id	sid	tid	token	lemma	pos
ejpam-2418	1	1	compile	compile	NOUN
ejpam-2418	1	2	/	/	SYM
ejpam-2418	1	3	output.dvi	output.dvi	NOUN
ejpam-2418	1	4	european	european	ADJ
ejpam-2418	1	5	journal	journal	NOUN
ejpam-2418	1	6	of	of	ADP
ejpam-2418	1	7	pure	pure	ADJ
ejpam-2418	1	8	and	and	CCONJ
ejpam-2418	1	9	applied	apply	VERB
ejpam-2418	1	10	mathematics	mathematic	NOUN
ejpam-2418	1	11	vol	vol	NOUN
ejpam-2418	1	12	.	.	PROPN
ejpam-2418	2	1	9	9	NUM
ejpam-2418	2	2	,	,	PUNCT
ejpam-2418	2	3	no	no	INTJ
ejpam-2418	2	4	.	.	NOUN
ejpam-2418	2	5	1	1	NUM
ejpam-2418	2	6	,	,	PUNCT
ejpam-2418	2	7	2016	2016	NUM
ejpam-2418	2	8	,	,	PUNCT
ejpam-2418	2	9	19	19	NUM
ejpam-2418	2	10	-	-	SYM
ejpam-2418	2	11	26	26	NUM
ejpam-2418	2	12	issn	issn	PROPN
ejpam-2418	2	13	1307	1307	NUM
ejpam-2418	2	14	-	-	SYM
ejpam-2418	2	15	5543	5543	NUM
ejpam-2418	2	16	–	–	PUNCT
ejpam-2418	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2418	2	18	essentiality	essentiality	NOUN
ejpam-2418	2	19	in	in	ADP
ejpam-2418	2	20	the	the	DET
ejpam-2418	2	21	category	category	NOUN
ejpam-2418	2	22	of	of	ADP
ejpam-2418	2	23	s	s	NOUN
ejpam-2418	2	24	-	-	PUNCT
ejpam-2418	2	25	acts	act	NOUN
ejpam-2418	2	26	hasan	hasan	PROPN
ejpam-2418	2	27	barzegar	barzegar	PROPN
ejpam-2418	2	28	department	department	PROPN
ejpam-2418	2	29	of	of	ADP
ejpam-2418	2	30	mathematics	mathematics	PROPN
ejpam-2418	2	31	,	,	PUNCT
ejpam-2418	2	32	tafresh	tafresh	PROPN
ejpam-2418	2	33	university	university	NOUN
ejpam-2418	2	34	,	,	PUNCT
ejpam-2418	2	35	tafresh	tafresh	NOUN
ejpam-2418	2	36	,	,	PUNCT
ejpam-2418	2	37	iran	iran	PROPN
ejpam-2418	2	38	.	.	PUNCT
ejpam-2418	3	1	abstract	abstract	ADJ
ejpam-2418	3	2	.	.	PUNCT
ejpam-2418	4	1	essentiality	essentiality	NOUN
ejpam-2418	4	2	is	be	AUX
ejpam-2418	4	3	an	an	DET
ejpam-2418	4	4	important	important	ADJ
ejpam-2418	4	5	notion	notion	NOUN
ejpam-2418	4	6	closely	closely	ADV
ejpam-2418	4	7	related	relate	VERB
ejpam-2418	4	8	to	to	ADP
ejpam-2418	4	9	injectivity	injectivity	NOUN
ejpam-2418	4	10	.	.	PUNCT
ejpam-2418	5	1	in	in	ADP
ejpam-2418	5	2	this	this	DET
ejpam-2418	5	3	paper	paper	NOUN
ejpam-2418	5	4	,	,	PUNCT
ejpam-2418	5	5	we	we	PRON
ejpam-2418	5	6	study	study	VERB
ejpam-2418	5	7	essentiality	essentiality	NOUN
ejpam-2418	5	8	with	with	ADP
ejpam-2418	5	9	respect	respect	NOUN
ejpam-2418	5	10	to	to	ADP
ejpam-2418	5	11	monomorphisms	monomorphism	NOUN
ejpam-2418	5	12	of	of	ADP
ejpam-2418	5	13	acts	act	NOUN
ejpam-2418	5	14	.	.	PUNCT
ejpam-2418	6	1	we	we	PRON
ejpam-2418	6	2	give	give	VERB
ejpam-2418	6	3	some	some	DET
ejpam-2418	6	4	criterion	criterion	NOUN
ejpam-2418	6	5	to	to	PART
ejpam-2418	6	6	characterize	characterize	VERB
ejpam-2418	6	7	and	and	CCONJ
ejpam-2418	6	8	describe	describe	VERB
ejpam-2418	6	9	essentiality	essentiality	NOUN
ejpam-2418	6	10	explicitly	explicitly	ADV
ejpam-2418	6	11	.	.	PUNCT
ejpam-2418	7	1	2010	2010	NUM
ejpam-2418	7	2	mathematics	mathematic	NOUN
ejpam-2418	7	3	subject	subject	NOUN
ejpam-2418	7	4	classifications	classification	NOUN
ejpam-2418	7	5	:	:	PUNCT
ejpam-2418	7	6	primary	primary	ADJ
ejpam-2418	7	7	20m30	20m30	NOUN
ejpam-2418	7	8	,	,	PUNCT
ejpam-2418	7	9	08a60	08a60	NUM
ejpam-2418	7	10	;	;	PUNCT
ejpam-2418	7	11	secondary	secondary	ADJ
ejpam-2418	7	12	08b30	08b30	NOUN
ejpam-2418	7	13	.	.	PUNCT
ejpam-2418	8	1	key	key	ADJ
ejpam-2418	8	2	words	word	NOUN
ejpam-2418	8	3	and	and	CCONJ
ejpam-2418	8	4	phrases	phrase	NOUN
ejpam-2418	8	5	:	:	PUNCT
ejpam-2418	8	6	essential	essential	ADJ
ejpam-2418	8	7	extension	extension	NOUN
ejpam-2418	8	8	,	,	PUNCT
ejpam-2418	8	9	s	s	NOUN
ejpam-2418	8	10	-	-	PUNCT
ejpam-2418	8	11	acts	act	VERB
ejpam-2418	8	12	1	1	NUM
ejpam-2418	8	13	.	.	PUNCT
ejpam-2418	9	1	introduction	introduction	NOUN
ejpam-2418	9	2	and	and	CCONJ
ejpam-2418	9	3	preliminaries	preliminary	NOUN
ejpam-2418	9	4	an	an	DET
ejpam-2418	9	5	important	important	ADJ
ejpam-2418	9	6	notion	notion	NOUN
ejpam-2418	9	7	related	relate	VERB
ejpam-2418	9	8	to	to	ADP
ejpam-2418	9	9	injectivity	injectivity	NOUN
ejpam-2418	9	10	with	with	ADP
ejpam-2418	9	11	respect	respect	NOUN
ejpam-2418	9	12	to	to	ADP
ejpam-2418	9	13	monomorphisms	monomorphism	NOUN
ejpam-2418	9	14	or	or	CCONJ
ejpam-2418	9	15	any	any	DET
ejpam-2418	9	16	other	other	ADJ
ejpam-2418	9	17	classm	classm	NOUN
ejpam-2418	9	18	of	of	ADP
ejpam-2418	9	19	morphisms	morphism	NOUN
ejpam-2418	9	20	in	in	ADP
ejpam-2418	9	21	a	a	DET
ejpam-2418	9	22	categorya	categorya	NOUN
ejpam-2418	9	23	,	,	PUNCT
ejpam-2418	9	24	is	be	AUX
ejpam-2418	9	25	essentiality	essentiality	NOUN
ejpam-2418	9	26	.	.	PUNCT
ejpam-2418	10	1	in	in	ADP
ejpam-2418	10	2	fact	fact	NOUN
ejpam-2418	10	3	,	,	PUNCT
ejpam-2418	10	4	injectivity	injectivity	PROPN
ejpam-2418	10	5	is	be	AUX
ejpam-2418	10	6	characterized	characterize	VERB
ejpam-2418	10	7	and	and	CCONJ
ejpam-2418	10	8	injective	injective	ADJ
ejpam-2418	10	9	hulls	hull	NOUN
ejpam-2418	10	10	are	be	AUX
ejpam-2418	10	11	defined	define	VERB
ejpam-2418	10	12	using	use	VERB
ejpam-2418	10	13	essentiality	essentiality	NOUN
ejpam-2418	10	14	(	(	PUNCT
ejpam-2418	10	15	see	see	VERB
ejpam-2418	10	16	,	,	PUNCT
ejpam-2418	10	17	for	for	ADP
ejpam-2418	10	18	example	example	NOUN
ejpam-2418	10	19	,	,	PUNCT
ejpam-2418	10	20	[	[	X
ejpam-2418	10	21	1	1	NUM
ejpam-2418	10	22	,	,	PUNCT
ejpam-2418	10	23	10	10	NUM
ejpam-2418	10	24	]	]	PUNCT
ejpam-2418	10	25	and	and	CCONJ
ejpam-2418	10	26	[	[	X
ejpam-2418	10	27	5	5	NUM
ejpam-2418	10	28	]	]	PUNCT
ejpam-2418	10	29	)	)	PUNCT
ejpam-2418	10	30	.	.	PUNCT
ejpam-2418	11	1	throughout	throughout	ADP
ejpam-2418	11	2	this	this	DET
ejpam-2418	11	3	paper	paper	NOUN
ejpam-2418	11	4	s	s	VERB
ejpam-2418	11	5	will	will	AUX
ejpam-2418	11	6	be	be	AUX
ejpam-2418	11	7	denoted	denote	VERB
ejpam-2418	11	8	by	by	ADP
ejpam-2418	11	9	the	the	DET
ejpam-2418	11	10	semigroup	semigroup	NOUN
ejpam-2418	11	11	with	with	ADP
ejpam-2418	11	12	or	or	CCONJ
ejpam-2418	11	13	without	without	ADP
ejpam-2418	11	14	identity	identity	NOUN
ejpam-2418	11	15	.	.	PUNCT
ejpam-2418	12	1	we	we	PRON
ejpam-2418	12	2	take	take	VERB
ejpam-2418	12	3	a	a	DET
ejpam-2418	12	4	=	=	PUNCT
ejpam-2418	12	5	act	act	NOUN
ejpam-2418	12	6	-	-	PUNCT
ejpam-2418	12	7	s	s	NOUN
ejpam-2418	12	8	to	to	PART
ejpam-2418	12	9	be	be	AUX
ejpam-2418	12	10	the	the	DET
ejpam-2418	12	11	category	category	NOUN
ejpam-2418	12	12	of	of	ADP
ejpam-2418	12	13	right	right	ADJ
ejpam-2418	12	14	acts	act	NOUN
ejpam-2418	12	15	over	over	ADP
ejpam-2418	12	16	a	a	DET
ejpam-2418	12	17	semigroup	semigroup	NOUN
ejpam-2418	12	18	s	s	NOUN
ejpam-2418	12	19	and	and	CCONJ
ejpam-2418	12	20	m	m	PROPN
ejpam-2418	12	21	ono	ono	PROPN
ejpam-2418	12	22	to	to	PART
ejpam-2418	12	23	be	be	AUX
ejpam-2418	12	24	the	the	DET
ejpam-2418	12	25	class	class	NOUN
ejpam-2418	12	26	of	of	ADP
ejpam-2418	12	27	all	all	DET
ejpam-2418	12	28	monomorphisms	monomorphism	NOUN
ejpam-2418	12	29	of	of	ADP
ejpam-2418	12	30	right	right	ADJ
ejpam-2418	12	31	s	s	NOUN
ejpam-2418	12	32	-	-	PUNCT
ejpam-2418	12	33	acts	act	NOUN
ejpam-2418	12	34	,	,	PUNCT
ejpam-2418	12	35	and	and	CCONJ
ejpam-2418	12	36	then	then	ADV
ejpam-2418	12	37	,	,	PUNCT
ejpam-2418	12	38	we	we	PRON
ejpam-2418	12	39	study	study	VERB
ejpam-2418	12	40	the	the	DET
ejpam-2418	12	41	notion	notion	NOUN
ejpam-2418	12	42	of	of	ADP
ejpam-2418	12	43	essentiality	essentiality	NOUN
ejpam-2418	12	44	with	with	ADP
ejpam-2418	12	45	respect	respect	NOUN
ejpam-2418	12	46	to	to	ADP
ejpam-2418	12	47	this	this	DET
ejpam-2418	12	48	class	class	NOUN
ejpam-2418	12	49	.	.	PUNCT
ejpam-2418	13	1	essentiality	essentiality	NOUN
ejpam-2418	13	2	with	with	ADP
ejpam-2418	13	3	respect	respect	NOUN
ejpam-2418	13	4	to	to	ADP
ejpam-2418	13	5	the	the	DET
ejpam-2418	13	6	subclass	subclass	NOUN
ejpam-2418	13	7	m	m	NOUN
ejpam-2418	13	8	of	of	ADP
ejpam-2418	13	9	monomorphisms	monomorphism	NOUN
ejpam-2418	13	10	have	have	AUX
ejpam-2418	13	11	studied	study	VERB
ejpam-2418	13	12	and	and	CCONJ
ejpam-2418	13	13	some	some	DET
ejpam-2418	13	14	equivalent	equivalent	ADJ
ejpam-2418	13	15	conditions	condition	NOUN
ejpam-2418	13	16	,	,	PUNCT
ejpam-2418	13	17	so	so	ADV
ejpam-2418	13	18	called	call	VERB
ejpam-2418	13	19	“	"	PUNCT
ejpam-2418	13	20	essential	essential	ADJ
ejpam-2418	13	21	test	test	NOUN
ejpam-2418	13	22	lemma	lemma	PROPN
ejpam-2418	13	23	for	for	ADP
ejpam-2418	13	24	essentiality	essentiality	NOUN
ejpam-2418	13	25	"	"	PUNCT
ejpam-2418	13	26	,	,	PUNCT
ejpam-2418	13	27	have	have	AUX
ejpam-2418	13	28	introduced(see	introduced(see	VERB
ejpam-2418	13	29	,	,	PUNCT
ejpam-2418	13	30	[	[	X
ejpam-2418	13	31	7	7	NUM
ejpam-2418	13	32	,	,	PUNCT
ejpam-2418	13	33	9	9	NUM
ejpam-2418	13	34	]	]	PUNCT
ejpam-2418	13	35	)	)	PUNCT
ejpam-2418	13	36	.	.	PUNCT
ejpam-2418	14	1	we	we	PRON
ejpam-2418	14	2	substantially	substantially	ADV
ejpam-2418	14	3	improve	improve	VERB
ejpam-2418	14	4	the	the	DET
ejpam-2418	14	5	usual	usual	ADJ
ejpam-2418	14	6	characterization	characterization	NOUN
ejpam-2418	14	7	of	of	ADP
ejpam-2418	14	8	essentiality	essentiality	NOUN
ejpam-2418	14	9	in	in	ADP
ejpam-2418	14	10	terms	term	NOUN
ejpam-2418	14	11	of	of	ADP
ejpam-2418	14	12	congruences	congruence	NOUN
ejpam-2418	14	13	,	,	PUNCT
ejpam-2418	14	14	lemma	lemma	PROPN
ejpam-2418	14	15	1	1	NUM
ejpam-2418	14	16	,	,	PUNCT
ejpam-2418	14	17	of	of	ADP
ejpam-2418	14	18	an	an	DET
ejpam-2418	14	19	extension	extension	NOUN
ejpam-2418	14	20	b	b	NOUN
ejpam-2418	14	21	of	of	ADP
ejpam-2418	14	22	a	a	PRON
ejpam-2418	14	23	by	by	ADP
ejpam-2418	14	24	giving	give	VERB
ejpam-2418	14	25	a	a	DET
ejpam-2418	14	26	characterization	characterization	NOUN
ejpam-2418	14	27	in	in	ADP
ejpam-2418	14	28	terms	term	NOUN
ejpam-2418	14	29	of	of	ADP
ejpam-2418	14	30	the	the	DET
ejpam-2418	14	31	elements	element	NOUN
ejpam-2418	14	32	of	of	ADP
ejpam-2418	14	33	b	b	NOUN
ejpam-2418	14	34	,	,	PUNCT
ejpam-2418	14	35	theorems	theorem	NOUN
ejpam-2418	14	36	5	5	NUM
ejpam-2418	14	37	and	and	CCONJ
ejpam-2418	14	38	6	6	NUM
ejpam-2418	14	39	,	,	PUNCT
ejpam-2418	14	40	which	which	PRON
ejpam-2418	14	41	are	be	AUX
ejpam-2418	14	42	essential	essential	ADJ
ejpam-2418	14	43	test	test	NOUN
ejpam-2418	14	44	lemmas	lemmas	ADJ
ejpam-2418	14	45	.	.	PUNCT
ejpam-2418	15	1	also	also	ADV
ejpam-2418	15	2	,	,	PUNCT
ejpam-2418	15	3	similar	similar	ADJ
ejpam-2418	15	4	to	to	ADP
ejpam-2418	15	5	the	the	DET
ejpam-2418	15	6	case	case	NOUN
ejpam-2418	15	7	of	of	ADP
ejpam-2418	15	8	modules	module	NOUN
ejpam-2418	15	9	,	,	PUNCT
ejpam-2418	15	10	which	which	DET
ejpam-2418	15	11	essentiality	essentiality	NOUN
ejpam-2418	15	12	has	have	VERB
ejpam-2418	15	13	an	an	DET
ejpam-2418	15	14	expression	expression	NOUN
ejpam-2418	15	15	by	by	ADP
ejpam-2418	15	16	submodules	submodule	NOUN
ejpam-2418	15	17	,	,	PUNCT
ejpam-2418	15	18	in	in	ADP
ejpam-2418	15	19	theorem	theorem	NOUN
ejpam-2418	15	20	1	1	NUM
ejpam-2418	15	21	an	an	DET
ejpam-2418	15	22	equivalent	equivalent	ADJ
ejpam-2418	15	23	condition	condition	NOUN
ejpam-2418	15	24	in	in	ADP
ejpam-2418	15	25	terms	term	NOUN
ejpam-2418	15	26	of	of	ADP
ejpam-2418	15	27	ress	ress	NOUN
ejpam-2418	15	28	congruences	congruence	NOUN
ejpam-2418	15	29	is	be	AUX
ejpam-2418	15	30	obtained	obtain	VERB
ejpam-2418	15	31	for	for	ADP
ejpam-2418	15	32	essentiality	essentiality	NOUN
ejpam-2418	15	33	.	.	PUNCT
ejpam-2418	16	1	although	although	SCONJ
ejpam-2418	16	2	the	the	DET
ejpam-2418	16	3	baer	baer	PROPN
ejpam-2418	16	4	criterion	criterion	NOUN
ejpam-2418	16	5	for	for	ADP
ejpam-2418	16	6	injectivity	injectivity	NOUN
ejpam-2418	16	7	(	(	PUNCT
ejpam-2418	16	8	weak	weak	ADJ
ejpam-2418	16	9	injectivity	injectivity	NOUN
ejpam-2418	16	10	implies	imply	VERB
ejpam-2418	16	11	injectivity	injectivity	NOUN
ejpam-2418	16	12	)	)	PUNCT
ejpam-2418	16	13	is	be	AUX
ejpam-2418	16	14	true	true	ADJ
ejpam-2418	16	15	for	for	ADP
ejpam-2418	16	16	modules	module	NOUN
ejpam-2418	16	17	over	over	ADP
ejpam-2418	16	18	a	a	DET
ejpam-2418	16	19	ring	ring	NOUN
ejpam-2418	16	20	(	(	PUNCT
ejpam-2418	16	21	with	with	ADP
ejpam-2418	16	22	an	an	DET
ejpam-2418	16	23	identity	identity	NOUN
ejpam-2418	16	24	)	)	PUNCT
ejpam-2418	16	25	,	,	PUNCT
ejpam-2418	16	26	it	it	PRON
ejpam-2418	16	27	is	be	AUX
ejpam-2418	16	28	an	an	DET
ejpam-2418	16	29	open	open	ADJ
ejpam-2418	16	30	problem	problem	NOUN
ejpam-2418	16	31	for	for	ADP
ejpam-2418	16	32	acts	act	NOUN
ejpam-2418	16	33	over	over	ADP
ejpam-2418	16	34	a	a	DET
ejpam-2418	16	35	semigroup	semigroup	NOUN
ejpam-2418	16	36	s	s	X
ejpam-2418	16	37	(	(	PUNCT
ejpam-2418	16	38	with	with	ADP
ejpam-2418	16	39	or	or	CCONJ
ejpam-2418	16	40	without	without	ADP
ejpam-2418	16	41	identity	identity	NOUN
ejpam-2418	16	42	)	)	PUNCT
ejpam-2418	16	43	.	.	PUNCT
ejpam-2418	17	1	in	in	ADP
ejpam-2418	17	2	fact	fact	NOUN
ejpam-2418	17	3	,	,	PUNCT
ejpam-2418	17	4	we	we	PRON
ejpam-2418	17	5	are	be	AUX
ejpam-2418	17	6	not	not	PART
ejpam-2418	17	7	aware	aware	ADJ
ejpam-2418	17	8	of	of	ADP
ejpam-2418	17	9	any	any	DET
ejpam-2418	17	10	type	type	NOUN
ejpam-2418	17	11	of	of	ADP
ejpam-2418	17	12	weak	weak	ADJ
ejpam-2418	17	13	injectivity	injectivity	NOUN
ejpam-2418	17	14	implying	imply	VERB
ejpam-2418	17	15	injectivity	injectivity	NOUN
ejpam-2418	17	16	of	of	ADP
ejpam-2418	17	17	s	s	NOUN
ejpam-2418	17	18	-	-	PUNCT
ejpam-2418	17	19	acts	act	NOUN
ejpam-2418	17	20	,	,	PUNCT
ejpam-2418	17	21	in	in	ADP
ejpam-2418	17	22	general	general	ADJ
ejpam-2418	17	23	,	,	PUNCT
ejpam-2418	17	24	other	other	ADJ
ejpam-2418	17	25	than	than	ADP
ejpam-2418	17	26	skornjakov	skornjakov	NOUN
ejpam-2418	17	27	-	-	PUNCT
ejpam-2418	17	28	baer	baer	PROPN
ejpam-2418	17	29	criterion	criterion	NOUN
ejpam-2418	17	30	,	,	PUNCT
ejpam-2418	17	31	which	which	PRON
ejpam-2418	17	32	says	say	VERB
ejpam-2418	17	33	that	that	SCONJ
ejpam-2418	17	34	injectivity	injectivity	NOUN
ejpam-2418	17	35	with	with	ADP
ejpam-2418	17	36	respect	respect	NOUN
ejpam-2418	17	37	to	to	ADP
ejpam-2418	17	38	subacts	subact	NOUN
ejpam-2418	17	39	of	of	ADP
ejpam-2418	17	40	cyclic	cyclic	ADJ
ejpam-2418	17	41	acts	act	NOUN
ejpam-2418	17	42	implies	imply	VERB
ejpam-2418	17	43	injectivity	injectivity	NOUN
ejpam-2418	17	44	with	with	ADP
ejpam-2418	17	45	respect	respect	NOUN
ejpam-2418	17	46	to	to	ADP
ejpam-2418	17	47	all	all	DET
ejpam-2418	17	48	monomorphisms	monomorphism	NOUN
ejpam-2418	17	49	.	.	PUNCT
ejpam-2418	18	1	email	email	NOUN
ejpam-2418	18	2	address	address	NOUN
ejpam-2418	18	3	:	:	PUNCT
ejpam-2418	18	4	h56bar@tafreshu.ac.ir	h56bar@tafreshu.ac.ir	PROPN
ejpam-2418	18	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2418	19	1	19	19	NUM
ejpam-2418	19	2	c	c	NOUN
ejpam-2418	19	3	©	©	PROPN
ejpam-2418	19	4	2016	2016	NUM
ejpam-2418	19	5	ejpam	ejpam	VERB
ejpam-2418	19	6	all	all	DET
ejpam-2418	19	7	rights	right	NOUN
ejpam-2418	19	8	reserved	reserve	VERB
ejpam-2418	19	9	.	.	PUNCT
ejpam-2418	20	1	h.	h.	PROPN
ejpam-2418	20	2	barzegar	barzegar	PROPN
ejpam-2418	20	3	/	/	SYM
ejpam-2418	20	4	eur	eur	PROPN
ejpam-2418	20	5	.	.	PUNCT
ejpam-2418	21	1	j.	j.	PROPN
ejpam-2418	21	2	pure	pure	PROPN
ejpam-2418	21	3	appl	appl	PROPN
ejpam-2418	21	4	.	.	PROPN
ejpam-2418	21	5	math	math	PROPN
ejpam-2418	21	6	,	,	PUNCT
ejpam-2418	21	7	9	9	NUM
ejpam-2418	21	8	(	(	PUNCT
ejpam-2418	21	9	2016	2016	NUM
ejpam-2418	21	10	)	)	PUNCT
ejpam-2418	21	11	,	,	PUNCT
ejpam-2418	21	12	19	19	NUM
ejpam-2418	21	13	-	-	SYM
ejpam-2418	21	14	26	26	NUM
ejpam-2418	21	15	20	20	NUM
ejpam-2418	21	16	one	one	NUM
ejpam-2418	21	17	of	of	ADP
ejpam-2418	21	18	the	the	DET
ejpam-2418	21	19	well	well	ADV
ejpam-2418	21	20	known	know	VERB
ejpam-2418	21	21	theorem	theorem	NOUN
ejpam-2418	21	22	about	about	ADP
ejpam-2418	21	23	the	the	DET
ejpam-2418	21	24	injectivity	injectivity	NOUN
ejpam-2418	21	25	says	say	VERB
ejpam-2418	21	26	that	that	SCONJ
ejpam-2418	21	27	,	,	PUNCT
ejpam-2418	21	28	an	an	DET
ejpam-2418	21	29	s	s	NOUN
ejpam-2418	21	30	-	-	PUNCT
ejpam-2418	21	31	act	act	NOUN
ejpam-2418	21	32	a	a	PRON
ejpam-2418	21	33	is	be	AUX
ejpam-2418	21	34	injective	injective	ADJ
ejpam-2418	21	35	if	if	SCONJ
ejpam-2418	21	36	and	and	CCONJ
ejpam-2418	21	37	only	only	ADV
ejpam-2418	21	38	if	if	SCONJ
ejpam-2418	21	39	it	it	PRON
ejpam-2418	21	40	has	have	VERB
ejpam-2418	21	41	no	no	DET
ejpam-2418	21	42	proper	proper	ADJ
ejpam-2418	21	43	essential	essential	ADJ
ejpam-2418	21	44	extension(see	extension(see	NOUN
ejpam-2418	21	45	,	,	PUNCT
ejpam-2418	21	46	[	[	X
ejpam-2418	21	47	8	8	NUM
ejpam-2418	21	48	]	]	PUNCT
ejpam-2418	21	49	or	or	CCONJ
ejpam-2418	21	50	[	[	X
ejpam-2418	21	51	4	4	NUM
ejpam-2418	21	52	]	]	NUM
ejpam-2418	21	53	)	)	PUNCT
ejpam-2418	21	54	.	.	PUNCT
ejpam-2418	22	1	so	so	ADV
ejpam-2418	22	2	essentiality	essentiality	NOUN
ejpam-2418	22	3	play	play	VERB
ejpam-2418	22	4	an	an	DET
ejpam-2418	22	5	important	important	ADJ
ejpam-2418	22	6	role	role	NOUN
ejpam-2418	22	7	in	in	ADP
ejpam-2418	22	8	the	the	DET
ejpam-2418	22	9	study	study	NOUN
ejpam-2418	22	10	of	of	ADP
ejpam-2418	22	11	the	the	DET
ejpam-2418	22	12	baer	baer	PROPN
ejpam-2418	22	13	problem	problem	NOUN
ejpam-2418	22	14	.	.	PUNCT
ejpam-2418	23	1	in	in	ADP
ejpam-2418	23	2	section	section	NOUN
ejpam-2418	23	3	2	2	NUM
ejpam-2418	23	4	some	some	DET
ejpam-2418	23	5	necessity	necessity	NOUN
ejpam-2418	23	6	conditions	condition	NOUN
ejpam-2418	23	7	on	on	ADP
ejpam-2418	23	8	essentiality	essentiality	NOUN
ejpam-2418	23	9	are	be	AUX
ejpam-2418	23	10	obtained	obtain	VERB
ejpam-2418	23	11	and	and	CCONJ
ejpam-2418	23	12	theorem	theorem	VERB
ejpam-2418	23	13	5	5	NUM
ejpam-2418	23	14	,	,	PUNCT
ejpam-2418	23	15	“	"	PUNCT
ejpam-2418	23	16	which	which	PRON
ejpam-2418	23	17	is	be	AUX
ejpam-2418	23	18	the	the	DET
ejpam-2418	23	19	main	main	ADJ
ejpam-2418	23	20	result	result	NOUN
ejpam-2418	23	21	of	of	ADP
ejpam-2418	23	22	this	this	DET
ejpam-2418	23	23	article	article	NOUN
ejpam-2418	23	24	"	"	PUNCT
ejpam-2418	23	25	,	,	PUNCT
ejpam-2418	23	26	is	be	AUX
ejpam-2418	23	27	in	in	ADP
ejpam-2418	23	28	fact	fact	NOUN
ejpam-2418	23	29	an	an	DET
ejpam-2418	23	30	essential	essential	ADJ
ejpam-2418	23	31	test	test	NOUN
ejpam-2418	23	32	lemma	lemma	PROPN
ejpam-2418	23	33	which	which	PRON
ejpam-2418	23	34	introduces	introduce	VERB
ejpam-2418	23	35	an	an	DET
ejpam-2418	23	36	equivalent	equivalent	ADJ
ejpam-2418	23	37	condition	condition	NOUN
ejpam-2418	23	38	to	to	ADP
ejpam-2418	23	39	essentiality	essentiality	NOUN
ejpam-2418	23	40	.	.	PUNCT
ejpam-2418	24	1	let	let	VERB
ejpam-2418	24	2	us	we	PRON
ejpam-2418	24	3	first	first	ADV
ejpam-2418	24	4	recall	recall	VERB
ejpam-2418	24	5	the	the	DET
ejpam-2418	24	6	definition	definition	NOUN
ejpam-2418	24	7	and	and	CCONJ
ejpam-2418	24	8	some	some	DET
ejpam-2418	24	9	ingredients	ingredient	NOUN
ejpam-2418	24	10	of	of	ADP
ejpam-2418	24	11	the	the	DET
ejpam-2418	24	12	category	category	NOUN
ejpam-2418	24	13	act−	act−	ADP
ejpam-2418	24	14	s	s	PROPN
ejpam-2418	24	15	of	of	ADP
ejpam-2418	24	16	acts	act	NOUN
ejpam-2418	24	17	over	over	ADP
ejpam-2418	24	18	a	a	DET
ejpam-2418	24	19	semigroup	semigroup	NOUN
ejpam-2418	24	20	s	s	PRON
ejpam-2418	24	21	needed	need	VERB
ejpam-2418	24	22	in	in	ADP
ejpam-2418	24	23	the	the	DET
ejpam-2418	24	24	sequel	sequel	NOUN
ejpam-2418	24	25	.	.	PUNCT
ejpam-2418	25	1	for	for	ADP
ejpam-2418	25	2	more	more	ADJ
ejpam-2418	25	3	information	information	NOUN
ejpam-2418	25	4	and	and	CCONJ
ejpam-2418	25	5	the	the	DET
ejpam-2418	25	6	notions	notion	NOUN
ejpam-2418	25	7	not	not	PART
ejpam-2418	25	8	mentioned	mention	VERB
ejpam-2418	25	9	here	here	ADV
ejpam-2418	25	10	see	see	VERB
ejpam-2418	25	11	,	,	PUNCT
ejpam-2418	25	12	for	for	ADP
ejpam-2418	25	13	example	example	NOUN
ejpam-2418	25	14	,	,	PUNCT
ejpam-2418	25	15	[	[	X
