id	sid	tid	token	lemma	pos
ejpam-1745	1	1	european	european	PROPN
ejpam-1745	1	2	journal	journal	PROPN
ejpam-1745	1	3	of	of	ADP
ejpam-1745	1	4	pure	pure	ADJ
ejpam-1745	1	5	and	and	CCONJ
ejpam-1745	1	6	applied	apply	VERB
ejpam-1745	1	7	mathematics	mathematic	NOUN
ejpam-1745	1	8	vol	vol	NOUN
ejpam-1745	1	9	.	.	PROPN
ejpam-1745	2	1	6	6	NUM
ejpam-1745	2	2	,	,	PUNCT
ejpam-1745	2	3	no	no	INTJ
ejpam-1745	2	4	.	.	NOUN
ejpam-1745	2	5	2	2	NUM
ejpam-1745	2	6	,	,	PUNCT
ejpam-1745	2	7	2013	2013	NUM
ejpam-1745	2	8	,	,	PUNCT
ejpam-1745	2	9	211	211	NUM
ejpam-1745	2	10	-	-	SYM
ejpam-1745	2	11	221	221	NUM
ejpam-1745	2	12	issn	issn	PROPN
ejpam-1745	2	13	1307	1307	NUM
ejpam-1745	2	14	-	-	SYM
ejpam-1745	2	15	5543	5543	NUM
ejpam-1745	2	16	–	–	PUNCT
ejpam-1745	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1745	2	18	sequentially	sequentially	ADV
ejpam-1745	2	19	complete	complete	ADJ
ejpam-1745	2	20	s	s	NOUN
ejpam-1745	2	21	-	-	PUNCT
ejpam-1745	2	22	acts	act	NOUN
ejpam-1745	2	23	and	and	CCONJ
ejpam-1745	2	24	baer	baer	PROPN
ejpam-1745	2	25	type	type	NOUN
ejpam-1745	2	26	criteria	criterion	NOUN
ejpam-1745	2	27	over	over	ADP
ejpam-1745	2	28	semigroups	semigroups	PROPN
ejpam-1745	2	29	h.	h.	PROPN
ejpam-1745	2	30	barzegar	barzegar	PROPN
ejpam-1745	2	31	department	department	PROPN
ejpam-1745	2	32	of	of	ADP
ejpam-1745	2	33	mathematics	mathematics	PROPN
ejpam-1745	2	34	,	,	PUNCT
ejpam-1745	2	35	tafresh	tafresh	PROPN
ejpam-1745	2	36	university	university	NOUN
ejpam-1745	2	37	,	,	PUNCT
ejpam-1745	2	38	tafresh	tafresh	NOUN
ejpam-1745	2	39	,	,	PUNCT
ejpam-1745	2	40	iran	iran	PROPN
ejpam-1745	2	41	.	.	PUNCT
ejpam-1745	3	1	abstract	abstract	ADJ
ejpam-1745	3	2	.	.	PUNCT
ejpam-1745	4	1	dedicated	dedicate	VERB
ejpam-1745	4	2	to	to	ADP
ejpam-1745	4	3	professor	professor	NOUN
ejpam-1745	4	4	m.	m.	NOUN
ejpam-1745	4	5	mehdi	mehdi	PROPN
ejpam-1745	4	6	ebrahimi	ebrahimi	PROPN
ejpam-1745	4	7	on	on	ADP
ejpam-1745	4	8	his	his	PRON
ejpam-1745	4	9	65th	65th	ADJ
ejpam-1745	4	10	birthday	birthday	NOUN
ejpam-1745	4	11	although	although	SCONJ
ejpam-1745	4	12	the	the	DET
ejpam-1745	4	13	baer	baer	PROPN
ejpam-1745	4	14	criterion	criterion	NOUN
ejpam-1745	4	15	for	for	ADP
ejpam-1745	4	16	injectivity	injectivity	NOUN
ejpam-1745	4	17	is	be	AUX
ejpam-1745	4	18	true	true	ADJ
ejpam-1745	4	19	for	for	ADP
ejpam-1745	4	20	modules	module	NOUN
ejpam-1745	4	21	over	over	ADP
ejpam-1745	4	22	a	a	DET
ejpam-1745	4	23	ring	ring	NOUN
ejpam-1745	4	24	with	with	ADP
ejpam-1745	4	25	an	an	DET
ejpam-1745	4	26	identity	identity	NOUN
ejpam-1745	4	27	,	,	PUNCT
ejpam-1745	4	28	it	it	PRON
ejpam-1745	4	29	is	be	AUX
ejpam-1745	4	30	an	an	DET
ejpam-1745	4	31	open	open	ADJ
ejpam-1745	4	32	problem	problem	NOUN
ejpam-1745	4	33	for	for	ADP
ejpam-1745	4	34	acts	act	NOUN
ejpam-1745	4	35	over	over	ADP
ejpam-1745	4	36	a	a	DET
ejpam-1745	4	37	semigroup	semigroup	NOUN
ejpam-1745	4	38	s	s	X
ejpam-1745	4	39	(	(	PUNCT
ejpam-1745	4	40	with	with	ADP
ejpam-1745	4	41	or	or	CCONJ
ejpam-1745	4	42	without	without	ADP
ejpam-1745	4	43	identity	identity	NOUN
ejpam-1745	4	44	)	)	PUNCT
ejpam-1745	4	45	.	.	PUNCT
ejpam-1745	5	1	in	in	ADP
ejpam-1745	5	2	this	this	DET
ejpam-1745	5	3	work	work	NOUN
ejpam-1745	5	4	,	,	PUNCT
ejpam-1745	5	5	we	we	PRON
ejpam-1745	5	6	study	study	VERB
ejpam-1745	5	7	a	a	DET
ejpam-1745	5	8	kind	kind	NOUN
ejpam-1745	5	9	of	of	ADP
ejpam-1745	5	10	baer	baer	PROPN
ejpam-1745	5	11	criterion	criterion	NOUN
ejpam-1745	5	12	for	for	ADP
ejpam-1745	5	13	injectivity	injectivity	NOUN
ejpam-1745	5	14	of	of	ADP
ejpam-1745	5	15	acts	act	NOUN
ejpam-1745	5	16	over	over	ADP
ejpam-1745	5	17	a	a	DET
ejpam-1745	5	18	semigroup	semigroup	NOUN
ejpam-1745	5	19	s.	s.	PROPN
ejpam-1745	5	20	we	we	PRON
ejpam-1745	5	21	consider	consider	VERB
ejpam-1745	5	22	a	a	DET
ejpam-1745	5	23	kind	kind	NOUN
ejpam-1745	5	24	of	of	ADP
ejpam-1745	5	25	weak	weak	ADJ
ejpam-1745	5	26	injectivity	injectivity	NOUN
ejpam-1745	5	27	which	which	PRON
ejpam-1745	5	28	we	we	PRON
ejpam-1745	5	29	call	call	VERB
ejpam-1745	5	30	s	s	NOUN
ejpam-1745	5	31	-completeness	-completeness	NOUN
ejpam-1745	5	32	and	and	CCONJ
ejpam-1745	5	33	give	give	VERB
ejpam-1745	5	34	some	some	DET
ejpam-1745	5	35	conditions	condition	NOUN
ejpam-1745	5	36	under	under	ADP
ejpam-1745	5	37	which	which	PRON
ejpam-1745	5	38	s	s	NOUN
ejpam-1745	5	39	-	-	PUNCT
ejpam-1745	5	40	completeness	completeness	NOUN
ejpam-1745	5	41	coincides	coincide	VERB
ejpam-1745	5	42	with	with	ADP
ejpam-1745	5	43	injectivity	injectivity	NOUN
ejpam-1745	5	44	.	.	PUNCT
ejpam-1745	6	1	2010	2010	NUM
ejpam-1745	6	2	mathematics	mathematic	NOUN
ejpam-1745	6	3	subject	subject	NOUN
ejpam-1745	6	4	classifications	classification	NOUN
ejpam-1745	6	5	:	:	PUNCT
ejpam-1745	6	6	20m30	20m30	NUM
ejpam-1745	6	7	,	,	PUNCT
ejpam-1745	6	8	08a60	08a60	NUM
ejpam-1745	6	9	;	;	PUNCT
ejpam-1745	6	10	08b30	08b30	DET
ejpam-1745	6	11	key	key	ADJ
ejpam-1745	6	12	words	word	NOUN
ejpam-1745	6	13	and	and	CCONJ
ejpam-1745	6	14	phrases	phrase	NOUN
ejpam-1745	6	15	:	:	PUNCT
ejpam-1745	6	16	sequentially	sequentially	ADV
ejpam-1745	6	17	pure	pure	ADJ
ejpam-1745	6	18	,	,	PUNCT
ejpam-1745	6	19	injectivity	injectivity	NOUN
ejpam-1745	6	20	,	,	PUNCT
ejpam-1745	6	21	sequentially	sequentially	ADV
ejpam-1745	6	22	complete	complete	ADJ
ejpam-1745	6	23	1	1	NUM
ejpam-1745	6	24	.	.	PUNCT
ejpam-1745	6	25	introduction	introduction	NOUN
ejpam-1745	6	26	throughout	throughout	ADP
ejpam-1745	6	27	this	this	DET
ejpam-1745	6	28	paper	paper	NOUN
ejpam-1745	6	29	s	s	NOUN
ejpam-1745	6	30	will	will	AUX
ejpam-1745	6	31	denote	denote	VERB
ejpam-1745	6	32	a	a	DET
ejpam-1745	6	33	given	give	VERB
ejpam-1745	6	34	semigroup	semigroup	NOUN
ejpam-1745	6	35	and	and	CCONJ
ejpam-1745	6	36	recall	recall	VERB
ejpam-1745	6	37	that	that	PRON
ejpam-1745	6	38	,	,	PUNCT
ejpam-1745	6	39	for	for	ADP
ejpam-1745	6	40	a	a	DET
ejpam-1745	6	41	semigroup	semigroup	NOUN
ejpam-1745	6	42	s	s	PROPN
ejpam-1745	6	43	,	,	PUNCT
ejpam-1745	6	44	a	a	DET
ejpam-1745	6	45	set	set	NOUN
ejpam-1745	6	46	a	a	PRON
ejpam-1745	6	47	is	be	AUX
ejpam-1745	6	48	a	a	DET
ejpam-1745	6	49	right	right	ADJ
ejpam-1745	6	50	s	s	NOUN
ejpam-1745	6	51	-	-	NOUN
ejpam-1745	6	52	act	act	NOUN
ejpam-1745	6	53	(	(	PUNCT
ejpam-1745	6	54	or	or	CCONJ
ejpam-1745	6	55	an	an	DET
ejpam-1745	6	56	s	s	NOUN
ejpam-1745	6	57	-	-	NOUN
ejpam-1745	6	58	act	act	NOUN
ejpam-1745	6	59	)	)	PUNCT
ejpam-1745	6	60	if	if	SCONJ
ejpam-1745	6	61	there	there	PRON
ejpam-1745	6	62	is	be	VERB
ejpam-1745	6	63	a	a	DET
ejpam-1745	6	64	,	,	PUNCT
ejpam-1745	6	65	so	so	ADV
ejpam-1745	6	66	called	call	VERB
ejpam-1745	6	67	,	,	PUNCT
ejpam-1745	6	68	action	action	NOUN
ejpam-1745	6	69	µ	µ	NOUN
ejpam-1745	6	70	:	:	PUNCT
ejpam-1745	6	71	a×	a×	PROPN
ejpam-1745	6	72	s	s	PART
ejpam-1745	6	73	→	→	PUNCT
ejpam-1745	6	74	a	a	DET
ejpam-1745	6	75	such	such	ADJ
ejpam-1745	6	76	that	that	PRON
ejpam-1745	6	77	,	,	PUNCT
ejpam-1745	6	78	denoting	denote	VERB
ejpam-1745	6	79	µ(a	µ(a	PROPN
ejpam-1745	6	80	,	,	PUNCT
ejpam-1745	6	81	s	s	PROPN
ejpam-1745	6	82	)	)	PUNCT
ejpam-1745	6	83	:	:	PUNCT
ejpam-1745	6	84	=	=	PUNCT
ejpam-1745	6	85	as	as	ADP
ejpam-1745	6	86	,	,	PUNCT
ejpam-1745	6	87	a(st	a(st	PROPN
ejpam-1745	6	88	)	)	PUNCT
ejpam-1745	6	89	=	=	PUNCT
ejpam-1745	6	90	(	(	PUNCT
ejpam-1745	6	91	as)t	as)t	PROPN
ejpam-1745	6	92	and	and	CCONJ
ejpam-1745	6	93	if	if	SCONJ
ejpam-1745	6	94	s	s	VERB
ejpam-1745	6	95	is	be	AUX
ejpam-1745	6	96	a	a	DET
ejpam-1745	6	97	monoid	monoid	NOUN
ejpam-1745	6	98	with	with	ADP
ejpam-1745	6	99	1	1	NUM
ejpam-1745	6	100	,	,	PUNCT
ejpam-1745	6	101	a1=	a1=	PROPN
ejpam-1745	6	102	a.	a.	NOUN
ejpam-1745	6	103	a	a	DET
ejpam-1745	6	104	morphism	morphism	NOUN
ejpam-1745	6	105	f	f	PROPN
ejpam-1745	6	106	:	:	PUNCT
ejpam-1745	6	107	a→	a→	PROPN
ejpam-1745	6	108	b	b	X
ejpam-1745	6	109	between	between	ADP
ejpam-1745	6	110	s	s	NOUN
ejpam-1745	6	111	-	-	PUNCT
ejpam-1745	6	112	acts	act	VERB
ejpam-1745	6	113	a	a	PRON
ejpam-1745	6	114	,	,	PUNCT
ejpam-1745	6	115	b	b	PROPN
ejpam-1745	6	116	is	be	AUX
ejpam-1745	6	117	called	call	VERB
ejpam-1745	6	118	a	a	DET
ejpam-1745	6	119	homomorphism	homomorphism	NOUN
ejpam-1745	6	120	if	if	SCONJ
ejpam-1745	6	121	,	,	PUNCT
ejpam-1745	6	122	for	for	ADP
ejpam-1745	6	123	each	each	DET
ejpam-1745	6	124	a	a	DET
ejpam-1745	6	125	∈	∈	PROPN
ejpam-1745	6	126	a	a	PRON
ejpam-1745	6	127	,	,	PUNCT
ejpam-1745	6	128	s	s	NOUN
ejpam-1745	6	129	∈	∈	PROPN
ejpam-1745	6	130	s	s	PROPN
ejpam-1745	6	131	,	,	PUNCT
ejpam-1745	6	132	f	f	X
ejpam-1745	6	133	(	(	PUNCT
ejpam-1745	6	134	as	as	ADP
ejpam-1745	6	135	)	)	PUNCT
ejpam-1745	6	136	=	=	SYM
ejpam-1745	6	137	f	f	PROPN
ejpam-1745	6	138	(	(	PUNCT
ejpam-1745	6	139	a)s	a)s	NOUN
ejpam-1745	6	140	.	.	PUNCT
ejpam-1745	7	1	the	the	DET
ejpam-1745	7	2	category	category	NOUN
ejpam-1745	7	3	of	of	ADP
ejpam-1745	7	4	all	all	PRON
ejpam-1745	7	5	(	(	PUNCT
ejpam-1745	7	6	right	right	ADJ
ejpam-1745	7	7	)	)	PUNCT
ejpam-1745	7	8	s	s	NOUN
ejpam-1745	7	9	-	-	PUNCT
ejpam-1745	7	10	acts	act	NOUN
ejpam-1745	7	11	and	and	CCONJ
ejpam-1745	7	12	homomorphisms	homomorphism	NOUN
ejpam-1745	7	13	between	between	ADP
ejpam-1745	7	14	them	they	PRON
ejpam-1745	7	15	is	be	AUX
ejpam-1745	7	16	denoted	denote	VERB
ejpam-1745	7	17	by	by	ADP
ejpam-1745	7	18	act	act	PROPN
ejpam-1745	7	19	-	-	PUNCT
ejpam-1745	7	20	s.	s.	PROPN
ejpam-1745	7	21	sequentially	sequentially	ADV
ejpam-1745	7	22	complete	complete	ADJ
ejpam-1745	7	23	s	s	NOUN
ejpam-1745	7	24	-	-	PUNCT
ejpam-1745	7	25	acts	act	NOUN
ejpam-1745	7	26	are	be	AUX
ejpam-1745	7	27	special	special	ADJ
ejpam-1745	7	28	objects	object	NOUN
ejpam-1745	7	29	of	of	ADP
ejpam-1745	7	30	this	this	DET
ejpam-1745	7	31	category	category	NOUN
ejpam-1745	7	32	which	which	PRON
ejpam-1745	7	33	will	will	AUX
ejpam-1745	7	34	be	be	AUX
ejpam-1745	7	35	studied	study	VERB
ejpam-1745	7	36	here	here	ADV
ejpam-1745	7	37	.	.	PUNCT
ejpam-1745	8	1	an	an	DET
ejpam-1745	8	2	s	s	NOUN
ejpam-1745	8	3	-	-	PUNCT
ejpam-1745	8	4	act	act	NOUN
ejpam-1745	8	5	a	a	PRON
ejpam-1745	8	6	is	be	AUX
ejpam-1745	8	7	called	call	VERB
ejpam-1745	8	8	pure	pure	ADJ
ejpam-1745	8	9	in	in	ADP
ejpam-1745	8	10	an	an	DET
ejpam-1745	8	11	extension	extension	NOUN
ejpam-1745	8	12	b	b	NOUN
ejpam-1745	8	13	of	of	ADP
ejpam-1745	8	14	a	a	PRON
ejpam-1745	8	15	if	if	SCONJ
ejpam-1745	8	16	any	any	DET
ejpam-1745	8	17	system	system	NOUN
ejpam-1745	8	18	of	of	ADP
ejpam-1745	8	19	finitely	finitely	ADV
ejpam-1745	8	20	many	many	ADJ
ejpam-1745	8	21	equations	equation	NOUN
ejpam-1745	8	22	over	over	ADP
ejpam-1745	8	23	a	a	PRON
ejpam-1745	8	24	has	have	VERB
ejpam-1745	8	25	a	a	DET
ejpam-1745	8	26	solution	solution	NOUN
ejpam-1745	8	27	in	in	ADP
ejpam-1745	8	28	a	a	PRON
ejpam-1745	8	29	whenever	whenever	SCONJ
ejpam-1745	8	30	this	this	PRON
ejpam-1745	8	31	is	be	AUX
ejpam-1745	8	32	the	the	DET
ejpam-1745	8	33	case	case	NOUN
ejpam-1745	8	34	for	for	ADP
ejpam-1745	8	35	b.	b.	PROPN
ejpam-1745	8	36	an	an	DET
ejpam-1745	8	37	s	s	NOUN
ejpam-1745	8	38	-	-	PUNCT
ejpam-1745	8	39	act	act	NOUN
ejpam-1745	9	1	a	a	PRON
ejpam-1745	9	2	is	be	AUX
ejpam-1745	9	3	called	call	VERB
ejpam-1745	9	4	absolutely	absolutely	ADV
ejpam-1745	9	5	pure	pure	ADJ
ejpam-1745	9	6	if	if	SCONJ
ejpam-1745	9	7	it	it	PRON
ejpam-1745	9	8	is	be	AUX
ejpam-1745	9	9	pure	pure	ADJ
ejpam-1745	9	10	in	in	ADP
ejpam-1745	9	11	all	all	PRON
ejpam-1745	9	12	of	of	ADP
ejpam-1745	9	13	which	which	DET
ejpam-1745	9	14	extensions	extension	NOUN
ejpam-1745	9	15	.	.	PUNCT
ejpam-1745	10	1	a	a	DET
ejpam-1745	10	2	monoid	monoid	NOUN
ejpam-1745	10	3	s	s	NOUN
ejpam-1745	10	4	is	be	AUX
ejpam-1745	10	5	said	say	VERB
ejpam-1745	10	6	to	to	PART
ejpam-1745	10	7	be	be	AUX
ejpam-1745	10	8	completely	completely	ADV
ejpam-1745	10	9	right	right	ADJ
ejpam-1745	10	10	pure	pure	ADJ
ejpam-1745	10	11	if	if	SCONJ
ejpam-1745	10	12	all	all	DET
ejpam-1745	10	13	its	its	PRON
ejpam-1745	10	14	right	right	ADJ
ejpam-1745	10	15	s	s	NOUN
ejpam-1745	10	16	-	-	PUNCT
ejpam-1745	10	17	acts	act	NOUN
ejpam-1745	10	18	are	be	AUX
ejpam-1745	10	19	absolutely	absolutely	ADV
ejpam-1745	10	20	pure	pure	ADJ
ejpam-1745	10	21	.	.	PUNCT
ejpam-1745	11	1	completely	completely	ADV
ejpam-1745	11	2	right	right	ADJ
ejpam-1745	11	3	pure	pure	ADJ
ejpam-1745	11	4	monoids	monoid	NOUN
ejpam-1745	11	5	have	have	AUX
ejpam-1745	11	6	further	far	ADV
ejpam-1745	11	7	been	be	AUX
ejpam-1745	11	8	studied	study	VERB
ejpam-1745	11	9	in	in	ADP
ejpam-1745	11	10	literature	literature	NOUN
ejpam-1745	11	11	[	[	X
ejpam-1745	11	12	see	see	VERB
ejpam-1745	11	13	e.g.	e.g.	ADV
ejpam-1745	11	14	4	4	NUM
ejpam-1745	11	15	,	,	PUNCT
ejpam-1745	11	16	7	7	NUM
ejpam-1745	11	17	,	,	PUNCT
ejpam-1745	11	18	8	8	NUM
ejpam-1745	11	19	]	]	PUNCT
ejpam-1745	11	20	.	.	PUNCT
ejpam-1745	12	1	a	a	DET
ejpam-1745	12	2	characterization	characterization	NOUN
ejpam-1745	12	3	of	of	ADP
ejpam-1745	12	4	completely	completely	ADV
ejpam-1745	12	5	right	right	ADJ
ejpam-1745	12	6	pure	pure	ADJ
ejpam-1745	12	7	monoids	monoid	NOUN
ejpam-1745	12	8	was	be	AUX
ejpam-1745	12	9	given	give	VERB
ejpam-1745	12	10	in	in	ADP
ejpam-1745	12	11	[	[	X
ejpam-1745	12	12	7	7	NUM
ejpam-1745	12	13	]	]	PUNCT
ejpam-1745	12	14	,	,	PUNCT
ejpam-1745	12	15	but	but	CCONJ
ejpam-1745	12	16	clearly	clearly	ADV
ejpam-1745	12	17	not	not	PART
ejpam-1745	12	18	satisfactory	satisfactory	ADJ
ejpam-1745	12	19	.	.	PUNCT
ejpam-1745	13	1	gould	gould	PROPN
ejpam-1745	13	2	in	in	ADP
ejpam-1745	13	3	[	[	X
ejpam-1745	13	4	8	8	NUM
ejpam-1745	13	5	]	]	PUNCT
ejpam-1745	13	6	attempts	attempt	VERB
ejpam-1745	13	7	to	to	PART
ejpam-1745	13	8	remedy	remedy	VERB
ejpam-1745	13	9	this	this	PRON
ejpam-1745	13	10	by	by	ADP
ejpam-1745	13	11	giving	give	VERB
ejpam-1745	13	12	a	a	DET
ejpam-1745	13	13	characterization	characterization	NOUN
ejpam-1745	13	14	of	of	ADP
ejpam-1745	13	15	completely	completely	ADV
ejpam-1745	13	16	right	right	ADJ
ejpam-1745	13	17	pure	pure	ADJ
ejpam-1745	13	18	monoids	monoid	NOUN
ejpam-1745	13	19	in	in	ADP
ejpam-1745	13	20	terms	term	NOUN
ejpam-1745	13	21	of	of	ADP
ejpam-1745	13	22	right	right	ADJ
ejpam-1745	13	23	ideals	ideal	NOUN
ejpam-1745	13	24	and	and	CCONJ
ejpam-1745	13	25	right	right	ADJ
ejpam-1745	13	26	congruences	congruence	NOUN
ejpam-1745	13	27	that	that	PRON
ejpam-1745	13	28	is	be	AUX
ejpam-1745	13	29	a	a	DET
ejpam-1745	13	30	closer	close	ADJ
ejpam-1745	13	31	analogue	analogue	NOUN
ejpam-1745	13	32	of	of	ADP
ejpam-1745	13	33	proposition	proposition	NOUN
ejpam-1745	13	34	2.1	2.1	NUM
ejpam-1745	13	35	of	of	ADP
ejpam-1745	13	36	[	[	X
ejpam-1745	13	37	7	7	NUM
ejpam-1745	13	38	]	]	PUNCT
ejpam-1745	13	39	.	.	PUNCT
ejpam-1745	14	1	email	email	NOUN
ejpam-1745	14	2	address	address	NOUN
ejpam-1745	14	3	:	:	PUNCT
ejpam-1745	14	4	h56bar@tafreshu.ac.ir	h56bar@tafreshu.ac.ir	VERB
ejpam-1745	14	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1745	15	1	211	211	NUM
ejpam-1745	15	2	c	c	X
ejpam-1745	15	3	©	©	PROPN
ejpam-1745	15	4	2013	2013	NUM
ejpam-1745	15	5	ejpam	ejpam	NOUN
ejpam-1745	15	6	all	all	DET
ejpam-1745	15	7	rights	right	NOUN
ejpam-1745	15	8	reserved	reserve	VERB
ejpam-1745	15	9	.	.	PUNCT
ejpam-1745	16	1	h.	h.	PROPN
ejpam-1745	16	2	barzegar	barzegar	PROPN
ejpam-1745	16	3	/	/	SYM
ejpam-1745	16	4	eur	eur	PROPN
ejpam-1745	16	5	.	.	PUNCT
ejpam-1745	17	1	j.	j.	PROPN
ejpam-1745	17	2	pure	pure	PROPN
ejpam-1745	17	3	appl	appl	PROPN
ejpam-1745	17	4	.	.	PROPN
ejpam-1745	17	5	math	math	PROPN
ejpam-1745	17	6	,	,	PUNCT
ejpam-1745	17	7	6	6	NUM
ejpam-1745	17	8	(	(	PUNCT
ejpam-1745	17	9	2013	2013	NUM
ejpam-1745	17	10	)	)	PUNCT
ejpam-1745	17	11	,	,	PUNCT
ejpam-1745	17	12	211	211	NUM
ejpam-1745	17	13	-	-	SYM
ejpam-1745	17	14	221	221	NUM
ejpam-1745	17	15	212	212	NUM
ejpam-1745	17	16	proposition	proposition	NOUN
ejpam-1745	17	17	2.1	2.1	NUM
ejpam-1745	17	18	of	of	ADP
ejpam-1745	17	19	[	[	X
ejpam-1745	17	20	8	8	NUM
ejpam-1745	17	21	]	]	PUNCT
ejpam-1745	17	22	shows	show	VERB
ejpam-1745	17	23	that	that	SCONJ
ejpam-1745	17	24	the	the	DET
ejpam-1745	17	25	monoid	monoid	PROPN
ejpam-1745	17	26	s	s	X
ejpam-1745	17	27	is	be	AUX
ejpam-1745	17	28	completely	completely	ADV
ejpam-1745	17	29	right	right	ADJ
ejpam-1745	17	30	pure	pure	ADJ
ejpam-1745	17	31	if	if	SCONJ
ejpam-1745	18	1	and	and	CCONJ
ejpam-1745	18	2	only	only	ADV
ejpam-1745	18	3	if	if	SCONJ
ejpam-1745	18	4	every	every	DET
ejpam-1745	18	5	s	s	NOUN
ejpam-1745	18	6	-	-	NOUN
ejpam-1745	18	7	act	act	NOUN
ejpam-1745	18	8	a	a	PRON
ejpam-1745	18	9	is	be	AUX
ejpam-1745	18	10	pure	pure	ADJ
ejpam-1745	18	11	with	with	ADP
ejpam-1745	18	12	one	one	NUM
ejpam-1745	18	13	variable	variable	NOUN
ejpam-1745	18	14	in	in	ADP
ejpam-1745	18	15	any	any	DET
ejpam-1745	18	16	extension	extension	NOUN
ejpam-1745	18	17	.	.	PUNCT
ejpam-1745	19	1	ebrahimi	ebrahimi	PROPN
ejpam-1745	19	2	and	and	CCONJ
ejpam-1745	19	3	mahmoudi	mahmoudi	ADJ
ejpam-1745	20	1	[	[	X
ejpam-1745	20	2	4	4	X
ejpam-1745	20	3	]	]	PUNCT
ejpam-1745	20	4	has	have	AUX
ejpam-1745	20	5	introduced	introduce	VERB
ejpam-1745	20	6	the	the	DET
ejpam-1745	20	7	concept	concept	NOUN
ejpam-1745	20	8	of	of	ADP
ejpam-1745	20	9	s	s	NOUN
ejpam-1745	20	10	-	-	ADJ
ejpam-1745	20	11	pure	pure	ADJ
ejpam-1745	20	12	monomorphism	monomorphism	NOUN
ejpam-1745	20	13	in	in	ADP
ejpam-1745	20	14	the	the	DET
ejpam-1745	20	15	category	category	NOUN
ejpam-1745	20	16	of	of	ADP
ejpam-1745	20	17	projection	projection	NOUN
ejpam-1745	20	18	algebras	algebra	NOUN
ejpam-1745	20	19	by	by	ADP
ejpam-1745	20	20	a	a	DET
ejpam-1745	20	21	system	system	NOUN
ejpam-1745	20	22	of	of	ADP
ejpam-1745	20	23	equations	equation	NOUN
ejpam-1745	20	24	such	such	ADJ
ejpam-1745	20	25	as	as	ADP
ejpam-1745	20	26	xs	xs	PROPN
ejpam-1745	20	27	=	=	PUNCT
ejpam-1745	20	28	as(s	as(s	X
ejpam-1745	20	29	∈	∈	PROPN
ejpam-1745	20	30	s	s	NOUN
ejpam-1745	20	31	,	,	PUNCT
ejpam-1745	20	32	as	as	SCONJ
ejpam-1745	20	33	∈	∈	PROPN
ejpam-1745	20	34	a	a	PRON
ejpam-1745	20	35	)	)	PUNCT
ejpam-1745	20	36	.	.	PUNCT
ejpam-1745	21	1	so	so	ADV
ejpam-1745	21	2	we	we	PRON
ejpam-1745	21	3	are	be	AUX
ejpam-1745	21	4	persuaded	persuade	VERB
ejpam-1745	21	5	to	to	PART
ejpam-1745	21	6	study	study	VERB
ejpam-1745	21	7	a	a	DET
ejpam-1745	21	8	kind	kind	NOUN
ejpam-1745	21	9	of	of	ADP
ejpam-1745	21	10	completely	completely	ADV
ejpam-1745	21	11	right	right	ADJ
ejpam-1745	21	12	purity	purity	NOUN
ejpam-1745	21	13	for	for	ADP
ejpam-1745	21	14	semigrops	semigrop	NOUN
ejpam-1745	21	15	for	for	ADP
ejpam-1745	21	16	these	these	DET
ejpam-1745	21	17	equations	equation	NOUN
ejpam-1745	21	18	in	in	ADP
ejpam-1745	21	19	general	general	ADJ
ejpam-1745	21	20	in	in	ADP
ejpam-1745	21	21	the	the	DET
ejpam-1745	21	22	category	category	NOUN
ejpam-1745	21	23	act	act	PROPN
ejpam-1745	21	24	-	-	PUNCT
ejpam-1745	21	25	s.	s.	PROPN
ejpam-1745	21	26	the	the	DET
ejpam-1745	21	27	sense	sense	NOUN
ejpam-1745	21	28	of	of	ADP
ejpam-1745	21	29	s	s	NOUN
ejpam-1745	21	30	-	-	PUNCT
ejpam-1745	21	31	complete	complete	ADJ
ejpam-1745	21	32	is	be	AUX
ejpam-1745	21	33	equivalent	equivalent	ADJ
ejpam-1745	21	34	to	to	ADP
ejpam-1745	21	35	a	a	DET
ejpam-1745	21	36	kind	kind	NOUN
ejpam-1745	21	37	of	of	ADP
ejpam-1745	21	38	injectivity	injectivity	NOUN
ejpam-1745	21	39	which	which	PRON
ejpam-1745	21	40	is	be	AUX
ejpam-1745	21	41	called	call	VERB
ejpam-1745	21	42	s	s	NOUN
ejpam-1745	21	43	-	-	NOUN
ejpam-1745	21	44	injectivity	injectivity	NOUN
ejpam-1745	21	45	and	and	CCONJ
ejpam-1745	21	46	studied	study	VERB
ejpam-1745	21	47	in	in	ADP
ejpam-1745	21	48	[	[	X
ejpam-1745	21	49	12	12	NUM
ejpam-1745	21	50	]	]	PUNCT
ejpam-1745	21	51	.	.	PUNCT
ejpam-1745	22	1	here	here	ADV
ejpam-1745	22	2	in	in	ADV
ejpam-1745	22	3	,	,	PUNCT
ejpam-1745	22	4	we	we	PRON
ejpam-1745	22	5	characterize	characterize	VERB
ejpam-1745	22	6	the	the	DET
ejpam-1745	22	7	semigroups	semigroup	NOUN
ejpam-1745	22	8	s	s	VERB
ejpam-1745	22	9	over	over	ADP
ejpam-1745	22	10	which	which	PRON
ejpam-1745	22	11	all	all	DET
ejpam-1745	22	12	s	s	NOUN
ejpam-1745	22	13	-	-	PUNCT
ejpam-1745	22	14	acts	act	NOUN
ejpam-1745	22	15	are	be	AUX
ejpam-1745	22	16	s	s	NOUN
ejpam-1745	22	17	-	-	NOUN
ejpam-1745	22	18	complete	complete	ADJ
ejpam-1745	22	19	.	.	PUNCT
ejpam-1745	23	1	also	also	ADV
ejpam-1745	23	2	,	,	PUNCT
ejpam-1745	23	3	every	every	DET
ejpam-1745	23	4	injective	injective	ADJ
ejpam-1745	23	5	s	s	NOUN
ejpam-1745	23	6	-	-	PUNCT
ejpam-1745	23	7	act	act	NOUN
ejpam-1745	23	8	is	be	AUX
ejpam-1745	23	9	s	s	NOUN
ejpam-1745	23	10	-	-	NOUN
ejpam-1745	23	11	complete	complete	ADJ
ejpam-1745	23	12	but	but	CCONJ
ejpam-1745	23	13	the	the	DET
ejpam-1745	23	14	converse	converse	NOUN
ejpam-1745	23	15	is	be	AUX
ejpam-1745	23	16	not	not	PART
ejpam-1745	23	17	true	true	ADJ
ejpam-1745	23	18	in	in	ADP
ejpam-1745	23	19	general	general	ADJ
ejpam-1745	23	20	.	.	PUNCT
ejpam-1745	24	1	the	the	DET
ejpam-1745	24	2	baer	baer	PROPN
ejpam-1745	24	3	criterion	criterion	NOUN
ejpam-1745	24	4	for	for	ADP
ejpam-1745	24	5	injectivity	injectivity	NOUN
ejpam-1745	24	6	(	(	PUNCT
ejpam-1745	24	7	weak	weak	ADJ
ejpam-1745	24	8	injectivity	injectivity	NOUN
ejpam-1745	24	9	implies	imply	VERB
ejpam-1745	24	10	injectivity	injectivity	NOUN
ejpam-1745	24	11	)	)	PUNCT
ejpam-1745	24	12	of	of	ADP
ejpam-1745	24	13	s	s	NOUN
ejpam-1745	24	14	-	-	PUNCT
ejpam-1745	24	15	acts	act	NOUN
ejpam-1745	24	16	,	,	PUNCT
ejpam-1745	24	17	which	which	PRON
ejpam-1745	24	18	is	be	AUX
ejpam-1745	24	19	true	true	ADJ
ejpam-1745	24	20	for	for	ADP
ejpam-1745	24	21	modules	module	NOUN
ejpam-1745	24	22	over	over	ADP
ejpam-1745	24	23	a	a	DET
ejpam-1745	24	24	ring	ring	NOUN
ejpam-1745	24	25	with	with	ADP
ejpam-1745	24	26	an	an	DET
ejpam-1745	24	27	identity	identity	NOUN
ejpam-1745	24	28	,	,	PUNCT
ejpam-1745	24	29	is	be	AUX
ejpam-1745	24	30	an	an	DET
ejpam-1745	24	31	open	open	ADJ
ejpam-1745	24	32	problem	problem	NOUN
ejpam-1745	24	33	for	for	ADP
ejpam-1745	24	34	acts	act	NOUN
ejpam-1745	24	35	over	over	ADP
ejpam-1745	24	36	a	a	DET
ejpam-1745	24	37	semigroup	semigroup	NOUN
ejpam-1745	24	38	s	s	X
ejpam-1745	24	39	(	(	PUNCT
ejpam-1745	24	40	with	with	ADP
ejpam-1745	24	41	or	or	CCONJ
ejpam-1745	24	42	without	without	ADP
ejpam-1745	24	43	identity	identity	NOUN
ejpam-1745	24	44	)	)	PUNCT
ejpam-1745	24	45	.	.	PUNCT
ejpam-1745	25	1	furthermore	furthermore	ADV
ejpam-1745	25	2	in	in	ADP
ejpam-1745	25	3	this	this	DET
ejpam-1745	25	4	paper	paper	NOUN
ejpam-1745	25	5	a	a	DET
ejpam-1745	25	6	weaker	weak	ADJ
ejpam-1745	25	7	kind	kind	NOUN
ejpam-1745	25	8	of	of	ADP
ejpam-1745	25	9	baer	baer	PROPN
ejpam-1745	25	10	criterion	criterion	NOUN
ejpam-1745	25	11	(	(	PUNCT
ejpam-1745	25	12	s	s	NOUN
ejpam-1745	25	13	-	-	ADJ
ejpam-1745	25	14	completeness	completeness	NOUN
ejpam-1745	25	15	implies	imply	VERB
ejpam-1745	25	16	injectivity	injectivity	NOUN
ejpam-1745	25	17	)	)	PUNCT
ejpam-1745	25	18	is	be	AUX
ejpam-1745	25	19	investigated	investigate	VERB
ejpam-1745	25	20	and	and	CCONJ
ejpam-1745	25	21	some	some	DET
ejpam-1745	25	22	semigroups	semigroup	NOUN
ejpam-1745	25	23	over	over	ADP
ejpam-1745	25	24	all	all	PRON
ejpam-1745	25	25	of	of	ADP
ejpam-1745	25	26	which	which	PRON
ejpam-1745	25	27	every	every	DET
ejpam-1745	25	28	s	s	NOUN
ejpam-1745	25	29	-	-	ADJ
ejpam-1745	25	30	complete	complete	ADJ
ejpam-1745	25	31	s	s	NOUN
ejpam-1745	25	32	-	-	NOUN
ejpam-1745	25	33	act	act	NOUN
ejpam-1745	25	34	is	be	AUX
ejpam-1745	25	35	injective	injective	ADJ
ejpam-1745	25	36	is	be	AUX
ejpam-1745	25	37	introduced	introduce	VERB
ejpam-1745	25	38	.	.	PUNCT
ejpam-1745	26	1	these	these	DET
ejpam-1745	26	2	conclusions	conclusion	NOUN
ejpam-1745	26	3	are	be	AUX
ejpam-1745	26	4	the	the	DET
ejpam-1745	26	5	main	main	ADJ
ejpam-1745	26	6	part	part	NOUN
ejpam-1745	26	7	of	of	ADP
ejpam-1745	26	8	this	this	DET
ejpam-1745	26	9	article	article	NOUN
ejpam-1745	26	10	,	,	PUNCT
ejpam-1745	26	11	which	which	PRON
ejpam-1745	26	12	appear	appear	VERB
ejpam-1745	26	13	in	in	ADP
ejpam-1745	26	14	section	section	NOUN
ejpam-1745	26	15	4	4	NUM
ejpam-1745	26	16	.	.	NOUN
ejpam-1745	27	1	2	2	NUM
ejpam-1745	27	2	.	.	X
ejpam-1745	27	3	preliminary	preliminary	ADJ
ejpam-1745	27	4	in	in	ADP
ejpam-1745	27	5	this	this	DET
ejpam-1745	27	6	section	section	NOUN
ejpam-1745	27	7	we	we	PRON
ejpam-1745	27	8	briefly	briefly	ADV
ejpam-1745	27	9	recall	recall	VERB
ejpam-1745	27	10	the	the	DET
ejpam-1745	27	11	definition	definition	NOUN
ejpam-1745	27	12	and	and	CCONJ
ejpam-1745	27	13	the	the	DET
ejpam-1745	27	14	categorical	categorical	ADJ
ejpam-1745	27	15	and	and	CCONJ
ejpam-1745	27	16	algebraic	algebraic	ADJ
ejpam-1745	27	17	ingredients	ingredient	NOUN
ejpam-1745	27	18	of	of	ADP
ejpam-1745	27	19	the	the	DET
ejpam-1745	27	20	category	category	NOUN
ejpam-1745	27	21	act	act	NOUN
ejpam-1745	27	22	-	-	PUNCT
ejpam-1745	27	23	s	s	PROPN
ejpam-1745	27	24	of	of	ADP
ejpam-1745	27	25	(	(	PUNCT
ejpam-1745	27	26	right	right	ADJ
ejpam-1745	27	27	)	)	PUNCT
ejpam-1745	27	28	s	s	NOUN
ejpam-1745	27	29	-	-	PUNCT
ejpam-1745	27	30	acts	act	VERB
ejpam-1745	27	31	over	over	ADP
ejpam-1745	27	32	a	a	DET
ejpam-1745	27	33	semigroup	semigroup	NOUN
ejpam-1745	27	34	s	s	NOUN
ejpam-1745	27	35	and	and	CCONJ
ejpam-1745	27	36	recall	recall	VERB
ejpam-1745	27	37	sequentially	sequentially	ADV
ejpam-1745	27	38	pure	pure	ADJ
ejpam-1745	27	39	monomorphisms	monomorphism	NOUN
ejpam-1745	27	40	in	in	ADP
ejpam-1745	27	41	this	this	DET
ejpam-1745	27	42	category	category	NOUN
ejpam-1745	27	43	.	.	PUNCT
ejpam-1745	28	1	for	for	ADP
ejpam-1745	28	2	more	more	ADJ
ejpam-1745	28	3	information	information	NOUN
ejpam-1745	28	4	and	and	CCONJ
ejpam-1745	28	5	the	the	DET
ejpam-1745	28	6	notions	notion	NOUN
ejpam-1745	28	7	not	not	PART
ejpam-1745	28	8	mentioned	mention	VERB
ejpam-1745	28	9	here	here	ADV
ejpam-1745	28	10	about	about	ADP
ejpam-1745	28	11	this	this	DET
ejpam-1745	28	12	category	category	NOUN
ejpam-1745	28	13	see	see	VERB
ejpam-1745	28	14	,	,	PUNCT
