id	sid	tid	token	lemma	pos
ejpam-2010	1	1	european	european	PROPN
ejpam-2010	1	2	journal	journal	PROPN
ejpam-2010	1	3	of	of	ADP
ejpam-2010	1	4	pure	pure	ADJ
ejpam-2010	1	5	and	and	CCONJ
ejpam-2010	1	6	applied	apply	VERB
ejpam-2010	1	7	mathematics	mathematic	NOUN
ejpam-2010	1	8	vol	vol	NOUN
ejpam-2010	1	9	.	.	PROPN
ejpam-2010	2	1	6	6	NUM
ejpam-2010	2	2	,	,	PUNCT
ejpam-2010	2	3	no	no	INTJ
ejpam-2010	2	4	.	.	NOUN
ejpam-2010	2	5	3	3	NUM
ejpam-2010	2	6	,	,	PUNCT
ejpam-2010	2	7	2013	2013	NUM
ejpam-2010	2	8	,	,	PUNCT
ejpam-2010	2	9	256	256	NUM
ejpam-2010	2	10	-	-	SYM
ejpam-2010	2	11	281	281	NUM
ejpam-2010	2	12	issn	issn	PROPN
ejpam-2010	2	13	1307	1307	NUM
ejpam-2010	2	14	-	-	SYM
ejpam-2010	2	15	5543	5543	NUM
ejpam-2010	2	16	–	–	PUNCT
ejpam-2010	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2010	2	18	morita	morita	PROPN
ejpam-2010	2	19	theory	theory	NOUN
ejpam-2010	2	20	for	for	ADP
ejpam-2010	2	21	rings	ring	NOUN
ejpam-2010	2	22	and	and	CCONJ
ejpam-2010	2	23	semigroups	semigroups	PROPN
ejpam-2010	2	24	yan	yan	PROPN
ejpam-2010	2	25	hui	hui	PROPN
ejpam-2010	2	26	wang1	wang1	PROPN
ejpam-2010	2	27	,	,	PUNCT
ejpam-2010	2	28	kar	kar	PROPN
ejpam-2010	2	29	ping	ping	PROPN
ejpam-2010	2	30	shum2,∗	shum2,∗	PROPN
ejpam-2010	2	31	,	,	PUNCT
ejpam-2010	2	32	xue	xue	PROPN
ejpam-2010	2	33	ming	ming	PROPN
ejpam-2010	2	34	ren	ren	PROPN
ejpam-2010	2	35	3	3	NUM
ejpam-2010	2	36	1	1	NUM
ejpam-2010	2	37	college	college	NOUN
ejpam-2010	2	38	of	of	ADP
ejpam-2010	2	39	information	information	NOUN
ejpam-2010	2	40	and	and	CCONJ
ejpam-2010	2	41	engineering	engineering	NOUN
ejpam-2010	2	42	science	science	NOUN
ejpam-2010	2	43	,	,	PUNCT
ejpam-2010	2	44	shangdong	shangdong	PROPN
ejpam-2010	2	45	university	university	PROPN
ejpam-2010	2	46	of	of	ADP
ejpam-2010	2	47	science	science	NOUN
ejpam-2010	2	48	and	and	CCONJ
ejpam-2010	2	49	technology	technology	NOUN
ejpam-2010	2	50	,	,	PUNCT
ejpam-2010	2	51	qingdao	qingdao	PROPN
ejpam-2010	2	52	,	,	PUNCT
ejpam-2010	2	53	266590	266590	NUM
ejpam-2010	2	54	,	,	PUNCT
ejpam-2010	2	55	p.	p.	PROPN
ejpam-2010	2	56	r.	r.	PROPN
ejpam-2010	3	1	china	china	PROPN
ejpam-2010	3	2	2	2	NUM
ejpam-2010	3	3	instutute	instutute	NOUN
ejpam-2010	3	4	of	of	ADP
ejpam-2010	3	5	mathematics	mathematics	PROPN
ejpam-2010	3	6	,	,	PUNCT
ejpam-2010	3	7	yunnan	yunnan	PROPN
ejpam-2010	3	8	university	university	PROPN
ejpam-2010	3	9	,	,	PUNCT
ejpam-2010	3	10	kunming	kunming	NOUN
ejpam-2010	3	11	,	,	PUNCT
ejpam-2010	3	12	650091	650091	NUM
ejpam-2010	3	13	,	,	PUNCT
ejpam-2010	3	14	p.	p.	PROPN
ejpam-2010	3	15	r.	r.	PROPN
ejpam-2010	4	1	china	china	PROPN
ejpam-2010	4	2	3	3	NUM
ejpam-2010	4	3	department	department	PROPN
ejpam-2010	4	4	of	of	ADP
ejpam-2010	4	5	mathematics	mathematics	PROPN
ejpam-2010	4	6	,	,	PUNCT
ejpam-2010	4	7	xi’an	xi’an	PROPN
ejpam-2010	4	8	university	university	PROPN
ejpam-2010	4	9	of	of	ADP
ejpam-2010	4	10	architecture	architecture	NOUN
ejpam-2010	4	11	and	and	CCONJ
ejpam-2010	4	12	technology	technology	NOUN
ejpam-2010	4	13	,	,	PUNCT
ejpam-2010	4	14	xi’an	xi’an	PROPN
ejpam-2010	4	15	,	,	PUNCT
ejpam-2010	4	16	710055	710055	NUM
ejpam-2010	4	17	,	,	PUNCT
ejpam-2010	4	18	p.	p.	NOUN
ejpam-2010	4	19	r.china	r.china	NOUN
ejpam-2010	4	20	abstract	abstract	ADJ
ejpam-2010	4	21	.	.	PUNCT
ejpam-2010	5	1	the	the	DET
ejpam-2010	5	2	notion	notion	NOUN
ejpam-2010	5	3	of	of	ADP
ejpam-2010	5	4	morita	morita	PROPN
ejpam-2010	5	5	equivalence	equivalence	NOUN
ejpam-2010	5	6	for	for	ADP
ejpam-2010	5	7	rings	ring	NOUN
ejpam-2010	5	8	defines	define	VERB
ejpam-2010	5	9	a	a	DET
ejpam-2010	5	10	relationship	relationship	NOUN
ejpam-2010	5	11	between	between	ADP
ejpam-2010	5	12	rings	ring	NOUN
ejpam-2010	5	13	in	in	ADP
ejpam-2010	5	14	terms	term	NOUN
ejpam-2010	5	15	of	of	ADP
ejpam-2010	5	16	their	their	PRON
ejpam-2010	5	17	module	module	NOUN
ejpam-2010	5	18	categories	category	NOUN
ejpam-2010	5	19	being	be	AUX
ejpam-2010	5	20	equivalent	equivalent	ADJ
ejpam-2010	5	21	in	in	ADP
ejpam-2010	5	22	the	the	DET
ejpam-2010	5	23	sense	sense	NOUN
ejpam-2010	5	24	of	of	ADP
ejpam-2010	5	25	category	category	NOUN
ejpam-2010	5	26	theory	theory	NOUN
ejpam-2010	5	27	.	.	PUNCT
ejpam-2010	6	1	to	to	PART
ejpam-2010	6	2	characterise	characterise	VERB
ejpam-2010	6	3	morita	morita	PROPN
ejpam-2010	6	4	equivalence	equivalence	NOUN
ejpam-2010	6	5	for	for	ADP
ejpam-2010	6	6	rings	ring	NOUN
ejpam-2010	6	7	,	,	PUNCT
ejpam-2010	6	8	morita	morita	PROPN
ejpam-2010	6	9	contexts	contexts	PROPN
ejpam-2010	6	10	and	and	CCONJ
ejpam-2010	6	11	factors	factor	NOUN
ejpam-2010	6	12	on	on	ADP
ejpam-2010	6	13	various	various	ADJ
ejpam-2010	6	14	bimodules	bimodule	NOUN
ejpam-2010	6	15	have	have	AUX
ejpam-2010	6	16	emerged	emerge	VERB
ejpam-2010	6	17	.	.	PUNCT
ejpam-2010	7	1	as	as	ADP
ejpam-2010	7	2	a	a	DET
ejpam-2010	7	3	generalisation	generalisation	NOUN
ejpam-2010	7	4	of	of	ADP
ejpam-2010	7	5	morita	morita	PROPN
ejpam-2010	7	6	equivalence	equivalence	PROPN
ejpam-2010	7	7	,	,	PUNCT
ejpam-2010	7	8	the	the	DET
ejpam-2010	7	9	concept	concept	NOUN
ejpam-2010	7	10	of	of	ADP
ejpam-2010	7	11	morita	morita	PROPN
ejpam-2010	7	12	-	-	PUNCT
ejpam-2010	7	13	like	like	ADJ
ejpam-2010	7	14	equivalences	equivalence	NOUN
ejpam-2010	7	15	was	be	AUX
ejpam-2010	7	16	developed	develop	VERB
ejpam-2010	7	17	to	to	PART
ejpam-2010	7	18	investigate	investigate	VERB
ejpam-2010	7	19	xst	xst	NOUN
ejpam-2010	7	20	-	-	PUNCT
ejpam-2010	7	21	rings	ring	NOUN
ejpam-2010	7	22	.	.	PUNCT
ejpam-2010	8	1	the	the	DET
ejpam-2010	8	2	study	study	NOUN
ejpam-2010	8	3	of	of	ADP
ejpam-2010	8	4	morita	morita	PROPN
ejpam-2010	8	5	invariants	invariants	PROPN
ejpam-2010	8	6	is	be	AUX
ejpam-2010	8	7	also	also	ADV
ejpam-2010	8	8	an	an	DET
ejpam-2010	8	9	important	important	ADJ
ejpam-2010	8	10	branch	branch	NOUN
ejpam-2010	8	11	in	in	ADP
ejpam-2010	8	12	the	the	DET
ejpam-2010	8	13	morita	morita	PROPN
ejpam-2010	8	14	theory	theory	NOUN
ejpam-2010	8	15	for	for	ADP
ejpam-2010	8	16	rings	ring	NOUN
ejpam-2010	8	17	.	.	PUNCT
ejpam-2010	9	1	analogous	analogous	ADJ
ejpam-2010	9	2	to	to	ADP
ejpam-2010	9	3	the	the	DET
ejpam-2010	9	4	morita	morita	PROPN
ejpam-2010	9	5	theory	theory	NOUN
ejpam-2010	9	6	for	for	ADP
ejpam-2010	9	7	rings	ring	NOUN
ejpam-2010	9	8	,	,	PUNCT
ejpam-2010	9	9	morita	morita	PROPN
ejpam-2010	9	10	equivalence	equivalence	NOUN
ejpam-2010	9	11	and	and	CCONJ
ejpam-2010	9	12	morita	morita	PROPN
ejpam-2010	9	13	invariants	invariants	PROPN
ejpam-2010	9	14	for	for	ADP
ejpam-2010	9	15	semigroups	semigroup	NOUN
ejpam-2010	9	16	have	have	AUX
ejpam-2010	9	17	been	be	AUX
ejpam-2010	9	18	developed	develop	VERB
ejpam-2010	9	19	.	.	PUNCT
ejpam-2010	10	1	four	four	NUM
ejpam-2010	10	2	major	major	ADJ
ejpam-2010	10	3	approaches	approach	NOUN
ejpam-2010	10	4	to	to	ADP
ejpam-2010	10	5	the	the	DET
ejpam-2010	10	6	characterisations	characterisation	NOUN
ejpam-2010	10	7	of	of	ADP
ejpam-2010	10	8	morita	morita	PROPN
ejpam-2010	10	9	equivalence	equivalence	NOUN
ejpam-2010	10	10	between	between	ADP
ejpam-2010	10	11	semigroups	semigroup	NOUN
ejpam-2010	10	12	have	have	AUX
ejpam-2010	10	13	appeared	appear	VERB
ejpam-2010	10	14	.	.	PUNCT
ejpam-2010	11	1	they	they	PRON
ejpam-2010	11	2	are	be	AUX
ejpam-2010	11	3	categories	category	NOUN
ejpam-2010	11	4	of	of	ADP
ejpam-2010	11	5	acts	act	NOUN
ejpam-2010	11	6	over	over	ADP
ejpam-2010	11	7	semigroups	semigroup	NOUN
ejpam-2010	11	8	,	,	PUNCT
ejpam-2010	11	9	morita	morita	PROPN
ejpam-2010	11	10	contexts	contexts	PROPN
ejpam-2010	11	11	,	,	PUNCT
ejpam-2010	11	12	cauchy	cauchy	ADJ
ejpam-2010	11	13	completions	completion	NOUN
ejpam-2010	11	14	and	and	CCONJ
ejpam-2010	11	15	enlargements	enlargement	NOUN
ejpam-2010	11	16	.	.	PUNCT
ejpam-2010	12	1	the	the	DET
ejpam-2010	12	2	aim	aim	NOUN
ejpam-2010	12	3	of	of	ADP
ejpam-2010	12	4	this	this	DET
ejpam-2010	12	5	article	article	NOUN
ejpam-2010	12	6	is	be	AUX
ejpam-2010	12	7	to	to	PART
ejpam-2010	12	8	make	make	VERB
ejpam-2010	12	9	a	a	DET
ejpam-2010	12	10	brief	brief	ADJ
ejpam-2010	12	11	survey	survey	NOUN
ejpam-2010	12	12	of	of	ADP
ejpam-2010	12	13	morita	morita	PROPN
ejpam-2010	12	14	equivalence	equivalence	NOUN
ejpam-2010	12	15	for	for	ADP
ejpam-2010	12	16	rings	ring	NOUN
ejpam-2010	12	17	not	not	PART
ejpam-2010	12	18	necessary	necessary	ADJ
ejpam-2010	12	19	with	with	ADP
ejpam-2010	12	20	an	an	DET
ejpam-2010	12	21	identity	identity	NOUN
ejpam-2010	12	22	and	and	CCONJ
ejpam-2010	12	23	semigroups	semigroup	NOUN
ejpam-2010	12	24	.	.	PUNCT
ejpam-2010	13	1	2010	2010	NUM
ejpam-2010	13	2	mathematics	mathematic	NOUN
ejpam-2010	13	3	subject	subject	NOUN
ejpam-2010	13	4	classifications	classification	NOUN
ejpam-2010	13	5	:	:	PUNCT
ejpam-2010	13	6	20m10	20m10	NUM
ejpam-2010	13	7	key	key	ADJ
ejpam-2010	13	8	words	word	NOUN
ejpam-2010	13	9	and	and	CCONJ
ejpam-2010	13	10	phrases	phrase	NOUN
ejpam-2010	13	11	:	:	PUNCT
ejpam-2010	13	12	morita	morita	PROPN
ejpam-2010	13	13	equivalence	equivalence	PROPN
ejpam-2010	13	14	,	,	PUNCT
ejpam-2010	13	15	morita	morita	NOUN
ejpam-2010	13	16	-	-	PUNCT
ejpam-2010	13	17	like	like	ADJ
ejpam-2010	13	18	equivalence	equivalence	NOUN
ejpam-2010	13	19	,	,	PUNCT
ejpam-2010	13	20	acts	act	NOUN
ejpam-2010	13	21	,	,	PUNCT
ejpam-2010	13	22	modules	module	NOUN
ejpam-2010	13	23	,	,	PUNCT
ejpam-2010	13	24	xst	xst	PROPN
ejpam-2010	13	25	-	-	PUNCT
ejpam-2010	13	26	rings	ring	NOUN
ejpam-2010	13	27	1	1	NUM
ejpam-2010	13	28	.	.	PUNCT
ejpam-2010	13	29	introduction	introduction	NOUN
ejpam-2010	13	30	the	the	DET
ejpam-2010	13	31	classical	classical	ADJ
ejpam-2010	13	32	morita	morita	PROPN
ejpam-2010	13	33	theory	theory	NOUN
ejpam-2010	13	34	for	for	ADP
ejpam-2010	13	35	rings	ring	NOUN
ejpam-2010	13	36	has	have	AUX
ejpam-2010	13	37	been	be	AUX
ejpam-2010	13	38	recognised	recognise	VERB
ejpam-2010	13	39	as	as	ADP
ejpam-2010	13	40	one	one	NUM
ejpam-2010	13	41	of	of	ADP
ejpam-2010	13	42	the	the	DET
ejpam-2010	13	43	most	most	ADV
ejpam-2010	13	44	important	important	ADJ
ejpam-2010	13	45	and	and	CCONJ
ejpam-2010	13	46	fundamental	fundamental	ADJ
ejpam-2010	13	47	tools	tool	NOUN
ejpam-2010	13	48	in	in	ADP
ejpam-2010	13	49	studying	study	VERB
ejpam-2010	13	50	the	the	DET
ejpam-2010	13	51	structure	structure	NOUN
ejpam-2010	13	52	of	of	ADP
ejpam-2010	13	53	rings	ring	NOUN
ejpam-2010	13	54	.	.	PUNCT
ejpam-2010	14	1	in	in	ADP
ejpam-2010	14	2	the	the	DET
ejpam-2010	14	3	paper	paper	NOUN
ejpam-2010	14	4	[	[	X
ejpam-2010	14	5	34	34	NUM
ejpam-2010	14	6	]	]	X
ejpam-2010	14	7	morita	morita	PROPN
ejpam-2010	14	8	firstly	firstly	ADV
ejpam-2010	14	9	established	establish	VERB
ejpam-2010	14	10	the	the	DET
ejpam-2010	14	11	morita	morita	PROPN
ejpam-2010	14	12	equivalent	equivalent	PROPN
ejpam-2010	14	13	theory	theory	NOUN
ejpam-2010	14	14	for	for	ADP
ejpam-2010	14	15	unital	unital	ADJ
ejpam-2010	14	16	rings	ring	NOUN
ejpam-2010	14	17	,	,	PUNCT
ejpam-2010	14	18	that	that	ADV
ejpam-2010	14	19	is	is	ADV
ejpam-2010	14	20	,	,	PUNCT
ejpam-2010	14	21	rings	ring	NOUN
ejpam-2010	14	22	with	with	ADP
ejpam-2010	14	23	identity	identity	NOUN
ejpam-2010	14	24	.	.	PUNCT
ejpam-2010	15	1	there	there	PRON
ejpam-2010	15	2	exist	exist	VERB
ejpam-2010	15	3	two	two	NUM
ejpam-2010	15	4	angles	angle	NOUN
ejpam-2010	15	5	to	to	PART
ejpam-2010	15	6	generalise	generalise	VERB
ejpam-2010	15	7	the	the	DET
ejpam-2010	15	8	morita	morita	PROPN
ejpam-2010	15	9	theory	theory	NOUN
ejpam-2010	15	10	for	for	ADP
ejpam-2010	15	11	rings	ring	NOUN
ejpam-2010	15	12	.	.	PUNCT
ejpam-2010	16	1	one	one	NUM
ejpam-2010	16	2	is	be	AUX
ejpam-2010	16	3	to	to	PART
ejpam-2010	16	4	investigate	investigate	VERB
ejpam-2010	16	5	the	the	DET
ejpam-2010	16	6	morita	morita	PROPN
ejpam-2010	16	7	theory	theory	NOUN
ejpam-2010	16	8	for	for	ADP
ejpam-2010	16	9	different	different	ADJ
ejpam-2010	16	10	rings	ring	NOUN
ejpam-2010	16	11	.	.	PUNCT
ejpam-2010	17	1	in	in	ADP
ejpam-2010	17	2	1974	1974	NUM
ejpam-2010	17	3	,	,	PUNCT
ejpam-2010	17	4	fuller	full	ADJ
ejpam-2010	17	5	[	[	X
ejpam-2010	17	6	10	10	NUM
ejpam-2010	17	7	]	]	PUNCT
ejpam-2010	17	8	made	make	VERB
ejpam-2010	17	9	a	a	DET
ejpam-2010	17	10	first	first	ADJ
ejpam-2010	17	11	step	step	NOUN
ejpam-2010	17	12	in	in	ADP
ejpam-2010	17	13	extending	extend	VERB
ejpam-2010	17	14	the	the	DET
ejpam-2010	17	15	theory	theory	NOUN
ejpam-2010	17	16	of	of	ADP
ejpam-2010	17	17	morita	morita	PROPN
ejpam-2010	17	18	equivalence	equivalence	NOUN
ejpam-2010	17	19	to	to	ADP
ejpam-2010	17	20	rings	ring	NOUN
ejpam-2010	17	21	without	without	ADP
ejpam-2010	17	22	identity	identity	NOUN
ejpam-2010	17	23	.	.	PUNCT
ejpam-2010	18	1	he	he	PRON
ejpam-2010	18	2	considered	consider	VERB
ejpam-2010	18	3	the	the	DET
ejpam-2010	18	4	categorical	categorical	ADJ
ejpam-2010	18	5	equivalences	equivalence	NOUN
ejpam-2010	18	6	between	between	ADP
ejpam-2010	18	7	∗corresponding	∗corresponde	VERB
ejpam-2010	18	8	author	author	NOUN
ejpam-2010	18	9	.	.	PUNCT
ejpam-2010	19	1	email	email	NOUN
ejpam-2010	19	2	addresses	address	NOUN
ejpam-2010	19	3	:	:	PUNCT
ejpam-2010	19	4	yanhuiwang@sdust.edu.cn	yanhuiwang@sdust.edu.cn	PROPN
ejpam-2010	19	5	(	(	PUNCT
ejpam-2010	19	6	y.	y.	PROPN
ejpam-2010	19	7	wang	wang	PROPN
ejpam-2010	19	8	)	)	PUNCT
ejpam-2010	19	9	,	,	PUNCT
ejpam-2010	19	10	kpshum@ynu.edu.cn	kpshum@ynu.edu.cn	PROPN
ejpam-2010	19	11	(	(	PUNCT
ejpam-2010	19	12	k.	k.	PROPN
ejpam-2010	19	13	shum	shum	PROPN
ejpam-2010	19	14	)	)	PUNCT
ejpam-2010	19	15	,	,	PUNCT
ejpam-2010	19	16	xmren@xauat.edu.cn	xmren@xauat.edu.cn	X
ejpam-2010	19	17	(	(	PUNCT
ejpam-2010	19	18	x.	x.	NOUN
ejpam-2010	19	19	ren	ren	PROPN
ejpam-2010	19	20	)	)	PUNCT
ejpam-2010	19	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2010	20	1	256	256	NUM
ejpam-2010	20	2	c	c	X
ejpam-2010	20	3	©	©	PROPN
ejpam-2010	20	4	2013	2013	NUM
ejpam-2010	20	5	ejpam	ejpam	NOUN
ejpam-2010	20	6	all	all	DET
ejpam-2010	20	7	rights	right	NOUN
ejpam-2010	20	8	reserved	reserve	VERB
ejpam-2010	20	9	.	.	PUNCT
ejpam-2010	21	1	y.	y.	PROPN
ejpam-2010	21	2	wang	wang	PROPN
ejpam-2010	21	3	,	,	PUNCT
ejpam-2010	21	4	k.	k.	PROPN
ejpam-2010	21	5	shum	shum	PROPN
ejpam-2010	21	6	,	,	PUNCT
ejpam-2010	21	7	x.	x.	PROPN
ejpam-2010	21	8	ren	ren	PROPN
ejpam-2010	21	9	/	/	SYM
ejpam-2010	21	10	eur	eur	PROPN
ejpam-2010	21	11	.	.	PUNCT
ejpam-2010	22	1	j.	j.	PROPN
ejpam-2010	22	2	pure	pure	PROPN
ejpam-2010	22	3	appl	appl	PROPN
ejpam-2010	22	4	.	.	PROPN
ejpam-2010	22	5	math	math	PROPN
ejpam-2010	22	6	,	,	PUNCT
ejpam-2010	22	7	6	6	NUM
ejpam-2010	22	8	(	(	PUNCT
ejpam-2010	22	9	2013	2013	NUM
ejpam-2010	22	10	)	)	PUNCT
ejpam-2010	22	11	,	,	PUNCT
ejpam-2010	22	12	256	256	NUM
ejpam-2010	22	13	-	-	SYM
ejpam-2010	22	14	281	281	NUM
ejpam-2010	22	15	257	257	NUM
ejpam-2010	22	16	the	the	DET
ejpam-2010	22	17	complete	complete	ADJ
ejpam-2010	22	18	additive	additive	ADJ
ejpam-2010	22	19	subcategory	subcategory	NOUN
ejpam-2010	22	20	of	of	ADP
ejpam-2010	22	21	rings	ring	NOUN
ejpam-2010	22	22	which	which	PRON
ejpam-2010	22	23	do	do	AUX
ejpam-2010	22	24	not	not	PART
ejpam-2010	22	25	necessarily	necessarily	ADV
ejpam-2010	22	26	possess	possess	VERB
ejpam-2010	22	27	an	an	DET
ejpam-2010	22	28	identity	identity	NOUN
ejpam-2010	22	29	,	,	PUNCT
ejpam-2010	22	30	and	and	CCONJ
ejpam-2010	22	31	the	the	DET
ejpam-2010	22	32	category	category	NOUN
ejpam-2010	22	33	of	of	ADP
ejpam-2010	22	34	unital	unital	ADJ
ejpam-2010	22	35	modules	module	NOUN
ejpam-2010	22	36	over	over	ADP
ejpam-2010	22	37	rings	ring	NOUN
ejpam-2010	22	38	with	with	ADP
ejpam-2010	22	39	identity	identity	NOUN
ejpam-2010	22	40	.	.	PUNCT
ejpam-2010	23	1	such	such	DET
ejpam-2010	23	2	a	a	DET
ejpam-2010	23	3	result	result	NOUN
ejpam-2010	23	4	was	be	AUX
ejpam-2010	23	5	further	far	ADV
ejpam-2010	23	6	strengthened	strengthen	VERB
ejpam-2010	23	7	and	and	CCONJ
ejpam-2010	23	8	enriched	enrich	VERB
ejpam-2010	23	9	by	by	ADP
ejpam-2010	23	10	sato	sato	NOUN
ejpam-2010	23	11	[	[	X
ejpam-2010	23	12	41	41	NUM
ejpam-2010	23	13	]	]	PUNCT
ejpam-2010	23	14	and	and	CCONJ
ejpam-2010	23	15	azumaya	azumaya	NOUN
ejpam-2010	24	1	[	[	X
ejpam-2010	24	2	4	4	NUM
ejpam-2010	24	3	]	]	PUNCT
ejpam-2010	24	4	.	.	PUNCT
ejpam-2010	25	1	along	along	ADP
ejpam-2010	25	2	this	this	DET
ejpam-2010	25	3	direction	direction	NOUN
ejpam-2010	25	4	fruitful	fruitful	ADJ
ejpam-2010	25	5	results	result	NOUN
ejpam-2010	25	6	about	about	ADP
ejpam-2010	25	7	morita	morita	PROPN
ejpam-2010	25	8	theory	theory	NOUN
ejpam-2010	25	9	for	for	ADP
ejpam-2010	25	10	various	various	ADJ
ejpam-2010	25	11	rings	ring	NOUN
ejpam-2010	25	12	have	have	AUX
ejpam-2010	25	13	been	be	AUX
ejpam-2010	25	14	obtained	obtain	VERB
ejpam-2010	25	15	by	by	ADP
ejpam-2010	25	16	many	many	ADJ
ejpam-2010	25	17	authors	author	NOUN
ejpam-2010	25	18	.	.	PUNCT
ejpam-2010	26	1	in	in	ADP
ejpam-2010	26	2	1983	1983	NUM
ejpam-2010	26	3	,	,	PUNCT
ejpam-2010	26	4	abrams	abrams	PROPN
ejpam-2010	26	5	initiated	initiate	VERB
ejpam-2010	26	6	the	the	DET
ejpam-2010	26	7	study	study	NOUN
ejpam-2010	26	8	of	of	ADP
ejpam-2010	26	9	morita	morita	PROPN
ejpam-2010	26	10	theory	theory	PROPN
ejpam-2010	26	11	for	for	ADP
ejpam-2010	26	12	rings	ring	NOUN
ejpam-2010	26	13	in	in	ADP
ejpam-2010	26	14	which	which	PRON
ejpam-2010	26	15	a	a	DET
ejpam-2010	26	16	set	set	NOUN
ejpam-2010	26	17	of	of	ADP
ejpam-2010	26	18	commuting	commute	VERB
ejpam-2010	26	19	idempotents	idempotent	NOUN
ejpam-2010	26	20	is	be	AUX
ejpam-2010	26	21	given	give	VERB
ejpam-2010	26	22	such	such	ADJ
ejpam-2010	26	23	that	that	SCONJ
ejpam-2010	26	24	every	every	DET
ejpam-2010	26	25	element	element	NOUN
ejpam-2010	26	26	of	of	ADP
ejpam-2010	26	27	the	the	DET
ejpam-2010	26	28	ring	ring	NOUN
ejpam-2010	26	29	admits	admit	VERB
ejpam-2010	26	30	one	one	NUM
ejpam-2010	26	31	of	of	ADP
ejpam-2010	26	32	these	these	DET
ejpam-2010	26	33	idempotents	idempotent	NOUN
ejpam-2010	26	34	as	as	ADP
ejpam-2010	26	35	a	a	DET
ejpam-2010	26	36	two	two	NUM
ejpam-2010	26	37	-	-	PUNCT
ejpam-2010	26	38	sided	sided	ADJ
ejpam-2010	26	39	unit	unit	NOUN
ejpam-2010	26	40	,	,	PUNCT
ejpam-2010	26	41	and	and	CCONJ
ejpam-2010	26	42	the	the	DET
ejpam-2010	26	43	categories	category	NOUN
ejpam-2010	26	44	of	of	ADP
ejpam-2010	26	45	all	all	DET
ejpam-2010	26	46	left	leave	VERB
ejpam-2010	26	47	modules	module	NOUN
ejpam-2010	26	48	over	over	ADP
ejpam-2010	26	49	these	these	DET
ejpam-2010	26	50	rings	ring	NOUN
ejpam-2010	26	51	which	which	PRON
ejpam-2010	26	52	are	be	AUX
ejpam-2010	26	53	unitary	unitary	ADJ
ejpam-2010	26	54	in	in	ADP
ejpam-2010	26	55	a	a	DET
ejpam-2010	26	56	natural	natural	ADJ
ejpam-2010	26	57	sense	sense	NOUN
ejpam-2010	26	58	.	.	PUNCT
ejpam-2010	27	1	ánh	ánh	NOUN
ejpam-2010	27	2	and	and	CCONJ
ejpam-2010	27	3	márki	márki	NOUN
ejpam-2010	28	1	[	[	X
ejpam-2010	28	2	3	3	NUM
ejpam-2010	28	3	]	]	X
ejpam-2010	28	4	further	further	ADJ
ejpam-2010	28	5	generalised	generalise	VERB
ejpam-2010	28	6	abrams	abrams	PROPN
ejpam-2010	28	7	’s	’s	PART
ejpam-2010	28	8	result	result	NOUN
ejpam-2010	28	9	to	to	ADP
ejpam-2010	28	10	rings	ring	NOUN
ejpam-2010	28	11	with	with	ADP
ejpam-2010	28	12	local	local	ADJ
ejpam-2010	28	13	units	unit	NOUN
ejpam-2010	28	14	by	by	ADP
ejpam-2010	28	15	weaken	weaken	VERB
ejpam-2010	28	16	the	the	DET
ejpam-2010	28	17	condition	condition	NOUN
ejpam-2010	28	18	of	of	ADP
ejpam-2010	28	19	commutativity	commutativity	NOUN
ejpam-2010	28	20	of	of	ADP
ejpam-2010	28	21	idempotents	idempotent	NOUN
ejpam-2010	28	22	.	.	PUNCT
ejpam-2010	29	1	in	in	ADP
ejpam-2010	29	2	1991	1991	NUM
ejpam-2010	29	3	,	,	PUNCT
ejpam-2010	29	4	garcia	garcia	PROPN
ejpam-2010	29	5	and	and	CCONJ
ejpam-2010	29	6	simòn	simòn	VERB
ejpam-2010	29	7	[	[	X
ejpam-2010	29	8	14	14	NUM
ejpam-2010	29	9	]	]	PUNCT
ejpam-2010	29	10	made	make	VERB
ejpam-2010	29	11	use	use	NOUN
ejpam-2010	29	12	of	of	ADP
ejpam-2010	29	13	a	a	DET
ejpam-2010	29	14	completely	completely	ADV
ejpam-2010	29	15	new	new	ADJ
ejpam-2010	29	16	technique	technique	NOUN
ejpam-2010	29	17	of	of	ADP
ejpam-2010	29	18	non	non	ADJ
ejpam-2010	29	19	-	-	ADJ
ejpam-2010	29	20	commutative	commutative	ADJ
ejpam-2010	29	21	localisations	localisation	NOUN
ejpam-2010	29	22	to	to	PART
ejpam-2010	29	23	build	build	VERB
ejpam-2010	29	24	the	the	DET
ejpam-2010	29	25	morita	morita	PROPN
ejpam-2010	29	26	theory	theory	NOUN
ejpam-2010	29	27	for	for	ADP
ejpam-2010	29	28	idempotent	idempotent	ADJ
ejpam-2010	29	29	rings	ring	NOUN
ejpam-2010	29	30	.	.	PUNCT
ejpam-2010	30	1	in	in	ADP
ejpam-2010	30	2	the	the	DET
ejpam-2010	30	3	last	last	ADJ
ejpam-2010	30	4	two	two	NUM
ejpam-2010	30	5	decades	decade	NOUN
ejpam-2010	30	6	,	,	PUNCT
ejpam-2010	30	7	other	other	ADJ
ejpam-2010	30	8	generalisations	generalisation	NOUN
ejpam-2010	30	9	of	of	ADP
ejpam-2010	30	10	morita	morita	PROPN
ejpam-2010	30	11	theory	theory	NOUN
ejpam-2010	30	12	have	have	AUX
ejpam-2010	30	13	been	be	AUX
ejpam-2010	30	14	widely	widely	ADV
ejpam-2010	30	15	studied	study	VERB
ejpam-2010	30	16	by	by	ADP
ejpam-2010	30	17	komatsu	komatsu	NOUN
ejpam-2010	30	18	[	[	X
ejpam-2010	30	19	17	17	NUM
ejpam-2010	30	20	]	]	PUNCT
ejpam-2010	30	21	,	,	PUNCT
ejpam-2010	30	22	kguno	kguno	VERB
ejpam-2010	31	1	[	[	X
ejpam-2010	31	2	18	18	NUM
ejpam-2010	31	3	]	]	PUNCT
ejpam-2010	31	4	,	,	PUNCT
ejpam-2010	31	5	nobusawa	nobusawa	PROPN
ejpam-2010	32	1	[	[	X
ejpam-2010	32	2	35	35	NUM
ejpam-2010	32	3	]	]	PUNCT
ejpam-2010	32	4	,	,	PUNCT
ejpam-2010	32	5	pawathi	pawathi	ADJ
ejpam-2010	32	6	and	and	CCONJ
ejpam-2010	32	7	ramakrishra	ramakrishra	NOUN
ejpam-2010	32	8	rao	rao	NOUN
ejpam-2010	33	1	[	[	X
ejpam-2010	33	2	36	36	NUM
ejpam-2010	33	3	]	]	PUNCT
ejpam-2010	33	4	,	,	PUNCT
ejpam-2010	33	5	garcia	garcia	PROPN
ejpam-2010	34	1	[	[	X
ejpam-2010	34	2	12	12	NUM
ejpam-2010	34	3	]	]	PUNCT
ejpam-2010	34	4	,	,	PUNCT
ejpam-2010	34	5	xu	xu	INTJ
ejpam-2010	34	6	,	,	PUNCT
ejpam-2010	34	7	shum	shum	NOUN
ejpam-2010	34	8	and	and	CCONJ
ejpam-2010	34	9	turner	turner	PROPN
ejpam-2010	34	10	-	-	PUNCT
ejpam-2010	34	11	smith	smith	PROPN
ejpam-2010	35	1	[	[	X
ejpam-2010	35	2	49	49	NUM
ejpam-2010	35	3	]	]	PUNCT
ejpam-2010	35	4	and	and	CCONJ
ejpam-2010	35	5	so	so	ADV
ejpam-2010	35	6	on	on	ADV
ejpam-2010	35	7	.	.	PUNCT
ejpam-2010	36	1	recently	recently	ADV
ejpam-2010	36	2	,	,	PUNCT
ejpam-2010	36	3	quillen	quillen	VERB
ejpam-2010	37	1	[	[	X
ejpam-2010	37	2	38	38	NUM
ejpam-2010	37	3	]	]	PUNCT
ejpam-2010	37	4	studied	study	VERB
ejpam-2010	37	5	non	non	ADJ
ejpam-2010	37	6	-	-	ADJ
ejpam-2010	37	7	unital	unital	ADJ
ejpam-2010	37	8	rings	ring	NOUN
ejpam-2010	37	9	and	and	CCONJ
ejpam-2010	37	10	morita	morita	PROPN
ejpam-2010	37	11	invariance	invariance	PROPN
ejpam-2010	37	12	by	by	ADP
ejpam-2010	37	13	homotopy	homotopy	NOUN
ejpam-2010	37	14	categories	category	NOUN
ejpam-2010	37	15	.	.	PUNCT
ejpam-2010	38	1	the	the	DET
ejpam-2010	38	2	other	other	ADJ
ejpam-2010	38	3	way	way	NOUN
ejpam-2010	38	4	to	to	PART
ejpam-2010	38	5	generalise	generalise	VERB
ejpam-2010	38	6	the	the	DET
ejpam-2010	38	7	morita	morita	PROPN
ejpam-2010	38	8	theory	theory	NOUN
ejpam-2010	38	9	for	for	ADP
ejpam-2010	38	10	rings	ring	NOUN
ejpam-2010	38	11	is	be	AUX
ejpam-2010	38	12	to	to	PART
ejpam-2010	38	13	describe	describe	VERB
ejpam-2010	38	14	the	the	DET
ejpam-2010	38	15	morita	morita	NOUN
ejpam-2010	38	16	equivalence	equivalence	NOUN
ejpam-2010	38	17	in	in	ADP
ejpam-2010	38	18	terms	term	NOUN
ejpam-2010	38	19	of	of	ADP
ejpam-2010	38	20	different	different	ADJ
ejpam-2010	38	21	full	full	ADJ
ejpam-2010	38	22	subcategories	subcategorie	NOUN
ejpam-2010	38	23	of	of	ADP
ejpam-2010	38	24	rings	ring	NOUN
ejpam-2010	38	25	.	.	PUNCT
ejpam-2010	39	1	for	for	ADP
ejpam-2010	39	2	example	example	NOUN
ejpam-2010	39	3	,	,	PUNCT
ejpam-2010	39	4	in	in	ADP
ejpam-2010	39	5	[	[	X
ejpam-2010	39	6	10	10	NUM
ejpam-2010	39	7	]	]	PUNCT
ejpam-2010	39	8	and	and	CCONJ
ejpam-2010	39	9	[	[	X
ejpam-2010	39	10	32	32	NUM
ejpam-2010	39	11	]	]	PUNCT
ejpam-2010	39	12	they	they	PRON
ejpam-2010	39	13	chose	choose	VERB
ejpam-2010	39	14	a	a	DET
ejpam-2010	39	15	different	different	ADJ
ejpam-2010	39	16	bimodule	bimodule	NOUN
ejpam-2010	39	17	p	p	NOUN
ejpam-2010	39	18	to	to	PART
ejpam-2010	39	19	describe	describe	VERB
ejpam-2010	39	20	the	the	DET
ejpam-2010	39	21	category	category	NOUN
ejpam-2010	39	22	equivalences	equivalence	NOUN
ejpam-2010	39	23	of	of	ADP
ejpam-2010	39	24	modules	module	NOUN
ejpam-2010	39	25	via	via	ADP
ejpam-2010	39	26	the	the	DET
ejpam-2010	39	27	functors	functors	PROPN
ejpam-2010	39	28	p⊗−	p⊗−	PROPN
ejpam-2010	39	29	and	and	CCONJ
ejpam-2010	39	30	hom(p,−	hom(p,−	NOUN
ejpam-2010	39	31	)	)	PUNCT
ejpam-2010	39	32	.	.	PUNCT
ejpam-2010	40	1	the	the	DET
ejpam-2010	40	2	bimodule	bimodule	NOUN
ejpam-2010	40	3	p	p	PROPN
ejpam-2010	40	4	discussed	discuss	VERB
ejpam-2010	40	5	in	in	ADP
ejpam-2010	40	6	[	[	X
ejpam-2010	40	7	10	10	NUM
ejpam-2010	40	8	]	]	PUNCT
ejpam-2010	40	9	is	be	AUX
ejpam-2010	40	10	a	a	DET
ejpam-2010	40	11	quasi	quasi	NOUN
ejpam-2010	40	12	-	-	NOUN
ejpam-2010	40	13	progenerator	progenerator	NOUN
ejpam-2010	40	14	and	and	CCONJ
ejpam-2010	40	15	the	the	DET
ejpam-2010	40	16	bimodule	bimodule	NOUN
ejpam-2010	40	17	p	p	PROPN
ejpam-2010	40	18	considered	consider	VERB
ejpam-2010	40	19	in	in	ADP
ejpam-2010	40	20	[	[	X
ejpam-2010	40	21	32	32	NUM
ejpam-2010	40	22	]	]	PUNCT
ejpam-2010	40	23	is	be	AUX
ejpam-2010	40	24	a	a	DET
ejpam-2010	40	25	∗-module	∗-module	NOUN
ejpam-2010	40	26	.	.	PUNCT
ejpam-2010	41	1	in	in	ADP
ejpam-2010	41	2	[	[	X
ejpam-2010	41	3	47	47	NUM
ejpam-2010	41	4	]	]	PUNCT
ejpam-2010	41	5	,	,	PUNCT
ejpam-2010	41	6	trlifaj	trlifaj	NOUN
ejpam-2010	41	7	remarked	remark	VERB
ejpam-2010	41	8	that	that	SCONJ
ejpam-2010	41	9	every	every	DET
ejpam-2010	41	10	∗-module	∗-module	NOUN
ejpam-2010	41	11	is	be	AUX
ejpam-2010	41	12	finitely	finitely	ADV
ejpam-2010	41	13	generated	generate	VERB
ejpam-2010	41	14	and	and	CCONJ
ejpam-2010	41	15	colpi	colpi	PROPN
ejpam-2010	42	1	[	[	X
ejpam-2010	42	2	8	8	NUM
ejpam-2010	42	3	]	]	PUNCT
ejpam-2010	42	4	noticed	notice	VERB
ejpam-2010	42	5	that	that	SCONJ
ejpam-2010	42	6	the	the	DET
ejpam-2010	42	7	tilting	tilting	NOUN
ejpam-2010	42	8	modules	module	NOUN
ejpam-2010	42	9	are	be	AUX
ejpam-2010	42	10	closely	closely	ADV
ejpam-2010	42	11	related	relate	VERB
ejpam-2010	42	12	with	with	ADP
ejpam-2010	42	13	the	the	DET
ejpam-2010	42	14	∗-modules	∗-module	NOUN
ejpam-2010	42	15	.	.	PUNCT
ejpam-2010	43	1	this	this	DET
ejpam-2010	43	2	fact	fact	NOUN
ejpam-2010	43	3	builds	build	VERB
ejpam-2010	43	4	a	a	DET
ejpam-2010	43	5	connection	connection	NOUN
ejpam-2010	43	6	between	between	ADP
ejpam-2010	43	7	finite	finite	ADJ
ejpam-2010	43	8	dimensional	dimensional	ADJ
ejpam-2010	43	9	algebras	algebra	NOUN
ejpam-2010	43	10	via	via	ADP
ejpam-2010	43	11	equivalent	equivalent	ADJ
ejpam-2010	43	12	representable	representable	ADJ
ejpam-2010	43	13	functor	functor	PROPN
ejpam-2010	43	14	equivalences	equivalence	VERB
ejpam-2010	43	15	between	between	ADP
ejpam-2010	43	16	categories	category	NOUN
ejpam-2010	43	17	of	of	ADP
ejpam-2010	43	18	modules	module	NOUN
ejpam-2010	43	19	.	.	PUNCT
ejpam-2010	44	1	in	in	ADP
ejpam-2010	44	2	[	[	X
ejpam-2010	44	3	15	15	NUM
ejpam-2010	44	4	]	]	PUNCT
ejpam-2010	44	5	,	,	PUNCT
ejpam-2010	44	6	jacobson	jacobson	PROPN
ejpam-2010	44	7	remarked	remark	VERB
ejpam-2010	44	8	that	that	SCONJ
ejpam-2010	44	9	classical	classical	ADJ
ejpam-2010	44	10	morita	morita	NOUN
ejpam-2010	44	11	theory	theory	NOUN
ejpam-2010	44	12	for	for	ADP
ejpam-2010	44	13	rings	ring	NOUN
ejpam-2010	44	14	can	can	AUX
ejpam-2010	44	15	be	be	AUX
ejpam-2010	44	16	expressed	express	VERB
ejpam-2010	44	17	as	as	ADP
ejpam-2010	44	18	a	a	DET
ejpam-2010	44	19	theory	theory	NOUN
ejpam-2010	44	20	for	for	ADP
ejpam-2010	44	21	equivalent	equivalent	ADJ
ejpam-2010	44	22	matrix	matrix	NOUN
ejpam-2010	44	23	rings	ring	NOUN
ejpam-2010	44	24	.	.	PUNCT
ejpam-2010	45	1	in	in	ADP
ejpam-2010	45	2	fact	fact	NOUN
ejpam-2010	45	3	,	,	PUNCT
ejpam-2010	45	4	in	in	ADP
ejpam-2010	45	5	view	view	NOUN
ejpam-2010	45	6	of	of	ADP
ejpam-2010	45	7	morita	morita	PROPN
ejpam-2010	45	8	equivalence	equivalence	NOUN
ejpam-2010	45	9	,	,	PUNCT
ejpam-2010	45	10	we	we	PRON
ejpam-2010	45	11	can	can	AUX
ejpam-2010	45	12	describe	describe	VERB
ejpam-2010	45	13	the	the	DET
ejpam-2010	45	14	common	common	ADJ
ejpam-2010	45	15	“	"	PUNCT
ejpam-2010	45	16	two	two	NUM
ejpam-2010	45	17	-	-	PUNCT
ejpam-2010	45	18	sided	sided	ADJ
ejpam-2010	45	19	”	"	PUNCT
ejpam-2010	45	20	algebraic	algebraic	ADJ
ejpam-2010	45	21	structures	structure	NOUN
ejpam-2010	45	22	of	of	ADP
ejpam-2010	45	23	various	various	ADJ
ejpam-2010	45	24	finite	finite	ADJ
ejpam-2010	45	25	matrix	matrix	NOUN
ejpam-2010	45	26	rings	ring	NOUN
ejpam-2010	45	27	with	with	ADP
ejpam-2010	45	28	different	different	ADJ
ejpam-2010	45	29	ranks	rank	NOUN
ejpam-2010	45	30	,	,	PUNCT
ejpam-2010	45	31	for	for	ADP
ejpam-2010	45	32	instance	instance	NOUN
ejpam-2010	45	33	,	,	PUNCT
ejpam-2010	45	34	the	the	DET
ejpam-2010	45	35	simple	simple	ADJ
ejpam-2010	45	36	,	,	PUNCT
ejpam-2010	45	37	left	left	ADJ
ejpam-2010	45	38	artinean	artinean	ADJ
ejpam-2010	45	39	,	,	PUNCT
ejpam-2010	45	40	left	leave	VERB
ejpam-2010	45	41	notherian	notherian	ADJ
ejpam-2010	45	42	,	,	PUNCT
ejpam-2010	45	43	primitive	primitive	ADJ
ejpam-2010	45	44	and	and	CCONJ
ejpam-2010	45	45	semi	semi	ADJ
ejpam-2010	45	46	-	-	ADJ
ejpam-2010	45	47	simple	simple	ADJ
ejpam-2010	45	48	ring	ring	NOUN
ejpam-2010	45	49	between	between	ADP
ejpam-2010	45	50	rings	ring	NOUN
ejpam-2010	45	51	,	,	PUNCT
ejpam-2010	45	52	and	and	CCONJ
ejpam-2010	45	53	also	also	ADV
ejpam-2010	45	54	these	these	DET
ejpam-2010	45	55	ring	ring	NOUN
ejpam-2010	45	56	properties	property	NOUN
ejpam-2010	45	57	are	be	AUX
ejpam-2010	45	58	invariant	invariant	ADJ
ejpam-2010	45	59	and	and	CCONJ
ejpam-2010	45	60	preserved	preserve	VERB
ejpam-2010	45	61	if	if	SCONJ
ejpam-2010	45	62	they	they	PRON
ejpam-2010	45	63	are	be	AUX
ejpam-2010	45	64	morita	morita	PROPN
ejpam-2010	45	65	equivalent	equivalent	NOUN
ejpam-2010	45	66	.	.	PUNCT
ejpam-2010	46	1	in	in	ADP
ejpam-2010	46	2	[	[	X
ejpam-2010	46	3	49	49	NUM
ejpam-2010	46	4	]	]	PUNCT
ejpam-2010	46	5	,	,	PUNCT
ejpam-2010	46	6	xu	xu	INTJ
ejpam-2010	46	7	,	,	PUNCT
ejpam-2010	46	8	shum	shum	NOUN
ejpam-2010	46	9	and	and	CCONJ
ejpam-2010	46	10	turner	turner	PROPN
ejpam-2010	46	11	-	-	PUNCT
ejpam-2010	46	12	smith	smith	PROPN
ejpam-2010	46	13	generalised	generalise	VERB
ejpam-2010	46	14	the	the	DET
ejpam-2010	46	15	classcal	classcal	ADJ
ejpam-2010	46	16	morita	morita	PROPN
ejpam-2010	46	17	theory	theory	PROPN
ejpam-2010	46	18	for	for	ADP
ejpam-2010	46	19	finite	finite	ADJ
ejpam-2010	46	20	matrix	matrix	NOUN
ejpam-2010	46	21	rings	ring	NOUN
ejpam-2010	46	22	to	to	PART
ejpam-2010	46	23	infinite	infinite	VERB
ejpam-2010	46	24	matrix	matrix	NOUN
ejpam-2010	46	25	rings	ring	NOUN
ejpam-2010	46	26	using	use	VERB
ejpam-2010	46	27	the	the	DET
ejpam-2010	46	28	matrix	matrix	NOUN
ejpam-2010	46	29	approach	approach	NOUN
ejpam-2010	46	30	and	and	CCONJ
ejpam-2010	46	31	replacement	replacement	NOUN
ejpam-2010	46	32	techniques	technique	NOUN
ejpam-2010	46	33	.	.	PUNCT
ejpam-2010	47	1	they	they	PRON
ejpam-2010	47	2	also	also	ADV
ejpam-2010	47	3	defined	define	VERB
ejpam-2010	47	4	a	a	DET
ejpam-2010	47	5	class	class	NOUN
ejpam-2010	47	6	of	of	ADP
ejpam-2010	47	7	rings	ring	NOUN
ejpam-2010	47	8	called	call	VERB
ejpam-2010	47	9	xst	xst	PROPN
ejpam-2010	47	10	-	-	PUNCT
ejpam-2010	47	11	rings	ring	NOUN
ejpam-2010	47	12	which	which	PRON
ejpam-2010	47	13	contain	contain	VERB
ejpam-2010	47	14	the	the	DET
ejpam-2010	47	15	class	class	NOUN
ejpam-2010	47	16	of	of	ADP
ejpam-2010	47	17	rings	ring	NOUN
ejpam-2010	47	18	with	with	ADP
ejpam-2010	47	19	local	local	ADJ
ejpam-2010	47	20	units	unit	NOUN
ejpam-2010	47	21	.	.	PUNCT
ejpam-2010	48	1	to	to	PART
ejpam-2010	48	2	investigate	investigate	VERB
ejpam-2010	48	3	xst	xst	PROPN
ejpam-2010	48	4	-	-	PUNCT
ejpam-2010	48	5	rings	ring	NOUN
ejpam-2010	48	6	,	,	PUNCT
ejpam-2010	48	7	they	they	PRON
ejpam-2010	48	8	defined	define	VERB
ejpam-2010	48	9	a	a	DET
ejpam-2010	48	10	new	new	ADJ
ejpam-2010	48	11	equivalence	equivalence	NOUN
ejpam-2010	48	12	,	,	PUNCT
ejpam-2010	48	13	namely	namely	ADV
ejpam-2010	48	14	morita	morita	NOUN
ejpam-2010	48	15	-	-	PUNCT
ejpam-2010	48	16	like	like	ADJ
ejpam-2010	48	17	equivalence	equivalence	NOUN
ejpam-2010	48	18	,	,	PUNCT
ejpam-2010	48	19	which	which	PRON
ejpam-2010	48	20	is	be	AUX
ejpam-2010	48	21	a	a	DET
ejpam-2010	48	22	generalisation	generalisation	NOUN
ejpam-2010	48	23	of	of	ADP
ejpam-2010	48	24	morita	morita	PROPN
ejpam-2010	48	25	equivalence	equivalence	NOUN
ejpam-2010	48	26	.	.	PUNCT
ejpam-2010	49	1	the	the	DET
ejpam-2010	49	2	morita	morita	PROPN
ejpam-2010	49	3	theory	theory	NOUN
ejpam-2010	49	4	for	for	ADP
ejpam-2010	49	5	rings	ring	NOUN
ejpam-2010	49	6	was	be	AUX
ejpam-2010	49	7	first	first	ADV
ejpam-2010	49	8	extended	extend	VERB
ejpam-2010	49	9	independently	independently	ADV
ejpam-2010	49	10	to	to	ADP
ejpam-2010	49	11	monoids	monoid	NOUN
ejpam-2010	49	12	by	by	ADP
ejpam-2010	49	13	banaschewski	banaschewski	NOUN
ejpam-2010	50	1	[	[	X
ejpam-2010	50	2	5	5	NUM
ejpam-2010	50	3	]	]	PUNCT
ejpam-2010	50	4	and	and	CCONJ
ejpam-2010	50	5	knauer	knauer	NOUN
ejpam-2010	51	1	[	[	X
ejpam-2010	51	2	16	16	NUM
ejpam-2010	51	3	]	]	PUNCT
ejpam-2010	51	4	.	.	PUNCT
ejpam-2010	52	1	in	in	ADP
ejpam-2010	52	2	[	[	X
ejpam-2010	52	3	5	5	NUM
ejpam-2010	52	4	]	]	PUNCT
ejpam-2010	52	5	banaschewski	banaschewski	NOUN
ejpam-2010	52	6	showed	show	VERB
ejpam-2010	52	7	that	that	SCONJ
ejpam-2010	52	8	the	the	DET
ejpam-2010	52	9	generalisation	generalisation	NOUN
ejpam-2010	52	10	of	of	ADP
ejpam-2010	52	11	the	the	DET
ejpam-2010	52	12	morita	morita	PROPN
ejpam-2010	52	13	theory	theory	NOUN
ejpam-2010	52	14	for	for	ADP
ejpam-2010	52	15	rings	ring	NOUN
ejpam-2010	52	16	to	to	ADP
ejpam-2010	52	17	semigroups	semigroups	X
ejpam-2010	52	18	is	be	AUX
ejpam-2010	52	19	in	in	ADP
ejpam-2010	52	20	fact	fact	NOUN
ejpam-2010	52	21	isomorphic	isomorphic	ADJ
ejpam-2010	52	22	in	in	SCONJ
ejpam-2010	52	23	case	case	NOUN
ejpam-2010	52	24	r	r	NOUN
ejpam-2010	52	25	-	-	PUNCT
ejpam-2010	52	26	act	act	NOUN
ejpam-2010	52	27	and	and	CCONJ
ejpam-2010	52	28	s	s	NOUN
ejpam-2010	52	29	-	-	PUNCT
ejpam-2010	52	30	act	act	NOUN
ejpam-2010	52	31	are	be	AUX
ejpam-2010	52	32	equivalent	equivalent	ADJ
ejpam-2010	52	33	,	,	PUNCT
ejpam-2010	52	34	with	with	ADP
ejpam-2010	52	35	no	no	DET
ejpam-2010	52	36	requirement	requirement	NOUN
ejpam-2010	52	37	that	that	PRON
ejpam-2010	52	38	acts	act	VERB
ejpam-2010	52	39	be	be	VERB
ejpam-2010	52	40	unitary	unitary	ADJ
ejpam-2010	52	41	in	in	ADP
ejpam-2010	52	42	any	any	DET
ejpam-2010	52	43	sense	sense	NOUN
ejpam-2010	52	44	.	.	PUNCT
ejpam-2010	53	1	so	so	ADV
ejpam-2010	53	2	one	one	NOUN
ejpam-2010	53	3	is	be	AUX
ejpam-2010	53	4	forced	force	VERB
ejpam-2010	53	5	to	to	PART
ejpam-2010	53	6	define	define	VERB
ejpam-2010	53	7	morita	morita	NOUN
ejpam-2010	53	8	equivalence	equivalence	NOUN
ejpam-2010	53	9	in	in	ADP
ejpam-2010	53	10	terms	term	NOUN
ejpam-2010	53	11	of	of	ADP
ejpam-2010	53	12	subcategories	subcategorie	NOUN
ejpam-2010	53	13	if	if	SCONJ
ejpam-2010	53	14	a	a	DET
ejpam-2010	53	15	notion	notion	NOUN
ejpam-2010	53	16	differing	differ	VERB
ejpam-2010	53	17	from	from	ADP
ejpam-2010	53	18	isomorphism	isomorphism	NOUN
ejpam-2010	53	19	is	be	AUX
ejpam-2010	53	20	to	to	PART
ejpam-2010	53	21	be	be	AUX
ejpam-2010	53	22	obtained	obtain	VERB
ejpam-2010	53	23	.	.	PUNCT
ejpam-2010	54	1	based	base	VERB
ejpam-2010	54	2	on	on	ADP
ejpam-2010	54	3	the	the	DET
ejpam-2010	54	4	ideal	ideal	NOUN
ejpam-2010	54	5	of	of	ADP
ejpam-2010	54	6	developing	develop	VERB
ejpam-2010	54	7	the	the	DET
ejpam-2010	54	8	morita	morita	PROPN
ejpam-2010	54	9	theory	theory	NOUN
ejpam-2010	54	10	for	for	ADP
ejpam-2010	54	11	rings	ring	NOUN
ejpam-2010	54	12	with	with	ADP
ejpam-2010	54	13	identity	identity	NOUN
ejpam-2010	54	14	to	to	ADP
ejpam-2010	54	15	the	the	DET
ejpam-2010	54	16	rings	ring	NOUN
ejpam-2010	54	17	without	without	ADP
ejpam-2010	54	18	identity	identity	NOUN
ejpam-2010	54	19	,	,	PUNCT
ejpam-2010	54	20	tarlwar	tarlwar	VERB
ejpam-2010	54	21	[	[	NOUN
ejpam-2010	54	22	43	43	NUM
ejpam-2010	54	23	]	]	PUNCT
ejpam-2010	54	24	initiated	initiate	VERB
ejpam-2010	54	25	a	a	DET
ejpam-2010	54	26	new	new	ADJ
ejpam-2010	54	27	way	way	NOUN
ejpam-2010	54	28	to	to	PART
ejpam-2010	54	29	define	define	VERB
ejpam-2010	54	30	the	the	DET
ejpam-2010	54	31	morita	morita	PROPN
ejpam-2010	54	32	theory	theory	NOUN
ejpam-2010	54	33	for	for	ADP
ejpam-2010	54	34	semigroups	semigroup	NOUN
ejpam-2010	54	35	with	with	ADP
ejpam-2010	54	36	local	local	ADJ
ejpam-2010	54	37	units	unit	NOUN
ejpam-2010	54	38	,	,	PUNCT
ejpam-2010	54	39	where	where	SCONJ
ejpam-2010	54	40	a	a	DET
ejpam-2010	54	41	semigroup	semigroup	NOUN
ejpam-2010	54	42	s	s	NOUN
ejpam-2010	54	43	is	be	AUX
ejpam-2010	54	44	said	say	VERB
ejpam-2010	54	45	to	to	PART
ejpam-2010	54	46	be	be	AUX
ejpam-2010	54	47	with	with	ADP
ejpam-2010	54	48	local	local	ADJ
ejpam-2010	54	49	units	unit	NOUN
ejpam-2010	54	50	if	if	SCONJ
ejpam-2010	54	51	for	for	ADP
ejpam-2010	54	52	each	each	DET
ejpam-2010	54	53	s	s	X
ejpam-2010	54	54	∈	∈	PROPN
ejpam-2010	54	55	s	s	VERB
ejpam-2010	54	56	there	there	PRON
ejpam-2010	54	57	exist	exist	VERB
ejpam-2010	54	58	idempotents	idempotent	NOUN
ejpam-2010	54	59	e	e	NOUN
ejpam-2010	54	60	and	and	CCONJ
ejpam-2010	54	61	f	f	PROPN
ejpam-2010	55	1	such	such	ADJ
ejpam-2010	55	2	that	that	PRON
ejpam-2010	55	3	es	es	NOUN
ejpam-2010	55	4	=	=	SYM
ejpam-2010	55	5	s	s	PART
ejpam-2010	55	6	=	=	X
ejpam-2010	55	7	s	s	X
ejpam-2010	55	8	f	f	NOUN
ejpam-2010	55	9	.	.	PUNCT
ejpam-2010	56	1	to	to	PART
ejpam-2010	56	2	generalise	generalise	VERB
ejpam-2010	56	3	the	the	DET
ejpam-2010	56	4	morita	morita	PROPN
ejpam-2010	56	5	theory	theory	NOUN
ejpam-2010	56	6	for	for	ADP
ejpam-2010	56	7	semigroups	semigroup	NOUN
ejpam-2010	56	8	,	,	PUNCT
ejpam-2010	56	9	there	there	PRON
ejpam-2010	56	10	exist	exist	VERB
ejpam-2010	56	11	two	two	NUM
ejpam-2010	56	12	directions	direction	NOUN
ejpam-2010	56	13	.	.	PUNCT
ejpam-2010	57	1	one	one	NUM
ejpam-2010	57	2	is	be	AUX
ejpam-2010	57	3	to	to	ADP
ejpam-2010	57	4	a	a	DET
ejpam-2010	57	5	larger	large	ADJ
ejpam-2010	57	6	class	class	NOUN
ejpam-2010	57	7	of	of	ADP
ejpam-2010	57	8	semigroups	semigroup	NOUN
ejpam-2010	57	9	.	.	PUNCT
ejpam-2010	58	1	observe	observe	VERB
ejpam-2010	58	2	that	that	SCONJ
ejpam-2010	58	3	if	if	SCONJ
ejpam-2010	58	4	s	s	NOUN
ejpam-2010	58	5	is	be	AUX
ejpam-2010	58	6	a	a	DET
ejpam-2010	58	7	semigroup	semigroup	NOUN
ejpam-2010	58	8	with	with	ADP
ejpam-2010	58	9	local	local	ADJ
ejpam-2010	58	10	units	unit	NOUN
ejpam-2010	58	11	then	then	ADV
ejpam-2010	58	12	it	it	PRON
ejpam-2010	58	13	is	be	AUX
ejpam-2010	58	14	a	a	DET
ejpam-2010	58	15	factorisable	factorisable	ADJ
ejpam-2010	58	16	semigroup	semigroup	NOUN
ejpam-2010	58	17	as	as	SCONJ
ejpam-2010	58	18	it	it	PRON
ejpam-2010	58	19	has	have	VERB
ejpam-2010	58	20	the	the	DET
ejpam-2010	58	21	property	property	NOUN
ejpam-2010	58	22	s2	s2	NOUN
ejpam-2010	58	23	=	=	PUNCT
ejpam-2010	58	24	s.	s.	PROPN
ejpam-2010	58	25	in	in	ADP
ejpam-2010	58	26	[	[	X
ejpam-2010	58	27	44	44	NUM
ejpam-2010	58	28	,	,	PUNCT
ejpam-2010	58	29	45	45	NUM
ejpam-2010	58	30	]	]	X
ejpam-2010	58	31	y.	y.	PROPN
ejpam-2010	58	32	wang	wang	PROPN
ejpam-2010	58	33	,	,	PUNCT
ejpam-2010	58	34	k.	k.	PROPN
ejpam-2010	58	35	shum	shum	PROPN
ejpam-2010	58	36	,	,	PUNCT
ejpam-2010	58	37	x.	x.	PROPN
ejpam-2010	58	38	ren	ren	PROPN
ejpam-2010	58	39	/	/	SYM
ejpam-2010	58	40	eur	eur	PROPN
ejpam-2010	58	41	.	.	PUNCT
ejpam-2010	59	1	j.	j.	PROPN
ejpam-2010	59	2	pure	pure	PROPN
ejpam-2010	59	3	appl	appl	PROPN
ejpam-2010	59	4	.	.	PROPN
ejpam-2010	59	5	math	math	PROPN
ejpam-2010	59	6	,	,	PUNCT
ejpam-2010	59	7	6	6	NUM
ejpam-2010	59	8	(	(	PUNCT
ejpam-2010	59	9	2013	2013	NUM
ejpam-2010	59	10	)	)	PUNCT
ejpam-2010	59	11	,	,	PUNCT
ejpam-2010	59	12	256	256	NUM
ejpam-2010	59	13	-	-	SYM
ejpam-2010	59	14	281	281	NUM
ejpam-2010	59	15	258	258	NUM
ejpam-2010	59	16	tarlwar	tarlwar	VERB
ejpam-2010	59	17	further	far	ADV
ejpam-2010	59	18	generalised	generalise	VERB
ejpam-2010	59	19	his	his	PRON
ejpam-2010	59	20	theory	theory	NOUN
ejpam-2010	59	21	to	to	ADP
ejpam-2010	59	22	factorisable	factorisable	ADJ
ejpam-2010	59	23	semigroups	semigroup	NOUN
ejpam-2010	59	24	.	.	PUNCT
ejpam-2010	60	1	then	then	ADV
ejpam-2010	60	2	chen	chen	PROPN
ejpam-2010	60	3	and	and	CCONJ
ejpam-2010	60	4	shum	shum	ADJ
ejpam-2010	61	1	[	[	X
ejpam-2010	61	2	6	6	NUM
ejpam-2010	61	3	]	]	PUNCT
ejpam-2010	61	4	studied	study	VERB
ejpam-2010	61	5	the	the	DET
ejpam-2010	61	6	mortia	mortia	NOUN
ejpam-2010	61	7	equivalence	equivalence	NOUN
ejpam-2010	61	8	of	of	ADP
ejpam-2010	61	9	factorisable	factorisable	ADJ
ejpam-2010	61	10	semigroups	semigroup	NOUN
ejpam-2010	61	11	using	use	VERB
ejpam-2010	61	12	a	a	DET
ejpam-2010	61	13	different	different	ADJ
ejpam-2010	61	14	technique	technique	NOUN
ejpam-2010	61	15	from	from	ADP
ejpam-2010	61	16	tarlwar	tarlwar	VERB
ejpam-2010	61	17	’s	’s	PART
ejpam-2010	61	18	[	[	X
ejpam-2010	61	19	45	45	NUM
ejpam-2010	61	20	]	]	PUNCT
ejpam-2010	61	21	.	.	PUNCT
ejpam-2010	62	1	subsequetly	subsequetly	ADV
ejpam-2010	62	2	,	,	PUNCT
ejpam-2010	62	3	laan	laan	PROPN
ejpam-2010	62	4	and	and	CCONJ
ejpam-2010	62	5	márki	márki	ADJ
ejpam-2010	63	1	[	[	X
ejpam-2010	63	2	20	20	NUM
ejpam-2010	63	3	]	]	PUNCT
ejpam-2010	63	4	investigated	investigate	VERB
ejpam-2010	63	5	various	various	ADJ
ejpam-2010	63	6	classes	class	NOUN
ejpam-2010	63	7	of	of	ADP
ejpam-2010	63	8	factorisable	factorisable	ADJ
ejpam-2010	63	9	semigroups	semigroup	NOUN
ejpam-2010	63	10	.	.	PUNCT
ejpam-2010	64	1	the	the	DET
ejpam-2010	64	2	other	other	ADJ
ejpam-2010	64	3	way	way	NOUN
ejpam-2010	64	4	to	to	PART
ejpam-2010	64	5	generalise	generalise	VERB
ejpam-2010	64	6	the	the	DET
ejpam-2010	64	7	morita	morita	PROPN
ejpam-2010	64	8	theory	theory	NOUN
ejpam-2010	64	9	for	for	ADP
ejpam-2010	64	10	semigroups	semigroup	NOUN
ejpam-2010	64	11	with	with	ADP
ejpam-2010	64	12	local	local	ADJ
ejpam-2010	64	13	units	unit	NOUN
ejpam-2010	64	14	is	be	AUX
ejpam-2010	64	15	to	to	PART
ejpam-2010	64	16	investigate	investigate	VERB
ejpam-2010	64	17	some	some	DET
ejpam-2010	64	18	special	special	ADJ
ejpam-2010	64	19	kinds	kind	NOUN
ejpam-2010	64	20	of	of	ADP
ejpam-2010	64	21	semigroups	semigroup	NOUN
ejpam-2010	64	22	with	with	ADP
ejpam-2010	64	23	local	local	ADJ
ejpam-2010	64	24	units	unit	NOUN
ejpam-2010	64	25	.	.	PUNCT
ejpam-2010	65	1	inverse	inverse	NOUN
ejpam-2010	65	2	semigroups	semigroup	NOUN
ejpam-2010	65	3	can	can	AUX
ejpam-2010	65	4	be	be	AUX
ejpam-2010	65	5	considered	consider	VERB
ejpam-2010	65	6	as	as	ADP
ejpam-2010	65	7	an	an	DET
ejpam-2010	65	8	important	important	ADJ
ejpam-2010	65	9	class	class	NOUN
ejpam-2010	65	10	of	of	ADP
ejpam-2010	65	11	semigroups	semigroup	NOUN
ejpam-2010	65	12	with	with	ADP
ejpam-2010	65	13	local	local	ADJ
ejpam-2010	65	14	units	unit	NOUN
ejpam-2010	65	15	.	.	PUNCT
ejpam-2010	66	1	in	in	ADP
ejpam-2010	66	2	[	[	X
ejpam-2010	66	3	42	42	NUM
ejpam-2010	66	4	]	]	X
ejpam-2010	66	5	steinberg	steinberg	PROPN
ejpam-2010	66	6	introduced	introduce	VERB
ejpam-2010	66	7	a	a	DET
ejpam-2010	66	8	strong	strong	ADJ
ejpam-2010	66	9	morita	morita	NOUN
ejpam-2010	66	10	theory	theory	NOUN
ejpam-2010	66	11	for	for	ADP
ejpam-2010	66	12	inverse	inverse	NOUN
ejpam-2010	66	13	semigroups	semigroup	NOUN
ejpam-2010	66	14	in	in	ADP
ejpam-2010	66	15	terms	term	NOUN
ejpam-2010	66	16	of	of	ADP
ejpam-2010	66	17	morita	morita	PROPN
ejpam-2010	66	18	contexts	contexts	PROPN
ejpam-2010	66	19	,	,	PUNCT
ejpam-2010	66	20	which	which	PRON
ejpam-2010	66	21	turns	turn	VERB
ejpam-2010	66	22	out	out	ADP
ejpam-2010	66	23	to	to	PART
ejpam-2010	66	24	be	be	AUX
ejpam-2010	66	25	equivalent	equivalent	ADJ
ejpam-2010	66	26	with	with	ADP
ejpam-2010	66	27	the	the	DET
ejpam-2010	66	28	usual	usual	ADJ
ejpam-2010	66	29	morita	morita	NOUN
ejpam-2010	66	30	equivalence	equivalence	NOUN
ejpam-2010	66	31	of	of	ADP
ejpam-2010	66	32	inverse	inverse	NOUN
ejpam-2010	66	33	semigroups	semigroup	NOUN
ejpam-2010	66	34	.	.	PUNCT
ejpam-2010	67	1	recently	recently	ADV
ejpam-2010	67	2	,	,	PUNCT
ejpam-2010	67	3	lawson	lawson	PROPN
ejpam-2010	67	4	[	[	X
ejpam-2010	67	5	25	25	NUM
ejpam-2010	67	6	]	]	PUNCT
ejpam-2010	67	7	reformulate	reformulate	NOUN
ejpam-2010	67	8	tarlwar	tarlwar	NOUN
ejpam-2010	67	9	’s	’s	PART
ejpam-2010	67	10	theory	theory	NOUN
ejpam-2010	67	11	for	for	ADP
ejpam-2010	67	12	semigroups	semigroup	NOUN
ejpam-2010	67	13	with	with	ADP
ejpam-2010	67	14	local	local	ADJ
ejpam-2010	67	15	units	unit	NOUN
ejpam-2010	67	16	and	and	CCONJ
ejpam-2010	67	17	also	also	ADV
ejpam-2010	67	18	gave	give	VERB
ejpam-2010	67	19	equivalent	equivalent	ADJ
ejpam-2010	67	20	characterisations	characterisation	NOUN
ejpam-2010	67	21	of	of	ADP
ejpam-2010	67	22	morita	morita	PROPN
ejpam-2010	67	23	equivalence	equivalence	NOUN
ejpam-2010	67	24	in	in	ADP
ejpam-2010	67	25	terms	term	NOUN
ejpam-2010	67	26	of	of	ADP
ejpam-2010	67	27	categories	category	NOUN
ejpam-2010	67	28	of	of	ADP
ejpam-2010	67	29	acts	act	NOUN
ejpam-2010	67	30	over	over	ADP
ejpam-2010	67	31	them	they	PRON
ejpam-2010	67	32	,	,	PUNCT
ejpam-2010	67	33	morita	morita	PROPN
ejpam-2010	67	34	contexts	contexts	PROPN
ejpam-2010	67	35	,	,	PUNCT
ejpam-2010	67	36	cauchy	cauchy	ADJ
ejpam-2010	67	37	completions	completion	NOUN
ejpam-2010	67	38	and	and	CCONJ
ejpam-2010	67	39	enlargements	enlargement	NOUN
ejpam-2010	67	40	.	.	PUNCT
ejpam-2010	68	1	to	to	PART
ejpam-2010	68	2	study	study	VERB
ejpam-2010	68	3	morita	morita	PROPN
ejpam-2010	68	4	invariants	invariants	PROPN
ejpam-2010	68	5	for	for	ADP
ejpam-2010	68	6	semigroups	semigroup	NOUN
ejpam-2010	68	7	is	be	AUX
ejpam-2010	68	8	also	also	ADV
ejpam-2010	68	9	a	a	DET
ejpam-2010	68	10	focus	focus	NOUN
ejpam-2010	68	11	which	which	PRON
ejpam-2010	68	12	many	many	ADJ
ejpam-2010	68	13	authors	author	NOUN
ejpam-2010	68	14	pay	pay	VERB
ejpam-2010	68	15	attention	attention	NOUN
ejpam-2010	68	16	to	to	ADP
ejpam-2010	68	17	.	.	PUNCT
ejpam-2010	69	1	in	in	ADP
ejpam-2010	69	2	[	[	X
ejpam-2010	69	3	25	25	NUM
ejpam-2010	69	4	]	]	X
ejpam-2010	69	5	lawson	lawson	PROPN
ejpam-2010	69	6	showed	show	VERB
ejpam-2010	69	7	that	that	SCONJ
ejpam-2010	69	8	some	some	DET
ejpam-2010	69	9	important	important	ADJ
ejpam-2010	69	10	subclasses	subclass	NOUN
ejpam-2010	69	11	of	of	ADP
ejpam-2010	69	12	regular	regular	ADJ
ejpam-2010	69	13	semigroups	semigroup	NOUN
ejpam-2010	69	14	are	be	AUX
ejpam-2010	69	15	morita	morita	PROPN
ejpam-2010	69	16	invariant	invariant	PROPN
ejpam-2010	69	17	,	,	PUNCT
ejpam-2010	69	18	under	under	ADP
ejpam-2010	69	19	the	the	DET
ejpam-2010	69	20	assumption	assumption	NOUN
ejpam-2010	69	21	that	that	SCONJ
ejpam-2010	69	22	these	these	DET
ejpam-2010	69	23	semigroups	semigroup	NOUN
ejpam-2010	69	24	have	have	AUX
ejpam-2010	69	25	local	local	ADJ
ejpam-2010	69	26	units	unit	NOUN
ejpam-2010	69	27	.	.	PUNCT
ejpam-2010	70	1	to	to	PART
ejpam-2010	70	2	get	get	AUX
ejpam-2010	70	3	rid	rid	VERB
ejpam-2010	70	4	of	of	ADP
ejpam-2010	70	5	the	the	DET
ejpam-2010	70	6	assumption	assumption	NOUN
ejpam-2010	70	7	that	that	PRON
ejpam-2010	70	8	semigroups	semigroup	VERB
ejpam-2010	70	9	with	with	ADP
ejpam-2010	70	10	local	local	ADJ
ejpam-2010	70	11	units	unit	NOUN
ejpam-2010	70	12	laan	laan	PROPN
ejpam-2010	71	1	[	[	X
ejpam-2010	71	2	19	19	NUM
ejpam-2010	71	3	]	]	PUNCT
ejpam-2010	71	4	has	have	AUX
ejpam-2010	71	5	got	get	VERB
ejpam-2010	71	6	some	some	DET
ejpam-2010	71	7	nice	nice	ADJ
ejpam-2010	71	8	results	result	NOUN
ejpam-2010	71	9	.	.	PUNCT
ejpam-2010	72	1	in	in	ADP
ejpam-2010	72	2	[	[	X
ejpam-2010	72	3	20	20	NUM
ejpam-2010	72	4	]	]	PUNCT
ejpam-2010	72	5	the	the	DET
ejpam-2010	72	6	lattice	lattice	NOUN
ejpam-2010	72	7	of	of	ADP
ejpam-2010	72	8	congruences	congruence	NOUN
ejpam-2010	72	9	,	,	PUNCT
ejpam-2010	72	10	the	the	DET
ejpam-2010	72	11	lattice	lattice	NOUN
ejpam-2010	72	12	of	of	ADP
ejpam-2010	72	13	ideals	ideal	NOUN
ejpam-2010	72	14	and	and	CCONJ
ejpam-2010	72	15	so	so	ADV
ejpam-2010	72	16	on	on	ADV
ejpam-2010	72	17	were	be	AUX
ejpam-2010	72	18	discussed	discuss	VERB
ejpam-2010	72	19	based	base	VERB
ejpam-2010	72	20	on	on	ADP
ejpam-2010	72	21	strongly	strongly	ADV
ejpam-2010	72	22	morita	morita	PROPN
ejpam-2010	72	23	equivalent	equivalent	PROPN
ejpam-2010	72	24	semigroups	semigroup	NOUN
ejpam-2010	72	25	.	.	PUNCT
ejpam-2010	73	1	in	in	ADP
ejpam-2010	73	2	this	this	DET
ejpam-2010	73	3	paper	paper	NOUN
ejpam-2010	73	4	we	we	PRON
ejpam-2010	73	5	mainly	mainly	ADV
ejpam-2010	73	6	make	make	VERB
ejpam-2010	73	7	a	a	DET
ejpam-2010	73	8	survey	survey	NOUN
ejpam-2010	73	9	of	of	ADP
ejpam-2010	73	10	the	the	DET
ejpam-2010	73	11	morita	morita	PROPN
ejpam-2010	73	12	theory	theory	NOUN
ejpam-2010	73	13	for	for	ADP
ejpam-2010	73	14	rings	ring	NOUN
ejpam-2010	73	15	and	and	CCONJ
ejpam-2010	73	16	semigroups	semigroup	NOUN
ejpam-2010	73	17	.	.	PUNCT
ejpam-2010	74	1	the	the	DET
ejpam-2010	74	2	structure	structure	NOUN
ejpam-2010	74	3	of	of	ADP
ejpam-2010	74	4	this	this	DET
ejpam-2010	74	5	paper	paper	NOUN
ejpam-2010	74	6	is	be	AUX
ejpam-2010	74	7	as	as	SCONJ
ejpam-2010	74	8	follows	follow	VERB
ejpam-2010	74	9	.	.	PUNCT
ejpam-2010	75	1	in	in	ADP
ejpam-2010	75	2	section	section	NOUN
ejpam-2010	75	3	2	2	NUM
ejpam-2010	75	4	we	we	PRON
ejpam-2010	75	5	recall	recall	VERB
ejpam-2010	75	6	some	some	DET
ejpam-2010	75	7	basic	basic	ADJ
ejpam-2010	75	8	concepts	concept	NOUN
ejpam-2010	75	9	for	for	ADP
ejpam-2010	75	10	rings	ring	NOUN
ejpam-2010	75	11	and	and	CCONJ
ejpam-2010	75	12	semigroups	semigroup	NOUN
ejpam-2010	75	13	.	.	PUNCT
ejpam-2010	76	1	to	to	PART
ejpam-2010	76	2	study	study	VERB
ejpam-2010	76	3	morita	morita	PROPN
ejpam-2010	76	4	equivalence	equivalence	NOUN
ejpam-2010	76	5	we	we	PRON
ejpam-2010	76	6	also	also	ADV
ejpam-2010	76	7	introduce	introduce	VERB
ejpam-2010	76	8	several	several	ADJ
ejpam-2010	76	9	notions	notion	NOUN
ejpam-2010	76	10	and	and	CCONJ
ejpam-2010	76	11	terminology	terminology	NOUN
ejpam-2010	76	12	of	of	ADP
ejpam-2010	76	13	acts	act	NOUN
ejpam-2010	76	14	over	over	ADP
ejpam-2010	76	15	semigroups	semigroup	NOUN
ejpam-2010	76	16	and	and	CCONJ
ejpam-2010	76	17	modules	module	NOUN
ejpam-2010	76	18	.	.	PUNCT
ejpam-2010	77	1	section	section	NOUN
ejpam-2010	77	2	3	3	NUM
ejpam-2010	77	3	discusses	discuss	VERB
ejpam-2010	77	4	the	the	DET
ejpam-2010	77	5	morita	morita	PROPN
ejpam-2010	77	6	equivalence	equivalence	NOUN
ejpam-2010	77	7	and	and	CCONJ
ejpam-2010	77	8	morita	morita	PROPN
ejpam-2010	77	9	invariants	invariants	PROPN
ejpam-2010	77	10	for	for	ADP
ejpam-2010	77	11	rings	ring	NOUN
ejpam-2010	77	12	with	with	ADP
ejpam-2010	77	13	local	local	ADJ
ejpam-2010	77	14	units	unit	NOUN
ejpam-2010	77	15	and	and	CCONJ
ejpam-2010	77	16	xst	xst	PROPN
ejpam-2010	77	17	-	-	PUNCT
ejpam-2010	77	18	rings	ring	NOUN
ejpam-2010	77	19	.	.	PUNCT
ejpam-2010	78	1	morita	morita	PROPN
ejpam-2010	78	2	equivalence	equivalence	NOUN
ejpam-2010	78	3	for	for	ADP
ejpam-2010	78	4	semigroups	semigroup	NOUN
ejpam-2010	78	5	such	such	ADJ
ejpam-2010	78	6	as	as	ADP
ejpam-2010	78	7	semigroups	semigroup	NOUN
ejpam-2010	78	8	with	with	ADP
ejpam-2010	78	9	local	local	ADJ
ejpam-2010	78	10	units	unit	NOUN
ejpam-2010	78	11	,	,	PUNCT
ejpam-2010	78	12	inverse	inverse	NOUN
ejpam-2010	78	13	semigroups	semigroup	NOUN
ejpam-2010	78	14	,	,	PUNCT
ejpam-2010	78	15	factorisable	factorisable	ADJ
ejpam-2010	78	16	semigroups	semigroup	NOUN
ejpam-2010	78	17	and	and	CCONJ
ejpam-2010	78	18	so	so	ADV
ejpam-2010	78	19	on	on	ADV
ejpam-2010	78	20	is	be	AUX
ejpam-2010	78	21	investigate	investigate	VERB
ejpam-2010	78	22	in	in	ADP
ejpam-2010	78	23	section	section	NOUN
ejpam-2010	78	24	4	4	NUM
ejpam-2010	78	25	.	.	NOUN
ejpam-2010	78	26	2	2	NUM
ejpam-2010	78	27	.	.	NUM
ejpam-2010	78	28	preliminaries	preliminary	NOUN
ejpam-2010	78	29	in	in	ADP
ejpam-2010	78	30	this	this	DET
ejpam-2010	78	31	section	section	NOUN
ejpam-2010	78	32	we	we	PRON
ejpam-2010	78	33	mainly	mainly	ADV
ejpam-2010	78	34	present	present	VERB
ejpam-2010	78	35	a	a	DET
ejpam-2010	78	36	number	number	NOUN
ejpam-2010	78	37	of	of	ADP
ejpam-2010	78	38	definitions	definition	NOUN
ejpam-2010	78	39	and	and	CCONJ
ejpam-2010	78	40	elementary	elementary	ADJ
ejpam-2010	78	41	observations	observation	NOUN
ejpam-2010	78	42	concerning	concern	VERB
ejpam-2010	78	43	rings	ring	NOUN
ejpam-2010	78	44	and	and	CCONJ
ejpam-2010	78	45	semigroups	semigroup	NOUN
ejpam-2010	78	46	.	.	PUNCT
ejpam-2010	79	1	for	for	ADP
ejpam-2010	79	2	further	further	ADJ
ejpam-2010	79	3	details	detail	NOUN
ejpam-2010	79	4	of	of	ADP
ejpam-2010	79	5	rings	ring	NOUN
ejpam-2010	79	6	,	,	PUNCT
ejpam-2010	79	7	we	we	PRON
ejpam-2010	79	8	refer	refer	VERB
ejpam-2010	79	9	the	the	DET
ejpam-2010	79	10	reader	reader	NOUN
ejpam-2010	79	11	to	to	ADP
ejpam-2010	79	12	[	[	PUNCT
ejpam-2010	79	13	22	22	NUM
ejpam-2010	79	14	]	]	PUNCT
ejpam-2010	79	15	,	,	PUNCT
ejpam-2010	79	16	for	for	ADP
ejpam-2010	79	17	semigroup	semigroup	ADJ
ejpam-2010	79	18	theory	theory	NOUN
ejpam-2010	79	19	to	to	ADP
ejpam-2010	79	20	[	[	X
ejpam-2010	79	21	39	39	NUM
ejpam-2010	79	22	]	]	PUNCT
ejpam-2010	79	23	and	and	CCONJ
ejpam-2010	79	24	for	for	ADP
ejpam-2010	79	25	category	category	NOUN
ejpam-2010	79	26	theory	theory	NOUN
ejpam-2010	79	27	to	to	ADP
ejpam-2010	79	28	[	[	X
ejpam-2010	79	29	33	33	NUM
ejpam-2010	79	30	]	]	PUNCT
ejpam-2010	79	31	.	.	PUNCT
ejpam-2010	80	1	in	in	ADP
ejpam-2010	80	2	this	this	DET
ejpam-2010	80	3	paper	paper	NOUN
ejpam-2010	80	4	,	,	PUNCT
ejpam-2010	80	5	let	let	VERB
ejpam-2010	80	6	k	k	PRON
ejpam-2010	80	7	be	be	AUX
ejpam-2010	80	8	an	an	DET
ejpam-2010	80	9	algebra	algebra	NOUN
ejpam-2010	80	10	system	system	NOUN
ejpam-2010	80	11	.	.	PUNCT
ejpam-2010	81	1	we	we	PRON
ejpam-2010	81	2	denote	denote	VERB
ejpam-2010	81	3	by	by	ADP
ejpam-2010	81	4	e(k	e(k	NOUN
ejpam-2010	81	5	)	)	PUNCT
ejpam-2010	81	6	the	the	DET
ejpam-2010	81	7	set	set	NOUN
ejpam-2010	81	8	of	of	ADP
ejpam-2010	81	9	all	all	DET
ejpam-2010	81	10	its	its	PRON
ejpam-2010	81	11	idempotents	idempotent	NOUN
ejpam-2010	81	12	.	.	PUNCT
ejpam-2010	82	1	2.1	2.1	NUM
ejpam-2010	82	2	.	.	PUNCT
ejpam-2010	82	3	rings	ring	NOUN
ejpam-2010	82	4	and	and	CCONJ
ejpam-2010	82	5	modules	module	VERB
ejpam-2010	82	6	a	a	DET
ejpam-2010	82	7	ring	ring	NOUN
ejpam-2010	82	8	is	be	AUX
ejpam-2010	82	9	unital	unital	ADJ
ejpam-2010	82	10	if	if	SCONJ
ejpam-2010	82	11	it	it	PRON
ejpam-2010	82	12	has	have	VERB
ejpam-2010	82	13	an	an	DET
ejpam-2010	82	14	identity	identity	NOUN
ejpam-2010	82	15	for	for	ADP
ejpam-2010	82	16	multiplication	multiplication	NOUN
ejpam-2010	82	17	.	.	PUNCT
ejpam-2010	83	1	a	a	DET
ejpam-2010	83	2	ring	ring	NOUN
ejpam-2010	83	3	is	be	AUX
ejpam-2010	83	4	commutative	commutative	ADJ
ejpam-2010	83	5	if	if	SCONJ
ejpam-2010	83	6	the	the	DET
ejpam-2010	83	7	multiplication	multiplication	NOUN
ejpam-2010	83	8	is	be	AUX
ejpam-2010	83	9	commutative	commutative	ADJ
ejpam-2010	83	10	.	.	PUNCT
ejpam-2010	84	1	we	we	PRON
ejpam-2010	84	2	say	say	VERB
ejpam-2010	84	3	that	that	SCONJ
ejpam-2010	84	4	r	r	NOUN
ejpam-2010	84	5	is	be	AUX
ejpam-2010	84	6	a	a	DET
ejpam-2010	84	7	ring	ring	NOUN
ejpam-2010	84	8	with	with	ADP
ejpam-2010	84	9	local	local	ADJ
ejpam-2010	84	10	units	unit	NOUN
ejpam-2010	84	11	if	if	SCONJ
ejpam-2010	84	12	every	every	DET
ejpam-2010	84	13	finite	finite	NOUN
ejpam-2010	84	14	subset	subset	NOUN
ejpam-2010	84	15	of	of	ADP
ejpam-2010	84	16	r	r	NOUN
ejpam-2010	84	17	is	be	AUX
ejpam-2010	84	18	contained	contain	VERB
ejpam-2010	84	19	in	in	ADP
ejpam-2010	84	20	a	a	DET
ejpam-2010	84	21	subring	subring	NOUN
ejpam-2010	84	22	of	of	ADP
ejpam-2010	84	23	the	the	DET
ejpam-2010	84	24	form	form	NOUN
ejpam-2010	84	25	ere	ere	INTJ
ejpam-2010	84	26	where	where	SCONJ
ejpam-2010	84	27	e	e	X
ejpam-2010	84	28	∈	∈	PROPN
ejpam-2010	84	29	e(r	e(r	NUM
ejpam-2010	84	30	)	)	PUNCT
ejpam-2010	84	31	.	.	PUNCT
ejpam-2010	85	1	a	a	DET
ejpam-2010	85	2	subset	subset	NOUN
ejpam-2010	85	3	e	e	NOUN
ejpam-2010	85	4	of	of	ADP
ejpam-2010	85	5	r	r	NOUN
ejpam-2010	85	6	is	be	AUX
ejpam-2010	85	7	called	call	VERB
ejpam-2010	85	8	a	a	DET
ejpam-2010	85	9	set	set	NOUN
ejpam-2010	85	10	of	of	ADP
ejpam-2010	85	11	local	local	ADJ
ejpam-2010	85	12	units	unit	NOUN
ejpam-2010	85	13	(	(	PUNCT
ejpam-2010	85	14	slu	slu	NOUN
ejpam-2010	85	15	)	)	PUNCT
ejpam-2010	85	16	for	for	ADP
ejpam-2010	85	17	r	r	NOUN
ejpam-2010	85	18	in	in	ADP
ejpam-2010	85	19	case	case	NOUN
ejpam-2010	85	20	e	e	NOUN
ejpam-2010	85	21	is	be	AUX
ejpam-2010	85	22	a	a	DET
ejpam-2010	85	23	set	set	NOUN
ejpam-2010	85	24	of	of	ADP
ejpam-2010	85	25	commuting	commute	VERB
ejpam-2010	85	26	idempotents	idempotent	NOUN
ejpam-2010	85	27	such	such	ADJ
ejpam-2010	85	28	that	that	PRON
ejpam-2010	85	29	for	for	ADP
ejpam-2010	85	30	each	each	PRON
ejpam-2010	85	31	x	x	PUNCT
ejpam-2010	85	32	in	in	ADP
ejpam-2010	85	33	r	r	NOUN
ejpam-2010	85	34	there	there	PRON
ejpam-2010	85	35	exists	exist	VERB
ejpam-2010	85	36	an	an	DET
ejpam-2010	85	37	e	e	NOUN
ejpam-2010	85	38	in	in	ADP
ejpam-2010	85	39	e	e	PROPN
ejpam-2010	85	40	with	with	ADP
ejpam-2010	85	41	ex	ex	X
ejpam-2010	86	1	=	=	PUNCT
ejpam-2010	86	2	xe	xe	PROPN
ejpam-2010	86	3	=	=	SYM
ejpam-2010	86	4	x	x	PROPN
ejpam-2010	86	5	.	.	PUNCT
ejpam-2010	87	1	note	note	VERB
ejpam-2010	87	2	that	that	SCONJ
ejpam-2010	87	3	if	if	SCONJ
ejpam-2010	87	4	r	r	NOUN
ejpam-2010	87	5	is	be	AUX
ejpam-2010	87	6	a	a	DET
ejpam-2010	87	7	unital	unital	ADJ
ejpam-2010	87	8	ring	ring	NOUN
ejpam-2010	87	9	with	with	ADP
ejpam-2010	87	10	identity	identity	NOUN
ejpam-2010	87	11	1	1	NUM
ejpam-2010	87	12	,	,	PUNCT
ejpam-2010	87	13	then	then	ADV
ejpam-2010	87	14	{	{	PUNCT
ejpam-2010	87	15	1	1	X
ejpam-2010	87	16	}	}	PUNCT
ejpam-2010	87	17	is	be	AUX
ejpam-2010	87	18	an	an	DET
ejpam-2010	87	19	slu	slu	NOUN
ejpam-2010	87	20	for	for	ADP
ejpam-2010	87	21	r.	r.	PROPN
ejpam-2010	87	22	if	if	SCONJ
ejpam-2010	87	23	r	r	NOUN
ejpam-2010	87	24	is	be	AUX
ejpam-2010	87	25	a	a	DET
ejpam-2010	87	26	ring	ring	NOUN
ejpam-2010	87	27	with	with	ADP
ejpam-2010	87	28	slu	slu	NOUN
ejpam-2010	87	29	then	then	ADV
ejpam-2010	87	30	it	it	PRON
ejpam-2010	87	31	is	be	AUX
ejpam-2010	87	32	a	a	DET
ejpam-2010	87	33	ring	ring	NOUN
ejpam-2010	87	34	with	with	ADP
ejpam-2010	87	35	local	local	ADJ
ejpam-2010	87	36	units	unit	NOUN
ejpam-2010	87	37	,	,	PUNCT
