-3206	87	8	definition	definition	NOUN
ejpam-3206	87	9	of	of	ADP
ejpam-3206	87	10	the	the	DET
ejpam-3206	87	11	weak	weak	ADJ
ejpam-3206	87	12	ps	ps	NOUN
ejpam-3206	87	13	-	-	NOUN
ejpam-3206	87	14	condition	condition	NOUN
ejpam-3206	87	15	,	,	PUNCT
ejpam-3206	87	16	we	we	PRON
ejpam-3206	87	17	use	use	VERB
ejpam-3206	87	18	”	"	PUNCT
ejpam-3206	87	19	or	or	CCONJ
ejpam-3206	87	20	”	"	PUNCT
ejpam-3206	87	21	to	to	PART
ejpam-3206	87	22	mean	mean	VERB
ejpam-3206	87	23	that	that	SCONJ
ejpam-3206	87	24	one	one	NUM
ejpam-3206	87	25	of	of	ADP
ejpam-3206	87	26	the	the	DET
ejpam-3206	87	27	two	two	NUM
ejpam-3206	87	28	options	option	NOUN
ejpam-3206	87	29	only	only	ADV
ejpam-3206	87	30	holds	hold	VERB
ejpam-3206	87	31	,	,	PUNCT
ejpam-3206	87	32	but	but	CCONJ
ejpam-3206	87	33	not	not	PART
ejpam-3206	87	34	both	both	PRON
ejpam-3206	87	35	,	,	PUNCT
ejpam-3206	87	36	unless	unless	SCONJ
ejpam-3206	87	37	that	that	PRON
ejpam-3206	87	38	nr	nr	PROPN
ejpam-3206	87	39	(	(	PUNCT
ejpam-3206	87	40	l	l	NOUN
ejpam-3206	87	41	)	)	PUNCT
ejpam-3206	87	42	=	=	SYM
ejpam-3206	87	43	(	(	PUNCT
ejpam-3206	87	44	0	0	NUM
ejpam-3206	87	45	)	)	PUNCT
ejpam-3206	87	46	.	.	PUNCT
ejpam-3206	88	1	since	since	SCONJ
ejpam-3206	88	2	nil	nil	NOUN
ejpam-3206	88	3	(	(	PUNCT
ejpam-3206	88	4	r	r	NOUN
ejpam-3206	88	5	)	)	PUNCT
ejpam-3206	88	6	⋂	⋂	PROPN
ejpam-3206	88	7	i	i	PROPN
ejpam-3206	88	8	d	d	PROPN
ejpam-3206	88	9	(	(	PUNCT
ejpam-3206	88	10	r	r	NOUN
ejpam-3206	88	11	)	)	PUNCT
ejpam-3206	88	12	=	=	SYM
ejpam-3206	88	13	(	(	PUNCT
ejpam-3206	88	14	0	0	NUM
ejpam-3206	88	15	)	)	PUNCT
ejpam-3206	88	16	.	.	PUNCT
ejpam-3206	89	1	2	2	X
ejpam-3206	89	2	)	)	PUNCT
ejpam-3206	89	3	it	it	PRON
ejpam-3206	89	4	is	be	AUX
ejpam-3206	89	5	clear	clear	ADJ
ejpam-3206	89	6	that	that	SCONJ
ejpam-3206	89	7	in	in	ADP
ejpam-3206	89	8	reduced	reduce	VERB
ejpam-3206	89	9	rings	ring	NOUN
ejpam-3206	89	10	weak	weak	ADJ
ejpam-3206	89	11	ps	ps	NOUN
ejpam-3206	89	12	-	-	PUNCT
ejpam-3206	89	13	condition	condition	NOUN
ejpam-3206	89	14	and	and	CCONJ
ejpam-3206	89	15	ps	ps	NOUN
ejpam-3206	89	16	-	-	PUNCT
ejpam-3206	89	17	condition	condition	NOUN
ejpam-3206	89	18	are	be	AUX
ejpam-3206	89	19	equivalent	equivalent	ADJ
ejpam-3206	89	20	.	.	PUNCT
ejpam-3206	90	1	example	example	NOUN
ejpam-3206	90	2	4	4	NUM
ejpam-3206	90	3	.	.	PUNCT
ejpam-3206	91	1	every	every	DET
ejpam-3206	91	2	domain	domain	NOUN
ejpam-3206	91	3	(	(	PUNCT
ejpam-3206	91	4	which	which	PRON
ejpam-3206	91	5	is	be	AUX
ejpam-3206	91	6	not	not	PART
ejpam-3206	91	7	a	a	DET
ejpam-3206	91	8	field	field	NOUN
ejpam-3206	91	9	)	)	PUNCT
ejpam-3206	91	10	is	be	AUX
ejpam-3206	91	11	a	a	DET
ejpam-3206	91	12	reduced	reduce	VERB
ejpam-3206	91	13	weak	weak	ADJ
ejpam-3206	91	14	ps	ps	NOUN
ejpam-3206	91	15	-	-	NOUN
ejpam-3206	91	16	ring	ring	NOUN
ejpam-3206	91	17	,	,	PUNCT
ejpam-3206	91	18	since	since	SCONJ
ejpam-3206	91	19	the	the	DET
ejpam-3206	91	20	left	left	NOUN
ejpam-3206	91	21	(	(	PUNCT
ejpam-3206	91	22	right	right	ADJ
ejpam-3206	91	23	)	)	PUNCT
ejpam-3206	91	24	annihilator	annihilator	NOUN
ejpam-3206	91	25	of	of	ADP
ejpam-3206	91	26	every	every	DET
ejpam-3206	91	27	right	right	NOUN
ejpam-3206	91	28	(	(	PUNCT
ejpam-3206	91	29	left	left	ADJ
ejpam-3206	91	30	)	)	PUNCT
ejpam-3206	91	31	maximal	maximal	ADJ
ejpam-3206	91	32	ideal	ideal	NOUN
ejpam-3206	91	33	is	be	AUX
ejpam-3206	91	34	zero	zero	NUM
ejpam-3206	91	35	and	and	CCONJ
ejpam-3206	91	36	hence	hence	ADV
ejpam-3206	91	37	generated	generate	VERB
ejpam-3206	91	38	by	by	ADP
ejpam-3206	91	39	idempotent	idempotent	NOUN
ejpam-3206	91	40	.	.	PUNCT
ejpam-3206	92	1	also	also	ADV
ejpam-3206	92	2	,	,	PUNCT
ejpam-3206	92	3	every	every	DET
ejpam-3206	92	4	field	field	NOUN
ejpam-3206	92	5	is	be	AUX
ejpam-3206	92	6	a	a	DET
ejpam-3206	92	7	reduced	reduce	VERB
ejpam-3206	92	8	weak	weak	ADJ
ejpam-3206	92	9	ps	ps	NOUN
ejpam-3206	92	10	-	-	NOUN
ejpam-3206	92	11	ring	ring	NOUN
ejpam-3206	92	12	,	,	PUNCT
ejpam-3206	92	13	since	since	SCONJ
ejpam-3206	92	14	the	the	DET
ejpam-3206	92	15	zero	zero	NUM
ejpam-3206	92	16	ideal	ideal	NOUN
ejpam-3206	92	17	is	be	AUX
ejpam-3206	92	18	the	the	DET
ejpam-3206	92	19	only	only	ADJ
ejpam-3206	92	20	maximal	maximal	ADJ
ejpam-3206	92	21	ideal	ideal	NOUN
ejpam-3206	92	22	in	in	ADP
ejpam-3206	92	23	a	a	DET
ejpam-3206	92	24	field	field	NOUN
ejpam-3206	93	1	f	f	X
ejpam-3206	93	2	,	,	PUNCT
ejpam-3206	93	3	clearly	clearly	ADV
ejpam-3206	93	4	the	the	DET
ejpam-3206	93	5	left	left	ADJ
ejpam-3206	93	6	(	(	PUNCT
ejpam-3206	93	7	right	right	ADJ
ejpam-3206	93	8	)	)	PUNCT
ejpam-3206	93	9	annihilator	annihilator	NOUN
ejpam-3206	93	10	of	of	ADP
ejpam-3206	93	11	the	the	DET
ejpam-3206	93	12	zero	zero	NUM
ejpam-3206	93	13	ideal	ideal	NOUN
ejpam-3206	93	14	is	be	AUX
ejpam-3206	93	15	f	f	PROPN
ejpam-3206	93	16	which	which	PRON
ejpam-3206	93	17	is	be	AUX
ejpam-3206	93	18	generated	generate	VERB
ejpam-3206	93	19	by	by	ADP
ejpam-3206	93	20	1	1	NUM
ejpam-3206	93	21	which	which	PRON
ejpam-3206	93	22	is	be	AUX
ejpam-3206	93	23	an	an	DET
ejpam-3206	93	24	idempotent	idempotent	NOUN
ejpam-3206	93	25	in	in	ADP
ejpam-3206	93	26	f.	f.	PROPN
ejpam-3206	93	27	example	example	PROPN
ejpam-3206	94	1	5	5	X
ejpam-3206	94	2	.	.	PUNCT
ejpam-3206	95	1	if	if	SCONJ
ejpam-3206	95	2	r	r	NOUN
ejpam-3206	95	3	is	be	AUX
ejpam-3206	95	4	a	a	DET
ejpam-3206	95	5	commutative	commutative	ADJ
ejpam-3206	95	6	local	local	ADJ
ejpam-3206	95	7	ring	ring	NOUN
ejpam-3206	95	8	with	with	ADP
ejpam-3206	95	9	a	a	DET
ejpam-3206	95	10	unique	unique	ADJ
ejpam-3206	95	11	maximal	maximal	ADJ
ejpam-3206	95	12	ideal	ideal	NOUN
ejpam-3206	95	13	l	l	NOUN
ejpam-3206	95	14	,	,	PUNCT
ejpam-3206	95	15	then	then	ADV
ejpam-3206	95	16	:	:	PUNCT
ejpam-3206	95	17	1	1	X
ejpam-3206	95	18	)	)	PUNCT
ejpam-3206	95	19	r	r	NOUN
ejpam-3206	95	20	is	be	AUX
ejpam-3206	95	21	an	an	DET
ejpam-3206	95	22	ni	ni	NOUN
ejpam-3206	95	23	-	-	PUNCT
ejpam-3206	95	24	ring	ring	NOUN
ejpam-3206	95	25	and	and	CCONJ
ejpam-3206	95	26	l	l	NOUN
ejpam-3206	95	27	=	=	SYM
ejpam-3206	95	28	nil(r	nil(r	PROPN
ejpam-3206	95	29	)	)	PUNCT
ejpam-3206	95	30	,	,	PUNCT
ejpam-3206	95	31	2	2	X
ejpam-3206	95	32	)	)	PUNCT
ejpam-3206	95	33	nr	nr	NOUN
ejpam-3206	95	34	(	(	PUNCT
ejpam-3206	95	35	l	l	NOUN
ejpam-3206	95	36	)	)	PUNCT
ejpam-3206	95	37	=	=	SYM
ejpam-3206	95	38	r	r	NOUN
ejpam-3206	95	39	=	=	SYM
ejpam-3206	95	40	〈	〈	PROPN
ejpam-3206	95	41	1	1	NUM
ejpam-3206	95	42	〉	〉	NUM
ejpam-3206	95	43	,	,	PUNCT
ejpam-3206	95	44	the	the	DET
ejpam-3206	95	45	principal	principal	ADJ
ejpam-3206	95	46	ideal	ideal	NOUN
ejpam-3206	95	47	generated	generate	VERB
ejpam-3206	95	48	by	by	ADP
ejpam-3206	95	49	1	1	NUM
ejpam-3206	95	50	,	,	PUNCT
ejpam-3206	95	51	which	which	PRON
ejpam-3206	95	52	proves	prove	VERB
ejpam-3206	95	53	that	that	SCONJ
ejpam-3206	95	54	a	a	DET
ejpam-3206	95	55	commutative	commutative	ADJ
ejpam-3206	95	56	local	local	ADJ
ejpam-3206	95	57	ring	ring	NOUN
ejpam-3206	95	58	is	be	AUX
ejpam-3206	95	59	a	a	DET
ejpam-3206	95	60	weak	weak	ADJ
ejpam-3206	95	61	ps	ps	NOUN
ejpam-3206	95	62	-	-	NOUN
ejpam-3206	95	63	ring	ring	NOUN
ejpam-3206	95	64	.	.	PUNCT
ejpam-3206	96	1	3	3	X
ejpam-3206	96	2	)	)	PUNCT
ejpam-3206	96	3	by	by	ADP
ejpam-3206	96	4	above	above	ADV
ejpam-3206	96	5	we	we	PRON
ejpam-3206	96	6	get	get	VERB
ejpam-3206	96	7	many	many	ADJ
ejpam-3206	96	8	examples	example	NOUN
ejpam-3206	96	9	of	of	ADP
ejpam-3206	96	10	weak	weak	ADJ
ejpam-3206	96	11	ps	ps	NOUN
ejpam-3206	96	12	-	-	PUNCT
ejpam-3206	96	13	rings	ring	NOUN
ejpam-3206	96	14	,	,	PUNCT
ejpam-3206	96	15	e.g.	e.g.	ADV
ejpam-3206	96	16	,	,	PUNCT
ejpam-3206	96	17	r	r	NOUN
ejpam-3206	96	18	=	=	PUNCT
ejpam-3206	96	19	zpn	zpn	NOUN
ejpam-3206	96	20	,	,	PUNCT
ejpam-3206	96	21	for	for	ADP
ejpam-3206	96	22	any	any	DET
ejpam-3206	96	23	prime	prime	ADJ
ejpam-3206	96	24	number	number	NOUN
ejpam-3206	96	25	p	p	NOUN
ejpam-3206	96	26	and	and	CCONJ
ejpam-3206	96	27	for	for	ADP
ejpam-3206	96	28	any	any	DET
ejpam-3206	96	29	positive	positive	ADJ
ejpam-3206	96	30	integer	integer	NOUN
ejpam-3206	96	31	n.	n.	NOUN
ejpam-3206	96	32	the	the	DET
ejpam-3206	96	33	unique	unique	ADJ
ejpam-3206	96	34	maximal	maximal	ADJ
ejpam-3206	96	35	ideal	ideal	NOUN
ejpam-3206	96	36	of	of	ADP
ejpam-3206	96	37	r	r	NOUN
ejpam-3206	96	38	=	=	PUNCT
ejpam-3206	96	39	zpn	zpn	NOUN
ejpam-3206	96	40	is	be	AUX
ejpam-3206	96	41	l	l	NOUN
ejpam-3206	96	42	=	=	PUNCT
ejpam-3206	96	43	〈	〈	PROPN
ejpam-3206	96	44	p	p	PROPN
ejpam-3206	96	45	〉	〉	PROPN
ejpam-3206	96	46	=	=	SYM
ejpam-3206	96	47	j(r	j(r	PROPN
ejpam-3206	96	48	)	)	PUNCT
ejpam-3206	96	49	.	.	PUNCT
ejpam-3206	97	1	also	also	ADV
ejpam-3206	97	2	,	,	PUNCT
ejpam-3206	97	3	a	a	DET
ejpam-3206	97	4	local	local	ADJ
ejpam-3206	97	5	domain	domain	NOUN
ejpam-3206	97	6	r	r	NOUN
ejpam-3206	97	7	=	=	SYM
ejpam-3206	97	8	f	f	X
ejpam-3206	98	1	[	[	X
ejpam-3206	98	2	[	[	X
ejpam-3206	98	3	x	x	X
ejpam-3206	98	4	]	]	X
ejpam-3206	98	5	]	]	X
ejpam-3206	98	6	,	,	PUNCT
ejpam-3206	98	7	where	where	SCONJ
ejpam-3206	98	8	f	f	PROPN
ejpam-3206	98	9	is	be	AUX
ejpam-3206	98	10	any	any	DET
ejpam-3206	98	11	field	field	NOUN
ejpam-3206	98	12	with	with	ADP
ejpam-3206	98	13	unique	unique	ADJ
ejpam-3206	98	14	maximal	maximal	ADJ
ejpam-3206	98	15	ideal	ideal	NOUN
ejpam-3206	98	16	l	l	NOUN
ejpam-3206	98	17	=	=	SYM
ejpam-3206	98	18	〈	〈	PROPN
ejpam-3206	98	19	x	x	SYM
ejpam-3206	98	20	〉	〉	NOUN
ejpam-3206	98	21	=	=	SYM
ejpam-3206	98	22	j(r	j(r	PROPN
ejpam-3206	98	23	)	)	PUNCT
ejpam-3206	98	24	.	.	PUNCT
ejpam-3206	99	1	example	example	NOUN
ejpam-3206	100	1	6	6	NUM
ejpam-3206	100	2	.	.	PUNCT
ejpam-3206	100	3	consider	consider	VERB
ejpam-3206	100	4	the	the	DET
ejpam-3206	100	5	commutative	commutative	ADJ
ejpam-3206	100	6	reduced	reduce	VERB
ejpam-3206	100	7	ring	ring	NOUN
ejpam-3206	100	8	r	r	NOUN
ejpam-3206	100	9	=	=	SYM
ejpam-3206	100	10	z6	z6	PROPN
ejpam-3206	100	11	,	,	PUNCT
ejpam-3206	100	12	since	since	SCONJ
ejpam-3206	100	13	nil(r	nil(r	PROPN
ejpam-3206	100	14	)	)	PUNCT
ejpam-3206	100	15	=	=	PRON
ejpam-3206	100	16	{	{	PUNCT
ejpam-3206	100	17	0	0	NUM
ejpam-3206	100	18	}	}	PUNCT
ejpam-3206	100	19	.	.	PUNCT
ejpam-3206	101	1	r	r	NOUN
ejpam-3206	101	2	has	have	VERB
ejpam-3206	101	3	two	two	NUM
ejpam-3206	101	4	maximal	maximal	ADJ
ejpam-3206	101	5	ideals	ideal	NOUN
ejpam-3206	101	6	which	which	PRON
ejpam-3206	101	7	are	be	AUX
ejpam-3206	101	8	l1	l1	PROPN
ejpam-3206	101	9	=	=	SYM
ejpam-3206	101	10	{	{	PUNCT
ejpam-3206	101	11	0	0	NUM
ejpam-3206	101	12	,	,	PUNCT
ejpam-3206	101	13	2	2	NUM
ejpam-3206	101	14	,	,	PUNCT
ejpam-3206	101	15	4	4	NUM
ejpam-3206	101	16	}	}	PUNCT
ejpam-3206	101	17	and	and	CCONJ
ejpam-3206	101	18	l2	l2	NOUN
ejpam-3206	101	19	=	=	SYM
ejpam-3206	101	20	{	{	PUNCT
ejpam-3206	101	21	0	0	NUM
ejpam-3206	101	22	,	,	PUNCT
ejpam-3206	101	23	3	3	NUM
ejpam-3206	101	24	}	}	PUNCT
ejpam-3206	101	25	.	.	PUNCT
ejpam-3206	102	1	note	note	VERB
ejpam-3206	102	2	that	that	SCONJ
ejpam-3206	102	3	id(r	id(r	NOUN
ejpam-3206	102	4	)	)	PUNCT
ejpam-3206	102	5	=	=	PUNCT
ejpam-3206	102	6	{	{	PUNCT
ejpam-3206	102	7	0	0	NUM
ejpam-3206	102	8	,	,	PUNCT
ejpam-3206	102	9	1	1	NUM
ejpam-3206	102	10	,	,	PUNCT
ejpam-3206	102	11	3	3	NUM
ejpam-3206	102	12	,	,	PUNCT
ejpam-3206	102	13	4	4	NUM
ejpam-3206	102	14	}	}	PUNCT
ejpam-3206	102	15	.	.	PUNCT
ejpam-3206	103	1	now	now	ADV
ejpam-3206	103	2	we	we	PRON
ejpam-3206	103	3	compute	compute	VERB
ejpam-3206	103	4	the	the	DET
ejpam-3206	103	5	weak	weak	ADJ
ejpam-3206	103	6	annihilator	annihilator	NOUN
ejpam-3206	103	7	for	for	ADP
ejpam-3206	103	8	these	these	DET
ejpam-3206	103	9	ideals	ideal	NOUN
ejpam-3206	103	10	as	as	SCONJ
ejpam-3206	103	11	follows	follow	VERB
ejpam-3206	103	12	:	:	PUNCT
ejpam-3206	103	13	nr	nr	PROPN
ejpam-3206	103	14	(	(	PUNCT
ejpam-3206	103	15	l1	l1	PROPN
ejpam-3206	103	16	)	)	PUNCT
ejpam-3206	103	17	=	=	PUNCT
ejpam-3206	103	18	`	`	PUNCT
ejpam-3206	103	19	r(l1	r(l1	PROPN
ejpam-3206	103	20	)	)	PUNCT
ejpam-3206	103	21	=	=	SYM
ejpam-3206	103	22	rr(l1	rr(l1	NOUN
ejpam-3206	103	23	)	)	PUNCT
ejpam-3206	103	24	=	=	SYM
ejpam-3206	103	25	l2	l2	NOUN
ejpam-3206	103	26	=	=	SYM
ejpam-3206	103	27	{	{	PUNCT
ejpam-3206	103	28	0	0	NUM
ejpam-3206	103	29	,	,	PUNCT
ejpam-3206	103	30	3	3	NUM
ejpam-3206	103	31	}	}	PUNCT
ejpam-3206	103	32	=	=	PUNCT
ejpam-3206	103	33	〈	〈	PROPN
ejpam-3206	103	34	3	3	NUM
ejpam-3206	103	35	〉	〉	NOUN
ejpam-3206	103	36	,	,	PUNCT
ejpam-3206	103	37	and	and	CCONJ
ejpam-3206	103	38	nr	nr	PROPN
ejpam-3206	103	39	(	(	PUNCT
ejpam-3206	103	40	l2	l2	PROPN
ejpam-3206	103	41	)	)	PUNCT
ejpam-3206	103	42	=	=	PUNCT
ejpam-3206	103	43	`	`	PUNCT
ejpam-3206	103	44	r(l2	r(l2	NOUN
ejpam-3206	103	45	)	)	PUNCT
ejpam-3206	103	46	=	=	SYM
ejpam-3206	104	1	rr(l2	rr(l2	NOUN
ejpam-3206	104	2	)	)	PUNCT
ejpam-3206	104	3	=	=	SYM
ejpam-3206	104	4	l1	l1	PROPN
ejpam-3206	104	5	=	=	SYM
ejpam-3206	104	6	{	{	PUNCT
ejpam-3206	104	7	0	0	NUM
ejpam-3206	104	8	,	,	PUNCT
ejpam-3206	104	9	2	2	NUM
ejpam-3206	104	10	,	,	PUNCT
ejpam-3206	104	11	4	4	NUM
ejpam-3206	104	12	}	}	PUNCT
ejpam-3206	104	13	=	=	PUNCT
ejpam-3206	104	14	〈	〈	PROPN
ejpam-3206	104	15	4	4	NUM
ejpam-3206	104	16	〉	〉	NOUN
ejpam-3206	104	17	.	.	PUNCT
ejpam-3206	105	1	hence	hence	ADV
ejpam-3206	105	2	z6	z6	PROPN
ejpam-3206	105	3	is	be	AUX
ejpam-3206	105	4	a	a	DET
ejpam-3206	105	5	(	(	PUNCT
ejpam-3206	105	6	weak	weak	ADJ
ejpam-3206	105	7	)	)	PUNCT
ejpam-3206	105	8	ps	ps	NOUN
ejpam-3206	105	9	-	-	PUNCT
ejpam-3206	105	10	ring	ring	NOUN
ejpam-3206	105	11	.	.	PUNCT
ejpam-3206	105	12	example	example	NOUN
ejpam-3206	106	1	7	7	NUM
ejpam-3206	106	2	.	.	X
ejpam-3206	106	3	consider	consider	VERB
ejpam-3206	106	4	the	the	DET
ejpam-3206	106	5	commutative	commutative	ADJ
ejpam-3206	106	6	reduced	reduce	VERB
ejpam-3206	106	7	ring	ring	NOUN
ejpam-3206	106	8	r	r	NOUN
ejpam-3206	106	9	=	=	SYM
ejpam-3206	106	10	z10	z10	NOUN
ejpam-3206	106	11	with	with	ADP
ejpam-3206	106	12	nil(r	nil(r	NOUN
ejpam-3206	106	13	)	)	PUNCT
ejpam-3206	106	14	=	=	PRON
ejpam-3206	106	15	{	{	PUNCT
ejpam-3206	106	16	0	0	NUM
ejpam-3206	106	17	}	}	PUNCT
ejpam-3206	106	18	and	and	CCONJ
ejpam-3206	106	19	id(r	id(r	NOUN
ejpam-3206	106	20	)	)	PUNCT
ejpam-3206	106	21	=	=	PUNCT
ejpam-3206	106	22	{	{	PUNCT
ejpam-3206	106	23	0	0	NUM
ejpam-3206	106	24	,	,	PUNCT
ejpam-3206	106	25	5	5	NUM
ejpam-3206	106	26	,	,	PUNCT
ejpam-3206	106	27	6	6	NUM
ejpam-3206	106	28	}	}	PUNCT
ejpam-3206	106	29	.	.	PUNCT
ejpam-3206	107	1	we	we	PRON
ejpam-3206	107	2	can	can	AUX
ejpam-3206	107	3	check	check	VERB
ejpam-3206	107	4	that	that	PRON
ejpam-3206	107	5	,	,	PUNCT
ejpam-3206	107	6	r	r	NOUN
ejpam-3206	107	7	has	have	VERB
ejpam-3206	107	8	two	two	NUM
ejpam-3206	107	9	maximal	maximal	ADJ
ejpam-3206	107	10	ideals	ideal	NOUN
ejpam-3206	107	11	only	only	ADV
ejpam-3206	107	12	which	which	PRON
ejpam-3206	107	13	are	be	AUX
ejpam-3206	107	14	l1	l1	PROPN
ejpam-3206	107	15	=	=	SYM
ejpam-3206	107	16	{	{	PUNCT
ejpam-3206	107	17	0	0	NUM
ejpam-3206	107	18	,	,	PUNCT
ejpam-3206	107	19	2	2	NUM
ejpam-3206	107	20	,	,	PUNCT
ejpam-3206	107	21	4	4	NUM
ejpam-3206	107	22	,	,	PUNCT
ejpam-3206	107	23	6	6	NUM
ejpam-3206	107	24	,	,	PUNCT
ejpam-3206	107	25	8	8	NUM
ejpam-3206	107	26	}	}	PUNCT
ejpam-3206	107	27	and	and	CCONJ
ejpam-3206	107	28	l2	l2	NOUN
ejpam-3206	107	29	=	=	SYM
ejpam-3206	107	30	{	{	PUNCT
ejpam-3206	107	31	0	0	NUM
ejpam-3206	107	32	,	,	PUNCT
ejpam-3206	107	33	5	5	NUM
ejpam-3206	107	34	}	}	PUNCT
ejpam-3206	107	35	.	.	PUNCT
ejpam-3206	108	1	now	now	ADV
ejpam-3206	108	2	we	we	PRON
ejpam-3206	108	3	compute	compute	VERB
ejpam-3206	108	4	the	the	DET
ejpam-3206	108	5	weak	weak	ADJ
ejpam-3206	108	6	annihilator	annihilator	NOUN
ejpam-3206	108	7	for	for	ADP
ejpam-3206	108	8	these	these	DET
ejpam-3206	108	9	two	two	NUM
ejpam-3206	108	10	ideals	ideal	NOUN
ejpam-3206	108	11	as	as	SCONJ
ejpam-3206	108	12	follows	follow	VERB
ejpam-3206	108	13	:	:	PUNCT
ejpam-3206	108	14	nr	nr	PROPN
ejpam-3206	108	15	(	(	PUNCT
ejpam-3206	108	16	l1	l1	PROPN
ejpam-3206	108	17	)	)	PUNCT
ejpam-3206	108	18	=	=	SYM
ejpam-3206	108	19	l2	l2	NOUN
ejpam-3206	108	20	=	=	SYM
ejpam-3206	108	21	{	{	PUNCT
ejpam-3206	108	22	0	0	NUM
ejpam-3206	108	23	,	,	PUNCT
ejpam-3206	108	24	5	5	NUM
ejpam-3206	108	25	}	}	PUNCT
ejpam-3206	108	26	=	=	PUNCT
ejpam-3206	108	27	〈	〈	PROPN
ejpam-3206	108	28	5	5	NUM
ejpam-3206	108	29	〉	〉	NOUN
ejpam-3206	108	30	,	,	PUNCT
ejpam-3206	108	31	m.	m.	NOUN
ejpam-3206	108	32	a.	a.	NOUN
ejpam-3206	108	33	farahat	farahat	PROPN
ejpam-3206	108	34	,	,	PUNCT
ejpam-3206	108	35	s.	s.	PROPN
ejpam-3206	108	36	t.	t.	PROPN
ejpam-3206	108	37	al	al	PROPN
ejpam-3206	108	38	-	-	PUNCT
ejpam-3206	108	39	bogamy	bogamy	PROPN
ejpam-3206	108	40	/	/	SYM
ejpam-3206	108	41	eur	eur	PROPN
ejpam-3206	108	42	.	.	PUNCT
ejpam-3206	109	1	j.	j.	PROPN
ejpam-3206	109	2	pure	pure	PROPN
ejpam-3206	109	3	appl	appl	PROPN
ejpam-3206	109	4	.	.	PROPN
ejpam-3206	109	5	math	math	PROPN
ejpam-3206	109	6	,	,	PUNCT
ejpam-3206	109	7	11	11	NUM
ejpam-3206	109	8	(	(	PUNCT
ejpam-3206	109	9	1	1	NUM
ejpam-3206	109	10	)	)	PUNCT
ejpam-3206	109	11	(	(	PUNCT
ejpam-3206	109	12	2018	2018	NUM
ejpam-3206	109	13	)	)	PUNCT
ejpam-3206	109	14	,	,	PUNCT
ejpam-3206	109	15	244	244	NUM
ejpam-3206	109	16	-	-	SYM
ejpam-3206	109	17	259	259	NUM
ejpam-3206	109	18	248	248	NUM
ejpam-3206	109	19	and	and	CCONJ
ejpam-3206	109	20	nr	nr	PRON
ejpam-3206	109	21	(	(	PUNCT
ejpam-3206	109	22	l2	l2	PROPN
ejpam-3206	109	23	)	)	PUNCT
ejpam-3206	109	24	=	=	SYM
ejpam-3206	109	25	l1	l1	PROPN
ejpam-3206	109	26	=	=	SYM
ejpam-3206	109	27	{	{	PUNCT
ejpam-3206	109	28	0	0	NUM
ejpam-3206	109	29	,	,	PUNCT
ejpam-3206	109	30	2	2	NUM
ejpam-3206	109	31	,	,	PUNCT
ejpam-3206	109	32	4	4	NUM
ejpam-3206	109	33	,	,	PUNCT
ejpam-3206	109	34	6	6	NUM
ejpam-3206	109	35	,	,	PUNCT
ejpam-3206	109	36	8	8	NUM
ejpam-3206	109	37	}	}	PUNCT
ejpam-3206	109	38	=	=	SYM
ejpam-3206	109	39	〈	〈	PROPN
ejpam-3206	109	40	6	6	NUM
ejpam-3206	109	41	〉	〉	NOUN
ejpam-3206	109	42	.	.	PUNCT
ejpam-3206	110	1	hence	hence	ADV
ejpam-3206	110	2	z10	z10	NOUN
ejpam-3206	110	3	is	be	AUX
ejpam-3206	110	4	a	a	DET
ejpam-3206	110	5	(	(	PUNCT
ejpam-3206	110	6	weak	weak	ADJ
ejpam-3206	110	7	)	)	PUNCT
ejpam-3206	110	8	ps	ps	NOUN
ejpam-3206	110	9	-	-	PUNCT
ejpam-3206	110	10	ring	ring	NOUN
ejpam-3206	110	11	.	.	PUNCT
ejpam-3206	110	12	example	example	NOUN
ejpam-3206	110	13	8	8	NUM
ejpam-3206	110	14	.	.	PUNCT
ejpam-3206	111	1	consider	consider	VERB
ejpam-3206	111	2	the	the	DET
ejpam-3206	111	3	commutative	commutative	ADJ
ejpam-3206	111	4	nonreduced	nonreduce	VERB
ejpam-3206	111	5	ring	ring	NOUN
ejpam-3206	111	6	r	r	NOUN
ejpam-3206	111	7	=	=	SYM
ejpam-3206	111	8	z12	z12	PROPN
ejpam-3206	111	9	with	with	ADP
ejpam-3206	111	10	nil(r	nil(r	NOUN
ejpam-3206	111	11	)	)	PUNCT
ejpam-3206	111	12	=	=	PRON
ejpam-3206	111	13	{	{	PUNCT
ejpam-3206	111	14	0	0	NUM
ejpam-3206	111	15	,	,	PUNCT
ejpam-3206	111	16	6	6	NUM
ejpam-3206	111	17	}	}	PUNCT
ejpam-3206	111	18	and	and	CCONJ
ejpam-3206	111	19	id(r	id(r	NOUN
ejpam-3206	111	20	)	)	PUNCT
ejpam-3206	111	21	=	=	PUNCT
ejpam-3206	112	1	{	{	PUNCT
ejpam-3206	112	2	0	0	NUM
ejpam-3206	112	3	,	,	PUNCT
ejpam-3206	112	4	1	1	NUM
ejpam-3206	112	5	,	,	PUNCT
ejpam-3206	112	6	9	9	NUM
ejpam-3206	112	7	}	}	PUNCT
ejpam-3206	112	8	.	.	PUNCT
ejpam-3206	113	1	we	we	PRON
ejpam-3206	113	2	can	can	AUX
ejpam-3206	113	3	check	check	VERB
ejpam-3206	113	4	that	that	PRON
ejpam-3206	113	5	,	,	PUNCT
ejpam-3206	113	6	r	r	NOUN
ejpam-3206	113	7	has	have	VERB
ejpam-3206	113	8	two	two	NUM
ejpam-3206	113	9	maximal	maximal	ADJ
ejpam-3206	113	10	ideals	ideal	NOUN
ejpam-3206	113	11	only	only	ADV
ejpam-3206	113	12	which	which	PRON
ejpam-3206	113	13	are	be	AUX
ejpam-3206	113	14	l1	l1	PROPN
ejpam-3206	113	15	=	=	SYM
ejpam-3206	113	16	{	{	PUNCT
ejpam-3206	113	17	0	0	NUM
ejpam-3206	113	18	,	,	PUNCT
ejpam-3206	113	19	2	2	NUM
ejpam-3206	113	20	,	,	PUNCT
ejpam-3206	113	21	4	4	NUM
ejpam-3206	113	22	,	,	PUNCT
ejpam-3206	113	23	6	6	NUM
ejpam-3206	113	24	,	,	PUNCT
ejpam-3206	113	25	8	8	NUM
ejpam-3206	113	26	,	,	PUNCT
ejpam-3206	113	27	10	10	NUM
ejpam-3206	113	28	}	}	PUNCT
ejpam-3206	113	29	and	and	CCONJ
ejpam-3206	113	30	l2	l2	NOUN
ejpam-3206	113	31	=	=	SYM
ejpam-3206	113	32	{	{	PUNCT
ejpam-3206	113	33	0	0	NUM
ejpam-3206	113	34	,	,	PUNCT
ejpam-3206	113	35	3	3	NUM
ejpam-3206	113	36	,	,	PUNCT
ejpam-3206	113	37	6	6	NUM
ejpam-3206	113	38	,	,	PUNCT
ejpam-3206	113	39	9	9	NUM
ejpam-3206	113	40	}	}	PUNCT
ejpam-3206	113	41	.	.	PUNCT
ejpam-3206	114	1	now	now	ADV
ejpam-3206	114	2	we	we	PRON
ejpam-3206	114	3	compute	compute	VERB
ejpam-3206	114	4	the	the	DET
ejpam-3206	114	5	weak	weak	ADJ
ejpam-3206	114	6	annihilator	annihilator	NOUN
ejpam-3206	114	7	for	for	ADP
ejpam-3206	114	8	these	these	DET
ejpam-3206	114	9	two	two	NUM
ejpam-3206	114	10	ideals	ideal	NOUN
ejpam-3206	114	11	as	as	SCONJ
ejpam-3206	114	12	follows	follow	VERB
ejpam-3206	114	13	:	:	PUNCT
ejpam-3206	114	14	nr	nr	PROPN
ejpam-3206	114	15	(	(	PUNCT
ejpam-3206	114	16	l1	l1	PROPN
ejpam-3206	114	17	)	)	PUNCT
ejpam-3206	114	18	=	=	SYM
ejpam-3206	114	19	l2	l2	NOUN
ejpam-3206	114	20	=	=	SYM
ejpam-3206	114	21	{	{	PUNCT
ejpam-3206	114	22	0	0	NUM
ejpam-3206	114	23	,	,	PUNCT
ejpam-3206	114	24	3	3	NUM
ejpam-3206	114	25	,	,	PUNCT
ejpam-3206	114	26	6	6	NUM
ejpam-3206	114	27	,	,	PUNCT
ejpam-3206	114	28	9	9	NUM
ejpam-3206	114	29	}	}	PUNCT
ejpam-3206	114	30	=	=	PUNCT
ejpam-3206	114	31	〈	〈	PROPN
ejpam-3206	114	32	9	9	NUM
ejpam-3206	114	33	〉	〉	NOUN
ejpam-3206	114	34	,	,	PUNCT
ejpam-3206	114	35	and	and	CCONJ
ejpam-3206	114	36	nr	nr	PROPN
ejpam-3206	114	37	(	(	PUNCT
ejpam-3206	114	38	l2	l2	PROPN
ejpam-3206	114	39	)	)	PUNCT
ejpam-3206	114	40	=	=	SYM
ejpam-3206	114	41	l1	l1	PROPN
ejpam-3206	114	42	=	=	SYM
ejpam-3206	114	43	{	{	PUNCT
ejpam-3206	114	44	0	0	NUM
ejpam-3206	114	45	,	,	PUNCT
ejpam-3206	114	46	2	2	NUM
ejpam-3206	114	47	,	,	PUNCT
ejpam-3206	114	48	4	4	NUM
ejpam-3206	114	49	,	,	PUNCT
ejpam-3206	114	50	6	6	NUM
ejpam-3206	114	51	,	,	PUNCT
ejpam-3206	114	52	8	8	NUM
ejpam-3206	114	53	,	,	PUNCT
ejpam-3206	114	54	10	10	NUM
ejpam-3206	114	55	}	}	PUNCT
ejpam-3206	114	56	=	=	PUNCT
ejpam-3206	114	57	〈	〈	PROPN
ejpam-3206	114	58	2	2	NUM
ejpam-3206	114	59	〉	〉	NOUN
ejpam-3206	114	60	=	=	SYM
ejpam-3206	114	61	〈	〈	PROPN
ejpam-3206	114	62	10	10	NUM
ejpam-3206	114	63	〉	〉	NOUN
ejpam-3206	114	64	.	.	PUNCT
ejpam-3206	115	1	clearly	clearly	ADV
ejpam-3206	115	2	,	,	PUNCT
ejpam-3206	115	3	nr	nr	PROPN
ejpam-3206	115	4	(	(	PUNCT
ejpam-3206	115	5	l2	l2	PROPN
ejpam-3206	115	6	)	)	PUNCT
ejpam-3206	115	7	"	"	PUNCT
ejpam-3206	115	8	nil(r	nil(r	NOUN
ejpam-3206	115	9	)	)	PUNCT
ejpam-3206	115	10	and	and	CCONJ
ejpam-3206	115	11	nr	nr	PROPN
ejpam-3206	115	12	(	(	PUNCT
ejpam-3206	115	13	l2	l2	PROPN
ejpam-3206	115	14	)	)	PUNCT
ejpam-3206	115	15	not	not	PART
ejpam-3206	115	16	generated	generate	VERB
ejpam-3206	115	17	by	by	ADP
ejpam-3206	115	18	an	an	DET
ejpam-3206	115	19	idempotent	idempotent	NOUN
ejpam-3206	115	20	in	in	ADP
ejpam-3206	115	21	r.	r.	PROPN
ejpam-3206	115	22	hence	hence	ADV
ejpam-3206	115	23	z12	z12	PROPN
ejpam-3206	115	24	is	be	AUX
ejpam-3206	115	25	not	not	PART
ejpam-3206	115	26	a	a	DET
ejpam-3206	115	27	weak	weak	ADJ
ejpam-3206	115	28	ps	ps	NOUN
ejpam-3206	115	29	-	-	PUNCT
ejpam-3206	115	30	ring	ring	NOUN
ejpam-3206	115	31	.	.	PUNCT
ejpam-3206	116	1	now	now	ADV
ejpam-3206	116	2	we	we	PRON
ejpam-3206	116	3	turn	turn	VERB
ejpam-3206	116	4	to	to	PART
ejpam-3206	116	5	compute	compute	VERB
ejpam-3206	116	6	the	the	DET
ejpam-3206	116	7	left	left	ADJ
ejpam-3206	116	8	(	(	PUNCT
ejpam-3206	116	9	right	right	ADJ
ejpam-3206	116	10	)	)	PUNCT
ejpam-3206	116	11	annihilator	annihilator	NOUN
ejpam-3206	116	12	for	for	ADP
ejpam-3206	116	13	these	these	DET
ejpam-3206	116	14	maximal	maximal	ADJ
ejpam-3206	116	15	two	two	NUM
ejpam-3206	116	16	-	-	PUNCT
ejpam-3206	116	17	sided	sided	ADJ
ejpam-3206	116	18	ideals	ideal	NOUN
ejpam-3206	116	19	as	as	SCONJ
ejpam-3206	116	20	follows	follow	VERB
ejpam-3206	116	21	:	:	PUNCT
ejpam-3206	116	22	`	`	PUNCT
ejpam-3206	117	1	r	r	NOUN
ejpam-3206	117	2	(	(	PUNCT
ejpam-3206	117	3	l1	l1	PROPN
ejpam-3206	117	4	)	)	PUNCT
ejpam-3206	117	5	=	=	SYM
ejpam-3206	117	6	rr(l1	rr(l1	NOUN
ejpam-3206	117	7	)	)	PUNCT
ejpam-3206	117	8	=	=	PUNCT
ejpam-3206	117	9	{	{	PUNCT
ejpam-3206	117	10	0	0	NUM
ejpam-3206	117	11	,	,	PUNCT
ejpam-3206	117	12	6	6	NUM
ejpam-3206	117	13	}	}	PUNCT
ejpam-3206	117	14	=	=	SYM
ejpam-3206	117	15	nil(r	nil(r	PROPN
ejpam-3206	117	16	)	)	PUNCT
ejpam-3206	117	17	.	.	PUNCT
ejpam-3206	118	1	which	which	PRON
ejpam-3206	118	2	is	be	AUX
ejpam-3206	118	3	not	not	PART
ejpam-3206	118	4	generated	generate	VERB
ejpam-3206	118	5	by	by	ADP
ejpam-3206	118	6	an	an	DET
ejpam-3206	118	7	idempotent	idempotent	ADJ
ejpam-3206	118	8	element	element	NOUN
ejpam-3206	118	9	in	in	ADP
ejpam-3206	118	10	r	r	NOUN
ejpam-3206	118	11	,	,	PUNCT
ejpam-3206	118	12	and	and	CCONJ
ejpam-3206	118	13	`	`	PUNCT
ejpam-3206	118	14	r	r	NOUN
ejpam-3206	118	15	(	(	PUNCT
ejpam-3206	118	16	l2	l2	NOUN
ejpam-3206	118	17	)	)	PUNCT
ejpam-3206	119	1	=	=	SYM
ejpam-3206	119	2	rr(l2	rr(l2	NOUN
ejpam-3206	119	3	)	)	PUNCT
ejpam-3206	119	4	=	=	PUNCT
ejpam-3206	119	5	〈	〈	PROPN
ejpam-3206	119	6	0	0	NUM
ejpam-3206	119	7	〉	〉	NOUN
ejpam-3206	119	8	.	.	PUNCT
ejpam-3206	120	1	hence	hence	ADV
ejpam-3206	120	2	z12	z12	PROPN
ejpam-3206	120	3	is	be	AUX
ejpam-3206	120	4	not	not	PART
ejpam-3206	120	5	a	a	DET
ejpam-3206	120	6	ps	ps	NOUN
ejpam-3206	120	7	-	-	PUNCT
ejpam-3206	120	8	ring	ring	NOUN
ejpam-3206	120	9	.	.	PUNCT
ejpam-3206	120	10	example	example	NOUN
ejpam-3206	121	1	9	9	NUM
ejpam-3206	121	2	.	.	PUNCT
ejpam-3206	122	1	let	let	VERB
ejpam-3206	122	2	f	f	PRON
ejpam-3206	122	3	be	be	AUX
ejpam-3206	122	4	a	a	DET
ejpam-3206	122	5	field	field	NOUN
ejpam-3206	122	6	and	and	CCONJ
ejpam-3206	122	7	r	r	NOUN
ejpam-3206	122	8	=	=	SYM
ejpam-3206	122	9	(	(	PUNCT
ejpam-3206	122	10	f	f	NOUN
ejpam-3206	122	11	f	f	PROPN
ejpam-3206	122	12	f	f	PROPN
ejpam-3206	122	13	f	f	PROPN
ejpam-3206	122	14	)	)	PUNCT
ejpam-3206	122	15	.	.	PUNCT
ejpam-3206	123	1	the	the	DET
ejpam-3206	123	2	only	only	ADJ
ejpam-3206	123	3	maximal	maximal	ADJ
ejpam-3206	123	4	right	right	ADJ
ejpam-3206	123	5	ideals	ideal	NOUN
ejpam-3206	123	6	(	(	PUNCT
ejpam-3206	123	7	which	which	PRON
ejpam-3206	123	8	are	be	AUX
ejpam-3206	123	9	not	not	PART
ejpam-3206	123	10	left	leave	VERB
ejpam-3206	123	11	ideals	ideal	NOUN
ejpam-3206	123	12	)	)	PUNCT
ejpam-3206	123	13	of	of	ADP
ejpam-3206	123	14	r	r	NOUN
ejpam-3206	123	15	are	be	AUX
ejpam-3206	123	16	:	:	PUNCT
ejpam-3206	123	17	l1	l1	PROPN
ejpam-3206	123	18	=	=	PUNCT
ejpam-3206	124	1	(	(	PUNCT
ejpam-3206	124	2	f	f	NOUN
ejpam-3206	124	3	f	f	PROPN
ejpam-3206	124	4	0	0	PROPN
ejpam-3206	124	5	0	0	NUM
ejpam-3206	124	6	)	)	PUNCT
ejpam-3206	124	7	&	&	CCONJ
ejpam-3206	124	8	l2	l2	NOUN
ejpam-3206	124	9	=	=	SYM
ejpam-3206	124	10	(	(	PUNCT
ejpam-3206	124	11	0	0	NUM
ejpam-3206	124	12	0	0	NUM
ejpam-3206	124	13	f	f	PROPN
ejpam-3206	124	14	f	f	PROPN
ejpam-3206	124	15	)	)	PUNCT
ejpam-3206	124	16	,	,	PUNCT
ejpam-3206	124	17	also	also	ADV
ejpam-3206	124	18	,	,	PUNCT
ejpam-3206	124	19	j1	j1	PROPN
ejpam-3206	124	20	=	=	PUNCT
ejpam-3206	124	21	(	(	PUNCT
ejpam-3206	124	22	f	f	PROPN
ejpam-3206	124	23	0	0	PUNCT
ejpam-3206	124	24	f	f	PROPN
ejpam-3206	124	25	0	0	NUM
ejpam-3206	124	26	)	)	PUNCT
ejpam-3206	124	27	&	&	CCONJ
ejpam-3206	124	28	j2	j2	PROPN
ejpam-3206	124	29	=	=	SYM
ejpam-3206	124	30	(	(	PUNCT
ejpam-3206	124	31	0	0	NUM
ejpam-3206	124	32	f	f	NOUN
ejpam-3206	124	33	0	0	NUM
ejpam-3206	124	34	f	f	PROPN
ejpam-3206	124	35	)	)	PUNCT
ejpam-3206	124	36	,	,	PUNCT
ejpam-3206	124	37	are	be	AUX
ejpam-3206	124	38	the	the	DET
ejpam-3206	124	39	only	only	ADJ
ejpam-3206	124	40	maximal	maximal	ADJ
ejpam-3206	124	41	left	leave	VERB
ejpam-3206	124	42	ideals	ideal	NOUN
ejpam-3206	124	43	(	(	PUNCT
ejpam-3206	124	44	which	which	PRON
ejpam-3206	124	45	are	be	AUX
ejpam-3206	124	46	not	not	PART
ejpam-3206	124	47	right	right	ADJ
ejpam-3206	124	48	ideals	ideal	NOUN
ejpam-3206	124	49	)	)	PUNCT
ejpam-3206	124	50	of	of	ADP
ejpam-3206	124	51	r.	r.	PROPN
ejpam-3206	124	52	nil	nil	PROPN
ejpam-3206	124	53	(	(	PUNCT
ejpam-3206	124	54	r	r	NOUN
ejpam-3206	124	55	)	)	PUNCT
ejpam-3206	124	56	=	=	SYM
ejpam-3206	124	57	(	(	PUNCT
ejpam-3206	124	58	0	0	NUM
ejpam-3206	124	59	f	f	NOUN
ejpam-3206	124	60	0	0	NUM
ejpam-3206	124	61	0	0	NUM
ejpam-3206	124	62	)	)	PUNCT
ejpam-3206	124	63	⋃	⋃	PROPN
ejpam-3206	124	64	(	(	PUNCT
ejpam-3206	124	65	0	0	NUM
ejpam-3206	124	66	0	0	NUM
ejpam-3206	124	67	f	f	NOUN
ejpam-3206	124	68	0	0	NUM
ejpam-3206	124	69	)	)	PUNCT
ejpam-3206	124	70	,	,	PUNCT
ejpam-3206	124	71	which	which	PRON
ejpam-3206	124	72	is	be	AUX
ejpam-3206	124	73	neither	neither	CCONJ
ejpam-3206	124	74	a	a	DET
ejpam-3206	124	75	left	left	NOUN
ejpam-3206	124	76	nor	nor	CCONJ
ejpam-3206	124	77	a	a	DET
ejpam-3206	124	78	right	right	ADJ
ejpam-3206	124	79	ideal	ideal	NOUN
ejpam-3206	124	80	of	of	ADP
ejpam-3206	124	81	r.	r.	PROPN
ejpam-3206	124	82	hence	hence	ADV
ejpam-3206	124	83	r	r	NOUN
ejpam-3206	124	84	is	be	AUX
ejpam-3206	124	85	not	not	PART
ejpam-3206	124	86	an	an	DET
ejpam-3206	124	87	ni	ni	NOUN
ejpam-3206	124	88	-	-	NOUN
ejpam-3206	124	89	ring	ring	NOUN
ejpam-3206	124	90	.	.	PUNCT
ejpam-3206	125	1	we	we	PRON
ejpam-3206	125	2	can	can	AUX
ejpam-3206	125	3	check	check	VERB
ejpam-3206	125	4	the	the	DET
ejpam-3206	125	5	following	follow	VERB
ejpam-3206	125	6	facts	fact	NOUN
ejpam-3206	125	7	:	:	PUNCT
ejpam-3206	125	8	1	1	NUM
ejpam-3206	125	9	)	)	PUNCT
ejpam-3206	125	10	nr(l1	nr(l1	X
ejpam-3206	125	11	)	)	PUNCT
ejpam-3206	125	12	=	=	SYM
ejpam-3206	125	13	j2	j2	NOUN
ejpam-3206	125	14	=	=	SYM
ejpam-3206	125	15	re	re	X
