id	sid	tid	token	lemma	pos
ejpam-1726	1	1	1_shum.dvi	1_shum.dvi	NUM
ejpam-1726	1	2	european	european	ADJ
ejpam-1726	1	3	journal	journal	NOUN
ejpam-1726	1	4	of	of	ADP
ejpam-1726	1	5	pure	pure	ADJ
ejpam-1726	1	6	and	and	CCONJ
ejpam-1726	1	7	applied	apply	VERB
ejpam-1726	1	8	mathematics	mathematic	NOUN
ejpam-1726	1	9	vol	vol	NOUN
ejpam-1726	1	10	.	.	PROPN
ejpam-1726	2	1	6	6	NUM
ejpam-1726	2	2	,	,	PUNCT
ejpam-1726	2	3	no	no	INTJ
ejpam-1726	2	4	.	.	NOUN
ejpam-1726	2	5	1	1	NUM
ejpam-1726	2	6	,	,	PUNCT
ejpam-1726	2	7	2013	2013	NUM
ejpam-1726	2	8	,	,	PUNCT
ejpam-1726	2	9	1	1	NUM
ejpam-1726	2	10	-	-	SYM
ejpam-1726	2	11	10	10	NUM
ejpam-1726	2	12	issn	issn	PROPN
ejpam-1726	2	13	1307	1307	NUM
ejpam-1726	2	14	-	-	SYM
ejpam-1726	2	15	5543	5543	NUM
ejpam-1726	2	16	–	–	PUNCT
ejpam-1726	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1726	2	18	γ	γ	X
ejpam-1726	2	19	-	-	PUNCT
ejpam-1726	2	20	semigroups	semigroup	NOUN
ejpam-1726	2	21	with	with	ADP
ejpam-1726	2	22	unities	unity	NOUN
ejpam-1726	2	23	and	and	CCONJ
ejpam-1726	2	24	morita	morita	NOUN
ejpam-1726	2	25	equivalence	equivalence	NOUN
ejpam-1726	2	26	for	for	ADP
ejpam-1726	2	27	monoids	monoid	NOUN
ejpam-1726	2	28	sujit	sujit	PROPN
ejpam-1726	2	29	kumar	kumar	PROPN
ejpam-1726	2	30	sardar1,∗	sardar1,∗	PROPN
ejpam-1726	2	31	,	,	PUNCT
ejpam-1726	2	32	sugato	sugato	VERB
ejpam-1726	2	33	gupta1	gupta1	PROPN
ejpam-1726	2	34	,	,	PUNCT
ejpam-1726	2	35	kar	kar	PROPN
ejpam-1726	2	36	ping	ping	PROPN
ejpam-1726	2	37	shum2	shum2	PROPN
ejpam-1726	2	38	1	1	NUM
ejpam-1726	2	39	department	department	NOUN
ejpam-1726	2	40	of	of	ADP
ejpam-1726	2	41	mathematics	mathematic	NOUN
ejpam-1726	2	42	,	,	PUNCT
ejpam-1726	2	43	jadavpur	jadavpur	PROPN
ejpam-1726	2	44	university	university	PROPN
ejpam-1726	2	45	,	,	PUNCT
ejpam-1726	2	46	india	india	PROPN
ejpam-1726	2	47	2	2	NUM
ejpam-1726	2	48	institute	institute	NOUN
ejpam-1726	2	49	of	of	ADP
ejpam-1726	2	50	mathematics	mathematics	PROPN
ejpam-1726	2	51	,	,	PUNCT
ejpam-1726	2	52	yunnan	yunnan	PROPN
ejpam-1726	2	53	university	university	PROPN
ejpam-1726	2	54	,	,	PUNCT
ejpam-1726	2	55	china	china	PROPN
ejpam-1726	2	56	abstract	abstract	NOUN
ejpam-1726	2	57	.	.	PUNCT
ejpam-1726	3	1	in	in	ADP
ejpam-1726	3	2	this	this	DET
ejpam-1726	3	3	paper	paper	NOUN
ejpam-1726	3	4	we	we	PRON
ejpam-1726	3	5	show	show	VERB
ejpam-1726	3	6	that	that	SCONJ
ejpam-1726	3	7	the	the	DET
ejpam-1726	3	8	left	left	ADJ
ejpam-1726	3	9	operator	operator	NOUN
ejpam-1726	3	10	and	and	CCONJ
ejpam-1726	3	11	right	right	ADJ
ejpam-1726	3	12	operator	operator	NOUN
ejpam-1726	3	13	semigroups	semigroup	NOUN
ejpam-1726	3	14	of	of	ADP
ejpam-1726	3	15	a	a	DET
ejpam-1726	3	16	γ	γ	NOUN
ejpam-1726	3	17	-	-	PUNCT
ejpam-1726	3	18	semigroup	semigroup	NOUN
ejpam-1726	3	19	with	with	ADP
ejpam-1726	3	20	unities	unity	NOUN
ejpam-1726	3	21	are	be	AUX
ejpam-1726	3	22	morita	morita	PROPN
ejpam-1726	3	23	equivalent	equivalent	PROPN
ejpam-1726	3	24	monoids	monoids	PROPN
ejpam-1726	3	25	.	.	PUNCT
ejpam-1726	4	1	it	it	PRON
ejpam-1726	4	2	is	be	AUX
ejpam-1726	4	3	also	also	ADV
ejpam-1726	4	4	deduced	deduce	VERB
ejpam-1726	4	5	that	that	SCONJ
ejpam-1726	4	6	if	if	SCONJ
ejpam-1726	4	7	l	l	NOUN
ejpam-1726	4	8	and	and	CCONJ
ejpam-1726	4	9	r	r	NOUN
ejpam-1726	4	10	are	be	AUX
ejpam-1726	4	11	two	two	NUM
ejpam-1726	4	12	morita	morita	PROPN
ejpam-1726	4	13	equivalent	equivalent	PROPN
ejpam-1726	4	14	monoids	monoid	NOUN
ejpam-1726	4	15	then	then	ADV
ejpam-1726	4	16	a	a	DET
ejpam-1726	4	17	γ	γ	NOUN
ejpam-1726	4	18	-	-	PUNCT
ejpam-1726	4	19	semigroup	semigroup	NOUN
ejpam-1726	4	20	with	with	ADP
ejpam-1726	4	21	unities	unity	NOUN
ejpam-1726	4	22	can	can	AUX
ejpam-1726	4	23	be	be	AUX
ejpam-1726	4	24	constructed	construct	VERB
ejpam-1726	4	25	such	such	ADJ
ejpam-1726	4	26	that	that	SCONJ
ejpam-1726	4	27	its	its	PRON
ejpam-1726	4	28	left	left	ADJ
ejpam-1726	4	29	and	and	CCONJ
ejpam-1726	4	30	right	right	ADJ
ejpam-1726	4	31	operator	operator	NOUN
ejpam-1726	4	32	monoids	monoid	NOUN
ejpam-1726	4	33	are	be	AUX
ejpam-1726	4	34	isomorphic	isomorphic	ADJ
ejpam-1726	4	35	to	to	ADP
ejpam-1726	4	36	l	l	NOUN
ejpam-1726	4	37	and	and	CCONJ
ejpam-1726	4	38	r	r	NOUN
ejpam-1726	4	39	respectively	respectively	ADV
ejpam-1726	4	40	.	.	PUNCT
ejpam-1726	5	1	this	this	DET
ejpam-1726	5	2	result	result	NOUN
ejpam-1726	5	3	is	be	AUX
ejpam-1726	5	4	used	use	VERB
ejpam-1726	5	5	to	to	PART
ejpam-1726	5	6	obtain	obtain	VERB
ejpam-1726	5	7	some	some	DET
ejpam-1726	5	8	properties	property	NOUN
ejpam-1726	5	9	of	of	ADP
ejpam-1726	5	10	monoids	monoid	NOUN
ejpam-1726	5	11	which	which	PRON
ejpam-1726	5	12	remain	remain	VERB
ejpam-1726	5	13	invariant	invariant	ADJ
ejpam-1726	5	14	under	under	ADP
ejpam-1726	5	15	morita	morita	PROPN
ejpam-1726	5	16	equivalence	equivalence	NOUN
ejpam-1726	5	17	.	.	PUNCT
ejpam-1726	6	1	2010	2010	NUM
ejpam-1726	6	2	mathematics	mathematic	NOUN
ejpam-1726	6	3	subject	subject	NOUN
ejpam-1726	6	4	classifications	classification	NOUN
ejpam-1726	6	5	:	:	PUNCT
ejpam-1726	6	6	20m11	20m11	NUM
ejpam-1726	6	7	,	,	PUNCT
ejpam-1726	6	8	20m12	20m12	NUM
ejpam-1726	6	9	,	,	PUNCT
ejpam-1726	6	10	20m30	20m30	NUM
ejpam-1726	6	11	,	,	PUNCT
ejpam-1726	6	12	20m50	20m50	NUM
ejpam-1726	6	13	.	.	PUNCT
ejpam-1726	7	1	key	key	ADJ
ejpam-1726	7	2	words	word	NOUN
ejpam-1726	7	3	and	and	CCONJ
ejpam-1726	7	4	phrases	phrase	NOUN
ejpam-1726	7	5	:	:	PUNCT
ejpam-1726	7	6	γ	γ	NOUN
ejpam-1726	7	7	-	-	PUNCT
ejpam-1726	7	8	semigroup	semigroup	PROPN
ejpam-1726	7	9	,	,	PUNCT
ejpam-1726	7	10	morita	morita	PROPN
ejpam-1726	7	11	equivalence	equivalence	NOUN
ejpam-1726	7	12	for	for	ADP
ejpam-1726	7	13	monoids	monoid	NOUN
ejpam-1726	7	14	,	,	PUNCT
ejpam-1726	7	15	morita	morita	PROPN
ejpam-1726	7	16	invariant	invariant	PROPN
ejpam-1726	7	17	.	.	PUNCT
ejpam-1726	8	1	1	1	NUM
ejpam-1726	8	2	.	.	X
ejpam-1726	8	3	introduction	introduction	NOUN
ejpam-1726	8	4	if	if	SCONJ
ejpam-1726	8	5	someone	someone	PRON
ejpam-1726	8	6	asks	ask	VERB
ejpam-1726	8	7	"	"	PUNCT
ejpam-1726	8	8	what	what	PRON
ejpam-1726	8	9	is	be	AUX
ejpam-1726	8	10	the	the	DET
ejpam-1726	8	11	most	most	ADV
ejpam-1726	8	12	natural	natural	ADJ
ejpam-1726	8	13	example	example	NOUN
ejpam-1726	8	14	of	of	ADP
ejpam-1726	8	15	ring	ring	NOUN
ejpam-1726	8	16	?	?	PUNCT
ejpam-1726	8	17	"	"	PUNCT
ejpam-1726	8	18	,	,	PUNCT
ejpam-1726	8	19	the	the	DET
ejpam-1726	8	20	ring	ring	NOUN
ejpam-1726	8	21	of	of	ADP
ejpam-1726	8	22	integers	integer	NOUN
ejpam-1726	8	23	is	be	AUX
ejpam-1726	8	24	one	one	NUM
ejpam-1726	8	25	possible	possible	ADJ
ejpam-1726	8	26	answer	answer	NOUN
ejpam-1726	8	27	to	to	ADP
ejpam-1726	8	28	this	this	DET
ejpam-1726	8	29	question	question	NOUN
ejpam-1726	8	30	.	.	PUNCT
ejpam-1726	9	1	but	but	CCONJ
ejpam-1726	9	2	a	a	DET
ejpam-1726	9	3	more	more	ADV
ejpam-1726	9	4	interesting	interesting	ADJ
ejpam-1726	9	5	answer	answer	NOUN
ejpam-1726	9	6	will	will	AUX
ejpam-1726	9	7	be	be	AUX
ejpam-1726	9	8	the	the	DET
ejpam-1726	9	9	endomorphism	endomorphism	NOUN
ejpam-1726	9	10	ring	ring	NOUN
ejpam-1726	9	11	of	of	ADP
ejpam-1726	9	12	an	an	DET
ejpam-1726	9	13	abelian	abelian	ADJ
ejpam-1726	9	14	group	group	NOUN
ejpam-1726	9	15	,	,	PUNCT
ejpam-1726	9	16	i.e.	i.e.	X
ejpam-1726	9	17	,	,	PUNCT
ejpam-1726	9	18	endm	endm	NOUN
ejpam-1726	9	19	or	or	CCONJ
ejpam-1726	9	20	hom(m	hom(m	NOUN
ejpam-1726	9	21	,	,	PUNCT
ejpam-1726	9	22	m	m	PROPN
ejpam-1726	9	23	)	)	PUNCT
ejpam-1726	9	24	where	where	SCONJ
ejpam-1726	9	25	m	m	NOUN
ejpam-1726	9	26	is	be	AUX
ejpam-1726	9	27	an	an	DET
ejpam-1726	9	28	abelian	abelian	ADJ
ejpam-1726	9	29	group	group	NOUN
ejpam-1726	9	30	.	.	PUNCT
ejpam-1726	10	1	now	now	ADV
ejpam-1726	10	2	if	if	SCONJ
ejpam-1726	10	3	two	two	NUM
ejpam-1726	10	4	abelian	abelian	ADJ
ejpam-1726	10	5	groups	group	NOUN
ejpam-1726	10	6	,	,	PUNCT
ejpam-1726	10	7	say	say	VERB
ejpam-1726	10	8	a	a	DET
ejpam-1726	10	9	and	and	CCONJ
ejpam-1726	10	10	b	b	NOUN
ejpam-1726	10	11	instead	instead	ADV
ejpam-1726	10	12	of	of	ADP
ejpam-1726	10	13	one	one	NUM
ejpam-1726	10	14	are	be	AUX
ejpam-1726	10	15	taken	take	VERB
ejpam-1726	10	16	,	,	PUNCT
ejpam-1726	10	17	then	then	ADV
ejpam-1726	10	18	hom(a	hom(a	PROPN
ejpam-1726	10	19	,	,	PUNCT
ejpam-1726	10	20	b	b	NOUN
ejpam-1726	10	21	)	)	PUNCT
ejpam-1726	10	22	is	be	AUX
ejpam-1726	10	23	no	no	ADV
ejpam-1726	10	24	longer	long	ADV
ejpam-1726	10	25	a	a	DET
ejpam-1726	10	26	ring	ring	NOUN
ejpam-1726	10	27	in	in	ADP
ejpam-1726	10	28	the	the	DET
ejpam-1726	10	29	way	way	NOUN
ejpam-1726	10	30	as	as	SCONJ
ejpam-1726	10	31	endm	endm	NOUN
ejpam-1726	10	32	becomes	become	VERB
ejpam-1726	10	33	a	a	DET
ejpam-1726	10	34	ring	ring	NOUN
ejpam-1726	10	35	because	because	SCONJ
ejpam-1726	10	36	the	the	DET
ejpam-1726	10	37	composition	composition	NOUN
ejpam-1726	10	38	is	be	AUX
ejpam-1726	10	39	no	no	ADV
ejpam-1726	10	40	longer	long	ADV
ejpam-1726	10	41	defined	define	VERB
ejpam-1726	10	42	.	.	PUNCT
ejpam-1726	11	1	however	however	ADV
ejpam-1726	11	2	,	,	PUNCT
ejpam-1726	11	3	if	if	SCONJ
ejpam-1726	11	4	one	one	PRON
ejpam-1726	11	5	takes	take	VERB
ejpam-1726	11	6	an	an	DET
ejpam-1726	11	7	element	element	NOUN
ejpam-1726	11	8	of	of	ADP
ejpam-1726	11	9	hom(b	hom(b	ADJ
ejpam-1726	11	10	,	,	PUNCT
ejpam-1726	11	11	a	a	PRON
ejpam-1726	11	12	)	)	PUNCT
ejpam-1726	11	13	and	and	CCONJ
ejpam-1726	11	14	put	put	VERB
ejpam-1726	11	15	it	it	PRON
ejpam-1726	11	16	in	in	ADP
ejpam-1726	11	17	between	between	ADP
ejpam-1726	11	18	two	two	NUM
ejpam-1726	11	19	elements	element	NOUN
ejpam-1726	11	20	of	of	ADP
ejpam-1726	11	21	hom(a	hom(a	PROPN
ejpam-1726	11	22	,	,	PUNCT
ejpam-1726	11	23	b	b	NOUN
ejpam-1726	11	24	)	)	PUNCT
ejpam-1726	11	25	then	then	ADV
ejpam-1726	11	26	the	the	DET
ejpam-1726	11	27	composition	composition	NOUN
ejpam-1726	11	28	can	can	AUX
ejpam-1726	11	29	be	be	AUX
ejpam-1726	11	30	defined	define	VERB
ejpam-1726	11	31	.	.	PUNCT
ejpam-1726	12	1	taking	take	VERB
ejpam-1726	12	2	this	this	PRON
ejpam-1726	12	3	as	as	ADP
ejpam-1726	12	4	a	a	DET
ejpam-1726	12	5	motivating	motivating	NOUN
ejpam-1726	12	6	factor	factor	NOUN
ejpam-1726	12	7	n.	n.	PROPN
ejpam-1726	12	8	nobusawa	nobusawa	PROPN
ejpam-1726	13	1	[	[	X
ejpam-1726	13	2	15	15	NUM
ejpam-1726	13	3	]	]	X
ejpam-1726	13	4	generalized	generalize	VERB
ejpam-1726	13	5	the	the	DET
ejpam-1726	13	6	ring	ring	NOUN
ejpam-1726	13	7	theory	theory	NOUN
ejpam-1726	13	8	in	in	ADP
ejpam-1726	13	9	the	the	DET
ejpam-1726	13	10	form	form	NOUN
ejpam-1726	13	11	of	of	ADP
ejpam-1726	13	12	γ	γ	NOUN
ejpam-1726	13	13	-	-	NOUN
ejpam-1726	13	14	ring	ring	NOUN
ejpam-1726	13	15	in	in	ADP
ejpam-1726	13	16	1964	1964	NUM
ejpam-1726	13	17	.	.	PUNCT
ejpam-1726	14	1	later	later	ADV
ejpam-1726	14	2	m.k.sen	m.k.sen	VERB
ejpam-1726	14	3	[	[	X
ejpam-1726	14	4	18	18	NUM
ejpam-1726	14	5	]	]	PUNCT
ejpam-1726	14	6	introduced	introduce	VERB
ejpam-1726	14	7	the	the	DET
ejpam-1726	14	8	notion	notion	NOUN
ejpam-1726	14	9	of	of	ADP
ejpam-1726	14	10	γ	γ	NOUN
ejpam-1726	14	11	-	-	PUNCT
ejpam-1726	14	12	semigroup	semigroup	NOUN
ejpam-1726	14	13	by	by	ADP
ejpam-1726	14	14	taking	take	VERB
ejpam-1726	14	15	sets	set	NOUN
ejpam-1726	14	16	instead	instead	ADV
ejpam-1726	14	17	of	of	ADP
ejpam-1726	14	18	abelian	abelian	ADJ
ejpam-1726	14	19	groups	group	NOUN
ejpam-1726	14	20	.	.	PUNCT
ejpam-1726	15	1	it	it	PRON
ejpam-1726	15	2	is	be	AUX
ejpam-1726	15	3	well	well	ADV
ejpam-1726	15	4	known	know	VERB
ejpam-1726	15	5	that	that	SCONJ
ejpam-1726	15	6	with	with	ADP
ejpam-1726	15	7	every	every	DET
ejpam-1726	15	8	γ	γ	NOUN
ejpam-1726	15	9	-	-	NOUN
ejpam-1726	15	10	structure	structure	NOUN
ejpam-1726	15	11	,	,	PUNCT
ejpam-1726	15	12	there	there	PRON
ejpam-1726	15	13	always	always	ADV
ejpam-1726	15	14	exist	exist	VERB
ejpam-1726	15	15	two	two	NUM
ejpam-1726	15	16	corresponding	correspond	VERB
ejpam-1726	15	17	operator	operator	NOUN
ejpam-1726	15	18	structures	structure	NOUN
ejpam-1726	15	19	,	,	PUNCT
ejpam-1726	15	20	i.e.	i.e.	X
ejpam-1726	15	21	,	,	PUNCT
ejpam-1726	15	22	for	for	ADP
ejpam-1726	15	23	a	a	DET
ejpam-1726	15	24	γ	γ	NOUN
ejpam-1726	15	25	-	-	NOUN
ejpam-1726	15	26	ring	ring	NOUN
ejpam-1726	15	27	,	,	PUNCT
ejpam-1726	15	28	there	there	PRON
ejpam-1726	15	29	exist	exist	VERB
ejpam-1726	15	30	two	two	NUM
ejpam-1726	15	31	associated	associated	ADJ
ejpam-1726	15	32	operator	operator	NOUN
ejpam-1726	15	33	rings	ring	NOUN
ejpam-1726	15	34	,	,	PUNCT
ejpam-1726	15	35	for	for	ADP
ejpam-1726	15	36	a	a	DET
ejpam-1726	15	37	γ	γ	NOUN
ejpam-1726	15	38	-	-	PUNCT
ejpam-1726	15	39	semigroup	semigroup	NOUN
ejpam-1726	15	40	,	,	PUNCT
ejpam-1726	15	41	there	there	PRON
ejpam-1726	15	42	are	be	VERB
ejpam-1726	15	43	operator	operator	NOUN
ejpam-1726	15	44	semigroups	semigroup	NOUN
ejpam-1726	15	45	.	.	PUNCT
ejpam-1726	16	1	it	it	PRON
ejpam-1726	16	2	is	be	AUX
ejpam-1726	16	3	natural	natural	ADJ
ejpam-1726	16	4	to	to	PART
ejpam-1726	16	5	ask	ask	VERB
ejpam-1726	16	6	the	the	DET
ejpam-1726	16	7	reverse	reverse	ADJ
ejpam-1726	16	8	question	question	NOUN
ejpam-1726	16	9	i.e.	i.e.	ADV
ejpam-1726	16	10	,	,	PUNCT
ejpam-1726	16	11	what	what	DET
ejpam-1726	16	12	relation	relation	NOUN
ejpam-1726	16	13	is	be	AUX
ejpam-1726	16	14	to	to	PART
ejpam-1726	16	15	be	be	AUX
ejpam-1726	16	16	satisfied	satisfy	VERB
ejpam-1726	16	17	by	by	ADP
ejpam-1726	16	18	two	two	NUM
ejpam-1726	16	19	given	give	VERB
ejpam-1726	16	20	rings	ring	NOUN
ejpam-1726	16	21	or	or	CCONJ
ejpam-1726	16	22	semigroups	semigroup	NOUN
ejpam-1726	16	23	m	m	VERB
ejpam-1726	16	24	and	and	CCONJ
ejpam-1726	16	25	n	n	CCONJ
ejpam-1726	16	26	such	such	ADJ
ejpam-1726	16	27	that	that	SCONJ
ejpam-1726	16	28	one	one	PRON
ejpam-1726	16	29	can	can	AUX
ejpam-1726	16	30	find	find	VERB
ejpam-1726	16	31	a	a	DET
ejpam-1726	16	32	corresponding	correspond	VERB
ejpam-1726	16	33	γ	γ	X
ejpam-1726	16	34	-	-	PUNCT
ejpam-1726	16	35	structure(i.e	structure(i.e	NOUN
ejpam-1726	16	36	.	.	PUNCT
ejpam-1726	17	1	γ	γ	PROPN
ejpam-1726	17	2	-	-	PUNCT
ejpam-1726	17	3	ring	ring	NOUN
ejpam-1726	17	4	or	or	CCONJ
ejpam-1726	17	5	γ	γ	NOUN
ejpam-1726	17	6	-	-	PUNCT
ejpam-1726	17	7	semigroup	semigroup	NOUN
ejpam-1726	17	8	respectively	respectively	ADV
ejpam-1726	17	9	)	)	PUNCT
ejpam-1726	17	10	whose	whose	DET
ejpam-1726	17	11	∗corresponding	∗corresponde	VERB
ejpam-1726	17	12	author	author	NOUN
ejpam-1726	17	13	.	.	PUNCT
ejpam-1726	18	1	email	email	NOUN
ejpam-1726	18	2	addresses	address	NOUN
ejpam-1726	18	3	:	:	PUNCT
ejpam-1726	18	4	sksardarjumath	sksardarjumath	NOUN
ejpam-1726	18	5	�	�	NOUN
ejpam-1726	18	6	gmail	gmail	NOUN
ejpam-1726	18	7	.	.	PUNCT
ejpam-1726	19	1	om	om	PROPN
ejpam-1726	19	2	(	(	PUNCT
ejpam-1726	19	3	s.	s.	PROPN
ejpam-1726	19	4	sardar	sardar	PROPN
ejpam-1726	19	5	)	)	PUNCT
ejpam-1726	19	6	,	,	PUNCT
ejpam-1726	19	7	sguptaju	sguptaju	NOUN
ejpam-1726	19	8	�	�	NOUN
ejpam-1726	19	9	gmail	gmail	NOUN
ejpam-1726	19	10	.	.	PUNCT
ejpam-1726	20	1	om	om	PROPN
ejpam-1726	20	2	(	(	PUNCT
ejpam-1726	20	3	s.	s.	PROPN
ejpam-1726	20	4	gupta	gupta	PROPN
ejpam-1726	20	5	)	)	PUNCT
ejpam-1726	20	6	,	,	PUNCT
ejpam-1726	20	7	kpshum�ynu.edu	kpshum�ynu.edu	PROPN
ejpam-1726	20	8	.	.	PROPN
ejpam-1726	21	1	n	n	PROPN
ejpam-1726	21	2	(	(	PUNCT
ejpam-1726	21	3	k.	k.	NOUN
ejpam-1726	21	4	shum	shum	PROPN
ejpam-1726	21	5	)	)	PUNCT
ejpam-1726	21	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1726	22	1	1	1	NUM
ejpam-1726	22	2	c	c	X
ejpam-1726	22	3	©	©	PROPN
ejpam-1726	22	4	2013	2013	NUM
ejpam-1726	22	5	ejpam	ejpam	NOUN
ejpam-1726	22	6	all	all	DET
ejpam-1726	22	7	rights	right	NOUN
ejpam-1726	22	8	reserved	reserve	VERB
ejpam-1726	22	9	.	.	PUNCT
ejpam-1726	23	1	s.	s.	PROPN
ejpam-1726	23	2	sardar	sardar	PROPN
ejpam-1726	23	3	,	,	PUNCT
ejpam-1726	23	4	s.	s.	PROPN
ejpam-1726	23	5	gupta	gupta	PROPN
ejpam-1726	23	6	,	,	PUNCT
ejpam-1726	23	7	k.	k.	PROPN
ejpam-1726	23	8	shum	shum	PROPN
ejpam-1726	23	9	/	/	SYM
ejpam-1726	23	10	eur	eur	PROPN
ejpam-1726	23	11	.	.	PUNCT
ejpam-1726	24	1	j.	j.	PROPN
ejpam-1726	24	2	pure	pure	PROPN
ejpam-1726	24	3	appl	appl	PROPN
ejpam-1726	24	4	.	.	PROPN
ejpam-1726	24	5	math	math	PROPN
ejpam-1726	24	6	,	,	PUNCT
ejpam-1726	24	7	6	6	NUM
ejpam-1726	24	8	(	(	PUNCT
ejpam-1726	24	9	2013	2013	NUM
ejpam-1726	24	10	)	)	PUNCT
ejpam-1726	24	11	,	,	PUNCT
ejpam-1726	24	12	1	1	NUM
ejpam-1726	24	13	-	-	SYM
ejpam-1726	24	14	10	10	NUM
ejpam-1726	24	15	2	2	NUM
ejpam-1726	24	16	associated	associate	VERB
ejpam-1726	24	17	operator	operator	NOUN
ejpam-1726	24	18	structures	structure	NOUN
ejpam-1726	24	19	are	be	AUX
ejpam-1726	24	20	isomorphic	isomorphic	ADJ
ejpam-1726	24	21	to	to	ADP
ejpam-1726	24	22	m	m	PROPN
ejpam-1726	24	23	and	and	CCONJ
ejpam-1726	24	24	n	n	PRON
ejpam-1726	24	25	respectively	respectively	ADV
ejpam-1726	24	26	?	?	PUNCT
ejpam-1726	25	1	this	this	DET
ejpam-1726	25	2	problem	problem	NOUN
ejpam-1726	25	3	for	for	ADP
ejpam-1726	25	4	γ	γ	NOUN
ejpam-1726	25	5	-	-	PUNCT
ejpam-1726	25	6	ring	ring	NOUN
ejpam-1726	25	7	was	be	AUX
ejpam-1726	25	8	solved	solve	VERB
ejpam-1726	25	9	by	by	ADP
ejpam-1726	25	10	m.	m.	NOUN
ejpam-1726	25	11	parvati	parvati	PROPN
ejpam-1726	26	1	[	[	X
ejpam-1726	26	2	17	17	NUM
ejpam-1726	26	3	]	]	PUNCT
ejpam-1726	26	4	in	in	ADP
ejpam-1726	26	5	1984	1984	NUM
ejpam-1726	26	6	.	.	PUNCT
ejpam-1726	27	1	in	in	ADP
ejpam-1726	27	2	the	the	DET
ejpam-1726	27	3	same	same	ADJ
ejpam-1726	27	4	year	year	NOUN
ejpam-1726	27	5	,	,	PUNCT
ejpam-1726	27	6	n.	n.	PROPN
ejpam-1726	27	7	nobusawa	nobusawa	PROPN
ejpam-1726	28	1	[	[	X
ejpam-1726	28	2	16	16	NUM
ejpam-1726	28	3	]	]	PUNCT
ejpam-1726	28	4	stated	state	VERB
ejpam-1726	28	5	without	without	ADP
ejpam-1726	28	6	proof	proof	NOUN
ejpam-1726	28	7	that	that	SCONJ
ejpam-1726	28	8	the	the	DET
ejpam-1726	28	9	problem	problem	NOUN
ejpam-1726	28	10	would	would	AUX
ejpam-1726	28	11	have	have	AUX
ejpam-1726	28	12	some	some	DET
ejpam-1726	28	13	solution	solution	NOUN
ejpam-1726	28	14	.	.	PUNCT
ejpam-1726	29	1	while	while	SCONJ
ejpam-1726	29	2	answering	answer	VERB
ejpam-1726	29	3	the	the	DET
ejpam-1726	29	4	question	question	NOUN
ejpam-1726	29	5	for	for	ADP
ejpam-1726	29	6	γ	γ	NOUN
ejpam-1726	29	7	-	-	PUNCT
ejpam-1726	29	8	rings	ring	NOUN
ejpam-1726	29	9	,	,	PUNCT
ejpam-1726	29	10	m.	m.	NOUN
ejpam-1726	29	11	parvati	parvati	PROPN
ejpam-1726	29	12	adopted	adopt	VERB
ejpam-1726	29	13	the	the	DET
ejpam-1726	29	14	morita	morita	NOUN
ejpam-1726	29	15	equivalence	equivalence	NOUN
ejpam-1726	29	16	of	of	ADP
ejpam-1726	29	17	rings	ring	NOUN
ejpam-1726	29	18	[	[	X
ejpam-1726	29	19	6	6	NUM
ejpam-1726	29	20	]	]	PUNCT
ejpam-1726	29	21	,	,	PUNCT
ejpam-1726	29	22	in	in	ADP
ejpam-1726	29	23	the	the	DET
ejpam-1726	29	24	language	language	NOUN
ejpam-1726	29	25	of	of	ADP
ejpam-1726	29	26	category	category	NOUN
ejpam-1726	29	27	[	[	X
ejpam-1726	29	28	14	14	NUM
ejpam-1726	29	29	]	]	X
ejpam-1726	29	30	,	,	PUNCT
ejpam-1726	29	31	as	as	ADP
ejpam-1726	29	32	an	an	DET
ejpam-1726	29	33	important	important	ADJ
ejpam-1726	29	34	tool	tool	NOUN
ejpam-1726	29	35	.	.	PUNCT
ejpam-1726	30	1	this	this	DET
ejpam-1726	30	2	fact	fact	NOUN
ejpam-1726	30	3	together	together	ADV
ejpam-1726	30	4	with	with	ADP
ejpam-1726	30	5	the	the	DET
ejpam-1726	30	6	vast	vast	ADJ
ejpam-1726	30	7	literature	literature	NOUN
ejpam-1726	30	8	on	on	ADP
ejpam-1726	30	9	morita	morita	PROPN
ejpam-1726	30	10	equivalence	equivalence	NOUN
ejpam-1726	30	11	of	of	ADP
ejpam-1726	30	12	semigroups	semigroup	NOUN
ejpam-1726	30	13	and	and	CCONJ
ejpam-1726	30	14	monoids	monoid	VERB
ejpam-1726	31	1	[	[	X
ejpam-1726	31	2	7	7	NUM
ejpam-1726	31	3	,	,	PUNCT
ejpam-1726	31	4	8	8	NUM
ejpam-1726	31	5	,	,	PUNCT
ejpam-1726	31	6	12	12	NUM
ejpam-1726	31	7	,	,	PUNCT
ejpam-1726	31	8	13	13	NUM
ejpam-1726	31	9	,	,	PUNCT
ejpam-1726	31	10	19	19	NUM
ejpam-1726	31	11	,	,	PUNCT
ejpam-1726	31	12	20	20	NUM
ejpam-1726	31	13	]	]	PUNCT
ejpam-1726	31	14	has	have	AUX
ejpam-1726	31	15	motivated	motivate	VERB
ejpam-1726	31	16	us	we	PRON
ejpam-1726	31	17	to	to	PART
ejpam-1726	31	18	write	write	VERB
ejpam-1726	31	19	this	this	DET
ejpam-1726	31	20	paper	paper	NOUN
ejpam-1726	31	21	.	.	PUNCT
ejpam-1726	32	1	in	in	ADP
ejpam-1726	32	2	this	this	DET