ejpam-2010	87	38	but	but	CCONJ
ejpam-2010	87	39	the	the	DET
ejpam-2010	87	40	converse	converse	NOUN
ejpam-2010	87	41	is	be	AUX
ejpam-2010	87	42	not	not	PART
ejpam-2010	87	43	true	true	ADJ
ejpam-2010	87	44	.	.	PUNCT
ejpam-2010	88	1	in	in	ADP
ejpam-2010	88	2	addition	addition	NOUN
ejpam-2010	88	3	,	,	PUNCT
ejpam-2010	88	4	a	a	DET
ejpam-2010	88	5	ring	ring	NOUN
ejpam-2010	88	6	r	r	NOUN
ejpam-2010	88	7	with	with	ADP
ejpam-2010	88	8	slu	slu	NOUN
ejpam-2010	88	9	is	be	AUX
ejpam-2010	88	10	a	a	DET
ejpam-2010	88	11	ring	ring	NOUN
ejpam-2010	88	12	with	with	ADP
ejpam-2010	88	13	local	local	ADJ
ejpam-2010	88	14	units	unit	NOUN
ejpam-2010	88	15	whose	whose	DET
ejpam-2010	88	16	local	local	ADJ
ejpam-2010	88	17	units	unit	NOUN
ejpam-2010	88	18	commute	commute	VERB
ejpam-2010	88	19	.	.	PUNCT
ejpam-2010	89	1	let	let	VERB
ejpam-2010	89	2	r	r	PRON
ejpam-2010	89	3	be	be	AUX
ejpam-2010	89	4	a	a	DET
ejpam-2010	89	5	ring	ring	NOUN
ejpam-2010	89	6	.	.	PUNCT
ejpam-2010	90	1	if	if	SCONJ
ejpam-2010	90	2	m	m	NOUN
ejpam-2010	90	3	is	be	AUX
ejpam-2010	90	4	a	a	DET
ejpam-2010	90	5	left	left	ADJ
ejpam-2010	90	6	r	r	NOUN
ejpam-2010	90	7	-	-	PUNCT
ejpam-2010	90	8	module	module	NOUN
ejpam-2010	90	9	we	we	PRON
ejpam-2010	90	10	denote	denote	VERB
ejpam-2010	90	11	it	it	PRON
ejpam-2010	90	12	by	by	ADP
ejpam-2010	90	13	rm	rm	PROPN
ejpam-2010	90	14	.	.	PUNCT
ejpam-2010	91	1	let	let	VERB
ejpam-2010	91	2	m1	m1	PROPN
ejpam-2010	91	3	,	,	PUNCT
ejpam-2010	91	4	m2	m2	PROPN
ejpam-2010	91	5	,	,	PUNCT
ejpam-2010	91	6	.	.	PUNCT
ejpam-2010	91	7	.	.	PUNCT
ejpam-2010	92	1	.	.	PUNCT
ejpam-2010	93	1	,	,	PUNCT
ejpam-2010	93	2	mn	mn	PROPN
ejpam-2010	93	3	be	be	VERB
ejpam-2010	93	4	elements	element	NOUN
ejpam-2010	93	5	of	of	ADP
ejpam-2010	93	6	a	a	DET
ejpam-2010	93	7	left	left	ADJ
ejpam-2010	93	8	r	r	NOUN
ejpam-2010	93	9	-	-	PUNCT
ejpam-2010	93	10	module	module	NOUN
ejpam-2010	93	11	m	m	NOUN
ejpam-2010	93	12	.	.	PUNCT
ejpam-2010	94	1	then	then	ADV
ejpam-2010	94	2	m1	m1	PROPN
ejpam-2010	94	3	,	,	PUNCT
ejpam-2010	94	4	m2	m2	PROPN
ejpam-2010	94	5	,	,	PUNCT
ejpam-2010	94	6	.	.	PUNCT
ejpam-2010	94	7	.	.	PUNCT
ejpam-2010	94	8	.	.	PUNCT
ejpam-2010	95	1	,	,	PUNCT
ejpam-2010	95	2	mn	mn	PROPN
ejpam-2010	95	3	are	be	AUX
ejpam-2010	95	4	called	call	VERB
ejpam-2010	95	5	generators	generator	NOUN
ejpam-2010	95	6	of	of	ADP
ejpam-2010	95	7	m	m	PRON
ejpam-2010	95	8	if	if	SCONJ
ejpam-2010	95	9	for	for	ADP
ejpam-2010	95	10	each	each	DET
ejpam-2010	95	11	m	m	NOUN
ejpam-2010	95	12	∈	∈	NOUN
ejpam-2010	95	13	m	m	NOUN
ejpam-2010	95	14	,	,	PUNCT
ejpam-2010	95	15	there	there	PRON
ejpam-2010	95	16	exists	exist	VERB
ejpam-2010	95	17	r1	r1	NOUN
ejpam-2010	95	18	,	,	PUNCT
ejpam-2010	95	19	r2	r2	PROPN
ejpam-2010	95	20	,	,	PUNCT
ejpam-2010	95	21	.	.	PUNCT
ejpam-2010	95	22	.	.	PUNCT
ejpam-2010	96	1	.	.	PUNCT
ejpam-2010	97	1	,	,	PUNCT
ejpam-2010	97	2	rn	rn	PROPN
ejpam-2010	97	3	∈	∈	PROPN
ejpam-2010	97	4	r	r	NOUN
ejpam-2010	97	5	such	such	ADJ
ejpam-2010	97	6	that	that	PRON
ejpam-2010	97	7	m=	m=	NOUN
ejpam-2010	97	8	r1m1	r1m1	NOUN
ejpam-2010	97	9	+	+	CCONJ
ejpam-2010	97	10	r2m2	r2m2	ADJ
ejpam-2010	97	11	+	+	ADJ
ejpam-2010	97	12	.	.	PUNCT
ejpam-2010	97	13	.	.	PUNCT
ejpam-2010	98	1	.+	.+	NOUN
ejpam-2010	98	2	rnmn	rnmn	NOUN
ejpam-2010	98	3	,	,	PUNCT
ejpam-2010	98	4	meanwhile	meanwhile	ADV
ejpam-2010	98	5	m	m	VERB
ejpam-2010	98	6	is	be	AUX
ejpam-2010	98	7	called	call	VERB
ejpam-2010	98	8	finitely	finitely	ADV
ejpam-2010	98	9	y.	y.	PROPN
ejpam-2010	98	10	wang	wang	PROPN
ejpam-2010	98	11	,	,	PUNCT
ejpam-2010	98	12	k.	k.	PROPN
ejpam-2010	98	13	shum	shum	PROPN
ejpam-2010	98	14	,	,	PUNCT
ejpam-2010	98	15	x.	x.	PROPN
ejpam-2010	98	16	ren	ren	PROPN
ejpam-2010	98	17	/	/	SYM
ejpam-2010	98	18	eur	eur	PROPN
ejpam-2010	98	19	.	.	PUNCT
ejpam-2010	99	1	j.	j.	PROPN
ejpam-2010	99	2	pure	pure	PROPN
ejpam-2010	99	3	appl	appl	PROPN
ejpam-2010	99	4	.	.	PROPN
ejpam-2010	99	5	math	math	PROPN
ejpam-2010	99	6	,	,	PUNCT
ejpam-2010	99	7	6	6	NUM
ejpam-2010	99	8	(	(	PUNCT
ejpam-2010	99	9	2013	2013	NUM
ejpam-2010	99	10	)	)	PUNCT
ejpam-2010	99	11	,	,	PUNCT
ejpam-2010	99	12	256	256	NUM
ejpam-2010	99	13	-	-	SYM
ejpam-2010	99	14	281	281	NUM
ejpam-2010	99	15	259	259	NUM
ejpam-2010	99	16	generated	generate	VERB
ejpam-2010	99	17	.	.	PUNCT
ejpam-2010	100	1	we	we	PRON
ejpam-2010	100	2	call	call	VERB
ejpam-2010	100	3	a	a	DET
ejpam-2010	100	4	left	left	ADJ
ejpam-2010	100	5	r	r	NOUN
ejpam-2010	100	6	-	-	PUNCT
ejpam-2010	100	7	module	module	NOUN
ejpam-2010	100	8	unitary	unitary	ADJ
ejpam-2010	100	9	if	if	SCONJ
ejpam-2010	100	10	rm	rm	PROPN
ejpam-2010	100	11	=	=	NOUN
ejpam-2010	100	12	m	m	PROPN
ejpam-2010	100	13	,	,	PUNCT
ejpam-2010	100	14	that	that	ADV
ejpam-2010	100	15	is	is	ADV
ejpam-2010	100	16	,	,	PUNCT
ejpam-2010	100	17	for	for	ADP
ejpam-2010	100	18	each	each	DET
ejpam-2010	100	19	m	m	NOUN
ejpam-2010	100	20	∈	∈	NOUN
ejpam-2010	100	21	m	m	NOUN
ejpam-2010	100	22	,	,	PUNCT
ejpam-2010	100	23	there	there	PRON
ejpam-2010	100	24	exist	exist	VERB
ejpam-2010	100	25	r1	r1	NOUN
ejpam-2010	100	26	,	,	PUNCT
ejpam-2010	100	27	.	.	PUNCT
ejpam-2010	100	28	.	.	PUNCT
ejpam-2010	101	1	.	.	PUNCT
ejpam-2010	102	1	,	,	PUNCT
ejpam-2010	102	2	rn	rn	PROPN
ejpam-2010	102	3	∈	∈	PROPN
ejpam-2010	102	4	r	r	NOUN
ejpam-2010	102	5	and	and	CCONJ
ejpam-2010	102	6	m1	m1	NOUN
ejpam-2010	102	7	,	,	PUNCT
ejpam-2010	102	8	.	.	PUNCT
ejpam-2010	102	9	.	.	PUNCT
ejpam-2010	103	1	.	.	PUNCT
ejpam-2010	104	1	,	,	PUNCT
ejpam-2010	104	2	mn	mn	PROPN
ejpam-2010	104	3	∈	∈	PROPN
ejpam-2010	104	4	m	m	VERB
ejpam-2010	104	5	such	such	ADJ
ejpam-2010	104	6	that	that	SCONJ
ejpam-2010	104	7	r1m1	r1m1	NOUN
ejpam-2010	104	8	+	+	NOUN
ejpam-2010	104	9	.	.	PUNCT
ejpam-2010	104	10	.	.	PUNCT
ejpam-2010	105	1	.+rnmn	.+rnmn	PUNCT
ejpam-2010	106	1	=	=	PUNCT
ejpam-2010	106	2	m.	m.	NOUN
ejpam-2010	106	3	we	we	PRON
ejpam-2010	106	4	call	call	VERB
ejpam-2010	106	5	a	a	DET
ejpam-2010	106	6	bimodule	bimodule	NOUN
ejpam-2010	106	7	unitary	unitary	ADJ
ejpam-2010	106	8	if	if	SCONJ
ejpam-2010	106	9	it	it	PRON
ejpam-2010	106	10	is	be	AUX
ejpam-2010	106	11	unitary	unitary	ADJ
ejpam-2010	106	12	on	on	ADP
ejpam-2010	106	13	both	both	DET
ejpam-2010	106	14	sides	side	NOUN
ejpam-2010	106	15	.	.	PUNCT
ejpam-2010	107	1	a	a	DET
ejpam-2010	107	2	right	right	ADJ
ejpam-2010	107	3	r	r	NOUN
ejpam-2010	107	4	module	module	NOUN
ejpam-2010	107	5	mr	mr	PROPN
ejpam-2010	107	6	is	be	AUX
ejpam-2010	107	7	called	call	VERB
ejpam-2010	107	8	s	s	NOUN
ejpam-2010	107	9	-	-	NOUN
ejpam-2010	107	10	unital	unital	ADJ
ejpam-2010	107	11	if	if	SCONJ
ejpam-2010	107	12	for	for	ADP
ejpam-2010	107	13	every	every	DET
ejpam-2010	107	14	x	x	SYM
ejpam-2010	107	15	∈	∈	PROPN
ejpam-2010	107	16	m	m	VERB
ejpam-2010	107	17	there	there	PRON
ejpam-2010	107	18	exists	exist	VERB
ejpam-2010	107	19	r	r	NOUN
ejpam-2010	107	20	∈	∈	PROPN
ejpam-2010	107	21	r	r	NOUN
ejpam-2010	108	1	such	such	ADJ
ejpam-2010	108	2	that	that	SCONJ
ejpam-2010	108	3	x	x	SYM
ejpam-2010	108	4	r	r	NOUN
ejpam-2010	108	5	=	=	PUNCT
ejpam-2010	108	6	x	x	X
ejpam-2010	108	7	.	.	PUNCT
ejpam-2010	109	1	let	let	VERB
ejpam-2010	109	2	r	r	PRON
ejpam-2010	109	3	be	be	AUX
ejpam-2010	109	4	an	an	DET
ejpam-2010	109	5	arbitrary	arbitrary	ADJ
ejpam-2010	109	6	ring	ring	NOUN
ejpam-2010	109	7	.	.	PUNCT
ejpam-2010	110	1	for	for	ADP
ejpam-2010	110	2	convenience	convenience	NOUN
ejpam-2010	110	3	,	,	PUNCT
ejpam-2010	110	4	the	the	DET
ejpam-2010	110	5	category	category	NOUN
ejpam-2010	110	6	of	of	ADP
ejpam-2010	110	7	left	left	ADJ
ejpam-2010	110	8	r	r	NOUN
ejpam-2010	110	9	-	-	PUNCT
ejpam-2010	110	10	modules	module	NOUN
ejpam-2010	110	11	and	and	CCONJ
ejpam-2010	110	12	the	the	DET
ejpam-2010	110	13	usual	usual	ADJ
ejpam-2010	110	14	left	left	ADJ
ejpam-2010	110	15	r	r	NOUN
ejpam-2010	110	16	-	-	PUNCT
ejpam-2010	110	17	homomorphisms	homomorphism	NOUN
ejpam-2010	110	18	is	be	AUX
ejpam-2010	110	19	denoted	denote	VERB
ejpam-2010	110	20	by	by	ADP
ejpam-2010	110	21	r	r	NOUN
ejpam-2010	110	22	-	-	PUNCT
ejpam-2010	110	23	mod	mod	NOUN
ejpam-2010	110	24	.	.	PUNCT
ejpam-2010	111	1	if	if	SCONJ
ejpam-2010	111	2	m	m	PROPN
ejpam-2010	111	3	and	and	CCONJ
ejpam-2010	111	4	n	n	CCONJ
ejpam-2010	111	5	are	be	AUX
ejpam-2010	111	6	left	leave	VERB
ejpam-2010	111	7	r	r	NOUN
ejpam-2010	111	8	-	-	PUNCT
ejpam-2010	111	9	modules	module	NOUN
ejpam-2010	111	10	then	then	ADV
ejpam-2010	111	11	homr(m	homr(m	AUX
ejpam-2010	111	12	,	,	PUNCT
ejpam-2010	111	13	n	n	CCONJ
ejpam-2010	111	14	)	)	PUNCT
ejpam-2010	111	15	denotes	denote	VERB
ejpam-2010	111	16	the	the	DET
ejpam-2010	111	17	set	set	NOUN
ejpam-2010	111	18	of	of	ADP
ejpam-2010	111	19	all	all	PRON
ejpam-2010	111	20	left	leave	VERB
ejpam-2010	111	21	r	r	NOUN
ejpam-2010	111	22	-	-	PUNCT
ejpam-2010	111	23	homomorphisms	homomorphism	NOUN
ejpam-2010	111	24	from	from	ADP
ejpam-2010	111	25	m	m	PROPN
ejpam-2010	111	26	to	to	ADP
ejpam-2010	111	27	n	n	PROPN
ejpam-2010	111	28	.	.	PUNCT
ejpam-2010	112	1	we	we	PRON
ejpam-2010	112	2	use	use	VERB
ejpam-2010	112	3	rc	rc	PROPN
ejpam-2010	112	4	to	to	PART
ejpam-2010	112	5	denote	denote	VERB
ejpam-2010	112	6	the	the	DET
ejpam-2010	112	7	full	full	ADJ
ejpam-2010	112	8	subcategory	subcategory	NOUN
ejpam-2010	112	9	of	of	ADP
ejpam-2010	112	10	unital	unital	ADJ
ejpam-2010	112	11	left	left	ADJ
ejpam-2010	112	12	r	r	NOUN
ejpam-2010	112	13	-	-	PUNCT
ejpam-2010	112	14	modules	module	NOUN
ejpam-2010	112	15	,	,	PUNCT
ejpam-2010	112	16	which	which	PRON
ejpam-2010	112	17	is	be	AUX
ejpam-2010	112	18	complete	complete	ADJ
ejpam-2010	112	19	additive	additive	NOUN
ejpam-2010	112	20	,	,	PUNCT
ejpam-2010	112	21	that	that	ADV
ejpam-2010	112	22	is	is	ADV
ejpam-2010	112	23	,	,	PUNCT
ejpam-2010	112	24	it	it	PRON
ejpam-2010	112	25	is	be	AUX
ejpam-2010	112	26	closed	close	VERB
ejpam-2010	112	27	under	under	ADP
ejpam-2010	112	28	submodules	submodule	NOUN
ejpam-2010	112	29	,	,	PUNCT
ejpam-2010	112	30	epimorphic	epimorphic	ADJ
ejpam-2010	112	31	images	image	NOUN
ejpam-2010	112	32	and	and	CCONJ
ejpam-2010	112	33	direct	direct	ADJ
ejpam-2010	112	34	sums	sum	NOUN
ejpam-2010	112	35	.	.	PUNCT
ejpam-2010	113	1	dually	dually	PROPN
ejpam-2010	113	2	,	,	PUNCT
ejpam-2010	113	3	mod	mod	ADJ
ejpam-2010	113	4	-	-	PUNCT
ejpam-2010	113	5	r	r	NOUN
ejpam-2010	113	6	and	and	CCONJ
ejpam-2010	113	7	cr	cr	NOUN
ejpam-2010	113	8	denotes	denote	VERB
ejpam-2010	113	9	the	the	DET
ejpam-2010	113	10	category	category	NOUN
ejpam-2010	113	11	of	of	ADP
ejpam-2010	113	12	right	right	ADJ
ejpam-2010	113	13	r	r	NOUN
ejpam-2010	113	14	-	-	PUNCT
ejpam-2010	113	15	modules	module	NOUN
ejpam-2010	113	16	and	and	CCONJ
ejpam-2010	113	17	the	the	DET
ejpam-2010	113	18	closed	closed	ADJ
ejpam-2010	113	19	full	full	ADJ
ejpam-2010	113	20	subcategory	subcategory	ADJ
ejpam-2010	113	21	unital	unital	ADJ
ejpam-2010	113	22	ring	ring	NOUN
ejpam-2010	113	23	r	r	NOUN
ejpam-2010	113	24	-	-	PUNCT
ejpam-2010	113	25	modules	module	NOUN
ejpam-2010	113	26	.	.	PUNCT
ejpam-2010	114	1	notice	notice	VERB
ejpam-2010	114	2	that	that	SCONJ
ejpam-2010	114	3	for	for	ADP
ejpam-2010	114	4	a	a	DET
ejpam-2010	114	5	ring	ring	NOUN
ejpam-2010	114	6	with	with	ADP
ejpam-2010	114	7	local	local	ADJ
ejpam-2010	114	8	units	unit	NOUN
ejpam-2010	114	9	the	the	DET
ejpam-2010	114	10	category	category	NOUN
ejpam-2010	114	11	of	of	ADP
ejpam-2010	114	12	unital	unital	ADJ
ejpam-2010	114	13	left	left	ADJ
ejpam-2010	114	14	r	r	NOUN
ejpam-2010	114	15	-	-	PUNCT
ejpam-2010	114	16	modules	module	NOUN
ejpam-2010	114	17	is	be	AUX
ejpam-2010	114	18	naturally	naturally	ADV
ejpam-2010	114	19	closed	close	VERB
ejpam-2010	114	20	and	and	CCONJ
ejpam-2010	114	21	so	so	ADV
ejpam-2010	114	22	we	we	PRON
ejpam-2010	114	23	denote	denote	VERB
ejpam-2010	114	24	by	by	ADP
ejpam-2010	114	25	r	r	NOUN
ejpam-2010	114	26	-	-	PUNCT
ejpam-2010	114	27	umod	umod	VERB
ejpam-2010	114	28	the	the	DET
ejpam-2010	114	29	category	category	NOUN
ejpam-2010	114	30	of	of	ADP
ejpam-2010	114	31	unitary	unitary	ADJ
ejpam-2010	114	32	left	left	ADJ
ejpam-2010	114	33	r	r	NOUN
ejpam-2010	114	34	-	-	PUNCT
ejpam-2010	114	35	modules	module	NOUN
ejpam-2010	114	36	and	and	CCONJ
ejpam-2010	114	37	the	the	DET
ejpam-2010	114	38	usual	usual	ADJ
ejpam-2010	114	39	left	left	ADJ
ejpam-2010	114	40	r	r	NOUN
ejpam-2010	114	41	-	-	PUNCT
ejpam-2010	114	42	homomorphisms	homomorphism	NOUN
ejpam-2010	114	43	.	.	PUNCT
ejpam-2010	115	1	dually	dually	PROPN
ejpam-2010	115	2	,	,	PUNCT
ejpam-2010	115	3	umod	umod	PROPN
ejpam-2010	115	4	-	-	PUNCT
ejpam-2010	115	5	r	r	NOUN
ejpam-2010	115	6	denotes	denote	NOUN
ejpam-2010	115	7	the	the	DET
ejpam-2010	115	8	category	category	NOUN
ejpam-2010	115	9	of	of	ADP
ejpam-2010	115	10	unitary	unitary	ADJ
ejpam-2010	115	11	right	right	ADJ
ejpam-2010	115	12	r	r	NOUN
ejpam-2010	115	13	-	-	PUNCT
ejpam-2010	115	14	modules	module	NOUN
ejpam-2010	115	15	.	.	PUNCT
ejpam-2010	116	1	thus	thus	ADV
ejpam-2010	116	2	,	,	PUNCT
ejpam-2010	116	3	for	for	ADP
ejpam-2010	116	4	a	a	DET
ejpam-2010	116	5	ring	ring	NOUN
ejpam-2010	116	6	r	r	NOUN
ejpam-2010	116	7	with	with	ADP
ejpam-2010	116	8	local	local	ADJ
ejpam-2010	116	9	units	unit	NOUN
ejpam-2010	116	10	we	we	PRON
ejpam-2010	116	11	have	have	VERB
ejpam-2010	116	12	rc	rc	NOUN
ejpam-2010	116	13	=	=	SYM
ejpam-2010	116	14	r	r	X
ejpam-2010	116	15	-	-	PUNCT
ejpam-2010	116	16	umod	umod	PROPN
ejpam-2010	116	17	and	and	CCONJ
ejpam-2010	116	18	cr	cr	NOUN
ejpam-2010	116	19	=	=	SYM
ejpam-2010	116	20	umod	umod	PROPN
ejpam-2010	116	21	-	-	PUNCT
ejpam-2010	116	22	r.	r.	PROPN
ejpam-2010	116	23	let	let	VERB
ejpam-2010	116	24	c	c	PRON
ejpam-2010	116	25	be	be	AUX
ejpam-2010	116	26	an	an	DET
ejpam-2010	116	27	arbitrary	arbitrary	ADJ
ejpam-2010	116	28	subcategory	subcategory	NOUN
ejpam-2010	116	29	of	of	ADP
ejpam-2010	116	30	r	r	NOUN
ejpam-2010	116	31	-	-	PUNCT
ejpam-2010	116	32	mod	mod	NOUN
ejpam-2010	116	33	.	.	PUNCT
ejpam-2010	117	1	a	a	DET
ejpam-2010	117	2	left	left	ADJ
ejpam-2010	117	3	r	r	NOUN
ejpam-2010	117	4	-	-	PUNCT
ejpam-2010	117	5	module	module	NOUN
ejpam-2010	117	6	p	p	NOUN
ejpam-2010	117	7	∈	∈	PROPN
ejpam-2010	117	8	c	c	NOUN
ejpam-2010	117	9	is	be	AUX
ejpam-2010	117	10	projective	projective	ADJ
ejpam-2010	117	11	if	if	SCONJ
ejpam-2010	117	12	for	for	ADP
ejpam-2010	117	13	any	any	DET
ejpam-2010	117	14	n	n	NOUN
ejpam-2010	117	15	,	,	PUNCT
ejpam-2010	117	16	m	m	VERB
ejpam-2010	117	17	∈	∈	PROPN
ejpam-2010	117	18	c	c	NOUN
ejpam-2010	117	19	,	,	PUNCT
ejpam-2010	117	20	every	every	DET
ejpam-2010	117	21	surjective	surjective	ADJ
ejpam-2010	117	22	left	leave	VERB
ejpam-2010	117	23	r	r	NOUN
ejpam-2010	117	24	-	-	PUNCT
ejpam-2010	117	25	homomorphism	homomorphism	ADJ
ejpam-2010	117	26	f	f	X
ejpam-2010	117	27	:	:	PUNCT
ejpam-2010	117	28	n	n	X
ejpam-2010	117	29	→	→	SYM
ejpam-2010	117	30	m	m	NOUN
ejpam-2010	117	31	and	and	CCONJ
ejpam-2010	117	32	every	every	PRON
ejpam-2010	117	33	left	left	ADJ
ejpam-2010	117	34	r	r	NOUN
ejpam-2010	117	35	-	-	PUNCT
ejpam-2010	117	36	homomorphism	homomorphism	NOUN
ejpam-2010	117	37	g	g	NOUN
ejpam-2010	117	38	:	:	PUNCT
ejpam-2010	117	39	p	p	X
ejpam-2010	117	40	→	→	X
ejpam-2010	117	41	m	m	PROPN
ejpam-2010	117	42	,	,	PUNCT
ejpam-2010	117	43	there	there	PRON
ejpam-2010	117	44	exists	exist	VERB
ejpam-2010	117	45	a	a	DET
ejpam-2010	117	46	homomorphism	homomorphism	NOUN
ejpam-2010	117	47	h	h	NOUN
ejpam-2010	117	48	:	:	PUNCT
ejpam-2010	117	49	p	p	X
ejpam-2010	117	50	→	→	SYM
ejpam-2010	117	51	n	n	CCONJ
ejpam-2010	117	52	such	such	ADJ
ejpam-2010	117	53	that	that	SCONJ
ejpam-2010	117	54	f	f	PROPN
ejpam-2010	118	1	h=	h=	PROPN
ejpam-2010	118	2	g.	g.	PROPN
ejpam-2010	118	3	let	let	VERB
ejpam-2010	118	4	r	r	PRON
ejpam-2010	118	5	be	be	AUX
ejpam-2010	118	6	a	a	DET
ejpam-2010	118	7	ring	ring	NOUN
ejpam-2010	118	8	with	with	ADP
ejpam-2010	118	9	slu	slu	NOUN
ejpam-2010	118	10	.	.	PUNCT
ejpam-2010	119	1	we	we	PRON
ejpam-2010	119	2	say	say	VERB
ejpam-2010	119	3	that	that	SCONJ
ejpam-2010	119	4	a	a	DET
ejpam-2010	119	5	progenerator	progenerator	NOUN
ejpam-2010	119	6	for	for	ADP
ejpam-2010	119	7	r	r	NOUN
ejpam-2010	119	8	is	be	AUX
ejpam-2010	119	9	a	a	DET
ejpam-2010	119	10	compatible	compatible	ADJ
ejpam-2010	119	11	set	set	NOUN
ejpam-2010	119	12	{	{	PUNCT
ejpam-2010	119	13	x	x	PROPN
ejpam-2010	119	14	i	i	PRON
ejpam-2010	119	15	,	,	PUNCT
ejpam-2010	119	16	φi	φi	PROPN
ejpam-2010	119	17	j	j	PROPN
ejpam-2010	119	18	,	,	PUNCT
ejpam-2010	119	19	ψ	ψ	VERB
ejpam-2010	119	20	ji|i	ji|i	PROPN
ejpam-2010	119	21	∈	∈	PROPN
ejpam-2010	120	1	i	i	PRON
ejpam-2010	120	2	}	}	PUNCT
ejpam-2010	120	3	in	in	ADP
ejpam-2010	120	4	r	r	NOUN
ejpam-2010	120	5	-	-	PUNCT
ejpam-2010	120	6	umod	umod	NOUN
ejpam-2010	120	7	such	such	ADJ
ejpam-2010	120	8	that	that	SCONJ
ejpam-2010	120	9	(	(	PUNCT
ejpam-2010	120	10	1	1	X
ejpam-2010	120	11	)	)	PUNCT
ejpam-2010	120	12	for	for	ADP
ejpam-2010	120	13	each	each	DET
ejpam-2010	120	14	i	i	PRON
ejpam-2010	120	15	∈	∈	PROPN
ejpam-2010	120	16	i	i	PRON
ejpam-2010	120	17	,	,	PUNCT
ejpam-2010	120	18	x	x	VERB
ejpam-2010	120	19	i	i	PRON
ejpam-2010	120	20	is	be	AUX
ejpam-2010	120	21	a	a	DET
ejpam-2010	120	22	finitely	finitely	ADV
ejpam-2010	120	23	generated	generate	VERB
ejpam-2010	120	24	projective	projective	NOUN
ejpam-2010	120	25	left	leave	VERB
ejpam-2010	120	26	r	r	NOUN
ejpam-2010	120	27	-	-	PUNCT
ejpam-2010	120	28	module	module	NOUN
ejpam-2010	120	29	;	;	PUNCT
ejpam-2010	120	30	(	(	PUNCT
ejpam-2010	120	31	2	2	X
ejpam-2010	120	32	)	)	PUNCT
ejpam-2010	120	33	x	x	X
ejpam-2010	121	1	=	=	PUNCT
ejpam-2010	121	2	lim−→i(x	lim−→i(x	PROPN
ejpam-2010	122	1	i	i	PRON
ejpam-2010	122	2	,	,	PUNCT
ejpam-2010	122	3	φi	φi	PROPN
ejpam-2010	122	4	j	j	NOUN
ejpam-2010	122	5	)	)	PUNCT
ejpam-2010	122	6	is	be	AUX
ejpam-2010	122	7	a	a	DET
ejpam-2010	122	8	generator	generator	NOUN
ejpam-2010	122	9	for	for	ADP
ejpam-2010	122	10	r	r	NOUN
ejpam-2010	122	11	-	-	PUNCT
ejpam-2010	122	12	umod	umod	NOUN
ejpam-2010	122	13	.	.	PUNCT
ejpam-2010	123	1	let	let	VERB
ejpam-2010	123	2	r	r	PRON
ejpam-2010	123	3	be	be	AUX
ejpam-2010	123	4	a	a	DET
ejpam-2010	123	5	ring	ring	NOUN
ejpam-2010	123	6	with	with	ADP
ejpam-2010	123	7	local	local	ADJ
ejpam-2010	123	8	units	unit	NOUN
ejpam-2010	123	9	.	.	PUNCT
ejpam-2010	124	1	an	an	DET
ejpam-2010	124	2	r	r	NOUN
ejpam-2010	124	3	-	-	PUNCT
ejpam-2010	124	4	module	module	NOUN
ejpam-2010	124	5	p	p	NOUN
ejpam-2010	124	6	is	be	AUX
ejpam-2010	124	7	called	call	VERB
ejpam-2010	124	8	locally	locally	ADV
ejpam-2010	124	9	projective	projective	ADJ
ejpam-2010	124	10	in	in	ADP
ejpam-2010	124	11	case	case	NOUN
ejpam-2010	124	12	there	there	PRON
ejpam-2010	124	13	exists	exist	VERB
ejpam-2010	124	14	a	a	DET
ejpam-2010	124	15	compatible	compatible	ADJ
ejpam-2010	124	16	set	set	NOUN
ejpam-2010	124	17	{	{	PUNCT
ejpam-2010	124	18	pi	pi	NOUN
ejpam-2010	124	19	,	,	PUNCT
ejpam-2010	124	20	φi	φi	ADP
ejpam-2010	124	21	j	j	PROPN
ejpam-2010	124	22	,	,	PUNCT
ejpam-2010	124	23	ψ	ψ	PROPN
ejpam-2010	124	24	ji	ji	PROPN
ejpam-2010	124	25	,	,	PUNCT
ejpam-2010	124	26	i	i	PRON
ejpam-2010	124	27	}	}	PUNCT
ejpam-2010	124	28	such	such	ADJ
ejpam-2010	124	29	that	that	SCONJ
ejpam-2010	124	30	each	each	DET
ejpam-2010	124	31	pi	pi	NOUN
ejpam-2010	124	32	is	be	AUX
ejpam-2010	124	33	a	a	DET
ejpam-2010	124	34	finitely	finitely	ADV
ejpam-2010	124	35	generated	generate	VERB
ejpam-2010	124	36	projective	projective	ADJ
ejpam-2010	124	37	r	r	NOUN
ejpam-2010	124	38	-	-	PUNCT
ejpam-2010	124	39	module	module	NOUN
ejpam-2010	124	40	,	,	PUNCT
ejpam-2010	124	41	and	and	CCONJ
ejpam-2010	124	42	p	p	NOUN
ejpam-2010	124	43	=	=	NOUN
ejpam-2010	124	44	lim−→i(pi	lim−→i(pi	NOUN
ejpam-2010	124	45	,	,	PUNCT
ejpam-2010	124	46	φi	φi	PROPN
ejpam-2010	124	47	j	j	PROPN
ejpam-2010	124	48	)	)	PUNCT
ejpam-2010	124	49	.	.	PUNCT
ejpam-2010	125	1	for	for	ADP
ejpam-2010	125	2	convenience	convenience	NOUN
ejpam-2010	125	3	,	,	PUNCT
ejpam-2010	125	4	we	we	PRON
ejpam-2010	125	5	denote	denote	VERB
ejpam-2010	125	6	a	a	DET
ejpam-2010	125	7	locally	locally	ADV
ejpam-2010	125	8	projective	projective	NOUN
ejpam-2010	125	9	p	p	NOUN
ejpam-2010	125	10	by	by	ADP
ejpam-2010	125	11	{	{	PUNCT
ejpam-2010	125	12	p	p	X
ejpam-2010	125	13	,	,	PUNCT
ejpam-2010	125	14	φ	φ	PROPN
ejpam-2010	125	15	,	,	PUNCT
ejpam-2010	125	16	ψ	ψ	SYM
ejpam-2010	125	17	,	,	PUNCT
ejpam-2010	125	18	i	i	NOUN
ejpam-2010	125	19	}	}	PUNCT
ejpam-2010	125	20	.	.	PUNCT
ejpam-2010	126	1	let	let	VERB
ejpam-2010	126	2	{	{	PUNCT
ejpam-2010	126	3	p	p	X
ejpam-2010	126	4	,	,	PUNCT
ejpam-2010	126	5	φ	φ	PROPN
ejpam-2010	126	6	,	,	PUNCT
ejpam-2010	126	7	ψ	ψ	SYM
ejpam-2010	126	8	,	,	PUNCT
ejpam-2010	126	9	i	i	PRON
ejpam-2010	126	10	}	}	PUNCT
ejpam-2010	126	11	and	and	CCONJ
ejpam-2010	126	12	{	{	PUNCT
ejpam-2010	126	13	q	q	NOUN
ejpam-2010	126	14	,	,	PUNCT
ejpam-2010	126	15	τ	τ	PROPN
ejpam-2010	126	16	,	,	PUNCT
ejpam-2010	126	17	σ	σ	PROPN
ejpam-2010	126	18	,	,	PUNCT
ejpam-2010	126	19	k	k	NOUN
ejpam-2010	126	20	}	}	PUNCT
ejpam-2010	126	21	be	be	VERB
ejpam-2010	126	22	locally	locally	ADV
ejpam-2010	126	23	projective	projective	ADJ
ejpam-2010	126	24	r	r	NOUN
ejpam-2010	126	25	-	-	PUNCT
ejpam-2010	126	26	modules	module	NOUN
ejpam-2010	126	27	,	,	PUNCT
ejpam-2010	126	28	and	and	CCONJ
ejpam-2010	126	29	let	let	VERB
ejpam-2010	126	30	f	f	PROPN
ejpam-2010	126	31	∈	∈	PROPN
ejpam-2010	126	32	homr(p	homr(p	PROPN
ejpam-2010	126	33	,	,	PUNCT
ejpam-2010	126	34	q	q	NOUN
ejpam-2010	126	35	)	)	PUNCT
ejpam-2010	126	36	.	.	PUNCT
ejpam-2010	127	1	we	we	PRON
ejpam-2010	127	2	call	call	VERB
ejpam-2010	127	3	f	f	PROPN
ejpam-2010	127	4	a	a	DET
ejpam-2010	127	5	localized	localized	ADJ
ejpam-2010	127	6	morphism	morphism	NOUN
ejpam-2010	127	7	from	from	ADP
ejpam-2010	127	8	{	{	PUNCT
ejpam-2010	127	9	p	p	PROPN
ejpam-2010	127	10	,	,	PUNCT
ejpam-2010	127	11	φ	φ	PROPN
ejpam-2010	127	12	,	,	PUNCT
ejpam-2010	127	13	ψ	ψ	SYM
ejpam-2010	127	14	,	,	PUNCT
ejpam-2010	127	15	i	i	PRON
ejpam-2010	127	16	}	}	PUNCT
ejpam-2010	127	17	to	to	ADP
ejpam-2010	127	18	{	{	PUNCT
ejpam-2010	127	19	q	q	NOUN
ejpam-2010	127	20	,	,	PUNCT
ejpam-2010	127	21	τ	τ	PROPN
ejpam-2010	127	22	,	,	PUNCT
ejpam-2010	127	23	σ	σ	PROPN
ejpam-2010	127	24	,	,	PUNCT
ejpam-2010	127	25	k	k	PROPN
ejpam-2010	127	26	}	}	PUNCT
ejpam-2010	127	27	if	if	SCONJ
ejpam-2010	127	28	there	there	PRON
ejpam-2010	127	29	exists	exist	VERB
ejpam-2010	127	30	i	i	PRON
ejpam-2010	127	31	∈	∈	VERB
ejpam-2010	128	1	i	i	PRON
ejpam-2010	128	2	such	such	ADJ
ejpam-2010	128	3	that	that	SCONJ
ejpam-2010	128	4	f	f	PROPN
ejpam-2010	128	5	=	=	NOUN
ejpam-2010	128	6	ψiφi	ψiφi	VERB
ejpam-2010	128	7	f	f	PROPN
ejpam-2010	128	8	.	.	PUNCT
ejpam-2010	129	1	let	let	VERB
ejpam-2010	129	2	r	r	PRON
ejpam-2010	129	3	be	be	AUX
ejpam-2010	129	4	a	a	DET
ejpam-2010	129	5	ring	ring	NOUN
ejpam-2010	129	6	with	with	ADP
ejpam-2010	129	7	slu	slu	NOUN
ejpam-2010	129	8	.	.	PUNCT
ejpam-2010	130	1	abrams	abrams	PROPN
ejpam-2010	131	1	[	[	X
ejpam-2010	131	2	1	1	X
ejpam-2010	131	3	]	]	PUNCT
ejpam-2010	131	4	showed	show	VERB
ejpam-2010	131	5	that	that	SCONJ
ejpam-2010	131	6	the	the	DET
ejpam-2010	131	7	collection	collection	NOUN
ejpam-2010	131	8	of	of	ADP
ejpam-2010	131	9	locally	locally	ADV
ejpam-2010	131	10	projective	projective	ADJ
ejpam-2010	131	11	r	r	NOUN
ejpam-2010	131	12	-	-	PUNCT
ejpam-2010	131	13	modules	module	NOUN
ejpam-2010	131	14	,	,	PUNCT
ejpam-2010	131	15	together	together	ADV
ejpam-2010	131	16	with	with	ADP
ejpam-2010	131	17	localized	localized	ADJ
ejpam-2010	131	18	morphisms	morphism	NOUN
ejpam-2010	131	19	forms	form	NOUN
ejpam-2010	131	20	a	a	DET
ejpam-2010	131	21	category	category	NOUN
ejpam-2010	131	22	with	with	ADP
ejpam-2010	131	23	slu	slu	NOUN
ejpam-2010	131	24	.	.	PUNCT
ejpam-2010	132	1	denote	denote	VERB
ejpam-2010	132	2	such	such	DET
ejpam-2010	132	3	a	a	DET
ejpam-2010	132	4	category	category	NOUN
ejpam-2010	132	5	by	by	ADP
ejpam-2010	132	6	lp(r	lp(r	NOUN
ejpam-2010	132	7	)	)	PUNCT
ejpam-2010	132	8	.	.	PUNCT
ejpam-2010	133	1	let	let	VERB
ejpam-2010	133	2	r	r	NOUN
ejpam-2010	133	3	and	and	CCONJ
ejpam-2010	133	4	s	s	VERB
ejpam-2010	133	5	be	be	AUX
ejpam-2010	133	6	rings	ring	NOUN
ejpam-2010	133	7	.	.	PUNCT
ejpam-2010	134	1	a	a	DET
ejpam-2010	134	2	six	six	NUM
ejpam-2010	134	3	-	-	PUNCT
ejpam-2010	134	4	tuple	tuple	NOUN
ejpam-2010	134	5	〈	〈	PROPN
ejpam-2010	134	6	r	r	PROPN
ejpam-2010	134	7	,	,	PUNCT
ejpam-2010	134	8	s	s	PART
ejpam-2010	134	9	,	,	PUNCT
ejpam-2010	134	10	r	r	NOUN
ejpam-2010	134	11	ps	ps	PROPN
ejpam-2010	134	12	,	,	PUNCT
ejpam-2010	134	13	s	s	PROPN
ejpam-2010	134	14	qr	qr	NOUN
ejpam-2010	134	15	,	,	PUNCT
ejpam-2010	134	16	〈	〈	PROPN
ejpam-2010	134	17	,	,	PUNCT
ejpam-2010	134	18	〉	〉	NOUN
ejpam-2010	134	19	,	,	PUNCT
ejpam-2010	134	20	[	[	X
ejpam-2010	134	21	,	,	PUNCT
ejpam-2010	134	22	]	]	PUNCT
ejpam-2010	134	23	〉	〉	NOUN
ejpam-2010	134	24	is	be	AUX
ejpam-2010	134	25	said	say	VERB
ejpam-2010	134	26	to	to	PART
ejpam-2010	134	27	be	be	AUX
ejpam-2010	134	28	a	a	DET
ejpam-2010	134	29	morita	morita	NOUN
ejpam-2010	134	30	context	context	NOUN
ejpam-2010	134	31	if	if	SCONJ
ejpam-2010	134	32	the	the	DET
ejpam-2010	134	33	following	follow	VERB
ejpam-2010	134	34	conditions	condition	NOUN
ejpam-2010	134	35	hold	hold	VERB
ejpam-2010	134	36	:	:	PUNCT
ejpam-2010	134	37	(	(	PUNCT
ejpam-2010	134	38	1	1	X
ejpam-2010	134	39	)	)	PUNCT
ejpam-2010	134	40	rps	rps	NOUN
ejpam-2010	134	41	is	be	AUX
ejpam-2010	134	42	an	an	DET
ejpam-2010	134	43	r	r	NOUN
ejpam-2010	134	44	-	-	PUNCT
ejpam-2010	134	45	s	s	NOUN
ejpam-2010	134	46	-	-	PUNCT
ejpam-2010	134	47	bimodule	bimodule	NOUN
ejpam-2010	134	48	and	and	CCONJ
ejpam-2010	134	49	sqr	sqr	PROPN
ejpam-2010	134	50	is	be	AUX
ejpam-2010	134	51	an	an	DET
ejpam-2010	134	52	s	s	NOUN
ejpam-2010	134	53	-	-	PUNCT
ejpam-2010	134	54	r	r	NOUN
ejpam-2010	134	55	-	-	PUNCT
ejpam-2010	134	56	bimodule	bimodule	NOUN
ejpam-2010	134	57	;	;	PUNCT
ejpam-2010	134	58	(	(	PUNCT
ejpam-2010	134	59	2	2	X
ejpam-2010	134	60	)	)	PUNCT
ejpam-2010	134	61	〈	〈	PROPN
ejpam-2010	134	62	,	,	PUNCT
ejpam-2010	134	63	〉	〉	NOUN
ejpam-2010	134	64	is	be	AUX
ejpam-2010	134	65	an	an	DET
ejpam-2010	134	66	r	r	NOUN
ejpam-2010	134	67	-	-	PUNCT
ejpam-2010	134	68	r	r	NOUN
ejpam-2010	134	69	-	-	PUNCT
ejpam-2010	134	70	homomorphism	homomorphism	NOUN
ejpam-2010	134	71	of	of	ADP
ejpam-2010	134	72	p⊗sq	p⊗sq	NOUN
ejpam-2010	134	73	into	into	ADP
ejpam-2010	134	74	r	r	NOUN
ejpam-2010	134	75	,	,	PUNCT
ejpam-2010	134	76	and	and	CCONJ
ejpam-2010	134	77	[	[	X
ejpam-2010	134	78	,	,	PUNCT
ejpam-2010	134	79	]	]	PUNCT
ejpam-2010	134	80	is	be	AUX
ejpam-2010	134	81	an	an	DET
ejpam-2010	134	82	s	s	PROPN
ejpam-2010	134	83	-	-	PUNCT
ejpam-2010	134	84	s	s	NOUN
ejpam-2010	134	85	-	-	NOUN
ejpam-2010	134	86	homomorphism	homomorphism	NOUN
ejpam-2010	134	87	of	of	ADP
ejpam-2010	134	88	q⊗r	q⊗r	PROPN
ejpam-2010	134	89	p	p	NOUN
ejpam-2010	134	90	into	into	ADP
ejpam-2010	134	91	s	s	PRON
ejpam-2010	134	92	;	;	PUNCT
ejpam-2010	134	93	(	(	PUNCT
ejpam-2010	134	94	3	3	X
ejpam-2010	134	95	)	)	PUNCT
ejpam-2010	134	96	for	for	ADP
ejpam-2010	134	97	all	all	DET
ejpam-2010	134	98	p	p	NOUN
ejpam-2010	134	99	,	,	PUNCT
ejpam-2010	134	100	p′	p′	NOUN
ejpam-2010	134	101	∈	∈	PROPN
ejpam-2010	134	102	p	p	NOUN
ejpam-2010	134	103	and	and	CCONJ
ejpam-2010	134	104	q	q	NOUN
ejpam-2010	134	105	,	,	PUNCT
ejpam-2010	134	106	q′	q′	NOUN
ejpam-2010	134	107	∈q	∈q	NOUN
ejpam-2010	134	108	we	we	PRON
ejpam-2010	134	109	have	have	VERB
ejpam-2010	134	110	〈	〈	PROPN
ejpam-2010	134	111	p	p	NOUN
ejpam-2010	134	112	,	,	PUNCT
ejpam-2010	134	113	q〉p′	q〉p′	NUM
ejpam-2010	134	114	=	=	PROPN
ejpam-2010	134	115	p[q	p[q	PROPN
ejpam-2010	134	116	,	,	PUNCT
ejpam-2010	134	117	p′	p′	PROPN
ejpam-2010	134	118	]	]	PUNCT
ejpam-2010	134	119	and	and	CCONJ
ejpam-2010	134	120	q〈p	q〈p	PROPN
ejpam-2010	134	121	,	,	PUNCT
ejpam-2010	134	122	q′〉=	q′〉=	VERB
ejpam-2010	134	123	[	[	X
ejpam-2010	134	124	q	q	X
ejpam-2010	134	125	,	,	PUNCT
ejpam-2010	134	126	p]q′.	p]q′.	PROPN
ejpam-2010	134	127	y.	y.	PROPN
ejpam-2010	134	128	wang	wang	PROPN
ejpam-2010	134	129	,	,	PUNCT
ejpam-2010	134	130	k.	k.	PROPN
ejpam-2010	134	131	shum	shum	PROPN
ejpam-2010	134	132	,	,	PUNCT
ejpam-2010	134	133	x.	x.	PROPN
ejpam-2010	134	134	ren	ren	PROPN
ejpam-2010	134	135	/	/	SYM
ejpam-2010	134	136	eur	eur	PROPN
ejpam-2010	134	137	.	.	PUNCT
ejpam-2010	135	1	j.	j.	PROPN
ejpam-2010	135	2	pure	pure	PROPN
ejpam-2010	135	3	appl	appl	PROPN
ejpam-2010	135	4	.	.	PROPN
ejpam-2010	135	5	math	math	PROPN
ejpam-2010	135	6	,	,	PUNCT
ejpam-2010	135	7	6	6	NUM
ejpam-2010	135	8	(	(	PUNCT
ejpam-2010	135	9	2013	2013	NUM
ejpam-2010	135	10	)	)	PUNCT
ejpam-2010	135	11	,	,	PUNCT
ejpam-2010	135	12	256	256	NUM
ejpam-2010	135	13	-	-	SYM
ejpam-2010	135	14	281	281	NUM
ejpam-2010	135	15	260	260	NUM
ejpam-2010	135	16	for	for	ADP
ejpam-2010	135	17	convenience	convenience	NOUN
ejpam-2010	135	18	the	the	DET
ejpam-2010	135	19	images	image	NOUN
ejpam-2010	135	20	on	on	ADP
ejpam-2010	135	21	r	r	NOUN
ejpam-2010	135	22	and	and	CCONJ
ejpam-2010	135	23	s	s	PROPN
ejpam-2010	135	24	of	of	ADP
ejpam-2010	135	25	bimodule	bimodule	NOUN
ejpam-2010	135	26	homomorphisms	homomorphisms	PROPN
ejpam-2010	135	27	〈	〈	PROPN
ejpam-2010	135	28	,	,	PUNCT
ejpam-2010	135	29	〉	〉	NOUN
ejpam-2010	135	30	and	and	CCONJ
ejpam-2010	135	31	[	[	X
ejpam-2010	135	32	,	,	PUNCT
ejpam-2010	135	33	]	]	PUNCT
ejpam-2010	135	34	are	be	AUX
ejpam-2010	135	35	called	call	VERB
ejpam-2010	135	36	the	the	DET
ejpam-2010	135	37	traces	trace	NOUN
ejpam-2010	135	38	of	of	ADP
ejpam-2010	135	39	the	the	DET
ejpam-2010	135	40	context	context	NOUN
ejpam-2010	135	41	.	.	PUNCT
ejpam-2010	136	1	for	for	ADP
ejpam-2010	136	2	rings	ring	NOUN
ejpam-2010	136	3	with	with	ADP
ejpam-2010	136	4	local	local	ADJ
ejpam-2010	136	5	units	unit	NOUN
ejpam-2010	136	6	r	r	NOUN
ejpam-2010	136	7	and	and	CCONJ
ejpam-2010	136	8	s	s	PART
ejpam-2010	136	9	,	,	PUNCT
ejpam-2010	136	10	we	we	PRON
ejpam-2010	136	11	call	call	VERB
ejpam-2010	136	12	r	r	NOUN
ejpam-2010	136	13	and	and	CCONJ
ejpam-2010	136	14	s	s	NOUN
ejpam-2010	136	15	are	be	AUX
ejpam-2010	136	16	morita	morita	NOUN
ejpam-2010	136	17	equivalent	equivalent	ADJ
ejpam-2010	136	18	if	if	SCONJ
ejpam-2010	136	19	r	r	X
ejpam-2010	136	20	-	-	PUNCT
ejpam-2010	136	21	umod	umod	PROPN
ejpam-2010	136	22	is	be	AUX
ejpam-2010	136	23	equivalent	equivalent	ADJ
ejpam-2010	136	24	to	to	ADP
ejpam-2010	136	25	s	s	NOUN
ejpam-2010	136	26	-	-	PUNCT
ejpam-2010	136	27	umod	umod	PROPN
ejpam-2010	136	28	.	.	PUNCT
ejpam-2010	137	1	notice	notice	VERB
ejpam-2010	137	2	that	that	SCONJ
ejpam-2010	137	3	if	if	SCONJ
ejpam-2010	137	4	r	r	NOUN
ejpam-2010	137	5	and	and	CCONJ
ejpam-2010	137	6	s	s	NOUN
ejpam-2010	137	7	are	be	AUX
ejpam-2010	137	8	unital	unital	ADJ
ejpam-2010	137	9	then	then	ADV
ejpam-2010	137	10	r	r	NOUN
ejpam-2010	137	11	and	and	CCONJ
ejpam-2010	137	12	s	s	NOUN
ejpam-2010	137	13	are	be	AUX
ejpam-2010	137	14	morita	morita	NOUN
ejpam-2010	137	15	equivalent	equivalent	ADJ
ejpam-2010	137	16	if	if	SCONJ
ejpam-2010	137	17	and	and	CCONJ
ejpam-2010	137	18	only	only	ADV
ejpam-2010	137	19	if	if	SCONJ
ejpam-2010	137	20	r	r	NOUN
ejpam-2010	137	21	-	-	PUNCT
ejpam-2010	137	22	mod	mod	NOUN
ejpam-2010	137	23	is	be	AUX
ejpam-2010	137	24	equivalent	equivalent	ADJ
ejpam-2010	137	25	to	to	ADP
ejpam-2010	137	26	s	s	NOUN
ejpam-2010	137	27	-	-	NOUN
ejpam-2010	137	28	mod	mod	NOUN
ejpam-2010	137	29	.	.	PUNCT
ejpam-2010	138	1	we	we	PRON
ejpam-2010	138	2	say	say	VERB
ejpam-2010	138	3	that	that	SCONJ
ejpam-2010	138	4	arbitrary	arbitrary	ADJ
ejpam-2010	138	5	rings	ring	NOUN
ejpam-2010	138	6	r	r	NOUN
ejpam-2010	138	7	and	and	CCONJ
ejpam-2010	138	8	s	s	NOUN
ejpam-2010	138	9	are	be	AUX
ejpam-2010	138	10	morita	morita	NOUN
ejpam-2010	138	11	-	-	PUNCT
ejpam-2010	138	12	like	like	ADJ
ejpam-2010	138	13	equivalent	equivalent	NOUN
ejpam-2010	138	14	if	if	SCONJ
ejpam-2010	138	15	cr	cr	PROPN
ejpam-2010	138	16	and	and	CCONJ
ejpam-2010	138	17	cs	cs	PROPN
ejpam-2010	138	18	are	be	AUX
ejpam-2010	138	19	equivalent	equivalent	ADJ
ejpam-2010	138	20	.	.	PUNCT
ejpam-2010	139	1	clearly	clearly	ADV
ejpam-2010	139	2	,	,	PUNCT
ejpam-2010	139	3	for	for	ADP
ejpam-2010	139	4	rings	ring	NOUN
ejpam-2010	139	5	r	r	NOUN
ejpam-2010	139	6	with	with	ADP
ejpam-2010	139	7	local	local	ADJ
ejpam-2010	139	8	units	unit	NOUN
ejpam-2010	139	9	we	we	PRON
ejpam-2010	139	10	have	have	VERB
ejpam-2010	139	11	cr	cr	NOUN
ejpam-2010	139	12	=	=	PUNCT
ejpam-2010	139	13	umod	umod	PROPN
ejpam-2010	139	14	-	-	PUNCT
ejpam-2010	139	15	r.	r.	PROPN
ejpam-2010	139	16	thus	thus	ADV
ejpam-2010	139	17	,	,	PUNCT
ejpam-2010	139	18	the	the	DET
ejpam-2010	139	19	concept	concept	NOUN
ejpam-2010	139	20	of	of	ADP
ejpam-2010	139	21	morita	morita	PROPN
ejpam-2010	139	22	-	-	PUNCT
ejpam-2010	139	23	like	like	ADJ
ejpam-2010	139	24	equivalent	equivalent	NOUN
ejpam-2010	139	25	is	be	AUX
ejpam-2010	139	26	a	a	DET
ejpam-2010	139	27	generalisation	generalisation	NOUN
ejpam-2010	139	28	of	of	ADP
ejpam-2010	139	29	morita	morita	PROPN
ejpam-2010	139	30	equivalence	equivalence	NOUN
ejpam-2010	139	31	for	for	ADP
ejpam-2010	139	32	rings	ring	NOUN
ejpam-2010	139	33	with	with	ADP
ejpam-2010	139	34	local	local	ADJ
ejpam-2010	139	35	units	unit	NOUN
ejpam-2010	139	36	.	.	PUNCT
ejpam-2010	140	1	the	the	DET
ejpam-2010	140	2	morita	morita	PROPN
ejpam-2010	140	3	theory	theory	NOUN
ejpam-2010	140	4	is	be	AUX
ejpam-2010	140	5	not	not	PART
ejpam-2010	140	6	only	only	ADV
ejpam-2010	140	7	expressed	express	VERB
ejpam-2010	140	8	in	in	ADP
ejpam-2010	140	9	terms	term	NOUN
ejpam-2010	140	10	of	of	ADP
ejpam-2010	140	11	categories	category	NOUN
ejpam-2010	140	12	and	and	CCONJ
ejpam-2010	140	13	mortia	mortia	VERB
ejpam-2010	140	14	contexts	context	NOUN
ejpam-2010	140	15	as	as	ADP
ejpam-2010	140	16	above	above	ADV
ejpam-2010	140	17	,	,	PUNCT
ejpam-2010	140	18	but	but	CCONJ
ejpam-2010	140	19	also	also	ADV
ejpam-2010	140	20	described	describe	VERB
ejpam-2010	140	21	by	by	ADP
ejpam-2010	140	22	the	the	DET
ejpam-2010	140	23	matrix	matrix	NOUN
ejpam-2010	140	24	formulation	formulation	NOUN
ejpam-2010	140	25	.	.	PUNCT
ejpam-2010	141	1	let	let	VERB
ejpam-2010	141	2	r	r	PRON
ejpam-2010	141	3	be	be	AUX
ejpam-2010	141	4	a	a	DET
ejpam-2010	141	5	ring	ring	NOUN
ejpam-2010	141	6	and	and	CCONJ
ejpam-2010	141	7	γ	γ	NOUN
ejpam-2010	141	8	be	be	AUX
ejpam-2010	141	9	an	an	DET
ejpam-2010	141	10	arbitrary	arbitrary	ADJ
ejpam-2010	141	11	indexing	indexing	NOUN
ejpam-2010	141	12	set	set	NOUN
ejpam-2010	141	13	.	.	PUNCT
ejpam-2010	142	1	we	we	PRON
ejpam-2010	142	2	define	define	VERB
ejpam-2010	142	3	(	(	PUNCT
ejpam-2010	142	4	1	1	NUM
ejpam-2010	142	5	)	)	PUNCT
ejpam-2010	142	6	mγ(r	mγ(r	NOUN
ejpam-2010	142	7	)	)	PUNCT
ejpam-2010	142	8	to	to	PART
ejpam-2010	142	9	be	be	AUX
ejpam-2010	142	10	the	the	DET
ejpam-2010	142	11	matrix	matrix	NOUN
ejpam-2010	142	12	ring	ring	NOUN
ejpam-2010	142	13	of	of	ADP
ejpam-2010	142	14	all	all	PRON
ejpam-2010	142	15	γ×	γ×	NOUN
ejpam-2010	142	16	γ	γ	PROPN
ejpam-2010	142	17	row	row	NOUN
ejpam-2010	142	18	-	-	PUNCT
ejpam-2010	142	19	finite	finite	NOUN
ejpam-2010	142	20	matrices	matrix	NOUN
ejpam-2010	142	21	over	over	ADP
ejpam-2010	142	22	r	r	NOUN
ejpam-2010	142	23	(	(	PUNCT
ejpam-2010	142	24	i.e.	i.e.	X
ejpam-2010	142	25	,	,	PUNCT
ejpam-2010	142	26	if	if	SCONJ
ejpam-2010	142	27	m	m	VERB
ejpam-2010	142	28	∈	∈	NOUN
ejpam-2010	142	29	mγ(r	mγ(r	NOUN
ejpam-2010	142	30	)	)	PUNCT
ejpam-2010	142	31	then	then	ADV
ejpam-2010	142	32	each	each	DET
ejpam-2010	142	33	row	row	NOUN
ejpam-2010	142	34	of	of	ADP
ejpam-2010	142	35	m	m	PROPN
ejpam-2010	142	36	has	have	VERB
ejpam-2010	142	37	at	at	ADP
ejpam-2010	142	38	most	most	ADJ
ejpam-2010	142	39	a	a	DET
ejpam-2010	142	40	finite	finite	ADJ
ejpam-2010	142	41	number	number	NOUN
ejpam-2010	142	42	of	of	ADP
ejpam-2010	142	43	non	non	ADJ
ejpam-2010	142	44	-	-	ADJ
ejpam-2010	142	45	zero	zero	NUM
ejpam-2010	142	46	entries	entry	NOUN
ejpam-2010	142	47	)	)	PUNCT
ejpam-2010	142	48	;	;	PUNCT
ejpam-2010	142	49	(	(	PUNCT
ejpam-2010	142	50	2	2	X
ejpam-2010	142	51	)	)	PUNCT
ejpam-2010	142	52	m0	m0	PROPN
ejpam-2010	142	53	γ(r	γ(r	PROPN
ejpam-2010	142	54	)	)	PUNCT
ejpam-2010	142	55	to	to	PART
ejpam-2010	142	56	be	be	AUX
ejpam-2010	142	57	the	the	DET
ejpam-2010	142	58	subring	subring	NOUN
ejpam-2010	142	59	of	of	ADP
ejpam-2010	142	60	those	those	DET
ejpam-2010	142	61	matrices	matrix	NOUN
ejpam-2010	142	62	of	of	ADP
ejpam-2010	142	63	mγ(r	mγ(r	NOUN
ejpam-2010	142	64	)	)	PUNCT
ejpam-2010	142	65	with	with	ADP
ejpam-2010	142	66	at	at	ADP
ejpam-2010	142	67	most	most	ADJ
ejpam-2010	142	68	a	a	DET
ejpam-2010	142	69	finite	finite	ADJ
ejpam-2010	142	70	number	number	NOUN
ejpam-2010	142	71	of	of	ADP
ejpam-2010	142	72	non	non	ADJ
ejpam-2010	142	73	-	-	ADJ
ejpam-2010	142	74	zero	zero	ADJ
ejpam-2010	142	75	columns	column	NOUN
ejpam-2010	142	76	(	(	PUNCT
ejpam-2010	142	77	we	we	PRON
ejpam-2010	142	78	call	call	VERB
ejpam-2010	142	79	such	such	ADJ
ejpam-2010	142	80	matrices	matrix	NOUN
ejpam-2010	142	81	almost	almost	ADV
ejpam-2010	142	82	zero	zero	NUM
ejpam-2010	142	83	-	-	PUNCT
ejpam-2010	142	84	column	column	NOUN
ejpam-2010	142	85	matrices	matrix	NOUN
ejpam-2010	142	86	)	)	PUNCT
ejpam-2010	142	87	.	.	PUNCT
ejpam-2010	143	1	notice	notice	VERB
ejpam-2010	143	2	that	that	SCONJ
ejpam-2010	143	3	if	if	SCONJ
ejpam-2010	143	4	γ	γ	NOUN
ejpam-2010	143	5	is	be	AUX
ejpam-2010	143	6	finite	finite	NOUN
ejpam-2010	143	7	then	then	ADV
ejpam-2010	143	8	mγ(r	mγ(r	X
ejpam-2010	143	9	)	)	PUNCT
ejpam-2010	144	1	=	=	SYM
ejpam-2010	144	2	m0	m0	PROPN
ejpam-2010	144	3	γ(r	γ(r	PROPN
ejpam-2010	144	4	)	)	PUNCT
ejpam-2010	144	5	is	be	AUX
ejpam-2010	144	6	the	the	DET
ejpam-2010	144	7	matrix	matrix	NOUN
ejpam-2010	144	8	ring	ring	NOUN
ejpam-2010	144	9	of	of	ADP
ejpam-2010	144	10	all	all	PRON
ejpam-2010	144	11	γ×	γ×	NOUN
ejpam-2010	144	12	γ	γ	PROPN
ejpam-2010	144	13	matrices	matrice	VERB
ejpam-2010	144	14	over	over	ADP
ejpam-2010	144	15	r.	r.	PROPN
ejpam-2010	144	16	in	in	ADP
ejpam-2010	144	17	[	[	X
ejpam-2010	144	18	15	15	NUM
ejpam-2010	144	19	]	]	X
ejpam-2010	144	20	morita	morita	PROPN
ejpam-2010	144	21	’s	’s	PART
ejpam-2010	144	22	definition	definition	NOUN
ejpam-2010	144	23	of	of	ADP
ejpam-2010	144	24	equivalence	equivalence	NOUN
ejpam-2010	144	25	may	may	AUX
ejpam-2010	144	26	now	now	ADV
ejpam-2010	144	27	be	be	AUX
ejpam-2010	144	28	stated	state	VERB
ejpam-2010	144	29	as	as	SCONJ
ejpam-2010	144	30	follows	follow	VERB
ejpam-2010	144	31	:	:	PUNCT
ejpam-2010	144	32	rings	ring	NOUN
ejpam-2010	144	33	r	r	NOUN
ejpam-2010	144	34	and	and	CCONJ
ejpam-2010	144	35	s	s	NOUN
ejpam-2010	144	36	are	be	AUX
ejpam-2010	144	37	morita	morita	NOUN
ejpam-2010	144	38	equivalent	equivalent	ADJ
ejpam-2010	144	39	if	if	SCONJ
ejpam-2010	144	40	there	there	PRON
ejpam-2010	144	41	exists	exist	VERB
ejpam-2010	144	42	a	a	DET
ejpam-2010	144	43	natural	natural	ADJ
ejpam-2010	144	44	number	number	NOUN
ejpam-2010	144	45	n	n	NOUN
ejpam-2010	144	46	and	and	CCONJ
ejpam-2010	144	47	an	an	DET
ejpam-2010	144	48	idempotent	idempotent	ADJ
ejpam-2010	144	49	matrix	matrix	NOUN
ejpam-2010	144	50	l	l	NOUN
ejpam-2010	144	51	∈	∈	PROPN
ejpam-2010	144	52	mn(r	mn(r	NOUN
ejpam-2010	144	53	)	)	PUNCT
ejpam-2010	144	54	such	such	ADJ
ejpam-2010	144	55	that	that	SCONJ
ejpam-2010	144	56	(	(	PUNCT
ejpam-2010	144	57	1	1	X
ejpam-2010	144	58	)	)	PUNCT
ejpam-2010	144	59	s	s	VERB
ejpam-2010	144	60	∼=	∼=	PROPN
ejpam-2010	144	61	lmn(r)l	lmn(r)l	NOUN
ejpam-2010	144	62	;	;	PUNCT
ejpam-2010	144	63	(	(	PUNCT
ejpam-2010	144	64	2	2	X
ejpam-2010	144	65	)	)	PUNCT
ejpam-2010	144	66	mn(r)lmn(r	mn(r)lmn(r	NOUN
ejpam-2010	144	67	)	)	PUNCT
ejpam-2010	144	68	=	=	SYM
ejpam-2010	144	69	mn(r	mn(r	NOUN
ejpam-2010	144	70	)	)	PUNCT
ejpam-2010	144	71	.	.	PUNCT
ejpam-2010	145	1	2.2	2.2	NUM
ejpam-2010	145	2	.	.	PUNCT
ejpam-2010	145	3	semigroups	semigroup	NOUN
ejpam-2010	145	4	and	and	CCONJ
ejpam-2010	145	5	acts	act	NOUN
ejpam-2010	145	6	we	we	PRON
ejpam-2010	145	7	begin	begin	VERB
ejpam-2010	145	8	with	with	ADP
ejpam-2010	145	9	recalling	recall	VERB
ejpam-2010	145	10	some	some	DET
ejpam-2010	145	11	definitions	definition	NOUN
ejpam-2010	145	12	needed	need	VERB
ejpam-2010	145	13	in	in	ADP
ejpam-2010	145	14	the	the	DET
ejpam-2010	145	15	sequel	sequel	NOUN
ejpam-2010	145	16	.	.	PUNCT
ejpam-2010	146	1	an	an	DET
ejpam-2010	146	2	element	element	NOUN
ejpam-2010	146	3	s	s	NOUN
ejpam-2010	146	4	of	of	ADP
ejpam-2010	146	5	a	a	DET
ejpam-2010	146	6	semigroup	semigroup	NOUN
ejpam-2010	146	7	s	s	PART
ejpam-2010	146	8	is	be	AUX
ejpam-2010	146	9	called	call	VERB
ejpam-2010	146	10	regular	regular	ADJ
ejpam-2010	146	11	if	if	SCONJ
ejpam-2010	146	12	there	there	PRON
ejpam-2010	146	13	exists	exist	VERB
ejpam-2010	146	14	s′	s′	ADJ
ejpam-2010	146	15	∈	∈	PROPN
ejpam-2010	146	16	s	s	VERB
ejpam-2010	146	17	such	such	ADJ
ejpam-2010	146	18	that	that	DET
ejpam-2010	146	19	s	s	PART
ejpam-2010	146	20	=	=	X
ejpam-2010	146	21	ss′s	ss′s	NOUN
ejpam-2010	146	22	and	and	CCONJ
ejpam-2010	146	23	s′	s′	ADJ
ejpam-2010	146	24	=	=	PUNCT
ejpam-2010	146	25	s′ss′.	s′ss′.	NOUN
ejpam-2010	146	26	here	here	ADV
ejpam-2010	146	27	s′	s′	PRON
ejpam-2010	146	28	is	be	AUX
ejpam-2010	146	29	called	call	VERB
ejpam-2010	146	30	an	an	DET
ejpam-2010	146	31	inverse	inverse	NOUN
ejpam-2010	146	32	of	of	ADP
ejpam-2010	146	33	s.	s.	PROPN
ejpam-2010	146	34	a	a	DET
ejpam-2010	146	35	semigroup	semigroup	PROPN
ejpam-2010	146	36	s	s	VERB
ejpam-2010	146	37	is	be	AUX
ejpam-2010	146	38	regular	regular	ADJ
ejpam-2010	146	39	if	if	SCONJ
ejpam-2010	146	40	every	every	DET
ejpam-2010	146	41	element	element	NOUN
ejpam-2010	146	42	of	of	ADP
ejpam-2010	146	43	s	s	PROPN
ejpam-2010	146	44	is	be	AUX
ejpam-2010	146	45	regular	regular	ADJ
ejpam-2010	146	46	.	.	PUNCT
ejpam-2010	147	1	a	a	DET
ejpam-2010	147	2	regular	regular	ADJ
ejpam-2010	147	3	semigroup	semigroup	NOUN
ejpam-2010	147	4	s	s	PART
ejpam-2010	147	5	is	be	AUX
ejpam-2010	147	6	said	say	VERB
ejpam-2010	147	7	to	to	PART
ejpam-2010	147	8	be	be	AUX
ejpam-2010	147	9	inverse	inverse	ADJ
ejpam-2010	147	10	if	if	SCONJ
ejpam-2010	147	11	each	each	DET
ejpam-2010	147	12	element	element	NOUN
ejpam-2010	147	13	of	of	ADP
ejpam-2010	147	14	s	s	PROPN
ejpam-2010	147	15	has	have	VERB
ejpam-2010	147	16	a	a	DET
ejpam-2010	147	17	unique	unique	ADJ
ejpam-2010	147	18	inverse	inverse	NOUN
ejpam-2010	147	19	.	.	PUNCT
ejpam-2010	148	1	a	a	DET
ejpam-2010	148	2	semigroup	semigroup	NOUN
ejpam-2010	148	3	with	with	ADP
ejpam-2010	148	4	identity	identity	NOUN
ejpam-2010	148	5	is	be	AUX
ejpam-2010	148	6	called	call	VERB
ejpam-2010	148	7	a	a	DET
ejpam-2010	148	8	monoid	monoid	NOUN
ejpam-2010	148	9	.	.	PUNCT
ejpam-2010	149	1	in	in	ADP
ejpam-2010	149	2	[	[	X
ejpam-2010	149	3	21	21	NUM
ejpam-2010	149	4	]	]	X
ejpam-2010	149	5	a	a	DET
ejpam-2010	149	6	semigroup	semigroup	NOUN
ejpam-2010	149	7	s	s	NOUN
ejpam-2010	149	8	is	be	AUX
ejpam-2010	149	9	said	say	VERB
ejpam-2010	149	10	to	to	PART
ejpam-2010	149	11	have	have	VERB
ejpam-2010	149	12	local	local	ADJ
ejpam-2010	149	13	units	unit	NOUN
ejpam-2010	149	14	if	if	SCONJ
ejpam-2010	149	15	for	for	ADP
ejpam-2010	149	16	every	every	DET
ejpam-2010	149	17	s	s	X
ejpam-2010	149	18	∈	∈	NOUN
ejpam-2010	149	19	s	s	VERB
ejpam-2010	149	20	there	there	PRON
ejpam-2010	149	21	exist	exist	VERB
ejpam-2010	149	22	e	e	NOUN
ejpam-2010	149	23	,	,	PUNCT
ejpam-2010	149	24	f	f	PROPN
ejpam-2010	149	25	∈	∈	PROPN
ejpam-2010	149	26	e(s	e(s	PROPN
ejpam-2010	149	27	)	)	PUNCT
ejpam-2010	149	28	such	such	ADJ
ejpam-2010	149	29	that	that	DET
ejpam-2010	149	30	s	s	NOUN
ejpam-2010	149	31	=	=	X
ejpam-2010	149	32	es	es	X
ejpam-2010	149	33	=	=	SYM
ejpam-2010	149	34	s	s	PROPN
ejpam-2010	149	35	f	f	NOUN
ejpam-2010	149	36	.	.	PUNCT
ejpam-2010	150	1	certainly	certainly	ADV
ejpam-2010	150	2	,	,	PUNCT
ejpam-2010	150	3	a	a	DET
ejpam-2010	150	4	monoid	monoid	NOUN
ejpam-2010	150	5	is	be	AUX
ejpam-2010	150	6	a	a	DET
ejpam-2010	150	7	semigroup	semigroup	NOUN
ejpam-2010	150	8	with	with	ADP
ejpam-2010	150	9	local	local	ADJ
ejpam-2010	150	10	units	unit	NOUN
ejpam-2010	150	11	.	.	PUNCT
ejpam-2010	151	1	in	in	ADP
ejpam-2010	151	2	addition	addition	NOUN
ejpam-2010	151	3	,	,	PUNCT
ejpam-2010	151	4	we	we	PRON
ejpam-2010	151	5	have	have	VERB
ejpam-2010	151	6	:	:	PUNCT
ejpam-2010	151	7	definition	definition	NOUN
ejpam-2010	151	8	1	1	NUM
ejpam-2010	151	9	(	(	PUNCT
ejpam-2010	151	10	[	[	X
ejpam-2010	151	11	43	43	NUM
ejpam-2010	151	12	]	]	PUNCT
ejpam-2010	151	13	)	)	PUNCT
ejpam-2010	151	14	.	.	PUNCT
ejpam-2010	152	1	let	let	VERB
ejpam-2010	152	2	s	s	PRON
ejpam-2010	152	3	be	be	AUX
ejpam-2010	152	4	a	a	DET
ejpam-2010	152	5	semigroup	semigroup	NOUN
ejpam-2010	152	6	.	.	PUNCT
ejpam-2010	153	1	then	then	ADV
ejpam-2010	153	2	(	(	PUNCT
ejpam-2010	153	3	1	1	X
ejpam-2010	153	4	)	)	PUNCT
ejpam-2010	153	5	s	s	VERB
ejpam-2010	153	6	is	be	AUX
ejpam-2010	153	7	said	say	VERB
ejpam-2010	153	8	to	to	PART
ejpam-2010	153	9	be	be	AUX
ejpam-2010	153	10	a	a	DET
ejpam-2010	153	11	semigroup	semigroup	NOUN
ejpam-2010	153	12	with	with	ADP
ejpam-2010	153	13	weak	weak	ADJ
ejpam-2010	153	14	local	local	ADJ
ejpam-2010	153	15	units	unit	NOUN
ejpam-2010	153	16	if	if	SCONJ
ejpam-2010	153	17	for	for	ADP
ejpam-2010	153	18	every	every	DET
ejpam-2010	153	19	s	s	X
ejpam-2010	153	20	∈	∈	NOUN
ejpam-2010	153	21	s	s	VERB
ejpam-2010	153	22	there	there	PRON
ejpam-2010	153	23	exist	exist	VERB
ejpam-2010	153	24	u	u	NOUN
ejpam-2010	153	25	,	,	PUNCT
ejpam-2010	153	26	v	v	PROPN
ejpam-2010	153	27	∈	∈	NOUN
ejpam-2010	153	28	s	s	VERB
ejpam-2010	153	29	such	such	ADJ
ejpam-2010	153	30	that	that	PRON
ejpam-2010	153	31	s	s	PART
ejpam-2010	153	32	=	=	SYM
ejpam-2010	153	33	us	us	PROPN
ejpam-2010	153	34	=	=	PUNCT
ejpam-2010	153	35	sv(these	sv(these	PROPN
ejpam-2010	153	36	semigroups	semigroup	NOUN
ejpam-2010	153	37	are	be	AUX
ejpam-2010	153	38	called	call	VERB
ejpam-2010	153	39	semigroups	semigroup	NOUN
ejpam-2010	153	40	satisfying	satisfy	VERB
ejpam-2010	153	41	condition	condition	NOUN
ejpam-2010	153	42	(	(	PUNCT
ejpam-2010	153	43	p	p	NOUN
ejpam-2010	153	44	)	)	PUNCT
ejpam-2010	153	45	in	in	ADP
ejpam-2010	153	46	[	[	X
ejpam-2010	153	47	24	24	NUM
ejpam-2010	153	48	]	]	PUNCT
ejpam-2010	153	49	and	and	CCONJ
ejpam-2010	153	50	like	like	ADP
ejpam-2010	153	51	unity	unity	NOUN
ejpam-2010	153	52	semigroups	semigroup	NOUN
ejpam-2010	153	53	in	in	ADP
ejpam-2010	153	54	[	[	X
ejpam-2010	153	55	6	6	NUM
ejpam-2010	153	56	]	]	PUNCT
ejpam-2010	153	57	)	)	PUNCT
ejpam-2010	153	58	;	;	PUNCT
ejpam-2010	153	59	(	(	PUNCT
ejpam-2010	153	60	2	2	X
ejpam-2010	153	61	)	)	PUNCT
ejpam-2010	153	62	s	s	VERB
ejpam-2010	153	63	is	be	AUX
ejpam-2010	153	64	said	say	VERB
ejpam-2010	153	65	to	to	PART
ejpam-2010	153	66	be	be	AUX
ejpam-2010	153	67	a	a	DET
ejpam-2010	153	68	semigroup	semigroup	NOUN
ejpam-2010	153	69	with	with	ADP
ejpam-2010	153	70	common	common	ADJ
ejpam-2010	153	71	two	two	NUM
ejpam-2010	153	72	-	-	PUNCT
ejpam-2010	153	73	sided	sided	ADJ
ejpam-2010	153	74	local	local	ADJ
ejpam-2010	153	75	units	unit	NOUN
ejpam-2010	153	76	(	(	PUNCT
ejpam-2010	153	77	called	call	VERB
ejpam-2010	153	78	simply	simply	ADV
ejpam-2010	153	79	“	"	PUNCT
ejpam-2010	153	80	local	local	ADJ
ejpam-2010	153	81	units	unit	NOUN
ejpam-2010	153	82	”	"	PUNCT
ejpam-2010	153	83	in	in	ADP
ejpam-2010	153	84	the	the	DET
ejpam-2010	153	85	ring	ring	NOUN
ejpam-2010	153	86	case	case	NOUN
ejpam-2010	153	87	[	[	X
ejpam-2010	153	88	3	3	NUM
ejpam-2010	153	89	]	]	SYM
ejpam-2010	153	90	)	)	PUNCT
ejpam-2010	153	91	if	if	SCONJ
ejpam-2010	153	92	for	for	ADP
ejpam-2010	153	93	every	every	DET
ejpam-2010	153	94	finite	finite	NOUN
ejpam-2010	153	95	subset	subset	NOUN
ejpam-2010	153	96	s′	s′	ADJ
ejpam-2010	153	97	⊆	⊆	NUM
ejpam-2010	153	98	s	s	VERB
ejpam-2010	153	99	there	there	PRON
ejpam-2010	153	100	exists	exist	VERB
ejpam-2010	153	101	an	an	DET
ejpam-2010	153	102	idempotent	idempotent	NOUN
ejpam-2010	153	103	e	e	NOUN
ejpam-2010	153	104	∈	∈	NOUN
ejpam-2010	153	105	s	s	VERB
ejpam-2010	153	106	such	such	ADJ
ejpam-2010	153	107	that	that	SCONJ
ejpam-2010	153	108	s′	s′	ADJ
ejpam-2010	153	109	⊆	⊆	NUM
ejpam-2010	153	110	ese	ese	NOUN
ejpam-2010	153	111	;	;	PUNCT
ejpam-2010	153	112	that	that	ADV
ejpam-2010	153	113	is	be	AUX
ejpam-2010	153	114	,	,	PUNCT
ejpam-2010	153	115	s	s	PART
ejpam-2010	153	116	=	=	X
ejpam-2010	153	117	es	es	X
ejpam-2010	153	118	=	=	SYM
ejpam-2010	153	119	se	se	X
ejpam-2010	153	120	for	for	ADP
ejpam-2010	153	121	every	every	DET
ejpam-2010	153	122	s	s	PROPN
ejpam-2010	153	123	∈	∈	PROPN
ejpam-2010	153	124	s′	s′	NOUN
ejpam-2010	153	125	;	;	PUNCT
ejpam-2010	153	126	y.	y.	PROPN
ejpam-2010	153	127	wang	wang	PROPN
ejpam-2010	153	128	,	,	PUNCT
ejpam-2010	153	129	k.	k.	PROPN
ejpam-2010	153	130	shum	shum	PROPN
ejpam-2010	153	131	,	,	PUNCT
ejpam-2010	153	132	x.	x.	PROPN
ejpam-2010	153	133	ren	ren	PROPN
ejpam-2010	153	134	/	/	SYM
ejpam-2010	153	135	eur	eur	PROPN
ejpam-2010	153	136	.	.	PUNCT
ejpam-2010	154	1	j.	j.	PROPN
ejpam-2010	154	2	pure	pure	PROPN
ejpam-2010	154	3	appl	appl	PROPN
ejpam-2010	154	4	.	.	PROPN
ejpam-2010	154	5	math	math	PROPN
ejpam-2010	154	6	,	,	PUNCT
ejpam-2010	154	7	6	6	NUM
ejpam-2010	154	8	(	(	PUNCT
ejpam-2010	154	9	2013	2013	NUM
ejpam-2010	154	10	)	)	PUNCT
ejpam-2010	154	11	,	,	PUNCT
ejpam-2010	154	12	256	256	NUM
ejpam-2010	154	13	-	-	SYM
ejpam-2010	154	14	281	281	NUM
ejpam-2010	154	15	261	261	NUM
ejpam-2010	154	16	(	(	PUNCT
ejpam-2010	154	17	3	3	NUM
ejpam-2010	154	18	)	)	PUNCT
ejpam-2010	154	19	s	s	VERB
ejpam-2010	154	20	is	be	AUX
ejpam-2010	154	21	said	say	VERB
ejpam-2010	154	22	to	to	PART
ejpam-2010	154	23	be	be	AUX
ejpam-2010	154	24	a	a	DET
ejpam-2010	154	25	semigroup	semigroup	NOUN
ejpam-2010	154	26	with	with	ADP
ejpam-2010	154	27	common	common	ADJ
ejpam-2010	154	28	two	two	NUM
ejpam-2010	154	29	-	-	PUNCT
ejpam-2010	154	30	sided	side	VERB
ejpam-2010	154	31	weak	weak	ADJ
ejpam-2010	154	32	local	local	ADJ
ejpam-2010	154	33	units	unit	NOUN
ejpam-2010	154	34	if	if	SCONJ
ejpam-2010	154	35	for	for	ADP
ejpam-2010	154	36	all	all	DET
ejpam-2010	154	37	s	s	NOUN
ejpam-2010	154	38	,	,	PUNCT
ejpam-2010	154	39	s′	s′	PUNCT
ejpam-2010	154	40	∈	∈	PROPN
ejpam-2010	154	41	s	s	PART
ejpam-2010	154	42	there	there	PRON
ejpam-2010	154	43	exists	exist	VERB
ejpam-2010	154	44	u	u	PROPN
ejpam-2010	154	45	∈	∈	PROPN
ejpam-2010	154	46	s	s	VERB
ejpam-2010	154	47	such	such	ADJ
ejpam-2010	154	48	that	that	DET
ejpam-2010	154	49	s	s	PART
ejpam-2010	154	50	=	=	X
ejpam-2010	154	51	us	us	PROPN
ejpam-2010	154	52	=	=	SYM
ejpam-2010	154	53	su	su	PROPN
ejpam-2010	154	54	and	and	CCONJ
ejpam-2010	154	55	s′	s′	ADJ
ejpam-2010	154	56	=	=	SYM
ejpam-2010	154	57	us′	us′	ADJ
ejpam-2010	154	58	=	=	SYM
ejpam-2010	154	59	s′u	s′u	X
ejpam-2010	154	60	;	;	PUNCT
ejpam-2010	154	61	(	(	PUNCT
ejpam-2010	154	62	4	4	X
ejpam-2010	154	63	)	)	PUNCT
ejpam-2010	154	64	s	s	VERB
ejpam-2010	154	65	is	be	AUX
ejpam-2010	154	66	said	say	VERB
ejpam-2010	154	67	to	to	PART
ejpam-2010	154	68	be	be	AUX
ejpam-2010	154	69	a	a	DET
ejpam-2010	154	70	semigroup	semigroup	NOUN
ejpam-2010	154	71	with	with	ADP
ejpam-2010	154	72	common	common	ADJ
ejpam-2010	154	73	joint	joint	ADJ
ejpam-2010	154	74	weak	weak	ADJ
ejpam-2010	154	75	local	local	ADJ
ejpam-2010	154	76	units	unit	NOUN
ejpam-2010	154	77	if	if	SCONJ
ejpam-2010	154	78	for	for	ADP
ejpam-2010	154	79	all	all	DET
ejpam-2010	154	80	s	s	NOUN
ejpam-2010	154	81	,	,	PUNCT
ejpam-2010	154	82	s′	s′	PUNCT
ejpam-2010	154	83	∈	∈	PROPN
ejpam-2010	154	84	s	s	VERB
ejpam-2010	154	85	there	there	PRON
ejpam-2010	154	86	exist	exist	VERB
ejpam-2010	154	87	u	u	NOUN
ejpam-2010	154	88	,	,	PUNCT
ejpam-2010	154	89	v	v	PROPN
ejpam-2010	154	90	∈	∈	NOUN
ejpam-2010	154	91	s	s	VERB
ejpam-2010	154	92	such	such	ADJ
ejpam-2010	154	93	that	that	DET
ejpam-2010	154	94	s	s	PART
ejpam-2010	154	95	=	=	X
ejpam-2010	154	96	usv	usv	ADJ
ejpam-2010	154	97	and	and	CCONJ
ejpam-2010	154	98	s′	s′	NOUN
ejpam-2010	154	99	=	=	SYM
ejpam-2010	155	1	us′v	us′v	X
ejpam-2010	155	2	.	.	PUNCT
ejpam-2010	156	1	we	we	PRON
ejpam-2010	156	2	pause	pause	VERB
ejpam-2010	156	3	here	here	ADV
ejpam-2010	156	4	to	to	PART
ejpam-2010	156	5	make	make	VERB
ejpam-2010	156	6	a	a	DET
ejpam-2010	156	7	short	short	ADJ
ejpam-2010	156	8	observation	observation	NOUN
ejpam-2010	156	9	that	that	SCONJ
ejpam-2010	156	10	if	if	SCONJ
ejpam-2010	156	11	a	a	DET
ejpam-2010	156	12	semigroup	semigroup	NOUN
ejpam-2010	156	13	has	have	VERB
ejpam-2010	156	14	common	common	ADJ
ejpam-2010	156	15	two	two	NUM
ejpam-2010	156	16	-	-	PUNCT
ejpam-2010	156	17	sided	sided	ADJ
ejpam-2010	156	18	local	local	ADJ
ejpam-2010	156	19	units	unit	NOUN
ejpam-2010	156	20	then	then	ADV
ejpam-2010	156	21	it	it	PRON
ejpam-2010	156	22	has	have	VERB
ejpam-2010	156	23	local	local	ADJ
ejpam-2010	156	24	units	unit	NOUN
ejpam-2010	156	25	and	and	CCONJ
ejpam-2010	156	26	common	common	ADJ
ejpam-2010	156	27	two	two	NUM
ejpam-2010	156	28	-	-	PUNCT
ejpam-2010	156	29	sided	side	VERB
ejpam-2010	156	30	weak	weak	ADJ
ejpam-2010	156	31	local	local	ADJ
ejpam-2010	156	32	units	unit	NOUN
ejpam-2010	156	33	;	;	PUNCT
ejpam-2010	156	34	the	the	DET
ejpam-2010	156	35	latter	latter	ADJ
ejpam-2010	156	36	property	property	NOUN
ejpam-2010	156	37	implies	imply	VERB
ejpam-2010	156	38	having	have	VERB
ejpam-2010	156	39	weak	weak	ADJ
ejpam-2010	156	40	local	local	ADJ
ejpam-2010	156	41	units	unit	NOUN
ejpam-2010	156	42	as	as	ADV
ejpam-2010	156	43	well	well	ADV
ejpam-2010	156	44	as	as	ADP
ejpam-2010	156	45	common	common	ADJ
ejpam-2010	156	46	joint	joint	ADJ
ejpam-2010	156	47	weak	weak	ADJ
ejpam-2010	156	48	local	local	ADJ
ejpam-2010	156	49	units	unit	NOUN
ejpam-2010	156	50	;	;	PUNCT
ejpam-2010	156	51	having	have	VERB
ejpam-2010	156	52	local	local	ADJ
ejpam-2010	156	53	units	unit	NOUN
ejpam-2010	156	54	implies	imply	VERB
ejpam-2010	156	55	having	have	VERB
ejpam-2010	156	56	weak	weak	ADJ
ejpam-2010	156	57	local	local	ADJ
ejpam-2010	156	58	units	unit	NOUN
ejpam-2010	156	59	.	.	PUNCT
ejpam-2010	157	1	a	a	DET
ejpam-2010	157	2	semigroup	semigroup	PROPN
ejpam-2010	157	3	t	t	PROPN
ejpam-2010	157	4	is	be	AUX
ejpam-2010	157	5	said	say	VERB
ejpam-2010	157	6	to	to	PART
ejpam-2010	157	7	be	be	AUX
ejpam-2010	157	8	an	an	DET
ejpam-2010	157	9	enlargement	enlargement	NOUN
ejpam-2010	157	10	of	of	ADP
ejpam-2010	157	11	its	its	PRON
ejpam-2010	157	12	subsemigroup	subsemigroup	NOUN
ejpam-2010	157	13	s	s	X
ejpam-2010	157	14	if	if	SCONJ
ejpam-2010	157	15	s	s	PART
ejpam-2010	157	16	=	=	X
ejpam-2010	157	17	sts	st	NOUN
ejpam-2010	157	18	and	and	CCONJ
ejpam-2010	157	19	t	t	NOUN
ejpam-2010	157	20	=	=	PUNCT
ejpam-2010	157	21	tst	tst	NOUN
ejpam-2010	157	22	.	.	PUNCT
ejpam-2010	158	1	let	let	VERB
ejpam-2010	158	2	s	s	NOUN
ejpam-2010	158	3	,	,	PUNCT
ejpam-2010	158	4	t	t	PROPN
ejpam-2010	158	5	and	and	CCONJ
ejpam-2010	158	6	r	r	NOUN
ejpam-2010	158	7	be	be	VERB
ejpam-2010	158	8	semigroups	semigroup	NOUN
ejpam-2010	158	9	.	.	PUNCT
ejpam-2010	159	1	we	we	PRON
ejpam-2010	159	2	say	say	VERB
ejpam-2010	159	3	that	that	SCONJ
ejpam-2010	159	4	r	r	NOUN
ejpam-2010	159	5	is	be	AUX
ejpam-2010	159	6	a	a	DET
ejpam-2010	159	7	joint	joint	ADJ
ejpam-2010	159	8	enlargement	enlargement	NOUN
ejpam-2010	159	9	of	of	ADP
ejpam-2010	159	10	s	s	PRON
ejpam-2010	159	11	and	and	CCONJ
ejpam-2010	159	12	t	t	PROPN
ejpam-2010	159	13	if	if	SCONJ
ejpam-2010	159	14	it	it	PRON
ejpam-2010	159	15	is	be	AUX
ejpam-2010	159	16	an	an	DET
ejpam-2010	159	17	enlargement	enlargement	NOUN
ejpam-2010	159	18	of	of	ADP
ejpam-2010	159	19	subsemigroups	subsemigroup	NOUN
ejpam-2010	159	20	s′	s′	NUM
ejpam-2010	159	21	and	and	CCONJ
ejpam-2010	159	22	t	t	NOUN
ejpam-2010	159	23	′	′	NUM
ejpam-2010	159	24	which	which	PRON
ejpam-2010	159	25	are	be	AUX
ejpam-2010	159	26	isomorphic	isomorphic	ADJ
ejpam-2010	159	27	to	to	ADP
ejpam-2010	159	28	s	s	PRON
ejpam-2010	159	29	and	and	CCONJ
ejpam-2010	159	30	t	t	NOUN
ejpam-2010	159	31	respectively	respectively	ADV
ejpam-2010	159	32	.	.	PUNCT
ejpam-2010	160	1	if	if	SCONJ
ejpam-2010	160	2	r	r	NOUN
ejpam-2010	160	3	is	be	AUX
ejpam-2010	160	4	a	a	DET
ejpam-2010	160	5	regular	regular	ADJ
ejpam-2010	160	6	semigroups	semigroup	NOUN
ejpam-2010	160	7	we	we	PRON
ejpam-2010	160	8	say	say	VERB
ejpam-2010	160	9	that	that	SCONJ
ejpam-2010	160	10	it	it	PRON
ejpam-2010	160	11	is	be	AUX
ejpam-2010	160	12	a	a	DET
ejpam-2010	160	13	regular	regular	ADJ
ejpam-2010	160	14	joint	joint	ADJ
ejpam-2010	160	15	enlargement	enlargement	NOUN
ejpam-2010	160	16	.	.	PUNCT
ejpam-2010	161	1	recall	recall	VERB
ejpam-2010	161	2	that	that	SCONJ
ejpam-2010	161	3	the	the	DET
ejpam-2010	161	4	cauchy	cauchy	ADJ
ejpam-2010	161	5	completion	completion	NOUN
ejpam-2010	161	6	of	of	ADP
ejpam-2010	161	7	a	a	DET
ejpam-2010	161	8	semigroup	semigroup	NOUN
ejpam-2010	161	9	s	s	PART
ejpam-2010	161	10	is	be	AUX
ejpam-2010	161	11	a	a	DET
ejpam-2010	161	12	category	category	NOUN
ejpam-2010	161	13	with	with	ADP
ejpam-2010	161	14	object	object	NOUN
ejpam-2010	161	15	set	set	VERB
ejpam-2010	161	16	e(s	e(s	PROPN
ejpam-2010	161	17	)	)	PUNCT
ejpam-2010	161	18	,	,	PUNCT
ejpam-2010	161	19	homomorphism	homomorphism	NOUN
ejpam-2010	161	20	sets	set	VERB
ejpam-2010	161	21	c(s	c(	NOUN
ejpam-2010	161	22	)	)	PUNCT
ejpam-2010	161	23	=	=	SYM
ejpam-2010	161	24	{	{	PUNCT
ejpam-2010	161	25	(	(	PUNCT
ejpam-2010	161	26	e	e	NOUN
ejpam-2010	161	27	,	,	PUNCT
ejpam-2010	161	28	s	s	X
ejpam-2010	161	29	,	,	PUNCT
ejpam-2010	161	30	f	f	PROPN
ejpam-2010	161	31	)	)	PUNCT
ejpam-2010	161	32	∈	∈	PROPN
ejpam-2010	161	33	e(s)×	e(s)×	PROPN
ejpam-2010	161	34	s×	s×	VERB
ejpam-2010	161	35	e(s	e(s	PROPN
ejpam-2010	161	36	)	)	PUNCT
ejpam-2010	161	37	:	:	PUNCT
ejpam-2010	162	1	es	es	X
ejpam-2010	162	2	f	f	PROPN
ejpam-2010	162	3	=	=	SYM
ejpam-2010	162	4	s	s	PROPN
ejpam-2010	162	5	}	}	PUNCT
ejpam-2010	162	6	and	and	CCONJ
ejpam-2010	162	7	composition	composition	NOUN
ejpam-2010	162	8	(	(	PUNCT
ejpam-2010	162	9	e	e	NOUN
ejpam-2010	162	10	,	,	PUNCT
ejpam-2010	162	11	s	s	X
ejpam-2010	162	12	,	,	PUNCT
ejpam-2010	162	13	f	f	NOUN
ejpam-2010	162	14	)	)	PUNCT
ejpam-2010	162	15	(	(	PUNCT
ejpam-2010	162	16	f	f	PROPN
ejpam-2010	162	17	,	,	PUNCT
ejpam-2010	162	18	t	t	PROPN
ejpam-2010	162	19	,	,	PUNCT
ejpam-2010	162	20	h	h	NOUN
ejpam-2010	162	21	)	)	PUNCT
ejpam-2010	162	22	=	=	SYM
ejpam-2010	162	23	(	(	PUNCT
ejpam-2010	162	24	e	e	PROPN
ejpam-2010	162	25	,	,	PUNCT
ejpam-2010	162	26	st	st	PROPN
ejpam-2010	162	27	,	,	PUNCT
ejpam-2010	162	28	h	h	NOUN
ejpam-2010	162	29	)	)	PUNCT
ejpam-2010	162	30	.	.	PUNCT
ejpam-2010	163	1	let	let	VERB
ejpam-2010	163	2	s	s	PRON
ejpam-2010	163	3	be	be	AUX
ejpam-2010	163	4	an	an	DET