ejpam-3206	125	16	where	where	SCONJ
ejpam-3206	125	17	e	e	X
ejpam-3206	125	18	=	=	PRON
ejpam-3206	125	19	(	(	PUNCT
ejpam-3206	125	20	0	0	NUM
ejpam-3206	125	21	1	1	NUM
ejpam-3206	125	22	0	0	NUM
ejpam-3206	125	23	1	1	NUM
ejpam-3206	125	24	)	)	PUNCT
ejpam-3206	125	25	∈	∈	PROPN
ejpam-3206	125	26	id(r	id(r	NOUN
ejpam-3206	125	27	)	)	PUNCT
ejpam-3206	125	28	,	,	PUNCT
ejpam-3206	125	29	2	2	X
ejpam-3206	125	30	)	)	PUNCT
ejpam-3206	125	31	nr(l2	nr(l2	NOUN
ejpam-3206	125	32	)	)	PUNCT
ejpam-3206	125	33	=	=	SYM
ejpam-3206	125	34	j1	j1	PROPN
ejpam-3206	125	35	=	=	PUNCT
ejpam-3206	125	36	rf	rf	ADJ
ejpam-3206	125	37	where	where	SCONJ
ejpam-3206	125	38	f	f	AUX
ejpam-3206	125	39	=	=	PRON
ejpam-3206	125	40	(	(	PUNCT
ejpam-3206	125	41	1	1	NUM
ejpam-3206	125	42	0	0	NUM
ejpam-3206	125	43	1	1	NUM
ejpam-3206	125	44	0	0	NUM
ejpam-3206	125	45	)	)	PUNCT
ejpam-3206	125	46	∈	∈	PROPN
ejpam-3206	125	47	id(r	id(r	NOUN
ejpam-3206	125	48	)	)	PUNCT
ejpam-3206	125	49	.	.	PUNCT
ejpam-3206	126	1	using	use	VERB
ejpam-3206	126	2	the	the	DET
ejpam-3206	126	3	above	above	ADJ
ejpam-3206	126	4	discussion	discussion	NOUN
ejpam-3206	126	5	,	,	PUNCT
ejpam-3206	126	6	we	we	PRON
ejpam-3206	126	7	conclude	conclude	VERB
ejpam-3206	126	8	that	that	SCONJ
ejpam-3206	126	9	r	r	NOUN
ejpam-3206	126	10	is	be	AUX
ejpam-3206	126	11	a	a	DET
ejpam-3206	126	12	weak	weak	ADJ
ejpam-3206	126	13	right	right	ADJ
ejpam-3206	126	14	ps	ps	NOUN
ejpam-3206	126	15	-	-	NOUN
ejpam-3206	126	16	ring	ring	NOUN
ejpam-3206	126	17	.	.	PUNCT
ejpam-3206	127	1	by	by	ADP
ejpam-3206	127	2	the	the	DET
ejpam-3206	127	3	same	same	ADJ
ejpam-3206	127	4	way	way	NOUN
ejpam-3206	127	5	we	we	PRON
ejpam-3206	127	6	can	can	AUX
ejpam-3206	127	7	check	check	VERB
ejpam-3206	127	8	the	the	DET
ejpam-3206	127	9	following	following	NOUN
ejpam-3206	127	10	:	:	PUNCT
ejpam-3206	127	11	m.	m.	NOUN
ejpam-3206	127	12	a.	a.	PROPN
ejpam-3206	127	13	farahat	farahat	PROPN
ejpam-3206	127	14	,	,	PUNCT
ejpam-3206	127	15	s.	s.	PROPN
ejpam-3206	127	16	t.	t.	PROPN
ejpam-3206	127	17	al	al	PROPN
ejpam-3206	127	18	-	-	PUNCT
ejpam-3206	127	19	bogamy	bogamy	PROPN
ejpam-3206	127	20	/	/	SYM
ejpam-3206	127	21	eur	eur	PROPN
ejpam-3206	127	22	.	.	PUNCT
ejpam-3206	128	1	j.	j.	PROPN
ejpam-3206	128	2	pure	pure	PROPN
ejpam-3206	128	3	appl	appl	PROPN
ejpam-3206	128	4	.	.	PROPN
ejpam-3206	128	5	math	math	PROPN
ejpam-3206	128	6	,	,	PUNCT
ejpam-3206	128	7	11	11	NUM
ejpam-3206	128	8	(	(	PUNCT
ejpam-3206	128	9	1	1	NUM
ejpam-3206	128	10	)	)	PUNCT
ejpam-3206	128	11	(	(	PUNCT
ejpam-3206	128	12	2018	2018	NUM
ejpam-3206	128	13	)	)	PUNCT
ejpam-3206	128	14	,	,	PUNCT
ejpam-3206	128	15	244	244	NUM
ejpam-3206	128	16	-	-	SYM
ejpam-3206	128	17	259	259	NUM
ejpam-3206	128	18	249	249	NUM
ejpam-3206	128	19	3	3	NUM
ejpam-3206	128	20	)	)	PUNCT
ejpam-3206	128	21	nr(j1	nr(j1	NUM
ejpam-3206	128	22	)	)	PUNCT
ejpam-3206	128	23	=	=	SYM
ejpam-3206	128	24	l2	l2	NOUN
ejpam-3206	128	25	=	=	PUNCT
ejpam-3206	128	26	hr	hr	NOUN
ejpam-3206	129	1	where	where	SCONJ
ejpam-3206	129	2	h	h	NOUN
ejpam-3206	129	3	=	=	PUNCT
ejpam-3206	129	4	(	(	PUNCT
ejpam-3206	129	5	0	0	NUM
ejpam-3206	129	6	0	0	NUM
ejpam-3206	129	7	1	1	NUM
ejpam-3206	129	8	1	1	NUM
ejpam-3206	129	9	)	)	PUNCT
ejpam-3206	129	10	∈	∈	PROPN
ejpam-3206	129	11	id(r	id(r	NOUN
ejpam-3206	129	12	)	)	PUNCT
ejpam-3206	129	13	,	,	PUNCT
ejpam-3206	129	14	4	4	X
ejpam-3206	129	15	)	)	PUNCT
ejpam-3206	129	16	nr(j2	nr(j2	NOUN
ejpam-3206	129	17	)	)	PUNCT
ejpam-3206	129	18	=	=	SYM
ejpam-3206	129	19	l1	l1	PROPN
ejpam-3206	129	20	=	=	PROPN
ejpam-3206	129	21	kr	kr	PROPN
ejpam-3206	129	22	where	where	SCONJ
ejpam-3206	129	23	k	k	PROPN
ejpam-3206	129	24	=	=	PRON
ejpam-3206	129	25	(	(	PUNCT
ejpam-3206	129	26	1	1	NUM
ejpam-3206	129	27	1	1	NUM
ejpam-3206	129	28	0	0	NUM
ejpam-3206	129	29	0	0	NUM
ejpam-3206	129	30	)	)	PUNCT
ejpam-3206	129	31	∈	∈	PROPN
ejpam-3206	129	32	id(r	id(r	NOUN
ejpam-3206	129	33	)	)	PUNCT
ejpam-3206	129	34	.	.	PUNCT
ejpam-3206	130	1	by	by	ADP
ejpam-3206	130	2	the	the	DET
ejpam-3206	130	3	above	above	ADJ
ejpam-3206	130	4	discussion	discussion	NOUN
ejpam-3206	130	5	,	,	PUNCT
ejpam-3206	130	6	we	we	PRON
ejpam-3206	130	7	conclude	conclude	VERB
ejpam-3206	130	8	that	that	SCONJ
ejpam-3206	130	9	r	r	NOUN
ejpam-3206	130	10	is	be	AUX
ejpam-3206	130	11	a	a	DET
ejpam-3206	130	12	weak	weak	ADJ
ejpam-3206	130	13	left	left	ADJ
ejpam-3206	130	14	ps	ps	NOUN
ejpam-3206	130	15	-	-	PUNCT
ejpam-3206	130	16	ring	ring	NOUN
ejpam-3206	130	17	.	.	PUNCT
ejpam-3206	131	1	therefore	therefore	ADV
ejpam-3206	131	2	r	r	NOUN
ejpam-3206	131	3	is	be	AUX
ejpam-3206	131	4	a	a	DET
ejpam-3206	131	5	weak	weak	ADJ
ejpam-3206	131	6	ps	ps	NOUN
ejpam-3206	131	7	-	-	PUNCT
ejpam-3206	131	8	ring	ring	NOUN
ejpam-3206	131	9	.	.	PUNCT
ejpam-3206	131	10	example	example	NOUN
ejpam-3206	132	1	10	10	NUM
ejpam-3206	132	2	.	.	PUNCT
ejpam-3206	133	1	let	let	VERB
ejpam-3206	133	2	f	f	PRON
ejpam-3206	133	3	be	be	AUX
ejpam-3206	133	4	a	a	DET
ejpam-3206	133	5	filed	file	VERB
ejpam-3206	133	6	and	and	CCONJ
ejpam-3206	133	7	r	r	NOUN
ejpam-3206	133	8	=	=	SYM
ejpam-3206	133	9	t2	t2	PROPN
ejpam-3206	133	10	(	(	PUNCT
ejpam-3206	133	11	f	f	PROPN
ejpam-3206	133	12	)	)	PUNCT
ejpam-3206	134	1	=	=	PUNCT
ejpam-3206	135	1	(	(	PUNCT
ejpam-3206	135	2	f	f	NOUN
ejpam-3206	135	3	f	f	PROPN
ejpam-3206	135	4	0	0	NUM
ejpam-3206	135	5	f	f	PROPN
ejpam-3206	135	6	)	)	PUNCT
ejpam-3206	136	1	=	=	PRON
ejpam-3206	136	2	{	{	PUNCT
ejpam-3206	136	3	(	(	PUNCT
ejpam-3206	136	4	a	a	DET
ejpam-3206	136	5	b	b	NOUN
ejpam-3206	136	6	0	0	NUM
ejpam-3206	136	7	c	c	NOUN
ejpam-3206	136	8	)	)	PUNCT
ejpam-3206	136	9	|	|	ADV
ejpam-3206	136	10	a	a	DET
ejpam-3206	136	11	,	,	PUNCT
ejpam-3206	136	12	b	b	NOUN
ejpam-3206	136	13	,	,	PUNCT
ejpam-3206	136	14	c	c	PROPN
ejpam-3206	136	15	∈	∈	PROPN
ejpam-3206	136	16	f	f	PROPN
ejpam-3206	136	17	}	}	PUNCT
ejpam-3206	136	18	.	.	PUNCT
ejpam-3206	137	1	we	we	PRON
ejpam-3206	137	2	can	can	AUX
ejpam-3206	137	3	check	check	VERB
ejpam-3206	137	4	that	that	DET
ejpam-3206	137	5	nil	nil	NOUN
ejpam-3206	137	6	(	(	PUNCT
ejpam-3206	137	7	r	r	NOUN
ejpam-3206	137	8	)	)	PUNCT
ejpam-3206	137	9	=	=	SYM
ejpam-3206	137	10	{	{	PUNCT
ejpam-3206	137	11	(	(	PUNCT
ejpam-3206	137	12	0	0	NUM
ejpam-3206	137	13	b	b	NOUN
ejpam-3206	137	14	0	0	NUM
ejpam-3206	137	15	0	0	NUM
ejpam-3206	137	16	)	)	PUNCT
ejpam-3206	138	1	|	|	ADV
ejpam-3206	138	2	b	b	X
ejpam-3206	138	3	∈	∈	NOUN
ejpam-3206	138	4	f	f	X
ejpam-3206	138	5	}	}	PUNCT
ejpam-3206	138	6	=	=	SYM
ejpam-3206	138	7	(	(	PUNCT
ejpam-3206	138	8	0	0	NUM
ejpam-3206	138	9	f	f	NOUN
ejpam-3206	138	10	0	0	NUM
ejpam-3206	138	11	0	0	NUM
ejpam-3206	138	12	)	)	PUNCT
ejpam-3206	138	13	is	be	AUX
ejpam-3206	138	14	a	a	DET
ejpam-3206	138	15	two	two	NUM
ejpam-3206	138	16	sided	sided	ADJ
ejpam-3206	138	17	ideal	ideal	NOUN
ejpam-3206	138	18	in	in	ADP
ejpam-3206	138	19	r	r	NOUN
ejpam-3206	138	20	,	,	PUNCT
ejpam-3206	138	21	hence	hence	ADV
ejpam-3206	138	22	r	r	NOUN
ejpam-3206	138	23	is	be	AUX
ejpam-3206	138	24	an	an	DET
ejpam-3206	138	25	ni	ni	NOUN
ejpam-3206	138	26	-	-	PUNCT
ejpam-3206	138	27	ring	ring	NOUN
ejpam-3206	138	28	.	.	PUNCT
ejpam-3206	139	1	the	the	DET
ejpam-3206	139	2	only	only	ADJ
ejpam-3206	139	3	maximal	maximal	ADJ
ejpam-3206	139	4	(	(	PUNCT
ejpam-3206	139	5	two	two	NUM
ejpam-3206	139	6	sided	sided	ADJ
ejpam-3206	139	7	)	)	PUNCT
ejpam-3206	139	8	ideals	ideal	NOUN
ejpam-3206	139	9	of	of	ADP
ejpam-3206	139	10	r	r	NOUN
ejpam-3206	139	11	are	be	AUX
ejpam-3206	139	12	:	:	PUNCT
ejpam-3206	139	13	l	l	X
ejpam-3206	139	14	=	=	PUNCT
ejpam-3206	139	15	(	(	PUNCT
ejpam-3206	139	16	f	f	NOUN
ejpam-3206	139	17	f	f	PROPN
ejpam-3206	139	18	0	0	NUM
ejpam-3206	139	19	0	0	NUM
ejpam-3206	139	20	)	)	PUNCT
ejpam-3206	139	21	and	and	CCONJ
ejpam-3206	139	22	j	j	PROPN
ejpam-3206	140	1	=	=	PRON
ejpam-3206	140	2	(	(	PUNCT
ejpam-3206	140	3	0	0	NUM
ejpam-3206	140	4	f	f	NOUN
ejpam-3206	140	5	0	0	PUNCT
ejpam-3206	140	6	f	f	X
ejpam-3206	140	7	)	)	PUNCT
ejpam-3206	141	1	we	we	PRON
ejpam-3206	141	2	can	can	AUX
ejpam-3206	141	3	check	check	VERB
ejpam-3206	141	4	that	that	PRON
ejpam-3206	141	5	nr(l	nr(l	PUNCT
ejpam-3206	141	6	)	)	PUNCT
ejpam-3206	141	7	=	=	SYM
ejpam-3206	141	8	nil	nil	NOUN
ejpam-3206	141	9	(	(	PUNCT
ejpam-3206	141	10	r	r	NOUN
ejpam-3206	141	11	)	)	PUNCT
ejpam-3206	141	12	and	and	CCONJ
ejpam-3206	141	13	nr(j	nr(j	NUM
ejpam-3206	141	14	)	)	PUNCT
ejpam-3206	141	15	=	=	SYM
ejpam-3206	141	16	nil	nil	NOUN
ejpam-3206	141	17	(	(	PUNCT
ejpam-3206	141	18	r	r	NOUN
ejpam-3206	141	19	)	)	PUNCT
ejpam-3206	141	20	.	.	PUNCT
ejpam-3206	142	1	therefore	therefore	ADV
ejpam-3206	142	2	we	we	PRON
ejpam-3206	142	3	conclude	conclude	VERB
ejpam-3206	142	4	that	that	SCONJ
ejpam-3206	142	5	r	r	NOUN
ejpam-3206	142	6	is	be	AUX
ejpam-3206	142	7	a	a	DET
ejpam-3206	142	8	weak	weak	ADJ
ejpam-3206	142	9	ps	ps	NOUN
ejpam-3206	142	10	-	-	PUNCT
ejpam-3206	142	11	ring	ring	NOUN
ejpam-3206	142	12	.	.	PUNCT
ejpam-3206	142	13	example	example	NOUN
ejpam-3206	143	1	11	11	NUM
ejpam-3206	143	2	.	.	PUNCT
ejpam-3206	144	1	consider	consider	VERB
ejpam-3206	144	2	the	the	DET
ejpam-3206	144	3	semigroup	semigroup	PROPN
ejpam-3206	144	4	ring	ring	NOUN
ejpam-3206	144	5	v	v	NOUN
ejpam-3206	144	6	=	=	SYM
ejpam-3206	144	7	z2[s	z2[s	NOUN
ejpam-3206	144	8	]	]	X
ejpam-3206	145	1	=	=	SYM
ejpam-3206	145	2	{	{	PUNCT
ejpam-3206	145	3	αa+	αa+	NOUN
ejpam-3206	145	4	βb	βb	NOUN
ejpam-3206	145	5	:	:	PUNCT
ejpam-3206	145	6	α	α	X
ejpam-3206	145	7	,	,	PUNCT
ejpam-3206	145	8	β	β	PROPN
ejpam-3206	145	9	∈	∈	PROPN
ejpam-3206	145	10	z2	z2	PROPN
ejpam-3206	145	11	}	}	PUNCT
ejpam-3206	145	12	=	=	PUNCT
ejpam-3206	145	13	{	{	PUNCT
ejpam-3206	145	14	0	0	NUM
ejpam-3206	145	15	,	,	PUNCT
ejpam-3206	145	16	a	a	DET
ejpam-3206	145	17	,	,	PUNCT
ejpam-3206	145	18	b	b	NOUN
ejpam-3206	145	19	,	,	PUNCT
ejpam-3206	145	20	a+	a+	PRON
ejpam-3206	145	21	b	b	X
ejpam-3206	145	22	=	=	SYM
ejpam-3206	145	23	c	c	NOUN
ejpam-3206	145	24	}	}	PUNCT
ejpam-3206	145	25	,	,	PUNCT
ejpam-3206	145	26	where	where	SCONJ
ejpam-3206	145	27	s	s	VERB
ejpam-3206	145	28	=	=	X
ejpam-3206	145	29	{	{	PUNCT
ejpam-3206	145	30	a	a	DET
ejpam-3206	145	31	,	,	PUNCT
ejpam-3206	145	32	b	b	NOUN
ejpam-3206	145	33	}	}	PUNCT
ejpam-3206	145	34	is	be	AUX
ejpam-3206	145	35	the	the	DET
ejpam-3206	145	36	semigroup	semigroup	NOUN
ejpam-3206	145	37	with	with	ADP
ejpam-3206	145	38	the	the	DET
ejpam-3206	145	39	following	follow	VERB
ejpam-3206	145	40	cayley	cayley	ADJ
ejpam-3206	145	41	multiplication	multiplication	NOUN
ejpam-3206	145	42	table	table	NOUN
ejpam-3206	145	43	×	×	NOUN
ejpam-3206	145	44	a	a	DET
ejpam-3206	145	45	b	b	NOUN
ejpam-3206	145	46	a	a	DET
ejpam-3206	145	47	a	a	DET
ejpam-3206	145	48	b	b	PROPN
ejpam-3206	145	49	b	b	PROPN
ejpam-3206	145	50	a	a	DET
ejpam-3206	145	51	b	b	NOUN
ejpam-3206	145	52	clearly	clearly	ADV
ejpam-3206	145	53	,	,	PUNCT
ejpam-3206	145	54	id(v	id(v	NOUN
ejpam-3206	145	55	)	)	PUNCT
ejpam-3206	145	56	=	=	PRON
ejpam-3206	146	1	{	{	PUNCT
ejpam-3206	146	2	0	0	NUM
ejpam-3206	146	3	,	,	PUNCT
ejpam-3206	146	4	a	a	DET
ejpam-3206	146	5	,	,	PUNCT
ejpam-3206	146	6	b	b	NOUN
ejpam-3206	146	7	}	}	PUNCT
ejpam-3206	146	8	&	&	CCONJ
ejpam-3206	146	9	nil	nil	PROPN
ejpam-3206	146	10	(	(	PUNCT
ejpam-3206	146	11	v	v	NOUN
ejpam-3206	146	12	)	)	PUNCT
ejpam-3206	146	13	=	=	PUNCT
ejpam-3206	146	14	{	{	PUNCT
ejpam-3206	146	15	0	0	NUM
ejpam-3206	146	16	,	,	PUNCT
ejpam-3206	146	17	c	c	NOUN
ejpam-3206	146	18	}	}	PUNCT
ejpam-3206	146	19	.	.	PUNCT
ejpam-3206	147	1	we	we	PRON
ejpam-3206	147	2	can	can	AUX
ejpam-3206	147	3	check	check	VERB
ejpam-3206	147	4	the	the	DET
ejpam-3206	147	5	following	following	NOUN
ejpam-3206	147	6	:	:	PUNCT
ejpam-3206	147	7	1	1	X
ejpam-3206	147	8	)	)	PUNCT
ejpam-3206	147	9	i	i	PRON
ejpam-3206	147	10	=	=	PUNCT
ejpam-3206	147	11	{	{	PUNCT
ejpam-3206	147	12	0	0	NUM
ejpam-3206	147	13	,	,	PUNCT
ejpam-3206	147	14	a	a	PRON
ejpam-3206	147	15	}	}	PUNCT
ejpam-3206	147	16	is	be	AUX
ejpam-3206	147	17	a	a	DET
ejpam-3206	147	18	left	left	ADJ
ejpam-3206	147	19	maximal	maximal	ADJ
ejpam-3206	147	20	ideal	ideal	NOUN
ejpam-3206	147	21	in	in	ADP
ejpam-3206	147	22	v	v	ADP
ejpam-3206	147	23	which	which	PRON
ejpam-3206	147	24	is	be	AUX
ejpam-3206	147	25	not	not	PART
ejpam-3206	147	26	a	a	DET
ejpam-3206	147	27	right	right	ADJ
ejpam-3206	147	28	ideal	ideal	NOUN
ejpam-3206	147	29	,	,	PUNCT
ejpam-3206	147	30	2	2	X
ejpam-3206	147	31	)	)	PUNCT
ejpam-3206	147	32	j	j	NOUN
ejpam-3206	148	1	=	=	PUNCT
ejpam-3206	148	2	{	{	PUNCT
ejpam-3206	148	3	0	0	NUM
ejpam-3206	148	4	,	,	PUNCT
ejpam-3206	148	5	b	b	NOUN
ejpam-3206	148	6	}	}	PUNCT
ejpam-3206	148	7	is	be	AUX
ejpam-3206	148	8	a	a	DET
ejpam-3206	148	9	left	left	ADJ
ejpam-3206	148	10	maximal	maximal	ADJ
ejpam-3206	148	11	ideal	ideal	NOUN
ejpam-3206	148	12	in	in	ADP
ejpam-3206	148	13	v	v	ADP
ejpam-3206	148	14	which	which	PRON
ejpam-3206	148	15	is	be	AUX
ejpam-3206	148	16	not	not	PART
ejpam-3206	148	17	a	a	DET
ejpam-3206	148	18	right	right	ADJ
ejpam-3206	148	19	ideal	ideal	NOUN
ejpam-3206	148	20	,	,	PUNCT
ejpam-3206	148	21	3	3	X
ejpam-3206	148	22	)	)	PUNCT
ejpam-3206	148	23	k	k	NOUN
ejpam-3206	149	1	=	=	PUNCT
ejpam-3206	149	2	{	{	PUNCT
ejpam-3206	149	3	0	0	NUM
ejpam-3206	149	4	,	,	PUNCT
ejpam-3206	149	5	c	c	NOUN
ejpam-3206	149	6	}	}	PUNCT
ejpam-3206	149	7	=	=	SYM
ejpam-3206	149	8	nil	nil	ADJ
ejpam-3206	149	9	(	(	PUNCT
ejpam-3206	149	10	v	v	NOUN
ejpam-3206	149	11	)	)	PUNCT
ejpam-3206	149	12	is	be	AUX
ejpam-3206	149	13	a	a	DET
ejpam-3206	149	14	maximal	maximal	ADJ
ejpam-3206	149	15	2	2	NUM
ejpam-3206	149	16	-	-	PUNCT
ejpam-3206	149	17	sided	sided	ADJ
ejpam-3206	149	18	ideal	ideal	NOUN
ejpam-3206	149	19	in	in	ADP
ejpam-3206	149	20	v	v	NOUN
ejpam-3206	149	21	,	,	PUNCT
ejpam-3206	149	22	hence	hence	ADV
ejpam-3206	149	23	v	v	NOUN
ejpam-3206	149	24	is	be	AUX
ejpam-3206	149	25	an	an	DET
ejpam-3206	149	26	ni	ni	NOUN
ejpam-3206	149	27	-	-	PUNCT
ejpam-3206	149	28	ring	ring	NOUN
ejpam-3206	149	29	,	,	PUNCT
ejpam-3206	149	30	4	4	NUM
ejpam-3206	149	31	)	)	PUNCT
ejpam-3206	149	32	we	we	PRON
ejpam-3206	149	33	can	can	AUX
ejpam-3206	149	34	check	check	VERB
ejpam-3206	149	35	that	that	PRON
ejpam-3206	149	36	nv	nv	PROPN
ejpam-3206	149	37	(	(	PUNCT
ejpam-3206	149	38	i	i	NOUN
ejpam-3206	149	39	)	)	PUNCT
ejpam-3206	149	40	=	=	PUNCT
ejpam-3206	150	1	k	k	NOUN
ejpam-3206	150	2	=	=	PUNCT
ejpam-3206	150	3	nil	nil	ADJ
ejpam-3206	150	4	(	(	PUNCT
ejpam-3206	150	5	v	v	NOUN
ejpam-3206	150	6	)	)	PUNCT
ejpam-3206	150	7	,	,	PUNCT
ejpam-3206	150	8	nv	nv	PROPN
ejpam-3206	150	9	(	(	PUNCT
ejpam-3206	150	10	j	j	PROPN
ejpam-3206	150	11	)	)	PUNCT
ejpam-3206	150	12	=	=	PUNCT
ejpam-3206	151	1	k	k	NOUN
ejpam-3206	151	2	=	=	PUNCT
ejpam-3206	151	3	nil	nil	ADJ
ejpam-3206	151	4	(	(	PUNCT
ejpam-3206	151	5	v	v	NOUN
ejpam-3206	151	6	)	)	PUNCT
ejpam-3206	151	7	and	and	CCONJ
ejpam-3206	151	8	nv	nv	PROPN
ejpam-3206	151	9	(	(	PUNCT
ejpam-3206	151	10	k	k	NOUN
ejpam-3206	151	11	)	)	PUNCT
ejpam-3206	151	12	=	=	SYM
ejpam-3206	152	1	v	v	X
ejpam-3206	152	2	=	=	SYM
ejpam-3206	152	3	a×	a×	NOUN
ejpam-3206	152	4	v	v	NOUN
ejpam-3206	152	5	=	=	PUNCT
ejpam-3206	153	1	b×	b×	NOUN
ejpam-3206	153	2	v.	v.	CCONJ
ejpam-3206	153	3	therefore	therefore	ADV
ejpam-3206	153	4	v	v	NOUN
ejpam-3206	153	5	is	be	AUX
ejpam-3206	153	6	a	a	DET
ejpam-3206	153	7	weak	weak	ADJ
ejpam-3206	153	8	left	left	ADJ
ejpam-3206	153	9	ps	ps	NOUN
ejpam-3206	153	10	-	-	PUNCT
ejpam-3206	153	11	ring	ring	NOUN
ejpam-3206	153	12	.	.	PUNCT
ejpam-3206	154	1	since	since	SCONJ
ejpam-3206	154	2	the	the	DET
ejpam-3206	154	3	only	only	ADJ
ejpam-3206	154	4	right	right	ADJ
ejpam-3206	154	5	maximal	maximal	ADJ
ejpam-3206	154	6	ideal	ideal	NOUN
ejpam-3206	154	7	in	in	ADP
ejpam-3206	154	8	v	v	NOUN
ejpam-3206	154	9	,	,	PUNCT
ejpam-3206	154	10	is	be	AUX
ejpam-3206	154	11	k	k	NOUN
ejpam-3206	154	12	=	=	PUNCT
ejpam-3206	154	13	{	{	PUNCT
ejpam-3206	154	14	0	0	NUM
ejpam-3206	154	15	,	,	PUNCT
ejpam-3206	154	16	c	c	NOUN
ejpam-3206	154	17	}	}	PUNCT
ejpam-3206	154	18	=	=	SYM
ejpam-3206	154	19	nil	nil	ADJ
ejpam-3206	154	20	(	(	PUNCT
ejpam-3206	154	21	v	v	NOUN
ejpam-3206	154	22	)	)	PUNCT
ejpam-3206	154	23	and	and	CCONJ
ejpam-3206	154	24	nv	nv	PROPN
ejpam-3206	154	25	(	(	PUNCT
ejpam-3206	154	26	k	k	NOUN
ejpam-3206	154	27	)	)	PUNCT
ejpam-3206	154	28	=	=	SYM
ejpam-3206	154	29	v	v	NOUN
ejpam-3206	154	30	which	which	PRON
ejpam-3206	154	31	is	be	AUX
ejpam-3206	154	32	not	not	PART
ejpam-3206	154	33	generated	generate	VERB
ejpam-3206	154	34	by	by	ADP
ejpam-3206	154	35	an	an	DET
ejpam-3206	154	36	idempotent	idempotent	NOUN
ejpam-3206	154	37	as	as	ADP
ejpam-3206	154	38	a	a	DET
ejpam-3206	154	39	left	left	ADJ
ejpam-3206	154	40	ideal	ideal	NOUN
ejpam-3206	154	41	,	,	PUNCT
ejpam-3206	154	42	so	so	SCONJ
ejpam-3206	154	43	v	v	NOUN
ejpam-3206	154	44	is	be	AUX
ejpam-3206	154	45	not	not	PART
ejpam-3206	154	46	a	a	DET
ejpam-3206	154	47	right	right	ADJ
ejpam-3206	154	48	weak	weak	ADJ
ejpam-3206	154	49	ps	ps	NOUN
ejpam-3206	154	50	-	-	PUNCT
ejpam-3206	154	51	ring	ring	NOUN
ejpam-3206	154	52	.	.	PUNCT
ejpam-3206	155	1	also	also	ADV
ejpam-3206	155	2	,	,	PUNCT
ejpam-3206	155	3	we	we	PRON
ejpam-3206	155	4	can	can	AUX
ejpam-3206	155	5	check	check	VERB
ejpam-3206	155	6	the	the	DET
ejpam-3206	155	7	following	following	NOUN
ejpam-3206	155	8	:	:	PUNCT
ejpam-3206	156	1	rv	rv	PROPN
ejpam-3206	156	2	(	(	PUNCT
ejpam-3206	156	3	i	i	NOUN
ejpam-3206	156	4	)	)	PUNCT
ejpam-3206	156	5	=	=	SYM
ejpam-3206	156	6	0	0	PUNCT
ejpam-3206	157	1	=	=	SYM
ejpam-3206	157	2	0	0	NUM
ejpam-3206	157	3	×	×	PROPN
ejpam-3206	157	4	v	v	NOUN
ejpam-3206	157	5	,	,	PUNCT
ejpam-3206	157	6	rv	rv	PROPN
ejpam-3206	157	7	(	(	PUNCT
ejpam-3206	157	8	j	j	PROPN
ejpam-3206	157	9	)	)	PUNCT
ejpam-3206	157	10	=	=	SYM
ejpam-3206	157	11	0	0	PUNCT
ejpam-3206	158	1	=	=	SYM
ejpam-3206	158	2	0	0	NUM
ejpam-3206	158	3	×	×	NOUN
ejpam-3206	158	4	v	v	NOUN
ejpam-3206	158	5	,	,	PUNCT
ejpam-3206	158	6	and	and	CCONJ
ejpam-3206	158	7	rv	rv	PROPN
ejpam-3206	158	8	(	(	PUNCT
ejpam-3206	158	9	k	k	NOUN
ejpam-3206	158	10	)	)	PUNCT
ejpam-3206	158	11	=	=	SYM
ejpam-3206	158	12	v	v	NOUN
ejpam-3206	158	13	=	=	PUNCT
ejpam-3206	158	14	a	a	DET
ejpam-3206	158	15	×	×	NOUN
ejpam-3206	158	16	v	v	NOUN
ejpam-3206	158	17	=	=	SYM
ejpam-3206	158	18	b	b	PROPN
ejpam-3206	158	19	×	×	NOUN
ejpam-3206	158	20	v.	v.	ADP
ejpam-3206	158	21	hence	hence	ADV
ejpam-3206	158	22	v	v	NOUN
ejpam-3206	158	23	is	be	AUX
ejpam-3206	158	24	a	a	DET
ejpam-3206	158	25	left	left	ADJ
ejpam-3206	158	26	ps	ps	NOUN
ejpam-3206	158	27	-	-	PUNCT
ejpam-3206	158	28	ring	ring	NOUN
ejpam-3206	158	29	.	.	PUNCT
ejpam-3206	159	1	for	for	ADP
ejpam-3206	159	2	the	the	DET
ejpam-3206	159	3	unique	unique	ADJ
ejpam-3206	159	4	maximal	maximal	ADJ
ejpam-3206	159	5	right	right	ADJ
ejpam-3206	159	6	ideal	ideal	NOUN
ejpam-3206	159	7	k	k	PROPN
ejpam-3206	159	8	in	in	ADP
ejpam-3206	159	9	v	v	NUM
ejpam-3206	159	10	,	,	PUNCT
ejpam-3206	159	11	we	we	PRON
ejpam-3206	159	12	have	have	VERB
ejpam-3206	159	13	`	`	PUNCT
ejpam-3206	159	14	v	v	X
ejpam-3206	159	15	(	(	PUNCT
ejpam-3206	159	16	k	k	NOUN
ejpam-3206	159	17	)	)	PUNCT
ejpam-3206	159	18	=	=	SYM
ejpam-3206	159	19	v	v	NOUN
ejpam-3206	159	20	which	which	PRON
ejpam-3206	159	21	is	be	AUX
ejpam-3206	159	22	not	not	PART
ejpam-3206	159	23	generated	generate	VERB
ejpam-3206	159	24	by	by	ADP
ejpam-3206	159	25	an	an	DET
ejpam-3206	159	26	idempotent	idempotent	NOUN
ejpam-3206	159	27	as	as	ADP
ejpam-3206	159	28	a	a	DET
ejpam-3206	159	29	left	left	ADJ
ejpam-3206	159	30	ideal	ideal	NOUN
ejpam-3206	159	31	.	.	PUNCT
ejpam-3206	160	1	hence	hence	ADV
ejpam-3206	160	2	v	v	NOUN
ejpam-3206	160	3	is	be	AUX
ejpam-3206	160	4	not	not	PART
ejpam-3206	160	5	a	a	DET
ejpam-3206	160	6	right	right	ADJ
ejpam-3206	160	7	ps	ps	NOUN
ejpam-3206	160	8	-	-	NOUN
ejpam-3206	160	9	ring	ring	NOUN
ejpam-3206	160	10	.	.	PUNCT
ejpam-3206	161	1	m.	m.	NOUN
ejpam-3206	161	2	a.	a.	PROPN
ejpam-3206	161	3	farahat	farahat	PROPN
ejpam-3206	161	4	,	,	PUNCT
ejpam-3206	161	5	s.	s.	PROPN
ejpam-3206	161	6	t.	t.	PROPN
ejpam-3206	161	7	al	al	PROPN
ejpam-3206	161	8	-	-	PUNCT
ejpam-3206	161	9	bogamy	bogamy	PROPN
ejpam-3206	161	10	/	/	SYM
ejpam-3206	161	11	eur	eur	PROPN
ejpam-3206	161	12	.	.	PUNCT
ejpam-3206	162	1	j.	j.	PROPN
ejpam-3206	162	2	pure	pure	PROPN
ejpam-3206	162	3	appl	appl	PROPN
ejpam-3206	162	4	.	.	PROPN
ejpam-3206	162	5	math	math	PROPN
ejpam-3206	162	6	,	,	PUNCT
ejpam-3206	162	7	11	11	NUM
ejpam-3206	162	8	(	(	PUNCT
ejpam-3206	162	9	1	1	NUM
ejpam-3206	162	10	)	)	PUNCT
ejpam-3206	162	11	(	(	PUNCT
ejpam-3206	162	12	2018	2018	NUM
ejpam-3206	162	13	)	)	PUNCT
ejpam-3206	162	14	,	,	PUNCT
ejpam-3206	162	15	244	244	NUM
ejpam-3206	162	16	-	-	SYM
ejpam-3206	162	17	259	259	NUM
ejpam-3206	162	18	250	250	NUM
ejpam-3206	162	19	lemma	lemma	PROPN
ejpam-3206	162	20	2	2	NUM
ejpam-3206	162	21	.	.	PUNCT
ejpam-3206	163	1	let	let	VERB
ejpam-3206	163	2	r	r	PRON
ejpam-3206	163	3	be	be	AUX
ejpam-3206	163	4	an	an	DET
ejpam-3206	163	5	ni	ni	NOUN
ejpam-3206	163	6	-	-	PUNCT
ejpam-3206	163	7	ring	ring	NOUN
ejpam-3206	163	8	,	,	PUNCT
ejpam-3206	163	9	l	l	NOUN
ejpam-3206	163	10	a	a	DET
ejpam-3206	163	11	maximal	maximal	ADJ
ejpam-3206	163	12	right	right	ADJ
ejpam-3206	163	13	ideal	ideal	NOUN
ejpam-3206	163	14	in	in	ADP
ejpam-3206	163	15	r	r	NOUN
ejpam-3206	163	16	and	and	CCONJ
ejpam-3206	163	17	r	r	NOUN
ejpam-3206	163	18	=	=	NOUN
ejpam-3206	163	19	r	r	NOUN
ejpam-3206	163	20	/nil	/nil	PUNCT
ejpam-3206	163	21	(	(	PUNCT
ejpam-3206	163	22	r	r	NOUN
ejpam-3206	163	23	)	)	PUNCT
ejpam-3206	163	24	.	.	PUNCT
ejpam-3206	164	1	then	then	ADV
ejpam-3206	164	2	:	:	PUNCT
ejpam-3206	164	3	1	1	X
ejpam-3206	164	4	)	)	PUNCT
ejpam-3206	164	5	l	l	NOUN
ejpam-3206	164	6	contains	contain	VERB
ejpam-3206	164	7	n	n	PROPN
ejpam-3206	164	8	=	=	SYM
ejpam-3206	164	9	nil	nil	NOUN
ejpam-3206	164	10	(	(	PUNCT
ejpam-3206	164	11	r	r	NOUN
ejpam-3206	164	12	)	)	PUNCT
ejpam-3206	164	13	,	,	PUNCT
ejpam-3206	164	14	2	2	X
ejpam-3206	164	15	)	)	PUNCT
ejpam-3206	165	1	l	l	NOUN
ejpam-3206	165	2	=	=	PUNCT
ejpam-3206	165	3	l	l	NOUN
ejpam-3206	165	4	/n	/n	PUNCT
ejpam-3206	165	5	is	be	AUX
ejpam-3206	165	6	a	a	DET
ejpam-3206	165	7	maximal	maximal	ADJ
ejpam-3206	165	8	right	right	ADJ
ejpam-3206	165	9	ideal	ideal	NOUN
ejpam-3206	165	10	in	in	ADP
ejpam-3206	165	11	r	r	NOUN
ejpam-3206	165	12	,	,	PUNCT
ejpam-3206	165	13	and	and	CCONJ
ejpam-3206	165	14	3	3	X
ejpam-3206	165	15	)	)	PUNCT
ejpam-3206	165	16	if	if	SCONJ
ejpam-3206	165	17	e	e	PROPN
ejpam-3206	165	18	∈	∈	PROPN
ejpam-3206	165	19	i	i	PROPN
ejpam-3206	165	20	d	d	PROPN
ejpam-3206	165	21	(	(	PUNCT
ejpam-3206	165	22	r	r	NOUN
ejpam-3206	165	23	)	)	PUNCT
ejpam-3206	165	24	,	,	PUNCT
ejpam-3206	165	25	then	then	ADV
ejpam-3206	165	26	e	e	PROPN
ejpam-3206	165	27	∈	∈	PROPN
ejpam-3206	165	28	id(r	id(r	NOUN
ejpam-3206	165	29	)	)	PUNCT
ejpam-3206	165	30	.	.	PUNCT
ejpam-3206	166	1	proof	proof	NOUN
ejpam-3206	166	2	.	.	PUNCT
ejpam-3206	167	1	1	1	X
ejpam-3206	167	2	)	)	PUNCT
ejpam-3206	167	3	let	let	VERB
ejpam-3206	167	4	the	the	DET
ejpam-3206	167	5	contrary	contrary	NOUN
ejpam-3206	167	6	,	,	PUNCT
ejpam-3206	167	7	i.e.	i.e.	X
ejpam-3206	167	8	,	,	PUNCT
ejpam-3206	167	9	n	n	PROPN
ejpam-3206	167	10	=	=	SYM
ejpam-3206	167	11	nil	nil	NOUN
ejpam-3206	167	12	(	(	PUNCT
ejpam-3206	167	13	r	r	NOUN
ejpam-3206	167	14	)	)	PUNCT
ejpam-3206	167	15	"	"	PUNCT
ejpam-3206	167	16	l	l	NOUN
ejpam-3206	167	17	,	,	PUNCT
ejpam-3206	167	18	then	then	ADV
ejpam-3206	167	19	there	there	PRON
ejpam-3206	167	20	is	be	VERB
ejpam-3206	167	21	0	0	NUM
ejpam-3206	167	22	6=	6=	ADP
ejpam-3206	167	23	a	a	DET
ejpam-3206	167	24	∈	∈	PROPN
ejpam-3206	167	25	n	n	CCONJ
ejpam-3206	167	26	,	,	PUNCT
ejpam-3206	168	1	such	such	ADJ
ejpam-3206	168	2	that	that	SCONJ
ejpam-3206	168	3	a	a	DET
ejpam-3206	168	4	/∈	/∈	SYM
ejpam-3206	168	5	l.	l.	NOUN
ejpam-3206	169	1	so	so	ADV
ejpam-3206	169	2	l+	l+	X
ejpam-3206	169	3	ar	ar	PROPN
ejpam-3206	169	4	=	=	SYM
ejpam-3206	169	5	r	r	NOUN
ejpam-3206	169	6	,	,	PUNCT
ejpam-3206	169	7	thus	thus	ADV
ejpam-3206	169	8	b+	b+	X
ejpam-3206	169	9	ar	ar	NOUN
ejpam-3206	169	10	=	=	SYM
ejpam-3206	169	11	1	1	NUM
ejpam-3206	169	12	,	,	PUNCT
ejpam-3206	169	13	for	for	ADP
ejpam-3206	169	14	some	some	DET
ejpam-3206	169	15	b	b	NOUN
ejpam-3206	169	16	∈	∈	PROPN
ejpam-3206	169	17	l	l	NOUN
ejpam-3206	169	18	and	and	CCONJ
ejpam-3206	169	19	r	r	PROPN
ejpam-3206	169	20	∈	∈	PROPN
ejpam-3206	169	21	r.	r.	NOUN
ejpam-3206	169	22	since	since	SCONJ
ejpam-3206	169	23	every	every	DET
ejpam-3206	169	24	nilpotent	nilpotent	ADJ
ejpam-3206	169	25	element	element	NOUN
ejpam-3206	169	26	lies	lie	VERB
ejpam-3206	169	27	in	in	ADP
ejpam-3206	169	28	j(r	j(r	PROPN
ejpam-3206	169	29	)	)	PUNCT
ejpam-3206	169	30	,	,	PUNCT
ejpam-3206	169	31	we	we	PRON
ejpam-3206	169	32	have	have	VERB
ejpam-3206	169	33	b	b	NOUN
ejpam-3206	169	34	=	=	SYM
ejpam-3206	169	35	1−	1−	NUM
ejpam-3206	169	36	ar	ar	NOUN
ejpam-3206	169	37	is	be	AUX
ejpam-3206	169	38	a	a	DET
ejpam-3206	169	39	right	right	ADJ
ejpam-3206	169	40	invertible	invertible	ADJ
ejpam-3206	169	41	element	element	NOUN
ejpam-3206	169	42	in	in	ADP
ejpam-3206	169	43	r	r	NOUN
ejpam-3206	169	44	,	,	PUNCT
ejpam-3206	169	45	which	which	PRON
ejpam-3206	169	46	impossible	impossible	ADJ
ejpam-3206	169	47	since	since	SCONJ
ejpam-3206	169	48	b	b	PROPN
ejpam-3206	169	49	∈	∈	PROPN
ejpam-3206	169	50	l	l	NOUN
ejpam-3206	169	51	and	and	CCONJ
ejpam-3206	169	52	l	l	NOUN
ejpam-3206	169	53	is	be	AUX
ejpam-3206	169	54	a	a	DET
ejpam-3206	169	55	maximal	maximal	ADJ
ejpam-3206	169	56	right	right	ADJ
ejpam-3206	169	57	ideal	ideal	NOUN
ejpam-3206	169	58	in	in	ADP
ejpam-3206	169	59	r.	r.	PROPN
ejpam-3206	169	60	2	2	NUM
ejpam-3206	169	61	)	)	PUNCT
ejpam-3206	169	62	let	let	VERB
ejpam-3206	169	63	the	the	DET
ejpam-3206	169	64	contrary	contrary	NOUN
ejpam-3206	169	65	,	,	PUNCT
ejpam-3206	169	66	i.e.	i.e.	X
ejpam-3206	169	67	,	,	PUNCT
ejpam-3206	169	68	l	l	NOUN
ejpam-3206	169	69	=	=	SYM
ejpam-3206	169	70	l	l	NOUN
ejpam-3206	169	71	/n	/n	PUNCT
ejpam-3206	169	72	is	be	AUX
ejpam-3206	169	73	not	not	PART
ejpam-3206	169	74	a	a	DET
ejpam-3206	169	75	maximal	maximal	ADJ
ejpam-3206	169	76	right	right	ADJ
ejpam-3206	169	77	ideal	ideal	NOUN
ejpam-3206	169	78	in	in	ADP
ejpam-3206	169	79	r	r	NOUN
ejpam-3206	169	80	,	,	PUNCT
ejpam-3206	169	81	then	then	ADV
ejpam-3206	169	82	there	there	PRON
ejpam-3206	169	83	is	be	VERB
ejpam-3206	169	84	a	a	DET
ejpam-3206	169	85	proper	proper	ADJ
ejpam-3206	169	86	right	right	ADJ
ejpam-3206	169	87	ideal	ideal	NOUN
ejpam-3206	169	88	k	k	PROPN
ejpam-3206	170	1	=	=	PUNCT
ejpam-3206	170	2	k	k	PROPN
ejpam-3206	170	3	/n	/n	PUNCT
ejpam-3206	170	4	in	in	ADP
ejpam-3206	170	5	r	r	NOUN
ejpam-3206	170	6	,	,	PUNCT
ejpam-3206	170	7	for	for	ADP
ejpam-3206	170	8	some	some	DET
ejpam-3206	170	9	right	right	ADJ
ejpam-3206	170	10	ideal	ideal	NOUN
ejpam-3206	170	11	k	k	PROPN
ejpam-3206	170	12	in	in	ADP
ejpam-3206	170	13	r	r	NOUN
ejpam-3206	170	14	contain	contain	VERB
ejpam-3206	170	15	n	n	CCONJ
ejpam-3206	170	16	,	,	PUNCT
ejpam-3206	170	17	such	such	ADJ
ejpam-3206	170	18	that	that	SCONJ
ejpam-3206	170	19	l	l	NOUN
ejpam-3206	170	20	⊂	⊂	PROPN
ejpam-3206	171	1	k	k	X
ejpam-3206	171	2	in	in	ADP
ejpam-3206	171	3	r	r	NOUN
ejpam-3206	171	4	,	,	PUNCT
ejpam-3206	171	5	which	which	PRON
ejpam-3206	171	6	implies	imply	VERB
ejpam-3206	171	7	clearly	clearly	ADV
ejpam-3206	171	8	that	that	SCONJ
ejpam-3206	171	9	l	l	NOUN
ejpam-3206	172	1	⊂	⊂	PROPN
ejpam-3206	172	2	k	k	X
ejpam-3206	172	3	in	in	ADP
ejpam-3206	172	4	r	r	NOUN
ejpam-3206	172	5	,	,	PUNCT
ejpam-3206	172	6	which	which	PRON
ejpam-3206	172	7	contradicts	contradict	VERB
ejpam-3206	172	8	for	for	ADP
ejpam-3206	172	9	the	the	DET
ejpam-3206	172	10	maximality	maximality	NOUN
ejpam-3206	172	11	of	of	ADP
ejpam-3206	172	12	l.	l.	PROPN
ejpam-3206	172	13	3	3	NUM
ejpam-3206	172	14	)	)	PUNCT
ejpam-3206	172	15	let	let	VERB
ejpam-3206	172	16	e	e	PROPN
ejpam-3206	172	17	∈	∈	PROPN
ejpam-3206	172	18	id(r	id(r	NOUN
ejpam-3206	172	19	)	)	PUNCT
ejpam-3206	172	20	,	,	PUNCT
ejpam-3206	172	21	then	then	ADV
ejpam-3206	172	22	(	(	PUNCT
ejpam-3206	172	23	e)2	e)2	X
ejpam-3206	172	24	=	=	SYM
ejpam-3206	172	25	(	(	PUNCT
ejpam-3206	172	26	e+n	e+n	NUM
ejpam-3206	172	27	)	)	PUNCT
ejpam-3206	172	28	(	(	PUNCT
ejpam-3206	172	29	e+n	e+n	NUM
ejpam-3206	172	30	)	)	PUNCT
ejpam-3206	172	31	=	=	SYM
ejpam-3206	172	32	e2	e2	PROPN
ejpam-3206	172	33	+	+	PROPN
ejpam-3206	172	34	n	n	NOUN
ejpam-3206	172	35	=	=	SYM
ejpam-3206	172	36	e+n	e+n	NUM
ejpam-3206	172	37	=	=	SYM
ejpam-3206	172	38	e	e	NOUN
ejpam-3206	172	39	,	,	PUNCT
ejpam-3206	172	40	hence	hence	ADV
ejpam-3206	172	41	e	e	NOUN
ejpam-3206	172	42	∈	∈	PROPN
ejpam-3206	172	43	id(r	id(r	NOUN
ejpam-3206	172	44	)	)	PUNCT
ejpam-3206	172	45	.	.	PUNCT
ejpam-3206	173	1	theorem	theorem	NOUN
ejpam-3206	173	2	2	2	NUM
ejpam-3206	173	3	.	.	PUNCT
ejpam-3206	173	4	suppose	suppose	VERB
ejpam-3206	173	5	that	that	SCONJ
ejpam-3206	173	6	r	r	NOUN
ejpam-3206	173	7	is	be	AUX
ejpam-3206	173	8	an	an	DET
ejpam-3206	173	9	ni	ni	NOUN
ejpam-3206	173	10	-	-	PUNCT
ejpam-3206	173	11	ring	ring	NOUN
ejpam-3206	173	12	.	.	PUNCT
ejpam-3206	174	1	if	if	SCONJ
ejpam-3206	174	2	r	r	NOUN
ejpam-3206	174	3	is	be	AUX
ejpam-3206	174	4	a	a	DET
ejpam-3206	174	5	weak	weak	ADJ
ejpam-3206	174	6	right	right	ADJ
ejpam-3206	174	7	ps	ps	NOUN
ejpam-3206	174	8	-	-	NOUN
ejpam-3206	174	9	ring	ring	NOUN
ejpam-3206	174	10	,	,	PUNCT
ejpam-3206	174	11	then	then	ADV
ejpam-3206	174	12	r	r	NOUN
ejpam-3206	174	13	=	=	NOUN
ejpam-3206	174	14	r	r	NOUN
ejpam-3206	174	15	/nil	/nil	PUNCT
ejpam-3206	174	16	(	(	PUNCT
ejpam-3206	174	17	r	r	NOUN
ejpam-3206	174	18	)	)	PUNCT