ejpam-1745	28	15	for	for	ADP
ejpam-1745	28	16	example	example	NOUN
ejpam-1745	28	17	,	,	PUNCT
ejpam-1745	29	1	[	[	X
ejpam-1745	29	2	9	9	NUM
ejpam-1745	29	3	]	]	PUNCT
ejpam-1745	29	4	.	.	PUNCT
ejpam-1745	30	1	recall	recall	VERB
ejpam-1745	30	2	that	that	SCONJ
ejpam-1745	30	3	an	an	DET
ejpam-1745	30	4	element	element	NOUN
ejpam-1745	30	5	a	a	DET
ejpam-1745	30	6	∈	∈	NOUN
ejpam-1745	30	7	a(t	a(t	NOUN
ejpam-1745	30	8	∈	∈	PROPN
ejpam-1745	30	9	s	s	PART
ejpam-1745	30	10	)	)	PUNCT
ejpam-1745	30	11	is	be	AUX
ejpam-1745	30	12	said	say	VERB
ejpam-1745	30	13	to	to	PART
ejpam-1745	30	14	be	be	AUX
ejpam-1745	30	15	a	a	DET
ejpam-1745	30	16	fixed	fix	VERB
ejpam-1745	30	17	element	element	NOUN
ejpam-1745	30	18	(	(	PUNCT
ejpam-1745	30	19	left	leave	VERB
ejpam-1745	30	20	zero	zero	NUM
ejpam-1745	30	21	element	element	NOUN
ejpam-1745	30	22	)	)	PUNCT
ejpam-1745	30	23	if	if	SCONJ
ejpam-1745	30	24	as	as	ADP
ejpam-1745	30	25	=	=	PUNCT
ejpam-1745	30	26	a	a	X
ejpam-1745	30	27	(	(	PUNCT
ejpam-1745	30	28	ts	ts	PROPN
ejpam-1745	30	29	=	=	PUNCT
ejpam-1745	30	30	t	t	PROPN
ejpam-1745	30	31	)	)	PUNCT
ejpam-1745	30	32	for	for	ADP
ejpam-1745	30	33	all	all	DET
ejpam-1745	30	34	s	s	PROPN
ejpam-1745	30	35	∈	∈	PROPN
ejpam-1745	30	36	s.	s.	PROPN
ejpam-1745	30	37	the	the	DET
ejpam-1745	30	38	s	s	PROPN
ejpam-1745	30	39	-	-	NOUN
ejpam-1745	30	40	act	act	NOUN
ejpam-1745	30	41	a∪	a∪	CCONJ
ejpam-1745	30	42	{	{	PUNCT
ejpam-1745	30	43	0	0	NUM
ejpam-1745	30	44	}	}	PUNCT
ejpam-1745	30	45	with	with	ADP
ejpam-1745	30	46	a	a	DET
ejpam-1745	30	47	fixed	fix	VERB
ejpam-1745	30	48	element	element	NOUN
ejpam-1745	30	49	adjoined	adjoin	VERB
ejpam-1745	30	50	to	to	ADP
ejpam-1745	30	51	a	a	PRON
ejpam-1745	30	52	is	be	AUX
ejpam-1745	30	53	denoted	denote	VERB
ejpam-1745	30	54	by	by	ADP
ejpam-1745	30	55	a0	a0	PROPN
ejpam-1745	30	56	.	.	PUNCT
ejpam-1745	31	1	since	since	SCONJ
ejpam-1745	31	2	the	the	DET
ejpam-1745	31	3	class	class	NOUN
ejpam-1745	31	4	of	of	ADP
ejpam-1745	31	5	s	s	NOUN
ejpam-1745	31	6	-	-	PUNCT
ejpam-1745	31	7	acts	act	NOUN
ejpam-1745	31	8	is	be	AUX
ejpam-1745	31	9	an	an	DET
ejpam-1745	31	10	equational	equational	ADJ
ejpam-1745	31	11	class	class	NOUN
ejpam-1745	31	12	,	,	PUNCT
ejpam-1745	31	13	the	the	DET
ejpam-1745	31	14	category	category	NOUN
ejpam-1745	31	15	act	act	NOUN
ejpam-1745	31	16	-	-	PUNCT
ejpam-1745	31	17	s	s	PART
ejpam-1745	31	18	is	be	AUX
ejpam-1745	31	19	complete	complete	ADJ
ejpam-1745	31	20	(	(	PUNCT
ejpam-1745	31	21	has	have	AUX
ejpam-1745	31	22	all	all	DET
ejpam-1745	31	23	products	product	NOUN
ejpam-1745	31	24	and	and	CCONJ
ejpam-1745	31	25	equalizers	equalizer	NOUN
ejpam-1745	31	26	)	)	PUNCT
ejpam-1745	31	27	and	and	CCONJ
ejpam-1745	31	28	cocomplete	cocomplete	ADJ
ejpam-1745	31	29	(	(	PUNCT
ejpam-1745	31	30	has	have	VERB
ejpam-1745	31	31	all	all	DET
ejpam-1745	31	32	coproducts	coproduct	NOUN
ejpam-1745	31	33	and	and	CCONJ
ejpam-1745	31	34	coequalizers	coequalizer	NOUN
ejpam-1745	31	35	)	)	PUNCT
ejpam-1745	31	36	.	.	PUNCT
ejpam-1745	32	1	in	in	ADP
ejpam-1745	32	2	fact	fact	NOUN
ejpam-1745	32	3	,	,	PUNCT
ejpam-1745	32	4	limits	limit	NOUN
ejpam-1745	32	5	and	and	CCONJ
ejpam-1745	32	6	colimits	colimit	NOUN
ejpam-1745	32	7	in	in	ADP
ejpam-1745	32	8	this	this	DET
ejpam-1745	32	9	category	category	NOUN
ejpam-1745	32	10	are	be	AUX
ejpam-1745	32	11	computed	compute	VERB
ejpam-1745	32	12	as	as	ADP
ejpam-1745	32	13	in	in	ADP
ejpam-1745	32	14	the	the	DET
ejpam-1745	32	15	category	category	NOUN
ejpam-1745	32	16	set	set	VERB
ejpam-1745	32	17	of	of	ADP
ejpam-1745	32	18	sets	set	NOUN
ejpam-1745	32	19	and	and	CCONJ
ejpam-1745	32	20	equipped	equip	VERB
ejpam-1745	32	21	with	with	ADP
ejpam-1745	32	22	a	a	DET
ejpam-1745	32	23	natural	natural	ADJ
ejpam-1745	32	24	action	action	NOUN
ejpam-1745	32	25	.	.	PUNCT
ejpam-1745	33	1	in	in	ADP
ejpam-1745	33	2	particular	particular	ADJ
ejpam-1745	33	3	,	,	PUNCT
ejpam-1745	33	4	for	for	SCONJ
ejpam-1745	33	5	a	a	DET
ejpam-1745	33	6	family	family	NOUN
ejpam-1745	33	7	{	{	PUNCT
ejpam-1745	33	8	ai	ai	VERB
ejpam-1745	33	9	}	}	PUNCT
ejpam-1745	33	10	of	of	ADP
ejpam-1745	33	11	s	s	NOUN
ejpam-1745	33	12	-	-	PUNCT
ejpam-1745	33	13	acts	act	VERB
ejpam-1745	33	14	their	their	PRON
ejpam-1745	33	15	cartesian	cartesian	ADJ
ejpam-1745	33	16	product	product	NOUN
ejpam-1745	33	17	∏	∏	PROPN
ejpam-1745	33	18	ai	ai	VERB
ejpam-1745	33	19	with	with	ADP
ejpam-1745	33	20	the	the	DET
ejpam-1745	33	21	s	s	NOUN
ejpam-1745	33	22	-	-	PUNCT
ejpam-1745	33	23	action	action	NOUN
ejpam-1745	33	24	defined	define	VERB
ejpam-1745	33	25	by	by	ADP
ejpam-1745	33	26	(	(	PUNCT
ejpam-1745	33	27	ai)s	ai)	NOUN
ejpam-1745	33	28	=	=	SYM
ejpam-1745	33	29	(	(	PUNCT
ejpam-1745	33	30	ais	ais	PROPN
ejpam-1745	33	31	)	)	PUNCT
ejpam-1745	33	32	is	be	AUX
ejpam-1745	33	33	the	the	DET
ejpam-1745	33	34	product	product	NOUN
ejpam-1745	33	35	of	of	ADP
ejpam-1745	33	36	a	a	DET
ejpam-1745	33	37	family	family	NOUN
ejpam-1745	33	38	{	{	PUNCT
ejpam-1745	33	39	ai	ai	VERB
ejpam-1745	33	40	}	}	PUNCT
ejpam-1745	33	41	in	in	ADP
ejpam-1745	33	42	act	act	PROPN
ejpam-1745	33	43	-	-	PUNCT
ejpam-1745	33	44	s.	s.	PROPN
ejpam-1745	33	45	the	the	DET
ejpam-1745	33	46	coproduct	coproduct	NOUN
ejpam-1745	33	47	of	of	ADP
ejpam-1745	33	48	a	a	DET
ejpam-1745	33	49	family	family	NOUN
ejpam-1745	33	50	{	{	PUNCT
ejpam-1745	33	51	ai	ai	VERB
ejpam-1745	33	52	}	}	PUNCT
ejpam-1745	33	53	in	in	ADP
ejpam-1745	33	54	act	act	PROPN
ejpam-1745	33	55	-	-	PUNCT
ejpam-1745	33	56	s	s	PART
ejpam-1745	33	57	is	be	AUX
ejpam-1745	33	58	their	their	PRON
ejpam-1745	33	59	disjoint	disjoint	NOUN
ejpam-1745	33	60	union	union	NOUN
ejpam-1745	33	61	∐	∐	ADV
ejpam-1745	33	62	ai	ai	VERB
ejpam-1745	33	63	=	=	SYM
ejpam-1745	33	64	∪(ai	∪(ai	ADJ
ejpam-1745	33	65	×	×	NOUN
ejpam-1745	33	66	{	{	PUNCT
ejpam-1745	33	67	i	i	NOUN
ejpam-1745	33	68	}	}	PUNCT
ejpam-1745	33	69	)	)	PUNCT
ejpam-1745	33	70	with	with	ADP
ejpam-1745	33	71	the	the	DET
ejpam-1745	33	72	action	action	NOUN
ejpam-1745	33	73	of	of	ADP
ejpam-1745	33	74	s	s	PRON
ejpam-1745	33	75	defined	define	VERB
ejpam-1745	33	76	by	by	ADP
ejpam-1745	33	77	(	(	PUNCT
ejpam-1745	33	78	a	a	PRON
ejpam-1745	33	79	,	,	PUNCT
ejpam-1745	33	80	i)s	i)	NOUN
ejpam-1745	34	1	=	=	SYM
ejpam-1745	34	2	(	(	PUNCT
ejpam-1745	34	3	as	as	ADP
ejpam-1745	34	4	,	,	PUNCT
ejpam-1745	34	5	i	i	NOUN
ejpam-1745	34	6	)	)	PUNCT
ejpam-1745	34	7	for	for	ADP
ejpam-1745	34	8	s	s	PROPN
ejpam-1745	34	9	∈	∈	PROPN
ejpam-1745	34	10	s	s	PROPN
ejpam-1745	34	11	,	,	PUNCT
ejpam-1745	34	12	a	a	DET
ejpam-1745	34	13	∈	∈	NOUN
ejpam-1745	34	14	ai	ai	VERB
ejpam-1745	34	15	.	.	PUNCT
ejpam-1745	35	1	recall	recall	VERB
ejpam-1745	35	2	that	that	PRON
ejpam-1745	35	3	for	for	SCONJ
ejpam-1745	35	4	a	a	DET
ejpam-1745	35	5	family	family	NOUN
ejpam-1745	35	6	{	{	PUNCT
ejpam-1745	35	7	ai	ai	VERB
ejpam-1745	35	8	:	:	PUNCT
ejpam-1745	35	9	i	i	PRON
ejpam-1745	35	10	∈	∈	VERB
ejpam-1745	35	11	i	i	X
ejpam-1745	35	12	}	}	PUNCT
ejpam-1745	35	13	of	of	ADP
ejpam-1745	35	14	s	s	NOUN
ejpam-1745	35	15	-	-	PUNCT
ejpam-1745	35	16	acts	act	VERB
ejpam-1745	35	17	with	with	ADP
ejpam-1745	35	18	a	a	DET
ejpam-1745	35	19	unique	unique	ADJ
ejpam-1745	35	20	fixed	fix	VERB
ejpam-1745	35	21	element	element	NOUN
ejpam-1745	35	22	0	0	NUM
ejpam-1745	35	23	,	,	PUNCT
ejpam-1745	35	24	the	the	DET
ejpam-1745	35	25	direct	direct	ADJ
ejpam-1745	35	26	sum	sum	NOUN
ejpam-1745	35	27	⊕	⊕	PROPN
ejpam-1745	35	28	i∈i	i∈i	ADJ
ejpam-1745	35	29	ai	ai	VERB
ejpam-1745	35	30	is	be	AUX
ejpam-1745	35	31	defined	define	VERB
ejpam-1745	35	32	to	to	PART
ejpam-1745	35	33	be	be	AUX
ejpam-1745	35	34	the	the	DET
ejpam-1745	35	35	subact	subact	NOUN
ejpam-1745	35	36	of	of	ADP
ejpam-1745	35	37	the	the	DET
ejpam-1745	35	38	product	product	NOUN
ejpam-1745	35	39	∏	∏	PROPN
ejpam-1745	35	40	i∈i	i∈i	ADV
ejpam-1745	35	41	ai	ai	AUX
ejpam-1745	35	42	consisting	consist	VERB
ejpam-1745	35	43	of	of	ADP
ejpam-1745	35	44	all	all	PRON
ejpam-1745	35	45	(	(	PUNCT
ejpam-1745	35	46	ai)i∈i	ai)i∈i	NOUN
ejpam-1745	35	47	such	such	ADJ
ejpam-1745	35	48	that	that	SCONJ
ejpam-1745	35	49	ai	ai	VERB
ejpam-1745	35	50	=	=	NOUN
ejpam-1745	35	51	0	0	NUM
ejpam-1745	35	52	for	for	ADP
ejpam-1745	35	53	all	all	PRON
ejpam-1745	35	54	i	i	PRON
ejpam-1745	35	55	∈	∈	VERB
ejpam-1745	35	56	i	i	PRON
ejpam-1745	35	57	except	except	SCONJ
ejpam-1745	35	58	a	a	DET
ejpam-1745	35	59	finite	finite	ADJ
ejpam-1745	35	60	number	number	NOUN
ejpam-1745	35	61	.	.	PUNCT
ejpam-1745	36	1	we	we	PRON
ejpam-1745	36	2	use	use	VERB
ejpam-1745	36	3	⊕	⊕	PROPN
ejpam-1745	36	4	i∈i	i∈i	ADJ
ejpam-1745	36	5	ai	ai	VERB
ejpam-1745	36	6	only	only	ADV
ejpam-1745	36	7	for	for	ADP
ejpam-1745	36	8	s	s	NOUN
ejpam-1745	36	9	-	-	PUNCT
ejpam-1745	36	10	acts	act	NOUN
ejpam-1745	36	11	with	with	ADP
ejpam-1745	36	12	unique	unique	ADJ
ejpam-1745	36	13	fixed	fix	VERB
ejpam-1745	36	14	element	element	NOUN
ejpam-1745	36	15	.	.	PUNCT
ejpam-1745	37	1	an	an	DET
ejpam-1745	37	2	s	s	NOUN
ejpam-1745	37	3	-	-	PUNCT
ejpam-1745	37	4	act	act	NOUN
ejpam-1745	37	5	a	a	PRON
ejpam-1745	37	6	is	be	AUX
ejpam-1745	37	7	said	say	VERB
ejpam-1745	37	8	to	to	PART
ejpam-1745	37	9	be	be	AUX
ejpam-1745	37	10	injective	injective	ADJ
ejpam-1745	37	11	if	if	SCONJ
ejpam-1745	37	12	for	for	ADP
ejpam-1745	37	13	any	any	DET
ejpam-1745	37	14	monomorphism	monomorphism	NOUN
ejpam-1745	37	15	g	g	NOUN
ejpam-1745	37	16	:	:	PUNCT
ejpam-1745	37	17	b	b	X
ejpam-1745	37	18	→	→	SYM
ejpam-1745	37	19	c	c	PROPN
ejpam-1745	37	20	and	and	CCONJ
ejpam-1745	37	21	any	any	DET
ejpam-1745	37	22	homomorphism	homomorphism	PROPN
ejpam-1745	37	23	f	f	X
ejpam-1745	37	24	:	:	PUNCT
ejpam-1745	37	25	b→	b→	PROPN
ejpam-1745	37	26	a	a	PRON
ejpam-1745	37	27	there	there	PRON
ejpam-1745	37	28	exists	exist	VERB
ejpam-1745	37	29	a	a	DET
ejpam-1745	37	30	homomorphism	homomorphism	NOUN
ejpam-1745	37	31	h	h	NOUN
ejpam-1745	38	1	:	:	PUNCT
ejpam-1745	38	2	c	c	X
ejpam-1745	38	3	→	→	PUNCT
ejpam-1745	38	4	a	a	DET
ejpam-1745	38	5	such	such	ADJ
ejpam-1745	38	6	that	that	DET
ejpam-1745	38	7	hg	hg	NOUN
ejpam-1745	38	8	=	=	SYM
ejpam-1745	38	9	f	f	PROPN
ejpam-1745	38	10	.	.	PUNCT
ejpam-1745	39	1	an	an	DET
ejpam-1745	39	2	s	s	NOUN
ejpam-1745	39	3	-	-	PUNCT
ejpam-1745	39	4	act	act	NOUN
ejpam-1745	39	5	a	a	PRON
ejpam-1745	39	6	is	be	AUX
ejpam-1745	39	7	said	say	VERB
ejpam-1745	39	8	to	to	PART
ejpam-1745	39	9	be	be	AUX
ejpam-1745	39	10	weakly	weakly	ADV
ejpam-1745	39	11	injective	injective	ADJ
ejpam-1745	39	12	if	if	SCONJ
ejpam-1745	39	13	it	it	PRON
ejpam-1745	39	14	is	be	AUX
ejpam-1745	39	15	injective	injective	ADJ
ejpam-1745	39	16	with	with	ADP
ejpam-1745	39	17	respect	respect	NOUN
ejpam-1745	39	18	to	to	ADP
ejpam-1745	39	19	right	right	ADJ
ejpam-1745	39	20	ideals	ideal	NOUN
ejpam-1745	39	21	of	of	ADP
ejpam-1745	39	22	s.	s.	PROPN
ejpam-1745	39	23	in	in	ADP
ejpam-1745	39	24	this	this	DET
ejpam-1745	39	25	section	section	NOUN
ejpam-1745	39	26	we	we	PRON
ejpam-1745	39	27	recall	recall	VERB
ejpam-1745	39	28	the	the	DET
ejpam-1745	39	29	notion	notion	NOUN
ejpam-1745	39	30	of	of	ADP
ejpam-1745	39	31	sequentially	sequentially	ADV
ejpam-1745	39	32	pure	pure	ADJ
ejpam-1745	39	33	monomorphisms	monomorphism	NOUN
ejpam-1745	39	34	mainly	mainly	ADV
ejpam-1745	39	35	from	from	ADP
ejpam-1745	39	36	[	[	X
ejpam-1745	39	37	1	1	NUM
ejpam-1745	39	38	,	,	PUNCT
ejpam-1745	39	39	2	2	NUM
ejpam-1745	39	40	]	]	PUNCT
ejpam-1745	39	41	.	.	PUNCT
ejpam-1745	40	1	for	for	ADP
ejpam-1745	40	2	simplicity	simplicity	NOUN
ejpam-1745	40	3	,	,	PUNCT
ejpam-1745	40	4	we	we	PRON
ejpam-1745	40	5	let	let	VERB
ejpam-1745	40	6	the	the	DET
ejpam-1745	40	7	letter	letter	NOUN
ejpam-1745	40	8	“	"	PUNCT
ejpam-1745	40	9	s	s	PART
ejpam-1745	40	10	”	"	PUNCT
ejpam-1745	40	11	stand	stand	NOUN
ejpam-1745	40	12	for	for	ADP
ejpam-1745	40	13	the	the	DET
ejpam-1745	40	14	prefix	prefix	NOUN
ejpam-1745	40	15	“	"	PUNCT
ejpam-1745	40	16	sequentially	sequentially	ADV
ejpam-1745	40	17	”	"	PUNCT
ejpam-1745	40	18	.	.	PUNCT
ejpam-1745	41	1	definition	definition	NOUN
ejpam-1745	41	2	1	1	NUM
ejpam-1745	41	3	.	.	PUNCT
ejpam-1745	42	1	we	we	PRON
ejpam-1745	42	2	say	say	VERB
ejpam-1745	42	3	that	that	SCONJ
ejpam-1745	42	4	a	a	PRON
ejpam-1745	42	5	is	be	AUX
ejpam-1745	42	6	s	s	NOUN
ejpam-1745	42	7	-	-	ADJ
ejpam-1745	42	8	pure	pure	ADJ
ejpam-1745	42	9	in	in	ADP
ejpam-1745	42	10	an	an	DET
ejpam-1745	42	11	extension	extension	NOUN
ejpam-1745	42	12	b	b	NOUN
ejpam-1745	42	13	of	of	ADP
ejpam-1745	42	14	a	a	PRON
ejpam-1745	42	15	if	if	SCONJ
ejpam-1745	42	16	every	every	DET
ejpam-1745	42	17	sequential	sequential	ADJ
ejpam-1745	42	18	system	system	NOUN
ejpam-1745	42	19	of	of	ADP
ejpam-1745	42	20	equations	equation	NOUN
ejpam-1745	42	21	with	with	ADP
ejpam-1745	42	22	constants	constant	NOUN
ejpam-1745	42	23	from	from	ADP
ejpam-1745	42	24	a	a	DET
ejpam-1745	42	25	such	such	ADJ
ejpam-1745	42	26	as	as	ADP
ejpam-1745	42	27	σa	σa	PROPN
ejpam-1745	42	28	=	=	SYM
ejpam-1745	42	29	{	{	PUNCT
ejpam-1745	42	30	xs	xs	NOUN
ejpam-1745	42	31	=	=	PUNCT
ejpam-1745	42	32	as	as	ADP
ejpam-1745	42	33	:	:	PUNCT
ejpam-1745	42	34	s	s	VERB
ejpam-1745	42	35	∈	∈	PROPN
ejpam-1745	42	36	s	s	NOUN
ejpam-1745	42	37	,	,	PUNCT
ejpam-1745	42	38	as	as	SCONJ
ejpam-1745	42	39	∈	∈	PROPN
ejpam-1745	42	40	a	a	PRON
ejpam-1745	42	41	}	}	PUNCT
ejpam-1745	42	42	has	have	VERB
ejpam-1745	42	43	a	a	DET
ejpam-1745	42	44	solution	solution	NOUN
ejpam-1745	42	45	in	in	ADP
ejpam-1745	42	46	a	a	PRON
ejpam-1745	42	47	whenever	whenever	SCONJ
ejpam-1745	42	48	it	it	PRON
ejpam-1745	42	49	has	have	VERB
ejpam-1745	42	50	a	a	DET
ejpam-1745	42	51	solution	solution	NOUN
ejpam-1745	42	52	in	in	ADP
ejpam-1745	42	53	b.	b.	PROPN
ejpam-1745	43	1	the	the	DET
ejpam-1745	43	2	system	system	NOUN
ejpam-1745	43	3	σa	σa	PROPN
ejpam-1745	43	4	is	be	AUX
ejpam-1745	43	5	said	say	VERB
ejpam-1745	43	6	to	to	PART
ejpam-1745	43	7	be	be	AUX
ejpam-1745	43	8	consistent	consistent	ADJ
ejpam-1745	43	9	if	if	SCONJ
ejpam-1745	43	10	it	it	PRON
ejpam-1745	43	11	has	have	VERB
ejpam-1745	43	12	a	a	DET
ejpam-1745	43	13	solution	solution	NOUN
ejpam-1745	43	14	in	in	ADP
ejpam-1745	43	15	some	some	DET
ejpam-1745	43	16	extension	extension	NOUN
ejpam-1745	43	17	b	b	PROPN
ejpam-1745	43	18	of	of	ADP
ejpam-1745	43	19	a.	a.	PROPN
ejpam-1745	43	20	h.	h.	PROPN
ejpam-1745	43	21	barzegar	barzegar	PROPN
ejpam-1745	43	22	/	/	SYM
ejpam-1745	43	23	eur	eur	PROPN
ejpam-1745	43	24	.	.	PUNCT
ejpam-1745	44	1	j.	j.	PROPN
ejpam-1745	44	2	pure	pure	PROPN
ejpam-1745	44	3	appl	appl	PROPN
ejpam-1745	44	4	.	.	PROPN
ejpam-1745	44	5	math	math	PROPN
ejpam-1745	44	6	,	,	PUNCT
ejpam-1745	44	7	6	6	NUM
ejpam-1745	44	8	(	(	PUNCT
ejpam-1745	44	9	2013	2013	NUM
ejpam-1745	44	10	)	)	PUNCT
ejpam-1745	44	11	,	,	PUNCT
ejpam-1745	44	12	211	211	NUM
ejpam-1745	44	13	-	-	SYM
ejpam-1745	44	14	221	221	NUM
ejpam-1745	44	15	213	213	NUM
ejpam-1745	44	16	note	note	NOUN
ejpam-1745	44	17	that	that	SCONJ
ejpam-1745	44	18	there	there	PRON
ejpam-1745	44	19	is	be	VERB
ejpam-1745	44	20	a	a	DET
ejpam-1745	44	21	one	one	NUM
ejpam-1745	44	22	to	to	ADP
ejpam-1745	44	23	one	one	NUM
ejpam-1745	44	24	correspondence	correspondence	NOUN
ejpam-1745	44	25	between	between	ADP
ejpam-1745	44	26	the	the	DET
ejpam-1745	44	27	set	set	NOUN
ejpam-1745	44	28	of	of	ADP
ejpam-1745	44	29	all	all	DET
ejpam-1745	44	30	systems	system	NOUN
ejpam-1745	44	31	of	of	ADP
ejpam-1745	44	32	equations	equation	NOUN
ejpam-1745	44	33	σa	σa	VERB
ejpam-1745	44	34	of	of	ADP
ejpam-1745	44	35	the	the	DET
ejpam-1745	44	36	above	above	ADJ
ejpam-1745	44	37	form	form	NOUN
ejpam-1745	44	38	on	on	ADP
ejpam-1745	44	39	an	an	DET
ejpam-1745	44	40	s	s	NOUN
ejpam-1745	44	41	-	-	NOUN
ejpam-1745	44	42	act	act	NOUN
ejpam-1745	44	43	a	a	PRON
ejpam-1745	44	44	and	and	CCONJ
ejpam-1745	44	45	the	the	DET
ejpam-1745	44	46	set	set	NOUN
ejpam-1745	44	47	of	of	ADP
ejpam-1745	44	48	all	all	DET
ejpam-1745	44	49	functions	function	NOUN
ejpam-1745	44	50	k	k	NOUN
ejpam-1745	44	51	:	:	PUNCT
ejpam-1745	44	52	s→	s→	X
ejpam-1745	44	53	a.	a.	NOUN
ejpam-1745	44	54	for	for	ADP
ejpam-1745	44	55	any	any	DET
ejpam-1745	44	56	s	s	NOUN
ejpam-1745	44	57	-	-	PUNCT
ejpam-1745	44	58	act	act	NOUN
ejpam-1745	44	59	b	b	NOUN
ejpam-1745	44	60	and	and	CCONJ
ejpam-1745	44	61	b	b	PROPN
ejpam-1745	44	62	∈	∈	PROPN
ejpam-1745	44	63	b	b	NOUN
ejpam-1745	44	64	,	,	PUNCT
ejpam-1745	44	65	let	let	VERB
ejpam-1745	44	66	us	we	PRON
ejpam-1745	44	67	denote	denote	VERB
ejpam-1745	44	68	the	the	DET
ejpam-1745	44	69	homomorphism	homomorphism	NOUN
ejpam-1745	44	70	λb	λb	ADP
ejpam-1745	44	71	:	:	PUNCT
ejpam-1745	44	72	s	s	X
ejpam-1745	44	73	→	→	SYM
ejpam-1745	44	74	b	b	PROPN
ejpam-1745	44	75	,	,	PUNCT
ejpam-1745	44	76	defined	define	VERB
ejpam-1745	44	77	by	by	ADP
ejpam-1745	44	78	λb(s	λb(	NOUN
ejpam-1745	44	79	)	)	PUNCT
ejpam-1745	44	80	:	:	PUNCT
ejpam-1745	44	81	=	=	SYM
ejpam-1745	44	82	bs	b	NOUN
ejpam-1745	44	83	,	,	PUNCT
ejpam-1745	44	84	by	by	ADP
ejpam-1745	44	85	λb	λb	PROPN
ejpam-1745	44	86	.	.	PUNCT
ejpam-1745	45	1	in	in	ADP
ejpam-1745	45	2	these	these	DET
ejpam-1745	45	3	notations	notation	NOUN
ejpam-1745	45	4	,	,	PUNCT
ejpam-1745	45	5	we	we	PRON
ejpam-1745	45	6	have	have	VERB
ejpam-1745	45	7	lemma	lemma	PROPN
ejpam-1745	45	8	1	1	NUM
ejpam-1745	45	9	(	(	PUNCT
ejpam-1745	45	10	[	[	X
ejpam-1745	45	11	1	1	NUM
ejpam-1745	45	12	]	]	NUM
ejpam-1745	45	13	)	)	PUNCT
ejpam-1745	45	14	.	.	PUNCT
ejpam-1745	46	1	a	a	DET
ejpam-1745	46	2	map	map	NOUN
ejpam-1745	46	3	k	k	X
ejpam-1745	46	4	:	:	PUNCT
ejpam-1745	46	5	s→	s→	X
ejpam-1745	46	6	a	a	PRON
ejpam-1745	46	7	is	be	AUX
ejpam-1745	46	8	a	a	DET
ejpam-1745	46	9	homomorphism	homomorphism	NOUN
ejpam-1745	46	10	if	if	SCONJ
ejpam-1745	46	11	and	and	CCONJ
ejpam-1745	46	12	only	only	ADV
ejpam-1745	46	13	if	if	SCONJ
ejpam-1745	46	14	there	there	PRON
ejpam-1745	46	15	exists	exist	VERB
ejpam-1745	46	16	an	an	DET
ejpam-1745	46	17	extension	extension	NOUN
ejpam-1745	46	18	b	b	NOUN
ejpam-1745	46	19	of	of	ADP
ejpam-1745	46	20	a	a	PRON
ejpam-1745	46	21	and	and	CCONJ
ejpam-1745	46	22	b	b	NOUN
ejpam-1745	46	23	∈	∈	PROPN
ejpam-1745	46	24	b	b	NOUN
ejpam-1745	46	25	such	such	ADJ
ejpam-1745	46	26	that	that	PRON
ejpam-1745	46	27	k	k	PROPN
ejpam-1745	46	28	=	=	PUNCT
ejpam-1745	46	29	λb	λb	PROPN
ejpam-1745	46	30	.	.	PROPN
ejpam-1745	46	31	remark	remark	PROPN
ejpam-1745	46	32	1	1	NUM
ejpam-1745	46	33	(	(	PUNCT
ejpam-1745	46	34	[	[	X
ejpam-1745	46	35	1	1	NUM
ejpam-1745	46	36	]	]	PUNCT
ejpam-1745	46	37	)	)	PUNCT
ejpam-1745	46	38	.	.	PUNCT
ejpam-1745	47	1	for	for	ADP
ejpam-1745	47	2	a	a	DET
ejpam-1745	47	3	subact	subact	NOUN
ejpam-1745	47	4	a	a	PRON
ejpam-1745	47	5	of	of	ADP
ejpam-1745	47	6	b	b	NOUN
ejpam-1745	47	7	,	,	PUNCT
ejpam-1745	47	8	the	the	DET
ejpam-1745	47	9	following	follow	VERB
ejpam-1745	47	10	are	be	AUX
ejpam-1745	47	11	equivalent	equivalent	ADJ
ejpam-1745	47	12	:	:	PUNCT
ejpam-1745	47	13	(	(	PUNCT
ejpam-1745	47	14	i	i	NOUN
ejpam-1745	47	15	)	)	PUNCT
ejpam-1745	47	16	a	a	PRON
ejpam-1745	47	17	is	be	AUX
ejpam-1745	47	18	s	s	NOUN
ejpam-1745	47	19	-	-	ADJ
ejpam-1745	47	20	pure	pure	ADJ
ejpam-1745	47	21	in	in	ADP
ejpam-1745	47	22	b.	b.	PROPN
ejpam-1745	47	23	(	(	PUNCT
ejpam-1745	47	24	ii	ii	PROPN
ejpam-1745	47	25	)	)	PUNCT
ejpam-1745	47	26	for	for	ADP
ejpam-1745	47	27	every	every	DET
ejpam-1745	47	28	b	b	PROPN
ejpam-1745	47	29	∈	∈	PROPN
ejpam-1745	47	30	b	b	PROPN
ejpam-1745	47	31	with	with	ADP
ejpam-1745	47	32	bs	bs	PROPN
ejpam-1745	48	1	⊆	⊆	PROPN
ejpam-1745	48	2	a	a	PRON
ejpam-1745	48	3	there	there	PRON
ejpam-1745	48	4	is	be	VERB
ejpam-1745	48	5	an	an	DET
ejpam-1745	48	6	element	element	NOUN
ejpam-1745	48	7	a	a	DET
ejpam-1745	48	8	∈	∈	PROPN
ejpam-1745	48	9	a	a	PRON
ejpam-1745	48	10	with	with	ADP
ejpam-1745	48	11	λb	λb	PROPN
ejpam-1745	48	12	=	=	SYM
ejpam-1745	48	13	λa	λa	PROPN
ejpam-1745	48	14	.	.	PUNCT
ejpam-1745	49	1	(	(	PUNCT
ejpam-1745	49	2	iii	iii	X
ejpam-1745	49	3	)	)	PUNCT
ejpam-1745	49	4	every	every	DET
ejpam-1745	49	5	homomorphism	homomorphism	NOUN
ejpam-1745	50	1	k	k	X
ejpam-1745	50	2	:	:	PUNCT
ejpam-1745	50	3	s→	s→	X
ejpam-1745	50	4	a	a	PRON
ejpam-1745	50	5	is	be	AUX
ejpam-1745	50	6	of	of	ADP
ejpam-1745	50	7	the	the	DET
ejpam-1745	50	8	form	form	NOUN
ejpam-1745	50	9	λa	λa	INTJ
ejpam-1745	50	10	for	for	ADP
ejpam-1745	50	11	some	some	PRON
ejpam-1745	50	12	a	a	DET
ejpam-1745	50	13	∈	∈	NOUN
ejpam-1745	50	14	a	a	PRON
ejpam-1745	50	15	whenever	whenever	SCONJ
ejpam-1745	50	16	it	it	PRON
ejpam-1745	50	17	is	be	AUX
ejpam-1745	50	18	of	of	ADP
ejpam-1745	50	19	the	the	DET
ejpam-1745	50	20	form	form	NOUN
ejpam-1745	50	21	λb	λb	ADV
ejpam-1745	50	22	for	for	ADP
ejpam-1745	50	23	some	some	DET
ejpam-1745	50	24	b	b	PROPN
ejpam-1745	50	25	∈	∈	PROPN
ejpam-1745	50	26	b.	b.	PROPN
ejpam-1745	51	1	throughout	throughout	ADP
ejpam-1745	51	2	the	the	DET
ejpam-1745	51	3	paper	paper	NOUN
ejpam-1745	51	4	we	we	PRON
ejpam-1745	51	5	will	will	AUX
ejpam-1745	51	6	opt	opt	VERB
ejpam-1745	51	7	for	for	ADP
ejpam-1745	51	8	one	one	NUM
ejpam-1745	51	9	of	of	ADP
ejpam-1745	51	10	the	the	DET
ejpam-1745	51	11	three	three	NUM
ejpam-1745	51	12	equivalents	equivalent	NOUN
ejpam-1745	51	13	above	above	ADV
ejpam-1745	51	14	for	for	ADP
ejpam-1745	51	15	s	s	NOUN
ejpam-1745	51	16	-	-	NOUN
ejpam-1745	51	17	purity	purity	NOUN
ejpam-1745	51	18	.	.	PUNCT
ejpam-1745	52	1	the	the	DET
ejpam-1745	52	2	above	above	ADJ
ejpam-1745	52	3	remark	remark	NOUN
ejpam-1745	52	4	also	also	ADV
ejpam-1745	52	5	shows	show	VERB
ejpam-1745	52	6	that	that	SCONJ
ejpam-1745	52	7	if	if	SCONJ
ejpam-1745	52	8	one	one	NUM
ejpam-1745	52	9	defines	define	VERB
ejpam-1745	52	10	ã	ã	PROPN
ejpam-1745	52	11	:	:	PUNCT
ejpam-1745	52	12	=	=	SYM
ejpam-1745	52	13	{	{	PUNCT
ejpam-1745	52	14	b	b	PROPN
ejpam-1745	52	15	∈	∈	PROPN
ejpam-1745	52	16	b	b	PROPN
ejpam-1745	52	17	:	:	PUNCT
ejpam-1745	52	18	∃	∃	PROPN
ejpam-1745	52	19	a	a	PROPN
ejpam-1745	52	20	∈	∈	PROPN
ejpam-1745	52	21	a	a	PRON
ejpam-1745	52	22	,	,	PUNCT
ejpam-1745	52	23	λb	λb	PROPN
ejpam-1745	52	24	=	=	PUNCT
ejpam-1745	52	25	λa	λa	NOUN
ejpam-1745	52	26	}	}	PUNCT
ejpam-1745	52	27	and	and	CCONJ
ejpam-1745	52	28	ā	ā	ADJ
ejpam-1745	52	29	:	:	PUNCT
ejpam-1745	52	30	=	=	SYM
ejpam-1745	52	31	{	{	PUNCT
ejpam-1745	52	32	b	b	PROPN
ejpam-1745	52	33	∈	∈	PROPN
ejpam-1745	52	34	b	b	NOUN
ejpam-1745	52	35	:	:	PUNCT
ejpam-1745	52	36	bs	bs	PROPN
ejpam-1745	53	1	⊆	⊆	NUM
ejpam-1745	53	2	a	a	PRON
ejpam-1745	53	3	}	}	PUNCT
ejpam-1745	53	4	,	,	PUNCT
ejpam-1745	53	5	then	then	ADV
ejpam-1745	53	6	a	a	PRON
ejpam-1745	53	7	is	be	AUX
ejpam-1745	53	8	s	s	NOUN
ejpam-1745	53	9	-	-	ADJ
ejpam-1745	53	10	pure	pure	ADJ
ejpam-1745	53	11	in	in	ADP
ejpam-1745	53	12	b	b	NOUN
ejpam-1745	53	13	if	if	SCONJ
ejpam-1745	54	1	and	and	CCONJ
ejpam-1745	54	2	only	only	ADV
ejpam-1745	54	3	if	if	SCONJ
ejpam-1745	54	4	ã=	ã=	PROPN
ejpam-1745	54	5	ā.	ā.	PUNCT
ejpam-1745	54	6	for	for	ADP
ejpam-1745	54	7	more	more	ADJ
ejpam-1745	54	8	details	detail	NOUN
ejpam-1745	54	9	,	,	PUNCT
ejpam-1745	54	10	see	see	VERB
ejpam-1745	54	11	[	[	X
ejpam-1745	54	12	1	1	NUM
ejpam-1745	54	13	]	]	PUNCT
ejpam-1745	54	14	.	.	PUNCT
ejpam-1745	55	1	3	3	X
ejpam-1745	55	2	.	.	X
ejpam-1745	55	3	sequentially	sequentially	ADV
ejpam-1745	55	4	complete	complete	ADJ
ejpam-1745	55	5	s	s	NOUN
ejpam-1745	55	6	-	-	PUNCT
ejpam-1745	55	7	acts	act	NOUN
ejpam-1745	55	8	in	in	ADP
ejpam-1745	55	9	this	this	DET
ejpam-1745	55	10	section	section	NOUN
ejpam-1745	55	11	we	we	PRON
ejpam-1745	55	12	study	study	VERB
ejpam-1745	55	13	some	some	DET
ejpam-1745	55	14	algebraic	algebraic	ADJ
ejpam-1745	55	15	and	and	CCONJ
ejpam-1745	55	16	categorical	categorical	ADJ
ejpam-1745	55	17	properties	property	NOUN
ejpam-1745	55	18	of	of	ADP
ejpam-1745	55	19	s	s	NOUN
ejpam-1745	55	20	-	-	ADJ
ejpam-1745	55	21	complete	complete	ADJ
ejpam-1745	55	22	s	s	NOUN
ejpam-1745	55	23	-	-	PUNCT
ejpam-1745	55	24	acts	act	NOUN
ejpam-1745	55	25	and	and	CCONJ
ejpam-1745	55	26	characterize	characterize	VERB
ejpam-1745	55	27	the	the	DET
ejpam-1745	55	28	semigroups	semigroup	NOUN
ejpam-1745	55	29	s	s	VERB
ejpam-1745	55	30	over	over	ADP
ejpam-1745	55	31	which	which	PRON
ejpam-1745	55	32	all	all	DET
ejpam-1745	55	33	acts	act	NOUN
ejpam-1745	55	34	are	be	AUX
ejpam-1745	55	35	s	s	NOUN
ejpam-1745	55	36	-	-	NOUN
ejpam-1745	55	37	complete	complete	ADJ
ejpam-1745	55	38	.	.	PUNCT
ejpam-1745	56	1	the	the	DET
ejpam-1745	56	2	main	main	ADJ
ejpam-1745	56	3	result	result	NOUN
ejpam-1745	56	4	of	of	ADP
ejpam-1745	56	5	this	this	DET
ejpam-1745	56	6	section	section	NOUN
ejpam-1745	56	7	is	be	AUX
ejpam-1745	56	8	theorem	theorem	VERB
ejpam-1745	56	9	1	1	NUM
ejpam-1745	56	10	,	,	PUNCT
ejpam-1745	56	11	which	which	PRON
ejpam-1745	56	12	shows	show	VERB
ejpam-1745	56	13	that	that	SCONJ
ejpam-1745	56	14	s	s	NOUN
ejpam-1745	56	15	-	-	PUNCT
ejpam-1745	56	16	completeness	completeness	NOUN
ejpam-1745	56	17	is	be	AUX
ejpam-1745	56	18	equivalent	equivalent	ADJ
ejpam-1745	56	19	to	to	ADP
ejpam-1745	56	20	s	s	NOUN
ejpam-1745	56	21	-	-	PUNCT
ejpam-1745	56	22	injectivity	injectivity	NOUN
ejpam-1745	56	23	that	that	PRON
ejpam-1745	56	24	is	be	AUX
ejpam-1745	56	25	defined	define	VERB
ejpam-1745	56	26	and	and	CCONJ
ejpam-1745	56	27	studied	study	VERB
ejpam-1745	56	28	in	in	ADP
ejpam-1745	56	29	[	[	X
ejpam-1745	56	30	11	11	NUM
ejpam-1745	56	31	]	]	PUNCT
ejpam-1745	56	32	.	.	PUNCT
ejpam-1745	57	1	also	also	ADV
ejpam-1745	57	2	it	it	PRON
ejpam-1745	57	3	is	be	AUX
ejpam-1745	57	4	equivalent	equivalent	ADJ
ejpam-1745	57	5	to	to	ADP
ejpam-1745	57	6	absolutely	absolutely	ADV
ejpam-1745	57	7	s	s	NOUN
ejpam-1745	57	8	-	-	ADJ
ejpam-1745	57	9	pure	pure	ADJ
ejpam-1745	57	10	.	.	PUNCT
ejpam-1745	58	1	some	some	PRON
ejpam-1745	58	2	of	of	ADP
ejpam-1745	58	3	the	the	DET
ejpam-1745	58	4	following	following	ADJ
ejpam-1745	58	5	results	result	NOUN
ejpam-1745	58	6	will	will	AUX
ejpam-1745	58	7	be	be	AUX
ejpam-1745	58	8	used	use	VERB