ejpam-2010	163	5	inverse	inverse	NOUN
ejpam-2010	163	6	semigroup	semigroup	NOUN
ejpam-2010	163	7	.	.	PUNCT
ejpam-2010	164	1	we	we	PRON
ejpam-2010	164	2	can	can	AUX
ejpam-2010	164	3	construct	construct	VERB
ejpam-2010	164	4	a	a	DET
ejpam-2010	164	5	left	left	ADJ
ejpam-2010	164	6	cancellative	cancellative	ADJ
ejpam-2010	164	7	category	category	NOUN
ejpam-2010	164	8	with	with	ADP
ejpam-2010	164	9	object	object	NOUN
ejpam-2010	164	10	set	set	VERB
ejpam-2010	164	11	s	s	PART
ejpam-2010	164	12	,	,	PUNCT
ejpam-2010	164	13	homomorphism	homomorphism	NOUN
ejpam-2010	164	14	sets	set	VERB
ejpam-2010	164	15	l(s	l(s	PROPN
ejpam-2010	164	16	)	)	PUNCT
ejpam-2010	165	1	=	=	PRON
ejpam-2010	165	2	{	{	PUNCT
ejpam-2010	165	3	(	(	PUNCT
ejpam-2010	165	4	e	e	NOUN
ejpam-2010	165	5	,	,	PUNCT
ejpam-2010	165	6	s	s	PART
ejpam-2010	165	7	)	)	PUNCT
ejpam-2010	165	8	∈	∈	PROPN
ejpam-2010	165	9	e(s)×	e(s)×	PROPN
ejpam-2010	165	10	s	s	PART
ejpam-2010	165	11	:	:	PUNCT
ejpam-2010	165	12	se	se	X
ejpam-2010	165	13	=	=	SYM
ejpam-2010	165	14	s	s	X
ejpam-2010	165	15	}	}	PUNCT
ejpam-2010	165	16	and	and	CCONJ
ejpam-2010	165	17	composition	composition	NOUN
ejpam-2010	165	18	(	(	PUNCT
ejpam-2010	165	19	e	e	NOUN
ejpam-2010	165	20	,	,	PUNCT
ejpam-2010	165	21	s	s	PART
ejpam-2010	165	22	)	)	PUNCT
ejpam-2010	165	23	(	(	PUNCT
ejpam-2010	165	24	f	f	PROPN
ejpam-2010	165	25	,	,	PUNCT
ejpam-2010	165	26	t	t	PROPN
ejpam-2010	165	27	)	)	PUNCT
ejpam-2010	165	28	=	=	SYM
ejpam-2010	166	1	(	(	PUNCT
ejpam-2010	166	2	e	e	PROPN
ejpam-2010	166	3	,	,	PUNCT
ejpam-2010	166	4	st	st	PROPN
ejpam-2010	166	5	)	)	PUNCT
ejpam-2010	166	6	whenever	whenever	SCONJ
ejpam-2010	166	7	s	s	VERB
ejpam-2010	166	8	∗	∗	NOUN
ejpam-2010	166	9	s	s	PART
ejpam-2010	166	10	=	=	SYM
ejpam-2010	166	11	f	f	PROPN
ejpam-2010	166	12	.	.	PUNCT
ejpam-2010	167	1	in	in	ADP
ejpam-2010	167	2	addition	addition	NOUN
ejpam-2010	167	3	,	,	PUNCT
ejpam-2010	167	4	the	the	DET
ejpam-2010	167	5	regular	regular	ADJ
ejpam-2010	167	6	elements	element	NOUN
ejpam-2010	167	7	of	of	ADP
ejpam-2010	167	8	c(s	c(	NOUN
ejpam-2010	167	9	)	)	PUNCT
ejpam-2010	167	10	form	form	NOUN
ejpam-2010	167	11	an	an	DET
ejpam-2010	167	12	inverse	inverse	NOUN
ejpam-2010	167	13	category	category	NOUN
ejpam-2010	167	14	,	,	PUNCT
ejpam-2010	167	15	i(s	i(s	NOUN
ejpam-2010	167	16	)	)	PUNCT
ejpam-2010	167	17	,	,	PUNCT
ejpam-2010	167	18	given	give	VERB
ejpam-2010	167	19	by	by	ADP
ejpam-2010	167	20	i(s	i(s	NOUN
ejpam-2010	167	21	)	)	PUNCT
ejpam-2010	168	1	=	=	PRON
ejpam-2010	168	2	{	{	PUNCT
ejpam-2010	168	3	(	(	PUNCT
ejpam-2010	168	4	e	e	NOUN
ejpam-2010	168	5	,	,	PUNCT
ejpam-2010	168	6	a	a	PRON
ejpam-2010	168	7	,	,	PUNCT
ejpam-2010	168	8	f	f	PROPN
ejpam-2010	168	9	)	)	PUNCT
ejpam-2010	168	10	∈	∈	PROPN
ejpam-2010	168	11	c(s	c(	NOUN
ejpam-2010	168	12	)	)	PUNCT
ejpam-2010	168	13	:	:	PUNCT
ejpam-2010	168	14	a	a	DET
ejpam-2010	168	15	∈	∈	PROPN
ejpam-2010	168	16	reg(s	reg(s	NOUN
ejpam-2010	168	17	)	)	PUNCT
ejpam-2010	168	18	}	}	PUNCT
ejpam-2010	168	19	,	,	PUNCT
ejpam-2010	168	20	where	where	SCONJ
ejpam-2010	168	21	reg(s	reg(s	NOUN
ejpam-2010	168	22	)	)	PUNCT
ejpam-2010	168	23	is	be	AUX
ejpam-2010	168	24	the	the	DET
ejpam-2010	168	25	set	set	NOUN
ejpam-2010	168	26	of	of	ADP
ejpam-2010	168	27	regular	regular	ADJ
ejpam-2010	168	28	elements	element	NOUN
ejpam-2010	168	29	of	of	ADP
ejpam-2010	168	30	s.	s.	PROPN
ejpam-2010	168	31	we	we	PRON
ejpam-2010	168	32	shall	shall	AUX
ejpam-2010	168	33	build	build	VERB
ejpam-2010	168	34	semigroups	semigroup	NOUN
ejpam-2010	168	35	from	from	ADP
ejpam-2010	168	36	(	(	PUNCT
ejpam-2010	168	37	small	small	ADJ
ejpam-2010	168	38	)	)	PUNCT
ejpam-2010	168	39	categories	category	NOUN
ejpam-2010	168	40	using	use	VERB
ejpam-2010	168	41	the	the	DET
ejpam-2010	168	42	following	follow	VERB
ejpam-2010	168	43	technique	technique	NOUN
ejpam-2010	168	44	.	.	PUNCT
ejpam-2010	169	1	a	a	DET
ejpam-2010	169	2	category	category	NOUN
ejpam-2010	169	3	c	c	NOUN
ejpam-2010	169	4	is	be	AUX
ejpam-2010	169	5	said	say	VERB
ejpam-2010	169	6	to	to	PART
ejpam-2010	169	7	be	be	AUX
ejpam-2010	169	8	strongly	strongly	ADV
ejpam-2010	169	9	connected	connect	VERB
ejpam-2010	169	10	if	if	SCONJ
ejpam-2010	169	11	for	for	ADP
ejpam-2010	169	12	each	each	DET
ejpam-2010	169	13	pair	pair	NOUN
ejpam-2010	169	14	of	of	ADP
ejpam-2010	169	15	identities	identity	NOUN
ejpam-2010	169	16	e	e	NOUN
ejpam-2010	169	17	and	and	CCONJ
ejpam-2010	169	18	f	f	NOUN
ejpam-2010	169	19	there	there	PRON
ejpam-2010	169	20	is	be	VERB
ejpam-2010	169	21	an	an	DET
ejpam-2010	169	22	arrow	arrow	NOUN
ejpam-2010	169	23	from	from	ADP
ejpam-2010	169	24	e	e	NOUN
ejpam-2010	169	25	to	to	ADP
ejpam-2010	169	26	f	f	PROPN
ejpam-2010	169	27	.	.	PUNCT
ejpam-2010	170	1	let	let	VERB
ejpam-2010	170	2	c	c	PRON
ejpam-2010	170	3	be	be	AUX
ejpam-2010	170	4	a	a	DET
ejpam-2010	170	5	strongly	strongly	ADV
ejpam-2010	170	6	connected	connect	VERB
ejpam-2010	170	7	category	category	NOUN
ejpam-2010	170	8	.	.	PUNCT
ejpam-2010	171	1	a	a	DET
ejpam-2010	171	2	consolidation	consolidation	NOUN
ejpam-2010	171	3	for	for	ADP
ejpam-2010	171	4	c	c	PROPN
ejpam-2010	171	5	is	be	AUX
ejpam-2010	171	6	a	a	DET
ejpam-2010	171	7	function	function	NOUN
ejpam-2010	171	8	p	p	NOUN
ejpam-2010	171	9	:	:	PUNCT
ejpam-2010	171	10	c0	c0	PROPN
ejpam-2010	171	11	×	×	PROPN
ejpam-2010	171	12	c0	c0	PROPN
ejpam-2010	171	13	→	→	PROPN
ejpam-2010	171	14	c	c	PROPN
ejpam-2010	171	15	,	,	PUNCT
ejpam-2010	171	16	p(e	p(e	PROPN
ejpam-2010	171	17	,	,	PUNCT
ejpam-2010	171	18	f	f	X
ejpam-2010	171	19	)	)	PUNCT
ejpam-2010	172	1	=	=	SYM
ejpam-2010	172	2	pe	pe	PROPN
ejpam-2010	172	3	,	,	PUNCT
ejpam-2010	172	4	f	f	PROPN
ejpam-2010	172	5	,	,	PUNCT
ejpam-2010	172	6	where	where	SCONJ
ejpam-2010	172	7	pe	pe	X
ejpam-2010	172	8	,	,	PUNCT
ejpam-2010	172	9	f	f	PROPN
ejpam-2010	172	10	is	be	AUX
ejpam-2010	172	11	an	an	DET
ejpam-2010	172	12	arrow	arrow	NOUN
ejpam-2010	172	13	from	from	ADP
ejpam-2010	172	14	e	e	NOUN
ejpam-2010	172	15	to	to	ADP
ejpam-2010	172	16	f	f	PROPN
ejpam-2010	172	17	and	and	CCONJ
ejpam-2010	172	18	pe	pe	X
ejpam-2010	172	19	,	,	PUNCT
ejpam-2010	172	20	e	e	X
ejpam-2010	172	21	=	=	PROPN
ejpam-2010	172	22	e.	e.	PROPN
ejpam-2010	172	23	given	give	VERB
ejpam-2010	172	24	a	a	DET
ejpam-2010	172	25	category	category	NOUN
ejpam-2010	172	26	c	c	NOUN
ejpam-2010	172	27	equipped	equip	VERB
ejpam-2010	172	28	with	with	ADP
ejpam-2010	172	29	a	a	DET
ejpam-2010	172	30	consolidation	consolidation	NOUN
ejpam-2010	172	31	p	p	NOUN
ejpam-2010	172	32	we	we	PRON
ejpam-2010	172	33	can	can	AUX
ejpam-2010	172	34	define	define	VERB
ejpam-2010	172	35	a	a	DET
ejpam-2010	172	36	binary	binary	ADJ
ejpam-2010	172	37	operation	operation	NOUN
ejpam-2010	172	38	◦	◦	NOUN
ejpam-2010	172	39	on	on	ADP
ejpam-2010	172	40	c	c	NOUN
ejpam-2010	172	41	by	by	ADP
ejpam-2010	172	42	x	x	SYM
ejpam-2010	172	43	◦	◦	NOUN
ejpam-2010	172	44	y	y	NOUN
ejpam-2010	172	45	=	=	PUNCT
ejpam-2010	172	46	x	x	SYM
ejpam-2010	172	47	pe	pe	PROPN
ejpam-2010	172	48	,	,	PUNCT
ejpam-2010	172	49	f	f	PROPN
ejpam-2010	172	50	y	y	PROPN
ejpam-2010	172	51	where	where	SCONJ
ejpam-2010	172	52	x	x	PRON
ejpam-2010	172	53	has	have	VERB
ejpam-2010	172	54	codomain	codomain	ADJ
ejpam-2010	172	55	e	e	NOUN
ejpam-2010	172	56	and	and	CCONJ
ejpam-2010	172	57	y	y	PROPN
ejpam-2010	172	58	has	have	VERB
ejpam-2010	172	59	domain	domain	NOUN
ejpam-2010	172	60	f	f	X
ejpam-2010	172	61	.	.	PUNCT
ejpam-2010	173	1	it	it	PRON
ejpam-2010	173	2	is	be	AUX
ejpam-2010	173	3	easily	easily	ADV
ejpam-2010	173	4	checked	check	VERB
ejpam-2010	173	5	that	that	SCONJ
ejpam-2010	173	6	this	this	DET
ejpam-2010	173	7	converts	convert	NOUN
ejpam-2010	173	8	c	c	NOUN
ejpam-2010	173	9	into	into	ADP
ejpam-2010	173	10	a	a	DET
ejpam-2010	173	11	semigroup	semigroup	NOUN
ejpam-2010	173	12	.	.	PUNCT
ejpam-2010	174	1	we	we	PRON
ejpam-2010	174	2	denote	denote	VERB
ejpam-2010	174	3	this	this	DET
ejpam-2010	174	4	semigroup	semigroup	NOUN
ejpam-2010	174	5	by	by	ADP
ejpam-2010	174	6	c	c	PROPN
ejpam-2010	174	7	p.	p.	NOUN
ejpam-2010	174	8	if	if	SCONJ
ejpam-2010	174	9	we	we	PRON
ejpam-2010	174	10	omit	omit	VERB
ejpam-2010	174	11	◦	◦	NOUN
ejpam-2010	174	12	then	then	ADV
ejpam-2010	174	13	the	the	DET
ejpam-2010	174	14	product	product	NOUN
ejpam-2010	174	15	is	be	AUX
ejpam-2010	174	16	in	in	ADP
ejpam-2010	174	17	the	the	DET
ejpam-2010	174	18	category	category	NOUN
ejpam-2010	174	19	.	.	PUNCT
ejpam-2010	175	1	we	we	PRON
ejpam-2010	175	2	pause	pause	VERB
ejpam-2010	175	3	here	here	ADV
ejpam-2010	175	4	to	to	PART
ejpam-2010	175	5	recall	recall	VERB
ejpam-2010	175	6	a	a	DET
ejpam-2010	175	7	concept	concept	NOUN
ejpam-2010	175	8	.	.	PUNCT
ejpam-2010	176	1	let	let	VERB
ejpam-2010	176	2	c	c	PRON
ejpam-2010	176	3	be	be	AUX
ejpam-2010	176	4	a	a	DET
ejpam-2010	176	5	category	category	NOUN
ejpam-2010	176	6	.	.	PUNCT
ejpam-2010	177	1	we	we	PRON
ejpam-2010	177	2	say	say	VERB
ejpam-2010	177	3	that	that	PRON
ejpam-2010	177	4	c	c	NOUN
ejpam-2010	178	1	=	=	PUNCT
ejpam-2010	179	1	[	[	X
ejpam-2010	179	2	a	a	X
ejpam-2010	179	3	,	,	PUNCT
ejpam-2010	179	4	b	b	NOUN
ejpam-2010	179	5	]	]	X
ejpam-2010	179	6	is	be	AUX
ejpam-2010	179	7	bipartite	bipartite	ADJ
ejpam-2010	179	8	(	(	PUNCT
ejpam-2010	179	9	with	with	ADP
ejpam-2010	179	10	left	left	ADJ
ejpam-2010	179	11	part	part	NOUN
ejpam-2010	179	12	a	a	DET
ejpam-2010	179	13	and	and	CCONJ
ejpam-2010	179	14	right	right	ADJ
ejpam-2010	179	15	part	part	NOUN
ejpam-2010	179	16	b	b	X
ejpam-2010	179	17	)	)	PUNCT
ejpam-2010	179	18	if	if	SCONJ
ejpam-2010	179	19	it	it	PRON
ejpam-2010	179	20	satisfies	satisfy	VERB
ejpam-2010	179	21	the	the	DET
ejpam-2010	179	22	following	follow	VERB
ejpam-2010	179	23	conditions	condition	NOUN
ejpam-2010	179	24	:	:	PUNCT
ejpam-2010	179	25	(	(	PUNCT
ejpam-2010	179	26	b1	b1	NOUN
ejpam-2010	179	27	)	)	PUNCT
ejpam-2010	179	28	c	c	PROPN
ejpam-2010	179	29	has	have	VERB
ejpam-2010	179	30	full	full	ADJ
ejpam-2010	179	31	disjoint	disjoint	NOUN
ejpam-2010	179	32	subcategories	subcategorie	NOUN
ejpam-2010	179	33	a	a	PRON
ejpam-2010	179	34	and	and	CCONJ
ejpam-2010	179	35	b	b	NOUN
ejpam-2010	179	36	such	such	ADJ
ejpam-2010	179	37	that	that	DET
ejpam-2010	179	38	c0	c0	PROPN
ejpam-2010	179	39	=	=	SYM
ejpam-2010	179	40	a0	a0	PROPN
ejpam-2010	179	41	∪	∪	PROPN
ejpam-2010	179	42	b0	b0	PROPN
ejpam-2010	179	43	;	;	PUNCT
ejpam-2010	179	44	(	(	PUNCT
ejpam-2010	179	45	b2	b2	NOUN
ejpam-2010	179	46	)	)	PUNCT
ejpam-2010	179	47	for	for	ADP
ejpam-2010	179	48	each	each	DET
ejpam-2010	179	49	identity	identity	NOUN
ejpam-2010	179	50	e	e	NOUN
ejpam-2010	179	51	∈	∈	PROPN
ejpam-2010	179	52	a0	a0	NOUN
ejpam-2010	179	53	there	there	PRON
ejpam-2010	179	54	exists	exist	VERB
ejpam-2010	179	55	an	an	DET
ejpam-2010	179	56	isomorphism	isomorphism	NOUN
ejpam-2010	179	57	x	x	PUNCT
ejpam-2010	179	58	with	with	ADP
ejpam-2010	179	59	domain	domain	NOUN
ejpam-2010	179	60	e	e	NOUN
ejpam-2010	179	61	and	and	CCONJ
ejpam-2010	179	62	codomain	codomain	ADJ
ejpam-2010	179	63	in	in	ADP
ejpam-2010	179	64	b0	b0	NOUN
ejpam-2010	179	65	;	;	PUNCT
ejpam-2010	179	66	for	for	ADP
ejpam-2010	179	67	each	each	DET
ejpam-2010	179	68	identity	identity	NOUN
ejpam-2010	179	69	f	f	PROPN
ejpam-2010	179	70	∈	∈	PROPN
ejpam-2010	179	71	b0	b0	NOUN
ejpam-2010	179	72	there	there	PRON
ejpam-2010	179	73	exists	exist	VERB
ejpam-2010	179	74	an	an	DET
ejpam-2010	179	75	isomorphism	isomorphism	NOUN
ejpam-2010	179	76	y	y	PROPN
ejpam-2010	179	77	with	with	ADP
ejpam-2010	179	78	domain	domain	NOUN
ejpam-2010	179	79	f	f	NOUN
ejpam-2010	179	80	and	and	CCONJ
ejpam-2010	179	81	codomain	codomain	ADJ
ejpam-2010	179	82	in	in	ADP
ejpam-2010	179	83	a0	a0	PROPN
ejpam-2010	179	84	.	.	PUNCT
ejpam-2010	180	1	y.	y.	PROPN
ejpam-2010	180	2	wang	wang	PROPN
ejpam-2010	180	3	,	,	PUNCT
ejpam-2010	180	4	k.	k.	PROPN
ejpam-2010	180	5	shum	shum	PROPN
ejpam-2010	180	6	,	,	PUNCT
ejpam-2010	180	7	x.	x.	PROPN
ejpam-2010	180	8	ren	ren	PROPN
ejpam-2010	180	9	/	/	SYM
ejpam-2010	180	10	eur	eur	PROPN
ejpam-2010	180	11	.	.	PUNCT
ejpam-2010	181	1	j.	j.	PROPN
ejpam-2010	181	2	pure	pure	PROPN
ejpam-2010	181	3	appl	appl	PROPN
ejpam-2010	181	4	.	.	PROPN
ejpam-2010	181	5	math	math	PROPN
ejpam-2010	181	6	,	,	PUNCT
ejpam-2010	181	7	6	6	NUM
ejpam-2010	181	8	(	(	PUNCT
ejpam-2010	181	9	2013	2013	NUM
ejpam-2010	181	10	)	)	PUNCT
ejpam-2010	181	11	,	,	PUNCT
ejpam-2010	181	12	256	256	NUM
ejpam-2010	181	13	-	-	SYM
ejpam-2010	181	14	281	281	NUM
ejpam-2010	181	15	262	262	NUM
ejpam-2010	181	16	in	in	ADP
ejpam-2010	181	17	[	[	PUNCT
ejpam-2010	181	18	37	37	NUM
ejpam-2010	181	19	]	]	PUNCT
ejpam-2010	181	20	,	,	PUNCT
ejpam-2010	181	21	the	the	DET
ejpam-2010	181	22	categories	category	NOUN
ejpam-2010	181	23	a	a	PRON
ejpam-2010	181	24	and	and	CCONJ
ejpam-2010	181	25	b	b	NOUN
ejpam-2010	181	26	are	be	AUX
ejpam-2010	181	27	equivalent	equivalent	ADJ
ejpam-2010	181	28	if	if	SCONJ
ejpam-2010	181	29	and	and	CCONJ
ejpam-2010	181	30	only	only	ADV
ejpam-2010	181	31	if	if	SCONJ
ejpam-2010	181	32	there	there	PRON
ejpam-2010	181	33	is	be	VERB
ejpam-2010	181	34	a	a	DET
ejpam-2010	181	35	bipartite	bipartite	ADJ
ejpam-2010	181	36	category	category	NOUN
ejpam-2010	181	37	with	with	ADP
ejpam-2010	181	38	left	left	ADJ
ejpam-2010	181	39	part	part	NOUN
ejpam-2010	181	40	a	a	DET
ejpam-2010	181	41	and	and	CCONJ
ejpam-2010	181	42	right	right	ADJ
ejpam-2010	181	43	part	part	PROPN
ejpam-2010	181	44	b.	b.	PROPN
ejpam-2010	181	45	lemma	lemma	PROPN
ejpam-2010	182	1	1	1	NUM
ejpam-2010	182	2	.	.	PUNCT
ejpam-2010	183	1	[	[	X
ejpam-2010	183	2	25	25	NUM
ejpam-2010	183	3	,	,	PUNCT
ejpam-2010	183	4	theorem	theorem	VERB
ejpam-2010	183	5	3.7	3.7	NUM
ejpam-2010	183	6	]	]	PUNCT
ejpam-2010	183	7	let	let	VERB
ejpam-2010	183	8	c	c	NOUN
ejpam-2010	183	9	=	=	PUNCT
ejpam-2010	184	1	[	[	X
ejpam-2010	184	2	a	a	X
ejpam-2010	184	3	,	,	PUNCT
ejpam-2010	184	4	b	b	AUX
ejpam-2010	184	5	]	]	PUNCT
ejpam-2010	184	6	be	be	AUX
ejpam-2010	184	7	a	a	DET
ejpam-2010	184	8	bipartite	bipartite	ADJ
ejpam-2010	184	9	category	category	NOUN
ejpam-2010	184	10	and	and	CCONJ
ejpam-2010	184	11	let	let	VERB
ejpam-2010	184	12	r	r	PRON
ejpam-2010	184	13	be	be	AUX
ejpam-2010	184	14	a	a	DET
ejpam-2010	184	15	consolidation	consolidation	NOUN
ejpam-2010	184	16	defined	define	VERB
ejpam-2010	184	17	on	on	ADP
ejpam-2010	184	18	c.	c.	PROPN
ejpam-2010	184	19	then	then	ADV
ejpam-2010	184	20	cr	cr	PROPN
ejpam-2010	184	21	is	be	AUX
ejpam-2010	184	22	an	an	DET
ejpam-2010	184	23	enlargement	enlargement	NOUN
ejpam-2010	184	24	of	of	ADP
ejpam-2010	184	25	both	both	DET
ejpam-2010	184	26	ar	ar	NOUN
ejpam-2010	184	27	and	and	CCONJ
ejpam-2010	184	28	br	br	PROPN
ejpam-2010	184	29	.	.	PUNCT
ejpam-2010	185	1	an	an	DET
ejpam-2010	185	2	inverse	inverse	NOUN
ejpam-2010	185	3	semigroup	semigroup	NOUN
ejpam-2010	185	4	s	s	VERB
ejpam-2010	185	5	can	can	AUX
ejpam-2010	185	6	also	also	ADV
ejpam-2010	185	7	be	be	AUX
ejpam-2010	185	8	regarded	regard	VERB
ejpam-2010	185	9	as	as	ADP
ejpam-2010	185	10	an	an	DET
ejpam-2010	185	11	inductive	inductive	ADJ
ejpam-2010	185	12	groupoid	groupoid	PROPN
ejpam-2010	185	13	g(s	g(s	PROPN
ejpam-2010	185	14	)	)	PUNCT
ejpam-2010	185	15	.	.	PUNCT
ejpam-2010	186	1	inductive	inductive	ADJ
ejpam-2010	186	2	groupoids	groupoid	NOUN
ejpam-2010	186	3	are	be	AUX
ejpam-2010	186	4	ordered	order	VERB
ejpam-2010	186	5	groupoid	groupoid	PROPN
ejpam-2010	186	6	in	in	ADP
ejpam-2010	186	7	which	which	PRON
ejpam-2010	186	8	the	the	DET
ejpam-2010	186	9	set	set	NOUN
ejpam-2010	186	10	of	of	ADP
ejpam-2010	186	11	identities	identity	NOUN
ejpam-2010	186	12	forms	form	VERB
ejpam-2010	186	13	a	a	DET
ejpam-2010	186	14	semilattice	semilattice	NOUN
ejpam-2010	186	15	.	.	PUNCT
ejpam-2010	187	1	let	let	VERB
ejpam-2010	187	2	s	s	PRON
ejpam-2010	187	3	and	and	CCONJ
ejpam-2010	187	4	t	t	PROPN
ejpam-2010	187	5	be	be	AUX
ejpam-2010	187	6	inverse	inverse	ADJ
ejpam-2010	187	7	semigroups	semigroup	NOUN
ejpam-2010	187	8	with	with	ADP
ejpam-2010	187	9	associated	associated	ADJ
ejpam-2010	187	10	inductive	inductive	ADJ
ejpam-2010	187	11	groupoids	groupoid	NOUN
ejpam-2010	187	12	g(s	g(s	PROPN
ejpam-2010	187	13	)	)	PUNCT
ejpam-2010	187	14	and	and	CCONJ
ejpam-2010	187	15	g(t	g(t	PROPN
ejpam-2010	187	16	)	)	PUNCT
ejpam-2010	187	17	.	.	PUNCT
ejpam-2010	188	1	a	a	DET
ejpam-2010	188	2	bipartite	bipartite	NOUN
ejpam-2010	188	3	ordered	order	VERB
ejpam-2010	188	4	groupoid	groupoid	NOUN
ejpam-2010	188	5	enlargement	enlargement	NOUN
ejpam-2010	188	6	of	of	ADP
ejpam-2010	188	7	g(s	g(s	NOUN
ejpam-2010	188	8	)	)	PUNCT
ejpam-2010	188	9	and	and	CCONJ
ejpam-2010	188	10	g(t	g(t	PROPN
ejpam-2010	188	11	)	)	PUNCT
ejpam-2010	188	12	is	be	AUX
ejpam-2010	188	13	an	an	DET
ejpam-2010	188	14	ordered	order	VERB
ejpam-2010	188	15	groupoid	groupoid	NOUN
ejpam-2010	189	1	[	[	X
ejpam-2010	189	2	g(s	g(s	NOUN
ejpam-2010	189	3	)	)	PUNCT
ejpam-2010	189	4	,	,	PUNCT
ejpam-2010	189	5	g(t	g(t	PROPN
ejpam-2010	189	6	)	)	PUNCT
ejpam-2010	189	7	]	]	PUNCT
ejpam-2010	190	1	such	such	ADJ
ejpam-2010	190	2	that	that	SCONJ
ejpam-2010	190	3	the	the	DET
ejpam-2010	190	4	set	set	NOUN
ejpam-2010	190	5	of	of	ADP
ejpam-2010	190	6	identities	identity	NOUN
ejpam-2010	190	7	of	of	ADP
ejpam-2010	190	8	[	[	X
ejpam-2010	190	9	g(s	g(s	X
ejpam-2010	190	10	)	)	PUNCT
ejpam-2010	190	11	,	,	PUNCT
ejpam-2010	190	12	g(t	g(t	PROPN
ejpam-2010	190	13	)	)	PUNCT
ejpam-2010	190	14	]	]	PUNCT
ejpam-2010	190	15	is	be	AUX
ejpam-2010	190	16	the	the	DET
ejpam-2010	190	17	disjoint	disjoint	PROPN
ejpam-2010	190	18	union	union	NOUN
ejpam-2010	190	19	of	of	ADP
ejpam-2010	190	20	the	the	DET
ejpam-2010	190	21	set	set	NOUN
ejpam-2010	190	22	of	of	ADP
ejpam-2010	190	23	identities	identity	NOUN
ejpam-2010	190	24	of	of	ADP
ejpam-2010	190	25	g(s	g(s	NOUN
ejpam-2010	190	26	)	)	PUNCT
ejpam-2010	190	27	and	and	CCONJ
ejpam-2010	190	28	g(t	g(t	PROPN
ejpam-2010	190	29	)	)	PUNCT
ejpam-2010	190	30	and	and	CCONJ
ejpam-2010	190	31	for	for	ADP
ejpam-2010	190	32	each	each	DET
ejpam-2010	190	33	e	e	PROPN
ejpam-2010	190	34	∈	∈	PROPN
ejpam-2010	190	35	g(s)0	g(s)0	PROPN
ejpam-2010	190	36	there	there	PRON
ejpam-2010	190	37	exists	exist	VERB
ejpam-2010	190	38	an	an	DET
ejpam-2010	190	39	arrow	arrow	NOUN
ejpam-2010	190	40	x	x	PUNCT
ejpam-2010	190	41	such	such	ADJ
ejpam-2010	190	42	that	that	SCONJ
ejpam-2010	190	43	the	the	DET
ejpam-2010	190	44	domain	domain	NOUN
ejpam-2010	190	45	of	of	ADP
ejpam-2010	190	46	x	x	PROPN
ejpam-2010	190	47	is	be	AUX
ejpam-2010	190	48	e	e	NOUN
ejpam-2010	190	49	and	and	CCONJ
ejpam-2010	190	50	the	the	DET
ejpam-2010	190	51	codomain	codomain	NOUN
ejpam-2010	190	52	of	of	ADP
ejpam-2010	190	53	x	x	PUNCT
ejpam-2010	190	54	is	be	AUX
ejpam-2010	190	55	contained	contain	VERB
ejpam-2010	190	56	in	in	ADP
ejpam-2010	190	57	g(t	g(t	PROPN
ejpam-2010	190	58	)	)	PUNCT
ejpam-2010	190	59	0	0	NUM
ejpam-2010	190	60	and	and	CCONJ
ejpam-2010	190	61	dually	dually	ADV
ejpam-2010	190	62	.	.	PUNCT
ejpam-2010	191	1	let	let	VERB
ejpam-2010	191	2	s	s	PRON
ejpam-2010	191	3	and	and	CCONJ
ejpam-2010	191	4	t	t	PROPN
ejpam-2010	191	5	be	be	VERB
ejpam-2010	191	6	semigroups	semigroup	NOUN
ejpam-2010	191	7	with	with	ADP
ejpam-2010	191	8	local	local	ADJ
ejpam-2010	191	9	units	unit	NOUN
ejpam-2010	191	10	.	.	PUNCT
ejpam-2010	192	1	a	a	DET
ejpam-2010	192	2	homomorphism	homomorphism	NOUN
ejpam-2010	192	3	θ	θ	X
ejpam-2010	192	4	:	:	PUNCT
ejpam-2010	192	5	s	s	X
ejpam-2010	192	6	→	→	SYM
ejpam-2010	192	7	t	t	PROPN
ejpam-2010	192	8	is	be	AUX
ejpam-2010	192	9	said	say	VERB
ejpam-2010	192	10	to	to	PART
ejpam-2010	192	11	be	be	AUX
ejpam-2010	192	12	a	a	DET
ejpam-2010	192	13	local	local	ADJ
ejpam-2010	192	14	isomorphism	isomorphism	NOUN
ejpam-2010	192	15	if	if	SCONJ
ejpam-2010	192	16	the	the	DET
ejpam-2010	192	17	following	follow	VERB
ejpam-2010	192	18	conditions	condition	NOUN
ejpam-2010	192	19	are	be	AUX
ejpam-2010	192	20	satisfied	satisfied	ADJ
ejpam-2010	192	21	:	:	PUNCT
ejpam-2010	192	22	(	(	PUNCT
ejpam-2010	192	23	li1	li1	NOUN
ejpam-2010	192	24	)	)	PUNCT
ejpam-2010	192	25	the	the	DET
ejpam-2010	192	26	function	function	NOUN
ejpam-2010	192	27	θ	θ	PROPN
ejpam-2010	192	28	restricted	restrict	VERB
ejpam-2010	192	29	to	to	ADP
ejpam-2010	192	30	es	es	PROPN
ejpam-2010	192	31	f	f	PROPN
ejpam-2010	192	32	induces	induce	VERB
ejpam-2010	192	33	an	an	DET
ejpam-2010	192	34	isomorphism	isomorphism	NOUN
ejpam-2010	192	35	with	with	ADP
ejpam-2010	192	36	θ(e)tθ	θ(e)tθ	PROPN
ejpam-2010	192	37	(	(	PUNCT
ejpam-2010	192	38	f	f	PROPN
ejpam-2010	192	39	)	)	PUNCT
ejpam-2010	192	40	for	for	ADP
ejpam-2010	192	41	all	all	DET
ejpam-2010	192	42	idempotents	idempotent	NOUN
ejpam-2010	192	43	e	e	NOUN
ejpam-2010	192	44	and	and	CCONJ
ejpam-2010	192	45	f	f	PROPN
ejpam-2010	192	46	in	in	ADP
ejpam-2010	192	47	s	s	PROPN
ejpam-2010	192	48	;	;	PUNCT
ejpam-2010	192	49	(	(	PUNCT
ejpam-2010	192	50	li2	li2	NOUN
ejpam-2010	192	51	)	)	PUNCT
ejpam-2010	192	52	idempotents	idempotent	NOUN
ejpam-2010	192	53	lift	lift	VERB
ejpam-2010	192	54	along	along	ADP
ejpam-2010	192	55	θ	θ	PROPN
ejpam-2010	192	56	meaning	mean	VERB
ejpam-2010	192	57	that	that	SCONJ
ejpam-2010	192	58	if	if	SCONJ
ejpam-2010	192	59	e	e	NOUN
ejpam-2010	192	60	is	be	AUX
ejpam-2010	192	61	an	an	DET
ejpam-2010	192	62	idempotent	idempotent	NOUN
ejpam-2010	192	63	in	in	ADP
ejpam-2010	192	64	the	the	DET
ejpam-2010	192	65	image	image	NOUN
ejpam-2010	192	66	of	of	ADP
ejpam-2010	192	67	θ	θ	PROPN
ejpam-2010	192	68	then	then	ADV
ejpam-2010	192	69	there	there	PRON
ejpam-2010	192	70	is	be	VERB
ejpam-2010	192	71	an	an	DET
ejpam-2010	192	72	idempotent	idempotent	ADJ
ejpam-2010	192	73	e	e	NOUN
ejpam-2010	192	74	in	in	ADP
ejpam-2010	192	75	s	s	PRON
ejpam-2010	192	76	such	such	ADJ
ejpam-2010	192	77	that	that	DET
ejpam-2010	192	78	θ(e	θ(e	NOUN
ejpam-2010	192	79	)	)	PUNCT
ejpam-2010	192	80	=	=	SYM
ejpam-2010	193	1	e	e	NOUN
ejpam-2010	193	2	;	;	PUNCT
ejpam-2010	193	3	(	(	PUNCT
ejpam-2010	193	4	li3	li3	NOUN
ejpam-2010	193	5	)	)	PUNCT
ejpam-2010	193	6	for	for	ADP
ejpam-2010	193	7	each	each	DET
ejpam-2010	193	8	idempotent	idempotent	ADJ
ejpam-2010	193	9	e	e	PROPN
ejpam-2010	193	10	∈	∈	PROPN
ejpam-2010	193	11	t	t	NOUN
ejpam-2010	193	12	there	there	PRON
ejpam-2010	193	13	exists	exist	VERB
ejpam-2010	193	14	an	an	DET
ejpam-2010	193	15	idempotent	idempotent	NOUN
ejpam-2010	193	16	f	f	PROPN
ejpam-2010	193	17	∈	∈	PROPN
ejpam-2010	193	18	t	t	PROPN
ejpam-2010	193	19	in	in	ADP
ejpam-2010	193	20	the	the	DET
ejpam-2010	193	21	image	image	NOUN
ejpam-2010	193	22	of	of	ADP
ejpam-2010	193	23	θ	θ	PROPN
ejpam-2010	193	24	such	such	ADJ
ejpam-2010	193	25	that	that	SCONJ
ejpam-2010	193	26	e	e	PROPN
ejpam-2010	193	27	d	d	X
ejpam-2010	193	28	f	f	PROPN
ejpam-2010	193	29	.	.	PUNCT
ejpam-2010	194	1	this	this	PRON
ejpam-2010	194	2	is	be	AUX
ejpam-2010	194	3	a	a	DET
ejpam-2010	194	4	generalisation	generalisation	NOUN
ejpam-2010	194	5	of	of	ADP
ejpam-2010	194	6	the	the	DET
ejpam-2010	194	7	classical	classical	ADJ
ejpam-2010	194	8	definition	definition	NOUN
ejpam-2010	194	9	of	of	ADP
ejpam-2010	194	10	a	a	DET
ejpam-2010	194	11	local	local	ADJ
ejpam-2010	194	12	isomorphism	isomorphism	NOUN
ejpam-2010	194	13	between	between	ADP
ejpam-2010	194	14	regular	regular	ADJ
ejpam-2010	194	15	semigroups	semigroup	NOUN
ejpam-2010	194	16	[	[	X
ejpam-2010	194	17	27	27	NUM
ejpam-2010	194	18	,	,	PUNCT
ejpam-2010	194	19	28	28	NUM
ejpam-2010	194	20	]	]	PUNCT
ejpam-2010	194	21	and	and	CCONJ
ejpam-2010	194	22	has	have	VERB
ejpam-2010	194	23	its	its	PRON
ejpam-2010	194	24	origins	origin	NOUN
ejpam-2010	194	25	in	in	ADP
ejpam-2010	194	26	[	[	X
ejpam-2010	194	27	26	26	NUM
ejpam-2010	194	28	]	]	PUNCT
ejpam-2010	194	29	and	and	CCONJ
ejpam-2010	194	30	[	[	X
ejpam-2010	194	31	24	24	NUM
ejpam-2010	194	32	]	]	PUNCT
ejpam-2010	194	33	as	as	ADV
ejpam-2010	194	34	well	well	ADV
ejpam-2010	194	35	as	as	ADP
ejpam-2010	194	36	topos	topos	PROPN
ejpam-2010	194	37	theory	theory	NOUN
ejpam-2010	194	38	.	.	PUNCT
ejpam-2010	195	1	when	when	SCONJ
ejpam-2010	195	2	s	s	NOUN
ejpam-2010	195	3	is	be	AUX
ejpam-2010	195	4	regular	regular	ADJ
ejpam-2010	195	5	,	,	PUNCT
ejpam-2010	195	6	surjective	surjective	ADJ
ejpam-2010	195	7	local	local	ADJ
ejpam-2010	195	8	isomorphisms	isomorphism	NOUN
ejpam-2010	195	9	are	be	AUX
ejpam-2010	195	10	precisely	precisely	ADV
ejpam-2010	195	11	the	the	DET
ejpam-2010	195	12	surjective	surjective	ADJ
ejpam-2010	195	13	homomorphisms	homomorphism	NOUN
ejpam-2010	195	14	that	that	PRON
ejpam-2010	195	15	are	be	AUX
ejpam-2010	195	16	injective	injective	ADJ
ejpam-2010	195	17	when	when	SCONJ
ejpam-2010	195	18	restricted	restrict	VERB
ejpam-2010	195	19	to	to	ADP
ejpam-2010	195	20	each	each	DET
ejpam-2010	195	21	local	local	ADJ
ejpam-2010	195	22	submonoid	submonoid	ADJ
ejpam-2010	195	23	[	[	X
ejpam-2010	195	24	24	24	NUM
ejpam-2010	195	25	]	]	PUNCT
ejpam-2010	195	26	.	.	PUNCT
ejpam-2010	196	1	let	let	VERB
ejpam-2010	196	2	s	s	PRON
ejpam-2010	196	3	be	be	AUX
ejpam-2010	196	4	a	a	DET
ejpam-2010	196	5	semigroup	semigroup	NOUN
ejpam-2010	196	6	.	.	PUNCT
ejpam-2010	197	1	if	if	SCONJ
ejpam-2010	197	2	the	the	DET
ejpam-2010	197	3	action	action	NOUN
ejpam-2010	197	4	of	of	ADP
ejpam-2010	197	5	s	s	PRON
ejpam-2010	197	6	on	on	ADP
ejpam-2010	197	7	the	the	DET
ejpam-2010	197	8	left	left	NOUN
ejpam-2010	197	9	of	of	ADP
ejpam-2010	197	10	the	the	DET
ejpam-2010	197	11	set	set	NOUN
ejpam-2010	197	12	x	x	INTJ
ejpam-2010	197	13	we	we	PRON
ejpam-2010	197	14	say	say	VERB
ejpam-2010	197	15	that	that	SCONJ
ejpam-2010	197	16	x	x	PRON
ejpam-2010	197	17	is	be	AUX
ejpam-2010	197	18	a	a	DET
ejpam-2010	197	19	left	left	ADJ
ejpam-2010	197	20	s	s	NOUN
ejpam-2010	197	21	-	-	NOUN
ejpam-2010	197	22	act	act	NOUN
ejpam-2010	197	23	.	.	PUNCT
ejpam-2010	198	1	if	if	SCONJ
ejpam-2010	198	2	m	m	PROPN
ejpam-2010	198	3	and	and	CCONJ
ejpam-2010	198	4	n	n	CCONJ
ejpam-2010	198	5	are	be	AUX
ejpam-2010	198	6	left	leave	VERB
ejpam-2010	198	7	s	s	NOUN
ejpam-2010	198	8	-	-	PUNCT
ejpam-2010	198	9	acts	act	NOUN
ejpam-2010	198	10	then	then	ADV
ejpam-2010	198	11	homs(m	homs(m	VERB
ejpam-2010	198	12	,	,	PUNCT
ejpam-2010	198	13	n	n	CCONJ
ejpam-2010	198	14	)	)	PUNCT
ejpam-2010	198	15	denotes	denote	VERB
ejpam-2010	198	16	the	the	DET
ejpam-2010	198	17	set	set	NOUN
ejpam-2010	198	18	of	of	ADP
ejpam-2010	198	19	all	all	DET
ejpam-2010	198	20	left	leave	VERB
ejpam-2010	198	21	s	s	NOUN
ejpam-2010	198	22	-	-	PUNCT
ejpam-2010	198	23	homomorphisms	homomorphism	NOUN
ejpam-2010	198	24	from	from	ADP
ejpam-2010	198	25	m	m	PROPN
ejpam-2010	198	26	to	to	ADP
ejpam-2010	198	27	n	n	PROPN
ejpam-2010	198	28	.	.	PUNCT
ejpam-2010	199	1	if	if	SCONJ
ejpam-2010	199	2	m	m	NOUN
ejpam-2010	199	3	is	be	AUX
ejpam-2010	199	4	a	a	DET
ejpam-2010	199	5	right	right	ADJ
ejpam-2010	199	6	s	s	NOUN
ejpam-2010	199	7	-	-	PUNCT
ejpam-2010	199	8	act	act	NOUN
ejpam-2010	199	9	then	then	ADV
ejpam-2010	199	10	homs(m	homs(m	INTJ
ejpam-2010	199	11	,	,	PUNCT
ejpam-2010	199	12	n	n	CCONJ
ejpam-2010	199	13	)	)	PUNCT
ejpam-2010	199	14	becomes	become	VERB
ejpam-2010	199	15	a	a	DET
ejpam-2010	199	16	left	left	ADJ
ejpam-2010	199	17	s	s	NOUN
ejpam-2010	199	18	-	-	NOUN
ejpam-2010	199	19	act	act	NOUN
ejpam-2010	199	20	when	when	SCONJ
ejpam-2010	199	21	we	we	PRON
ejpam-2010	199	22	define	define	VERB
ejpam-2010	199	23	s	s	VERB
ejpam-2010	199	24	·	·	PUNCT
ejpam-2010	199	25	f	f	X
ejpam-2010	199	26	by	by	ADP
ejpam-2010	199	27	(	(	PUNCT
ejpam-2010	199	28	m)(s	m)(s	X
ejpam-2010	199	29	·	·	PUNCT
ejpam-2010	199	30	f	f	X
ejpam-2010	199	31	)	)	PUNCT
ejpam-2010	200	1	=	=	PRON
ejpam-2010	200	2	(	(	PUNCT
ejpam-2010	200	3	ms	ms	PROPN
ejpam-2010	200	4	)	)	PUNCT
ejpam-2010	200	5	f	f	PROPN
ejpam-2010	200	6	.	.	PUNCT
ejpam-2010	201	1	in	in	ADP
ejpam-2010	201	2	particular	particular	ADJ
ejpam-2010	201	3	,	,	PUNCT
ejpam-2010	201	4	homs(s	homs(s	PROPN
ejpam-2010	201	5	,	,	PUNCT
ejpam-2010	201	6	m	m	VERB
ejpam-2010	201	7	)	)	PUNCT
ejpam-2010	201	8	is	be	AUX
ejpam-2010	201	9	a	a	DET
ejpam-2010	201	10	left	left	ADJ
ejpam-2010	201	11	s	s	NOUN
ejpam-2010	201	12	-	-	NOUN
ejpam-2010	201	13	act	act	NOUN
ejpam-2010	201	14	.	.	PUNCT
ejpam-2010	202	1	we	we	PRON
ejpam-2010	202	2	denote	denote	VERB
ejpam-2010	202	3	by	by	ADP
ejpam-2010	202	4	s	s	NOUN
ejpam-2010	202	5	-	-	PUNCT
ejpam-2010	202	6	act	act	NOUN
ejpam-2010	202	7	the	the	DET
ejpam-2010	202	8	category	category	NOUN
ejpam-2010	202	9	of	of	ADP
ejpam-2010	202	10	left	left	ADJ
ejpam-2010	202	11	s	s	NOUN
ejpam-2010	202	12	-	-	PUNCT
ejpam-2010	202	13	acts	act	NOUN
ejpam-2010	202	14	and	and	CCONJ
ejpam-2010	202	15	left	leave	VERB
ejpam-2010	202	16	s	s	NOUN
ejpam-2010	202	17	-	-	PUNCT
ejpam-2010	202	18	homomorphisms	homomorphism	NOUN
ejpam-2010	202	19	.	.	PUNCT
ejpam-2010	203	1	a	a	DET
ejpam-2010	203	2	left	left	ADJ
ejpam-2010	203	3	s	s	NOUN
ejpam-2010	203	4	-	-	NOUN
ejpam-2010	203	5	act	act	NOUN
ejpam-2010	203	6	x	x	PUNCT
ejpam-2010	203	7	is	be	AUX
ejpam-2010	203	8	said	say	VERB
ejpam-2010	203	9	to	to	PART
ejpam-2010	203	10	be	be	AUX
ejpam-2010	203	11	left	leave	VERB
ejpam-2010	203	12	unitary	unitary	ADJ
ejpam-2010	203	13	if	if	SCONJ
ejpam-2010	203	14	and	and	CCONJ
ejpam-2010	203	15	only	only	ADV
ejpam-2010	203	16	if	if	SCONJ
ejpam-2010	203	17	sx	sx	PROPN
ejpam-2010	203	18	=	=	PUNCT
ejpam-2010	203	19	x	x	PROPN
ejpam-2010	203	20	.	.	PUNCT
ejpam-2010	204	1	if	if	SCONJ
ejpam-2010	204	2	s	s	PROPN
ejpam-2010	204	3	has	have	VERB
ejpam-2010	204	4	local	local	ADJ
ejpam-2010	204	5	units	unit	NOUN
ejpam-2010	204	6	and	and	CCONJ
ejpam-2010	204	7	x	x	NOUN
ejpam-2010	204	8	is	be	AUX
ejpam-2010	204	9	a	a	DET
ejpam-2010	204	10	unitary	unitary	ADJ
ejpam-2010	204	11	left	leave	VERB
ejpam-2010	204	12	s	s	NOUN
ejpam-2010	204	13	-	-	NOUN
ejpam-2010	204	14	act	act	NOUN
ejpam-2010	204	15	,	,	PUNCT
ejpam-2010	204	16	then	then	ADV
ejpam-2010	204	17	it	it	PRON
ejpam-2010	204	18	is	be	AUX
ejpam-2010	204	19	easy	easy	ADJ
ejpam-2010	204	20	to	to	PART
ejpam-2010	204	21	check	check	VERB
ejpam-2010	204	22	that	that	PRON
ejpam-2010	204	23	for	for	ADP
ejpam-2010	204	24	each	each	DET
ejpam-2010	204	25	x	x	SYM
ejpam-2010	204	26	∈	∈	PROPN
ejpam-2010	204	27	x	x	PUNCT
ejpam-2010	204	28	there	there	PRON
ejpam-2010	204	29	exists	exist	VERB
ejpam-2010	204	30	e	e	PROPN
ejpam-2010	204	31	∈	∈	PROPN
ejpam-2010	204	32	e(s	e(s	PROPN
ejpam-2010	204	33	)	)	PUNCT
ejpam-2010	205	1	such	such	ADJ
ejpam-2010	205	2	that	that	SCONJ
ejpam-2010	205	3	ex	ex	X
ejpam-2010	206	1	=	=	NOUN
ejpam-2010	206	2	x	x	X
ejpam-2010	206	3	.	.	PUNCT
ejpam-2010	207	1	we	we	PRON
ejpam-2010	207	2	denote	denote	VERB
ejpam-2010	207	3	by	by	ADP
ejpam-2010	207	4	s	s	NOUN
ejpam-2010	207	5	-	-	VERB
ejpam-2010	207	6	uact	uact	ADJ
ejpam-2010	207	7	the	the	DET
ejpam-2010	207	8	category	category	NOUN
ejpam-2010	207	9	consisting	consist	VERB
ejpam-2010	207	10	of	of	ADP
ejpam-2010	207	11	unitary	unitary	ADJ
ejpam-2010	207	12	left	leave	VERB
ejpam-2010	207	13	s	s	NOUN
ejpam-2010	207	14	-	-	PUNCT
ejpam-2010	207	15	acts	act	NOUN
ejpam-2010	207	16	and	and	CCONJ
ejpam-2010	207	17	s	s	NOUN
ejpam-2010	207	18	-	-	PUNCT
ejpam-2010	207	19	homomorphisms	homomorphism	NOUN
ejpam-2010	207	20	.	.	PUNCT
ejpam-2010	208	1	let	let	VERB
ejpam-2010	208	2	x	x	PRON
ejpam-2010	208	3	be	be	AUX
ejpam-2010	208	4	a	a	DET
ejpam-2010	208	5	left	left	ADJ
ejpam-2010	208	6	s	s	NOUN
ejpam-2010	208	7	-	-	NOUN
ejpam-2010	208	8	act	act	NOUN
ejpam-2010	208	9	.	.	PUNCT
ejpam-2010	209	1	the	the	DET
ejpam-2010	209	2	action	action	NOUN
ejpam-2010	209	3	of	of	ADP
ejpam-2010	209	4	s	s	PRON
ejpam-2010	209	5	on	on	ADV
ejpam-2010	209	6	x	x	PART
ejpam-2010	209	7	induces	induce	VERB
ejpam-2010	209	8	a	a	DET
ejpam-2010	209	9	map	map	NOUN
ejpam-2010	209	10	µx	µx	VERB
ejpam-2010	209	11	:	:	PUNCT
ejpam-2010	209	12	s	s	VERB
ejpam-2010	209	13	⊗	⊗	PROPN
ejpam-2010	209	14	x	x	PUNCT
ejpam-2010	209	15	→	→	SYM
ejpam-2010	209	16	x	x	SYM
ejpam-2010	209	17	,	,	PUNCT
ejpam-2010	209	18	where	where	SCONJ
ejpam-2010	209	19	s	s	AUX
ejpam-2010	209	20	⊗	⊗	PROPN
ejpam-2010	209	21	x	x	PUNCT
ejpam-2010	209	22	is	be	AUX
ejpam-2010	209	23	the	the	DET
ejpam-2010	209	24	tensor	tensor	NOUN
ejpam-2010	209	25	product	product	NOUN
ejpam-2010	209	26	of	of	ADP
ejpam-2010	209	27	s	s	PRON
ejpam-2010	209	28	and	and	CCONJ
ejpam-2010	209	29	x	x	INTJ
ejpam-2010	209	30	.	.	PUNCT
ejpam-2010	210	1	in	in	ADP
ejpam-2010	210	2	[	[	X
ejpam-2010	210	3	25	25	NUM
ejpam-2010	210	4	]	]	X
ejpam-2010	210	5	lawson	lawson	PROPN
ejpam-2010	210	6	showed	show	VERB
ejpam-2010	210	7	that	that	SCONJ
ejpam-2010	210	8	µx	µx	ADV
ejpam-2010	210	9	is	be	AUX
ejpam-2010	210	10	surjective	surjective	ADJ
ejpam-2010	210	11	if	if	SCONJ
ejpam-2010	210	12	and	and	CCONJ
ejpam-2010	210	13	only	only	ADV
ejpam-2010	210	14	if	if	SCONJ
ejpam-2010	210	15	x	x	PRON
ejpam-2010	210	16	is	be	AUX
ejpam-2010	210	17	left	leave	VERB
ejpam-2010	210	18	unitary	unitary	ADJ
ejpam-2010	210	19	.	.	PUNCT
ejpam-2010	211	1	the	the	DET
ejpam-2010	211	2	left	left	ADJ
ejpam-2010	211	3	s	s	NOUN
ejpam-2010	211	4	-	-	NOUN
ejpam-2010	211	5	act	act	NOUN
ejpam-2010	211	6	x	x	PUNCT
ejpam-2010	211	7	is	be	AUX
ejpam-2010	211	8	said	say	VERB
ejpam-2010	211	9	to	to	PART
ejpam-2010	211	10	be	be	AUX
ejpam-2010	211	11	closed	close	VERB
ejpam-2010	211	12	if	if	SCONJ
ejpam-2010	211	13	µx	µx	VERB
ejpam-2010	211	14	is	be	AUX
ejpam-2010	211	15	surjective	surjective	ADJ
ejpam-2010	211	16	and	and	CCONJ
ejpam-2010	211	17	injective	injective	ADJ
ejpam-2010	211	18	.	.	PUNCT
ejpam-2010	212	1	all	all	DET
ejpam-2010	212	2	the	the	DET
ejpam-2010	212	3	closed	closed	ADJ
ejpam-2010	212	4	left	leave	VERB
ejpam-2010	212	5	s	s	NOUN
ejpam-2010	212	6	-	-	PUNCT
ejpam-2010	212	7	acts	act	NOUN
ejpam-2010	212	8	form	form	VERB
ejpam-2010	212	9	a	a	DET
ejpam-2010	212	10	full	full	ADJ
ejpam-2010	212	11	-	-	PUNCT
ejpam-2010	212	12	subcategory	subcategory	NOUN
ejpam-2010	212	13	of	of	ADP
ejpam-2010	212	14	s	s	PROPN
ejpam-2010	212	15	-	-	PUNCT
ejpam-2010	212	16	act	act	NOUN
ejpam-2010	212	17	,	,	PUNCT
ejpam-2010	212	18	denoted	denote	VERB
ejpam-2010	212	19	by	by	ADP
ejpam-2010	212	20	s	s	NOUN
ejpam-2010	212	21	-	-	NOUN
ejpam-2010	212	22	fact	fact	NOUN
ejpam-2010	212	23	(	(	PUNCT
ejpam-2010	212	24	it	it	PRON
ejpam-2010	212	25	is	be	AUX
ejpam-2010	212	26	denoted	denote	VERB
ejpam-2010	212	27	by	by	ADP
ejpam-2010	212	28	s	s	NOUN
ejpam-2010	212	29	-	-	NOUN
ejpam-2010	212	30	fixact	fixact	NOUN
ejpam-2010	212	31	in	in	ADP
ejpam-2010	212	32	[	[	X
ejpam-2010	212	33	43	43	NUM
ejpam-2010	212	34	]	]	NUM
ejpam-2010	212	35	)	)	PUNCT
ejpam-2010	212	36	.	.	PUNCT
ejpam-2010	213	1	dually	dually	ADV
ejpam-2010	213	2	we	we	PRON
ejpam-2010	213	3	have	have	VERB
ejpam-2010	213	4	right	right	ADJ
ejpam-2010	213	5	s	s	NOUN
ejpam-2010	213	6	-	-	PUNCT
ejpam-2010	213	7	acts	act	NOUN
ejpam-2010	213	8	and	and	CCONJ
ejpam-2010	213	9	also	also	ADV
ejpam-2010	213	10	we	we	PRON
ejpam-2010	213	11	define	define	VERB
ejpam-2010	213	12	(	(	PUNCT
ejpam-2010	213	13	s	s	PROPN
ejpam-2010	213	14	,	,	PUNCT
ejpam-2010	213	15	t	t	NOUN
ejpam-2010	213	16	)	)	PUNCT
ejpam-2010	213	17	-biacts	-biact	NOUN
ejpam-2010	213	18	in	in	ADP
ejpam-2010	213	19	the	the	DET
ejpam-2010	213	20	usual	usual	ADJ
ejpam-2010	213	21	way	way	NOUN
ejpam-2010	213	22	.	.	PUNCT
ejpam-2010	214	1	a	a	DET
ejpam-2010	214	2	biact	biact	NOUN
ejpam-2010	214	3	is	be	AUX
ejpam-2010	214	4	unitary	unitary	ADJ
ejpam-2010	214	5	if	if	SCONJ
ejpam-2010	214	6	it	it	PRON
ejpam-2010	214	7	is	be	AUX
ejpam-2010	214	8	left	leave	VERB
ejpam-2010	214	9	-	-	PUNCT
ejpam-2010	214	10	right	right	NOUN
ejpam-2010	214	11	unitary	unitary	ADJ
ejpam-2010	214	12	.	.	PUNCT
ejpam-2010	215	1	a	a	DET
ejpam-2010	215	2	biact	biact	NOUN
ejpam-2010	215	3	is	be	AUX
ejpam-2010	215	4	closed	close	VERB
ejpam-2010	215	5	if	if	SCONJ
ejpam-2010	215	6	it	it	PRON
ejpam-2010	215	7	is	be	AUX
ejpam-2010	215	8	closed	close	VERB
ejpam-2010	215	9	as	as	ADP
ejpam-2010	215	10	a	a	DET
ejpam-2010	215	11	left	left	NOUN
ejpam-2010	215	12	and	and	CCONJ
ejpam-2010	215	13	as	as	ADP
ejpam-2010	215	14	a	a	DET
ejpam-2010	215	15	right	right	ADJ
ejpam-2010	215	16	act	act	NOUN
ejpam-2010	215	17	.	.	PUNCT
ejpam-2010	216	1	notice	notice	VERB
ejpam-2010	216	2	that	that	SCONJ
ejpam-2010	216	3	s	s	NOUN
ejpam-2010	216	4	-	-	PUNCT
ejpam-2010	216	5	fact	fact	NOUN
ejpam-2010	216	6	⊆	⊆	NUM
ejpam-2010	216	7	s	s	NOUN
ejpam-2010	216	8	-	-	NOUN
ejpam-2010	216	9	uact	uact	ADJ
ejpam-2010	216	10	,	,	PUNCT
ejpam-2010	216	11	where	where	SCONJ
ejpam-2010	216	12	the	the	DET
ejpam-2010	216	13	inclusion	inclusion	NOUN
ejpam-2010	216	14	is	be	AUX
ejpam-2010	216	15	as	as	ADP
ejpam-2010	216	16	full	full	ADJ
ejpam-2010	216	17	subcategories	subcategorie	NOUN
ejpam-2010	216	18	.	.	PUNCT
ejpam-2010	217	1	the	the	DET
ejpam-2010	217	2	full	full	ADJ
ejpam-2010	217	3	subcategory	subcategory	NOUN
ejpam-2010	217	4	which	which	PRON
ejpam-2010	217	5	consists	consist	VERB
ejpam-2010	217	6	of	of	ADP
ejpam-2010	217	7	all	all	DET
ejpam-2010	217	8	objects	object	NOUN
ejpam-2010	217	9	that	that	PRON
ejpam-2010	217	10	are	be	AUX
ejpam-2010	217	11	in	in	ADP
ejpam-2010	217	12	s	s	NOUN
ejpam-2010	217	13	-	-	ADJ
ejpam-2010	217	14	uact	uact	ADJ
ejpam-2010	217	15	and	and	CCONJ
ejpam-2010	217	16	are	be	AUX
ejpam-2010	217	17	fixed	fix	VERB
ejpam-2010	217	18	by	by	ADP
ejpam-2010	217	19	the	the	DET
ejpam-2010	217	20	functor	functor	PROPN
ejpam-2010	217	21	shoms(s,−	shoms(s,−	PROPN
ejpam-2010	217	22	)	)	PUNCT
ejpam-2010	217	23	is	be	AUX
ejpam-2010	217	24	denoted	denote	VERB
ejpam-2010	217	25	by	by	ADP
ejpam-2010	217	26	s	s	NOUN
ejpam-2010	217	27	-	-	NOUN
ejpam-2010	217	28	ufact	ufact	ADJ
ejpam-2010	217	29	.	.	PUNCT
ejpam-2010	218	1	y.	y.	PROPN
ejpam-2010	218	2	wang	wang	PROPN
ejpam-2010	218	3	,	,	PUNCT
ejpam-2010	218	4	k.	k.	PROPN
ejpam-2010	218	5	shum	shum	PROPN
ejpam-2010	218	6	,	,	PUNCT
ejpam-2010	218	7	x.	x.	PROPN
ejpam-2010	218	8	ren	ren	PROPN
ejpam-2010	218	9	/	/	SYM
ejpam-2010	218	10	eur	eur	PROPN
ejpam-2010	218	11	.	.	PUNCT
ejpam-2010	219	1	j.	j.	PROPN
ejpam-2010	219	2	pure	pure	PROPN
ejpam-2010	219	3	appl	appl	PROPN
ejpam-2010	219	4	.	.	PROPN
ejpam-2010	219	5	math	math	PROPN
ejpam-2010	219	6	,	,	PUNCT
ejpam-2010	219	7	6	6	NUM
ejpam-2010	219	8	(	(	PUNCT
ejpam-2010	219	9	2013	2013	NUM
ejpam-2010	219	10	)	)	PUNCT
ejpam-2010	219	11	,	,	PUNCT
ejpam-2010	219	12	256	256	NUM
ejpam-2010	219	13	-	-	SYM
ejpam-2010	219	14	281	281	NUM
ejpam-2010	219	15	263	263	NUM
ejpam-2010	219	16	we	we	PRON
ejpam-2010	219	17	say	say	VERB
ejpam-2010	219	18	that	that	SCONJ
ejpam-2010	219	19	a	a	DET
ejpam-2010	219	20	closed	closed	ADJ
ejpam-2010	219	21	left	leave	VERB
ejpam-2010	219	22	s	s	NOUN
ejpam-2010	219	23	-	-	PUNCT
ejpam-2010	219	24	act	act	NOUN
ejpam-2010	219	25	m	m	NOUN
ejpam-2010	219	26	is	be	AUX
ejpam-2010	219	27	indecomposable	indecomposable	ADJ
ejpam-2010	219	28	if	if	SCONJ
ejpam-2010	219	29	m	m	NOUN
ejpam-2010	219	30	is	be	AUX
ejpam-2010	219	31	not	not	PART
ejpam-2010	219	32	isomorphic	isomorphic	ADJ
ejpam-2010	219	33	to	to	ADP
ejpam-2010	219	34	any	any	DET
ejpam-2010	219	35	coproduct	coproduct	NOUN
ejpam-2010	219	36	n	n	ADP
ejpam-2010	219	37	t	t	NOUN
ejpam-2010	219	38	n	n	PROPN
ejpam-2010	219	39	where	where	SCONJ
ejpam-2010	219	40	n	n	NOUN
ejpam-2010	219	41	and	and	CCONJ
ejpam-2010	219	42	n	n	PROPN
ejpam-2010	219	43	are	be	AUX
ejpam-2010	219	44	non	non	ADJ
ejpam-2010	219	45	-	-	ADJ
ejpam-2010	219	46	empty	empty	ADJ
ejpam-2010	219	47	closed	closed	ADJ
ejpam-2010	219	48	left	leave	VERB
ejpam-2010	219	49	s	s	NOUN
ejpam-2010	219	50	-	-	PUNCT
ejpam-2010	219	51	acts	act	NOUN
ejpam-2010	219	52	.	.	PUNCT
ejpam-2010	220	1	proposition	proposition	NOUN
ejpam-2010	220	2	1	1	NUM
ejpam-2010	220	3	.	.	PUNCT
ejpam-2010	221	1	[	[	X
ejpam-2010	221	2	25	25	NUM
ejpam-2010	221	3	,	,	PUNCT
ejpam-2010	221	4	proposon	proposon	NOUN
ejpam-2010	221	5	3.3	3.3	NUM
ejpam-2010	221	6	]	]	PUNCT
ejpam-2010	221	7	in	in	ADP
ejpam-2010	221	8	the	the	DET
ejpam-2010	221	9	category	category	NOUN
ejpam-2010	221	10	s	s	NOUN
ejpam-2010	221	11	-	-	PUNCT
ejpam-2010	221	12	fact	fact	NOUN
ejpam-2010	221	13	,	,	PUNCT
ejpam-2010	221	14	p	p	NOUN
ejpam-2010	221	15	is	be	AUX
ejpam-2010	221	16	indecomposable	indecomposable	ADJ
ejpam-2010	221	17	and	and	CCONJ
ejpam-2010	221	18	projective	projective	ADJ
ejpam-2010	221	19	if	if	SCONJ
ejpam-2010	221	20	and	and	CCONJ
ejpam-2010	221	21	only	only	ADV
ejpam-2010	221	22	if	if	SCONJ
ejpam-2010	221	23	p	p	NOUN
ejpam-2010	221	24	is	be	AUX
ejpam-2010	221	25	isomorphic	isomorphic	ADJ
ejpam-2010	221	26	to	to	PART
ejpam-2010	221	27	se	se	VERB
ejpam-2010	221	28	for	for	ADP
ejpam-2010	221	29	some	some	DET
ejpam-2010	221	30	idempotent	idempotent	ADJ
ejpam-2010	221	31	e.	e.	PROPN
ejpam-2010	221	32	in	in	ADP
ejpam-2010	221	33	1972	1972	NUM
ejpam-2010	221	34	,	,	PUNCT
ejpam-2010	221	35	banaschewski	banaschewski	PROPN
ejpam-2010	221	36	showed	show	VERB
ejpam-2010	221	37	that	that	SCONJ
ejpam-2010	221	38	the	the	DET
ejpam-2010	221	39	generalisation	generalisation	NOUN
ejpam-2010	221	40	of	of	ADP
ejpam-2010	221	41	the	the	DET
ejpam-2010	221	42	morita	morita	PROPN
ejpam-2010	221	43	theory	theory	NOUN
ejpam-2010	221	44	for	for	ADP
ejpam-2010	221	45	rings	ring	NOUN
ejpam-2010	221	46	to	to	ADP
ejpam-2010	221	47	semigroups	semigroups	X
ejpam-2010	221	48	is	be	AUX
ejpam-2010	221	49	in	in	ADP
ejpam-2010	221	50	fact	fact	NOUN
ejpam-2010	221	51	isomorphic	isomorphic	ADJ
ejpam-2010	221	52	in	in	SCONJ
ejpam-2010	221	53	case	case	NOUN
ejpam-2010	221	54	r	r	NOUN
ejpam-2010	221	55	-	-	PUNCT
ejpam-2010	221	56	act	act	NOUN
ejpam-2010	221	57	and	and	CCONJ
ejpam-2010	221	58	s	s	NOUN
ejpam-2010	221	59	-	-	PUNCT
ejpam-2010	221	60	act	act	NOUN
ejpam-2010	221	61	are	be	AUX
ejpam-2010	221	62	equivalent	equivalent	ADJ
ejpam-2010	221	63	,	,	PUNCT
ejpam-2010	221	64	with	with	ADP
ejpam-2010	221	65	no	no	DET
ejpam-2010	221	66	requirement	requirement	NOUN
ejpam-2010	221	67	that	that	PRON
ejpam-2010	221	68	acts	act	VERB
ejpam-2010	221	69	be	be	VERB
ejpam-2010	221	70	unitary	unitary	ADJ
ejpam-2010	221	71	in	in	ADP
ejpam-2010	221	72	any	any	DET
ejpam-2010	221	73	sense	sense	NOUN
ejpam-2010	221	74	.	.	PUNCT
ejpam-2010	222	1	so	so	ADV
ejpam-2010	222	2	one	one	NOUN
ejpam-2010	222	3	is	be	AUX
ejpam-2010	222	4	forced	force	VERB
ejpam-2010	222	5	to	to	PART
ejpam-2010	222	6	define	define	VERB
ejpam-2010	222	7	morita	morita	NOUN
ejpam-2010	222	8	equivalence	equivalence	NOUN
ejpam-2010	222	9	in	in	ADP
ejpam-2010	222	10	terms	term	NOUN
ejpam-2010	222	11	of	of	ADP
ejpam-2010	222	12	subcategories	subcategorie	NOUN
ejpam-2010	222	13	if	if	SCONJ
ejpam-2010	222	14	a	a	DET
ejpam-2010	222	15	notion	notion	NOUN
ejpam-2010	222	16	differing	differ	VERB
ejpam-2010	222	17	from	from	ADP
ejpam-2010	222	18	isomorphism	isomorphism	NOUN
ejpam-2010	222	19	is	be	AUX
ejpam-2010	222	20	to	to	PART
ejpam-2010	222	21	be	be	AUX
ejpam-2010	222	22	obtained	obtain	VERB
ejpam-2010	222	23	.	.	PUNCT
ejpam-2010	223	1	in	in	ADP
ejpam-2010	223	2	1990	1990	NUM
ejpam-2010	223	3	,	,	PUNCT
ejpam-2010	223	4	knauer	knauer	NOUN
ejpam-2010	223	5	and	and	CCONJ
ejpam-2010	223	6	normak	normak	PROPN
ejpam-2010	223	7	showed	show	VERB
ejpam-2010	223	8	that	that	SCONJ
ejpam-2010	223	9	monoids	monoid	NOUN
ejpam-2010	223	10	m	m	VERB
ejpam-2010	223	11	and	and	CCONJ
ejpam-2010	223	12	n	n	PROPN
ejpam-2010	223	13	are	be	AUX
ejpam-2010	223	14	morita	morita	NOUN
ejpam-2010	223	15	equivalent	equivalent	ADJ
ejpam-2010	223	16	if	if	SCONJ
ejpam-2010	223	17	and	and	CCONJ
ejpam-2010	223	18	only	only	ADV
ejpam-2010	223	19	if	if	SCONJ
ejpam-2010	223	20	m	m	NOUN
ejpam-2010	223	21	-fact	-fact	ADJ
ejpam-2010	223	22	and	and	CCONJ
ejpam-2010	223	23	n	n	DET
ejpam-2010	223	24	-fact	-fact	NOUN
ejpam-2010	223	25	are	be	AUX
ejpam-2010	223	26	equivalent	equivalent	ADJ
ejpam-2010	223	27	categories	category	NOUN
ejpam-2010	223	28	.	.	PUNCT
ejpam-2010	224	1	as	as	ADP
ejpam-2010	224	2	a	a	DET
ejpam-2010	224	3	generalisation	generalisation	NOUN
ejpam-2010	224	4	of	of	ADP
ejpam-2010	224	5	morita	morita	PROPN
ejpam-2010	224	6	equivalence	equivalence	NOUN
ejpam-2010	224	7	for	for	ADP
ejpam-2010	224	8	rings	ring	NOUN
ejpam-2010	224	9	and	and	CCONJ
ejpam-2010	224	10	monoids	monoid	NOUN
ejpam-2010	224	11	tarlwar	tarlwar	VERB
ejpam-2010	224	12	first	first	ADV
ejpam-2010	224	13	defined	define	VERB
ejpam-2010	224	14	morita	morita	NOUN
ejpam-2010	224	15	theory	theory	NOUN
ejpam-2010	224	16	for	for	ADP
ejpam-2010	224	17	semigroups	semigroup	NOUN
ejpam-2010	224	18	with	with	ADP
ejpam-2010	224	19	local	local	ADJ
ejpam-2010	224	20	units	unit	NOUN
ejpam-2010	224	21	.	.	PUNCT
ejpam-2010	225	1	semigroups	semigroups	PROPN
ejpam-2010	225	2	r	r	NOUN
ejpam-2010	225	3	and	and	CCONJ
ejpam-2010	225	4	s	s	PROPN
ejpam-2010	225	5	with	with	ADP
ejpam-2010	225	6	local	local	ADJ
ejpam-2010	225	7	units	unit	NOUN
ejpam-2010	225	8	are	be	AUX
ejpam-2010	225	9	morita	morita	NOUN
ejpam-2010	225	10	equivalent	equivalent	ADJ
ejpam-2010	225	11	if	if	SCONJ
ejpam-2010	225	12	s	s	NOUN
ejpam-2010	225	13	-	-	PUNCT
ejpam-2010	225	14	fact	fact	NOUN
ejpam-2010	225	15	is	be	AUX
ejpam-2010	225	16	equivalent	equivalent	ADJ
ejpam-2010	225	17	to	to	ADP
ejpam-2010	225	18	r	r	NOUN
ejpam-2010	225	19	-	-	NOUN
ejpam-2010	225	20	fact	fact	NOUN
ejpam-2010	225	21	.	.	PUNCT
ejpam-2010	226	1	if	if	SCONJ
ejpam-2010	226	2	r	r	NOUN
ejpam-2010	226	3	and	and	CCONJ
ejpam-2010	226	4	s	s	PRON
ejpam-2010	226	5	both	both	PRON
ejpam-2010	226	6	have	have	VERB
ejpam-2010	226	7	a	a	DET
ejpam-2010	226	8	zero	zero	NUM
ejpam-2010	226	9	,	,	PUNCT
ejpam-2010	226	10	then	then	ADV
ejpam-2010	226	11	we	we	PRON
ejpam-2010	226	12	shall	shall	AUX
ejpam-2010	226	13	require	require	VERB
ejpam-2010	226	14	that	that	SCONJ
ejpam-2010	226	15	s0	s0	NOUN
ejpam-2010	226	16	-	-	PUNCT
ejpam-2010	226	17	fact	fact	NOUN
ejpam-2010	226	18	be	be	AUX
ejpam-2010	226	19	equivalent	equivalent	ADJ
ejpam-2010	226	20	to	to	ADP
ejpam-2010	226	21	r0	r0	NOUN
ejpam-2010	226	22	-	-	PUNCT
ejpam-2010	226	23	fact	fact	NOUN
ejpam-2010	226	24	.	.	PUNCT
ejpam-2010	227	1	let	let	VERB
ejpam-2010	227	2	r	r	NOUN
ejpam-2010	227	3	and	and	CCONJ
ejpam-2010	227	4	s	s	VERB
ejpam-2010	227	5	be	be	AUX
ejpam-2010	227	6	semigroups	semigroup	NOUN
ejpam-2010	227	7	.	.	PUNCT
ejpam-2010	228	1	a	a	DET
ejpam-2010	228	2	six	six	NUM
ejpam-2010	228	3	-	-	PUNCT
ejpam-2010	228	4	tuple	tuple	NOUN
ejpam-2010	228	5	〈	〈	PROPN
ejpam-2010	228	6	r	r	PROPN
ejpam-2010	228	7	,	,	PUNCT
ejpam-2010	228	8	s	s	PART
ejpam-2010	228	9	,	,	PUNCT
ejpam-2010	228	10	r	r	NOUN
ejpam-2010	228	11	ps	ps	PROPN
ejpam-2010	228	12	,	,	PUNCT
ejpam-2010	228	13	s	s	PROPN
ejpam-2010	228	14	qr	qr	NOUN
ejpam-2010	228	15	,	,	PUNCT
ejpam-2010	228	16	〈	〈	PROPN
ejpam-2010	228	17	,	,	PUNCT
ejpam-2010	228	18	〉	〉	NOUN
ejpam-2010	228	19	,	,	PUNCT
ejpam-2010	228	20	[	[	X
ejpam-2010	228	21	,	,	PUNCT
ejpam-2010	228	22	]	]	PUNCT
ejpam-2010	228	23	〉	〉	NOUN
ejpam-2010	228	24	is	be	AUX
ejpam-2010	228	25	said	say	VERB
ejpam-2010	228	26	to	to	PART
ejpam-2010	228	27	be	be	AUX
ejpam-2010	228	28	a	a	DET
ejpam-2010	228	29	morita	morita	NOUN
ejpam-2010	228	30	context	context	NOUN
ejpam-2010	228	31	if	if	SCONJ
ejpam-2010	228	32	the	the	DET
ejpam-2010	228	33	following	follow	VERB
ejpam-2010	228	34	conditions	condition	NOUN
ejpam-2010	228	35	hold	hold	VERB
ejpam-2010	228	36	:	:	PUNCT
ejpam-2010	228	37	(	(	PUNCT
ejpam-2010	228	38	1	1	X
ejpam-2010	228	39	)	)	PUNCT
ejpam-2010	228	40	rps	rps	NOUN
ejpam-2010	228	41	is	be	AUX
ejpam-2010	228	42	an	an	DET
ejpam-2010	228	43	r	r	NOUN
ejpam-2010	228	44	-	-	PUNCT
ejpam-2010	228	45	s	s	NOUN
ejpam-2010	228	46	-	-	PUNCT
ejpam-2010	228	47	biact	biact	NOUN
ejpam-2010	228	48	and	and	CCONJ
ejpam-2010	228	49	sqr	sqr	PROPN
ejpam-2010	228	50	is	be	AUX
ejpam-2010	228	51	an	an	DET
ejpam-2010	228	52	s	s	NOUN
ejpam-2010	228	53	-	-	PUNCT
ejpam-2010	228	54	r	r	NOUN
ejpam-2010	228	55	-	-	PUNCT
ejpam-2010	228	56	biact	biact	NOUN
ejpam-2010	228	57	;	;	PUNCT
ejpam-2010	228	58	(	(	PUNCT
ejpam-2010	228	59	2	2	X
ejpam-2010	228	60	)	)	PUNCT
ejpam-2010	228	61	〈	〈	PROPN
ejpam-2010	228	62	,	,	PUNCT
ejpam-2010	228	63	〉	〉	NOUN
ejpam-2010	228	64	is	be	AUX
ejpam-2010	228	65	an	an	DET
ejpam-2010	228	66	r	r	NOUN
ejpam-2010	228	67	-	-	PUNCT
ejpam-2010	228	68	r	r	NOUN
ejpam-2010	228	69	-	-	PUNCT
ejpam-2010	228	70	morphism	morphism	NOUN
ejpam-2010	228	71	of	of	ADP
ejpam-2010	228	72	p	p	NOUN
ejpam-2010	228	73	⊗s	⊗s	ADJ
ejpam-2010	228	74	q	q	NOUN
ejpam-2010	228	75	into	into	ADP
ejpam-2010	228	76	r	r	NOUN
ejpam-2010	228	77	,	,	PUNCT
ejpam-2010	228	78	and	and	CCONJ
ejpam-2010	228	79	[	[	X
ejpam-2010	228	80	,	,	PUNCT
ejpam-2010	228	81	]	]	PUNCT
ejpam-2010	228	82	is	be	AUX
ejpam-2010	228	83	an	an	DET
ejpam-2010	228	84	s	s	PROPN
ejpam-2010	228	85	-	-	PUNCT
ejpam-2010	228	86	s	s	NOUN
ejpam-2010	228	87	-	-	NOUN
ejpam-2010	228	88	morphism	morphism	NOUN
ejpam-2010	228	89	of	of	ADP
ejpam-2010	228	90	q⊗r	q⊗r	PROPN
ejpam-2010	228	91	p	p	NOUN
ejpam-2010	228	92	into	into	ADP
ejpam-2010	228	93	s	s	PRON
ejpam-2010	228	94	;	;	PUNCT
ejpam-2010	228	95	(	(	PUNCT
ejpam-2010	228	96	3	3	X
ejpam-2010	228	97	)	)	PUNCT
ejpam-2010	228	98	for	for	ADP
ejpam-2010	228	99	all	all	DET
ejpam-2010	228	100	p	p	NOUN
ejpam-2010	228	101	,	,	PUNCT
ejpam-2010	228	102	p′	p′	NOUN
ejpam-2010	228	103	∈	∈	PROPN
ejpam-2010	228	104	p	p	NOUN
ejpam-2010	228	105	and	and	CCONJ
ejpam-2010	228	106	q	q	NOUN
ejpam-2010	228	107	,	,	PUNCT
ejpam-2010	228	108	q′	q′	NOUN
ejpam-2010	228	109	∈q	∈q	NOUN
ejpam-2010	228	110	we	we	PRON
ejpam-2010	228	111	have	have	VERB
ejpam-2010	228	112	〈	〈	PROPN
ejpam-2010	228	113	p	p	NOUN
ejpam-2010	228	114	,	,	PUNCT
ejpam-2010	228	115	q〉p′	q〉p′	NUM
ejpam-2010	228	116	=	=	PROPN
ejpam-2010	228	117	p[q	p[q	PROPN
ejpam-2010	228	118	,	,	PUNCT
ejpam-2010	228	119	p′	p′	PROPN
ejpam-2010	228	120	]	]	PUNCT
ejpam-2010	228	121	and	and	CCONJ
ejpam-2010	228	122	q〈p	q〈p	PROPN
ejpam-2010	228	123	,	,	PUNCT
ejpam-2010	228	124	q′〉=	q′〉=	VERB
ejpam-2010	228	125	[	[	X
ejpam-2010	228	126	q	q	X
ejpam-2010	228	127	,	,	PUNCT
ejpam-2010	228	128	p]q′.	p]q′.	NOUN
ejpam-2010	228	129	we	we	PRON
ejpam-2010	228	130	say	say	VERB
ejpam-2010	228	131	that	that	SCONJ
ejpam-2010	228	132	a	a	DET
ejpam-2010	228	133	morita	morita	PROPN
ejpam-2010	228	134	context	context	PROPN
ejpam-2010	228	135	〈	〈	PROPN
ejpam-2010	228	136	r	r	PROPN
ejpam-2010	228	137	,	,	PUNCT
ejpam-2010	228	138	s	s	PART
ejpam-2010	228	139	,	,	PUNCT
ejpam-2010	228	140	r	r	NOUN
ejpam-2010	228	141	ps	ps	PROPN
ejpam-2010	228	142	,	,	PUNCT
ejpam-2010	228	143	s	s	PROPN
ejpam-2010	228	144	qr	qr	NOUN
ejpam-2010	228	145	,	,	PUNCT
ejpam-2010	228	146	〈	〈	PROPN
ejpam-2010	228	147	,	,	PUNCT
ejpam-2010	228	148	〉	〉	NOUN
ejpam-2010	228	149	,	,	PUNCT
ejpam-2010	228	150	[	[	X
ejpam-2010	228	151	,	,	PUNCT
ejpam-2010	228	152	]	]	PUNCT
ejpam-2010	228	153	〉	〉	NOUN
ejpam-2010	228	154	is	be	AUX
ejpam-2010	228	155	unitary	unitary	ADJ
ejpam-2010	228	156	if	if	SCONJ
ejpam-2010	228	157	rp	rp	NOUN
ejpam-2010	228	158	∈	∈	PROPN
ejpam-2010	228	159	s	s	NOUN
ejpam-2010	228	160	-	-	NOUN
ejpam-2010	228	161	fact	fact	NOUN
ejpam-2010	228	162	,	,	PUNCT
ejpam-2010	228	163	sq	sq	PROPN
ejpam-2010	228	164	∈	∈	PROPN
ejpam-2010	228	165	s	s	NOUN
ejpam-2010	228	166	-	-	NOUN
ejpam-2010	228	167	fact	fact	NOUN
ejpam-2010	228	168	and	and	CCONJ
ejpam-2010	228	169	the	the	DET
ejpam-2010	228	170	biacts	biact	NOUN
ejpam-2010	228	171	rps	rps	PROPN
ejpam-2010	228	172	and	and	CCONJ
ejpam-2010	228	173	sqr	sqr	PROPN
ejpam-2010	228	174	are	be	AUX
ejpam-2010	228	175	unitary	unitary	ADJ
ejpam-2010	228	176	.	.	PUNCT
ejpam-2010	229	1	two	two	NUM
ejpam-2010	229	2	semigroups	semigroup	NOUN
ejpam-2010	229	3	r	r	NOUN
ejpam-2010	229	4	and	and	CCONJ
ejpam-2010	229	5	s	s	NOUN
ejpam-2010	229	6	are	be	AUX
ejpam-2010	229	7	strongly1	strongly1	PROPN
ejpam-2010	229	8	morita	morita	PROPN
ejpam-2010	229	9	equivalent	equivalent	PROPN
ejpam-2010	229	10	if	if	SCONJ
ejpam-2010	229	11	there	there	PRON
ejpam-2010	229	12	exists	exist	VERB
ejpam-2010	229	13	a	a	DET
ejpam-2010	229	14	unitary	unitary	ADJ
ejpam-2010	229	15	morita	morita	NOUN
ejpam-2010	229	16	context	context	NOUN
ejpam-2010	229	17	such	such	ADJ
ejpam-2010	229	18	that	that	SCONJ
ejpam-2010	229	19	〈	〈	NOUN
ejpam-2010	229	20	,	,	PUNCT
ejpam-2010	229	21	〉	〉	NOUN
ejpam-2010	229	22	and	and	CCONJ
ejpam-2010	229	23	[	[	X
ejpam-2010	229	24	,	,	PUNCT
ejpam-2010	229	25	]	]	X
ejpam-2010	229	26	are	be	AUX
ejpam-2010	229	27	surjective	surjective	ADJ
ejpam-2010	229	28	.	.	PUNCT
ejpam-2010	230	1	the	the	DET
ejpam-2010	230	2	subscript	subscript	NOUN
ejpam-2010	230	3	is	be	AUX
ejpam-2010	230	4	used	use	VERB
ejpam-2010	230	5	to	to	PART
ejpam-2010	230	6	distinguish	distinguish	VERB
ejpam-2010	230	7	this	this	DET
ejpam-2010	230	8	meaning	meaning	NOUN
ejpam-2010	230	9	of	of	ADP
ejpam-2010	230	10	the	the	DET
ejpam-2010	230	11	word	word	NOUN
ejpam-2010	230	12	“	"	PUNCT
ejpam-2010	230	13	strongly	strongly	ADV
ejpam-2010	230	14	”	"	PUNCT
ejpam-2010	230	15	from	from	ADP
ejpam-2010	230	16	both	both	CCONJ
ejpam-2010	230	17	general	general	ADJ
ejpam-2010	230	18	semigroups	semigroup	NOUN
ejpam-2010	230	19	and	and	CCONJ
ejpam-2010	230	20	inverse	inverse	NOUN
ejpam-2010	230	21	semigroups	semigroup	NOUN
ejpam-2010	230	22	which	which	PRON
ejpam-2010	230	23	will	will	AUX
ejpam-2010	230	24	occur	occur	VERB
ejpam-2010	230	25	below	below	ADV
ejpam-2010	230	26	.	.	PUNCT
ejpam-2010	231	1	a	a	DET
ejpam-2010	231	2	5	5	NUM
ejpam-2010	231	3	-	-	PUNCT
ejpam-2010	231	4	tuple	tuple	NOUN
ejpam-2010	231	5	(	(	PUNCT
ejpam-2010	231	6	s	s	PROPN
ejpam-2010	231	7	,	,	PUNCT
ejpam-2010	231	8	t	t	PROPN
ejpam-2010	231	9	,	,	PUNCT
ejpam-2010	231	10	x	x	X
ejpam-2010	231	11	,	,	PUNCT
ejpam-2010	231	12	〈	〈	PROPN
ejpam-2010	231	13	,	,	PUNCT
ejpam-2010	231	14	〉	〉	NOUN
ejpam-2010	231	15	,	,	PUNCT
ejpam-2010	231	16	[	[	X
ejpam-2010	231	17	,	,	PUNCT
ejpam-2010	231	18	]	]	X
ejpam-2010	231	19	)	)	PUNCT
ejpam-2010	231	20	,	,	PUNCT
ejpam-2010	231	21	where	where	SCONJ
ejpam-2010	231	22	s	s	PRON
ejpam-2010	231	23	and	and	CCONJ
ejpam-2010	231	24	t	t	PROPN
ejpam-2010	231	25	are	be	AUX
ejpam-2010	231	26	inverse	inverse	NOUN
ejpam-2010	231	27	semigroups	semigroup	NOUN
ejpam-2010	231	28	and	and	CCONJ
ejpam-2010	231	29	x	x	X
ejpam-2010	231	30	is	be	AUX
ejpam-2010	231	31	a	a	DET
ejpam-2010	231	32	s	s	PROPN
ejpam-2010	231	33	-	-	PUNCT
ejpam-2010	231	34	t	t	NOUN
ejpam-2010	231	35	-biact	-biact	NOUN
ejpam-2010	231	36	,	,	PUNCT
ejpam-2010	231	37	is	be	AUX
ejpam-2010	231	38	said	say	VERB
ejpam-2010	231	39	to	to	PART
ejpam-2010	231	40	be	be	AUX
ejpam-2010	231	41	an	an	DET
ejpam-2010	231	42	inverse	inverse	NOUN
ejpam-2010	231	43	morita	morita	NOUN
ejpam-2010	231	44	context	context	NOUN
ejpam-2010	231	45	if	if	SCONJ
ejpam-2010	231	46	the	the	DET
ejpam-2010	231	47	following	follow	VERB
ejpam-2010	231	48	conditions	condition	NOUN
ejpam-2010	231	49	holds	hold	VERB
ejpam-2010	231	50	:	:	PUNCT
ejpam-2010	231	51	(	(	PUNCT
ejpam-2010	231	52	1	1	X
ejpam-2010	231	53	)	)	PUNCT
ejpam-2010	231	54	the	the	DET
ejpam-2010	231	55	left	left	ADJ
ejpam-2010	231	56	action	action	NOUN
ejpam-2010	231	57	of	of	ADP
ejpam-2010	231	58	s	s	PRON
ejpam-2010	231	59	on	on	ADP
ejpam-2010	231	60	x	x	PUNCT
ejpam-2010	231	61	and	and	CCONJ
ejpam-2010	231	62	the	the	DET
ejpam-2010	231	63	right	right	ADJ
ejpam-2010	231	64	action	action	NOUN
ejpam-2010	231	65	of	of	ADP
ejpam-2010	231	66	t	t	PROPN
ejpam-2010	231	67	on	on	ADP
ejpam-2010	231	68	x	x	PROPN
ejpam-2010	231	69	commute	commute	NOUN
ejpam-2010	231	70	;	;	PUNCT
ejpam-2010	231	71	(	(	PUNCT
ejpam-2010	231	72	2	2	X
ejpam-2010	231	73	)	)	PUNCT
ejpam-2010	231	74	〈	〈	PROPN
ejpam-2010	231	75	,	,	PUNCT
ejpam-2010	231	76	〉	〉	NOUN
ejpam-2010	231	77	:	:	PUNCT
ejpam-2010	231	78	x	x	X
ejpam-2010	231	79	×	×	NOUN
ejpam-2010	231	80	x	x	X
ejpam-2010	231	81	→	→	SYM
ejpam-2010	231	82	s	s	X
ejpam-2010	231	83	and	and	CCONJ
ejpam-2010	231	84	[	[	X
ejpam-2010	231	85	,	,	PUNCT
ejpam-2010	231	86	]	]	X
ejpam-2010	231	87	:	:	PUNCT
ejpam-2010	231	88	x	x	PUNCT
ejpam-2010	231	89	×	×	NOUN
ejpam-2010	231	90	x	x	X
ejpam-2010	231	91	→	→	SYM
ejpam-2010	231	92	t	t	PROPN
ejpam-2010	231	93	are	be	AUX
ejpam-2010	231	94	surjective	surjective	ADJ
ejpam-2010	231	95	functions	function	NOUN
ejpam-2010	231	96	;	;	PUNCT
ejpam-2010	231	97	(	(	PUNCT
ejpam-2010	231	98	3	3	X
ejpam-2010	231	99	)	)	PUNCT
ejpam-2010	231	100	for	for	ADP
ejpam-2010	231	101	any	any	DET
ejpam-2010	231	102	x	x	SYM
ejpam-2010	231	103	,	,	PUNCT
ejpam-2010	231	104	y	y	PROPN
ejpam-2010	231	105	,	,	PUNCT
ejpam-2010	231	106	z	z	NOUN
ejpam-2010	231	107	∈	∈	PROPN
ejpam-2010	231	108	x	x	X
ejpam-2010	231	109	,	,	PUNCT
ejpam-2010	231	110	s	s	PROPN
ejpam-2010	231	111	∈	∈	PROPN
ejpam-2010	231	112	s	s	X
ejpam-2010	231	113	and	and	CCONJ
ejpam-2010	231	114	t	t	PROPN
ejpam-2010	231	115	∈	∈	PROPN
ejpam-2010	231	116	t	t	NOUN
ejpam-2010	231	117	we	we	PRON
ejpam-2010	231	118	have	have	AUX
ejpam-2010	231	119	:	:	PUNCT
ejpam-2010	231	120	(	(	PUNCT
ejpam-2010	231	121	i	i	NOUN
ejpam-2010	231	122	)	)	PUNCT
ejpam-2010	231	123	〈	〈	PROPN
ejpam-2010	231	124	sx	sx	PROPN
ejpam-2010	231	125	,	,	PUNCT
ejpam-2010	231	126	y〉=	y〉=	NOUN
ejpam-2010	231	127	s〈x	s〈x	PROPN
ejpam-2010	231	128	,	,	PUNCT
ejpam-2010	231	129	y	y	PROPN
ejpam-2010	231	130	〉	〉	NOUN
ejpam-2010	231	131	;	;	PUNCT
ejpam-2010	231	132	(	(	PUNCT
ejpam-2010	231	133	ii	ii	NOUN
ejpam-2010	231	134	)	)	PUNCT
ejpam-2010	231	135	〈	〈	PROPN
ejpam-2010	231	136	y	y	PROPN
ejpam-2010	231	137	,	,	PUNCT
ejpam-2010	231	138	x〉=	x〉=	PUNCT
ejpam-2010	232	1	〈	〈	PROPN
ejpam-2010	232	2	x	x	SYM
ejpam-2010	232	3	,	,	PUNCT
ejpam-2010	232	4	y〉∗	y〉∗	PROPN
ejpam-2010	232	5	;	;	PUNCT
ejpam-2010	232	6	y.	y.	PROPN
ejpam-2010	232	7	wang	wang	PROPN
ejpam-2010	232	8	,	,	PUNCT
ejpam-2010	232	9	k.	k.	PROPN
ejpam-2010	232	10	shum	shum	PROPN
ejpam-2010	232	11	,	,	PUNCT
ejpam-2010	232	12	x.	x.	PROPN
ejpam-2010	232	13	ren	ren	PROPN
ejpam-2010	232	14	/	/	SYM
ejpam-2010	232	15	eur	eur	PROPN
ejpam-2010	232	16	.	.	PUNCT
ejpam-2010	233	1	j.	j.	PROPN
ejpam-2010	233	2	pure	pure	PROPN
ejpam-2010	233	3	appl	appl	PROPN
ejpam-2010	233	4	.	.	PROPN
ejpam-2010	233	5	math	math	PROPN
ejpam-2010	233	6	,	,	PUNCT
ejpam-2010	233	7	6	6	NUM
ejpam-2010	233	8	(	(	PUNCT
ejpam-2010	233	9	2013	2013	NUM
ejpam-2010	233	10	)	)	PUNCT
ejpam-2010	233	11	,	,	PUNCT
ejpam-2010	233	12	256	256	NUM
ejpam-2010	233	13	-	-	SYM
ejpam-2010	233	14	281	281	NUM
ejpam-2010	233	15	264	264	NUM
ejpam-2010	233	16	(	(	PUNCT
ejpam-2010	233	17	iii	iii	NOUN
ejpam-2010	233	18	)	)	PUNCT
ejpam-2010	233	19	〈	〈	NOUN
ejpam-2010	233	20	x	x	NOUN