ejpam-3206	174	19	is	be	AUX
ejpam-3206	174	20	a	a	DET
ejpam-3206	174	21	right	right	ADJ
ejpam-3206	174	22	ps	ps	NOUN
ejpam-3206	174	23	-	-	NOUN
ejpam-3206	174	24	ring	ring	NOUN
ejpam-3206	174	25	.	.	PUNCT
ejpam-3206	175	1	proof	proof	NOUN
ejpam-3206	175	2	.	.	PUNCT
ejpam-3206	176	1	let	let	VERB
ejpam-3206	176	2	r	r	PRON
ejpam-3206	176	3	be	be	AUX
ejpam-3206	176	4	a	a	DET
ejpam-3206	176	5	weak	weak	ADJ
ejpam-3206	176	6	right	right	ADJ
ejpam-3206	176	7	ps	ps	NOUN
ejpam-3206	176	8	-	-	PUNCT
ejpam-3206	176	9	ring	ring	NOUN
ejpam-3206	176	10	and	and	CCONJ
ejpam-3206	176	11	l	l	NOUN
ejpam-3206	176	12	be	be	AUX
ejpam-3206	176	13	a	a	DET
ejpam-3206	176	14	maximal	maximal	ADJ
ejpam-3206	176	15	right	right	ADJ
ejpam-3206	176	16	ideal	ideal	NOUN
ejpam-3206	176	17	in	in	ADP
ejpam-3206	176	18	r.	r.	PROPN
ejpam-3206	176	19	from	from	ADP
ejpam-3206	176	20	lemma	lemma	PROPN
ejpam-3206	176	21	2	2	NUM
ejpam-3206	176	22	,	,	PUNCT
ejpam-3206	176	23	we	we	PRON
ejpam-3206	176	24	have	have	VERB
ejpam-3206	176	25	l	l	NOUN
ejpam-3206	176	26	contains	contain	VERB
ejpam-3206	176	27	n	n	PRON
ejpam-3206	176	28	and	and	CCONJ
ejpam-3206	177	1	l	l	NOUN
ejpam-3206	177	2	=	=	SYM
ejpam-3206	177	3	l	l	NOUN
ejpam-3206	177	4	/n	/n	PUNCT
ejpam-3206	177	5	is	be	AUX
ejpam-3206	177	6	a	a	DET
ejpam-3206	177	7	maximal	maximal	ADJ
ejpam-3206	177	8	right	right	ADJ
ejpam-3206	177	9	ideal	ideal	NOUN
ejpam-3206	177	10	in	in	ADP
ejpam-3206	177	11	r.	r.	PROPN
ejpam-3206	177	12	since	since	SCONJ
ejpam-3206	177	13	r	r	NOUN
ejpam-3206	177	14	is	be	AUX
ejpam-3206	177	15	a	a	DET
ejpam-3206	177	16	weak	weak	ADJ
ejpam-3206	177	17	right	right	ADJ
ejpam-3206	177	18	ps	ps	NOUN
ejpam-3206	177	19	-	-	NOUN
ejpam-3206	177	20	ring	ring	NOUN
ejpam-3206	177	21	,	,	PUNCT
ejpam-3206	177	22	we	we	PRON
ejpam-3206	177	23	have	have	VERB
ejpam-3206	177	24	either	either	CCONJ
ejpam-3206	177	25	nr(l	nr(l	NOUN
ejpam-3206	177	26	)	)	PUNCT
ejpam-3206	177	27	⊆	⊆	NUM
ejpam-3206	177	28	nil	nil	NOUN
ejpam-3206	177	29	(	(	PUNCT
ejpam-3206	177	30	r	r	NOUN
ejpam-3206	177	31	)	)	PUNCT
ejpam-3206	177	32	or	or	CCONJ
ejpam-3206	177	33	nr(l	nr(l	NOUN
ejpam-3206	177	34	)	)	PUNCT
ejpam-3206	177	35	=	=	SYM
ejpam-3206	177	36	re	re	PROPN
ejpam-3206	177	37	,	,	PUNCT
ejpam-3206	177	38	for	for	ADP
ejpam-3206	177	39	some	some	DET
ejpam-3206	177	40	e	e	NOUN
ejpam-3206	177	41	∈	∈	PROPN
ejpam-3206	177	42	i	i	PROPN
ejpam-3206	177	43	d	d	PROPN
ejpam-3206	177	44	(	(	PUNCT
ejpam-3206	177	45	r	r	NOUN
ejpam-3206	177	46	)	)	PUNCT
ejpam-3206	177	47	.	.	PUNCT
ejpam-3206	178	1	case	case	NOUN
ejpam-3206	178	2	(	(	PUNCT
ejpam-3206	178	3	1	1	NUM
ejpam-3206	178	4	):	):	PUNCT
ejpam-3206	178	5	assume	assume	VERB
ejpam-3206	178	6	first	first	ADV
ejpam-3206	178	7	that	that	SCONJ
ejpam-3206	178	8	nr(l	nr(l	X
ejpam-3206	178	9	)	)	PUNCT
ejpam-3206	178	10	⊆	⊆	NUM
ejpam-3206	178	11	nil	nil	NOUN
ejpam-3206	178	12	(	(	PUNCT
ejpam-3206	178	13	r	r	NOUN
ejpam-3206	178	14	)	)	PUNCT
ejpam-3206	178	15	.	.	PUNCT
ejpam-3206	179	1	let	let	VERB
ejpam-3206	179	2	a	a	DET
ejpam-3206	179	3	∈	∈	ADJ
ejpam-3206	179	4	`	`	PUNCT
ejpam-3206	179	5	r	r	NOUN
ejpam-3206	179	6	(	(	PUNCT
ejpam-3206	179	7	l	l	NOUN
ejpam-3206	179	8	)	)	PUNCT
ejpam-3206	179	9	.	.	PUNCT
ejpam-3206	180	1	then	then	ADV
ejpam-3206	180	2	al	al	PROPN
ejpam-3206	180	3	=	=	SYM
ejpam-3206	180	4	0	0	PUNCT
ejpam-3206	181	1	=	=	SYM
ejpam-3206	181	2	nil	nil	NOUN
ejpam-3206	181	3	(	(	PUNCT
ejpam-3206	181	4	r	r	NOUN
ejpam-3206	181	5	)	)	PUNCT
ejpam-3206	181	6	,	,	PUNCT
ejpam-3206	181	7	which	which	PRON
ejpam-3206	181	8	implies	imply	VERB
ejpam-3206	181	9	that	that	SCONJ
ejpam-3206	181	10	al	al	PROPN
ejpam-3206	181	11	⊆	⊆	NUM
ejpam-3206	181	12	nil	nil	NOUN
ejpam-3206	181	13	(	(	PUNCT
ejpam-3206	181	14	r	r	NOUN
ejpam-3206	181	15	)	)	PUNCT
ejpam-3206	181	16	.	.	PUNCT
ejpam-3206	182	1	hence	hence	ADV
ejpam-3206	182	2	a	a	DET
ejpam-3206	182	3	∈	∈	PROPN
ejpam-3206	182	4	nr(l	nr(l	X
ejpam-3206	182	5	)	)	PUNCT
ejpam-3206	182	6	⊆	⊆	NUM
ejpam-3206	182	7	nil	nil	NOUN
ejpam-3206	182	8	(	(	PUNCT
ejpam-3206	182	9	r	r	NOUN
ejpam-3206	182	10	)	)	PUNCT
ejpam-3206	182	11	.	.	PUNCT
ejpam-3206	183	1	thus	thus	ADV
ejpam-3206	183	2	a	a	DET
ejpam-3206	183	3	=	=	SYM
ejpam-3206	183	4	0	0	NUM
ejpam-3206	183	5	which	which	PRON
ejpam-3206	183	6	implies	imply	VERB
ejpam-3206	183	7	that	that	SCONJ
ejpam-3206	183	8	`	`	PUNCT
ejpam-3206	183	9	r	r	NOUN
ejpam-3206	183	10	(	(	PUNCT
ejpam-3206	183	11	l	l	NOUN
ejpam-3206	183	12	)	)	PUNCT
ejpam-3206	184	1	=	=	SYM
ejpam-3206	184	2	(	(	PUNCT
ejpam-3206	184	3	0	0	NUM
ejpam-3206	184	4	)	)	PUNCT
ejpam-3206	184	5	and	and	CCONJ
ejpam-3206	184	6	we	we	PRON
ejpam-3206	184	7	conclude	conclude	VERB
ejpam-3206	184	8	that	that	SCONJ
ejpam-3206	184	9	r	r	NOUN
ejpam-3206	184	10	=	=	NOUN
ejpam-3206	184	11	r	r	NOUN
ejpam-3206	184	12	/nil	/nil	PUNCT
ejpam-3206	184	13	(	(	PUNCT
ejpam-3206	184	14	r	r	NOUN
ejpam-3206	184	15	)	)	PUNCT
ejpam-3206	184	16	is	be	AUX
ejpam-3206	184	17	a	a	DET
ejpam-3206	184	18	right	right	ADJ
ejpam-3206	184	19	ps	ps	NOUN
ejpam-3206	184	20	-	-	NOUN
ejpam-3206	184	21	ring	ring	NOUN
ejpam-3206	184	22	.	.	PUNCT
ejpam-3206	185	1	case	case	NOUN
ejpam-3206	185	2	(	(	PUNCT
ejpam-3206	185	3	2	2	NUM
ejpam-3206	185	4	):	):	PUNCT
ejpam-3206	185	5	assume	assume	VERB
ejpam-3206	185	6	that	that	SCONJ
ejpam-3206	185	7	nr(l	nr(l	NOUN
ejpam-3206	185	8	)	)	PUNCT
ejpam-3206	185	9	=	=	SYM
ejpam-3206	185	10	re	re	PROPN
ejpam-3206	185	11	,	,	PUNCT
ejpam-3206	185	12	for	for	ADP
ejpam-3206	185	13	some	some	DET
ejpam-3206	185	14	e	e	NOUN
ejpam-3206	185	15	∈	∈	PROPN
ejpam-3206	185	16	i	i	PROPN
ejpam-3206	185	17	d	d	PROPN
ejpam-3206	185	18	(	(	PUNCT
ejpam-3206	185	19	r	r	NOUN
ejpam-3206	185	20	)	)	PUNCT
ejpam-3206	185	21	.	.	PUNCT
ejpam-3206	186	1	let	let	VERB
ejpam-3206	186	2	a	a	DET
ejpam-3206	186	3	∈	∈	ADJ
ejpam-3206	186	4	`	`	PUNCT
ejpam-3206	186	5	r	r	NOUN
ejpam-3206	186	6	(	(	PUNCT
ejpam-3206	186	7	l	l	NOUN
ejpam-3206	186	8	)	)	PUNCT
ejpam-3206	186	9	.	.	PUNCT
ejpam-3206	187	1	then	then	ADV
ejpam-3206	187	2	al	al	PROPN
ejpam-3206	187	3	=	=	SYM
ejpam-3206	187	4	0	0	PUNCT
ejpam-3206	188	1	=	=	SYM
ejpam-3206	188	2	nil	nil	NOUN
ejpam-3206	188	3	(	(	PUNCT
ejpam-3206	188	4	r	r	NOUN
ejpam-3206	188	5	)	)	PUNCT
ejpam-3206	188	6	,	,	PUNCT
ejpam-3206	188	7	which	which	PRON
ejpam-3206	188	8	implies	imply	VERB
ejpam-3206	188	9	that	that	SCONJ
ejpam-3206	188	10	al	al	PROPN
ejpam-3206	188	11	⊆	⊆	NUM
ejpam-3206	188	12	nil	nil	NOUN
ejpam-3206	188	13	(	(	PUNCT
ejpam-3206	188	14	r	r	NOUN
ejpam-3206	188	15	)	)	PUNCT
ejpam-3206	188	16	.	.	PUNCT
ejpam-3206	189	1	hence	hence	ADV
ejpam-3206	189	2	a	a	DET
ejpam-3206	189	3	∈	∈	NOUN
ejpam-3206	189	4	nr(l	nr(l	X
ejpam-3206	189	5	)	)	PUNCT
ejpam-3206	189	6	=	=	SYM
ejpam-3206	189	7	re	re	NOUN
ejpam-3206	189	8	and	and	CCONJ
ejpam-3206	189	9	so	so	ADV
ejpam-3206	189	10	a	a	DET
ejpam-3206	189	11	=	=	SYM
ejpam-3206	189	12	re	re	NOUN
ejpam-3206	189	13	,	,	PUNCT
ejpam-3206	189	14	for	for	ADP
ejpam-3206	189	15	some	some	DET
ejpam-3206	189	16	r	r	NOUN
ejpam-3206	189	17	∈	∈	PROPN
ejpam-3206	189	18	r.	r.	NOUN
ejpam-3206	189	19	therefore	therefore	ADV
ejpam-3206	189	20	a	a	DET
ejpam-3206	189	21	=	=	PUNCT
ejpam-3206	189	22	re	re	NOUN
ejpam-3206	189	23	.	.	PUNCT
ejpam-3206	190	1	thus	thus	ADV
ejpam-3206	190	2	`	`	PUNCT
ejpam-3206	190	3	r	r	NOUN
ejpam-3206	190	4	(	(	PUNCT
ejpam-3206	190	5	l	l	NOUN
ejpam-3206	190	6	)	)	PUNCT
ejpam-3206	190	7	=	=	SYM
ejpam-3206	190	8	re	re	PRON
ejpam-3206	190	9	and	and	CCONJ
ejpam-3206	190	10	we	we	PRON
ejpam-3206	190	11	conclude	conclude	VERB
ejpam-3206	190	12	that	that	SCONJ
ejpam-3206	190	13	r	r	NOUN
ejpam-3206	190	14	=	=	NOUN
ejpam-3206	190	15	r	r	NOUN
ejpam-3206	190	16	/nil	/nil	PUNCT
ejpam-3206	190	17	(	(	PUNCT
ejpam-3206	190	18	r	r	NOUN
ejpam-3206	190	19	)	)	PUNCT
ejpam-3206	190	20	is	be	AUX
ejpam-3206	190	21	a	a	DET
ejpam-3206	190	22	right	right	ADJ
ejpam-3206	190	23	ps	ps	NOUN
ejpam-3206	190	24	-	-	NOUN
ejpam-3206	190	25	ring	ring	NOUN
ejpam-3206	190	26	.	.	PUNCT
ejpam-3206	191	1	example	example	NOUN
ejpam-3206	191	2	12	12	NUM
ejpam-3206	191	3	.	.	PUNCT
ejpam-3206	192	1	in	in	ADP
ejpam-3206	192	2	example	example	NOUN
ejpam-3206	192	3	8	8	NUM
ejpam-3206	192	4	we	we	PRON
ejpam-3206	192	5	conclude	conclude	VERB
ejpam-3206	192	6	that	that	SCONJ
ejpam-3206	192	7	the	the	DET
ejpam-3206	192	8	ring	ring	NOUN
ejpam-3206	192	9	r	r	NOUN
ejpam-3206	192	10	=	=	SYM
ejpam-3206	192	11	z12	z12	NOUN
ejpam-3206	192	12	is	be	AUX
ejpam-3206	192	13	not	not	PART
ejpam-3206	192	14	a	a	DET
ejpam-3206	192	15	weak	weak	ADJ
ejpam-3206	192	16	ps	ps	NOUN
ejpam-3206	192	17	-	-	NOUN
ejpam-3206	192	18	ring	ring	NOUN
ejpam-3206	192	19	.	.	PUNCT
ejpam-3206	193	1	we	we	PRON
ejpam-3206	193	2	can	can	AUX
ejpam-3206	193	3	check	check	VERB
ejpam-3206	193	4	that	that	DET
ejpam-3206	193	5	r	r	NOUN
ejpam-3206	193	6	=	=	NOUN
ejpam-3206	193	7	r	r	NOUN
ejpam-3206	193	8	/nil	/nil	PUNCT
ejpam-3206	193	9	(	(	PUNCT
ejpam-3206	193	10	r	r	NOUN
ejpam-3206	193	11	)	)	PUNCT
ejpam-3206	193	12	∼=	∼=	NOUN
ejpam-3206	193	13	z6	z6	NOUN
ejpam-3206	193	14	,	,	PUNCT
ejpam-3206	193	15	which	which	PRON
ejpam-3206	193	16	,	,	PUNCT
ejpam-3206	193	17	by	by	ADP
ejpam-3206	193	18	example	example	NOUN
ejpam-3206	193	19	6	6	NUM
ejpam-3206	193	20	,	,	PUNCT
ejpam-3206	193	21	is	be	AUX
ejpam-3206	193	22	a	a	DET
ejpam-3206	193	23	weak	weak	ADJ
ejpam-3206	193	24	ps	ps	NOUN
ejpam-3206	193	25	-	-	NOUN
ejpam-3206	193	26	ring	ring	NOUN
ejpam-3206	193	27	.	.	PUNCT
ejpam-3206	194	1	so	so	ADV
ejpam-3206	194	2	we	we	PRON
ejpam-3206	194	3	get	get	VERB
ejpam-3206	194	4	here	here	ADV
ejpam-3206	194	5	an	an	DET
ejpam-3206	194	6	example	example	NOUN
ejpam-3206	194	7	to	to	PART
ejpam-3206	194	8	show	show	VERB
ejpam-3206	194	9	that	that	SCONJ
ejpam-3206	194	10	the	the	DET
ejpam-3206	194	11	converse	converse	NOUN
ejpam-3206	194	12	direction	direction	NOUN
ejpam-3206	194	13	of	of	ADP
ejpam-3206	194	14	theorem	theorem	ADJ
ejpam-3206	194	15	2	2	NUM
ejpam-3206	194	16	does	do	AUX
ejpam-3206	194	17	not	not	PART
ejpam-3206	194	18	hold	hold	VERB
ejpam-3206	194	19	.	.	PUNCT
ejpam-3206	195	1	example	example	NOUN
ejpam-3206	195	2	13	13	NUM
ejpam-3206	195	3	.	.	PUNCT
ejpam-3206	196	1	in	in	ADP
ejpam-3206	196	2	example	example	NOUN
ejpam-3206	196	3	11	11	NUM
ejpam-3206	196	4	we	we	PRON
ejpam-3206	196	5	conclude	conclude	VERB
ejpam-3206	196	6	that	that	SCONJ
ejpam-3206	196	7	the	the	DET
ejpam-3206	196	8	ring	ring	NOUN
ejpam-3206	196	9	r	r	NOUN
ejpam-3206	196	10	=	=	NOUN
ejpam-3206	196	11	v	v	NOUN
ejpam-3206	196	12	is	be	AUX
ejpam-3206	196	13	a	a	DET
ejpam-3206	196	14	weak	weak	ADJ
ejpam-3206	196	15	left	left	ADJ
ejpam-3206	196	16	ps	ps	NOUN
ejpam-3206	196	17	-	-	PUNCT
ejpam-3206	196	18	ring	ring	NOUN
ejpam-3206	196	19	.	.	PUNCT
ejpam-3206	197	1	we	we	PRON
ejpam-3206	197	2	turn	turn	VERB
ejpam-3206	197	3	now	now	ADV
ejpam-3206	197	4	to	to	PART
ejpam-3206	197	5	check	check	VERB
ejpam-3206	197	6	the	the	DET
ejpam-3206	197	7	condition	condition	NOUN
ejpam-3206	197	8	of	of	ADP
ejpam-3206	197	9	weak	weak	ADJ
ejpam-3206	197	10	ps	ps	NOUN
ejpam-3206	197	11	-	-	NOUN
ejpam-3206	197	12	ring	ring	NOUN
ejpam-3206	197	13	on	on	ADP
ejpam-3206	197	14	the	the	DET
ejpam-3206	197	15	direct	direct	ADJ
ejpam-3206	197	16	sum	sum	NOUN
ejpam-3206	197	17	a	a	DET
ejpam-3206	197	18	=	=	SYM
ejpam-3206	197	19	v	v	ADP
ejpam-3206	197	20	⊕	⊕	PROPN
ejpam-3206	198	1	v.	v.	ADV
ejpam-3206	199	1	in	in	ADP
ejpam-3206	199	2	a	a	PRON
ejpam-3206	199	3	,	,	PUNCT
ejpam-3206	199	4	we	we	PRON
ejpam-3206	199	5	have	have	VERB
ejpam-3206	199	6	:	:	PUNCT
ejpam-3206	199	7	nil	nil	X
ejpam-3206	199	8	(	(	PUNCT
ejpam-3206	199	9	a	a	X
ejpam-3206	199	10	)	)	PUNCT
ejpam-3206	199	11	=	=	SYM
ejpam-3206	199	12	nil	nil	NOUN
ejpam-3206	199	13	(	(	PUNCT
ejpam-3206	199	14	v	v	NOUN
ejpam-3206	199	15	)	)	PUNCT
ejpam-3206	199	16	⊕	⊕	PROPN
ejpam-3206	199	17	nil	nil	NOUN
ejpam-3206	199	18	(	(	PUNCT
ejpam-3206	199	19	v	v	NOUN
ejpam-3206	199	20	)	)	PUNCT
ejpam-3206	199	21	=	=	SYM
ejpam-3206	199	22	{	{	PUNCT
ejpam-3206	199	23	(	(	PUNCT
ejpam-3206	199	24	0	0	NUM
ejpam-3206	199	25	,	,	PUNCT
ejpam-3206	199	26	0	0	NUM
ejpam-3206	199	27	)	)	PUNCT
ejpam-3206	199	28	,	,	PUNCT
ejpam-3206	199	29	(	(	PUNCT
ejpam-3206	199	30	0	0	NUM
ejpam-3206	199	31	,	,	PUNCT
ejpam-3206	199	32	c	c	NOUN
ejpam-3206	199	33	)	)	PUNCT
ejpam-3206	199	34	,	,	PUNCT
ejpam-3206	199	35	(	(	PUNCT
ejpam-3206	199	36	c	c	X
ejpam-3206	199	37	,	,	PUNCT
ejpam-3206	199	38	0	0	NUM
ejpam-3206	199	39	)	)	PUNCT
ejpam-3206	199	40	,	,	PUNCT
ejpam-3206	199	41	(	(	PUNCT
ejpam-3206	199	42	c	c	X
ejpam-3206	199	43	,	,	PUNCT
ejpam-3206	199	44	c	c	NOUN
ejpam-3206	199	45	)	)	PUNCT
ejpam-3206	199	46	}	}	PUNCT
ejpam-3206	199	47	,	,	PUNCT
ejpam-3206	199	48	and	and	CCONJ
ejpam-3206	199	49	i	i	PROPN
ejpam-3206	199	50	d	d	PROPN
ejpam-3206	199	51	(	(	PUNCT
ejpam-3206	199	52	a	a	X
ejpam-3206	199	53	)	)	PUNCT
ejpam-3206	200	1	=	=	PUNCT
ejpam-3206	200	2	i	i	PROPN
ejpam-3206	200	3	d	d	PROPN
ejpam-3206	200	4	(	(	PUNCT
ejpam-3206	200	5	v	v	NOUN
ejpam-3206	200	6	)	)	PUNCT
ejpam-3206	200	7	⊕	⊕	PROPN
ejpam-3206	201	1	i	i	PROPN
ejpam-3206	201	2	d	d	PROPN
ejpam-3206	201	3	(	(	PUNCT
ejpam-3206	201	4	v	v	NOUN
ejpam-3206	201	5	)	)	PUNCT
ejpam-3206	201	6	=	=	SYM
ejpam-3206	201	7	{	{	PUNCT
ejpam-3206	201	8	(	(	PUNCT
ejpam-3206	201	9	0	0	NUM
ejpam-3206	201	10	,	,	PUNCT
ejpam-3206	201	11	0	0	NUM
ejpam-3206	201	12	)	)	PUNCT
ejpam-3206	201	13	,	,	PUNCT
ejpam-3206	201	14	(	(	PUNCT
ejpam-3206	201	15	0	0	NUM
ejpam-3206	201	16	,	,	PUNCT
ejpam-3206	201	17	a	a	PRON
ejpam-3206	201	18	)	)	PUNCT
ejpam-3206	201	19	,	,	PUNCT
ejpam-3206	201	20	(	(	PUNCT
ejpam-3206	201	21	a	a	PRON
ejpam-3206	201	22	,	,	PUNCT
ejpam-3206	201	23	0	0	NUM
ejpam-3206	201	24	)	)	PUNCT
ejpam-3206	201	25	,	,	PUNCT
ejpam-3206	201	26	(	(	PUNCT
ejpam-3206	201	27	0	0	NUM
ejpam-3206	201	28	,	,	PUNCT
ejpam-3206	201	29	b	b	NOUN
ejpam-3206	201	30	)	)	PUNCT
ejpam-3206	201	31	,	,	PUNCT
ejpam-3206	201	32	(	(	PUNCT
ejpam-3206	201	33	b	b	NOUN
ejpam-3206	201	34	,	,	PUNCT
ejpam-3206	201	35	0	0	NUM
ejpam-3206	201	36	)	)	PUNCT
ejpam-3206	201	37	,	,	PUNCT
ejpam-3206	201	38	(	(	PUNCT
ejpam-3206	201	39	a	a	DET
ejpam-3206	201	40	,	,	PUNCT
ejpam-3206	201	41	b	b	NOUN
ejpam-3206	201	42	)	)	PUNCT
ejpam-3206	201	43	,	,	PUNCT
ejpam-3206	201	44	(	(	PUNCT
ejpam-3206	201	45	b	b	X
ejpam-3206	201	46	,	,	PUNCT
ejpam-3206	201	47	a	a	NOUN
ejpam-3206	201	48	)	)	PUNCT
ejpam-3206	201	49	}	}	PUNCT
ejpam-3206	201	50	.	.	PUNCT
ejpam-3206	202	1	consider	consider	VERB
ejpam-3206	202	2	now	now	ADV
ejpam-3206	202	3	the	the	DET
ejpam-3206	202	4	following	follow	VERB
ejpam-3206	202	5	maximal	maximal	ADJ
ejpam-3206	202	6	two	two	NUM
ejpam-3206	202	7	sided	sided	ADJ
ejpam-3206	202	8	ideal	ideal	NOUN
ejpam-3206	202	9	in	in	ADP
ejpam-3206	202	10	a	a	DET
ejpam-3206	202	11	,	,	PUNCT
ejpam-3206	202	12	l	l	NOUN
ejpam-3206	202	13	=	=	SYM
ejpam-3206	202	14	k	k	PROPN
ejpam-3206	202	15	⊕	⊕	PROPN
ejpam-3206	202	16	v	v	NOUN
ejpam-3206	202	17	=	=	PRON
ejpam-3206	202	18	{	{	PUNCT
ejpam-3206	202	19	(	(	PUNCT
ejpam-3206	202	20	0	0	NUM
ejpam-3206	202	21	,	,	PUNCT
ejpam-3206	202	22	0	0	NUM
ejpam-3206	202	23	)	)	PUNCT
ejpam-3206	202	24	,	,	PUNCT
ejpam-3206	202	25	(	(	PUNCT
ejpam-3206	202	26	0	0	NUM
ejpam-3206	202	27	,	,	PUNCT
ejpam-3206	202	28	c	c	NOUN
ejpam-3206	202	29	)	)	PUNCT
ejpam-3206	202	30	,	,	PUNCT
ejpam-3206	202	31	(	(	PUNCT
ejpam-3206	202	32	a	a	PRON
ejpam-3206	202	33	,	,	PUNCT
ejpam-3206	202	34	0	0	NUM
ejpam-3206	202	35	)	)	PUNCT
ejpam-3206	202	36	,	,	PUNCT
ejpam-3206	202	37	(	(	PUNCT
ejpam-3206	202	38	a	a	DET
ejpam-3206	202	39	,	,	PUNCT
ejpam-3206	202	40	c	c	NOUN
ejpam-3206	202	41	)	)	PUNCT
ejpam-3206	202	42	,	,	PUNCT
ejpam-3206	202	43	(	(	PUNCT
ejpam-3206	202	44	b	b	NOUN
ejpam-3206	202	45	,	,	PUNCT
ejpam-3206	202	46	0	0	NUM
ejpam-3206	202	47	)	)	PUNCT
ejpam-3206	202	48	,	,	PUNCT
ejpam-3206	202	49	(	(	PUNCT
ejpam-3206	202	50	b	b	X
ejpam-3206	202	51	,	,	PUNCT
ejpam-3206	202	52	c	c	NOUN
ejpam-3206	202	53	)	)	PUNCT
ejpam-3206	202	54	,	,	PUNCT
ejpam-3206	202	55	(	(	PUNCT
ejpam-3206	202	56	c	c	X
ejpam-3206	202	57	,	,	PUNCT
ejpam-3206	202	58	0	0	NUM
ejpam-3206	202	59	)	)	PUNCT
ejpam-3206	202	60	,	,	PUNCT
ejpam-3206	202	61	(	(	PUNCT
ejpam-3206	202	62	c	c	X
ejpam-3206	202	63	,	,	PUNCT
ejpam-3206	202	64	c	c	NOUN
ejpam-3206	202	65	)	)	PUNCT
ejpam-3206	202	66	}	}	PUNCT
ejpam-3206	202	67	.	.	PUNCT
ejpam-3206	203	1	m.	m.	NOUN
ejpam-3206	203	2	a.	a.	PROPN
ejpam-3206	203	3	farahat	farahat	PROPN
ejpam-3206	203	4	,	,	PUNCT
ejpam-3206	203	5	s.	s.	PROPN
ejpam-3206	203	6	t.	t.	PROPN
ejpam-3206	203	7	al	al	PROPN
ejpam-3206	203	8	-	-	PUNCT
ejpam-3206	203	9	bogamy	bogamy	PROPN
ejpam-3206	203	10	/	/	SYM
ejpam-3206	203	11	eur	eur	PROPN
ejpam-3206	203	12	.	.	PUNCT
ejpam-3206	204	1	j.	j.	PROPN
ejpam-3206	204	2	pure	pure	PROPN
ejpam-3206	204	3	appl	appl	PROPN
ejpam-3206	204	4	.	.	PROPN
ejpam-3206	204	5	math	math	PROPN
ejpam-3206	204	6	,	,	PUNCT
ejpam-3206	204	7	11	11	NUM
ejpam-3206	204	8	(	(	PUNCT
ejpam-3206	204	9	1	1	NUM
ejpam-3206	204	10	)	)	PUNCT
ejpam-3206	204	11	(	(	PUNCT
ejpam-3206	204	12	2018	2018	NUM
ejpam-3206	204	13	)	)	PUNCT
ejpam-3206	204	14	,	,	PUNCT
ejpam-3206	204	15	244	244	NUM
ejpam-3206	204	16	-	-	SYM
ejpam-3206	204	17	259	259	NUM
ejpam-3206	204	18	251	251	NUM
ejpam-3206	204	19	by	by	ADP
ejpam-3206	204	20	direct	direct	ADJ
ejpam-3206	204	21	computations	computation	NOUN
ejpam-3206	204	22	we	we	PRON
ejpam-3206	204	23	get	get	VERB
ejpam-3206	204	24	na	na	ADP
ejpam-3206	204	25	(	(	PUNCT
ejpam-3206	204	26	k	k	PROPN
ejpam-3206	204	27	⊕	⊕	PROPN
ejpam-3206	204	28	v	v	NOUN
ejpam-3206	204	29	)	)	PUNCT
ejpam-3206	204	30	=	=	SYM
ejpam-3206	204	31	nv	nv	PROPN
ejpam-3206	204	32	(	(	PUNCT
ejpam-3206	204	33	k)⊕nv	k)⊕nv	PROPN
ejpam-3206	204	34	(	(	PUNCT
ejpam-3206	204	35	v	v	NOUN
ejpam-3206	204	36	)	)	PUNCT
ejpam-3206	204	37	=	=	SYM
ejpam-3206	204	38	v	v	ADP
ejpam-3206	204	39	⊕k	⊕k	NOUN
ejpam-3206	204	40	=	=	SYM
ejpam-3206	204	41	{	{	PUNCT
ejpam-3206	204	42	(	(	PUNCT
ejpam-3206	204	43	0	0	NUM
ejpam-3206	204	44	,	,	PUNCT
ejpam-3206	204	45	0	0	NUM
ejpam-3206	204	46	)	)	PUNCT
ejpam-3206	204	47	,	,	PUNCT
ejpam-3206	204	48	(	(	PUNCT
ejpam-3206	204	49	0	0	NUM
ejpam-3206	204	50	,	,	PUNCT
ejpam-3206	204	51	a	a	PRON
ejpam-3206	204	52	)	)	PUNCT
ejpam-3206	204	53	,	,	PUNCT
ejpam-3206	204	54	(	(	PUNCT
ejpam-3206	204	55	0	0	NUM
ejpam-3206	204	56	,	,	PUNCT
ejpam-3206	204	57	b	b	NOUN
ejpam-3206	204	58	)	)	PUNCT
ejpam-3206	204	59	,	,	PUNCT
ejpam-3206	204	60	(	(	PUNCT
ejpam-3206	204	61	0	0	NUM
ejpam-3206	204	62	,	,	PUNCT
ejpam-3206	204	63	c	c	NOUN
ejpam-3206	204	64	)	)	PUNCT
ejpam-3206	204	65	,	,	PUNCT
ejpam-3206	204	66	(	(	PUNCT
ejpam-3206	204	67	c	c	X
ejpam-3206	204	68	,	,	PUNCT
ejpam-3206	204	69	0	0	NUM
ejpam-3206	204	70	)	)	PUNCT
ejpam-3206	204	71	,	,	PUNCT
ejpam-3206	204	72	(	(	PUNCT
ejpam-3206	204	73	c	c	X
ejpam-3206	204	74	,	,	PUNCT
ejpam-3206	204	75	a	a	NOUN
ejpam-3206	204	76	)	)	PUNCT
ejpam-3206	204	77	,	,	PUNCT
ejpam-3206	204	78	(	(	PUNCT
ejpam-3206	204	79	c	c	X
ejpam-3206	204	80	,	,	PUNCT
ejpam-3206	204	81	b	b	NOUN
ejpam-3206	204	82	)	)	PUNCT
ejpam-3206	204	83	,	,	PUNCT
ejpam-3206	204	84	(	(	PUNCT
ejpam-3206	204	85	c	c	X
ejpam-3206	204	86	,	,	PUNCT
ejpam-3206	204	87	c	c	NOUN
ejpam-3206	204	88	)	)	PUNCT
ejpam-3206	204	89	}	}	PUNCT
ejpam-3206	204	90	.	.	PUNCT
ejpam-3206	205	1	clearly	clearly	ADV
ejpam-3206	205	2	,	,	PUNCT
ejpam-3206	205	3	na	na	X
ejpam-3206	205	4	(	(	PUNCT
ejpam-3206	205	5	k	k	PROPN
ejpam-3206	205	6	⊕	⊕	PROPN
ejpam-3206	205	7	v	v	NOUN
ejpam-3206	205	8	)	)	PUNCT
ejpam-3206	205	9	is	be	AUX
ejpam-3206	205	10	not	not	PART
ejpam-3206	205	11	contained	contain	VERB
ejpam-3206	205	12	in	in	ADP
ejpam-3206	205	13	nil	nil	NOUN
ejpam-3206	205	14	(	(	PUNCT
ejpam-3206	205	15	a	a	NOUN
ejpam-3206	205	16	)	)	PUNCT
ejpam-3206	205	17	and	and	CCONJ
ejpam-3206	205	18	not	not	PART
ejpam-3206	205	19	generated	generate	VERB
ejpam-3206	205	20	by	by	ADP
ejpam-3206	205	21	idempotent	idempotent	NOUN
ejpam-3206	205	22	in	in	ADP
ejpam-3206	205	23	a.	a.	NOUN
ejpam-3206	205	24	therefore	therefore	ADV
ejpam-3206	205	25	a	a	DET
ejpam-3206	205	26	=	=	SYM
ejpam-3206	205	27	v	v	ADP
ejpam-3206	205	28	⊕	⊕	PROPN
ejpam-3206	205	29	v	v	NOUN
ejpam-3206	205	30	is	be	AUX
ejpam-3206	205	31	not	not	PART
ejpam-3206	205	32	a	a	DET
ejpam-3206	205	33	weak	weak	ADJ
ejpam-3206	205	34	left	left	NOUN
ejpam-3206	205	35	(	(	PUNCT
ejpam-3206	205	36	right	right	ADJ
ejpam-3206	205	37	)	)	PUNCT
ejpam-3206	205	38	ps	ps	NOUN
ejpam-3206	205	39	-	-	PUNCT
ejpam-3206	205	40	ring	ring	NOUN
ejpam-3206	205	41	,	,	PUNCT
ejpam-3206	205	42	i.e.	i.e.	X
ejpam-3206	205	43	,	,	PUNCT
ejpam-3206	205	44	the	the	DET
ejpam-3206	205	45	direct	direct	ADJ
ejpam-3206	205	46	sum	sum	NOUN
ejpam-3206	205	47	of	of	ADP
ejpam-3206	205	48	weak	weak	ADJ
ejpam-3206	205	49	left	left	NOUN
ejpam-3206	205	50	(	(	PUNCT
ejpam-3206	205	51	right	right	ADJ
ejpam-3206	205	52	)	)	PUNCT
ejpam-3206	205	53	ps	ps	NOUN
ejpam-3206	205	54	-	-	PUNCT
ejpam-3206	205	55	rings	ring	NOUN
ejpam-3206	205	56	not	not	PART
ejpam-3206	205	57	necessary	necessary	ADJ
ejpam-3206	205	58	be	be	AUX
ejpam-3206	205	59	a	a	DET
ejpam-3206	205	60	weak	weak	ADJ
ejpam-3206	205	61	left	left	NOUN
ejpam-3206	205	62	(	(	PUNCT
ejpam-3206	205	63	right	right	ADJ
ejpam-3206	205	64	)	)	PUNCT
ejpam-3206	205	65	ps	ps	NOUN
ejpam-3206	205	66	-	-	PUNCT
ejpam-3206	205	67	ring	ring	NOUN
ejpam-3206	205	68	.	.	PUNCT
ejpam-3206	206	1	recall	recall	VERB
ejpam-3206	206	2	that	that	SCONJ
ejpam-3206	206	3	a	a	DET
ejpam-3206	206	4	nonzero	nonzero	ADJ
ejpam-3206	206	5	right	right	ADJ
ejpam-3206	206	6	ideal	ideal	NOUN
ejpam-3206	206	7	i	i	PRON
ejpam-3206	206	8	of	of	ADP
ejpam-3206	206	9	r	r	NOUN
ejpam-3206	206	10	is	be	AUX
ejpam-3206	206	11	a	a	DET
ejpam-3206	206	12	right	right	ADJ
ejpam-3206	206	13	essential	essential	ADJ
ejpam-3206	206	14	ideal	ideal	NOUN
ejpam-3206	206	15	if	if	SCONJ
ejpam-3206	206	16	i	i	PRON
ejpam-3206	206	17	has	have	VERB
ejpam-3206	206	18	nonzero	nonzero	ADJ
ejpam-3206	206	19	intersection	intersection	NOUN
ejpam-3206	206	20	with	with	ADP
ejpam-3206	206	21	every	every	DET
ejpam-3206	206	22	nonzero	nonzero	ADJ
ejpam-3206	206	23	right	right	ADJ
ejpam-3206	206	24	ideal	ideal	NOUN
ejpam-3206	206	25	of	of	ADP
ejpam-3206	206	26	r.	r.	PROPN
ejpam-3206	206	27	a	a	DET
ejpam-3206	206	28	singular	singular	ADJ
ejpam-3206	206	29	right	right	PROPN
ejpam-3206	206	30	ideal	ideal	PROPN
ejpam-3206	206	31	sr	sr	PROPN
ejpam-3206	206	32	(	(	PUNCT
ejpam-3206	206	33	r	r	NOUN
ejpam-3206	206	34	)	)	PUNCT
ejpam-3206	206	35	of	of	ADP
ejpam-3206	206	36	r	r	NOUN
ejpam-3206	206	37	is	be	AUX
ejpam-3206	206	38	defined	define	VERB
ejpam-3206	206	39	by	by	ADP
ejpam-3206	206	40	sr	sr	PROPN
ejpam-3206	206	41	(	(	PUNCT
ejpam-3206	206	42	r	r	NOUN
ejpam-3206	206	43	)	)	PUNCT
ejpam-3206	206	44	=	=	NOUN
ejpam-3206	206	45	{	{	PUNCT
ejpam-3206	206	46	a	a	DET
ejpam-3206	206	47	∈	∈	NOUN
ejpam-3206	207	1	r	r	NOUN
ejpam-3206	207	2	|	|	NOUN
ejpam-3206	207	3	rr	rr	X
ejpam-3206	207	4	(	(	PUNCT
ejpam-3206	207	5	a	a	NOUN
ejpam-3206	207	6	)	)	PUNCT
ejpam-3206	207	7	is	be	AUX
ejpam-3206	207	8	an	an	DET
ejpam-3206	207	9	essential	essential	ADJ
ejpam-3206	207	10	right	right	ADJ
ejpam-3206	207	11	ideal	ideal	NOUN
ejpam-3206	207	12	of	of	ADP
ejpam-3206	207	13	r	r	NOUN
ejpam-3206	207	14	}	}	PUNCT
ejpam-3206	207	15	.	.	PUNCT
ejpam-3206	208	1	similarly	similarly	ADV
ejpam-3206	208	2	,	,	PUNCT
ejpam-3206	208	3	we	we	PRON
ejpam-3206	208	4	can	can	AUX
ejpam-3206	208	5	define	define	VERB
ejpam-3206	208	6	a	a	DET
ejpam-3206	208	7	singular	singular	NOUN
ejpam-3206	208	8	left	leave	VERB
ejpam-3206	208	9	ideal	ideal	NOUN
ejpam-3206	208	10	s	s	X
ejpam-3206	208	11	`	`	PUNCT
ejpam-3206	208	12	(	(	PUNCT
ejpam-3206	208	13	r	r	NOUN
ejpam-3206	208	14	)	)	PUNCT
ejpam-3206	208	15	of	of	ADP
ejpam-3206	208	16	r	r	NOUN
ejpam-3206	208	17	is	be	AUX
ejpam-3206	208	18	defined	define	VERB
ejpam-3206	208	19	by	by	ADP
ejpam-3206	208	20	s	s	NOUN
ejpam-3206	208	21	`	`	PUNCT
ejpam-3206	208	22	(	(	PUNCT
ejpam-3206	208	23	r	r	NOUN
ejpam-3206	208	24	)	)	PUNCT
ejpam-3206	208	25	=	=	NOUN
ejpam-3206	208	26	{	{	PUNCT
ejpam-3206	208	27	a	a	DET
ejpam-3206	208	28	∈	∈	PROPN
ejpam-3206	208	29	r	r	NOUN
ejpam-3206	208	30	|	|	NOUN
ejpam-3206	208	31	`	`	PUNCT
ejpam-3206	208	32	r	r	NOUN
ejpam-3206	208	33	(	(	PUNCT
ejpam-3206	208	34	a	a	NOUN
ejpam-3206	208	35	)	)	PUNCT
ejpam-3206	208	36	is	be	AUX
ejpam-3206	208	37	an	an	DET
ejpam-3206	208	38	essential	essential	ADJ
ejpam-3206	208	39	left	left	ADJ
ejpam-3206	208	40	ideal	ideal	NOUN
ejpam-3206	208	41	of	of	ADP
ejpam-3206	208	42	r	r	NOUN
ejpam-3206	208	43	}	}	PUNCT
ejpam-3206	208	44	.	.	PUNCT
ejpam-3206	209	1	a	a	DET
ejpam-3206	209	2	ring	ring	NOUN
ejpam-3206	209	3	r	r	NOUN
ejpam-3206	209	4	is	be	AUX
ejpam-3206	209	5	called	call	VERB
ejpam-3206	209	6	right	right	ADJ
ejpam-3206	209	7	(	(	PUNCT
ejpam-3206	209	8	left	left	ADJ
ejpam-3206	209	9	)	)	PUNCT
ejpam-3206	209	10	nonsingular	nonsingular	ADJ
ejpam-3206	210	1	if	if	SCONJ
ejpam-3206	210	2	sr	sr	PROPN
ejpam-3206	210	3	(	(	PUNCT
ejpam-3206	210	4	r	r	NOUN
ejpam-3206	210	5	)	)	PUNCT
ejpam-3206	210	6	=	=	SYM
ejpam-3206	210	7	0	0	PUNCT
ejpam-3206	210	8	(	(	PUNCT
ejpam-3206	210	9	s	s	NOUN
ejpam-3206	210	10	`	`	PUNCT
ejpam-3206	210	11	(	(	PUNCT
ejpam-3206	210	12	r	r	NOUN
ejpam-3206	210	13	)	)	PUNCT
ejpam-3206	210	14	=	=	SYM
ejpam-3206	210	15	0	0	NUM
ejpam-3206	210	16	)	)	PUNCT
ejpam-3206	210	17	and	and	CCONJ
ejpam-3206	210	18	right	right	ADJ
ejpam-3206	210	19	(	(	PUNCT
ejpam-3206	210	20	left	left	ADJ
ejpam-3206	210	21	)	)	PUNCT
ejpam-3206	210	22	singular	singular	NOUN
ejpam-3206	211	1	if	if	SCONJ
ejpam-3206	211	2	sr	sr	PROPN
ejpam-3206	211	3	(	(	PUNCT
ejpam-3206	211	4	r	r	NOUN
ejpam-3206	211	5	)	)	PUNCT
ejpam-3206	211	6	=	=	SYM
ejpam-3206	211	7	r	r	NOUN
ejpam-3206	211	8	(	(	PUNCT
ejpam-3206	211	9	s	s	NOUN
ejpam-3206	211	10	`	`	PUNCT
ejpam-3206	211	11	(	(	PUNCT
ejpam-3206	211	12	r	r	NOUN
ejpam-3206	211	13	)	)	PUNCT
ejpam-3206	211	14	=	=	SYM
ejpam-3206	211	15	r	r	NOUN
ejpam-3206	211	16	)	)	PUNCT
ejpam-3206	211	17	.	.	PUNCT
ejpam-3206	212	1	we	we	PRON
ejpam-3206	212	2	define	define	VERB
ejpam-3206	212	3	a	a	DET
ejpam-3206	212	4	weak	weak	ADJ
ejpam-3206	212	5	singular	singular	ADJ
ejpam-3206	212	6	ideal	ideal	NOUN
ejpam-3206	212	7	of	of	ADP
ejpam-3206	212	8	an	an	DET
ejpam-3206	212	9	ni	ni	NOUN
ejpam-3206	212	10	-	-	PUNCT
ejpam-3206	212	11	ring	ring	NOUN
ejpam-3206	212	12	r	r	NOUN
ejpam-3206	212	13	as	as	SCONJ
ejpam-3206	212	14	follows	follow	VERB
ejpam-3206	212	15	:	:	PUNCT
ejpam-3206	212	16	ns	ns	INTJ
ejpam-3206	212	17	(	(	PUNCT
ejpam-3206	212	18	r	r	NOUN
ejpam-3206	212	19	)	)	PUNCT
ejpam-3206	212	20	=	=	NOUN
ejpam-3206	212	21	{	{	PUNCT
ejpam-3206	212	22	a	a	DET
ejpam-3206	212	23	∈	∈	PROPN
ejpam-3206	212	24	r	r	NOUN
ejpam-3206	212	25	|	|	NOUN
ejpam-3206	212	26	nr	nr	PROPN
ejpam-3206	212	27	(	(	PUNCT
ejpam-3206	212	28	a	a	PRON
ejpam-3206	212	29	)	)	PUNCT
ejpam-3206	212	30	is	be	AUX
ejpam-3206	212	31	an	an	DET
ejpam-3206	212	32	essential	essential	ADJ
ejpam-3206	212	33	ideal	ideal	NOUN
ejpam-3206	212	34	of	of	ADP
ejpam-3206	212	35	r	r	NOUN
ejpam-3206	212	36	}	}	PUNCT
ejpam-3206	212	37	.	.	PUNCT
ejpam-3206	213	1	we	we	PRON
ejpam-3206	213	2	extend	extend	VERB
ejpam-3206	213	3	the	the	DET
ejpam-3206	213	4	definitions	definition	NOUN
ejpam-3206	213	5	of	of	ADP
ejpam-3206	213	6	a	a	DET
ejpam-3206	213	7	right	right	NOUN
ejpam-3206	213	8	(	(	PUNCT
ejpam-3206	213	9	left	left	ADJ
ejpam-3206	213	10	)	)	PUNCT
ejpam-3206	213	11	nonsingular	nonsingular	ADJ
ejpam-3206	213	12	ring	ring	NOUN
ejpam-3206	213	13	and	and	CCONJ
ejpam-3206	213	14	a	a	DET
ejpam-3206	213	15	right	right	NOUN
ejpam-3206	213	16	(	(	PUNCT
ejpam-3206	213	17	left	left	ADJ
ejpam-3206	213	18	)	)	PUNCT
ejpam-3206	213	19	singular	singular	PROPN
ejpam-3206	213	20	ring	ring	NOUN
ejpam-3206	213	21	to	to	ADP
ejpam-3206	213	22	a	a	DET
ejpam-3206	213	23	weak	weak	ADJ
ejpam-3206	213	24	nonsingular	nonsingular	ADJ
ejpam-3206	213	25	ring	ring	NOUN
ejpam-3206	213	26	and	and	CCONJ
ejpam-3206	213	27	a	a	DET
ejpam-3206	213	28	weak	weak	ADJ
ejpam-3206	213	29	singular	singular	ADJ
ejpam-3206	213	30	ring	ring	NOUN
ejpam-3206	213	31	,	,	PUNCT
ejpam-3206	213	32	respectively	respectively	ADV
ejpam-3206	213	33	,	,	PUNCT
ejpam-3206	213	34	as	as	SCONJ
ejpam-3206	213	35	follows	follow	VERB
ejpam-3206	213	36	:	:	PUNCT
ejpam-3206	213	37	definition	definition	NOUN
ejpam-3206	213	38	2	2	NUM
ejpam-3206	213	39	.	.	PUNCT
ejpam-3206	214	1	an	an	DET
ejpam-3206	214	2	ni	ni	NOUN
ejpam-3206	214	3	-	-	PUNCT
ejpam-3206	214	4	ring	ring	NOUN
ejpam-3206	214	5	r	r	NOUN
ejpam-3206	214	6	is	be	AUX
ejpam-3206	214	7	called	call	VERB
ejpam-3206	214	8	a	a	DET
ejpam-3206	214	9	weak	weak	ADJ
ejpam-3206	214	10	singular	singular	NOUN
ejpam-3206	214	11	ring	ring	NOUN
ejpam-3206	214	12	if	if	SCONJ
ejpam-3206	214	13	ns	ns	X
ejpam-3206	214	14	(	(	PUNCT
ejpam-3206	214	15	r	r	NOUN
ejpam-3206	214	16	)	)	PUNCT
ejpam-3206	214	17	=	=	SYM
ejpam-3206	215	1	r	r	NOUN
ejpam-3206	215	2	and	and	CCONJ
ejpam-3206	215	3	r	r	NOUN
ejpam-3206	215	4	is	be	AUX
ejpam-3206	215	5	called	call	VERB
ejpam-3206	215	6	a	a	DET
ejpam-3206	215	7	weak	weak	ADJ
ejpam-3206	215	8	nonsingular	nonsingular	ADJ
ejpam-3206	215	9	ring	ring	NOUN
ejpam-3206	215	10	if	if	SCONJ
ejpam-3206	215	11	ns	ns	X
ejpam-3206	215	12	(	(	PUNCT
ejpam-3206	215	13	r	r	NOUN
ejpam-3206	215	14	)	)	PUNCT
ejpam-3206	215	15	=	=	SYM
ejpam-3206	215	16	0	0	X
ejpam-3206	215	17	.	.	NOUN