ejpam-1745	58	9	in	in	ADP
ejpam-1745	58	10	the	the	DET
ejpam-1745	58	11	next	next	ADJ
ejpam-1745	58	12	section	section	NOUN
ejpam-1745	58	13	.	.	PUNCT
ejpam-1745	59	1	definition	definition	NOUN
ejpam-1745	59	2	2	2	NUM
ejpam-1745	59	3	.	.	PUNCT
ejpam-1745	60	1	an	an	DET
ejpam-1745	60	2	s	s	NOUN
ejpam-1745	60	3	-	-	PUNCT
ejpam-1745	60	4	act	act	NOUN
ejpam-1745	60	5	a	a	PRON
ejpam-1745	60	6	is	be	AUX
ejpam-1745	60	7	called	call	VERB
ejpam-1745	60	8	sequentially	sequentially	ADV
ejpam-1745	60	9	complete	complete	ADJ
ejpam-1745	60	10	or	or	CCONJ
ejpam-1745	60	11	(	(	PUNCT
ejpam-1745	60	12	s	s	NOUN
ejpam-1745	60	13	-	-	VERB
ejpam-1745	60	14	complete	complete	ADJ
ejpam-1745	60	15	)	)	PUNCT
ejpam-1745	60	16	if	if	SCONJ
ejpam-1745	60	17	every	every	DET
ejpam-1745	60	18	consistent	consistent	ADJ
ejpam-1745	60	19	system	system	NOUN
ejpam-1745	60	20	σa	σa	X
ejpam-1745	60	21	has	have	VERB
ejpam-1745	60	22	a	a	DET
ejpam-1745	60	23	solution	solution	NOUN
ejpam-1745	60	24	in	in	ADP
ejpam-1745	60	25	a.	a.	NOUN
ejpam-1745	60	26	theorem	theorem	NOUN
ejpam-1745	60	27	1	1	NUM
ejpam-1745	60	28	.	.	X
ejpam-1745	61	1	for	for	ADP
ejpam-1745	61	2	an	an	DET
ejpam-1745	61	3	s	s	NOUN
ejpam-1745	61	4	-	-	NOUN
ejpam-1745	61	5	act	act	NOUN
ejpam-1745	61	6	a	a	PRON
ejpam-1745	61	7	,	,	PUNCT
ejpam-1745	61	8	the	the	DET
ejpam-1745	61	9	following	follow	VERB
ejpam-1745	61	10	are	be	AUX
ejpam-1745	61	11	equivalent	equivalent	ADJ
ejpam-1745	61	12	:	:	PUNCT
ejpam-1745	61	13	(	(	PUNCT
ejpam-1745	61	14	i	i	NOUN
ejpam-1745	61	15	)	)	PUNCT
ejpam-1745	61	16	a	a	PRON
ejpam-1745	61	17	is	be	AUX
ejpam-1745	61	18	s	s	NOUN
ejpam-1745	61	19	-	-	NOUN
ejpam-1745	61	20	complete	complete	ADJ
ejpam-1745	61	21	.	.	PUNCT
ejpam-1745	62	1	(	(	PUNCT
ejpam-1745	62	2	ii	ii	NOUN
ejpam-1745	62	3	)	)	PUNCT
ejpam-1745	62	4	a	a	PRON
ejpam-1745	62	5	is	be	AUX
ejpam-1745	62	6	absolutely	absolutely	ADV
ejpam-1745	62	7	s	s	NOUN
ejpam-1745	62	8	-	-	ADJ
ejpam-1745	62	9	pure	pure	ADJ
ejpam-1745	62	10	(	(	PUNCT
ejpam-1745	62	11	that	that	PRON
ejpam-1745	62	12	is	is	ADV
ejpam-1745	62	13	,	,	PUNCT
ejpam-1745	62	14	it	it	PRON
ejpam-1745	62	15	is	be	AUX
ejpam-1745	62	16	s	s	NOUN
ejpam-1745	62	17	-	-	ADJ
ejpam-1745	62	18	pure	pure	ADJ
ejpam-1745	62	19	in	in	ADP
ejpam-1745	62	20	each	each	PRON
ejpam-1745	62	21	of	of	ADP
ejpam-1745	62	22	its	its	PRON
ejpam-1745	62	23	extension	extension	NOUN
ejpam-1745	62	24	)	)	PUNCT
ejpam-1745	62	25	.	.	PUNCT
ejpam-1745	63	1	(	(	PUNCT
ejpam-1745	63	2	iii	iii	X
ejpam-1745	63	3	)	)	PUNCT
ejpam-1745	63	4	a	a	PRON
ejpam-1745	63	5	is	be	AUX
ejpam-1745	63	6	s	s	NOUN
ejpam-1745	63	7	-	-	ADJ
ejpam-1745	63	8	pure	pure	ADJ
ejpam-1745	63	9	in	in	ADP
ejpam-1745	63	10	its	its	PRON
ejpam-1745	63	11	injective	injective	ADJ
ejpam-1745	63	12	hull	hull	NOUN
ejpam-1745	63	13	e(a	e(a	PROPN
ejpam-1745	63	14	)	)	PUNCT
ejpam-1745	63	15	.	.	PUNCT
ejpam-1745	64	1	(	(	PUNCT
ejpam-1745	64	2	iv	iv	X
ejpam-1745	64	3	)	)	PUNCT
ejpam-1745	64	4	a	a	PRON
ejpam-1745	64	5	is	be	AUX
ejpam-1745	64	6	s	s	NOUN
ejpam-1745	64	7	-	-	ADJ
ejpam-1745	64	8	injective	injective	ADJ
ejpam-1745	64	9	(	(	PUNCT
ejpam-1745	64	10	i.e	i.e	X
ejpam-1745	64	11	,	,	PUNCT
ejpam-1745	64	12	every	every	DET
ejpam-1745	64	13	homomorphism	homomorphism	NOUN
ejpam-1745	64	14	k	k	X
ejpam-1745	64	15	:	:	PUNCT
ejpam-1745	64	16	s	s	AUX
ejpam-1745	64	17	−→	−→	NOUN
ejpam-1745	64	18	a	a	PRON
ejpam-1745	64	19	is	be	AUX
ejpam-1745	64	20	of	of	ADP
ejpam-1745	64	21	the	the	DET
ejpam-1745	64	22	form	form	NOUN
ejpam-1745	64	23	λa	λa	INTJ
ejpam-1745	64	24	for	for	ADP
ejpam-1745	64	25	some	some	DET
ejpam-1745	64	26	a	a	DET
ejpam-1745	64	27	∈	∈	PROPN
ejpam-1745	64	28	a	a	PRON
ejpam-1745	64	29	)	)	PUNCT
ejpam-1745	64	30	.	.	PUNCT
ejpam-1745	65	1	(	(	PUNCT
ejpam-1745	65	2	v	v	NOUN
ejpam-1745	65	3	)	)	PUNCT
ejpam-1745	65	4	every	every	DET
ejpam-1745	65	5	homomorphism	homomorphism	NOUN
ejpam-1745	65	6	f	f	X
ejpam-1745	65	7	:	:	PUNCT
ejpam-1745	65	8	s→	s→	X
ejpam-1745	66	1	a	a	PRON
ejpam-1745	66	2	can	can	AUX
ejpam-1745	66	3	be	be	AUX
ejpam-1745	66	4	extended	extend	VERB
ejpam-1745	66	5	to	to	ADP
ejpam-1745	66	6	a	a	DET
ejpam-1745	66	7	homomorphism	homomorphism	NOUN
ejpam-1745	66	8	f	f	X
ejpam-1745	66	9	:	:	PUNCT
ejpam-1745	66	10	s1→	s1→	ADJ
ejpam-1745	66	11	a.	a.	NOUN
ejpam-1745	66	12	proof	proof	NOUN
ejpam-1745	66	13	.	.	PUNCT
ejpam-1745	67	1	(	(	PUNCT
ejpam-1745	67	2	i)⇒	i)⇒	PROPN
ejpam-1745	67	3	(	(	PUNCT
ejpam-1745	67	4	ii	ii	NOUN
ejpam-1745	67	5	)	)	PUNCT
ejpam-1745	67	6	let	let	VERB
ejpam-1745	67	7	b	b	X
ejpam-1745	67	8	be	be	AUX
ejpam-1745	67	9	an	an	DET
ejpam-1745	67	10	extension	extension	NOUN
ejpam-1745	67	11	of	of	ADP
ejpam-1745	67	12	a	a	PRON
ejpam-1745	67	13	and	and	CCONJ
ejpam-1745	67	14	for	for	ADP
ejpam-1745	67	15	b	b	PROPN
ejpam-1745	67	16	∈	∈	PROPN
ejpam-1745	67	17	b	b	PROPN
ejpam-1745	67	18	,	,	PUNCT
ejpam-1745	67	19	bs	bs	PROPN
ejpam-1745	67	20	⊆	⊆	NUM
ejpam-1745	67	21	a.	a.	NOUN
ejpam-1745	67	22	so	so	ADV
ejpam-1745	67	23	σa	σa	PROPN
ejpam-1745	67	24	=	=	SYM
ejpam-1745	67	25	{	{	PUNCT
ejpam-1745	68	1	xs	xs	NOUN
ejpam-1745	68	2	=	=	PUNCT
ejpam-1745	68	3	bs	bs	INTJ
ejpam-1745	69	1	|	|	NOUN
ejpam-1745	69	2	s	s	VERB
ejpam-1745	69	3	∈	∈	PROPN
ejpam-1745	69	4	s	s	AUX
ejpam-1745	69	5	}	}	PUNCT
ejpam-1745	69	6	is	be	AUX
ejpam-1745	69	7	a	a	DET
ejpam-1745	69	8	consistent	consistent	ADJ
ejpam-1745	69	9	system	system	NOUN
ejpam-1745	69	10	which	which	PRON
ejpam-1745	69	11	has	have	VERB
ejpam-1745	69	12	a	a	DET
ejpam-1745	69	13	solution	solution	NOUN
ejpam-1745	69	14	a	a	PRON
ejpam-1745	69	15	in	in	ADP
ejpam-1745	69	16	a.	a.	NOUN
ejpam-1745	69	17	thus	thus	ADV
ejpam-1745	69	18	a	a	DET
ejpam-1745	69	19	is	be	AUX
ejpam-1745	69	20	s	s	NOUN
ejpam-1745	69	21	-	-	ADJ
ejpam-1745	69	22	pure	pure	ADJ
ejpam-1745	69	23	in	in	ADP
ejpam-1745	69	24	b.	b.	PROPN
ejpam-1745	69	25	(	(	PUNCT
ejpam-1745	69	26	ii	ii	NOUN
ejpam-1745	69	27	)	)	PUNCT
ejpam-1745	69	28	⇒	⇒	NOUN
ejpam-1745	69	29	(	(	PUNCT
ejpam-1745	69	30	i	i	NOUN
ejpam-1745	69	31	)	)	PUNCT
ejpam-1745	69	32	let	let	VERB
ejpam-1745	69	33	the	the	DET
ejpam-1745	69	34	system	system	NOUN
ejpam-1745	69	35	σa	σa	VERB
ejpam-1745	69	36	has	have	VERB
ejpam-1745	69	37	a	a	DET
ejpam-1745	69	38	solution	solution	NOUN
ejpam-1745	69	39	in	in	ADP
ejpam-1745	69	40	an	an	DET
ejpam-1745	69	41	s	s	NOUN
ejpam-1745	69	42	-	-	ADJ
ejpam-1745	69	43	pure	pure	ADJ
ejpam-1745	69	44	extension	extension	NOUN
ejpam-1745	69	45	b	b	PROPN
ejpam-1745	69	46	of	of	ADP
ejpam-1745	69	47	a.	a.	NOUN
ejpam-1745	69	48	since	since	SCONJ
ejpam-1745	69	49	a	a	PRON
ejpam-1745	69	50	is	be	AUX
ejpam-1745	69	51	absolutely	absolutely	ADV
ejpam-1745	69	52	s	s	NOUN
ejpam-1745	69	53	-	-	ADJ
ejpam-1745	69	54	pure	pure	ADJ
ejpam-1745	69	55	,	,	PUNCT
ejpam-1745	69	56	σa	σa	PROPN
ejpam-1745	69	57	has	have	VERB
ejpam-1745	69	58	a	a	DET
ejpam-1745	69	59	solution	solution	NOUN
ejpam-1745	69	60	a	a	PRON
ejpam-1745	69	61	in	in	ADP
ejpam-1745	69	62	a.	a.	NOUN
ejpam-1745	69	63	h.	h.	PROPN
ejpam-1745	69	64	barzegar	barzegar	PROPN
ejpam-1745	69	65	/	/	SYM
ejpam-1745	69	66	eur	eur	PROPN
ejpam-1745	69	67	.	.	PUNCT
ejpam-1745	70	1	j.	j.	PROPN
ejpam-1745	70	2	pure	pure	PROPN
ejpam-1745	70	3	appl	appl	PROPN
ejpam-1745	70	4	.	.	PROPN
ejpam-1745	70	5	math	math	PROPN
ejpam-1745	70	6	,	,	PUNCT
ejpam-1745	70	7	6	6	NUM
ejpam-1745	70	8	(	(	PUNCT
ejpam-1745	70	9	2013	2013	NUM
ejpam-1745	70	10	)	)	PUNCT
ejpam-1745	70	11	,	,	PUNCT
ejpam-1745	70	12	211	211	NUM
ejpam-1745	70	13	-	-	SYM
ejpam-1745	70	14	221	221	NUM
ejpam-1745	70	15	214	214	NUM
ejpam-1745	70	16	the	the	DET
ejpam-1745	70	17	equivalency	equivalency	NOUN
ejpam-1745	70	18	of	of	ADP
ejpam-1745	70	19	(	(	PUNCT
ejpam-1745	70	20	ii	ii	NOUN
ejpam-1745	70	21	)	)	PUNCT
ejpam-1745	70	22	,	,	PUNCT
ejpam-1745	70	23	(	(	PUNCT
ejpam-1745	70	24	iii	iii	NOUN
ejpam-1745	70	25	)	)	PUNCT
ejpam-1745	70	26	and	and	CCONJ
ejpam-1745	70	27	(	(	PUNCT
ejpam-1745	70	28	iv	iv	X
ejpam-1745	70	29	)	)	PUNCT
ejpam-1745	70	30	is	be	AUX
ejpam-1745	70	31	obtained	obtain	VERB
ejpam-1745	70	32	from	from	ADP
ejpam-1745	70	33	theorem	theorem	ADJ
ejpam-1745	70	34	2.2	2.2	NUM
ejpam-1745	70	35	of	of	ADP
ejpam-1745	70	36	[	[	X
ejpam-1745	70	37	10	10	NUM
ejpam-1745	70	38	]	]	PUNCT
ejpam-1745	70	39	.	.	PUNCT
ejpam-1745	71	1	the	the	DET
ejpam-1745	71	2	equivalency	equivalency	NOUN
ejpam-1745	71	3	of	of	ADP
ejpam-1745	71	4	(	(	PUNCT
ejpam-1745	71	5	iv	iv	NOUN
ejpam-1745	71	6	)	)	PUNCT
ejpam-1745	71	7	and	and	CCONJ
ejpam-1745	71	8	(	(	PUNCT
ejpam-1745	71	9	v	v	NOUN
ejpam-1745	71	10	)	)	PUNCT
ejpam-1745	71	11	is	be	AUX
ejpam-1745	71	12	obtained	obtain	VERB
ejpam-1745	71	13	from	from	ADP
ejpam-1745	71	14	[	[	X
ejpam-1745	71	15	11	11	NUM
ejpam-1745	71	16	]	]	PUNCT
ejpam-1745	71	17	,	,	PUNCT
ejpam-1745	71	18	theorem	theorem	VERB
ejpam-1745	71	19	2.7	2.7	NUM
ejpam-1745	71	20	.	.	PUNCT
ejpam-1745	72	1	from	from	ADP
ejpam-1745	72	2	here	here	ADV
ejpam-1745	72	3	to	to	ADP
ejpam-1745	72	4	the	the	DET
ejpam-1745	72	5	end	end	NOUN
ejpam-1745	72	6	of	of	ADP
ejpam-1745	72	7	paper	paper	NOUN
ejpam-1745	72	8	we	we	PRON
ejpam-1745	72	9	use	use	VERB
ejpam-1745	72	10	some	some	DET
ejpam-1745	72	11	parts	part	NOUN
ejpam-1745	72	12	of	of	ADP
ejpam-1745	72	13	theorem	theorem	NOUN
ejpam-1745	72	14	1	1	NUM
ejpam-1745	72	15	for	for	ADP
ejpam-1745	72	16	s	s	NOUN
ejpam-1745	72	17	-	-	NOUN
ejpam-1745	72	18	completeness	completeness	NOUN
ejpam-1745	72	19	.	.	PUNCT
ejpam-1745	73	1	remark	remark	PROPN
ejpam-1745	73	2	2	2	NUM
ejpam-1745	73	3	.	.	PUNCT
ejpam-1745	74	1	having	have	VERB
ejpam-1745	74	2	parts	part	NOUN
ejpam-1745	74	3	(	(	PUNCT
ejpam-1745	74	4	iv	iv	NUM
ejpam-1745	74	5	)	)	PUNCT
ejpam-1745	74	6	and	and	CCONJ
ejpam-1745	74	7	(	(	PUNCT
ejpam-1745	74	8	v	v	NOUN
ejpam-1745	74	9	)	)	PUNCT
ejpam-1745	74	10	of	of	ADP
ejpam-1745	74	11	the	the	DET
ejpam-1745	74	12	above	above	ADJ
ejpam-1745	74	13	theorem	theorem	NOUN
ejpam-1745	74	14	,	,	PUNCT
ejpam-1745	74	15	one	one	PRON
ejpam-1745	74	16	can	can	AUX
ejpam-1745	74	17	easily	easily	ADV
ejpam-1745	74	18	get	get	VERB
ejpam-1745	74	19	some	some	DET
ejpam-1745	74	20	relations	relation	NOUN
ejpam-1745	74	21	between	between	ADP
ejpam-1745	74	22	s	s	NOUN
ejpam-1745	74	23	-	-	NOUN
ejpam-1745	74	24	completeness	completeness	NOUN
ejpam-1745	74	25	and	and	CCONJ
ejpam-1745	74	26	injectivity	injectivity	NOUN
ejpam-1745	74	27	or	or	CCONJ
ejpam-1745	74	28	any	any	DET
ejpam-1745	74	29	types	type	NOUN
ejpam-1745	74	30	of	of	ADP
ejpam-1745	74	31	weak	weak	ADJ
ejpam-1745	74	32	injectivity	injectivity	NOUN
ejpam-1745	74	33	[	[	X
ejpam-1745	74	34	see	see	VERB
ejpam-1745	74	35	9	9	NUM
ejpam-1745	74	36	]	]	PUNCT
ejpam-1745	74	37	.	.	PUNCT
ejpam-1745	75	1	for	for	ADP
ejpam-1745	75	2	example	example	NOUN
ejpam-1745	75	3	,	,	PUNCT
ejpam-1745	75	4	we	we	PRON
ejpam-1745	75	5	have	have	VERB
ejpam-1745	75	6	the	the	DET
ejpam-1745	75	7	following	following	NOUN
ejpam-1745	75	8	:	:	PUNCT
ejpam-1745	75	9	every	every	DET
ejpam-1745	75	10	injective	injective	ADJ
ejpam-1745	75	11	s	s	NOUN
ejpam-1745	75	12	-	-	PUNCT
ejpam-1745	75	13	act	act	NOUN
ejpam-1745	75	14	is	be	AUX
ejpam-1745	75	15	s	s	NOUN
ejpam-1745	75	16	-	-	NOUN
ejpam-1745	75	17	complete	complete	ADJ
ejpam-1745	75	18	.	.	PUNCT
ejpam-1745	76	1	but	but	CCONJ
ejpam-1745	76	2	the	the	DET
ejpam-1745	76	3	converse	converse	NOUN
ejpam-1745	76	4	is	be	AUX
ejpam-1745	76	5	not	not	PART
ejpam-1745	76	6	in	in	ADP
ejpam-1745	76	7	generally	generally	ADV
ejpam-1745	76	8	true	true	ADJ
ejpam-1745	76	9	,	,	PUNCT
ejpam-1745	76	10	indeed	indeed	ADV
ejpam-1745	76	11	,	,	PUNCT
ejpam-1745	76	12	the	the	DET
ejpam-1745	76	13	monoid	monoid	NOUN
ejpam-1745	76	14	s	s	X
ejpam-1745	76	15	=	=	NOUN
ejpam-1745	76	16	z	z	NOUN
ejpam-1745	76	17	with	with	ADP
ejpam-1745	76	18	the	the	DET
ejpam-1745	76	19	usual	usual	ADJ
ejpam-1745	76	20	multiplication	multiplication	NOUN
ejpam-1745	76	21	,	,	PUNCT
ejpam-1745	76	22	is	be	AUX
ejpam-1745	76	23	s	s	NOUN
ejpam-1745	76	24	-	-	NOUN
ejpam-1745	76	25	complete	complete	ADJ
ejpam-1745	76	26	as	as	ADP
ejpam-1745	76	27	an	an	DET
ejpam-1745	76	28	s	s	NOUN
ejpam-1745	76	29	-	-	NOUN
ejpam-1745	76	30	act	act	NOUN
ejpam-1745	76	31	but	but	CCONJ
ejpam-1745	76	32	it	it	PRON
ejpam-1745	76	33	is	be	AUX
ejpam-1745	76	34	not	not	PART
ejpam-1745	76	35	divisible	divisible	ADJ
ejpam-1745	76	36	.	.	PUNCT
ejpam-1745	77	1	so	so	ADV
ejpam-1745	77	2	it	it	PRON
ejpam-1745	77	3	is	be	AUX
ejpam-1745	77	4	not	not	PART
ejpam-1745	77	5	injective	injective	ADJ
ejpam-1745	77	6	s	s	NOUN
ejpam-1745	77	7	-	-	NOUN
ejpam-1745	77	8	act	act	NOUN
ejpam-1745	77	9	.	.	PUNCT
ejpam-1745	78	1	also	also	ADV
ejpam-1745	78	2	weak	weak	ADJ
ejpam-1745	78	3	injectivity	injectivity	NOUN
ejpam-1745	78	4	does	do	AUX
ejpam-1745	78	5	not	not	PART
ejpam-1745	78	6	imply	imply	VERB
ejpam-1745	78	7	s	s	NOUN
ejpam-1745	78	8	-	-	NOUN
ejpam-1745	78	9	completeness	completeness	NOUN
ejpam-1745	78	10	.	.	PUNCT
ejpam-1745	79	1	to	to	PART
ejpam-1745	79	2	show	show	VERB
ejpam-1745	79	3	this	this	DET
ejpam-1745	79	4	fact	fact	NOUN
ejpam-1745	79	5	,	,	PUNCT
ejpam-1745	79	6	consider	consider	VERB
ejpam-1745	79	7	s	s	PRON
ejpam-1745	79	8	=	=	X
ejpam-1745	79	9	(	(	PUNCT
ejpam-1745	79	10	n	n	CCONJ
ejpam-1745	79	11	,	,	PUNCT
ejpam-1745	79	12	min	min	NOUN
ejpam-1745	79	13	)	)	PUNCT
ejpam-1745	79	14	.	.	PUNCT
ejpam-1745	80	1	since	since	SCONJ
ejpam-1745	80	2	identity	identity	NOUN
ejpam-1745	80	3	homomorphism	homomorphism	NOUN
ejpam-1745	80	4	on	on	ADP
ejpam-1745	80	5	n	n	CCONJ
ejpam-1745	80	6	is	be	AUX
ejpam-1745	80	7	not	not	PART
ejpam-1745	80	8	of	of	ADP
ejpam-1745	80	9	the	the	DET
ejpam-1745	80	10	form	form	NOUN
ejpam-1745	80	11	λa	λa	ADP
ejpam-1745	80	12	,	,	PUNCT
ejpam-1745	80	13	then	then	ADV
ejpam-1745	80	14	nn	nn	PROPN
ejpam-1745	80	15	is	be	AUX
ejpam-1745	80	16	not	not	PART
ejpam-1745	80	17	s	s	NOUN
ejpam-1745	80	18	-	-	NOUN
ejpam-1745	80	19	complete	complete	ADJ
ejpam-1745	80	20	.	.	PUNCT
ejpam-1745	81	1	now	now	ADV
ejpam-1745	81	2	let	let	VERB
ejpam-1745	81	3	i	i	PRON
ejpam-1745	81	4	be	be	AUX
ejpam-1745	81	5	a	a	DET
ejpam-1745	81	6	right	right	ADJ
ejpam-1745	81	7	ideal	ideal	NOUN
ejpam-1745	81	8	of	of	ADP
ejpam-1745	81	9	s	s	PRON
ejpam-1745	81	10	and	and	CCONJ
ejpam-1745	81	11	f	f	NOUN
ejpam-1745	81	12	:	:	PUNCT
ejpam-1745	82	1	i	i	PRON
ejpam-1745	82	2	−→	−→	VERB
ejpam-1745	82	3	n	n	VERB
ejpam-1745	82	4	be	be	VERB
ejpam-1745	82	5	a	a	DET
ejpam-1745	82	6	homomorphism	homomorphism	NOUN
ejpam-1745	82	7	.	.	PUNCT
ejpam-1745	83	1	we	we	PRON
ejpam-1745	83	2	want	want	VERB
ejpam-1745	83	3	to	to	PART
ejpam-1745	83	4	extend	extend	VERB
ejpam-1745	83	5	f	f	PROPN
ejpam-1745	83	6	to	to	ADP
ejpam-1745	83	7	s.	s.	PROPN
ejpam-1745	83	8	the	the	DET
ejpam-1745	83	9	case	case	NOUN
ejpam-1745	84	1	i	i	PRON
ejpam-1745	84	2	=	=	X
ejpam-1745	84	3	s	s	VERB
ejpam-1745	84	4	is	be	AUX
ejpam-1745	84	5	obvious	obvious	ADJ
ejpam-1745	84	6	.	.	PUNCT
ejpam-1745	85	1	otherwise	otherwise	ADV
ejpam-1745	85	2	,	,	PUNCT
ejpam-1745	85	3	i	i	PRON
ejpam-1745	85	4	is	be	AUX
ejpam-1745	85	5	of	of	ADP
ejpam-1745	85	6	the	the	DET
ejpam-1745	85	7	form	form	NOUN
ejpam-1745	85	8	ms	ms	NOUN
ejpam-1745	85	9	=	=	X
ejpam-1745	85	10	{	{	PUNCT
ejpam-1745	85	11	ms	ms	NOUN
ejpam-1745	85	12	|	|	NOUN
ejpam-1745	85	13	s	s	NOUN
ejpam-1745	85	14	∈	∈	PROPN
ejpam-1745	85	15	s	s	PART
ejpam-1745	85	16	}	}	PUNCT
ejpam-1745	85	17	.	.	PUNCT
ejpam-1745	86	1	the	the	DET
ejpam-1745	86	2	homomorphism	homomorphism	PROPN
ejpam-1745	86	3	g	g	PROPN
ejpam-1745	86	4	:	:	PUNCT
ejpam-1745	86	5	n→	n→	PUNCT
ejpam-1745	86	6	n	n	CCONJ
ejpam-1745	86	7	defined	define	VERB
ejpam-1745	86	8	by	by	ADP
ejpam-1745	86	9	g(n	g(n	PROPN
ejpam-1745	86	10	)	)	PUNCT
ejpam-1745	86	11	=	=	SYM
ejpam-1745	87	1	f	f	PROPN
ejpam-1745	87	2	(	(	PUNCT
ejpam-1745	87	3	mn	mn	PROPN
ejpam-1745	87	4	)	)	PUNCT
ejpam-1745	87	5	is	be	AUX
ejpam-1745	87	6	an	an	DET
ejpam-1745	87	7	extension	extension	NOUN
ejpam-1745	87	8	of	of	ADP
ejpam-1745	87	9	f	f	PROPN
ejpam-1745	87	10	.	.	PUNCT
ejpam-1745	88	1	thus	thus	ADV
ejpam-1745	88	2	n	n	PRON
ejpam-1745	88	3	is	be	AUX
ejpam-1745	88	4	a	a	DET
ejpam-1745	88	5	weakly	weakly	ADV
ejpam-1745	88	6	injective	injective	ADJ
ejpam-1745	88	7	as	as	ADP
ejpam-1745	88	8	an	an	DET
ejpam-1745	88	9	s	s	NOUN
ejpam-1745	88	10	-	-	NOUN
ejpam-1745	88	11	act	act	NOUN
ejpam-1745	88	12	.	.	PUNCT
ejpam-1745	89	1	theorem	theorem	NOUN
ejpam-1745	89	2	2	2	NUM
ejpam-1745	89	3	.	.	PUNCT
ejpam-1745	90	1	an	an	DET
ejpam-1745	90	2	s	s	NOUN
ejpam-1745	90	3	-	-	NOUN
ejpam-1745	90	4	act	act	NOUN
ejpam-1745	90	5	a	a	PRON
ejpam-1745	90	6	is	be	AUX
ejpam-1745	90	7	s	s	NOUN
ejpam-1745	90	8	-	-	NOUN
ejpam-1745	90	9	complete	complete	ADJ
ejpam-1745	90	10	and	and	CCONJ
ejpam-1745	90	11	weakly	weakly	ADV
ejpam-1745	90	12	injective	injective	ADJ
ejpam-1745	90	13	if	if	SCONJ
ejpam-1745	91	1	and	and	CCONJ
ejpam-1745	91	2	only	only	ADV
ejpam-1745	91	3	if	if	SCONJ
ejpam-1745	91	4	for	for	ADP
ejpam-1745	91	5	every	every	DET
ejpam-1745	91	6	right	right	ADJ
ejpam-1745	91	7	ideal	ideal	NOUN
ejpam-1745	91	8	i	i	PRON
ejpam-1745	91	9	of	of	ADP
ejpam-1745	91	10	s	s	PROPN
ejpam-1745	91	11	,	,	PUNCT
ejpam-1745	91	12	every	every	DET
ejpam-1745	91	13	homomorphism	homomorphism	PROPN
ejpam-1745	91	14	f	f	X
ejpam-1745	91	15	:	:	PUNCT
ejpam-1745	91	16	i	i	PRON
ejpam-1745	91	17	→	→	PUNCT
ejpam-1745	91	18	a	a	DET
ejpam-1745	91	19	is	be	AUX
ejpam-1745	91	20	of	of	ADP
ejpam-1745	91	21	the	the	DET
ejpam-1745	91	22	form	form	NOUN
ejpam-1745	91	23	λa	λa	INTJ
ejpam-1745	91	24	for	for	ADP
ejpam-1745	91	25	some	some	DET
ejpam-1745	91	26	a	a	DET
ejpam-1745	91	27	∈	∈	NOUN
ejpam-1745	91	28	a.	a.	NOUN
ejpam-1745	91	29	proof	proof	NOUN
ejpam-1745	91	30	.	.	PUNCT
ejpam-1745	92	1	by	by	ADP
ejpam-1745	92	2	using	use	VERB
ejpam-1745	92	3	theorem	theorem	NOUN
ejpam-1745	92	4	1	1	NUM
ejpam-1745	92	5	the	the	DET
ejpam-1745	92	6	sufficiency	sufficiency	NOUN
ejpam-1745	92	7	is	be	AUX
ejpam-1745	92	8	clear	clear	ADJ
ejpam-1745	92	9	.	.	PUNCT
ejpam-1745	93	1	we	we	PRON
ejpam-1745	93	2	show	show	VERB
ejpam-1745	93	3	only	only	ADV
ejpam-1745	93	4	the	the	DET
ejpam-1745	93	5	necessity	necessity	NOUN
ejpam-1745	93	6	.	.	PUNCT
ejpam-1745	94	1	let	let	VERB
ejpam-1745	94	2	a	a	DET
ejpam-1745	94	3	be	be	AUX
ejpam-1745	94	4	an	an	DET
ejpam-1745	94	5	s	s	NOUN
ejpam-1745	94	6	-	-	NOUN
ejpam-1745	94	7	complete	complete	ADJ
ejpam-1745	94	8	and	and	CCONJ
ejpam-1745	94	9	weakly	weakly	ADJ
ejpam-1745	94	10	injective	injective	ADJ
ejpam-1745	94	11	s	s	NOUN
ejpam-1745	94	12	-	-	NOUN
ejpam-1745	94	13	act	act	NOUN
ejpam-1745	94	14	.	.	PUNCT
ejpam-1745	95	1	take	take	VERB
ejpam-1745	95	2	a	a	DET
ejpam-1745	95	3	homomorphism	homomorphism	NOUN
ejpam-1745	95	4	f	f	X
ejpam-1745	95	5	:	:	PUNCT
ejpam-1745	95	6	i	i	PRON
ejpam-1745	95	7	→	→	PUNCT
ejpam-1745	95	8	a	a	PRON
ejpam-1745	95	9	from	from	ADP
ejpam-1745	95	10	a	a	DET
ejpam-1745	95	11	right	right	ADJ
ejpam-1745	95	12	ideal	ideal	NOUN
ejpam-1745	95	13	i	i	PRON
ejpam-1745	95	14	of	of	ADP
ejpam-1745	95	15	s.	s.	PROPN
ejpam-1745	95	16	since	since	SCONJ
ejpam-1745	95	17	a	a	PRON
ejpam-1745	95	18	is	be	AUX
ejpam-1745	95	19	weakly	weakly	ADV
ejpam-1745	95	20	injective	injective	ADJ
ejpam-1745	95	21	,	,	PUNCT
ejpam-1745	95	22	f	f	PROPN
ejpam-1745	95	23	can	can	AUX
ejpam-1745	95	24	be	be	AUX
ejpam-1745	95	25	extended	extend	VERB
ejpam-1745	95	26	to	to	ADP
ejpam-1745	95	27	a	a	DET
ejpam-1745	95	28	homomorphism	homomorphism	NOUN
ejpam-1745	95	29	f	f	X
ejpam-1745	95	30	:	:	PUNCT
ejpam-1745	95	31	s	s	X
ejpam-1745	95	32	→	→	PUNCT
ejpam-1745	95	33	a.	a.	NOUN
ejpam-1745	95	34	now	now	ADV
ejpam-1745	95	35	,	,	PUNCT
ejpam-1745	95	36	since	since	SCONJ
ejpam-1745	95	37	a	a	PRON
ejpam-1745	95	38	is	be	AUX
ejpam-1745	95	39	s	s	NOUN
ejpam-1745	95	40	-	-	NOUN
ejpam-1745	95	41	complete	complete	ADJ
ejpam-1745	95	42	,	,	PUNCT
ejpam-1745	95	43	f	f	PROPN
ejpam-1745	95	44	=	=	PUNCT
ejpam-1745	95	45	λa	λa	PROPN
ejpam-1745	95	46	for	for	ADP
ejpam-1745	95	47	some	some	DET
ejpam-1745	95	48	a	a	DET
ejpam-1745	95	49	∈	∈	PROPN
ejpam-1745	95	50	a	a	PRON
ejpam-1745	95	51	,	,	PUNCT
ejpam-1745	95	52	and	and	CCONJ
ejpam-1745	95	53	hence	hence	ADV
ejpam-1745	95	54	so	so	ADV
ejpam-1745	95	55	is	be	AUX
ejpam-1745	95	56	f	f	PROPN
ejpam-1745	95	57	.	.	PUNCT
ejpam-1745	96	1	lemma	lemma	PROPN
ejpam-1745	97	1	2	2	X
ejpam-1745	97	2	.	.	PUNCT
ejpam-1745	98	1	if	if	SCONJ
ejpam-1745	98	2	a	a	PRON
ejpam-1745	98	3	is	be	AUX
ejpam-1745	98	4	s	s	NOUN
ejpam-1745	98	5	-	-	ADJ
ejpam-1745	98	6	pure	pure	ADJ
ejpam-1745	98	7	in	in	ADP
ejpam-1745	98	8	b	b	NOUN
ejpam-1745	98	9	and	and	CCONJ
ejpam-1745	98	10	b	b	PROPN
ejpam-1745	98	11	is	be	AUX
ejpam-1745	98	12	s	s	NOUN
ejpam-1745	98	13	-	-	NOUN
ejpam-1745	98	14	complete	complete	ADJ
ejpam-1745	98	15	,	,	PUNCT
ejpam-1745	98	16	then	then	ADV
ejpam-1745	98	17	a	a	PRON
ejpam-1745	98	18	is	be	AUX
ejpam-1745	98	19	s	s	NOUN
ejpam-1745	98	20	-	-	NOUN
ejpam-1745	98	21	complete	complete	ADJ
ejpam-1745	98	22	.	.	PUNCT
ejpam-1745	99	1	proof	proof	NOUN
ejpam-1745	99	2	.	.	PUNCT
ejpam-1745	100	1	let	let	VERB
ejpam-1745	100	2	f	f	NOUN
ejpam-1745	100	3	:	:	PUNCT
ejpam-1745	100	4	s	s	X
ejpam-1745	100	5	→	→	X
ejpam-1745	100	6	a	a	PRON
ejpam-1745	100	7	be	be	AUX
ejpam-1745	100	8	a	a	DET
ejpam-1745	100	9	homomorphism	homomorphism	NOUN
ejpam-1745	100	10	.	.	PUNCT
ejpam-1745	101	1	since	since	SCONJ
ejpam-1745	101	2	b	b	PROPN
ejpam-1745	101	3	is	be	AUX
ejpam-1745	101	4	s	s	NOUN
ejpam-1745	101	5	-	-	NOUN
ejpam-1745	101	6	complete	complete	ADJ
ejpam-1745	101	7	,	,	PUNCT
ejpam-1745	101	8	f	f	PROPN
ejpam-1745	101	9	is	be	AUX
ejpam-1745	101	10	of	of	ADP
ejpam-1745	101	11	the	the	DET
ejpam-1745	101	12	form	form	NOUN
ejpam-1745	101	13	λb	λb	ADV
ejpam-1745	101	14	for	for	ADP
ejpam-1745	101	15	some	some	DET
ejpam-1745	101	16	b	b	PROPN
ejpam-1745	101	17	∈	∈	PROPN
ejpam-1745	101	18	b	b	PROPN
ejpam-1745	101	19	and	and	CCONJ
ejpam-1745	101	20	since	since	SCONJ
ejpam-1745	101	21	a	a	PRON
ejpam-1745	101	22	is	be	AUX
ejpam-1745	101	23	s	s	NOUN
ejpam-1745	101	24	-	-	NOUN
ejpam-1745	101	25	pure	pure	ADJ
ejpam-1745	101	26	in	in	ADP
ejpam-1745	101	27	b	b	NUM
ejpam-1745	101	28	,	,	PUNCT
ejpam-1745	101	29	it	it	PRON
ejpam-1745	101	30	is	be	AUX
ejpam-1745	101	31	of	of	ADP
ejpam-1745	101	32	the	the	DET
ejpam-1745	101	33	form	form	NOUN
ejpam-1745	101	34	λa	λa	INTJ
ejpam-1745	101	35	for	for	ADP
ejpam-1745	101	36	some	some	PRON
ejpam-1745	101	37	a	a	DET
ejpam-1745	101	38	∈	∈	NOUN
ejpam-1745	101	39	a.	a.	NOUN
ejpam-1745	101	40	as	as	ADP
ejpam-1745	101	41	a	a	DET
ejpam-1745	101	42	result	result	NOUN
ejpam-1745	101	43	of	of	ADP
ejpam-1745	101	44	lemma	lemma	PROPN
ejpam-1745	101	45	2	2	NUM
ejpam-1745	101	46	,	,	PUNCT
ejpam-1745	101	47	we	we	PRON
ejpam-1745	101	48	have	have	VERB
ejpam-1745	101	49	the	the	DET
ejpam-1745	101	50	following	follow	VERB
ejpam-1745	101	51	corollary	corollary	NOUN
ejpam-1745	101	52	.	.	PUNCT
ejpam-1745	102	1	but	but	CCONJ
ejpam-1745	102	2	first	first	ADV
ejpam-1745	102	3	recall	recall	VERB
ejpam-1745	102	4	that	that	SCONJ
ejpam-1745	102	5	a	a	DET
ejpam-1745	102	6	subact	subact	NOUN
ejpam-1745	102	7	a	a	PRON
ejpam-1745	102	8	of	of	ADP
ejpam-1745	102	9	b	b	NOUN
ejpam-1745	102	10	is	be	AUX
ejpam-1745	102	11	a	a	DET
ejpam-1745	102	12	retract	retract	NOUN
ejpam-1745	102	13	of	of	ADP
ejpam-1745	102	14	b	b	NOUN
ejpam-1745	102	15	if	if	SCONJ
ejpam-1745	102	16	there	there	PRON
ejpam-1745	102	17	exists	exist	VERB
ejpam-1745	102	18	a	a	DET
ejpam-1745	102	19	homomorphism	homomorphism	NOUN
ejpam-1745	102	20	,	,	PUNCT
ejpam-1745	102	21	so	so	ADV
ejpam-1745	102	22	called	call	VERB
ejpam-1745	102	23	retraction	retraction	NOUN
ejpam-1745	102	24	,	,	PUNCT
ejpam-1745	102	25	g	g	NOUN
ejpam-1745	102	26	:	:	PUNCT
ejpam-1745	102	27	b	b	X
ejpam-1745	102	28	→	→	PUNCT
ejpam-1745	102	29	a	a	PRON
ejpam-1745	102	30	such	such	ADJ
ejpam-1745	102	31	that	that	DET
ejpam-1745	102	32	g|a	g|a	PROPN
ejpam-1745	102	33	=	=	SYM
ejpam-1745	102	34	ida	ida	PROPN
ejpam-1745	102	35	.	.	PUNCT
ejpam-1745	102	36	corollary	corollary	PROPN
ejpam-1745	103	1	1	1	NUM
ejpam-1745	103	2	.	.	PUNCT
ejpam-1745	104	1	a	a	DET
ejpam-1745	104	2	retract	retract	NOUN
ejpam-1745	104	3	of	of	ADP
ejpam-1745	104	4	an	an	DET
ejpam-1745	104	5	s	s	NOUN
ejpam-1745	104	6	-	-	ADJ
ejpam-1745	104	7	complete	complete	ADJ
ejpam-1745	104	8	s	s	NOUN
ejpam-1745	104	9	-	-	NOUN
ejpam-1745	104	10	act	act	NOUN
ejpam-1745	104	11	is	be	AUX
ejpam-1745	104	12	an	an	DET
ejpam-1745	104	13	s	s	NOUN
ejpam-1745	104	14	-	-	ADJ
ejpam-1745	104	15	complete	complete	ADJ
ejpam-1745	104	16	s	s	NOUN
ejpam-1745	104	17	-	-	NOUN
ejpam-1745	104	18	act	act	NOUN
ejpam-1745	104	19	.	.	PUNCT
ejpam-1745	105	1	proof	proof	NOUN
ejpam-1745	105	2	.	.	PUNCT
ejpam-1745	106	1	[	[	X
ejpam-1745	106	2	by	by	ADP
ejpam-1745	106	3	[	[	PUNCT
ejpam-1745	106	4	1	1	NUM
ejpam-1745	106	5	,	,	PUNCT
ejpam-1745	106	6	lemma	lemma	PROPN
ejpam-1745	106	7	2.4	2.4	NUM
ejpam-1745	106	8	]	]	X
ejpam-1745	106	9	]	]	X
ejpam-1745	106	10	if	if	SCONJ
ejpam-1745	106	11	an	an	DET
ejpam-1745	106	12	s	s	NOUN
ejpam-1745	106	13	-	-	NOUN
ejpam-1745	106	14	act	act	NOUN
ejpam-1745	106	15	a	a	PRON
ejpam-1745	106	16	is	be	AUX
ejpam-1745	106	17	a	a	DET
ejpam-1745	106	18	retract	retract	NOUN
ejpam-1745	106	19	of	of	ADP
ejpam-1745	106	20	b	b	NOUN
ejpam-1745	106	21	then	then	ADV
ejpam-1745	106	22	it	it	PRON
ejpam-1745	106	23	is	be	AUX
ejpam-1745	106	24	s	s	NOUN
ejpam-1745	106	25	-	-	ADJ
ejpam-1745	106	26	pure	pure	ADJ
ejpam-1745	106	27	in	in	ADP
ejpam-1745	106	28	b.	b.	PROPN
ejpam-1745	106	29	now	now	ADV
ejpam-1745	106	30	we	we	PRON
ejpam-1745	106	31	are	be	AUX
ejpam-1745	106	32	done	do	VERB
ejpam-1745	106	33	by	by	ADP
ejpam-1745	106	34	applying	apply	VERB
ejpam-1745	106	35	lemma	lemma	PROPN
ejpam-1745	106	36	2	2	NUM