ejpam-2010	233	21	,	,	PUNCT
ejpam-2010	233	22	x〉x	x〉x	X
ejpam-2010	233	23	=	=	PUNCT
ejpam-2010	234	1	x	x	X
ejpam-2010	234	2	;	;	PUNCT
ejpam-2010	234	3	(	(	PUNCT
ejpam-2010	234	4	iv	iv	X
ejpam-2010	234	5	)	)	PUNCT
ejpam-2010	235	1	[	[	X
ejpam-2010	235	2	x	x	X
ejpam-2010	235	3	,	,	PUNCT
ejpam-2010	235	4	y	y	PROPN
ejpam-2010	235	5	t	t	PROPN
ejpam-2010	235	6	]	]	PUNCT
ejpam-2010	235	7	=	=	PUNCT
ejpam-2010	236	1	[	[	X
ejpam-2010	236	2	x	x	X
ejpam-2010	236	3	,	,	PUNCT
ejpam-2010	236	4	y]t	y]t	NOUN
ejpam-2010	236	5	;	;	PUNCT
ejpam-2010	236	6	(	(	PUNCT
ejpam-2010	236	7	v	v	NOUN
ejpam-2010	236	8	)	)	PUNCT
ejpam-2010	237	1	[	[	X
ejpam-2010	237	2	y	y	X
ejpam-2010	237	3	,	,	PUNCT
ejpam-2010	237	4	x	x	X
ejpam-2010	237	5	]	]	X
ejpam-2010	237	6	=	=	PUNCT
ejpam-2010	238	1	[	[	X
ejpam-2010	238	2	x	x	X
ejpam-2010	238	3	,	,	PUNCT
ejpam-2010	238	4	y]∗	y]∗	PROPN
ejpam-2010	238	5	;	;	PUNCT
ejpam-2010	238	6	(	(	PUNCT
ejpam-2010	238	7	vi	vi	NOUN
ejpam-2010	238	8	)	)	PUNCT
ejpam-2010	238	9	x[x	x[x	NOUN
ejpam-2010	238	10	,	,	PUNCT
ejpam-2010	238	11	x	x	X
ejpam-2010	238	12	]	]	X
ejpam-2010	238	13	=	=	SYM
ejpam-2010	238	14	x	x	X
ejpam-2010	238	15	;	;	PUNCT
ejpam-2010	238	16	(	(	PUNCT
ejpam-2010	238	17	vii	vii	PROPN
ejpam-2010	238	18	)	)	PUNCT
ejpam-2010	238	19	〈	〈	PROPN
ejpam-2010	238	20	x	x	PROPN
ejpam-2010	238	21	,	,	PUNCT
ejpam-2010	238	22	y〉z	y〉z	PROPN
ejpam-2010	238	23	=	=	PROPN
ejpam-2010	238	24	x[y	x[y	PROPN
ejpam-2010	238	25	,	,	PUNCT
ejpam-2010	238	26	z	z	X
ejpam-2010	238	27	]	]	X
ejpam-2010	238	28	,	,	PUNCT
ejpam-2010	238	29	where	where	SCONJ
ejpam-2010	238	30	a∗	a∗	PROPN
ejpam-2010	238	31	is	be	AUX
ejpam-2010	238	32	the	the	DET
ejpam-2010	238	33	inverse	inverse	NOUN
ejpam-2010	238	34	of	of	ADP
ejpam-2010	238	35	a	a	PRON
ejpam-2010	238	36	for	for	ADP
ejpam-2010	238	37	all	all	DET
ejpam-2010	238	38	a	a	DET
ejpam-2010	238	39	∈	∈	NOUN
ejpam-2010	238	40	s.	s.	PROPN
ejpam-2010	238	41	here	here	ADV
ejpam-2010	238	42	we	we	PRON
ejpam-2010	238	43	call	call	VERB
ejpam-2010	238	44	x	x	VERB
ejpam-2010	238	45	(	(	PUNCT
ejpam-2010	238	46	together	together	ADV
ejpam-2010	238	47	with	with	ADP
ejpam-2010	238	48	the	the	DET
ejpam-2010	238	49	two	two	NUM
ejpam-2010	238	50	“	"	PUNCT
ejpam-2010	238	51	inner	inner	ADJ
ejpam-2010	238	52	products	product	NOUN
ejpam-2010	238	53	”	"	PUNCT
ejpam-2010	238	54	)	)	PUNCT
ejpam-2010	238	55	an	an	DET
ejpam-2010	238	56	equivalence	equivalence	NOUN
ejpam-2010	238	57	bimodule	bimodule	NOUN
ejpam-2010	238	58	.	.	PUNCT
ejpam-2010	239	1	two	two	NUM
ejpam-2010	239	2	inverse	inverse	NOUN
ejpam-2010	239	3	semigroups	semigroup	NOUN
ejpam-2010	239	4	s	s	PART
ejpam-2010	239	5	and	and	CCONJ
ejpam-2010	239	6	t	t	PROPN
ejpam-2010	239	7	are	be	AUX
ejpam-2010	239	8	said	say	VERB
ejpam-2010	239	9	to	to	ADP
ejpam-2010	239	10	strongly2	strongly2	PROPN
ejpam-2010	239	11	morita	morita	PROPN
ejpam-2010	239	12	equivalent	equivalent	PROPN
ejpam-2010	239	13	if	if	SCONJ
ejpam-2010	239	14	there	there	PRON
ejpam-2010	239	15	exists	exist	VERB
ejpam-2010	239	16	an	an	DET
ejpam-2010	239	17	equivalence	equivalence	NOUN
ejpam-2010	239	18	bimodule	bimodule	NOUN
ejpam-2010	239	19	for	for	ADP
ejpam-2010	239	20	them	they	PRON
ejpam-2010	239	21	,	,	PUNCT
ejpam-2010	239	22	that	that	ADV
ejpam-2010	239	23	is	is	ADV
ejpam-2010	239	24	,	,	PUNCT
ejpam-2010	239	25	there	there	PRON
ejpam-2010	239	26	exists	exist	VERB
ejpam-2010	239	27	an	an	DET
ejpam-2010	239	28	inverse	inverse	NOUN
ejpam-2010	239	29	morita	morita	NOUN
ejpam-2010	239	30	context	context	PROPN
ejpam-2010	239	31	(	(	PUNCT
ejpam-2010	239	32	s	s	PROPN
ejpam-2010	239	33	,	,	PUNCT
ejpam-2010	239	34	t	t	PROPN
ejpam-2010	239	35	,	,	PUNCT
ejpam-2010	239	36	x	x	X
ejpam-2010	239	37	,	,	PUNCT
ejpam-2010	239	38	〈	〈	PROPN
ejpam-2010	239	39	,	,	PUNCT
ejpam-2010	239	40	〉	〉	NOUN
ejpam-2010	239	41	,	,	PUNCT
ejpam-2010	239	42	[	[	X
ejpam-2010	239	43	,	,	PUNCT
ejpam-2010	239	44	]	]	X
ejpam-2010	239	45	)	)	PUNCT
ejpam-2010	239	46	.	.	PUNCT
ejpam-2010	240	1	3	3	X
ejpam-2010	240	2	.	.	X
ejpam-2010	240	3	morita	morita	PROPN
ejpam-2010	240	4	theory	theory	PROPN
ejpam-2010	240	5	for	for	ADP
ejpam-2010	240	6	rings	ring	NOUN
ejpam-2010	240	7	the	the	DET
ejpam-2010	240	8	main	main	ADJ
ejpam-2010	240	9	purpose	purpose	NOUN
ejpam-2010	240	10	of	of	ADP
ejpam-2010	240	11	this	this	DET
ejpam-2010	240	12	section	section	NOUN
ejpam-2010	240	13	is	be	AUX
ejpam-2010	240	14	to	to	PART
ejpam-2010	240	15	make	make	VERB
ejpam-2010	240	16	a	a	DET
ejpam-2010	240	17	survey	survey	NOUN
ejpam-2010	240	18	of	of	ADP
ejpam-2010	240	19	morita	morita	PROPN
ejpam-2010	240	20	theory	theory	NOUN
ejpam-2010	240	21	for	for	ADP
ejpam-2010	240	22	rings	ring	NOUN
ejpam-2010	240	23	.	.	PUNCT
ejpam-2010	241	1	the	the	DET
ejpam-2010	241	2	morita	morita	PROPN
ejpam-2010	241	3	theory	theory	NOUN
ejpam-2010	241	4	for	for	ADP
ejpam-2010	241	5	rings	ring	NOUN
ejpam-2010	241	6	has	have	AUX
ejpam-2010	241	7	been	be	AUX
ejpam-2010	241	8	widely	widely	ADV
ejpam-2010	241	9	studied	study	VERB
ejpam-2010	241	10	and	and	CCONJ
ejpam-2010	241	11	so	so	ADV
ejpam-2010	241	12	fruitful	fruitful	ADJ
ejpam-2010	241	13	results	result	NOUN
ejpam-2010	241	14	have	have	AUX
ejpam-2010	241	15	been	be	AUX
ejpam-2010	241	16	obtained	obtain	VERB
ejpam-2010	241	17	.	.	PUNCT
ejpam-2010	242	1	considering	consider	VERB
ejpam-2010	242	2	the	the	DET
ejpam-2010	242	3	length	length	NOUN
ejpam-2010	242	4	of	of	ADP
ejpam-2010	242	5	the	the	DET
ejpam-2010	242	6	paper	paper	NOUN
ejpam-2010	242	7	,	,	PUNCT
ejpam-2010	242	8	we	we	PRON
ejpam-2010	242	9	focus	focus	VERB
ejpam-2010	242	10	on	on	ADP
ejpam-2010	242	11	rings	ring	NOUN
ejpam-2010	242	12	with	with	ADP
ejpam-2010	242	13	local	local	ADJ
ejpam-2010	242	14	units	unit	NOUN
ejpam-2010	242	15	and	and	CCONJ
ejpam-2010	242	16	xst	xst	PROPN
ejpam-2010	242	17	-	-	PUNCT
ejpam-2010	242	18	rings	ring	NOUN
ejpam-2010	242	19	.	.	PUNCT
ejpam-2010	243	1	3.1	3.1	NUM
ejpam-2010	243	2	.	.	PUNCT
ejpam-2010	243	3	rings	ring	NOUN
ejpam-2010	243	4	with	with	ADP
ejpam-2010	243	5	local	local	ADJ
ejpam-2010	243	6	units	unit	NOUN
ejpam-2010	243	7	we	we	PRON
ejpam-2010	243	8	begin	begin	VERB
ejpam-2010	243	9	with	with	ADP
ejpam-2010	243	10	a	a	DET
ejpam-2010	243	11	well	well	ADV
ejpam-2010	243	12	-	-	PUNCT
ejpam-2010	243	13	known	know	VERB
ejpam-2010	243	14	theorem	theorem	NOUN
ejpam-2010	243	15	for	for	ADP
ejpam-2010	243	16	unital	unital	ADJ
ejpam-2010	243	17	rings	ring	NOUN
ejpam-2010	243	18	.	.	PUNCT
ejpam-2010	244	1	let	let	VERB
ejpam-2010	244	2	r	r	PRON
ejpam-2010	244	3	be	be	AUX
ejpam-2010	244	4	a	a	DET
ejpam-2010	244	5	unital	unital	ADJ
ejpam-2010	244	6	ring	ring	NOUN
ejpam-2010	244	7	and	and	CCONJ
ejpam-2010	244	8	let	let	VERB
ejpam-2010	244	9	p(r	p(r	PROPN
ejpam-2010	244	10	)	)	PUNCT
ejpam-2010	244	11	denote	denote	VERB
ejpam-2010	244	12	the	the	DET
ejpam-2010	244	13	full	full	ADJ
ejpam-2010	244	14	subcategory	subcategory	NOUN
ejpam-2010	244	15	of	of	ADP
ejpam-2010	244	16	r	r	NOUN
ejpam-2010	244	17	-	-	PUNCT
ejpam-2010	244	18	mod	mod	NOUN
ejpam-2010	244	19	consisting	consisting	NOUN
ejpam-2010	244	20	of	of	ADP
ejpam-2010	244	21	the	the	DET
ejpam-2010	244	22	finitely	finitely	ADV
ejpam-2010	244	23	generated	generate	VERB
ejpam-2010	244	24	projective	projective	NOUN
ejpam-2010	244	25	left	leave	VERB
ejpam-2010	244	26	r	r	NOUN
ejpam-2010	244	27	-	-	PUNCT
ejpam-2010	244	28	modules	module	NOUN
ejpam-2010	244	29	.	.	PUNCT
ejpam-2010	245	1	theorem	theorem	NOUN
ejpam-2010	245	2	1	1	NUM
ejpam-2010	245	3	.	.	PUNCT
ejpam-2010	246	1	[	[	X
ejpam-2010	246	2	34	34	NUM
ejpam-2010	246	3	,	,	PUNCT
ejpam-2010	246	4	theorem	theorem	VERB
ejpam-2010	246	5	3.4	3.4	NUM
ejpam-2010	246	6	]	]	PUNCT
ejpam-2010	246	7	let	let	VERB
ejpam-2010	246	8	r	r	NOUN
ejpam-2010	246	9	and	and	CCONJ
ejpam-2010	246	10	s	s	AUX
ejpam-2010	246	11	be	be	AUX
ejpam-2010	246	12	unital	unital	ADJ
ejpam-2010	246	13	rings	ring	NOUN
ejpam-2010	246	14	.	.	PUNCT
ejpam-2010	247	1	then	then	ADV
ejpam-2010	247	2	the	the	DET
ejpam-2010	247	3	following	follow	VERB
ejpam-2010	247	4	statements	statement	NOUN
ejpam-2010	247	5	are	be	AUX
ejpam-2010	247	6	equivalent	equivalent	ADJ
ejpam-2010	247	7	:	:	PUNCT
ejpam-2010	247	8	(	(	PUNCT
ejpam-2010	247	9	1	1	X
ejpam-2010	247	10	)	)	PUNCT
ejpam-2010	247	11	r	r	NOUN
ejpam-2010	247	12	and	and	CCONJ
ejpam-2010	247	13	s	s	NOUN
ejpam-2010	247	14	are	be	AUX
ejpam-2010	247	15	morita	morita	PROPN
ejpam-2010	247	16	equivalent	equivalent	NOUN
ejpam-2010	247	17	;	;	PUNCT
ejpam-2010	247	18	(	(	PUNCT
ejpam-2010	247	19	2	2	X
ejpam-2010	247	20	)	)	PUNCT
ejpam-2010	247	21	there	there	PRON
ejpam-2010	247	22	exists	exist	VERB
ejpam-2010	247	23	a	a	DET
ejpam-2010	247	24	finitely	finitely	ADV
ejpam-2010	247	25	generated	generate	VERB
ejpam-2010	247	26	projective	projective	ADJ
ejpam-2010	247	27	generator	generator	PROPN
ejpam-2010	247	28	rp	rp	NOUN
ejpam-2010	247	29	for	for	ADP
ejpam-2010	247	30	r	r	NOUN
ejpam-2010	247	31	-	-	PUNCT
ejpam-2010	247	32	mod	mod	NOUN
ejpam-2010	247	33	such	such	ADJ
ejpam-2010	247	34	that	that	PRON
ejpam-2010	247	35	s	s	VERB
ejpam-2010	247	36	∼=	∼=	PROPN
ejpam-2010	247	37	endr(p	endr(p	NOUN
ejpam-2010	247	38	)	)	PUNCT
ejpam-2010	247	39	;	;	PUNCT
ejpam-2010	247	40	(	(	PUNCT
ejpam-2010	247	41	3	3	X
ejpam-2010	247	42	)	)	PUNCT
ejpam-2010	247	43	there	there	PRON
ejpam-2010	247	44	exists	exist	VERB
ejpam-2010	247	45	p	p	NOUN
ejpam-2010	247	46	in	in	ADP
ejpam-2010	247	47	p(r	p(r	PROPN
ejpam-2010	247	48	)	)	PUNCT
ejpam-2010	247	49	,	,	PUNCT
ejpam-2010	247	50	with	with	ADP
ejpam-2010	247	51	p	p	PROPN
ejpam-2010	247	52	a	a	DET
ejpam-2010	247	53	generator	generator	NOUN
ejpam-2010	247	54	for	for	ADP
ejpam-2010	247	55	r	r	NOUN
ejpam-2010	247	56	-	-	PUNCT
ejpam-2010	247	57	mod	mod	ADJ
ejpam-2010	247	58	,	,	PUNCT
ejpam-2010	247	59	such	such	ADJ
ejpam-2010	247	60	that	that	PRON
ejpam-2010	247	61	s	s	VERB
ejpam-2010	247	62	∼=	∼=	NOUN
ejpam-2010	247	63	endp(r)(p	endp(r)(p	NOUN
ejpam-2010	247	64	)	)	PUNCT
ejpam-2010	247	65	.	.	PUNCT
ejpam-2010	248	1	in	in	ADP
ejpam-2010	248	2	1983	1983	NUM
ejpam-2010	248	3	,	,	PUNCT
ejpam-2010	248	4	abrams	abrams	PROPN
ejpam-2010	248	5	extent	extent	PROPN
ejpam-2010	248	6	theorem	theorem	VERB
ejpam-2010	248	7	1	1	NUM
ejpam-2010	248	8	from	from	ADP
ejpam-2010	248	9	unital	unital	ADJ
ejpam-2010	248	10	rings	ring	NOUN
ejpam-2010	248	11	to	to	ADP
ejpam-2010	248	12	rings	ring	NOUN
ejpam-2010	248	13	with	with	ADP
ejpam-2010	248	14	slu	slu	NOUN
ejpam-2010	248	15	.	.	PUNCT
ejpam-2010	249	1	we	we	PRON
ejpam-2010	249	2	now	now	ADV
ejpam-2010	249	3	give	give	VERB
ejpam-2010	249	4	a	a	DET
ejpam-2010	249	5	brief	brief	ADJ
ejpam-2010	249	6	description	description	NOUN
ejpam-2010	249	7	.	.	PUNCT
ejpam-2010	250	1	let	let	VERB
ejpam-2010	250	2	r	r	NOUN
ejpam-2010	250	3	and	and	CCONJ
ejpam-2010	250	4	s	s	AUX
ejpam-2010	250	5	be	be	AUX
ejpam-2010	250	6	mortia	mortia	X
ejpam-2010	250	7	equivalent	equivalent	ADJ
ejpam-2010	250	8	rings	ring	NOUN
ejpam-2010	250	9	with	with	ADP
ejpam-2010	250	10	slu	slu	NOUN
ejpam-2010	250	11	.	.	PUNCT
ejpam-2010	251	1	b.abrams	b.abram	VERB
ejpam-2010	251	2	[	[	X
ejpam-2010	251	3	1	1	NUM
ejpam-2010	251	4	]	]	PUNCT
ejpam-2010	251	5	further	far	ADV
ejpam-2010	251	6	showed	show	VERB
ejpam-2010	251	7	that	that	SCONJ
ejpam-2010	251	8	s	s	VERB
ejpam-2010	251	9	can	can	AUX
ejpam-2010	251	10	be	be	AUX
ejpam-2010	251	11	considered	consider	VERB
ejpam-2010	251	12	as	as	ADP
ejpam-2010	251	13	limiend(q	limiend(q	NOUN
ejpam-2010	251	14	i	i	PRON
ejpam-2010	251	15	)	)	PUNCT
ejpam-2010	251	16	,	,	PUNCT
ejpam-2010	251	17	where	where	SCONJ
ejpam-2010	251	18	{	{	PUNCT
ejpam-2010	251	19	q	q	NOUN
ejpam-2010	251	20	i	i	PRON
ejpam-2010	251	21	,	,	PUNCT
ejpam-2010	251	22	φi	φi	PROPN
ejpam-2010	251	23	j	j	PROPN
ejpam-2010	251	24	,	,	PUNCT
ejpam-2010	251	25	ψ	ψ	VERB
ejpam-2010	251	26	ji|i	ji|i	PROPN
ejpam-2010	251	27	∈	∈	PROPN
ejpam-2010	251	28	i	i	PRON
ejpam-2010	251	29	}	}	PUNCT
ejpam-2010	251	30	is	be	AUX
ejpam-2010	251	31	a	a	DET
ejpam-2010	251	32	progenerator	progenerator	NOUN
ejpam-2010	251	33	for	for	ADP
ejpam-2010	251	34	r.	r.	NOUN
ejpam-2010	251	35	conversely	conversely	ADV
ejpam-2010	251	36	,	,	PUNCT
ejpam-2010	251	37	if	if	SCONJ
ejpam-2010	251	38	s	s	VERB
ejpam-2010	251	39	∼=	∼=	VERB
ejpam-2010	251	40	limiend(q	limiend(q	NOUN
ejpam-2010	251	41	i	i	PRON
ejpam-2010	251	42	)	)	PUNCT
ejpam-2010	251	43	,	,	PUNCT
ejpam-2010	252	1	where	where	SCONJ
ejpam-2010	252	2	{	{	PUNCT
ejpam-2010	252	3	q	q	NOUN
ejpam-2010	252	4	i	i	PRON
ejpam-2010	252	5	,	,	PUNCT
ejpam-2010	252	6	φi	φi	PROPN
ejpam-2010	252	7	j	j	PROPN
ejpam-2010	252	8	,	,	PUNCT
ejpam-2010	252	9	ψ	ψ	VERB
ejpam-2010	252	10	ji|i	ji|i	PROPN
ejpam-2010	252	11	∈	∈	PROPN
ejpam-2010	253	1	i	i	PRON
ejpam-2010	253	2	}	}	PUNCT
ejpam-2010	253	3	is	be	AUX
ejpam-2010	253	4	a	a	DET
ejpam-2010	253	5	progenerator	progenerator	NOUN
ejpam-2010	253	6	.	.	PUNCT
ejpam-2010	254	1	we	we	PRON
ejpam-2010	254	2	define	define	VERB
ejpam-2010	254	3	si	si	X
ejpam-2010	254	4	=	=	SYM
ejpam-2010	254	5	endr(x	endr(x	PROPN
ejpam-2010	254	6	i	i	NOUN
ejpam-2010	254	7	)	)	PUNCT
ejpam-2010	254	8	.	.	PUNCT
ejpam-2010	255	1	then	then	ADV
ejpam-2010	255	2	s	s	VERB
ejpam-2010	255	3	∼=	∼=	PROPN
ejpam-2010	255	4	lim−→i((si	lim−→i((si	NOUN
ejpam-2010	255	5	,	,	PUNCT
ejpam-2010	255	6	1	1	NUM
ejpam-2010	255	7	j),ωi	j),ωi	NUM
ejpam-2010	255	8	j	j	PROPN
ejpam-2010	255	9	)	)	PUNCT
ejpam-2010	255	10	where	where	SCONJ
ejpam-2010	255	11	ωi	ωi	PROPN
ejpam-2010	255	12	j	j	PROPN
ejpam-2010	255	13	:	:	PUNCT
ejpam-2010	255	14	si	si	PROPN
ejpam-2010	255	15	→	→	SYM
ejpam-2010	255	16	s	s	PART
ejpam-2010	255	17	j	j	NOUN
ejpam-2010	255	18	defined	define	VERB
ejpam-2010	255	19	by	by	ADP
ejpam-2010	255	20	r	r	NOUN
ejpam-2010	255	21	7→ψ	7→ψ	NUM
ejpam-2010	255	22	ji	ji	PROPN
ejpam-2010	255	23	rφi	rφi	PROPN
ejpam-2010	255	24	j	j	PROPN
ejpam-2010	255	25	.	.	PUNCT
ejpam-2010	256	1	let	let	VERB
ejpam-2010	256	2	fi	fi	NOUN
ejpam-2010	256	3	denote	denote	VERB
ejpam-2010	257	1	[	[	X
ejpam-2010	257	2	1x	1x	X
ejpam-2010	257	3	i	i	X
ejpam-2010	257	4	]	]	PUNCT
ejpam-2010	257	5	in	in	ADP
ejpam-2010	257	6	limiend(x	limiend(x	PROPN
ejpam-2010	257	7	i	i	PROPN
ejpam-2010	257	8	)	)	PUNCT
ejpam-2010	257	9	.	.	PUNCT
ejpam-2010	258	1	then	then	ADV
ejpam-2010	258	2	endr(x	endr(x	PROPN
ejpam-2010	258	3	i)∼=	i)∼=	VERB
ejpam-2010	258	4	fis	fis	PROPN
ejpam-2010	258	5	fi	fi	PROPN
ejpam-2010	258	6	y.	y.	PROPN
ejpam-2010	258	7	wang	wang	PROPN
ejpam-2010	258	8	,	,	PUNCT
ejpam-2010	258	9	k.	k.	PROPN
ejpam-2010	258	10	shum	shum	PROPN
ejpam-2010	258	11	,	,	PUNCT
ejpam-2010	258	12	x.	x.	PROPN
ejpam-2010	258	13	ren	ren	PROPN
ejpam-2010	258	14	/	/	SYM
ejpam-2010	258	15	eur	eur	PROPN
ejpam-2010	258	16	.	.	PUNCT
ejpam-2010	259	1	j.	j.	PROPN
ejpam-2010	259	2	pure	pure	PROPN
ejpam-2010	259	3	appl	appl	PROPN
ejpam-2010	259	4	.	.	PROPN
ejpam-2010	259	5	math	math	PROPN
ejpam-2010	259	6	,	,	PUNCT
ejpam-2010	259	7	6	6	NUM
ejpam-2010	259	8	(	(	PUNCT
ejpam-2010	259	9	2013	2013	NUM
ejpam-2010	259	10	)	)	PUNCT
ejpam-2010	259	11	,	,	PUNCT
ejpam-2010	259	12	256	256	NUM
ejpam-2010	259	13	-	-	SYM
ejpam-2010	259	14	281	281	NUM
ejpam-2010	259	15	265	265	NUM
ejpam-2010	259	16	given	give	VERB
ejpam-2010	259	17	by	by	ADP
ejpam-2010	259	18	r	r	NOUN
ejpam-2010	259	19	7→	7→	PROPN
ejpam-2010	259	20	[	[	X
ejpam-2010	259	21	r	r	X
ejpam-2010	259	22	]	]	PUNCT
ejpam-2010	259	23	.	.	PUNCT
ejpam-2010	259	24	suppose	suppose	VERB
ejpam-2010	259	25	that	that	SCONJ
ejpam-2010	259	26	m	m	PROPN
ejpam-2010	259	27	is	be	AUX
ejpam-2010	259	28	a	a	DET
ejpam-2010	259	29	left	left	ADJ
ejpam-2010	259	30	r	r	NOUN
ejpam-2010	259	31	-	-	PUNCT
ejpam-2010	259	32	modules	module	NOUN
ejpam-2010	259	33	.	.	PUNCT
ejpam-2010	260	1	let	let	VERB
ejpam-2010	260	2	i	i	PRON
ejpam-2010	260	3	≤	≤	VERB
ejpam-2010	260	4	j	j	PROPN
ejpam-2010	260	5	in	in	ADP
ejpam-2010	260	6	i	i	PRON
ejpam-2010	260	7	.	.	PUNCT
ejpam-2010	261	1	then	then	ADV
ejpam-2010	261	2	there	there	PRON
ejpam-2010	261	3	exists	exist	VERB
ejpam-2010	261	4	a	a	DET
ejpam-2010	261	5	unique	unique	ADJ
ejpam-2010	261	6	left	leave	VERB
ejpam-2010	261	7	s	s	NOUN
ejpam-2010	261	8	-	-	PUNCT
ejpam-2010	261	9	module	module	NOUN
ejpam-2010	261	10	homomorphism	homomorphism	NOUN
ejpam-2010	261	11	gm	gm	PROPN
ejpam-2010	262	1	i	i	PRON
ejpam-2010	262	2	j	j	PROPN
ejpam-2010	262	3	:	:	PUNCT
ejpam-2010	262	4	s	s	PART
ejpam-2010	262	5	fi	fi	NOUN
ejpam-2010	262	6	⊗i	⊗i	PROPN
ejpam-2010	262	7	homr(x	homr(x	PROPN
ejpam-2010	262	8	i	i	PRON
ejpam-2010	262	9	,	,	PUNCT
ejpam-2010	262	10	m)→	m)→	VERB
ejpam-2010	262	11	s	s	VERB
ejpam-2010	263	1	f	f	PROPN
ejpam-2010	263	2	j	j	PROPN
ejpam-2010	264	1	⊗	⊗	PROPN
ejpam-2010	264	2	j	j	PROPN
ejpam-2010	264	3	homr(x	homr(x	PROPN
ejpam-2010	264	4	j	j	PROPN
ejpam-2010	264	5	,	,	PUNCT
ejpam-2010	264	6	m	m	PROPN
ejpam-2010	264	7	)	)	PUNCT
ejpam-2010	264	8	such	such	ADJ
ejpam-2010	264	9	that	that	SCONJ
ejpam-2010	264	10	gm	gm	PROPN
ejpam-2010	265	1	i	i	PRON
ejpam-2010	265	2	j	j	PROPN
ejpam-2010	265	3	:	:	PUNCT
ejpam-2010	265	4	s	s	PART
ejpam-2010	265	5	fi	fi	NOUN
ejpam-2010	265	6	⊗i	⊗i	PROPN
ejpam-2010	265	7	v	v	ADP
ejpam-2010	265	8	7→	7→	PROPN
ejpam-2010	265	9	s	s	PART
ejpam-2010	265	10	fi	fi	NOUN
ejpam-2010	265	11	⊗	⊗	PROPN
ejpam-2010	265	12	j	j	PROPN
ejpam-2010	265	13	ψ	ψ	X
ejpam-2010	265	14	ji	ji	PROPN
ejpam-2010	266	1	v.	v.	ADV
ejpam-2010	266	2	in	in	ADP
ejpam-2010	266	3	fact	fact	NOUN
ejpam-2010	266	4	,	,	PUNCT
ejpam-2010	266	5	for	for	ADP
ejpam-2010	266	6	i	i	PROPN
ejpam-2010	266	7	≤	≤	NUM
ejpam-2010	266	8	j	j	PROPN
ejpam-2010	266	9	≤	≤	PROPN
ejpam-2010	266	10	k	k	PROPN
ejpam-2010	266	11	in	in	ADP
ejpam-2010	266	12	i	i	PRON
ejpam-2010	266	13	,	,	PUNCT
ejpam-2010	266	14	gm	gm	PROPN
ejpam-2010	267	1	i	i	PRON
ejpam-2010	267	2	j	j	PROPN
ejpam-2010	268	1	◦	◦	NOUN
ejpam-2010	268	2	gm	gm	PROPN
ejpam-2010	268	3	jk	jk	PROPN
ejpam-2010	269	1	=	=	PRON
ejpam-2010	269	2	gm	gm	PROPN
ejpam-2010	269	3	ik	ik	PROPN
ejpam-2010	269	4	.	.	PUNCT
ejpam-2010	270	1	we	we	PRON
ejpam-2010	270	2	define	define	VERB
ejpam-2010	270	3	g(m	g(m	NOUN
ejpam-2010	270	4	)	)	PUNCT
ejpam-2010	271	1	=	=	PUNCT
ejpam-2010	271	2	lim−→i(s	lim−→i(s	PROPN
ejpam-2010	271	3	fi	fi	NOUN
ejpam-2010	271	4	⊗i	⊗i	PROPN
ejpam-2010	271	5	homr(x	homr(x	PROPN
ejpam-2010	271	6	i	i	PRON
ejpam-2010	271	7	,	,	PUNCT
ejpam-2010	271	8	m	m	PROPN
ejpam-2010	271	9	)	)	PUNCT
ejpam-2010	271	10	,	,	PUNCT
ejpam-2010	271	11	gm	gm	PROPN
ejpam-2010	272	1	i	i	PRON
ejpam-2010	272	2	j	j	PROPN
ejpam-2010	272	3	)	)	PUNCT
ejpam-2010	272	4	.	.	PUNCT
ejpam-2010	273	1	then	then	ADV
ejpam-2010	273	2	g(m	g(m	VERB
ejpam-2010	273	3	)	)	PUNCT
ejpam-2010	273	4	is	be	AUX
ejpam-2010	273	5	a	a	DET
ejpam-2010	273	6	left	left	ADJ
ejpam-2010	273	7	s	s	NOUN
ejpam-2010	273	8	-	-	NOUN
ejpam-2010	273	9	module	module	NOUN
ejpam-2010	273	10	.	.	PUNCT
ejpam-2010	274	1	for	for	ADP
ejpam-2010	274	2	each	each	DET
ejpam-2010	274	3	i	i	PRON
ejpam-2010	274	4	∈	∈	PROPN
ejpam-2010	274	5	i	i	PRON
ejpam-2010	274	6	let	let	VERB
ejpam-2010	274	7	gm	gm	PROPN
ejpam-2010	275	1	i	i	PRON
ejpam-2010	275	2	:	:	PUNCT
ejpam-2010	275	3	s	s	PART
ejpam-2010	276	1	fi	fi	NOUN
ejpam-2010	276	2	⊗i	⊗i	PROPN
ejpam-2010	276	3	homr(x	homr(x	PROPN
ejpam-2010	276	4	i	i	PROPN
ejpam-2010	276	5	,	,	PUNCT
ejpam-2010	276	6	m)→	m)→	VERB
ejpam-2010	276	7	mg	mg	PROPN
ejpam-2010	276	8	denote	denote	VERB
ejpam-2010	276	9	the	the	DET
ejpam-2010	276	10	limit	limit	NOUN
ejpam-2010	276	11	map	map	NOUN
ejpam-2010	276	12	;	;	PUNCT
ejpam-2010	276	13	so	so	CCONJ
ejpam-2010	276	14	for	for	ADP
ejpam-2010	276	15	each	each	DET
ejpam-2010	276	16	i	i	PROPN
ejpam-2010	276	17	≤	≤	PROPN
ejpam-2010	277	1	j	j	PROPN
ejpam-2010	277	2	,	,	PUNCT
ejpam-2010	277	3	we	we	PRON
ejpam-2010	277	4	have	have	VERB
ejpam-2010	277	5	gm	gm	PROPN
ejpam-2010	278	1	i	i	PRON
ejpam-2010	278	2	j	j	PROPN
ejpam-2010	279	1	◦	◦	NOUN
ejpam-2010	279	2	gm	gm	PROPN
ejpam-2010	279	3	j	j	PROPN
ejpam-2010	280	1	=	=	PUNCT
ejpam-2010	280	2	gm	gm	PROPN
ejpam-2010	281	1	i	i	INTJ
ejpam-2010	281	2	.	.	PUNCT
ejpam-2010	282	1	suppose	suppose	VERB
ejpam-2010	282	2	that	that	SCONJ
ejpam-2010	282	3	m	m	PROPN
ejpam-2010	282	4	and	and	CCONJ
ejpam-2010	282	5	m	m	VERB
ejpam-2010	282	6	′	′	NOUN
ejpam-2010	282	7	are	be	AUX
ejpam-2010	282	8	left	leave	VERB
ejpam-2010	282	9	r	r	NOUN
ejpam-2010	282	10	-	-	PUNCT
ejpam-2010	282	11	modules	module	NOUN
ejpam-2010	282	12	,	,	PUNCT
ejpam-2010	282	13	and	and	CCONJ
ejpam-2010	282	14	α	α	DET
ejpam-2010	282	15	∈	∈	NOUN
ejpam-2010	282	16	homr(m	homr(m	NOUN
ejpam-2010	282	17	,	,	PUNCT
ejpam-2010	282	18	m	m	VERB
ejpam-2010	282	19	′	′	NUM
ejpam-2010	282	20	)	)	PUNCT
ejpam-2010	282	21	.	.	PUNCT
ejpam-2010	283	1	for	for	ADP
ejpam-2010	283	2	i	i	PRON
ejpam-2010	283	3	∈	∈	PROPN
ejpam-2010	284	1	i	i	PRON
ejpam-2010	284	2	,	,	PUNCT
ejpam-2010	284	3	we	we	PRON
ejpam-2010	284	4	define	define	VERB
ejpam-2010	284	5	αi	αi	PRON
ejpam-2010	284	6	∗	∗	NOUN
ejpam-2010	284	7	:	:	PUNCT
ejpam-2010	285	1	homr(x	homr(x	X
ejpam-2010	285	2	i	i	PRON
ejpam-2010	285	3	,	,	PUNCT
ejpam-2010	285	4	m)→	m)→	VERB
ejpam-2010	286	1	homr(x	homr(x	NOUN
ejpam-2010	286	2	i	i	PRON
ejpam-2010	286	3	,	,	PUNCT
ejpam-2010	286	4	m	m	VERB
ejpam-2010	286	5	′	′	NUM
ejpam-2010	286	6	)	)	PUNCT
ejpam-2010	286	7	via	via	ADP
ejpam-2010	286	8	vαi	vαi	ADJ
ejpam-2010	286	9	∗	∗	NOUN
ejpam-2010	287	1	=	=	SYM
ejpam-2010	287	2	vα	vα	PROPN
ejpam-2010	287	3	,	,	PUNCT
ejpam-2010	287	4	where	where	SCONJ
ejpam-2010	287	5	v	v	X
ejpam-2010	287	6	∈	∈	PROPN
ejpam-2010	287	7	homr(x	homr(x	NOUN
ejpam-2010	287	8	i	i	PRON
ejpam-2010	287	9	,	,	PUNCT
ejpam-2010	287	10	m	m	PROPN
ejpam-2010	287	11	)	)	PUNCT
ejpam-2010	287	12	.	.	PUNCT
ejpam-2010	288	1	this	this	PRON
ejpam-2010	288	2	induces	induce	VERB
ejpam-2010	288	3	the	the	DET
ejpam-2010	288	4	map	map	NOUN
ejpam-2010	288	5	1⊗αi	1⊗αi	NUM
ejpam-2010	288	6	∗	∗	NOUN
ejpam-2010	288	7	:	:	PUNCT
ejpam-2010	288	8	s	s	PART
ejpam-2010	288	9	fi	fi	NOUN
ejpam-2010	288	10	⊗i	⊗i	PROPN
ejpam-2010	288	11	homr(x	homr(x	PROPN
ejpam-2010	288	12	i	i	PRON
ejpam-2010	288	13	,	,	PUNCT
ejpam-2010	288	14	m)→	m)→	VERB
ejpam-2010	288	15	s	s	PART
ejpam-2010	289	1	fi	fi	NOUN
ejpam-2010	289	2	⊗i	⊗i	PROPN
ejpam-2010	289	3	homr(x	homr(x	PROPN
ejpam-2010	290	1	i	i	PRON
ejpam-2010	290	2	,	,	PUNCT
ejpam-2010	290	3	m	m	VERB
ejpam-2010	290	4	′	′	NUM
ejpam-2010	290	5	)	)	PUNCT
ejpam-2010	290	6	.	.	PUNCT
ejpam-2010	291	1	thus	thus	ADV
ejpam-2010	291	2	,	,	PUNCT
ejpam-2010	291	3	we	we	PRON
ejpam-2010	291	4	get	get	VERB
ejpam-2010	291	5	a	a	DET
ejpam-2010	291	6	unique	unique	ADJ
ejpam-2010	291	7	s	s	NOUN
ejpam-2010	291	8	-	-	PUNCT
ejpam-2010	291	9	homomorphism	homomorphism	NOUN
ejpam-2010	291	10	g(α	g(α	NOUN
ejpam-2010	291	11	)	)	PUNCT
ejpam-2010	291	12	with	with	ADP
ejpam-2010	291	13	certain	certain	ADJ
ejpam-2010	291	14	properties	property	NOUN
ejpam-2010	291	15	as	as	SCONJ
ejpam-2010	291	16	required	require	VERB
ejpam-2010	291	17	.	.	PUNCT
ejpam-2010	292	1	dually	dually	PROPN
ejpam-2010	292	2	,	,	PUNCT
ejpam-2010	292	3	we	we	PRON
ejpam-2010	292	4	can	can	AUX
ejpam-2010	292	5	define	define	VERB
ejpam-2010	292	6	a	a	DET
ejpam-2010	292	7	functor	functor	PROPN
ejpam-2010	292	8	h	h	NOUN
ejpam-2010	292	9	:	:	PUNCT
ejpam-2010	292	10	s	s	X
ejpam-2010	292	11	-	-	PUNCT
ejpam-2010	292	12	mod→	mod→	NOUN
ejpam-2010	292	13	r	r	NOUN
ejpam-2010	292	14	-	-	PUNCT
ejpam-2010	292	15	mod	mod	NOUN
ejpam-2010	292	16	which	which	PRON
ejpam-2010	292	17	is	be	AUX
ejpam-2010	292	18	an	an	DET
ejpam-2010	292	19	inverse	inverse	NOUN
ejpam-2010	292	20	for	for	ADP
ejpam-2010	292	21	g.	g.	PROPN
ejpam-2010	292	22	so	so	ADV
ejpam-2010	292	23	r	r	PROPN
ejpam-2010	292	24	-	-	PUNCT
ejpam-2010	292	25	mod	mod	ADJ
ejpam-2010	292	26	and	and	CCONJ
ejpam-2010	292	27	s	s	PROPN
ejpam-2010	292	28	-	-	ADJ
ejpam-2010	292	29	mod	mod	NOUN
ejpam-2010	292	30	are	be	AUX
ejpam-2010	292	31	equivalent	equivalent	ADJ
ejpam-2010	292	32	.	.	PUNCT
ejpam-2010	293	1	thus	thus	ADV
ejpam-2010	293	2	,	,	PUNCT
ejpam-2010	293	3	we	we	PRON
ejpam-2010	293	4	obtain	obtain	VERB
ejpam-2010	293	5	an	an	DET
ejpam-2010	293	6	analogue	analogue	NOUN
ejpam-2010	293	7	of	of	ADP
ejpam-2010	293	8	theorem	theorem	ADJ
ejpam-2010	293	9	1	1	NUM
ejpam-2010	293	10	.	.	PUNCT
ejpam-2010	293	11	theorem	theorem	NOUN
ejpam-2010	293	12	2	2	NUM
ejpam-2010	293	13	.	.	PUNCT
ejpam-2010	294	1	[	[	X
ejpam-2010	294	2	1	1	NUM
ejpam-2010	294	3	,	,	PUNCT
ejpam-2010	294	4	theorem	theorem	VERB
ejpam-2010	294	5	4.2	4.2	NUM
ejpam-2010	294	6	]	]	PUNCT
ejpam-2010	294	7	let	let	VERB
ejpam-2010	294	8	r	r	NOUN
ejpam-2010	294	9	and	and	CCONJ
ejpam-2010	294	10	s	s	AUX
ejpam-2010	294	11	be	be	AUX
ejpam-2010	294	12	rings	ring	NOUN
ejpam-2010	294	13	with	with	ADP
ejpam-2010	294	14	slu	slu	NOUN
ejpam-2010	294	15	.	.	PUNCT
ejpam-2010	295	1	then	then	ADV
ejpam-2010	295	2	the	the	DET
ejpam-2010	295	3	following	follow	VERB
ejpam-2010	295	4	statements	statement	NOUN
ejpam-2010	295	5	are	be	AUX
ejpam-2010	295	6	equivalent	equivalent	ADJ
ejpam-2010	295	7	:	:	PUNCT
ejpam-2010	295	8	(	(	PUNCT
ejpam-2010	295	9	1	1	X
ejpam-2010	295	10	)	)	PUNCT
ejpam-2010	295	11	r	r	NOUN
ejpam-2010	295	12	and	and	CCONJ
ejpam-2010	295	13	s	s	NOUN
ejpam-2010	295	14	are	be	AUX
ejpam-2010	295	15	morita	morita	PROPN
ejpam-2010	295	16	equivalent	equivalent	NOUN
ejpam-2010	295	17	;	;	PUNCT
ejpam-2010	295	18	(	(	PUNCT
ejpam-2010	295	19	2	2	X
ejpam-2010	295	20	)	)	PUNCT
ejpam-2010	295	21	there	there	PRON
ejpam-2010	295	22	exists	exist	VERB
ejpam-2010	295	23	a	a	DET
ejpam-2010	295	24	progenerator	progenerator	NOUN
ejpam-2010	295	25	{	{	PUNCT
ejpam-2010	295	26	x	x	NOUN
ejpam-2010	295	27	i	i	NOUN
ejpam-2010	295	28	:	:	PUNCT
ejpam-2010	295	29	φi	φi	PROPN
ejpam-2010	295	30	j	j	PROPN
ejpam-2010	295	31	,	,	PUNCT
ejpam-2010	295	32	ψ	ψ	VERB
ejpam-2010	295	33	ji|i	ji|i	PROPN
ejpam-2010	295	34	∈	∈	PROPN
ejpam-2010	296	1	i	i	X
ejpam-2010	296	2	}	}	PUNCT
ejpam-2010	296	3	for	for	ADP
ejpam-2010	296	4	r	r	NOUN
ejpam-2010	296	5	such	such	ADJ
ejpam-2010	296	6	that	that	PRON
ejpam-2010	296	7	s	s	VERB
ejpam-2010	296	8	∼=	∼=	PROPN
ejpam-2010	296	9	limi	limi	NOUN
ejpam-2010	296	10	end(x	end(x	NOUN
ejpam-2010	296	11	i	i	NOUN
ejpam-2010	296	12	)	)	PUNCT
ejpam-2010	296	13	.	.	PUNCT
ejpam-2010	297	1	(	(	PUNCT
ejpam-2010	297	2	3	3	X
ejpam-2010	297	3	)	)	PUNCT
ejpam-2010	297	4	there	there	PRON
ejpam-2010	297	5	exists	exist	VERB
ejpam-2010	297	6	a	a	DET
ejpam-2010	297	7	locally	locally	ADV
ejpam-2010	297	8	projective	projective	ADJ
ejpam-2010	297	9	r	r	NOUN
ejpam-2010	297	10	-	-	PUNCT
ejpam-2010	297	11	module	module	NOUN
ejpam-2010	297	12	(	(	PUNCT
ejpam-2010	297	13	p	p	PROPN
ejpam-2010	297	14	,	,	PUNCT
ejpam-2010	297	15	φ	φ	PROPN
ejpam-2010	297	16	,	,	PUNCT
ejpam-2010	297	17	ψ	ψ	SYM
ejpam-2010	297	18	,	,	PUNCT
ejpam-2010	297	19	i	i	PROPN
ejpam-2010	297	20	)	)	PUNCT
ejpam-2010	297	21	,	,	PUNCT
ejpam-2010	297	22	with	with	ADP
ejpam-2010	297	23	p	p	PROPN
ejpam-2010	297	24	a	a	DET
ejpam-2010	297	25	generator	generator	NOUN
ejpam-2010	297	26	for	for	ADP
ejpam-2010	297	27	r	r	NOUN
ejpam-2010	297	28	-	-	PUNCT
ejpam-2010	297	29	mod	mod	ADJ
ejpam-2010	297	30	,	,	PUNCT
ejpam-2010	297	31	such	such	ADJ
ejpam-2010	297	32	that	that	PRON
ejpam-2010	297	33	s	s	VERB
ejpam-2010	297	34	∼=	∼=	PROPN
ejpam-2010	297	35	endlp(r)((p	endlp(r)((p	NOUN
ejpam-2010	297	36	,	,	PUNCT
ejpam-2010	297	37	φ	φ	PROPN
ejpam-2010	297	38	,	,	PUNCT
ejpam-2010	297	39	ψ	ψ	SYM
ejpam-2010	297	40	,	,	PUNCT
ejpam-2010	297	41	i	i	NOUN
ejpam-2010	297	42	)	)	PUNCT
ejpam-2010	297	43	)	)	PUNCT
ejpam-2010	297	44	.	.	PUNCT
ejpam-2010	298	1	in	in	ADP
ejpam-2010	298	2	the	the	DET
ejpam-2010	298	3	following	following	NOUN
ejpam-2010	298	4	we	we	PRON
ejpam-2010	298	5	describe	describe	VERB
ejpam-2010	298	6	morita	morita	NOUN
ejpam-2010	298	7	equivalence	equivalence	NOUN
ejpam-2010	298	8	in	in	ADP
ejpam-2010	298	9	terms	term	NOUN
ejpam-2010	298	10	of	of	ADP
ejpam-2010	298	11	mortia	mortia	PROPN
ejpam-2010	298	12	context	context	NOUN
ejpam-2010	298	13	.	.	PUNCT
ejpam-2010	299	1	let	let	VERB
ejpam-2010	299	2	r	r	NOUN
ejpam-2010	299	3	and	and	CCONJ
ejpam-2010	299	4	s	s	AUX
ejpam-2010	299	5	be	be	AUX
ejpam-2010	299	6	morita	morita	PROPN
ejpam-2010	299	7	equivalent	equivalent	PROPN
ejpam-2010	299	8	rings	ring	NOUN
ejpam-2010	299	9	with	with	ADP
ejpam-2010	299	10	local	local	ADJ
ejpam-2010	299	11	units	unit	NOUN
ejpam-2010	299	12	via	via	ADP
ejpam-2010	299	13	inverse	inverse	NOUN
ejpam-2010	299	14	equivalences	equivalence	VERB
ejpam-2010	299	15	g	g	NOUN
ejpam-2010	299	16	:	:	PUNCT
ejpam-2010	299	17	r	r	X
ejpam-2010	299	18	-	-	PUNCT
ejpam-2010	299	19	mod→	mod→	NOUN
ejpam-2010	299	20	s	s	NOUN
ejpam-2010	299	21	-	-	NOUN
ejpam-2010	299	22	mod	mod	NOUN
ejpam-2010	299	23	and	and	CCONJ
ejpam-2010	299	24	h	h	NOUN
ejpam-2010	299	25	:	:	PUNCT
ejpam-2010	299	26	s	s	X
ejpam-2010	299	27	-	-	PUNCT
ejpam-2010	299	28	mod→	mod→	NOUN
ejpam-2010	299	29	r	r	NOUN
ejpam-2010	299	30	-	-	PUNCT
ejpam-2010	299	31	mod	mod	NOUN
ejpam-2010	299	32	.	.	PUNCT
ejpam-2010	300	1	set	set	VERB
ejpam-2010	300	2	p	p	NOUN
ejpam-2010	300	3	=	=	PUNCT
ejpam-2010	300	4	h(ss	h(ss	PROPN
ejpam-2010	300	5	)	)	PUNCT
ejpam-2010	300	6	and	and	CCONJ
ejpam-2010	300	7	q	q	NOUN
ejpam-2010	300	8	=	=	SYM
ejpam-2010	300	9	g(rr	g(rr	PROPN
ejpam-2010	300	10	)	)	PUNCT
ejpam-2010	300	11	.	.	PUNCT
ejpam-2010	301	1	then	then	ADV
ejpam-2010	301	2	p	p	PROPN
ejpam-2010	301	3	and	and	CCONJ
ejpam-2010	301	4	q	q	NOUN
ejpam-2010	301	5	are	be	AUX
ejpam-2010	301	6	naturally	naturally	ADV
ejpam-2010	301	7	unitary	unitary	ADJ
ejpam-2010	301	8	bimodules	bimodule	NOUN
ejpam-2010	301	9	rps	rps	PROPN
ejpam-2010	301	10	and	and	CCONJ
ejpam-2010	301	11	sqr	sqr	PROPN
ejpam-2010	301	12	.	.	PUNCT
ejpam-2010	302	1	we	we	PRON
ejpam-2010	302	2	define	define	VERB
ejpam-2010	302	3	two	two	NUM
ejpam-2010	302	4	bilinear	bilinear	NOUN
ejpam-2010	302	5	products	product	NOUN
ejpam-2010	302	6	(	(	PUNCT
ejpam-2010	302	7	−,−	−,−	X
ejpam-2010	302	8	)	)	PUNCT
ejpam-2010	302	9	:	:	PUNCT
ejpam-2010	303	1	p	p	X
ejpam-2010	303	2	×q→	×q→	NOUN
ejpam-2010	303	3	r	r	NOUN
ejpam-2010	303	4	:	:	PUNCT
ejpam-2010	303	5	(	(	PUNCT
ejpam-2010	303	6	p	p	X
ejpam-2010	303	7	,	,	PUNCT
ejpam-2010	303	8	q	q	NOUN
ejpam-2010	303	9	)	)	PUNCT
ejpam-2010	303	10	=	=	PUNCT
ejpam-2010	303	11	pq	pq	NOUN
ejpam-2010	303	12	∈	∈	PROPN
ejpam-2010	303	13	r	r	NOUN
ejpam-2010	303	14	,	,	PUNCT
ejpam-2010	303	15	y.	y.	PROPN
ejpam-2010	303	16	wang	wang	PROPN
ejpam-2010	303	17	,	,	PUNCT
ejpam-2010	303	18	k.	k.	PROPN
ejpam-2010	303	19	shum	shum	PROPN
ejpam-2010	303	20	,	,	PUNCT
ejpam-2010	303	21	x.	x.	PROPN
ejpam-2010	303	22	ren	ren	PROPN
ejpam-2010	303	23	/	/	SYM
ejpam-2010	303	24	eur	eur	PROPN
ejpam-2010	303	25	.	.	PUNCT
ejpam-2010	304	1	j.	j.	PROPN
ejpam-2010	304	2	pure	pure	PROPN
ejpam-2010	304	3	appl	appl	PROPN
ejpam-2010	304	4	.	.	PROPN
ejpam-2010	304	5	math	math	PROPN
ejpam-2010	304	6	,	,	PUNCT
ejpam-2010	304	7	6	6	NUM
ejpam-2010	304	8	(	(	PUNCT
ejpam-2010	304	9	2013	2013	NUM
ejpam-2010	304	10	)	)	PUNCT
ejpam-2010	304	11	,	,	PUNCT
ejpam-2010	304	12	256	256	NUM
ejpam-2010	304	13	-	-	SYM
ejpam-2010	304	14	281	281	NUM
ejpam-2010	304	15	266	266	NUM
ejpam-2010	304	16	〈	〈	NOUN
ejpam-2010	304	17	−,−	−,−	NOUN
ejpam-2010	304	18	〉	〉	NOUN
ejpam-2010	304	19	:	:	PUNCT
ejpam-2010	304	20	q×	q×	PUNCT
ejpam-2010	304	21	p	p	X
ejpam-2010	304	22	→	→	SYM
ejpam-2010	304	23	s	s	PART
ejpam-2010	304	24	:	:	PUNCT
ejpam-2010	304	25	〈	〈	ADJ
ejpam-2010	304	26	q	q	PROPN
ejpam-2010	304	27	,	,	PUNCT
ejpam-2010	304	28	p〉=	p〉=	NOUN
ejpam-2010	304	29	(	(	PUNCT
ejpam-2010	304	30	−	−	PROPN
ejpam-2010	304	31	,	,	PUNCT
ejpam-2010	304	32	q)p	q)p	NOUN
ejpam-2010	304	33	∈	∈	PROPN
ejpam-2010	304	34	s.	s.	PROPN
ejpam-2010	304	35	put	put	VERB
ejpam-2010	304	36	(	(	PUNCT
ejpam-2010	304	37	p1⊗	p1⊗	PROPN
ejpam-2010	304	38	q1)(p2⊗	q1)(p2⊗	PROPN
ejpam-2010	304	39	q2	q2	NOUN
ejpam-2010	304	40	)	)	PUNCT
ejpam-2010	305	1	=	=	SYM
ejpam-2010	305	2	p1⊗	p1⊗	NUM
ejpam-2010	305	3	〈	〈	PROPN
ejpam-2010	305	4	q1	q1	PROPN
ejpam-2010	305	5	,	,	PUNCT
ejpam-2010	305	6	p2〉q2	p2〉q2	NOUN
ejpam-2010	305	7	and	and	CCONJ
ejpam-2010	305	8	(	(	PUNCT
ejpam-2010	305	9	q1⊗	q1⊗	PROPN
ejpam-2010	305	10	p1)(q2⊗	p1)(q2⊗	NOUN
ejpam-2010	305	11	p2	p2	NOUN
ejpam-2010	305	12	)	)	PUNCT
ejpam-2010	305	13	=	=	SYM
ejpam-2010	305	14	q1⊗	q1⊗	NOUN
ejpam-2010	305	15	(	(	PUNCT
ejpam-2010	305	16	p1	p1	NOUN
ejpam-2010	305	17	,	,	PUNCT
ejpam-2010	305	18	q2)p2	q2)p2	NOUN
ejpam-2010	305	19	.	.	PUNCT
ejpam-2010	306	1	then	then	ADV
ejpam-2010	306	2	,	,	PUNCT
ejpam-2010	306	3	p	p	NOUN
ejpam-2010	306	4	⊗s	⊗s	ADJ
ejpam-2010	306	5	q	q	NOUN
ejpam-2010	306	6	and	and	CCONJ
ejpam-2010	306	7	q	q	ADJ
ejpam-2010	306	8	⊗r	⊗r	PROPN
ejpam-2010	307	1	p	p	NOUN
ejpam-2010	307	2	become	become	VERB
ejpam-2010	307	3	rings	ring	NOUN
ejpam-2010	307	4	,	,	PUNCT
ejpam-2010	307	5	and	and	CCONJ
ejpam-2010	307	6	we	we	PRON
ejpam-2010	307	7	have	have	VERB
ejpam-2010	307	8	r	r	NOUN
ejpam-2010	307	9	∼=	∼=	PROPN
ejpam-2010	307	10	p	p	NOUN
ejpam-2010	307	11	⊗s	⊗s	ADJ
ejpam-2010	307	12	q	q	NOUN
ejpam-2010	307	13	and	and	CCONJ
ejpam-2010	307	14	s	s	VERB
ejpam-2010	307	15	∼=	∼=	PROPN
ejpam-2010	307	16	q	q	NOUN
ejpam-2010	308	1	⊗r	⊗r	NOUN
ejpam-2010	308	2	p.	p.	NOUN
ejpam-2010	309	1	so	so	CCONJ
ejpam-2010	309	2	(	(	PUNCT
ejpam-2010	309	3	r	r	NOUN
ejpam-2010	309	4	,	,	PUNCT
ejpam-2010	309	5	s	s	PART
ejpam-2010	309	6	,	,	PUNCT
ejpam-2010	309	7	r	r	NOUN
ejpam-2010	309	8	ps	ps	PROPN
ejpam-2010	309	9	,	,	PUNCT
ejpam-2010	309	10	s	s	PROPN
ejpam-2010	309	11	qr	qr	NOUN
ejpam-2010	309	12	,	,	PUNCT
ejpam-2010	309	13	〈	〈	PROPN
ejpam-2010	309	14	,	,	PUNCT
ejpam-2010	309	15	〉	〉	NOUN
ejpam-2010	309	16	,	,	PUNCT
ejpam-2010	309	17	[	[	X
ejpam-2010	309	18	,	,	PUNCT
ejpam-2010	309	19	]	]	X
ejpam-2010	309	20	)	)	PUNCT
ejpam-2010	309	21	forms	form	VERB
ejpam-2010	309	22	a	a	DET
ejpam-2010	309	23	mortia	mortia	NOUN
ejpam-2010	309	24	context	context	NOUN
ejpam-2010	309	25	with	with	ADP
ejpam-2010	309	26	surjective	surjective	ADJ
ejpam-2010	309	27	mappings	mapping	NOUN
ejpam-2010	309	28	.	.	PUNCT
ejpam-2010	310	1	conversely	conversely	ADV
ejpam-2010	310	2	,	,	PUNCT
ejpam-2010	310	3	let	let	VERB
ejpam-2010	310	4	r	r	NOUN
ejpam-2010	310	5	,	,	PUNCT
ejpam-2010	310	6	s	s	X
ejpam-2010	310	7	,	,	PUNCT
ejpam-2010	310	8	rps	rps	PROPN
ejpam-2010	310	9	,	,	PUNCT
ejpam-2010	310	10	sqr	sqr	PROPN
ejpam-2010	310	11	,	,	PUNCT
ejpam-2010	310	12	(	(	PUNCT
ejpam-2010	310	13	,	,	PUNCT
ejpam-2010	310	14	)	)	PUNCT
ejpam-2010	310	15	:	:	PUNCT
ejpam-2010	311	1	p	p	X
ejpam-2010	311	2	×q→	×q→	PROPN
ejpam-2010	311	3	r	r	NOUN
ejpam-2010	311	4	,	,	PUNCT
ejpam-2010	311	5	〈	〈	PROPN
ejpam-2010	311	6	,	,	PUNCT
ejpam-2010	311	7	〉	〉	NOUN
ejpam-2010	311	8	:	:	PUNCT
ejpam-2010	311	9	q×	q×	PUNCT
ejpam-2010	311	10	p	p	X
ejpam-2010	311	11	→	→	X
ejpam-2010	311	12	s	s	AUX
ejpam-2010	311	13	be	be	AUX
ejpam-2010	311	14	a	a	DET
ejpam-2010	311	15	morita	morita	NOUN
ejpam-2010	311	16	context	context	NOUN
ejpam-2010	311	17	where	where	SCONJ
ejpam-2010	311	18	r	r	NOUN
ejpam-2010	311	19	,	,	PUNCT
ejpam-2010	311	20	s	s	VERB
ejpam-2010	311	21	are	be	AUX
ejpam-2010	311	22	rings	ring	NOUN
ejpam-2010	311	23	with	with	ADP
ejpam-2010	311	24	local	local	ADJ
ejpam-2010	311	25	units	unit	NOUN
ejpam-2010	311	26	and	and	CCONJ
ejpam-2010	311	27	p	p	X
ejpam-2010	311	28	,	,	PUNCT
ejpam-2010	311	29	q	q	X
ejpam-2010	311	30	are	be	AUX
ejpam-2010	311	31	unitary	unitary	ADJ
ejpam-2010	311	32	bimodules	bimodule	NOUN
ejpam-2010	311	33	.	.	PUNCT
ejpam-2010	312	1	then	then	ADV
ejpam-2010	312	2	p	p	X
ejpam-2010	312	3	⊗s	⊗s	ADJ
ejpam-2010	312	4	−	−	NOUN
ejpam-2010	312	5	:	:	PUNCT
ejpam-2010	312	6	smod→	smod→	PROPN
ejpam-2010	312	7	rmod	rmod	PROPN
ejpam-2010	312	8	and	and	CCONJ
ejpam-2010	312	9	q⊗r	q⊗r	PROPN
ejpam-2010	312	10	−	−	NOUN
ejpam-2010	312	11	:	:	PUNCT
ejpam-2010	312	12	rmod→	rmod→	PROPN
ejpam-2010	312	13	smod	smod	PROPN
ejpam-2010	312	14	are	be	AUX
ejpam-2010	312	15	equivalence	equivalence	NOUN
ejpam-2010	312	16	inverse	inverse	NOUN
ejpam-2010	312	17	to	to	ADP
ejpam-2010	312	18	each	each	DET
ejpam-2010	312	19	other	other	ADJ
ejpam-2010	312	20	if	if	SCONJ
ejpam-2010	312	21	and	and	CCONJ
ejpam-2010	312	22	only	only	ADV
ejpam-2010	312	23	if	if	SCONJ
ejpam-2010	312	24	both	both	PRON
ejpam-2010	312	25	(	(	PUNCT
ejpam-2010	312	26	,	,	PUNCT
ejpam-2010	312	27	)	)	PUNCT
ejpam-2010	312	28	and	and	CCONJ
ejpam-2010	312	29	〈	〈	PROPN
ejpam-2010	312	30	,	,	PUNCT
ejpam-2010	312	31	〉	〉	NOUN
ejpam-2010	312	32	are	be	AUX
ejpam-2010	312	33	surjective	surjective	ADJ
ejpam-2010	312	34	.	.	PUNCT
ejpam-2010	313	1	thus	thus	ADV
ejpam-2010	313	2	,	,	PUNCT
ejpam-2010	313	3	we	we	PRON
ejpam-2010	313	4	have	have	AUX
ejpam-2010	313	5	:	:	PUNCT
ejpam-2010	313	6	theorem	theorem	VERB
ejpam-2010	313	7	3	3	NUM
ejpam-2010	313	8	.	.	PUNCT
ejpam-2010	314	1	[	[	X
ejpam-2010	314	2	3	3	X
ejpam-2010	314	3	]	]	PUNCT
ejpam-2010	314	4	let	let	VERB
ejpam-2010	314	5	r	r	NOUN
ejpam-2010	314	6	and	and	CCONJ
ejpam-2010	314	7	s	s	AUX
ejpam-2010	314	8	be	be	AUX
ejpam-2010	314	9	rings	ring	NOUN
ejpam-2010	314	10	with	with	ADP
ejpam-2010	314	11	local	local	ADJ
ejpam-2010	314	12	units	unit	NOUN
ejpam-2010	314	13	.	.	PUNCT
ejpam-2010	315	1	then	then	ADV
ejpam-2010	315	2	the	the	DET
ejpam-2010	315	3	following	follow	VERB
ejpam-2010	315	4	statements	statement	NOUN
ejpam-2010	315	5	are	be	AUX
ejpam-2010	315	6	equivalent	equivalent	ADJ
ejpam-2010	315	7	:	:	PUNCT
ejpam-2010	315	8	(	(	PUNCT
ejpam-2010	315	9	1	1	X
ejpam-2010	315	10	)	)	PUNCT
ejpam-2010	315	11	r	r	NOUN
ejpam-2010	315	12	and	and	CCONJ
ejpam-2010	315	13	s	s	NOUN
ejpam-2010	315	14	are	be	AUX
ejpam-2010	315	15	morita	morita	PROPN
ejpam-2010	315	16	equivalent	equivalent	NOUN
ejpam-2010	315	17	;	;	PUNCT
ejpam-2010	315	18	(	(	PUNCT
ejpam-2010	315	19	2	2	X
ejpam-2010	315	20	)	)	PUNCT
ejpam-2010	315	21	there	there	PRON
ejpam-2010	315	22	exists	exist	VERB
ejpam-2010	315	23	a	a	DET
ejpam-2010	315	24	morita	morita	PROPN
ejpam-2010	315	25	context	context	PROPN
ejpam-2010	315	26	(	(	PUNCT
ejpam-2010	315	27	r	r	NOUN
ejpam-2010	315	28	,	,	PUNCT
ejpam-2010	315	29	s	s	PROPN
ejpam-2010	315	30	,	,	PUNCT
ejpam-2010	315	31	p	p	X
ejpam-2010	315	32	,	,	PUNCT
ejpam-2010	315	33	q	q	ADJ
ejpam-2010	315	34	,	,	PUNCT
ejpam-2010	315	35	〈	〈	PROPN
ejpam-2010	315	36	,	,	PUNCT
ejpam-2010	315	37	〉	〉	NOUN
ejpam-2010	315	38	,	,	PUNCT
ejpam-2010	315	39	[	[	X
ejpam-2010	315	40	,	,	PUNCT
ejpam-2010	315	41	]	]	X
ejpam-2010	315	42	)	)	PUNCT
ejpam-2010	315	43	with	with	ADP
ejpam-2010	315	44	surjective	surjective	ADJ
ejpam-2010	315	45	mappings	mapping	NOUN
ejpam-2010	315	46	.	.	PUNCT
ejpam-2010	316	1	we	we	PRON
ejpam-2010	316	2	pause	pause	VERB
ejpam-2010	316	3	here	here	ADV
ejpam-2010	316	4	to	to	PART
ejpam-2010	316	5	remark	remark	VERB
ejpam-2010	316	6	that	that	SCONJ
ejpam-2010	316	7	morita	morita	PROPN
ejpam-2010	316	8	contexts	contexts	PROPN
ejpam-2010	316	9	with	with	ADP
ejpam-2010	316	10	surjective	surjective	ADJ
ejpam-2010	316	11	mappings	mapping	NOUN
ejpam-2010	316	12	are	be	AUX
ejpam-2010	316	13	shown	show	VERB
ejpam-2010	316	14	to	to	PART
ejpam-2010	316	15	yield	yield	VERB
ejpam-2010	316	16	morita	morita	PROPN
ejpam-2010	316	17	equivalence	equivalence	NOUN
ejpam-2010	316	18	,	,	PUNCT
ejpam-2010	316	19	and	and	CCONJ
ejpam-2010	316	20	vice	vice	ADV
ejpam-2010	316	21	versa	versa	ADV
ejpam-2010	316	22	,	,	PUNCT
ejpam-2010	316	23	for	for	ADP
ejpam-2010	316	24	central	central	ADJ
ejpam-2010	316	25	separable	separable	ADJ
ejpam-2010	316	26	algebras	algebra	NOUN
ejpam-2010	316	27	over	over	ADP
ejpam-2010	316	28	a	a	DET
ejpam-2010	316	29	commutative	commutative	ADJ
ejpam-2010	316	30	ring	ring	NOUN
ejpam-2010	316	31	with	with	ADP
ejpam-2010	316	32	identity	identity	NOUN
ejpam-2010	316	33	.	.	PUNCT
ejpam-2010	317	1	however	however	ADV
ejpam-2010	317	2	,	,	PUNCT
ejpam-2010	317	3	central	central	ADJ
ejpam-2010	317	4	separable	separable	NOUN
ejpam-2010	317	5	algebras	algebra	NOUN
ejpam-2010	317	6	need	need	AUX
ejpam-2010	317	7	not	not	PART
ejpam-2010	317	8	have	have	VERB
ejpam-2010	317	9	local	local	ADJ
ejpam-2010	317	10	units	unit	NOUN
ejpam-2010	317	11	and	and	CCONJ
ejpam-2010	317	12	the	the	DET
ejpam-2010	317	13	converse	converse	NOUN
ejpam-2010	317	14	implication	implication	NOUN
ejpam-2010	317	15	does	do	AUX
ejpam-2010	317	16	not	not	PART
ejpam-2010	317	17	hold	hold	VERB
ejpam-2010	317	18	either	either	ADV
ejpam-2010	317	19	.	.	PUNCT
ejpam-2010	318	1	more	more	ADJ
ejpam-2010	318	2	details	detail	NOUN
ejpam-2010	318	3	are	be	AUX
ejpam-2010	318	4	referred	refer	VERB
ejpam-2010	318	5	to	to	ADP
ejpam-2010	318	6	[	[	X
ejpam-2010	318	7	46	46	NUM
ejpam-2010	318	8	]	]	PUNCT
ejpam-2010	318	9	.	.	PUNCT
ejpam-2010	319	1	corollary	corollary	ADJ
ejpam-2010	319	2	1	1	NUM
ejpam-2010	319	3	.	.	PUNCT
ejpam-2010	320	1	[	[	X
ejpam-2010	320	2	3	3	NUM
ejpam-2010	320	3	,	,	PUNCT
ejpam-2010	320	4	corollary	corollary	ADJ
ejpam-2010	320	5	2.3	2.3	NUM
ejpam-2010	320	6	]	]	PUNCT
ejpam-2010	320	7	for	for	ADP
ejpam-2010	320	8	any	any	DET
ejpam-2010	320	9	rings	ring	NOUN
ejpam-2010	320	10	r	r	NOUN
ejpam-2010	320	11	,	,	PUNCT
ejpam-2010	320	12	s	s	VERB
ejpam-2010	320	13	with	with	ADP
ejpam-2010	320	14	local	local	ADJ
ejpam-2010	320	15	units	unit	NOUN
ejpam-2010	320	16	,	,	PUNCT
ejpam-2010	320	17	r	r	X
ejpam-2010	320	18	-	-	PUNCT
ejpam-2010	320	19	umod	umod	PROPN
ejpam-2010	320	20	and	and	CCONJ
ejpam-2010	320	21	sumod	sumod	NOUN
ejpam-2010	320	22	are	be	AUX
ejpam-2010	320	23	equivalent	equivalent	ADJ
ejpam-2010	320	24	if	if	SCONJ
ejpam-2010	321	1	and	and	CCONJ
ejpam-2010	321	2	only	only	ADV
ejpam-2010	321	3	if	if	SCONJ
ejpam-2010	321	4	umodr	umodr	ADJ
ejpam-2010	321	5	and	and	CCONJ
ejpam-2010	321	6	umods	umod	NOUN
ejpam-2010	321	7	are	be	AUX
ejpam-2010	321	8	equivalent	equivalent	ADJ
ejpam-2010	321	9	.	.	PUNCT
ejpam-2010	322	1	we	we	PRON
ejpam-2010	322	2	recall	recall	VERB
ejpam-2010	322	3	that	that	SCONJ
ejpam-2010	322	4	a	a	DET
ejpam-2010	322	5	unitary	unitary	ADJ
ejpam-2010	322	6	bimodule	bimodule	NOUN
ejpam-2010	322	7	rms	rm	NOUN
ejpam-2010	322	8	is	be	AUX
ejpam-2010	322	9	balanced	balanced	ADJ
ejpam-2010	322	10	if	if	SCONJ
ejpam-2010	322	11	the	the	DET
ejpam-2010	322	12	canonical	canonical	ADJ
ejpam-2010	322	13	homomorphisms	homomorphism	NOUN
ejpam-2010	322	14	s	s	PART
ejpam-2010	322	15	→	→	SYM
ejpam-2010	322	16	endrm	endrm	NOUN
ejpam-2010	322	17	and	and	CCONJ
ejpam-2010	322	18	r	r	NOUN
ejpam-2010	322	19	→	→	PUNCT
ejpam-2010	322	20	ends	end	VERB
ejpam-2010	322	21	m	m	NOUN
ejpam-2010	322	22	are	be	AUX
ejpam-2010	322	23	injective	injective	ADJ
ejpam-2010	322	24	and	and	CCONJ
ejpam-2010	322	25	,	,	PUNCT
ejpam-2010	322	26	identifying	identify	VERB
ejpam-2010	322	27	r	r	NOUN
ejpam-2010	322	28	and	and	CCONJ
ejpam-2010	322	29	s	s	NOUN
ejpam-2010	322	30	with	with	ADP
ejpam-2010	322	31	the	the	DET
ejpam-2010	322	32	corresponding	correspond	VERB
ejpam-2010	322	33	subrings	subring	NOUN
ejpam-2010	322	34	of	of	ADP
ejpam-2010	322	35	endomorphisms	endomorphism	NOUN
ejpam-2010	322	36	of	of	ADP
ejpam-2010	322	37	m	m	PRON
ejpam-2010	322	38	,	,	PUNCT
ejpam-2010	322	39	it	it	PRON
ejpam-2010	322	40	holds	hold	VERB
ejpam-2010	322	41	sends	send	VERB
ejpam-2010	322	42	m	m	PROPN
ejpam-2010	322	43	=	=	SYM
ejpam-2010	322	44	s	s	NOUN
ejpam-2010	322	45	and	and	CCONJ
ejpam-2010	322	46	(	(	PUNCT
ejpam-2010	322	47	ends	end	VERB
ejpam-2010	322	48	m)r=	m)r=	PROPN
ejpam-2010	322	49	r.	r.	PROPN
ejpam-2010	322	50	it	it	PRON
ejpam-2010	322	51	is	be	AUX
ejpam-2010	322	52	known	know	VERB
ejpam-2010	322	53	[	[	PUNCT
ejpam-2010	322	54	9	9	NUM
ejpam-2010	322	55	]	]	PUNCT
ejpam-2010	322	56	that	that	SCONJ
ejpam-2010	322	57	untial	untial	ADJ
ejpam-2010	322	58	rings	ring	NOUN
ejpam-2010	322	59	r	r	NOUN
ejpam-2010	322	60	and	and	CCONJ
ejpam-2010	322	61	s	s	NOUN
ejpam-2010	322	62	are	be	AUX
ejpam-2010	322	63	morita	morita	NOUN
ejpam-2010	322	64	equivalent	equivalent	ADJ
ejpam-2010	322	65	if	if	SCONJ
ejpam-2010	323	1	and	and	CCONJ
ejpam-2010	323	2	only	only	ADV
ejpam-2010	323	3	if	if	SCONJ
ejpam-2010	323	4	there	there	PRON
ejpam-2010	323	5	exists	exist	VERB
ejpam-2010	323	6	a	a	DET
ejpam-2010	323	7	balanced	balanced	ADJ
ejpam-2010	323	8	bimodule	bimodule	NOUN
ejpam-2010	323	9	rps	rps	PROPN
ejpam-2010	323	10	such	such	ADJ
ejpam-2010	323	11	that	that	SCONJ
ejpam-2010	323	12	(	(	PUNCT
ejpam-2010	323	13	1	1	X
ejpam-2010	323	14	)	)	PUNCT
ejpam-2010	323	15	ps	ps	NOUN
ejpam-2010	323	16	and	and	CCONJ
ejpam-2010	323	17	rp	rp	NOUN
ejpam-2010	323	18	are	be	AUX
ejpam-2010	323	19	progenerators	progenerator	NOUN
ejpam-2010	323	20	;	;	PUNCT
ejpam-2010	323	21	(	(	PUNCT
ejpam-2010	323	22	2	2	X
ejpam-2010	323	23	)	)	PUNCT
ejpam-2010	323	24	the	the	DET
ejpam-2010	323	25	functor	functor	PROPN
ejpam-2010	323	26	pair	pair	NOUN
ejpam-2010	323	27	(	(	PUNCT
ejpam-2010	323	28	⊗rp,⊗sq	⊗rp,⊗sq	NUM
ejpam-2010	323	29	)	)	PUNCT
ejpam-2010	323	30	defines	define	VERB
ejpam-2010	323	31	an	an	DET
ejpam-2010	323	32	equivalence	equivalence	NOUN
ejpam-2010	323	33	of	of	ADP
ejpam-2010	323	34	the	the	DET
ejpam-2010	323	35	categories	category	NOUN
ejpam-2010	323	36	r	r	NOUN
ejpam-2010	323	37	-	-	PUNCT
ejpam-2010	323	38	mod	mod	ADJ
ejpam-2010	323	39	and	and	CCONJ
ejpam-2010	323	40	s	s	NOUN
ejpam-2010	323	41	-	-	NOUN
ejpam-2010	323	42	mod	mod	ADJ
ejpam-2010	323	43	,	,	PUNCT
ejpam-2010	323	44	where	where	SCONJ
ejpam-2010	323	45	q	q	NOUN
ejpam-2010	323	46	=	=	SYM
ejpam-2010	323	47	homs(p	homs(p	PROPN
ejpam-2010	323	48	,	,	PUNCT
ejpam-2010	323	49	s	s	PROPN
ejpam-2010	323	50	)	)	PUNCT
ejpam-2010	323	51	.	.	PUNCT
ejpam-2010	324	1	such	such	DET
ejpam-2010	324	2	a	a	DET
ejpam-2010	324	3	result	result	NOUN
ejpam-2010	324	4	was	be	AUX
ejpam-2010	324	5	extended	extend	VERB
ejpam-2010	324	6	by	by	ADP
ejpam-2010	324	7	fuller	full	ADJ
ejpam-2010	324	8	[	[	X
ejpam-2010	324	9	9	9	NUM
ejpam-2010	324	10	]	]	PUNCT
ejpam-2010	324	11	.	.	PUNCT
ejpam-2010	325	1	fuller	full	ADJ
ejpam-2010	325	2	investigated	investigate	VERB
ejpam-2010	325	3	the	the	DET
ejpam-2010	325	4	categorical	categorical	ADJ
ejpam-2010	325	5	equivalence	equivalence	NOUN
ejpam-2010	325	6	between	between	ADP
ejpam-2010	325	7	r	r	NOUN
ejpam-2010	325	8	-	-	PUNCT
ejpam-2010	325	9	mod	mod	NOUN
ejpam-2010	325	10	and	and	CCONJ
ejpam-2010	325	11	r	r	NOUN
ejpam-2010	325	12	-	-	PUNCT
ejpam-2010	325	13	umod	umod	NOUN
ejpam-2010	325	14	.	.	PUNCT
ejpam-2010	326	1	he	he	PRON
ejpam-2010	326	2	showed	show	VERB
ejpam-2010	326	3	that	that	SCONJ
ejpam-2010	326	4	if	if	SCONJ
ejpam-2010	326	5	r	r	NOUN
ejpam-2010	326	6	-	-	PUNCT
ejpam-2010	326	7	mod	mod	NOUN
ejpam-2010	326	8	is	be	AUX
ejpam-2010	326	9	equivalent	equivalent	ADJ
ejpam-2010	326	10	to	to	ADP
ejpam-2010	326	11	s	s	NOUN
ejpam-2010	326	12	-	-	PUNCT
ejpam-2010	326	13	mod	mod	NOUN
ejpam-2010	326	14	then	then	ADV
ejpam-2010	326	15	there	there	PRON
ejpam-2010	326	16	exists	exist	VERB
ejpam-2010	326	17	a	a	DET
ejpam-2010	326	18	bimodule	bimodule	NOUN
ejpam-2010	326	19	rus	rus	NOUN
ejpam-2010	326	20	such	such	ADJ
ejpam-2010	326	21	that	that	SCONJ
ejpam-2010	326	22	(	(	PUNCT
ejpam-2010	326	23	1	1	X
ejpam-2010	326	24	)	)	PUNCT
ejpam-2010	326	25	us	we	PRON
ejpam-2010	326	26	is	be	AUX
ejpam-2010	326	27	finitely	finitely	ADV
ejpam-2010	326	28	generated	generate	VERB
ejpam-2010	326	29	and	and	CCONJ
ejpam-2010	326	30	quasi	quasi	ADJ
ejpam-2010	326	31	-	-	ADJ
ejpam-2010	326	32	projective	projective	ADJ
ejpam-2010	326	33	and	and	CCONJ
ejpam-2010	326	34	generates	generate	VERB
ejpam-2010	326	35	each	each	PRON
ejpam-2010	326	36	of	of	ADP
ejpam-2010	326	37	its	its	PRON
ejpam-2010	326	38	submodules	submodule	NOUN
ejpam-2010	326	39	;	;	PUNCT
ejpam-2010	326	40	(	(	PUNCT
ejpam-2010	326	41	2	2	X
ejpam-2010	326	42	)	)	PUNCT
ejpam-2010	326	43	ru	ru	NOUN
ejpam-2010	326	44	is	be	AUX
ejpam-2010	326	45	faithful	faithful	ADJ
ejpam-2010	326	46	and	and	CCONJ
ejpam-2010	326	47	flat	flat	ADJ
ejpam-2010	326	48	;	;	PUNCT
ejpam-2010	327	1	y.	y.	PROPN
ejpam-2010	327	2	wang	wang	PROPN
ejpam-2010	327	3	,	,	PUNCT
ejpam-2010	327	4	k.	k.	PROPN
ejpam-2010	327	5	shum	shum	PROPN
ejpam-2010	327	6	,	,	PUNCT
ejpam-2010	327	7	x.	x.	PROPN
ejpam-2010	327	8	ren	ren	PROPN
ejpam-2010	327	9	/	/	SYM
ejpam-2010	327	10	eur	eur	PROPN
ejpam-2010	327	11	.	.	PUNCT
ejpam-2010	328	1	j.	j.	PROPN
ejpam-2010	328	2	pure	pure	PROPN
ejpam-2010	328	3	appl	appl	PROPN
ejpam-2010	328	4	.	.	PROPN
ejpam-2010	328	5	math	math	PROPN
ejpam-2010	328	6	,	,	PUNCT
ejpam-2010	328	7	6	6	NUM
ejpam-2010	328	8	(	(	PUNCT
ejpam-2010	328	9	2013	2013	NUM
ejpam-2010	328	10	)	)	PUNCT
ejpam-2010	328	11	,	,	PUNCT
ejpam-2010	328	12	256	256	NUM
ejpam-2010	328	13	-	-	SYM
ejpam-2010	328	14	281	281	NUM
ejpam-2010	328	15	267	267	NUM
ejpam-2010	328	16	(	(	PUNCT
ejpam-2010	328	17	3	3	NUM
ejpam-2010	328	18	)	)	PUNCT
ejpam-2010	328	19	the	the	DET
ejpam-2010	328	20	functor	functor	PROPN
ejpam-2010	328	21	pair	pair	NOUN
ejpam-2010	328	22	(	(	PUNCT
ejpam-2010	328	23	⊗ru	⊗ru	NOUN
ejpam-2010	328	24	,	,	PUNCT
ejpam-2010	328	25	homs(u	homs(u	NOUN
ejpam-2010	328	26	,	,	PUNCT
ejpam-2010	328	27	−	−	PROPN
ejpam-2010	328	28	)	)	PUNCT
ejpam-2010	328	29	)	)	PUNCT
ejpam-2010	328	30	defines	define	VERB
ejpam-2010	328	31	an	an	DET
ejpam-2010	328	32	equivalence	equivalence	NOUN
ejpam-2010	328	33	between	between	ADP
ejpam-2010	328	34	r	r	NOUN
ejpam-2010	328	35	-	-	PUNCT
ejpam-2010	328	36	mod	mod	NOUN
ejpam-2010	328	37	and	and	CCONJ
ejpam-2010	328	38	sumod	sumod	NOUN
ejpam-2010	328	39	.	.	PUNCT
ejpam-2010	329	1	analogous	analogous	ADJ
ejpam-2010	329	2	to	to	ADP
ejpam-2010	329	3	such	such	DET
ejpam-2010	329	4	a	a	DET
ejpam-2010	329	5	result	result	NOUN
ejpam-2010	329	6	we	we	PRON
ejpam-2010	329	7	proceed	proceed	VERB
ejpam-2010	329	8	to	to	PART
ejpam-2010	329	9	study	study	VERB
ejpam-2010	329	10	morita	morita	PROPN
ejpam-2010	329	11	equivalence	equivalence	NOUN
ejpam-2010	329	12	in	in	ADP
ejpam-2010	329	13	terms	term	NOUN
ejpam-2010	329	14	of	of	ADP
ejpam-2010	329	15	locally	locally	ADV
ejpam-2010	329	16	projective	projective	ADJ
ejpam-2010	329	17	generators	generator	NOUN
ejpam-2010	329	18	instead	instead	ADV
ejpam-2010	329	19	of	of	ADP
ejpam-2010	329	20	progenerators	progenerator	NOUN
ejpam-2010	329	21	.	.	PUNCT
ejpam-2010	330	1	theorem	theorem	VERB
ejpam-2010	330	2	4	4	NUM
ejpam-2010	330	3	.	.	PUNCT
ejpam-2010	331	1	[	[	X
ejpam-2010	331	2	3	3	NUM
ejpam-2010	331	3	,	,	PUNCT
ejpam-2010	331	4	theorem	theorem	VERB
ejpam-2010	331	5	2.4	2.4	NUM
ejpam-2010	331	6	]	]	PUNCT
ejpam-2010	331	7	let	let	VERB
ejpam-2010	331	8	r	r	NOUN
ejpam-2010	331	9	,	,	PUNCT
ejpam-2010	331	10	s	s	AUX
ejpam-2010	331	11	be	be	AUX
ejpam-2010	331	12	rings	ring	NOUN
ejpam-2010	331	13	with	with	ADP
ejpam-2010	331	14	local	local	ADJ
ejpam-2010	331	15	units	unit	NOUN
ejpam-2010	331	16	,	,	PUNCT
ejpam-2010	331	17	and	and	CCONJ
ejpam-2010	331	18	let	let	VERB
ejpam-2010	331	19	g	g	NOUN
ejpam-2010	331	20	:	:	PUNCT
ejpam-2010	331	21	r−umod→	r−umod→	PROPN
ejpam-2010	331	22	s	s	PROPN
ejpam-2010	331	23	−umod	−umod	NOUN
ejpam-2010	331	24	,	,	PUNCT
ejpam-2010	331	25	h	h	NOUN
ejpam-2010	331	26	:	:	PUNCT
ejpam-2010	331	27	s	s	AUX
ejpam-2010	331	28	−umod→	−umod→	VERB
ejpam-2010	331	29	r−umod	r−umod	PART
ejpam-2010	331	30	be	be	AUX
ejpam-2010	331	31	additive	additive	ADJ
ejpam-2010	331	32	functors	functor	NOUN
ejpam-2010	331	33	.	.	PUNCT
ejpam-2010	332	1	then	then	ADV
ejpam-2010	332	2	g	g	PROPN
ejpam-2010	332	3	and	and	CCONJ
ejpam-2010	332	4	h	h	NOUN
ejpam-2010	332	5	are	be	AUX
ejpam-2010	332	6	equivalences	equivalence	NOUN
ejpam-2010	332	7	inverse	inverse	ADJ
ejpam-2010	332	8	to	to	ADP
ejpam-2010	332	9	each	each	DET
ejpam-2010	332	10	other	other	ADJ
ejpam-2010	332	11	if	if	SCONJ
ejpam-2010	333	1	and	and	CCONJ
ejpam-2010	333	2	only	only	ADV
ejpam-2010	333	3	if	if	SCONJ
ejpam-2010	333	4	there	there	PRON
ejpam-2010	333	5	exists	exist	VERB
ejpam-2010	333	6	a	a	DET
ejpam-2010	333	7	unitary	unitary	ADJ
ejpam-2010	333	8	bimodule	bimodule	NOUN
ejpam-2010	333	9	rps	rps	NOUN
ejpam-2010	333	10	such	such	ADJ
ejpam-2010	333	11	that	that	SCONJ
ejpam-2010	333	12	(	(	PUNCT
ejpam-2010	333	13	1	1	X
ejpam-2010	333	14	)	)	PUNCT
ejpam-2010	333	15	both	both	DET
ejpam-2010	333	16	rp	rp	NOUN
ejpam-2010	333	17	,	,	PUNCT
ejpam-2010	333	18	ps	ps	PROPN
ejpam-2010	333	19	are	be	AUX
ejpam-2010	333	20	locally	locally	ADV
ejpam-2010	333	21	projective	projective	ADJ
ejpam-2010	333	22	generators	generator	NOUN
ejpam-2010	333	23	;	;	PUNCT
ejpam-2010	333	24	(	(	PUNCT
ejpam-2010	333	25	2	2	X
ejpam-2010	333	26	)	)	PUNCT
ejpam-2010	333	27	rps	rps	NOUN
ejpam-2010	333	28	is	be	AUX
ejpam-2010	333	29	balanced	balanced	ADJ
ejpam-2010	333	30	;	;	PUNCT
ejpam-2010	333	31	(	(	PUNCT
ejpam-2010	333	32	3	3	X
ejpam-2010	333	33	)	)	PUNCT
ejpam-2010	333	34	g	g	NOUN
ejpam-2010	333	35	∼=	∼=	PROPN
ejpam-2010	333	36	shomr(p,−	shomr(p,−	NOUN
ejpam-2010	333	37	)	)	PUNCT
ejpam-2010	333	38	and	and	CCONJ
ejpam-2010	333	39	h	h	NOUN
ejpam-2010	333	40	∼=	∼=	ADV
ejpam-2010	333	41	p	p	NOUN
ejpam-2010	333	42	⊗s	⊗s	NOUN
ejpam-2010	334	1	−.	−.	ADV
ejpam-2010	334	2	moreover	moreover	ADV
ejpam-2010	334	3	,	,	PUNCT
ejpam-2010	334	4	if	if	SCONJ
ejpam-2010	334	5	p	p	NOUN
ejpam-2010	334	6	satisfies	satisfy	VERB
ejpam-2010	334	7	these	these	DET
ejpam-2010	334	8	conditions	condition	NOUN
ejpam-2010	334	9	then	then	ADV
ejpam-2010	334	10	,	,	PUNCT
ejpam-2010	334	11	putting	put	VERB
ejpam-2010	334	12	q	q	NOUN
ejpam-2010	334	13	=	=	SYM
ejpam-2010	334	14	shomr(p	shomr(p	PROPN
ejpam-2010	334	15	,	,	PUNCT
ejpam-2010	334	16	r	r	NOUN
ejpam-2010	334	17	)	)	PUNCT
ejpam-2010	334	18	,	,	PUNCT
ejpam-2010	334	19	sqr	sqr	PROPN
ejpam-2010	334	20	is	be	AUX
ejpam-2010	334	21	a	a	DET
ejpam-2010	334	22	balanced	balanced	ADJ
ejpam-2010	334	23	bimodule	bimodule	NOUN
ejpam-2010	334	24	,	,	PUNCT
ejpam-2010	334	25	both	both	CCONJ
ejpam-2010	334	26	sq	sq	NOUN
ejpam-2010	334	27	and	and	CCONJ
ejpam-2010	334	28	qr	qr	PROPN
ejpam-2010	334	29	are	be	AUX
ejpam-2010	334	30	locally	locally	ADV
ejpam-2010	334	31	projective	projective	ADJ
ejpam-2010	334	32	generators	generator	NOUN
ejpam-2010	334	33	,	,	PUNCT
ejpam-2010	334	34	h	h	NOUN
ejpam-2010	334	35	∼=	∼=	NOUN
ejpam-2010	334	36	rhoms(q,−	rhoms(q,−	NOUN
ejpam-2010	334	37	)	)	PUNCT
ejpam-2010	334	38	and	and	CCONJ
ejpam-2010	334	39	g	g	PROPN
ejpam-2010	334	40	∼=q⊗r−.	∼=q⊗r−.	PRON
ejpam-2010	334	41	building	build	VERB
ejpam-2010	334	42	on	on	ADP
ejpam-2010	334	43	this	this	DET
ejpam-2010	334	44	idea	idea	NOUN
ejpam-2010	334	45	garcia	garcia	PROPN
ejpam-2010	335	1	[	[	X
ejpam-2010	335	2	12	12	NUM
ejpam-2010	335	3	]	]	X
ejpam-2010	335	4	reintroduced	reintroduce	VERB
ejpam-2010	335	5	matrices	matrix	NOUN
ejpam-2010	335	6	by	by	ADP
ejpam-2010	335	7	showing	show	VERB
ejpam-2010	335	8	that	that	SCONJ
ejpam-2010	335	9	if	if	SCONJ
ejpam-2010	335	10	n	n	PRON
ejpam-2010	335	11	is	be	AUX
ejpam-2010	335	12	the	the	DET
ejpam-2010	335	13	set	set	NOUN
ejpam-2010	335	14	of	of	ADP
ejpam-2010	335	15	natural	natural	ADJ
ejpam-2010	335	16	numbers	number	NOUN
ejpam-2010	335	17	and	and	CCONJ
ejpam-2010	335	18	t	t	NOUN
ejpam-2010	335	19	is	be	AUX
ejpam-2010	335	20	the	the	DET
ejpam-2010	335	21	matrix	matrix	NOUN
ejpam-2010	335	22	ring	ring	NOUN
ejpam-2010	335	23	m0	m0	NOUN
ejpam-2010	335	24	n(r	n(r	NOUN
ejpam-2010	335	25	)	)	PUNCT
ejpam-2010	335	26	,	,	PUNCT
ejpam-2010	335	27	then	then	ADV
ejpam-2010	335	28	,	,	PUNCT
ejpam-2010	335	29	r	r	X
ejpam-2010	335	30	-	-	PUNCT
ejpam-2010	335	31	mod	mod	NOUN
ejpam-2010	335	32	is	be	AUX
ejpam-2010	335	33	equivalent	equivalent	ADJ
ejpam-2010	335	34	to	to	ADP
ejpam-2010	335	35	t	t	PROPN
ejpam-2010	335	36	-umod	-umod	PROPN
ejpam-2010	335	37	.	.	PUNCT
ejpam-2010	336	1	xu	xu	PROPN
ejpam-2010	336	2	,	,	PUNCT
ejpam-2010	336	3	shum	shum	NOUN
ejpam-2010	336	4	and	and	CCONJ
ejpam-2010	336	5	turner	turner	PROPN
ejpam-2010	336	6	-	-	PUNCT
ejpam-2010	336	7	smith	smith	PROPN
ejpam-2010	336	8	further	further	PROPN
ejpam-2010	336	9	generalised	generalise	VERB
ejpam-2010	336	10	garcia	garcia	PROPN
ejpam-2010	336	11	’s	’s	PART
ejpam-2010	336	12	result	result	NOUN
ejpam-2010	336	13	by	by	ADP
ejpam-2010	336	14	replacing	replace	VERB
ejpam-2010	336	15	the	the	DET
ejpam-2010	336	16	index	index	NOUN
ejpam-2010	336	17	set	set	VERB
ejpam-2010	336	18	n	n	NOUN
ejpam-2010	336	19	with	with	ADP
ejpam-2010	336	20	an	an	DET
ejpam-2010	336	21	arbitrary	arbitrary	ADJ
ejpam-2010	336	22	set	set	NOUN
ejpam-2010	336	23	γ	γ	NOUN
ejpam-2010	336	24	as	as	SCONJ
ejpam-2010	336	25	follows	follow	VERB
ejpam-2010	336	26	:	:	PUNCT
ejpam-2010	336	27	theorem	theorem	NOUN
ejpam-2010	336	28	5	5	NUM
ejpam-2010	336	29	.	.	PUNCT
ejpam-2010	337	1	[	[	X
ejpam-2010	337	2	49	49	NUM
ejpam-2010	337	3	,	,	PUNCT
ejpam-2010	337	4	theorem	theorem	VERB
ejpam-2010	337	5	3.2	3.2	NUM
ejpam-2010	337	6	]	]	PUNCT
ejpam-2010	337	7	let	let	VERB
ejpam-2010	337	8	r	r	PRON
ejpam-2010	337	9	be	be	AUX
ejpam-2010	337	10	a	a	DET
ejpam-2010	337	11	unital	unital	ADJ
ejpam-2010	337	12	ring	ring	NOUN
ejpam-2010	337	13	.	.	PUNCT
ejpam-2010	338	1	if	if	SCONJ
ejpam-2010	338	2	l	l	PROPN
ejpam-2010	338	3	∈	∈	PROPN
ejpam-2010	338	4	mγ(r	mγ(r	X
ejpam-2010	338	5	)	)	PUNCT
ejpam-2010	338	6	is	be	AUX
ejpam-2010	338	7	idempotent	idempotent	ADJ
ejpam-2010	338	8	and	and	CCONJ
ejpam-2010	338	9	such	such	ADJ
ejpam-2010	338	10	that	that	DET
ejpam-2010	338	11	m0	m0	NOUN
ejpam-2010	338	12	γ(r)/m	γ(r)/m	PROPN
ejpam-2010	338	13	0	0	NUM
ejpam-2010	338	14	γ(r	γ(r	PROPN
ejpam-2010	338	15	)	)	PUNCT
ejpam-2010	339	1	=	=	SYM
ejpam-2010	339	2	m0	m0	PROPN
ejpam-2010	339	3	γ(r	γ(r	PROPN
ejpam-2010	339	4	)	)	PUNCT
ejpam-2010	339	5	,	,	PUNCT
ejpam-2010	339	6	then	then	ADV
ejpam-2010	339	7	lm0	lm0	PROPN
ejpam-2010	339	8	γ(r)l	γ(r)l	PUNCT
ejpam-2010	339	9	and	and	CCONJ
ejpam-2010	339	10	m0	m0	PROPN
ejpam-2010	339	11	γ(r	γ(r	PROPN
ejpam-2010	339	12	)	)	PUNCT
ejpam-2010	339	13	are	be	AUX
ejpam-2010	339	14	morita	morita	NOUN
ejpam-2010	339	15	-	-	PUNCT
ejpam-2010	339	16	like	like	ADJ
ejpam-2010	339	17	equivalent	equivalent	NOUN
ejpam-2010	339	18	.	.	PUNCT
ejpam-2010	340	1	moreover	moreover	ADV
ejpam-2010	340	2	,	,	PUNCT
ejpam-2010	340	3	the	the	DET
ejpam-2010	340	4	functor	functor	PROPN
ejpam-2010	340	5	pair	pair	NOUN
ejpam-2010	340	6	(	(	PUNCT
ejpam-2010	340	7	⊗s	⊗s	ADJ
ejpam-2010	340	8	lm0	lm0	NOUN
ejpam-2010	340	9	γ(r),⊗t	γ(r),⊗t	PUNCT
ejpam-2010	340	10	m0	m0	PROPN
ejpam-2010	340	11	γ(r)l	γ(r)l	PROPN