ejpam-1726	32	3	paper	paper	NOUN
ejpam-1726	32	4	,	,	PUNCT
ejpam-1726	32	5	among	among	ADP
ejpam-1726	32	6	other	other	ADJ
ejpam-1726	32	7	results	result	NOUN
ejpam-1726	32	8	we	we	PRON
ejpam-1726	32	9	deduce	deduce	VERB
ejpam-1726	32	10	that	that	SCONJ
ejpam-1726	32	11	two	two	NUM
ejpam-1726	32	12	monoids	monoid	NOUN
ejpam-1726	32	13	l	l	NOUN
ejpam-1726	32	14	and	and	CCONJ
ejpam-1726	32	15	r	r	NOUN
ejpam-1726	32	16	are	be	AUX
ejpam-1726	32	17	morita	morita	NOUN
ejpam-1726	32	18	equivalent	equivalent	ADJ
ejpam-1726	33	1	if	if	SCONJ
ejpam-1726	33	2	and	and	CCONJ
ejpam-1726	33	3	only	only	ADV
ejpam-1726	33	4	if	if	SCONJ
ejpam-1726	33	5	there	there	PRON
ejpam-1726	33	6	exists	exist	VERB
ejpam-1726	33	7	a	a	DET
ejpam-1726	33	8	γ	γ	NOUN
ejpam-1726	33	9	-	-	PUNCT
ejpam-1726	33	10	semigroup	semigroup	NOUN
ejpam-1726	33	11	with	with	ADP
ejpam-1726	33	12	unities	unity	NOUN
ejpam-1726	33	13	whose	whose	DET
ejpam-1726	33	14	operator	operator	NOUN
ejpam-1726	33	15	monoids	monoid	NOUN
ejpam-1726	33	16	are	be	AUX
ejpam-1726	33	17	isomorphic	isomorphic	ADJ
ejpam-1726	33	18	to	to	ADP
ejpam-1726	33	19	l	l	PROPN
ejpam-1726	33	20	and	and	CCONJ
ejpam-1726	33	21	r.	r.	NOUN
ejpam-1726	33	22	this	this	DET
ejpam-1726	33	23	result	result	NOUN
ejpam-1726	33	24	appears	appear	VERB
ejpam-1726	33	25	to	to	PART
ejpam-1726	33	26	be	be	AUX
ejpam-1726	33	27	very	very	ADV
ejpam-1726	33	28	useful	useful	ADJ
ejpam-1726	33	29	to	to	PART
ejpam-1726	33	30	study	study	VERB
ejpam-1726	33	31	the	the	DET
ejpam-1726	33	32	γ	γ	NOUN
ejpam-1726	33	33	-	-	PUNCT
ejpam-1726	33	34	semigroups	semigroup	NOUN
ejpam-1726	33	35	via	via	ADP
ejpam-1726	33	36	morita	morita	PROPN
ejpam-1726	33	37	theory	theory	PROPN
ejpam-1726	33	38	for	for	ADP
ejpam-1726	33	39	monoids	monoid	NOUN
ejpam-1726	33	40	by	by	ADP
ejpam-1726	33	41	using	use	VERB
ejpam-1726	33	42	operator	operator	NOUN
ejpam-1726	33	43	semigroups	semigroup	NOUN
ejpam-1726	33	44	and	and	CCONJ
ejpam-1726	33	45	conversely	conversely	ADV
ejpam-1726	33	46	the	the	DET
ejpam-1726	33	47	morita	morita	PROPN
ejpam-1726	33	48	theory	theory	NOUN
ejpam-1726	33	49	for	for	ADP
ejpam-1726	33	50	monoids	monoid	NOUN
ejpam-1726	33	51	via	via	ADP
ejpam-1726	33	52	γsemigroups	γsemigroup	NOUN
ejpam-1726	33	53	.	.	PUNCT
ejpam-1726	34	1	we	we	PRON
ejpam-1726	34	2	will	will	AUX
ejpam-1726	34	3	apply	apply	VERB
ejpam-1726	34	4	this	this	DET
ejpam-1726	34	5	result	result	NOUN
ejpam-1726	34	6	to	to	PART
ejpam-1726	34	7	obtain	obtain	VERB
ejpam-1726	34	8	some	some	DET
ejpam-1726	34	9	results	result	NOUN
ejpam-1726	34	10	concerning	concern	VERB
ejpam-1726	34	11	the	the	DET
ejpam-1726	34	12	morita	morita	PROPN
ejpam-1726	34	13	invariants	invariant	NOUN
ejpam-1726	34	14	of	of	ADP
ejpam-1726	34	15	monoids	monoid	NOUN
ejpam-1726	34	16	.	.	PUNCT
ejpam-1726	35	1	2	2	X
ejpam-1726	35	2	.	.	X
ejpam-1726	35	3	preliminaries	preliminary	NOUN
ejpam-1726	35	4	we	we	PRON
ejpam-1726	35	5	recall	recall	VERB
ejpam-1726	35	6	here	here	ADV
ejpam-1726	35	7	some	some	DET
ejpam-1726	35	8	basic	basic	ADJ
ejpam-1726	35	9	definitions	definition	NOUN
ejpam-1726	35	10	and	and	CCONJ
ejpam-1726	35	11	results	result	NOUN
ejpam-1726	35	12	on	on	ADP
ejpam-1726	35	13	morita	morita	NOUN
ejpam-1726	35	14	equivalence	equivalence	NOUN
ejpam-1726	35	15	for	for	ADP
ejpam-1726	35	16	monoids	monoid	NOUN
ejpam-1726	35	17	as	as	ADV
ejpam-1726	35	18	well	well	ADV
ejpam-1726	35	19	as	as	ADP
ejpam-1726	35	20	some	some	DET
ejpam-1726	35	21	notions	notion	NOUN
ejpam-1726	35	22	of	of	ADP
ejpam-1726	35	23	γ	γ	NOUN
ejpam-1726	35	24	-	-	PUNCT
ejpam-1726	35	25	semigroups	semigroup	NOUN
ejpam-1726	35	26	with	with	ADP
ejpam-1726	35	27	unities	unity	NOUN
ejpam-1726	35	28	for	for	ADP
ejpam-1726	35	29	their	their	PRON
ejpam-1726	35	30	use	use	NOUN
ejpam-1726	35	31	in	in	ADP
ejpam-1726	35	32	the	the	DET
ejpam-1726	35	33	sequel	sequel	NOUN
ejpam-1726	35	34	.	.	PUNCT
ejpam-1726	36	1	throughout	throughout	ADP
ejpam-1726	36	2	this	this	DET
ejpam-1726	36	3	paper	paper	NOUN
ejpam-1726	36	4	,	,	PUNCT
ejpam-1726	36	5	we	we	PRON
ejpam-1726	36	6	assumed	assume	VERB
ejpam-1726	36	7	the	the	DET
ejpam-1726	36	8	mappings	mapping	NOUN
ejpam-1726	36	9	to	to	PART
ejpam-1726	36	10	act	act	VERB
ejpam-1726	36	11	from	from	ADP
ejpam-1726	36	12	the	the	DET
ejpam-1726	36	13	right	right	NOUN
ejpam-1726	36	14	.	.	PUNCT
ejpam-1726	37	1	definition	definition	NOUN
ejpam-1726	37	2	1	1	NUM
ejpam-1726	37	3	(	(	PUNCT
ejpam-1726	37	4	[	[	X
ejpam-1726	37	5	12	12	NUM
ejpam-1726	37	6	]	]	PUNCT
ejpam-1726	37	7	)	)	PUNCT
ejpam-1726	37	8	.	.	PUNCT
ejpam-1726	38	1	let	let	VERB
ejpam-1726	38	2	a	a	PRON
ejpam-1726	38	3	be	be	AUX
ejpam-1726	38	4	a	a	DET
ejpam-1726	38	5	monoid	monoid	NOUN
ejpam-1726	38	6	with	with	ADP
ejpam-1726	38	7	identity	identity	NOUN
ejpam-1726	38	8	1	1	NUM
ejpam-1726	38	9	.	.	PUNCT
ejpam-1726	39	1	then	then	ADV
ejpam-1726	39	2	a	a	DET
ejpam-1726	39	3	nonempty	nonempty	ADV
ejpam-1726	39	4	set	set	VERB
ejpam-1726	39	5	m	m	PRON
ejpam-1726	39	6	together	together	ADV
ejpam-1726	39	7	with	with	ADP
ejpam-1726	39	8	a	a	DET
ejpam-1726	39	9	map	map	NOUN
ejpam-1726	39	10	a×m	a×m	PUNCT
ejpam-1726	39	11	→	→	SYM
ejpam-1726	39	12	m	m	PROPN
ejpam-1726	39	13	,	,	PUNCT
ejpam-1726	39	14	denoted	denote	VERB
ejpam-1726	39	15	(	(	PUNCT
ejpam-1726	39	16	a	a	PRON
ejpam-1726	39	17	,	,	PUNCT
ejpam-1726	39	18	x	x	NOUN
ejpam-1726	39	19	)	)	PUNCT
ejpam-1726	39	20	7→	7→	NUM
ejpam-1726	39	21	ax	ax	NOUN
ejpam-1726	39	22	,	,	PUNCT
ejpam-1726	39	23	satisfying	satisfy	VERB
ejpam-1726	39	24	(	(	PUNCT
ejpam-1726	39	25	ab)x	ab)x	PROPN
ejpam-1726	39	26	=	=	SYM
ejpam-1726	39	27	a(bx	a(bx	PROPN
ejpam-1726	39	28	)	)	PUNCT
ejpam-1726	39	29	and	and	CCONJ
ejpam-1726	39	30	1x	1x	NUM
ejpam-1726	40	1	=	=	PUNCT
ejpam-1726	40	2	x	x	PROPN
ejpam-1726	40	3	for	for	ADP
ejpam-1726	40	4	all	all	DET
ejpam-1726	40	5	a	a	PRON
ejpam-1726	40	6	,	,	PUNCT
ejpam-1726	40	7	b	b	X
ejpam-1726	40	8	∈	∈	PROPN
ejpam-1726	40	9	a	a	PRON
ejpam-1726	40	10	and	and	CCONJ
ejpam-1726	40	11	x	x	SYM
ejpam-1726	40	12	∈	∈	PROPN
ejpam-1726	40	13	m	m	PROPN
ejpam-1726	40	14	,	,	PUNCT
ejpam-1726	40	15	is	be	AUX
ejpam-1726	40	16	called	call	VERB
ejpam-1726	40	17	a	a	DET
ejpam-1726	40	18	(	(	PUNCT
ejpam-1726	40	19	left	left	ADJ
ejpam-1726	40	20	)	)	PUNCT
ejpam-1726	40	21	a	a	DET
ejpam-1726	40	22	-	-	PUNCT
ejpam-1726	40	23	act	act	NOUN
ejpam-1726	40	24	and	and	CCONJ
ejpam-1726	40	25	is	be	AUX
ejpam-1726	40	26	denoted	denote	VERB
ejpam-1726	40	27	by	by	ADP
ejpam-1726	40	28	am	am	NOUN
ejpam-1726	40	29	.	.	PUNCT
ejpam-1726	41	1	definition	definition	NOUN
ejpam-1726	41	2	2	2	NUM
ejpam-1726	41	3	(	(	PUNCT
ejpam-1726	41	4	[	[	X
ejpam-1726	41	5	12	12	NUM
ejpam-1726	41	6	]	]	PUNCT
ejpam-1726	41	7	)	)	PUNCT
ejpam-1726	41	8	.	.	PUNCT
ejpam-1726	42	1	let	let	VERB
ejpam-1726	42	2	m	m	PRON
ejpam-1726	42	3	and	and	CCONJ
ejpam-1726	42	4	n	n	CCONJ
ejpam-1726	42	5	be	be	VERB
ejpam-1726	42	6	two	two	NUM
ejpam-1726	42	7	a	a	DET
ejpam-1726	42	8	-	-	PUNCT
ejpam-1726	42	9	acts	act	NOUN
ejpam-1726	42	10	.	.	PUNCT
ejpam-1726	43	1	then	then	ADV
ejpam-1726	43	2	a	a	DET
ejpam-1726	43	3	mapping	mapping	NOUN
ejpam-1726	43	4	f	f	X
ejpam-1726	43	5	:	:	PUNCT
ejpam-1726	43	6	m	m	VERB
ejpam-1726	43	7	→	→	SYM
ejpam-1726	43	8	n	n	X
ejpam-1726	43	9	is	be	AUX
ejpam-1726	43	10	called	call	VERB
ejpam-1726	43	11	a	a	DET
ejpam-1726	43	12	(	(	PUNCT
ejpam-1726	43	13	left	left	ADJ
ejpam-1726	43	14	)	)	PUNCT
ejpam-1726	43	15	a	a	DET
ejpam-1726	43	16	-	-	PUNCT
ejpam-1726	43	17	morphism	morphism	NOUN
ejpam-1726	43	18	if	if	SCONJ
ejpam-1726	43	19	for	for	ADP
ejpam-1726	43	20	all	all	DET
ejpam-1726	43	21	a	a	DET
ejpam-1726	43	22	∈	∈	PROPN
ejpam-1726	43	23	a	a	DET
ejpam-1726	43	24	and	and	CCONJ
ejpam-1726	43	25	x	x	SYM
ejpam-1726	43	26	∈	∈	PROPN
ejpam-1726	43	27	m	m	NOUN
ejpam-1726	43	28	,	,	PUNCT
ejpam-1726	43	29	(	(	PUNCT
ejpam-1726	43	30	ax	ax	NOUN
ejpam-1726	43	31	)	)	PUNCT
ejpam-1726	43	32	f	f	NOUN
ejpam-1726	43	33	=	=	PUNCT
ejpam-1726	43	34	a(x	a(x	PROPN
ejpam-1726	43	35	f	f	PROPN
ejpam-1726	43	36	)	)	PUNCT
ejpam-1726	43	37	.	.	PUNCT
ejpam-1726	44	1	the	the	DET
ejpam-1726	44	2	notions	notion	NOUN
ejpam-1726	44	3	of	of	ADP
ejpam-1726	44	4	a−b	a−b	NOUN
ejpam-1726	44	5	-	-	PUNCT
ejpam-1726	44	6	biact	biact	NOUN
ejpam-1726	44	7	and	and	CCONJ
ejpam-1726	44	8	a−b	a−b	NOUN
ejpam-1726	44	9	-	-	PUNCT
ejpam-1726	44	10	morphism	morphism	NOUN
ejpam-1726	44	11	are	be	AUX
ejpam-1726	44	12	defined	define	VERB
ejpam-1726	44	13	in	in	ADP
ejpam-1726	44	14	an	an	DET
ejpam-1726	44	15	obvious	obvious	ADJ
ejpam-1726	44	16	manner	manner	NOUN
ejpam-1726	44	17	.	.	PUNCT
ejpam-1726	45	1	the	the	DET
ejpam-1726	45	2	category	category	NOUN
ejpam-1726	45	3	formed	form	VERB
ejpam-1726	45	4	by	by	ADP
ejpam-1726	45	5	left	leave	VERB
ejpam-1726	45	6	a	a	PRON
ejpam-1726	45	7	-	-	PUNCT
ejpam-1726	45	8	acts	act	NOUN
ejpam-1726	45	9	together	together	ADV
ejpam-1726	45	10	with	with	ADP
ejpam-1726	45	11	the	the	DET
ejpam-1726	45	12	a	a	PRON
ejpam-1726	45	13	-	-	PUNCT
ejpam-1726	45	14	morphisms	morphism	NOUN
ejpam-1726	45	15	is	be	AUX
ejpam-1726	45	16	denoted	denote	VERB
ejpam-1726	45	17	by	by	ADP
ejpam-1726	45	18	a	a	DET
ejpam-1726	45	19	-	-	PUNCT
ejpam-1726	45	20	act	act	NOUN
ejpam-1726	45	21	.	.	PUNCT
ejpam-1726	46	1	analogously	analogously	ADV
ejpam-1726	46	2	,	,	PUNCT
ejpam-1726	46	3	the	the	DET
ejpam-1726	46	4	right	right	ADJ
ejpam-1726	46	5	a	a	NOUN
ejpam-1726	46	6	-	-	PUNCT
ejpam-1726	46	7	acts	act	NOUN
ejpam-1726	46	8	(	(	PUNCT
ejpam-1726	46	9	denoted	denote	VERB
ejpam-1726	46	10	by	by	ADP
ejpam-1726	46	11	ma	ma	PROPN
ejpam-1726	46	12	)	)	PUNCT
ejpam-1726	46	13	and	and	CCONJ
ejpam-1726	46	14	the	the	DET
ejpam-1726	46	15	right	right	ADJ
ejpam-1726	46	16	a	a	NOUN
ejpam-1726	46	17	-	-	PUNCT
ejpam-1726	46	18	morphisms	morphism	NOUN
ejpam-1726	46	19	can	can	AUX
ejpam-1726	46	20	be	be	AUX
ejpam-1726	46	21	defined	define	VERB
ejpam-1726	46	22	.	.	PUNCT
ejpam-1726	47	1	their	their	PRON
ejpam-1726	47	2	category	category	NOUN
ejpam-1726	47	3	is	be	AUX
ejpam-1726	47	4	denoted	denote	VERB
ejpam-1726	47	5	by	by	ADP
ejpam-1726	47	6	act	act	PROPN
ejpam-1726	47	7	-	-	PUNCT
ejpam-1726	47	8	a.	a.	NOUN
ejpam-1726	47	9	definition	definition	NOUN
ejpam-1726	47	10	3	3	NUM
ejpam-1726	47	11	(	(	PUNCT
ejpam-1726	47	12	[	[	X
ejpam-1726	47	13	12	12	NUM
ejpam-1726	47	14	]	]	PUNCT
ejpam-1726	47	15	)	)	PUNCT
ejpam-1726	47	16	.	.	PUNCT
ejpam-1726	48	1	let	let	VERB
ejpam-1726	48	2	a	a	PRON
ejpam-1726	48	3	and	and	CCONJ
ejpam-1726	48	4	b	b	NOUN
ejpam-1726	48	5	be	be	AUX
ejpam-1726	48	6	two	two	NUM
ejpam-1726	48	7	monoids	monoid	NOUN
ejpam-1726	48	8	.	.	PUNCT
ejpam-1726	49	1	then	then	ADV
ejpam-1726	49	2	a	a	PRON
ejpam-1726	49	3	and	and	CCONJ
ejpam-1726	49	4	b	b	NOUN
ejpam-1726	49	5	are	be	AUX
ejpam-1726	49	6	said	say	VERB
ejpam-1726	49	7	to	to	PART
ejpam-1726	49	8	be	be	AUX
ejpam-1726	49	9	morita	morita	NOUN
ejpam-1726	49	10	equivalent	equivalent	ADJ
ejpam-1726	49	11	if	if	SCONJ
ejpam-1726	49	12	a	a	DET
ejpam-1726	49	13	-	-	PUNCT
ejpam-1726	49	14	act	act	NOUN
ejpam-1726	49	15	and	and	CCONJ
ejpam-1726	49	16	b	b	X
ejpam-1726	49	17	-	-	PUNCT
ejpam-1726	49	18	act	act	NOUN
ejpam-1726	49	19	are	be	AUX
ejpam-1726	49	20	two	two	NUM
ejpam-1726	49	21	equivalent	equivalent	ADJ
ejpam-1726	49	22	categories	category	NOUN
ejpam-1726	49	23	.	.	PUNCT
ejpam-1726	50	1	theorem	theorem	NOUN
ejpam-1726	50	2	1	1	NUM
ejpam-1726	50	3	(	(	PUNCT
ejpam-1726	50	4	[	[	X
ejpam-1726	50	5	19	19	NUM
ejpam-1726	50	6	]	]	NUM
ejpam-1726	50	7	)	)	PUNCT
ejpam-1726	50	8	.	.	PUNCT
ejpam-1726	51	1	let	let	VERB
ejpam-1726	51	2	r	r	NOUN
ejpam-1726	51	3	and	and	CCONJ
ejpam-1726	51	4	s	s	AUX
ejpam-1726	51	5	be	be	AUX
ejpam-1726	51	6	two	two	NUM
ejpam-1726	51	7	morita	morita	PROPN
ejpam-1726	51	8	equivalent	equivalent	PROPN
ejpam-1726	51	9	monoids	monoid	NOUN
ejpam-1726	51	10	via	via	ADP
ejpam-1726	51	11	inverse	inverse	NOUN
ejpam-1726	51	12	equivalences	equivalence	VERB
ejpam-1726	52	1	f	f	X
ejpam-1726	52	2	:	:	PUNCT
ejpam-1726	52	3	r−	r−	PROPN
ejpam-1726	52	4	act	act	PROPN
ejpam-1726	52	5	→	→	SYM
ejpam-1726	52	6	s	s	PART
ejpam-1726	52	7	−	−	PROPN
ejpam-1726	52	8	act	act	NOUN
ejpam-1726	52	9	and	and	CCONJ
ejpam-1726	52	10	g	g	NOUN
ejpam-1726	52	11	:	:	PUNCT
ejpam-1726	52	12	s	s	PROPN
ejpam-1726	52	13	−	−	PROPN
ejpam-1726	52	14	act	act	PROPN
ejpam-1726	52	15	→	→	SYM
ejpam-1726	52	16	r−	r−	PROPN
ejpam-1726	52	17	act	act	PROPN
ejpam-1726	52	18	.	.	PUNCT
ejpam-1726	53	1	set	set	VERB
ejpam-1726	53	2	p	p	NOUN
ejpam-1726	53	3	=	=	PUNCT
ejpam-1726	53	4	f(r	f(r	X
ejpam-1726	53	5	)	)	PUNCT
ejpam-1726	53	6	and	and	CCONJ
ejpam-1726	53	7	q	q	ADJ
ejpam-1726	53	8	=	=	SYM
ejpam-1726	53	9	g(s	g(s	PROPN
ejpam-1726	53	10	)	)	PUNCT
ejpam-1726	53	11	.	.	PUNCT
ejpam-1726	54	1	then	then	ADV
ejpam-1726	54	2	p	p	PROPN
ejpam-1726	54	3	and	and	CCONJ
ejpam-1726	54	4	q	q	NOUN
ejpam-1726	54	5	are	be	AUX
ejpam-1726	54	6	unitary	unitary	ADJ
ejpam-1726	54	7	biacts	biact	NOUN
ejpam-1726	54	8	s	s	PART
ejpam-1726	54	9	pr	pr	NOUN
ejpam-1726	54	10	and	and	CCONJ
ejpam-1726	54	11	rqs	rqs	X
ejpam-1726	54	12	such	such	ADJ
ejpam-1726	54	13	that	that	PRON
ejpam-1726	54	14	,	,	PUNCT
ejpam-1726	54	15	(	(	PUNCT
ejpam-1726	54	16	1	1	X
ejpam-1726	54	17	)	)	PUNCT
ejpam-1726	54	18	s	s	VERB
ejpam-1726	54	19	p	p	NOUN
ejpam-1726	54	20	,	,	PUNCT
ejpam-1726	54	21	rq	rq	NOUN
ejpam-1726	54	22	are	be	AUX
ejpam-1726	54	23	respectively	respectively	ADV
ejpam-1726	54	24	generators	generator	NOUN
ejpam-1726	54	25	for	for	ADP
ejpam-1726	54	26	s	s	NOUN
ejpam-1726	54	27	-	-	PUNCT
ejpam-1726	54	28	act	act	NOUN
ejpam-1726	54	29	and	and	CCONJ
ejpam-1726	54	30	r	r	NOUN
ejpam-1726	54	31	-	-	PUNCT
ejpam-1726	54	32	act	act	NOUN
ejpam-1726	54	33	;	;	PUNCT
ejpam-1726	54	34	(	(	PUNCT
ejpam-1726	54	35	2	2	X
ejpam-1726	54	36	)	)	PUNCT
ejpam-1726	54	37	r∼=	r∼=	NUM
ejpam-1726	54	38	ends(p	ends(p	NOUN
ejpam-1726	54	39	)	)	PUNCT
ejpam-1726	54	40	and	and	CCONJ
ejpam-1726	54	41	s	s	AUX
ejpam-1726	54	42	∼=	∼=	NOUN
ejpam-1726	54	43	endr(q	endr(q	NOUN
ejpam-1726	54	44	)	)	PUNCT
ejpam-1726	54	45	;	;	PUNCT
ejpam-1726	54	46	(	(	PUNCT
ejpam-1726	54	47	3	3	X
ejpam-1726	54	48	)	)	PUNCT
ejpam-1726	54	49	f	f	NOUN
ejpam-1726	54	50	∼=	∼=	NOUN
ejpam-1726	54	51	homr(q	homr(q	NOUN
ejpam-1726	54	52	,	,	PUNCT
ejpam-1726	54	53	)	)	PUNCT
ejpam-1726	54	54	and	and	CCONJ
ejpam-1726	54	55	g	g	PROPN
ejpam-1726	54	56	∼=	∼=	PROPN
ejpam-1726	54	57	homs(p	homs(p	NOUN
ejpam-1726	54	58	,	,	PUNCT
ejpam-1726	54	59	)	)	PUNCT
ejpam-1726	54	60	;	;	PUNCT
ejpam-1726	54	61	s.	s.	PROPN
ejpam-1726	54	62	sardar	sardar	PROPN
ejpam-1726	54	63	,	,	PUNCT
ejpam-1726	54	64	s.	s.	PROPN
ejpam-1726	54	65	gupta	gupta	PROPN
ejpam-1726	54	66	,	,	PUNCT
ejpam-1726	54	67	k.	k.	PROPN
ejpam-1726	54	68	shum	shum	PROPN
ejpam-1726	54	69	/	/	SYM
ejpam-1726	54	70	eur	eur	PROPN
ejpam-1726	54	71	.	.	PUNCT
ejpam-1726	55	1	j.	j.	PROPN
ejpam-1726	55	2	pure	pure	PROPN
ejpam-1726	55	3	appl	appl	PROPN
ejpam-1726	55	4	.	.	PROPN
ejpam-1726	55	5	math	math	PROPN
ejpam-1726	55	6	,	,	PUNCT
ejpam-1726	55	7	6	6	NUM
ejpam-1726	55	8	(	(	PUNCT
ejpam-1726	55	9	2013	2013	NUM
ejpam-1726	55	10	)	)	PUNCT
ejpam-1726	55	11	,	,	PUNCT
ejpam-1726	55	12	1	1	NUM
ejpam-1726	55	13	-	-	SYM
ejpam-1726	55	14	10	10	NUM
ejpam-1726	55	15	3	3	NUM
ejpam-1726	55	16	(	(	PUNCT
ejpam-1726	55	17	4	4	NUM
ejpam-1726	55	18	)	)	PUNCT
ejpam-1726	55	19	s	s	AUX
ejpam-1726	55	20	pr	pr	NOUN
ejpam-1726	55	21	∼=	∼=	NOUN
ejpam-1726	55	22	homr(q	homr(q	NOUN
ejpam-1726	55	23	,	,	PUNCT
ejpam-1726	55	24	r	r	NOUN
ejpam-1726	55	25	)	)	PUNCT
ejpam-1726	55	26	and	and	CCONJ
ejpam-1726	55	27	rqs	rqs	PROPN
ejpam-1726	55	28	∼=	∼=	PART
ejpam-1726	55	29	homs(p	homs(p	NOUN
ejpam-1726	55	30	,	,	PUNCT
ejpam-1726	55	31	s	s	NOUN
ejpam-1726	55	32	)	)	PUNCT
ejpam-1726	55	33	.	.	PUNCT
ejpam-1726	56	1	the	the	DET
ejpam-1726	56	2	following	follow	VERB
ejpam-1726	56	3	theorem	theorem	NOUN
ejpam-1726	56	4	characterizes	characterize	VERB
ejpam-1726	56	5	the	the	DET
ejpam-1726	56	6	generators	generator	NOUN
ejpam-1726	56	7	of	of	ADP
ejpam-1726	56	8	a	a	DET
ejpam-1726	56	9	-	-	PUNCT
ejpam-1726	56	10	act	act	NOUN
ejpam-1726	56	11	.	.	PUNCT
ejpam-1726	57	1	theorem	theorem	ADJ
ejpam-1726	57	2	2	2	NUM
ejpam-1726	57	3	(	(	PUNCT
ejpam-1726	57	4	[	[	X
ejpam-1726	57	5	12	12	NUM
ejpam-1726	57	6	]	]	NUM
ejpam-1726	57	7	)	)	PUNCT
ejpam-1726	57	8	.	.	PUNCT
ejpam-1726	58	1	an	an	DET
ejpam-1726	58	2	a	a	DET
ejpam-1726	58	3	-	-	PUNCT
ejpam-1726	58	4	act	act	NOUN
ejpam-1726	58	5	g	g	NOUN
ejpam-1726	58	6	is	be	AUX
ejpam-1726	58	7	a	a	DET
ejpam-1726	58	8	generator	generator	NOUN
ejpam-1726	58	9	for	for	ADP
ejpam-1726	58	10	the	the	DET
ejpam-1726	58	11	category	category	NOUN
ejpam-1726	58	12	a	a	DET
ejpam-1726	58	13	-	-	PUNCT
ejpam-1726	58	14	act	act	NOUN
ejpam-1726	58	15	if	if	SCONJ
ejpam-1726	58	16	and	and	CCONJ
ejpam-1726	58	17	only	only	ADV
ejpam-1726	58	18	if	if	SCONJ
ejpam-1726	58	19	there	there	PRON
ejpam-1726	58	20	exists	exist	VERB
ejpam-1726	58	21	an	an	DET
ejpam-1726	58	22	epimorphism	epimorphism	NOUN
ejpam-1726	58	23	g	g	NOUN
ejpam-1726	58	24	:	:	PUNCT
ejpam-1726	58	25	g→	g→	NOUN
ejpam-1726	58	26	a.	a.	NOUN
ejpam-1726	58	27	definition	definition	NOUN
ejpam-1726	58	28	4	4	NUM
ejpam-1726	58	29	(	(	PUNCT
ejpam-1726	58	30	[	[	X
ejpam-1726	58	31	12	12	NUM
ejpam-1726	58	32	]	]	PUNCT
ejpam-1726	58	33	)	)	PUNCT
ejpam-1726	58	34	.	.	PUNCT
ejpam-1726	59	1	for	for	ADP
ejpam-1726	59	2	a	a	DET
ejpam-1726	59	3	right	right	ADJ
ejpam-1726	59	4	a	a	DET
ejpam-1726	59	5	-	-	PUNCT
ejpam-1726	59	6	act	act	NOUN
ejpam-1726	59	7	ma	ma	PROPN
ejpam-1726	59	8	and	and	CCONJ
ejpam-1726	59	9	a	a	DET
ejpam-1726	59	10	left	left	ADJ
ejpam-1726	59	11	a	a	DET
ejpam-1726	59	12	-	-	PUNCT
ejpam-1726	59	13	act	act	NOUN
ejpam-1726	59	14	an	an	PRON
ejpam-1726	59	15	,	,	PUNCT
ejpam-1726	59	16	the	the	DET
ejpam-1726	59	17	tensor	tensor	NOUN
ejpam-1726	59	18	product	product	NOUN
ejpam-1726	59	19	of	of	ADP
ejpam-1726	59	20	these	these	DET
ejpam-1726	59	21	two	two	NUM
ejpam-1726	59	22	acts	act	NOUN
ejpam-1726	59	23	,	,	PUNCT
ejpam-1726	59	24	denoted	denote	VERB
ejpam-1726	59	25	by	by	ADP
ejpam-1726	59	26	m⊗an	m⊗an	NOUN
ejpam-1726	59	27	,	,	PUNCT
ejpam-1726	59	28	is	be	AUX
ejpam-1726	59	29	the	the	DET
ejpam-1726	59	30	unique	unique	ADJ
ejpam-1726	59	31	solution	solution	NOUN
ejpam-1726	59	32	of	of	ADP
ejpam-1726	59	33	the	the	DET
ejpam-1726	59	34	usual	usual	ADJ
ejpam-1726	59	35	universal	universal	ADJ
ejpam-1726	59	36	problem	problem	NOUN
ejpam-1726	59	37	:	:	PUNCT
ejpam-1726	59	38	that	that	PRON
ejpam-1726	59	39	is	be	AUX
ejpam-1726	59	40	,	,	PUNCT
ejpam-1726	59	41	m⊗a	m⊗a	NOUN
ejpam-1726	59	42	n	n	NOUN
ejpam-1726	59	43	=	=	SYM
ejpam-1726	59	44	(	(	PUNCT
ejpam-1726	59	45	m×n)/σ	m×n)/σ	NOUN
ejpam-1726	59	46	,	,	PUNCT
ejpam-1726	59	47	where	where	SCONJ
ejpam-1726	59	48	σ	σ	PROPN
ejpam-1726	59	49	is	be	AUX
ejpam-1726	59	50	the	the	DET
ejpam-1726	59	51	equivalence	equivalence	NOUN
ejpam-1726	59	52	relation	relation	NOUN
ejpam-1726	59	53	on	on	ADP
ejpam-1726	59	54	m×n	m×n	PROPN
ejpam-1726	59	55	generated	generate	VERB
ejpam-1726	59	56	by	by	ADP
ejpam-1726	59	57	σ	σ	PROPN
ejpam-1726	59	58	=	=	SYM
ejpam-1726	59	59	{	{	PUNCT
ejpam-1726	59	60	(	(	PUNCT
ejpam-1726	59	61	(	(	PUNCT
ejpam-1726	59	62	xa	xa	PROPN
ejpam-1726	59	63	,	,	PUNCT
ejpam-1726	59	64	y	y	PROPN
ejpam-1726	59	65	)	)	PUNCT
ejpam-1726	59	66	,	,	PUNCT
ejpam-1726	59	67	(	(	PUNCT
ejpam-1726	59	68	x	x	X
ejpam-1726	59	69	,	,	PUNCT
ejpam-1726	59	70	a	a	DET
ejpam-1726	59	71	y	y	NOUN
ejpam-1726	59	72	)	)	PUNCT
ejpam-1726	59	73	)	)	PUNCT
ejpam-1726	59	74	:	:	PUNCT
ejpam-1726	60	1	x	x	X
ejpam-1726	60	2	∈	∈	NOUN
ejpam-1726	60	3	m	m	NOUN
ejpam-1726	60	4	,	,	PUNCT
ejpam-1726	60	5	y	y	PROPN
ejpam-1726	60	6	∈	∈	PROPN
ejpam-1726	60	7	n	n	PRON
ejpam-1726	60	8	,	,	PUNCT
ejpam-1726	60	9	a	a	DET
ejpam-1726	60	10	∈	∈	PROPN
ejpam-1726	60	11	a	a	PRON
ejpam-1726	60	12	}	}	PUNCT
ejpam-1726	60	13	.	.	PUNCT
ejpam-1726	61	1	we	we	PRON
ejpam-1726	61	2	denote	denote	VERB
ejpam-1726	61	3	the	the	DET
ejpam-1726	61	4	class	class	NOUN
