id	sid	tid	token	lemma	pos
ejpam-3229	1	1	european	european	PROPN
ejpam-3229	1	2	journal	journal	PROPN
ejpam-3229	1	3	of	of	ADP
ejpam-3229	1	4	pure	pure	ADJ
ejpam-3229	1	5	and	and	CCONJ
ejpam-3229	1	6	applied	apply	VERB
ejpam-3229	1	7	mathematics	mathematic	NOUN
ejpam-3229	1	8	vol	vol	NOUN
ejpam-3229	1	9	.	.	PUNCT
ejpam-3229	2	1	11	11	NUM
ejpam-3229	2	2	,	,	PUNCT
ejpam-3229	2	3	no	no	INTJ
ejpam-3229	2	4	.	.	NOUN
ejpam-3229	2	5	2	2	NUM
ejpam-3229	2	6	,	,	PUNCT
ejpam-3229	2	7	2018	2018	NUM
ejpam-3229	2	8	,	,	PUNCT
ejpam-3229	2	9	431	431	NUM
ejpam-3229	2	10	-	-	SYM
ejpam-3229	2	11	443	443	NUM
ejpam-3229	2	12	issn	issn	PROPN
ejpam-3229	2	13	1307	1307	NUM
ejpam-3229	2	14	-	-	SYM
ejpam-3229	2	15	5543	5543	NUM
ejpam-3229	2	16	–	–	PUNCT
ejpam-3229	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3229	2	18	published	publish	VERB
ejpam-3229	2	19	by	by	ADP
ejpam-3229	2	20	new	new	PROPN
ejpam-3229	2	21	york	york	PROPN
ejpam-3229	2	22	business	business	PROPN
ejpam-3229	2	23	global	global	PROPN
ejpam-3229	2	24	on	on	ADP
ejpam-3229	2	25	m	m	NOUN
ejpam-3229	2	26	-	-	ADJ
ejpam-3229	2	27	principally	principally	ADV
ejpam-3229	2	28	injective	injective	ADJ
ejpam-3229	2	29	and	and	CCONJ
ejpam-3229	2	30	projective	projective	ADJ
ejpam-3229	2	31	s	s	NOUN
ejpam-3229	2	32	-	-	PUNCT
ejpam-3229	2	33	acts	act	VERB
ejpam-3229	2	34	javed	javed	ADJ
ejpam-3229	2	35	hussain1,∗	hussain1,∗	PROPN
ejpam-3229	2	36	,	,	PUNCT
ejpam-3229	2	37	muhammad	muhammad	PROPN
ejpam-3229	2	38	shabir2	shabir2	PROPN
ejpam-3229	2	39	1	1	NUM
ejpam-3229	2	40	department	department	NOUN
ejpam-3229	2	41	of	of	ADP
ejpam-3229	2	42	mathematics	mathematic	NOUN
ejpam-3229	2	43	,	,	PUNCT
ejpam-3229	2	44	sukkur	sukkur	PROPN
ejpam-3229	2	45	iba	iba	PROPN
ejpam-3229	2	46	university	university	PROPN
ejpam-3229	2	47	,	,	PUNCT
ejpam-3229	2	48	sukkur	sukkur	PROPN
ejpam-3229	2	49	,	,	PUNCT
ejpam-3229	2	50	pakistan	pakistan	PROPN
ejpam-3229	2	51	2	2	NUM
ejpam-3229	2	52	department	department	NOUN
ejpam-3229	2	53	of	of	ADP
ejpam-3229	2	54	mathematics	mathematic	NOUN
ejpam-3229	2	55	,	,	PUNCT
ejpam-3229	2	56	quaid	quaid	PROPN
ejpam-3229	2	57	-	-	PUNCT
ejpam-3229	2	58	i	i	PROPN
ejpam-3229	2	59	-	-	PUNCT
ejpam-3229	2	60	azam	azam	PROPN
ejpam-3229	2	61	university	university	PROPN
ejpam-3229	2	62	,	,	PUNCT
ejpam-3229	2	63	islamabad	islamabad	PROPN
ejpam-3229	2	64	,	,	PUNCT
ejpam-3229	2	65	pakistan	pakistan	PROPN
ejpam-3229	2	66	abstract	abstract	NOUN
ejpam-3229	2	67	.	.	PUNCT
ejpam-3229	3	1	in	in	ADP
ejpam-3229	3	2	this	this	DET
ejpam-3229	3	3	paper	paper	NOUN
ejpam-3229	3	4	,	,	PUNCT
ejpam-3229	3	5	we	we	PRON
ejpam-3229	3	6	have	have	AUX
ejpam-3229	3	7	introduced	introduce	VERB
ejpam-3229	3	8	the	the	DET
ejpam-3229	3	9	notions	notion	NOUN
ejpam-3229	3	10	of	of	ADP
ejpam-3229	3	11	m	m	NOUN
ejpam-3229	3	12	-	-	ADJ
ejpam-3229	3	13	cyclic	cyclic	ADJ
ejpam-3229	3	14	s	s	NOUN
ejpam-3229	3	15	-	-	PUNCT
ejpam-3229	3	16	acts	act	NOUN
ejpam-3229	3	17	,	,	PUNCT
ejpam-3229	3	18	m	m	NOUN
ejpam-3229	3	19	-	-	ADJ
ejpam-3229	3	20	principally	principally	ADV
ejpam-3229	3	21	projective	projective	ADJ
ejpam-3229	3	22	and	and	CCONJ
ejpam-3229	3	23	injective	injective	ADJ
ejpam-3229	3	24	s	s	NOUN
ejpam-3229	3	25	-	-	PUNCT
ejpam-3229	3	26	acts	act	NOUN
ejpam-3229	3	27	,	,	PUNCT
ejpam-3229	3	28	semi	semi	ADJ
ejpam-3229	3	29	-	-	ADJ
ejpam-3229	3	30	projective	projective	ADJ
ejpam-3229	3	31	s	s	NOUN
ejpam-3229	3	32	-	-	PUNCT
ejpam-3229	3	33	acts	act	NOUN
ejpam-3229	3	34	and	and	CCONJ
ejpam-3229	3	35	co	co	NOUN
ejpam-3229	3	36	-	-	NOUN
ejpam-3229	3	37	cyclic	cyclic	ADJ
ejpam-3229	3	38	s	s	NOUN
ejpam-3229	3	39	-	-	PUNCT
ejpam-3229	3	40	acts	act	NOUN
ejpam-3229	3	41	,	,	PUNCT
ejpam-3229	3	42	wherem	wherem	PROPN
ejpam-3229	3	43	is	be	AUX
ejpam-3229	3	44	a	a	DET
ejpam-3229	3	45	right	right	ADJ
ejpam-3229	3	46	s	s	NOUN
ejpam-3229	3	47	-	-	NOUN
ejpam-3229	3	48	act	act	NOUN
ejpam-3229	3	49	.	.	PUNCT
ejpam-3229	4	1	several	several	ADJ
ejpam-3229	4	2	interesting	interesting	ADJ
ejpam-3229	4	3	properties	property	NOUN
ejpam-3229	4	4	,	,	PUNCT
ejpam-3229	4	5	characterizations	characterization	VERB
ejpam-3229	4	6	relations	relation	NOUN
ejpam-3229	4	7	between	between	ADP
ejpam-3229	4	8	newly	newly	ADV
ejpam-3229	4	9	defined	define	VERB
ejpam-3229	4	10	structures	structure	NOUN
ejpam-3229	4	11	have	have	AUX
ejpam-3229	4	12	been	be	AUX
ejpam-3229	4	13	investigated	investigate	VERB
ejpam-3229	4	14	.	.	PUNCT
ejpam-3229	5	1	2010	2010	NUM
ejpam-3229	5	2	mathematics	mathematic	NOUN
ejpam-3229	5	3	subject	subject	NOUN
ejpam-3229	5	4	classifications	classification	NOUN
ejpam-3229	5	5	:	:	PUNCT
ejpam-3229	5	6	20m30	20m30	NUM
ejpam-3229	5	7	,	,	PUNCT
ejpam-3229	5	8	08a60	08a60	NUM
ejpam-3229	5	9	,	,	PUNCT
ejpam-3229	5	10	08b30	08b30	DET
ejpam-3229	5	11	key	key	ADJ
ejpam-3229	5	12	words	word	NOUN
ejpam-3229	5	13	and	and	CCONJ
ejpam-3229	5	14	phrases	phrase	NOUN
ejpam-3229	5	15	:	:	PUNCT
ejpam-3229	5	16	semigroups	semigroup	NOUN
ejpam-3229	5	17	,	,	PUNCT
ejpam-3229	5	18	s	s	NOUN
ejpam-3229	5	19	-	-	PUNCT
ejpam-3229	5	20	acts	act	NOUN
ejpam-3229	5	21	,	,	PUNCT
ejpam-3229	5	22	endomorphism	endomorphism	PROPN
ejpam-3229	5	23	monoids	monoids	PROPN
ejpam-3229	5	24	.	.	PUNCT
ejpam-3229	6	1	1	1	X
ejpam-3229	6	2	.	.	X
ejpam-3229	6	3	introduction	introduction	NOUN
ejpam-3229	6	4	group	group	NOUN
ejpam-3229	6	5	action	action	NOUN
ejpam-3229	6	6	has	have	AUX
ejpam-3229	6	7	played	play	VERB
ejpam-3229	6	8	a	a	DET
ejpam-3229	6	9	very	very	ADV
ejpam-3229	6	10	significant	significant	ADJ
ejpam-3229	6	11	role	role	NOUN
ejpam-3229	6	12	in	in	ADP
ejpam-3229	6	13	the	the	DET
ejpam-3229	6	14	development	development	NOUN
ejpam-3229	6	15	of	of	ADP
ejpam-3229	6	16	the	the	DET
ejpam-3229	6	17	theory	theory	NOUN
ejpam-3229	6	18	of	of	ADP
ejpam-3229	6	19	groups	group	NOUN
ejpam-3229	6	20	.	.	PUNCT
ejpam-3229	7	1	similarly	similarly	ADV
ejpam-3229	7	2	representation	representation	NOUN
ejpam-3229	7	3	of	of	ADP
ejpam-3229	7	4	the	the	DET
ejpam-3229	7	5	semi	semi	ADJ
ejpam-3229	7	6	group	group	NOUN
ejpam-3229	7	7	s	s	VERB
ejpam-3229	7	8	by	by	ADP
ejpam-3229	7	9	transformation	transformation	NOUN
ejpam-3229	7	10	of	of	ADP
ejpam-3229	7	11	a	a	DET
ejpam-3229	7	12	set	set	NOUN
ejpam-3229	7	13	,	,	PUNCT
ejpam-3229	7	14	i.e.	i.e.	X
ejpam-3229	7	15	acts	act	NOUN
ejpam-3229	7	16	plays	play	VERB
ejpam-3229	7	17	an	an	DET
ejpam-3229	7	18	essential	essential	ADJ
ejpam-3229	7	19	role	role	NOUN
ejpam-3229	7	20	in	in	ADP
ejpam-3229	7	21	semigroup	semigroup	PROPN
ejpam-3229	7	22	theory	theory	NOUN
ejpam-3229	7	23	from	from	ADP
ejpam-3229	7	24	the	the	DET
ejpam-3229	7	25	beginning	beginning	NOUN
ejpam-3229	7	26	(	(	PUNCT
ejpam-3229	7	27	as	as	SCONJ
ejpam-3229	7	28	can	can	AUX
ejpam-3229	7	29	be	be	AUX
ejpam-3229	7	30	seen	see	VERB
ejpam-3229	7	31	from	from	ADP
ejpam-3229	7	32	the	the	DET
ejpam-3229	7	33	title	title	NOUN
ejpam-3229	7	34	of	of	ADP
ejpam-3229	7	35	a.	a.	PROPN
ejpam-3229	7	36	k.	k.	PROPN
ejpam-3229	7	37	suschkewitsch	suschkewitsch	PROPN
ejpam-3229	7	38	’s	’s	PART
ejpam-3229	7	39	dissertation	dissertation	NOUN
ejpam-3229	7	40	”	"	PUNCT
ejpam-3229	7	41	the	the	DET
ejpam-3229	7	42	action	action	NOUN
ejpam-3229	7	43	of	of	ADP
ejpam-3229	7	44	generalized	generalized	ADJ
ejpam-3229	7	45	group	group	NOUN
ejpam-3229	7	46	theory	theory	NOUN
ejpam-3229	7	47	”	"	PUNCT
ejpam-3229	7	48	(	(	PUNCT
ejpam-3229	7	49	in	in	ADP
ejpam-3229	7	50	russian	russian	PROPN
ejpam-3229	7	51	)	)	PUNCT
ejpam-3229	7	52	,	,	PUNCT
ejpam-3229	7	53	1992	1992	NUM
ejpam-3229	7	54	)	)	PUNCT
ejpam-3229	7	55	.	.	PUNCT
ejpam-3229	8	1	a	a	DET
ejpam-3229	8	2	representation	representation	NOUN
ejpam-3229	8	3	of	of	ADP
ejpam-3229	8	4	a	a	DET
ejpam-3229	8	5	semigroup	semigroup	NOUN
ejpam-3229	8	6	s	s	NOUN
ejpam-3229	8	7	by	by	ADP
ejpam-3229	8	8	a	a	DET
ejpam-3229	8	9	transformation	transformation	NOUN
ejpam-3229	8	10	of	of	ADP
ejpam-3229	8	11	a	a	DET
ejpam-3229	8	12	set	set	NOUN
ejpam-3229	8	13	defines	define	VERB
ejpam-3229	8	14	an	an	DET
ejpam-3229	8	15	s	s	NOUN
ejpam-3229	8	16	-	-	NOUN
ejpam-3229	8	17	act	act	NOUN
ejpam-3229	8	18	just	just	ADV
ejpam-3229	8	19	as	as	SCONJ
ejpam-3229	8	20	the	the	DET
ejpam-3229	8	21	representation	representation	NOUN
ejpam-3229	8	22	of	of	ADP
ejpam-3229	8	23	a	a	DET
ejpam-3229	8	24	ring	ring	NOUN
ejpam-3229	8	25	r	r	NOUN
ejpam-3229	8	26	by	by	ADP
ejpam-3229	8	27	endomorphisms	endomorphism	NOUN
ejpam-3229	8	28	of	of	ADP
ejpam-3229	8	29	an	an	DET
ejpam-3229	8	30	abelian	abelian	ADJ
ejpam-3229	8	31	group	group	NOUN
ejpam-3229	8	32	defines	define	VERB
ejpam-3229	8	33	an	an	DET
ejpam-3229	8	34	r	r	NOUN
ejpam-3229	8	35	-	-	PUNCT
ejpam-3229	8	36	module	module	NOUN
ejpam-3229	8	37	.	.	PUNCT
ejpam-3229	9	1	probably	probably	ADV
ejpam-3229	9	2	first	first	ADJ
ejpam-3229	9	3	time	time	NOUN
ejpam-3229	9	4	,	,	PUNCT
ejpam-3229	9	5	the	the	DET
ejpam-3229	9	6	definition	definition	NOUN
ejpam-3229	9	7	of	of	ADP
ejpam-3229	9	8	s	s	NOUN
ejpam-3229	9	9	-	-	PUNCT
ejpam-3229	9	10	acts	act	NOUN
ejpam-3229	9	11	appeared	appear	VERB
ejpam-3229	9	12	in	in	ADP
ejpam-3229	9	13	two	two	NUM
ejpam-3229	9	14	papers	paper	NOUN
ejpam-3229	9	15	of	of	ADP
ejpam-3229	9	16	the	the	DET
ejpam-3229	9	17	h.	h.	PROPN
ejpam-3229	9	18	j.	j.	PROPN
ejpam-3229	9	19	hoehnke	hoehnke	PROPN
ejpam-3229	9	20	with	with	ADP
ejpam-3229	9	21	a	a	DET
ejpam-3229	9	22	different	different	ADJ
ejpam-3229	9	23	name	name	NOUN
ejpam-3229	9	24	in	in	ADP
ejpam-3229	9	25	connection	connection	NOUN
ejpam-3229	9	26	with	with	ADP
ejpam-3229	9	27	the	the	DET
ejpam-3229	9	28	consideration	consideration	NOUN
ejpam-3229	9	29	of	of	ADP
ejpam-3229	9	30	radicals	radical	NOUN
ejpam-3229	9	31	of	of	ADP
ejpam-3229	9	32	a	a	DET
ejpam-3229	9	33	semigroup	semigroup	NOUN
ejpam-3229	9	34	.	.	PUNCT
ejpam-3229	10	1	acts	act	VERB
ejpam-3229	10	2	over	over	ADP
ejpam-3229	10	3	the	the	DET
ejpam-3229	10	4	semigroups	semigroup	NOUN
ejpam-3229	10	5	appeared	appear	VERB
ejpam-3229	10	6	and	and	CCONJ
ejpam-3229	10	7	were	be	AUX
ejpam-3229	10	8	used	use	VERB
ejpam-3229	10	9	in	in	ADP
ejpam-3229	10	10	various	various	ADJ
ejpam-3229	10	11	applications	application	NOUN
ejpam-3229	10	12	like	like	ADP
ejpam-3229	10	13	algebra	algebra	NOUN
ejpam-3229	10	14	automata	automata	NOUN
ejpam-3229	10	15	theory	theory	NOUN
ejpam-3229	10	16	,	,	PUNCT
ejpam-3229	10	17	mathematical	mathematical	ADJ
ejpam-3229	10	18	linguistics	linguistic	NOUN
ejpam-3229	10	19	,	,	PUNCT
ejpam-3229	10	20	graph	graph	NOUN
ejpam-3229	10	21	theory	theory	NOUN
ejpam-3229	10	22	,	,	PUNCT
ejpam-3229	10	23	system	system	NOUN
ejpam-3229	10	24	theory	theory	NOUN
ejpam-3229	10	25	,	,	PUNCT
ejpam-3229	10	26	information	information	NOUN
ejpam-3229	10	27	theory	theory	NOUN
ejpam-3229	10	28	,	,	PUNCT
ejpam-3229	10	29	the	the	DET
ejpam-3229	10	30	theory	theory	NOUN
ejpam-3229	10	31	of	of	ADP
ejpam-3229	10	32	communications	communication	NOUN
ejpam-3229	10	33	and	and	CCONJ
ejpam-3229	10	34	electronic	electronic	ADJ
ejpam-3229	10	35	circuits	circuit	NOUN
ejpam-3229	10	36	,	,	PUNCT
ejpam-3229	10	37	databases	database	NOUN
ejpam-3229	10	38	and	and	CCONJ
ejpam-3229	10	39	other	other	ADJ
ejpam-3229	10	40	fields	field	NOUN
ejpam-3229	10	41	of	of	ADP
ejpam-3229	10	42	theoretical	theoretical	ADJ
ejpam-3229	10	43	computer	computer	NOUN
ejpam-3229	10	44	science	science	NOUN
ejpam-3229	10	45	.	.	PUNCT
ejpam-3229	11	1	in	in	ADP
ejpam-3229	11	2	ring	ring	NOUN
ejpam-3229	11	3	theory	theory	NOUN
ejpam-3229	11	4	,	,	PUNCT
ejpam-3229	11	5	nowadays	nowadays	ADV
ejpam-3229	11	6	it	it	PRON
ejpam-3229	11	7	is	be	AUX
ejpam-3229	11	8	impossible	impossible	ADJ
ejpam-3229	11	9	to	to	PART
ejpam-3229	11	10	imagine	imagine	VERB
ejpam-3229	11	11	the	the	DET
ejpam-3229	11	12	main	main	ADJ
ejpam-3229	11	13	directions	direction	NOUN
ejpam-3229	11	14	without	without	ADP
ejpam-3229	11	15	homological	homological	ADJ
ejpam-3229	11	16	methods	method	NOUN
ejpam-3229	11	17	using	use	VERB
ejpam-3229	11	18	categories	category	NOUN
ejpam-3229	11	19	of	of	ADP
ejpam-3229	11	20	modules	module	NOUN
ejpam-3229	11	21	.	.	PUNCT
ejpam-3229	12	1	similarly	similarly	ADV
ejpam-3229	12	2	,	,	PUNCT
ejpam-3229	12	3	it	it	PRON
ejpam-3229	12	4	is	be	AUX
ejpam-3229	12	5	important	important	ADJ
ejpam-3229	12	6	for	for	SCONJ
ejpam-3229	12	7	monoids	monoid	NOUN
ejpam-3229	12	8	to	to	PART
ejpam-3229	12	9	consider	consider	VERB
ejpam-3229	12	10	an	an	DET
ejpam-3229	12	11	associated	associated	ADJ
ejpam-3229	12	12	category	category	NOUN
ejpam-3229	12	13	of	of	ADP
ejpam-3229	12	14	s	s	NOUN
ejpam-3229	12	15	-	-	PUNCT
ejpam-3229	12	16	acts	act	NOUN
ejpam-3229	12	17	projective	projective	ADJ
ejpam-3229	12	18	and	and	CCONJ
ejpam-3229	12	19	injective	injective	ADJ
ejpam-3229	12	20	s	s	NOUN
ejpam-3229	12	21	-	-	PUNCT
ejpam-3229	12	22	acts	act	NOUN
ejpam-3229	12	23	,	,	PUNCT
ejpam-3229	12	24	injective	injective	ADJ
ejpam-3229	12	25	envelopes	envelope	NOUN
ejpam-3229	12	26	,	,	PUNCT
ejpam-3229	12	27	projective	projective	ADJ
ejpam-3229	12	28	covers	cover	NOUN
ejpam-3229	12	29	were	be	AUX
ejpam-3229	12	30	mainly	mainly	ADV
ejpam-3229	12	31	developed	develop	VERB
ejpam-3229	12	32	by	by	ADP
ejpam-3229	12	33	p.	p.	NOUN
ejpam-3229	12	34	berthiaume	berthiaume	NOUN
ejpam-3229	13	1	[	[	X
ejpam-3229	13	2	11	11	NUM
ejpam-3229	13	3	]	]	PUNCT
ejpam-3229	13	4	,	,	PUNCT
ejpam-3229	13	5	c.	c.	PROPN
ejpam-3229	13	6	s.	s.	PROPN
ejpam-3229	13	7	johnson	johnson	PROPN
ejpam-3229	13	8	&	&	CCONJ
ejpam-3229	13	9	f.	f.	PROPN
ejpam-3229	13	10	mc	mc	PROPN
ejpam-3229	13	11	.	.	PROPN
ejpam-3229	13	12	morris	morris	PROPN
ejpam-3229	14	1	[	[	X
ejpam-3229	14	2	3	3	NUM
ejpam-3229	14	3	]	]	PUNCT
ejpam-3229	14	4	,	,	PUNCT
ejpam-3229	14	5	b.m	b.m	PROPN
ejpam-3229	14	6	schein	schein	PROPN
ejpam-3229	15	1	[	[	X
ejpam-3229	15	2	10	10	NUM
ejpam-3229	15	3	]	]	PUNCT
ejpam-3229	15	4	.	.	PUNCT
ejpam-3229	16	1	the	the	DET
ejpam-3229	16	2	monoids	monoid	NOUN
ejpam-3229	16	3	over	over	ADP
ejpam-3229	16	4	which	which	PRON
ejpam-3229	16	5	all	all	DET
ejpam-3229	16	6	s	s	NOUN
ejpam-3229	16	7	-	-	PUNCT
ejpam-3229	16	8	acts	act	NOUN
ejpam-3229	16	9	are	be	AUX
ejpam-3229	16	10	(	(	PUNCT
ejpam-3229	16	11	injective	injective	ADJ
ejpam-3229	16	12	)	)	PUNCT
ejpam-3229	16	13	projective	projective	NOUN
ejpam-3229	16	14	were	be	AUX
ejpam-3229	16	15	investigated	investigate	VERB
ejpam-3229	16	16	by	by	ADP
ejpam-3229	16	17	l.skronjakov	l.skronjakov	NOUN
ejpam-3229	16	18	.	.	PUNCT
ejpam-3229	17	1	the	the	DET
ejpam-3229	17	2	most	most	ADV
ejpam-3229	17	3	notable	notable	ADJ
ejpam-3229	17	4	difference	difference	NOUN
ejpam-3229	17	5	between	between	ADP
ejpam-3229	17	6	the	the	DET
ejpam-3229	17	7	theory	theory	NOUN
ejpam-3229	17	8	of	of	ADP
ejpam-3229	17	9	s	s	NOUN
ejpam-3229	17	10	-	-	PUNCT
ejpam-3229	17	11	acts	act	NOUN
ejpam-3229	17	12	and	and	CCONJ
ejpam-3229	17	13	the	the	DET
ejpam-3229	17	14	theory	theory	NOUN
ejpam-3229	17	15	of	of	ADP
ejpam-3229	17	16	modules	module	NOUN
ejpam-3229	17	17	was	be	AUX
ejpam-3229	17	18	discovered	discover	VERB
ejpam-3229	17	19	by	by	ADP
ejpam-3229	17	20	t	t	PROPN
ejpam-3229	17	21	.g	.g	PROPN
ejpam-3229	17	22	mustfin	mustfin	PROPN
ejpam-3229	17	23	,	,	PUNCT
ejpam-3229	17	24	j.	j.	PROPN
ejpam-3229	17	25	∗corresponding	∗corresponding	PROPN
ejpam-3229	17	26	author	author	NOUN
ejpam-3229	17	27	.	.	PUNCT
ejpam-3229	18	1	email	email	NOUN
ejpam-3229	18	2	addresses	address	NOUN
ejpam-3229	18	3	:	:	PUNCT
ejpam-3229	19	1	javed.brohi@iba-suk.edu.pk	javed.brohi@iba-suk.edu.pk	PROPN
ejpam-3229	19	2	(	(	PUNCT
ejpam-3229	19	3	j.	j.	PROPN
ejpam-3229	19	4	hussain	hussain	PROPN
ejpam-3229	19	5	)	)	PUNCT
ejpam-3229	19	6	,	,	PUNCT
ejpam-3229	19	7	mshabirbhatti@yahoo.co.uk	mshabirbhatti@yahoo.co.uk	PROPN
ejpam-3229	19	8	(	(	PUNCT
ejpam-3229	19	9	m.	m.	NOUN
ejpam-3229	19	10	shabir	shabir	PROPN
ejpam-3229	19	11	)	)	PUNCT
ejpam-3229	19	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3229	19	13	431	431	NUM
ejpam-3229	20	1	c	c	X
ejpam-3229	20	2	©	©	PROPN
ejpam-3229	20	3	2018	2018	NUM
ejpam-3229	20	4	ejpam	ejpam	VERB
ejpam-3229	20	5	all	all	DET
ejpam-3229	20	6	rights	right	NOUN
ejpam-3229	20	7	reserved	reserve	VERB
ejpam-3229	20	8	.	.	PUNCT
ejpam-3229	21	1	j.	j.	PROPN
ejpam-3229	21	2	hussain	hussain	PROPN
ejpam-3229	21	3	,	,	PUNCT
ejpam-3229	21	4	m.shabir	m.shabir	PROPN
ejpam-3229	21	5	/	/	SYM
ejpam-3229	21	6	eur	eur	PROPN
ejpam-3229	21	7	.	.	PUNCT
ejpam-3229	22	1	j.	j.	PROPN
ejpam-3229	22	2	pure	pure	PROPN
ejpam-3229	22	3	appl	appl	PROPN
ejpam-3229	22	4	.	.	PROPN
ejpam-3229	22	5	math	math	PROPN
ejpam-3229	22	6	,	,	PUNCT
ejpam-3229	22	7	11	11	NUM
ejpam-3229	22	8	(	(	PUNCT
ejpam-3229	22	9	2	2	NUM
ejpam-3229	22	10	)	)	PUNCT
ejpam-3229	22	11	(	(	PUNCT
ejpam-3229	22	12	2018	2018	NUM
ejpam-3229	22	13	)	)	PUNCT
ejpam-3229	22	14	,	,	PUNCT
ejpam-3229	22	15	431	431	NUM
ejpam-3229	22	16	-	-	SYM
ejpam-3229	22	17	443	443	NUM
ejpam-3229	22	18	432	432	NUM
ejpam-3229	22	19	fountain	fountain	NOUN
ejpam-3229	22	20	and	and	CCONJ
ejpam-3229	22	21	v.	v.	ADP
ejpam-3229	22	22	gould	gould	PROPN
ejpam-3229	22	23	,	,	PUNCT
ejpam-3229	22	24	that	that	SCONJ
ejpam-3229	22	25	there	there	PRON
ejpam-3229	22	26	exist	exist	VERB
ejpam-3229	22	27	s	s	NOUN
ejpam-3229	22	28	-	-	PUNCT
ejpam-3229	22	29	acts	act	NOUN
ejpam-3229	22	30	which	which	PRON
ejpam-3229	22	31	have	have	VERB
ejpam-3229	22	32	unstable	unstable	ADJ
ejpam-3229	22	33	theories	theory	NOUN
ejpam-3229	22	34	whereas	whereas	SCONJ
ejpam-3229	22	35	,	,	PUNCT
ejpam-3229	22	36	all	all	DET
ejpam-3229	22	37	complete	complete	ADJ
ejpam-3229	22	38	theories	theory	NOUN
ejpam-3229	22	39	of	of	ADP
ejpam-3229	22	40	modules	module	NOUN
ejpam-3229	22	41	are	be	AUX
ejpam-3229	22	42	stable	stable	ADJ
ejpam-3229	22	43	.	.	PUNCT
ejpam-3229	23	1	principally	principally	ADV
ejpam-3229	23	2	injective	injective	ADJ
ejpam-3229	23	3	s	s	NOUN
ejpam-3229	23	4	-	-	PUNCT
ejpam-3229	23	5	acts	act	NOUN
ejpam-3229	23	6	were	be	AUX
ejpam-3229	23	7	first	first	ADV
ejpam-3229	23	8	considered	consider	VERB
ejpam-3229	23	9	by	by	ADP
ejpam-3229	23	10	j.	j.	PROPN
ejpam-3229	23	11	luedeman	luedeman	PROPN
ejpam-3229	24	1	[	[	X
ejpam-3229	24	2	8	8	NUM
ejpam-3229	24	3	]	]	PUNCT
ejpam-3229	24	4	,	,	PUNCT
ejpam-3229	24	5	f.	f.	PROPN
ejpam-3229	24	6	mc	mc	PROPN
ejpam-3229	24	7	.	.	PROPN
ejpam-3229	24	8	morris	morris	PROPN
ejpam-3229	24	9	,	,	PUNCT
ejpam-3229	24	10	and	and	CCONJ
ejpam-3229	24	11	s.	s.	PROPN
ejpam-3229	24	12	k.	k.	PROPN
ejpam-3229	24	13	sim	sim	VERB
ejpam-3229	25	1	[	[	X
ejpam-3229	25	2	13	13	NUM
ejpam-3229	25	3	]	]	PUNCT
ejpam-3229	25	4	,	,	PUNCT
ejpam-3229	25	5	p.	p.	NOUN
ejpam-3229	25	6	berthiaume	berthiaume	NOUN
ejpam-3229	26	1	[	[	X
ejpam-3229	26	2	11	11	NUM
ejpam-3229	26	3	]	]	PUNCT
ejpam-3229	26	4	,	,	PUNCT
ejpam-3229	26	5	introduced	introduce	VERB
ejpam-3229	26	6	the	the	DET
ejpam-3229	26	7	notion	notion	NOUN
ejpam-3229	26	8	of	of	ADP
ejpam-3229	26	9	weak	weak	ADJ
ejpam-3229	26	10	injectivity	injectivity	NOUN
ejpam-3229	26	11	.	.	PUNCT
ejpam-3229	27	1	m.	m.	NOUN
ejpam-3229	27	2	shabir	shabir	PROPN
ejpam-3229	27	3	and	and	CCONJ
ejpam-3229	27	4	j.	j.	PROPN
ejpam-3229	27	5	ahsan	ahsan	PROPN
ejpam-3229	27	6	in	in	ADP
ejpam-3229	27	7	[	[	X
ejpam-3229	27	8	2	2	NUM
ejpam-3229	27	9	]	]	PUNCT
ejpam-3229	27	10	have	have	AUX
ejpam-3229	27	11	characterized	characterize	VERB
ejpam-3229	27	12	the	the	DET
ejpam-3229	27	13	monoids	monoid	NOUN
ejpam-3229	27	14	by	by	ADP
ejpam-3229	27	15	p	p	NOUN
ejpam-3229	27	16	-injective	-injective	ADJ
ejpam-3229	27	17	s	s	NOUN
ejpam-3229	27	18	-	-	PUNCT
ejpam-3229	27	19	acts	act	NOUN
ejpam-3229	27	20	and	and	CCONJ
ejpam-3229	27	21	a	a	DET
ejpam-3229	27	22	normal	normal	ADJ
ejpam-3229	27	23	system	system	NOUN
ejpam-3229	27	24	.	.	PUNCT
ejpam-3229	28	1	the	the	DET
ejpam-3229	28	2	novelity	novelity	NOUN
ejpam-3229	28	3	of	of	ADP
ejpam-3229	28	4	this	this	DET
ejpam-3229	28	5	work	work	NOUN
ejpam-3229	28	6	is	be	AUX
ejpam-3229	28	7	not	not	PART
ejpam-3229	28	8	only	only	ADV
ejpam-3229	28	9	that	that	SCONJ
ejpam-3229	28	10	new	new	ADJ
ejpam-3229	28	11	sturctures	sturcture	NOUN
ejpam-3229	28	12	has	have	AUX
ejpam-3229	28	13	been	be	AUX
ejpam-3229	28	14	defined	define	VERB
ejpam-3229	28	15	and	and	CCONJ
ejpam-3229	28	16	several	several	ADJ
ejpam-3229	28	17	of	of	ADP
ejpam-3229	28	18	their	their	PRON
ejpam-3229	28	19	nontrivial	nontrivial	ADJ
ejpam-3229	28	20	and	and	CCONJ
ejpam-3229	28	21	interesting	interesting	ADJ
ejpam-3229	28	22	properties	property	NOUN
ejpam-3229	28	23	has	have	AUX
ejpam-3229	28	24	been	be	AUX
ejpam-3229	28	25	studied	study	VERB
ejpam-3229	28	26	but	but	CCONJ
ejpam-3229	28	27	also	also	ADV
ejpam-3229	28	28	that	that	SCONJ
ejpam-3229	28	29	several	several	ADJ
ejpam-3229	28	30	of	of	ADP
ejpam-3229	28	31	connections	connection	NOUN
ejpam-3229	28	32	of	of	ADP
ejpam-3229	28	33	our	our	PRON
ejpam-3229	28	34	defined	define	VERB
ejpam-3229	28	35	structures	structure	NOUN
ejpam-3229	28	36	has	have	AUX
ejpam-3229	28	37	been	be	AUX
ejpam-3229	28	38	eastablsihed	eastablsihe	VERB
ejpam-3229	28	39	with	with	ADP
ejpam-3229	28	40	existing	exist	VERB
ejpam-3229	28	41	sturctures	sturcture	NOUN
ejpam-3229	28	42	like	like	ADP
ejpam-3229	28	43	injective	injective	ADJ
ejpam-3229	28	44	,	,	PUNCT
ejpam-3229	28	45	projective	projective	ADJ
ejpam-3229	28	46	,	,	PUNCT
ejpam-3229	28	47	co	co	ADJ
ejpam-3229	28	48	-	-	ADJ
ejpam-3229	28	49	hereditary	hereditary	ADJ
ejpam-3229	28	50	s	s	NOUN
ejpam-3229	28	51	-	-	PUNCT
ejpam-3229	28	52	acts	act	NOUN
ejpam-3229	28	53	and	and	CCONJ
ejpam-3229	28	54	pp	pp	NOUN
ejpam-3229	28	55	-	-	PUNCT
ejpam-3229	28	56	semigroups	semigroup	NOUN
ejpam-3229	28	57	.	.	PUNCT
ejpam-3229	29	1	for	for	ADP
ejpam-3229	29	2	example	example	NOUN
ejpam-3229	29	3	see	see	VERB
ejpam-3229	29	4	theorems	theorem	NOUN
ejpam-3229	29	5	9	9	NUM
ejpam-3229	29	6	,	,	PUNCT
ejpam-3229	29	7	10	10	NUM
ejpam-3229	29	8	,	,	PUNCT
ejpam-3229	29	9	11	11	NUM
ejpam-3229	29	10	,	,	PUNCT
ejpam-3229	29	11	14	14	NUM
ejpam-3229	29	12	and	and	CCONJ
ejpam-3229	29	13	corollary	corollary	ADJ
ejpam-3229	29	14	4	4	NUM
ejpam-3229	29	15	.	.	PUNCT
ejpam-3229	30	1	in	in	ADP
ejpam-3229	30	2	this	this	DET
ejpam-3229	30	3	paper	paper	NOUN
ejpam-3229	30	4	,	,	PUNCT
ejpam-3229	30	5	we	we	PRON
ejpam-3229	30	6	have	have	AUX
ejpam-3229	30	7	introduced	introduce	VERB
ejpam-3229	30	8	the	the	DET
ejpam-3229	30	9	notions	notion	NOUN
ejpam-3229	30	10	of	of	ADP
ejpam-3229	30	11	m	m	NOUN
ejpam-3229	30	12	-	-	ADJ
ejpam-3229	30	13	cyclic	cyclic	ADJ
ejpam-3229	30	14	s	s	NOUN
ejpam-3229	30	15	-	-	PUNCT
ejpam-3229	30	16	acts	act	NOUN
ejpam-3229	30	17	,	,	PUNCT
ejpam-3229	30	18	m	m	NOUN
ejpam-3229	30	19	-	-	ADJ
ejpam-3229	30	20	principally	principally	ADV
ejpam-3229	30	21	projective	projective	ADJ
ejpam-3229	30	22	and	and	CCONJ
ejpam-3229	30	23	injective	injective	ADJ
ejpam-3229	30	24	s	s	NOUN
ejpam-3229	30	25	-	-	PUNCT
ejpam-3229	30	26	acts	act	NOUN
ejpam-3229	30	27	and	and	CCONJ
ejpam-3229	30	28	semi	semi	ADJ
ejpam-3229	30	29	-	-	ADJ
ejpam-3229	30	30	projective	projective	ADJ
ejpam-3229	30	31	s	s	NOUN
ejpam-3229	30	32	-	-	NOUN
ejpam-3229	30	33	acts	act	NOUN
ejpam-3229	30	34	,	,	PUNCT
ejpam-3229	30	35	wherem	wherem	PROPN
ejpam-3229	30	36	is	be	AUX
ejpam-3229	30	37	a	a	DET
ejpam-3229	30	38	right	right	ADJ
ejpam-3229	30	39	s	s	NOUN
ejpam-3229	30	40	-	-	NOUN
ejpam-3229	30	41	act	act	NOUN
ejpam-3229	30	42	.	.	PUNCT
ejpam-3229	31	1	the	the	DET
ejpam-3229	31	2	paper	paper	NOUN
ejpam-3229	31	3	consists	consist	VERB
ejpam-3229	31	4	of	of	ADP
ejpam-3229	31	5	4	4	NUM
ejpam-3229	31	6	sections	section	NOUN
ejpam-3229	31	7	.	.	PUNCT
ejpam-3229	32	1	we	we	PRON
ejpam-3229	32	2	are	be	AUX
ejpam-3229	32	3	giving	give	VERB
ejpam-3229	32	4	a	a	DET
ejpam-3229	32	5	section	section	NOUN
ejpam-3229	32	6	-	-	PUNCT
ejpam-3229	32	7	wise	wise	ADJ
ejpam-3229	32	8	description	description	NOUN
ejpam-3229	32	9	of	of	ADP
ejpam-3229	32	10	the	the	DET
ejpam-3229	32	11	paper	paper	NOUN
ejpam-3229	32	12	.	.	PUNCT
ejpam-3229	33	1	first	first	ADJ
ejpam-3229	33	2	section	section	NOUN
ejpam-3229	33	3	is	be	AUX
ejpam-3229	33	4	running	run	VERB
ejpam-3229	33	5	introduction	introduction	NOUN
ejpam-3229	33	6	.	.	PUNCT
ejpam-3229	34	1	in	in	ADP
ejpam-3229	34	2	section	section	NOUN
ejpam-3229	34	3	2	2	NUM
ejpam-3229	34	4	,	,	PUNCT
ejpam-3229	34	5	we	we	PRON
ejpam-3229	34	6	have	have	AUX
ejpam-3229	34	7	defined	define	VERB
ejpam-3229	34	8	m	m	ADV
ejpam-3229	34	9	-	-	ADJ
ejpam-3229	34	10	principally	principally	ADV
ejpam-3229	34	11	injective	injective	ADJ
ejpam-3229	34	12	s	s	NOUN
ejpam-3229	34	13	-	-	PUNCT
ejpam-3229	34	14	acts	act	NOUN
ejpam-3229	34	15	and	and	CCONJ
ejpam-3229	34	16	established	establish	VERB
ejpam-3229	34	17	the	the	DET
ejpam-3229	34	18	connection	connection	NOUN
ejpam-3229	34	19	between	between	ADP
ejpam-3229	34	20	the	the	DET
ejpam-3229	34	21	m	m	NOUN
ejpam-3229	34	22	-	-	PUNCT
ejpam-3229	34	23	cyclic	cyclic	ADJ
ejpam-3229	34	24	sub	sub	NOUN
ejpam-3229	34	25	-	-	NOUN
ejpam-3229	34	26	acts	act	NOUN
ejpam-3229	34	27	and	and	CCONJ
ejpam-3229	34	28	the	the	DET
ejpam-3229	34	29	ideals	ideal	NOUN
ejpam-3229	34	30	of	of	ADP
ejpam-3229	34	31	endomorphism	endomorphism	PROPN
ejpam-3229	34	32	monoid	monoid	NOUN
ejpam-3229	34	33	of	of	ADP
ejpam-3229	34	34	a	a	DET
ejpam-3229	34	35	quasi	quasi	ADJ
ejpam-3229	34	36	-	-	ADJ
ejpam-3229	34	37	principally	principally	ADV
ejpam-3229	34	38	injective	injective	ADJ
ejpam-3229	34	39	s	s	NOUN
ejpam-3229	34	40	-	-	PUNCT
ejpam-3229	34	41	act	act	NOUN
ejpam-3229	34	42	m.	m.	NOUN
ejpam-3229	34	43	further	far	ADV
ejpam-3229	34	44	a	a	DET
ejpam-3229	34	45	relation	relation	NOUN
ejpam-3229	34	46	between	between	ADP
ejpam-3229	34	47	the	the	DET
ejpam-3229	34	48	kernel	kernel	PROPN
ejpam-3229	34	49	congruence	congruence	NOUN
ejpam-3229	34	50	induced	induce	VERB
ejpam-3229	34	51	by	by	ADP
ejpam-3229	34	52	endomorphisms	endomorphism	NOUN
ejpam-3229	34	53	on	on	ADP
ejpam-3229	34	54	quasi	quasi	ADJ
ejpam-3229	34	55	-	-	ADJ
ejpam-3229	34	56	principally	principally	ADV
ejpam-3229	34	57	injective	injective	ADJ
ejpam-3229	34	58	s	s	NOUN
ejpam-3229	34	59	-	-	PUNCT
ejpam-3229	34	60	act	act	NOUN
ejpam-3229	34	61	m	m	PROPN
ejpam-3229	34	62	and	and	CCONJ
ejpam-3229	34	63	the	the	DET
ejpam-3229	34	64	ideals	ideal	NOUN
ejpam-3229	34	65	of	of	ADP
ejpam-3229	34	66	its	its	PRON
ejpam-3229	34	67	endomorphism	endomorphism	NOUN
ejpam-3229	34	68	monoid	monoid	NOUN
ejpam-3229	34	69	.	.	PUNCT
ejpam-3229	35	1	after	after	ADP
ejpam-3229	35	2	that	that	PRON
ejpam-3229	35	3	,	,	PUNCT
ejpam-3229	35	4	some	some	PRON
ejpam-3229	35	5	of	of	ADP
ejpam-3229	35	6	the	the	DET
ejpam-3229	35	7	properties	property	NOUN
ejpam-3229	35	8	of	of	ADP
ejpam-3229	35	9	mprincipally	mprincipally	ADV
ejpam-3229	35	10	injective	injective	ADJ
ejpam-3229	35	11	s	s	NOUN
ejpam-3229	35	12	-	-	PUNCT
ejpam-3229	35	13	acts	act	NOUN
ejpam-3229	35	14	have	have	AUX
ejpam-3229	35	15	also	also	ADV
ejpam-3229	35	16	been	be	AUX
ejpam-3229	35	17	investigated	investigate	VERB
ejpam-3229	35	18	.	.	PUNCT
ejpam-3229	36	1	in	in	ADP
ejpam-3229	36	2	section	section	NOUN
ejpam-3229	36	3	2	2	NUM
ejpam-3229	36	4	,	,	PUNCT
ejpam-3229	36	5	we	we	PRON
ejpam-3229	36	6	have	have	AUX
ejpam-3229	36	7	defined	define	VERB
ejpam-3229	36	8	m	m	ADV
ejpam-3229	36	9	-	-	ADJ
ejpam-3229	36	10	principally	principally	ADV
ejpam-3229	36	11	projective	projective	ADJ
ejpam-3229	36	12	s	s	NOUN
ejpam-3229	36	13	-	-	PUNCT
ejpam-3229	36	14	acts	act	NOUN
ejpam-3229	36	15	and	and	CCONJ
ejpam-3229	36	16	investigated	investigate	VERB
ejpam-3229	36	17	some	some	DET
ejpam-3229	36	18	interesting	interesting	ADJ
ejpam-3229	36	19	results	result	NOUN
ejpam-3229	36	20	and	and	CCONJ
ejpam-3229	36	21	connection	connection	NOUN
ejpam-3229	36	22	with	with	ADP
ejpam-3229	36	23	m	m	NOUN
ejpam-3229	36	24	-	-	ADJ
ejpam-3229	36	25	principally	principally	ADV
ejpam-3229	36	26	injective	injective	ADJ
ejpam-3229	36	27	s	s	NOUN
ejpam-3229	36	28	-	-	PUNCT
ejpam-3229	36	29	acts	act	NOUN
ejpam-3229	36	30	.	.	PUNCT
ejpam-3229	37	1	a	a	DET
ejpam-3229	37	2	note	note	NOUN
ejpam-3229	37	3	on	on	ADP
ejpam-3229	37	4	co	co	NOUN
ejpam-3229	37	5	-	-	ADJ
ejpam-3229	37	6	hereditary	hereditary	ADJ
ejpam-3229	37	7	s	s	NOUN
ejpam-3229	37	8	-	-	PUNCT
ejpam-3229	37	9	acts	act	NOUN
ejpam-3229	37	10	is	be	AUX
ejpam-3229	37	11	included	include	VERB
ejpam-3229	37	12	at	at	ADP
ejpam-3229	37	13	the	the	DET
ejpam-3229	37	14	end	end	NOUN
ejpam-3229	37	15	of	of	ADP
ejpam-3229	37	16	the	the	DET
ejpam-3229	37	17	section	section	NOUN
ejpam-3229	37	18	.	.	PUNCT
ejpam-3229	38	1	in	in	ADP
ejpam-3229	38	2	section	section	NOUN
ejpam-3229	38	3	4	4	NUM
ejpam-3229	38	4	,	,	PUNCT
ejpam-3229	38	5	semi	semi	ADJ
ejpam-3229	38	6	-	-	ADJ
ejpam-3229	38	7	projective	projective	ADJ
ejpam-3229	38	8	s	s	NOUN
ejpam-3229	38	9	-	-	PUNCT
ejpam-3229	38	10	acts	act	NOUN
ejpam-3229	38	11	have	have	AUX
ejpam-3229	38	12	been	be	AUX
ejpam-3229	38	13	defined	define	VERB
ejpam-3229	38	14	and	and	CCONJ
ejpam-3229	38	15	connections	connection	NOUN
ejpam-3229	38	16	with	with	ADP
ejpam-3229	38	17	its	its	PRON
ejpam-3229	38	18	endomorphism	endomorphism	NOUN
ejpam-3229	38	19	monoid	monoid	NOUN
ejpam-3229	38	20	are	be	AUX
ejpam-3229	38	21	investigated	investigate	VERB
ejpam-3229	38	22	and	and	CCONJ
ejpam-3229	38	23	significant	significant	ADJ
ejpam-3229	38	24	results	result	NOUN
ejpam-3229	38	25	are	be	AUX
ejpam-3229	38	26	proved	prove	VERB
ejpam-3229	38	27	.	.	PUNCT
ejpam-3229	39	1	2	2	X
ejpam-3229	39	2	.	.	X
ejpam-3229	39	3	m	m	VERB
ejpam-3229	39	4	-	-	PUNCT
ejpam-3229	39	5	principally	principally	ADV
ejpam-3229	39	6	injective	injective	ADJ
ejpam-3229	39	7	s	s	NOUN
ejpam-3229	39	8	-	-	PUNCT
ejpam-3229	39	9	acts	act	NOUN
ejpam-3229	39	10	and	and	CCONJ
ejpam-3229	39	11	their	their	PRON
ejpam-3229	39	12	properties	property	NOUN
ejpam-3229	39	13	in	in	ADP
ejpam-3229	39	14	terms	term	NOUN
ejpam-3229	39	15	of	of	ADP
ejpam-3229	39	16	m	m	NOUN
ejpam-3229	39	17	-	-	PUNCT
ejpam-3229	39	18	cyclic	cyclic	ADJ
ejpam-3229	39	19	sub	sub	NOUN
ejpam-3229	39	20	-	-	NOUN
ejpam-3229	39	21	acts	act	NOUN
ejpam-3229	39	22	throughout	throughout	ADP
ejpam-3229	39	23	the	the	DET
ejpam-3229	39	24	paper	paper	NOUN
ejpam-3229	39	25	s	s	PART
ejpam-3229	39	26	will	will	AUX
ejpam-3229	39	27	denote	denote	VERB
ejpam-3229	39	28	the	the	DET
ejpam-3229	39	29	semigroup	semigroup	NOUN
ejpam-3229	39	30	with	with	ADP
ejpam-3229	39	31	fixed	fix	VERB
ejpam-3229	39	32	element	element	NOUN
ejpam-3229	39	33	θ	θ	PROPN
ejpam-3229	39	34	and	and	CCONJ
ejpam-3229	39	35	e	e	NOUN
ejpam-3229	39	36	will	will	AUX
ejpam-3229	39	37	denote	denote	VERB
ejpam-3229	39	38	the	the	DET
ejpam-3229	39	39	endomorphism	endomorphism	PROPN
ejpam-3229	39	40	monoid	monoid	NOUN
ejpam-3229	39	41	of	of	ADP
ejpam-3229	39	42	a	a	DET
ejpam-3229	39	43	right	right	ADJ
ejpam-3229	39	44	s	s	NOUN
ejpam-3229	39	45	-	-	NOUN
ejpam-3229	39	46	act	act	NOUN
ejpam-3229	39	47	m	m	PROPN
ejpam-3229	39	48	,	,	PUNCT
ejpam-3229	39	49	i.e.	i.e.	X
ejpam-3229	39	50	e	e	X
ejpam-3229	39	51	=	=	PRON
ejpam-3229	39	52	ends	end	NOUN
ejpam-3229	39	53	(	(	PUNCT
ejpam-3229	39	54	m	m	NOUN
ejpam-3229	39	55	)	)	PUNCT
ejpam-3229	39	56	.	.	PUNCT
ejpam-3229	40	1	moreover	moreover	ADV
ejpam-3229	40	2	,	,	PUNCT
ejpam-3229	40	3	by	by	ADP
ejpam-3229	40	4	ker	ker	PROPN
ejpam-3229	40	5	γ	γ	NOUN
ejpam-3229	40	6	we	we	PRON
ejpam-3229	40	7	mean	mean	VERB
ejpam-3229	40	8	the	the	DET
ejpam-3229	40	9	usual	usual	ADJ
ejpam-3229	40	10	kernel	kernel	NOUN
ejpam-3229	40	11	congruence	congruence	NOUN
ejpam-3229	40	12	on	on	ADP
ejpam-3229	40	13	m	m	AUX
ejpam-3229	40	14	induced	induce	VERB
ejpam-3229	40	15	by	by	ADP
ejpam-3229	40	16	γ	γ	PROPN
ejpam-3229	40	17	∈	∈	PROPN
ejpam-3229	40	18	e.	e.	PROPN
ejpam-3229	40	19	definition	definition	NOUN
ejpam-3229	40	20	1	1	X
ejpam-3229	40	21	.	.	PUNCT
ejpam-3229	41	1	let	let	VERB
ejpam-3229	41	2	n	n	PRON
ejpam-3229	41	3	be	be	AUX
ejpam-3229	41	4	a	a	DET
ejpam-3229	41	5	sub	sub	NOUN
ejpam-3229	41	6	-	-	NOUN
ejpam-3229	41	7	act	act	NOUN
ejpam-3229	41	8	of	of	ADP
ejpam-3229	41	9	a	a	DET
ejpam-3229	41	10	right	right	ADJ
ejpam-3229	41	11	s	s	NOUN
ejpam-3229	41	12	-	-	PUNCT
ejpam-3229	41	13	act	act	NOUN
ejpam-3229	41	14	m.	m.	NOUN
ejpam-3229	41	15	then	then	ADV
ejpam-3229	41	16	n	n	PRON
ejpam-3229	41	17	is	be	AUX
ejpam-3229	41	18	called	call	VERB
ejpam-3229	41	19	an	an	DET
ejpam-3229	41	20	m	m	NOUN
ejpam-3229	41	21	-	-	PUNCT
ejpam-3229	41	22	cyclic	cyclic	ADJ
ejpam-3229	41	23	sub	sub	NOUN
ejpam-3229	41	24	-	-	NOUN
ejpam-3229	41	25	act	act	NOUN
ejpam-3229	41	26	of	of	ADP
ejpam-3229	41	27	m	m	PROPN
ejpam-3229	41	28	if	if	SCONJ
ejpam-3229	41	29	n	n	NOUN
ejpam-3229	41	30	∼=m	∼=m	ADJ
ejpam-3229	41	31	/	/	SYM
ejpam-3229	41	32	ρ	ρ	NOUN
ejpam-3229	41	33	for	for	ADP
ejpam-3229	41	34	some	some	DET
ejpam-3229	41	35	congruence	congruence	NOUN
ejpam-3229	41	36	ρ	ρ	NOUN
ejpam-3229	41	37	on	on	ADP
ejpam-3229	41	38	m.	m.	NOUN
ejpam-3229	41	39	lemma	lemma	PROPN
ejpam-3229	41	40	1	1	X
ejpam-3229	41	41	.	.	PUNCT
ejpam-3229	42	1	let	let	VERB
ejpam-3229	42	2	m	m	PRON
ejpam-3229	42	3	be	be	AUX
ejpam-3229	42	4	a	a	DET
ejpam-3229	42	5	right	right	ADJ
ejpam-3229	42	6	s	s	NOUN
ejpam-3229	42	7	-	-	NOUN
ejpam-3229	42	8	act	act	NOUN
ejpam-3229	42	9	and	and	CCONJ
ejpam-3229	42	10	n	n	PRON
ejpam-3229	42	11	be	be	AUX
ejpam-3229	42	12	a	a	DET
ejpam-3229	42	13	sub	sub	NOUN
ejpam-3229	42	14	-	-	NOUN
ejpam-3229	42	15	act	act	NOUN
ejpam-3229	42	16	of	of	ADP
ejpam-3229	42	17	m.	m.	NOUN
ejpam-3229	42	18	then	then	ADV
ejpam-3229	42	19	the	the	DET
ejpam-3229	42	20	following	following	NOUN
ejpam-3229	42	21	are	be	AUX
ejpam-3229	42	22	equivalent	equivalent	ADJ
ejpam-3229	42	23	.	.	PUNCT
ejpam-3229	43	1	1	1	X
ejpam-3229	43	2	)	)	PUNCT
ejpam-3229	43	3	n	n	PRON
ejpam-3229	43	4	∼=m	∼=m	ADJ
ejpam-3229	43	5	/	/	SYM
ejpam-3229	43	6	ρ	ρ	NOUN
ejpam-3229	43	7	.	.	NOUN
ejpam-3229	43	8	2	2	NUM
ejpam-3229	43	9	)	)	PUNCT
ejpam-3229	44	1	n	n	NOUN
ejpam-3229	44	2	=	=	SYM
ejpam-3229	44	3	α	α	PROPN
ejpam-3229	44	4	(	(	PUNCT
ejpam-3229	44	5	m	m	NOUN
ejpam-3229	44	6	)	)	PUNCT
ejpam-3229	44	7	,	,	PUNCT
ejpam-3229	44	8	for	for	ADP
ejpam-3229	44	9	some	some	DET
ejpam-3229	44	10	α	α	PROPN
ejpam-3229	44	11	∈	∈	PROPN
ejpam-3229	44	12	e.	e.	PROPN
ejpam-3229	44	13	proof	proof	PROPN
ejpam-3229	44	14	.	.	PUNCT
ejpam-3229	45	1	1)⇒	1)⇒	NUM
ejpam-3229	45	2	2	2	NUM
ejpam-3229	45	3	)	)	PUNCT
ejpam-3229	45	4	let	let	VERB
ejpam-3229	45	5	π	π	NOUN
ejpam-3229	45	6	:	:	PUNCT
ejpam-3229	45	7	m→m	m→m	PROPN
ejpam-3229	45	8	/	/	SYM
ejpam-3229	45	9	ρ	ρ	PROPN
ejpam-3229	45	10	be	be	VERB
ejpam-3229	45	11	a	a	DET
ejpam-3229	45	12	natural	natural	ADJ
ejpam-3229	45	13	epimorphism	epimorphism	NOUN
ejpam-3229	45	14	and	and	CCONJ
ejpam-3229	45	15	γ	γ	NOUN
ejpam-3229	45	16	:	:	PUNCT
ejpam-3229	45	17	m	m	PROPN
ejpam-3229	45	18	/	/	SYM
ejpam-3229	45	19	ρ→	ρ→	PROPN
ejpam-3229	45	20	n	n	VERB