ejpam-2010	340	12	)	)	PUNCT
ejpam-2010	340	13	defines	define	VERB
ejpam-2010	340	14	an	an	DET
ejpam-2010	340	15	equivalence	equivalence	NOUN
ejpam-2010	340	16	between	between	ADP
ejpam-2010	340	17	s	s	NOUN
ejpam-2010	340	18	-	-	PUNCT
ejpam-2010	340	19	mod	mod	ADJ
ejpam-2010	340	20	and	and	CCONJ
ejpam-2010	340	21	t	t	PROPN
ejpam-2010	340	22	-	-	PUNCT
ejpam-2010	340	23	mod	mod	PROPN
ejpam-2010	340	24	,	,	PUNCT
ejpam-2010	340	25	where	where	SCONJ
ejpam-2010	340	26	s	s	VERB
ejpam-2010	340	27	=	=	VERB
ejpam-2010	340	28	lm0	lm0	NOUN
ejpam-2010	340	29	γ(r)l	γ(r)l	PUNCT
ejpam-2010	340	30	and	and	CCONJ
ejpam-2010	340	31	t	t	NOUN
ejpam-2010	340	32	=	=	SYM
ejpam-2010	340	33	m0	m0	PROPN
ejpam-2010	340	34	γ(r	γ(r	PROPN
ejpam-2010	340	35	)	)	PUNCT
ejpam-2010	340	36	.	.	PUNCT
ejpam-2010	341	1	the	the	DET
ejpam-2010	341	2	following	follow	VERB
ejpam-2010	341	3	corollary	corollary	NOUN
ejpam-2010	341	4	not	not	PART
ejpam-2010	341	5	only	only	ADV
ejpam-2010	341	6	includes	include	VERB
ejpam-2010	341	7	the	the	DET
ejpam-2010	341	8	result	result	NOUN
ejpam-2010	341	9	of	of	ADP
ejpam-2010	341	10	xu	xu	PROPN
ejpam-2010	342	1	[	[	X
ejpam-2010	342	2	48	48	NUM
ejpam-2010	342	3	]	]	PUNCT
ejpam-2010	342	4	but	but	CCONJ
ejpam-2010	342	5	also	also	ADV
ejpam-2010	342	6	that	that	PRON
ejpam-2010	342	7	of	of	ADP
ejpam-2010	342	8	garcia	garcia	PROPN
ejpam-2010	342	9	[	[	X
ejpam-2010	342	10	12	12	NUM
ejpam-2010	342	11	]	]	X
ejpam-2010	342	12	,	,	PUNCT
ejpam-2010	342	13	who	who	PRON
ejpam-2010	342	14	considers	consider	VERB
ejpam-2010	342	15	γ	γ	X
ejpam-2010	342	16	=	=	SYM
ejpam-2010	342	17	n.	n.	NOUN
ejpam-2010	342	18	corollary	corollary	NOUN
ejpam-2010	342	19	2	2	NUM
ejpam-2010	342	20	.	.	PUNCT
ejpam-2010	343	1	[	[	X
ejpam-2010	343	2	49	49	NUM
ejpam-2010	343	3	,	,	PUNCT
ejpam-2010	343	4	corollary	corollary	ADJ
ejpam-2010	343	5	3.3	3.3	NUM
ejpam-2010	343	6	]	]	PUNCT
ejpam-2010	343	7	let	let	VERB
ejpam-2010	343	8	r	r	PRON
ejpam-2010	343	9	be	be	AUX
ejpam-2010	343	10	a	a	DET
ejpam-2010	343	11	unital	unital	ADJ
ejpam-2010	343	12	ring	ring	NOUN
ejpam-2010	343	13	.	.	PUNCT
ejpam-2010	344	1	then	then	ADV
ejpam-2010	344	2	r	r	NOUN
ejpam-2010	344	3	and	and	CCONJ
ejpam-2010	344	4	m0	m0	PROPN
ejpam-2010	344	5	γ(r	γ(r	PROPN
ejpam-2010	344	6	)	)	PUNCT
ejpam-2010	344	7	are	be	AUX
ejpam-2010	344	8	morita	morita	NOUN
ejpam-2010	344	9	-	-	PUNCT
ejpam-2010	344	10	like	like	ADJ
ejpam-2010	344	11	equivalent	equivalent	NOUN
ejpam-2010	344	12	.	.	PUNCT
ejpam-2010	345	1	if	if	SCONJ
ejpam-2010	345	2	|γ|=	|γ|=	ADJ
ejpam-2010	345	3	n	n	CCONJ
ejpam-2010	345	4	,	,	PUNCT
ejpam-2010	345	5	then	then	ADV
ejpam-2010	345	6	we	we	PRON
ejpam-2010	345	7	have	have	VERB
ejpam-2010	345	8	mn(r	mn(r	NOUN
ejpam-2010	345	9	)	)	PUNCT
ejpam-2010	346	1	=	=	SYM
ejpam-2010	346	2	m0	m0	PROPN
ejpam-2010	346	3	n	n	CCONJ
ejpam-2010	346	4	(	(	PUNCT
ejpam-2010	346	5	r	r	NOUN
ejpam-2010	346	6	)	)	PUNCT
ejpam-2010	346	7	.	.	PUNCT
ejpam-2010	347	1	thus	thus	ADV
ejpam-2010	347	2	,	,	PUNCT
ejpam-2010	347	3	we	we	PRON
ejpam-2010	347	4	have	have	AUX
ejpam-2010	347	5	:	:	PUNCT
ejpam-2010	347	6	corollary	corollary	ADJ
ejpam-2010	347	7	3	3	X
ejpam-2010	347	8	.	.	PUNCT
ejpam-2010	348	1	[	[	X
ejpam-2010	348	2	49	49	NUM
ejpam-2010	348	3	,	,	PUNCT
ejpam-2010	348	4	corollary	corollary	ADJ
ejpam-2010	348	5	3.3	3.3	NUM
ejpam-2010	348	6	]	]	PUNCT
ejpam-2010	348	7	let	let	VERB
ejpam-2010	348	8	r	r	PRON
ejpam-2010	348	9	be	be	AUX
ejpam-2010	348	10	a	a	DET
ejpam-2010	348	11	unital	unital	ADJ
ejpam-2010	348	12	ring	ring	NOUN
ejpam-2010	348	13	,	,	PUNCT
ejpam-2010	348	14	and	and	CCONJ
ejpam-2010	348	15	let	let	VERB
ejpam-2010	348	16	l	l	NOUN
ejpam-2010	348	17	be	be	AUX
ejpam-2010	348	18	an	an	DET
ejpam-2010	348	19	idempotent	idempotent	NOUN
ejpam-2010	348	20	in	in	ADP
ejpam-2010	348	21	mn(r	mn(r	NOUN
ejpam-2010	348	22	)	)	PUNCT
ejpam-2010	348	23	such	such	ADJ
ejpam-2010	348	24	that	that	DET
ejpam-2010	348	25	mn(r)lmn(r	mn(r)lmn(r	NOUN
ejpam-2010	348	26	)	)	PUNCT
ejpam-2010	348	27	=	=	SYM
ejpam-2010	348	28	mn(r	mn(r	NOUN
ejpam-2010	348	29	)	)	PUNCT
ejpam-2010	348	30	.	.	PUNCT
ejpam-2010	349	1	then	then	ADV
ejpam-2010	349	2	r	r	NOUN
ejpam-2010	349	3	and	and	CCONJ
ejpam-2010	349	4	lmn(r)l	lmn(r)l	VERB
ejpam-2010	349	5	are	be	AUX
ejpam-2010	349	6	morita	morita	PROPN
ejpam-2010	349	7	equivalent	equivalent	NOUN
ejpam-2010	349	8	.	.	PUNCT
ejpam-2010	350	1	we	we	PRON
ejpam-2010	350	2	now	now	ADV
ejpam-2010	350	3	list	list	VERB
ejpam-2010	350	4	from	from	ADP
ejpam-2010	350	5	[	[	X
ejpam-2010	350	6	3	3	NUM
ejpam-2010	350	7	]	]	PUNCT
ejpam-2010	350	8	two	two	NUM
ejpam-2010	350	9	properties	property	NOUN
ejpam-2010	350	10	of	of	ADP
ejpam-2010	350	11	morita	morita	PROPN
ejpam-2010	350	12	equivalent	equivalent	PROPN
ejpam-2010	350	13	rings	ring	NOUN
ejpam-2010	350	14	with	with	ADP
ejpam-2010	350	15	local	local	ADJ
ejpam-2010	350	16	units	unit	NOUN
ejpam-2010	350	17	.	.	PUNCT
ejpam-2010	351	1	proposition	proposition	NOUN
ejpam-2010	351	2	2	2	NUM
ejpam-2010	351	3	.	.	PUNCT
ejpam-2010	352	1	let	let	VERB
ejpam-2010	352	2	r	r	NOUN
ejpam-2010	352	3	and	and	CCONJ
ejpam-2010	352	4	s	s	AUX
ejpam-2010	352	5	be	be	AUX
ejpam-2010	352	6	morita	morita	PROPN
ejpam-2010	352	7	equivalent	equivalent	PROPN
ejpam-2010	352	8	rings	ring	NOUN
ejpam-2010	352	9	with	with	ADP
ejpam-2010	352	10	local	local	ADJ
ejpam-2010	352	11	units	unit	NOUN
ejpam-2010	352	12	.	.	PUNCT
ejpam-2010	353	1	then	then	ADV
ejpam-2010	353	2	(	(	PUNCT
ejpam-2010	353	3	1	1	X
ejpam-2010	353	4	)	)	PUNCT
ejpam-2010	353	5	if	if	SCONJ
ejpam-2010	353	6	r	r	NOUN
ejpam-2010	353	7	is	be	AUX
ejpam-2010	353	8	regular	regular	ADJ
ejpam-2010	353	9	then	then	ADV
ejpam-2010	353	10	s	s	VERB
ejpam-2010	353	11	is	be	AUX
ejpam-2010	353	12	also	also	ADV
ejpam-2010	353	13	regular	regular	ADJ
ejpam-2010	353	14	;	;	PUNCT
ejpam-2010	353	15	(	(	PUNCT
ejpam-2010	353	16	2	2	X
ejpam-2010	353	17	)	)	PUNCT
ejpam-2010	353	18	r	r	NOUN
ejpam-2010	353	19	is	be	AUX
ejpam-2010	353	20	primitive	primitive	ADJ
ejpam-2010	353	21	or	or	CCONJ
ejpam-2010	353	22	a	a	DET
ejpam-2010	353	23	ring	ring	NOUN
ejpam-2010	353	24	with	with	ADP
ejpam-2010	353	25	zero	zero	NUM
ejpam-2010	353	26	jacobson	jacobson	PROPN
ejpam-2010	353	27	radical	radical	PROPN
ejpam-2010	353	28	if	if	SCONJ
ejpam-2010	353	29	and	and	CCONJ
ejpam-2010	353	30	only	only	ADV
ejpam-2010	353	31	if	if	SCONJ
ejpam-2010	353	32	s	s	NOUN
ejpam-2010	353	33	is	be	AUX
ejpam-2010	353	34	such	such	ADJ
ejpam-2010	353	35	.	.	PUNCT
ejpam-2010	354	1	y.	y.	PROPN
ejpam-2010	354	2	wang	wang	PROPN
ejpam-2010	354	3	,	,	PUNCT
ejpam-2010	354	4	k.	k.	PROPN
ejpam-2010	354	5	shum	shum	PROPN
ejpam-2010	354	6	,	,	PUNCT
ejpam-2010	354	7	x.	x.	PROPN
ejpam-2010	354	8	ren	ren	PROPN
ejpam-2010	354	9	/	/	SYM
ejpam-2010	354	10	eur	eur	PROPN
ejpam-2010	354	11	.	.	PUNCT
ejpam-2010	355	1	j.	j.	PROPN
ejpam-2010	355	2	pure	pure	PROPN
ejpam-2010	355	3	appl	appl	PROPN
ejpam-2010	355	4	.	.	PROPN
ejpam-2010	355	5	math	math	PROPN
ejpam-2010	355	6	,	,	PUNCT
ejpam-2010	355	7	6	6	NUM
ejpam-2010	355	8	(	(	PUNCT
ejpam-2010	355	9	2013	2013	NUM
ejpam-2010	355	10	)	)	PUNCT
ejpam-2010	355	11	,	,	PUNCT
ejpam-2010	355	12	256	256	NUM
ejpam-2010	355	13	-	-	SYM
ejpam-2010	355	14	281	281	NUM
ejpam-2010	355	15	268	268	NUM
ejpam-2010	355	16	it	it	PRON
ejpam-2010	355	17	is	be	AUX
ejpam-2010	355	18	a	a	DET
ejpam-2010	355	19	good	good	ADJ
ejpam-2010	355	20	place	place	NOUN
ejpam-2010	355	21	to	to	PART
ejpam-2010	355	22	cite	cite	VERB
ejpam-2010	355	23	from	from	ADP
ejpam-2010	355	24	[	[	X
ejpam-2010	355	25	3	3	X
ejpam-2010	355	26	]	]	X
ejpam-2010	355	27	very	very	ADV
ejpam-2010	355	28	interesting	interesting	ADJ
ejpam-2010	355	29	results	result	NOUN
ejpam-2010	355	30	characterising	characterise	VERB
ejpam-2010	355	31	rings	ring	NOUN
ejpam-2010	355	32	which	which	PRON
ejpam-2010	355	33	are	be	AUX
ejpam-2010	355	34	morita	morita	PROPN
ejpam-2010	355	35	equivalent	equivalent	ADJ
ejpam-2010	355	36	to	to	ADP
ejpam-2010	355	37	rings	ring	NOUN
ejpam-2010	355	38	of	of	ADP
ejpam-2010	355	39	certain	certain	ADJ
ejpam-2010	355	40	kinds	kind	NOUN
ejpam-2010	355	41	.	.	PUNCT
ejpam-2010	356	1	we	we	PRON
ejpam-2010	356	2	say	say	VERB
ejpam-2010	356	3	that	that	SCONJ
ejpam-2010	356	4	a	a	DET
ejpam-2010	356	5	unital	unital	ADJ
ejpam-2010	356	6	ring	ring	NOUN
ejpam-2010	356	7	r	r	NOUN
ejpam-2010	356	8	is	be	AUX
ejpam-2010	356	9	primary	primary	ADJ
ejpam-2010	356	10	if	if	SCONJ
ejpam-2010	356	11	the	the	DET
ejpam-2010	356	12	factor	factor	NOUN
ejpam-2010	356	13	r	r	NOUN
ejpam-2010	356	14	/	/	SYM
ejpam-2010	356	15	j(r	j(r	PROPN
ejpam-2010	356	16	)	)	PUNCT
ejpam-2010	356	17	is	be	AUX
ejpam-2010	356	18	a	a	DET
ejpam-2010	356	19	simple	simple	ADJ
ejpam-2010	356	20	artinian	artinian	ADJ
ejpam-2010	356	21	ring	ring	NOUN
ejpam-2010	356	22	such	such	ADJ
ejpam-2010	356	23	that	that	SCONJ
ejpam-2010	356	24	the	the	DET
ejpam-2010	356	25	idempotents	idempotent	NOUN
ejpam-2010	356	26	can	can	AUX
ejpam-2010	356	27	be	be	AUX
ejpam-2010	356	28	lifted	lift	VERB
ejpam-2010	356	29	,	,	PUNCT
ejpam-2010	356	30	where	where	SCONJ
ejpam-2010	356	31	j(r	j(r	PROPN
ejpam-2010	356	32	)	)	PUNCT
ejpam-2010	356	33	is	be	AUX
ejpam-2010	356	34	its	its	PRON
ejpam-2010	356	35	jacobson	jacobson	PROPN
ejpam-2010	356	36	radical	radical	NOUN
ejpam-2010	356	37	.	.	PUNCT
ejpam-2010	357	1	in	in	ADP
ejpam-2010	357	2	addition	addition	NOUN
ejpam-2010	357	3	,	,	PUNCT
ejpam-2010	357	4	if	if	SCONJ
ejpam-2010	357	5	r	r	NOUN
ejpam-2010	357	6	/	/	SYM
ejpam-2010	357	7	j(r	j(r	PROPN
ejpam-2010	357	8	)	)	PUNCT
ejpam-2010	357	9	is	be	AUX
ejpam-2010	357	10	a	a	DET
ejpam-2010	357	11	division	division	NOUN
ejpam-2010	357	12	ring	ring	NOUN
ejpam-2010	357	13	then	then	ADV
ejpam-2010	357	14	r	r	NOUN
ejpam-2010	357	15	is	be	AUX
ejpam-2010	357	16	said	say	VERB
ejpam-2010	357	17	to	to	PART
ejpam-2010	357	18	be	be	AUX
ejpam-2010	357	19	a	a	DET
ejpam-2010	357	20	local	local	ADJ
ejpam-2010	357	21	ring	ring	NOUN
ejpam-2010	357	22	.	.	PUNCT
ejpam-2010	358	1	a	a	DET
ejpam-2010	358	2	ring	ring	NOUN
ejpam-2010	358	3	r	r	NOUN
ejpam-2010	358	4	is	be	AUX
ejpam-2010	358	5	said	say	VERB
ejpam-2010	358	6	to	to	PART
ejpam-2010	358	7	be	be	AUX
ejpam-2010	358	8	a	a	DET
ejpam-2010	358	9	strongly	strongly	ADV
ejpam-2010	358	10	locally	locally	ADV
ejpam-2010	358	11	matrix	matrix	NOUN
ejpam-2010	358	12	ring	ring	NOUN
ejpam-2010	358	13	over	over	ADP
ejpam-2010	358	14	a	a	DET
ejpam-2010	358	15	(	(	PUNCT
ejpam-2010	358	16	unital	unital	ADJ
ejpam-2010	358	17	)	)	PUNCT
ejpam-2010	358	18	ring	ring	NOUN
ejpam-2010	358	19	s	s	PRON
ejpam-2010	358	20	if	if	SCONJ
ejpam-2010	358	21	every	every	DET
ejpam-2010	358	22	finite	finite	NOUN
ejpam-2010	358	23	subset	subset	VERB
ejpam-2010	358	24	u	u	NOUN
ejpam-2010	358	25	⊆	⊆	NUM
ejpam-2010	358	26	r	r	NOUN
ejpam-2010	358	27	there	there	PRON
ejpam-2010	358	28	is	be	VERB
ejpam-2010	358	29	an	an	DET
ejpam-2010	358	30	idempotent	idempotent	ADJ
ejpam-2010	358	31	e	e	NOUN
ejpam-2010	358	32	∈	∈	NOUN
ejpam-2010	358	33	r	r	NOUN
ejpam-2010	358	34	such	such	ADJ
ejpam-2010	358	35	that	that	DET
ejpam-2010	358	36	u	u	PROPN
ejpam-2010	358	37	⊆	⊆	NUM
ejpam-2010	358	38	ere	ere	NOUN
ejpam-2010	358	39	and	and	CCONJ
ejpam-2010	358	40	ere	ere	NOUN
ejpam-2010	358	41	is	be	AUX
ejpam-2010	358	42	isomorphic	isomorphic	ADJ
ejpam-2010	358	43	to	to	ADP
ejpam-2010	358	44	the	the	DET
ejpam-2010	358	45	matrix	matrix	NOUN
ejpam-2010	358	46	ring	ring	NOUN
ejpam-2010	358	47	sn	sn	PROPN
ejpam-2010	358	48	for	for	ADP
ejpam-2010	358	49	some	some	DET
ejpam-2010	358	50	n.	n.	NOUN
ejpam-2010	358	51	proposition	proposition	NOUN
ejpam-2010	359	1	3	3	X
ejpam-2010	359	2	.	.	PUNCT
ejpam-2010	360	1	let	let	VERB
ejpam-2010	360	2	r	r	PRON
ejpam-2010	360	3	be	be	AUX
ejpam-2010	360	4	a	a	DET
ejpam-2010	360	5	ring	ring	NOUN
ejpam-2010	360	6	with	with	ADP
ejpam-2010	360	7	local	local	ADJ
ejpam-2010	360	8	units	unit	NOUN
ejpam-2010	360	9	.	.	PUNCT
ejpam-2010	361	1	then	then	ADV
ejpam-2010	361	2	(	(	PUNCT
ejpam-2010	361	3	1	1	X
ejpam-2010	361	4	)	)	PUNCT
ejpam-2010	361	5	r	r	NOUN
ejpam-2010	361	6	is	be	AUX
ejpam-2010	361	7	morita	morita	NOUN
ejpam-2010	361	8	equivalent	equivalent	ADJ
ejpam-2010	361	9	to	to	ADP
ejpam-2010	361	10	a	a	DET
ejpam-2010	361	11	untial	untial	ADJ
ejpam-2010	361	12	ring	ring	NOUN
ejpam-2010	361	13	if	if	SCONJ
ejpam-2010	362	1	and	and	CCONJ
ejpam-2010	362	2	only	only	ADV
ejpam-2010	362	3	if	if	SCONJ
ejpam-2010	362	4	there	there	PRON
ejpam-2010	362	5	exists	exist	VERB
ejpam-2010	362	6	an	an	DET
ejpam-2010	362	7	idempotent	idempotent	ADJ
ejpam-2010	362	8	e	e	NOUN
ejpam-2010	362	9	in	in	ADP
ejpam-2010	362	10	r	r	NOUN
ejpam-2010	362	11	with	with	ADP
ejpam-2010	362	12	r=	r=	ADJ
ejpam-2010	362	13	rer	rer	NOUN
ejpam-2010	362	14	.	.	PUNCT
ejpam-2010	363	1	moreover	moreover	ADV
ejpam-2010	363	2	,	,	PUNCT
ejpam-2010	363	3	r	r	NOUN
ejpam-2010	363	4	is	be	AUX
ejpam-2010	363	5	morita	morita	PROPN
ejpam-2010	363	6	equivalent	equivalent	NOUN
ejpam-2010	363	7	to	to	ADP
ejpam-2010	363	8	ere	ere	PROPN
ejpam-2010	363	9	;	;	PUNCT
ejpam-2010	363	10	(	(	PUNCT
ejpam-2010	363	11	2	2	X
ejpam-2010	363	12	)	)	PUNCT
ejpam-2010	363	13	r	r	NOUN
ejpam-2010	363	14	is	be	AUX
ejpam-2010	363	15	mortia	mortia	VERB
ejpam-2010	363	16	equivalent	equivalent	ADJ
ejpam-2010	363	17	to	to	ADP
ejpam-2010	363	18	a	a	DET
ejpam-2010	363	19	division	division	NOUN
ejpam-2010	363	20	ring	ring	NOUN
ejpam-2010	363	21	if	if	SCONJ
ejpam-2010	363	22	and	and	CCONJ
ejpam-2010	363	23	only	only	ADV
ejpam-2010	363	24	if	if	SCONJ
ejpam-2010	363	25	it	it	PRON
ejpam-2010	363	26	is	be	AUX
ejpam-2010	363	27	a	a	DET
ejpam-2010	363	28	simple	simple	ADJ
ejpam-2010	363	29	ring	ring	NOUN
ejpam-2010	363	30	with	with	ADP
ejpam-2010	363	31	minimal	minimal	ADJ
ejpam-2010	363	32	one	one	NUM
ejpam-2010	363	33	-	-	PUNCT
ejpam-2010	363	34	sided	sided	ADJ
ejpam-2010	363	35	ideals	ideal	NOUN
ejpam-2010	363	36	;	;	PUNCT
ejpam-2010	363	37	(	(	PUNCT
ejpam-2010	363	38	3	3	X
ejpam-2010	363	39	)	)	PUNCT
ejpam-2010	363	40	r	r	NOUN
ejpam-2010	363	41	is	be	AUX
ejpam-2010	363	42	morita	morita	NOUN
ejpam-2010	363	43	equivalent	equivalent	ADJ
ejpam-2010	363	44	to	to	ADP
ejpam-2010	363	45	a	a	DET
ejpam-2010	363	46	primary	primary	ADJ
ejpam-2010	363	47	ring	ring	NOUN
ejpam-2010	363	48	if	if	SCONJ
ejpam-2010	363	49	and	and	CCONJ
ejpam-2010	363	50	only	only	ADV
ejpam-2010	363	51	if	if	SCONJ
ejpam-2010	363	52	r	r	NOUN
ejpam-2010	363	53	is	be	AUX
ejpam-2010	363	54	isomorphic	isomorphic	ADJ
ejpam-2010	363	55	to	to	ADP
ejpam-2010	363	56	a	a	DET
ejpam-2010	363	57	strongly	strongly	ADV
ejpam-2010	363	58	locally	locally	ADV
ejpam-2010	363	59	matrix	matrix	NOUN
ejpam-2010	363	60	ring	ring	NOUN
ejpam-2010	363	61	over	over	ADP
ejpam-2010	363	62	a	a	DET
ejpam-2010	363	63	local	local	ADJ
ejpam-2010	363	64	ring	ring	NOUN
ejpam-2010	363	65	.	.	PUNCT
ejpam-2010	364	1	3.2	3.2	NUM
ejpam-2010	364	2	.	.	PUNCT
ejpam-2010	365	1	xst	xst	PROPN
ejpam-2010	365	2	-rings	-ring	VERB
ejpam-2010	365	3	the	the	DET
ejpam-2010	365	4	aim	aim	NOUN
ejpam-2010	365	5	of	of	ADP
ejpam-2010	365	6	this	this	DET
ejpam-2010	365	7	subsection	subsection	NOUN
ejpam-2010	365	8	is	be	AUX
ejpam-2010	365	9	to	to	PART
ejpam-2010	365	10	give	give	VERB
ejpam-2010	365	11	a	a	DET
ejpam-2010	365	12	number	number	NOUN
ejpam-2010	365	13	of	of	ADP
ejpam-2010	365	14	important	important	ADJ
ejpam-2010	365	15	and	and	CCONJ
ejpam-2010	365	16	useful	useful	ADJ
ejpam-2010	365	17	results	result	NOUN
ejpam-2010	365	18	concerning	concern	VERB
ejpam-2010	365	19	xst	xst	NOUN
ejpam-2010	365	20	-	-	PUNCT
ejpam-2010	365	21	rings	ring	NOUN
ejpam-2010	365	22	.	.	PUNCT
ejpam-2010	366	1	we	we	PRON
ejpam-2010	366	2	recall	recall	VERB
ejpam-2010	366	3	that	that	SCONJ
ejpam-2010	366	4	a	a	DET
ejpam-2010	366	5	ring	ring	NOUN
ejpam-2010	366	6	r	r	NOUN
ejpam-2010	366	7	is	be	AUX
ejpam-2010	366	8	called	call	VERB
ejpam-2010	366	9	a	a	DET
ejpam-2010	366	10	right	right	ADJ
ejpam-2010	366	11	xst	xst	NOUN
ejpam-2010	366	12	-	-	NOUN
ejpam-2010	366	13	ring	ring	NOUN
ejpam-2010	366	14	if	if	SCONJ
ejpam-2010	366	15	every	every	DET
ejpam-2010	366	16	submodule	submodule	NOUN
ejpam-2010	366	17	of	of	ADP
ejpam-2010	366	18	a	a	DET
ejpam-2010	366	19	unitary	unitary	ADJ
ejpam-2010	366	20	right	right	ADJ
ejpam-2010	366	21	rmodule	rmodule	NOUN
ejpam-2010	366	22	is	be	AUX
ejpam-2010	366	23	again	again	ADV
ejpam-2010	366	24	unitary	unitary	ADJ
ejpam-2010	366	25	.	.	PUNCT
ejpam-2010	367	1	a	a	DET
ejpam-2010	367	2	ring	ring	NOUN
ejpam-2010	367	3	r	r	NOUN
ejpam-2010	367	4	is	be	AUX
ejpam-2010	367	5	an	an	DET
ejpam-2010	367	6	xst	xst	NOUN
ejpam-2010	367	7	-	-	PUNCT
ejpam-2010	367	8	ring	ring	NOUN
ejpam-2010	367	9	if	if	SCONJ
ejpam-2010	367	10	it	it	PRON
ejpam-2010	367	11	is	be	AUX
ejpam-2010	367	12	both	both	ADV
ejpam-2010	367	13	right	right	ADJ
ejpam-2010	367	14	and	and	CCONJ
ejpam-2010	367	15	left	leave	VERB
ejpam-2010	367	16	xst	xst	PROPN
ejpam-2010	367	17	.	.	PUNCT
ejpam-2010	368	1	in	in	ADP
ejpam-2010	368	2	[	[	X
ejpam-2010	368	3	13	13	NUM
ejpam-2010	368	4	]	]	PUNCT
ejpam-2010	368	5	,	,	PUNCT
ejpam-2010	368	6	a	a	DET
ejpam-2010	368	7	ring	ring	NOUN
ejpam-2010	368	8	r	r	NOUN
ejpam-2010	368	9	is	be	AUX
ejpam-2010	368	10	right	right	ADJ
ejpam-2010	368	11	xst	xst	NOUN
ejpam-2010	369	1	if	if	SCONJ
ejpam-2010	370	1	and	and	CCONJ
ejpam-2010	370	2	only	only	ADV
ejpam-2010	370	3	if	if	SCONJ
ejpam-2010	370	4	umod	umod	PROPN
ejpam-2010	370	5	-	-	PUNCT
ejpam-2010	370	6	r	r	NOUN
ejpam-2010	370	7	is	be	AUX
ejpam-2010	370	8	complete	complete	ADJ
ejpam-2010	370	9	additive	additive	NOUN
ejpam-2010	370	10	,	,	PUNCT
ejpam-2010	370	11	if	if	SCONJ
ejpam-2010	370	12	and	and	CCONJ
ejpam-2010	370	13	only	only	ADV
ejpam-2010	370	14	if	if	SCONJ
ejpam-2010	370	15	every	every	DET
ejpam-2010	370	16	unitary	unitary	ADJ
ejpam-2010	370	17	ring	ring	NOUN
ejpam-2010	370	18	r	r	NOUN
ejpam-2010	370	19	-	-	PUNCT
ejpam-2010	370	20	module	module	NOUN
ejpam-2010	370	21	is	be	AUX
ejpam-2010	370	22	s	s	NOUN
ejpam-2010	370	23	-	-	NOUN
ejpam-2010	370	24	unital	unital	ADJ
ejpam-2010	370	25	.	.	PUNCT
ejpam-2010	371	1	in	in	ADP
ejpam-2010	371	2	addition	addition	NOUN
ejpam-2010	371	3	,	,	PUNCT
ejpam-2010	371	4	if	if	SCONJ
ejpam-2010	371	5	r	r	NOUN
ejpam-2010	371	6	is	be	AUX
ejpam-2010	371	7	a	a	DET
ejpam-2010	371	8	right	right	ADJ
ejpam-2010	371	9	xst	xst	NOUN
ejpam-2010	371	10	ring	ring	NOUN
ejpam-2010	371	11	then	then	ADV
ejpam-2010	371	12	mod	mod	PROPN
ejpam-2010	371	13	-	-	PUNCT
ejpam-2010	371	14	r	r	NOUN
ejpam-2010	371	15	coincides	coincide	VERB
ejpam-2010	371	16	with	with	ADP
ejpam-2010	371	17	cr	cr	PROPN
ejpam-2010	371	18	.	.	PUNCT
ejpam-2010	372	1	thus	thus	ADV
ejpam-2010	372	2	rings	ring	VERB
ejpam-2010	372	3	r	r	NOUN
ejpam-2010	372	4	and	and	CCONJ
ejpam-2010	372	5	s	s	NOUN
ejpam-2010	372	6	are	be	AUX
ejpam-2010	372	7	right	right	ADJ
ejpam-2010	372	8	morita	morita	NOUN
ejpam-2010	372	9	-	-	PUNCT
ejpam-2010	372	10	like	like	ADJ
ejpam-2010	372	11	equivalent	equivalent	NOUN
ejpam-2010	372	12	if	if	SCONJ
ejpam-2010	373	1	and	and	CCONJ
ejpam-2010	373	2	only	only	ADV
ejpam-2010	373	3	if	if	SCONJ
ejpam-2010	373	4	r	r	NOUN
ejpam-2010	373	5	and	and	CCONJ
ejpam-2010	373	6	s	s	NOUN
ejpam-2010	373	7	are	be	AUX
ejpam-2010	373	8	right	right	ADJ
ejpam-2010	373	9	xst	xst	PROPN
ejpam-2010	373	10	and	and	CCONJ
ejpam-2010	373	11	mod	mod	PROPN
ejpam-2010	373	12	-	-	PUNCT
ejpam-2010	373	13	r	r	NOUN
ejpam-2010	373	14	and	and	CCONJ
ejpam-2010	373	15	mod	mod	PROPN
ejpam-2010	373	16	-	-	PUNCT
ejpam-2010	373	17	s	s	NOUN
ejpam-2010	373	18	are	be	AUX
ejpam-2010	373	19	equivalent	equivalent	ADJ
ejpam-2010	373	20	.	.	PUNCT
ejpam-2010	374	1	observe	observe	VERB
ejpam-2010	374	2	that	that	SCONJ
ejpam-2010	374	3	for	for	ADP
ejpam-2010	374	4	right	right	ADJ
ejpam-2010	374	5	xst	xst	PROPN
ejpam-2010	374	6	-	-	PUNCT
ejpam-2010	374	7	rings	ring	NOUN
ejpam-2010	374	8	r	r	NOUN
ejpam-2010	374	9	and	and	CCONJ
ejpam-2010	374	10	s	s	PROPN
ejpam-2010	374	11	,	,	PUNCT
ejpam-2010	374	12	they	they	PRON
ejpam-2010	374	13	are	be	AUX
ejpam-2010	374	14	right	right	ADJ
ejpam-2010	374	15	morita	morita	PROPN
ejpam-2010	374	16	-	-	PUNCT
ejpam-2010	374	17	like	like	ADJ
ejpam-2010	374	18	equivalent	equivalent	NOUN
ejpam-2010	374	19	if	if	SCONJ
ejpam-2010	375	1	and	and	CCONJ
ejpam-2010	375	2	only	only	ADV
ejpam-2010	375	3	if	if	SCONJ
ejpam-2010	375	4	mod	mod	ADJ
ejpam-2010	375	5	-	-	PUNCT
ejpam-2010	375	6	r	r	NOUN
ejpam-2010	375	7	and	and	CCONJ
ejpam-2010	375	8	mod	mod	PROPN
ejpam-2010	375	9	-	-	PUNCT
ejpam-2010	375	10	s	s	NOUN
ejpam-2010	375	11	are	be	AUX
ejpam-2010	375	12	equivalent	equivalent	ADJ
ejpam-2010	375	13	,	,	PUNCT
ejpam-2010	375	14	that	that	ADV
ejpam-2010	375	15	is	is	ADV
ejpam-2010	375	16	,	,	PUNCT
ejpam-2010	375	17	r	r	NOUN
ejpam-2010	375	18	and	and	CCONJ
ejpam-2010	375	19	s	s	NOUN
ejpam-2010	375	20	are	be	AUX
ejpam-2010	375	21	morita	morita	PROPN
ejpam-2010	375	22	equivalent	equivalent	NOUN
ejpam-2010	375	23	.	.	PUNCT
ejpam-2010	376	1	so	so	ADV
ejpam-2010	376	2	for	for	ADP
ejpam-2010	376	3	xst	xst	PROPN
ejpam-2010	376	4	-	-	PUNCT
ejpam-2010	376	5	rings	ring	NOUN
ejpam-2010	376	6	,	,	PUNCT
ejpam-2010	376	7	morita	morita	NOUN
ejpam-2010	376	8	-	-	PUNCT
ejpam-2010	376	9	like	like	ADJ
ejpam-2010	376	10	equivalence	equivalence	NOUN
ejpam-2010	376	11	and	and	CCONJ
ejpam-2010	376	12	morita	morita	PROPN
ejpam-2010	376	13	equivalence	equivalence	NOUN
ejpam-2010	376	14	coincide	coincide	NOUN
ejpam-2010	376	15	.	.	PUNCT
ejpam-2010	377	1	theorem	theorem	NOUN
ejpam-2010	377	2	5	5	NUM
ejpam-2010	377	3	can	can	AUX
ejpam-2010	377	4	be	be	AUX
ejpam-2010	377	5	restated	restate	VERB
ejpam-2010	377	6	in	in	ADP
ejpam-2010	377	7	the	the	DET
ejpam-2010	377	8	following	follow	VERB
ejpam-2010	377	9	form	form	NOUN
ejpam-2010	377	10	cited	cite	VERB
ejpam-2010	377	11	from	from	ADP
ejpam-2010	377	12	[	[	X
ejpam-2010	377	13	13	13	NUM
ejpam-2010	377	14	]	]	PUNCT
ejpam-2010	377	15	.	.	PUNCT
ejpam-2010	378	1	theorem	theorem	ADJ
ejpam-2010	378	2	6	6	NUM
ejpam-2010	378	3	.	.	PUNCT
ejpam-2010	379	1	let	let	VERB
ejpam-2010	379	2	r	r	PRON
ejpam-2010	379	3	be	be	AUX
ejpam-2010	379	4	a	a	DET
ejpam-2010	379	5	unital	unital	ADJ
ejpam-2010	379	6	ring	ring	NOUN
ejpam-2010	379	7	,	,	PUNCT
ejpam-2010	379	8	λ	λ	X
ejpam-2010	379	9	any	any	DET
ejpam-2010	379	10	non	non	ADJ
ejpam-2010	379	11	-	-	ADJ
ejpam-2010	379	12	empty	empty	ADJ
ejpam-2010	379	13	set	set	NOUN
ejpam-2010	379	14	,	,	PUNCT
ejpam-2010	379	15	rf	rf	VERB
ejpam-2010	379	16	a	a	DET
ejpam-2010	379	17	free	free	ADJ
ejpam-2010	379	18	left	left	ADJ
ejpam-2010	379	19	r	r	NOUN
ejpam-2010	379	20	-	-	PUNCT
ejpam-2010	379	21	module	module	NOUN
ejpam-2010	379	22	of	of	ADP
ejpam-2010	379	23	rank	rank	PROPN
ejpam-2010	379	24	λ	λ	PROPN
ejpam-2010	379	25	,	,	PUNCT
ejpam-2010	379	26	e	e	NOUN
ejpam-2010	379	27	=	=	SYM
ejpam-2010	379	28	end(rf	end(rf	NOUN
ejpam-2010	379	29	)	)	PUNCT
ejpam-2010	379	30	its	its	PRON
ejpam-2010	379	31	endomorphism	endomorphism	NOUN
ejpam-2010	379	32	ring	ring	NOUN
ejpam-2010	379	33	,	,	PUNCT
ejpam-2010	379	34	and	and	CCONJ
ejpam-2010	379	35	e	e	X
ejpam-2010	379	36	f	f	PROPN
ejpam-2010	379	37	=	=	SYM
ejpam-2010	379	38	f	f	PROPN
ejpam-2010	379	39	end(rf	end(rf	NOUN
ejpam-2010	379	40	)	)	PUNCT
ejpam-2010	379	41	the	the	DET
ejpam-2010	379	42	ring	ring	NOUN
ejpam-2010	379	43	of	of	ADP
ejpam-2010	379	44	the	the	DET
ejpam-2010	379	45	finite	finite	ADJ
ejpam-2010	379	46	endomorphisms	endomorphism	NOUN
ejpam-2010	379	47	of	of	ADP
ejpam-2010	379	48	f.	f.	PROPN
ejpam-2010	379	49	moreover	moreover	ADV
ejpam-2010	379	50	,	,	PUNCT
ejpam-2010	379	51	let	let	VERB
ejpam-2010	379	52	rp	rp	NOUN
ejpam-2010	379	53	be	be	AUX
ejpam-2010	379	54	a	a	DET
ejpam-2010	379	55	projective	projective	ADJ
ejpam-2010	379	56	generator	generator	NOUN
ejpam-2010	379	57	which	which	PRON
ejpam-2010	379	58	is	be	AUX
ejpam-2010	379	59	isomorphic	isomorphic	ADJ
ejpam-2010	379	60	to	to	ADP
ejpam-2010	379	61	a	a	DET
ejpam-2010	379	62	direct	direct	ADJ
ejpam-2010	379	63	summand	summand	NOUN
ejpam-2010	379	64	of	of	ADP
ejpam-2010	379	65	rf	rf	PROPN
ejpam-2010	379	66	.	.	PUNCT
ejpam-2010	380	1	then	then	ADV
ejpam-2010	380	2	(	(	PUNCT
ejpam-2010	380	3	1	1	X
ejpam-2010	380	4	)	)	PUNCT
ejpam-2010	380	5	e	e	NOUN
ejpam-2010	380	6	f	f	PROPN
ejpam-2010	380	7	and	and	CCONJ
ejpam-2010	380	8	f	f	PROPN
ejpam-2010	380	9	end(rp	end(rp	PROPN
ejpam-2010	380	10	)	)	PUNCT
ejpam-2010	380	11	are	be	AUX
ejpam-2010	380	12	right	right	ADJ
ejpam-2010	380	13	xst	xst	PROPN
ejpam-2010	380	14	-	-	PUNCT
ejpam-2010	380	15	rings	ring	NOUN
ejpam-2010	380	16	;	;	PUNCT
ejpam-2010	380	17	(	(	PUNCT
ejpam-2010	380	18	2	2	X
ejpam-2010	380	19	)	)	PUNCT
ejpam-2010	380	20	mod	mod	ADJ
ejpam-2010	380	21	-	-	PUNCT
ejpam-2010	380	22	e	e	NOUN
ejpam-2010	380	23	f	f	PROPN
ejpam-2010	380	24	and	and	CCONJ
ejpam-2010	380	25	modf	modf	NOUN
ejpam-2010	380	26	end(rp	end(rp	PROPN
ejpam-2010	380	27	)	)	PUNCT
ejpam-2010	380	28	are	be	AUX
ejpam-2010	380	29	equivalent	equivalent	ADJ
ejpam-2010	380	30	categories	category	NOUN
ejpam-2010	380	31	.	.	PUNCT
ejpam-2010	381	1	that	that	PRON
ejpam-2010	381	2	is	be	AUX
ejpam-2010	381	3	,	,	PUNCT
ejpam-2010	381	4	e	e	PROPN
ejpam-2010	381	5	f	f	PROPN
ejpam-2010	381	6	and	and	CCONJ
ejpam-2010	381	7	f	f	PROPN
ejpam-2010	381	8	end(rp	end(rp	PROPN
ejpam-2010	381	9	)	)	PUNCT
ejpam-2010	381	10	are	be	AUX
ejpam-2010	381	11	right	right	ADJ
ejpam-2010	381	12	morita	morita	PROPN
ejpam-2010	381	13	-	-	PUNCT
ejpam-2010	381	14	like	like	ADJ
ejpam-2010	381	15	equivalent	equivalent	ADJ
ejpam-2010	381	16	rings	ring	NOUN
ejpam-2010	381	17	.	.	PUNCT
ejpam-2010	382	1	y.	y.	PROPN
ejpam-2010	382	2	wang	wang	PROPN
ejpam-2010	382	3	,	,	PUNCT
ejpam-2010	382	4	k.	k.	PROPN
ejpam-2010	382	5	shum	shum	PROPN
ejpam-2010	382	6	,	,	PUNCT
ejpam-2010	382	7	x.	x.	PROPN
ejpam-2010	382	8	ren	ren	PROPN
ejpam-2010	382	9	/	/	SYM
ejpam-2010	382	10	eur	eur	PROPN
ejpam-2010	382	11	.	.	PUNCT
ejpam-2010	383	1	j.	j.	PROPN
ejpam-2010	383	2	pure	pure	PROPN
ejpam-2010	383	3	appl	appl	PROPN
ejpam-2010	383	4	.	.	PROPN
ejpam-2010	383	5	math	math	PROPN
ejpam-2010	383	6	,	,	PUNCT
ejpam-2010	383	7	6	6	NUM
ejpam-2010	383	8	(	(	PUNCT
ejpam-2010	383	9	2013	2013	NUM
ejpam-2010	383	10	)	)	PUNCT
ejpam-2010	383	11	,	,	PUNCT
ejpam-2010	383	12	256	256	NUM
ejpam-2010	383	13	-	-	SYM
ejpam-2010	383	14	281	281	NUM
ejpam-2010	383	15	269	269	NUM
ejpam-2010	383	16	the	the	DET
ejpam-2010	383	17	following	follow	VERB
ejpam-2010	383	18	theorem	theorem	NOUN
ejpam-2010	383	19	identifies	identify	VERB
ejpam-2010	383	20	all	all	DET
ejpam-2010	383	21	rings	ring	NOUN
ejpam-2010	383	22	which	which	PRON
ejpam-2010	383	23	are	be	AUX
ejpam-2010	383	24	right	right	ADJ
ejpam-2010	383	25	morita	morita	NOUN
ejpam-2010	383	26	-	-	PUNCT
ejpam-2010	383	27	like	like	ADJ
ejpam-2010	383	28	equivalent	equivalent	NOUN
ejpam-2010	383	29	to	to	ADP
ejpam-2010	383	30	unital	unital	ADJ
ejpam-2010	383	31	rings	ring	NOUN
ejpam-2010	383	32	.	.	PUNCT
ejpam-2010	384	1	theorem	theorem	VERB
ejpam-2010	384	2	7	7	NUM
ejpam-2010	384	3	.	.	PUNCT
ejpam-2010	385	1	[	[	X
ejpam-2010	385	2	13	13	NUM
ejpam-2010	385	3	,	,	PUNCT
ejpam-2010	385	4	corollary	corollary	ADJ
ejpam-2010	385	5	3	3	NUM
ejpam-2010	385	6	]	]	PUNCT
ejpam-2010	385	7	let	let	VERB
ejpam-2010	385	8	r	r	PRON
ejpam-2010	385	9	be	be	AUX
ejpam-2010	385	10	an	an	DET
ejpam-2010	385	11	idempotent	idempotent	ADJ
ejpam-2010	385	12	ring	ring	NOUN
ejpam-2010	385	13	.	.	PUNCT
ejpam-2010	386	1	then	then	ADV
ejpam-2010	386	2	r	r	NOUN
ejpam-2010	386	3	is	be	AUX
ejpam-2010	386	4	a	a	DET
ejpam-2010	386	5	right	right	ADJ
ejpam-2010	386	6	xst	xst	NOUN
ejpam-2010	386	7	-	-	NOUN
ejpam-2010	386	8	ring	ring	NOUN
ejpam-2010	386	9	such	such	ADJ
ejpam-2010	386	10	that	that	SCONJ
ejpam-2010	386	11	r	r	NOUN
ejpam-2010	386	12	is	be	AUX
ejpam-2010	386	13	right	right	ADJ
ejpam-2010	386	14	morita	morita	NOUN
ejpam-2010	386	15	-	-	PUNCT
ejpam-2010	386	16	like	like	ADJ
ejpam-2010	386	17	equivalent	equivalent	NOUN
ejpam-2010	386	18	to	to	ADP
ejpam-2010	386	19	a	a	DET
ejpam-2010	386	20	unital	unital	ADJ
ejpam-2010	386	21	ring	ring	NOUN
ejpam-2010	386	22	a	a	DET
ejpam-2010	386	23	if	if	NOUN
ejpam-2010	387	1	and	and	CCONJ
ejpam-2010	387	2	only	only	ADV
ejpam-2010	387	3	if	if	SCONJ
ejpam-2010	387	4	there	there	PRON
ejpam-2010	387	5	exists	exist	VERB
ejpam-2010	387	6	a	a	DET
ejpam-2010	387	7	generator	generator	NOUN
ejpam-2010	387	8	am	am	NOUN
ejpam-2010	387	9	of	of	ADP
ejpam-2010	387	10	a	a	DET
ejpam-2010	387	11	-	-	PUNCT
ejpam-2010	387	12	mod	mod	NOUN
ejpam-2010	387	13	such	such	ADJ
ejpam-2010	387	14	that	that	SCONJ
ejpam-2010	387	15	r	r	NOUN
ejpam-2010	387	16	t	t	PROPN
ejpam-2010	387	17	(	(	PUNCT
ejpam-2010	387	18	rr	rr	NOUN
ejpam-2010	387	19	)	)	PUNCT
ejpam-2010	387	20	is	be	AUX
ejpam-2010	387	21	isomorphic	isomorphic	ADJ
ejpam-2010	387	22	to	to	ADP
ejpam-2010	387	23	a	a	DET
ejpam-2010	387	24	dense	dense	ADJ
ejpam-2010	387	25	right	right	ADJ
ejpam-2010	387	26	ideal	ideal	NOUN
ejpam-2010	387	27	of	of	ADP
ejpam-2010	387	28	end(am	end(am	NOUN
ejpam-2010	387	29	)	)	PUNCT
ejpam-2010	387	30	which	which	PRON
ejpam-2010	387	31	is	be	AUX
ejpam-2010	387	32	contained	contain	VERB
ejpam-2010	387	33	in	in	ADP
ejpam-2010	387	34	f	f	PROPN
ejpam-2010	387	35	end(am	end(am	PROPN
ejpam-2010	387	36	)	)	PUNCT
ejpam-2010	387	37	,	,	PUNCT
ejpam-2010	387	38	where	where	SCONJ
ejpam-2010	387	39	r	r	NOUN
ejpam-2010	387	40	t	t	PROPN
ejpam-2010	387	41	(	(	PUNCT
ejpam-2010	387	42	rr	rr	NOUN
ejpam-2010	387	43	)	)	PUNCT
ejpam-2010	387	44	is	be	AUX
ejpam-2010	387	45	the	the	DET
ejpam-2010	387	46	quotient	quotient	NOUN
ejpam-2010	387	47	module	module	NOUN
ejpam-2010	387	48	of	of	ADP
ejpam-2010	387	49	r	r	NOUN
ejpam-2010	387	50	factored	factor	VERB
ejpam-2010	387	51	by	by	ADP
ejpam-2010	387	52	t	t	PROPN
ejpam-2010	387	53	(	(	PUNCT
ejpam-2010	387	54	rr	rr	NOUN
ejpam-2010	387	55	)	)	PUNCT
ejpam-2010	387	56	,	,	PUNCT
ejpam-2010	387	57	and	and	CCONJ
ejpam-2010	387	58	f	f	PROPN
ejpam-2010	387	59	end(am	end(am	PROPN
ejpam-2010	387	60	)	)	PUNCT
ejpam-2010	387	61	is	be	AUX
ejpam-2010	387	62	the	the	DET
ejpam-2010	387	63	ring	ring	NOUN
ejpam-2010	387	64	of	of	ADP
ejpam-2010	387	65	the	the	DET
ejpam-2010	387	66	finite	finite	ADJ
ejpam-2010	387	67	endomorphisms	endomorphism	NOUN
ejpam-2010	387	68	of	of	ADP
ejpam-2010	387	69	m.	m.	NOUN
ejpam-2010	387	70	if	if	SCONJ
ejpam-2010	387	71	r	r	NOUN
ejpam-2010	387	72	is	be	AUX
ejpam-2010	387	73	an	an	DET
ejpam-2010	387	74	xst	xst	NOUN
ejpam-2010	387	75	-	-	PUNCT
ejpam-2010	387	76	ring	ring	NOUN
ejpam-2010	387	77	,	,	PUNCT
ejpam-2010	387	78	we	we	PRON
ejpam-2010	387	79	shall	shall	AUX
ejpam-2010	387	80	use	use	VERB
ejpam-2010	387	81	u(r	u(r	NOUN
ejpam-2010	387	82	)	)	PUNCT
ejpam-2010	387	83	to	to	PART
ejpam-2010	387	84	denote	denote	VERB
ejpam-2010	387	85	the	the	DET
ejpam-2010	387	86	ideal	ideal	NOUN
ejpam-2010	387	87	of	of	ADP
ejpam-2010	387	88	r.	r.	PROPN
ejpam-2010	387	89	then	then	ADV
ejpam-2010	387	90	proposition	proposition	VERB
ejpam-2010	387	91	4	4	NUM
ejpam-2010	387	92	.	.	PUNCT
ejpam-2010	388	1	[	[	X
ejpam-2010	388	2	13	13	NUM
ejpam-2010	388	3	,	,	PUNCT
ejpam-2010	388	4	proposition	proposition	NOUN
ejpam-2010	388	5	8	8	NUM
ejpam-2010	388	6	]	]	PUNCT
ejpam-2010	388	7	let	let	VERB
ejpam-2010	388	8	r	r	NOUN
ejpam-2010	388	9	and	and	CCONJ
ejpam-2010	388	10	s	s	AUX
ejpam-2010	388	11	be	be	AUX
ejpam-2010	388	12	xst	xst	NOUN
ejpam-2010	388	13	-	-	PUNCT
ejpam-2010	388	14	rings	ring	NOUN
ejpam-2010	388	15	.	.	PUNCT
ejpam-2010	389	1	then	then	ADV
ejpam-2010	389	2	the	the	DET
ejpam-2010	389	3	following	follow	VERB
ejpam-2010	389	4	statements	statement	NOUN
ejpam-2010	389	5	are	be	AUX
ejpam-2010	389	6	equivalent	equivalent	ADJ
ejpam-2010	389	7	:	:	PUNCT
ejpam-2010	389	8	(	(	PUNCT
ejpam-2010	389	9	1	1	X
ejpam-2010	389	10	)	)	PUNCT
ejpam-2010	389	11	mod	mod	ADJ
ejpam-2010	389	12	-	-	PUNCT
ejpam-2010	389	13	r	r	NOUN
ejpam-2010	389	14	and	and	CCONJ
ejpam-2010	389	15	mod	mod	PROPN
ejpam-2010	389	16	-	-	PUNCT
ejpam-2010	389	17	s	s	NOUN
ejpam-2010	389	18	are	be	AUX
ejpam-2010	389	19	equivalent	equivalent	ADJ
ejpam-2010	389	20	;	;	PUNCT
ejpam-2010	389	21	(	(	PUNCT
ejpam-2010	389	22	2	2	X
ejpam-2010	389	23	)	)	PUNCT
ejpam-2010	389	24	mod	mod	ADJ
ejpam-2010	389	25	-	-	PUNCT
ejpam-2010	389	26	u(r	u(r	NOUN
ejpam-2010	389	27	)	)	PUNCT
ejpam-2010	389	28	and	and	CCONJ
ejpam-2010	389	29	mod	mod	PROPN
ejpam-2010	389	30	-	-	PUNCT
ejpam-2010	389	31	u(s	u(s	ADJ
ejpam-2010	389	32	)	)	PUNCT
ejpam-2010	389	33	are	be	AUX
ejpam-2010	389	34	equivalent	equivalent	ADJ
ejpam-2010	389	35	;	;	PUNCT
ejpam-2010	389	36	(	(	PUNCT
ejpam-2010	389	37	3	3	X
ejpam-2010	389	38	)	)	PUNCT
ejpam-2010	389	39	r	r	NOUN
ejpam-2010	389	40	-	-	PUNCT
ejpam-2010	389	41	mod	mod	ADJ
ejpam-2010	389	42	and	and	CCONJ
ejpam-2010	389	43	s	s	PROPN
ejpam-2010	389	44	-	-	ADJ
ejpam-2010	389	45	mod	mod	NOUN
ejpam-2010	389	46	are	be	AUX
ejpam-2010	389	47	equivalent	equivalent	ADJ
ejpam-2010	389	48	;	;	PUNCT
ejpam-2010	389	49	(	(	PUNCT
ejpam-2010	389	50	4	4	X
ejpam-2010	389	51	)	)	PUNCT
ejpam-2010	389	52	u(r)-mod	u(r)-mod	PROPN
ejpam-2010	389	53	and	and	CCONJ
ejpam-2010	389	54	u(s)-mod	u(s)-mod	PROPN
ejpam-2010	389	55	are	be	AUX
ejpam-2010	389	56	equivalent	equivalent	ADJ
ejpam-2010	389	57	.	.	PUNCT
ejpam-2010	390	1	proposition	proposition	NOUN
ejpam-2010	390	2	5	5	NUM
ejpam-2010	390	3	.	.	PUNCT
ejpam-2010	391	1	[	[	X
ejpam-2010	391	2	13	13	NUM
ejpam-2010	391	3	,	,	PUNCT
ejpam-2010	391	4	proposition	proposition	NOUN
ejpam-2010	391	5	9	9	NUM
ejpam-2010	391	6	]	]	PUNCT
ejpam-2010	391	7	let	let	VERB
ejpam-2010	391	8	r	r	NOUN
ejpam-2010	391	9	and	and	CCONJ
ejpam-2010	391	10	s	s	AUX
ejpam-2010	391	11	be	be	AUX
ejpam-2010	391	12	xst	xst	NOUN
ejpam-2010	391	13	-	-	PUNCT
ejpam-2010	391	14	rings	ring	NOUN
ejpam-2010	391	15	.	.	PUNCT
ejpam-2010	392	1	then	then	ADV
ejpam-2010	392	2	mod	mod	PROPN
ejpam-2010	392	3	-	-	PUNCT
ejpam-2010	392	4	r	r	NOUN
ejpam-2010	392	5	and	and	CCONJ
ejpam-2010	392	6	mod	mod	PROPN
ejpam-2010	392	7	-	-	PUNCT
ejpam-2010	392	8	s	s	NOUN
ejpam-2010	392	9	are	be	AUX
ejpam-2010	392	10	equivalent	equivalent	ADJ
ejpam-2010	392	11	if	if	SCONJ
ejpam-2010	392	12	and	and	CCONJ
ejpam-2010	392	13	only	only	ADV
ejpam-2010	392	14	if	if	SCONJ
ejpam-2010	392	15	there	there	PRON
ejpam-2010	392	16	exists	exist	VERB
ejpam-2010	392	17	a	a	DET
ejpam-2010	392	18	morita	morita	PROPN
ejpam-2010	392	19	context	context	NOUN
ejpam-2010	392	20	between	between	ADP
ejpam-2010	392	21	r	r	NOUN
ejpam-2010	392	22	and	and	CCONJ
ejpam-2010	392	23	s	s	PROPN
ejpam-2010	392	24	,	,	PUNCT
ejpam-2010	392	25	given	give	VERB
ejpam-2010	392	26	by	by	ADP
ejpam-2010	392	27	(	(	PUNCT
ejpam-2010	392	28	on	on	ADP
ejpam-2010	392	29	both	both	DET
ejpam-2010	392	30	sides	side	NOUN
ejpam-2010	392	31	)	)	PUNCT
ejpam-2010	392	32	bimodules	bimodule	VERB
ejpam-2010	392	33	rps	rps	PROPN
ejpam-2010	392	34	and	and	CCONJ
ejpam-2010	392	35	sqr	sqr	PROPN
ejpam-2010	392	36	such	such	ADJ
ejpam-2010	392	37	that	that	SCONJ
ejpam-2010	392	38	the	the	DET
ejpam-2010	392	39	traces	trace	NOUN
ejpam-2010	392	40	of	of	ADP
ejpam-2010	392	41	the	the	DET
ejpam-2010	392	42	context	context	NOUN
ejpam-2010	392	43	are	be	AUX
ejpam-2010	392	44	,	,	PUNCT
ejpam-2010	392	45	respectively	respectively	ADV
ejpam-2010	392	46	,	,	PUNCT
ejpam-2010	392	47	u(r	u(r	NOUN
ejpam-2010	392	48	)	)	PUNCT
ejpam-2010	392	49	and	and	CCONJ
ejpam-2010	392	50	u(s	u(s	NUM
ejpam-2010	392	51	)	)	PUNCT
ejpam-2010	392	52	.	.	PUNCT
ejpam-2010	393	1	let	let	VERB
ejpam-2010	393	2	r	r	PRON
ejpam-2010	393	3	be	be	AUX
ejpam-2010	393	4	a	a	DET
ejpam-2010	393	5	ring	ring	NOUN
ejpam-2010	393	6	,	,	PUNCT
ejpam-2010	393	7	rp	rp	ADP
ejpam-2010	393	8	a	a	DET
ejpam-2010	393	9	unitary	unitary	ADJ
ejpam-2010	393	10	left	left	ADJ
ejpam-2010	393	11	r	r	NOUN
ejpam-2010	393	12	-	-	PUNCT
ejpam-2010	393	13	module	module	NOUN
ejpam-2010	393	14	and	and	CCONJ
ejpam-2010	393	15	s	s	NOUN
ejpam-2010	393	16	=	=	NOUN
ejpam-2010	393	17	end(rp	end(rp	PROPN
ejpam-2010	393	18	)	)	PUNCT
ejpam-2010	393	19	.	.	PUNCT
ejpam-2010	394	1	we	we	PRON
ejpam-2010	394	2	denote	denote	VERB
ejpam-2010	394	3	by	by	ADP
ejpam-2010	394	4	f	f	PROPN
ejpam-2010	394	5	end(rp	end(rp	PROPN
ejpam-2010	394	6	)	)	PUNCT
ejpam-2010	394	7	to	to	ADP
ejpam-2010	394	8	the	the	DET
ejpam-2010	394	9	following	follow	VERB
ejpam-2010	394	10	(	(	PUNCT
ejpam-2010	394	11	non	non	ADJ
ejpam-2010	394	12	-	-	ADJ
ejpam-2010	394	13	unital	unital	ADJ
ejpam-2010	394	14	,	,	PUNCT
ejpam-2010	394	15	in	in	ADP
ejpam-2010	394	16	general	general	ADJ
ejpam-2010	394	17	)	)	PUNCT
ejpam-2010	394	18	subring	subring	NOUN
ejpam-2010	394	19	of	of	ADP
ejpam-2010	394	20	rp	rp	NOUN
ejpam-2010	394	21	:	:	PUNCT
ejpam-2010	394	22	{	{	PUNCT
ejpam-2010	395	1	α	α	NOUN
ejpam-2010	395	2	∈	∈	NOUN
ejpam-2010	395	3	s|∃x	s|∃x	PROPN
ejpam-2010	395	4	i	i	PRON
ejpam-2010	395	5	∈	∈	VERB
ejpam-2010	395	6	p,∃	p,∃	X
ejpam-2010	395	7	fi	fi	NOUN
ejpam-2010	395	8	∈	∈	PROPN
ejpam-2010	395	9	homr(p	homr(p	NOUN
ejpam-2010	395	10	,	,	PUNCT
ejpam-2010	395	11	r),∀u	r),∀u	PROPN
ejpam-2010	395	12	∈	∈	PROPN
ejpam-2010	395	13	p	p	X
ejpam-2010	395	14	,	,	PUNCT
ejpam-2010	395	15	uα=	uα=	NOUN
ejpam-2010	395	16	n	n	CCONJ
ejpam-2010	395	17	∑	∑	PROPN
ejpam-2010	395	18	i=1	i=1	PROPN
ejpam-2010	395	19	(	(	PUNCT
ejpam-2010	395	20	ufi)x	ufi)x	PROPN
ejpam-2010	395	21	i	i	PROPN
ejpam-2010	395	22	}	}	PUNCT
ejpam-2010	395	23	.	.	PUNCT
ejpam-2010	396	1	theorem	theorem	VERB
ejpam-2010	396	2	8	8	NUM
ejpam-2010	396	3	.	.	PUNCT
ejpam-2010	397	1	[	[	X
ejpam-2010	397	2	13	13	NUM
ejpam-2010	397	3	,	,	PUNCT
ejpam-2010	397	4	theorem	theorem	VERB
ejpam-2010	397	5	6	6	NUM
ejpam-2010	397	6	]	]	PUNCT
ejpam-2010	397	7	let	let	VERB
ejpam-2010	397	8	r	r	NOUN
ejpam-2010	397	9	and	and	CCONJ
ejpam-2010	397	10	s	s	AUX
ejpam-2010	397	11	be	be	AUX
ejpam-2010	397	12	xst	xst	NOUN
ejpam-2010	397	13	-	-	PUNCT
ejpam-2010	397	14	rings	ring	NOUN
ejpam-2010	397	15	.	.	PUNCT
ejpam-2010	398	1	r	r	NOUN
ejpam-2010	398	2	and	and	CCONJ
ejpam-2010	398	3	s	s	NOUN
ejpam-2010	398	4	are	be	AUX
ejpam-2010	398	5	morita	morita	NOUN
ejpam-2010	398	6	-	-	PUNCT
ejpam-2010	398	7	like	like	ADJ
ejpam-2010	398	8	equivalent	equivalent	NOUN
ejpam-2010	398	9	if	if	SCONJ
ejpam-2010	399	1	and	and	CCONJ
ejpam-2010	399	2	only	only	ADV
ejpam-2010	399	3	if	if	SCONJ
ejpam-2010	399	4	there	there	PRON
ejpam-2010	399	5	exists	exist	VERB
ejpam-2010	399	6	a	a	DET
ejpam-2010	399	7	generator	generator	NOUN
ejpam-2010	399	8	rp	rp	NOUN
ejpam-2010	399	9	of	of	ADP
ejpam-2010	399	10	the	the	DET
ejpam-2010	399	11	category	category	NOUN
ejpam-2010	399	12	r	r	NOUN
ejpam-2010	399	13	-	-	PUNCT
ejpam-2010	399	14	mod	mod	NOUN
ejpam-2010	399	15	such	such	ADJ
ejpam-2010	399	16	that	that	DET
ejpam-2010	399	17	u(s	u(s	PROPN
ejpam-2010	399	18	)	)	PUNCT
ejpam-2010	399	19	is	be	AUX
ejpam-2010	399	20	isomorphic	isomorphic	ADJ
ejpam-2010	399	21	to	to	ADP
ejpam-2010	399	22	a	a	DET
ejpam-2010	399	23	dense	dense	ADJ
ejpam-2010	399	24	right	right	ADJ
ejpam-2010	399	25	ideal	ideal	NOUN
ejpam-2010	399	26	t	t	PROPN
ejpam-2010	399	27	of	of	ADP
ejpam-2010	399	28	endrp	endrp	NOUN
ejpam-2010	399	29	,	,	PUNCT
ejpam-2010	399	30	such	such	ADJ
ejpam-2010	399	31	that	that	SCONJ
ejpam-2010	399	32	t	t	PROPN
ejpam-2010	399	33	⊆	⊆	NUM
ejpam-2010	399	34	f	f	PROPN
ejpam-2010	399	35	end(rp	end(rp	NOUN
ejpam-2010	399	36	)	)	PUNCT
ejpam-2010	399	37	.	.	PUNCT
ejpam-2010	400	1	4	4	X
ejpam-2010	400	2	.	.	X
ejpam-2010	400	3	morita	morita	PROPN
ejpam-2010	400	4	theory	theory	NOUN
ejpam-2010	400	5	for	for	ADP
ejpam-2010	400	6	semigroups	semigroup	NOUN
ejpam-2010	400	7	in	in	ADP
ejpam-2010	400	8	this	this	DET
ejpam-2010	400	9	section	section	NOUN
ejpam-2010	400	10	we	we	PRON
ejpam-2010	400	11	describe	describe	VERB
ejpam-2010	400	12	the	the	DET
ejpam-2010	400	13	development	development	NOUN
ejpam-2010	400	14	of	of	ADP
ejpam-2010	400	15	morita	morita	PROPN
ejpam-2010	400	16	theory	theory	NOUN
ejpam-2010	400	17	for	for	ADP
ejpam-2010	400	18	semigroups	semigroup	NOUN
ejpam-2010	400	19	.	.	PUNCT
ejpam-2010	401	1	there	there	PRON
ejpam-2010	401	2	mainly	mainly	ADV
ejpam-2010	401	3	exist	exist	VERB
ejpam-2010	401	4	four	four	NUM
ejpam-2010	401	5	ways	way	NOUN
ejpam-2010	401	6	of	of	ADP
ejpam-2010	401	7	investigating	investigate	VERB
ejpam-2010	401	8	morita	morita	NOUN
ejpam-2010	401	9	equivalence	equivalence	NOUN
ejpam-2010	401	10	for	for	ADP
ejpam-2010	401	11	semigroups	semigroup	NOUN
ejpam-2010	401	12	:	:	PUNCT
ejpam-2010	401	13	using	use	VERB
ejpam-2010	401	14	categories	category	NOUN
ejpam-2010	401	15	of	of	ADP
ejpam-2010	401	16	acts	act	NOUN
ejpam-2010	401	17	over	over	ADP
ejpam-2010	401	18	them	they	PRON
ejpam-2010	401	19	,	,	PUNCT
ejpam-2010	401	20	morita	morita	PROPN
ejpam-2010	401	21	contexts	contexts	PROPN
ejpam-2010	401	22	,	,	PUNCT
ejpam-2010	401	23	cauchy	cauchy	ADJ
ejpam-2010	401	24	completions	completion	NOUN
ejpam-2010	401	25	and	and	CCONJ
ejpam-2010	401	26	enlargements	enlargement	NOUN
ejpam-2010	401	27	.	.	PUNCT
ejpam-2010	402	1	y.	y.	PROPN
ejpam-2010	402	2	wang	wang	PROPN
ejpam-2010	402	3	,	,	PUNCT
ejpam-2010	402	4	k.	k.	PROPN
ejpam-2010	402	5	shum	shum	PROPN
ejpam-2010	402	6	,	,	PUNCT
ejpam-2010	402	7	x.	x.	PROPN
ejpam-2010	402	8	ren	ren	PROPN
ejpam-2010	402	9	/	/	SYM
ejpam-2010	402	10	eur	eur	PROPN
ejpam-2010	402	11	.	.	PUNCT
ejpam-2010	403	1	j.	j.	PROPN
ejpam-2010	403	2	pure	pure	PROPN
ejpam-2010	403	3	appl	appl	PROPN
ejpam-2010	403	4	.	.	PROPN
ejpam-2010	403	5	math	math	PROPN
ejpam-2010	403	6	,	,	PUNCT
ejpam-2010	403	7	6	6	NUM
ejpam-2010	403	8	(	(	PUNCT
ejpam-2010	403	9	2013	2013	NUM
ejpam-2010	403	10	)	)	PUNCT
ejpam-2010	403	11	,	,	PUNCT
ejpam-2010	403	12	256	256	NUM
ejpam-2010	403	13	-	-	SYM
ejpam-2010	403	14	281	281	NUM
ejpam-2010	403	15	270	270	NUM
ejpam-2010	403	16	4.1	4.1	NUM
ejpam-2010	403	17	.	.	PUNCT
ejpam-2010	404	1	semigroups	semigroup	NOUN
ejpam-2010	404	2	with	with	ADP
ejpam-2010	404	3	local	local	ADJ
ejpam-2010	404	4	units	unit	NOUN
ejpam-2010	404	5	in	in	ADP
ejpam-2010	404	6	[	[	X
ejpam-2010	404	7	25	25	NUM
ejpam-2010	404	8	]	]	PUNCT
ejpam-2010	404	9	,	,	PUNCT
ejpam-2010	404	10	lawson	lawson	PROPN
ejpam-2010	404	11	gave	give	VERB
ejpam-2010	404	12	a	a	DET
ejpam-2010	404	13	list	list	NOUN
ejpam-2010	404	14	of	of	ADP
ejpam-2010	404	15	equivalent	equivalent	ADJ
ejpam-2010	404	16	characterisations	characterisation	NOUN
ejpam-2010	404	17	of	of	ADP
ejpam-2010	404	18	morita	morita	PROPN
ejpam-2010	404	19	equivalence	equivalence	NOUN
ejpam-2010	404	20	for	for	ADP
ejpam-2010	404	21	semigroups	semigroup	NOUN
ejpam-2010	404	22	with	with	ADP
ejpam-2010	404	23	local	local	ADJ
ejpam-2010	404	24	units	unit	NOUN
ejpam-2010	404	25	.	.	PUNCT
ejpam-2010	405	1	we	we	PRON
ejpam-2010	405	2	reformulate	reformulate	VERB
ejpam-2010	405	3	them	they	PRON
ejpam-2010	405	4	in	in	ADP
ejpam-2010	405	5	theorem	theorem	NOUN
ejpam-2010	405	6	9	9	NUM
ejpam-2010	405	7	appearing	appear	VERB
ejpam-2010	405	8	in	in	ADP
ejpam-2010	405	9	the	the	DET
ejpam-2010	405	10	follow	follow	NOUN
ejpam-2010	405	11	.	.	PUNCT
ejpam-2010	406	1	theorem	theorem	VERB
ejpam-2010	406	2	9	9	NUM
ejpam-2010	406	3	.	.	PUNCT
ejpam-2010	407	1	[	[	X
ejpam-2010	407	2	25	25	NUM
ejpam-2010	407	3	,	,	PUNCT
ejpam-2010	407	4	theorem	theorem	VERB
ejpam-2010	407	5	1.1	1.1	NUM
ejpam-2010	407	6	]	]	PUNCT
ejpam-2010	407	7	let	let	VERB
ejpam-2010	407	8	s	s	PRON
ejpam-2010	407	9	and	and	CCONJ
ejpam-2010	407	10	t	t	PROPN
ejpam-2010	407	11	be	be	VERB
ejpam-2010	407	12	semigroups	semigroup	NOUN
ejpam-2010	407	13	with	with	ADP
ejpam-2010	407	14	local	local	ADJ
ejpam-2010	407	15	units	unit	NOUN
ejpam-2010	407	16	.	.	PUNCT
ejpam-2010	408	1	then	then	ADV
ejpam-2010	408	2	the	the	DET
ejpam-2010	408	3	following	follow	VERB
ejpam-2010	408	4	statements	statement	NOUN
ejpam-2010	408	5	are	be	AUX
ejpam-2010	408	6	equivalent	equivalent	ADJ
ejpam-2010	408	7	:	:	PUNCT
ejpam-2010	408	8	(	(	PUNCT
ejpam-2010	408	9	1	1	X
ejpam-2010	408	10	)	)	PUNCT
ejpam-2010	408	11	s	s	NOUN
ejpam-2010	408	12	and	and	CCONJ
ejpam-2010	408	13	t	t	PROPN
ejpam-2010	408	14	are	be	AUX
ejpam-2010	408	15	morita	morita	PROPN
ejpam-2010	408	16	equivalent	equivalent	NOUN
ejpam-2010	408	17	;	;	PUNCT
ejpam-2010	408	18	(	(	PUNCT
ejpam-2010	408	19	2	2	X
ejpam-2010	408	20	)	)	PUNCT
ejpam-2010	408	21	the	the	DET
ejpam-2010	408	22	categories	category	NOUN
ejpam-2010	408	23	c(s	c(	VERB
ejpam-2010	408	24	)	)	PUNCT
ejpam-2010	408	25	and	and	CCONJ
ejpam-2010	408	26	c(t	c(t	PROPN
ejpam-2010	408	27	)	)	PUNCT
ejpam-2010	408	28	are	be	AUX
ejpam-2010	408	29	equivalent	equivalent	ADJ
ejpam-2010	408	30	;	;	PUNCT
ejpam-2010	408	31	(	(	PUNCT
ejpam-2010	408	32	3	3	X
ejpam-2010	408	33	)	)	PUNCT
ejpam-2010	408	34	s	s	NOUN
ejpam-2010	408	35	and	and	CCONJ
ejpam-2010	408	36	t	t	PROPN
ejpam-2010	408	37	have	have	VERB
ejpam-2010	408	38	a	a	DET
ejpam-2010	408	39	joint	joint	ADJ
ejpam-2010	408	40	enlargement	enlargement	NOUN
ejpam-2010	408	41	which	which	PRON
ejpam-2010	408	42	can	can	AUX
ejpam-2010	408	43	be	be	AUX
ejpam-2010	408	44	chosen	choose	VERB
ejpam-2010	408	45	to	to	PART
ejpam-2010	408	46	be	be	AUX
ejpam-2010	408	47	regular	regular	ADJ
ejpam-2010	408	48	if	if	SCONJ
ejpam-2010	408	49	s	s	NOUN
ejpam-2010	408	50	and	and	CCONJ
ejpam-2010	408	51	t	t	PROPN
ejpam-2010	408	52	are	be	AUX
ejpam-2010	408	53	both	both	ADV
ejpam-2010	408	54	regular	regular	ADJ
ejpam-2010	408	55	;	;	PUNCT
ejpam-2010	408	56	(	(	PUNCT
ejpam-2010	408	57	4	4	X
ejpam-2010	408	58	)	)	PUNCT
ejpam-2010	408	59	there	there	PRON
ejpam-2010	408	60	exists	exist	VERB
ejpam-2010	408	61	a	a	DET
ejpam-2010	408	62	unitary	unitary	ADJ
ejpam-2010	408	63	morita	morita	NOUN
ejpam-2010	408	64	context	context	NOUN
ejpam-2010	408	65	(	(	PUNCT
ejpam-2010	408	66	s	s	PROPN
ejpam-2010	408	67	,	,	PUNCT
ejpam-2010	408	68	t	t	PROPN
ejpam-2010	408	69	,	,	PUNCT
ejpam-2010	408	70	p	p	X
ejpam-2010	408	71	,	,	PUNCT
ejpam-2010	408	72	q	q	ADJ
ejpam-2010	408	73	,	,	PUNCT
ejpam-2010	408	74	〈	〈	PROPN
ejpam-2010	408	75	,	,	PUNCT
ejpam-2010	408	76	〉	〉	NOUN
ejpam-2010	408	77	,	,	PUNCT
ejpam-2010	408	78	[	[	X
ejpam-2010	408	79	,	,	PUNCT
ejpam-2010	408	80	]	]	X
ejpam-2010	408	81	)	)	PUNCT
ejpam-2010	408	82	with	with	ADP
ejpam-2010	408	83	surjective	surjective	ADJ
ejpam-2010	408	84	mappings	mapping	NOUN
ejpam-2010	408	85	.	.	PUNCT
ejpam-2010	409	1	it	it	PRON
ejpam-2010	409	2	is	be	AUX
ejpam-2010	409	3	now	now	ADV
ejpam-2010	409	4	worth	worth	ADJ
ejpam-2010	409	5	to	to	PART
ejpam-2010	409	6	give	give	VERB
ejpam-2010	409	7	a	a	DET
ejpam-2010	409	8	short	short	ADJ
ejpam-2010	409	9	remark	remark	NOUN
ejpam-2010	409	10	about	about	ADP
ejpam-2010	409	11	the	the	DET
ejpam-2010	409	12	proof	proof	NOUN
ejpam-2010	409	13	of	of	ADP
ejpam-2010	409	14	theorem	theorem	NOUN
ejpam-2010	409	15	9	9	NUM
ejpam-2010	409	16	.	.	PUNCT
ejpam-2010	409	17	from	from	ADP
ejpam-2010	409	18	(	(	PUNCT
ejpam-2010	409	19	1	1	NUM
ejpam-2010	409	20	)	)	PUNCT
ejpam-2010	409	21	to	to	ADP
ejpam-2010	409	22	(	(	PUNCT
ejpam-2010	409	23	2	2	NUM
ejpam-2010	409	24	)	)	PUNCT
ejpam-2010	409	25	.	.	PUNCT
ejpam-2010	410	1	let	let	VERB
ejpam-2010	410	2	s	s	PRON
ejpam-2010	410	3	and	and	CCONJ
ejpam-2010	410	4	t	t	PROPN
ejpam-2010	410	5	be	be	AUX
ejpam-2010	410	6	morita	morita	PROPN
ejpam-2010	410	7	equivalent	equivalent	ADJ
ejpam-2010	410	8	via	via	ADP
ejpam-2010	410	9	inverse	inverse	NOUN
ejpam-2010	410	10	functors	functors	PROPN
ejpam-2010	410	11	g	g	NOUN
ejpam-2010	410	12	:	:	PUNCT
ejpam-2010	410	13	s	s	VERB
ejpam-2010	410	14	−	−	PROPN
ejpam-2010	410	15	fact	fact	NOUN
ejpam-2010	410	16	→	→	PUNCT
ejpam-2010	410	17	t	t	NOUN
ejpam-2010	410	18	−	−	DET
ejpam-2010	410	19	fact	fact	NOUN
ejpam-2010	410	20	and	and	CCONJ
ejpam-2010	410	21	h	h	NOUN
ejpam-2010	411	1	:	:	PUNCT
ejpam-2010	411	2	t	t	PROPN
ejpam-2010	412	1	−	−	DET
ejpam-2010	412	2	fact	fact	NOUN
ejpam-2010	412	3	→	→	SYM
ejpam-2010	412	4	s	s	VERB
ejpam-2010	412	5	−	−	NOUN
ejpam-2010	412	6	fact	fact	NOUN
ejpam-2010	412	7	.	.	PUNCT
ejpam-2010	413	1	notice	notice	VERB
ejpam-2010	413	2	that	that	SCONJ
ejpam-2010	413	3	if	if	SCONJ
ejpam-2010	413	4	m	m	NOUN
ejpam-2010	413	5	is	be	AUX
ejpam-2010	413	6	an	an	DET
ejpam-2010	413	7	indecomposable	indecomposable	ADJ
ejpam-2010	413	8	projective	projective	NOUN
ejpam-2010	413	9	in	in	ADP
ejpam-2010	413	10	s	s	NOUN
ejpam-2010	413	11	-	-	NOUN
ejpam-2010	413	12	fact	fact	NOUN
ejpam-2010	413	13	then	then	ADV
ejpam-2010	413	14	g(m	g(m	VERB
ejpam-2010	413	15	)	)	PUNCT
ejpam-2010	413	16	is	be	AUX
ejpam-2010	413	17	an	an	DET
ejpam-2010	413	18	indecomposable	indecomposable	ADJ
ejpam-2010	413	19	projective	projective	NOUN
ejpam-2010	413	20	in	in	ADP
ejpam-2010	413	21	t	t	PROPN
ejpam-2010	413	22	-fact	-fact	NOUN
ejpam-2010	413	23	.	.	PUNCT
ejpam-2010	414	1	thus	thus	ADV
ejpam-2010	414	2	g	g	PROPN
ejpam-2010	414	3	maps	map	VERB
ejpam-2010	414	4	the	the	DET
ejpam-2010	414	5	full	full	ADJ
ejpam-2010	414	6	subcategory	subcategory	NOUN
ejpam-2010	414	7	of	of	ADP
ejpam-2010	414	8	indecomposable	indecomposable	ADJ
ejpam-2010	414	9	projectives	projective	NOUN
ejpam-2010	414	10	in	in	ADP
ejpam-2010	414	11	s	s	NOUN
ejpam-2010	414	12	-	-	NOUN
ejpam-2010	414	13	fact	fact	NOUN
ejpam-2010	414	14	to	to	ADP
ejpam-2010	414	15	the	the	DET
ejpam-2010	414	16	full	full	ADJ
ejpam-2010	414	17	subcategory	subcategory	NOUN
ejpam-2010	414	18	of	of	ADP
ejpam-2010	414	19	indecomposable	indecomposable	ADJ
ejpam-2010	414	20	projectives	projective	NOUN
ejpam-2010	414	21	in	in	ADP
ejpam-2010	414	22	t	t	NOUN
ejpam-2010	414	23	-fact	-fact	NOUN
ejpam-2010	414	24	,	,	PUNCT
ejpam-2010	414	25	and	and	CCONJ
ejpam-2010	414	26	h	h	NOUN
ejpam-2010	414	27	does	do	VERB
ejpam-2010	414	28	the	the	DET
ejpam-2010	414	29	same	same	ADJ
ejpam-2010	414	30	in	in	ADP
ejpam-2010	414	31	the	the	DET
ejpam-2010	414	32	opposite	opposite	ADJ
ejpam-2010	414	33	direction	direction	NOUN
ejpam-2010	414	34	.	.	PUNCT
ejpam-2010	415	1	so	so	ADV
ejpam-2010	415	2	the	the	DET
ejpam-2010	415	3	full	full	ADJ
ejpam-2010	415	4	subcategory	subcategory	NOUN
ejpam-2010	415	5	of	of	ADP
ejpam-2010	415	6	indecomposable	indecomposable	ADJ
ejpam-2010	415	7	projectives	projective	NOUN
ejpam-2010	415	8	in	in	ADP
ejpam-2010	415	9	s	s	NOUN
ejpam-2010	415	10	-	-	PUNCT
ejpam-2010	415	11	fact	fact	NOUN
ejpam-2010	415	12	is	be	AUX
ejpam-2010	415	13	equivalent	equivalent	ADJ
ejpam-2010	415	14	to	to	ADP
ejpam-2010	415	15	the	the	DET
ejpam-2010	415	16	full	full	ADJ
ejpam-2010	415	17	subcategory	subcategory	NOUN
ejpam-2010	415	18	of	of	ADP
ejpam-2010	415	19	indecomposable	indecomposable	ADJ
ejpam-2010	415	20	projectives	projective	NOUN
ejpam-2010	415	21	in	in	ADP
ejpam-2010	415	22	t	t	NOUN
ejpam-2010	415	23	-fact	-fact	NOUN
ejpam-2010	415	24	.	.	PUNCT
ejpam-2010	416	1	by	by	ADP
ejpam-2010	416	2	proposition	proposition	NOUN
ejpam-2010	416	3	1	1	NUM
ejpam-2010	416	4	,	,	PUNCT
ejpam-2010	416	5	every	every	DET
ejpam-2010	416	6	indecomposable	indecomposable	ADJ
ejpam-2010	416	7	projective	projective	NOUN
ejpam-2010	416	8	in	in	ADP
ejpam-2010	416	9	s	s	NOUN
ejpam-2010	416	10	-	-	PUNCT
ejpam-2010	416	11	fact	fact	NOUN
ejpam-2010	416	12	is	be	AUX
ejpam-2010	416	13	isomorphic	isomorphic	ADJ
ejpam-2010	416	14	to	to	ADP
ejpam-2010	416	15	one	one	NUM
ejpam-2010	416	16	of	of	ADP
ejpam-2010	416	17	the	the	DET
ejpam-2010	416	18	form	form	NOUN
ejpam-2010	416	19	se	se	ADV
ejpam-2010	416	20	for	for	ADP
ejpam-2010	416	21	some	some	DET
ejpam-2010	416	22	idempotent	idempotent	NOUN
ejpam-2010	416	23	e.	e.	PROPN
ejpam-2010	416	24	let	let	VERB
ejpam-2010	416	25	ips	ip	NOUN
ejpam-2010	416	26	be	be	AUX
ejpam-2010	416	27	the	the	DET
ejpam-2010	416	28	full	full	ADJ
ejpam-2010	416	29	subcategory	subcategory	NOUN
ejpam-2010	416	30	of	of	ADP
ejpam-2010	416	31	s	s	NOUN
ejpam-2010	416	32	-	-	VERB
ejpam-2010	416	33	fact	fact	NOUN
ejpam-2010	416	34	whose	whose	DET
ejpam-2010	416	35	objects	object	NOUN
ejpam-2010	416	36	are	be	AUX
ejpam-2010	416	37	all	all	DET
ejpam-2010	416	38	the	the	DET
ejpam-2010	416	39	left	left	ADJ
ejpam-2010	416	40	closed	closed	ADJ
ejpam-2010	416	41	s	s	NOUN
ejpam-2010	416	42	-	-	PUNCT
ejpam-2010	416	43	acts	act	NOUN
ejpam-2010	416	44	of	of	ADP
ejpam-2010	416	45	the	the	DET
ejpam-2010	416	46	form	form	NOUN
ejpam-2010	416	47	se	se	X
ejpam-2010	416	48	where	where	SCONJ
ejpam-2010	416	49	e	e	PROPN
ejpam-2010	416	50	ranges	range	VERB
ejpam-2010	416	51	over	over	ADP
ejpam-2010	416	52	all	all	DET
ejpam-2010	416	53	idempotents	idempotent	NOUN
ejpam-2010	416	54	of	of	ADP
ejpam-2010	416	55	s.	s.	PROPN
ejpam-2010	416	56	then	then	ADV
ejpam-2010	416	57	the	the	DET
ejpam-2010	416	58	full	full	ADJ
ejpam-2010	416	59	subcategory	subcategory	NOUN
ejpam-2010	416	60	of	of	ADP
ejpam-2010	416	61	indecomposable	indecomposable	ADJ
ejpam-2010	416	62	projectives	projective	NOUN
ejpam-2010	416	63	in	in	ADP
ejpam-2010	416	64	s	s	NOUN
ejpam-2010	416	65	-	-	PUNCT
ejpam-2010	416	66	fact	fact	NOUN
ejpam-2010	416	67	is	be	AUX
ejpam-2010	416	68	equivalent	equivalent	ADJ
ejpam-2010	416	69	to	to	ADP
ejpam-2010	416	70	ips	ip	NOUN
ejpam-2010	416	71	.	.	PUNCT
ejpam-2010	417	1	similarly	similarly	ADV
ejpam-2010	417	2	,	,	PUNCT
ejpam-2010	417	3	the	the	DET
ejpam-2010	417	4	full	full	ADJ
ejpam-2010	417	5	subcategory	subcategory	NOUN
ejpam-2010	417	6	of	of	ADP
ejpam-2010	417	7	indecomposable	indecomposable	ADJ
ejpam-2010	417	8	projectives	projective	NOUN
ejpam-2010	417	9	in	in	ADP
ejpam-2010	417	10	t	t	PROPN
ejpam-2010	417	11	fact	fact	NOUN
ejpam-2010	417	12	is	be	AUX
ejpam-2010	417	13	equivalent	equivalent	ADJ
ejpam-2010	417	14	to	to	PART
ejpam-2010	417	15	ipt	ipt	VERB
ejpam-2010	417	16	.	.	PUNCT
ejpam-2010	418	1	it	it	PRON
ejpam-2010	418	2	follows	follow	VERB
ejpam-2010	418	3	that	that	SCONJ
ejpam-2010	418	4	ips	ip	NOUN
ejpam-2010	418	5	is	be	AUX
ejpam-2010	418	6	equivalent	equivalent	ADJ
ejpam-2010	418	7	to	to	PART
ejpam-2010	418	8	ipt	ipt	VERB
ejpam-2010	418	9	.	.	PUNCT
ejpam-2010	419	1	let	let	VERB
ejpam-2010	419	2	α	α	NOUN
ejpam-2010	419	3	:	:	PUNCT
ejpam-2010	419	4	se→	se→	PROPN
ejpam-2010	419	5	s	s	X
ejpam-2010	419	6	f	f	AUX
ejpam-2010	419	7	be	be	AUX
ejpam-2010	419	8	a	a	DET
ejpam-2010	419	9	left	left	ADJ
ejpam-2010	419	10	s	s	NOUN
ejpam-2010	419	11	-	-	NOUN
ejpam-2010	419	12	homomorphism	homomorphism	NOUN
ejpam-2010	419	13	.	.	PUNCT
ejpam-2010	420	1	put	put	AUX
ejpam-2010	420	2	a	a	DET
ejpam-2010	420	3	=	=	NOUN
ejpam-2010	420	4	eα	eα	NOUN
ejpam-2010	420	5	.	.	NOUN
ejpam-2010	420	6	define	define	VERB
ejpam-2010	420	7	a	a	DET
ejpam-2010	420	8	functor	functor	PROPN
ejpam-2010	420	9	f	f	PROPN
ejpam-2010	420	10	of	of	ADP
ejpam-2010	420	11	c(s	c(	NOUN
ejpam-2010	420	12	)	)	PUNCT
ejpam-2010	420	13	by	by	ADP
ejpam-2010	420	14	:	:	PUNCT
ejpam-2010	420	15	f(e	f(e	NOUN
ejpam-2010	420	16	)	)	PUNCT
ejpam-2010	420	17	=	=	PUNCT
ejpam-2010	420	18	se	se	X
ejpam-2010	420	19	for	for	ADP
ejpam-2010	420	20	all	all	DET
ejpam-2010	420	21	e	e	PROPN
ejpam-2010	420	22	∈	∈	PROPN
ejpam-2010	420	23	e(s	e(s	PROPN
ejpam-2010	420	24	)	)	PUNCT
ejpam-2010	420	25	,	,	PUNCT
ejpam-2010	420	26	f(e	f(e	PROPN
ejpam-2010	420	27	,	,	PUNCT
ejpam-2010	420	28	a	a	PRON
ejpam-2010	420	29	,	,	PUNCT
ejpam-2010	420	30	f	f	NOUN
ejpam-2010	420	31	)	)	PUNCT
ejpam-2010	421	1	=	=	SYM
ejpam-2010	421	2	ρa	ρa	PROPN
ejpam-2010	421	3	:	:	PUNCT
ejpam-2010	421	4	se→	se→	PROPN
ejpam-2010	421	5	s	s	X
ejpam-2010	421	6	f	f	PROPN
ejpam-2010	421	7	,	,	PUNCT
ejpam-2010	421	8	xρa	xρa	PROPN
ejpam-2010	422	1	=	=	SYM
ejpam-2010	423	1	xa	xa	PROPN
ejpam-2010	423	2	for	for	ADP
ejpam-2010	423	3	all	all	DET
ejpam-2010	423	4	x	x	SYM
ejpam-2010	423	5	∈	∈	PROPN
ejpam-2010	423	6	se	se	X
ejpam-2010	423	7	.	.	PUNCT
ejpam-2010	424	1	then	then	ADV
ejpam-2010	424	2	f	f	PROPN
ejpam-2010	424	3	is	be	AUX
ejpam-2010	424	4	a	a	DET
ejpam-2010	424	5	full	full	ADJ
ejpam-2010	424	6	and	and	CCONJ
ejpam-2010	424	7	faithful	faithful	ADJ
ejpam-2010	424	8	functor	functor	NOUN
ejpam-2010	424	9	and	and	CCONJ
ejpam-2010	424	10	so	so	ADV
ejpam-2010	424	11	c(s	c(	NOUN
ejpam-2010	424	12	)	)	PUNCT
ejpam-2010	424	13	is	be	AUX
ejpam-2010	424	14	equivalent	equivalent	ADJ
ejpam-2010	424	15	to	to	ADP
ejpam-2010	424	16	ips	ip	NOUN
ejpam-2010	424	17	.	.	PUNCT
ejpam-2010	425	1	hence	hence	ADV
ejpam-2010	425	2	c(s	c(	NOUN
ejpam-2010	425	3	)	)	PUNCT
ejpam-2010	425	4	and	and	CCONJ
ejpam-2010	425	5	c(t	c(t	PROPN
ejpam-2010	425	6	)	)	PUNCT
ejpam-2010	425	7	are	be	AUX
ejpam-2010	425	8	equivalent	equivalent	ADJ
ejpam-2010	425	9	.	.	PUNCT
ejpam-2010	426	1	from	from	ADP
ejpam-2010	426	2	(	(	PUNCT
ejpam-2010	426	3	2	2	NUM
ejpam-2010	426	4	)	)	PUNCT
ejpam-2010	426	5	to	to	ADP
ejpam-2010	426	6	(	(	PUNCT
ejpam-2010	426	7	3	3	NUM
ejpam-2010	426	8	)	)	PUNCT
ejpam-2010	426	9	.	.	PUNCT
ejpam-2010	427	1	let	let	VERB
ejpam-2010	427	2	s	s	PRON
ejpam-2010	427	3	and	and	CCONJ
ejpam-2010	427	4	t	t	PROPN
ejpam-2010	427	5	be	be	VERB
ejpam-2010	427	6	semigroups	semigroup	NOUN
ejpam-2010	427	7	with	with	ADP
ejpam-2010	427	8	local	local	ADJ
ejpam-2010	427	9	units	unit	NOUN
ejpam-2010	427	10	.	.	PUNCT
ejpam-2010	428	1	if	if	SCONJ
ejpam-2010	428	2	the	the	DET
ejpam-2010	428	3	categories	category	NOUN
ejpam-2010	428	4	c(s	c(	VERB
ejpam-2010	428	5	)	)	PUNCT
ejpam-2010	428	6	and	and	CCONJ
ejpam-2010	428	7	c(t	c(t	PROPN
ejpam-2010	428	8	)	)	PUNCT
ejpam-2010	428	9	are	be	AUX
ejpam-2010	428	10	equivalent	equivalent	ADJ
ejpam-2010	428	11	,	,	PUNCT
ejpam-2010	428	12	then	then	ADV
ejpam-2010	428	13	we	we	PRON
ejpam-2010	428	14	can	can	AUX
ejpam-2010	428	15	construct	construct	VERB
ejpam-2010	428	16	a	a	DET
ejpam-2010	428	17	bipartite	bipartite	ADJ
ejpam-2010	428	18	category	category	NOUN
ejpam-2010	428	19	c	c	NOUN
ejpam-2010	429	1	=	=	PUNCT
ejpam-2010	430	1	[	[	X
ejpam-2010	430	2	c(s	c(	NOUN
ejpam-2010	430	3	)	)	PUNCT
ejpam-2010	430	4	,	,	PUNCT
ejpam-2010	430	5	c(t	c(t	PROPN
ejpam-2010	430	6	)	)	PUNCT
ejpam-2010	430	7	]	]	PUNCT
ejpam-2010	430	8	where	where	SCONJ
ejpam-2010	430	9	c(s	c(	NOUN
ejpam-2010	430	10	)	)	PUNCT
ejpam-2010	430	11	and	and	CCONJ
ejpam-2010	430	12	c(t	c(t	PROPN
ejpam-2010	430	13	)	)	PUNCT
ejpam-2010	430	14	are	be	AUX
ejpam-2010	430	15	strongly	strongly	ADV
ejpam-2010	430	16	connected	connect	VERB
ejpam-2010	430	17	,	,	PUNCT
ejpam-2010	430	18	and	and	CCONJ
ejpam-2010	430	19	so	so	ADV
ejpam-2010	430	20	c	c	PROPN