ejpam-1726	61	5	of	of	ADP
ejpam-1726	61	6	(	(	PUNCT
ejpam-1726	61	7	x	x	PROPN
ejpam-1726	61	8	,	,	PUNCT
ejpam-1726	61	9	y	y	PROPN
ejpam-1726	61	10	)	)	PUNCT
ejpam-1726	61	11	by	by	ADP
ejpam-1726	61	12	x	x	PROPN
ejpam-1726	61	13	⊗	⊗	PROPN
ejpam-1726	61	14	y.	y.	PROPN
ejpam-1726	61	15	when	when	SCONJ
ejpam-1726	61	16	there	there	PRON
ejpam-1726	61	17	is	be	VERB
ejpam-1726	61	18	no	no	DET
ejpam-1726	61	19	ambiguity	ambiguity	NOUN
ejpam-1726	61	20	about	about	ADP
ejpam-1726	61	21	the	the	DET
ejpam-1726	61	22	monoid	monoid	PROPN
ejpam-1726	61	23	a	a	NOUN
ejpam-1726	61	24	,	,	PUNCT
ejpam-1726	61	25	we	we	PRON
ejpam-1726	61	26	write	write	VERB
ejpam-1726	61	27	the	the	DET
ejpam-1726	61	28	tensor	tensor	NOUN
ejpam-1726	61	29	product	product	NOUN
ejpam-1726	61	30	as	as	ADP
ejpam-1726	61	31	m	m	PROPN
ejpam-1726	61	32	⊗	⊗	PROPN
ejpam-1726	61	33	n.	n.	PROPN
ejpam-1726	61	34	definition	definition	NOUN
ejpam-1726	61	35	5	5	NUM
ejpam-1726	61	36	(	(	PUNCT
ejpam-1726	61	37	[	[	X
ejpam-1726	61	38	2	2	NUM
ejpam-1726	61	39	]	]	PUNCT
ejpam-1726	61	40	)	)	PUNCT
ejpam-1726	61	41	.	.	PUNCT
ejpam-1726	62	1	let	let	VERB
ejpam-1726	62	2	a	a	PRON
ejpam-1726	62	3	and	and	CCONJ
ejpam-1726	62	4	γ	γ	NOUN
ejpam-1726	62	5	be	be	AUX
ejpam-1726	62	6	two	two	NUM
ejpam-1726	62	7	non	non	ADJ
ejpam-1726	62	8	-	-	ADJ
ejpam-1726	62	9	empty	empty	ADJ
ejpam-1726	62	10	sets	set	NOUN
ejpam-1726	62	11	.	.	PUNCT
ejpam-1726	63	1	then	then	ADV
ejpam-1726	63	2	a	a	PRON
ejpam-1726	63	3	is	be	AUX
ejpam-1726	63	4	said	say	VERB
ejpam-1726	63	5	to	to	PART
ejpam-1726	63	6	be	be	AUX
ejpam-1726	63	7	a	a	DET
ejpam-1726	63	8	γ	γ	NOUN
ejpam-1726	63	9	-	-	PUNCT
ejpam-1726	63	10	semigroup	semigroup	NOUN
ejpam-1726	63	11	if	if	SCONJ
ejpam-1726	63	12	there	there	PRON
ejpam-1726	63	13	exist	exist	VERB
ejpam-1726	63	14	mappings	mapping	NOUN
ejpam-1726	63	15	a×γ×a→	a×γ×a→	PROPN
ejpam-1726	63	16	a	a	PRON
ejpam-1726	63	17	,	,	PUNCT
ejpam-1726	63	18	denoted	denote	VERB
ejpam-1726	63	19	by	by	ADP
ejpam-1726	63	20	(	(	PUNCT
ejpam-1726	63	21	a	a	PRON
ejpam-1726	63	22	,	,	PUNCT
ejpam-1726	63	23	γ	γ	PROPN
ejpam-1726	63	24	,	,	PUNCT
ejpam-1726	63	25	b	b	NOUN
ejpam-1726	63	26	)	)	PUNCT
ejpam-1726	63	27	7→	7→	NUM
ejpam-1726	63	28	aγb	aγb	NOUN
ejpam-1726	63	29	,	,	PUNCT
ejpam-1726	63	30	and	and	CCONJ
ejpam-1726	63	31	γ×a×γ→	γ×a×γ→	PROPN
ejpam-1726	63	32	γ	γ	PROPN
ejpam-1726	63	33	,	,	PUNCT
ejpam-1726	63	34	denoted	denote	VERB
ejpam-1726	63	35	by	by	ADP
ejpam-1726	63	36	(	(	PUNCT
ejpam-1726	63	37	α	α	X
ejpam-1726	63	38	,	,	PUNCT
ejpam-1726	63	39	a	a	PRON
ejpam-1726	63	40	,	,	PUNCT
ejpam-1726	63	41	β	β	NOUN
ejpam-1726	63	42	)	)	PUNCT
ejpam-1726	63	43	7→	7→	NUM
ejpam-1726	63	44	αaβ	αaβ	NOUN
ejpam-1726	63	45	,	,	PUNCT
ejpam-1726	63	46	satisfying	satisfy	VERB
ejpam-1726	63	47	(	(	PUNCT
ejpam-1726	63	48	aαb)β	aαb)β	NOUN
ejpam-1726	63	49	c	c	NOUN
ejpam-1726	63	50	=	=	SYM
ejpam-1726	63	51	a(αbβ)c	a(αbβ)c	PROPN
ejpam-1726	63	52	=	=	PUNCT
ejpam-1726	63	53	aα(bβ	aα(bβ	PROPN
ejpam-1726	63	54	c	c	PROPN
ejpam-1726	63	55	)	)	PUNCT
ejpam-1726	63	56	for	for	ADP
ejpam-1726	63	57	all	all	DET
ejpam-1726	63	58	a	a	DET
ejpam-1726	63	59	,	,	PUNCT
ejpam-1726	63	60	b	b	NOUN
ejpam-1726	63	61	,	,	PUNCT
ejpam-1726	63	62	c	c	PROPN
ejpam-1726	63	63	∈	∈	PROPN
ejpam-1726	63	64	a	a	PRON
ejpam-1726	63	65	and	and	CCONJ
ejpam-1726	63	66	α	α	NOUN
ejpam-1726	63	67	,	,	PUNCT
ejpam-1726	63	68	β	β	PROPN
ejpam-1726	63	69	∈	∈	PROPN
ejpam-1726	63	70	γ	γ	PROPN
ejpam-1726	63	71	.	.	PROPN
ejpam-1726	63	72	definition	definition	NOUN
ejpam-1726	63	73	6	6	NUM
ejpam-1726	63	74	(	(	PUNCT
ejpam-1726	63	75	[	[	X
ejpam-1726	63	76	2	2	NUM
ejpam-1726	63	77	]	]	PUNCT
ejpam-1726	63	78	)	)	PUNCT
ejpam-1726	63	79	.	.	PUNCT
ejpam-1726	64	1	let	let	VERB
ejpam-1726	64	2	a	a	PRON
ejpam-1726	64	3	be	be	AUX
ejpam-1726	64	4	a	a	DET
ejpam-1726	64	5	γ	γ	NOUN
ejpam-1726	64	6	-	-	PUNCT
ejpam-1726	64	7	semigroup	semigroup	NOUN
ejpam-1726	64	8	and	and	CCONJ
ejpam-1726	64	9	ρ	ρ	PROPN
ejpam-1726	64	10	be	be	AUX
ejpam-1726	64	11	a	a	DET
ejpam-1726	64	12	relation	relation	NOUN
ejpam-1726	64	13	on	on	ADP
ejpam-1726	64	14	γ×a	γ×a	PROPN
ejpam-1726	64	15	defined	define	VERB
ejpam-1726	64	16	by	by	ADP
ejpam-1726	64	17	(	(	PUNCT
ejpam-1726	64	18	α	α	X
ejpam-1726	64	19	,	,	PUNCT
ejpam-1726	64	20	a)ρ(β	a)ρ(β	PROPN
ejpam-1726	64	21	,	,	PUNCT
ejpam-1726	64	22	b)⇔	b)⇔	PROPN
ejpam-1726	64	23	xαa	xαa	NOUN
ejpam-1726	65	1	=	=	PUNCT
ejpam-1726	65	2	xβ	xβ	PROPN
ejpam-1726	65	3	b	b	NOUN
ejpam-1726	65	4	and	and	CCONJ
ejpam-1726	65	5	αaγ	αaγ	NOUN
ejpam-1726	66	1	=	=	SYM
ejpam-1726	66	2	β	β	AUX
ejpam-1726	66	3	bγ	bγ	ADV
ejpam-1726	66	4	for	for	ADP
ejpam-1726	66	5	all	all	DET
ejpam-1726	66	6	x	x	SYM
ejpam-1726	66	7	∈	∈	PROPN
ejpam-1726	66	8	a	a	PRON
ejpam-1726	66	9	and	and	CCONJ
ejpam-1726	66	10	γ	γ	PROPN
ejpam-1726	66	11	∈	∈	PROPN
ejpam-1726	66	12	γ	γ	X
ejpam-1726	66	13	.	.	PROPN
ejpam-1726	67	1	then	then	ADV
ejpam-1726	67	2	ρ	ρ	PROPN
ejpam-1726	67	3	is	be	AUX
ejpam-1726	67	4	an	an	DET
ejpam-1726	67	5	equivalence	equivalence	NOUN
ejpam-1726	67	6	relation	relation	NOUN
ejpam-1726	67	7	.	.	PUNCT
ejpam-1726	68	1	let	let	VERB
ejpam-1726	68	2	us	we	PRON
ejpam-1726	68	3	denote	denote	VERB
ejpam-1726	68	4	the	the	DET
ejpam-1726	68	5	equivalence	equivalence	NOUN
ejpam-1726	68	6	class	class	NOUN
ejpam-1726	68	7	of	of	ADP
ejpam-1726	68	8	(	(	PUNCT
ejpam-1726	68	9	α	α	NOUN
ejpam-1726	68	10	,	,	PUNCT
ejpam-1726	68	11	a	a	NOUN
ejpam-1726	68	12	)	)	PUNCT
ejpam-1726	68	13	by	by	ADP
ejpam-1726	68	14	[	[	X
ejpam-1726	68	15	α	α	X
ejpam-1726	68	16	,	,	PUNCT
ejpam-1726	68	17	a	a	PRON
ejpam-1726	68	18	]	]	X
ejpam-1726	68	19	.	.	PUNCT
ejpam-1726	69	1	then	then	ADV
ejpam-1726	69	2	the	the	DET
ejpam-1726	69	3	right	right	ADJ
ejpam-1726	69	4	operator	operator	NOUN
ejpam-1726	69	5	semigroup	semigroup	NOUN
ejpam-1726	69	6	of	of	ADP
ejpam-1726	69	7	the	the	DET
ejpam-1726	69	8	γ	γ	PROPN
ejpam-1726	69	9	-	-	PUNCT
ejpam-1726	69	10	semigroup	semigroup	NOUN
ejpam-1726	69	11	a	a	PRON
ejpam-1726	69	12	is	be	AUX
ejpam-1726	69	13	defined	define	VERB
ejpam-1726	69	14	to	to	PART
ejpam-1726	69	15	be	be	AUX
ejpam-1726	69	16	r	r	NOUN
ejpam-1726	69	17	=	=	SYM
ejpam-1726	69	18	(	(	PUNCT
ejpam-1726	69	19	γ×	γ×	NUM
ejpam-1726	69	20	a)/ρ	a)/ρ	PROPN
ejpam-1726	69	21	=	=	SYM
ejpam-1726	70	1	{	{	PUNCT
ejpam-1726	70	2	[	[	X
ejpam-1726	70	3	α	α	X
ejpam-1726	70	4	,	,	PUNCT
ejpam-1726	70	5	a	a	PRON
ejpam-1726	70	6	]	]	X
ejpam-1726	70	7	|	|	ADP
ejpam-1726	70	8	a	a	DET
ejpam-1726	70	9	∈	∈	PROPN
ejpam-1726	70	10	a	a	PRON
ejpam-1726	70	11	,	,	PUNCT
ejpam-1726	70	12	α	α	PROPN
ejpam-1726	70	13	∈	∈	PROPN
ejpam-1726	70	14	γ	γ	X
ejpam-1726	70	15	}	}	PUNCT
ejpam-1726	70	16	,	,	PUNCT
ejpam-1726	70	17	where	where	SCONJ
ejpam-1726	70	18	the	the	DET
ejpam-1726	70	19	composition	composition	NOUN
ejpam-1726	70	20	is	be	AUX
ejpam-1726	70	21	defined	define	VERB
ejpam-1726	70	22	as	as	ADP
ejpam-1726	70	23	[	[	X
ejpam-1726	70	24	α	α	NOUN
ejpam-1726	70	25	,	,	PUNCT
ejpam-1726	70	26	a][β	a][β	VERB
ejpam-1726	70	27	,	,	PUNCT
ejpam-1726	70	28	b	b	X
ejpam-1726	70	29	]	]	X
ejpam-1726	70	30	=	=	PUNCT
ejpam-1726	71	1	[	[	X
ejpam-1726	71	2	α	α	NOUN
ejpam-1726	71	3	,	,	PUNCT
ejpam-1726	71	4	aβ	aβ	PROPN
ejpam-1726	71	5	b	b	NOUN
ejpam-1726	71	6	]	]	PUNCT
ejpam-1726	71	7	and	and	CCONJ
ejpam-1726	71	8	the	the	DET
ejpam-1726	71	9	associativity	associativity	NOUN
ejpam-1726	71	10	of	of	ADP
ejpam-1726	71	11	this	this	DET
ejpam-1726	71	12	composition	composition	NOUN
ejpam-1726	71	13	comes	come	VERB
ejpam-1726	71	14	from	from	ADP
ejpam-1726	71	15	the	the	DET
ejpam-1726	71	16	associativity	associativity	NOUN
ejpam-1726	71	17	of	of	ADP
ejpam-1726	71	18	γ	γ	PROPN
ejpam-1726	71	19	-	-	PUNCT
ejpam-1726	71	20	semigroup	semigroup	PROPN
ejpam-1726	71	21	a.	a.	NOUN
ejpam-1726	71	22	analogously	analogously	ADV
ejpam-1726	71	23	,	,	PUNCT
ejpam-1726	71	24	the	the	DET
ejpam-1726	71	25	left	left	ADJ
ejpam-1726	71	26	operator	operator	NOUN
ejpam-1726	71	27	semigroup	semigroup	PROPN
ejpam-1726	71	28	l	l	PROPN
ejpam-1726	71	29	is	be	AUX
ejpam-1726	71	30	defined	define	VERB
ejpam-1726	71	31	and	and	CCONJ
ejpam-1726	71	32	its	its	PRON
ejpam-1726	71	33	elements	element	NOUN
ejpam-1726	71	34	are	be	AUX
ejpam-1726	71	35	denoted	denote	VERB
ejpam-1726	71	36	by	by	ADP
ejpam-1726	71	37	[	[	X
ejpam-1726	71	38	a	a	X
ejpam-1726	71	39	,	,	PUNCT
ejpam-1726	71	40	α	α	NOUN
ejpam-1726	71	41	]	]	X
ejpam-1726	71	42	,	,	PUNCT
ejpam-1726	71	43	|	|	ADV
ejpam-1726	71	44	a	a	DET
ejpam-1726	71	45	∈	∈	PROPN
ejpam-1726	71	46	a	a	PRON
ejpam-1726	71	47	,	,	PUNCT
ejpam-1726	71	48	α	α	PROPN
ejpam-1726	71	49	∈	∈	PROPN
ejpam-1726	71	50	γ	γ	X
ejpam-1726	71	51	}	}	PUNCT
ejpam-1726	71	52	.	.	PUNCT
ejpam-1726	72	1	definition	definition	NOUN
ejpam-1726	72	2	7	7	NUM
ejpam-1726	72	3	(	(	PUNCT
ejpam-1726	72	4	[	[	X
ejpam-1726	72	5	2	2	NUM
ejpam-1726	72	6	]	]	PUNCT
ejpam-1726	72	7	)	)	PUNCT
ejpam-1726	72	8	.	.	PUNCT
ejpam-1726	73	1	if	if	SCONJ
ejpam-1726	73	2	there	there	PRON
ejpam-1726	73	3	exists	exist	VERB
ejpam-1726	73	4	an	an	DET
ejpam-1726	73	5	element	element	NOUN
ejpam-1726	73	6	[	[	X
ejpam-1726	73	7	γ	γ	X
ejpam-1726	73	8	,	,	PUNCT
ejpam-1726	73	9	f	f	X
ejpam-1726	73	10	]	]	PUNCT
ejpam-1726	73	11	in	in	ADP
ejpam-1726	73	12	the	the	DET
ejpam-1726	73	13	right	right	ADJ
ejpam-1726	73	14	operator	operator	NOUN
ejpam-1726	73	15	semigroup	semigroup	NOUN
ejpam-1726	73	16	r	r	NOUN
ejpam-1726	73	17	of	of	ADP
ejpam-1726	73	18	a	a	DET
ejpam-1726	73	19	γsemigroup	γsemigroup	NOUN
ejpam-1726	74	1	a	a	DET
ejpam-1726	74	2	such	such	ADJ
ejpam-1726	74	3	that	that	PRON
ejpam-1726	74	4	xγ	xγ	PROPN
ejpam-1726	74	5	f	f	X
ejpam-1726	75	1	=	=	PUNCT
ejpam-1726	75	2	x	x	PROPN
ejpam-1726	75	3	for	for	ADP
ejpam-1726	75	4	all	all	DET
ejpam-1726	75	5	x	x	SYM
ejpam-1726	75	6	∈	∈	PROPN
ejpam-1726	75	7	a	a	PRON
ejpam-1726	75	8	,	,	PUNCT
ejpam-1726	75	9	then	then	ADV
ejpam-1726	75	10	that	that	DET
ejpam-1726	75	11	element	element	NOUN
ejpam-1726	75	12	is	be	AUX
ejpam-1726	75	13	called	call	VERB
ejpam-1726	75	14	the	the	DET
ejpam-1726	75	15	right	right	ADJ
ejpam-1726	75	16	unity	unity	NOUN
ejpam-1726	75	17	of	of	ADP
ejpam-1726	75	18	a.	a.	NOUN
ejpam-1726	75	19	similar	similar	ADJ
ejpam-1726	75	20	is	be	AUX
ejpam-1726	75	21	the	the	DET
ejpam-1726	75	22	definition	definition	NOUN
ejpam-1726	75	23	of	of	ADP
ejpam-1726	75	24	the	the	DET
ejpam-1726	75	25	left	left	ADJ
ejpam-1726	75	26	unity	unity	NOUN
ejpam-1726	75	27	of	of	ADP
ejpam-1726	75	28	a.	a.	NOUN
ejpam-1726	75	29	a	a	PRON
ejpam-1726	75	30	is	be	AUX
ejpam-1726	75	31	said	say	VERB
ejpam-1726	75	32	to	to	PART
ejpam-1726	75	33	be	be	AUX
ejpam-1726	75	34	a	a	DET
ejpam-1726	75	35	γ	γ	NOUN
ejpam-1726	75	36	-	-	PUNCT
ejpam-1726	75	37	semigroup	semigroup	NOUN
ejpam-1726	75	38	with	with	ADP
ejpam-1726	75	39	unities	unity	NOUN
ejpam-1726	75	40	if	if	SCONJ
ejpam-1726	75	41	it	it	PRON
ejpam-1726	75	42	has	have	AUX
ejpam-1726	75	43	both	both	CCONJ
ejpam-1726	75	44	left	leave	VERB
ejpam-1726	75	45	and	and	CCONJ
ejpam-1726	75	46	right	right	ADJ
ejpam-1726	75	47	unities	unity	NOUN
ejpam-1726	75	48	.	.	PUNCT
ejpam-1726	76	1	it	it	PRON
ejpam-1726	76	2	may	may	AUX
ejpam-1726	76	3	be	be	AUX
ejpam-1726	76	4	noted	note	VERB
ejpam-1726	76	5	that	that	SCONJ
ejpam-1726	76	6	the	the	DET
ejpam-1726	76	7	left	left	ADJ
ejpam-1726	76	8	unity	unity	NOUN
ejpam-1726	76	9	(	(	PUNCT
ejpam-1726	76	10	right	right	ADJ
ejpam-1726	76	11	unity	unity	NOUN
ejpam-1726	76	12	)	)	PUNCT
ejpam-1726	76	13	of	of	ADP
ejpam-1726	76	14	a	a	PRON
ejpam-1726	76	15	becomes	become	VERB
ejpam-1726	76	16	the	the	DET
ejpam-1726	76	17	identity	identity	NOUN
ejpam-1726	76	18	of	of	ADP
ejpam-1726	76	19	l	l	NOUN
ejpam-1726	76	20	(	(	PUNCT
ejpam-1726	76	21	respectively	respectively	ADV
ejpam-1726	76	22	,	,	PUNCT
ejpam-1726	76	23	r	r	NOUN
ejpam-1726	76	24	)	)	PUNCT
ejpam-1726	76	25	.	.	PUNCT
ejpam-1726	77	1	for	for	ADP
ejpam-1726	77	2	more	more	ADJ
ejpam-1726	77	3	preliminaries	preliminary	NOUN
ejpam-1726	77	4	on	on	ADP
ejpam-1726	77	5	morita	morita	PROPN
ejpam-1726	77	6	theory	theory	NOUN
ejpam-1726	77	7	of	of	ADP
ejpam-1726	77	8	monoids	monoid	NOUN
ejpam-1726	77	9	and	and	CCONJ
ejpam-1726	77	10	on	on	ADP
ejpam-1726	77	11	γ	γ	NOUN
ejpam-1726	77	12	-	-	PUNCT
ejpam-1726	77	13	semigroups	semigroup	NOUN
ejpam-1726	77	14	we	we	PRON
ejpam-1726	77	15	refer	refer	VERB
ejpam-1726	77	16	to	to	ADP
ejpam-1726	77	17	[	[	X
ejpam-1726	77	18	7	7	NUM
ejpam-1726	77	19	,	,	PUNCT
ejpam-1726	77	20	12	12	NUM
ejpam-1726	77	21	,	,	PUNCT
ejpam-1726	77	22	13	13	NUM
ejpam-1726	77	23	,	,	PUNCT
ejpam-1726	77	24	19	19	NUM
ejpam-1726	77	25	]	]	PUNCT
ejpam-1726	77	26	and	and	CCONJ
ejpam-1726	77	27	[	[	X
ejpam-1726	77	28	1	1	NUM
ejpam-1726	77	29	,	,	PUNCT
ejpam-1726	77	30	2	2	NUM
ejpam-1726	77	31	,	,	PUNCT
ejpam-1726	77	32	3	3	NUM
ejpam-1726	77	33	,	,	PUNCT
ejpam-1726	77	34	4	4	NUM
ejpam-1726	77	35	,	,	PUNCT
ejpam-1726	77	36	5	5	NUM
ejpam-1726	77	37	]	]	PUNCT
ejpam-1726	77	38	,	,	PUNCT
ejpam-1726	77	39	respectively	respectively	ADV
ejpam-1726	77	40	.	.	PUNCT
ejpam-1726	78	1	3	3	X
ejpam-1726	78	2	.	.	X
ejpam-1726	78	3	relating	relate	VERB
ejpam-1726	78	4	γ	γ	NOUN
ejpam-1726	78	5	-	-	PUNCT
ejpam-1726	78	6	semigroups	semigroup	NOUN
ejpam-1726	78	7	with	with	ADP
ejpam-1726	78	8	morita	morita	NOUN
ejpam-1726	78	9	equivalence	equivalence	NOUN
ejpam-1726	78	10	in	in	ADP
ejpam-1726	78	11	this	this	DET
ejpam-1726	78	12	section	section	NOUN
ejpam-1726	78	13	we	we	PRON
ejpam-1726	78	14	are	be	AUX
ejpam-1726	78	15	going	go	VERB
ejpam-1726	78	16	to	to	PART
ejpam-1726	78	17	explore	explore	VERB
ejpam-1726	78	18	the	the	DET
ejpam-1726	78	19	relationship	relationship	NOUN
ejpam-1726	78	20	between	between	ADP
ejpam-1726	78	21	γ	γ	NOUN
ejpam-1726	78	22	-	-	PUNCT
ejpam-1726	78	23	semigroups	semigroup	NOUN
ejpam-1726	78	24	with	with	ADP
ejpam-1726	78	25	unities	unity	NOUN
ejpam-1726	78	26	and	and	CCONJ
ejpam-1726	78	27	the	the	DET
ejpam-1726	78	28	morita	morita	NOUN
ejpam-1726	78	29	equivalence	equivalence	NOUN
ejpam-1726	78	30	for	for	ADP
ejpam-1726	78	31	monoids	monoid	NOUN
ejpam-1726	78	32	.	.	PUNCT
ejpam-1726	79	1	definition	definition	NOUN
ejpam-1726	79	2	8	8	NUM
ejpam-1726	79	3	.	.	PUNCT
ejpam-1726	80	1	a	a	DET
ejpam-1726	80	2	six	six	NUM
ejpam-1726	80	3	-	-	PUNCT
ejpam-1726	80	4	tuple	tuple	NOUN
ejpam-1726	80	5	〈	〈	PROPN
ejpam-1726	80	6	a	a	PROPN
ejpam-1726	80	7	,	,	PUNCT
ejpam-1726	80	8	b	b	NOUN
ejpam-1726	80	9	,	,	PUNCT
ejpam-1726	80	10	a	a	DET
ejpam-1726	80	11	pb	pb	PROPN
ejpam-1726	80	12	,	,	PUNCT
ejpam-1726	80	13	b	b	PROPN
ejpam-1726	80	14	qa	qa	PROPN
ejpam-1726	80	15	,	,	PUNCT
ejpam-1726	80	16	τ,µ	τ,µ	ADJ
ejpam-1726	80	17	〉	〉	NOUN
ejpam-1726	80	18	is	be	AUX
ejpam-1726	80	19	said	say	VERB
ejpam-1726	80	20	to	to	PART
ejpam-1726	80	21	be	be	AUX
ejpam-1726	80	22	a	a	DET
ejpam-1726	80	23	morita	morita	NOUN
ejpam-1726	80	24	context	context	NOUN
ejpam-1726	80	25	,	,	PUNCT
ejpam-1726	80	26	where	where	SCONJ
ejpam-1726	80	27	a	a	PRON
ejpam-1726	80	28	and	and	CCONJ
ejpam-1726	80	29	b	b	NOUN
ejpam-1726	80	30	are	be	AUX
ejpam-1726	80	31	monoids	monoid	NOUN
ejpam-1726	80	32	,	,	PUNCT
ejpam-1726	80	33	apb	apb	PROPN
ejpam-1726	80	34	and	and	CCONJ
ejpam-1726	80	35	bqa	bqa	NOUN
ejpam-1726	80	36	are	be	AUX
ejpam-1726	80	37	biacts	biact	NOUN
ejpam-1726	80	38	,	,	PUNCT
ejpam-1726	80	39	τ	τ	PROPN
ejpam-1726	80	40	is	be	AUX
ejpam-1726	80	41	an	an	DET
ejpam-1726	80	42	a−	a−	PROPN
ejpam-1726	80	43	a	a	NOUN
ejpam-1726	80	44	-	-	PUNCT
ejpam-1726	80	45	morphism	morphism	NOUN
ejpam-1726	80	46	of	of	ADP
ejpam-1726	80	47	p	p	PROPN
ejpam-1726	80	48	⊗b	⊗b	PROPN
ejpam-1726	80	49	q	q	PUNCT
ejpam-1726	80	50	into	into	ADP
ejpam-1726	80	51	a	a	PRON
ejpam-1726	80	52	and	and	CCONJ
ejpam-1726	80	53	µ	µ	NOUN
ejpam-1726	80	54	is	be	AUX
ejpam-1726	80	55	an	an	DET
ejpam-1726	80	56	b	b	NOUN
ejpam-1726	80	57	−	−	NOUN
ejpam-1726	80	58	bmorphism	bmorphism	NOUN
ejpam-1726	80	59	of	of	ADP
ejpam-1726	80	60	q⊗a	q⊗a	NOUN
ejpam-1726	80	61	p	p	NOUN
ejpam-1726	80	62	into	into	ADP
ejpam-1726	80	63	b	b	NOUN
ejpam-1726	80	64	such	such	ADJ
ejpam-1726	80	65	that	that	SCONJ
ejpam-1726	80	66	if	if	SCONJ
ejpam-1726	80	67	we	we	PRON
ejpam-1726	80	68	write	write	VERB
ejpam-1726	80	69	(	(	PUNCT
ejpam-1726	80	70	p⊗	p⊗	NOUN
ejpam-1726	80	71	q)τ	q)τ	PUNCT
ejpam-1726	81	1	=	=	NOUN
ejpam-1726	81	2	<	<	X
ejpam-1726	81	3	p	p	X
ejpam-1726	81	4	,	,	PUNCT
ejpam-1726	81	5	q	q	X
ejpam-1726	81	6	>	>	X
ejpam-1726	81	7	and	and	CCONJ
ejpam-1726	81	8	(	(	PUNCT
ejpam-1726	81	9	q⊗	q⊗	NOUN
ejpam-1726	81	10	p)µ	p)µ	NOUN
ejpam-1726	82	1	=	=	PUNCT
ejpam-1726	83	1	[	[	X
ejpam-1726	83	2	q	q	X
ejpam-1726	83	3	,	,	PUNCT
ejpam-1726	83	4	p	p	X
ejpam-1726	83	5	]	]	X
ejpam-1726	83	6	,	,	PUNCT
ejpam-1726	83	7	then	then	ADV
ejpam-1726	83	8	for	for	ADP
ejpam-1726	83	9	all	all	DET
ejpam-1726	83	10	p	p	NOUN
ejpam-1726	83	11	,	,	PUNCT
ejpam-1726	83	12	p′	p′	NOUN
ejpam-1726	83	13	∈	∈	PROPN
ejpam-1726	83	14	p	p	NOUN
ejpam-1726	83	15	and	and	CCONJ
ejpam-1726	83	16	q	q	NOUN
ejpam-1726	83	17	,	,	PUNCT
ejpam-1726	83	18	q′	q′	NOUN
ejpam-1726	83	19	∈q	∈q	NOUN
ejpam-1726	83	20	we	we	PRON
ejpam-1726	83	21	have	have	VERB
ejpam-1726	83	22	<	<	X
ejpam-1726	83	23	p	p	X
ejpam-1726	83	24	,	,	PUNCT
ejpam-1726	83	25	q	q	X
ejpam-1726	83	26	>	>	X
ejpam-1726	83	27	p′	p′	PROPN
ejpam-1726	83	28	=	=	SYM
ejpam-1726	83	29	p[q	p[q	PROPN
ejpam-1726	83	30	,	,	PUNCT
ejpam-1726	83	31	p′	p′	NOUN
ejpam-1726	83	32	]	]	PUNCT
ejpam-1726	83	33	and	and	CCONJ
ejpam-1726	83	34	q	q	ADJ
ejpam-1726	83	35	<	<	X
ejpam-1726	83	36	p	p	X
ejpam-1726	83	37	,	,	PUNCT
ejpam-1726	83	38	q′	q′	NOUN
ejpam-1726	83	39	>	>	PUNCT
ejpam-1726	83	40	=	=	PUNCT
ejpam-1726	84	1	[	[	X
ejpam-1726	84	2	q	q	X
ejpam-1726	84	3	,	,	PUNCT
ejpam-1726	84	4	p]q′.	p]q′.	PROPN
ejpam-1726	84	5	s.	s.	PROPN
ejpam-1726	84	6	sardar	sardar	PROPN
ejpam-1726	84	7	,	,	PUNCT
ejpam-1726	84	8	s.	s.	PROPN
ejpam-1726	84	9	gupta	gupta	PROPN
ejpam-1726	84	10	,	,	PUNCT
ejpam-1726	84	11	k.	k.	PROPN
ejpam-1726	84	12	shum	shum	PROPN
ejpam-1726	84	13	/	/	SYM
ejpam-1726	84	14	eur	eur	PROPN
ejpam-1726	84	15	.	.	PUNCT
ejpam-1726	85	1	j.	j.	PROPN
ejpam-1726	85	2	pure	pure	PROPN
ejpam-1726	85	3	appl	appl	PROPN
ejpam-1726	85	4	.	.	PROPN
ejpam-1726	85	5	math	math	PROPN
ejpam-1726	85	6	,	,	PUNCT
ejpam-1726	85	7	6	6	NUM
ejpam-1726	85	8	(	(	PUNCT
ejpam-1726	85	9	2013	2013	NUM
ejpam-1726	85	10	)	)	PUNCT
ejpam-1726	85	11	,	,	PUNCT
ejpam-1726	85	12	1	1	NUM
ejpam-1726	85	13	-	-	SYM
ejpam-1726	85	14	10	10	NUM
ejpam-1726	85	15	4	4	NUM
ejpam-1726	85	16	this	this	DET
ejpam-1726	85	17	definition	definition	NOUN
ejpam-1726	85	18	is	be	AUX
ejpam-1726	85	19	analogous	analogous	ADJ
ejpam-1726	85	20	to	to	ADP
ejpam-1726	85	21	the	the	DET
ejpam-1726	85	22	case	case	NOUN
ejpam-1726	85	23	of	of	ADP
ejpam-1726	85	24	semigroups	semigroup	NOUN
ejpam-1726	85	25	in	in	ADP
ejpam-1726	85	26	[	[	X
ejpam-1726	85	27	19	19	NUM
ejpam-1726	85	28	]	]	PUNCT
ejpam-1726	85	29	.	.	PUNCT
ejpam-1726	86	1	it	it	PRON
ejpam-1726	86	2	can	can	AUX
ejpam-1726	86	3	be	be	AUX
ejpam-1726	86	4	easily	easily	ADV
ejpam-1726	86	5	seen	see	VERB
ejpam-1726	86	6	that	that	SCONJ
ejpam-1726	86	7	the	the	DET
ejpam-1726	86	8	morita	morita	PROPN
ejpam-1726	86	9	context	context	PROPN
ejpam-1726	86	10	presented	present	VERB
ejpam-1726	86	11	here	here	ADV
ejpam-1726	86	12	is	be	AUX
ejpam-1726	86	13	"	"	PUNCT
ejpam-1726	86	14	unitary	unitary	ADJ
ejpam-1726	86	15	"	"	PUNCT
ejpam-1726	86	16	in	in	ADP
ejpam-1726	86	17	the	the	DET
ejpam-1726	86	18	sense	sense	NOUN
ejpam-1726	86	19	given	give	VERB
ejpam-1726	86	20	by	by	ADP
ejpam-1726	86	21	s.talwar	s.talwar	NOUN
ejpam-1726	86	22	[	[	X
ejpam-1726	86	23	19	19	NUM
ejpam-1726	86	24	]	]	PUNCT
ejpam-1726	86	25	.	.	PUNCT
ejpam-1726	87	1	the	the	DET
ejpam-1726	87	2	following	following	ADJ
ejpam-1726	87	3	result	result	NOUN
ejpam-1726	87	4	is	be	AUX
ejpam-1726	87	5	a	a	DET
ejpam-1726	87	6	simple	simple	ADJ
ejpam-1726	87	7	consequence	consequence	NOUN
ejpam-1726	87	8	of	of	ADP
ejpam-1726	87	9	theorem	theorem	NOUN
ejpam-1726	87	10	8.3	8.3	NUM