ejpam-3206	215	18	example	example	NOUN
ejpam-3206	216	1	14	14	NUM
ejpam-3206	216	2	.	.	NOUN
ejpam-3206	216	3	1	1	NUM
ejpam-3206	216	4	)	)	PUNCT
ejpam-3206	216	5	in	in	ADP
ejpam-3206	216	6	example	example	NOUN
ejpam-3206	216	7	5	5	NUM
ejpam-3206	216	8	,	,	PUNCT
ejpam-3206	216	9	r	r	NOUN
ejpam-3206	216	10	=	=	SYM
ejpam-3206	216	11	z4	z4	X
ejpam-3206	216	12	,	,	PUNCT
ejpam-3206	216	13	we	we	PRON
ejpam-3206	216	14	can	can	AUX
ejpam-3206	216	15	check	check	VERB
ejpam-3206	216	16	that	that	PRON
ejpam-3206	216	17	ns	ns	INTJ
ejpam-3206	216	18	(	(	PUNCT
ejpam-3206	216	19	r	r	NOUN
ejpam-3206	216	20	)	)	PUNCT
ejpam-3206	216	21	=	=	SYM
ejpam-3206	216	22	r	r	NOUN
ejpam-3206	216	23	,	,	PUNCT
ejpam-3206	216	24	hence	hence	ADV
ejpam-3206	216	25	r	r	NOUN
ejpam-3206	216	26	is	be	AUX
ejpam-3206	216	27	a	a	DET
ejpam-3206	216	28	weak	weak	ADJ
ejpam-3206	216	29	singular	singular	ADJ
ejpam-3206	216	30	ring	ring	NOUN
ejpam-3206	216	31	.	.	PUNCT
ejpam-3206	217	1	but	but	CCONJ
ejpam-3206	217	2	sr	sr	PROPN
ejpam-3206	217	3	(	(	PUNCT
ejpam-3206	217	4	r	r	NOUN
ejpam-3206	217	5	)	)	PUNCT
ejpam-3206	217	6	=	=	SYM
ejpam-3206	217	7	s	s	X
ejpam-3206	217	8	`	`	PUNCT
ejpam-3206	217	9	(	(	PUNCT
ejpam-3206	217	10	r	r	NOUN
ejpam-3206	217	11	)	)	PUNCT
ejpam-3206	217	12	=	=	SYM
ejpam-3206	217	13	{	{	PUNCT
ejpam-3206	217	14	0	0	NUM
ejpam-3206	217	15	,	,	PUNCT
ejpam-3206	217	16	2	2	NUM
ejpam-3206	217	17	}	}	PUNCT
ejpam-3206	217	18	=	=	NOUN
ejpam-3206	217	19	nil	nil	NOUN
ejpam-3206	217	20	(	(	PUNCT
ejpam-3206	217	21	r	r	NOUN
ejpam-3206	217	22	)	)	PUNCT
ejpam-3206	217	23	,	,	PUNCT
ejpam-3206	217	24	hence	hence	ADV
ejpam-3206	217	25	r	r	NOUN
ejpam-3206	217	26	is	be	AUX
ejpam-3206	217	27	neither	neither	CCONJ
ejpam-3206	217	28	a	a	DET
ejpam-3206	217	29	nonsingular	nonsingular	ADJ
ejpam-3206	217	30	ring	ring	NOUN
ejpam-3206	217	31	nor	nor	CCONJ
ejpam-3206	217	32	a	a	DET
ejpam-3206	217	33	singular	singular	ADJ
ejpam-3206	217	34	ring	ring	NOUN
ejpam-3206	217	35	.	.	PUNCT
ejpam-3206	218	1	2	2	NUM
ejpam-3206	218	2	)	)	PUNCT
ejpam-3206	218	3	in	in	ADP
ejpam-3206	218	4	example	example	NOUN
ejpam-3206	218	5	6	6	NUM
ejpam-3206	218	6	,	,	PUNCT
ejpam-3206	218	7	r	r	NOUN
ejpam-3206	218	8	=	=	SYM
ejpam-3206	218	9	z6	z6	PROPN
ejpam-3206	218	10	,	,	PUNCT
ejpam-3206	218	11	we	we	PRON
ejpam-3206	218	12	can	can	AUX
ejpam-3206	218	13	check	check	VERB
ejpam-3206	218	14	that	that	PRON
ejpam-3206	218	15	ns	ns	INTJ
ejpam-3206	218	16	(	(	PUNCT
ejpam-3206	218	17	r	r	NOUN
ejpam-3206	218	18	)	)	PUNCT
ejpam-3206	218	19	=	=	SYM
ejpam-3206	218	20	sr	sr	PROPN
ejpam-3206	218	21	(	(	PUNCT
ejpam-3206	218	22	r	r	NOUN
ejpam-3206	218	23	)	)	PUNCT
ejpam-3206	218	24	=	=	SYM
ejpam-3206	218	25	s	s	X
ejpam-3206	218	26	`	`	PUNCT
ejpam-3206	218	27	(	(	PUNCT
ejpam-3206	218	28	r	r	NOUN
ejpam-3206	218	29	)	)	PUNCT
ejpam-3206	218	30	=	=	SYM
ejpam-3206	218	31	(	(	PUNCT
ejpam-3206	218	32	0	0	NUM
ejpam-3206	218	33	)	)	PUNCT
ejpam-3206	218	34	,	,	PUNCT
ejpam-3206	218	35	hence	hence	ADV
ejpam-3206	218	36	r	r	NOUN
ejpam-3206	218	37	is	be	AUX
ejpam-3206	218	38	a	a	DET
ejpam-3206	218	39	(	(	PUNCT
ejpam-3206	218	40	weak	weak	ADJ
ejpam-3206	218	41	)	)	PUNCT
ejpam-3206	218	42	nonsingular	nonsingular	ADJ
ejpam-3206	218	43	ring	ring	NOUN
ejpam-3206	218	44	.	.	PUNCT
ejpam-3206	219	1	3	3	X
ejpam-3206	219	2	)	)	PUNCT
ejpam-3206	219	3	in	in	ADP
ejpam-3206	219	4	example	example	NOUN
ejpam-3206	219	5	7	7	NUM
ejpam-3206	219	6	,	,	PUNCT
ejpam-3206	219	7	r	r	NOUN
ejpam-3206	219	8	=	=	SYM
ejpam-3206	219	9	z10	z10	NOUN
ejpam-3206	219	10	,	,	PUNCT
ejpam-3206	219	11	we	we	PRON
ejpam-3206	219	12	can	can	AUX
ejpam-3206	219	13	check	check	VERB
ejpam-3206	219	14	that	that	PRON
ejpam-3206	219	15	ns	ns	INTJ
ejpam-3206	219	16	(	(	PUNCT
ejpam-3206	219	17	r	r	NOUN
ejpam-3206	219	18	)	)	PUNCT
ejpam-3206	219	19	=	=	SYM
ejpam-3206	219	20	sr	sr	PROPN
ejpam-3206	219	21	(	(	PUNCT
ejpam-3206	219	22	r	r	NOUN
ejpam-3206	219	23	)	)	PUNCT
ejpam-3206	219	24	=	=	SYM
ejpam-3206	219	25	s	s	X
ejpam-3206	219	26	`	`	PUNCT
ejpam-3206	219	27	(	(	PUNCT
ejpam-3206	219	28	r	r	NOUN
ejpam-3206	219	29	)	)	PUNCT
ejpam-3206	219	30	=	=	SYM
ejpam-3206	219	31	(	(	PUNCT
ejpam-3206	219	32	0	0	NUM
ejpam-3206	219	33	)	)	PUNCT
ejpam-3206	219	34	,	,	PUNCT
ejpam-3206	219	35	hence	hence	ADV
ejpam-3206	219	36	r	r	NOUN
ejpam-3206	219	37	is	be	AUX
ejpam-3206	219	38	a	a	DET
ejpam-3206	219	39	(	(	PUNCT
ejpam-3206	219	40	weak	weak	ADJ
ejpam-3206	219	41	)	)	PUNCT
ejpam-3206	219	42	nonsingular	nonsingular	ADJ
ejpam-3206	219	43	ring	ring	NOUN
ejpam-3206	219	44	.	.	PUNCT
ejpam-3206	220	1	4	4	NUM
ejpam-3206	220	2	)	)	PUNCT
ejpam-3206	220	3	in	in	ADP
ejpam-3206	220	4	example	example	NOUN
ejpam-3206	220	5	8	8	NUM
ejpam-3206	220	6	,	,	PUNCT
ejpam-3206	220	7	r	r	NOUN
ejpam-3206	220	8	=	=	SYM
ejpam-3206	220	9	z12	z12	NUM
ejpam-3206	220	10	,	,	PUNCT
ejpam-3206	220	11	we	we	PRON
ejpam-3206	220	12	can	can	AUX
ejpam-3206	220	13	check	check	VERB
ejpam-3206	220	14	that	that	PRON
ejpam-3206	220	15	ns	ns	INTJ
ejpam-3206	220	16	(	(	PUNCT
ejpam-3206	220	17	r	r	NOUN
ejpam-3206	220	18	)	)	PUNCT
ejpam-3206	220	19	=	=	SYM
ejpam-3206	220	20	{	{	PUNCT
ejpam-3206	220	21	0	0	NUM
ejpam-3206	220	22	,	,	PUNCT
ejpam-3206	220	23	6	6	NUM
ejpam-3206	220	24	}	}	PUNCT
ejpam-3206	220	25	=	=	SYM
ejpam-3206	220	26	nil	nil	NOUN
ejpam-3206	220	27	(	(	PUNCT
ejpam-3206	220	28	r	r	NOUN
ejpam-3206	220	29	)	)	PUNCT
ejpam-3206	220	30	,	,	PUNCT
ejpam-3206	220	31	hence	hence	ADV
ejpam-3206	220	32	r	r	NOUN
ejpam-3206	220	33	is	be	AUX
ejpam-3206	220	34	neither	neither	CCONJ
ejpam-3206	220	35	a	a	DET
ejpam-3206	220	36	weak	weak	ADJ
ejpam-3206	220	37	nonsingular	nonsingular	ADJ
ejpam-3206	220	38	ring	ring	NOUN
ejpam-3206	220	39	nor	nor	CCONJ
ejpam-3206	220	40	a	a	DET
ejpam-3206	220	41	weak	weak	ADJ
ejpam-3206	220	42	singular	singular	ADJ
ejpam-3206	220	43	ring	ring	NOUN
ejpam-3206	220	44	.	.	PUNCT
ejpam-3206	221	1	but	but	CCONJ
ejpam-3206	221	2	sr	sr	PROPN
ejpam-3206	221	3	(	(	PUNCT
ejpam-3206	221	4	r	r	NOUN
ejpam-3206	221	5	)	)	PUNCT
ejpam-3206	221	6	=	=	SYM
ejpam-3206	221	7	s	s	X
ejpam-3206	221	8	`	`	PUNCT
ejpam-3206	221	9	(	(	PUNCT
ejpam-3206	221	10	r	r	NOUN
ejpam-3206	221	11	)	)	PUNCT
ejpam-3206	221	12	=	=	SYM
ejpam-3206	221	13	{	{	PUNCT
ejpam-3206	221	14	0	0	NUM
ejpam-3206	221	15	,	,	PUNCT
ejpam-3206	221	16	6	6	NUM
ejpam-3206	221	17	}	}	PUNCT
ejpam-3206	221	18	=	=	SYM
ejpam-3206	221	19	nil	nil	NOUN
ejpam-3206	221	20	(	(	PUNCT
ejpam-3206	221	21	r	r	NOUN
ejpam-3206	221	22	)	)	PUNCT
ejpam-3206	221	23	,	,	PUNCT
ejpam-3206	221	24	hence	hence	ADV
ejpam-3206	221	25	r	r	NOUN
ejpam-3206	221	26	is	be	AUX
ejpam-3206	221	27	neither	neither	CCONJ
ejpam-3206	221	28	a	a	DET
ejpam-3206	221	29	nonsingular	nonsingular	ADJ
ejpam-3206	221	30	ring	ring	NOUN
ejpam-3206	221	31	nor	nor	CCONJ
ejpam-3206	221	32	a	a	DET
ejpam-3206	221	33	singular	singular	ADJ
ejpam-3206	221	34	ring	ring	NOUN
ejpam-3206	221	35	.	.	PUNCT
ejpam-3206	222	1	5	5	NUM
ejpam-3206	222	2	)	)	PUNCT
ejpam-3206	222	3	in	in	ADP
ejpam-3206	222	4	example	example	NOUN
ejpam-3206	222	5	11	11	NUM
ejpam-3206	222	6	,	,	PUNCT
ejpam-3206	222	7	r	r	NOUN
ejpam-3206	222	8	=	=	SYM
ejpam-3206	222	9	v	v	NOUN
ejpam-3206	222	10	,	,	PUNCT
ejpam-3206	222	11	we	we	PRON
ejpam-3206	222	12	can	can	AUX
ejpam-3206	222	13	check	check	VERB
ejpam-3206	222	14	that	that	DET
ejpam-3206	222	15	ns	ns	INTJ
ejpam-3206	222	16	(	(	PUNCT
ejpam-3206	222	17	v	v	NOUN
ejpam-3206	222	18	)	)	PUNCT
ejpam-3206	222	19	=	=	PUNCT
ejpam-3206	222	20	{	{	PUNCT
ejpam-3206	222	21	0	0	NUM
ejpam-3206	222	22	,	,	PUNCT
ejpam-3206	222	23	c	c	NOUN
ejpam-3206	222	24	}	}	PUNCT
ejpam-3206	222	25	=	=	SYM
ejpam-3206	222	26	k	k	NOUN
ejpam-3206	222	27	=	=	PUNCT
ejpam-3206	222	28	nil	nil	ADJ
ejpam-3206	222	29	(	(	PUNCT
ejpam-3206	222	30	v	v	NOUN
ejpam-3206	222	31	)	)	PUNCT
ejpam-3206	222	32	,	,	PUNCT
ejpam-3206	222	33	hence	hence	ADV
ejpam-3206	222	34	v	v	NOUN
ejpam-3206	222	35	is	be	AUX
ejpam-3206	222	36	neither	neither	CCONJ
ejpam-3206	222	37	a	a	DET
ejpam-3206	222	38	weak	weak	ADJ
ejpam-3206	222	39	nonsingular	nonsingular	ADJ
ejpam-3206	222	40	ring	ring	NOUN
ejpam-3206	222	41	nor	nor	CCONJ
ejpam-3206	222	42	a	a	DET
ejpam-3206	222	43	weak	weak	ADJ
ejpam-3206	222	44	singular	singular	ADJ
ejpam-3206	222	45	ring	ring	NOUN
ejpam-3206	222	46	.	.	PUNCT
ejpam-3206	223	1	but	but	CCONJ
ejpam-3206	223	2	sr(v	sr(v	PUNCT
ejpam-3206	223	3	)	)	PUNCT
ejpam-3206	224	1	=	=	PUNCT
ejpam-3206	224	2	{	{	PUNCT
ejpam-3206	224	3	0	0	NUM
ejpam-3206	224	4	,	,	PUNCT
ejpam-3206	224	5	c	c	NOUN
ejpam-3206	224	6	}	}	PUNCT
ejpam-3206	224	7	=	=	SYM
ejpam-3206	224	8	k	k	PROPN
ejpam-3206	224	9	and	and	CCONJ
ejpam-3206	224	10	s	s	PROPN
ejpam-3206	224	11	`	`	PUNCT
ejpam-3206	224	12	(	(	PUNCT
ejpam-3206	224	13	v	v	NOUN
ejpam-3206	224	14	)	)	PUNCT
ejpam-3206	224	15	=	=	SYM
ejpam-3206	224	16	(	(	PUNCT
ejpam-3206	224	17	0	0	NUM
ejpam-3206	224	18	)	)	PUNCT
ejpam-3206	224	19	,	,	PUNCT
ejpam-3206	224	20	hence	hence	ADV
ejpam-3206	224	21	v	v	NOUN
ejpam-3206	224	22	is	be	AUX
ejpam-3206	224	23	a	a	DET
ejpam-3206	224	24	left	left	ADJ
ejpam-3206	224	25	nonsingular	nonsingular	ADJ
ejpam-3206	224	26	ring	ring	NOUN
ejpam-3206	224	27	which	which	PRON
ejpam-3206	224	28	is	be	AUX
ejpam-3206	224	29	not	not	PART
ejpam-3206	224	30	a	a	DET
ejpam-3206	224	31	right	right	ADJ
ejpam-3206	224	32	nonsingular	nonsingular	ADJ
ejpam-3206	224	33	ring	ring	NOUN
ejpam-3206	224	34	.	.	PUNCT
ejpam-3206	225	1	lemma	lemma	PROPN
ejpam-3206	225	2	3	3	NUM
ejpam-3206	225	3	.	.	X
ejpam-3206	226	1	for	for	ADP
ejpam-3206	226	2	any	any	DET
ejpam-3206	226	3	ring	ring	NOUN
ejpam-3206	226	4	r	r	NOUN
ejpam-3206	226	5	,	,	PUNCT
ejpam-3206	226	6	we	we	PRON
ejpam-3206	226	7	have	have	VERB
ejpam-3206	226	8	sr	sr	PROPN
ejpam-3206	226	9	(	(	PUNCT
ejpam-3206	226	10	r	r	NOUN
ejpam-3206	226	11	)	)	PUNCT
ejpam-3206	226	12	⊆	⊆	NUM
ejpam-3206	226	13	ns	ns	NUM
ejpam-3206	226	14	(	(	PUNCT
ejpam-3206	226	15	r	r	NOUN
ejpam-3206	226	16	)	)	PUNCT
ejpam-3206	226	17	.	.	PUNCT
ejpam-3206	227	1	m.	m.	NOUN
ejpam-3206	227	2	a.	a.	PROPN
ejpam-3206	227	3	farahat	farahat	PROPN
ejpam-3206	227	4	,	,	PUNCT
ejpam-3206	227	5	s.	s.	PROPN
ejpam-3206	227	6	t.	t.	PROPN
ejpam-3206	227	7	al	al	PROPN
ejpam-3206	227	8	-	-	PUNCT
ejpam-3206	227	9	bogamy	bogamy	PROPN
ejpam-3206	227	10	/	/	SYM
ejpam-3206	227	11	eur	eur	PROPN
ejpam-3206	227	12	.	.	PUNCT
ejpam-3206	228	1	j.	j.	PROPN
ejpam-3206	228	2	pure	pure	PROPN
ejpam-3206	228	3	appl	appl	PROPN
ejpam-3206	228	4	.	.	PROPN
ejpam-3206	228	5	math	math	PROPN
ejpam-3206	228	6	,	,	PUNCT
ejpam-3206	228	7	11	11	NUM
ejpam-3206	228	8	(	(	PUNCT
ejpam-3206	228	9	1	1	NUM
ejpam-3206	228	10	)	)	PUNCT
ejpam-3206	228	11	(	(	PUNCT
ejpam-3206	228	12	2018	2018	NUM
ejpam-3206	228	13	)	)	PUNCT
ejpam-3206	228	14	,	,	PUNCT
ejpam-3206	228	15	244	244	NUM
ejpam-3206	228	16	-	-	SYM
ejpam-3206	228	17	259	259	NUM
ejpam-3206	228	18	252	252	NUM
ejpam-3206	228	19	proof	proof	NOUN
ejpam-3206	228	20	.	.	PUNCT
ejpam-3206	229	1	if	if	SCONJ
ejpam-3206	229	2	a	a	DET
ejpam-3206	229	3	∈	∈	PROPN
ejpam-3206	229	4	sr	sr	NOUN
ejpam-3206	229	5	(	(	PUNCT
ejpam-3206	229	6	r	r	NOUN
ejpam-3206	229	7	)	)	PUNCT
ejpam-3206	229	8	,	,	PUNCT
ejpam-3206	229	9	then	then	ADV
ejpam-3206	229	10	rr	rr	X
ejpam-3206	229	11	(	(	PUNCT
ejpam-3206	229	12	a	a	NOUN
ejpam-3206	229	13	)	)	PUNCT
ejpam-3206	229	14	is	be	AUX
ejpam-3206	229	15	an	an	DET
ejpam-3206	229	16	essential	essential	ADJ
ejpam-3206	229	17	right	right	ADJ
ejpam-3206	229	18	ideal	ideal	NOUN
ejpam-3206	229	19	.	.	PUNCT
ejpam-3206	230	1	since	since	SCONJ
ejpam-3206	230	2	rr	rr	PROPN
ejpam-3206	230	3	(	(	PUNCT
ejpam-3206	230	4	a	a	NOUN
ejpam-3206	230	5	)	)	PUNCT
ejpam-3206	230	6	⊆	⊆	NUM
ejpam-3206	230	7	nr	nr	PROPN
ejpam-3206	230	8	(	(	PUNCT
ejpam-3206	230	9	a	a	NOUN
ejpam-3206	230	10	)	)	PUNCT
ejpam-3206	230	11	,	,	PUNCT
ejpam-3206	230	12	we	we	PRON
ejpam-3206	230	13	conclude	conclude	VERB
ejpam-3206	230	14	that	that	SCONJ
ejpam-3206	230	15	nr	nr	PROPN
ejpam-3206	230	16	(	(	PUNCT
ejpam-3206	230	17	a	a	PRON
ejpam-3206	230	18	)	)	PUNCT
ejpam-3206	230	19	is	be	AUX
ejpam-3206	230	20	also	also	ADV
ejpam-3206	230	21	essential	essential	ADJ
ejpam-3206	230	22	ideal	ideal	NOUN
ejpam-3206	230	23	.	.	PUNCT
ejpam-3206	231	1	thus	thus	ADV
ejpam-3206	231	2	a	a	DET
ejpam-3206	231	3	∈	∈	ADJ
ejpam-3206	231	4	ns	ns	INTJ
ejpam-3206	231	5	(	(	PUNCT
ejpam-3206	231	6	r	r	NOUN
ejpam-3206	231	7	)	)	PUNCT
ejpam-3206	231	8	.	.	PUNCT
ejpam-3206	232	1	therefore	therefore	ADV
ejpam-3206	232	2	sr	sr	PROPN
ejpam-3206	232	3	(	(	PUNCT
ejpam-3206	232	4	r	r	NOUN
ejpam-3206	232	5	)	)	PUNCT
ejpam-3206	232	6	⊆	⊆	NUM
ejpam-3206	232	7	ns	ns	NUM
ejpam-3206	232	8	(	(	PUNCT
ejpam-3206	232	9	r	r	NOUN
ejpam-3206	232	10	)	)	PUNCT
ejpam-3206	232	11	.	.	PUNCT
ejpam-3206	233	1	corollary	corollary	ADJ
ejpam-3206	233	2	1	1	NUM
ejpam-3206	233	3	.	.	NOUN
ejpam-3206	233	4	1	1	NUM
ejpam-3206	233	5	)	)	PUNCT
ejpam-3206	233	6	every	every	DET
ejpam-3206	233	7	weak	weak	ADJ
ejpam-3206	233	8	nonsingular	nonsingular	ADJ
ejpam-3206	233	9	ring	ring	NOUN
ejpam-3206	233	10	is	be	AUX
ejpam-3206	233	11	a	a	DET
ejpam-3206	233	12	right	right	NOUN
ejpam-3206	233	13	(	(	PUNCT
ejpam-3206	233	14	left	left	ADJ
ejpam-3206	233	15	)	)	PUNCT
ejpam-3206	233	16	nonsingular	nonsingular	ADJ
ejpam-3206	233	17	ring	ring	NOUN
ejpam-3206	233	18	.	.	PUNCT
ejpam-3206	234	1	2	2	NUM
ejpam-3206	234	2	)	)	PUNCT
ejpam-3206	234	3	every	every	PRON
ejpam-3206	234	4	right	right	NOUN
ejpam-3206	234	5	(	(	PUNCT
ejpam-3206	234	6	left	left	ADJ
ejpam-3206	234	7	)	)	PUNCT
ejpam-3206	234	8	singular	singular	PROPN
ejpam-3206	234	9	ring	ring	NOUN
ejpam-3206	234	10	is	be	AUX
ejpam-3206	234	11	a	a	DET
ejpam-3206	234	12	weak	weak	ADJ
ejpam-3206	234	13	singular	singular	ADJ
ejpam-3206	234	14	ring	ring	NOUN
ejpam-3206	234	15	.	.	PUNCT
ejpam-3206	235	1	remark	remark	PROPN
ejpam-3206	235	2	3	3	NUM
ejpam-3206	235	3	.	.	PUNCT
ejpam-3206	236	1	the	the	DET
ejpam-3206	236	2	converse	converse	NOUN
ejpam-3206	236	3	of	of	ADP
ejpam-3206	236	4	the	the	DET
ejpam-3206	236	5	last	last	ADJ
ejpam-3206	236	6	corollary	corollary	NOUN
ejpam-3206	236	7	need	need	AUX
ejpam-3206	236	8	not	not	PART
ejpam-3206	236	9	be	be	AUX
ejpam-3206	236	10	true	true	ADJ
ejpam-3206	236	11	by	by	ADP
ejpam-3206	236	12	the	the	DET
ejpam-3206	236	13	following	following	ADJ
ejpam-3206	236	14	examples	example	NOUN
ejpam-3206	236	15	:	:	PUNCT
ejpam-3206	236	16	1	1	X
ejpam-3206	236	17	)	)	PUNCT
ejpam-3206	236	18	in	in	ADP
ejpam-3206	236	19	example	example	NOUN
ejpam-3206	236	20	14	14	NUM
ejpam-3206	236	21	,	,	PUNCT
ejpam-3206	236	22	(	(	PUNCT
ejpam-3206	236	23	1	1	NUM
ejpam-3206	236	24	)	)	PUNCT
ejpam-3206	236	25	,	,	PUNCT
ejpam-3206	236	26	r	r	NOUN
ejpam-3206	236	27	=	=	SYM
ejpam-3206	236	28	z4	z4	X
ejpam-3206	236	29	,	,	PUNCT
ejpam-3206	236	30	is	be	AUX
ejpam-3206	236	31	a	a	DET
ejpam-3206	236	32	weak	weak	ADJ
ejpam-3206	236	33	singular	singular	ADJ
ejpam-3206	236	34	ring	ring	NOUN
ejpam-3206	236	35	.	.	PUNCT
ejpam-3206	237	1	but	but	CCONJ
ejpam-3206	237	2	r	r	NOUN
ejpam-3206	237	3	is	be	AUX
ejpam-3206	237	4	not	not	PART
ejpam-3206	237	5	a	a	DET
ejpam-3206	237	6	singular	singular	ADJ
ejpam-3206	237	7	ring	ring	NOUN
ejpam-3206	237	8	.	.	PUNCT
ejpam-3206	238	1	2	2	NUM
ejpam-3206	238	2	)	)	PUNCT
ejpam-3206	238	3	in	in	ADP
ejpam-3206	238	4	example	example	NOUN
ejpam-3206	238	5	14	14	NUM
ejpam-3206	238	6	,	,	PUNCT
ejpam-3206	238	7	(	(	PUNCT
ejpam-3206	238	8	5	5	NUM
ejpam-3206	238	9	)	)	PUNCT
ejpam-3206	238	10	,	,	PUNCT
ejpam-3206	238	11	r	r	NOUN
ejpam-3206	238	12	=	=	SYM
ejpam-3206	238	13	v	v	NOUN
ejpam-3206	238	14	,	,	PUNCT
ejpam-3206	238	15	is	be	AUX
ejpam-3206	238	16	a	a	DET
ejpam-3206	238	17	left	left	ADJ
ejpam-3206	238	18	nonsingular	nonsingular	ADJ
ejpam-3206	238	19	ring	ring	NOUN
ejpam-3206	238	20	.	.	PUNCT
ejpam-3206	239	1	but	but	CCONJ
ejpam-3206	239	2	r	r	NOUN
ejpam-3206	239	3	is	be	AUX
ejpam-3206	239	4	not	not	PART
ejpam-3206	239	5	a	a	DET
ejpam-3206	239	6	weak	weak	ADJ
ejpam-3206	239	7	singular	singular	ADJ
ejpam-3206	239	8	ring	ring	NOUN
ejpam-3206	239	9	.	.	PUNCT
ejpam-3206	240	1	corollary	corollary	ADJ
ejpam-3206	240	2	2	2	NUM
ejpam-3206	240	3	.	.	PUNCT
ejpam-3206	241	1	every	every	DET
ejpam-3206	241	2	weak	weak	ADJ
ejpam-3206	241	3	nonsingular	nonsingular	ADJ
ejpam-3206	241	4	ring	ring	NOUN
ejpam-3206	241	5	is	be	AUX
ejpam-3206	241	6	a	a	DET
ejpam-3206	241	7	ps	ps	NOUN
ejpam-3206	241	8	-	-	PUNCT
ejpam-3206	241	9	ring	ring	NOUN
ejpam-3206	241	10	.	.	PUNCT
ejpam-3206	242	1	proof	proof	NOUN
ejpam-3206	242	2	.	.	PUNCT
ejpam-3206	243	1	since	since	SCONJ
ejpam-3206	243	2	every	every	DET
ejpam-3206	243	3	nonsingular	nonsingular	ADJ
ejpam-3206	243	4	ring	ring	NOUN
ejpam-3206	243	5	is	be	AUX
ejpam-3206	243	6	a	a	DET
ejpam-3206	243	7	ps	ps	NOUN
ejpam-3206	243	8	-	-	PUNCT
ejpam-3206	243	9	ring	ring	NOUN
ejpam-3206	243	10	,	,	PUNCT
ejpam-3206	243	11	the	the	DET
ejpam-3206	243	12	result	result	NOUN
ejpam-3206	243	13	follows	follow	VERB
ejpam-3206	243	14	.	.	PUNCT
ejpam-3206	244	1	theorem	theorem	NOUN
ejpam-3206	244	2	3	3	NUM
ejpam-3206	244	3	.	.	PUNCT
ejpam-3206	244	4	a	a	DET
ejpam-3206	244	5	semisimple	semisimple	ADJ
ejpam-3206	244	6	ni	ni	NOUN
ejpam-3206	244	7	-	-	PUNCT
ejpam-3206	244	8	ring	ring	NOUN
ejpam-3206	244	9	is	be	AUX
ejpam-3206	244	10	a	a	DET
ejpam-3206	244	11	weak	weak	ADJ
ejpam-3206	244	12	right	right	NOUN
ejpam-3206	244	13	(	(	PUNCT
ejpam-3206	244	14	left	left	ADJ
ejpam-3206	244	15	)	)	PUNCT
ejpam-3206	244	16	ps	ps	NOUN
ejpam-3206	244	17	-	-	PUNCT
ejpam-3206	244	18	ring	ring	NOUN
ejpam-3206	244	19	.	.	PUNCT
ejpam-3206	245	1	proof	proof	NOUN
ejpam-3206	245	2	.	.	PUNCT
ejpam-3206	246	1	it	it	PRON
ejpam-3206	246	2	is	be	AUX
ejpam-3206	246	3	well	well	ADV
ejpam-3206	246	4	-	-	PUNCT
ejpam-3206	246	5	known	know	VERB
ejpam-3206	246	6	that	that	SCONJ
ejpam-3206	246	7	any	any	DET
ejpam-3206	246	8	right	right	NOUN
ejpam-3206	246	9	(	(	PUNCT
ejpam-3206	246	10	resp	resp	NOUN
ejpam-3206	246	11	.	.	PUNCT
ejpam-3206	246	12	left	left	ADJ
ejpam-3206	246	13	)	)	PUNCT
ejpam-3206	246	14	ideal	ideal	NOUN
ejpam-3206	246	15	i	i	PRON
ejpam-3206	246	16	in	in	ADP
ejpam-3206	246	17	a	a	DET
ejpam-3206	246	18	semisimple	semisimple	NOUN
ejpam-3206	246	19	ring	ring	NOUN
ejpam-3206	246	20	r	r	NOUN
ejpam-3206	246	21	has	have	VERB
ejpam-3206	246	22	the	the	DET
ejpam-3206	246	23	form	form	NOUN
ejpam-3206	247	1	i	i	PRON
ejpam-3206	247	2	=	=	SYM
ejpam-3206	247	3	er	er	INTJ
ejpam-3206	247	4	(	(	PUNCT
ejpam-3206	247	5	resp	resp	NOUN
ejpam-3206	247	6	.	.	PUNCT
ejpam-3206	248	1	i	i	PRON
ejpam-3206	248	2	=	=	SYM
ejpam-3206	248	3	re	re	NOUN
ejpam-3206	248	4	)	)	PUNCT
ejpam-3206	248	5	,	,	PUNCT
ejpam-3206	248	6	where	where	SCONJ
ejpam-3206	248	7	e	e	PROPN
ejpam-3206	248	8	∈	∈	PROPN
ejpam-3206	248	9	i	i	PROPN
ejpam-3206	248	10	d	d	PROPN
ejpam-3206	248	11	(	(	PUNCT
ejpam-3206	248	12	r	r	NOUN
ejpam-3206	248	13	)	)	PUNCT
ejpam-3206	248	14	.	.	PUNCT
ejpam-3206	249	1	since	since	SCONJ
ejpam-3206	249	2	r	r	NOUN
ejpam-3206	249	3	is	be	AUX
ejpam-3206	249	4	an	an	DET
ejpam-3206	249	5	ni	ni	NOUN
ejpam-3206	249	6	-	-	NOUN
ejpam-3206	249	7	ring	ring	NOUN
ejpam-3206	249	8	,	,	PUNCT
ejpam-3206	249	9	we	we	PRON
ejpam-3206	249	10	have	have	VERB
ejpam-3206	249	11	nr	nr	PRON
ejpam-3206	249	12	(	(	PUNCT
ejpam-3206	249	13	l	l	NOUN
ejpam-3206	249	14	)	)	PUNCT
ejpam-3206	249	15	is	be	AUX
ejpam-3206	249	16	an	an	DET
ejpam-3206	249	17	ideal	ideal	NOUN
ejpam-3206	249	18	of	of	ADP
ejpam-3206	249	19	r	r	NOUN
ejpam-3206	249	20	and	and	CCONJ
ejpam-3206	249	21	the	the	DET
ejpam-3206	249	22	proof	proof	NOUN
ejpam-3206	249	23	is	be	AUX
ejpam-3206	249	24	complete	complete	ADJ
ejpam-3206	249	25	.	.	PUNCT
ejpam-3206	250	1	remark	remark	PROPN
ejpam-3206	250	2	4	4	NUM
ejpam-3206	250	3	.	.	PUNCT
ejpam-3206	251	1	a	a	DET
ejpam-3206	251	2	ring	ring	NOUN
ejpam-3206	251	3	r	r	NOUN
ejpam-3206	251	4	,	,	PUNCT
ejpam-3206	251	5	in	in	ADP
ejpam-3206	251	6	example	example	NOUN
ejpam-3206	251	7	9	9	NUM
ejpam-3206	251	8	,	,	PUNCT
ejpam-3206	251	9	is	be	AUX
ejpam-3206	251	10	a	a	DET
ejpam-3206	251	11	simple	simple	ADJ
ejpam-3206	251	12	ring	ring	NOUN
ejpam-3206	251	13	,	,	PUNCT
ejpam-3206	251	14	hence	hence	ADV
ejpam-3206	251	15	r	r	NOUN
ejpam-3206	251	16	is	be	AUX
ejpam-3206	251	17	a	a	DET
ejpam-3206	251	18	semisimple	semisimple	NOUN
ejpam-3206	251	19	ring	ring	NOUN
ejpam-3206	251	20	which	which	PRON
ejpam-3206	251	21	is	be	AUX
ejpam-3206	251	22	not	not	PART
ejpam-3206	251	23	an	an	DET
ejpam-3206	251	24	ni	ni	NOUN
ejpam-3206	251	25	-	-	NOUN
ejpam-3206	251	26	ring	ring	NOUN
ejpam-3206	251	27	.	.	PUNCT
ejpam-3206	252	1	but	but	CCONJ
ejpam-3206	252	2	r	r	NOUN
ejpam-3206	252	3	is	be	AUX
ejpam-3206	252	4	a	a	DET
ejpam-3206	252	5	weak	weak	ADJ
ejpam-3206	252	6	right	right	NOUN
ejpam-3206	252	7	(	(	PUNCT
ejpam-3206	252	8	left	left	ADJ
ejpam-3206	252	9	)	)	PUNCT
ejpam-3206	252	10	ps	ps	NOUN
ejpam-3206	252	11	-	-	PUNCT
ejpam-3206	252	12	ring	ring	NOUN
ejpam-3206	252	13	.	.	PUNCT
ejpam-3206	252	14	example	example	NOUN
ejpam-3206	253	1	15	15	NUM
ejpam-3206	253	2	.	.	PUNCT
ejpam-3206	254	1	in	in	ADP
ejpam-3206	254	2	example	example	NOUN
ejpam-3206	254	3	11	11	NUM
ejpam-3206	254	4	,	,	PUNCT
ejpam-3206	254	5	r	r	NOUN
ejpam-3206	254	6	=	=	SYM
ejpam-3206	254	7	v	v	NOUN
ejpam-3206	254	8	,	,	PUNCT
ejpam-3206	254	9	we	we	PRON
ejpam-3206	254	10	have	have	AUX
ejpam-3206	254	11	v	v	NOUN
ejpam-3206	254	12	is	be	AUX
ejpam-3206	254	13	a	a	DET
ejpam-3206	254	14	left	left	ADJ
ejpam-3206	254	15	nonsingular	nonsingular	ADJ
ejpam-3206	254	16	ring	ring	NOUN
ejpam-3206	254	17	which	which	PRON
ejpam-3206	254	18	is	be	AUX
ejpam-3206	254	19	not	not	PART
ejpam-3206	254	20	a	a	DET
ejpam-3206	254	21	right	right	ADJ
ejpam-3206	254	22	nonsingular	nonsingular	ADJ
ejpam-3206	254	23	ring	ring	NOUN
ejpam-3206	254	24	.	.	PUNCT
ejpam-3206	255	1	therefore	therefore	ADV
ejpam-3206	255	2	v	v	NOUN
ejpam-3206	255	3	is	be	AUX
ejpam-3206	255	4	a	a	DET
ejpam-3206	255	5	left	left	ADJ
ejpam-3206	255	6	ps	ps	NOUN
ejpam-3206	255	7	-	-	PUNCT
ejpam-3206	255	8	ring	ring	NOUN
ejpam-3206	255	9	which	which	PRON
ejpam-3206	255	10	is	be	AUX
ejpam-3206	255	11	not	not	PART
ejpam-3206	255	12	a	a	DET
ejpam-3206	255	13	reduced	reduce	VERB
ejpam-3206	255	14	ring	ring	NOUN
ejpam-3206	255	15	.	.	PUNCT
ejpam-3206	256	1	given	give	VERB
ejpam-3206	256	2	a	a	DET
ejpam-3206	256	3	ring	ring	NOUN
ejpam-3206	256	4	r	r	NOUN
ejpam-3206	256	5	and	and	CCONJ
ejpam-3206	256	6	rmr	rmr	PROPN
ejpam-3206	256	7	an	an	DET
ejpam-3206	256	8	r	r	NOUN
ejpam-3206	256	9	-	-	PUNCT
ejpam-3206	256	10	r	r	NOUN
ejpam-3206	256	11	-	-	PUNCT
ejpam-3206	256	12	bimodule	bimodule	NOUN
ejpam-3206	256	13	,	,	PUNCT
ejpam-3206	256	14	the	the	DET
ejpam-3206	256	15	trivial	trivial	ADJ
ejpam-3206	256	16	extension	extension	NOUN
ejpam-3206	256	17	of	of	ADP
ejpam-3206	256	18	r	r	NOUN
ejpam-3206	256	19	by	by	ADP
ejpam-3206	256	20	m	m	PROPN
ejpam-3206	256	21	is	be	AUX
ejpam-3206	256	22	the	the	DET
ejpam-3206	256	23	ring	ring	NOUN
ejpam-3206	256	24	t	t	PROPN
ejpam-3206	256	25	(	(	PUNCT
ejpam-3206	256	26	r	r	NOUN
ejpam-3206	256	27	,	,	PUNCT
ejpam-3206	256	28	m	m	NOUN
ejpam-3206	256	29	)	)	PUNCT
ejpam-3206	256	30	=	=	PRON
ejpam-3206	256	31	r⊕m	r⊕m	VERB
ejpam-3206	256	32	with	with	ADP
ejpam-3206	256	33	the	the	DET
ejpam-3206	256	34	usual	usual	ADJ
ejpam-3206	256	35	addition	addition	NOUN
ejpam-3206	256	36	and	and	CCONJ
ejpam-3206	256	37	the	the	DET
ejpam-3206	256	38	multiplication	multiplication	NOUN
ejpam-3206	256	39	(	(	PUNCT
ejpam-3206	256	40	r1,m1	r1,m1	PROPN
ejpam-3206	256	41	)	)	PUNCT
ejpam-3206	256	42	(	(	PUNCT
ejpam-3206	256	43	r2,m2	r2,m2	PROPN
ejpam-3206	256	44	)	)	PUNCT
ejpam-3206	256	45	=	=	PRON
ejpam-3206	256	46	(	(	PUNCT
ejpam-3206	256	47	r1r2	r1r2	X
ejpam-3206	256	48	,	,	PUNCT
ejpam-3206	256	49	r1m2	r1m2	ADJ
ejpam-3206	256	50	+	+	NOUN
ejpam-3206	256	51	m1r2	m1r2	NUM
ejpam-3206	256	52	)	)	PUNCT
ejpam-3206	256	53	,	,	PUNCT
ejpam-3206	256	54	where	where	SCONJ
ejpam-3206	256	55	r1	r1	PROPN
ejpam-3206	256	56	,	,	PUNCT
ejpam-3206	256	57	r2	r2	PROPN
ejpam-3206	256	58	∈	∈	PROPN
ejpam-3206	256	59	r	r	NOUN
ejpam-3206	256	60	and	and	CCONJ
ejpam-3206	256	61	m1,m2	m1,m2	PROPN
ejpam-3206	256	62	∈m	∈m	NOUN
ejpam-3206	256	63	.	.	PUNCT
ejpam-3206	257	1	this	this	PRON
ejpam-3206	257	2	is	be	AUX
ejpam-3206	257	3	isomorphic	isomorphic	ADJ
ejpam-3206	257	4	to	to	ADP
ejpam-3206	257	5	the	the	DET
ejpam-3206	257	6	ring	ring	NOUN
ejpam-3206	257	7	of	of	ADP
ejpam-3206	257	8	all	all	DET
ejpam-3206	257	9	matrices	matrix	NOUN
ejpam-3206	257	10	(	(	PUNCT
ejpam-3206	257	11	r	r	NOUN
ejpam-3206	257	12	m	m	VERB
ejpam-3206	257	13	0	0	NUM
ejpam-3206	257	14	r	r	NOUN
ejpam-3206	257	15	)	)	PUNCT
ejpam-3206	257	16	,	,	PUNCT
ejpam-3206	257	17	where	where	SCONJ
ejpam-3206	257	18	r	r	NOUN
ejpam-3206	257	19	∈	∈	PROPN
ejpam-3206	257	20	r	r	NOUN
ejpam-3206	257	21	and	and	CCONJ
ejpam-3206	257	22	m	m	PROPN
ejpam-3206	257	23	∈	∈	NOUN
ejpam-3206	257	24	m	m	VERB
ejpam-3206	257	25	with	with	ADP
ejpam-3206	257	26	the	the	DET
ejpam-3206	257	27	usual	usual	ADJ
ejpam-3206	257	28	matrix	matrix	NOUN
ejpam-3206	257	29	operations	operation	NOUN
ejpam-3206	257	30	.	.	PUNCT
ejpam-3206	258	1	trivial	trivial	ADJ
ejpam-3206	258	2	extensions	extension	NOUN
ejpam-3206	258	3	attracted	attract	VERB
ejpam-3206	258	4	attention	attention	NOUN
ejpam-3206	258	5	when	when	SCONJ
ejpam-3206	258	6	people	people	NOUN
ejpam-3206	258	7	searched	search	VERB
ejpam-3206	258	8	for	for	ADP
ejpam-3206	258	9	nonreduced	nonreduce	VERB
ejpam-3206	258	10	rings	ring	NOUN
ejpam-3206	258	11	which	which	PRON
ejpam-3206	258	12	are	be	AUX
ejpam-3206	258	13	armendraiz	armendraiz	ADJ
ejpam-3206	258	14	[	[	X
ejpam-3206	258	15	2	2	NUM
ejpam-3206	258	16	]	]	PUNCT
ejpam-3206	258	17	.	.	PUNCT
ejpam-3206	259	1	the	the	DET
ejpam-3206	259	2	article	article	NOUN
ejpam-3206	259	3	of	of	ADP
ejpam-3206	259	4	rege	rege	PROPN
ejpam-3206	259	5	and	and	CCONJ
ejpam-3206	259	6	chhawchharia	chhawchharia	PROPN
ejpam-3206	259	7	(	(	PUNCT
ejpam-3206	259	8	[	[	X
ejpam-3206	259	9	19	19	NUM
ejpam-3206	259	10	]	]	PUNCT
ejpam-3206	259	11	,	,	PUNCT
ejpam-3206	259	12	1997	1997	NUM
ejpam-3206	259	13	)	)	PUNCT
ejpam-3206	259	14	seems	seem	VERB
ejpam-3206	259	15	to	to	PART
ejpam-3206	259	16	be	be	AUX
ejpam-3206	259	17	the	the	DET
ejpam-3206	259	18	first	first	ADJ
ejpam-3206	259	19	to	to	PART
ejpam-3206	259	20	consider	consider	VERB
ejpam-3206	259	21	the	the	DET
ejpam-3206	259	22	armendraiz	armendraiz	ADJ
ejpam-3206	259	23	property	property	NOUN
ejpam-3206	259	24	of	of	ADP
ejpam-3206	259	25	trivial	trivial	ADJ
ejpam-3206	259	26	extensions	extension	NOUN
ejpam-3206	259	27	.	.	PUNCT
ejpam-3206	260	1	proposition	proposition	NOUN
ejpam-3206	260	2	2	2	NUM
ejpam-3206	260	3	.	.	PUNCT
ejpam-3206	261	1	let	let	VERB
ejpam-3206	261	2	r	r	PRON
ejpam-3206	261	3	be	be	AUX
ejpam-3206	261	4	a	a	DET
ejpam-3206	261	5	reduced	reduce	VERB
ejpam-3206	261	6	ring	ring	NOUN
ejpam-3206	261	7	.	.	PUNCT
ejpam-3206	262	1	if	if	SCONJ
ejpam-3206	262	2	t	t	PROPN
ejpam-3206	262	3	(	(	PUNCT
ejpam-3206	262	4	r	r	NOUN
ejpam-3206	262	5	,	,	PUNCT
ejpam-3206	262	6	m	m	NOUN
ejpam-3206	262	7	)	)	PUNCT
ejpam-3206	262	8	is	be	AUX
ejpam-3206	262	9	a	a	DET
ejpam-3206	262	10	weak	weak	ADJ
ejpam-3206	262	11	right	right	ADJ
ejpam-3206	262	12	ps	ps	NOUN
ejpam-3206	262	13	-	-	NOUN
ejpam-3206	262	14	ring	ring	NOUN
ejpam-3206	262	15	,	,	PUNCT
ejpam-3206	262	16	then	then	ADV
ejpam-3206	262	17	r	r	NOUN
ejpam-3206	262	18	is	be	AUX
ejpam-3206	262	19	a	a	DET
ejpam-3206	262	20	right	right	ADJ
ejpam-3206	262	21	ps	ps	NOUN
ejpam-3206	262	22	-	-	NOUN
ejpam-3206	262	23	ring	ring	NOUN
ejpam-3206	262	24	.	.	PUNCT
ejpam-3206	263	1	proof	proof	NOUN
ejpam-3206	263	2	.	.	PUNCT
ejpam-3206	264	1	set	set	VERB
ejpam-3206	264	2	a	a	DET
ejpam-3206	264	3	=	=	X
ejpam-3206	264	4	t	t	X
ejpam-3206	264	5	(	(	PUNCT
ejpam-3206	264	6	r	r	NOUN
ejpam-3206	264	7	,	,	PUNCT
ejpam-3206	264	8	m	m	NOUN
ejpam-3206	264	9	)	)	PUNCT
ejpam-3206	264	10	.	.	PUNCT
ejpam-3206	265	1	since	since	SCONJ
ejpam-3206	265	2	r	r	NOUN
ejpam-3206	265	3	is	be	AUX
ejpam-3206	265	4	a	a	DET
ejpam-3206	265	5	reduced	reduced	ADJ
ejpam-3206	265	6	ring	ring	NOUN
ejpam-3206	265	7	,	,	PUNCT
ejpam-3206	265	8	we	we	PRON
ejpam-3206	265	9	can	can	AUX
ejpam-3206	265	10	easily	easily	ADV
ejpam-3206	265	11	conclude	conclude	VERB
ejpam-3206	265	12	that	that	DET
ejpam-3206	265	13	nil	nil	NOUN
ejpam-3206	265	14	(	(	PUNCT
ejpam-3206	265	15	a	a	X
ejpam-3206	265	16	)	)	PUNCT
ejpam-3206	265	17	∼=	∼=	PROPN
ejpam-3206	265	18	{	{	PUNCT
ejpam-3206	265	19	(	(	PUNCT
ejpam-3206	265	20	0	0	NUM
ejpam-3206	265	21	m	m	NOUN
ejpam-3206	265	22	0	0	NUM
ejpam-3206	265	23	0	0	NUM
ejpam-3206	265	24	)	)	PUNCT
ejpam-3206	265	25	|m	|m	NOUN
ejpam-3206	265	26	∈m	∈m	NOUN
ejpam-3206	265	27	}	}	PUNCT
ejpam-3206	265	28	and	and	CCONJ
ejpam-3206	265	29	hence	hence	ADV
ejpam-3206	265	30	a	a	PRON
ejpam-3206	265	31	=	=	X
ejpam-3206	265	32	a	a	PRON
ejpam-3206	265	33	/nil	/nil	PUNCT
ejpam-3206	265	34	(	(	PUNCT
ejpam-3206	265	35	a	a	X
ejpam-3206	265	36	)	)	PUNCT
ejpam-3206	265	37	∼=	∼=	NOUN
ejpam-3206	265	38	r	r	NOUN
ejpam-3206	265	39	,	,	PUNCT
ejpam-3206	265	40	which	which	PRON
ejpam-3206	265	41	completes	complete	VERB
ejpam-3206	265	42	the	the	DET
ejpam-3206	265	43	proof	proof	NOUN
ejpam-3206	265	44	.	.	PUNCT
ejpam-3206	266	1	m.	m.	NOUN
ejpam-3206	266	2	a.	a.	PROPN
ejpam-3206	266	3	farahat	farahat	PROPN
ejpam-3206	266	4	,	,	PUNCT
ejpam-3206	266	5	s.	s.	PROPN
ejpam-3206	266	6	t.	t.	PROPN
ejpam-3206	266	7	al	al	PROPN
