id	sid	tid	token	lemma	pos
ejpam-2696	1	1	european	european	PROPN
ejpam-2696	1	2	journal	journal	PROPN
ejpam-2696	1	3	of	of	ADP
ejpam-2696	1	4	pure	pure	ADJ
ejpam-2696	1	5	and	and	CCONJ
ejpam-2696	1	6	applied	apply	VERB
ejpam-2696	1	7	mathematics	mathematic	NOUN
ejpam-2696	1	8	vol	vol	NOUN
ejpam-2696	1	9	.	.	PROPN
ejpam-2696	2	1	10	10	NUM
ejpam-2696	2	2	,	,	PUNCT
ejpam-2696	2	3	no	no	INTJ
ejpam-2696	2	4	.	.	NOUN
ejpam-2696	2	5	4	4	NUM
ejpam-2696	2	6	,	,	PUNCT
ejpam-2696	2	7	2017	2017	NUM
ejpam-2696	2	8	,	,	PUNCT
ejpam-2696	2	9	739	739	NUM
ejpam-2696	2	10	-	-	SYM
ejpam-2696	2	11	748	748	NUM
ejpam-2696	2	12	issn	issn	PROPN
ejpam-2696	2	13	1307	1307	NUM
ejpam-2696	2	14	-	-	SYM
ejpam-2696	2	15	5543	5543	NUM
ejpam-2696	2	16	–	–	PUNCT
ejpam-2696	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2696	2	18	published	publish	VERB
ejpam-2696	2	19	by	by	ADP
ejpam-2696	2	20	new	new	PROPN
ejpam-2696	2	21	york	york	PROPN
ejpam-2696	2	22	business	business	PROPN
ejpam-2696	2	23	global	global	PROPN
ejpam-2696	2	24	on	on	ADP
ejpam-2696	2	25	gamma	gamma	PROPN
ejpam-2696	2	26	acts	act	NOUN
ejpam-2696	2	27	over	over	ADP
ejpam-2696	2	28	gamma	gamma	PROPN
ejpam-2696	2	29	semigroups	semigroups	PROPN
ejpam-2696	2	30	hamid	hamid	PROPN
ejpam-2696	2	31	rasouli1,∗	rasouli1,∗	PROPN
ejpam-2696	2	32	,	,	PUNCT
ejpam-2696	2	33	ali	ali	PROPN
ejpam-2696	2	34	reza	reza	PROPN
ejpam-2696	2	35	shabani2	shabani2	NOUN
ejpam-2696	2	36	1	1	NUM
ejpam-2696	2	37	department	department	NOUN
ejpam-2696	2	38	of	of	ADP
ejpam-2696	2	39	mathematics	mathematic	NOUN
ejpam-2696	2	40	,	,	PUNCT
ejpam-2696	2	41	science	science	NOUN
ejpam-2696	2	42	and	and	CCONJ
ejpam-2696	2	43	research	research	NOUN
ejpam-2696	2	44	branch	branch	NOUN
ejpam-2696	2	45	,	,	PUNCT
ejpam-2696	2	46	islamic	islamic	PROPN
ejpam-2696	2	47	azad	azad	PROPN
ejpam-2696	2	48	university	university	PROPN
ejpam-2696	2	49	tehran	tehran	PROPN
ejpam-2696	2	50	,	,	PUNCT
ejpam-2696	2	51	iran	iran	PROPN
ejpam-2696	2	52	2	2	NUM
ejpam-2696	2	53	department	department	NOUN
ejpam-2696	2	54	of	of	ADP
ejpam-2696	2	55	mathematics	mathematic	NOUN
ejpam-2696	2	56	,	,	PUNCT
ejpam-2696	2	57	imam	imam	PROPN
ejpam-2696	2	58	khomeini	khomeini	PROPN
ejpam-2696	2	59	maritime	maritime	PROPN
ejpam-2696	2	60	university	university	PROPN
ejpam-2696	2	61	of	of	ADP
ejpam-2696	2	62	nowshahr	nowshahr	PROPN
ejpam-2696	2	63	nowshahr	nowshahr	PROPN
ejpam-2696	2	64	,	,	PUNCT
ejpam-2696	2	65	iran	iran	PROPN
ejpam-2696	2	66	abstract	abstract	ADJ
ejpam-2696	2	67	.	.	PUNCT
ejpam-2696	3	1	for	for	ADP
ejpam-2696	3	2	a	a	DET
ejpam-2696	3	3	semigroup	semigroup	NOUN
ejpam-2696	3	4	s	s	NOUN
ejpam-2696	3	5	,	,	PUNCT
ejpam-2696	3	6	actions	action	NOUN
ejpam-2696	3	7	of	of	ADP
ejpam-2696	3	8	s	s	PRON
ejpam-2696	3	9	on	on	ADP
ejpam-2696	3	10	non	non	ADJ
ejpam-2696	3	11	-	-	ADJ
ejpam-2696	3	12	empty	empty	ADJ
ejpam-2696	3	13	sets	set	NOUN
ejpam-2696	3	14	,	,	PUNCT
ejpam-2696	3	15	namely	namely	ADV
ejpam-2696	3	16	s	s	NOUN
ejpam-2696	3	17	-	-	PUNCT
ejpam-2696	3	18	acts	act	NOUN
ejpam-2696	3	19	,	,	PUNCT
ejpam-2696	3	20	are	be	AUX
ejpam-2696	3	21	of	of	ADP
ejpam-2696	3	22	interest	interest	NOUN
ejpam-2696	3	23	to	to	PART
ejpam-2696	3	24	consider	consider	VERB
ejpam-2696	3	25	for	for	ADP
ejpam-2696	3	26	their	their	PRON
ejpam-2696	3	27	applications	application	NOUN
ejpam-2696	3	28	in	in	ADP
ejpam-2696	3	29	many	many	ADJ
ejpam-2696	3	30	branches	branch	NOUN
ejpam-2696	3	31	of	of	ADP
ejpam-2696	3	32	science	science	NOUN
ejpam-2696	3	33	.	.	PUNCT
ejpam-2696	4	1	the	the	DET
ejpam-2696	4	2	well	well	ADV
ejpam-2696	4	3	known	know	VERB
ejpam-2696	4	4	generalization	generalization	NOUN
ejpam-2696	4	5	of	of	ADP
ejpam-2696	4	6	a	a	DET
ejpam-2696	4	7	semigroup	semigroup	NOUN
ejpam-2696	4	8	is	be	AUX
ejpam-2696	4	9	the	the	DET
ejpam-2696	4	10	γ	γ	NOUN
ejpam-2696	4	11	-	-	PUNCT
ejpam-2696	4	12	semigroup	semigroup	NOUN
ejpam-2696	4	13	.	.	PUNCT
ejpam-2696	5	1	the	the	DET
ejpam-2696	5	2	notion	notion	NOUN
ejpam-2696	5	3	of	of	ADP
ejpam-2696	5	4	a	a	DET
ejpam-2696	5	5	γ	γ	NOUN
ejpam-2696	5	6	-	-	NOUN
ejpam-2696	5	7	act	act	NOUN
ejpam-2696	5	8	over	over	ADP
ejpam-2696	5	9	a	a	DET
ejpam-2696	5	10	γ	γ	NOUN
ejpam-2696	5	11	-	-	PUNCT
ejpam-2696	5	12	semigroup	semigroup	NOUN
ejpam-2696	5	13	is	be	AUX
ejpam-2696	5	14	a	a	DET
ejpam-2696	5	15	generalization	generalization	NOUN
ejpam-2696	5	16	of	of	ADP
ejpam-2696	5	17	actions	action	NOUN
ejpam-2696	5	18	over	over	ADP
ejpam-2696	5	19	semigroups	semigroup	NOUN
ejpam-2696	5	20	.	.	PUNCT
ejpam-2696	6	1	in	in	ADP
ejpam-2696	6	2	this	this	DET
ejpam-2696	6	3	paper	paper	NOUN
ejpam-2696	6	4	,	,	PUNCT
ejpam-2696	6	5	certain	certain	ADJ
ejpam-2696	6	6	intrinsic	intrinsic	ADJ
ejpam-2696	6	7	and	and	CCONJ
ejpam-2696	6	8	basic	basic	ADJ
ejpam-2696	6	9	properties	property	NOUN
ejpam-2696	6	10	of	of	ADP
ejpam-2696	6	11	γ	γ	NOUN
ejpam-2696	6	12	-	-	PUNCT
ejpam-2696	6	13	acts	act	NOUN
ejpam-2696	6	14	including	include	VERB
ejpam-2696	6	15	cyclic	cyclic	ADJ
ejpam-2696	6	16	,	,	PUNCT
ejpam-2696	6	17	indecomposable	indecomposable	ADJ
ejpam-2696	6	18	and	and	CCONJ
ejpam-2696	6	19	free	free	ADJ
ejpam-2696	6	20	are	be	AUX
ejpam-2696	6	21	studied	study	VERB
ejpam-2696	6	22	as	as	ADV
ejpam-2696	6	23	well	well	ADV
ejpam-2696	6	24	.	.	PUNCT
ejpam-2696	7	1	among	among	ADP
ejpam-2696	7	2	other	other	ADJ
ejpam-2696	7	3	results	result	NOUN
ejpam-2696	7	4	,	,	PUNCT
ejpam-2696	7	5	it	it	PRON
ejpam-2696	7	6	is	be	AUX
ejpam-2696	7	7	shown	show	VERB
ejpam-2696	7	8	that	that	SCONJ
ejpam-2696	7	9	a	a	DET
ejpam-2696	7	10	γ	γ	NOUN
ejpam-2696	7	11	-	-	PUNCT
ejpam-2696	7	12	act	act	NOUN
ejpam-2696	7	13	is	be	AUX
ejpam-2696	7	14	free	free	ADJ
ejpam-2696	7	15	only	only	ADV
ejpam-2696	7	16	if	if	SCONJ
ejpam-2696	7	17	|γ|	|γ|	PROPN
ejpam-2696	7	18	=	=	SYM
ejpam-2696	7	19	1	1	X
ejpam-2696	7	20	.	.	NUM
ejpam-2696	7	21	2010	2010	NUM
ejpam-2696	7	22	mathematics	mathematic	NOUN
ejpam-2696	7	23	subject	subject	NOUN
ejpam-2696	7	24	classifications	classification	NOUN
ejpam-2696	7	25	:	:	PUNCT
ejpam-2696	7	26	20n99	20n99	NUM
ejpam-2696	7	27	,	,	PUNCT
ejpam-2696	7	28	20m30	20m30	NUM
ejpam-2696	7	29	,	,	PUNCT
ejpam-2696	7	30	20m05	20m05	NUM
ejpam-2696	7	31	,	,	PUNCT
ejpam-2696	7	32	08a30	08a30	VERB
ejpam-2696	7	33	key	key	ADJ
ejpam-2696	7	34	words	word	NOUN
ejpam-2696	7	35	and	and	CCONJ
ejpam-2696	7	36	phrases	phrase	NOUN
ejpam-2696	7	37	:	:	PUNCT
ejpam-2696	7	38	γ	γ	NOUN
ejpam-2696	7	39	-	-	PUNCT
ejpam-2696	7	40	semigroup	semigroup	NOUN
ejpam-2696	7	41	,	,	PUNCT
ejpam-2696	7	42	γ	γ	PROPN
ejpam-2696	7	43	-	-	PUNCT
ejpam-2696	7	44	act	act	NOUN
ejpam-2696	7	45	,	,	PUNCT
ejpam-2696	7	46	γ	γ	PROPN
ejpam-2696	7	47	-	-	ADJ
ejpam-2696	7	48	congruence	congruence	ADJ
ejpam-2696	7	49	1	1	NUM
ejpam-2696	7	50	.	.	PUNCT
ejpam-2696	8	1	introduction	introduction	NOUN
ejpam-2696	8	2	nobusawa	nobusawa	PROPN
ejpam-2696	9	1	[	[	X
ejpam-2696	9	2	10	10	NUM
ejpam-2696	9	3	]	]	PUNCT
ejpam-2696	9	4	introduced	introduce	VERB
ejpam-2696	9	5	the	the	DET
ejpam-2696	9	6	notion	notion	NOUN
ejpam-2696	9	7	of	of	ADP
ejpam-2696	9	8	a	a	DET
ejpam-2696	9	9	γ	γ	NOUN
ejpam-2696	9	10	-	-	NOUN
ejpam-2696	9	11	ring	ring	NOUN
ejpam-2696	9	12	,	,	PUNCT
ejpam-2696	9	13	which	which	PRON
ejpam-2696	9	14	is	be	AUX
ejpam-2696	9	15	more	more	ADV
ejpam-2696	9	16	general	general	ADJ
ejpam-2696	9	17	than	than	ADP
ejpam-2696	9	18	a	a	DET
ejpam-2696	9	19	ring	ring	NOUN
ejpam-2696	9	20	.	.	PUNCT
ejpam-2696	10	1	then	then	ADV
ejpam-2696	10	2	barnes	barne	VERB
ejpam-2696	11	1	[	[	X
ejpam-2696	11	2	2	2	NUM
ejpam-2696	11	3	]	]	PUNCT
ejpam-2696	11	4	studied	study	VERB
ejpam-2696	11	5	γ	γ	PROPN
ejpam-2696	11	6	-	-	PUNCT
ejpam-2696	11	7	rings	ring	NOUN
ejpam-2696	11	8	in	in	ADP
ejpam-2696	11	9	a	a	DET
ejpam-2696	11	10	different	different	ADJ
ejpam-2696	11	11	way	way	NOUN
ejpam-2696	11	12	than	than	ADP
ejpam-2696	11	13	that	that	PRON
ejpam-2696	11	14	of	of	ADP
ejpam-2696	11	15	nobusawa	nobusawa	PROPN
ejpam-2696	11	16	.	.	PUNCT
ejpam-2696	12	1	motivated	motivate	VERB
ejpam-2696	12	2	by	by	ADP
ejpam-2696	12	3	these	these	DET
ejpam-2696	12	4	generalizations	generalization	NOUN
ejpam-2696	12	5	of	of	ADP
ejpam-2696	12	6	rings	ring	NOUN
ejpam-2696	12	7	,	,	PUNCT
ejpam-2696	12	8	sen	sen	PROPN
ejpam-2696	13	1	[	[	X
ejpam-2696	13	2	12	12	NUM
ejpam-2696	13	3	]	]	PUNCT
ejpam-2696	13	4	defined	define	VERB
ejpam-2696	13	5	the	the	DET
ejpam-2696	13	6	concept	concept	NOUN
ejpam-2696	13	7	of	of	ADP
ejpam-2696	13	8	a	a	DET
ejpam-2696	13	9	γ	γ	NOUN
ejpam-2696	13	10	-	-	PUNCT
ejpam-2696	13	11	semigroup	semigroup	NOUN
ejpam-2696	13	12	,	,	PUNCT
ejpam-2696	13	13	as	as	ADP
ejpam-2696	13	14	a	a	DET
ejpam-2696	13	15	generalization	generalization	NOUN
ejpam-2696	13	16	of	of	ADP
ejpam-2696	13	17	a	a	DET
ejpam-2696	13	18	semigroup	semigroup	NOUN
ejpam-2696	13	19	.	.	PUNCT
ejpam-2696	14	1	the	the	DET
ejpam-2696	14	2	investigation	investigation	NOUN
ejpam-2696	14	3	on	on	ADP
ejpam-2696	14	4	γ	γ	NOUN
ejpam-2696	14	5	-	-	PUNCT
ejpam-2696	14	6	semigroups	semigroup	NOUN
ejpam-2696	14	7	was	be	AUX
ejpam-2696	14	8	done	do	VERB
ejpam-2696	14	9	by	by	ADP
ejpam-2696	14	10	certain	certain	ADJ
ejpam-2696	14	11	mathematicians	mathematician	NOUN
ejpam-2696	14	12	which	which	PRON
ejpam-2696	14	13	are	be	AUX
ejpam-2696	14	14	parallel	parallel	ADJ
ejpam-2696	14	15	to	to	ADP
ejpam-2696	14	16	the	the	DET
ejpam-2696	14	17	results	result	NOUN
ejpam-2696	14	18	in	in	ADP
ejpam-2696	14	19	semigroup	semigroup	PROPN
ejpam-2696	14	20	theory	theory	NOUN
ejpam-2696	14	21	,	,	PUNCT
ejpam-2696	14	22	for	for	ADP
ejpam-2696	14	23	example	example	NOUN
ejpam-2696	14	24	,	,	PUNCT
ejpam-2696	14	25	one	one	PRON
ejpam-2696	14	26	may	may	AUX
ejpam-2696	14	27	see	see	VERB
ejpam-2696	14	28	[	[	X
ejpam-2696	14	29	11	11	NUM
ejpam-2696	14	30	,	,	PUNCT
ejpam-2696	14	31	13	13	NUM
ejpam-2696	14	32	,	,	PUNCT
ejpam-2696	14	33	14	14	NUM
ejpam-2696	14	34	]	]	PUNCT
ejpam-2696	14	35	.	.	PUNCT
ejpam-2696	15	1	recently	recently	ADV
ejpam-2696	15	2	on	on	ADP
ejpam-2696	15	3	this	this	DET
ejpam-2696	15	4	area	area	NOUN
ejpam-2696	15	5	some	some	DET
ejpam-2696	15	6	new	new	ADJ
ejpam-2696	15	7	papers	paper	NOUN
ejpam-2696	15	8	appeared	appear	VERB
ejpam-2696	15	9	,	,	PUNCT
ejpam-2696	15	10	such	such	ADJ
ejpam-2696	15	11	as	as	ADP
ejpam-2696	15	12	[	[	X
ejpam-2696	15	13	3–5	3–5	NOUN
ejpam-2696	15	14	]	]	PUNCT
ejpam-2696	15	15	.	.	PUNCT
ejpam-2696	16	1	the	the	DET
ejpam-2696	16	2	algebraic	algebraic	ADJ
ejpam-2696	16	3	structure	structure	NOUN
ejpam-2696	16	4	of	of	ADP
ejpam-2696	16	5	a	a	DET
ejpam-2696	16	6	module	module	NOUN
ejpam-2696	16	7	over	over	ADP
ejpam-2696	16	8	a	a	DET
ejpam-2696	16	9	ring	ring	NOUN
ejpam-2696	16	10	has	have	AUX
ejpam-2696	16	11	also	also	ADV
ejpam-2696	16	12	been	be	AUX
ejpam-2696	16	13	generalized	generalize	VERB
ejpam-2696	16	14	to	to	ADP
ejpam-2696	16	15	the	the	DET
ejpam-2696	16	16	γ	γ	NOUN
ejpam-2696	16	17	-	-	NOUN
ejpam-2696	16	18	module	module	NOUN
ejpam-2696	16	19	over	over	ADP
ejpam-2696	16	20	a	a	DET
ejpam-2696	16	21	γ	γ	NOUN
ejpam-2696	16	22	-	-	NOUN
ejpam-2696	16	23	ring	ring	NOUN
ejpam-2696	16	24	in	in	ADP
ejpam-2696	16	25	[	[	X
ejpam-2696	16	26	1	1	NUM
ejpam-2696	16	27	]	]	PUNCT
ejpam-2696	16	28	.	.	PUNCT
ejpam-2696	17	1	a	a	DET
ejpam-2696	17	2	useful	useful	ADJ
ejpam-2696	17	3	algebraic	algebraic	ADJ
ejpam-2696	17	4	structure	structure	NOUN
ejpam-2696	17	5	in	in	ADP
ejpam-2696	17	6	a	a	DET
ejpam-2696	17	7	variety	variety	NOUN
ejpam-2696	17	8	of	of	ADP
ejpam-2696	17	9	applications	application	NOUN
ejpam-2696	17	10	like	like	ADP
ejpam-2696	17	11	algebraic	algebraic	ADJ
ejpam-2696	17	12	automata	automata	NOUN
ejpam-2696	17	13	theory	theory	NOUN
ejpam-2696	17	14	,	,	PUNCT
ejpam-2696	17	15	theoretical	theoretical	ADJ
ejpam-2696	17	16	computer	computer	NOUN
ejpam-2696	17	17	science	science	NOUN
ejpam-2696	17	18	and	and	CCONJ
ejpam-2696	17	19	information	information	NOUN
ejpam-2696	17	20	theory	theory	NOUN
ejpam-2696	17	21	is	be	AUX
ejpam-2696	17	22	the	the	DET
ejpam-2696	17	23	notion	notion	NOUN
ejpam-2696	17	24	of	of	ADP
ejpam-2696	17	25	sact	sact	NOUN
ejpam-2696	17	26	over	over	ADP
ejpam-2696	17	27	a	a	DET
ejpam-2696	17	28	semigroup	semigroup	NOUN
ejpam-2696	17	29	s	s	X
ejpam-2696	17	30	which	which	PRON
ejpam-2696	17	31	is	be	AUX
ejpam-2696	17	32	more	more	ADV
ejpam-2696	17	33	general	general	ADJ
ejpam-2696	17	34	than	than	ADP
ejpam-2696	17	35	a	a	DET
ejpam-2696	17	36	module	module	NOUN
ejpam-2696	17	37	over	over	ADP
ejpam-2696	17	38	a	a	DET
ejpam-2696	17	39	ring	ring	NOUN
ejpam-2696	17	40	(	(	PUNCT
ejpam-2696	17	41	see	see	VERB
ejpam-2696	17	42	,	,	PUNCT
ejpam-2696	17	43	for	for	ADP
ejpam-2696	17	44	example	example	NOUN
ejpam-2696	17	45	,	,	PUNCT
ejpam-2696	17	46	[	[	X
ejpam-2696	17	47	8	8	NUM
ejpam-2696	17	48	]	]	NUM
ejpam-2696	17	49	)	)	PUNCT
ejpam-2696	17	50	.	.	PUNCT
ejpam-2696	18	1	a	a	DET
ejpam-2696	18	2	generalization	generalization	NOUN
ejpam-2696	18	3	of	of	ADP
ejpam-2696	18	4	an	an	DET
ejpam-2696	18	5	s	s	NOUN
ejpam-2696	18	6	-	-	NOUN
ejpam-2696	18	7	act	act	NOUN
ejpam-2696	18	8	to	to	ADP
ejpam-2696	18	9	the	the	DET
ejpam-2696	18	10	γ	γ	NOUN
ejpam-2696	18	11	-	-	NOUN
ejpam-2696	18	12	act	act	NOUN
ejpam-2696	18	13	over	over	ADP
ejpam-2696	18	14	a	a	DET
ejpam-2696	18	15	γ	γ	PROPN
ejpam-2696	18	16	-	-	PUNCT
ejpam-2696	18	17	semigroup	semigroup	NOUN
ejpam-2696	18	18	can	can	AUX
ejpam-2696	18	19	be	be	AUX
ejpam-2696	18	20	found	find	VERB
ejpam-2696	18	21	in	in	ADP
ejpam-2696	18	22	[	[	X
ejpam-2696	18	23	14	14	NUM
ejpam-2696	18	24	]	]	PUNCT
ejpam-2696	18	25	in	in	ADP
ejpam-2696	18	26	connection	connection	NOUN
ejpam-2696	18	27	with	with	ADP
ejpam-2696	18	28	the	the	DET
ejpam-2696	18	29	consideration	consideration	NOUN
ejpam-2696	18	30	of	of	ADP
ejpam-2696	18	31	radicals	radical	NOUN
ejpam-2696	18	32	of	of	ADP
ejpam-2696	18	33	γ	γ	NOUN
ejpam-2696	18	34	-	-	PUNCT
ejpam-2696	18	35	semigroups	semigroup	NOUN
ejpam-2696	18	36	.	.	PUNCT
ejpam-2696	19	1	here	here	ADV
ejpam-2696	19	2	we	we	PRON
ejpam-2696	19	3	study	study	VERB
ejpam-2696	19	4	some	some	DET
ejpam-2696	19	5	properties	property	NOUN
ejpam-2696	19	6	of	of	ADP
ejpam-2696	19	7	γ	γ	NOUN
ejpam-2696	19	8	-	-	PUNCT
ejpam-2696	19	9	acts	act	NOUN
ejpam-2696	19	10	originating	originate	VERB
ejpam-2696	19	11	by	by	ADP
ejpam-2696	19	12	the	the	DET
ejpam-2696	19	13	basic	basic	ADJ
ejpam-2696	19	14	properties	property	NOUN
ejpam-2696	19	15	of	of	ADP
ejpam-2696	19	16	s	s	NOUN
ejpam-2696	19	17	-	-	PUNCT
ejpam-2696	19	18	acts	act	NOUN
ejpam-2696	19	19	.	.	PUNCT
ejpam-2696	20	1	first	first	ADV
ejpam-2696	20	2	,	,	PUNCT
ejpam-2696	20	3	we	we	PRON
ejpam-2696	20	4	describe	describe	VERB
ejpam-2696	20	5	a	a	DET
ejpam-2696	20	6	γ	γ	NOUN
ejpam-2696	20	7	-	-	NOUN
ejpam-2696	20	8	act	act	NOUN
ejpam-2696	20	9	in	in	ADP
ejpam-2696	20	10	terms	term	NOUN
ejpam-2696	20	11	of	of	ADP
ejpam-2696	20	12	a	a	DET
ejpam-2696	20	13	γ	γ	NOUN
ejpam-2696	20	14	-	-	PUNCT
ejpam-2696	20	15	representation	representation	NOUN
ejpam-2696	20	16	of	of	ADP
ejpam-2696	20	17	a	a	DET
ejpam-2696	20	18	γ	γ	NOUN
ejpam-2696	20	19	-	-	PUNCT
ejpam-2696	20	20	semigroup	semigroup	NOUN
ejpam-2696	20	21	by	by	ADP
ejpam-2696	20	22	γ	γ	NOUN
ejpam-2696	20	23	-	-	PUNCT