ejpam-3229	45	21	be	be	AUX
ejpam-3229	45	22	an	an	DET
ejpam-3229	45	23	isomorphism	isomorphism	NOUN
ejpam-3229	45	24	then	then	ADV
ejpam-3229	45	25	it	it	PRON
ejpam-3229	45	26	follows	follow	VERB
ejpam-3229	45	27	that	that	SCONJ
ejpam-3229	45	28	γπ	γπ	ADV
ejpam-3229	45	29	:	:	PUNCT
ejpam-3229	45	30	m→n	m→n	NOUN
ejpam-3229	45	31	is	be	AUX
ejpam-3229	45	32	an	an	DET
ejpam-3229	45	33	epimorphism	epimorphism	NOUN
ejpam-3229	45	34	and	and	CCONJ
ejpam-3229	45	35	γπ	γπ	ADV
ejpam-3229	45	36	(	(	PUNCT
ejpam-3229	45	37	m	m	NOUN
ejpam-3229	45	38	)	)	PUNCT
ejpam-3229	45	39	=	=	SYM
ejpam-3229	46	1	n	n	NOUN
ejpam-3229	46	2	.	.	NOUN
ejpam-3229	46	3	2)⇒1	2)⇒1	NUM
ejpam-3229	46	4	)	)	PUNCT
ejpam-3229	46	5	suppose	suppose	VERB
ejpam-3229	46	6	n	n	PRON
ejpam-3229	46	7	=	=	SYM
ejpam-3229	46	8	α	α	PROPN
ejpam-3229	46	9	(	(	PUNCT
ejpam-3229	46	10	m	m	NOUN
ejpam-3229	46	11	)	)	PUNCT
ejpam-3229	46	12	for	for	ADP
ejpam-3229	46	13	some	some	DET
ejpam-3229	46	14	α	α	PROPN
ejpam-3229	46	15	∈	∈	PROPN
ejpam-3229	46	16	e.	e.	PROPN
ejpam-3229	46	17	let	let	VERB
ejpam-3229	46	18	k	k	PROPN
ejpam-3229	46	19	=	=	PUNCT
ejpam-3229	46	20	kerα	kerα	PROPN
ejpam-3229	46	21	.	.	PUNCT
ejpam-3229	47	1	define	define	VERB
ejpam-3229	47	2	φ	φ	NOUN
ejpam-3229	47	3	:	:	PUNCT
ejpam-3229	47	4	n	n	PROPN
ejpam-3229	47	5	=	=	SYM
ejpam-3229	47	6	α	α	PROPN
ejpam-3229	47	7	(	(	PUNCT
ejpam-3229	47	8	m)→	m)→	VERB
ejpam-3229	47	9	m	m	PROPN
ejpam-3229	47	10	/	/	SYM
ejpam-3229	47	11	k	k	X
ejpam-3229	47	12	by	by	ADP
ejpam-3229	47	13	φ(α(m	φ(α(m	VERB
ejpam-3229	47	14	)	)	PUNCT
ejpam-3229	47	15	)	)	PUNCT
ejpam-3229	48	1	=	=	PUNCT
ejpam-3229	49	1	[	[	X
ejpam-3229	49	2	m]k	m]k	X
ejpam-3229	49	3	.	.	PUNCT
ejpam-3229	50	1	indeed	indeed	ADV
ejpam-3229	50	2	φ	φ	PROPN
ejpam-3229	50	3	is	be	AUX
ejpam-3229	50	4	an	an	DET
ejpam-3229	50	5	s	s	NOUN
ejpam-3229	50	6	-	-	NOUN
ejpam-3229	50	7	isomorphism	isomorphism	NOUN
ejpam-3229	50	8	.	.	PUNCT
ejpam-3229	51	1	thus	thus	ADV
ejpam-3229	51	2	by	by	ADP
ejpam-3229	51	3	lemma	lemma	PROPN
ejpam-3229	51	4	(	(	PUNCT
ejpam-3229	51	5	1	1	X
ejpam-3229	51	6	)	)	PUNCT
ejpam-3229	51	7	we	we	PRON
ejpam-3229	51	8	conclude	conclude	VERB
ejpam-3229	51	9	that	that	SCONJ
ejpam-3229	51	10	α	α	PROPN
ejpam-3229	51	11	(	(	PUNCT
ejpam-3229	51	12	m	m	PROPN
ejpam-3229	51	13	)	)	PUNCT
ejpam-3229	51	14	,	,	PUNCT
ejpam-3229	51	15	where	where	SCONJ
ejpam-3229	51	16	α	α	PRON
ejpam-3229	51	17	∈	∈	PROPN
ejpam-3229	51	18	e	e	NOUN
ejpam-3229	51	19	,	,	PUNCT
ejpam-3229	51	20	can	can	AUX
ejpam-3229	51	21	also	also	ADV
ejpam-3229	51	22	be	be	AUX
ejpam-3229	51	23	used	use	VERB
ejpam-3229	51	24	as	as	ADP
ejpam-3229	51	25	an	an	DET
ejpam-3229	51	26	alternate	alternate	ADJ
ejpam-3229	51	27	notion	notion	NOUN
ejpam-3229	51	28	for	for	ADP
ejpam-3229	51	29	m	m	NOUN
ejpam-3229	51	30	-	-	PUNCT
ejpam-3229	51	31	cyclic	cyclic	ADJ
ejpam-3229	51	32	sub	sub	NOUN
ejpam-3229	51	33	-	-	NOUN
ejpam-3229	51	34	act	act	NOUN
ejpam-3229	51	35	of	of	ADP
ejpam-3229	51	36	m.	m.	NOUN
ejpam-3229	51	37	j.	j.	PROPN
ejpam-3229	51	38	hussain	hussain	PROPN
ejpam-3229	51	39	,	,	PUNCT
ejpam-3229	51	40	m.shabir	m.shabir	PROPN
ejpam-3229	51	41	/	/	SYM
ejpam-3229	51	42	eur	eur	PROPN
ejpam-3229	51	43	.	.	PUNCT
ejpam-3229	52	1	j.	j.	PROPN
ejpam-3229	52	2	pure	pure	PROPN
ejpam-3229	52	3	appl	appl	PROPN
ejpam-3229	52	4	.	.	PROPN
ejpam-3229	52	5	math	math	PROPN
ejpam-3229	52	6	,	,	PUNCT
ejpam-3229	52	7	11	11	NUM
ejpam-3229	52	8	(	(	PUNCT
ejpam-3229	52	9	2	2	NUM
ejpam-3229	52	10	)	)	PUNCT
ejpam-3229	52	11	(	(	PUNCT
ejpam-3229	52	12	2018	2018	NUM
ejpam-3229	52	13	)	)	PUNCT
ejpam-3229	52	14	,	,	PUNCT
ejpam-3229	52	15	431	431	NUM
ejpam-3229	52	16	-	-	SYM
ejpam-3229	52	17	443	443	NUM
ejpam-3229	52	18	433	433	NUM
ejpam-3229	52	19	definition	definition	NOUN
ejpam-3229	52	20	2	2	NUM
ejpam-3229	52	21	.	.	PUNCT
ejpam-3229	53	1	let	let	VERB
ejpam-3229	53	2	m	m	PRON
ejpam-3229	53	3	be	be	AUX
ejpam-3229	53	4	a	a	DET
ejpam-3229	53	5	right	right	ADJ
ejpam-3229	53	6	s	s	NOUN
ejpam-3229	53	7	-	-	NOUN
ejpam-3229	53	8	act	act	NOUN
ejpam-3229	53	9	.	.	PUNCT
ejpam-3229	54	1	a	a	DET
ejpam-3229	54	2	right	right	ADJ
ejpam-3229	54	3	s	s	NOUN
ejpam-3229	54	4	-	-	NOUN
ejpam-3229	54	5	act	act	NOUN
ejpam-3229	54	6	n	n	VERB
ejpam-3229	54	7	is	be	AUX
ejpam-3229	54	8	called	call	VERB
ejpam-3229	54	9	m	m	ADV
ejpam-3229	54	10	-	-	PUNCT
ejpam-3229	54	11	principally	principally	ADV
ejpam-3229	54	12	injective	injective	ADJ
ejpam-3229	54	13	if	if	SCONJ
ejpam-3229	54	14	every	every	DET
ejpam-3229	54	15	s	s	NOUN
ejpam-3229	54	16	-	-	PUNCT
ejpam-3229	54	17	homomorphism	homomorphism	NOUN
ejpam-3229	54	18	from	from	ADP
ejpam-3229	54	19	an	an	DET
ejpam-3229	54	20	m	m	NOUN
ejpam-3229	54	21	-	-	PUNCT
ejpam-3229	54	22	cyclic	cyclic	ADJ
ejpam-3229	54	23	sub	sub	NOUN
ejpam-3229	54	24	-	-	NOUN
ejpam-3229	54	25	act	act	NOUN
ejpam-3229	54	26	to	to	ADP
ejpam-3229	54	27	n	n	NUM
ejpam-3229	54	28	can	can	AUX
ejpam-3229	54	29	be	be	AUX
ejpam-3229	54	30	extended	extend	VERB
ejpam-3229	54	31	to	to	ADP
ejpam-3229	54	32	an	an	DET
ejpam-3229	54	33	s	s	NOUN
ejpam-3229	54	34	-	-	PUNCT
ejpam-3229	54	35	homomorphism	homomorphism	NOUN
ejpam-3229	54	36	from	from	ADP
ejpam-3229	54	37	m	m	PROPN
ejpam-3229	54	38	to	to	ADP
ejpam-3229	54	39	n	n	PROPN
ejpam-3229	54	40	.	.	PUNCT
ejpam-3229	55	1	definition	definition	NOUN
ejpam-3229	55	2	3	3	NUM
ejpam-3229	55	3	.	.	PUNCT
ejpam-3229	56	1	a	a	DET
ejpam-3229	56	2	right	right	NOUN
ejpam-3229	56	3	s	s	NOUN
ejpam-3229	56	4	-	-	ADJ
ejpam-3229	56	5	actm	actm	ADJ
ejpam-3229	56	6	is	be	AUX
ejpam-3229	56	7	called	call	VERB
ejpam-3229	56	8	quasi	quasi	ADJ
ejpam-3229	56	9	-	-	ADJ
ejpam-3229	56	10	principally	principally	ADV
ejpam-3229	56	11	injective	injective	ADJ
ejpam-3229	56	12	if	if	SCONJ
ejpam-3229	56	13	it	it	PRON
ejpam-3229	56	14	ism	ism	NOUN
ejpam-3229	56	15	-	-	PUNCT
ejpam-3229	56	16	principally	principally	ADV
ejpam-3229	56	17	injective	injective	ADJ
ejpam-3229	56	18	.	.	PUNCT
ejpam-3229	57	1	definition	definition	NOUN
ejpam-3229	57	2	4	4	NUM
ejpam-3229	57	3	.	.	PUNCT
ejpam-3229	58	1	a	a	DET
ejpam-3229	58	2	semigroup	semigroup	NOUN
ejpam-3229	58	3	s	s	NOUN
ejpam-3229	58	4	with	with	ADP
ejpam-3229	58	5	a	a	DET
ejpam-3229	58	6	fixed	fix	VERB
ejpam-3229	58	7	element	element	NOUN
ejpam-3229	58	8	θ	θ	PROPN
ejpam-3229	58	9	is	be	AUX
ejpam-3229	58	10	called	call	VERB
ejpam-3229	58	11	self	self	NOUN
ejpam-3229	58	12	principally	principally	ADV
ejpam-3229	58	13	injective	injective	ADJ
ejpam-3229	58	14	if	if	SCONJ
ejpam-3229	58	15	s	s	VERB
ejpam-3229	58	16	is	be	AUX
ejpam-3229	58	17	s	s	NOUN
ejpam-3229	58	18	-	-	PUNCT
ejpam-3229	58	19	principally	principally	ADV
ejpam-3229	58	20	injective	injective	ADJ
ejpam-3229	58	21	.	.	PUNCT
ejpam-3229	59	1	theorem	theorem	NOUN
ejpam-3229	59	2	1	1	X
ejpam-3229	59	3	.	.	PUNCT
ejpam-3229	60	1	let	let	VERB
ejpam-3229	60	2	m	m	PRON
ejpam-3229	60	3	be	be	AUX
ejpam-3229	60	4	a	a	DET
ejpam-3229	60	5	quasi	quasi	ADJ
ejpam-3229	60	6	-	-	ADJ
ejpam-3229	60	7	principally	principally	ADV
ejpam-3229	60	8	injective	injective	ADJ
ejpam-3229	60	9	s	s	NOUN
ejpam-3229	60	10	-	-	PUNCT
ejpam-3229	60	11	act	act	NOUN
ejpam-3229	60	12	and	and	CCONJ
ejpam-3229	60	13	α	α	NOUN
ejpam-3229	60	14	,	,	PUNCT
ejpam-3229	60	15	β	β	PROPN
ejpam-3229	60	16	∈	∈	PROPN
ejpam-3229	60	17	e.	e.	PROPN
ejpam-3229	60	18	1	1	NUM
ejpam-3229	60	19	)	)	PUNCT
ejpam-3229	60	20	if	if	SCONJ
ejpam-3229	60	21	α	α	PROPN
ejpam-3229	60	22	(	(	PUNCT
ejpam-3229	60	23	m	m	NOUN
ejpam-3229	60	24	)	)	PUNCT
ejpam-3229	60	25	can	can	AUX
ejpam-3229	60	26	be	be	AUX
ejpam-3229	60	27	embedded	embed	VERB
ejpam-3229	60	28	into	into	ADP
ejpam-3229	60	29	β	β	PROPN
ejpam-3229	60	30	(	(	PUNCT
ejpam-3229	60	31	m	m	PROPN
ejpam-3229	60	32	)	)	PUNCT
ejpam-3229	60	33	then	then	ADV
ejpam-3229	60	34	eα	eα	PROPN
ejpam-3229	60	35	is	be	AUX
ejpam-3229	60	36	the	the	DET
ejpam-3229	60	37	e	e	ADJ
ejpam-3229	60	38	-	-	ADJ
ejpam-3229	60	39	homomorphic	homomorphic	ADJ
ejpam-3229	60	40	image	image	NOUN
ejpam-3229	60	41	of	of	ADP
ejpam-3229	60	42	eβ	eβ	NOUN
ejpam-3229	60	43	.	.	PROPN
ejpam-3229	60	44	2	2	NUM
ejpam-3229	60	45	)	)	PUNCT
ejpam-3229	60	46	if	if	SCONJ
ejpam-3229	60	47	β	β	X
ejpam-3229	60	48	(	(	PUNCT
ejpam-3229	60	49	m	m	NOUN
ejpam-3229	60	50	)	)	PUNCT
ejpam-3229	60	51	is	be	AUX
ejpam-3229	60	52	the	the	DET
ejpam-3229	60	53	e	e	ADJ
ejpam-3229	60	54	-	-	ADJ
ejpam-3229	60	55	homomorphic	homomorphic	ADJ
ejpam-3229	60	56	image	image	NOUN
ejpam-3229	60	57	of	of	ADP
ejpam-3229	60	58	α	α	PROPN
ejpam-3229	60	59	(	(	PUNCT
ejpam-3229	60	60	m	m	NOUN
ejpam-3229	60	61	)	)	PUNCT
ejpam-3229	60	62	then	then	ADV
ejpam-3229	60	63	eβ	eβ	NOUN
ejpam-3229	60	64	can	can	AUX
ejpam-3229	60	65	be	be	AUX
ejpam-3229	60	66	embedded	embed	VERB
ejpam-3229	60	67	into	into	ADP
ejpam-3229	60	68	eα	eα	PRON
ejpam-3229	60	69	.	.	PROPN
ejpam-3229	60	70	3	3	NUM
ejpam-3229	60	71	)	)	PUNCT
ejpam-3229	60	72	if	if	SCONJ
ejpam-3229	60	73	α	α	PROPN
ejpam-3229	60	74	(	(	PUNCT
ejpam-3229	60	75	m	m	NOUN
ejpam-3229	60	76	)	)	PUNCT
ejpam-3229	60	77	∼=	∼=	PROPN
ejpam-3229	60	78	β	β	X
ejpam-3229	60	79	(	(	PUNCT
ejpam-3229	60	80	m	m	PROPN
ejpam-3229	60	81	)	)	PUNCT
ejpam-3229	60	82	then	then	ADV
ejpam-3229	60	83	eα	eα	VERB
ejpam-3229	60	84	∼=	∼=	PROPN
ejpam-3229	60	85	eβ	eβ	NOUN
ejpam-3229	60	86	.	.	PUNCT
ejpam-3229	61	1	here	here	ADV
ejpam-3229	61	2	eα	eα	PROPN
ejpam-3229	62	1	=	=	SYM
ejpam-3229	62	2	{	{	PUNCT
ejpam-3229	62	3	uα	uα	X
ejpam-3229	62	4	:	:	PUNCT
ejpam-3229	62	5	u	u	PROPN
ejpam-3229	62	6	∈	∈	PROPN
ejpam-3229	62	7	e	e	NOUN
ejpam-3229	62	8	}	}	PUNCT
ejpam-3229	62	9	and	and	CCONJ
ejpam-3229	62	10	eβ	eβ	NOUN
ejpam-3229	62	11	=	=	PUNCT
ejpam-3229	62	12	{	{	PUNCT
ejpam-3229	62	13	uβ	uβ	NOUN
ejpam-3229	62	14	:	:	PUNCT
ejpam-3229	62	15	u	u	NOUN
ejpam-3229	62	16	∈	∈	PROPN
ejpam-3229	62	17	e	e	NOUN
ejpam-3229	62	18	}	}	PUNCT
ejpam-3229	62	19	.	.	PUNCT
ejpam-3229	63	1	proof	proof	NOUN
ejpam-3229	63	2	.	.	PUNCT
ejpam-3229	64	1	1	1	X
ejpam-3229	64	2	)	)	PUNCT
ejpam-3229	64	3	suppose	suppose	VERB
ejpam-3229	64	4	f	f	X
ejpam-3229	64	5	:	:	PUNCT
ejpam-3229	64	6	α	α	PROPN
ejpam-3229	64	7	(	(	PUNCT
ejpam-3229	64	8	m)→	m)→	PROPN
ejpam-3229	64	9	β	β	X
ejpam-3229	64	10	(	(	PUNCT
ejpam-3229	64	11	m	m	NOUN
ejpam-3229	64	12	)	)	PUNCT
ejpam-3229	64	13	is	be	AUX
ejpam-3229	64	14	an	an	DET
ejpam-3229	64	15	s	s	NOUN
ejpam-3229	64	16	-	-	NOUN
ejpam-3229	64	17	monomorphism	monomorphism	NOUN
ejpam-3229	64	18	.	.	PUNCT
ejpam-3229	65	1	consider	consider	VERB
ejpam-3229	65	2	the	the	DET
ejpam-3229	65	3	inclusions	inclusion	NOUN
ejpam-3229	66	1	i	i	PRON
ejpam-3229	66	2	:	:	PUNCT
ejpam-3229	66	3	α	α	PROPN
ejpam-3229	66	4	(	(	PUNCT
ejpam-3229	66	5	m	m	NOUN
ejpam-3229	66	6	)	)	PUNCT
ejpam-3229	66	7	→	→	SYM
ejpam-3229	66	8	m	m	PROPN
ejpam-3229	66	9	,	,	PUNCT
ejpam-3229	66	10	j	j	NOUN
ejpam-3229	66	11	:	:	PUNCT
ejpam-3229	66	12	β	β	X
ejpam-3229	66	13	(	(	PUNCT
ejpam-3229	66	14	m	m	PROPN
ejpam-3229	66	15	)	)	PUNCT
ejpam-3229	66	16	→	→	SYM
ejpam-3229	66	17	m	m	NOUN
ejpam-3229	66	18	and	and	CCONJ
ejpam-3229	66	19	maps	map	NOUN
ejpam-3229	66	20	α′	α′	NUM
ejpam-3229	66	21	:	:	PUNCT
ejpam-3229	66	22	m	m	VERB
ejpam-3229	66	23	→	→	SYM
ejpam-3229	66	24	α	α	PROPN
ejpam-3229	66	25	(	(	PUNCT
ejpam-3229	66	26	m	m	NOUN
ejpam-3229	66	27	)	)	PUNCT
ejpam-3229	66	28	,	,	PUNCT
ejpam-3229	66	29	β′	β′	NUM
ejpam-3229	66	30	:	:	PUNCT
ejpam-3229	66	31	m	m	VERB
ejpam-3229	66	32	→	→	SYM
ejpam-3229	66	33	β	β	X
ejpam-3229	66	34	(	(	PUNCT
ejpam-3229	66	35	m	m	NOUN
ejpam-3229	66	36	)	)	PUNCT
ejpam-3229	67	1	such	such	ADJ
ejpam-3229	67	2	that	that	SCONJ
ejpam-3229	67	3	α	α	PRON
ejpam-3229	67	4	=	=	NOUN
ejpam-3229	67	5	iα	iα	NOUN
ejpam-3229	67	6	′	′	NOUN
ejpam-3229	68	1	and	and	CCONJ
ejpam-3229	68	2	β	β	X
ejpam-3229	68	3	=	=	SYM
ejpam-3229	68	4	jβ	jβ	PROPN
ejpam-3229	68	5	′	′	INTJ
ejpam-3229	68	6	.	.	PUNCT
ejpam-3229	69	1	now	now	ADV
ejpam-3229	69	2	since	since	ADV
ejpam-3229	69	3	,	,	PUNCT
ejpam-3229	69	4	m	m	VERB
ejpam-3229	69	5	is	be	AUX
ejpam-3229	69	6	quasi	quasi	ADJ
ejpam-3229	69	7	-	-	ADJ
ejpam-3229	69	8	principally	principally	ADV
ejpam-3229	69	9	injective	injective	ADJ
ejpam-3229	69	10	so	so	SCONJ
ejpam-3229	69	11	there	there	PRON
ejpam-3229	69	12	exists	exist	VERB
ejpam-3229	69	13	an	an	DET
ejpam-3229	69	14	s	s	NOUN
ejpam-3229	69	15	-	-	PUNCT
ejpam-3229	69	16	homomorphism	homomorphism	NOUN
ejpam-3229	69	17	g	g	NOUN
ejpam-3229	69	18	:	:	PUNCT
ejpam-3229	69	19	m	m	VERB
ejpam-3229	69	20	→	→	NOUN
ejpam-3229	69	21	m	m	VERB
ejpam-3229	69	22	such	such	ADJ
ejpam-3229	69	23	that	that	SCONJ
ejpam-3229	69	24	,	,	PUNCT
ejpam-3229	69	25	jf	jf	PROPN
ejpam-3229	69	26	=	=	NOUN
ejpam-3229	69	27	gi	gi	PROPN
ejpam-3229	69	28	,	,	PUNCT
ejpam-3229	69	29	where	where	SCONJ
ejpam-3229	69	30	g	g	PROPN
ejpam-3229	69	31	extends	extend	VERB
ejpam-3229	69	32	f	f	PROPN
ejpam-3229	69	33	.	.	PUNCT
ejpam-3229	70	1	moreover	moreover	ADV
ejpam-3229	70	2	,	,	PUNCT
ejpam-3229	70	3	since	since	SCONJ
ejpam-3229	70	4	g(α(m	g(α(m	PROPN
ejpam-3229	70	5	)	)	PUNCT
ejpam-3229	70	6	)	)	PUNCT
ejpam-3229	70	7	=	=	PUNCT
ejpam-3229	70	8	β(m′	β(m′	X
ejpam-3229	70	9	)	)	PUNCT
ejpam-3229	70	10	∈	∈	PROPN
ejpam-3229	70	11	β	β	X
ejpam-3229	70	12	(	(	PUNCT
ejpam-3229	70	13	m	m	PROPN
ejpam-3229	70	14	)	)	PUNCT
ejpam-3229	70	15	,	,	PUNCT
ejpam-3229	70	16	for	for	ADP
ejpam-3229	70	17	some	some	DET
ejpam-3229	70	18	m′	m′	NUM
ejpam-3229	70	19	∈m	∈m	NOUN
ejpam-3229	70	20	,	,	PUNCT
ejpam-3229	70	21	therefore	therefore	ADV
ejpam-3229	70	22	gα	gα	ADP
ejpam-3229	70	23	(	(	PUNCT
ejpam-3229	70	24	m	m	NOUN
ejpam-3229	70	25	)	)	PUNCT
ejpam-3229	70	26	⊆	⊆	NUM
ejpam-3229	70	27	β	β	X
ejpam-3229	70	28	(	(	PUNCT
ejpam-3229	70	29	m	m	NOUN
ejpam-3229	70	30	)	)	PUNCT
ejpam-3229	70	31	.	.	PUNCT
ejpam-3229	71	1	define	define	VERB
ejpam-3229	71	2	φ	φ	NOUN
ejpam-3229	71	3	:	:	PUNCT
ejpam-3229	71	4	eβ	eβ	NOUN
ejpam-3229	71	5	→	→	SYM
ejpam-3229	71	6	eα	eα	NOUN
ejpam-3229	71	7	by	by	ADP
ejpam-3229	71	8	φ(uβ	φ(uβ	NOUN
ejpam-3229	71	9	)	)	PUNCT
ejpam-3229	71	10	=	=	SYM
ejpam-3229	72	1	ugα	ugα	NOUN
ejpam-3229	72	2	.	.	PUNCT
ejpam-3229	73	1	we	we	PRON
ejpam-3229	73	2	claim	claim	VERB
ejpam-3229	73	3	that	that	SCONJ
ejpam-3229	73	4	φ	φ	PROPN
ejpam-3229	73	5	is	be	AUX
ejpam-3229	73	6	e	e	NOUN
ejpam-3229	73	7	-	-	NOUN
ejpam-3229	73	8	epimorphism	epimorphism	NOUN
ejpam-3229	73	9	.	.	PUNCT
ejpam-3229	74	1	in	in	ADP
ejpam-3229	74	2	order	order	NOUN
ejpam-3229	74	3	to	to	PART
ejpam-3229	74	4	see	see	VERB
ejpam-3229	74	5	that	that	SCONJ
ejpam-3229	74	6	φ	φ	PROPN
ejpam-3229	74	7	is	be	AUX
ejpam-3229	74	8	well	well	ADV
ejpam-3229	74	9	-	-	PUNCT
ejpam-3229	74	10	defined	define	VERB
ejpam-3229	74	11	,	,	PUNCT
ejpam-3229	74	12	take	take	VERB
ejpam-3229	74	13	uβ	uβ	PROPN
ejpam-3229	74	14	,	,	PUNCT
ejpam-3229	74	15	vβ	vβ	PRON
ejpam-3229	74	16	∈	∈	PROPN
ejpam-3229	74	17	eβ	eβ	VERB
ejpam-3229	74	18	such	such	ADJ
ejpam-3229	74	19	that	that	PRON
ejpam-3229	74	20	uβ	uβ	NOUN
ejpam-3229	74	21	=	=	NOUN
ejpam-3229	74	22	vβ	vβ	PROPN
ejpam-3229	74	23	.	.	PUNCT
ejpam-3229	74	24	suppose	suppose	VERB
ejpam-3229	74	25	contrary	contrary	ADJ
ejpam-3229	74	26	that	that	SCONJ
ejpam-3229	74	27	φ(uβ	φ(uβ	NOUN
ejpam-3229	74	28	)	)	PUNCT
ejpam-3229	74	29	6=	6=	ADP
ejpam-3229	74	30	φ(vβ	φ(vβ	NOUN
ejpam-3229	74	31	)	)	PUNCT
ejpam-3229	74	32	i.e.	i.e.	X
ejpam-3229	74	33	ugα	ugα	PROPN
ejpam-3229	74	34	6=	6=	SYM
ejpam-3229	74	35	vgα	vgα	NOUN
ejpam-3229	74	36	,	,	PUNCT
ejpam-3229	74	37	so	so	SCONJ
ejpam-3229	74	38	there	there	PRON
ejpam-3229	74	39	exists	exist	VERB
ejpam-3229	74	40	m	m	VERB
ejpam-3229	74	41	∈	∈	PROPN
ejpam-3229	74	42	m	m	VERB
ejpam-3229	74	43	such	such	ADJ
ejpam-3229	74	44	that	that	PRON
ejpam-3229	74	45	ugα(m	ugα(m	PROPN
ejpam-3229	74	46	)	)	PUNCT
ejpam-3229	74	47	6=	6=	NUM
ejpam-3229	74	48	vgα(m	vgα(m	PROPN
ejpam-3229	74	49	)	)	PUNCT
ejpam-3229	74	50	,	,	PUNCT
ejpam-3229	74	51	but	but	CCONJ
ejpam-3229	74	52	g(m	g(m	X
ejpam-3229	74	53	)	)	PUNCT
ejpam-3229	74	54	=	=	PUNCT
ejpam-3229	74	55	β(m′	β(m′	NOUN
ejpam-3229	74	56	)	)	PUNCT
ejpam-3229	74	57	for	for	ADP
ejpam-3229	74	58	some	some	DET
ejpam-3229	74	59	m′	m′	NUM
ejpam-3229	74	60	∈	∈	PROPN
ejpam-3229	74	61	m.	m.	NOUN
ejpam-3229	74	62	thus	thus	ADV
ejpam-3229	74	63	uβ(m′	uβ(m′	PROPN
ejpam-3229	74	64	)	)	PUNCT
ejpam-3229	74	65	6=	6=	ADP
ejpam-3229	75	1	vβ(m′	vβ(m′	NOUN
ejpam-3229	75	2	)	)	PUNCT
ejpam-3229	75	3	this	this	PRON
ejpam-3229	75	4	leads	lead	VERB
ejpam-3229	75	5	to	to	ADP
ejpam-3229	75	6	a	a	DET
ejpam-3229	75	7	contradiction	contradiction	NOUN
ejpam-3229	75	8	.	.	PUNCT
ejpam-3229	76	1	now	now	ADV
ejpam-3229	76	2	for	for	ADP
ejpam-3229	76	3	any	any	DET
ejpam-3229	76	4	uβ	uβ	PROPN
ejpam-3229	76	5	∈	∈	PROPN
ejpam-3229	76	6	eβ	eβ	NOUN
ejpam-3229	76	7	,	,	PUNCT
ejpam-3229	76	8	φ(γ(uβ	φ(γ(uβ	NOUN
ejpam-3229	76	9	)	)	PUNCT
ejpam-3229	76	10	)	)	PUNCT
ejpam-3229	77	1	=	=	PUNCT
ejpam-3229	77	2	φ((γu)β	φ((γu)β	PROPN
ejpam-3229	77	3	)	)	PUNCT
ejpam-3229	77	4	=	=	SYM
ejpam-3229	77	5	(	(	PUNCT
ejpam-3229	77	6	γu)gα	γu)gα	PUNCT
ejpam-3229	77	7	=	=	SYM
ejpam-3229	77	8	γ(ugα	γ(ugα	PROPN
ejpam-3229	77	9	)	)	PUNCT
ejpam-3229	77	10	=	=	SYM
ejpam-3229	77	11	γφ(uβ	γφ(uβ	NOUN
ejpam-3229	77	12	)	)	PUNCT
ejpam-3229	77	13	,	,	PUNCT
ejpam-3229	77	14	for	for	ADP
ejpam-3229	77	15	all	all	DET
ejpam-3229	77	16	γ	γ	PROPN
ejpam-3229	77	17	∈	∈	PROPN
ejpam-3229	77	18	e.	e.	PROPN
ejpam-3229	77	19	so	so	PROPN
ejpam-3229	77	20	φ	φ	PROPN
ejpam-3229	77	21	is	be	AUX
ejpam-3229	77	22	an	an	DET
ejpam-3229	77	23	e	e	NOUN
ejpam-3229	77	24	-	-	NOUN
ejpam-3229	77	25	homomorphism	homomorphism	NOUN
ejpam-3229	77	26	.	.	PUNCT
ejpam-3229	78	1	to	to	PART
ejpam-3229	78	2	see	see	VERB
ejpam-3229	78	3	surjectivity	surjectivity	NOUN
ejpam-3229	78	4	of	of	ADP
ejpam-3229	78	5	φ	φ	PROPN
ejpam-3229	78	6	,	,	PUNCT
ejpam-3229	78	7	let	let	VERB
ejpam-3229	78	8	uα	uα	PRON
ejpam-3229	78	9	∈	∈	PROPN
ejpam-3229	78	10	eα	eα	NOUN
ejpam-3229	78	11	,	,	PUNCT
ejpam-3229	78	12	where	where	SCONJ
ejpam-3229	78	13	u	u	PROPN
ejpam-3229	78	14	∈	∈	PROPN
ejpam-3229	78	15	m.	m.	NOUN
ejpam-3229	78	16	consider	consider	VERB
ejpam-3229	78	17	ui	ui	PROPN
ejpam-3229	78	18	:	:	PUNCT
ejpam-3229	78	19	α	α	PROPN
ejpam-3229	78	20	(	(	PUNCT
ejpam-3229	78	21	m	m	NOUN
ejpam-3229	78	22	)	)	PUNCT
ejpam-3229	78	23	→m	→m	PROPN
ejpam-3229	78	24	,	,	PUNCT
ejpam-3229	78	25	since	since	SCONJ
ejpam-3229	78	26	m	m	PROPN
ejpam-3229	78	27	is	be	AUX
ejpam-3229	78	28	quasi	quasi	ADJ
ejpam-3229	78	29	-	-	ADJ
ejpam-3229	78	30	principally	principally	ADV
ejpam-3229	78	31	injective	injective	ADJ
ejpam-3229	78	32	so	so	SCONJ
ejpam-3229	78	33	there	there	PRON
ejpam-3229	78	34	exists	exist	VERB
ejpam-3229	78	35	γ	γ	X
ejpam-3229	78	36	:	:	PUNCT
ejpam-3229	78	37	m→m	m→m	VERB
ejpam-3229	78	38	such	such	ADJ
ejpam-3229	78	39	that	that	SCONJ
ejpam-3229	78	40	γjf	γjf	ADP
ejpam-3229	78	41	=	=	SYM
ejpam-3229	78	42	ui	ui	PROPN
ejpam-3229	78	43	.	.	PROPN
ejpam-3229	78	44	consider	consider	VERB
ejpam-3229	78	45	φ(γβ	φ(γβ	NOUN
ejpam-3229	78	46	)	)	PUNCT
ejpam-3229	78	47	=	=	SYM
ejpam-3229	78	48	γgα	γgα	NOUN
ejpam-3229	78	49	=	=	SYM
ejpam-3229	78	50	γgiα′	γgiα′	X
ejpam-3229	79	1	=	=	PUNCT
ejpam-3229	79	2	γjfα′	γjfα′	NOUN
ejpam-3229	80	1	=	=	PUNCT
ejpam-3229	80	2	uiα′	uiα′	ADJ
ejpam-3229	80	3	=	=	PUNCT
ejpam-3229	80	4	uα	uα	PROPN
ejpam-3229	80	5	.	.	PUNCT
ejpam-3229	81	1	thus	thus	ADV
ejpam-3229	81	2	φ	φ	PRON
ejpam-3229	81	3	:	:	PUNCT
ejpam-3229	81	4	eβ	eβ	NOUN
ejpam-3229	81	5	→	→	SYM
ejpam-3229	81	6	eα	eα	PROPN
ejpam-3229	81	7	is	be	AUX
ejpam-3229	81	8	an	an	DET
ejpam-3229	81	9	e	e	NOUN
ejpam-3229	81	10	-	-	NOUN
ejpam-3229	81	11	epimorphism	epimorphism	NOUN
ejpam-3229	81	12	.	.	PUNCT
ejpam-3229	82	1	2	2	X
ejpam-3229	82	2	)	)	PUNCT
ejpam-3229	82	3	let	let	VERB
ejpam-3229	82	4	us	we	PRON
ejpam-3229	82	5	keep	keep	VERB
ejpam-3229	82	6	the	the	DET
ejpam-3229	82	7	same	same	ADJ
ejpam-3229	82	8	notation	notation	NOUN
ejpam-3229	82	9	as	as	ADP
ejpam-3229	82	10	in	in	ADP
ejpam-3229	82	11	part	part	NOUN
ejpam-3229	82	12	1	1	NUM
ejpam-3229	82	13	)	)	PUNCT
ejpam-3229	82	14	of	of	ADP
ejpam-3229	82	15	proof	proof	NOUN
ejpam-3229	82	16	.	.	PUNCT
ejpam-3229	83	1	let	let	VERB
ejpam-3229	83	2	f	f	NOUN
ejpam-3229	83	3	:	:	PUNCT
ejpam-3229	83	4	α	α	PROPN
ejpam-3229	83	5	(	(	PUNCT
ejpam-3229	83	6	m	m	NOUN
ejpam-3229	83	7	)	)	PUNCT
ejpam-3229	83	8	→	→	SYM
ejpam-3229	83	9	β	β	X
ejpam-3229	83	10	(	(	PUNCT
ejpam-3229	83	11	m	m	NOUN
ejpam-3229	83	12	)	)	PUNCT
ejpam-3229	83	13	be	be	AUX
ejpam-3229	83	14	an	an	DET
ejpam-3229	83	15	s	s	NOUN
ejpam-3229	83	16	-	-	PUNCT
ejpam-3229	83	17	epimorphism	epimorphism	NOUN
ejpam-3229	83	18	and	and	CCONJ
ejpam-3229	83	19	we	we	PRON
ejpam-3229	83	20	also	also	ADV
ejpam-3229	83	21	have	have	VERB
ejpam-3229	83	22	jf	jf	PROPN
ejpam-3229	83	23	=	=	NOUN
ejpam-3229	83	24	gi	gi	PROPN
ejpam-3229	83	25	.	.	PUNCT
ejpam-3229	84	1	define	define	VERB
ejpam-3229	84	2	φ	φ	PROPN
ejpam-3229	84	3	:	:	PUNCT
ejpam-3229	84	4	eβ	eβ	NOUN
ejpam-3229	84	5	→	→	SYM
ejpam-3229	84	6	eα	eα	NOUN
ejpam-3229	84	7	by	by	ADP
ejpam-3229	84	8	φ(uβ	φ(uβ	NOUN
ejpam-3229	84	9	)	)	PUNCT
ejpam-3229	84	10	=	=	SYM
ejpam-3229	84	11	ugα	ugα	NOUN
ejpam-3229	84	12	.	.	PUNCT
ejpam-3229	85	1	the	the	DET
ejpam-3229	85	2	map	map	NOUN
ejpam-3229	85	3	is	be	AUX
ejpam-3229	85	4	well	well	ADV
ejpam-3229	85	5	-	-	PUNCT
ejpam-3229	85	6	defined	define	VERB
ejpam-3229	85	7	and	and	CCONJ
ejpam-3229	85	8	an	an	DET
ejpam-3229	85	9	e	e	NOUN
ejpam-3229	85	10	-	-	NOUN
ejpam-3229	85	11	homomorphism	homomorphism	NOUN
ejpam-3229	85	12	as	as	SCONJ
ejpam-3229	85	13	is	be	AUX
ejpam-3229	85	14	in	in	ADP
ejpam-3229	85	15	1	1	NUM
ejpam-3229	85	16	)	)	PUNCT
ejpam-3229	85	17	.	.	PUNCT
ejpam-3229	86	1	moreover	moreover	ADV
ejpam-3229	86	2	,	,	PUNCT
ejpam-3229	86	3	β	β	X
ejpam-3229	86	4	(	(	PUNCT
ejpam-3229	86	5	m	m	NOUN
ejpam-3229	86	6	)	)	PUNCT
ejpam-3229	86	7	=	=	NOUN
ejpam-3229	86	8	gα	gα	NOUN
ejpam-3229	86	9	(	(	PUNCT
ejpam-3229	86	10	m	m	NOUN
ejpam-3229	86	11	)	)	PUNCT
ejpam-3229	86	12	.	.	PUNCT
ejpam-3229	87	1	to	to	PART
ejpam-3229	87	2	show	show	VERB
ejpam-3229	87	3	injectivity	injectivity	NOUN
ejpam-3229	87	4	of	of	ADP
ejpam-3229	87	5	φ	φ	PROPN
ejpam-3229	87	6	,	,	PUNCT
ejpam-3229	87	7	we	we	PRON
ejpam-3229	87	8	let	let	VERB
ejpam-3229	87	9	uβ	uβ	PRON
ejpam-3229	87	10	,	,	PUNCT
ejpam-3229	87	11	vβ	vβ	PRON
ejpam-3229	87	12	∈	∈	PROPN
ejpam-3229	87	13	eβ	eβ	VERB
ejpam-3229	87	14	such	such	ADJ
ejpam-3229	87	15	that	that	DET
ejpam-3229	87	16	uβ	uβ	PROPN
ejpam-3229	87	17	6=	6=	ADP
ejpam-3229	87	18	vβ	vβ	ADP
ejpam-3229	87	19	so	so	ADV
ejpam-3229	87	20	uβ(m′	uβ(m′	ADJ
ejpam-3229	87	21	)	)	PUNCT
ejpam-3229	87	22	6=	6=	ADP
ejpam-3229	88	1	vβ(m′	vβ(m′	NOUN
ejpam-3229	88	2	)	)	PUNCT
ejpam-3229	88	3	for	for	ADP
ejpam-3229	88	4	some	some	DET
ejpam-3229	88	5	m′	m′	NUM
ejpam-3229	88	6	∈	∈	PROPN
ejpam-3229	88	7	m.	m.	NOUN
ejpam-3229	88	8	now	now	ADV
ejpam-3229	88	9	gα(m	gα(m	VERB
ejpam-3229	88	10	)	)	PUNCT
ejpam-3229	88	11	=	=	SYM
ejpam-3229	89	1	β(m′	β(m′	NOUN
ejpam-3229	89	2	)	)	PUNCT
ejpam-3229	89	3	for	for	ADP
ejpam-3229	89	4	some	some	DET
ejpam-3229	89	5	m	m	NOUN
ejpam-3229	89	6	∈	∈	NOUN
ejpam-3229	89	7	m	m	NOUN
ejpam-3229	89	8	,	,	PUNCT
ejpam-3229	89	9	which	which	PRON
ejpam-3229	89	10	implies	imply	VERB
ejpam-3229	89	11	that	that	SCONJ
ejpam-3229	89	12	ugα(m	ugα(m	PROPN
ejpam-3229	89	13	)	)	PUNCT
ejpam-3229	89	14	6=	6=	NUM
ejpam-3229	90	1	vgα(m	vgα(m	PROPN
ejpam-3229	90	2	)	)	PUNCT
ejpam-3229	90	3	and	and	CCONJ
ejpam-3229	90	4	therefore	therefore	ADV
ejpam-3229	90	5	ugα	ugα	PROPN
ejpam-3229	90	6	6=	6=	PROPN
ejpam-3229	90	7	vgα	vgα	NOUN
ejpam-3229	90	8	hence	hence	ADV
ejpam-3229	90	9	φ(uβ	φ(uβ	NOUN
ejpam-3229	90	10	)	)	PUNCT
ejpam-3229	90	11	6=	6=	ADP
ejpam-3229	90	12	φ(vβ	φ(vβ	NOUN
ejpam-3229	90	13	)	)	PUNCT
ejpam-3229	90	14	.	.	PUNCT
ejpam-3229	91	1	3	3	X
ejpam-3229	91	2	)	)	PUNCT
ejpam-3229	91	3	a	a	DET
ejpam-3229	91	4	direct	direct	ADJ
ejpam-3229	91	5	consequence	consequence	NOUN
ejpam-3229	91	6	of	of	ADP
ejpam-3229	91	7	1	1	NUM
ejpam-3229	91	8	)	)	PUNCT
ejpam-3229	91	9	and	and	CCONJ
ejpam-3229	91	10	2	2	NUM
ejpam-3229	91	11	)	)	PUNCT
ejpam-3229	91	12	.	.	PUNCT
ejpam-3229	92	1	an	an	DET
ejpam-3229	92	2	immediate	immediate	ADJ
ejpam-3229	92	3	corollary	corollary	NOUN
ejpam-3229	92	4	of	of	ADP
ejpam-3229	92	5	last	last	ADJ
ejpam-3229	92	6	theorem	theorem	NOUN
ejpam-3229	92	7	is	be	AUX
ejpam-3229	92	8	following	follow	VERB
ejpam-3229	92	9	.	.	PUNCT
ejpam-3229	93	1	j.	j.	PROPN
ejpam-3229	93	2	hussain	hussain	PROPN
ejpam-3229	93	3	,	,	PUNCT
ejpam-3229	93	4	m.shabir	m.shabir	PROPN
ejpam-3229	93	5	/	/	SYM
ejpam-3229	93	6	eur	eur	PROPN
ejpam-3229	93	7	.	.	PUNCT
ejpam-3229	94	1	j.	j.	PROPN
ejpam-3229	94	2	pure	pure	PROPN
ejpam-3229	94	3	appl	appl	PROPN
ejpam-3229	94	4	.	.	PROPN
ejpam-3229	94	5	math	math	PROPN
ejpam-3229	94	6	,	,	PUNCT
ejpam-3229	94	7	11	11	NUM
ejpam-3229	94	8	(	(	PUNCT
ejpam-3229	94	9	2	2	NUM
ejpam-3229	94	10	)	)	PUNCT
ejpam-3229	94	11	(	(	PUNCT
ejpam-3229	94	12	2018	2018	NUM
ejpam-3229	94	13	)	)	PUNCT
ejpam-3229	94	14	,	,	PUNCT
ejpam-3229	94	15	431	431	NUM
ejpam-3229	94	16	-	-	SYM
ejpam-3229	94	17	443	443	NUM
ejpam-3229	94	18	434	434	NUM
ejpam-3229	94	19	corollary	corollary	ADJ
ejpam-3229	94	20	1	1	NUM
ejpam-3229	94	21	.	.	PUNCT
ejpam-3229	95	1	let	let	VERB
ejpam-3229	95	2	s	s	PRON
ejpam-3229	95	3	be	be	AUX
ejpam-3229	95	4	a	a	DET
ejpam-3229	95	5	right	right	ADJ
ejpam-3229	95	6	self	self	NOUN
ejpam-3229	95	7	-	-	PUNCT
ejpam-3229	95	8	principally	principally	ADV
ejpam-3229	95	9	injective	injective	ADJ
ejpam-3229	95	10	semigroup	semigroup	NOUN
ejpam-3229	95	11	and	and	CCONJ
ejpam-3229	95	12	a	a	DET
ejpam-3229	95	13	,	,	PUNCT
ejpam-3229	95	14	b	b	X
ejpam-3229	95	15	∈	∈	PROPN
ejpam-3229	95	16	s	s	AUX
ejpam-3229	95	17	then	then	ADV
ejpam-3229	95	18	following	follow	VERB
ejpam-3229	95	19	are	be	AUX
ejpam-3229	95	20	equivalent	equivalent	ADJ
ejpam-3229	95	21	:	:	PUNCT
ejpam-3229	95	22	1	1	X
ejpam-3229	95	23	)	)	PUNCT
ejpam-3229	95	24	if	if	SCONJ
ejpam-3229	95	25	bs	bs	PROPN
ejpam-3229	95	26	embeds	embed	VERB
ejpam-3229	95	27	in	in	ADP
ejpam-3229	95	28	as	as	SCONJ
ejpam-3229	95	29	then	then	ADV
ejpam-3229	95	30	sb	sb	PROPN
ejpam-3229	95	31	is	be	AUX
ejpam-3229	95	32	a	a	DET
ejpam-3229	95	33	homomorphic	homomorphic	ADJ
ejpam-3229	95	34	image	image	NOUN
ejpam-3229	95	35	of	of	ADP
ejpam-3229	95	36	sa	sa	PROPN
ejpam-3229	95	37	.	.	PROPN
ejpam-3229	95	38	2	2	NUM
ejpam-3229	95	39	)	)	PUNCT
ejpam-3229	95	40	if	if	SCONJ
ejpam-3229	95	41	as	as	SCONJ
ejpam-3229	95	42	is	be	AUX
ejpam-3229	95	43	a	a	DET
ejpam-3229	95	44	homomorphic	homomorphic	ADJ
ejpam-3229	95	45	image	image	NOUN
ejpam-3229	95	46	of	of	ADP
ejpam-3229	95	47	bs	bs	PROPN
ejpam-3229	95	48	then	then	ADV
ejpam-3229	95	49	sb	sb	PROPN
ejpam-3229	95	50	can	can	AUX
ejpam-3229	95	51	be	be	AUX
ejpam-3229	95	52	embedded	embed	VERB
ejpam-3229	95	53	in	in	ADP
ejpam-3229	95	54	sa	sa	PROPN
ejpam-3229	95	55	.	.	PROPN
ejpam-3229	96	1	3	3	X
ejpam-3229	96	2	)	)	PUNCT
ejpam-3229	96	3	if	if	SCONJ
ejpam-3229	96	4	bs	bs	NOUN
ejpam-3229	96	5	∼=	∼=	PROPN
ejpam-3229	96	6	as	as	SCONJ
ejpam-3229	96	7	then	then	ADV
ejpam-3229	96	8	sb	sb	PROPN
ejpam-3229	96	9	∼=	∼=	PROPN
ejpam-3229	96	10	sa	sa	PROPN
ejpam-3229	96	11	.	.	PUNCT
ejpam-3229	96	12	theorem	theorem	NOUN
ejpam-3229	96	13	2	2	NUM
ejpam-3229	96	14	.	.	PUNCT
ejpam-3229	97	1	if	if	SCONJ
ejpam-3229	97	2	m	m	NOUN
ejpam-3229	97	3	be	be	VERB
ejpam-3229	97	4	a	a	DET
ejpam-3229	97	5	right	right	ADJ
ejpam-3229	97	6	s	s	NOUN
ejpam-3229	97	7	-	-	PUNCT
ejpam-3229	97	8	act	act	NOUN
ejpam-3229	97	9	then	then	ADV
ejpam-3229	97	10	,	,	PUNCT
ejpam-3229	97	11	for	for	ADP
ejpam-3229	97	12	all	all	DET
ejpam-3229	97	13	α	α	NOUN
ejpam-3229	97	14	,	,	PUNCT
ejpam-3229	97	15	β	β	X
ejpam-3229	97	16	∈	∈	PROPN
ejpam-3229	97	17	e	e	NOUN
ejpam-3229	97	18	,	,	PUNCT
ejpam-3229	97	19	following	follow	VERB
ejpam-3229	97	20	are	be	AUX
ejpam-3229	97	21	equivalent	equivalent	ADJ
ejpam-3229	97	22	.	.	PUNCT
ejpam-3229	98	1	1	1	X
ejpam-3229	98	2	)	)	PUNCT
ejpam-3229	98	3	m	m	VERB
ejpam-3229	98	4	is	be	AUX
ejpam-3229	98	5	quasi	quasi	ADJ
ejpam-3229	98	6	-	-	ADJ
ejpam-3229	98	7	principally	principally	ADV
ejpam-3229	98	8	injective	injective	ADJ
ejpam-3229	98	9	.	.	PUNCT
ejpam-3229	99	1	2	2	X
ejpam-3229	99	2	)	)	PUNCT
ejpam-3229	99	3	if	if	SCONJ
ejpam-3229	99	4	anne(kerα	anne(kerα	PROPN
ejpam-3229	99	5	)	)	PUNCT
ejpam-3229	100	1	=	=	PRON
ejpam-3229	100	2	{	{	PUNCT
ejpam-3229	100	3	β	β	X
ejpam-3229	100	4	∈	∈	PROPN
ejpam-3229	100	5	e	e	NOUN
ejpam-3229	100	6	:	:	PUNCT
ejpam-3229	100	7	kerα	kerα	PROPN
ejpam-3229	100	8	⊆	⊆	NUM
ejpam-3229	100	9	kerβ	kerβ	PROPN
ejpam-3229	100	10	}	}	PUNCT
ejpam-3229	100	11	then	then	ADV
ejpam-3229	100	12	anne(kerα	anne(kerα	PROPN
ejpam-3229	100	13	)	)	PUNCT
ejpam-3229	100	14	=	=	SYM
ejpam-3229	100	15	eα	eα	X
ejpam-3229	100	16	.	.	NOUN
ejpam-3229	100	17	3	3	NUM
ejpam-3229	100	18	)	)	PUNCT
ejpam-3229	100	19	if	if	SCONJ
ejpam-3229	100	20	kerβ	kerβ	PROPN
ejpam-3229	100	21	⊆	⊆	NUM
ejpam-3229	100	22	kerα	kerα	NOUN
ejpam-3229	100	23	then	then	ADV
ejpam-3229	100	24	eα	eα	VERB
ejpam-3229	100	25	⊆	⊆	NUM
ejpam-3229	100	26	eβ	eβ	NOUN
ejpam-3229	100	27	.	.	PUNCT
ejpam-3229	101	1	proof	proof	NOUN
ejpam-3229	101	2	.	.	PUNCT
ejpam-3229	102	1	1)⇒2	1)⇒2	NUM
ejpam-3229	102	2	)	)	PUNCT
ejpam-3229	102	3	let	let	VERB
ejpam-3229	102	4	uα	uα	PROPN
ejpam-3229	102	5	∈	∈	PROPN
ejpam-3229	102	6	eα	eα	NOUN
ejpam-3229	102	7	,	,	PUNCT
ejpam-3229	102	8	where	where	SCONJ
ejpam-3229	102	9	u	u	PROPN
ejpam-3229	102	10	∈	∈	PROPN
ejpam-3229	102	11	e.	e.	PROPN
ejpam-3229	102	12	to	to	PART
ejpam-3229	102	13	show	show	VERB
ejpam-3229	102	14	that	that	SCONJ
ejpam-3229	102	15	uα	uα	PROPN
ejpam-3229	102	16	∈	∈	PROPN
ejpam-3229	102	17	anne(kerα	anne(kerα	PROPN
ejpam-3229	102	18	)	)	PUNCT
ejpam-3229	102	19	,	,	PUNCT
ejpam-3229	102	20	we	we	PRON
ejpam-3229	102	21	need	need	VERB
ejpam-3229	102	22	to	to	PART
ejpam-3229	102	23	show	show	VERB
ejpam-3229	102	24	that	that	SCONJ
ejpam-3229	102	25	kerα	kerα	ADJ
ejpam-3229	102	26	⊆	⊆	NUM
ejpam-3229	102	27	keruα	keruα	NOUN
ejpam-3229	102	28	.	.	PUNCT
ejpam-3229	103	1	let	let	VERB
ejpam-3229	103	2	(	(	PUNCT
ejpam-3229	103	3	x	x	NOUN
ejpam-3229	103	4	,	,	PUNCT
ejpam-3229	103	5	y	y	NOUN
ejpam-3229	103	6	)	)	PUNCT
ejpam-3229	103	7	∈	∈	PROPN
ejpam-3229	103	8	kerα	kerα	NOUN
ejpam-3229	103	9	,	,	PUNCT
ejpam-3229	103	10	we	we	PRON
ejpam-3229	103	11	have	have	VERB
ejpam-3229	103	12	α(x	α(x	NOUN
ejpam-3229	103	13	)	)	PUNCT
ejpam-3229	104	1	=	=	SYM
ejpam-3229	104	2	α(y	α(y	NOUN
ejpam-3229	104	3	)	)	PUNCT
ejpam-3229	104	4	so	so	ADV
ejpam-3229	104	5	uα(x	uα(x	NOUN
ejpam-3229	104	6	)	)	PUNCT
ejpam-3229	104	7	=	=	SYM
ejpam-3229	104	8	uα(y	uα(y	NOUN
ejpam-3229	104	9	)	)	PUNCT
ejpam-3229	104	10	,	,	PUNCT
ejpam-3229	104	11	which	which	PRON
ejpam-3229	104	12	implies	imply	VERB
ejpam-3229	104	13	(	(	PUNCT
ejpam-3229	104	14	x	x	X
ejpam-3229	104	15	,	,	PUNCT
ejpam-3229	104	16	y	y	NOUN
ejpam-3229	104	17	)	)	PUNCT
ejpam-3229	104	18	∈	∈	PROPN
ejpam-3229	104	19	keruα	keruα	NOUN
ejpam-3229	104	20	,	,	PUNCT
ejpam-3229	104	21	it	it	PRON
ejpam-3229	104	22	follows	follow	VERB
ejpam-3229	104	23	that	that	SCONJ
ejpam-3229	104	24	kerα	kerα	ADV
ejpam-3229	104	25	⊆	⊆	NUM
ejpam-3229	104	26	keruα	keruα	ADJ
ejpam-3229	104	27	and	and	CCONJ
ejpam-3229	104	28	so	so	ADV
ejpam-3229	104	29	uα	uα	PROPN
ejpam-3229	104	30	∈	∈	PROPN
ejpam-3229	104	31	anne(kerα	anne(kerα	PROPN
ejpam-3229	104	32	)	)	PUNCT
ejpam-3229	104	33	.	.	PUNCT
ejpam-3229	105	1	for	for	ADP
ejpam-3229	105	2	reverse	reverse	ADJ
ejpam-3229	105	3	inclusion	inclusion	NOUN
ejpam-3229	105	4	,	,	PUNCT
ejpam-3229	105	5	let	let	VERB
ejpam-3229	105	6	β	β	X
ejpam-3229	105	7	∈	∈	PROPN
ejpam-3229	105	8	anne(kerα	anne(kerα	PROPN
ejpam-3229	105	9	)	)	PUNCT
ejpam-3229	105	10	so	so	ADV
ejpam-3229	105	11	kerα	kerα	ADV
ejpam-3229	105	12	⊆	⊆	NUM
ejpam-3229	105	13	kerβ	kerβ	NOUN
ejpam-3229	105	14	.	.	PUNCT
ejpam-3229	106	1	consider	consider	VERB
ejpam-3229	106	2	α′	α′	NUM
ejpam-3229	106	3	:	:	PUNCT
ejpam-3229	106	4	m	m	VERB
ejpam-3229	106	5	→	→	SYM
ejpam-3229	106	6	α	α	PROPN
ejpam-3229	106	7	(	(	PUNCT
ejpam-3229	106	8	m	m	NOUN
ejpam-3229	106	9	)	)	PUNCT
ejpam-3229	106	10	and	and	CCONJ
ejpam-3229	106	11	β′	β′	NUM
ejpam-3229	106	12	:	:	PUNCT
ejpam-3229	107	1	m	m	VERB
ejpam-3229	107	2	→	→	SYM
ejpam-3229	107	3	β	β	X
ejpam-3229	107	4	(	(	PUNCT
ejpam-3229	107	5	m)induced	m)induce	VERB
ejpam-3229	107	6	by	by	ADP
ejpam-3229	107	7	α	α	PROPN
ejpam-3229	107	8	and	and	CCONJ
ejpam-3229	107	9	β	β	X
ejpam-3229	107	10	.	.	PUNCT
ejpam-3229	108	1	if	if	SCONJ
ejpam-3229	108	2	i	i	PRON
ejpam-3229	108	3	:	:	PUNCT
ejpam-3229	108	4	α	α	PROPN
ejpam-3229	108	5	(	(	PUNCT
ejpam-3229	108	6	m	m	NOUN
ejpam-3229	108	7	)	)	PUNCT
ejpam-3229	108	8	→	→	SYM
ejpam-3229	108	9	m	m	PROPN
ejpam-3229	108	10	and	and	CCONJ
ejpam-3229	108	11	j	j	PROPN
ejpam-3229	108	12	:	:	PUNCT
ejpam-3229	108	13	β	β	X
ejpam-3229	108	14	(	(	PUNCT
ejpam-3229	108	15	m	m	PROPN
ejpam-3229	108	16	)	)	PUNCT
ejpam-3229	108	17	→	→	PUNCT
ejpam-3229	108	18	m	m	NOUN
ejpam-3229	108	19	are	be	AUX
ejpam-3229	108	20	inclusions	inclusion	NOUN
ejpam-3229	108	21	then	then	ADV
ejpam-3229	108	22	α	α	X
ejpam-3229	108	23	=	=	PUNCT
ejpam-3229	108	24	iα	iα	NOUN
ejpam-3229	109	1	′	′	NOUN
ejpam-3229	109	2	and	and	CCONJ
ejpam-3229	109	3	β	β	X
ejpam-3229	109	4	=	=	SYM
ejpam-3229	109	5	jβ′.	jβ′.	PROPN
ejpam-3229	109	6	since	since	SCONJ
ejpam-3229	109	7	α′	α′	NUM
ejpam-3229	109	8	is	be	AUX
ejpam-3229	109	9	an	an	DET
ejpam-3229	109	10	epimorphism	epimorphism	NOUN
ejpam-3229	109	11	so	so	SCONJ
ejpam-3229	109	12	there	there	PRON
ejpam-3229	109	13	exists	exist	VERB
ejpam-3229	109	14	an	an	DET
ejpam-3229	109	15	s	s	NOUN
ejpam-3229	109	16	-	-	PUNCT
ejpam-3229	109	17	homomorphism	homomorphism	NOUN
ejpam-3229	109	18	φ	φ	NOUN
ejpam-3229	109	19	:	:	PUNCT
ejpam-3229	109	20	α	α	PROPN
ejpam-3229	109	21	(	(	PUNCT
ejpam-3229	109	22	m	m	NOUN
ejpam-3229	109	23	)	)	PUNCT
ejpam-3229	109	24	→	→	SYM
ejpam-3229	109	25	β	β	X
ejpam-3229	109	26	(	(	PUNCT
ejpam-3229	109	27	m	m	NOUN
ejpam-3229	109	28	)	)	PUNCT
ejpam-3229	110	1	such	such	ADJ
ejpam-3229	110	2	that	that	DET
ejpam-3229	110	3	φα′	φα′	PROPN
ejpam-3229	111	1	=	=	NOUN
ejpam-3229	111	2	β′.	β′.	PROPN
ejpam-3229	111	3	since	since	SCONJ
ejpam-3229	111	4	m	m	PROPN
ejpam-3229	111	5	is	be	AUX
ejpam-3229	111	6	quasi	quasi	ADJ
ejpam-3229	111	7	-	-	ADJ
ejpam-3229	111	8	principally	principally	ADV
ejpam-3229	111	9	injective	injective	ADJ
ejpam-3229	111	10	so	so	SCONJ
ejpam-3229	111	11	there	there	PRON
ejpam-3229	111	12	exists	exist	VERB
ejpam-3229	111	13	ψ	ψ	X
ejpam-3229	111	14	∈	∈	NOUN
ejpam-3229	111	15	e	e	NOUN
ejpam-3229	111	16	such	such	ADJ
ejpam-3229	111	17	that	that	PRON
ejpam-3229	111	18	ψi	ψi	NOUN
ejpam-3229	111	19	=	=	SYM
ejpam-3229	111	20	jφ	jφ	PROPN
ejpam-3229	111	21	.	.	PUNCT
ejpam-3229	111	22	finally	finally	ADV
ejpam-3229	111	23	consider	consider	VERB
ejpam-3229	111	24	,	,	PUNCT