ejpam-3206	266	8	-	-	PUNCT
ejpam-3206	266	9	bogamy	bogamy	PROPN
ejpam-3206	266	10	/	/	SYM
ejpam-3206	266	11	eur	eur	PROPN
ejpam-3206	266	12	.	.	PUNCT
ejpam-3206	267	1	j.	j.	PROPN
ejpam-3206	267	2	pure	pure	PROPN
ejpam-3206	267	3	appl	appl	PROPN
ejpam-3206	267	4	.	.	PROPN
ejpam-3206	267	5	math	math	PROPN
ejpam-3206	267	6	,	,	PUNCT
ejpam-3206	267	7	11	11	NUM
ejpam-3206	267	8	(	(	PUNCT
ejpam-3206	267	9	1	1	NUM
ejpam-3206	267	10	)	)	PUNCT
ejpam-3206	267	11	(	(	PUNCT
ejpam-3206	267	12	2018	2018	NUM
ejpam-3206	267	13	)	)	PUNCT
ejpam-3206	267	14	,	,	PUNCT
ejpam-3206	267	15	244	244	NUM
ejpam-3206	267	16	-	-	SYM
ejpam-3206	267	17	259	259	NUM
ejpam-3206	267	18	253	253	NUM
ejpam-3206	267	19	proposition	proposition	NOUN
ejpam-3206	267	20	3	3	NUM
ejpam-3206	267	21	.	.	PUNCT
ejpam-3206	268	1	let	let	VERB
ejpam-3206	268	2	r	r	PRON
ejpam-3206	268	3	be	be	AUX
ejpam-3206	268	4	a	a	DET
ejpam-3206	268	5	reduced	reduce	VERB
ejpam-3206	268	6	ring	ring	NOUN
ejpam-3206	268	7	.	.	PUNCT
ejpam-3206	269	1	if	if	SCONJ
ejpam-3206	269	2	t	t	PROPN
ejpam-3206	269	3	(	(	PUNCT
ejpam-3206	269	4	r	r	NOUN
ejpam-3206	269	5	,	,	PUNCT
ejpam-3206	269	6	r	r	NOUN
ejpam-3206	269	7	)	)	PUNCT
ejpam-3206	269	8	is	be	AUX
ejpam-3206	269	9	a	a	DET
ejpam-3206	269	10	weak	weak	ADJ
ejpam-3206	269	11	right	right	ADJ
ejpam-3206	269	12	ps	ps	NOUN
ejpam-3206	269	13	-	-	NOUN
ejpam-3206	269	14	ring	ring	NOUN
ejpam-3206	269	15	,	,	PUNCT
ejpam-3206	269	16	then	then	ADV
ejpam-3206	269	17	r	r	NOUN
ejpam-3206	269	18	is	be	AUX
ejpam-3206	269	19	a	a	DET
ejpam-3206	269	20	right	right	ADJ
ejpam-3206	269	21	ps	ps	NOUN
ejpam-3206	269	22	-	-	NOUN
ejpam-3206	269	23	ring	ring	NOUN
ejpam-3206	269	24	.	.	PUNCT
ejpam-3206	270	1	observe	observe	VERB
ejpam-3206	270	2	that	that	SCONJ
ejpam-3206	270	3	t	t	NOUN
ejpam-3206	270	4	(	(	PUNCT
ejpam-3206	270	5	r	r	NOUN
ejpam-3206	270	6	,	,	PUNCT
ejpam-3206	270	7	r	r	NOUN
ejpam-3206	270	8	)	)	PUNCT
ejpam-3206	270	9	∼=	∼=	PROPN
ejpam-3206	270	10	r[x	r[x	NOUN
ejpam-3206	270	11	]	]	X
ejpam-3206	270	12	/	/	SYM
ejpam-3206	270	13	〈	〈	PROPN
ejpam-3206	270	14	x2	x2	ADJ
ejpam-3206	270	15	〉	〉	NOUN
ejpam-3206	270	16	,	,	PUNCT
ejpam-3206	270	17	so	so	ADV
ejpam-3206	270	18	we	we	PRON
ejpam-3206	270	19	get	get	VERB
ejpam-3206	270	20	the	the	DET
ejpam-3206	270	21	following	follow	VERB
ejpam-3206	270	22	corollary	corollary	ADJ
ejpam-3206	270	23	:	:	PUNCT
ejpam-3206	270	24	corollary	corollary	ADJ
ejpam-3206	270	25	3	3	X
ejpam-3206	270	26	.	.	PUNCT
ejpam-3206	271	1	let	let	VERB
ejpam-3206	271	2	r	r	PRON
ejpam-3206	271	3	be	be	AUX
ejpam-3206	271	4	a	a	DET
ejpam-3206	271	5	reduced	reduce	VERB
ejpam-3206	271	6	ring	ring	NOUN
ejpam-3206	271	7	.	.	PUNCT
ejpam-3206	272	1	if	if	SCONJ
ejpam-3206	272	2	r[x	r[x	PROPN
ejpam-3206	272	3	]	]	X
ejpam-3206	272	4	/	/	SYM
ejpam-3206	272	5	〈	〈	PROPN
ejpam-3206	272	6	x2	x2	ADJ
ejpam-3206	272	7	〉	〉	NOUN
ejpam-3206	272	8	is	be	AUX
ejpam-3206	272	9	a	a	DET
ejpam-3206	272	10	weak	weak	ADJ
ejpam-3206	272	11	right	right	ADJ
ejpam-3206	272	12	ps	ps	NOUN
ejpam-3206	272	13	-	-	NOUN
ejpam-3206	272	14	ring	ring	NOUN
ejpam-3206	272	15	,	,	PUNCT
ejpam-3206	272	16	then	then	ADV
ejpam-3206	272	17	r	r	NOUN
ejpam-3206	272	18	is	be	AUX
ejpam-3206	272	19	a	a	DET
ejpam-3206	272	20	right	right	ADJ
ejpam-3206	272	21	ps	ps	NOUN
ejpam-3206	272	22	-	-	NOUN
ejpam-3206	272	23	ring	ring	NOUN
ejpam-3206	272	24	.	.	PUNCT
ejpam-3206	273	1	3	3	X
ejpam-3206	273	2	.	.	X
ejpam-3206	273	3	skew	skew	PROPN
ejpam-3206	273	4	hurwitz	hurwitz	PROPN
ejpam-3206	273	5	series	series	PROPN
ejpam-3206	273	6	rings	ring	NOUN
ejpam-3206	273	7	satisfy	satisfy	VERB
ejpam-3206	273	8	the	the	DET
ejpam-3206	273	9	weak	weak	ADJ
ejpam-3206	273	10	ps	ps	NOUN
ejpam-3206	273	11	-	-	PUNCT
ejpam-3206	273	12	condition	condition	NOUN
ejpam-3206	273	13	rings	ring	NOUN
ejpam-3206	273	14	of	of	ADP
ejpam-3206	273	15	formal	formal	ADJ
ejpam-3206	273	16	power	power	NOUN
ejpam-3206	273	17	series	series	NOUN
ejpam-3206	273	18	have	have	AUX
ejpam-3206	273	19	been	be	AUX
ejpam-3206	273	20	of	of	ADP
ejpam-3206	273	21	interest	interest	NOUN
ejpam-3206	273	22	and	and	CCONJ
ejpam-3206	273	23	have	have	AUX
ejpam-3206	273	24	had	have	VERB
ejpam-3206	273	25	important	important	ADJ
ejpam-3206	273	26	applications	application	NOUN
ejpam-3206	273	27	in	in	ADP
ejpam-3206	273	28	many	many	ADJ
ejpam-3206	273	29	areas	area	NOUN
ejpam-3206	273	30	,	,	PUNCT
ejpam-3206	273	31	one	one	NUM
ejpam-3206	273	32	of	of	ADP
ejpam-3206	273	33	which	which	PRON
ejpam-3206	273	34	has	have	AUX
ejpam-3206	273	35	been	be	AUX
ejpam-3206	273	36	differential	differential	ADJ
ejpam-3206	273	37	algebra	algebra	NOUN
ejpam-3206	273	38	.	.	PUNCT
ejpam-3206	274	1	in	in	ADP
ejpam-3206	274	2	an	an	DET
ejpam-3206	274	3	earlier	early	ADJ
ejpam-3206	274	4	paper	paper	NOUN
ejpam-3206	274	5	by	by	ADP
ejpam-3206	274	6	keigher	keigher	ADJ
ejpam-3206	274	7	[	[	X
ejpam-3206	274	8	10	10	NUM
ejpam-3206	274	9	]	]	PUNCT
ejpam-3206	274	10	,	,	PUNCT
ejpam-3206	274	11	the	the	DET
ejpam-3206	274	12	ring	ring	NOUN
ejpam-3206	274	13	of	of	ADP
ejpam-3206	274	14	hurwitz	hurwitz	PROPN
ejpam-3206	274	15	series	series	PROPN
ejpam-3206	274	16	,	,	PUNCT
ejpam-3206	274	17	a	a	DET
ejpam-3206	274	18	variant	variant	NOUN
ejpam-3206	274	19	of	of	ADP
ejpam-3206	274	20	the	the	DET
ejpam-3206	274	21	ring	ring	NOUN
ejpam-3206	274	22	of	of	ADP
ejpam-3206	274	23	formal	formal	ADJ
ejpam-3206	274	24	power	power	NOUN
ejpam-3206	274	25	series	series	NOUN
ejpam-3206	274	26	was	be	AUX
ejpam-3206	274	27	considered	consider	VERB
ejpam-3206	274	28	,	,	PUNCT
ejpam-3206	274	29	and	and	CCONJ
ejpam-3206	274	30	some	some	PRON
ejpam-3206	274	31	of	of	ADP
ejpam-3206	274	32	its	its	PRON
ejpam-3206	274	33	properties	property	NOUN
ejpam-3206	274	34	,	,	PUNCT
ejpam-3206	274	35	especially	especially	ADV
ejpam-3206	274	36	its	its	PRON
ejpam-3206	274	37	categorical	categorical	ADJ
ejpam-3206	274	38	properties	property	NOUN
ejpam-3206	274	39	,	,	PUNCT
ejpam-3206	274	40	were	be	AUX
ejpam-3206	274	41	studied	study	VERB
ejpam-3206	274	42	.	.	PUNCT
ejpam-3206	275	1	in	in	ADP
ejpam-3206	275	2	the	the	DET
ejpam-3206	275	3	papers	paper	NOUN
ejpam-3206	275	4	(	(	PUNCT
ejpam-3206	275	5	[	[	X
ejpam-3206	275	6	11	11	NUM
ejpam-3206	275	7	,	,	PUNCT
ejpam-3206	275	8	12	12	NUM
ejpam-3206	275	9	]	]	PUNCT
ejpam-3206	275	10	)	)	PUNCT
ejpam-3206	275	11	keigher	keigher	PROPN
ejpam-3206	275	12	demonstrated	demonstrate	VERB
ejpam-3206	275	13	that	that	SCONJ
ejpam-3206	275	14	the	the	DET
ejpam-3206	275	15	ring	ring	NOUN
ejpam-3206	275	16	of	of	ADP
ejpam-3206	275	17	hurwitz	hurwitz	PROPN
ejpam-3206	275	18	series	series	PROPN
ejpam-3206	275	19	has	have	VERB
ejpam-3206	275	20	many	many	ADJ
ejpam-3206	275	21	interesting	interesting	ADJ
ejpam-3206	275	22	applications	application	NOUN
ejpam-3206	275	23	in	in	ADP
ejpam-3206	275	24	differential	differential	ADJ
ejpam-3206	275	25	algebra	algebra	NOUN
ejpam-3206	275	26	and	and	CCONJ
ejpam-3206	275	27	in	in	ADP
ejpam-3206	275	28	the	the	DET
ejpam-3206	275	29	discussion	discussion	NOUN
ejpam-3206	275	30	about	about	ADP
ejpam-3206	275	31	weak	weak	ADJ
ejpam-3206	275	32	normalization	normalization	NOUN
ejpam-3206	275	33	.	.	PUNCT
ejpam-3206	276	1	the	the	DET
ejpam-3206	276	2	product	product	NOUN
ejpam-3206	276	3	of	of	ADP
ejpam-3206	276	4	series	series	NOUN
ejpam-3206	276	5	using	use	VERB
ejpam-3206	276	6	the	the	DET
ejpam-3206	276	7	binomial	binomial	ADJ
ejpam-3206	276	8	coefficients	coefficient	NOUN
ejpam-3206	276	9	,	,	PUNCT
ejpam-3206	276	10	was	be	AUX
ejpam-3206	276	11	studied	study	VERB
ejpam-3206	276	12	also	also	ADV
ejpam-3206	276	13	in	in	ADP
ejpam-3206	276	14	papers	paper	NOUN
ejpam-3206	276	15	by	by	ADP
ejpam-3206	276	16	fliess	fliess	NOUN
ejpam-3206	276	17	[	[	X
ejpam-3206	276	18	5	5	NUM
ejpam-3206	276	19	]	]	PUNCT
ejpam-3206	276	20	and	and	CCONJ
ejpam-3206	276	21	taft	taft	X
ejpam-3206	277	1	[	[	X
ejpam-3206	277	2	21	21	NUM
ejpam-3206	277	3	]	]	PUNCT
ejpam-3206	277	4	.	.	PUNCT
ejpam-3206	278	1	ring	ring	NOUN
ejpam-3206	278	2	-	-	PUNCT
ejpam-3206	278	3	theoretical	theoretical	ADJ
ejpam-3206	278	4	properties	property	NOUN
ejpam-3206	278	5	of	of	ADP
ejpam-3206	278	6	hurwitz	hurwitz	PROPN
ejpam-3206	278	7	series	series	PROPN
ejpam-3206	278	8	rings	ring	NOUN
ejpam-3206	278	9	and	and	CCONJ
ejpam-3206	278	10	its	its	PRON
ejpam-3206	278	11	skew	skew	NOUN
ejpam-3206	278	12	have	have	AUX
ejpam-3206	278	13	been	be	AUX
ejpam-3206	278	14	investigated	investigate	VERB
ejpam-3206	278	15	by	by	ADP
ejpam-3206	278	16	many	many	ADJ
ejpam-3206	278	17	authors	author	NOUN
ejpam-3206	278	18	(	(	PUNCT
ejpam-3206	278	19	[	[	X
ejpam-3206	278	20	10	10	NUM
ejpam-3206	278	21	,	,	PUNCT
ejpam-3206	278	22	11	11	NUM
ejpam-3206	278	23	,	,	PUNCT
ejpam-3206	278	24	12	12	NUM
ejpam-3206	278	25	,	,	PUNCT
ejpam-3206	278	26	7	7	NUM
ejpam-3206	278	27	,	,	PUNCT
ejpam-3206	278	28	8	8	NUM
ejpam-3206	278	29	,	,	PUNCT
ejpam-3206	278	30	4	4	NUM
ejpam-3206	278	31	]	]	NUM
ejpam-3206	278	32	)	)	PUNCT
ejpam-3206	278	33	.	.	PUNCT
ejpam-3206	279	1	in	in	ADP
ejpam-3206	279	2	this	this	DET
ejpam-3206	279	3	section	section	NOUN
ejpam-3206	279	4	we	we	PRON
ejpam-3206	279	5	study	study	VERB
ejpam-3206	279	6	the	the	DET
ejpam-3206	279	7	skew	skew	PROPN
ejpam-3206	279	8	hurwitz	hurwitz	PROPN
ejpam-3206	279	9	series	series	PROPN
ejpam-3206	279	10	rings	ring	NOUN
ejpam-3206	279	11	over	over	ADP
ejpam-3206	279	12	a	a	DET
ejpam-3206	279	13	noncommutative	noncommutative	ADJ
ejpam-3206	279	14	rings	ring	NOUN
ejpam-3206	279	15	and	and	CCONJ
ejpam-3206	279	16	examine	examine	VERB
ejpam-3206	279	17	their	their	PRON
ejpam-3206	279	18	structures	structure	NOUN
ejpam-3206	279	19	and	and	CCONJ
ejpam-3206	279	20	properties	property	NOUN
ejpam-3206	279	21	.	.	PUNCT
ejpam-3206	280	1	the	the	DET
ejpam-3206	280	2	elements	element	NOUN
ejpam-3206	280	3	of	of	ADP
ejpam-3206	280	4	hr	hr	NOUN
ejpam-3206	280	5	are	be	AUX
ejpam-3206	280	6	ordinary	ordinary	ADJ
ejpam-3206	280	7	formal	formal	ADJ
ejpam-3206	280	8	series	series	NOUN
ejpam-3206	280	9	,	,	PUNCT
ejpam-3206	280	10	i.e.	i.e.	X
ejpam-3206	280	11	,	,	PUNCT
ejpam-3206	280	12	hr	hr	NOUN
ejpam-3206	280	13	=	=	PUNCT
ejpam-3206	280	14	{	{	PUNCT
ejpam-3206	280	15	∞∑	∞∑	NUM
ejpam-3206	280	16	i=0	i=0	PROPN
ejpam-3206	280	17	aix	aix	NOUN
ejpam-3206	280	18	i	i	NOUN
ejpam-3206	280	19	|ai	|ai	NUM
ejpam-3206	280	20	∈	∈	PROPN
ejpam-3206	280	21	r	r	NOUN
ejpam-3206	280	22	}	}	PUNCT
ejpam-3206	280	23	.	.	PUNCT
ejpam-3206	281	1	the	the	DET
ejpam-3206	281	2	operation	operation	NOUN
ejpam-3206	281	3	of	of	ADP
ejpam-3206	281	4	addition	addition	NOUN
ejpam-3206	281	5	in	in	ADP
ejpam-3206	281	6	hr	hr	NOUN
ejpam-3206	281	7	is	be	AUX
ejpam-3206	281	8	a	a	DET
ejpam-3206	281	9	componentwise	componentwise	NOUN
ejpam-3206	281	10	addition	addition	NOUN
ejpam-3206	281	11	and	and	CCONJ
ejpam-3206	281	12	the	the	DET
ejpam-3206	281	13	operation	operation	NOUN
ejpam-3206	281	14	of	of	ADP
ejpam-3206	281	15	multiplication	multiplication	NOUN
ejpam-3206	281	16	is	be	AUX
ejpam-3206	281	17	defined	define	VERB
ejpam-3206	281	18	by	by	ADP
ejpam-3206	281	19	the	the	DET
ejpam-3206	281	20	following	following	NOUN
ejpam-3206	281	21	:	:	PUNCT
ejpam-3206	281	22	for	for	ADP
ejpam-3206	281	23	each	each	DET
ejpam-3206	281	24	two	two	NUM
ejpam-3206	281	25	hurwitz	hurwitz	PROPN
ejpam-3206	281	26	series	series	PROPN
ejpam-3206	281	27	f(x	f(x	PROPN
ejpam-3206	281	28	)	)	PUNCT
ejpam-3206	281	29	=	=	PUNCT
ejpam-3206	282	1	∞∑	∞∑	NUM
ejpam-3206	282	2	i=0	i=0	PROPN
ejpam-3206	282	3	aix	aix	NOUN
ejpam-3206	282	4	i	i	PROPN
ejpam-3206	282	5	and	and	CCONJ
ejpam-3206	282	6	g(x	g(x	NOUN
ejpam-3206	282	7	)	)	PUNCT
ejpam-3206	283	1	=	=	NOUN
ejpam-3206	284	1	∞∑	∞∑	NUM
ejpam-3206	284	2	j=0	j=0	PROPN
ejpam-3206	284	3	bjx	bjx	PROPN
ejpam-3206	284	4	j	j	PROPN
ejpam-3206	284	5	∈	∈	PROPN
ejpam-3206	284	6	hr	hr	PROPN
ejpam-3206	284	7	,	,	PUNCT
ejpam-3206	284	8	(	(	PUNCT
ejpam-3206	284	9	∞∑	∞∑	NUM
ejpam-3206	284	10	i=0	i=0	PROPN
ejpam-3206	284	11	aix	aix	NOUN
ejpam-3206	284	12	i	i	NOUN
ejpam-3206	284	13	)	)	PUNCT
ejpam-3206	285	1			PROPN
ejpam-3206	285	2	∞∑	∞∑	NUM
ejpam-3206	285	3	j=0	j=0	PROPN
ejpam-3206	285	4	bjx	bjx	PROPN
ejpam-3206	285	5	j	j	PROPN
ejpam-3206	285	6			PROPN
ejpam-3206	285	7	=	=	PUNCT
ejpam-3206	286	1	∞∑	∞∑	NUM
ejpam-3206	286	2	n=0	n=0	NUM
ejpam-3206	286	3	(	(	PUNCT
ejpam-3206	286	4	n∑	n∑	NOUN
ejpam-3206	286	5	i=0	i=0	PROPN
ejpam-3206	286	6	(	(	PUNCT
ejpam-3206	286	7	n	n	X
ejpam-3206	286	8	i	i	NOUN
ejpam-3206	286	9	)	)	PUNCT
ejpam-3206	286	10	aibn−i	aibn−i	ADV
ejpam-3206	286	11	)	)	PUNCT
ejpam-3206	286	12	xn	xn	PROPN
ejpam-3206	286	13	,	,	PUNCT
ejpam-3206	286	14	where	where	SCONJ
ejpam-3206	286	15	(	(	PUNCT
ejpam-3206	286	16	n	n	NOUN
ejpam-3206	286	17	i	i	PRON
ejpam-3206	286	18	)	)	PUNCT
ejpam-3206	287	1	=	=	PUNCT
ejpam-3206	287	2	cn	cn	INTJ
ejpam-3206	288	1	i	i	NOUN
ejpam-3206	288	2	=	=	PUNCT
ejpam-3206	288	3	n	n	X
ejpam-3206	288	4	!	!	PUNCT
ejpam-3206	288	5	i!×(n−i	i!×(n−i	NOUN
ejpam-3206	288	6	)	)	PUNCT
ejpam-3206	288	7	!	!	PUNCT
ejpam-3206	289	1	,	,	PUNCT
ejpam-3206	289	2	is	be	AUX
ejpam-3206	289	3	the	the	DET
ejpam-3206	289	4	binomial	binomial	ADJ
ejpam-3206	289	5	coefficient	coefficient	NOUN
ejpam-3206	289	6	.	.	PUNCT
ejpam-3206	290	1	from	from	ADP
ejpam-3206	290	2	the	the	DET
ejpam-3206	290	3	above	above	ADJ
ejpam-3206	290	4	discussion	discussion	NOUN
ejpam-3206	290	5	we	we	PRON
ejpam-3206	290	6	can	can	AUX
ejpam-3206	290	7	say	say	VERB
ejpam-3206	290	8	that	that	PRON
ejpam-3206	290	9	:	:	PUNCT
ejpam-3206	290	10	the	the	DET
ejpam-3206	290	11	multiplication	multiplication	NOUN
ejpam-3206	290	12	is	be	AUX
ejpam-3206	290	13	subject	subject	ADJ
ejpam-3206	290	14	to	to	ADP
ejpam-3206	290	15	the	the	DET
ejpam-3206	290	16	relation	relation	NOUN
ejpam-3206	290	17	(	(	PUNCT
ejpam-3206	290	18	hurwitz	hurwitz	PROPN
ejpam-3206	290	19	multiplication	multiplication	NOUN
ejpam-3206	290	20	rule	rule	NOUN
ejpam-3206	290	21	)	)	PUNCT
ejpam-3206	290	22	(	(	PUNCT
ejpam-3206	290	23	aix	aix	NOUN
ejpam-3206	290	24	i	i	PROPN
ejpam-3206	290	25	)	)	PUNCT
ejpam-3206	291	1	(	(	PUNCT
ejpam-3206	291	2	bjx	bjx	INTJ
ejpam-3206	291	3	j	j	PROPN
ejpam-3206	291	4	)	)	PUNCT
ejpam-3206	292	1	=	=	PRON
ejpam-3206	293	1	(	(	PUNCT
ejpam-3206	293	2	i+	i+	NUM
ejpam-3206	293	3	j	j	NOUN
ejpam-3206	293	4	i	i	PROPN
ejpam-3206	293	5	)	)	PUNCT
ejpam-3206	293	6	aibjx	aibjx	PROPN
ejpam-3206	293	7	i+j	i+j	NUM
ejpam-3206	294	1	=	=	SYM
ejpam-3206	295	1	(	(	PUNCT
ejpam-3206	295	2	i+	i+	NUM
ejpam-3206	295	3	j	j	PROPN
ejpam-3206	295	4	j	j	PROPN
ejpam-3206	295	5	)	)	PUNCT
ejpam-3206	295	6	aibjx	aibjx	PROPN
ejpam-3206	295	7	i+j	i+j	NUM
ejpam-3206	295	8	.	.	PUNCT
ejpam-3206	296	1	it	it	PRON
ejpam-3206	296	2	is	be	AUX
ejpam-3206	296	3	now	now	ADV
ejpam-3206	296	4	routine	routine	ADJ
ejpam-3206	296	5	to	to	PART
ejpam-3206	296	6	check	check	VERB
ejpam-3206	296	7	that	that	PRON
ejpam-3206	296	8	hr	hr	NOUN
ejpam-3206	296	9	is	be	AUX
ejpam-3206	296	10	a	a	DET
ejpam-3206	296	11	ring	ring	NOUN
ejpam-3206	296	12	with	with	ADP
ejpam-3206	296	13	identity	identity	NOUN
ejpam-3206	296	14	1r	1r	NUM
ejpam-3206	296	15	which	which	PRON
ejpam-3206	296	16	is	be	AUX
ejpam-3206	296	17	called	call	VERB
ejpam-3206	296	18	the	the	DET
ejpam-3206	296	19	hurwitz	hurwitz	PROPN
ejpam-3206	296	20	series	series	PROPN
ejpam-3206	296	21	rings	ring	NOUN
ejpam-3206	296	22	over	over	ADP
ejpam-3206	296	23	r.	r.	PROPN
ejpam-3206	296	24	clearly	clearly	ADV
ejpam-3206	296	25	,	,	PUNCT
ejpam-3206	296	26	r	r	NOUN
ejpam-3206	296	27	is	be	AUX
ejpam-3206	296	28	a	a	DET
ejpam-3206	296	29	subring	subring	NOUN
ejpam-3206	296	30	of	of	ADP
ejpam-3206	296	31	hr	hr	NOUN
ejpam-3206	296	32	.	.	PUNCT
ejpam-3206	297	1	despite	despite	SCONJ
ejpam-3206	297	2	the	the	DET
ejpam-3206	297	3	apparent	apparent	ADJ
ejpam-3206	297	4	similarity	similarity	NOUN
ejpam-3206	297	5	between	between	ADP
ejpam-3206	297	6	the	the	DET
ejpam-3206	297	7	formal	formal	ADJ
ejpam-3206	297	8	power	power	NOUN
ejpam-3206	297	9	series	series	PROPN
ejpam-3206	297	10	rings	rings	PROPN
ejpam-3206	297	11	r[[x	r[[x	PROPN
ejpam-3206	297	12	]	]	X
ejpam-3206	297	13	]	]	PUNCT
ejpam-3206	297	14	and	and	CCONJ
ejpam-3206	297	15	the	the	DET
ejpam-3206	297	16	hurwitz	hurwitz	PROPN
ejpam-3206	297	17	series	series	PROPN
ejpam-3206	297	18	rings	ring	NOUN
ejpam-3206	297	19	hr	hr	PROPN
ejpam-3206	298	1	but	but	CCONJ
ejpam-3206	298	2	there	there	PRON
ejpam-3206	298	3	are	be	VERB
ejpam-3206	298	4	substantial	substantial	ADJ
ejpam-3206	298	5	difference	difference	NOUN
ejpam-3206	298	6	between	between	ADP
ejpam-3206	298	7	them	they	PRON
ejpam-3206	298	8	for	for	ADP
ejpam-3206	298	9	example	example	NOUN
ejpam-3206	298	10	,	,	PUNCT
ejpam-3206	298	11	m.	m.	NOUN
ejpam-3206	298	12	a.	a.	NOUN
ejpam-3206	298	13	farahat	farahat	PROPN
ejpam-3206	298	14	,	,	PUNCT
ejpam-3206	298	15	s.	s.	PROPN
ejpam-3206	298	16	t.	t.	PROPN
ejpam-3206	298	17	al	al	PROPN
ejpam-3206	298	18	-	-	PUNCT
ejpam-3206	298	19	bogamy	bogamy	PROPN
ejpam-3206	298	20	/	/	SYM
ejpam-3206	298	21	eur	eur	PROPN
ejpam-3206	298	22	.	.	PUNCT
ejpam-3206	299	1	j.	j.	PROPN
ejpam-3206	299	2	pure	pure	PROPN
ejpam-3206	299	3	appl	appl	PROPN
ejpam-3206	299	4	.	.	PROPN
ejpam-3206	299	5	math	math	PROPN
ejpam-3206	299	6	,	,	PUNCT
ejpam-3206	299	7	11	11	NUM
ejpam-3206	299	8	(	(	PUNCT
ejpam-3206	299	9	1	1	NUM
ejpam-3206	299	10	)	)	PUNCT
ejpam-3206	299	11	(	(	PUNCT
ejpam-3206	299	12	2018	2018	NUM
ejpam-3206	299	13	)	)	PUNCT
ejpam-3206	299	14	,	,	PUNCT
ejpam-3206	299	15	244	244	NUM
ejpam-3206	299	16	-	-	SYM
ejpam-3206	299	17	259	259	NUM
ejpam-3206	299	18	254	254	NUM
ejpam-3206	299	19	the	the	DET
ejpam-3206	299	20	ideal	ideal	ADJ
ejpam-3206	299	21	〈	〈	PROPN
ejpam-3206	299	22	x	x	SYM
ejpam-3206	299	23	,	,	PUNCT
ejpam-3206	299	24	x2	x2	PROPN
ejpam-3206	299	25	,	,	PUNCT
ejpam-3206	299	26	x3	x3	ADJ
ejpam-3206	299	27	,	,	PUNCT
ejpam-3206	299	28	...	...	PUNCT
ejpam-3206	299	29	〉	〉	NOUN
ejpam-3206	299	30	is	be	AUX
ejpam-3206	299	31	principal	principal	ADJ
ejpam-3206	299	32	in	in	ADP
ejpam-3206	299	33	r[[x	r[[x	PROPN
ejpam-3206	299	34	]	]	X
ejpam-3206	299	35	]	]	PUNCT
ejpam-3206	299	36	which	which	PRON
ejpam-3206	299	37	is	be	AUX
ejpam-3206	299	38	the	the	DET
ejpam-3206	299	39	same	same	ADJ
ejpam-3206	299	40	as	as	ADP
ejpam-3206	299	41	the	the	DET
ejpam-3206	299	42	ideal	ideal	ADJ
ejpam-3206	299	43	〈	〈	PROPN
ejpam-3206	299	44	x	x	PROPN
ejpam-3206	299	45	〉	〉	PROPN
ejpam-3206	299	46	but	but	CCONJ
ejpam-3206	299	47	the	the	DET
ejpam-3206	299	48	ideal	ideal	ADJ
ejpam-3206	299	49	〈	〈	PROPN
ejpam-3206	299	50	x	x	SYM
ejpam-3206	299	51	,	,	PUNCT
ejpam-3206	299	52	x2	x2	PROPN
ejpam-3206	299	53	,	,	PUNCT
ejpam-3206	299	54	x3	x3	ADJ
ejpam-3206	299	55	,	,	PUNCT
ejpam-3206	299	56	...	...	PUNCT
ejpam-3206	299	57	〉	〉	NOUN
ejpam-3206	299	58	in	in	ADP
ejpam-3206	299	59	hr	hr	NOUN
ejpam-3206	299	60	is	be	AUX
ejpam-3206	299	61	not	not	PART
ejpam-3206	299	62	a	a	DET
ejpam-3206	299	63	finitely	finitely	ADV
ejpam-3206	299	64	generated	generate	VERB
ejpam-3206	299	65	.	.	PUNCT
ejpam-3206	300	1	here	here	ADV
ejpam-3206	301	1	x2	x2	INTJ
ejpam-3206	301	2	/∈	/∈	PUNCT
ejpam-3206	302	1	〈	〈	PROPN
ejpam-3206	302	2	x	x	X
ejpam-3206	302	3	〉	〉	PROPN
ejpam-3206	302	4	since	since	SCONJ
ejpam-3206	302	5	x.x	x.x	PROPN
ejpam-3206	302	6	=	=	SYM
ejpam-3206	302	7	2x2	2x2	X
ejpam-3206	302	8	.	.	PUNCT
ejpam-3206	303	1	clearly	clearly	ADV
ejpam-3206	303	2	,	,	PUNCT
ejpam-3206	303	3	if	if	SCONJ
ejpam-3206	303	4	r	r	NOUN
ejpam-3206	303	5	has	have	VERB
ejpam-3206	303	6	q	q	X
ejpam-3206	303	7	as	as	ADP
ejpam-3206	303	8	a	a	DET
ejpam-3206	303	9	subring	subring	NOUN
ejpam-3206	303	10	,	,	PUNCT
ejpam-3206	303	11	then	then	ADV
ejpam-3206	303	12	the	the	DET
ejpam-3206	303	13	ideal	ideal	ADJ
ejpam-3206	303	14	〈	〈	PROPN
ejpam-3206	303	15	x	x	SYM
ejpam-3206	303	16	,	,	PUNCT
ejpam-3206	303	17	x2	x2	PROPN
ejpam-3206	303	18	,	,	PUNCT
ejpam-3206	303	19	x3	x3	ADJ
ejpam-3206	303	20	,	,	PUNCT
ejpam-3206	303	21	...	...	PUNCT
ejpam-3206	303	22	〉	〉	NOUN
ejpam-3206	303	23	in	in	ADP
ejpam-3206	303	24	hr	hr	NOUN
ejpam-3206	303	25	will	will	AUX
ejpam-3206	303	26	be	be	AUX
ejpam-3206	303	27	the	the	DET
ejpam-3206	303	28	same	same	ADJ
ejpam-3206	303	29	as	as	ADP
ejpam-3206	303	30	the	the	DET
ejpam-3206	303	31	principal	principal	ADJ
ejpam-3206	303	32	ideal	ideal	NOUN
ejpam-3206	303	33	〈	〈	PROPN
ejpam-3206	303	34	x	x	PROPN
ejpam-3206	303	35	〉	〉	PROPN
ejpam-3206	303	36	.	.	PUNCT
ejpam-3206	304	1	let	let	VERB
ejpam-3206	304	2	σ	σ	NOUN
ejpam-3206	304	3	be	be	AUX
ejpam-3206	304	4	an	an	DET
ejpam-3206	304	5	endomorphism	endomorphism	NOUN
ejpam-3206	304	6	of	of	ADP
ejpam-3206	304	7	the	the	DET
ejpam-3206	304	8	ring	ring	NOUN
ejpam-3206	304	9	r	r	NOUN
ejpam-3206	304	10	,	,	PUNCT
ejpam-3206	304	11	with	with	ADP
ejpam-3206	304	12	σ(1	σ(1	PROPN
ejpam-3206	304	13	)	)	PUNCT
ejpam-3206	304	14	=	=	SYM
ejpam-3206	305	1	1	1	X
ejpam-3206	305	2	.	.	PUNCT
ejpam-3206	306	1	the	the	DET
ejpam-3206	306	2	elements	element	NOUN
ejpam-3206	306	3	of	of	ADP
ejpam-3206	306	4	a	a	DET
ejpam-3206	306	5	=	=	X
ejpam-3206	306	6	(	(	PUNCT
ejpam-3206	306	7	hr	hr	PROPN
ejpam-3206	306	8	,	,	PUNCT
ejpam-3206	306	9	σ	σ	PROPN
ejpam-3206	306	10	)	)	PUNCT
ejpam-3206	306	11	,	,	PUNCT
ejpam-3206	306	12	the	the	DET
ejpam-3206	306	13	ring	ring	NOUN
ejpam-3206	306	14	of	of	ADP
ejpam-3206	306	15	skew	skew	ADJ
ejpam-3206	306	16	hurwitz	hurwitz	PROPN
ejpam-3206	306	17	series	series	PROPN
ejpam-3206	306	18	,	,	PUNCT
ejpam-3206	306	19	are	be	AUX
ejpam-3206	306	20	the	the	DET
ejpam-3206	306	21	ordinary	ordinary	ADJ
ejpam-3206	306	22	formal	formal	ADJ
ejpam-3206	306	23	series	series	NOUN
ejpam-3206	306	24	∞∑	∞∑	PROPN
ejpam-3206	306	25	i=0	i=0	PROPN
ejpam-3206	306	26	aix	aix	NOUN
ejpam-3206	306	27	i	i	PRON
ejpam-3206	306	28	,	,	PUNCT
ejpam-3206	306	29	where	where	SCONJ
ejpam-3206	306	30	ai	ai	VERB
ejpam-3206	306	31	∈	∈	PROPN
ejpam-3206	306	32	r	r	NOUN
ejpam-3206	306	33	,	,	PUNCT
ejpam-3206	306	34	with	with	ADP
ejpam-3206	306	35	component	component	NOUN
ejpam-3206	306	36	wise	wise	ADJ
ejpam-3206	306	37	addition	addition	NOUN
ejpam-3206	306	38	and	and	CCONJ
ejpam-3206	306	39	the	the	DET
ejpam-3206	306	40	following	follow	VERB
ejpam-3206	306	41	operation	operation	NOUN
ejpam-3206	306	42	of	of	ADP
ejpam-3206	306	43	multiplication	multiplication	NOUN
ejpam-3206	306	44	:	:	PUNCT
ejpam-3206	306	45	for	for	ADP
ejpam-3206	306	46	each	each	DET
ejpam-3206	306	47	two	two	NUM
ejpam-3206	306	48	hurwitz	hurwitz	PROPN
ejpam-3206	306	49	series	series	PROPN
ejpam-3206	306	50	f(x	f(x	PROPN
ejpam-3206	306	51	)	)	PUNCT
ejpam-3206	307	1	=	=	PUNCT
ejpam-3206	308	1	∞∑	∞∑	NUM
ejpam-3206	308	2	i=0	i=0	PROPN
ejpam-3206	308	3	aix	aix	NOUN
ejpam-3206	308	4	i	i	PROPN
ejpam-3206	308	5	and	and	CCONJ
ejpam-3206	308	6	g(x	g(x	NOUN
ejpam-3206	308	7	)	)	PUNCT
ejpam-3206	309	1	=	=	NOUN
ejpam-3206	310	1	∞∑	∞∑	NUM
ejpam-3206	310	2	j=0	j=0	PROPN
ejpam-3206	310	3	bjx	bjx	PROPN
ejpam-3206	310	4	j	j	PROPN
ejpam-3206	310	5	∈	∈	PROPN
ejpam-3206	310	6	a	a	DET
ejpam-3206	310	7	=	=	X
ejpam-3206	310	8	(	(	PUNCT
ejpam-3206	310	9	hr	hr	PROPN
ejpam-3206	310	10	,	,	PUNCT
ejpam-3206	310	11	σ	σ	PROPN
ejpam-3206	310	12	)	)	PUNCT
ejpam-3206	310	13	,	,	PUNCT
ejpam-3206	310	14	(	(	PUNCT
ejpam-3206	310	15	∞∑	∞∑	NUM
ejpam-3206	310	16	i=0	i=0	PROPN
ejpam-3206	310	17	aix	aix	NOUN
ejpam-3206	310	18	i	i	NOUN
ejpam-3206	310	19	)	)	PUNCT
ejpam-3206	311	1			PROPN
ejpam-3206	311	2	∞∑	∞∑	NUM
ejpam-3206	311	3	j=0	j=0	PROPN
ejpam-3206	311	4	bjx	bjx	PROPN
ejpam-3206	311	5	j	j	PROPN
ejpam-3206	311	6			PROPN
ejpam-3206	311	7	=	=	PUNCT
ejpam-3206	312	1	∞∑	∞∑	NUM
ejpam-3206	312	2	n=0	n=0	NUM
ejpam-3206	312	3	(	(	PUNCT
ejpam-3206	312	4	n∑	n∑	NOUN
ejpam-3206	312	5	i=0	i=0	PROPN
ejpam-3206	312	6	(	(	PUNCT
ejpam-3206	312	7	n	n	NOUN
ejpam-3206	312	8	i	i	PROPN
ejpam-3206	312	9	)	)	PUNCT
ejpam-3206	312	10	aiσ	aiσ	ADP
ejpam-3206	312	11	i(bn−i	i(bn−i	NOUN
ejpam-3206	312	12	)	)	PUNCT
ejpam-3206	312	13	)	)	PUNCT
ejpam-3206	312	14	xn	xn	PROPN
ejpam-3206	312	15	.	.	PUNCT
ejpam-3206	313	1	from	from	ADP
ejpam-3206	313	2	the	the	DET
ejpam-3206	313	3	above	above	ADJ
ejpam-3206	313	4	discussion	discussion	NOUN
ejpam-3206	313	5	we	we	PRON
ejpam-3206	313	6	can	can	AUX
ejpam-3206	313	7	say	say	VERB
ejpam-3206	313	8	that	that	PRON
ejpam-3206	313	9	:	:	PUNCT
ejpam-3206	313	10	the	the	DET
ejpam-3206	313	11	multiplication	multiplication	NOUN
ejpam-3206	313	12	is	be	AUX
ejpam-3206	313	13	subject	subject	ADJ
ejpam-3206	313	14	to	to	ADP
ejpam-3206	313	15	the	the	DET
ejpam-3206	313	16	relation	relation	NOUN
ejpam-3206	313	17	(	(	PUNCT
ejpam-3206	313	18	hurwitz	hurwitz	PROPN
ejpam-3206	313	19	multiplication	multiplication	NOUN
ejpam-3206	313	20	rule	rule	NOUN
ejpam-3206	313	21	)	)	PUNCT
ejpam-3206	313	22	(	(	PUNCT
ejpam-3206	313	23	aix	aix	NOUN
ejpam-3206	313	24	i	i	PROPN
ejpam-3206	313	25	)	)	PUNCT
ejpam-3206	314	1	(	(	PUNCT
ejpam-3206	314	2	bjx	bjx	INTJ
ejpam-3206	314	3	j	j	PROPN
ejpam-3206	314	4	)	)	PUNCT
ejpam-3206	315	1	=	=	PRON
ejpam-3206	316	1	(	(	PUNCT
ejpam-3206	316	2	i+	i+	NUM
ejpam-3206	316	3	j	j	NOUN
ejpam-3206	316	4	i	i	PROPN
ejpam-3206	316	5	)	)	PUNCT
ejpam-3206	316	6	aiσ	aiσ	ADP
ejpam-3206	316	7	i(bj)x	i(bj)x	NOUN
ejpam-3206	316	8	i+j	i+j	NUM
ejpam-3206	316	9	=	=	SYM
ejpam-3206	316	10	(	(	PUNCT
ejpam-3206	316	11	i+	i+	NUM
ejpam-3206	316	12	j	j	PROPN
ejpam-3206	316	13	j	j	PROPN
ejpam-3206	316	14	)	)	PUNCT
ejpam-3206	316	15	aiσ	aiσ	ADP
ejpam-3206	316	16	i(bj)x	i(bj)x	PROPN
ejpam-3206	316	17	i+j	i+j	NUM
ejpam-3206	316	18	.	.	PUNCT
ejpam-3206	317	1	by	by	ADP
ejpam-3206	317	2	hr	hr	NOUN
ejpam-3206	317	3	and	and	CCONJ
ejpam-3206	317	4	p	p	NOUN
ejpam-3206	317	5	=	=	PUNCT
ejpam-3206	317	6	(	(	PUNCT
ejpam-3206	317	7	hr	hr	PROPN
ejpam-3206	317	8	,	,	PUNCT
ejpam-3206	317	9	σ	σ	PROPN
ejpam-3206	317	10	)	)	PUNCT
ejpam-3206	317	11	,	,	PUNCT
ejpam-3206	317	12	we	we	PRON
ejpam-3206	317	13	denote	denote	VERB
ejpam-3206	317	14	the	the	DET
ejpam-3206	317	15	polynomial	polynomial	ADJ
ejpam-3206	317	16	hurwitz	hurwitz	PROPN
ejpam-3206	317	17	ring	ring	NOUN
ejpam-3206	317	18	and	and	CCONJ
ejpam-3206	317	19	skew	skew	ADJ
ejpam-3206	317	20	polynomial	polynomial	PROPN
ejpam-3206	317	21	hurwitz	hurwitz	PROPN
ejpam-3206	317	22	ring	ring	NOUN
ejpam-3206	317	23	,	,	PUNCT
ejpam-3206	317	24	respectively	respectively	ADV
ejpam-3206	317	25	.	.	PUNCT
ejpam-3206	318	1	the	the	DET
ejpam-3206	318	2	product	product	NOUN
ejpam-3206	318	3	,	,	PUNCT
ejpam-3206	318	4	in	in	ADP
ejpam-3206	318	5	this	this	DET
ejpam-3206	318	6	case	case	NOUN
ejpam-3206	318	7	will	will	AUX
ejpam-3206	318	8	be	be	AUX
ejpam-3206	318	9	as	as	SCONJ
ejpam-3206	318	10	follows	follow	VERB
ejpam-3206	318	11	:	:	PUNCT
ejpam-3206	318	12	for	for	ADP
ejpam-3206	318	13	each	each	DET
ejpam-3206	318	14	two	two	NUM
ejpam-3206	318	15	polynomial	polynomial	ADJ
ejpam-3206	318	16	hurwitz	hurwitz	PROPN
ejpam-3206	318	17	f(x	f(x	PROPN
ejpam-3206	318	18	)	)	PUNCT
ejpam-3206	319	1	=	=	SYM
ejpam-3206	320	1	v∑	v∑	NUM
ejpam-3206	320	2	i=0	i=0	PROPN
ejpam-3206	320	3	aix	aix	NOUN
ejpam-3206	320	4	i	i	PROPN
ejpam-3206	320	5	and	and	CCONJ
ejpam-3206	320	6	g(x	g(x	NOUN
ejpam-3206	320	7	)	)	PUNCT
ejpam-3206	321	1	=	=	SYM
ejpam-3206	321	2	u∑	u∑	PROPN
ejpam-3206	321	3	j=0	j=0	PROPN
ejpam-3206	321	4	bjx	bjx	PROPN
ejpam-3206	321	5	j	j	PROPN
ejpam-3206	321	6	∈	∈	PROPN
ejpam-3206	321	7	p	p	X
ejpam-3206	321	8	,	,	PUNCT
ejpam-3206	321	9	(	(	PUNCT
ejpam-3206	321	10	v∑	v∑	ADP
ejpam-3206	321	11	i=0	i=0	PROPN
ejpam-3206	321	12	aix	aix	NOUN
ejpam-3206	321	13	i	i	NOUN
ejpam-3206	321	14	)	)	PUNCT
ejpam-3206	322	1			PROPN
ejpam-3206	322	2	u∑	u∑	PUNCT
ejpam-3206	322	3	j=0	j=0	PROPN
ejpam-3206	322	4	bjx	bjx	PROPN
ejpam-3206	322	5	j	j	PROPN
ejpam-3206	322	6			PROPN
ejpam-3206	322	7	=	=	SYM
ejpam-3206	322	8	v+u∑	v+u∑	PROPN
ejpam-3206	322	9	n=0	n=0	NUM
ejpam-3206	322	10	(	(	PUNCT
ejpam-3206	322	11	n∑	n∑	NOUN
ejpam-3206	322	12	i=0	i=0	PROPN
ejpam-3206	322	13	(	(	PUNCT
ejpam-3206	322	14	n	n	NOUN
ejpam-3206	322	15	i	i	PROPN
ejpam-3206	322	16	)	)	PUNCT
ejpam-3206	322	17	aiσ	aiσ	ADP
ejpam-3206	322	18	i(bn−i	i(bn−i	NOUN
ejpam-3206	322	19	)	)	PUNCT
ejpam-3206	322	20	)	)	PUNCT
ejpam-3206	323	1	xn	xn	X
ejpam-3206	323	2	.	.	PUNCT
ejpam-3206	324	1	annin	annin	ADJ
ejpam-3206	324	2	[	[	X
ejpam-3206	324	3	1	1	NUM
ejpam-3206	324	4	]	]	PUNCT
ejpam-3206	324	5	introduced	introduce	VERB
ejpam-3206	324	6	the	the	DET
ejpam-3206	324	7	notion	notion	NOUN
ejpam-3206	324	8	of	of	ADP
ejpam-3206	324	9	σ	σ	PROPN
ejpam-3206	324	10	-	-	PUNCT
ejpam-3206	324	11	compatibility	compatibility	NOUN
ejpam-3206	324	12	of	of	ADP
ejpam-3206	324	13	rings	ring	NOUN
ejpam-3206	324	14	as	as	SCONJ
ejpam-3206	324	15	follows	follow	VERB
ejpam-3206	324	16	.	.	PUNCT
ejpam-3206	325	1	definition	definition	NOUN
ejpam-3206	325	2	3	3	NUM
ejpam-3206	325	3	(	(	PUNCT
ejpam-3206	325	4	[	[	X
ejpam-3206	325	5	1	1	NUM
ejpam-3206	325	6	]	]	NUM
ejpam-3206	325	7	)	)	PUNCT
ejpam-3206	325	8	.	.	PUNCT
ejpam-3206	326	1	a	a	DET
ejpam-3206	326	2	ring	ring	NOUN
ejpam-3206	326	3	r	r	NOUN
ejpam-3206	326	4	is	be	AUX
ejpam-3206	326	5	said	say	VERB
ejpam-3206	326	6	to	to	PART
ejpam-3206	326	7	be	be	AUX
ejpam-3206	326	8	σ	σ	NOUN
ejpam-3206	326	9	-	-	ADJ
ejpam-3206	326	10	compatible	compatible	ADJ
ejpam-3206	326	11	if	if	SCONJ
ejpam-3206	326	12	ab	ab	PROPN
ejpam-3206	326	13	=	=	SYM
ejpam-3206	326	14	0	0	NUM
ejpam-3206	326	15	⇔	⇔	NUM
ejpam-3206	326	16	aσ(b	aσ(b	NUM
ejpam-3206	326	17	)	)	PUNCT
ejpam-3206	326	18	=	=	SYM
ejpam-3206	326	19	0	0	NUM