ejpam-1726	87	11	of	of	ADP
ejpam-1726	87	12	s.	s.	PROPN
ejpam-1726	87	13	talwar	talwar	PROPN
ejpam-1726	87	14	in	in	ADP
ejpam-1726	87	15	[	[	X
ejpam-1726	87	16	19	19	NUM
ejpam-1726	87	17	]	]	PUNCT
ejpam-1726	87	18	when	when	SCONJ
ejpam-1726	87	19	the	the	DET
ejpam-1726	87	20	semigroups	semigroup	NOUN
ejpam-1726	87	21	are	be	AUX
ejpam-1726	87	22	replaced	replace	VERB
ejpam-1726	87	23	by	by	ADP
ejpam-1726	87	24	monoids	monoid	NOUN
ejpam-1726	87	25	.	.	PUNCT
ejpam-1726	88	1	theorem	theorem	NOUN
ejpam-1726	88	2	3	3	X
ejpam-1726	88	3	.	.	PUNCT
ejpam-1726	89	1	let	let	VERB
ejpam-1726	89	2	〈	〈	PROPN
ejpam-1726	89	3	r	r	NOUN
ejpam-1726	89	4	,	,	PUNCT
ejpam-1726	89	5	s	s	PART
ejpam-1726	89	6	,	,	PUNCT
ejpam-1726	89	7	r	r	NOUN
ejpam-1726	89	8	ps	ps	PROPN
ejpam-1726	89	9	,	,	PUNCT
ejpam-1726	89	10	s	s	PROPN
ejpam-1726	89	11	qr	qr	NOUN
ejpam-1726	89	12	,	,	PUNCT
ejpam-1726	89	13	τ,µ	τ,µ	ADJ
ejpam-1726	89	14	〉	〉	NOUN
ejpam-1726	89	15	be	be	VERB
ejpam-1726	89	16	a	a	DET
ejpam-1726	89	17	morita	morita	NOUN
ejpam-1726	89	18	context	context	NOUN
ejpam-1726	89	19	with	with	ADP
ejpam-1726	89	20	τ,µ	τ,µ	PROPN
ejpam-1726	89	21	surjective	surjective	NOUN
ejpam-1726	89	22	.	.	PUNCT
ejpam-1726	90	1	then	then	ADV
ejpam-1726	90	2	the	the	DET
ejpam-1726	90	3	following	follow	VERB
ejpam-1726	90	4	statements	statement	NOUN
ejpam-1726	90	5	hold	hold	VERB
ejpam-1726	90	6	:	:	PUNCT
ejpam-1726	90	7	(	(	PUNCT
ejpam-1726	90	8	i	i	NOUN
ejpam-1726	90	9	)	)	PUNCT
ejpam-1726	90	10	the	the	DET
ejpam-1726	90	11	categories	category	NOUN
ejpam-1726	90	12	r	r	NOUN
ejpam-1726	90	13	-	-	PUNCT
ejpam-1726	90	14	act	act	NOUN
ejpam-1726	90	15	and	and	CCONJ
ejpam-1726	90	16	s	s	NOUN
ejpam-1726	90	17	-	-	PUNCT
ejpam-1726	90	18	act	act	NOUN
ejpam-1726	90	19	are	be	AUX
ejpam-1726	90	20	equivalent	equivalent	ADJ
ejpam-1726	90	21	;	;	PUNCT
ejpam-1726	90	22	(	(	PUNCT
ejpam-1726	90	23	ii	ii	NOUN
ejpam-1726	90	24	)	)	PUNCT
ejpam-1726	90	25	s	s	PART
ejpam-1726	90	26	p	p	NOUN
ejpam-1726	90	27	and	and	CCONJ
ejpam-1726	90	28	rq	rq	NOUN
ejpam-1726	90	29	are	be	AUX
ejpam-1726	90	30	respectively	respectively	ADV
ejpam-1726	90	31	generators	generator	NOUN
ejpam-1726	90	32	for	for	ADP
ejpam-1726	90	33	s	s	NOUN
ejpam-1726	90	34	-	-	PUNCT
ejpam-1726	90	35	act	act	NOUN
ejpam-1726	90	36	and	and	CCONJ
ejpam-1726	90	37	r	r	NOUN
ejpam-1726	90	38	-	-	PUNCT
ejpam-1726	90	39	act	act	NOUN
ejpam-1726	90	40	;	;	PUNCT
ejpam-1726	90	41	(	(	PUNCT
ejpam-1726	90	42	iii	iii	X
ejpam-1726	90	43	)	)	PUNCT
ejpam-1726	90	44	r∼=	r∼=	NUM
ejpam-1726	90	45	ends(p	ends(p	NOUN
ejpam-1726	90	46	)	)	PUNCT
ejpam-1726	90	47	and	and	CCONJ
ejpam-1726	90	48	s	s	VERB
ejpam-1726	90	49	∼=	∼=	NOUN
ejpam-1726	90	50	endr(q	endr(q	NOUN
ejpam-1726	90	51	)	)	PUNCT
ejpam-1726	90	52	as	as	ADP
ejpam-1726	90	53	semigroups	semigroup	NOUN
ejpam-1726	90	54	;	;	PUNCT
ejpam-1726	90	55	(	(	PUNCT
ejpam-1726	90	56	iv	iv	X
ejpam-1726	90	57	)	)	PUNCT
ejpam-1726	90	58	s	s	AUX
ejpam-1726	90	59	pr	pr	NOUN
ejpam-1726	90	60	∼=	∼=	NOUN
ejpam-1726	90	61	homr(q	homr(q	NOUN
ejpam-1726	90	62	,	,	PUNCT
ejpam-1726	90	63	r	r	NOUN
ejpam-1726	90	64	)	)	PUNCT
ejpam-1726	90	65	and	and	CCONJ
ejpam-1726	90	66	rqs	rqs	PROPN
ejpam-1726	90	67	∼=	∼=	PART
ejpam-1726	90	68	homs(p	homs(p	NOUN
ejpam-1726	90	69	,	,	PUNCT
ejpam-1726	90	70	s	s	PART
ejpam-1726	90	71	)	)	PUNCT
ejpam-1726	90	72	as	as	ADP
ejpam-1726	90	73	biacts	biact	NOUN
ejpam-1726	90	74	.	.	PUNCT
ejpam-1726	91	1	theorem	theorem	ADJ
ejpam-1726	91	2	4	4	NUM
ejpam-1726	91	3	.	.	PUNCT
ejpam-1726	92	1	let	let	VERB
ejpam-1726	92	2	a	a	PRON
ejpam-1726	92	3	be	be	AUX
ejpam-1726	92	4	a	a	DET
ejpam-1726	92	5	γ	γ	NOUN
ejpam-1726	92	6	-	-	PUNCT
ejpam-1726	92	7	semigroup	semigroup	NOUN
ejpam-1726	92	8	with	with	ADP
ejpam-1726	92	9	unities	unity	NOUN
ejpam-1726	92	10	and	and	CCONJ
ejpam-1726	92	11	its	its	PRON
ejpam-1726	92	12	left	left	ADJ
ejpam-1726	92	13	and	and	CCONJ
ejpam-1726	92	14	right	right	ADJ
ejpam-1726	92	15	operator	operator	NOUN
ejpam-1726	92	16	monoids	monoid	NOUN
ejpam-1726	92	17	are	be	AUX
ejpam-1726	92	18	respectively	respectively	ADV
ejpam-1726	92	19	l	l	NOUN
ejpam-1726	92	20	and	and	CCONJ
ejpam-1726	92	21	r.	r.	PROPN
ejpam-1726	92	22	then	then	ADV
ejpam-1726	92	23	the	the	DET
ejpam-1726	92	24	following	follow	VERB
ejpam-1726	92	25	conditions	condition	NOUN
ejpam-1726	92	26	hold	hold	VERB
ejpam-1726	92	27	:	:	PUNCT
ejpam-1726	92	28	(	(	PUNCT
ejpam-1726	92	29	1	1	X
ejpam-1726	92	30	)	)	PUNCT
ejpam-1726	92	31	l	l	NOUN
ejpam-1726	92	32	and	and	CCONJ
ejpam-1726	92	33	r	r	NOUN
ejpam-1726	92	34	are	be	AUX
ejpam-1726	92	35	morita	morita	PROPN
ejpam-1726	92	36	equivalent	equivalent	NOUN
ejpam-1726	92	37	;	;	PUNCT
ejpam-1726	92	38	(	(	PUNCT
ejpam-1726	92	39	2	2	X
ejpam-1726	92	40	)	)	PUNCT
ejpam-1726	92	41	la	la	NOUN
ejpam-1726	92	42	and	and	CCONJ
ejpam-1726	92	43	rγ	rγ	PRON
ejpam-1726	92	44	are	be	AUX
ejpam-1726	92	45	respectively	respectively	ADV
ejpam-1726	92	46	generators	generator	NOUN
ejpam-1726	92	47	for	for	ADP
ejpam-1726	92	48	l	l	NOUN
ejpam-1726	92	49	-	-	NOUN
ejpam-1726	92	50	act	act	NOUN
ejpam-1726	92	51	and	and	CCONJ
ejpam-1726	92	52	r	r	NOUN
ejpam-1726	92	53	-	-	PUNCT
ejpam-1726	92	54	act	act	NOUN
ejpam-1726	92	55	;	;	PUNCT
ejpam-1726	92	56	(	(	PUNCT
ejpam-1726	92	57	3	3	X
ejpam-1726	92	58	)	)	PUNCT
ejpam-1726	92	59	r∼=	r∼=	NUM
ejpam-1726	92	60	endl(a	endl(a	X
ejpam-1726	92	61	)	)	PUNCT
ejpam-1726	92	62	and	and	CCONJ
ejpam-1726	92	63	l	l	NOUN
ejpam-1726	92	64	∼=	∼=	NOUN
ejpam-1726	92	65	endr(γ	endr(γ	NOUN
ejpam-1726	92	66	)	)	PUNCT
ejpam-1726	92	67	as	as	ADP
ejpam-1726	92	68	semigroups	semigroup	NOUN
ejpam-1726	92	69	;	;	PUNCT
ejpam-1726	92	70	(	(	PUNCT
ejpam-1726	92	71	4	4	X
ejpam-1726	92	72	)	)	PUNCT
ejpam-1726	92	73	lar	lar	ADJ
ejpam-1726	92	74	∼=	∼=	PROPN
ejpam-1726	92	75	homr(γ	homr(γ	PROPN
ejpam-1726	92	76	,	,	PUNCT
ejpam-1726	92	77	r	r	NOUN
ejpam-1726	92	78	)	)	PUNCT
ejpam-1726	92	79	and	and	CCONJ
ejpam-1726	92	80	rγl	rγl	VERB
ejpam-1726	92	81	∼=	∼=	PROPN
ejpam-1726	92	82	homl(a	homl(a	PROPN
ejpam-1726	92	83	,	,	PUNCT
ejpam-1726	92	84	l	l	NOUN
ejpam-1726	92	85	)	)	PUNCT
ejpam-1726	92	86	as	as	ADP
ejpam-1726	92	87	biacts	biact	NOUN
ejpam-1726	92	88	.	.	PUNCT
ejpam-1726	93	1	proof	proof	NOUN
ejpam-1726	93	2	.	.	PUNCT
ejpam-1726	94	1	we	we	PRON
ejpam-1726	94	2	first	first	ADV
ejpam-1726	94	3	prove	prove	VERB
ejpam-1726	94	4	that	that	SCONJ
ejpam-1726	94	5	lar	lar	ADJ
ejpam-1726	94	6	and	and	CCONJ
ejpam-1726	94	7	rγl	rγl	NOUN
ejpam-1726	94	8	are	be	AUX
ejpam-1726	94	9	biacts	biact	NOUN
ejpam-1726	94	10	.	.	PUNCT
ejpam-1726	95	1	for	for	ADP
ejpam-1726	95	2	this	this	PRON
ejpam-1726	95	3	we	we	PRON
ejpam-1726	95	4	define	define	VERB
ejpam-1726	95	5	l×	l×	PROPN
ejpam-1726	95	6	a→	a→	PUNCT
ejpam-1726	95	7	a	a	PRON
ejpam-1726	95	8	and	and	CCONJ
ejpam-1726	95	9	a×	a×	PROPN
ejpam-1726	95	10	r→	r→	VERB
ejpam-1726	95	11	a	a	PRON
ejpam-1726	95	12	respectively	respectively	ADV
ejpam-1726	95	13	as	as	SCONJ
ejpam-1726	95	14	follows	follow	VERB
ejpam-1726	95	15	[	[	X
ejpam-1726	95	16	a	a	X
ejpam-1726	95	17	,	,	PUNCT
ejpam-1726	95	18	α]b	α]b	NOUN
ejpam-1726	95	19	:	:	PUNCT
ejpam-1726	95	20	=	=	PUNCT
ejpam-1726	95	21	aαb	aαb	NOUN
ejpam-1726	95	22	and	and	CCONJ
ejpam-1726	95	23	a[β	a[β	PROPN
ejpam-1726	95	24	,	,	PUNCT
ejpam-1726	96	1	b	b	X
ejpam-1726	96	2	]	]	X
ejpam-1726	96	3	:	:	PUNCT
ejpam-1726	96	4	=	=	PUNCT
ejpam-1726	96	5	aβ	aβ	PROPN
ejpam-1726	96	6	b.	b.	PROPN
ejpam-1726	96	7	then	then	ADV
ejpam-1726	96	8	for	for	ADP
ejpam-1726	96	9	all	all	DET
ejpam-1726	96	10	a	a	DET
ejpam-1726	96	11	,	,	PUNCT
ejpam-1726	96	12	b	b	NOUN
ejpam-1726	96	13	,	,	PUNCT
ejpam-1726	96	14	c	c	PROPN
ejpam-1726	96	15	∈	∈	PROPN
ejpam-1726	96	16	a	a	PRON
ejpam-1726	96	17	and	and	CCONJ
ejpam-1726	96	18	α	α	NOUN
ejpam-1726	96	19	,	,	PUNCT
ejpam-1726	96	20	β	β	PROPN
ejpam-1726	96	21	∈	∈	PROPN
ejpam-1726	96	22	γ	γ	X
ejpam-1726	96	23	,	,	PUNCT
ejpam-1726	96	24	we	we	PRON
ejpam-1726	96	25	have	have	VERB
ejpam-1726	96	26	a([α	a([α	NOUN
ejpam-1726	96	27	,	,	PUNCT
ejpam-1726	96	28	b][β	b][β	NOUN
ejpam-1726	96	29	,	,	PUNCT
ejpam-1726	96	30	c	c	X
ejpam-1726	96	31	]	]	X
ejpam-1726	96	32	)	)	PUNCT
ejpam-1726	96	33	=	=	SYM
ejpam-1726	96	34	a[α	a[α	PROPN
ejpam-1726	96	35	,	,	PUNCT
ejpam-1726	96	36	bβ	bβ	NOUN
ejpam-1726	96	37	c	c	NOUN
ejpam-1726	96	38	]	]	X
ejpam-1726	96	39	=	=	PUNCT
ejpam-1726	96	40	aα(bβ	aα(bβ	PROPN
ejpam-1726	96	41	c	c	PROPN
ejpam-1726	96	42	)	)	PUNCT
ejpam-1726	96	43	=	=	SYM
ejpam-1726	96	44	(	(	PUNCT
ejpam-1726	96	45	aαb)β	aαb)β	NOUN
ejpam-1726	96	46	c	c	NOUN
ejpam-1726	96	47	=	=	PUNCT
ejpam-1726	96	48	(	(	PUNCT
ejpam-1726	96	49	a[α	a[α	PROPN
ejpam-1726	96	50	,	,	PUNCT
ejpam-1726	96	51	b])[β	b])[β	X
ejpam-1726	96	52	,	,	PUNCT
ejpam-1726	96	53	c	c	X
ejpam-1726	96	54	]	]	PUNCT
ejpam-1726	96	55	.	.	PUNCT
ejpam-1726	97	1	hence	hence	ADV
ejpam-1726	97	2	a	a	PRON
ejpam-1726	97	3	is	be	AUX
ejpam-1726	97	4	a	a	DET
ejpam-1726	97	5	right	right	ADJ
ejpam-1726	97	6	r	r	NOUN
ejpam-1726	97	7	-	-	NOUN
ejpam-1726	97	8	act	act	NOUN
ejpam-1726	97	9	.	.	PUNCT
ejpam-1726	98	1	similarly	similarly	ADV
ejpam-1726	98	2	we	we	PRON
ejpam-1726	98	3	can	can	AUX
ejpam-1726	98	4	show	show	VERB
ejpam-1726	98	5	that	that	SCONJ
ejpam-1726	98	6	a	a	PRON
ejpam-1726	98	7	is	be	AUX
ejpam-1726	98	8	a	a	DET
ejpam-1726	98	9	left	left	ADJ
ejpam-1726	98	10	l	l	NOUN
ejpam-1726	98	11	-	-	NOUN
ejpam-1726	98	12	act	act	NOUN
ejpam-1726	98	13	.	.	PUNCT
ejpam-1726	99	1	that	that	PRON
ejpam-1726	99	2	a	a	PRON
ejpam-1726	99	3	is	be	AUX
ejpam-1726	99	4	a	a	DET
ejpam-1726	99	5	biact	biact	NOUN
ejpam-1726	99	6	follows	follow	VERB
ejpam-1726	99	7	from	from	ADP
ejpam-1726	99	8	the	the	DET
ejpam-1726	99	9	generalized	generalize	VERB
ejpam-1726	99	10	associative	associative	ADJ
ejpam-1726	99	11	property(gap	property(gap	NOUN
ejpam-1726	99	12	)	)	PUNCT
ejpam-1726	99	13	of	of	ADP
ejpam-1726	99	14	the	the	DET
ejpam-1726	99	15	γ	γ	PROPN
ejpam-1726	99	16	-	-	PUNCT
ejpam-1726	99	17	semigroup	semigroup	ADJ
ejpam-1726	99	18	a.	a.	NOUN
ejpam-1726	99	19	similarly	similarly	ADV
ejpam-1726	99	20	we	we	PRON
ejpam-1726	99	21	can	can	AUX
ejpam-1726	99	22	show	show	VERB
ejpam-1726	99	23	that	that	SCONJ
ejpam-1726	99	24	rγl	rγl	NOUN
ejpam-1726	99	25	is	be	AUX
ejpam-1726	99	26	a	a	DET
ejpam-1726	99	27	biact	biact	NOUN
ejpam-1726	99	28	.	.	PUNCT
ejpam-1726	100	1	now	now	ADV
ejpam-1726	100	2	consider	consider	VERB
ejpam-1726	100	3	the	the	DET
ejpam-1726	100	4	mappings	mapping	NOUN
ejpam-1726	100	5	τ	τ	X
ejpam-1726	100	6	:	:	PUNCT
ejpam-1726	100	7	a⊗	a⊗	PROPN
ejpam-1726	100	8	γ→	γ→	PROPN
ejpam-1726	100	9	l	l	PROPN
ejpam-1726	100	10	and	and	CCONJ
ejpam-1726	100	11	µ	µ	NOUN
ejpam-1726	100	12	:	:	PUNCT
ejpam-1726	100	13	γ⊗	γ⊗	NOUN
ejpam-1726	100	14	a→	a→	PUNCT
ejpam-1726	100	15	r	r	NOUN
ejpam-1726	100	16	s.	s.	PROPN
ejpam-1726	100	17	sardar	sardar	PROPN
ejpam-1726	100	18	,	,	PUNCT
ejpam-1726	100	19	s.	s.	PROPN
ejpam-1726	100	20	gupta	gupta	PROPN
ejpam-1726	100	21	,	,	PUNCT
ejpam-1726	100	22	k.	k.	PROPN
ejpam-1726	100	23	shum	shum	PROPN
ejpam-1726	100	24	/	/	SYM
ejpam-1726	100	25	eur	eur	PROPN
ejpam-1726	100	26	.	.	PUNCT
ejpam-1726	101	1	j.	j.	PROPN
ejpam-1726	101	2	pure	pure	PROPN
ejpam-1726	101	3	appl	appl	PROPN
ejpam-1726	101	4	.	.	PROPN
ejpam-1726	101	5	math	math	PROPN
ejpam-1726	101	6	,	,	PUNCT
ejpam-1726	101	7	6	6	NUM
ejpam-1726	101	8	(	(	PUNCT
ejpam-1726	101	9	2013	2013	NUM
ejpam-1726	101	10	)	)	PUNCT
ejpam-1726	101	11	,	,	PUNCT
ejpam-1726	101	12	1	1	NUM
ejpam-1726	101	13	-	-	SYM
ejpam-1726	101	14	10	10	NUM
ejpam-1726	101	15	5	5	NUM
ejpam-1726	101	16	respectively	respectively	ADV
ejpam-1726	101	17	defined	define	VERB
ejpam-1726	101	18	as	as	SCONJ
ejpam-1726	101	19	follows	follow	VERB
ejpam-1726	101	20	(	(	PUNCT
ejpam-1726	101	21	a⊗α)τ=	a⊗α)τ=	X
ejpam-1726	101	22	[	[	X
ejpam-1726	101	23	a	a	X
ejpam-1726	101	24	,	,	PUNCT
ejpam-1726	101	25	α	α	X
ejpam-1726	101	26	]	]	PUNCT
ejpam-1726	101	27	and	and	CCONJ
ejpam-1726	101	28	(	(	PUNCT
ejpam-1726	101	29	α⊗	α⊗	NOUN
ejpam-1726	101	30	a)µ=	a)µ=	NOUN
ejpam-1726	102	1	[	[	X
ejpam-1726	102	2	α	α	NOUN
ejpam-1726	102	3	,	,	PUNCT
ejpam-1726	102	4	a	a	PRON
ejpam-1726	102	5	]	]	X
ejpam-1726	102	6	.	.	PUNCT
ejpam-1726	103	1	now	now	ADV
ejpam-1726	103	2	we	we	PRON
ejpam-1726	103	3	prove	prove	VERB
ejpam-1726	103	4	that	that	SCONJ
ejpam-1726	103	5	the	the	DET
ejpam-1726	103	6	mapping	mapping	NOUN
ejpam-1726	103	7	τ	τ	X
ejpam-1726	103	8	is	be	AUX
ejpam-1726	103	9	well	well	ADV
ejpam-1726	103	10	-	-	PUNCT
ejpam-1726	103	11	defined	define	VERB
ejpam-1726	103	12	.	.	PUNCT
ejpam-1726	104	1	let	let	VERB
ejpam-1726	104	2	a	a	DET
ejpam-1726	104	3	⊗	⊗	PROPN
ejpam-1726	104	4	α	α	NOUN
ejpam-1726	104	5	=	=	SYM
ejpam-1726	104	6	b	b	PROPN
ejpam-1726	104	7	⊗	⊗	NUM
ejpam-1726	104	8	β	β	X
ejpam-1726	104	9	.	.	PUNCT
ejpam-1726	105	1	then	then	ADV
ejpam-1726	105	2	either	either	CCONJ
ejpam-1726	105	3	(	(	PUNCT
ejpam-1726	105	4	a	a	DET
ejpam-1726	105	5	,	,	PUNCT
ejpam-1726	105	6	α	α	NOUN
ejpam-1726	105	7	)	)	PUNCT
ejpam-1726	105	8	=	=	SYM
ejpam-1726	105	9	(	(	PUNCT
ejpam-1726	105	10	b	b	NOUN
ejpam-1726	105	11	,	,	PUNCT
ejpam-1726	105	12	β	β	NOUN
ejpam-1726	105	13	)	)	PUNCT
ejpam-1726	105	14	in	in	ADP
ejpam-1726	105	15	which	which	DET
ejpam-1726	105	16	case	case	NOUN
ejpam-1726	105	17	[	[	X
ejpam-1726	105	18	a	a	X
ejpam-1726	105	19	,	,	PUNCT
ejpam-1726	105	20	α	α	NOUN
ejpam-1726	105	21	]	]	X
ejpam-1726	106	1	=	=	PUNCT
ejpam-1726	107	1	[	[	X
ejpam-1726	107	2	b	b	X
ejpam-1726	107	3	,	,	PUNCT
ejpam-1726	107	4	β	β	X
ejpam-1726	107	5	]	]	X
ejpam-1726	107	6	;	;	PUNCT
ejpam-1726	107	7	or	or	CCONJ
ejpam-1726	107	8	for	for	ADP
ejpam-1726	107	9	some	some	DET
ejpam-1726	107	10	positive	positive	ADJ
ejpam-1726	107	11	integer	integer	NOUN
ejpam-1726	107	12	n≥	n≥	NOUN
ejpam-1726	107	13	2	2	NUM
ejpam-1726	107	14	there	there	PRON
ejpam-1726	107	15	is	be	VERB
ejpam-1726	107	16	a	a	DET
ejpam-1726	107	17	sequence	sequence	NOUN
ejpam-1726	107	18	(	(	PUNCT
ejpam-1726	107	19	a	a	DET
ejpam-1726	107	20	,	,	PUNCT
ejpam-1726	107	21	α	α	NOUN
ejpam-1726	107	22	)	)	PUNCT
ejpam-1726	107	23	=	=	SYM
ejpam-1726	107	24	(	(	PUNCT
ejpam-1726	107	25	a1,α1)→	a1,α1)→	PROPN
ejpam-1726	107	26	(	(	PUNCT
ejpam-1726	107	27	a2,α2)→	a2,α2)→	PROPN
ejpam-1726	107	28	.	.	PUNCT
ejpam-1726	107	29	.	.	PUNCT
ejpam-1726	108	1	.→	.→	PUNCT
ejpam-1726	108	2	(	(	PUNCT
ejpam-1726	108	3	an	an	DET
ejpam-1726	108	4	,	,	PUNCT
ejpam-1726	108	5	αn	αn	NOUN
ejpam-1726	108	6	)	)	PUNCT
ejpam-1726	108	7	=	=	SYM
ejpam-1726	109	1	(	(	PUNCT
ejpam-1726	109	2	b	b	NOUN
ejpam-1726	109	3	,	,	PUNCT
ejpam-1726	109	4	β	β	NOUN
ejpam-1726	109	5	)	)	PUNCT
ejpam-1726	109	6	in	in	ADP
ejpam-1726	109	7	which	which	PRON
ejpam-1726	109	8	for	for	ADP
ejpam-1726	109	9	each	each	DET
ejpam-1726	109	10	i	i	PRON
ejpam-1726	109	11	∈	∈	PROPN
ejpam-1726	109	12	{	{	PUNCT
ejpam-1726	109	13	1	1	NUM
ejpam-1726	109	14	,	,	PUNCT
ejpam-1726	109	15	.	.	PUNCT
ejpam-1726	109	16	.	.	PUNCT
ejpam-1726	110	1	.	.	PUNCT
ejpam-1726	111	1	,	,	PUNCT
ejpam-1726	111	2	n−	n−	NOUN
ejpam-1726	111	3	1	1	NUM
ejpam-1726	111	4	}	}	PUNCT
ejpam-1726	111	5	either	either	CCONJ
ejpam-1726	111	6	(	(	PUNCT
ejpam-1726	111	7	(	(	PUNCT
ejpam-1726	111	8	ai	ai	VERB
ejpam-1726	111	9	,	,	PUNCT
ejpam-1726	111	10	αi	αi	NOUN
ejpam-1726	111	11	)	)	PUNCT
ejpam-1726	111	12	,	,	PUNCT
ejpam-1726	111	13	(	(	PUNCT
ejpam-1726	111	14	ai+1,αi+1	ai+1,αi+1	ADJ
ejpam-1726	111	15	)	)	PUNCT
ejpam-1726	111	16	)	)	PUNCT
ejpam-1726	112	1	∈	∈	PROPN
ejpam-1726	112	2	σ	σ	NOUN
ejpam-1726	112	3	or	or	CCONJ
ejpam-1726	112	4	(	(	PUNCT
ejpam-1726	112	5	(	(	PUNCT
ejpam-1726	112	6	ai+1,αi+1	ai+1,αi+1	NOUN
ejpam-1726	112	7	)	)	PUNCT
ejpam-1726	112	8	,	,	PUNCT
ejpam-1726	112	9	(	(	PUNCT
ejpam-1726	112	10	ai	ai	NOUN
ejpam-1726	112	11	,	,	PUNCT
ejpam-1726	112	12	αi	αi	NOUN
ejpam-1726	112	13	)	)	PUNCT
ejpam-1726	112	14	)	)	PUNCT
ejpam-1726	113	1	∈	∈	PROPN
ejpam-1726	113	2	σ	σ	PROPN
ejpam-1726	113	3	.	.	PUNCT
ejpam-1726	114	1	here	here	ADV
ejpam-1726	114	2	(	(	PUNCT
ejpam-1726	114	3	(	(	PUNCT
ejpam-1726	114	4	ai	ai	VERB
ejpam-1726	114	5	,	,	PUNCT
ejpam-1726	114	6	αi	αi	NOUN
ejpam-1726	114	7	)	)	PUNCT
ejpam-1726	114	8	,	,	PUNCT
ejpam-1726	114	9	(	(	PUNCT
ejpam-1726	114	10	ai+1,αi+1	ai+1,αi+1	ADJ
ejpam-1726	114	11	)	)	PUNCT
ejpam-1726	114	12	)	)	PUNCT
ejpam-1726	115	1	∈	∈	PROPN
ejpam-1726	115	2	σ	σ	NOUN
ejpam-1726	115	3	means	mean	VERB
ejpam-1726	115	4	that	that	SCONJ
ejpam-1726	115	5	for	for	ADP
ejpam-1726	115	6	some	some	DET
ejpam-1726	115	7	ri	ri	NOUN
ejpam-1726	115	8	∈	∈	PROPN
ejpam-1726	115	9	r	r	NOUN
ejpam-1726	115	10	,	,	PUNCT
ejpam-1726	115	11	ai	ai	NOUN
ejpam-1726	115	12	=	=	PUNCT
ejpam-1726	115	13	ai+1ri	ai+1ri	NOUN
ejpam-1726	115	14	,	,	PUNCT
ejpam-1726	115	15	αi+1	αi+1	NOUN
ejpam-1726	115	16	=	=	NOUN
ejpam-1726	115	17	riαi	riαi	NOUN
ejpam-1726	115	18	.	.	PUNCT
ejpam-1726	116	1	then	then	ADV
ejpam-1726	116	2	for	for	ADP
ejpam-1726	116	3	all	all	DET
ejpam-1726	116	4	c	c	NOUN
ejpam-1726	116	5	∈	∈	PROPN
ejpam-1726	116	6	a	a	DET
ejpam-1726	116	7	aiαic	aiαic	NOUN
ejpam-1726	116	8	=	=	PUNCT
ejpam-1726	116	9	(	(	PUNCT
ejpam-1726	116	10	ai+1ri)αic	ai+1ri)αic	NOUN
ejpam-1726	116	11	=	=	SYM
ejpam-1726	116	12	ai+1(riαi)c	ai+1(riαi)c	PROPN
ejpam-1726	116	13	=	=	SYM
ejpam-1726	116	14	ai+1αi+1c	ai+1αi+1c	NOUN
ejpam-1726	116	15	.	.	PUNCT
ejpam-1726	117	1	also	also	ADV
ejpam-1726	117	2	for	for	ADP
ejpam-1726	117	3	all	all	DET
ejpam-1726	117	4	γ	γ	PROPN
ejpam-1726	117	5	∈	∈	PROPN
ejpam-1726	117	6	γ	γ	X
ejpam-1726	117	7	,	,	PUNCT
ejpam-1726	117	8	γaiαi	γaiαi	NOUN
ejpam-1726	117	9	=	=	SYM
ejpam-1726	117	10	γ(ai+1ri)αi	γ(ai+1ri)αi	NOUN
ejpam-1726	117	11	=	=	SYM
ejpam-1726	117	12	γai+1(riαi	γai+1(riαi	PROPN
ejpam-1726	117	13	)	)	PUNCT
ejpam-1726	117	14	=	=	PUNCT
ejpam-1726	117	15	γai+1αi+1	γai+1αi+1	PROPN
ejpam-1726	117	16	.	.	PUNCT
ejpam-1726	118	1	so	so	ADV
ejpam-1726	118	2	we	we	PRON
ejpam-1726	118	3	have	have	VERB
ejpam-1726	118	4	[	[	X
ejpam-1726	118	5	ai	ai	VERB
ejpam-1726	118	6	,	,	PUNCT
ejpam-1726	118	7	αi	αi	X
ejpam-1726	118	8	]	]	PUNCT
ejpam-1726	118	9	=	=	PUNCT
ejpam-1726	119	1	[	[	X
ejpam-1726	119	2	ai+1,αi+1	ai+1,αi+1	X
ejpam-1726	119	3	]	]	X
ejpam-1726	119	4	for	for	ADP
ejpam-1726	119	5	each	each	DET
ejpam-1726	119	6	i	i	PRON
ejpam-1726	119	7	∈	∈	PROPN
ejpam-1726	119	8	{	{	PUNCT
ejpam-1726	119	9	1	1	NUM
ejpam-1726	119	10	,	,	PUNCT
ejpam-1726	119	11	.	.	PUNCT
ejpam-1726	119	12	.	.	PUNCT
ejpam-1726	119	13	.	.	PUNCT
ejpam-1726	120	1	,	,	PUNCT
ejpam-1726	120	2	n−	n−	NOUN
ejpam-1726	120	3	1	1	NUM
ejpam-1726	120	4	}	}	PUNCT
ejpam-1726	120	5	.	.	PUNCT
ejpam-1726	121	1	the	the	DET
ejpam-1726	121	2	same	same	ADJ
ejpam-1726	121	3	happens	happen	VERB
ejpam-1726	121	4	for	for	ADP
ejpam-1726	121	5	the	the	DET
ejpam-1726	121	6	other	other	ADJ
ejpam-1726	121	7	case	case	NOUN
ejpam-1726	121	8	also	also	ADV
ejpam-1726	121	9	.	.	PUNCT
ejpam-1726	122	1	using	use	VERB
ejpam-1726	122	2	these	these	DET
ejpam-1726	122	3	results	result	NOUN
ejpam-1726	122	4	we	we	PRON
ejpam-1726	122	5	have	have	VERB
ejpam-1726	122	6	[	[	X
ejpam-1726	122	7	a	a	X
ejpam-1726	122	8	,	,	PUNCT
ejpam-1726	122	9	α	α	NOUN
ejpam-1726	122	10	]	]	X
ejpam-1726	122	11	=	=	PUNCT
ejpam-1726	123	1	[	[	X
ejpam-1726	123	2	a1,α1	a1,α1	X
ejpam-1726	123	3	]	]	X
ejpam-1726	123	4	=	=	PUNCT
ejpam-1726	123	5	·	·	PUNCT
ejpam-1726	123	6	·	·	PUNCT
ejpam-1726	123	7	·	·	PUNCT
ejpam-1726	123	8	=	=	PUNCT
ejpam-1726	124	1	[	[	X
ejpam-1726	124	2	an	an	DET
ejpam-1726	124	3	,	,	PUNCT
ejpam-1726	124	4	αn	αn	NOUN
ejpam-1726	124	5	]	]	X
ejpam-1726	124	6	=	=	PUNCT
ejpam-1726	125	1	[	[	X
ejpam-1726	125	2	b	b	X
ejpam-1726	125	3	,	,	PUNCT
ejpam-1726	125	4	β	β	X
ejpam-1726	125	5	]	]	X
ejpam-1726	125	6	.	.	PUNCT
ejpam-1726	126	1	similarly	similarly	ADV
ejpam-1726	126	2	µ	µ	X
ejpam-1726	126	3	is	be	AUX
ejpam-1726	126	4	also	also	ADV
ejpam-1726	126	5	well	well	ADV
ejpam-1726	126	6	defined	define	VERB
ejpam-1726	126	7	.	.	PUNCT
ejpam-1726	127	1	again	again	ADV
ejpam-1726	127	2	,	,	PUNCT
ejpam-1726	127	3	by	by	ADP
ejpam-1726	127	4	the	the	DET
ejpam-1726	127	5	definition	definition	NOUN