ejpam-1745	106	37	.	.	PUNCT
ejpam-1745	107	1	in	in	ADP
ejpam-1745	107	2	the	the	DET
ejpam-1745	107	3	next	next	ADJ
ejpam-1745	107	4	theorem	theorem	NOUN
ejpam-1745	107	5	,	,	PUNCT
ejpam-1745	107	6	we	we	PRON
ejpam-1745	107	7	mention	mention	VERB
ejpam-1745	107	8	a	a	DET
ejpam-1745	107	9	characterization	characterization	NOUN
ejpam-1745	107	10	of	of	ADP
ejpam-1745	107	11	semigroup	semigroup	PROPN
ejpam-1745	107	12	s	s	PROPN
ejpam-1745	107	13	over	over	ADP
ejpam-1745	107	14	which	which	PRON
ejpam-1745	107	15	all	all	DET
ejpam-1745	107	16	acts	act	NOUN
ejpam-1745	107	17	are	be	AUX
ejpam-1745	107	18	s	s	NOUN
ejpam-1745	107	19	-	-	NOUN
ejpam-1745	107	20	complete	complete	ADJ
ejpam-1745	107	21	.	.	PUNCT
ejpam-1745	108	1	definition	definition	NOUN
ejpam-1745	108	2	3	3	NUM
ejpam-1745	108	3	.	.	PUNCT
ejpam-1745	109	1	an	an	DET
ejpam-1745	109	2	s	s	NOUN
ejpam-1745	109	3	-	-	PUNCT
ejpam-1745	109	4	act	act	NOUN
ejpam-1745	109	5	a	a	PRON
ejpam-1745	109	6	is	be	AUX
ejpam-1745	109	7	said	say	VERB
ejpam-1745	109	8	to	to	PART
ejpam-1745	109	9	be	be	AUX
ejpam-1745	109	10	principally	principally	ADV
ejpam-1745	109	11	s	s	NOUN
ejpam-1745	109	12	-	-	NOUN
ejpam-1745	109	13	complete	complete	ADJ
ejpam-1745	109	14	if	if	SCONJ
ejpam-1745	109	15	a	a	PRON
ejpam-1745	109	16	is	be	AUX
ejpam-1745	109	17	s	s	NOUN
ejpam-1745	109	18	-	-	ADJ
ejpam-1745	109	19	pure	pure	ADJ
ejpam-1745	109	20	in	in	ADP
ejpam-1745	109	21	each	each	PRON
ejpam-1745	109	22	of	of	ADP
ejpam-1745	109	23	its	its	PRON
ejpam-1745	109	24	cyclic	cyclic	ADJ
ejpam-1745	109	25	extension	extension	NOUN
ejpam-1745	109	26	.	.	PUNCT
ejpam-1745	110	1	theorem	theorem	NOUN
ejpam-1745	110	2	3	3	NUM
ejpam-1745	110	3	.	.	X
ejpam-1745	110	4	for	for	ADP
ejpam-1745	110	5	a	a	DET
ejpam-1745	110	6	semigroup	semigroup	NOUN
ejpam-1745	110	7	s	s	PART
ejpam-1745	110	8	the	the	DET
ejpam-1745	110	9	following	following	NOUN
ejpam-1745	110	10	are	be	AUX
ejpam-1745	110	11	equivalent	equivalent	ADJ
ejpam-1745	110	12	:	:	PUNCT
ejpam-1745	110	13	h.	h.	PROPN
ejpam-1745	110	14	barzegar	barzegar	PROPN
ejpam-1745	110	15	/	/	SYM
ejpam-1745	110	16	eur	eur	PROPN
ejpam-1745	110	17	.	.	PUNCT
ejpam-1745	111	1	j.	j.	PROPN
ejpam-1745	111	2	pure	pure	PROPN
ejpam-1745	111	3	appl	appl	PROPN
ejpam-1745	111	4	.	.	PROPN
ejpam-1745	111	5	math	math	PROPN
ejpam-1745	111	6	,	,	PUNCT
ejpam-1745	111	7	6	6	NUM
ejpam-1745	111	8	(	(	PUNCT
ejpam-1745	111	9	2013	2013	NUM
ejpam-1745	111	10	)	)	PUNCT
ejpam-1745	111	11	,	,	PUNCT
ejpam-1745	111	12	211	211	NUM
ejpam-1745	111	13	-	-	SYM
ejpam-1745	111	14	221	221	NUM
ejpam-1745	111	15	215	215	NUM
ejpam-1745	111	16	(	(	PUNCT
ejpam-1745	111	17	i	i	NOUN
ejpam-1745	111	18	)	)	PUNCT
ejpam-1745	111	19	all	all	PRON
ejpam-1745	111	20	right	right	ADJ
ejpam-1745	111	21	s	s	NOUN
ejpam-1745	111	22	-	-	PUNCT
ejpam-1745	111	23	acts	act	NOUN
ejpam-1745	111	24	are	be	AUX
ejpam-1745	111	25	s	s	NOUN
ejpam-1745	111	26	-	-	NOUN
ejpam-1745	111	27	complete	complete	ADJ
ejpam-1745	111	28	.	.	PUNCT
ejpam-1745	112	1	(	(	PUNCT
ejpam-1745	112	2	ii	ii	NOUN
ejpam-1745	112	3	)	)	PUNCT
ejpam-1745	112	4	all	all	PRON
ejpam-1745	112	5	right	right	NOUN
ejpam-1745	112	6	s	s	NOUN
ejpam-1745	112	7	-	-	PUNCT
ejpam-1745	112	8	acts	act	NOUN
ejpam-1745	112	9	are	be	AUX
ejpam-1745	112	10	principally	principally	ADV
ejpam-1745	112	11	s	s	NOUN
ejpam-1745	112	12	-	-	NOUN
ejpam-1745	112	13	complete	complete	ADJ
ejpam-1745	112	14	.	.	PUNCT
ejpam-1745	113	1	(	(	PUNCT
ejpam-1745	113	2	iii	iii	X
ejpam-1745	113	3	)	)	PUNCT
ejpam-1745	113	4	s	s	VERB
ejpam-1745	113	5	is	be	AUX
ejpam-1745	113	6	an	an	DET
ejpam-1745	113	7	s	s	NOUN
ejpam-1745	113	8	-	-	ADJ
ejpam-1745	113	9	complete	complete	ADJ
ejpam-1745	113	10	s	s	NOUN
ejpam-1745	113	11	-	-	NOUN
ejpam-1745	113	12	act	act	NOUN
ejpam-1745	113	13	.	.	PUNCT
ejpam-1745	114	1	(	(	PUNCT
ejpam-1745	114	2	iv	iv	X
ejpam-1745	114	3	)	)	PUNCT
ejpam-1745	114	4	s	s	VERB
ejpam-1745	114	5	is	be	AUX
ejpam-1745	114	6	s	s	NOUN
ejpam-1745	114	7	-	-	ADJ
ejpam-1745	114	8	pure	pure	ADJ
ejpam-1745	114	9	in	in	ADP
ejpam-1745	114	10	s1	s1	NOUN
ejpam-1745	114	11	.	.	PUNCT
ejpam-1745	115	1	(	(	PUNCT
ejpam-1745	115	2	v	v	NOUN
ejpam-1745	115	3	)	)	PUNCT
ejpam-1745	115	4	s	s	AUX
ejpam-1745	115	5	has	have	VERB
ejpam-1745	115	6	a	a	DET
ejpam-1745	115	7	left	left	ADJ
ejpam-1745	115	8	identity	identity	NOUN
ejpam-1745	115	9	element	element	NOUN
ejpam-1745	115	10	.	.	PUNCT
ejpam-1745	116	1	(	(	PUNCT
ejpam-1745	116	2	vi	vi	NOUN
ejpam-1745	116	3	)	)	PUNCT
ejpam-1745	116	4	pullbacks	pullback	NOUN
ejpam-1745	116	5	preserve	preserve	VERB
ejpam-1745	116	6	s	s	NOUN
ejpam-1745	116	7	-	-	ADJ
ejpam-1745	116	8	pure	pure	ADJ
ejpam-1745	116	9	monomorphisms	monomorphism	NOUN
ejpam-1745	116	10	.	.	PUNCT
ejpam-1745	117	1	proof	proof	NOUN
ejpam-1745	117	2	.	.	PUNCT
ejpam-1745	118	1	the	the	DET
ejpam-1745	118	2	implications	implication	NOUN
ejpam-1745	118	3	(	(	PUNCT
ejpam-1745	118	4	i	i	NOUN
ejpam-1745	118	5	)	)	PUNCT
ejpam-1745	119	1	=	=	NOUN
ejpam-1745	119	2	⇒	⇒	NOUN
ejpam-1745	119	3	(	(	PUNCT
ejpam-1745	119	4	ii	ii	NOUN
ejpam-1745	119	5	)	)	PUNCT
ejpam-1745	120	1	=	=	NOUN
ejpam-1745	120	2	⇒	⇒	NOUN
ejpam-1745	120	3	(	(	PUNCT
ejpam-1745	120	4	iv	iv	NUM
ejpam-1745	120	5	)	)	PUNCT
ejpam-1745	120	6	,	,	PUNCT
ejpam-1745	120	7	(	(	PUNCT
ejpam-1745	120	8	i	i	NOUN
ejpam-1745	120	9	)	)	PUNCT
ejpam-1745	121	1	=	=	NOUN
ejpam-1745	121	2	⇒	⇒	NOUN
ejpam-1745	121	3	(	(	PUNCT
ejpam-1745	121	4	iii	iii	NOUN
ejpam-1745	121	5	)	)	PUNCT
ejpam-1745	121	6	and	and	CCONJ
ejpam-1745	121	7	(	(	PUNCT
ejpam-1745	121	8	iii	iii	X
ejpam-1745	121	9	)	)	PUNCT
ejpam-1745	121	10	=	=	NOUN
ejpam-1745	121	11	⇒	⇒	NOUN
ejpam-1745	121	12	(	(	PUNCT
ejpam-1745	121	13	iv	iv	X
ejpam-1745	121	14	)	)	PUNCT
ejpam-1745	121	15	are	be	AUX
ejpam-1745	121	16	obtained	obtain	VERB
ejpam-1745	121	17	by	by	ADP
ejpam-1745	121	18	using	use	VERB
ejpam-1745	121	19	theorem	theorem	NOUN
ejpam-1745	121	20	1	1	NUM
ejpam-1745	121	21	.	.	PUNCT
ejpam-1745	121	22	by	by	ADP
ejpam-1745	121	23	[	[	X
ejpam-1745	121	24	1	1	NUM
ejpam-1745	121	25	,	,	PUNCT
ejpam-1745	121	26	theorem	theorem	VERB
ejpam-1745	121	27	3.1	3.1	NUM
ejpam-1745	121	28	]	]	PUNCT
ejpam-1745	121	29	,	,	PUNCT
ejpam-1745	121	30	(	(	PUNCT
ejpam-1745	121	31	iv	iv	X
ejpam-1745	121	32	)	)	PUNCT
ejpam-1745	121	33	and	and	CCONJ
ejpam-1745	121	34	(	(	PUNCT
ejpam-1745	121	35	v	v	NOUN
ejpam-1745	121	36	)	)	PUNCT
ejpam-1745	121	37	are	be	AUX
ejpam-1745	121	38	equivalent	equivalent	ADJ
ejpam-1745	121	39	.	.	PUNCT
ejpam-1745	122	1	(	(	PUNCT
ejpam-1745	122	2	v	v	NOUN
ejpam-1745	122	3	)	)	PUNCT
ejpam-1745	122	4	=	=	NOUN
ejpam-1745	122	5	⇒	⇒	NOUN
ejpam-1745	122	6	(	(	PUNCT
ejpam-1745	122	7	i	i	NOUN
ejpam-1745	122	8	)	)	PUNCT
ejpam-1745	122	9	for	for	ADP
ejpam-1745	122	10	every	every	DET
ejpam-1745	122	11	s	s	NOUN
ejpam-1745	122	12	-	-	NOUN
ejpam-1745	122	13	act	act	NOUN
ejpam-1745	122	14	a	a	DET
ejpam-1745	122	15	every	every	DET
ejpam-1745	122	16	homomorphism	homomorphism	NOUN
ejpam-1745	122	17	k	k	X
ejpam-1745	122	18	:	:	PUNCT
ejpam-1745	122	19	s	s	AUX
ejpam-1745	122	20	−→	−→	NOUN
ejpam-1745	122	21	a	a	PRON
ejpam-1745	122	22	is	be	AUX
ejpam-1745	122	23	of	of	ADP
ejpam-1745	122	24	the	the	DET
ejpam-1745	122	25	form	form	NOUN
ejpam-1745	123	1	k	k	NOUN
ejpam-1745	123	2	=	=	PUNCT
ejpam-1745	123	3	λk(1	λk(1	PROPN
ejpam-1745	123	4	)	)	PUNCT
ejpam-1745	123	5	.	.	PUNCT
ejpam-1745	124	1	so	so	ADV
ejpam-1745	124	2	by	by	ADP
ejpam-1745	124	3	theorem	theorem	NOUN
ejpam-1745	124	4	1.(iv	1.(iv	NUM
ejpam-1745	124	5	)	)	PUNCT
ejpam-1745	124	6	the	the	DET
ejpam-1745	124	7	result	result	NOUN
ejpam-1745	124	8	is	be	AUX
ejpam-1745	124	9	true	true	ADJ
ejpam-1745	124	10	.	.	PUNCT
ejpam-1745	125	1	(	(	PUNCT
ejpam-1745	125	2	v)	v)	NUM
ejpam-1745	125	3	⇐	⇐	ADJ
ejpam-1745	125	4	⇒	⇒	NOUN
ejpam-1745	125	5	(	(	PUNCT
ejpam-1745	125	6	vi	vi	X
ejpam-1745	125	7	)	)	PUNCT
ejpam-1745	125	8	apply	apply	VERB
ejpam-1745	125	9	[	[	X
ejpam-1745	125	10	1	1	NUM
ejpam-1745	125	11	,	,	PUNCT
ejpam-1745	125	12	lemma	lemma	PROPN
ejpam-1745	125	13	3.3	3.3	NUM
ejpam-1745	125	14	]	]	PUNCT
ejpam-1745	125	15	.	.	PUNCT
ejpam-1745	126	1	the	the	DET
ejpam-1745	126	2	following	follow	VERB
ejpam-1745	126	3	lemma	lemma	PROPN
ejpam-1745	126	4	will	will	AUX
ejpam-1745	126	5	be	be	AUX
ejpam-1745	126	6	used	use	VERB
ejpam-1745	126	7	in	in	ADP
ejpam-1745	126	8	corollary	corollary	ADJ
ejpam-1745	126	9	2	2	NUM
ejpam-1745	126	10	and	and	CCONJ
ejpam-1745	126	11	in	in	ADP
ejpam-1745	126	12	section	section	NOUN
ejpam-1745	126	13	4	4	NUM
ejpam-1745	126	14	.	.	PUNCT
ejpam-1745	127	1	lemma	lemma	PROPN
ejpam-1745	127	2	3	3	X
ejpam-1745	127	3	.	.	PUNCT
ejpam-1745	128	1	let	let	VERB
ejpam-1745	128	2	ai(i	ai(i	PRON
ejpam-1745	128	3	∈	∈	PROPN
ejpam-1745	128	4	i	i	PRON
ejpam-1745	128	5	)	)	PUNCT
ejpam-1745	128	6	be	be	VERB
ejpam-1745	128	7	a	a	DET
ejpam-1745	128	8	family	family	NOUN
ejpam-1745	128	9	of	of	ADP
ejpam-1745	128	10	s	s	NOUN
ejpam-1745	128	11	-	-	PUNCT
ejpam-1745	128	12	acts	act	NOUN
ejpam-1745	128	13	and	and	CCONJ
ejpam-1745	128	14	s	s	AUX
ejpam-1745	128	15	be	be	AUX
ejpam-1745	128	16	a	a	DET
ejpam-1745	128	17	finitely	finitely	ADV
ejpam-1745	128	18	generated	generate	VERB
ejpam-1745	128	19	as	as	ADP
ejpam-1745	128	20	an	an	DET
ejpam-1745	128	21	s	s	NOUN
ejpam-1745	128	22	-	-	NOUN
ejpam-1745	128	23	act	act	NOUN
ejpam-1745	128	24	.	.	PUNCT
ejpam-1745	129	1	then	then	ADV
ejpam-1745	129	2	⊕	⊕	PROPN
ejpam-1745	129	3	ai	ai	VERB
ejpam-1745	129	4	is	be	AUX
ejpam-1745	129	5	s	s	NOUN
ejpam-1745	129	6	-	-	ADJ
ejpam-1745	129	7	pure	pure	ADJ
ejpam-1745	129	8	in	in	ADP
ejpam-1745	129	9	∏	∏	NUM
ejpam-1745	129	10	ai	ai	NOUN
ejpam-1745	129	11	.	.	PUNCT
ejpam-1745	130	1	proof	proof	NOUN
ejpam-1745	130	2	.	.	PUNCT
ejpam-1745	131	1	consider	consider	VERB
ejpam-1745	131	2	s	s	PRON
ejpam-1745	131	3	k−→	k−→	NOUN
ejpam-1745	131	4	⊕	⊕	NOUN
ejpam-1745	131	5	ai	ai	VERB
ejpam-1745	131	6	,	,	PUNCT
ejpam-1745	131	7	→	→	SYM
ejpam-1745	131	8	∏	∏	PROPN
ejpam-1745	131	9	ai	ai	VERB
ejpam-1745	131	10	such	such	ADJ
ejpam-1745	131	11	that	that	SCONJ
ejpam-1745	131	12	k	k	PROPN
ejpam-1745	131	13	=	=	PUNCT
ejpam-1745	131	14	λ{ai}({ai	λ{ai}({ai	PROPN
ejpam-1745	131	15	}	}	PUNCT
ejpam-1745	131	16	∈	∈	PROPN
ejpam-1745	131	17	∏	∏	PROPN
ejpam-1745	131	18	ai	ai	NOUN
ejpam-1745	131	19	)	)	PUNCT
ejpam-1745	131	20	,	,	PUNCT
ejpam-1745	131	21	and	and	CCONJ
ejpam-1745	131	22	s	s	X
ejpam-1745	131	23	=	=	SYM
ejpam-1745	131	24	⋃n	⋃n	PROPN
ejpam-1745	131	25	i=1	i=1	PROPN
ejpam-1745	131	26	t	t	PROPN
ejpam-1745	131	27	is	be	AUX
ejpam-1745	131	28	1	1	NUM
ejpam-1745	131	29	.	.	PUNCT
ejpam-1745	132	1	so	so	ADV
ejpam-1745	132	2	there	there	PRON
ejpam-1745	132	3	exists	exist	VERB
ejpam-1745	132	4	a	a	DET
ejpam-1745	132	5	finite	finite	NOUN
ejpam-1745	132	6	subset	subset	VERB
ejpam-1745	133	1	j	j	PROPN
ejpam-1745	133	2	⊂	⊂	PROPN
ejpam-1745	133	3	i	i	PRON
ejpam-1745	133	4	such	such	ADJ
ejpam-1745	133	5	that	that	PRON
ejpam-1745	133	6	for	for	ADP
ejpam-1745	133	7	every	every	DET
ejpam-1745	133	8	s	s	X
ejpam-1745	133	9	∈	∈	PROPN
ejpam-1745	133	10	s	s	NOUN
ejpam-1745	133	11	,	,	PUNCT
ejpam-1745	133	12	k(s)i	k(s)i	PROPN
ejpam-1745	133	13	=	=	SYM
ejpam-1745	133	14	0(i	0(i	NUM
ejpam-1745	133	15	6∈	6∈	PROPN
ejpam-1745	133	16	j	j	PROPN
ejpam-1745	133	17	)	)	PUNCT
ejpam-1745	133	18	.	.	PUNCT
ejpam-1745	134	1	thus	thus	ADV
ejpam-1745	134	2	k	k	X
ejpam-1745	134	3	=	=	SYM
ejpam-1745	134	4	λ{bi	λ{bi	PROPN
ejpam-1745	134	5	}	}	PUNCT
ejpam-1745	134	6	for	for	ADP
ejpam-1745	134	7	bi	bi	NOUN
ejpam-1745	134	8	=	=	PUNCT
ejpam-1745	134	9	(	(	PUNCT
ejpam-1745	134	10	ai	ai	VERB
ejpam-1745	134	11	for	for	ADP
ejpam-1745	134	12	i	i	PROPN
ejpam-1745	134	13	∈	∈	PROPN
ejpam-1745	134	14	j	j	PROPN
ejpam-1745	134	15	0	0	NUM
ejpam-1745	134	16	for	for	ADP
ejpam-1745	134	17	i	i	PRON
ejpam-1745	134	18	/∈	/∈	PUNCT
ejpam-1745	135	1	j	j	PROPN
ejpam-1745	135	2	.	.	PUNCT
ejpam-1745	136	1	now	now	ADV
ejpam-1745	136	2	theorem	theorem	VERB
ejpam-1745	136	3	1.(iv	1.(iv	NUM
ejpam-1745	136	4	)	)	PUNCT
ejpam-1745	136	5	completes	complete	VERB
ejpam-1745	136	6	the	the	DET
ejpam-1745	136	7	proof	proof	NOUN
ejpam-1745	136	8	.	.	PUNCT
ejpam-1745	137	1	theorem	theorem	ADJ
ejpam-1745	137	2	4	4	NUM
ejpam-1745	137	3	.	.	X
ejpam-1745	137	4	for	for	ADP
ejpam-1745	137	5	a	a	DET
ejpam-1745	137	6	semigroup	semigroup	NOUN
ejpam-1745	137	7	s	s	PROPN
ejpam-1745	137	8	,	,	PUNCT
ejpam-1745	137	9	the	the	DET
ejpam-1745	137	10	following	follow	VERB
ejpam-1745	137	11	statements	statement	NOUN
ejpam-1745	137	12	are	be	AUX
ejpam-1745	137	13	equivalent	equivalent	ADJ
ejpam-1745	137	14	:	:	PUNCT
ejpam-1745	137	15	(	(	PUNCT
ejpam-1745	137	16	i	i	NOUN
ejpam-1745	137	17	)	)	PUNCT
ejpam-1745	137	18	every	every	DET
ejpam-1745	137	19	direct	direct	ADJ
ejpam-1745	137	20	sum	sum	NOUN
ejpam-1745	137	21	of	of	ADP
ejpam-1745	137	22	s	s	NOUN
ejpam-1745	137	23	-	-	ADJ
ejpam-1745	137	24	complete	complete	ADJ
ejpam-1745	137	25	s	s	NOUN
ejpam-1745	137	26	-	-	PUNCT
ejpam-1745	137	27	acts	act	NOUN
ejpam-1745	137	28	is	be	AUX
ejpam-1745	137	29	s	s	NOUN
ejpam-1745	137	30	-	-	NOUN
ejpam-1745	137	31	complete	complete	ADJ
ejpam-1745	137	32	.	.	PUNCT
ejpam-1745	138	1	(	(	PUNCT
ejpam-1745	138	2	ii	ii	NOUN
ejpam-1745	138	3	)	)	PUNCT
ejpam-1745	138	4	every	every	DET
ejpam-1745	138	5	direct	direct	ADJ
ejpam-1745	138	6	sum	sum	NOUN
ejpam-1745	138	7	of	of	ADP
ejpam-1745	138	8	s	s	NOUN
ejpam-1745	138	9	-	-	ADJ
ejpam-1745	138	10	complete	complete	ADJ
ejpam-1745	138	11	s	s	NOUN
ejpam-1745	138	12	-	-	PUNCT
ejpam-1745	138	13	acts	act	NOUN
ejpam-1745	138	14	is	be	AUX
ejpam-1745	138	15	s	s	NOUN
ejpam-1745	138	16	-	-	ADJ
ejpam-1745	138	17	pure	pure	ADJ
ejpam-1745	138	18	in	in	ADP
ejpam-1745	138	19	their	their	PRON
ejpam-1745	138	20	direct	direct	ADJ
ejpam-1745	138	21	.	.	PUNCT
ejpam-1745	139	1	proof	proof	NOUN
ejpam-1745	139	2	.	.	PUNCT
ejpam-1745	140	1	(	(	PUNCT
ejpam-1745	140	2	i	i	NOUN
ejpam-1745	140	3	)	)	PUNCT
ejpam-1745	141	1	=	=	NOUN
ejpam-1745	141	2	⇒	⇒	NOUN
ejpam-1745	141	3	(	(	PUNCT
ejpam-1745	141	4	ii	ii	NOUN
ejpam-1745	141	5	)	)	PUNCT
ejpam-1745	141	6	let	let	AUX
ejpam-1745	141	7	{	{	PUNCT
ejpam-1745	141	8	ai	ai	AUX
ejpam-1745	141	9	}	}	PUNCT
ejpam-1745	141	10	be	be	AUX
ejpam-1745	141	11	a	a	DET
ejpam-1745	141	12	family	family	NOUN
ejpam-1745	141	13	of	of	ADP
ejpam-1745	141	14	s	s	NOUN
ejpam-1745	141	15	-	-	ADJ
ejpam-1745	141	16	complete	complete	ADJ
ejpam-1745	141	17	s	s	NOUN
ejpam-1745	141	18	-	-	NOUN
ejpam-1745	141	19	acts	act	NOUN
ejpam-1745	141	20	.	.	PUNCT
ejpam-1745	142	1	then	then	ADV
ejpam-1745	142	2	⊕	⊕	PROPN
ejpam-1745	142	3	ai	ai	VERB
ejpam-1745	142	4	is	be	AUX
ejpam-1745	142	5	s	s	NOUN
ejpam-1745	142	6	-	-	NOUN
ejpam-1745	142	7	complete	complete	ADJ
ejpam-1745	142	8	and	and	CCONJ
ejpam-1745	142	9	by	by	ADP
ejpam-1745	142	10	theorem	theorem	NOUN
ejpam-1745	142	11	1	1	NUM
ejpam-1745	142	12	it	it	PRON
ejpam-1745	142	13	is	be	AUX
ejpam-1745	142	14	s	s	NOUN
ejpam-1745	142	15	-	-	ADJ
ejpam-1745	142	16	pure	pure	ADJ
ejpam-1745	142	17	in	in	ADP
ejpam-1745	142	18	∏	∏	NUM
ejpam-1745	142	19	ai	ai	NOUN
ejpam-1745	142	20	.	.	PUNCT
ejpam-1745	143	1	(	(	PUNCT
ejpam-1745	143	2	ii	ii	NOUN
ejpam-1745	143	3	)	)	PUNCT
ejpam-1745	144	1	=	=	NOUN
ejpam-1745	144	2	⇒	⇒	NOUN
ejpam-1745	144	3	(	(	PUNCT
ejpam-1745	144	4	i	i	NOUN
ejpam-1745	144	5	)	)	PUNCT
ejpam-1745	144	6	this	this	DET
ejpam-1745	144	7	implication	implication	NOUN
ejpam-1745	144	8	is	be	AUX
ejpam-1745	144	9	obtained	obtain	VERB
ejpam-1745	144	10	by	by	ADP
ejpam-1745	144	11	applying	apply	VERB
ejpam-1745	144	12	[	[	X
ejpam-1745	144	13	11	11	NUM
ejpam-1745	144	14	,	,	PUNCT
ejpam-1745	144	15	theorem	theorem	VERB
ejpam-1745	144	16	3.1	3.1	NUM
ejpam-1745	144	17	]	]	PUNCT
ejpam-1745	144	18	,	,	PUNCT
ejpam-1745	144	19	theorem	theorem	VERB
ejpam-1745	144	20	1	1	NUM
ejpam-1745	144	21	and	and	CCONJ
ejpam-1745	144	22	lemma	lemma	PROPN
ejpam-1745	144	23	2	2	NUM
ejpam-1745	144	24	.	.	PUNCT
ejpam-1745	144	25	corollary	corollary	ADJ
ejpam-1745	144	26	2	2	NUM
ejpam-1745	144	27	.	.	PUNCT
ejpam-1745	145	1	if	if	SCONJ
ejpam-1745	145	2	the	the	DET
ejpam-1745	145	3	semigroup	semigroup	NOUN
ejpam-1745	145	4	s	s	VERB
ejpam-1745	145	5	is	be	AUX
ejpam-1745	145	6	a	a	DET
ejpam-1745	145	7	finitely	finitely	ADV
ejpam-1745	145	8	generated	generate	VERB
ejpam-1745	145	9	as	as	ADP
ejpam-1745	145	10	an	an	DET
ejpam-1745	145	11	s	s	NOUN
ejpam-1745	145	12	-	-	NOUN
ejpam-1745	145	13	act	act	NOUN
ejpam-1745	145	14	,	,	PUNCT
ejpam-1745	145	15	then	then	ADV
ejpam-1745	145	16	every	every	DET
ejpam-1745	145	17	direct	direct	ADJ
ejpam-1745	145	18	sum	sum	NOUN
ejpam-1745	145	19	of	of	ADP
ejpam-1745	145	20	s	s	NOUN
ejpam-1745	145	21	-	-	ADJ
ejpam-1745	145	22	complete	complete	ADJ
ejpam-1745	145	23	s	s	NOUN
ejpam-1745	145	24	-	-	PUNCT
ejpam-1745	145	25	acts	act	NOUN
ejpam-1745	145	26	is	be	AUX
ejpam-1745	145	27	s	s	NOUN
ejpam-1745	145	28	-	-	NOUN
ejpam-1745	145	29	complete	complete	ADJ
ejpam-1745	145	30	.	.	PUNCT
ejpam-1745	146	1	lemma	lemma	PROPN
ejpam-1745	146	2	4	4	X
ejpam-1745	146	3	.	.	PUNCT
ejpam-1745	147	1	let	let	VERB
ejpam-1745	147	2	g	g	NOUN
ejpam-1745	147	3	:	:	PUNCT
ejpam-1745	147	4	s	s	X
ejpam-1745	147	5	→	→	SYM
ejpam-1745	147	6	t	t	PROPN
ejpam-1745	147	7	be	be	AUX
ejpam-1745	147	8	an	an	DET
ejpam-1745	147	9	epimorphism	epimorphism	NOUN
ejpam-1745	147	10	.	.	PUNCT
ejpam-1745	148	1	if	if	SCONJ
ejpam-1745	148	2	right	right	ADJ
ejpam-1745	148	3	t	t	PROPN
ejpam-1745	148	4	-	-	PUNCT
ejpam-1745	148	5	act	act	NOUN
ejpam-1745	148	6	a	a	DET
ejpam-1745	148	7	be	be	NOUN
ejpam-1745	148	8	s	s	NOUN
ejpam-1745	148	9	-	-	NOUN
ejpam-1745	148	10	complete	complete	ADJ
ejpam-1745	148	11	as	as	ADP
ejpam-1745	148	12	an	an	DET
ejpam-1745	148	13	s	s	NOUN
ejpam-1745	148	14	-	-	NOUN
ejpam-1745	148	15	act	act	NOUN
ejpam-1745	148	16	,	,	PUNCT
ejpam-1745	148	17	then	then	ADV
ejpam-1745	148	18	it	it	PRON
ejpam-1745	148	19	is	be	AUX
ejpam-1745	148	20	s	s	NOUN
ejpam-1745	148	21	-	-	NOUN
ejpam-1745	148	22	complete	complete	ADJ
ejpam-1745	148	23	as	as	ADP
ejpam-1745	148	24	a	a	DET
ejpam-1745	148	25	t	t	NOUN
ejpam-1745	148	26	-	-	PUNCT
ejpam-1745	148	27	act	act	NOUN
ejpam-1745	148	28	.	.	PUNCT
ejpam-1745	149	1	h.	h.	PROPN
ejpam-1745	149	2	barzegar	barzegar	PROPN
ejpam-1745	149	3	/	/	SYM
ejpam-1745	149	4	eur	eur	PROPN
ejpam-1745	149	5	.	.	PUNCT
ejpam-1745	150	1	j.	j.	PROPN
ejpam-1745	150	2	pure	pure	PROPN
ejpam-1745	150	3	appl	appl	PROPN
ejpam-1745	150	4	.	.	PROPN
ejpam-1745	150	5	math	math	PROPN
ejpam-1745	150	6	,	,	PUNCT
ejpam-1745	150	7	6	6	NUM
ejpam-1745	150	8	(	(	PUNCT
ejpam-1745	150	9	2013	2013	NUM
ejpam-1745	150	10	)	)	PUNCT
ejpam-1745	150	11	,	,	PUNCT
ejpam-1745	150	12	211	211	NUM
ejpam-1745	150	13	-	-	SYM
ejpam-1745	150	14	221	221	NUM
ejpam-1745	150	15	216	216	NUM
ejpam-1745	150	16	proof	proof	NOUN
ejpam-1745	150	17	.	.	PUNCT
ejpam-1745	151	1	let	let	VERB
ejpam-1745	151	2	f	f	NOUN
ejpam-1745	151	3	:	:	PUNCT
ejpam-1745	151	4	t	t	PROPN
ejpam-1745	151	5	→	→	PUNCT
ejpam-1745	151	6	a	a	DET
ejpam-1745	151	7	be	be	AUX
ejpam-1745	151	8	a	a	DET
ejpam-1745	151	9	t	t	NOUN
ejpam-1745	151	10	-	-	PUNCT
ejpam-1745	151	11	homomorphism	homomorphism	NOUN
ejpam-1745	151	12	.	.	PUNCT
ejpam-1745	152	1	since	since	SCONJ
ejpam-1745	152	2	a	a	PRON
ejpam-1745	152	3	is	be	AUX
ejpam-1745	152	4	s	s	NOUN
ejpam-1745	152	5	-	-	NOUN
ejpam-1745	152	6	complete	complete	ADJ
ejpam-1745	152	7	as	as	ADP
ejpam-1745	152	8	an	an	DET
ejpam-1745	152	9	s	s	NOUN
ejpam-1745	152	10	-	-	NOUN
ejpam-1745	152	11	act	act	NOUN
ejpam-1745	152	12	,	,	PUNCT
ejpam-1745	152	13	then	then	ADV
ejpam-1745	152	14	f	f	PROPN
ejpam-1745	152	15	g	g	PROPN
ejpam-1745	152	16	=	=	SYM
ejpam-1745	152	17	λa	λa	PROPN
ejpam-1745	152	18	for	for	ADP
ejpam-1745	152	19	some	some	PRON
ejpam-1745	152	20	a	a	DET
ejpam-1745	152	21	∈	∈	PROPN
ejpam-1745	152	22	a	a	PRON
ejpam-1745	152	23	which	which	PRON
ejpam-1745	152	24	implies	imply	VERB
ejpam-1745	152	25	that	that	SCONJ
ejpam-1745	152	26	for	for	ADP
ejpam-1745	152	27	every	every	DET
ejpam-1745	152	28	t	t	NOUN
ejpam-1745	152	29	∈	∈	PROPN
ejpam-1745	152	30	t	t	PROPN
ejpam-1745	152	31	,	,	PUNCT
ejpam-1745	152	32	f	f	PROPN
ejpam-1745	152	33	(	(	PUNCT
ejpam-1745	152	34	t	t	PROPN
ejpam-1745	152	35	)	)	PUNCT
ejpam-1745	152	36	=	=	SYM
ejpam-1745	152	37	f	f	PROPN
ejpam-1745	152	38	(	(	PUNCT
ejpam-1745	152	39	g(st	g(st	NOUN
ejpam-1745	152	40	)	)	PUNCT
ejpam-1745	152	41	)	)	PUNCT
ejpam-1745	153	1	=	=	SYM
ejpam-1745	153	2	asst	asst	NOUN
ejpam-1745	153	3	=	=	PUNCT
ejpam-1745	153	4	at	at	ADP
ejpam-1745	153	5	g(st	g(st	NOUN
ejpam-1745	153	6	)	)	PUNCT
ejpam-1745	153	7	=	=	PUNCT
ejpam-1745	153	8	at	at	ADP
ejpam-1745	153	9	t	t	PROPN
ejpam-1745	153	10	=	=	PUNCT
ejpam-1745	153	11	λa(t	λa(t	X
ejpam-1745	153	12	)	)	PUNCT
ejpam-1745	153	13	.	.	PUNCT
ejpam-1745	154	1	remark	remark	PROPN
ejpam-1745	154	2	3	3	NUM
ejpam-1745	154	3	.	.	PUNCT
ejpam-1745	155	1	as	as	SCONJ
ejpam-1745	155	2	we	we	PRON
ejpam-1745	155	3	saw	see	VERB
ejpam-1745	155	4	in	in	ADP
ejpam-1745	155	5	theorem	theorem	ADJ
ejpam-1745	155	6	1	1	NUM
ejpam-1745	155	7	,	,	PUNCT
ejpam-1745	155	8	s	s	NOUN
ejpam-1745	155	9	-	-	NOUN
ejpam-1745	155	10	completeness	completeness	NOUN
ejpam-1745	155	11	is	be	AUX
ejpam-1745	155	12	equivalent	equivalent	ADJ
ejpam-1745	155	13	to	to	ADP
ejpam-1745	155	14	s	s	NOUN
ejpam-1745	155	15	-	-	PUNCT
ejpam-1745	155	16	injectivity	injectivity	NOUN
ejpam-1745	155	17	which	which	PRON
ejpam-1745	155	18	defined	define	VERB
ejpam-1745	155	19	in	in	ADP
ejpam-1745	155	20	[	[	X
ejpam-1745	155	21	11	11	NUM
ejpam-1745	155	22	]	]	PUNCT
ejpam-1745	155	23	.	.	PUNCT
ejpam-1745	156	1	some	some	DET
ejpam-1745	156	2	categorical	categorical	ADJ
ejpam-1745	156	3	properties	property	NOUN
ejpam-1745	156	4	such	such	ADJ
ejpam-1745	156	5	as	as	ADP
ejpam-1745	156	6	product	product	NOUN
ejpam-1745	156	7	,	,	PUNCT
ejpam-1745	156	8	coproduct	coproduct	NOUN
ejpam-1745	156	9	and	and	CCONJ
ejpam-1745	156	10	direct	direct	ADJ
ejpam-1745	156	11	sum	sum	NOUN
ejpam-1745	156	12	of	of	ADP
ejpam-1745	156	13	s	s	NOUN
ejpam-1745	156	14	-	-	ADJ
ejpam-1745	156	15	injective	injective	ADJ
ejpam-1745	156	16	s	s	NOUN
ejpam-1745	156	17	-	-	PUNCT
ejpam-1745	156	18	acts	act	NOUN
ejpam-1745	156	19	were	be	AUX
ejpam-1745	156	20	checked	check	VERB
ejpam-1745	156	21	in	in	ADP
ejpam-1745	156	22	[	[	X
ejpam-1745	156	23	11	11	NUM
ejpam-1745	156	24	]	]	PUNCT
ejpam-1745	156	25	.	.	PUNCT
ejpam-1745	157	1	4	4	X
ejpam-1745	157	2	.	.	X
ejpam-1745	158	1	some	some	DET
ejpam-1745	158	2	baer	baer	PROPN
ejpam-1745	158	3	type	type	NOUN
ejpam-1745	158	4	criteria	criterion	NOUN
ejpam-1745	158	5	for	for	ADP
ejpam-1745	158	6	injectivity	injectivity	NOUN
ejpam-1745	158	7	of	of	ADP
ejpam-1745	158	8	s	s	NOUN
ejpam-1745	158	9	-	-	PUNCT
ejpam-1745	158	10	acts	act	NOUN
ejpam-1745	158	11	although	although	SCONJ
ejpam-1745	158	12	the	the	DET
ejpam-1745	158	13	baer	baer	PROPN
ejpam-1745	158	14	criterion	criterion	NOUN
ejpam-1745	158	15	for	for	ADP
ejpam-1745	158	16	injectivity	injectivity	NOUN
ejpam-1745	158	17	(	(	PUNCT
ejpam-1745	158	18	weak	weak	ADJ
ejpam-1745	158	19	injectivity	injectivity	NOUN
ejpam-1745	158	20	implies	imply	VERB
ejpam-1745	158	21	injectivity	injectivity	NOUN
ejpam-1745	158	22	)	)	PUNCT
ejpam-1745	158	23	is	be	AUX
ejpam-1745	158	24	true	true	ADJ
ejpam-1745	158	25	for	for	ADP
ejpam-1745	158	26	modules	module	NOUN
ejpam-1745	158	27	over	over	ADP
ejpam-1745	158	28	a	a	DET
ejpam-1745	158	29	ring	ring	NOUN
ejpam-1745	158	30	(	(	PUNCT
ejpam-1745	158	31	with	with	ADP
ejpam-1745	158	32	an	an	DET
ejpam-1745	158	33	identity	identity	NOUN
ejpam-1745	158	34	)	)	PUNCT
ejpam-1745	158	35	,	,	PUNCT
ejpam-1745	158	36	it	it	PRON
ejpam-1745	158	37	is	be	AUX
ejpam-1745	158	38	an	an	DET
ejpam-1745	158	39	open	open	ADJ
ejpam-1745	158	40	problem	problem	NOUN
ejpam-1745	158	41	for	for	ADP
ejpam-1745	158	42	acts	act	NOUN
ejpam-1745	158	43	over	over	ADP
ejpam-1745	158	44	a	a	DET
ejpam-1745	158	45	semigroup	semigroup	NOUN
ejpam-1745	158	46	s	s	X
ejpam-1745	158	47	(	(	PUNCT
ejpam-1745	158	48	with	with	ADP
ejpam-1745	158	49	or	or	CCONJ
ejpam-1745	158	50	without	without	ADP
ejpam-1745	158	51	identity	identity	NOUN
ejpam-1745	158	52	)	)	PUNCT
ejpam-1745	158	53	.	.	PUNCT
ejpam-1745	159	1	in	in	ADP
ejpam-1745	159	2	fact	fact	NOUN
ejpam-1745	159	3	,	,	PUNCT
ejpam-1745	159	4	we	we	PRON
ejpam-1745	159	5	are	be	AUX
ejpam-1745	159	6	not	not	PART
ejpam-1745	159	7	aware	aware	ADJ
ejpam-1745	159	8	of	of	ADP
ejpam-1745	159	9	any	any	DET
ejpam-1745	159	10	type	type	NOUN
ejpam-1745	159	11	of	of	ADP
ejpam-1745	159	12	weak	weak	ADJ
ejpam-1745	159	13	injectivity	injectivity	NOUN
ejpam-1745	159	14	implying	imply	VERB
ejpam-1745	159	15	injectivity	injectivity	NOUN
ejpam-1745	159	16	of	of	ADP
ejpam-1745	159	17	s	s	NOUN
ejpam-1745	159	18	-	-	PUNCT
ejpam-1745	159	19	acts	act	NOUN
ejpam-1745	159	20	,	,	PUNCT
ejpam-1745	159	21	in	in	ADP
ejpam-1745	159	22	general	general	ADJ
ejpam-1745	159	23	,	,	PUNCT
ejpam-1745	159	24	other	other	ADJ
ejpam-1745	159	25	than	than	ADP
ejpam-1745	159	26	skornjakov	skornjakov	NOUN
ejpam-1745	159	27	-	-	PUNCT
ejpam-1745	159	28	baer	baer	PROPN
ejpam-1745	159	29	criterion	criterion	NOUN
ejpam-1745	159	30	,	,	PUNCT
ejpam-1745	159	31	which	which	PRON
ejpam-1745	159	32	says	say	VERB
ejpam-1745	159	33	that	that	SCONJ
ejpam-1745	159	34	injectivity	injectivity	NOUN
ejpam-1745	159	35	with	with	ADP
ejpam-1745	159	36	respect	respect	NOUN
ejpam-1745	159	37	to	to	ADP
ejpam-1745	159	38	subacts	subact	NOUN
ejpam-1745	159	39	of	of	ADP
ejpam-1745	159	40	cyclic	cyclic	ADJ
ejpam-1745	159	41	acts	act	NOUN
ejpam-1745	159	42	implies	imply	VERB
ejpam-1745	159	43	injectivity	injectivity	NOUN
ejpam-1745	159	44	with	with	ADP
ejpam-1745	159	45	respect	respect	NOUN