ejpam-3206	326	20	,	,	PUNCT
ejpam-3206	326	21	where	where	SCONJ
ejpam-3206	326	22	a	a	PRON
ejpam-3206	326	23	,	,	PUNCT
ejpam-3206	326	24	b	b	PROPN
ejpam-3206	326	25	∈	∈	PROPN
ejpam-3206	326	26	r.	r.	VERB
ejpam-3206	326	27	some	some	PRON
ejpam-3206	326	28	of	of	ADP
ejpam-3206	326	29	the	the	DET
ejpam-3206	326	30	basic	basic	ADJ
ejpam-3206	326	31	properties	property	NOUN
ejpam-3206	326	32	of	of	ADP
ejpam-3206	326	33	a	a	DET
ejpam-3206	326	34	σ	σ	PROPN
ejpam-3206	326	35	-	-	PUNCT
ejpam-3206	326	36	compatible	compatible	ADJ
ejpam-3206	326	37	ring	ring	NOUN
ejpam-3206	326	38	was	be	AUX
ejpam-3206	326	39	given	give	VERB
ejpam-3206	326	40	in	in	ADP
ejpam-3206	326	41	the	the	DET
ejpam-3206	326	42	following	follow	VERB
ejpam-3206	326	43	lemmas	lemmas	PROPN
ejpam-3206	326	44	.	.	PUNCT
ejpam-3206	327	1	lemma	lemma	PROPN
ejpam-3206	327	2	4	4	NUM
ejpam-3206	327	3	(	(	PUNCT
ejpam-3206	327	4	[	[	X
ejpam-3206	327	5	1	1	NUM
ejpam-3206	327	6	]	]	PUNCT
ejpam-3206	327	7	)	)	PUNCT
ejpam-3206	327	8	.	.	PUNCT
ejpam-3206	328	1	if	if	SCONJ
ejpam-3206	328	2	r	r	NOUN
ejpam-3206	328	3	is	be	AUX
ejpam-3206	328	4	a	a	DET
ejpam-3206	328	5	σ	σ	PROPN
ejpam-3206	328	6	-	-	PUNCT
ejpam-3206	328	7	compatible	compatible	ADJ
ejpam-3206	328	8	ring	ring	NOUN
ejpam-3206	328	9	,	,	PUNCT
ejpam-3206	328	10	then	then	ADV
ejpam-3206	328	11	:	:	PUNCT
ejpam-3206	328	12	1	1	X
ejpam-3206	328	13	)	)	PUNCT
ejpam-3206	328	14	σ(1	σ(1	NOUN
ejpam-3206	328	15	)	)	PUNCT
ejpam-3206	329	1	=	=	SYM
ejpam-3206	329	2	1	1	NUM
ejpam-3206	329	3	,	,	PUNCT
ejpam-3206	329	4	2	2	NUM
ejpam-3206	329	5	)	)	PUNCT
ejpam-3206	329	6	σ	σ	NOUN
ejpam-3206	329	7	is	be	AUX
ejpam-3206	329	8	a	a	DET
ejpam-3206	329	9	monomorphism	monomorphism	NOUN
ejpam-3206	329	10	,	,	PUNCT
ejpam-3206	329	11	3	3	NUM
ejpam-3206	329	12	)	)	PUNCT
ejpam-3206	329	13	ab	ab	NOUN
ejpam-3206	329	14	=	=	PUNCT
ejpam-3206	329	15	0⇔	0⇔	NOUN
ejpam-3206	329	16	σ(a)b	σ(a)b	PROPN
ejpam-3206	329	17	=	=	SYM
ejpam-3206	329	18	0	0	PROPN
ejpam-3206	329	19	,	,	PUNCT
ejpam-3206	329	20	where	where	SCONJ
ejpam-3206	329	21	a	a	DET
ejpam-3206	329	22	,	,	PUNCT
ejpam-3206	329	23	b	b	PROPN
ejpam-3206	329	24	∈	∈	PROPN
ejpam-3206	329	25	r.	r.	PROPN
ejpam-3206	329	26	lemma	lemma	PROPN
ejpam-3206	329	27	5	5	NUM
ejpam-3206	329	28	(	(	PUNCT
ejpam-3206	329	29	[	[	X
ejpam-3206	329	30	1	1	NUM
ejpam-3206	329	31	]	]	PUNCT
ejpam-3206	329	32	)	)	PUNCT
ejpam-3206	329	33	.	.	PUNCT
ejpam-3206	330	1	let	let	VERB
ejpam-3206	330	2	r	r	PRON
ejpam-3206	330	3	be	be	AUX
ejpam-3206	330	4	a	a	DET
ejpam-3206	330	5	σ	σ	NOUN
ejpam-3206	330	6	-	-	PUNCT
ejpam-3206	330	7	compatible	compatible	ADJ
ejpam-3206	330	8	ring	ring	NOUN
ejpam-3206	330	9	.	.	PUNCT
ejpam-3206	331	1	then	then	ADV
ejpam-3206	331	2	ab	ab	PROPN
ejpam-3206	331	3	=	=	SYM
ejpam-3206	331	4	0	0	PROPN
ejpam-3206	331	5	⇔	⇔	PROPN
ejpam-3206	331	6	aσi	aσi	PROPN
ejpam-3206	331	7	(	(	PUNCT
ejpam-3206	331	8	b	b	NOUN
ejpam-3206	331	9	)	)	PUNCT
ejpam-3206	331	10	=	=	SYM
ejpam-3206	331	11	0	0	NUM
ejpam-3206	331	12	⇔	⇔	X
ejpam-3206	331	13	σi(a)b	σi(a)b	PROPN
ejpam-3206	332	1	=	=	SYM
ejpam-3206	332	2	0	0	PROPN
ejpam-3206	332	3	for	for	ADP
ejpam-3206	332	4	all	all	PRON
ejpam-3206	332	5	i	i	PRON
ejpam-3206	332	6	≥	≥	VERB
ejpam-3206	332	7	0	0	NUM
ejpam-3206	332	8	and	and	CCONJ
ejpam-3206	332	9	a	a	DET
ejpam-3206	332	10	,	,	PUNCT
ejpam-3206	332	11	b	b	PROPN
ejpam-3206	332	12	∈	∈	PROPN
ejpam-3206	332	13	r.	r.	NOUN
ejpam-3206	332	14	in	in	ADP
ejpam-3206	332	15	[	[	X
ejpam-3206	332	16	13	13	NUM
ejpam-3206	332	17	]	]	PUNCT
ejpam-3206	332	18	,	,	PUNCT
ejpam-3206	332	19	the	the	DET
ejpam-3206	332	20	author	author	NOUN
ejpam-3206	332	21	introduced	introduce	VERB
ejpam-3206	332	22	the	the	DET
ejpam-3206	332	23	concept	concept	NOUN
ejpam-3206	332	24	of	of	ADP
ejpam-3206	332	25	σ	σ	PROPN
ejpam-3206	332	26	-	-	ADJ
ejpam-3206	332	27	rigid	rigid	ADJ
ejpam-3206	332	28	rings	ring	NOUN
ejpam-3206	332	29	for	for	ADP
ejpam-3206	332	30	rings	ring	NOUN
ejpam-3206	332	31	with	with	ADP
ejpam-3206	332	32	an	an	DET
ejpam-3206	332	33	endomorphism	endomorphism	PROPN
ejpam-3206	332	34	σ	σ	PROPN
ejpam-3206	332	35	,	,	PUNCT
ejpam-3206	332	36	as	as	SCONJ
ejpam-3206	332	37	follows	follow	VERB
ejpam-3206	332	38	:	:	PUNCT
ejpam-3206	332	39	m.	m.	NOUN
ejpam-3206	332	40	a.	a.	PROPN
ejpam-3206	332	41	farahat	farahat	PROPN
ejpam-3206	332	42	,	,	PUNCT
ejpam-3206	332	43	s.	s.	PROPN
ejpam-3206	332	44	t.	t.	PROPN
ejpam-3206	332	45	al	al	PROPN
ejpam-3206	332	46	-	-	PUNCT
ejpam-3206	332	47	bogamy	bogamy	PROPN
ejpam-3206	332	48	/	/	SYM
ejpam-3206	332	49	eur	eur	PROPN
ejpam-3206	332	50	.	.	PUNCT
ejpam-3206	333	1	j.	j.	PROPN
ejpam-3206	333	2	pure	pure	PROPN
ejpam-3206	333	3	appl	appl	PROPN
ejpam-3206	333	4	.	.	PROPN
ejpam-3206	333	5	math	math	PROPN
ejpam-3206	333	6	,	,	PUNCT
ejpam-3206	333	7	11	11	NUM
ejpam-3206	333	8	(	(	PUNCT
ejpam-3206	333	9	1	1	NUM
ejpam-3206	333	10	)	)	PUNCT
ejpam-3206	333	11	(	(	PUNCT
ejpam-3206	333	12	2018	2018	NUM
ejpam-3206	333	13	)	)	PUNCT
ejpam-3206	333	14	,	,	PUNCT
ejpam-3206	333	15	244	244	NUM
ejpam-3206	333	16	-	-	SYM
ejpam-3206	333	17	259	259	NUM
ejpam-3206	333	18	255	255	NUM
ejpam-3206	333	19	definition	definition	NOUN
ejpam-3206	333	20	4	4	NUM
ejpam-3206	333	21	(	(	PUNCT
ejpam-3206	333	22	[	[	X
ejpam-3206	333	23	13	13	NUM
ejpam-3206	333	24	]	]	NUM
ejpam-3206	333	25	)	)	PUNCT
ejpam-3206	333	26	.	.	PUNCT
ejpam-3206	334	1	let	let	VERB
ejpam-3206	334	2	r	r	PRON
ejpam-3206	334	3	be	be	AUX
ejpam-3206	334	4	a	a	DET
ejpam-3206	334	5	ring	ring	NOUN
ejpam-3206	334	6	with	with	ADP
ejpam-3206	334	7	an	an	DET
ejpam-3206	334	8	endomorphism	endomorphism	PROPN
ejpam-3206	334	9	σ	σ	PROPN
ejpam-3206	334	10	.	.	PUNCT
ejpam-3206	335	1	if	if	SCONJ
ejpam-3206	335	2	aσ(a	aσ(a	NUM
ejpam-3206	335	3	)	)	PUNCT
ejpam-3206	335	4	=	=	SYM
ejpam-3206	335	5	0⇒	0⇒	VERB
ejpam-3206	335	6	a	a	DET
ejpam-3206	335	7	=	=	NOUN
ejpam-3206	335	8	0	0	NUM
ejpam-3206	335	9	,	,	PUNCT
ejpam-3206	335	10	for	for	ADP
ejpam-3206	335	11	a	a	DET
ejpam-3206	335	12	∈	∈	PROPN
ejpam-3206	335	13	r	r	NOUN
ejpam-3206	335	14	,	,	PUNCT
ejpam-3206	335	15	then	then	ADV
ejpam-3206	335	16	r	r	NOUN
ejpam-3206	335	17	is	be	AUX
ejpam-3206	335	18	called	call	VERB
ejpam-3206	335	19	a	a	DET
ejpam-3206	335	20	σ	σ	PROPN
ejpam-3206	335	21	-	-	ADJ
ejpam-3206	335	22	rigid	rigid	ADJ
ejpam-3206	335	23	ring	ring	NOUN
ejpam-3206	335	24	.	.	PUNCT
ejpam-3206	336	1	some	some	PRON
ejpam-3206	336	2	of	of	ADP
ejpam-3206	336	3	the	the	DET
ejpam-3206	336	4	basic	basic	ADJ
ejpam-3206	336	5	properties	property	NOUN
ejpam-3206	336	6	of	of	ADP
ejpam-3206	336	7	a	a	DET
ejpam-3206	336	8	σ	σ	PROPN
ejpam-3206	336	9	-	-	ADJ
ejpam-3206	336	10	rigid	rigid	ADJ
ejpam-3206	336	11	ring	ring	NOUN
ejpam-3206	336	12	was	be	AUX
ejpam-3206	336	13	given	give	VERB
ejpam-3206	336	14	in	in	ADP
ejpam-3206	336	15	the	the	DET
ejpam-3206	336	16	following	follow	VERB
ejpam-3206	336	17	lemma	lemma	PROPN
ejpam-3206	336	18	.	.	PUNCT
ejpam-3206	337	1	lemma	lemma	PROPN
ejpam-3206	337	2	6	6	NUM
ejpam-3206	337	3	(	(	PUNCT
ejpam-3206	337	4	[	[	X
ejpam-3206	337	5	9	9	NUM
ejpam-3206	337	6	]	]	PUNCT
ejpam-3206	337	7	)	)	PUNCT
ejpam-3206	337	8	.	.	PUNCT
ejpam-3206	338	1	if	if	SCONJ
ejpam-3206	338	2	r	r	NOUN
ejpam-3206	338	3	is	be	AUX
ejpam-3206	338	4	a	a	DET
ejpam-3206	338	5	σ	σ	PROPN
ejpam-3206	338	6	-	-	ADJ
ejpam-3206	338	7	rigid	rigid	ADJ
ejpam-3206	338	8	ring	ring	NOUN
ejpam-3206	338	9	,	,	PUNCT
ejpam-3206	338	10	then	then	ADV
ejpam-3206	338	11	:	:	PUNCT
ejpam-3206	338	12	1	1	X
ejpam-3206	338	13	)	)	PUNCT
ejpam-3206	338	14	r	r	NOUN
ejpam-3206	338	15	is	be	AUX
ejpam-3206	338	16	a	a	DET
ejpam-3206	338	17	reduced	reduced	ADJ
ejpam-3206	338	18	ring	ring	NOUN
ejpam-3206	338	19	,	,	PUNCT
ejpam-3206	338	20	2	2	NUM
ejpam-3206	338	21	)	)	PUNCT
ejpam-3206	338	22	σ	σ	NOUN
ejpam-3206	338	23	is	be	AUX
ejpam-3206	338	24	a	a	DET
ejpam-3206	338	25	monomorphism	monomorphism	NOUN
ejpam-3206	338	26	.	.	PUNCT
ejpam-3206	339	1	the	the	DET
ejpam-3206	339	2	relation	relation	NOUN
ejpam-3206	339	3	between	between	ADP
ejpam-3206	339	4	a	a	DET
ejpam-3206	339	5	σ	σ	PROPN
ejpam-3206	339	6	-	-	PUNCT
ejpam-3206	339	7	compatible	compatible	ADJ
ejpam-3206	339	8	ring	ring	NOUN
ejpam-3206	339	9	and	and	CCONJ
ejpam-3206	339	10	a	a	DET
ejpam-3206	339	11	σ	σ	PROPN
ejpam-3206	339	12	-	-	ADJ
ejpam-3206	339	13	rigid	rigid	ADJ
ejpam-3206	339	14	ring	ring	NOUN
ejpam-3206	339	15	was	be	AUX
ejpam-3206	339	16	studied	study	VERB
ejpam-3206	339	17	in	in	ADP
ejpam-3206	339	18	the	the	DET
ejpam-3206	339	19	following	follow	VERB
ejpam-3206	339	20	lemma	lemma	PROPN
ejpam-3206	339	21	.	.	PUNCT
ejpam-3206	340	1	lemma	lemma	PROPN
ejpam-3206	340	2	7	7	NUM
ejpam-3206	340	3	(	(	PUNCT
ejpam-3206	340	4	[	[	X
ejpam-3206	340	5	9	9	NUM
ejpam-3206	340	6	]	]	NUM
ejpam-3206	340	7	)	)	PUNCT
ejpam-3206	340	8	.	.	PUNCT
ejpam-3206	341	1	a	a	DET
ejpam-3206	341	2	ring	ring	NOUN
ejpam-3206	341	3	r	r	NOUN
ejpam-3206	341	4	is	be	AUX
ejpam-3206	341	5	a	a	DET
ejpam-3206	341	6	reduced	reduce	VERB
ejpam-3206	341	7	σ	σ	VERB
ejpam-3206	341	8	-	-	PUNCT
ejpam-3206	341	9	compatible	compatible	ADJ
ejpam-3206	341	10	ring	ring	NOUN
ejpam-3206	341	11	if	if	SCONJ
ejpam-3206	341	12	and	and	CCONJ
ejpam-3206	341	13	only	only	ADV
ejpam-3206	341	14	if	if	SCONJ
ejpam-3206	341	15	r	r	NOUN
ejpam-3206	341	16	is	be	AUX
ejpam-3206	341	17	σ	σ	NOUN
ejpam-3206	341	18	-	-	ADJ
ejpam-3206	341	19	rigid	rigid	ADJ
ejpam-3206	341	20	.	.	PUNCT
ejpam-3206	342	1	hong	hong	PROPN
ejpam-3206	342	2	,	,	PUNCT
ejpam-3206	342	3	et	et	PROPN
ejpam-3206	342	4	.	.	PUNCT
ejpam-3206	343	1	al	al	PROPN
ejpam-3206	343	2	.	.	PROPN
ejpam-3206	343	3	,	,	PUNCT
ejpam-3206	343	4	in	in	ADP
ejpam-3206	343	5	(	(	PUNCT
ejpam-3206	343	6	[	[	X
ejpam-3206	343	7	9	9	NUM
ejpam-3206	343	8	]	]	PUNCT
ejpam-3206	343	9	,	,	PUNCT
ejpam-3206	343	10	proposition	proposition	NOUN
ejpam-3206	343	11	5	5	NUM
ejpam-3206	343	12	)	)	PUNCT
ejpam-3206	343	13	,	,	PUNCT
ejpam-3206	343	14	proved	prove	VERB
ejpam-3206	343	15	that	that	SCONJ
ejpam-3206	343	16	:	:	PUNCT
ejpam-3206	343	17	if	if	SCONJ
ejpam-3206	343	18	r	r	NOUN
ejpam-3206	343	19	is	be	AUX
ejpam-3206	343	20	a	a	DET
ejpam-3206	343	21	σ	σ	PROPN
ejpam-3206	343	22	-	-	ADJ
ejpam-3206	343	23	rigid	rigid	ADJ
ejpam-3206	343	24	ring	ring	NOUN
ejpam-3206	343	25	,	,	PUNCT
ejpam-3206	343	26	then	then	ADV
ejpam-3206	343	27	for	for	ADP
ejpam-3206	343	28	each	each	DET
ejpam-3206	343	29	e	e	PROPN
ejpam-3206	343	30	∈	∈	PROPN
ejpam-3206	343	31	i	i	PROPN
ejpam-3206	343	32	d	d	PROPN
ejpam-3206	343	33	(	(	PUNCT
ejpam-3206	343	34	r	r	NOUN
ejpam-3206	343	35	)	)	PUNCT
ejpam-3206	343	36	,	,	PUNCT
ejpam-3206	343	37	we	we	PRON
ejpam-3206	343	38	have	have	VERB
ejpam-3206	343	39	σ(e	σ(e	PROPN
ejpam-3206	343	40	)	)	PUNCT
ejpam-3206	344	1	=	=	SYM
ejpam-3206	344	2	e.	e.	PROPN
ejpam-3206	345	1	in	in	ADP
ejpam-3206	345	2	what	what	PRON
ejpam-3206	345	3	follows	follow	VERB
ejpam-3206	345	4	,	,	PUNCT
ejpam-3206	345	5	we	we	PRON
ejpam-3206	345	6	characterize	characterize	VERB
ejpam-3206	345	7	skew	skew	NOUN
ejpam-3206	345	8	hurwitz	hurwitz	PROPN
ejpam-3206	345	9	series	series	PROPN
ejpam-3206	345	10	rings	ring	NOUN
ejpam-3206	345	11	that	that	PRON
ejpam-3206	345	12	satisfy	satisfy	VERB
ejpam-3206	345	13	the	the	DET
ejpam-3206	345	14	weak	weak	ADJ
ejpam-3206	345	15	pscondition	pscondition	NOUN
ejpam-3206	345	16	.	.	PUNCT
ejpam-3206	346	1	we	we	PRON
ejpam-3206	346	2	shall	shall	AUX
ejpam-3206	346	3	need	need	VERB
ejpam-3206	346	4	the	the	DET
ejpam-3206	346	5	following	follow	VERB
ejpam-3206	346	6	auxiliary	auxiliary	ADJ
ejpam-3206	346	7	result	result	NOUN
ejpam-3206	346	8	in	in	ADP
ejpam-3206	346	9	the	the	DET
ejpam-3206	346	10	proof	proof	NOUN
ejpam-3206	346	11	of	of	ADP
ejpam-3206	346	12	our	our	PRON
ejpam-3206	346	13	theorems	theorem	NOUN
ejpam-3206	346	14	.	.	PUNCT
ejpam-3206	347	1	lemma	lemma	PROPN
ejpam-3206	347	2	8	8	NUM
ejpam-3206	347	3	(	(	PUNCT
ejpam-3206	347	4	2.5	2.5	NUM
ejpam-3206	347	5	and	and	CCONJ
ejpam-3206	347	6	2.6	2.6	NUM
ejpam-3206	348	1	[	[	X
ejpam-3206	348	2	17	17	NUM
ejpam-3206	348	3	]	]	PUNCT
ejpam-3206	348	4	)	)	PUNCT
ejpam-3206	348	5	.	.	PUNCT
ejpam-3206	349	1	let	let	VERB
ejpam-3206	349	2	r	r	PRON
ejpam-3206	349	3	be	be	AUX
ejpam-3206	349	4	a	a	DET
ejpam-3206	349	5	σ	σ	NOUN
ejpam-3206	349	6	-	-	PUNCT
ejpam-3206	349	7	compatible	compatible	ADJ
ejpam-3206	349	8	ni	ni	NOUN
ejpam-3206	349	9	-	-	NOUN
ejpam-3206	349	10	ring	ring	NOUN
ejpam-3206	349	11	with	with	ADP
ejpam-3206	349	12	nil(r	nil(r	NOUN
ejpam-3206	349	13	)	)	PUNCT
ejpam-3206	349	14	nilpotent	nilpotent	NOUN
ejpam-3206	349	15	and	and	CCONJ
ejpam-3206	349	16	r	r	NOUN
ejpam-3206	349	17	a	a	DET
ejpam-3206	349	18	torsion	torsion	NOUN
ejpam-3206	349	19	free	free	ADJ
ejpam-3206	349	20	as	as	ADP
ejpam-3206	349	21	a	a	DET
ejpam-3206	349	22	z	z	NOUN
ejpam-3206	349	23	-	-	PUNCT
ejpam-3206	349	24	module	module	NOUN
ejpam-3206	349	25	.	.	PUNCT
ejpam-3206	350	1	set	set	VERB
ejpam-3206	350	2	k	k	PROPN
ejpam-3206	350	3	=	=	PUNCT
ejpam-3206	350	4	nil	nil	NOUN
ejpam-3206	350	5	(	(	PUNCT
ejpam-3206	350	6	r	r	NOUN
ejpam-3206	350	7	)	)	PUNCT
ejpam-3206	350	8	.	.	PUNCT
ejpam-3206	351	1	then	then	ADV
ejpam-3206	351	2	we	we	PRON
ejpam-3206	351	3	have	have	VERB
ejpam-3206	351	4	:	:	PUNCT
ejpam-3206	351	5	(	(	PUNCT
ejpam-3206	351	6	1	1	X
ejpam-3206	351	7	)	)	PUNCT
ejpam-3206	351	8	nil	nil	NOUN
ejpam-3206	351	9	(	(	PUNCT
ejpam-3206	351	10	a	a	X
ejpam-3206	351	11	)	)	PUNCT
ejpam-3206	351	12	=	=	SYM
ejpam-3206	351	13	(	(	PUNCT
ejpam-3206	351	14	hk	hk	PROPN
ejpam-3206	351	15	,	,	PUNCT
ejpam-3206	351	16	σ	σ	PROPN
ejpam-3206	351	17	)	)	PUNCT
ejpam-3206	351	18	.	.	PUNCT
ejpam-3206	352	1	(	(	PUNCT
ejpam-3206	352	2	2	2	X
ejpam-3206	352	3	)	)	PUNCT
ejpam-3206	352	4	f	f	NOUN
ejpam-3206	352	5	(	(	PUNCT
ejpam-3206	352	6	x	x	X
ejpam-3206	352	7	)	)	PUNCT
ejpam-3206	352	8	=	=	PUNCT
ejpam-3206	353	1	∞∑	∞∑	NUM
ejpam-3206	353	2	i=0	i=0	PROPN
ejpam-3206	353	3	aix	aix	NOUN
ejpam-3206	353	4	i	i	NOUN
ejpam-3206	353	5	∈	∈	PROPN
ejpam-3206	353	6	nil	nil	NOUN
ejpam-3206	353	7	(	(	PUNCT
ejpam-3206	353	8	a	a	X
ejpam-3206	353	9	)	)	PUNCT
ejpam-3206	353	10	if	if	SCONJ
ejpam-3206	354	1	and	and	CCONJ
ejpam-3206	354	2	only	only	ADV
ejpam-3206	354	3	if	if	SCONJ
ejpam-3206	354	4	ai	ai	VERB
ejpam-3206	354	5	∈	∈	PROPN
ejpam-3206	354	6	nil	nil	NOUN
ejpam-3206	354	7	(	(	PUNCT
ejpam-3206	354	8	r	r	NOUN
ejpam-3206	354	9	)	)	PUNCT
ejpam-3206	354	10	for	for	ADP
ejpam-3206	354	11	all	all	PRON
ejpam-3206	354	12	i	i	PRON
ejpam-3206	354	13	≥	≥	NOUN
ejpam-3206	354	14	0	0	NUM
ejpam-3206	354	15	.	.	PUNCT
ejpam-3206	355	1	(	(	PUNCT
ejpam-3206	355	2	3	3	X
ejpam-3206	355	3	)	)	PUNCT
ejpam-3206	355	4	if	if	SCONJ
ejpam-3206	355	5	f	f	PROPN
ejpam-3206	355	6	(	(	PUNCT
ejpam-3206	355	7	x	x	X
ejpam-3206	355	8	)	)	PUNCT
ejpam-3206	355	9	=	=	PUNCT
ejpam-3206	356	1	∞∑	∞∑	NUM
ejpam-3206	356	2	i=0	i=0	PROPN
ejpam-3206	356	3	aix	aix	NOUN
ejpam-3206	356	4	i	i	PROPN
ejpam-3206	356	5	and	and	CCONJ
ejpam-3206	356	6	g	g	PROPN
ejpam-3206	356	7	(	(	PUNCT
ejpam-3206	356	8	x	x	NOUN
ejpam-3206	356	9	)	)	PUNCT
ejpam-3206	356	10	=	=	SYM
ejpam-3206	357	1	∞∑	∞∑	NUM
ejpam-3206	357	2	j=0	j=0	PROPN
ejpam-3206	357	3	bjx	bjx	PROPN
ejpam-3206	357	4	j	j	PROPN
ejpam-3206	357	5	∈	∈	PROPN
ejpam-3206	357	6	a	a	DET
ejpam-3206	357	7	such	such	ADJ
ejpam-3206	357	8	that	that	SCONJ
ejpam-3206	357	9	f	f	PROPN
ejpam-3206	357	10	(	(	PUNCT
ejpam-3206	357	11	x	x	NOUN
ejpam-3206	357	12	)	)	PUNCT
ejpam-3206	357	13	g	g	NOUN
ejpam-3206	357	14	(	(	PUNCT
ejpam-3206	357	15	x	x	NOUN
ejpam-3206	357	16	)	)	PUNCT
ejpam-3206	357	17	∈	∈	PROPN
ejpam-3206	357	18	nil	nil	NOUN
ejpam-3206	357	19	(	(	PUNCT
ejpam-3206	357	20	a	a	NOUN
ejpam-3206	357	21	)	)	PUNCT
ejpam-3206	357	22	,	,	PUNCT
ejpam-3206	357	23	then	then	ADV
ejpam-3206	357	24	aibj	aibj	PROPN
ejpam-3206	357	25	∈	∈	PROPN
ejpam-3206	357	26	k	k	PROPN
ejpam-3206	357	27	=	=	PUNCT
ejpam-3206	357	28	nil	nil	NOUN
ejpam-3206	357	29	(	(	PUNCT
ejpam-3206	357	30	r	r	NOUN
ejpam-3206	357	31	)	)	PUNCT
ejpam-3206	357	32	for	for	ADP
ejpam-3206	357	33	all	all	DET
ejpam-3206	357	34	i	i	PROPN
ejpam-3206	357	35	,	,	PUNCT
ejpam-3206	357	36	j	j	PROPN
ejpam-3206	357	37	≥	≥	PROPN
ejpam-3206	357	38	0	0	NUM
ejpam-3206	357	39	.	.	PUNCT
ejpam-3206	358	1	as	as	ADP
ejpam-3206	358	2	a	a	DET
ejpam-3206	358	3	corollary	corollary	NOUN
ejpam-3206	358	4	we	we	PRON
ejpam-3206	358	5	get	get	VERB
ejpam-3206	358	6	the	the	DET
ejpam-3206	358	7	following	following	ADJ
ejpam-3206	358	8	result	result	NOUN
ejpam-3206	358	9	in	in	ADP
ejpam-3206	358	10	the	the	DET
ejpam-3206	358	11	finite	finite	ADJ
ejpam-3206	358	12	case	case	NOUN
ejpam-3206	358	13	.	.	PUNCT
ejpam-3206	359	1	lemma	lemma	PROPN
ejpam-3206	359	2	9	9	NUM
ejpam-3206	359	3	.	.	PUNCT
ejpam-3206	360	1	let	let	VERB
ejpam-3206	360	2	r	r	PRON
ejpam-3206	360	3	be	be	AUX
ejpam-3206	360	4	a	a	DET
ejpam-3206	360	5	σ	σ	NOUN
ejpam-3206	360	6	-	-	PUNCT
ejpam-3206	360	7	compatible	compatible	ADJ
ejpam-3206	360	8	ni	ni	NOUN
ejpam-3206	360	9	-	-	NOUN
ejpam-3206	360	10	ring	ring	NOUN
ejpam-3206	360	11	with	with	ADP
ejpam-3206	360	12	nil(r	nil(r	NOUN
ejpam-3206	360	13	)	)	PUNCT
ejpam-3206	360	14	nilpotent	nilpotent	NOUN
ejpam-3206	360	15	and	and	CCONJ
ejpam-3206	360	16	r	r	NOUN
ejpam-3206	360	17	a	a	DET
ejpam-3206	360	18	torsion	torsion	NOUN
ejpam-3206	360	19	free	free	ADJ
ejpam-3206	360	20	as	as	ADP
ejpam-3206	360	21	a	a	DET
ejpam-3206	360	22	z	z	NOUN
ejpam-3206	360	23	-	-	PUNCT
ejpam-3206	360	24	module	module	NOUN
ejpam-3206	360	25	.	.	PUNCT
ejpam-3206	361	1	set	set	VERB
ejpam-3206	361	2	k	k	PROPN
ejpam-3206	361	3	=	=	PUNCT
ejpam-3206	361	4	nil	nil	NOUN
ejpam-3206	361	5	(	(	PUNCT
ejpam-3206	361	6	r	r	NOUN
ejpam-3206	361	7	)	)	PUNCT
ejpam-3206	361	8	.	.	PUNCT
ejpam-3206	362	1	then	then	ADV
ejpam-3206	362	2	we	we	PRON
ejpam-3206	362	3	have	have	VERB
ejpam-3206	362	4	:	:	PUNCT
ejpam-3206	362	5	(	(	PUNCT
ejpam-3206	362	6	1	1	X
ejpam-3206	362	7	)	)	PUNCT
ejpam-3206	362	8	nil	nil	NOUN
ejpam-3206	362	9	(	(	PUNCT
ejpam-3206	362	10	p	p	NOUN
ejpam-3206	362	11	)	)	PUNCT
ejpam-3206	362	12	=	=	SYM
ejpam-3206	362	13	(	(	PUNCT
ejpam-3206	362	14	hk	hk	PROPN
ejpam-3206	362	15	,	,	PUNCT
ejpam-3206	362	16	σ	σ	PROPN
ejpam-3206	362	17	)	)	PUNCT
ejpam-3206	362	18	.	.	PUNCT
ejpam-3206	363	1	(	(	PUNCT
ejpam-3206	363	2	2	2	X
ejpam-3206	363	3	)	)	PUNCT
ejpam-3206	363	4	f	f	NOUN
ejpam-3206	363	5	(	(	PUNCT
ejpam-3206	363	6	x	x	X
ejpam-3206	363	7	)	)	PUNCT
ejpam-3206	363	8	=	=	SYM
ejpam-3206	363	9	k∑	k∑	PROPN
ejpam-3206	364	1	i=0	i=0	PROPN
ejpam-3206	364	2	aix	aix	PROPN
ejpam-3206	364	3	i	i	PROPN
ejpam-3206	364	4	∈	∈	PROPN
ejpam-3206	364	5	nil	nil	NOUN
ejpam-3206	364	6	(	(	PUNCT
ejpam-3206	364	7	p	p	NOUN
ejpam-3206	364	8	)	)	PUNCT
ejpam-3206	364	9	if	if	SCONJ
ejpam-3206	365	1	and	and	CCONJ
ejpam-3206	365	2	only	only	ADV
ejpam-3206	365	3	if	if	SCONJ
ejpam-3206	365	4	ai	ai	VERB
ejpam-3206	365	5	∈	∈	PROPN
ejpam-3206	365	6	nil	nil	NOUN
ejpam-3206	365	7	(	(	PUNCT
ejpam-3206	365	8	r	r	NOUN
ejpam-3206	365	9	)	)	PUNCT
ejpam-3206	365	10	for	for	ADP
ejpam-3206	365	11	all	all	PRON
ejpam-3206	365	12	i	i	PRON
ejpam-3206	365	13	≥	≥	NOUN
ejpam-3206	365	14	0	0	NUM
ejpam-3206	365	15	.	.	PUNCT
ejpam-3206	366	1	(	(	PUNCT
ejpam-3206	366	2	3	3	X
ejpam-3206	366	3	)	)	PUNCT
ejpam-3206	366	4	if	if	SCONJ
ejpam-3206	366	5	f	f	PROPN
ejpam-3206	366	6	(	(	PUNCT
ejpam-3206	366	7	x	x	X
ejpam-3206	366	8	)	)	PUNCT
ejpam-3206	366	9	=	=	SYM
ejpam-3206	366	10	k∑	k∑	PROPN
ejpam-3206	366	11	i=0	i=0	PROPN
ejpam-3206	366	12	aix	aix	PROPN
ejpam-3206	366	13	i	i	PROPN
ejpam-3206	366	14	and	and	CCONJ
ejpam-3206	366	15	g	g	PROPN
ejpam-3206	366	16	(	(	PUNCT
ejpam-3206	366	17	x	x	NOUN
ejpam-3206	366	18	)	)	PUNCT
ejpam-3206	366	19	=	=	SYM
ejpam-3206	366	20	n∑	n∑	NOUN
ejpam-3206	366	21	j=0	j=0	PROPN
ejpam-3206	366	22	bjx	bjx	PROPN
ejpam-3206	366	23	j	j	PROPN
ejpam-3206	366	24	∈	∈	PROPN
ejpam-3206	366	25	p	p	NOUN
ejpam-3206	367	1	such	such	ADJ
ejpam-3206	367	2	that	that	SCONJ
ejpam-3206	367	3	f	f	PROPN
ejpam-3206	367	4	(	(	PUNCT
ejpam-3206	367	5	x	x	NOUN
ejpam-3206	367	6	)	)	PUNCT
ejpam-3206	367	7	g	g	NOUN
ejpam-3206	367	8	(	(	PUNCT
ejpam-3206	367	9	x	x	NOUN
ejpam-3206	367	10	)	)	PUNCT
ejpam-3206	367	11	∈	∈	PROPN
ejpam-3206	367	12	nil	nil	NOUN
ejpam-3206	367	13	(	(	PUNCT
ejpam-3206	367	14	p	p	NOUN
ejpam-3206	367	15	)	)	PUNCT
ejpam-3206	367	16	,	,	PUNCT
ejpam-3206	367	17	then	then	ADV
ejpam-3206	367	18	aibj	aibj	PROPN
ejpam-3206	367	19	∈	∈	PROPN
ejpam-3206	367	20	k	k	PROPN
ejpam-3206	367	21	=	=	PUNCT
ejpam-3206	367	22	nil	nil	NOUN
ejpam-3206	367	23	(	(	PUNCT
ejpam-3206	367	24	r	r	NOUN
ejpam-3206	367	25	)	)	PUNCT
ejpam-3206	367	26	for	for	ADP
ejpam-3206	367	27	all	all	PRON
ejpam-3206	367	28	0	0	NUM
ejpam-3206	367	29	≤	≤	NUM
ejpam-3206	367	30	i	i	PRON
ejpam-3206	367	31	≤	≤	NOUN
ejpam-3206	367	32	k	k	PRON
ejpam-3206	367	33	and	and	CCONJ
ejpam-3206	367	34	0	0	NUM
ejpam-3206	367	35	≤	≤	NUM
ejpam-3206	367	36	j	j	PROPN
ejpam-3206	367	37	≤	≤	PROPN
ejpam-3206	367	38	n.	n.	NOUN
ejpam-3206	367	39	now	now	ADV
ejpam-3206	367	40	,	,	PUNCT
ejpam-3206	367	41	we	we	PRON
ejpam-3206	367	42	can	can	AUX
ejpam-3206	367	43	prove	prove	VERB
ejpam-3206	367	44	our	our	PRON
ejpam-3206	367	45	result	result	NOUN
ejpam-3206	367	46	in	in	ADP
ejpam-3206	367	47	the	the	DET
ejpam-3206	367	48	infinite	infinite	ADJ
ejpam-3206	367	49	case	case	NOUN
ejpam-3206	367	50	:	:	PUNCT
ejpam-3206	367	51	theorem	theorem	NOUN
ejpam-3206	367	52	4	4	NUM
ejpam-3206	367	53	.	.	PUNCT
ejpam-3206	368	1	let	let	VERB
ejpam-3206	368	2	r	r	PRON
ejpam-3206	368	3	be	be	AUX
ejpam-3206	368	4	a	a	DET
ejpam-3206	368	5	σ	σ	NOUN
ejpam-3206	368	6	-	-	PUNCT
ejpam-3206	368	7	compatible	compatible	ADJ
ejpam-3206	368	8	ni	ni	NOUN
ejpam-3206	368	9	-	-	NOUN
ejpam-3206	368	10	ring	ring	NOUN
ejpam-3206	368	11	with	with	ADP
ejpam-3206	368	12	nil(r	nil(r	NOUN
ejpam-3206	368	13	)	)	PUNCT
ejpam-3206	368	14	nilpotent	nilpotent	NOUN
ejpam-3206	368	15	,	,	PUNCT
ejpam-3206	368	16	σ(e	σ(e	PROPN
ejpam-3206	368	17	)	)	PUNCT
ejpam-3206	369	1	=	=	PUNCT
ejpam-3206	369	2	e	e	NOUN
ejpam-3206	369	3	for	for	ADP
ejpam-3206	369	4	every	every	DET
ejpam-3206	369	5	e	e	PROPN
ejpam-3206	369	6	∈	∈	PROPN
ejpam-3206	369	7	id(r	id(r	NOUN
ejpam-3206	369	8	)	)	PUNCT
ejpam-3206	369	9	and	and	CCONJ
ejpam-3206	369	10	r	r	NOUN
ejpam-3206	369	11	a	a	DET
ejpam-3206	369	12	torsion	torsion	NOUN
ejpam-3206	369	13	free	free	ADJ
ejpam-3206	369	14	as	as	ADP
ejpam-3206	369	15	a	a	DET
ejpam-3206	369	16	z	z	NOUN
ejpam-3206	369	17	-	-	PUNCT
ejpam-3206	369	18	module	module	NOUN
ejpam-3206	369	19	.	.	PUNCT
ejpam-3206	370	1	if	if	SCONJ
ejpam-3206	370	2	r	r	NOUN
ejpam-3206	370	3	is	be	AUX
ejpam-3206	370	4	a	a	DET
ejpam-3206	370	5	weak	weak	ADJ
ejpam-3206	370	6	right	right	ADJ
ejpam-3206	370	7	ps	ps	NOUN
ejpam-3206	370	8	-	-	NOUN
ejpam-3206	370	9	ring	ring	NOUN
ejpam-3206	370	10	,	,	PUNCT
ejpam-3206	370	11	then	then	ADV
ejpam-3206	370	12	a	a	PRON
ejpam-3206	370	13	=	=	SYM
ejpam-3206	370	14	(	(	PUNCT
ejpam-3206	370	15	hr	hr	PROPN
ejpam-3206	370	16	,	,	PUNCT
ejpam-3206	370	17	σ	σ	PROPN
ejpam-3206	370	18	)	)	PUNCT
ejpam-3206	370	19	is	be	AUX
ejpam-3206	370	20	a	a	DET
ejpam-3206	370	21	weak	weak	ADJ
ejpam-3206	370	22	right	right	ADJ
ejpam-3206	370	23	ps	ps	NOUN
ejpam-3206	370	24	-	-	PUNCT
ejpam-3206	370	25	ring	ring	NOUN
ejpam-3206	370	26	.	.	PUNCT
ejpam-3206	371	1	m.	m.	NOUN
ejpam-3206	371	2	a.	a.	PROPN
ejpam-3206	371	3	farahat	farahat	PROPN
ejpam-3206	371	4	,	,	PUNCT
ejpam-3206	371	5	s.	s.	PROPN
ejpam-3206	371	6	t.	t.	PROPN
ejpam-3206	371	7	al	al	PROPN
ejpam-3206	371	8	-	-	PUNCT
ejpam-3206	371	9	bogamy	bogamy	PROPN
ejpam-3206	371	10	/	/	SYM
ejpam-3206	371	11	eur	eur	PROPN
ejpam-3206	371	12	.	.	PUNCT
ejpam-3206	372	1	j.	j.	PROPN
ejpam-3206	372	2	pure	pure	PROPN
ejpam-3206	372	3	appl	appl	PROPN
ejpam-3206	372	4	.	.	PROPN
ejpam-3206	372	5	math	math	PROPN
ejpam-3206	372	6	,	,	PUNCT
ejpam-3206	372	7	11	11	NUM
ejpam-3206	372	8	(	(	PUNCT
ejpam-3206	372	9	1	1	NUM
ejpam-3206	372	10	)	)	PUNCT
ejpam-3206	372	11	(	(	PUNCT
ejpam-3206	372	12	2018	2018	NUM
ejpam-3206	372	13	)	)	PUNCT
ejpam-3206	372	14	,	,	PUNCT
ejpam-3206	372	15	244	244	NUM
ejpam-3206	372	16	-	-	SYM
ejpam-3206	372	17	259	259	NUM
ejpam-3206	372	18	256	256	NUM
ejpam-3206	372	19	proof	proof	NOUN
ejpam-3206	372	20	.	.	PUNCT
ejpam-3206	373	1	let	let	VERB
ejpam-3206	373	2	l	l	NOUN
ejpam-3206	373	3	be	be	AUX
ejpam-3206	373	4	a	a	DET
ejpam-3206	373	5	maximal	maximal	ADJ
ejpam-3206	373	6	right	right	ADJ
ejpam-3206	373	7	ideal	ideal	NOUN
ejpam-3206	373	8	of	of	ADP
ejpam-3206	373	9	a	a	DET
ejpam-3206	373	10	=	=	X
ejpam-3206	373	11	(	(	PUNCT
ejpam-3206	373	12	hr	hr	PROPN
ejpam-3206	373	13	,	,	PUNCT
ejpam-3206	373	14	σ	σ	PROPN
ejpam-3206	373	15	)	)	PUNCT
ejpam-3206	373	16	.	.	PUNCT
ejpam-3206	374	1	we	we	PRON
ejpam-3206	374	2	will	will	AUX
ejpam-3206	374	3	show	show	VERB
ejpam-3206	374	4	that	that	SCONJ
ejpam-3206	374	5	either	either	CCONJ
ejpam-3206	374	6	na	na	INTJ
ejpam-3206	374	7	(	(	PUNCT
ejpam-3206	374	8	l	l	NOUN
ejpam-3206	374	9	)	)	PUNCT
ejpam-3206	374	10	⊆	⊆	NUM
ejpam-3206	374	11	nil(a	nil(a	NUM
ejpam-3206	374	12	)	)	PUNCT
ejpam-3206	374	13	or	or	CCONJ
ejpam-3206	374	14	na	na	ADP
ejpam-3206	374	15	(	(	PUNCT
ejpam-3206	374	16	l	l	NOUN
ejpam-3206	374	17	)	)	PUNCT
ejpam-3206	374	18	=	=	SYM
ejpam-3206	374	19	aq	aq	PROPN
ejpam-3206	374	20	,	,	PUNCT
ejpam-3206	374	21	where	where	SCONJ
ejpam-3206	374	22	q	q	PROPN
ejpam-3206	374	23	∈	∈	PROPN
ejpam-3206	374	24	id(a	id(a	NOUN
ejpam-3206	374	25	)	)	PUNCT
ejpam-3206	374	26	.	.	PUNCT
ejpam-3206	375	1	let	let	VERB
ejpam-3206	375	2	i	i	PRON
ejpam-3206	375	3	be	be	AUX
ejpam-3206	375	4	the	the	DET
ejpam-3206	375	5	set	set	NOUN
ejpam-3206	375	6	of	of	ADP
ejpam-3206	375	7	all	all	DET
ejpam-3206	375	8	coefficients	coefficient	NOUN
ejpam-3206	375	9	of	of	ADP
ejpam-3206	375	10	all	all	DET
ejpam-3206	375	11	hurwitz	hurwitz	PROPN
ejpam-3206	375	12	series	series	PROPN
ejpam-3206	375	13	in	in	ADP
ejpam-3206	375	14	l	l	PROPN
ejpam-3206	375	15	and	and	CCONJ
ejpam-3206	375	16	let	let	VERB
ejpam-3206	375	17	j	j	PROPN
ejpam-3206	375	18	be	be	AUX
ejpam-3206	375	19	the	the	DET
ejpam-3206	375	20	right	right	ADJ
ejpam-3206	375	21	ideal	ideal	NOUN
ejpam-3206	375	22	of	of	ADP
ejpam-3206	375	23	r	r	NOUN
ejpam-3206	375	24	generated	generate	VERB
ejpam-3206	375	25	by	by	ADP
ejpam-3206	375	26	i	i	PRON
ejpam-3206	375	27	,	,	PUNCT
ejpam-3206	376	1	i.e.	i.e.	X
ejpam-3206	376	2	,	,	PUNCT
ejpam-3206	376	3	j	j	PROPN
ejpam-3206	376	4	=	=	SYM
ejpam-3206	376	5	〈	〈	PROPN
ejpam-3206	376	6	i〉r	i〉r	PROPN
ejpam-3206	376	7	=	=	SYM
ejpam-3206	376	8	ir	ir	PROPN
ejpam-3206	376	9	.	.	PUNCT
ejpam-3206	377	1	if	if	SCONJ
ejpam-3206	377	2	j	j	PROPN
ejpam-3206	377	3	=	=	SYM
ejpam-3206	377	4	r	r	NOUN
ejpam-3206	377	5	,	,	PUNCT
ejpam-3206	377	6	then	then	ADV
ejpam-3206	377	7	there	there	PRON
ejpam-3206	377	8	exist	exist	VERB
ejpam-3206	377	9	a1	a1	NOUN
ejpam-3206	377	10	,	,	PUNCT
ejpam-3206	377	11	a2	a2	PROPN
ejpam-3206	377	12	,	,	PUNCT
ejpam-3206	377	13	...	...	PUNCT
ejpam-3206	377	14	,	,	PUNCT
ejpam-3206	377	15	an	an	DET
ejpam-3206	377	16	∈	∈	NOUN
ejpam-3206	377	17	i	i	PRON
ejpam-3206	377	18	and	and	CCONJ
ejpam-3206	377	19	r1	r1	PROPN
ejpam-3206	377	20	,	,	PUNCT
ejpam-3206	377	21	r2	r2	PROPN
ejpam-3206	377	22	,	,	PUNCT
ejpam-3206	377	23	...	...	PUNCT
ejpam-3206	377	24	,	,	PUNCT
ejpam-3206	377	25	rn	rn	PROPN
ejpam-3206	377	26	∈	∈	PROPN
ejpam-3206	377	27	r	r	NOUN
ejpam-3206	377	28	,	,	PUNCT
ejpam-3206	377	29	such	such	ADJ
ejpam-3206	377	30	that	that	SCONJ
ejpam-3206	377	31	1	1	NUM
ejpam-3206	377	32	=	=	SYM
ejpam-3206	377	33	a1r1	a1r1	PROPN
ejpam-3206	377	34	+	+	ADJ
ejpam-3206	377	35	a2r2	a2r2	X
ejpam-3206	377	36	+	+	NUM
ejpam-3206	377	37	...	...	PUNCT
ejpam-3206	377	38	+	+	NUM
ejpam-3206	377	39	anrn	anrn	NOUN
ejpam-3206	377	40	.	.	PUNCT
ejpam-3206	378	1	suppose	suppose	VERB
ejpam-3206	378	2	that	that	SCONJ
ejpam-3206	378	3	ϕ(x	ϕ(x	X
ejpam-3206	378	4	)	)	PUNCT
ejpam-3206	378	5	=	=	PUNCT
ejpam-3206	379	1	∞∑	∞∑	NUM
ejpam-3206	379	2	i=0	i=0	PROPN
ejpam-3206	379	3	bix	bix	PROPN
ejpam-3206	379	4	i	i	PRON
ejpam-3206	379	5	∈	∈	PROPN
ejpam-3206	379	6	na	na	X
ejpam-3206	379	7	(	(	PUNCT
ejpam-3206	379	8	l	l	NOUN
ejpam-3206	379	9	)	)	PUNCT
ejpam-3206	379	10	,	,	PUNCT
ejpam-3206	379	11	then	then	ADV
ejpam-3206	379	12	for	for	ADP
ejpam-3206	379	13	every	every	DET
ejpam-3206	379	14	f(x	f(x	PROPN
ejpam-3206	379	15	)	)	PUNCT
ejpam-3206	379	16	=	=	PUNCT
ejpam-3206	380	1	∞∑	∞∑	NUM
ejpam-3206	380	2	j=0	j=0	PROPN
ejpam-3206	380	3	ajx	ajx	NOUN
ejpam-3206	380	4	j	j	PROPN
ejpam-3206	380	5	∈	∈	PROPN
ejpam-3206	380	6	l	l	PROPN
ejpam-3206	380	7	,	,	PUNCT
ejpam-3206	380	8	we	we	PRON
ejpam-3206	380	9	have	have	VERB
ejpam-3206	380	10	ϕ(x)f(x	ϕ(x)f(x	NOUN
ejpam-3206	380	11	)	)	PUNCT
ejpam-3206	381	1	=	=	PUNCT
ejpam-3206	382	1	(	(	PUNCT
ejpam-3206	382	2	∞∑	∞∑	NUM
ejpam-3206	382	3	i=0	i=0	PROPN
ejpam-3206	382	4	bix	bix	PROPN
ejpam-3206	382	5	i	i	PRON
ejpam-3206	382	6	)	)	PUNCT
ejpam-3206	382	7			PROPN
ejpam-3206	382	8	∞∑	∞∑	NUM
ejpam-3206	382	9	j=0	j=0	PROPN
ejpam-3206	382	10	ajx	ajx	NUM
ejpam-3206	382	11	j	j	PROPN
ejpam-3206	382	12			PROPN
ejpam-3206	382	13	∈	∈	PROPN
ejpam-3206	382	14	nil(a	nil(a	PROPN
ejpam-3206	382	15	)	)	PUNCT
ejpam-3206	382	16	.	.	PUNCT
ejpam-3206	383	1	since	since	SCONJ
ejpam-3206	383	2	r	r	NOUN
ejpam-3206	383	3	is	be	AUX
ejpam-3206	383	4	a	a	DET
ejpam-3206	383	5	σ	σ	PROPN
ejpam-3206	383	6	-	-	PUNCT
ejpam-3206	383	7	compatible	compatible	ADJ
ejpam-3206	383	8	ni	ni	NOUN
ejpam-3206	383	9	-	-	NOUN
ejpam-3206	383	10	ring	ring	NOUN