ejpam-3229	111	25	ψα	ψα	ADP
ejpam-3229	111	26	=	=	NOUN
ejpam-3229	111	27	ψ(iα	ψ(iα	NOUN
ejpam-3229	111	28	′	′	NUM
ejpam-3229	111	29	)	)	PUNCT
ejpam-3229	112	1	=	=	SYM
ejpam-3229	112	2	(	(	PUNCT
ejpam-3229	112	3	ψi)α	ψi)α	NOUN
ejpam-3229	112	4	′	′	NOUN
ejpam-3229	112	5	=	=	SYM
ejpam-3229	112	6	(	(	PUNCT
ejpam-3229	112	7	jφ)α	jφ)α	NUM
ejpam-3229	112	8	′	′	NUM
ejpam-3229	112	9	=	=	SYM
ejpam-3229	112	10	j(φα	j(φα	PROPN
ejpam-3229	112	11	′	′	NUM
ejpam-3229	112	12	)	)	PUNCT
ejpam-3229	113	1	=	=	PUNCT
ejpam-3229	114	1	jβ′	jβ′	X
ejpam-3229	114	2	=	=	PUNCT
ejpam-3229	114	3	β	β	X
ejpam-3229	114	4	this	this	PRON
ejpam-3229	114	5	shows	show	VERB
ejpam-3229	114	6	that	that	SCONJ
ejpam-3229	114	7	β	β	PROPN
ejpam-3229	114	8	∈	∈	PROPN
ejpam-3229	114	9	eα	eα	INTJ
ejpam-3229	114	10	.	.	PUNCT
ejpam-3229	114	11	thus	thus	ADV
ejpam-3229	114	12	anne(kerα	anne(kerα	PROPN
ejpam-3229	114	13	)	)	PUNCT
ejpam-3229	114	14	=	=	SYM
ejpam-3229	115	1	eα	eα	PROPN
ejpam-3229	115	2	.	.	NOUN
ejpam-3229	115	3	2)⇒3	2)⇒3	NUM
ejpam-3229	115	4	)	)	PUNCT
ejpam-3229	115	5	suppose	suppose	VERB
ejpam-3229	115	6	kerβ	kerβ	PROPN
ejpam-3229	115	7	⊆	⊆	NUM
ejpam-3229	115	8	kerα	kerα	NOUN
ejpam-3229	115	9	.	.	PUNCT
ejpam-3229	116	1	by	by	ADP
ejpam-3229	116	2	hypothesis	hypothesis	NOUN
ejpam-3229	116	3	it	it	PRON
ejpam-3229	116	4	is	be	AUX
ejpam-3229	116	5	sufficient	sufficient	ADJ
ejpam-3229	116	6	to	to	PART
ejpam-3229	116	7	show	show	VERB
ejpam-3229	116	8	that	that	SCONJ
ejpam-3229	116	9	anne(kerα	anne(kerα	PROPN
ejpam-3229	116	10	)	)	PUNCT
ejpam-3229	116	11	⊆	⊆	NUM
ejpam-3229	116	12	anne(kerβ	anne(kerβ	PROPN
ejpam-3229	116	13	)	)	PUNCT
ejpam-3229	116	14	.	.	PUNCT
ejpam-3229	117	1	let	let	VERB
ejpam-3229	117	2	u	u	PRON
ejpam-3229	117	3	∈	∈	PROPN
ejpam-3229	117	4	anne(kerα	anne(kerα	PROPN
ejpam-3229	117	5	)	)	PUNCT
ejpam-3229	117	6	so	so	ADV
ejpam-3229	117	7	kerα	kerα	ADV
ejpam-3229	117	8	⊆	⊆	NUM
ejpam-3229	117	9	keru	keru	NOUN
ejpam-3229	117	10	then	then	ADV
ejpam-3229	117	11	kerβ	kerβ	PROPN
ejpam-3229	117	12	⊆	⊆	NUM
ejpam-3229	117	13	keru	keru	NOUN
ejpam-3229	118	1	and	and	CCONJ
ejpam-3229	118	2	therefore	therefore	ADV
ejpam-3229	118	3	u	u	X
ejpam-3229	118	4	∈	∈	PROPN
ejpam-3229	118	5	anne(kerβ	anne(kerβ	PROPN
ejpam-3229	118	6	)	)	PUNCT
ejpam-3229	118	7	.	.	PUNCT
ejpam-3229	119	1	thus	thus	ADV
ejpam-3229	119	2	anne(kerα	anne(kerα	PROPN
ejpam-3229	119	3	)	)	PUNCT
ejpam-3229	119	4	⊆	⊆	NUM
ejpam-3229	119	5	anne(kerβ	anne(kerβ	PROPN
ejpam-3229	119	6	)	)	PUNCT
ejpam-3229	119	7	.	.	PUNCT
ejpam-3229	120	1	3)⇒1	3)⇒1	NUM
ejpam-3229	120	2	)	)	PUNCT
ejpam-3229	120	3	suppose	suppose	VERB
ejpam-3229	120	4	φ	φ	X
ejpam-3229	120	5	:	:	PUNCT
ejpam-3229	120	6	α	α	PROPN
ejpam-3229	120	7	(	(	PUNCT
ejpam-3229	120	8	m)→m	m)→m	X
ejpam-3229	120	9	is	be	AUX
ejpam-3229	120	10	an	an	DET
ejpam-3229	120	11	s	s	NOUN
ejpam-3229	120	12	-	-	NOUN
ejpam-3229	120	13	homomorphism	homomorphism	NOUN
ejpam-3229	120	14	.	.	PUNCT
ejpam-3229	121	1	now	now	ADV
ejpam-3229	121	2	φα′	φα′	PROPN
ejpam-3229	122	1	∈	∈	PROPN
ejpam-3229	122	2	e.	e.	PROPN
ejpam-3229	122	3	we	we	PRON
ejpam-3229	122	4	can	can	AUX
ejpam-3229	122	5	easily	easily	ADV
ejpam-3229	122	6	see	see	VERB
ejpam-3229	122	7	kerα	kerα	ADJ
ejpam-3229	122	8	⊆	⊆	NUM
ejpam-3229	122	9	ker	ker	NOUN
ejpam-3229	122	10	φα′.	φα′.	NOUN
ejpam-3229	122	11	so	so	ADV
ejpam-3229	122	12	by	by	ADP
ejpam-3229	122	13	hypothesis	hypothesis	NOUN
ejpam-3229	122	14	eφα′	eφα′	NOUN
ejpam-3229	122	15	⊆	⊆	NUM
ejpam-3229	122	16	eα	eα	NOUN
ejpam-3229	122	17	.	.	PUNCT
ejpam-3229	123	1	since	since	SCONJ
ejpam-3229	123	2	φα′	φα′	PROPN
ejpam-3229	123	3	∈	∈	PROPN
ejpam-3229	123	4	eφα′	eφα′	NOUN
ejpam-3229	123	5	⊆	⊆	NUM
ejpam-3229	123	6	eα	eα	NOUN
ejpam-3229	123	7	so	so	ADV
ejpam-3229	123	8	φα′	φα′	PROPN
ejpam-3229	123	9	=	=	SYM
ejpam-3229	123	10	uα	uα	PROPN
ejpam-3229	123	11	for	for	ADP
ejpam-3229	123	12	some	some	DET
ejpam-3229	123	13	u	u	NOUN
ejpam-3229	123	14	∈	∈	PROPN
ejpam-3229	123	15	e	e	NOUN
ejpam-3229	123	16	,	,	PUNCT
ejpam-3229	123	17	which	which	PRON
ejpam-3229	123	18	implies	imply	VERB
ejpam-3229	123	19	the	the	DET
ejpam-3229	123	20	desired	desire	VERB
ejpam-3229	123	21	result	result	NOUN
ejpam-3229	123	22	.	.	PUNCT
ejpam-3229	124	1	if	if	SCONJ
ejpam-3229	124	2	annrs(a	annrs(a	NOUN
ejpam-3229	124	3	)	)	PUNCT
ejpam-3229	124	4	=	=	PRON
ejpam-3229	124	5	{	{	PUNCT
ejpam-3229	124	6	s	s	X
ejpam-3229	124	7	∈	∈	NOUN
ejpam-3229	124	8	s	s	PART
ejpam-3229	124	9	:	:	PUNCT
ejpam-3229	124	10	as	as	SCONJ
ejpam-3229	124	11	=	=	PROPN
ejpam-3229	124	12	θ	θ	PROPN
ejpam-3229	124	13	}	}	PUNCT
ejpam-3229	124	14	is	be	AUX
ejpam-3229	124	15	a	a	DET
ejpam-3229	124	16	right	right	ADJ
ejpam-3229	124	17	annihilator	annihilator	NOUN
ejpam-3229	124	18	and	and	CCONJ
ejpam-3229	124	19	annls(a	annls(a	PROPN
ejpam-3229	124	20	)	)	PUNCT
ejpam-3229	124	21	=	=	PRON
ejpam-3229	124	22	{	{	PUNCT
ejpam-3229	124	23	s	s	X
ejpam-3229	124	24	∈	∈	NOUN
ejpam-3229	124	25	s	s	PART
ejpam-3229	124	26	:	:	PUNCT
ejpam-3229	124	27	sa	sa	PROPN
ejpam-3229	124	28	=	=	SYM
ejpam-3229	124	29	θ	θ	PROPN
ejpam-3229	124	30	}	}	PUNCT
ejpam-3229	124	31	a	a	DET
ejpam-3229	124	32	left	left	ADJ
ejpam-3229	124	33	annihilator	annihilator	NOUN
ejpam-3229	124	34	then	then	ADV
ejpam-3229	124	35	we	we	PRON
ejpam-3229	124	36	can	can	AUX
ejpam-3229	124	37	have	have	AUX
ejpam-3229	124	38	following	follow	VERB
ejpam-3229	124	39	corollary	corollary	NOUN
ejpam-3229	124	40	from	from	ADP
ejpam-3229	124	41	theorem	theorem	ADJ
ejpam-3229	124	42	2	2	NUM
ejpam-3229	124	43	.	.	PUNCT
ejpam-3229	124	44	corollary	corollary	ADJ
ejpam-3229	124	45	2	2	NUM
ejpam-3229	124	46	.	.	PUNCT
ejpam-3229	125	1	the	the	DET
ejpam-3229	125	2	following	follow	VERB
ejpam-3229	125	3	are	be	AUX
ejpam-3229	125	4	equivalent	equivalent	ADJ
ejpam-3229	125	5	for	for	ADP
ejpam-3229	125	6	a	a	DET
ejpam-3229	125	7	semigroup	semigroup	PROPN
ejpam-3229	125	8	s.	s.	PROPN
ejpam-3229	125	9	a	a	PRON
ejpam-3229	125	10	)	)	PUNCT
ejpam-3229	125	11	s	s	VERB
ejpam-3229	125	12	is	be	AUX
ejpam-3229	125	13	right	right	ADJ
ejpam-3229	125	14	self	self	NOUN
ejpam-3229	125	15	-	-	PUNCT
ejpam-3229	125	16	principally	principally	ADV
ejpam-3229	125	17	injective	injective	ADJ
ejpam-3229	125	18	.	.	PUNCT
ejpam-3229	126	1	b	b	X
ejpam-3229	126	2	)	)	PUNCT
ejpam-3229	126	3	annls(a	annls(a	NOUN
ejpam-3229	126	4	)	)	PUNCT
ejpam-3229	126	5	=	=	SYM
ejpam-3229	127	1	sa	sa	PROPN
ejpam-3229	127	2	.	.	PUNCT
ejpam-3229	128	1	c	c	X
ejpam-3229	128	2	)	)	PUNCT
ejpam-3229	128	3	annrs(b	annrs(b	PROPN
ejpam-3229	128	4	)	)	PUNCT
ejpam-3229	128	5	⊆	⊆	NUM
ejpam-3229	128	6	annrs(a	annrs(a	NOUN
ejpam-3229	128	7	)	)	PUNCT
ejpam-3229	128	8	implies	imply	VERB
ejpam-3229	128	9	that	that	SCONJ
ejpam-3229	128	10	sb	sb	PROPN
ejpam-3229	128	11	⊆	⊆	NUM
ejpam-3229	128	12	sa	sa	PROPN
ejpam-3229	128	13	.	.	PUNCT
ejpam-3229	129	1	we	we	PRON
ejpam-3229	129	2	denote	denote	VERB
ejpam-3229	129	3	the	the	DET
ejpam-3229	129	4	set	set	NOUN
ejpam-3229	129	5	of	of	ADP
ejpam-3229	129	6	all	all	DET
ejpam-3229	129	7	homomorphisms	homomorphism	NOUN
ejpam-3229	129	8	from	from	ADP
ejpam-3229	129	9	a	a	DET
ejpam-3229	129	10	right	right	ADJ
ejpam-3229	129	11	s	s	NOUN
ejpam-3229	129	12	-	-	PUNCT
ejpam-3229	129	13	act	act	NOUN
ejpam-3229	129	14	m	m	VERB
ejpam-3229	129	15	to	to	ADP
ejpam-3229	129	16	a	a	DET
ejpam-3229	129	17	right	right	ADJ
ejpam-3229	129	18	s	s	NOUN
ejpam-3229	129	19	-	-	NOUN
ejpam-3229	129	20	act	act	NOUN
ejpam-3229	129	21	n	n	CCONJ
ejpam-3229	129	22	,	,	PUNCT
ejpam-3229	129	23	by	by	ADP
ejpam-3229	129	24	homs(m	homs(m	PROPN
ejpam-3229	129	25	,	,	PUNCT
ejpam-3229	129	26	n	n	NOUN
ejpam-3229	129	27	)	)	PUNCT
ejpam-3229	129	28	.	.	PUNCT
ejpam-3229	130	1	moreover	moreover	ADV
ejpam-3229	130	2	,	,	PUNCT
ejpam-3229	130	3	homs(m	homs(m	PROPN
ejpam-3229	130	4	,	,	PUNCT
ejpam-3229	130	5	n	n	CCONJ
ejpam-3229	130	6	)	)	PUNCT
ejpam-3229	130	7	is	be	AUX
ejpam-3229	130	8	a	a	DET
ejpam-3229	130	9	right	right	ADJ
ejpam-3229	130	10	e	e	NOUN
ejpam-3229	130	11	-	-	NOUN
ejpam-3229	130	12	act	act	NOUN
ejpam-3229	130	13	by	by	ADP
ejpam-3229	130	14	action	action	NOUN
ejpam-3229	130	15	(	(	PUNCT
ejpam-3229	130	16	u	u	NOUN
ejpam-3229	130	17	,	,	PUNCT
ejpam-3229	130	18	α	α	NOUN
ejpam-3229	130	19	)	)	PUNCT
ejpam-3229	130	20	→	→	SYM
ejpam-3229	130	21	uα	uα	PROPN
ejpam-3229	130	22	,	,	PUNCT
ejpam-3229	130	23	the	the	DET
ejpam-3229	130	24	usual	usual	ADJ
ejpam-3229	130	25	composition	composition	NOUN
ejpam-3229	130	26	of	of	ADP
ejpam-3229	130	27	functions	function	NOUN
ejpam-3229	130	28	.	.	PUNCT
ejpam-3229	131	1	lemma	lemma	PROPN
ejpam-3229	131	2	2	2	X
ejpam-3229	131	3	.	.	PUNCT
ejpam-3229	132	1	let	let	VERB
ejpam-3229	132	2	m	m	PRON
ejpam-3229	132	3	and	and	CCONJ
ejpam-3229	132	4	n	n	CCONJ
ejpam-3229	132	5	be	be	AUX
ejpam-3229	132	6	two	two	NUM
ejpam-3229	132	7	right	right	ADJ
ejpam-3229	132	8	s	s	NOUN
ejpam-3229	132	9	-	-	PUNCT
ejpam-3229	132	10	acts	act	VERB
ejpam-3229	132	11	then	then	ADV
ejpam-3229	132	12	n	n	AUX
ejpam-3229	132	13	is	be	AUX
ejpam-3229	132	14	m	m	NOUN
ejpam-3229	132	15	-	-	ADJ
ejpam-3229	132	16	principally	principally	ADV
ejpam-3229	132	17	injective	injective	ADJ
ejpam-3229	132	18	iff	iff	NOUN
ejpam-3229	132	19	for	for	ADP
ejpam-3229	132	20	all	all	DET
ejpam-3229	132	21	α	α	NOUN
ejpam-3229	132	22	∈	∈	PROPN
ejpam-3229	132	23	e	e	NOUN
ejpam-3229	132	24	,	,	PUNCT
ejpam-3229	132	25	homs(m	homs(m	PROPN
ejpam-3229	132	26	,	,	PUNCT
ejpam-3229	132	27	n	n	NOUN
ejpam-3229	132	28	)	)	PUNCT
ejpam-3229	132	29	α	α	NOUN
ejpam-3229	132	30	=	=	SYM
ejpam-3229	132	31	{	{	PUNCT
ejpam-3229	132	32	β	β	NOUN
ejpam-3229	132	33	∈	∈	PROPN
ejpam-3229	132	34	homs(m	homs(m	PROPN
ejpam-3229	132	35	,	,	PUNCT
ejpam-3229	132	36	n	n	NUM
ejpam-3229	132	37	):	):	PUNCT
ejpam-3229	132	38	kerα	kerα	ADV
ejpam-3229	132	39	⊆	⊆	NUM
ejpam-3229	132	40	kerβ	kerβ	NOUN
ejpam-3229	132	41	}	}	PUNCT
ejpam-3229	132	42	.	.	PUNCT
ejpam-3229	133	1	j.	j.	PROPN
ejpam-3229	133	2	hussain	hussain	PROPN
ejpam-3229	133	3	,	,	PUNCT
ejpam-3229	133	4	m.shabir	m.shabir	PROPN
ejpam-3229	133	5	/	/	SYM
ejpam-3229	133	6	eur	eur	PROPN
ejpam-3229	133	7	.	.	PUNCT
ejpam-3229	134	1	j.	j.	PROPN
ejpam-3229	134	2	pure	pure	PROPN
ejpam-3229	134	3	appl	appl	PROPN
ejpam-3229	134	4	.	.	PROPN
ejpam-3229	134	5	math	math	PROPN
ejpam-3229	134	6	,	,	PUNCT
ejpam-3229	134	7	11	11	NUM
ejpam-3229	134	8	(	(	PUNCT
ejpam-3229	134	9	2	2	NUM
ejpam-3229	134	10	)	)	PUNCT
ejpam-3229	134	11	(	(	PUNCT
ejpam-3229	134	12	2018	2018	NUM
ejpam-3229	134	13	)	)	PUNCT
ejpam-3229	134	14	,	,	PUNCT
ejpam-3229	134	15	431	431	NUM
ejpam-3229	134	16	-	-	SYM
ejpam-3229	134	17	443	443	NUM
ejpam-3229	134	18	435	435	NUM
ejpam-3229	134	19	proof	proof	NOUN
ejpam-3229	134	20	.	.	PUNCT
ejpam-3229	135	1	let	let	VERB
ejpam-3229	135	2	k	k	NOUN
ejpam-3229	135	3	=	=	PUNCT
ejpam-3229	135	4	β	β	X
ejpam-3229	135	5	∈	∈	PROPN
ejpam-3229	135	6	homs	hom	NOUN
ejpam-3229	135	7	(	(	PUNCT
ejpam-3229	135	8	m	m	PROPN
ejpam-3229	135	9	,	,	PUNCT
ejpam-3229	135	10	n	n	PROPN
ejpam-3229	135	11	)	)	PUNCT
ejpam-3229	135	12	:	:	PUNCT
ejpam-3229	135	13	kerα	kerα	PROPN
ejpam-3229	135	14	⊆	⊆	NUM
ejpam-3229	135	15	kerβ	kerβ	NOUN
ejpam-3229	135	16	}	}	PUNCT
ejpam-3229	135	17	.	.	PUNCT
ejpam-3229	136	1	let	let	VERB
ejpam-3229	136	2	β	β	PRON
ejpam-3229	136	3	∈	∈	PROPN
ejpam-3229	137	1	k	k	NOUN
ejpam-3229	137	2	then	then	ADV
ejpam-3229	137	3	kerα	kerα	VERB
ejpam-3229	137	4	⊆	⊆	NUM
ejpam-3229	137	5	kerβ	kerβ	NOUN
ejpam-3229	137	6	.	.	PUNCT
ejpam-3229	138	1	define	define	VERB
ejpam-3229	138	2	φ	φ	NOUN
ejpam-3229	138	3	:	:	PUNCT
ejpam-3229	138	4	α	α	PROPN
ejpam-3229	138	5	(	(	PUNCT
ejpam-3229	138	6	m	m	NOUN
ejpam-3229	138	7	)	)	PUNCT
ejpam-3229	138	8	→	→	SYM
ejpam-3229	138	9	n	n	CCONJ
ejpam-3229	138	10	by	by	ADP
ejpam-3229	138	11	φ(α(m	φ(α(m	VERB
ejpam-3229	138	12	)	)	PUNCT
ejpam-3229	138	13	)	)	PUNCT
ejpam-3229	139	1	=	=	PUNCT
ejpam-3229	139	2	β(m	β(m	NOUN
ejpam-3229	139	3	)	)	PUNCT
ejpam-3229	139	4	.	.	PUNCT
ejpam-3229	140	1	clearly	clearly	ADV
ejpam-3229	140	2	φ	φ	PROPN
ejpam-3229	140	3	is	be	AUX
ejpam-3229	140	4	well	well	ADV
ejpam-3229	140	5	-	-	PUNCT
ejpam-3229	140	6	defined	define	VERB
ejpam-3229	140	7	and	and	CCONJ
ejpam-3229	140	8	an	an	DET
ejpam-3229	140	9	shomomorphism	shomomorphism	NOUN
ejpam-3229	140	10	.	.	PUNCT
ejpam-3229	141	1	since	since	SCONJ
ejpam-3229	141	2	n	n	NUM
ejpam-3229	141	3	is	be	AUX
ejpam-3229	141	4	m	m	NOUN
ejpam-3229	141	5	-	-	ADJ
ejpam-3229	141	6	principally	principally	ADV
ejpam-3229	141	7	injective	injective	ADJ
ejpam-3229	141	8	so	so	SCONJ
ejpam-3229	141	9	there	there	PRON
ejpam-3229	141	10	exists	exist	VERB
ejpam-3229	141	11	γ	γ	X
ejpam-3229	141	12	:	:	PUNCT
ejpam-3229	141	13	m	m	VERB
ejpam-3229	141	14	→	→	SYM
ejpam-3229	141	15	n	n	CCONJ
ejpam-3229	141	16	such	such	ADJ
ejpam-3229	141	17	that	that	DET
ejpam-3229	141	18	γi	γi	NOUN
ejpam-3229	141	19	=	=	SYM
ejpam-3229	141	20	φ	φ	X
ejpam-3229	141	21	i.e.	i.e.	X
ejpam-3229	141	22	γ	γ	X
ejpam-3229	141	23	extendsφ	extendsφ	PROPN
ejpam-3229	141	24	,	,	PUNCT
ejpam-3229	141	25	where	where	SCONJ
ejpam-3229	141	26	i	i	PRON
ejpam-3229	141	27	:	:	PUNCT
ejpam-3229	141	28	α	α	X
ejpam-3229	141	29	(	(	PUNCT
ejpam-3229	141	30	m)→mis	m)→mis	VERB
ejpam-3229	141	31	the	the	DET
ejpam-3229	141	32	inclusion	inclusion	NOUN
ejpam-3229	141	33	.	.	PUNCT
ejpam-3229	142	1	consider	consider	VERB
ejpam-3229	142	2	,	,	PUNCT
ejpam-3229	142	3	β(m	β(m	PROPN
ejpam-3229	142	4	)	)	PUNCT
ejpam-3229	142	5	=	=	SYM
ejpam-3229	142	6	φ(α(m	φ(α(m	VERB
ejpam-3229	142	7	)	)	PUNCT
ejpam-3229	142	8	)	)	PUNCT
ejpam-3229	143	1	=	=	SYM
ejpam-3229	143	2	γi(α(m	γi(α(m	NOUN
ejpam-3229	143	3	)	)	PUNCT
ejpam-3229	143	4	)	)	PUNCT
ejpam-3229	144	1	=	=	PUNCT
ejpam-3229	144	2	γ(α(m	γ(α(m	NOUN
ejpam-3229	144	3	)	)	PUNCT
ejpam-3229	144	4	)	)	PUNCT
ejpam-3229	145	1	=	=	SYM
ejpam-3229	145	2	γα(m	γα(m	X
ejpam-3229	145	3	)	)	PUNCT
ejpam-3229	145	4	for	for	ADP
ejpam-3229	145	5	all	all	DET
ejpam-3229	145	6	m	m	NOUN
ejpam-3229	145	7	∈	∈	NOUN
ejpam-3229	145	8	m	m	NOUN
ejpam-3229	145	9	,	,	PUNCT
ejpam-3229	145	10	hence	hence	ADV
ejpam-3229	145	11	β	β	X
ejpam-3229	145	12	=	=	SYM
ejpam-3229	145	13	γα	γα	ADP
ejpam-3229	145	14	∈	∈	PROPN
ejpam-3229	145	15	homs	hom	NOUN
ejpam-3229	145	16	(	(	PUNCT
ejpam-3229	145	17	m	m	PROPN
ejpam-3229	145	18	,	,	PUNCT
ejpam-3229	145	19	n	n	CCONJ
ejpam-3229	145	20	)	)	PUNCT
ejpam-3229	145	21	α	α	X
ejpam-3229	145	22	.	.	PUNCT
ejpam-3229	146	1	for	for	ADP
ejpam-3229	146	2	the	the	DET
ejpam-3229	146	3	reverse	reverse	ADJ
ejpam-3229	146	4	inclusion	inclusion	NOUN
ejpam-3229	146	5	let	let	VERB
ejpam-3229	146	6	uα	uα	PROPN
ejpam-3229	146	7	∈	∈	PROPN
ejpam-3229	146	8	homs	hom	NOUN
ejpam-3229	146	9	(	(	PUNCT
ejpam-3229	146	10	m	m	PROPN
ejpam-3229	146	11	,	,	PUNCT
ejpam-3229	146	12	n	n	CCONJ
ejpam-3229	146	13	)	)	PUNCT
ejpam-3229	146	14	α	α	X
ejpam-3229	146	15	.	.	PUNCT
ejpam-3229	147	1	we	we	PRON
ejpam-3229	147	2	claim	claim	VERB
ejpam-3229	147	3	that	that	SCONJ
ejpam-3229	147	4	kerα	kerα	ADV
ejpam-3229	147	5	⊆	⊆	NUM
ejpam-3229	147	6	keruα	keruα	NOUN
ejpam-3229	147	7	.	.	PUNCT
ejpam-3229	147	8	,	,	PUNCT
ejpam-3229	147	9	which	which	PRON
ejpam-3229	147	10	is	be	AUX
ejpam-3229	147	11	sufficient	sufficient	ADJ
ejpam-3229	147	12	to	to	PART
ejpam-3229	147	13	show	show	VERB
ejpam-3229	147	14	that	that	SCONJ
ejpam-3229	147	15	uα	uα	PROPN
ejpam-3229	147	16	∈	∈	PROPN
ejpam-3229	147	17	k.	k.	PROPN
ejpam-3229	147	18	to	to	PART
ejpam-3229	147	19	do	do	VERB
ejpam-3229	147	20	so	so	ADV
ejpam-3229	147	21	,	,	PUNCT
ejpam-3229	147	22	let	let	VERB
ejpam-3229	147	23	(	(	PUNCT
ejpam-3229	147	24	x	x	NOUN
ejpam-3229	147	25	,	,	PUNCT
ejpam-3229	147	26	y	y	NOUN
ejpam-3229	147	27	)	)	PUNCT
ejpam-3229	147	28	∈	∈	PROPN
ejpam-3229	147	29	kerα	kerα	NOUN
ejpam-3229	147	30	so	so	ADV
ejpam-3229	147	31	α(x	α(x	NOUN
ejpam-3229	147	32	)	)	PUNCT
ejpam-3229	147	33	=	=	SYM
ejpam-3229	148	1	α(y	α(y	NOUN
ejpam-3229	148	2	)	)	PUNCT
ejpam-3229	148	3	and	and	CCONJ
ejpam-3229	148	4	therefore	therefore	ADV
ejpam-3229	148	5	uα(x	uα(x	PUNCT
ejpam-3229	148	6	)	)	PUNCT
ejpam-3229	148	7	=	=	SYM
ejpam-3229	148	8	uα(y	uα(y	NOUN
ejpam-3229	148	9	)	)	PUNCT
ejpam-3229	148	10	which	which	PRON
ejpam-3229	148	11	shows	show	VERB
ejpam-3229	148	12	(	(	PUNCT
ejpam-3229	148	13	x	x	NOUN
ejpam-3229	148	14	,	,	PUNCT
ejpam-3229	148	15	y	y	NOUN
ejpam-3229	148	16	)	)	PUNCT
ejpam-3229	148	17	∈	∈	PROPN
ejpam-3229	148	18	keruα	keruα	NOUN
ejpam-3229	148	19	,	,	PUNCT
ejpam-3229	148	20	hence	hence	ADV
ejpam-3229	148	21	kerα	kerα	VERB
ejpam-3229	148	22	⊆	⊆	NUM
ejpam-3229	148	23	keruα	keruα	ADJ
ejpam-3229	148	24	.	.	PUNCT
ejpam-3229	149	1	hence	hence	ADV
ejpam-3229	149	2	homs(m	homs(m	PROPN
ejpam-3229	149	3	,	,	PUNCT
ejpam-3229	149	4	n	n	NOUN
ejpam-3229	149	5	)	)	PUNCT
ejpam-3229	149	6	α	α	PROPN
ejpam-3229	149	7	=	=	PUNCT
ejpam-3229	149	8	k.	k.	PROPN
ejpam-3229	149	9	for	for	ADP
ejpam-3229	149	10	the	the	DET
ejpam-3229	149	11	converse	converse	NOUN
ejpam-3229	149	12	,	,	PUNCT
ejpam-3229	149	13	let	let	VERB
ejpam-3229	149	14	φ	φ	PROPN
ejpam-3229	149	15	:	:	PUNCT
ejpam-3229	149	16	α	α	PROPN
ejpam-3229	149	17	(	(	PUNCT
ejpam-3229	149	18	m	m	NOUN
ejpam-3229	149	19	)	)	PUNCT
ejpam-3229	149	20	→	→	SYM
ejpam-3229	149	21	n	n	CCONJ
ejpam-3229	149	22	be	be	AUX
ejpam-3229	149	23	a	a	DET
ejpam-3229	149	24	s	s	NOUN
ejpam-3229	149	25	-	-	NOUN
ejpam-3229	149	26	homomorphism	homomorphism	NOUN
ejpam-3229	149	27	.	.	PUNCT
ejpam-3229	150	1	consider	consider	VERB
ejpam-3229	150	2	the	the	DET
ejpam-3229	150	3	map	map	NOUN
ejpam-3229	150	4	φα	φα	ADP
ejpam-3229	150	5	∈	∈	PROPN
ejpam-3229	150	6	homs(m	homs(m	PROPN
ejpam-3229	150	7	,	,	PUNCT
ejpam-3229	150	8	n	n	PROPN
ejpam-3229	150	9	)	)	PUNCT
ejpam-3229	150	10	.	.	PUNCT
ejpam-3229	151	1	clearly	clearly	ADV
ejpam-3229	151	2	,	,	PUNCT
ejpam-3229	151	3	kerα	kerα	ADV
ejpam-3229	151	4	⊆	⊆	NUM
ejpam-3229	151	5	ker	ker	NOUN
ejpam-3229	151	6	φα	φα	PROPN
ejpam-3229	151	7	.	.	PUNCT
ejpam-3229	152	1	therefore	therefore	ADV
ejpam-3229	152	2	φα	φα	PROPN
ejpam-3229	152	3	∈	∈	PROPN
ejpam-3229	152	4	k	k	X
ejpam-3229	152	5	=	=	SYM
ejpam-3229	152	6	homs(m	homs(m	PROPN
ejpam-3229	152	7	,	,	PUNCT
ejpam-3229	152	8	n	n	NOUN
ejpam-3229	152	9	)	)	PUNCT
ejpam-3229	152	10	α	α	NOUN
ejpam-3229	153	1	so	so	ADV
ejpam-3229	153	2	φα	φα	PROPN
ejpam-3229	153	3	=	=	SYM
ejpam-3229	153	4	uα	uα	PROPN
ejpam-3229	153	5	,	,	PUNCT
ejpam-3229	153	6	for	for	ADP
ejpam-3229	153	7	some	some	DET
ejpam-3229	153	8	u	u	PROPN
ejpam-3229	153	9	∈	∈	PROPN
ejpam-3229	153	10	homs(m	homs(m	PROPN
ejpam-3229	153	11	,	,	PUNCT
ejpam-3229	153	12	n	n	PRON
ejpam-3229	153	13	)	)	PUNCT
ejpam-3229	153	14	.	.	PUNCT
ejpam-3229	154	1	hence	hence	ADV
ejpam-3229	154	2	n	n	NOUN
ejpam-3229	154	3	is	be	AUX
ejpam-3229	154	4	m	m	NOUN
ejpam-3229	154	5	-	-	PUNCT
ejpam-3229	154	6	principally	principally	ADV
ejpam-3229	154	7	injective	injective	ADJ
ejpam-3229	154	8	.	.	PUNCT
ejpam-3229	155	1	lemma	lemma	PROPN
ejpam-3229	155	2	3	3	NUM
ejpam-3229	155	3	.	.	PUNCT
ejpam-3229	156	1	every	every	DET
ejpam-3229	156	2	x	x	ADJ
ejpam-3229	156	3	-	-	ADJ
ejpam-3229	156	4	cyclic	cyclic	ADJ
ejpam-3229	156	5	sub	sub	NOUN
ejpam-3229	156	6	-	-	NOUN
ejpam-3229	156	7	act	act	NOUN
ejpam-3229	156	8	of	of	ADP
ejpam-3229	156	9	x	x	PROPN
ejpam-3229	156	10	is	be	AUX
ejpam-3229	156	11	anm	anm	NOUN
ejpam-3229	156	12	-	-	PUNCT
ejpam-3229	156	13	cyclic	cyclic	ADJ
ejpam-3229	156	14	sub	sub	ADJ
ejpam-3229	156	15	-	-	ADJ
ejpam-3229	156	16	act	act	ADJ
ejpam-3229	156	17	ofm	ofm	PROPN
ejpam-3229	156	18	,	,	PUNCT
ejpam-3229	156	19	for	for	ADP
ejpam-3229	156	20	everym	everym	NOUN
ejpam-3229	156	21	-	-	PUNCT
ejpam-3229	156	22	cyclic	cyclic	ADJ
ejpam-3229	156	23	sub	sub	NOUN
ejpam-3229	156	24	-	-	NOUN
ejpam-3229	156	25	act	act	NOUN
ejpam-3229	156	26	x	x	PUNCT
ejpam-3229	156	27	of	of	ADP
ejpam-3229	156	28	m.	m.	NOUN
ejpam-3229	156	29	proof	proof	NOUN
ejpam-3229	156	30	.	.	PUNCT
ejpam-3229	157	1	supposen	supposen	NOUN
ejpam-3229	157	2	is	be	AUX
ejpam-3229	157	3	anx	anx	ADJ
ejpam-3229	157	4	-	-	PUNCT
ejpam-3229	157	5	cyclic	cyclic	ADJ
ejpam-3229	157	6	sub	sub	ADJ
ejpam-3229	157	7	-	-	ADJ
ejpam-3229	157	8	act	act	ADJ
ejpam-3229	157	9	ofx	ofx	PROPN
ejpam-3229	157	10	son	son	NOUN
ejpam-3229	157	11	=	=	PROPN
ejpam-3229	157	12	α(x	α(x	PROPN
ejpam-3229	157	13	)	)	PUNCT
ejpam-3229	157	14	for	for	ADP
ejpam-3229	157	15	some	some	DET
ejpam-3229	157	16	α	α	NOUN
ejpam-3229	157	17	∈	∈	NOUN
ejpam-3229	157	18	ends(x).now	ends(x).now	PROPN
ejpam-3229	157	19	since	since	SCONJ
ejpam-3229	157	20	x	x	PROPN
ejpam-3229	157	21	is	be	AUX
ejpam-3229	157	22	m	m	NOUN
ejpam-3229	157	23	-	-	NOUN
ejpam-3229	157	24	cyclic	cyclic	ADJ
ejpam-3229	158	1	so	so	NOUN
ejpam-3229	158	2	x	x	SYM
ejpam-3229	158	3	=	=	SYM
ejpam-3229	158	4	γ	γ	X
ejpam-3229	158	5	(	(	PUNCT
ejpam-3229	158	6	m	m	PROPN
ejpam-3229	158	7	)	)	PUNCT
ejpam-3229	158	8	for	for	ADP
ejpam-3229	158	9	some	some	DET
ejpam-3229	158	10	γ	γ	NOUN
ejpam-3229	158	11	∈	∈	PROPN
ejpam-3229	158	12	e	e	NOUN
ejpam-3229	158	13	,	,	PUNCT
ejpam-3229	158	14	hence	hence	ADV
ejpam-3229	158	15	n	n	NOUN
ejpam-3229	158	16	=	=	SYM
ejpam-3229	158	17	αγ	αγ	PROPN
ejpam-3229	158	18	(	(	PUNCT
ejpam-3229	158	19	m	m	NOUN
ejpam-3229	158	20	)	)	PUNCT
ejpam-3229	158	21	so	so	CCONJ
ejpam-3229	158	22	n	n	PROPN
ejpam-3229	158	23	is	be	AUX
ejpam-3229	158	24	m	m	NOUN
ejpam-3229	158	25	-	-	ADJ
ejpam-3229	158	26	cyclic	cyclic	ADJ
ejpam-3229	158	27	.	.	PUNCT
ejpam-3229	159	1	theorem	theorem	NOUN
ejpam-3229	159	2	3	3	X
ejpam-3229	159	3	.	.	PUNCT
ejpam-3229	160	1	let	let	VERB
ejpam-3229	160	2	n	n	PRON
ejpam-3229	160	3	and	and	CCONJ
ejpam-3229	160	4	m	m	AUX
ejpam-3229	160	5	be	be	AUX
ejpam-3229	160	6	right	right	ADJ
ejpam-3229	160	7	s	s	NOUN
ejpam-3229	160	8	-	-	PUNCT
ejpam-3229	160	9	acts	act	VERB
ejpam-3229	160	10	then	then	ADV
ejpam-3229	160	11	n	n	AUX
ejpam-3229	160	12	is	be	AUX
ejpam-3229	160	13	m	m	NOUN
ejpam-3229	160	14	-	-	ADJ
ejpam-3229	160	15	principally	principally	ADV
ejpam-3229	160	16	injective	injective	ADJ
ejpam-3229	160	17	iff	iff	PROPN
ejpam-3229	160	18	n	n	PART
ejpam-3229	160	19	is	be	AUX
ejpam-3229	160	20	x−principally	x−principally	ADV
ejpam-3229	160	21	injective	injective	ADJ
ejpam-3229	160	22	for	for	ADP
ejpam-3229	160	23	every	every	DET
ejpam-3229	160	24	m	m	NOUN
ejpam-3229	160	25	-	-	PUNCT
ejpam-3229	160	26	cyclic	cyclic	ADJ
ejpam-3229	160	27	sub	sub	NOUN
ejpam-3229	160	28	-	-	NOUN
ejpam-3229	160	29	act	act	NOUN
ejpam-3229	160	30	x	x	PUNCT
ejpam-3229	160	31	of	of	ADP
ejpam-3229	160	32	m.	m.	NOUN
ejpam-3229	160	33	proof	proof	NOUN
ejpam-3229	160	34	.	.	PUNCT
ejpam-3229	161	1	let	let	VERB
ejpam-3229	161	2	n	n	PRON
ejpam-3229	161	3	be	be	AUX
ejpam-3229	161	4	m	m	ADJ
ejpam-3229	161	5	-	-	ADJ
ejpam-3229	161	6	principally	principally	ADV
ejpam-3229	161	7	injective	injective	ADJ
ejpam-3229	161	8	and	and	CCONJ
ejpam-3229	161	9	x	x	PART
ejpam-3229	161	10	be	be	AUX
ejpam-3229	161	11	an	an	DET
ejpam-3229	161	12	m	m	NOUN
ejpam-3229	161	13	-	-	PUNCT
ejpam-3229	161	14	cyclic	cyclic	ADJ
ejpam-3229	161	15	sub	sub	NOUN
ejpam-3229	161	16	-	-	NOUN
ejpam-3229	161	17	act	act	NOUN
ejpam-3229	161	18	of	of	ADP
ejpam-3229	161	19	m	m	PROPN
ejpam-3229	161	20	,	,	PUNCT
ejpam-3229	161	21	so	so	ADV
ejpam-3229	161	22	x	x	SYM
ejpam-3229	161	23	=	=	SYM
ejpam-3229	161	24	γ	γ	X
ejpam-3229	161	25	(	(	PUNCT
ejpam-3229	161	26	m	m	PROPN
ejpam-3229	161	27	)	)	PUNCT
ejpam-3229	161	28	,	,	PUNCT
ejpam-3229	161	29	for	for	ADP
ejpam-3229	161	30	some	some	DET
ejpam-3229	161	31	γ	γ	PROPN
ejpam-3229	161	32	∈	∈	PROPN
ejpam-3229	161	33	e.	e.	PROPN
ejpam-3229	161	34	let	let	VERB
ejpam-3229	161	35	φ	φ	PROPN
ejpam-3229	161	36	:	:	PUNCT
ejpam-3229	161	37	α(x	α(x	NOUN
ejpam-3229	161	38	)	)	PUNCT
ejpam-3229	161	39	→	→	SYM
ejpam-3229	162	1	n	n	CCONJ
ejpam-3229	162	2	where	where	SCONJ
ejpam-3229	162	3	α	α	DET
ejpam-3229	162	4	∈	∈	PROPN
ejpam-3229	162	5	ends(x	ends(x	NOUN
ejpam-3229	162	6	)	)	PUNCT
ejpam-3229	162	7	so	so	ADV
ejpam-3229	162	8	α(x	α(x	NOUN
ejpam-3229	162	9	)	)	PUNCT
ejpam-3229	163	1	=	=	SYM
ejpam-3229	163	2	α	α	PROPN
ejpam-3229	163	3	(	(	PUNCT
ejpam-3229	163	4	γ	γ	X
ejpam-3229	163	5	(	(	PUNCT
ejpam-3229	163	6	m	m	NOUN
ejpam-3229	163	7	)	)	PUNCT
ejpam-3229	163	8	)	)	PUNCT
ejpam-3229	164	1	=	=	PUNCT
ejpam-3229	164	2	αγ	αγ	PROPN
ejpam-3229	164	3	(	(	PUNCT
ejpam-3229	164	4	m	m	NOUN
ejpam-3229	164	5	)	)	PUNCT
ejpam-3229	164	6	,	,	PUNCT
ejpam-3229	164	7	since	since	SCONJ
ejpam-3229	164	8	n	n	ADV
ejpam-3229	164	9	is	be	AUX
ejpam-3229	164	10	m	m	NOUN
ejpam-3229	164	11	-	-	ADJ
ejpam-3229	164	12	principally	principally	ADV
ejpam-3229	164	13	injective	injective	ADJ
ejpam-3229	164	14	so	so	ADV
ejpam-3229	164	15	φ̂	φ̂	PUNCT
ejpam-3229	164	16	:	:	PUNCT
ejpam-3229	164	17	m→n	m→n	NOUN
ejpam-3229	164	18	extends	extend	VERB
ejpam-3229	164	19	φ	φ	PROPN
ejpam-3229	164	20	.	.	PUNCT
ejpam-3229	165	1	now	now	ADV
ejpam-3229	165	2	φ̂/x	φ̂/x	PROPN
ejpam-3229	165	3	=	=	SYM
ejpam-3229	165	4	ψ	ψ	NOUN
ejpam-3229	165	5	,	,	PUNCT
ejpam-3229	165	6	clearly	clearly	ADV
ejpam-3229	165	7	ψ	ψ	X
ejpam-3229	165	8	:	:	PUNCT
ejpam-3229	165	9	x	x	SYM
ejpam-3229	165	10	→	→	SYM
ejpam-3229	165	11	n	n	NUM
ejpam-3229	165	12	extends	extend	VERB
ejpam-3229	165	13	φ	φ	NUM
ejpam-3229	165	14	,	,	PUNCT
ejpam-3229	165	15	hence	hence	ADV
ejpam-3229	165	16	n	n	PRON
ejpam-3229	165	17	is	be	AUX
ejpam-3229	165	18	x	x	NOUN
ejpam-3229	165	19	-	-	NOUN
ejpam-3229	165	20	cyclic	cyclic	ADJ
ejpam-3229	165	21	.	.	PUNCT
ejpam-3229	166	1	conversely	conversely	ADV
ejpam-3229	166	2	assume	assume	VERB
ejpam-3229	166	3	as	as	SCONJ
ejpam-3229	166	4	mentioned	mention	VERB
ejpam-3229	166	5	in	in	ADP
ejpam-3229	166	6	the	the	DET
ejpam-3229	166	7	statement	statement	NOUN
ejpam-3229	166	8	.	.	PUNCT
ejpam-3229	167	1	since	since	SCONJ
ejpam-3229	167	2	i	i	PRON
ejpam-3229	167	3	(	(	PUNCT
ejpam-3229	167	4	m	m	NOUN
ejpam-3229	167	5	)	)	PUNCT
ejpam-3229	167	6	=	=	SYM
ejpam-3229	167	7	m	m	PROPN
ejpam-3229	167	8	,	,	PUNCT
ejpam-3229	167	9	where	where	SCONJ
ejpam-3229	167	10	i	i	PRON
ejpam-3229	167	11	is	be	AUX
ejpam-3229	167	12	an	an	DET
ejpam-3229	167	13	identity	identity	NOUN
ejpam-3229	167	14	s	s	NOUN
ejpam-3229	167	15	-	-	NOUN
ejpam-3229	167	16	homomorphism	homomorphism	NOUN
ejpam-3229	167	17	on	on	ADP
ejpam-3229	167	18	m	m	PROPN
ejpam-3229	167	19	,	,	PUNCT
ejpam-3229	167	20	so	so	ADV
ejpam-3229	167	21	m	m	ADV
ejpam-3229	167	22	,	,	PUNCT
ejpam-3229	167	23	itself	itself	PRON
ejpam-3229	167	24	is	be	AUX
ejpam-3229	167	25	an	an	DET
ejpam-3229	167	26	m	m	NOUN
ejpam-3229	167	27	-	-	PUNCT
ejpam-3229	167	28	cyclic	cyclic	ADJ
ejpam-3229	167	29	sub	sub	NOUN
ejpam-3229	167	30	-	-	NOUN
ejpam-3229	167	31	act	act	NOUN
ejpam-3229	167	32	of	of	ADP
ejpam-3229	167	33	m.	m.	NOUN
ejpam-3229	167	34	thus	thus	ADV
ejpam-3229	167	35	n	n	ADV
ejpam-3229	167	36	is	be	AUX
ejpam-3229	167	37	m	m	NOUN
ejpam-3229	167	38	-	-	PUNCT
ejpam-3229	167	39	principally	principally	ADV
ejpam-3229	167	40	injective	injective	ADJ
ejpam-3229	167	41	.	.	PUNCT
ejpam-3229	168	1	the	the	DET
ejpam-3229	168	2	direct	direct	ADJ
ejpam-3229	168	3	product	product	NOUN
ejpam-3229	168	4	of	of	ADP
ejpam-3229	168	5	s	s	NOUN
ejpam-3229	168	6	-	-	PUNCT
ejpam-3229	168	7	acts	act	NOUN
ejpam-3229	168	8	is	be	AUX
ejpam-3229	168	9	defined	define	VERB
ejpam-3229	168	10	in	in	ADP
ejpam-3229	168	11	[	[	X
ejpam-3229	168	12	4	4	NUM
ejpam-3229	168	13	]	]	PUNCT
ejpam-3229	168	14	.	.	PUNCT
ejpam-3229	169	1	if	if	SCONJ
ejpam-3229	169	2	n	n	NUM
ejpam-3229	169	3	=	=	PROPN
ejpam-3229	169	4	⊕	⊕	PROPN
ejpam-3229	169	5	i∈i	i∈i	ADJ
ejpam-3229	169	6	ni	ni	PROPN
ejpam-3229	169	7	is	be	AUX
ejpam-3229	169	8	the	the	DET
ejpam-3229	169	9	direct	direct	ADJ
ejpam-3229	169	10	sum	sum	NOUN
ejpam-3229	169	11	of	of	ADP
ejpam-3229	169	12	right	right	ADJ
ejpam-3229	169	13	s	s	NOUN
ejpam-3229	169	14	-	-	PUNCT
ejpam-3229	169	15	acts	act	NOUN
ejpam-3229	169	16	ni	ni	PROPN
ejpam-3229	169	17	,	,	PUNCT
ejpam-3229	169	18	for	for	ADP
ejpam-3229	169	19	each	each	DET
ejpam-3229	169	20	i	i	PROPN
ejpam-3229	169	21	∈	∈	PROPN
ejpam-3229	169	22	i.	i.	NOUN
ejpam-3229	169	23	moreover	moreover	ADV
ejpam-3229	169	24	,	,	PUNCT
ejpam-3229	169	25	we	we	PRON
ejpam-3229	169	26	treat	treat	VERB
ejpam-3229	169	27	λi	λi	ADP
ejpam-3229	169	28	:	:	PUNCT
ejpam-3229	169	29	ni	ni	PROPN
ejpam-3229	169	30	→	→	SYM
ejpam-3229	169	31	n	n	PROPN
ejpam-3229	169	32	as	as	ADP
ejpam-3229	169	33	a	a	DET
ejpam-3229	169	34	natural	natural	ADJ
ejpam-3229	169	35	s	s	NOUN
ejpam-3229	169	36	-	-	PUNCT
ejpam-3229	169	37	injection	injection	NOUN
ejpam-3229	169	38	and	and	CCONJ
ejpam-3229	169	39	πj	πj	INTJ
ejpam-3229	169	40	:	:	PUNCT
ejpam-3229	169	41	n	n	X
ejpam-3229	169	42	→	→	SYM
ejpam-3229	169	43	nj	nj	PROPN
ejpam-3229	169	44	as	as	ADP
ejpam-3229	169	45	a	a	DET
ejpam-3229	169	46	natural	natural	ADJ
ejpam-3229	169	47	s	s	NOUN
ejpam-3229	169	48	-	-	NOUN
ejpam-3229	169	49	projection	projection	NOUN
ejpam-3229	169	50	such	such	ADJ
ejpam-3229	169	51	that	that	DET
ejpam-3229	169	52	πjλj	πjλj	NOUN
ejpam-3229	169	53	=	=	SYM
ejpam-3229	169	54	inj	inj	NOUN
ejpam-3229	169	55	,	,	PUNCT
ejpam-3229	169	56	where	where	SCONJ
ejpam-3229	169	57	inj	inj	NOUN
ejpam-3229	169	58	is	be	AUX
ejpam-3229	169	59	the	the	DET
ejpam-3229	169	60	identity	identity	NOUN
ejpam-3229	169	61	s	s	NOUN
ejpam-3229	169	62	-	-	PUNCT
ejpam-3229	169	63	homomorphism	homomorphism	NOUN
ejpam-3229	169	64	on	on	ADP
ejpam-3229	169	65	nj	nj	PROPN
ejpam-3229	169	66	.	.	PUNCT
ejpam-3229	170	1	theorem	theorem	VERB
ejpam-3229	170	2	4	4	NUM
ejpam-3229	170	3	.	.	PUNCT
ejpam-3229	170	4	n	n	NOUN
ejpam-3229	170	5	=	=	PROPN
ejpam-3229	170	6	⊕	⊕	PROPN
ejpam-3229	170	7	i∈i	i∈i	ADJ
ejpam-3229	170	8	ni	ni	PROPN
ejpam-3229	170	9	is	be	AUX
ejpam-3229	170	10	m	m	NOUN
ejpam-3229	170	11	-	-	ADJ
ejpam-3229	170	12	principally	principally	ADV
ejpam-3229	170	13	injective	injective	ADJ
ejpam-3229	170	14	iff	iff	PROPN
ejpam-3229	170	15	each	each	DET
ejpam-3229	170	16	ni	ni	PROPN
ejpam-3229	170	17	is	be	AUX
ejpam-3229	170	18	m	m	NOUN
ejpam-3229	170	19	-	-	ADJ
ejpam-3229	170	20	principally	principally	ADV
ejpam-3229	170	21	injective	injective	ADJ
ejpam-3229	170	22	,	,	PUNCT
ejpam-3229	170	23	for	for	ADP
ejpam-3229	170	24	all	all	PRON
ejpam-3229	170	25	i	i	PRON
ejpam-3229	170	26	∈	∈	PROPN
ejpam-3229	170	27	i.	i.	NOUN
ejpam-3229	170	28	proof	proof	PROPN
ejpam-3229	170	29	.	.	PUNCT
ejpam-3229	171	1	suppose	suppose	VERB
ejpam-3229	171	2	φj	φj	X
ejpam-3229	171	3	:	:	PUNCT
ejpam-3229	171	4	α	α	PROPN
ejpam-3229	171	5	(	(	PUNCT
ejpam-3229	171	6	m)→	m)→	PROPN
ejpam-3229	171	7	nj	nj	PROPN
ejpam-3229	171	8	is	be	AUX
ejpam-3229	171	9	an	an	DET
ejpam-3229	171	10	s	s	NOUN
ejpam-3229	171	11	-	-	PUNCT
ejpam-3229	171	12	homomorphism	homomorphism	NOUN
ejpam-3229	171	13	for	for	SCONJ
ejpam-3229	171	14	each	each	DET
ejpam-3229	171	15	j	j	PROPN
ejpam-3229	171	16	∈	∈	PROPN
ejpam-3229	171	17	i.	i.	NOUN
ejpam-3229	171	18	now	now	ADV
ejpam-3229	171	19	sincen	sincen	VERB
ejpam-3229	171	20	is	be	AUX
ejpam-3229	171	21	m	m	NOUN
ejpam-3229	171	22	-	-	ADJ
ejpam-3229	171	23	principally	principally	ADV
ejpam-3229	171	24	injective	injective	ADJ
ejpam-3229	171	25	so	so	SCONJ
ejpam-3229	171	26	we	we	PRON
ejpam-3229	171	27	have	have	VERB
ejpam-3229	171	28	γ	γ	NOUN
ejpam-3229	171	29	:	:	PUNCT
ejpam-3229	171	30	m→n	m→n	NOUN
ejpam-3229	171	31	such	such	ADJ
ejpam-3229	171	32	that	that	DET
ejpam-3229	171	33	γi	γi	NOUN
ejpam-3229	171	34	=	=	SYM
ejpam-3229	171	35	λjφj	λjφj	NOUN
ejpam-3229	171	36	,	,	PUNCT
ejpam-3229	171	37	where	where	SCONJ
ejpam-3229	171	38	i	i	PRON
ejpam-3229	171	39	:	:	PUNCT
ejpam-3229	171	40	α	α	X
ejpam-3229	171	41	(	(	PUNCT
ejpam-3229	171	42	m)→m	m)→m	X
ejpam-3229	171	43	is	be	AUX
ejpam-3229	171	44	inclusion	inclusion	NOUN
ejpam-3229	171	45	.	.	PUNCT
ejpam-3229	172	1	using	use	VERB
ejpam-3229	172	2	πjγ	πjγ	PROPN
ejpam-3229	172	3	:	:	PUNCT
ejpam-3229	172	4	m→nj	m→nj	NUM
ejpam-3229	172	5	it	it	PRON
ejpam-3229	172	6	follows	follow	VERB
ejpam-3229	172	7	that	that	SCONJ
ejpam-3229	172	8	,	,	PUNCT
ejpam-3229	172	9	(	(	PUNCT
ejpam-3229	172	10	πjγ)i	πjγ)i	PROPN
ejpam-3229	172	11	=	=	SYM
ejpam-3229	172	12	πj(γi	πj(γi	PROPN
ejpam-3229	172	13	)	)	PUNCT
ejpam-3229	172	14	=	=	SYM
ejpam-3229	173	1	πj(λjφj	πj(λjφj	X
ejpam-3229	173	2	)	)	PUNCT
ejpam-3229	173	3	=	=	SYM
ejpam-3229	173	4	(	(	PUNCT
ejpam-3229	173	5	πjλj)φj	πjλj)φj	NOUN
ejpam-3229	173	6	=	=	NOUN
ejpam-3229	173	7	φj	φj	PROPN
ejpam-3229	173	8	.	.	PUNCT
ejpam-3229	174	1	j.	j.	PROPN
ejpam-3229	174	2	hussain	hussain	PROPN
ejpam-3229	174	3	,	,	PUNCT
ejpam-3229	174	4	m.shabir	m.shabir	PROPN
ejpam-3229	174	5	/	/	SYM
ejpam-3229	174	6	eur	eur	PROPN
ejpam-3229	174	7	.	.	PUNCT
ejpam-3229	175	1	j.	j.	PROPN
ejpam-3229	175	2	pure	pure	PROPN
ejpam-3229	175	3	appl	appl	PROPN
ejpam-3229	175	4	.	.	PROPN
ejpam-3229	175	5	math	math	PROPN
ejpam-3229	175	6	,	,	PUNCT
ejpam-3229	175	7	11	11	NUM
ejpam-3229	175	8	(	(	PUNCT
ejpam-3229	175	9	2	2	NUM
ejpam-3229	175	10	)	)	PUNCT
ejpam-3229	175	11	(	(	PUNCT
ejpam-3229	175	12	2018	2018	NUM
ejpam-3229	175	13	)	)	PUNCT
ejpam-3229	175	14	,	,	PUNCT
ejpam-3229	175	15	431	431	NUM
ejpam-3229	175	16	-	-	SYM
ejpam-3229	175	17	443	443	NUM
ejpam-3229	175	18	436	436	NUM
ejpam-3229	175	19	conversely	conversely	ADV
ejpam-3229	175	20	assume	assume	VERB
ejpam-3229	175	21	that	that	SCONJ
ejpam-3229	175	22	φ	φ	PROPN
ejpam-3229	175	23	:	:	PUNCT
ejpam-3229	175	24	α	α	X
ejpam-3229	175	25	(	(	PUNCT
ejpam-3229	175	26	m)→	m)→	VERB
ejpam-3229	175	27	n	n	PRON
ejpam-3229	175	28	is	be	AUX
ejpam-3229	175	29	an	an	DET
ejpam-3229	175	30	s	s	NOUN
ejpam-3229	175	31	-	-	NOUN
ejpam-3229	175	32	homomorphism	homomorphism	NOUN
ejpam-3229	175	33	.	.	PUNCT
ejpam-3229	176	1	now	now	ADV
ejpam-3229	176	2	πjφ	πjφ	ADV
ejpam-3229	176	3	:	:	PUNCT
ejpam-3229	176	4	α	α	X
ejpam-3229	176	5	(	(	PUNCT
ejpam-3229	176	6	m)→	m)→	PROPN
ejpam-3229	176	7	nj	nj	PROPN
ejpam-3229	176	8	is	be	AUX
ejpam-3229	176	9	also	also	ADV
ejpam-3229	176	10	an	an	DET
ejpam-3229	176	11	s	s	NOUN
ejpam-3229	176	12	-	-	NOUN
ejpam-3229	176	13	homomorphism	homomorphism	NOUN
ejpam-3229	176	14	.	.	PUNCT
ejpam-3229	177	1	since	since	SCONJ
ejpam-3229	177	2	each	each	DET
ejpam-3229	177	3	nj	nj	PROPN
ejpam-3229	177	4	is	be	AUX
ejpam-3229	177	5	m	m	NOUN
ejpam-3229	177	6	-	-	PUNCT
ejpam-3229	177	7	principally	principally	ADV
ejpam-3229	177	8	injective	injective	ADJ
ejpam-3229	177	9	,	,	PUNCT
ejpam-3229	177	10	so	so	SCONJ
ejpam-3229	177	11	we	we	PRON
ejpam-3229	177	12	have	have	AUX
ejpam-3229	177	13	γj	γj	ADP
ejpam-3229	177	14	:	:	PUNCT
ejpam-3229	177	15	m	m	PROPN
ejpam-3229	177	16	→	→	SYM
ejpam-3229	177	17	nj	nj	PROPN
ejpam-3229	177	18	such	such	ADJ
ejpam-3229	177	19	that	that	DET
ejpam-3229	177	20	γji	γji	ADJ
ejpam-3229	177	21	=	=	SYM
ejpam-3229	177	22	πjφ	πjφ	NOUN
ejpam-3229	177	23	.	.	PUNCT
ejpam-3229	177	24	define	define	VERB
ejpam-3229	177	25	γ	γ	X
ejpam-3229	177	26	:	:	PUNCT
ejpam-3229	177	27	m	m	PROPN
ejpam-3229	177	28	→	→	SYM
ejpam-3229	177	29	n	n	X