ejpam-2696	20	24	transformations	transformation	NOUN
ejpam-2696	20	25	of	of	ADP
ejpam-2696	20	26	a	a	DET
ejpam-2696	20	27	set	set	NOUN
ejpam-2696	20	28	.	.	PUNCT
ejpam-2696	21	1	then	then	ADV
ejpam-2696	21	2	∗corresponding	∗corresponde	VERB
ejpam-2696	21	3	author	author	NOUN
ejpam-2696	21	4	.	.	PUNCT
ejpam-2696	22	1	email	email	NOUN
ejpam-2696	22	2	addresses	address	NOUN
ejpam-2696	22	3	:	:	PUNCT
ejpam-2696	22	4	hrasouli@srbiau.ac.ir	hrasouli@srbiau.ac.ir	NOUN
ejpam-2696	22	5	;	;	PUNCT
ejpam-2696	22	6	hrasouli5@yahoo.com	hrasouli5@yahoo.com	X
ejpam-2696	22	7	(	(	PUNCT
ejpam-2696	22	8	h.	h.	PROPN
ejpam-2696	22	9	rasouli	rasouli	PROPN
ejpam-2696	22	10	)	)	PUNCT
ejpam-2696	22	11	,	,	PUNCT
ejpam-2696	22	12	ashabani@srbiau.ac.ir	ashabani@srbiau.ac.ir	PROPN
ejpam-2696	22	13	(	(	PUNCT
ejpam-2696	22	14	a.r	a.r	PROPN
ejpam-2696	22	15	.	.	PROPN
ejpam-2696	22	16	shabani	shabani	PROPN
ejpam-2696	22	17	)	)	PUNCT
ejpam-2696	22	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2696	23	1	739	739	NUM
ejpam-2696	23	2	c	c	X
ejpam-2696	23	3	©	©	PROPN
ejpam-2696	23	4	2017	2017	NUM
ejpam-2696	23	5	ejpam	ejpam	VERB
ejpam-2696	23	6	all	all	DET
ejpam-2696	23	7	rights	right	NOUN
ejpam-2696	23	8	reserved	reserve	VERB
ejpam-2696	23	9	.	.	PUNCT
ejpam-2696	24	1	h.	h.	PROPN
ejpam-2696	24	2	rasouli	rasouli	PROPN
ejpam-2696	24	3	,	,	PUNCT
ejpam-2696	24	4	a.r	a.r	PROPN
ejpam-2696	24	5	.	.	PROPN
ejpam-2696	24	6	shabani	shabani	PROPN
ejpam-2696	24	7	/	/	SYM
ejpam-2696	24	8	eur	eur	PROPN
ejpam-2696	24	9	.	.	PUNCT
ejpam-2696	25	1	j.	j.	PROPN
ejpam-2696	25	2	pure	pure	PROPN
ejpam-2696	25	3	appl	appl	PROPN
ejpam-2696	25	4	.	.	PROPN
ejpam-2696	25	5	math	math	PROPN
ejpam-2696	25	6	,	,	PUNCT
ejpam-2696	25	7	10	10	NUM
ejpam-2696	25	8	(	(	PUNCT
ejpam-2696	25	9	4	4	NUM
ejpam-2696	25	10	)	)	PUNCT
ejpam-2696	25	11	(	(	PUNCT
ejpam-2696	25	12	2017	2017	NUM
ejpam-2696	25	13	)	)	PUNCT
ejpam-2696	25	14	,	,	PUNCT
ejpam-2696	25	15	739	739	NUM
ejpam-2696	25	16	-	-	SYM
ejpam-2696	25	17	748	748	NUM
ejpam-2696	25	18	740	740	NUM
ejpam-2696	25	19	some	some	DET
ejpam-2696	25	20	particular	particular	ADJ
ejpam-2696	25	21	morphisms	morphism	NOUN
ejpam-2696	25	22	in	in	ADP
ejpam-2696	25	23	the	the	DET
ejpam-2696	25	24	category	category	NOUN
ejpam-2696	25	25	of	of	ADP
ejpam-2696	25	26	γ	γ	NOUN
ejpam-2696	25	27	-	-	PUNCT
ejpam-2696	25	28	acts	act	NOUN
ejpam-2696	25	29	are	be	AUX
ejpam-2696	25	30	characterized	characterize	VERB
ejpam-2696	25	31	.	.	PUNCT
ejpam-2696	26	1	finally	finally	ADV
ejpam-2696	26	2	,	,	PUNCT
ejpam-2696	26	3	some	some	DET
ejpam-2696	26	4	results	result	NOUN
ejpam-2696	26	5	concerning	concern	VERB
ejpam-2696	26	6	cyclic	cyclic	ADJ
ejpam-2696	26	7	,	,	PUNCT
ejpam-2696	26	8	indecomposable	indecomposable	ADJ
ejpam-2696	26	9	and	and	CCONJ
ejpam-2696	26	10	free	free	ADJ
ejpam-2696	26	11	γ	γ	NOUN
ejpam-2696	26	12	-	-	PUNCT
ejpam-2696	26	13	acts	act	NOUN
ejpam-2696	26	14	are	be	AUX
ejpam-2696	26	15	presented	present	VERB
ejpam-2696	26	16	.	.	PUNCT
ejpam-2696	27	1	in	in	ADP
ejpam-2696	27	2	the	the	DET
ejpam-2696	27	3	sequel	sequel	NOUN
ejpam-2696	27	4	we	we	PRON
ejpam-2696	27	5	recall	recall	VERB
ejpam-2696	27	6	the	the	DET
ejpam-2696	27	7	definitions	definition	NOUN
ejpam-2696	27	8	of	of	ADP
ejpam-2696	27	9	s	s	NOUN
ejpam-2696	27	10	-	-	NOUN
ejpam-2696	27	11	act	act	NOUN
ejpam-2696	27	12	and	and	CCONJ
ejpam-2696	27	13	γ	γ	NOUN
ejpam-2696	27	14	-	-	PUNCT
ejpam-2696	27	15	semigroup	semigroup	NOUN
ejpam-2696	27	16	.	.	PUNCT
ejpam-2696	28	1	for	for	ADP
ejpam-2696	28	2	a	a	DET
ejpam-2696	28	3	semigroup	semigroup	PROPN
ejpam-2696	28	4	s	s	PROPN
ejpam-2696	28	5	,	,	PUNCT
ejpam-2696	28	6	a	a	DET
ejpam-2696	28	7	non	non	ADJ
ejpam-2696	28	8	-	-	ADJ
ejpam-2696	28	9	empty	empty	ADJ
ejpam-2696	28	10	set	set	NOUN
ejpam-2696	28	11	a	a	DET
ejpam-2696	28	12	together	together	NOUN
ejpam-2696	28	13	with	with	ADP
ejpam-2696	28	14	a	a	DET
ejpam-2696	28	15	mapping	mapping	NOUN
ejpam-2696	28	16	µ	µ	NOUN
ejpam-2696	28	17	:	:	PUNCT
ejpam-2696	28	18	s	s	AUX
ejpam-2696	28	19	×a→	×a→	PROPN
ejpam-2696	28	20	a	a	DET
ejpam-2696	28	21	where	where	SCONJ
ejpam-2696	28	22	(	(	PUNCT
ejpam-2696	28	23	s	s	X
ejpam-2696	28	24	,	,	PUNCT
ejpam-2696	28	25	a	a	PRON
ejpam-2696	28	26	)	)	PUNCT
ejpam-2696	28	27	7→	7→	NUM
ejpam-2696	28	28	sa	sa	NOUN
ejpam-2696	28	29	:	:	PUNCT
ejpam-2696	28	30	=	=	SYM
ejpam-2696	28	31	µ(s	µ(s	X
ejpam-2696	28	32	,	,	PUNCT
ejpam-2696	28	33	a	a	PRON
ejpam-2696	28	34	)	)	PUNCT
ejpam-2696	28	35	is	be	AUX
ejpam-2696	28	36	called	call	VERB
ejpam-2696	28	37	a	a	DET
ejpam-2696	28	38	(	(	PUNCT
ejpam-2696	28	39	left	left	ADJ
ejpam-2696	28	40	)	)	PUNCT
ejpam-2696	28	41	s	s	PART
ejpam-2696	28	42	-	-	PUNCT
ejpam-2696	28	43	act	act	NOUN
ejpam-2696	28	44	if	if	SCONJ
ejpam-2696	28	45	for	for	ADP
ejpam-2696	28	46	all	all	DET
ejpam-2696	28	47	s	s	PROPN
ejpam-2696	28	48	,	,	PUNCT
ejpam-2696	28	49	t	t	PROPN
ejpam-2696	28	50	∈	∈	PROPN
ejpam-2696	28	51	s	s	PART
ejpam-2696	28	52	and	and	CCONJ
ejpam-2696	28	53	a	a	DET
ejpam-2696	28	54	∈	∈	PROPN
ejpam-2696	28	55	a	a	PRON
ejpam-2696	28	56	,	,	PUNCT
ejpam-2696	28	57	(	(	PUNCT
ejpam-2696	28	58	st)a	st)a	PROPN
ejpam-2696	28	59	=	=	SYM
ejpam-2696	28	60	s(ta	s(ta	NUM
ejpam-2696	28	61	)	)	PUNCT
ejpam-2696	28	62	holds	hold	VERB
ejpam-2696	28	63	.	.	PUNCT
ejpam-2696	29	1	this	this	PRON
ejpam-2696	29	2	is	be	AUX
ejpam-2696	29	3	written	write	VERB
ejpam-2696	29	4	as	as	ADP
ejpam-2696	29	5	sa	sa	PROPN
ejpam-2696	29	6	.	.	PUNCT
ejpam-2696	29	7	for	for	ADP
ejpam-2696	29	8	a	a	DET
ejpam-2696	29	9	monoid	monoid	NOUN
ejpam-2696	29	10	s	s	NOUN
ejpam-2696	29	11	with	with	ADP
ejpam-2696	29	12	an	an	DET
ejpam-2696	29	13	identity	identity	NOUN
ejpam-2696	29	14	1	1	NUM
ejpam-2696	29	15	,	,	PUNCT
ejpam-2696	29	16	we	we	PRON
ejpam-2696	29	17	add	add	VERB
ejpam-2696	29	18	the	the	DET
ejpam-2696	29	19	condition	condition	NOUN
ejpam-2696	29	20	1a	1a	NOUN
ejpam-2696	29	21	=	=	SYM
ejpam-2696	29	22	a	a	X
ejpam-2696	29	23	,	,	PUNCT
ejpam-2696	29	24	for	for	ADP
ejpam-2696	29	25	all	all	DET
ejpam-2696	29	26	a	a	DET
ejpam-2696	29	27	∈	∈	NOUN
ejpam-2696	29	28	a.	a.	NOUN
ejpam-2696	29	29	the	the	DET
ejpam-2696	29	30	definition	definition	NOUN
ejpam-2696	29	31	of	of	ADP
ejpam-2696	29	32	an	an	DET
ejpam-2696	29	33	s	s	NOUN
ejpam-2696	29	34	-	-	NOUN
ejpam-2696	29	35	act	act	NOUN
ejpam-2696	29	36	,	,	PUNCT
ejpam-2696	29	37	in	in	ADP
ejpam-2696	29	38	this	this	DET
ejpam-2696	29	39	form	form	NOUN
ejpam-2696	29	40	,	,	PUNCT
ejpam-2696	29	41	first	first	ADV
ejpam-2696	29	42	proposed	propose	VERB
ejpam-2696	29	43	by	by	ADP
ejpam-2696	29	44	hoehnke	hoehnke	ADV
ejpam-2696	29	45	in	in	ADP
ejpam-2696	29	46	[	[	X
ejpam-2696	29	47	6	6	NUM
ejpam-2696	29	48	,	,	PUNCT
ejpam-2696	29	49	7	7	NUM
ejpam-2696	29	50	]	]	PUNCT
ejpam-2696	29	51	,	,	PUNCT
ejpam-2696	29	52	with	with	ADP
ejpam-2696	29	53	a	a	DET
ejpam-2696	29	54	different	different	ADJ
ejpam-2696	29	55	name	name	NOUN
ejpam-2696	29	56	in	in	ADP
ejpam-2696	29	57	connection	connection	NOUN
ejpam-2696	29	58	with	with	ADP
ejpam-2696	29	59	the	the	DET
ejpam-2696	29	60	consideration	consideration	NOUN
ejpam-2696	29	61	of	of	ADP
ejpam-2696	29	62	radicals	radical	NOUN
ejpam-2696	29	63	of	of	ADP
ejpam-2696	29	64	semigroups	semigroup	NOUN
ejpam-2696	29	65	.	.	PUNCT
ejpam-2696	30	1	for	for	ADP
ejpam-2696	30	2	more	more	ADJ
ejpam-2696	30	3	information	information	NOUN
ejpam-2696	30	4	on	on	ADP
ejpam-2696	30	5	this	this	DET
ejpam-2696	30	6	basic	basic	ADJ
ejpam-2696	30	7	concept	concept	NOUN
ejpam-2696	30	8	,	,	PUNCT
ejpam-2696	30	9	see	see	VERB
ejpam-2696	30	10	[	[	X
ejpam-2696	30	11	9	9	NUM
ejpam-2696	30	12	]	]	PUNCT
ejpam-2696	30	13	.	.	PUNCT
ejpam-2696	31	1	there	there	PRON
ejpam-2696	31	2	are	be	VERB
ejpam-2696	31	3	some	some	DET
ejpam-2696	31	4	different	different	ADJ
ejpam-2696	31	5	definitions	definition	NOUN
ejpam-2696	31	6	for	for	ADP
ejpam-2696	31	7	a	a	DET
ejpam-2696	31	8	γ	γ	NOUN
ejpam-2696	31	9	-	-	PUNCT
ejpam-2696	31	10	semigroup	semigroup	NOUN
ejpam-2696	31	11	in	in	ADP
ejpam-2696	31	12	the	the	DET
ejpam-2696	31	13	literature	literature	NOUN
ejpam-2696	31	14	(	(	PUNCT
ejpam-2696	31	15	see	see	VERB
ejpam-2696	31	16	for	for	ADP
ejpam-2696	31	17	example	example	NOUN
ejpam-2696	31	18	[	[	X
ejpam-2696	31	19	11–14	11–14	NUM
ejpam-2696	31	20	]	]	PUNCT
ejpam-2696	31	21	)	)	PUNCT
ejpam-2696	31	22	.	.	PUNCT
ejpam-2696	32	1	here	here	ADV
ejpam-2696	32	2	we	we	PRON
ejpam-2696	32	3	consider	consider	VERB
ejpam-2696	32	4	the	the	DET
ejpam-2696	32	5	one	one	NOUN
ejpam-2696	32	6	which	which	PRON
ejpam-2696	32	7	is	be	AUX
ejpam-2696	32	8	introduced	introduce	VERB
ejpam-2696	32	9	in	in	ADP
ejpam-2696	32	10	[	[	X
ejpam-2696	32	11	11	11	NUM
ejpam-2696	32	12	]	]	PUNCT
ejpam-2696	32	13	as	as	SCONJ
ejpam-2696	32	14	follows	follow	VERB
ejpam-2696	32	15	.	.	PUNCT
ejpam-2696	33	1	let	let	VERB
ejpam-2696	33	2	s	s	PRON
ejpam-2696	33	3	and	and	CCONJ
ejpam-2696	33	4	γ	γ	NOUN
ejpam-2696	33	5	be	be	AUX
ejpam-2696	33	6	non	non	ADJ
ejpam-2696	33	7	-	-	ADJ
ejpam-2696	33	8	empty	empty	ADJ
ejpam-2696	33	9	sets	set	NOUN
ejpam-2696	33	10	.	.	PUNCT
ejpam-2696	34	1	then	then	ADV
ejpam-2696	34	2	s	s	VERB
ejpam-2696	34	3	is	be	AUX
ejpam-2696	34	4	said	say	VERB
ejpam-2696	34	5	to	to	PART
ejpam-2696	34	6	be	be	AUX
ejpam-2696	34	7	a	a	DET
ejpam-2696	34	8	γ	γ	NOUN
ejpam-2696	34	9	-	-	PUNCT
ejpam-2696	34	10	semigroup	semigroup	NOUN
ejpam-2696	34	11	if	if	SCONJ
ejpam-2696	34	12	there	there	PRON
ejpam-2696	34	13	exists	exist	VERB
ejpam-2696	34	14	a	a	DET
ejpam-2696	34	15	mapping	mapping	NOUN
ejpam-2696	34	16	λ	λ	NOUN
ejpam-2696	34	17	:	:	PUNCT
ejpam-2696	34	18	s	s	VERB
ejpam-2696	34	19	×	×	NOUN
ejpam-2696	34	20	γ	γ	X
ejpam-2696	34	21	×	×	NOUN
ejpam-2696	34	22	s	s	PROPN
ejpam-2696	34	23	→	→	SYM
ejpam-2696	34	24	s	s	PROPN
ejpam-2696	34	25	,	,	PUNCT
ejpam-2696	34	26	writing	write	VERB
ejpam-2696	34	27	λ(a	λ(a	NOUN
ejpam-2696	34	28	,	,	PUNCT
ejpam-2696	34	29	γ	γ	X
ejpam-2696	34	30	,	,	PUNCT
ejpam-2696	34	31	b	b	NOUN
ejpam-2696	34	32	)	)	PUNCT
ejpam-2696	34	33	as	as	ADP
ejpam-2696	34	34	aγb	aγb	NOUN
ejpam-2696	34	35	satisfying	satisfy	VERB
ejpam-2696	34	36	the	the	DET
ejpam-2696	34	37	identity	identity	NOUN
ejpam-2696	34	38	(	(	PUNCT
ejpam-2696	34	39	aγb)βc	aγb)βc	NOUN
ejpam-2696	34	40	=	=	PUNCT
ejpam-2696	34	41	aγ(bβc	aγ(bβc	PROPN
ejpam-2696	34	42	)	)	PUNCT
ejpam-2696	34	43	for	for	ADP
ejpam-2696	34	44	all	all	DET
ejpam-2696	34	45	a	a	DET
ejpam-2696	34	46	,	,	PUNCT
ejpam-2696	34	47	b	b	NOUN
ejpam-2696	34	48	,	,	PUNCT
ejpam-2696	34	49	c	c	PROPN
ejpam-2696	34	50	∈	∈	PROPN
ejpam-2696	34	51	s	s	X
ejpam-2696	34	52	and	and	CCONJ
ejpam-2696	34	53	γ	γ	X
ejpam-2696	34	54	,	,	PUNCT
ejpam-2696	34	55	β	β	PROPN
ejpam-2696	34	56	∈	∈	PROPN
ejpam-2696	34	57	γ	γ	X
ejpam-2696	34	58	.	.	PUNCT
ejpam-2696	35	1	let	let	VERB
ejpam-2696	35	2	s	s	PRON
ejpam-2696	35	3	be	be	AUX
ejpam-2696	35	4	a	a	DET
ejpam-2696	35	5	γ	γ	NOUN
ejpam-2696	35	6	-	-	PUNCT
ejpam-2696	35	7	semigroup	semigroup	NOUN
ejpam-2696	35	8	.	.	PUNCT
ejpam-2696	36	1	an	an	DET
ejpam-2696	36	2	element	element	NOUN
ejpam-2696	36	3	e	e	NOUN
ejpam-2696	36	4	of	of	ADP
ejpam-2696	36	5	s	s	PROPN
ejpam-2696	36	6	is	be	AUX
ejpam-2696	36	7	said	say	VERB
ejpam-2696	36	8	to	to	PART
ejpam-2696	36	9	be	be	AUX
ejpam-2696	36	10	a	a	DET
ejpam-2696	36	11	left	left	ADJ
ejpam-2696	36	12	(	(	PUNCT
ejpam-2696	36	13	right	right	ADJ
ejpam-2696	36	14	)	)	PUNCT
ejpam-2696	36	15	identity	identity	NOUN
ejpam-2696	36	16	of	of	ADP
ejpam-2696	36	17	s	s	PRON
ejpam-2696	36	18	if	if	SCONJ
ejpam-2696	36	19	,	,	PUNCT
ejpam-2696	36	20	eγs	eγs	VERB
ejpam-2696	36	21	=	=	SYM
ejpam-2696	36	22	s	s	X
ejpam-2696	36	23	(	(	PUNCT
ejpam-2696	36	24	sγe	sγe	NOUN
ejpam-2696	36	25	=	=	SYM
ejpam-2696	36	26	s	s	NOUN
ejpam-2696	36	27	)	)	PUNCT
ejpam-2696	36	28	for	for	ADP
ejpam-2696	36	29	all	all	DET
ejpam-2696	36	30	s	s	PART
ejpam-2696	36	31	∈	∈	PROPN
ejpam-2696	36	32	s	s	NOUN
ejpam-2696	36	33	and	and	CCONJ
ejpam-2696	36	34	γ	γ	PROPN
ejpam-2696	36	35	∈	∈	PROPN
ejpam-2696	36	36	γ	γ	X
ejpam-2696	36	37	.	.	PUNCT
ejpam-2696	37	1	a	a	DET
ejpam-2696	37	2	left	left	NOUN
ejpam-2696	37	3	as	as	ADV
ejpam-2696	37	4	well	well	ADV
ejpam-2696	37	5	as	as	ADP
ejpam-2696	37	6	right	right	ADJ
ejpam-2696	37	7	identify	identify	NOUN
ejpam-2696	37	8	is	be	AUX
ejpam-2696	37	9	an	an	DET
ejpam-2696	37	10	identity	identity	NOUN
ejpam-2696	37	11	of	of	ADP
ejpam-2696	37	12	s.	s.	PROPN
ejpam-2696	37	13	a	a	DET
ejpam-2696	37	14	γ	γ	PROPN
ejpam-2696	37	15	-	-	PUNCT
ejpam-2696	37	16	semigroup	semigroup	NOUN
ejpam-2696	37	17	with	with	ADP
ejpam-2696	37	18	an	an	DET
ejpam-2696	37	19	identity	identity	NOUN
ejpam-2696	37	20	is	be	AUX
ejpam-2696	37	21	called	call	VERB
ejpam-2696	37	22	a	a	DET
ejpam-2696	37	23	γ	γ	PROPN
ejpam-2696	37	24	-	-	PUNCT
ejpam-2696	37	25	monoid	monoid	NOUN
ejpam-2696	37	26	.	.	PUNCT
ejpam-2696	38	1	a	a	DET
ejpam-2696	38	2	non	non	ADJ
ejpam-2696	38	3	-	-	ADJ
ejpam-2696	38	4	empty	empty	ADJ
ejpam-2696	38	5	subset	subset	NOUN
ejpam-2696	38	6	i	i	PRON
ejpam-2696	38	7	of	of	ADP
ejpam-2696	38	8	s	s	PRON
ejpam-2696	38	9	satisfying	satisfy	VERB
ejpam-2696	38	10	sγi	sγi	NOUN
ejpam-2696	38	11	⊆	⊆	NUM
ejpam-2696	38	12	i	i	PRON
ejpam-2696	38	13	is	be	AUX
ejpam-2696	38	14	called	call	VERB
ejpam-2696	38	15	a	a	DET
ejpam-2696	38	16	left	left	ADJ
ejpam-2696	38	17	γ	γ	NOUN
ejpam-2696	38	18	-	-	NOUN
ejpam-2696	38	19	ideal	ideal	NOUN
ejpam-2696	38	20	of	of	ADP
ejpam-2696	38	21	s.	s.	PROPN
ejpam-2696	38	22	by	by	ADP
ejpam-2696	38	23	a	a	DET
ejpam-2696	38	24	left	left	ADJ
ejpam-2696	38	25	γ	γ	NOUN
ejpam-2696	38	26	-	-	NOUN
ejpam-2696	38	27	congruence	congruence	NOUN
ejpam-2696	38	28	on	on	ADP
ejpam-2696	38	29	s	s	PRON
ejpam-2696	38	30	we	we	PRON
ejpam-2696	38	31	mean	mean	VERB
ejpam-2696	38	32	an	an	DET
ejpam-2696	38	33	equivalence	equivalence	NOUN
ejpam-2696	38	34	relation	relation	NOUN
ejpam-2696	38	35	ρ	ρ	PROPN
ejpam-2696	38	36	on	on	ADP
ejpam-2696	38	37	s	s	PRON
ejpam-2696	38	38	for	for	ADP
ejpam-2696	38	39	which	which	PRON
ejpam-2696	38	40	sρs′	sρs′	PROPN
ejpam-2696	38	41	implies	imply	VERB
ejpam-2696	38	42	(	(	PUNCT
ejpam-2696	38	43	tγs)ρ(tγs′	tγs)ρ(tγs′	NUM
ejpam-2696	38	44	)	)	PUNCT
ejpam-2696	38	45	for	for	ADP
ejpam-2696	38	46	s	s	PROPN
ejpam-2696	38	47	,	,	PUNCT
ejpam-2696	38	48	s′	s′	NUM
ejpam-2696	38	49	,	,	PUNCT
ejpam-2696	38	50	t	t	PROPN
ejpam-2696	38	51	∈	∈	PROPN
ejpam-2696	38	52	s	s	PART
ejpam-2696	38	53	and	and	CCONJ
ejpam-2696	38	54	γ	γ	PROPN
ejpam-2696	38	55	∈	∈	PROPN
ejpam-2696	38	56	γ	γ	X
ejpam-2696	38	57	.	.	PUNCT
ejpam-2696	39	1	let	let	VERB
ejpam-2696	39	2	s	s	PRON
ejpam-2696	39	3	and	and	CCONJ
ejpam-2696	39	4	t	t	PROPN
ejpam-2696	39	5	be	be	AUX
ejpam-2696	39	6	two	two	NUM
ejpam-2696	39	7	γ	γ	NOUN
ejpam-2696	39	8	-	-	PUNCT
ejpam-2696	39	9	semigroups	semigroup	NOUN
ejpam-2696	39	10	with	with	ADP
ejpam-2696	39	11	left	left	ADJ
ejpam-2696	39	12	identities	identity	NOUN
ejpam-2696	39	13	e	e	NOUN
ejpam-2696	39	14	and	and	CCONJ
ejpam-2696	39	15	e′	e′	PROPN
ejpam-2696	39	16	,	,	PUNCT
ejpam-2696	39	17	respectively	respectively	ADV
ejpam-2696	39	18	.	.	PUNCT
ejpam-2696	40	1	a	a	DET
ejpam-2696	40	2	map	map	NOUN
ejpam-2696	40	3	f	f	X
ejpam-2696	40	4	:	:	PUNCT
ejpam-2696	40	5	s	s	X
ejpam-2696	40	6	→	→	SYM
ejpam-2696	40	7	t	t	X
ejpam-2696	40	8	satisfying	satisfy	VERB