ejpam-3206	383	11	with	with	ADP
ejpam-3206	383	12	nil(r	nil(r	NOUN
ejpam-3206	383	13	)	)	PUNCT
ejpam-3206	383	14	a	a	DET
ejpam-3206	383	15	nilpotent	nilpotent	NOUN
ejpam-3206	383	16	and	and	CCONJ
ejpam-3206	383	17	r	r	NOUN
ejpam-3206	383	18	a	a	DET
ejpam-3206	383	19	torsion	torsion	NOUN
ejpam-3206	383	20	free	free	ADJ
ejpam-3206	383	21	as	as	ADP
ejpam-3206	383	22	a	a	DET
ejpam-3206	383	23	zmodule	zmodule	NOUN
ejpam-3206	383	24	from	from	ADP
ejpam-3206	383	25	lemma	lemma	PROPN
ejpam-3206	383	26	8	8	NUM
ejpam-3206	383	27	,	,	PUNCT
ejpam-3206	383	28	we	we	PRON
ejpam-3206	383	29	get	get	VERB
ejpam-3206	383	30	that	that	DET
ejpam-3206	383	31	biaj	biaj	PROPN
ejpam-3206	383	32	∈	∈	PROPN
ejpam-3206	383	33	nil(r	nil(r	PROPN
ejpam-3206	383	34	)	)	PUNCT
ejpam-3206	383	35	,	,	PUNCT
ejpam-3206	383	36	for	for	ADP
ejpam-3206	383	37	all	all	DET
ejpam-3206	383	38	integers	integer	NOUN
ejpam-3206	383	39	0	0	NUM
ejpam-3206	383	40	≤	≤	NUM
ejpam-3206	383	41	i	i	PRON
ejpam-3206	383	42	and	and	CCONJ
ejpam-3206	383	43	0	0	NUM
ejpam-3206	383	44	≤	≤	NOUN
ejpam-3206	383	45	j.	j.	PROPN
ejpam-3206	383	46	consequently	consequently	ADV
ejpam-3206	383	47	,	,	PUNCT
ejpam-3206	383	48	for	for	ADP
ejpam-3206	383	49	every	every	DET
ejpam-3206	383	50	a	a	DET
ejpam-3206	383	51	∈	∈	PROPN
ejpam-3206	383	52	i	i	NOUN
ejpam-3206	383	53	,	,	PUNCT
ejpam-3206	383	54	bia	bia	PROPN
ejpam-3206	383	55	∈	∈	PROPN
ejpam-3206	383	56	nil(r	nil(r	PROPN
ejpam-3206	383	57	)	)	PUNCT
ejpam-3206	383	58	,	,	PUNCT
ejpam-3206	383	59	for	for	ADP
ejpam-3206	383	60	all	all	DET
ejpam-3206	383	61	integers	integer	NOUN
ejpam-3206	383	62	0	0	NUM
ejpam-3206	383	63	≤	≤	NUM
ejpam-3206	383	64	i.	i.	NOUN
ejpam-3206	383	65	hence	hence	ADV
ejpam-3206	384	1	bi	bi	PROPN
ejpam-3206	384	2	∈	∈	PROPN
ejpam-3206	384	3	nr	nr	PROPN
ejpam-3206	384	4	(	(	PUNCT
ejpam-3206	384	5	j	j	PROPN
ejpam-3206	384	6	)	)	PUNCT
ejpam-3206	384	7	=	=	SYM
ejpam-3206	384	8	nr	nr	PROPN
ejpam-3206	384	9	(	(	PUNCT
ejpam-3206	384	10	r	r	NOUN
ejpam-3206	384	11	)	)	PUNCT
ejpam-3206	384	12	=	=	SYM
ejpam-3206	384	13	nil(r	nil(r	NOUN
ejpam-3206	384	14	)	)	PUNCT
ejpam-3206	384	15	,	,	PUNCT
ejpam-3206	384	16	for	for	ADP
ejpam-3206	384	17	all	all	DET
ejpam-3206	384	18	integers	integer	NOUN
ejpam-3206	384	19	0	0	NUM
ejpam-3206	384	20	≤	≤	NUM
ejpam-3206	384	21	i.	i.	NOUN
ejpam-3206	384	22	therefore	therefore	ADV
ejpam-3206	384	23	ϕ(x	ϕ(x	PROPN
ejpam-3206	384	24	)	)	PUNCT
ejpam-3206	384	25	∈	∈	PROPN
ejpam-3206	384	26	nil(a	nil(a	PROPN
ejpam-3206	384	27	)	)	PUNCT
ejpam-3206	384	28	.	.	PUNCT
ejpam-3206	385	1	hence	hence	ADV
ejpam-3206	385	2	na	na	PROPN
ejpam-3206	385	3	(	(	PUNCT
ejpam-3206	385	4	l	l	NOUN
ejpam-3206	385	5	)	)	PUNCT
ejpam-3206	385	6	⊆	⊆	NUM
ejpam-3206	385	7	nil(a	nil(a	NUM
ejpam-3206	385	8	)	)	PUNCT
ejpam-3206	385	9	.	.	PUNCT
ejpam-3206	386	1	if	if	SCONJ
ejpam-3206	386	2	j	j	PROPN
ejpam-3206	386	3	6=	6=	PROPN
ejpam-3206	386	4	r	r	NOUN
ejpam-3206	386	5	,	,	PUNCT
ejpam-3206	386	6	we	we	PRON
ejpam-3206	386	7	show	show	VERB
ejpam-3206	386	8	that	that	SCONJ
ejpam-3206	386	9	j	j	PROPN
ejpam-3206	386	10	is	be	AUX
ejpam-3206	386	11	a	a	DET
ejpam-3206	386	12	maximal	maximal	ADJ
ejpam-3206	386	13	right	right	ADJ
ejpam-3206	386	14	ideal	ideal	NOUN
ejpam-3206	386	15	of	of	ADP
ejpam-3206	386	16	r.	r.	PROPN
ejpam-3206	386	17	let	let	VERB
ejpam-3206	386	18	r	r	NOUN
ejpam-3206	386	19	∈	∈	PROPN
ejpam-3206	386	20	r−j	r−j	NOUN
ejpam-3206	386	21	.	.	PUNCT
ejpam-3206	387	1	if	if	SCONJ
ejpam-3206	387	2	r	r	NOUN
ejpam-3206	387	3	∈	∈	PROPN
ejpam-3206	387	4	l	l	NOUN
ejpam-3206	387	5	,	,	PUNCT
ejpam-3206	387	6	then	then	ADV
ejpam-3206	387	7	r	r	NOUN
ejpam-3206	387	8	∈	∈	PROPN
ejpam-3206	388	1	i	i	PRON
ejpam-3206	388	2	and	and	CCONJ
ejpam-3206	388	3	so	so	ADV
ejpam-3206	388	4	r	r	NOUN
ejpam-3206	388	5	∈	∈	PROPN
ejpam-3206	388	6	j	j	PROPN
ejpam-3206	388	7	,	,	PUNCT
ejpam-3206	388	8	which	which	PRON
ejpam-3206	388	9	is	be	AUX
ejpam-3206	388	10	a	a	DET
ejpam-3206	388	11	contradiction	contradiction	NOUN
ejpam-3206	388	12	.	.	PUNCT
ejpam-3206	389	1	thus	thus	ADV
ejpam-3206	389	2	r	r	NOUN
ejpam-3206	389	3	/∈	/∈	PUNCT
ejpam-3206	389	4	l.	l.	NOUN
ejpam-3206	389	5	since	since	SCONJ
ejpam-3206	389	6	l	l	PROPN
ejpam-3206	389	7	is	be	AUX
ejpam-3206	389	8	a	a	DET
ejpam-3206	389	9	maximal	maximal	ADJ
ejpam-3206	389	10	right	right	ADJ
ejpam-3206	389	11	ideal	ideal	NOUN
ejpam-3206	389	12	of	of	ADP
ejpam-3206	389	13	a	a	PRON
ejpam-3206	389	14	,	,	PUNCT
ejpam-3206	389	15	we	we	PRON
ejpam-3206	389	16	have	have	VERB
ejpam-3206	389	17	a	a	DET
ejpam-3206	389	18	=	=	PUNCT
ejpam-3206	389	19	l+	l+	PUNCT
ejpam-3206	389	20	ra	ra	NOUN
ejpam-3206	389	21	.	.	PUNCT
ejpam-3206	390	1	it	it	PRON
ejpam-3206	390	2	follows	follow	VERB
ejpam-3206	390	3	that	that	SCONJ
ejpam-3206	390	4	there	there	PRON
ejpam-3206	390	5	exist	exist	VERB
ejpam-3206	390	6	f(x	f(x	NOUN
ejpam-3206	390	7	)	)	PUNCT
ejpam-3206	391	1	=	=	PUNCT
ejpam-3206	392	1	∞∑	∞∑	NUM
ejpam-3206	392	2	i=0	i=0	PROPN
ejpam-3206	392	3	aix	aix	NOUN
ejpam-3206	392	4	i	i	NOUN
ejpam-3206	392	5	∈	∈	PROPN
ejpam-3206	392	6	l	l	NOUN
ejpam-3206	392	7	and	and	CCONJ
ejpam-3206	392	8	g(x	g(x	NOUN
ejpam-3206	392	9	)	)	PUNCT
ejpam-3206	393	1	=	=	NOUN
ejpam-3206	394	1	∞∑	∞∑	NUM
ejpam-3206	394	2	j=0	j=0	PROPN
ejpam-3206	394	3	bjx	bjx	PROPN
ejpam-3206	394	4	j	j	PROPN
ejpam-3206	394	5	∈	∈	PROPN
ejpam-3206	394	6	a	a	PRON
ejpam-3206	394	7	,	,	PUNCT
ejpam-3206	394	8	such	such	ADJ
ejpam-3206	394	9	that	that	SCONJ
ejpam-3206	394	10	1	1	NUM
ejpam-3206	394	11	=	=	SYM
ejpam-3206	394	12	a0	a0	PROPN
ejpam-3206	394	13	+	+	CCONJ
ejpam-3206	394	14	rb0	rb0	PROPN
ejpam-3206	394	15	.	.	PUNCT
ejpam-3206	395	1	if	if	SCONJ
ejpam-3206	395	2	a0	a0	PROPN
ejpam-3206	395	3	=	=	SYM
ejpam-3206	395	4	0	0	PROPN
ejpam-3206	395	5	,	,	PUNCT
ejpam-3206	395	6	then	then	ADV
ejpam-3206	395	7	1	1	X
ejpam-3206	395	8	=	=	SYM
ejpam-3206	395	9	rb0	rb0	NOUN
ejpam-3206	395	10	∈	∈	PROPN
ejpam-3206	395	11	r.r	r.r	PROPN
ejpam-3206	395	12	and	and	CCONJ
ejpam-3206	395	13	so	so	ADV
ejpam-3206	395	14	r	r	NOUN
ejpam-3206	395	15	=	=	SYM
ejpam-3206	395	16	j	j	PROPN
ejpam-3206	395	17	+	+	NUM
ejpam-3206	395	18	rr	rr	PROPN
ejpam-3206	395	19	.	.	PUNCT
ejpam-3206	396	1	if	if	SCONJ
ejpam-3206	396	2	a0	a0	PROPN
ejpam-3206	396	3	6=	6=	PROPN
ejpam-3206	396	4	0	0	NUM
ejpam-3206	396	5	,	,	PUNCT
ejpam-3206	396	6	then	then	ADV
ejpam-3206	396	7	a0	a0	PROPN
ejpam-3206	396	8	∈	∈	PROPN
ejpam-3206	397	1	i	i	PRON
ejpam-3206	397	2	⊂	⊂	PROPN
ejpam-3206	397	3	j	j	PROPN
ejpam-3206	397	4	which	which	PRON
ejpam-3206	397	5	implies	imply	VERB
ejpam-3206	397	6	that	that	SCONJ
ejpam-3206	397	7	r	r	NOUN
ejpam-3206	397	8	=	=	SYM
ejpam-3206	397	9	j	j	PROPN
ejpam-3206	397	10	+	+	NUM
ejpam-3206	397	11	rr	rr	PROPN
ejpam-3206	397	12	.	.	PUNCT
ejpam-3206	398	1	hence	hence	ADV
ejpam-3206	398	2	j	j	PROPN
ejpam-3206	398	3	is	be	AUX
ejpam-3206	398	4	a	a	DET
ejpam-3206	398	5	maximal	maximal	ADJ
ejpam-3206	398	6	right	right	ADJ
ejpam-3206	398	7	ideal	ideal	NOUN
ejpam-3206	398	8	of	of	ADP
ejpam-3206	398	9	r.	r.	PROPN
ejpam-3206	398	10	since	since	SCONJ
ejpam-3206	398	11	r	r	NOUN
ejpam-3206	398	12	is	be	AUX
ejpam-3206	398	13	a	a	DET
ejpam-3206	398	14	weak	weak	ADJ
ejpam-3206	398	15	right	right	ADJ
ejpam-3206	398	16	ps	ps	NOUN
ejpam-3206	398	17	-	-	NOUN
ejpam-3206	398	18	ring	ring	NOUN
ejpam-3206	398	19	,	,	PUNCT
ejpam-3206	398	20	it	it	PRON
ejpam-3206	398	21	follows	follow	VERB
ejpam-3206	398	22	that	that	SCONJ
ejpam-3206	398	23	either	either	CCONJ
ejpam-3206	398	24	nr	nr	PROPN
ejpam-3206	398	25	(	(	PUNCT
ejpam-3206	398	26	j	j	PROPN
ejpam-3206	398	27	)	)	PUNCT
ejpam-3206	398	28	⊆	⊆	NUM
ejpam-3206	398	29	nil(r	nil(r	NUM
ejpam-3206	398	30	)	)	PUNCT
ejpam-3206	398	31	or	or	CCONJ
ejpam-3206	398	32	nr	nr	PRON
ejpam-3206	398	33	(	(	PUNCT
ejpam-3206	398	34	j	j	PROPN
ejpam-3206	398	35	)	)	PUNCT
ejpam-3206	398	36	=	=	PUNCT
ejpam-3206	398	37	re	re	PROPN
ejpam-3206	398	38	,	,	PUNCT
ejpam-3206	398	39	where	where	SCONJ
ejpam-3206	398	40	e	e	PROPN
ejpam-3206	398	41	∈	∈	PROPN
ejpam-3206	398	42	id(r	id(r	NOUN
ejpam-3206	398	43	)	)	PUNCT
ejpam-3206	398	44	.	.	PUNCT
ejpam-3206	399	1	case	case	NOUN
ejpam-3206	399	2	(	(	PUNCT
ejpam-3206	399	3	1	1	NUM
ejpam-3206	399	4	):	):	PUNCT
ejpam-3206	399	5	assume	assume	VERB
ejpam-3206	399	6	that	that	SCONJ
ejpam-3206	399	7	nr	nr	PRON
ejpam-3206	399	8	(	(	PUNCT
ejpam-3206	399	9	j	j	PROPN
ejpam-3206	399	10	)	)	PUNCT
ejpam-3206	399	11	⊆	⊆	NUM
ejpam-3206	399	12	nil(r	nil(r	NOUN
ejpam-3206	399	13	)	)	PUNCT
ejpam-3206	399	14	.	.	PUNCT
ejpam-3206	400	1	we	we	PRON
ejpam-3206	400	2	will	will	AUX
ejpam-3206	400	3	show	show	VERB
ejpam-3206	400	4	that	that	SCONJ
ejpam-3206	400	5	na	na	ADP
ejpam-3206	400	6	(	(	PUNCT
ejpam-3206	400	7	l	l	NOUN
ejpam-3206	400	8	)	)	PUNCT
ejpam-3206	400	9	⊆	⊆	NUM
ejpam-3206	400	10	nil(a	nil(a	NUM
ejpam-3206	400	11	)	)	PUNCT
ejpam-3206	400	12	.	.	PUNCT
ejpam-3206	401	1	let	let	VERB
ejpam-3206	401	2	ϕ	ϕ	NOUN
ejpam-3206	401	3	(	(	PUNCT
ejpam-3206	401	4	x	x	NOUN
ejpam-3206	401	5	)	)	PUNCT
ejpam-3206	401	6	=	=	SYM
ejpam-3206	402	1	∞∑	∞∑	NUM
ejpam-3206	402	2	i=0	i=0	ADJ
ejpam-3206	402	3	mix	mix	NOUN
ejpam-3206	402	4	i	i	NOUN
ejpam-3206	402	5	∈	∈	NOUN
ejpam-3206	402	6	na	na	X
ejpam-3206	402	7	(	(	PUNCT
ejpam-3206	402	8	l	l	NOUN
ejpam-3206	402	9	)	)	PUNCT
ejpam-3206	402	10	.	.	PUNCT
ejpam-3206	403	1	then	then	ADV
ejpam-3206	403	2	for	for	ADP
ejpam-3206	403	3	every	every	DET
ejpam-3206	403	4	g	g	PROPN
ejpam-3206	403	5	(	(	PUNCT
ejpam-3206	403	6	x	x	NOUN
ejpam-3206	403	7	)	)	PUNCT
ejpam-3206	403	8	=	=	SYM
ejpam-3206	403	9	∞∑	∞∑	NUM
ejpam-3206	403	10	j=0	j=0	PROPN
ejpam-3206	403	11	ajx	ajx	NOUN
ejpam-3206	403	12	j	j	PROPN
ejpam-3206	403	13	∈	∈	PROPN
ejpam-3206	403	14	l	l	PROPN
ejpam-3206	403	15	,	,	PUNCT
ejpam-3206	403	16	we	we	PRON
ejpam-3206	403	17	have	have	VERB
ejpam-3206	403	18	ϕ	ϕ	NOUN
ejpam-3206	403	19	(	(	PUNCT
ejpam-3206	403	20	x	x	NOUN
ejpam-3206	403	21	)	)	PUNCT
ejpam-3206	403	22	g	g	NOUN
ejpam-3206	403	23	(	(	PUNCT
ejpam-3206	403	24	x	x	NOUN
ejpam-3206	403	25	)	)	PUNCT
ejpam-3206	403	26	=	=	SYM
ejpam-3206	404	1	(	(	PUNCT
ejpam-3206	404	2	∞∑	∞∑	NUM
ejpam-3206	404	3	i=0	i=0	PROPN
ejpam-3206	404	4	bix	bix	PROPN
ejpam-3206	404	5	i	i	PRON
ejpam-3206	404	6	)	)	PUNCT
ejpam-3206	404	7			PROPN
ejpam-3206	404	8	∞∑	∞∑	NUM
ejpam-3206	404	9	j=0	j=0	PROPN
ejpam-3206	404	10	ajx	ajx	NUM
ejpam-3206	404	11	j	j	PROPN
ejpam-3206	404	12			PROPN
ejpam-3206	404	13	∈	∈	PROPN
ejpam-3206	404	14	nil(a	nil(a	PROPN
ejpam-3206	404	15	)	)	PUNCT
ejpam-3206	404	16	.	.	PUNCT
ejpam-3206	405	1	since	since	SCONJ
ejpam-3206	405	2	r	r	NOUN
ejpam-3206	405	3	is	be	AUX
ejpam-3206	405	4	a	a	DET
ejpam-3206	405	5	σ	σ	PROPN
ejpam-3206	405	6	-	-	PUNCT
ejpam-3206	405	7	compatible	compatible	ADJ
ejpam-3206	405	8	ni	ni	NOUN
ejpam-3206	405	9	-	-	NOUN
ejpam-3206	405	10	ring	ring	NOUN
ejpam-3206	405	11	with	with	ADP
ejpam-3206	405	12	nil(r	nil(r	NOUN
ejpam-3206	405	13	)	)	PUNCT
ejpam-3206	405	14	a	a	DET
ejpam-3206	405	15	nilpotent	nilpotent	NOUN
ejpam-3206	405	16	,	,	PUNCT
ejpam-3206	405	17	from	from	ADP
ejpam-3206	405	18	lemma	lemma	PROPN
ejpam-3206	405	19	8	8	NUM
ejpam-3206	405	20	,	,	PUNCT
ejpam-3206	405	21	we	we	PRON
ejpam-3206	405	22	get	get	VERB
ejpam-3206	405	23	that	that	DET
ejpam-3206	405	24	biaj	biaj	PROPN
ejpam-3206	405	25	∈	∈	PROPN
ejpam-3206	405	26	nil(r	nil(r	PROPN
ejpam-3206	405	27	)	)	PUNCT
ejpam-3206	405	28	,	,	PUNCT
ejpam-3206	405	29	for	for	ADP
ejpam-3206	405	30	all	all	DET
ejpam-3206	405	31	integers	integer	NOUN
ejpam-3206	405	32	0	0	NUM
ejpam-3206	405	33	≤	≤	NUM
ejpam-3206	405	34	i	i	PRON
ejpam-3206	405	35	and	and	CCONJ
ejpam-3206	405	36	0	0	NUM
ejpam-3206	405	37	≤	≤	NOUN
ejpam-3206	405	38	j.	j.	PROPN
ejpam-3206	405	39	consequently	consequently	ADV
ejpam-3206	405	40	,	,	PUNCT
ejpam-3206	405	41	for	for	ADP
ejpam-3206	405	42	every	every	DET
ejpam-3206	405	43	a	a	DET
ejpam-3206	405	44	∈	∈	PROPN
ejpam-3206	405	45	i	i	NOUN
ejpam-3206	405	46	,	,	PUNCT
ejpam-3206	405	47	bia	bia	PROPN
ejpam-3206	405	48	∈	∈	PROPN
ejpam-3206	405	49	nil(r	nil(r	PROPN
ejpam-3206	405	50	)	)	PUNCT
ejpam-3206	405	51	,	,	PUNCT
ejpam-3206	405	52	m.	m.	NOUN
ejpam-3206	405	53	a.	a.	NOUN
ejpam-3206	405	54	farahat	farahat	PROPN
ejpam-3206	405	55	,	,	PUNCT
ejpam-3206	405	56	s.	s.	PROPN
ejpam-3206	405	57	t.	t.	PROPN
ejpam-3206	405	58	al	al	PROPN
ejpam-3206	405	59	-	-	PUNCT
ejpam-3206	405	60	bogamy	bogamy	PROPN
ejpam-3206	405	61	/	/	SYM
ejpam-3206	405	62	eur	eur	PROPN
ejpam-3206	405	63	.	.	PUNCT
ejpam-3206	406	1	j.	j.	PROPN
ejpam-3206	406	2	pure	pure	PROPN
ejpam-3206	406	3	appl	appl	PROPN
ejpam-3206	406	4	.	.	PROPN
ejpam-3206	406	5	math	math	PROPN
ejpam-3206	406	6	,	,	PUNCT
ejpam-3206	406	7	11	11	NUM
ejpam-3206	406	8	(	(	PUNCT
ejpam-3206	406	9	1	1	NUM
ejpam-3206	406	10	)	)	PUNCT
ejpam-3206	406	11	(	(	PUNCT
ejpam-3206	406	12	2018	2018	NUM
ejpam-3206	406	13	)	)	PUNCT
ejpam-3206	406	14	,	,	PUNCT
ejpam-3206	406	15	244	244	NUM
ejpam-3206	406	16	-	-	SYM
ejpam-3206	406	17	259	259	NUM
ejpam-3206	406	18	257	257	NUM
ejpam-3206	406	19	for	for	ADP
ejpam-3206	406	20	all	all	DET
ejpam-3206	406	21	integers	integer	NOUN
ejpam-3206	406	22	0	0	NUM
ejpam-3206	406	23	≤	≤	NUM
ejpam-3206	406	24	i.	i.	NOUN
ejpam-3206	407	1	hence	hence	ADV
ejpam-3206	407	2	bi	bi	PROPN
ejpam-3206	407	3	∈	∈	PROPN
ejpam-3206	407	4	nr	nr	PROPN
ejpam-3206	407	5	(	(	PUNCT
ejpam-3206	407	6	j	j	PROPN
ejpam-3206	407	7	)	)	PUNCT
ejpam-3206	407	8	=	=	SYM
ejpam-3206	407	9	nr	nr	PROPN
ejpam-3206	407	10	(	(	PUNCT
ejpam-3206	407	11	r	r	NOUN
ejpam-3206	407	12	)	)	PUNCT
ejpam-3206	407	13	=	=	SYM
ejpam-3206	407	14	nil(r	nil(r	NOUN
ejpam-3206	407	15	)	)	PUNCT
ejpam-3206	407	16	,	,	PUNCT
ejpam-3206	407	17	for	for	ADP
ejpam-3206	407	18	all	all	DET
ejpam-3206	407	19	integers	integer	NOUN
ejpam-3206	407	20	0	0	NUM
ejpam-3206	407	21	≤	≤	NUM
ejpam-3206	407	22	i.	i.	NOUN
ejpam-3206	407	23	therefore	therefore	ADV
ejpam-3206	407	24	ϕ(x	ϕ(x	PROPN
ejpam-3206	407	25	)	)	PUNCT
ejpam-3206	407	26	∈	∈	PROPN
ejpam-3206	407	27	nil(a	nil(a	PROPN
ejpam-3206	407	28	)	)	PUNCT
ejpam-3206	407	29	and	and	CCONJ
ejpam-3206	407	30	we	we	PRON
ejpam-3206	407	31	have	have	VERB
ejpam-3206	407	32	na	na	PART
ejpam-3206	407	33	(	(	PUNCT
ejpam-3206	407	34	l	l	NOUN
ejpam-3206	407	35	)	)	PUNCT
ejpam-3206	407	36	⊆	⊆	NUM
ejpam-3206	407	37	nil(a	nil(a	NUM
ejpam-3206	407	38	)	)	PUNCT
ejpam-3206	407	39	.	.	PUNCT
ejpam-3206	408	1	case	case	NOUN
ejpam-3206	408	2	(	(	PUNCT
ejpam-3206	408	3	2	2	NUM
ejpam-3206	408	4	):	):	PUNCT
ejpam-3206	408	5	assume	assume	VERB
ejpam-3206	408	6	that	that	SCONJ
ejpam-3206	408	7	nr	nr	PRON
ejpam-3206	408	8	(	(	PUNCT
ejpam-3206	408	9	j	j	PROPN
ejpam-3206	408	10	)	)	PUNCT
ejpam-3206	408	11	=	=	PUNCT
ejpam-3206	408	12	re	re	PROPN
ejpam-3206	408	13	,	,	PUNCT
ejpam-3206	408	14	where	where	SCONJ
ejpam-3206	408	15	e	e	PROPN
ejpam-3206	408	16	∈	∈	PROPN
ejpam-3206	408	17	id(r	id(r	NOUN
ejpam-3206	408	18	)	)	PUNCT
ejpam-3206	408	19	.	.	PUNCT
ejpam-3206	409	1	we	we	PRON
ejpam-3206	409	2	will	will	AUX
ejpam-3206	409	3	show	show	VERB
ejpam-3206	409	4	that	that	SCONJ
ejpam-3206	409	5	na	na	ADP
ejpam-3206	409	6	(	(	PUNCT
ejpam-3206	409	7	l	l	NOUN
ejpam-3206	409	8	)	)	PUNCT
ejpam-3206	409	9	=	=	SYM
ejpam-3206	409	10	aq	aq	PROPN
ejpam-3206	409	11	,	,	PUNCT
ejpam-3206	409	12	where	where	SCONJ
ejpam-3206	409	13	q	q	PROPN
ejpam-3206	409	14	∈	∈	PROPN
ejpam-3206	409	15	id(a	id(a	NOUN
ejpam-3206	409	16	)	)	PUNCT
ejpam-3206	409	17	.	.	PUNCT
ejpam-3206	410	1	let	let	VERB
ejpam-3206	410	2	ϕ(x	ϕ(x	PRON
ejpam-3206	410	3	)	)	PUNCT
ejpam-3206	410	4	=	=	PUNCT
ejpam-3206	411	1	∞∑	∞∑	NUM
ejpam-3206	411	2	i=0	i=0	PROPN
ejpam-3206	411	3	bix	bix	PROPN
ejpam-3206	411	4	i	i	PRON
ejpam-3206	411	5	∈	∈	PROPN
ejpam-3206	411	6	na	na	X
ejpam-3206	411	7	(	(	PUNCT
ejpam-3206	411	8	l	l	NOUN
ejpam-3206	411	9	)	)	PUNCT
ejpam-3206	411	10	and	and	CCONJ
ejpam-3206	411	11	ϕ(x	ϕ(x	NOUN
ejpam-3206	411	12	)	)	PUNCT
ejpam-3206	411	13	/∈	/∈	PUNCT
ejpam-3206	411	14	nil(a	nil(a	NUM
ejpam-3206	411	15	)	)	PUNCT
ejpam-3206	411	16	,	,	PUNCT
ejpam-3206	411	17	then	then	ADV
ejpam-3206	411	18	for	for	ADP
ejpam-3206	411	19	every	every	DET
ejpam-3206	411	20	f(x	f(x	PROPN
ejpam-3206	411	21	)	)	PUNCT
ejpam-3206	411	22	=	=	PUNCT
ejpam-3206	412	1	∞∑	∞∑	NUM
ejpam-3206	412	2	j=0	j=0	PROPN
ejpam-3206	412	3	ajx	ajx	NOUN
ejpam-3206	412	4	j	j	PROPN
ejpam-3206	412	5	∈	∈	PROPN
ejpam-3206	412	6	l	l	PROPN
ejpam-3206	412	7	,	,	PUNCT
ejpam-3206	412	8	we	we	PRON
ejpam-3206	412	9	have	have	VERB
ejpam-3206	412	10	ϕ(x)f(x	ϕ(x)f(x	NOUN
ejpam-3206	412	11	)	)	PUNCT
ejpam-3206	413	1	=	=	PUNCT
ejpam-3206	414	1	(	(	PUNCT
ejpam-3206	414	2	∞∑	∞∑	NUM
ejpam-3206	414	3	i=0	i=0	PROPN
ejpam-3206	414	4	bix	bix	PROPN
ejpam-3206	414	5	i	i	PRON
ejpam-3206	414	6	)	)	PUNCT
ejpam-3206	414	7			PROPN
ejpam-3206	414	8	∞∑	∞∑	NUM
ejpam-3206	414	9	j=0	j=0	PROPN
ejpam-3206	414	10	ajx	ajx	NUM
ejpam-3206	414	11	j	j	PROPN
ejpam-3206	414	12			PROPN
ejpam-3206	414	13	∈	∈	PROPN
ejpam-3206	414	14	nil(a	nil(a	PROPN
ejpam-3206	414	15	)	)	PUNCT
ejpam-3206	414	16	.	.	PUNCT
ejpam-3206	415	1	since	since	SCONJ
ejpam-3206	415	2	r	r	NOUN
ejpam-3206	415	3	is	be	AUX
ejpam-3206	415	4	a	a	DET
ejpam-3206	415	5	σ	σ	PROPN
ejpam-3206	415	6	-	-	PUNCT
ejpam-3206	415	7	compatible	compatible	ADJ
ejpam-3206	415	8	ni	ni	NOUN
ejpam-3206	415	9	-	-	NOUN
ejpam-3206	415	10	ring	ring	NOUN
ejpam-3206	415	11	with	with	ADP
ejpam-3206	415	12	nil(r	nil(r	NOUN
ejpam-3206	415	13	)	)	PUNCT
ejpam-3206	415	14	a	a	DET
ejpam-3206	415	15	nilpotent	nilpotent	NOUN
ejpam-3206	415	16	,	,	PUNCT
ejpam-3206	415	17	from	from	ADP
ejpam-3206	415	18	lemma	lemma	PROPN
ejpam-3206	415	19	8	8	NUM
ejpam-3206	415	20	,	,	PUNCT
ejpam-3206	415	21	we	we	PRON
ejpam-3206	415	22	get	get	VERB
ejpam-3206	415	23	that	that	DET
ejpam-3206	415	24	biaj	biaj	PROPN
ejpam-3206	415	25	∈	∈	PROPN
ejpam-3206	415	26	nil(r	nil(r	PROPN
ejpam-3206	415	27	)	)	PUNCT
ejpam-3206	415	28	,	,	PUNCT
ejpam-3206	415	29	for	for	ADP
ejpam-3206	415	30	all	all	DET
ejpam-3206	415	31	integers	integer	NOUN
ejpam-3206	415	32	0	0	NUM
ejpam-3206	415	33	≤	≤	NUM
ejpam-3206	415	34	i	i	PRON
ejpam-3206	415	35	and	and	CCONJ
ejpam-3206	415	36	0	0	NUM
ejpam-3206	415	37	≤	≤	NOUN
ejpam-3206	415	38	j.	j.	PROPN
ejpam-3206	415	39	consequently	consequently	ADV
ejpam-3206	415	40	,	,	PUNCT
ejpam-3206	415	41	for	for	ADP
ejpam-3206	415	42	every	every	DET
ejpam-3206	415	43	a	a	DET
ejpam-3206	415	44	∈	∈	PROPN
ejpam-3206	415	45	i	i	NOUN
ejpam-3206	415	46	,	,	PUNCT
ejpam-3206	415	47	bia	bia	PROPN
ejpam-3206	415	48	∈	∈	PROPN
ejpam-3206	415	49	nil(r	nil(r	PROPN
ejpam-3206	415	50	)	)	PUNCT
ejpam-3206	415	51	,	,	PUNCT
ejpam-3206	415	52	for	for	ADP
ejpam-3206	415	53	all	all	DET
ejpam-3206	415	54	integers	integer	NOUN
ejpam-3206	415	55	0	0	NUM
ejpam-3206	415	56	≤	≤	NUM
ejpam-3206	415	57	i.	i.	NOUN
ejpam-3206	415	58	for	for	ADP
ejpam-3206	415	59	any	any	DET
ejpam-3206	415	60	m	m	PROPN
ejpam-3206	415	61	∈	∈	PROPN
ejpam-3206	415	62	j	j	NOUN
ejpam-3206	415	63	,	,	PUNCT
ejpam-3206	415	64	there	there	PRON
ejpam-3206	415	65	exist	exist	VERB
ejpam-3206	415	66	a1	a1	NOUN
ejpam-3206	415	67	,	,	PUNCT
ejpam-3206	415	68	a2	a2	PROPN
ejpam-3206	415	69	,	,	PUNCT
ejpam-3206	415	70	...	...	PUNCT
ejpam-3206	415	71	,	,	PUNCT
ejpam-3206	415	72	an	an	DET
ejpam-3206	415	73	∈	∈	NOUN
ejpam-3206	415	74	i	i	PRON
ejpam-3206	415	75	and	and	CCONJ
ejpam-3206	415	76	r1	r1	PROPN
ejpam-3206	415	77	,	,	PUNCT
ejpam-3206	415	78	r2	r2	PROPN
ejpam-3206	415	79	,	,	PUNCT
ejpam-3206	415	80	...	...	PUNCT
ejpam-3206	415	81	,	,	PUNCT
ejpam-3206	415	82	rn	rn	PROPN
ejpam-3206	415	83	∈	∈	PROPN
ejpam-3206	415	84	r	r	NOUN
ejpam-3206	415	85	,	,	PUNCT
ejpam-3206	415	86	such	such	ADJ
ejpam-3206	415	87	that	that	SCONJ
ejpam-3206	415	88	m	m	VERB
ejpam-3206	415	89	=	=	PUNCT
ejpam-3206	415	90	a1r1	a1r1	PROPN
ejpam-3206	415	91	+	+	ADJ
ejpam-3206	415	92	a2r2	a2r2	X
ejpam-3206	415	93	+	+	NUM
ejpam-3206	415	94	...	...	PUNCT
ejpam-3206	415	95	+	+	NUM
ejpam-3206	415	96	anrn	anrn	NOUN
ejpam-3206	415	97	,	,	PUNCT
ejpam-3206	415	98	bim	bim	NOUN
ejpam-3206	415	99	=	=	SYM
ejpam-3206	415	100	(	(	PUNCT
ejpam-3206	415	101	bia1	bia1	PROPN
ejpam-3206	415	102	)	)	PUNCT
ejpam-3206	415	103	r1	r1	PROPN
ejpam-3206	415	104	+	+	CCONJ
ejpam-3206	415	105	(	(	PUNCT
ejpam-3206	415	106	bia2	bia2	PROPN
ejpam-3206	415	107	)	)	PUNCT
ejpam-3206	415	108	r2	r2	PROPN
ejpam-3206	416	1	+	+	CCONJ
ejpam-3206	416	2	...	...	PUNCT
ejpam-3206	417	1	+	+	CCONJ
ejpam-3206	417	2	(	(	PUNCT
ejpam-3206	417	3	bian	bian	ADJ
ejpam-3206	417	4	)	)	PUNCT
ejpam-3206	417	5	rn	rn	PROPN
ejpam-3206	417	6	,	,	PUNCT
ejpam-3206	417	7	hence	hence	ADV
ejpam-3206	417	8	bim	bim	VERB
ejpam-3206	417	9	∈	∈	PROPN
ejpam-3206	417	10	nil(r	nil(r	PROPN
ejpam-3206	417	11	)	)	PUNCT
ejpam-3206	417	12	,	,	PUNCT
ejpam-3206	417	13	for	for	ADP
ejpam-3206	417	14	all	all	DET
ejpam-3206	417	15	integers	integer	NOUN
ejpam-3206	417	16	0	0	NUM
ejpam-3206	417	17	≤	≤	NUM
ejpam-3206	418	1	i	i	PRON
ejpam-3206	418	2	,	,	PUNCT
ejpam-3206	418	3	so	so	CCONJ
ejpam-3206	418	4	bi	bi	PROPN
ejpam-3206	418	5	∈	∈	PROPN
ejpam-3206	418	6	nr	nr	PROPN
ejpam-3206	418	7	(	(	PUNCT
ejpam-3206	418	8	j	j	PROPN
ejpam-3206	418	9	)	)	PUNCT
ejpam-3206	418	10	=	=	SYM
ejpam-3206	418	11	re	re	PROPN
ejpam-3206	418	12	,	,	PUNCT
ejpam-3206	418	13	for	for	ADP
ejpam-3206	418	14	all	all	DET
ejpam-3206	418	15	integers	integer	NOUN
ejpam-3206	418	16	0	0	NUM
ejpam-3206	418	17	≤	≤	NUM
ejpam-3206	418	18	i.	i.	NOUN
ejpam-3206	418	19	therefore	therefore	ADV
ejpam-3206	418	20	there	there	PRON
ejpam-3206	418	21	exist	exist	VERB
ejpam-3206	418	22	ti	ti	NOUN
ejpam-3206	418	23	∈	∈	NOUN
ejpam-3206	418	24	r	r	NOUN
ejpam-3206	418	25	such	such	ADJ
ejpam-3206	418	26	that	that	DET
ejpam-3206	418	27	bi	bi	NOUN
ejpam-3206	418	28	=	=	NOUN
ejpam-3206	418	29	tie	tie	NOUN
ejpam-3206	418	30	,	,	PUNCT
ejpam-3206	418	31	for	for	ADP
ejpam-3206	418	32	all	all	DET
ejpam-3206	418	33	integers	integer	NOUN
ejpam-3206	418	34	0	0	NUM
ejpam-3206	418	35	≤	≤	NOUN
ejpam-3206	418	36	i	i	PRON
ejpam-3206	418	37	,	,	PUNCT
ejpam-3206	418	38	and	and	CCONJ
ejpam-3206	418	39	we	we	PRON
ejpam-3206	418	40	have	have	VERB
ejpam-3206	418	41	σ(e	σ(e	PROPN
ejpam-3206	418	42	)	)	PUNCT
ejpam-3206	419	1	=	=	SYM
ejpam-3206	419	2	e.	e.	PROPN
ejpam-3206	419	3	hence	hence	ADV
ejpam-3206	419	4	ϕ(x	ϕ(x	PROPN
ejpam-3206	419	5	)	)	PUNCT
ejpam-3206	419	6	=	=	PUNCT
ejpam-3206	420	1	∞∑	∞∑	NUM
ejpam-3206	420	2	i=0	i=0	PROPN
ejpam-3206	420	3	bix	bix	PROPN
ejpam-3206	420	4	i	i	PRON
ejpam-3206	420	5	=	=	SYM
ejpam-3206	420	6	∞∑	∞∑	NUM
ejpam-3206	420	7	i=0	i=0	PROPN
ejpam-3206	420	8	tiex	tiex	NOUN
ejpam-3206	420	9	i	i	NOUN
ejpam-3206	420	10	=	=	PUNCT
ejpam-3206	420	11	(	(	PUNCT
ejpam-3206	420	12	∞∑	∞∑	DET
ejpam-3206	420	13	i=0	i=0	PROPN
ejpam-3206	420	14	tix	tix	NOUN
ejpam-3206	420	15	i	i	PRON
ejpam-3206	420	16	)	)	PUNCT
ejpam-3206	420	17	e	e	PROPN
ejpam-3206	420	18	∈	∈	PROPN
ejpam-3206	420	19	aq	aq	ADP
ejpam-3206	420	20	,	,	PUNCT
ejpam-3206	420	21	where	where	SCONJ
ejpam-3206	420	22	q2	q2	NOUN
ejpam-3206	420	23	=	=	SYM
ejpam-3206	420	24	e2	e2	PROPN
ejpam-3206	420	25	=	=	PUNCT
ejpam-3206	420	26	e	e	X
ejpam-3206	420	27	=	=	PUNCT
ejpam-3206	420	28	q	q	PUNCT
ejpam-3206	420	29	∈	∈	PROPN
ejpam-3206	420	30	a.	a.	NOUN
ejpam-3206	420	31	therefore	therefore	ADV
ejpam-3206	420	32	na	na	X
ejpam-3206	420	33	(	(	PUNCT
ejpam-3206	420	34	l	l	NOUN
ejpam-3206	420	35	)	)	PUNCT
ejpam-3206	420	36	=	=	SYM
ejpam-3206	420	37	aq	aq	PROPN
ejpam-3206	420	38	,	,	PUNCT
ejpam-3206	420	39	where	where	SCONJ
ejpam-3206	420	40	q	q	PROPN
ejpam-3206	420	41	∈	∈	PROPN
ejpam-3206	420	42	id(a	id(a	NOUN
ejpam-3206	420	43	)	)	PUNCT
ejpam-3206	420	44	and	and	CCONJ
ejpam-3206	420	45	the	the	DET
ejpam-3206	420	46	result	result	NOUN
ejpam-3206	420	47	is	be	AUX
ejpam-3206	420	48	proved	prove	VERB
ejpam-3206	420	49	.	.	PUNCT
ejpam-3206	421	1	as	as	ADP
ejpam-3206	421	2	a	a	DET
ejpam-3206	421	3	corollary	corollary	NOUN
ejpam-3206	421	4	we	we	PRON
ejpam-3206	421	5	get	get	VERB
ejpam-3206	421	6	the	the	DET
ejpam-3206	421	7	following	following	ADJ
ejpam-3206	421	8	result	result	NOUN
ejpam-3206	421	9	in	in	ADP
ejpam-3206	421	10	the	the	DET
ejpam-3206	421	11	finite	finite	ADJ
ejpam-3206	421	12	case	case	NOUN
ejpam-3206	421	13	.	.	PUNCT
ejpam-3206	422	1	corollary	corollary	ADJ
ejpam-3206	422	2	4	4	NUM
ejpam-3206	422	3	.	.	PUNCT
ejpam-3206	423	1	let	let	VERB
ejpam-3206	423	2	r	r	PRON
ejpam-3206	423	3	be	be	AUX
ejpam-3206	423	4	a	a	DET
ejpam-3206	423	5	σ	σ	NOUN
ejpam-3206	423	6	-	-	PUNCT
ejpam-3206	423	7	compatible	compatible	ADJ
ejpam-3206	423	8	ni	ni	NOUN
ejpam-3206	423	9	-	-	NOUN
ejpam-3206	423	10	ring	ring	NOUN
ejpam-3206	423	11	with	with	ADP
ejpam-3206	423	12	nil(r	nil(r	NOUN
ejpam-3206	423	13	)	)	PUNCT
ejpam-3206	423	14	nilpotent	nilpotent	NOUN
ejpam-3206	423	15	,	,	PUNCT
ejpam-3206	423	16	σ(e	σ(e	PROPN
ejpam-3206	423	17	)	)	PUNCT
ejpam-3206	424	1	=	=	PUNCT
ejpam-3206	424	2	e	e	NOUN
ejpam-3206	424	3	for	for	ADP
ejpam-3206	424	4	every	every	DET
ejpam-3206	424	5	e	e	PROPN
ejpam-3206	424	6	∈	∈	PROPN
ejpam-3206	424	7	id(r	id(r	NOUN
ejpam-3206	424	8	)	)	PUNCT
ejpam-3206	424	9	and	and	CCONJ
ejpam-3206	424	10	r	r	NOUN
ejpam-3206	424	11	a	a	DET
ejpam-3206	424	12	torsion	torsion	NOUN
ejpam-3206	424	13	free	free	ADJ
ejpam-3206	424	14	as	as	ADP
ejpam-3206	424	15	a	a	DET
ejpam-3206	424	16	z	z	NOUN
ejpam-3206	424	17	-	-	PUNCT
ejpam-3206	424	18	module	module	NOUN
ejpam-3206	424	19	.	.	PUNCT
ejpam-3206	425	1	if	if	SCONJ
ejpam-3206	425	2	r	r	NOUN
ejpam-3206	425	3	is	be	AUX
ejpam-3206	425	4	a	a	DET
ejpam-3206	425	5	weak	weak	ADJ
ejpam-3206	425	6	right	right	ADJ
ejpam-3206	425	7	ps	ps	NOUN
ejpam-3206	425	8	-	-	NOUN
ejpam-3206	425	9	ring	ring	NOUN
ejpam-3206	425	10	,	,	PUNCT
ejpam-3206	425	11	then	then	ADV
ejpam-3206	425	12	p	p	NOUN
ejpam-3206	425	13	=	=	SYM
ejpam-3206	425	14	(	(	PUNCT
ejpam-3206	425	15	hr	hr	PROPN
ejpam-3206	425	16	,	,	PUNCT
ejpam-3206	425	17	σ	σ	PROPN
ejpam-3206	425	18	)	)	PUNCT
ejpam-3206	425	19	is	be	AUX
ejpam-3206	425	20	a	a	DET
ejpam-3206	425	21	weak	weak	ADJ
ejpam-3206	425	22	right	right	ADJ
ejpam-3206	425	23	ps	ps	NOUN
ejpam-3206	425	24	-	-	PUNCT
ejpam-3206	425	25	ring	ring	NOUN
ejpam-3206	425	26	.	.	PUNCT
ejpam-3206	426	1	theorem	theorem	NOUN
ejpam-3206	426	2	5	5	NUM
ejpam-3206	426	3	.	.	PUNCT
ejpam-3206	427	1	let	let	VERB
ejpam-3206	427	2	r	r	PRON
ejpam-3206	427	3	be	be	AUX
ejpam-3206	427	4	a	a	DET
ejpam-3206	427	5	σ	σ	NOUN
ejpam-3206	427	6	-	-	PUNCT
ejpam-3206	427	7	compatible	compatible	ADJ
ejpam-3206	427	8	ni	ni	NOUN
ejpam-3206	427	9	-	-	NOUN
ejpam-3206	427	10	ring	ring	NOUN
ejpam-3206	427	11	with	with	ADP
ejpam-3206	427	12	nil(r	nil(r	NOUN
ejpam-3206	427	13	)	)	PUNCT
ejpam-3206	427	14	nilpotent	nilpotent	NOUN
ejpam-3206	427	15	and	and	CCONJ
ejpam-3206	427	16	r	r	NOUN
ejpam-3206	427	17	a	a	DET
ejpam-3206	427	18	torsion	torsion	NOUN
ejpam-3206	427	19	free	free	ADJ
ejpam-3206	427	20	as	as	ADP
ejpam-3206	427	21	a	a	DET
ejpam-3206	427	22	z	z	NOUN
ejpam-3206	427	23	-	-	PUNCT
ejpam-3206	427	24	module	module	NOUN
ejpam-3206	427	25	.	.	PUNCT
ejpam-3206	428	1	if	if	SCONJ
ejpam-3206	428	2	r	r	NOUN
ejpam-3206	428	3	is	be	AUX
ejpam-3206	428	4	a	a	DET
ejpam-3206	428	5	weak	weak	ADJ
ejpam-3206	428	6	left	left	ADJ
ejpam-3206	428	7	ps	ps	NOUN
ejpam-3206	428	8	-	-	PUNCT
ejpam-3206	428	9	ring	ring	NOUN
ejpam-3206	428	10	,	,	PUNCT
ejpam-3206	428	11	then	then	ADV
ejpam-3206	428	12	a	a	PRON
ejpam-3206	428	13	=	=	SYM
ejpam-3206	428	14	(	(	PUNCT
ejpam-3206	428	15	hr	hr	PROPN
ejpam-3206	428	16	,	,	PUNCT
ejpam-3206	428	17	σ	σ	PROPN
ejpam-3206	428	18	)	)	PUNCT
ejpam-3206	428	19	is	be	AUX
ejpam-3206	428	20	a	a	DET
ejpam-3206	428	21	weak	weak	ADJ
ejpam-3206	428	22	left	left	ADJ
ejpam-3206	428	23	ps	ps	NOUN
ejpam-3206	428	24	-	-	PUNCT
ejpam-3206	428	25	ring	ring	NOUN
ejpam-3206	428	26	.	.	PUNCT
ejpam-3206	429	1	proof	proof	NOUN
ejpam-3206	429	2	.	.	PUNCT
ejpam-3206	430	1	the	the	DET
ejpam-3206	430	2	proof	proof	NOUN
ejpam-3206	430	3	is	be	AUX
ejpam-3206	430	4	similar	similar	ADJ
ejpam-3206	430	5	to	to	ADP
ejpam-3206	430	6	the	the	DET
ejpam-3206	430	7	previous	previous	ADJ
ejpam-3206	430	8	proof	proof	NOUN
ejpam-3206	430	9	of	of	ADP
ejpam-3206	430	10	theorem	theorem	ADJ
ejpam-3206	430	11	4	4	NUM
ejpam-3206	430	12	.	.	PUNCT
ejpam-3206	431	1	the	the	DET
ejpam-3206	431	2	only	only	ADJ
ejpam-3206	431	3	thing	thing	NOUN
ejpam-3206	431	4	we	we	PRON
ejpam-3206	431	5	need	need	VERB
ejpam-3206	431	6	to	to	PART
ejpam-3206	431	7	note	note	VERB
ejpam-3206	431	8	here	here	ADV
ejpam-3206	431	9	is	be	AUX
ejpam-3206	431	10	that	that	SCONJ
ejpam-3206	431	11	,	,	PUNCT
ejpam-3206	431	12	if	if	SCONJ
ejpam-3206	431	13	l	l	NOUN
ejpam-3206	431	14	is	be	AUX
ejpam-3206	431	15	a	a	DET
ejpam-3206	431	16	maximal	maximal	ADJ
ejpam-3206	431	17	left	leave	VERB
ejpam-3206	431	18	ideal	ideal	NOUN
ejpam-3206	431	19	of	of	ADP
ejpam-3206	431	20	a	a	PRON
ejpam-3206	431	21	=	=	X
ejpam-3206	431	22	(	(	PUNCT
ejpam-3206	431	23	hr	hr	PROPN
ejpam-3206	431	24	,	,	PUNCT
ejpam-3206	431	25	σ	σ	PROPN
ejpam-3206	431	26	)	)	PUNCT
ejpam-3206	431	27	,	,	PUNCT
ejpam-3206	431	28	then	then	ADV
ejpam-3206	431	29	,	,	PUNCT
ejpam-3206	431	30	by	by	ADP
ejpam-3206	431	31	the	the	DET
ejpam-3206	431	32	analogue	analogue	NOUN
ejpam-3206	431	33	manner	manner	NOUN
ejpam-3206	431	34	as	as	ADP
ejpam-3206	431	35	above	above	ADV
ejpam-3206	431	36	,	,	PUNCT
ejpam-3206	431	37	we	we	PRON
ejpam-3206	431	38	get	get	VERB
ejpam-3206	431	39	in	in	ADP
ejpam-3206	431	40	case	case	NOUN
ejpam-3206	431	41	(	(	PUNCT
ejpam-3206	431	42	2	2	NUM