ejpam-3229	177	30	by	by	ADP
ejpam-3229	177	31	γ(t	γ(t	NOUN
ejpam-3229	177	32	)	)	PUNCT
ejpam-3229	177	33	=	=	SYM
ejpam-3229	177	34	(	(	PUNCT
ejpam-3229	177	35	γj(t	γj(t	PROPN
ejpam-3229	177	36	)	)	PUNCT
ejpam-3229	177	37	)	)	PUNCT
ejpam-3229	177	38	,	,	PUNCT
ejpam-3229	177	39	for	for	ADP
ejpam-3229	177	40	t	t	PROPN
ejpam-3229	177	41	∈	∈	PROPN
ejpam-3229	177	42	α	α	PROPN
ejpam-3229	177	43	(	(	PUNCT
ejpam-3229	177	44	m	m	PROPN
ejpam-3229	177	45	)	)	PUNCT
ejpam-3229	177	46	.	.	PUNCT
ejpam-3229	178	1	clearly	clearly	ADV
ejpam-3229	178	2	γ	γ	PROPN
ejpam-3229	178	3	is	be	AUX
ejpam-3229	178	4	an	an	DET
ejpam-3229	178	5	s	s	NOUN
ejpam-3229	178	6	-	-	PUNCT
ejpam-3229	178	7	homomorphism	homomorphism	NOUN
ejpam-3229	178	8	and	and	CCONJ
ejpam-3229	178	9	γ(i(t	γ(i(t	NOUN
ejpam-3229	178	10	)	)	PUNCT
ejpam-3229	178	11	)	)	PUNCT
ejpam-3229	179	1	=	=	SYM
ejpam-3229	179	2	(	(	PUNCT
ejpam-3229	179	3	γj(i(t	γj(i(t	NOUN
ejpam-3229	179	4	)	)	PUNCT
ejpam-3229	179	5	)	)	PUNCT
ejpam-3229	179	6	)	)	PUNCT
ejpam-3229	180	1	=	=	PUNCT
ejpam-3229	180	2	(	(	PUNCT
ejpam-3229	180	3	γji(t	γji(t	NOUN
ejpam-3229	180	4	)	)	PUNCT
ejpam-3229	180	5	)	)	PUNCT
ejpam-3229	181	1	=	=	SYM
ejpam-3229	181	2	(	(	PUNCT
ejpam-3229	181	3	πjφ(t	πjφ(t	NOUN
ejpam-3229	181	4	)	)	PUNCT
ejpam-3229	181	5	)	)	PUNCT
ejpam-3229	182	1	=	=	SYM
ejpam-3229	182	2	φ(t	φ(t	PROPN
ejpam-3229	182	3	)	)	PUNCT
ejpam-3229	182	4	,	,	PUNCT
ejpam-3229	182	5	for	for	ADP
ejpam-3229	182	6	all	all	DET
ejpam-3229	182	7	t	t	NOUN
ejpam-3229	182	8	∈	∈	PROPN
ejpam-3229	182	9	α	α	PROPN
ejpam-3229	182	10	(	(	PUNCT
ejpam-3229	182	11	m	m	NOUN
ejpam-3229	182	12	)	)	PUNCT
ejpam-3229	182	13	.	.	PUNCT
ejpam-3229	183	1	thus	thus	ADV
ejpam-3229	183	2	γ	γ	PROPN
ejpam-3229	183	3	extends	extend	VERB
ejpam-3229	183	4	φ	φ	NUM
ejpam-3229	183	5	,	,	PUNCT
ejpam-3229	183	6	so	so	ADV
ejpam-3229	183	7	n	n	PROPN
ejpam-3229	183	8	is	be	AUX
ejpam-3229	183	9	m	m	NOUN
ejpam-3229	183	10	-	-	PUNCT
ejpam-3229	183	11	principally	principally	ADV
ejpam-3229	183	12	injective	injective	ADJ
ejpam-3229	183	13	.	.	PUNCT
ejpam-3229	184	1	corollary	corollary	ADJ
ejpam-3229	184	2	3	3	NUM
ejpam-3229	184	3	.	.	PUNCT
ejpam-3229	185	1	n	n	PROPN
ejpam-3229	185	2	=	=	PROPN
ejpam-3229	185	3	⊕	⊕	PROPN
ejpam-3229	185	4	i∈i	i∈i	ADJ
ejpam-3229	185	5	ni	ni	PROPN
ejpam-3229	185	6	is	be	AUX
ejpam-3229	185	7	quasi	quasi	ADJ
ejpam-3229	185	8	-	-	ADJ
ejpam-3229	185	9	principally	principally	ADV
ejpam-3229	185	10	injective	injective	ADJ
ejpam-3229	185	11	iff	iff	PROPN
ejpam-3229	185	12	each	each	DET
ejpam-3229	185	13	ni	ni	PROPN
ejpam-3229	185	14	is	be	AUX
ejpam-3229	185	15	quasi	quasi	ADJ
ejpam-3229	185	16	-	-	ADJ
ejpam-3229	185	17	principally	principally	ADV
ejpam-3229	185	18	injective	injective	ADJ
ejpam-3229	185	19	,	,	PUNCT
ejpam-3229	185	20	for	for	ADP
ejpam-3229	185	21	all	all	PRON
ejpam-3229	185	22	i	i	PRON
ejpam-3229	185	23	∈	∈	PROPN
ejpam-3229	185	24	i.	i.	NOUN
ejpam-3229	185	25	3	3	NUM
ejpam-3229	185	26	.	.	PUNCT
ejpam-3229	186	1	m	m	VERB
ejpam-3229	186	2	-	-	PUNCT
ejpam-3229	186	3	principally	principally	ADV
ejpam-3229	186	4	projective	projective	ADJ
ejpam-3229	186	5	s	s	NOUN
ejpam-3229	186	6	-	-	PUNCT
ejpam-3229	186	7	acts	act	NOUN
ejpam-3229	186	8	in	in	ADP
ejpam-3229	186	9	this	this	DET
ejpam-3229	186	10	section	section	NOUN
ejpam-3229	186	11	we	we	PRON
ejpam-3229	186	12	have	have	VERB
ejpam-3229	186	13	definedm	definedm	NOUN
ejpam-3229	186	14	-	-	PUNCT
ejpam-3229	186	15	principally	principally	ADV
ejpam-3229	186	16	injective	injective	ADJ
ejpam-3229	186	17	s	s	NOUN
ejpam-3229	186	18	-	-	PUNCT
ejpam-3229	186	19	acts	act	NOUN
ejpam-3229	186	20	and	and	CCONJ
ejpam-3229	186	21	characterized	characterize	VERB
ejpam-3229	186	22	them	they	PRON
ejpam-3229	186	23	in	in	ADP
ejpam-3229	186	24	terms	term	NOUN
ejpam-3229	186	25	ofm	ofm	PROPN
ejpam-3229	186	26	-	-	PUNCT
ejpam-3229	186	27	cyclic	cyclic	ADJ
ejpam-3229	186	28	sub	sub	NOUN
ejpam-3229	186	29	-	-	NOUN
ejpam-3229	186	30	acts	act	NOUN
ejpam-3229	186	31	.	.	PUNCT
ejpam-3229	187	1	further	far	ADV
ejpam-3229	187	2	we	we	PRON
ejpam-3229	187	3	have	have	AUX
ejpam-3229	187	4	also	also	ADV
ejpam-3229	187	5	investigated	investigate	VERB
ejpam-3229	187	6	few	few	ADJ
ejpam-3229	187	7	basic	basic	ADJ
ejpam-3229	187	8	and	and	CCONJ
ejpam-3229	187	9	important	important	ADJ
ejpam-3229	187	10	properties	property	NOUN
ejpam-3229	187	11	of	of	ADP
ejpam-3229	187	12	the	the	DET
ejpam-3229	187	13	mentioned	mention	VERB
ejpam-3229	187	14	structure	structure	NOUN
ejpam-3229	187	15	.	.	PUNCT
ejpam-3229	188	1	3.1	3.1	NUM
ejpam-3229	188	2	.	.	PUNCT
ejpam-3229	189	1	m	m	VERB
ejpam-3229	189	2	-	-	PUNCT
ejpam-3229	189	3	principally	principally	ADV
ejpam-3229	189	4	and	and	CCONJ
ejpam-3229	189	5	quasi	quasi	ADJ
ejpam-3229	189	6	-	-	ADJ
ejpam-3229	189	7	principally	principally	ADV
ejpam-3229	189	8	projective	projective	ADJ
ejpam-3229	189	9	s	s	NOUN
ejpam-3229	189	10	-	-	PUNCT
ejpam-3229	189	11	act	act	NOUN
ejpam-3229	189	12	definition	definition	NOUN
ejpam-3229	189	13	5	5	NUM
ejpam-3229	189	14	.	.	PUNCT
ejpam-3229	190	1	a	a	DET
ejpam-3229	190	2	right	right	ADJ
ejpam-3229	190	3	s	s	NOUN
ejpam-3229	190	4	-	-	PUNCT
ejpam-3229	190	5	act	act	NOUN
ejpam-3229	190	6	n	n	PRON
ejpam-3229	190	7	is	be	AUX
ejpam-3229	190	8	calledm	calledm	NOUN
ejpam-3229	190	9	-	-	PUNCT
ejpam-3229	190	10	principally	principally	ADV
ejpam-3229	190	11	projective	projective	ADJ
ejpam-3229	190	12	if	if	SCONJ
ejpam-3229	190	13	every	every	DET
ejpam-3229	190	14	s	s	NOUN
ejpam-3229	190	15	-	-	PUNCT
ejpam-3229	190	16	homomorphism	homomorphism	NOUN
ejpam-3229	190	17	from	from	ADP
ejpam-3229	190	18	n	n	PRON
ejpam-3229	190	19	to	to	ADP
ejpam-3229	190	20	an	an	DET
ejpam-3229	190	21	m	m	NOUN
ejpam-3229	190	22	-	-	PUNCT
ejpam-3229	190	23	cyclic	cyclic	ADJ
ejpam-3229	190	24	sub	sub	NOUN
ejpam-3229	190	25	-	-	NOUN
ejpam-3229	190	26	act	act	NOUN
ejpam-3229	190	27	of	of	ADP
ejpam-3229	190	28	m	m	PROPN
ejpam-3229	190	29	can	can	AUX
ejpam-3229	190	30	be	be	AUX
ejpam-3229	190	31	lifted	lift	VERB
ejpam-3229	190	32	to	to	ADP
ejpam-3229	190	33	an	an	DET
ejpam-3229	190	34	s	s	NOUN
ejpam-3229	190	35	-	-	PUNCT
ejpam-3229	190	36	homomorphism	homomorphism	NOUN
ejpam-3229	190	37	from	from	ADP
ejpam-3229	190	38	n	n	PART
ejpam-3229	190	39	to	to	PART
ejpam-3229	190	40	m.	m.	VERB
ejpam-3229	190	41	lemma	lemma	PROPN
ejpam-3229	190	42	4	4	X
ejpam-3229	190	43	.	.	PUNCT
ejpam-3229	191	1	let	let	VERB
ejpam-3229	191	2	m	m	PRON
ejpam-3229	191	3	and	and	CCONJ
ejpam-3229	191	4	n	n	ADV
ejpam-3229	191	5	be	be	AUX
ejpam-3229	191	6	right	right	ADJ
ejpam-3229	191	7	s	s	NOUN
ejpam-3229	191	8	-	-	PUNCT
ejpam-3229	191	9	acts	act	VERB
ejpam-3229	191	10	then	then	ADV
ejpam-3229	191	11	n	n	AUX
ejpam-3229	191	12	is	be	AUX
ejpam-3229	191	13	m	m	NOUN
ejpam-3229	191	14	-	-	ADJ
ejpam-3229	191	15	principally	principally	ADV
ejpam-3229	191	16	projective	projective	ADJ
ejpam-3229	191	17	iff	iff	PROPN
ejpam-3229	191	18	homs	hom	NOUN
ejpam-3229	191	19	(	(	PUNCT
ejpam-3229	191	20	n	n	X
ejpam-3229	191	21	,	,	PUNCT
ejpam-3229	191	22	α	α	PROPN
ejpam-3229	191	23	(	(	PUNCT
ejpam-3229	191	24	m	m	NOUN
ejpam-3229	191	25	)	)	PUNCT
ejpam-3229	191	26	)	)	PUNCT
ejpam-3229	192	1	=	=	SYM
ejpam-3229	192	2	αhoms(n	αhoms(n	NUM
ejpam-3229	192	3	,	,	PUNCT
ejpam-3229	192	4	m	m	PROPN
ejpam-3229	192	5	)	)	PUNCT
ejpam-3229	192	6	,	,	PUNCT
ejpam-3229	192	7	for	for	ADP
ejpam-3229	192	8	all	all	DET
ejpam-3229	192	9	α	α	PRON
ejpam-3229	192	10	∈	∈	PROPN
ejpam-3229	192	11	e.	e.	PROPN
ejpam-3229	192	12	proof	proof	PROPN
ejpam-3229	192	13	.	.	PUNCT
ejpam-3229	193	1	assume	assume	VERB
ejpam-3229	193	2	thatn	thatn	ADJ
ejpam-3229	193	3	ism	ism	NOUN
ejpam-3229	193	4	-	-	PUNCT
ejpam-3229	193	5	principally	principally	ADV
ejpam-3229	193	6	projective	projective	ADJ
ejpam-3229	193	7	.	.	PUNCT
ejpam-3229	194	1	let	let	VERB
ejpam-3229	194	2	α	α	PRON
ejpam-3229	194	3	∈	∈	PROPN
ejpam-3229	194	4	e	e	X
ejpam-3229	194	5	and	and	CCONJ
ejpam-3229	194	6	αu	αu	PRON
ejpam-3229	194	7	∈	∈	PROPN
ejpam-3229	194	8	αhoms(n	αhoms(n	PROPN
ejpam-3229	194	9	,	,	PUNCT
ejpam-3229	194	10	m	m	PROPN
ejpam-3229	194	11	)	)	PUNCT
ejpam-3229	194	12	where	where	SCONJ
ejpam-3229	194	13	u	u	PROPN
ejpam-3229	194	14	∈	∈	PROPN
ejpam-3229	194	15	homs	hom	NOUN
ejpam-3229	194	16	(	(	PUNCT
ejpam-3229	194	17	n	n	X
ejpam-3229	194	18	,	,	PUNCT
ejpam-3229	194	19	m	m	PROPN
ejpam-3229	194	20	)	)	PUNCT
ejpam-3229	194	21	.	.	PUNCT
ejpam-3229	195	1	since	since	SCONJ
ejpam-3229	195	2	α	α	NOUN
ejpam-3229	195	3	:	:	PUNCT
ejpam-3229	195	4	m	m	VERB
ejpam-3229	195	5	→	→	SYM
ejpam-3229	195	6	α	α	PROPN
ejpam-3229	195	7	(	(	PUNCT
ejpam-3229	195	8	m	m	NOUN
ejpam-3229	195	9	)	)	PUNCT
ejpam-3229	195	10	so	so	ADV
ejpam-3229	195	11	αu	αu	VERB
ejpam-3229	195	12	:	:	PUNCT
ejpam-3229	195	13	n	n	X
ejpam-3229	195	14	→	→	SYM
ejpam-3229	195	15	α	α	PROPN
ejpam-3229	195	16	(	(	PUNCT
ejpam-3229	195	17	m	m	NOUN
ejpam-3229	195	18	)	)	PUNCT
ejpam-3229	195	19	this	this	PRON
ejpam-3229	195	20	means	mean	VERB
ejpam-3229	195	21	αu	αu	ADP
ejpam-3229	195	22	∈	∈	PROPN
ejpam-3229	195	23	homs	hom	NOUN
ejpam-3229	195	24	(	(	PUNCT
ejpam-3229	195	25	n	n	X
ejpam-3229	195	26	,	,	PUNCT
ejpam-3229	195	27	α	α	PROPN
ejpam-3229	195	28	(	(	PUNCT
ejpam-3229	195	29	m	m	NOUN
ejpam-3229	195	30	)	)	PUNCT
ejpam-3229	195	31	)	)	PUNCT
ejpam-3229	195	32	which	which	PRON
ejpam-3229	195	33	gives	give	VERB
ejpam-3229	195	34	homs	hom	NOUN
ejpam-3229	195	35	(	(	PUNCT
ejpam-3229	195	36	n	n	X
ejpam-3229	195	37	,	,	PUNCT
ejpam-3229	195	38	α	α	PROPN
ejpam-3229	195	39	(	(	PUNCT
ejpam-3229	195	40	m	m	NOUN
ejpam-3229	195	41	)	)	PUNCT
ejpam-3229	195	42	)	)	PUNCT
ejpam-3229	195	43	⊇	⊇	PROPN
ejpam-3229	195	44	αhoms	αhom	NOUN
ejpam-3229	195	45	(	(	PUNCT
ejpam-3229	195	46	n	n	CCONJ
ejpam-3229	195	47	,	,	PUNCT
ejpam-3229	195	48	m	m	PROPN
ejpam-3229	195	49	)	)	PUNCT
ejpam-3229	195	50	.	.	PUNCT
ejpam-3229	196	1	for	for	ADP
ejpam-3229	196	2	the	the	DET
ejpam-3229	196	3	converse	converse	NOUN
ejpam-3229	196	4	inclusion	inclusion	NOUN
ejpam-3229	196	5	,	,	PUNCT
ejpam-3229	196	6	let	let	VERB
ejpam-3229	196	7	φ	φ	PROPN
ejpam-3229	196	8	∈	∈	PROPN
ejpam-3229	196	9	homs	hom	NOUN
ejpam-3229	196	10	(	(	PUNCT
ejpam-3229	196	11	n	n	X
ejpam-3229	196	12	,	,	PUNCT
ejpam-3229	196	13	α	α	PROPN
ejpam-3229	196	14	(	(	PUNCT
ejpam-3229	196	15	m	m	NOUN
ejpam-3229	196	16	)	)	PUNCT
ejpam-3229	196	17	)	)	PUNCT
ejpam-3229	196	18	.	.	PUNCT
ejpam-3229	197	1	since	since	SCONJ
ejpam-3229	197	2	n	n	ADV
ejpam-3229	197	3	ism	ism	NOUN
ejpam-3229	197	4	principally	principally	ADV
ejpam-3229	197	5	projective	projective	ADJ
ejpam-3229	197	6	so	so	SCONJ
ejpam-3229	197	7	we	we	PRON
ejpam-3229	197	8	have	have	VERB
ejpam-3229	197	9	an	an	DET
ejpam-3229	197	10	s	s	NOUN
ejpam-3229	197	11	-	-	PUNCT
ejpam-3229	197	12	homomorphism	homomorphism	NOUN
ejpam-3229	197	13	γ	γ	X
ejpam-3229	197	14	:	:	PUNCT
ejpam-3229	197	15	n	n	CCONJ
ejpam-3229	197	16	→m	→m	PROPN
ejpam-3229	198	1	such	such	ADJ
ejpam-3229	198	2	that	that	SCONJ
ejpam-3229	198	3	φ	φ	PROPN
ejpam-3229	198	4	=	=	SYM
ejpam-3229	198	5	αγ	αγ	PROPN
ejpam-3229	198	6	which	which	PRON
ejpam-3229	198	7	implies	imply	VERB
ejpam-3229	198	8	φ	φ	PROPN
ejpam-3229	198	9	∈	∈	PROPN
ejpam-3229	198	10	αhoms	αhom	NOUN
ejpam-3229	198	11	(	(	PUNCT
ejpam-3229	198	12	n	n	CCONJ
ejpam-3229	198	13	,	,	PUNCT
ejpam-3229	198	14	m	m	PROPN
ejpam-3229	198	15	)	)	PUNCT
ejpam-3229	198	16	.	.	PUNCT
ejpam-3229	199	1	thus	thus	ADV
ejpam-3229	199	2	equality	equality	NOUN
ejpam-3229	199	3	holds	hold	VERB
ejpam-3229	199	4	.	.	PUNCT
ejpam-3229	200	1	conversely	conversely	ADV
ejpam-3229	200	2	assume	assume	VERB
ejpam-3229	200	3	that	that	SCONJ
ejpam-3229	200	4	homs	hom	NOUN
ejpam-3229	200	5	(	(	PUNCT
ejpam-3229	200	6	n	n	X
ejpam-3229	200	7	,	,	PUNCT
ejpam-3229	200	8	α	α	PROPN
ejpam-3229	200	9	(	(	PUNCT
ejpam-3229	200	10	m	m	NOUN
ejpam-3229	200	11	)	)	PUNCT
ejpam-3229	200	12	)	)	PUNCT
ejpam-3229	201	1	=	=	SYM
ejpam-3229	201	2	αhoms	αhom	NOUN
ejpam-3229	201	3	(	(	PUNCT
ejpam-3229	201	4	n	n	CCONJ
ejpam-3229	201	5	,	,	PUNCT
ejpam-3229	201	6	m	m	PROPN
ejpam-3229	201	7	)	)	PUNCT
ejpam-3229	201	8	for	for	ADP
ejpam-3229	201	9	all	all	DET
ejpam-3229	201	10	α	α	PROPN
ejpam-3229	201	11	∈	∈	PROPN
ejpam-3229	201	12	e.	e.	PROPN
ejpam-3229	201	13	let	let	VERB
ejpam-3229	201	14	φ	φ	PROPN
ejpam-3229	201	15	:	:	PUNCT
ejpam-3229	201	16	n	n	PROPN
ejpam-3229	201	17	→	→	SYM
ejpam-3229	201	18	α	α	PROPN
ejpam-3229	201	19	(	(	PUNCT
ejpam-3229	201	20	m	m	NOUN
ejpam-3229	201	21	)	)	PUNCT
ejpam-3229	201	22	so	so	ADV
ejpam-3229	201	23	by	by	ADP
ejpam-3229	201	24	hypothesis	hypothesis	NOUN
ejpam-3229	201	25	φ	φ	NOUN
ejpam-3229	201	26	=	=	SYM
ejpam-3229	201	27	αu	αu	PROPN
ejpam-3229	201	28	for	for	ADP
ejpam-3229	201	29	some	some	DET
ejpam-3229	201	30	u	u	PROPN
ejpam-3229	201	31	∈	∈	PROPN
ejpam-3229	201	32	homs	hom	NOUN
ejpam-3229	201	33	(	(	PUNCT
ejpam-3229	201	34	n	n	X
ejpam-3229	201	35	,	,	PUNCT
ejpam-3229	201	36	m	m	PROPN
ejpam-3229	201	37	)	)	PUNCT
ejpam-3229	201	38	.	.	PUNCT
ejpam-3229	202	1	hence	hence	ADV
ejpam-3229	202	2	n	n	NOUN
ejpam-3229	202	3	is	be	AUX
ejpam-3229	202	4	m	m	NOUN
ejpam-3229	202	5	-	-	PUNCT
ejpam-3229	202	6	principally	principally	ADV
ejpam-3229	202	7	projective	projective	ADJ
ejpam-3229	202	8	.	.	PUNCT
ejpam-3229	203	1	theorem	theorem	NOUN
ejpam-3229	203	2	5	5	NUM
ejpam-3229	203	3	.	.	PUNCT
ejpam-3229	204	1	if	if	SCONJ
ejpam-3229	204	2	k	k	PROPN
ejpam-3229	204	3	∼=	∼=	PROPN
ejpam-3229	204	4	n	n	PRON
ejpam-3229	204	5	,	,	PUNCT
ejpam-3229	204	6	m	m	VERB
ejpam-3229	204	7	∼=	∼=	NOUN
ejpam-3229	204	8	m′	m′	NOUN
ejpam-3229	204	9	and	and	CCONJ
ejpam-3229	204	10	n	n	NOUN
ejpam-3229	204	11	is	be	AUX
ejpam-3229	204	12	m	m	NOUN
ejpam-3229	204	13	-	-	ADJ
ejpam-3229	204	14	principally	principally	ADV
ejpam-3229	204	15	projective	projective	ADJ
ejpam-3229	204	16	then	then	ADV
ejpam-3229	204	17	k	k	PROPN
ejpam-3229	204	18	is	be	AUX
ejpam-3229	204	19	mprincipally	mprincipally	ADV
ejpam-3229	204	20	projective	projective	ADJ
ejpam-3229	204	21	and	and	CCONJ
ejpam-3229	204	22	n	n	PRON
ejpam-3229	204	23	is	be	AUX
ejpam-3229	204	24	m′-principally	m′-principally	ADV
ejpam-3229	204	25	projective	projective	ADJ
ejpam-3229	204	26	.	.	PUNCT
ejpam-3229	205	1	proof	proof	NOUN
ejpam-3229	205	2	.	.	PUNCT
ejpam-3229	206	1	straight	straight	ADV
ejpam-3229	206	2	forward	forward	ADV
ejpam-3229	206	3	.	.	PUNCT
ejpam-3229	207	1	lemma	lemma	PROPN
ejpam-3229	207	2	5	5	X
ejpam-3229	207	3	.	.	PUNCT
ejpam-3229	208	1	let	let	VERB
ejpam-3229	208	2	m	m	PRON
ejpam-3229	208	3	and	and	CCONJ
ejpam-3229	208	4	n	n	CCONJ
ejpam-3229	208	5	be	be	AUX
ejpam-3229	208	6	two	two	NUM
ejpam-3229	208	7	right	right	ADJ
ejpam-3229	208	8	s	s	NOUN
ejpam-3229	208	9	-	-	PUNCT
ejpam-3229	208	10	acts	act	VERB
ejpam-3229	208	11	then	then	ADV
ejpam-3229	208	12	n	n	AUX
ejpam-3229	208	13	is	be	AUX
ejpam-3229	208	14	m	m	NOUN
ejpam-3229	208	15	-	-	ADJ
ejpam-3229	208	16	principally	principally	ADV
ejpam-3229	208	17	projective	projective	ADJ
ejpam-3229	208	18	iff	iff	PROPN
ejpam-3229	208	19	n	n	PRON
ejpam-3229	208	20	is	be	AUX
ejpam-3229	208	21	x	x	ADJ
ejpam-3229	208	22	-	-	ADJ
ejpam-3229	208	23	principally	principally	ADV
ejpam-3229	208	24	projective	projective	ADJ
ejpam-3229	208	25	for	for	ADP
ejpam-3229	208	26	every	every	DET
ejpam-3229	208	27	m	m	NOUN
ejpam-3229	208	28	-	-	PUNCT
ejpam-3229	208	29	cyclic	cyclic	ADJ
ejpam-3229	208	30	sub	sub	NOUN
ejpam-3229	208	31	-	-	NOUN
ejpam-3229	208	32	act	act	NOUN
ejpam-3229	208	33	x	x	PUNCT
ejpam-3229	208	34	of	of	ADP
ejpam-3229	208	35	m.	m.	NOUN
ejpam-3229	208	36	j.	j.	PROPN
ejpam-3229	208	37	hussain	hussain	PROPN
ejpam-3229	208	38	,	,	PUNCT
ejpam-3229	208	39	m.shabir	m.shabir	PROPN
ejpam-3229	208	40	/	/	SYM
ejpam-3229	208	41	eur	eur	PROPN
ejpam-3229	208	42	.	.	PUNCT
ejpam-3229	209	1	j.	j.	PROPN
ejpam-3229	209	2	pure	pure	PROPN
ejpam-3229	209	3	appl	appl	PROPN
ejpam-3229	209	4	.	.	PROPN
ejpam-3229	209	5	math	math	PROPN
ejpam-3229	209	6	,	,	PUNCT
ejpam-3229	209	7	11	11	NUM
ejpam-3229	209	8	(	(	PUNCT
ejpam-3229	209	9	2	2	NUM
ejpam-3229	209	10	)	)	PUNCT
ejpam-3229	209	11	(	(	PUNCT
ejpam-3229	209	12	2018	2018	NUM
ejpam-3229	209	13	)	)	PUNCT
ejpam-3229	209	14	,	,	PUNCT
ejpam-3229	209	15	431	431	NUM
ejpam-3229	209	16	-	-	SYM
ejpam-3229	209	17	443	443	NUM
ejpam-3229	209	18	437	437	NUM
ejpam-3229	209	19	proof	proof	NOUN
ejpam-3229	209	20	.	.	PUNCT
ejpam-3229	210	1	suppose	suppose	VERB
ejpam-3229	210	2	n	n	PRON
ejpam-3229	210	3	is	be	AUX
ejpam-3229	210	4	x	x	ADJ
ejpam-3229	210	5	-	-	ADJ
ejpam-3229	210	6	principally	principally	ADV
ejpam-3229	210	7	projective	projective	ADJ
ejpam-3229	210	8	.	.	PUNCT
ejpam-3229	211	1	as	as	SCONJ
ejpam-3229	211	2	x	x	X
ejpam-3229	211	3	x	x	X
ejpam-3229	211	4	is	be	AUX
ejpam-3229	211	5	a	a	DET
ejpam-3229	211	6	m	m	NOUN
ejpam-3229	211	7	-	-	PUNCT
ejpam-3229	211	8	cyclic	cyclic	ADJ
ejpam-3229	211	9	sub	sub	NOUN
ejpam-3229	211	10	-	-	NOUN
ejpam-3229	211	11	act	act	NOUN
ejpam-3229	211	12	of	of	ADP
ejpam-3229	211	13	m	m	NOUN
ejpam-3229	211	14	so	so	ADJ
ejpam-3229	211	15	x	x	X
ejpam-3229	211	16	=	=	SYM
ejpam-3229	211	17	α	α	PROPN
ejpam-3229	211	18	(	(	PUNCT
ejpam-3229	211	19	m	m	NOUN
ejpam-3229	211	20	)	)	PUNCT
ejpam-3229	211	21	,	,	PUNCT
ejpam-3229	211	22	for	for	ADP
ejpam-3229	211	23	some	some	DET
ejpam-3229	211	24	α	α	NOUN
ejpam-3229	211	25	.	.	PUNCT
ejpam-3229	212	1	moreover	moreover	ADV
ejpam-3229	212	2	,	,	PUNCT
ejpam-3229	212	3	φ	φ	PROPN
ejpam-3229	212	4	:	:	PUNCT
ejpam-3229	212	5	n	n	PROPN
ejpam-3229	212	6	→	→	SYM
ejpam-3229	212	7	β(x	β(x	NOUN
ejpam-3229	212	8	)	)	PUNCT
ejpam-3229	212	9	be	be	AUX
ejpam-3229	212	10	an	an	DET
ejpam-3229	212	11	s	s	NOUN
ejpam-3229	212	12	-	-	NOUN
ejpam-3229	212	13	homomorphism	homomorphism	NOUN
ejpam-3229	212	14	,	,	PUNCT
ejpam-3229	212	15	where	where	SCONJ
ejpam-3229	212	16	β	β	X
ejpam-3229	212	17	∈	∈	PROPN
ejpam-3229	212	18	end(x	end(x	PROPN
ejpam-3229	212	19	)	)	PUNCT
ejpam-3229	212	20	.	.	PUNCT
ejpam-3229	213	1	now	now	ADV
ejpam-3229	213	2	β(x	β(x	NOUN
ejpam-3229	213	3	)	)	PUNCT
ejpam-3229	213	4	=	=	SYM
ejpam-3229	213	5	βα	βα	X
ejpam-3229	213	6	(	(	PUNCT
ejpam-3229	213	7	m	m	NOUN
ejpam-3229	213	8	)	)	PUNCT
ejpam-3229	213	9	so	so	ADV
ejpam-3229	213	10	β(x	β(x	NOUN
ejpam-3229	213	11	)	)	PUNCT
ejpam-3229	213	12	is	be	AUX
ejpam-3229	213	13	m	m	NOUN
ejpam-3229	213	14	-	-	NOUN
ejpam-3229	213	15	cyclic	cyclic	ADJ
ejpam-3229	213	16	and	and	CCONJ
ejpam-3229	213	17	since	since	SCONJ
ejpam-3229	213	18	n	n	NUM
ejpam-3229	213	19	is	be	AUX
ejpam-3229	213	20	m	m	NOUN
ejpam-3229	213	21	-	-	ADJ
ejpam-3229	213	22	principally	principally	ADV
ejpam-3229	213	23	projective	projective	ADJ
ejpam-3229	213	24	so	so	SCONJ
ejpam-3229	213	25	there	there	PRON
ejpam-3229	213	26	exists	exist	VERB
ejpam-3229	213	27	φ	φ	NOUN
ejpam-3229	213	28	:	:	PUNCT
ejpam-3229	213	29	n	n	CCONJ
ejpam-3229	213	30	→m	→m	PROPN
ejpam-3229	214	1	such	such	ADJ
ejpam-3229	214	2	that	that	SCONJ
ejpam-3229	214	3	(	(	PUNCT
ejpam-3229	214	4	βα)φ	βα)φ	PROPN
ejpam-3229	214	5	=	=	SYM
ejpam-3229	214	6	φ	φ	PROPN
ejpam-3229	214	7	.	.	PUNCT
ejpam-3229	215	1	now	now	ADV
ejpam-3229	215	2	consider	consider	VERB
ejpam-3229	215	3	αφ	αφ	NUM
ejpam-3229	215	4	:	:	PUNCT
ejpam-3229	215	5	n	n	X
ejpam-3229	215	6	→	→	SYM
ejpam-3229	215	7	x	x	X
ejpam-3229	215	8	which	which	PRON
ejpam-3229	215	9	clearly	clearly	ADV
ejpam-3229	215	10	lifts	lift	VERB
ejpam-3229	215	11	φ	φ	NUM
ejpam-3229	215	12	i.e.	i.e.	X
ejpam-3229	215	13	β(αφ	β(αφ	NOUN
ejpam-3229	215	14	)	)	PUNCT
ejpam-3229	215	15	=	=	SYM
ejpam-3229	216	1	(	(	PUNCT
ejpam-3229	216	2	βα)φ	βα)φ	PROPN
ejpam-3229	216	3	=	=	SYM
ejpam-3229	216	4	φ	φ	PROPN
ejpam-3229	216	5	.	.	PUNCT
ejpam-3229	217	1	hence	hence	ADV
ejpam-3229	217	2	n	n	ADV
ejpam-3229	217	3	is	be	AUX
ejpam-3229	217	4	x	x	ADJ
ejpam-3229	217	5	-	-	ADJ
ejpam-3229	217	6	principally	principally	ADV
ejpam-3229	217	7	projective	projective	ADJ
ejpam-3229	217	8	.	.	PUNCT
ejpam-3229	218	1	converse	converse	NOUN
ejpam-3229	218	2	is	be	AUX
ejpam-3229	218	3	trivially	trivially	ADV
ejpam-3229	218	4	follows	follow	VERB
ejpam-3229	218	5	by	by	ADP
ejpam-3229	218	6	taking	take	VERB
ejpam-3229	218	7	particular	particular	ADJ
ejpam-3229	218	8	x	x	PUNCT
ejpam-3229	218	9	=	=	ADJ
ejpam-3229	218	10	m.	m.	NOUN
ejpam-3229	218	11	theorem	theorem	VERB
ejpam-3229	218	12	6	6	NUM
ejpam-3229	218	13	.	.	PUNCT
ejpam-3229	219	1	let	let	VERB
ejpam-3229	219	2	n	n	PRON
ejpam-3229	219	3	be	be	AUX
ejpam-3229	219	4	anm	anm	NOUN
ejpam-3229	219	5	-	-	PUNCT
ejpam-3229	219	6	principally	principally	ADV
ejpam-3229	219	7	projective	projective	ADJ
ejpam-3229	219	8	s	s	NOUN
ejpam-3229	219	9	-	-	NOUN
ejpam-3229	219	10	act	act	NOUN
ejpam-3229	219	11	.	.	PUNCT
ejpam-3229	220	1	if	if	SCONJ
ejpam-3229	220	2	φ	φ	PROPN
ejpam-3229	220	3	is	be	AUX
ejpam-3229	220	4	idempotent	idempotent	ADJ
ejpam-3229	220	5	(	(	PUNCT
ejpam-3229	220	6	i.e.	i.e.	X
ejpam-3229	220	7	φ2	φ2	PROPN
ejpam-3229	220	8	=	=	SYM
ejpam-3229	220	9	φ	φ	PROPN
ejpam-3229	220	10	)	)	PUNCT
ejpam-3229	220	11	then	then	ADV
ejpam-3229	220	12	the	the	DET
ejpam-3229	220	13	homomorphic	homomorphic	ADJ
ejpam-3229	220	14	image	image	NOUN
ejpam-3229	220	15	φ(n	φ(n	ADJ
ejpam-3229	220	16	)	)	PUNCT
ejpam-3229	220	17	is	be	AUX
ejpam-3229	220	18	also	also	ADV
ejpam-3229	220	19	m	m	NOUN
ejpam-3229	220	20	-	-	PUNCT
ejpam-3229	220	21	principally	principally	ADV
ejpam-3229	220	22	projective	projective	ADJ
ejpam-3229	220	23	.	.	PUNCT
ejpam-3229	221	1	proof	proof	NOUN
ejpam-3229	221	2	.	.	PUNCT
ejpam-3229	222	1	let	let	VERB
ejpam-3229	222	2	γ	γ	NOUN
ejpam-3229	222	3	:	:	PUNCT
ejpam-3229	222	4	φ(n	φ(n	PROPN
ejpam-3229	222	5	)	)	PUNCT
ejpam-3229	222	6	→	→	SYM
ejpam-3229	222	7	α	α	PROPN
ejpam-3229	222	8	(	(	PUNCT
ejpam-3229	222	9	m	m	NOUN
ejpam-3229	222	10	)	)	PUNCT
ejpam-3229	222	11	be	be	AUX
ejpam-3229	222	12	an	an	DET
ejpam-3229	222	13	s	s	NOUN
ejpam-3229	222	14	-	-	NOUN
ejpam-3229	222	15	homomorphism	homomorphism	NOUN
ejpam-3229	222	16	.	.	PUNCT
ejpam-3229	223	1	consider	consider	VERB
ejpam-3229	223	2	γφ	γφ	NOUN
ejpam-3229	223	3	:	:	PUNCT
ejpam-3229	223	4	n	n	X
ejpam-3229	223	5	→	→	SYM
ejpam-3229	223	6	α	α	PROPN
ejpam-3229	223	7	(	(	PUNCT
ejpam-3229	223	8	m	m	PROPN
ejpam-3229	223	9	)	)	PUNCT
ejpam-3229	223	10	,	,	PUNCT
ejpam-3229	223	11	is	be	AUX
ejpam-3229	223	12	an	an	DET
ejpam-3229	223	13	s	s	NOUN
ejpam-3229	223	14	-	-	PUNCT
ejpam-3229	223	15	homomorphism	homomorphism	NOUN
ejpam-3229	223	16	,	,	PUNCT
ejpam-3229	223	17	since	since	SCONJ
ejpam-3229	223	18	n	n	ADV
ejpam-3229	223	19	is	be	AUX
ejpam-3229	223	20	m	m	NOUN
ejpam-3229	223	21	-	-	ADJ
ejpam-3229	223	22	principally	principally	ADV
ejpam-3229	223	23	projective	projective	ADJ
ejpam-3229	223	24	so	so	SCONJ
ejpam-3229	223	25	there	there	PRON
ejpam-3229	223	26	exists	exist	VERB
ejpam-3229	223	27	θ	θ	NOUN
ejpam-3229	223	28	:	:	PUNCT
ejpam-3229	223	29	n	n	X
ejpam-3229	223	30	→	→	PUNCT
ejpam-3229	223	31	m	m	AUX
ejpam-3229	223	32	lifting	lift	VERB
ejpam-3229	223	33	γφ	γφ	ADP
ejpam-3229	223	34	i.e.	i.e.	X
ejpam-3229	223	35	αθ	αθ	X
ejpam-3229	223	36	=	=	ADJ
ejpam-3229	223	37	γφ	γφ	NOUN
ejpam-3229	223	38	.	.	PUNCT
ejpam-3229	223	39	note	note	VERB
ejpam-3229	223	40	that	that	PRON
ejpam-3229	223	41	θi	θi	X
ejpam-3229	223	42	:	:	PUNCT
ejpam-3229	223	43	φ(n	φ(n	PROPN
ejpam-3229	223	44	)	)	PUNCT
ejpam-3229	224	1	→m	→m	PROPN
ejpam-3229	224	2	,	,	PUNCT
ejpam-3229	224	3	where	where	SCONJ
ejpam-3229	224	4	i	i	PRON
ejpam-3229	224	5	:	:	PUNCT
ejpam-3229	224	6	φ(n	φ(n	PROPN
ejpam-3229	224	7	)	)	PUNCT
ejpam-3229	224	8	→	→	SYM
ejpam-3229	224	9	n	n	X
ejpam-3229	224	10	is	be	AUX
ejpam-3229	224	11	inclusion	inclusion	NOUN
ejpam-3229	224	12	.	.	PUNCT
ejpam-3229	225	1	it	it	PRON
ejpam-3229	225	2	follows	follow	VERB
ejpam-3229	225	3	that	that	SCONJ
ejpam-3229	225	4	for	for	ADP
ejpam-3229	225	5	all	all	DET
ejpam-3229	225	6	φ(n	φ(n	NOUN
ejpam-3229	225	7	)	)	PUNCT
ejpam-3229	225	8	∈	∈	NOUN
ejpam-3229	225	9	φ(n	φ(n	PROPN
ejpam-3229	225	10	)	)	PUNCT
ejpam-3229	225	11	we	we	PRON
ejpam-3229	225	12	have	have	AUX
ejpam-3229	225	13	,	,	PUNCT
ejpam-3229	225	14	(	(	PUNCT
ejpam-3229	225	15	α(θi))(φ(n	α(θi))(φ(n	NOUN
ejpam-3229	225	16	)	)	PUNCT
ejpam-3229	225	17	)	)	PUNCT
ejpam-3229	226	1	=	=	SYM
ejpam-3229	226	2	(	(	PUNCT
ejpam-3229	226	3	αθ)i(φ(n	αθ)i(φ(n	ADJ
ejpam-3229	226	4	)	)	PUNCT
ejpam-3229	226	5	)	)	PUNCT
ejpam-3229	227	1	=	=	PUNCT
ejpam-3229	227	2	αθ(φ(n	αθ(φ(n	NOUN
ejpam-3229	227	3	)	)	PUNCT
ejpam-3229	227	4	)	)	PUNCT
ejpam-3229	227	5	=	=	SYM
ejpam-3229	227	6	γφ(φ(n	γφ(φ(n	X
ejpam-3229	227	7	)	)	PUNCT
ejpam-3229	227	8	)	)	PUNCT
ejpam-3229	227	9	=	=	SYM
ejpam-3229	227	10	γ(φ(n	γ(φ(n	NOUN
ejpam-3229	227	11	)	)	PUNCT
ejpam-3229	227	12	)	)	PUNCT
ejpam-3229	227	13	,	,	PUNCT
ejpam-3229	227	14	which	which	PRON
ejpam-3229	227	15	simply	simply	ADV
ejpam-3229	227	16	implies	imply	VERB
ejpam-3229	227	17	that	that	SCONJ
ejpam-3229	227	18	α(θi	α(θi	ADV
ejpam-3229	227	19	)	)	PUNCT
ejpam-3229	227	20	=	=	SYM
ejpam-3229	228	1	γ	γ	X
ejpam-3229	228	2	.	.	NOUN
ejpam-3229	228	3	hence	hence	ADV
ejpam-3229	228	4	φ(n	φ(n	PROPN
ejpam-3229	228	5	)	)	PUNCT
ejpam-3229	228	6	is	be	AUX
ejpam-3229	228	7	m	m	NOUN
ejpam-3229	228	8	-	-	PUNCT
ejpam-3229	228	9	principally	principally	ADV
ejpam-3229	228	10	projective	projective	ADJ
ejpam-3229	228	11	.	.	PUNCT
ejpam-3229	229	1	theorem	theorem	VERB
ejpam-3229	229	2	7	7	NUM
ejpam-3229	229	3	.	.	NOUN
ejpam-3229	229	4	letm	letm	NOUN
ejpam-3229	229	5	and	and	CCONJ
ejpam-3229	229	6	n	n	CCONJ
ejpam-3229	229	7	be	be	AUX
ejpam-3229	229	8	right	right	ADJ
ejpam-3229	229	9	s	s	NOUN
ejpam-3229	229	10	-	-	PUNCT
ejpam-3229	229	11	acts	act	NOUN
ejpam-3229	229	12	,	,	PUNCT
ejpam-3229	229	13	thenm	thenm	PROPN
ejpam-3229	229	14	is	be	AUX
ejpam-3229	229	15	n	n	PRON
ejpam-3229	229	16	-principally	-principally	ADV
ejpam-3229	229	17	projective	projective	ADJ
ejpam-3229	229	18	and	and	CCONJ
ejpam-3229	229	19	every	every	DET
ejpam-3229	229	20	n	n	PRON
ejpam-3229	229	21	-cyclic	-cyclic	ADJ
ejpam-3229	229	22	sub	sub	NOUN
ejpam-3229	229	23	-	-	NOUN
ejpam-3229	229	24	act	act	NOUN
ejpam-3229	229	25	of	of	ADP
ejpam-3229	229	26	n	n	PRON
ejpam-3229	229	27	ism	ism	NOUN
ejpam-3229	229	28	-	-	PUNCT
ejpam-3229	229	29	principally	principally	ADV
ejpam-3229	229	30	injective	injective	ADJ
ejpam-3229	229	31	iff	iff	PROPN
ejpam-3229	229	32	n	n	CCONJ
ejpam-3229	229	33	ism	ism	NOUN
ejpam-3229	229	34	-	-	PUNCT
ejpam-3229	229	35	principally	principally	ADV
ejpam-3229	229	36	injective	injective	ADJ
ejpam-3229	229	37	and	and	CCONJ
ejpam-3229	229	38	every	every	DET
ejpam-3229	229	39	m	m	NOUN
ejpam-3229	229	40	-	-	ADJ
ejpam-3229	229	41	cyclic	cyclic	ADJ
ejpam-3229	229	42	sub	sub	NOUN
ejpam-3229	229	43	-	-	NOUN
ejpam-3229	229	44	act	act	NOUN
ejpam-3229	229	45	of	of	ADP
ejpam-3229	229	46	m	m	PROPN
ejpam-3229	229	47	is	be	AUX
ejpam-3229	229	48	n	n	PRON
ejpam-3229	229	49	-principally	-principally	ADV
ejpam-3229	229	50	projective	projective	ADJ
ejpam-3229	229	51	.	.	PUNCT
ejpam-3229	230	1	proof	proof	NOUN
ejpam-3229	230	2	.	.	PUNCT
ejpam-3229	231	1	assume	assume	VERB
ejpam-3229	231	2	that	that	SCONJ
ejpam-3229	231	3	m	m	PROPN
ejpam-3229	231	4	is	be	AUX
ejpam-3229	231	5	n	n	PRON
ejpam-3229	231	6	-principally	-principally	ADV
ejpam-3229	231	7	projective	projective	ADJ
ejpam-3229	231	8	and	and	CCONJ
ejpam-3229	231	9	each	each	DET
ejpam-3229	231	10	n	n	PRON
ejpam-3229	231	11	-cyclic	-cyclic	NOUN
ejpam-3229	231	12	sub	sub	NOUN
ejpam-3229	231	13	-	-	NOUN
ejpam-3229	231	14	act	act	NOUN
ejpam-3229	231	15	of	of	ADP
ejpam-3229	231	16	n	n	PROPN
ejpam-3229	231	17	is	be	AUX
ejpam-3229	231	18	m	m	NOUN
ejpam-3229	231	19	-	-	ADJ
ejpam-3229	231	20	principally	principally	ADV
ejpam-3229	231	21	injective	injective	ADJ
ejpam-3229	231	22	.	.	PUNCT
ejpam-3229	232	1	since	since	SCONJ
ejpam-3229	232	2	i(n	i(n	NOUN
ejpam-3229	232	3	)	)	PUNCT
ejpam-3229	232	4	=	=	SYM
ejpam-3229	232	5	n	n	NOUN
ejpam-3229	232	6	,	,	PUNCT
ejpam-3229	232	7	where	where	SCONJ
ejpam-3229	232	8	i	i	PRON
ejpam-3229	232	9	is	be	AUX
ejpam-3229	232	10	the	the	DET
ejpam-3229	232	11	identity	identity	NOUN
ejpam-3229	232	12	on	on	ADP
ejpam-3229	232	13	n	n	PROPN
ejpam-3229	232	14	,	,	PUNCT
ejpam-3229	232	15	so	so	CCONJ
ejpam-3229	232	16	n	n	PROPN
ejpam-3229	232	17	is	be	AUX
ejpam-3229	232	18	itself	itself	PRON
ejpam-3229	232	19	n	n	PRON
ejpam-3229	232	20	cyclic	cyclic	ADJ
ejpam-3229	232	21	sub	sub	NOUN
ejpam-3229	232	22	-	-	NOUN
ejpam-3229	232	23	act	act	NOUN
ejpam-3229	232	24	of	of	ADP
ejpam-3229	232	25	n	n	NUM
ejpam-3229	232	26	and	and	CCONJ
ejpam-3229	232	27	hencem	hencem	ADV
ejpam-3229	232	28	-	-	PUNCT
ejpam-3229	232	29	principally	principally	ADV
ejpam-3229	232	30	injective	injective	ADJ
ejpam-3229	232	31	.	.	PUNCT
ejpam-3229	233	1	let	let	VERB
ejpam-3229	233	2	α	α	PROPN
ejpam-3229	233	3	(	(	PUNCT
ejpam-3229	233	4	m	m	NOUN
ejpam-3229	233	5	)	)	PUNCT
ejpam-3229	233	6	be	be	VERB
ejpam-3229	233	7	anm	anm	NOUN
ejpam-3229	233	8	-	-	PUNCT
ejpam-3229	233	9	cyclic	cyclic	ADJ
ejpam-3229	233	10	sub	sub	ADJ
ejpam-3229	233	11	-	-	ADJ
ejpam-3229	233	12	act	act	ADJ
ejpam-3229	233	13	ofm	ofm	PROPN
ejpam-3229	233	14	,	,	PUNCT
ejpam-3229	233	15	where	where	SCONJ
ejpam-3229	233	16	α	α	PROPN
ejpam-3229	233	17	∈	∈	PROPN
ejpam-3229	233	18	e.	e.	PROPN
ejpam-3229	233	19	to	to	PART
ejpam-3229	233	20	show	show	VERB
ejpam-3229	233	21	α	α	PROPN
ejpam-3229	233	22	(	(	PUNCT
ejpam-3229	233	23	m	m	NOUN
ejpam-3229	233	24	)	)	PUNCT
ejpam-3229	233	25	is	be	AUX
ejpam-3229	233	26	n	n	PRON
ejpam-3229	233	27	-principally	-principally	ADV
ejpam-3229	233	28	projective	projective	ADJ
ejpam-3229	233	29	,	,	PUNCT
ejpam-3229	233	30	we	we	PRON
ejpam-3229	233	31	let	let	VERB
ejpam-3229	233	32	γ	γ	X
ejpam-3229	233	33	:	:	PUNCT
ejpam-3229	233	34	α	α	PROPN
ejpam-3229	233	35	(	(	PUNCT
ejpam-3229	233	36	m)→	m)→	PROPN
ejpam-3229	233	37	β(n	β(n	PUNCT
ejpam-3229	233	38	)	)	PUNCT
ejpam-3229	233	39	be	be	AUX
ejpam-3229	233	40	an	an	DET
ejpam-3229	233	41	s	s	NOUN
ejpam-3229	233	42	-	-	NOUN
ejpam-3229	233	43	homomorphism	homomorphism	NOUN
ejpam-3229	233	44	,	,	PUNCT
ejpam-3229	233	45	where	where	SCONJ
ejpam-3229	233	46	β	β	PROPN
ejpam-3229	233	47	is	be	AUX
ejpam-3229	233	48	an	an	DET
ejpam-3229	233	49	endomorphism	endomorphism	NOUN
ejpam-3229	233	50	on	on	ADP
ejpam-3229	233	51	n	n	PROPN
ejpam-3229	233	52	.	.	PUNCT
ejpam-3229	234	1	since	since	SCONJ
ejpam-3229	234	2	β(n	β(n	NUM
ejpam-3229	234	3	)	)	PUNCT
ejpam-3229	234	4	ism	ism	NOUN
ejpam-3229	234	5	-	-	PUNCT
ejpam-3229	234	6	principally	principally	ADV
ejpam-3229	234	7	injective	injective	ADJ
ejpam-3229	234	8	so	so	SCONJ
ejpam-3229	234	9	there	there	PRON
ejpam-3229	234	10	exists	exist	VERB
ejpam-3229	234	11	θ	θ	NOUN
ejpam-3229	234	12	:	:	PUNCT
ejpam-3229	235	1	m	m	VERB
ejpam-3229	235	2	→	→	SYM
ejpam-3229	235	3	β(n	β(n	NUM
ejpam-3229	235	4	)	)	PUNCT
ejpam-3229	236	1	such	such	ADJ
ejpam-3229	236	2	that	that	PRON
ejpam-3229	236	3	θi	θi	X
ejpam-3229	236	4	=	=	SYM
ejpam-3229	236	5	γ	γ	PROPN
ejpam-3229	236	6	,	,	PUNCT
ejpam-3229	236	7	where	where	SCONJ
ejpam-3229	236	8	i	i	PRON
ejpam-3229	236	9	:	:	PUNCT
ejpam-3229	236	10	α	α	PROPN
ejpam-3229	236	11	(	(	PUNCT
ejpam-3229	236	12	m	m	NOUN
ejpam-3229	236	13	)	)	PUNCT
ejpam-3229	236	14	→	→	PUNCT
ejpam-3229	236	15	m	m	PROPN
ejpam-3229	236	16	is	be	AUX
ejpam-3229	236	17	inclusion	inclusion	NOUN
ejpam-3229	236	18	.	.	PUNCT
ejpam-3229	237	1	now	now	ADV
ejpam-3229	237	2	since	since	SCONJ
ejpam-3229	237	3	m	m	PROPN
ejpam-3229	237	4	is	be	AUX
ejpam-3229	237	5	n	n	PRON
ejpam-3229	237	6	-principally	-principally	ADV
ejpam-3229	237	7	projective	projective	ADJ
ejpam-3229	237	8	so	so	ADV
ejpam-3229	237	9	there	there	PRON
ejpam-3229	237	10	exists	exist	VERB
ejpam-3229	237	11	φ	φ	NOUN
ejpam-3229	237	12	:	:	PUNCT
ejpam-3229	237	13	m→n	m→n	NOUN
ejpam-3229	237	14	such	such	ADJ
ejpam-3229	237	15	that	that	SCONJ
ejpam-3229	237	16	βφ	βφ	ADP
ejpam-3229	237	17	=	=	SYM
ejpam-3229	237	18	θ	θ	PROPN
ejpam-3229	237	19	.	.	PUNCT
ejpam-3229	237	20	now	now	ADV
ejpam-3229	237	21	consider	consider	VERB
ejpam-3229	237	22	φi	φi	ADV
ejpam-3229	237	23	:	:	PUNCT
ejpam-3229	237	24	α	α	PROPN
ejpam-3229	237	25	(	(	PUNCT
ejpam-3229	237	26	m	m	NOUN
ejpam-3229	237	27	)	)	PUNCT
ejpam-3229	237	28	→	→	SYM
ejpam-3229	237	29	n	n	CCONJ
ejpam-3229	237	30	which	which	PRON
ejpam-3229	237	31	lifts	lift	VERB
ejpam-3229	237	32	γ	γ	X
ejpam-3229	237	33	,	,	PUNCT
ejpam-3229	237	34	i.e.	i.e.	X
ejpam-3229	237	35	β(φi	β(φi	NOUN
ejpam-3229	237	36	)	)	PUNCT
ejpam-3229	237	37	=	=	PUNCT
ejpam-3229	237	38	(	(	PUNCT
ejpam-3229	237	39	βφ)i	βφ)i	NUM
ejpam-3229	237	40	=	=	SYM
ejpam-3229	237	41	θi	θi	NOUN
ejpam-3229	237	42	=	=	SYM
ejpam-3229	237	43	γ	γ	PROPN
ejpam-3229	237	44	.	.	PROPN
ejpam-3229	237	45	hence	hence	ADV
ejpam-3229	237	46	α	α	PROPN
ejpam-3229	237	47	(	(	PUNCT
ejpam-3229	237	48	m	m	NOUN
ejpam-3229	237	49	)	)	PUNCT
ejpam-3229	237	50	is	be	AUX
ejpam-3229	237	51	n	n	PRON
ejpam-3229	237	52	-principally	-principally	ADV
ejpam-3229	237	53	projective	projective	ADJ
ejpam-3229	237	54	.	.	PUNCT
ejpam-3229	238	1	conversely	conversely	ADV
ejpam-3229	238	2	assume	assume	VERB
ejpam-3229	238	3	that	that	SCONJ
ejpam-3229	238	4	n	n	PRON
ejpam-3229	238	5	is	be	AUX
ejpam-3229	238	6	m	m	NOUN
ejpam-3229	238	7	-	-	ADJ
ejpam-3229	238	8	principally	principally	ADV
ejpam-3229	238	9	injective	injective	ADJ
ejpam-3229	238	10	and	and	CCONJ
ejpam-3229	238	11	every	every	DET
ejpam-3229	238	12	m	m	NOUN
ejpam-3229	238	13	-	-	ADJ
ejpam-3229	238	14	cyclic	cyclic	ADJ
ejpam-3229	238	15	sub	sub	NOUN
ejpam-3229	238	16	-	-	NOUN
ejpam-3229	238	17	act	act	NOUN
ejpam-3229	238	18	of	of	ADP
ejpam-3229	238	19	m	m	PROPN
ejpam-3229	238	20	is	be	AUX
ejpam-3229	238	21	n	n	PRON
ejpam-3229	238	22	-principally	-principally	ADV
ejpam-3229	238	23	projective	projective	ADJ
ejpam-3229	238	24	.	.	PUNCT
ejpam-3229	239	1	trivially	trivially	ADV
ejpam-3229	239	2	m	m	VERB
ejpam-3229	239	3	is	be	AUX
ejpam-3229	239	4	n	n	PRON
ejpam-3229	239	5	-principally	-principally	ADV
ejpam-3229	239	6	projective	projective	ADJ
ejpam-3229	239	7	.	.	PUNCT
ejpam-3229	240	1	let	let	AUX
ejpam-3229	240	2	β(n	β(n	PUNCT
ejpam-3229	240	3	)	)	PUNCT
ejpam-3229	240	4	be	be	AUX
ejpam-3229	240	5	n	n	PRON
ejpam-3229	240	6	cyclic	cyclic	ADJ
ejpam-3229	240	7	sub	sub	NOUN
ejpam-3229	240	8	-	-	NOUN
ejpam-3229	240	9	act	act	NOUN
ejpam-3229	240	10	of	of	ADP
ejpam-3229	240	11	n	n	PROPN
ejpam-3229	240	12	and	and	CCONJ
ejpam-3229	240	13	γ	γ	X
ejpam-3229	240	14	:	:	PUNCT
ejpam-3229	240	15	α	α	PROPN
ejpam-3229	240	16	(	(	PUNCT
ejpam-3229	240	17	m	m	NOUN
ejpam-3229	240	18	)	)	PUNCT
ejpam-3229	240	19	→	→	SYM
ejpam-3229	240	20	β(n	β(n	NUM
ejpam-3229	240	21	)	)	PUNCT
ejpam-3229	240	22	be	be	AUX
ejpam-3229	240	23	an	an	DET
ejpam-3229	240	24	s	s	NOUN
ejpam-3229	240	25	-	-	NOUN
ejpam-3229	240	26	homomorphism	homomorphism	NOUN
ejpam-3229	240	27	.	.	PUNCT
ejpam-3229	241	1	since	since	SCONJ