ejpam-2696	40	9	f(e	f(e	NOUN
ejpam-2696	40	10	)	)	PUNCT
ejpam-2696	40	11	=	=	SYM
ejpam-2696	40	12	e′	e′	NOUN
ejpam-2696	40	13	and	and	CCONJ
ejpam-2696	40	14	f(sγs′	f(sγs′	NUM
ejpam-2696	40	15	)	)	PUNCT
ejpam-2696	40	16	=	=	SYM
ejpam-2696	40	17	f(s)γf(s′	f(s)γf(s′	NOUN
ejpam-2696	40	18	)	)	PUNCT
ejpam-2696	40	19	for	for	ADP
ejpam-2696	40	20	all	all	DET
ejpam-2696	40	21	s	s	PROPN
ejpam-2696	40	22	,	,	PUNCT
ejpam-2696	40	23	s′	s′	PUNCT
ejpam-2696	40	24	∈	∈	PROPN
ejpam-2696	40	25	s	s	PROPN
ejpam-2696	40	26	,	,	PUNCT
ejpam-2696	40	27	γ	γ	PROPN
ejpam-2696	40	28	∈	∈	PROPN
ejpam-2696	40	29	γ	γ	PROPN
ejpam-2696	40	30	,	,	PUNCT
ejpam-2696	40	31	is	be	AUX
ejpam-2696	40	32	called	call	VERB
ejpam-2696	40	33	a	a	DET
ejpam-2696	40	34	γ	γ	NOUN
ejpam-2696	40	35	-	-	PUNCT
ejpam-2696	40	36	semigroup	semigroup	ADJ
ejpam-2696	40	37	homomorphism	homomorphism	NOUN
ejpam-2696	40	38	.	.	PUNCT
ejpam-2696	41	1	2	2	X
ejpam-2696	41	2	.	.	X
ejpam-2696	41	3	the	the	DET
ejpam-2696	41	4	structure	structure	NOUN
ejpam-2696	41	5	of	of	ADP
ejpam-2696	41	6	γ	γ	PROPN
ejpam-2696	41	7	-	-	PUNCT
ejpam-2696	41	8	s	s	NOUN
ejpam-2696	41	9	-	-	PUNCT
ejpam-2696	41	10	acts	act	VERB
ejpam-2696	41	11	the	the	DET
ejpam-2696	41	12	purpose	purpose	NOUN
ejpam-2696	41	13	of	of	ADP
ejpam-2696	41	14	this	this	DET
ejpam-2696	41	15	section	section	NOUN
ejpam-2696	41	16	is	be	AUX
ejpam-2696	41	17	to	to	PART
ejpam-2696	41	18	study	study	VERB
ejpam-2696	41	19	some	some	DET
ejpam-2696	41	20	basic	basic	ADJ
ejpam-2696	41	21	properties	property	NOUN
ejpam-2696	41	22	of	of	ADP
ejpam-2696	41	23	γ	γ	PROPN
ejpam-2696	41	24	-	-	PUNCT
ejpam-2696	41	25	s	s	NOUN
ejpam-2696	41	26	-	-	PUNCT
ejpam-2696	41	27	acts	act	NOUN
ejpam-2696	41	28	.	.	PUNCT
ejpam-2696	42	1	let	let	VERB
ejpam-2696	42	2	us	we	PRON
ejpam-2696	42	3	first	first	ADV
ejpam-2696	42	4	give	give	VERB
ejpam-2696	42	5	some	some	DET
ejpam-2696	42	6	definitions	definition	NOUN
ejpam-2696	42	7	.	.	PUNCT
ejpam-2696	43	1	let	let	VERB
ejpam-2696	43	2	s	s	PRON
ejpam-2696	43	3	be	be	AUX
ejpam-2696	43	4	a	a	DET
ejpam-2696	43	5	γ	γ	NOUN
ejpam-2696	43	6	-	-	PUNCT
ejpam-2696	43	7	semigroup	semigroup	NOUN
ejpam-2696	43	8	and	and	CCONJ
ejpam-2696	43	9	a	a	DET
ejpam-2696	43	10	be	be	AUX
ejpam-2696	43	11	a	a	DET
ejpam-2696	43	12	non	non	ADJ
ejpam-2696	43	13	-	-	ADJ
ejpam-2696	43	14	empty	empty	ADJ
ejpam-2696	43	15	set	set	NOUN
ejpam-2696	43	16	.	.	PUNCT
ejpam-2696	44	1	recall	recall	NOUN
ejpam-2696	44	2	from	from	ADP
ejpam-2696	44	3	[	[	X
ejpam-2696	44	4	14	14	NUM
ejpam-2696	44	5	]	]	PUNCT
ejpam-2696	44	6	that	that	SCONJ
ejpam-2696	44	7	if	if	SCONJ
ejpam-2696	44	8	there	there	PRON
ejpam-2696	44	9	exists	exist	VERB
ejpam-2696	44	10	a	a	DET
ejpam-2696	44	11	mapping	mapping	NOUN
ejpam-2696	44	12	λ	λ	NOUN
ejpam-2696	44	13	:	:	PUNCT
ejpam-2696	44	14	s×γ×a→	s×γ×a→	INTJ
ejpam-2696	44	15	a	a	DET
ejpam-2696	44	16	where	where	SCONJ
ejpam-2696	44	17	(	(	PUNCT
ejpam-2696	44	18	s	s	X
ejpam-2696	44	19	,	,	PUNCT
ejpam-2696	44	20	γ	γ	PROPN
ejpam-2696	44	21	,	,	PUNCT
ejpam-2696	44	22	a	a	PRON
ejpam-2696	44	23	)	)	PUNCT
ejpam-2696	44	24	7→	7→	NUM
ejpam-2696	44	25	sγa	sγa	NOUN
ejpam-2696	44	26	:	:	PUNCT
ejpam-2696	44	27	=	=	SYM
ejpam-2696	44	28	λ(s	λ(s	PROPN
ejpam-2696	44	29	,	,	PUNCT
ejpam-2696	44	30	γ	γ	PROPN
ejpam-2696	44	31	,	,	PUNCT
ejpam-2696	44	32	a	a	PRON
ejpam-2696	44	33	)	)	PUNCT
ejpam-2696	44	34	such	such	ADJ
ejpam-2696	44	35	that	that	SCONJ
ejpam-2696	44	36	(	(	PUNCT
ejpam-2696	44	37	sγt)βa	sγt)βa	ADJ
ejpam-2696	44	38	=	=	SYM
ejpam-2696	44	39	sγ(tβa	sγ(tβa	NOUN
ejpam-2696	44	40	)	)	PUNCT
ejpam-2696	44	41	for	for	ADP
ejpam-2696	44	42	all	all	DET
ejpam-2696	44	43	a	a	DET
ejpam-2696	44	44	∈	∈	PROPN
ejpam-2696	44	45	a	a	DET
ejpam-2696	44	46	,	,	PUNCT
ejpam-2696	44	47	s	s	PROPN
ejpam-2696	44	48	,	,	PUNCT
ejpam-2696	44	49	t	t	PROPN
ejpam-2696	44	50	∈	∈	PROPN
ejpam-2696	44	51	s	s	PART
ejpam-2696	44	52	and	and	CCONJ
ejpam-2696	44	53	γ	γ	PROPN
ejpam-2696	44	54	,	,	PUNCT
ejpam-2696	44	55	β	β	PROPN
ejpam-2696	44	56	∈	∈	PROPN
ejpam-2696	44	57	γ	γ	X
ejpam-2696	44	58	,	,	PUNCT
ejpam-2696	44	59	and	and	CCONJ
ejpam-2696	44	60	if	if	SCONJ
ejpam-2696	44	61	s	s	PROPN
ejpam-2696	44	62	has	have	VERB
ejpam-2696	44	63	a	a	DET
ejpam-2696	44	64	left	left	ADJ
ejpam-2696	44	65	identity	identity	NOUN
ejpam-2696	44	66	e	e	NOUN
ejpam-2696	44	67	,	,	PUNCT
ejpam-2696	44	68	eγa	eγa	NOUN
ejpam-2696	44	69	=	=	PUNCT
ejpam-2696	44	70	a	a	NOUN
ejpam-2696	44	71	for	for	ADP
ejpam-2696	44	72	every	every	DET
ejpam-2696	44	73	a	a	DET
ejpam-2696	44	74	∈	∈	PROPN
ejpam-2696	44	75	a	a	PRON
ejpam-2696	44	76	and	and	CCONJ
ejpam-2696	44	77	γ	γ	PROPN
ejpam-2696	44	78	∈	∈	PROPN
ejpam-2696	44	79	γ	γ	X
ejpam-2696	44	80	,	,	PUNCT
ejpam-2696	44	81	then	then	ADV
ejpam-2696	44	82	a	a	PRON
ejpam-2696	44	83	is	be	AUX
ejpam-2696	44	84	called	call	VERB
ejpam-2696	44	85	a	a	DET
ejpam-2696	44	86	(	(	PUNCT
ejpam-2696	44	87	left	left	ADJ
ejpam-2696	44	88	)	)	PUNCT
ejpam-2696	44	89	γ	γ	PROPN
ejpam-2696	44	90	-	-	PUNCT
ejpam-2696	44	91	s	s	NOUN
ejpam-2696	44	92	-	-	PUNCT
ejpam-2696	44	93	act	act	NOUN
ejpam-2696	44	94	.	.	PUNCT
ejpam-2696	45	1	if	if	SCONJ
ejpam-2696	45	2	no	no	DET
ejpam-2696	45	3	confusion	confusion	NOUN
ejpam-2696	45	4	arises	arise	VERB
ejpam-2696	45	5	,	,	PUNCT
ejpam-2696	45	6	a	a	DET
ejpam-2696	45	7	γ	γ	PROPN
ejpam-2696	45	8	-	-	PUNCT
ejpam-2696	45	9	s	s	NOUN
ejpam-2696	45	10	-	-	PUNCT
ejpam-2696	45	11	act	act	NOUN
ejpam-2696	45	12	a	a	PRON
ejpam-2696	45	13	is	be	AUX
ejpam-2696	45	14	simply	simply	ADV
ejpam-2696	45	15	called	call	VERB
ejpam-2696	45	16	a	a	DET
ejpam-2696	45	17	γ	γ	NOUN
ejpam-2696	45	18	-	-	NOUN
ejpam-2696	45	19	act	act	NOUN
ejpam-2696	45	20	and	and	CCONJ
ejpam-2696	45	21	is	be	AUX
ejpam-2696	45	22	denoted	denote	VERB
ejpam-2696	45	23	by	by	ADP
ejpam-2696	45	24	γa	γa	PROPN
ejpam-2696	45	25	.	.	PUNCT
ejpam-2696	46	1	a	a	DET
ejpam-2696	46	2	non	non	ADJ
ejpam-2696	46	3	-	-	ADJ
ejpam-2696	46	4	empty	empty	ADJ
ejpam-2696	46	5	subset	subset	NOUN
ejpam-2696	46	6	a′	a′	NOUN
ejpam-2696	46	7	of	of	ADP
ejpam-2696	46	8	a	a	PRON
ejpam-2696	46	9	is	be	AUX
ejpam-2696	46	10	said	say	VERB
ejpam-2696	46	11	to	to	PART
ejpam-2696	46	12	be	be	AUX
ejpam-2696	46	13	a	a	DET
ejpam-2696	46	14	γ	γ	NOUN
ejpam-2696	46	15	-	-	NOUN
ejpam-2696	46	16	subact	subact	NOUN
ejpam-2696	46	17	of	of	ADP
ejpam-2696	46	18	a	a	PRON
ejpam-2696	46	19	if	if	SCONJ
ejpam-2696	46	20	sγa′	sγa′	VERB
ejpam-2696	46	21	⊆	⊆	NUM
ejpam-2696	46	22	a′	a′	PROPN
ejpam-2696	46	23	,	,	PUNCT
ejpam-2696	46	24	that	that	ADV
ejpam-2696	46	25	is	is	ADV
ejpam-2696	46	26	,	,	PUNCT
ejpam-2696	46	27	sγa′	sγa′	PROPN
ejpam-2696	46	28	∈	∈	PRON
ejpam-2696	46	29	a′	a′	NOUN
ejpam-2696	46	30	for	for	ADP
ejpam-2696	46	31	all	all	DET
ejpam-2696	46	32	s	s	PART
ejpam-2696	46	33	∈	∈	PROPN
ejpam-2696	46	34	s	s	NOUN
ejpam-2696	46	35	,	,	PUNCT
ejpam-2696	46	36	a′	a′	PROPN
ejpam-2696	46	37	∈	∈	PROPN
ejpam-2696	46	38	a′	a′	PROPN
ejpam-2696	46	39	and	and	CCONJ
ejpam-2696	46	40	γ	γ	PROPN
ejpam-2696	46	41	∈	∈	PROPN
ejpam-2696	46	42	γ	γ	X
ejpam-2696	46	43	.	.	PUNCT
ejpam-2696	46	44	clearly	clearly	ADV
ejpam-2696	46	45	,	,	PUNCT
ejpam-2696	46	46	s	s	VERB
ejpam-2696	46	47	itself	itself	PRON
ejpam-2696	46	48	is	be	AUX
ejpam-2696	46	49	a	a	DET
ejpam-2696	46	50	γ	γ	PROPN
ejpam-2696	46	51	-	-	PUNCT
ejpam-2696	46	52	s	s	NOUN
ejpam-2696	46	53	-	-	NOUN
ejpam-2696	46	54	act	act	NOUN
ejpam-2696	46	55	with	with	ADP
ejpam-2696	46	56	its	its	PRON
ejpam-2696	46	57	γ	γ	NOUN
ejpam-2696	46	58	-	-	NOUN
ejpam-2696	46	59	operation	operation	NOUN
ejpam-2696	46	60	as	as	ADP
ejpam-2696	46	61	the	the	DET
ejpam-2696	46	62	γ	γ	NOUN
ejpam-2696	46	63	-	-	NOUN
ejpam-2696	46	64	action	action	NOUN
ejpam-2696	46	65	.	.	PUNCT
ejpam-2696	47	1	also	also	ADV
ejpam-2696	47	2	any	any	DET
ejpam-2696	47	3	left	left	ADJ
ejpam-2696	47	4	γ	γ	NOUN
ejpam-2696	47	5	-	-	NOUN
ejpam-2696	47	6	ideal	ideal	NOUN
ejpam-2696	47	7	of	of	ADP
ejpam-2696	47	8	s	s	PROPN
ejpam-2696	47	9	is	be	AUX
ejpam-2696	47	10	a	a	DET
ejpam-2696	47	11	γ	γ	NOUN
ejpam-2696	47	12	-	-	NOUN
ejpam-2696	47	13	subact	subact	NOUN
ejpam-2696	47	14	of	of	ADP
ejpam-2696	47	15	s.	s.	PROPN
ejpam-2696	47	16	let	let	VERB
ejpam-2696	47	17	a	a	PRON
ejpam-2696	47	18	be	be	AUX
ejpam-2696	47	19	a	a	DET
ejpam-2696	47	20	γ	γ	PROPN
ejpam-2696	47	21	-	-	PUNCT
ejpam-2696	47	22	s	s	NOUN
ejpam-2696	47	23	-	-	PUNCT
ejpam-2696	47	24	act	act	NOUN
ejpam-2696	47	25	.	.	PUNCT
ejpam-2696	48	1	an	an	DET
ejpam-2696	48	2	element	element	NOUN
ejpam-2696	48	3	θ	θ	PROPN
ejpam-2696	48	4	∈	∈	PROPN
ejpam-2696	48	5	a	a	PRON
ejpam-2696	48	6	is	be	AUX
ejpam-2696	48	7	called	call	VERB
ejpam-2696	48	8	a	a	DET
ejpam-2696	48	9	zero	zero	NUM
ejpam-2696	48	10	element	element	NOUN
ejpam-2696	48	11	of	of	ADP
ejpam-2696	48	12	a	a	DET
ejpam-2696	48	13	if	if	SCONJ
ejpam-2696	48	14	sγθ	sγθ	NOUN
ejpam-2696	48	15	=	=	SYM
ejpam-2696	48	16	θ	θ	NOUN
ejpam-2696	48	17	for	for	ADP
ejpam-2696	48	18	every	every	DET
ejpam-2696	48	19	s	s	X
ejpam-2696	48	20	∈	∈	PROPN
ejpam-2696	48	21	s	s	NOUN
ejpam-2696	48	22	and	and	CCONJ
ejpam-2696	48	23	γ	γ	PROPN
ejpam-2696	48	24	∈	∈	PROPN
ejpam-2696	48	25	γ	γ	PROPN
ejpam-2696	48	26	.	.	PROPN
ejpam-2696	49	1	let	let	VERB
ejpam-2696	49	2	γa	γa	NOUN
ejpam-2696	49	3	,	,	PUNCT
ejpam-2696	49	4	γb	γb	INTJ
ejpam-2696	49	5	be	be	AUX
ejpam-2696	49	6	two	two	NUM
ejpam-2696	49	7	γ	γ	PROPN
ejpam-2696	49	8	-	-	PUNCT
ejpam-2696	49	9	s	s	NOUN
ejpam-2696	49	10	-	-	PUNCT
ejpam-2696	49	11	acts	act	NOUN
ejpam-2696	49	12	.	.	PUNCT
ejpam-2696	50	1	a	a	DET
ejpam-2696	50	2	mapping	mapping	NOUN
ejpam-2696	50	3	f	f	NOUN
ejpam-2696	50	4	:	:	PUNCT
ejpam-2696	50	5	γa	γa	PROPN
ejpam-2696	50	6	→	→	SYM
ejpam-2696	50	7	γb	γb	PROPN
ejpam-2696	50	8	is	be	AUX
ejpam-2696	50	9	called	call	VERB
ejpam-2696	50	10	a	a	DET
ejpam-2696	50	11	γs	γs	NOUN
ejpam-2696	50	12	-	-	PUNCT
ejpam-2696	50	13	homomorphism	homomorphism	NOUN
ejpam-2696	50	14	,	,	PUNCT
ejpam-2696	50	15	or	or	CCONJ
ejpam-2696	50	16	simply	simply	ADV
ejpam-2696	50	17	γ	γ	NOUN
ejpam-2696	50	18	-	-	PUNCT
ejpam-2696	50	19	homomorphism	homomorphism	NOUN
ejpam-2696	50	20	,	,	PUNCT
ejpam-2696	50	21	if	if	SCONJ
ejpam-2696	50	22	f(sγa	f(sγa	NOUN
ejpam-2696	50	23	)	)	PUNCT
ejpam-2696	50	24	=	=	SYM
ejpam-2696	50	25	sγf(a	sγf(a	PROPN
ejpam-2696	50	26	)	)	PUNCT
ejpam-2696	50	27	for	for	ADP
ejpam-2696	50	28	every	every	DET
ejpam-2696	50	29	s	s	PROPN
ejpam-2696	50	30	∈	∈	PROPN
ejpam-2696	50	31	s	s	NOUN
ejpam-2696	50	32	,	,	PUNCT
ejpam-2696	50	33	a	a	DET
ejpam-2696	50	34	∈	∈	PROPN
ejpam-2696	50	35	a	a	PRON
ejpam-2696	50	36	and	and	CCONJ
ejpam-2696	50	37	γ	γ	PROPN
ejpam-2696	50	38	∈	∈	PROPN
ejpam-2696	50	39	γ	γ	X
ejpam-2696	50	40	.	.	PUNCT
ejpam-2696	51	1	if	if	SCONJ
ejpam-2696	51	2	s	s	PROPN
ejpam-2696	51	3	is	be	AUX
ejpam-2696	51	4	a	a	DET
ejpam-2696	51	5	γ	γ	NOUN
ejpam-2696	51	6	-	-	PUNCT
ejpam-2696	51	7	monoid	monoid	NOUN
ejpam-2696	51	8	with	with	ADP
ejpam-2696	51	9	identity	identity	NOUN
ejpam-2696	51	10	1	1	NUM
ejpam-2696	51	11	and	and	CCONJ
ejpam-2696	51	12	a	a	PRON
ejpam-2696	51	13	is	be	AUX
ejpam-2696	51	14	a	a	DET
ejpam-2696	51	15	γ	γ	PROPN
ejpam-2696	51	16	-	-	PUNCT
ejpam-2696	51	17	s	s	NOUN
ejpam-2696	51	18	-	-	PUNCT
ejpam-2696	51	19	act	act	NOUN
ejpam-2696	51	20	,	,	PUNCT
ejpam-2696	51	21	then	then	ADV
ejpam-2696	51	22	for	for	SCONJ
ejpam-2696	51	23	every	every	DET
ejpam-2696	51	24	s	s	PROPN
ejpam-2696	51	25	,	,	PUNCT
ejpam-2696	51	26	t	t	PROPN
ejpam-2696	51	27	∈	∈	PROPN
ejpam-2696	51	28	s	s	PART
ejpam-2696	51	29	and	and	CCONJ
ejpam-2696	51	30	γ	γ	PROPN
ejpam-2696	51	31	,	,	PUNCT
ejpam-2696	51	32	β	β	PROPN
ejpam-2696	51	33	∈	∈	PROPN
ejpam-2696	51	34	γ	γ	X
ejpam-2696	51	35	,	,	PUNCT
ejpam-2696	51	36	we	we	PRON
ejpam-2696	51	37	have	have	AUX
ejpam-2696	51	38	sγt	sγt	VERB
ejpam-2696	51	39	=	=	NOUN
ejpam-2696	51	40	sβt	sβt	NOUN
ejpam-2696	51	41	and	and	CCONJ
ejpam-2696	51	42	sγa	sγa	NOUN
ejpam-2696	51	43	=	=	SYM
ejpam-2696	51	44	sβa	sβa	PROPN
ejpam-2696	51	45	.	.	PUNCT
ejpam-2696	52	1	indeed	indeed	ADV
ejpam-2696	52	2	,	,	PUNCT
ejpam-2696	52	3	sγt	sγt	X
ejpam-2696	52	4	=	=	PUNCT
ejpam-2696	52	5	(	(	PUNCT
ejpam-2696	52	6	sβ1)γt	sβ1)γt	ADV
ejpam-2696	52	7	=	=	SYM
ejpam-2696	52	8	sβ(1γt	sβ(1γt	NOUN
ejpam-2696	52	9	)	)	PUNCT
ejpam-2696	52	10	=	=	SYM
ejpam-2696	52	11	sβt	sβt	NOUN
ejpam-2696	52	12	;	;	PUNCT
ejpam-2696	52	13	and	and	CCONJ
ejpam-2696	52	14	sγa	sγa	NOUN
ejpam-2696	52	15	=	=	SYM
ejpam-2696	52	16	(	(	PUNCT
ejpam-2696	52	17	sβ1)γa	sβ1)γa	X
ejpam-2696	52	18	=	=	SYM
ejpam-2696	52	19	sβ(1γa	sβ(1γa	NOUN
ejpam-2696	52	20	)	)	PUNCT
ejpam-2696	52	21	=	=	SYM
ejpam-2696	52	22	sβa	sβa	PROPN
ejpam-2696	52	23	.	.	PUNCT
ejpam-2696	53	1	then	then	ADV
ejpam-2696	53	2	it	it	PRON
ejpam-2696	53	3	is	be	AUX
ejpam-2696	53	4	more	more	ADV
ejpam-2696	53	5	interesting	interesting	ADJ
ejpam-2696	53	6	to	to	PART
ejpam-2696	53	7	consider	consider	VERB
ejpam-2696	53	8	γ	γ	X
ejpam-2696	53	9	-	-	PUNCT
ejpam-2696	53	10	s	s	NOUN
ejpam-2696	53	11	-	-	PUNCT
ejpam-2696	53	12	acts	act	NOUN
ejpam-2696	53	13	for	for	ADP
ejpam-2696	53	14	a	a	DET
ejpam-2696	53	15	γ	γ	NOUN
ejpam-2696	53	16	-	-	PUNCT
ejpam-2696	53	17	semigroup	semigroup	NOUN
ejpam-2696	53	18	s	s	NOUN
ejpam-2696	53	19	with	with	ADP
ejpam-2696	53	20	a	a	DET
ejpam-2696	53	21	left	left	ADJ
ejpam-2696	53	22	identity	identity	NOUN
ejpam-2696	53	23	(	(	PUNCT
ejpam-2696	53	24	not	not	PART
ejpam-2696	53	25	necessarily	necessarily	ADV
ejpam-2696	53	26	an	an	DET
ejpam-2696	53	27	identity	identity	NOUN
ejpam-2696	53	28	)	)	PUNCT
ejpam-2696	53	29	.	.	PUNCT
ejpam-2696	54	1	therefore	therefore	ADV
ejpam-2696	54	2	,	,	PUNCT
ejpam-2696	54	3	from	from	ADP
ejpam-2696	54	4	now	now	ADV
ejpam-2696	54	5	on	on	ADV
ejpam-2696	54	6	,	,	PUNCT
ejpam-2696	54	7	s	s	AUX
ejpam-2696	54	8	stands	stand	NOUN
ejpam-2696	54	9	for	for	ADP
ejpam-2696	54	10	a	a	DET
ejpam-2696	54	11	γ	γ	NOUN
ejpam-2696	54	12	-	-	PUNCT
ejpam-2696	54	13	semigroup	semigroup	NOUN
ejpam-2696	54	14	with	with	ADP
ejpam-2696	54	15	a	a	DET
ejpam-2696	54	16	left	left	ADJ
ejpam-2696	54	17	identity	identity	NOUN
ejpam-2696	54	18	e	e	NOUN
ejpam-2696	54	19	unless	unless	SCONJ
ejpam-2696	54	20	otherwise	otherwise	ADV
ejpam-2696	54	21	stated	state	VERB
ejpam-2696	54	22	.	.	PUNCT
ejpam-2696	55	1	the	the	DET
ejpam-2696	55	2	idea	idea	NOUN
ejpam-2696	55	3	of	of	ADP
ejpam-2696	55	4	representing	represent	VERB
ejpam-2696	55	5	something	something	PRON
ejpam-2696	55	6	by	by	ADP
ejpam-2696	55	7	some	some	DET
ejpam-2696	55	8	other	other	ADJ
ejpam-2696	55	9	objects	object	NOUN
ejpam-2696	55	10	which	which	PRON
ejpam-2696	55	11	are	be	AUX
ejpam-2696	55	12	better	well	ADV
ejpam-2696	55	13	known	know	VERB
ejpam-2696	55	14	at	at	ADP
ejpam-2696	55	15	h.	h.	PROPN
ejpam-2696	55	16	rasouli	rasouli	PROPN
ejpam-2696	55	17	,	,	PUNCT
ejpam-2696	55	18	a.r	a.r	PROPN
ejpam-2696	55	19	.	.	PROPN
ejpam-2696	55	20	shabani	shabani	PROPN
ejpam-2696	55	21	/	/	SYM
ejpam-2696	55	22	eur	eur	PROPN
ejpam-2696	55	23	.	.	PUNCT
ejpam-2696	56	1	j.	j.	PROPN
ejpam-2696	56	2	pure	pure	PROPN
ejpam-2696	56	3	appl	appl	PROPN
ejpam-2696	56	4	.	.	PROPN
ejpam-2696	56	5	math	math	PROPN
ejpam-2696	56	6	,	,	PUNCT
ejpam-2696	56	7	10	10	NUM
ejpam-2696	56	8	(	(	PUNCT
ejpam-2696	56	9	4	4	NUM
ejpam-2696	56	10	)	)	PUNCT
ejpam-2696	56	11	(	(	PUNCT