ejpam-2418	25	16	6	6	NUM
ejpam-2418	25	17	]	]	PUNCT
ejpam-2418	25	18	and	and	CCONJ
ejpam-2418	26	1	[	[	X
ejpam-2418	26	2	8	8	NUM
ejpam-2418	26	3	]	]	PUNCT
ejpam-2418	26	4	.	.	PUNCT
ejpam-2418	27	1	recall	recall	VERB
ejpam-2418	27	2	that	that	PRON
ejpam-2418	27	3	,	,	PUNCT
ejpam-2418	27	4	for	for	ADP
ejpam-2418	27	5	a	a	DET
ejpam-2418	27	6	semigroup	semigroup	NOUN
ejpam-2418	27	7	s	s	PROPN
ejpam-2418	27	8	,	,	PUNCT
ejpam-2418	27	9	a	a	DET
ejpam-2418	27	10	set	set	NOUN
ejpam-2418	27	11	a	a	PRON
ejpam-2418	27	12	is	be	AUX
ejpam-2418	27	13	an	an	DET
ejpam-2418	27	14	s	s	NOUN
ejpam-2418	27	15	-	-	NOUN
ejpam-2418	27	16	act	act	NOUN
ejpam-2418	27	17	(	(	PUNCT
ejpam-2418	27	18	or	or	CCONJ
ejpam-2418	27	19	an	an	DET
ejpam-2418	27	20	s	s	NOUN
ejpam-2418	27	21	-	-	PUNCT
ejpam-2418	27	22	set	set	NOUN
ejpam-2418	27	23	)	)	PUNCT
ejpam-2418	27	24	if	if	SCONJ
ejpam-2418	27	25	there	there	PRON
ejpam-2418	27	26	is	be	VERB
ejpam-2418	27	27	a	a	DET
ejpam-2418	27	28	,	,	PUNCT
ejpam-2418	27	29	so	so	ADV
ejpam-2418	27	30	called	call	VERB
ejpam-2418	27	31	,	,	PUNCT
ejpam-2418	27	32	action	action	NOUN
ejpam-2418	27	33	µ	µ	NOUN
ejpam-2418	27	34	:	:	PUNCT
ejpam-2418	27	35	a×	a×	PROPN
ejpam-2418	27	36	s	s	PART
ejpam-2418	27	37	→	→	PUNCT
ejpam-2418	27	38	a	a	DET
ejpam-2418	27	39	such	such	ADJ
ejpam-2418	27	40	that	that	PRON
ejpam-2418	27	41	,	,	PUNCT
ejpam-2418	27	42	denoting	denote	VERB
ejpam-2418	27	43	µ(a	µ(a	PROPN
ejpam-2418	27	44	,	,	PUNCT
ejpam-2418	27	45	s	s	PROPN
ejpam-2418	27	46	)	)	PUNCT
ejpam-2418	27	47	:	:	PUNCT
ejpam-2418	27	48	=	=	PUNCT
ejpam-2418	27	49	as	as	ADP
ejpam-2418	27	50	,	,	PUNCT
ejpam-2418	27	51	a(st	a(st	PROPN
ejpam-2418	27	52	)	)	PUNCT
ejpam-2418	27	53	=	=	PUNCT
ejpam-2418	28	1	(	(	PUNCT
ejpam-2418	28	2	as)t	as)t	PROPN
ejpam-2418	28	3	and	and	CCONJ
ejpam-2418	28	4	if	if	SCONJ
ejpam-2418	28	5	s	s	VERB
ejpam-2418	28	6	is	be	AUX
ejpam-2418	28	7	a	a	DET
ejpam-2418	28	8	monoid	monoid	NOUN
ejpam-2418	28	9	with	with	ADP
ejpam-2418	28	10	1	1	NUM
ejpam-2418	28	11	,	,	PUNCT
ejpam-2418	28	12	a1=	a1=	PROPN
ejpam-2418	28	13	a.	a.	NOUN
ejpam-2418	28	14	each	each	DET
ejpam-2418	28	15	semigroup	semigroup	PROPN
ejpam-2418	28	16	s	s	VERB
ejpam-2418	28	17	can	can	AUX
ejpam-2418	28	18	be	be	AUX
ejpam-2418	28	19	considered	consider	VERB
ejpam-2418	28	20	as	as	ADP
ejpam-2418	28	21	an	an	DET
ejpam-2418	28	22	s	s	NOUN
ejpam-2418	28	23	-	-	NOUN
ejpam-2418	28	24	act	act	NOUN
ejpam-2418	28	25	with	with	ADP
ejpam-2418	28	26	the	the	DET
ejpam-2418	28	27	action	action	NOUN
ejpam-2418	28	28	given	give	VERB
ejpam-2418	28	29	by	by	ADP
ejpam-2418	28	30	its	its	PRON
ejpam-2418	28	31	multiplication	multiplication	NOUN
ejpam-2418	28	32	.	.	PUNCT
ejpam-2418	29	1	notice	notice	VERB
ejpam-2418	29	2	that	that	SCONJ
ejpam-2418	29	3	,	,	PUNCT
ejpam-2418	29	4	adjoining	adjoin	VERB
ejpam-2418	29	5	an	an	DET
ejpam-2418	29	6	external	external	ADJ
ejpam-2418	29	7	left	leave	VERB
ejpam-2418	29	8	identity	identity	NOUN
ejpam-2418	29	9	1	1	NUM
ejpam-2418	29	10	to	to	ADP
ejpam-2418	29	11	a	a	DET
ejpam-2418	29	12	semigroup	semigroup	NOUN
ejpam-2418	29	13	s	s	VERB
ejpam-2418	29	14	an	an	DET
ejpam-2418	29	15	s	s	NOUN
ejpam-2418	29	16	-	-	PUNCT
ejpam-2418	29	17	act	act	NOUN
ejpam-2418	29	18	s1	s1	NOUN
ejpam-2418	29	19	:	:	PUNCT
ejpam-2418	29	20	=	=	SYM
ejpam-2418	29	21	s	s	X
ejpam-2418	29	22	∪	∪	X
ejpam-2418	29	23	{	{	PUNCT
ejpam-2418	29	24	1	1	NUM
ejpam-2418	29	25	}	}	PUNCT
ejpam-2418	29	26	is	be	AUX
ejpam-2418	29	27	obtained	obtain	VERB
ejpam-2418	29	28	.	.	PUNCT
ejpam-2418	30	1	also	also	ADV
ejpam-2418	30	2	,	,	PUNCT
ejpam-2418	30	3	recall	recall	VERB
ejpam-2418	30	4	that	that	SCONJ
ejpam-2418	30	5	an	an	DET
ejpam-2418	30	6	element	element	NOUN
ejpam-2418	30	7	a	a	DET
ejpam-2418	30	8	∈	∈	NOUN
ejpam-2418	30	9	a	a	PRON
ejpam-2418	30	10	is	be	AUX
ejpam-2418	30	11	said	say	VERB
ejpam-2418	30	12	to	to	PART
ejpam-2418	30	13	be	be	AUX
ejpam-2418	30	14	fixed	fix	VERB
ejpam-2418	30	15	if	if	SCONJ
ejpam-2418	30	16	as	as	SCONJ
ejpam-2418	30	17	=	=	X
ejpam-2418	30	18	a	a	PRON
ejpam-2418	30	19	for	for	ADP
ejpam-2418	30	20	all	all	PRON
ejpam-2418	30	21	s	s	PART
ejpam-2418	30	22	∈	∈	PROPN
ejpam-2418	30	23	s.	s.	PROPN
ejpam-2418	30	24	the	the	DET
ejpam-2418	30	25	s	s	PROPN
ejpam-2418	30	26	-	-	NOUN
ejpam-2418	30	27	act	act	NOUN
ejpam-2418	30	28	a∪{0	a∪{0	NOUN
ejpam-2418	30	29	}	}	PUNCT
ejpam-2418	30	30	with	with	ADP
ejpam-2418	30	31	a	a	DET
ejpam-2418	30	32	fixed	fix	VERB
ejpam-2418	30	33	adjoined	adjoin	VERB
ejpam-2418	30	34	to	to	ADP
ejpam-2418	30	35	a	a	PRON
ejpam-2418	30	36	is	be	AUX
ejpam-2418	30	37	denoted	denote	VERB
ejpam-2418	30	38	by	by	ADP
ejpam-2418	30	39	a0	a0	PROPN
ejpam-2418	30	40	.	.	PUNCT
ejpam-2418	31	1	all	all	DET
ejpam-2418	31	2	fixed	fix	VERB
ejpam-2418	31	3	elements	element	NOUN
ejpam-2418	31	4	of	of	ADP
ejpam-2418	31	5	as	as	ADP
ejpam-2418	31	6	an	an	DET
ejpam-2418	31	7	s	s	NOUN
ejpam-2418	31	8	-	-	NOUN
ejpam-2418	31	9	act	act	NOUN
ejpam-2418	31	10	a	a	PRON
ejpam-2418	31	11	is	be	AUX
ejpam-2418	31	12	a	a	DET
ejpam-2418	31	13	subact	subact	NOUN
ejpam-2418	31	14	of	of	ADP
ejpam-2418	31	15	a	a	PRON
ejpam-2418	31	16	and	and	CCONJ
ejpam-2418	31	17	denoted	denote	VERB
ejpam-2418	31	18	by	by	ADP
ejpam-2418	31	19	f	f	PROPN
ejpam-2418	31	20	ix(a	ix(a	PROPN
ejpam-2418	31	21	)	)	PUNCT
ejpam-2418	31	22	.	.	PUNCT
ejpam-2418	32	1	a	a	DET
ejpam-2418	32	2	fixed	fix	VERB
ejpam-2418	32	3	element	element	NOUN
ejpam-2418	32	4	of	of	ADP
ejpam-2418	32	5	a	a	DET
ejpam-2418	32	6	semigroup	semigroup	NOUN
ejpam-2418	32	7	s	s	PART
ejpam-2418	32	8	is	be	AUX
ejpam-2418	32	9	called	call	VERB
ejpam-2418	32	10	a	a	DET
ejpam-2418	32	11	left	left	ADJ
ejpam-2418	32	12	zero	zero	NUM
ejpam-2418	32	13	element	element	NOUN
ejpam-2418	32	14	.	.	PUNCT
ejpam-2418	33	1	all	all	PRON
ejpam-2418	33	2	left	leave	VERB
ejpam-2418	33	3	zero	zero	NUM
ejpam-2418	33	4	elements	element	NOUN
ejpam-2418	33	5	of	of	ADP
ejpam-2418	33	6	a	a	DET
ejpam-2418	33	7	semigroup	semigroup	NOUN
ejpam-2418	33	8	s	s	PART
ejpam-2418	33	9	is	be	AUX
ejpam-2418	33	10	a	a	DET
ejpam-2418	33	11	right	right	ADJ
ejpam-2418	33	12	ideal	ideal	NOUN
ejpam-2418	33	13	of	of	ADP
ejpam-2418	33	14	s	s	PRON
ejpam-2418	33	15	and	and	CCONJ
ejpam-2418	33	16	denoted	denote	VERB
ejpam-2418	33	17	by	by	ADP
ejpam-2418	33	18	z(s	z(s	PROPN
ejpam-2418	33	19	)	)	PUNCT
ejpam-2418	33	20	.	.	PUNCT
ejpam-2418	34	1	the	the	DET
ejpam-2418	34	2	definitions	definition	NOUN
ejpam-2418	34	3	of	of	ADP
ejpam-2418	34	4	a	a	DET
ejpam-2418	34	5	homomorphism	homomorphism	NOUN
ejpam-2418	34	6	of	of	ADP
ejpam-2418	34	7	s	s	NOUN
ejpam-2418	34	8	-	-	PUNCT
ejpam-2418	34	9	acts	act	NOUN
ejpam-2418	34	10	or	or	CCONJ
ejpam-2418	34	11	s	s	NOUN
ejpam-2418	34	12	-	-	NOUN
ejpam-2418	34	13	maps	map	NOUN
ejpam-2418	34	14	,	,	PUNCT
ejpam-2418	34	15	subact	subact	VERB
ejpam-2418	34	16	a	a	PRON
ejpam-2418	34	17	of	of	ADP
ejpam-2418	34	18	b	b	NOUN
ejpam-2418	34	19	,	,	PUNCT
ejpam-2418	34	20	written	write	VERB
ejpam-2418	34	21	as	as	ADP
ejpam-2418	34	22	a≤	a≤	DET
ejpam-2418	34	23	b	b	PROPN
ejpam-2418	34	24	,	,	PUNCT
ejpam-2418	34	25	an	an	DET
ejpam-2418	34	26	extension	extension	NOUN
ejpam-2418	34	27	of	of	ADP
ejpam-2418	34	28	a	a	PRON
ejpam-2418	34	29	,	,	PUNCT
ejpam-2418	34	30	a	a	DET
ejpam-2418	34	31	congruence	congruence	NOUN
ejpam-2418	34	32	ρ	ρ	NOUN
ejpam-2418	34	33	on	on	ADP
ejpam-2418	34	34	a	a	PRON
ejpam-2418	34	35	and	and	CCONJ
ejpam-2418	34	36	a	a	DET
ejpam-2418	34	37	quotient	quotient	NOUN
ejpam-2418	34	38	a	a	PRON
ejpam-2418	34	39	/	/	SYM
ejpam-2418	34	40	ρ	ρ	NOUN
ejpam-2418	34	41	of	of	ADP
ejpam-2418	34	42	a	a	PRON
ejpam-2418	34	43	are	be	AUX
ejpam-2418	34	44	all	all	ADV
ejpam-2418	34	45	clear	clear	ADJ
ejpam-2418	34	46	.	.	PUNCT
ejpam-2418	35	1	for	for	ADP
ejpam-2418	35	2	h	h	NOUN
ejpam-2418	35	3	⊆	⊆	NUM
ejpam-2418	35	4	a×	a×	PROPN
ejpam-2418	35	5	a	a	X
ejpam-2418	35	6	,	,	PUNCT
ejpam-2418	35	7	the	the	DET
ejpam-2418	35	8	congruence	congruence	NOUN
ejpam-2418	35	9	generated	generate	VERB
ejpam-2418	35	10	by	by	ADP
ejpam-2418	35	11	h	h	PROPN
ejpam-2418	35	12	,	,	PUNCT
ejpam-2418	35	13	that	that	PRON
ejpam-2418	35	14	is	be	AUX
ejpam-2418	35	15	the	the	DET
ejpam-2418	35	16	smallest	small	ADJ
ejpam-2418	35	17	congruence	congruence	NOUN
ejpam-2418	35	18	on	on	ADP
ejpam-2418	35	19	a	a	DET
ejpam-2418	35	20	containing	contain	VERB
ejpam-2418	35	21	h	h	NOUN
ejpam-2418	35	22	,	,	PUNCT
ejpam-2418	35	23	is	be	AUX
ejpam-2418	35	24	denoted	denote	VERB
ejpam-2418	35	25	by	by	ADP
ejpam-2418	35	26	ρ(h	ρ(h	NOUN
ejpam-2418	35	27	)	)	PUNCT
ejpam-2418	35	28	.	.	PUNCT
ejpam-2418	36	1	let	let	VERB
ejpam-2418	36	2	h	h	NOUN
ejpam-2418	36	3	⊆	⊆	NUM
ejpam-2418	36	4	a×a	a×a	PROPN
ejpam-2418	36	5	and	and	CCONJ
ejpam-2418	36	6	ρ	ρ	PROPN
ejpam-2418	36	7	=	=	SYM
ejpam-2418	36	8	ρ(h	ρ(h	NOUN
ejpam-2418	36	9	)	)	PUNCT
ejpam-2418	36	10	.	.	PUNCT
ejpam-2418	37	1	then	then	ADV
ejpam-2418	37	2	,	,	PUNCT
ejpam-2418	37	3	for	for	ADP
ejpam-2418	37	4	a	a	PRON
ejpam-2418	37	5	,	,	PUNCT
ejpam-2418	37	6	b	b	PROPN
ejpam-2418	37	7	∈	∈	PROPN
ejpam-2418	37	8	a	a	PRON
ejpam-2418	37	9	,	,	PUNCT
ejpam-2418	37	10	one	one	NOUN
ejpam-2418	37	11	has	have	AUX
ejpam-2418	37	12	aρb	aρb	VERB
ejpam-2418	37	13	if	if	SCONJ
ejpam-2418	37	14	and	and	CCONJ
ejpam-2418	37	15	only	only	ADV
ejpam-2418	37	16	if	if	SCONJ
ejpam-2418	37	17	either	either	CCONJ
ejpam-2418	37	18	a	a	DET
ejpam-2418	37	19	=	=	SYM
ejpam-2418	37	20	b	b	NOUN
ejpam-2418	37	21	or	or	CCONJ
ejpam-2418	37	22	there	there	ADV
ejpam-2418	37	23	exist	exist	VERB
ejpam-2418	37	24	p1	p1	NOUN
ejpam-2418	37	25	,	,	PUNCT
ejpam-2418	37	26	p2	p2	NOUN
ejpam-2418	37	27	,	,	PUNCT
ejpam-2418	37	28	.	.	PUNCT
ejpam-2418	37	29	.	.	PUNCT
ejpam-2418	38	1	.	.	PUNCT
ejpam-2418	39	1	,	,	PUNCT
ejpam-2418	39	2	pn	pn	INTJ
ejpam-2418	39	3	,	,	PUNCT
ejpam-2418	39	4	q1,q2	q1,q2	PROPN
ejpam-2418	39	5	,	,	PUNCT
ejpam-2418	39	6	.	.	PUNCT
ejpam-2418	39	7	.	.	PUNCT
ejpam-2418	39	8	.	.	PUNCT
ejpam-2418	40	1	,	,	PUNCT
ejpam-2418	40	2	qn	qn	NOUN
ejpam-2418	40	3	∈	∈	PROPN
ejpam-2418	40	4	a	a	DET
ejpam-2418	40	5	,	,	PUNCT
ejpam-2418	40	6	s1	s1	NOUN
ejpam-2418	40	7	,	,	PUNCT
ejpam-2418	40	8	s2	s2	NOUN
ejpam-2418	40	9	,	,	PUNCT
ejpam-2418	40	10	.	.	PUNCT
ejpam-2418	40	11	.	.	PUNCT
ejpam-2418	41	1	.	.	PUNCT
ejpam-2418	42	1	,	,	PUNCT
ejpam-2418	42	2	sn	sn	PROPN
ejpam-2418	42	3	∈	∈	PROPN
ejpam-2418	42	4	s1	s1	NOUN
ejpam-2418	42	5	where	where	SCONJ
ejpam-2418	42	6	for	for	ADP
ejpam-2418	42	7	i	i	PROPN
ejpam-2418	42	8	=	=	NOUN
ejpam-2418	42	9	1	1	NUM
ejpam-2418	42	10	,	,	PUNCT
ejpam-2418	42	11	.	.	PUNCT
ejpam-2418	42	12	.	.	PUNCT
ejpam-2418	43	1	.	.	PUNCT
ejpam-2418	44	1	,	,	PUNCT
ejpam-2418	44	2	n	n	CCONJ
ejpam-2418	44	3	,	,	PUNCT
ejpam-2418	44	4	(	(	PUNCT
ejpam-2418	44	5	pi	pi	NOUN
ejpam-2418	44	6	,	,	PUNCT
ejpam-2418	44	7	qi	qi	PROPN
ejpam-2418	44	8	)	)	PUNCT
ejpam-2418	44	9	∈	∈	PROPN
ejpam-2418	44	10	h	h	NOUN
ejpam-2418	44	11	∪	∪	VERB
ejpam-2418	44	12	h−1	h−1	PROPN
ejpam-2418	44	13	,	,	PUNCT
ejpam-2418	44	14	such	such	ADJ
ejpam-2418	44	15	that	that	SCONJ
ejpam-2418	44	16	a	a	DET
ejpam-2418	44	17	=	=	NOUN
ejpam-2418	44	18	p1s1,q1s1	p1s1,q1s1	NOUN
ejpam-2418	44	19	=	=	NOUN
ejpam-2418	44	20	p2s2,q2s2	p2s2,q2s2	NOUN
ejpam-2418	44	21	=	=	SYM
ejpam-2418	44	22	p3s3	p3s3	NOUN
ejpam-2418	44	23	,	,	PUNCT
ejpam-2418	44	24	.	.	PUNCT
ejpam-2418	44	25	.	.	PUNCT
ejpam-2418	44	26	.	.	PUNCT
ejpam-2418	45	1	,	,	PUNCT
ejpam-2418	45	2	qnsn	qnsn	X
ejpam-2418	45	3	=	=	SYM
ejpam-2418	45	4	b.	b.	PROPN
ejpam-2418	45	5	2	2	X
ejpam-2418	45	6	.	.	X
ejpam-2418	45	7	essentiality	essentiality	NOUN
ejpam-2418	45	8	of	of	ADP
ejpam-2418	45	9	acts	act	NOUN
ejpam-2418	45	10	here	here	ADV
ejpam-2418	45	11	,	,	PUNCT
ejpam-2418	45	12	some	some	DET
ejpam-2418	45	13	characterizations	characterization	NOUN
ejpam-2418	45	14	and	and	CCONJ
ejpam-2418	45	15	some	some	DET
ejpam-2418	45	16	properties	property	NOUN
ejpam-2418	45	17	of	of	ADP
ejpam-2418	45	18	essentiality	essentiality	NOUN
ejpam-2418	45	19	are	be	AUX
ejpam-2418	45	20	given	give	VERB
ejpam-2418	45	21	.	.	PUNCT
ejpam-2418	46	1	many	many	ADJ
ejpam-2418	46	2	of	of	ADP
ejpam-2418	46	3	results	result	NOUN
ejpam-2418	46	4	of	of	ADP
ejpam-2418	46	5	this	this	DET
ejpam-2418	46	6	section	section	NOUN
ejpam-2418	46	7	are	be	AUX
ejpam-2418	46	8	similar	similar	ADJ
ejpam-2418	46	9	to	to	ADP
ejpam-2418	46	10	the	the	DET
ejpam-2418	46	11	work	work	NOUN
ejpam-2418	46	12	done	do	VERB
ejpam-2418	46	13	in	in	ADP
ejpam-2418	46	14	[	[	X
ejpam-2418	46	15	3	3	NUM
ejpam-2418	46	16	]	]	PUNCT
ejpam-2418	46	17	.	.	PUNCT
ejpam-2418	47	1	definition	definition	NOUN
ejpam-2418	47	2	1	1	NUM
ejpam-2418	47	3	.	.	PUNCT
ejpam-2418	48	1	a	a	DET
ejpam-2418	48	2	monomorphism	monomorphism	NOUN
ejpam-2418	48	3	f	f	X
ejpam-2418	48	4	:	:	PUNCT
ejpam-2418	48	5	a→	a→	PROPN
ejpam-2418	48	6	b	b	X
ejpam-2418	48	7	of	of	ADP
ejpam-2418	48	8	s	s	NOUN
ejpam-2418	48	9	-	-	PUNCT
ejpam-2418	48	10	acts	act	NOUN
ejpam-2418	48	11	is	be	AUX
ejpam-2418	48	12	said	say	VERB
ejpam-2418	48	13	to	to	PART
ejpam-2418	48	14	be	be	AUX
ejpam-2418	48	15	essential	essential	ADJ
ejpam-2418	48	16	if	if	SCONJ
ejpam-2418	48	17	for	for	ADP
ejpam-2418	48	18	each	each	DET
ejpam-2418	48	19	homomorphism	homomorphism	NOUN
ejpam-2418	48	20	g	g	NOUN
ejpam-2418	48	21	:	:	PUNCT
ejpam-2418	48	22	b→	b→	PROPN
ejpam-2418	48	23	c	c	NOUN
ejpam-2418	48	24	which	which	PRON
ejpam-2418	48	25	g	g	NOUN
ejpam-2418	48	26	f	f	PROPN
ejpam-2418	48	27	is	be	AUX
ejpam-2418	48	28	a	a	DET
ejpam-2418	48	29	monomorphism	monomorphism	NOUN
ejpam-2418	48	30	,	,	PUNCT
ejpam-2418	48	31	then	then	ADV
ejpam-2418	48	32	g	g	PROPN
ejpam-2418	48	33	is	be	AUX
ejpam-2418	48	34	so	so	ADV
ejpam-2418	48	35	.	.	PUNCT
ejpam-2418	49	1	if	if	SCONJ
ejpam-2418	49	2	f	f	PROPN
ejpam-2418	49	3	is	be	AUX
ejpam-2418	49	4	an	an	DET
ejpam-2418	49	5	inclusion	inclusion	NOUN
ejpam-2418	49	6	map	map	NOUN
ejpam-2418	49	7	,	,	PUNCT
ejpam-2418	49	8	then	then	ADV
ejpam-2418	49	9	b	b	PROPN
ejpam-2418	49	10	is	be	AUX
ejpam-2418	49	11	said	say	VERB
ejpam-2418	49	12	to	to	PART
ejpam-2418	49	13	be	be	AUX
ejpam-2418	49	14	an	an	DET
ejpam-2418	49	15	essential	essential	ADJ
ejpam-2418	49	16	extension	extension	NOUN
ejpam-2418	49	17	of	of	ADP
ejpam-2418	49	18	a.	a.	NOUN
ejpam-2418	49	19	the	the	DET
ejpam-2418	49	20	following	follow	VERB
ejpam-2418	49	21	two	two	NUM
ejpam-2418	49	22	theorems	theorem	NOUN
ejpam-2418	49	23	give	give	VERB
ejpam-2418	49	24	the	the	DET
ejpam-2418	49	25	usual	usual	ADJ
ejpam-2418	49	26	(	(	PUNCT
ejpam-2418	49	27	external	external	ADJ
ejpam-2418	49	28	)	)	PUNCT
ejpam-2418	49	29	characterizations	characterization	NOUN
ejpam-2418	49	30	for	for	ADP
ejpam-2418	49	31	the	the	DET
ejpam-2418	49	32	essentiality	essentiality	NOUN
ejpam-2418	49	33	(	(	PUNCT
ejpam-2418	49	34	mainly	mainly	ADV
ejpam-2418	49	35	in	in	ADP
ejpam-2418	49	36	terms	term	NOUN
ejpam-2418	49	37	of	of	ADP
ejpam-2418	49	38	congruences	congruence	NOUN
ejpam-2418	49	39	)	)	PUNCT
ejpam-2418	49	40	.	.	PUNCT
ejpam-2418	50	1	more	more	ADJ
ejpam-2418	50	2	(	(	PUNCT
ejpam-2418	50	3	internal	internal	ADJ
ejpam-2418	50	4	)	)	PUNCT
ejpam-2418	50	5	characterizations	characterization	NOUN
ejpam-2418	50	6	(	(	PUNCT
ejpam-2418	50	7	in	in	ADP
ejpam-2418	50	8	terms	term	NOUN
ejpam-2418	50	9	of	of	ADP
ejpam-2418	50	10	elements	element	NOUN
ejpam-2418	50	11	)	)	PUNCT
ejpam-2418	50	12	will	will	AUX
ejpam-2418	50	13	be	be	AUX
ejpam-2418	50	14	given	give	VERB
ejpam-2418	50	15	later	later	ADV
ejpam-2418	50	16	in	in	ADP
ejpam-2418	50	17	this	this	DET
ejpam-2418	50	18	section	section	NOUN
ejpam-2418	50	19	.	.	PUNCT
ejpam-2418	51	1	the	the	DET
ejpam-2418	51	2	set	set	NOUN
ejpam-2418	51	3	of	of	ADP
ejpam-2418	51	4	all	all	DET
ejpam-2418	51	5	congruences	congruence	NOUN
ejpam-2418	51	6	on	on	ADP
ejpam-2418	51	7	an	an	DET
ejpam-2418	51	8	s	s	PROPN
ejpam-2418	51	9	-	-	PUNCT
ejpam-2418	51	10	act	act	NOUN
ejpam-2418	51	11	b	b	NOUN
ejpam-2418	51	12	is	be	AUX
ejpam-2418	51	13	denoted	denote	VERB
ejpam-2418	51	14	by	by	ADP
ejpam-2418	51	15	con(b	con(b	PROPN
ejpam-2418	51	16	)	)	PUNCT
ejpam-2418	51	17	and	and	CCONJ
ejpam-2418	51	18	∆	∆	PROPN
ejpam-2418	51	19	is	be	AUX
ejpam-2418	51	20	the	the	DET
ejpam-2418	51	21	trivial	trivial	ADJ
ejpam-2418	51	22	congruence(i.e	congruence(i.e	NOUN
ejpam-2418	51	23	.	.	PUNCT
ejpam-2418	52	1	a∆b	a∆b	VERB
ejpam-2418	52	2	if	if	SCONJ
ejpam-2418	52	3	and	and	CCONJ
ejpam-2418	52	4	only	only	ADV
ejpam-2418	52	5	if	if	SCONJ
ejpam-2418	52	6	a	a	DET
ejpam-2418	52	7	=	=	SYM
ejpam-2418	52	8	b.	b.	NOUN
ejpam-2418	52	9	)	)	PUNCT
ejpam-2418	52	10	lemma	lemma	PROPN
ejpam-2418	53	1	1	1	NUM
ejpam-2418	53	2	.	.	PUNCT
ejpam-2418	53	3	for	for	ADP
ejpam-2418	53	4	a	a	DET
ejpam-2418	53	5	monomorphism	monomorphism	NOUN
ejpam-2418	53	6	f	f	X
ejpam-2418	53	7	:	:	PUNCT
ejpam-2418	53	8	a→	a→	PROPN
ejpam-2418	53	9	b	b	X
ejpam-2418	53	10	,	,	PUNCT
ejpam-2418	53	11	the	the	DET
ejpam-2418	53	12	following	follow	VERB
ejpam-2418	53	13	are	be	AUX
ejpam-2418	53	14	equivalent	equivalent	ADJ
ejpam-2418	53	15	:	:	PUNCT
ejpam-2418	53	16	(	(	PUNCT
ejpam-2418	53	17	i	i	NOUN
ejpam-2418	53	18	)	)	PUNCT
ejpam-2418	53	19	f	f	PROPN
ejpam-2418	53	20	is	be	AUX
ejpam-2418	53	21	an	an	DET
ejpam-2418	53	22	essential	essential	ADJ
ejpam-2418	53	23	monomorphism	monomorphism	NOUN
ejpam-2418	53	24	.	.	PUNCT
ejpam-2418	54	1	h.	h.	PROPN
ejpam-2418	54	2	barzegar	barzegar	PROPN
ejpam-2418	54	3	/	/	SYM
ejpam-2418	54	4	eur	eur	PROPN
ejpam-2418	54	5	.	.	PUNCT
ejpam-2418	55	1	j.	j.	PROPN
ejpam-2418	55	2	pure	pure	PROPN
ejpam-2418	55	3	appl	appl	PROPN
ejpam-2418	55	4	.	.	PROPN
ejpam-2418	55	5	math	math	PROPN
ejpam-2418	55	6	,	,	PUNCT
ejpam-2418	55	7	9	9	NUM
ejpam-2418	55	8	(	(	PUNCT
ejpam-2418	55	9	2016	2016	NUM
ejpam-2418	55	10	)	)	PUNCT
ejpam-2418	55	11	,	,	PUNCT
ejpam-2418	55	12	19	19	NUM
ejpam-2418	55	13	-	-	SYM
ejpam-2418	55	14	26	26	NUM
ejpam-2418	55	15	21	21	NUM
ejpam-2418	55	16	(	(	PUNCT
ejpam-2418	55	17	ii	ii	NOUN
ejpam-2418	55	18	)	)	PUNCT
ejpam-2418	55	19	for	for	ADP
ejpam-2418	55	20	every	every	DET
ejpam-2418	55	21	epimorphism	epimorphism	NOUN
ejpam-2418	55	22	g	g	NOUN
ejpam-2418	55	23	:	:	PUNCT
ejpam-2418	55	24	b→	b→	PROPN
ejpam-2418	55	25	c	c	NOUN
ejpam-2418	55	26	such	such	ADJ
ejpam-2418	55	27	that	that	SCONJ
ejpam-2418	55	28	g	g	PROPN
ejpam-2418	55	29	f	f	PROPN
ejpam-2418	55	30	is	be	AUX
ejpam-2418	55	31	a	a	DET
ejpam-2418	55	32	monomorphism	monomorphism	NOUN
ejpam-2418	55	33	,	,	PUNCT
ejpam-2418	55	34	g	g	PROPN
ejpam-2418	55	35	itself	itself	PRON
ejpam-2418	55	36	is	be	AUX
ejpam-2418	55	37	a	a	DET
ejpam-2418	55	38	monomorphism	monomorphism	NOUN
ejpam-2418	55	39	.	.	PUNCT
ejpam-2418	56	1	(	(	PUNCT
ejpam-2418	56	2	iii	iii	NOUN
ejpam-2418	56	3	)	)	PUNCT
ejpam-2418	56	4	for	for	ADP
ejpam-2418	56	5	every	every	DET
ejpam-2418	56	6	congruence	congruence	NOUN
ejpam-2418	56	7	ρ	ρ	NOUN
ejpam-2418	56	8	on	on	ADP
ejpam-2418	56	9	b	b	NOUN
ejpam-2418	56	10	such	such	ADJ
ejpam-2418	56	11	that	that	DET
ejpam-2418	56	12	for	for	ADP
ejpam-2418	56	13	the	the	DET
ejpam-2418	56	14	canonical	canonical	ADJ
ejpam-2418	56	15	epimorphism	epimorphism	NOUN
ejpam-2418	56	16	π	π	NOUN
ejpam-2418	56	17	:	:	PUNCT
ejpam-2418	56	18	b→	b→	PROPN
ejpam-2418	56	19	b	b	X
ejpam-2418	56	20	/	/	SYM
ejpam-2418	56	21	ρ	ρ	PROPN
ejpam-2418	56	22	,	,	PUNCT
ejpam-2418	56	23	π	π	PROPN
ejpam-2418	56	24	f	f	PROPN
ejpam-2418	56	25	is	be	AUX
ejpam-2418	56	26	a	a	DET
ejpam-2418	56	27	monomorphism	monomorphism	NOUN
ejpam-2418	56	28	,	,	PUNCT
ejpam-2418	56	29	we	we	PRON
ejpam-2418	56	30	get	get	VERB
ejpam-2418	56	31	ρ	ρ	NOUN