ejpam-3229	241	2	α	α	PROPN
ejpam-3229	241	3	(	(	PUNCT
ejpam-3229	241	4	m	m	NOUN
ejpam-3229	241	5	)	)	PUNCT
ejpam-3229	241	6	is	be	AUX
ejpam-3229	241	7	n	n	PRON
ejpam-3229	241	8	-principally	-principally	ADV
ejpam-3229	241	9	projective	projective	ADJ
ejpam-3229	241	10	so	so	SCONJ
ejpam-3229	241	11	there	there	PRON
ejpam-3229	241	12	exists	exist	VERB
ejpam-3229	241	13	θ	θ	NOUN
ejpam-3229	241	14	:	:	PUNCT
ejpam-3229	241	15	α	α	PROPN
ejpam-3229	241	16	(	(	PUNCT
ejpam-3229	241	17	m	m	NOUN
ejpam-3229	241	18	)	)	PUNCT
ejpam-3229	241	19	→	→	PUNCT
ejpam-3229	241	20	n	n	X
ejpam-3229	241	21	such	such	ADJ
ejpam-3229	241	22	that	that	SCONJ
ejpam-3229	241	23	βθ	βθ	PROPN
ejpam-3229	241	24	=	=	SYM
ejpam-3229	241	25	γ	γ	X
ejpam-3229	241	26	.	.	PUNCT
ejpam-3229	241	27	now	now	ADV
ejpam-3229	241	28	since	since	SCONJ
ejpam-3229	241	29	n	n	NUM
ejpam-3229	241	30	is	be	AUX
ejpam-3229	241	31	m	m	NOUN
ejpam-3229	241	32	-	-	ADJ
ejpam-3229	241	33	principally	principally	ADV
ejpam-3229	241	34	injective	injective	ADJ
ejpam-3229	241	35	so	so	SCONJ
ejpam-3229	241	36	there	there	PRON
ejpam-3229	241	37	exists	exist	VERB
ejpam-3229	241	38	φ	φ	NOUN
ejpam-3229	241	39	:	:	PUNCT
ejpam-3229	241	40	m	m	VERB
ejpam-3229	241	41	→	→	SYM
ejpam-3229	241	42	n	n	CCONJ
ejpam-3229	241	43	such	such	ADJ
ejpam-3229	241	44	that	that	PRON
ejpam-3229	241	45	φi	φi	PROPN
ejpam-3229	241	46	=	=	ADJ
ejpam-3229	241	47	θ	θ	X
ejpam-3229	241	48	.	.	PUNCT
ejpam-3229	241	49	consider	consider	VERB
ejpam-3229	241	50	s	s	NOUN
ejpam-3229	241	51	-	-	PUNCT
ejpam-3229	241	52	homomorphism	homomorphism	NOUN
ejpam-3229	241	53	βφ	βφ	X
ejpam-3229	241	54	:	:	PUNCT
ejpam-3229	241	55	α	α	PROPN
ejpam-3229	241	56	(	(	PUNCT
ejpam-3229	241	57	m	m	NOUN
ejpam-3229	241	58	)	)	PUNCT
ejpam-3229	241	59	→	→	SYM
ejpam-3229	241	60	n	n	CCONJ
ejpam-3229	241	61	which	which	PRON
ejpam-3229	241	62	extends	extend	VERB
ejpam-3229	241	63	γ	γ	X
ejpam-3229	241	64	i.e.	i.e.	X
ejpam-3229	241	65	(	(	PUNCT
ejpam-3229	241	66	βφ)i	βφ)i	NUM
ejpam-3229	241	67	=	=	SYM
ejpam-3229	241	68	β(φi	β(φi	NOUN
ejpam-3229	241	69	)	)	PUNCT
ejpam-3229	242	1	=	=	PUNCT
ejpam-3229	242	2	βθ	βθ	NOUN
ejpam-3229	242	3	=	=	SYM
ejpam-3229	242	4	γ	γ	X
ejpam-3229	242	5	.	.	PROPN
ejpam-3229	242	6	hence	hence	ADV
ejpam-3229	242	7	β(n	β(n	PUNCT
ejpam-3229	242	8	)	)	PUNCT
ejpam-3229	242	9	is	be	AUX
ejpam-3229	242	10	m	m	NOUN
ejpam-3229	242	11	-	-	PUNCT
ejpam-3229	242	12	principally	principally	ADV
ejpam-3229	242	13	injective	injective	ADJ
ejpam-3229	242	14	.	.	PUNCT
ejpam-3229	243	1	theorem	theorem	ADJ
ejpam-3229	243	2	8	8	NUM
ejpam-3229	243	3	.	.	PUNCT
ejpam-3229	244	1	n	n	NOUN
ejpam-3229	244	2	=	=	PROPN
ejpam-3229	244	3	⊕	⊕	PROPN
ejpam-3229	244	4	i∈i	i∈i	ADJ
ejpam-3229	244	5	ni	ni	PROPN
ejpam-3229	244	6	is	be	AUX
ejpam-3229	244	7	m	m	NOUN
ejpam-3229	244	8	-	-	ADJ
ejpam-3229	244	9	principally	principally	ADV
ejpam-3229	244	10	projective	projective	ADJ
ejpam-3229	244	11	where	where	SCONJ
ejpam-3229	244	12	each	each	DET
ejpam-3229	244	13	ni	ni	PROPN
ejpam-3229	244	14	is	be	AUX
ejpam-3229	244	15	m	m	NOUN
ejpam-3229	244	16	-	-	ADJ
ejpam-3229	244	17	principally	principally	ADV
ejpam-3229	244	18	projective	projective	ADJ
ejpam-3229	244	19	for	for	ADP
ejpam-3229	244	20	all	all	PRON
ejpam-3229	244	21	i	i	PRON
ejpam-3229	244	22	∈	∈	PROPN
ejpam-3229	244	23	i.	i.	NOUN
ejpam-3229	244	24	proof	proof	PROPN
ejpam-3229	244	25	.	.	PUNCT
ejpam-3229	245	1	follows	follow	VERB
ejpam-3229	245	2	on	on	ADP
ejpam-3229	245	3	the	the	DET
ejpam-3229	245	4	same	same	ADJ
ejpam-3229	245	5	lines	line	NOUN
ejpam-3229	245	6	of	of	ADP
ejpam-3229	245	7	theorem	theorem	ADJ
ejpam-3229	245	8	4	4	NUM
ejpam-3229	245	9	.	.	PUNCT
ejpam-3229	245	10	j.	j.	PROPN
ejpam-3229	245	11	hussain	hussain	PROPN
ejpam-3229	245	12	,	,	PUNCT
ejpam-3229	245	13	m.shabir	m.shabir	PROPN
ejpam-3229	245	14	/	/	SYM
ejpam-3229	245	15	eur	eur	PROPN
ejpam-3229	245	16	.	.	PUNCT
ejpam-3229	246	1	j.	j.	PROPN
ejpam-3229	246	2	pure	pure	PROPN
ejpam-3229	246	3	appl	appl	PROPN
ejpam-3229	246	4	.	.	PROPN
ejpam-3229	246	5	math	math	PROPN
ejpam-3229	246	6	,	,	PUNCT
ejpam-3229	246	7	11	11	NUM
ejpam-3229	246	8	(	(	PUNCT
ejpam-3229	246	9	2	2	NUM
ejpam-3229	246	10	)	)	PUNCT
ejpam-3229	246	11	(	(	PUNCT
ejpam-3229	246	12	2018	2018	NUM
ejpam-3229	246	13	)	)	PUNCT
ejpam-3229	246	14	,	,	PUNCT
ejpam-3229	246	15	431	431	NUM
ejpam-3229	246	16	-	-	SYM
ejpam-3229	246	17	443	443	NUM
ejpam-3229	246	18	438	438	NUM
ejpam-3229	246	19	definition	definition	NOUN
ejpam-3229	246	20	6	6	NUM
ejpam-3229	246	21	.	.	PUNCT
ejpam-3229	247	1	for	for	ADP
ejpam-3229	247	2	right	right	ADJ
ejpam-3229	247	3	s	s	NOUN
ejpam-3229	247	4	-	-	PUNCT
ejpam-3229	247	5	acts	act	VERB
ejpam-3229	247	6	m	m	VERB
ejpam-3229	247	7	and	and	CCONJ
ejpam-3229	247	8	n	n	CCONJ
ejpam-3229	247	9	,	,	PUNCT
ejpam-3229	247	10	m	m	VERB
ejpam-3229	247	11	is	be	AUX
ejpam-3229	247	12	called	call	VERB
ejpam-3229	247	13	n	n	CCONJ
ejpam-3229	247	14	-projective	-projective	ADJ
ejpam-3229	247	15	or	or	CCONJ
ejpam-3229	247	16	projective	projective	ADJ
ejpam-3229	247	17	relative	relative	ADJ
ejpam-3229	247	18	to	to	ADP
ejpam-3229	247	19	n	n	PROPN
ejpam-3229	247	20	,	,	PUNCT
ejpam-3229	247	21	if	if	SCONJ
ejpam-3229	247	22	every	every	DET
ejpam-3229	247	23	right	right	NOUN
ejpam-3229	247	24	s	s	NOUN
ejpam-3229	247	25	-	-	NOUN
ejpam-3229	247	26	act	act	NOUN
ejpam-3229	247	27	c	c	NOUN
ejpam-3229	247	28	,	,	PUNCT
ejpam-3229	247	29	every	every	DET
ejpam-3229	247	30	homomorphism	homomorphism	PROPN
ejpam-3229	247	31	f	f	X
ejpam-3229	247	32	:	:	PUNCT
ejpam-3229	247	33	m	m	VERB
ejpam-3229	247	34	→	→	SYM
ejpam-3229	247	35	c	c	NOUN
ejpam-3229	247	36	can	can	AUX
ejpam-3229	247	37	be	be	AUX
ejpam-3229	247	38	lifted	lift	VERB
ejpam-3229	247	39	w.r.t	w.r.t	NOUN
ejpam-3229	247	40	every	every	DET
ejpam-3229	247	41	g	g	NOUN
ejpam-3229	247	42	:	:	PUNCT
ejpam-3229	247	43	n	n	PROPN
ejpam-3229	247	44	→	→	SYM
ejpam-3229	247	45	c	c	NOUN
ejpam-3229	247	46	i.e.	i.e.	X
ejpam-3229	247	47	there	there	PRON
ejpam-3229	247	48	exists	exist	VERB
ejpam-3229	247	49	a	a	DET
ejpam-3229	247	50	homomorphism	homomorphism	ADJ
ejpam-3229	247	51	h	h	NOUN
ejpam-3229	247	52	:	:	PUNCT
ejpam-3229	247	53	m→n	m→n	NOUN
ejpam-3229	247	54	such	such	ADJ
ejpam-3229	247	55	that	that	SCONJ
ejpam-3229	247	56	f	f	PROPN
ejpam-3229	247	57	=	=	SYM
ejpam-3229	247	58	gh	gh	PROPN
ejpam-3229	247	59	.	.	PUNCT
ejpam-3229	248	1	moreover	moreover	ADV
ejpam-3229	248	2	,	,	PUNCT
ejpam-3229	248	3	m	m	VERB
ejpam-3229	248	4	is	be	AUX
ejpam-3229	248	5	called	call	VERB
ejpam-3229	248	6	n	n	ADV
ejpam-3229	248	7	-injective	-injective	ADJ
ejpam-3229	248	8	right	right	ADJ
ejpam-3229	248	9	s	s	NOUN
ejpam-3229	248	10	-	-	NOUN
ejpam-3229	248	11	act	act	NOUN
ejpam-3229	248	12	,	,	PUNCT
ejpam-3229	248	13	if	if	SCONJ
ejpam-3229	248	14	for	for	ADP
ejpam-3229	248	15	any	any	DET
ejpam-3229	248	16	sub	sub	NOUN
ejpam-3229	248	17	-	-	NOUN
ejpam-3229	248	18	act	act	ADJ
ejpam-3229	248	19	c	c	NOUN
ejpam-3229	248	20	of	of	ADP
ejpam-3229	248	21	n	n	PROPN
ejpam-3229	248	22	,	,	PUNCT
ejpam-3229	248	23	and	and	CCONJ
ejpam-3229	248	24	any	any	DET
ejpam-3229	248	25	homormorphism	homormorphism	NOUN
ejpam-3229	248	26	f	f	NOUN
ejpam-3229	248	27	:	:	PUNCT
ejpam-3229	248	28	c	c	X
ejpam-3229	248	29	→m	→m	PUNCT
ejpam-3229	248	30	there	there	PRON
ejpam-3229	248	31	exists	exist	VERB
ejpam-3229	248	32	a	a	DET
ejpam-3229	248	33	homormophism	homormophism	NOUN
ejpam-3229	248	34	g	g	NOUN
ejpam-3229	248	35	:	:	PUNCT
ejpam-3229	248	36	n	n	CCONJ
ejpam-3229	248	37	→m	→m	PUNCT
ejpam-3229	248	38	extending	extend	VERB
ejpam-3229	248	39	f	f	PROPN
ejpam-3229	248	40	.	.	PUNCT
ejpam-3229	249	1	theorem	theorem	ADJ
ejpam-3229	249	2	9	9	NUM
ejpam-3229	249	3	.	.	PUNCT
ejpam-3229	250	1	let	let	VERB
ejpam-3229	250	2	m	m	PRON
ejpam-3229	250	3	and	and	CCONJ
ejpam-3229	250	4	n	n	CCONJ
ejpam-3229	250	5	be	be	AUX
ejpam-3229	250	6	two	two	NUM
ejpam-3229	250	7	right	right	ADJ
ejpam-3229	250	8	s	s	NOUN
ejpam-3229	250	9	-	-	PUNCT
ejpam-3229	250	10	acts	act	VERB
ejpam-3229	250	11	,	,	PUNCT
ejpam-3229	250	12	then	then	ADV
ejpam-3229	250	13	m	m	PROPN
ejpam-3229	250	14	is	be	AUX
ejpam-3229	250	15	n	n	ADV
ejpam-3229	250	16	-injective	-injective	ADJ
ejpam-3229	250	17	and	and	CCONJ
ejpam-3229	250	18	each	each	DET
ejpam-3229	250	19	subact	subact	NOUN
ejpam-3229	250	20	of	of	ADP
ejpam-3229	250	21	n	n	NUM
ejpam-3229	250	22	is	be	AUX
ejpam-3229	250	23	m	m	NOUN
ejpam-3229	250	24	-	-	ADJ
ejpam-3229	250	25	principally	principally	ADV
ejpam-3229	250	26	projective	projective	ADJ
ejpam-3229	250	27	iff	iff	PROPN
ejpam-3229	250	28	n	n	PART
ejpam-3229	250	29	is	be	AUX
ejpam-3229	250	30	m	m	NOUN
ejpam-3229	250	31	-	-	ADJ
ejpam-3229	250	32	principally	principally	ADV
ejpam-3229	250	33	projective	projective	ADJ
ejpam-3229	250	34	and	and	CCONJ
ejpam-3229	250	35	each	each	DET
ejpam-3229	250	36	m	m	NOUN
ejpam-3229	250	37	-	-	PUNCT
ejpam-3229	250	38	cyclic	cyclic	ADJ
ejpam-3229	250	39	sub	sub	NOUN
ejpam-3229	250	40	-	-	NOUN
ejpam-3229	250	41	act	act	NOUN
ejpam-3229	250	42	of	of	ADP
ejpam-3229	250	43	m	m	PROPN
ejpam-3229	250	44	is	be	AUX
ejpam-3229	251	1	n	n	ADV
ejpam-3229	251	2	-injective	-injective	ADJ
ejpam-3229	251	3	.	.	PUNCT
ejpam-3229	252	1	proof	proof	NOUN
ejpam-3229	252	2	.	.	PUNCT
ejpam-3229	253	1	assume	assume	VERB
ejpam-3229	253	2	that	that	SCONJ
ejpam-3229	253	3	m	m	PROPN
ejpam-3229	253	4	is	be	AUX
ejpam-3229	253	5	n	n	ADV
ejpam-3229	253	6	-injective	-injective	ADJ
ejpam-3229	253	7	and	and	CCONJ
ejpam-3229	253	8	each	each	DET
ejpam-3229	253	9	sub	sub	NOUN
ejpam-3229	253	10	-	-	NOUN
ejpam-3229	253	11	act	act	NOUN
ejpam-3229	253	12	of	of	ADP
ejpam-3229	253	13	n	n	PROPN
ejpam-3229	253	14	is	be	AUX
ejpam-3229	253	15	m	m	NOUN
ejpam-3229	253	16	-	-	PUNCT
ejpam-3229	253	17	principally	principally	ADV
ejpam-3229	253	18	projective	projective	ADJ
ejpam-3229	253	19	.	.	PUNCT
ejpam-3229	254	1	sincen	sincen	NOUN
ejpam-3229	254	2	is	be	AUX
ejpam-3229	254	3	a	a	DET
ejpam-3229	254	4	sub	sub	NOUN
ejpam-3229	254	5	-	-	NOUN
ejpam-3229	254	6	act	act	NOUN
ejpam-3229	254	7	of	of	ADP
ejpam-3229	254	8	itself	itself	PRON
ejpam-3229	254	9	andm	andm	NOUN
ejpam-3229	254	10	-	-	PUNCT
ejpam-3229	254	11	principally	principally	ADV
ejpam-3229	254	12	projective	projective	ADJ
ejpam-3229	254	13	.	.	PUNCT
ejpam-3229	255	1	let	let	VERB
ejpam-3229	255	2	α	α	PROPN
ejpam-3229	255	3	(	(	PUNCT
ejpam-3229	255	4	m	m	NOUN
ejpam-3229	255	5	)	)	PUNCT
ejpam-3229	255	6	be	be	VERB
ejpam-3229	255	7	anm	anm	NOUN
ejpam-3229	255	8	-	-	PUNCT
ejpam-3229	255	9	cyclic	cyclic	ADJ
ejpam-3229	255	10	sub	sub	NOUN
ejpam-3229	255	11	-	-	NOUN
ejpam-3229	255	12	act	act	NOUN
ejpam-3229	255	13	of	of	ADP
ejpam-3229	255	14	m	m	PROPN
ejpam-3229	255	15	,	,	PUNCT
ejpam-3229	255	16	where	where	SCONJ
ejpam-3229	255	17	α	α	PROPN
ejpam-3229	255	18	∈	∈	PROPN
ejpam-3229	255	19	e.	e.	PROPN
ejpam-3229	255	20	to	to	PART
ejpam-3229	255	21	show	show	VERB
ejpam-3229	255	22	α	α	PROPN
ejpam-3229	255	23	(	(	PUNCT
ejpam-3229	255	24	m	m	NOUN
ejpam-3229	255	25	)	)	PUNCT
ejpam-3229	255	26	is	be	AUX
ejpam-3229	255	27	n	n	ADV
ejpam-3229	255	28	-injective	-injective	ADJ
ejpam-3229	255	29	,	,	PUNCT
ejpam-3229	255	30	we	we	PRON
ejpam-3229	255	31	let	let	VERB
ejpam-3229	255	32	β	β	PRON
ejpam-3229	255	33	:	:	PUNCT
ejpam-3229	255	34	n	n	CCONJ
ejpam-3229	255	35	′	′	NUM
ejpam-3229	255	36	→	→	SYM
ejpam-3229	255	37	α	α	PROPN
ejpam-3229	255	38	(	(	PUNCT
ejpam-3229	255	39	m	m	NOUN
ejpam-3229	255	40	)	)	PUNCT
ejpam-3229	255	41	be	be	AUX
ejpam-3229	255	42	an	an	DET
ejpam-3229	255	43	s	s	NOUN
ejpam-3229	255	44	-	-	NOUN
ejpam-3229	255	45	homomorphism	homomorphism	NOUN
ejpam-3229	255	46	,	,	PUNCT
ejpam-3229	255	47	where	where	SCONJ
ejpam-3229	255	48	n	n	PRON
ejpam-3229	255	49	′	′	NOUN
ejpam-3229	255	50	is	be	AUX
ejpam-3229	255	51	a	a	DET
ejpam-3229	255	52	sub	sub	NOUN
ejpam-3229	255	53	-	-	NOUN
ejpam-3229	255	54	act	act	NOUN
ejpam-3229	255	55	of	of	ADP
ejpam-3229	255	56	n	n	PROPN
ejpam-3229	255	57	.	.	PUNCT
ejpam-3229	256	1	since	since	SCONJ
ejpam-3229	256	2	each	each	DET
ejpam-3229	256	3	sub	sub	NOUN
ejpam-3229	256	4	-	-	NOUN
ejpam-3229	256	5	act	act	NOUN
ejpam-3229	256	6	of	of	ADP
ejpam-3229	256	7	n	n	PROPN
ejpam-3229	256	8	is	be	AUX
ejpam-3229	256	9	m	m	NOUN
ejpam-3229	256	10	-	-	ADJ
ejpam-3229	256	11	principally	principally	ADV
ejpam-3229	256	12	projective	projective	ADJ
ejpam-3229	256	13	so	so	SCONJ
ejpam-3229	256	14	n	n	ADJ
ejpam-3229	256	15	′	′	NOUN
ejpam-3229	256	16	is	be	AUX
ejpam-3229	256	17	alsom	alsom	NOUN
ejpam-3229	256	18	-	-	PUNCT
ejpam-3229	256	19	principally	principally	ADV
ejpam-3229	256	20	projective	projective	ADJ
ejpam-3229	256	21	.	.	PUNCT
ejpam-3229	257	1	therefore	therefore	ADV
ejpam-3229	257	2	there	there	PRON
ejpam-3229	257	3	exists	exist	VERB
ejpam-3229	257	4	γ	γ	X
ejpam-3229	257	5	:	:	PUNCT
ejpam-3229	257	6	n	n	PRON
ejpam-3229	257	7	′	′	NOUN
ejpam-3229	257	8	→m	→m	PUNCT
ejpam-3229	257	9	such	such	ADJ
ejpam-3229	257	10	that	that	SCONJ
ejpam-3229	257	11	αγ	αγ	PROPN
ejpam-3229	257	12	=	=	SYM
ejpam-3229	257	13	β	β	X
ejpam-3229	257	14	.	.	PUNCT
ejpam-3229	258	1	since	since	SCONJ
ejpam-3229	258	2	m	m	PROPN
ejpam-3229	258	3	is	be	AUX
ejpam-3229	258	4	n	n	ADV
ejpam-3229	258	5	-injective	-injective	ADJ
ejpam-3229	258	6	so	so	SCONJ
ejpam-3229	258	7	there	there	PRON
ejpam-3229	258	8	exists	exist	VERB
ejpam-3229	258	9	φ	φ	NOUN
ejpam-3229	258	10	:	:	PUNCT
ejpam-3229	258	11	n	n	X
ejpam-3229	258	12	→	→	SYM
ejpam-3229	258	13	m	m	VERB
ejpam-3229	258	14	such	such	ADJ
ejpam-3229	258	15	that	that	SCONJ
ejpam-3229	258	16	φi	φi	ADP
ejpam-3229	258	17	=	=	SYM
ejpam-3229	258	18	γ	γ	X
ejpam-3229	258	19	.	.	PROPN
ejpam-3229	258	20	now	now	ADV
ejpam-3229	258	21	consider	consider	VERB
ejpam-3229	258	22	αφ	αφ	NUM
ejpam-3229	258	23	:	:	PUNCT
ejpam-3229	258	24	n	n	PROPN
ejpam-3229	258	25	→	→	SYM
ejpam-3229	258	26	α	α	PROPN
ejpam-3229	258	27	(	(	PUNCT
ejpam-3229	258	28	m	m	NOUN
ejpam-3229	258	29	)	)	PUNCT
ejpam-3229	258	30	and	and	CCONJ
ejpam-3229	258	31	(	(	PUNCT
ejpam-3229	258	32	αφ)i	αφ)i	NOUN
ejpam-3229	258	33	=	=	SYM
ejpam-3229	258	34	α(φi	α(φi	PROPN
ejpam-3229	258	35	)	)	PUNCT
ejpam-3229	259	1	=	=	PUNCT
ejpam-3229	259	2	αγ	αγ	X
ejpam-3229	259	3	=	=	SYM
ejpam-3229	259	4	β	β	X
ejpam-3229	259	5	.	.	PUNCT
ejpam-3229	260	1	hence	hence	ADV
ejpam-3229	260	2	α	α	PROPN
ejpam-3229	260	3	(	(	PUNCT
ejpam-3229	260	4	m	m	NOUN
ejpam-3229	260	5	)	)	PUNCT
ejpam-3229	260	6	is	be	AUX
ejpam-3229	260	7	n	n	ADV
ejpam-3229	260	8	-injective	-injective	ADJ
ejpam-3229	260	9	.	.	PUNCT
ejpam-3229	261	1	conversely	conversely	ADV
ejpam-3229	261	2	assume	assume	VERB
ejpam-3229	261	3	that	that	SCONJ
ejpam-3229	261	4	n	n	PRON
ejpam-3229	261	5	is	be	AUX
ejpam-3229	261	6	m	m	NOUN
ejpam-3229	261	7	-	-	ADJ
ejpam-3229	261	8	principally	principally	ADV
ejpam-3229	261	9	projective	projective	ADJ
ejpam-3229	261	10	and	and	CCONJ
ejpam-3229	261	11	each	each	DET
ejpam-3229	261	12	m	m	NOUN
ejpam-3229	261	13	-	-	PUNCT
ejpam-3229	261	14	cyclic	cyclic	ADJ
ejpam-3229	261	15	sub	sub	NOUN
ejpam-3229	261	16	-	-	NOUN
ejpam-3229	261	17	act	act	NOUN
ejpam-3229	261	18	of	of	ADP
ejpam-3229	261	19	m	m	PROPN
ejpam-3229	261	20	is	be	AUX
ejpam-3229	262	1	n	n	ADV
ejpam-3229	262	2	-injective	-injective	ADJ
ejpam-3229	262	3	.	.	PUNCT
ejpam-3229	263	1	m	m	VERB
ejpam-3229	263	2	itself	itself	PRON
ejpam-3229	263	3	is	be	AUX
ejpam-3229	263	4	an	an	DET
ejpam-3229	263	5	m	m	NOUN
ejpam-3229	263	6	-	-	PUNCT
ejpam-3229	263	7	cyclic	cyclic	ADJ
ejpam-3229	263	8	sub	sub	NOUN
ejpam-3229	263	9	-	-	NOUN
ejpam-3229	263	10	act	act	NOUN
ejpam-3229	263	11	and	and	CCONJ
ejpam-3229	263	12	n	n	PRON
ejpam-3229	263	13	-injective	-injective	ADJ
ejpam-3229	263	14	.	.	PUNCT
ejpam-3229	264	1	let	let	VERB
ejpam-3229	264	2	n	n	PRON
ejpam-3229	264	3	′	′	AUX
ejpam-3229	264	4	be	be	AUX
ejpam-3229	264	5	a	a	DET
ejpam-3229	264	6	sub	sub	NOUN
ejpam-3229	264	7	-	-	NOUN
ejpam-3229	264	8	act	act	NOUN
ejpam-3229	264	9	of	of	ADP
ejpam-3229	264	10	n	n	PROPN
ejpam-3229	264	11	and	and	CCONJ
ejpam-3229	264	12	β	β	X
ejpam-3229	264	13	:	:	PUNCT
ejpam-3229	264	14	n	n	X
ejpam-3229	264	15	′	′	NUM
ejpam-3229	264	16	→	→	SYM
ejpam-3229	264	17	α	α	PROPN
ejpam-3229	264	18	(	(	PUNCT
ejpam-3229	264	19	m	m	NOUN
ejpam-3229	264	20	)	)	PUNCT
ejpam-3229	264	21	be	be	AUX
ejpam-3229	264	22	an	an	DET
ejpam-3229	264	23	s	s	NOUN
ejpam-3229	264	24	-	-	NOUN
ejpam-3229	264	25	homomorphism	homomorphism	NOUN
ejpam-3229	264	26	.	.	PUNCT
ejpam-3229	265	1	since	since	SCONJ
ejpam-3229	265	2	α	α	PROPN
ejpam-3229	265	3	(	(	PUNCT
ejpam-3229	265	4	m	m	NOUN
ejpam-3229	265	5	)	)	PUNCT
ejpam-3229	265	6	is	be	AUX
ejpam-3229	265	7	n	n	ADV
ejpam-3229	265	8	-injective	-injective	ADJ
ejpam-3229	265	9	so	so	SCONJ
ejpam-3229	265	10	there	there	PRON
ejpam-3229	265	11	exists	exist	VERB
ejpam-3229	265	12	γ	γ	X
ejpam-3229	265	13	:	:	PUNCT
ejpam-3229	265	14	n	n	PROPN
ejpam-3229	265	15	→	→	SYM
ejpam-3229	265	16	α	α	PROPN
ejpam-3229	265	17	(	(	PUNCT
ejpam-3229	265	18	m	m	NOUN
ejpam-3229	265	19	)	)	PUNCT
ejpam-3229	266	1	such	such	ADJ
ejpam-3229	266	2	that	that	PRON
ejpam-3229	266	3	γi	γi	NOUN
ejpam-3229	266	4	=	=	SYM
ejpam-3229	266	5	β	β	NOUN
ejpam-3229	266	6	,	,	PUNCT
ejpam-3229	266	7	where	where	SCONJ
ejpam-3229	266	8	i	i	PRON
ejpam-3229	266	9	:	:	PUNCT
ejpam-3229	266	10	n	n	X
ejpam-3229	266	11	′	′	NUM
ejpam-3229	266	12	→	→	PUNCT
ejpam-3229	266	13	n	n	X
ejpam-3229	266	14	is	be	AUX
ejpam-3229	266	15	inclusion	inclusion	NOUN
ejpam-3229	266	16	.	.	PUNCT
ejpam-3229	267	1	since	since	SCONJ
ejpam-3229	267	2	n	n	NUM
ejpam-3229	267	3	is	be	AUX
ejpam-3229	267	4	m	m	NOUN
ejpam-3229	267	5	-	-	ADJ
ejpam-3229	267	6	principally	principally	ADV
ejpam-3229	267	7	projective	projective	ADJ
ejpam-3229	267	8	so	so	SCONJ
ejpam-3229	267	9	we	we	PRON
ejpam-3229	267	10	have	have	VERB
ejpam-3229	267	11	φ	φ	NOUN
ejpam-3229	267	12	:	:	PUNCT
ejpam-3229	267	13	n	n	X
ejpam-3229	267	14	→	→	SYM
ejpam-3229	267	15	m	m	VERB
ejpam-3229	267	16	such	such	ADJ
ejpam-3229	267	17	that	that	SCONJ
ejpam-3229	267	18	αφ	αφ	PROPN
ejpam-3229	267	19	=	=	SYM
ejpam-3229	267	20	γ	γ	X
ejpam-3229	267	21	.	.	PROPN
ejpam-3229	267	22	now	now	ADV
ejpam-3229	267	23	keep	keep	VERB
ejpam-3229	267	24	in	in	ADP
ejpam-3229	267	25	view	view	NOUN
ejpam-3229	267	26	φi	φi	ADP
ejpam-3229	267	27	:	:	PUNCT
ejpam-3229	267	28	n	n	PRON
ejpam-3229	267	29	′	′	NOUN
ejpam-3229	267	30	→m	→m	PROPN
ejpam-3229	267	31	and	and	CCONJ
ejpam-3229	267	32	α(φi	α(φi	NOUN
ejpam-3229	267	33	)	)	PUNCT
ejpam-3229	268	1	=	=	PUNCT
ejpam-3229	268	2	(	(	PUNCT
ejpam-3229	268	3	αφ)i	αφ)i	X
ejpam-3229	268	4	=	=	SYM
ejpam-3229	268	5	γi	γi	NOUN
ejpam-3229	268	6	=	=	SYM
ejpam-3229	268	7	β	β	X
ejpam-3229	268	8	.	.	PUNCT
ejpam-3229	269	1	hence	hence	ADV
ejpam-3229	269	2	n	n	ADV
ejpam-3229	269	3	′	′	NOUN
ejpam-3229	269	4	is	be	AUX
ejpam-3229	269	5	m	m	NOUN
ejpam-3229	269	6	-	-	PUNCT
ejpam-3229	269	7	principally	principally	ADV
ejpam-3229	269	8	projective	projective	ADJ
ejpam-3229	269	9	.	.	PUNCT
ejpam-3229	270	1	theorem	theorem	ADJ
ejpam-3229	270	2	10	10	NUM
ejpam-3229	270	3	.	.	PUNCT
ejpam-3229	271	1	the	the	DET
ejpam-3229	271	2	following	follow	VERB
ejpam-3229	271	3	statements	statement	NOUN
ejpam-3229	271	4	are	be	AUX
ejpam-3229	271	5	equivalent	equivalent	ADJ
ejpam-3229	271	6	for	for	ADP
ejpam-3229	271	7	a	a	DET
ejpam-3229	271	8	projective	projective	ADJ
ejpam-3229	271	9	right	right	NOUN
ejpam-3229	271	10	s	s	NOUN
ejpam-3229	271	11	-	-	PUNCT
ejpam-3229	271	12	act	act	NOUN
ejpam-3229	271	13	m.	m.	NOUN
ejpam-3229	271	14	1	1	NUM
ejpam-3229	271	15	)	)	PUNCT
ejpam-3229	271	16	every	every	DET
ejpam-3229	271	17	m	m	NOUN
ejpam-3229	271	18	-	-	PUNCT
ejpam-3229	271	19	cyclic	cyclic	ADJ
ejpam-3229	271	20	sub	sub	NOUN
ejpam-3229	271	21	-	-	NOUN
ejpam-3229	271	22	act	act	NOUN
ejpam-3229	271	23	of	of	ADP
ejpam-3229	271	24	m	m	PROPN
ejpam-3229	271	25	is	be	AUX
ejpam-3229	271	26	projective	projective	ADJ
ejpam-3229	271	27	.	.	PUNCT
ejpam-3229	272	1	2	2	X
ejpam-3229	272	2	)	)	PUNCT
ejpam-3229	272	3	every	every	DET
ejpam-3229	272	4	factor	factor	NOUN
ejpam-3229	272	5	s	s	NOUN
ejpam-3229	272	6	-	-	NOUN
ejpam-3229	272	7	act	act	NOUN
ejpam-3229	272	8	of	of	ADP
ejpam-3229	272	9	an	an	PRON
ejpam-3229	272	10	m	m	ADV
ejpam-3229	272	11	-	-	ADJ
ejpam-3229	272	12	principally	principally	ADV
ejpam-3229	272	13	injective	injective	ADJ
ejpam-3229	272	14	s	s	NOUN
ejpam-3229	272	15	-	-	PUNCT
ejpam-3229	272	16	act	act	NOUN
ejpam-3229	272	17	is	be	AUX
ejpam-3229	272	18	m	m	NOUN
ejpam-3229	272	19	-	-	PUNCT
ejpam-3229	272	20	principally	principally	ADV
ejpam-3229	272	21	injective	injective	ADJ
ejpam-3229	272	22	.	.	PUNCT
ejpam-3229	273	1	3	3	X
ejpam-3229	273	2	)	)	PUNCT
ejpam-3229	273	3	every	every	DET
ejpam-3229	273	4	factor	factor	NOUN
ejpam-3229	273	5	s	s	NOUN
ejpam-3229	273	6	-	-	NOUN
ejpam-3229	273	7	act	act	NOUN
ejpam-3229	273	8	of	of	ADP
ejpam-3229	273	9	an	an	DET
ejpam-3229	273	10	injective	injective	ADJ
ejpam-3229	273	11	s	s	NOUN
ejpam-3229	273	12	-	-	PUNCT
ejpam-3229	273	13	act	act	NOUN
ejpam-3229	273	14	is	be	AUX
ejpam-3229	273	15	m	m	NOUN
ejpam-3229	273	16	-	-	PUNCT
ejpam-3229	273	17	principally	principally	ADV
ejpam-3229	273	18	injective	injective	ADJ
ejpam-3229	273	19	.	.	PUNCT
ejpam-3229	274	1	proof	proof	NOUN
ejpam-3229	274	2	.	.	PUNCT
ejpam-3229	275	1	1)⇒2	1)⇒2	NUM
ejpam-3229	275	2	)	)	PUNCT
ejpam-3229	275	3	let	let	VERB
ejpam-3229	275	4	n	n	PRON
ejpam-3229	275	5	be	be	AUX
ejpam-3229	275	6	anm	anm	NOUN
ejpam-3229	275	7	-	-	PUNCT
ejpam-3229	275	8	principally	principally	ADV
ejpam-3229	275	9	injective	injective	ADJ
ejpam-3229	275	10	s	s	NOUN
ejpam-3229	275	11	-	-	PUNCT
ejpam-3229	275	12	act	act	NOUN
ejpam-3229	275	13	and	and	CCONJ
ejpam-3229	275	14	ρ	ρ	NOUN
ejpam-3229	275	15	be	be	AUX
ejpam-3229	275	16	a	a	DET
ejpam-3229	275	17	congruence	congruence	NOUN
ejpam-3229	275	18	on	on	ADP
ejpam-3229	275	19	n	n	PROPN
ejpam-3229	275	20	.	.	PUNCT
ejpam-3229	276	1	let	let	VERB
ejpam-3229	276	2	φ	φ	PROPN
ejpam-3229	276	3	:	:	PUNCT
ejpam-3229	276	4	α	α	PROPN
ejpam-3229	276	5	(	(	PUNCT
ejpam-3229	276	6	m	m	NOUN
ejpam-3229	276	7	)	)	PUNCT
ejpam-3229	276	8	→	→	SYM
ejpam-3229	276	9	n	n	CCONJ
ejpam-3229	276	10	/	/	SYM
ejpam-3229	276	11	ρ	ρ	PROPN
ejpam-3229	276	12	be	be	AUX
ejpam-3229	276	13	an	an	DET
ejpam-3229	276	14	s	s	NOUN
ejpam-3229	276	15	-	-	NOUN
ejpam-3229	276	16	homomorphism	homomorphism	NOUN
ejpam-3229	276	17	,	,	PUNCT
ejpam-3229	276	18	where	where	SCONJ
ejpam-3229	276	19	α	α	PROPN
ejpam-3229	276	20	∈	∈	PROPN
ejpam-3229	276	21	e.	e.	PROPN
ejpam-3229	276	22	since	since	SCONJ
ejpam-3229	276	23	α	α	PROPN
ejpam-3229	276	24	(	(	PUNCT
ejpam-3229	276	25	m	m	NOUN
ejpam-3229	276	26	)	)	PUNCT
ejpam-3229	276	27	is	be	AUX
ejpam-3229	276	28	projective	projective	ADJ
ejpam-3229	276	29	so	so	ADV
ejpam-3229	276	30	there	there	PRON
ejpam-3229	276	31	exists	exist	VERB
ejpam-3229	276	32	φ	φ	NOUN
ejpam-3229	276	33	:	:	PUNCT
ejpam-3229	276	34	α	α	PROPN
ejpam-3229	276	35	(	(	PUNCT
ejpam-3229	276	36	m	m	NOUN
ejpam-3229	276	37	)	)	PUNCT
ejpam-3229	276	38	→	→	PUNCT
ejpam-3229	276	39	n	n	X
ejpam-3229	276	40	such	such	ADJ
ejpam-3229	276	41	that	that	DET
ejpam-3229	276	42	πφ	πφ	PROPN
ejpam-3229	276	43	=	=	SYM
ejpam-3229	276	44	φ	φ	PROPN
ejpam-3229	276	45	,	,	PUNCT
ejpam-3229	276	46	where	where	SCONJ
ejpam-3229	276	47	π	π	NOUN
ejpam-3229	276	48	:	:	PUNCT
ejpam-3229	276	49	n	n	PROPN
ejpam-3229	276	50	→	→	SYM
ejpam-3229	276	51	n	n	CCONJ
ejpam-3229	276	52	/	/	SYM
ejpam-3229	276	53	ρ	ρ	PROPN
ejpam-3229	276	54	is	be	AUX
ejpam-3229	276	55	a	a	DET
ejpam-3229	276	56	canonical	canonical	ADJ
ejpam-3229	276	57	epimorphism	epimorphism	NOUN
ejpam-3229	276	58	.	.	PUNCT
ejpam-3229	277	1	now	now	ADV
ejpam-3229	277	2	as	as	SCONJ
ejpam-3229	277	3	n	n	PRON
ejpam-3229	277	4	is	be	AUX
ejpam-3229	277	5	m	m	NOUN
ejpam-3229	277	6	-	-	ADJ
ejpam-3229	277	7	principally	principally	ADV
ejpam-3229	277	8	injective	injective	ADJ
ejpam-3229	277	9	so	so	SCONJ
ejpam-3229	277	10	there	there	PRON
ejpam-3229	277	11	exists	exist	VERB
ejpam-3229	277	12	γ	γ	X
ejpam-3229	277	13	:	:	PUNCT
ejpam-3229	277	14	m	m	PROPN
ejpam-3229	277	15	→	→	SYM
ejpam-3229	277	16	n	n	X
ejpam-3229	277	17	which	which	PRON
ejpam-3229	277	18	extends	extend	VERB
ejpam-3229	277	19	φ	φ	PROPN
ejpam-3229	277	20	.	.	PUNCT
ejpam-3229	278	1	consider	consider	VERB
ejpam-3229	278	2	πγ	πγ	NOUN
ejpam-3229	278	3	:	:	PUNCT
ejpam-3229	278	4	m	m	PROPN
ejpam-3229	278	5	→	→	SYM
ejpam-3229	278	6	n	n	CCONJ
ejpam-3229	278	7	/	/	SYM
ejpam-3229	278	8	ρ	ρ	PROPN
ejpam-3229	278	9	which	which	PRON
ejpam-3229	278	10	extends	extend	VERB
ejpam-3229	278	11	φ	φ	PROPN
ejpam-3229	278	12	.	.	PUNCT
ejpam-3229	279	1	hence	hence	ADV
ejpam-3229	279	2	n	n	CCONJ
ejpam-3229	279	3	/	/	SYM
ejpam-3229	279	4	ρ	ρ	PROPN
ejpam-3229	279	5	is	be	AUX
ejpam-3229	279	6	m	m	NOUN
ejpam-3229	279	7	-	-	ADJ
ejpam-3229	279	8	principally	principally	ADV
ejpam-3229	279	9	injective	injective	ADJ
ejpam-3229	279	10	.	.	PUNCT
ejpam-3229	280	1	2)⇒3	2)⇒3	NUM
ejpam-3229	280	2	)	)	PUNCT
ejpam-3229	280	3	letn	letn	NOUN
ejpam-3229	280	4	be	be	VERB
ejpam-3229	280	5	an	an	DET
ejpam-3229	280	6	injective	injective	ADJ
ejpam-3229	280	7	right	right	ADJ
ejpam-3229	280	8	s	s	NOUN
ejpam-3229	280	9	-	-	PUNCT
ejpam-3229	280	10	act	act	NOUN
ejpam-3229	280	11	and	and	CCONJ
ejpam-3229	280	12	ρ	ρ	PROPN
ejpam-3229	280	13	be	be	AUX
ejpam-3229	280	14	congruence	congruence	PROPN
ejpam-3229	280	15	onn	onn	PROPN
ejpam-3229	280	16	.	.	PUNCT
ejpam-3229	281	1	let	let	VERB
ejpam-3229	281	2	φ	φ	PROPN
ejpam-3229	281	3	:	:	PUNCT
ejpam-3229	281	4	α	α	X
ejpam-3229	281	5	(	(	PUNCT
ejpam-3229	281	6	m)→	m)→	AUX
ejpam-3229	281	7	n	n	PRON
ejpam-3229	281	8	be	be	AUX
ejpam-3229	281	9	an	an	DET
ejpam-3229	281	10	s	s	NOUN
ejpam-3229	281	11	-	-	PUNCT
ejpam-3229	281	12	homomorphism	homomorphism	NOUN
ejpam-3229	281	13	and	and	CCONJ
ejpam-3229	281	14	n	n	CCONJ
ejpam-3229	281	15	be	be	AUX
ejpam-3229	281	16	injective	injective	ADJ
ejpam-3229	281	17	,	,	PUNCT
ejpam-3229	281	18	so	so	SCONJ
ejpam-3229	281	19	there	there	PRON
ejpam-3229	281	20	exists	exist	VERB
ejpam-3229	281	21	γ	γ	X
ejpam-3229	281	22	:	:	PUNCT
ejpam-3229	281	23	m→n	m→n	NUM
ejpam-3229	281	24	extending	extend	VERB
ejpam-3229	281	25	φ	φ	NUM
ejpam-3229	281	26	.	.	PUNCT
ejpam-3229	282	1	by	by	ADP
ejpam-3229	282	2	hypothesis	hypothesis	NOUN
ejpam-3229	282	3	n	n	NOUN
ejpam-3229	282	4	is	be	AUX
ejpam-3229	282	5	m	m	NOUN
ejpam-3229	282	6	-	-	PUNCT
ejpam-3229	282	7	principally	principally	ADV
ejpam-3229	282	8	injective	injective	ADJ
ejpam-3229	282	9	.	.	PUNCT
ejpam-3229	283	1	thus	thus	ADV
ejpam-3229	283	2	n	n	CCONJ
ejpam-3229	283	3	/	/	SYM
ejpam-3229	283	4	ρ	ρ	PROPN
ejpam-3229	283	5	is	be	AUX
ejpam-3229	283	6	m	m	NOUN
ejpam-3229	283	7	-	-	ADJ
ejpam-3229	283	8	principally	principally	ADV
ejpam-3229	283	9	injective	injective	ADJ
ejpam-3229	283	10	.	.	PUNCT
ejpam-3229	284	1	3)⇒1	3)⇒1	NUM
ejpam-3229	284	2	)	)	PUNCT
ejpam-3229	284	3	let	let	VERB
ejpam-3229	284	4	α	α	PROPN
ejpam-3229	284	5	(	(	PUNCT
ejpam-3229	284	6	m	m	NOUN
ejpam-3229	284	7	)	)	PUNCT
ejpam-3229	284	8	be	be	AUX
ejpam-3229	284	9	an	an	DET
ejpam-3229	284	10	m	m	NOUN
ejpam-3229	284	11	-	-	PUNCT
ejpam-3229	284	12	cyclic	cyclic	ADJ
ejpam-3229	284	13	sub	sub	NOUN
ejpam-3229	284	14	-	-	NOUN
ejpam-3229	284	15	act	act	NOUN
ejpam-3229	284	16	of	of	ADP
ejpam-3229	284	17	m	m	PROPN
ejpam-3229	284	18	,	,	PUNCT
ejpam-3229	284	19	h	h	NOUN
ejpam-3229	284	20	:	:	PUNCT
ejpam-3229	284	21	a	a	DET
ejpam-3229	284	22	→	→	SYM
ejpam-3229	284	23	b	b	X
ejpam-3229	284	24	be	be	AUX
ejpam-3229	284	25	an	an	DET
ejpam-3229	284	26	s	s	NOUN
ejpam-3229	284	27	-	-	PUNCT
ejpam-3229	284	28	epimorphism	epimorphism	NOUN
ejpam-3229	284	29	and	and	CCONJ
ejpam-3229	284	30	β	β	X
ejpam-3229	284	31	:	:	PUNCT
ejpam-3229	284	32	α	α	PROPN
ejpam-3229	284	33	(	(	PUNCT
ejpam-3229	284	34	m	m	NOUN
ejpam-3229	284	35	)	)	PUNCT
ejpam-3229	284	36	→	→	SYM
ejpam-3229	285	1	b	b	X
ejpam-3229	285	2	be	be	AUX
ejpam-3229	285	3	an	an	DET
ejpam-3229	285	4	s	s	NOUN
ejpam-3229	285	5	-	-	NOUN
ejpam-3229	285	6	homomorphism	homomorphism	NOUN
ejpam-3229	285	7	.	.	PUNCT
ejpam-3229	286	1	by	by	ADP
ejpam-3229	286	2	corollary	corollary	ADJ
ejpam-3229	286	3	2.1.2	2.1.2	NUM
ejpam-3229	286	4	of	of	ADP
ejpam-3229	286	5	[	[	X
ejpam-3229	286	6	1	1	X
ejpam-3229	286	7	]	]	PUNCT
ejpam-3229	286	8	there	there	PRON
ejpam-3229	286	9	exists	exist	VERB
ejpam-3229	286	10	an	an	DET
ejpam-3229	286	11	injective	injective	ADJ
ejpam-3229	286	12	s	s	NOUN
ejpam-3229	286	13	-	-	PUNCT
ejpam-3229	286	14	act	act	NOUN
ejpam-3229	286	15	q	q	NOUN
ejpam-3229	286	16	in	in	ADP
ejpam-3229	286	17	which	which	PRON
ejpam-3229	286	18	a	a	PRON
ejpam-3229	286	19	can	can	AUX
ejpam-3229	286	20	be	be	AUX
ejpam-3229	286	21	embedded	embed	VERB
ejpam-3229	286	22	.	.	PUNCT
ejpam-3229	287	1	now	now	ADV
ejpam-3229	287	2	define	define	VERB
ejpam-3229	287	3	φ	φ	NOUN
ejpam-3229	287	4	:	:	PUNCT
ejpam-3229	287	5	b	b	X
ejpam-3229	287	6	=	=	SYM
ejpam-3229	287	7	h(a	h(a	PROPN
ejpam-3229	287	8	)	)	PUNCT
ejpam-3229	287	9	→	→	PUNCT
ejpam-3229	287	10	a	a	X
ejpam-3229	287	11	/	/	SYM
ejpam-3229	287	12	k	k	NOUN
ejpam-3229	287	13	by	by	ADP
ejpam-3229	287	14	φ(h(a	φ(h(a	PROPN
ejpam-3229	287	15	)	)	PUNCT
ejpam-3229	287	16	)	)	PUNCT
ejpam-3229	288	1	=	=	PUNCT
ejpam-3229	289	1	[	[	X
ejpam-3229	289	2	a]k	a]k	INTJ
ejpam-3229	289	3	,	,	PUNCT
ejpam-3229	289	4	where	where	SCONJ
ejpam-3229	289	5	k	k	PROPN
ejpam-3229	289	6	=	=	SYM
ejpam-3229	289	7	kerh	kerh	PROPN
ejpam-3229	289	8	,	,	PUNCT
ejpam-3229	289	9	the	the	DET
ejpam-3229	289	10	kernel	kernel	PROPN
ejpam-3229	289	11	congruence	congruence	NOUN
ejpam-3229	289	12	on	on	ADP
ejpam-3229	289	13	a	a	DET
ejpam-3229	289	14	induced	induce	VERB
ejpam-3229	289	15	by	by	ADP
ejpam-3229	289	16	h.	h.	PROPN
ejpam-3229	289	17	clearly	clearly	ADV
ejpam-3229	289	18	φ	φ	PROPN
ejpam-3229	289	19	is	be	AUX
ejpam-3229	289	20	an	an	DET
ejpam-3229	289	21	s	s	NOUN
ejpam-3229	289	22	-	-	NOUN
ejpam-3229	289	23	isomorphism	isomorphism	NOUN
ejpam-3229	289	24	.	.	PUNCT
ejpam-3229	290	1	let	let	VERB
ejpam-3229	290	2	k	k	NOUN
ejpam-3229	291	1	′	′	NUM
ejpam-3229	292	1	=	=	PUNCT
ejpam-3229	292	2	k	k	NOUN
ejpam-3229	292	3	∪	∪	ADP
ejpam-3229	292	4	4q	4q	NOUN
ejpam-3229	292	5	be	be	VERB
ejpam-3229	292	6	a	a	DET
ejpam-3229	292	7	congruence	congruence	NOUN
ejpam-3229	292	8	on	on	ADP
ejpam-3229	292	9	q	q	NOUN
ejpam-3229	292	10	,	,	PUNCT
ejpam-3229	292	11	where	where	SCONJ
ejpam-3229	292	12	4q	4q	NOUN
ejpam-3229	292	13	is	be	AUX
ejpam-3229	292	14	a	a	DET
ejpam-3229	292	15	diagonal	diagonal	ADJ
ejpam-3229	292	16	congruence	congruence	NOUN
ejpam-3229	292	17	on	on	ADP
ejpam-3229	292	18	q.	q.	PROPN
ejpam-3229	292	19	moreover	moreover	ADV
ejpam-3229	292	20	,	,	PUNCT
ejpam-3229	292	21	a	a	PRON
ejpam-3229	292	22	/	/	SYM
ejpam-3229	292	23	k	k	PROPN
ejpam-3229	292	24	is	be	AUX
ejpam-3229	292	25	a	a	DET
ejpam-3229	292	26	sub	sub	NOUN
ejpam-3229	292	27	-	-	NOUN
ejpam-3229	292	28	act	act	NOUN
ejpam-3229	292	29	of	of	ADP
ejpam-3229	292	30	q	q	PROPN
ejpam-3229	292	31	/	/	SYM
ejpam-3229	292	32	k	k	PROPN
ejpam-3229	292	33	′.	′.	NOUN
ejpam-3229	292	34	thus	thus	ADV
ejpam-3229	292	35	β	β	X
ejpam-3229	292	36	:	:	PUNCT
ejpam-3229	292	37	α	α	X
ejpam-3229	292	38	(	(	PUNCT
ejpam-3229	292	39	m)→	m)→	PROPN
ejpam-3229	292	40	b	b	NOUN
ejpam-3229	292	41	can	can	AUX
ejpam-3229	292	42	also	also	ADV
ejpam-3229	292	43	be	be	AUX
ejpam-3229	292	44	j.	j.	PROPN
ejpam-3229	292	45	hussain	hussain	PROPN
ejpam-3229	292	46	,	,	PUNCT
ejpam-3229	292	47	m.shabir	m.shabir	PROPN
ejpam-3229	292	48	/	/	SYM
ejpam-3229	292	49	eur	eur	PROPN
ejpam-3229	292	50	.	.	PUNCT
ejpam-3229	293	1	j.	j.	PROPN
ejpam-3229	293	2	pure	pure	PROPN
ejpam-3229	293	3	appl	appl	PROPN
ejpam-3229	293	4	.	.	PROPN
ejpam-3229	293	5	math	math	PROPN
ejpam-3229	293	6	,	,	PUNCT
ejpam-3229	293	7	11	11	NUM
ejpam-3229	293	8	(	(	PUNCT
ejpam-3229	293	9	2	2	NUM
ejpam-3229	293	10	)	)	PUNCT
ejpam-3229	293	11	(	(	PUNCT
ejpam-3229	293	12	2018	2018	NUM
ejpam-3229	293	13	)	)	PUNCT
ejpam-3229	293	14	,	,	PUNCT
ejpam-3229	293	15	431	431	NUM
ejpam-3229	293	16	-	-	SYM
ejpam-3229	293	17	443	443	NUM
ejpam-3229	293	18	439	439	NUM
ejpam-3229	293	19	viewed	view	VERB
ejpam-3229	293	20	as	as	ADP
ejpam-3229	293	21	β	β	X
ejpam-3229	293	22	:	:	PUNCT
ejpam-3229	293	23	α	α	PROPN
ejpam-3229	293	24	(	(	PUNCT
ejpam-3229	293	25	m	m	NOUN
ejpam-3229	293	26	)	)	PUNCT
ejpam-3229	293	27	→	→	SYM
ejpam-3229	293	28	q	q	X
ejpam-3229	293	29	/	/	SYM
ejpam-3229	293	30	k	k	PROPN
ejpam-3229	293	31	′.	′.	NOUN
ejpam-3229	293	32	by	by	ADP
ejpam-3229	293	33	hypothesis	hypothesis	NOUN
ejpam-3229	293	34	q	q	NOUN
ejpam-3229	293	35	/	/	SYM
ejpam-3229	293	36	k	k	NOUN
ejpam-3229	293	37	′	′	NOUN
ejpam-3229	293	38	is	be	AUX
ejpam-3229	293	39	m	m	NOUN
ejpam-3229	293	40	-	-	ADJ
ejpam-3229	293	41	principally	principally	ADV
ejpam-3229	293	42	injective	injective	ADJ
ejpam-3229	293	43	,	,	PUNCT
ejpam-3229	293	44	so	so	SCONJ
ejpam-3229	293	45	there	there	PRON
ejpam-3229	293	46	exists	exist	VERB
ejpam-3229	293	47	β	β	X
ejpam-3229	293	48	:	:	PUNCT
ejpam-3229	293	49	m→	m→	NOUN
ejpam-3229	293	50	q	q	PROPN
ejpam-3229	293	51	/	/	SYM
ejpam-3229	293	52	k	k	NOUN
ejpam-3229	293	53	′	′	NUM
ejpam-3229	293	54	which	which	PRON
ejpam-3229	293	55	extends	extend	VERB
ejpam-3229	293	56	β	β	X
ejpam-3229	293	57	.	.	PUNCT
ejpam-3229	294	1	since	since	SCONJ
ejpam-3229	294	2	m	m	PROPN
ejpam-3229	294	3	is	be	AUX
ejpam-3229	294	4	projective	projective	ADJ
ejpam-3229	294	5	so	so	ADV
ejpam-3229	294	6	there	there	PRON
ejpam-3229	294	7	exists	exist	VERB
ejpam-3229	294	8	γ	γ	X
ejpam-3229	294	9	:	:	PUNCT
ejpam-3229	294	10	m→	m→	NOUN
ejpam-3229	294	11	q	q	PUNCT
ejpam-3229	294	12	such	such	ADJ
ejpam-3229	294	13	that	that	PRON
ejpam-3229	294	14	πγ	πγ	NOUN
ejpam-3229	294	15	=	=	SYM
ejpam-3229	294	16	β	β	NOUN
ejpam-3229	294	17	,	,	PUNCT
ejpam-3229	294	18	where	where	SCONJ
ejpam-3229	294	19	π	π	X
ejpam-3229	294	20	:	:	PUNCT
ejpam-3229	294	21	q→	q→	PROPN
ejpam-3229	294	22	q	q	NOUN
ejpam-3229	294	23	/	/	SYM
ejpam-3229	294	24	k	k	NOUN
ejpam-3229	294	25	′	′	NOUN
ejpam-3229	294	26	is	be	AUX
ejpam-3229	294	27	a	a	DET
ejpam-3229	294	28	canonical	canonical	ADJ
ejpam-3229	294	29	epimorphism	epimorphism	NOUN
ejpam-3229	294	30	i.e.	i.e.	X
ejpam-3229	294	31	γ	γ	X
ejpam-3229	294	32	lifts	lift	VERB
ejpam-3229	294	33	β	β	X
ejpam-3229	294	34	.	.	PUNCT
ejpam-3229	294	35	clearly	clearly	ADV
ejpam-3229	294	36	γ(α	γ(α	PROPN
ejpam-3229	294	37	(	(	PUNCT
ejpam-3229	294	38	m	m	NOUN
ejpam-3229	294	39	)	)	PUNCT
ejpam-3229	294	40	)	)	PUNCT
ejpam-3229	294	41	lies	lie	VERB
ejpam-3229	294	42	in	in	ADP
ejpam-3229	294	43	the	the	DET
ejpam-3229	294	44	domain	domain	NOUN
ejpam-3229	294	45	of	of	ADP
ejpam-3229	294	46	h	h	NOUN
ejpam-3229	294	47	,	,	PUNCT
ejpam-3229	294	48	so	so	SCONJ
ejpam-3229	294	49	we	we	PRON
ejpam-3229	294	50	must	must	AUX
ejpam-3229	294	51	have	have	VERB
ejpam-3229	294	52	γ(α	γ(α	PROPN
ejpam-3229	294	53	(	(	PUNCT