ejpam-1745	159	46	to	to	ADP
ejpam-1745	159	47	all	all	DET
ejpam-1745	159	48	monomorphisms	monomorphism	NOUN
ejpam-1745	159	49	.	.	PUNCT
ejpam-1745	160	1	one	one	NUM
ejpam-1745	160	2	line	line	NOUN
ejpam-1745	160	3	of	of	ADP
ejpam-1745	160	4	study	study	NOUN
ejpam-1745	160	5	in	in	ADP
ejpam-1745	160	6	this	this	DET
ejpam-1745	160	7	regard	regard	NOUN
ejpam-1745	160	8	is	be	AUX
ejpam-1745	160	9	to	to	PART
ejpam-1745	160	10	investigate	investigate	VERB
ejpam-1745	160	11	the	the	DET
ejpam-1745	160	12	relation	relation	NOUN
ejpam-1745	160	13	between	between	ADP
ejpam-1745	160	14	m1	m1	NOUN
ejpam-1745	160	15	-	-	PUNCT
ejpam-1745	160	16	injectivity	injectivity	PROPN
ejpam-1745	160	17	and	and	CCONJ
ejpam-1745	160	18	injectivity	injectivity	NOUN
ejpam-1745	160	19	with	with	ADP
ejpam-1745	160	20	respect	respect	NOUN
ejpam-1745	160	21	to	to	ADP
ejpam-1745	160	22	another	another	DET
ejpam-1745	160	23	subclassm2	subclassm2	NOUN
ejpam-1745	160	24	of	of	ADP
ejpam-1745	160	25	monomorphisms	monomorphism	NOUN
ejpam-1745	160	26	,	,	PUNCT
ejpam-1745	160	27	the	the	DET
ejpam-1745	160	28	results	result	NOUN
ejpam-1745	160	29	of	of	ADP
ejpam-1745	160	30	which	which	PRON
ejpam-1745	160	31	may	may	AUX
ejpam-1745	160	32	be	be	AUX
ejpam-1745	160	33	called	call	VERB
ejpam-1745	160	34	the	the	DET
ejpam-1745	160	35	baer	baer	PROPN
ejpam-1745	160	36	type	type	NOUN
ejpam-1745	160	37	criteria	criterion	NOUN
ejpam-1745	160	38	.	.	PUNCT
ejpam-1745	161	1	note	note	VERB
ejpam-1745	161	2	that	that	SCONJ
ejpam-1745	161	3	if	if	SCONJ
ejpam-1745	161	4	m2	m2	PROPN
ejpam-1745	161	5	⊆	⊆	NUM
ejpam-1745	161	6	m1	m1	NOUN
ejpam-1745	161	7	,	,	PUNCT
ejpam-1745	161	8	then	then	ADV
ejpam-1745	161	9	m1	m1	NOUN
ejpam-1745	161	10	-	-	PUNCT
ejpam-1745	161	11	injectivity	injectivity	PROPN
ejpam-1745	161	12	implies	imply	VERB
ejpam-1745	161	13	m2injectivity	m2injectivity	PROPN
ejpam-1745	161	14	.	.	PUNCT
ejpam-1745	162	1	the	the	DET
ejpam-1745	162	2	baer	baer	PROPN
ejpam-1745	162	3	type	type	NOUN
ejpam-1745	162	4	problem	problem	NOUN
ejpam-1745	162	5	is	be	AUX
ejpam-1745	162	6	about	about	ADP
ejpam-1745	162	7	the	the	DET
ejpam-1745	162	8	converse	converse	NOUN
ejpam-1745	162	9	of	of	ADP
ejpam-1745	162	10	this	this	DET
ejpam-1745	162	11	fact	fact	NOUN
ejpam-1745	162	12	.	.	PUNCT
ejpam-1745	163	1	by	by	ADP
ejpam-1745	163	2	using	use	VERB
ejpam-1745	163	3	theorem	theorem	NOUN
ejpam-1745	163	4	1	1	NUM
ejpam-1745	163	5	in	in	ADP
ejpam-1745	163	6	this	this	DET
ejpam-1745	163	7	paper	paper	NOUN
ejpam-1745	163	8	in	in	ADP
ejpam-1745	163	9	fact	fact	NOUN
ejpam-1745	163	10	we	we	PRON
ejpam-1745	163	11	use	use	VERB
ejpam-1745	163	12	injectivity	injectivity	NOUN
ejpam-1745	163	13	only	only	ADV
ejpam-1745	163	14	with	with	ADP
ejpam-1745	163	15	respect	respect	NOUN
ejpam-1745	163	16	to	to	ADP
ejpam-1745	163	17	a	a	DET
ejpam-1745	163	18	monomorphism	monomorphism	NOUN
ejpam-1745	163	19	s→	s→	X
ejpam-1745	163	20	s1	s1	NOUN
ejpam-1745	163	21	which	which	PRON
ejpam-1745	163	22	is	be	AUX
ejpam-1745	163	23	s	s	NOUN
ejpam-1745	163	24	-	-	NOUN
ejpam-1745	163	25	completeness	completeness	NOUN
ejpam-1745	163	26	.	.	PUNCT
ejpam-1745	164	1	as	as	SCONJ
ejpam-1745	164	2	we	we	PRON
ejpam-1745	164	3	saw	see	VERB
ejpam-1745	164	4	in	in	ADP
ejpam-1745	164	5	remark	remark	NOUN
ejpam-1745	164	6	2	2	NUM
ejpam-1745	164	7	,	,	PUNCT
ejpam-1745	164	8	every	every	DET
ejpam-1745	164	9	injective	injective	ADJ
ejpam-1745	164	10	s	s	NOUN
ejpam-1745	164	11	-	-	PUNCT
ejpam-1745	164	12	acts	act	NOUN
ejpam-1745	164	13	is	be	AUX
ejpam-1745	164	14	s	s	NOUN
ejpam-1745	164	15	-	-	NOUN
ejpam-1745	164	16	complete	complete	ADJ
ejpam-1745	164	17	but	but	CCONJ
ejpam-1745	164	18	the	the	DET
ejpam-1745	164	19	converse	converse	NOUN
ejpam-1745	164	20	is	be	AUX
ejpam-1745	164	21	not	not	PART
ejpam-1745	164	22	true	true	ADJ
ejpam-1745	164	23	in	in	ADP
ejpam-1745	164	24	general	general	ADJ
ejpam-1745	164	25	.	.	PUNCT
ejpam-1745	165	1	in	in	ADP
ejpam-1745	165	2	this	this	DET
ejpam-1745	165	3	final	final	ADJ
ejpam-1745	165	4	section	section	NOUN
ejpam-1745	165	5	,	,	PUNCT
ejpam-1745	165	6	we	we	PRON
ejpam-1745	165	7	use	use	VERB
ejpam-1745	165	8	s	s	NOUN
ejpam-1745	165	9	-	-	NOUN
ejpam-1745	165	10	completeness	completeness	ADJ
ejpam-1745	165	11	to	to	PART
ejpam-1745	165	12	give	give	VERB
ejpam-1745	165	13	some	some	DET
ejpam-1745	165	14	baer	baer	PROPN
ejpam-1745	165	15	type	type	NOUN
ejpam-1745	165	16	results	result	NOUN
ejpam-1745	165	17	about	about	ADP
ejpam-1745	165	18	injectivity	injectivity	NOUN
ejpam-1745	165	19	of	of	ADP
ejpam-1745	165	20	s	s	NOUN
ejpam-1745	165	21	-	-	PUNCT
ejpam-1745	165	22	acts	act	NOUN
ejpam-1745	165	23	.	.	PUNCT
ejpam-1745	166	1	we	we	PRON
ejpam-1745	166	2	introduce	introduce	VERB
ejpam-1745	166	3	some	some	DET
ejpam-1745	166	4	semigroups	semigroup	NOUN
ejpam-1745	166	5	over	over	ADP
ejpam-1745	166	6	all	all	PRON
ejpam-1745	166	7	of	of	ADP
ejpam-1745	166	8	which	which	PRON
ejpam-1745	166	9	every	every	DET
ejpam-1745	166	10	s	s	NOUN
ejpam-1745	166	11	-	-	ADJ
ejpam-1745	166	12	complete	complete	ADJ
ejpam-1745	166	13	s	s	NOUN
ejpam-1745	166	14	-	-	PUNCT
ejpam-1745	166	15	acts	act	NOUN
ejpam-1745	166	16	is	be	AUX
ejpam-1745	166	17	injective	injective	ADJ
ejpam-1745	166	18	.	.	PUNCT
ejpam-1745	167	1	first	first	ADV
ejpam-1745	167	2	recall	recall	VERB
ejpam-1745	167	3	the	the	DET
ejpam-1745	167	4	following	follow	VERB
ejpam-1745	167	5	definition	definition	NOUN
ejpam-1745	167	6	from	from	ADP
ejpam-1745	167	7	the	the	DET
ejpam-1745	167	8	closure	closure	NOUN
ejpam-1745	167	9	operator	operator	NOUN
ejpam-1745	167	10	given	give	VERB
ejpam-1745	167	11	in	in	ADP
ejpam-1745	167	12	[	[	X
ejpam-1745	167	13	6	6	NUM
ejpam-1745	167	14	]	]	PUNCT
ejpam-1745	167	15	.	.	PUNCT
ejpam-1745	168	1	definition	definition	NOUN
ejpam-1745	168	2	4	4	NUM
ejpam-1745	168	3	.	.	PUNCT
ejpam-1745	168	4	for	for	ADP
ejpam-1745	168	5	a	a	DET
ejpam-1745	168	6	subact	subact	NOUN
ejpam-1745	168	7	a	a	PRON
ejpam-1745	168	8	of	of	ADP
ejpam-1745	168	9	b	b	NOUN
ejpam-1745	168	10	,	,	PUNCT
ejpam-1745	168	11	let	let	VERB
ejpam-1745	168	12	ā	ā	ADJ
ejpam-1745	168	13	:	:	PUNCT
ejpam-1745	168	14	=	=	SYM
ejpam-1745	168	15	{	{	PUNCT
ejpam-1745	168	16	b	b	PROPN
ejpam-1745	168	17	∈	∈	PROPN
ejpam-1745	168	18	b	b	NOUN
ejpam-1745	168	19	:	:	PUNCT
ejpam-1745	168	20	bs	bs	PROPN
ejpam-1745	168	21	⊆	⊆	SYM
ejpam-1745	168	22	a	a	PRON
ejpam-1745	168	23	}	}	PUNCT
ejpam-1745	168	24	.	.	PUNCT
ejpam-1745	169	1	then	then	ADV
ejpam-1745	169	2	,	,	PUNCT
ejpam-1745	169	3	a	a	PRON
ejpam-1745	169	4	is	be	AUX
ejpam-1745	169	5	said	say	VERB
ejpam-1745	169	6	to	to	PART
ejpam-1745	169	7	be	be	AUX
ejpam-1745	169	8	s	s	NOUN
ejpam-1745	169	9	-	-	NOUN
ejpam-1745	169	10	dense	dense	ADJ
ejpam-1745	169	11	in	in	ADP
ejpam-1745	169	12	b	b	NOUN
ejpam-1745	169	13	if	if	SCONJ
ejpam-1745	169	14	ā=	ā=	ADJ
ejpam-1745	169	15	b.	b.	NOUN
ejpam-1745	169	16	the	the	DET
ejpam-1745	169	17	following	follow	VERB
ejpam-1745	169	18	definition	definition	NOUN
ejpam-1745	169	19	is	be	AUX
ejpam-1745	169	20	a	a	DET
ejpam-1745	169	21	well	well	ADV
ejpam-1745	169	22	known	know	VERB
ejpam-1745	169	23	definition	definition	NOUN
ejpam-1745	169	24	in	in	ADP
ejpam-1745	169	25	the	the	DET
ejpam-1745	169	26	literature	literature	NOUN
ejpam-1745	169	27	as	as	SCONJ
ejpam-1745	169	28	we	we	PRON
ejpam-1745	169	29	use	use	VERB
ejpam-1745	169	30	here	here	ADV
ejpam-1745	169	31	.	.	PUNCT
ejpam-1745	170	1	definition	definition	NOUN
ejpam-1745	170	2	5	5	NUM
ejpam-1745	170	3	.	.	PUNCT
ejpam-1745	171	1	for	for	ADP
ejpam-1745	171	2	a	a	DET
ejpam-1745	171	3	subclass	subclass	NOUN
ejpam-1745	171	4	m	m	NOUN
ejpam-1745	171	5	of	of	ADP
ejpam-1745	171	6	monomorphisms	monomorphism	NOUN
ejpam-1745	171	7	we	we	PRON
ejpam-1745	171	8	say	say	VERB
ejpam-1745	171	9	that	that	SCONJ
ejpam-1745	171	10	the	the	DET
ejpam-1745	171	11	m	m	PROPN
ejpam-1745	171	12	morphism	morphism	NOUN
ejpam-1745	171	13	f	f	PROPN
ejpam-1745	171	14	:	:	PUNCT
ejpam-1745	171	15	a→	a→	PROPN
ejpam-1745	171	16	b	b	NOUN
ejpam-1745	171	17	is	be	AUX
ejpam-1745	171	18	m	m	PRON
ejpam-1745	171	19	-essential	-essential	ADJ
ejpam-1745	171	20	if	if	SCONJ
ejpam-1745	171	21	every	every	DET
ejpam-1745	171	22	g	g	NOUN
ejpam-1745	171	23	:	:	PUNCT
ejpam-1745	171	24	b	b	X
ejpam-1745	171	25	→	→	SYM
ejpam-1745	171	26	c	c	PROPN
ejpam-1745	171	27	is	be	AUX
ejpam-1745	171	28	a	a	DET
ejpam-1745	171	29	monomorphism	monomorphism	NOUN
ejpam-1745	171	30	whenever	whenever	SCONJ
ejpam-1745	171	31	g	g	PROPN
ejpam-1745	171	32	f	f	PROPN
ejpam-1745	171	33	is	be	AUX
ejpam-1745	171	34	a	a	DET
ejpam-1745	171	35	monomorphism	monomorphism	NOUN
ejpam-1745	171	36	.	.	PUNCT
ejpam-1745	172	1	for	for	ADP
ejpam-1745	172	2	simplicity	simplicity	NOUN
ejpam-1745	172	3	,	,	PUNCT
ejpam-1745	172	4	we	we	PRON
ejpam-1745	172	5	say	say	VERB
ejpam-1745	172	6	essential	essential	ADJ
ejpam-1745	172	7	whenm	whenm	NOUN
ejpam-1745	172	8	is	be	AUX
ejpam-1745	172	9	the	the	DET
ejpam-1745	172	10	class	class	NOUN
ejpam-1745	172	11	of	of	ADP
ejpam-1745	172	12	all	all	DET
ejpam-1745	172	13	monomorphism	monomorphism	NOUN
ejpam-1745	172	14	.	.	PUNCT
ejpam-1745	173	1	we	we	PRON
ejpam-1745	173	2	have	have	VERB
ejpam-1745	173	3	the	the	DET
ejpam-1745	173	4	following	follow	VERB
ejpam-1745	173	5	result	result	NOUN
ejpam-1745	173	6	from	from	ADP
ejpam-1745	173	7	[	[	X
ejpam-1745	173	8	3	3	NUM
ejpam-1745	173	9	]	]	PUNCT
ejpam-1745	173	10	.	.	PUNCT
ejpam-1745	174	1	theorem	theorem	ADJ
ejpam-1745	174	2	5	5	NUM
ejpam-1745	174	3	.	.	PUNCT
ejpam-1745	175	1	an	an	DET
ejpam-1745	175	2	s	s	NOUN
ejpam-1745	175	3	-	-	PUNCT
ejpam-1745	175	4	act	act	NOUN
ejpam-1745	175	5	a	a	PRON
ejpam-1745	175	6	is	be	AUX
ejpam-1745	175	7	injective	injective	ADJ
ejpam-1745	175	8	if	if	SCONJ
ejpam-1745	175	9	and	and	CCONJ
ejpam-1745	175	10	only	only	ADV
ejpam-1745	175	11	if	if	SCONJ
ejpam-1745	175	12	it	it	PRON
ejpam-1745	175	13	has	have	VERB
ejpam-1745	175	14	no	no	DET
ejpam-1745	175	15	proper	proper	ADJ
ejpam-1745	175	16	essential	essential	ADJ
ejpam-1745	175	17	extension	extension	NOUN
ejpam-1745	175	18	.	.	PUNCT
ejpam-1745	176	1	henceforth	henceforth	ADV
ejpam-1745	176	2	in	in	ADP
ejpam-1745	176	3	this	this	DET
ejpam-1745	176	4	section	section	NOUN
ejpam-1745	176	5	,	,	PUNCT
ejpam-1745	176	6	we	we	PRON
ejpam-1745	176	7	have	have	VERB
ejpam-1745	176	8	some	some	DET
ejpam-1745	176	9	conditions	condition	NOUN
ejpam-1745	176	10	for	for	ADP
ejpam-1745	176	11	which	which	PRON
ejpam-1745	176	12	every	every	DET
ejpam-1745	176	13	s	s	NOUN
ejpam-1745	176	14	-	-	ADJ
ejpam-1745	176	15	complete	complete	ADJ
ejpam-1745	176	16	s	s	NOUN
ejpam-1745	176	17	-	-	NOUN
ejpam-1745	176	18	act	act	NOUN
ejpam-1745	176	19	is	be	AUX
ejpam-1745	176	20	injective	injective	ADJ
ejpam-1745	176	21	.	.	PUNCT
ejpam-1745	177	1	but	but	CCONJ
ejpam-1745	177	2	first	first	ADV
ejpam-1745	177	3	recall	recall	VERB
ejpam-1745	177	4	the	the	DET
ejpam-1745	177	5	following	follow	VERB
ejpam-1745	177	6	lemma	lemma	PROPN
ejpam-1745	177	7	:	:	PUNCT
ejpam-1745	177	8	lemma	lemma	PROPN
ejpam-1745	177	9	5	5	NUM
ejpam-1745	177	10	.	.	PUNCT
ejpam-1745	178	1	[	[	X
ejpam-1745	178	2	[	[	X
ejpam-1745	178	3	1	1	NUM
ejpam-1745	178	4	]	]	X
ejpam-1745	178	5	]	]	X
ejpam-1745	178	6	any	any	DET
ejpam-1745	178	7	s	s	NOUN
ejpam-1745	178	8	-	-	PUNCT
ejpam-1745	178	9	dense	dense	ADJ
ejpam-1745	178	10	,	,	PUNCT
ejpam-1745	178	11	s	s	NOUN
ejpam-1745	178	12	-	-	ADJ
ejpam-1745	178	13	pure	pure	ADJ
ejpam-1745	178	14	monomorphism	monomorphism	NOUN
ejpam-1745	178	15	has	have	VERB
ejpam-1745	178	16	a	a	DET
ejpam-1745	178	17	retraction	retraction	NOUN
ejpam-1745	178	18	.	.	PUNCT
ejpam-1745	179	1	h.	h.	PROPN
ejpam-1745	179	2	barzegar	barzegar	PROPN
ejpam-1745	179	3	/	/	SYM
ejpam-1745	179	4	eur	eur	PROPN
ejpam-1745	179	5	.	.	PUNCT
ejpam-1745	180	1	j.	j.	PROPN
ejpam-1745	180	2	pure	pure	PROPN
ejpam-1745	180	3	appl	appl	PROPN
ejpam-1745	180	4	.	.	PROPN
ejpam-1745	180	5	math	math	PROPN
ejpam-1745	180	6	,	,	PUNCT
ejpam-1745	180	7	6	6	NUM
ejpam-1745	180	8	(	(	PUNCT
ejpam-1745	180	9	2013	2013	NUM
ejpam-1745	180	10	)	)	PUNCT
ejpam-1745	180	11	,	,	PUNCT
ejpam-1745	180	12	211	211	NUM
ejpam-1745	180	13	-	-	SYM
ejpam-1745	180	14	221	221	NUM
ejpam-1745	180	15	217	217	NUM
ejpam-1745	180	16	theorem	theorem	NOUN
ejpam-1745	180	17	6	6	NUM
ejpam-1745	180	18	.	.	PUNCT
ejpam-1745	181	1	if	if	SCONJ
ejpam-1745	181	2	every	every	DET
ejpam-1745	181	3	essential	essential	ADJ
ejpam-1745	181	4	extension	extension	NOUN
ejpam-1745	181	5	is	be	AUX
ejpam-1745	181	6	s	s	NOUN
ejpam-1745	181	7	-	-	PUNCT
ejpam-1745	181	8	dense	dense	ADJ
ejpam-1745	181	9	,	,	PUNCT
ejpam-1745	181	10	then	then	ADV
ejpam-1745	181	11	every	every	DET
ejpam-1745	181	12	nonempty	nonempty	ADJ
ejpam-1745	181	13	right	right	ADJ
ejpam-1745	181	14	ideal	ideal	NOUN
ejpam-1745	181	15	of	of	ADP
ejpam-1745	181	16	s	s	PROPN
ejpam-1745	181	17	has	have	VERB
ejpam-1745	181	18	a	a	DET
ejpam-1745	181	19	left	left	ADJ
ejpam-1745	181	20	zero	zero	NUM
ejpam-1745	181	21	element	element	NOUN
ejpam-1745	181	22	.	.	PUNCT
ejpam-1745	182	1	in	in	ADP
ejpam-1745	182	2	particular	particular	ADJ
ejpam-1745	182	3	,	,	PUNCT
ejpam-1745	182	4	s	s	AUX
ejpam-1745	182	5	has	have	VERB
ejpam-1745	182	6	a	a	DET
ejpam-1745	182	7	left	left	ADJ
ejpam-1745	182	8	zero	zero	NUM
ejpam-1745	182	9	element	element	NOUN
ejpam-1745	182	10	and	and	CCONJ
ejpam-1745	182	11	every	every	DET
ejpam-1745	182	12	s	s	NOUN
ejpam-1745	182	13	-	-	PUNCT
ejpam-1745	182	14	act	act	NOUN
ejpam-1745	182	15	a	a	PRON
ejpam-1745	182	16	has	have	VERB
ejpam-1745	182	17	a	a	DET
ejpam-1745	182	18	fixed	fix	VERB
ejpam-1745	182	19	element	element	NOUN
ejpam-1745	182	20	.	.	PUNCT
ejpam-1745	183	1	proof	proof	NOUN
ejpam-1745	183	2	.	.	PUNCT
ejpam-1745	184	1	let	let	VERB
ejpam-1745	184	2	i	i	PRON
ejpam-1745	184	3	be	be	AUX
ejpam-1745	184	4	a	a	DET
ejpam-1745	184	5	nonempty	nonempty	ADJ
ejpam-1745	184	6	right	right	ADJ
ejpam-1745	184	7	ideal	ideal	NOUN
ejpam-1745	184	8	of	of	ADP
ejpam-1745	184	9	s	s	PRON
ejpam-1745	184	10	that	that	PRON
ejpam-1745	184	11	does	do	AUX
ejpam-1745	184	12	not	not	PART
ejpam-1745	184	13	have	have	VERB
ejpam-1745	184	14	a	a	DET
ejpam-1745	184	15	left	left	ADJ
ejpam-1745	184	16	zero	zero	NUM
ejpam-1745	184	17	element	element	NOUN
ejpam-1745	184	18	.	.	PUNCT
ejpam-1745	185	1	by	by	ADP
ejpam-1745	185	2	[	[	X
ejpam-1745	185	3	2	2	NUM
ejpam-1745	185	4	]	]	PUNCT
ejpam-1745	185	5	,	,	PUNCT
ejpam-1745	185	6	lemma	lemma	PROPN
ejpam-1745	185	7	4.1	4.1	NUM
ejpam-1745	185	8	,	,	PUNCT
ejpam-1745	185	9	i0	i0	PROPN
ejpam-1745	185	10	is	be	AUX
ejpam-1745	185	11	an	an	DET
ejpam-1745	185	12	essential	essential	ADJ
ejpam-1745	185	13	extension	extension	NOUN
ejpam-1745	185	14	and	and	CCONJ
ejpam-1745	185	15	hence	hence	ADV
ejpam-1745	185	16	s	s	NOUN
ejpam-1745	185	17	-	-	PUNCT
ejpam-1745	185	18	dense	dense	ADJ
ejpam-1745	185	19	extension	extension	NOUN
ejpam-1745	185	20	of	of	ADP
ejpam-1745	185	21	i	i	PRON
ejpam-1745	185	22	.	.	PUNCT
ejpam-1745	186	1	thus	thus	ADV
ejpam-1745	186	2	for	for	ADP
ejpam-1745	186	3	every	every	DET
ejpam-1745	186	4	s	s	X
ejpam-1745	186	5	∈	∈	NOUN
ejpam-1745	186	6	s	s	NOUN
ejpam-1745	186	7	,	,	PUNCT
ejpam-1745	186	8	0=	0=	NOUN
ejpam-1745	186	9	0s	0s	NUM
ejpam-1745	186	10	∈	∈	PROPN
ejpam-1745	186	11	i	i	PRON
ejpam-1745	186	12	which	which	PRON
ejpam-1745	186	13	is	be	AUX
ejpam-1745	186	14	a	a	DET
ejpam-1745	186	15	contradiction	contradiction	NOUN
ejpam-1745	186	16	.	.	PUNCT
ejpam-1745	187	1	similar	similar	ADJ
ejpam-1745	187	2	to	to	ADP
ejpam-1745	187	3	the	the	DET
ejpam-1745	187	4	proof	proof	NOUN
ejpam-1745	187	5	of	of	ADP
ejpam-1745	187	6	[	[	X
ejpam-1745	187	7	2	2	NUM
ejpam-1745	187	8	,	,	PUNCT
ejpam-1745	187	9	proposition	proposition	NOUN
ejpam-1745	187	10	3.6(ii	3.6(ii	NUM
ejpam-1745	187	11	)	)	PUNCT
ejpam-1745	187	12	and	and	CCONJ
ejpam-1745	187	13	lemma	lemma	PROPN
ejpam-1745	187	14	3.9	3.9	NUM
ejpam-1745	187	15	]	]	SYM
ejpam-1745	187	16	one	one	PRON
ejpam-1745	187	17	gets	get	VERB
ejpam-1745	187	18	:	:	PUNCT
ejpam-1745	187	19	lemma	lemma	PROPN
ejpam-1745	187	20	6	6	X
ejpam-1745	187	21	.	.	PUNCT
ejpam-1745	188	1	let	let	VERB
ejpam-1745	188	2	a	a	PRON
ejpam-1745	188	3	be	be	AUX
ejpam-1745	188	4	a	a	DET
ejpam-1745	188	5	subact	subact	NOUN
ejpam-1745	188	6	of	of	ADP
ejpam-1745	188	7	b	b	NOUN
ejpam-1745	188	8	:	:	PUNCT
ejpam-1745	188	9	(	(	PUNCT
ejpam-1745	188	10	i	i	NOUN
ejpam-1745	188	11	)	)	PUNCT
ejpam-1745	188	12	if	if	SCONJ
ejpam-1745	188	13	c	c	PRON
ejpam-1745	188	14	be	be	VERB
ejpam-1745	188	15	a	a	DET
ejpam-1745	188	16	subact	subact	NOUN
ejpam-1745	188	17	of	of	ADP
ejpam-1745	188	18	b	b	NOUN
ejpam-1745	188	19	that	that	PRON
ejpam-1745	188	20	|c	|c	VERB
ejpam-1745	188	21	|	|	NOUN
ejpam-1745	188	22	≥	≥	NOUN
ejpam-1745	188	23	2	2	NUM
ejpam-1745	188	24	and	and	CCONJ
ejpam-1745	188	25	|c	|c	NOUN
ejpam-1745	188	26	∩a|	∩a|	ADP
ejpam-1745	188	27	≤	≤	NOUN
ejpam-1745	188	28	1	1	NUM
ejpam-1745	188	29	,	,	PUNCT
ejpam-1745	188	30	then	then	ADV
ejpam-1745	188	31	b	b	NOUN
ejpam-1745	188	32	is	be	AUX
ejpam-1745	188	33	not	not	PART
ejpam-1745	188	34	an	an	DET
ejpam-1745	188	35	essential	essential	ADJ
ejpam-1745	188	36	extension	extension	NOUN
ejpam-1745	188	37	of	of	ADP
ejpam-1745	188	38	a.	a.	PROPN
ejpam-1745	188	39	(	(	PUNCT
ejpam-1745	188	40	ii	ii	PROPN
ejpam-1745	188	41	)	)	PUNCT
ejpam-1745	188	42	if	if	SCONJ
ejpam-1745	188	43	a	a	PRON
ejpam-1745	188	44	and	and	CCONJ
ejpam-1745	188	45	b	b	NOUN
ejpam-1745	188	46	\	\	NOUN
ejpam-1745	188	47	a	a	DET
ejpam-1745	188	48	have	have	AUX
ejpam-1745	188	49	fixed	fix	VERB
ejpam-1745	188	50	element	element	NOUN
ejpam-1745	188	51	,	,	PUNCT
ejpam-1745	188	52	then	then	ADV
ejpam-1745	188	53	b	b	NOUN
ejpam-1745	188	54	is	be	AUX
ejpam-1745	188	55	not	not	PART
ejpam-1745	188	56	an	an	DET
ejpam-1745	188	57	essential	essential	ADJ
ejpam-1745	188	58	extension	extension	NOUN
ejpam-1745	188	59	of	of	ADP
ejpam-1745	188	60	a.	a.	NOUN
ejpam-1745	188	61	for	for	ADP
ejpam-1745	188	62	a	a	DET
ejpam-1745	188	63	subact	subact	NOUN
ejpam-1745	188	64	a	a	PRON
ejpam-1745	188	65	of	of	ADP
ejpam-1745	188	66	an	an	DET
ejpam-1745	188	67	s	s	NOUN
ejpam-1745	188	68	-	-	PUNCT
ejpam-1745	188	69	act	act	NOUN
ejpam-1745	188	70	b	b	NOUN
ejpam-1745	188	71	and	and	CCONJ
ejpam-1745	188	72	b	b	PROPN
ejpam-1745	188	73	∈	∈	PROPN
ejpam-1745	188	74	b	b	NOUN
ejpam-1745	188	75	,	,	PUNCT
ejpam-1745	188	76	we	we	PRON
ejpam-1745	188	77	use	use	VERB
ejpam-1745	188	78	the	the	DET
ejpam-1745	188	79	notation	notation	NOUN
ejpam-1745	188	80	ib	ib	NOUN
ejpam-1745	188	81	=	=	PRON
ejpam-1745	188	82	{	{	PUNCT
ejpam-1745	188	83	s	s	NOUN
ejpam-1745	188	84	∈	∈	NOUN
ejpam-1745	188	85	s	s	VERB
ejpam-1745	188	86	|	|	ADV
ejpam-1745	188	87	bs	bs	NOUN
ejpam-1745	188	88	∈	∈	PROPN
ejpam-1745	188	89	a	a	PRON
ejpam-1745	188	90	}	}	PUNCT
ejpam-1745	188	91	.	.	PUNCT
ejpam-1745	189	1	also	also	ADV
ejpam-1745	189	2	the	the	DET
ejpam-1745	189	3	set	set	NOUN
ejpam-1745	189	4	of	of	ADP
ejpam-1745	189	5	all	all	DET
ejpam-1745	189	6	fixed	fix	VERB
ejpam-1745	189	7	elements	element	NOUN
ejpam-1745	189	8	of	of	ADP
ejpam-1745	189	9	an	an	DET
ejpam-1745	189	10	s	s	NOUN
ejpam-1745	189	11	-	-	PUNCT
ejpam-1745	189	12	act	act	NOUN
ejpam-1745	189	13	b	b	NOUN
ejpam-1745	189	14	and	and	CCONJ
ejpam-1745	189	15	the	the	DET
ejpam-1745	189	16	set	set	NOUN
ejpam-1745	189	17	of	of	ADP
ejpam-1745	189	18	all	all	DET
ejpam-1745	189	19	left	leave	VERB
ejpam-1745	189	20	zero	zero	NUM
ejpam-1745	189	21	elements	element	NOUN
ejpam-1745	189	22	of	of	ADP
ejpam-1745	189	23	a	a	DET
ejpam-1745	189	24	semigroup	semigroup	NOUN
ejpam-1745	189	25	s	s	VERB
ejpam-1745	189	26	are	be	AUX
ejpam-1745	189	27	denoted	denote	VERB
ejpam-1745	189	28	respectively	respectively	ADV
ejpam-1745	189	29	by	by	ADP
ejpam-1745	189	30	f	f	PROPN
ejpam-1745	189	31	ix(b	ix(b	PROPN
ejpam-1745	189	32	)	)	PUNCT
ejpam-1745	189	33	and	and	CCONJ
ejpam-1745	189	34	z(s	z(s	PROPN
ejpam-1745	189	35	)	)	PUNCT
ejpam-1745	189	36	.	.	PUNCT
ejpam-1745	190	1	corollary	corollary	ADJ
ejpam-1745	190	2	3	3	X
ejpam-1745	190	3	.	.	PUNCT
ejpam-1745	191	1	let	let	VERB
ejpam-1745	191	2	a	a	DET
ejpam-1745	191	3	have	have	AUX
ejpam-1745	191	4	at	at	ADV
ejpam-1745	191	5	least	least	ADV
ejpam-1745	191	6	one	one	NUM
ejpam-1745	191	7	fixed	fix	VERB
ejpam-1745	191	8	element	element	NOUN
ejpam-1745	191	9	and	and	CCONJ
ejpam-1745	191	10	b	b	NOUN
ejpam-1745	191	11	be	be	AUX
ejpam-1745	191	12	an	an	DET
ejpam-1745	191	13	s	s	NOUN
ejpam-1745	191	14	-	-	ADJ
ejpam-1745	191	15	pure	pure	ADJ
ejpam-1745	191	16	essential	essential	ADJ
ejpam-1745	191	17	(	(	PUNCT
ejpam-1745	191	18	essential	essential	ADJ
ejpam-1745	191	19	)	)	PUNCT
ejpam-1745	191	20	extension	extension	NOUN
ejpam-1745	191	21	of	of	ADP
ejpam-1745	191	22	a.	a.	NOUN
ejpam-1745	191	23	then	then	ADV
ejpam-1745	191	24	:	:	PUNCT
ejpam-1745	191	25	(	(	PUNCT
ejpam-1745	191	26	i	i	NOUN
ejpam-1745	191	27	)	)	PUNCT
ejpam-1745	191	28	f	f	PROPN
ejpam-1745	191	29	ix(b)⊆	ix(b)⊆	PROPN
ejpam-1745	191	30	a.	a.	PROPN
ejpam-1745	191	31	(	(	PUNCT
ejpam-1745	191	32	ii	ii	NOUN
ejpam-1745	191	33	)	)	PUNCT
ejpam-1745	191	34	for	for	ADP
ejpam-1745	191	35	every	every	DET
ejpam-1745	191	36	b	b	PROPN
ejpam-1745	191	37	∈	∈	PROPN
ejpam-1745	191	38	b	b	PROPN
ejpam-1745	191	39	,	,	PUNCT
ejpam-1745	191	40	ib	ib	NOUN
ejpam-1745	191	41	6=	6=	NUM
ejpam-1745	191	42	;	;	PUNCT
ejpam-1745	191	43	.	.	PUNCT
ejpam-1745	192	1	corollary	corollary	ADJ
ejpam-1745	192	2	4	4	NUM
ejpam-1745	192	3	.	.	PUNCT
ejpam-1745	193	1	if	if	SCONJ
ejpam-1745	193	2	s	s	PROPN
ejpam-1745	193	3	has	have	VERB
ejpam-1745	193	4	a	a	DET
ejpam-1745	193	5	left	left	ADJ
ejpam-1745	193	6	zero	zero	NUM
ejpam-1745	193	7	element	element	NOUN
ejpam-1745	193	8	and	and	CCONJ
ejpam-1745	193	9	s	s	NOUN
ejpam-1745	193	10	is	be	AUX
ejpam-1745	193	11	an	an	DET
ejpam-1745	193	12	essential	essential	ADJ
ejpam-1745	193	13	extension	extension	NOUN
ejpam-1745	193	14	of	of	ADP
ejpam-1745	193	15	a	a	DET
ejpam-1745	193	16	right	right	ADJ
ejpam-1745	193	17	ideal	ideal	NOUN
ejpam-1745	194	1	i	i	PRON
ejpam-1745	194	2	,	,	PUNCT
ejpam-1745	194	3	then	then	ADV
ejpam-1745	194	4	z(s)⊆	z(s)⊆	PROPN
ejpam-1745	194	5	i	i	PRON
ejpam-1745	194	6	.	.	PUNCT
ejpam-1745	195	1	if	if	SCONJ
ejpam-1745	195	2	s	s	NOUN
ejpam-1745	195	3	is	be	AUX
ejpam-1745	195	4	a	a	DET
ejpam-1745	195	5	left	left	ADJ
ejpam-1745	195	6	zero	zero	NUM
ejpam-1745	195	7	semigroup	semigroup	NOUN
ejpam-1745	195	8	,	,	PUNCT
ejpam-1745	195	9	then	then	ADV
ejpam-1745	195	10	i	i	PRON
ejpam-1745	195	11	=	=	SYM
ejpam-1745	195	12	s.	s.	PROPN
ejpam-1745	195	13	theorem	theorem	VERB
ejpam-1745	195	14	7	7	NUM
ejpam-1745	195	15	.	.	PUNCT
ejpam-1745	196	1	if	if	SCONJ
ejpam-1745	196	2	every	every	DET
ejpam-1745	196	3	essential	essential	ADJ
ejpam-1745	196	4	extension	extension	NOUN
ejpam-1745	196	5	is	be	AUX
ejpam-1745	196	6	s	s	NOUN
ejpam-1745	196	7	-	-	PUNCT
ejpam-1745	196	8	dense	dense	ADJ
ejpam-1745	196	9	,	,	PUNCT
ejpam-1745	196	10	then	then	ADV
ejpam-1745	196	11	every	every	DET
ejpam-1745	196	12	s	s	NOUN
ejpam-1745	196	13	-	-	PUNCT
ejpam-1745	196	14	act	act	NOUN
ejpam-1745	196	15	has	have	VERB
ejpam-1745	196	16	an	an	DET
ejpam-1745	196	17	s	s	NOUN
ejpam-1745	196	18	-	-	PUNCT
ejpam-1745	196	19	dense	dense	ADJ
ejpam-1745	196	20	injective	injective	NOUN
ejpam-1745	196	21	(	(	PUNCT
ejpam-1745	196	22	which	which	PRON
ejpam-1745	196	23	is	be	AUX
ejpam-1745	196	24	injective	injective	ADJ
ejpam-1745	196	25	with	with	ADP
ejpam-1745	196	26	respect	respect	NOUN
ejpam-1745	196	27	to	to	ADP
ejpam-1745	196	28	s	s	NOUN
ejpam-1745	196	29	-	-	PUNCT
ejpam-1745	196	30	dense	dense	ADJ
ejpam-1745	196	31	monomorphisms	monomorphism	NOUN
ejpam-1745	196	32	)	)	PUNCT
ejpam-1745	196	33	s	s	NOUN
ejpam-1745	196	34	-	-	PUNCT
ejpam-1745	196	35	dense	dense	ADJ
ejpam-1745	196	36	extension	extension	NOUN
ejpam-1745	196	37	.	.	PUNCT
ejpam-1745	197	1	proof	proof	NOUN
ejpam-1745	197	2	.	.	PUNCT
ejpam-1745	198	1	let	let	VERB
ejpam-1745	198	2	a	a	DET
ejpam-1745	198	3	∈act	∈act	NOUN
ejpam-1745	198	4	-	-	PUNCT
ejpam-1745	198	5	s	s	NOUN
ejpam-1745	198	6	and	and	CCONJ
ejpam-1745	198	7	ι	ι	X
ejpam-1745	198	8	:	:	PUNCT
ejpam-1745	198	9	a→	a→	X
ejpam-1745	198	10	e(a	e(a	NOUN
ejpam-1745	198	11	)	)	PUNCT
ejpam-1745	198	12	be	be	AUX
ejpam-1745	198	13	an	an	DET
ejpam-1745	198	14	injective	injective	ADJ
ejpam-1745	198	15	hull	hull	NOUN
ejpam-1745	198	16	of	of	ADP
ejpam-1745	198	17	a(which	a(which	NOUN
ejpam-1745	198	18	exists	exist	VERB
ejpam-1745	198	19	as	as	SCONJ
ejpam-1745	198	20	proved	prove	VERB
ejpam-1745	198	21	in	in	ADP
ejpam-1745	198	22	[	[	X
ejpam-1745	198	23	3	3	NUM
ejpam-1745	198	24	]	]	NUM
ejpam-1745	198	25	)	)	PUNCT
ejpam-1745	198	26	.	.	PUNCT
ejpam-1745	199	1	so	so	ADV
ejpam-1745	199	2	ι	ι	PROPN
ejpam-1745	199	3	is	be	AUX
ejpam-1745	199	4	s	s	NOUN
ejpam-1745	199	5	-	-	PUNCT
ejpam-1745	199	6	dense	dense	ADJ
ejpam-1745	199	7	and	and	CCONJ
ejpam-1745	199	8	e(a	e(a	PROPN
ejpam-1745	199	9	)	)	PUNCT
ejpam-1745	199	10	is	be	AUX
ejpam-1745	199	11	an	an	DET
ejpam-1745	199	12	s	s	NOUN
ejpam-1745	199	13	-	-	PUNCT
ejpam-1745	199	14	dense	dense	ADJ
ejpam-1745	199	15	injective	injective	ADJ
ejpam-1745	199	16	s	s	NOUN
ejpam-1745	199	17	-	-	PUNCT
ejpam-1745	199	18	dense	dense	ADJ
ejpam-1745	199	19	essential	essential	ADJ
ejpam-1745	199	20	extension	extension	NOUN
ejpam-1745	199	21	of	of	ADP
ejpam-1745	199	22	a.	a.	PROPN
ejpam-1745	199	23	lemma	lemma	PROPN
ejpam-1745	199	24	7	7	X
ejpam-1745	199	25	.	.	PUNCT
ejpam-1745	200	1	let	let	VERB
ejpam-1745	200	2	a	a	DET
ejpam-1745	200	3	have	have	AUX
ejpam-1745	200	4	at	at	ADV
ejpam-1745	200	5	least	least	ADV
ejpam-1745	200	6	one	one	NUM
ejpam-1745	200	7	fixed	fix	VERB
ejpam-1745	200	8	element	element	NOUN