ejpam-2418	56	32	=	=	PROPN
ejpam-2418	56	33	∆.	∆.	X
ejpam-2418	56	34	(	(	PUNCT
ejpam-2418	56	35	iv	iv	X
ejpam-2418	56	36	)	)	PUNCT
ejpam-2418	56	37	for	for	ADP
ejpam-2418	56	38	every	every	DET
ejpam-2418	56	39	monogenic	monogenic	ADJ
ejpam-2418	56	40	congruence	congruence	NOUN
ejpam-2418	56	41	ρ	ρ	PROPN
ejpam-2418	56	42	on	on	ADP
ejpam-2418	56	43	b	b	NOUN
ejpam-2418	56	44	such	such	ADJ
ejpam-2418	56	45	that	that	DET
ejpam-2418	56	46	for	for	ADP
ejpam-2418	56	47	the	the	DET
ejpam-2418	56	48	canonical	canonical	ADJ
ejpam-2418	56	49	epimorphism	epimorphism	NOUN
ejpam-2418	56	50	π	π	NOUN
ejpam-2418	56	51	:	:	PUNCT
ejpam-2418	56	52	b→	b→	PROPN
ejpam-2418	56	53	b	b	X
ejpam-2418	56	54	/	/	SYM
ejpam-2418	56	55	ρ	ρ	PROPN
ejpam-2418	56	56	,	,	PUNCT
ejpam-2418	56	57	π	π	PROPN
ejpam-2418	56	58	f	f	PROPN
ejpam-2418	56	59	is	be	AUX
ejpam-2418	56	60	a	a	DET
ejpam-2418	56	61	monomorphism	monomorphism	NOUN
ejpam-2418	56	62	,	,	PUNCT
ejpam-2418	56	63	we	we	PRON
ejpam-2418	56	64	get	get	VERB
ejpam-2418	56	65	ρ	ρ	NOUN
ejpam-2418	56	66	=	=	NOUN
ejpam-2418	56	67	∆.	∆.	NOUN
ejpam-2418	56	68	proof	proof	NOUN
ejpam-2418	56	69	.	.	PUNCT
ejpam-2418	57	1	we	we	PRON
ejpam-2418	57	2	just	just	ADV
ejpam-2418	57	3	prove	prove	VERB
ejpam-2418	57	4	(	(	PUNCT
ejpam-2418	57	5	iv)⇒	iv)⇒	X
ejpam-2418	57	6	(	(	PUNCT
ejpam-2418	57	7	i	i	NOUN
ejpam-2418	57	8	)	)	PUNCT
ejpam-2418	57	9	.	.	PUNCT
ejpam-2418	58	1	let	let	VERB
ejpam-2418	58	2	g	g	NOUN
ejpam-2418	58	3	:	:	PUNCT
ejpam-2418	58	4	b→	b→	PROPN
ejpam-2418	58	5	c	c	AUX
ejpam-2418	58	6	be	be	AUX
ejpam-2418	58	7	a	a	DET
ejpam-2418	58	8	homomorphism	homomorphism	NOUN
ejpam-2418	58	9	with	with	ADP
ejpam-2418	58	10	g	g	PROPN
ejpam-2418	58	11	f	f	PROPN
ejpam-2418	58	12	a	a	DET
ejpam-2418	58	13	monomorphism	monomorphism	NOUN
ejpam-2418	58	14	,	,	PUNCT
ejpam-2418	58	15	and	and	CCONJ
ejpam-2418	58	16	g(b	g(b	PROPN
ejpam-2418	58	17	)	)	PUNCT
ejpam-2418	58	18	=	=	SYM
ejpam-2418	58	19	g(b′	g(b′	PROPN
ejpam-2418	58	20	)	)	PUNCT
ejpam-2418	58	21	.	.	PUNCT
ejpam-2418	59	1	then	then	ADV
ejpam-2418	59	2	,	,	PUNCT
ejpam-2418	59	3	sinceρ(b	sinceρ(b	PROPN
ejpam-2418	59	4	,	,	PUNCT
ejpam-2418	59	5	b′	b′	NUM
ejpam-2418	59	6	)	)	PUNCT
ejpam-2418	59	7	⊆	⊆	NUM
ejpam-2418	59	8	ker(g	ker(g	PROPN
ejpam-2418	59	9	)	)	PUNCT
ejpam-2418	59	10	,	,	PUNCT
ejpam-2418	59	11	we	we	PRON
ejpam-2418	59	12	can	can	AUX
ejpam-2418	59	13	factorize	factorize	VERB
ejpam-2418	59	14	g	g	NOUN
ejpam-2418	59	15	through	through	ADP
ejpam-2418	59	16	b	b	PROPN
ejpam-2418	59	17	/	/	SYM
ejpam-2418	59	18	ρ(b	ρ(b	NOUN
ejpam-2418	59	19	,	,	PUNCT
ejpam-2418	59	20	b′	b′	NUM
ejpam-2418	59	21	)	)	PUNCT
ejpam-2418	59	22	,	,	PUNCT
ejpam-2418	59	23	and	and	CCONJ
ejpam-2418	59	24	hence	hence	ADV
ejpam-2418	59	25	π	π	X
ejpam-2418	59	26	f	f	PROPN
ejpam-2418	59	27	is	be	AUX
ejpam-2418	59	28	a	a	DET
ejpam-2418	59	29	monomorphism	monomorphism	NOUN
ejpam-2418	59	30	,	,	PUNCT
ejpam-2418	59	31	where	where	SCONJ
ejpam-2418	59	32	π	π	X
ejpam-2418	59	33	:	:	PUNCT
ejpam-2418	60	1	b→	b→	PROPN
ejpam-2418	60	2	b	b	X
ejpam-2418	60	3	/	/	SYM
ejpam-2418	60	4	ρ(b	ρ(b	NOUN
ejpam-2418	60	5	,	,	PUNCT
ejpam-2418	60	6	b′	b′	NUM
ejpam-2418	60	7	)	)	PUNCT
ejpam-2418	60	8	.	.	PUNCT
ejpam-2418	61	1	so	so	ADV
ejpam-2418	61	2	,	,	PUNCT
ejpam-2418	61	3	by	by	ADP
ejpam-2418	61	4	(	(	PUNCT
ejpam-2418	61	5	iv	iv	X
ejpam-2418	61	6	)	)	PUNCT
ejpam-2418	61	7	,	,	PUNCT
ejpam-2418	61	8	ρ(b	ρ(b	NOUN
ejpam-2418	61	9	,	,	PUNCT
ejpam-2418	61	10	b′	b′	NUM
ejpam-2418	61	11	)	)	PUNCT
ejpam-2418	61	12	=	=	SYM
ejpam-2418	61	13	∆	∆	NOUN
ejpam-2418	61	14	,	,	PUNCT
ejpam-2418	61	15	and	and	CCONJ
ejpam-2418	61	16	thus	thus	ADV
ejpam-2418	61	17	b	b	X
ejpam-2418	61	18	=	=	SYM
ejpam-2418	61	19	b′.	b′.	PROPN
ejpam-2418	61	20	corollary	corollary	NOUN
ejpam-2418	61	21	1	1	NUM
ejpam-2418	61	22	.	.	PUNCT
ejpam-2418	62	1	an	an	DET
ejpam-2418	62	2	s	s	NOUN
ejpam-2418	62	3	-	-	PUNCT
ejpam-2418	62	4	act	act	NOUN
ejpam-2418	62	5	b	b	NOUN
ejpam-2418	62	6	is	be	AUX
ejpam-2418	62	7	an	an	DET
ejpam-2418	62	8	essential	essential	ADJ
ejpam-2418	62	9	extension	extension	NOUN
ejpam-2418	62	10	of	of	ADP
ejpam-2418	62	11	a	a	DET
ejpam-2418	62	12	if	if	NOUN
ejpam-2418	62	13	and	and	CCONJ
ejpam-2418	62	14	only	only	ADV
ejpam-2418	62	15	if	if	SCONJ
ejpam-2418	62	16	for	for	ADP
ejpam-2418	62	17	each	each	DET
ejpam-2418	62	18	congruence	congruence	NOUN
ejpam-2418	62	19	ρ	ρ	PROPN
ejpam-2418	62	20	on	on	ADP
ejpam-2418	62	21	b	b	NUM
ejpam-2418	62	22	,	,	PUNCT
ejpam-2418	62	23	if	if	SCONJ
ejpam-2418	62	24	ρ	ρ	PROPN
ejpam-2418	62	25	|	|	NOUN
ejpam-2418	62	26	a	a	DET
ejpam-2418	62	27	=	=	NOUN
ejpam-2418	62	28	∆	∆	X
ejpam-2418	62	29	,	,	PUNCT
ejpam-2418	62	30	then	then	ADV
ejpam-2418	62	31	ρ	ρ	PROPN
ejpam-2418	62	32	=	=	PROPN
ejpam-2418	62	33	∆.	∆.	PROPN
ejpam-2418	62	34	theorem	theorem	NOUN
ejpam-2418	62	35	1	1	NUM
ejpam-2418	62	36	.	.	PUNCT
ejpam-2418	63	1	an	an	DET
ejpam-2418	63	2	extension	extension	NOUN
ejpam-2418	63	3	b	b	NOUN
ejpam-2418	63	4	of	of	ADP
ejpam-2418	63	5	a	a	PRON
ejpam-2418	63	6	is	be	AUX
ejpam-2418	63	7	an	an	DET
ejpam-2418	63	8	essential	essential	ADJ
ejpam-2418	63	9	extension	extension	NOUN
ejpam-2418	63	10	if	if	SCONJ
ejpam-2418	63	11	and	and	CCONJ
ejpam-2418	63	12	only	only	ADV
ejpam-2418	63	13	if	if	SCONJ
ejpam-2418	63	14	for	for	ADP
ejpam-2418	63	15	every	every	DET
ejpam-2418	63	16	non	non	ADJ
ejpam-2418	63	17	trivial	trivial	ADJ
ejpam-2418	63	18	θ	θ	PROPN
ejpam-2418	63	19	∈	∈	PROPN
ejpam-2418	63	20	con(b	con(b	PROPN
ejpam-2418	63	21	)	)	PUNCT
ejpam-2418	63	22	,	,	PUNCT
ejpam-2418	63	23	θ	θ	PROPN
ejpam-2418	63	24	∩ρ	∩ρ	PROPN
ejpam-2418	63	25	a	a	DET
ejpam-2418	63	26	6=∆	6=∆	NOUN
ejpam-2418	63	27	,	,	PUNCT
ejpam-2418	63	28	where	where	SCONJ
ejpam-2418	63	29	ρa	ρa	PRON
ejpam-2418	63	30	is	be	AUX
ejpam-2418	63	31	the	the	DET
ejpam-2418	63	32	rees	rees	PROPN
ejpam-2418	63	33	congruence	congruence	VERB
ejpam-2418	63	34	on	on	ADP
ejpam-2418	63	35	b.	b.	PROPN
ejpam-2418	63	36	proof	proof	NOUN
ejpam-2418	63	37	.	.	PUNCT
ejpam-2418	64	1	(	(	PUNCT
ejpam-2418	64	2	⇒	⇒	PROPN
ejpam-2418	64	3	)	)	PUNCT
ejpam-2418	64	4	let	let	VERB
ejpam-2418	64	5	θ	θ	PROPN
ejpam-2418	64	6	6=	6=	NUM
ejpam-2418	64	7	∆	∆	PROPN
ejpam-2418	64	8	and	and	CCONJ
ejpam-2418	64	9	θ	θ	PROPN
ejpam-2418	64	10	∩	∩	X
ejpam-2418	64	11	ρ	ρ	VERB
ejpam-2418	64	12	a	a	X
ejpam-2418	64	13	=	=	X
ejpam-2418	64	14	∆.	∆.	X
ejpam-2418	64	15	then	then	ADV
ejpam-2418	64	16	,	,	PUNCT
ejpam-2418	64	17	considering	consider	VERB
ejpam-2418	64	18	the	the	DET
ejpam-2418	64	19	canonical	canonical	ADJ
ejpam-2418	64	20	epimorphism	epimorphism	NOUN
ejpam-2418	64	21	π	π	NOUN
ejpam-2418	64	22	:	:	PUNCT
ejpam-2418	64	23	b	b	X
ejpam-2418	64	24	→	→	SYM
ejpam-2418	64	25	b	b	X
ejpam-2418	64	26	/	/	SYM
ejpam-2418	64	27	θ	θ	PROPN
ejpam-2418	64	28	,	,	PUNCT
ejpam-2418	64	29	we	we	PRON
ejpam-2418	64	30	see	see	VERB
ejpam-2418	64	31	that	that	SCONJ
ejpam-2418	64	32	π|a	π|a	PROPN
ejpam-2418	64	33	is	be	AUX
ejpam-2418	64	34	a	a	DET
ejpam-2418	64	35	monomorphism	monomorphism	NOUN
ejpam-2418	64	36	,	,	PUNCT
ejpam-2418	64	37	and	and	CCONJ
ejpam-2418	64	38	so	so	ADV
ejpam-2418	64	39	by	by	ADP
ejpam-2418	64	40	hypothesis	hypothesis	NOUN
ejpam-2418	64	41	θ	θ	NOUN
ejpam-2418	64	42	=	=	PUNCT
ejpam-2418	64	43	∆	∆	PROPN
ejpam-2418	64	44	which	which	PRON
ejpam-2418	64	45	is	be	AUX
ejpam-2418	64	46	a	a	DET
ejpam-2418	64	47	contradiction	contradiction	NOUN
ejpam-2418	64	48	.	.	PUNCT
ejpam-2418	65	1	(	(	PUNCT
ejpam-2418	65	2	⇐	⇐	NOUN
ejpam-2418	65	3	)	)	PUNCT
ejpam-2418	65	4	let	let	VERB
ejpam-2418	65	5	g	g	NOUN
ejpam-2418	65	6	:	:	PUNCT
ejpam-2418	65	7	b→	b→	PROPN
ejpam-2418	65	8	c	c	AUX
ejpam-2418	65	9	be	be	AUX
ejpam-2418	65	10	a	a	DET
ejpam-2418	65	11	homomorphism	homomorphism	NOUN
ejpam-2418	65	12	such	such	ADJ
ejpam-2418	65	13	that	that	DET
ejpam-2418	65	14	g|a	g|a	NOUN
ejpam-2418	65	15	is	be	AUX
ejpam-2418	65	16	a	a	DET
ejpam-2418	65	17	monomorphism	monomorphism	NOUN
ejpam-2418	65	18	.	.	PUNCT
ejpam-2418	66	1	it	it	PRON
ejpam-2418	66	2	is	be	AUX
ejpam-2418	66	3	clear	clear	ADJ
ejpam-2418	66	4	that	that	SCONJ
ejpam-2418	66	5	ker(g)∩ρa	ker(g)∩ρa	PROPN
ejpam-2418	66	6	=	=	PUNCT
ejpam-2418	66	7	∆.	∆.	PROPN
ejpam-2418	66	8	so	so	ADV
ejpam-2418	66	9	by	by	ADP
ejpam-2418	66	10	hypothesis	hypothesis	NOUN
ejpam-2418	66	11	,	,	PUNCT
ejpam-2418	66	12	ker(g	ker(g	PROPN
ejpam-2418	66	13	)	)	PUNCT
ejpam-2418	66	14	=	=	SYM
ejpam-2418	67	1	∆	∆	PROPN
ejpam-2418	68	1	and	and	CCONJ
ejpam-2418	68	2	hence	hence	ADV
ejpam-2418	68	3	g	g	PROPN
ejpam-2418	68	4	is	be	AUX
ejpam-2418	68	5	a	a	DET
ejpam-2418	68	6	monomorphism	monomorphism	NOUN
ejpam-2418	68	7	.	.	PUNCT
ejpam-2418	69	1	theorem	theorem	NOUN
ejpam-2418	69	2	2	2	NUM
ejpam-2418	69	3	.	.	PUNCT
ejpam-2418	70	1	the	the	DET
ejpam-2418	70	2	monomorphisms	monomorphism	NOUN
ejpam-2418	70	3	f	f	X
ejpam-2418	70	4	:	:	PUNCT
ejpam-2418	70	5	a→	a→	PROPN
ejpam-2418	70	6	b	b	NOUN
ejpam-2418	70	7	and	and	CCONJ
ejpam-2418	70	8	g	g	NOUN
ejpam-2418	70	9	:	:	PUNCT
ejpam-2418	70	10	b→	b→	PROPN
ejpam-2418	70	11	c	c	PROPN
ejpam-2418	70	12	are	be	AUX
ejpam-2418	70	13	essential	essential	ADJ
ejpam-2418	70	14	monomorphisms	monomorphism	NOUN
ejpam-2418	70	15	if	if	SCONJ
ejpam-2418	70	16	and	and	CCONJ
ejpam-2418	70	17	only	only	ADV
ejpam-2418	70	18	if	if	SCONJ
ejpam-2418	70	19	g	g	PROPN
ejpam-2418	70	20	f	f	PROPN
ejpam-2418	70	21	is	be	AUX
ejpam-2418	70	22	so	so	ADV
ejpam-2418	70	23	.	.	PUNCT
ejpam-2418	71	1	proof	proof	NOUN
ejpam-2418	71	2	.	.	PUNCT
ejpam-2418	72	1	we	we	PRON
ejpam-2418	72	2	just	just	ADV
ejpam-2418	72	3	prove	prove	VERB
ejpam-2418	72	4	the	the	DET
ejpam-2418	72	5	case	case	NOUN
ejpam-2418	72	6	that	that	SCONJ
ejpam-2418	72	7	if	if	SCONJ
ejpam-2418	72	8	g	g	PROPN
ejpam-2418	72	9	f	f	PROPN
ejpam-2418	72	10	is	be	AUX
ejpam-2418	72	11	an	an	DET
ejpam-2418	72	12	essential	essential	ADJ
ejpam-2418	72	13	monomorphism	monomorphism	NOUN
ejpam-2418	72	14	,	,	PUNCT
ejpam-2418	72	15	then	then	ADV
ejpam-2418	72	16	f	f	PROPN
ejpam-2418	72	17	is	be	AUX
ejpam-2418	72	18	so	so	ADV
ejpam-2418	72	19	.	.	PUNCT
ejpam-2418	73	1	let	let	VERB
ejpam-2418	73	2	h	h	NOUN
ejpam-2418	73	3	:	:	PUNCT
ejpam-2418	73	4	b→	b→	PROPN
ejpam-2418	73	5	d	d	PART
ejpam-2418	73	6	be	be	AUX
ejpam-2418	73	7	a	a	DET
ejpam-2418	73	8	homomorphism	homomorphism	NOUN
ejpam-2418	73	9	such	such	ADJ
ejpam-2418	73	10	that	that	SCONJ
ejpam-2418	73	11	hf	hf	PROPN
ejpam-2418	73	12	is	be	AUX
ejpam-2418	73	13	a	a	DET
ejpam-2418	73	14	monomorphism	monomorphism	NOUN
ejpam-2418	73	15	.	.	PUNCT
ejpam-2418	74	1	then	then	ADV
ejpam-2418	74	2	there	there	PRON
ejpam-2418	74	3	exists	exist	VERB
ejpam-2418	74	4	an	an	DET
ejpam-2418	74	5	extension	extension	NOUN
ejpam-2418	74	6	h̄	h̄	NOUN
ejpam-2418	74	7	:	:	PUNCT
ejpam-2418	74	8	c	c	X
ejpam-2418	74	9	→	→	SYM
ejpam-2418	74	10	e(d	e(d	PROPN
ejpam-2418	74	11	)	)	PUNCT
ejpam-2418	74	12	of	of	ADP
ejpam-2418	74	13	h	h	NOUN
ejpam-2418	74	14	to	to	ADP
ejpam-2418	74	15	the	the	DET
ejpam-2418	74	16	injective	injective	ADJ
ejpam-2418	74	17	hull	hull	NOUN
ejpam-2418	74	18	of	of	ADP
ejpam-2418	74	19	d	d	PROPN
ejpam-2418	74	20	,	,	PUNCT
ejpam-2418	74	21	and	and	CCONJ
ejpam-2418	74	22	since	since	SCONJ
ejpam-2418	74	23	g	g	PROPN
ejpam-2418	74	24	f	f	PROPN
ejpam-2418	74	25	is	be	AUX
ejpam-2418	74	26	essential	essential	ADJ
ejpam-2418	74	27	,	,	PUNCT
ejpam-2418	74	28	h̄	h̄	NOUN
ejpam-2418	74	29	is	be	AUX
ejpam-2418	74	30	a	a	DET
ejpam-2418	74	31	monomorphism	monomorphism	NOUN
ejpam-2418	74	32	,	,	PUNCT
ejpam-2418	74	33	and	and	CCONJ
ejpam-2418	74	34	hence	hence	ADV
ejpam-2418	74	35	so	so	ADV
ejpam-2418	74	36	is	be	AUX
ejpam-2418	74	37	h.	h.	PROPN
ejpam-2418	74	38	proposition	proposition	PROPN
ejpam-2418	74	39	1	1	X
ejpam-2418	74	40	.	.	PUNCT
ejpam-2418	75	1	let	let	VERB
ejpam-2418	75	2	a	a	PRON
ejpam-2418	75	3	and	and	CCONJ
ejpam-2418	75	4	c	c	AUX
ejpam-2418	75	5	be	be	AUX
ejpam-2418	75	6	subacts	subact	NOUN
ejpam-2418	75	7	of	of	ADP
ejpam-2418	75	8	b	b	NOUN
ejpam-2418	75	9	such	such	ADJ
ejpam-2418	75	10	that	that	PRON
ejpam-2418	75	11	|c	|c	VERB
ejpam-2418	75	12	|	|	NOUN
ejpam-2418	75	13	≥	≥	NOUN
ejpam-2418	75	14	2	2	NUM
ejpam-2418	75	15	and	and	CCONJ
ejpam-2418	75	16	b	b	NOUN
ejpam-2418	75	17	is	be	AUX
ejpam-2418	75	18	an	an	DET
ejpam-2418	75	19	essential	essential	ADJ
ejpam-2418	75	20	extension	extension	NOUN
ejpam-2418	75	21	of	of	ADP
ejpam-2418	75	22	a.	a.	NOUN
ejpam-2418	75	23	then	then	ADV
ejpam-2418	75	24	|c	|c	VERB
ejpam-2418	75	25	∩	∩	NOUN
ejpam-2418	75	26	a|	a|	X
ejpam-2418	75	27	≥	≥	NUM
ejpam-2418	75	28	2	2	NUM
ejpam-2418	75	29	.	.	PUNCT
ejpam-2418	76	1	in	in	ADP
ejpam-2418	76	2	particular	particular	ADJ
ejpam-2418	76	3	,	,	PUNCT
ejpam-2418	76	4	b	b	PROPN
ejpam-2418	76	5	\	\	PROPN
ejpam-2418	76	6	a	a	PRON
ejpam-2418	76	7	does	do	AUX
ejpam-2418	76	8	not	not	PART
ejpam-2418	76	9	have	have	VERB
ejpam-2418	76	10	two	two	NUM
ejpam-2418	76	11	fixed	fix	VERB
ejpam-2418	76	12	elements	element	NOUN
ejpam-2418	76	13	.	.	PUNCT
ejpam-2418	77	1	proof	proof	NOUN
ejpam-2418	77	2	.	.	PUNCT
ejpam-2418	78	1	let	let	VERB
ejpam-2418	78	2	|c∩a|	|c∩a|	NOUN
ejpam-2418	78	3	≤	≤	ADV
ejpam-2418	78	4	1	1	NUM
ejpam-2418	78	5	.	.	PUNCT
ejpam-2418	79	1	it	it	PRON
ejpam-2418	79	2	is	be	AUX
ejpam-2418	79	3	clear	clear	ADJ
ejpam-2418	79	4	thatπ|a	thatπ|a	NOUN
ejpam-2418	79	5	:	:	PUNCT
ejpam-2418	79	6	a→	a→	PROPN
ejpam-2418	79	7	b	b	X
ejpam-2418	79	8	/	/	SYM
ejpam-2418	79	9	ρ	ρ	PROPN
ejpam-2418	79	10	c	c	NOUN
ejpam-2418	79	11	,	,	PUNCT
ejpam-2418	79	12	in	in	ADP
ejpam-2418	79	13	which	which	PRON
ejpam-2418	79	14	ρ	ρ	NOUN
ejpam-2418	79	15	c	c	PROPN
ejpam-2418	79	16	is	be	AUX
ejpam-2418	79	17	a	a	DET
ejpam-2418	79	18	ress	ress	NOUN
ejpam-2418	79	19	congruence	congruence	NOUN
ejpam-2418	79	20	on	on	ADP
ejpam-2418	79	21	c	c	PROPN
ejpam-2418	79	22	,	,	PUNCT
ejpam-2418	79	23	is	be	AUX
ejpam-2418	79	24	a	a	DET
ejpam-2418	79	25	monomorphism	monomorphism	NOUN
ejpam-2418	79	26	.	.	PUNCT
ejpam-2418	80	1	hence	hence	ADV
ejpam-2418	80	2	,	,	PUNCT
ejpam-2418	80	3	π	π	PROPN
ejpam-2418	80	4	is	be	AUX
ejpam-2418	80	5	a	a	DET
ejpam-2418	80	6	monomorphism	monomorphism	NOUN
ejpam-2418	80	7	and	and	CCONJ
ejpam-2418	80	8	so	so	ADV
ejpam-2418	80	9	|c	|c	ADJ
ejpam-2418	80	10	|=	|=	NOUN
ejpam-2418	80	11	1	1	NUM
ejpam-2418	80	12	,	,	PUNCT
ejpam-2418	80	13	which	which	PRON
ejpam-2418	80	14	is	be	AUX
ejpam-2418	80	15	a	a	DET
ejpam-2418	80	16	contradiction	contradiction	NOUN
ejpam-2418	80	17	.	.	PUNCT
ejpam-2418	81	1	corollary	corollary	ADJ
ejpam-2418	81	2	2	2	NUM
ejpam-2418	81	3	.	.	PUNCT
ejpam-2418	82	1	if	if	SCONJ
ejpam-2418	82	2	a0	a0	PROPN
ejpam-2418	82	3	∈	∈	PROPN
ejpam-2418	82	4	a	a	DET
ejpam-2418	82	5	and	and	CCONJ
ejpam-2418	82	6	b0	b0	ADP
ejpam-2418	82	7	∈	∈	PROPN
ejpam-2418	82	8	b	b	NOUN
ejpam-2418	82	9	\	\	PROPN
ejpam-2418	82	10	a	a	PRON
ejpam-2418	82	11	are	be	AUX
ejpam-2418	82	12	fixed	fix	VERB
ejpam-2418	82	13	elements	element	NOUN
ejpam-2418	82	14	,	,	PUNCT
ejpam-2418	82	15	then	then	ADV
ejpam-2418	82	16	b	b	X
ejpam-2418	82	17	is	be	AUX
ejpam-2418	82	18	not	not	PART
ejpam-2418	82	19	an	an	DET
ejpam-2418	82	20	essential	essential	ADJ
ejpam-2418	82	21	extension	extension	NOUN
ejpam-2418	82	22	of	of	ADP
ejpam-2418	82	23	a.	a.	NOUN
ejpam-2418	82	24	for	for	ADP
ejpam-2418	82	25	a	a	DET
ejpam-2418	82	26	subact	subact	NOUN
ejpam-2418	82	27	a	a	PRON
ejpam-2418	82	28	of	of	ADP
ejpam-2418	82	29	an	an	DET
ejpam-2418	82	30	s	s	NOUN
ejpam-2418	82	31	-	-	PUNCT
ejpam-2418	82	32	act	act	NOUN
ejpam-2418	82	33	b	b	NOUN
ejpam-2418	82	34	and	and	CCONJ
ejpam-2418	82	35	b	b	PROPN
ejpam-2418	82	36	∈	∈	PROPN
ejpam-2418	82	37	b	b	NOUN
ejpam-2418	82	38	,	,	PUNCT
ejpam-2418	82	39	we	we	PRON
ejpam-2418	82	40	use	use	VERB
ejpam-2418	82	41	the	the	DET
ejpam-2418	82	42	notation	notation	NOUN
ejpam-2418	82	43	ib	ib	NOUN
ejpam-2418	82	44	=	=	PRON
ejpam-2418	82	45	{	{	PUNCT
ejpam-2418	82	46	s	s	NOUN
ejpam-2418	82	47	∈	∈	NOUN
ejpam-2418	82	48	s	s	VERB
ejpam-2418	82	49	|	|	ADV
ejpam-2418	82	50	bs	bs	NOUN
ejpam-2418	82	51	∈	∈	PROPN
ejpam-2418	82	52	a	a	PRON
ejpam-2418	82	53	}	}	PUNCT
ejpam-2418	82	54	.	.	PUNCT
ejpam-2418	83	1	corollary	corollary	ADJ
ejpam-2418	83	2	3	3	X
ejpam-2418	83	3	.	.	PUNCT
ejpam-2418	83	4	let	let	VERB
ejpam-2418	83	5	a	a	DET
ejpam-2418	83	6	have	have	AUX
ejpam-2418	83	7	at	at	ADV
ejpam-2418	83	8	least	least	ADV
ejpam-2418	83	9	one	one	NUM
ejpam-2418	83	10	fixed	fix	VERB
ejpam-2418	83	11	element	element	NOUN
ejpam-2418	83	12	and	and	CCONJ
ejpam-2418	83	13	b	b	NOUN
ejpam-2418	83	14	be	be	AUX
ejpam-2418	83	15	an	an	DET
ejpam-2418	83	16	essential	essential	ADJ
ejpam-2418	83	17	extension	extension	NOUN
ejpam-2418	83	18	of	of	ADP
ejpam-2418	83	19	a.	a.	NOUN
ejpam-2418	83	20	then	then	ADV
ejpam-2418	83	21	:	:	PUNCT
ejpam-2418	83	22	h.	h.	PROPN
ejpam-2418	83	23	barzegar	barzegar	PROPN
ejpam-2418	83	24	/	/	SYM
ejpam-2418	83	25	eur	eur	PROPN
ejpam-2418	83	26	.	.	PUNCT
ejpam-2418	84	1	j.	j.	PROPN
ejpam-2418	84	2	pure	pure	PROPN
ejpam-2418	84	3	appl	appl	PROPN
ejpam-2418	84	4	.	.	PROPN
ejpam-2418	84	5	math	math	PROPN
ejpam-2418	84	6	,	,	PUNCT
ejpam-2418	84	7	9	9	NUM
ejpam-2418	84	8	(	(	PUNCT
ejpam-2418	84	9	2016	2016	NUM
ejpam-2418	84	10	)	)	PUNCT
ejpam-2418	84	11	,	,	PUNCT
ejpam-2418	84	12	19	19	NUM
ejpam-2418	84	13	-	-	SYM
ejpam-2418	84	14	26	26	NUM
ejpam-2418	84	15	22	22	NUM
ejpam-2418	84	16	(	(	PUNCT
ejpam-2418	84	17	i	i	NOUN
ejpam-2418	84	18	)	)	PUNCT
ejpam-2418	84	19	f	f	PROPN
ejpam-2418	84	20	ix(b	ix(b	PROPN
ejpam-2418	84	21	)	)	PUNCT
ejpam-2418	85	1	⊆	⊆	NUM
ejpam-2418	85	2	a.	a.	NOUN
ejpam-2418	85	3	(	(	PUNCT
ejpam-2418	85	4	ii	ii	NOUN
ejpam-2418	85	5	)	)	PUNCT
ejpam-2418	85	6	for	for	ADP
ejpam-2418	85	7	every	every	DET
ejpam-2418	85	8	b	b	PROPN
ejpam-2418	85	9	∈	∈	PROPN
ejpam-2418	85	10	b	b	PROPN
ejpam-2418	85	11	,	,	PUNCT
ejpam-2418	85	12	ib	ib	NOUN
ejpam-2418	85	13	6=	6=	NUM
ejpam-2418	85	14	;	;	PUNCT
ejpam-2418	85	15	.	.	PUNCT
ejpam-2418	86	1	corollary	corollary	ADJ
ejpam-2418	86	2	4	4	NUM
ejpam-2418	86	3	.	.	PUNCT
ejpam-2418	87	1	if	if	SCONJ
ejpam-2418	87	2	s	s	PROPN
ejpam-2418	87	3	has	have	AUX
ejpam-2418	87	4	at	at	ADV
ejpam-2418	87	5	least	least	ADJ
ejpam-2418	87	6	one	one	NUM
ejpam-2418	87	7	left	leave	VERB
ejpam-2418	87	8	zero	zero	NUM
ejpam-2418	87	9	element	element	NOUN
ejpam-2418	87	10	and	and	CCONJ
ejpam-2418	87	11	s	s	NOUN
ejpam-2418	87	12	is	be	AUX
ejpam-2418	87	13	an	an	DET
ejpam-2418	87	14	essential	essential	ADJ
ejpam-2418	87	15	extension	extension	NOUN
ejpam-2418	87	16	of	of	ADP
ejpam-2418	87	17	a	a	DET
ejpam-2418	87	18	right	right	ADJ
ejpam-2418	87	19	ideal	ideal	NOUN
ejpam-2418	88	1	i	i	PRON
ejpam-2418	88	2	,	,	PUNCT
ejpam-2418	88	3	then	then	ADV
ejpam-2418	88	4	z(s	z(s	PROPN
ejpam-2418	88	5	)	)	PUNCT
ejpam-2418	88	6	⊆	⊆	NUM
ejpam-2418	88	7	i	i	PRON
ejpam-2418	88	8	.	.	PUNCT
ejpam-2418	89	1	if	if	SCONJ
ejpam-2418	89	2	s	s	NOUN
ejpam-2418	89	3	is	be	AUX
ejpam-2418	89	4	a	a	DET
ejpam-2418	89	5	left	left	ADJ
ejpam-2418	89	6	zero	zero	NUM
ejpam-2418	89	7	semigroup	semigroup	NOUN
ejpam-2418	89	8	,	,	PUNCT
ejpam-2418	89	9	then	then	ADV
ejpam-2418	89	10	i	i	PRON
ejpam-2418	89	11	=	=	PUNCT
ejpam-2418	89	12	s.	s.	PROPN
ejpam-2418	89	13	lemma	lemma	PROPN
ejpam-2418	90	1	2	2	X
ejpam-2418	90	2	.	.	PUNCT
ejpam-2418	91	1	if	if	SCONJ
ejpam-2418	91	2	a	a	PRON
ejpam-2418	91	3	has	have	VERB
ejpam-2418	91	4	no	no	DET
ejpam-2418	91	5	fixed	fix	VERB
ejpam-2418	91	6	element	element	NOUN
ejpam-2418	91	7	,	,	PUNCT
ejpam-2418	91	8	then	then	ADV
ejpam-2418	91	9	a0	a0	PROPN
ejpam-2418	91	10	is	be	AUX
ejpam-2418	91	11	an	an	DET