ejpam-1726	127	6	it	it	PRON
ejpam-1726	127	7	is	be	AUX
ejpam-1726	127	8	clear	clear	ADJ
ejpam-1726	127	9	that	that	SCONJ
ejpam-1726	127	10	these	these	DET
ejpam-1726	127	11	mappings	mapping	NOUN
ejpam-1726	127	12	are	be	AUX
ejpam-1726	127	13	surjective	surjective	ADJ
ejpam-1726	127	14	.	.	PUNCT
ejpam-1726	128	1	now	now	ADV
ejpam-1726	128	2	we	we	PRON
ejpam-1726	128	3	see	see	VERB
ejpam-1726	128	4	that	that	PRON
ejpam-1726	128	5	for	for	ADP
ejpam-1726	128	6	all	all	DET
ejpam-1726	128	7	a	a	PRON
ejpam-1726	128	8	,	,	PUNCT
ejpam-1726	128	9	b	b	X
ejpam-1726	128	10	∈	∈	PROPN
ejpam-1726	128	11	a	a	DET
ejpam-1726	128	12	,	,	PUNCT
ejpam-1726	128	13	α	α	X
ejpam-1726	128	14	,	,	PUNCT
ejpam-1726	128	15	β	β	PROPN
ejpam-1726	128	16	∈	∈	PROPN
ejpam-1726	128	17	γ	γ	X
ejpam-1726	128	18	,	,	PUNCT
ejpam-1726	128	19	(	(	PUNCT
ejpam-1726	128	20	a⊗α)τb	a⊗α)τb	PROPN
ejpam-1726	128	21	=	=	PUNCT
ejpam-1726	129	1	[	[	X
ejpam-1726	129	2	a	a	X
ejpam-1726	129	3	,	,	PUNCT
ejpam-1726	129	4	α]b	α]b	NUM
ejpam-1726	129	5	=	=	NOUN
ejpam-1726	129	6	aαb	aαb	NOUN
ejpam-1726	129	7	=	=	SYM
ejpam-1726	129	8	a[α	a[α	PROPN
ejpam-1726	129	9	,	,	PUNCT
ejpam-1726	129	10	b	b	AUX
ejpam-1726	129	11	]	]	X
ejpam-1726	129	12	=	=	PUNCT
ejpam-1726	129	13	a(α⊗	a(α⊗	PROPN
ejpam-1726	129	14	b)µand	b)µand	PROPN
ejpam-1726	129	15	α(a⊗	α(a⊗	ADJ
ejpam-1726	129	16	β)τ	β)τ	PUNCT
ejpam-1726	129	17	=	=	SYM
ejpam-1726	129	18	α[a	α[a	PROPN
ejpam-1726	129	19	,	,	PUNCT
ejpam-1726	129	20	β	β	X
ejpam-1726	129	21	]	]	X
ejpam-1726	129	22	=	=	SYM
ejpam-1726	129	23	αaβ	αaβ	NOUN
ejpam-1726	129	24	=	=	PUNCT
ejpam-1726	130	1	[	[	X
ejpam-1726	130	2	α	α	NOUN
ejpam-1726	130	3	,	,	PUNCT
ejpam-1726	130	4	a]β	a]β	NOUN
ejpam-1726	130	5	=	=	SYM
ejpam-1726	130	6	(	(	PUNCT
ejpam-1726	130	7	α⊗	α⊗	NOUN
ejpam-1726	130	8	a)µβ	a)µβ	PROPN
ejpam-1726	130	9	.	.	PUNCT
ejpam-1726	131	1	thus	thus	ADV
ejpam-1726	131	2	〈	〈	PROPN
ejpam-1726	131	3	l	l	NOUN
ejpam-1726	131	4	,	,	PUNCT
ejpam-1726	131	5	r	r	NOUN
ejpam-1726	131	6	,	,	PUNCT
ejpam-1726	131	7	l	l	PROPN
ejpam-1726	131	8	ar	ar	PROPN
ejpam-1726	131	9	,	,	PUNCT
ejpam-1726	131	10	r	r	NOUN
ejpam-1726	131	11	γl	γl	NOUN
ejpam-1726	131	12	,	,	PUNCT
ejpam-1726	131	13	τ,µ	τ,µ	ADJ
ejpam-1726	131	14	〉	〉	NOUN
ejpam-1726	131	15	is	be	AUX
ejpam-1726	131	16	a	a	DET
ejpam-1726	131	17	morita	morita	PROPN
ejpam-1726	131	18	context	context	NOUN
ejpam-1726	131	19	with	with	ADP
ejpam-1726	131	20	τ	τ	PROPN
ejpam-1726	131	21	and	and	CCONJ
ejpam-1726	131	22	µ	µ	X
ejpam-1726	131	23	surjective	surjective	NOUN
ejpam-1726	131	24	.	.	PUNCT
ejpam-1726	132	1	now	now	ADV
ejpam-1726	132	2	from	from	ADP
ejpam-1726	132	3	theorem	theorem	ADJ
ejpam-1726	132	4	3	3	NUM
ejpam-1726	132	5	we	we	PRON
ejpam-1726	132	6	can	can	AUX
ejpam-1726	132	7	prove	prove	VERB
ejpam-1726	132	8	the	the	DET
ejpam-1726	132	9	following	following	ADJ
ejpam-1726	132	10	statements	statement	NOUN
ejpam-1726	132	11	:	:	PUNCT
ejpam-1726	132	12	(	(	PUNCT
ejpam-1726	132	13	1	1	X
ejpam-1726	132	14	)	)	PUNCT
ejpam-1726	132	15	l	l	NOUN
ejpam-1726	132	16	and	and	CCONJ
ejpam-1726	132	17	r	r	NOUN
ejpam-1726	132	18	are	be	AUX
ejpam-1726	132	19	morita	morita	PROPN
ejpam-1726	132	20	equivalent	equivalent	NOUN
ejpam-1726	132	21	;	;	PUNCT
ejpam-1726	132	22	(	(	PUNCT
ejpam-1726	132	23	2	2	X
ejpam-1726	132	24	)	)	PUNCT
ejpam-1726	132	25	la	la	NOUN
ejpam-1726	132	26	and	and	CCONJ
ejpam-1726	132	27	rγ	rγ	PRON
ejpam-1726	132	28	are	be	AUX
ejpam-1726	132	29	respectively	respectively	ADV
ejpam-1726	132	30	the	the	DET
ejpam-1726	132	31	generators	generator	NOUN
ejpam-1726	132	32	for	for	ADP
ejpam-1726	132	33	the	the	DET
ejpam-1726	132	34	l	l	NOUN
ejpam-1726	132	35	-	-	NOUN
ejpam-1726	132	36	act	act	NOUN
ejpam-1726	132	37	and	and	CCONJ
ejpam-1726	132	38	the	the	DET
ejpam-1726	132	39	r	r	NOUN
ejpam-1726	132	40	-	-	PUNCT
ejpam-1726	132	41	act	act	NOUN
ejpam-1726	132	42	;	;	PUNCT
ejpam-1726	132	43	(	(	PUNCT
ejpam-1726	132	44	3	3	X
ejpam-1726	132	45	)	)	PUNCT
ejpam-1726	132	46	r∼=	r∼=	NUM
ejpam-1726	132	47	endl(a	endl(a	X
ejpam-1726	132	48	)	)	PUNCT
ejpam-1726	132	49	and	and	CCONJ
ejpam-1726	132	50	l	l	NOUN
ejpam-1726	132	51	∼=	∼=	NOUN
ejpam-1726	132	52	endr(γ	endr(γ	NOUN
ejpam-1726	132	53	)	)	PUNCT
ejpam-1726	132	54	as	as	ADP
ejpam-1726	132	55	semigroups	semigroup	NOUN
ejpam-1726	132	56	;	;	PUNCT
ejpam-1726	132	57	(	(	PUNCT
ejpam-1726	132	58	4	4	X
ejpam-1726	132	59	)	)	PUNCT
ejpam-1726	132	60	lar	lar	ADJ
ejpam-1726	132	61	∼=	∼=	PROPN
ejpam-1726	132	62	homr(γ	homr(γ	PROPN
ejpam-1726	132	63	,	,	PUNCT
ejpam-1726	132	64	r	r	NOUN
ejpam-1726	132	65	)	)	PUNCT
ejpam-1726	132	66	and	and	CCONJ
ejpam-1726	132	67	rγl	rγl	VERB
ejpam-1726	132	68	∼=	∼=	PROPN
ejpam-1726	132	69	homl(a	homl(a	PROPN
ejpam-1726	132	70	,	,	PUNCT
ejpam-1726	132	71	l	l	NOUN
ejpam-1726	132	72	)	)	PUNCT
ejpam-1726	132	73	as	as	ADP
ejpam-1726	132	74	biacts	biact	NOUN
ejpam-1726	132	75	.	.	PUNCT
ejpam-1726	133	1	hence	hence	ADV
ejpam-1726	133	2	the	the	DET
ejpam-1726	133	3	theorem	theorem	NOUN
ejpam-1726	133	4	is	be	AUX
ejpam-1726	133	5	proved	prove	VERB
ejpam-1726	133	6	.	.	PUNCT
ejpam-1726	134	1	in	in	ADP
ejpam-1726	134	2	the	the	DET
ejpam-1726	134	3	following	follow	VERB
ejpam-1726	134	4	theorem	theorem	NOUN
ejpam-1726	134	5	we	we	PRON
ejpam-1726	134	6	consider	consider	VERB
ejpam-1726	134	7	two	two	NUM
ejpam-1726	134	8	monoids	monoid	NOUN
ejpam-1726	134	9	l	l	NOUN
ejpam-1726	134	10	and	and	CCONJ
ejpam-1726	134	11	r	r	NOUN
ejpam-1726	134	12	which	which	PRON
ejpam-1726	134	13	are	be	AUX
ejpam-1726	134	14	morita	morita	PROPN
ejpam-1726	134	15	equivalent	equivalent	NOUN
ejpam-1726	134	16	.	.	PUNCT
ejpam-1726	135	1	s.	s.	PROPN
ejpam-1726	135	2	sardar	sardar	PROPN
ejpam-1726	135	3	,	,	PUNCT
ejpam-1726	135	4	s.	s.	PROPN
ejpam-1726	135	5	gupta	gupta	PROPN
ejpam-1726	135	6	,	,	PUNCT
ejpam-1726	135	7	k.	k.	PROPN
ejpam-1726	135	8	shum	shum	PROPN
ejpam-1726	135	9	/	/	SYM
ejpam-1726	135	10	eur	eur	PROPN
ejpam-1726	135	11	.	.	PUNCT
ejpam-1726	136	1	j.	j.	PROPN
ejpam-1726	136	2	pure	pure	PROPN
ejpam-1726	136	3	appl	appl	PROPN
ejpam-1726	136	4	.	.	PROPN
ejpam-1726	136	5	math	math	PROPN
ejpam-1726	136	6	,	,	PUNCT
ejpam-1726	136	7	6	6	NUM
ejpam-1726	136	8	(	(	PUNCT
ejpam-1726	136	9	2013	2013	NUM
ejpam-1726	136	10	)	)	PUNCT
ejpam-1726	136	11	,	,	PUNCT
ejpam-1726	136	12	1	1	NUM
ejpam-1726	136	13	-	-	SYM
ejpam-1726	136	14	10	10	NUM
ejpam-1726	136	15	6	6	NUM
ejpam-1726	136	16	theorem	theorem	NOUN
ejpam-1726	136	17	5	5	NUM
ejpam-1726	136	18	.	.	PUNCT
ejpam-1726	137	1	let	let	VERB
ejpam-1726	137	2	l	l	NOUN
ejpam-1726	137	3	and	and	CCONJ
ejpam-1726	137	4	r	r	NOUN
ejpam-1726	137	5	be	be	VERB
ejpam-1726	137	6	two	two	NUM
ejpam-1726	137	7	monoids	monoid	NOUN
ejpam-1726	137	8	which	which	PRON
ejpam-1726	137	9	are	be	AUX
ejpam-1726	137	10	morita	morita	PROPN
ejpam-1726	137	11	equivalent	equivalent	NOUN
ejpam-1726	137	12	.	.	PUNCT
ejpam-1726	138	1	then	then	ADV
ejpam-1726	138	2	there	there	PRON
ejpam-1726	138	3	exists	exist	VERB
ejpam-1726	138	4	a	a	DET
ejpam-1726	138	5	γsemigroup	γsemigroup	NOUN
ejpam-1726	138	6	with	with	ADP
ejpam-1726	138	7	unities	unity	NOUN
ejpam-1726	138	8	whose	whose	DET
ejpam-1726	138	9	left	left	ADJ
ejpam-1726	138	10	and	and	CCONJ
ejpam-1726	138	11	right	right	ADJ
ejpam-1726	138	12	operator	operator	NOUN
ejpam-1726	138	13	monoids	monoid	NOUN
ejpam-1726	138	14	are	be	AUX
ejpam-1726	138	15	respectively	respectively	ADV
ejpam-1726	138	16	isomorphic	isomorphic	ADJ
ejpam-1726	138	17	to	to	ADP
ejpam-1726	138	18	l	l	NOUN
ejpam-1726	138	19	and	and	CCONJ
ejpam-1726	138	20	r	r	NOUN
ejpam-1726	138	21	respectively	respectively	ADV
ejpam-1726	138	22	.	.	PUNCT
ejpam-1726	139	1	proof	proof	NOUN
ejpam-1726	139	2	.	.	PUNCT
ejpam-1726	140	1	as	as	SCONJ
ejpam-1726	140	2	l	l	PROPN
ejpam-1726	140	3	and	and	CCONJ
ejpam-1726	140	4	r	r	NOUN
ejpam-1726	140	5	are	be	AUX
ejpam-1726	140	6	morita	morita	PROPN
ejpam-1726	140	7	equivalent	equivalent	NOUN
ejpam-1726	140	8	the	the	DET
ejpam-1726	140	9	categories	category	NOUN
ejpam-1726	140	10	l	l	NOUN
ejpam-1726	140	11	-	-	NOUN
ejpam-1726	140	12	act	act	NOUN
ejpam-1726	140	13	and	and	CCONJ
ejpam-1726	140	14	r	r	NOUN
ejpam-1726	140	15	-	-	PUNCT
ejpam-1726	140	16	act	act	NOUN
ejpam-1726	140	17	are	be	AUX
ejpam-1726	140	18	equivalent	equivalent	ADJ
ejpam-1726	140	19	categories	category	NOUN
ejpam-1726	140	20	via	via	ADP
ejpam-1726	140	21	functors	functor	NOUN
ejpam-1726	140	22	,	,	PUNCT
ejpam-1726	140	23	say	say	VERB
ejpam-1726	140	24	f	f	X
ejpam-1726	140	25	:	:	PUNCT
ejpam-1726	140	26	r	r	X
ejpam-1726	140	27	-	-	PUNCT
ejpam-1726	140	28	act→	act→	NOUN
ejpam-1726	140	29	l	l	NOUN
ejpam-1726	140	30	-	-	NOUN
ejpam-1726	140	31	act	act	NOUN
ejpam-1726	140	32	and	and	CCONJ
ejpam-1726	140	33	g	g	NOUN
ejpam-1726	140	34	:	:	PUNCT
ejpam-1726	140	35	l	l	NOUN
ejpam-1726	140	36	-	-	NOUN
ejpam-1726	140	37	act→	act→	ADJ
ejpam-1726	140	38	r	r	NOUN
ejpam-1726	140	39	-	-	PUNCT
ejpam-1726	140	40	act	act	NOUN
ejpam-1726	140	41	.	.	PUNCT
ejpam-1726	141	1	now	now	ADV
ejpam-1726	141	2	let	let	VERB
ejpam-1726	141	3	a=	a=	ADJ
ejpam-1726	141	4	f(r	f(r	X
ejpam-1726	141	5	)	)	PUNCT
ejpam-1726	141	6	and	and	CCONJ
ejpam-1726	141	7	γ	γ	X
ejpam-1726	141	8	=	=	SYM
ejpam-1726	141	9	g(l	g(l	PROPN
ejpam-1726	141	10	)	)	PUNCT
ejpam-1726	141	11	.	.	PUNCT
ejpam-1726	142	1	then	then	ADV
ejpam-1726	142	2	by	by	ADP
ejpam-1726	142	3	theorem	theorem	NOUN
ejpam-1726	142	4	1	1	NUM
ejpam-1726	142	5	the	the	DET
ejpam-1726	142	6	following	following	ADJ
ejpam-1726	142	7	statements	statement	NOUN
ejpam-1726	142	8	follow	follow	VERB
ejpam-1726	142	9	:	:	PUNCT
ejpam-1726	142	10	(	(	PUNCT
ejpam-1726	142	11	1	1	X
ejpam-1726	142	12	)	)	PUNCT
ejpam-1726	142	13	lar	lar	NOUN
ejpam-1726	142	14	and	and	CCONJ
ejpam-1726	142	15	rγl	rγl	NOUN
ejpam-1726	142	16	are	be	AUX
ejpam-1726	142	17	biacts	biact	NOUN
ejpam-1726	142	18	;	;	PUNCT
ejpam-1726	142	19	(	(	PUNCT
ejpam-1726	142	20	2	2	X
ejpam-1726	142	21	)	)	PUNCT
ejpam-1726	142	22	la	la	NOUN
ejpam-1726	142	23	and	and	CCONJ
ejpam-1726	142	24	rγ	rγ	PRON
ejpam-1726	142	25	are	be	AUX
ejpam-1726	142	26	generators	generator	NOUN
ejpam-1726	142	27	for	for	ADP
ejpam-1726	142	28	l	l	NOUN
ejpam-1726	142	29	-	-	NOUN
ejpam-1726	142	30	act	act	NOUN
ejpam-1726	142	31	and	and	CCONJ
ejpam-1726	142	32	r	r	NOUN
ejpam-1726	142	33	-	-	PUNCT
ejpam-1726	142	34	act	act	NOUN
ejpam-1726	142	35	;	;	PUNCT
ejpam-1726	142	36	(	(	PUNCT
ejpam-1726	142	37	3	3	X
ejpam-1726	142	38	)	)	PUNCT
ejpam-1726	142	39	lar	lar	ADJ
ejpam-1726	142	40	∼=	∼=	PROPN
ejpam-1726	142	41	homr(γ	homr(γ	PROPN
ejpam-1726	142	42	,	,	PUNCT
ejpam-1726	142	43	r	r	NOUN
ejpam-1726	142	44	)	)	PUNCT
ejpam-1726	142	45	and	and	CCONJ
ejpam-1726	142	46	rγl	rγl	VERB
ejpam-1726	142	47	∼=	∼=	PROPN
ejpam-1726	142	48	homl(a	homl(a	PROPN
ejpam-1726	142	49	,	,	PUNCT
ejpam-1726	142	50	l	l	PROPN
ejpam-1726	142	51	)	)	PUNCT
ejpam-1726	142	52	;	;	PUNCT
ejpam-1726	142	53	(	(	PUNCT
ejpam-1726	142	54	4	4	X
ejpam-1726	142	55	)	)	PUNCT
ejpam-1726	142	56	f	f	NOUN
ejpam-1726	142	57	∼=	∼=	PROPN
ejpam-1726	142	58	homr(γ	homr(γ	PROPN
ejpam-1726	142	59	,	,	PUNCT
ejpam-1726	142	60	)	)	PUNCT
ejpam-1726	142	61	and	and	CCONJ
ejpam-1726	142	62	g	g	PROPN
ejpam-1726	142	63	∼=	∼=	PROPN
ejpam-1726	142	64	homl(a	homl(a	PROPN
ejpam-1726	142	65	,	,	PUNCT
ejpam-1726	142	66	)	)	PUNCT
ejpam-1726	142	67	;	;	PUNCT
ejpam-1726	142	68	(	(	PUNCT
ejpam-1726	142	69	5	5	X
ejpam-1726	142	70	)	)	PUNCT
ejpam-1726	142	71	l	l	NOUN
ejpam-1726	142	72	∼=	∼=	PROPN
ejpam-1726	142	73	endrγ	endrγ	NOUN
ejpam-1726	142	74	,	,	PUNCT
ejpam-1726	142	75	r∼=	r∼=	NUM
ejpam-1726	142	76	endla	endla	NOUN
ejpam-1726	142	77	.	.	PUNCT
ejpam-1726	143	1	now	now	ADV
ejpam-1726	143	2	considering	consider	VERB
ejpam-1726	143	3	γ	γ	NOUN
ejpam-1726	143	4	as	as	ADP
ejpam-1726	143	5	homl(a	homl(a	PROPN
ejpam-1726	143	6	,	,	PUNCT
ejpam-1726	143	7	l	l	NOUN
ejpam-1726	143	8	)	)	PUNCT
ejpam-1726	143	9	we	we	PRON
ejpam-1726	143	10	define	define	VERB
ejpam-1726	143	11	the	the	DET
ejpam-1726	143	12	mappings	mapping	NOUN
ejpam-1726	143	13	a×γ×a→	a×γ×a→	PROPN
ejpam-1726	143	14	a	a	PRON
ejpam-1726	143	15	and	and	CCONJ
ejpam-1726	143	16	γ×	γ×	NOUN
ejpam-1726	143	17	a×	a×	PROPN
ejpam-1726	143	18	γ→	γ→	PROPN
ejpam-1726	143	19	γ	γ	X
ejpam-1726	143	20	such	such	ADJ
ejpam-1726	143	21	that	that	PRON
ejpam-1726	143	22	for	for	ADP
ejpam-1726	143	23	a	a	DET
ejpam-1726	143	24	,	,	PUNCT
ejpam-1726	143	25	b	b	NOUN
ejpam-1726	143	26	,	,	PUNCT
ejpam-1726	143	27	x	x	SYM
ejpam-1726	143	28	∈	∈	PROPN
ejpam-1726	143	29	a	a	PRON
ejpam-1726	143	30	and	and	CCONJ
ejpam-1726	143	31	α	α	NOUN
ejpam-1726	143	32	,	,	PUNCT
ejpam-1726	143	33	β	β	X
ejpam-1726	143	34	,	,	PUNCT
ejpam-1726	143	35	γ	γ	PROPN
ejpam-1726	143	36	∈	∈	PROPN
ejpam-1726	143	37	γ	γ	X
ejpam-1726	143	38	(	(	PUNCT
ejpam-1726	143	39	a	a	PROPN
ejpam-1726	143	40	,	,	PUNCT
ejpam-1726	143	41	γ	γ	PROPN
ejpam-1726	143	42	,	,	PUNCT
ejpam-1726	143	43	b	b	NOUN
ejpam-1726	143	44	)	)	PUNCT
ejpam-1726	143	45	7→	7→	NUM
ejpam-1726	143	46	(	(	PUNCT
ejpam-1726	143	47	(	(	PUNCT
ejpam-1726	143	48	a)γ)b	a)γ)b	NOUN
ejpam-1726	143	49	and	and	CCONJ
ejpam-1726	143	50	(	(	PUNCT
ejpam-1726	143	51	α	α	NOUN
ejpam-1726	143	52	,	,	PUNCT
ejpam-1726	143	53	x	x	X
ejpam-1726	143	54	,	,	PUNCT
ejpam-1726	143	55	β	β	NOUN
ejpam-1726	143	56	)	)	PUNCT
ejpam-1726	143	57	7→	7→	NUM
ejpam-1726	143	58	α((x)β	α((x)β	NOUN
ejpam-1726	143	59	)	)	PUNCT
ejpam-1726	143	60	.	.	PUNCT
ejpam-1726	144	1	now	now	ADV
ejpam-1726	144	2	we	we	PRON
ejpam-1726	144	3	have	have	VERB
ejpam-1726	144	4	(	(	PUNCT
ejpam-1726	144	5	aαb)β	aαb)β	NOUN
ejpam-1726	144	6	c	c	NOUN
ejpam-1726	144	7	=	=	SYM
ejpam-1726	144	8	(	(	PUNCT
ejpam-1726	144	9	(	(	PUNCT
ejpam-1726	144	10	(	(	PUNCT
ejpam-1726	144	11	a)αb)β)c	a)αb)β)c	X
ejpam-1726	144	12	=	=	SYM
ejpam-1726	144	13	(	(	PUNCT
ejpam-1726	144	14	(	(	PUNCT
ejpam-1726	144	15	a)α(b)β)c	a)α(b)β)c	NOUN
ejpam-1726	144	16	,	,	PUNCT
ejpam-1726	144	17	since	since	SCONJ
ejpam-1726	144	18	β	β	NOUN
ejpam-1726	144	19	is	be	AUX
ejpam-1726	144	20	a	a	DET
ejpam-1726	144	21	left	left	ADJ
ejpam-1726	144	22	l	l	NOUN
ejpam-1726	144	23	-	-	NOUN
ejpam-1726	144	24	morphism	morphism	NOUN
ejpam-1726	144	25	.	.	PUNCT
ejpam-1726	145	1	aα(bβ	aα(bβ	ADP
ejpam-1726	145	2	c	c	PROPN
ejpam-1726	145	3	)	)	PUNCT
ejpam-1726	145	4	=	=	SYM
ejpam-1726	145	5	(	(	PUNCT
ejpam-1726	145	6	(	(	PUNCT
ejpam-1726	145	7	a)α)(((b)β)c	a)α)(((b)β)c	NOUN
ejpam-1726	145	8	)	)	PUNCT
ejpam-1726	145	9	=	=	SYM
ejpam-1726	145	10	(	(	PUNCT
ejpam-1726	145	11	(	(	PUNCT
ejpam-1726	145	12	a)α(b)β)c	a)α(b)β)c	NOUN
ejpam-1726	145	13	,	,	PUNCT
ejpam-1726	145	14	since	since	SCONJ
ejpam-1726	145	15	a	a	PRON
ejpam-1726	145	16	is	be	AUX
ejpam-1726	145	17	a	a	DET
ejpam-1726	145	18	left	left	ADJ
ejpam-1726	145	19	l	l	NOUN
ejpam-1726	145	20	-	-	NOUN
ejpam-1726	145	21	act	act	NOUN
ejpam-1726	145	22	.	.	PUNCT
ejpam-1726	146	1	a(αbβ)c	a(αbβ)c	NOUN
ejpam-1726	146	2	=	=	PUNCT
ejpam-1726	146	3	(	(	PUNCT
ejpam-1726	146	4	(	(	PUNCT
ejpam-1726	146	5	a)(α((b)β)))c	a)(α((b)β)))c	PROPN
ejpam-1726	146	6	=	=	SYM
ejpam-1726	146	7	(	(	PUNCT
ejpam-1726	146	8	(	(	PUNCT
ejpam-1726	146	9	a)α(b)β)c	a)α(b)β)c	PROPN
ejpam-1726	146	10	,	,	PUNCT
ejpam-1726	146	11	this	this	PRON
ejpam-1726	146	12	comes	come	VERB
ejpam-1726	146	13	from	from	ADP
ejpam-1726	146	14	how	how	SCONJ
ejpam-1726	146	15	we	we	PRON
ejpam-1726	146	16	have	have	AUX
ejpam-1726	146	17	considered	consider	VERB
ejpam-1726	146	18	homl(a	homl(a	PROPN
ejpam-1726	146	19	,	,	PUNCT
ejpam-1726	146	20	l	l	NOUN
ejpam-1726	146	21	)	)	PUNCT
ejpam-1726	146	22	as	as	ADP
ejpam-1726	146	23	a	a	DET
ejpam-1726	146	24	right	right	ADJ
ejpam-1726	146	25	l	l	NOUN
ejpam-1726	146	26	-	-	NOUN
ejpam-1726	146	27	act	act	NOUN
ejpam-1726	146	28	.	.	PUNCT
ejpam-1726	147	1	hence	hence	ADV
ejpam-1726	147	2	a	a	PRON
ejpam-1726	147	3	is	be	AUX
ejpam-1726	147	4	a	a	DET
ejpam-1726	147	5	γ	γ	NOUN
ejpam-1726	147	6	-	-	PUNCT
ejpam-1726	147	7	semigroup	semigroup	NOUN
ejpam-1726	147	8	.	.	PUNCT
ejpam-1726	148	1	now	now	ADV
ejpam-1726	148	2	it	it	PRON
ejpam-1726	148	3	remains	remain	VERB
ejpam-1726	148	4	to	to	PART
ejpam-1726	148	5	prove	prove	VERB
ejpam-1726	148	6	that	that	SCONJ
ejpam-1726	148	7	the	the	DET
ejpam-1726	148	8	operator	operator	NOUN
ejpam-1726	148	9	semigroups	semigroup	NOUN
ejpam-1726	148	10	are	be	AUX
ejpam-1726	148	11	isomorphic	isomorphic	ADJ
ejpam-1726	148	12	to	to	ADP
ejpam-1726	148	13	l	l	PROPN
ejpam-1726	148	14	and	and	CCONJ
ejpam-1726	148	15	r.	r.	PROPN
ejpam-1726	148	16	let	let	VERB
ejpam-1726	148	17	l′	l′	PROPN
ejpam-1726	148	18	and	and	CCONJ
ejpam-1726	148	19	r′	r′	PROPN
ejpam-1726	148	20	be	be	AUX
ejpam-1726	148	21	the	the	DET
ejpam-1726	148	22	left	left	ADJ
ejpam-1726	148	23	and	and	CCONJ
ejpam-1726	148	24	right	right	ADJ
ejpam-1726	148	25	operator	operator	NOUN
ejpam-1726	148	26	semigroups	semigroup	NOUN
ejpam-1726	148	27	of	of	ADP
ejpam-1726	148	28	the	the	DET
ejpam-1726	148	29	γ	γ	PROPN
ejpam-1726	148	30	-	-	PUNCT
ejpam-1726	148	31	semigroup	semigroup	ADJ
ejpam-1726	148	32	a.	a.	NOUN
ejpam-1726	148	33	we	we	PRON
ejpam-1726	148	34	define	define	VERB
ejpam-1726	148	35	f	f	X
ejpam-1726	148	36	:	:	PUNCT
ejpam-1726	148	37	l′→	l′→	ADJ
ejpam-1726	148	38	l	l	NOUN
ejpam-1726	148	39	by	by	X
ejpam-1726	148	40	(	(	PUNCT
ejpam-1726	148	41	[	[	X
ejpam-1726	148	42	a	a	X
ejpam-1726	148	43	,	,	PUNCT
ejpam-1726	148	44	α	α	NOUN
ejpam-1726	148	45	]	]	X
ejpam-1726	148	46	)	)	PUNCT
ejpam-1726	148	47	f	f	PROPN
ejpam-1726	148	48	=	=	PUNCT
ejpam-1726	148	49	(	(	PUNCT
ejpam-1726	148	50	a)α	a)α	X
ejpam-1726	148	51	.	.	PUNCT
ejpam-1726	149	1	the	the	DET
ejpam-1726	149	2	mapping	mapping	NOUN
ejpam-1726	149	3	f	f	PROPN
ejpam-1726	149	4	is	be	AUX
ejpam-1726	149	5	well	well	ADV
ejpam-1726	149	6	-	-	PUNCT
ejpam-1726	149	7	defined	define	VERB
ejpam-1726	149	8	,	,	PUNCT
ejpam-1726	149	9	since	since	SCONJ
ejpam-1726	149	10	[	[	X
ejpam-1726	149	11	a	a	X
ejpam-1726	149	12	,	,	PUNCT
ejpam-1726	149	13	α	α	NOUN
ejpam-1726	149	14	]	]	X
ejpam-1726	149	15	=	=	PUNCT
ejpam-1726	150	1	[	[	X
ejpam-1726	150	2	b	b	NOUN
ejpam-1726	150	3	,	,	PUNCT
ejpam-1726	150	4	β]⇒γaα	β]⇒γaα	PUNCT
ejpam-1726	150	5	=	=	SYM
ejpam-1726	150	6	γbβ	γbβ	NOUN
ejpam-1726	150	7	for	for	ADP
ejpam-1726	150	8	all	all	DET
ejpam-1726	150	9	γ	γ	PROPN
ejpam-1726	150	10	∈	∈	PROPN
ejpam-1726	150	11	γ	γ	X
ejpam-1726	150	12	⇒γ((a)α	⇒γ((a)α	PROPN
ejpam-1726	150	13	)	)	PUNCT
ejpam-1726	151	1	=	=	SYM
ejpam-1726	151	2	γ((b)β	γ((b)β	PROPN
ejpam-1726	151	3	)	)	PUNCT
ejpam-1726	151	4	for	for	ADP
ejpam-1726	151	5	all	all	DET
ejpam-1726	151	6	γ	γ	PROPN
ejpam-1726	151	7	∈	∈	PROPN
ejpam-1726	151	8	γ	γ	PROPN
ejpam-1726	151	9	s.	s.	PROPN
ejpam-1726	151	10	sardar	sardar	PROPN
ejpam-1726	151	11	,	,	PUNCT
ejpam-1726	151	12	s.	s.	PROPN
ejpam-1726	151	13	gupta	gupta	PROPN
ejpam-1726	151	14	,	,	PUNCT
ejpam-1726	151	15	k.	k.	PROPN
ejpam-1726	151	16	shum	shum	PROPN
ejpam-1726	151	17	/	/	SYM
ejpam-1726	151	18	eur	eur	PROPN
ejpam-1726	151	19	.	.	PUNCT
ejpam-1726	152	1	j.	j.	PROPN
ejpam-1726	152	2	pure	pure	PROPN
ejpam-1726	152	3	appl	appl	PROPN
ejpam-1726	152	4	.	.	PROPN
ejpam-1726	152	5	math	math	PROPN
ejpam-1726	152	6	,	,	PUNCT
ejpam-1726	152	7	6	6	NUM
ejpam-1726	152	8	(	(	PUNCT
ejpam-1726	152	9	2013	2013	NUM
ejpam-1726	152	10	)	)	PUNCT
ejpam-1726	152	11	,	,	PUNCT
ejpam-1726	152	12	1	1	NUM
ejpam-1726	152	13	-	-	SYM
ejpam-1726	152	14	10	10	NUM
ejpam-1726	152	15	7	7	NUM
ejpam-1726	152	16	⇒(a)α=	⇒(a)α=	NOUN
ejpam-1726	152	17	(	(	PUNCT
ejpam-1726	152	18	b)β	b)β	VERB
ejpam-1726	152	19	.	.	PUNCT
ejpam-1726	153	1	it	it	PRON
ejpam-1726	153	2	is	be	AUX
ejpam-1726	153	3	also	also	ADV
ejpam-1726	153	4	clear	clear	ADJ
ejpam-1726	153	5	that	that	SCONJ
ejpam-1726	153	6	the	the	DET
ejpam-1726	153	7	mapping	mapping	NOUN
ejpam-1726	153	8	is	be	AUX
ejpam-1726	153	9	injective	injective	ADJ
ejpam-1726	153	10	,	,	PUNCT
ejpam-1726	153	11	since	since	SCONJ
ejpam-1726	153	12	(	(	PUNCT
ejpam-1726	153	13	a)α=	a)α=	PROPN
ejpam-1726	153	14	(	(	PUNCT
ejpam-1726	153	15	b)β	b)β	X
ejpam-1726	153	16	⇒γ((a)α	⇒γ((a)α	PROPN