ejpam-2696	56	12	2017	2017	NUM
ejpam-2696	56	13	)	)	PUNCT
ejpam-2696	56	14	,	,	PUNCT
ejpam-2696	56	15	739	739	NUM
ejpam-2696	56	16	-	-	SYM
ejpam-2696	56	17	748	748	NUM
ejpam-2696	56	18	741	741	NUM
ejpam-2696	56	19	least	least	ADJ
ejpam-2696	56	20	in	in	ADP
ejpam-2696	56	21	some	some	DET
ejpam-2696	56	22	respects	respect	NOUN
ejpam-2696	56	23	is	be	AUX
ejpam-2696	56	24	quite	quite	ADV
ejpam-2696	56	25	familiar	familiar	ADJ
ejpam-2696	56	26	in	in	ADP
ejpam-2696	56	27	mathematics	mathematic	NOUN
ejpam-2696	56	28	.	.	PUNCT
ejpam-2696	57	1	it	it	PRON
ejpam-2696	57	2	is	be	AUX
ejpam-2696	57	3	well	well	ADV
ejpam-2696	57	4	known	know	VERB
ejpam-2696	57	5	that	that	SCONJ
ejpam-2696	57	6	every	every	DET
ejpam-2696	57	7	representation	representation	NOUN
ejpam-2696	57	8	of	of	ADP
ejpam-2696	57	9	a	a	DET
ejpam-2696	57	10	ring	ring	NOUN
ejpam-2696	57	11	by	by	ADP
ejpam-2696	57	12	endomorphisms	endomorphism	NOUN
ejpam-2696	57	13	of	of	ADP
ejpam-2696	57	14	an	an	DET
ejpam-2696	57	15	abelian	abelian	ADJ
ejpam-2696	57	16	group	group	NOUN
ejpam-2696	57	17	gives	give	VERB
ejpam-2696	57	18	a	a	DET
ejpam-2696	57	19	module	module	NOUN
ejpam-2696	57	20	over	over	ADP
ejpam-2696	57	21	that	that	DET
ejpam-2696	57	22	ring	ring	NOUN
ejpam-2696	57	23	and	and	CCONJ
ejpam-2696	57	24	vice	vice	NOUN
ejpam-2696	57	25	versa	versa	ADV
ejpam-2696	57	26	.	.	PUNCT
ejpam-2696	58	1	analogously	analogously	ADV
ejpam-2696	58	2	,	,	PUNCT
ejpam-2696	58	3	representations	representation	NOUN
ejpam-2696	58	4	of	of	ADP
ejpam-2696	58	5	semigroups	semigroup	NOUN
ejpam-2696	58	6	(	(	PUNCT
ejpam-2696	58	7	monoids	monoid	NOUN
ejpam-2696	58	8	)	)	PUNCT
ejpam-2696	58	9	by	by	ADP
ejpam-2696	58	10	transformations	transformation	NOUN
ejpam-2696	58	11	of	of	ADP
ejpam-2696	58	12	sets	set	NOUN
ejpam-2696	58	13	give	give	VERB
ejpam-2696	58	14	rise	rise	NOUN
ejpam-2696	58	15	to	to	ADP
ejpam-2696	58	16	the	the	DET
ejpam-2696	58	17	notion	notion	NOUN
ejpam-2696	58	18	of	of	ADP
ejpam-2696	58	19	acts	act	NOUN
ejpam-2696	58	20	over	over	ADP
ejpam-2696	58	21	semigroups	semigroup	NOUN
ejpam-2696	58	22	(	(	PUNCT
ejpam-2696	58	23	monoids	monoid	NOUN
ejpam-2696	58	24	)	)	PUNCT
ejpam-2696	58	25	(	(	PUNCT
ejpam-2696	58	26	see	see	VERB
ejpam-2696	58	27	[	[	X
ejpam-2696	58	28	9	9	NUM
ejpam-2696	58	29	,	,	PUNCT
ejpam-2696	58	30	proposition	proposition	NOUN
ejpam-2696	58	31	i.4.4	i.4.4	NOUN
ejpam-2696	58	32	]	]	X
ejpam-2696	58	33	)	)	PUNCT
ejpam-2696	58	34	.	.	PUNCT
ejpam-2696	59	1	in	in	ADP
ejpam-2696	59	2	the	the	DET
ejpam-2696	59	3	same	same	ADJ
ejpam-2696	59	4	way	way	NOUN
ejpam-2696	59	5	,	,	PUNCT
ejpam-2696	59	6	we	we	PRON
ejpam-2696	59	7	here	here	ADV
ejpam-2696	59	8	describe	describe	VERB
ejpam-2696	59	9	γ	γ	NOUN
ejpam-2696	59	10	-	-	NOUN
ejpam-2696	59	11	acts	act	NOUN
ejpam-2696	59	12	in	in	ADP
ejpam-2696	59	13	terms	term	NOUN
ejpam-2696	59	14	of	of	ADP
ejpam-2696	59	15	γ	γ	NOUN
ejpam-2696	59	16	-	-	PUNCT
ejpam-2696	59	17	representations	representation	NOUN
ejpam-2696	59	18	of	of	ADP
ejpam-2696	59	19	γ	γ	NOUN
ejpam-2696	59	20	-	-	PUNCT
ejpam-2696	59	21	semigroups	semigroup	NOUN
ejpam-2696	59	22	.	.	PUNCT
ejpam-2696	60	1	let	let	VERB
ejpam-2696	60	2	a	a	PRON
ejpam-2696	60	3	be	be	AUX
ejpam-2696	60	4	a	a	DET
ejpam-2696	60	5	non	non	ADJ
ejpam-2696	60	6	-	-	ADJ
ejpam-2696	60	7	empty	empty	ADJ
ejpam-2696	60	8	set	set	NOUN
ejpam-2696	60	9	and	and	CCONJ
ejpam-2696	60	10	a	a	DET
ejpam-2696	60	11	denote	denote	NOUN
ejpam-2696	60	12	the	the	DET
ejpam-2696	60	13	set	set	NOUN
ejpam-2696	60	14	of	of	ADP
ejpam-2696	60	15	all	all	DET
ejpam-2696	60	16	maps	map	NOUN
ejpam-2696	60	17	ϕ	ϕ	NOUN
ejpam-2696	60	18	:	:	PUNCT
ejpam-2696	60	19	γ→	γ→	PROPN
ejpam-2696	60	20	aa	aa	PROPN
ejpam-2696	60	21	,	,	PUNCT
ejpam-2696	60	22	the	the	DET
ejpam-2696	60	23	so	so	ADV
ejpam-2696	60	24	called	call	VERB
ejpam-2696	60	25	γ	γ	NOUN
ejpam-2696	60	26	-	-	PUNCT
ejpam-2696	60	27	transformations	transformation	NOUN
ejpam-2696	60	28	of	of	ADP
ejpam-2696	60	29	a	a	PRON
ejpam-2696	60	30	,	,	PUNCT
ejpam-2696	60	31	where	where	SCONJ
ejpam-2696	60	32	aa	aa	PROPN
ejpam-2696	60	33	is	be	AUX
ejpam-2696	60	34	the	the	DET
ejpam-2696	60	35	monoid	monoid	NOUN
ejpam-2696	60	36	of	of	ADP
ejpam-2696	60	37	all	all	DET
ejpam-2696	60	38	transformations	transformation	NOUN
ejpam-2696	60	39	of	of	ADP
ejpam-2696	60	40	a	a	PRON
ejpam-2696	60	41	with	with	ADP
ejpam-2696	60	42	the	the	DET
ejpam-2696	60	43	usual	usual	ADJ
ejpam-2696	60	44	composition	composition	NOUN
ejpam-2696	60	45	of	of	ADP
ejpam-2696	60	46	mappings	mapping	NOUN
ejpam-2696	60	47	as	as	ADP
ejpam-2696	60	48	its	its	PRON
ejpam-2696	60	49	operation	operation	NOUN
ejpam-2696	60	50	.	.	PUNCT
ejpam-2696	61	1	now	now	ADV
ejpam-2696	61	2	we	we	PRON
ejpam-2696	61	3	have	have	VERB
ejpam-2696	61	4	lemma	lemma	PROPN
ejpam-2696	61	5	1	1	NUM
ejpam-2696	61	6	.	.	PUNCT
ejpam-2696	62	1	the	the	DET
ejpam-2696	62	2	set	set	NOUN
ejpam-2696	62	3	a	a	PRON
ejpam-2696	62	4	is	be	AUX
ejpam-2696	62	5	a	a	DET
ejpam-2696	62	6	γ	γ	NOUN
ejpam-2696	62	7	-	-	PUNCT
ejpam-2696	62	8	semigroup	semigroup	NOUN
ejpam-2696	62	9	with	with	ADP
ejpam-2696	62	10	a	a	DET
ejpam-2696	62	11	left	left	ADJ
ejpam-2696	62	12	(	(	PUNCT
ejpam-2696	62	13	not	not	PART
ejpam-2696	62	14	necessarily	necessarily	ADV
ejpam-2696	62	15	right	right	ADJ
ejpam-2696	62	16	)	)	PUNCT
ejpam-2696	62	17	identity	identity	NOUN
ejpam-2696	62	18	under	under	ADP
ejpam-2696	62	19	the	the	DET
ejpam-2696	62	20	γ	γ	NOUN
ejpam-2696	62	21	-	-	NOUN
ejpam-2696	62	22	operation	operation	NOUN
ejpam-2696	62	23	ϕγϕ′	ϕγϕ′	NOUN
ejpam-2696	62	24	:	:	PUNCT
ejpam-2696	62	25	γ	γ	X
ejpam-2696	62	26	→	→	SYM
ejpam-2696	62	27	aa	aa	NOUN
ejpam-2696	62	28	defined	define	VERB
ejpam-2696	62	29	by	by	ADP
ejpam-2696	62	30	ϕγϕ′(γ′	ϕγϕ′(γ′	NOUN
ejpam-2696	62	31	)	)	PUNCT
ejpam-2696	62	32	:	:	PUNCT
ejpam-2696	62	33	=	=	PUNCT
ejpam-2696	62	34	ϕ(γ)ϕ′(γ′	ϕ(γ)ϕ′(γ′	PROPN
ejpam-2696	62	35	)	)	PUNCT
ejpam-2696	62	36	for	for	ADP
ejpam-2696	62	37	all	all	DET
ejpam-2696	62	38	ϕ,ϕ′	ϕ,ϕ′	NOUN
ejpam-2696	62	39	∈	∈	PROPN
ejpam-2696	62	40	a	a	PRON
ejpam-2696	62	41	and	and	CCONJ
ejpam-2696	62	42	γ	γ	X
ejpam-2696	62	43	,	,	PUNCT
ejpam-2696	62	44	γ′	γ′	PROPN
ejpam-2696	62	45	∈	∈	PROPN
ejpam-2696	62	46	γ	γ	X
ejpam-2696	62	47	.	.	PUNCT
ejpam-2696	62	48	proof	proof	NOUN
ejpam-2696	62	49	.	.	PUNCT
ejpam-2696	63	1	let	let	VERB
ejpam-2696	63	2	ϕ,ϕ′	ϕ,ϕ′	ADJ
ejpam-2696	63	3	,	,	PUNCT
ejpam-2696	63	4	ϕ′′	ϕ′′	PROPN
ejpam-2696	63	5	∈	∈	PROPN
ejpam-2696	63	6	a	a	PRON
ejpam-2696	63	7	and	and	CCONJ
ejpam-2696	63	8	γ	γ	X
ejpam-2696	63	9	,	,	PUNCT
ejpam-2696	63	10	γ′.	γ′.	VERB
ejpam-2696	63	11	then	then	ADV
ejpam-2696	63	12	(	(	PUNCT
ejpam-2696	63	13	ϕγϕ′)γ′ϕ′′	ϕγϕ′)γ′ϕ′′	PROPN
ejpam-2696	63	14	=	=	PUNCT
ejpam-2696	63	15	ϕγ(ϕ′γ′ϕ′′	ϕγ(ϕ′γ′ϕ′′	NUM
ejpam-2696	63	16	)	)	PUNCT
ejpam-2696	63	17	.	.	PUNCT
ejpam-2696	64	1	indeed	indeed	ADV
ejpam-2696	64	2	,	,	PUNCT
ejpam-2696	64	3	for	for	ADP
ejpam-2696	64	4	any	any	DET
ejpam-2696	64	5	γ′′	γ′′	PROPN
ejpam-2696	64	6	∈	∈	PROPN
ejpam-2696	64	7	γ	γ	NOUN
ejpam-2696	64	8	we	we	PRON
ejpam-2696	64	9	have	have	VERB
ejpam-2696	64	10	[	[	X
ejpam-2696	64	11	(	(	PUNCT
ejpam-2696	64	12	ϕγϕ′)γ′ϕ′′](γ′′	ϕγϕ′)γ′ϕ′′](γ′′	NOUN
ejpam-2696	64	13	)	)	PUNCT
ejpam-2696	64	14	=	=	SYM
ejpam-2696	65	1	(	(	PUNCT
ejpam-2696	65	2	ϕγϕ′)(γ′)ϕ′′(γ′′	ϕγϕ′)(γ′)ϕ′′(γ′′	PROPN
ejpam-2696	65	3	)	)	PUNCT
ejpam-2696	65	4	=	=	SYM
ejpam-2696	65	5	ϕ(γ)ϕ′(γ′)ϕ′′(γ′′	ϕ(γ)ϕ′(γ′)ϕ′′(γ′′	NOUN
ejpam-2696	65	6	)	)	PUNCT
ejpam-2696	65	7	=	=	SYM
ejpam-2696	65	8	ϕ(γ)(ϕ′γ′ϕ′′)(γ′′	ϕ(γ)(ϕ′γ′ϕ′′)(γ′′	PROPN
ejpam-2696	65	9	)	)	PUNCT
ejpam-2696	65	10	=	=	PUNCT
ejpam-2696	66	1	[	[	X
ejpam-2696	66	2	ϕγ(ϕ′γ′ϕ′′)](γ′′	ϕγ(ϕ′γ′ϕ′′)](γ′′	NOUN
ejpam-2696	66	3	)	)	PUNCT
ejpam-2696	66	4	,	,	PUNCT
ejpam-2696	66	5	as	as	SCONJ
ejpam-2696	66	6	desired	desire	VERB
ejpam-2696	66	7	.	.	PUNCT
ejpam-2696	67	1	also	also	ADV
ejpam-2696	67	2	the	the	DET
ejpam-2696	67	3	constant	constant	ADJ
ejpam-2696	67	4	mapping	mapping	NOUN
ejpam-2696	67	5	ε	ε	PROPN
ejpam-2696	67	6	:	:	PUNCT
ejpam-2696	67	7	γ→	γ→	PROPN
ejpam-2696	67	8	aa	aa	NOUN
ejpam-2696	67	9	which	which	PRON
ejpam-2696	67	10	maps	map	VERB
ejpam-2696	67	11	every	every	DET
ejpam-2696	67	12	element	element	NOUN
ejpam-2696	67	13	of	of	ADP
ejpam-2696	67	14	γ	γ	PROPN
ejpam-2696	67	15	to	to	ADP
ejpam-2696	67	16	ida	ida	PROPN
ejpam-2696	67	17	is	be	AUX
ejpam-2696	67	18	a	a	DET
ejpam-2696	67	19	left	left	ADJ
ejpam-2696	67	20	identity	identity	NOUN
ejpam-2696	67	21	element	element	NOUN
ejpam-2696	67	22	of	of	ADP
ejpam-2696	67	23	a	a	PRON
ejpam-2696	67	24	which	which	PRON
ejpam-2696	67	25	is	be	AUX
ejpam-2696	67	26	not	not	PART
ejpam-2696	67	27	necessarily	necessarily	ADV
ejpam-2696	67	28	a	a	DET
ejpam-2696	67	29	right	right	ADJ
ejpam-2696	67	30	identity	identity	NOUN
ejpam-2696	67	31	.	.	PUNCT
ejpam-2696	68	1	in	in	ADP
ejpam-2696	68	2	the	the	DET
ejpam-2696	68	3	following	following	NOUN
ejpam-2696	68	4	,	,	PUNCT
ejpam-2696	68	5	the	the	DET
ejpam-2696	68	6	notion	notion	NOUN
ejpam-2696	68	7	of	of	ADP
ejpam-2696	68	8	representations	representation	NOUN
ejpam-2696	68	9	of	of	ADP
ejpam-2696	68	10	a	a	DET
ejpam-2696	68	11	semigroup	semigroup	NOUN
ejpam-2696	68	12	by	by	ADP
ejpam-2696	68	13	transformations	transformation	NOUN
ejpam-2696	68	14	of	of	ADP
ejpam-2696	68	15	a	a	DET
ejpam-2696	68	16	set	set	NOUN
ejpam-2696	68	17	is	be	AUX
ejpam-2696	68	18	generalized	generalize	VERB
ejpam-2696	68	19	.	.	PUNCT
ejpam-2696	69	1	definition	definition	NOUN
ejpam-2696	69	2	1	1	NUM
ejpam-2696	69	3	.	.	PUNCT
ejpam-2696	70	1	a	a	DET
ejpam-2696	70	2	γ	γ	NOUN
ejpam-2696	70	3	-	-	PUNCT
ejpam-2696	70	4	representation	representation	NOUN
ejpam-2696	70	5	of	of	ADP
ejpam-2696	70	6	a	a	DET
ejpam-2696	70	7	γ	γ	NOUN
ejpam-2696	70	8	-	-	PUNCT
ejpam-2696	70	9	semigroup	semigroup	NOUN
ejpam-2696	70	10	s	s	NOUN
ejpam-2696	70	11	by	by	ADP
ejpam-2696	70	12	γ	γ	NOUN
ejpam-2696	70	13	-	-	PUNCT
ejpam-2696	70	14	transformations	transformation	NOUN
ejpam-2696	70	15	of	of	ADP
ejpam-2696	70	16	a	a	DET
ejpam-2696	70	17	nonempty	nonempty	NOUN
ejpam-2696	70	18	set	set	VERB
ejpam-2696	70	19	a	a	PRON
ejpam-2696	70	20	is	be	AUX
ejpam-2696	70	21	a	a	DET
ejpam-2696	70	22	γ	γ	NOUN
ejpam-2696	70	23	-	-	PUNCT
ejpam-2696	70	24	semigroup	semigroup	NOUN
ejpam-2696	70	25	homomorphism	homomorphism	NOUN
ejpam-2696	70	26	φ	φ	X
ejpam-2696	70	27	:	:	PUNCT
ejpam-2696	70	28	s	s	X
ejpam-2696	70	29	→	→	X
ejpam-2696	70	30	a	a	X
ejpam-2696	70	31	,	,	PUNCT
ejpam-2696	70	32	where	where	SCONJ
ejpam-2696	70	33	a	a	PRON
ejpam-2696	70	34	is	be	AUX
ejpam-2696	70	35	the	the	DET
ejpam-2696	70	36	γ	γ	PROPN
ejpam-2696	70	37	-	-	PUNCT
ejpam-2696	70	38	semigroup	semigroup	PROPN
ejpam-2696	70	39	described	describe	VERB
ejpam-2696	70	40	in	in	ADP
ejpam-2696	70	41	lemma	lemma	PROPN
ejpam-2696	70	42	1	1	NUM
ejpam-2696	70	43	.	.	PUNCT
ejpam-2696	70	44	proposition	proposition	NOUN
ejpam-2696	70	45	1	1	NUM
ejpam-2696	70	46	.	.	PUNCT
ejpam-2696	71	1	every	every	DET
ejpam-2696	71	2	γ	γ	NOUN
ejpam-2696	71	3	-	-	PUNCT
ejpam-2696	71	4	representation	representation	NOUN
ejpam-2696	71	5	of	of	ADP
ejpam-2696	71	6	a	a	DET
ejpam-2696	71	7	γ	γ	NOUN
ejpam-2696	71	8	-	-	PUNCT
ejpam-2696	71	9	semigroup	semigroup	NOUN
ejpam-2696	71	10	s	s	NOUN
ejpam-2696	71	11	by	by	ADP
ejpam-2696	71	12	γ	γ	NOUN
ejpam-2696	71	13	-	-	PUNCT
ejpam-2696	71	14	transformations	transformation	NOUN
ejpam-2696	71	15	of	of	ADP
ejpam-2696	71	16	a	a	DET
ejpam-2696	71	17	non	non	ADJ
ejpam-2696	71	18	-	-	ADJ
ejpam-2696	71	19	empty	empty	ADJ
ejpam-2696	71	20	set	set	NOUN
ejpam-2696	71	21	a	a	PRON
ejpam-2696	71	22	in	in	ADP
ejpam-2696	71	23	a	a	DET
ejpam-2696	71	24	turns	turn	NOUN
ejpam-2696	71	25	a	a	PRON
ejpam-2696	71	26	into	into	ADP
ejpam-2696	71	27	a	a	DET
ejpam-2696	71	28	γ	γ	X
ejpam-2696	71	29	-	-	PUNCT
ejpam-2696	71	30	s	s	NOUN
ejpam-2696	71	31	-	-	PUNCT
ejpam-2696	71	32	act	act	NOUN
ejpam-2696	71	33	.	.	PUNCT
ejpam-2696	72	1	conversely	conversely	ADV
ejpam-2696	72	2	,	,	PUNCT
ejpam-2696	72	3	for	for	ADP
ejpam-2696	72	4	every	every	DET
ejpam-2696	72	5	γ	γ	PROPN
ejpam-2696	72	6	-	-	PUNCT
ejpam-2696	72	7	s	s	NOUN
ejpam-2696	72	8	-	-	PUNCT
ejpam-2696	72	9	act	act	NOUN
ejpam-2696	72	10	γa	γa	NOUN
ejpam-2696	72	11	,	,	PUNCT
ejpam-2696	72	12	there	there	PRON
ejpam-2696	72	13	is	be	VERB
ejpam-2696	72	14	an	an	DET
ejpam-2696	72	15	associated	associated	ADJ
ejpam-2696	72	16	γ	γ	NOUN
ejpam-2696	72	17	-	-	NOUN
ejpam-2696	72	18	representation	representation	NOUN
ejpam-2696	72	19	of	of	ADP
ejpam-2696	72	20	s	s	NUM
ejpam-2696	72	21	by	by	ADP
ejpam-2696	72	22	γ	γ	NOUN
ejpam-2696	72	23	-	-	PUNCT
ejpam-2696	72	24	transformations	transformation	NOUN
ejpam-2696	72	25	of	of	ADP
ejpam-2696	72	26	a	a	PRON
ejpam-2696	72	27	in	in	ADP
ejpam-2696	72	28	a.	a.	NOUN
ejpam-2696	72	29	proof	proof	NOUN
ejpam-2696	72	30	.	.	PUNCT
ejpam-2696	73	1	let	let	VERB
ejpam-2696	73	2	a	a	PRON
ejpam-2696	73	3	be	be	AUX
ejpam-2696	73	4	a	a	DET
ejpam-2696	73	5	non	non	ADJ
ejpam-2696	73	6	-	-	ADJ
ejpam-2696	73	7	empty	empty	ADJ
ejpam-2696	73	8	set	set	NOUN
ejpam-2696	73	9	and	and	CCONJ
ejpam-2696	73	10	s	s	AUX
ejpam-2696	73	11	be	be	AUX
ejpam-2696	73	12	a	a	DET
ejpam-2696	73	13	γ	γ	NOUN
ejpam-2696	73	14	-	-	PUNCT
ejpam-2696	73	15	semigroup	semigroup	NOUN
ejpam-2696	73	16	.	.	PUNCT
ejpam-2696	74	1	if	if	SCONJ
ejpam-2696	74	2	φ	φ	PROPN
ejpam-2696	74	3	:	:	PUNCT
ejpam-2696	74	4	s	s	X
ejpam-2696	74	5	→	→	X
ejpam-2696	74	6	a	a	PRON
ejpam-2696	74	7	is	be	AUX
ejpam-2696	74	8	a	a	DET
ejpam-2696	74	9	γrepresentation	γrepresentation	NOUN
ejpam-2696	74	10	,	,	PUNCT
ejpam-2696	74	11	define	define	VERB
ejpam-2696	74	12	λ	λ	X
ejpam-2696	74	13	:	:	PUNCT
ejpam-2696	74	14	s	s	AUX
ejpam-2696	74	15	×	×	PROPN
ejpam-2696	74	16	γ	γ	X
ejpam-2696	74	17	×	×	PROPN
ejpam-2696	74	18	a	a	DET
ejpam-2696	74	19	→	→	PUNCT
ejpam-2696	74	20	a	a	PRON
ejpam-2696	74	21	by	by	ADP
ejpam-2696	74	22	sγa	sγa	PROPN
ejpam-2696	74	23	=	=	SYM
ejpam-2696	74	24	λ(s	λ(s	PROPN
ejpam-2696	74	25	,	,	PUNCT
ejpam-2696	74	26	γ	γ	PROPN
ejpam-2696	74	27	,	,	PUNCT
ejpam-2696	74	28	a	a	PRON
ejpam-2696	74	29	)	)	PUNCT
ejpam-2696	74	30	:	:	PUNCT
ejpam-2696	74	31	=	=	SYM
ejpam-2696	74	32	φ(s)(γ)(a	φ(s)(γ)(a	NOUN
ejpam-2696	74	33	)	)	PUNCT
ejpam-2696	74	34	,	,	PUNCT
ejpam-2696	74	35	for	for	ADP
ejpam-2696	74	36	all	all	DET
ejpam-2696	74	37	s	s	PART
ejpam-2696	74	38	∈	∈	PROPN
ejpam-2696	74	39	s	s	NOUN
ejpam-2696	74	40	,	,	PUNCT
ejpam-2696	74	41	γ	γ	PROPN
ejpam-2696	74	42	∈	∈	PROPN
ejpam-2696	74	43	γ	γ	X
ejpam-2696	74	44	,	,	PUNCT
ejpam-2696	74	45	a	a	DET
ejpam-2696	74	46	∈	∈	NOUN
ejpam-2696	74	47	a.	a.	NOUN
ejpam-2696	74	48	then	then	ADV
ejpam-2696	74	49	a	a	PRON
ejpam-2696	74	50	is	be	AUX
ejpam-2696	74	51	a	a	DET
ejpam-2696	74	52	γ	γ	PROPN
ejpam-2696	74	53	-	-	PUNCT
ejpam-2696	74	54	s	s	NOUN
ejpam-2696	74	55	-	-	PUNCT
ejpam-2696	74	56	act	act	NOUN
ejpam-2696	74	57	.	.	PUNCT
ejpam-2696	75	1	for	for	ADP
ejpam-2696	75	2	this	this	PRON
ejpam-2696	75	3	,	,	PUNCT
ejpam-2696	75	4	let	let	VERB
ejpam-2696	75	5	s	s	NOUN
ejpam-2696	75	6	,	,	PUNCT
ejpam-2696	75	7	s′	s′	ADJ
ejpam-2696	75	8	∈	∈	PROPN
ejpam-2696	75	9	s	s	NOUN
ejpam-2696	75	10	,	,	PUNCT
ejpam-2696	75	11	γ	γ	X
ejpam-2696	75	12	,	,	PUNCT
ejpam-2696	75	13	γ′	γ′	PROPN