ejpam-2418	91	12	essential	essential	ADJ
ejpam-2418	91	13	extension	extension	NOUN
ejpam-2418	91	14	of	of	ADP
ejpam-2418	91	15	a.	a.	NOUN
ejpam-2418	91	16	proof	proof	NOUN
ejpam-2418	91	17	.	.	PUNCT
ejpam-2418	92	1	let	let	VERB
ejpam-2418	92	2	g	g	NOUN
ejpam-2418	92	3	:	:	PUNCT
ejpam-2418	92	4	a0→	a0→	NUM
ejpam-2418	93	1	b	b	AUX
ejpam-2418	93	2	be	be	AUX
ejpam-2418	93	3	a	a	DET
ejpam-2418	93	4	homomorphism	homomorphism	NOUN
ejpam-2418	93	5	such	such	ADJ
ejpam-2418	93	6	that	that	DET
ejpam-2418	93	7	g|a	g|a	NOUN
ejpam-2418	93	8	is	be	AUX
ejpam-2418	93	9	a	a	DET
ejpam-2418	93	10	monomorphism	monomorphism	NOUN
ejpam-2418	93	11	.	.	PUNCT
ejpam-2418	94	1	then	then	ADV
ejpam-2418	94	2	g	g	PROPN
ejpam-2418	94	3	itself	itself	PRON
ejpam-2418	94	4	is	be	AUX
ejpam-2418	94	5	one	one	NUM
ejpam-2418	94	6	-	-	PUNCT
ejpam-2418	94	7	one	one	NUM
ejpam-2418	94	8	.	.	PUNCT
ejpam-2418	95	1	in	in	ADP
ejpam-2418	95	2	fact	fact	NOUN
ejpam-2418	95	3	,	,	PUNCT
ejpam-2418	95	4	if	if	SCONJ
ejpam-2418	95	5	g(a	g(a	PROPN
ejpam-2418	95	6	)	)	PUNCT
ejpam-2418	95	7	=	=	SYM
ejpam-2418	95	8	g(0	g(0	PROPN
ejpam-2418	95	9	)	)	PUNCT
ejpam-2418	95	10	for	for	ADP
ejpam-2418	95	11	some	some	DET
ejpam-2418	95	12	a	a	DET
ejpam-2418	95	13	∈	∈	PROPN
ejpam-2418	95	14	a	a	PRON
ejpam-2418	95	15	,	,	PUNCT
ejpam-2418	95	16	then	then	ADV
ejpam-2418	95	17	for	for	ADP
ejpam-2418	95	18	every	every	DET
ejpam-2418	95	19	s	s	X
ejpam-2418	95	20	∈	∈	PROPN
ejpam-2418	95	21	s	s	NOUN
ejpam-2418	95	22	,	,	PUNCT
ejpam-2418	95	23	g(as	g(as	NOUN
ejpam-2418	95	24	)	)	PUNCT
ejpam-2418	95	25	=	=	SYM
ejpam-2418	96	1	g(a)s	g(a)s	NOUN
ejpam-2418	96	2	=	=	SYM
ejpam-2418	96	3	g(0)s	g(0)s	PROPN
ejpam-2418	96	4	=	=	SYM
ejpam-2418	96	5	g(0s	g(0s	NOUN
ejpam-2418	96	6	)	)	PUNCT
ejpam-2418	96	7	=	=	SYM
ejpam-2418	96	8	g(0	g(0	PROPN
ejpam-2418	96	9	)	)	PUNCT
ejpam-2418	96	10	=	=	SYM
ejpam-2418	96	11	g(a	g(a	PROPN
ejpam-2418	96	12	)	)	PUNCT
ejpam-2418	96	13	and	and	CCONJ
ejpam-2418	96	14	so	so	ADV
ejpam-2418	96	15	as	as	SCONJ
ejpam-2418	96	16	=	=	NOUN
ejpam-2418	96	17	a.	a.	NOUN
ejpam-2418	96	18	this	this	PRON
ejpam-2418	96	19	means	mean	VERB
ejpam-2418	96	20	that	that	SCONJ
ejpam-2418	96	21	a	a	PRON
ejpam-2418	96	22	is	be	AUX
ejpam-2418	96	23	a	a	DET
ejpam-2418	96	24	fixed	fix	VERB
ejpam-2418	96	25	element	element	NOUN
ejpam-2418	96	26	,	,	PUNCT
ejpam-2418	96	27	which	which	PRON
ejpam-2418	96	28	is	be	AUX
ejpam-2418	96	29	a	a	DET
ejpam-2418	96	30	contradiction	contradiction	NOUN
ejpam-2418	96	31	.	.	PUNCT
ejpam-2418	97	1	thus	thus	ADV
ejpam-2418	97	2	g	g	PROPN
ejpam-2418	97	3	is	be	AUX
ejpam-2418	97	4	an	an	DET
ejpam-2418	97	5	injection	injection	NOUN
ejpam-2418	97	6	.	.	PUNCT
ejpam-2418	98	1	lemma	lemma	PROPN
ejpam-2418	98	2	3	3	NUM
ejpam-2418	98	3	.	.	PUNCT
ejpam-2418	98	4	pushouts	pushout	NOUN
ejpam-2418	98	5	do	do	AUX
ejpam-2418	98	6	not	not	PART
ejpam-2418	98	7	necessarily	necessarily	ADV
ejpam-2418	98	8	transfer	transfer	VERB
ejpam-2418	98	9	essential	essential	ADJ
ejpam-2418	98	10	monomorphisms	monomorphism	NOUN
ejpam-2418	98	11	.	.	PUNCT
ejpam-2418	99	1	proof	proof	NOUN
ejpam-2418	99	2	.	.	PUNCT
ejpam-2418	100	1	let	let	VERB
ejpam-2418	100	2	a	a	PRON
ejpam-2418	100	3	have	have	VERB
ejpam-2418	100	4	no	no	DET
ejpam-2418	100	5	fixed	fix	VERB
ejpam-2418	100	6	element	element	NOUN
ejpam-2418	100	7	.	.	PUNCT
ejpam-2418	101	1	by	by	ADP
ejpam-2418	101	2	lemma	lemma	PROPN
ejpam-2418	101	3	2	2	NUM
ejpam-2418	101	4	,	,	PUNCT
ejpam-2418	101	5	the	the	DET
ejpam-2418	101	6	inclusion	inclusion	NOUN
ejpam-2418	101	7	τ	τ	X
ejpam-2418	101	8	:	:	PUNCT
ejpam-2418	101	9	a→	a→	PUNCT
ejpam-2418	101	10	a0	a0	PROPN
ejpam-2418	101	11	is	be	AUX
ejpam-2418	101	12	an	an	DET
ejpam-2418	101	13	essential	essential	ADJ
ejpam-2418	101	14	extension	extension	NOUN
ejpam-2418	101	15	.	.	PUNCT
ejpam-2418	102	1	consider	consider	VERB
ejpam-2418	102	2	the	the	DET
ejpam-2418	102	3	pushout	pushout	NOUN
ejpam-2418	102	4	diagram	diagram	NOUN
ejpam-2418	102	5	a	a	PRON
ejpam-2418	102	6	τ	τ	PROPN
ejpam-2418	102	7	→	→	SYM
ejpam-2418	102	8	a0	a0	PROPN
ejpam-2418	102	9	τ	τ	PROPN
ejpam-2418	102	10	↓	↓	PROPN
ejpam-2418	102	11	↓	↓	PROPN
ejpam-2418	102	12	q	q	PROPN
ejpam-2418	102	13	a0	a0	PROPN
ejpam-2418	102	14	p	p	PROPN
ejpam-2418	102	15	→	→	SYM
ejpam-2418	102	16	az1,z2	az1,z2	NOUN
ejpam-2418	102	17	where	where	SCONJ
ejpam-2418	102	18	z1	z1	ADJ
ejpam-2418	102	19	,	,	PUNCT
ejpam-2418	102	20	z2	z2	PROPN
ejpam-2418	102	21	are	be	AUX
ejpam-2418	102	22	two	two	NUM
ejpam-2418	102	23	fixed	fix	VERB
ejpam-2418	102	24	elements	element	NOUN
ejpam-2418	102	25	adjoint	adjoint	VERB
ejpam-2418	102	26	to	to	ADP
ejpam-2418	102	27	a	a	PRON
ejpam-2418	102	28	and	and	CCONJ
ejpam-2418	102	29	p(a	p(a	NOUN
ejpam-2418	102	30	)	)	PUNCT
ejpam-2418	102	31	=	=	SYM
ejpam-2418	102	32	q(a	q(a	PROPN
ejpam-2418	102	33	)	)	PUNCT
ejpam-2418	103	1	=	=	SYM
ejpam-2418	103	2	a	a	DET
ejpam-2418	103	3	(	(	PUNCT
ejpam-2418	103	4	a	a	DET
ejpam-2418	103	5	∈	∈	PROPN
ejpam-2418	103	6	a	a	NOUN
ejpam-2418	103	7	)	)	PUNCT
ejpam-2418	103	8	and	and	CCONJ
ejpam-2418	103	9	p(0	p(0	PROPN
ejpam-2418	103	10	)	)	PUNCT
ejpam-2418	103	11	=	=	SYM
ejpam-2418	103	12	z1	z1	PROPN
ejpam-2418	103	13	,	,	PUNCT
ejpam-2418	103	14	q(0	q(0	PROPN
ejpam-2418	103	15	)	)	PUNCT
ejpam-2418	103	16	=	=	SYM
ejpam-2418	103	17	z2	z2	PROPN
ejpam-2418	103	18	.	.	PUNCT
ejpam-2418	104	1	by	by	ADP
ejpam-2418	104	2	[	[	X
ejpam-2418	104	3	2	2	NUM
ejpam-2418	104	4	,	,	PUNCT
ejpam-2418	104	5	theorem	theorem	ADJ
ejpam-2418	104	6	3.2(1	3.2(1	NUM
ejpam-2418	104	7	)	)	PUNCT
ejpam-2418	104	8	]	]	PUNCT
ejpam-2418	104	9	,	,	PUNCT
ejpam-2418	104	10	p	p	NOUN
ejpam-2418	104	11	and	and	CCONJ
ejpam-2418	104	12	q	q	NOUN
ejpam-2418	104	13	are	be	AUX
ejpam-2418	104	14	monomorphisms	monomorphism	NOUN
ejpam-2418	104	15	.	.	PUNCT
ejpam-2418	105	1	define	define	VERB
ejpam-2418	105	2	a	a	DET
ejpam-2418	105	3	homomorphism	homomorphism	NOUN
ejpam-2418	105	4	h	h	NOUN
ejpam-2418	105	5	:	:	PUNCT
ejpam-2418	105	6	az1,z2	az1,z2	PROPN
ejpam-2418	105	7	→	→	SYM
ejpam-2418	105	8	a0	a0	PROPN
ejpam-2418	105	9	by	by	ADP
ejpam-2418	105	10	h(a	h(a	PROPN
ejpam-2418	105	11	)	)	PUNCT
ejpam-2418	106	1	=	=	PUNCT
ejpam-2418	106	2	a	a	PRON
ejpam-2418	106	3	and	and	CCONJ
ejpam-2418	106	4	h(z1	h(z1	NOUN
ejpam-2418	106	5	)	)	PUNCT
ejpam-2418	106	6	=	=	SYM
ejpam-2418	106	7	h(z2	h(z2	NOUN
ejpam-2418	106	8	)	)	PUNCT
ejpam-2418	106	9	=	=	PUNCT
ejpam-2418	107	1	0	0	X
ejpam-2418	107	2	.	.	PUNCT
ejpam-2418	107	3	then	then	ADV
ejpam-2418	107	4	hp	hp	PROPN
ejpam-2418	107	5	=	=	PUNCT
ejpam-2418	107	6	ida0	ida0	PROPN
ejpam-2418	107	7	.	.	PUNCT
ejpam-2418	108	1	but	but	CCONJ
ejpam-2418	108	2	,	,	PUNCT
ejpam-2418	108	3	h	h	NOUN
ejpam-2418	108	4	is	be	AUX
ejpam-2418	108	5	not	not	PART
ejpam-2418	108	6	one	one	NUM
ejpam-2418	108	7	-	-	PUNCT
ejpam-2418	108	8	one	one	NUM
ejpam-2418	108	9	,	,	PUNCT
ejpam-2418	108	10	and	and	CCONJ
ejpam-2418	108	11	hence	hence	ADV
ejpam-2418	108	12	p	p	NOUN
ejpam-2418	108	13	is	be	AUX
ejpam-2418	108	14	not	not	PART
ejpam-2418	108	15	an	an	DET
ejpam-2418	108	16	essential	essential	ADJ
ejpam-2418	108	17	extension	extension	NOUN
ejpam-2418	108	18	.	.	PUNCT
ejpam-2418	109	1	recall	recall	VERB
ejpam-2418	109	2	that	that	SCONJ
ejpam-2418	109	3	a	a	DET
ejpam-2418	109	4	directed	direct	VERB
ejpam-2418	109	5	system	system	NOUN
ejpam-2418	109	6	of	of	ADP
ejpam-2418	109	7	s	s	NOUN
ejpam-2418	109	8	-	-	PUNCT
ejpam-2418	109	9	acts	act	NOUN
ejpam-2418	109	10	and	and	CCONJ
ejpam-2418	109	11	s	s	NOUN
ejpam-2418	109	12	-	-	NOUN
ejpam-2418	109	13	maps	map	NOUN
ejpam-2418	109	14	is	be	AUX
ejpam-2418	109	15	a	a	DET
ejpam-2418	109	16	family	family	NOUN
ejpam-2418	109	17	(	(	PUNCT
ejpam-2418	109	18	bα)α∈i	bα)α∈i	NOUN
ejpam-2418	109	19	of	of	ADP
ejpam-2418	109	20	s	s	NOUN
ejpam-2418	109	21	-	-	PUNCT
ejpam-2418	109	22	acts	act	NOUN
ejpam-2418	109	23	indexed	index	VERB
ejpam-2418	109	24	by	by	ADP
ejpam-2418	109	25	an	an	DET
ejpam-2418	109	26	updirected	updirected	ADJ
ejpam-2418	109	27	set	set	NOUN
ejpam-2418	109	28	i	i	PRON
ejpam-2418	109	29	endowed	endow	VERB
ejpam-2418	109	30	by	by	ADP
ejpam-2418	109	31	a	a	DET
ejpam-2418	109	32	family	family	NOUN
ejpam-2418	109	33	(	(	PUNCT
ejpam-2418	109	34	gαβ	gαβ	NOUN
ejpam-2418	109	35	:	:	PUNCT
ejpam-2418	109	36	bα	bα	PROPN
ejpam-2418	109	37	→	→	SYM
ejpam-2418	109	38	bβ	bβ	NOUN
ejpam-2418	109	39	)	)	PUNCT
ejpam-2418	109	40	α≤β∈i	α≤β∈i	NOUN
ejpam-2418	109	41	of	of	ADP
ejpam-2418	109	42	s	s	NOUN
ejpam-2418	109	43	-	-	NOUN
ejpam-2418	109	44	maps	map	NOUN
ejpam-2418	110	1	such	such	ADJ
ejpam-2418	110	2	that	that	SCONJ
ejpam-2418	110	3	given	give	VERB
ejpam-2418	110	4	α≤	α≤	PROPN
ejpam-2418	110	5	β	β	NOUN
ejpam-2418	110	6	≤	≤	NUM
ejpam-2418	110	7	γ	γ	X
ejpam-2418	110	8	∈	∈	PROPN
ejpam-2418	111	1	i	i	PRON
ejpam-2418	111	2	we	we	PRON
ejpam-2418	111	3	have	have	VERB
ejpam-2418	111	4	gβγgαβ	gβγgαβ	NOUN
ejpam-2418	111	5	=	=	SYM
ejpam-2418	111	6	gαγ	gαγ	PROPN
ejpam-2418	111	7	.	.	PUNCT
ejpam-2418	112	1	note	note	VERB
ejpam-2418	112	2	that	that	SCONJ
ejpam-2418	112	3	the	the	DET
ejpam-2418	112	4	direct	direct	ADJ
ejpam-2418	112	5	limit	limit	NOUN
ejpam-2418	112	6	(	(	PUNCT
ejpam-2418	112	7	directed	direct	VERB
ejpam-2418	112	8	colimit	colimit	NOUN
ejpam-2418	112	9	)	)	PUNCT
ejpam-2418	112	10	of	of	ADP
ejpam-2418	112	11	a	a	DET
ejpam-2418	112	12	directed	direct	VERB
ejpam-2418	112	13	system	system	NOUN
ejpam-2418	112	14	(	(	PUNCT
ejpam-2418	112	15	(	(	PUNCT
ejpam-2418	112	16	bα)α∈i	bα)α∈i	X
ejpam-2418	112	17	,	,	PUNCT
ejpam-2418	112	18	(	(	PUNCT
ejpam-2418	112	19	gαβ	gαβ	NOUN
ejpam-2418	112	20	)	)	PUNCT
ejpam-2418	112	21	α≤β∈i	α≤β∈i	PROPN
ejpam-2418	112	22	)	)	PUNCT
ejpam-2418	112	23	in	in	ADP
ejpam-2418	112	24	act	act	PROPN
ejpam-2418	112	25	-	-	PUNCT
ejpam-2418	112	26	s	s	PART
ejpam-2418	112	27	is	be	AUX
ejpam-2418	112	28	given	give	VERB
ejpam-2418	112	29	as	as	ADP
ejpam-2418	112	30	l	l	NOUN
ejpam-2418	112	31	i	i	NOUN
ejpam-2418	112	32	m	m	VERB
ejpam-2418	112	33	−→α	−→α	ADJ
ejpam-2418	112	34	bα	bα	NOUN
ejpam-2418	113	1	=	=	PUNCT
ejpam-2418	113	2	∐	∐	ADJ
ejpam-2418	113	3	α	α	PROPN
ejpam-2418	113	4	bα	bα	PROPN
ejpam-2418	113	5	/	/	SYM
ejpam-2418	113	6	ρ	ρ	PROPN
ejpam-2418	113	7	where	where	SCONJ
ejpam-2418	113	8	the	the	DET
ejpam-2418	113	9	congruence	congruence	NOUN
ejpam-2418	113	10	ρ	ρ	NOUN
ejpam-2418	113	11	is	be	AUX
ejpam-2418	113	12	given	give	VERB
ejpam-2418	113	13	by	by	ADP
ejpam-2418	113	14	bαρbβ	bαρbβ	PROPN
ejpam-2418	114	1	if	if	SCONJ
ejpam-2418	114	2	and	and	CCONJ
ejpam-2418	114	3	only	only	ADV
ejpam-2418	114	4	if	if	SCONJ
ejpam-2418	114	5	there	there	PRON
ejpam-2418	114	6	exists	exist	VERB
ejpam-2418	114	7	γ	γ	PROPN
ejpam-2418	114	8	≥	≥	PROPN
ejpam-2418	114	9	α	α	X
ejpam-2418	114	10	,	,	PUNCT
ejpam-2418	114	11	β	β	PROPN
ejpam-2418	114	12	such	such	ADJ
ejpam-2418	114	13	that	that	DET
ejpam-2418	114	14	uγgαγ(bα	uγgαγ(bα	NOUN
ejpam-2418	114	15	)	)	PUNCT
ejpam-2418	114	16	=	=	PUNCT
ejpam-2418	114	17	uγgβγ(bβ	uγgβγ(bβ	PROPN
ejpam-2418	114	18	)	)	PUNCT
ejpam-2418	114	19	in	in	ADP
ejpam-2418	114	20	which	which	PRON
ejpam-2418	114	21	each	each	DET
ejpam-2418	114	22	uα	uα	X
ejpam-2418	114	23	:	:	PUNCT
ejpam-2418	114	24	bα→	bα→	NOUN
ejpam-2418	114	25	∐	∐	X
ejpam-2418	115	1	α	α	DET
ejpam-2418	115	2	bα	bα	PROPN
ejpam-2418	115	3	is	be	AUX
ejpam-2418	115	4	an	an	DET
ejpam-2418	115	5	injection	injection	NOUN
ejpam-2418	115	6	map	map	NOUN
ejpam-2418	115	7	of	of	ADP
ejpam-2418	115	8	the	the	DET
ejpam-2418	115	9	coproduct	coproduct	NOUN
ejpam-2418	115	10	.	.	PUNCT
ejpam-2418	116	1	notice	notice	VERB
ejpam-2418	116	2	that	that	SCONJ
ejpam-2418	116	3	the	the	DET
ejpam-2418	116	4	family	family	NOUN
ejpam-2418	116	5	gα	gα	NOUN
ejpam-2418	116	6	=	=	PUNCT
ejpam-2418	116	7	πuα	πuα	NOUN
ejpam-2418	116	8	:	:	PUNCT
ejpam-2418	116	9	bα→	bα→	X
ejpam-2418	116	10	l	l	PUNCT
ejpam-2418	117	1	i	i	PRON
ejpam-2418	117	2	m	m	VERB
ejpam-2418	117	3	−→α	−→α	ADJ
ejpam-2418	117	4	bα	bα	NOUN
ejpam-2418	117	5	of	of	ADP
ejpam-2418	117	6	s	s	NOUN
ejpam-2418	117	7	-	-	PUNCT
ejpam-2418	117	8	maps	map	NOUN
ejpam-2418	117	9	satisfies	satisfie	NOUN
ejpam-2418	117	10	gβ	gβ	ADP
ejpam-2418	117	11	gαβ	gαβ	PROPN
ejpam-2418	117	12	=	=	PUNCT
ejpam-2418	117	13	gα	gα	NOUN
ejpam-2418	117	14	for	for	ADP
ejpam-2418	117	15	α≤	α≤	PROPN
ejpam-2418	117	16	β	β	PROPN
ejpam-2418	117	17	,	,	PUNCT
ejpam-2418	117	18	where	where	SCONJ
ejpam-2418	117	19	π	π	X
ejpam-2418	117	20	:	:	PUNCT
ejpam-2418	117	21	∐	∐	X
ejpam-2418	117	22	α	α	X
ejpam-2418	117	23	bα→	bα→	X
ejpam-2418	118	1	l	l	NOUN
ejpam-2418	119	1	i	i	PRON
ejpam-2418	119	2	m	m	VERB
ejpam-2418	119	3	−→α	−→α	ADJ
ejpam-2418	119	4	bα	bα	NOUN
ejpam-2418	119	5	is	be	AUX
ejpam-2418	119	6	the	the	DET
ejpam-2418	119	7	natural	natural	ADJ
ejpam-2418	119	8	s	s	NOUN
ejpam-2418	119	9	-	-	PUNCT
ejpam-2418	119	10	map	map	NOUN
ejpam-2418	119	11	.	.	PUNCT
ejpam-2418	120	1	theorem	theorem	NOUN
ejpam-2418	120	2	3	3	NUM
ejpam-2418	120	3	.	.	PUNCT
ejpam-2418	121	1	any	any	DET
ejpam-2418	121	2	direct	direct	ADJ
ejpam-2418	121	3	limit	limit	NOUN
ejpam-2418	121	4	of	of	ADP
ejpam-2418	121	5	essential	essential	ADJ
ejpam-2418	121	6	monomorphisms	monomorphism	NOUN
ejpam-2418	121	7	is	be	AUX
ejpam-2418	121	8	an	an	DET
ejpam-2418	121	9	essential	essential	ADJ
ejpam-2418	121	10	monomorphism	monomorphism	NOUN
ejpam-2418	121	11	.	.	PUNCT
ejpam-2418	122	1	proof	proof	NOUN
ejpam-2418	122	2	.	.	PUNCT
ejpam-2418	123	1	let	let	VERB
ejpam-2418	123	2	f	f	NOUN
ejpam-2418	123	3	:	:	PUNCT
ejpam-2418	123	4	a→	a→	PUNCT
ejpam-2418	123	5	l	l	X
ejpam-2418	124	1	i	i	NOUN
ejpam-2418	124	2	m	m	VERB
ejpam-2418	124	3	−→α	−→α	ADJ
ejpam-2418	124	4	bα	bα	NOUN
ejpam-2418	124	5	be	be	AUX
ejpam-2418	124	6	a	a	DET
ejpam-2418	124	7	direct	direct	ADJ
ejpam-2418	124	8	limit	limit	NOUN
ejpam-2418	124	9	in	in	ADP
ejpam-2418	124	10	act	act	PROPN
ejpam-2418	124	11	-	-	PUNCT
ejpam-2418	124	12	s	s	PROPN
ejpam-2418	124	13	of	of	ADP
ejpam-2418	124	14	essential	essential	ADJ
ejpam-2418	124	15	monomorphisms	monomorphism	NOUN
ejpam-2418	124	16	fα	fα	ADP
ejpam-2418	124	17	:	:	PUNCT
ejpam-2418	124	18	a→	a→	PROPN
ejpam-2418	124	19	bα	bα	PROPN
ejpam-2418	124	20	,	,	PUNCT
ejpam-2418	124	21	α	α	PROPN
ejpam-2418	124	22	∈	∈	X
ejpam-2418	125	1	i	i	PRON
ejpam-2418	125	2	,	,	PUNCT
ejpam-2418	125	3	and	and	CCONJ
ejpam-2418	125	4	directed	direct	VERB
ejpam-2418	125	5	s	s	NOUN
ejpam-2418	125	6	-	-	PUNCT
ejpam-2418	125	7	maps	map	NOUN
ejpam-2418	125	8	gαβ	gαβ	NOUN
ejpam-2418	125	9	:	:	PUNCT
ejpam-2418	125	10	bα→	bα→	PUNCT
ejpam-2418	125	11	bβ	bβ	NOUN
ejpam-2418	125	12	(	(	PUNCT
ejpam-2418	125	13	α≤	α≤	PROPN
ejpam-2418	125	14	β	β	NOUN
ejpam-2418	125	15	)	)	PUNCT
ejpam-2418	125	16	,	,	PUNCT
ejpam-2418	125	17	and	and	CCONJ
ejpam-2418	125	18	consider	consider	VERB
ejpam-2418	125	19	gα	gα	ADP
ejpam-2418	125	20	:	:	PUNCT
ejpam-2418	125	21	bα→	bα→	X
ejpam-2418	125	22	l	l	NOUN
ejpam-2418	126	1	i	i	PRON
ejpam-2418	126	2	m	m	VERB
ejpam-2418	126	3	−→α	−→α	ADJ
ejpam-2418	126	4	bα	bα	NOUN
ejpam-2418	126	5	as	as	ADP
ejpam-2418	126	6	before	before	ADV
ejpam-2418	126	7	.	.	PUNCT
ejpam-2418	127	1	to	to	PART
ejpam-2418	127	2	show	show	VERB
ejpam-2418	127	3	that	that	SCONJ
ejpam-2418	127	4	f	f	X
ejpam-2418	127	5	:	:	PUNCT
ejpam-2418	127	6	a→	a→	PUNCT
ejpam-2418	127	7	l	l	NOUN
ejpam-2418	128	1	i	i	PRON
ejpam-2418	128	2	m	m	VERB
ejpam-2418	128	3	−→	−→	ADJ
ejpam-2418	128	4	bα	bα	NOUN
ejpam-2418	128	5	is	be	AUX
ejpam-2418	128	6	essential	essential	ADJ
ejpam-2418	128	7	,	,	PUNCT
ejpam-2418	128	8	let	let	VERB
ejpam-2418	128	9	hf	hf	ADV
ejpam-2418	128	10	,	,	PUNCT
ejpam-2418	128	11	for	for	ADP
ejpam-2418	128	12	h	h	NOUN
ejpam-2418	128	13	:	:	PUNCT
ejpam-2418	128	14	l	l	PUNCT
ejpam-2418	129	1	i	i	VERB
ejpam-2418	129	2	m	m	VERB
ejpam-2418	129	3	−→α	−→α	ADJ
ejpam-2418	129	4	bα	bα	PROPN
ejpam-2418	129	5	→	→	SYM
ejpam-2418	129	6	c	c	NOUN
ejpam-2418	129	7	,	,	PUNCT
ejpam-2418	129	8	be	be	AUX
ejpam-2418	129	9	a	a	DET
ejpam-2418	129	10	monomorphism	monomorphism	NOUN
ejpam-2418	129	11	.	.	PUNCT
ejpam-2418	130	1	then	then	ADV
ejpam-2418	130	2	,	,	PUNCT
ejpam-2418	130	3	for	for	ADP
ejpam-2418	130	4	every	every	DET
ejpam-2418	130	5	α	α	NOUN
ejpam-2418	130	6	∈	∈	X
ejpam-2418	130	7	i	i	PRON
ejpam-2418	130	8	,	,	PUNCT
ejpam-2418	130	9	hgα	hgα	VERB
ejpam-2418	130	10	fα	fα	ADP
ejpam-2418	130	11	∈	∈	NOUN
ejpam-2418	130	12	m	m	NOUN
ejpam-2418	130	13	.	.	PUNCT
ejpam-2418	131	1	since	since	SCONJ
ejpam-2418	131	2	each	each	DET
ejpam-2418	131	3	fα	fα	NOUN
ejpam-2418	131	4	is	be	AUX
ejpam-2418	131	5	essential	essential	ADJ
ejpam-2418	131	6	,	,	PUNCT
ejpam-2418	131	7	each	each	DET
ejpam-2418	131	8	hgα	hgα	NOUN
ejpam-2418	131	9	is	be	AUX
ejpam-2418	131	10	a	a	DET
ejpam-2418	131	11	monomorphism	monomorphism	NOUN
ejpam-2418	131	12	.	.	PUNCT
ejpam-2418	132	1	now	now	ADV
ejpam-2418	132	2	if	if	SCONJ
ejpam-2418	132	3	h([bα	h([bα	PROPN
ejpam-2418	132	4	]	]	X
ejpam-2418	132	5	)	)	PUNCT
ejpam-2418	132	6	=	=	SYM
ejpam-2418	132	7	h([bβ	h([bβ	PROPN
ejpam-2418	132	8	]	]	PUNCT
ejpam-2418	132	9	)	)	PUNCT
ejpam-2418	132	10	,	,	PUNCT
ejpam-2418	132	11	then	then	ADV
ejpam-2418	132	12	hgγgαγ(bα	hgγgαγ(bα	PROPN
ejpam-2418	132	13	)	)	PUNCT
ejpam-2418	132	14	=	=	SYM
ejpam-2418	132	15	hgγgβγ(bβ	hgγgβγ(bβ	ADJ
ejpam-2418	132	16	)	)	PUNCT
ejpam-2418	132	17	,	,	PUNCT
ejpam-2418	132	18	for	for	ADP
ejpam-2418	132	19	some	some	DET
ejpam-2418	132	20	γ	γ	NOUN
ejpam-2418	132	21	≥	≥	NUM
ejpam-2418	132	22	α	α	NOUN
ejpam-2418	132	23	,	,	PUNCT
ejpam-2418	132	24	β	β	X
ejpam-2418	132	25	.	.	PUNCT
ejpam-2418	133	1	thus	thus	ADV
ejpam-2418	133	2	gαγ(bα	gαγ(bα	VERB
ejpam-2418	133	3	)	)	PUNCT
ejpam-2418	133	4	=	=	SYM
ejpam-2418	133	5	gβγ(bβ	gβγ(bβ	NOUN
ejpam-2418	133	6	)	)	PUNCT
ejpam-2418	133	7	which	which	PRON
ejpam-2418	133	8	means	mean	VERB
ejpam-2418	133	9	that	that	SCONJ
ejpam-2418	133	10	bαρbβ	bαρbβ	PROPN
ejpam-2418	133	11	,	,	PUNCT
ejpam-2418	133	12	and	and	CCONJ
ejpam-2418	133	13	hence	hence	ADV
ejpam-2418	133	14	h	h	NOUN
ejpam-2418	133	15	is	be	AUX
ejpam-2418	133	16	a	a	DET
ejpam-2418	133	17	monomorphism	monomorphism	NOUN
ejpam-2418	133	18	and	and	CCONJ
ejpam-2418	133	19	f	f	PROPN
ejpam-2418	133	20	is	be	AUX
ejpam-2418	133	21	essential	essential	ADJ
ejpam-2418	133	22	.	.	PUNCT
ejpam-2418	134	1	h.	h.	PROPN
ejpam-2418	134	2	barzegar	barzegar	PROPN
ejpam-2418	134	3	/	/	SYM
ejpam-2418	134	4	eur	eur	PROPN
ejpam-2418	134	5	.	.	PUNCT
ejpam-2418	135	1	j.	j.	PROPN
ejpam-2418	135	2	pure	pure	PROPN
ejpam-2418	135	3	appl	appl	PROPN
ejpam-2418	135	4	.	.	PROPN
ejpam-2418	135	5	math	math	PROPN
ejpam-2418	135	6	,	,	PUNCT
ejpam-2418	135	7	9	9	NUM
ejpam-2418	135	8	(	(	PUNCT
ejpam-2418	135	9	2016	2016	NUM
ejpam-2418	135	10	)	)	PUNCT
ejpam-2418	135	11	,	,	PUNCT
ejpam-2418	135	12	19	19	NUM
ejpam-2418	135	13	-	-	SYM
ejpam-2418	135	14	26	26	NUM
ejpam-2418	135	15	23	23	NUM
ejpam-2418	135	16	definition	definition	NOUN
ejpam-2418	135	17	2	2	NUM
ejpam-2418	135	18	.	.	PUNCT
ejpam-2418	136	1	the	the	DET
ejpam-2418	136	2	category	category	NOUN
ejpam-2418	136	3	a	a	PRON
ejpam-2418	136	4	is	be	AUX
ejpam-2418	136	5	called	call	VERB
ejpam-2418	136	6	essentially	essentially	ADV
ejpam-2418	136	7	bounded	bound	VERB
ejpam-2418	136	8	,	,	PUNCT
ejpam-2418	136	9	if	if	SCONJ
ejpam-2418	136	10	every	every	DET
ejpam-2418	136	11	a	a	DET
ejpam-2418	136	12	∈	∈	PROPN
ejpam-2418	136	13	a	a	PRON
ejpam-2418	136	14	has	have	VERB
ejpam-2418	136	15	only	only	ADV
ejpam-2418	136	16	a	a	DET
ejpam-2418	136	17	set	set	NOUN
ejpam-2418	136	18	of	of	ADP
ejpam-2418	136	19	essential	essential	ADJ
ejpam-2418	136	20	extensions	extension	NOUN