ejpam-1745	200	9	and	and	CCONJ
ejpam-1745	200	10	b	b	NOUN
ejpam-1745	200	11	be	be	AUX
ejpam-1745	200	12	an	an	DET
ejpam-1745	200	13	s	s	NOUN
ejpam-1745	200	14	-	-	ADJ
ejpam-1745	200	15	pure	pure	ADJ
ejpam-1745	200	16	essential	essential	ADJ
ejpam-1745	200	17	extension	extension	NOUN
ejpam-1745	200	18	of	of	ADP
ejpam-1745	200	19	a.	a.	NOUN
ejpam-1745	200	20	then	then	ADV
ejpam-1745	200	21	(	(	PUNCT
ejpam-1745	200	22	i	i	NOUN
ejpam-1745	200	23	)	)	PUNCT
ejpam-1745	200	24	ā=	ā=	NUM
ejpam-1745	200	25	a.	a.	NOUN
ejpam-1745	200	26	(	(	PUNCT
ejpam-1745	200	27	ii	ii	NOUN
ejpam-1745	200	28	)	)	PUNCT
ejpam-1745	200	29	for	for	ADP
ejpam-1745	200	30	each	each	DET
ejpam-1745	200	31	b	b	PROPN
ejpam-1745	200	32	∈	∈	PROPN
ejpam-1745	200	33	b	b	X
ejpam-1745	200	34	\	\	PROPN
ejpam-1745	200	35	a	a	PRON
ejpam-1745	200	36	,	,	PUNCT
ejpam-1745	200	37	;	;	PUNCT
ejpam-1745	200	38	6=	6=	NUM
ejpam-1745	200	39	ib	ib	NOUN
ejpam-1745	200	40	6=	6=	ADP
ejpam-1745	200	41	s	s	PART
ejpam-1745	200	42	proof	proof	NOUN
ejpam-1745	200	43	.	.	PUNCT
ejpam-1745	201	1	(	(	PUNCT
ejpam-1745	201	2	i	i	NOUN
ejpam-1745	201	3	)	)	PUNCT
ejpam-1745	201	4	by	by	ADP
ejpam-1745	201	5	[	[	X
ejpam-1745	201	6	2	2	NUM
ejpam-1745	201	7	,	,	PUNCT
ejpam-1745	201	8	lemma	lemma	PROPN
ejpam-1745	201	9	4.7.(v	4.7.(v	NUM
ejpam-1745	201	10	)	)	PUNCT
ejpam-1745	201	11	]	]	PUNCT
ejpam-1745	201	12	,	,	PUNCT
ejpam-1745	201	13	a	a	PRON
ejpam-1745	201	14	is	be	AUX
ejpam-1745	201	15	s	s	NOUN
ejpam-1745	201	16	-	-	ADJ
ejpam-1745	201	17	pure	pure	ADJ
ejpam-1745	201	18	essential	essential	ADJ
ejpam-1745	201	19	in	in	ADP
ejpam-1745	201	20	ā.	ā.	PUNCT
ejpam-1745	201	21	since	since	SCONJ
ejpam-1745	201	22	a	a	PRON
ejpam-1745	201	23	is	be	AUX
ejpam-1745	201	24	s	s	NOUN
ejpam-1745	201	25	-	-	ADJ
ejpam-1745	201	26	dense	dense	ADJ
ejpam-1745	201	27	in	in	ADP
ejpam-1745	201	28	ā	ā	NOUN
ejpam-1745	201	29	,	,	PUNCT
ejpam-1745	201	30	by	by	ADP
ejpam-1745	201	31	lemma	lemma	PROPN
ejpam-1745	201	32	5	5	NUM
ejpam-1745	201	33	,	,	PUNCT
ejpam-1745	201	34	a	a	PRON
ejpam-1745	201	35	is	be	AUX
ejpam-1745	201	36	a	a	DET
ejpam-1745	201	37	retract	retract	NOUN
ejpam-1745	201	38	of	of	ADP
ejpam-1745	201	39	ā	ā	NOUN
ejpam-1745	201	40	which	which	PRON
ejpam-1745	201	41	is	be	AUX
ejpam-1745	201	42	an	an	DET
ejpam-1745	201	43	isomorphism	isomorphism	NOUN
ejpam-1745	201	44	by	by	ADP
ejpam-1745	201	45	essentiality	essentiality	NOUN
ejpam-1745	201	46	.	.	PUNCT
ejpam-1745	202	1	thus	thus	ADV
ejpam-1745	202	2	a=	a=	VERB
ejpam-1745	202	3	ā.	ā.	PUNCT
ejpam-1745	202	4	(	(	PUNCT
ejpam-1745	202	5	ii	ii	NOUN
ejpam-1745	202	6	)	)	PUNCT
ejpam-1745	202	7	by	by	ADP
ejpam-1745	202	8	part	part	NOUN
ejpam-1745	202	9	(	(	PUNCT
ejpam-1745	202	10	i	i	NOUN
ejpam-1745	202	11	)	)	PUNCT
ejpam-1745	202	12	,	,	PUNCT
ejpam-1745	202	13	ā=	ā=	DET
ejpam-1745	202	14	a	a	DET
ejpam-1745	202	15	,	,	PUNCT
ejpam-1745	202	16	so	so	SCONJ
ejpam-1745	202	17	ib	ib	PROPN
ejpam-1745	202	18	6=	6=	NUM
ejpam-1745	202	19	s	s	PART
ejpam-1745	202	20	and	and	CCONJ
ejpam-1745	202	21	by	by	ADP
ejpam-1745	202	22	corollary	corollary	ADJ
ejpam-1745	202	23	3	3	NUM
ejpam-1745	202	24	,	,	PUNCT
ejpam-1745	202	25	;	;	PUNCT
ejpam-1745	202	26	6=	6=	NUM
ejpam-1745	202	27	ib	ib	PROPN
ejpam-1745	202	28	.	.	PUNCT
ejpam-1745	202	29	theorem	theorem	PROPN
ejpam-1745	202	30	8	8	NUM
ejpam-1745	202	31	.	.	PUNCT
ejpam-1745	203	1	if	if	SCONJ
ejpam-1745	203	2	a	a	PRON
ejpam-1745	203	3	is	be	AUX
ejpam-1745	203	4	s	s	NOUN
ejpam-1745	203	5	-	-	ADJ
ejpam-1745	203	6	complete	complete	ADJ
ejpam-1745	203	7	s	s	NOUN
ejpam-1745	203	8	-	-	NOUN
ejpam-1745	203	9	act	act	NOUN
ejpam-1745	203	10	and	and	CCONJ
ejpam-1745	203	11	every	every	DET
ejpam-1745	203	12	s	s	NOUN
ejpam-1745	203	13	-	-	ADJ
ejpam-1745	203	14	pure	pure	ADJ
ejpam-1745	203	15	essential	essential	ADJ
ejpam-1745	203	16	extension	extension	NOUN
ejpam-1745	203	17	of	of	ADP
ejpam-1745	203	18	a	a	DET
ejpam-1745	203	19	is	be	AUX
ejpam-1745	203	20	s	s	NOUN
ejpam-1745	203	21	-	-	PUNCT
ejpam-1745	203	22	dense	dense	ADJ
ejpam-1745	203	23	,	,	PUNCT
ejpam-1745	203	24	then	then	ADV
ejpam-1745	203	25	a	a	PRON
ejpam-1745	203	26	is	be	AUX
ejpam-1745	203	27	injective	injective	ADJ
ejpam-1745	203	28	.	.	PUNCT
ejpam-1745	204	1	h.	h.	PROPN
ejpam-1745	204	2	barzegar	barzegar	PROPN
ejpam-1745	204	3	/	/	SYM
ejpam-1745	204	4	eur	eur	PROPN
ejpam-1745	204	5	.	.	PUNCT
ejpam-1745	205	1	j.	j.	PROPN
ejpam-1745	205	2	pure	pure	PROPN
ejpam-1745	205	3	appl	appl	PROPN
ejpam-1745	205	4	.	.	PROPN
ejpam-1745	205	5	math	math	PROPN
ejpam-1745	205	6	,	,	PUNCT
ejpam-1745	205	7	6	6	NUM
ejpam-1745	205	8	(	(	PUNCT
ejpam-1745	205	9	2013	2013	NUM
ejpam-1745	205	10	)	)	PUNCT
ejpam-1745	205	11	,	,	PUNCT
ejpam-1745	205	12	211	211	NUM
ejpam-1745	205	13	-	-	SYM
ejpam-1745	205	14	221	221	NUM
ejpam-1745	205	15	218	218	NUM
ejpam-1745	205	16	proof	proof	NOUN
ejpam-1745	205	17	.	.	PUNCT
ejpam-1745	206	1	let	let	AUX
ejpam-1745	206	2	e(a	e(a	NOUN
ejpam-1745	206	3	)	)	PUNCT
ejpam-1745	206	4	be	be	AUX
ejpam-1745	206	5	an	an	DET
ejpam-1745	206	6	injective	injective	ADJ
ejpam-1745	206	7	hull	hull	NOUN
ejpam-1745	206	8	of	of	ADP
ejpam-1745	206	9	a.	a.	NOUN
ejpam-1745	206	10	since	since	SCONJ
ejpam-1745	206	11	a	a	PRON
ejpam-1745	206	12	is	be	AUX
ejpam-1745	206	13	an	an	DET
ejpam-1745	206	14	s	s	NOUN
ejpam-1745	206	15	-	-	NOUN
ejpam-1745	206	16	complete	complete	ADJ
ejpam-1745	206	17	and	and	CCONJ
ejpam-1745	206	18	e(a	e(a	PROPN
ejpam-1745	206	19	)	)	PUNCT
ejpam-1745	206	20	is	be	AUX
ejpam-1745	206	21	an	an	DET
ejpam-1745	206	22	essential	essential	ADJ
ejpam-1745	206	23	extension	extension	NOUN
ejpam-1745	206	24	of	of	ADP
ejpam-1745	206	25	a	a	DET
ejpam-1745	206	26	,	,	PUNCT
ejpam-1745	206	27	then	then	ADV
ejpam-1745	206	28	e(a	e(a	PROPN
ejpam-1745	206	29	)	)	PUNCT
ejpam-1745	206	30	is	be	AUX
ejpam-1745	206	31	an	an	DET
ejpam-1745	206	32	s	s	NOUN
ejpam-1745	206	33	-	-	ADJ
ejpam-1745	206	34	pure	pure	ADJ
ejpam-1745	206	35	essential	essential	ADJ
ejpam-1745	206	36	extension	extension	NOUN
ejpam-1745	206	37	of	of	ADP
ejpam-1745	206	38	a.	a.	NOUN
ejpam-1745	206	39	thus	thus	ADV
ejpam-1745	206	40	a	a	PRON
ejpam-1745	206	41	is	be	AUX
ejpam-1745	206	42	a	a	DET
ejpam-1745	206	43	retract	retract	NOUN
ejpam-1745	206	44	of	of	ADP
ejpam-1745	206	45	e(a	e(a	NOUN
ejpam-1745	206	46	)	)	PUNCT
ejpam-1745	206	47	by	by	ADP
ejpam-1745	206	48	lemma	lemma	PROPN
ejpam-1745	206	49	5	5	NUM
ejpam-1745	206	50	,	,	PUNCT
ejpam-1745	206	51	which	which	PRON
ejpam-1745	206	52	implies	imply	VERB
ejpam-1745	206	53	a	a	DET
ejpam-1745	206	54	is	be	AUX
ejpam-1745	206	55	an	an	DET
ejpam-1745	206	56	injective	injective	ADJ
ejpam-1745	206	57	s	s	NOUN
ejpam-1745	206	58	-	-	PUNCT
ejpam-1745	206	59	act	act	NOUN
ejpam-1745	206	60	.	.	PUNCT
ejpam-1745	207	1	theorem	theorem	VERB
ejpam-1745	207	2	9	9	NUM
ejpam-1745	207	3	.	.	PUNCT
ejpam-1745	208	1	if	if	SCONJ
ejpam-1745	208	2	s2	s2	VERB
ejpam-1745	208	3	=	=	SYM
ejpam-1745	208	4	s	s	PROPN
ejpam-1745	208	5	,	,	PUNCT
ejpam-1745	208	6	then	then	ADV
ejpam-1745	208	7	the	the	DET
ejpam-1745	208	8	following	following	NOUN
ejpam-1745	208	9	are	be	AUX
ejpam-1745	208	10	equivalent	equivalent	ADJ
ejpam-1745	208	11	:	:	PUNCT
ejpam-1745	208	12	(	(	PUNCT
ejpam-1745	208	13	i	i	NOUN
ejpam-1745	208	14	)	)	PUNCT
ejpam-1745	208	15	every	every	DET
ejpam-1745	208	16	s	s	NOUN
ejpam-1745	208	17	-	-	ADJ
ejpam-1745	208	18	complete	complete	ADJ
ejpam-1745	208	19	s	s	NOUN
ejpam-1745	208	20	-	-	NOUN
ejpam-1745	208	21	act	act	NOUN
ejpam-1745	208	22	is	be	AUX
ejpam-1745	208	23	injective	injective	ADJ
ejpam-1745	208	24	.	.	PUNCT
ejpam-1745	209	1	(	(	PUNCT
ejpam-1745	209	2	ii	ii	NOUN
ejpam-1745	209	3	)	)	PUNCT
ejpam-1745	209	4	every	every	DET
ejpam-1745	209	5	essential	essential	ADJ
ejpam-1745	209	6	extension	extension	NOUN
ejpam-1745	209	7	is	be	AUX
ejpam-1745	209	8	s	s	NOUN
ejpam-1745	209	9	-	-	PUNCT
ejpam-1745	209	10	dense	dense	ADJ
ejpam-1745	209	11	.	.	PUNCT
ejpam-1745	210	1	(	(	PUNCT
ejpam-1745	210	2	iii	iii	X
ejpam-1745	210	3	)	)	PUNCT
ejpam-1745	210	4	every	every	PRON
ejpam-1745	210	5	s	s	NOUN
ejpam-1745	210	6	-	-	ADJ
ejpam-1745	210	7	pure	pure	ADJ
ejpam-1745	210	8	essential	essential	ADJ
ejpam-1745	210	9	extension	extension	NOUN
ejpam-1745	210	10	is	be	AUX
ejpam-1745	210	11	s	s	NOUN
ejpam-1745	210	12	-	-	PUNCT
ejpam-1745	210	13	dense	dense	ADJ
ejpam-1745	210	14	.	.	PUNCT
ejpam-1745	211	1	(	(	PUNCT
ejpam-1745	211	2	iv	iv	X
ejpam-1745	211	3	)	)	PUNCT
ejpam-1745	211	4	every	every	DET
ejpam-1745	211	5	s	s	NOUN
ejpam-1745	211	6	-	-	ADJ
ejpam-1745	211	7	pure	pure	ADJ
ejpam-1745	211	8	essential	essential	ADJ
ejpam-1745	211	9	extension	extension	NOUN
ejpam-1745	211	10	is	be	AUX
ejpam-1745	211	11	isomorphism	isomorphism	NOUN
ejpam-1745	211	12	.	.	PUNCT
ejpam-1745	212	1	proof	proof	NOUN
ejpam-1745	212	2	.	.	PUNCT
ejpam-1745	213	1	(	(	PUNCT
ejpam-1745	213	2	i	i	NOUN
ejpam-1745	213	3	)	)	PUNCT
ejpam-1745	213	4	⇒	⇒	PROPN
ejpam-1745	213	5	(	(	PUNCT
ejpam-1745	213	6	ii	ii	NOUN
ejpam-1745	213	7	)	)	PUNCT
ejpam-1745	213	8	let	let	VERB
ejpam-1745	213	9	b	b	X
ejpam-1745	213	10	be	be	AUX
ejpam-1745	213	11	an	an	DET
ejpam-1745	213	12	essential	essential	ADJ
ejpam-1745	213	13	extension	extension	NOUN
ejpam-1745	213	14	of	of	ADP
ejpam-1745	213	15	a.	a.	NOUN
ejpam-1745	213	16	by	by	ADP
ejpam-1745	213	17	[	[	X
ejpam-1745	213	18	5	5	NUM
ejpam-1745	213	19	,	,	PUNCT
ejpam-1745	213	20	theorem	theorem	VERB
ejpam-1745	213	21	3.10	3.10	NUM
ejpam-1745	213	22	]	]	PUNCT
ejpam-1745	213	23	,	,	PUNCT
ejpam-1745	213	24	a	a	PRON
ejpam-1745	213	25	has	have	VERB
ejpam-1745	213	26	an	an	DET
ejpam-1745	213	27	s	s	NOUN
ejpam-1745	213	28	-	-	PUNCT
ejpam-1745	213	29	dense	dense	ADJ
ejpam-1745	213	30	injective	injective	ADJ
ejpam-1745	213	31	hull	hull	NOUN
ejpam-1745	213	32	such	such	ADJ
ejpam-1745	213	33	as	as	ADP
ejpam-1745	213	34	ι	ι	PROPN
ejpam-1745	213	35	:	:	PUNCT
ejpam-1745	213	36	a→	a→	X
ejpam-1745	213	37	ed(a	ed(a	NOUN
ejpam-1745	213	38	)	)	PUNCT
ejpam-1745	213	39	.	.	PUNCT
ejpam-1745	214	1	by	by	ADP
ejpam-1745	214	2	theorem	theorem	NOUN
ejpam-1745	214	3	1	1	NUM
ejpam-1745	214	4	,	,	PUNCT
ejpam-1745	214	5	ed(a	ed(a	NOUN
ejpam-1745	214	6	)	)	PUNCT
ejpam-1745	214	7	is	be	AUX
ejpam-1745	214	8	s	s	NOUN
ejpam-1745	214	9	-	-	NOUN
ejpam-1745	214	10	complete	complete	ADJ
ejpam-1745	214	11	and	and	CCONJ
ejpam-1745	214	12	hence	hence	ADV
ejpam-1745	214	13	it	it	PRON
ejpam-1745	214	14	is	be	AUX
ejpam-1745	214	15	injective	injective	ADJ
ejpam-1745	214	16	.	.	PUNCT
ejpam-1745	215	1	so	so	ADV
ejpam-1745	215	2	there	there	PRON
ejpam-1745	215	3	exists	exist	VERB
ejpam-1745	215	4	g	g	NOUN
ejpam-1745	215	5	:	:	PUNCT
ejpam-1745	215	6	b→	b→	PROPN
ejpam-1745	215	7	ed(a	ed(a	ADJ
ejpam-1745	215	8	)	)	PUNCT
ejpam-1745	215	9	such	such	ADJ
ejpam-1745	215	10	that	that	DET
ejpam-1745	215	11	g|a	g|a	PROPN
ejpam-1745	216	1	=	=	SYM
ejpam-1745	216	2	ι	ι	PROPN
ejpam-1745	216	3	which	which	PRON
ejpam-1745	216	4	implies	imply	VERB
ejpam-1745	216	5	g	g	PROPN
ejpam-1745	216	6	is	be	AUX
ejpam-1745	216	7	a	a	DET
ejpam-1745	216	8	monomorphism	monomorphism	NOUN
ejpam-1745	216	9	.	.	PUNCT
ejpam-1745	217	1	since	since	SCONJ
ejpam-1745	217	2	g|a	g|a	PROPN
ejpam-1745	217	3	=	=	SYM
ejpam-1745	217	4	ι	ι	PROPN
ejpam-1745	217	5	is	be	AUX
ejpam-1745	217	6	an	an	DET
ejpam-1745	217	7	s	s	NOUN
ejpam-1745	217	8	-	-	PUNCT
ejpam-1745	217	9	dense	dense	ADJ
ejpam-1745	217	10	monomorphism	monomorphism	NOUN
ejpam-1745	217	11	,	,	PUNCT
ejpam-1745	217	12	it	it	PRON
ejpam-1745	217	13	is	be	AUX
ejpam-1745	217	14	clear	clear	ADJ
ejpam-1745	217	15	that	that	SCONJ
ejpam-1745	217	16	b	b	NOUN
ejpam-1745	217	17	is	be	AUX
ejpam-1745	217	18	an	an	DET
ejpam-1745	217	19	s	s	NOUN
ejpam-1745	217	20	-	-	PUNCT
ejpam-1745	217	21	dense	dense	ADJ
ejpam-1745	217	22	extension	extension	NOUN
ejpam-1745	217	23	of	of	ADP
ejpam-1745	217	24	a.	a.	NOUN
ejpam-1745	217	25	(	(	PUNCT
ejpam-1745	217	26	iii	iii	NOUN
ejpam-1745	217	27	)	)	PUNCT
ejpam-1745	217	28	⇒	⇒	NOUN
ejpam-1745	217	29	(	(	PUNCT
ejpam-1745	217	30	iv	iv	X
ejpam-1745	217	31	)	)	PUNCT
ejpam-1745	217	32	let	let	VERB
ejpam-1745	217	33	b	b	X
ejpam-1745	217	34	be	be	AUX
ejpam-1745	217	35	an	an	DET
ejpam-1745	217	36	s	s	NOUN
ejpam-1745	217	37	-	-	ADJ
ejpam-1745	217	38	pure	pure	ADJ
ejpam-1745	217	39	essential	essential	ADJ
ejpam-1745	217	40	extension	extension	NOUN
ejpam-1745	217	41	of	of	ADP
ejpam-1745	217	42	a.	a.	NOUN
ejpam-1745	217	43	then	then	ADV
ejpam-1745	217	44	a	a	PRON
ejpam-1745	217	45	is	be	AUX
ejpam-1745	217	46	s	s	NOUN
ejpam-1745	217	47	-	-	ADJ
ejpam-1745	217	48	dense	dense	ADJ
ejpam-1745	217	49	in	in	ADP
ejpam-1745	217	50	b	b	PROPN
ejpam-1745	217	51	and	and	CCONJ
ejpam-1745	217	52	by	by	ADP
ejpam-1745	217	53	lemma	lemma	PROPN
ejpam-1745	217	54	5	5	NUM
ejpam-1745	217	55	,	,	PUNCT
ejpam-1745	217	56	it	it	PRON
ejpam-1745	217	57	is	be	AUX
ejpam-1745	217	58	a	a	DET
ejpam-1745	217	59	retract	retract	NOUN
ejpam-1745	217	60	of	of	ADP
ejpam-1745	217	61	b.	b.	NOUN
ejpam-1745	218	1	so	so	ADV
ejpam-1745	218	2	there	there	PRON
ejpam-1745	218	3	is	be	VERB
ejpam-1745	218	4	a	a	DET
ejpam-1745	218	5	homomorphism	homomorphism	NOUN
ejpam-1745	218	6	g	g	NOUN
ejpam-1745	218	7	:	:	PUNCT
ejpam-1745	218	8	b	b	X
ejpam-1745	218	9	→	→	PUNCT
ejpam-1745	218	10	a	a	DET
ejpam-1745	218	11	such	such	ADJ
ejpam-1745	218	12	that	that	DET
ejpam-1745	218	13	g|a	g|a	NOUN
ejpam-1745	218	14	is	be	AUX
ejpam-1745	218	15	a	a	DET
ejpam-1745	218	16	monomorphism	monomorphism	NOUN
ejpam-1745	218	17	,	,	PUNCT
ejpam-1745	218	18	which	which	PRON
ejpam-1745	218	19	implies	imply	VERB
ejpam-1745	218	20	g	g	PROPN
ejpam-1745	218	21	is	be	AUX
ejpam-1745	218	22	an	an	DET
ejpam-1745	218	23	isomorphism	isomorphism	NOUN
ejpam-1745	218	24	.	.	PUNCT
ejpam-1745	219	1	(	(	PUNCT
ejpam-1745	219	2	iv)⇒	iv)⇒	X
ejpam-1745	219	3	(	(	PUNCT
ejpam-1745	219	4	i	i	NOUN
ejpam-1745	219	5	)	)	PUNCT
ejpam-1745	219	6	it	it	PRON
ejpam-1745	219	7	is	be	AUX
ejpam-1745	219	8	concluded	conclude	VERB
ejpam-1745	219	9	from	from	ADP
ejpam-1745	219	10	theorem	theorem	ADJ
ejpam-1745	219	11	8	8	NUM
ejpam-1745	219	12	.	.	PUNCT
ejpam-1745	220	1	theorem	theorem	NOUN
ejpam-1745	220	2	10	10	NUM
ejpam-1745	220	3	.	.	PUNCT
ejpam-1745	221	1	if	if	SCONJ
ejpam-1745	221	2	for	for	ADP
ejpam-1745	221	3	every	every	DET
ejpam-1745	221	4	nontrivial	nontrivial	ADJ
ejpam-1745	221	5	right	right	ADJ
ejpam-1745	221	6	ideal	ideal	NOUN
ejpam-1745	221	7	i	i	PRON
ejpam-1745	221	8	of	of	ADP
ejpam-1745	221	9	s	s	PROPN
ejpam-1745	221	10	,	,	PUNCT
ejpam-1745	221	11	ī	ī	PROPN
ejpam-1745	221	12	6=	6=	NOUN
ejpam-1745	222	1	i	i	PRON
ejpam-1745	222	2	,	,	PUNCT
ejpam-1745	222	3	then	then	ADV
ejpam-1745	222	4	every	every	DET
ejpam-1745	222	5	s	s	NOUN
ejpam-1745	222	6	-	-	ADJ
ejpam-1745	222	7	complete	complete	ADJ
ejpam-1745	222	8	s	s	NOUN
ejpam-1745	222	9	-	-	NOUN
ejpam-1745	222	10	act	act	NOUN
ejpam-1745	222	11	with	with	ADP
ejpam-1745	222	12	at	at	ADV
ejpam-1745	222	13	least	least	ADV
ejpam-1745	222	14	one	one	NUM
ejpam-1745	222	15	fixed	fix	VERB
ejpam-1745	222	16	element	element	NOUN
ejpam-1745	222	17	is	be	AUX
ejpam-1745	222	18	injective	injective	ADJ
ejpam-1745	222	19	.	.	PUNCT
ejpam-1745	223	1	proof	proof	NOUN
ejpam-1745	223	2	.	.	PUNCT
ejpam-1745	224	1	let	let	VERB
ejpam-1745	224	2	b	b	X
ejpam-1745	224	3	be	be	AUX
ejpam-1745	224	4	an	an	DET
ejpam-1745	224	5	s	s	NOUN
ejpam-1745	224	6	-	-	ADJ
ejpam-1745	224	7	pure	pure	ADJ
ejpam-1745	224	8	essential	essential	ADJ
ejpam-1745	224	9	extension	extension	NOUN
ejpam-1745	224	10	of	of	ADP
ejpam-1745	224	11	an	an	DET
ejpam-1745	224	12	s	s	NOUN
ejpam-1745	224	13	-	-	ADJ
ejpam-1745	224	14	complete	complete	ADJ
ejpam-1745	224	15	s	s	NOUN
ejpam-1745	224	16	-	-	NOUN
ejpam-1745	224	17	act	act	NOUN
ejpam-1745	224	18	a	a	PRON
ejpam-1745	224	19	and	and	CCONJ
ejpam-1745	225	1	b	b	NOUN
ejpam-1745	225	2	∈	∈	ADP
ejpam-1745	225	3	b	b	X
ejpam-1745	225	4	\	\	PROPN
ejpam-1745	225	5	a.	a.	NOUN
ejpam-1745	225	6	by	by	ADP
ejpam-1745	225	7	lemma	lemma	PROPN
ejpam-1745	225	8	7	7	NUM
ejpam-1745	225	9	,	,	PUNCT
ejpam-1745	225	10	;	;	PUNCT
ejpam-1745	225	11	6=	6=	NUM
ejpam-1745	225	12	ib	ib	PROPN
ejpam-1745	225	13	6=	6=	ADP
ejpam-1745	225	14	s.	s.	PROPN
ejpam-1745	225	15	by	by	ADP
ejpam-1745	225	16	hypothesis	hypothesis	NOUN
ejpam-1745	225	17	īb	īb	PROPN
ejpam-1745	225	18	6=	6=	PROPN
ejpam-1745	225	19	ib	ib	NOUN
ejpam-1745	225	20	and	and	CCONJ
ejpam-1745	225	21	there	there	PRON
ejpam-1745	225	22	exists	exist	VERB
ejpam-1745	225	23	x	x	X
ejpam-1745	225	24	∈	∈	PROPN
ejpam-1745	225	25	īb	īb	PROPN
ejpam-1745	225	26	\	\	PROPN
ejpam-1745	225	27	ib	ib	NOUN
ejpam-1745	225	28	.	.	PUNCT
ejpam-1745	226	1	since	since	SCONJ
ejpam-1745	226	2	a	a	DET
ejpam-1745	226	3	→	→	SYM
ejpam-1745	226	4	b	b	NOUN
ejpam-1745	226	5	is	be	AUX
ejpam-1745	226	6	an	an	DET
ejpam-1745	226	7	s	s	NOUN
ejpam-1745	226	8	-	-	ADJ
ejpam-1745	226	9	pure	pure	ADJ
ejpam-1745	226	10	essential	essential	ADJ
ejpam-1745	226	11	extension	extension	NOUN
ejpam-1745	226	12	,	,	PUNCT
ejpam-1745	226	13	the	the	DET
ejpam-1745	226	14	inclusion	inclusion	NOUN
ejpam-1745	226	15	map	map	NOUN
ejpam-1745	226	16	ι	ι	X
ejpam-1745	226	17	:	:	PUNCT
ejpam-1745	226	18	a→	a→	X
ejpam-1745	226	19	a∪	a∪	X
ejpam-1745	226	20	{	{	PUNCT
ejpam-1745	226	21	bx	bx	X
ejpam-1745	226	22	}	}	PUNCT
ejpam-1745	226	23	is	be	AUX
ejpam-1745	226	24	also	also	ADV
ejpam-1745	226	25	s	s	NOUN
ejpam-1745	226	26	-	-	ADJ
ejpam-1745	226	27	pure	pure	ADJ
ejpam-1745	226	28	essential	essential	ADJ
ejpam-1745	226	29	and	and	CCONJ
ejpam-1745	226	30	s	s	NOUN
ejpam-1745	226	31	-	-	PUNCT
ejpam-1745	226	32	dense	dense	ADJ
ejpam-1745	226	33	which	which	PRON
ejpam-1745	226	34	is	be	AUX
ejpam-1745	226	35	a	a	DET
ejpam-1745	226	36	retraction	retraction	NOUN
ejpam-1745	226	37	by	by	ADP
ejpam-1745	226	38	lemma	lemma	PROPN
ejpam-1745	226	39	5	5	NUM
ejpam-1745	226	40	.	.	PUNCT
ejpam-1745	226	41	essentiality	essentiality	NOUN
ejpam-1745	226	42	of	of	ADP
ejpam-1745	226	43	ι	ι	PROPN
ejpam-1745	226	44	implies	imply	VERB
ejpam-1745	226	45	that	that	SCONJ
ejpam-1745	226	46	it	it	PRON
ejpam-1745	226	47	is	be	AUX
ejpam-1745	226	48	an	an	DET
ejpam-1745	226	49	isomorphism	isomorphism	NOUN
ejpam-1745	226	50	.	.	PUNCT
ejpam-1745	227	1	so	so	ADV
ejpam-1745	227	2	bx	bx	PROPN
ejpam-1745	227	3	∈	∈	PROPN
ejpam-1745	227	4	a	a	PRON
ejpam-1745	228	1	and	and	CCONJ
ejpam-1745	228	2	x	x	SYM
ejpam-1745	228	3	∈	∈	NOUN
ejpam-1745	228	4	ib	ib	NOUN
ejpam-1745	228	5	which	which	PRON
ejpam-1745	228	6	is	be	AUX
ejpam-1745	228	7	a	a	DET
ejpam-1745	228	8	contradiction	contradiction	NOUN
ejpam-1745	228	9	.	.	PUNCT
ejpam-1745	229	1	thus	thus	ADV
ejpam-1745	229	2	a=	a=	PROPN
ejpam-1745	229	3	b	b	NOUN
ejpam-1745	229	4	and	and	CCONJ
ejpam-1745	229	5	by	by	ADP
ejpam-1745	229	6	theorem	theorem	NOUN
ejpam-1745	229	7	8	8	NUM
ejpam-1745	229	8	,	,	PUNCT
ejpam-1745	229	9	a	a	PRON
ejpam-1745	229	10	is	be	AUX
ejpam-1745	229	11	an	an	DET
ejpam-1745	229	12	injective	injective	ADJ
ejpam-1745	229	13	s	s	NOUN
ejpam-1745	229	14	-	-	NOUN
ejpam-1745	229	15	act	act	NOUN
ejpam-1745	229	16	.	.	PUNCT
ejpam-1745	230	1	corollary	corollary	ADJ
ejpam-1745	230	2	5	5	NUM
ejpam-1745	230	3	.	.	PUNCT
ejpam-1745	231	1	if	if	SCONJ
ejpam-1745	231	2	s	s	NOUN
ejpam-1745	231	3	is	be	AUX
ejpam-1745	231	4	an	an	DET
ejpam-1745	231	5	infinite	infinite	ADJ
ejpam-1745	231	6	monogenic	monogenic	ADJ
ejpam-1745	231	7	semigroup	semigroup	NOUN
ejpam-1745	231	8	,	,	PUNCT
ejpam-1745	231	9	then	then	ADV
ejpam-1745	231	10	every	every	DET
ejpam-1745	231	11	s	s	NOUN
ejpam-1745	231	12	-	-	ADJ
ejpam-1745	231	13	complete	complete	ADJ
ejpam-1745	231	14	s	s	NOUN
ejpam-1745	231	15	-	-	NOUN
ejpam-1745	231	16	act	act	NOUN
ejpam-1745	231	17	with	with	ADP
ejpam-1745	231	18	at	at	ADV
ejpam-1745	231	19	least	least	ADV
ejpam-1745	231	20	one	one	NUM
ejpam-1745	231	21	fixed	fix	VERB
ejpam-1745	231	22	element	element	NOUN
ejpam-1745	231	23	is	be	AUX
ejpam-1745	231	24	injective	injective	ADJ
ejpam-1745	231	25	.	.	PUNCT
ejpam-1745	232	1	proof	proof	NOUN
ejpam-1745	232	2	.	.	PUNCT
ejpam-1745	233	1	first	first	ADV
ejpam-1745	233	2	recall	recall	VERB
ejpam-1745	233	3	that	that	SCONJ
ejpam-1745	233	4	every	every	DET
ejpam-1745	233	5	infinite	infinite	ADJ
ejpam-1745	233	6	cyclic	cyclic	ADJ
ejpam-1745	233	7	semigroup	semigroup	NOUN
ejpam-1745	233	8	is	be	AUX
ejpam-1745	233	9	isomorphic	isomorphic	ADJ
ejpam-1745	233	10	to	to	ADP
ejpam-1745	233	11	(	(	PUNCT
ejpam-1745	233	12	n,+	n,+	NUM
ejpam-1745	233	13	)	)	PUNCT
ejpam-1745	234	1	[	[	X
ejpam-1745	234	2	see	see	VERB
ejpam-1745	234	3	9	9	NUM
ejpam-1745	234	4	]	]	PUNCT
ejpam-1745	234	5	.	.	PUNCT
ejpam-1745	235	1	let	let	VERB
ejpam-1745	235	2	i	i	PRON
ejpam-1745	235	3	be	be	AUX
ejpam-1745	235	4	a	a	DET
ejpam-1745	235	5	nontrivial	nontrivial	ADJ
ejpam-1745	235	6	right	right	ADJ
ejpam-1745	235	7	ideal	ideal	NOUN
ejpam-1745	235	8	of	of	ADP
ejpam-1745	235	9	s.	s.	PROPN
ejpam-1745	235	10	so	so	ADV
ejpam-1745	235	11	there	there	PRON
ejpam-1745	235	12	exists	exist	VERB
ejpam-1745	235	13	1	1	NUM
ejpam-1745	235	14	≤	≤	NUM
ejpam-1745	235	15	n0	n0	NUM
ejpam-1745	235	16	∈	∈	PROPN
ejpam-1745	236	1	n	n	PRON
ejpam-1745	236	2	such	such	ADJ
ejpam-1745	236	3	that	that	SCONJ
ejpam-1745	236	4	i	i	PRON
ejpam-1745	236	5	=	=	PUNCT
ejpam-1745	236	6	{	{	PUNCT
ejpam-1745	236	7	n	n	CCONJ
ejpam-1745	236	8	∈	∈	PROPN
ejpam-1745	236	9	n	n	CCONJ
ejpam-1745	236	10	|	|	ADV
ejpam-1745	236	11	n0	n0	NUM
ejpam-1745	236	12	≤	≤	NOUN
ejpam-1745	236	13	n	n	CCONJ
ejpam-1745	236	14	}	}	PUNCT
ejpam-1745	236	15	and	and	CCONJ
ejpam-1745	236	16	s	s	VERB
ejpam-1745	236	17	\	\	ADJ
ejpam-1745	237	1	i	i	NOUN
ejpam-1745	237	2	=	=	SYM
ejpam-1745	237	3	{	{	PUNCT
ejpam-1745	237	4	1,2	1,2	NUM
ejpam-1745	237	5	,	,	PUNCT
ejpam-1745	237	6	.	.	PUNCT
ejpam-1745	237	7	.	.	PUNCT
ejpam-1745	237	8	.	.	PUNCT
ejpam-1745	238	1	,	,	PUNCT
ejpam-1745	238	2	n0−	n0−	NOUN
ejpam-1745	238	3	1	1	NUM
ejpam-1745	238	4	}	}	PUNCT
ejpam-1745	238	5	.	.	PUNCT
ejpam-1745	239	1	thus	thus	ADV
ejpam-1745	239	2	ī	ī	X
ejpam-1745	239	3	=	=	PUNCT
ejpam-1745	239	4	i	i	PRON
ejpam-1745	239	5	∪	∪	VERB
ejpam-1745	239	6	{	{	PUNCT
ejpam-1745	239	7	n0−	n0−	NOUN
ejpam-1745	239	8	1	1	NUM
ejpam-1745	239	9	}	}	PUNCT
ejpam-1745	239	10	.	.	PUNCT
ejpam-1745	240	1	now	now	ADV
ejpam-1745	240	2	we	we	PRON
ejpam-1745	240	3	get	get	VERB
ejpam-1745	240	4	the	the	DET
ejpam-1745	240	5	result	result	NOUN
ejpam-1745	240	6	by	by	ADP
ejpam-1745	240	7	using	use	VERB
ejpam-1745	240	8	theorem	theorem	ADJ
ejpam-1745	240	9	10	10	NUM
ejpam-1745	240	10	.	.	PUNCT
ejpam-1745	241	1	corollary	corollary	ADJ
ejpam-1745	241	2	6	6	NUM
ejpam-1745	241	3	.	.	PUNCT
ejpam-1745	242	1	if	if	SCONJ
ejpam-1745	242	2	s	s	PROPN
ejpam-1745	242	3	is	be	AUX
ejpam-1745	242	4	a	a	DET
ejpam-1745	242	5	finite	finite	ADJ
ejpam-1745	242	6	monogenic	monogenic	ADJ
ejpam-1745	242	7	semigroup	semigroup	NOUN
ejpam-1745	242	8	,	,	PUNCT
ejpam-1745	242	9	then	then	ADV
ejpam-1745	242	10	every	every	DET
ejpam-1745	242	11	s	s	NOUN
ejpam-1745	242	12	-	-	ADJ
ejpam-1745	242	13	complete	complete	ADJ
ejpam-1745	242	14	s	s	NOUN
ejpam-1745	242	15	-	-	NOUN
ejpam-1745	242	16	act	act	NOUN
ejpam-1745	242	17	with	with	ADP
ejpam-1745	242	18	at	at	ADV
ejpam-1745	242	19	least	least	ADV
ejpam-1745	242	20	one	one	NUM
ejpam-1745	242	21	fixed	fix	VERB
ejpam-1745	242	22	element	element	NOUN
ejpam-1745	242	23	is	be	AUX
ejpam-1745	242	24	injective	injective	ADJ
ejpam-1745	242	25	.	.	PUNCT
ejpam-1745	243	1	proof	proof	NOUN
ejpam-1745	243	2	.	.	PUNCT
ejpam-1745	244	1	the	the	DET
ejpam-1745	244	2	proof	proof	NOUN
ejpam-1745	244	3	is	be	AUX
ejpam-1745	244	4	similar	similar	ADJ
ejpam-1745	244	5	to	to	ADP
ejpam-1745	244	6	the	the	DET
ejpam-1745	244	7	proof	proof	NOUN
ejpam-1745	244	8	of	of	ADP
ejpam-1745	244	9	theorem	theorem	ADJ
ejpam-1745	244	10	5	5	NUM
ejpam-1745	244	11	.	.	PUNCT
ejpam-1745	244	12	h.	h.	PROPN
ejpam-1745	244	13	barzegar	barzegar	PROPN
ejpam-1745	244	14	/	/	SYM
ejpam-1745	244	15	eur	eur	PROPN
ejpam-1745	244	16	.	.	PUNCT
ejpam-1745	245	1	j.	j.	PROPN
ejpam-1745	245	2	pure	pure	PROPN
ejpam-1745	245	3	appl	appl	PROPN
ejpam-1745	245	4	.	.	PROPN
ejpam-1745	245	5	math	math	PROPN
ejpam-1745	245	6	,	,	PUNCT
ejpam-1745	245	7	6	6	NUM
ejpam-1745	245	8	(	(	PUNCT
ejpam-1745	245	9	2013	2013	NUM
ejpam-1745	245	10	)	)	PUNCT
ejpam-1745	245	11	,	,	PUNCT
ejpam-1745	245	12	211	211	NUM
ejpam-1745	245	13	-	-	SYM
ejpam-1745	245	14	221	221	NUM
ejpam-1745	245	15	219	219	NUM
ejpam-1745	245	16	corollary	corollary	NOUN
ejpam-1745	245	17	7	7	NUM
ejpam-1745	245	18	.	.	PUNCT
ejpam-1745	246	1	let	let	VERB
ejpam-1745	246	2	s	s	PRON
ejpam-1745	246	3	be	be	AUX
ejpam-1745	246	4	a	a	DET
ejpam-1745	246	5	semigroup	semigroup	NOUN
ejpam-1745	246	6	and	and	CCONJ
ejpam-1745	246	7	s0	s0	PROPN
ejpam-1745	246	8	∈	∈	PROPN
ejpam-1745	246	9	s	s	PROPN
ejpam-1745	246	10	,	,	PUNCT
ejpam-1745	246	11	such	such	ADJ
ejpam-1745	246	12	that	that	SCONJ
ejpam-1745	246	13	for	for	ADP
ejpam-1745	246	14	all	all	DET
ejpam-1745	246	15	s	s	PROPN
ejpam-1745	246	16	,	,	PUNCT
ejpam-1745	246	17	t	t	PROPN
ejpam-1745	246	18	∈	∈	PROPN
ejpam-1745	246	19	s	s	PROPN
ejpam-1745	246	20	,	,	PUNCT
ejpam-1745	246	21	st	st	PROPN
ejpam-1745	246	22	=	=	PROPN
ejpam-1745	246	23	s0	s0	PROPN
ejpam-1745	246	24	.	.	PUNCT
ejpam-1745	247	1	then	then	ADV
ejpam-1745	247	2	every	every	DET
ejpam-1745	247	3	s	s	NOUN
ejpam-1745	247	4	-	-	ADJ
ejpam-1745	247	5	complete	complete	ADJ
ejpam-1745	247	6	s	s	NOUN
ejpam-1745	247	7	-	-	NOUN
ejpam-1745	247	8	act	act	NOUN
ejpam-1745	247	9	is	be	AUX
ejpam-1745	247	10	injective	injective	ADJ
ejpam-1745	247	11	.	.	PUNCT
ejpam-1745	248	1	proof	proof	NOUN
ejpam-1745	248	2	.	.	PUNCT
ejpam-1745	249	1	it	it	PRON
ejpam-1745	249	2	is	be	AUX
ejpam-1745	249	3	clear	clear	ADJ
ejpam-1745	249	4	that	that	SCONJ