ejpam-2696	75	14	∈	∈	PROPN
ejpam-2696	75	15	γ	γ	X
ejpam-2696	75	16	,	,	PUNCT
ejpam-2696	75	17	a	a	DET
ejpam-2696	75	18	∈	∈	NOUN
ejpam-2696	75	19	a.	a.	NOUN
ejpam-2696	75	20	we	we	PRON
ejpam-2696	75	21	have	have	VERB
ejpam-2696	75	22	(	(	PUNCT
ejpam-2696	75	23	sγs′)γ′a	sγs′)γ′a	PROPN
ejpam-2696	75	24	=	=	SYM
ejpam-2696	75	25	φ(sγs′)(γ′)(a	φ(sγs′)(γ′)(a	PROPN
ejpam-2696	75	26	)	)	PUNCT
ejpam-2696	75	27	=	=	SYM
ejpam-2696	75	28	(	(	PUNCT
ejpam-2696	75	29	φ(s)γφ(s′))(γ′)(a	φ(s)γφ(s′))(γ′)(a	NUM
ejpam-2696	75	30	)	)	PUNCT
ejpam-2696	75	31	=	=	SYM
ejpam-2696	75	32	(	(	PUNCT
ejpam-2696	75	33	φ(s)(γ))(φ(s′)(γ′)(a	φ(s)(γ))(φ(s′)(γ′)(a	NOUN
ejpam-2696	75	34	)	)	PUNCT
ejpam-2696	75	35	)	)	PUNCT
ejpam-2696	76	1	=	=	PRON
ejpam-2696	76	2	(	(	PUNCT
ejpam-2696	76	3	φ(s)(γ))(s′γ′a	φ(s)(γ))(s′γ′a	NOUN
ejpam-2696	76	4	)	)	PUNCT
ejpam-2696	76	5	=	=	SYM
ejpam-2696	77	1	sγ(s′γ′a	sγ(s′γ′a	NOUN
ejpam-2696	77	2	)	)	PUNCT
ejpam-2696	77	3	.	.	PUNCT
ejpam-2696	78	1	also	also	ADV
ejpam-2696	78	2	if	if	SCONJ
ejpam-2696	78	3	e	e	PROPN
ejpam-2696	78	4	and	and	CCONJ
ejpam-2696	78	5	ε	ε	PROPN
ejpam-2696	78	6	are	be	AUX
ejpam-2696	78	7	left	leave	VERB
ejpam-2696	78	8	identities	identity	NOUN
ejpam-2696	78	9	of	of	ADP
ejpam-2696	78	10	s	s	PRON
ejpam-2696	78	11	and	and	CCONJ
ejpam-2696	78	12	a	a	PRON
ejpam-2696	78	13	,	,	PUNCT
ejpam-2696	78	14	respectively	respectively	ADV
ejpam-2696	78	15	,	,	PUNCT
ejpam-2696	78	16	then	then	ADV
ejpam-2696	78	17	eγa	eγa	NOUN
ejpam-2696	78	18	=	=	SYM
ejpam-2696	78	19	φ(e)(γ)(a	φ(e)(γ)(a	NOUN
ejpam-2696	78	20	)	)	PUNCT
ejpam-2696	78	21	=	=	PUNCT
ejpam-2696	79	1	ε(γ)(a	ε(γ)(a	NUM
ejpam-2696	79	2	)	)	PUNCT
ejpam-2696	79	3	=	=	SYM
ejpam-2696	79	4	ida(a	ida(a	PROPN
ejpam-2696	79	5	)	)	PUNCT
ejpam-2696	79	6	=	=	SYM
ejpam-2696	80	1	a.	a.	NOUN
ejpam-2696	80	2	for	for	ADP
ejpam-2696	80	3	the	the	DET
ejpam-2696	80	4	converse	converse	NOUN
ejpam-2696	80	5	,	,	PUNCT
ejpam-2696	80	6	consider	consider	VERB
ejpam-2696	80	7	any	any	DET
ejpam-2696	80	8	γ	γ	PROPN
ejpam-2696	80	9	-	-	PUNCT
ejpam-2696	80	10	s	s	NOUN
ejpam-2696	80	11	-	-	PUNCT
ejpam-2696	80	12	act	act	NOUN
ejpam-2696	80	13	γa	γa	PROPN
ejpam-2696	80	14	.	.	PUNCT
ejpam-2696	81	1	define	define	VERB
ejpam-2696	81	2	φ	φ	NOUN
ejpam-2696	81	3	:	:	PUNCT
ejpam-2696	81	4	s	s	X
ejpam-2696	81	5	→	→	SYM
ejpam-2696	81	6	a	a	DET
ejpam-2696	81	7	h.	h.	PROPN
ejpam-2696	81	8	rasouli	rasouli	PROPN
ejpam-2696	81	9	,	,	PUNCT
ejpam-2696	81	10	a.r	a.r	PROPN
ejpam-2696	81	11	.	.	PROPN
ejpam-2696	81	12	shabani	shabani	PROPN
ejpam-2696	81	13	/	/	SYM
ejpam-2696	81	14	eur	eur	PROPN
ejpam-2696	81	15	.	.	PUNCT
ejpam-2696	82	1	j.	j.	PROPN
ejpam-2696	82	2	pure	pure	PROPN
ejpam-2696	82	3	appl	appl	PROPN
ejpam-2696	82	4	.	.	PROPN
ejpam-2696	82	5	math	math	PROPN
ejpam-2696	82	6	,	,	PUNCT
ejpam-2696	82	7	10	10	NUM
ejpam-2696	82	8	(	(	PUNCT
ejpam-2696	82	9	4	4	NUM
ejpam-2696	82	10	)	)	PUNCT
ejpam-2696	82	11	(	(	PUNCT
ejpam-2696	82	12	2017	2017	NUM
ejpam-2696	82	13	)	)	PUNCT
ejpam-2696	82	14	,	,	PUNCT
ejpam-2696	82	15	739	739	NUM
ejpam-2696	82	16	-	-	SYM
ejpam-2696	82	17	748	748	NUM
ejpam-2696	82	18	742	742	NUM
ejpam-2696	82	19	by	by	ADP
ejpam-2696	82	20	φ(s	φ(	VERB
ejpam-2696	82	21	)	)	PUNCT
ejpam-2696	82	22	=	=	VERB
ejpam-2696	83	1	ϕs	ϕs	ADP
ejpam-2696	83	2	:	:	PUNCT
ejpam-2696	83	3	γ	γ	X
ejpam-2696	83	4	→	→	SYM
ejpam-2696	83	5	aa	aa	PROPN
ejpam-2696	83	6	,	,	PUNCT
ejpam-2696	83	7	where	where	SCONJ
ejpam-2696	83	8	ϕs(γ)(a	ϕs(γ)(a	NOUN
ejpam-2696	83	9	)	)	PUNCT
ejpam-2696	83	10	:	:	PUNCT
ejpam-2696	83	11	=	=	PUNCT
ejpam-2696	83	12	sγa	sγa	ADJ
ejpam-2696	83	13	for	for	ADP
ejpam-2696	83	14	all	all	DET
ejpam-2696	83	15	s	s	PART
ejpam-2696	83	16	∈	∈	PROPN
ejpam-2696	83	17	s	s	NOUN
ejpam-2696	83	18	,	,	PUNCT
ejpam-2696	83	19	γ	γ	PROPN
ejpam-2696	83	20	∈	∈	PROPN
ejpam-2696	83	21	γ	γ	X
ejpam-2696	83	22	,	,	PUNCT
ejpam-2696	83	23	a	a	DET
ejpam-2696	83	24	∈	∈	NOUN
ejpam-2696	83	25	a.	a.	NOUN
ejpam-2696	83	26	it	it	PRON
ejpam-2696	83	27	must	must	AUX
ejpam-2696	83	28	be	be	AUX
ejpam-2696	83	29	shown	show	VERB
ejpam-2696	83	30	that	that	SCONJ
ejpam-2696	83	31	φ	φ	PROPN
ejpam-2696	83	32	is	be	AUX
ejpam-2696	83	33	a	a	DET
ejpam-2696	83	34	γ	γ	NOUN
ejpam-2696	83	35	-	-	PUNCT
ejpam-2696	83	36	semigroup	semigroup	ADJ
ejpam-2696	83	37	homomorphism	homomorphism	NOUN
ejpam-2696	83	38	.	.	PUNCT
ejpam-2696	84	1	let	let	VERB
ejpam-2696	84	2	s	s	NOUN
ejpam-2696	84	3	,	,	PUNCT
ejpam-2696	84	4	s′	s′	ADJ
ejpam-2696	84	5	∈	∈	PROPN
ejpam-2696	84	6	s	s	NOUN
ejpam-2696	84	7	and	and	CCONJ
ejpam-2696	84	8	γ	γ	PROPN
ejpam-2696	84	9	∈	∈	PROPN
ejpam-2696	84	10	γ	γ	X
ejpam-2696	84	11	.	.	PROPN
ejpam-2696	84	12	then	then	ADV
ejpam-2696	84	13	φ(sγs′	φ(sγs′	NUM
ejpam-2696	84	14	)	)	PUNCT
ejpam-2696	85	1	=	=	SYM
ejpam-2696	86	1	φ(s)γφ(s′	φ(s)γφ(s′	ADJ
ejpam-2696	86	2	)	)	PUNCT
ejpam-2696	86	3	,	,	PUNCT
ejpam-2696	86	4	or	or	CCONJ
ejpam-2696	86	5	equivalently	equivalently	ADV
ejpam-2696	86	6	,	,	PUNCT
ejpam-2696	86	7	ϕsγs′	ϕsγs′	PUNCT
ejpam-2696	87	1	=	=	SYM
ejpam-2696	87	2	ϕsγϕs′	ϕsγϕs′	PROPN
ejpam-2696	87	3	.	.	PUNCT
ejpam-2696	88	1	to	to	PART
ejpam-2696	88	2	see	see	VERB
ejpam-2696	88	3	this	this	PRON
ejpam-2696	88	4	,	,	PUNCT
ejpam-2696	88	5	let	let	VERB
ejpam-2696	88	6	β	β	PRON
ejpam-2696	88	7	∈	∈	PROPN
ejpam-2696	88	8	γ	γ	NOUN
ejpam-2696	88	9	and	and	CCONJ
ejpam-2696	88	10	a	a	DET
ejpam-2696	88	11	∈	∈	NOUN
ejpam-2696	88	12	a.	a.	NOUN
ejpam-2696	88	13	we	we	PRON
ejpam-2696	88	14	get	get	VERB
ejpam-2696	88	15	ϕsγs′(β)(a	ϕsγs′(β)(a	PRON
ejpam-2696	88	16	)	)	PUNCT
ejpam-2696	89	1	=	=	SYM
ejpam-2696	89	2	(	(	PUNCT
ejpam-2696	89	3	sγs′)βa	sγs′)βa	PROPN
ejpam-2696	89	4	=	=	PUNCT
ejpam-2696	89	5	sγ(s′βa	sγ(s′βa	PROPN
ejpam-2696	89	6	)	)	PUNCT
ejpam-2696	89	7	=	=	SYM
ejpam-2696	89	8	sγ(ϕs′(β)(a	sγ(ϕs′(β)(a	NOUN
ejpam-2696	89	9	)	)	PUNCT
ejpam-2696	89	10	)	)	PUNCT
ejpam-2696	90	1	=	=	PUNCT
ejpam-2696	90	2	ϕs(γ)ϕs′(β)(a	ϕs(γ)ϕs′(β)(a	NUM
ejpam-2696	90	3	)	)	PUNCT
ejpam-2696	90	4	=	=	SYM
ejpam-2696	90	5	(	(	PUNCT
ejpam-2696	90	6	ϕsγϕs′)(β)(a	ϕsγϕs′)(β)(a	NOUN
ejpam-2696	90	7	)	)	PUNCT
ejpam-2696	90	8	.	.	PUNCT
ejpam-2696	91	1	therefore	therefore	ADV
ejpam-2696	91	2	,	,	PUNCT
ejpam-2696	91	3	φ	φ	PROPN
ejpam-2696	91	4	is	be	AUX
ejpam-2696	91	5	a	a	DET
ejpam-2696	91	6	γ	γ	NOUN
ejpam-2696	91	7	-	-	NOUN
ejpam-2696	91	8	representation	representation	NOUN
ejpam-2696	91	9	.	.	PUNCT
ejpam-2696	92	1	remark	remark	NOUN
ejpam-2696	92	2	1	1	NUM
ejpam-2696	92	3	.	.	PUNCT
ejpam-2696	93	1	(	(	PUNCT
ejpam-2696	93	2	i	i	NOUN
ejpam-2696	93	3	)	)	PUNCT
ejpam-2696	93	4	every	every	DET
ejpam-2696	93	5	s	s	PROPN
ejpam-2696	93	6	-	-	NOUN
ejpam-2696	93	7	act	act	NOUN
ejpam-2696	93	8	a	a	PRON
ejpam-2696	93	9	over	over	ADP
ejpam-2696	93	10	a	a	DET
ejpam-2696	93	11	semigroup	semigroup	NOUN
ejpam-2696	93	12	s	s	VERB
ejpam-2696	93	13	can	can	AUX
ejpam-2696	93	14	be	be	AUX
ejpam-2696	93	15	generalized	generalize	VERB
ejpam-2696	93	16	to	to	ADP
ejpam-2696	93	17	a	a	DET
ejpam-2696	93	18	γ	γ	X
ejpam-2696	93	19	-	-	PUNCT
ejpam-2696	93	20	s	s	NOUN
ejpam-2696	93	21	-	-	PUNCT
ejpam-2696	93	22	act	act	NOUN
ejpam-2696	93	23	over	over	ADP
ejpam-2696	93	24	the	the	DET
ejpam-2696	93	25	induced	induced	ADJ
ejpam-2696	93	26	γ	γ	PROPN
ejpam-2696	93	27	-	-	PUNCT
ejpam-2696	93	28	semigroup	semigroup	PROPN
ejpam-2696	93	29	s.	s.	PROPN
ejpam-2696	93	30	indeed	indeed	ADV
ejpam-2696	93	31	,	,	PUNCT
ejpam-2696	93	32	first	first	ADV
ejpam-2696	93	33	note	note	VERB
ejpam-2696	93	34	that	that	SCONJ
ejpam-2696	93	35	a	a	DET
ejpam-2696	93	36	semigroup	semigroup	NOUN
ejpam-2696	93	37	s	s	VERB
ejpam-2696	93	38	can	can	AUX
ejpam-2696	93	39	be	be	AUX
ejpam-2696	93	40	made	make	VERB
ejpam-2696	93	41	into	into	ADP
ejpam-2696	93	42	a	a	DET
ejpam-2696	93	43	γ	γ	NOUN
ejpam-2696	93	44	-	-	PUNCT
ejpam-2696	93	45	semigroup	semigroup	NOUN
ejpam-2696	93	46	by	by	ADP
ejpam-2696	93	47	setting	set	VERB
ejpam-2696	93	48	sγt	sγt	NOUN
ejpam-2696	93	49	:	:	PUNCT
ejpam-2696	93	50	=	=	SYM
ejpam-2696	93	51	st	st	PROPN
ejpam-2696	93	52	for	for	ADP
ejpam-2696	93	53	every	every	DET
ejpam-2696	93	54	s	s	PROPN
ejpam-2696	93	55	,	,	PUNCT
ejpam-2696	93	56	t	t	PROPN
ejpam-2696	93	57	∈	∈	PROPN
ejpam-2696	93	58	s	s	PART
ejpam-2696	93	59	and	and	CCONJ
ejpam-2696	93	60	γ	γ	PROPN
ejpam-2696	93	61	∈	∈	PROPN
ejpam-2696	93	62	γ	γ	X
ejpam-2696	93	63	.	.	PUNCT
ejpam-2696	93	64	now	now	ADV
ejpam-2696	93	65	define	define	VERB
ejpam-2696	93	66	a	a	DET
ejpam-2696	93	67	mapping	mapping	NOUN
ejpam-2696	93	68	from	from	ADP
ejpam-2696	93	69	s	s	PROPN
ejpam-2696	93	70	×	×	PROPN
ejpam-2696	93	71	γ	γ	X
ejpam-2696	93	72	×	×	NOUN
ejpam-2696	93	73	a	a	PRON
ejpam-2696	93	74	to	to	ADP
ejpam-2696	93	75	a	a	PRON
ejpam-2696	93	76	by	by	ADP
ejpam-2696	93	77	sγa	sγa	NOUN
ejpam-2696	93	78	:	:	PUNCT
ejpam-2696	93	79	=	=	SYM
ejpam-2696	93	80	sa	sa	NOUN
ejpam-2696	93	81	for	for	ADP
ejpam-2696	93	82	every	every	DET
ejpam-2696	93	83	s	s	X
ejpam-2696	93	84	∈	∈	PROPN
ejpam-2696	93	85	s	s	PROPN
ejpam-2696	93	86	,	,	PUNCT
ejpam-2696	93	87	γ	γ	PROPN
ejpam-2696	93	88	∈	∈	PROPN
ejpam-2696	93	89	γ	γ	NOUN
ejpam-2696	93	90	and	and	CCONJ
ejpam-2696	93	91	a	a	DET
ejpam-2696	93	92	∈	∈	PROPN
ejpam-2696	93	93	a.	a.	NOUN
ejpam-2696	93	94	then	then	ADV
ejpam-2696	93	95	a	a	PRON
ejpam-2696	93	96	is	be	AUX
ejpam-2696	93	97	a	a	DET
ejpam-2696	93	98	γ	γ	PROPN
ejpam-2696	93	99	-	-	PUNCT
ejpam-2696	93	100	s	s	NOUN
ejpam-2696	93	101	-	-	PUNCT
ejpam-2696	93	102	act	act	NOUN
ejpam-2696	93	103	.	.	PUNCT
ejpam-2696	94	1	moreover	moreover	ADV
ejpam-2696	94	2	,	,	PUNCT
ejpam-2696	94	3	if	if	SCONJ
ejpam-2696	94	4	a	a	PRON
ejpam-2696	94	5	is	be	AUX
ejpam-2696	94	6	a	a	DET
ejpam-2696	94	7	γ	γ	PROPN
ejpam-2696	94	8	-	-	PUNCT
ejpam-2696	94	9	s	s	NOUN
ejpam-2696	94	10	-	-	NOUN
ejpam-2696	94	11	act	act	NOUN
ejpam-2696	94	12	over	over	ADP
ejpam-2696	94	13	a	a	DET
ejpam-2696	94	14	γ	γ	NOUN
ejpam-2696	94	15	-	-	PUNCT
ejpam-2696	94	16	semigroup	semigroup	NOUN
ejpam-2696	94	17	s	s	NOUN
ejpam-2696	94	18	and	and	CCONJ
ejpam-2696	94	19	γ	γ	PROPN
ejpam-2696	94	20	is	be	AUX
ejpam-2696	94	21	a	a	DET
ejpam-2696	94	22	fixed	fix	VERB
ejpam-2696	94	23	element	element	NOUN
ejpam-2696	94	24	of	of	ADP
ejpam-2696	94	25	γ	γ	PROPN
ejpam-2696	94	26	,	,	PUNCT
ejpam-2696	94	27	then	then	ADV
ejpam-2696	94	28	s	s	VERB
ejpam-2696	94	29	is	be	AUX
ejpam-2696	94	30	a	a	DET
ejpam-2696	94	31	semigroup	semigroup	NOUN
ejpam-2696	94	32	under	under	ADP
ejpam-2696	94	33	the	the	DET
ejpam-2696	94	34	operation	operation	NOUN
ejpam-2696	94	35	st	st	PROPN
ejpam-2696	94	36	:	:	PUNCT
ejpam-2696	94	37	=	=	SYM
ejpam-2696	94	38	sγt	sγt	VERB
ejpam-2696	94	39	for	for	ADP
ejpam-2696	94	40	all	all	DET
ejpam-2696	94	41	s	s	PROPN
ejpam-2696	94	42	,	,	PUNCT
ejpam-2696	94	43	t	t	PROPN
ejpam-2696	94	44	∈	∈	PROPN
ejpam-2696	94	45	s	s	PROPN
ejpam-2696	94	46	,	,	PUNCT
ejpam-2696	94	47	and	and	CCONJ
ejpam-2696	94	48	a	a	PRON
ejpam-2696	94	49	with	with	ADP
ejpam-2696	94	50	the	the	DET
ejpam-2696	94	51	action	action	NOUN
ejpam-2696	94	52	sa	sa	NOUN
ejpam-2696	94	53	:	:	PUNCT
ejpam-2696	94	54	=	=	SYM
ejpam-2696	94	55	sγa	sγa	PROPN
ejpam-2696	94	56	,	,	PUNCT
ejpam-2696	94	57	for	for	ADP
ejpam-2696	94	58	every	every	DET
ejpam-2696	94	59	s	s	X
ejpam-2696	94	60	∈	∈	PROPN
ejpam-2696	94	61	s	s	NOUN
ejpam-2696	94	62	and	and	CCONJ
ejpam-2696	94	63	a	a	DET
ejpam-2696	94	64	∈	∈	PROPN
ejpam-2696	94	65	a	a	PRON
ejpam-2696	94	66	,	,	PUNCT
ejpam-2696	94	67	is	be	AUX
ejpam-2696	94	68	an	an	DET
ejpam-2696	94	69	s	s	NOUN
ejpam-2696	94	70	-	-	NOUN
ejpam-2696	94	71	act	act	NOUN
ejpam-2696	94	72	.	.	PUNCT
ejpam-2696	95	1	(	(	PUNCT
ejpam-2696	95	2	ii	ii	NOUN
ejpam-2696	95	3	)	)	PUNCT
ejpam-2696	95	4	a	a	DET
ejpam-2696	95	5	γ	γ	PROPN
ejpam-2696	95	6	-	-	PUNCT
ejpam-2696	95	7	s	s	NOUN
ejpam-2696	95	8	-	-	PUNCT
ejpam-2696	95	9	act	act	NOUN
ejpam-2696	95	10	can	can	AUX
ejpam-2696	95	11	have	have	VERB
ejpam-2696	95	12	more	more	ADJ
ejpam-2696	95	13	than	than	ADP
ejpam-2696	95	14	one	one	NUM
ejpam-2696	95	15	zero	zero	NUM
ejpam-2696	95	16	,	,	PUNCT
ejpam-2696	95	17	for	for	ADP
ejpam-2696	95	18	instance	instance	NOUN
ejpam-2696	95	19	,	,	PUNCT
ejpam-2696	95	20	any	any	DET
ejpam-2696	95	21	non	non	ADJ
ejpam-2696	95	22	-	-	ADJ
ejpam-2696	95	23	empty	empty	ADJ
ejpam-2696	95	24	set	set	NOUN
ejpam-2696	95	25	a	a	PRON
ejpam-2696	95	26	becomes	become	VERB
ejpam-2696	95	27	a	a	DET
ejpam-2696	95	28	γ	γ	PROPN
ejpam-2696	95	29	-	-	PUNCT
ejpam-2696	95	30	s	s	NOUN
ejpam-2696	95	31	-	-	NOUN
ejpam-2696	95	32	act	act	NOUN
ejpam-2696	95	33	by	by	ADP
ejpam-2696	95	34	definition	definition	NOUN
ejpam-2696	95	35	sγa	sγa	NOUN
ejpam-2696	96	1	=	=	PUNCT
ejpam-2696	96	2	a	a	PRON
ejpam-2696	96	3	for	for	ADP
ejpam-2696	96	4	every	every	DET
ejpam-2696	96	5	a	a	DET
ejpam-2696	96	6	∈	∈	PROPN
ejpam-2696	96	7	a	a	PRON
ejpam-2696	96	8	,	,	PUNCT
ejpam-2696	96	9	s	s	NOUN
ejpam-2696	96	10	∈	∈	PROPN
ejpam-2696	96	11	s	s	NOUN
ejpam-2696	96	12	and	and	CCONJ
ejpam-2696	96	13	γ	γ	PROPN
ejpam-2696	96	14	∈	∈	PROPN
ejpam-2696	96	15	γ	γ	X
ejpam-2696	96	16	,	,	PUNCT
ejpam-2696	96	17	i.e.	i.e.	X
ejpam-2696	96	18	all	all	DET
ejpam-2696	96	19	elements	element	NOUN
ejpam-2696	96	20	of	of	ADP
ejpam-2696	96	21	a	a	PRON
ejpam-2696	96	22	are	be	AUX
ejpam-2696	96	23	zero	zero	NUM
ejpam-2696	96	24	.	.	PUNCT
ejpam-2696	97	1	if	if	SCONJ
ejpam-2696	97	2	s	s	PROPN
ejpam-2696	97	3	has	have	VERB
ejpam-2696	97	4	a	a	DET
ejpam-2696	97	5	right	right	ADJ
ejpam-2696	97	6	zero	zero	NUM
ejpam-2696	97	7	z	z	NOUN
ejpam-2696	97	8	,	,	PUNCT
ejpam-2696	97	9	i.e.	i.e.	X
ejpam-2696	97	10	sαz	sαz	X
ejpam-2696	97	11	=	=	SYM
ejpam-2696	97	12	z	z	NOUN
ejpam-2696	97	13	for	for	ADP
ejpam-2696	97	14	any	any	DET
ejpam-2696	97	15	s	s	X
ejpam-2696	97	16	∈	∈	PROPN
ejpam-2696	97	17	s	s	NOUN
ejpam-2696	97	18	,	,	PUNCT
ejpam-2696	97	19	α	α	PROPN
ejpam-2696	97	20	∈	∈	PROPN
ejpam-2696	97	21	γ	γ	X
ejpam-2696	97	22	,	,	PUNCT
ejpam-2696	97	23	then	then	ADV
ejpam-2696	97	24	every	every	DET
ejpam-2696	97	25	element	element	NOUN
ejpam-2696	97	26	zγa	zγa	NOUN
ejpam-2696	97	27	for	for	ADP
ejpam-2696	97	28	a	a	DET
ejpam-2696	97	29	∈	∈	PROPN
ejpam-2696	97	30	a	a	PRON
ejpam-2696	97	31	and	and	CCONJ
ejpam-2696	97	32	γ	γ	PROPN
ejpam-2696	97	33	∈	∈	PROPN
ejpam-2696	97	34	γ	γ	X
ejpam-2696	97	35	is	be	AUX
ejpam-2696	97	36	a	a	DET
ejpam-2696	97	37	zero	zero	NUM
ejpam-2696	97	38	element	element	NOUN
ejpam-2696	97	39	of	of	ADP
ejpam-2696	97	40	a.	a.	NOUN
ejpam-2696	97	41	indeed	indeed	ADV
ejpam-2696	97	42	,	,	PUNCT
ejpam-2696	97	43	for	for	ADP
ejpam-2696	97	44	every	every	DET
ejpam-2696	97	45	s	s	X
ejpam-2696	97	46	∈	∈	PROPN
ejpam-2696	97	47	s	s	NOUN
ejpam-2696	97	48	and	and	CCONJ
ejpam-2696	97	49	α	α	PRON
ejpam-2696	97	50	∈	∈	PROPN
ejpam-2696	97	51	γ	γ	X
ejpam-2696	97	52	,	,	PUNCT
ejpam-2696	97	53	sα(zγa	sα(zγa	ADJ
ejpam-2696	97	54	)	)	PUNCT
ejpam-2696	97	55	=	=	SYM
ejpam-2696	97	56	(	(	PUNCT
ejpam-2696	98	1	sαz)γa	sαz)γa	NOUN
ejpam-2696	98	2	=	=	SYM
ejpam-2696	98	3	zγa	zγa	NOUN
ejpam-2696	98	4	.	.	PUNCT
ejpam-2696	99	1	note	note	VERB
ejpam-2696	99	2	that	that	SCONJ
ejpam-2696	99	3	every	every	DET
ejpam-2696	99	4	γ	γ	PROPN
ejpam-2696	99	5	-	-	PUNCT
ejpam-2696	99	6	s	s	NOUN
ejpam-2696	99	7	-	-	PUNCT
ejpam-2696	99	8	act	act	NOUN
ejpam-2696	99	9	a	a	PRON
ejpam-2696	99	10	can	can	AUX
ejpam-2696	99	11	be	be	AUX