ejpam-2010	430	21	is	be	AUX
ejpam-2010	430	22	strongly	strongly	ADV
ejpam-2010	430	23	connected	connect	VERB
ejpam-2010	430	24	.	.	PUNCT
ejpam-2010	431	1	for	for	ADP
ejpam-2010	431	2	any	any	DET
ejpam-2010	431	3	e	e	PROPN
ejpam-2010	431	4	∈	∈	PROPN
ejpam-2010	431	5	e(s	e(s	PROPN
ejpam-2010	431	6	)	)	PUNCT
ejpam-2010	431	7	,	,	PUNCT
ejpam-2010	431	8	we	we	PRON
ejpam-2010	431	9	denote	denote	VERB
ejpam-2010	431	10	the	the	DET
ejpam-2010	431	11	identity	identity	NOUN
ejpam-2010	431	12	(	(	PUNCT
ejpam-2010	431	13	e	e	NOUN
ejpam-2010	431	14	,	,	PUNCT
ejpam-2010	431	15	e	e	NOUN
ejpam-2010	431	16	,	,	PUNCT
ejpam-2010	431	17	e	e	NOUN
ejpam-2010	431	18	)	)	PUNCT
ejpam-2010	431	19	of	of	ADP
ejpam-2010	431	20	c(s	c(	NOUN
ejpam-2010	431	21	)	)	PUNCT
ejpam-2010	431	22	by	by	ADP
ejpam-2010	431	23	ē.	ē.	NOUN
ejpam-2010	431	24	on	on	ADP
ejpam-2010	431	25	c(s	c(	NOUN
ejpam-2010	431	26	)	)	PUNCT
ejpam-2010	431	27	we	we	PRON
ejpam-2010	431	28	define	define	VERB
ejpam-2010	431	29	the	the	DET
ejpam-2010	431	30	consolidation	consolidation	NOUN
ejpam-2010	431	31	p	p	NOUN
ejpam-2010	431	32	by	by	ADP
ejpam-2010	431	33	pe	pe	PROPN
ejpam-2010	431	34	,	,	PUNCT
ejpam-2010	431	35	f	f	PROPN
ejpam-2010	431	36	=	=	SYM
ejpam-2010	431	37	(	(	PUNCT
ejpam-2010	431	38	e	e	NOUN
ejpam-2010	431	39	,	,	PUNCT
ejpam-2010	431	40	e	e	PROPN
ejpam-2010	431	41	f	f	PROPN
ejpam-2010	431	42	,	,	PUNCT
ejpam-2010	431	43	f	f	PROPN
ejpam-2010	431	44	)	)	PUNCT
ejpam-2010	431	45	.	.	PUNCT
ejpam-2010	432	1	the	the	DET
ejpam-2010	432	2	function	function	NOUN
ejpam-2010	432	3	π\1	π\1	NOUN
ejpam-2010	432	4	:	:	PUNCT
ejpam-2010	432	5	c(s)p	c(s)p	PROPN
ejpam-2010	432	6	→	→	PUNCT
ejpam-2010	432	7	s	s	AUX
ejpam-2010	432	8	given	give	VERB
ejpam-2010	432	9	by	by	ADP
ejpam-2010	432	10	(	(	PUNCT
ejpam-2010	432	11	e	e	NOUN
ejpam-2010	432	12	,	,	PUNCT
ejpam-2010	432	13	s	s	X
ejpam-2010	432	14	,	,	PUNCT
ejpam-2010	432	15	f	f	PROPN
ejpam-2010	432	16	)	)	PUNCT
ejpam-2010	432	17	→	→	X
ejpam-2010	432	18	s	s	PART
ejpam-2010	432	19	is	be	AUX
ejpam-2010	432	20	a	a	DET
ejpam-2010	432	21	surjective	surjective	ADJ
ejpam-2010	432	22	homomorphism	homomorphism	NOUN
ejpam-2010	432	23	.	.	PUNCT
ejpam-2010	433	1	for	for	ADP
ejpam-2010	433	2	any	any	DET
ejpam-2010	433	3	i	i	NOUN
ejpam-2010	433	4	∈	∈	PROPN
ejpam-2010	433	5	e(t	e(t	PROPN
ejpam-2010	433	6	)	)	PUNCT
ejpam-2010	433	7	,	,	PUNCT
ejpam-2010	433	8	we	we	PRON
ejpam-2010	433	9	denote	denote	VERB
ejpam-2010	433	10	the	the	DET
ejpam-2010	433	11	identity	identity	NOUN
ejpam-2010	433	12	(	(	PUNCT
ejpam-2010	433	13	i	i	PRON
ejpam-2010	433	14	,	,	PUNCT
ejpam-2010	433	15	i	i	PRON
ejpam-2010	433	16	,	,	PUNCT
ejpam-2010	433	17	i	i	PROPN
ejpam-2010	433	18	)	)	PUNCT
ejpam-2010	433	19	of	of	ADP
ejpam-2010	433	20	c(s	c(	NOUN
ejpam-2010	433	21	)	)	PUNCT
ejpam-2010	433	22	by	by	ADP
ejpam-2010	433	23	î.	î.	VERB
ejpam-2010	433	24	on	on	ADP
ejpam-2010	433	25	c(t	c(t	PROPN
ejpam-2010	433	26	)	)	PUNCT
ejpam-2010	433	27	we	we	PRON
ejpam-2010	433	28	define	define	VERB
ejpam-2010	433	29	the	the	DET
ejpam-2010	433	30	consolidation	consolidation	NOUN
ejpam-2010	433	31	q	q	PUNCT
ejpam-2010	433	32	by	by	ADP
ejpam-2010	433	33	qi	qi	PROPN
ejpam-2010	433	34	,	,	PUNCT
ejpam-2010	433	35	j	j	PROPN
ejpam-2010	434	1	=	=	PRON
ejpam-2010	434	2	(	(	PUNCT
ejpam-2010	434	3	i	i	PROPN
ejpam-2010	434	4	,	,	PUNCT
ejpam-2010	434	5	i	i	PROPN
ejpam-2010	434	6	j	j	PROPN
ejpam-2010	434	7	,	,	PUNCT
ejpam-2010	434	8	j	j	PROPN
ejpam-2010	434	9	)	)	PUNCT
ejpam-2010	434	10	.	.	PUNCT
ejpam-2010	435	1	the	the	DET
ejpam-2010	435	2	function	function	NOUN
ejpam-2010	435	3	π\2	π\2	PROPN
ejpam-2010	435	4	:	:	PUNCT
ejpam-2010	435	5	c(t	c(t	PROPN
ejpam-2010	435	6	)	)	PUNCT
ejpam-2010	435	7	q→	q→	PROPN
ejpam-2010	435	8	t	t	PROPN
ejpam-2010	435	9	given	give	VERB
ejpam-2010	435	10	by	by	ADP
ejpam-2010	435	11	(	(	PUNCT
ejpam-2010	435	12	i	i	PROPN
ejpam-2010	435	13	,	,	PUNCT
ejpam-2010	435	14	t	t	PROPN
ejpam-2010	435	15	,	,	PUNCT
ejpam-2010	435	16	j)→	j)→	PROPN
ejpam-2010	435	17	t	t	PROPN
ejpam-2010	435	18	is	be	AUX
ejpam-2010	435	19	a	a	DET
ejpam-2010	435	20	surjective	surjective	ADJ
ejpam-2010	435	21	homomorphism	homomorphism	NOUN
ejpam-2010	435	22	.	.	PUNCT
ejpam-2010	436	1	let	let	VERB
ejpam-2010	436	2	π	π	X
ejpam-2010	436	3	be	be	AUX
ejpam-2010	436	4	the	the	DET
ejpam-2010	436	5	congruence	congruence	NOUN
ejpam-2010	436	6	on	on	ADP
ejpam-2010	436	7	c	c	NOUN
ejpam-2010	436	8	r	r	NOUN
ejpam-2010	436	9	generated	generate	VERB
ejpam-2010	436	10	by	by	ADP
ejpam-2010	436	11	π\1	π\1	PROPN
ejpam-2010	436	12	∪π	∪π	CCONJ
ejpam-2010	436	13	\	\	PROPN
ejpam-2010	436	14	2	2	NUM
ejpam-2010	436	15	.	.	PUNCT
ejpam-2010	437	1	then	then	ADV
ejpam-2010	437	2	c	c	X
ejpam-2010	437	3	r	r	PROPN
ejpam-2010	437	4	/	/	SYM
ejpam-2010	437	5	π	π	PROPN
ejpam-2010	437	6	is	be	AUX
ejpam-2010	437	7	a	a	DET
ejpam-2010	437	8	semigroup	semigroup	NOUN
ejpam-2010	437	9	with	with	ADP
ejpam-2010	437	10	local	local	ADJ
ejpam-2010	437	11	units	unit	NOUN
ejpam-2010	437	12	that	that	PRON
ejpam-2010	437	13	is	be	AUX
ejpam-2010	437	14	an	an	DET
ejpam-2010	437	15	enlargement	enlargement	NOUN
ejpam-2010	437	16	of	of	ADP
ejpam-2010	437	17	(	(	PUNCT
ejpam-2010	437	18	isomorphic	isomorphic	ADJ
ejpam-2010	437	19	copies	copy	NOUN
ejpam-2010	437	20	of	of	ADP
ejpam-2010	437	21	)	)	PUNCT
ejpam-2010	437	22	s	s	PROPN
ejpam-2010	437	23	and	and	CCONJ
ejpam-2010	437	24	t	t	PROPN
ejpam-2010	437	25	.	.	PUNCT
ejpam-2010	438	1	y.	y.	PROPN
ejpam-2010	438	2	wang	wang	PROPN
ejpam-2010	438	3	,	,	PUNCT
ejpam-2010	438	4	k.	k.	PROPN
ejpam-2010	438	5	shum	shum	PROPN
ejpam-2010	438	6	,	,	PUNCT
ejpam-2010	438	7	x.	x.	PROPN
ejpam-2010	438	8	ren	ren	PROPN
ejpam-2010	438	9	/	/	SYM
ejpam-2010	438	10	eur	eur	PROPN
ejpam-2010	438	11	.	.	PUNCT
ejpam-2010	439	1	j.	j.	PROPN
ejpam-2010	439	2	pure	pure	PROPN
ejpam-2010	439	3	appl	appl	PROPN
ejpam-2010	439	4	.	.	PROPN
ejpam-2010	439	5	math	math	PROPN
ejpam-2010	439	6	,	,	PUNCT
ejpam-2010	439	7	6	6	NUM
ejpam-2010	439	8	(	(	PUNCT
ejpam-2010	439	9	2013	2013	NUM
ejpam-2010	439	10	)	)	PUNCT
ejpam-2010	439	11	,	,	PUNCT
ejpam-2010	439	12	256	256	NUM
ejpam-2010	439	13	-	-	SYM
ejpam-2010	439	14	281	281	NUM
ejpam-2010	439	15	271	271	NUM
ejpam-2010	439	16	from	from	ADP
ejpam-2010	439	17	(	(	PUNCT
ejpam-2010	439	18	3	3	NUM
ejpam-2010	439	19	)	)	PUNCT
ejpam-2010	439	20	to	to	ADP
ejpam-2010	439	21	(	(	PUNCT
ejpam-2010	439	22	4	4	NUM
ejpam-2010	439	23	)	)	PUNCT
ejpam-2010	439	24	.	.	PUNCT
ejpam-2010	440	1	let	let	VERB
ejpam-2010	440	2	s	s	PRON
ejpam-2010	440	3	and	and	CCONJ
ejpam-2010	440	4	t	t	PROPN
ejpam-2010	440	5	have	have	VERB
ejpam-2010	440	6	a	a	DET
ejpam-2010	440	7	joint	joint	ADJ
ejpam-2010	440	8	enlargement	enlargement	NOUN
ejpam-2010	440	9	r.	r.	PROPN
ejpam-2010	440	10	put	put	VERB
ejpam-2010	440	11	p	p	NOUN
ejpam-2010	440	12	=	=	NOUN
ejpam-2010	440	13	srt	srt	NOUN
ejpam-2010	440	14	and	and	CCONJ
ejpam-2010	440	15	q	q	NOUN
ejpam-2010	440	16	=	=	PROPN
ejpam-2010	440	17	trs	trs	PROPN
ejpam-2010	440	18	.	.	PUNCT
ejpam-2010	441	1	we	we	PRON
ejpam-2010	441	2	define	define	VERB
ejpam-2010	441	3	two	two	NUM
ejpam-2010	441	4	maps	map	NOUN
ejpam-2010	441	5	〈	〈	NOUN
ejpam-2010	441	6	−,−	−,−	NOUN
ejpam-2010	441	7	〉	〉	NOUN
ejpam-2010	441	8	:	:	PUNCT
ejpam-2010	441	9	p	p	X
ejpam-2010	441	10	⊗q→	⊗q→	X
ejpam-2010	441	11	s	s	X
ejpam-2010	442	1	and	and	CCONJ
ejpam-2010	443	1	[	[	X
ejpam-2010	443	2	−,−	−,−	X
ejpam-2010	443	3	]	]	X
ejpam-2010	443	4	:	:	PUNCT
ejpam-2010	443	5	q⊗	q⊗	PROPN
ejpam-2010	443	6	p	p	PROPN
ejpam-2010	443	7	→	→	SYM
ejpam-2010	443	8	t	t	NOUN
ejpam-2010	443	9	by	by	ADP
ejpam-2010	443	10	〈	〈	PROPN
ejpam-2010	443	11	p	p	PROPN
ejpam-2010	443	12	,	,	PUNCT
ejpam-2010	443	13	q	q	SYM
ejpam-2010	443	14	〉	〉	NOUN
ejpam-2010	443	15	=	=	SYM
ejpam-2010	443	16	pq	pq	NOUN
ejpam-2010	443	17	and	and	CCONJ
ejpam-2010	443	18	[	[	X
ejpam-2010	443	19	q	q	X
ejpam-2010	443	20	,	,	PUNCT
ejpam-2010	443	21	p	p	X
ejpam-2010	443	22	]	]	X
ejpam-2010	443	23	=	=	PUNCT
ejpam-2010	443	24	qp	qp	NOUN
ejpam-2010	443	25	,	,	PUNCT
ejpam-2010	443	26	where	where	SCONJ
ejpam-2010	443	27	p	p	PROPN
ejpam-2010	443	28	∈	∈	PROPN
ejpam-2010	443	29	p	p	NOUN
ejpam-2010	443	30	and	and	CCONJ
ejpam-2010	443	31	q	q	PROPN
ejpam-2010	443	32	∈	∈	PROPN
ejpam-2010	443	33	q.	q.	NOUN
ejpam-2010	443	34	then	then	ADV
ejpam-2010	443	35	〈	〈	PROPN
ejpam-2010	443	36	s	s	PROPN
ejpam-2010	443	37	,	,	PUNCT
ejpam-2010	443	38	t	t	PROPN
ejpam-2010	443	39	,	,	PUNCT
ejpam-2010	443	40	p	p	X
ejpam-2010	443	41	,	,	PUNCT
ejpam-2010	443	42	q	q	NOUN
ejpam-2010	443	43	,	,	PUNCT
ejpam-2010	443	44	〈	〈	NOUN
ejpam-2010	443	45	−,−	−,−	X
ejpam-2010	443	46	〉	〉	NOUN
ejpam-2010	443	47	,	,	PUNCT
ejpam-2010	443	48	[	[	X
ejpam-2010	443	49	−,−	−,−	X
ejpam-2010	443	50	]	]	X
ejpam-2010	443	51	〉	〉	NOUN
ejpam-2010	443	52	forms	form	VERB
ejpam-2010	443	53	a	a	DET
ejpam-2010	443	54	unitary	unitary	ADJ
ejpam-2010	443	55	morita	morita	NOUN
ejpam-2010	443	56	context	context	NOUN
ejpam-2010	443	57	with	with	ADP
ejpam-2010	443	58	surjective	surjective	ADJ
ejpam-2010	443	59	maps	map	NOUN
ejpam-2010	443	60	.	.	PUNCT
ejpam-2010	444	1	from	from	ADP
ejpam-2010	444	2	(	(	PUNCT
ejpam-2010	444	3	4	4	NUM
ejpam-2010	444	4	)	)	PUNCT
ejpam-2010	444	5	to	to	ADP
ejpam-2010	444	6	(	(	PUNCT
ejpam-2010	444	7	1	1	NUM
ejpam-2010	444	8	)	)	PUNCT
ejpam-2010	444	9	.	.	PUNCT
ejpam-2010	445	1	let	let	VERB
ejpam-2010	445	2	〈	〈	PROPN
ejpam-2010	445	3	s	s	PART
ejpam-2010	445	4	,	,	PUNCT
ejpam-2010	445	5	t	t	PROPN
ejpam-2010	445	6	,	,	PUNCT
ejpam-2010	445	7	p	p	X
ejpam-2010	445	8	,	,	PUNCT
ejpam-2010	445	9	q	q	NOUN
ejpam-2010	445	10	,	,	PUNCT
ejpam-2010	445	11	〈	〈	NOUN
ejpam-2010	445	12	−,−	−,−	X
ejpam-2010	445	13	〉	〉	NOUN
ejpam-2010	445	14	,	,	PUNCT
ejpam-2010	445	15	[	[	X
ejpam-2010	445	16	−,−	−,−	X
ejpam-2010	445	17	]	]	X
ejpam-2010	445	18	〉	〉	NOUN
ejpam-2010	445	19	be	be	VERB
ejpam-2010	445	20	a	a	DET
ejpam-2010	445	21	unitary	unitary	ADJ
ejpam-2010	445	22	morita	morita	NOUN
ejpam-2010	445	23	context	context	NOUN
ejpam-2010	445	24	with	with	ADP
ejpam-2010	445	25	surjective	surjective	ADJ
ejpam-2010	445	26	maps	map	NOUN
ejpam-2010	445	27	.	.	PUNCT
ejpam-2010	446	1	then	then	ADV
ejpam-2010	446	2	there	there	PRON
ejpam-2010	446	3	exist	exist	VERB
ejpam-2010	446	4	two	two	NUM
ejpam-2010	446	5	inverse	inverse	NOUN
ejpam-2010	446	6	functors	functor	NOUN
ejpam-2010	446	7	q⊗−	q⊗−	PROPN
ejpam-2010	446	8	:	:	PUNCT
ejpam-2010	446	9	s−fact→	s−fact→	NOUN
ejpam-2010	446	10	t−	t−	DET
ejpam-2010	446	11	fact	fact	NOUN
ejpam-2010	446	12	and	and	CCONJ
ejpam-2010	446	13	p	p	NOUN
ejpam-2010	446	14	⊗−	⊗−	NOUN
ejpam-2010	446	15	:	:	PUNCT
ejpam-2010	446	16	t−fact→	t−fact→	PROPN
ejpam-2010	446	17	s−	s−	PROPN
ejpam-2010	446	18	fact	fact	NOUN
ejpam-2010	446	19	,	,	PUNCT
ejpam-2010	446	20	and	and	CCONJ
ejpam-2010	446	21	thus	thus	ADV
ejpam-2010	446	22	s	s	PART
ejpam-2010	446	23	and	and	CCONJ
ejpam-2010	446	24	t	t	PROPN
ejpam-2010	446	25	are	be	AUX
ejpam-2010	446	26	morita	morita	PROPN
ejpam-2010	446	27	equivalent	equivalent	PROPN
ejpam-2010	446	28	.	.	PUNCT
ejpam-2010	447	1	observe	observe	VERB
ejpam-2010	447	2	that	that	PRON
ejpam-2010	447	3	to	to	PART
ejpam-2010	447	4	characterise	characterise	VERB
ejpam-2010	447	5	two	two	NUM
ejpam-2010	447	6	semigroups	semigroup	NOUN
ejpam-2010	447	7	being	be	AUX
ejpam-2010	447	8	morita	morita	NOUN
ejpam-2010	447	9	equivalent	equivalent	NOUN
ejpam-2010	447	10	there	there	PRON
ejpam-2010	447	11	exists	exist	VERB
ejpam-2010	447	12	another	another	DET
ejpam-2010	447	13	method	method	NOUN
ejpam-2010	447	14	using	use	VERB
ejpam-2010	447	15	a	a	DET
ejpam-2010	447	16	consolidation	consolidation	NOUN
ejpam-2010	447	17	and	and	CCONJ
ejpam-2010	447	18	a	a	DET
ejpam-2010	447	19	local	local	ADJ
ejpam-2010	447	20	isomorphism	isomorphism	NOUN
ejpam-2010	447	21	as	as	SCONJ
ejpam-2010	447	22	follows	follow	VERB
ejpam-2010	447	23	:	:	PUNCT
ejpam-2010	447	24	theorem	theorem	NOUN
ejpam-2010	447	25	10	10	NUM
ejpam-2010	447	26	.	.	PUNCT
ejpam-2010	448	1	[	[	X
ejpam-2010	448	2	25	25	NUM
ejpam-2010	448	3	,	,	PUNCT
ejpam-2010	448	4	theorem	theorem	VERB
ejpam-2010	448	5	1.2	1.2	NUM
ejpam-2010	448	6	]	]	PUNCT
ejpam-2010	448	7	let	let	VERB
ejpam-2010	448	8	s	s	PRON
ejpam-2010	448	9	and	and	CCONJ
ejpam-2010	448	10	t	t	PROPN
ejpam-2010	448	11	be	be	VERB
ejpam-2010	448	12	semigroups	semigroup	NOUN
ejpam-2010	448	13	with	with	ADP
ejpam-2010	448	14	local	local	ADJ
ejpam-2010	448	15	units	unit	NOUN
ejpam-2010	448	16	.	.	PUNCT
ejpam-2010	449	1	then	then	ADV
ejpam-2010	449	2	s	s	VERB
ejpam-2010	449	3	and	and	CCONJ
ejpam-2010	449	4	t	t	PROPN
ejpam-2010	449	5	are	be	AUX
ejpam-2010	449	6	morita	morita	NOUN
ejpam-2010	449	7	equivalent	equivalent	ADJ
ejpam-2010	449	8	if	if	SCONJ
ejpam-2010	450	1	and	and	CCONJ
ejpam-2010	450	2	only	only	ADV
ejpam-2010	450	3	if	if	SCONJ
ejpam-2010	450	4	there	there	PRON
ejpam-2010	450	5	is	be	VERB
ejpam-2010	450	6	a	a	DET
ejpam-2010	450	7	consolidation	consolidation	NOUN
ejpam-2010	450	8	q	q	NOUN
ejpam-2010	450	9	on	on	ADP
ejpam-2010	450	10	c(s	c(	NOUN
ejpam-2010	450	11	)	)	PUNCT
ejpam-2010	450	12	and	and	CCONJ
ejpam-2010	450	13	a	a	DET
ejpam-2010	450	14	local	local	ADJ
ejpam-2010	450	15	isomorphism	isomorphism	NOUN
ejpam-2010	450	16	ψ	ψ	X
ejpam-2010	450	17	:	:	PUNCT
ejpam-2010	450	18	c(s)q→	c(s)q→	X
ejpam-2010	450	19	t.	t.	NOUN
ejpam-2010	450	20	the	the	DET
ejpam-2010	450	21	following	follow	VERB
ejpam-2010	450	22	is	be	AUX
ejpam-2010	450	23	a	a	DET
ejpam-2010	450	24	list	list	NOUN
ejpam-2010	450	25	of	of	ADP
ejpam-2010	450	26	morita	morita	PROPN
ejpam-2010	450	27	invariant	invariant	PROPN
ejpam-2010	450	28	properties	property	NOUN
ejpam-2010	450	29	.	.	PUNCT
ejpam-2010	451	1	these	these	PRON
ejpam-2010	451	2	go	go	VERB
ejpam-2010	451	3	back	back	ADV
ejpam-2010	451	4	to	to	ADP
ejpam-2010	451	5	results	result	NOUN
ejpam-2010	451	6	obtained	obtain	VERB
ejpam-2010	451	7	for	for	ADP
ejpam-2010	451	8	enlargements	enlargement	NOUN
ejpam-2010	451	9	[	[	X
ejpam-2010	451	10	23	23	NUM
ejpam-2010	451	11	]	]	PUNCT
ejpam-2010	451	12	,	,	PUNCT
ejpam-2010	451	13	and	and	CCONJ
ejpam-2010	451	14	they	they	PRON
ejpam-2010	451	15	were	be	AUX
ejpam-2010	451	16	known	know	VERB
ejpam-2010	451	17	from	from	ADP
ejpam-2010	451	18	the	the	DET
ejpam-2010	451	19	morita	morita	PROPN
ejpam-2010	451	20	framework	framework	NOUN
ejpam-2010	451	21	to	to	ADP
ejpam-2010	451	22	talwar	talwar	PROPN
ejpam-2010	452	1	[	[	X
ejpam-2010	452	2	43	43	NUM
ejpam-2010	452	3	,	,	PUNCT
ejpam-2010	452	4	45	45	NUM
ejpam-2010	452	5	]	]	PUNCT
ejpam-2010	452	6	.	.	PUNCT
ejpam-2010	453	1	proposition	proposition	NOUN
ejpam-2010	453	2	6	6	NUM
ejpam-2010	453	3	.	.	PUNCT
ejpam-2010	454	1	[	[	X
ejpam-2010	454	2	25	25	NUM
ejpam-2010	454	3	,	,	PUNCT
ejpam-2010	454	4	proposition	proposition	NOUN
ejpam-2010	454	5	5.1	5.1	NUM
ejpam-2010	454	6	]	]	PUNCT
ejpam-2010	454	7	let	let	VERB
ejpam-2010	454	8	s	s	PRON
ejpam-2010	454	9	and	and	CCONJ
ejpam-2010	454	10	t	t	PROPN
ejpam-2010	454	11	be	be	VERB
ejpam-2010	454	12	semigroups	semigroup	NOUN
ejpam-2010	454	13	with	with	ADP
ejpam-2010	454	14	local	local	ADJ
ejpam-2010	454	15	units	unit	NOUN
ejpam-2010	454	16	which	which	PRON
ejpam-2010	454	17	are	be	AUX
ejpam-2010	454	18	morita	morita	PROPN
ejpam-2010	454	19	equivalent	equivalent	NOUN
ejpam-2010	454	20	.	.	PUNCT
ejpam-2010	455	1	then	then	ADV
ejpam-2010	455	2	(	(	PUNCT
ejpam-2010	455	3	1	1	X
ejpam-2010	455	4	)	)	PUNCT
ejpam-2010	455	5	each	each	DET
ejpam-2010	455	6	local	local	ADJ
ejpam-2010	455	7	submonoid	submonoid	NOUN
ejpam-2010	455	8	of	of	ADP
ejpam-2010	455	9	s	s	NOUN
ejpam-2010	455	10	is	be	AUX
ejpam-2010	455	11	isomorphic	isomorphic	ADJ
ejpam-2010	455	12	to	to	ADP
ejpam-2010	455	13	a	a	DET
ejpam-2010	455	14	local	local	ADJ
ejpam-2010	455	15	submonoid	submonoid	NOUN
ejpam-2010	455	16	of	of	ADP
ejpam-2010	455	17	t	t	PROPN
ejpam-2010	455	18	,	,	PUNCT
ejpam-2010	455	19	and	and	CCONJ
ejpam-2010	455	20	vice	vice	NOUN
ejpam-2010	455	21	-	-	NOUN
ejpam-2010	455	22	versa	versa	ADV
ejpam-2010	455	23	;	;	PUNCT
ejpam-2010	455	24	(	(	PUNCT
ejpam-2010	455	25	2	2	X
ejpam-2010	455	26	)	)	PUNCT
ejpam-2010	455	27	s	s	VERB
ejpam-2010	455	28	is	be	AUX
ejpam-2010	455	29	regular	regular	ADJ
ejpam-2010	455	30	if	if	SCONJ
ejpam-2010	455	31	and	and	CCONJ
ejpam-2010	455	32	only	only	ADV
ejpam-2010	455	33	if	if	SCONJ
ejpam-2010	455	34	t	t	PROPN
ejpam-2010	455	35	is	be	AUX
ejpam-2010	455	36	regular	regular	ADJ
ejpam-2010	455	37	;	;	PUNCT
ejpam-2010	455	38	(	(	PUNCT
ejpam-2010	455	39	3	3	X
ejpam-2010	455	40	)	)	PUNCT
ejpam-2010	455	41	the	the	DET
ejpam-2010	455	42	cardinalities	cardinality	NOUN
ejpam-2010	455	43	of	of	ADP
ejpam-2010	455	44	the	the	DET
ejpam-2010	455	45	sets	set	NOUN
ejpam-2010	455	46	of	of	ADP
ejpam-2010	455	47	regular	regular	ADJ
ejpam-2010	455	48	d	d	NOUN
ejpam-2010	455	49	-	-	PUNCT
ejpam-2010	455	50	classes	class	NOUN
ejpam-2010	455	51	in	in	ADP
ejpam-2010	455	52	s	s	PRON
ejpam-2010	455	53	and	and	CCONJ
ejpam-2010	455	54	t	t	PROPN
ejpam-2010	455	55	are	be	AUX
ejpam-2010	455	56	the	the	DET
ejpam-2010	455	57	same	same	ADJ
ejpam-2010	455	58	;	;	PUNCT
ejpam-2010	455	59	(	(	PUNCT
ejpam-2010	455	60	4	4	X
ejpam-2010	455	61	)	)	PUNCT
ejpam-2010	455	62	the	the	DET
ejpam-2010	455	63	posets	poset	NOUN
ejpam-2010	455	64	of	of	ADP
ejpam-2010	455	65	two	two	NUM
ejpam-2010	455	66	-	-	PUNCT
ejpam-2010	455	67	sided	sided	ADJ
ejpam-2010	455	68	ideals	ideal	NOUN
ejpam-2010	455	69	in	in	ADP
ejpam-2010	455	70	s	s	PRON
ejpam-2010	455	71	and	and	CCONJ
ejpam-2010	455	72	t	t	PROPN
ejpam-2010	455	73	are	be	AUX
ejpam-2010	455	74	order	order	NOUN
ejpam-2010	455	75	-	-	PUNCT
ejpam-2010	455	76	isomorphic	isomorphic	ADJ
ejpam-2010	455	77	.	.	PUNCT
ejpam-2010	456	1	(	(	PUNCT
ejpam-2010	456	2	5	5	X
ejpam-2010	456	3	)	)	PUNCT
ejpam-2010	456	4	the	the	DET
ejpam-2010	456	5	posets	poset	NOUN
ejpam-2010	456	6	of	of	ADP
ejpam-2010	456	7	principal	principal	ADJ
ejpam-2010	456	8	two	two	NUM
ejpam-2010	456	9	-	-	PUNCT
ejpam-2010	456	10	sided	sided	ADJ
ejpam-2010	456	11	ideals	ideal	NOUN
ejpam-2010	456	12	in	in	ADP
ejpam-2010	456	13	s	s	PRON
ejpam-2010	456	14	and	and	CCONJ
ejpam-2010	456	15	t	t	PROPN
ejpam-2010	456	16	are	be	AUX
ejpam-2010	456	17	order	order	NOUN
ejpam-2010	456	18	-	-	PUNCT
ejpam-2010	456	19	isomorphic	isomorphic	ADJ
ejpam-2010	456	20	.	.	PUNCT
ejpam-2010	457	1	the	the	DET
ejpam-2010	457	2	following	following	ADJ
ejpam-2010	457	3	result	result	NOUN
ejpam-2010	457	4	was	be	AUX
ejpam-2010	457	5	known	know	VERB
ejpam-2010	457	6	to	to	ADP
ejpam-2010	457	7	talwar	talwar	PROPN
ejpam-2010	457	8	[	[	X
ejpam-2010	457	9	44	44	NUM
ejpam-2010	457	10	]	]	PUNCT
ejpam-2010	457	11	.	.	PUNCT
ejpam-2010	458	1	it	it	PRON
ejpam-2010	458	2	shows	show	VERB
ejpam-2010	458	3	how	how	SCONJ
ejpam-2010	458	4	the	the	DET
ejpam-2010	458	5	theory	theory	NOUN
ejpam-2010	458	6	simplifies	simplify	VERB
ejpam-2010	458	7	radically	radically	ADV
ejpam-2010	458	8	when	when	SCONJ
ejpam-2010	458	9	at	at	ADV
ejpam-2010	458	10	least	least	ADV
ejpam-2010	458	11	one	one	NUM
ejpam-2010	458	12	of	of	ADP
ejpam-2010	458	13	the	the	DET
ejpam-2010	458	14	semigroups	semigroup	NOUN
ejpam-2010	458	15	is	be	AUX
ejpam-2010	458	16	a	a	DET
ejpam-2010	458	17	monoid	monoid	NOUN
ejpam-2010	458	18	.	.	PUNCT
ejpam-2010	459	1	proposition	proposition	NOUN
ejpam-2010	459	2	7	7	NUM
ejpam-2010	459	3	.	.	PUNCT
ejpam-2010	460	1	[	[	X
ejpam-2010	460	2	25	25	NUM
ejpam-2010	460	3	,	,	PUNCT
ejpam-2010	460	4	proposition	proposition	NOUN
ejpam-2010	460	5	5.2	5.2	NUM
ejpam-2010	460	6	]	]	PUNCT
ejpam-2010	460	7	let	let	VERB
ejpam-2010	460	8	s	s	PRON
ejpam-2010	460	9	be	be	AUX
ejpam-2010	460	10	a	a	DET
ejpam-2010	460	11	monoid	monoid	NOUN
ejpam-2010	460	12	and	and	CCONJ
ejpam-2010	460	13	t	t	X
ejpam-2010	460	14	a	a	DET
ejpam-2010	460	15	semigroup	semigroup	NOUN
ejpam-2010	460	16	with	with	ADP
ejpam-2010	460	17	local	local	ADJ
ejpam-2010	460	18	units	unit	NOUN
ejpam-2010	460	19	.	.	PUNCT
ejpam-2010	461	1	then	then	ADV
ejpam-2010	461	2	s	s	VERB
ejpam-2010	461	3	and	and	CCONJ
ejpam-2010	461	4	t	t	PROPN
ejpam-2010	461	5	are	be	AUX
ejpam-2010	461	6	morita	morita	NOUN
ejpam-2010	461	7	equivalent	equivalent	ADJ
ejpam-2010	461	8	if	if	SCONJ
ejpam-2010	462	1	and	and	CCONJ
ejpam-2010	462	2	only	only	ADV
ejpam-2010	462	3	if	if	SCONJ
ejpam-2010	462	4	there	there	PRON
ejpam-2010	462	5	is	be	VERB
ejpam-2010	462	6	an	an	DET
ejpam-2010	462	7	idempotent	idempotent	ADJ
ejpam-2010	462	8	f	f	NOUN
ejpam-2010	462	9	in	in	ADP
ejpam-2010	462	10	t	t	PROPN
ejpam-2010	462	11	such	such	ADJ
ejpam-2010	462	12	that	that	DET
ejpam-2010	462	13	t	t	NOUN
ejpam-2010	463	1	=	=	SYM
ejpam-2010	463	2	t	t	PROPN
ejpam-2010	463	3	f	f	PROPN
ejpam-2010	463	4	t	t	PROPN
ejpam-2010	464	1	and	and	CCONJ
ejpam-2010	464	2	f	f	PROPN
ejpam-2010	464	3	t	t	PROPN
ejpam-2010	464	4	f	f	PROPN
ejpam-2010	464	5	is	be	AUX
ejpam-2010	464	6	isomorphic	isomorphic	ADJ
ejpam-2010	464	7	to	to	ADP
ejpam-2010	464	8	s.	s.	PROPN
ejpam-2010	464	9	thus	thus	ADV
ejpam-2010	464	10	t	t	PROPN
ejpam-2010	464	11	is	be	AUX
ejpam-2010	464	12	an	an	DET
ejpam-2010	464	13	enlargement	enlargement	NOUN
ejpam-2010	464	14	of	of	ADP
ejpam-2010	464	15	s.	s.	PROPN
ejpam-2010	464	16	as	as	ADP
ejpam-2010	464	17	a	a	DET
ejpam-2010	464	18	monoid	monoid	NOUN
ejpam-2010	464	19	is	be	AUX
ejpam-2010	464	20	a	a	DET
ejpam-2010	464	21	semigroup	semigroup	NOUN
ejpam-2010	464	22	with	with	ADP
ejpam-2010	464	23	local	local	ADJ
ejpam-2010	464	24	units	unit	NOUN
ejpam-2010	464	25	,	,	PUNCT
ejpam-2010	464	26	we	we	PRON
ejpam-2010	464	27	have	have	VERB
ejpam-2010	464	28	the	the	DET
ejpam-2010	464	29	following	follow	VERB
ejpam-2010	464	30	corollaries	corollary	NOUN
ejpam-2010	464	31	.	.	PUNCT
ejpam-2010	465	1	corollary	corollary	ADJ
ejpam-2010	465	2	4	4	NUM
ejpam-2010	465	3	.	.	PUNCT
ejpam-2010	466	1	[	[	X
ejpam-2010	466	2	43	43	NUM
ejpam-2010	466	3	,	,	PUNCT
ejpam-2010	466	4	corollary	corollary	NOUN
ejpam-2010	466	5	9.2	9.2	NUM
ejpam-2010	466	6	]	]	PUNCT
ejpam-2010	466	7	the	the	DET
ejpam-2010	466	8	monoids	monoid	NOUN
ejpam-2010	466	9	m	m	VERB
ejpam-2010	466	10	and	and	CCONJ
ejpam-2010	466	11	n	n	PROPN
ejpam-2010	466	12	are	be	AUX
ejpam-2010	466	13	morita	morita	NOUN
ejpam-2010	466	14	equivalent	equivalent	ADJ
ejpam-2010	467	1	if	if	SCONJ
ejpam-2010	467	2	and	and	CCONJ
ejpam-2010	467	3	only	only	ADV
ejpam-2010	467	4	if	if	SCONJ
ejpam-2010	467	5	there	there	PRON
ejpam-2010	467	6	exists	exist	VERB
ejpam-2010	467	7	an	an	DET
ejpam-2010	467	8	idempotent	idempotent	NOUN
ejpam-2010	467	9	e	e	NOUN
ejpam-2010	467	10	∈	∈	PROPN
ejpam-2010	467	11	m	m	VERB
ejpam-2010	467	12	such	such	ADJ
ejpam-2010	467	13	that	that	SCONJ
ejpam-2010	467	14	m	m	ADV
ejpam-2010	467	15	=	=	SYM
ejpam-2010	467	16	mem	mem	ADJ
ejpam-2010	467	17	and	and	CCONJ
ejpam-2010	467	18	n	n	PRON
ejpam-2010	467	19	∼=	∼=	PART
ejpam-2010	467	20	eme	eme	NOUN
ejpam-2010	467	21	.	.	PUNCT
ejpam-2010	468	1	y.	y.	PROPN
ejpam-2010	468	2	wang	wang	PROPN
ejpam-2010	468	3	,	,	PUNCT
ejpam-2010	468	4	k.	k.	PROPN
ejpam-2010	468	5	shum	shum	PROPN
ejpam-2010	468	6	,	,	PUNCT
ejpam-2010	468	7	x.	x.	PROPN
ejpam-2010	468	8	ren	ren	PROPN
ejpam-2010	468	9	/	/	SYM
ejpam-2010	468	10	eur	eur	PROPN
ejpam-2010	468	11	.	.	PUNCT
ejpam-2010	469	1	j.	j.	PROPN
ejpam-2010	469	2	pure	pure	PROPN
ejpam-2010	469	3	appl	appl	PROPN
ejpam-2010	469	4	.	.	PROPN
ejpam-2010	469	5	math	math	PROPN
ejpam-2010	469	6	,	,	PUNCT
ejpam-2010	469	7	6	6	NUM
ejpam-2010	469	8	(	(	PUNCT
ejpam-2010	469	9	2013	2013	NUM
ejpam-2010	469	10	)	)	PUNCT
ejpam-2010	469	11	,	,	PUNCT
ejpam-2010	469	12	256	256	NUM
ejpam-2010	469	13	-	-	SYM
ejpam-2010	469	14	281	281	NUM
ejpam-2010	469	15	272	272	NUM
ejpam-2010	469	16	if	if	SCONJ
ejpam-2010	469	17	m	m	ADJ
ejpam-2010	469	18	is	be	AUX
ejpam-2010	469	19	a	a	DET
ejpam-2010	469	20	monoid	monoid	NOUN
ejpam-2010	469	21	then	then	ADV
ejpam-2010	469	22	m	m	NOUN
ejpam-2010	469	23	-fact	-fact	NOUN
ejpam-2010	469	24	is	be	AUX
ejpam-2010	469	25	in	in	ADP
ejpam-2010	469	26	fact	fact	NOUN
ejpam-2010	469	27	m	m	NOUN
ejpam-2010	469	28	-act	-act	PUNCT
ejpam-2010	469	29	as	as	SCONJ
ejpam-2010	469	30	studied	study	VERB
ejpam-2010	469	31	by	by	ADP
ejpam-2010	469	32	knauer	knauer	NOUN
ejpam-2010	469	33	.	.	PUNCT
ejpam-2010	470	1	corollary	corollary	ADJ
ejpam-2010	470	2	4	4	NUM
ejpam-2010	470	3	is	be	AUX
ejpam-2010	470	4	therefore	therefore	ADV
ejpam-2010	470	5	just	just	ADV
ejpam-2010	470	6	knauer	knauer	PROPN
ejpam-2010	470	7	’s	’s	PART
ejpam-2010	470	8	theorem	theorem	VERB
ejpam-2010	470	9	on	on	ADP
ejpam-2010	470	10	morita	morita	PROPN
ejpam-2010	470	11	equivalence	equivalence	PROPN
ejpam-2010	470	12	.	.	PUNCT
ejpam-2010	471	1	for	for	ADP
ejpam-2010	471	2	morita	morita	PROPN
ejpam-2010	471	3	equivalent	equivalent	PROPN
ejpam-2010	471	4	monoids	monoid	NOUN
ejpam-2010	471	5	we	we	PRON
ejpam-2010	471	6	still	still	ADV
ejpam-2010	471	7	have	have	VERB
ejpam-2010	471	8	the	the	DET
ejpam-2010	471	9	following	follow	VERB
ejpam-2010	471	10	properties	property	NOUN
ejpam-2010	471	11	.	.	PUNCT
ejpam-2010	472	1	corollary	corollary	ADJ
ejpam-2010	472	2	5	5	NUM
ejpam-2010	472	3	.	.	PUNCT
ejpam-2010	473	1	[	[	X
ejpam-2010	473	2	43	43	NUM
ejpam-2010	473	3	,	,	PUNCT
ejpam-2010	473	4	corollary	corollary	NOUN
ejpam-2010	473	5	9.3	9.3	NUM
ejpam-2010	473	6	]	]	PUNCT
ejpam-2010	473	7	let	let	VERB
ejpam-2010	473	8	s	s	PRON
ejpam-2010	473	9	and	and	CCONJ
ejpam-2010	473	10	t	t	PROPN
ejpam-2010	473	11	be	be	AUX
ejpam-2010	473	12	morita	morita	PROPN
ejpam-2010	473	13	equivalent	equivalent	PROPN
ejpam-2010	473	14	monoids	monoids	PROPN
ejpam-2010	473	15	.	.	PUNCT
ejpam-2010	474	1	then	then	ADV
ejpam-2010	474	2	s	s	VERB
ejpam-2010	474	3	and	and	CCONJ
ejpam-2010	474	4	t	t	PROPN
ejpam-2010	474	5	are	be	AUX
ejpam-2010	474	6	isomorphic	isomorphic	ADJ
ejpam-2010	474	7	in	in	ADP
ejpam-2010	474	8	any	any	PRON
ejpam-2010	474	9	of	of	ADP
ejpam-2010	474	10	the	the	DET
ejpam-2010	474	11	following	following	ADJ
ejpam-2010	474	12	cases	case	NOUN
ejpam-2010	474	13	:	:	PUNCT
ejpam-2010	474	14	(	(	PUNCT
ejpam-2010	474	15	1	1	X
ejpam-2010	474	16	)	)	PUNCT
ejpam-2010	474	17	s	s	VERB
ejpam-2010	474	18	is	be	AUX
ejpam-2010	474	19	a	a	DET
ejpam-2010	474	20	commutative	commutative	ADJ
ejpam-2010	474	21	monoid	monoid	NOUN
ejpam-2010	474	22	;	;	PUNCT
ejpam-2010	474	23	(	(	PUNCT
ejpam-2010	474	24	2	2	X
ejpam-2010	474	25	)	)	PUNCT
ejpam-2010	474	26	there	there	PRON
ejpam-2010	474	27	exists	exist	VERB
ejpam-2010	474	28	at	at	ADP
ejpam-2010	474	29	most	most	ADV
ejpam-2010	474	30	one	one	NUM
ejpam-2010	474	31	element	element	NOUN
ejpam-2010	474	32	of	of	ADP
ejpam-2010	474	33	s	s	PRON
ejpam-2010	474	34	which	which	PRON
ejpam-2010	474	35	has	have	VERB
ejpam-2010	474	36	a	a	DET
ejpam-2010	474	37	finite	finite	ADJ
ejpam-2010	474	38	order	order	NOUN
ejpam-2010	474	39	;	;	PUNCT
ejpam-2010	474	40	(	(	PUNCT
ejpam-2010	474	41	3	3	X
ejpam-2010	474	42	)	)	PUNCT
ejpam-2010	474	43	the	the	DET
ejpam-2010	474	44	identity	identity	NOUN
ejpam-2010	474	45	element	element	NOUN
ejpam-2010	474	46	e	e	NOUN
ejpam-2010	474	47	of	of	ADP
ejpam-2010	474	48	s	s	PROPN
ejpam-2010	474	49	is	be	AUX
ejpam-2010	474	50	externally	externally	ADV
ejpam-2010	474	51	adjoined	adjoin	VERB
ejpam-2010	474	52	,	,	PUNCT
ejpam-2010	474	53	that	that	ADV
ejpam-2010	474	54	is	is	ADV
ejpam-2010	474	55	,	,	PUNCT
ejpam-2010	474	56	if	if	SCONJ
ejpam-2010	474	57	ab	ab	PROPN
ejpam-2010	474	58	=	=	SYM
ejpam-2010	474	59	e	e	PROPN
ejpam-2010	474	60	,	,	PUNCT
ejpam-2010	474	61	for	for	ADP
ejpam-2010	474	62	all	all	DET
ejpam-2010	474	63	a	a	PRON
ejpam-2010	474	64	,	,	PUNCT
ejpam-2010	474	65	b	b	X
ejpam-2010	474	66	∈	∈	PROPN
ejpam-2010	474	67	s	s	PROPN
ejpam-2010	474	68	,	,	PUNCT
ejpam-2010	474	69	then	then	ADV
ejpam-2010	474	70	we	we	PRON
ejpam-2010	474	71	have	have	VERB
ejpam-2010	474	72	a	a	DET
ejpam-2010	474	73	=	=	SYM
ejpam-2010	474	74	b	b	NOUN
ejpam-2010	474	75	=	=	SYM
ejpam-2010	474	76	e	e	NOUN
ejpam-2010	474	77	;	;	PUNCT
ejpam-2010	474	78	(	(	PUNCT
ejpam-2010	474	79	4	4	X
ejpam-2010	474	80	)	)	PUNCT
ejpam-2010	474	81	s	s	VERB
ejpam-2010	474	82	is	be	AUX
ejpam-2010	474	83	a	a	DET
ejpam-2010	474	84	group	group	NOUN
ejpam-2010	474	85	.	.	PUNCT
ejpam-2010	475	1	the	the	DET
ejpam-2010	475	2	morita	morita	PROPN
ejpam-2010	475	3	theory	theory	NOUN
ejpam-2010	475	4	of	of	ADP
ejpam-2010	475	5	unital	unital	ADJ
ejpam-2010	475	6	rings	ring	NOUN
ejpam-2010	475	7	provides	provide	VERB
ejpam-2010	475	8	a	a	DET
ejpam-2010	475	9	framework	framework	NOUN
ejpam-2010	475	10	for	for	ADP
ejpam-2010	475	11	understanding	understand	VERB
ejpam-2010	475	12	the	the	DET
ejpam-2010	475	13	wedderburnartin	wedderburnartin	NOUN
ejpam-2010	475	14	theorem	theorem	NOUN
ejpam-2010	475	15	[	[	X
ejpam-2010	475	16	22	22	NUM
ejpam-2010	475	17	]	]	PUNCT
ejpam-2010	475	18	.	.	PUNCT
ejpam-2010	476	1	as	as	ADP
ejpam-2010	476	2	an	an	DET
ejpam-2010	476	3	analogue	analogue	NOUN
ejpam-2010	476	4	of	of	ADP
ejpam-2010	476	5	simple	simple	ADJ
ejpam-2010	476	6	artinian	artinian	ADJ
ejpam-2010	476	7	rings	ring	NOUN
ejpam-2010	476	8	in	in	ADP
ejpam-2010	476	9	the	the	DET
ejpam-2010	476	10	range	range	NOUN
ejpam-2010	476	11	of	of	ADP
ejpam-2010	476	12	semigroups	semigroup	NOUN
ejpam-2010	476	13	is	be	AUX
ejpam-2010	476	14	the	the	DET
ejpam-2010	476	15	class	class	NOUN
ejpam-2010	476	16	of	of	ADP
ejpam-2010	476	17	completely	completely	ADV
ejpam-2010	476	18	simple	simple	ADJ
ejpam-2010	476	19	semigroups	semigroup	NOUN
ejpam-2010	476	20	.	.	PUNCT
ejpam-2010	477	1	the	the	DET
ejpam-2010	477	2	following	follow	VERB
ejpam-2010	477	3	theorem	theorem	NOUN
ejpam-2010	477	4	gives	give	VERB
ejpam-2010	477	5	a	a	DET
ejpam-2010	477	6	number	number	NOUN
ejpam-2010	477	7	of	of	ADP
ejpam-2010	477	8	equivalent	equivalent	ADJ
ejpam-2010	477	9	characterisations	characterisation	NOUN
ejpam-2010	477	10	of	of	ADP
ejpam-2010	477	11	completely	completely	ADV
ejpam-2010	477	12	simple	simple	ADJ
ejpam-2010	477	13	semigroups	semigroup	NOUN
ejpam-2010	477	14	.	.	PUNCT
ejpam-2010	478	1	we	we	PRON
ejpam-2010	478	2	first	first	ADV
ejpam-2010	478	3	recall	recall	VERB
ejpam-2010	478	4	that	that	SCONJ
ejpam-2010	478	5	a	a	DET
ejpam-2010	478	6	semigroup	semigroup	NOUN
ejpam-2010	478	7	s	s	NOUN
ejpam-2010	478	8	is	be	AUX
ejpam-2010	478	9	said	say	VERB
ejpam-2010	478	10	to	to	PART
ejpam-2010	478	11	have	have	VERB
ejpam-2010	478	12	a	a	DET
ejpam-2010	478	13	property	property	NOUN
ejpam-2010	478	14	locally	locally	ADV
ejpam-2010	478	15	if	if	SCONJ
ejpam-2010	478	16	each	each	DET
ejpam-2010	478	17	local	local	ADJ
ejpam-2010	478	18	submonoid	submonoid	ADJ
ejpam-2010	478	19	ese	ese	NOUN
ejpam-2010	478	20	has	have	VERB
ejpam-2010	478	21	that	that	DET
ejpam-2010	478	22	property	property	NOUN
ejpam-2010	478	23	.	.	PUNCT
ejpam-2010	479	1	by	by	ADP
ejpam-2010	479	2	the	the	DET
ejpam-2010	479	3	local	local	ADJ
ejpam-2010	479	4	structure	structure	NOUN
ejpam-2010	479	5	of	of	ADP
ejpam-2010	479	6	a	a	DET
ejpam-2010	479	7	semigroup	semigroup	NOUN
ejpam-2010	479	8	s	s	NOUN
ejpam-2010	479	9	,	,	PUNCT
ejpam-2010	479	10	we	we	PRON
ejpam-2010	479	11	mean	mean	VERB
ejpam-2010	479	12	the	the	DET
ejpam-2010	479	13	structure	structure	NOUN
ejpam-2010	479	14	of	of	ADP
ejpam-2010	479	15	the	the	DET
ejpam-2010	479	16	local	local	ADJ
ejpam-2010	479	17	submonoids	submonoid	NOUN
ejpam-2010	479	18	ese	ese	NOUN
ejpam-2010	479	19	as	as	SCONJ
ejpam-2010	479	20	e	e	NOUN
ejpam-2010	479	21	varies	vary	VERB
ejpam-2010	479	22	over	over	ADP
ejpam-2010	479	23	the	the	DET
ejpam-2010	479	24	set	set	NOUN
ejpam-2010	479	25	of	of	ADP
ejpam-2010	479	26	idempotents	idempotent	NOUN
ejpam-2010	479	27	of	of	ADP
ejpam-2010	479	28	s.	s.	PROPN
ejpam-2010	479	29	theorem	theorem	VERB
ejpam-2010	479	30	11	11	NUM
ejpam-2010	479	31	.	.	PUNCT
ejpam-2010	480	1	[	[	X
ejpam-2010	480	2	25	25	NUM
ejpam-2010	480	3	,	,	PUNCT
ejpam-2010	480	4	theorem	theorem	VERB
ejpam-2010	480	5	5.3]let	5.3]let	NUM
ejpam-2010	480	6	s	s	VERB
ejpam-2010	480	7	be	be	AUX
ejpam-2010	480	8	a	a	DET
ejpam-2010	480	9	semigroup	semigroup	NOUN
ejpam-2010	480	10	with	with	ADP
ejpam-2010	480	11	local	local	ADJ
ejpam-2010	480	12	units	unit	NOUN
ejpam-2010	480	13	.	.	PUNCT
ejpam-2010	481	1	then	then	ADV
ejpam-2010	481	2	the	the	DET
ejpam-2010	481	3	following	follow	VERB
ejpam-2010	481	4	statements	statement	NOUN
ejpam-2010	481	5	are	be	AUX
ejpam-2010	481	6	equivalent	equivalent	ADJ
ejpam-2010	481	7	:	:	PUNCT
ejpam-2010	481	8	(	(	PUNCT
ejpam-2010	481	9	1	1	X
ejpam-2010	481	10	)	)	PUNCT
ejpam-2010	481	11	s	s	VERB
ejpam-2010	481	12	is	be	AUX
ejpam-2010	481	13	completely	completely	ADV
ejpam-2010	481	14	simple	simple	ADJ
ejpam-2010	481	15	;	;	PUNCT
ejpam-2010	481	16	(	(	PUNCT
ejpam-2010	481	17	2	2	X
ejpam-2010	481	18	)	)	PUNCT
ejpam-2010	481	19	s	s	VERB
ejpam-2010	481	20	is	be	AUX
ejpam-2010	481	21	regular	regular	ADJ
ejpam-2010	481	22	and	and	CCONJ
ejpam-2010	481	23	locally	locally	ADV
ejpam-2010	481	24	a	a	DET
ejpam-2010	481	25	group	group	NOUN
ejpam-2010	481	26	;	;	PUNCT
ejpam-2010	481	27	(	(	PUNCT
ejpam-2010	481	28	3	3	X
ejpam-2010	481	29	)	)	PUNCT
ejpam-2010	481	30	there	there	PRON
ejpam-2010	481	31	exists	exist	VERB
ejpam-2010	481	32	an	an	DET
ejpam-2010	481	33	idempotent	idempotent	NOUN
ejpam-2010	481	34	e	e	NOUN
ejpam-2010	481	35	such	such	ADJ
ejpam-2010	481	36	that	that	DET
ejpam-2010	481	37	s	s	PART
ejpam-2010	481	38	=	=	X
ejpam-2010	481	39	ses	se	NOUN
ejpam-2010	481	40	and	and	CCONJ
ejpam-2010	481	41	ese	ese	NOUN
ejpam-2010	481	42	is	be	AUX
ejpam-2010	481	43	a	a	DET
ejpam-2010	481	44	group	group	NOUN
ejpam-2010	481	45	;	;	PUNCT
ejpam-2010	481	46	(	(	PUNCT
ejpam-2010	481	47	4	4	X
ejpam-2010	481	48	)	)	PUNCT
ejpam-2010	481	49	s	s	VERB
ejpam-2010	481	50	is	be	AUX
ejpam-2010	481	51	morita	morita	NOUN
ejpam-2010	481	52	equivalent	equivalent	ADJ
ejpam-2010	481	53	to	to	ADP
ejpam-2010	481	54	a	a	DET
ejpam-2010	481	55	group	group	NOUN
ejpam-2010	481	56	.	.	PUNCT
ejpam-2010	482	1	in	in	ADP
ejpam-2010	482	2	1940	1940	NUM
ejpam-2010	482	3	,	,	PUNCT
ejpam-2010	482	4	rees	ree	NOUN
ejpam-2010	482	5	showed	show	VERB
ejpam-2010	482	6	that	that	SCONJ
ejpam-2010	482	7	every	every	DET
ejpam-2010	482	8	completely	completely	ADV
ejpam-2010	482	9	0	0	NUM
ejpam-2010	482	10	-	-	PUNCT
ejpam-2010	482	11	simple	simple	ADJ
ejpam-2010	482	12	semigroup	semigroup	NOUN
ejpam-2010	482	13	is	be	AUX
ejpam-2010	482	14	isomorphic	isomorphic	ADJ
ejpam-2010	482	15	to	to	ADP
ejpam-2010	482	16	a	a	DET
ejpam-2010	482	17	rees	rees	PROPN
ejpam-2010	482	18	matrix	matrix	NOUN
ejpam-2010	482	19	semigroup	semigroup	NOUN
ejpam-2010	482	20	.	.	PUNCT
ejpam-2010	483	1	we	we	PRON
ejpam-2010	483	2	now	now	ADV
ejpam-2010	483	3	proceed	proceed	VERB
ejpam-2010	483	4	to	to	PART
ejpam-2010	483	5	recover	recover	VERB
ejpam-2010	483	6	the	the	DET
ejpam-2010	483	7	rees	rees	PROPN
ejpam-2010	483	8	theorem	theorem	VERB
ejpam-2010	483	9	as	as	SCONJ
ejpam-2010	483	10	follows	follow	VERB
ejpam-2010	483	11	:	:	PUNCT
ejpam-2010	483	12	theorem	theorem	NOUN
ejpam-2010	483	13	12	12	NUM
ejpam-2010	483	14	.	.	PUNCT
ejpam-2010	484	1	[	[	X
ejpam-2010	484	2	43	43	NUM
ejpam-2010	484	3	,	,	PUNCT
ejpam-2010	484	4	theorem	theorem	VERB
ejpam-2010	484	5	9.8	9.8	NUM
ejpam-2010	484	6	]	]	PUNCT
ejpam-2010	484	7	a	a	DET
ejpam-2010	484	8	regular	regular	ADJ
ejpam-2010	484	9	semigroup	semigroup	NOUN
ejpam-2010	484	10	s	s	NOUN
ejpam-2010	484	11	with	with	ADP
ejpam-2010	484	12	zero	zero	NUM
ejpam-2010	484	13	is	be	AUX
ejpam-2010	484	14	completely	completely	ADV
ejpam-2010	484	15	0	0	NUM
ejpam-2010	484	16	-	-	NOUN
ejpam-2010	484	17	simple	simple	ADJ
ejpam-2010	484	18	if	if	SCONJ
ejpam-2010	484	19	and	and	CCONJ
ejpam-2010	484	20	only	only	ADV
ejpam-2010	484	21	if	if	SCONJ
ejpam-2010	484	22	s	s	NOUN
ejpam-2010	484	23	is	be	AUX
ejpam-2010	484	24	morita	morita	NOUN
ejpam-2010	484	25	equivalent	equivalent	ADJ
ejpam-2010	484	26	to	to	ADP
ejpam-2010	484	27	a	a	DET
ejpam-2010	484	28	group	group	NOUN
ejpam-2010	484	29	g	g	NOUN
ejpam-2010	484	30	with	with	ADP
ejpam-2010	484	31	zero	zero	NUM
ejpam-2010	484	32	.	.	PUNCT
ejpam-2010	485	1	further	far	ADV
ejpam-2010	485	2	,	,	PUNCT
ejpam-2010	485	3	we	we	PRON
ejpam-2010	485	4	have	have	VERB
ejpam-2010	485	5	the	the	DET
ejpam-2010	485	6	following	follow	VERB
ejpam-2010	485	7	theorem	theorem	VERB
ejpam-2010	485	8	.	.	PUNCT
ejpam-2010	485	9	theorem	theorem	VERB
ejpam-2010	485	10	13	13	NUM
ejpam-2010	485	11	.	.	PUNCT
ejpam-2010	486	1	[	[	X
ejpam-2010	486	2	43	43	NUM
ejpam-2010	486	3	,	,	PUNCT
ejpam-2010	486	4	theorem	theorem	VERB
ejpam-2010	486	5	9.11	9.11	NUM
ejpam-2010	486	6	]	]	PUNCT
ejpam-2010	486	7	a	a	DET
ejpam-2010	486	8	regular	regular	ADJ
ejpam-2010	486	9	semigroup	semigroup	NOUN
ejpam-2010	486	10	s	s	NOUN
ejpam-2010	486	11	with	with	ADP
ejpam-2010	486	12	zero	zero	NUM
ejpam-2010	486	13	is	be	AUX
ejpam-2010	486	14	bisimple	bisimple	ADJ
ejpam-2010	486	15	if	if	SCONJ
ejpam-2010	487	1	and	and	CCONJ
ejpam-2010	487	2	only	only	ADV
ejpam-2010	487	3	if	if	SCONJ
ejpam-2010	487	4	s	s	NOUN
ejpam-2010	487	5	is	be	AUX
ejpam-2010	487	6	morita	morita	NOUN
ejpam-2010	487	7	equivalent	equivalent	ADJ
ejpam-2010	487	8	to	to	ADP
ejpam-2010	487	9	a	a	DET
ejpam-2010	487	10	regular	regular	ADJ
ejpam-2010	487	11	bisimple	bisimple	NOUN
ejpam-2010	487	12	monoid	monoid	NOUN
ejpam-2010	487	13	with	with	ADP
ejpam-2010	487	14	zero	zero	NUM
ejpam-2010	487	15	.	.	PUNCT
ejpam-2010	488	1	y.	y.	PROPN
ejpam-2010	488	2	wang	wang	PROPN
ejpam-2010	488	3	,	,	PUNCT
ejpam-2010	488	4	k.	k.	PROPN
ejpam-2010	488	5	shum	shum	PROPN
ejpam-2010	488	6	,	,	PUNCT
ejpam-2010	488	7	x.	x.	PROPN
ejpam-2010	488	8	ren	ren	PROPN
ejpam-2010	488	9	/	/	SYM
ejpam-2010	488	10	eur	eur	PROPN
ejpam-2010	488	11	.	.	PUNCT
ejpam-2010	489	1	j.	j.	PROPN
ejpam-2010	489	2	pure	pure	PROPN
ejpam-2010	489	3	appl	appl	PROPN
ejpam-2010	489	4	.	.	PROPN
ejpam-2010	489	5	math	math	PROPN
ejpam-2010	489	6	,	,	PUNCT
ejpam-2010	489	7	6	6	NUM
ejpam-2010	489	8	(	(	PUNCT
ejpam-2010	489	9	2013	2013	NUM
ejpam-2010	489	10	)	)	PUNCT
ejpam-2010	489	11	,	,	PUNCT
ejpam-2010	489	12	256	256	NUM
ejpam-2010	489	13	-	-	SYM
ejpam-2010	489	14	281	281	NUM
ejpam-2010	489	15	273	273	NUM
ejpam-2010	489	16	from	from	ADP
ejpam-2010	489	17	theorem	theorem	ADJ
ejpam-2010	489	18	13	13	NUM
ejpam-2010	489	19	,	,	PUNCT
ejpam-2010	489	20	we	we	PRON
ejpam-2010	489	21	are	be	AUX
ejpam-2010	489	22	able	able	ADJ
ejpam-2010	489	23	to	to	PART
ejpam-2010	489	24	deduce	deduce	VERB
ejpam-2010	489	25	that	that	SCONJ
ejpam-2010	489	26	a	a	DET
ejpam-2010	489	27	regular	regular	ADJ
ejpam-2010	489	28	semigroup	semigroup	NOUN
ejpam-2010	489	29	s	s	PART
ejpam-2010	489	30	is	be	AUX
ejpam-2010	489	31	bisimple	bisimple	ADJ
ejpam-2010	489	32	if	if	SCONJ
ejpam-2010	490	1	and	and	CCONJ
ejpam-2010	490	2	only	only	ADV
ejpam-2010	490	3	if	if	SCONJ
ejpam-2010	490	4	s	s	NOUN
ejpam-2010	490	5	is	be	AUX
ejpam-2010	490	6	morita	morita	NOUN
ejpam-2010	490	7	equivalent	equivalent	ADJ
ejpam-2010	490	8	to	to	ADP
ejpam-2010	490	9	a	a	DET
ejpam-2010	490	10	regular	regular	ADJ
ejpam-2010	490	11	bisimple	bisimple	NOUN
ejpam-2010	490	12	monoid	monoid	NOUN
ejpam-2010	490	13	.	.	PUNCT
ejpam-2010	491	1	mcalister	mcalister	PROPN
ejpam-2010	492	1	[	[	X
ejpam-2010	492	2	27–31	27–31	PROPN
ejpam-2010	492	3	]	]	PUNCT
ejpam-2010	492	4	investigated	investigate	VERB
ejpam-2010	492	5	regular	regular	ADJ
ejpam-2010	492	6	semigroups	semigroup	NOUN
ejpam-2010	492	7	which	which	PRON
ejpam-2010	492	8	are	be	AUX
ejpam-2010	492	9	locally	locally	ADV
ejpam-2010	492	10	groups	group	NOUN
ejpam-2010	492	11	.	.	PUNCT
ejpam-2010	493	1	such	such	ADJ
ejpam-2010	493	2	results	result	NOUN
ejpam-2010	493	3	are	be	AUX
ejpam-2010	493	4	generalisations	generalisation	NOUN
ejpam-2010	493	5	of	of	ADP
ejpam-2010	493	6	the	the	DET
ejpam-2010	493	7	theorem	theorem	NOUN
ejpam-2010	493	8	of	of	ADP
ejpam-2010	493	9	completely	completely	ADV
ejpam-2010	493	10	simple	simple	ADJ
ejpam-2010	493	11	semigroups	semigroup	NOUN
ejpam-2010	493	12	.	.	PUNCT
ejpam-2010	494	1	for	for	ADP
ejpam-2010	494	2	instance	instance	NOUN
ejpam-2010	494	3	,	,	PUNCT
ejpam-2010	494	4	mcalister	mcalister	PROPN
ejpam-2010	494	5	[	[	X
ejpam-2010	494	6	27	27	NUM
ejpam-2010	494	7	,	,	PUNCT
ejpam-2010	494	8	28	28	NUM
ejpam-2010	494	9	]	]	PUNCT
ejpam-2010	494	10	studied	study	VERB
ejpam-2010	494	11	locally	locally	ADV
ejpam-2010	494	12	inverse	inverse	ADJ
ejpam-2010	494	13	semigroups	semigroup	NOUN
ejpam-2010	494	14	which	which	PRON
ejpam-2010	494	15	are	be	AUX
ejpam-2010	494	16	analogous	analogous	ADJ
ejpam-2010	494	17	to	to	ADP
ejpam-2010	494	18	both	both	PRON
ejpam-2010	494	19	completely	completely	ADV
ejpam-2010	494	20	simple	simple	ADJ
ejpam-2010	494	21	semigroups	semigroup	NOUN
ejpam-2010	494	22	and	and	CCONJ
ejpam-2010	494	23	inverse	inverse	NOUN
ejpam-2010	494	24	semigroups	semigroup	NOUN
ejpam-2010	494	25	.	.	PUNCT
ejpam-2010	495	1	we	we	PRON
ejpam-2010	495	2	will	will	AUX
ejpam-2010	495	3	interpret	interpret	VERB
ejpam-2010	495	4	mcalister	mcalister	PROPN
ejpam-2010	495	5	’s	’s	PART
ejpam-2010	495	6	results	result	NOUN
ejpam-2010	495	7	in	in	ADP
ejpam-2010	495	8	terms	term	NOUN
ejpam-2010	495	9	of	of	ADP
ejpam-2010	495	10	morita	morita	PROPN
ejpam-2010	495	11	equivalence	equivalence	NOUN
ejpam-2010	495	12	as	as	SCONJ
ejpam-2010	495	13	follows	follow	VERB
ejpam-2010	495	14	:	:	PUNCT
ejpam-2010	495	15	theorem	theorem	NOUN
ejpam-2010	495	16	14	14	NUM
ejpam-2010	495	17	.	.	PUNCT
ejpam-2010	496	1	[	[	X
ejpam-2010	496	2	25	25	NUM
ejpam-2010	496	3	,	,	PUNCT
ejpam-2010	496	4	theorem	theorem	VERB
ejpam-2010	496	5	5.5	5.5	NUM
ejpam-2010	496	6	]	]	PUNCT
ejpam-2010	496	7	let	let	VERB
ejpam-2010	496	8	s	s	PRON
ejpam-2010	496	9	be	be	AUX
ejpam-2010	496	10	a	a	DET
ejpam-2010	496	11	semigroup	semigroup	NOUN
ejpam-2010	496	12	with	with	ADP
ejpam-2010	496	13	local	local	ADJ
ejpam-2010	496	14	units	unit	NOUN
ejpam-2010	496	15	.	.	PUNCT
ejpam-2010	497	1	then	then	ADV
ejpam-2010	497	2	(	(	PUNCT
ejpam-2010	497	3	1	1	X
ejpam-2010	497	4	)	)	PUNCT
ejpam-2010	497	5	s	s	VERB
ejpam-2010	497	6	is	be	AUX
ejpam-2010	497	7	morita	morita	NOUN
ejpam-2010	497	8	equivalent	equivalent	ADJ
ejpam-2010	497	9	to	to	ADP
ejpam-2010	497	10	a	a	DET
ejpam-2010	497	11	group	group	NOUN
ejpam-2010	497	12	if	if	SCONJ
ejpam-2010	497	13	and	and	CCONJ
ejpam-2010	497	14	only	only	ADV
ejpam-2010	497	15	if	if	SCONJ
ejpam-2010	497	16	it	it	PRON
ejpam-2010	497	17	is	be	AUX
ejpam-2010	497	18	completely	completely	ADV
ejpam-2010	497	19	simple	simple	ADJ
ejpam-2010	497	20	;	;	PUNCT
ejpam-2010	497	21	(	(	PUNCT
ejpam-2010	497	22	2	2	X
ejpam-2010	497	23	)	)	PUNCT
ejpam-2010	497	24	s	s	VERB
ejpam-2010	497	25	is	be	AUX
ejpam-2010	497	26	morita	morita	NOUN
ejpam-2010	497	27	equivalent	equivalent	ADJ
ejpam-2010	497	28	to	to	ADP
ejpam-2010	497	29	an	an	DET
ejpam-2010	497	30	inverse	inverse	NOUN
ejpam-2010	497	31	semigroup	semigroup	NOUN
ejpam-2010	498	1	if	if	SCONJ
ejpam-2010	498	2	and	and	CCONJ
ejpam-2010	498	3	only	only	ADV
ejpam-2010	498	4	if	if	SCONJ
ejpam-2010	498	5	it	it	PRON
ejpam-2010	498	6	is	be	AUX
ejpam-2010	498	7	regular	regular	ADJ
ejpam-2010	498	8	and	and	CCONJ
ejpam-2010	498	9	locally	locally	ADV
ejpam-2010	498	10	inverse	inverse	ADJ
ejpam-2010	498	11	;	;	PUNCT
ejpam-2010	498	12	(	(	PUNCT
ejpam-2010	498	13	3	3	X
ejpam-2010	498	14	)	)	PUNCT
ejpam-2010	498	15	s	s	VERB
ejpam-2010	498	16	is	be	AUX
ejpam-2010	498	17	morita	morita	NOUN
ejpam-2010	498	18	equivalent	equivalent	ADJ
ejpam-2010	498	19	to	to	ADP
ejpam-2010	498	20	a	a	DET
ejpam-2010	498	21	semilattice	semilattice	NOUN
ejpam-2010	498	22	if	if	SCONJ
ejpam-2010	498	23	and	and	CCONJ
ejpam-2010	498	24	only	only	ADV
ejpam-2010	498	25	if	if	SCONJ
ejpam-2010	498	26	it	it	PRON
ejpam-2010	498	27	is	be	AUX
ejpam-2010	498	28	regular	regular	ADJ
ejpam-2010	498	29	,	,	PUNCT
ejpam-2010	498	30	locally	locally	ADV
ejpam-2010	498	31	a	a	DET
ejpam-2010	498	32	semilattice	semilattice	NOUN
ejpam-2010	498	33	,	,	PUNCT
ejpam-2010	498	34	and	and	CCONJ
ejpam-2010	498	35	s	s	PROPN
ejpam-2010	498	36	/	/	SYM
ejpam-2010	498	37	j	j	PROPN
ejpam-2010	498	38	is	be	AUX
ejpam-2010	498	39	a	a	DET
ejpam-2010	498	40	meet	meet	ADJ
ejpam-2010	498	41	semilattice	semilattice	NOUN
ejpam-2010	498	42	under	under	ADP
ejpam-2010	498	43	subset	subset	NOUN
ejpam-2010	498	44	inclusion	inclusion	NOUN
ejpam-2010	498	45	;	;	PUNCT
ejpam-2010	498	46	(	(	PUNCT
ejpam-2010	498	47	4	4	X
ejpam-2010	498	48	)	)	PUNCT
ejpam-2010	498	49	s	s	VERB
ejpam-2010	498	50	is	be	AUX
ejpam-2010	498	51	morita	morita	NOUN
ejpam-2010	498	52	equivalent	equivalent	ADJ
ejpam-2010	498	53	to	to	ADP
ejpam-2010	498	54	an	an	DET
ejpam-2010	498	55	orthodox	orthodox	NOUN
ejpam-2010	498	56	semigroup	semigroup	NOUN
ejpam-2010	498	57	if	if	SCONJ
ejpam-2010	498	58	and	and	CCONJ
ejpam-2010	498	59	only	only	ADV
ejpam-2010	498	60	if	if	SCONJ
ejpam-2010	498	61	it	it	PRON
ejpam-2010	498	62	is	be	AUX
ejpam-2010	498	63	regular	regular	ADJ
ejpam-2010	498	64	and	and	CCONJ
ejpam-2010	498	65	locally	locally	ADV
ejpam-2010	498	66	orthodox	orthodox	ADJ
ejpam-2010	498	67	;	;	PUNCT
ejpam-2010	498	68	(	(	PUNCT
ejpam-2010	498	69	5	5	X
ejpam-2010	498	70	)	)	PUNCT
ejpam-2010	498	71	s	s	VERB
ejpam-2010	498	72	is	be	AUX
ejpam-2010	498	73	morita	morita	NOUN
ejpam-2010	498	74	equivalent	equivalent	ADJ
ejpam-2010	498	75	to	to	ADP
ejpam-2010	498	76	an	an	DET
ejpam-2010	498	77	l	l	NOUN
ejpam-2010	498	78	-	-	ADJ
ejpam-2010	498	79	unipotent	unipotent	ADJ
ejpam-2010	498	80	semigroup	semigroup	NOUN
ejpam-2010	499	1	if	if	SCONJ
ejpam-2010	499	2	and	and	CCONJ
ejpam-2010	499	3	only	only	ADV
ejpam-2010	499	4	if	if	SCONJ
ejpam-2010	499	5	it	it	PRON
ejpam-2010	499	6	is	be	AUX
ejpam-2010	499	7	regular	regular	ADJ
ejpam-2010	499	8	and	and	CCONJ
ejpam-2010	499	9	locally	locally	ADV
ejpam-2010	499	10	l	l	NOUN
ejpam-2010	499	11	-	-	NOUN
ejpam-2010	499	12	unipotent	unipotent	ADJ
ejpam-2010	499	13	;	;	PUNCT
ejpam-2010	499	14	(	(	PUNCT
ejpam-2010	499	15	6	6	X
ejpam-2010	499	16	)	)	PUNCT
ejpam-2010	499	17	s	s	VERB
ejpam-2010	499	18	is	be	AUX
ejpam-2010	499	19	morita	morita	NOUN
ejpam-2010	499	20	equivalent	equivalent	ADJ
ejpam-2010	499	21	to	to	ADP
ejpam-2010	499	22	an	an	DET
ejpam-2010	499	23	e	e	NOUN
ejpam-2010	499	24	-	-	NOUN
ejpam-2010	499	25	solid	solid	ADJ
ejpam-2010	499	26	semigroup	semigroup	NOUN
ejpam-2010	499	27	if	if	SCONJ
ejpam-2010	499	28	and	and	CCONJ
ejpam-2010	499	29	only	only	ADV
ejpam-2010	499	30	if	if	SCONJ
ejpam-2010	499	31	it	it	PRON
ejpam-2010	499	32	is	be	AUX
ejpam-2010	499	33	regular	regular	ADJ
ejpam-2010	499	34	and	and	CCONJ
ejpam-2010	499	35	locally	locally	ADV
ejpam-2010	499	36	e	e	NOUN
ejpam-2010	499	37	-	-	NOUN
ejpam-2010	499	38	solid	solid	ADJ
ejpam-2010	499	39	;	;	PUNCT
ejpam-2010	499	40	(	(	PUNCT
ejpam-2010	499	41	7	7	X
ejpam-2010	499	42	)	)	PUNCT
ejpam-2010	499	43	s	s	VERB
ejpam-2010	499	44	is	be	AUX
ejpam-2010	499	45	morita	morita	NOUN
ejpam-2010	499	46	equivalent	equivalent	ADJ
ejpam-2010	499	47	to	to	ADP
ejpam-2010	499	48	a	a	DET
ejpam-2010	499	49	union	union	NOUN
ejpam-2010	499	50	of	of	ADP
ejpam-2010	499	51	groups	group	NOUN
ejpam-2010	499	52	if	if	SCONJ
ejpam-2010	499	53	and	and	CCONJ
ejpam-2010	499	54	only	only	ADV
ejpam-2010	499	55	if	if	SCONJ
ejpam-2010	499	56	it	it	PRON
ejpam-2010	499	57	is	be	AUX
ejpam-2010	499	58	regular	regular	ADJ
ejpam-2010	499	59	,	,	PUNCT
ejpam-2010	499	60	locally	locally	ADV
ejpam-2010	499	61	a	a	DET
ejpam-2010	499	62	union	union	NOUN
ejpam-2010	499	63	of	of	ADP
ejpam-2010	499	64	groups	group	NOUN
ejpam-2010	499	65	,	,	PUNCT
ejpam-2010	499	66	and	and	CCONJ
ejpam-2010	499	67	s	s	PROPN
ejpam-2010	499	68	/	/	SYM
ejpam-2010	499	69	j	j	PROPN
ejpam-2010	499	70	is	be	AUX
ejpam-2010	499	71	a	a	DET
ejpam-2010	499	72	meet	meet	ADJ
ejpam-2010	499	73	semilattice	semilattice	NOUN
ejpam-2010	499	74	under	under	ADP
ejpam-2010	499	75	subset	subset	NOUN
ejpam-2010	499	76	inclusion	inclusion	NOUN
ejpam-2010	499	77	.	.	PUNCT
ejpam-2010	500	1	let	let	VERB
ejpam-2010	500	2	s	s	PRON
ejpam-2010	500	3	be	be	AUX
ejpam-2010	500	4	a	a	DET
ejpam-2010	500	5	semigroup	semigroup	NOUN
ejpam-2010	500	6	having	having	AUX
ejpam-2010	500	7	locally	locally	ADV
ejpam-2010	500	8	commuting	commute	VERB
ejpam-2010	500	9	idempotents	idempotent	NOUN
ejpam-2010	500	10	.	.	PUNCT
ejpam-2010	501	1	a	a	DET
ejpam-2010	501	2	function	function	NOUN
ejpam-2010	501	3	p	p	NOUN
ejpam-2010	501	4	:	:	PUNCT
ejpam-2010	501	5	e(s	e(s	NUM
ejpam-2010	501	6	)	)	PUNCT
ejpam-2010	501	7	×	×	PROPN
ejpam-2010	501	8	e(s	e(s	PROPN
ejpam-2010	501	9	)	)	PUNCT
ejpam-2010	502	1	→	→	SYM
ejpam-2010	502	2	s	s	AUX
ejpam-2010	502	3	given	give	VERB
ejpam-2010	502	4	by	by	ADP
ejpam-2010	502	5	p(u	p(u	ADJ
ejpam-2010	502	6	,	,	PUNCT
ejpam-2010	502	7	v	v	NOUN
ejpam-2010	502	8	)	)	PUNCT
ejpam-2010	502	9	=	=	SYM
ejpam-2010	502	10	pu	pu	PROPN
ejpam-2010	502	11	,	,	PUNCT
ejpam-2010	502	12	v	v	NOUN
ejpam-2010	502	13	for	for	ADP
ejpam-2010	502	14	all	all	DET
ejpam-2010	502	15	u	u	NOUN
ejpam-2010	502	16	,	,	PUNCT
ejpam-2010	502	17	v	v	ADP
ejpam-2010	502	18	∈	∈	PROPN
ejpam-2010	502	19	s	s	NOUN
ejpam-2010	502	20	,	,	PUNCT
ejpam-2010	502	21	is	be	AUX
ejpam-2010	502	22	called	call	VERB
ejpam-2010	502	23	a	a	DET
ejpam-2010	502	24	mcalister	mcalister	NOUN
ejpam-2010	502	25	sandwich	sandwich	NOUN
ejpam-2010	502	26	function	function	NOUN
ejpam-2010	502	27	if	if	SCONJ
ejpam-2010	502	28	it	it	PRON
ejpam-2010	502	29	satisfies	satisfy	VERB
ejpam-2010	502	30	the	the	DET
ejpam-2010	502	31	following	follow	VERB
ejpam-2010	502	32	conditions	condition	NOUN
ejpam-2010	502	33	:	:	PUNCT
ejpam-2010	502	34	(	(	PUNCT
ejpam-2010	502	35	1	1	X
ejpam-2010	502	36	)	)	PUNCT
ejpam-2010	502	37	pu	pu	PROPN
ejpam-2010	502	38	,	,	PUNCT
ejpam-2010	502	39	v	v	NOUN
ejpam-2010	502	40	∈	∈	PROPN
ejpam-2010	502	41	usv	usv	ADJ
ejpam-2010	502	42	and	and	CCONJ
ejpam-2010	502	43	pu	pu	PROPN
ejpam-2010	502	44	,	,	PUNCT
ejpam-2010	502	45	u	u	NOUN
ejpam-2010	502	46	=	=	SYM
ejpam-2010	502	47	u	u	PROPN
ejpam-2010	502	48	;	;	PUNCT
ejpam-2010	502	49	(	(	PUNCT
ejpam-2010	502	50	2	2	X
ejpam-2010	502	51	)	)	PUNCT
ejpam-2010	502	52	pu	pu	PROPN
ejpam-2010	502	53	,	,	PUNCT
ejpam-2010	502	54	v	v	NOUN
ejpam-2010	502	55	∈	∈	NOUN
ejpam-2010	502	56	v	v	NOUN
ejpam-2010	502	57	(	(	PUNCT
ejpam-2010	502	58	pv	pv	INTJ
ejpam-2010	502	59	,	,	PUNCT
ejpam-2010	502	60	u	u	NOUN
ejpam-2010	502	61	)	)	PUNCT
ejpam-2010	502	62	;	;	PUNCT
ejpam-2010	502	63	(	(	PUNCT
ejpam-2010	502	64	3	3	X
ejpam-2010	502	65	)	)	PUNCT
ejpam-2010	502	66	pu	pu	PROPN
ejpam-2010	502	67	,	,	PUNCT
ejpam-2010	502	68	v	v	X
ejpam-2010	502	69	pv	pv	NOUN
ejpam-2010	502	70	,	,	PUNCT
ejpam-2010	502	71	f	f	PROPN
ejpam-2010	502	72	≤	≤	PROPN
ejpam-2010	502	73	pu	pu	PROPN
ejpam-2010	502	74	,	,	PUNCT
ejpam-2010	502	75	f	f	PROPN
ejpam-2010	502	76	.	.	PUNCT
ejpam-2010	503	1	theorem	theorem	VERB
ejpam-2010	503	2	15	15	NUM
ejpam-2010	503	3	.	.	PUNCT
ejpam-2010	504	1	[	[	X
ejpam-2010	504	2	2	2	NUM
ejpam-2010	504	3	,	,	PUNCT
ejpam-2010	504	4	theorem	theorem	VERB
ejpam-2010	504	5	3.10	3.10	NUM
ejpam-2010	504	6	]	]	PUNCT
ejpam-2010	504	7	a	a	DET
ejpam-2010	504	8	semigroup	semigroup	NOUN
ejpam-2010	504	9	s	s	NOUN
ejpam-2010	504	10	with	with	ADP
ejpam-2010	504	11	local	local	ADJ
ejpam-2010	504	12	unitsis	unitsis	NOUN
ejpam-2010	504	13	morita	morita	PROPN
ejpam-2010	504	14	equivalent	equivalent	NOUN
ejpam-2010	504	15	to	to	ADP
ejpam-2010	504	16	a	a	DET
ejpam-2010	504	17	semigroup	semigroup	NOUN
ejpam-2010	504	18	with	with	ADP
ejpam-2010	504	19	local	local	ADJ
ejpam-2010	504	20	units	unit	NOUN
ejpam-2010	504	21	having	have	VERB
ejpam-2010	504	22	commuting	commute	VERB
ejpam-2010	504	23	idempotents	idempotent	NOUN
ejpam-2010	504	24	if	if	SCONJ
ejpam-2010	504	25	and	and	CCONJ
ejpam-2010	504	26	only	only	ADV
ejpam-2010	504	27	if	if	SCONJ
ejpam-2010	504	28	it	it	PRON
ejpam-2010	504	29	has	have	AUX
ejpam-2010	504	30	locally	locally	ADV
ejpam-2010	504	31	commuting	commute	VERB
ejpam-2010	504	32	idempotents	idempotent	NOUN
ejpam-2010	504	33	and	and	CCONJ
ejpam-2010	504	34	is	be	AUX
ejpam-2010	504	35	equipped	equip	VERB
ejpam-2010	504	36	with	with	ADP
ejpam-2010	504	37	a	a	DET
ejpam-2010	504	38	mcalister	mcalister	NOUN
ejpam-2010	504	39	sandwich	sandwich	NOUN
ejpam-2010	504	40	function	function	PROPN
ejpam-2010	504	41	.	.	PUNCT
ejpam-2010	505	1	notice	notice	VERB
ejpam-2010	505	2	that	that	SCONJ
ejpam-2010	505	3	if	if	SCONJ
ejpam-2010	505	4	s	s	NOUN
ejpam-2010	505	5	is	be	AUX
ejpam-2010	505	6	a	a	DET
ejpam-2010	505	7	semigroup	semigroup	NOUN
ejpam-2010	505	8	with	with	ADP
ejpam-2010	505	9	local	local	ADJ
ejpam-2010	505	10	units	unit	NOUN
ejpam-2010	505	11	and	and	CCONJ
ejpam-2010	505	12	with	with	ADP
ejpam-2010	505	13	locally	locally	ADV
ejpam-2010	505	14	commuting	commuting	NOUN
ejpam-2010	505	15	idempotents	idempotent	NOUN
ejpam-2010	505	16	,	,	PUNCT
ejpam-2010	505	17	then	then	ADV
ejpam-2010	505	18	s	s	VERB
ejpam-2010	505	19	has	have	VERB
ejpam-2010	505	20	a	a	DET
ejpam-2010	505	21	mcalister	mcalister	NOUN
ejpam-2010	505	22	sandwich	sandwich	NOUN
ejpam-2010	505	23	function	function	NOUN
ejpam-2010	505	24	if	if	SCONJ
ejpam-2010	505	25	and	and	CCONJ
ejpam-2010	505	26	only	only	ADV
ejpam-2010	505	27	if	if	SCONJ
ejpam-2010	505	28	the	the	DET
ejpam-2010	505	29	inverse	inverse	NOUN
ejpam-2010	505	30	category	category	NOUN
ejpam-2010	505	31	i(s	i(s	NOUN
ejpam-2010	505	32	)	)	PUNCT
ejpam-2010	505	33	is	be	AUX
ejpam-2010	505	34	equipped	equip	VERB
ejpam-2010	505	35	with	with	ADP
ejpam-2010	505	36	a	a	DET
ejpam-2010	505	37	mcalister	mcalister	NOUN
ejpam-2010	505	38	consolidation	consolidation	NOUN
ejpam-2010	505	39	.	.	PUNCT
ejpam-2010	506	1	if	if	SCONJ
ejpam-2010	506	2	i(s	i(s	NOUN
ejpam-2010	506	3	)	)	PUNCT
ejpam-2010	506	4	is	be	AUX
ejpam-2010	506	5	strongly	strongly	ADV
ejpam-2010	506	6	connected	connect	VERB
ejpam-2010	506	7	and	and	CCONJ
ejpam-2010	506	8	is	be	AUX
ejpam-2010	506	9	equipped	equip	VERB
ejpam-2010	506	10	with	with	ADP
ejpam-2010	506	11	a	a	DET
ejpam-2010	506	12	mcalister	mcalister	NOUN
ejpam-2010	506	13	consolidation	consolidation	NOUN
ejpam-2010	506	14	,	,	PUNCT
ejpam-2010	506	15	then	then	ADV
ejpam-2010	506	16	i(s	i(s	PROPN
ejpam-2010	506	17	)	)	PUNCT
ejpam-2010	506	18	is	be	AUX
ejpam-2010	506	19	morita	morita	PROPN
ejpam-2010	506	20	equivalent	equivalent	ADJ
ejpam-2010	506	21	to	to	ADP
ejpam-2010	506	22	the	the	DET
ejpam-2010	506	23	cauchy	cauchy	ADJ
ejpam-2010	506	24	completion	completion	NOUN
ejpam-2010	506	25	of	of	ADP
ejpam-2010	506	26	an	an	DET
ejpam-2010	506	27	inverse	inverse	NOUN
ejpam-2010	506	28	semigroup	semigroup	NOUN
ejpam-2010	506	29	.	.	PUNCT
ejpam-2010	507	1	thus	thus	ADV
ejpam-2010	507	2	,	,	PUNCT
ejpam-2010	507	3	we	we	PRON
ejpam-2010	507	4	have	have	VERB
ejpam-2010	507	5	the	the	DET
ejpam-2010	507	6	following	follow	VERB
ejpam-2010	507	7	theorem	theorem	VERB
ejpam-2010	507	8	.	.	PUNCT
ejpam-2010	508	1	y.	y.	PROPN
ejpam-2010	508	2	wang	wang	PROPN
ejpam-2010	508	3	,	,	PUNCT
ejpam-2010	508	4	k.	k.	PROPN
ejpam-2010	508	5	shum	shum	PROPN
ejpam-2010	508	6	,	,	PUNCT
ejpam-2010	508	7	x.	x.	PROPN
ejpam-2010	508	8	ren	ren	PROPN
ejpam-2010	508	9	/	/	SYM
ejpam-2010	508	10	eur	eur	PROPN
ejpam-2010	508	11	.	.	PUNCT
ejpam-2010	509	1	j.	j.	PROPN
ejpam-2010	509	2	pure	pure	PROPN
ejpam-2010	509	3	appl	appl	PROPN
ejpam-2010	509	4	.	.	PROPN
ejpam-2010	509	5	math	math	PROPN
ejpam-2010	509	6	,	,	PUNCT
ejpam-2010	509	7	6	6	NUM
ejpam-2010	509	8	(	(	PUNCT
ejpam-2010	509	9	2013	2013	NUM
ejpam-2010	509	10	)	)	PUNCT
ejpam-2010	509	11	,	,	PUNCT
ejpam-2010	509	12	256	256	NUM
ejpam-2010	509	13	-	-	SYM
ejpam-2010	509	14	281	281	NUM
ejpam-2010	509	15	274	274	NUM
ejpam-2010	509	16	theorem	theorem	NOUN
ejpam-2010	509	17	16	16	NUM
ejpam-2010	509	18	.	.	PUNCT
ejpam-2010	510	1	[	[	X
ejpam-2010	510	2	2	2	NUM
ejpam-2010	510	3	,	,	PUNCT
ejpam-2010	510	4	theorem	theorem	VERB
ejpam-2010	510	5	3.11	3.11	NUM
ejpam-2010	510	6	]	]	PUNCT
ejpam-2010	510	7	the	the	DET
ejpam-2010	510	8	semigroup	semigroup	NOUN
ejpam-2010	510	9	with	with	ADP
ejpam-2010	510	10	local	local	ADJ
ejpam-2010	510	11	units	unit	NOUN
ejpam-2010	510	12	s	s	PART
ejpam-2010	510	13	is	be	AUX
ejpam-2010	510	14	morita	morita	NOUN
ejpam-2010	510	15	equivalent	equivalent	ADJ
ejpam-2010	510	16	to	to	ADP
ejpam-2010	510	17	a	a	DET
ejpam-2010	510	18	semigroup	semigroup	NOUN
ejpam-2010	510	19	with	with	ADP
ejpam-2010	510	20	local	local	ADJ
ejpam-2010	510	21	units	unit	NOUN
ejpam-2010	510	22	and	and	CCONJ
ejpam-2010	510	23	with	with	ADP
ejpam-2010	510	24	commuting	commute	VERB
ejpam-2010	510	25	idempotents	idempotent	NOUN
ejpam-2010	510	26	if	if	SCONJ
ejpam-2010	510	27	and	and	CCONJ
ejpam-2010	510	28	only	only	ADV
ejpam-2010	510	29	if	if	SCONJ
ejpam-2010	510	30	the	the	DET
ejpam-2010	510	31	following	follow	VERB
ejpam-2010	510	32	two	two	NUM
ejpam-2010	510	33	conditions	condition	NOUN
ejpam-2010	510	34	hold	hold	VERB
ejpam-2010	510	35	:	:	PUNCT
ejpam-2010	510	36	(	(	PUNCT
ejpam-2010	510	37	1	1	X
ejpam-2010	510	38	)	)	PUNCT
ejpam-2010	510	39	s	s	VERB
ejpam-2010	510	40	has	have	AUX
ejpam-2010	510	41	locally	locally	ADV
ejpam-2010	510	42	commuting	commute	VERB
ejpam-2010	510	43	idempotents	idempotent	NOUN
ejpam-2010	510	44	;	;	PUNCT
ejpam-2010	510	45	(	(	PUNCT
ejpam-2010	510	46	2	2	X
ejpam-2010	510	47	)	)	PUNCT
ejpam-2010	510	48	the	the	DET
ejpam-2010	510	49	inverse	inverse	NOUN
ejpam-2010	510	50	category	category	NOUN
ejpam-2010	510	51	i(s	i(s	NOUN
ejpam-2010	510	52	)	)	PUNCT
ejpam-2010	510	53	is	be	AUX
ejpam-2010	510	54	equivalent	equivalent	ADJ
ejpam-2010	510	55	to	to	ADP
ejpam-2010	510	56	a	a	DET
ejpam-2010	510	57	category	category	NOUN
ejpam-2010	510	58	of	of	ADP
ejpam-2010	510	59	the	the	DET
ejpam-2010	510	60	form	form	NOUN
ejpam-2010	510	61	c(t	c(t	PROPN
ejpam-2010	510	62	)	)	PUNCT
ejpam-2010	510	63	,	,	PUNCT
ejpam-2010	510	64	where	where	SCONJ
ejpam-2010	510	65	t	t	PROPN
ejpam-2010	510	66	is	be	AUX
ejpam-2010	510	67	an	an	DET
ejpam-2010	510	68	inverse	inverse	NOUN
ejpam-2010	510	69	semigroup	semigroup	NOUN
ejpam-2010	510	70	.	.	PUNCT
ejpam-2010	511	1	theorem	theorem	VERB
ejpam-2010	511	2	17	17	NUM
ejpam-2010	511	3	.	.	PUNCT
ejpam-2010	512	1	[	[	X
ejpam-2010	512	2	2	2	NUM
ejpam-2010	512	3	,	,	PUNCT
ejpam-2010	512	4	theorem	theorem	VERB
ejpam-2010	512	5	3.12	3.12	NUM