ejpam-1726	153	17	)	)	PUNCT
ejpam-1726	154	1	=	=	SYM
ejpam-1726	154	2	γ((b)β	γ((b)β	PROPN
ejpam-1726	154	3	)	)	PUNCT
ejpam-1726	154	4	and	and	CCONJ
ejpam-1726	154	5	(	(	PUNCT
ejpam-1726	154	6	(	(	PUNCT
ejpam-1726	154	7	a)α)x	a)α)x	ADV
ejpam-1726	154	8	=	=	SYM
ejpam-1726	154	9	(	(	PUNCT
ejpam-1726	154	10	(	(	PUNCT
ejpam-1726	154	11	b)β)x	b)β)x	NOUN
ejpam-1726	154	12	for	for	ADP
ejpam-1726	154	13	all	all	DET
ejpam-1726	154	14	x	x	PROPN
ejpam-1726	154	15	∈	∈	PROPN
ejpam-1726	154	16	a	a	PRON
ejpam-1726	154	17	,	,	PUNCT
ejpam-1726	154	18	γ	γ	PROPN
ejpam-1726	154	19	∈	∈	PROPN
ejpam-1726	154	20	γ	γ	NOUN
ejpam-1726	154	21	⇒γaα	⇒γaα	NOUN
ejpam-1726	154	22	=	=	SYM
ejpam-1726	154	23	γbβ	γbβ	NOUN
ejpam-1726	154	24	and	and	CCONJ
ejpam-1726	154	25	aαx	aαx	PROPN
ejpam-1726	154	26	=	=	SYM
ejpam-1726	154	27	bβ	bβ	NOUN
ejpam-1726	154	28	x	x	PUNCT
ejpam-1726	154	29	for	for	ADP
ejpam-1726	154	30	all	all	DET
ejpam-1726	154	31	x	x	SYM
ejpam-1726	154	32	∈	∈	PROPN
ejpam-1726	154	33	a	a	PRON
ejpam-1726	154	34	,	,	PUNCT
ejpam-1726	154	35	γ	γ	PROPN
ejpam-1726	154	36	∈	∈	PROPN
ejpam-1726	154	37	γ	γ	PROPN
ejpam-1726	154	38	⇒[a	⇒[a	PROPN
ejpam-1726	154	39	,	,	PUNCT
ejpam-1726	154	40	α	α	X
ejpam-1726	154	41	]	]	X
ejpam-1726	154	42	=	=	PUNCT
ejpam-1726	155	1	[	[	X
ejpam-1726	155	2	b	b	X
ejpam-1726	155	3	,	,	PUNCT
ejpam-1726	155	4	β	β	X
ejpam-1726	155	5	]	]	X
ejpam-1726	155	6	.	.	PUNCT
ejpam-1726	156	1	again	again	ADV
ejpam-1726	156	2	,	,	PUNCT
ejpam-1726	156	3	since	since	SCONJ
ejpam-1726	156	4	la	la	X
ejpam-1726	156	5	is	be	AUX
ejpam-1726	156	6	a	a	DET
ejpam-1726	156	7	generator	generator	NOUN
ejpam-1726	156	8	of	of	ADP
ejpam-1726	156	9	l	l	PROPN
ejpam-1726	156	10	-	-	NOUN
ejpam-1726	156	11	act	act	NOUN
ejpam-1726	156	12	so	so	ADV
ejpam-1726	156	13	by	by	ADP
ejpam-1726	156	14	theorem	theorem	NOUN
ejpam-1726	156	15	2	2	NUM
ejpam-1726	156	16	there	there	ADV
ejpam-1726	156	17	exists	exist	VERB
ejpam-1726	156	18	a	a	DET
ejpam-1726	156	19	left	left	ADJ
ejpam-1726	156	20	l	l	NOUN
ejpam-1726	156	21	-	-	NOUN
ejpam-1726	156	22	morphism	morphism	ADJ
ejpam-1726	156	23	ψ	ψ	NOUN
ejpam-1726	156	24	:	:	PUNCT
ejpam-1726	156	25	a→	a→	X
ejpam-1726	156	26	l.	l.	NOUN
ejpam-1726	156	27	hence	hence	ADV
ejpam-1726	156	28	for	for	ADP
ejpam-1726	156	29	any	any	DET
ejpam-1726	156	30	l	l	NOUN
ejpam-1726	156	31	∈	∈	NOUN
ejpam-1726	156	32	l	l	NOUN
ejpam-1726	156	33	there	there	PRON
ejpam-1726	156	34	exists	exist	VERB
ejpam-1726	156	35	a	a	DET
ejpam-1726	156	36	∈	∈	NOUN
ejpam-1726	156	37	a	a	DET
ejpam-1726	156	38	such	such	ADJ
ejpam-1726	156	39	that	that	PRON
ejpam-1726	156	40	(	(	PUNCT
ejpam-1726	156	41	a)ψ=	a)ψ=	NOUN
ejpam-1726	156	42	l.	l.	PROPN
ejpam-1726	156	43	then	then	ADV
ejpam-1726	156	44	we	we	PRON
ejpam-1726	156	45	have	have	VERB
ejpam-1726	156	46	(	(	PUNCT
ejpam-1726	156	47	[	[	X
ejpam-1726	156	48	a	a	X
ejpam-1726	156	49	,	,	PUNCT
ejpam-1726	156	50	ψ	ψ	X
ejpam-1726	156	51	]	]	X
ejpam-1726	156	52	f	f	X
ejpam-1726	156	53	=	=	SYM
ejpam-1726	156	54	l.	l.	PROPN
ejpam-1726	157	1	this	this	PRON
ejpam-1726	157	2	shows	show	VERB
ejpam-1726	157	3	that	that	SCONJ
ejpam-1726	157	4	the	the	DET
ejpam-1726	157	5	mapping	mapping	NOUN
ejpam-1726	157	6	f	f	PROPN
ejpam-1726	157	7	is	be	AUX
ejpam-1726	157	8	surjective	surjective	ADJ
ejpam-1726	157	9	.	.	PUNCT
ejpam-1726	158	1	also	also	ADV
ejpam-1726	158	2	f	f	PROPN
ejpam-1726	158	3	is	be	AUX
ejpam-1726	158	4	a	a	DET
ejpam-1726	158	5	semigroup	semigroup	ADJ
ejpam-1726	158	6	morphism	morphism	NOUN
ejpam-1726	158	7	because	because	SCONJ
ejpam-1726	158	8	for	for	ADP
ejpam-1726	158	9	all	all	DET
ejpam-1726	158	10	a	a	PRON
ejpam-1726	158	11	,	,	PUNCT
ejpam-1726	158	12	b	b	X
ejpam-1726	158	13	∈	∈	PROPN
ejpam-1726	158	14	a	a	PRON
ejpam-1726	158	15	and	and	CCONJ
ejpam-1726	158	16	α	α	NOUN
ejpam-1726	158	17	,	,	PUNCT
ejpam-1726	158	18	β	β	PROPN
ejpam-1726	158	19	∈	∈	PROPN
ejpam-1726	158	20	γ	γ	X
ejpam-1726	158	21	(	(	PUNCT
ejpam-1726	158	22	[	[	X
ejpam-1726	158	23	a	a	DET
ejpam-1726	158	24	,	,	PUNCT
ejpam-1726	158	25	α][b	α][b	PROPN
ejpam-1726	158	26	,	,	PUNCT
ejpam-1726	158	27	β	β	NOUN
ejpam-1726	158	28	]	]	X
ejpam-1726	158	29	)	)	PUNCT
ejpam-1726	158	30	f	f	PROPN
ejpam-1726	159	1	=	=	PUNCT
ejpam-1726	159	2	(	(	PUNCT
ejpam-1726	159	3	[	[	X
ejpam-1726	159	4	aαb	aαb	NOUN
ejpam-1726	159	5	,	,	PUNCT
ejpam-1726	159	6	β	β	X
ejpam-1726	159	7	]	]	X
ejpam-1726	159	8	)	)	PUNCT
ejpam-1726	159	9	f	f	PROPN
ejpam-1726	159	10	=	=	PUNCT
ejpam-1726	159	11	(	(	PUNCT
ejpam-1726	159	12	(	(	PUNCT
ejpam-1726	159	13	(	(	PUNCT
ejpam-1726	159	14	a)α)b)β	a)α)b)β	NOUN
ejpam-1726	159	15	=	=	SYM
ejpam-1726	159	16	(	(	PUNCT
ejpam-1726	159	17	a)α(b)β	a)α(b)β	X
ejpam-1726	159	18	=	=	SYM
ejpam-1726	159	19	(	(	PUNCT
ejpam-1726	159	20	[	[	X
ejpam-1726	159	21	a	a	X
ejpam-1726	159	22	,	,	PUNCT
ejpam-1726	159	23	α	α	NOUN
ejpam-1726	159	24	]	]	X
ejpam-1726	159	25	)	)	PUNCT
ejpam-1726	159	26	f	f	NOUN
ejpam-1726	159	27	(	(	PUNCT
ejpam-1726	159	28	[	[	X
ejpam-1726	159	29	b	b	NOUN
ejpam-1726	159	30	,	,	PUNCT
ejpam-1726	159	31	β	β	NOUN
ejpam-1726	159	32	]	]	X
ejpam-1726	159	33	)	)	PUNCT
ejpam-1726	159	34	f	f	PROPN
ejpam-1726	159	35	.	.	PUNCT
ejpam-1726	160	1	hence	hence	ADV
ejpam-1726	160	2	l	l	NOUN
ejpam-1726	160	3	and	and	CCONJ
ejpam-1726	160	4	l′	l′	NOUN
ejpam-1726	160	5	are	be	AUX
ejpam-1726	160	6	isomorphic	isomorphic	ADJ
ejpam-1726	160	7	as	as	ADP
ejpam-1726	160	8	monoids	monoid	NOUN
ejpam-1726	160	9	.	.	PUNCT
ejpam-1726	161	1	similarly	similarly	ADV
ejpam-1726	161	2	we	we	PRON
ejpam-1726	161	3	can	can	AUX
ejpam-1726	161	4	prove	prove	VERB
ejpam-1726	161	5	that	that	SCONJ
ejpam-1726	161	6	r′	r′	NOUN
ejpam-1726	161	7	is	be	AUX
ejpam-1726	161	8	isomorphic	isomorphic	ADJ
ejpam-1726	161	9	to	to	ADP
ejpam-1726	161	10	r.	r.	NOUN
ejpam-1726	161	11	hence	hence	ADV
ejpam-1726	161	12	the	the	DET
ejpam-1726	161	13	proof	proof	NOUN
ejpam-1726	161	14	follows	follow	VERB
ejpam-1726	161	15	.	.	PUNCT
ejpam-1726	162	1	we	we	PRON
ejpam-1726	162	2	conclude	conclude	VERB
ejpam-1726	162	3	this	this	DET
ejpam-1726	162	4	section	section	NOUN
ejpam-1726	162	5	by	by	ADP
ejpam-1726	162	6	combining	combine	VERB
ejpam-1726	162	7	the	the	DET
ejpam-1726	162	8	above	above	ADJ
ejpam-1726	162	9	two	two	NUM
ejpam-1726	162	10	results	result	NOUN
ejpam-1726	162	11	into	into	ADP
ejpam-1726	162	12	one	one	NUM
ejpam-1726	162	13	theorem	theorem	NOUN
ejpam-1726	162	14	.	.	PUNCT
ejpam-1726	163	1	theorem	theorem	ADJ
ejpam-1726	163	2	6	6	NUM
ejpam-1726	163	3	.	.	PUNCT
ejpam-1726	163	4	two	two	NUM
ejpam-1726	163	5	monoids	monoid	NOUN
ejpam-1726	163	6	l	l	NOUN
ejpam-1726	163	7	and	and	CCONJ
ejpam-1726	163	8	r	r	NOUN
ejpam-1726	163	9	are	be	AUX
ejpam-1726	163	10	morita	morita	NOUN
ejpam-1726	163	11	equivalent	equivalent	ADJ
ejpam-1726	164	1	if	if	SCONJ
ejpam-1726	164	2	and	and	CCONJ
ejpam-1726	164	3	only	only	ADV
ejpam-1726	164	4	if	if	SCONJ
ejpam-1726	164	5	there	there	PRON
ejpam-1726	164	6	exists	exist	VERB
ejpam-1726	164	7	a	a	DET
ejpam-1726	164	8	γ	γ	NOUN
ejpam-1726	164	9	-	-	PUNCT
ejpam-1726	164	10	semigroup	semigroup	NOUN
ejpam-1726	164	11	with	with	ADP
ejpam-1726	164	12	unities	unity	NOUN
ejpam-1726	164	13	whose	whose	DET
ejpam-1726	164	14	operator	operator	NOUN
ejpam-1726	164	15	monoids	monoid	NOUN
ejpam-1726	164	16	are	be	AUX
ejpam-1726	164	17	isomorphic	isomorphic	ADJ
ejpam-1726	164	18	to	to	ADP
ejpam-1726	164	19	l	l	PROPN
ejpam-1726	164	20	and	and	CCONJ
ejpam-1726	164	21	r.	r.	PROPN
ejpam-1726	164	22	4	4	NUM
ejpam-1726	164	23	.	.	PUNCT
ejpam-1726	165	1	applications	application	NOUN
ejpam-1726	165	2	in	in	ADP
ejpam-1726	165	3	this	this	DET
ejpam-1726	165	4	section	section	NOUN
ejpam-1726	165	5	we	we	PRON
ejpam-1726	165	6	give	give	VERB
ejpam-1726	165	7	some	some	DET
ejpam-1726	165	8	applications	application	NOUN
ejpam-1726	165	9	of	of	ADP
ejpam-1726	165	10	the	the	DET
ejpam-1726	165	11	theorem	theorem	NOUN
ejpam-1726	165	12	6	6	NUM
ejpam-1726	165	13	.	.	PUNCT
ejpam-1726	165	14	by	by	ADP
ejpam-1726	165	15	using	use	VERB
ejpam-1726	165	16	our	our	PRON
ejpam-1726	165	17	result	result	NOUN
ejpam-1726	165	18	and	and	CCONJ
ejpam-1726	165	19	some	some	DET
ejpam-1726	165	20	well	well	ADV
ejpam-1726	165	21	-	-	PUNCT
ejpam-1726	165	22	known	know	VERB
ejpam-1726	165	23	theories	theory	NOUN
ejpam-1726	165	24	of	of	ADP
ejpam-1726	165	25	γ	γ	NOUN
ejpam-1726	165	26	-	-	PUNCT
ejpam-1726	165	27	semigroups	semigroup	NOUN
ejpam-1726	165	28	we	we	PRON
ejpam-1726	165	29	are	be	AUX
ejpam-1726	165	30	able	able	ADJ
ejpam-1726	165	31	to	to	PART
ejpam-1726	165	32	deduce	deduce	VERB
ejpam-1726	165	33	some	some	DET
ejpam-1726	165	34	properties	property	NOUN
ejpam-1726	165	35	of	of	ADP
ejpam-1726	165	36	monoids	monoid	NOUN
ejpam-1726	165	37	which	which	PRON
ejpam-1726	165	38	remain	remain	VERB
ejpam-1726	165	39	invariant	invariant	ADJ
ejpam-1726	165	40	under	under	ADP
ejpam-1726	165	41	morita	morita	PROPN
ejpam-1726	165	42	equivalence	equivalence	NOUN
ejpam-1726	165	43	.	.	PUNCT
ejpam-1726	166	1	the	the	DET
ejpam-1726	166	2	reader	reader	NOUN
ejpam-1726	166	3	is	be	AUX
ejpam-1726	166	4	referred	refer	VERB
ejpam-1726	166	5	to	to	ADP
ejpam-1726	166	6	[	[	X
ejpam-1726	166	7	1	1	NUM
ejpam-1726	166	8	,	,	PUNCT
ejpam-1726	166	9	2	2	NUM
ejpam-1726	166	10	,	,	PUNCT
ejpam-1726	166	11	3	3	NUM
ejpam-1726	166	12	,	,	PUNCT
ejpam-1726	166	13	4	4	NUM
ejpam-1726	166	14	,	,	PUNCT
ejpam-1726	166	15	5	5	NUM
ejpam-1726	166	16	]	]	PUNCT
ejpam-1726	166	17	for	for	ADP
ejpam-1726	166	18	the	the	DET
ejpam-1726	166	19	results	result	NOUN
ejpam-1726	166	20	of	of	ADP
ejpam-1726	166	21	γ	γ	NOUN
ejpam-1726	166	22	-	-	PUNCT
ejpam-1726	166	23	semigroups	semigroup	NOUN
ejpam-1726	166	24	and	and	CCONJ
ejpam-1726	166	25	to	to	ADP
ejpam-1726	166	26	[	[	X
ejpam-1726	166	27	9	9	NUM
ejpam-1726	166	28	,	,	PUNCT
ejpam-1726	166	29	10	10	NUM
ejpam-1726	166	30	,	,	PUNCT
ejpam-1726	166	31	11	11	NUM
ejpam-1726	166	32	]	]	PUNCT
ejpam-1726	166	33	for	for	ADP
ejpam-1726	166	34	preliminaries	preliminary	NOUN
ejpam-1726	166	35	of	of	ADP
ejpam-1726	166	36	semigroups	semigroup	NOUN
ejpam-1726	166	37	used	use	VERB
ejpam-1726	166	38	in	in	ADP
ejpam-1726	166	39	this	this	DET
ejpam-1726	166	40	section	section	NOUN
ejpam-1726	166	41	.	.	PUNCT
ejpam-1726	167	1	theorem	theorem	VERB
ejpam-1726	167	2	7	7	NUM
ejpam-1726	167	3	.	.	PUNCT
ejpam-1726	168	1	let	let	VERB
ejpam-1726	168	2	l	l	NOUN
ejpam-1726	168	3	and	and	CCONJ
ejpam-1726	168	4	r	r	NOUN
ejpam-1726	168	5	be	be	AUX
ejpam-1726	168	6	two	two	NUM
ejpam-1726	168	7	morita	morita	PROPN
ejpam-1726	168	8	equivalent	equivalent	PROPN
ejpam-1726	168	9	monoids	monoids	PROPN
ejpam-1726	168	10	.	.	PUNCT
ejpam-1726	169	1	then	then	ADV
ejpam-1726	169	2	there	there	PRON
ejpam-1726	169	3	exists	exist	VERB
ejpam-1726	169	4	an	an	DET
ejpam-1726	169	5	inclusion	inclusion	NOUN
ejpam-1726	169	6	preserving	preserve	VERB
ejpam-1726	169	7	bijection	bijection	NOUN
ejpam-1726	169	8	between	between	ADP
ejpam-1726	169	9	the	the	DET
ejpam-1726	169	10	set	set	NOUN
ejpam-1726	169	11	of	of	ADP
ejpam-1726	169	12	all	all	DET
ejpam-1726	169	13	ideals	ideal	NOUN
ejpam-1726	169	14	of	of	ADP
ejpam-1726	169	15	r	r	NOUN
ejpam-1726	169	16	and	and	CCONJ
ejpam-1726	169	17	the	the	DET
ejpam-1726	169	18	set	set	NOUN
ejpam-1726	169	19	of	of	ADP
ejpam-1726	169	20	all	all	DET
ejpam-1726	169	21	ideals	ideal	NOUN
ejpam-1726	169	22	of	of	ADP
ejpam-1726	169	23	l.	l.	PROPN
ejpam-1726	169	24	proof	proof	NOUN
ejpam-1726	169	25	.	.	PUNCT
ejpam-1726	170	1	by	by	ADP
ejpam-1726	170	2	theorem	theorem	NOUN
ejpam-1726	170	3	6	6	NUM
ejpam-1726	170	4	there	there	ADV
ejpam-1726	170	5	exists	exist	VERB
ejpam-1726	170	6	a	a	DET
ejpam-1726	170	7	γ	γ	NOUN
ejpam-1726	170	8	-	-	PUNCT
ejpam-1726	170	9	semigroup	semigroup	NOUN
ejpam-1726	170	10	a	a	PRON
ejpam-1726	170	11	with	with	ADP
ejpam-1726	170	12	left	left	ADJ
ejpam-1726	170	13	and	and	CCONJ
ejpam-1726	170	14	right	right	ADJ
ejpam-1726	170	15	unities	unity	NOUN
ejpam-1726	170	16	whose	whose	DET
ejpam-1726	170	17	left	left	ADJ
ejpam-1726	170	18	and	and	CCONJ
ejpam-1726	170	19	right	right	ADJ
ejpam-1726	170	20	operator	operator	NOUN
ejpam-1726	170	21	monoids	monoid	NOUN
ejpam-1726	170	22	l1	l1	PROPN
ejpam-1726	170	23	and	and	CCONJ
ejpam-1726	170	24	r1	r1	PROPN
ejpam-1726	170	25	are	be	AUX
ejpam-1726	170	26	isomorphic	isomorphic	ADJ
ejpam-1726	170	27	to	to	ADP
ejpam-1726	170	28	l	l	NOUN
ejpam-1726	170	29	and	and	CCONJ
ejpam-1726	170	30	r	r	NOUN
ejpam-1726	170	31	respectively	respectively	ADV
ejpam-1726	170	32	.	.	PUNCT
ejpam-1726	171	1	hence	hence	ADV
ejpam-1726	171	2	it	it	PRON
ejpam-1726	171	3	suffices	suffice	VERB
ejpam-1726	171	4	to	to	PART
ejpam-1726	171	5	prove	prove	VERB
ejpam-1726	171	6	the	the	DET
ejpam-1726	171	7	result	result	NOUN
ejpam-1726	171	8	for	for	ADP
ejpam-1726	171	9	l1	l1	PROPN
ejpam-1726	171	10	and	and	CCONJ
ejpam-1726	171	11	r1	r1	PROPN
ejpam-1726	171	12	.	.	PUNCT
ejpam-1726	172	1	now	now	ADV
ejpam-1726	172	2	for	for	ADP
ejpam-1726	172	3	each	each	DET
ejpam-1726	172	4	p	p	PROPN
ejpam-1726	172	5	⊆	⊆	NUM
ejpam-1726	172	6	l1	l1	PROPN
ejpam-1726	172	7	and	and	CCONJ
ejpam-1726	172	8	m	m	PROPN
ejpam-1726	172	9	⊆	⊆	NUM
ejpam-1726	172	10	r1	r1	NOUN
ejpam-1726	172	11	we	we	PRON
ejpam-1726	172	12	define	define	VERB
ejpam-1726	172	13	p+	p+	NOUN
ejpam-1726	172	14	=	=	SYM
ejpam-1726	172	15	{	{	PUNCT
ejpam-1726	172	16	x	x	SYM
ejpam-1726	172	17	∈	∈	PROPN
ejpam-1726	173	1	a	a	DET
ejpam-1726	173	2	|	|	NOUN
ejpam-1726	174	1	[	[	X
ejpam-1726	174	2	x	x	X
ejpam-1726	174	3	,	,	PUNCT
ejpam-1726	174	4	α	α	X
ejpam-1726	174	5	]	]	X
ejpam-1726	174	6	∈	∈	NOUN
ejpam-1726	174	7	for	for	ADP
ejpam-1726	174	8	all	all	DET
ejpam-1726	174	9	α	α	PRON
ejpam-1726	174	10	∈	∈	PROPN
ejpam-1726	174	11	γ	γ	X
ejpam-1726	174	12	}	}	PUNCT
ejpam-1726	174	13	and	and	CCONJ
ejpam-1726	174	14	m∗	m∗	VERB
ejpam-1726	174	15	=	=	SYM
ejpam-1726	174	16	{	{	PUNCT
ejpam-1726	174	17	x	x	SYM
ejpam-1726	174	18	∈	∈	PROPN
ejpam-1726	175	1	a	a	DET
ejpam-1726	175	2	|	|	NOUN
ejpam-1726	175	3	[	[	X
ejpam-1726	175	4	α	α	X
ejpam-1726	175	5	,	,	PUNCT
ejpam-1726	175	6	x	x	X
ejpam-1726	175	7	]	]	X
ejpam-1726	175	8	∈	∈	PROPN
ejpam-1726	175	9	m	m	VERB
ejpam-1726	175	10	,	,	PUNCT
ejpam-1726	175	11	for	for	ADP
ejpam-1726	175	12	all	all	PRON
ejpam-1726	175	13	α	α	DET
ejpam-1726	175	14	∈	∈	PROPN
ejpam-1726	175	15	γ	γ	X
ejpam-1726	175	16	}	}	PUNCT
ejpam-1726	175	17	.	.	PUNCT
ejpam-1726	176	1	also	also	ADV
ejpam-1726	176	2	for	for	ADP
ejpam-1726	176	3	each	each	DET
ejpam-1726	176	4	q	q	NOUN
ejpam-1726	176	5	⊆	⊆	NUM
ejpam-1726	176	6	a	a	DET
ejpam-1726	176	7	define	define	NOUN
ejpam-1726	176	8	q+	q+	ADV
ejpam-1726	176	9	′	′	NUM
ejpam-1726	176	10	=	=	PUNCT
ejpam-1726	176	11	{	{	PUNCT
ejpam-1726	176	12	[	[	X
ejpam-1726	176	13	x	x	X
ejpam-1726	176	14	,	,	PUNCT
ejpam-1726	176	15	α	α	X
ejpam-1726	176	16	]	]	X
ejpam-1726	176	17	∈	∈	PROPN
ejpam-1726	176	18	l1	l1	PROPN
ejpam-1726	176	19	|	|	PROPN
ejpam-1726	176	20	xαa	xαa	PROPN
ejpam-1726	176	21	∈q	∈q	NOUN
ejpam-1726	176	22	,	,	PUNCT
ejpam-1726	176	23	for	for	ADP
ejpam-1726	176	24	all	all	DET
ejpam-1726	176	25	a	a	DET
ejpam-1726	176	26	∈	∈	PROPN
ejpam-1726	176	27	a	a	PRON
ejpam-1726	176	28	}	}	PUNCT
ejpam-1726	176	29	and	and	CCONJ
ejpam-1726	176	30	q∗	q∗	VERB
ejpam-1726	177	1	′	′	NUM
ejpam-1726	177	2	=	=	PUNCT
ejpam-1726	178	1	{	{	PUNCT
ejpam-1726	178	2	[	[	X
ejpam-1726	178	3	α	α	X
ejpam-1726	178	4	,	,	PUNCT
ejpam-1726	178	5	x	x	X
ejpam-1726	178	6	]	]	X
ejpam-1726	178	7	∈	∈	PROPN
ejpam-1726	178	8	r1	r1	NOUN
ejpam-1726	178	9	|	|	ADV
ejpam-1726	178	10	aαx	aαx	PROPN
ejpam-1726	178	11	∈q	∈q	NOUN
ejpam-1726	178	12	,	,	PUNCT
ejpam-1726	178	13	for	for	ADP
ejpam-1726	178	14	all	all	DET
ejpam-1726	178	15	a	a	DET
ejpam-1726	178	16	∈	∈	PROPN
ejpam-1726	178	17	a	a	PRON
ejpam-1726	178	18	}	}	PUNCT
ejpam-1726	178	19	.	.	PUNCT
ejpam-1726	179	1	s.	s.	PROPN
ejpam-1726	179	2	sardar	sardar	PROPN
ejpam-1726	179	3	,	,	PUNCT
ejpam-1726	179	4	s.	s.	PROPN
ejpam-1726	179	5	gupta	gupta	PROPN
ejpam-1726	179	6	,	,	PUNCT
ejpam-1726	179	7	k.	k.	PROPN
ejpam-1726	179	8	shum	shum	PROPN
ejpam-1726	179	9	/	/	SYM
ejpam-1726	179	10	eur	eur	PROPN
ejpam-1726	179	11	.	.	PUNCT
ejpam-1726	180	1	j.	j.	PROPN
ejpam-1726	180	2	pure	pure	PROPN
ejpam-1726	180	3	appl	appl	PROPN
ejpam-1726	180	4	.	.	PROPN
ejpam-1726	180	5	math	math	PROPN
ejpam-1726	180	6	,	,	PUNCT
ejpam-1726	180	7	6	6	NUM
ejpam-1726	180	8	(	(	PUNCT
ejpam-1726	180	9	2013	2013	NUM
ejpam-1726	180	10	)	)	PUNCT
ejpam-1726	180	11	,	,	PUNCT
ejpam-1726	180	12	1	1	NUM
ejpam-1726	180	13	-	-	SYM
ejpam-1726	180	14	10	10	NUM
ejpam-1726	180	15	8	8	NUM
ejpam-1726	180	16	now	now	ADV
ejpam-1726	180	17	there	there	PRON
ejpam-1726	180	18	exists	exist	VERB
ejpam-1726	180	19	an	an	DET
ejpam-1726	180	20	inclusion	inclusion	NOUN
ejpam-1726	180	21	preserving	preserve	VERB
ejpam-1726	180	22	bijection	bijection	NOUN
ejpam-1726	180	23	between	between	ADP
ejpam-1726	180	24	the	the	DET
ejpam-1726	180	25	set	set	NOUN
ejpam-1726	180	26	of	of	ADP
ejpam-1726	180	27	all	all	DET
ejpam-1726	180	28	ideals	ideal	NOUN
ejpam-1726	180	29	of	of	ADP
ejpam-1726	180	30	a	a	PRON
ejpam-1726	180	31	and	and	CCONJ
ejpam-1726	180	32	the	the	DET
ejpam-1726	180	33	set	set	NOUN
ejpam-1726	180	34	of	of	ADP
ejpam-1726	180	35	all	all	DET
ejpam-1726	180	36	ideals	ideal	NOUN
ejpam-1726	180	37	of	of	ADP
ejpam-1726	180	38	l1	l1	PROPN
ejpam-1726	180	39	[	[	X
ejpam-1726	180	40	see	see	VERB
ejpam-1726	180	41	2	2	NUM
ejpam-1726	180	42	]	]	PUNCT
ejpam-1726	180	43	via	via	ADP
ejpam-1726	180	44	the	the	DET
ejpam-1726	180	45	mapping	mapping	NOUN
ejpam-1726	180	46	q	q	PROPN
ejpam-1726	180	47	7→	7→	NUM
ejpam-1726	180	48	q+	q+	ADP
ejpam-1726	180	49	′	′	VERB
ejpam-1726	180	50	with	with	ADP
ejpam-1726	180	51	the	the	DET
ejpam-1726	180	52	inverse	inverse	NOUN
ejpam-1726	180	53	p	p	PROPN
ejpam-1726	180	54	7→	7→	PROPN
ejpam-1726	180	55	p+	p+	NOUN
ejpam-1726	180	56	.	.	PUNCT
ejpam-1726	181	1	and	and	CCONJ
ejpam-1726	181	2	also	also	ADV
ejpam-1726	181	3	there	there	PRON
ejpam-1726	181	4	exists	exist	VERB
ejpam-1726	181	5	an	an	DET
ejpam-1726	181	6	inclusion	inclusion	NOUN
ejpam-1726	181	7	preserving	preserve	VERB
ejpam-1726	181	8	bijection	bijection	NOUN
ejpam-1726	181	9	between	between	ADP
ejpam-1726	181	10	the	the	DET
ejpam-1726	181	11	set	set	NOUN
ejpam-1726	181	12	of	of	ADP
ejpam-1726	181	13	all	all	DET
ejpam-1726	181	14	ideals	ideal	NOUN
ejpam-1726	181	15	of	of	ADP
ejpam-1726	181	16	a	a	PRON
ejpam-1726	181	17	and	and	CCONJ
ejpam-1726	181	18	the	the	DET
ejpam-1726	181	19	set	set	NOUN
ejpam-1726	181	20	of	of	ADP
ejpam-1726	181	21	all	all	DET
ejpam-1726	181	22	ideals	ideal	NOUN
ejpam-1726	181	23	of	of	ADP
ejpam-1726	181	24	r1	r1	PROPN
ejpam-1726	181	25	via	via	ADP
ejpam-1726	181	26	the	the	DET
ejpam-1726	181	27	mapping	mapping	NOUN
ejpam-1726	181	28	q	q	PROPN
ejpam-1726	181	29	7→	7→	NUM
ejpam-1726	181	30	q∗	q∗	NOUN
ejpam-1726	181	31	′	′	NOUN
ejpam-1726	181	32	with	with	ADP
ejpam-1726	181	33	the	the	DET
ejpam-1726	181	34	inverse	inverse	NOUN
ejpam-1726	181	35	m	m	PROPN
ejpam-1726	181	36	7→	7→	NUM
ejpam-1726	181	37	m∗.	m∗.	NOUN
ejpam-1726	181	38	thus	thus	ADV
ejpam-1726	181	39	we	we	PRON
ejpam-1726	181	40	find	find	VERB
ejpam-1726	181	41	an	an	DET
ejpam-1726	181	42	inclusion	inclusion	NOUN
ejpam-1726	181	43	preserving	preserve	VERB
ejpam-1726	181	44	bijection	bijection	NOUN
ejpam-1726	181	45	between	between	ADP
ejpam-1726	181	46	the	the	DET
ejpam-1726	181	47	set	set	NOUN
ejpam-1726	181	48	of	of	ADP
ejpam-1726	181	49	all	all	DET
ejpam-1726	181	50	ideals	ideal	NOUN
ejpam-1726	181	51	of	of	ADP
ejpam-1726	181	52	r1	r1	PROPN
ejpam-1726	181	53	and	and	CCONJ
ejpam-1726	181	54	the	the	DET
ejpam-1726	181	55	set	set	NOUN
ejpam-1726	181	56	of	of	ADP
ejpam-1726	181	57	all	all	DET
ejpam-1726	181	58	ideals	ideal	NOUN
ejpam-1726	181	59	of	of	ADP
ejpam-1726	181	60	l1	l1	PROPN
ejpam-1726	181	61	via	via	ADP
ejpam-1726	181	62	the	the	DET
ejpam-1726	181	63	composition	composition	NOUN
ejpam-1726	181	64	mapping	mapping	NOUN
ejpam-1726	181	65	j	j	PROPN
ejpam-1726	181	66	7→	7→	NUM