ejpam-2696	99	12	extended	extend	VERB
ejpam-2696	99	13	to	to	ADP
ejpam-2696	99	14	a	a	DET
ejpam-2696	99	15	γ	γ	PROPN
ejpam-2696	99	16	-	-	PUNCT
ejpam-2696	99	17	s	s	NOUN
ejpam-2696	99	18	-	-	NOUN
ejpam-2696	99	19	act	act	NOUN
ejpam-2696	99	20	with	with	ADP
ejpam-2696	99	21	a	a	DET
ejpam-2696	99	22	zero	zero	NUM
ejpam-2696	99	23	θ	θ	NOUN
ejpam-2696	99	24	by	by	ADP
ejpam-2696	99	25	taking	take	VERB
ejpam-2696	99	26	the	the	DET
ejpam-2696	99	27	disjoint	disjoint	NOUN
ejpam-2696	99	28	union	union	NOUN
ejpam-2696	99	29	a	a	PRON
ejpam-2696	99	30	∪	∪	X
ejpam-2696	99	31	{	{	PUNCT
ejpam-2696	99	32	θ	θ	NOUN
ejpam-2696	99	33	}	}	PUNCT
ejpam-2696	99	34	.	.	PUNCT
ejpam-2696	100	1	in	in	ADP
ejpam-2696	100	2	the	the	DET
ejpam-2696	100	3	following	following	NOUN
ejpam-2696	100	4	,	,	PUNCT
ejpam-2696	100	5	we	we	PRON
ejpam-2696	100	6	give	give	VERB
ejpam-2696	100	7	some	some	DET
ejpam-2696	100	8	examples	example	NOUN
ejpam-2696	100	9	of	of	ADP
ejpam-2696	100	10	γ	γ	PROPN
ejpam-2696	100	11	-	-	PUNCT
ejpam-2696	100	12	s	s	NOUN
ejpam-2696	100	13	-	-	PUNCT
ejpam-2696	100	14	acts	act	NOUN
ejpam-2696	100	15	.	.	PUNCT
ejpam-2696	101	1	example	example	NOUN
ejpam-2696	102	1	1	1	NUM
ejpam-2696	102	2	.	.	PUNCT
ejpam-2696	103	1	(	(	PUNCT
ejpam-2696	103	2	i	i	NOUN
ejpam-2696	103	3	)	)	PUNCT
ejpam-2696	103	4	let	let	VERB
ejpam-2696	103	5	s	s	NOUN
ejpam-2696	103	6	,	,	PUNCT
ejpam-2696	103	7	γ	γ	PROPN
ejpam-2696	103	8	and	and	CCONJ
ejpam-2696	103	9	m	m	VERB
ejpam-2696	103	10	be	be	VERB
ejpam-2696	103	11	the	the	DET
ejpam-2696	103	12	sets	set	NOUN
ejpam-2696	103	13	of	of	ADP
ejpam-2696	103	14	all	all	DET
ejpam-2696	103	15	3	3	NUM
ejpam-2696	103	16	×	×	NOUN
ejpam-2696	103	17	2	2	NUM
ejpam-2696	103	18	,	,	PUNCT
ejpam-2696	103	19	2	2	NUM
ejpam-2696	103	20	×	×	NOUN
ejpam-2696	103	21	3	3	NUM
ejpam-2696	103	22	and	and	CCONJ
ejpam-2696	103	23	3	3	NUM
ejpam-2696	103	24	×	×	NOUN
ejpam-2696	103	25	3	3	NUM
ejpam-2696	103	26	matrices	matrix	NOUN
ejpam-2696	103	27	over	over	ADP
ejpam-2696	103	28	z	z	NOUN
ejpam-2696	103	29	,	,	PUNCT
ejpam-2696	103	30	respectively	respectively	ADV
ejpam-2696	103	31	.	.	PUNCT
ejpam-2696	104	1	under	under	ADP
ejpam-2696	104	2	the	the	DET
ejpam-2696	104	3	usual	usual	ADJ
ejpam-2696	104	4	matrix	matrix	NOUN
ejpam-2696	104	5	products	product	NOUN
ejpam-2696	104	6	,	,	PUNCT
ejpam-2696	104	7	s	s	VERB
ejpam-2696	104	8	is	be	AUX
ejpam-2696	104	9	a	a	DET
ejpam-2696	104	10	γ	γ	NOUN
ejpam-2696	104	11	-	-	PUNCT
ejpam-2696	104	12	semigroup	semigroup	NOUN
ejpam-2696	104	13	and	and	CCONJ
ejpam-2696	104	14	m	m	PROPN
ejpam-2696	104	15	is	be	AUX
ejpam-2696	104	16	a	a	DET
ejpam-2696	104	17	γ	γ	PROPN
ejpam-2696	104	18	-	-	PUNCT
ejpam-2696	104	19	s	s	NOUN
ejpam-2696	104	20	-	-	PUNCT
ejpam-2696	104	21	act	act	NOUN
ejpam-2696	104	22	but	but	CCONJ
ejpam-2696	104	23	not	not	PART
ejpam-2696	104	24	an	an	DET
ejpam-2696	104	25	s	s	NOUN
ejpam-2696	104	26	-	-	NOUN
ejpam-2696	104	27	act	act	NOUN
ejpam-2696	104	28	.	.	PUNCT
ejpam-2696	105	1	(	(	PUNCT
ejpam-2696	105	2	ii	ii	NOUN
ejpam-2696	105	3	)	)	PUNCT
ejpam-2696	105	4	let	let	VERB
ejpam-2696	105	5	s	s	PRON
ejpam-2696	105	6	=	=	PUNCT
ejpam-2696	105	7	{	{	PUNCT
ejpam-2696	105	8	5n	5n	NOUN
ejpam-2696	105	9	+	+	ADP
ejpam-2696	105	10	4	4	NUM
ejpam-2696	105	11	:	:	PUNCT
ejpam-2696	105	12	n	n	CCONJ
ejpam-2696	105	13	∈	∈	PROPN
ejpam-2696	105	14	n	n	CCONJ
ejpam-2696	105	15	}	}	PUNCT
ejpam-2696	105	16	,	,	PUNCT
ejpam-2696	105	17	γ	γ	X
ejpam-2696	105	18	=	=	SYM
ejpam-2696	105	19	{	{	PUNCT
ejpam-2696	105	20	5n	5n	NOUN
ejpam-2696	105	21	+	+	CCONJ
ejpam-2696	105	22	1	1	NUM
ejpam-2696	105	23	:	:	PUNCT
ejpam-2696	105	24	n	n	CCONJ
ejpam-2696	105	25	∈	∈	PROPN
ejpam-2696	105	26	n	n	CCONJ
ejpam-2696	105	27	}	}	PUNCT
ejpam-2696	105	28	and	and	CCONJ
ejpam-2696	105	29	a	a	DET
ejpam-2696	105	30	=	=	NOUN
ejpam-2696	105	31	{	{	PUNCT
ejpam-2696	105	32	5n	5n	NOUN
ejpam-2696	105	33	:	:	PUNCT
ejpam-2696	105	34	n	n	CCONJ
ejpam-2696	105	35	∈	∈	PROPN
ejpam-2696	105	36	n	n	CCONJ
ejpam-2696	105	37	}	}	PUNCT
ejpam-2696	105	38	.	.	PUNCT
ejpam-2696	106	1	under	under	ADP
ejpam-2696	106	2	the	the	DET
ejpam-2696	106	3	usual	usual	ADJ
ejpam-2696	106	4	addition	addition	NOUN
ejpam-2696	106	5	of	of	ADP
ejpam-2696	106	6	natural	natural	ADJ
ejpam-2696	106	7	numbers	number	NOUN
ejpam-2696	106	8	,	,	PUNCT
ejpam-2696	106	9	s	s	VERB
ejpam-2696	106	10	is	be	AUX
ejpam-2696	106	11	a	a	DET
ejpam-2696	106	12	γ	γ	NOUN
ejpam-2696	106	13	-	-	PUNCT
ejpam-2696	106	14	semigroup	semigroup	NOUN
ejpam-2696	106	15	and	and	CCONJ
ejpam-2696	106	16	a	a	PRON
ejpam-2696	106	17	is	be	AUX
ejpam-2696	106	18	a	a	DET
ejpam-2696	106	19	γ	γ	PROPN
ejpam-2696	106	20	-	-	PUNCT
ejpam-2696	106	21	s	s	NOUN
ejpam-2696	106	22	-	-	PUNCT
ejpam-2696	106	23	act	act	NOUN
ejpam-2696	106	24	but	but	CCONJ
ejpam-2696	106	25	not	not	PART
ejpam-2696	106	26	an	an	DET
ejpam-2696	106	27	s	s	NOUN
ejpam-2696	106	28	-	-	NOUN
ejpam-2696	106	29	act	act	NOUN
ejpam-2696	106	30	.	.	PUNCT
ejpam-2696	107	1	(	(	PUNCT
ejpam-2696	107	2	iii	iii	X
ejpam-2696	107	3	)	)	PUNCT
ejpam-2696	107	4	if	if	SCONJ
ejpam-2696	107	5	a	a	PRON
ejpam-2696	107	6	is	be	AUX
ejpam-2696	107	7	a	a	DET
ejpam-2696	107	8	γ	γ	PROPN
ejpam-2696	107	9	-	-	PUNCT
ejpam-2696	107	10	s	s	NOUN
ejpam-2696	107	11	-	-	PUNCT
ejpam-2696	107	12	act	act	NOUN
ejpam-2696	107	13	,	,	PUNCT
ejpam-2696	107	14	then	then	ADV
ejpam-2696	107	15	the	the	DET
ejpam-2696	107	16	power	power	NOUN
ejpam-2696	107	17	set	set	NOUN
ejpam-2696	107	18	of	of	ADP
ejpam-2696	107	19	a	a	PRON
ejpam-2696	107	20	,	,	PUNCT
ejpam-2696	107	21	p	p	X
ejpam-2696	107	22	(	(	PUNCT
ejpam-2696	107	23	a	a	NOUN
ejpam-2696	107	24	)	)	PUNCT
ejpam-2696	107	25	,	,	PUNCT
ejpam-2696	107	26	is	be	AUX
ejpam-2696	107	27	a	a	DET
ejpam-2696	107	28	γ	γ	PROPN
ejpam-2696	107	29	-	-	PUNCT
ejpam-2696	107	30	s	s	NOUN
ejpam-2696	107	31	-	-	NOUN
ejpam-2696	107	32	act	act	NOUN
ejpam-2696	107	33	under	under	ADP
ejpam-2696	107	34	the	the	DET
ejpam-2696	107	35	γ	γ	NOUN
ejpam-2696	107	36	-	-	NOUN
ejpam-2696	107	37	action	action	NOUN
ejpam-2696	107	38	sγx	sγx	NOUN
ejpam-2696	107	39	=	=	NOUN
ejpam-2696	107	40	:	:	PUNCT
ejpam-2696	107	41	{	{	PUNCT
ejpam-2696	107	42	sγx	sγx	INTJ
ejpam-2696	107	43	|	|	ADV
ejpam-2696	107	44	x	x	SYM
ejpam-2696	107	45	∈	∈	NOUN
ejpam-2696	107	46	x	x	X
ejpam-2696	107	47	}	}	PUNCT
ejpam-2696	107	48	for	for	ADP
ejpam-2696	107	49	s	s	PROPN
ejpam-2696	107	50	∈	∈	PROPN
ejpam-2696	107	51	s	s	NOUN
ejpam-2696	107	52	,	,	PUNCT
ejpam-2696	107	53	x	x	SYM
ejpam-2696	107	54	∈	∈	PROPN
ejpam-2696	107	55	p	p	X
ejpam-2696	107	56	(	(	PUNCT
ejpam-2696	107	57	a	a	NOUN
ejpam-2696	107	58	)	)	PUNCT
ejpam-2696	107	59	and	and	CCONJ
ejpam-2696	107	60	γ	γ	PROPN
ejpam-2696	107	61	∈	∈	PROPN
ejpam-2696	107	62	γ	γ	X
ejpam-2696	107	63	.	.	PROPN
ejpam-2696	107	64	(	(	PUNCT
ejpam-2696	107	65	iv	iv	X
ejpam-2696	107	66	)	)	PUNCT
ejpam-2696	107	67	let	let	VERB
ejpam-2696	107	68	s	s	PRON
ejpam-2696	107	69	be	be	AUX
ejpam-2696	107	70	a	a	DET
ejpam-2696	107	71	γ	γ	NOUN
ejpam-2696	107	72	-	-	PUNCT
ejpam-2696	107	73	semigroup	semigroup	NOUN
ejpam-2696	107	74	.	.	PUNCT
ejpam-2696	108	1	then	then	ADV
ejpam-2696	108	2	the	the	DET
ejpam-2696	108	3	set	set	NOUN
ejpam-2696	108	4	of	of	ADP
ejpam-2696	108	5	all	all	DET
ejpam-2696	108	6	2	2	NUM
ejpam-2696	108	7	×	×	NOUN
ejpam-2696	108	8	2	2	NUM
ejpam-2696	108	9	matrices	matrix	NOUN
ejpam-2696	108	10	over	over	ADP
ejpam-2696	108	11	s	s	NOUN
ejpam-2696	108	12	is	be	AUX
ejpam-2696	108	13	a	a	DET
ejpam-2696	108	14	γ	γ	PROPN
ejpam-2696	108	15	-	-	PUNCT
ejpam-2696	108	16	s	s	NOUN
ejpam-2696	108	17	-	-	NOUN
ejpam-2696	108	18	act	act	NOUN
ejpam-2696	108	19	under	under	ADP
ejpam-2696	108	20	the	the	DET
ejpam-2696	108	21	γ	γ	NOUN
ejpam-2696	108	22	-	-	NOUN
ejpam-2696	108	23	action	action	NOUN
ejpam-2696	108	24	:	:	PUNCT
ejpam-2696	108	25	s1γ	s1γ	ADV
ejpam-2696	108	26	(	(	PUNCT
ejpam-2696	108	27	s	s	AUX
ejpam-2696	108	28	s′	s′	PROPN
ejpam-2696	108	29	t	t	PROPN
ejpam-2696	108	30	t′	t′	NUM
ejpam-2696	108	31	)	)	PUNCT
ejpam-2696	109	1	:	:	PUNCT
ejpam-2696	109	2	=	=	SYM
ejpam-2696	109	3	(	(	PUNCT
ejpam-2696	109	4	s1γs	s1γs	PUNCT
ejpam-2696	109	5	s1γs	s1γs	PUNCT
ejpam-2696	109	6	′	′	NUM
ejpam-2696	109	7	s1γt	s1γt	PUNCT
ejpam-2696	109	8	s1γt	s1γt	NUM
ejpam-2696	109	9	′	′	NUM
ejpam-2696	109	10	)	)	PUNCT
ejpam-2696	109	11	for	for	ADP
ejpam-2696	109	12	s1	s1	PROPN
ejpam-2696	109	13	,	,	PUNCT
ejpam-2696	109	14	s	s	X
ejpam-2696	109	15	,	,	PUNCT
ejpam-2696	109	16	s	s	NOUN
ejpam-2696	109	17	′	′	NUM
ejpam-2696	109	18	,	,	PUNCT
ejpam-2696	109	19	t	t	PROPN
ejpam-2696	109	20	,	,	PUNCT
ejpam-2696	109	21	t′	t′	X
ejpam-2696	109	22	∈	∈	PROPN
ejpam-2696	109	23	s	s	X
ejpam-2696	109	24	and	and	CCONJ
ejpam-2696	109	25	γ	γ	PROPN
ejpam-2696	109	26	∈	∈	PROPN
ejpam-2696	109	27	γ	γ	X
ejpam-2696	109	28	.	.	PUNCT
ejpam-2696	110	1	(	(	PUNCT
ejpam-2696	110	2	v	v	NOUN
ejpam-2696	110	3	)	)	PUNCT
ejpam-2696	110	4	let	let	VERB
ejpam-2696	110	5	s	s	PRON
ejpam-2696	110	6	and	and	CCONJ
ejpam-2696	110	7	t	t	PROPN
ejpam-2696	110	8	be	be	AUX
ejpam-2696	110	9	γ	γ	NOUN
ejpam-2696	110	10	-	-	PUNCT
ejpam-2696	110	11	semigroups	semigroup	NOUN
ejpam-2696	110	12	.	.	PUNCT
ejpam-2696	111	1	clearly	clearly	ADV
ejpam-2696	111	2	,	,	PUNCT
ejpam-2696	111	3	the	the	DET
ejpam-2696	111	4	cartesian	cartesian	ADJ
ejpam-2696	111	5	product	product	NOUN
ejpam-2696	111	6	s×t	s×t	PRON
ejpam-2696	111	7	is	be	AUX
ejpam-2696	111	8	a	a	DET
ejpam-2696	111	9	γ	γ	NOUN
ejpam-2696	111	10	-	-	PUNCT
ejpam-2696	111	11	semigroup	semigroup	NOUN
ejpam-2696	111	12	with	with	ADP
ejpam-2696	111	13	the	the	DET
ejpam-2696	111	14	γ	γ	NOUN
ejpam-2696	111	15	-	-	NOUN
ejpam-2696	111	16	operation	operation	NOUN
ejpam-2696	111	17	(	(	PUNCT
ejpam-2696	111	18	s1	s1	NOUN
ejpam-2696	111	19	,	,	PUNCT
ejpam-2696	111	20	t1)γ(s2	t1)γ(s2	PROPN
ejpam-2696	111	21	,	,	PUNCT
ejpam-2696	111	22	t2	t2	NOUN
ejpam-2696	111	23	)	)	PUNCT
ejpam-2696	111	24	:	:	PUNCT
ejpam-2696	112	1	=	=	SYM
ejpam-2696	112	2	(	(	PUNCT
ejpam-2696	112	3	s1γs2	s1γs2	NOUN
ejpam-2696	112	4	,	,	PUNCT
ejpam-2696	112	5	t1γt2	t1γt2	ADJ
ejpam-2696	112	6	)	)	PUNCT
ejpam-2696	112	7	for	for	ADP
ejpam-2696	112	8	every	every	DET
ejpam-2696	112	9	s1	s1	NOUN
ejpam-2696	112	10	,	,	PUNCT
ejpam-2696	112	11	s2	s2	NOUN
ejpam-2696	112	12	∈	∈	PROPN
ejpam-2696	112	13	s	s	PROPN
ejpam-2696	112	14	,	,	PUNCT
ejpam-2696	112	15	t1	t1	PROPN
ejpam-2696	112	16	,	,	PUNCT
ejpam-2696	112	17	t2	t2	PROPN
ejpam-2696	112	18	∈	∈	PROPN
ejpam-2696	112	19	t	t	PROPN
ejpam-2696	112	20	and	and	CCONJ
ejpam-2696	112	21	h.	h.	PROPN
ejpam-2696	112	22	rasouli	rasouli	PROPN
ejpam-2696	112	23	,	,	PUNCT
ejpam-2696	112	24	a.r	a.r	PROPN
ejpam-2696	112	25	.	.	PROPN
ejpam-2696	112	26	shabani	shabani	PROPN
ejpam-2696	112	27	/	/	SYM
ejpam-2696	112	28	eur	eur	PROPN
ejpam-2696	112	29	.	.	PUNCT
ejpam-2696	113	1	j.	j.	PROPN
ejpam-2696	113	2	pure	pure	PROPN
ejpam-2696	113	3	appl	appl	PROPN
ejpam-2696	113	4	.	.	PROPN
ejpam-2696	113	5	math	math	PROPN
ejpam-2696	113	6	,	,	PUNCT
ejpam-2696	113	7	10	10	NUM
ejpam-2696	113	8	(	(	PUNCT
ejpam-2696	113	9	4	4	NUM
ejpam-2696	113	10	)	)	PUNCT
ejpam-2696	113	11	(	(	PUNCT
ejpam-2696	113	12	2017	2017	NUM
ejpam-2696	113	13	)	)	PUNCT
ejpam-2696	113	14	,	,	PUNCT
ejpam-2696	113	15	739	739	NUM
ejpam-2696	113	16	-	-	SYM
ejpam-2696	113	17	748	748	NUM
ejpam-2696	113	18	743	743	NUM
ejpam-2696	113	19	γ	γ	PROPN
ejpam-2696	113	20	∈	∈	PROPN
ejpam-2696	113	21	γ	γ	X
ejpam-2696	113	22	.	.	PUNCT
ejpam-2696	113	23	now	now	ADV
ejpam-2696	113	24	suppose	suppose	VERB
ejpam-2696	113	25	s	s	PRON
ejpam-2696	113	26	and	and	CCONJ
ejpam-2696	113	27	t	t	PROPN
ejpam-2696	113	28	contain	contain	VERB
ejpam-2696	113	29	right	right	ADJ
ejpam-2696	113	30	zero	zero	NUM
ejpam-2696	113	31	elements	element	NOUN
ejpam-2696	113	32	z	z	NOUN
ejpam-2696	113	33	,	,	PUNCT
ejpam-2696	113	34	z′	z′	PROPN
ejpam-2696	113	35	,	,	PUNCT
ejpam-2696	113	36	respectively	respectively	ADV
ejpam-2696	113	37	.	.	PUNCT
ejpam-2696	114	1	then	then	ADV
ejpam-2696	114	2	the	the	DET
ejpam-2696	114	3	set	set	NOUN
ejpam-2696	114	4	a	a	X
ejpam-2696	114	5	=	=	X
ejpam-2696	114	6	{	{	PUNCT
ejpam-2696	114	7	(	(	PUNCT
ejpam-2696	114	8	s	s	X
ejpam-2696	114	9	z	z	NOUN
ejpam-2696	114	10	z′	z′	NUM
ejpam-2696	114	11	t	t	NOUN
ejpam-2696	114	12	)	)	PUNCT
ejpam-2696	114	13	:	:	PUNCT
ejpam-2696	114	14	s	s	VERB
ejpam-2696	114	15	∈	∈	PROPN
ejpam-2696	114	16	s	s	PROPN
ejpam-2696	114	17	,	,	PUNCT
ejpam-2696	114	18	t	t	PROPN
ejpam-2696	114	19	∈	∈	PROPN
ejpam-2696	114	20	t	t	PROPN
ejpam-2696	114	21	}	}	PUNCT
ejpam-2696	114	22	is	be	AUX
ejpam-2696	114	23	a	a	DET
ejpam-2696	114	24	γ	γ	PROPN
ejpam-2696	114	25	-	-	PUNCT
ejpam-2696	114	26	s	s	NOUN
ejpam-2696	114	27	×	×	NOUN
ejpam-2696	114	28	t	t	NOUN
ejpam-2696	114	29	-act	-act	PUNCT
ejpam-2696	114	30	under	under	ADP
ejpam-2696	114	31	the	the	DET
ejpam-2696	114	32	γ	γ	NOUN
ejpam-2696	114	33	-	-	NOUN
ejpam-2696	114	34	action	action	NOUN
ejpam-2696	114	35	:	:	PUNCT
ejpam-2696	114	36	(	(	PUNCT
ejpam-2696	114	37	s1	s1	NOUN
ejpam-2696	114	38	,	,	PUNCT
ejpam-2696	114	39	t1)γ	t1)γ	NOUN
ejpam-2696	114	40	(	(	PUNCT
ejpam-2696	114	41	s2	s2	NOUN
ejpam-2696	114	42	z	z	NOUN
ejpam-2696	114	43	z′	z′	NUM
ejpam-2696	114	44	t2	t2	PROPN
ejpam-2696	114	45	)	)	PUNCT
ejpam-2696	114	46	:	:	PUNCT
ejpam-2696	115	1	=	=	SYM
ejpam-2696	115	2	(	(	PUNCT
ejpam-2696	115	3	s1γs2	s1γs2	PROPN
ejpam-2696	115	4	z	z	PROPN
ejpam-2696	115	5	z′	z′	NOUN
ejpam-2696	115	6	t1γt2	t1γt2	NOUN
ejpam-2696	115	7	)	)	PUNCT
ejpam-2696	115	8	for	for	ADP
ejpam-2696	115	9	s1	s1	NOUN
ejpam-2696	115	10	,	,	PUNCT
ejpam-2696	115	11	s2	s2	NOUN
ejpam-2696	115	12	∈	∈	PROPN
ejpam-2696	115	13	s	s	PROPN
ejpam-2696	115	14	,	,	PUNCT
ejpam-2696	115	15	t1	t1	PROPN
ejpam-2696	115	16	,	,	PUNCT
ejpam-2696	115	17	t2	t2	PROPN
ejpam-2696	115	18	∈	∈	PROPN
ejpam-2696	115	19	t	t	PROPN
ejpam-2696	115	20	and	and	CCONJ
ejpam-2696	115	21	γ	γ	PROPN
ejpam-2696	115	22	∈	∈	PROPN
ejpam-2696	115	23	γ	γ	X
ejpam-2696	115	24	.	.	PROPN
ejpam-2696	115	25	to	to	PART
ejpam-2696	115	26	see	see	VERB
ejpam-2696	115	27	this	this	PRON
ejpam-2696	115	28	,	,	PUNCT
ejpam-2696	115	29	let	let	VERB
ejpam-2696	115	30	s1	s1	NOUN
ejpam-2696	115	31	,	,	PUNCT
ejpam-2696	115	32	s2	s2	PROPN
ejpam-2696	115	33	,	,	PUNCT
ejpam-2696	115	34	s	s	PART
ejpam-2696	115	35	∈	∈	PROPN
ejpam-2696	115	36	s	s	NOUN
ejpam-2696	115	37	,	,	PUNCT
ejpam-2696	115	38	t1	t1	NOUN
ejpam-2696	115	39	,	,	PUNCT
ejpam-2696	115	40	t2	t2	NOUN
ejpam-2696	115	41	,	,	PUNCT
ejpam-2696	115	42	t	t	PROPN
ejpam-2696	115	43	∈	∈	PROPN
ejpam-2696	115	44	t	t	PROPN
ejpam-2696	115	45	and	and	CCONJ
ejpam-2696	115	46	α	α	NOUN
ejpam-2696	115	47	,	,	PUNCT
ejpam-2696	115	48	γ	γ	PROPN
ejpam-2696	115	49	∈	∈	PROPN
ejpam-2696	115	50	γ	γ	X
ejpam-2696	115	51	.	.	PUNCT
ejpam-2696	116	1	we	we	PRON
ejpam-2696	116	2	have	have	VERB
ejpam-2696	116	3	:	:	PUNCT
ejpam-2696	116	4	(	(	PUNCT
ejpam-2696	116	5	(	(	PUNCT
ejpam-2696	116	6	s1	s1	NOUN
ejpam-2696	116	7	,	,	PUNCT
ejpam-2696	116	8	t1)α(s2	t1)α(s2	PROPN
ejpam-2696	116	9	,	,	PUNCT
ejpam-2696	116	10	t2))γ	t2))γ	PUNCT
ejpam-2696	116	11	(	(	PUNCT
ejpam-2696	116	12	s	s	X
ejpam-2696	116	13	z	z	NOUN
ejpam-2696	116	14	z′	z′	NUM
ejpam-2696	116	15	t	t	NOUN
ejpam-2696	116	16	)	)	PUNCT
ejpam-2696	117	1	=	=	PRON
ejpam-2696	117	2	(	(	PUNCT