ejpam-2418	136	21	.	.	PUNCT
ejpam-2418	137	1	proposition	proposition	NOUN
ejpam-2418	137	2	2	2	NUM
ejpam-2418	137	3	.	.	PUNCT
ejpam-2418	138	1	the	the	DET
ejpam-2418	138	2	category	category	NOUN
ejpam-2418	138	3	act	act	NOUN
ejpam-2418	138	4	-	-	PUNCT
ejpam-2418	138	5	s	s	PART
ejpam-2418	138	6	is	be	AUX
ejpam-2418	138	7	essentially	essentially	ADV
ejpam-2418	138	8	bounded	bound	VERB
ejpam-2418	138	9	.	.	PUNCT
ejpam-2418	139	1	proof	proof	NOUN
ejpam-2418	139	2	.	.	PUNCT
ejpam-2418	140	1	any	any	DET
ejpam-2418	140	2	essential	essential	ADJ
ejpam-2418	140	3	extension	extension	NOUN
ejpam-2418	140	4	b	b	PROPN
ejpam-2418	140	5	of	of	ADP
ejpam-2418	140	6	a	a	PRON
ejpam-2418	140	7	can	can	AUX
ejpam-2418	140	8	be	be	AUX
ejpam-2418	140	9	clearly	clearly	ADV
ejpam-2418	140	10	embedded	embed	VERB
ejpam-2418	140	11	into	into	ADP
ejpam-2418	140	12	the	the	DET
ejpam-2418	140	13	injective	injective	ADJ
ejpam-2418	140	14	hull	hull	NOUN
ejpam-2418	140	15	e(a	e(a	PROPN
ejpam-2418	140	16	)	)	PUNCT
ejpam-2418	140	17	of	of	ADP
ejpam-2418	140	18	a.	a.	NOUN
ejpam-2418	141	1	so	so	ADV
ejpam-2418	141	2	,	,	PUNCT
ejpam-2418	141	3	we	we	PRON
ejpam-2418	141	4	get	get	VERB
ejpam-2418	141	5	the	the	DET
ejpam-2418	141	6	result	result	NOUN
ejpam-2418	141	7	.	.	PUNCT
ejpam-2418	142	1	the	the	DET
ejpam-2418	142	2	following	follow	VERB
ejpam-2418	142	3	theorem	theorem	NOUN
ejpam-2418	142	4	is	be	AUX
ejpam-2418	142	5	an	an	DET
ejpam-2418	142	6	other	other	ADJ
ejpam-2418	142	7	form	form	NOUN
ejpam-2418	142	8	of	of	ADP
ejpam-2418	142	9	[	[	X
ejpam-2418	142	10	4	4	NUM
ejpam-2418	142	11	,	,	PUNCT
ejpam-2418	142	12	theorem	theorem	VERB
ejpam-2418	142	13	8	8	NUM
ejpam-2418	142	14	]	]	PUNCT
ejpam-2418	142	15	.	.	PUNCT
ejpam-2418	143	1	theorem	theorem	ADJ
ejpam-2418	143	2	4	4	NUM
ejpam-2418	143	3	.	.	PUNCT
ejpam-2418	143	4	act	act	PROPN
ejpam-2418	143	5	-	-	PUNCT
ejpam-2418	143	6	s	s	PART
ejpam-2418	143	7	fulfills	fulfill	VERB
ejpam-2418	143	8	banaschewski	banaschewski	PROPN
ejpam-2418	143	9	’s	’s	PART
ejpam-2418	143	10	condition	condition	NOUN
ejpam-2418	143	11	,	,	PUNCT
ejpam-2418	143	12	that	that	ADV
ejpam-2418	143	13	is	is	ADV
ejpam-2418	143	14	,	,	PUNCT
ejpam-2418	143	15	for	for	ADP
ejpam-2418	143	16	every	every	DET
ejpam-2418	143	17	monomorphism	monomorphism	NOUN
ejpam-2418	143	18	f	f	X
ejpam-2418	143	19	:	:	PUNCT
ejpam-2418	143	20	a→	a→	PROPN
ejpam-2418	143	21	b	b	X
ejpam-2418	143	22	there	there	PRON
ejpam-2418	143	23	exists	exist	VERB
ejpam-2418	143	24	a	a	DET
ejpam-2418	143	25	homomorphism	homomorphism	NOUN
ejpam-2418	143	26	g	g	NOUN
ejpam-2418	143	27	:	:	PUNCT
ejpam-2418	143	28	b→	b→	PROPN
ejpam-2418	143	29	c	c	NOUN
ejpam-2418	143	30	such	such	ADJ
ejpam-2418	143	31	that	that	SCONJ
ejpam-2418	143	32	g	g	PROPN
ejpam-2418	143	33	f	f	PROPN
ejpam-2418	143	34	is	be	AUX
ejpam-2418	143	35	an	an	DET
ejpam-2418	143	36	essential	essential	ADJ
ejpam-2418	143	37	monomorphism	monomorphism	NOUN
ejpam-2418	143	38	.	.	PUNCT
ejpam-2418	144	1	for	for	ADP
ejpam-2418	144	2	an	an	DET
ejpam-2418	144	3	s	s	NOUN
ejpam-2418	144	4	-	-	NOUN
ejpam-2418	144	5	act	act	NOUN
ejpam-2418	144	6	a	a	PRON
ejpam-2418	144	7	and	and	CCONJ
ejpam-2418	144	8	a	a	DET
ejpam-2418	144	9	∈	∈	PROPN
ejpam-2418	144	10	a	a	PRON
ejpam-2418	144	11	we	we	PRON
ejpam-2418	144	12	denote	denote	VERB
ejpam-2418	144	13	the	the	DET
ejpam-2418	144	14	homomorphism	homomorphism	PROPN
ejpam-2418	144	15	f	f	X
ejpam-2418	144	16	:	:	PUNCT
ejpam-2418	144	17	s→	s→	X
ejpam-2418	144	18	a	a	PRON
ejpam-2418	144	19	,	,	PUNCT
ejpam-2418	144	20	given	give	VERB
ejpam-2418	144	21	by	by	ADP
ejpam-2418	144	22	f	f	PROPN
ejpam-2418	144	23	(	(	PUNCT
ejpam-2418	144	24	s	s	NOUN
ejpam-2418	144	25	)	)	PUNCT
ejpam-2418	144	26	=	=	PUNCT
ejpam-2418	144	27	as	as	ADP
ejpam-2418	144	28	for	for	ADP
ejpam-2418	144	29	all	all	DET
ejpam-2418	144	30	s	s	PART
ejpam-2418	144	31	∈	∈	PROPN
ejpam-2418	144	32	s	s	NOUN
ejpam-2418	144	33	,	,	PUNCT
ejpam-2418	144	34	by	by	ADP
ejpam-2418	144	35	λa	λa	PROPN
ejpam-2418	144	36	.	.	PUNCT
ejpam-2418	145	1	lemma	lemma	PROPN
ejpam-2418	145	2	4	4	X
ejpam-2418	145	3	.	.	PUNCT
ejpam-2418	146	1	let	let	VERB
ejpam-2418	146	2	b	b	X
ejpam-2418	146	3	be	be	AUX
ejpam-2418	146	4	an	an	DET
ejpam-2418	146	5	essential	essential	ADJ
ejpam-2418	146	6	extension	extension	NOUN
ejpam-2418	146	7	of	of	ADP
ejpam-2418	146	8	a	a	PRON
ejpam-2418	146	9	and	and	CCONJ
ejpam-2418	146	10	c	c	NOUN
ejpam-2418	146	11	p(a	p(a	PROPN
ejpam-2418	146	12	)	)	PUNCT
ejpam-2418	147	1	=	=	PRON
ejpam-2418	147	2	{	{	PUNCT
ejpam-2418	147	3	b	b	X
ejpam-2418	147	4	∈	∈	PROPN
ejpam-2418	147	5	b	b	NOUN
ejpam-2418	148	1	|	|	ADV
ejpam-2418	148	2	∃a	∃a	NOUN
ejpam-2418	148	3	∈	∈	PROPN
ejpam-2418	148	4	a	a	PRON
ejpam-2418	148	5	,	,	PUNCT
ejpam-2418	148	6	λb	λb	NOUN
ejpam-2418	148	7	=	=	PUNCT
ejpam-2418	148	8	λa	λa	NOUN
ejpam-2418	148	9	}	}	PUNCT
ejpam-2418	148	10	.	.	PUNCT
ejpam-2418	149	1	then	then	ADV
ejpam-2418	149	2	c	c	PROPN
ejpam-2418	149	3	p(a	p(a	PROPN
ejpam-2418	149	4	)	)	PUNCT
ejpam-2418	149	5	=	=	NOUN
ejpam-2418	149	6	a.	a.	NOUN
ejpam-2418	149	7	proof	proof	NOUN
ejpam-2418	149	8	.	.	PUNCT
ejpam-2418	150	1	since	since	SCONJ
ejpam-2418	150	2	b	b	PROPN
ejpam-2418	150	3	is	be	AUX
ejpam-2418	150	4	an	an	DET
ejpam-2418	150	5	essential	essential	ADJ
ejpam-2418	150	6	extension	extension	NOUN
ejpam-2418	150	7	of	of	ADP
ejpam-2418	150	8	a	a	DET
ejpam-2418	150	9	,	,	PUNCT
ejpam-2418	150	10	c	c	PROPN
ejpam-2418	150	11	p(a	p(a	PROPN
ejpam-2418	150	12	)	)	PUNCT
ejpam-2418	150	13	is	be	AUX
ejpam-2418	150	14	an	an	DET
ejpam-2418	150	15	essential	essential	ADJ
ejpam-2418	150	16	extension	extension	NOUN
ejpam-2418	150	17	of	of	ADP
ejpam-2418	150	18	a	a	DET
ejpam-2418	150	19	too	too	ADV
ejpam-2418	150	20	.	.	PUNCT
ejpam-2418	151	1	let	let	VERB
ejpam-2418	151	2	c	c	PROPN
ejpam-2418	151	3	p(a	p(a	VERB
ejpam-2418	151	4	)	)	PUNCT
ejpam-2418	151	5	6=	6=	ADP
ejpam-2418	151	6	a	a	DET
ejpam-2418	151	7	and	and	CCONJ
ejpam-2418	151	8	b	b	NOUN
ejpam-2418	151	9	∈	∈	PROPN
ejpam-2418	151	10	c	c	X
ejpam-2418	151	11	p(a	p(a	NOUN
ejpam-2418	151	12	)	)	PUNCT
ejpam-2418	151	13	\	\	PROPN
ejpam-2418	151	14	a.	a.	NOUN
ejpam-2418	151	15	by	by	ADP
ejpam-2418	151	16	the	the	DET
ejpam-2418	151	17	axiom	axiom	NOUN
ejpam-2418	151	18	of	of	ADP
ejpam-2418	151	19	choice	choice	NOUN
ejpam-2418	151	20	,	,	PUNCT
ejpam-2418	151	21	choose	choose	VERB
ejpam-2418	151	22	and	and	CCONJ
ejpam-2418	151	23	fix	fix	VERB
ejpam-2418	151	24	an	an	DET
ejpam-2418	151	25	element	element	NOUN
ejpam-2418	151	26	ab	ab	PROPN
ejpam-2418	151	27	∈	∈	PROPN
ejpam-2418	151	28	a	a	DET
ejpam-2418	151	29	such	such	ADJ
ejpam-2418	151	30	that	that	DET
ejpam-2418	151	31	λb	λb	NOUN
ejpam-2418	151	32	=	=	PUNCT
ejpam-2418	151	33	λab	λab	PROPN
ejpam-2418	151	34	.	.	PUNCT
ejpam-2418	152	1	consider	consider	VERB
ejpam-2418	152	2	the	the	DET
ejpam-2418	152	3	homomorphism	homomorphism	NOUN
ejpam-2418	152	4	g	g	NOUN
ejpam-2418	152	5	:	:	PUNCT
ejpam-2418	152	6	c	c	X
ejpam-2418	152	7	p(a)→	p(a)→	PUNCT
ejpam-2418	153	1	a	a	PRON
ejpam-2418	153	2	defined	define	VERB
ejpam-2418	153	3	by	by	ADP
ejpam-2418	153	4	g(b	g(b	PROPN
ejpam-2418	153	5	)	)	PUNCT
ejpam-2418	153	6	=	=	SYM
ejpam-2418	153	7	¨	¨	NOUN
ejpam-2418	153	8	b	b	X
ejpam-2418	153	9	,	,	PUNCT
ejpam-2418	153	10	if	if	SCONJ
ejpam-2418	153	11	b	b	X
ejpam-2418	153	12	∈	∈	PROPN
ejpam-2418	153	13	a	a	DET
ejpam-2418	153	14	ab	ab	NOUN
ejpam-2418	153	15	,	,	PUNCT
ejpam-2418	153	16	if	if	SCONJ
ejpam-2418	153	17	b	b	PROPN
ejpam-2418	153	18	6∈	6∈	NOUN
ejpam-2418	153	19	a	a	X
ejpam-2418	153	20	.	.	PUNCT
ejpam-2418	154	1	it	it	PRON
ejpam-2418	154	2	is	be	AUX
ejpam-2418	154	3	clear	clear	ADJ
ejpam-2418	154	4	that	that	SCONJ
ejpam-2418	154	5	g	g	PROPN
ejpam-2418	154	6	|	|	ADV
ejpam-2418	154	7	a	a	DET
ejpam-2418	154	8	=	=	X
ejpam-2418	154	9	i	i	PROPN
ejpam-2418	154	10	d	d	PROPN
ejpam-2418	154	11	a	a	PROPN
ejpam-2418	154	12	and	and	CCONJ
ejpam-2418	154	13	hence	hence	ADV
ejpam-2418	154	14	g	g	PROPN
ejpam-2418	154	15	is	be	AUX
ejpam-2418	154	16	an	an	DET
ejpam-2418	154	17	isomorphism	isomorphism	NOUN
ejpam-2418	154	18	.	.	PUNCT
ejpam-2418	155	1	so	so	ADV
ejpam-2418	155	2	b	b	X
ejpam-2418	155	3	=	=	SYM
ejpam-2418	155	4	ab	ab	PROPN
ejpam-2418	155	5	which	which	PRON
ejpam-2418	155	6	is	be	AUX
ejpam-2418	155	7	a	a	DET
ejpam-2418	155	8	contradiction	contradiction	NOUN
ejpam-2418	155	9	.	.	PUNCT
ejpam-2418	156	1	thus	thus	ADV
ejpam-2418	156	2	c	c	X
ejpam-2418	156	3	p(a	p(a	PROPN
ejpam-2418	156	4	)	)	PUNCT
ejpam-2418	156	5	=	=	SYM
ejpam-2418	156	6	a.	a.	NOUN
ejpam-2418	156	7	proposition	proposition	NOUN
ejpam-2418	156	8	3	3	X
ejpam-2418	156	9	.	.	PUNCT
ejpam-2418	156	10	suppose	suppose	VERB
ejpam-2418	156	11	that	that	SCONJ
ejpam-2418	156	12	b	b	PROPN
ejpam-2418	156	13	is	be	AUX
ejpam-2418	156	14	an	an	DET
ejpam-2418	156	15	essential	essential	ADJ
ejpam-2418	156	16	extension	extension	NOUN
ejpam-2418	156	17	of	of	ADP
ejpam-2418	156	18	a	a	PRON
ejpam-2418	156	19	and	and	CCONJ
ejpam-2418	157	1	b	b	NOUN
ejpam-2418	157	2	∈	∈	PROPN
ejpam-2418	157	3	b	b	X
ejpam-2418	157	4	\	\	PROPN
ejpam-2418	157	5	a	a	DET
ejpam-2418	157	6	,	,	PUNCT
ejpam-2418	157	7	b′	b′	NUM
ejpam-2418	157	8	∈	∈	PROPN
ejpam-2418	157	9	b	b	NOUN
ejpam-2418	157	10	such	such	ADJ
ejpam-2418	157	11	that	that	DET
ejpam-2418	157	12	ib	ib	NOUN
ejpam-2418	158	1	=	=	NOUN
ejpam-2418	158	2	ib′	ib′	INTJ
ejpam-2418	158	3	.	.	PUNCT
ejpam-2418	159	1	if	if	SCONJ
ejpam-2418	159	2	for	for	ADP
ejpam-2418	159	3	each	each	DET
ejpam-2418	159	4	s	s	X
ejpam-2418	159	5	∈	∈	NOUN
ejpam-2418	159	6	ib	ib	NOUN
ejpam-2418	159	7	=	=	NOUN
ejpam-2418	159	8	ib′	ib′	ADV
ejpam-2418	159	9	,	,	PUNCT
ejpam-2418	159	10	bs	bs	PROPN
ejpam-2418	159	11	=	=	SYM
ejpam-2418	159	12	b′s	b′s	PROPN
ejpam-2418	159	13	,	,	PUNCT
ejpam-2418	159	14	then	then	ADV
ejpam-2418	159	15	b	b	X
ejpam-2418	159	16	=	=	SYM
ejpam-2418	159	17	b′.	b′.	PROPN
ejpam-2418	159	18	proof	proof	NOUN
ejpam-2418	159	19	.	.	PUNCT
ejpam-2418	160	1	if	if	SCONJ
ejpam-2418	160	2	b′	b′	NUM
ejpam-2418	160	3	∈	∈	PROPN
ejpam-2418	160	4	a	a	X
ejpam-2418	160	5	,	,	PUNCT
ejpam-2418	160	6	then	then	ADV
ejpam-2418	160	7	ib	ib	NOUN
ejpam-2418	160	8	=	=	PUNCT
ejpam-2418	160	9	ib′	ib′	X
ejpam-2418	161	1	=	=	SYM
ejpam-2418	161	2	s	s	X
ejpam-2418	161	3	and	and	CCONJ
ejpam-2418	161	4	b	b	PROPN
ejpam-2418	161	5	∈	∈	PROPN
ejpam-2418	161	6	c	c	PROPN
ejpam-2418	161	7	p(a	p(a	NOUN
ejpam-2418	161	8	)	)	PUNCT
ejpam-2418	161	9	.	.	PUNCT
ejpam-2418	162	1	by	by	ADP
ejpam-2418	162	2	lemma	lemma	PROPN
ejpam-2418	162	3	4	4	NUM
ejpam-2418	162	4	,	,	PUNCT
ejpam-2418	162	5	b	b	X
ejpam-2418	162	6	∈	∈	PROPN
ejpam-2418	162	7	a	a	PRON
ejpam-2418	162	8	,	,	PUNCT
ejpam-2418	162	9	which	which	PRON
ejpam-2418	162	10	is	be	AUX
ejpam-2418	162	11	impossible	impossible	ADJ
ejpam-2418	162	12	.	.	PUNCT
ejpam-2418	163	1	so	so	ADV
ejpam-2418	163	2	b′	b′	ADJ
ejpam-2418	163	3	/∈	/∈	PUNCT
ejpam-2418	164	1	a.	a.	NOUN
ejpam-2418	164	2	consider	consider	VERB
ejpam-2418	164	3	the	the	DET
ejpam-2418	164	4	canonical	canonical	ADJ
ejpam-2418	164	5	epimorphism	epimorphism	NOUN
ejpam-2418	164	6	π	π	NOUN
ejpam-2418	164	7	:	:	PUNCT
ejpam-2418	164	8	b	b	X
ejpam-2418	164	9	→	→	SYM
ejpam-2418	164	10	b	b	PROPN
ejpam-2418	164	11	/	/	SYM
ejpam-2418	164	12	ρ(b	ρ(b	NOUN
ejpam-2418	164	13	,	,	PUNCT
ejpam-2418	164	14	b′	b′	NUM
ejpam-2418	164	15	)	)	PUNCT
ejpam-2418	164	16	.	.	PUNCT
ejpam-2418	165	1	let	let	VERB
ejpam-2418	165	2	a	a	PRON
ejpam-2418	165	3	,	,	PUNCT
ejpam-2418	165	4	a′	a′	PROPN
ejpam-2418	165	5	∈	∈	PROPN
ejpam-2418	165	6	a	a	PRON
ejpam-2418	165	7	and	and	CCONJ
ejpam-2418	165	8	aρ(b	aρ(b	NOUN
ejpam-2418	165	9	,	,	PUNCT
ejpam-2418	165	10	b′)a′.	b′)a′.	PROPN
ejpam-2418	165	11	then	then	ADV
ejpam-2418	165	12	a	a	DET
ejpam-2418	165	13	=	=	PUNCT
ejpam-2418	165	14	a′	a′	NOUN
ejpam-2418	165	15	or	or	CCONJ
ejpam-2418	165	16	there	there	PRON
ejpam-2418	165	17	exist	exist	VERB
ejpam-2418	165	18	pi	pi	NOUN
ejpam-2418	165	19	,	,	PUNCT
ejpam-2418	165	20	qi	qi	PROPN
ejpam-2418	165	21	∈	∈	PROPN
ejpam-2418	165	22	{	{	PUNCT
ejpam-2418	165	23	b	b	NOUN
ejpam-2418	165	24	,	,	PUNCT
ejpam-2418	165	25	b′	b′	NUM
ejpam-2418	165	26	}	}	PUNCT
ejpam-2418	165	27	,	,	PUNCT
ejpam-2418	165	28	si	si	PROPN
ejpam-2418	165	29	∈	∈	PROPN
ejpam-2418	165	30	s1	s1	NOUN
ejpam-2418	165	31	and	and	CCONJ
ejpam-2418	165	32	n	n	CCONJ
ejpam-2418	165	33	∈	∈	PROPN
ejpam-2418	165	34	n	n	PRON
ejpam-2418	165	35	such	such	ADJ
ejpam-2418	165	36	that	that	SCONJ
ejpam-2418	165	37	a	a	DET
ejpam-2418	165	38	=	=	X
ejpam-2418	165	39	p1s1	p1s1	NOUN
ejpam-2418	165	40	,	,	PUNCT
ejpam-2418	165	41	q1s1	q1s1	NOUN
ejpam-2418	165	42	=	=	PUNCT
ejpam-2418	165	43	p2s2,q2s2	p2s2,q2s2	NOUN
ejpam-2418	165	44	=	=	SYM
ejpam-2418	165	45	p3s3	p3s3	NOUN
ejpam-2418	165	46	,	,	PUNCT
ejpam-2418	165	47	.	.	PUNCT
ejpam-2418	165	48	.	.	PUNCT
ejpam-2418	165	49	.	.	PUNCT
ejpam-2418	166	1	,	,	PUNCT
ejpam-2418	166	2	qnsn	qnsn	NOUN
ejpam-2418	166	3	=	=	NOUN
ejpam-2418	166	4	a′.	a′.	NOUN
ejpam-2418	166	5	if	if	SCONJ
ejpam-2418	166	6	s1	s1	PROPN
ejpam-2418	166	7	=	=	SYM
ejpam-2418	166	8	1	1	NUM
ejpam-2418	166	9	,	,	PUNCT
ejpam-2418	166	10	then	then	ADV
ejpam-2418	166	11	a	a	DET
ejpam-2418	166	12	=	=	X
ejpam-2418	166	13	p1s1	p1s1	NOUN
ejpam-2418	166	14	=	=	PROPN
ejpam-2418	166	15	p1	p1	PROPN
ejpam-2418	166	16	∈	∈	PROPN
ejpam-2418	166	17	{	{	PUNCT
ejpam-2418	166	18	b	b	NOUN
ejpam-2418	166	19	,	,	PUNCT
ejpam-2418	166	20	b′	b′	NUM
ejpam-2418	166	21	}	}	PUNCT
ejpam-2418	166	22	,	,	PUNCT
ejpam-2418	166	23	which	which	PRON
ejpam-2418	166	24	is	be	AUX
ejpam-2418	166	25	impossible	impossible	ADJ
ejpam-2418	166	26	.	.	PUNCT
ejpam-2418	167	1	let	let	VERB
ejpam-2418	167	2	for	for	ADP
ejpam-2418	167	3	i	i	PRON
ejpam-2418	167	4	≥	≥	NOUN
ejpam-2418	167	5	2	2	NUM
ejpam-2418	167	6	,	,	PUNCT
ejpam-2418	167	7	si	si	NOUN
ejpam-2418	167	8	=	=	SYM
ejpam-2418	167	9	1	1	NUM
ejpam-2418	167	10	and	and	CCONJ
ejpam-2418	167	11	for	for	ADP
ejpam-2418	167	12	each	each	DET
ejpam-2418	167	13	j	j	NOUN
ejpam-2418	167	14	<	<	X
ejpam-2418	167	15	i	i	PROPN
ejpam-2418	167	16	,	,	PUNCT
ejpam-2418	167	17	s	s	PROPN
ejpam-2418	167	18	j	j	PROPN
ejpam-2418	167	19	6=	6=	PROPN
ejpam-2418	167	20	1	1	NUM
ejpam-2418	167	21	.	.	PUNCT
ejpam-2418	168	1	so	so	ADV
ejpam-2418	168	2	s1	s1	PROPN
ejpam-2418	168	3	∈	∈	PROPN
ejpam-2418	168	4	ip1	ip1	PROPN
ejpam-2418	168	5	=	=	SYM
ejpam-2418	168	6	iq1	iq1	PROPN
ejpam-2418	168	7	and	and	CCONJ
ejpam-2418	168	8	a	a	DET
ejpam-2418	168	9	=	=	X
ejpam-2418	168	10	p1s1	p1s1	NOUN
ejpam-2418	168	11	=	=	SYM
ejpam-2418	168	12	q1s1	q1s1	NOUN
ejpam-2418	168	13	=	=	SYM
ejpam-2418	168	14	p2s2	p2s2	PROPN
ejpam-2418	168	15	,	,	PUNCT
ejpam-2418	168	16	which	which	PRON
ejpam-2418	168	17	implies	imply	VERB
ejpam-2418	168	18	s2	s2	PROPN
ejpam-2418	168	19	∈	∈	PROPN
ejpam-2418	168	20	ip2	ip2	PROPN
ejpam-2418	168	21	=	=	SYM
ejpam-2418	168	22	iq2	iq2	PROPN
ejpam-2418	168	23	and	and	CCONJ
ejpam-2418	168	24	p2s2	p2s2	PROPN
ejpam-2418	168	25	=	=	SYM
ejpam-2418	168	26	q2s2	q2s2	PROPN
ejpam-2418	169	1	=	=	SYM
ejpam-2418	169	2	p3s3	p3s3	NOUN
ejpam-2418	169	3	.	.	PUNCT
ejpam-2418	169	4	by	by	ADP
ejpam-2418	169	5	continuing	continue	VERB
ejpam-2418	169	6	with	with	ADP
ejpam-2418	169	7	this	this	DET
ejpam-2418	169	8	way	way	NOUN
ejpam-2418	169	9	,	,	PUNCT
ejpam-2418	169	10	we	we	PRON
ejpam-2418	169	11	have	have	VERB
ejpam-2418	169	12	a	a	DET
ejpam-2418	169	13	=	=	X
ejpam-2418	169	14	p1s1	p1s1	NOUN
ejpam-2418	169	15	=	=	PUNCT
ejpam-2418	169	16	q1s1	q1s1	NOUN
ejpam-2418	169	17	=	=	PUNCT
ejpam-2418	169	18	p2s2	p2s2	X
ejpam-2418	169	19	=	=	SYM
ejpam-2418	169	20	q2s2	q2s2	PROPN
ejpam-2418	169	21	=	=	SYM
ejpam-2418	170	1	p3s3	p3s3	NOUN
ejpam-2418	170	2	=	=	PUNCT
ejpam-2418	170	3	.	.	PUNCT
ejpam-2418	170	4	.	.	PUNCT
ejpam-2418	171	1	.=	.=	VERB
ejpam-2418	171	2	qi−1si−1	qi−1si−1	PROPN
ejpam-2418	171	3	=	=	SYM
ejpam-2418	171	4	pisi	pisi	X
ejpam-2418	171	5	=	=	PROPN
ejpam-2418	171	6	pi	pi	NOUN
ejpam-2418	171	7	∈	∈	PROPN
ejpam-2418	171	8	{	{	PUNCT
ejpam-2418	171	9	b	b	NOUN
ejpam-2418	171	10	,	,	PUNCT
ejpam-2418	171	11	b′	b′	NUM
ejpam-2418	171	12	}	}	PUNCT
ejpam-2418	171	13	.	.	PUNCT
ejpam-2418	172	1	so	so	ADV
ejpam-2418	172	2	b	b	NOUN
ejpam-2418	172	3	or	or	CCONJ
ejpam-2418	172	4	b′	b′	NUM
ejpam-2418	172	5	belongs	belong	VERB
ejpam-2418	172	6	to	to	ADP
ejpam-2418	172	7	a	a	PRON
ejpam-2418	172	8	,	,	PUNCT
ejpam-2418	172	9	which	which	PRON
ejpam-2418	172	10	is	be	AUX
ejpam-2418	172	11	a	a	DET
ejpam-2418	172	12	contradiction	contradiction	NOUN
ejpam-2418	172	13	.	.	PUNCT
ejpam-2418	173	1	thus	thus	ADV
ejpam-2418	173	2	for	for	ADP
ejpam-2418	173	3	each	each	DET
ejpam-2418	173	4	1	1	NUM
ejpam-2418	173	5	≤	≤	NUM
ejpam-2418	173	6	i	i	PRON
ejpam-2418	173	7	≤	≤	PROPN
ejpam-2418	173	8	n	n	CCONJ
ejpam-2418	173	9	,	,	PUNCT
ejpam-2418	173	10	si	si	PROPN
ejpam-2418	173	11	6=	6=	ADP
ejpam-2418	173	12	1	1	NUM
ejpam-2418	173	13	,	,	PUNCT
ejpam-2418	173	14	which	which	PRON
ejpam-2418	173	15	deduced	deduce	VERB
ejpam-2418	173	16	that	that	SCONJ
ejpam-2418	173	17	a	a	DET
ejpam-2418	173	18	=	=	X
ejpam-2418	173	19	p1s1	p1s1	NOUN
ejpam-2418	173	20	=	=	PUNCT
ejpam-2418	173	21	q1s1	q1s1	NOUN
ejpam-2418	173	22	=	=	PUNCT
ejpam-2418	173	23	p2s2	p2s2	X
ejpam-2418	173	24	=	=	SYM
ejpam-2418	173	25	q2s2	q2s2	PROPN
ejpam-2418	173	26	=	=	SYM
ejpam-2418	173	27	p3s3	p3s3	NOUN
ejpam-2418	173	28	=	=	PUNCT
ejpam-2418	173	29	.	.	PUNCT
ejpam-2418	173	30	.	.	PUNCT
ejpam-2418	174	1	.=	.=	NOUN
ejpam-2418	174	2	a′.	a′.	NOUN
ejpam-2418	175	1	so	so	SCONJ
ejpam-2418	175	2	π	π	PROPN
ejpam-2418	175	3	|a	|a	VERB
ejpam-2418	175	4	is	be	AUX
ejpam-2418	175	5	a	a	DET
ejpam-2418	175	6	monomorphism	monomorphism	NOUN
ejpam-2418	175	7	.	.	PUNCT
ejpam-2418	176	1	by	by	ADP
ejpam-2418	176	2	the	the	DET
ejpam-2418	176	3	hypothesize	hypothesize	NOUN
ejpam-2418	176	4	π	π	NOUN
ejpam-2418	176	5	is	be	AUX
ejpam-2418	176	6	a	a	DET
ejpam-2418	176	7	monomorphism	monomorphism	NOUN
ejpam-2418	176	8	and	and	CCONJ
ejpam-2418	176	9	hence	hence	ADV
ejpam-2418	176	10	b	b	X
ejpam-2418	177	1	=	=	X
ejpam-2418	177	2	b′.	b′.	PROPN
ejpam-2418	177	3	an	an	DET
ejpam-2418	177	4	s	s	PROPN
ejpam-2418	177	5	-	-	PUNCT
ejpam-2418	177	6	act	act	NOUN
ejpam-2418	177	7	a	a	PRON
ejpam-2418	177	8	is	be	AUX
ejpam-2418	177	9	called	call	VERB
ejpam-2418	177	10	s	s	NOUN
ejpam-2418	177	11	-	-	PUNCT
ejpam-2418	177	12	dense	dense	ADJ
ejpam-2418	177	13	in	in	ADP
ejpam-2418	177	14	an	an	DET
ejpam-2418	177	15	extension	extension	NOUN
ejpam-2418	177	16	b	b	NOUN
ejpam-2418	177	17	,	,	PUNCT
ejpam-2418	177	18	if	if	SCONJ
ejpam-2418	177	19	for	for	ADP
ejpam-2418	177	20	each	each	DET
ejpam-2418	177	21	b	b	PROPN
ejpam-2418	177	22	∈	∈	PROPN
ejpam-2418	177	23	b	b	PROPN
ejpam-2418	177	24	,	,	PUNCT
ejpam-2418	177	25	bs	bs	PROPN
ejpam-2418	177	26	⊆	⊆	NUM
ejpam-2418	177	27	a.	a.	NOUN
ejpam-2418	177	28	also	also	ADV
ejpam-2418	177	29	b	b	PROPN
ejpam-2418	177	30	is	be	AUX
ejpam-2418	177	31	said	say	VERB
ejpam-2418	177	32	to	to	PART
ejpam-2418	177	33	be	be	AUX
ejpam-2418	177	34	an	an	DET
ejpam-2418	177	35	s	s	NOUN
ejpam-2418	177	36	-	-	PUNCT
ejpam-2418	177	37	dense	dense	ADJ
ejpam-2418	177	38	essential	essential	ADJ
ejpam-2418	177	39	extension	extension	NOUN
ejpam-2418	177	40	of	of	ADP
ejpam-2418	177	41	a	a	PRON
ejpam-2418	177	42	,	,	PUNCT
ejpam-2418	177	43	if	if	SCONJ
ejpam-2418	177	44	b	b	NOUN
ejpam-2418	177	45	is	be	AUX
ejpam-2418	177	46	an	an	DET
ejpam-2418	177	47	s	s	NOUN
ejpam-2418	177	48	-	-	PUNCT
ejpam-2418	177	49	dense	dense	ADJ
ejpam-2418	177	50	extension	extension	NOUN
ejpam-2418	177	51	as	as	ADV