ejpam-3229	294	54	m	m	NOUN
ejpam-3229	294	55	)	)	PUNCT
ejpam-3229	294	56	)	)	PUNCT
ejpam-3229	295	1	⊆	⊆	NUM
ejpam-3229	295	2	a.	a.	NOUN
ejpam-3229	295	3	thus	thus	ADV
ejpam-3229	295	4	we	we	PRON
ejpam-3229	295	5	have	have	AUX
ejpam-3229	295	6	lifted	lift	VERB
ejpam-3229	295	7	β	β	NOUN
ejpam-3229	295	8	.	.	PUNCT
ejpam-3229	296	1	this	this	PRON
ejpam-3229	296	2	completes	complete	VERB
ejpam-3229	296	3	the	the	DET
ejpam-3229	296	4	proof	proof	NOUN
ejpam-3229	296	5	of	of	ADP
ejpam-3229	296	6	the	the	DET
ejpam-3229	296	7	theorem	theorem	PROPN
ejpam-3229	296	8	.	.	PROPN
ejpam-3229	296	9	corollary	corollary	ADJ
ejpam-3229	296	10	4	4	NUM
ejpam-3229	296	11	.	.	PUNCT
ejpam-3229	297	1	the	the	DET
ejpam-3229	297	2	following	follow	VERB
ejpam-3229	297	3	statements	statement	NOUN
ejpam-3229	297	4	are	be	AUX
ejpam-3229	297	5	equivalent	equivalent	ADJ
ejpam-3229	297	6	for	for	ADP
ejpam-3229	297	7	a	a	DET
ejpam-3229	297	8	semigroup	semigroup	PROPN
ejpam-3229	297	9	s.	s.	PROPN
ejpam-3229	297	10	1	1	NUM
ejpam-3229	297	11	)	)	PUNCT
ejpam-3229	297	12	s	s	VERB
ejpam-3229	297	13	is	be	AUX
ejpam-3229	297	14	a	a	DET
ejpam-3229	297	15	right	right	ADJ
ejpam-3229	297	16	pp	pp	ADJ
ejpam-3229	297	17	-	-	PUNCT
ejpam-3229	297	18	semigroup	semigroup	NOUN
ejpam-3229	297	19	.	.	PUNCT
ejpam-3229	298	1	2	2	NUM
ejpam-3229	298	2	)	)	PUNCT
ejpam-3229	298	3	every	every	DET
ejpam-3229	298	4	factor	factor	NOUN
ejpam-3229	298	5	s	s	NOUN
ejpam-3229	298	6	-	-	NOUN
ejpam-3229	298	7	act	act	NOUN
ejpam-3229	298	8	of	of	ADP
ejpam-3229	298	9	pm	pm	NOUN
ejpam-3229	298	10	-	-	PUNCT
ejpam-3229	298	11	injective	injective	ADJ
ejpam-3229	298	12	s	s	NOUN
ejpam-3229	298	13	-	-	PUNCT
ejpam-3229	298	14	act	act	NOUN
ejpam-3229	298	15	is	be	AUX
ejpam-3229	298	16	pm	pm	NOUN
ejpam-3229	298	17	-	-	PUNCT
ejpam-3229	298	18	injective	injective	ADJ
ejpam-3229	298	19	.	.	PUNCT
ejpam-3229	299	1	3	3	X
ejpam-3229	299	2	)	)	PUNCT
ejpam-3229	299	3	every	every	DET
ejpam-3229	299	4	factor	factor	NOUN
ejpam-3229	299	5	s	s	NOUN
ejpam-3229	299	6	-	-	NOUN
ejpam-3229	299	7	act	act	NOUN
ejpam-3229	299	8	of	of	ADP
ejpam-3229	299	9	an	an	DET
ejpam-3229	299	10	injective	injective	ADJ
ejpam-3229	299	11	s	s	NOUN
ejpam-3229	299	12	-	-	PUNCT
ejpam-3229	299	13	act	act	NOUN
ejpam-3229	299	14	is	be	AUX
ejpam-3229	299	15	pm	pm	NOUN
ejpam-3229	299	16	-	-	PUNCT
ejpam-3229	299	17	injective	injective	ADJ
ejpam-3229	299	18	.	.	PUNCT
ejpam-3229	300	1	theorem	theorem	NOUN
ejpam-3229	300	2	11	11	NUM
ejpam-3229	300	3	.	.	PUNCT
ejpam-3229	301	1	let	let	VERB
ejpam-3229	301	2	n	n	PRON
ejpam-3229	301	3	be	be	AUX
ejpam-3229	301	4	an	an	DET
ejpam-3229	301	5	m	m	ADV
ejpam-3229	301	6	-	-	ADJ
ejpam-3229	301	7	principally	principally	ADV
ejpam-3229	301	8	projective	projective	ADJ
ejpam-3229	301	9	s	s	NOUN
ejpam-3229	301	10	-	-	NOUN
ejpam-3229	301	11	act	act	NOUN
ejpam-3229	301	12	.	.	PUNCT
ejpam-3229	302	1	if	if	SCONJ
ejpam-3229	302	2	m0	m0	PROPN
ejpam-3229	302	3	is	be	AUX
ejpam-3229	302	4	either	either	CCONJ
ejpam-3229	302	5	an	an	DET
ejpam-3229	302	6	shomomorphic	shomomorphic	ADJ
ejpam-3229	302	7	image	image	NOUN
ejpam-3229	302	8	or	or	CCONJ
ejpam-3229	302	9	an	an	DET
ejpam-3229	302	10	s	s	NOUN
ejpam-3229	302	11	-	-	PUNCT
ejpam-3229	302	12	sub	sub	NOUN
ejpam-3229	302	13	-	-	NOUN
ejpam-3229	302	14	act	act	NOUN
ejpam-3229	302	15	of	of	ADP
ejpam-3229	302	16	m	m	PROPN
ejpam-3229	302	17	,	,	PUNCT
ejpam-3229	302	18	then	then	ADV
ejpam-3229	302	19	n	n	PROPN
ejpam-3229	302	20	is	be	AUX
ejpam-3229	302	21	m0	m0	NOUN
ejpam-3229	302	22	-	-	PUNCT
ejpam-3229	302	23	principally	principally	ADV
ejpam-3229	302	24	projective	projective	ADJ
ejpam-3229	302	25	.	.	PUNCT
ejpam-3229	303	1	proof	proof	NOUN
ejpam-3229	303	2	.	.	PUNCT
ejpam-3229	304	1	if	if	SCONJ
ejpam-3229	304	2	n	n	PRON
ejpam-3229	304	3	is	be	AUX
ejpam-3229	304	4	a	a	DET
ejpam-3229	304	5	homomorphic	homomorphic	ADJ
ejpam-3229	304	6	image	image	NOUN
ejpam-3229	304	7	of	of	ADP
ejpam-3229	304	8	m0	m0	NOUN
ejpam-3229	304	9	then	then	ADV
ejpam-3229	304	10	the	the	DET
ejpam-3229	304	11	result	result	NOUN
ejpam-3229	304	12	follows	follow	VERB
ejpam-3229	304	13	directly	directly	ADV
ejpam-3229	304	14	from	from	ADP
ejpam-3229	304	15	the	the	DET
ejpam-3229	304	16	lemma	lemma	PROPN
ejpam-3229	304	17	5	5	NUM
ejpam-3229	304	18	.	.	PUNCT
ejpam-3229	305	1	now	now	ADV
ejpam-3229	305	2	assume	assume	VERB
ejpam-3229	305	3	that	that	SCONJ
ejpam-3229	305	4	m0	m0	PROPN
ejpam-3229	305	5	is	be	AUX
ejpam-3229	305	6	ssub	ssub	ADJ
ejpam-3229	305	7	-	-	PUNCT
ejpam-3229	305	8	act	act	NOUN
ejpam-3229	305	9	of	of	ADP
ejpam-3229	305	10	m.	m.	NOUN
ejpam-3229	305	11	to	to	PART
ejpam-3229	305	12	show	show	VERB
ejpam-3229	305	13	that	that	SCONJ
ejpam-3229	305	14	n	n	PRON
ejpam-3229	305	15	is	be	AUX
ejpam-3229	305	16	m0	m0	NOUN
ejpam-3229	305	17	-	-	PUNCT
ejpam-3229	305	18	principally	principally	ADV
ejpam-3229	305	19	projective	projective	ADJ
ejpam-3229	305	20	,	,	PUNCT
ejpam-3229	305	21	we	we	PRON
ejpam-3229	305	22	let	let	VERB
ejpam-3229	305	23	φ	φ	NOUN
ejpam-3229	305	24	:	:	PUNCT
ejpam-3229	305	25	n	n	PROPN
ejpam-3229	305	26	→	→	SYM
ejpam-3229	305	27	α(m0	α(m0	NOUN
ejpam-3229	305	28	)	)	PUNCT
ejpam-3229	305	29	be	be	AUX
ejpam-3229	305	30	an	an	DET
ejpam-3229	305	31	s	s	NOUN
ejpam-3229	305	32	-	-	NOUN
ejpam-3229	305	33	homomorphism	homomorphism	NOUN
ejpam-3229	305	34	,	,	PUNCT
ejpam-3229	305	35	where	where	SCONJ
ejpam-3229	305	36	α	α	PROPN
ejpam-3229	305	37	∈	∈	PROPN
ejpam-3229	305	38	end(m0	end(m0	NOUN
ejpam-3229	305	39	)	)	PUNCT
ejpam-3229	305	40	.	.	PUNCT
ejpam-3229	306	1	by	by	ADP
ejpam-3229	306	2	lemma	lemma	PROPN
ejpam-3229	306	3	1	1	NUM
ejpam-3229	306	4	,	,	PUNCT
ejpam-3229	306	5	it	it	PRON
ejpam-3229	306	6	is	be	AUX
ejpam-3229	306	7	clear	clear	ADJ
ejpam-3229	306	8	that	that	SCONJ
ejpam-3229	306	9	α(m0	α(m0	NOUN
ejpam-3229	306	10	)	)	PUNCT
ejpam-3229	306	11	'	'	PUNCT
ejpam-3229	307	1	m0/	m0/	NUM
ejpam-3229	307	2	kerα	kerα	ADV
ejpam-3229	307	3	.	.	PUNCT
ejpam-3229	308	1	consider	consider	VERB
ejpam-3229	308	2	π0	π0	NOUN
ejpam-3229	308	3	:	:	PUNCT
ejpam-3229	308	4	m0	m0	PROPN
ejpam-3229	308	5	→	→	PUNCT
ejpam-3229	308	6	m0/	m0/	NOUN
ejpam-3229	308	7	kerα	kerα	ADV
ejpam-3229	308	8	be	be	AUX
ejpam-3229	308	9	the	the	DET
ejpam-3229	308	10	natural	natural	ADJ
ejpam-3229	308	11	epimorphism	epimorphism	NOUN
ejpam-3229	308	12	.	.	PUNCT
ejpam-3229	309	1	let	let	VERB
ejpam-3229	309	2	ρ	ρ	NOUN
ejpam-3229	309	3	be	be	AUX
ejpam-3229	309	4	the	the	DET
ejpam-3229	309	5	congruence	congruence	NOUN
ejpam-3229	309	6	onm	onm	NOUN
ejpam-3229	309	7	defined	define	VERB
ejpam-3229	309	8	by	by	ADP
ejpam-3229	309	9	ρ	ρ	PROPN
ejpam-3229	309	10	=	=	SYM
ejpam-3229	309	11	kerα∪4	kerα∪4	PROPN
ejpam-3229	309	12	m	m	PROPN
ejpam-3229	309	13	,	,	PUNCT
ejpam-3229	309	14	where	where	SCONJ
ejpam-3229	309	15	4	4	NUM
ejpam-3229	309	16	m	m	NOUN
ejpam-3229	309	17	is	be	AUX
ejpam-3229	309	18	a	a	DET
ejpam-3229	309	19	diagonal	diagonal	ADJ
ejpam-3229	309	20	congruence	congruence	NOUN
ejpam-3229	309	21	on	on	ADP
ejpam-3229	309	22	m.	m.	NOUN
ejpam-3229	309	23	let	let	VERB
ejpam-3229	309	24	π	π	NOUN
ejpam-3229	309	25	:	:	PUNCT
ejpam-3229	309	26	m→m	m→m	PROPN
ejpam-3229	309	27	/	/	SYM
ejpam-3229	309	28	ρ	ρ	PROPN
ejpam-3229	309	29	'	'	PART
ejpam-3229	309	30	γ	γ	X
ejpam-3229	309	31	(	(	PUNCT
ejpam-3229	309	32	m	m	PROPN
ejpam-3229	309	33	)	)	PUNCT
ejpam-3229	309	34	for	for	ADP
ejpam-3229	309	35	some	some	DET
ejpam-3229	309	36	endomorphism	endomorphism	PROPN
ejpam-3229	309	37	γ	γ	X
ejpam-3229	309	38	on	on	ADP
ejpam-3229	309	39	m.	m.	NOUN
ejpam-3229	309	40	we	we	PRON
ejpam-3229	309	41	can	can	AUX
ejpam-3229	309	42	take	take	VERB
ejpam-3229	309	43	another	another	DET
ejpam-3229	309	44	view	view	NOUN
ejpam-3229	309	45	of	of	ADP
ejpam-3229	309	46	φ	φ	NUM
ejpam-3229	309	47	,	,	PUNCT
ejpam-3229	309	48	notice	notice	VERB
ejpam-3229	309	49	that	that	SCONJ
ejpam-3229	309	50	α(m0	α(m0	NOUN
ejpam-3229	309	51	)	)	PUNCT
ejpam-3229	310	1	'	'	PUNCT
ejpam-3229	310	2	m0/	m0/	NOUN
ejpam-3229	310	3	kerα	kerα	VERB
ejpam-3229	310	4	⊂m	⊂m	PROPN
ejpam-3229	310	5	/	/	SYM
ejpam-3229	310	6	ρ	ρ	PROPN
ejpam-3229	310	7	'	'	PART
ejpam-3229	310	8	γ	γ	X
ejpam-3229	310	9	(	(	PUNCT
ejpam-3229	310	10	m	m	NOUN
ejpam-3229	310	11	)	)	PUNCT
ejpam-3229	310	12	thus	thus	ADV
ejpam-3229	310	13	we	we	PRON
ejpam-3229	310	14	can	can	AUX
ejpam-3229	310	15	treat	treat	VERB
ejpam-3229	310	16	φ	φ	PROPN
ejpam-3229	310	17	as	as	ADP
ejpam-3229	310	18	an	an	DET
ejpam-3229	310	19	s	s	NOUN
ejpam-3229	310	20	-	-	PUNCT
ejpam-3229	310	21	homomorphism	homomorphism	NOUN
ejpam-3229	310	22	φ	φ	NOUN
ejpam-3229	310	23	:	:	PUNCT
ejpam-3229	310	24	n	n	X
ejpam-3229	310	25	→	→	SYM
ejpam-3229	310	26	γ	γ	X
ejpam-3229	310	27	(	(	PUNCT
ejpam-3229	310	28	m	m	PROPN
ejpam-3229	310	29	)	)	PUNCT
ejpam-3229	310	30	,	,	PUNCT
ejpam-3229	310	31	also	also	ADV
ejpam-3229	310	32	surely	surely	ADV
ejpam-3229	310	33	π	π	X
ejpam-3229	310	34	extends	extend	VERB
ejpam-3229	310	35	π0	π0	NOUN
ejpam-3229	310	36	.	.	PUNCT
ejpam-3229	311	1	since	since	SCONJ
ejpam-3229	311	2	n	n	NUM
ejpam-3229	311	3	is	be	AUX
ejpam-3229	311	4	m	m	NOUN
ejpam-3229	311	5	-	-	ADJ
ejpam-3229	311	6	principally	principally	ADV
ejpam-3229	311	7	projective	projective	ADJ
ejpam-3229	311	8	so	so	SCONJ
ejpam-3229	311	9	there	there	PRON
ejpam-3229	311	10	exists	exist	VERB
ejpam-3229	311	11	β	β	X
ejpam-3229	311	12	:	:	PUNCT
ejpam-3229	311	13	n	n	CCONJ
ejpam-3229	311	14	→m	→m	PROPN
ejpam-3229	311	15	such	such	ADJ
ejpam-3229	311	16	that	that	SCONJ
ejpam-3229	311	17	πβ	πβ	PROPN
ejpam-3229	311	18	=	=	ADJ
ejpam-3229	311	19	φ	φ	PROPN
ejpam-3229	311	20	.	.	PUNCT
ejpam-3229	312	1	but	but	CCONJ
ejpam-3229	312	2	π(β(n	π(β(n	NOUN
ejpam-3229	312	3	)	)	PUNCT
ejpam-3229	312	4	)	)	PUNCT
ejpam-3229	313	1	=	=	SYM
ejpam-3229	313	2	πβ(n	πβ(n	X
ejpam-3229	313	3	)	)	PUNCT
ejpam-3229	314	1	=	=	SYM
ejpam-3229	314	2	φ(n	φ(n	PROPN
ejpam-3229	314	3	)	)	PUNCT
ejpam-3229	314	4	⊂	⊂	PROPN
ejpam-3229	314	5	α(m0	α(m0	PROPN
ejpam-3229	314	6	)	)	PUNCT
ejpam-3229	314	7	'	'	PUNCT
ejpam-3229	314	8	m0/	m0/	NUM
ejpam-3229	314	9	kerα	kerα	ADJ
ejpam-3229	314	10	,	,	PUNCT
ejpam-3229	314	11	which	which	PRON
ejpam-3229	314	12	clearly	clearly	ADV
ejpam-3229	314	13	shows	show	VERB
ejpam-3229	314	14	that	that	PRON
ejpam-3229	314	15	β(n	β(n	PUNCT
ejpam-3229	314	16	)	)	PUNCT
ejpam-3229	315	1	⊂	⊂	PROPN
ejpam-3229	315	2	m0	m0	PROPN
ejpam-3229	315	3	.	.	PUNCT
ejpam-3229	316	1	thus	thus	ADV
ejpam-3229	316	2	we	we	PRON
ejpam-3229	316	3	can	can	AUX
ejpam-3229	316	4	treat	treat	VERB
ejpam-3229	316	5	β	β	PRON
ejpam-3229	316	6	from	from	ADP
ejpam-3229	316	7	n	n	PROPN
ejpam-3229	316	8	to	to	ADP
ejpam-3229	316	9	m0	m0	PROPN
ejpam-3229	316	10	.	.	PUNCT
ejpam-3229	317	1	since	since	SCONJ
ejpam-3229	317	2	π	π	PROPN
ejpam-3229	317	3	and	and	CCONJ
ejpam-3229	317	4	π0	π0	NOUN
ejpam-3229	317	5	agrees	agree	VERB
ejpam-3229	317	6	at	at	ADP
ejpam-3229	317	7	m0	m0	PROPN
ejpam-3229	317	8	,	,	PUNCT
ejpam-3229	317	9	so	so	ADV
ejpam-3229	317	10	π0β(n	π0β(n	NOUN
ejpam-3229	317	11	)	)	PUNCT
ejpam-3229	317	12	=	=	PUNCT
ejpam-3229	318	1	π0(β(n	π0(β(n	NOUN
ejpam-3229	318	2	)	)	PUNCT
ejpam-3229	318	3	)	)	PUNCT
ejpam-3229	319	1	=	=	SYM
ejpam-3229	319	2	π(β(n	π(β(n	NOUN
ejpam-3229	319	3	)	)	PUNCT
ejpam-3229	319	4	)	)	PUNCT
ejpam-3229	320	1	=	=	PUNCT
ejpam-3229	320	2	πβ(n	πβ(n	X
ejpam-3229	320	3	)	)	PUNCT
ejpam-3229	320	4	=	=	SYM
ejpam-3229	320	5	φ(n	φ(n	NOUN
ejpam-3229	320	6	)	)	PUNCT
ejpam-3229	320	7	for	for	ADP
ejpam-3229	320	8	all	all	PRON
ejpam-3229	320	9	n	n	PRON
ejpam-3229	320	10	∈	∈	PROPN
ejpam-3229	320	11	n	n	NOUN
ejpam-3229	320	12	,	,	PUNCT
ejpam-3229	320	13	which	which	PRON
ejpam-3229	320	14	implies	imply	VERB
ejpam-3229	320	15	that	that	SCONJ
ejpam-3229	321	1	π0β	π0β	PROPN
ejpam-3229	321	2	=	=	PUNCT
ejpam-3229	321	3	φ	φ	PROPN
ejpam-3229	321	4	.	.	PUNCT
ejpam-3229	322	1	hence	hence	ADV
ejpam-3229	322	2	n	n	PROPN
ejpam-3229	322	3	is	be	AUX
ejpam-3229	322	4	m0	m0	NOUN
ejpam-3229	322	5	-	-	PUNCT
ejpam-3229	322	6	principally	principally	ADV
ejpam-3229	322	7	projective	projective	ADJ
ejpam-3229	322	8	.	.	PUNCT
ejpam-3229	323	1	theorem	theorem	NOUN
ejpam-3229	323	2	12	12	NUM
ejpam-3229	323	3	.	.	PUNCT
ejpam-3229	324	1	let	let	VERB
ejpam-3229	324	2	m	m	PRON
ejpam-3229	324	3	be	be	AUX
ejpam-3229	324	4	a	a	DET
ejpam-3229	324	5	projective	projective	ADJ
ejpam-3229	324	6	s	s	NOUN
ejpam-3229	324	7	-	-	NOUN
ejpam-3229	324	8	act	act	NOUN
ejpam-3229	324	9	and	and	CCONJ
ejpam-3229	324	10	e	e	NOUN
ejpam-3229	324	11	=	=	SYM
ejpam-3229	324	12	e	e	X
ejpam-3229	324	13	(	(	PUNCT
ejpam-3229	324	14	m	m	NOUN
ejpam-3229	324	15	)	)	PUNCT
ejpam-3229	324	16	be	be	AUX
ejpam-3229	324	17	an	an	DET
ejpam-3229	324	18	injective	injective	ADJ
ejpam-3229	324	19	hull	hull	NOUN
ejpam-3229	324	20	of	of	ADP
ejpam-3229	324	21	m.	m.	NOUN
ejpam-3229	324	22	if	if	SCONJ
ejpam-3229	324	23	e	e	NOUN
ejpam-3229	324	24	is	be	AUX
ejpam-3229	324	25	completely	completely	ADV
ejpam-3229	324	26	m	m	ADJ
ejpam-3229	324	27	-	-	ADJ
ejpam-3229	324	28	principally	principally	ADV
ejpam-3229	324	29	injective	injective	ADJ
ejpam-3229	324	30	i.e.	i.e.	X
ejpam-3229	324	31	each	each	DET
ejpam-3229	324	32	factor	factor	NOUN
ejpam-3229	324	33	s	s	PART
ejpam-3229	324	34	-	-	NOUN
ejpam-3229	324	35	act	act	NOUN
ejpam-3229	324	36	of	of	ADP
ejpam-3229	324	37	e	e	PROPN
ejpam-3229	324	38	is	be	AUX
ejpam-3229	324	39	m	m	NOUN
ejpam-3229	324	40	-	-	ADJ
ejpam-3229	324	41	principally	principally	ADV
ejpam-3229	324	42	injective	injective	ADJ
ejpam-3229	324	43	,	,	PUNCT
ejpam-3229	324	44	then	then	ADV
ejpam-3229	324	45	each	each	DET
ejpam-3229	324	46	m	m	NOUN
ejpam-3229	324	47	-	-	PUNCT
ejpam-3229	324	48	cyclic	cyclic	ADJ
ejpam-3229	324	49	sub	sub	NOUN
ejpam-3229	324	50	-	-	NOUN
ejpam-3229	324	51	act	act	NOUN
ejpam-3229	324	52	of	of	ADP
ejpam-3229	324	53	m	m	PROPN
ejpam-3229	324	54	is	be	AUX
ejpam-3229	324	55	m	m	ADJ
ejpam-3229	324	56	-	-	PUNCT
ejpam-3229	324	57	principally	principally	ADV
ejpam-3229	324	58	projective	projective	ADJ
ejpam-3229	324	59	.	.	PUNCT
ejpam-3229	325	1	proof	proof	NOUN
ejpam-3229	325	2	.	.	PUNCT
ejpam-3229	326	1	let	let	VERB
ejpam-3229	326	2	α	α	PRON
ejpam-3229	326	3	(	(	PUNCT
ejpam-3229	326	4	m	m	NOUN
ejpam-3229	326	5	)	)	PUNCT
ejpam-3229	326	6	be	be	AUX
ejpam-3229	326	7	an	an	DET
ejpam-3229	326	8	m	m	NOUN
ejpam-3229	326	9	-	-	PUNCT
ejpam-3229	326	10	cyclic	cyclic	ADJ
ejpam-3229	326	11	sub	sub	NOUN
ejpam-3229	326	12	-	-	NOUN
ejpam-3229	326	13	act	act	NOUN
ejpam-3229	326	14	of	of	ADP
ejpam-3229	326	15	m	m	PROPN
ejpam-3229	326	16	,	,	PUNCT
ejpam-3229	326	17	α	α	PROPN
ejpam-3229	326	18	∈	∈	PROPN
ejpam-3229	326	19	ends	end	VERB
ejpam-3229	326	20	(	(	PUNCT
ejpam-3229	326	21	m	m	NOUN
ejpam-3229	326	22	)	)	PUNCT
ejpam-3229	326	23	and	and	CCONJ
ejpam-3229	326	24	i	i	PRON
ejpam-3229	326	25	:	:	PUNCT
ejpam-3229	326	26	α	α	PROPN
ejpam-3229	326	27	(	(	PUNCT
ejpam-3229	326	28	m	m	NOUN
ejpam-3229	326	29	)	)	PUNCT
ejpam-3229	326	30	→m	→m	PUNCT
ejpam-3229	326	31	be	be	AUX
ejpam-3229	326	32	an	an	DET
ejpam-3229	326	33	inclusion	inclusion	NOUN
ejpam-3229	326	34	map	map	NOUN
ejpam-3229	326	35	.	.	PUNCT
ejpam-3229	327	1	consider	consider	VERB
ejpam-3229	327	2	π	π	NOUN
ejpam-3229	327	3	:	:	PUNCT
ejpam-3229	327	4	e→	e→	PROPN
ejpam-3229	327	5	e	e	PROPN
ejpam-3229	327	6	/	/	SYM
ejpam-3229	327	7	ρ	ρ	PROPN
ejpam-3229	327	8	,	,	PUNCT
ejpam-3229	327	9	where	where	SCONJ
ejpam-3229	327	10	ρ	ρ	PROPN
ejpam-3229	327	11	is	be	AUX
ejpam-3229	327	12	congruence	congruence	NOUN
ejpam-3229	327	13	on	on	ADP
ejpam-3229	327	14	e.	e.	PROPN
ejpam-3229	327	15	let	let	VERB
ejpam-3229	327	16	γ	γ	X
ejpam-3229	327	17	:	:	PUNCT
ejpam-3229	327	18	α	α	PROPN
ejpam-3229	327	19	(	(	PUNCT
ejpam-3229	327	20	m)→	m)→	VERB
ejpam-3229	327	21	β(e	β(e	DET
ejpam-3229	327	22	)	)	PUNCT
ejpam-3229	327	23	,	,	PUNCT
ejpam-3229	327	24	where	where	SCONJ
ejpam-3229	327	25	β	β	PROPN
ejpam-3229	327	26	is	be	AUX
ejpam-3229	327	27	an	an	DET
ejpam-3229	327	28	endomorphism	endomorphism	NOUN
ejpam-3229	327	29	on	on	ADP
ejpam-3229	327	30	e.	e.	PROPN
ejpam-3229	327	31	clearly	clearly	ADV
ejpam-3229	327	32	β(e	β(e	PROPN
ejpam-3229	327	33	)	)	PUNCT
ejpam-3229	327	34	'	'	PUNCT
ejpam-3229	327	35	e/	e/	ADV
ejpam-3229	327	36	kerβ	kerβ	PROPN
ejpam-3229	327	37	.	.	PUNCT
ejpam-3229	328	1	since	since	SCONJ
ejpam-3229	328	2	e	e	PROPN
ejpam-3229	328	3	is	be	AUX
ejpam-3229	328	4	completely	completely	ADV
ejpam-3229	328	5	m	m	ADJ
ejpam-3229	328	6	-	-	ADJ
ejpam-3229	328	7	principally	principally	ADV
ejpam-3229	328	8	injective	injective	ADJ
ejpam-3229	328	9	which	which	PRON
ejpam-3229	328	10	implies	imply	VERB
ejpam-3229	328	11	e/	e/	ADV
ejpam-3229	328	12	kerβ	kerβ	PROPN
ejpam-3229	328	13	ism	ism	NOUN
ejpam-3229	328	14	-	-	PUNCT
ejpam-3229	328	15	principally	principally	ADV
ejpam-3229	328	16	injective	injective	ADJ
ejpam-3229	328	17	.	.	PUNCT
ejpam-3229	329	1	therefore	therefore	ADV
ejpam-3229	329	2	,	,	PUNCT
ejpam-3229	329	3	there	there	PRON
ejpam-3229	329	4	exists	exist	VERB
ejpam-3229	329	5	φ	φ	NOUN
ejpam-3229	329	6	:	:	PUNCT
ejpam-3229	329	7	m→	m→	NOUN
ejpam-3229	329	8	e/	e/	PROPN
ejpam-3229	329	9	kerβ	kerβ	PROPN
ejpam-3229	329	10	'	'	PUNCT
ejpam-3229	329	11	β(e	β(e	PROPN
ejpam-3229	329	12	)	)	PUNCT
ejpam-3229	329	13	,	,	PUNCT
ejpam-3229	329	14	such	such	ADJ
ejpam-3229	329	15	that	that	DET
ejpam-3229	329	16	φi	φi	ADP
ejpam-3229	329	17	=	=	SYM
ejpam-3229	329	18	γ	γ	X
ejpam-3229	329	19	.	.	PROPN
ejpam-3229	329	20	since	since	SCONJ
ejpam-3229	329	21	m	m	PROPN
ejpam-3229	329	22	is	be	AUX
ejpam-3229	329	23	projective	projective	ADJ
ejpam-3229	329	24	so	so	SCONJ
ejpam-3229	329	25	there	there	PRON
ejpam-3229	329	26	exists	exist	VERB
ejpam-3229	329	27	ψ	ψ	X
ejpam-3229	329	28	:	:	PUNCT
ejpam-3229	329	29	m	m	VERB
ejpam-3229	329	30	→	→	SYM
ejpam-3229	329	31	e	e	X
ejpam-3229	330	1	such	such	ADJ
ejpam-3229	330	2	that	that	PRON
ejpam-3229	330	3	βψ	βψ	X
ejpam-3229	330	4	=	=	SYM
ejpam-3229	330	5	φ	φ	PROPN
ejpam-3229	330	6	.	.	PUNCT
ejpam-3229	331	1	let	let	VERB
ejpam-3229	331	2	θ	θ	NOUN
ejpam-3229	331	3	:	:	PUNCT
ejpam-3229	331	4	=	=	SYM
ejpam-3229	331	5	ψi	ψi	ADP
ejpam-3229	331	6	:	:	PUNCT
ejpam-3229	331	7	α	α	PROPN
ejpam-3229	331	8	(	(	PUNCT
ejpam-3229	331	9	m	m	NOUN
ejpam-3229	331	10	)	)	PUNCT
ejpam-3229	331	11	→	→	PUNCT
ejpam-3229	331	12	e	e	X
ejpam-3229	331	13	so	so	ADV
ejpam-3229	331	14	βθ	βθ	VERB
ejpam-3229	331	15	=	=	SYM
ejpam-3229	331	16	βψi	βψi	NOUN
ejpam-3229	332	1	=	=	PUNCT
ejpam-3229	332	2	φi	φi	PROPN
ejpam-3229	332	3	=	=	SYM
ejpam-3229	332	4	γ	γ	X
ejpam-3229	332	5	.	.	PUNCT
ejpam-3229	332	6	thus	thus	ADV
ejpam-3229	332	7	α	α	PROPN
ejpam-3229	332	8	(	(	PUNCT
ejpam-3229	332	9	m	m	NOUN
ejpam-3229	332	10	)	)	PUNCT
ejpam-3229	332	11	is	be	AUX
ejpam-3229	332	12	e	e	VERB
ejpam-3229	332	13	-	-	ADJ
ejpam-3229	332	14	principally	principally	ADV
ejpam-3229	332	15	projective	projective	ADJ
ejpam-3229	332	16	.	.	PUNCT
ejpam-3229	333	1	now	now	ADV
ejpam-3229	333	2	since	since	SCONJ
ejpam-3229	333	3	m	m	PROPN
ejpam-3229	333	4	can	can	AUX
ejpam-3229	333	5	be	be	AUX
ejpam-3229	333	6	embedded	embed	VERB
ejpam-3229	333	7	in	in	ADP
ejpam-3229	333	8	e	e	X
ejpam-3229	333	9	so	so	ADV
ejpam-3229	333	10	we	we	PRON
ejpam-3229	333	11	can	can	AUX
ejpam-3229	333	12	treat	treat	VERB
ejpam-3229	333	13	m	m	PRON
ejpam-3229	333	14	as	as	ADP
ejpam-3229	333	15	the	the	DET
ejpam-3229	333	16	sub	sub	NOUN
ejpam-3229	333	17	-	-	NOUN
ejpam-3229	333	18	act	act	NOUN
ejpam-3229	333	19	of	of	ADP
ejpam-3229	333	20	e	e	PROPN
ejpam-3229	333	21	and	and	CCONJ
ejpam-3229	333	22	so	so	ADV
ejpam-3229	333	23	by	by	ADP
ejpam-3229	333	24	theorem	theorem	NOUN
ejpam-3229	333	25	11	11	NUM
ejpam-3229	333	26	,	,	PUNCT
ejpam-3229	333	27	it	it	PRON
ejpam-3229	333	28	follows	follow	VERB
ejpam-3229	333	29	that	that	SCONJ
ejpam-3229	333	30	α	α	PROPN
ejpam-3229	333	31	(	(	PUNCT
ejpam-3229	333	32	m	m	NOUN
ejpam-3229	333	33	)	)	PUNCT
ejpam-3229	333	34	is	be	AUX
ejpam-3229	333	35	m	m	NOUN
ejpam-3229	333	36	-	-	PUNCT
ejpam-3229	333	37	principally	principally	ADV
ejpam-3229	333	38	projective	projective	ADJ
ejpam-3229	333	39	.	.	PUNCT
ejpam-3229	334	1	j.	j.	PROPN
ejpam-3229	334	2	hussain	hussain	PROPN
ejpam-3229	334	3	,	,	PUNCT
ejpam-3229	334	4	m.shabir	m.shabir	PROPN
ejpam-3229	334	5	/	/	SYM
ejpam-3229	334	6	eur	eur	PROPN
ejpam-3229	334	7	.	.	PUNCT
ejpam-3229	335	1	j.	j.	PROPN
ejpam-3229	335	2	pure	pure	PROPN
ejpam-3229	335	3	appl	appl	PROPN
ejpam-3229	335	4	.	.	PROPN
ejpam-3229	335	5	math	math	PROPN
ejpam-3229	335	6	,	,	PUNCT
ejpam-3229	335	7	11	11	NUM
ejpam-3229	335	8	(	(	PUNCT
ejpam-3229	335	9	2	2	NUM
ejpam-3229	335	10	)	)	PUNCT
ejpam-3229	335	11	(	(	PUNCT
ejpam-3229	335	12	2018	2018	NUM
ejpam-3229	335	13	)	)	PUNCT
ejpam-3229	335	14	,	,	PUNCT
ejpam-3229	335	15	431	431	NUM
ejpam-3229	335	16	-	-	SYM
ejpam-3229	335	17	443	443	NUM
ejpam-3229	335	18	440	440	NUM
ejpam-3229	335	19	theorem	theorem	NOUN
ejpam-3229	335	20	13	13	NUM
ejpam-3229	335	21	.	.	PUNCT
ejpam-3229	336	1	a	a	X
ejpam-3229	336	2	)	)	PUNCT
ejpam-3229	336	3	let	let	VERB
ejpam-3229	336	4	m	m	PRON
ejpam-3229	336	5	be	be	AUX
ejpam-3229	336	6	a	a	DET
ejpam-3229	336	7	right	right	ADJ
ejpam-3229	336	8	s	s	NOUN
ejpam-3229	336	9	-	-	NOUN
ejpam-3229	336	10	act	act	NOUN
ejpam-3229	336	11	,	,	PUNCT
ejpam-3229	336	12	if	if	SCONJ
ejpam-3229	336	13	every	every	DET
ejpam-3229	336	14	m	m	NOUN
ejpam-3229	336	15	-	-	PUNCT
ejpam-3229	336	16	cyclic	cyclic	ADJ
ejpam-3229	336	17	sub	sub	NOUN
ejpam-3229	336	18	-	-	NOUN
ejpam-3229	336	19	act	act	ADJ
ejpam-3229	336	20	α	α	PROPN
ejpam-3229	336	21	(	(	PUNCT
ejpam-3229	336	22	m	m	NOUN
ejpam-3229	336	23	)	)	PUNCT
ejpam-3229	336	24	(	(	PUNCT
ejpam-3229	336	25	where	where	SCONJ
ejpam-3229	336	26	α	α	PROPN
ejpam-3229	336	27	∈	∈	PROPN
ejpam-3229	336	28	ends	end	VERB
ejpam-3229	336	29	(	(	PUNCT
ejpam-3229	336	30	m	m	NOUN
ejpam-3229	336	31	)	)	PUNCT
ejpam-3229	336	32	)	)	PUNCT
ejpam-3229	336	33	of	of	ADP
ejpam-3229	336	34	m	m	PROPN
ejpam-3229	336	35	is	be	AUX
ejpam-3229	336	36	a	a	DET
ejpam-3229	336	37	-	-	PUNCT
ejpam-3229	336	38	principally	principally	ADV
ejpam-3229	336	39	projective	projective	ADJ
ejpam-3229	336	40	and	and	CCONJ
ejpam-3229	336	41	a	a	DET
ejpam-3229	336	42	is	be	AUX
ejpam-3229	336	43	m	m	NOUN
ejpam-3229	336	44	-	-	ADJ
ejpam-3229	336	45	principally	principally	ADV
ejpam-3229	336	46	injective	injective	ADJ
ejpam-3229	336	47	then	then	ADV
ejpam-3229	336	48	every	every	DET
ejpam-3229	336	49	a	a	DET
ejpam-3229	336	50	-	-	PUNCT
ejpam-3229	336	51	cyclic	cyclic	ADJ
ejpam-3229	336	52	sub	sub	ADJ
ejpam-3229	336	53	-	-	ADJ
ejpam-3229	336	54	act	act	ADJ
ejpam-3229	336	55	β(a	β(a	PROPN
ejpam-3229	336	56	)	)	PUNCT
ejpam-3229	336	57	(	(	PUNCT
ejpam-3229	336	58	where	where	SCONJ
ejpam-3229	336	59	β	β	X
ejpam-3229	336	60	∈	∈	PROPN
ejpam-3229	336	61	ends(a	ends(a	PROPN
ejpam-3229	336	62	)	)	PUNCT
ejpam-3229	336	63	)	)	PUNCT
ejpam-3229	336	64	of	of	ADP
ejpam-3229	336	65	a	a	DET
ejpam-3229	336	66	is	be	AUX
ejpam-3229	336	67	m	m	NOUN
ejpam-3229	336	68	-	-	ADJ
ejpam-3229	336	69	principally	principally	ADV
ejpam-3229	336	70	injective	injective	ADJ
ejpam-3229	336	71	.	.	PUNCT
ejpam-3229	337	1	b	b	X
ejpam-3229	337	2	)	)	PUNCT
ejpam-3229	337	3	let	let	VERB
ejpam-3229	337	4	i	i	PRON
ejpam-3229	337	5	:	:	PUNCT
ejpam-3229	337	6	β(a	β(a	PROPN
ejpam-3229	337	7	)	)	PUNCT
ejpam-3229	337	8	→	→	SYM
ejpam-3229	337	9	a	a	DET
ejpam-3229	337	10	(	(	PUNCT
ejpam-3229	337	11	where	where	SCONJ
ejpam-3229	337	12	β	β	X
ejpam-3229	337	13	∈	∈	PROPN
ejpam-3229	337	14	ends(a	ends(a	PROPN
ejpam-3229	337	15	)	)	PUNCT
ejpam-3229	337	16	)	)	PUNCT
ejpam-3229	337	17	be	be	AUX
ejpam-3229	337	18	an	an	DET
ejpam-3229	337	19	inclusion	inclusion	NOUN
ejpam-3229	337	20	map	map	NOUN
ejpam-3229	337	21	and	and	CCONJ
ejpam-3229	337	22	m	m	AUX
ejpam-3229	337	23	be	be	AUX
ejpam-3229	337	24	an	an	DET
ejpam-3229	337	25	s	s	NOUN
ejpam-3229	337	26	-	-	NOUN
ejpam-3229	337	27	act	act	NOUN
ejpam-3229	337	28	.	.	PUNCT
ejpam-3229	338	1	if	if	SCONJ
ejpam-3229	338	2	every	every	DET
ejpam-3229	338	3	m	m	NOUN
ejpam-3229	338	4	-	-	PUNCT
ejpam-3229	338	5	cyclic	cyclic	ADJ
ejpam-3229	338	6	sub	sub	NOUN
ejpam-3229	338	7	-	-	NOUN
ejpam-3229	338	8	act	act	NOUN
ejpam-3229	338	9	of	of	ADP
ejpam-3229	338	10	m	m	PROPN
ejpam-3229	338	11	is	be	AUX
ejpam-3229	338	12	a	a	PRON
ejpam-3229	338	13	-	-	PUNCT
ejpam-3229	338	14	principally	principally	ADV
ejpam-3229	338	15	injective	injective	ADJ
ejpam-3229	338	16	and	and	CCONJ
ejpam-3229	338	17	a	a	PRON
ejpam-3229	338	18	is	be	AUX
ejpam-3229	338	19	m	m	NOUN
ejpam-3229	338	20	-	-	ADJ
ejpam-3229	338	21	principally	principally	ADV
ejpam-3229	338	22	projective	projective	ADJ
ejpam-3229	338	23	then	then	ADV
ejpam-3229	338	24	β(a	β(a	PROPN
ejpam-3229	338	25	)	)	PUNCT
ejpam-3229	338	26	is	be	AUX
ejpam-3229	338	27	m	m	NOUN
ejpam-3229	338	28	-	-	PUNCT
ejpam-3229	338	29	principally	principally	ADV
ejpam-3229	338	30	projective	projective	ADJ
ejpam-3229	338	31	.	.	PUNCT
ejpam-3229	339	1	proof	proof	NOUN
ejpam-3229	339	2	.	.	PUNCT
ejpam-3229	340	1	a	a	PRON
ejpam-3229	340	2	)	)	PUNCT
ejpam-3229	340	3	let	let	VERB
ejpam-3229	340	4	i	i	PRON
ejpam-3229	340	5	:	:	PUNCT
ejpam-3229	340	6	α	α	PROPN
ejpam-3229	340	7	(	(	PUNCT
ejpam-3229	340	8	m	m	NOUN
ejpam-3229	340	9	)	)	PUNCT
ejpam-3229	340	10	→	→	PUNCT
ejpam-3229	340	11	m	m	AUX
ejpam-3229	340	12	be	be	VERB
ejpam-3229	340	13	an	an	DET
ejpam-3229	340	14	inclusion	inclusion	NOUN
ejpam-3229	340	15	map	map	NOUN
ejpam-3229	340	16	and	and	CCONJ
ejpam-3229	340	17	let	let	VERB
ejpam-3229	340	18	γ	γ	X
ejpam-3229	340	19	:	:	PUNCT
ejpam-3229	340	20	α	α	PROPN
ejpam-3229	340	21	(	(	PUNCT
ejpam-3229	340	22	m	m	NOUN
ejpam-3229	340	23	)	)	PUNCT
ejpam-3229	340	24	→	→	SYM
ejpam-3229	340	25	β(a	β(a	PROPN
ejpam-3229	340	26	)	)	PUNCT
ejpam-3229	340	27	be	be	VERB
ejpam-3229	340	28	an	an	DET
ejpam-3229	340	29	s	s	NOUN
ejpam-3229	340	30	-	-	NOUN
ejpam-3229	340	31	homomorphism	homomorphism	NOUN
ejpam-3229	340	32	,	,	PUNCT
ejpam-3229	340	33	where	where	SCONJ
ejpam-3229	340	34	β	β	X
ejpam-3229	340	35	∈	∈	PROPN
ejpam-3229	340	36	ends(a	ends(a	PROPN
ejpam-3229	340	37	)	)	PUNCT
ejpam-3229	340	38	.	.	PUNCT
ejpam-3229	341	1	since	since	SCONJ
ejpam-3229	341	2	α	α	PROPN
ejpam-3229	341	3	(	(	PUNCT
ejpam-3229	341	4	m	m	NOUN
ejpam-3229	341	5	)	)	PUNCT
ejpam-3229	341	6	is	be	AUX
ejpam-3229	341	7	a	a	PRON
ejpam-3229	341	8	-	-	PUNCT
ejpam-3229	341	9	principally	principally	ADV
ejpam-3229	341	10	projective	projective	ADJ
ejpam-3229	341	11	so	so	SCONJ
ejpam-3229	341	12	there	there	PRON
ejpam-3229	341	13	exists	exist	VERB
ejpam-3229	341	14	h	h	NOUN
ejpam-3229	341	15	:	:	PUNCT
ejpam-3229	341	16	α	α	X
ejpam-3229	341	17	(	(	PUNCT
ejpam-3229	341	18	m)→	m)→	VERB
ejpam-3229	341	19	a	a	DET
ejpam-3229	341	20	such	such	ADJ
ejpam-3229	341	21	that	that	PRON
ejpam-3229	341	22	βh	βh	ADP
ejpam-3229	341	23	=	=	SYM
ejpam-3229	341	24	γ	γ	X
ejpam-3229	341	25	.	.	PROPN
ejpam-3229	342	1	since	since	SCONJ
ejpam-3229	342	2	a	a	DET
ejpam-3229	342	3	ism	ism	NOUN
ejpam-3229	342	4	-	-	PUNCT
ejpam-3229	342	5	principally	principally	ADV
ejpam-3229	342	6	injective	injective	ADJ
ejpam-3229	342	7	so	so	SCONJ
ejpam-3229	342	8	there	there	PRON
ejpam-3229	342	9	exists	exist	VERB
ejpam-3229	342	10	λ	λ	X
ejpam-3229	342	11	:	:	PUNCT
ejpam-3229	342	12	m→	m→	NOUN
ejpam-3229	342	13	a	a	DET
ejpam-3229	342	14	such	such	ADJ
ejpam-3229	343	1	that	that	PRON
ejpam-3229	343	2	λi	λi	ADP
ejpam-3229	343	3	=	=	X
ejpam-3229	343	4	h.	h.	PROPN
ejpam-3229	343	5	let	let	VERB
ejpam-3229	343	6	µ	µ	X
ejpam-3229	343	7	=	=	X
ejpam-3229	343	8	βλ	βλ	NOUN
ejpam-3229	343	9	:	:	PUNCT
ejpam-3229	343	10	m→	m→	NOUN
ejpam-3229	343	11	β(a	β(a	PROPN
ejpam-3229	343	12	)	)	PUNCT
ejpam-3229	343	13	,	,	PUNCT
ejpam-3229	343	14	since	since	SCONJ
ejpam-3229	343	15	µi	µi	PROPN
ejpam-3229	343	16	=	=	PUNCT
ejpam-3229	343	17	βλi	βλi	NOUN
ejpam-3229	343	18	=	=	PUNCT
ejpam-3229	343	19	βh	βh	NOUN
ejpam-3229	344	1	=	=	SYM
ejpam-3229	344	2	γ	γ	X
ejpam-3229	344	3	.	.	PROPN
ejpam-3229	344	4	hence	hence	ADV
ejpam-3229	344	5	β(a	β(a	PROPN
ejpam-3229	344	6	)	)	PUNCT
ejpam-3229	344	7	is	be	AUX
ejpam-3229	344	8	m	m	NOUN
ejpam-3229	344	9	-	-	PUNCT
ejpam-3229	344	10	principally	principally	ADV
ejpam-3229	344	11	injective	injective	ADJ
ejpam-3229	344	12	.	.	PUNCT
ejpam-3229	345	1	b	b	X
ejpam-3229	345	2	)	)	PUNCT
ejpam-3229	345	3	to	to	PART
ejpam-3229	345	4	show	show	VERB
ejpam-3229	345	5	that	that	SCONJ
ejpam-3229	345	6	β(a	β(a	PROPN
ejpam-3229	345	7	)	)	PUNCT
ejpam-3229	345	8	is	be	AUX
ejpam-3229	345	9	m	m	NOUN
ejpam-3229	345	10	-	-	PUNCT
ejpam-3229	345	11	principally	principally	ADV
ejpam-3229	345	12	projective	projective	ADJ
ejpam-3229	345	13	,	,	PUNCT
ejpam-3229	345	14	we	we	PRON
ejpam-3229	345	15	let	let	VERB
ejpam-3229	345	16	γ	γ	X
ejpam-3229	345	17	:	:	PUNCT
ejpam-3229	345	18	β(a	β(a	PROPN
ejpam-3229	345	19	)	)	PUNCT
ejpam-3229	345	20	→	→	SYM
ejpam-3229	345	21	α	α	PROPN
ejpam-3229	345	22	(	(	PUNCT
ejpam-3229	345	23	m	m	NOUN
ejpam-3229	345	24	)	)	PUNCT
ejpam-3229	345	25	be	be	AUX
ejpam-3229	345	26	an	an	DET
ejpam-3229	345	27	shomomorphism	shomomorphism	NOUN
ejpam-3229	345	28	,	,	PUNCT
ejpam-3229	345	29	where	where	SCONJ
ejpam-3229	345	30	α	α	PROPN
ejpam-3229	345	31	∈	∈	PROPN
ejpam-3229	345	32	e.	e.	NOUN
ejpam-3229	345	33	keeping	keep	VERB
ejpam-3229	345	34	γ	γ	NOUN
ejpam-3229	345	35	in	in	ADP
ejpam-3229	345	36	view	view	NOUN
ejpam-3229	345	37	,	,	PUNCT
ejpam-3229	345	38	since	since	SCONJ
ejpam-3229	345	39	α	α	PROPN
ejpam-3229	345	40	(	(	PUNCT
ejpam-3229	345	41	m	m	NOUN
ejpam-3229	345	42	)	)	PUNCT
ejpam-3229	345	43	is	be	AUX
ejpam-3229	345	44	a	a	PRON
ejpam-3229	345	45	-	-	PUNCT
ejpam-3229	345	46	principally	principally	ADV
ejpam-3229	345	47	injective	injective	ADJ
ejpam-3229	345	48	so	so	SCONJ
ejpam-3229	345	49	there	there	PRON
ejpam-3229	345	50	exists	exist	VERB
ejpam-3229	345	51	φ	φ	NOUN
ejpam-3229	345	52	:	:	PUNCT
ejpam-3229	346	1	a	a	DET
ejpam-3229	346	2	→	→	SYM
ejpam-3229	346	3	α	α	X
ejpam-3229	346	4	(	(	PUNCT
ejpam-3229	346	5	m	m	NOUN
ejpam-3229	346	6	)	)	PUNCT
ejpam-3229	346	7	such	such	ADJ
ejpam-3229	346	8	that	that	SCONJ
ejpam-3229	346	9	φi	φi	ADP
ejpam-3229	346	10	=	=	SYM
ejpam-3229	346	11	γ	γ	X
ejpam-3229	346	12	.	.	NOUN
ejpam-3229	346	13	since	since	SCONJ
ejpam-3229	346	14	a	a	DET
ejpam-3229	346	15	ism	ism	NOUN
ejpam-3229	346	16	-	-	PUNCT
ejpam-3229	346	17	principally	principally	ADV
ejpam-3229	346	18	projective	projective	ADJ
ejpam-3229	346	19	so	so	SCONJ
ejpam-3229	346	20	there	there	PRON
ejpam-3229	346	21	exists	exist	VERB
ejpam-3229	346	22	θ	θ	NOUN
ejpam-3229	346	23	:	:	PUNCT
ejpam-3229	346	24	a→m	a→m	X
ejpam-3229	346	25	such	such	ADJ
ejpam-3229	346	26	that	that	SCONJ
ejpam-3229	346	27	αθ	αθ	PROPN
ejpam-3229	346	28	=	=	SYM
ejpam-3229	346	29	φ	φ	PROPN
ejpam-3229	346	30	.	.	PUNCT
ejpam-3229	347	1	consider	consider	VERB
ejpam-3229	347	2	θi	θi	NUM
ejpam-3229	347	3	:	:	SYM
ejpam-3229	347	4	β(a)→m	β(a)→m	X
ejpam-3229	347	5	and	and	CCONJ
ejpam-3229	347	6	α(θi	α(θi	PROPN
ejpam-3229	347	7	)	)	PUNCT
ejpam-3229	347	8	=	=	PUNCT
ejpam-3229	347	9	(	(	PUNCT
ejpam-3229	347	10	αθ)i	αθ)i	PROPN
ejpam-3229	347	11	=	=	PUNCT
ejpam-3229	347	12	φi	φi	ADP
ejpam-3229	347	13	=	=	SYM
ejpam-3229	347	14	γ	γ	X
ejpam-3229	347	15	.	.	NOUN
ejpam-3229	347	16	hence	hence	ADV
ejpam-3229	347	17	β(a	β(a	PROPN
ejpam-3229	347	18	)	)	PUNCT
ejpam-3229	347	19	is	be	AUX
ejpam-3229	347	20	m	m	NOUN
ejpam-3229	347	21	-	-	PUNCT
ejpam-3229	347	22	principally	principally	ADV
ejpam-3229	347	23	projective	projective	ADJ
ejpam-3229	347	24	.	.	PUNCT
ejpam-3229	348	1	3.2	3.2	NUM
ejpam-3229	348	2	.	.	PUNCT
ejpam-3229	349	1	a	a	DET
ejpam-3229	349	2	note	note	NOUN
ejpam-3229	349	3	on	on	ADP
ejpam-3229	349	4	co	co	NOUN
ejpam-3229	349	5	-	-	ADJ
ejpam-3229	349	6	hereditary	hereditary	ADJ
ejpam-3229	349	7	s	s	NOUN
ejpam-3229	349	8	-	-	PUNCT
ejpam-3229	349	9	acts	act	NOUN
ejpam-3229	349	10	remark	remark	NOUN
ejpam-3229	349	11	1	1	NUM
ejpam-3229	349	12	.	.	PUNCT
ejpam-3229	349	13	usually	usually	ADV
ejpam-3229	349	14	co	co	ADJ
ejpam-3229	349	15	-	-	ADJ
ejpam-3229	349	16	hereditary	hereditary	ADJ
ejpam-3229	349	17	s	s	NOUN
ejpam-3229	349	18	-	-	PUNCT
ejpam-3229	349	19	acts	act	NOUN
ejpam-3229	349	20	are	be	AUX
ejpam-3229	349	21	defined	define	VERB
ejpam-3229	349	22	as	as	ADP
ejpam-3229	349	23	those	those	DET
ejpam-3229	349	24	s	s	NOUN
ejpam-3229	349	25	-	-	PUNCT
ejpam-3229	349	26	acts	act	VERB
ejpam-3229	349	27	whose	whose	DET
ejpam-3229	349	28	every	every	DET
ejpam-3229	349	29	proper	proper	ADJ
ejpam-3229	349	30	factor	factor	NOUN
ejpam-3229	349	31	s	s	PART
ejpam-3229	349	32	-	-	PUNCT
ejpam-3229	349	33	act	act	NOUN
ejpam-3229	349	34	is	be	AUX
ejpam-3229	349	35	injective	injective	ADJ
ejpam-3229	349	36	.	.	PUNCT
ejpam-3229	350	1	keeping	keep	VERB
ejpam-3229	350	2	in	in	ADP
ejpam-3229	350	3	view	view	NOUN
ejpam-3229	350	4	lemma	lemma	PROPN
ejpam-3229	350	5	1	1	NUM
ejpam-3229	350	6	we	we	PRON
ejpam-3229	350	7	can	can	AUX
ejpam-3229	350	8	redefine	redefine	VERB
ejpam-3229	350	9	the	the	DET
ejpam-3229	350	10	co	co	NOUN
ejpam-3229	350	11	-	-	ADJ
ejpam-3229	350	12	hereditary	hereditary	ADJ
ejpam-3229	350	13	s	s	NOUN
ejpam-3229	350	14	-	-	PUNCT
ejpam-3229	350	15	acts	act	NOUN
ejpam-3229	350	16	as	as	ADP
ejpam-3229	350	17	following	follow	VERB
ejpam-3229	350	18	.	.	PUNCT
ejpam-3229	351	1	definition	definition	NOUN
ejpam-3229	351	2	7	7	NUM
ejpam-3229	351	3	.	.	PUNCT
ejpam-3229	352	1	a	a	DET
ejpam-3229	352	2	right	right	ADJ
ejpam-3229	352	3	s	s	NOUN
ejpam-3229	352	4	-	-	NOUN
ejpam-3229	352	5	act	act	NOUN
ejpam-3229	352	6	m	m	VERB
ejpam-3229	352	7	is	be	AUX
ejpam-3229	352	8	called	call	VERB
ejpam-3229	352	9	co	co	ADJ
ejpam-3229	352	10	-	-	ADJ
ejpam-3229	352	11	hereditary	hereditary	ADJ
ejpam-3229	352	12	s	s	NOUN
ejpam-3229	352	13	-	-	NOUN
ejpam-3229	352	14	act	act	NOUN
ejpam-3229	352	15	,	,	PUNCT
ejpam-3229	352	16	if	if	SCONJ
ejpam-3229	352	17	each	each	DET
ejpam-3229	352	18	m	m	NOUN
ejpam-3229	352	19	-	-	PUNCT
ejpam-3229	352	20	cyclic	cyclic	ADJ
ejpam-3229	352	21	sub	sub	NOUN
ejpam-3229	352	22	-	-	NOUN
ejpam-3229	352	23	act	act	NOUN
ejpam-3229	352	24	is	be	AUX
ejpam-3229	352	25	injective	injective	ADJ
ejpam-3229	352	26	.	.	PUNCT
ejpam-3229	353	1	definition	definition	NOUN
ejpam-3229	353	2	8	8	NUM
ejpam-3229	353	3	.	.	PUNCT
ejpam-3229	354	1	a	a	DET
ejpam-3229	354	2	right	right	ADJ
ejpam-3229	354	3	s	s	NOUN
ejpam-3229	354	4	-	-	NOUN
ejpam-3229	354	5	act	act	NOUN
ejpam-3229	354	6	m	m	VERB
ejpam-3229	354	7	is	be	AUX
ejpam-3229	354	8	npi	npi	PROPN
ejpam-3229	354	9	-	-	ADJ
ejpam-3229	354	10	co	co	NOUN
ejpam-3229	354	11	-	-	NOUN
ejpam-3229	354	12	hereditary	hereditary	ADJ
ejpam-3229	354	13	if	if	SCONJ
ejpam-3229	354	14	every	every	DET
ejpam-3229	354	15	m	m	NOUN
ejpam-3229	354	16	-	-	PUNCT
ejpam-3229	354	17	cyclic	cyclic	ADJ
ejpam-3229	354	18	sub	sub	NOUN
ejpam-3229	354	19	-	-	NOUN
ejpam-3229	354	20	act	act	NOUN