ejpam-2696	117	3	s1αs2	s1αs2	NOUN
ejpam-2696	117	4	,	,	PUNCT
ejpam-2696	117	5	t1αt2)γ	t1αt2)γ	NOUN
ejpam-2696	117	6	(	(	PUNCT
ejpam-2696	117	7	s	s	X
ejpam-2696	117	8	z	z	NOUN
ejpam-2696	117	9	z′	z′	NUM
ejpam-2696	117	10	t	t	NOUN
ejpam-2696	117	11	)	)	PUNCT
ejpam-2696	117	12	=	=	PUNCT
ejpam-2696	118	1	(	(	PUNCT
ejpam-2696	118	2	(	(	PUNCT
ejpam-2696	118	3	s1αs2)γs	s1αs2)γs	X
ejpam-2696	118	4	z	z	NOUN
ejpam-2696	118	5	z′	z′	NUM
ejpam-2696	118	6	(	(	PUNCT
ejpam-2696	118	7	t1αt2)γt	t1αt2)γt	PROPN
ejpam-2696	118	8	)	)	PUNCT
ejpam-2696	118	9	=	=	SYM
ejpam-2696	118	10	(	(	PUNCT
ejpam-2696	118	11	s1α(s2γs	s1α(s2γs	NOUN
ejpam-2696	118	12	)	)	PUNCT
ejpam-2696	118	13	z	z	NOUN
ejpam-2696	118	14	z′	z′	NUM
ejpam-2696	118	15	t1α(t2γt	t1α(t2γt	NOUN
ejpam-2696	118	16	)	)	PUNCT
ejpam-2696	118	17	)	)	PUNCT
ejpam-2696	119	1	=	=	SYM
ejpam-2696	119	2	(	(	PUNCT
ejpam-2696	119	3	s1	s1	PROPN
ejpam-2696	119	4	,	,	PUNCT
ejpam-2696	119	5	t1)α((s2	t1)α((s2	NOUN
ejpam-2696	119	6	,	,	PUNCT
ejpam-2696	119	7	t2)γ	t2)γ	NOUN
ejpam-2696	119	8	(	(	PUNCT
ejpam-2696	119	9	s	s	NOUN
ejpam-2696	119	10	z	z	NOUN
ejpam-2696	119	11	z′	z′	NUM
ejpam-2696	119	12	t	t	PROPN
ejpam-2696	119	13	)	)	PUNCT
ejpam-2696	119	14	)	)	PUNCT
ejpam-2696	119	15	.	.	PUNCT
ejpam-2696	120	1	hence	hence	ADV
ejpam-2696	120	2	,	,	PUNCT
ejpam-2696	120	3	a	a	PRON
ejpam-2696	120	4	is	be	AUX
ejpam-2696	120	5	a	a	DET
ejpam-2696	120	6	γ	γ	PROPN
ejpam-2696	120	7	-	-	PUNCT
ejpam-2696	120	8	s	s	PART
ejpam-2696	120	9	×	×	NOUN
ejpam-2696	120	10	u	u	NOUN
ejpam-2696	120	11	-act	-act	NOUN
ejpam-2696	120	12	.	.	PUNCT
ejpam-2696	121	1	we	we	PRON
ejpam-2696	121	2	here	here	ADV
ejpam-2696	121	3	generalize	generalize	VERB
ejpam-2696	121	4	some	some	DET
ejpam-2696	121	5	basic	basic	ADJ
ejpam-2696	121	6	properties	property	NOUN
ejpam-2696	121	7	of	of	ADP
ejpam-2696	121	8	s	s	NOUN
ejpam-2696	121	9	-	-	PUNCT
ejpam-2696	121	10	acts	act	NOUN
ejpam-2696	121	11	to	to	ADP
ejpam-2696	121	12	γ	γ	PROPN
ejpam-2696	121	13	-	-	PUNCT
ejpam-2696	121	14	s	s	NOUN
ejpam-2696	121	15	-	-	PUNCT
ejpam-2696	121	16	acts	act	NOUN
ejpam-2696	121	17	.	.	PUNCT
ejpam-2696	122	1	since	since	SCONJ
ejpam-2696	122	2	the	the	DET
ejpam-2696	122	3	composition	composition	NOUN
ejpam-2696	122	4	of	of	ADP
ejpam-2696	122	5	two	two	NUM
ejpam-2696	122	6	γ	γ	NOUN
ejpam-2696	122	7	-	-	PUNCT
ejpam-2696	122	8	homomorphisms	homomorphism	NOUN
ejpam-2696	122	9	is	be	AUX
ejpam-2696	122	10	a	a	DET
ejpam-2696	122	11	γ	γ	NOUN
ejpam-2696	122	12	-	-	PUNCT
ejpam-2696	122	13	homomorphism	homomorphism	NOUN
ejpam-2696	122	14	,	,	PUNCT
ejpam-2696	122	15	and	and	CCONJ
ejpam-2696	122	16	the	the	DET
ejpam-2696	122	17	identity	identity	NOUN
ejpam-2696	122	18	map	map	NOUN
ejpam-2696	122	19	on	on	ADP
ejpam-2696	122	20	a	a	DET
ejpam-2696	122	21	γ	γ	NOUN
ejpam-2696	122	22	-	-	PUNCT
ejpam-2696	122	23	act	act	NOUN
ejpam-2696	122	24	is	be	AUX
ejpam-2696	122	25	a	a	DET
ejpam-2696	122	26	γ	γ	NOUN
ejpam-2696	122	27	-	-	PUNCT
ejpam-2696	122	28	homomorphism	homomorphism	NOUN
ejpam-2696	122	29	,	,	PUNCT
ejpam-2696	122	30	we	we	PRON
ejpam-2696	122	31	conclude	conclude	VERB
ejpam-2696	122	32	that	that	SCONJ
ejpam-2696	122	33	all	all	DET
ejpam-2696	122	34	γ	γ	NOUN
ejpam-2696	122	35	-	-	NOUN
ejpam-2696	122	36	acts	act	VERB
ejpam-2696	122	37	together	together	ADV
ejpam-2696	122	38	with	with	ADP
ejpam-2696	122	39	all	all	DET
ejpam-2696	122	40	γ	γ	NOUN
ejpam-2696	122	41	-	-	PUNCT
ejpam-2696	122	42	homomorphisms	homomorphism	NOUN
ejpam-2696	122	43	between	between	ADP
ejpam-2696	122	44	them	they	PRON
ejpam-2696	122	45	forms	form	VERB
ejpam-2696	122	46	a	a	DET
ejpam-2696	122	47	category	category	NOUN
ejpam-2696	122	48	which	which	PRON
ejpam-2696	122	49	is	be	AUX
ejpam-2696	122	50	denoted	denote	VERB
ejpam-2696	122	51	by	by	ADP
ejpam-2696	122	52	γ	γ	PROPN
ejpam-2696	122	53	-	-	PUNCT
ejpam-2696	122	54	s	s	NOUN
ejpam-2696	122	55	-	-	PUNCT
ejpam-2696	122	56	act	act	NOUN
ejpam-2696	122	57	,	,	PUNCT
ejpam-2696	122	58	or	or	CCONJ
ejpam-2696	122	59	simply	simply	ADV
ejpam-2696	122	60	γ	γ	PROPN
ejpam-2696	122	61	-	-	PUNCT
ejpam-2696	122	62	act	act	NOUN
ejpam-2696	122	63	if	if	SCONJ
ejpam-2696	122	64	no	no	DET
ejpam-2696	122	65	confusion	confusion	NOUN
ejpam-2696	122	66	arise	arise	VERB
ejpam-2696	122	67	.	.	PUNCT
ejpam-2696	123	1	the	the	DET
ejpam-2696	123	2	notions	notion	NOUN
ejpam-2696	123	3	of	of	ADP
ejpam-2696	123	4	γ	γ	NOUN
ejpam-2696	123	5	-	-	PUNCT
ejpam-2696	123	6	monomorphisms	monomorphism	NOUN
ejpam-2696	123	7	,	,	PUNCT
ejpam-2696	123	8	γ	γ	NOUN
ejpam-2696	123	9	-	-	PUNCT
ejpam-2696	123	10	epimorphisms	epimorphism	NOUN
ejpam-2696	123	11	and	and	CCONJ
ejpam-2696	123	12	γ	γ	NOUN
ejpam-2696	123	13	-	-	PUNCT
ejpam-2696	123	14	isomorphisms	isomorphism	NOUN
ejpam-2696	123	15	in	in	ADP
ejpam-2696	123	16	their	their	PRON
ejpam-2696	123	17	categorical	categorical	ADJ
ejpam-2696	123	18	forms	form	NOUN
ejpam-2696	123	19	are	be	AUX
ejpam-2696	123	20	defined	define	VERB
ejpam-2696	123	21	as	as	ADP
ejpam-2696	123	22	monomorphisms	monomorphism	NOUN
ejpam-2696	123	23	,	,	PUNCT
ejpam-2696	123	24	epimorphisms	epimorphism	NOUN
ejpam-2696	123	25	and	and	CCONJ
ejpam-2696	123	26	isomorphisms	isomorphism	NOUN
ejpam-2696	123	27	,	,	PUNCT
ejpam-2696	123	28	respectively	respectively	ADV
ejpam-2696	123	29	,	,	PUNCT
ejpam-2696	123	30	in	in	ADP
ejpam-2696	123	31	the	the	DET
ejpam-2696	123	32	category	category	NOUN
ejpam-2696	123	33	γ	γ	NOUN
ejpam-2696	123	34	-	-	NOUN
ejpam-2696	123	35	act	act	NOUN
ejpam-2696	123	36	.	.	PUNCT
ejpam-2696	124	1	here	here	ADV
ejpam-2696	124	2	we	we	PRON
ejpam-2696	124	3	characterize	characterize	VERB
ejpam-2696	124	4	these	these	DET
ejpam-2696	124	5	notions	notion	NOUN
ejpam-2696	124	6	in	in	ADP
ejpam-2696	124	7	terms	term	NOUN
ejpam-2696	124	8	of	of	ADP
ejpam-2696	124	9	injective	injective	ADJ
ejpam-2696	124	10	,	,	PUNCT
ejpam-2696	124	11	surjective	surjective	ADJ
ejpam-2696	124	12	and	and	CCONJ
ejpam-2696	124	13	bijective	bijective	ADJ
ejpam-2696	124	14	γ	γ	NOUN
ejpam-2696	124	15	-	-	PUNCT
ejpam-2696	124	16	homomorphisms	homomorphism	NOUN
ejpam-2696	124	17	.	.	PUNCT
ejpam-2696	125	1	let	let	VERB
ejpam-2696	125	2	us	we	PRON
ejpam-2696	125	3	list	list	VERB
ejpam-2696	125	4	some	some	DET
ejpam-2696	125	5	preliminaries	preliminary	NOUN
ejpam-2696	125	6	.	.	PUNCT
ejpam-2696	126	1	if	if	SCONJ
ejpam-2696	126	2	γa	γa	PROPN
ejpam-2696	126	3	is	be	AUX
ejpam-2696	126	4	a	a	DET
ejpam-2696	126	5	γ	γ	NOUN
ejpam-2696	126	6	-	-	PUNCT
ejpam-2696	126	7	act	act	NOUN
ejpam-2696	126	8	,	,	PUNCT
ejpam-2696	126	9	a	a	DET
ejpam-2696	126	10	∈	∈	NOUN
ejpam-2696	126	11	γa	γa	NOUN
ejpam-2696	126	12	and	and	CCONJ
ejpam-2696	126	13	γ	γ	PROPN
ejpam-2696	126	14	∈	∈	PROPN
ejpam-2696	126	15	γ	γ	X
ejpam-2696	126	16	,	,	PUNCT
ejpam-2696	126	17	then	then	ADV
ejpam-2696	126	18	the	the	DET
ejpam-2696	126	19	map	map	NOUN
ejpam-2696	126	20	λa	λa	ADP
ejpam-2696	126	21	,	,	PUNCT
ejpam-2696	126	22	γ	γ	X
ejpam-2696	126	23	:	:	PUNCT
ejpam-2696	126	24	γs	γs	ADP
ejpam-2696	126	25	→	→	SYM
ejpam-2696	126	26	γa	γa	PROPN
ejpam-2696	126	27	defined	define	VERB
ejpam-2696	126	28	by	by	ADP
ejpam-2696	126	29	λa	λa	ADP
ejpam-2696	126	30	,	,	PUNCT
ejpam-2696	126	31	γ(s	γ(	NOUN
ejpam-2696	126	32	)	)	PUNCT
ejpam-2696	127	1	=	=	SYM
ejpam-2696	127	2	sγa	sγa	ADJ
ejpam-2696	127	3	for	for	ADP
ejpam-2696	127	4	every	every	DET
ejpam-2696	127	5	s	s	X
ejpam-2696	127	6	∈	∈	NOUN
ejpam-2696	127	7	s	s	NOUN
ejpam-2696	127	8	is	be	AUX
ejpam-2696	127	9	a	a	DET
ejpam-2696	127	10	γ	γ	NOUN
ejpam-2696	127	11	-	-	PUNCT
ejpam-2696	127	12	homomorphism	homomorphism	NOUN
ejpam-2696	127	13	.	.	PUNCT
ejpam-2696	128	1	to	to	PART
ejpam-2696	128	2	see	see	VERB
ejpam-2696	128	3	this	this	PRON
ejpam-2696	128	4	,	,	PUNCT
ejpam-2696	128	5	for	for	ADP
ejpam-2696	128	6	every	every	DET
ejpam-2696	128	7	t	t	NOUN
ejpam-2696	128	8	∈	∈	PROPN
ejpam-2696	128	9	s	s	PART
ejpam-2696	128	10	and	and	CCONJ
ejpam-2696	128	11	β	β	X
ejpam-2696	128	12	∈	∈	NOUN
ejpam-2696	128	13	γ	γ	NOUN
ejpam-2696	128	14	we	we	PRON
ejpam-2696	128	15	have	have	VERB
ejpam-2696	128	16	λa	λa	ADP
ejpam-2696	128	17	,	,	PUNCT
ejpam-2696	128	18	γ(tβs	γ(tβs	PROPN
ejpam-2696	128	19	)	)	PUNCT
ejpam-2696	129	1	=	=	PUNCT
ejpam-2696	129	2	(	(	PUNCT
ejpam-2696	129	3	tβs)γa	tβs)γa	NOUN
ejpam-2696	129	4	=	=	SYM
ejpam-2696	129	5	tβ(sγa	tβ(sγa	NOUN
ejpam-2696	129	6	)	)	PUNCT
ejpam-2696	129	7	=	=	PUNCT
ejpam-2696	129	8	tβλa	tβλa	PROPN
ejpam-2696	129	9	,	,	PUNCT
ejpam-2696	129	10	γ(s	γ(	NOUN
ejpam-2696	129	11	)	)	PUNCT
ejpam-2696	129	12	.	.	PUNCT
ejpam-2696	130	1	let	let	VERB
ejpam-2696	130	2	γa	γa	PRON
ejpam-2696	130	3	be	be	AUX
ejpam-2696	130	4	a	a	DET
ejpam-2696	130	5	γ	γ	PROPN
ejpam-2696	130	6	-	-	PUNCT
ejpam-2696	130	7	s	s	NOUN
ejpam-2696	130	8	-	-	PUNCT
ejpam-2696	130	9	act	act	NOUN
ejpam-2696	130	10	.	.	PUNCT
ejpam-2696	131	1	an	an	DET
ejpam-2696	131	2	equivalence	equivalence	NOUN
ejpam-2696	131	3	relation	relation	NOUN
ejpam-2696	131	4	ρ	ρ	NOUN
ejpam-2696	131	5	on	on	ADP
ejpam-2696	131	6	a	a	PRON
ejpam-2696	131	7	is	be	AUX
ejpam-2696	131	8	called	call	VERB
ejpam-2696	131	9	a	a	DET
ejpam-2696	131	10	γ	γ	PROPN
ejpam-2696	131	11	-	-	PUNCT
ejpam-2696	131	12	s	s	NOUN
ejpam-2696	131	13	-	-	PUNCT
ejpam-2696	131	14	congruence	congruence	NOUN
ejpam-2696	131	15	,	,	PUNCT
ejpam-2696	131	16	or	or	CCONJ
ejpam-2696	131	17	simply	simply	ADV
ejpam-2696	131	18	a	a	DET
ejpam-2696	131	19	γ	γ	NOUN
ejpam-2696	131	20	-	-	PUNCT
ejpam-2696	131	21	congruence	congruence	NOUN
ejpam-2696	131	22	,	,	PUNCT
ejpam-2696	131	23	on	on	ADP
ejpam-2696	131	24	γa	γa	PRON
ejpam-2696	131	25	if	if	SCONJ
ejpam-2696	131	26	aρa′	aρa′	PRON
ejpam-2696	131	27	implies	imply	VERB
ejpam-2696	131	28	(	(	PUNCT
ejpam-2696	131	29	sγa)ρ(sγa′	sγa)ρ(sγa′	NUM
ejpam-2696	131	30	)	)	PUNCT
ejpam-2696	131	31	for	for	ADP
ejpam-2696	131	32	every	every	DET
ejpam-2696	131	33	a	a	NOUN
ejpam-2696	131	34	,	,	PUNCT
ejpam-2696	131	35	a′	a′	PROPN
ejpam-2696	131	36	∈	∈	PROPN
ejpam-2696	131	37	γa	γa	PROPN
ejpam-2696	131	38	,	,	PUNCT
ejpam-2696	131	39	s	s	VERB
ejpam-2696	131	40	∈	∈	PROPN
ejpam-2696	131	41	s	s	NOUN
ejpam-2696	131	42	and	and	CCONJ
ejpam-2696	131	43	γ	γ	PROPN
ejpam-2696	131	44	∈	∈	PROPN
ejpam-2696	131	45	γ	γ	X
ejpam-2696	131	46	.	.	PUNCT
ejpam-2696	132	1	the	the	DET
ejpam-2696	132	2	set	set	NOUN
ejpam-2696	132	3	γa	γa	PROPN
ejpam-2696	132	4	ρ	ρ	PROPN
ejpam-2696	132	5	=	=	PUNCT
ejpam-2696	132	6	{	{	PUNCT
ejpam-2696	133	1	[	[	X
ejpam-2696	133	2	a]ρ	a]ρ	NOUN
ejpam-2696	133	3	:	:	PUNCT
ejpam-2696	133	4	a	a	DET
ejpam-2696	133	5	∈	∈	PROPN
ejpam-2696	133	6	γa	γa	NOUN
ejpam-2696	133	7	}	}	PUNCT
ejpam-2696	133	8	with	with	ADP
ejpam-2696	133	9	the	the	DET
ejpam-2696	133	10	γ	γ	NOUN
ejpam-2696	133	11	-	-	NOUN
ejpam-2696	133	12	action	action	NOUN
ejpam-2696	133	13	sγ[a]ρ	sγ[a]ρ	PROPN
ejpam-2696	133	14	=	=	PUNCT
ejpam-2696	134	1	[	[	X
ejpam-2696	134	2	sγa]ρ	sγa]ρ	PROPN
ejpam-2696	134	3	for	for	ADP
ejpam-2696	134	4	every	every	DET
ejpam-2696	134	5	s	s	X
ejpam-2696	134	6	∈	∈	PROPN
ejpam-2696	134	7	s	s	NOUN
ejpam-2696	134	8	and	and	CCONJ
ejpam-2696	134	9	γ	γ	PROPN
ejpam-2696	134	10	∈	∈	PROPN
ejpam-2696	134	11	γ	γ	NOUN
ejpam-2696	134	12	is	be	AUX
ejpam-2696	134	13	called	call	VERB
ejpam-2696	134	14	the	the	DET
ejpam-2696	134	15	factor	factor	NOUN
ejpam-2696	134	16	γ	γ	NOUN
ejpam-2696	134	17	-	-	NOUN
ejpam-2696	134	18	act	act	NOUN
ejpam-2696	134	19	of	of	ADP
ejpam-2696	134	20	γa	γa	NOUN
ejpam-2696	134	21	by	by	ADP
ejpam-2696	134	22	ρ	ρ	PROPN
ejpam-2696	134	23	,	,	PUNCT
ejpam-2696	134	24	and	and	CCONJ
ejpam-2696	134	25	the	the	DET
ejpam-2696	134	26	canonical	canonical	ADJ
ejpam-2696	134	27	surjection	surjection	NOUN
ejpam-2696	134	28	πρ	πρ	VERB
ejpam-2696	134	29	:	:	PUNCT
ejpam-2696	134	30	γa	γa	PROPN
ejpam-2696	134	31	→	→	SYM
ejpam-2696	134	32	γa	γa	PROPN
ejpam-2696	134	33	ρ	ρ	NUM
ejpam-2696	134	34	where	where	SCONJ
ejpam-2696	134	35	a	a	DET
ejpam-2696	134	36	7→	7→	NOUN
ejpam-2696	135	1	[	[	X
ejpam-2696	135	2	a]ρ	a]ρ	PROPN
ejpam-2696	135	3	is	be	AUX
ejpam-2696	135	4	called	call	VERB
ejpam-2696	135	5	the	the	DET
ejpam-2696	135	6	canonical	canonical	ADJ
ejpam-2696	135	7	γ	γ	NOUN
ejpam-2696	135	8	-	-	PUNCT
ejpam-2696	135	9	epimorphism	epimorphism	NOUN
ejpam-2696	135	10	.	.	PUNCT
ejpam-2696	136	1	also	also	ADV
ejpam-2696	136	2	for	for	ADP
ejpam-2696	136	3	a	a	DET
ejpam-2696	136	4	γhomomorphism	γhomomorphism	NOUN
ejpam-2696	136	5	f	f	NOUN
ejpam-2696	136	6	:	:	PUNCT
ejpam-2696	136	7	γa→	γa→	PROPN
ejpam-2696	136	8	γb	γb	PROPN
ejpam-2696	136	9	,	,	PUNCT
ejpam-2696	136	10	the	the	DET
ejpam-2696	136	11	γ	γ	PROPN
ejpam-2696	136	12	-	-	ADJ
ejpam-2696	136	13	congruence	congruence	ADJ
ejpam-2696	136	14	ρ	ρ	NOUN
ejpam-2696	136	15	=	=	SYM
ejpam-2696	136	16	kerf	kerf	NOUN
ejpam-2696	136	17	on	on	ADP
ejpam-2696	136	18	γa	γa	PRON
ejpam-2696	137	1	where	where	SCONJ
ejpam-2696	137	2	aρa′	aρa′	ADJ
ejpam-2696	137	3	if	if	SCONJ
ejpam-2696	138	1	and	and	CCONJ
ejpam-2696	138	2	only	only	ADV
ejpam-2696	138	3	if	if	SCONJ
ejpam-2696	138	4	f(a	f(a	NOUN
ejpam-2696	138	5	)	)	PUNCT
ejpam-2696	138	6	=	=	SYM
ejpam-2696	138	7	f(a′	f(a′	PROPN
ejpam-2696	138	8	)	)	PUNCT
ejpam-2696	138	9	,	,	PUNCT
ejpam-2696	138	10	for	for	ADP
ejpam-2696	138	11	all	all	DET
ejpam-2696	138	12	a	a	PRON
ejpam-2696	138	13	,	,	PUNCT
ejpam-2696	138	14	a′	a′	PROPN
ejpam-2696	138	15	∈	∈	PROPN
ejpam-2696	138	16	a	a	PRON
ejpam-2696	138	17	,	,	PUNCT
ejpam-2696	138	18	is	be	AUX
ejpam-2696	138	19	called	call	VERB
ejpam-2696	138	20	the	the	DET
ejpam-2696	138	21	kernel	kernel	PROPN
ejpam-2696	138	22	γ	γ	PROPN
ejpam-2696	138	23	-	-	NOUN
ejpam-2696	138	24	congruence	congruence	NOUN
ejpam-2696	138	25	of	of	ADP
ejpam-2696	138	26	f	f	PROPN
ejpam-2696	138	27	.	.	PUNCT
ejpam-2696	139	1	for	for	ADP
ejpam-2696	139	2	each	each	DET
ejpam-2696	139	3	γ	γ	ADJ
ejpam-2696	139	4	-	-	ADJ
ejpam-2696	139	5	subact	subact	ADJ
ejpam-2696	139	6	γb	γb	NOUN
ejpam-2696	139	7	of	of	ADP
ejpam-2696	139	8	γa	γa	PROPN
ejpam-2696	139	9	,	,	PUNCT
ejpam-2696	139	10	the	the	DET
ejpam-2696	139	11	rees	rees	PROPN
ejpam-2696	139	12	γ	γ	PROPN
ejpam-2696	139	13	-	-	ADJ
ejpam-2696	139	14	congruence	congruence	ADJ
ejpam-2696	139	15	ρb	ρb	NOUN
ejpam-2696	139	16	on	on	ADP
ejpam-2696	139	17	a	a	PRON
ejpam-2696	139	18	is	be	AUX
ejpam-2696	139	19	given	give	VERB
ejpam-2696	139	20	as	as	ADP
ejpam-2696	139	21	aρba	aρba	PROPN
ejpam-2696	139	22	′	′	VERB
ejpam-2696	140	1	if	if	SCONJ
ejpam-2696	140	2	and	and	CCONJ
ejpam-2696	140	3	only	only	ADV
ejpam-2696	140	4	if	if	SCONJ
ejpam-2696	140	5	a	a	DET
ejpam-2696	140	6	=	=	PUNCT
ejpam-2696	140	7	a′	a′	NOUN
ejpam-2696	140	8	or	or	CCONJ
ejpam-2696	140	9	a	a	PRON
ejpam-2696	140	10	,	,	PUNCT
ejpam-2696	140	11	a′	a′	PROPN
ejpam-2696	140	12	∈	∈	PROPN
ejpam-2696	140	13	b	b	PROPN
ejpam-2696	140	14	,	,	PUNCT
ejpam-2696	140	15	for	for	ADP
ejpam-2696	140	16	any	any	DET
ejpam-2696	140	17	a	a	NOUN
ejpam-2696	140	18	,	,	PUNCT
ejpam-2696	140	19	a′	a′	PROPN
ejpam-2696	140	20	∈	∈	PROPN
ejpam-2696	140	21	a.	a.	NOUN
ejpam-2696	140	22	the	the	DET
ejpam-2696	140	23	resulting	result	VERB
ejpam-2696	140	24	factor	factor	NOUN
ejpam-2696	140	25	γ	γ	NOUN
ejpam-2696	140	26	-	-	PUNCT
ejpam-2696	140	27	act	act	NOUN
ejpam-2696	140	28	γa	γa	NOUN
ejpam-2696	140	29	ρb	ρb	NOUN
ejpam-2696	140	30	is	be	AUX