ejpam-2418	177	52	well	well	ADV
ejpam-2418	177	53	as	as	ADP
ejpam-2418	177	54	essential	essential	ADJ
ejpam-2418	177	55	extension	extension	NOUN
ejpam-2418	177	56	of	of	ADP
ejpam-2418	177	57	a.	a.	NOUN
ejpam-2418	177	58	the	the	DET
ejpam-2418	177	59	following	follow	VERB
ejpam-2418	177	60	lemma	lemma	PROPN
ejpam-2418	177	61	is	be	AUX
ejpam-2418	177	62	an	an	DET
ejpam-2418	177	63	essential	essential	ADJ
ejpam-2418	177	64	test	test	NOUN
ejpam-2418	177	65	lemma	lemma	PROPN
ejpam-2418	177	66	for	for	ADP
ejpam-2418	177	67	s	s	NOUN
ejpam-2418	177	68	-	-	PUNCT
ejpam-2418	177	69	dense	dense	ADJ
ejpam-2418	177	70	essentiality	essentiality	NOUN
ejpam-2418	177	71	.	.	PUNCT
ejpam-2418	178	1	h.	h.	PROPN
ejpam-2418	178	2	barzegar	barzegar	PROPN
ejpam-2418	178	3	/	/	SYM
ejpam-2418	178	4	eur	eur	PROPN
ejpam-2418	178	5	.	.	PUNCT
ejpam-2418	179	1	j.	j.	PROPN
ejpam-2418	179	2	pure	pure	PROPN
ejpam-2418	179	3	appl	appl	PROPN
ejpam-2418	179	4	.	.	PROPN
ejpam-2418	179	5	math	math	PROPN
ejpam-2418	179	6	,	,	PUNCT
ejpam-2418	179	7	9	9	NUM
ejpam-2418	179	8	(	(	PUNCT
ejpam-2418	179	9	2016	2016	NUM
ejpam-2418	179	10	)	)	PUNCT
ejpam-2418	179	11	,	,	PUNCT
ejpam-2418	179	12	19	19	NUM
ejpam-2418	179	13	-	-	SYM
ejpam-2418	179	14	26	26	NUM
ejpam-2418	179	15	24	24	NUM
ejpam-2418	179	16	lemma	lemma	PROPN
ejpam-2418	179	17	5	5	NUM
ejpam-2418	179	18	.	.	PUNCT
ejpam-2418	180	1	an	an	DET
ejpam-2418	180	2	s	s	NOUN
ejpam-2418	180	3	-	-	PUNCT
ejpam-2418	180	4	dense	dense	ADJ
ejpam-2418	180	5	extension	extension	NOUN
ejpam-2418	180	6	τ	τ	X
ejpam-2418	180	7	:	:	PUNCT
ejpam-2418	180	8	a→	a→	PROPN
ejpam-2418	180	9	b	b	NOUN
ejpam-2418	180	10	is	be	AUX
ejpam-2418	180	11	s	s	NOUN
ejpam-2418	180	12	-	-	PUNCT
ejpam-2418	180	13	dense	dense	ADJ
ejpam-2418	180	14	essential	essential	ADJ
ejpam-2418	180	15	if	if	SCONJ
ejpam-2418	180	16	and	and	CCONJ
ejpam-2418	180	17	only	only	ADV
ejpam-2418	180	18	if	if	SCONJ
ejpam-2418	180	19	for	for	ADP
ejpam-2418	180	20	each	each	DET
ejpam-2418	180	21	b	b	PROPN
ejpam-2418	180	22	∈	∈	PROPN
ejpam-2418	180	23	b	b	X
ejpam-2418	180	24	\	\	PROPN
ejpam-2418	180	25	a	a	DET
ejpam-2418	180	26	,	,	PUNCT
ejpam-2418	180	27	b′	b′	NUM
ejpam-2418	180	28	∈	∈	PROPN
ejpam-2418	180	29	b	b	NOUN
ejpam-2418	180	30	,	,	PUNCT
ejpam-2418	180	31	if	if	SCONJ
ejpam-2418	180	32	λb	λb	ADJ
ejpam-2418	180	33	=	=	PUNCT
ejpam-2418	180	34	λb′	λb′	NOUN
ejpam-2418	180	35	,	,	PUNCT
ejpam-2418	180	36	then	then	ADV
ejpam-2418	180	37	b	b	X
ejpam-2418	180	38	=	=	SYM
ejpam-2418	180	39	b′.	b′.	PROPN
ejpam-2418	180	40	proof	proof	NOUN
ejpam-2418	180	41	.	.	PUNCT
ejpam-2418	181	1	(	(	PUNCT
ejpam-2418	181	2	⇒	⇒	PROPN
ejpam-2418	181	3	)	)	PUNCT
ejpam-2418	181	4	since	since	SCONJ
ejpam-2418	181	5	a	a	PRON
ejpam-2418	181	6	is	be	AUX
ejpam-2418	181	7	s	s	NOUN
ejpam-2418	181	8	-	-	NOUN
ejpam-2418	181	9	dense	dense	ADJ
ejpam-2418	181	10	in	in	ADP
ejpam-2418	181	11	b	b	NOUN
ejpam-2418	181	12	,	,	PUNCT
ejpam-2418	181	13	ib	ib	X
ejpam-2418	181	14	=	=	PUNCT
ejpam-2418	181	15	ib′	ib′	PROPN
ejpam-2418	181	16	=	=	PUNCT
ejpam-2418	181	17	s.	s.	PROPN
ejpam-2418	181	18	now	now	ADV
ejpam-2418	181	19	we	we	PRON
ejpam-2418	181	20	are	be	AUX
ejpam-2418	181	21	done	do	VERB
ejpam-2418	181	22	by	by	ADP
ejpam-2418	181	23	using	use	VERB
ejpam-2418	181	24	proposition	proposition	NOUN
ejpam-2418	181	25	3	3	NUM
ejpam-2418	181	26	.	.	PUNCT
ejpam-2418	182	1	(	(	PUNCT
ejpam-2418	182	2	⇐	⇐	NOUN
ejpam-2418	182	3	)	)	PUNCT
ejpam-2418	182	4	consider	consider	VERB
ejpam-2418	182	5	a	a	DET
ejpam-2418	182	6	τ	τ	PROPN
ejpam-2418	182	7	→	→	SYM
ejpam-2418	182	8	b	b	PROPN
ejpam-2418	182	9	g	g	PROPN
ejpam-2418	182	10	→	→	SYM
ejpam-2418	182	11	c	c	PROPN
ejpam-2418	182	12	,	,	PUNCT
ejpam-2418	182	13	which	which	PRON
ejpam-2418	182	14	τ	τ	PROPN
ejpam-2418	182	15	is	be	AUX
ejpam-2418	182	16	inclusion	inclusion	NOUN
ejpam-2418	182	17	map	map	NOUN
ejpam-2418	182	18	and	and	CCONJ
ejpam-2418	182	19	gτ	gτ	PROPN
ejpam-2418	182	20	is	be	AUX
ejpam-2418	182	21	a	a	DET
ejpam-2418	182	22	monomorphism	monomorphism	NOUN
ejpam-2418	182	23	.	.	PUNCT
ejpam-2418	183	1	let	let	VERB
ejpam-2418	183	2	g(b	g(b	X
ejpam-2418	183	3	)	)	PUNCT
ejpam-2418	183	4	=	=	SYM
ejpam-2418	183	5	g(b′	g(b′	PROPN
ejpam-2418	183	6	)	)	PUNCT
ejpam-2418	183	7	such	such	ADJ
ejpam-2418	183	8	that	that	DET
ejpam-2418	183	9	b	b	X
ejpam-2418	183	10	∈	∈	PROPN
ejpam-2418	183	11	b	b	X
ejpam-2418	183	12	\	\	PROPN
ejpam-2418	183	13	a.	a.	NOUN
ejpam-2418	183	14	for	for	ADP
ejpam-2418	183	15	each	each	DET
ejpam-2418	183	16	s	s	X
ejpam-2418	183	17	∈	∈	NOUN
ejpam-2418	183	18	s	s	X
ejpam-2418	183	19	we	we	PRON
ejpam-2418	183	20	have	have	VERB
ejpam-2418	183	21	g(bs	g(bs	PRON
ejpam-2418	183	22	)	)	PUNCT
ejpam-2418	183	23	=	=	SYM
ejpam-2418	183	24	g(b′s	g(b′s	NOUN
ejpam-2418	183	25	)	)	PUNCT
ejpam-2418	183	26	and	and	CCONJ
ejpam-2418	183	27	{	{	PUNCT
ejpam-2418	183	28	bs	bs	NOUN
ejpam-2418	183	29	,	,	PUNCT
ejpam-2418	183	30	b′s	b′s	NOUN
ejpam-2418	183	31	}	}	PUNCT
ejpam-2418	183	32	∈	∈	PROPN
ejpam-2418	183	33	a.	a.	NOUN
ejpam-2418	183	34	since	since	SCONJ
ejpam-2418	183	35	g	g	PROPN
ejpam-2418	183	36	|	|	ADV
ejpam-2418	183	37	a	a	PRON
ejpam-2418	183	38	is	be	AUX
ejpam-2418	183	39	one	one	NUM
ejpam-2418	183	40	to	to	ADP
ejpam-2418	183	41	one	one	NUM
ejpam-2418	183	42	,	,	PUNCT
ejpam-2418	183	43	λb	λb	ADP
ejpam-2418	183	44	=	=	PUNCT
ejpam-2418	183	45	λb′	λb′	ADJ
ejpam-2418	183	46	and	and	CCONJ
ejpam-2418	183	47	hence	hence	ADV
ejpam-2418	183	48	b	b	X
ejpam-2418	183	49	=	=	X
ejpam-2418	183	50	b′.	b′.	PROPN
ejpam-2418	183	51	lemma	lemma	PROPN
ejpam-2418	183	52	6	6	NUM
ejpam-2418	183	53	.	.	PUNCT
ejpam-2418	184	1	let	let	VERB
ejpam-2418	184	2	a	a	PRON
ejpam-2418	184	3	have	have	VERB
ejpam-2418	184	4	a	a	DET
ejpam-2418	184	5	fixed	fix	VERB
ejpam-2418	184	6	element	element	NOUN
ejpam-2418	184	7	and	and	CCONJ
ejpam-2418	184	8	b	b	NOUN
ejpam-2418	184	9	be	be	AUX
ejpam-2418	184	10	a	a	DET
ejpam-2418	184	11	proper	proper	ADJ
ejpam-2418	184	12	essential	essential	ADJ
ejpam-2418	184	13	extension	extension	NOUN
ejpam-2418	184	14	of	of	ADP
ejpam-2418	184	15	a.	a.	NOUN
ejpam-2418	184	16	then	then	ADV
ejpam-2418	184	17	for	for	ADP
ejpam-2418	184	18	every	every	DET
ejpam-2418	184	19	b	b	PROPN
ejpam-2418	184	20	∈	∈	PROPN
ejpam-2418	184	21	b	b	PROPN
ejpam-2418	184	22	and	and	CCONJ
ejpam-2418	184	23	every	every	PRON
ejpam-2418	184	24	nonempty	nonempty	ADJ
ejpam-2418	184	25	right	right	ADJ
ejpam-2418	184	26	ideal	ideal	ADJ
ejpam-2418	184	27	j	j	PROPN
ejpam-2418	184	28	of	of	ADP
ejpam-2418	184	29	s	s	PROPN
ejpam-2418	184	30	,	,	PUNCT
ejpam-2418	184	31	ib	ib	PROPN
ejpam-2418	184	32	∩	∩	PROPN
ejpam-2418	184	33	j	j	PROPN
ejpam-2418	184	34	6=	6=	NUM
ejpam-2418	184	35	;	;	PUNCT
ejpam-2418	184	36	.	.	PUNCT
ejpam-2418	185	1	proof	proof	NOUN
ejpam-2418	185	2	.	.	PUNCT
ejpam-2418	186	1	for	for	ADP
ejpam-2418	186	2	b	b	PROPN
ejpam-2418	186	3	∈	∈	PROPN
ejpam-2418	186	4	a	a	X
ejpam-2418	186	5	,	,	PUNCT
ejpam-2418	186	6	ib	ib	NOUN
ejpam-2418	186	7	=	=	SYM
ejpam-2418	186	8	s	s	PROPN
ejpam-2418	186	9	and	and	CCONJ
ejpam-2418	186	10	the	the	DET
ejpam-2418	186	11	result	result	NOUN
ejpam-2418	186	12	is	be	AUX
ejpam-2418	186	13	obvious	obvious	ADJ
ejpam-2418	186	14	.	.	PUNCT
ejpam-2418	187	1	for	for	ADP
ejpam-2418	187	2	b	b	PROPN
ejpam-2418	187	3	/∈	/∈	PROPN
ejpam-2418	187	4	a	a	PRON
ejpam-2418	187	5	,	,	PUNCT
ejpam-2418	187	6	let	let	VERB
ejpam-2418	187	7	j	j	PRON
ejpam-2418	187	8	be	be	AUX
ejpam-2418	187	9	a	a	DET
ejpam-2418	187	10	nonempty	nonempty	ADJ
ejpam-2418	187	11	right	right	ADJ
ejpam-2418	187	12	ideal	ideal	NOUN
ejpam-2418	187	13	of	of	ADP
ejpam-2418	187	14	s	s	PRON
ejpam-2418	187	15	and	and	CCONJ
ejpam-2418	187	16	ib∩	ib∩	PROPN
ejpam-2418	187	17	j	j	PROPN
ejpam-2418	187	18	=	=	PUNCT
ejpam-2418	187	19	;	;	PUNCT
ejpam-2418	187	20	.	.	PUNCT
ejpam-2418	188	1	by	by	ADP
ejpam-2418	188	2	corollary	corollary	ADJ
ejpam-2418	188	3	3	3	NUM
ejpam-2418	188	4	,	,	PUNCT
ejpam-2418	188	5	ib	ib	NOUN
ejpam-2418	188	6	6=	6=	NUM
ejpam-2418	188	7	;	;	PUNCT
ejpam-2418	188	8	and	and	CCONJ
ejpam-2418	188	9	f	f	PROPN
ejpam-2418	188	10	ix(b	ix(b	PROPN
ejpam-2418	188	11	)	)	PUNCT
ejpam-2418	188	12	⊆	⊆	NUM
ejpam-2418	188	13	a.	a.	NOUN
ejpam-2418	188	14	it	it	PRON
ejpam-2418	188	15	is	be	AUX
ejpam-2418	188	16	clear	clear	ADJ
ejpam-2418	188	17	that	that	SCONJ
ejpam-2418	188	18	b′	b′	NOUN
ejpam-2418	188	19	=	=	PUNCT
ejpam-2418	188	20	{	{	PUNCT
ejpam-2418	188	21	bs|s	bs|s	NOUN
ejpam-2418	188	22	∈	∈	PROPN
ejpam-2418	188	23	j	j	PROPN
ejpam-2418	188	24	}	}	PUNCT
ejpam-2418	188	25	is	be	AUX
ejpam-2418	188	26	a	a	DET
ejpam-2418	188	27	subact	subact	NOUN
ejpam-2418	188	28	of	of	ADP
ejpam-2418	188	29	b	b	NOUN
ejpam-2418	188	30	and	and	CCONJ
ejpam-2418	188	31	b′	b′	NUM
ejpam-2418	188	32	∩	∩	NOUN
ejpam-2418	188	33	a=	a=	NOUN
ejpam-2418	188	34	;	;	PUNCT
ejpam-2418	188	35	.	.	PUNCT
ejpam-2418	189	1	by	by	ADP
ejpam-2418	189	2	proposition	proposition	NOUN
ejpam-2418	189	3	1	1	NUM
ejpam-2418	189	4	,	,	PUNCT
ejpam-2418	189	5	|b′|	|b′|	PROPN
ejpam-2418	189	6	=	=	SYM
ejpam-2418	189	7	1	1	NUM
ejpam-2418	189	8	and	and	CCONJ
ejpam-2418	189	9	hence	hence	ADV
ejpam-2418	189	10	for	for	ADP
ejpam-2418	189	11	every	every	DET
ejpam-2418	189	12	s	s	PROPN
ejpam-2418	189	13	∈	∈	PROPN
ejpam-2418	189	14	j	j	NOUN
ejpam-2418	189	15	,	,	PUNCT
ejpam-2418	189	16	bs	bs	PROPN
ejpam-2418	189	17	=	=	SYM
ejpam-2418	189	18	b0	b0	NOUN
ejpam-2418	189	19	for	for	ADP
ejpam-2418	189	20	some	some	DET
ejpam-2418	189	21	b0	b0	NOUN
ejpam-2418	189	22	∈	∈	PROPN
ejpam-2418	189	23	b	b	NOUN
ejpam-2418	189	24	\	\	PROPN
ejpam-2418	189	25	a.	a.	NOUN
ejpam-2418	189	26	consider	consider	VERB
ejpam-2418	189	27	s0	s0	PROPN
ejpam-2418	189	28	∈	∈	PROPN
ejpam-2418	189	29	j	j	PROPN
ejpam-2418	189	30	.	.	PUNCT
ejpam-2418	190	1	then	then	ADV
ejpam-2418	190	2	for	for	ADP
ejpam-2418	190	3	every	every	DET
ejpam-2418	190	4	t	t	NOUN
ejpam-2418	190	5	∈	∈	PROPN
ejpam-2418	190	6	s	s	PROPN
ejpam-2418	190	7	,	,	PUNCT
ejpam-2418	190	8	b0	b0	NOUN
ejpam-2418	190	9	t	t	NOUN
ejpam-2418	191	1	=	=	PUNCT
ejpam-2418	191	2	(	(	PUNCT
ejpam-2418	191	3	bs0)t	bs0)t	PROPN
ejpam-2418	191	4	=	=	PUNCT
ejpam-2418	191	5	b(s0	b(s0	PROPN
ejpam-2418	191	6	t	t	PROPN
ejpam-2418	191	7	)	)	PUNCT
ejpam-2418	191	8	=	=	SYM
ejpam-2418	191	9	b0	b0	NOUN
ejpam-2418	191	10	.	.	PUNCT
ejpam-2418	192	1	so	so	ADV
ejpam-2418	192	2	b0	b0	NOUN
ejpam-2418	192	3	∈	∈	PROPN
ejpam-2418	192	4	f	f	PROPN
ejpam-2418	192	5	ix(b	ix(b	PROPN
ejpam-2418	192	6	)	)	PUNCT
ejpam-2418	193	1	⊆	⊆	NUM
ejpam-2418	193	2	a	a	PRON
ejpam-2418	193	3	,	,	PUNCT
ejpam-2418	193	4	which	which	PRON
ejpam-2418	193	5	is	be	AUX
ejpam-2418	193	6	impossible	impossible	ADJ
ejpam-2418	193	7	.	.	PUNCT
ejpam-2418	194	1	the	the	DET
ejpam-2418	194	2	following	follow	VERB
ejpam-2418	194	3	two	two	NUM
ejpam-2418	194	4	theorems	theorem	NOUN
ejpam-2418	194	5	are	be	AUX
ejpam-2418	194	6	the	the	DET
ejpam-2418	194	7	main	main	ADJ
ejpam-2418	194	8	results	result	NOUN
ejpam-2418	194	9	of	of	ADP
ejpam-2418	194	10	this	this	DET
ejpam-2418	194	11	article	article	NOUN
ejpam-2418	194	12	,	,	PUNCT
ejpam-2418	194	13	which	which	PRON
ejpam-2418	194	14	is	be	AUX
ejpam-2418	194	15	in	in	ADP
ejpam-2418	194	16	fact	fact	NOUN
ejpam-2418	194	17	a	a	DET
ejpam-2418	194	18	kind	kind	NOUN
ejpam-2418	194	19	of	of	ADP
ejpam-2418	194	20	essential	essential	ADJ
ejpam-2418	194	21	test	test	NOUN
ejpam-2418	194	22	lemma	lemma	PROPN
ejpam-2418	194	23	.	.	PUNCT
ejpam-2418	195	1	in	in	ADP
ejpam-2418	195	2	these	these	DET
ejpam-2418	195	3	theorems	theorem	NOUN
ejpam-2418	195	4	we	we	PRON
ejpam-2418	195	5	give	give	VERB
ejpam-2418	195	6	an	an	DET
ejpam-2418	195	7	(	(	PUNCT
ejpam-2418	195	8	internal	internal	ADJ
ejpam-2418	195	9	)	)	PUNCT
ejpam-2418	195	10	characterization	characterization	NOUN
ejpam-2418	195	11	for	for	ADP
ejpam-2418	195	12	essential	essential	ADJ
ejpam-2418	195	13	monomorphisms	monomorphism	NOUN
ejpam-2418	195	14	(	(	PUNCT
ejpam-2418	195	15	in	in	ADP
ejpam-2418	195	16	terms	term	NOUN
ejpam-2418	195	17	of	of	ADP
ejpam-2418	195	18	elements	element	NOUN
ejpam-2418	195	19	rather	rather	ADV
ejpam-2418	195	20	than	than	ADP
ejpam-2418	195	21	congruences	congruence	NOUN
ejpam-2418	195	22	)	)	PUNCT
ejpam-2418	195	23	.	.	PUNCT
ejpam-2418	196	1	theorem	theorem	ADJ
ejpam-2418	196	2	5	5	NUM
ejpam-2418	196	3	.	.	PUNCT
ejpam-2418	197	1	(	(	PUNCT
ejpam-2418	197	2	essential	essential	ADJ
ejpam-2418	197	3	test	test	NOUN
ejpam-2418	197	4	lemma	lemma	PROPN
ejpam-2418	197	5	1	1	NUM
ejpam-2418	197	6	)	)	PUNCT
ejpam-2418	197	7	an	an	DET
ejpam-2418	197	8	s	s	PROPN
ejpam-2418	197	9	-	-	PUNCT
ejpam-2418	197	10	act	act	NOUN
ejpam-2418	197	11	b	b	NOUN
ejpam-2418	197	12	is	be	AUX
ejpam-2418	197	13	an	an	DET
ejpam-2418	197	14	essential	essential	ADJ
ejpam-2418	197	15	extension	extension	NOUN
ejpam-2418	197	16	of	of	ADP
ejpam-2418	197	17	a	a	DET
ejpam-2418	197	18	if	if	NOUN
ejpam-2418	197	19	and	and	CCONJ
ejpam-2418	197	20	only	only	ADV
ejpam-2418	197	21	if	if	SCONJ
ejpam-2418	197	22	for	for	ADP
ejpam-2418	197	23	every	every	DET
ejpam-2418	197	24	x	x	SYM
ejpam-2418	197	25	∈	∈	PROPN
ejpam-2418	197	26	b	b	PROPN
ejpam-2418	197	27	and	and	CCONJ
ejpam-2418	197	28	y	y	PROPN
ejpam-2418	197	29	∈	∈	PROPN
ejpam-2418	198	1	b	b	PROPN
ejpam-2418	198	2	\	\	PROPN
ejpam-2418	198	3	a	a	PRON
ejpam-2418	198	4	whenever	whenever	SCONJ
ejpam-2418	198	5	the	the	DET
ejpam-2418	198	6	following	follow	VERB
ejpam-2418	198	7	two	two	NUM
ejpam-2418	198	8	conditions	condition	NOUN
ejpam-2418	198	9	hold	hold	VERB
ejpam-2418	198	10	then	then	ADV
ejpam-2418	198	11	x	x	X
ejpam-2418	198	12	=	=	SYM
ejpam-2418	198	13	y	y	PROPN
ejpam-2418	198	14	:	:	PUNCT
ejpam-2418	198	15	(	(	PUNCT
ejpam-2418	198	16	i	i	NOUN
ejpam-2418	198	17	)	)	PUNCT
ejpam-2418	198	18	for	for	ADP
ejpam-2418	198	19	each	each	DET
ejpam-2418	198	20	s	s	X
ejpam-2418	198	21	∈	∈	NOUN
ejpam-2418	198	22	s	s	VERB
ejpam-2418	198	23	with	with	ADP
ejpam-2418	198	24	s	s	PROPN
ejpam-2418	198	25	∈	∈	NOUN
ejpam-2418	198	26	ix	ix	ADP
ejpam-2418	198	27	∩	∩	NOUN
ejpam-2418	198	28	i	i	PRON
ejpam-2418	198	29	y	y	PROPN
ejpam-2418	198	30	,	,	PUNCT
ejpam-2418	198	31	we	we	PRON
ejpam-2418	198	32	have	have	VERB
ejpam-2418	198	33	xs	xs	NOUN
ejpam-2418	198	34	=	=	SYM
ejpam-2418	198	35	ys	ys	PROPN
ejpam-2418	198	36	.	.	PUNCT
ejpam-2418	199	1	(	(	PUNCT
ejpam-2418	199	2	ii	ii	NOUN
ejpam-2418	199	3	)	)	PUNCT
ejpam-2418	199	4	if	if	SCONJ
ejpam-2418	199	5	i1	i1	PROPN
ejpam-2418	199	6	=	=	PUNCT
ejpam-2418	199	7	ix	ix	ADV
ejpam-2418	199	8	\	\	PROPN
ejpam-2418	200	1	i	i	PROPN
ejpam-2418	200	2	y	y	PROPN
ejpam-2418	200	3	and	and	CCONJ
ejpam-2418	200	4	i2	i2	PROPN
ejpam-2418	201	1	=	=	PUNCT
ejpam-2418	202	1	i	i	NOUN
ejpam-2418	202	2	y	y	NOUN
ejpam-2418	202	3	\	\	PUNCT
ejpam-2418	202	4	ix	ix	ADV
ejpam-2418	202	5	,	,	PUNCT
ejpam-2418	202	6	then	then	ADV
ejpam-2418	202	7	kerλy	kerλy	VERB
ejpam-2418	202	8	|i1	|i1	PROPN
ejpam-2418	202	9	⊆	⊆	NUM
ejpam-2418	202	10	kerλx	kerλx	NOUN
ejpam-2418	202	11	and	and	CCONJ
ejpam-2418	202	12	kerλx	kerλx	NOUN
ejpam-2418	202	13	|i2	|i2	ADP
ejpam-2418	202	14	⊆	⊆	NUM
ejpam-2418	202	15	kerλy	kerλy	NOUN
ejpam-2418	202	16	.	.	PUNCT
ejpam-2418	203	1	proof	proof	NOUN
ejpam-2418	203	2	.	.	PUNCT
ejpam-2418	204	1	(	(	PUNCT
ejpam-2418	204	2	⇐	⇐	NOUN
ejpam-2418	204	3	)	)	PUNCT
ejpam-2418	204	4	let	let	VERB
ejpam-2418	204	5	g	g	NOUN
ejpam-2418	204	6	:	:	PUNCT
ejpam-2418	204	7	b→	b→	PROPN
ejpam-2418	204	8	c	c	AUX
ejpam-2418	204	9	be	be	AUX
ejpam-2418	204	10	a	a	DET
ejpam-2418	204	11	homomorphism	homomorphism	NOUN
ejpam-2418	204	12	with	with	ADP
ejpam-2418	204	13	g|a	g|a	PROPN
ejpam-2418	204	14	a	a	DET
ejpam-2418	204	15	monomorphism	monomorphism	NOUN
ejpam-2418	204	16	,	,	PUNCT
ejpam-2418	204	17	and	and	CCONJ
ejpam-2418	204	18	g(x	g(x	NOUN
ejpam-2418	204	19	)	)	PUNCT
ejpam-2418	205	1	=	=	SYM
ejpam-2418	205	2	g(y	g(y	NOUN
ejpam-2418	205	3	)	)	PUNCT
ejpam-2418	205	4	for	for	ADP
ejpam-2418	205	5	x	x	SYM
ejpam-2418	205	6	,	,	PUNCT
ejpam-2418	205	7	y	y	PROPN
ejpam-2418	205	8	∈	∈	PROPN
ejpam-2418	205	9	b	b	PROPN
ejpam-2418	205	10	.	.	PUNCT
ejpam-2418	206	1	then	then	ADV
ejpam-2418	206	2	,	,	PUNCT
ejpam-2418	206	3	clearly	clearly	ADV
ejpam-2418	206	4	conditions	condition	NOUN
ejpam-2418	206	5	(	(	PUNCT
ejpam-2418	206	6	i	i	NOUN
ejpam-2418	206	7	)	)	PUNCT
ejpam-2418	206	8	and	and	CCONJ
ejpam-2418	206	9	(	(	PUNCT
ejpam-2418	206	10	ii	ii	NOUN
ejpam-2418	206	11	)	)	PUNCT
ejpam-2418	206	12	hold	hold	VERB
ejpam-2418	206	13	for	for	ADP
ejpam-2418	206	14	x	x	PROPN
ejpam-2418	206	15	∈	∈	PROPN
ejpam-2418	206	16	b	b	PROPN
ejpam-2418	206	17	,	,	PUNCT
ejpam-2418	206	18	y	y	PROPN
ejpam-2418	206	19	∈	∈	PROPN
ejpam-2418	206	20	b	b	X
ejpam-2418	206	21	\	\	PROPN
ejpam-2418	206	22	a.	a.	NOUN
ejpam-2418	206	23	thus	thus	ADV
ejpam-2418	206	24	x	x	X
ejpam-2418	206	25	=	=	SYM
ejpam-2418	206	26	y	y	PROPN
ejpam-2418	206	27	,	,	PUNCT
ejpam-2418	206	28	and	and	CCONJ
ejpam-2418	206	29	so	so	ADV
ejpam-2418	206	30	b	b	PROPN
ejpam-2418	206	31	is	be	AUX
ejpam-2418	206	32	an	an	DET
ejpam-2418	206	33	essential	essential	ADJ
ejpam-2418	206	34	extension	extension	NOUN
ejpam-2418	206	35	of	of	ADP
ejpam-2418	206	36	a.	a.	NOUN
ejpam-2418	206	37	(	(	PUNCT
ejpam-2418	206	38	⇒	⇒	PROPN
ejpam-2418	206	39	)	)	PUNCT
ejpam-2418	206	40	let	let	VERB
ejpam-2418	206	41	b	b	X
ejpam-2418	206	42	be	be	AUX
ejpam-2418	206	43	an	an	DET
ejpam-2418	206	44	essential	essential	ADJ
ejpam-2418	206	45	extension	extension	NOUN
ejpam-2418	206	46	of	of	ADP
ejpam-2418	206	47	a	a	DET
ejpam-2418	206	48	,	,	PUNCT
ejpam-2418	206	49	x	x	SYM
ejpam-2418	206	50	∈	∈	PROPN
ejpam-2418	206	51	b	b	NOUN
ejpam-2418	206	52	,	,	PUNCT
ejpam-2418	206	53	and	and	CCONJ
ejpam-2418	206	54	y	y	PROPN
ejpam-2418	206	55	∈	∈	PROPN
ejpam-2418	206	56	b	b	X
ejpam-2418	206	57	\	\	PROPN
ejpam-2418	206	58	a.	a.	NOUN
ejpam-2418	206	59	let	let	VERB
ejpam-2418	206	60	the	the	DET
ejpam-2418	206	61	conditions	condition	NOUN
ejpam-2418	206	62	(	(	PUNCT
ejpam-2418	206	63	i	i	NOUN
ejpam-2418	206	64	)	)	PUNCT
ejpam-2418	206	65	and	and	CCONJ
ejpam-2418	206	66	(	(	PUNCT
ejpam-2418	206	67	ii	ii	NOUN
ejpam-2418	206	68	)	)	PUNCT
ejpam-2418	206	69	hold	hold	VERB
ejpam-2418	206	70	.	.	PUNCT
ejpam-2418	207	1	at	at	ADP
ejpam-2418	207	2	first	first	ADV
ejpam-2418	207	3	we	we	PRON
ejpam-2418	207	4	show	show	VERB
ejpam-2418	207	5	that	that	SCONJ
ejpam-2418	207	6	ix	ix	ADV
ejpam-2418	207	7	=	=	PUNCT
ejpam-2418	207	8	i	i	NOUN
ejpam-2418	207	9	y	y	PROPN
ejpam-2418	207	10	.	.	PUNCT
ejpam-2418	208	1	on	on	ADP
ejpam-2418	208	2	the	the	DET
ejpam-2418	208	3	contrary	contrary	NOUN
ejpam-2418	208	4	,	,	PUNCT
ejpam-2418	208	5	let	let	VERB
ejpam-2418	208	6	ix	ix	PRON
ejpam-2418	208	7	6=	6=	PRON
ejpam-2418	209	1	i	i	PRON
ejpam-2418	209	2	y	y	PROPN
ejpam-2418	209	3	.	.	PUNCT
ejpam-2418	210	1	in	in	ADP
ejpam-2418	210	2	this	this	DET
ejpam-2418	210	3	case	case	NOUN
ejpam-2418	210	4	,	,	PUNCT
ejpam-2418	210	5	there	there	PRON
ejpam-2418	210	6	exists	exist	VERB
ejpam-2418	210	7	t	t	PROPN
ejpam-2418	210	8	∈	∈	PROPN
ejpam-2418	210	9	s	s	VERB
ejpam-2418	210	10	such	such	ADJ
ejpam-2418	210	11	that	that	SCONJ
ejpam-2418	210	12	a	a	DET
ejpam-2418	210	13	=	=	SYM
ejpam-2418	210	14	x	x	SYM
ejpam-2418	210	15	t	t	NOUN
ejpam-2418	210	16	∈	∈	PROPN
ejpam-2418	210	17	a	a	PRON
ejpam-2418	210	18	and	and	CCONJ
ejpam-2418	210	19	b	b	X
ejpam-2418	210	20	=	=	SYM
ejpam-2418	210	21	y	y	PROPN
ejpam-2418	210	22	t	t	PROPN
ejpam-2418	210	23	/∈	/∈	PUNCT
ejpam-2418	211	1	a	a	DET
ejpam-2418	211	2	(	(	PUNCT
ejpam-2418	211	3	or	or	CCONJ
ejpam-2418	211	4	x	x	SYM
ejpam-2418	211	5	t	t	NOUN