ejpam-3229	354	21	of	of	ADP
ejpam-3229	354	22	m	m	PROPN
ejpam-3229	354	23	is	be	AUX
ejpam-3229	354	24	n	n	PRON
ejpam-3229	354	25	-principally	-principally	ADV
ejpam-3229	354	26	injective	injective	ADJ
ejpam-3229	354	27	.	.	PUNCT
ejpam-3229	355	1	definition	definition	NOUN
ejpam-3229	355	2	9	9	NUM
ejpam-3229	355	3	.	.	PUNCT
ejpam-3229	356	1	a	a	DET
ejpam-3229	356	2	right	right	ADJ
ejpam-3229	356	3	s	s	NOUN
ejpam-3229	356	4	-	-	NOUN
ejpam-3229	356	5	act	act	NOUN
ejpam-3229	356	6	is	be	AUX
ejpam-3229	356	7	quasi	quasi	ADJ
ejpam-3229	356	8	pi	pi	NOUN
ejpam-3229	356	9	-	-	PUNCT
ejpam-3229	356	10	co	co	NOUN
ejpam-3229	356	11	-	-	NOUN
ejpam-3229	356	12	hereditary	hereditary	ADJ
ejpam-3229	356	13	if	if	SCONJ
ejpam-3229	356	14	every	every	DET
ejpam-3229	356	15	m	m	NOUN
ejpam-3229	356	16	-	-	PUNCT
ejpam-3229	356	17	cyclic	cyclic	ADJ
ejpam-3229	356	18	sub	sub	NOUN
ejpam-3229	356	19	-	-	NOUN
ejpam-3229	356	20	act	act	NOUN
ejpam-3229	356	21	of	of	ADP
ejpam-3229	356	22	m	m	PROPN
ejpam-3229	356	23	is	be	AUX
ejpam-3229	356	24	m	m	ADJ
ejpam-3229	356	25	-	-	ADJ
ejpam-3229	356	26	principally	principally	ADV
ejpam-3229	356	27	injective	injective	ADJ
ejpam-3229	356	28	.	.	PUNCT
ejpam-3229	357	1	remark	remark	PROPN
ejpam-3229	357	2	2	2	NUM
ejpam-3229	357	3	.	.	PUNCT
ejpam-3229	357	4	co	co	NOUN
ejpam-3229	357	5	-	-	NOUN
ejpam-3229	357	6	hereditary	hereditary	ADJ
ejpam-3229	357	7	→	→	SYM
ejpam-3229	357	8	npi	npi	PROPN
ejpam-3229	357	9	-	-	PUNCT
ejpam-3229	357	10	co	co	NOUN
ejpam-3229	357	11	-	-	ADJ
ejpam-3229	357	12	hereditary	hereditary	ADJ
ejpam-3229	357	13	→pico	→pico	NOUN
ejpam-3229	357	14	-	-	NOUN
ejpam-3229	357	15	hereditary	hereditary	ADJ
ejpam-3229	357	16	.	.	PUNCT
ejpam-3229	358	1	theorem	theorem	VERB
ejpam-3229	358	2	14	14	NUM
ejpam-3229	358	3	.	.	PUNCT
ejpam-3229	359	1	if	if	SCONJ
ejpam-3229	359	2	an	an	DET
ejpam-3229	359	3	s	s	NOUN
ejpam-3229	359	4	-	-	PUNCT
ejpam-3229	359	5	act	act	NOUN
ejpam-3229	359	6	m	m	NOUN
ejpam-3229	359	7	is	be	AUX
ejpam-3229	359	8	api	api	NOUN
ejpam-3229	359	9	-	-	PUNCT
ejpam-3229	359	10	co	co	NOUN
ejpam-3229	359	11	-	-	NOUN
ejpam-3229	359	12	hereditary	hereditary	ADJ
ejpam-3229	359	13	,	,	PUNCT
ejpam-3229	359	14	then	then	ADV
ejpam-3229	359	15	every	every	DET
ejpam-3229	359	16	a	a	DET
ejpam-3229	359	17	-	-	PUNCT
ejpam-3229	359	18	cyclic	cyclic	ADJ
ejpam-3229	359	19	sub	sub	NOUN
ejpam-3229	359	20	-	-	NOUN
ejpam-3229	359	21	act	act	NOUN
ejpam-3229	359	22	of	of	ADP
ejpam-3229	359	23	an	an	DET
ejpam-3229	359	24	m	m	ADV
ejpam-3229	359	25	-	-	ADJ
ejpam-3229	359	26	principally	principally	ADV
ejpam-3229	359	27	projective	projective	ADJ
ejpam-3229	359	28	s	s	NOUN
ejpam-3229	359	29	-	-	PUNCT
ejpam-3229	359	30	act	act	NOUN
ejpam-3229	359	31	a	a	PRON
ejpam-3229	359	32	is	be	AUX
ejpam-3229	359	33	m	m	NOUN
ejpam-3229	359	34	-	-	PUNCT
ejpam-3229	359	35	principally	principally	ADV
ejpam-3229	359	36	projective	projective	ADJ
ejpam-3229	359	37	.	.	PUNCT
ejpam-3229	360	1	proof	proof	NOUN
ejpam-3229	360	2	.	.	PUNCT
ejpam-3229	361	1	let	let	AUX
ejpam-3229	361	2	α(a	α(a	NOUN
ejpam-3229	361	3	)	)	PUNCT
ejpam-3229	361	4	be	be	AUX
ejpam-3229	361	5	an	an	DET
ejpam-3229	361	6	a	a	PRON
ejpam-3229	361	7	-	-	PUNCT
ejpam-3229	361	8	cyclic	cyclic	ADJ
ejpam-3229	361	9	sub	sub	NOUN
ejpam-3229	361	10	-	-	NOUN
ejpam-3229	361	11	act	act	NOUN
ejpam-3229	361	12	of	of	ADP
ejpam-3229	361	13	a.	a.	NOUN
ejpam-3229	361	14	we	we	PRON
ejpam-3229	361	15	show	show	VERB
ejpam-3229	361	16	it	it	PRON
ejpam-3229	361	17	is	be	AUX
ejpam-3229	361	18	m	m	NOUN
ejpam-3229	361	19	-	-	PUNCT
ejpam-3229	361	20	principally	principally	ADV
ejpam-3229	361	21	projective	projective	ADJ
ejpam-3229	361	22	.	.	PUNCT
ejpam-3229	362	1	by	by	ADP
ejpam-3229	362	2	definition	definition	NOUN
ejpam-3229	362	3	every	every	DET
ejpam-3229	362	4	m	m	NOUN
ejpam-3229	362	5	-	-	PUNCT
ejpam-3229	362	6	cyclic	cyclic	ADJ
ejpam-3229	362	7	sub	sub	NOUN
ejpam-3229	362	8	-	-	NOUN
ejpam-3229	362	9	act	act	NOUN
ejpam-3229	362	10	of	of	ADP
ejpam-3229	362	11	m	m	PROPN
ejpam-3229	362	12	is	be	AUX
ejpam-3229	362	13	a	a	PRON
ejpam-3229	362	14	-	-	PUNCT
ejpam-3229	362	15	principally	principally	ADV
ejpam-3229	362	16	injective	injective	ADJ
ejpam-3229	362	17	.	.	PUNCT
ejpam-3229	363	1	since	since	SCONJ
ejpam-3229	363	2	m	m	PROPN
ejpam-3229	363	3	is	be	AUX
ejpam-3229	363	4	itself	itself	PRON
ejpam-3229	363	5	m	m	ADJ
ejpam-3229	363	6	-	-	ADJ
ejpam-3229	363	7	cyclic	cyclic	ADJ
ejpam-3229	363	8	sub	sub	NOUN
ejpam-3229	363	9	-	-	NOUN
ejpam-3229	363	10	act	act	NOUN
ejpam-3229	363	11	of	of	ADP
ejpam-3229	363	12	m	m	NOUN
ejpam-3229	363	13	so	so	ADV
ejpam-3229	363	14	is	be	AUX
ejpam-3229	363	15	a	a	PRON
ejpam-3229	363	16	-	-	PUNCT
ejpam-3229	363	17	principally	principally	ADV
ejpam-3229	363	18	injective	injective	ADJ
ejpam-3229	363	19	thus	thus	ADV
ejpam-3229	363	20	by	by	ADP
ejpam-3229	363	21	theorem	theorem	NOUN
ejpam-3229	363	22	13	13	NUM
ejpam-3229	363	23	again	again	ADV
ejpam-3229	363	24	,	,	PUNCT
ejpam-3229	363	25	α(a	α(a	NOUN
ejpam-3229	363	26	)	)	PUNCT
ejpam-3229	363	27	is	be	AUX
ejpam-3229	363	28	m	m	NOUN
ejpam-3229	363	29	-	-	PUNCT
ejpam-3229	363	30	principally	principally	ADV
ejpam-3229	363	31	projective	projective	ADJ
ejpam-3229	363	32	.	.	PUNCT
ejpam-3229	364	1	corollary	corollary	ADJ
ejpam-3229	364	2	5	5	NUM
ejpam-3229	364	3	.	.	PUNCT
ejpam-3229	365	1	if	if	SCONJ
ejpam-3229	365	2	an	an	DET
ejpam-3229	365	3	s	s	NOUN
ejpam-3229	365	4	-	-	PUNCT
ejpam-3229	365	5	act	act	NOUN
ejpam-3229	365	6	m	m	NOUN
ejpam-3229	365	7	is	be	AUX
ejpam-3229	365	8	pi	pi	ADJ
ejpam-3229	365	9	-	-	PUNCT
ejpam-3229	365	10	cohereditary	cohereditary	ADJ
ejpam-3229	365	11	and	and	CCONJ
ejpam-3229	365	12	m	m	NOUN
ejpam-3229	365	13	-	-	ADJ
ejpam-3229	365	14	principally	principally	ADV
ejpam-3229	365	15	projective	projective	ADJ
ejpam-3229	365	16	,	,	PUNCT
ejpam-3229	365	17	then	then	ADV
ejpam-3229	365	18	every	every	DET
ejpam-3229	365	19	m	m	NOUN
ejpam-3229	365	20	-	-	PUNCT
ejpam-3229	365	21	cyclic	cyclic	ADJ
ejpam-3229	365	22	sub	sub	NOUN
ejpam-3229	365	23	-	-	NOUN
ejpam-3229	365	24	act	act	NOUN
ejpam-3229	365	25	of	of	ADP
ejpam-3229	365	26	m	m	PROPN
ejpam-3229	365	27	is	be	AUX
ejpam-3229	365	28	m	m	ADJ
ejpam-3229	365	29	-	-	PUNCT
ejpam-3229	365	30	principally	principally	ADV
ejpam-3229	365	31	projective	projective	ADJ
ejpam-3229	365	32	.	.	PUNCT
ejpam-3229	366	1	j.	j.	PROPN
ejpam-3229	366	2	hussain	hussain	PROPN
ejpam-3229	366	3	,	,	PUNCT
ejpam-3229	366	4	m.shabir	m.shabir	PROPN
ejpam-3229	366	5	/	/	SYM
ejpam-3229	366	6	eur	eur	PROPN
ejpam-3229	366	7	.	.	PUNCT
ejpam-3229	367	1	j.	j.	PROPN
ejpam-3229	367	2	pure	pure	PROPN
ejpam-3229	367	3	appl	appl	PROPN
ejpam-3229	367	4	.	.	PROPN
ejpam-3229	367	5	math	math	PROPN
ejpam-3229	367	6	,	,	PUNCT
ejpam-3229	367	7	11	11	NUM
ejpam-3229	367	8	(	(	PUNCT
ejpam-3229	367	9	2	2	NUM
ejpam-3229	367	10	)	)	PUNCT
ejpam-3229	367	11	(	(	PUNCT
ejpam-3229	367	12	2018	2018	NUM
ejpam-3229	367	13	)	)	PUNCT
ejpam-3229	367	14	,	,	PUNCT
ejpam-3229	367	15	431	431	NUM
ejpam-3229	367	16	-	-	SYM
ejpam-3229	367	17	443	443	NUM
ejpam-3229	367	18	441	441	NUM
ejpam-3229	367	19	4	4	NUM
ejpam-3229	367	20	.	.	PUNCT
ejpam-3229	368	1	semi	semi	ADJ
ejpam-3229	368	2	-	-	ADJ
ejpam-3229	368	3	projective	projective	ADJ
ejpam-3229	368	4	s	s	NOUN
ejpam-3229	368	5	-	-	PUNCT
ejpam-3229	368	6	acts	act	NOUN
ejpam-3229	368	7	definition	definition	NOUN
ejpam-3229	368	8	10	10	NUM
ejpam-3229	368	9	.	.	PUNCT
ejpam-3229	369	1	a	a	DET
ejpam-3229	369	2	right	right	NOUN
ejpam-3229	369	3	s	s	NOUN
ejpam-3229	369	4	-	-	ADJ
ejpam-3229	369	5	actm	actm	ADV
ejpam-3229	369	6	is	be	AUX
ejpam-3229	369	7	called	call	VERB
ejpam-3229	369	8	a	a	DET
ejpam-3229	369	9	semi	semi	ADJ
ejpam-3229	369	10	-	-	ADJ
ejpam-3229	369	11	projective	projective	ADJ
ejpam-3229	369	12	s	s	NOUN
ejpam-3229	369	13	-	-	NOUN
ejpam-3229	369	14	act	act	NOUN
ejpam-3229	369	15	if	if	SCONJ
ejpam-3229	369	16	αe	αe	NUM
ejpam-3229	369	17	=	=	SYM
ejpam-3229	369	18	homs(m	homs(m	PROPN
ejpam-3229	369	19	,	,	PUNCT
ejpam-3229	369	20	α	α	PROPN
ejpam-3229	369	21	(	(	PUNCT
ejpam-3229	369	22	m	m	NOUN
ejpam-3229	369	23	)	)	PUNCT
ejpam-3229	369	24	)	)	PUNCT
ejpam-3229	369	25	for	for	ADP
ejpam-3229	369	26	all	all	DET
ejpam-3229	369	27	α	α	PROPN
ejpam-3229	369	28	∈	∈	PROPN
ejpam-3229	369	29	e.	e.	PROPN
ejpam-3229	369	30	theorem	theorem	PROPN
ejpam-3229	369	31	15	15	NUM
ejpam-3229	369	32	.	.	PUNCT
ejpam-3229	370	1	let	let	VERB
ejpam-3229	370	2	m	m	PRON
ejpam-3229	370	3	be	be	AUX
ejpam-3229	370	4	an	an	DET
ejpam-3229	370	5	s	s	NOUN
ejpam-3229	370	6	-	-	NOUN
ejpam-3229	370	7	act	act	NOUN
ejpam-3229	370	8	then	then	ADV
ejpam-3229	370	9	the	the	DET
ejpam-3229	370	10	following	follow	VERB
ejpam-3229	370	11	conditions	condition	NOUN
ejpam-3229	370	12	are	be	AUX
ejpam-3229	370	13	equivalent	equivalent	ADJ
ejpam-3229	370	14	.	.	PUNCT
ejpam-3229	371	1	1	1	X
ejpam-3229	371	2	)	)	PUNCT
ejpam-3229	371	3	m	m	VERB
ejpam-3229	371	4	is	be	AUX
ejpam-3229	371	5	quasi	quasi	ADJ
ejpam-3229	371	6	-	-	ADJ
ejpam-3229	371	7	principally	principally	ADV
ejpam-3229	371	8	projective	projective	ADJ
ejpam-3229	371	9	.	.	PUNCT
ejpam-3229	372	1	2	2	X
ejpam-3229	372	2	)	)	PUNCT
ejpam-3229	372	3	m	m	VERB
ejpam-3229	372	4	is	be	AUX
ejpam-3229	372	5	semi	semi	ADJ
ejpam-3229	372	6	-	-	ADJ
ejpam-3229	372	7	projective	projective	ADJ
ejpam-3229	372	8	.	.	PUNCT
ejpam-3229	373	1	3	3	NUM
ejpam-3229	373	2	)	)	PUNCT
ejpam-3229	373	3	for	for	ADP
ejpam-3229	373	4	α	α	NOUN
ejpam-3229	373	5	,	,	PUNCT
ejpam-3229	373	6	β	β	X
ejpam-3229	373	7	∈	∈	X
ejpam-3229	373	8	e	e	X
ejpam-3229	373	9	if	if	SCONJ
ejpam-3229	373	10	α	α	PROPN
ejpam-3229	373	11	(	(	PUNCT
ejpam-3229	373	12	m	m	NOUN
ejpam-3229	373	13	)	)	PUNCT
ejpam-3229	373	14	⊆	⊆	NUM
ejpam-3229	373	15	β	β	X
ejpam-3229	373	16	(	(	PUNCT
ejpam-3229	373	17	m	m	NOUN
ejpam-3229	373	18	)	)	PUNCT
ejpam-3229	373	19	then	then	ADV
ejpam-3229	373	20	αe	αe	PROPN
ejpam-3229	373	21	⊆	⊆	NUM
ejpam-3229	373	22	βe	βe	PROPN
ejpam-3229	373	23	.	.	PUNCT
ejpam-3229	374	1	proof	proof	NOUN
ejpam-3229	374	2	.	.	PUNCT
ejpam-3229	375	1	1)⇒2	1)⇒2	NUM
ejpam-3229	375	2	)	)	PUNCT
ejpam-3229	375	3	follows	follow	VERB
ejpam-3229	375	4	directly	directly	ADV
ejpam-3229	375	5	from	from	ADP
ejpam-3229	375	6	lemma	lemma	PROPN
ejpam-3229	375	7	4	4	NUM
ejpam-3229	375	8	,	,	PUNCT
ejpam-3229	375	9	for	for	ADP
ejpam-3229	375	10	n	n	PRON
ejpam-3229	375	11	=	=	NOUN
ejpam-3229	375	12	m.	m.	NOUN
ejpam-3229	375	13	2)⇒3	2)⇒3	NUM
ejpam-3229	375	14	)	)	PUNCT
ejpam-3229	375	15	let	let	VERB
ejpam-3229	375	16	α	α	PROPN
ejpam-3229	375	17	(	(	PUNCT
ejpam-3229	375	18	m	m	NOUN
ejpam-3229	375	19	)	)	PUNCT
ejpam-3229	375	20	⊆	⊆	NUM
ejpam-3229	375	21	β	β	X
ejpam-3229	375	22	(	(	PUNCT
ejpam-3229	375	23	m	m	NOUN
ejpam-3229	375	24	)	)	PUNCT
ejpam-3229	375	25	then	then	ADV
ejpam-3229	375	26	for	for	ADP
ejpam-3229	375	27	u	u	PROPN
ejpam-3229	375	28	∈	∈	PROPN
ejpam-3229	375	29	homs(m	homs(m	PROPN
ejpam-3229	375	30	,	,	PUNCT
ejpam-3229	375	31	α	α	PROPN
ejpam-3229	375	32	(	(	PUNCT
ejpam-3229	375	33	m	m	NOUN
ejpam-3229	375	34	)	)	PUNCT
ejpam-3229	375	35	)	)	PUNCT
ejpam-3229	375	36	since	since	SCONJ
ejpam-3229	375	37	α	α	PROPN
ejpam-3229	375	38	(	(	PUNCT
ejpam-3229	375	39	m	m	NOUN
ejpam-3229	375	40	)	)	PUNCT
ejpam-3229	375	41	⊆	⊆	NUM
ejpam-3229	375	42	β	β	X
ejpam-3229	375	43	(	(	PUNCT
ejpam-3229	375	44	m	m	NOUN
ejpam-3229	375	45	)	)	PUNCT
ejpam-3229	375	46	so	so	SCONJ
ejpam-3229	375	47	we	we	PRON
ejpam-3229	375	48	may	may	AUX
ejpam-3229	375	49	also	also	ADV
ejpam-3229	375	50	view	view	VERB
ejpam-3229	375	51	u	u	NOUN
ejpam-3229	375	52	as	as	ADP
ejpam-3229	375	53	an	an	DET
ejpam-3229	375	54	s	s	NOUN
ejpam-3229	375	55	-	-	ADJ
ejpam-3229	375	56	homomorphism	homomorphism	ADJ
ejpam-3229	375	57	u	u	NOUN
ejpam-3229	375	58	:	:	PUNCT
ejpam-3229	375	59	m→	m→	NOUN
ejpam-3229	375	60	β	β	X
ejpam-3229	375	61	(	(	PUNCT
ejpam-3229	375	62	m	m	NOUN
ejpam-3229	375	63	)	)	PUNCT
ejpam-3229	375	64	i.e.	i.e.	X
ejpam-3229	375	65	u	u	X
ejpam-3229	375	66	∈	∈	PROPN
ejpam-3229	375	67	homs(m	homs(m	PROPN
ejpam-3229	375	68	,	,	PUNCT
ejpam-3229	375	69	β	β	X
ejpam-3229	375	70	(	(	PUNCT
ejpam-3229	375	71	m	m	NOUN
ejpam-3229	375	72	)	)	PUNCT
ejpam-3229	375	73	)	)	PUNCT
ejpam-3229	375	74	.	.	PUNCT
ejpam-3229	376	1	so	so	ADV
ejpam-3229	376	2	we	we	PRON
ejpam-3229	376	3	have	have	VERB
ejpam-3229	376	4	homs(m	homs(m	PROPN
ejpam-3229	376	5	,	,	PUNCT
ejpam-3229	376	6	α	α	PROPN
ejpam-3229	376	7	(	(	PUNCT
ejpam-3229	376	8	m	m	NOUN
ejpam-3229	376	9	)	)	PUNCT
ejpam-3229	376	10	)	)	PUNCT
ejpam-3229	377	1	⊆	⊆	NUM
ejpam-3229	377	2	homs(m	homs(m	NOUN
ejpam-3229	377	3	,	,	PUNCT
ejpam-3229	377	4	β	β	X
ejpam-3229	377	5	(	(	PUNCT
ejpam-3229	377	6	m	m	NOUN
ejpam-3229	377	7	)	)	PUNCT
ejpam-3229	377	8	)	)	PUNCT
ejpam-3229	377	9	and	and	CCONJ
ejpam-3229	377	10	therefore	therefore	ADV
ejpam-3229	377	11	by	by	ADP
ejpam-3229	377	12	hypothesis	hypothesis	NOUN
ejpam-3229	377	13	αe	αe	PROPN
ejpam-3229	377	14	⊆	⊆	NUM
ejpam-3229	377	15	βe	βe	PROPN
ejpam-3229	377	16	.	.	PROPN
ejpam-3229	377	17	3)⇒1	3)⇒1	NUM
ejpam-3229	377	18	)	)	PUNCT
ejpam-3229	377	19	consider	consider	VERB
ejpam-3229	377	20	φ	φ	NOUN
ejpam-3229	377	21	:	:	PUNCT
ejpam-3229	377	22	m→	m→	NOUN
ejpam-3229	377	23	α	α	PROPN
ejpam-3229	377	24	(	(	PUNCT
ejpam-3229	377	25	m	m	NOUN
ejpam-3229	377	26	)	)	PUNCT
ejpam-3229	377	27	an	an	DET
ejpam-3229	377	28	s	s	NOUN
ejpam-3229	377	29	-	-	PUNCT
ejpam-3229	377	30	homomorphism	homomorphism	NOUN
ejpam-3229	377	31	,	,	PUNCT
ejpam-3229	377	32	so	so	SCONJ
ejpam-3229	377	33	φ	φ	PROPN
ejpam-3229	377	34	(	(	PUNCT
ejpam-3229	377	35	m	m	PROPN
ejpam-3229	377	36	)	)	PUNCT
ejpam-3229	377	37	⊆	⊆	NUM
ejpam-3229	377	38	α	α	PROPN
ejpam-3229	377	39	(	(	PUNCT
ejpam-3229	377	40	m	m	NOUN
ejpam-3229	377	41	)	)	PUNCT
ejpam-3229	377	42	by	by	ADP
ejpam-3229	377	43	hypothesis	hypothesis	NOUN
ejpam-3229	377	44	φe	φe	ADP
ejpam-3229	377	45	⊆	⊆	NUM
ejpam-3229	377	46	αe	αe	NOUN
ejpam-3229	377	47	.	.	PUNCT
ejpam-3229	378	1	since	since	SCONJ
ejpam-3229	378	2	φ	φ	PROPN
ejpam-3229	378	3	∈	∈	PROPN
ejpam-3229	378	4	φe	φe	ADP
ejpam-3229	378	5	⊆	⊆	NUM
ejpam-3229	378	6	αe	αe	NOUN
ejpam-3229	378	7	so	so	ADV
ejpam-3229	378	8	φ	φ	PROPN
ejpam-3229	378	9	=	=	SYM
ejpam-3229	378	10	αu	αu	PROPN
ejpam-3229	378	11	,	,	PUNCT
ejpam-3229	378	12	for	for	ADP
ejpam-3229	378	13	some	some	DET
ejpam-3229	378	14	u	u	PROPN
ejpam-3229	378	15	∈	∈	PROPN
ejpam-3229	378	16	e.	e.	PROPN
ejpam-3229	378	17	hence	hence	ADV
ejpam-3229	378	18	m	m	VERB
ejpam-3229	378	19	is	be	AUX
ejpam-3229	378	20	quasi	quasi	ADJ
ejpam-3229	378	21	-	-	ADJ
ejpam-3229	378	22	principally	principally	ADV
ejpam-3229	378	23	projective	projective	ADJ
ejpam-3229	378	24	.	.	PUNCT
ejpam-3229	379	1	theorem	theorem	VERB
ejpam-3229	379	2	16	16	NUM
ejpam-3229	379	3	.	.	PUNCT
ejpam-3229	380	1	let	let	VERB
ejpam-3229	380	2	m	m	PRON
ejpam-3229	380	3	be	be	AUX
ejpam-3229	380	4	a	a	DET
ejpam-3229	380	5	semi	semi	ADJ
ejpam-3229	380	6	-	-	ADJ
ejpam-3229	380	7	projective	projective	ADJ
ejpam-3229	380	8	right	right	ADJ
ejpam-3229	380	9	s	s	NOUN
ejpam-3229	380	10	-	-	PUNCT
ejpam-3229	380	11	act	act	NOUN
ejpam-3229	380	12	and	and	CCONJ
ejpam-3229	380	13	α	α	NOUN
ejpam-3229	380	14	,	,	PUNCT
ejpam-3229	380	15	β	β	PROPN
ejpam-3229	380	16	∈	∈	PROPN
ejpam-3229	380	17	e.	e.	PROPN
ejpam-3229	380	18	then	then	ADV
ejpam-3229	380	19	:	:	PUNCT
ejpam-3229	380	20	1	1	X
ejpam-3229	380	21	)	)	PUNCT
ejpam-3229	380	22	if	if	SCONJ
ejpam-3229	380	23	α	α	PROPN
ejpam-3229	380	24	(	(	PUNCT
ejpam-3229	380	25	m	m	NOUN
ejpam-3229	380	26	)	)	PUNCT
ejpam-3229	380	27	embeds	embed	VERB
ejpam-3229	380	28	into	into	ADP
ejpam-3229	380	29	β	β	PROPN
ejpam-3229	380	30	(	(	PUNCT
ejpam-3229	380	31	m	m	PROPN
ejpam-3229	380	32	)	)	PUNCT
ejpam-3229	380	33	then	then	ADV
ejpam-3229	380	34	αe	αe	PRON
ejpam-3229	380	35	can	can	AUX
ejpam-3229	380	36	be	be	AUX
ejpam-3229	380	37	embedded	embed	VERB
ejpam-3229	380	38	into	into	ADP
ejpam-3229	380	39	βe	βe	PRON
ejpam-3229	380	40	.	.	PROPN
ejpam-3229	380	41	2	2	NUM
ejpam-3229	380	42	)	)	PUNCT
ejpam-3229	380	43	if	if	SCONJ
ejpam-3229	380	44	β	β	X
ejpam-3229	380	45	(	(	PUNCT
ejpam-3229	380	46	m	m	NOUN
ejpam-3229	380	47	)	)	PUNCT
ejpam-3229	380	48	is	be	AUX
ejpam-3229	380	49	a	a	DET
ejpam-3229	380	50	homomorphic	homomorphic	ADJ
ejpam-3229	380	51	image	image	NOUN
ejpam-3229	380	52	of	of	ADP
ejpam-3229	380	53	α	α	PROPN
ejpam-3229	380	54	(	(	PUNCT
ejpam-3229	380	55	m	m	NOUN
ejpam-3229	380	56	)	)	PUNCT
ejpam-3229	380	57	then	then	ADV
ejpam-3229	380	58	βe	βe	PRON
ejpam-3229	380	59	is	be	AUX
ejpam-3229	380	60	a	a	DET
ejpam-3229	380	61	homomorphic	homomorphic	ADJ
ejpam-3229	380	62	image	image	NOUN
ejpam-3229	380	63	of	of	ADP
ejpam-3229	380	64	αe	αe	PRON
ejpam-3229	380	65	.	.	PUNCT
ejpam-3229	381	1	3	3	X
ejpam-3229	381	2	)	)	PUNCT
ejpam-3229	381	3	if	if	SCONJ
ejpam-3229	381	4	α	α	PROPN
ejpam-3229	381	5	(	(	PUNCT
ejpam-3229	381	6	m	m	NOUN
ejpam-3229	381	7	)	)	PUNCT
ejpam-3229	381	8	∼=	∼=	PROPN
ejpam-3229	381	9	β	β	X
ejpam-3229	381	10	(	(	PUNCT
ejpam-3229	381	11	m	m	PROPN
ejpam-3229	381	12	)	)	PUNCT
ejpam-3229	381	13	then	then	ADV
ejpam-3229	381	14	αe	αe	X
ejpam-3229	381	15	∼=	∼=	PROPN
ejpam-3229	381	16	βe	βe	PRON
ejpam-3229	381	17	.	.	PUNCT
ejpam-3229	382	1	proof	proof	NOUN
ejpam-3229	382	2	.	.	PUNCT
ejpam-3229	383	1	1	1	X
ejpam-3229	383	2	)	)	PUNCT
ejpam-3229	383	3	let	let	VERB
ejpam-3229	383	4	f	f	PRON
ejpam-3229	383	5	:	:	PUNCT
ejpam-3229	383	6	α	α	PROPN
ejpam-3229	383	7	(	(	PUNCT
ejpam-3229	383	8	m)→	m)→	PROPN
ejpam-3229	383	9	β	β	X
ejpam-3229	383	10	(	(	PUNCT
ejpam-3229	383	11	m	m	NOUN
ejpam-3229	383	12	)	)	PUNCT
ejpam-3229	383	13	be	be	AUX
ejpam-3229	383	14	an	an	DET
ejpam-3229	383	15	s	s	NOUN
ejpam-3229	383	16	-	-	NOUN
ejpam-3229	383	17	homomorphism	homomorphism	NOUN
ejpam-3229	383	18	.	.	PUNCT
ejpam-3229	384	1	sincem	sincem	NOUN
ejpam-3229	384	2	is	be	AUX
ejpam-3229	384	3	semi	semi	ADV
ejpam-3229	384	4	projective	projective	ADJ
ejpam-3229	384	5	so	so	SCONJ
ejpam-3229	384	6	βe	βe	PROPN
ejpam-3229	384	7	=	=	PUNCT
ejpam-3229	384	8	homs	hom	NOUN
ejpam-3229	384	9	(	(	PUNCT
ejpam-3229	384	10	m	m	PROPN
ejpam-3229	384	11	,	,	PUNCT
ejpam-3229	384	12	β	β	X
ejpam-3229	384	13	(	(	PUNCT
ejpam-3229	384	14	m	m	NOUN
ejpam-3229	384	15	)	)	PUNCT
ejpam-3229	384	16	)	)	PUNCT
ejpam-3229	384	17	.	.	PUNCT
ejpam-3229	385	1	as	as	ADP
ejpam-3229	385	2	fα	fα	ADP
ejpam-3229	385	3	:	:	PUNCT
ejpam-3229	385	4	m→	m→	NOUN
ejpam-3229	385	5	β	β	X
ejpam-3229	385	6	(	(	PUNCT
ejpam-3229	385	7	m	m	PROPN
ejpam-3229	385	8	)	)	PUNCT
ejpam-3229	385	9	,	,	PUNCT
ejpam-3229	385	10	so	so	ADV
ejpam-3229	385	11	fα	fα	ADP
ejpam-3229	385	12	∈	∈	NOUN
ejpam-3229	385	13	homs	hom	NOUN
ejpam-3229	385	14	(	(	PUNCT
ejpam-3229	385	15	m	m	PROPN
ejpam-3229	385	16	,	,	PUNCT
ejpam-3229	385	17	β	β	X
ejpam-3229	385	18	(	(	PUNCT
ejpam-3229	385	19	m	m	NOUN
ejpam-3229	385	20	)	)	PUNCT
ejpam-3229	385	21	)	)	PUNCT
ejpam-3229	386	1	=	=	SYM
ejpam-3229	387	1	βe	βe	PROPN
ejpam-3229	388	1	and	and	CCONJ
ejpam-3229	388	2	so	so	ADV
ejpam-3229	388	3	fα	fα	ADV
ejpam-3229	388	4	=	=	SYM
ejpam-3229	388	5	βg	βg	ADJ
ejpam-3229	388	6	,	,	PUNCT
ejpam-3229	388	7	for	for	ADP
ejpam-3229	388	8	some	some	DET
ejpam-3229	388	9	g	g	PROPN
ejpam-3229	388	10	∈	∈	PROPN
ejpam-3229	388	11	e.	e.	PROPN
ejpam-3229	388	12	define	define	VERB
ejpam-3229	388	13	φ	φ	PROPN
ejpam-3229	388	14	:	:	PUNCT
ejpam-3229	388	15	αe	αe	X
ejpam-3229	388	16	→	→	SYM
ejpam-3229	388	17	βe	βe	X
ejpam-3229	388	18	by	by	ADP
ejpam-3229	388	19	φ(αu	φ(αu	NOUN
ejpam-3229	388	20	)	)	PUNCT
ejpam-3229	388	21	=	=	SYM
ejpam-3229	388	22	βgu	βgu	NOUN
ejpam-3229	388	23	for	for	ADP
ejpam-3229	388	24	u	u	PROPN
ejpam-3229	388	25	∈	∈	PROPN
ejpam-3229	388	26	e.	e.	PROPN
ejpam-3229	389	1	we	we	PRON
ejpam-3229	389	2	can	can	AUX
ejpam-3229	389	3	see	see	VERB
ejpam-3229	389	4	that	that	SCONJ
ejpam-3229	389	5	φ	φ	PROPN
ejpam-3229	389	6	is	be	AUX
ejpam-3229	389	7	well	well	ADV
ejpam-3229	389	8	-	-	PUNCT
ejpam-3229	389	9	defined	define	VERB
ejpam-3229	389	10	.	.	PUNCT
ejpam-3229	390	1	indeed	indeed	ADV
ejpam-3229	390	2	,	,	PUNCT
ejpam-3229	390	3	for	for	ADP
ejpam-3229	390	4	any	any	DET
ejpam-3229	390	5	u	u	NOUN
ejpam-3229	390	6	,	,	PUNCT
ejpam-3229	390	7	v	v	NOUN
ejpam-3229	390	8	∈	∈	NOUN
ejpam-3229	390	9	e	e	NOUN
ejpam-3229	390	10	such	such	ADJ
ejpam-3229	390	11	that	that	DET
ejpam-3229	390	12	αu	αu	NOUN
ejpam-3229	390	13	=	=	PUNCT
ejpam-3229	390	14	αv	αv	NOUN
ejpam-3229	390	15	we	we	PRON
ejpam-3229	390	16	have	have	VERB
ejpam-3229	390	17	fαu	fαu	NOUN
ejpam-3229	390	18	=	=	SYM
ejpam-3229	391	1	fαv	fαv	NOUN
ejpam-3229	391	2	implies	imply	VERB
ejpam-3229	391	3	βgu	βgu	NOUN
ejpam-3229	392	1	=	=	PRON
ejpam-3229	392	2	βgv	βgv	PROPN
ejpam-3229	393	1	and	and	CCONJ
ejpam-3229	393	2	so	so	ADV
ejpam-3229	393	3	φ(αu	φ(αu	X
ejpam-3229	393	4	)	)	PUNCT
ejpam-3229	393	5	=	=	SYM
ejpam-3229	393	6	φ(αv	φ(αv	PROPN
ejpam-3229	393	7	)	)	PUNCT
ejpam-3229	393	8	.	.	PUNCT
ejpam-3229	394	1	clearly	clearly	ADV
ejpam-3229	394	2	e	e	X
ejpam-3229	394	3	-	-	NOUN
ejpam-3229	394	4	homomorphism	homomorphism	NOUN
ejpam-3229	394	5	.	.	PUNCT
ejpam-3229	395	1	to	to	PART
ejpam-3229	395	2	show	show	VERB
ejpam-3229	395	3	injectivity	injectivity	NOUN
ejpam-3229	395	4	we	we	PRON
ejpam-3229	395	5	take	take	VERB
ejpam-3229	395	6	φ(αu	φ(αu	NOUN
ejpam-3229	395	7	)	)	PUNCT
ejpam-3229	395	8	=	=	SYM
ejpam-3229	395	9	φ(αv	φ(αv	NOUN
ejpam-3229	395	10	)	)	PUNCT
ejpam-3229	395	11	then	then	ADV
ejpam-3229	395	12	βgu	βgu	PUNCT
ejpam-3229	396	1	=	=	PUNCT
ejpam-3229	396	2	βgv	βgv	PROPN
ejpam-3229	396	3	.	.	PUNCT
ejpam-3229	397	1	as	as	SCONJ
ejpam-3229	397	2	fα	fα	ADV
ejpam-3229	397	3	=	=	VERB
ejpam-3229	397	4	βg	βg	ADP
ejpam-3229	397	5	therefore	therefore	ADV
ejpam-3229	397	6	fαu	fαu	NOUN
ejpam-3229	397	7	=	=	SYM
ejpam-3229	397	8	fαv	fαv	NOUN
ejpam-3229	397	9	.	.	PUNCT
ejpam-3229	398	1	since	since	SCONJ
ejpam-3229	398	2	f	f	PROPN
ejpam-3229	398	3	is	be	AUX
ejpam-3229	398	4	1	1	NUM
ejpam-3229	398	5	-	-	SYM
ejpam-3229	398	6	1	1	NUM
ejpam-3229	398	7	αu	αu	NOUN
ejpam-3229	398	8	=	=	SYM
ejpam-3229	398	9	αv	αv	NOUN
ejpam-3229	398	10	.	.	PUNCT
ejpam-3229	399	1	hence	hence	ADV
ejpam-3229	399	2	φ	φ	PROPN
ejpam-3229	399	3	is	be	AUX
ejpam-3229	399	4	embbedding	embbedde	VERB
ejpam-3229	399	5	.	.	PUNCT
ejpam-3229	400	1	2	2	X
ejpam-3229	400	2	)	)	PUNCT
ejpam-3229	400	3	let	let	VERB
ejpam-3229	400	4	f	f	X
ejpam-3229	400	5	,	,	PUNCT
ejpam-3229	400	6	g	g	PROPN
ejpam-3229	400	7	and	and	CCONJ
ejpam-3229	400	8	φ	φ	PROPN
ejpam-3229	400	9	be	be	VERB
ejpam-3229	400	10	as	as	ADP
ejpam-3229	400	11	in	in	ADP
ejpam-3229	400	12	part	part	NOUN
ejpam-3229	400	13	1	1	NUM
ejpam-3229	400	14	)	)	PUNCT
ejpam-3229	400	15	.	.	PUNCT
ejpam-3229	401	1	for	for	ADP
ejpam-3229	401	2	βu	βu	PRON
ejpam-3229	401	3	∈	∈	NOUN
ejpam-3229	401	4	βe	βe	ADP
ejpam-3229	401	5	there	there	PRON
ejpam-3229	401	6	exists	exist	VERB
ejpam-3229	401	7	ψ	ψ	X
ejpam-3229	401	8	∈	∈	PROPN
ejpam-3229	401	9	homs(m	homs(m	PROPN
ejpam-3229	401	10	,	,	PUNCT
ejpam-3229	401	11	β	β	X
ejpam-3229	401	12	(	(	PUNCT
ejpam-3229	401	13	m	m	NOUN
ejpam-3229	401	14	)	)	PUNCT
ejpam-3229	401	15	)	)	PUNCT
ejpam-3229	401	16	such	such	ADJ
ejpam-3229	401	17	that	that	PRON
ejpam-3229	401	18	βu	βu	PUNCT
ejpam-3229	401	19	=	=	SYM
ejpam-3229	401	20	ψ	ψ	X
ejpam-3229	401	21	.	.	NOUN
ejpam-3229	401	22	for	for	ADP
ejpam-3229	401	23	m	m	PROPN
ejpam-3229	401	24	∈	∈	NOUN
ejpam-3229	401	25	m	m	VERB
ejpam-3229	401	26	we	we	PRON
ejpam-3229	401	27	have	have	VERB
ejpam-3229	401	28	βu(m	βu(m	PUNCT
ejpam-3229	401	29	)	)	PUNCT
ejpam-3229	401	30	=	=	SYM
ejpam-3229	401	31	ψ(m	ψ(m	PROPN
ejpam-3229	401	32	)	)	PUNCT
ejpam-3229	401	33	∈	∈	PROPN
ejpam-3229	401	34	β(m	β(m	PROPN
ejpam-3229	401	35	)	)	PUNCT
ejpam-3229	401	36	so	so	SCONJ
ejpam-3229	401	37	there	there	PRON
ejpam-3229	401	38	exist	exist	VERB
ejpam-3229	401	39	m′	m′	NOUN
ejpam-3229	401	40	such	such	ADJ
ejpam-3229	401	41	that	that	SCONJ
ejpam-3229	401	42	βu(m	βu(m	PRON
ejpam-3229	401	43	)	)	PUNCT
ejpam-3229	401	44	=	=	SYM
ejpam-3229	401	45	ψ(m	ψ(m	PROPN
ejpam-3229	401	46	)	)	PUNCT
ejpam-3229	401	47	=	=	SYM
ejpam-3229	401	48	β(m′	β(m′	NOUN
ejpam-3229	401	49	)	)	PUNCT
ejpam-3229	401	50	.	.	PUNCT
ejpam-3229	402	1	as	as	ADP
ejpam-3229	402	2	fα	fα	ADP
ejpam-3229	402	3	(	(	PUNCT
ejpam-3229	402	4	m	m	NOUN
ejpam-3229	402	5	)	)	PUNCT
ejpam-3229	402	6	=	=	SYM
ejpam-3229	402	7	β	β	X
ejpam-3229	402	8	(	(	PUNCT
ejpam-3229	402	9	m	m	NOUN
ejpam-3229	402	10	)	)	PUNCT
ejpam-3229	402	11	so	so	ADV
ejpam-3229	402	12	there	there	PRON
ejpam-3229	402	13	exists	exist	VERB
ejpam-3229	402	14	m′′	m′′	VERB
ejpam-3229	402	15	such	such	ADJ
ejpam-3229	402	16	that	that	SCONJ
ejpam-3229	402	17	βu(m	βu(m	PRON
ejpam-3229	402	18	)	)	PUNCT
ejpam-3229	402	19	=	=	SYM
ejpam-3229	402	20	ψ(m	ψ(m	PROPN
ejpam-3229	402	21	)	)	PUNCT
ejpam-3229	402	22	=	=	SYM
ejpam-3229	402	23	β(m′	β(m′	NOUN
ejpam-3229	402	24	)	)	PUNCT
ejpam-3229	402	25	=	=	PUNCT
ejpam-3229	402	26	fα(m′′	fα(m′′	X
ejpam-3229	402	27	)	)	PUNCT
ejpam-3229	402	28	=	=	PUNCT
ejpam-3229	402	29	βg(m′′	βg(m′′	PROPN
ejpam-3229	402	30	)	)	PUNCT
ejpam-3229	402	31	.	.	PUNCT
ejpam-3229	403	1	hence	hence	ADV
ejpam-3229	403	2	we	we	PRON
ejpam-3229	403	3	can	can	AUX
ejpam-3229	403	4	define	define	VERB
ejpam-3229	403	5	γ	γ	NOUN
ejpam-3229	403	6	:	:	PUNCT
ejpam-3229	403	7	m	m	PROPN
ejpam-3229	403	8	→	→	SYM
ejpam-3229	403	9	m	m	VERB
ejpam-3229	403	10	by	by	ADP
ejpam-3229	403	11	γ(m	γ(m	PROPN
ejpam-3229	403	12	)	)	PUNCT
ejpam-3229	403	13	=	=	PUNCT
ejpam-3229	404	1	m′′,for	m′′,for	PROPN
ejpam-3229	404	2	m	m	PROPN
ejpam-3229	404	3	,	,	PUNCT
ejpam-3229	404	4	m′′	m′′	PROPN
ejpam-3229	404	5	∈	∈	PROPN
ejpam-3229	404	6	m	m	PRON
ejpam-3229	404	7	,	,	PUNCT
ejpam-3229	404	8	whenever	whenever	SCONJ
ejpam-3229	404	9	βu(m	βu(m	PRON
ejpam-3229	404	10	)	)	PUNCT
ejpam-3229	404	11	=	=	PUNCT
ejpam-3229	405	1	βg(m′′	βg(m′′	NOUN
ejpam-3229	405	2	)	)	PUNCT
ejpam-3229	405	3	.	.	PUNCT
ejpam-3229	406	1	let	let	VERB
ejpam-3229	406	2	us	we	PRON
ejpam-3229	406	3	see	see	VERB
ejpam-3229	406	4	that	that	SCONJ
ejpam-3229	406	5	γ	γ	PROPN
ejpam-3229	406	6	is	be	AUX
ejpam-3229	406	7	well	well	ADV
ejpam-3229	406	8	-	-	PUNCT
ejpam-3229	406	9	defined	define	VERB
ejpam-3229	406	10	.	.	PUNCT
ejpam-3229	407	1	let	let	VERB
ejpam-3229	407	2	m1	m1	PROPN
ejpam-3229	407	3	=	=	SYM
ejpam-3229	407	4	m2	m2	PROPN
ejpam-3229	407	5	,	,	PUNCT
ejpam-3229	407	6	where	where	SCONJ
ejpam-3229	407	7	γ(m1	γ(m1	VERB
ejpam-3229	407	8	)	)	PUNCT
ejpam-3229	407	9	=	=	SYM
ejpam-3229	407	10	m′′1	m′′1	NOUN
ejpam-3229	407	11	and	and	CCONJ
ejpam-3229	407	12	γ(m2	γ(m2	NOUN
ejpam-3229	407	13	)	)	PUNCT
ejpam-3229	407	14	=	=	PUNCT
ejpam-3229	408	1	m′′2	m′′2	PROPN
ejpam-3229	408	2	.	.	PUNCT
ejpam-3229	409	1	this	this	PRON
ejpam-3229	409	2	holds	hold	VERB
ejpam-3229	409	3	only	only	ADV
ejpam-3229	409	4	when	when	SCONJ
ejpam-3229	409	5	βu(m1	βu(m1	NOUN
ejpam-3229	409	6	)	)	PUNCT
ejpam-3229	409	7	=	=	SYM
ejpam-3229	409	8	βg(m′′1	βg(m′′1	NOUN
ejpam-3229	409	9	)	)	PUNCT
ejpam-3229	409	10	and	and	CCONJ
ejpam-3229	409	11	βu(m2	βu(m2	NUM
ejpam-3229	409	12	)	)	PUNCT
ejpam-3229	409	13	=	=	PUNCT
ejpam-3229	409	14	βg(m′′2	βg(m′′2	PROPN
ejpam-3229	409	15	)	)	PUNCT
ejpam-3229	409	16	,	,	PUNCT
ejpam-3229	409	17	βu(m2	βu(m2	NUM
ejpam-3229	409	18	)	)	PUNCT
ejpam-3229	409	19	=	=	SYM
ejpam-3229	409	20	βu(m1	βu(m1	NOUN
ejpam-3229	409	21	)	)	PUNCT
ejpam-3229	409	22	=	=	SYM
ejpam-3229	410	1	βg(m′′1	βg(m′′1	NOUN
ejpam-3229	410	2	)	)	PUNCT
ejpam-3229	410	3	,	,	PUNCT
ejpam-3229	410	4	which	which	PRON
ejpam-3229	410	5	implies	imply	VERB
ejpam-3229	410	6	γ(m2	γ(m2	ADJ
ejpam-3229	410	7	)	)	PUNCT
ejpam-3229	410	8	=	=	SYM
ejpam-3229	411	1	m′′1	m′′1	NOUN
ejpam-3229	411	2	=	=	PUNCT
ejpam-3229	411	3	γ(m1	γ(m1	NOUN
ejpam-3229	411	4	)	)	PUNCT
ejpam-3229	411	5	,	,	PUNCT
ejpam-3229	411	6	hence	hence	ADV
ejpam-3229	411	7	γ	γ	PROPN
ejpam-3229	411	8	is	be	AUX
ejpam-3229	411	9	well	well	ADV
ejpam-3229	411	10	defined	define	VERB
ejpam-3229	411	11	.	.	PUNCT
ejpam-3229	412	1	moreover	moreover	ADV
ejpam-3229	412	2	βu(m	βu(m	PRON
ejpam-3229	412	3	)	)	PUNCT
ejpam-3229	412	4	=	=	PUNCT
ejpam-3229	413	1	βg(m′′	βg(m′′	X
ejpam-3229	413	2	)	)	PUNCT
ejpam-3229	413	3	=	=	SYM
ejpam-3229	413	4	βgγ(m	βgγ(m	PROPN
ejpam-3229	413	5	)	)	PUNCT
ejpam-3229	413	6	for	for	ADP
ejpam-3229	413	7	all	all	DET
ejpam-3229	413	8	m	m	NOUN
ejpam-3229	413	9	∈m	∈m	NOUN
ejpam-3229	413	10	.	.	PUNCT
ejpam-3229	414	1	thus	thus	ADV
ejpam-3229	414	2	βu	βu	X
ejpam-3229	414	3	=	=	PUNCT
ejpam-3229	414	4	βgγ	βgγ	NOUN
ejpam-3229	414	5	=	=	SYM
ejpam-3229	414	6	φ(αγ	φ(αγ	NOUN
ejpam-3229	414	7	)	)	PUNCT
ejpam-3229	414	8	so	so	SCONJ
ejpam-3229	414	9	φ	φ	PROPN
ejpam-3229	414	10	is	be	AUX
ejpam-3229	414	11	epimorphism	epimorphism	NOUN
ejpam-3229	414	12	.	.	PUNCT
ejpam-3229	415	1	3	3	X
ejpam-3229	415	2	)	)	PUNCT
ejpam-3229	415	3	follows	follow	VERB
ejpam-3229	415	4	directly	directly	ADV
ejpam-3229	415	5	form	form	VERB
ejpam-3229	415	6	1	1	NUM
ejpam-3229	415	7	)	)	PUNCT
ejpam-3229	415	8	and	and	CCONJ
ejpam-3229	415	9	2	2	NUM
ejpam-3229	415	10	)	)	PUNCT
ejpam-3229	415	11	.	.	PUNCT
ejpam-3229	416	1	j.	j.	PROPN
ejpam-3229	416	2	hussain	hussain	PROPN
ejpam-3229	416	3	,	,	PUNCT
ejpam-3229	416	4	m.shabir	m.shabir	PROPN
ejpam-3229	416	5	/	/	SYM
ejpam-3229	416	6	eur	eur	PROPN
ejpam-3229	416	7	.	.	PUNCT
ejpam-3229	417	1	j.	j.	PROPN
ejpam-3229	417	2	pure	pure	PROPN
ejpam-3229	417	3	appl	appl	PROPN
ejpam-3229	417	4	.	.	PROPN
ejpam-3229	417	5	math	math	PROPN
ejpam-3229	417	6	,	,	PUNCT
ejpam-3229	417	7	11	11	NUM
ejpam-3229	417	8	(	(	PUNCT
ejpam-3229	417	9	2	2	NUM
ejpam-3229	417	10	)	)	PUNCT
ejpam-3229	417	11	(	(	PUNCT
ejpam-3229	417	12	2018	2018	NUM
ejpam-3229	417	13	)	)	PUNCT
ejpam-3229	417	14	,	,	PUNCT
ejpam-3229	417	15	431	431	NUM
ejpam-3229	417	16	-	-	SYM
ejpam-3229	417	17	443	443	NUM
ejpam-3229	417	18	442	442	NUM
ejpam-3229	417	19	theorem	theorem	NOUN
ejpam-3229	417	20	17	17	NUM
ejpam-3229	417	21	.	.	PUNCT
ejpam-3229	418	1	let	let	VERB
ejpam-3229	418	2	m	m	PRON
ejpam-3229	418	3	be	be	AUX
ejpam-3229	418	4	a	a	DET
ejpam-3229	418	5	semi	semi	ADJ
ejpam-3229	418	6	-	-	ADJ
ejpam-3229	418	7	projective(quasi	projective(quasi	ADJ
ejpam-3229	418	8	-	-	PUNCT
ejpam-3229	418	9	principally	principally	ADV
ejpam-3229	418	10	projective	projective	ADJ
ejpam-3229	418	11	)	)	PUNCT
ejpam-3229	419	1	right	right	ADJ
ejpam-3229	419	2	s	s	NOUN
ejpam-3229	419	3	-	-	PUNCT
ejpam-3229	419	4	act	act	NOUN
ejpam-3229	419	5	then	then	ADV
ejpam-3229	419	6	there	there	PRON
ejpam-3229	419	7	is	be	VERB
ejpam-3229	419	8	a	a	DET
ejpam-3229	419	9	one	one	NUM
ejpam-3229	419	10	-	-	PUNCT
ejpam-3229	419	11	one	one	NUM
ejpam-3229	419	12	correspondence	correspondence	NOUN
ejpam-3229	419	13	between	between	ADP
ejpam-3229	419	14	m	m	NOUN
ejpam-3229	419	15	-	-	PUNCT
ejpam-3229	419	16	cyclic	cyclic	ADJ
ejpam-3229	419	17	sub	sub	NOUN
ejpam-3229	419	18	-	-	NOUN
ejpam-3229	419	19	acts	act	NOUN
ejpam-3229	419	20	of	of	ADP
ejpam-3229	419	21	m	m	NOUN
ejpam-3229	419	22	and	and	CCONJ
ejpam-3229	419	23	principal	principal	ADJ
ejpam-3229	419	24	right	right	ADJ
ejpam-3229	419	25	ideals	ideal	NOUN
ejpam-3229	419	26	of	of	ADP
ejpam-3229	419	27	e.	e.	PROPN
ejpam-3229	419	28	proof	proof	PROPN
ejpam-3229	419	29	.	.	PUNCT
ejpam-3229	420	1	let	let	VERB
ejpam-3229	420	2	ã	ã	PROPN
ejpam-3229	420	3	be	be	AUX
ejpam-3229	420	4	a	a	DET
ejpam-3229	420	5	collection	collection	NOUN
ejpam-3229	420	6	of	of	ADP
ejpam-3229	420	7	all	all	DET
ejpam-3229	420	8	m	m	NOUN
ejpam-3229	420	9	-	-	ADJ
ejpam-3229	420	10	cyclic	cyclic	ADJ
ejpam-3229	420	11	sub	sub	NOUN
ejpam-3229	420	12	-	-	NOUN
ejpam-3229	420	13	acts	act	NOUN
ejpam-3229	420	14	of	of	ADP
ejpam-3229	420	15	m	m	NOUN
ejpam-3229	420	16	and	and	CCONJ
ejpam-3229	420	17	b̃	b̃	PROPN
ejpam-3229	420	18	be	be	AUX
ejpam-3229	420	19	a	a	DET
ejpam-3229	420	20	collection	collection	NOUN
ejpam-3229	420	21	all	all	DET
ejpam-3229	420	22	principal	principal	ADJ
ejpam-3229	420	23	right	right	ADJ
ejpam-3229	420	24	ideals	ideal	NOUN
ejpam-3229	420	25	of	of	ADP
ejpam-3229	420	26	e.	e.	PROPN
ejpam-3229	420	27	define	define	VERB
ejpam-3229	420	28	φ	φ	PROPN
ejpam-3229	420	29	:	:	PUNCT
ejpam-3229	420	30	ã	ã	PROPN
ejpam-3229	420	31	→	→	SYM
ejpam-3229	420	32	b̃	b̃	PROPN
ejpam-3229	420	33	by	by	ADP
ejpam-3229	420	34	φ(α	φ(α	PROPN
ejpam-3229	420	35	(	(	PUNCT
ejpam-3229	420	36	m	m	NOUN
ejpam-3229	420	37	)	)	PUNCT
ejpam-3229	420	38	)	)	PUNCT
ejpam-3229	421	1	=	=	SYM
ejpam-3229	422	1	αe	αe	X
ejpam-3229	422	2	.	.	PROPN
ejpam-3229	423	1	now	now	ADV
ejpam-3229	423	2	φ	φ	PROPN
ejpam-3229	423	3	is	be	AUX
ejpam-3229	423	4	well	well	ADV
ejpam-3229	423	5	defined	define	VERB
ejpam-3229	423	6	because	because	SCONJ
ejpam-3229	423	7	if	if	SCONJ
ejpam-3229	423	8	α	α	PROPN
ejpam-3229	423	9	(	(	PUNCT
ejpam-3229	423	10	m	m	NOUN
ejpam-3229	423	11	)	)	PUNCT
ejpam-3229	423	12	=	=	SYM
ejpam-3229	424	1	β	β	X
ejpam-3229	424	2	(	(	PUNCT
ejpam-3229	424	3	m	m	PROPN
ejpam-3229	424	4	)	)	PUNCT
ejpam-3229	424	5	for	for	ADP
ejpam-3229	424	6	α	α	NOUN
ejpam-3229	424	7	,	,	PUNCT
ejpam-3229	424	8	β	β	X
ejpam-3229	424	9	∈	∈	PROPN
ejpam-3229	424	10	e	e	NOUN
ejpam-3229	424	11	,	,	PUNCT
ejpam-3229	424	12	then	then	ADV
ejpam-3229	424	13	homs	hom	NOUN
ejpam-3229	424	14	(	(	PUNCT
ejpam-3229	424	15	m	m	PROPN
ejpam-3229	424	16	,	,	PUNCT
ejpam-3229	424	17	α	α	PROPN
ejpam-3229	424	18	(	(	PUNCT
ejpam-3229	424	19	m	m	NOUN
ejpam-3229	424	20	)	)	PUNCT
ejpam-3229	424	21	)	)	PUNCT
ejpam-3229	425	1	=	=	NOUN
ejpam-3229	425	2	homs	hom	NOUN
ejpam-3229	425	3	(	(	PUNCT
ejpam-3229	425	4	m	m	PROPN
ejpam-3229	425	5	,	,	PUNCT
ejpam-3229	425	6	β	β	X
ejpam-3229	425	7	(	(	PUNCT
ejpam-3229	425	8	m	m	NOUN
ejpam-3229	425	9	)	)	PUNCT
ejpam-3229	425	10	)	)	PUNCT
ejpam-3229	425	11	,	,	PUNCT
ejpam-3229	425	12	since	since	SCONJ
ejpam-3229	425	13	m	m	PROPN
ejpam-3229	425	14	is	be	AUX
ejpam-3229	425	15	semi	semi	ADJ
ejpam-3229	425	16	-	-	ADJ
ejpam-3229	425	17	projective	projective	ADJ
ejpam-3229	425	18	so	so	SCONJ
ejpam-3229	425	19	αe	αe	PROPN
ejpam-3229	425	20	=	=	SYM
ejpam-3229	425	21	βe	βe	PROPN
ejpam-3229	425	22	and	and	CCONJ
ejpam-3229	425	23	φ	φ	PROPN
ejpam-3229	425	24	(	(	PUNCT
ejpam-3229	425	25	α	α	PROPN
ejpam-3229	425	26	(	(	PUNCT
ejpam-3229	425	27	m	m	NOUN
ejpam-3229	425	28	)	)	PUNCT
ejpam-3229	425	29	)	)	PUNCT
ejpam-3229	426	1	=	=	SYM
ejpam-3229	426	2	φ(β	φ(β	PROPN
ejpam-3229	426	3	(	(	PUNCT
ejpam-3229	426	4	m	m	NOUN
ejpam-3229	426	5	)	)	PUNCT
ejpam-3229	426	6	)	)	PUNCT
ejpam-3229	426	7	.	.	PUNCT
ejpam-3229	427	1	to	to	PART
ejpam-3229	427	2	show	show	VERB
ejpam-3229	427	3	injectivity	injectivity	NOUN
ejpam-3229	427	4	we	we	PRON
ejpam-3229	427	5	let	let	VERB
ejpam-3229	427	6	φ(α	φ(α	PROPN
ejpam-3229	427	7	(	(	PUNCT
ejpam-3229	427	8	m	m	NOUN
ejpam-3229	427	9	)	)	PUNCT
ejpam-3229	427	10	)	)	PUNCT
ejpam-3229	428	1	=	=	SYM
ejpam-3229	428	2	φ(β	φ(β	PROPN
ejpam-3229	428	3	(	(	PUNCT
ejpam-3229	428	4	m	m	NOUN
ejpam-3229	428	5	)	)	PUNCT