ejpam-1726	181	67	j∗	j∗	NOUN
ejpam-1726	181	68	7→	7→	NUM
ejpam-1726	181	69	(	(	PUNCT
ejpam-1726	181	70	j∗)+	j∗)+	PROPN
ejpam-1726	181	71	′	′	NUM
ejpam-1726	181	72	with	with	ADP
ejpam-1726	181	73	the	the	DET
ejpam-1726	181	74	inverse	inverse	NOUN
ejpam-1726	182	1	i	i	NOUN
ejpam-1726	182	2	7→	7→	NUM
ejpam-1726	182	3	i+	i+	NUM
ejpam-1726	182	4	7→	7→	NUM
ejpam-1726	182	5	(	(	PUNCT
ejpam-1726	182	6	i+)∗	i+)∗	PROPN
ejpam-1726	182	7	′	′	NUM
ejpam-1726	182	8	.	.	PUNCT
ejpam-1726	183	1	hence	hence	ADV
ejpam-1726	183	2	the	the	DET
ejpam-1726	183	3	proof	proof	NOUN
ejpam-1726	183	4	is	be	AUX
ejpam-1726	183	5	completed	complete	VERB
ejpam-1726	183	6	.	.	PUNCT
ejpam-1726	184	1	now	now	ADV
ejpam-1726	184	2	from	from	ADP
ejpam-1726	184	3	[	[	X
ejpam-1726	184	4	1	1	NUM
ejpam-1726	184	5	,	,	PUNCT
ejpam-1726	184	6	3	3	NUM
ejpam-1726	184	7	,	,	PUNCT
ejpam-1726	184	8	5	5	NUM
ejpam-1726	184	9	]	]	PUNCT
ejpam-1726	184	10	we	we	PRON
ejpam-1726	184	11	know	know	VERB
ejpam-1726	184	12	that	that	SCONJ
ejpam-1726	184	13	all	all	DET
ejpam-1726	184	14	the	the	DET
ejpam-1726	184	15	mappings	mapping	NOUN
ejpam-1726	184	16	+	+	PROPN
ejpam-1726	184	17	,	,	PUNCT
ejpam-1726	184	18	+	+	NOUN
ejpam-1726	184	19	′	′	NOUN
ejpam-1726	184	20	,	,	PUNCT
ejpam-1726	184	21	∗	∗	NOUN
ejpam-1726	184	22	and	and	CCONJ
ejpam-1726	184	23	∗′	∗′	PROPN
ejpam-1726	184	24	carry	carry	VERB
ejpam-1726	184	25	the	the	DET
ejpam-1726	184	26	prime	prime	ADJ
ejpam-1726	184	27	ideal	ideal	NOUN
ejpam-1726	184	28	to	to	ADP
ejpam-1726	184	29	prime	prime	ADJ
ejpam-1726	184	30	ideal	ideal	NOUN
ejpam-1726	184	31	;	;	PUNCT
ejpam-1726	184	32	the	the	DET
ejpam-1726	184	33	maximal	maximal	ADJ
ejpam-1726	184	34	ideal	ideal	NOUN
ejpam-1726	184	35	to	to	ADP
ejpam-1726	184	36	maximal	maximal	ADJ
ejpam-1726	184	37	ideal	ideal	NOUN
ejpam-1726	184	38	;	;	PUNCT
ejpam-1726	184	39	the	the	DET
ejpam-1726	184	40	nilpotent	nilpotent	ADJ
ejpam-1726	184	41	ideal	ideal	NOUN
ejpam-1726	184	42	to	to	PART
ejpam-1726	184	43	nilpotent	nilpotent	VERB
ejpam-1726	184	44	ideal	ideal	NOUN
ejpam-1726	184	45	;	;	PUNCT
ejpam-1726	184	46	the	the	DET
ejpam-1726	184	47	nil	nil	ADJ
ejpam-1726	184	48	ideal	ideal	NOUN
ejpam-1726	184	49	to	to	PART
ejpam-1726	184	50	nil	nil	VERB
ejpam-1726	184	51	ideal	ideal	ADJ
ejpam-1726	184	52	;	;	PUNCT
ejpam-1726	184	53	the	the	DET
ejpam-1726	184	54	primary	primary	ADJ
ejpam-1726	184	55	ideal	ideal	NOUN
ejpam-1726	184	56	to	to	ADP
ejpam-1726	184	57	primary	primary	ADJ
ejpam-1726	184	58	ideal	ideal	NOUN
ejpam-1726	184	59	;	;	PUNCT
ejpam-1726	184	60	the	the	DET
ejpam-1726	184	61	semiprimary	semiprimary	ADJ
ejpam-1726	184	62	ideal	ideal	NOUN
ejpam-1726	184	63	to	to	ADP
ejpam-1726	184	64	semiprimary	semiprimary	ADJ
ejpam-1726	184	65	ideal	ideal	NOUN
ejpam-1726	184	66	and	and	CCONJ
ejpam-1726	184	67	the	the	DET
ejpam-1726	184	68	semiprime	semiprime	NOUN
ejpam-1726	184	69	ideal	ideal	NOUN
ejpam-1726	184	70	to	to	ADP
ejpam-1726	184	71	semiprime	semiprime	NOUN
ejpam-1726	184	72	ideal	ideal	NOUN
ejpam-1726	184	73	.	.	PUNCT
ejpam-1726	185	1	thus	thus	ADV
ejpam-1726	185	2	by	by	ADP
ejpam-1726	185	3	applying	apply	VERB
ejpam-1726	185	4	the	the	DET
ejpam-1726	185	5	same	same	ADJ
ejpam-1726	185	6	arguments	argument	NOUN
ejpam-1726	185	7	as	as	SCONJ
ejpam-1726	185	8	given	give	VERB
ejpam-1726	185	9	in	in	ADP
ejpam-1726	185	10	the	the	DET
ejpam-1726	185	11	above	above	ADJ
ejpam-1726	185	12	theorems	theorem	NOUN
ejpam-1726	185	13	we	we	PRON
ejpam-1726	185	14	see	see	VERB
ejpam-1726	185	15	that	that	SCONJ
ejpam-1726	185	16	the	the	DET
ejpam-1726	185	17	composition	composition	NOUN
ejpam-1726	185	18	mappings	mapping	NOUN
ejpam-1726	185	19	j	j	PROPN
ejpam-1726	185	20	7→	7→	NUM
ejpam-1726	185	21	j∗	j∗	NOUN
ejpam-1726	185	22	7→	7→	NUM
ejpam-1726	185	23	(	(	PUNCT
ejpam-1726	185	24	j∗)+	j∗)+	PROPN
ejpam-1726	185	25	′	′	NOUN
ejpam-1726	185	26	and	and	CCONJ
ejpam-1726	185	27	its	its	PRON
ejpam-1726	185	28	inverse	inverse	NOUN
ejpam-1726	186	1	i	i	NOUN
ejpam-1726	186	2	7→	7→	NUM
ejpam-1726	186	3	i+	i+	NUM
ejpam-1726	186	4	7→	7→	NUM
ejpam-1726	186	5	(	(	PUNCT
ejpam-1726	186	6	i+)∗	i+)∗	PROPN
ejpam-1726	186	7	′	′	NUM
ejpam-1726	186	8	.	.	PUNCT
ejpam-1726	187	1	carry	carry	VERB
ejpam-1726	187	2	the	the	DET
ejpam-1726	187	3	prime	prime	ADJ
ejpam-1726	187	4	ideal	ideal	NOUN
ejpam-1726	187	5	to	to	ADP
ejpam-1726	187	6	prime	prime	ADJ
ejpam-1726	187	7	ideal	ideal	NOUN
ejpam-1726	187	8	;	;	PUNCT
ejpam-1726	187	9	the	the	DET
ejpam-1726	187	10	maximal	maximal	ADJ
ejpam-1726	187	11	ideal	ideal	NOUN
ejpam-1726	187	12	to	to	ADP
ejpam-1726	187	13	maximal	maximal	ADJ
ejpam-1726	187	14	ideal	ideal	NOUN
ejpam-1726	187	15	;	;	PUNCT
ejpam-1726	187	16	the	the	DET
ejpam-1726	187	17	nilpotent	nilpotent	ADJ
ejpam-1726	187	18	ideal	ideal	NOUN
ejpam-1726	187	19	to	to	PART
ejpam-1726	187	20	nilpotent	nilpotent	VERB
ejpam-1726	187	21	ideal	ideal	NOUN
ejpam-1726	187	22	;	;	PUNCT
ejpam-1726	187	23	the	the	DET
ejpam-1726	187	24	nil	nil	ADJ
ejpam-1726	187	25	ideal	ideal	NOUN
ejpam-1726	187	26	to	to	PART
ejpam-1726	187	27	nil	nil	VERB
ejpam-1726	187	28	ideal	ideal	ADJ
ejpam-1726	187	29	;	;	PUNCT
ejpam-1726	187	30	the	the	DET
ejpam-1726	187	31	primary	primary	ADJ
ejpam-1726	187	32	ideal	ideal	NOUN
ejpam-1726	187	33	to	to	ADP
ejpam-1726	187	34	primary	primary	ADJ
ejpam-1726	187	35	ideal	ideal	NOUN
ejpam-1726	187	36	;	;	PUNCT
ejpam-1726	187	37	the	the	DET
ejpam-1726	187	38	semiprimary	semiprimary	ADJ
ejpam-1726	187	39	ideal	ideal	NOUN
ejpam-1726	187	40	to	to	ADP
ejpam-1726	187	41	semiprimary	semiprimary	ADJ
ejpam-1726	187	42	ideal	ideal	NOUN
ejpam-1726	187	43	and	and	CCONJ
ejpam-1726	187	44	the	the	DET
ejpam-1726	187	45	semiprime	semiprime	NOUN
ejpam-1726	187	46	ideal	ideal	NOUN
ejpam-1726	187	47	to	to	ADP
ejpam-1726	187	48	semiprime	semiprime	NOUN
ejpam-1726	187	49	ideal	ideal	NOUN
ejpam-1726	187	50	from	from	ADP
ejpam-1726	187	51	r1	r1	PROPN
ejpam-1726	187	52	to	to	ADP
ejpam-1726	187	53	l1	l1	PROPN
ejpam-1726	187	54	and	and	CCONJ
ejpam-1726	187	55	from	from	ADP
ejpam-1726	187	56	l1	l1	PROPN
ejpam-1726	187	57	to	to	ADP
ejpam-1726	187	58	r1	r1	PROPN
ejpam-1726	187	59	,	,	PUNCT
ejpam-1726	187	60	respectively	respectively	ADV
ejpam-1726	187	61	.	.	PUNCT
ejpam-1726	188	1	this	this	DET
ejpam-1726	188	2	fact	fact	NOUN
ejpam-1726	188	3	gives	give	VERB
ejpam-1726	188	4	rise	rise	NOUN
ejpam-1726	188	5	to	to	ADP
ejpam-1726	188	6	the	the	DET
ejpam-1726	188	7	following	following	ADJ
ejpam-1726	188	8	result	result	NOUN
ejpam-1726	188	9	for	for	ADP
ejpam-1726	188	10	the	the	DET
ejpam-1726	188	11	morita	morita	PROPN
ejpam-1726	188	12	equivalent	equivalent	PROPN
ejpam-1726	188	13	monoids	monoids	PROPN
ejpam-1726	188	14	.	.	PUNCT
ejpam-1726	189	1	theorem	theorem	VERB
ejpam-1726	189	2	8	8	NUM
ejpam-1726	189	3	.	.	PUNCT
ejpam-1726	190	1	let	let	VERB
ejpam-1726	190	2	l	l	NOUN
ejpam-1726	190	3	and	and	CCONJ
ejpam-1726	190	4	r	r	NOUN
ejpam-1726	190	5	be	be	AUX
ejpam-1726	190	6	two	two	NUM
ejpam-1726	190	7	morita	morita	PROPN
ejpam-1726	190	8	equivalent	equivalent	PROPN
ejpam-1726	190	9	monoids	monoids	PROPN
ejpam-1726	190	10	.	.	PUNCT
ejpam-1726	191	1	then	then	ADV
ejpam-1726	191	2	there	there	PRON
ejpam-1726	191	3	exists	exist	VERB
ejpam-1726	191	4	an	an	DET
ejpam-1726	191	5	inclusion	inclusion	NOUN
ejpam-1726	191	6	preserving	preserve	VERB
ejpam-1726	191	7	bijection	bijection	NOUN
ejpam-1726	191	8	between	between	ADP
ejpam-1726	191	9	the	the	DET
ejpam-1726	191	10	set	set	NOUN
ejpam-1726	191	11	of	of	ADP
ejpam-1726	191	12	all	all	DET
ejpam-1726	191	13	prime	prime	ADJ
ejpam-1726	191	14	(	(	PUNCT
ejpam-1726	191	15	maximal	maximal	ADJ
ejpam-1726	191	16	,	,	PUNCT
ejpam-1726	191	17	nilpotent	nilpotent	ADJ
ejpam-1726	191	18	,	,	PUNCT
ejpam-1726	191	19	nil	nil	ADJ
ejpam-1726	191	20	,	,	PUNCT
ejpam-1726	191	21	primary	primary	ADJ
ejpam-1726	191	22	,	,	PUNCT
ejpam-1726	191	23	semiprimary	semiprimary	ADJ
ejpam-1726	191	24	,	,	PUNCT
ejpam-1726	191	25	semiprime	semiprime	NOUN
ejpam-1726	191	26	)	)	PUNCT
ejpam-1726	191	27	ideals	ideal	NOUN
ejpam-1726	191	28	of	of	ADP
ejpam-1726	191	29	r	r	NOUN
ejpam-1726	191	30	and	and	CCONJ
ejpam-1726	191	31	the	the	DET
ejpam-1726	191	32	set	set	NOUN
ejpam-1726	191	33	of	of	ADP
ejpam-1726	191	34	all	all	DET
ejpam-1726	191	35	prime	prime	ADJ
ejpam-1726	191	36	(	(	PUNCT
ejpam-1726	191	37	maximal	maximal	ADJ
ejpam-1726	191	38	,	,	PUNCT
ejpam-1726	191	39	nilpotent	nilpotent	ADJ
ejpam-1726	191	40	,	,	PUNCT
ejpam-1726	191	41	nil	nil	ADJ
ejpam-1726	191	42	,	,	PUNCT
ejpam-1726	191	43	primary	primary	ADJ
ejpam-1726	191	44	,	,	PUNCT
ejpam-1726	191	45	semiprimary	semiprimary	ADJ
ejpam-1726	191	46	,	,	PUNCT
ejpam-1726	191	47	semiprime	semiprime	NOUN
ejpam-1726	191	48	,	,	PUNCT
ejpam-1726	191	49	respectively	respectively	ADV
ejpam-1726	191	50	)	)	PUNCT
ejpam-1726	191	51	ideals	ideal	NOUN
ejpam-1726	191	52	of	of	ADP
ejpam-1726	191	53	l.	l.	PROPN
ejpam-1726	191	54	also	also	ADV
ejpam-1726	191	55	combining	combine	VERB
ejpam-1726	191	56	the	the	DET
ejpam-1726	191	57	respective	respective	ADJ
ejpam-1726	191	58	results	result	NOUN
ejpam-1726	191	59	of	of	ADP
ejpam-1726	191	60	[	[	X
ejpam-1726	191	61	3	3	NUM
ejpam-1726	191	62	,	,	PUNCT
ejpam-1726	191	63	5	5	NUM
ejpam-1726	191	64	]	]	PUNCT
ejpam-1726	191	65	for	for	ADP
ejpam-1726	191	66	left	left	ADJ
ejpam-1726	191	67	operator	operator	NOUN
ejpam-1726	191	68	l	l	NOUN
ejpam-1726	191	69	and	and	CCONJ
ejpam-1726	191	70	right	right	ADJ
ejpam-1726	191	71	operator	operator	NOUN
ejpam-1726	191	72	r	r	NOUN
ejpam-1726	191	73	of	of	ADP
ejpam-1726	191	74	a	a	DET
ejpam-1726	191	75	γ	γ	NOUN
ejpam-1726	191	76	-	-	PUNCT
ejpam-1726	191	77	semigroup	semigroup	NOUN
ejpam-1726	191	78	a	a	PRON
ejpam-1726	191	79	we	we	PRON
ejpam-1726	191	80	find	find	VERB
ejpam-1726	191	81	that	that	SCONJ
ejpam-1726	191	82	different	different	ADJ
ejpam-1726	191	83	types	type	NOUN
ejpam-1726	191	84	of	of	ADP
ejpam-1726	191	85	radicals	radical	NOUN
ejpam-1726	191	86	viz	viz	PROPN
ejpam-1726	191	87	.	.	PUNCT
ejpam-1726	192	1	prime	prime	PROPN
ejpam-1726	192	2	radical	radical	ADJ
ejpam-1726	192	3	,	,	PUNCT
ejpam-1726	192	4	schwarz	schwarz	NOUN
ejpam-1726	192	5	radical	radical	ADJ
ejpam-1726	192	6	,	,	PUNCT
ejpam-1726	192	7	clifford	clifford	PROPN
ejpam-1726	192	8	radical	radical	PROPN
ejpam-1726	192	9	are	be	AUX
ejpam-1726	192	10	also	also	ADV
ejpam-1726	192	11	preserved	preserve	VERB
ejpam-1726	192	12	by	by	ADP
ejpam-1726	192	13	the	the	DET
ejpam-1726	192	14	mappings	mapping	NOUN
ejpam-1726	192	15	j	j	PROPN
ejpam-1726	192	16	7→	7→	NUM
ejpam-1726	192	17	j∗	j∗	NOUN
ejpam-1726	192	18	7→	7→	NUM
ejpam-1726	192	19	(	(	PUNCT
ejpam-1726	192	20	j∗)+	j∗)+	PROPN
ejpam-1726	192	21	′	′	NOUN
ejpam-1726	192	22	and	and	CCONJ
ejpam-1726	192	23	its	its	PRON
ejpam-1726	192	24	inverse	inverse	NOUN
ejpam-1726	192	25	i	i	NOUN
ejpam-1726	192	26	7→	7→	NUM
ejpam-1726	192	27	i+	i+	NUM
ejpam-1726	192	28	7→	7→	NUM
ejpam-1726	192	29	(	(	PUNCT
ejpam-1726	192	30	i+)∗	i+)∗	PROPN
ejpam-1726	192	31	′	′	NUM
ejpam-1726	192	32	.	.	PUNCT
ejpam-1726	193	1	hence	hence	ADV
ejpam-1726	193	2	,	,	PUNCT
ejpam-1726	193	3	we	we	PRON
ejpam-1726	193	4	obtain	obtain	VERB
ejpam-1726	193	5	the	the	DET
ejpam-1726	193	6	following	follow	VERB
ejpam-1726	193	7	theorem	theorem	VERB
ejpam-1726	193	8	.	.	PUNCT
ejpam-1726	193	9	theorem	theorem	NOUN
ejpam-1726	193	10	9	9	NUM
ejpam-1726	193	11	.	.	PUNCT
ejpam-1726	194	1	let	let	VERB
ejpam-1726	194	2	l	l	NOUN
ejpam-1726	194	3	and	and	CCONJ
ejpam-1726	194	4	r	r	NOUN
ejpam-1726	194	5	be	be	VERB
ejpam-1726	194	6	morita	morita	PROPN
ejpam-1726	194	7	equivalent	equivalent	PROPN
ejpam-1726	194	8	monoids	monoids	PROPN
ejpam-1726	194	9	.	.	PUNCT
ejpam-1726	195	1	then	then	ADV
ejpam-1726	195	2	the	the	DET
ejpam-1726	195	3	prime	prime	NOUN
ejpam-1726	195	4	(	(	PUNCT
ejpam-1726	195	5	schwarz	schwarz	PROPN
ejpam-1726	195	6	,	,	PUNCT
ejpam-1726	195	7	clifford	clifford	PROPN
ejpam-1726	195	8	)	)	PUNCT
ejpam-1726	195	9	radical	radical	NOUN
ejpam-1726	195	10	of	of	ADP
ejpam-1726	195	11	r(l	r(l	NOUN
ejpam-1726	195	12	)	)	PUNCT
ejpam-1726	195	13	is	be	AUX
ejpam-1726	195	14	taken	take	VERB
ejpam-1726	195	15	to	to	PART
ejpam-1726	195	16	be	be	AUX
ejpam-1726	195	17	the	the	DET
ejpam-1726	195	18	prime	prime	NOUN
ejpam-1726	195	19	(	(	PUNCT
ejpam-1726	195	20	schwarz	schwarz	PROPN
ejpam-1726	195	21	,	,	PUNCT
ejpam-1726	195	22	clifford	clifford	PROPN
ejpam-1726	195	23	)	)	PUNCT
ejpam-1726	195	24	radical	radical	NOUN
ejpam-1726	195	25	of	of	ADP
ejpam-1726	195	26	l	l	PROPN
ejpam-1726	195	27	(	(	PUNCT
ejpam-1726	195	28	respectively	respectively	ADV
ejpam-1726	195	29	,	,	PUNCT
ejpam-1726	195	30	r	r	NOUN
ejpam-1726	195	31	)	)	PUNCT
ejpam-1726	195	32	via	via	ADP
ejpam-1726	195	33	the	the	DET
ejpam-1726	195	34	mapping	mapping	NOUN
ejpam-1726	195	35	j	j	PROPN
ejpam-1726	195	36	7→	7→	NUM
ejpam-1726	195	37	j∗	j∗	NOUN
ejpam-1726	195	38	7→	7→	NUM
ejpam-1726	195	39	(	(	PUNCT
ejpam-1726	195	40	j∗)+	j∗)+	PROPN
ejpam-1726	195	41	′	′	NUM
ejpam-1726	195	42	(	(	PUNCT
ejpam-1726	195	43	respectively	respectively	ADV
ejpam-1726	195	44	,	,	PUNCT
ejpam-1726	195	45	i	i	PROPN
ejpam-1726	195	46	7→	7→	NUM
ejpam-1726	195	47	i+	i+	NUM
ejpam-1726	195	48	7→	7→	NUM
ejpam-1726	195	49	(	(	PUNCT
ejpam-1726	195	50	i+)∗	i+)∗	PROPN
ejpam-1726	195	51	′	′	NUM
ejpam-1726	195	52	)	)	PUNCT
ejpam-1726	195	53	.	.	PUNCT
ejpam-1726	196	1	references	reference	NOUN
ejpam-1726	196	2	9	9	NUM
ejpam-1726	196	3	in	in	ADP
ejpam-1726	196	4	the	the	DET
ejpam-1726	196	5	following	follow	VERB
ejpam-1726	196	6	theorem	theorem	NOUN
ejpam-1726	196	7	we	we	PRON
ejpam-1726	196	8	characterize	characterize	VERB
ejpam-1726	196	9	the	the	DET
ejpam-1726	196	10	noetherian	noetherian	ADJ
ejpam-1726	196	11	morita	morita	PROPN
ejpam-1726	196	12	equivalent	equivalent	PROPN
ejpam-1726	196	13	monoids	monoids	PROPN
ejpam-1726	196	14	.	.	PUNCT
ejpam-1726	197	1	theorem	theorem	NOUN
ejpam-1726	197	2	10	10	NUM
ejpam-1726	197	3	.	.	PUNCT
ejpam-1726	198	1	let	let	VERB
ejpam-1726	198	2	l	l	NOUN
ejpam-1726	198	3	and	and	CCONJ
ejpam-1726	198	4	r	r	NOUN
ejpam-1726	198	5	be	be	VERB
ejpam-1726	198	6	morita	morita	PROPN
ejpam-1726	198	7	equivalent	equivalent	PROPN
ejpam-1726	198	8	monoids	monoids	PROPN
ejpam-1726	198	9	.	.	PUNCT
ejpam-1726	199	1	then	then	ADV
ejpam-1726	199	2	l	l	NOUN
ejpam-1726	199	3	is	be	AUX
ejpam-1726	199	4	noetherian	noetherian	ADJ
ejpam-1726	199	5	if	if	SCONJ
ejpam-1726	199	6	and	and	CCONJ
ejpam-1726	199	7	only	only	ADV
ejpam-1726	199	8	if	if	SCONJ
ejpam-1726	199	9	r	r	NOUN
ejpam-1726	199	10	is	be	AUX
ejpam-1726	199	11	noetherian	noetherian	ADJ
ejpam-1726	199	12	.	.	PUNCT
ejpam-1726	200	1	proof	proof	NOUN
ejpam-1726	200	2	.	.	PUNCT
ejpam-1726	201	1	by	by	ADP
ejpam-1726	201	2	theorem	theorem	NOUN
ejpam-1726	201	3	6	6	NUM
ejpam-1726	201	4	there	there	ADV
ejpam-1726	201	5	exists	exist	VERB
ejpam-1726	201	6	a	a	DET
ejpam-1726	201	7	γ	γ	NOUN
ejpam-1726	201	8	-	-	PUNCT
ejpam-1726	201	9	semigroup	semigroup	NOUN
ejpam-1726	201	10	a	a	PRON
ejpam-1726	201	11	with	with	ADP
ejpam-1726	201	12	left	left	ADJ
ejpam-1726	201	13	and	and	CCONJ
ejpam-1726	201	14	right	right	ADJ
ejpam-1726	201	15	unities	unity	NOUN
ejpam-1726	201	16	whose	whose	DET
ejpam-1726	201	17	left	left	ADJ
ejpam-1726	201	18	and	and	CCONJ
ejpam-1726	201	19	right	right	ADJ
ejpam-1726	201	20	operator	operator	NOUN
ejpam-1726	201	21	monoids	monoid	NOUN
ejpam-1726	201	22	l1	l1	PROPN
ejpam-1726	201	23	and	and	CCONJ
ejpam-1726	201	24	r1	r1	PROPN
ejpam-1726	201	25	are	be	AUX
ejpam-1726	201	26	isomorphic	isomorphic	ADJ
ejpam-1726	201	27	to	to	ADP
ejpam-1726	201	28	l	l	NOUN
ejpam-1726	201	29	and	and	CCONJ
ejpam-1726	201	30	r	r	NOUN
ejpam-1726	201	31	respectively	respectively	ADV
ejpam-1726	201	32	.	.	PUNCT
ejpam-1726	202	1	now	now	ADV
ejpam-1726	202	2	according	accord	VERB
ejpam-1726	202	3	to	to	ADP
ejpam-1726	202	4	[	[	X
ejpam-1726	202	5	4	4	NUM
ejpam-1726	202	6	]	]	X
ejpam-1726	202	7	l1	l1	PROPN
ejpam-1726	202	8	is	be	AUX
ejpam-1726	202	9	noetherian	noetherian	ADJ
ejpam-1726	202	10	⇔	⇔	X
ejpam-1726	202	11	a	a	PRON
ejpam-1726	202	12	is	be	AUX
ejpam-1726	202	13	noetherian	noetherian	ADJ
ejpam-1726	202	14	⇔	⇔	X
ejpam-1726	202	15	r1is	r1is	PUNCT
ejpam-1726	202	16	noetherian	noetherian	NOUN
ejpam-1726	202	17	.	.	PUNCT
ejpam-1726	203	1	hence	hence	ADV
ejpam-1726	203	2	the	the	DET
ejpam-1726	203	3	result	result	NOUN
ejpam-1726	203	4	follows	follow	VERB
ejpam-1726	203	5	.	.	PUNCT
ejpam-1726	204	1	in	in	ADP
ejpam-1726	204	2	a	a	DET
ejpam-1726	204	3	similar	similar	ADJ
ejpam-1726	204	4	way	way	NOUN
ejpam-1726	204	5	by	by	ADP
ejpam-1726	204	6	using	use	VERB
ejpam-1726	204	7	the	the	DET
ejpam-1726	204	8	result	result	NOUN
ejpam-1726	204	9	of	of	ADP
ejpam-1726	204	10	[	[	X
ejpam-1726	204	11	1	1	NUM
ejpam-1726	204	12	]	]	PUNCT
ejpam-1726	204	13	regarding	regard	VERB
ejpam-1726	204	14	primary	primary	ADJ
ejpam-1726	204	15	and	and	CCONJ
ejpam-1726	204	16	semiprimary	semiprimary	ADJ
ejpam-1726	204	17	γ	γ	PROPN
ejpam-1726	204	18	-	-	PUNCT
ejpam-1726	204	19	semigroup	semigroup	NOUN
ejpam-1726	204	20	we	we	PRON
ejpam-1726	204	21	get	get	VERB
ejpam-1726	204	22	the	the	DET
ejpam-1726	204	23	following	follow	VERB
ejpam-1726	204	24	theorem	theorem	VERB
ejpam-1726	204	25	.	.	PUNCT
ejpam-1726	204	26	theorem	theorem	NOUN
ejpam-1726	204	27	11	11	NUM
ejpam-1726	204	28	.	.	PUNCT
ejpam-1726	205	1	let	let	VERB
ejpam-1726	205	2	l	l	NOUN
ejpam-1726	205	3	and	and	CCONJ
ejpam-1726	205	4	r	r	NOUN
ejpam-1726	205	5	be	be	VERB
ejpam-1726	205	6	morita	morita	PROPN
ejpam-1726	205	7	equivalent	equivalent	PROPN
ejpam-1726	205	8	monoids	monoids	PROPN
ejpam-1726	205	9	.	.	PUNCT
ejpam-1726	206	1	then	then	ADV
ejpam-1726	206	2	l	l	PROPN
ejpam-1726	206	3	is	be	AUX
ejpam-1726	206	4	primary	primary	ADJ
ejpam-1726	206	5	(	(	PUNCT
ejpam-1726	206	6	semiprimary	semiprimary	ADJ
ejpam-1726	206	7	)	)	PUNCT
ejpam-1726	206	8	if	if	SCONJ
ejpam-1726	207	1	and	and	CCONJ
ejpam-1726	207	2	only	only	ADV
ejpam-1726	207	3	if	if	SCONJ
ejpam-1726	207	4	r	r	NOUN
ejpam-1726	207	5	is	be	AUX
ejpam-1726	207	6	primary	primary	ADJ
ejpam-1726	207	7	(	(	PUNCT
ejpam-1726	207	8	semiprimary	semiprimary	ADJ
ejpam-1726	207	9	)	)	PUNCT
ejpam-1726	207	10	.	.	PUNCT
ejpam-1726	208	1	remark	remark	PROPN
ejpam-1726	208	2	1	1	NUM
ejpam-1726	208	3	.	.	PUNCT
ejpam-1726	209	1	since	since	SCONJ
ejpam-1726	209	2	we	we	PRON
ejpam-1726	209	3	have	have	AUX
ejpam-1726	209	4	deduced	deduce	VERB
ejpam-1726	209	5	that	that	SCONJ
ejpam-1726	209	6	the	the	DET
ejpam-1726	209	7	operator	operator	NOUN
ejpam-1726	209	8	monoids	monoid	NOUN
ejpam-1726	209	9	of	of	ADP
ejpam-1726	209	10	a	a	DET
ejpam-1726	209	11	γ	γ	NOUN
ejpam-1726	209	12	-	-	PUNCT
ejpam-1726	209	13	semigroup	semigroup	NOUN
ejpam-1726	209	14	a	a	PRON
ejpam-1726	209	15	with	with	ADP
ejpam-1726	209	16	unities	unity	NOUN
ejpam-1726	209	17	are	be	AUX
ejpam-1726	209	18	morita	morita	PROPN
ejpam-1726	209	19	equivalent	equivalent	NOUN
ejpam-1726	209	20	it	it	PRON
ejpam-1726	209	21	is	be	AUX
ejpam-1726	209	22	noteworthy	noteworthy	ADJ
ejpam-1726	209	23	that	that	SCONJ
ejpam-1726	209	24	the	the	DET
ejpam-1726	209	25	examples	example	NOUN
ejpam-1726	209	26	of	of	ADP
ejpam-1726	209	27	non	non	ADJ
ejpam-1726	209	28	-	-	ADJ
ejpam-1726	209	29	isomorphic	isomorphic	ADJ
ejpam-1726	209	30	operator	operator	NOUN
ejpam-1726	209	31	monoids	monoid	NOUN
ejpam-1726	209	32	will	will	AUX
ejpam-1726	209	33	also	also	ADV
ejpam-1726	209	34	become	become	VERB
ejpam-1726	209	35	examples	example	NOUN
ejpam-1726	209	36	of	of	ADP
ejpam-1726	209	37	non	non	ADJ
ejpam-1726	209	38	-	-	ADJ
ejpam-1726	209	39	isomorphic	isomorphic	ADJ
ejpam-1726	209	40	morita	morita	NOUN
ejpam-1726	209	41	equivalent	equivalent	PROPN
ejpam-1726	209	42	monoids	monoid	NOUN
ejpam-1726	209	43	.	.	PUNCT
ejpam-1726	210	1	5	5	X
ejpam-1726	210	2	.	.	X
ejpam-1726	210	3	conclusion	conclusion	NOUN
ejpam-1726	210	4	it	it	PRON
ejpam-1726	210	5	is	be	AUX
ejpam-1726	210	6	evident	evident	ADJ
ejpam-1726	210	7	from	from	ADP