ejpam-2418	211	6	/∈	/∈	PUNCT
ejpam-2418	212	1	a	a	X
ejpam-2418	212	2	,	,	PUNCT
ejpam-2418	212	3	y	y	PROPN
ejpam-2418	212	4	t	t	PROPN
ejpam-2418	212	5	∈	∈	PROPN
ejpam-2418	212	6	a	a	PRON
ejpam-2418	212	7	)	)	PUNCT
ejpam-2418	212	8	.	.	PUNCT
ejpam-2418	213	1	so	so	ADV
ejpam-2418	213	2	,	,	PUNCT
ejpam-2418	213	3	by	by	ADP
ejpam-2418	213	4	(	(	PUNCT
ejpam-2418	213	5	i	i	NOUN
ejpam-2418	213	6	)	)	PUNCT
ejpam-2418	213	7	,	,	PUNCT
ejpam-2418	213	8	we	we	PRON
ejpam-2418	213	9	have	have	VERB
ejpam-2418	213	10	(	(	PUNCT
ejpam-2418	213	11	∗	∗	NOUN
ejpam-2418	213	12	)	)	PUNCT
ejpam-2418	213	13	for	for	ADP
ejpam-2418	213	14	every	every	DET
ejpam-2418	213	15	s	s	X
ejpam-2418	213	16	∈	∈	NOUN
ejpam-2418	213	17	ib	ib	NOUN
ejpam-2418	213	18	,	,	PUNCT
ejpam-2418	213	19	as	as	ADP
ejpam-2418	213	20	=	=	NOUN
ejpam-2418	213	21	x	x	X
ejpam-2418	213	22	ts	ts	ADP
ejpam-2418	213	23	=	=	PUNCT
ejpam-2418	213	24	y	y	PROPN
ejpam-2418	213	25	ts	ts	X
ejpam-2418	214	1	=	=	NOUN
ejpam-2418	214	2	bs	bs	PROPN
ejpam-2418	214	3	.	.	PUNCT
ejpam-2418	215	1	now	now	ADV
ejpam-2418	215	2	,	,	PUNCT
ejpam-2418	215	3	consider	consider	VERB
ejpam-2418	215	4	the	the	DET
ejpam-2418	215	5	congruence	congruence	NOUN
ejpam-2418	215	6	ρ	ρ	PROPN
ejpam-2418	215	7	=	=	SYM
ejpam-2418	215	8	ρ(a	ρ(a	PROPN
ejpam-2418	215	9	,	,	PUNCT
ejpam-2418	215	10	b	b	NOUN
ejpam-2418	215	11	)	)	PUNCT
ejpam-2418	215	12	on	on	ADP
ejpam-2418	215	13	b	b	PROPN
ejpam-2418	215	14	and	and	CCONJ
ejpam-2418	215	15	(	(	PUNCT
ejpam-2418	215	16	a1	a1	PROPN
ejpam-2418	215	17	,	,	PUNCT
ejpam-2418	215	18	a2	a2	NOUN
ejpam-2418	215	19	)	)	PUNCT
ejpam-2418	215	20	∈	∈	PROPN
ejpam-2418	215	21	ρ	ρ	PROPN
ejpam-2418	215	22	with	with	ADP
ejpam-2418	215	23	a1	a1	NOUN
ejpam-2418	215	24	,	,	PUNCT
ejpam-2418	215	25	a2	a2	PROPN
ejpam-2418	215	26	∈	∈	PROPN
ejpam-2418	215	27	a.	a.	NOUN
ejpam-2418	215	28	then	then	ADV
ejpam-2418	215	29	a1	a1	NOUN
ejpam-2418	215	30	=	=	PROPN
ejpam-2418	215	31	a2	a2	PROPN
ejpam-2418	215	32	or	or	CCONJ
ejpam-2418	215	33	there	there	ADV
ejpam-2418	215	34	exist	exist	VERB
ejpam-2418	215	35	p1	p1	NOUN
ejpam-2418	215	36	,	,	PUNCT
ejpam-2418	215	37	p2	p2	NOUN
ejpam-2418	215	38	,	,	PUNCT
ejpam-2418	215	39	.	.	PUNCT
ejpam-2418	215	40	.	.	PUNCT
ejpam-2418	216	1	.	.	PUNCT
ejpam-2418	217	1	,	,	PUNCT
ejpam-2418	217	2	pn	pn	PROPN
ejpam-2418	217	3	and	and	CCONJ
ejpam-2418	217	4	q1,q2	q1,q2	PROPN
ejpam-2418	217	5	,	,	PUNCT
ejpam-2418	217	6	.	.	PUNCT
ejpam-2418	217	7	.	.	PUNCT
ejpam-2418	218	1	.	.	PUNCT
ejpam-2418	219	1	,	,	PUNCT
ejpam-2418	219	2	qn	qn	VERB
ejpam-2418	219	3	in	in	ADP
ejpam-2418	219	4	b	b	NOUN
ejpam-2418	219	5	with	with	ADP
ejpam-2418	219	6	{	{	PUNCT
ejpam-2418	219	7	pi	pi	NOUN
ejpam-2418	219	8	,	,	PUNCT
ejpam-2418	219	9	qi}=	qi}=	X
ejpam-2418	219	10	{	{	PUNCT
ejpam-2418	219	11	a	a	PROPN
ejpam-2418	219	12	,	,	PUNCT
ejpam-2418	219	13	b	b	NOUN
ejpam-2418	219	14	}	}	PUNCT
ejpam-2418	219	15	and	and	CCONJ
ejpam-2418	219	16	s1	s1	NOUN
ejpam-2418	219	17	,	,	PUNCT
ejpam-2418	219	18	s2	s2	PROPN
ejpam-2418	219	19	,	,	PUNCT
ejpam-2418	219	20	.	.	PUNCT
ejpam-2418	219	21	.	.	PUNCT
ejpam-2418	220	1	.	.	PUNCT
ejpam-2418	221	1	,	,	PUNCT
ejpam-2418	221	2	sn	sn	PROPN
ejpam-2418	221	3	∈	∈	PROPN
ejpam-2418	221	4	s1	s1	NOUN
ejpam-2418	221	5	such	such	ADJ
ejpam-2418	221	6	that	that	DET
ejpam-2418	221	7	a1	a1	NOUN
ejpam-2418	221	8	=	=	NOUN
ejpam-2418	221	9	p1s1,q1s1	p1s1,q1s1	NOUN
ejpam-2418	221	10	=	=	SYM
ejpam-2418	221	11	p2s2	p2s2	NOUN
ejpam-2418	221	12	,	,	PUNCT
ejpam-2418	221	13	.	.	PUNCT
ejpam-2418	221	14	.	.	PUNCT
ejpam-2418	221	15	.	.	PUNCT
ejpam-2418	222	1	,	,	PUNCT
ejpam-2418	222	2	qnsn	qnsn	NOUN
ejpam-2418	222	3	=	=	SYM
ejpam-2418	222	4	a2	a2	PROPN
ejpam-2418	222	5	.	.	PUNCT
ejpam-2418	223	1	we	we	PRON
ejpam-2418	223	2	prove	prove	VERB
ejpam-2418	223	3	,	,	PUNCT
ejpam-2418	223	4	by	by	ADP
ejpam-2418	223	5	induction	induction	NOUN
ejpam-2418	223	6	on	on	ADP
ejpam-2418	223	7	n	n	CCONJ
ejpam-2418	223	8	,	,	PUNCT
ejpam-2418	223	9	that	that	DET
ejpam-2418	223	10	a1	a1	NOUN
ejpam-2418	223	11	=	=	NOUN
ejpam-2418	223	12	a2	a2	PROPN
ejpam-2418	223	13	,	,	PUNCT
ejpam-2418	223	14	.	.	PUNCT
ejpam-2418	224	1	if	if	SCONJ
ejpam-2418	224	2	n	n	NOUN
ejpam-2418	224	3	=	=	SYM
ejpam-2418	224	4	1	1	NUM
ejpam-2418	224	5	,	,	PUNCT
ejpam-2418	224	6	then	then	ADV
ejpam-2418	224	7	a1	a1	NOUN
ejpam-2418	224	8	=	=	SYM
ejpam-2418	224	9	p1s1	p1s1	NOUN
ejpam-2418	224	10	,	,	PUNCT
ejpam-2418	224	11	a2	a2	PROPN
ejpam-2418	224	12	=	=	SYM
ejpam-2418	224	13	q1s1	q1s1	PROPN
ejpam-2418	224	14	(	(	PUNCT
ejpam-2418	224	15	where	where	SCONJ
ejpam-2418	224	16	s1	s1	PROPN
ejpam-2418	224	17	6=	6=	ADP
ejpam-2418	224	18	1	1	NUM
ejpam-2418	224	19	,	,	PUNCT
ejpam-2418	224	20	since	since	SCONJ
ejpam-2418	224	21	otherwise	otherwise	ADV
ejpam-2418	224	22	p1	p1	PROPN
ejpam-2418	224	23	=	=	PUNCT
ejpam-2418	224	24	a	a	PRON
ejpam-2418	224	25	and	and	CCONJ
ejpam-2418	224	26	hence	hence	ADV
ejpam-2418	224	27	a2	a2	PROPN
ejpam-2418	224	28	=	=	SYM
ejpam-2418	224	29	q1	q1	PROPN
ejpam-2418	224	30	=	=	SYM
ejpam-2418	224	31	b	b	PROPN
ejpam-2418	224	32	which	which	PRON
ejpam-2418	224	33	is	be	AUX
ejpam-2418	224	34	a	a	DET
ejpam-2418	224	35	contradiction	contradiction	NOUN
ejpam-2418	224	36	)	)	PUNCT
ejpam-2418	224	37	.	.	PUNCT
ejpam-2418	225	1	but	but	CCONJ
ejpam-2418	225	2	,	,	PUNCT
ejpam-2418	225	3	one	one	NUM
ejpam-2418	225	4	of	of	ADP
ejpam-2418	225	5	p1	p1	PROPN
ejpam-2418	225	6	or	or	CCONJ
ejpam-2418	225	7	q1	q1	PROPN
ejpam-2418	225	8	is	be	AUX
ejpam-2418	225	9	b	b	NOUN
ejpam-2418	225	10	,	,	PUNCT
ejpam-2418	225	11	so	so	ADV
ejpam-2418	225	12	bs1	bs1	NOUN
ejpam-2418	225	13	∈	∈	PROPN
ejpam-2418	225	14	a	a	PRON
ejpam-2418	225	15	and	and	CCONJ
ejpam-2418	225	16	hence	hence	ADV
ejpam-2418	225	17	using	use	VERB
ejpam-2418	225	18	(	(	PUNCT
ejpam-2418	225	19	∗	∗	NOUN
ejpam-2418	225	20	)	)	PUNCT
ejpam-2418	225	21	a1	a1	NOUN
ejpam-2418	225	22	=	=	PUNCT
ejpam-2418	225	23	p1s1	p1s1	NOUN
ejpam-2418	225	24	=	=	SYM
ejpam-2418	225	25	q1s1	q1s1	NOUN
ejpam-2418	225	26	=	=	PUNCT
ejpam-2418	225	27	a2	a2	PROPN
ejpam-2418	225	28	.	.	PUNCT
ejpam-2418	226	1	now	now	ADV
ejpam-2418	226	2	,	,	PUNCT
ejpam-2418	226	3	let	let	VERB
ejpam-2418	226	4	the	the	DET
ejpam-2418	226	5	result	result	NOUN
ejpam-2418	226	6	be	be	AUX
ejpam-2418	226	7	true	true	ADJ
ejpam-2418	226	8	when	when	SCONJ
ejpam-2418	226	9	the	the	DET
ejpam-2418	226	10	path	path	NOUN
ejpam-2418	226	11	connecting	connect	VERB
ejpam-2418	226	12	a1	a1	NOUN
ejpam-2418	226	13	to	to	ADP
ejpam-2418	226	14	a2	a2	PROPN
ejpam-2418	226	15	has	have	VERB
ejpam-2418	226	16	length	length	NOUN
ejpam-2418	226	17	less	less	ADJ
ejpam-2418	226	18	than	than	SCONJ
ejpam-2418	226	19	n.	n.	NOUN
ejpam-2418	226	20	assume	assume	VERB
ejpam-2418	226	21	we	we	PRON
ejpam-2418	226	22	have	have	VERB
ejpam-2418	226	23	the	the	DET
ejpam-2418	226	24	above	above	ADJ
ejpam-2418	226	25	path	path	NOUN
ejpam-2418	226	26	of	of	ADP
ejpam-2418	226	27	length	length	NOUN
ejpam-2418	226	28	n≥	n≥	NOUN
ejpam-2418	226	29	1	1	NUM
ejpam-2418	226	30	.	.	PUNCT
ejpam-2418	227	1	then	then	ADV
ejpam-2418	227	2	:	:	PUNCT
ejpam-2418	227	3	if	if	SCONJ
ejpam-2418	227	4	q1s1	q1s1	PROPN
ejpam-2418	227	5	∈	∈	PROPN
ejpam-2418	227	6	a	a	DET
ejpam-2418	227	7	then	then	ADV
ejpam-2418	227	8	s1	s1	PROPN
ejpam-2418	227	9	6=	6=	ADP
ejpam-2418	227	10	1	1	NUM
ejpam-2418	227	11	(	(	PUNCT
ejpam-2418	227	12	because	because	SCONJ
ejpam-2418	227	13	otherwise	otherwise	ADV
ejpam-2418	227	14	q1	q1	PROPN
ejpam-2418	227	15	=	=	PUNCT
ejpam-2418	227	16	a	a	PRON
ejpam-2418	227	17	and	and	CCONJ
ejpam-2418	227	18	p1	p1	PROPN
ejpam-2418	227	19	=	=	SYM
ejpam-2418	227	20	b	b	PROPN
ejpam-2418	227	21	which	which	PRON
ejpam-2418	227	22	contradicts	contradict	VERB
ejpam-2418	227	23	a1	a1	NOUN
ejpam-2418	227	24	=	=	SYM
ejpam-2418	227	25	p1s1	p1s1	NOUN
ejpam-2418	227	26	)	)	PUNCT
ejpam-2418	227	27	.	.	PUNCT
ejpam-2418	228	1	also	also	ADV
ejpam-2418	228	2	bs1	bs1	VERB
ejpam-2418	228	3	∈	∈	PROPN
ejpam-2418	228	4	a	a	PRON
ejpam-2418	228	5	because	because	SCONJ
ejpam-2418	228	6	it	it	PRON
ejpam-2418	228	7	is	be	AUX
ejpam-2418	228	8	one	one	NUM
ejpam-2418	228	9	of	of	ADP
ejpam-2418	228	10	p1s1	p1s1	NOUN
ejpam-2418	228	11	or	or	CCONJ
ejpam-2418	228	12	q1s1	q1s1	NOUN
ejpam-2418	228	13	.	.	PUNCT
ejpam-2418	228	14	thus	thus	ADV
ejpam-2418	228	15	a1	a1	NOUN
ejpam-2418	228	16	=	=	PUNCT
ejpam-2418	228	17	p1s1	p1s1	NOUN
ejpam-2418	228	18	=	=	ADJ
ejpam-2418	228	19	q1s1	q1s1	PROPN
ejpam-2418	228	20	.	.	PUNCT
ejpam-2418	229	1	this	this	PRON
ejpam-2418	229	2	means	mean	VERB
ejpam-2418	229	3	p2s2	p2s2	PROPN
ejpam-2418	229	4	=	=	NOUN
ejpam-2418	229	5	a1	a1	NOUN
ejpam-2418	230	1	and	and	CCONJ
ejpam-2418	230	2	so	so	ADV
ejpam-2418	230	3	we	we	PRON
ejpam-2418	230	4	get	get	VERB
ejpam-2418	230	5	a	a	DET
ejpam-2418	230	6	path	path	NOUN
ejpam-2418	230	7	with	with	ADP
ejpam-2418	230	8	length	length	NOUN
ejpam-2418	230	9	n−1	n−1	PROPN
ejpam-2418	230	10	which	which	PRON
ejpam-2418	230	11	connects	connect	VERB
ejpam-2418	230	12	a1	a1	NOUN
ejpam-2418	230	13	to	to	ADP
ejpam-2418	230	14	a2	a2	PROPN
ejpam-2418	230	15	.	.	PUNCT
ejpam-2418	231	1	then	then	ADV
ejpam-2418	231	2	,	,	PUNCT
ejpam-2418	231	3	by	by	ADP
ejpam-2418	231	4	induction	induction	NOUN
ejpam-2418	231	5	hypothesis	hypothesis	NOUN
ejpam-2418	231	6	,	,	PUNCT
ejpam-2418	231	7	a1	a1	NOUN
ejpam-2418	231	8	=	=	PROPN
ejpam-2418	231	9	a2	a2	PROPN
ejpam-2418	231	10	.	.	PUNCT
ejpam-2418	232	1	references	reference	NOUN
ejpam-2418	232	2	25	25	NUM
ejpam-2418	232	3	if	if	SCONJ
ejpam-2418	232	4	q1s1	q1s1	PROPN
ejpam-2418	232	5	/∈	/∈	PUNCT
ejpam-2418	233	1	a	a	DET
ejpam-2418	233	2	then	then	ADV
ejpam-2418	233	3	p2	p2	PROPN
ejpam-2418	233	4	=	=	SYM
ejpam-2418	233	5	q1	q1	PROPN
ejpam-2418	233	6	=	=	SYM
ejpam-2418	233	7	b	b	PROPN
ejpam-2418	233	8	and	and	CCONJ
ejpam-2418	233	9	q2	q2	NOUN
ejpam-2418	233	10	=	=	SYM
ejpam-2418	233	11	p1	p1	PROPN
ejpam-2418	233	12	=	=	PUNCT
ejpam-2418	233	13	a.	a.	NOUN
ejpam-2418	233	14	hence	hence	ADV
ejpam-2418	233	15	,	,	PUNCT
ejpam-2418	233	16	q2s2	q2s2	PROPN
ejpam-2418	233	17	∈	∈	PROPN
ejpam-2418	233	18	a.	a.	NOUN
ejpam-2418	234	1	so	so	CCONJ
ejpam-2418	234	2	y	y	PROPN
ejpam-2418	234	3	ts1	ts1	PROPN
ejpam-2418	235	1	=	=	PUNCT
ejpam-2418	236	1	bs1	bs1	NOUN
ejpam-2418	236	2	=	=	SYM
ejpam-2418	236	3	q1s1	q1s1	NOUN
ejpam-2418	236	4	=	=	PUNCT
ejpam-2418	236	5	p2s2	p2s2	X
ejpam-2418	236	6	=	=	NOUN
ejpam-2418	236	7	bs2	bs2	PROPN
ejpam-2418	236	8	=	=	PUNCT
ejpam-2418	236	9	y	y	PROPN
ejpam-2418	236	10	ts2	ts2	PROPN
ejpam-2418	236	11	where	where	SCONJ
ejpam-2418	236	12	{	{	PUNCT
ejpam-2418	236	13	x	x	PROPN
ejpam-2418	236	14	ts1	ts1	PROPN
ejpam-2418	236	15	,	,	PUNCT
ejpam-2418	236	16	x	x	PROPN
ejpam-2418	236	17	ts2	ts2	ADJ
ejpam-2418	236	18	}	}	PUNCT
ejpam-2418	236	19	⊆	⊆	NUM
ejpam-2418	236	20	a	a	PRON
ejpam-2418	236	21	and	and	CCONJ
ejpam-2418	236	22	y	y	PROPN
ejpam-2418	236	23	ts2	ts2	PROPN
ejpam-2418	237	1	=	=	PUNCT
ejpam-2418	237	2	y	y	PROPN
ejpam-2418	237	3	ts1	ts1	PROPN
ejpam-2418	237	4	/∈	/∈	PUNCT
ejpam-2418	238	1	a.	a.	PROPN
ejpam-2418	239	1	thus	thus	ADV
ejpam-2418	239	2	,	,	PUNCT
ejpam-2418	239	3	by	by	ADP
ejpam-2418	239	4	(	(	PUNCT
ejpam-2418	239	5	ii	ii	NOUN
ejpam-2418	239	6	)	)	PUNCT
ejpam-2418	239	7	,	,	PUNCT
ejpam-2418	239	8	we	we	PRON
ejpam-2418	239	9	get	get	VERB
ejpam-2418	239	10	x	x	X
ejpam-2418	239	11	ts1	ts1	PROPN
ejpam-2418	239	12	=	=	PUNCT
ejpam-2418	239	13	x	x	SYM
ejpam-2418	239	14	ts2	ts2	NOUN
ejpam-2418	239	15	and	and	CCONJ
ejpam-2418	239	16	so	so	ADV
ejpam-2418	239	17	a1	a1	NOUN
ejpam-2418	239	18	=	=	PUNCT
ejpam-2418	239	19	p1s1	p1s1	NOUN
ejpam-2418	239	20	=	=	PUNCT
ejpam-2418	239	21	as1	as1	PROPN
ejpam-2418	239	22	=	=	PROPN
ejpam-2418	239	23	as2	as2	PROPN
ejpam-2418	239	24	=	=	PUNCT
ejpam-2418	240	1	q2s2	q2s2	PROPN
ejpam-2418	240	2	.	.	PUNCT
ejpam-2418	241	1	this	this	PRON
ejpam-2418	241	2	gives	give	VERB
ejpam-2418	241	3	p3s3	p3s3	NOUN
ejpam-2418	241	4	=	=	NOUN
ejpam-2418	241	5	a1	a1	NOUN
ejpam-2418	241	6	and	and	CCONJ
ejpam-2418	241	7	hence	hence	ADV
ejpam-2418	241	8	we	we	PRON
ejpam-2418	241	9	get	get	VERB
ejpam-2418	241	10	a	a	DET
ejpam-2418	241	11	path	path	NOUN
ejpam-2418	241	12	with	with	ADP
ejpam-2418	241	13	a	a	DET
ejpam-2418	241	14	lower	low	ADJ
ejpam-2418	241	15	length	length	NOUN
ejpam-2418	241	16	than	than	ADP
ejpam-2418	241	17	n	n	NUM
ejpam-2418	241	18	which	which	PRON
ejpam-2418	241	19	yields	yield	VERB
ejpam-2418	241	20	a1	a1	NOUN
ejpam-2418	241	21	=	=	PROPN
ejpam-2418	241	22	a2	a2	PROPN
ejpam-2418	241	23	,	,	PUNCT
ejpam-2418	241	24	by	by	ADP
ejpam-2418	241	25	induction	induction	NOUN
ejpam-2418	241	26	hypothesis	hypothesis	NOUN
ejpam-2418	241	27	.	.	PUNCT
ejpam-2418	242	1	therefore	therefore	ADV
ejpam-2418	242	2	,	,	PUNCT
ejpam-2418	242	3	a1	a1	NOUN
ejpam-2418	242	4	=	=	PROPN
ejpam-2418	242	5	a2	a2	PROPN
ejpam-2418	242	6	.	.	PUNCT
ejpam-2418	243	1	so	so	ADV
ejpam-2418	243	2	ρ	ρ	PROPN
ejpam-2418	243	3	is	be	AUX
ejpam-2418	243	4	identity	identity	NOUN
ejpam-2418	243	5	on	on	ADP
ejpam-2418	243	6	a.	a.	NOUN
ejpam-2418	243	7	thus	thus	ADV
ejpam-2418	243	8	it	it	PRON
ejpam-2418	243	9	is	be	AUX
ejpam-2418	243	10	identity	identity	NOUN
ejpam-2418	243	11	on	on	ADP
ejpam-2418	243	12	b	b	NOUN
ejpam-2418	243	13	and	and	CCONJ
ejpam-2418	243	14	hence	hence	ADV
ejpam-2418	243	15	a	a	DET
ejpam-2418	243	16	=	=	SYM
ejpam-2418	243	17	b	b	NOUN
ejpam-2418	243	18	,	,	PUNCT
ejpam-2418	243	19	which	which	PRON
ejpam-2418	243	20	is	be	AUX
ejpam-2418	243	21	a	a	DET
ejpam-2418	243	22	contradiction	contradiction	NOUN
ejpam-2418	243	23	.	.	PUNCT
ejpam-2418	244	1	so	so	ADV
ejpam-2418	244	2	,	,	PUNCT
ejpam-2418	244	3	ix	ix	PROPN
ejpam-2418	244	4	=	=	PUNCT
ejpam-2418	245	1	i	i	NOUN
ejpam-2418	245	2	y	y	PROPN
ejpam-2418	245	3	.	.	PUNCT
ejpam-2418	246	1	now	now	ADV
ejpam-2418	246	2	using	use	VERB
ejpam-2418	246	3	proposition	proposition	NOUN
ejpam-2418	246	4	3	3	NUM
ejpam-2418	246	5	deduced	deduce	VERB
ejpam-2418	246	6	the	the	DET
ejpam-2418	246	7	result	result	NOUN
ejpam-2418	246	8	.	.	PUNCT
ejpam-2418	247	1	theorem	theorem	ADJ
ejpam-2418	247	2	6	6	NUM
ejpam-2418	247	3	.	.	PUNCT
ejpam-2418	248	1	(	(	PUNCT
ejpam-2418	248	2	essential	essential	ADJ
ejpam-2418	248	3	test	test	NOUN
ejpam-2418	248	4	lemma	lemma	PROPN
ejpam-2418	248	5	2	2	NUM
ejpam-2418	248	6	)	)	PUNCT
ejpam-2418	248	7	an	an	DET
ejpam-2418	248	8	s	s	NOUN
ejpam-2418	248	9	-	-	PUNCT
ejpam-2418	248	10	act	act	NOUN
ejpam-2418	248	11	b	b	NOUN
ejpam-2418	248	12	is	be	AUX
ejpam-2418	248	13	an	an	DET
ejpam-2418	248	14	essential	essential	ADJ
ejpam-2418	248	15	extension	extension	NOUN
ejpam-2418	248	16	of	of	ADP
ejpam-2418	248	17	a	a	DET
ejpam-2418	248	18	if	if	NOUN
ejpam-2418	248	19	and	and	CCONJ
ejpam-2418	248	20	only	only	ADV
ejpam-2418	248	21	if	if	SCONJ
ejpam-2418	248	22	the	the	DET
ejpam-2418	248	23	following	follow	VERB
ejpam-2418	248	24	hold	hold	NOUN
ejpam-2418	248	25	:	:	PUNCT
ejpam-2418	248	26	(	(	PUNCT
ejpam-2418	248	27	i	i	NOUN
ejpam-2418	248	28	)	)	PUNCT
ejpam-2418	248	29	for	for	ADP
ejpam-2418	248	30	every	every	DET
ejpam-2418	248	31	b	b	PROPN
ejpam-2418	248	32	,	,	PUNCT
ejpam-2418	248	33	b′	b′	NUM
ejpam-2418	248	34	∈	∈	PROPN
ejpam-2418	248	35	b	b	NOUN
ejpam-2418	248	36	,	,	PUNCT
ejpam-2418	248	37	if	if	SCONJ
ejpam-2418	248	38	ρ(b	ρ(b	PROPN
ejpam-2418	248	39	,	,	PUNCT
ejpam-2418	248	40	b′)∩	b′)∩	PROPN
ejpam-2418	248	41	a×	a×	NOUN
ejpam-2418	248	42	a=∆	a=∆	PROPN
ejpam-2418	248	43	,	,	PUNCT
ejpam-2418	248	44	then	then	ADV
ejpam-2418	248	45	λb	λb	ADP
ejpam-2418	248	46	=	=	ADJ
ejpam-2418	248	47	λb′	λb′	NOUN
ejpam-2418	248	48	.	.	PUNCT
ejpam-2418	249	1	(	(	PUNCT
ejpam-2418	249	2	ii	ii	NOUN
ejpam-2418	249	3	)	)	PUNCT
ejpam-2418	249	4	for	for	ADP
ejpam-2418	249	5	every	every	DET
ejpam-2418	249	6	b	b	PROPN
ejpam-2418	249	7	,	,	PUNCT
ejpam-2418	249	8	b′	b′	NUM
ejpam-2418	249	9	∈	∈	PROPN
ejpam-2418	249	10	b	b	NOUN
ejpam-2418	249	11	\	\	PROPN
ejpam-2418	249	12	a	a	PRON
ejpam-2418	249	13	,	,	PUNCT
ejpam-2418	249	14	if	if	SCONJ
ejpam-2418	249	15	λb	λb	ADJ
ejpam-2418	249	16	=	=	PUNCT
ejpam-2418	249	17	λb′	λb′	NOUN
ejpam-2418	249	18	,	,	PUNCT
ejpam-2418	249	19	then	then	ADV
ejpam-2418	249	20	b	b	X
ejpam-2418	249	21	=	=	X
ejpam-2418	249	22	b′.	b′.	PROPN
ejpam-2418	249	23	(	(	PUNCT
ejpam-2418	249	24	iii	iii	NOUN
ejpam-2418	249	25	)	)	PUNCT
ejpam-2418	249	26	c	c	PROPN
ejpam-2418	249	27	p	p	PROPN
ejpam-2418	249	28	b	b	PROPN
ejpam-2418	249	29	(	(	PUNCT
ejpam-2418	249	30	a	a	NOUN
ejpam-2418	249	31	)	)	PUNCT
ejpam-2418	249	32	=	=	NOUN
ejpam-2418	249	33	a.	a.	NOUN
ejpam-2418	249	34	proof	proof	NOUN
ejpam-2418	249	35	.	.	PUNCT
ejpam-2418	250	1	(	(	PUNCT
ejpam-2418	250	2	⇒	⇒	PROPN
ejpam-2418	250	3	)	)	PUNCT
ejpam-2418	250	4	to	to	PART
ejpam-2418	250	5	prove	prove	VERB
ejpam-2418	250	6	(	(	PUNCT
ejpam-2418	250	7	i	i	NOUN
ejpam-2418	250	8	)	)	PUNCT
ejpam-2418	250	9	,	,	PUNCT
ejpam-2418	250	10	let	let	VERB
ejpam-2418	250	11	b	b	NUM
ejpam-2418	250	12	,	,	PUNCT
ejpam-2418	250	13	b′	b′	NUM
ejpam-2418	250	14	∈	∈	PROPN
ejpam-2418	250	15	b	b	PROPN
ejpam-2418	250	16	and	and	CCONJ
ejpam-2418	250	17	ρ(b	ρ(b	PROPN
ejpam-2418	250	18	,	,	PUNCT
ejpam-2418	250	19	b′	b′	NUM
ejpam-2418	250	20	)	)	PUNCT
ejpam-2418	250	21	∩	∩	NOUN
ejpam-2418	250	22	a×	a×	PRON
ejpam-2418	250	23	a=	a=	VERB
ejpam-2418	250	24	∆.	∆.	X
ejpam-2418	250	25	so	so	ADV
ejpam-2418	250	26	for	for	ADP
ejpam-2418	250	27	the	the	DET
ejpam-2418	250	28	canonical	canonical	ADJ
ejpam-2418	250	29	map	map	NOUN
ejpam-2418	250	30	π	π	X
ejpam-2418	250	31	:	:	PUNCT
ejpam-2418	250	32	b→	b→	PROPN
ejpam-2418	250	33	b	b	X
ejpam-2418	250	34	/	/	SYM
ejpam-2418	250	35	ρ(b	ρ(b	NOUN
ejpam-2418	250	36	,	,	PUNCT
ejpam-2418	250	37	b′	b′	NUM
ejpam-2418	250	38	)	)	PUNCT
ejpam-2418	250	39	,	,	PUNCT
ejpam-2418	250	40	π	π	PROPN
ejpam-2418	250	41	|	|	ADV
ejpam-2418	250	42	a	a	PRON
ejpam-2418	250	43	and	and	CCONJ
ejpam-2418	251	1	so	so	ADV
ejpam-2418	251	2	π	π	PROPN
ejpam-2418	251	3	is	be	AUX
ejpam-2418	251	4	a	a	DET
ejpam-2418	251	5	monomorphism	monomorphism	NOUN
ejpam-2418	251	6	.	.	PUNCT
ejpam-2418	252	1	therefore	therefore	ADV
ejpam-2418	252	2	b	b	X
ejpam-2418	252	3	=	=	PUNCT
ejpam-2418	252	4	b′	b′	NUM
ejpam-2418	252	5	and	and	CCONJ
ejpam-2418	252	6	hence	hence	ADV
ejpam-2418	252	7	λb	λb	ADV
ejpam-2418	252	8	=	=	ADJ
ejpam-2418	252	9	λb′	λb′	NOUN
ejpam-2418	252	10	.	.	PUNCT
ejpam-2418	253	1	to	to	PART
ejpam-2418	253	2	prove	prove	VERB
ejpam-2418	253	3	(	(	PUNCT
ejpam-2418	253	4	ii	ii	NOUN
ejpam-2418	253	5	)	)	PUNCT
ejpam-2418	253	6	,	,	PUNCT
ejpam-2418	253	7	let	let	VERB
ejpam-2418	253	8	b	b	NUM
ejpam-2418	253	9	,	,	PUNCT
ejpam-2418	253	10	b′	b′	NUM
ejpam-2418	253	11	∈	∈	PROPN
ejpam-2418	253	12	b	b	NOUN
ejpam-2418	253	13	\	\	PROPN
ejpam-2418	253	14	a	a	PRON
ejpam-2418	253	15	with	with	ADP
ejpam-2418	253	16	λb	λb	NOUN
ejpam-2418	253	17	=	=	PUNCT
ejpam-2418	253	18	λb′	λb′	NOUN
ejpam-2418	253	19	.	.	PUNCT
ejpam-2418	254	1	for	for	ADP
ejpam-2418	254	2	the	the	DET
ejpam-2418	254	3	canonical	canonical	ADJ
ejpam-2418	254	4	map	map	NOUN
ejpam-2418	254	5	π	π	X
ejpam-2418	254	6	:	:	PUNCT
ejpam-2418	254	7	b	b	X
ejpam-2418	254	8	→	→	SYM
ejpam-2418	254	9	b	b	PROPN
ejpam-2418	254	10	/	/	SYM
ejpam-2418	254	11	ρ(b	ρ(b	NOUN
ejpam-2418	254	12	,	,	PUNCT
ejpam-2418	254	13	b′	b′	NUM
ejpam-2418	254	14	)	)	PUNCT
ejpam-2418	254	15	,	,	PUNCT
ejpam-2418	254	16	π	π	PROPN
ejpam-2418	254	17	|	|	ADV
ejpam-2418	254	18	a	a	PRON
ejpam-2418	254	19	is	be	AUX
ejpam-2418	254	20	a	a	DET
ejpam-2418	254	21	monomorphism	monomorphism	NOUN
ejpam-2418	254	22	,	,	PUNCT
ejpam-2418	254	23	indeed	indeed	ADV