ejpam-1745	249	5	every	every	DET
ejpam-1745	249	6	nonempty	nonempty	ADJ
ejpam-1745	249	7	right	right	ADJ
ejpam-1745	249	8	ideal	ideal	NOUN
ejpam-1745	249	9	of	of	ADP
ejpam-1745	249	10	s	s	PROPN
ejpam-1745	249	11	is	be	AUX
ejpam-1745	249	12	a	a	DET
ejpam-1745	249	13	subset	subset	NOUN
ejpam-1745	249	14	of	of	ADP
ejpam-1745	249	15	s	s	PRON
ejpam-1745	249	16	containing	contain	VERB
ejpam-1745	249	17	an	an	DET
ejpam-1745	249	18	element	element	NOUN
ejpam-1745	249	19	s0	s0	NOUN
ejpam-1745	249	20	and	and	CCONJ
ejpam-1745	249	21	for	for	ADP
ejpam-1745	249	22	every	every	DET
ejpam-1745	249	23	nonempty	nonempty	ADJ
ejpam-1745	249	24	proper	proper	ADJ
ejpam-1745	249	25	right	right	ADJ
ejpam-1745	249	26	ideal	ideal	NOUN
ejpam-1745	249	27	i	i	PRON
ejpam-1745	249	28	of	of	ADP
ejpam-1745	249	29	s	s	PROPN
ejpam-1745	249	30	,	,	PUNCT
ejpam-1745	249	31	i	i	PROPN
ejpam-1745	249	32	6=	6=	PROPN
ejpam-1745	249	33	ī	ī	NOUN
ejpam-1745	249	34	=	=	SYM
ejpam-1745	249	35	s.	s.	PROPN
ejpam-1745	250	1	so	so	SCONJ
ejpam-1745	250	2	the	the	DET
ejpam-1745	250	3	proof	proof	NOUN
ejpam-1745	250	4	is	be	AUX
ejpam-1745	250	5	complete	complete	ADJ
ejpam-1745	250	6	by	by	ADP
ejpam-1745	250	7	theorem	theorem	ADJ
ejpam-1745	250	8	10	10	NUM
ejpam-1745	250	9	.	.	PUNCT
ejpam-1745	251	1	theorem	theorem	VERB
ejpam-1745	251	2	11	11	NUM
ejpam-1745	251	3	.	.	PUNCT
ejpam-1745	252	1	if	if	SCONJ
ejpam-1745	252	2	every	every	PRON
ejpam-1745	252	3	nonempty	nonempty	VERB
ejpam-1745	252	4	proper	proper	ADJ
ejpam-1745	252	5	right	right	ADJ
ejpam-1745	252	6	ideal	ideal	NOUN
ejpam-1745	252	7	of	of	ADP
ejpam-1745	252	8	s	s	PRON
ejpam-1745	252	9	generates	generate	NOUN
ejpam-1745	252	10	by	by	ADP
ejpam-1745	252	11	a	a	DET
ejpam-1745	252	12	central	central	ADJ
ejpam-1745	252	13	idempotent	idempotent	NOUN
ejpam-1745	252	14	element	element	NOUN
ejpam-1745	252	15	,	,	PUNCT
ejpam-1745	252	16	then	then	ADV
ejpam-1745	252	17	every	every	DET
ejpam-1745	252	18	s	s	NOUN
ejpam-1745	252	19	-	-	ADJ
ejpam-1745	252	20	complete	complete	ADJ
ejpam-1745	252	21	s	s	NOUN
ejpam-1745	252	22	-	-	NOUN
ejpam-1745	252	23	act	act	NOUN
ejpam-1745	252	24	with	with	ADP
ejpam-1745	252	25	at	at	ADV
ejpam-1745	252	26	least	least	ADV
ejpam-1745	252	27	one	one	NUM
ejpam-1745	252	28	fixed	fix	VERB
ejpam-1745	252	29	element	element	NOUN
ejpam-1745	252	30	is	be	AUX
ejpam-1745	252	31	injective	injective	ADJ
ejpam-1745	252	32	.	.	PUNCT
ejpam-1745	253	1	proof	proof	NOUN
ejpam-1745	253	2	.	.	PUNCT
ejpam-1745	254	1	let	let	VERB
ejpam-1745	254	2	a	a	DET
ejpam-1745	254	3	be	be	AUX
ejpam-1745	254	4	an	an	DET
ejpam-1745	254	5	s	s	NOUN
ejpam-1745	254	6	-	-	ADJ
ejpam-1745	254	7	complete	complete	ADJ
ejpam-1745	254	8	s	s	NOUN
ejpam-1745	254	9	-	-	NOUN
ejpam-1745	254	10	act	act	NOUN
ejpam-1745	254	11	with	with	ADP
ejpam-1745	254	12	at	at	ADV
ejpam-1745	254	13	least	least	ADV
ejpam-1745	254	14	one	one	NUM
ejpam-1745	254	15	fixed	fix	VERB
ejpam-1745	254	16	element	element	NOUN
ejpam-1745	254	17	and	and	CCONJ
ejpam-1745	254	18	b	b	NOUN
ejpam-1745	254	19	be	be	AUX
ejpam-1745	254	20	an	an	DET
ejpam-1745	254	21	essential	essential	ADJ
ejpam-1745	254	22	extension	extension	NOUN
ejpam-1745	254	23	of	of	ADP
ejpam-1745	254	24	a.	a.	NOUN
ejpam-1745	254	25	by	by	ADP
ejpam-1745	254	26	using	use	VERB
ejpam-1745	254	27	theorem	theorem	ADJ
ejpam-1745	254	28	1	1	NUM
ejpam-1745	254	29	and	and	CCONJ
ejpam-1745	254	30	lemma	lemma	PROPN
ejpam-1745	254	31	7	7	NUM
ejpam-1745	254	32	,	,	PUNCT
ejpam-1745	254	33	for	for	ADP
ejpam-1745	254	34	every	every	DET
ejpam-1745	254	35	b	b	PROPN
ejpam-1745	254	36	∈	∈	PROPN
ejpam-1745	254	37	b\a	b\a	NOUN
ejpam-1745	254	38	,	,	PUNCT
ejpam-1745	254	39	;	;	PUNCT
ejpam-1745	254	40	6=	6=	NUM
ejpam-1745	254	41	ib	ib	PROPN
ejpam-1745	254	42	6=	6=	AUX
ejpam-1745	254	43	s.	s.	PROPN
ejpam-1745	255	1	so	so	ADV
ejpam-1745	255	2	ib	ib	PROPN
ejpam-1745	255	3	=	=	PUNCT
ejpam-1745	255	4	ebs1	ebs1	PROPN
ejpam-1745	255	5	such	such	ADJ
ejpam-1745	255	6	that	that	SCONJ
ejpam-1745	255	7	eb	eb	PROPN
ejpam-1745	255	8	is	be	AUX
ejpam-1745	255	9	a	a	DET
ejpam-1745	255	10	central	central	ADJ
ejpam-1745	255	11	idempotent	idempotent	ADJ
ejpam-1745	255	12	element	element	NOUN
ejpam-1745	255	13	.	.	PUNCT
ejpam-1745	256	1	consider	consider	VERB
ejpam-1745	256	2	the	the	DET
ejpam-1745	256	3	map	map	NOUN
ejpam-1745	256	4	g	g	PROPN
ejpam-1745	256	5	:	:	PUNCT
ejpam-1745	256	6	b→	b→	PROPN
ejpam-1745	257	1	a	a	PRON
ejpam-1745	257	2	defined	define	VERB
ejpam-1745	257	3	by	by	ADP
ejpam-1745	257	4	g(b	g(b	PROPN
ejpam-1745	257	5	)	)	PUNCT
ejpam-1745	257	6	=	=	PRON
ejpam-1745	257	7	(	(	PUNCT
ejpam-1745	257	8	b	b	X
ejpam-1745	257	9	,	,	PUNCT
ejpam-1745	257	10	if	if	SCONJ
ejpam-1745	257	11	b	b	X
ejpam-1745	257	12	∈	∈	PROPN
ejpam-1745	257	13	a	a	DET
ejpam-1745	257	14	beb	beb	NOUN
ejpam-1745	257	15	,	,	PUNCT
ejpam-1745	257	16	if	if	SCONJ
ejpam-1745	257	17	b	b	PROPN
ejpam-1745	257	18	6∈	6∈	PROPN
ejpam-1745	257	19	a	a	DET
ejpam-1745	257	20	let	let	NOUN
ejpam-1745	257	21	b	b	NOUN
ejpam-1745	257	22	∈	∈	PROPN
ejpam-1745	257	23	b	b	PROPN
ejpam-1745	257	24	and	and	CCONJ
ejpam-1745	257	25	s	s	PROPN
ejpam-1745	257	26	∈	∈	PROPN
ejpam-1745	257	27	s.	s.	PROPN
ejpam-1745	257	28	if	if	SCONJ
ejpam-1745	257	29	b	b	PROPN
ejpam-1745	257	30	∈	∈	PROPN
ejpam-1745	257	31	a	a	PRON
ejpam-1745	257	32	,	,	PUNCT
ejpam-1745	257	33	g(bs	g(bs	PROPN
ejpam-1745	257	34	)	)	PUNCT
ejpam-1745	257	35	=	=	SYM
ejpam-1745	257	36	bs	bs	NOUN
ejpam-1745	257	37	=	=	SYM
ejpam-1745	257	38	g(b)s	g(b)s	PROPN
ejpam-1745	257	39	.	.	PUNCT
ejpam-1745	258	1	if	if	SCONJ
ejpam-1745	258	2	b	b	PROPN
ejpam-1745	258	3	6∈	6∈	NOUN
ejpam-1745	258	4	a	a	PRON
ejpam-1745	258	5	,	,	PUNCT
ejpam-1745	258	6	g(b)s	g(b)s	PROPN
ejpam-1745	258	7	=	=	SYM
ejpam-1745	258	8	bebs	bebs	NOUN
ejpam-1745	258	9	.	.	PUNCT
ejpam-1745	259	1	two	two	NUM
ejpam-1745	259	2	cases	case	NOUN
ejpam-1745	259	3	may	may	AUX
ejpam-1745	259	4	happen	happen	VERB
ejpam-1745	259	5	:	:	PUNCT
ejpam-1745	259	6	case	case	NOUN
ejpam-1745	259	7	(	(	PUNCT
ejpam-1745	259	8	1	1	NUM
ejpam-1745	259	9	):	):	PUNCT
ejpam-1745	259	10	s	s	VERB
ejpam-1745	259	11	∈	∈	NOUN
ejpam-1745	259	12	ib	ib	NOUN
ejpam-1745	259	13	.	.	PUNCT
ejpam-1745	260	1	so	so	ADV
ejpam-1745	260	2	s	s	PART
ejpam-1745	260	3	=	=	NOUN
ejpam-1745	260	4	ebs1	ebs1	PROPN
ejpam-1745	260	5	=	=	SYM
ejpam-1745	260	6	eb(ebs1	eb(ebs1	PROPN
ejpam-1745	260	7	)	)	PUNCT
ejpam-1745	260	8	=	=	SYM
ejpam-1745	260	9	ebs	ebs	PROPN
ejpam-1745	260	10	and	and	CCONJ
ejpam-1745	260	11	g(bs	g(bs	PROPN
ejpam-1745	260	12	)	)	PUNCT
ejpam-1745	260	13	=	=	SYM
ejpam-1745	260	14	bs	bs	NOUN
ejpam-1745	260	15	=	=	PUNCT
ejpam-1745	260	16	b(ebs	b(ebs	PROPN
ejpam-1745	260	17	)	)	PUNCT
ejpam-1745	260	18	=	=	SYM
ejpam-1745	260	19	g(b)s	g(b)s	PROPN
ejpam-1745	260	20	.	.	PUNCT
ejpam-1745	261	1	case	case	NOUN
ejpam-1745	261	2	(	(	PUNCT
ejpam-1745	261	3	2	2	NUM
ejpam-1745	261	4	):	):	PUNCT
ejpam-1745	261	5	s	s	NOUN
ejpam-1745	261	6	/∈	/∈	NOUN
ejpam-1745	261	7	ib	ib	NOUN
ejpam-1745	261	8	.	.	PUNCT
ejpam-1745	262	1	then	then	ADV
ejpam-1745	262	2	bs	bs	INTJ
ejpam-1745	262	3	/∈	/∈	PUNCT
ejpam-1745	262	4	a	a	PRON
ejpam-1745	262	5	and	and	CCONJ
ejpam-1745	262	6	ibs	ibs	PROPN
ejpam-1745	262	7	=	=	PUNCT
ejpam-1745	262	8	ebss	ebss	PROPN
ejpam-1745	262	9	1	1	NUM
ejpam-1745	262	10	.	.	PUNCT
ejpam-1745	263	1	since	since	SCONJ
ejpam-1745	263	2	(	(	PUNCT
ejpam-1745	263	3	bs)eb	bs)eb	X
ejpam-1745	263	4	=	=	SYM
ejpam-1745	263	5	(	(	PUNCT
ejpam-1745	263	6	beb)s	beb)s	ADP
ejpam-1745	263	7	∈	∈	PROPN
ejpam-1745	263	8	a	a	PRON
ejpam-1745	263	9	,	,	PUNCT
ejpam-1745	263	10	eb	eb	PROPN
ejpam-1745	263	11	∈	∈	PROPN
ejpam-1745	263	12	ibs	ibs	PROPN
ejpam-1745	263	13	and	and	CCONJ
ejpam-1745	263	14	hence	hence	ADV
ejpam-1745	263	15	ib	ib	PROPN
ejpam-1745	263	16	⊆	⊆	NUM
ejpam-1745	263	17	ibs	ib	NOUN
ejpam-1745	263	18	.	.	PUNCT
ejpam-1745	264	1	so	so	ADV
ejpam-1745	264	2	ebs	ebs	PROPN
ejpam-1745	264	3	=	=	PUNCT
ejpam-1745	264	4	ebs	ebs	PROPN
ejpam-1745	264	5	t	t	NOUN
ejpam-1745	264	6	for	for	ADP
ejpam-1745	264	7	some	some	DET
ejpam-1745	264	8	t	t	NOUN
ejpam-1745	264	9	∈	∈	PROPN
ejpam-1745	264	10	s.	s.	PROPN
ejpam-1745	264	11	on	on	ADP
ejpam-1745	264	12	the	the	DET
ejpam-1745	264	13	other	other	ADJ
ejpam-1745	264	14	hand	hand	NOUN
ejpam-1745	264	15	sebs	sebs	NOUN
ejpam-1745	264	16	∈	∈	PROPN
ejpam-1745	264	17	ib	ib	NOUN
ejpam-1745	264	18	implies	imply	VERB
ejpam-1745	264	19	sebs	sebs	NOUN
ejpam-1745	264	20	=	=	SYM
ejpam-1745	264	21	eb	eb	PROPN
ejpam-1745	264	22	t1(t1	t1(t1	NUM
ejpam-1745	264	23	∈	∈	PROPN
ejpam-1745	264	24	s	s	PART
ejpam-1745	264	25	)	)	PUNCT
ejpam-1745	264	26	=	=	SYM
ejpam-1745	264	27	eb(eb	eb(eb	PROPN
ejpam-1745	264	28	t1	t1	PROPN
ejpam-1745	264	29	)	)	PUNCT
ejpam-1745	264	30	=	=	SYM
ejpam-1745	264	31	eb(sebs	eb(sebs	NOUN
ejpam-1745	264	32	)	)	PUNCT
ejpam-1745	264	33	.	.	PUNCT
ejpam-1745	265	1	thus	thus	ADV
ejpam-1745	265	2	g(bs	g(bs	PROPN
ejpam-1745	265	3	)	)	PUNCT
ejpam-1745	265	4	=	=	SYM
ejpam-1745	265	5	(	(	PUNCT
ejpam-1745	265	6	bs)ebs	bs)ebs	NOUN
ejpam-1745	265	7	=	=	SYM
ejpam-1745	265	8	beb(sebs	beb(sebs	NOUN
ejpam-1745	265	9	)	)	PUNCT
ejpam-1745	265	10	=	=	SYM
ejpam-1745	265	11	b(ebs)ebs	b(ebs)ebs	NUM
ejpam-1745	266	1	=	=	NOUN
ejpam-1745	266	2	b(ebs	b(ebs	X
ejpam-1745	266	3	t)ebs	t)ebs	NOUN
ejpam-1745	266	4	=	=	SYM
ejpam-1745	266	5	bebs(ebs	bebs(ebs	NOUN
ejpam-1745	266	6	t	t	PROPN
ejpam-1745	266	7	)	)	PUNCT
ejpam-1745	266	8	=	=	SYM
ejpam-1745	266	9	bebs	bebs	PROPN
ejpam-1745	266	10	t	t	PROPN
ejpam-1745	266	11	=	=	SYM
ejpam-1745	266	12	bebs	bebs	PROPN
ejpam-1745	266	13	=	=	SYM
ejpam-1745	266	14	g(b)s	g(b)s	PROPN
ejpam-1745	266	15	.	.	PUNCT
ejpam-1745	267	1	therefore	therefore	ADV
ejpam-1745	267	2	g	g	PROPN
ejpam-1745	267	3	is	be	AUX
ejpam-1745	267	4	a	a	DET
ejpam-1745	267	5	homomorphism	homomorphism	NOUN
ejpam-1745	267	6	and	and	CCONJ
ejpam-1745	267	7	since	since	SCONJ
ejpam-1745	267	8	b	b	PROPN
ejpam-1745	267	9	is	be	AUX
ejpam-1745	267	10	an	an	DET
ejpam-1745	267	11	essential	essential	ADJ
ejpam-1745	267	12	extension	extension	NOUN
ejpam-1745	267	13	of	of	ADP
ejpam-1745	267	14	a	a	PRON
ejpam-1745	267	15	,	,	PUNCT
ejpam-1745	267	16	g	g	PROPN
ejpam-1745	267	17	is	be	AUX
ejpam-1745	267	18	an	an	DET
ejpam-1745	267	19	isomorphism	isomorphism	NOUN
ejpam-1745	267	20	.	.	PUNCT
ejpam-1745	268	1	so	so	ADV
ejpam-1745	268	2	we	we	PRON
ejpam-1745	268	3	get	get	VERB
ejpam-1745	268	4	the	the	DET
ejpam-1745	268	5	result	result	NOUN
ejpam-1745	268	6	by	by	ADP
ejpam-1745	268	7	theorem	theorem	NOUN
ejpam-1745	268	8	9	9	NUM
ejpam-1745	268	9	.	.	PUNCT
ejpam-1745	269	1	as	as	ADP
ejpam-1745	269	2	usual	usual	ADJ
ejpam-1745	269	3	s	s	X
ejpam-1745	269	4	is	be	AUX
ejpam-1745	269	5	a	a	DET
ejpam-1745	269	6	clifford	clifford	PROPN
ejpam-1745	269	7	semigroup	semigroup	NOUN
ejpam-1745	270	1	[	[	X
ejpam-1745	270	2	see	see	VERB
ejpam-1745	270	3	9	9	NUM
ejpam-1745	270	4	]	]	PUNCT
ejpam-1745	270	5	if	if	SCONJ
ejpam-1745	270	6	each	each	DET
ejpam-1745	270	7	α	α	NOUN
ejpam-1745	270	8	∈	∈	NOUN
ejpam-1745	271	1	s	s	PART
ejpam-1745	271	2	has	have	VERB
ejpam-1745	271	3	an	an	DET
ejpam-1745	271	4	inverse	inverse	ADJ
ejpam-1745	271	5	element(i.e	element(i.e	NOUN
ejpam-1745	271	6	,	,	PUNCT
ejpam-1745	271	7	there	there	PRON
ejpam-1745	271	8	exists	exist	VERB
ejpam-1745	271	9	α−1	α−1	PROPN
ejpam-1745	271	10	∈	∈	PROPN
ejpam-1745	271	11	s	s	VERB
ejpam-1745	271	12	such	such	ADJ
ejpam-1745	271	13	that	that	SCONJ
ejpam-1745	271	14	αα−1α	αα−1α	NUM
ejpam-1745	271	15	=	=	SYM
ejpam-1745	271	16	α−1αα−1	α−1αα−1	NOUN
ejpam-1745	271	17	)	)	PUNCT
ejpam-1745	271	18	and	and	CCONJ
ejpam-1745	271	19	the	the	DET
ejpam-1745	271	20	set	set	NOUN
ejpam-1745	271	21	of	of	ADP
ejpam-1745	271	22	all	all	DET
ejpam-1745	271	23	idempotents	idempotent	NOUN
ejpam-1745	271	24	is	be	AUX
ejpam-1745	271	25	equal	equal	ADJ
ejpam-1745	271	26	to	to	ADP
ejpam-1745	271	27	the	the	DET
ejpam-1745	271	28	set	set	NOUN
ejpam-1745	271	29	of	of	ADP
ejpam-1745	271	30	all	all	DET
ejpam-1745	271	31	central	central	ADJ
ejpam-1745	271	32	elements	element	NOUN
ejpam-1745	271	33	.	.	PUNCT
ejpam-1745	272	1	it	it	PRON
ejpam-1745	272	2	is	be	AUX
ejpam-1745	272	3	easy	easy	ADJ
ejpam-1745	272	4	to	to	PART
ejpam-1745	272	5	check	check	VERB
ejpam-1745	272	6	that	that	PRON
ejpam-1745	272	7	for	for	ADP
ejpam-1745	272	8	every	every	DET
ejpam-1745	272	9	α	α	PROPN
ejpam-1745	272	10	∈	∈	PROPN
ejpam-1745	272	11	s	s	PROPN
ejpam-1745	272	12	,	,	PUNCT
ejpam-1745	272	13	αα−1	αα−1	PROPN
ejpam-1745	272	14	is	be	AUX
ejpam-1745	272	15	an	an	DET
ejpam-1745	272	16	idempotent	idempotent	ADJ
ejpam-1745	272	17	element	element	NOUN
ejpam-1745	272	18	and	and	CCONJ
ejpam-1745	272	19	αs1	αs1	NOUN
ejpam-1745	273	1	=	=	ADJ
ejpam-1745	273	2	αα−1s1	αα−1s1	NOUN
ejpam-1745	273	3	.	.	PUNCT
ejpam-1745	274	1	so	so	ADV
ejpam-1745	274	2	we	we	PRON
ejpam-1745	274	3	conclude	conclude	VERB
ejpam-1745	274	4	the	the	DET
ejpam-1745	274	5	following	follow	VERB
ejpam-1745	274	6	corollary	corollary	ADJ
ejpam-1745	274	7	;	;	PUNCT
ejpam-1745	274	8	corollary	corollary	ADJ
ejpam-1745	274	9	8	8	NUM
ejpam-1745	274	10	.	.	PUNCT
ejpam-1745	275	1	let	let	VERB
ejpam-1745	275	2	s	s	PRON
ejpam-1745	275	3	be	be	AUX
ejpam-1745	275	4	a	a	DET
ejpam-1745	275	5	clifford	clifford	PROPN
ejpam-1745	275	6	semigroup	semigroup	NOUN
ejpam-1745	275	7	.	.	PUNCT
ejpam-1745	276	1	if	if	SCONJ
ejpam-1745	276	2	each	each	PRON
ejpam-1745	276	3	of	of	ADP
ejpam-1745	276	4	proper	proper	ADJ
ejpam-1745	276	5	nonempty	nonempty	ADJ
ejpam-1745	276	6	right	right	ADJ
ejpam-1745	276	7	ideals	ideal	NOUN
ejpam-1745	276	8	of	of	ADP
ejpam-1745	276	9	s	s	NOUN
ejpam-1745	276	10	is	be	AUX
ejpam-1745	276	11	principal	principal	ADJ
ejpam-1745	276	12	,	,	PUNCT
ejpam-1745	276	13	then	then	ADV
ejpam-1745	276	14	every	every	DET
ejpam-1745	276	15	s	s	NOUN
ejpam-1745	276	16	-	-	ADJ
ejpam-1745	276	17	complete	complete	ADJ
ejpam-1745	276	18	s	s	NOUN
ejpam-1745	276	19	-	-	NOUN
ejpam-1745	276	20	act	act	NOUN
ejpam-1745	276	21	with	with	ADP
ejpam-1745	276	22	at	at	ADV
ejpam-1745	276	23	least	least	ADV
ejpam-1745	276	24	one	one	NUM
ejpam-1745	276	25	fixed	fix	VERB
ejpam-1745	276	26	element	element	NOUN
ejpam-1745	276	27	is	be	AUX
ejpam-1745	276	28	injective	injective	ADJ
ejpam-1745	276	29	.	.	PUNCT
ejpam-1745	277	1	the	the	DET
ejpam-1745	277	2	following	follow	VERB
ejpam-1745	277	3	two	two	NUM
ejpam-1745	277	4	corollaries	corollary	NOUN
ejpam-1745	277	5	are	be	AUX
ejpam-1745	277	6	special	special	ADJ
ejpam-1745	277	7	cases	case	NOUN
ejpam-1745	277	8	of	of	ADP
ejpam-1745	277	9	clifford	clifford	PROPN
ejpam-1745	277	10	semigroup	semigroup	PROPN
ejpam-1745	277	11	.	.	PUNCT
ejpam-1745	278	1	corollary	corollary	ADJ
ejpam-1745	278	2	9	9	NUM
ejpam-1745	278	3	.	.	PUNCT
ejpam-1745	279	1	let	let	VERB
ejpam-1745	279	2	the	the	DET
ejpam-1745	279	3	semigroup	semigroup	NOUN
ejpam-1745	279	4	s	s	AUX
ejpam-1745	279	5	be	be	AUX
ejpam-1745	279	6	a	a	DET
ejpam-1745	279	7	commutative	commutative	ADJ
ejpam-1745	279	8	chain	chain	NOUN
ejpam-1745	279	9	with	with	ADP
ejpam-1745	279	10	the	the	DET
ejpam-1745	279	11	relation	relation	NOUN
ejpam-1745	279	12	(	(	PUNCT
ejpam-1745	279	13	x	x	SYM
ejpam-1745	279	14	≤	≤	NUM
ejpam-1745	280	1	y⇔	y⇔	NOUN
ejpam-1745	280	2	x	x	PUNCT
ejpam-1745	280	3	y	y	NOUN
ejpam-1745	280	4	=	=	PUNCT
ejpam-1745	280	5	x	x	NOUN
ejpam-1745	280	6	)	)	PUNCT
ejpam-1745	280	7	or	or	CCONJ
ejpam-1745	280	8	(	(	PUNCT
ejpam-1745	280	9	x	x	SYM
ejpam-1745	280	10	≤	≤	NUM
ejpam-1745	280	11	y⇔	y⇔	NOUN
ejpam-1745	280	12	x	x	PUNCT
ejpam-1745	280	13	y	y	PROPN
ejpam-1745	280	14	=	=	SYM
ejpam-1745	280	15	y	y	PROPN
ejpam-1745	280	16	)	)	PUNCT
ejpam-1745	280	17	.	.	PUNCT
ejpam-1745	281	1	then	then	ADV
ejpam-1745	281	2	every	every	DET
ejpam-1745	281	3	s	s	NOUN
ejpam-1745	281	4	-	-	ADJ
ejpam-1745	281	5	complete	complete	ADJ
ejpam-1745	281	6	s	s	NOUN
ejpam-1745	281	7	-	-	NOUN
ejpam-1745	281	8	act	act	NOUN
ejpam-1745	281	9	with	with	ADP
ejpam-1745	281	10	at	at	ADV
ejpam-1745	281	11	least	least	ADV
ejpam-1745	281	12	one	one	NUM
ejpam-1745	281	13	fixed	fix	VERB
ejpam-1745	281	14	element	element	NOUN
ejpam-1745	281	15	is	be	AUX
ejpam-1745	281	16	injective	injective	ADJ
ejpam-1745	281	17	.	.	PUNCT
ejpam-1745	282	1	corollary	corollary	ADJ
ejpam-1745	282	2	10	10	NUM
ejpam-1745	282	3	.	.	PUNCT
ejpam-1745	283	1	let	let	VERB
ejpam-1745	283	2	the	the	DET
ejpam-1745	283	3	semigroup	semigroup	NOUN
ejpam-1745	283	4	s	s	AUX
ejpam-1745	283	5	be	be	AUX
ejpam-1745	283	6	a	a	DET
ejpam-1745	283	7	commutative	commutative	ADJ
ejpam-1745	283	8	band	band	NOUN
ejpam-1745	283	9	.	.	PUNCT
ejpam-1745	284	1	then	then	ADV
ejpam-1745	284	2	every	every	DET
ejpam-1745	284	3	s	s	NOUN
ejpam-1745	284	4	-	-	ADJ
ejpam-1745	284	5	complete	complete	ADJ
ejpam-1745	284	6	s	s	NOUN
ejpam-1745	284	7	-	-	NOUN
ejpam-1745	284	8	act	act	NOUN
ejpam-1745	284	9	with	with	ADP
ejpam-1745	284	10	at	at	ADV
ejpam-1745	284	11	least	least	ADV
ejpam-1745	284	12	one	one	NUM
ejpam-1745	284	13	fixed	fix	VERB
ejpam-1745	284	14	element	element	NOUN
ejpam-1745	284	15	is	be	AUX
ejpam-1745	284	16	injective	injective	ADJ
ejpam-1745	284	17	.	.	PUNCT
ejpam-1745	285	1	h.	h.	PROPN
ejpam-1745	285	2	barzegar	barzegar	PROPN
ejpam-1745	285	3	/	/	SYM
ejpam-1745	285	4	eur	eur	PROPN
ejpam-1745	285	5	.	.	PUNCT
ejpam-1745	286	1	j.	j.	PROPN
ejpam-1745	286	2	pure	pure	PROPN
ejpam-1745	286	3	appl	appl	PROPN
ejpam-1745	286	4	.	.	PROPN
ejpam-1745	286	5	math	math	PROPN
ejpam-1745	286	6	,	,	PUNCT
ejpam-1745	286	7	6	6	NUM
ejpam-1745	286	8	(	(	PUNCT
ejpam-1745	286	9	2013	2013	NUM
ejpam-1745	286	10	)	)	PUNCT
ejpam-1745	286	11	,	,	PUNCT
ejpam-1745	286	12	211	211	NUM
ejpam-1745	286	13	-	-	SYM
ejpam-1745	286	14	221	221	NUM
ejpam-1745	286	15	220	220	NUM
ejpam-1745	286	16	an	an	DET
ejpam-1745	286	17	important	important	ADJ
ejpam-1745	286	18	semigroup	semigroup	NOUN
ejpam-1745	286	19	satisfying	satisfying	NOUN
ejpam-1745	286	20	to	to	ADP
ejpam-1745	286	21	these	these	DET
ejpam-1745	286	22	corollaries	corollary	NOUN
ejpam-1745	286	23	is	be	AUX
ejpam-1745	286	24	s	s	NOUN
ejpam-1745	286	25	=	=	PUNCT
ejpam-1745	286	26	(	(	PUNCT
ejpam-1745	286	27	n	n	CCONJ
ejpam-1745	286	28	,	,	PUNCT
ejpam-1745	286	29	min	min	NOUN
ejpam-1745	286	30	)	)	PUNCT
ejpam-1745	286	31	.	.	PUNCT
ejpam-1745	287	1	the	the	DET
ejpam-1745	287	2	category	category	NOUN
ejpam-1745	287	3	of	of	ADP
ejpam-1745	287	4	all	all	DET
ejpam-1745	287	5	s	s	NOUN
ejpam-1745	287	6	-	-	PUNCT
ejpam-1745	287	7	acts	act	NOUN
ejpam-1745	287	8	for	for	ADP
ejpam-1745	287	9	this	this	DET
ejpam-1745	287	10	semigroup	semigroup	NOUN
ejpam-1745	287	11	,	,	PUNCT
ejpam-1745	287	12	so	so	ADV
ejpam-1745	287	13	called	call	VERB
ejpam-1745	287	14	projection	projection	NOUN
ejpam-1745	287	15	algebras	algebra	NOUN
ejpam-1745	287	16	,	,	PUNCT
ejpam-1745	287	17	has	have	AUX
ejpam-1745	287	18	been	be	AUX
ejpam-1745	287	19	studied	study	VERB
ejpam-1745	287	20	by	by	ADP
ejpam-1745	287	21	ebrahimi	ebrahimi	PROPN
ejpam-1745	287	22	and	and	CCONJ
ejpam-1745	287	23	mahmoud	mahmoud	PROPN
ejpam-1745	288	1	[	[	X
ejpam-1745	288	2	4	4	NUM
ejpam-1745	288	3	]	]	PUNCT
ejpam-1745	288	4	and	and	CCONJ
ejpam-1745	288	5	giuli	giuli	ADJ
ejpam-1745	289	1	[	[	PUNCT
ejpam-1745	289	2	6].these	6].these	NUM
ejpam-1745	289	3	types	type	NOUN
ejpam-1745	289	4	of	of	ADP
ejpam-1745	289	5	s	s	NOUN
ejpam-1745	289	6	-	-	PUNCT
ejpam-1745	289	7	acts	act	NOUN
ejpam-1745	289	8	are	be	AUX
ejpam-1745	289	9	mostly	mostly	ADV
ejpam-1745	289	10	used	use	VERB
ejpam-1745	289	11	in	in	ADP
ejpam-1745	289	12	computer	computer	NOUN
ejpam-1745	289	13	science	science	NOUN
ejpam-1745	289	14	.	.	PUNCT
ejpam-1745	290	1	lemma	lemma	PROPN
ejpam-1745	290	2	8	8	NUM
ejpam-1745	290	3	.	.	PUNCT
ejpam-1745	291	1	let	let	VERB
ejpam-1745	291	2	a	a	PRON
ejpam-1745	291	3	have	have	VERB
ejpam-1745	291	4	a	a	DET
ejpam-1745	291	5	fixed	fix	VERB
ejpam-1745	291	6	element	element	NOUN
ejpam-1745	291	7	and	and	CCONJ
ejpam-1745	291	8	b	b	NOUN
ejpam-1745	291	9	be	be	AUX
ejpam-1745	291	10	a	a	DET
ejpam-1745	291	11	proper	proper	ADJ
ejpam-1745	291	12	s	s	NOUN
ejpam-1745	291	13	-	-	ADJ
ejpam-1745	291	14	pure	pure	ADJ
ejpam-1745	291	15	essential	essential	ADJ
ejpam-1745	291	16	extension	extension	NOUN
ejpam-1745	291	17	of	of	ADP
ejpam-1745	291	18	a.	a.	NOUN
ejpam-1745	291	19	then	then	ADV
ejpam-1745	291	20	for	for	ADP
ejpam-1745	291	21	every	every	DET
ejpam-1745	291	22	b	b	PROPN
ejpam-1745	291	23	∈	∈	PROPN
ejpam-1745	291	24	b	b	PROPN
ejpam-1745	291	25	and	and	CCONJ
ejpam-1745	291	26	every	every	PRON
ejpam-1745	291	27	nonempty	nonempty	ADJ
ejpam-1745	291	28	right	right	ADJ
ejpam-1745	291	29	ideal	ideal	ADJ
ejpam-1745	291	30	j	j	PROPN
ejpam-1745	291	31	of	of	ADP
ejpam-1745	291	32	s	s	PROPN
ejpam-1745	291	33	,	,	PUNCT
ejpam-1745	291	34	ib	ib	PROPN
ejpam-1745	291	35	∩	∩	PROPN
ejpam-1745	291	36	j	j	PROPN
ejpam-1745	291	37	6=	6=	NUM
ejpam-1745	291	38	;	;	PUNCT
ejpam-1745	291	39	.	.	PUNCT
ejpam-1745	292	1	proof	proof	NOUN
ejpam-1745	292	2	.	.	PUNCT
ejpam-1745	293	1	for	for	ADP
ejpam-1745	293	2	b	b	PROPN
ejpam-1745	293	3	∈	∈	PROPN
ejpam-1745	293	4	a	a	X
ejpam-1745	293	5	,	,	PUNCT
ejpam-1745	293	6	ib	ib	NOUN
ejpam-1745	293	7	=	=	SYM
ejpam-1745	293	8	s	s	PROPN
ejpam-1745	293	9	and	and	CCONJ
ejpam-1745	293	10	the	the	DET
ejpam-1745	293	11	result	result	NOUN
ejpam-1745	293	12	is	be	AUX
ejpam-1745	293	13	obvious	obvious	ADJ
ejpam-1745	293	14	.	.	PUNCT
ejpam-1745	294	1	for	for	ADP
ejpam-1745	294	2	b	b	PROPN
ejpam-1745	294	3	/∈	/∈	PROPN
ejpam-1745	294	4	a	a	PRON
ejpam-1745	294	5	,	,	PUNCT
ejpam-1745	294	6	let	let	VERB
ejpam-1745	294	7	j	j	PRON
ejpam-1745	294	8	be	be	AUX
ejpam-1745	294	9	a	a	DET
ejpam-1745	294	10	nonempty	nonempty	ADJ
ejpam-1745	294	11	right	right	ADJ
ejpam-1745	294	12	ideal	ideal	NOUN
ejpam-1745	294	13	of	of	ADP
ejpam-1745	294	14	s	s	PRON
ejpam-1745	294	15	and	and	CCONJ
ejpam-1745	294	16	ib∩j	ib∩j	PROPN
ejpam-1745	294	17	=	=	SYM
ejpam-1745	294	18	;	;	PUNCT
ejpam-1745	294	19	.	.	PUNCT
ejpam-1745	295	1	by	by	ADP
ejpam-1745	295	2	corollary	corollary	ADJ
ejpam-1745	295	3	3	3	NUM
ejpam-1745	295	4	,	,	PUNCT
ejpam-1745	295	5	ib	ib	NOUN
ejpam-1745	295	6	6=	6=	NUM
ejpam-1745	295	7	;	;	PUNCT
ejpam-1745	295	8	and	and	CCONJ
ejpam-1745	295	9	f	f	PROPN
ejpam-1745	295	10	ix(b)⊆	ix(b)⊆	PROPN
ejpam-1745	295	11	a.	a.	NOUN
ejpam-1745	295	12	it	it	PRON
ejpam-1745	295	13	is	be	AUX
ejpam-1745	295	14	clear	clear	ADJ
ejpam-1745	295	15	that	that	SCONJ
ejpam-1745	295	16	b′	b′	NOUN
ejpam-1745	295	17	=	=	PUNCT
ejpam-1745	295	18	{	{	PUNCT
ejpam-1745	295	19	bs|s	bs|s	NOUN
ejpam-1745	295	20	∈	∈	PROPN
ejpam-1745	295	21	j	j	PROPN
ejpam-1745	295	22	}	}	PUNCT
ejpam-1745	295	23	is	be	AUX
ejpam-1745	295	24	a	a	DET
ejpam-1745	295	25	subact	subact	NOUN
ejpam-1745	295	26	of	of	ADP
ejpam-1745	295	27	b	b	NOUN
ejpam-1745	295	28	and	and	CCONJ
ejpam-1745	295	29	b′	b′	NUM
ejpam-1745	295	30	∩	∩	NOUN
ejpam-1745	295	31	a	a	NOUN
ejpam-1745	295	32	=	=	X
ejpam-1745	295	33	;	;	PUNCT
ejpam-1745	295	34	.	.	PUNCT
ejpam-1745	296	1	by	by	ADP
ejpam-1745	296	2	lemma	lemma	PROPN
ejpam-1745	296	3	6	6	NUM
ejpam-1745	296	4	,	,	PUNCT
ejpam-1745	296	5	|b′|	|b′|	PROPN
ejpam-1745	296	6	=	=	SYM
ejpam-1745	296	7	1	1	NUM
ejpam-1745	296	8	and	and	CCONJ
ejpam-1745	296	9	hence	hence	ADV
ejpam-1745	296	10	for	for	ADP
ejpam-1745	296	11	every	every	DET
ejpam-1745	296	12	s	s	PROPN
ejpam-1745	296	13	∈	∈	PROPN
ejpam-1745	296	14	j	j	NOUN
ejpam-1745	296	15	,	,	PUNCT
ejpam-1745	296	16	bs	bs	PROPN
ejpam-1745	296	17	=	=	SYM
ejpam-1745	296	18	b0	b0	NOUN
ejpam-1745	296	19	for	for	ADP
ejpam-1745	296	20	some	some	DET
ejpam-1745	296	21	b0	b0	PROPN
ejpam-1745	296	22	∈	∈	PROPN
ejpam-1745	296	23	b.	b.	PROPN
ejpam-1745	296	24	consider	consider	VERB
ejpam-1745	296	25	s0	s0	PROPN
ejpam-1745	296	26	∈	∈	PROPN
ejpam-1745	296	27	j	j	PROPN
ejpam-1745	296	28	.	.	PUNCT
ejpam-1745	297	1	then	then	ADV
ejpam-1745	297	2	for	for	ADP
ejpam-1745	297	3	every	every	DET
ejpam-1745	297	4	t	t	NOUN
ejpam-1745	297	5	∈	∈	PROPN
ejpam-1745	297	6	s	s	PROPN
ejpam-1745	297	7	,	,	PUNCT
ejpam-1745	297	8	b0	b0	NOUN
ejpam-1745	297	9	t	t	NOUN
ejpam-1745	298	1	=	=	PUNCT
ejpam-1745	298	2	(	(	PUNCT
ejpam-1745	298	3	bs0)t	bs0)t	PROPN
ejpam-1745	298	4	=	=	PUNCT
ejpam-1745	298	5	b(s0	b(s0	PROPN
ejpam-1745	298	6	t	t	PROPN
ejpam-1745	298	7	)	)	PUNCT
ejpam-1745	298	8	=	=	SYM
ejpam-1745	298	9	b0	b0	NOUN
ejpam-1745	298	10	.	.	PUNCT
ejpam-1745	299	1	so	so	ADV
ejpam-1745	299	2	b0	b0	NOUN
ejpam-1745	299	3	∈	∈	PROPN
ejpam-1745	299	4	f	f	PROPN
ejpam-1745	299	5	ix(b)⊆	ix(b)⊆	PROPN
ejpam-1745	299	6	a	a	PRON
ejpam-1745	299	7	,	,	PUNCT
ejpam-1745	299	8	which	which	PRON
ejpam-1745	299	9	is	be	AUX
ejpam-1745	299	10	impossible	impossible	ADJ
ejpam-1745	299	11	.	.	PUNCT
ejpam-1745	300	1	theorem	theorem	NOUN
ejpam-1745	300	2	12	12	NUM
ejpam-1745	300	3	.	.	PUNCT
ejpam-1745	300	4	suppose	suppose	VERB
ejpam-1745	300	5	that	that	SCONJ
ejpam-1745	300	6	every	every	DET
ejpam-1745	300	7	nonempty	nonempty	ADJ
ejpam-1745	300	8	nontrivial	nontrivial	ADJ
ejpam-1745	300	9	right	right	ADJ
ejpam-1745	300	10	ideal	ideal	NOUN
ejpam-1745	300	11	i	i	PRON
ejpam-1745	300	12	of	of	ADP
ejpam-1745	300	13	s	s	PROPN
ejpam-1745	300	14	is	be	AUX
ejpam-1745	300	15	maximal	maximal	ADJ
ejpam-1745	300	16	.	.	PUNCT
ejpam-1745	301	1	then	then	ADV
ejpam-1745	301	2	every	every	DET
ejpam-1745	301	3	s	s	NOUN
ejpam-1745	301	4	-	-	ADJ
ejpam-1745	301	5	complete	complete	ADJ
ejpam-1745	301	6	s	s	NOUN
ejpam-1745	301	7	-	-	NOUN
ejpam-1745	301	8	act	act	NOUN
ejpam-1745	301	9	with	with	ADP
ejpam-1745	301	10	at	at	ADV
ejpam-1745	301	11	least	least	ADV
ejpam-1745	301	12	one	one	NUM
ejpam-1745	301	13	fixed	fix	VERB
ejpam-1745	301	14	element	element	NOUN
ejpam-1745	301	15	is	be	AUX
ejpam-1745	301	16	injective	injective	ADJ
ejpam-1745	301	17	.	.	PUNCT