ejpam-1726	210	8	theorem	theorem	NOUN
ejpam-1726	210	9	6	6	NUM
ejpam-1726	210	10	that	that	SCONJ
ejpam-1726	210	11	there	there	PRON
ejpam-1726	210	12	is	be	VERB
ejpam-1726	210	13	a	a	DET
ejpam-1726	210	14	close	close	ADJ
ejpam-1726	210	15	connection	connection	NOUN
ejpam-1726	210	16	between	between	ADP
ejpam-1726	210	17	the	the	DET
ejpam-1726	210	18	morita	morita	PROPN
ejpam-1726	210	19	equivalence	equivalence	NOUN
ejpam-1726	210	20	of	of	ADP
ejpam-1726	210	21	monoids	monoid	NOUN
ejpam-1726	210	22	and	and	CCONJ
ejpam-1726	210	23	γ	γ	NOUN
ejpam-1726	210	24	-	-	PUNCT
ejpam-1726	210	25	semigroups	semigroup	NOUN
ejpam-1726	210	26	with	with	ADP
ejpam-1726	210	27	unities	unity	NOUN
ejpam-1726	210	28	which	which	PRON
ejpam-1726	210	29	supplement	supplement	VERB
ejpam-1726	210	30	the	the	DET
ejpam-1726	210	31	study	study	NOUN
ejpam-1726	210	32	of	of	ADP
ejpam-1726	210	33	the	the	DET
ejpam-1726	210	34	other	other	ADJ
ejpam-1726	210	35	.	.	PUNCT
ejpam-1726	211	1	in	in	ADP
ejpam-1726	211	2	this	this	DET
ejpam-1726	211	3	paper	paper	NOUN
ejpam-1726	211	4	we	we	PRON
ejpam-1726	211	5	have	have	AUX
ejpam-1726	211	6	already	already	ADV
ejpam-1726	211	7	shown	show	VERB
ejpam-1726	211	8	how	how	SCONJ
ejpam-1726	211	9	the	the	DET
ejpam-1726	211	10	results	result	NOUN
ejpam-1726	211	11	of	of	ADP
ejpam-1726	211	12	γ	γ	NOUN
ejpam-1726	211	13	-	-	PUNCT
ejpam-1726	211	14	semigroups	semigroup	NOUN
ejpam-1726	211	15	can	can	AUX
ejpam-1726	211	16	be	be	AUX
ejpam-1726	211	17	used	use	VERB
ejpam-1726	211	18	to	to	PART
ejpam-1726	211	19	enrich	enrich	VERB
ejpam-1726	211	20	the	the	DET
ejpam-1726	211	21	morita	morita	PROPN
ejpam-1726	211	22	theory	theory	NOUN
ejpam-1726	211	23	for	for	ADP
ejpam-1726	211	24	monoids	monoid	NOUN
ejpam-1726	211	25	.	.	PUNCT
ejpam-1726	212	1	it	it	PRON
ejpam-1726	212	2	will	will	AUX
ejpam-1726	212	3	be	be	AUX
ejpam-1726	212	4	nice	nice	ADJ
ejpam-1726	212	5	to	to	PART
ejpam-1726	212	6	see	see	VERB
ejpam-1726	212	7	whether	whether	SCONJ
ejpam-1726	212	8	similar	similar	ADJ
ejpam-1726	212	9	results	result	NOUN
ejpam-1726	212	10	will	will	AUX
ejpam-1726	212	11	hold	hold	VERB
ejpam-1726	212	12	when	when	SCONJ
ejpam-1726	212	13	we	we	PRON
ejpam-1726	212	14	replace	replace	VERB
ejpam-1726	212	15	the	the	DET
ejpam-1726	212	16	morita	morita	NOUN
ejpam-1726	212	17	equivalence	equivalence	NOUN
ejpam-1726	212	18	by	by	ADP
ejpam-1726	212	19	morita	morita	PROPN
ejpam-1726	212	20	-	-	PUNCT
ejpam-1726	212	21	like	like	ADJ
ejpam-1726	212	22	equivalence	equivalence	NOUN
ejpam-1726	212	23	[	[	X
ejpam-1726	212	24	20	20	NUM
ejpam-1726	212	25	]	]	PUNCT
ejpam-1726	212	26	.	.	PUNCT
ejpam-1726	213	1	references	reference	NOUN
ejpam-1726	213	2	[	[	X
ejpam-1726	213	3	1	1	NUM
ejpam-1726	213	4	]	]	PUNCT
ejpam-1726	213	5	n	n	PRON
ejpam-1726	213	6	c	c	NOUN
ejpam-1726	213	7	adhikari	adhikari	PROPN
ejpam-1726	213	8	.	.	PUNCT
ejpam-1726	214	1	primary	primary	ADJ
ejpam-1726	214	2	and	and	CCONJ
ejpam-1726	214	3	semiprimary	semiprimary	ADJ
ejpam-1726	214	4	γ	γ	PROPN
ejpam-1726	214	5	-	-	PUNCT
ejpam-1726	214	6	semigroup	semigroup	NOUN
ejpam-1726	214	7	.	.	PUNCT
ejpam-1726	215	1	analele	analele	ADP
ejpam-1726	215	2	stiintifice	stiintifice	PROPN
ejpam-1726	215	3	ale	ale	NOUN
ejpam-1726	215	4	universitatii	universitatii	PROPN
ejpam-1726	215	5	"	"	PUNCT
ejpam-1726	215	6	al	al	PROPN
ejpam-1726	215	7	.	.	PROPN
ejpam-1726	215	8	i.	i.	PROPN
ejpam-1726	215	9	cuze	cuze	PROPN
ejpam-1726	215	10	"	"	PUNCT
ejpam-1726	215	11	din	din	PROPN
ejpam-1726	215	12	iasi	iasi	PROPN
ejpam-1726	215	13	.	.	PROPN
ejpam-1726	215	14	serie	serie	PROPN
ejpam-1726	215	15	noua	noua	PROPN
ejpam-1726	215	16	.	.	PROPN
ejpam-1726	215	17	matematica	matematica	PROPN
ejpam-1726	215	18	,	,	PUNCT
ejpam-1726	215	19	42(2):273–280	42(2):273–280	NOUN
ejpam-1726	215	20	,	,	PUNCT
ejpam-1726	215	21	1998	1998	NUM
ejpam-1726	215	22	.	.	PUNCT
ejpam-1726	216	1	[	[	X
ejpam-1726	216	2	2	2	NUM
ejpam-1726	216	3	]	]	PUNCT
ejpam-1726	216	4	n	n	PRON
ejpam-1726	216	5	c	c	NOUN
ejpam-1726	216	6	adhikari	adhikari	PROPN
ejpam-1726	216	7	and	and	CCONJ
ejpam-1726	216	8	t	t	PROPN
ejpam-1726	216	9	k	k	PROPN
ejpam-1726	216	10	dutta	dutta	PROPN
ejpam-1726	216	11	.	.	PUNCT
ejpam-1726	217	1	on	on	ADP
ejpam-1726	217	2	γ	γ	PROPN
ejpam-1726	217	3	-	-	PUNCT
ejpam-1726	217	4	semigroup	semigroup	NOUN
ejpam-1726	217	5	with	with	ADP
ejpam-1726	217	6	right	right	NOUN
ejpam-1726	217	7	and	and	CCONJ
ejpam-1726	217	8	left	leave	VERB
ejpam-1726	217	9	unities	unity	NOUN
ejpam-1726	217	10	.	.	PUNCT
ejpam-1726	218	1	soochow	soochow	PROPN
ejpam-1726	218	2	journal	journal	PROPN
ejpam-1726	218	3	of	of	ADP
ejpam-1726	218	4	mathematics	mathematics	PROPN
ejpam-1726	218	5	,	,	PUNCT
ejpam-1726	218	6	19(4):461–474	19(4):461–474	PROPN
ejpam-1726	218	7	,	,	PUNCT
ejpam-1726	218	8	1993	1993	NUM
ejpam-1726	218	9	.	.	PUNCT
ejpam-1726	219	1	[	[	X
ejpam-1726	219	2	3	3	X
ejpam-1726	219	3	]	]	PUNCT
ejpam-1726	219	4	n	n	PRON
ejpam-1726	219	5	c	c	NOUN
ejpam-1726	219	6	adhikari	adhikari	PROPN
ejpam-1726	219	7	and	and	CCONJ
ejpam-1726	219	8	t	t	PROPN
ejpam-1726	219	9	k	k	PROPN
ejpam-1726	219	10	dutta	dutta	PROPN
ejpam-1726	219	11	.	.	PUNCT
ejpam-1726	220	1	on	on	ADP
ejpam-1726	220	2	prime	prime	ADJ
ejpam-1726	220	3	radical	radical	ADJ
ejpam-1726	220	4	of	of	ADP
ejpam-1726	220	5	γ	γ	PROPN
ejpam-1726	220	6	-	-	PUNCT
ejpam-1726	220	7	semigroup	semigroup	NOUN
ejpam-1726	220	8	.	.	PUNCT
ejpam-1726	220	9	bulletin	bulletin	NOUN
ejpam-1726	220	10	of	of	ADP
ejpam-1726	220	11	calcutta	calcutta	PROPN
ejpam-1726	220	12	mathematical	mathematical	ADJ
ejpam-1726	220	13	society	society	NOUN
ejpam-1726	220	14	,	,	PUNCT
ejpam-1726	220	15	86(5):437–444	86(5):437–444	PROPN
ejpam-1726	220	16	,	,	PUNCT
ejpam-1726	220	17	1994	1994	NUM
ejpam-1726	220	18	.	.	PUNCT
ejpam-1726	221	1	[	[	X
ejpam-1726	221	2	4	4	X
ejpam-1726	221	3	]	]	PUNCT
ejpam-1726	221	4	n	n	PRON
ejpam-1726	221	5	c	c	NOUN
ejpam-1726	221	6	adhikari	adhikari	PROPN
ejpam-1726	221	7	and	and	CCONJ
ejpam-1726	221	8	t	t	PROPN
ejpam-1726	221	9	k	k	PROPN
ejpam-1726	221	10	dutta	dutta	PROPN
ejpam-1726	221	11	.	.	PUNCT
ejpam-1726	222	1	on	on	ADP
ejpam-1726	222	2	noetherian	noetherian	ADJ
ejpam-1726	222	3	γ	γ	X
ejpam-1726	222	4	-	-	PUNCT
ejpam-1726	222	5	semigroup	semigroup	NOUN
ejpam-1726	222	6	.	.	PUNCT
ejpam-1726	223	1	kyunpook	kyunpook	PROPN
ejpam-1726	223	2	mathematical	mathematical	PROPN
ejpam-1726	223	3	journal	journal	PROPN
ejpam-1726	223	4	,	,	PUNCT
ejpam-1726	223	5	36(1):89–95	36(1):89–95	NUM
ejpam-1726	223	6	,	,	PUNCT
ejpam-1726	223	7	1996	1996	NUM
ejpam-1726	223	8	.	.	PUNCT
ejpam-1726	224	1	[	[	X
ejpam-1726	224	2	5	5	NUM
ejpam-1726	224	3	]	]	PUNCT
ejpam-1726	224	4	n	n	PRON
ejpam-1726	224	5	c	c	NOUN
ejpam-1726	224	6	adhikari	adhikari	PROPN
ejpam-1726	224	7	and	and	CCONJ
ejpam-1726	224	8	t	t	PROPN
ejpam-1726	224	9	k	k	PROPN
ejpam-1726	224	10	dutta	dutta	PROPN
ejpam-1726	224	11	.	.	PUNCT
ejpam-1726	225	1	on	on	ADP
ejpam-1726	225	2	the	the	DET
ejpam-1726	225	3	radicals	radical	NOUN
ejpam-1726	225	4	of	of	ADP
ejpam-1726	225	5	γ	γ	PROPN
ejpam-1726	225	6	-	-	PUNCT
ejpam-1726	225	7	semigroup	semigroup	NOUN
ejpam-1726	225	8	.	.	PUNCT
ejpam-1726	225	9	bulletin	bulletin	NOUN
ejpam-1726	225	10	of	of	ADP
ejpam-1726	225	11	calcutta	calcutta	PROPN
ejpam-1726	225	12	mathematical	mathematical	ADJ
ejpam-1726	225	13	society	society	NOUN
ejpam-1726	225	14	,	,	PUNCT
ejpam-1726	225	15	88(3):189–194	88(3):189–194	PROPN
ejpam-1726	225	16	,	,	PUNCT
ejpam-1726	225	17	1996	1996	NUM
ejpam-1726	225	18	.	.	PUNCT
ejpam-1726	226	1	references	reference	NOUN
ejpam-1726	226	2	10	10	NUM
ejpam-1726	227	1	[	[	X
ejpam-1726	227	2	6	6	NUM
ejpam-1726	227	3	]	]	X
ejpam-1726	227	4	f	f	PROPN
ejpam-1726	227	5	w	w	PROPN
ejpam-1726	227	6	anderson	anderson	PROPN
ejpam-1726	227	7	and	and	CCONJ
ejpam-1726	227	8	k	k	PROPN
ejpam-1726	227	9	r	r	NOUN
ejpam-1726	227	10	fuller	full	ADJ
ejpam-1726	227	11	.	.	PUNCT
ejpam-1726	228	1	rings	ring	NOUN
ejpam-1726	228	2	and	and	CCONJ
ejpam-1726	228	3	categories	category	NOUN
ejpam-1726	228	4	of	of	ADP
ejpam-1726	228	5	modules	module	NOUN
ejpam-1726	228	6	.	.	PUNCT
ejpam-1726	229	1	springer	springer	NOUN
ejpam-1726	229	2	,	,	PUNCT
ejpam-1726	229	3	berlin	berlin	PROPN
ejpam-1726	229	4	,	,	PUNCT
ejpam-1726	229	5	1974	1974	NUM
ejpam-1726	229	6	.	.	PUNCT
ejpam-1726	230	1	[	[	X
ejpam-1726	230	2	7	7	NUM
ejpam-1726	230	3	]	]	SYM
ejpam-1726	230	4	b	b	X
ejpam-1726	230	5	banaschewski	banaschewski	NOUN
ejpam-1726	230	6	.	.	PUNCT
ejpam-1726	231	1	functors	functor	NOUN
ejpam-1726	231	2	into	into	ADP
ejpam-1726	231	3	the	the	DET
ejpam-1726	231	4	category	category	NOUN
ejpam-1726	231	5	of	of	ADP
ejpam-1726	231	6	m	m	NOUN
ejpam-1726	231	7	-	-	PUNCT
ejpam-1726	231	8	sets	set	NOUN
ejpam-1726	231	9	.	.	PUNCT
ejpam-1726	232	1	abhandlungen	abhandlungen	PROPN
ejpam-1726	232	2	aus	aus	PROPN
ejpam-1726	232	3	dem	dem	PROPN
ejpam-1726	232	4	mathematischen	mathematischen	PROPN
ejpam-1726	232	5	seminar	seminar	PROPN
ejpam-1726	232	6	der	der	NOUN
ejpam-1726	232	7	universitat	universitat	PROPN
ejpam-1726	232	8	hamburg	hamburg	PROPN
ejpam-1726	232	9	,	,	PUNCT
ejpam-1726	232	10	8:49–64	8:49–64	NUM
ejpam-1726	232	11	,	,	PUNCT
ejpam-1726	232	12	1972	1972	NUM
ejpam-1726	232	13	.	.	PUNCT
ejpam-1726	233	1	[	[	X
ejpam-1726	233	2	8	8	NUM
ejpam-1726	233	3	]	]	X
ejpam-1726	233	4	y	y	PROPN
ejpam-1726	233	5	q	q	PROPN
ejpam-1726	233	6	chen	chen	PROPN
ejpam-1726	233	7	and	and	CCONJ
ejpam-1726	233	8	k	k	PROPN
ejpam-1726	233	9	p	p	X
ejpam-1726	233	10	shum	shum	PROPN
ejpam-1726	233	11	.	.	PUNCT
ejpam-1726	234	1	morita	morita	PROPN
ejpam-1726	234	2	equivalence	equivalence	NOUN
ejpam-1726	234	3	for	for	ADP
ejpam-1726	234	4	factorisable	factorisable	ADJ
ejpam-1726	234	5	semigroups	semigroup	NOUN
ejpam-1726	234	6	.	.	PUNCT
ejpam-1726	235	1	acta	acta	PROPN
ejpam-1726	235	2	mathematica	mathematica	PROPN
ejpam-1726	235	3	sinica	sinica	PROPN
ejpam-1726	235	4	(	(	PUNCT
ejpam-1726	235	5	english	english	PROPN
ejpam-1726	235	6	series	series	PROPN
ejpam-1726	235	7	)	)	PUNCT
ejpam-1726	235	8	,	,	PUNCT
ejpam-1726	235	9	17:437–454	17:437–454	NUM
ejpam-1726	235	10	,	,	PUNCT
ejpam-1726	235	11	2001	2001	NUM
ejpam-1726	235	12	.	.	PUNCT
ejpam-1726	236	1	[	[	X
ejpam-1726	236	2	9	9	NUM
ejpam-1726	236	3	]	]	PUNCT
ejpam-1726	236	4	a	a	DET
ejpam-1726	236	5	h	h	NOUN
ejpam-1726	236	6	clifford	clifford	PROPN
ejpam-1726	236	7	and	and	CCONJ
ejpam-1726	236	8	g	g	PROPN
ejpam-1726	236	9	b	b	PROPN
ejpam-1726	236	10	preston	preston	PROPN
ejpam-1726	236	11	.	.	PUNCT
ejpam-1726	237	1	the	the	DET
ejpam-1726	237	2	algebraic	algebraic	PROPN
ejpam-1726	237	3	theory	theory	NOUN
ejpam-1726	237	4	of	of	ADP
ejpam-1726	237	5	semigroups	semigroup	NOUN
ejpam-1726	237	6	,	,	PUNCT
ejpam-1726	237	7	vol	vol	NOUN
ejpam-1726	237	8	-	-	PUNCT
ejpam-1726	237	9	i.	i.	NOUN
ejpam-1726	237	10	american	american	PROPN
ejpam-1726	237	11	mathematical	mathematical	PROPN
ejpam-1726	237	12	society	society	NOUN
ejpam-1726	237	13	,	,	PUNCT
ejpam-1726	237	14	1961	1961	NUM
ejpam-1726	237	15	.	.	PUNCT
ejpam-1726	238	1	[	[	X
ejpam-1726	238	2	10	10	NUM
ejpam-1726	238	3	]	]	X
ejpam-1726	238	4	a	a	DET
ejpam-1726	238	5	h	h	NOUN
ejpam-1726	238	6	clifford	clifford	PROPN
ejpam-1726	238	7	and	and	CCONJ
ejpam-1726	238	8	g	g	PROPN
ejpam-1726	238	9	b	b	PROPN
ejpam-1726	238	10	preston	preston	PROPN
ejpam-1726	238	11	.	.	PUNCT
ejpam-1726	239	1	the	the	DET
ejpam-1726	239	2	algebraic	algebraic	PROPN
ejpam-1726	239	3	theory	theory	NOUN
ejpam-1726	239	4	of	of	ADP
ejpam-1726	239	5	semigroups	semigroup	NOUN
ejpam-1726	239	6	,	,	PUNCT
ejpam-1726	239	7	vol	vol	NOUN
ejpam-1726	239	8	-	-	PUNCT
ejpam-1726	239	9	ii	ii	NOUN
ejpam-1726	239	10	.	.	PUNCT
ejpam-1726	240	1	american	american	PROPN
ejpam-1726	240	2	mathematical	mathematical	PROPN
ejpam-1726	240	3	society	society	NOUN
ejpam-1726	240	4	,	,	PUNCT
ejpam-1726	240	5	1967	1967	NUM
ejpam-1726	240	6	.	.	PUNCT
ejpam-1726	241	1	[	[	X
ejpam-1726	241	2	11	11	NUM
ejpam-1726	241	3	]	]	X
ejpam-1726	241	4	j	j	PROPN
ejpam-1726	241	5	m	m	NOUN
ejpam-1726	241	6	howie	howie	NOUN
ejpam-1726	241	7	.	.	PUNCT
ejpam-1726	242	1	an	an	DET
ejpam-1726	242	2	introduction	introduction	NOUN
ejpam-1726	242	3	to	to	ADP
ejpam-1726	242	4	semigroup	semigroup	PROPN
ejpam-1726	242	5	theory	theory	NOUN
ejpam-1726	242	6	.	.	PUNCT
ejpam-1726	243	1	academic	academic	ADJ
ejpam-1726	243	2	press	press	PROPN
ejpam-1726	243	3	,	,	PUNCT
ejpam-1726	243	4	london	london	PROPN
ejpam-1726	243	5	,	,	PUNCT
ejpam-1726	243	6	1976	1976	NUM
ejpam-1726	243	7	.	.	PUNCT
ejpam-1726	244	1	[	[	X
ejpam-1726	244	2	12	12	NUM
ejpam-1726	244	3	]	]	X
ejpam-1726	244	4	u	u	NOUN
ejpam-1726	244	5	knauer	knauer	NOUN
ejpam-1726	244	6	.	.	PUNCT
ejpam-1726	244	7	projectivity	projectivity	NOUN
ejpam-1726	244	8	of	of	ADP
ejpam-1726	244	9	acts	act	NOUN
ejpam-1726	244	10	and	and	CCONJ
ejpam-1726	244	11	morita	morita	PROPN
ejpam-1726	244	12	equivalence	equivalence	NOUN
ejpam-1726	244	13	of	of	ADP
ejpam-1726	244	14	monoids	monoid	NOUN
ejpam-1726	244	15	.	.	PUNCT
ejpam-1726	245	1	semigroup	semigroup	PROPN
ejpam-1726	245	2	forum	forum	PROPN
ejpam-1726	245	3	,	,	PUNCT
ejpam-1726	245	4	3:359–370	3:359–370	NUM
ejpam-1726	245	5	,	,	PUNCT
ejpam-1726	245	6	1972	1972	NUM
ejpam-1726	245	7	.	.	PUNCT
ejpam-1726	246	1	[	[	X
ejpam-1726	246	2	13	13	NUM
ejpam-1726	246	3	]	]	SYM
ejpam-1726	246	4	u	u	NOUN
ejpam-1726	246	5	knauer	knauer	NOUN
ejpam-1726	246	6	and	and	CCONJ
ejpam-1726	246	7	p	p	PROPN
ejpam-1726	246	8	normak	normak	PROPN
ejpam-1726	246	9	.	.	PUNCT
ejpam-1726	247	1	morita	morita	PROPN
ejpam-1726	247	2	duality	duality	NOUN
ejpam-1726	247	3	of	of	ADP
ejpam-1726	247	4	monoids	monoid	NOUN
ejpam-1726	247	5	.	.	PUNCT
ejpam-1726	248	1	semigroup	semigroup	PROPN
ejpam-1726	248	2	forum	forum	PROPN
ejpam-1726	248	3	,	,	PUNCT
ejpam-1726	248	4	40:39–57	40:39–57	PROPN
ejpam-1726	248	5	,	,	PUNCT
ejpam-1726	248	6	1990	1990	NUM
ejpam-1726	248	7	.	.	PUNCT
ejpam-1726	249	1	[	[	X
ejpam-1726	249	2	14	14	NUM
ejpam-1726	249	3	]	]	SYM
ejpam-1726	249	4	b	b	PROPN
ejpam-1726	249	5	mitchell	mitchell	PROPN
ejpam-1726	249	6	.	.	PUNCT
ejpam-1726	250	1	theory	theory	NOUN
ejpam-1726	250	2	of	of	ADP
ejpam-1726	250	3	categories	category	NOUN
ejpam-1726	250	4	.	.	PUNCT
ejpam-1726	251	1	academic	academic	PROPN
ejpam-1726	251	2	press	press	PROPN
ejpam-1726	251	3	inc	inc	PROPN
ejpam-1726	251	4	.	.	PROPN
ejpam-1726	251	5	,	,	PUNCT
ejpam-1726	251	6	new	new	PROPN
ejpam-1726	251	7	york	york	PROPN
ejpam-1726	251	8	,	,	PUNCT
ejpam-1726	251	9	1965	1965	NUM
ejpam-1726	251	10	.	.	PUNCT
ejpam-1726	252	1	[	[	X
ejpam-1726	252	2	15	15	NUM
ejpam-1726	252	3	]	]	X
ejpam-1726	252	4	n	n	DET
ejpam-1726	252	5	nobusawa	nobusawa	NOUN
ejpam-1726	252	6	.	.	PUNCT
ejpam-1726	253	1	on	on	ADP
ejpam-1726	253	2	a	a	DET
ejpam-1726	253	3	generalization	generalization	NOUN
ejpam-1726	253	4	of	of	ADP
ejpam-1726	253	5	the	the	DET
ejpam-1726	253	6	ring	ring	NOUN
ejpam-1726	253	7	theory	theory	NOUN
ejpam-1726	253	8	.	.	PUNCT
ejpam-1726	254	1	osaka	osaka	PROPN
ejpam-1726	254	2	journal	journal	PROPN
ejpam-1726	254	3	of	of	ADP
ejpam-1726	254	4	mathematics	mathematic	NOUN
ejpam-1726	254	5	,	,	PUNCT
ejpam-1726	254	6	1:81–89	1:81–89	NUM
ejpam-1726	254	7	,	,	PUNCT
ejpam-1726	254	8	1964	1964	NUM
ejpam-1726	254	9	.	.	PUNCT
ejpam-1726	255	1	[	[	X
ejpam-1726	255	2	16	16	NUM
ejpam-1726	255	3	]	]	PUNCT
ejpam-1726	255	4	n	n	DET
ejpam-1726	255	5	nobusawa	nobusawa	NOUN
ejpam-1726	255	6	.	.	PUNCT
ejpam-1726	256	1	γ	γ	NOUN
ejpam-1726	256	2	-	-	PUNCT
ejpam-1726	256	3	rings	ring	NOUN
ejpam-1726	256	4	and	and	CCONJ
ejpam-1726	256	5	morita	morita	PROPN
ejpam-1726	256	6	equivalence	equivalence	NOUN
ejpam-1726	256	7	of	of	ADP
ejpam-1726	256	8	rings	ring	NOUN
ejpam-1726	256	9	.	.	PUNCT
ejpam-1726	257	1	mathematical	mathematical	ADJ
ejpam-1726	257	2	journal	journal	PROPN
ejpam-1726	257	3	of	of	ADP
ejpam-1726	257	4	okayama	okayama	PROPN
ejpam-1726	257	5	university	university	PROPN
ejpam-1726	257	6	,	,	PUNCT
ejpam-1726	257	7	26:151–156	26:151–156	PROPN
ejpam-1726	257	8	,	,	PUNCT
ejpam-1726	257	9	1984	1984	NUM
ejpam-1726	257	10	.	.	PUNCT
ejpam-1726	258	1	[	[	X
ejpam-1726	258	2	17	17	NUM
ejpam-1726	258	3	]	]	X
ejpam-1726	258	4	m	m	VERB
ejpam-1726	258	5	parvathi	parvathi	PROPN
ejpam-1726	258	6	and	and	CCONJ
ejpam-1726	258	7	p	p	X
ejpam-1726	258	8	a	a	DET
ejpam-1726	258	9	rajendran	rajendran	NOUN
ejpam-1726	258	10	.	.	PUNCT
ejpam-1726	259	1	gamma	gamma	NOUN
ejpam-1726	259	2	-	-	PUNCT
ejpam-1726	259	3	ring	ring	NOUN
ejpam-1726	259	4	and	and	CCONJ
ejpam-1726	259	5	morita	morita	PROPN
ejpam-1726	259	6	equivalence	equivalence	NOUN
ejpam-1726	259	7	.	.	PUNCT
ejpam-1726	260	1	communications	communication	NOUN
ejpam-1726	260	2	in	in	ADP
ejpam-1726	260	3	algebra	algebra	NOUN
ejpam-1726	260	4	,	,	PUNCT
ejpam-1726	260	5	12(14):1781–1786	12(14):1781–1786	NUM
ejpam-1726	260	6	,	,	PUNCT
ejpam-1726	260	7	1984	1984	NUM
ejpam-1726	260	8	.	.	PUNCT
ejpam-1726	261	1	[	[	X
ejpam-1726	261	2	18	18	NUM
ejpam-1726	261	3	]	]	X
ejpam-1726	261	4	m	m	VERB
ejpam-1726	261	5	k	k	PROPN
ejpam-1726	261	6	sen	sen	PROPN
ejpam-1726	261	7	.	.	PROPN
ejpam-1726	261	8	on	on	ADP
ejpam-1726	261	9	γ	γ	PROPN
ejpam-1726	261	10	-	-	PUNCT
ejpam-1726	261	11	semigroup	semigroup	NOUN
ejpam-1726	261	12	.	.	PUNCT
ejpam-1726	262	1	in	in	ADP
ejpam-1726	262	2	proceedings	proceeding	NOUN
ejpam-1726	262	3	of	of	ADP
ejpam-1726	262	4	international	international	ADJ
ejpam-1726	262	5	conference	conference	NOUN
ejpam-1726	262	6	on	on	ADP
ejpam-1726	262	7	algebra	algebra	NOUN
ejpam-1726	262	8	and	and	CCONJ
ejpam-1726	262	9	it	it	PRON
ejpam-1726	262	10	’s	’	VERB
ejpam-1726	262	11	aplication	aplication	NOUN
ejpam-1726	262	12	.	.	PUNCT
ejpam-1726	263	1	,	,	PUNCT
ejpam-1726	263	2	pages	page	NOUN
ejpam-1726	263	3	301–308	301–308	NUM
ejpam-1726	263	4	,	,	PUNCT
ejpam-1726	263	5	new	new	PROPN
ejpam-1726	263	6	york	york	PROPN
ejpam-1726	263	7	,	,	PUNCT
ejpam-1726	263	8	1981	1981	NUM
ejpam-1726	263	9	.	.	PUNCT
ejpam-1726	264	1	decker	decker	PROPN
ejpam-1726	264	2	publication	publication	NOUN
ejpam-1726	264	3	.	.	PUNCT
ejpam-1726	265	1	[	[	X
ejpam-1726	265	2	19	19	NUM
ejpam-1726	265	3	]	]	X
ejpam-1726	265	4	s	s	PART
ejpam-1726	265	5	talwar	talwar	PROPN
ejpam-1726	265	6	.	.	PUNCT
ejpam-1726	265	7	morita	morita	PROPN
ejpam-1726	265	8	equivalence	equivalence	NOUN
ejpam-1726	265	9	for	for	ADP
ejpam-1726	265	10	semigroups	semigroup	NOUN
ejpam-1726	265	11	.	.	PUNCT
ejpam-1726	266	1	journal	journal	NOUN
ejpam-1726	266	2	of	of	ADP
ejpam-1726	266	3	the	the	DET
ejpam-1726	266	4	australian	australian	ADJ
ejpam-1726	266	5	mathematical	mathematical	ADJ
ejpam-1726	266	6	society	society	NOUN
ejpam-1726	266	7	(	(	PUNCT
ejpam-1726	266	8	series	series	PROPN
ejpam-1726	266	9	a	a	PROPN
ejpam-1726	266	10	)	)	PUNCT
ejpam-1726	266	11	,	,	PUNCT
ejpam-1726	266	12	59:81–111	59:81–111	NUM
ejpam-1726	266	13	,	,	PUNCT
ejpam-1726	266	14	1995	1995	NUM
ejpam-1726	266	15	.	.	PUNCT
ejpam-1726	267	1	[	[	X
ejpam-1726	267	2	20	20	NUM
ejpam-1726	267	3	]	]	X
ejpam-1726	267	4	y	y	PROPN
ejpam-1726	267	5	h	h	PROPN
ejpam-1726	268	1	xu	xu	PROPN
ejpam-1726	268	2	,	,	PUNCT
ejpam-1726	268	3	k	k	PROPN
ejpam-1726	268	4	p	p	X
ejpam-1726	268	5	shum	shum	NOUN
ejpam-1726	268	6	,	,	PUNCT
ejpam-1726	268	7	and	and	CCONJ
ejpam-1726	268	8	r	r	NOUN
ejpam-1726	268	9	f	f	PROPN
ejpam-1726	268	10	turner	turner	PROPN
ejpam-1726	268	11	-	-	PUNCT
ejpam-1726	268	12	smith	smith	PROPN
ejpam-1726	268	13	.	.	PUNCT
ejpam-1726	269	1	morita	morita	PROPN
ejpam-1726	269	2	-	-	PUNCT
ejpam-1726	269	3	like	like	ADJ
ejpam-1726	269	4	equivalence	equivalence	NOUN
ejpam-1726	269	5	of	of	ADP
ejpam-1726	269	6	infinite	infinite	ADJ
ejpam-1726	269	7	matrix	matrix	NOUN
ejpam-1726	269	8	subrings	subring	NOUN
ejpam-1726	269	9	.	.	PUNCT
ejpam-1726	270	1	journal	journal	PROPN
ejpam-1726	270	2	of	of	ADP
ejpam-1726	270	3	algebra	algebra	PROPN
ejpam-1726	270	4	,	,	PUNCT
ejpam-1726	270	5	159(2):425–435	159(2):425–435	NUM
ejpam-1726	270	6	,	,	PUNCT
ejpam-1726	270	7	1993	1993	NUM
ejpam-1726	270	8	.	.	PUNCT