ejpam-2010	512	6	]	]	PUNCT
ejpam-2010	512	7	suppose	suppose	VERB
ejpam-2010	512	8	that	that	SCONJ
ejpam-2010	512	9	the	the	DET
ejpam-2010	512	10	set	set	NOUN
ejpam-2010	512	11	of	of	ADP
ejpam-2010	512	12	regular	regular	ADJ
ejpam-2010	512	13	elements	element	NOUN
ejpam-2010	512	14	of	of	ADP
ejpam-2010	512	15	a	a	DET
ejpam-2010	512	16	semigroup	semigroup	NOUN
ejpam-2010	512	17	s	s	NOUN
ejpam-2010	512	18	with	with	ADP
ejpam-2010	512	19	local	local	ADJ
ejpam-2010	512	20	units	unit	NOUN
ejpam-2010	512	21	forms	form	VERB
ejpam-2010	512	22	a	a	DET
ejpam-2010	512	23	regular	regular	ADJ
ejpam-2010	512	24	subsemigroup	subsemigroup	NOUN
ejpam-2010	512	25	.	.	PUNCT
ejpam-2010	513	1	then	then	ADV
ejpam-2010	513	2	s	s	VERB
ejpam-2010	513	3	is	be	AUX
ejpam-2010	513	4	morita	morita	NOUN
ejpam-2010	513	5	equivalent	equivalent	ADJ
ejpam-2010	513	6	to	to	ADP
ejpam-2010	513	7	a	a	DET
ejpam-2010	513	8	semigroup	semigroup	NOUN
ejpam-2010	513	9	with	with	ADP
ejpam-2010	513	10	commuting	commute	VERB
ejpam-2010	513	11	idempotents	idempotent	NOUN
ejpam-2010	513	12	if	if	SCONJ
ejpam-2010	513	13	and	and	CCONJ
ejpam-2010	513	14	only	only	ADV
ejpam-2010	513	15	if	if	SCONJ
ejpam-2010	513	16	s	s	NOUN
ejpam-2010	513	17	has	have	AUX
ejpam-2010	513	18	locally	locally	ADV
ejpam-2010	513	19	commuting	commute	VERB
ejpam-2010	513	20	idempotents	idempotent	NOUN
ejpam-2010	513	21	.	.	PUNCT
ejpam-2010	514	1	to	to	PART
ejpam-2010	514	2	end	end	VERB
ejpam-2010	514	3	this	this	DET
ejpam-2010	514	4	subsection	subsection	NOUN
ejpam-2010	514	5	we	we	PRON
ejpam-2010	514	6	discuss	discuss	VERB
ejpam-2010	514	7	the	the	DET
ejpam-2010	514	8	properties	property	NOUN
ejpam-2010	514	9	of	of	ADP
ejpam-2010	514	10	strongly1	strongly1	PROPN
ejpam-2010	514	11	morita	morita	PROPN
ejpam-2010	514	12	equivalent	equivalent	PROPN
ejpam-2010	514	13	semigroups	semigroup	NOUN
ejpam-2010	514	14	,	,	PUNCT
ejpam-2010	514	15	which	which	PRON
ejpam-2010	514	16	are	be	AUX
ejpam-2010	514	17	cited	cite	VERB
ejpam-2010	514	18	from	from	ADP
ejpam-2010	514	19	[	[	X
ejpam-2010	514	20	21	21	NUM
ejpam-2010	514	21	]	]	PUNCT
ejpam-2010	514	22	.	.	PUNCT
ejpam-2010	515	1	proposition	proposition	NOUN
ejpam-2010	515	2	8	8	NUM
ejpam-2010	515	3	.	.	PUNCT
ejpam-2010	516	1	let	let	VERB
ejpam-2010	516	2	s	s	PRON
ejpam-2010	516	3	and	and	CCONJ
ejpam-2010	516	4	t	t	PROPN
ejpam-2010	516	5	be	be	AUX
ejpam-2010	516	6	strongly1	strongly1	PROPN
ejpam-2010	516	7	morita	morita	PROPN
ejpam-2010	516	8	equivalent	equivalent	PROPN
ejpam-2010	516	9	semigroups	semigroup	NOUN
ejpam-2010	516	10	.	.	PUNCT
ejpam-2010	517	1	then	then	ADV
ejpam-2010	517	2	(	(	PUNCT
ejpam-2010	517	3	1	1	X
ejpam-2010	517	4	)	)	PUNCT
ejpam-2010	517	5	if	if	SCONJ
ejpam-2010	517	6	s	s	PRON
ejpam-2010	517	7	and	and	CCONJ
ejpam-2010	517	8	t	t	PROPN
ejpam-2010	517	9	are	be	AUX
ejpam-2010	517	10	semigroups	semigroup	NOUN
ejpam-2010	517	11	with	with	ADP
ejpam-2010	517	12	weak	weak	ADJ
ejpam-2010	517	13	local	local	ADJ
ejpam-2010	517	14	units	unit	NOUN
ejpam-2010	517	15	,	,	PUNCT
ejpam-2010	517	16	then	then	ADV
ejpam-2010	517	17	there	there	PRON
ejpam-2010	517	18	exists	exist	VERB
ejpam-2010	517	19	an	an	DET
ejpam-2010	517	20	isomorphism	isomorphism	NOUN
ejpam-2010	517	21	φ	φ	NOUN
ejpam-2010	517	22	:	:	PUNCT
ejpam-2010	517	23	id(s)→	id(s)→	NOUN
ejpam-2010	517	24	id(t	id(t	ADV
ejpam-2010	517	25	)	)	PUNCT
ejpam-2010	517	26	between	between	ADP
ejpam-2010	517	27	their	their	PRON
ejpam-2010	517	28	lattices	lattice	NOUN
ejpam-2010	517	29	of	of	ADP
ejpam-2010	517	30	ideals	ideal	NOUN
ejpam-2010	517	31	which	which	PRON
ejpam-2010	517	32	takes	take	VERB
ejpam-2010	517	33	finitely	finitely	ADV
ejpam-2010	517	34	generated	generate	VERB
ejpam-2010	517	35	ideals	ideal	NOUN
ejpam-2010	517	36	to	to	PART
ejpam-2010	517	37	finitely	finitely	ADV
ejpam-2010	517	38	generated	generate	VERB
ejpam-2010	517	39	ideals	ideal	NOUN
ejpam-2010	517	40	and	and	CCONJ
ejpam-2010	517	41	principal	principal	ADJ
ejpam-2010	517	42	ideals	ideal	NOUN
ejpam-2010	517	43	to	to	ADP
ejpam-2010	517	44	principal	principal	ADJ
ejpam-2010	517	45	ideals	ideal	NOUN
ejpam-2010	517	46	;	;	PUNCT
ejpam-2010	517	47	(	(	PUNCT
ejpam-2010	517	48	2	2	X
ejpam-2010	517	49	)	)	PUNCT
ejpam-2010	517	50	if	if	SCONJ
ejpam-2010	517	51	s	s	PRON
ejpam-2010	517	52	and	and	CCONJ
ejpam-2010	517	53	t	t	PROPN
ejpam-2010	517	54	are	be	AUX
ejpam-2010	517	55	semigroups	semigroup	NOUN
ejpam-2010	517	56	with	with	ADP
ejpam-2010	517	57	common	common	ADJ
ejpam-2010	517	58	two	two	NUM
ejpam-2010	517	59	-	-	PUNCT
ejpam-2010	517	60	sided	side	VERB
ejpam-2010	517	61	weak	weak	ADJ
ejpam-2010	517	62	local	local	ADJ
ejpam-2010	517	63	units	unit	NOUN
ejpam-2010	517	64	then	then	ADV
ejpam-2010	517	65	their	their	PRON
ejpam-2010	517	66	greatest	great	ADJ
ejpam-2010	517	67	commutative	commutative	ADJ
ejpam-2010	517	68	images	image	NOUN
ejpam-2010	517	69	are	be	AUX
ejpam-2010	517	70	isomorphic	isomorphic	ADJ
ejpam-2010	517	71	semigroups	semigroup	NOUN
ejpam-2010	517	72	;	;	PUNCT
ejpam-2010	517	73	(	(	PUNCT
ejpam-2010	517	74	3	3	X
ejpam-2010	517	75	)	)	PUNCT
ejpam-2010	517	76	if	if	SCONJ
ejpam-2010	517	77	s	s	PRON
ejpam-2010	517	78	and	and	CCONJ
ejpam-2010	517	79	t	t	PROPN
ejpam-2010	517	80	are	be	AUX
ejpam-2010	517	81	commutative	commutative	ADJ
ejpam-2010	517	82	semigroups	semigroup	NOUN
ejpam-2010	517	83	with	with	ADP
ejpam-2010	517	84	common	common	ADJ
ejpam-2010	517	85	two	two	NUM
ejpam-2010	517	86	-	-	PUNCT
ejpam-2010	517	87	sided	side	VERB
ejpam-2010	517	88	weak	weak	ADJ
ejpam-2010	517	89	local	local	ADJ
ejpam-2010	517	90	units	unit	NOUN
ejpam-2010	517	91	then	then	ADV
ejpam-2010	517	92	s	s	PRON
ejpam-2010	517	93	and	and	CCONJ
ejpam-2010	517	94	t	t	PROPN
ejpam-2010	517	95	are	be	AUX
ejpam-2010	517	96	isomorphic	isomorphic	ADJ
ejpam-2010	517	97	;	;	PUNCT
ejpam-2010	517	98	(	(	PUNCT
ejpam-2010	517	99	4	4	X
ejpam-2010	517	100	)	)	PUNCT
ejpam-2010	517	101	if	if	SCONJ
ejpam-2010	517	102	s	s	PRON
ejpam-2010	517	103	and	and	CCONJ
ejpam-2010	517	104	t	t	PROPN
ejpam-2010	517	105	are	be	AUX
ejpam-2010	517	106	semigroups	semigroup	NOUN
ejpam-2010	517	107	with	with	ADP
ejpam-2010	517	108	common	common	ADJ
ejpam-2010	517	109	two	two	NUM
ejpam-2010	517	110	-	-	PUNCT
ejpam-2010	517	111	sided	sided	ADJ
ejpam-2010	517	112	local	local	ADJ
ejpam-2010	517	113	units	unit	NOUN
ejpam-2010	517	114	then	then	ADV
ejpam-2010	517	115	s	s	VERB
ejpam-2010	517	116	and	and	CCONJ
ejpam-2010	517	117	t	t	PROPN
ejpam-2010	517	118	satisfy	satisfy	VERB
ejpam-2010	517	119	the	the	DET
ejpam-2010	517	120	same	same	ADJ
ejpam-2010	517	121	identities	identity	NOUN
ejpam-2010	517	122	.	.	PUNCT
ejpam-2010	518	1	from	from	ADP
ejpam-2010	518	2	(	(	PUNCT
ejpam-2010	518	3	3	3	X
ejpam-2010	518	4	)	)	PUNCT
ejpam-2010	518	5	in	in	ADP
ejpam-2010	518	6	proposition	proposition	NOUN
ejpam-2010	518	7	8	8	NUM
ejpam-2010	518	8	,	,	PUNCT
ejpam-2010	518	9	we	we	PRON
ejpam-2010	518	10	observe	observe	VERB
ejpam-2010	518	11	that	that	SCONJ
ejpam-2010	518	12	if	if	SCONJ
ejpam-2010	518	13	s	s	PRON
ejpam-2010	518	14	and	and	CCONJ
ejpam-2010	518	15	t	t	PROPN
ejpam-2010	518	16	are	be	AUX
ejpam-2010	518	17	strongly1	strongly1	PROPN
ejpam-2010	518	18	morita	morita	PROPN
ejpam-2010	518	19	equivalent	equivalent	PROPN
ejpam-2010	518	20	semigroups	semigroup	NOUN
ejpam-2010	518	21	with	with	ADP
ejpam-2010	518	22	common	common	ADJ
ejpam-2010	518	23	two	two	NUM
ejpam-2010	518	24	-	-	PUNCT
ejpam-2010	518	25	sided	side	VERB
ejpam-2010	518	26	weak	weak	ADJ
ejpam-2010	518	27	local	local	ADJ
ejpam-2010	518	28	units	unit	NOUN
ejpam-2010	518	29	then	then	ADV
ejpam-2010	518	30	their	their	PRON
ejpam-2010	518	31	greatest	great	ADJ
ejpam-2010	518	32	semilattice	semilattice	NOUN
ejpam-2010	518	33	images	image	NOUN
ejpam-2010	518	34	are	be	AUX
ejpam-2010	518	35	isomorphic	isomorphic	ADJ
ejpam-2010	518	36	.	.	PUNCT
ejpam-2010	519	1	the	the	DET
ejpam-2010	519	2	following	follow	VERB
ejpam-2010	519	3	theorem	theorem	NOUN
ejpam-2010	519	4	shows	show	NOUN
ejpam-2010	519	5	that	that	SCONJ
ejpam-2010	519	6	rees	ree	NOUN
ejpam-2010	519	7	congruences	congruence	VERB
ejpam-2010	519	8	correspond	correspond	ADV
ejpam-2010	519	9	to	to	ADP
ejpam-2010	519	10	rees	rees	PROPN
ejpam-2010	519	11	congruences	congruence	VERB
ejpam-2010	519	12	under	under	ADP
ejpam-2010	519	13	strongly1	strongly1	PROPN
ejpam-2010	519	14	morita	morita	PROPN
ejpam-2010	519	15	equivalence	equivalence	NOUN
ejpam-2010	519	16	and	and	CCONJ
ejpam-2010	519	17	also	also	ADV
ejpam-2010	519	18	implies	imply	VERB
ejpam-2010	519	19	that	that	SCONJ
ejpam-2010	519	20	the	the	DET
ejpam-2010	519	21	ideal	ideal	ADJ
ejpam-2010	519	22	lattices	lattice	NOUN
ejpam-2010	519	23	of	of	ADP
ejpam-2010	519	24	strongly1	strongly1	PROPN
ejpam-2010	519	25	morita	morita	PROPN
ejpam-2010	519	26	equivalent	equivalent	PROPN
ejpam-2010	519	27	semigroups	semigroup	NOUN
ejpam-2010	519	28	with	with	ADP
ejpam-2010	519	29	common	common	ADJ
ejpam-2010	519	30	joint	joint	ADJ
ejpam-2010	519	31	weak	weak	ADJ
ejpam-2010	519	32	local	local	ADJ
ejpam-2010	519	33	units	unit	NOUN
ejpam-2010	519	34	are	be	AUX
ejpam-2010	519	35	isomorphic	isomorphic	ADJ
ejpam-2010	519	36	.	.	PUNCT
ejpam-2010	520	1	theorem	theorem	PROPN
ejpam-2010	520	2	18	18	NUM
ejpam-2010	520	3	.	.	PUNCT
ejpam-2010	521	1	[	[	X
ejpam-2010	521	2	21	21	NUM
ejpam-2010	521	3	,	,	PUNCT
ejpam-2010	521	4	theorem	theorem	VERB
ejpam-2010	521	5	6	6	NUM
ejpam-2010	521	6	]	]	PUNCT
ejpam-2010	521	7	if	if	SCONJ
ejpam-2010	521	8	s	s	PROPN
ejpam-2010	521	9	and	and	CCONJ
ejpam-2010	521	10	t	t	PROPN
ejpam-2010	521	11	are	be	AUX
ejpam-2010	521	12	strongly1	strongly1	PROPN
ejpam-2010	521	13	morita	morita	PROPN
ejpam-2010	521	14	equivalent	equivalent	PROPN
ejpam-2010	521	15	semigroups	semigroup	NOUN
ejpam-2010	521	16	with	with	ADP
ejpam-2010	521	17	common	common	ADJ
ejpam-2010	521	18	joint	joint	ADJ
ejpam-2010	521	19	weak	weak	ADJ
ejpam-2010	521	20	local	local	ADJ
ejpam-2010	521	21	units	unit	NOUN
ejpam-2010	521	22	then	then	ADV
ejpam-2010	521	23	there	there	PRON
ejpam-2010	521	24	exists	exist	VERB
ejpam-2010	521	25	an	an	DET
ejpam-2010	521	26	isomorphism	isomorphism	NOUN
ejpam-2010	521	27	∏	∏	PROPN
ejpam-2010	521	28	:	:	PUNCT
ejpam-2010	522	1	con(s)→	con(s)→	PROPN
ejpam-2010	522	2	con(t	con(t	PROPN
ejpam-2010	522	3	)	)	PUNCT
ejpam-2010	522	4	between	between	ADP
ejpam-2010	522	5	their	their	PRON
ejpam-2010	522	6	congruence	congruence	NOUN
ejpam-2010	522	7	lattices	lattice	NOUN
ejpam-2010	522	8	such	such	ADJ
ejpam-2010	522	9	that	that	SCONJ
ejpam-2010	522	10	if	if	SCONJ
ejpam-2010	522	11	ρ	ρ	PROPN
ejpam-2010	522	12	∈	∈	PROPN
ejpam-2010	522	13	con(s	con(s	PROPN
ejpam-2010	522	14	)	)	PUNCT
ejpam-2010	522	15	then	then	ADV
ejpam-2010	522	16	the	the	DET
ejpam-2010	522	17	semigroups	semigroups	X
ejpam-2010	522	18	s	s	X
ejpam-2010	522	19	/	/	SYM
ejpam-2010	522	20	ρ	ρ	PROPN
ejpam-2010	522	21	and	and	CCONJ
ejpam-2010	522	22	t/	t/	PROPN
ejpam-2010	522	23	∏	∏	PROPN
ejpam-2010	522	24	(	(	PUNCT
ejpam-2010	522	25	ρ	ρ	PROPN
ejpam-2010	522	26	)	)	PUNCT
ejpam-2010	522	27	are	be	AUX
ejpam-2010	522	28	strongly1	strongly1	PROPN
ejpam-2010	522	29	morita	morita	PROPN
ejpam-2010	522	30	equivalent	equivalent	NOUN
ejpam-2010	522	31	,	,	PUNCT
ejpam-2010	522	32	and	and	CCONJ
ejpam-2010	522	33	∏	∏	NUM
ejpam-2010	522	34	takes	take	VERB
ejpam-2010	522	35	(	(	PUNCT
ejpam-2010	522	36	1	1	NUM
ejpam-2010	522	37	)	)	PUNCT
ejpam-2010	522	38	rees	ree	NOUN
ejpam-2010	522	39	congruences	congruence	VERB
ejpam-2010	522	40	to	to	ADP
ejpam-2010	522	41	rees	ree	NOUN
ejpam-2010	522	42	congruences	congruence	NOUN
ejpam-2010	522	43	;	;	PUNCT
ejpam-2010	522	44	(	(	PUNCT
ejpam-2010	522	45	2	2	X
ejpam-2010	522	46	)	)	PUNCT
ejpam-2010	522	47	finitely	finitely	ADV
ejpam-2010	522	48	generated	generate	VERB
ejpam-2010	522	49	congruences	congruence	NOUN
ejpam-2010	522	50	to	to	PART
ejpam-2010	522	51	finitely	finitely	ADV
ejpam-2010	522	52	generated	generate	VERB
ejpam-2010	522	53	congruences	congruence	NOUN
ejpam-2010	522	54	;	;	PUNCT
ejpam-2010	522	55	(	(	PUNCT
ejpam-2010	522	56	3	3	X
ejpam-2010	522	57	)	)	PUNCT
ejpam-2010	522	58	principal	principal	NOUN
ejpam-2010	522	59	congruences	congruence	VERB
ejpam-2010	522	60	to	to	ADP
ejpam-2010	522	61	principal	principal	ADJ
ejpam-2010	522	62	congruences	congruence	NOUN
ejpam-2010	522	63	.	.	PUNCT
ejpam-2010	523	1	y.	y.	PROPN
ejpam-2010	523	2	wang	wang	PROPN
ejpam-2010	523	3	,	,	PUNCT
ejpam-2010	523	4	k.	k.	PROPN
ejpam-2010	523	5	shum	shum	PROPN
ejpam-2010	523	6	,	,	PUNCT
ejpam-2010	523	7	x.	x.	PROPN
ejpam-2010	523	8	ren	ren	PROPN
ejpam-2010	523	9	/	/	SYM
ejpam-2010	523	10	eur	eur	PROPN
ejpam-2010	523	11	.	.	PUNCT
ejpam-2010	524	1	j.	j.	PROPN
ejpam-2010	524	2	pure	pure	PROPN
ejpam-2010	524	3	appl	appl	PROPN
ejpam-2010	524	4	.	.	PROPN
ejpam-2010	524	5	math	math	PROPN
ejpam-2010	524	6	,	,	PUNCT
ejpam-2010	524	7	6	6	NUM
ejpam-2010	524	8	(	(	PUNCT
ejpam-2010	524	9	2013	2013	NUM
ejpam-2010	524	10	)	)	PUNCT
ejpam-2010	524	11	,	,	PUNCT
ejpam-2010	524	12	256	256	NUM
ejpam-2010	524	13	-	-	SYM
ejpam-2010	524	14	281	281	NUM
ejpam-2010	524	15	275	275	NUM
ejpam-2010	524	16	4.2	4.2	NUM
ejpam-2010	524	17	.	.	PUNCT
ejpam-2010	525	1	inverse	inverse	NOUN
ejpam-2010	525	2	semigroups	semigroup	NOUN
ejpam-2010	525	3	let	let	VERB
ejpam-2010	525	4	s	s	PRON
ejpam-2010	525	5	be	be	AUX
ejpam-2010	525	6	an	an	DET
ejpam-2010	525	7	inverse	inverse	NOUN
ejpam-2010	525	8	semigroups	semigroup	NOUN
ejpam-2010	525	9	with	with	ADP
ejpam-2010	525	10	semilattice	semilattice	NOUN
ejpam-2010	525	11	of	of	ADP
ejpam-2010	525	12	idempotents	idempotent	NOUN
ejpam-2010	525	13	e(s	e(s	PROPN
ejpam-2010	525	14	)	)	PUNCT
ejpam-2010	525	15	.	.	PUNCT
ejpam-2010	526	1	we	we	PRON
ejpam-2010	526	2	define	define	VERB
ejpam-2010	526	3	an	an	DET
ejpam-2010	526	4	action	action	NOUN
ejpam-2010	526	5	of	of	ADP
ejpam-2010	526	6	s	s	PRON
ejpam-2010	526	7	on	on	ADP
ejpam-2010	526	8	e(s	e(s	PROPN
ejpam-2010	526	9	)	)	PUNCT
ejpam-2010	526	10	by	by	ADP
ejpam-2010	526	11	the	the	DET
ejpam-2010	526	12	rule	rule	NOUN
ejpam-2010	526	13	that	that	SCONJ
ejpam-2010	526	14	for	for	ADP
ejpam-2010	526	15	any	any	DET
ejpam-2010	526	16	s	s	X
ejpam-2010	526	17	∈	∈	NOUN
ejpam-2010	526	18	s	s	PART
ejpam-2010	526	19	and	and	CCONJ
ejpam-2010	526	20	e	e	PROPN
ejpam-2010	526	21	∈	∈	PROPN
ejpam-2010	526	22	e(s	e(s	PROPN
ejpam-2010	526	23	)	)	PUNCT
ejpam-2010	526	24	,	,	PUNCT
ejpam-2010	526	25	s	s	X
ejpam-2010	526	26	·	·	PUNCT
ejpam-2010	526	27	e	e	X
ejpam-2010	526	28	=	=	SYM
ejpam-2010	526	29	ses−1	ses−1	PROPN
ejpam-2010	526	30	,	,	PUNCT
ejpam-2010	526	31	where	where	SCONJ
ejpam-2010	526	32	s−1	s−1	PROPN
ejpam-2010	526	33	is	be	AUX
ejpam-2010	526	34	the	the	DET
ejpam-2010	526	35	unique	unique	ADJ
ejpam-2010	526	36	inverse	inverse	NOUN
ejpam-2010	526	37	of	of	ADP
ejpam-2010	526	38	s.	s.	PROPN
ejpam-2010	526	39	then	then	ADV
ejpam-2010	526	40	e(s	e(s	PROPN
ejpam-2010	526	41	)	)	PUNCT
ejpam-2010	526	42	together	together	ADV
ejpam-2010	526	43	with	with	ADP
ejpam-2010	526	44	the	the	DET
ejpam-2010	526	45	action	action	NOUN
ejpam-2010	526	46	is	be	AUX
ejpam-2010	526	47	called	call	VERB
ejpam-2010	526	48	the	the	DET
ejpam-2010	526	49	munn	munn	PROPN
ejpam-2010	526	50	module	module	NOUN
ejpam-2010	526	51	.	.	PUNCT
ejpam-2010	527	1	a	a	DET
ejpam-2010	527	2	left	left	ADJ
ejpam-2010	527	3	s	s	NOUN
ejpam-2010	527	4	-	-	NOUN
ejpam-2010	527	5	act	act	NOUN
ejpam-2010	527	6	x	x	PUNCT
ejpam-2010	527	7	paired	pair	VERB
ejpam-2010	527	8	with	with	ADP
ejpam-2010	527	9	an	an	DET
ejpam-2010	527	10	s	s	NOUN
ejpam-2010	527	11	-	-	PUNCT
ejpam-2010	527	12	homomorphism	homomorphism	NOUN
ejpam-2010	527	13	p	p	NOUN
ejpam-2010	527	14	to	to	ADP
ejpam-2010	527	15	e(s	e(s	PROPN
ejpam-2010	527	16	)	)	PUNCT
ejpam-2010	527	17	the	the	DET
ejpam-2010	527	18	munn	munn	PROPN
ejpam-2010	527	19	module	module	NOUN
ejpam-2010	527	20	,	,	PUNCT
ejpam-2010	527	21	such	such	ADJ
ejpam-2010	527	22	that	that	DET
ejpam-2010	527	23	p(x	p(x	NOUN
ejpam-2010	527	24	)	)	PUNCT
ejpam-2010	527	25	·	·	PUNCT
ejpam-2010	527	26	x	x	PUNCT
ejpam-2010	528	1	=	=	PUNCT
ejpam-2010	528	2	x	x	X
ejpam-2010	528	3	,	,	PUNCT
ejpam-2010	528	4	is	be	AUX
ejpam-2010	528	5	what	what	PRON
ejpam-2010	528	6	we	we	PRON
ejpam-2010	528	7	call	call	VERB
ejpam-2010	528	8	an	an	DET
ejpam-2010	528	9	étale	étale	ADJ
ejpam-2010	528	10	left	leave	VERB
ejpam-2010	528	11	s	s	NOUN
ejpam-2010	528	12	-	-	NOUN
ejpam-2010	528	13	act	act	NOUN
ejpam-2010	528	14	.	.	PUNCT
ejpam-2010	529	1	we	we	PRON
ejpam-2010	529	2	denote	denote	VERB
ejpam-2010	529	3	the	the	DET
ejpam-2010	529	4	category	category	NOUN
ejpam-2010	529	5	of	of	ADP
ejpam-2010	529	6	étale	étale	PROPN
ejpam-2010	529	7	left	left	ADJ
ejpam-2010	529	8	s	s	NOUN
ejpam-2010	529	9	-	-	PUNCT
ejpam-2010	529	10	acts	act	NOUN
ejpam-2010	529	11	by	by	ADP
ejpam-2010	529	12	étale	étale	PROPN
ejpam-2010	529	13	.	.	PUNCT
ejpam-2010	530	1	étale	étale	PROPN
ejpam-2010	530	2	can	can	AUX
ejpam-2010	530	3	be	be	AUX
ejpam-2010	530	4	taken	take	VERB
ejpam-2010	530	5	as	as	ADP
ejpam-2010	530	6	the	the	DET
ejpam-2010	530	7	definition	definition	NOUN
ejpam-2010	530	8	of	of	ADP
ejpam-2010	530	9	the	the	DET
ejpam-2010	530	10	classifying	classify	VERB
ejpam-2010	530	11	topos	topos	NOUN
ejpam-2010	530	12	of	of	ADP
ejpam-2010	530	13	s	s	PROPN
ejpam-2010	530	14	,	,	PUNCT
ejpam-2010	530	15	denoted	denote	VERB
ejpam-2010	530	16	b(s	b(	NOUN
ejpam-2010	530	17	)	)	PUNCT
ejpam-2010	530	18	.	.	PUNCT
ejpam-2010	531	1	étale	étale	PROPN
ejpam-2010	531	2	(	(	PUNCT
ejpam-2010	531	3	or	or	CCONJ
ejpam-2010	531	4	b(s	b(	NOUN
ejpam-2010	531	5	)	)	PUNCT
ejpam-2010	531	6	)	)	PUNCT
ejpam-2010	531	7	is	be	AUX
ejpam-2010	531	8	equivalent	equivalent	ADJ
ejpam-2010	531	9	to	to	ADP
ejpam-2010	531	10	the	the	DET
ejpam-2010	531	11	category	category	NOUN
ejpam-2010	531	12	psh(l(s	psh(l(s	NOUN
ejpam-2010	531	13	)	)	PUNCT
ejpam-2010	531	14	)	)	PUNCT
ejpam-2010	531	15	of	of	ADP
ejpam-2010	531	16	presheaves	presheave	NOUN
ejpam-2010	531	17	on	on	ADP
ejpam-2010	531	18	l(s	l(s	PROPN
ejpam-2010	531	19	)	)	PUNCT
ejpam-2010	531	20	.	.	PUNCT
ejpam-2010	532	1	theorem	theorem	VERB
ejpam-2010	532	2	19	19	NUM
ejpam-2010	532	3	.	.	PUNCT
ejpam-2010	533	1	[	[	X
ejpam-2010	533	2	11	11	NUM
ejpam-2010	533	3	,	,	PUNCT
ejpam-2010	533	4	theorem	theorem	VERB
ejpam-2010	533	5	1.1	1.1	NUM
ejpam-2010	533	6	]	]	PUNCT
ejpam-2010	533	7	let	let	VERB
ejpam-2010	533	8	s	s	PRON
ejpam-2010	533	9	and	and	CCONJ
ejpam-2010	533	10	t	t	PROPN
ejpam-2010	533	11	be	be	AUX
ejpam-2010	533	12	inverse	inverse	NOUN
ejpam-2010	533	13	semigroups	semigroup	NOUN
ejpam-2010	533	14	.	.	PUNCT
ejpam-2010	534	1	then	then	ADV
ejpam-2010	534	2	the	the	DET
ejpam-2010	534	3	following	follow	VERB
ejpam-2010	534	4	are	be	AUX
ejpam-2010	534	5	equivalent	equivalent	ADJ
ejpam-2010	534	6	:	:	PUNCT
ejpam-2010	534	7	(	(	PUNCT
ejpam-2010	534	8	1	1	X
ejpam-2010	534	9	)	)	PUNCT
ejpam-2010	534	10	s	s	NOUN
ejpam-2010	534	11	and	and	CCONJ
ejpam-2010	534	12	t	t	PROPN
ejpam-2010	534	13	are	be	AUX
ejpam-2010	534	14	strongly2	strongly2	PROPN
ejpam-2010	534	15	morita	morita	PROPN
ejpam-2010	534	16	equivalent	equivalent	PROPN
ejpam-2010	534	17	;	;	PUNCT
ejpam-2010	534	18	(	(	PUNCT
ejpam-2010	534	19	2	2	X
ejpam-2010	534	20	)	)	PUNCT
ejpam-2010	534	21	the	the	DET
ejpam-2010	534	22	classifying	classify	VERB
ejpam-2010	534	23	toposes	topos	NOUN
ejpam-2010	534	24	of	of	ADP
ejpam-2010	534	25	s	s	NOUN
ejpam-2010	534	26	and	and	CCONJ
ejpam-2010	534	27	t	t	PROPN
ejpam-2010	534	28	are	be	AUX
ejpam-2010	534	29	equivalent	equivalent	ADJ
ejpam-2010	534	30	;	;	PUNCT
ejpam-2010	534	31	(	(	PUNCT
ejpam-2010	534	32	3	3	X
ejpam-2010	534	33	)	)	PUNCT
ejpam-2010	534	34	the	the	DET
ejpam-2010	534	35	inductive	inductive	ADJ
ejpam-2010	534	36	groupoids	groupoid	NOUN
ejpam-2010	534	37	s	s	PART
ejpam-2010	534	38	and	and	CCONJ
ejpam-2010	534	39	t	t	PROPN
ejpam-2010	534	40	have	have	VERB
ejpam-2010	534	41	an	an	DET
ejpam-2010	534	42	ordered	order	VERB
ejpam-2010	534	43	groupoid	groupoid	NOUN
ejpam-2010	534	44	joint	joint	ADJ
ejpam-2010	534	45	enlargement	enlargement	NOUN
ejpam-2010	534	46	,	,	PUNCT
ejpam-2010	534	47	which	which	PRON
ejpam-2010	534	48	can	can	AUX
ejpam-2010	534	49	be	be	AUX
ejpam-2010	534	50	chosen	choose	VERB
ejpam-2010	534	51	to	to	PART
ejpam-2010	534	52	be	be	AUX
ejpam-2010	534	53	bipartite	bipartite	ADJ
ejpam-2010	534	54	;	;	PUNCT
ejpam-2010	534	55	(	(	PUNCT
ejpam-2010	534	56	4	4	X
ejpam-2010	534	57	)	)	PUNCT
ejpam-2010	534	58	the	the	DET
ejpam-2010	534	59	categories	category	NOUN
ejpam-2010	534	60	c(s	c(	VERB
ejpam-2010	534	61	)	)	PUNCT
ejpam-2010	534	62	and	and	CCONJ
ejpam-2010	534	63	c(t	c(t	PROPN
ejpam-2010	534	64	)	)	PUNCT
ejpam-2010	534	65	are	be	AUX
ejpam-2010	534	66	equivalent	equivalent	ADJ
ejpam-2010	534	67	;	;	PUNCT
ejpam-2010	534	68	(	(	PUNCT
ejpam-2010	534	69	5	5	X
ejpam-2010	534	70	)	)	PUNCT
ejpam-2010	534	71	s	s	VERB
ejpam-2010	534	72	and	and	CCONJ
ejpam-2010	534	73	thave	thave	VERB
ejpam-2010	534	74	a	a	DET
ejpam-2010	534	75	regular	regular	ADJ
ejpam-2010	534	76	joint	joint	ADJ
ejpam-2010	534	77	enlargement	enlargement	NOUN
ejpam-2010	534	78	;	;	PUNCT
ejpam-2010	534	79	(	(	PUNCT
ejpam-2010	534	80	6	6	NUM
ejpam-2010	534	81	)	)	PUNCT
ejpam-2010	534	82	s	s	NOUN
ejpam-2010	534	83	and	and	CCONJ
ejpam-2010	534	84	t	t	PROPN
ejpam-2010	534	85	are	be	AUX
ejpam-2010	534	86	morita	morita	PROPN
ejpam-2010	534	87	equivalent	equivalent	PROPN
ejpam-2010	534	88	.	.	PUNCT
ejpam-2010	535	1	observe	observe	VERB
ejpam-2010	535	2	that	that	SCONJ
ejpam-2010	535	3	the	the	DET
ejpam-2010	535	4	usual	usual	ADJ
ejpam-2010	535	5	morita	morita	NOUN
ejpam-2010	535	6	equivalence	equivalence	NOUN
ejpam-2010	535	7	and	and	CCONJ
ejpam-2010	535	8	the	the	DET
ejpam-2010	535	9	strongly2	strongly2	PROPN
ejpam-2010	535	10	morita	morita	PROPN
ejpam-2010	535	11	equivalence	equivalence	NOUN
ejpam-2010	535	12	coincide	coincide	NOUN
ejpam-2010	535	13	with	with	ADP
ejpam-2010	535	14	each	each	DET
ejpam-2010	535	15	other	other	ADJ
ejpam-2010	535	16	for	for	ADP
ejpam-2010	535	17	inverse	inverse	NOUN
ejpam-2010	535	18	semigroups	semigroup	NOUN
ejpam-2010	535	19	.	.	PUNCT
ejpam-2010	536	1	inverse	inverse	NOUN
ejpam-2010	536	2	semigroups	semigroup	NOUN
ejpam-2010	536	3	form	form	VERB
ejpam-2010	536	4	a	a	DET
ejpam-2010	536	5	special	special	ADJ
ejpam-2010	536	6	subclass	subclass	NOUN
ejpam-2010	536	7	of	of	ADP
ejpam-2010	536	8	semigroups	semigroup	NOUN
ejpam-2010	536	9	with	with	ADP
ejpam-2010	536	10	local	local	ADJ
ejpam-2010	536	11	units	unit	NOUN
ejpam-2010	536	12	so	so	SCONJ
ejpam-2010	536	13	we	we	PRON
ejpam-2010	536	14	have	have	VERB
ejpam-2010	536	15	the	the	DET
ejpam-2010	536	16	following	following	NOUN
ejpam-2010	536	17	theorem	theorem	NOUN
ejpam-2010	536	18	as	as	ADP
ejpam-2010	536	19	an	an	DET
ejpam-2010	536	20	analogue	analogue	NOUN
ejpam-2010	536	21	of	of	ADP
ejpam-2010	536	22	theorem	theorem	ADJ
ejpam-2010	536	23	10	10	NUM
ejpam-2010	536	24	.	.	PUNCT
ejpam-2010	537	1	theorem	theorem	VERB
ejpam-2010	537	2	20	20	NUM
ejpam-2010	537	3	.	.	PUNCT
ejpam-2010	538	1	[	[	X
ejpam-2010	538	2	2	2	NUM
ejpam-2010	538	3	,	,	PUNCT
ejpam-2010	538	4	theorem	theorem	VERB
ejpam-2010	538	5	2.15	2.15	NUM
ejpam-2010	538	6	]	]	PUNCT
ejpam-2010	538	7	let	let	VERB
ejpam-2010	538	8	s	s	PRON
ejpam-2010	538	9	and	and	CCONJ
ejpam-2010	538	10	t	t	PROPN
ejpam-2010	538	11	be	be	AUX
ejpam-2010	538	12	inverse	inverse	NOUN
ejpam-2010	538	13	semigroups	semigroup	NOUN
ejpam-2010	538	14	.	.	PUNCT
ejpam-2010	539	1	then	then	ADV
ejpam-2010	539	2	s	s	VERB
ejpam-2010	539	3	and	and	CCONJ
ejpam-2010	539	4	t	t	PROPN
ejpam-2010	539	5	are	be	AUX
ejpam-2010	539	6	morita	morita	NOUN
ejpam-2010	539	7	equivalent	equivalent	ADJ
ejpam-2010	539	8	if	if	SCONJ
ejpam-2010	540	1	and	and	CCONJ
ejpam-2010	540	2	only	only	ADV
ejpam-2010	540	3	if	if	SCONJ
ejpam-2010	540	4	there	there	PRON
ejpam-2010	540	5	is	be	VERB
ejpam-2010	540	6	a	a	DET
ejpam-2010	540	7	local	local	ADJ
ejpam-2010	540	8	isomorphism	isomorphism	NOUN
ejpam-2010	540	9	θ	θ	NOUN
ejpam-2010	540	10	:	:	PUNCT
ejpam-2010	540	11	c(s)p	c(s)p	PROPN
ejpam-2010	540	12	→	→	SYM
ejpam-2010	540	13	t	t	NOUN
ejpam-2010	540	14	for	for	ADP
ejpam-2010	540	15	some	some	DET
ejpam-2010	540	16	consolidation	consolidation	NOUN
ejpam-2010	540	17	p	p	NOUN
ejpam-2010	540	18	defined	define	VERB
ejpam-2010	540	19	on	on	ADP
ejpam-2010	540	20	c(s	c(	NOUN
ejpam-2010	540	21	)	)	PUNCT
ejpam-2010	540	22	.	.	PUNCT
ejpam-2010	541	1	corollary	corollary	ADJ
ejpam-2010	541	2	6	6	NUM
ejpam-2010	541	3	.	.	PUNCT
ejpam-2010	542	1	[	[	X
ejpam-2010	542	2	42	42	NUM
ejpam-2010	542	3	,	,	PUNCT
ejpam-2010	542	4	corollary	corollary	ADJ
ejpam-2010	542	5	5.5	5.5	NUM
ejpam-2010	542	6	]	]	PUNCT
ejpam-2010	542	7	suppose	suppose	VERB
ejpam-2010	542	8	s	s	PRON
ejpam-2010	542	9	and	and	CCONJ
ejpam-2010	542	10	t	t	PROPN
ejpam-2010	542	11	are	be	AUX
ejpam-2010	542	12	inverse	inverse	NOUN
ejpam-2010	542	13	semigroups	semigroup	NOUN
ejpam-2010	542	14	such	such	ADJ
ejpam-2010	542	15	that	that	SCONJ
ejpam-2010	542	16	t	t	PROPN
ejpam-2010	542	17	is	be	AUX
ejpam-2010	542	18	a	a	DET
ejpam-2010	542	19	monoid	monoid	NOUN
ejpam-2010	542	20	.	.	PUNCT
ejpam-2010	543	1	then	then	ADV
ejpam-2010	543	2	the	the	DET
ejpam-2010	543	3	following	following	NOUN
ejpam-2010	543	4	are	be	AUX
ejpam-2010	543	5	equivalent	equivalent	ADJ
ejpam-2010	543	6	:	:	PUNCT
ejpam-2010	543	7	(	(	PUNCT
ejpam-2010	543	8	1	1	X
ejpam-2010	543	9	)	)	PUNCT
ejpam-2010	543	10	there	there	PRON
ejpam-2010	543	11	exists	exist	VERB
ejpam-2010	543	12	an	an	DET
ejpam-2010	543	13	idempotent	idempotent	ADJ
ejpam-2010	543	14	e	e	NOUN
ejpam-2010	543	15	∈	∈	PROPN
ejpam-2010	543	16	e(s	e(s	PROPN
ejpam-2010	543	17	)	)	PUNCT
ejpam-2010	543	18	such	such	ADJ
ejpam-2010	543	19	that	that	DET
ejpam-2010	543	20	s	s	PART
ejpam-2010	543	21	=	=	X
ejpam-2010	543	22	ses	se	NOUN
ejpam-2010	543	23	and	and	CCONJ
ejpam-2010	543	24	t	t	NOUN
ejpam-2010	543	25	∼=	∼=	PROPN
ejpam-2010	543	26	ese	ese	NOUN
ejpam-2010	543	27	;	;	PUNCT
ejpam-2010	543	28	(	(	PUNCT
ejpam-2010	543	29	2	2	X
ejpam-2010	543	30	)	)	PUNCT
ejpam-2010	543	31	s	s	NOUN
ejpam-2010	543	32	and	and	CCONJ
ejpam-2010	543	33	t	t	PROPN
ejpam-2010	543	34	are	be	AUX
ejpam-2010	543	35	strongly2	strongly2	PROPN
ejpam-2010	543	36	morita	morita	PROPN
ejpam-2010	543	37	equivalent	equivalent	PROPN
ejpam-2010	543	38	;	;	PUNCT
ejpam-2010	543	39	(	(	PUNCT
ejpam-2010	543	40	3	3	X
ejpam-2010	543	41	)	)	PUNCT
ejpam-2010	543	42	the	the	DET
ejpam-2010	543	43	categories	category	NOUN
ejpam-2010	543	44	c(s	c(	VERB
ejpam-2010	543	45	)	)	PUNCT
ejpam-2010	543	46	and	and	CCONJ
ejpam-2010	543	47	c(t	c(t	PROPN
ejpam-2010	543	48	)	)	PUNCT
ejpam-2010	543	49	are	be	AUX
ejpam-2010	543	50	equivalent	equivalent	ADJ
ejpam-2010	543	51	.	.	PUNCT
ejpam-2010	544	1	y.	y.	PROPN
ejpam-2010	544	2	wang	wang	PROPN
ejpam-2010	544	3	,	,	PUNCT
ejpam-2010	544	4	k.	k.	PROPN
ejpam-2010	544	5	shum	shum	PROPN
ejpam-2010	544	6	,	,	PUNCT
ejpam-2010	544	7	x.	x.	PROPN
ejpam-2010	544	8	ren	ren	PROPN
ejpam-2010	544	9	/	/	SYM
ejpam-2010	544	10	eur	eur	PROPN
ejpam-2010	544	11	.	.	PUNCT
ejpam-2010	545	1	j.	j.	PROPN
ejpam-2010	545	2	pure	pure	PROPN
ejpam-2010	545	3	appl	appl	PROPN
ejpam-2010	545	4	.	.	PROPN
ejpam-2010	545	5	math	math	PROPN
ejpam-2010	545	6	,	,	PUNCT
ejpam-2010	545	7	6	6	NUM
ejpam-2010	545	8	(	(	PUNCT
ejpam-2010	545	9	2013	2013	NUM
ejpam-2010	545	10	)	)	PUNCT
ejpam-2010	545	11	,	,	PUNCT
ejpam-2010	545	12	256	256	NUM
ejpam-2010	545	13	-	-	SYM
ejpam-2010	545	14	281	281	NUM
ejpam-2010	545	15	276	276	NUM
ejpam-2010	545	16	we	we	PRON
ejpam-2010	545	17	remark	remark	VERB
ejpam-2010	545	18	that	that	SCONJ
ejpam-2010	545	19	if	if	SCONJ
ejpam-2010	545	20	an	an	DET
ejpam-2010	545	21	inverse	inverse	NOUN
ejpam-2010	545	22	semigroup	semigroup	NOUN
ejpam-2010	545	23	s	s	PART
ejpam-2010	545	24	is	be	AUX
ejpam-2010	545	25	strongly2	strongly2	PROPN
ejpam-2010	545	26	morita	morita	PROPN
ejpam-2010	545	27	equivalent	equivalent	PROPN
ejpam-2010	545	28	to	to	ADP
ejpam-2010	545	29	an	an	DET
ejpam-2010	545	30	inverse	inverse	NOUN
ejpam-2010	545	31	monoid	monoid	NOUN
ejpam-2010	545	32	t	t	PROPN
ejpam-2010	545	33	,	,	PUNCT
ejpam-2010	545	34	then	then	ADV
ejpam-2010	545	35	s	s	VERB
ejpam-2010	545	36	is	be	AUX
ejpam-2010	545	37	an	an	DET
ejpam-2010	545	38	enlargement	enlargement	NOUN
ejpam-2010	545	39	of	of	ADP
ejpam-2010	545	40	t	t	PROPN
ejpam-2010	545	41	.	.	PUNCT
ejpam-2010	546	1	in	in	ADP
ejpam-2010	546	2	particular	particular	ADJ
ejpam-2010	546	3	,	,	PUNCT
ejpam-2010	546	4	if	if	SCONJ
ejpam-2010	546	5	s	s	PRON
ejpam-2010	546	6	and	and	CCONJ
ejpam-2010	546	7	t	t	PROPN
ejpam-2010	546	8	are	be	AUX
ejpam-2010	546	9	inverse	inverse	ADJ
ejpam-2010	546	10	monoids	monoid	NOUN
ejpam-2010	546	11	,	,	PUNCT
ejpam-2010	546	12	then	then	ADV
ejpam-2010	546	13	s	s	VERB
ejpam-2010	546	14	is	be	AUX
ejpam-2010	546	15	strongly2	strongly2	PROPN
ejpam-2010	546	16	morita	morita	PROPN
ejpam-2010	546	17	equivalent	equivalent	PROPN
ejpam-2010	546	18	to	to	ADP
ejpam-2010	546	19	t	t	PROPN
ejpam-2010	546	20	if	if	SCONJ
ejpam-2010	546	21	and	and	CCONJ
ejpam-2010	546	22	only	only	ADV
ejpam-2010	546	23	if	if	SCONJ
ejpam-2010	546	24	there	there	PRON
ejpam-2010	546	25	exist	exist	VERB
ejpam-2010	546	26	e	e	PROPN
ejpam-2010	546	27	∈	∈	PROPN
ejpam-2010	546	28	e(s	e(s	PROPN
ejpam-2010	546	29	)	)	PUNCT
ejpam-2010	546	30	and	and	CCONJ
ejpam-2010	546	31	f	f	PROPN
ejpam-2010	546	32	∈	∈	PROPN
ejpam-2010	546	33	e(t	e(t	PROPN
ejpam-2010	546	34	)	)	PUNCT
ejpam-2010	547	1	so	so	SCONJ
ejpam-2010	547	2	that	that	PRON
ejpam-2010	547	3	s	s	VERB
ejpam-2010	547	4	=	=	SYM
ejpam-2010	547	5	ses	ses	PROPN
ejpam-2010	547	6	,	,	PUNCT
ejpam-2010	547	7	ese	ese	NOUN
ejpam-2010	547	8	∼=	∼=	PROPN
ejpam-2010	547	9	t	t	NOUN
ejpam-2010	547	10	and	and	CCONJ
ejpam-2010	547	11	t	t	PROPN
ejpam-2010	547	12	=	=	SYM
ejpam-2010	547	13	t	t	PROPN
ejpam-2010	547	14	f	f	PROPN
ejpam-2010	547	15	t	t	PROPN
ejpam-2010	547	16	and	and	CCONJ
ejpam-2010	547	17	f	f	PROPN
ejpam-2010	547	18	t	t	PROPN
ejpam-2010	547	19	f	f	PROPN
ejpam-2010	547	20	∼=	∼=	PROPN
ejpam-2010	547	21	s.	s.	PROPN
ejpam-2010	547	22	in	in	ADP
ejpam-2010	547	23	the	the	DET
ejpam-2010	547	24	following	following	NOUN
ejpam-2010	547	25	we	we	PRON
ejpam-2010	547	26	give	give	VERB
ejpam-2010	547	27	a	a	DET
ejpam-2010	547	28	list	list	NOUN
ejpam-2010	547	29	of	of	ADP
ejpam-2010	547	30	properties	property	NOUN
ejpam-2010	547	31	of	of	ADP
ejpam-2010	547	32	strongly2	strongly2	PROPN
ejpam-2010	547	33	morita	morita	PROPN
ejpam-2010	547	34	equivalent	equivalent	ADJ
ejpam-2010	547	35	inverse	inverse	NOUN
ejpam-2010	547	36	semigroups	semigroup	NOUN
ejpam-2010	547	37	which	which	PRON
ejpam-2010	547	38	was	be	AUX
ejpam-2010	547	39	taken	take	VERB
ejpam-2010	547	40	as	as	ADP
ejpam-2010	547	41	a	a	DET
ejpam-2010	547	42	corollary	corollary	NOUN
ejpam-2010	547	43	in	in	ADP
ejpam-2010	547	44	[	[	X
ejpam-2010	547	45	42	42	NUM
ejpam-2010	547	46	]	]	PUNCT
ejpam-2010	547	47	.	.	PUNCT
ejpam-2010	548	1	proposition	proposition	NOUN
ejpam-2010	548	2	9	9	NUM
ejpam-2010	548	3	.	.	PUNCT
ejpam-2010	549	1	[	[	X
ejpam-2010	549	2	42	42	NUM
ejpam-2010	549	3	,	,	PUNCT
ejpam-2010	549	4	corollary	corollary	ADJ
ejpam-2010	549	5	5.2	5.2	NUM
ejpam-2010	549	6	]	]	PUNCT
ejpam-2010	549	7	let	let	VERB
ejpam-2010	549	8	s	s	PRON
ejpam-2010	549	9	and	and	CCONJ
ejpam-2010	549	10	t	t	PROPN
ejpam-2010	549	11	be	be	AUX
ejpam-2010	549	12	strongly2	strongly2	PROPN
ejpam-2010	549	13	morita	morita	PROPN
ejpam-2010	549	14	equivalent	equivalent	ADJ
ejpam-2010	549	15	inverse	inverse	NOUN
ejpam-2010	549	16	semigroups	semigroup	NOUN
ejpam-2010	549	17	.	.	PUNCT
ejpam-2010	550	1	then	then	ADV
ejpam-2010	550	2	the	the	DET
ejpam-2010	550	3	following	following	ADJ
ejpam-2010	550	4	statements	statement	NOUN
ejpam-2010	550	5	hold	hold	VERB
ejpam-2010	550	6	:	:	PUNCT
ejpam-2010	550	7	(	(	PUNCT
ejpam-2010	550	8	1	1	X
ejpam-2010	550	9	)	)	PUNCT
ejpam-2010	550	10	the	the	DET
ejpam-2010	550	11	categories	category	NOUN
ejpam-2010	550	12	c(s	c(	VERB
ejpam-2010	550	13	)	)	PUNCT
ejpam-2010	550	14	and	and	CCONJ
ejpam-2010	550	15	c(t	c(t	PROPN
ejpam-2010	550	16	)	)	PUNCT
ejpam-2010	550	17	are	be	AUX
ejpam-2010	550	18	equivalent	equivalent	ADJ
ejpam-2010	550	19	;	;	PUNCT
ejpam-2010	550	20	(	(	PUNCT
ejpam-2010	550	21	2	2	X
ejpam-2010	550	22	)	)	PUNCT
ejpam-2010	550	23	the	the	DET
ejpam-2010	550	24	categories	category	NOUN
ejpam-2010	550	25	l(s	l(s	PROPN
ejpam-2010	550	26	)	)	PUNCT
ejpam-2010	550	27	and	and	CCONJ
ejpam-2010	550	28	l(t	l(t	PROPN
ejpam-2010	550	29	)	)	PUNCT
ejpam-2010	550	30	are	be	AUX
ejpam-2010	550	31	equivalent	equivalent	ADJ
ejpam-2010	550	32	;	;	PUNCT
ejpam-2010	550	33	(	(	PUNCT
ejpam-2010	550	34	3	3	X
ejpam-2010	550	35	)	)	PUNCT
ejpam-2010	550	36	for	for	ADP
ejpam-2010	550	37	each	each	DET
ejpam-2010	550	38	e	e	PROPN
ejpam-2010	550	39	∈	∈	PROPN
ejpam-2010	550	40	e(s	e(s	PROPN
ejpam-2010	550	41	)	)	PUNCT
ejpam-2010	550	42	,	,	PUNCT
ejpam-2010	550	43	there	there	PRON
ejpam-2010	550	44	exists	exist	VERB
ejpam-2010	550	45	an	an	DET
ejpam-2010	550	46	idempotent	idempotent	NOUN
ejpam-2010	550	47	f	f	PROPN
ejpam-2010	550	48	∈	∈	PROPN
ejpam-2010	550	49	e(t	e(t	PROPN
ejpam-2010	550	50	)	)	PUNCT
ejpam-2010	551	1	such	such	ADJ
ejpam-2010	551	2	that	that	SCONJ
ejpam-2010	551	3	ese	ese	NOUN
ejpam-2010	551	4	∼=	∼=	PROPN
ejpam-2010	551	5	f	f	PROPN
ejpam-2010	551	6	s	s	PROPN
ejpam-2010	551	7	f	f	X
ejpam-2010	551	8	and	and	CCONJ
ejpam-2010	551	9	conversely	conversely	ADV
ejpam-2010	551	10	;	;	PUNCT
ejpam-2010	551	11	(	(	PUNCT
ejpam-2010	551	12	4	4	X
ejpam-2010	551	13	)	)	PUNCT
ejpam-2010	551	14	the	the	DET
ejpam-2010	551	15	underlying	underlie	VERB
ejpam-2010	551	16	groupoids	groupoid	NOUN
ejpam-2010	551	17	of	of	ADP
ejpam-2010	551	18	s	s	PRON
ejpam-2010	551	19	and	and	CCONJ
ejpam-2010	551	20	t	t	PROPN
ejpam-2010	551	21	are	be	AUX
ejpam-2010	551	22	naturally	naturally	ADV
ejpam-2010	551	23	equivalent	equivalent	ADJ
ejpam-2010	551	24	;	;	PUNCT
ejpam-2010	551	25	(	(	PUNCT
ejpam-2010	551	26	5	5	X
ejpam-2010	551	27	)	)	PUNCT
ejpam-2010	551	28	there	there	PRON
ejpam-2010	551	29	is	be	VERB
ejpam-2010	551	30	a	a	DET
ejpam-2010	551	31	bijection	bijection	ADJ
ejpam-2010	551	32	f	f	NOUN
ejpam-2010	551	33	:	:	PUNCT
ejpam-2010	551	34	e(s)/d	e(s)/d	PROPN
ejpam-2010	551	35	→	→	SYM
ejpam-2010	551	36	e(t	e(t	PROPN
ejpam-2010	551	37	)	)	PUNCT
ejpam-2010	551	38	/d	/d	PUNCT
ejpam-2010	551	39	such	such	ADJ
ejpam-2010	551	40	that	that	SCONJ
ejpam-2010	551	41	if	if	SCONJ
ejpam-2010	551	42	d	d	NOUN
ejpam-2010	551	43	is	be	AUX
ejpam-2010	551	44	a	a	DET
ejpam-2010	551	45	d	d	NOUN
ejpam-2010	551	46	-	-	PUNCT
ejpam-2010	551	47	class	class	NOUN
ejpam-2010	551	48	of	of	ADP
ejpam-2010	551	49	s	s	PRON
ejpam-2010	551	50	with	with	ADP
ejpam-2010	551	51	maximal	maximal	ADJ
ejpam-2010	551	52	subgroup	subgroup	NOUN
ejpam-2010	551	53	g	g	NOUN
ejpam-2010	551	54	,	,	PUNCT
ejpam-2010	551	55	then	then	ADV
ejpam-2010	551	56	f(d	f(d	PROPN
ejpam-2010	551	57	)	)	PUNCT
ejpam-2010	551	58	is	be	AUX
ejpam-2010	551	59	a	a	DET
ejpam-2010	551	60	d	d	NOUN
ejpam-2010	551	61	-	-	PUNCT
ejpam-2010	551	62	class	class	NOUN
ejpam-2010	551	63	of	of	ADP
ejpam-2010	551	64	t	t	PROPN
ejpam-2010	551	65	with	with	ADP
ejpam-2010	551	66	maximal	maximal	ADJ
ejpam-2010	551	67	subgroup	subgroup	NOUN
ejpam-2010	551	68	isomorphic	isomorphic	ADJ
ejpam-2010	551	69	to	to	ADP
ejpam-2010	551	70	g	g	NOUN
ejpam-2010	551	71	;	;	PUNCT
ejpam-2010	551	72	(	(	PUNCT
ejpam-2010	551	73	6	6	X
ejpam-2010	551	74	)	)	PUNCT
ejpam-2010	551	75	the	the	DET
ejpam-2010	551	76	posets	poset	NOUN
ejpam-2010	551	77	e(s)/j	e(s)/j	PROPN
ejpam-2010	551	78	and	and	CCONJ
ejpam-2010	551	79	e(t	e(t	NOUN
ejpam-2010	551	80	)	)	PUNCT
ejpam-2010	552	1	/j	/j	X
ejpam-2010	552	2	are	be	AUX
ejpam-2010	552	3	isomorphic	isomorphic	ADJ
ejpam-2010	552	4	;	;	PUNCT
ejpam-2010	552	5	(	(	PUNCT
ejpam-2010	552	6	7	7	X
ejpam-2010	552	7	)	)	PUNCT
ejpam-2010	552	8	s	s	NOUN
ejpam-2010	552	9	and	and	CCONJ
ejpam-2010	552	10	t	t	PROPN
ejpam-2010	552	11	have	have	VERB
ejpam-2010	552	12	isomorphic	isomorphic	ADJ
ejpam-2010	552	13	lattices	lattice	NOUN
ejpam-2010	552	14	of	of	ADP
ejpam-2010	552	15	two	two	NUM
ejpam-2010	552	16	-	-	PUNCT
ejpam-2010	552	17	sided	sided	ADJ
ejpam-2010	552	18	ideals	ideal	NOUN
ejpam-2010	552	19	;	;	PUNCT
ejpam-2010	552	20	(	(	PUNCT
ejpam-2010	552	21	8)	8)	NUM
ejpam-2010	552	22	the	the	DET
ejpam-2010	552	23	classifying	classify	VERB
ejpam-2010	552	24	toposesb(s	toposesb(s	NOUN
ejpam-2010	552	25	)	)	PUNCT
ejpam-2010	552	26	andb(t	andb(t	NOUN
ejpam-2010	552	27	)	)	PUNCT
ejpam-2010	552	28	are	be	AUX
ejpam-2010	552	29	equivalent	equivalent	ADJ
ejpam-2010	552	30	;	;	PUNCT
ejpam-2010	552	31	(	(	PUNCT
ejpam-2010	552	32	9	9	X
ejpam-2010	552	33	)	)	PUNCT
ejpam-2010	552	34	s	s	NOUN
ejpam-2010	552	35	and	and	CCONJ
ejpam-2010	552	36	t	t	PROPN
ejpam-2010	552	37	have	have	VERB
ejpam-2010	552	38	the	the	DET
ejpam-2010	552	39	same	same	ADJ
ejpam-2010	552	40	cohomology	cohomology	NOUN
ejpam-2010	552	41	groups	group	NOUN
ejpam-2010	552	42	;	;	PUNCT
ejpam-2010	552	43	(	(	PUNCT
ejpam-2010	552	44	10	10	NUM
ejpam-2010	552	45	)	)	PUNCT
ejpam-2010	552	46	s	s	AUX
ejpam-2010	552	47	has	have	VERB
ejpam-2010	552	48	a	a	DET
ejpam-2010	552	49	zero	zero	NUM
ejpam-2010	552	50	if	if	SCONJ
ejpam-2010	552	51	and	and	CCONJ
ejpam-2010	552	52	only	only	ADV
ejpam-2010	552	53	if	if	SCONJ
ejpam-2010	552	54	t	t	PROPN
ejpam-2010	552	55	has	have	VERB
ejpam-2010	552	56	a	a	DET
ejpam-2010	552	57	zero	zero	NUM
ejpam-2010	552	58	;	;	PUNCT
ejpam-2010	552	59	(	(	PUNCT
ejpam-2010	552	60	11	11	X
ejpam-2010	552	61	)	)	PUNCT
ejpam-2010	552	62	they	they	PRON
ejpam-2010	552	63	have	have	VERB
ejpam-2010	552	64	isomorphic	isomorphic	ADJ
ejpam-2010	552	65	maximal	maximal	ADJ
ejpam-2010	552	66	group	group	NOUN
ejpam-2010	552	67	images	image	NOUN
ejpam-2010	552	68	.	.	PUNCT
ejpam-2010	553	1	if	if	SCONJ
ejpam-2010	553	2	e	e	PROPN
ejpam-2010	553	3	is	be	AUX
ejpam-2010	553	4	a	a	DET
ejpam-2010	553	5	semilattice	semilattice	NOUN
ejpam-2010	553	6	,	,	PUNCT
ejpam-2010	553	7	then	then	ADV
ejpam-2010	553	8	(	(	PUNCT
ejpam-2010	553	9	e,≤)∼=	e,≤)∼=	X
ejpam-2010	553	10	(	(	PUNCT
ejpam-2010	553	11	e	e	NOUN
ejpam-2010	553	12	/	/	SYM
ejpam-2010	553	13	j	j	PROPN
ejpam-2010	553	14	,	,	PUNCT
ejpam-2010	553	15	≤j	≤j	PROPN
ejpam-2010	553	16	)	)	PUNCT
ejpam-2010	553	17	and	and	CCONJ
ejpam-2010	553	18	so	so	ADV
ejpam-2010	553	19	we	we	PRON
ejpam-2010	553	20	have	have	VERB
ejpam-2010	553	21	the	the	DET
ejpam-2010	553	22	following	follow	VERB
ejpam-2010	553	23	corollaries	corollary	NOUN
ejpam-2010	553	24	.	.	PUNCT
ejpam-2010	554	1	corollary	corollary	ADJ
ejpam-2010	554	2	7	7	NUM
ejpam-2010	554	3	.	.	PUNCT
ejpam-2010	555	1	[	[	X
ejpam-2010	555	2	42	42	NUM
ejpam-2010	555	3	,	,	PUNCT
ejpam-2010	555	4	corollary	corollary	ADJ
ejpam-2010	555	5	5.3	5.3	NUM
ejpam-2010	555	6	]	]	PUNCT
ejpam-2010	555	7	let	let	VERB
ejpam-2010	555	8	e	e	NOUN
ejpam-2010	555	9	and	and	CCONJ
ejpam-2010	555	10	f	f	PROPN
ejpam-2010	555	11	be	be	AUX
ejpam-2010	555	12	strongly2	strongly2	PROPN
ejpam-2010	555	13	morita	morita	PROPN
ejpam-2010	555	14	equivalent	equivalent	PROPN
ejpam-2010	555	15	semilattices	semilattice	NOUN
ejpam-2010	555	16	.	.	PUNCT
ejpam-2010	556	1	then	then	ADV
ejpam-2010	556	2	e	e	PROPN
ejpam-2010	556	3	is	be	AUX
ejpam-2010	556	4	isomorphic	isomorphic	ADJ
ejpam-2010	556	5	to	to	ADP
ejpam-2010	556	6	f.	f.	PROPN
ejpam-2010	556	7	corollary	corollary	PROPN
ejpam-2010	556	8	8	8	NUM
ejpam-2010	556	9	.	.	PUNCT
ejpam-2010	557	1	[	[	X
ejpam-2010	557	2	42	42	NUM
ejpam-2010	557	3	,	,	PUNCT
ejpam-2010	557	4	corollary	corollary	NOUN
ejpam-2010	557	5	4.8	4.8	NUM
ejpam-2010	557	6	]	]	PUNCT
ejpam-2010	557	7	let	let	VERB
ejpam-2010	557	8	s	s	PRON
ejpam-2010	557	9	and	and	CCONJ
ejpam-2010	557	10	t	t	PROPN
ejpam-2010	557	11	be	be	AUX
ejpam-2010	557	12	strongly2	strongly2	PROPN
ejpam-2010	557	13	morita	morita	PROPN
ejpam-2010	557	14	equivalent	equivalent	ADJ
ejpam-2010	557	15	inverse	inverse	NOUN
ejpam-2010	557	16	semigroups	semigroup	NOUN
ejpam-2010	557	17	.	.	PUNCT
ejpam-2010	558	1	then	then	ADV
ejpam-2010	558	2	the	the	DET
ejpam-2010	558	3	universal	universal	ADJ
ejpam-2010	558	4	and	and	CCONJ
ejpam-2010	558	5	reduced	reduce	VERB
ejpam-2010	558	6	c∗-algebras	c∗-algebra	NOUN
ejpam-2010	558	7	of	of	ADP
ejpam-2010	558	8	s	s	NOUN
ejpam-2010	558	9	and	and	CCONJ
ejpam-2010	558	10	t	t	PROPN
ejpam-2010	558	11	are	be	AUX
ejpam-2010	558	12	strongly2	strongly2	PROPN
ejpam-2010	558	13	morita	morita	PROPN
ejpam-2010	558	14	equivalent	equivalent	PROPN
ejpam-2010	558	15	.	.	PUNCT
ejpam-2010	559	1	for	for	ADP
ejpam-2010	559	2	strongly	strongly	ADV
ejpam-2010	559	3	morita	morita	PROPN
ejpam-2010	559	4	equivalent	equivalent	ADJ
ejpam-2010	559	5	modules	module	NOUN
ejpam-2010	559	6	,	,	PUNCT
ejpam-2010	559	7	we	we	PRON
ejpam-2010	559	8	have	have	VERB
ejpam-2010	559	9	the	the	DET
ejpam-2010	559	10	following	follow	VERB
ejpam-2010	559	11	theorems	theorem	NOUN
ejpam-2010	559	12	.	.	PUNCT
ejpam-2010	560	1	theorem	theorem	NOUN
ejpam-2010	560	2	21	21	NUM
ejpam-2010	560	3	.	.	PUNCT
ejpam-2010	561	1	[	[	X
ejpam-2010	561	2	42	42	NUM
ejpam-2010	561	3	,	,	PUNCT
ejpam-2010	561	4	theorem	theorem	VERB
ejpam-2010	561	5	4.13	4.13	NUM
ejpam-2010	561	6	]	]	PUNCT
ejpam-2010	561	7	let	let	VERB
ejpam-2010	561	8	s	s	PRON
ejpam-2010	561	9	and	and	CCONJ
ejpam-2010	561	10	t	t	PROPN
ejpam-2010	561	11	be	be	AUX
ejpam-2010	561	12	strongly	strongly	ADV
ejpam-2010	561	13	morita	morita	PROPN
ejpam-2010	561	14	equivalent	equivalent	ADJ
ejpam-2010	561	15	inverse	inverse	NOUN
ejpam-2010	561	16	semigroups	semigroup	NOUN
ejpam-2010	561	17	and	and	CCONJ
ejpam-2010	561	18	let	let	VERB
ejpam-2010	561	19	k	k	PRON
ejpam-2010	561	20	be	be	AUX
ejpam-2010	561	21	a	a	DET
ejpam-2010	561	22	commutative	commutative	ADJ
ejpam-2010	561	23	unital	unital	ADJ
ejpam-2010	561	24	ring	ring	NOUN
ejpam-2010	561	25	.	.	PUNCT
ejpam-2010	562	1	then	then	ADV
ejpam-2010	562	2	the	the	DET
ejpam-2010	562	3	semigroup	semigroup	PROPN
ejpam-2010	562	4	algebras	algebras	PROPN
ejpam-2010	562	5	ks	ks	PROPN
ejpam-2010	562	6	and	and	CCONJ
ejpam-2010	562	7	kt	kt	PROPN
ejpam-2010	562	8	are	be	AUX
ejpam-2010	562	9	morita	morita	PROPN
ejpam-2010	562	10	equivalent	equivalent	NOUN
ejpam-2010	562	11	.	.	PUNCT
ejpam-2010	563	1	y.	y.	PROPN
ejpam-2010	563	2	wang	wang	PROPN
ejpam-2010	563	3	,	,	PUNCT
ejpam-2010	563	4	k.	k.	PROPN
ejpam-2010	563	5	shum	shum	PROPN
ejpam-2010	563	6	,	,	PUNCT
ejpam-2010	563	7	x.	x.	PROPN
ejpam-2010	563	8	ren	ren	PROPN
ejpam-2010	563	9	/	/	SYM
ejpam-2010	563	10	eur	eur	PROPN
ejpam-2010	563	11	.	.	PUNCT
ejpam-2010	564	1	j.	j.	PROPN
ejpam-2010	564	2	pure	pure	PROPN
ejpam-2010	564	3	appl	appl	PROPN
ejpam-2010	564	4	.	.	PROPN
ejpam-2010	564	5	math	math	PROPN
ejpam-2010	564	6	,	,	PUNCT
ejpam-2010	564	7	6	6	NUM
ejpam-2010	564	8	(	(	PUNCT
ejpam-2010	564	9	2013	2013	NUM
ejpam-2010	564	10	)	)	PUNCT
ejpam-2010	564	11	,	,	PUNCT
ejpam-2010	564	12	256	256	NUM
ejpam-2010	564	13	-	-	SYM
ejpam-2010	564	14	281	281	NUM
ejpam-2010	564	15	277	277	NUM
ejpam-2010	564	16	every	every	DET
ejpam-2010	564	17	proper	proper	ADJ
ejpam-2010	564	18	image	image	NOUN
ejpam-2010	564	19	of	of	ADP
ejpam-2010	564	20	the	the	DET
ejpam-2010	564	21	bicyclic	bicyclic	NOUN
ejpam-2010	564	22	monoid	monoid	NOUN
ejpam-2010	564	23	is	be	AUX
ejpam-2010	564	24	a	a	DET
ejpam-2010	564	25	group	group	NOUN
ejpam-2010	564	26	[	[	X
ejpam-2010	564	27	7	7	NUM
ejpam-2010	564	28	]	]	PUNCT
ejpam-2010	564	29	,	,	PUNCT
ejpam-2010	564	30	so	so	CCONJ
ejpam-2010	564	31	no	no	DET
ejpam-2010	564	32	residually	residually	ADV
ejpam-2010	564	33	finite	finite	ADJ
ejpam-2010	564	34	inverse	inverse	NOUN
ejpam-2010	564	35	semigroup	semigroup	NOUN
ejpam-2010	564	36	can	can	AUX
ejpam-2010	564	37	contain	contain	VERB
ejpam-2010	564	38	a	a	DET
ejpam-2010	564	39	copy	copy	NOUN
ejpam-2010	564	40	of	of	ADP
ejpam-2010	564	41	the	the	DET
ejpam-2010	564	42	bicyclic	bicyclic	NOUN
ejpam-2010	564	43	monoid	monoid	NOUN
ejpam-2010	564	44	.	.	PUNCT
ejpam-2010	565	1	(	(	PUNCT
ejpam-2010	565	2	actually	actually	ADV
ejpam-2010	565	3	it	it	PRON
ejpam-2010	565	4	is	be	AUX
ejpam-2010	565	5	known	know	VERB
ejpam-2010	565	6	that	that	SCONJ
ejpam-2010	565	7	the	the	DET
ejpam-2010	565	8	bicyclic	bicyclic	NOUN
ejpam-2010	565	9	monoid	monoid	NOUN
ejpam-2010	565	10	can	can	AUX
ejpam-2010	565	11	not	not	PART
ejpam-2010	565	12	embed	embed	VERB
ejpam-2010	565	13	in	in	ADP
ejpam-2010	565	14	any	any	DET
ejpam-2010	565	15	compact	compact	ADJ
ejpam-2010	565	16	semigroup	semigroup	NOUN
ejpam-2010	565	17	since	since	SCONJ
ejpam-2010	565	18	compact	compact	ADJ
ejpam-2010	565	19	semigroups	semigroup	NOUN
ejpam-2010	565	20	are	be	AUX
ejpam-2010	565	21	stable	stable	ADJ
ejpam-2010	565	22	and	and	CCONJ
ejpam-2010	565	23	the	the	DET
ejpam-2010	565	24	bicyclic	bicyclic	NOUN
ejpam-2010	565	25	monoid	monoid	NOUN
ejpam-2010	565	26	can	can	AUX
ejpam-2010	565	27	not	not	PART
ejpam-2010	565	28	embed	embed	VERB
ejpam-2010	565	29	in	in	ADP
ejpam-2010	565	30	any	any	DET
ejpam-2010	565	31	stable	stable	ADJ
ejpam-2010	565	32	semigroup	semigroup	NOUN
ejpam-2010	566	1	[	[	X
ejpam-2010	566	2	40	40	NUM
ejpam-2010	566	3	]	]	PUNCT
ejpam-2010	566	4	.	.	PUNCT
ejpam-2010	566	5	)	)	PUNCT
ejpam-2010	566	6	also	also	ADV
ejpam-2010	566	7	no	no	DET
ejpam-2010	566	8	semigroup	semigroup	NOUN
ejpam-2010	566	9	with	with	ADP
ejpam-2010	566	10	central	central	ADJ
ejpam-2010	566	11	idempotents	idempotent	NOUN
ejpam-2010	566	12	contains	contain	VERB
ejpam-2010	566	13	a	a	DET
ejpam-2010	566	14	copy	copy	NOUN
ejpam-2010	566	15	of	of	ADP
ejpam-2010	566	16	the	the	DET
ejpam-2010	566	17	bicyclic	bicyclic	NOUN
ejpam-2010	566	18	monoid	monoid	NOUN
ejpam-2010	566	19	since	since	SCONJ
ejpam-2010	566	20	its	its	PRON
ejpam-2010	566	21	idempotents	idempotent	NOUN
ejpam-2010	566	22	are	be	AUX
ejpam-2010	566	23	not	not	PART
ejpam-2010	566	24	central	central	ADJ
ejpam-2010	566	25	.	.	PUNCT
ejpam-2010	567	1	hence	hence	ADV
ejpam-2010	567	2	we	we	PRON
ejpam-2010	567	3	have	have	VERB
ejpam-2010	567	4	the	the	DET
ejpam-2010	567	5	following	follow	VERB
ejpam-2010	567	6	corollary	corollary	NOUN
ejpam-2010	567	7	.	.	PUNCT
ejpam-2010	568	1	corollary	corollary	ADJ
ejpam-2010	568	2	9	9	NUM
ejpam-2010	568	3	.	.	PUNCT
ejpam-2010	569	1	[	[	X
ejpam-2010	569	2	42	42	NUM
ejpam-2010	569	3	,	,	PUNCT
ejpam-2010	569	4	corollary	corollary	ADJ
ejpam-2010	569	5	5.7	5.7	NUM
ejpam-2010	569	6	]	]	PUNCT
ejpam-2010	569	7	suppose	suppose	VERB
ejpam-2010	569	8	that	that	SCONJ
ejpam-2010	569	9	s	s	PROPN
ejpam-2010	569	10	and	and	CCONJ
ejpam-2010	569	11	t	t	PROPN
ejpam-2010	569	12	are	be	AUX
ejpam-2010	569	13	strongly2	strongly2	PROPN
ejpam-2010	569	14	morita	morita	PROPN
ejpam-2010	569	15	equivalent	equivalent	PROPN
ejpam-2010	569	16	monoids	monoid	VERB
ejpam-2010	569	17	such	such	ADJ
ejpam-2010	569	18	that	that	DET
ejpam-2010	569	19	s	s	PART
ejpam-2010	569	20	is	be	AUX
ejpam-2010	569	21	either	either	ADV
ejpam-2010	569	22	:	:	PUNCT
ejpam-2010	569	23	(	(	PUNCT
ejpam-2010	569	24	1	1	X
ejpam-2010	569	25	)	)	PUNCT
ejpam-2010	569	26	a	a	DET
ejpam-2010	569	27	group	group	NOUN
ejpam-2010	569	28	;	;	PUNCT
ejpam-2010	569	29	(	(	PUNCT
ejpam-2010	569	30	2	2	X
ejpam-2010	569	31	)	)	PUNCT
ejpam-2010	569	32	commutative	commutative	ADJ
ejpam-2010	569	33	;	;	PUNCT
ejpam-2010	569	34	(	(	PUNCT
ejpam-2010	569	35	3	3	X
ejpam-2010	569	36	)	)	PUNCT
ejpam-2010	569	37	has	have	VERB
ejpam-2010	569	38	central	central	ADJ
ejpam-2010	569	39	idempotents	idempotent	NOUN
ejpam-2010	569	40	;	;	PUNCT
ejpam-2010	569	41	(	(	PUNCT
ejpam-2010	569	42	4	4	X
ejpam-2010	569	43	)	)	PUNCT
ejpam-2010	569	44	is	be	AUX
ejpam-2010	569	45	residually	residually	ADV
ejpam-2010	569	46	finite	finite	ADJ
ejpam-2010	569	47	.	.	PUNCT
ejpam-2010	570	1	then	then	ADV
ejpam-2010	570	2	s	s	VERB
ejpam-2010	570	3	and	and	CCONJ
ejpam-2010	570	4	t	t	PROPN
ejpam-2010	570	5	are	be	AUX
ejpam-2010	570	6	isomorphic	isomorphic	ADJ
ejpam-2010	570	7	.	.	PUNCT
ejpam-2010	571	1	4.3	4.3	NUM
ejpam-2010	571	2	.	.	PUNCT
ejpam-2010	571	3	factorisable	factorisable	ADJ
ejpam-2010	571	4	semigroups	semigroup	NOUN
ejpam-2010	571	5	we	we	PRON
ejpam-2010	571	6	recall	recall	VERB
ejpam-2010	571	7	that	that	SCONJ
ejpam-2010	571	8	a	a	DET
ejpam-2010	571	9	semigroup	semigroup	NOUN
ejpam-2010	571	10	s	s	VERB
ejpam-2010	571	11	is	be	AUX
ejpam-2010	571	12	factorisable	factorisable	ADJ
ejpam-2010	571	13	if	if	SCONJ
ejpam-2010	571	14	s	s	PART
ejpam-2010	571	15	=	=	SYM
ejpam-2010	571	16	s2	s2	PROPN
ejpam-2010	571	17	,	,	PUNCT
ejpam-2010	571	18	that	that	ADV
ejpam-2010	571	19	is	is	ADV
ejpam-2010	571	20	,	,	PUNCT
ejpam-2010	571	21	every	every	DET
ejpam-2010	571	22	element	element	NOUN
ejpam-2010	571	23	of	of	ADP
ejpam-2010	571	24	s	s	PRON
ejpam-2010	571	25	can	can	AUX
ejpam-2010	571	26	be	be	AUX
ejpam-2010	571	27	written	write	VERB
ejpam-2010	571	28	as	as	ADP
ejpam-2010	571	29	a	a	DET
ejpam-2010	571	30	product	product	NOUN
ejpam-2010	571	31	of	of	ADP
ejpam-2010	571	32	two	two	NUM
ejpam-2010	571	33	elements	element	NOUN
ejpam-2010	571	34	.	.	PUNCT
ejpam-2010	572	1	to	to	PART
ejpam-2010	572	2	proceed	proceed	VERB
ejpam-2010	572	3	the	the	DET
ejpam-2010	572	4	following	following	NOUN
ejpam-2010	572	5	,	,	PUNCT
ejpam-2010	572	6	we	we	PRON
ejpam-2010	572	7	first	first	ADV
ejpam-2010	572	8	recall	recall	VERB
ejpam-2010	572	9	a	a	DET
ejpam-2010	572	10	construction	construction	NOUN
ejpam-2010	572	11	from	from	ADP
ejpam-2010	572	12	[	[	X
ejpam-2010	572	13	44	44	NUM
ejpam-2010	572	14	]	]	PUNCT
ejpam-2010	572	15	.	.	PUNCT
ejpam-2010	573	1	let	let	VERB
ejpam-2010	573	2	r	r	PRON
ejpam-2010	573	3	be	be	AUX
ejpam-2010	573	4	a	a	DET
ejpam-2010	573	5	semigroup	semigroup	NOUN
ejpam-2010	573	6	,	,	PUNCT
ejpam-2010	573	7	let	let	VERB
ejpam-2010	573	8	x	x	PRON
ejpam-2010	573	9	and	and	CCONJ
ejpam-2010	573	10	y	y	PROPN
ejpam-2010	573	11	be	be	AUX
ejpam-2010	573	12	finite	finite	ADJ
ejpam-2010	573	13	non	non	ADJ
ejpam-2010	573	14	-	-	ADJ
ejpam-2010	573	15	empty	empty	ADJ
ejpam-2010	573	16	sets	set	NOUN
ejpam-2010	573	17	,	,	PUNCT
ejpam-2010	573	18	and	and	CCONJ
ejpam-2010	573	19	let	let	VERB
ejpam-2010	573	20	〈	〈	NOUN
ejpam-2010	573	21	,	,	PUNCT
ejpam-2010	573	22	〉	〉	NOUN
ejpam-2010	573	23	:	:	PUNCT
ejpam-2010	573	24	y	y	PROPN
ejpam-2010	573	25	×	×	NOUN
ejpam-2010	573	26	y	y	PROPN
ejpam-2010	573	27	→	→	PUNCT
ejpam-2010	573	28	r	r	NOUN
ejpam-2010	573	29	be	be	AUX
ejpam-2010	573	30	a	a	DET
ejpam-2010	573	31	function	function	NOUN
ejpam-2010	573	32	(	(	PUNCT
ejpam-2010	573	33	with	with	ADP
ejpam-2010	573	34	values	value	NOUN
ejpam-2010	573	35	denoted	denote	VERB
ejpam-2010	573	36	〈	〈	PROPN
ejpam-2010	573	37	y	y	PROPN
ejpam-2010	573	38	,	,	PUNCT
ejpam-2010	573	39	x	x	NOUN
ejpam-2010	573	40	〉	〉	NOUN
ejpam-2010	573	41	)	)	PUNCT
ejpam-2010	573	42	.	.	PUNCT
ejpam-2010	574	1	then	then	ADV
ejpam-2010	574	2	the	the	DET
ejpam-2010	574	3	set	set	NOUN
ejpam-2010	574	4	m	m	NOUN
ejpam-2010	574	5	=	=	PUNCT
ejpam-2010	574	6	x	x	SYM
ejpam-2010	574	7	×	×	PROPN
ejpam-2010	574	8	r×	r×	NOUN
ejpam-2010	574	9	y	y	PROPN
ejpam-2010	574	10	equipped	equip	VERB
ejpam-2010	574	11	with	with	ADP
ejpam-2010	574	12	the	the	DET
ejpam-2010	574	13	associative	associative	ADJ
ejpam-2010	574	14	product	product	NOUN
ejpam-2010	574	15	(	(	PUNCT
ejpam-2010	574	16	x	x	X
ejpam-2010	574	17	,	,	PUNCT
ejpam-2010	574	18	s	s	PROPN
ejpam-2010	574	19	,	,	PUNCT
ejpam-2010	574	20	y)(x	y)(x	PROPN
ejpam-2010	574	21	′	′	NUM
ejpam-2010	574	22	,	,	PUNCT
ejpam-2010	574	23	s′	s′	NUM
ejpam-2010	574	24	,	,	PUNCT
ejpam-2010	574	25	y	y	PROPN
ejpam-2010	574	26	′	′	NOUN
ejpam-2010	574	27	)	)	PUNCT
ejpam-2010	574	28	=	=	PRON
ejpam-2010	575	1	(	(	PUNCT
ejpam-2010	575	2	x	x	INTJ
ejpam-2010	575	3	,	,	PUNCT
ejpam-2010	575	4	s〈y	s〈y	PROPN
ejpam-2010	575	5	,	,	PUNCT
ejpam-2010	575	6	x	x	PUNCT
ejpam-2010	575	7	′〉)s′	′〉)s′	ADJ
ejpam-2010	575	8	,	,	PUNCT
ejpam-2010	575	9	y	y	PROPN
ejpam-2010	575	10	′	′	NOUN
ejpam-2010	575	11	)	)	PUNCT
ejpam-2010	575	12	is	be	AUX
ejpam-2010	575	13	a	a	DET
ejpam-2010	575	14	semigroup	semigroup	NOUN
ejpam-2010	575	15	,	,	PUNCT
ejpam-2010	575	16	known	know	VERB
ejpam-2010	575	17	as	as	ADP
ejpam-2010	575	18	the	the	DET
ejpam-2010	575	19	rees	rees	PROPN
ejpam-2010	575	20	matrix	matrix	NOUN
ejpam-2010	575	21	semigroup	semigroup	NOUN
ejpam-2010	575	22	over	over	ADP
ejpam-2010	575	23	r	r	NOUN
ejpam-2010	575	24	defined	define	VERB
ejpam-2010	575	25	by	by	ADP
ejpam-2010	575	26	〈	〈	PROPN
ejpam-2010	575	27	,	,	PUNCT
ejpam-2010	575	28	〉	〉	NOUN
ejpam-2010	575	29	.	.	PUNCT
ejpam-2010	576	1	we	we	PRON
ejpam-2010	576	2	formulate	formulate	VERB
ejpam-2010	576	3	the	the	DET
ejpam-2010	576	4	following	following	NOUN
ejpam-2010	576	5	:	:	PUNCT
ejpam-2010	576	6	let	let	VERB
ejpam-2010	576	7	r	r	PRON
ejpam-2010	576	8	be	be	AUX
ejpam-2010	576	9	a	a	DET
ejpam-2010	576	10	semigroup	semigroup	NOUN
ejpam-2010	576	11	,	,	PUNCT
ejpam-2010	576	12	let	let	VERB
ejpam-2010	576	13	rp	rp	NOUN
ejpam-2010	576	14	and	and	CCONJ
ejpam-2010	576	15	qr	qr	PROPN
ejpam-2010	576	16	be	be	AUX
ejpam-2010	576	17	respectively	respectively	ADV
ejpam-2010	576	18	left	leave	VERB
ejpam-2010	576	19	and	and	CCONJ
ejpam-2010	576	20	right	right	ADJ
ejpam-2010	576	21	r	r	NOUN
ejpam-2010	576	22	-	-	PUNCT
ejpam-2010	576	23	acts	act	NOUN
ejpam-2010	576	24	.	.	PUNCT
ejpam-2010	577	1	also	also	ADV
ejpam-2010	577	2	,	,	PUNCT
ejpam-2010	577	3	let	let	VERB
ejpam-2010	577	4	〈	〈	NOUN
ejpam-2010	577	5	,	,	PUNCT
ejpam-2010	577	6	〉	〉	NOUN
ejpam-2010	577	7	:	:	PUNCT
ejpam-2010	577	8	r	r	NOUN
ejpam-2010	577	9	p	p	NOUN
ejpam-2010	577	10	×qr→	×qr→	PROPN
ejpam-2010	577	11	r	r	NOUN
ejpam-2010	577	12	be	be	AUX
ejpam-2010	577	13	an	an	DET
ejpam-2010	577	14	r	r	NOUN
ejpam-2010	577	15	-	-	PUNCT
ejpam-2010	577	16	r	r	NOUN
ejpam-2010	577	17	-	-	PUNCT
ejpam-2010	577	18	bilinear	bilinear	NOUN
ejpam-2010	577	19	,	,	PUNCT
ejpam-2010	577	20	that	that	ADV
ejpam-2010	577	21	is	is	ADV
ejpam-2010	577	22	,	,	PUNCT
ejpam-2010	577	23	〈	〈	NOUN
ejpam-2010	577	24	rp	rp	NOUN
ejpam-2010	577	25	,	,	PUNCT
ejpam-2010	577	26	q〉=	q〉=	VERB
ejpam-2010	577	27	r〈p	r〈p	PROPN
ejpam-2010	577	28	,	,	PUNCT
ejpam-2010	577	29	q	q	SYM
ejpam-2010	577	30	〉	〉	NOUN
ejpam-2010	577	31	and	and	CCONJ
ejpam-2010	577	32	〈	〈	NOUN
ejpam-2010	577	33	p	p	PROPN
ejpam-2010	577	34	,	,	PUNCT
ejpam-2010	577	35	qs〉=	qs〉=	PROPN
ejpam-2010	577	36	〈	〈	PROPN
ejpam-2010	577	37	p	p	NOUN
ejpam-2010	577	38	,	,	PUNCT
ejpam-2010	577	39	q〉s	q〉s	PROPN
ejpam-2010	577	40	.	.	PUNCT
ejpam-2010	578	1	then	then	ADV
ejpam-2010	578	2	the	the	DET
ejpam-2010	578	3	set	set	NOUN
ejpam-2010	578	4	q⊗r	q⊗r	PROPN
ejpam-2010	578	5	p	p	NOUN
ejpam-2010	578	6	becomes	become	VERB
ejpam-2010	578	7	a	a	DET
ejpam-2010	578	8	semigroup	semigroup	NOUN
ejpam-2010	578	9	with	with	ADP
ejpam-2010	578	10	product	product	NOUN
ejpam-2010	578	11	(	(	PUNCT
ejpam-2010	578	12	q⊗	q⊗	PROPN
ejpam-2010	578	13	p)(q′⊗	p)(q′⊗	PROPN
ejpam-2010	578	14	p′	p′	NOUN
ejpam-2010	578	15	)	)	PUNCT
ejpam-2010	579	1	=	=	VERB
ejpam-2010	579	2	q⊗	q⊗	NOUN
ejpam-2010	579	3	〈	〈	PROPN
ejpam-2010	579	4	p	p	NOUN
ejpam-2010	579	5	,	,	PUNCT
ejpam-2010	579	6	q′〉p′.	q′〉p′.	VERB
ejpam-2010	579	7	the	the	DET
ejpam-2010	579	8	multiplication	multiplication	NOUN
ejpam-2010	579	9	is	be	AUX
ejpam-2010	579	10	well	well	ADV
ejpam-2010	579	11	defined	define	VERB
ejpam-2010	579	12	since	since	SCONJ
ejpam-2010	579	13	〈	〈	PROPN
ejpam-2010	579	14	,	,	PUNCT
ejpam-2010	579	15	〉	〉	NOUN
ejpam-2010	579	16	is	be	AUX
ejpam-2010	579	17	an	an	DET
ejpam-2010	579	18	r−	r−	PROPN
ejpam-2010	579	19	r	r	NOUN
ejpam-2010	579	20	-	-	PUNCT
ejpam-2010	579	21	bilinear	bilinear	NOUN
ejpam-2010	579	22	map	map	NOUN
ejpam-2010	579	23	.	.	PUNCT
ejpam-2010	580	1	it	it	PRON
ejpam-2010	580	2	is	be	AUX
ejpam-2010	580	3	easy	easy	ADJ
ejpam-2010	580	4	to	to	PART
ejpam-2010	580	5	verify	verify	VERB
ejpam-2010	580	6	that	that	SCONJ
ejpam-2010	580	7	it	it	PRON
ejpam-2010	580	8	is	be	AUX
ejpam-2010	580	9	associative	associative	ADJ
ejpam-2010	580	10	.	.	PUNCT
ejpam-2010	581	1	we	we	PRON
ejpam-2010	581	2	shall	shall	AUX
ejpam-2010	581	3	refer	refer	VERB
ejpam-2010	581	4	to	to	ADP
ejpam-2010	581	5	q⊗r	q⊗r	PROPN
ejpam-2010	581	6	p	p	NOUN
ejpam-2010	581	7	as	as	ADP
ejpam-2010	581	8	the	the	DET
ejpam-2010	581	9	morita	morita	PROPN
ejpam-2010	581	10	semigroup	semigroup	PROPN
ejpam-2010	581	11	over	over	ADP
ejpam-2010	581	12	r	r	NOUN
ejpam-2010	581	13	defined	define	VERB
ejpam-2010	581	14	by	by	ADP
ejpam-2010	581	15	〈	〈	PROPN
ejpam-2010	581	16	,	,	PUNCT
ejpam-2010	581	17	〉	〉	NOUN
ejpam-2010	581	18	.	.	PUNCT
ejpam-2010	581	19	references	reference	NOUN
ejpam-2010	581	20	278	278	NUM
ejpam-2010	581	21	theorem	theorem	NOUN
ejpam-2010	581	22	22	22	NUM
ejpam-2010	581	23	.	.	PUNCT
ejpam-2010	582	1	[	[	X
ejpam-2010	582	2	44	44	NUM
ejpam-2010	582	3	]	]	PUNCT
ejpam-2010	582	4	let	let	VERB
ejpam-2010	582	5	r	r	PRON
ejpam-2010	582	6	be	be	AUX
ejpam-2010	582	7	a	a	DET
ejpam-2010	582	8	factorisable	factorisable	ADJ
ejpam-2010	582	9	semigroup	semigroup	NOUN
ejpam-2010	582	10	,	,	PUNCT
ejpam-2010	582	11	and	and	CCONJ
ejpam-2010	582	12	let	let	VERB
ejpam-2010	582	13	rp	rp	NOUN
ejpam-2010	582	14	and	and	CCONJ
ejpam-2010	582	15	qr	qr	PROPN
ejpam-2010	582	16	be	be	AUX
ejpam-2010	582	17	respectively	respectively	ADV
ejpam-2010	582	18	unitary	unitary	ADJ
ejpam-2010	582	19	left	leave	VERB
ejpam-2010	582	20	and	and	CCONJ
ejpam-2010	582	21	right	right	ADJ
ejpam-2010	582	22	r	r	NOUN
ejpam-2010	582	23	-	-	PUNCT
ejpam-2010	582	24	acts	act	NOUN
ejpam-2010	582	25	.	.	PUNCT
ejpam-2010	583	1	also	also	ADV
ejpam-2010	583	2	,	,	PUNCT
ejpam-2010	583	3	let	let	VERB
ejpam-2010	583	4	〈	〈	NOUN
ejpam-2010	583	5	,	,	PUNCT
ejpam-2010	583	6	〉	〉	NOUN
ejpam-2010	583	7	:	:	PUNCT
ejpam-2010	583	8	r	r	NOUN
ejpam-2010	583	9	p	p	NOUN
ejpam-2010	583	10	×qr→	×qr→	PROPN
ejpam-2010	583	11	r	r	NOUN
ejpam-2010	583	12	be	be	VERB
ejpam-2010	583	13	a	a	DET
ejpam-2010	583	14	surjective	surjective	ADJ
ejpam-2010	583	15	r	r	NOUN
ejpam-2010	583	16	-	-	PUNCT
ejpam-2010	583	17	r	r	NOUN
ejpam-2010	583	18	-	-	PUNCT
ejpam-2010	583	19	bilinear	bilinear	NOUN
ejpam-2010	583	20	map	map	NOUN
ejpam-2010	583	21	.	.	PUNCT
ejpam-2010	584	1	the	the	DET