ejpam-3206	431	43	)	)	PUNCT
ejpam-3206	431	44	that	that	SCONJ
ejpam-3206	431	45	bi	bi	PROPN
ejpam-3206	431	46	∈	∈	PROPN
ejpam-3206	431	47	nr	nr	PROPN
ejpam-3206	431	48	(	(	PUNCT
ejpam-3206	431	49	j	j	PROPN
ejpam-3206	431	50	)	)	PUNCT
ejpam-3206	431	51	=	=	SYM
ejpam-3206	432	1	er	er	INTJ
ejpam-3206	432	2	,	,	PUNCT
ejpam-3206	432	3	for	for	ADP
ejpam-3206	432	4	all	all	DET
ejpam-3206	432	5	integers	integer	NOUN
ejpam-3206	432	6	0	0	NUM
ejpam-3206	432	7	≤	≤	NUM
ejpam-3206	432	8	i.	i.	NOUN
ejpam-3206	432	9	therefore	therefore	ADV
ejpam-3206	432	10	there	there	PRON
ejpam-3206	432	11	exist	exist	VERB
ejpam-3206	432	12	ti	ti	NOUN
ejpam-3206	432	13	∈	∈	NOUN
ejpam-3206	432	14	r	r	NOUN
ejpam-3206	432	15	such	such	ADJ
ejpam-3206	432	16	that	that	DET
ejpam-3206	432	17	bi	bi	NOUN
ejpam-3206	432	18	=	=	PROPN
ejpam-3206	432	19	eti	eti	PROPN
ejpam-3206	432	20	,	,	PUNCT
ejpam-3206	432	21	for	for	ADP
ejpam-3206	432	22	all	all	DET
ejpam-3206	432	23	integers	integer	NOUN
ejpam-3206	432	24	0	0	NUM
ejpam-3206	432	25	≤	≤	NUM
ejpam-3206	432	26	i.	i.	NOUN
ejpam-3206	432	27	so	so	ADV
ejpam-3206	432	28	ϕ(x	ϕ(x	PROPN
ejpam-3206	432	29	)	)	PUNCT
ejpam-3206	433	1	=	=	PUNCT
ejpam-3206	434	1	∞∑	∞∑	NUM
ejpam-3206	434	2	i=0	i=0	PROPN
ejpam-3206	434	3	bix	bix	PROPN
ejpam-3206	434	4	i	i	PRON
ejpam-3206	434	5	=	=	SYM
ejpam-3206	434	6	∞∑	∞∑	NUM
ejpam-3206	434	7	i=0	i=0	ADJ
ejpam-3206	434	8	etix	etix	NOUN
ejpam-3206	434	9	i	i	PRON
ejpam-3206	434	10	=	=	SYM
ejpam-3206	434	11	e	e	X
ejpam-3206	434	12	(	(	PUNCT
ejpam-3206	434	13	∞∑	∞∑	PRON
ejpam-3206	434	14	i=0	i=0	PROPN
ejpam-3206	434	15	tix	tix	NOUN
ejpam-3206	434	16	i	i	PRON
ejpam-3206	434	17	)	)	PUNCT
ejpam-3206	434	18	∈	∈	PROPN
ejpam-3206	434	19	qa	qa	PROPN
ejpam-3206	434	20	,	,	PUNCT
ejpam-3206	434	21	where	where	SCONJ
ejpam-3206	434	22	q2	q2	NOUN
ejpam-3206	434	23	=	=	SYM
ejpam-3206	434	24	e2	e2	PROPN
ejpam-3206	434	25	=	=	PUNCT
ejpam-3206	434	26	e	e	X
ejpam-3206	434	27	=	=	PUNCT
ejpam-3206	434	28	q	q	PUNCT
ejpam-3206	434	29	∈	∈	PROPN
ejpam-3206	434	30	a.	a.	NOUN
ejpam-3206	434	31	therefore	therefore	ADV
ejpam-3206	434	32	na	na	X
ejpam-3206	434	33	(	(	PUNCT
ejpam-3206	434	34	l	l	NOUN
ejpam-3206	434	35	)	)	PUNCT
ejpam-3206	434	36	=	=	SYM
ejpam-3206	434	37	qa	qa	PROPN
ejpam-3206	434	38	,	,	PUNCT
ejpam-3206	434	39	where	where	SCONJ
ejpam-3206	434	40	q	q	PROPN
ejpam-3206	434	41	∈	∈	PROPN
ejpam-3206	434	42	id(a	id(a	NOUN
ejpam-3206	434	43	)	)	PUNCT
ejpam-3206	434	44	and	and	CCONJ
ejpam-3206	434	45	the	the	DET
ejpam-3206	434	46	result	result	NOUN
ejpam-3206	434	47	is	be	AUX
ejpam-3206	434	48	proved	prove	VERB
ejpam-3206	434	49	.	.	PUNCT
ejpam-3206	435	1	as	as	ADP
ejpam-3206	435	2	a	a	DET
ejpam-3206	435	3	corollary	corollary	NOUN
ejpam-3206	435	4	we	we	PRON
ejpam-3206	435	5	get	get	VERB
ejpam-3206	435	6	the	the	DET
ejpam-3206	435	7	following	following	ADJ
ejpam-3206	435	8	result	result	NOUN
ejpam-3206	435	9	in	in	ADP
ejpam-3206	435	10	the	the	DET
ejpam-3206	435	11	finite	finite	ADJ
ejpam-3206	435	12	case	case	NOUN
ejpam-3206	435	13	.	.	PUNCT
ejpam-3206	436	1	references	reference	NOUN
ejpam-3206	436	2	258	258	NUM
ejpam-3206	436	3	corollary	corollary	ADJ
ejpam-3206	436	4	5	5	NUM
ejpam-3206	436	5	.	.	PUNCT
ejpam-3206	437	1	let	let	VERB
ejpam-3206	437	2	r	r	PRON
ejpam-3206	437	3	be	be	AUX
ejpam-3206	437	4	a	a	DET
ejpam-3206	437	5	σ	σ	NOUN
ejpam-3206	437	6	-	-	PUNCT
ejpam-3206	437	7	compatible	compatible	ADJ
ejpam-3206	437	8	ni	ni	NOUN
ejpam-3206	437	9	-	-	NOUN
ejpam-3206	437	10	ring	ring	NOUN
ejpam-3206	437	11	with	with	ADP
ejpam-3206	437	12	nil(r	nil(r	NOUN
ejpam-3206	437	13	)	)	PUNCT
ejpam-3206	437	14	nilpotent	nilpotent	NOUN
ejpam-3206	437	15	and	and	CCONJ
ejpam-3206	437	16	r	r	NOUN
ejpam-3206	437	17	a	a	DET
ejpam-3206	437	18	torsion	torsion	NOUN
ejpam-3206	437	19	free	free	ADJ
ejpam-3206	437	20	as	as	ADP
ejpam-3206	437	21	a	a	DET
ejpam-3206	437	22	z	z	NOUN
ejpam-3206	437	23	-	-	PUNCT
ejpam-3206	437	24	module	module	NOUN
ejpam-3206	437	25	.	.	PUNCT
ejpam-3206	438	1	if	if	SCONJ
ejpam-3206	438	2	r	r	NOUN
ejpam-3206	438	3	is	be	AUX
ejpam-3206	438	4	a	a	DET
ejpam-3206	438	5	weak	weak	ADJ
ejpam-3206	438	6	left	left	ADJ
ejpam-3206	438	7	ps	ps	NOUN
ejpam-3206	438	8	-	-	PUNCT
ejpam-3206	438	9	ring	ring	NOUN
ejpam-3206	438	10	,	,	PUNCT
ejpam-3206	438	11	then	then	ADV
ejpam-3206	438	12	p	p	NOUN
ejpam-3206	438	13	=	=	SYM
ejpam-3206	438	14	(	(	PUNCT
ejpam-3206	438	15	hr	hr	PROPN
ejpam-3206	438	16	,	,	PUNCT
ejpam-3206	438	17	σ	σ	PROPN
ejpam-3206	438	18	)	)	PUNCT
ejpam-3206	438	19	is	be	AUX
ejpam-3206	438	20	a	a	DET
ejpam-3206	438	21	weak	weak	ADJ
ejpam-3206	438	22	left	left	ADJ
ejpam-3206	438	23	ps	ps	NOUN
ejpam-3206	438	24	-	-	PUNCT
ejpam-3206	438	25	ring	ring	NOUN
ejpam-3206	438	26	.	.	PUNCT
ejpam-3206	439	1	assume	assume	VERB
ejpam-3206	439	2	that	that	SCONJ
ejpam-3206	439	3	σ	σ	PROPN
ejpam-3206	439	4	is	be	AUX
ejpam-3206	439	5	the	the	DET
ejpam-3206	439	6	identity	identity	NOUN
ejpam-3206	439	7	map	map	NOUN
ejpam-3206	439	8	,	,	PUNCT
ejpam-3206	439	9	then	then	ADV
ejpam-3206	439	10	the	the	DET
ejpam-3206	439	11	skew	skew	PROPN
ejpam-3206	439	12	hurwitz	hurwitz	PROPN
ejpam-3206	439	13	series	series	PROPN
ejpam-3206	439	14	ring	ring	VERB
ejpam-3206	439	15	a	a	DET
ejpam-3206	439	16	=	=	X
ejpam-3206	439	17	(	(	PUNCT
ejpam-3206	439	18	hr	hr	PROPN
ejpam-3206	439	19	,	,	PUNCT
ejpam-3206	439	20	σ	σ	PROPN
ejpam-3206	439	21	)	)	PUNCT
ejpam-3206	439	22	is	be	AUX
ejpam-3206	439	23	hr	hr	NOUN
ejpam-3206	439	24	,	,	PUNCT
ejpam-3206	439	25	the	the	DET
ejpam-3206	439	26	usual	usual	ADJ
ejpam-3206	439	27	hurwitz	hurwitz	PROPN
ejpam-3206	439	28	series	series	PROPN
ejpam-3206	439	29	ring	ring	NOUN
ejpam-3206	439	30	over	over	ADP
ejpam-3206	439	31	r	r	NOUN
ejpam-3206	439	32	,	,	PUNCT
ejpam-3206	439	33	and	and	CCONJ
ejpam-3206	439	34	the	the	DET
ejpam-3206	439	35	skew	skew	ADJ
ejpam-3206	439	36	hurwitz	hurwitz	PROPN
ejpam-3206	439	37	polynomial	polynomial	PROPN
ejpam-3206	439	38	ring	ring	PROPN
ejpam-3206	439	39	p	p	PROPN
ejpam-3206	439	40	=	=	X
ejpam-3206	439	41	(	(	PUNCT
ejpam-3206	439	42	hr	hr	PROPN
ejpam-3206	439	43	,	,	PUNCT
ejpam-3206	439	44	σ	σ	PROPN
ejpam-3206	439	45	)	)	PUNCT
ejpam-3206	439	46	is	be	AUX
ejpam-3206	439	47	hr	hr	NOUN
ejpam-3206	439	48	,	,	PUNCT
ejpam-3206	439	49	the	the	DET
ejpam-3206	439	50	usual	usual	ADJ
ejpam-3206	439	51	hurwitz	hurwitz	PROPN
ejpam-3206	439	52	polynomial	polynomial	ADJ
ejpam-3206	439	53	ring	ring	NOUN
ejpam-3206	439	54	over	over	ADP
ejpam-3206	439	55	r	r	NOUN
ejpam-3206	439	56	,	,	PUNCT
ejpam-3206	439	57	so	so	SCONJ
ejpam-3206	439	58	we	we	PRON
ejpam-3206	439	59	get	get	VERB
ejpam-3206	439	60	the	the	DET
ejpam-3206	439	61	following	follow	VERB
ejpam-3206	439	62	corollaries	corollary	NOUN
ejpam-3206	439	63	:	:	PUNCT
ejpam-3206	439	64	corollary	corollary	ADJ
ejpam-3206	439	65	6	6	NUM
ejpam-3206	439	66	.	.	PUNCT
ejpam-3206	440	1	let	let	VERB
ejpam-3206	440	2	r	r	PRON
ejpam-3206	440	3	be	be	AUX
ejpam-3206	440	4	an	an	DET
ejpam-3206	440	5	ni	ni	NOUN
ejpam-3206	440	6	-	-	NOUN
ejpam-3206	440	7	ring	ring	NOUN
ejpam-3206	440	8	with	with	ADP
ejpam-3206	440	9	nil(r	nil(r	NOUN
ejpam-3206	440	10	)	)	PUNCT
ejpam-3206	440	11	nilpotent	nilpotent	NOUN
ejpam-3206	440	12	and	and	CCONJ
ejpam-3206	440	13	r	r	NOUN
ejpam-3206	440	14	a	a	DET
ejpam-3206	440	15	torsion	torsion	NOUN
ejpam-3206	440	16	free	free	ADJ
ejpam-3206	440	17	as	as	ADP
ejpam-3206	440	18	a	a	DET
ejpam-3206	440	19	zmodule	zmodule	NOUN
ejpam-3206	440	20	.	.	PUNCT
ejpam-3206	441	1	if	if	SCONJ
ejpam-3206	441	2	r	r	NOUN
ejpam-3206	441	3	is	be	AUX
ejpam-3206	441	4	a	a	DET
ejpam-3206	441	5	weak	weak	ADJ
ejpam-3206	441	6	right	right	NOUN
ejpam-3206	441	7	(	(	PUNCT
ejpam-3206	441	8	left	left	ADJ
ejpam-3206	441	9	)	)	PUNCT
ejpam-3206	441	10	ps	ps	NOUN
ejpam-3206	441	11	-	-	PUNCT
ejpam-3206	441	12	ring	ring	NOUN
ejpam-3206	441	13	,	,	PUNCT
ejpam-3206	441	14	then	then	ADV
ejpam-3206	441	15	usual	usual	ADJ
ejpam-3206	441	16	hurwitz	hurwitz	PROPN
ejpam-3206	441	17	series	series	PROPN
ejpam-3206	441	18	ring	ring	NOUN
ejpam-3206	441	19	over	over	ADP
ejpam-3206	441	20	hr	hr	PROPN
ejpam-3206	441	21	is	be	AUX
ejpam-3206	441	22	a	a	DET
ejpam-3206	441	23	weak	weak	ADJ
ejpam-3206	441	24	right	right	NOUN
ejpam-3206	441	25	(	(	PUNCT
ejpam-3206	441	26	left	left	ADJ
ejpam-3206	441	27	)	)	PUNCT
ejpam-3206	441	28	ps	ps	NOUN
ejpam-3206	441	29	-	-	PUNCT
ejpam-3206	441	30	ring	ring	NOUN
ejpam-3206	441	31	.	.	PUNCT
ejpam-3206	442	1	corollary	corollary	ADJ
ejpam-3206	442	2	7	7	NUM
ejpam-3206	442	3	.	.	PUNCT
ejpam-3206	443	1	let	let	VERB
ejpam-3206	443	2	r	r	PRON
ejpam-3206	443	3	be	be	AUX
ejpam-3206	443	4	an	an	DET
ejpam-3206	443	5	ni	ni	NOUN
ejpam-3206	443	6	-	-	NOUN
ejpam-3206	443	7	ring	ring	NOUN
ejpam-3206	443	8	with	with	ADP
ejpam-3206	443	9	nil(r	nil(r	NOUN
ejpam-3206	443	10	)	)	PUNCT
ejpam-3206	443	11	nilpotent	nilpotent	NOUN
ejpam-3206	443	12	and	and	CCONJ
ejpam-3206	443	13	r	r	NOUN
ejpam-3206	443	14	a	a	DET
ejpam-3206	443	15	torsion	torsion	NOUN
ejpam-3206	443	16	free	free	ADJ
ejpam-3206	443	17	as	as	ADP
ejpam-3206	443	18	a	a	DET
ejpam-3206	443	19	zmodule	zmodule	NOUN
ejpam-3206	443	20	.	.	PUNCT
ejpam-3206	444	1	if	if	SCONJ
ejpam-3206	444	2	r	r	NOUN
ejpam-3206	444	3	is	be	AUX
ejpam-3206	444	4	a	a	DET
ejpam-3206	444	5	weak	weak	ADJ
ejpam-3206	444	6	right	right	NOUN
ejpam-3206	444	7	(	(	PUNCT
ejpam-3206	444	8	left	left	ADJ
ejpam-3206	444	9	)	)	PUNCT
ejpam-3206	444	10	ps	ps	NOUN
ejpam-3206	444	11	-	-	PUNCT
ejpam-3206	444	12	ring	ring	NOUN
ejpam-3206	444	13	,	,	PUNCT
ejpam-3206	444	14	then	then	ADV
ejpam-3206	444	15	usual	usual	ADJ
ejpam-3206	444	16	hurwitz	hurwitz	PROPN
ejpam-3206	444	17	polynomial	polynomial	ADJ
ejpam-3206	444	18	ring	ring	NOUN
ejpam-3206	444	19	over	over	ADP
ejpam-3206	444	20	hr	hr	NOUN
ejpam-3206	444	21	is	be	AUX
ejpam-3206	444	22	a	a	DET
ejpam-3206	444	23	weak	weak	ADJ
ejpam-3206	444	24	right	right	NOUN
ejpam-3206	444	25	(	(	PUNCT
ejpam-3206	444	26	left	left	ADJ
ejpam-3206	444	27	)	)	PUNCT
ejpam-3206	444	28	ps	ps	NOUN
ejpam-3206	444	29	-	-	PUNCT
ejpam-3206	444	30	ring	ring	NOUN
ejpam-3206	444	31	.	.	PUNCT
ejpam-3206	445	1	acknowledgements	acknowledgement	NOUN
ejpam-3206	445	2	the	the	DET
ejpam-3206	445	3	authors	author	NOUN
ejpam-3206	445	4	wish	wish	VERB
ejpam-3206	445	5	to	to	PART
ejpam-3206	445	6	express	express	VERB
ejpam-3206	445	7	their	their	PRON
ejpam-3206	445	8	sincere	sincere	ADJ
ejpam-3206	445	9	thanks	thank	NOUN
ejpam-3206	445	10	to	to	ADP
ejpam-3206	445	11	the	the	DET
ejpam-3206	445	12	referee	referee	NOUN
ejpam-3206	445	13	for	for	ADP
ejpam-3206	445	14	his	his	PRON
ejpam-3206	445	15	/	/	SYM
ejpam-3206	445	16	her	her	PRON
ejpam-3206	445	17	helpful	helpful	ADJ
ejpam-3206	445	18	comments	comment	NOUN
ejpam-3206	445	19	and	and	CCONJ
ejpam-3206	445	20	valuable	valuable	ADJ
ejpam-3206	445	21	suggestions	suggestion	NOUN
ejpam-3206	445	22	.	.	PUNCT
ejpam-3206	446	1	references	reference	NOUN
ejpam-3206	446	2	[	[	X
ejpam-3206	446	3	1	1	X
ejpam-3206	446	4	]	]	PUNCT
ejpam-3206	446	5	s.	s.	PROPN
ejpam-3206	446	6	annin	annin	PROPN
ejpam-3206	446	7	.	.	PUNCT
ejpam-3206	447	1	associated	associate	VERB
ejpam-3206	447	2	primes	prime	NOUN
ejpam-3206	447	3	over	over	ADP
ejpam-3206	447	4	ore	ore	NOUN
ejpam-3206	447	5	extension	extension	NOUN
ejpam-3206	447	6	rings	ring	NOUN
ejpam-3206	447	7	.	.	PUNCT
ejpam-3206	448	1	j.	j.	PROPN
ejpam-3206	448	2	algebr	algebr	PROPN
ejpam-3206	448	3	.	.	PUNCT
ejpam-3206	449	1	appl	appl	PROPN
ejpam-3206	449	2	.	.	PROPN
ejpam-3206	449	3	,	,	PUNCT
ejpam-3206	449	4	3:193–205	3:193–205	NUM
ejpam-3206	449	5	,	,	PUNCT
ejpam-3206	449	6	2004	2004	NUM
ejpam-3206	449	7	.	.	PUNCT
ejpam-3206	450	1	[	[	X
ejpam-3206	450	2	2	2	X
ejpam-3206	450	3	]	]	X
ejpam-3206	450	4	e.	e.	PROPN
ejpam-3206	450	5	armendariz	armendariz	PROPN
ejpam-3206	450	6	.	.	PUNCT
ejpam-3206	451	1	a	a	DET
ejpam-3206	451	2	note	note	NOUN
ejpam-3206	451	3	on	on	ADP
ejpam-3206	451	4	extensions	extension	NOUN
ejpam-3206	451	5	of	of	ADP
ejpam-3206	451	6	baer	baer	PROPN
ejpam-3206	451	7	and	and	CCONJ
ejpam-3206	451	8	p.p.-ring	p.p.-ring	PROPN
ejpam-3206	451	9	.	.	PUNCT
ejpam-3206	452	1	j.	j.	PROPN
ejpam-3206	452	2	aust	aust	PROPN
ejpam-3206	452	3	.	.	PUNCT
ejpam-3206	453	1	math	math	PROPN
ejpam-3206	453	2	.	.	PUNCT
ejpam-3206	454	1	soc	soc	PROPN
ejpam-3206	454	2	.	.	PUNCT
ejpam-3206	454	3	,	,	PUNCT
ejpam-3206	454	4	18:470–473	18:470–473	NUM
ejpam-3206	454	5	,	,	PUNCT
ejpam-3206	454	6	1974	1974	NUM
ejpam-3206	454	7	.	.	PUNCT
ejpam-3206	455	1	[	[	X
ejpam-3206	455	2	3	3	X
ejpam-3206	455	3	]	]	PUNCT
ejpam-3206	455	4	m.	m.	NOUN
ejpam-3206	455	5	farahat	farahat	PROPN
ejpam-3206	455	6	and	and	CCONJ
ejpam-3206	455	7	n.	n.	PROPN
ejpam-3206	455	8	al	al	PROPN
ejpam-3206	455	9	-	-	PUNCT
ejpam-3206	455	10	harthy	harthy	ADJ
ejpam-3206	455	11	.	.	PUNCT
ejpam-3206	456	1	ps	ps	NOUN
ejpam-3206	456	2	-	-	PUNCT
ejpam-3206	456	3	modules	module	NOUN
ejpam-3206	456	4	of	of	ADP
ejpam-3206	456	5	generalized	generalized	ADJ
ejpam-3206	456	6	mal’cev	mal’cev	PROPN
ejpam-3206	456	7	-	-	PUNCT
ejpam-3206	456	8	neumann	neumann	PROPN
ejpam-3206	456	9	series	series	PROPN
ejpam-3206	456	10	rings	rings	PROPN
ejpam-3206	456	11	.	.	PUNCT
ejpam-3206	457	1	hacettepe	hacettepe	PROPN
ejpam-3206	457	2	journal	journal	PROPN
ejpam-3206	457	3	of	of	ADP
ejpam-3206	457	4	mathematics	mathematic	NOUN
ejpam-3206	457	5	and	and	CCONJ
ejpam-3206	457	6	statistics	statistic	NOUN
ejpam-3206	457	7	,	,	PUNCT
ejpam-3206	457	8	46(5):1–6	46(5):1–6	NUM
ejpam-3206	457	9	,	,	PUNCT
ejpam-3206	457	10	2017	2017	NUM
ejpam-3206	457	11	.	.	PUNCT
ejpam-3206	458	1	[	[	X
ejpam-3206	458	2	4	4	X
ejpam-3206	458	3	]	]	PUNCT
ejpam-3206	458	4	m.	m.	NOUN
ejpam-3206	458	5	farahat	farahat	PROPN
ejpam-3206	458	6	and	and	CCONJ
ejpam-3206	458	7	s.	s.	PROPN
ejpam-3206	458	8	al	al	PROPN
ejpam-3206	458	9	-	-	PROPN
ejpam-3206	458	10	nafaie	nafaie	PROPN
ejpam-3206	458	11	.	.	PUNCT
ejpam-3206	459	1	some	some	DET
ejpam-3206	459	2	results	result	NOUN
ejpam-3206	459	3	on	on	ADP
ejpam-3206	459	4	skew	skew	ADJ
ejpam-3206	459	5	hurwitz	hurwitz	PROPN
ejpam-3206	459	6	series	series	PROPN
ejpam-3206	459	7	rings	rings	PROPN
ejpam-3206	459	8	.	.	PUNCT
ejpam-3206	460	1	far	far	PROPN
ejpam-3206	460	2	east	east	PROPN
ejpam-3206	460	3	journal	journal	PROPN
ejpam-3206	460	4	of	of	ADP
ejpam-3206	460	5	mathematical	mathematical	ADJ
ejpam-3206	460	6	sciences	science	NOUN
ejpam-3206	460	7	,	,	PUNCT
ejpam-3206	460	8	101(12):2767–2784	101(12):2767–2784	NUM
ejpam-3206	460	9	,	,	PUNCT
ejpam-3206	460	10	2017	2017	NUM
ejpam-3206	460	11	.	.	PUNCT
ejpam-3206	461	1	[	[	X
ejpam-3206	461	2	5	5	NUM
ejpam-3206	461	3	]	]	PUNCT
ejpam-3206	461	4	m.	m.	NOUN
ejpam-3206	461	5	fliess	fliess	NOUN
ejpam-3206	461	6	.	.	PUNCT
ejpam-3206	462	1	sur	sur	PROPN
ejpam-3206	462	2	divers	diver	NOUN
ejpam-3206	462	3	produits	produits	X
ejpam-3206	462	4	de	de	X
ejpam-3206	462	5	series	series	NOUN
ejpam-3206	462	6	fonnelles	fonnelle	NOUN
ejpam-3206	462	7	.	.	PUNCT
ejpam-3206	463	1	bull	bull	NOUN
ejpam-3206	463	2	.	.	PUNCT
ejpam-3206	464	1	soc	soc	PROPN
ejpam-3206	464	2	.	.	PUNCT
ejpam-3206	465	1	math	math	NOUN
ejpam-3206	465	2	.	.	PUNCT
ejpam-3206	466	1	fr	fr	INTJ
ejpam-3206	466	2	.	.	PROPN
ejpam-3206	466	3	,	,	PUNCT
ejpam-3206	467	1	102:181–191	102:181–191	NUM
ejpam-3206	467	2	,	,	PUNCT
ejpam-3206	467	3	1974	1974	NUM
ejpam-3206	467	4	.	.	PUNCT
ejpam-3206	468	1	[	[	X
ejpam-3206	468	2	6	6	NUM
ejpam-3206	468	3	]	]	PUNCT
ejpam-3206	468	4	r.	r.	PROPN
ejpam-3206	468	5	gordon	gordon	PROPN
ejpam-3206	468	6	.	.	PUNCT
ejpam-3206	468	7	rings	ring	NOUN
ejpam-3206	468	8	in	in	ADP
ejpam-3206	468	9	which	which	PRON
ejpam-3206	468	10	minimal	minimal	ADJ
ejpam-3206	468	11	left	left	ADJ
ejpam-3206	468	12	ideals	ideal	NOUN
ejpam-3206	468	13	are	be	AUX
ejpam-3206	468	14	projective	projective	ADJ
ejpam-3206	468	15	.	.	PUNCT
ejpam-3206	469	1	pac	pac	PROPN
ejpam-3206	469	2	.	.	PUNCT
ejpam-3206	470	1	j.	j.	PROPN
ejpam-3206	470	2	math	math	PROPN
ejpam-3206	470	3	.	.	PUNCT
ejpam-3206	470	4	,	,	PUNCT
ejpam-3206	470	5	31:679	31:679	NUM
ejpam-3206	470	6	–	–	PUNCT
ejpam-3206	470	7	692	692	NUM
ejpam-3206	470	8	,	,	PUNCT
ejpam-3206	470	9	1969	1969	NUM
ejpam-3206	470	10	.	.	PUNCT
ejpam-3206	471	1	[	[	X
ejpam-3206	471	2	7	7	X
ejpam-3206	471	3	]	]	X
ejpam-3206	471	4	e.	e.	PROPN
ejpam-3206	471	5	hashemi	hashemi	PROPN
ejpam-3206	471	6	.	.	PUNCT
ejpam-3206	472	1	extensions	extension	NOUN
ejpam-3206	472	2	of	of	ADP
ejpam-3206	472	3	baer	baer	PROPN
ejpam-3206	472	4	and	and	CCONJ
ejpam-3206	472	5	quasi	quasi	PROPN
ejpam-3206	472	6	-	-	ADJ
ejpam-3206	472	7	baer	baer	ADJ
ejpam-3206	472	8	modules	module	NOUN
ejpam-3206	472	9	.	.	PUNCT
ejpam-3206	473	1	bull	bull	NOUN
ejpam-3206	473	2	.	.	PUNCT
ejpam-3206	474	1	iranian	iranian	ADJ
ejpam-3206	474	2	math	math	PROPN
ejpam-3206	474	3	.	.	PUNCT
ejpam-3206	475	1	soc	soc	PROPN
ejpam-3206	475	2	.	.	PUNCT
ejpam-3206	475	3	,	,	PUNCT
ejpam-3206	475	4	37(1):1–13	37(1):1–13	NUM
ejpam-3206	475	5	,	,	PUNCT
ejpam-3206	475	6	2011	2011	NUM
ejpam-3206	475	7	.	.	PUNCT
ejpam-3206	476	1	[	[	X
ejpam-3206	476	2	8	8	NUM
ejpam-3206	476	3	]	]	PUNCT
ejpam-3206	476	4	a.	a.	NOUN
ejpam-3206	476	5	hassanein	hassanein	PROPN
ejpam-3206	476	6	and	and	CCONJ
ejpam-3206	476	7	m.	m.	NOUN
ejpam-3206	476	8	farahat	farahat	PROPN
ejpam-3206	476	9	.	.	PUNCT
ejpam-3206	477	1	some	some	DET
ejpam-3206	477	2	properties	property	NOUN
ejpam-3206	477	3	of	of	ADP
ejpam-3206	477	4	skew	skew	ADJ
ejpam-3206	477	5	hurwitz	hurwitz	PROPN
ejpam-3206	477	6	series	series	PROPN
ejpam-3206	477	7	.	.	PUNCT
ejpam-3206	478	1	le	le	PROPN
ejpam-3206	478	2	matematiche	matematiche	PROPN
ejpam-3206	478	3	,	,	PUNCT
ejpam-3206	478	4	lxix(i):169–178	lxix(i):169–178	PROPN
ejpam-3206	478	5	,	,	PUNCT
ejpam-3206	478	6	2014	2014	NUM
ejpam-3206	478	7	.	.	PUNCT
ejpam-3206	479	1	references	reference	NOUN
ejpam-3206	479	2	259	259	NUM
ejpam-3206	479	3	[	[	X
ejpam-3206	479	4	9	9	NUM
ejpam-3206	479	5	]	]	X
ejpam-3206	479	6	c.	c.	PROPN
ejpam-3206	479	7	hong	hong	PROPN
ejpam-3206	479	8	,	,	PUNCT
ejpam-3206	479	9	n.	n.	PROPN
ejpam-3206	479	10	kim	kim	PROPN
ejpam-3206	479	11	,	,	PUNCT
ejpam-3206	479	12	and	and	CCONJ
ejpam-3206	479	13	t.	t.	PROPN
ejpam-3206	479	14	kwak	kwak	PROPN
ejpam-3206	479	15	.	.	PUNCT
ejpam-3206	480	1	ore	ore	NOUN
ejpam-3206	480	2	extensions	extension	NOUN
ejpam-3206	480	3	of	of	ADP
ejpam-3206	480	4	baer	baer	PROPN
ejpam-3206	480	5	and	and	CCONJ
ejpam-3206	480	6	p.p.-rings	p.p.-ring	NOUN
ejpam-3206	480	7	.	.	PUNCT
ejpam-3206	481	1	j.	j.	PROPN
ejpam-3206	481	2	pure	pure	PROPN
ejpam-3206	481	3	and	and	CCONJ
ejpam-3206	481	4	appl	appl	PROPN
ejpam-3206	481	5	.	.	PUNCT
ejpam-3206	481	6	alg	alg	PROPN
ejpam-3206	481	7	.	.	PROPN
ejpam-3206	481	8	,	,	PUNCT
ejpam-3206	481	9	151:215–226	151:215–226	NUM
ejpam-3206	481	10	,	,	PUNCT
ejpam-3206	481	11	2000	2000	NUM
ejpam-3206	481	12	.	.	PUNCT
ejpam-3206	482	1	[	[	X
ejpam-3206	482	2	10	10	NUM
ejpam-3206	482	3	]	]	X
ejpam-3206	482	4	w.	w.	PROPN
ejpam-3206	482	5	keigher	keigher	PROPN
ejpam-3206	482	6	.	.	PUNCT
ejpam-3206	483	1	adjunctions	adjunction	NOUN
ejpam-3206	483	2	and	and	CCONJ
ejpam-3206	483	3	comonads	comonad	NOUN
ejpam-3206	483	4	in	in	ADP
ejpam-3206	483	5	differential	differential	ADJ
ejpam-3206	483	6	algebra	algebra	NOUN
ejpam-3206	483	7	.	.	PUNCT
ejpam-3206	484	1	pacific	pacific	PROPN
ejpam-3206	484	2	.	.	PUNCT
ejpam-3206	485	1	j.	j.	PROPN
ejpam-3206	485	2	math	math	PROPN
ejpam-3206	485	3	,	,	PUNCT
ejpam-3206	485	4	248:99–112	248:99–112	NUM
ejpam-3206	485	5	,	,	PUNCT
ejpam-3206	485	6	1975	1975	NUM
ejpam-3206	485	7	.	.	PUNCT
ejpam-3206	486	1	[	[	X
ejpam-3206	486	2	11	11	NUM
ejpam-3206	486	3	]	]	X
ejpam-3206	486	4	w.	w.	PROPN
ejpam-3206	486	5	keigher	keigher	PROPN
ejpam-3206	486	6	.	.	PUNCT
ejpam-3206	487	1	on	on	ADP
ejpam-3206	487	2	the	the	DET
ejpam-3206	487	3	ring	ring	NOUN
ejpam-3206	487	4	of	of	ADP
ejpam-3206	487	5	hurwitz	hurwitz	PROPN
ejpam-3206	487	6	series	series	PROPN
ejpam-3206	487	7	.	.	PUNCT
ejpam-3206	488	1	comm	comm	NOUN
ejpam-3206	488	2	.	.	PUNCT
ejpam-3206	489	1	alg	alg	PROPN
ejpam-3206	489	2	.	.	PROPN
ejpam-3206	489	3	,	,	PUNCT
ejpam-3206	489	4	25(6):1845–1859	25(6):1845–1859	NUM
ejpam-3206	489	5	,	,	PUNCT
ejpam-3206	489	6	1997	1997	NUM
ejpam-3206	489	7	.	.	PUNCT
ejpam-3206	490	1	[	[	X
ejpam-3206	490	2	12	12	NUM
ejpam-3206	490	3	]	]	X
ejpam-3206	490	4	w.	w.	PROPN
ejpam-3206	490	5	keigher	keigher	PROPN
ejpam-3206	490	6	and	and	CCONJ
ejpam-3206	490	7	f.	f.	PROPN
ejpam-3206	490	8	pritchard	pritchard	PROPN
ejpam-3206	490	9	.	.	PUNCT
ejpam-3206	491	1	hurwitz	hurwitz	PROPN
ejpam-3206	491	2	series	series	PROPN
ejpam-3206	491	3	as	as	ADP
ejpam-3206	491	4	formal	formal	ADJ
ejpam-3206	491	5	functions	function	NOUN
ejpam-3206	491	6	.	.	PUNCT
ejpam-3206	492	1	j.	j.	PROPN
ejpam-3206	492	2	pure	pure	PROPN
ejpam-3206	492	3	appl	appl	PROPN
ejpam-3206	492	4	.	.	PUNCT
ejpam-3206	493	1	alg	alg	PROPN
ejpam-3206	493	2	.	.	PROPN
ejpam-3206	493	3	,	,	PUNCT
ejpam-3206	493	4	146:291–304	146:291–304	NUM
ejpam-3206	493	5	,	,	PUNCT
ejpam-3206	493	6	2000	2000	NUM
ejpam-3206	493	7	.	.	PUNCT
ejpam-3206	494	1	[	[	X
ejpam-3206	494	2	13	13	NUM
ejpam-3206	494	3	]	]	PUNCT
ejpam-3206	494	4	j.	j.	PROPN
ejpam-3206	494	5	krempa	krempa	PROPN
ejpam-3206	494	6	.	.	PUNCT
ejpam-3206	495	1	some	some	DET
ejpam-3206	495	2	examples	example	NOUN
ejpam-3206	495	3	of	of	ADP
ejpam-3206	495	4	reduced	reduce	VERB
ejpam-3206	495	5	rings	ring	NOUN
ejpam-3206	495	6	.	.	PUNCT
ejpam-3206	496	1	algebra	algebra	PROPN
ejpam-3206	496	2	colloq	colloq	PROPN
ejpam-3206	496	3	.	.	PUNCT
ejpam-3206	496	4	,	,	PUNCT
ejpam-3206	496	5	3:289–300	3:289–300	NUM
ejpam-3206	496	6	,	,	PUNCT
ejpam-3206	496	7	1996	1996	NUM
ejpam-3206	496	8	.	.	PUNCT
ejpam-3206	497	1	[	[	X
ejpam-3206	497	2	14	14	NUM
ejpam-3206	497	3	]	]	PUNCT
ejpam-3206	497	4	z.	z.	PROPN
ejpam-3206	497	5	liu	liu	PROPN
ejpam-3206	497	6	and	and	CCONJ
ejpam-3206	497	7	f.	f.	PROPN
ejpam-3206	497	8	li	li	PROPN
ejpam-3206	497	9	.	.	PROPN
ejpam-3206	497	10	ps	ps	PROPN
ejpam-3206	497	11	-	-	PUNCT
ejpam-3206	497	12	rings	ring	NOUN
ejpam-3206	497	13	of	of	ADP
ejpam-3206	497	14	generalized	generalized	ADJ
ejpam-3206	497	15	power	power	NOUN
ejpam-3206	497	16	series	series	NOUN
ejpam-3206	497	17	.	.	PUNCT
ejpam-3206	498	1	comm	comm	NOUN
ejpam-3206	498	2	.	.	PUNCT
ejpam-3206	499	1	algebra	algebra	PROPN
ejpam-3206	499	2	,	,	PUNCT
ejpam-3206	499	3	26:2283–2291	26:2283–2291	NUM
ejpam-3206	499	4	,	,	PUNCT
ejpam-3206	499	5	1998	1998	NUM
ejpam-3206	499	6	.	.	PUNCT
ejpam-3206	500	1	[	[	X
ejpam-3206	500	2	15	15	NUM
ejpam-3206	500	3	]	]	X
ejpam-3206	500	4	w.	w.	PROPN
ejpam-3206	500	5	nicholson	nicholson	PROPN
ejpam-3206	500	6	and	and	CCONJ
ejpam-3206	500	7	j.	j.	PROPN
ejpam-3206	500	8	watters	watters	PROPN
ejpam-3206	500	9	.	.	PUNCT
ejpam-3206	501	1	rings	ring	NOUN
ejpam-3206	501	2	with	with	ADP
ejpam-3206	501	3	projective	projective	ADJ
ejpam-3206	501	4	socle	socle	NOUN
ejpam-3206	501	5	.	.	PUNCT
ejpam-3206	502	1	proc	proc	PROPN
ejpam-3206	502	2	.	.	PUNCT
ejpam-3206	503	1	amer	amer	PROPN
ejpam-3206	503	2	.	.	PUNCT
ejpam-3206	503	3	math	math	PROPN
ejpam-3206	503	4	.	.	PUNCT
ejpam-3206	504	1	soc	soc	PROPN
ejpam-3206	504	2	.	.	PUNCT
ejpam-3206	504	3	,	,	PUNCT
ejpam-3206	504	4	102:443–450	102:443–450	NUM
ejpam-3206	504	5	,	,	PUNCT
ejpam-3206	504	6	1988	1988	NUM
ejpam-3206	504	7	.	.	PUNCT
ejpam-3206	505	1	[	[	X
ejpam-3206	505	2	16	16	NUM
ejpam-3206	505	3	]	]	PUNCT
ejpam-3206	505	4	l.	l.	PROPN
ejpam-3206	505	5	ouyang	ouyang	PROPN
ejpam-3206	505	6	.	.	PUNCT
ejpam-3206	505	7	ore	ore	NOUN
ejpam-3206	505	8	extensions	extension	NOUN
ejpam-3206	505	9	of	of	ADP
ejpam-3206	505	10	weak	weak	ADJ
ejpam-3206	505	11	zip	zip	NOUN
ejpam-3206	505	12	rings	ring	NOUN
ejpam-3206	505	13	.	.	PUNCT
ejpam-3206	505	14	glasg	glasg	PROPN
ejpam-3206	505	15	.	.	PUNCT
ejpam-3206	506	1	math	math	NOUN
ejpam-3206	506	2	.	.	PUNCT
ejpam-3206	507	1	j.	j.	PROPN
ejpam-3206	507	2	,	,	PUNCT
ejpam-3206	507	3	51:525–537	51:525–537	PROPN
ejpam-3206	507	4	,	,	PUNCT
ejpam-3206	507	5	2009	2009	NUM
ejpam-3206	507	6	.	.	PUNCT
ejpam-3206	508	1	[	[	X
ejpam-3206	508	2	17	17	NUM
ejpam-3206	508	3	]	]	PUNCT
ejpam-3206	508	4	k.	k.	PROPN
ejpam-3206	509	1	paykan	paykan	PROPN
ejpam-3206	509	2	.	.	PUNCT
ejpam-3206	510	1	nilpotent	nilpotent	ADJ
ejpam-3206	510	2	elements	element	NOUN
ejpam-3206	510	3	of	of	ADP
ejpam-3206	510	4	skew	skew	ADJ
ejpam-3206	510	5	hurwitz	hurwitz	PROPN
ejpam-3206	510	6	series	series	PROPN
ejpam-3206	510	7	rings	rings	PROPN
ejpam-3206	510	8	.	.	PUNCT
ejpam-3206	511	1	rend	rend	VERB
ejpam-3206	511	2	.	.	PUNCT
ejpam-3206	512	1	circ	circ	PROPN
ejpam-3206	512	2	.	.	PUNCT
ejpam-3206	513	1	mat	mat	NOUN
ejpam-3206	513	2	.	.	PUNCT
ejpam-3206	513	3	palermo	palermo	PROPN
ejpam-3206	513	4	.	.	PUNCT
ejpam-3206	513	5	,	,	PUNCT
ejpam-3206	513	6	2016	2016	NUM
ejpam-3206	513	7	.	.	PUNCT
ejpam-3206	514	1	[	[	X
ejpam-3206	514	2	18	18	NUM
ejpam-3206	514	3	]	]	PUNCT
ejpam-3206	514	4	k.	k.	PROPN
ejpam-3206	515	1	paykan	paykan	PROPN
ejpam-3206	515	2	.	.	PUNCT
ejpam-3206	516	1	skew	skew	ADJ
ejpam-3206	516	2	inverse	inverse	NOUN
ejpam-3206	516	3	power	power	NOUN
ejpam-3206	516	4	series	series	PROPN
ejpam-3206	516	5	rings	ring	NOUN
ejpam-3206	516	6	over	over	ADP
ejpam-3206	516	7	a	a	DET
ejpam-3206	516	8	ring	ring	NOUN
ejpam-3206	516	9	with	with	ADP
ejpam-3206	516	10	projective	projective	ADJ
ejpam-3206	516	11	socle	socle	NOUN
ejpam-3206	516	12	.	.	PUNCT
ejpam-3206	517	1	czec	czec	ADJ
ejpam-3206	517	2	.	.	PUNCT
ejpam-3206	518	1	math	math	NOUN
ejpam-3206	518	2	.	.	PUNCT
ejpam-3206	519	1	j.	j.	PROPN
ejpam-3206	519	2	,	,	PUNCT
ejpam-3206	519	3	67(142):389–398	67(142):389–398	PROPN
ejpam-3206	519	4	,	,	PUNCT
ejpam-3206	519	5	2017	2017	NUM
ejpam-3206	519	6	.	.	PUNCT
ejpam-3206	520	1	[	[	X
ejpam-3206	520	2	19	19	NUM
ejpam-3206	520	3	]	]	PUNCT
ejpam-3206	520	4	m.	m.	NOUN
ejpam-3206	520	5	rege	rege	PROPN
ejpam-3206	520	6	and	and	CCONJ
ejpam-3206	520	7	s.	s.	PROPN
ejpam-3206	520	8	chhawchharia	chhawchharia	PROPN
ejpam-3206	520	9	.	.	PUNCT
ejpam-3206	521	1	armendariz	armendariz	PROPN
ejpam-3206	521	2	rings	ring	NOUN
ejpam-3206	521	3	.	.	PUNCT
ejpam-3206	522	1	proc	proc	PROPN
ejpam-3206	522	2	.	.	PUNCT
ejpam-3206	523	1	japan	japan	PROPN
ejpam-3206	523	2	acad	acad	PROPN
ejpam-3206	523	3	.	.	PUNCT
ejpam-3206	524	1	ser	ser	PROPN
ejpam-3206	524	2	.	.	PUNCT
ejpam-3206	525	1	a	a	DET
ejpam-3206	525	2	math	math	NOUN
ejpam-3206	525	3	.	.	PUNCT
ejpam-3206	526	1	sci	sci	PROPN
ejpam-3206	526	2	.	.	PROPN
ejpam-3206	526	3	,	,	PUNCT
ejpam-3206	526	4	73:14–17	73:14–17	NUM
ejpam-3206	526	5	,	,	PUNCT
ejpam-3206	526	6	1997	1997	NUM
ejpam-3206	526	7	.	.	PUNCT
ejpam-3206	527	1	[	[	X
ejpam-3206	527	2	20	20	NUM
ejpam-3206	527	3	]	]	X
ejpam-3206	527	4	r.	r.	PROPN
ejpam-3206	527	5	salem	salem	PROPN
ejpam-3206	527	6	,	,	PUNCT
ejpam-3206	527	7	m.	m.	NOUN
ejpam-3206	527	8	farahat	farahat	NOUN
ejpam-3206	527	9	,	,	PUNCT
ejpam-3206	527	10	and	and	CCONJ
ejpam-3206	527	11	h.	h.	PROPN
ejpam-3206	527	12	abd	abd	PROPN
ejpam-3206	527	13	-	-	PUNCT
ejpam-3206	527	14	elmalk	elmalk	NOUN
ejpam-3206	527	15	.	.	PUNCT
ejpam-3206	528	1	ps	ps	NOUN
ejpam-3206	528	2	-	-	PUNCT
ejpam-3206	528	3	modules	module	NOUN
ejpam-3206	528	4	over	over	ADP
ejpam-3206	528	5	ore	ore	NOUN
ejpam-3206	528	6	extensions	extension	NOUN
ejpam-3206	528	7	and	and	CCONJ
ejpam-3206	528	8	skew	skew	VERB
ejpam-3206	528	9	generalized	generalized	ADJ
ejpam-3206	528	10	power	power	NOUN
ejpam-3206	528	11	series	series	PROPN
ejpam-3206	528	12	rings	ring	NOUN
ejpam-3206	528	13	.	.	PUNCT
ejpam-3206	529	1	int	int	NOUN
ejpam-3206	529	2	.	.	PUNCT
ejpam-3206	530	1	j.	j.	PROPN
ejpam-3206	530	2	math	math	PROPN
ejpam-3206	530	3	.	.	PUNCT
ejpam-3206	531	1	math	math	NOUN
ejpam-3206	531	2	.	.	PUNCT
ejpam-3206	532	1	sci	sci	PROPN
ejpam-3206	532	2	.	.	PROPN
ejpam-3206	532	3	,	,	PUNCT
ejpam-3206	532	4	2015	2015	NUM
ejpam-3206	532	5	.	.	PUNCT
ejpam-3206	533	1	[	[	X
ejpam-3206	533	2	21	21	NUM
ejpam-3206	533	3	]	]	X
ejpam-3206	533	4	e.	e.	PROPN
ejpam-3206	533	5	taft	taft	PROPN
ejpam-3206	533	6	.	.	PUNCT
ejpam-3206	534	1	hurwitz	hurwitz	PROPN
ejpam-3206	534	2	invertibility	invertibility	PROPN
ejpam-3206	534	3	of	of	ADP
ejpam-3206	534	4	linearly	linearly	ADV
ejpam-3206	534	5	recursive	recursive	ADJ
ejpam-3206	534	6	sequences	sequence	NOUN
ejpam-3206	534	7	.	.	PUNCT
ejpam-3206	535	1	congr	congr	PROPN
ejpam-3206	535	2	.	.	PUNCT
ejpam-3206	536	1	numerantium	numerantium	ADJ
ejpam-3206	536	2	,	,	PUNCT
ejpam-3206	536	3	73:37–40	73:37–40	NUM
ejpam-3206	536	4	,	,	PUNCT
ejpam-3206	536	5	1990	1990	NUM
ejpam-3206	536	6	.	.	PUNCT
ejpam-3206	537	1	[	[	X
ejpam-3206	537	2	22	22	NUM
ejpam-3206	537	3	]	]	X
ejpam-3206	537	4	x.	x.	NOUN
ejpam-3206	537	5	weimin	weimin	PROPN
ejpam-3206	537	6	.	.	PUNCT
ejpam-3206	538	1	modules	module	NOUN
ejpam-3206	538	2	with	with	ADP
ejpam-3206	538	3	projective	projective	ADJ
ejpam-3206	538	4	socles	socle	NOUN
ejpam-3206	538	5	.	.	PUNCT
ejpam-3206	539	1	riv	riv	PROPN
ejpam-3206	539	2	.	.	PROPN
ejpam-3206	539	3	math	math	PROPN
ejpam-3206	539	4	.	.	PUNCT
ejpam-3206	540	1	univ	univ	PROPN
ejpam-3206	540	2	.	.	PUNCT
ejpam-3206	541	1	parma	parma	PROPN
ejpam-3206	541	2	(	(	PUNCT
ejpam-3206	541	3	n.s	n.s	PROPN
ejpam-3206	541	4	.	.	PROPN
ejpam-3206	541	5	)	)	PUNCT
ejpam-3206	541	6	,	,	PUNCT
ejpam-3206	541	7	1(5):311	1(5):311	NUM
ejpam-3206	541	8	–	–	PUNCT
ejpam-3206	541	9	315	315	NUM
ejpam-3206	541	10	,	,	PUNCT
ejpam-3206	541	11	1992	1992	NUM
ejpam-3206	541	12	.	.	PUNCT