ejpam-1745	302	1	proof	proof	NOUN
ejpam-1745	302	2	.	.	PUNCT
ejpam-1745	303	1	let	let	VERB
ejpam-1745	303	2	a	a	DET
ejpam-1745	303	3	be	be	AUX
ejpam-1745	303	4	an	an	DET
ejpam-1745	303	5	s	s	NOUN
ejpam-1745	303	6	-	-	ADJ
ejpam-1745	303	7	complete	complete	ADJ
ejpam-1745	303	8	s	s	NOUN
ejpam-1745	303	9	-	-	NOUN
ejpam-1745	303	10	act	act	NOUN
ejpam-1745	303	11	and	and	CCONJ
ejpam-1745	303	12	b	b	NOUN
ejpam-1745	303	13	be	be	AUX
ejpam-1745	303	14	an	an	DET
ejpam-1745	303	15	s	s	NOUN
ejpam-1745	303	16	-	-	ADJ
ejpam-1745	303	17	pure	pure	ADJ
ejpam-1745	303	18	essential	essential	ADJ
ejpam-1745	303	19	extension	extension	NOUN
ejpam-1745	303	20	of	of	ADP
ejpam-1745	303	21	a.	a.	NOUN
ejpam-1745	303	22	let	let	VERB
ejpam-1745	303	23	there	there	PRON
ejpam-1745	303	24	exist	exist	VERB
ejpam-1745	303	25	an	an	DET
ejpam-1745	303	26	element	element	NOUN
ejpam-1745	303	27	b	b	PROPN
ejpam-1745	303	28	∈	∈	PROPN
ejpam-1745	303	29	b	b	PROPN
ejpam-1745	303	30	\a	\a	VERB
ejpam-1745	303	31	.	.	PUNCT
ejpam-1745	304	1	by	by	ADP
ejpam-1745	304	2	using	use	VERB
ejpam-1745	304	3	lemma	lemma	PROPN
ejpam-1745	304	4	7	7	NUM
ejpam-1745	304	5	,	,	PUNCT
ejpam-1745	304	6	;	;	PUNCT
ejpam-1745	304	7	6=	6=	NUM
ejpam-1745	304	8	ib	ib	PROPN
ejpam-1745	304	9	6=	6=	PROPN
ejpam-1745	304	10	s.	s.	PROPN
ejpam-1745	304	11	consider	consider	VERB
ejpam-1745	304	12	t	t	PROPN
ejpam-1745	304	13	∈	∈	PROPN
ejpam-1745	304	14	s	s	PART
ejpam-1745	304	15	\	\	PROPN
ejpam-1745	304	16	ib	ib	NOUN
ejpam-1745	304	17	,	,	PUNCT
ejpam-1745	304	18	so	so	SCONJ
ejpam-1745	304	19	ib	ib	PROPN
ejpam-1745	304	20	∩	∩	PROPN
ejpam-1745	304	21	ts1	ts1	PROPN
ejpam-1745	304	22	6=	6=	PROPN
ejpam-1745	304	23	;	;	PUNCT
ejpam-1745	304	24	.	.	PUNCT
ejpam-1745	305	1	if	if	SCONJ
ejpam-1745	305	2	ts1	ts1	PROPN
ejpam-1745	305	3	6=	6=	PROPN
ejpam-1745	305	4	s	s	PROPN
ejpam-1745	305	5	,	,	PUNCT
ejpam-1745	305	6	ib	ib	NOUN
ejpam-1745	305	7	=	=	PUNCT
ejpam-1745	305	8	ib∩	ib∩	PROPN
ejpam-1745	305	9	ts1	ts1	PROPN
ejpam-1745	305	10	=	=	SYM
ejpam-1745	305	11	ts1	ts1	PROPN
ejpam-1745	305	12	.	.	PUNCT
ejpam-1745	306	1	thus	thus	ADV
ejpam-1745	306	2	t	t	X
ejpam-1745	306	3	∈	∈	PROPN
ejpam-1745	306	4	ib	ib	NOUN
ejpam-1745	306	5	,	,	PUNCT
ejpam-1745	306	6	which	which	PRON
ejpam-1745	306	7	is	be	AUX
ejpam-1745	306	8	a	a	DET
ejpam-1745	306	9	contradiction	contradiction	NOUN
ejpam-1745	306	10	.	.	PUNCT
ejpam-1745	307	1	if	if	SCONJ
ejpam-1745	307	2	ts1	ts1	PROPN
ejpam-1745	307	3	=	=	SYM
ejpam-1745	307	4	s	s	PROPN
ejpam-1745	307	5	,	,	PUNCT
ejpam-1745	307	6	then	then	ADV
ejpam-1745	307	7	ib	ib	VERB
ejpam-1745	307	8	⊆	⊆	NUM
ejpam-1745	307	9	ts1	ts1	PROPN
ejpam-1745	307	10	and	and	CCONJ
ejpam-1745	307	11	since	since	SCONJ
ejpam-1745	307	12	ib	ib	PROPN
ejpam-1745	307	13	is	be	AUX
ejpam-1745	307	14	maximal	maximal	ADJ
ejpam-1745	307	15	right	right	ADJ
ejpam-1745	307	16	ideal	ideal	NOUN
ejpam-1745	307	17	,	,	PUNCT
ejpam-1745	307	18	ib	ib	NOUN
ejpam-1745	307	19	=	=	PUNCT
ejpam-1745	307	20	ts	ts	PROPN
ejpam-1745	307	21	.	.	PUNCT
ejpam-1745	308	1	since	since	SCONJ
ejpam-1745	308	2	a→	a→	NUM
ejpam-1745	308	3	b	b	NOUN
ejpam-1745	308	4	is	be	AUX
ejpam-1745	308	5	an	an	DET
ejpam-1745	308	6	s	s	NOUN
ejpam-1745	308	7	-	-	ADJ
ejpam-1745	308	8	pure	pure	ADJ
ejpam-1745	308	9	essential	essential	ADJ
ejpam-1745	308	10	extension	extension	NOUN
ejpam-1745	308	11	,	,	PUNCT
ejpam-1745	308	12	the	the	DET
ejpam-1745	308	13	inclusion	inclusion	NOUN
ejpam-1745	308	14	map	map	NOUN
ejpam-1745	308	15	ι	ι	X
ejpam-1745	308	16	:	:	PUNCT
ejpam-1745	308	17	a→	a→	X
ejpam-1745	308	18	a∪	a∪	X
ejpam-1745	308	19	{	{	PUNCT
ejpam-1745	308	20	bt	bt	NOUN
ejpam-1745	308	21	}	}	PUNCT
ejpam-1745	308	22	is	be	AUX
ejpam-1745	308	23	also	also	ADV
ejpam-1745	308	24	s	s	NOUN
ejpam-1745	308	25	-	-	ADJ
ejpam-1745	308	26	pure	pure	ADJ
ejpam-1745	308	27	essential	essential	ADJ
ejpam-1745	308	28	and	and	CCONJ
ejpam-1745	308	29	s	s	NOUN
ejpam-1745	308	30	-	-	PUNCT
ejpam-1745	308	31	dense	dense	ADJ
ejpam-1745	308	32	which	which	PRON
ejpam-1745	308	33	is	be	AUX
ejpam-1745	308	34	a	a	DET
ejpam-1745	308	35	retraction	retraction	NOUN
ejpam-1745	308	36	by	by	ADP
ejpam-1745	308	37	lemma	lemma	PROPN
ejpam-1745	308	38	5	5	NUM
ejpam-1745	308	39	.	.	PUNCT
ejpam-1745	308	40	essentiality	essentiality	NOUN
ejpam-1745	308	41	of	of	ADP
ejpam-1745	308	42	ι	ι	PROPN
ejpam-1745	308	43	implies	imply	VERB
ejpam-1745	308	44	that	that	SCONJ
ejpam-1745	308	45	it	it	PRON
ejpam-1745	308	46	is	be	AUX
ejpam-1745	308	47	an	an	DET
ejpam-1745	308	48	isomorphism	isomorphism	NOUN
ejpam-1745	308	49	.	.	PUNCT
ejpam-1745	309	1	so	so	ADV
ejpam-1745	309	2	bt	bt	VERB
ejpam-1745	309	3	∈	∈	PROPN
ejpam-1745	310	1	a	a	PRON
ejpam-1745	311	1	and	and	CCONJ
ejpam-1745	311	2	t	t	PROPN
ejpam-1745	311	3	∈	∈	PROPN
ejpam-1745	311	4	ib	ib	NOUN
ejpam-1745	311	5	which	which	PRON
ejpam-1745	311	6	is	be	AUX
ejpam-1745	311	7	a	a	DET
ejpam-1745	311	8	contradiction	contradiction	NOUN
ejpam-1745	311	9	.	.	PUNCT
ejpam-1745	312	1	thus	thus	ADV
ejpam-1745	312	2	a=	a=	PROPN
ejpam-1745	312	3	b	b	NOUN
ejpam-1745	312	4	and	and	CCONJ
ejpam-1745	312	5	by	by	ADP
ejpam-1745	312	6	theorem	theorem	NOUN
ejpam-1745	312	7	8	8	NUM
ejpam-1745	312	8	,	,	PUNCT
ejpam-1745	312	9	a	a	PRON
ejpam-1745	312	10	is	be	AUX
ejpam-1745	312	11	an	an	DET
ejpam-1745	312	12	injective	injective	ADJ
ejpam-1745	312	13	s	s	NOUN
ejpam-1745	312	14	-	-	NOUN
ejpam-1745	312	15	act	act	NOUN
ejpam-1745	312	16	.	.	PUNCT
ejpam-1745	313	1	corollary	corollary	ADJ
ejpam-1745	313	2	11	11	NUM
ejpam-1745	313	3	.	.	PUNCT
ejpam-1745	314	1	if	if	SCONJ
ejpam-1745	314	2	s	s	PROPN
ejpam-1745	314	3	is	be	AUX
ejpam-1745	314	4	a	a	DET
ejpam-1745	314	5	simple	simple	ADJ
ejpam-1745	314	6	semigroup	semigroup	NOUN
ejpam-1745	314	7	,	,	PUNCT
ejpam-1745	314	8	then	then	ADV
ejpam-1745	314	9	every	every	DET
ejpam-1745	314	10	s	s	NOUN
ejpam-1745	314	11	-	-	ADJ
ejpam-1745	314	12	complete	complete	ADJ
ejpam-1745	314	13	s	s	NOUN
ejpam-1745	314	14	-	-	NOUN
ejpam-1745	314	15	act	act	NOUN
ejpam-1745	314	16	with	with	ADP
ejpam-1745	314	17	at	at	ADV
ejpam-1745	314	18	least	least	ADV
ejpam-1745	314	19	one	one	NUM
ejpam-1745	314	20	fixed	fix	VERB
ejpam-1745	314	21	element	element	NOUN
ejpam-1745	314	22	is	be	AUX
ejpam-1745	314	23	injective	injective	ADJ
ejpam-1745	314	24	.	.	PUNCT
ejpam-1745	315	1	corollary	corollary	ADJ
ejpam-1745	315	2	12	12	NUM
ejpam-1745	315	3	.	.	PUNCT
ejpam-1745	316	1	let	let	VERB
ejpam-1745	316	2	s	s	PRON
ejpam-1745	316	3	be	be	AUX
ejpam-1745	316	4	a	a	DET
ejpam-1745	316	5	semigroup	semigroup	NOUN
ejpam-1745	316	6	with	with	ADP
ejpam-1745	316	7	one	one	NUM
ejpam-1745	316	8	zero	zero	NUM
ejpam-1745	316	9	element	element	NOUN
ejpam-1745	316	10	s0	s0	NOUN
ejpam-1745	316	11	,	,	PUNCT
ejpam-1745	316	12	such	such	ADJ
ejpam-1745	316	13	that	that	SCONJ
ejpam-1745	316	14	the	the	DET
ejpam-1745	316	15	set	set	NOUN
ejpam-1745	316	16	of	of	ADP
ejpam-1745	316	17	whose	whose	DET
ejpam-1745	316	18	ideals	ideal	NOUN
ejpam-1745	316	19	be	be	VERB
ejpam-1745	316	20	{	{	PUNCT
ejpam-1745	316	21	;	;	PUNCT
ejpam-1745	316	22	,	,	PUNCT
ejpam-1745	316	23	{	{	PUNCT
ejpam-1745	316	24	s0	s0	PROPN
ejpam-1745	316	25	}	}	PUNCT
ejpam-1745	316	26	,	,	PUNCT
ejpam-1745	316	27	s	s	X
ejpam-1745	316	28	}	}	PUNCT
ejpam-1745	316	29	.	.	PUNCT
ejpam-1745	317	1	then	then	ADV
ejpam-1745	317	2	every	every	DET
ejpam-1745	317	3	s	s	NOUN
ejpam-1745	317	4	-	-	ADJ
ejpam-1745	317	5	complete	complete	ADJ
ejpam-1745	317	6	s	s	NOUN
ejpam-1745	317	7	-	-	NOUN
ejpam-1745	317	8	act	act	NOUN
ejpam-1745	317	9	is	be	AUX
ejpam-1745	317	10	injective	injective	ADJ
ejpam-1745	317	11	.	.	PUNCT
ejpam-1745	318	1	theorem	theorem	NOUN
ejpam-1745	318	2	13	13	NUM
ejpam-1745	318	3	.	.	PUNCT
ejpam-1745	319	1	assume	assume	VERB
ejpam-1745	319	2	that	that	SCONJ
ejpam-1745	319	3	for	for	ADP
ejpam-1745	319	4	every	every	DET
ejpam-1745	319	5	proper	proper	ADJ
ejpam-1745	319	6	nonempty	nonempty	ADJ
ejpam-1745	319	7	right	right	ADJ
ejpam-1745	319	8	ideal	ideal	NOUN
ejpam-1745	319	9	i	i	PRON
ejpam-1745	319	10	of	of	ADP
ejpam-1745	319	11	s	s	PRON
ejpam-1745	319	12	there	there	PRON
ejpam-1745	319	13	exists	exist	VERB
ejpam-1745	319	14	a	a	DET
ejpam-1745	319	15	nonempty	nonempty	ADJ
ejpam-1745	319	16	right	right	ADJ
ejpam-1745	319	17	ideal	ideal	ADJ
ejpam-1745	319	18	j	j	PROPN
ejpam-1745	319	19	of	of	ADP
ejpam-1745	319	20	s	s	PRON
ejpam-1745	319	21	such	such	ADJ
ejpam-1745	319	22	that	that	SCONJ
ejpam-1745	319	23	i	i	PROPN
ejpam-1745	319	24	∩	∩	NOUN
ejpam-1745	319	25	j	j	PROPN
ejpam-1745	320	1	=	=	PUNCT
ejpam-1745	320	2	;	;	PUNCT
ejpam-1745	320	3	.	.	PUNCT
ejpam-1745	321	1	then	then	ADV
ejpam-1745	321	2	every	every	DET
ejpam-1745	321	3	s	s	NOUN
ejpam-1745	321	4	-	-	ADJ
ejpam-1745	321	5	complete	complete	ADJ
ejpam-1745	321	6	s	s	NOUN
ejpam-1745	321	7	-	-	NOUN
ejpam-1745	321	8	act	act	NOUN
ejpam-1745	321	9	with	with	ADP
ejpam-1745	321	10	at	at	ADV
ejpam-1745	321	11	least	least	ADV
ejpam-1745	321	12	one	one	NUM
ejpam-1745	321	13	fixed	fix	VERB
ejpam-1745	321	14	element	element	NOUN
ejpam-1745	321	15	is	be	AUX
ejpam-1745	321	16	injective	injective	ADJ
ejpam-1745	321	17	.	.	PUNCT
ejpam-1745	322	1	proof	proof	NOUN
ejpam-1745	322	2	.	.	PUNCT
ejpam-1745	323	1	we	we	PRON
ejpam-1745	323	2	begin	begin	VERB
ejpam-1745	323	3	by	by	ADP
ejpam-1745	323	4	proving	prove	VERB
ejpam-1745	323	5	s2	s2	NOUN
ejpam-1745	323	6	=	=	PUNCT
ejpam-1745	323	7	s.	s.	PROPN
ejpam-1745	323	8	let	let	VERB
ejpam-1745	323	9	s2	s2	PROPN
ejpam-1745	323	10	6=	6=	NUM
ejpam-1745	323	11	s.	s.	PROPN
ejpam-1745	323	12	then	then	ADV
ejpam-1745	323	13	there	there	PRON
ejpam-1745	323	14	exists	exist	VERB
ejpam-1745	323	15	a	a	DET
ejpam-1745	323	16	right	right	ADJ
ejpam-1745	323	17	ideal	ideal	NOUN
ejpam-1745	323	18	j	j	PROPN
ejpam-1745	323	19	of	of	ADP
ejpam-1745	323	20	s	s	PRON
ejpam-1745	323	21	such	such	ADJ
ejpam-1745	323	22	that	that	DET
ejpam-1745	323	23	s2	s2	PROPN
ejpam-1745	323	24	∩	∩	NOUN
ejpam-1745	323	25	j	j	PROPN
ejpam-1745	323	26	=	=	PUNCT
ejpam-1745	323	27	;	;	PUNCT
ejpam-1745	323	28	.	.	PUNCT
ejpam-1745	324	1	consider	consider	VERB
ejpam-1745	324	2	x	x	X
ejpam-1745	324	3	∈	∈	PROPN
ejpam-1745	324	4	j	j	PROPN
ejpam-1745	324	5	.	.	PUNCT
ejpam-1745	325	1	for	for	ADP
ejpam-1745	325	2	every	every	DET
ejpam-1745	325	3	s	s	PROPN
ejpam-1745	325	4	∈	∈	PROPN
ejpam-1745	325	5	s	s	PROPN
ejpam-1745	325	6	,	,	PUNCT
ejpam-1745	325	7	xs	xs	PROPN
ejpam-1745	325	8	∈	∈	PROPN
ejpam-1745	325	9	j	j	PROPN
ejpam-1745	325	10	∩	∩	PROPN
ejpam-1745	325	11	s2	s2	PROPN
ejpam-1745	325	12	,	,	PUNCT
ejpam-1745	325	13	which	which	PRON
ejpam-1745	325	14	is	be	AUX
ejpam-1745	325	15	impossible	impossible	ADJ
ejpam-1745	325	16	.	.	PUNCT
ejpam-1745	326	1	now	now	ADV
ejpam-1745	326	2	the	the	DET
ejpam-1745	326	3	proof	proof	NOUN
ejpam-1745	326	4	is	be	AUX
ejpam-1745	326	5	straightforward	straightforward	ADJ
ejpam-1745	326	6	by	by	ADP
ejpam-1745	326	7	using	use	VERB
ejpam-1745	326	8	theorem	theorem	ADJ
ejpam-1745	326	9	9	9	NUM
ejpam-1745	326	10	and	and	CCONJ
ejpam-1745	326	11	lemma	lemma	PROPN
ejpam-1745	326	12	8	8	NUM
ejpam-1745	326	13	.	.	PUNCT
ejpam-1745	326	14	corollary	corollary	ADJ
ejpam-1745	326	15	13	13	NUM
ejpam-1745	326	16	.	.	PUNCT
ejpam-1745	327	1	let	let	VERB
ejpam-1745	327	2	s	s	PRON
ejpam-1745	327	3	be	be	AUX
ejpam-1745	327	4	a	a	DET
ejpam-1745	327	5	boolean	boolean	ADJ
ejpam-1745	327	6	algebra	algebra	NOUN
ejpam-1745	327	7	on	on	ADP
ejpam-1745	327	8	ideals(i.e	ideals(i.e	PROPN
ejpam-1745	327	9	compliment	compliment	NOUN
ejpam-1745	327	10	of	of	ADP
ejpam-1745	327	11	every	every	DET
ejpam-1745	327	12	right	right	ADJ
ejpam-1745	327	13	ideal	ideal	NOUN
ejpam-1745	327	14	is	be	AUX
ejpam-1745	327	15	a	a	DET
ejpam-1745	327	16	right	right	ADJ
ejpam-1745	327	17	ideal	ideal	NOUN
ejpam-1745	327	18	)	)	PUNCT
ejpam-1745	327	19	.	.	PUNCT
ejpam-1745	328	1	then	then	ADV
ejpam-1745	328	2	every	every	DET
ejpam-1745	328	3	s	s	NOUN
ejpam-1745	328	4	-	-	ADJ
ejpam-1745	328	5	complete	complete	ADJ
ejpam-1745	328	6	s	s	NOUN
ejpam-1745	328	7	-	-	NOUN
ejpam-1745	328	8	act	act	NOUN
ejpam-1745	328	9	with	with	ADP
ejpam-1745	328	10	at	at	ADV
ejpam-1745	328	11	least	least	ADV
ejpam-1745	328	12	one	one	NUM
ejpam-1745	328	13	fixed	fix	VERB
ejpam-1745	328	14	element	element	NOUN
ejpam-1745	328	15	is	be	AUX
ejpam-1745	328	16	injective	injective	ADJ
ejpam-1745	328	17	.	.	PUNCT
ejpam-1745	329	1	corollary	corollary	ADJ
ejpam-1745	329	2	14	14	NUM
ejpam-1745	329	3	.	.	PUNCT
ejpam-1745	330	1	if	if	SCONJ
ejpam-1745	330	2	s	s	NOUN
ejpam-1745	330	3	is	be	AUX
ejpam-1745	330	4	a	a	DET
ejpam-1745	330	5	left	left	ADJ
ejpam-1745	330	6	zero	zero	NUM
ejpam-1745	330	7	semigroup	semigroup	NOUN
ejpam-1745	330	8	,	,	PUNCT
ejpam-1745	330	9	then	then	ADV
ejpam-1745	330	10	every	every	DET
ejpam-1745	330	11	s	s	NOUN
ejpam-1745	330	12	-	-	ADJ
ejpam-1745	330	13	complete	complete	ADJ
ejpam-1745	330	14	s	s	NOUN
ejpam-1745	330	15	-	-	NOUN
ejpam-1745	330	16	act	act	NOUN
ejpam-1745	330	17	is	be	AUX
ejpam-1745	330	18	injective	injective	ADJ
ejpam-1745	330	19	.	.	PUNCT
ejpam-1745	331	1	there	there	PRON
ejpam-1745	331	2	is	be	VERB
ejpam-1745	331	3	still	still	ADV
ejpam-1745	331	4	an	an	DET
ejpam-1745	331	5	open	open	ADJ
ejpam-1745	331	6	question	question	NOUN
ejpam-1745	331	7	concerning	concern	VERB
ejpam-1745	331	8	s	s	NOUN
ejpam-1745	331	9	-	-	NOUN
ejpam-1745	331	10	complete	complete	ADJ
ejpam-1745	331	11	:	:	PUNCT
ejpam-1745	331	12	is	be	AUX
ejpam-1745	331	13	there	there	PRON
ejpam-1745	331	14	a	a	DET
ejpam-1745	331	15	necessary	necessary	ADJ
ejpam-1745	331	16	and	and	CCONJ
ejpam-1745	331	17	sufficient	sufficient	ADJ
ejpam-1745	331	18	condition	condition	NOUN
ejpam-1745	331	19	on	on	ADP
ejpam-1745	331	20	s	s	PRON
ejpam-1745	331	21	such	such	ADJ
ejpam-1745	331	22	that	that	SCONJ
ejpam-1745	331	23	all	all	DET
ejpam-1745	331	24	s	s	NOUN
ejpam-1745	331	25	-	-	ADJ
ejpam-1745	331	26	complete	complete	ADJ
ejpam-1745	331	27	s	s	NOUN
ejpam-1745	331	28	-	-	PUNCT
ejpam-1745	331	29	acts	act	VERB
ejpam-1745	331	30	a	a	PRON
ejpam-1745	331	31	with	with	ADP
ejpam-1745	331	32	at	at	ADV
ejpam-1745	331	33	least	least	ADV
ejpam-1745	331	34	one	one	NUM
ejpam-1745	331	35	fixed	fix	VERB
ejpam-1745	331	36	element	element	NOUN
ejpam-1745	331	37	is	be	AUX
ejpam-1745	331	38	injective	injective	ADJ
ejpam-1745	331	39	?	?	PUNCT
ejpam-1745	332	1	references	reference	NOUN
ejpam-1745	332	2	221	221	NUM
ejpam-1745	332	3	acknowledgements	acknowledgement	NOUN
ejpam-1745	332	4	i	i	PRON
ejpam-1745	332	5	would	would	AUX
ejpam-1745	332	6	like	like	VERB
ejpam-1745	332	7	to	to	PART
ejpam-1745	332	8	express	express	VERB
ejpam-1745	332	9	my	my	PRON
ejpam-1745	332	10	appreciation	appreciation	NOUN
ejpam-1745	332	11	to	to	ADP
ejpam-1745	332	12	the	the	DET
ejpam-1745	332	13	referee	referee	NOUN
ejpam-1745	332	14	for	for	ADP
ejpam-1745	332	15	carefully	carefully	ADV
ejpam-1745	332	16	reading	read	VERB
ejpam-1745	332	17	the	the	DET
ejpam-1745	332	18	paper	paper	NOUN
ejpam-1745	332	19	.	.	PUNCT
ejpam-1745	333	1	references	reference	NOUN
ejpam-1745	333	2	[	[	X
ejpam-1745	333	3	1	1	NUM
ejpam-1745	333	4	]	]	X
ejpam-1745	333	5	h.	h.	NOUN
ejpam-1745	333	6	barzegar	barzegar	PROPN
ejpam-1745	333	7	and	and	CCONJ
ejpam-1745	333	8	m.m	m.m	PROPN
ejpam-1745	333	9	.	.	PROPN
ejpam-1745	333	10	ebrahimi	ebrahimi	PROPN
ejpam-1745	333	11	.	.	PUNCT
ejpam-1745	334	1	sequentially	sequentially	ADV
ejpam-1745	334	2	pure	pure	ADJ
ejpam-1745	334	3	monomorphism	monomorphism	NOUN
ejpam-1745	334	4	of	of	ADP
ejpam-1745	334	5	acts	act	NOUN
ejpam-1745	334	6	over	over	ADP
ejpam-1745	334	7	semigroups	semigroup	NOUN
ejpam-1745	334	8	.	.	PUNCT
ejpam-1745	335	1	european	european	ADJ
ejpam-1745	335	2	journal	journal	PROPN
ejpam-1745	335	3	of	of	ADP
ejpam-1745	335	4	pure	pure	ADJ
ejpam-1745	335	5	and	and	CCONJ
ejpam-1745	335	6	applied	applied	ADJ
ejpam-1745	335	7	mathematics	mathematic	NOUN
ejpam-1745	335	8	,	,	PUNCT
ejpam-1745	335	9	1(4):41–55	1(4):41–55	NUM
ejpam-1745	335	10	,	,	PUNCT
ejpam-1745	335	11	2008	2008	NUM
ejpam-1745	335	12	.	.	PUNCT
ejpam-1745	336	1	[	[	X
ejpam-1745	336	2	2	2	X
ejpam-1745	336	3	]	]	PUNCT
ejpam-1745	336	4	h.	h.	NOUN
ejpam-1745	336	5	barzegar	barzegar	PROPN
ejpam-1745	336	6	,	,	PUNCT
ejpam-1745	336	7	m.m	m.m	PROPN
ejpam-1745	336	8	.	.	PROPN
ejpam-1745	336	9	ebrahimi	ebrahimi	PROPN
ejpam-1745	336	10	,	,	PUNCT
ejpam-1745	336	11	and	and	CCONJ
ejpam-1745	336	12	m.	m.	NOUN
ejpam-1745	336	13	mahmoudi	mahmoudi	NOUN
ejpam-1745	336	14	.	.	PUNCT
ejpam-1745	337	1	essentiality	essentiality	NOUN
ejpam-1745	337	2	and	and	CCONJ
ejpam-1745	337	3	injectivity	injectivity	NOUN
ejpam-1745	337	4	relative	relative	ADJ
ejpam-1745	337	5	to	to	ADP
ejpam-1745	337	6	sequential	sequential	ADJ
ejpam-1745	337	7	purity	purity	NOUN
ejpam-1745	337	8	of	of	ADP
ejpam-1745	337	9	acts	act	NOUN
ejpam-1745	337	10	.	.	PUNCT
ejpam-1745	338	1	semigroup	semigroup	PROPN
ejpam-1745	338	2	forum	forum	PROPN
ejpam-1745	338	3	,	,	PUNCT
ejpam-1745	338	4	79:128–144	79:128–144	PROPN
ejpam-1745	338	5	,	,	PUNCT
ejpam-1745	338	6	2009	2009	NUM
ejpam-1745	338	7	.	.	PUNCT
ejpam-1745	339	1	[	[	X
ejpam-1745	339	2	3	3	X
ejpam-1745	339	3	]	]	PUNCT
ejpam-1745	339	4	p.	p.	NOUN
ejpam-1745	339	5	berthiaume	berthiaume	PROPN
ejpam-1745	339	6	.	.	PUNCT
ejpam-1745	340	1	the	the	DET
ejpam-1745	340	2	injective	injective	ADJ
ejpam-1745	340	3	envelope	envelope	NOUN
ejpam-1745	340	4	of	of	ADP
ejpam-1745	340	5	s	s	NOUN
ejpam-1745	340	6	-	-	PUNCT
ejpam-1745	340	7	sets	set	NOUN
ejpam-1745	340	8	.	.	PUNCT
ejpam-1745	341	1	canad	canad	PROPN
ejpam-1745	341	2	.	.	PUNCT
ejpam-1745	342	1	math	math	NOUN
ejpam-1745	342	2	.	.	PUNCT
ejpam-1745	343	1	bull	bull	PROPN
ejpam-1745	343	2	.	.	PUNCT
ejpam-1745	343	3	,	,	PUNCT
ejpam-1745	343	4	10(2):261–273	10(2):261–273	NUM
ejpam-1745	343	5	,	,	PUNCT
ejpam-1745	343	6	1967	1967	NUM
ejpam-1745	343	7	.	.	PUNCT
ejpam-1745	344	1	[	[	X
ejpam-1745	344	2	4	4	NUM
ejpam-1745	344	3	]	]	X
ejpam-1745	344	4	m.m	m.m	PROPN
ejpam-1745	344	5	.	.	PROPN
ejpam-1745	344	6	ebrahimi	ebrahimi	PROPN
ejpam-1745	344	7	and	and	CCONJ
ejpam-1745	344	8	m.	m.	NOUN
ejpam-1745	344	9	mahmoudi	mahmoudi	PROPN
ejpam-1745	344	10	.	.	PUNCT
ejpam-1745	344	11	purity	purity	NOUN
ejpam-1745	344	12	and	and	CCONJ
ejpam-1745	344	13	equational	equational	ADJ
ejpam-1745	344	14	compactness	compactness	NOUN
ejpam-1745	344	15	of	of	ADP
ejpam-1745	344	16	projection	projection	NOUN
ejpam-1745	344	17	algebras	algebra	NOUN
ejpam-1745	344	18	.	.	PUNCT
ejpam-1745	344	19	applied	apply	VERB
ejpam-1745	344	20	categorical	categorical	ADJ
ejpam-1745	344	21	structure	structure	NOUN
ejpam-1745	344	22	,	,	PUNCT
ejpam-1745	344	23	9:381–394	9:381–394	NOUN
ejpam-1745	344	24	,	,	PUNCT
ejpam-1745	344	25	2001	2001	NUM
ejpam-1745	344	26	.	.	PUNCT
ejpam-1745	345	1	[	[	X
ejpam-1745	345	2	5	5	NUM
ejpam-1745	345	3	]	]	X
ejpam-1745	345	4	m.m	m.m	PROPN
ejpam-1745	345	5	.	.	PROPN
ejpam-1745	345	6	ebrahimi	ebrahimi	PROPN
ejpam-1745	345	7	,	,	PUNCT
ejpam-1745	345	8	m.	m.	NOUN
ejpam-1745	345	9	mahmoudi	mahmoudi	NOUN
ejpam-1745	345	10	,	,	PUNCT
ejpam-1745	345	11	and	and	CCONJ
ejpam-1745	345	12	l.	l.	PROPN
ejpam-1745	345	13	shahbaz	shahbaz	PROPN
ejpam-1745	345	14	.	.	PUNCT
ejpam-1745	346	1	proper	proper	ADJ
ejpam-1745	346	2	behaviour	behaviour	NOUN
ejpam-1745	346	3	of	of	ADP
ejpam-1745	346	4	sequential	sequential	ADJ
ejpam-1745	346	5	injectivity	injectivity	NOUN
ejpam-1745	346	6	of	of	ADP
ejpam-1745	346	7	acts	act	NOUN
ejpam-1745	346	8	over	over	ADP
ejpam-1745	346	9	semigroups	semigroup	NOUN
ejpam-1745	346	10	.	.	PUNCT
ejpam-1745	347	1	communication	communication	NOUN
ejpam-1745	347	2	in	in	ADP
ejpam-1745	347	3	algebra	algebra	PROPN
ejpam-1745	347	4	,	,	PUNCT
ejpam-1745	347	5	37(7):2511–2521	37(7):2511–2521	PROPN
ejpam-1745	347	6	,	,	PUNCT
ejpam-1745	347	7	2009	2009	NUM
ejpam-1745	347	8	.	.	PUNCT
ejpam-1745	348	1	[	[	X
ejpam-1745	348	2	6	6	NUM
ejpam-1745	348	3	]	]	PUNCT
ejpam-1745	348	4	e.	e.	PROPN
ejpam-1745	348	5	giuli	giuli	PROPN
ejpam-1745	348	6	.	.	PUNCT
ejpam-1745	349	1	on	on	ADP
ejpam-1745	349	2	m	m	ADV
ejpam-1745	349	3	-	-	PUNCT
ejpam-1745	349	4	separated	separate	VERB
ejpam-1745	349	5	projection	projection	NOUN
ejpam-1745	349	6	spaces	space	NOUN
ejpam-1745	349	7	.	.	PUNCT
ejpam-1745	350	1	applied	apply	VERB
ejpam-1745	350	2	categorical	categorical	ADJ
ejpam-1745	350	3	structure	structure	NOUN
ejpam-1745	350	4	,	,	PUNCT
ejpam-1745	350	5	2:91–99	2:91–99	NUM
ejpam-1745	350	6	,	,	PUNCT
ejpam-1745	350	7	1994	1994	NUM
ejpam-1745	350	8	.	.	PUNCT
ejpam-1745	351	1	[	[	X
ejpam-1745	351	2	7	7	X
ejpam-1745	351	3	]	]	X
ejpam-1745	351	4	v.	v.	PROPN
ejpam-1745	351	5	gould	gould	PROPN
ejpam-1745	351	6	.	.	PUNCT
ejpam-1745	352	1	the	the	DET
ejpam-1745	352	2	characterisation	characterisation	NOUN
ejpam-1745	352	3	of	of	ADP
ejpam-1745	352	4	monoids	monoid	NOUN
ejpam-1745	352	5	by	by	ADP
ejpam-1745	352	6	properties	property	NOUN
ejpam-1745	352	7	of	of	ADP
ejpam-1745	352	8	their	their	PRON
ejpam-1745	352	9	s	s	NOUN
ejpam-1745	352	10	-	-	NOUN
ejpam-1745	352	11	systems	system	NOUN
ejpam-1745	352	12	.	.	PUNCT
ejpam-1745	353	1	semigroup	semigroup	PROPN
ejpam-1745	353	2	forum	forum	PROPN
ejpam-1745	353	3	,	,	PUNCT
ejpam-1745	353	4	32(3):251–265	32(3):251–265	NUM
ejpam-1745	353	5	,	,	PUNCT
ejpam-1745	353	6	1985	1985	NUM
ejpam-1745	353	7	.	.	PUNCT
ejpam-1745	354	1	[	[	X
ejpam-1745	354	2	8	8	NUM
ejpam-1745	354	3	]	]	X
ejpam-1745	354	4	v.	v.	PROPN
ejpam-1745	354	5	gould	gould	PROPN
ejpam-1745	354	6	.	.	PUNCT
ejpam-1745	355	1	completely	completely	ADV
ejpam-1745	355	2	right	right	ADJ
ejpam-1745	355	3	pure	pure	ADJ
ejpam-1745	355	4	monoids	monoid	NOUN
ejpam-1745	355	5	.	.	PUNCT
ejpam-1745	356	1	proc.roy	proc.roy	PROPN
ejpam-1745	356	2	.	.	PROPN
ejpam-1745	356	3	irish	irish	PROPN
ejpam-1745	356	4	acad	acad	PROPN
ejpam-1745	356	5	,	,	PUNCT
ejpam-1745	356	6	section	section	NOUN
ejpam-1745	356	7	a	a	PRON
ejpam-1745	356	8	,	,	PUNCT
ejpam-1745	356	9	87:73–82	87:73–82	NUM
ejpam-1745	356	10	,	,	PUNCT
ejpam-1745	356	11	1987	1987	NUM
ejpam-1745	356	12	.	.	PUNCT
ejpam-1745	357	1	[	[	X
ejpam-1745	357	2	9	9	NUM
ejpam-1745	357	3	]	]	PUNCT
ejpam-1745	357	4	m.	m.	NOUN
ejpam-1745	357	5	kilp	kilp	PROPN
ejpam-1745	357	6	,	,	PUNCT
ejpam-1745	357	7	u.	u.	PROPN
ejpam-1745	357	8	knauer	knauer	PROPN
ejpam-1745	357	9	,	,	PUNCT
ejpam-1745	357	10	and	and	CCONJ
ejpam-1745	357	11	a.	a.	NOUN
ejpam-1745	357	12	mikhalev	mikhalev	PROPN
ejpam-1745	357	13	.	.	PUNCT
ejpam-1745	358	1	monoids	monoids	PROPN
ejpam-1745	358	2	,	,	PUNCT
ejpam-1745	358	3	acts	act	NOUN
ejpam-1745	358	4	and	and	CCONJ
ejpam-1745	358	5	categories	category	NOUN
ejpam-1745	358	6	.	.	PUNCT
ejpam-1745	359	1	walter	walter	PROPN
ejpam-1745	359	2	de	de	PROPN
ejpam-1745	359	3	gruyter	gruyter	PROPN
ejpam-1745	359	4	,	,	PUNCT
ejpam-1745	359	5	berlin	berlin	PROPN
ejpam-1745	359	6	,	,	PUNCT
ejpam-1745	359	7	new	new	PROPN
ejpam-1745	359	8	york	york	PROPN
ejpam-1745	359	9	,	,	PUNCT
ejpam-1745	359	10	2000	2000	NUM
ejpam-1745	359	11	.	.	PUNCT
ejpam-1745	360	1	[	[	X
ejpam-1745	360	2	10	10	NUM
ejpam-1745	360	3	]	]	PUNCT
ejpam-1745	360	4	m.	m.	NOUN
ejpam-1745	360	5	mahmoudi	mahmoudi	NOUN
ejpam-1745	360	6	and	and	CCONJ
ejpam-1745	360	7	gh	gh	PROPN
ejpam-1745	360	8	.	.	PROPN
ejpam-1745	360	9	moghaddasi	moghaddasi	PROPN
ejpam-1745	360	10	.	.	PUNCT
ejpam-1745	361	1	sequential	sequential	ADJ
ejpam-1745	361	2	purity	purity	NOUN
ejpam-1745	361	3	and	and	CCONJ
ejpam-1745	361	4	injectivity	injectivity	NOUN
ejpam-1745	361	5	of	of	ADP
ejpam-1745	361	6	acts	act	NOUN
ejpam-1745	361	7	over	over	ADP
ejpam-1745	361	8	some	some	DET
ejpam-1745	361	9	classes	class	NOUN
ejpam-1745	361	10	of	of	ADP
ejpam-1745	361	11	semigroups	semigroup	NOUN
ejpam-1745	361	12	.	.	PUNCT
ejpam-1745	362	1	taiwanese	taiwanese	ADJ
ejpam-1745	362	2	journal	journal	NOUN
ejpam-1745	362	3	of	of	ADP
ejpam-1745	362	4	mathematics	mathematic	NOUN
ejpam-1745	362	5	,	,	PUNCT
ejpam-1745	362	6	15(2):733–744	15(2):733–744	NUM
ejpam-1745	362	7	,	,	PUNCT
ejpam-1745	362	8	2011	2011	NUM
ejpam-1745	362	9	.	.	PUNCT
ejpam-1745	363	1	[	[	X
ejpam-1745	363	2	11	11	NUM
ejpam-1745	363	3	]	]	PUNCT
ejpam-1745	363	4	m.	m.	NOUN
ejpam-1745	363	5	mahmoudi	mahmoudi	NOUN
ejpam-1745	363	6	and	and	CCONJ
ejpam-1745	363	7	l.	l.	PROPN
ejpam-1745	363	8	shahbaz	shahbaz	PROPN
ejpam-1745	363	9	.	.	PUNCT
ejpam-1745	364	1	characterizing	characterize	VERB
ejpam-1745	364	2	semigroups	semigroup	NOUN
ejpam-1745	364	3	by	by	ADP
ejpam-1745	364	4	sequentially	sequentially	ADV
ejpam-1745	364	5	dense	dense	ADJ
ejpam-1745	364	6	injective	injective	ADJ
ejpam-1745	364	7	acts	act	NOUN
ejpam-1745	364	8	.	.	PUNCT
ejpam-1745	365	1	semigroup	semigroup	PROPN
ejpam-1745	365	2	forum	forum	PROPN
ejpam-1745	365	3	,	,	PUNCT
ejpam-1745	365	4	75(1):116–128	75(1):116–128	PROPN
ejpam-1745	365	5	,	,	PUNCT
ejpam-1745	365	6	2007	2007	NUM
ejpam-1745	365	7	.	.	PUNCT
ejpam-1745	366	1	[	[	X
ejpam-1745	366	2	12	12	NUM
ejpam-1745	366	3	]	]	PUNCT
ejpam-1745	366	4	m.	m.	NOUN
ejpam-1745	366	5	mahmoudi	mahmoudi	NOUN
ejpam-1745	366	6	and	and	CCONJ
ejpam-1745	366	7	l.	l.	PROPN
ejpam-1745	366	8	shahbaz	shahbaz	PROPN
ejpam-1745	366	9	.	.	PUNCT
ejpam-1745	367	1	sequential	sequential	ADJ
ejpam-1745	367	2	dense	dense	ADJ
ejpam-1745	367	3	essential	essential	ADJ
ejpam-1745	367	4	monomorphisms	monomorphism	NOUN
ejpam-1745	367	5	of	of	ADP
ejpam-1745	367	6	acts	act	NOUN
ejpam-1745	367	7	over	over	ADP
ejpam-1745	367	8	semigroups	semigroup	NOUN
ejpam-1745	367	9	.	.	PUNCT
ejpam-1745	368	1	applied	apply	VERB
ejpam-1745	368	2	categorical	categorical	ADJ
ejpam-1745	368	3	structure	structure	NOUN
ejpam-1745	368	4	,	,	PUNCT
ejpam-1745	368	5	18:461–471	18:461–471	NUM
ejpam-1745	368	6	,	,	PUNCT
ejpam-1745	368	7	2010	2010	NUM
ejpam-1745	368	8	.	.	PUNCT