ejpam-2418	254	24	,	,	PUNCT
ejpam-2418	254	25	let	let	VERB
ejpam-2418	254	26	aρ(b	aρ(b	NOUN
ejpam-2418	254	27	,	,	PUNCT
ejpam-2418	254	28	b′)a′(a	b′)a′(a	PROPN
ejpam-2418	254	29	,	,	PUNCT
ejpam-2418	254	30	a′	a′	PROPN
ejpam-2418	254	31	∈	∈	PROPN
ejpam-2418	254	32	a	a	PRON
ejpam-2418	254	33	)	)	PUNCT
ejpam-2418	254	34	.	.	PUNCT
ejpam-2418	255	1	so	so	ADV
ejpam-2418	255	2	there	there	PRON
ejpam-2418	255	3	are	be	VERB
ejpam-2418	255	4	p1	p1	NOUN
ejpam-2418	255	5	,	,	PUNCT
ejpam-2418	255	6	p2	p2	NOUN
ejpam-2418	255	7	,	,	PUNCT
ejpam-2418	255	8	.	.	PUNCT
ejpam-2418	255	9	.	.	PUNCT
ejpam-2418	256	1	.	.	PUNCT
ejpam-2418	257	1	,	,	PUNCT
ejpam-2418	257	2	pn	pn	INTJ
ejpam-2418	257	3	,	,	PUNCT
ejpam-2418	257	4	q1,q2	q1,q2	PROPN
ejpam-2418	257	5	,	,	PUNCT
ejpam-2418	257	6	.	.	PUNCT
ejpam-2418	257	7	.	.	PUNCT
ejpam-2418	257	8	.	.	PUNCT
ejpam-2418	258	1	,	,	PUNCT
ejpam-2418	258	2	qn	qn	PROPN
ejpam-2418	258	3	∈	∈	PROPN
ejpam-2418	258	4	{	{	PUNCT
ejpam-2418	258	5	b	b	NOUN
ejpam-2418	258	6	,	,	PUNCT
ejpam-2418	258	7	b′	b′	NUM
ejpam-2418	258	8	}	}	PUNCT
ejpam-2418	258	9	and	and	CCONJ
ejpam-2418	258	10	s1	s1	NOUN
ejpam-2418	258	11	,	,	PUNCT
ejpam-2418	258	12	s2	s2	PROPN
ejpam-2418	258	13	,	,	PUNCT
ejpam-2418	258	14	.	.	PUNCT
ejpam-2418	258	15	.	.	PUNCT
ejpam-2418	258	16	.	.	PUNCT
ejpam-2418	259	1	,	,	PUNCT
ejpam-2418	259	2	sn	sn	PROPN
ejpam-2418	259	3	∈	∈	PROPN
ejpam-2418	259	4	s1	s1	NOUN
ejpam-2418	259	5	such	such	ADJ
ejpam-2418	259	6	that	that	SCONJ
ejpam-2418	259	7	a	a	DET
ejpam-2418	259	8	=	=	NOUN
ejpam-2418	259	9	p1s1,q1s1	p1s1,q1s1	NOUN
ejpam-2418	259	10	=	=	SYM
ejpam-2418	259	11	p2s2	p2s2	NOUN
ejpam-2418	259	12	,	,	PUNCT
ejpam-2418	259	13	.	.	PUNCT
ejpam-2418	259	14	.	.	PUNCT
ejpam-2418	259	15	.	.	PUNCT
ejpam-2418	260	1	,	,	PUNCT
ejpam-2418	260	2	qnsn	qnsn	NOUN
ejpam-2418	260	3	=	=	SYM
ejpam-2418	260	4	a′.	a′.	NOUN
ejpam-2418	260	5	since	since	SCONJ
ejpam-2418	260	6	p1s1	p1s1	ADP
ejpam-2418	260	7	=	=	PUNCT
ejpam-2418	260	8	a	a	PRON
ejpam-2418	260	9	∈	∈	PROPN
ejpam-2418	260	10	a	a	PRON
ejpam-2418	260	11	,	,	PUNCT
ejpam-2418	260	12	s1	s1	PROPN
ejpam-2418	260	13	6=	6=	ADP
ejpam-2418	260	14	1	1	NUM
ejpam-2418	260	15	and	and	CCONJ
ejpam-2418	260	16	hence	hence	ADV
ejpam-2418	260	17	p2s2	p2s2	PROPN
ejpam-2418	260	18	=	=	SYM
ejpam-2418	260	19	q1s1	q1s1	NOUN
ejpam-2418	261	1	=	=	PUNCT
ejpam-2418	261	2	p1s1	p1s1	AUX
ejpam-2418	261	3	=	=	PUNCT
ejpam-2418	261	4	a	a	PRON
ejpam-2418	261	5	which	which	PRON
ejpam-2418	261	6	implies	imply	VERB
ejpam-2418	261	7	s2	s2	PROPN
ejpam-2418	261	8	6=	6=	ADP
ejpam-2418	261	9	1	1	NUM
ejpam-2418	261	10	.	.	PUNCT
ejpam-2418	261	11	by	by	AUX
ejpam-2418	261	12	continue	continue	VERB
ejpam-2418	261	13	to	to	ADP
ejpam-2418	261	14	this	this	DET
ejpam-2418	261	15	process	process	NOUN
ejpam-2418	261	16	,	,	PUNCT
ejpam-2418	261	17	for	for	ADP
ejpam-2418	261	18	each	each	DET
ejpam-2418	261	19	1	1	NUM
ejpam-2418	261	20	≤	≤	NUM
ejpam-2418	261	21	i	i	PRON
ejpam-2418	261	22	≤	≤	PROPN
ejpam-2418	261	23	n	n	CCONJ
ejpam-2418	261	24	,	,	PUNCT
ejpam-2418	261	25	si	si	PROPN
ejpam-2418	261	26	6=	6=	ADP
ejpam-2418	261	27	1	1	NUM
ejpam-2418	261	28	,	,	PUNCT
ejpam-2418	261	29	which	which	PRON
ejpam-2418	261	30	deduced	deduce	VERB
ejpam-2418	261	31	a	a	DET
ejpam-2418	261	32	=	=	NOUN
ejpam-2418	261	33	a′.	a′.	NOUN
ejpam-2418	261	34	by	by	ADP
ejpam-2418	261	35	essentiality	essentiality	NOUN
ejpam-2418	261	36	π	π	PROPN
ejpam-2418	261	37	is	be	AUX
ejpam-2418	261	38	a	a	DET
ejpam-2418	261	39	monomorphism	monomorphism	NOUN
ejpam-2418	261	40	and	and	CCONJ
ejpam-2418	261	41	thus	thus	ADV
ejpam-2418	261	42	ρ(b	ρ(b	ADJ
ejpam-2418	261	43	,	,	PUNCT
ejpam-2418	261	44	b′	b′	NUM
ejpam-2418	261	45	)	)	PUNCT
ejpam-2418	262	1	=	=	SYM
ejpam-2418	263	1	∆	∆	PROPN
ejpam-2418	263	2	and	and	CCONJ
ejpam-2418	263	3	b	b	X
ejpam-2418	263	4	=	=	SYM
ejpam-2418	263	5	b′.	b′.	PROPN
ejpam-2418	263	6	to	to	PART
ejpam-2418	263	7	prove	prove	VERB
ejpam-2418	263	8	(	(	PUNCT
ejpam-2418	263	9	iii	iii	NOUN
ejpam-2418	263	10	)	)	PUNCT
ejpam-2418	263	11	,	,	PUNCT
ejpam-2418	263	12	let	let	VERB
ejpam-2418	263	13	b	b	NOUN
ejpam-2418	263	14	∈	∈	PROPN
ejpam-2418	263	15	c	c	PROPN
ejpam-2418	263	16	p	p	PROPN
ejpam-2418	263	17	b	b	PROPN
ejpam-2418	263	18	(	(	PUNCT
ejpam-2418	263	19	a	a	NOUN
ejpam-2418	263	20	)	)	PUNCT
ejpam-2418	263	21	.	.	PUNCT
ejpam-2418	264	1	so	so	ADV
ejpam-2418	264	2	there	there	PRON
ejpam-2418	264	3	exists	exist	VERB
ejpam-2418	264	4	a	a	DET
ejpam-2418	264	5	∈	∈	NOUN
ejpam-2418	264	6	a	a	DET
ejpam-2418	264	7	such	such	ADJ
ejpam-2418	264	8	that	that	PRON
ejpam-2418	264	9	for	for	ADP
ejpam-2418	264	10	each	each	DET
ejpam-2418	264	11	s	s	X
ejpam-2418	264	12	∈	∈	PROPN
ejpam-2418	264	13	s	s	NOUN
ejpam-2418	264	14	,	,	PUNCT
ejpam-2418	264	15	as	as	SCONJ
ejpam-2418	264	16	=	=	NOUN
ejpam-2418	264	17	bs	b	NOUN
ejpam-2418	264	18	.	.	PUNCT
ejpam-2418	264	19	similarly	similarly	ADV
ejpam-2418	264	20	,	,	PUNCT
ejpam-2418	264	21	to	to	PART
ejpam-2418	264	22	prove	prove	VERB
ejpam-2418	264	23	(	(	PUNCT
ejpam-2418	264	24	ii	ii	NOUN
ejpam-2418	264	25	)	)	PUNCT
ejpam-2418	264	26	,	,	PUNCT
ejpam-2418	264	27	for	for	ADP
ejpam-2418	264	28	the	the	DET
ejpam-2418	264	29	canonical	canonical	ADJ
ejpam-2418	264	30	map	map	NOUN
ejpam-2418	264	31	π	π	X
ejpam-2418	264	32	:	:	PUNCT
ejpam-2418	264	33	b	b	X
ejpam-2418	264	34	→	→	SYM
ejpam-2418	264	35	b	b	X
ejpam-2418	264	36	/	/	SYM
ejpam-2418	264	37	ρ(a	ρ(a	PROPN
ejpam-2418	264	38	,	,	PUNCT
ejpam-2418	264	39	b	b	NOUN
ejpam-2418	264	40	)	)	PUNCT
ejpam-2418	264	41	,	,	PUNCT
ejpam-2418	264	42	π	π	PROPN
ejpam-2418	264	43	|	|	ADV
ejpam-2418	264	44	a	a	PRON
ejpam-2418	264	45	is	be	AUX
ejpam-2418	264	46	a	a	DET
ejpam-2418	264	47	monomorphism	monomorphism	NOUN
ejpam-2418	264	48	.	.	PUNCT
ejpam-2418	265	1	thus	thus	ADV
ejpam-2418	265	2	by	by	ADP
ejpam-2418	265	3	essentiality	essentiality	NOUN
ejpam-2418	265	4	,	,	PUNCT
ejpam-2418	265	5	π	π	PROPN
ejpam-2418	265	6	is	be	AUX
ejpam-2418	265	7	a	a	DET
ejpam-2418	265	8	monomorphism	monomorphism	NOUN
ejpam-2418	265	9	and	and	CCONJ
ejpam-2418	265	10	hence	hence	ADV
ejpam-2418	265	11	a	a	DET
ejpam-2418	265	12	=	=	X
ejpam-2418	265	13	b.	b.	PROPN
ejpam-2418	265	14	(	(	PUNCT
ejpam-2418	265	15	⇐	⇐	PROPN
ejpam-2418	265	16	)	)	PUNCT
ejpam-2418	265	17	by	by	ADP
ejpam-2418	265	18	lemma	lemma	PROPN
ejpam-2418	265	19	1	1	NUM
ejpam-2418	265	20	,	,	PUNCT
ejpam-2418	265	21	it	it	PRON
ejpam-2418	265	22	is	be	AUX
ejpam-2418	265	23	enough	enough	ADJ
ejpam-2418	265	24	to	to	PART
ejpam-2418	265	25	show	show	VERB
ejpam-2418	265	26	that	that	SCONJ
ejpam-2418	265	27	for	for	ADP
ejpam-2418	265	28	every	every	DET
ejpam-2418	265	29	monogenic	monogenic	ADJ
ejpam-2418	265	30	congruence	congruence	NOUN
ejpam-2418	265	31	ρ	ρ	PROPN
ejpam-2418	265	32	=	=	SYM
ejpam-2418	265	33	ρ(b	ρ(b	PROPN
ejpam-2418	265	34	,	,	PUNCT
ejpam-2418	265	35	b′	b′	NUM
ejpam-2418	265	36	)	)	PUNCT
ejpam-2418	265	37	on	on	ADP
ejpam-2418	265	38	b	b	X
ejpam-2418	265	39	such	such	ADJ
ejpam-2418	265	40	that	that	PRON
ejpam-2418	265	41	for	for	ADP
ejpam-2418	265	42	the	the	DET
ejpam-2418	265	43	canonical	canonical	ADJ
ejpam-2418	265	44	epimorphism	epimorphism	NOUN
ejpam-2418	265	45	π	π	NOUN
ejpam-2418	265	46	:	:	PUNCT
ejpam-2418	265	47	b→	b→	PROPN
ejpam-2418	265	48	b	b	X
ejpam-2418	265	49	/	/	SYM
ejpam-2418	265	50	ρ	ρ	PROPN
ejpam-2418	265	51	,	,	PUNCT
ejpam-2418	265	52	π	π	PROPN
ejpam-2418	265	53	|	|	ADV
ejpam-2418	265	54	a	a	PRON
ejpam-2418	265	55	is	be	AUX
ejpam-2418	265	56	a	a	DET
ejpam-2418	265	57	monomorphism	monomorphism	NOUN
ejpam-2418	265	58	,	,	PUNCT
ejpam-2418	265	59	we	we	PRON
ejpam-2418	265	60	get	get	VERB
ejpam-2418	265	61	b	b	NOUN
ejpam-2418	265	62	=	=	SYM
ejpam-2418	265	63	b′.	b′.	PROPN
ejpam-2418	265	64	since	since	SCONJ
ejpam-2418	265	65	π	π	PROPN
ejpam-2418	265	66	|	|	ADV
ejpam-2418	265	67	a	a	PRON
ejpam-2418	265	68	is	be	AUX
ejpam-2418	265	69	a	a	DET
ejpam-2418	265	70	monomorphism	monomorphism	NOUN
ejpam-2418	265	71	,	,	PUNCT
ejpam-2418	265	72	by	by	ADP
ejpam-2418	265	73	(	(	PUNCT
ejpam-2418	265	74	i	i	NOUN
ejpam-2418	265	75	)	)	PUNCT
ejpam-2418	265	76	,	,	PUNCT
ejpam-2418	265	77	λb	λb	ADP
ejpam-2418	265	78	=	=	PUNCT
ejpam-2418	265	79	λb′	λb′	NOUN
ejpam-2418	265	80	and	and	CCONJ
ejpam-2418	266	1	if	if	SCONJ
ejpam-2418	266	2	{	{	PUNCT
ejpam-2418	266	3	b	b	NOUN
ejpam-2418	266	4	,	,	PUNCT
ejpam-2418	266	5	b′	b′	NUM
ejpam-2418	266	6	}	}	PUNCT
ejpam-2418	266	7	⊆	⊆	NUM
ejpam-2418	266	8	a	a	PRON
ejpam-2418	266	9	,	,	PUNCT
ejpam-2418	266	10	then	then	ADV
ejpam-2418	266	11	b	b	X
ejpam-2418	266	12	=	=	SYM
ejpam-2418	266	13	b′.	b′.	PROPN
ejpam-2418	266	14	in	in	ADP
ejpam-2418	266	15	the	the	DET
ejpam-2418	266	16	case	case	NOUN
ejpam-2418	266	17	where	where	SCONJ
ejpam-2418	266	18	b	b	NOUN
ejpam-2418	266	19	,	,	PUNCT
ejpam-2418	266	20	b′	b′	NUM
ejpam-2418	266	21	∈	∈	PROPN
ejpam-2418	266	22	b	b	NOUN
ejpam-2418	266	23	\	\	PROPN
ejpam-2418	266	24	a	a	PRON
ejpam-2418	266	25	,	,	PUNCT
ejpam-2418	266	26	by	by	ADP
ejpam-2418	266	27	(	(	PUNCT
ejpam-2418	266	28	ii	ii	NOUN
ejpam-2418	266	29	)	)	PUNCT
ejpam-2418	266	30	,	,	PUNCT
ejpam-2418	266	31	b	b	X
ejpam-2418	266	32	=	=	X
ejpam-2418	266	33	b′.	b′.	PROPN
ejpam-2418	266	34	at	at	ADP
ejpam-2418	266	35	last	last	ADJ
ejpam-2418	266	36	condition	condition	NOUN
ejpam-2418	266	37	(	(	PUNCT
ejpam-2418	266	38	iii	iii	NOUN
ejpam-2418	266	39	)	)	PUNCT
ejpam-2418	266	40	shows	show	VERB
ejpam-2418	266	41	that	that	SCONJ
ejpam-2418	266	42	the	the	DET
ejpam-2418	266	43	case	case	NOUN
ejpam-2418	266	44	where	where	SCONJ
ejpam-2418	266	45	b	b	X
ejpam-2418	266	46	∈	∈	PROPN
ejpam-2418	266	47	a	a	DET
ejpam-2418	266	48	,	,	PUNCT
ejpam-2418	266	49	b′	b′	NUM
ejpam-2418	266	50	/∈	/∈	PUNCT
ejpam-2418	267	1	a	a	PRON
ejpam-2418	267	2	may	may	AUX
ejpam-2418	267	3	not	not	PART
ejpam-2418	267	4	occur	occur	VERB
ejpam-2418	267	5	.	.	PUNCT
ejpam-2418	268	1	acknowledgements	acknowledgement	VERB
ejpam-2418	268	2	the	the	DET
ejpam-2418	268	3	author	author	NOUN
ejpam-2418	268	4	gratefully	gratefully	ADV
ejpam-2418	268	5	acknowledges	acknowledge	VERB
ejpam-2418	268	6	to	to	ADP
ejpam-2418	268	7	the	the	DET
ejpam-2418	268	8	referee	referee	NOUN
ejpam-2418	268	9	for	for	ADP
ejpam-2418	268	10	carefully	carefully	ADV
ejpam-2418	268	11	reading	read	VERB
ejpam-2418	268	12	the	the	DET
ejpam-2418	268	13	paper	paper	NOUN
ejpam-2418	268	14	.	.	PUNCT
ejpam-2418	269	1	references	reference	NOUN
ejpam-2418	269	2	[	[	X
ejpam-2418	269	3	1	1	NUM
ejpam-2418	269	4	]	]	PUNCT
ejpam-2418	269	5	b.	b.	PROPN
ejpam-2418	269	6	banaschewski	banaschewski	PROPN
ejpam-2418	269	7	.	.	PUNCT
ejpam-2418	270	1	injectivity	injectivity	PROPN
ejpam-2418	270	2	and	and	CCONJ
ejpam-2418	270	3	essential	essential	ADJ
ejpam-2418	270	4	extensions	extension	NOUN
ejpam-2418	270	5	in	in	ADP
ejpam-2418	270	6	equational	equational	ADJ
ejpam-2418	270	7	classes	class	NOUN
ejpam-2418	270	8	of	of	ADP
ejpam-2418	270	9	algebras	algebras	PROPN
ejpam-2418	270	10	.	.	PUNCT
ejpam-2418	271	1	queen	queen	PROPN
ejpam-2418	271	2	’s	’s	PART
ejpam-2418	271	3	papers	paper	NOUN
ejpam-2418	271	4	in	in	ADP
ejpam-2418	271	5	pure	pure	ADJ
ejpam-2418	271	6	and	and	CCONJ
ejpam-2418	271	7	applied	applied	ADJ
ejpam-2418	271	8	mathematics	mathematic	NOUN
ejpam-2418	271	9	,	,	PUNCT
ejpam-2418	271	10	25:131–147	25:131–147	PROPN
ejpam-2418	271	11	,	,	PUNCT
ejpam-2418	271	12	1970	1970	NUM
ejpam-2418	271	13	.	.	PUNCT
ejpam-2418	272	1	references	reference	NOUN
ejpam-2418	272	2	26	26	NUM
ejpam-2418	272	3	[	[	X
ejpam-2418	272	4	2	2	NUM
ejpam-2418	272	5	]	]	X
ejpam-2418	272	6	h.	h.	NOUN
ejpam-2418	272	7	barzegar	barzegar	PROPN
ejpam-2418	272	8	and	and	CCONJ
ejpam-2418	272	9	m.m	m.m	PROPN
ejpam-2418	272	10	.	.	PROPN
ejpam-2418	272	11	ebrahimi	ebrahimi	PROPN
ejpam-2418	272	12	.	.	PUNCT
ejpam-2418	273	1	sequential	sequential	ADJ
ejpam-2418	273	2	pure	pure	ADJ
ejpam-2418	273	3	monomorphism	monomorphism	NOUN
ejpam-2418	273	4	of	of	ADP
ejpam-2418	273	5	acts	act	NOUN
ejpam-2418	273	6	over	over	ADP
ejpam-2418	273	7	semigroups	semigroup	NOUN
ejpam-2418	273	8	.	.	PUNCT
ejpam-2418	274	1	european	european	ADJ
ejpam-2418	274	2	journal	journal	PROPN
ejpam-2418	274	3	of	of	ADP
ejpam-2418	274	4	pure	pure	ADJ
ejpam-2418	274	5	and	and	CCONJ
ejpam-2418	274	6	applied	applied	ADJ
ejpam-2418	274	7	mathematics	mathematic	NOUN
ejpam-2418	274	8	,	,	PUNCT
ejpam-2418	274	9	1(4):91–99	1(4):91–99	NUM
ejpam-2418	274	10	,	,	PUNCT
ejpam-2418	274	11	2009	2009	NUM
ejpam-2418	274	12	.	.	PUNCT
ejpam-2418	275	1	[	[	X
ejpam-2418	275	2	3	3	X
ejpam-2418	275	3	]	]	X
ejpam-2418	275	4	h.	h.	NOUN
ejpam-2418	275	5	barzegar	barzegar	PROPN
ejpam-2418	275	6	,	,	PUNCT
ejpam-2418	275	7	m.m	m.m	PROPN
ejpam-2418	275	8	.	.	PROPN
ejpam-2418	275	9	ebrahimi	ebrahimi	PROPN
ejpam-2418	275	10	,	,	PUNCT
ejpam-2418	275	11	and	and	CCONJ
ejpam-2418	275	12	m.	m.	NOUN
ejpam-2418	275	13	mahmoudi	mahmoudi	NOUN
ejpam-2418	275	14	.	.	PUNCT
ejpam-2418	276	1	essentiality	essentiality	NOUN
ejpam-2418	276	2	and	and	CCONJ
ejpam-2418	276	3	injectivity	injectivity	NOUN
ejpam-2418	276	4	relative	relative	ADJ
ejpam-2418	276	5	to	to	ADP
ejpam-2418	276	6	sequential	sequential	ADJ
ejpam-2418	276	7	purity	purity	NOUN
ejpam-2418	276	8	of	of	ADP
ejpam-2418	276	9	acts	act	NOUN
ejpam-2418	276	10	.	.	PUNCT
ejpam-2418	277	1	semigroup	semigroup	PROPN
ejpam-2418	277	2	forum	forum	PROPN
ejpam-2418	277	3	,	,	PUNCT
ejpam-2418	277	4	79:128–144	79:128–144	PROPN
ejpam-2418	277	5	,	,	PUNCT
ejpam-2418	277	6	2009	2009	NUM
ejpam-2418	277	7	.	.	PUNCT
ejpam-2418	278	1	[	[	X
ejpam-2418	278	2	4	4	X
ejpam-2418	278	3	]	]	PUNCT
ejpam-2418	278	4	p.	p.	NOUN
ejpam-2418	278	5	berthiaume	berthiaume	PROPN
ejpam-2418	278	6	.	.	PUNCT
ejpam-2418	279	1	the	the	DET
ejpam-2418	279	2	injective	injective	ADJ
ejpam-2418	279	3	envelope	envelope	NOUN
ejpam-2418	279	4	of	of	ADP
ejpam-2418	279	5	s	s	NOUN
ejpam-2418	279	6	-	-	PUNCT
ejpam-2418	279	7	sets	set	NOUN
ejpam-2418	279	8	.	.	PUNCT
ejpam-2418	280	1	canadian	canadian	ADJ
ejpam-2418	280	2	mathematical	mathematical	ADJ
ejpam-2418	280	3	bulletin	bulletin	NOUN
ejpam-2418	280	4	,	,	PUNCT
ejpam-2418	280	5	10(2):261–273	10(2):261–273	NUM
ejpam-2418	280	6	,	,	PUNCT
ejpam-2418	280	7	1967	1967	NUM
ejpam-2418	280	8	.	.	PUNCT
ejpam-2418	281	1	[	[	X
ejpam-2418	281	2	5	5	NUM
ejpam-2418	281	3	]	]	X
ejpam-2418	281	4	m.m	m.m	PROPN
ejpam-2418	281	5	.	.	PROPN
ejpam-2418	281	6	ebrahimi	ebrahimi	PROPN
ejpam-2418	281	7	.	.	PUNCT
ejpam-2418	282	1	algebra	algebra	NOUN
ejpam-2418	282	2	in	in	ADP
ejpam-2418	282	3	a	a	DET
ejpam-2418	282	4	grothendieck	grothendieck	NOUN
ejpam-2418	282	5	topos	topos	NOUN
ejpam-2418	282	6	:	:	PUNCT
ejpam-2418	282	7	injectivity	injectivity	NOUN
ejpam-2418	282	8	in	in	ADP
ejpam-2418	282	9	quasi	quasi	ADJ
ejpam-2418	282	10	-	-	ADJ
ejpam-2418	282	11	equational	equational	ADJ
ejpam-2418	282	12	classes	class	NOUN
ejpam-2418	282	13	.	.	PUNCT
ejpam-2418	283	1	jounal	jounal	NOUN
ejpam-2418	283	2	of	of	ADP
ejpam-2418	283	3	pure	pure	ADJ
ejpam-2418	283	4	and	and	CCONJ
ejpam-2418	283	5	applied	applied	ADJ
ejpam-2418	283	6	algebra	algebra	NOUN
ejpam-2418	283	7	,	,	PUNCT
ejpam-2418	283	8	26(3):269–280	26(3):269–280	PROPN
ejpam-2418	283	9	,	,	PUNCT
ejpam-2418	283	10	1982	1982	NUM
ejpam-2418	283	11	.	.	PUNCT
ejpam-2418	284	1	[	[	X
ejpam-2418	284	2	6	6	NUM
ejpam-2418	284	3	]	]	X
ejpam-2418	284	4	m.m	m.m	PROPN
ejpam-2418	284	5	.	.	PROPN
ejpam-2418	284	6	ebrahimi	ebrahimi	PROPN
ejpam-2418	284	7	and	and	CCONJ
ejpam-2418	284	8	m.	m.	NOUN
ejpam-2418	284	9	mahmoudi	mahmoudi	NOUN
ejpam-2418	284	10	.	.	PUNCT
ejpam-2418	285	1	the	the	DET
ejpam-2418	285	2	category	category	NOUN
ejpam-2418	285	3	of	of	ADP
ejpam-2418	285	4	m	m	NOUN
ejpam-2418	285	5	-	-	PUNCT
ejpam-2418	285	6	sets	set	NOUN
ejpam-2418	285	7	.	.	PUNCT
ejpam-2418	286	1	itallian	itallian	ADJ
ejpam-2418	286	2	journal	journal	PROPN
ejpam-2418	286	3	of	of	ADP
ejpam-2418	286	4	pure	pure	ADJ
ejpam-2418	286	5	and	and	CCONJ
ejpam-2418	286	6	applied	applied	ADJ
ejpam-2418	286	7	mathematics	mathematic	NOUN
ejpam-2418	286	8	,	,	PUNCT
ejpam-2418	286	9	9:123–132	9:123–132	NUM
ejpam-2418	286	10	,	,	PUNCT
ejpam-2418	286	11	2001	2001	NUM
ejpam-2418	286	12	.	.	PUNCT
ejpam-2418	287	1	[	[	X
ejpam-2418	287	2	7	7	NUM
ejpam-2418	287	3	]	]	X
ejpam-2418	287	4	m.m	m.m	PROPN
ejpam-2418	287	5	.	.	PROPN
ejpam-2418	287	6	ebrahimi	ebrahimi	PROPN
ejpam-2418	287	7	and	and	CCONJ
ejpam-2418	287	8	m.	m.	NOUN
ejpam-2418	287	9	mahmoudi	mahmoudi	PROPN
ejpam-2418	287	10	.	.	PUNCT
ejpam-2418	288	1	purity	purity	NOUN
ejpam-2418	288	2	and	and	CCONJ
ejpam-2418	288	3	equational	equational	ADJ
ejpam-2418	288	4	compactness	compactness	NOUN
ejpam-2418	288	5	of	of	ADP
ejpam-2418	288	6	projection	projection	NOUN
ejpam-2418	288	7	algebras	algebra	NOUN
ejpam-2418	288	8	.	.	PUNCT
ejpam-2418	289	1	applied	apply	VERB
ejpam-2418	289	2	categorical	categorical	ADJ
ejpam-2418	289	3	structure	structure	NOUN
ejpam-2418	289	4	,	,	PUNCT
ejpam-2418	289	5	9:381–394	9:381–394	NOUN
ejpam-2418	289	6	,	,	PUNCT
ejpam-2418	289	7	2001	2001	NUM
ejpam-2418	289	8	.	.	PUNCT
ejpam-2418	290	1	[	[	X
ejpam-2418	290	2	8	8	NUM
ejpam-2418	290	3	]	]	PUNCT
ejpam-2418	290	4	m.	m.	NOUN
ejpam-2418	290	5	kilp	kilp	PROPN
ejpam-2418	290	6	,	,	PUNCT
ejpam-2418	290	7	u.	u.	PROPN
ejpam-2418	290	8	knauer	knauer	PROPN
ejpam-2418	290	9	,	,	PUNCT
ejpam-2418	290	10	and	and	CCONJ
ejpam-2418	290	11	a.	a.	NOUN
ejpam-2418	290	12	mikhalev	mikhalev	PROPN
ejpam-2418	290	13	.	.	PUNCT
ejpam-2418	291	1	monoids	monoids	PROPN
ejpam-2418	291	2	,	,	PUNCT
ejpam-2418	291	3	acts	act	NOUN
ejpam-2418	291	4	and	and	CCONJ
ejpam-2418	291	5	categories	category	NOUN
ejpam-2418	291	6	.	.	PUNCT
ejpam-2418	292	1	walter	walter	PROPN
ejpam-2418	292	2	de	de	PROPN
ejpam-2418	292	3	gruyter	gruyter	PROPN
ejpam-2418	292	4	,	,	PUNCT
ejpam-2418	292	5	berlin	berlin	PROPN
ejpam-2418	292	6	,	,	PUNCT
ejpam-2418	292	7	new	new	PROPN
ejpam-2418	292	8	york	york	PROPN
ejpam-2418	292	9	,	,	PUNCT
ejpam-2418	292	10	2000	2000	NUM
ejpam-2418	292	11	.	.	PUNCT
ejpam-2418	293	1	[	[	X
ejpam-2418	293	2	9	9	NUM
ejpam-2418	293	3	]	]	PUNCT
ejpam-2418	293	4	m.	m.	NOUN
ejpam-2418	293	5	mahmoudi	mahmoudi	NOUN
ejpam-2418	293	6	and	and	CCONJ
ejpam-2418	293	7	l.	l.	PROPN
ejpam-2418	293	8	shahbaz	shahbaz	PROPN
ejpam-2418	293	9	.	.	PUNCT
ejpam-2418	294	1	sequential	sequential	ADJ
ejpam-2418	294	2	dense	dense	ADJ
ejpam-2418	294	3	essential	essential	ADJ
ejpam-2418	294	4	monomorphisms	monomorphism	NOUN
ejpam-2418	294	5	of	of	ADP
ejpam-2418	294	6	acts	act	NOUN
ejpam-2418	294	7	over	over	ADP
ejpam-2418	294	8	semigroups	semigroup	NOUN
ejpam-2418	294	9	.	.	PUNCT
ejpam-2418	295	1	applied	apply	VERB
ejpam-2418	295	2	categorical	categorical	ADJ
ejpam-2418	295	3	structure	structure	NOUN
ejpam-2418	295	4	,	,	PUNCT
ejpam-2418	295	5	18(5):461–471	18(5):461–471	PROPN
ejpam-2418	295	6	,	,	PUNCT
ejpam-2418	295	7	2010	2010	NUM
ejpam-2418	295	8	.	.	PUNCT
ejpam-2418	296	1	[	[	X
ejpam-2418	296	2	10	10	NUM
ejpam-2418	296	3	]	]	X
ejpam-2418	296	4	w.	w.	PROPN
ejpam-2418	296	5	tholen	tholen	PROPN
ejpam-2418	296	6	.	.	PUNCT
ejpam-2418	297	1	injective	injective	ADJ
ejpam-2418	297	2	objects	object	NOUN
ejpam-2418	297	3	and	and	CCONJ
ejpam-2418	297	4	cogenerating	cogenerating	NOUN
ejpam-2418	297	5	sets	set	NOUN
ejpam-2418	297	6	.	.	PUNCT
ejpam-2418	298	1	journal	journal	NOUN
ejpam-2418	298	2	of	of	ADP
ejpam-2418	298	3	algebra	algebra	PROPN
ejpam-2418	298	4	,	,	PUNCT
ejpam-2418	298	5	73(1):139–155	73(1):139–155	PROPN
ejpam-2418	298	6	,	,	PUNCT
ejpam-2418	298	7	1981	1981	NUM
ejpam-2418	298	8	.	.	PUNCT