ejpam-3229	428	6	)	)	PUNCT
ejpam-3229	429	1	so	so	CCONJ
ejpam-3229	429	2	αe	αe	X
ejpam-3229	429	3	=	=	SYM
ejpam-3229	429	4	βe	βe	PROPN
ejpam-3229	429	5	and	and	CCONJ
ejpam-3229	429	6	homs(m	homs(m	PROPN
ejpam-3229	429	7	,	,	PUNCT
ejpam-3229	429	8	α	α	PROPN
ejpam-3229	429	9	(	(	PUNCT
ejpam-3229	429	10	m	m	NOUN
ejpam-3229	429	11	)	)	PUNCT
ejpam-3229	429	12	)	)	PUNCT
ejpam-3229	430	1	=	=	SYM
ejpam-3229	430	2	hom(m	hom(m	PROPN
ejpam-3229	430	3	,	,	PUNCT
ejpam-3229	430	4	β	β	X
ejpam-3229	430	5	(	(	PUNCT
ejpam-3229	430	6	m	m	NOUN
ejpam-3229	430	7	)	)	PUNCT
ejpam-3229	430	8	)	)	PUNCT
ejpam-3229	430	9	which	which	PRON
ejpam-3229	430	10	clearly	clearly	ADV
ejpam-3229	430	11	implies	imply	VERB
ejpam-3229	430	12	α	α	PROPN
ejpam-3229	430	13	(	(	PUNCT
ejpam-3229	430	14	m	m	NOUN
ejpam-3229	430	15	)	)	PUNCT
ejpam-3229	430	16	=	=	SYM
ejpam-3229	430	17	β	β	X
ejpam-3229	430	18	(	(	PUNCT
ejpam-3229	430	19	m	m	PROPN
ejpam-3229	430	20	)	)	PUNCT
ejpam-3229	430	21	.	.	PUNCT
ejpam-3229	431	1	surjection	surjection	PROPN
ejpam-3229	431	2	is	be	AUX
ejpam-3229	431	3	trivial	trivial	ADJ
ejpam-3229	431	4	.	.	PUNCT
ejpam-3229	432	1	theorem	theorem	NOUN
ejpam-3229	432	2	18	18	NUM
ejpam-3229	432	3	.	.	PUNCT
ejpam-3229	433	1	there	there	PRON
ejpam-3229	433	2	is	be	VERB
ejpam-3229	433	3	a	a	DET
ejpam-3229	433	4	one	one	NUM
ejpam-3229	433	5	-	-	PUNCT
ejpam-3229	433	6	one	one	NUM
ejpam-3229	433	7	correspondence	correspondence	NOUN
ejpam-3229	433	8	between	between	ADP
ejpam-3229	433	9	f	f	PROPN
ejpam-3229	433	10	∈	∈	PROPN
ejpam-3229	433	11	homs	hom	NOUN
ejpam-3229	433	12	(	(	PUNCT
ejpam-3229	433	13	α	α	PROPN
ejpam-3229	433	14	(	(	PUNCT
ejpam-3229	433	15	m	m	NOUN
ejpam-3229	433	16	)	)	PUNCT
ejpam-3229	433	17	,	,	PUNCT
ejpam-3229	433	18	m	m	PROPN
ejpam-3229	433	19	)	)	PUNCT
ejpam-3229	433	20	and	and	CCONJ
ejpam-3229	433	21	f	f	PROPN
ejpam-3229	433	22	∈	∈	PROPN
ejpam-3229	433	23	homs	hom	NOUN
ejpam-3229	433	24	(	(	PUNCT
ejpam-3229	433	25	αe	αe	NOUN
ejpam-3229	433	26	,	,	PUNCT
ejpam-3229	433	27	e	e	NOUN
ejpam-3229	433	28	)	)	PUNCT
ejpam-3229	433	29	with	with	ADP
ejpam-3229	433	30	kerf	kerf	NOUN
ejpam-3229	433	31	(	(	PUNCT
ejpam-3229	433	32	α	α	NOUN
ejpam-3229	433	33	)	)	PUNCT
ejpam-3229	433	34	⊃	⊃	NOUN
ejpam-3229	433	35	kerα	kerα	ADV
ejpam-3229	433	36	in	in	ADP
ejpam-3229	433	37	such	such	ADJ
ejpam-3229	433	38	away	away	ADV
ejpam-3229	433	39	that	that	SCONJ
ejpam-3229	433	40	f	f	PROPN
ejpam-3229	433	41	(	(	PUNCT
ejpam-3229	433	42	αu	αu	NOUN
ejpam-3229	433	43	)	)	PUNCT
ejpam-3229	433	44	=	=	SYM
ejpam-3229	433	45	fαu	fαu	NOUN
ejpam-3229	433	46	,	,	PUNCT
ejpam-3229	433	47	for	for	ADP
ejpam-3229	433	48	all	all	DET
ejpam-3229	433	49	u	u	PRON
ejpam-3229	433	50	∈	∈	PROPN
ejpam-3229	433	51	e	e	NOUN
ejpam-3229	433	52	and	and	CCONJ
ejpam-3229	433	53	f(α(m	f(α(m	NOUN
ejpam-3229	433	54	)	)	PUNCT
ejpam-3229	433	55	)	)	PUNCT
ejpam-3229	434	1	=	=	SYM
ejpam-3229	434	2	f	f	PROPN
ejpam-3229	434	3	(	(	PUNCT
ejpam-3229	434	4	α)(m	α)(m	NUM
ejpam-3229	434	5	)	)	PUNCT
ejpam-3229	434	6	,	,	PUNCT
ejpam-3229	434	7	for	for	ADP
ejpam-3229	434	8	all	all	DET
ejpam-3229	434	9	α	α	DET
ejpam-3229	434	10	∈	∈	NOUN
ejpam-3229	434	11	e	e	NOUN
ejpam-3229	434	12	and	and	CCONJ
ejpam-3229	434	13	m	m	PROPN
ejpam-3229	434	14	∈m	∈m	NOUN
ejpam-3229	434	15	.	.	PUNCT
ejpam-3229	435	1	proof	proof	NOUN
ejpam-3229	435	2	.	.	PUNCT
ejpam-3229	436	1	let	let	VERB
ejpam-3229	436	2	us	we	PRON
ejpam-3229	436	3	fix	fix	VERB
ejpam-3229	436	4	α	α	PRON
ejpam-3229	436	5	∈	∈	PROPN
ejpam-3229	436	6	e.	e.	NOUN
ejpam-3229	436	7	we	we	PRON
ejpam-3229	436	8	claim	claim	VERB
ejpam-3229	436	9	that	that	SCONJ
ejpam-3229	436	10	for	for	ADP
ejpam-3229	436	11	every	every	DET
ejpam-3229	436	12	f	f	PROPN
ejpam-3229	436	13	∈	∈	PROPN
ejpam-3229	436	14	homs	hom	NOUN
ejpam-3229	436	15	(	(	PUNCT
ejpam-3229	436	16	α	α	PROPN
ejpam-3229	436	17	(	(	PUNCT
ejpam-3229	436	18	m	m	NOUN
ejpam-3229	436	19	)	)	PUNCT
ejpam-3229	436	20	,	,	PUNCT
ejpam-3229	436	21	m	m	PROPN
ejpam-3229	436	22	)	)	PUNCT
ejpam-3229	436	23	.	.	PUNCT
ejpam-3229	437	1	we	we	PRON
ejpam-3229	437	2	can	can	AUX
ejpam-3229	437	3	define	define	VERB
ejpam-3229	437	4	a	a	DET
ejpam-3229	437	5	unique	unique	ADJ
ejpam-3229	437	6	f	f	NOUN
ejpam-3229	437	7	:	:	PUNCT
ejpam-3229	437	8	αe	αe	X
ejpam-3229	437	9	→	→	SYM
ejpam-3229	437	10	e	e	X
ejpam-3229	437	11	by	by	ADP
ejpam-3229	437	12	f	f	PROPN
ejpam-3229	437	13	(	(	PUNCT
ejpam-3229	437	14	αu	αu	NOUN
ejpam-3229	437	15	)	)	PUNCT
ejpam-3229	437	16	=	=	SYM
ejpam-3229	437	17	fαu	fαu	NOUN
ejpam-3229	437	18	,	,	PUNCT
ejpam-3229	437	19	for	for	ADP
ejpam-3229	437	20	all	all	DET
ejpam-3229	437	21	u	u	PROPN
ejpam-3229	437	22	∈	∈	PROPN
ejpam-3229	437	23	e.	e.	PROPN
ejpam-3229	437	24	also	also	ADV
ejpam-3229	437	25	we	we	PRON
ejpam-3229	437	26	can	can	AUX
ejpam-3229	437	27	see	see	VERB
ejpam-3229	437	28	that	that	DET
ejpam-3229	437	29	ker	ker	PROPN
ejpam-3229	437	30	f	f	X
ejpam-3229	437	31	(	(	PUNCT
ejpam-3229	437	32	α	α	X
ejpam-3229	437	33	)	)	PUNCT
ejpam-3229	437	34	⊃	⊃	PROPN
ejpam-3229	437	35	kerα	kerα	ADJ
ejpam-3229	437	36	.	.	PUNCT
ejpam-3229	438	1	indeed	indeed	ADV
ejpam-3229	438	2	,	,	PUNCT
ejpam-3229	438	3	for	for	ADP
ejpam-3229	438	4	(	(	PUNCT
ejpam-3229	438	5	x	x	NOUN
ejpam-3229	438	6	,	,	PUNCT
ejpam-3229	438	7	y	y	NOUN
ejpam-3229	438	8	)	)	PUNCT
ejpam-3229	438	9	∈	∈	PROPN
ejpam-3229	438	10	kerα	kerα	NOUN
ejpam-3229	438	11	we	we	PRON
ejpam-3229	438	12	have	have	VERB
ejpam-3229	438	13	α(x	α(x	NOUN
ejpam-3229	438	14	)	)	PUNCT
ejpam-3229	438	15	=	=	SYM
ejpam-3229	438	16	α(y	α(y	NOUN
ejpam-3229	438	17	)	)	PUNCT
ejpam-3229	438	18	,	,	PUNCT
ejpam-3229	438	19	which	which	PRON
ejpam-3229	438	20	implies	imply	VERB
ejpam-3229	438	21	fα(x	fα(x	NOUN
ejpam-3229	438	22	)	)	PUNCT
ejpam-3229	438	23	=	=	SYM
ejpam-3229	438	24	fα(y	fα(y	X
ejpam-3229	438	25	)	)	PUNCT
ejpam-3229	438	26	and	and	CCONJ
ejpam-3229	438	27	therefore	therefore	ADV
ejpam-3229	438	28	f	f	X
ejpam-3229	438	29	(	(	PUNCT
ejpam-3229	438	30	α)(x	α)(x	PROPN
ejpam-3229	438	31	)	)	PUNCT
ejpam-3229	438	32	=	=	SYM
ejpam-3229	439	1	f	f	PROPN
ejpam-3229	439	2	(	(	PUNCT
ejpam-3229	439	3	α)(y	α)(y	PROPN
ejpam-3229	439	4	)	)	PUNCT
ejpam-3229	439	5	i.e.(x	i.e.(x	PROPN
ejpam-3229	439	6	,	,	PUNCT
ejpam-3229	439	7	y	y	NOUN
ejpam-3229	439	8	)	)	PUNCT
ejpam-3229	439	9	∈	∈	NOUN
ejpam-3229	439	10	kerf	kerf	NOUN
ejpam-3229	439	11	(	(	PUNCT
ejpam-3229	439	12	α	α	NOUN
ejpam-3229	439	13	)	)	PUNCT
ejpam-3229	439	14	.	.	PUNCT
ejpam-3229	440	1	hence	hence	ADV
ejpam-3229	440	2	we	we	PRON
ejpam-3229	440	3	can	can	AUX
ejpam-3229	440	4	define	define	VERB
ejpam-3229	440	5	a	a	DET
ejpam-3229	440	6	map	map	NOUN
ejpam-3229	440	7	φ	φ	NOUN
ejpam-3229	440	8	:	:	PUNCT
ejpam-3229	440	9	homs(α	homs(α	VERB
ejpam-3229	440	10	(	(	PUNCT
ejpam-3229	440	11	m	m	NOUN
ejpam-3229	440	12	)	)	PUNCT
ejpam-3229	440	13	,	,	PUNCT
ejpam-3229	440	14	m)→	m)→	VERB
ejpam-3229	440	15	homs(αe	homs(αe	NOUN
ejpam-3229	440	16	,	,	PUNCT
ejpam-3229	440	17	e	e	NOUN
ejpam-3229	440	18	)	)	PUNCT
ejpam-3229	440	19	as	as	ADP
ejpam-3229	440	20	φ(f	φ(f	X
ejpam-3229	440	21	)	)	PUNCT
ejpam-3229	441	1	=	=	VERB
ejpam-3229	441	2	f.	f.	NOUN
ejpam-3229	441	3	we	we	PRON
ejpam-3229	441	4	will	will	AUX
ejpam-3229	441	5	show	show	VERB
ejpam-3229	441	6	that	that	SCONJ
ejpam-3229	441	7	φ	φ	PROPN
ejpam-3229	441	8	is	be	AUX
ejpam-3229	441	9	the	the	DET
ejpam-3229	441	10	required	require	VERB
ejpam-3229	441	11	one	one	NUM
ejpam-3229	441	12	-	-	PUNCT
ejpam-3229	441	13	one	one	NUM
ejpam-3229	441	14	correspondence	correspondence	NOUN
ejpam-3229	441	15	.	.	PUNCT
ejpam-3229	442	1	let	let	VERB
ejpam-3229	442	2	us	we	PRON
ejpam-3229	442	3	begin	begin	VERB
ejpam-3229	442	4	by	by	ADP
ejpam-3229	442	5	proving	prove	VERB
ejpam-3229	442	6	that	that	SCONJ
ejpam-3229	442	7	φ	φ	PROPN
ejpam-3229	442	8	is	be	AUX
ejpam-3229	442	9	well	well	ADV
ejpam-3229	442	10	defined	define	VERB
ejpam-3229	442	11	.	.	PUNCT
ejpam-3229	443	1	let	let	VERB
ejpam-3229	443	2	f	f	X
ejpam-3229	443	3	,	,	PUNCT
ejpam-3229	443	4	f	f	PROPN
ejpam-3229	443	5	′	′	NUM
ejpam-3229	443	6	∈	∈	PROPN
ejpam-3229	443	7	homs(α	homs(α	NOUN
ejpam-3229	443	8	(	(	PUNCT
ejpam-3229	443	9	m	m	NOUN
ejpam-3229	443	10	)	)	PUNCT
ejpam-3229	443	11	,	,	PUNCT
ejpam-3229	443	12	m	m	NOUN
ejpam-3229	443	13	)	)	PUNCT
ejpam-3229	443	14	such	such	ADJ
ejpam-3229	443	15	that	that	SCONJ
ejpam-3229	443	16	f	f	PROPN
ejpam-3229	443	17	=	=	SYM
ejpam-3229	443	18	f	f	PROPN
ejpam-3229	443	19	′.	′.	NOUN
ejpam-3229	443	20	then	then	ADV
ejpam-3229	443	21	fαu	fαu	VERB
ejpam-3229	443	22	=	=	SYM
ejpam-3229	443	23	f	f	PROPN
ejpam-3229	443	24	′αu	′αu	NOUN
ejpam-3229	443	25	and	and	CCONJ
ejpam-3229	443	26	so	so	ADV
ejpam-3229	443	27	f	f	PROPN
ejpam-3229	443	28	(	(	PUNCT
ejpam-3229	443	29	αu	αu	NOUN
ejpam-3229	443	30	)	)	PUNCT
ejpam-3229	443	31	=	=	SYM
ejpam-3229	443	32	f	f	PROPN
ejpam-3229	443	33	′(αu),for	′(αu),for	VERB
ejpam-3229	443	34	all	all	PRON
ejpam-3229	443	35	αu	αu	ADP
ejpam-3229	443	36	∈	∈	PROPN
ejpam-3229	443	37	αe	αe	NOUN
ejpam-3229	443	38	.	.	PROPN
ejpam-3229	444	1	hence	hence	ADV
ejpam-3229	444	2	f	f	PROPN
ejpam-3229	444	3	=	=	SYM
ejpam-3229	444	4	f	f	PROPN
ejpam-3229	444	5	′	′	NUM
ejpam-3229	444	6	i.e.	i.e.	X
ejpam-3229	444	7	φ(f	φ(f	PROPN
ejpam-3229	444	8	)	)	PUNCT
ejpam-3229	445	1	=	=	SYM
ejpam-3229	445	2	φ(f	φ(f	PROPN
ejpam-3229	445	3	′	′	NUM
ejpam-3229	445	4	)	)	PUNCT
ejpam-3229	445	5	.	.	PUNCT
ejpam-3229	446	1	to	to	PART
ejpam-3229	446	2	show	show	VERB
ejpam-3229	446	3	that	that	SCONJ
ejpam-3229	446	4	φ	φ	PROPN
ejpam-3229	446	5	is	be	AUX
ejpam-3229	446	6	1	1	NUM
ejpam-3229	446	7	-	-	SYM
ejpam-3229	446	8	1	1	NUM
ejpam-3229	446	9	.	.	PUNCT
ejpam-3229	447	1	let	let	VERB
ejpam-3229	447	2	f	f	X
ejpam-3229	447	3	,	,	PUNCT
ejpam-3229	447	4	f	f	PROPN
ejpam-3229	447	5	′	′	NUM
ejpam-3229	447	6	∈	∈	PROPN
ejpam-3229	447	7	homs(α	homs(α	NOUN
ejpam-3229	447	8	(	(	PUNCT
ejpam-3229	447	9	m	m	NOUN
ejpam-3229	447	10	)	)	PUNCT
ejpam-3229	447	11	,	,	PUNCT
ejpam-3229	447	12	m	m	NOUN
ejpam-3229	447	13	)	)	PUNCT
ejpam-3229	447	14	such	such	ADJ
ejpam-3229	447	15	that	that	SCONJ
ejpam-3229	447	16	φ(f	φ(f	PROPN
ejpam-3229	447	17	)	)	PUNCT
ejpam-3229	448	1	=	=	SYM
ejpam-3229	448	2	φ(f	φ(f	PROPN
ejpam-3229	448	3	′	′	NOUN
ejpam-3229	448	4	)	)	PUNCT
ejpam-3229	448	5	i.e.	i.e.	X
ejpam-3229	448	6	f	f	X
ejpam-3229	448	7	=	=	SYM
ejpam-3229	448	8	f	f	PROPN
ejpam-3229	448	9	′.	′.	NOUN
ejpam-3229	448	10	this	this	PRON
ejpam-3229	448	11	implies	imply	VERB
ejpam-3229	448	12	that	that	SCONJ
ejpam-3229	448	13	f	f	PROPN
ejpam-3229	448	14	(	(	PUNCT
ejpam-3229	448	15	αu	αu	NOUN
ejpam-3229	448	16	)	)	PUNCT
ejpam-3229	448	17	=	=	SYM
ejpam-3229	448	18	f	f	X
ejpam-3229	448	19	′(αu	′(αu	NOUN
ejpam-3229	448	20	)	)	PUNCT
ejpam-3229	448	21	,	,	PUNCT
ejpam-3229	448	22	for	for	ADP
ejpam-3229	448	23	all	all	DET
ejpam-3229	448	24	αu	αu	ADP
ejpam-3229	448	25	∈	∈	PROPN
ejpam-3229	448	26	αe	αe	PROPN
ejpam-3229	448	27	.	.	PROPN
ejpam-3229	448	28	therefore	therefore	ADV
ejpam-3229	448	29	fαu	fαu	AUX
ejpam-3229	448	30	=	=	SYM
ejpam-3229	448	31	f	f	PROPN
ejpam-3229	448	32	′αu	′αu	NOUN
ejpam-3229	448	33	,	,	PUNCT
ejpam-3229	448	34	for	for	ADP
ejpam-3229	448	35	all	all	DET
ejpam-3229	448	36	u	u	PROPN
ejpam-3229	448	37	∈	∈	PROPN
ejpam-3229	448	38	e.	e.	PROPN
ejpam-3229	448	39	in	in	ADP
ejpam-3229	448	40	particular	particular	ADJ
ejpam-3229	448	41	for	for	ADP
ejpam-3229	448	42	u	u	X
ejpam-3229	448	43	=	=	PROPN
ejpam-3229	448	44	i	i	PRON
ejpam-3229	448	45	m	m	VERB
ejpam-3229	448	46	,	,	PUNCT
ejpam-3229	448	47	it	it	PRON
ejpam-3229	448	48	follows	follow	VERB
ejpam-3229	448	49	that	that	PRON
ejpam-3229	448	50	fα	fα	ADP
ejpam-3229	448	51	=	=	SYM
ejpam-3229	448	52	f	f	PROPN
ejpam-3229	448	53	′α	′α	NOUN
ejpam-3229	448	54	and	and	CCONJ
ejpam-3229	448	55	hence	hence	ADV
ejpam-3229	448	56	f(α(m	f(α(m	NOUN
ejpam-3229	448	57	)	)	PUNCT
ejpam-3229	448	58	)	)	PUNCT
ejpam-3229	449	1	=	=	SYM
ejpam-3229	449	2	f	f	PROPN
ejpam-3229	449	3	′(α(m	′(α(m	NOUN
ejpam-3229	449	4	)	)	PUNCT
ejpam-3229	449	5	)	)	PUNCT
ejpam-3229	449	6	for	for	ADP
ejpam-3229	449	7	all	all	PRON
ejpam-3229	449	8	α(m	α(m	PROPN
ejpam-3229	449	9	)	)	PUNCT
ejpam-3229	449	10	∈	∈	PROPN
ejpam-3229	449	11	α	α	PROPN
ejpam-3229	449	12	(	(	PUNCT
ejpam-3229	449	13	m	m	NOUN
ejpam-3229	449	14	)	)	PUNCT
ejpam-3229	449	15	,	,	PUNCT
ejpam-3229	449	16	and	and	CCONJ
ejpam-3229	449	17	f	f	X
ejpam-3229	449	18	=	=	SYM
ejpam-3229	449	19	f	f	PROPN
ejpam-3229	449	20	′.	′.	NOUN
ejpam-3229	449	21	hence	hence	ADV
ejpam-3229	449	22	φ	φ	PROPN
ejpam-3229	449	23	is	be	AUX
ejpam-3229	449	24	1	1	NUM
ejpam-3229	449	25	-	-	SYM
ejpam-3229	449	26	1	1	NUM
ejpam-3229	449	27	.	.	PUNCT
ejpam-3229	449	28	to	to	PART
ejpam-3229	449	29	see	see	VERB
ejpam-3229	449	30	surjectivity	surjectivity	NOUN
ejpam-3229	449	31	,	,	PUNCT
ejpam-3229	449	32	let	let	VERB
ejpam-3229	449	33	f	f	PROPN
ejpam-3229	449	34	∈	∈	PROPN
ejpam-3229	449	35	homs	hom	NOUN
ejpam-3229	449	36	(	(	PUNCT
ejpam-3229	449	37	αe	αe	NOUN
ejpam-3229	449	38	,	,	PUNCT
ejpam-3229	449	39	e	e	NOUN
ejpam-3229	449	40	)	)	PUNCT
ejpam-3229	449	41	.	.	PUNCT
ejpam-3229	450	1	define	define	VERB
ejpam-3229	450	2	f(αm(m	f(αm(m	NOUN
ejpam-3229	450	3	)	)	PUNCT
ejpam-3229	450	4	)	)	PUNCT
ejpam-3229	451	1	=	=	SYM
ejpam-3229	451	2	f	f	PROPN
ejpam-3229	451	3	(	(	PUNCT
ejpam-3229	451	4	α)(m	α)(m	NUM
ejpam-3229	451	5	)	)	PUNCT
ejpam-3229	451	6	for	for	ADP
ejpam-3229	451	7	all	all	DET
ejpam-3229	451	8	m	m	PROPN
ejpam-3229	451	9	∈	∈	NOUN
ejpam-3229	451	10	m.	m.	NOUN
ejpam-3229	451	11	clearly	clearly	ADV
ejpam-3229	451	12	f	f	PROPN
ejpam-3229	451	13	is	be	AUX
ejpam-3229	451	14	s	s	NOUN
ejpam-3229	451	15	-	-	PUNCT
ejpam-3229	451	16	homomorphism	homomorphism	NOUN
ejpam-3229	451	17	and	and	CCONJ
ejpam-3229	451	18	φ(f	φ(f	PROPN
ejpam-3229	451	19	)	)	PUNCT
ejpam-3229	452	1	=	=	SYM
ejpam-3229	452	2	f.	f.	PROPN
ejpam-3229	452	3	thus	thus	ADV
ejpam-3229	452	4	we	we	PRON
ejpam-3229	452	5	established	establish	VERB
ejpam-3229	452	6	the	the	DET
ejpam-3229	452	7	1	1	NUM
ejpam-3229	452	8	-	-	SYM
ejpam-3229	452	9	1	1	NUM
ejpam-3229	452	10	correspondence	correspondence	NOUN
ejpam-3229	452	11	.	.	PUNCT
ejpam-3229	453	1	theorem	theorem	VERB
ejpam-3229	453	2	19	19	NUM
ejpam-3229	453	3	.	.	PUNCT
ejpam-3229	454	1	for	for	ADP
ejpam-3229	454	2	a	a	DET
ejpam-3229	454	3	semi	semi	ADJ
ejpam-3229	454	4	-	-	ADJ
ejpam-3229	454	5	projective	projective	ADJ
ejpam-3229	454	6	s	s	NOUN
ejpam-3229	454	7	-	-	NOUN
ejpam-3229	454	8	act	act	NOUN
ejpam-3229	454	9	and	and	CCONJ
ejpam-3229	454	10	α	α	PRON
ejpam-3229	454	11	∈	∈	PROPN
ejpam-3229	454	12	e	e	NOUN
ejpam-3229	454	13	,	,	PUNCT
ejpam-3229	454	14	α	α	PROPN
ejpam-3229	454	15	(	(	PUNCT
ejpam-3229	454	16	m	m	NOUN
ejpam-3229	454	17	)	)	PUNCT
ejpam-3229	454	18	is	be	AUX
ejpam-3229	454	19	simple	simple	ADJ
ejpam-3229	454	20	.	.	PUNCT
ejpam-3229	455	1	converse	converse	NOUN
ejpam-3229	455	2	is	be	AUX
ejpam-3229	455	3	true	true	ADJ
ejpam-3229	455	4	for	for	ADP
ejpam-3229	455	5	those	those	DET
ejpam-3229	455	6	s	s	NOUN
ejpam-3229	455	7	-	-	PUNCT
ejpam-3229	455	8	acts	act	NOUN
ejpam-3229	455	9	for	for	ADP
ejpam-3229	455	10	which	which	PRON
ejpam-3229	455	11	ms	ms	NOUN
ejpam-3229	455	12	is	be	AUX
ejpam-3229	455	13	m	m	NOUN
ejpam-3229	455	14	-	-	NOUN
ejpam-3229	455	15	cyclic	cyclic	ADJ
ejpam-3229	455	16	for	for	ADP
ejpam-3229	455	17	all	all	DET
ejpam-3229	455	18	m	m	NOUN
ejpam-3229	455	19	∈m	∈m	NOUN
ejpam-3229	455	20	.	.	PUNCT
ejpam-3229	456	1	proof	proof	NOUN
ejpam-3229	456	2	.	.	PUNCT
ejpam-3229	457	1	let	let	VERB
ejpam-3229	457	2	α	α	PRON
ejpam-3229	457	3	(	(	PUNCT
ejpam-3229	457	4	m	m	NOUN
ejpam-3229	457	5	)	)	PUNCT
ejpam-3229	457	6	be	be	AUX
ejpam-3229	457	7	simple	simple	ADJ
ejpam-3229	457	8	.	.	PUNCT
ejpam-3229	458	1	suppose	suppose	VERB
ejpam-3229	458	2	contrary	contrary	ADV
ejpam-3229	458	3	that	that	SCONJ
ejpam-3229	458	4	αe	αe	NOUN
ejpam-3229	458	5	is	be	AUX
ejpam-3229	458	6	not	not	PART
ejpam-3229	458	7	simple	simple	ADJ
ejpam-3229	458	8	,	,	PUNCT
ejpam-3229	458	9	so	so	SCONJ
ejpam-3229	458	10	there	there	PRON
ejpam-3229	458	11	exists	exist	VERB
ejpam-3229	458	12	γ	γ	PROPN
ejpam-3229	458	13	∈	∈	PROPN
ejpam-3229	458	14	e	e	NOUN
ejpam-3229	458	15	such	such	ADJ
ejpam-3229	458	16	that	that	SCONJ
ejpam-3229	458	17	θ	θ	PROPN
ejpam-3229	458	18	6=	6=	NUM
ejpam-3229	458	19	αγe	αγe	X
ejpam-3229	458	20	(	(	PUNCT
ejpam-3229	458	21	αe	αe	NOUN
ejpam-3229	458	22	,	,	PUNCT
ejpam-3229	458	23	and	and	CCONJ
ejpam-3229	458	24	therefore	therefore	ADV
ejpam-3229	458	25	αγ	αγ	PROPN
ejpam-3229	458	26	(	(	PUNCT
ejpam-3229	458	27	m	m	NOUN
ejpam-3229	458	28	)	)	PUNCT
ejpam-3229	458	29	(	(	PUNCT
ejpam-3229	458	30	α	α	PROPN
ejpam-3229	458	31	(	(	PUNCT
ejpam-3229	458	32	m	m	NOUN
ejpam-3229	458	33	)	)	PUNCT
ejpam-3229	458	34	contradiction	contradiction	NOUN
ejpam-3229	458	35	.	.	PUNCT
ejpam-3229	459	1	hence	hence	ADV
ejpam-3229	459	2	αe	αe	PROPN
ejpam-3229	459	3	is	be	AUX
ejpam-3229	459	4	simple	simple	ADJ
ejpam-3229	459	5	.	.	PUNCT
ejpam-3229	460	1	conversely	conversely	ADV
ejpam-3229	460	2	assume	assume	VERB
ejpam-3229	460	3	that	that	SCONJ
ejpam-3229	460	4	αe	αe	NOUN
ejpam-3229	460	5	is	be	AUX
ejpam-3229	460	6	simple	simple	ADJ
ejpam-3229	460	7	and	and	CCONJ
ejpam-3229	460	8	m	m	NOUN
ejpam-3229	460	9	is	be	AUX
ejpam-3229	460	10	,	,	PUNCT
ejpam-3229	460	11	as	as	SCONJ
ejpam-3229	460	12	mentioned	mention	VERB
ejpam-3229	460	13	in	in	ADP
ejpam-3229	460	14	the	the	DET
ejpam-3229	460	15	theorem	theorem	NOUN
ejpam-3229	460	16	.	.	PUNCT
ejpam-3229	461	1	let	let	VERB
ejpam-3229	461	2	ms	ms	NOUN
ejpam-3229	461	3	=	=	PROPN
ejpam-3229	461	4	γ	γ	X
ejpam-3229	461	5	(	(	PUNCT
ejpam-3229	461	6	m	m	PROPN
ejpam-3229	461	7	)	)	PUNCT
ejpam-3229	461	8	,	,	PUNCT
ejpam-3229	461	9	γ	γ	PROPN
ejpam-3229	461	10	∈	∈	PROPN
ejpam-3229	461	11	e.	e.	PROPN
ejpam-3229	461	12	now	now	ADV
ejpam-3229	461	13	θ	θ	PROPN
ejpam-3229	461	14	6=	6=	ADP
ejpam-3229	461	15	αγ	αγ	PROPN
ejpam-3229	461	16	(	(	PUNCT
ejpam-3229	461	17	m	m	NOUN
ejpam-3229	461	18	)	)	PUNCT
ejpam-3229	461	19	(	(	PUNCT
ejpam-3229	461	20	α	α	PROPN
ejpam-3229	461	21	(	(	PUNCT
ejpam-3229	461	22	m	m	NOUN
ejpam-3229	461	23	)	)	PUNCT
ejpam-3229	461	24	→	→	SYM
ejpam-3229	461	25	θ	θ	PROPN
ejpam-3229	461	26	6=	6=	NUM
ejpam-3229	461	27	αγe	αγe	NOUN
ejpam-3229	461	28	(	(	PUNCT
ejpam-3229	461	29	αe	αe	NUM
ejpam-3229	461	30	contradiction	contradiction	NOUN
ejpam-3229	461	31	.	.	PUNCT
ejpam-3229	462	1	hence	hence	ADV
ejpam-3229	462	2	the	the	DET
ejpam-3229	462	3	result	result	NOUN
ejpam-3229	462	4	.	.	PUNCT
ejpam-3229	463	1	theorem	theorem	ADJ
ejpam-3229	463	2	20	20	NUM
ejpam-3229	463	3	.	.	PUNCT
ejpam-3229	464	1	if	if	SCONJ
ejpam-3229	464	2	n	n	NUM
ejpam-3229	464	3	=	=	PROPN
ejpam-3229	464	4	⊕	⊕	PROPN
ejpam-3229	464	5	i∈i	i∈i	ADJ
ejpam-3229	464	6	ni	ni	PROPN
ejpam-3229	464	7	is	be	AUX
ejpam-3229	464	8	quasi	quasi	ADJ
ejpam-3229	464	9	-	-	ADJ
ejpam-3229	464	10	principally	principally	ADV
ejpam-3229	464	11	projective	projective	ADJ
ejpam-3229	464	12	(	(	PUNCT
ejpam-3229	464	13	respectively	respectively	ADV
ejpam-3229	464	14	semi	semi	ADJ
ejpam-3229	464	15	-	-	ADJ
ejpam-3229	464	16	projective	projective	ADJ
ejpam-3229	464	17	)	)	PUNCT
ejpam-3229	464	18	then	then	ADV
ejpam-3229	464	19	each	each	DET
ejpam-3229	464	20	ni	ni	PROPN
ejpam-3229	464	21	is	be	AUX
ejpam-3229	464	22	quasi	quasi	ADJ
ejpam-3229	464	23	-	-	ADJ
ejpam-3229	464	24	principally	principally	ADV
ejpam-3229	464	25	projective	projective	ADJ
ejpam-3229	464	26	(	(	PUNCT
ejpam-3229	464	27	respectively	respectively	ADV
ejpam-3229	464	28	semi	semi	ADJ
ejpam-3229	464	29	-	-	ADJ
ejpam-3229	464	30	projective	projective	ADJ
ejpam-3229	464	31	)	)	PUNCT
ejpam-3229	464	32	,	,	PUNCT
ejpam-3229	464	33	for	for	ADP
ejpam-3229	464	34	all	all	DET
ejpam-3229	464	35	i	i	PRON
ejpam-3229	464	36	∈	∈	PROPN
ejpam-3229	464	37	i.	i.	NOUN
ejpam-3229	464	38	references	reference	VERB
ejpam-3229	464	39	443	443	NUM
ejpam-3229	464	40	references	reference	NOUN
ejpam-3229	464	41	[	[	X
ejpam-3229	464	42	1	1	NUM
ejpam-3229	464	43	]	]	PUNCT
ejpam-3229	464	44	j.	j.	PROPN
ejpam-3229	464	45	ahsan	ahsan	PROPN
ejpam-3229	464	46	,	,	PUNCT
ejpam-3229	464	47	l.	l.	PROPN
ejpam-3229	464	48	zhongkui	zhongkui	PROPN
ejpam-3229	464	49	,	,	PUNCT
ejpam-3229	464	50	a	a	DET
ejpam-3229	464	51	homological	homological	ADJ
ejpam-3229	464	52	approach	approach	NOUN
ejpam-3229	464	53	to	to	ADP
ejpam-3229	464	54	the	the	DET
ejpam-3229	464	55	theory	theory	NOUN
ejpam-3229	464	56	of	of	ADP
ejpam-3229	464	57	monoids	monoid	NOUN
ejpam-3229	464	58	,	,	PUNCT
ejpam-3229	464	59	science	science	NOUN
ejpam-3229	464	60	press	press	PROPN
ejpam-3229	464	61	bejing	bejing	PROPN
ejpam-3229	464	62	.	.	PUNCT
ejpam-3229	465	1	[	[	X
ejpam-3229	465	2	2	2	X
ejpam-3229	465	3	]	]	PUNCT
ejpam-3229	465	4	j.	j.	PROPN
ejpam-3229	465	5	ahsan	ahsan	PROPN
ejpam-3229	465	6	,	,	PUNCT
ejpam-3229	465	7	m.	m.	PROPN
ejpam-3229	465	8	f.	f.	PROPN
ejpam-3229	465	9	khan	khan	PROPN
ejpam-3229	465	10	,	,	PUNCT
ejpam-3229	465	11	m.	m.	NOUN
ejpam-3229	465	12	shabir	shabir	PROPN
ejpam-3229	465	13	and	and	CCONJ
ejpam-3229	465	14	m.	m.	PROPN
ejpam-3229	465	15	takahashi	takahashi	PROPN
ejpam-3229	465	16	,	,	PUNCT
ejpam-3229	465	17	characterizations	characterization	NOUN
ejpam-3229	465	18	of	of	ADP
ejpam-3229	465	19	monoids	monoid	NOUN
ejpam-3229	465	20	by	by	ADP
ejpam-3229	465	21	p	p	X
ejpam-3229	465	22	-	-	PUNCT
ejpam-3229	465	23	injective	injective	ADJ
ejpam-3229	465	24	and	and	CCONJ
ejpam-3229	465	25	normal	normal	ADJ
ejpam-3229	465	26	s	s	NOUN
ejpam-3229	465	27	-	-	NOUN
ejpam-3229	465	28	system	system	NOUN
ejpam-3229	465	29	,	,	PUNCT
ejpam-3229	465	30	kobe	kobe	PROPN
ejpam-3229	465	31	j.	j.	PROPN
ejpam-3229	465	32	math	math	PROPN
ejpam-3229	465	33	,	,	PUNCT
ejpam-3229	465	34	(	(	PUNCT
ejpam-3229	465	35	1991)8:173	1991)8:173	NUM
ejpam-3229	465	36	-	-	SYM
ejpam-3229	465	37	192	192	NUM
ejpam-3229	465	38	.	.	PUNCT
ejpam-3229	466	1	[	[	X
ejpam-3229	466	2	3	3	X
ejpam-3229	466	3	]	]	PUNCT
ejpam-3229	466	4	c.	c.	PROPN
ejpam-3229	466	5	s.	s.	PROPN
ejpam-3229	466	6	johnson	johnson	PROPN
ejpam-3229	466	7	,	,	PUNCT
ejpam-3229	466	8	jr	jr	PROPN
ejpam-3229	466	9	.	.	PROPN
ejpam-3229	466	10	and	and	CCONJ
ejpam-3229	466	11	f.r	f.r	PROPN
ejpam-3229	466	12	.	.	PROPN
ejpam-3229	466	13	mcmorris	mcmorris	PROPN
ejpam-3229	466	14	:	:	PUNCT
ejpam-3229	466	15	completely	completely	ADV
ejpam-3229	466	16	cyclic	cyclic	ADJ
ejpam-3229	466	17	injective	injective	ADJ
ejpam-3229	466	18	semilattices	semilattice	NOUN
ejpam-3229	466	19	,	,	PUNCT
ejpam-3229	466	20	proc	proc	NOUN
ejpam-3229	466	21	.	.	PUNCT
ejpam-3229	467	1	amer	amer	PROPN
ejpam-3229	467	2	.	.	PUNCT
ejpam-3229	467	3	math	math	PROPN
ejpam-3229	467	4	.	.	PUNCT
ejpam-3229	468	1	soc	soc	PROPN
ejpam-3229	468	2	36(1972	36(1972	NUM
ejpam-3229	468	3	)	)	PUNCT
ejpam-3229	468	4	,	,	PUNCT
ejpam-3229	468	5	385	385	NUM
ejpam-3229	468	6	-	-	SYM
ejpam-3229	468	7	388	388	NUM
ejpam-3229	468	8	.	.	PUNCT
ejpam-3229	469	1	[	[	X
ejpam-3229	469	2	4	4	X
ejpam-3229	469	3	]	]	PUNCT
ejpam-3229	469	4	fakhruddin	fakhruddin	ADJ
ejpam-3229	469	5	s.m	s.m	PROPN
ejpam-3229	469	6	.	.	PROPN
ejpam-3229	469	7	,	,	PUNCT
ejpam-3229	469	8	on	on	ADP
ejpam-3229	469	9	the	the	DET
ejpam-3229	469	10	category	category	NOUN
ejpam-3229	469	11	of	of	ADP
ejpam-3229	469	12	s	s	NOUN
ejpam-3229	469	13	-	-	NOUN
ejpam-3229	469	14	posets	poset	NOUN
ejpam-3229	469	15	.	.	PUNCT
ejpam-3229	470	1	acta	acta	PROPN
ejpam-3229	470	2	sci	sci	PROPN
ejpam-3229	470	3	.	.	PROPN
ejpam-3229	470	4	math	math	PROPN
ejpam-3229	470	5	.	.	PUNCT
ejpam-3229	470	6	,	,	PUNCT
ejpam-3229	470	7	1988	1988	NUM
ejpam-3229	470	8	,	,	PUNCT
ejpam-3229	470	9	52	52	NUM
ejpam-3229	470	10	,	,	PUNCT
ejpam-3229	470	11	85	85	NUM
ejpam-3229	470	12	-	-	SYM
ejpam-3229	470	13	92	92	NUM
ejpam-3229	470	14	.	.	PUNCT
ejpam-3229	471	1	[	[	X
ejpam-3229	471	2	5	5	X
ejpam-3229	471	3	]	]	X
ejpam-3229	471	4	c.s	c.s	PROPN
ejpam-3229	471	5	.	.	PROPN
ejpam-3229	471	6	johnson	johnson	PROPN
ejpam-3229	471	7	,	,	PUNCT
ejpam-3229	471	8	j.r	j.r	PROPN
ejpam-3229	471	9	.	.	PROPN
ejpam-3229	471	10	,	,	PUNCT
ejpam-3229	471	11	mcmorris	mcmorris	PROPN
ejpam-3229	471	12	f.r	f.r	PROPN
ejpam-3229	471	13	.	.	PROPN
ejpam-3229	471	14	,	,	PUNCT
ejpam-3229	471	15	injective	injective	ADJ
ejpam-3229	471	16	hulls	hull	NOUN
ejpam-3229	471	17	on	on	ADP
ejpam-3229	471	18	certain	certain	ADJ
ejpam-3229	471	19	s	s	NOUN
ejpam-3229	471	20	-	-	NOUN
ejpam-3229	471	21	systems	system	NOUN
ejpam-3229	471	22	over	over	ADP
ejpam-3229	471	23	a	a	DET
ejpam-3229	471	24	semilattice	semilattice	NOUN
ejpam-3229	471	25	.	.	PUNCT
ejpam-3229	472	1	proc	proc	PROPN
ejpam-3229	472	2	.	.	PUNCT
ejpam-3229	473	1	amer	amer	PROPN
ejpam-3229	473	2	.	.	PUNCT
ejpam-3229	473	3	math	math	PROPN
ejpam-3229	473	4	.	.	PUNCT
ejpam-3229	474	1	soc	soc	PROPN
ejpam-3229	474	2	.	.	PROPN
ejpam-3229	474	3	,	,	PUNCT
ejpam-3229	474	4	1972	1972	NUM
ejpam-3229	474	5	,	,	PUNCT
ejpam-3229	474	6	32	32	NUM
ejpam-3229	474	7	,	,	PUNCT
ejpam-3229	474	8	371	371	NUM
ejpam-3229	474	9	-	-	SYM
ejpam-3229	474	10	375	375	NUM
ejpam-3229	474	11	.	.	PUNCT
ejpam-3229	475	1	[	[	X
ejpam-3229	475	2	6	6	NUM
ejpam-3229	475	3	]	]	PUNCT
ejpam-3229	475	4	j.	j.	PROPN
ejpam-3229	475	5	fountain	fountain	PROPN
ejpam-3229	475	6	,	,	PUNCT
ejpam-3229	475	7	a	a	DET
ejpam-3229	475	8	class	class	NOUN
ejpam-3229	475	9	of	of	ADP
ejpam-3229	475	10	right	right	ADJ
ejpam-3229	475	11	pp	pp	ADP
ejpam-3229	475	12	monoids	monoids	PROPN
ejpam-3229	475	13	,	,	PUNCT
ejpam-3229	475	14	quart	quart	NOUN
ejpam-3229	475	15	.	.	PUNCT
ejpam-3229	476	1	j.	j.	PROPN
ejpam-3229	476	2	math	math	PROPN
ejpam-3229	476	3	.	.	PUNCT
ejpam-3229	477	1	oxford	oxford	PROPN
ejpam-3229	477	2	(	(	PUNCT
ejpam-3229	477	3	2	2	NUM
ejpam-3229	477	4	)	)	SYM
ejpam-3229	477	5	28	28	NUM
ejpam-3229	477	6	(	(	PUNCT
ejpam-3229	477	7	1977	1977	NUM
ejpam-3229	477	8	)	)	PUNCT
ejpam-3229	477	9	,	,	PUNCT
ejpam-3229	477	10	285	285	NUM
ejpam-3229	477	11	-	-	SYM
ejpam-3229	477	12	300	300	NUM
ejpam-3229	477	13	[	[	X
ejpam-3229	477	14	7	7	NUM
ejpam-3229	477	15	]	]	X
ejpam-3229	477	16	j.	j.	PROPN
ejpam-3229	477	17	fountain	fountain	PROPN
ejpam-3229	477	18	:	:	PUNCT
ejpam-3229	477	19	completely	completely	ADV
ejpam-3229	477	20	right	right	ADJ
ejpam-3229	477	21	infective	infective	ADJ
ejpam-3229	477	22	semigroups	semigroup	NOUN
ejpam-3229	477	23	,	,	PUNCT
ejpam-3229	477	24	proc	proc	NOUN
ejpam-3229	477	25	.	.	PUNCT
ejpam-3229	478	1	london	london	PROPN
ejpam-3229	478	2	math	math	PROPN
ejpam-3229	478	3	.	.	PUNCT
ejpam-3229	479	1	soc	soc	PROPN
ejpam-3229	479	2	.	.	PUNCT
ejpam-3229	480	1	28(1974	28(1974	NUM
ejpam-3229	480	2	)	)	PUNCT
ejpam-3229	480	3	,	,	PUNCT
ejpam-3229	480	4	28	28	NUM
ejpam-3229	480	5	-	-	SYM
ejpam-3229	480	6	44	44	NUM
ejpam-3229	480	7	.	.	PUNCT
ejpam-3229	481	1	[	[	X
ejpam-3229	481	2	8	8	NUM
ejpam-3229	481	3	]	]	X
ejpam-3229	481	4	j.k	j.k	PROPN
ejpam-3229	481	5	.	.	PROPN
ejpam-3229	481	6	luedeman	luedeman	PROPN
ejpam-3229	481	7	,	,	PUNCT
ejpam-3229	481	8	f.r	f.r	PROPN
ejpam-3229	481	9	.	.	PROPN
ejpam-3229	481	10	mcmorris	mcmorris	PROPN
ejpam-3229	481	11	and	and	CCONJ
ejpam-3229	481	12	s.k	s.k	PROPN
ejpam-3229	481	13	.	.	PROPN
ejpam-3229	481	14	sim	sim	PROPN
ejpam-3229	481	15	,	,	PUNCT
ejpam-3229	481	16	semi	semi	NOUN
ejpam-3229	481	17	-	-	NOUN
ejpam-3229	481	18	groups	group	NOUN
ejpam-3229	481	19	for	for	ADP
ejpam-3229	481	20	which	which	PRON
ejpam-3229	481	21	every	every	DET
ejpam-3229	481	22	totally	totally	ADV
ejpam-3229	481	23	irreducible	irreducible	ADJ
ejpam-3229	481	24	s	s	NOUN
ejpam-3229	481	25	-	-	NOUN
ejpam-3229	481	26	system	system	NOUN
ejpam-3229	481	27	is	be	AUX
ejpam-3229	481	28	injective	injective	ADJ
ejpam-3229	481	29	,	,	PUNCT
ejpam-3229	481	30	comment	comment	NOUN
ejpam-3229	481	31	.	.	PUNCT
ejpam-3229	482	1	math	math	NOUN
ejpam-3229	482	2	.	.	PUNCT
ejpam-3229	483	1	univ	univ	PROPN
ejpam-3229	483	2	.	.	PUNCT
ejpam-3229	484	1	carolinae	carolinae	PROPN
ejpam-3229	484	2	19	19	NUM
ejpam-3229	484	3	(	(	PUNCT
ejpam-3229	484	4	1978	1978	NUM
ejpam-3229	484	5	)	)	PUNCT
ejpam-3229	484	6	,	,	PUNCT
ejpam-3229	484	7	27–35	27–35	NUM
ejpam-3229	484	8	.	.	PUNCT
ejpam-3229	485	1	[	[	X
ejpam-3229	485	2	9	9	NUM
ejpam-3229	485	3	]	]	X
ejpam-3229	485	4	j.j	j.j	PROPN
ejpam-3229	485	5	.	.	PROPN
ejpam-3229	485	6	rotman	rotman	PROPN
ejpam-3229	485	7	.	.	PUNCT
ejpam-3229	486	1	an	an	DET
ejpam-3229	486	2	introduction	introduction	NOUN
ejpam-3229	486	3	to	to	ADP
ejpam-3229	486	4	homological	homological	ADJ
ejpam-3229	486	5	algebra	algebra	NOUN
ejpam-3229	486	6	,	,	PUNCT
ejpam-3229	486	7	academic	academic	ADJ
ejpam-3229	486	8	press	press	NOUN
ejpam-3229	486	9	,	,	PUNCT
ejpam-3229	486	10	new	new	PROPN
ejpam-3229	486	11	york	york	PROPN
ejpam-3229	486	12	(	(	PUNCT
ejpam-3229	486	13	1979	1979	NUM
ejpam-3229	486	14	)	)	PUNCT
ejpam-3229	486	15	.	.	PUNCT
ejpam-3229	487	1	[	[	X
ejpam-3229	487	2	10	10	NUM
ejpam-3229	487	3	]	]	X
ejpam-3229	487	4	schein	schein	PROPN
ejpam-3229	487	5	b.m	b.m	PROPN
ejpam-3229	487	6	.	.	PROPN
ejpam-3229	487	7	injectives	injective	VERB
ejpam-3229	487	8	in	in	ADP
ejpam-3229	487	9	certain	certain	ADJ
ejpam-3229	487	10	classes	class	NOUN
ejpam-3229	487	11	of	of	ADP
ejpam-3229	487	12	semigroups	semigroup	NOUN
ejpam-3229	487	13	.	.	PUNCT
ejpam-3229	488	1	semigroup	semigroup	PROPN
ejpam-3229	488	2	forum	forum	PROPN
ejpam-3229	488	3	,	,	PUNCT
ejpam-3229	488	4	1974	1974	NUM
ejpam-3229	488	5	,	,	PUNCT
ejpam-3229	488	6	9	9	NUM
ejpam-3229	488	7	,	,	PUNCT
ejpam-3229	488	8	159	159	NUM
ejpam-3229	488	9	-	-	SYM
ejpam-3229	488	10	171	171	NUM
ejpam-3229	488	11	.	.	PUNCT
ejpam-3229	489	1	[	[	X
ejpam-3229	489	2	11	11	NUM
ejpam-3229	489	3	]	]	X
ejpam-3229	489	4	p.	p.	NOUN
ejpam-3229	489	5	brathiaume	brathiaume	PROPN
ejpam-3229	489	6	,	,	PUNCT
ejpam-3229	489	7	the	the	DET
ejpam-3229	489	8	injective	injective	ADJ
ejpam-3229	489	9	envelope	envelope	NOUN
ejpam-3229	489	10	of	of	ADP
ejpam-3229	489	11	s	s	NOUN
ejpam-3229	489	12	-	-	PUNCT
ejpam-3229	489	13	acts	act	NOUN
ejpam-3229	489	14	,	,	PUNCT
ejpam-3229	489	15	canad	canad	PROPN
ejpam-3229	489	16	.	.	PUNCT
ejpam-3229	490	1	math	math	NOUN
ejpam-3229	490	2	.	.	PUNCT
ejpam-3229	491	1	bull	bull	PROPN
ejpam-3229	491	2	,	,	PUNCT
ejpam-3229	491	3	(	(	PUNCT
ejpam-3229	491	4	1967)10:261273	1967)10:261273	NUM
ejpam-3229	491	5	.	.	PUNCT
ejpam-3229	492	1	[	[	X
ejpam-3229	492	2	12	12	NUM
ejpam-3229	492	3	]	]	X
ejpam-3229	492	4	r.	r.	PROPN
ejpam-3229	492	5	wisbauer	wisbauer	NOUN
ejpam-3229	492	6	,	,	PUNCT
ejpam-3229	492	7	foundations	foundation	NOUN
ejpam-3229	492	8	of	of	ADP
ejpam-3229	492	9	module	module	NOUN
ejpam-3229	492	10	and	and	CCONJ
ejpam-3229	492	11	ring	ring	NOUN
ejpam-3229	492	12	theory	theory	NOUN
ejpam-3229	492	13	,	,	PUNCT
ejpam-3229	492	14	gordon	gordon	PROPN
ejpam-3229	492	15	and	and	CCONJ
ejpam-3229	492	16	breach	breach	PROPN
ejpam-3229	492	17	,	,	PUNCT
ejpam-3229	492	18	philadelphia	philadelphia	PROPN
ejpam-3229	492	19	,	,	PUNCT
ejpam-3229	492	20	(	(	PUNCT
ejpam-3229	492	21	1991	1991	NUM
ejpam-3229	492	22	)	)	PUNCT
ejpam-3229	492	23	.	.	PUNCT
ejpam-3229	493	1	[	[	X
ejpam-3229	493	2	13	13	NUM
ejpam-3229	493	3	]	]	X
ejpam-3229	493	4	n.v	n.v	PROPN
ejpam-3229	493	5	.	.	PROPN
ejpam-3229	493	6	sanh	sanh	PROPN
ejpam-3229	493	7	n.	n.	PROPN
ejpam-3229	493	8	v.	v.	PROPN
ejpam-3229	493	9	,	,	PUNCT
ejpam-3229	493	10	shum	shum	PROPN
ejpam-3229	493	11	k.	k.	PROPN
ejpam-3229	493	12	p.	p.	PROPN
ejpam-3229	493	13	,	,	PUNCT
ejpam-3229	493	14	dhompongsa	dhompongsa	VERB
ejpam-3229	493	15	s.	s.	PROPN
ejpam-3229	493	16	and	and	CCONJ
ejpam-3229	493	17	wongwai	wongwai	PROPN
ejpam-3229	493	18	s.	s.	PROPN
ejpam-3229	493	19	,	,	PUNCT
ejpam-3229	493	20	on	on	ADP
ejpam-3229	493	21	quasi	quasi	ADJ
ejpam-3229	493	22	-	-	ADJ
ejpam-3229	493	23	principally	principally	ADV
ejpam-3229	493	24	injective	injective	ADJ
ejpam-3229	493	25	modules	module	NOUN
ejpam-3229	493	26	,	,	PUNCT
ejpam-3229	493	27	algebra	algebra	PROPN
ejpam-3229	493	28	coll	coll	PROPN
ejpam-3229	493	29	.	.	PUNCT
ejpam-3229	494	1	6(3)(1999),269	6(3)(1999),269	PROPN
ejpam-3229	494	2	-	-	PUNCT
ejpam-3229	494	3	276	276	NUM
ejpam-3229	494	4	.	.	PUNCT
ejpam-3229	495	1	[	[	X
ejpam-3229	495	2	14	14	NUM
ejpam-3229	495	3	]	]	X
ejpam-3229	495	4	v.	v.	PROPN
ejpam-3229	495	5	gould	gould	PROPN
ejpam-3229	495	6	,	,	PUNCT
ejpam-3229	495	7	divisible	divisible	ADJ
ejpam-3229	495	8	s	s	NOUN
ejpam-3229	495	9	-	-	PUNCT
ejpam-3229	495	10	systems	system	NOUN
ejpam-3229	495	11	and	and	CCONJ
ejpam-3229	495	12	r	r	NOUN
ejpam-3229	495	13	-	-	PUNCT
ejpam-3229	495	14	modules	module	NOUN
ejpam-3229	495	15	,	,	PUNCT
ejpam-3229	495	16	proc	proc	NOUN
ejpam-3229	495	17	.	.	PUNCT
ejpam-3229	496	1	edinburgh	edinburgh	PROPN
ejpam-3229	496	2	math	math	PROPN
ejpam-3229	496	3	.	.	PUNCT
ejpam-3229	497	1	soc	soc	PROPN
ejpam-3229	497	2	.	.	PUNCT
ejpam-3229	498	1	30	30	NUM
ejpam-3229	498	2	(	(	PUNCT
ejpam-3229	498	3	1987	1987	NUM
ejpam-3229	498	4	)	)	PUNCT
ejpam-3229	498	5	,	,	PUNCT
ejpam-3229	498	6	187–200	187–200	NUM
ejpam-3229	498	7	.	.	PUNCT
ejpam-3229	499	1	[	[	X
ejpam-3229	499	2	15	15	NUM
ejpam-3229	499	3	]	]	X
ejpam-3229	499	4	s.	s.	PROPN
ejpam-3229	499	5	wongwai	wongwai	PROPN
ejpam-3229	499	6	,	,	PUNCT
ejpam-3229	499	7	on	on	ADP
ejpam-3229	499	8	the	the	DET
ejpam-3229	499	9	endomorphism	endomorphism	NOUN
ejpam-3229	499	10	ring	ring	NOUN
ejpam-3229	499	11	of	of	ADP
ejpam-3229	499	12	a	a	DET
ejpam-3229	499	13	semi	semi	ADJ
ejpam-3229	499	14	-	-	ADJ
ejpam-3229	499	15	injective	injective	ADJ
ejpam-3229	499	16	module	module	NOUN
ejpam-3229	499	17	,	,	PUNCT
ejpam-3229	499	18	acta	acta	PROPN
ejpam-3229	499	19	math.univ.comenianae	math.univ.comenianae	PROPN
ejpam-3229	499	20	vol.lxxi	vol.lxxi	ADV
ejpam-3229	499	21	,	,	PUNCT
ejpam-3229	499	22	1(2002	1(2002	NUM
ejpam-3229	499	23	)	)	PUNCT
ejpam-3229	499	24	,	,	PUNCT
ejpam-3229	499	25	pp.27	pp.27	PROPN
ejpam-3229	499	26	-	-	SYM
ejpam-3229	499	27	33	33	NUM
ejpam-3229	499	28	[	[	SYM
ejpam-3229	499	29	16	16	NUM
ejpam-3229	499	30	]	]	X
ejpam-3229	499	31	tansee	tansee	PROPN
ejpam-3229	499	32	h.	h.	PROPN
ejpam-3229	499	33	and	and	CCONJ
ejpam-3229	499	34	wongwai	wongwai	PROPN
ejpam-3229	499	35	s.	s.	PROPN
ejpam-3229	499	36	,	,	PUNCT
ejpam-3229	499	37	on	on	ADP
ejpam-3229	499	38	the	the	DET
ejpam-3229	499	39	endomorphism	endomorphism	NOUN
ejpam-3229	499	40	ring	ring	NOUN
ejpam-3229	499	41	of	of	ADP
ejpam-3229	499	42	a	a	DET
ejpam-3229	499	43	semi	semi	ADJ
ejpam-3229	499	44	-	-	ADJ
ejpam-3229	499	45	projective	projective	ADJ
ejpam-3229	499	46	module	module	NOUN
ejpam-3229	499	47	,	,	PUNCT
ejpam-3229	499	48	kyungpook	kyungpook	PROPN
ejpam-3229	499	49	math	math	PROPN
ejpam-3229	499	50	j.	j.	PROPN
ejpam-3229	499	51	42(2002	42(2002	PROPN
ejpam-3229	499	52	)	)	PUNCT
ejpam-3229	499	53	,	,	PUNCT
ejpam-3229	499	54	369	369	NUM
ejpam-3229	499	55	-	-	SYM
ejpam-3229	499	56	38	38	NUM
ejpam-3229	499	57	.	.	PUNCT