ejpam-2010	584	2	morita	morita	PROPN
ejpam-2010	584	3	semigroup	semigroup	PROPN
ejpam-2010	584	4	q⊗r	q⊗r	PROPN
ejpam-2010	584	5	p	p	PROPN
ejpam-2010	584	6	is	be	AUX
ejpam-2010	584	7	strongly1	strongly1	PROPN
ejpam-2010	584	8	morita	morita	PROPN
ejpam-2010	584	9	equivalent	equivalent	PROPN
ejpam-2010	584	10	to	to	PART
ejpam-2010	584	11	r.	r.	VERB
ejpam-2010	584	12	let	let	VERB
ejpam-2010	584	13	s	s	PRON
ejpam-2010	584	14	be	be	AUX
ejpam-2010	584	15	an	an	DET
ejpam-2010	584	16	arbitrary	arbitrary	ADJ
ejpam-2010	584	17	semigroup	semigroup	NOUN
ejpam-2010	584	18	and	and	CCONJ
ejpam-2010	584	19	m	m	PROPN
ejpam-2010	584	20	∈	∈	PROPN
ejpam-2010	584	21	s	s	PROPN
ejpam-2010	584	22	-	-	NOUN
ejpam-2010	584	23	act	act	NOUN
ejpam-2010	584	24	.	.	PUNCT
ejpam-2010	585	1	we	we	PRON
ejpam-2010	585	2	set	set	VERB
ejpam-2010	585	3	ζm	ζm	ADP
ejpam-2010	585	4	=	=	PRON
ejpam-2010	585	5	{	{	PUNCT
ejpam-2010	585	6	(	(	PUNCT
ejpam-2010	585	7	m1	m1	NOUN
ejpam-2010	585	8	,	,	PUNCT
ejpam-2010	585	9	m2)|sm1	m2)|sm1	NOUN
ejpam-2010	585	10	=	=	PUNCT
ejpam-2010	585	11	sm2,∀s	sm2,∀s	NOUN
ejpam-2010	585	12	∈	∈	PROPN
ejpam-2010	585	13	s	s	PART
ejpam-2010	585	14	}	}	PUNCT
ejpam-2010	585	15	.	.	PUNCT
ejpam-2010	586	1	then	then	ADV
ejpam-2010	586	2	it	it	PRON
ejpam-2010	586	3	is	be	AUX
ejpam-2010	586	4	clear	clear	ADJ
ejpam-2010	586	5	that	that	SCONJ
ejpam-2010	586	6	ζm	ζm	NOUN
ejpam-2010	586	7	is	be	AUX
ejpam-2010	586	8	an	an	DET
ejpam-2010	586	9	s	s	NOUN
ejpam-2010	586	10	-	-	NOUN
ejpam-2010	586	11	congruence	congruence	NOUN
ejpam-2010	586	12	on	on	ADP
ejpam-2010	586	13	s	s	NOUN
ejpam-2010	586	14	m	m	NOUN
ejpam-2010	586	15	and	and	CCONJ
ejpam-2010	586	16	ζs	ζs	PROPN
ejpam-2010	586	17	is	be	AUX
ejpam-2010	586	18	a	a	DET
ejpam-2010	586	19	two	two	NUM
ejpam-2010	586	20	-	-	PUNCT
ejpam-2010	586	21	sided	sided	ADJ
ejpam-2010	586	22	congruence	congruence	NOUN
ejpam-2010	586	23	on	on	ADP
ejpam-2010	586	24	s.	s.	PROPN
ejpam-2010	586	25	we	we	PRON
ejpam-2010	586	26	can	can	AUX
ejpam-2010	586	27	denote	denote	VERB
ejpam-2010	586	28	the	the	DET
ejpam-2010	586	29	quotient	quotient	NOUN
ejpam-2010	586	30	semigroup	semigroup	NOUN
ejpam-2010	587	1	s	s	PART
ejpam-2010	587	2	/	/	SYM
ejpam-2010	587	3	ζs	ζs	NOUN
ejpam-2010	587	4	by	by	ADP
ejpam-2010	587	5	s′.	s′.	PROPN
ejpam-2010	588	1	it	it	PRON
ejpam-2010	588	2	is	be	AUX
ejpam-2010	588	3	clear	clear	ADJ
ejpam-2010	588	4	that	that	SCONJ
ejpam-2010	588	5	s′	s′	ADJ
ejpam-2010	588	6	is	be	AUX
ejpam-2010	588	7	an	an	DET
ejpam-2010	588	8	s	s	PROPN
ejpam-2010	588	9	-	-	PUNCT
ejpam-2010	588	10	s	s	NOUN
ejpam-2010	588	11	-	-	NOUN
ejpam-2010	588	12	biact	biact	NOUN
ejpam-2010	588	13	in	in	ADP
ejpam-2010	588	14	a	a	DET
ejpam-2010	588	15	natural	natural	ADJ
ejpam-2010	588	16	way	way	NOUN
ejpam-2010	588	17	:	:	PUNCT
ejpam-2010	588	18	for	for	ADP
ejpam-2010	588	19	any	any	DET
ejpam-2010	588	20	s	s	NOUN
ejpam-2010	588	21	,	,	PUNCT
ejpam-2010	588	22	t	t	PROPN
ejpam-2010	588	23	∈	∈	PROPN
ejpam-2010	588	24	s	s	PROPN
ejpam-2010	588	25	,	,	PUNCT
ejpam-2010	588	26	t	t	NOUN
ejpam-2010	588	27	s̄	s̄	NOUN
ejpam-2010	588	28	=	=	SYM
ejpam-2010	588	29	ts	ts	NOUN
ejpam-2010	588	30	,	,	PUNCT
ejpam-2010	588	31	s̄	s̄	NOUN
ejpam-2010	588	32	t	t	PROPN
ejpam-2010	588	33	=	=	SYM
ejpam-2010	588	34	st	st	PROPN
ejpam-2010	588	35	.	.	PROPN
ejpam-2010	588	36	theorem	theorem	PROPN
ejpam-2010	588	37	23	23	NUM
ejpam-2010	588	38	.	.	PUNCT
ejpam-2010	589	1	[	[	X
ejpam-2010	589	2	6	6	NUM
ejpam-2010	589	3	,	,	PUNCT
ejpam-2010	589	4	theorem	theorem	VERB
ejpam-2010	589	5	3	3	NUM
ejpam-2010	589	6	]	]	PUNCT
ejpam-2010	589	7	let	let	VERB
ejpam-2010	589	8	r	r	NOUN
ejpam-2010	589	9	,	,	PUNCT
ejpam-2010	589	10	s	s	AUX
ejpam-2010	589	11	be	be	AUX
ejpam-2010	589	12	factorisable	factorisable	ADJ
ejpam-2010	589	13	semigroups	semigroup	NOUN
ejpam-2010	589	14	.	.	PUNCT
ejpam-2010	590	1	then	then	ADV
ejpam-2010	590	2	the	the	DET
ejpam-2010	590	3	category	category	NOUN
ejpam-2010	590	4	r	r	NOUN
ejpam-2010	590	5	-	-	PUNCT
ejpam-2010	590	6	ufact	ufact	NOUN
ejpam-2010	590	7	is	be	AUX
ejpam-2010	590	8	equivalent	equivalent	ADJ
ejpam-2010	590	9	to	to	ADP
ejpam-2010	590	10	the	the	DET
ejpam-2010	590	11	category	category	NOUN
ejpam-2010	590	12	s	s	NOUN
ejpam-2010	590	13	-	-	PUNCT
ejpam-2010	590	14	ufact	ufact	ADJ
ejpam-2010	590	15	if	if	SCONJ
ejpam-2010	590	16	and	and	CCONJ
ejpam-2010	590	17	only	only	ADV
ejpam-2010	590	18	if	if	SCONJ
ejpam-2010	590	19	there	there	PRON
ejpam-2010	590	20	exists	exist	VERB
ejpam-2010	590	21	a	a	DET
ejpam-2010	590	22	unitary	unitary	ADJ
ejpam-2010	590	23	morita	morita	NOUN
ejpam-2010	590	24	context	context	PROPN
ejpam-2010	590	25	(	(	PUNCT
ejpam-2010	590	26	r′	r′	PROPN
ejpam-2010	590	27	,	,	PUNCT
ejpam-2010	590	28	s′,r′	s′,r′	PROPN
ejpam-2010	590	29	ps′	ps′	PROPN
ejpam-2010	590	30	,	,	PUNCT
ejpam-2010	590	31	s′	s′	X
ejpam-2010	590	32	qr′	qr′	PROPN
ejpam-2010	590	33	,	,	PUNCT
ejpam-2010	590	34	〈	〈	NOUN
ejpam-2010	590	35	〉	〉	NOUN
ejpam-2010	590	36	,	,	PUNCT
ejpam-2010	590	37	de	de	NOUN
ejpam-2010	590	38	)	)	PUNCT
ejpam-2010	590	39	with	with	ADP
ejpam-2010	590	40	〈	〈	NOUN
ejpam-2010	590	41	〉	〉	NOUN
ejpam-2010	590	42	and	and	CCONJ
ejpam-2010	590	43	de	de	X
ejpam-2010	590	44	surjective	surjective	NOUN
ejpam-2010	590	45	,	,	PUNCT
ejpam-2010	590	46	where	where	SCONJ
ejpam-2010	590	47	r′	r′	NUM
ejpam-2010	590	48	and	and	CCONJ
ejpam-2010	590	49	s′	s′	VERB
ejpam-2010	590	50	constructed	construct	VERB
ejpam-2010	590	51	as	as	ADP
ejpam-2010	590	52	above	above	ADV
ejpam-2010	590	53	.	.	PUNCT
ejpam-2010	591	1	moreover	moreover	ADV
ejpam-2010	591	2	,	,	PUNCT
ejpam-2010	591	3	if	if	SCONJ
ejpam-2010	591	4	this	this	PRON
ejpam-2010	591	5	is	be	AUX
ejpam-2010	591	6	the	the	DET
ejpam-2010	591	7	case	case	NOUN
ejpam-2010	591	8	,	,	PUNCT
ejpam-2010	591	9	then	then	ADV
ejpam-2010	591	10	we	we	PRON
ejpam-2010	591	11	have	have	VERB
ejpam-2010	591	12	the	the	DET
ejpam-2010	591	13	following	follow	VERB
ejpam-2010	591	14	category	category	NOUN
ejpam-2010	591	15	inverse	inverse	NOUN
ejpam-2010	591	16	equivalence	equivalence	NOUN
ejpam-2010	591	17	:	:	PUNCT
ejpam-2010	591	18	r−ufact	r−ufact	PROPN
ejpam-2010	591	19	f	f	PROPN
ejpam-2010	591	20	ggggbfgggg	ggggbfgggg	NOUN
ejpam-2010	591	21	g	g	PROPN
ejpam-2010	591	22	s−ufact	s−ufact	PROPN
ejpam-2010	591	23	,	,	PUNCT
ejpam-2010	591	24	where	where	SCONJ
ejpam-2010	591	25	f	f	PROPN
ejpam-2010	591	26	=	=	SYM
ejpam-2010	591	27	shomr(rp,−	shomr(rp,−	PROPN
ejpam-2010	591	28	)	)	PUNCT
ejpam-2010	591	29	and	and	CCONJ
ejpam-2010	591	30	g	g	NOUN
ejpam-2010	591	31	=	=	NOUN
ejpam-2010	591	32	rhoms(sq,−	rhoms(sq,−	NUM
ejpam-2010	591	33	)	)	PUNCT
ejpam-2010	591	34	.	.	PUNCT
ejpam-2010	592	1	let	let	VERB
ejpam-2010	592	2	s	s	PRON
ejpam-2010	592	3	be	be	AUX
ejpam-2010	592	4	a	a	DET
ejpam-2010	592	5	monoid	monoid	NOUN
ejpam-2010	592	6	with	with	ADP
ejpam-2010	592	7	identity	identity	NOUN
ejpam-2010	592	8	1	1	NUM
ejpam-2010	592	9	.	.	PUNCT
ejpam-2010	593	1	then	then	ADV
ejpam-2010	593	2	it	it	PRON
ejpam-2010	593	3	is	be	AUX
ejpam-2010	593	4	clear	clear	ADJ
ejpam-2010	593	5	that	that	SCONJ
ejpam-2010	593	6	for	for	ADP
ejpam-2010	593	7	any	any	DET
ejpam-2010	593	8	unitary	unitary	ADJ
ejpam-2010	593	9	s	s	NOUN
ejpam-2010	593	10	-	-	NOUN
ejpam-2010	593	11	act	act	NOUN
ejpam-2010	593	12	s	s	PART
ejpam-2010	593	13	m	m	NOUN
ejpam-2010	593	14	,	,	PUNCT
ejpam-2010	593	15	1	1	NUM
ejpam-2010	593	16	m	m	NOUN
ejpam-2010	593	17	=	=	VERB
ejpam-2010	593	18	m	m	VERB
ejpam-2010	593	19	for	for	ADP
ejpam-2010	593	20	any	any	DET
ejpam-2010	593	21	m	m	NOUN
ejpam-2010	593	22	∈	∈	NOUN
ejpam-2010	593	23	m	m	NOUN
ejpam-2010	593	24	.	.	PUNCT
ejpam-2010	594	1	therefore	therefore	ADV
ejpam-2010	594	2	,	,	PUNCT
ejpam-2010	594	3	s	s	NOUN
ejpam-2010	594	4	-	-	ADJ
ejpam-2010	594	5	ufact	ufact	ADJ
ejpam-2010	594	6	=	=	SYM
ejpam-2010	594	7	s	s	NOUN
ejpam-2010	594	8	-	-	PUNCT
ejpam-2010	594	9	uact	uact	ADJ
ejpam-2010	594	10	if	if	SCONJ
ejpam-2010	594	11	s	s	VERB
ejpam-2010	594	12	is	be	AUX
ejpam-2010	594	13	a	a	DET
ejpam-2010	594	14	monoid	monoid	NOUN
ejpam-2010	594	15	.	.	PUNCT
ejpam-2010	594	16	corollary	corollary	ADJ
ejpam-2010	594	17	10	10	NUM
ejpam-2010	594	18	.	.	PUNCT
ejpam-2010	595	1	[	[	X
ejpam-2010	595	2	6	6	NUM
ejpam-2010	595	3	,	,	PUNCT
ejpam-2010	595	4	16	16	NUM
ejpam-2010	595	5	]	]	PUNCT
ejpam-2010	595	6	let	let	VERB
ejpam-2010	595	7	r	r	NOUN
ejpam-2010	595	8	,	,	PUNCT
ejpam-2010	595	9	s	s	AUX
ejpam-2010	595	10	be	be	AUX
ejpam-2010	595	11	monoids	monoid	NOUN
ejpam-2010	595	12	.	.	PUNCT
ejpam-2010	596	1	then	then	ADV
ejpam-2010	596	2	the	the	DET
ejpam-2010	596	3	category	category	NOUN
ejpam-2010	596	4	r	r	NOUN
ejpam-2010	596	5	-	-	PUNCT
ejpam-2010	596	6	uact	uact	NOUN
ejpam-2010	596	7	is	be	AUX
ejpam-2010	596	8	equivalent	equivalent	ADJ
ejpam-2010	596	9	to	to	ADP
ejpam-2010	596	10	the	the	DET
ejpam-2010	596	11	category	category	NOUN
ejpam-2010	596	12	s	s	PART
ejpam-2010	596	13	-	-	PUNCT
ejpam-2010	596	14	uact	uact	ADJ
ejpam-2010	596	15	if	if	SCONJ
ejpam-2010	596	16	and	and	CCONJ
ejpam-2010	596	17	only	only	ADV
ejpam-2010	596	18	if	if	SCONJ
ejpam-2010	596	19	there	there	PRON
ejpam-2010	596	20	exists	exist	VERB
ejpam-2010	596	21	a	a	DET
ejpam-2010	596	22	unitary	unitary	ADJ
ejpam-2010	596	23	morita	morita	NOUN
ejpam-2010	596	24	context	context	NOUN
ejpam-2010	596	25	(	(	PUNCT
ejpam-2010	596	26	r	r	NOUN
ejpam-2010	596	27	,	,	PUNCT
ejpam-2010	596	28	s	s	PART
ejpam-2010	596	29	,	,	PUNCT
ejpam-2010	596	30	r	r	NOUN
ejpam-2010	596	31	ps	ps	PROPN
ejpam-2010	596	32	,	,	PUNCT
ejpam-2010	596	33	s	s	PROPN
ejpam-2010	596	34	qr	qr	NOUN
ejpam-2010	596	35	,	,	PUNCT
ejpam-2010	596	36	〈	〈	NOUN
ejpam-2010	596	37	〉	〉	NOUN
ejpam-2010	596	38	,	,	PUNCT
ejpam-2010	596	39	de	de	NOUN
ejpam-2010	596	40	)	)	PUNCT
ejpam-2010	596	41	with	with	ADP
ejpam-2010	596	42	〈	〈	NOUN
ejpam-2010	596	43	〉	〉	NOUN
ejpam-2010	596	44	and	and	CCONJ
ejpam-2010	596	45	de	de	X
ejpam-2010	596	46	surjective	surjective	NOUN
ejpam-2010	596	47	.	.	PUNCT
ejpam-2010	597	1	moreover	moreover	ADV
ejpam-2010	597	2	,	,	PUNCT
ejpam-2010	597	3	if	if	SCONJ
ejpam-2010	597	4	this	this	PRON
ejpam-2010	597	5	is	be	AUX
ejpam-2010	597	6	the	the	DET
ejpam-2010	597	7	case	case	NOUN
ejpam-2010	597	8	,	,	PUNCT
ejpam-2010	597	9	then	then	ADV
ejpam-2010	597	10	we	we	PRON
ejpam-2010	597	11	have	have	VERB
ejpam-2010	597	12	the	the	DET
ejpam-2010	597	13	following	follow	VERB
ejpam-2010	597	14	category	category	NOUN
ejpam-2010	597	15	inverse	inverse	NOUN
ejpam-2010	597	16	equivalence	equivalence	NOUN
ejpam-2010	597	17	:	:	PUNCT
ejpam-2010	597	18	r−uact	r−uact	PROPN
ejpam-2010	597	19	f	f	X
ejpam-2010	597	20	ggggbfgggg	ggggbfgggg	VERB
ejpam-2010	597	21	g	g	PROPN
ejpam-2010	597	22	s−uact	s−uact	PROPN
ejpam-2010	597	23	,	,	PUNCT
ejpam-2010	597	24	where	where	SCONJ
ejpam-2010	597	25	f	f	NOUN
ejpam-2010	597	26	=	=	PUNCT
ejpam-2010	597	27	homr(rp,−	homr(rp,−	PROPN
ejpam-2010	597	28	)	)	PUNCT
ejpam-2010	597	29	and	and	CCONJ
ejpam-2010	597	30	g	g	NOUN
ejpam-2010	597	31	=	=	NOUN
ejpam-2010	597	32	homs(sq,−	homs(sq,−	NOUN
ejpam-2010	597	33	)	)	PUNCT
ejpam-2010	597	34	.	.	PUNCT
ejpam-2010	598	1	acknowledgements	acknowledgement	NOUN
ejpam-2010	598	2	the	the	DET
ejpam-2010	598	3	first	first	ADJ
ejpam-2010	598	4	author	author	NOUN
ejpam-2010	598	5	was	be	AUX
ejpam-2010	598	6	supported	support	VERB
ejpam-2010	598	7	by	by	ADP
ejpam-2010	598	8	scientific	scientific	ADJ
ejpam-2010	598	9	research	research	NOUN
ejpam-2010	598	10	foundation	foundation	PROPN
ejpam-2010	598	11	of	of	ADP
ejpam-2010	598	12	shandong	shandong	PROPN
ejpam-2010	598	13	university	university	PROPN
ejpam-2010	598	14	of	of	ADP
ejpam-2010	598	15	science	science	NOUN
ejpam-2010	598	16	and	and	CCONJ
ejpam-2010	598	17	technology	technology	NOUN
ejpam-2010	598	18	for	for	ADP
ejpam-2010	598	19	recruited	recruit	VERB
ejpam-2010	598	20	talents	talent	NOUN
ejpam-2010	598	21	.	.	PUNCT
ejpam-2010	599	1	the	the	DET
ejpam-2010	599	2	third	third	ADJ
ejpam-2010	599	3	author	author	NOUN
ejpam-2010	599	4	was	be	AUX
ejpam-2010	599	5	supported	support	VERB
ejpam-2010	599	6	by	by	ADP
ejpam-2010	599	7	the	the	DET
ejpam-2010	599	8	national	national	ADJ
ejpam-2010	599	9	natural	natural	PROPN
ejpam-2010	599	10	science	science	PROPN
ejpam-2010	599	11	foundation	foundation	PROPN
ejpam-2010	599	12	of	of	ADP
ejpam-2010	599	13	china	china	PROPN
ejpam-2010	599	14	(	(	PUNCT
ejpam-2010	599	15	grant	grant	PROPN
ejpam-2010	599	16	no:10971160	no:10971160	NUM
ejpam-2010	599	17	)	)	PUNCT
ejpam-2010	599	18	.	.	PUNCT
ejpam-2010	600	1	references	reference	NOUN
ejpam-2010	600	2	[	[	X
ejpam-2010	600	3	1	1	NUM
ejpam-2010	600	4	]	]	X
ejpam-2010	600	5	g	g	PROPN
ejpam-2010	600	6	d	d	PROPN
ejpam-2010	600	7	abrams	abrams	PROPN
ejpam-2010	600	8	.	.	PROPN
ejpam-2010	600	9	morita	morita	PROPN
ejpam-2010	600	10	equivalence	equivalence	NOUN
ejpam-2010	600	11	for	for	ADP
ejpam-2010	600	12	rings	ring	NOUN
ejpam-2010	600	13	with	with	ADP
ejpam-2010	600	14	local	local	ADJ
ejpam-2010	600	15	units	unit	NOUN
ejpam-2010	600	16	.	.	PUNCT
ejpam-2010	601	1	communications	communication	NOUN
ejpam-2010	601	2	in	in	ADP
ejpam-2010	601	3	algebra	algebra	NOUN
ejpam-2010	601	4	,	,	PUNCT
ejpam-2010	601	5	11	11	NUM
ejpam-2010	601	6	:	:	SYM
ejpam-2010	601	7	801	801	NUM
ejpam-2010	601	8	-	-	NUM
ejpam-2010	601	9	837	837	NUM
ejpam-2010	601	10	,	,	PUNCT
ejpam-2010	601	11	1983	1983	NUM
ejpam-2010	601	12	.	.	PUNCT
ejpam-2010	602	1	[	[	X
ejpam-2010	602	2	2	2	NUM
ejpam-2010	602	3	]	]	SYM
ejpam-2010	602	4	b	b	PROPN
ejpam-2010	602	5	afara	afara	PROPN
ejpam-2010	602	6	and	and	CCONJ
ejpam-2010	602	7	m	m	PROPN
ejpam-2010	602	8	v	v	ADP
ejpam-2010	602	9	lawson	lawson	PROPN
ejpam-2010	602	10	.	.	PUNCT
ejpam-2010	603	1	morita	morita	PROPN
ejpam-2010	603	2	equivalence	equivalence	NOUN
ejpam-2010	603	3	of	of	ADP
ejpam-2010	603	4	semigroups	semigroup	NOUN
ejpam-2010	603	5	with	with	ADP
ejpam-2010	603	6	commuting	commute	VERB
ejpam-2010	603	7	idempotents	idempotent	NOUN
ejpam-2010	603	8	.	.	PUNCT
ejpam-2010	604	1	communications	communication	NOUN
ejpam-2010	604	2	in	in	ADP
ejpam-2010	604	3	algebra	algebra	NOUN
ejpam-2010	604	4	,	,	PUNCT
ejpam-2010	604	5	40:1982	40:1982	NOUN
ejpam-2010	604	6	-	-	SYM
ejpam-2010	604	7	1996	1996	NUM
ejpam-2010	604	8	,	,	PUNCT
ejpam-2010	604	9	2012	2012	NUM
ejpam-2010	604	10	.	.	PUNCT
ejpam-2010	605	1	[	[	X
ejpam-2010	605	2	3	3	X
ejpam-2010	605	3	]	]	X
ejpam-2010	605	4	p	p	NOUN
ejpam-2010	605	5	n	n	NUM
ejpam-2010	605	6	ánh	ánh	NOUN
ejpam-2010	605	7	and	and	CCONJ
ejpam-2010	605	8	l	l	NOUN
ejpam-2010	605	9	márki	márki	NOUN
ejpam-2010	605	10	.	.	PUNCT
ejpam-2010	606	1	morita	morita	PROPN
ejpam-2010	606	2	equivalence	equivalence	NOUN
ejpam-2010	606	3	for	for	ADP
ejpam-2010	606	4	rings	ring	NOUN
ejpam-2010	606	5	without	without	ADP
ejpam-2010	606	6	identity	identity	NOUN
ejpam-2010	606	7	.	.	PUNCT
ejpam-2010	607	1	tsukuba	tsukuba	PROPN
ejpam-2010	607	2	journal	journal	PROPN
ejpam-2010	607	3	of	of	ADP
ejpam-2010	607	4	mathematics	mathematic	NOUN
ejpam-2010	607	5	,	,	PUNCT
ejpam-2010	607	6	11	11	NUM
ejpam-2010	607	7	:	:	SYM
ejpam-2010	607	8	1	1	NUM
ejpam-2010	607	9	-	-	SYM
ejpam-2010	607	10	16	16	NUM
ejpam-2010	607	11	,	,	PUNCT
ejpam-2010	607	12	1987	1987	NUM
ejpam-2010	607	13	.	.	PUNCT
ejpam-2010	608	1	references	reference	NOUN
ejpam-2010	608	2	279	279	NUM
ejpam-2010	608	3	[	[	X
ejpam-2010	608	4	4	4	NUM
ejpam-2010	608	5	]	]	X
ejpam-2010	608	6	g	g	PROPN
ejpam-2010	608	7	azumaya	azumaya	NOUN
ejpam-2010	608	8	.	.	PUNCT
ejpam-2010	609	1	some	some	DET
ejpam-2010	609	2	aspects	aspect	NOUN
ejpam-2010	609	3	of	of	ADP
ejpam-2010	609	4	fuller	full	ADJ
ejpam-2010	609	5	’s	’s	PART
ejpam-2010	609	6	theorem	theorem	ADJ
ejpam-2010	609	7	,	,	PUNCT
ejpam-2010	609	8	module	module	NOUN
ejpam-2010	609	9	theory	theory	NOUN
ejpam-2010	609	10	.	.	PUNCT
ejpam-2010	610	1	lecture	lecture	NOUN
ejpam-2010	610	2	notes	note	NOUN
ejpam-2010	610	3	in	in	ADP
ejpam-2010	610	4	mathematics	mathematic	NOUN
ejpam-2010	610	5	,	,	PUNCT
ejpam-2010	610	6	700	700	NUM
ejpam-2010	610	7	:	:	PUNCT
ejpam-2010	610	8	34	34	NUM
ejpam-2010	610	9	-	-	SYM
ejpam-2010	610	10	45	45	NUM
ejpam-2010	610	11	,	,	PUNCT
ejpam-2010	610	12	1979	1979	NUM
ejpam-2010	610	13	.	.	PUNCT
ejpam-2010	611	1	[	[	X
ejpam-2010	611	2	5	5	NUM
ejpam-2010	611	3	]	]	X
ejpam-2010	611	4	s	s	VERB
ejpam-2010	611	5	bulman	bulman	NOUN
ejpam-2010	611	6	-	-	PUNCT
ejpam-2010	611	7	fleming	fleming	NOUN
ejpam-2010	611	8	and	and	CCONJ
ejpam-2010	611	9	m	m	NOUN
ejpam-2010	611	10	mahmoudi	mahmoudi	NOUN
ejpam-2010	611	11	.	.	PUNCT
ejpam-2010	612	1	the	the	DET
ejpam-2010	612	2	category	category	NOUN
ejpam-2010	612	3	of	of	ADP
ejpam-2010	612	4	s	s	NOUN
ejpam-2010	612	5	-	-	NOUN
ejpam-2010	612	6	posets	poset	NOUN
ejpam-2010	612	7	.	.	PUNCT
ejpam-2010	613	1	semigroup	semigroup	PROPN
ejpam-2010	613	2	forum	forum	PROPN
ejpam-2010	613	3	,	,	PUNCT
ejpam-2010	613	4	71	71	NUM
ejpam-2010	613	5	:	:	SYM
ejpam-2010	613	6	443	443	NUM
ejpam-2010	613	7	-	-	SYM
ejpam-2010	613	8	461	461	NUM
ejpam-2010	613	9	,	,	PUNCT
ejpam-2010	613	10	2005	2005	NUM
ejpam-2010	613	11	.	.	PUNCT
ejpam-2010	614	1	[	[	X
ejpam-2010	614	2	6	6	NUM
ejpam-2010	614	3	]	]	X
ejpam-2010	614	4	y	y	PROPN
ejpam-2010	614	5	q	q	PROPN
ejpam-2010	614	6	chen	chen	PROPN
ejpam-2010	614	7	and	and	CCONJ
ejpam-2010	614	8	k	k	PROPN
ejpam-2010	614	9	p	p	X
ejpam-2010	614	10	shum	shum	PROPN
ejpam-2010	614	11	.	.	PUNCT
ejpam-2010	615	1	morita	morita	PROPN
ejpam-2010	615	2	equivalence	equivalence	NOUN
ejpam-2010	615	3	for	for	ADP
ejpam-2010	615	4	factorisable	factorisable	ADJ
ejpam-2010	615	5	semigroups	semigroup	NOUN
ejpam-2010	615	6	.	.	PUNCT
ejpam-2010	616	1	acta	acta	PROPN
ejpam-2010	616	2	mathematica	mathematica	PROPN
ejpam-2010	616	3	sinica	sinica	PROPN
ejpam-2010	616	4	,	,	PUNCT
ejpam-2010	616	5	english	english	ADJ
ejpam-2010	616	6	series	series	NOUN
ejpam-2010	616	7	,	,	PUNCT
ejpam-2010	616	8	17	17	NUM
ejpam-2010	616	9	:	:	SYM
ejpam-2010	616	10	437	437	NUM
ejpam-2010	616	11	-	-	SYM
ejpam-2010	616	12	454	454	NUM
ejpam-2010	616	13	,	,	PUNCT
ejpam-2010	616	14	2001	2001	NUM
ejpam-2010	616	15	.	.	PUNCT
ejpam-2010	617	1	[	[	X
ejpam-2010	617	2	7	7	X
ejpam-2010	617	3	]	]	X
ejpam-2010	617	4	a	a	DET
ejpam-2010	617	5	h	h	NOUN
ejpam-2010	617	6	clifford	clifford	PROPN
ejpam-2010	617	7	and	and	CCONJ
ejpam-2010	617	8	g	g	PROPN
ejpam-2010	617	9	b	b	PROPN
ejpam-2010	617	10	preston	preston	PROPN
ejpam-2010	617	11	.	.	PUNCT
ejpam-2010	618	1	the	the	DET
ejpam-2010	618	2	algebraic	algebraic	PROPN
ejpam-2010	618	3	theory	theory	NOUN
ejpam-2010	618	4	of	of	ADP
ejpam-2010	618	5	semigroups	semigroup	NOUN
ejpam-2010	618	6	.	.	PUNCT
ejpam-2010	619	1	american	american	PROPN
ejpam-2010	619	2	mathematical	mathematical	PROPN
ejpam-2010	619	3	society	society	NOUN
ejpam-2010	619	4	,	,	PUNCT
ejpam-2010	619	5	providence	providence	NOUN
ejpam-2010	619	6	,	,	PUNCT
ejpam-2010	619	7	r.i	r.i	PROPN
ejpam-2010	619	8	.	.	PROPN
ejpam-2010	619	9	,	,	PUNCT
ejpam-2010	619	10	1961	1961	NUM
ejpam-2010	619	11	.	.	PUNCT
ejpam-2010	620	1	[	[	X
ejpam-2010	620	2	8	8	NUM
ejpam-2010	620	3	]	]	X
ejpam-2010	620	4	r	r	NOUN
ejpam-2010	620	5	colpi	colpi	NOUN
ejpam-2010	620	6	.	.	PUNCT
ejpam-2010	621	1	some	some	DET
ejpam-2010	621	2	remarks	remark	NOUN
ejpam-2010	621	3	on	on	ADP
ejpam-2010	621	4	equivalences	equivalence	NOUN
ejpam-2010	621	5	between	between	ADP
ejpam-2010	621	6	categories	category	NOUN
ejpam-2010	621	7	of	of	ADP
ejpam-2010	621	8	modules	module	NOUN
ejpam-2010	621	9	,	,	PUNCT
ejpam-2010	621	10	communications	communication	NOUN
ejpam-2010	621	11	in	in	ADP
ejpam-2010	621	12	algebra	algebra	NOUN
ejpam-2010	621	13	,	,	PUNCT
ejpam-2010	621	14	18	18	NUM
ejpam-2010	621	15	:	:	SYM
ejpam-2010	621	16	1935	1935	NUM
ejpam-2010	621	17	-	-	SYM
ejpam-2010	621	18	1951	1951	NUM
ejpam-2010	621	19	,	,	PUNCT
ejpam-2010	621	20	1990	1990	NUM
ejpam-2010	621	21	.	.	PUNCT
ejpam-2010	622	1	[	[	X
ejpam-2010	622	2	9	9	NUM
ejpam-2010	622	3	]	]	X
ejpam-2010	622	4	k	k	NOUN
ejpam-2010	622	5	r	r	NOUN
ejpam-2010	622	6	fuller	full	ADJ
ejpam-2010	622	7	.	.	PUNCT
ejpam-2010	623	1	rings	ring	NOUN
ejpam-2010	623	2	and	and	CCONJ
ejpam-2010	623	3	categories	category	NOUN
ejpam-2010	623	4	of	of	ADP
ejpam-2010	623	5	modulers	moduler	NOUN
ejpam-2010	623	6	.	.	PUNCT
ejpam-2010	624	1	springer	springer	NOUN
ejpam-2010	624	2	-	-	PUNCT
ejpam-2010	624	3	verlag	verlag	PROPN
ejpam-2010	624	4	,	,	PUNCT
ejpam-2010	624	5	new	new	PROPN
ejpam-2010	624	6	york	york	PROPN
ejpam-2010	624	7	.	.	PUNCT
ejpam-2010	625	1	heidelberg	heidelberg	PROPN
ejpam-2010	625	2	,	,	PUNCT
ejpam-2010	625	3	berlin	berlin	PROPN
ejpam-2010	625	4	,	,	PUNCT
ejpam-2010	625	5	1974	1974	NUM
ejpam-2010	625	6	.	.	PUNCT
ejpam-2010	626	1	[	[	X
ejpam-2010	626	2	10	10	NUM
ejpam-2010	626	3	]	]	X
ejpam-2010	626	4	k	k	NOUN
ejpam-2010	626	5	r	r	NOUN
ejpam-2010	626	6	fuller	full	ADJ
ejpam-2010	626	7	.	.	PUNCT
ejpam-2010	627	1	density	density	NOUN
ejpam-2010	627	2	and	and	CCONJ
ejpam-2010	627	3	equivalence	equivalence	NOUN
ejpam-2010	627	4	.	.	PUNCT
ejpam-2010	628	1	journal	journal	NOUN
ejpam-2010	628	2	of	of	ADP
ejpam-2010	628	3	algebra	algebra	PROPN
ejpam-2010	628	4	,	,	PUNCT
ejpam-2010	628	5	29	29	NUM
ejpam-2010	628	6	:	:	SYM
ejpam-2010	628	7	528	528	NUM
ejpam-2010	628	8	-	-	SYM
ejpam-2010	628	9	550	550	NUM
ejpam-2010	628	10	,	,	PUNCT
ejpam-2010	628	11	1974	1974	NUM
ejpam-2010	628	12	.	.	PUNCT
ejpam-2010	629	1	[	[	X
ejpam-2010	629	2	11	11	NUM
ejpam-2010	629	3	]	]	X
ejpam-2010	629	4	j	j	PROPN
ejpam-2010	629	5	funk	funk	NOUN
ejpam-2010	629	6	,	,	PUNCT
ejpam-2010	629	7	m	m	PROPN
ejpam-2010	629	8	v	v	ADP
ejpam-2010	629	9	lawson	lawson	PROPN
ejpam-2010	629	10	and	and	CCONJ
ejpam-2010	629	11	b	b	PROPN
ejpam-2010	629	12	steinberg	steinberg	PROPN
ejpam-2010	629	13	.	.	PUNCT
ejpam-2010	630	1	charaterizations	charaterization	NOUN
ejpam-2010	630	2	of	of	ADP
ejpam-2010	630	3	morita	morita	PROPN
ejpam-2010	630	4	equivalent	equivalent	ADJ
ejpam-2010	630	5	inverse	inverse	NOUN
ejpam-2010	630	6	semigroups	semigroup	NOUN
ejpam-2010	630	7	.	.	PUNCT
ejpam-2010	631	1	journal	journal	NOUN
ejpam-2010	631	2	of	of	ADP
ejpam-2010	631	3	pure	pure	ADJ
ejpam-2010	631	4	and	and	CCONJ
ejpam-2010	631	5	applied	applied	ADJ
ejpam-2010	631	6	algebra	algebra	NOUN
ejpam-2010	631	7	,	,	PUNCT
ejpam-2010	631	8	215	215	NUM
ejpam-2010	631	9	:	:	SYM
ejpam-2010	631	10	2262	2262	NUM
ejpam-2010	631	11	-	-	SYM
ejpam-2010	631	12	2279	2279	NUM
ejpam-2010	631	13	,	,	PUNCT
ejpam-2010	631	14	2011	2011	NUM
ejpam-2010	631	15	.	.	PUNCT
ejpam-2010	632	1	[	[	X
ejpam-2010	632	2	12	12	NUM
ejpam-2010	632	3	]	]	X
ejpam-2010	632	4	j	j	PROPN
ejpam-2010	632	5	l	l	PROPN
ejpam-2010	632	6	garcia	garcia	PROPN
ejpam-2010	632	7	.	.	PUNCT
ejpam-2010	633	1	the	the	DET
ejpam-2010	633	2	finite	finite	ADJ
ejpam-2010	633	3	column	column	NOUN
ejpam-2010	633	4	matrix	matrix	NOUN
ejpam-2010	633	5	ring	ring	NOUN
ejpam-2010	633	6	of	of	ADP
ejpam-2010	633	7	a	a	DET
ejpam-2010	633	8	ring	ring	NOUN
ejpam-2010	633	9	,	,	PUNCT
ejpam-2010	633	10	proceedings	proceeding	NOUN
ejpam-2010	633	11	,	,	PUNCT
ejpam-2010	633	12	1st	1st	ADJ
ejpam-2010	633	13	belgian	belgian	ADJ
ejpam-2010	633	14	-	-	PUNCT
ejpam-2010	633	15	spanish	spanish	ADJ
ejpam-2010	633	16	week	week	NOUN
ejpam-2010	633	17	on	on	ADP
ejpam-2010	633	18	algebra	algebra	NOUN
ejpam-2010	633	19	and	and	CCONJ
ejpam-2010	633	20	geometry	geometry	NOUN
ejpam-2010	633	21	,	,	PUNCT
ejpam-2010	633	22	64	64	NUM
ejpam-2010	633	23	-	-	SYM
ejpam-2010	633	24	74	74	NUM
ejpam-2010	633	25	,	,	PUNCT
ejpam-2010	633	26	1988	1988	NUM
ejpam-2010	633	27	.	.	PUNCT
ejpam-2010	634	1	[	[	X
ejpam-2010	634	2	13	13	NUM
ejpam-2010	634	3	]	]	SYM
ejpam-2010	634	4	j	j	PROPN
ejpam-2010	634	5	l	l	PROPN
ejpam-2010	634	6	garcia	garcia	PROPN
ejpam-2010	634	7	and	and	CCONJ
ejpam-2010	634	8	l	l	PROPN
ejpam-2010	634	9	marín	marín	PROPN
ejpam-2010	634	10	.	.	PUNCT
ejpam-2010	634	11	rings	ring	NOUN
ejpam-2010	634	12	having	have	VERB
ejpam-2010	634	13	a	a	DET
ejpam-2010	634	14	morita	morita	NOUN
ejpam-2010	634	15	-	-	PUNCT
ejpam-2010	634	16	like	like	ADJ
ejpam-2010	634	17	equivalence	equivalence	NOUN
ejpam-2010	634	18	.	.	PUNCT
ejpam-2010	635	1	communications	communication	NOUN
ejpam-2010	635	2	in	in	ADP
ejpam-2010	635	3	algebra	algebra	NOUN
ejpam-2010	635	4	,	,	PUNCT
ejpam-2010	635	5	27	27	NUM
ejpam-2010	635	6	:	:	PUNCT
ejpam-2010	635	7	665	665	NUM
ejpam-2010	635	8	-	-	SYM
ejpam-2010	635	9	680	680	NUM
ejpam-2010	635	10	,	,	PUNCT
ejpam-2010	635	11	1999	1999	NUM
ejpam-2010	635	12	.	.	PUNCT
ejpam-2010	636	1	[	[	X
ejpam-2010	636	2	14	14	NUM
ejpam-2010	636	3	]	]	X
ejpam-2010	636	4	j	j	PROPN
ejpam-2010	636	5	l	l	PROPN
ejpam-2010	636	6	garcia	garcia	PROPN
ejpam-2010	636	7	and	and	CCONJ
ejpam-2010	636	8	j	j	PROPN
ejpam-2010	636	9	j	j	PROPN
ejpam-2010	636	10	simòn	simòn	PROPN
ejpam-2010	636	11	.	.	PUNCT
ejpam-2010	637	1	morita	morita	PROPN
ejpam-2010	637	2	equivalence	equivalence	NOUN
ejpam-2010	637	3	for	for	ADP
ejpam-2010	637	4	idempotent	idempotent	ADJ
ejpam-2010	637	5	rings	ring	NOUN
ejpam-2010	637	6	.	.	PUNCT
ejpam-2010	638	1	journal	journal	PROPN
ejpam-2010	638	2	of	of	ADP
ejpam-2010	638	3	pure	pure	ADJ
ejpam-2010	638	4	and	and	CCONJ
ejpam-2010	638	5	applied	applied	ADJ
ejpam-2010	638	6	algebra	algebra	NOUN
ejpam-2010	638	7	,	,	PUNCT
ejpam-2010	638	8	76	76	NUM
ejpam-2010	638	9	:	:	SYM
ejpam-2010	638	10	39	39	NUM
ejpam-2010	638	11	-	-	SYM
ejpam-2010	638	12	56	56	NUM
ejpam-2010	638	13	,	,	PUNCT
ejpam-2010	638	14	1991	1991	NUM
ejpam-2010	638	15	.	.	PUNCT
ejpam-2010	639	1	[	[	X
ejpam-2010	639	2	15	15	NUM
ejpam-2010	639	3	]	]	X
ejpam-2010	639	4	n	n	PRON
ejpam-2010	639	5	jacobson	jacobson	PROPN
ejpam-2010	639	6	.	.	PUNCT
ejpam-2010	640	1	basic	basic	ADJ
ejpam-2010	640	2	algebra	algebra	PROPN
ejpam-2010	640	3	ii	ii	PROPN
ejpam-2010	640	4	.	.	PUNCT
ejpam-2010	641	1	van	van	PROPN
ejpam-2010	641	2	nostrand	nostrand	PROPN
ejpam-2010	641	3	/	/	SYM
ejpam-2010	641	4	freeman	freeman	PROPN
ejpam-2010	641	5	,	,	PUNCT
ejpam-2010	641	6	san	san	PROPN
ejpam-2010	641	7	franciso	franciso	PROPN
ejpam-2010	641	8	,	,	PUNCT
ejpam-2010	641	9	1976	1976	NUM
ejpam-2010	641	10	.	.	PUNCT
ejpam-2010	642	1	[	[	X
ejpam-2010	642	2	16	16	NUM
ejpam-2010	642	3	]	]	X
ejpam-2010	642	4	u	u	PROPN
ejpam-2010	642	5	knauer	knauer	NOUN
ejpam-2010	642	6	.	.	PUNCT
ejpam-2010	643	1	projectivity	projectivity	NOUN
ejpam-2010	643	2	of	of	ADP
ejpam-2010	643	3	acts	act	NOUN
ejpam-2010	643	4	and	and	CCONJ
ejpam-2010	643	5	morita	morita	PROPN
ejpam-2010	643	6	equivalence	equivalence	NOUN
ejpam-2010	643	7	of	of	ADP
ejpam-2010	643	8	monoids	monoid	NOUN
ejpam-2010	643	9	.	.	PUNCT
ejpam-2010	644	1	semigroup	semigroup	PROPN
ejpam-2010	644	2	forum	forum	PROPN
ejpam-2010	644	3	,	,	PUNCT
ejpam-2010	644	4	3	3	NUM
ejpam-2010	644	5	:	:	PUNCT
ejpam-2010	644	6	359	359	NUM
ejpam-2010	644	7	-	-	SYM
ejpam-2010	644	8	370	370	NUM
ejpam-2010	644	9	,	,	PUNCT
ejpam-2010	644	10	1972	1972	NUM
ejpam-2010	644	11	.	.	PUNCT
ejpam-2010	645	1	[	[	X
ejpam-2010	645	2	17	17	NUM
ejpam-2010	645	3	]	]	X
ejpam-2010	645	4	h	h	PROPN
ejpam-2010	645	5	komatsu	komatsu	PROPN
ejpam-2010	645	6	.	.	PUNCT
ejpam-2010	646	1	the	the	DET
ejpam-2010	646	2	category	category	NOUN
ejpam-2010	646	3	of	of	ADP
ejpam-2010	646	4	s	s	NOUN
ejpam-2010	646	5	-	-	ADJ
ejpam-2010	646	6	unital	unital	ADJ
ejpam-2010	646	7	modules	module	NOUN
ejpam-2010	646	8	.	.	PUNCT
ejpam-2010	647	1	mathematical	mathematical	ADJ
ejpam-2010	647	2	journal	journal	PROPN
ejpam-2010	647	3	of	of	ADP
ejpam-2010	647	4	okayama	okayama	PROPN
ejpam-2010	647	5	university	university	PROPN
ejpam-2010	647	6	,	,	PUNCT
ejpam-2010	647	7	28	28	NUM
ejpam-2010	647	8	:	:	PUNCT
ejpam-2010	647	9	54	54	NUM
ejpam-2010	647	10	-	-	SYM
ejpam-2010	647	11	91	91	NUM
ejpam-2010	647	12	,	,	PUNCT
ejpam-2010	647	13	1986	1986	NUM
ejpam-2010	647	14	.	.	PUNCT
ejpam-2010	648	1	[	[	X
ejpam-2010	648	2	18	18	NUM
ejpam-2010	648	3	]	]	X
ejpam-2010	648	4	s	s	VERB
ejpam-2010	649	1	kguno	kguno	PROPN
ejpam-2010	649	2	.	.	PUNCT
ejpam-2010	650	1	equivalence	equivalence	NOUN
ejpam-2010	650	2	of	of	ADP
ejpam-2010	650	3	module	module	NOUN
ejpam-2010	650	4	categories	category	NOUN
ejpam-2010	650	5	.	.	PUNCT
ejpam-2010	651	1	mathematical	mathematical	ADJ
ejpam-2010	651	2	journal	journal	PROPN
ejpam-2010	651	3	of	of	ADP
ejpam-2010	651	4	okayama	okayama	PROPN
ejpam-2010	651	5	university	university	PROPN
ejpam-2010	651	6	,	,	PUNCT
ejpam-2010	651	7	28	28	NUM
ejpam-2010	651	8	:	:	PUNCT
ejpam-2010	651	9	147	147	NUM
ejpam-2010	651	10	-	-	SYM
ejpam-2010	651	11	150	150	NUM
ejpam-2010	651	12	,	,	PUNCT
ejpam-2010	651	13	1986	1986	NUM
ejpam-2010	651	14	.	.	PUNCT
ejpam-2010	652	1	[	[	X
ejpam-2010	652	2	19	19	NUM
ejpam-2010	652	3	]	]	SYM
ejpam-2010	652	4	v	v	X
ejpam-2010	652	5	lann	lann	PROPN
ejpam-2010	652	6	.	.	PUNCT
ejpam-2010	653	1	morita	morita	PROPN
ejpam-2010	653	2	theorem	theorem	VERB
ejpam-2010	653	3	for	for	ADP
ejpam-2010	653	4	partially	partially	ADV
ejpam-2010	653	5	ordered	order	VERB
ejpam-2010	653	6	monoids	monoid	NOUN
ejpam-2010	653	7	.	.	PUNCT
ejpam-2010	654	1	proceedings	proceeding	NOUN
ejpam-2010	654	2	of	of	ADP
ejpam-2010	654	3	the	the	DET
ejpam-2010	654	4	estonian	estonian	ADJ
ejpam-2010	654	5	academy	academy	PROPN
ejpam-2010	654	6	of	of	ADP
ejpam-2010	654	7	sciences	sciences	PROPN
ejpam-2010	654	8	,	,	PUNCT
ejpam-2010	654	9	60	60	NUM
ejpam-2010	654	10	:	:	PUNCT
ejpam-2010	654	11	221	221	NUM
ejpam-2010	654	12	-	-	SYM
ejpam-2010	654	13	237	237	NUM
ejpam-2010	654	14	,	,	PUNCT
ejpam-2010	654	15	2011	2011	NUM
ejpam-2010	654	16	.	.	PUNCT
ejpam-2010	655	1	[	[	X
ejpam-2010	655	2	20	20	NUM
ejpam-2010	655	3	]	]	SYM
ejpam-2010	655	4	v	v	ADP
ejpam-2010	655	5	laan	laan	PROPN
ejpam-2010	655	6	and	and	CCONJ
ejpam-2010	655	7	l	l	PROPN
ejpam-2010	655	8	márki	márki	NOUN
ejpam-2010	655	9	.	.	PUNCT
ejpam-2010	656	1	strong	strong	ADJ
ejpam-2010	656	2	morita	morita	PROPN
ejpam-2010	656	3	equivalence	equivalence	NOUN
ejpam-2010	656	4	of	of	ADP
ejpam-2010	656	5	semigroups	semigroup	NOUN
ejpam-2010	656	6	with	with	ADP
ejpam-2010	656	7	local	local	ADJ
ejpam-2010	656	8	units	unit	NOUN
ejpam-2010	656	9	.	.	PUNCT
ejpam-2010	657	1	journal	journal	NOUN
ejpam-2010	657	2	of	of	ADP
ejpam-2010	657	3	pure	pure	ADJ
ejpam-2010	657	4	and	and	CCONJ
ejpam-2010	657	5	applied	applied	ADJ
ejpam-2010	657	6	algebra	algebra	NOUN
ejpam-2010	657	7	,	,	PUNCT
ejpam-2010	657	8	215	215	NUM
ejpam-2010	657	9	:	:	PUNCT
ejpam-2010	657	10	2538	2538	NUM
ejpam-2010	657	11	-	-	SYM
ejpam-2010	657	12	2546	2546	NUM
ejpam-2010	657	13	,	,	PUNCT
ejpam-2010	657	14	2011	2011	NUM
ejpam-2010	657	15	.	.	PUNCT
ejpam-2010	658	1	references	reference	NOUN
ejpam-2010	658	2	280	280	NUM
ejpam-2010	659	1	[	[	X
ejpam-2010	659	2	21	21	NUM
ejpam-2010	659	3	]	]	SYM
ejpam-2010	659	4	v	v	ADP
ejpam-2010	659	5	laan	laan	PROPN
ejpam-2010	659	6	and	and	CCONJ
ejpam-2010	659	7	l	l	PROPN
ejpam-2010	659	8	márki	márki	NOUN
ejpam-2010	659	9	.	.	PUNCT
ejpam-2010	660	1	morita	morita	PROPN
ejpam-2010	660	2	invariants	invariants	PROPN
ejpam-2010	660	3	for	for	ADP
ejpam-2010	660	4	semigroups	semigroup	NOUN
ejpam-2010	660	5	with	with	ADP
ejpam-2010	660	6	local	local	ADJ
ejpam-2010	660	7	units	unit	NOUN
ejpam-2010	660	8	.	.	PUNCT
ejpam-2010	661	1	monatsh	monatsh	ADJ
ejpam-2010	661	2	math	math	NOUN
ejpam-2010	661	3	,	,	PUNCT
ejpam-2010	661	4	166	166	NUM
ejpam-2010	661	5	:	:	PUNCT
ejpam-2010	661	6	441	441	NUM
ejpam-2010	661	7	-	-	SYM
ejpam-2010	661	8	451	451	NUM
ejpam-2010	661	9	,	,	PUNCT
ejpam-2010	661	10	2012	2012	NUM
ejpam-2010	661	11	.	.	PUNCT
ejpam-2010	662	1	[	[	X
ejpam-2010	662	2	22	22	NUM
ejpam-2010	662	3	]	]	PUNCT
ejpam-2010	662	4	t	t	PROPN
ejpam-2010	662	5	y	y	PROPN
ejpam-2010	662	6	lam	lam	PROPN
ejpam-2010	662	7	.	.	PUNCT
ejpam-2010	663	1	lectures	lecture	NOUN
ejpam-2010	663	2	on	on	ADP
ejpam-2010	663	3	rings	ring	NOUN
ejpam-2010	663	4	and	and	CCONJ
ejpam-2010	663	5	modules	module	NOUN
ejpam-2010	663	6	.	.	PUNCT
ejpam-2010	664	1	springer	springer	NOUN
ejpam-2010	664	2	-	-	PUNCT
ejpam-2010	664	3	verlag	verlag	PROPN
ejpam-2010	664	4	,	,	PUNCT
ejpam-2010	664	5	new	new	PROPN
ejpam-2010	664	6	york	york	PROPN
ejpam-2010	664	7	,	,	PUNCT
ejpam-2010	664	8	1999	1999	NUM
ejpam-2010	664	9	.	.	PUNCT
ejpam-2010	665	1	[	[	X
ejpam-2010	665	2	23	23	NUM
ejpam-2010	665	3	]	]	X
ejpam-2010	665	4	m	m	VERB
ejpam-2010	665	5	v	v	ADP
ejpam-2010	665	6	lawson	lawson	PROPN
ejpam-2010	665	7	.	.	PUNCT
ejpam-2010	666	1	enlargements	enlargement	NOUN
ejpam-2010	666	2	of	of	ADP
ejpam-2010	666	3	regular	regular	ADJ
ejpam-2010	666	4	semigroups	semigroup	NOUN
ejpam-2010	666	5	.	.	PUNCT
ejpam-2010	667	1	proceedings	proceeding	NOUN
ejpam-2010	667	2	of	of	ADP
ejpam-2010	667	3	the	the	DET
ejpam-2010	667	4	edinburgh	edinburgh	PROPN
ejpam-2010	667	5	mathematical	mathematical	PROPN
ejpam-2010	667	6	society	society	NOUN
ejpam-2010	667	7	,	,	PUNCT
ejpam-2010	667	8	39	39	NUM
ejpam-2010	667	9	:	:	SYM
ejpam-2010	667	10	425	425	NUM
ejpam-2010	667	11	-	-	SYM
ejpam-2010	667	12	460	460	NUM
ejpam-2010	667	13	,	,	PUNCT
ejpam-2010	667	14	1996	1996	NUM
ejpam-2010	667	15	.	.	PUNCT
ejpam-2010	668	1	[	[	X
ejpam-2010	668	2	24	24	NUM
ejpam-2010	668	3	]	]	X
ejpam-2010	668	4	m	m	VERB
ejpam-2010	668	5	v	v	ADP
ejpam-2010	668	6	lawson	lawson	PROPN
ejpam-2010	668	7	and	and	CCONJ
ejpam-2010	668	8	l	l	PROPN
ejpam-2010	668	9	márki	márki	NOUN
ejpam-2010	668	10	.	.	PUNCT
ejpam-2010	669	1	enlargements	enlargement	NOUN
ejpam-2010	669	2	and	and	CCONJ
ejpam-2010	669	3	coverings	covering	NOUN
ejpam-2010	669	4	by	by	ADP
ejpam-2010	669	5	rees	ree	NOUN
ejpam-2010	669	6	matrix	matrix	NOUN
ejpam-2010	669	7	semigroups	semigroup	NOUN
ejpam-2010	669	8	.	.	PUNCT
ejpam-2010	670	1	monatshefte	monatshefte	PROPN
ejpam-2010	670	2	fur	fur	NOUN
ejpam-2010	670	3	mathematik	mathematik	PROPN
ejpam-2010	670	4	,	,	PUNCT
ejpam-2010	670	5	129	129	NUM
ejpam-2010	670	6	:	:	SYM
ejpam-2010	670	7	191	191	NUM
ejpam-2010	670	8	-	-	SYM
ejpam-2010	670	9	195	195	NUM
ejpam-2010	670	10	,	,	PUNCT
ejpam-2010	670	11	2000	2000	NUM
ejpam-2010	670	12	.	.	PUNCT
ejpam-2010	671	1	[	[	X
ejpam-2010	671	2	25	25	NUM
ejpam-2010	671	3	]	]	X
ejpam-2010	671	4	m	m	VERB
ejpam-2010	671	5	v	v	ADP
ejpam-2010	671	6	lawson	lawson	PROPN
ejpam-2010	671	7	.	.	PUNCT
ejpam-2010	672	1	morita	morita	PROPN
ejpam-2010	672	2	equivalence	equivalence	NOUN
ejpam-2010	672	3	of	of	ADP
ejpam-2010	672	4	semigroups	semigroup	NOUN
ejpam-2010	672	5	with	with	ADP
ejpam-2010	672	6	local	local	ADJ
ejpam-2010	672	7	units	unit	NOUN
ejpam-2010	672	8	.	.	PUNCT
ejpam-2010	673	1	journal	journal	NOUN
ejpam-2010	673	2	of	of	ADP
ejpam-2010	673	3	pure	pure	ADJ
ejpam-2010	673	4	and	and	CCONJ
ejpam-2010	673	5	applied	applied	ADJ
ejpam-2010	673	6	algebra	algebra	NOUN
ejpam-2010	673	7	,	,	PUNCT
ejpam-2010	673	8	215	215	NUM
ejpam-2010	673	9	:	:	SYM
ejpam-2010	673	10	455	455	NUM
ejpam-2010	673	11	-	-	SYM
ejpam-2010	673	12	470	470	NUM
ejpam-2010	673	13	,	,	PUNCT
ejpam-2010	673	14	2011	2011	NUM
ejpam-2010	673	15	.	.	PUNCT
ejpam-2010	674	1	nj	nj	PROPN
ejpam-2010	674	2	,	,	PUNCT
ejpam-2010	674	3	1998	1998	NUM
ejpam-2010	674	4	.	.	PUNCT
ejpam-2010	675	1	[	[	X
ejpam-2010	675	2	26	26	NUM
ejpam-2010	675	3	]	]	PUNCT
ejpam-2010	675	4	l	l	NOUN
ejpam-2010	675	5	márki	márki	NOUN
ejpam-2010	675	6	and	and	CCONJ
ejpam-2010	675	7	o	o	PROPN
ejpam-2010	675	8	steinfeld	steinfeld	PROPN
ejpam-2010	675	9	.	.	PUNCT
ejpam-2010	676	1	a	a	DET
ejpam-2010	676	2	rees	rees	PROPN
ejpam-2010	676	3	construction	construction	NOUN
ejpam-2010	676	4	without	without	ADP
ejpam-2010	676	5	regularity	regularity	NOUN
ejpam-2010	676	6	.	.	PUNCT
ejpam-2010	677	1	in	in	ADP
ejpam-2010	677	2	contributions	contribution	NOUN
ejpam-2010	677	3	to	to	ADP
ejpam-2010	677	4	general	general	ADJ
ejpam-2010	677	5	algebra	algebra	NOUN
ejpam-2010	677	6	,	,	PUNCT
ejpam-2010	677	7	hölder	hölder	NOUN
ejpam-2010	677	8	-	-	PUNCT
ejpam-2010	677	9	pichler	pichler	NOUN
ejpam-2010	677	10	-	-	PUNCT
ejpam-2010	677	11	temsky	temsky	NOUN
ejpam-2010	677	12	,	,	PUNCT
ejpam-2010	677	13	wien	wien	NOUN
ejpam-2010	677	14	and	and	CCONJ
ejpam-2010	677	15	teubner	teubner	NOUN
ejpam-2010	677	16	,	,	PUNCT
ejpam-2010	677	17	stuttgart	stuttgart	PROPN
ejpam-2010	677	18	,	,	PUNCT
ejpam-2010	677	19	1988	1988	NUM
ejpam-2010	677	20	.	.	PUNCT
ejpam-2010	678	1	[	[	X
ejpam-2010	678	2	27	27	NUM
ejpam-2010	678	3	]	]	X
ejpam-2010	678	4	d	d	PROPN
ejpam-2010	678	5	b	b	PROPN
ejpam-2010	678	6	mcalister	mcalister	PROPN
ejpam-2010	678	7	.	.	PUNCT
ejpam-2010	679	1	regular	regular	ADJ
ejpam-2010	679	2	rees	ree	NOUN
ejpam-2010	679	3	matrix	matrix	NOUN
ejpam-2010	679	4	semigroups	semigroup	NOUN
ejpam-2010	679	5	and	and	CCONJ
ejpam-2010	679	6	regular	regular	ADJ
ejpam-2010	679	7	dubreil	dubreil	NOUN
ejpam-2010	679	8	-	-	PUNCT
ejpam-2010	679	9	jacotin	jacotin	NOUN
ejpam-2010	679	10	semigroups	semigroup	NOUN
ejpam-2010	679	11	.	.	PUNCT
ejpam-2010	680	1	journal	journal	NOUN
ejpam-2010	680	2	of	of	ADP
ejpam-2010	680	3	the	the	DET
ejpam-2010	680	4	australian	australian	ADJ
ejpam-2010	680	5	mathematical	mathematical	ADJ
ejpam-2010	680	6	society	society	NOUN
ejpam-2010	680	7	(	(	PUNCT
ejpam-2010	680	8	series	series	PROPN
ejpam-2010	680	9	a	a	PROPN
ejpam-2010	680	10	)	)	PUNCT
ejpam-2010	680	11	,	,	PUNCT
ejpam-2010	680	12	31	31	NUM
ejpam-2010	680	13	:	:	PUNCT
ejpam-2010	680	14	325	325	NUM
ejpam-2010	680	15	-	-	SYM
ejpam-2010	680	16	336	336	NUM
ejpam-2010	680	17	,	,	PUNCT
ejpam-2010	680	18	1981	1981	NUM
ejpam-2010	680	19	.	.	PUNCT
ejpam-2010	681	1	[	[	X
ejpam-2010	681	2	28	28	NUM
ejpam-2010	681	3	]	]	X
ejpam-2010	681	4	d	d	PROPN
ejpam-2010	681	5	b	b	X
ejpam-2010	681	6	mcalister	mcalister	PROPN
ejpam-2010	681	7	.	.	PUNCT
ejpam-2010	682	1	rees	rees	PROPN
ejpam-2010	682	2	matrix	matrix	NOUN
ejpam-2010	682	3	covers	cover	NOUN
ejpam-2010	682	4	for	for	ADP
ejpam-2010	682	5	locally	locally	ADV
ejpam-2010	682	6	inverse	inverse	NOUN
ejpam-2010	682	7	semigroups	semigroup	NOUN
ejpam-2010	682	8	.	.	PUNCT
ejpam-2010	683	1	transactions	transaction	NOUN
ejpam-2010	683	2	of	of	ADP
ejpam-2010	683	3	the	the	DET
ejpam-2010	683	4	american	american	PROPN
ejpam-2010	683	5	mathematical	mathematical	PROPN
ejpam-2010	683	6	society	society	NOUN
ejpam-2010	683	7	,	,	PUNCT
ejpam-2010	683	8	277	277	NUM
ejpam-2010	683	9	:	:	PUNCT
ejpam-2010	683	10	727	727	NUM
ejpam-2010	683	11	-	-	SYM
ejpam-2010	683	12	738	738	NUM
ejpam-2010	683	13	,	,	PUNCT
ejpam-2010	683	14	1983	1983	NUM
ejpam-2010	683	15	.	.	PUNCT
ejpam-2010	684	1	[	[	X
ejpam-2010	684	2	29	29	NUM
ejpam-2010	684	3	]	]	X
ejpam-2010	684	4	d	d	PROPN
ejpam-2010	684	5	b	b	X
ejpam-2010	684	6	mcalister	mcalister	PROPN
ejpam-2010	684	7	.	.	PUNCT
ejpam-2010	685	1	rees	rees	PROPN
ejpam-2010	685	2	matrix	matrix	NOUN
ejpam-2010	685	3	covers	cover	NOUN
ejpam-2010	685	4	for	for	ADP
ejpam-2010	685	5	regular	regular	ADJ
ejpam-2010	685	6	semigroups	semigroup	NOUN
ejpam-2010	685	7	.	.	PUNCT
ejpam-2010	686	1	journal	journal	NOUN
ejpam-2010	686	2	of	of	ADP
ejpam-2010	686	3	algebra	algebra	PROPN
ejpam-2010	686	4	,	,	PUNCT
ejpam-2010	686	5	89	89	NUM
ejpam-2010	686	6	:	:	SYM
ejpam-2010	686	7	264279	264279	NUM
ejpam-2010	686	8	,	,	PUNCT
ejpam-2010	686	9	1984	1984	NUM
ejpam-2010	686	10	.	.	PUNCT
ejpam-2010	687	1	[	[	X
ejpam-2010	687	2	30	30	NUM
ejpam-2010	687	3	]	]	X
ejpam-2010	687	4	d	d	PROPN
ejpam-2010	687	5	b	b	X
ejpam-2010	687	6	mcalister	mcalister	PROPN
ejpam-2010	687	7	.	.	PUNCT
ejpam-2010	688	1	rees	rees	PROPN
ejpam-2010	688	2	matrix	matrix	NOUN
ejpam-2010	688	3	covers	cover	NOUN
ejpam-2010	688	4	for	for	ADP
ejpam-2010	688	5	regular	regular	ADJ
ejpam-2010	688	6	semigroups	semigroup	NOUN
ejpam-2010	688	7	.	.	PUNCT
ejpam-2010	689	1	in	in	ADP
ejpam-2010	689	2	byleen	byleen	PROPN
ejpam-2010	689	3	,	,	PUNCT
ejpam-2010	689	4	jones	jones	PROPN
ejpam-2010	689	5	and	and	CCONJ
ejpam-2010	689	6	pastijn	pastijn	NOUN
ejpam-2010	689	7	,	,	PUNCT
ejpam-2010	689	8	editors	editor	NOUN
ejpam-2010	689	9	,	,	PUNCT
ejpam-2010	689	10	proceedings	proceeding	NOUN
ejpam-2010	689	11	of	of	ADP
ejpam-2010	689	12	1984	1984	NUM
ejpam-2010	689	13	marquette	marquette	PROPN
ejpam-2010	689	14	conference	conference	NOUN
ejpam-2010	689	15	on	on	ADP
ejpam-2010	689	16	semigroups	semigroup	NOUN
ejpam-2010	689	17	,	,	PUNCT
ejpam-2010	689	18	131	131	NUM
ejpam-2010	689	19	-	-	SYM
ejpam-2010	689	20	141	141	NUM
ejpam-2010	689	21	,	,	PUNCT
ejpam-2010	689	22	marquette	marquette	NOUN
ejpam-2010	689	23	university	university	NOUN
ejpam-2010	689	24	,	,	PUNCT
ejpam-2010	689	25	1985	1985	NUM
ejpam-2010	689	26	,	,	PUNCT
ejpam-2010	689	27	milwaukee	milwaukee	PROPN
ejpam-2010	689	28	.	.	PUNCT
ejpam-2010	690	1	[	[	X
ejpam-2010	690	2	31	31	NUM
ejpam-2010	690	3	]	]	X
ejpam-2010	690	4	d	d	PROPN
ejpam-2010	690	5	b	b	PROPN
ejpam-2010	690	6	mcalister	mcalister	PROPN
ejpam-2010	690	7	.	.	PUNCT
ejpam-2010	691	1	quasi	quasi	ADJ
ejpam-2010	691	2	-	-	ADJ
ejpam-2010	691	3	ideal	ideal	ADJ
ejpam-2010	691	4	embeddings	embedding	NOUN
ejpam-2010	691	5	and	and	CCONJ
ejpam-2010	691	6	rees	ree	NOUN
ejpam-2010	691	7	matrix	matrix	NOUN
ejpam-2010	691	8	covers	cover	NOUN
ejpam-2010	691	9	for	for	ADP
ejpam-2010	691	10	regular	regular	ADJ
ejpam-2010	691	11	semigroups	semigroup	NOUN
ejpam-2010	691	12	.	.	PUNCT
ejpam-2010	692	1	journal	journal	NOUN
ejpam-2010	692	2	of	of	ADP
ejpam-2010	692	3	algebra	algebra	PROPN
ejpam-2010	692	4	,	,	PUNCT
ejpam-2010	692	5	152	152	NUM
ejpam-2010	692	6	:	:	SYM
ejpam-2010	692	7	166	166	NUM
ejpam-2010	692	8	-	-	SYM
ejpam-2010	692	9	183	183	NUM
ejpam-2010	692	10	,	,	PUNCT
ejpam-2010	692	11	1992	1992	NUM
ejpam-2010	692	12	.	.	PUNCT
ejpam-2010	693	1	[	[	X
ejpam-2010	693	2	32	32	NUM
ejpam-2010	693	3	]	]	X
ejpam-2010	693	4	r	r	NOUN
ejpam-2010	693	5	mckenzie	mckenzie	NOUN
ejpam-2010	693	6	.	.	PUNCT
ejpam-2010	694	1	an	an	DET
ejpam-2010	694	2	algebraic	algebraic	ADJ
ejpam-2010	694	3	version	version	NOUN
ejpam-2010	694	4	of	of	ADP
ejpam-2010	694	5	categorical	categorical	ADJ
ejpam-2010	694	6	equivalence	equivalence	NOUN
ejpam-2010	694	7	for	for	ADP
ejpam-2010	694	8	varieties	variety	NOUN
ejpam-2010	694	9	and	and	CCONJ
ejpam-2010	694	10	more	more	ADV
ejpam-2010	694	11	general	general	ADJ
ejpam-2010	694	12	algebraic	algebraic	ADJ
ejpam-2010	694	13	categories	category	NOUN
ejpam-2010	694	14	.	.	PUNCT
ejpam-2010	695	1	in	in	ADP
ejpam-2010	695	2	s.p	s.p	PROPN
ejpam-2010	695	3	.	.	PROPN
ejpam-2010	695	4	agliano	agliano	PROPN
ejpam-2010	695	5	,	,	PUNCT
ejpam-2010	695	6	a.	a.	NOUN
ejpam-2010	695	7	ursini	ursini	NOUN
ejpam-2010	695	8	and	and	CCONJ
ejpam-2010	695	9	m.	m.	NOUN
ejpam-2010	695	10	dekker	dekker	PROPN
ejpam-2010	695	11	,	,	PUNCT
ejpam-2010	695	12	editors	editor	NOUN
ejpam-2010	695	13	,	,	PUNCT
ejpam-2010	695	14	logic	logic	NOUN
ejpam-2010	695	15	and	and	CCONJ
ejpam-2010	695	16	algebra	algebra	NOUN
ejpam-2010	695	17	:	:	PUNCT
ejpam-2010	695	18	proceedings	proceeding	NOUN
ejpam-2010	695	19	of	of	ADP
ejpam-2010	695	20	the	the	DET
ejpam-2010	695	21	magari	magari	PROPN
ejpam-2010	695	22	conference	conference	PROPN
ejpam-2010	695	23	,	,	PUNCT
ejpam-2010	695	24	siena	siena	PROPN
ejpam-2010	695	25	,	,	PUNCT
ejpam-2010	695	26	1996	1996	NUM
ejpam-2010	695	27	.	.	PUNCT
ejpam-2010	696	1	[	[	X
ejpam-2010	696	2	33	33	NUM
ejpam-2010	696	3	]	]	SYM
ejpam-2010	696	4	b	b	PROPN
ejpam-2010	696	5	mitchell	mitchell	PROPN
ejpam-2010	696	6	.	.	PUNCT
ejpam-2010	697	1	theory	theory	NOUN
ejpam-2010	697	2	of	of	ADP
ejpam-2010	697	3	categories	category	NOUN
ejpam-2010	697	4	,	,	PUNCT
ejpam-2010	697	5	academic	academic	ADJ
ejpam-2010	697	6	press	press	NOUN
ejpam-2010	697	7	,	,	PUNCT
ejpam-2010	697	8	1965	1965	NUM
ejpam-2010	697	9	.	.	PUNCT
ejpam-2010	698	1	[	[	X
ejpam-2010	698	2	34	34	NUM
ejpam-2010	698	3	]	]	X
ejpam-2010	698	4	k	k	PROPN
ejpam-2010	698	5	morita	morita	PROPN
ejpam-2010	698	6	.	.	PUNCT
ejpam-2010	699	1	duality	duality	NOUN
ejpam-2010	699	2	of	of	ADP
ejpam-2010	699	3	modules	module	NOUN
ejpam-2010	699	4	and	and	CCONJ
ejpam-2010	699	5	its	its	PRON
ejpam-2010	699	6	applications	application	NOUN
ejpam-2010	699	7	to	to	ADP
ejpam-2010	699	8	the	the	DET
ejpam-2010	699	9	theory	theory	NOUN
ejpam-2010	699	10	of	of	ADP
ejpam-2010	699	11	rings	ring	NOUN
ejpam-2010	699	12	with	with	ADP
ejpam-2010	699	13	minimum	minimum	ADJ
ejpam-2010	699	14	condition	condition	NOUN
ejpam-2010	699	15	.	.	PUNCT
ejpam-2010	700	1	science	science	PROPN
ejpam-2010	700	2	rep	rep	PROPN
ejpam-2010	700	3	.	.	PROPN
ejpam-2010	700	4	tokyo	tokyo	PROPN
ejpam-2010	700	5	kyoiku	kyoiku	PROPN
ejpam-2010	700	6	daigaku	daigaku	PROPN
ejpam-2010	700	7	sect	sect	PROPN
ejpam-2010	700	8	.	.	PUNCT
ejpam-2010	700	9	,	,	PUNCT
ejpam-2010	701	1	a6	a6	NOUN
ejpam-2010	701	2	:	:	PUNCT
ejpam-2010	701	3	85	85	NUM
ejpam-2010	701	4	-	-	SYM
ejpam-2010	701	5	142	142	NUM
ejpam-2010	701	6	,	,	PUNCT
ejpam-2010	701	7	1958	1958	NUM
ejpam-2010	701	8	.	.	PUNCT
ejpam-2010	702	1	[	[	X
ejpam-2010	702	2	35	35	NUM
ejpam-2010	702	3	]	]	X
ejpam-2010	702	4	n	n	DET
ejpam-2010	702	5	nobusawa	nobusawa	PROPN
ejpam-2010	702	6	.	.	PUNCT
ejpam-2010	702	7	gamma	gamma	NOUN
ejpam-2010	702	8	-	-	PUNCT
ejpam-2010	702	9	rings	ring	NOUN
ejpam-2010	702	10	and	and	CCONJ
ejpam-2010	702	11	morita	morita	PROPN
ejpam-2010	702	12	equivalence	equivalence	NOUN
ejpam-2010	702	13	of	of	ADP
ejpam-2010	702	14	rings	ring	NOUN
ejpam-2010	702	15	.	.	PUNCT
ejpam-2010	703	1	mathematical	mathematical	ADJ
ejpam-2010	703	2	journal	journal	PROPN
ejpam-2010	703	3	of	of	ADP
ejpam-2010	703	4	okayama	okayama	PROPN
ejpam-2010	703	5	university	university	PROPN
ejpam-2010	703	6	,	,	PUNCT
ejpam-2010	703	7	26	26	NUM
ejpam-2010	703	8	:	:	SYM
ejpam-2010	703	9	151	151	NUM
ejpam-2010	703	10	-	-	SYM
ejpam-2010	703	11	156	156	NUM
ejpam-2010	703	12	,	,	PUNCT
ejpam-2010	703	13	1984	1984	NUM
ejpam-2010	703	14	.	.	PUNCT
ejpam-2010	704	1	[	[	X
ejpam-2010	704	2	36	36	NUM
ejpam-2010	704	3	]	]	X
ejpam-2010	704	4	m	m	VERB
ejpam-2010	704	5	parvathi	parvathi	PROPN
ejpam-2010	704	6	and	and	CCONJ
ejpam-2010	704	7	a	a	DET
ejpam-2010	704	8	ranvakrishna	ranvakrishna	PROPN
ejpam-2010	704	9	rao	rao	PROPN
ejpam-2010	704	10	.	.	PUNCT
ejpam-2010	704	11	morita	morita	PROPN
ejpam-2010	704	12	equivalence	equivalence	NOUN
ejpam-2010	704	13	for	for	ADP
ejpam-2010	704	14	a	a	DET
ejpam-2010	704	15	large	large	ADJ
ejpam-2010	704	16	class	class	NOUN
ejpam-2010	704	17	of	of	ADP
ejpam-2010	704	18	rings	ring	NOUN
ejpam-2010	704	19	.	.	PUNCT
ejpam-2010	705	1	publicationes	publicatione	NOUN
ejpam-2010	705	2	mathematicae	mathematicae	PROPN
ejpam-2010	705	3	-	-	PUNCT
ejpam-2010	705	4	debrecen	debrecen	PROPN
ejpam-2010	705	5	,	,	PUNCT
ejpam-2010	705	6	35	35	NUM
ejpam-2010	705	7	:	:	SYM
ejpam-2010	705	8	65	65	NUM
ejpam-2010	705	9	-	-	SYM
ejpam-2010	705	10	71	71	NUM
ejpam-2010	705	11	,	,	PUNCT
ejpam-2010	705	12	1988	1988	NUM
ejpam-2010	705	13	.	.	PUNCT
ejpam-2010	706	1	references	reference	NOUN
ejpam-2010	706	2	281	281	NUM
ejpam-2010	707	1	[	[	X
ejpam-2010	707	2	37	37	NUM
ejpam-2010	707	3	]	]	X
ejpam-2010	707	4	b	b	NOUN
ejpam-2010	707	5	pécsi	pécsi	NOUN
ejpam-2010	707	6	.	.	PUNCT
ejpam-2010	708	1	on	on	ADP
ejpam-2010	708	2	morita	morita	PROPN
ejpam-2010	708	3	contexts	contexts	PROPN
ejpam-2010	708	4	in	in	ADP
ejpam-2010	708	5	bicategories	bicategorie	NOUN
ejpam-2010	708	6	.	.	PUNCT
ejpam-2010	709	1	applied	apply	VERB
ejpam-2010	709	2	categorical	categorical	ADJ
ejpam-2010	709	3	structures	structure	NOUN
ejpam-2010	709	4	,	,	PUNCT
ejpam-2010	709	5	20	20	NUM
ejpam-2010	709	6	:	:	PUNCT
ejpam-2010	709	7	415–432	415–432	NUM
ejpam-2010	709	8	.	.	NOUN
ejpam-2010	709	9	2012	2012	NUM
ejpam-2010	709	10	.	.	PUNCT
ejpam-2010	710	1	[	[	X
ejpam-2010	710	2	38	38	NUM
ejpam-2010	710	3	]	]	X
ejpam-2010	710	4	d	d	X
ejpam-2010	710	5	quillen	quillen	ADJ
ejpam-2010	710	6	.	.	PUNCT
ejpam-2010	711	1	k0	k0	PROPN
ejpam-2010	711	2	nonunital	nonunital	PROPN
ejpam-2010	711	3	rings	rings	PROPN
ejpam-2010	711	4	and	and	CCONJ
ejpam-2010	711	5	morita	morita	PROPN
ejpam-2010	711	6	invariance	invariance	PROPN
ejpam-2010	711	7	.	.	PUNCT
ejpam-2010	712	1	journal	journal	PROPN
ejpam-2010	712	2	für	für	PROPN
ejpam-2010	712	3	die	die	VERB
ejpam-2010	712	4	reine	reine	PROPN
ejpam-2010	712	5	and	and	CCONJ
ejpam-2010	712	6	angewandte	angewandte	PROPN
ejpam-2010	712	7	matliematik	matliematik	PROPN
ejpam-2010	712	8	,	,	PUNCT
ejpam-2010	712	9	472	472	NUM
ejpam-2010	712	10	:	:	PUNCT
ejpam-2010	712	11	197	197	NUM
ejpam-2010	712	12	-	-	SYM
ejpam-2010	712	13	217	217	NUM
ejpam-2010	712	14	,	,	PUNCT
ejpam-2010	712	15	1996	1996	NUM
ejpam-2010	712	16	.	.	PUNCT
ejpam-2010	713	1	[	[	X
ejpam-2010	713	2	39	39	NUM
ejpam-2010	713	3	]	]	X
ejpam-2010	713	4	d	d	X
ejpam-2010	713	5	rees	rees	PROPN
ejpam-2010	713	6	.	.	PUNCT
ejpam-2010	714	1	on	on	ADP
ejpam-2010	714	2	semigroups	semigroup	NOUN
ejpam-2010	714	3	.	.	PUNCT
ejpam-2010	715	1	proceedings	proceeding	NOUN
ejpam-2010	715	2	of	of	ADP
ejpam-2010	715	3	the	the	DET
ejpam-2010	715	4	cambridge	cambridge	PROPN
ejpam-2010	715	5	philosophical	philosophical	ADJ
ejpam-2010	715	6	society	society	NOUN
ejpam-2010	715	7	,	,	PUNCT
ejpam-2010	715	8	36	36	NUM
ejpam-2010	715	9	:	:	SYM
ejpam-2010	715	10	387	387	NUM
ejpam-2010	715	11	-	-	SYM
ejpam-2010	715	12	400	400	NUM
ejpam-2010	715	13	,	,	PUNCT
ejpam-2010	715	14	1940	1940	NUM
ejpam-2010	715	15	.	.	PUNCT
ejpam-2010	716	1	[	[	X
ejpam-2010	716	2	40	40	NUM
ejpam-2010	716	3	]	]	X
ejpam-2010	716	4	j	j	PROPN
ejpam-2010	716	5	rhodes	rhodes	PROPN
ejpam-2010	716	6	and	and	CCONJ
ejpam-2010	716	7	b	b	PROPN
ejpam-2010	716	8	steinberg	steinberg	PROPN
ejpam-2010	716	9	.	.	PUNCT
ejpam-2010	717	1	the	the	DET
ejpam-2010	717	2	q	q	NOUN
ejpam-2010	717	3	-	-	NOUN
ejpam-2010	717	4	theory	theory	NOUN
ejpam-2010	717	5	of	of	ADP
ejpam-2010	717	6	finite	finite	PROPN
ejpam-2010	717	7	semigroups	semigroup	NOUN
ejpam-2010	717	8	.	.	PUNCT
ejpam-2010	718	1	springer	springer	NOUN
ejpam-2010	718	2	monographs	monograph	NOUN
ejpam-2010	718	3	in	in	ADP
ejpam-2010	718	4	mathematics	mathematic	NOUN
ejpam-2010	718	5	,	,	PUNCT
ejpam-2010	718	6	springer	springer	NOUN
ejpam-2010	718	7	,	,	PUNCT
ejpam-2010	718	8	2009	2009	NUM
ejpam-2010	718	9	.	.	PUNCT
ejpam-2010	719	1	[	[	X
ejpam-2010	719	2	41	41	NUM
ejpam-2010	719	3	]	]	X
ejpam-2010	719	4	m	m	VERB
ejpam-2010	719	5	sato	sato	NOUN
ejpam-2010	719	6	.	.	PUNCT
ejpam-2010	720	1	fuller	full	ADJ
ejpam-2010	720	2	’s	’s	PART
ejpam-2010	720	3	theorem	theorem	NOUN
ejpam-2010	720	4	on	on	ADP
ejpam-2010	720	5	equivalences	equivalence	NOUN
ejpam-2010	720	6	.	.	PUNCT
ejpam-2010	721	1	journal	journal	NOUN
ejpam-2010	721	2	of	of	ADP
ejpam-2010	721	3	algebra	algebra	PROPN
ejpam-2010	721	4	,	,	PUNCT
ejpam-2010	721	5	52	52	NUM
ejpam-2010	721	6	:	:	SYM
ejpam-2010	721	7	274	274	NUM
ejpam-2010	721	8	-	-	SYM
ejpam-2010	721	9	284	284	NUM
ejpam-2010	721	10	,	,	PUNCT
ejpam-2010	721	11	1978	1978	NUM
ejpam-2010	721	12	.	.	PUNCT
ejpam-2010	722	1	[	[	X
ejpam-2010	722	2	42	42	NUM
ejpam-2010	722	3	]	]	SYM
ejpam-2010	722	4	b	b	PROPN
ejpam-2010	722	5	steinberg	steinberg	PROPN
ejpam-2010	722	6	.	.	PUNCT
ejpam-2010	723	1	strong	strong	ADJ
ejpam-2010	723	2	morita	morita	PROPN
ejpam-2010	723	3	equivalence	equivalence	NOUN
ejpam-2010	723	4	of	of	ADP
ejpam-2010	723	5	inverse	inverse	NOUN
ejpam-2010	723	6	semigroups	semigroup	NOUN
ejpam-2010	723	7	.	.	PUNCT
ejpam-2010	724	1	to	to	PART
ejpam-2010	724	2	appear	appear	VERB
ejpam-2010	724	3	in	in	ADP
ejpam-2010	724	4	houston	houston	PROPN
ejpam-2010	724	5	journal	journal	PROPN
ejpam-2010	724	6	of	of	ADP
ejpam-2010	724	7	mathematics	mathematic	NOUN
ejpam-2010	724	8	.	.	PUNCT
ejpam-2010	725	1	[	[	X
ejpam-2010	725	2	43	43	NUM
ejpam-2010	725	3	]	]	X
ejpam-2010	725	4	s	s	PART
ejpam-2010	725	5	talwar	talwar	PROPN
ejpam-2010	725	6	.	.	PUNCT
ejpam-2010	725	7	morita	morita	PROPN
ejpam-2010	725	8	equivalence	equivalence	NOUN
ejpam-2010	725	9	for	for	ADP
ejpam-2010	725	10	semigroups	semigroup	NOUN
ejpam-2010	725	11	.	.	PUNCT
ejpam-2010	726	1	journal	journal	NOUN
ejpam-2010	726	2	of	of	ADP
ejpam-2010	726	3	the	the	DET
ejpam-2010	726	4	australian	australian	ADJ
ejpam-2010	726	5	mathematical	mathematical	ADJ
ejpam-2010	726	6	society	society	NOUN
ejpam-2010	726	7	(	(	PUNCT
ejpam-2010	726	8	series	series	PROPN
ejpam-2010	726	9	a	a	PROPN
ejpam-2010	726	10	)	)	PUNCT
ejpam-2010	726	11	,	,	PUNCT
ejpam-2010	726	12	59	59	NUM
ejpam-2010	726	13	:	:	SYM
ejpam-2010	726	14	81	81	NUM
ejpam-2010	726	15	-	-	PUNCT
ejpam-2010	726	16	111	111	NUM
ejpam-2010	726	17	,	,	PUNCT
ejpam-2010	726	18	1995	1995	NUM
ejpam-2010	726	19	.	.	PUNCT
ejpam-2010	727	1	[	[	X
ejpam-2010	727	2	44	44	NUM
ejpam-2010	727	3	]	]	SYM
ejpam-2010	727	4	s	s	PART
ejpam-2010	728	1	talwar	talwar	PROPN
ejpam-2010	728	2	.	.	PUNCT
ejpam-2010	728	3	strong	strong	ADJ
ejpam-2010	728	4	morita	morita	PROPN
ejpam-2010	728	5	equivalence	equivalence	NOUN
ejpam-2010	728	6	and	and	CCONJ
ejpam-2010	728	7	a	a	DET
ejpam-2010	728	8	generalisation	generalisation	NOUN
ejpam-2010	728	9	of	of	ADP
ejpam-2010	728	10	the	the	DET
ejpam-2010	728	11	rees	rees	PROPN
ejpam-2010	728	12	theorem	theorem	VERB
ejpam-2010	728	13	.	.	PROPN
ejpam-2010	728	14	journal	journal	PROPN
ejpam-2010	728	15	of	of	ADP
ejpam-2010	728	16	algebra	algebra	PROPN
ejpam-2010	728	17	,	,	PUNCT
ejpam-2010	728	18	181	181	NUM
ejpam-2010	728	19	:	:	SYM
ejpam-2010	728	20	371	371	NUM
ejpam-2010	728	21	-	-	SYM
ejpam-2010	728	22	394	394	NUM
ejpam-2010	728	23	,	,	PUNCT
ejpam-2010	728	24	1996	1996	NUM
ejpam-2010	728	25	.	.	PUNCT
ejpam-2010	729	1	[	[	X
ejpam-2010	729	2	45	45	NUM
ejpam-2010	729	3	]	]	X
ejpam-2010	729	4	s	s	PART
ejpam-2010	729	5	talwar	talwar	PROPN
ejpam-2010	729	6	.	.	PUNCT
ejpam-2010	730	1	strong	strong	ADJ
ejpam-2010	730	2	morita	morita	PROPN
ejpam-2010	730	3	equivalence	equivalence	NOUN
ejpam-2010	730	4	and	and	CCONJ
ejpam-2010	730	5	the	the	DET
ejpam-2010	730	6	synthesis	synthesis	NOUN
ejpam-2010	730	7	theorem	theorem	NOUN
ejpam-2010	730	8	.	.	PUNCT
ejpam-2010	731	1	international	international	ADJ
ejpam-2010	731	2	journal	journal	NOUN
ejpam-2010	731	3	of	of	ADP
ejpam-2010	731	4	algebra	algebra	NOUN
ejpam-2010	731	5	and	and	CCONJ
ejpam-2010	731	6	computation	computation	NOUN
ejpam-2010	731	7	,	,	PUNCT
ejpam-2010	731	8	6	6	NUM
ejpam-2010	731	9	:	:	SYM
ejpam-2010	731	10	123	123	NUM
ejpam-2010	731	11	-	-	SYM
ejpam-2010	731	12	141	141	NUM
ejpam-2010	731	13	,	,	PUNCT
ejpam-2010	731	14	1996	1996	NUM
ejpam-2010	731	15	.	.	PUNCT
ejpam-2010	732	1	[	[	X
ejpam-2010	732	2	46	46	NUM
ejpam-2010	732	3	]	]	X
ejpam-2010	732	4	j	j	PROPN
ejpam-2010	732	5	l	l	PROPN
ejpam-2010	732	6	taylor	taylor	PROPN
ejpam-2010	732	7	.	.	PUNCT
ejpam-2010	733	1	a	a	DET
ejpam-2010	733	2	bigger	big	ADJ
ejpam-2010	733	3	brauer	brauer	PROPN
ejpam-2010	733	4	group	group	PROPN
ejpam-2010	733	5	.	.	PUNCT
ejpam-2010	734	1	pacific	pacific	PROPN
ejpam-2010	734	2	journal	journal	PROPN
ejpam-2010	734	3	of	of	ADP
ejpam-2010	734	4	mathematics	mathematic	NOUN
ejpam-2010	734	5	,	,	PUNCT
ejpam-2010	734	6	103	103	NUM
ejpam-2010	734	7	:	:	SYM
ejpam-2010	734	8	163	163	NUM
ejpam-2010	734	9	-	-	SYM
ejpam-2010	734	10	203	203	NUM
ejpam-2010	734	11	,	,	PUNCT
ejpam-2010	734	12	1982	1982	NUM
ejpam-2010	734	13	.	.	PUNCT
ejpam-2010	735	1	[	[	X
ejpam-2010	735	2	47	47	NUM
ejpam-2010	735	3	]	]	X
ejpam-2010	735	4	j	j	PROPN
ejpam-2010	735	5	trlifaj	trlifaj	NOUN
ejpam-2010	735	6	.	.	PUNCT
ejpam-2010	736	1	on	on	ADP
ejpam-2010	736	2	∗-modules	∗-module	NOUN
ejpam-2010	736	3	generating	generate	VERB
ejpam-2010	736	4	the	the	DET
ejpam-2010	736	5	injectives	injective	NOUN
ejpam-2010	736	6	.	.	PUNCT
ejpam-2010	737	1	rendiconti	rendiconti	PROPN
ejpam-2010	737	2	del	del	PROPN
ejpam-2010	737	3	seminario	seminario	PROPN
ejpam-2010	737	4	matematico	matematico	PROPN
ejpam-2010	737	5	della	della	PROPN
ejpam-2010	737	6	université	université	PROPN
ejpam-2010	737	7	di	di	PROPN
ejpam-2010	737	8	padova	padova	PROPN
ejpam-2010	737	9	,	,	PUNCT
ejpam-2010	737	10	88	88	NUM
ejpam-2010	737	11	:	:	PUNCT
ejpam-2010	737	12	211	211	NUM
ejpam-2010	737	13	-	-	SYM
ejpam-2010	737	14	220	220	NUM
ejpam-2010	737	15	,	,	PUNCT
ejpam-2010	737	16	1992	1992	NUM
ejpam-2010	737	17	.	.	PUNCT
ejpam-2010	738	1	[	[	X
ejpam-2010	738	2	48	48	NUM
ejpam-2010	738	3	]	]	X
ejpam-2010	738	4	y	y	PROPN
ejpam-2010	738	5	h	h	NOUN
ejpam-2010	738	6	xu	xu	PROPN
ejpam-2010	738	7	.	.	PUNCT
ejpam-2010	739	1	an	an	DET
ejpam-2010	739	2	equivalence	equivalence	NOUN
ejpam-2010	739	3	between	between	ADP
ejpam-2010	739	4	the	the	DET
ejpam-2010	739	5	ring	ring	NOUN
ejpam-2010	739	6	f	f	PROPN
ejpam-2010	739	7	and	and	CCONJ
ejpam-2010	739	8	infinite	infinite	ADJ
ejpam-2010	739	9	matrix	matrix	NOUN
ejpam-2010	739	10	subrings	subring	NOUN
ejpam-2010	739	11	over	over	ADP
ejpam-2010	739	12	f	f	PROPN
ejpam-2010	739	13	.	.	PUNCT
ejpam-2010	740	1	chinese	chinese	ADJ
ejpam-2010	740	2	annals	annal	NOUN
ejpam-2010	740	3	of	of	ADP
ejpam-2010	740	4	mathematics	mathematic	NOUN
ejpam-2010	740	5	,	,	PUNCT
ejpam-2010	740	6	series	series	NOUN
ejpam-2010	740	7	b	b	PROPN
ejpam-2010	740	8	,	,	PUNCT
ejpam-2010	740	9	1	1	NUM
ejpam-2010	740	10	:	:	PUNCT
ejpam-2010	740	11	66	66	NUM
ejpam-2010	740	12	-	-	SYM
ejpam-2010	740	13	69	69	NUM
ejpam-2010	740	14	,	,	PUNCT
ejpam-2010	740	15	1990	1990	NUM
ejpam-2010	740	16	.	.	PUNCT
ejpam-2010	741	1	[	[	X
ejpam-2010	741	2	49	49	NUM
ejpam-2010	741	3	]	]	X
ejpam-2010	741	4	y	y	PROPN
ejpam-2010	741	5	h	h	PROPN
ejpam-2010	742	1	xu	xu	PROPN
ejpam-2010	742	2	,	,	PUNCT
ejpam-2010	743	1	k	k	PROPN
ejpam-2010	743	2	p	p	X
ejpam-2010	743	3	shum	shum	NOUN
ejpam-2010	744	1	and	and	CCONJ
ejpam-2010	744	2	r	r	NOUN
ejpam-2010	744	3	f	f	PROPN
ejpam-2010	744	4	turner	turner	PROPN
ejpam-2010	744	5	-	-	PUNCT
ejpam-2010	744	6	smith	smith	PROPN
ejpam-2010	744	7	.	.	PUNCT
ejpam-2010	745	1	morita	morita	PROPN
ejpam-2010	745	2	-	-	PUNCT
ejpam-2010	745	3	like	like	ADJ
ejpam-2010	745	4	equivalence	equivalence	NOUN
ejpam-2010	745	5	of	of	ADP
ejpam-2010	745	6	infinite	infinite	ADJ
ejpam-2010	745	7	matrix	matrix	NOUN
ejpam-2010	745	8	subrings	subring	NOUN
ejpam-2010	745	9	.	.	PUNCT
ejpam-2010	746	1	journal	journal	PROPN
ejpam-2010	746	2	of	of	ADP
ejpam-2010	746	3	algebra	algebra	PROPN
ejpam-2010	746	4	,	,	PUNCT
ejpam-2010	746	5	159	159	NUM
ejpam-2010	746	6	:	:	SYM
ejpam-2010	746	7	425	425	NUM
ejpam-2010	746	8	-	-	SYM
ejpam-2010	746	9	435	435	NUM
ejpam-2010	746	10	,	,	PUNCT
ejpam-2010	746	11	1993	1993	NUM
ejpam-2010	746	12	.	.	PUNCT