ejpam-2696	140	31	simply	simply	ADV
ejpam-2696	140	32	denoted	denote	VERB
ejpam-2696	140	33	by	by	ADP
ejpam-2696	140	34	γa	γa	PROPN
ejpam-2696	140	35	γb	γb	PROPN
ejpam-2696	140	36	.	.	PUNCT
ejpam-2696	141	1	h.	h.	PROPN
ejpam-2696	141	2	rasouli	rasouli	PROPN
ejpam-2696	141	3	,	,	PUNCT
ejpam-2696	141	4	a.r	a.r	PROPN
ejpam-2696	141	5	.	.	PROPN
ejpam-2696	141	6	shabani	shabani	PROPN
ejpam-2696	141	7	/	/	SYM
ejpam-2696	141	8	eur	eur	PROPN
ejpam-2696	141	9	.	.	PUNCT
ejpam-2696	142	1	j.	j.	PROPN
ejpam-2696	142	2	pure	pure	PROPN
ejpam-2696	142	3	appl	appl	PROPN
ejpam-2696	142	4	.	.	PROPN
ejpam-2696	142	5	math	math	PROPN
ejpam-2696	142	6	,	,	PUNCT
ejpam-2696	142	7	10	10	NUM
ejpam-2696	142	8	(	(	PUNCT
ejpam-2696	142	9	4	4	NUM
ejpam-2696	142	10	)	)	PUNCT
ejpam-2696	142	11	(	(	PUNCT
ejpam-2696	142	12	2017	2017	NUM
ejpam-2696	142	13	)	)	PUNCT
ejpam-2696	142	14	,	,	PUNCT
ejpam-2696	142	15	739	739	NUM
ejpam-2696	142	16	-	-	SYM
ejpam-2696	142	17	748	748	NUM
ejpam-2696	142	18	744	744	NUM
ejpam-2696	142	19	proposition	proposition	NOUN
ejpam-2696	142	20	2	2	NUM
ejpam-2696	142	21	.	.	PUNCT
ejpam-2696	143	1	in	in	ADP
ejpam-2696	143	2	the	the	DET
ejpam-2696	143	3	category	category	NOUN
ejpam-2696	143	4	γ	γ	PROPN
ejpam-2696	143	5	-	-	PUNCT
ejpam-2696	143	6	act	act	NOUN
ejpam-2696	143	7	,	,	PUNCT
ejpam-2696	143	8	γ	γ	NOUN
ejpam-2696	143	9	-	-	PUNCT
ejpam-2696	143	10	monomorphisms	monomorphism	NOUN
ejpam-2696	143	11	,	,	PUNCT
ejpam-2696	143	12	γ	γ	NOUN
ejpam-2696	143	13	-	-	PUNCT
ejpam-2696	143	14	epimorphisms	epimorphism	NOUN
ejpam-2696	143	15	and	and	CCONJ
ejpam-2696	143	16	γ	γ	NOUN
ejpam-2696	143	17	-	-	PUNCT
ejpam-2696	143	18	isomorphisms	isomorphism	NOUN
ejpam-2696	143	19	are	be	AUX
ejpam-2696	143	20	exactly	exactly	ADV
ejpam-2696	143	21	injective	injective	ADJ
ejpam-2696	143	22	,	,	PUNCT
ejpam-2696	143	23	surjective	surjective	ADJ
ejpam-2696	143	24	and	and	CCONJ
ejpam-2696	143	25	bijective	bijective	ADJ
ejpam-2696	143	26	γ	γ	NOUN
ejpam-2696	143	27	-	-	PUNCT
ejpam-2696	143	28	homomorphisms	homomorphism	NOUN
ejpam-2696	143	29	,	,	PUNCT
ejpam-2696	143	30	respectively	respectively	ADV
ejpam-2696	143	31	.	.	PUNCT
ejpam-2696	144	1	proof	proof	NOUN
ejpam-2696	144	2	.	.	PUNCT
ejpam-2696	145	1	it	it	PRON
ejpam-2696	145	2	is	be	AUX
ejpam-2696	145	3	easy	easy	ADJ
ejpam-2696	145	4	to	to	PART
ejpam-2696	145	5	see	see	VERB
ejpam-2696	145	6	that	that	SCONJ
ejpam-2696	145	7	every	every	DET
ejpam-2696	145	8	injective	injective	ADJ
ejpam-2696	145	9	γ	γ	X
ejpam-2696	145	10	-	-	PUNCT
ejpam-2696	145	11	homomorphism	homomorphism	NOUN
ejpam-2696	145	12	is	be	AUX
ejpam-2696	145	13	a	a	DET
ejpam-2696	145	14	γ	γ	NOUN
ejpam-2696	145	15	-	-	PUNCT
ejpam-2696	145	16	monomorphism	monomorphism	NOUN
ejpam-2696	145	17	,	,	PUNCT
ejpam-2696	145	18	every	every	DET
ejpam-2696	145	19	surjective	surjective	ADJ
ejpam-2696	145	20	γ	γ	X
ejpam-2696	145	21	-	-	PUNCT
ejpam-2696	145	22	homomorphism	homomorphism	NOUN
ejpam-2696	145	23	is	be	AUX
ejpam-2696	145	24	a	a	DET
ejpam-2696	145	25	γ	γ	NOUN
ejpam-2696	145	26	-	-	PUNCT
ejpam-2696	145	27	epimorphism	epimorphism	NOUN
ejpam-2696	145	28	,	,	PUNCT
ejpam-2696	145	29	and	and	CCONJ
ejpam-2696	145	30	every	every	DET
ejpam-2696	145	31	γ	γ	PROPN
ejpam-2696	145	32	-	-	PUNCT
ejpam-2696	145	33	isomorphism	isomorphism	NOUN
ejpam-2696	145	34	is	be	AUX
ejpam-2696	145	35	bijective	bijective	ADJ
ejpam-2696	145	36	.	.	PUNCT
ejpam-2696	146	1	take	take	VERB
ejpam-2696	146	2	any	any	DET
ejpam-2696	146	3	γ	γ	NOUN
ejpam-2696	146	4	-	-	NOUN
ejpam-2696	146	5	homomorphism	homomorphism	ADJ
ejpam-2696	146	6	f	f	X
ejpam-2696	146	7	:	:	PUNCT
ejpam-2696	146	8	γa	γa	PROPN
ejpam-2696	146	9	→	→	SYM
ejpam-2696	146	10	γb	γb	AUX
ejpam-2696	146	11	.	.	PUNCT
ejpam-2696	146	12	suppose	suppose	VERB
ejpam-2696	146	13	f	f	PROPN
ejpam-2696	146	14	is	be	AUX
ejpam-2696	146	15	a	a	DET
ejpam-2696	146	16	γ	γ	NOUN
ejpam-2696	146	17	-	-	PUNCT
ejpam-2696	146	18	monomorphism	monomorphism	NOUN
ejpam-2696	146	19	and	and	CCONJ
ejpam-2696	146	20	f(a	f(a	NOUN
ejpam-2696	146	21	)	)	PUNCT
ejpam-2696	147	1	=	=	SYM
ejpam-2696	147	2	f(a′	f(a′	PROPN
ejpam-2696	147	3	)	)	PUNCT
ejpam-2696	147	4	for	for	ADP
ejpam-2696	147	5	any	any	DET
ejpam-2696	147	6	a	a	NOUN
ejpam-2696	147	7	,	,	PUNCT
ejpam-2696	147	8	a′	a′	PROPN
ejpam-2696	147	9	∈	∈	PROPN
ejpam-2696	147	10	a.	a.	NOUN
ejpam-2696	147	11	we	we	PRON
ejpam-2696	147	12	show	show	VERB
ejpam-2696	147	13	that	that	SCONJ
ejpam-2696	147	14	a	a	DET
ejpam-2696	147	15	=	=	NOUN
ejpam-2696	147	16	a′.	a′.	NOUN
ejpam-2696	147	17	let	let	VERB
ejpam-2696	147	18	γ	γ	X
ejpam-2696	147	19	∈	∈	PROPN
ejpam-2696	147	20	γ	γ	X
ejpam-2696	147	21	.	.	PUNCT
ejpam-2696	147	22	consider	consider	VERB
ejpam-2696	147	23	the	the	DET
ejpam-2696	147	24	γhomomorphisms	γhomomorphism	NOUN
ejpam-2696	147	25	λa	λa	PROPN
ejpam-2696	147	26	,	,	PUNCT
ejpam-2696	147	27	γ	γ	X
ejpam-2696	147	28	,	,	PUNCT
ejpam-2696	147	29	λa′,γ	λa′,γ	NOUN
ejpam-2696	147	30	:	:	PUNCT
ejpam-2696	147	31	γs	γs	VERB
ejpam-2696	147	32	→	→	SYM
ejpam-2696	147	33	γa	γa	PROPN
ejpam-2696	147	34	.	.	PUNCT
ejpam-2696	148	1	we	we	PRON
ejpam-2696	148	2	claim	claim	VERB
ejpam-2696	148	3	that	that	SCONJ
ejpam-2696	148	4	fλa	fλa	NOUN
ejpam-2696	148	5	,	,	PUNCT
ejpam-2696	148	6	γ	γ	NOUN
ejpam-2696	148	7	=	=	PUNCT
ejpam-2696	148	8	fλa′,γ	fλa′,γ	NOUN
ejpam-2696	148	9	.	.	PUNCT
ejpam-2696	149	1	for	for	ADP
ejpam-2696	149	2	every	every	DET
ejpam-2696	149	3	s	s	PROPN
ejpam-2696	149	4	∈	∈	PROPN
ejpam-2696	149	5	s	s	SYM
ejpam-2696	149	6	,	,	PUNCT
ejpam-2696	149	7	fλa	fλa	NOUN
ejpam-2696	149	8	,	,	PUNCT
ejpam-2696	149	9	γ(s	γ(s	PROPN
ejpam-2696	149	10	)	)	PUNCT
ejpam-2696	149	11	=	=	SYM
ejpam-2696	149	12	f(λa	f(λa	PROPN
ejpam-2696	149	13	,	,	PUNCT
ejpam-2696	149	14	γ(s	γ(	NOUN
ejpam-2696	149	15	)	)	PUNCT
ejpam-2696	149	16	)	)	PUNCT
ejpam-2696	149	17	=	=	SYM
ejpam-2696	149	18	f(sγa	f(sγa	NOUN
ejpam-2696	149	19	)	)	PUNCT
ejpam-2696	149	20	=	=	SYM
ejpam-2696	149	21	sγf(a	sγf(a	PROPN
ejpam-2696	149	22	)	)	PUNCT
ejpam-2696	149	23	=	=	PUNCT
ejpam-2696	149	24	sγf(a′	sγf(a′	NOUN
ejpam-2696	149	25	)	)	PUNCT
ejpam-2696	149	26	=	=	SYM
ejpam-2696	149	27	f(sγa′	f(sγa′	X
ejpam-2696	149	28	)	)	PUNCT
ejpam-2696	149	29	=	=	SYM
ejpam-2696	149	30	f(λa′,γ(s	f(λa′,γ(s	NUM
ejpam-2696	149	31	)	)	PUNCT
ejpam-2696	149	32	)	)	PUNCT
ejpam-2696	150	1	=	=	SYM
ejpam-2696	150	2	fλa′,γ(s	fλa′,γ(s	NOUN
ejpam-2696	150	3	)	)	PUNCT
ejpam-2696	150	4	.	.	PUNCT
ejpam-2696	151	1	since	since	SCONJ
ejpam-2696	151	2	f	f	PROPN
ejpam-2696	151	3	is	be	AUX
ejpam-2696	151	4	a	a	DET
ejpam-2696	151	5	γ	γ	NOUN
ejpam-2696	151	6	-	-	PUNCT
ejpam-2696	151	7	monomorphism	monomorphism	NOUN
ejpam-2696	151	8	,	,	PUNCT
ejpam-2696	151	9	λa	λa	PROPN
ejpam-2696	151	10	,	,	PUNCT
ejpam-2696	151	11	γ	γ	X
ejpam-2696	151	12	=	=	SYM
ejpam-2696	151	13	λa′,γ	λa′,γ	X
ejpam-2696	151	14	.	.	PUNCT
ejpam-2696	152	1	hence	hence	ADV
ejpam-2696	152	2	,	,	PUNCT
ejpam-2696	152	3	a	a	DET
ejpam-2696	152	4	=	=	NOUN
ejpam-2696	152	5	eγa	eγa	NOUN
ejpam-2696	152	6	=	=	SYM
ejpam-2696	152	7	λa	λa	NOUN
ejpam-2696	152	8	,	,	PUNCT
ejpam-2696	152	9	γ(e	γ(e	NOUN
ejpam-2696	152	10	)	)	PUNCT
ejpam-2696	153	1	=	=	SYM
ejpam-2696	153	2	λa′,γ(e	λa′,γ(e	NOUN
ejpam-2696	153	3	)	)	PUNCT
ejpam-2696	153	4	=	=	VERB
ejpam-2696	153	5	eγa′	eγa′	NOUN
ejpam-2696	153	6	=	=	PUNCT
ejpam-2696	153	7	a′	a′	PROPN
ejpam-2696	153	8	,	,	PUNCT
ejpam-2696	153	9	where	where	SCONJ
ejpam-2696	153	10	e	e	NOUN
ejpam-2696	153	11	is	be	AUX
ejpam-2696	153	12	a	a	DET
ejpam-2696	153	13	left	left	ADJ
ejpam-2696	153	14	identity	identity	NOUN
ejpam-2696	153	15	of	of	ADP
ejpam-2696	153	16	s.	s.	PROPN
ejpam-2696	153	17	then	then	ADV
ejpam-2696	153	18	f	f	PROPN
ejpam-2696	153	19	is	be	AUX
ejpam-2696	153	20	injective	injective	ADJ
ejpam-2696	153	21	.	.	PUNCT
ejpam-2696	154	1	now	now	ADV
ejpam-2696	154	2	let	let	VERB
ejpam-2696	154	3	f	f	PRON
ejpam-2696	154	4	be	be	AUX
ejpam-2696	154	5	a	a	DET
ejpam-2696	154	6	γ	γ	NOUN
ejpam-2696	154	7	-	-	PUNCT
ejpam-2696	154	8	epimorphism	epimorphism	NOUN
ejpam-2696	154	9	.	.	PUNCT
ejpam-2696	155	1	clearly	clearly	ADV
ejpam-2696	155	2	,	,	PUNCT
ejpam-2696	155	3	imf	imf	PROPN
ejpam-2696	155	4	is	be	AUX
ejpam-2696	155	5	a	a	DET
ejpam-2696	155	6	γ	γ	NOUN
ejpam-2696	155	7	-	-	NOUN
ejpam-2696	155	8	subact	subact	NOUN
ejpam-2696	155	9	of	of	ADP
ejpam-2696	155	10	b.	b.	PROPN
ejpam-2696	155	11	consider	consider	VERB
ejpam-2696	155	12	γ	γ	NOUN
ejpam-2696	155	13	-	-	PUNCT
ejpam-2696	155	14	homomorphisms	homomorphism	NOUN
ejpam-2696	155	15	g	g	NOUN
ejpam-2696	155	16	,	,	PUNCT
ejpam-2696	155	17	h	h	NOUN
ejpam-2696	155	18	:	:	PUNCT
ejpam-2696	155	19	γb	γb	INTJ
ejpam-2696	155	20	→	→	SYM
ejpam-2696	155	21	γb	γb	NOUN
ejpam-2696	155	22	imf	imf	NOUN
ejpam-2696	155	23	defined	define	VERB
ejpam-2696	155	24	by	by	ADP
ejpam-2696	155	25	g(b	g(b	PROPN
ejpam-2696	155	26	)	)	PUNCT
ejpam-2696	155	27	=	=	SYM
ejpam-2696	155	28	imf	imf	PROPN
ejpam-2696	155	29	and	and	CCONJ
ejpam-2696	155	30	h(b	h(b	PROPN
ejpam-2696	155	31	)	)	PUNCT
ejpam-2696	156	1	=	=	PUNCT
ejpam-2696	157	1	[	[	X
ejpam-2696	157	2	b]imf	b]imf	NOUN
ejpam-2696	157	3	for	for	ADP
ejpam-2696	157	4	every	every	DET
ejpam-2696	157	5	b	b	PROPN
ejpam-2696	157	6	∈	∈	PROPN
ejpam-2696	157	7	b	b	NOUN
ejpam-2696	157	8	,	,	PUNCT
ejpam-2696	157	9	respectively	respectively	ADV
ejpam-2696	157	10	.	.	PUNCT
ejpam-2696	158	1	clearly	clearly	ADV
ejpam-2696	158	2	,	,	PUNCT
ejpam-2696	158	3	gf	gf	PROPN
ejpam-2696	158	4	=	=	PUNCT
ejpam-2696	158	5	hf	hf	NOUN
ejpam-2696	158	6	and	and	CCONJ
ejpam-2696	158	7	then	then	ADV
ejpam-2696	158	8	g	g	PROPN
ejpam-2696	158	9	=	=	PROPN
ejpam-2696	158	10	h	h	NOUN
ejpam-2696	158	11	because	because	SCONJ
ejpam-2696	158	12	f	f	PROPN
ejpam-2696	158	13	is	be	AUX
ejpam-2696	158	14	a	a	DET
ejpam-2696	158	15	γ	γ	NOUN
ejpam-2696	158	16	-	-	PUNCT
ejpam-2696	158	17	epimorphism	epimorphism	NOUN
ejpam-2696	158	18	.	.	PUNCT
ejpam-2696	159	1	it	it	PRON
ejpam-2696	159	2	follows	follow	VERB
ejpam-2696	159	3	that	that	SCONJ
ejpam-2696	159	4	for	for	ADP
ejpam-2696	159	5	every	every	DET
ejpam-2696	159	6	b	b	PROPN
ejpam-2696	159	7	∈	∈	PROPN
ejpam-2696	159	8	b	b	PROPN
ejpam-2696	159	9	,	,	PUNCT
ejpam-2696	159	10	imf	imf	PROPN
ejpam-2696	159	11	=	=	SYM
ejpam-2696	159	12	g(b	g(b	X
ejpam-2696	159	13	)	)	PUNCT
ejpam-2696	159	14	=	=	SYM
ejpam-2696	159	15	h(b	h(b	ADJ
ejpam-2696	159	16	)	)	PUNCT
ejpam-2696	159	17	=	=	PUNCT
ejpam-2696	160	1	[	[	X
ejpam-2696	160	2	b]imf	b]imf	X
ejpam-2696	160	3	whence	whence	PROPN
ejpam-2696	160	4	imf	imf	PROPN
ejpam-2696	160	5	=	=	SYM
ejpam-2696	160	6	b	b	PROPN
ejpam-2696	160	7	,	,	PUNCT
ejpam-2696	160	8	i.e.	i.e.	X
ejpam-2696	160	9	f	f	PROPN
ejpam-2696	160	10	is	be	AUX
ejpam-2696	160	11	surjective	surjective	ADJ
ejpam-2696	160	12	.	.	PUNCT
ejpam-2696	161	1	finally	finally	ADV
ejpam-2696	161	2	,	,	PUNCT
ejpam-2696	161	3	assume	assume	VERB
ejpam-2696	161	4	that	that	SCONJ
ejpam-2696	161	5	f	f	PROPN
ejpam-2696	161	6	is	be	AUX
ejpam-2696	161	7	bijective	bijective	ADJ
ejpam-2696	161	8	.	.	PUNCT
ejpam-2696	162	1	it	it	PRON
ejpam-2696	162	2	suffices	suffice	VERB
ejpam-2696	162	3	to	to	PART
ejpam-2696	162	4	show	show	VERB
ejpam-2696	162	5	that	that	SCONJ
ejpam-2696	162	6	f−1	f−1	PROPN
ejpam-2696	162	7	is	be	AUX
ejpam-2696	162	8	a	a	DET
ejpam-2696	162	9	γ	γ	NOUN
ejpam-2696	162	10	-	-	PUNCT
ejpam-2696	162	11	homomorphism	homomorphism	NOUN
ejpam-2696	162	12	.	.	PUNCT
ejpam-2696	163	1	let	let	VERB
ejpam-2696	163	2	s	s	PRON
ejpam-2696	163	3	∈	∈	PROPN
ejpam-2696	163	4	s	s	PART
ejpam-2696	163	5	,	,	PUNCT
ejpam-2696	163	6	γ	γ	PROPN
ejpam-2696	163	7	∈	∈	PROPN
ejpam-2696	163	8	γ	γ	X
ejpam-2696	163	9	,	,	PUNCT
ejpam-2696	163	10	b	b	PROPN
ejpam-2696	163	11	∈	∈	PROPN
ejpam-2696	163	12	b.	b.	PROPN
ejpam-2696	163	13	then	then	ADV
ejpam-2696	163	14	there	there	PRON
ejpam-2696	163	15	exists	exist	VERB
ejpam-2696	163	16	a	a	DET
ejpam-2696	163	17	∈	∈	NOUN
ejpam-2696	163	18	a	a	DET
ejpam-2696	163	19	such	such	ADJ
ejpam-2696	163	20	that	that	DET
ejpam-2696	163	21	f(a	f(a	NOUN
ejpam-2696	163	22	)	)	PUNCT
ejpam-2696	164	1	=	=	SYM
ejpam-2696	164	2	b	b	PROPN
ejpam-2696	164	3	and	and	CCONJ
ejpam-2696	164	4	hence	hence	ADV
ejpam-2696	164	5	f−1(sγb	f−1(sγb	ADJ
ejpam-2696	164	6	)	)	PUNCT
ejpam-2696	164	7	=	=	SYM
ejpam-2696	164	8	f−1(sγf(a	f−1(sγf(a	NOUN
ejpam-2696	164	9	)	)	PUNCT
ejpam-2696	164	10	)	)	PUNCT
ejpam-2696	165	1	=	=	SYM
ejpam-2696	165	2	f−1(f(sγa	f−1(f(sγa	NOUN
ejpam-2696	165	3	)	)	PUNCT
ejpam-2696	165	4	)	)	PUNCT
ejpam-2696	166	1	=	=	SYM
ejpam-2696	166	2	sγa	sγa	PROPN
ejpam-2696	166	3	=	=	SYM
ejpam-2696	166	4	sγf−1(b	sγf−1(b	PROPN
ejpam-2696	166	5	)	)	PUNCT
ejpam-2696	166	6	.	.	PUNCT
ejpam-2696	167	1	this	this	PRON
ejpam-2696	167	2	implies	imply	VERB
ejpam-2696	167	3	that	that	SCONJ
ejpam-2696	167	4	f	f	PROPN
ejpam-2696	167	5	is	be	AUX
ejpam-2696	167	6	a	a	DET
ejpam-2696	167	7	γ	γ	NOUN
ejpam-2696	167	8	-	-	PUNCT
ejpam-2696	167	9	isomorphism	isomorphism	NOUN
ejpam-2696	167	10	.	.	PUNCT
ejpam-2696	168	1	remark	remark	PROPN
ejpam-2696	168	2	2	2	NUM
ejpam-2696	168	3	.	.	PUNCT
ejpam-2696	169	1	let	let	VERB
ejpam-2696	169	2	s	s	PRON
ejpam-2696	169	3	be	be	AUX
ejpam-2696	169	4	a	a	DET
ejpam-2696	169	5	γ	γ	NOUN
ejpam-2696	169	6	-	-	PUNCT
ejpam-2696	169	7	semigroup	semigroup	NOUN
ejpam-2696	169	8	,	,	PUNCT
ejpam-2696	169	9	γa	γa	PROPN
ejpam-2696	169	10	a	a	DET
ejpam-2696	169	11	γ	γ	PROPN
ejpam-2696	169	12	-	-	PUNCT
ejpam-2696	169	13	s	s	NOUN
ejpam-2696	169	14	-	-	PUNCT
ejpam-2696	169	15	act	act	NOUN
ejpam-2696	169	16	and	and	CCONJ
ejpam-2696	169	17	f	f	X
ejpam-2696	169	18	:	:	PUNCT
ejpam-2696	169	19	γa→	γa→	PROPN
ejpam-2696	169	20	γs	γ	VERB
ejpam-2696	169	21	a	a	DET
ejpam-2696	169	22	γ	γ	NOUN
ejpam-2696	169	23	-	-	PUNCT
ejpam-2696	169	24	homomorphism	homomorphism	NOUN
ejpam-2696	169	25	.	.	PUNCT
ejpam-2696	170	1	then	then	ADV
ejpam-2696	170	2	a	a	PRON
ejpam-2696	170	3	is	be	AUX
ejpam-2696	170	4	a	a	DET
ejpam-2696	170	5	γ	γ	NOUN
ejpam-2696	170	6	-	-	PUNCT
ejpam-2696	170	7	semigroup	semigroup	NOUN
ejpam-2696	170	8	under	under	ADP
ejpam-2696	170	9	the	the	DET
ejpam-2696	170	10	γ	γ	NOUN
ejpam-2696	170	11	-	-	PUNCT
ejpam-2696	170	12	operation	operation	NOUN
ejpam-2696	170	13	aγa′	aγa′	NOUN
ejpam-2696	170	14	:	:	PUNCT
ejpam-2696	170	15	=	=	PUNCT
ejpam-2696	170	16	f(a)γa′	f(a)γa′	PROPN
ejpam-2696	170	17	for	for	ADP
ejpam-2696	170	18	every	every	DET
ejpam-2696	170	19	a	a	NOUN
ejpam-2696	170	20	,	,	PUNCT
ejpam-2696	170	21	a′	a′	PROPN
ejpam-2696	170	22	∈	∈	PROPN
ejpam-2696	170	23	a	a	PRON
ejpam-2696	170	24	and	and	CCONJ
ejpam-2696	170	25	γ	γ	PROPN
ejpam-2696	170	26	∈	∈	PROPN
ejpam-2696	170	27	γ	γ	X
ejpam-2696	170	28	.	.	PROPN
ejpam-2696	170	29	for	for	ADP
ejpam-2696	170	30	this	this	PRON
ejpam-2696	170	31	,	,	PUNCT
ejpam-2696	170	32	let	let	VERB
ejpam-2696	170	33	a	a	DET
ejpam-2696	170	34	,	,	PUNCT
ejpam-2696	170	35	a′	a′	PROPN
ejpam-2696	170	36	,	,	PUNCT
ejpam-2696	170	37	a′′	a′′	PROPN
ejpam-2696	170	38	∈	∈	PROPN
ejpam-2696	170	39	a	a	PRON
ejpam-2696	170	40	and	and	CCONJ
ejpam-2696	170	41	α	α	NOUN
ejpam-2696	170	42	,	,	PUNCT
ejpam-2696	170	43	γ	γ	PROPN
ejpam-2696	170	44	∈	∈	PROPN
ejpam-2696	170	45	γ	γ	X
ejpam-2696	170	46	.	.	PROPN
ejpam-2696	171	1	then	then	ADV
ejpam-2696	171	2	(	(	PUNCT
ejpam-2696	171	3	aαa′)γa′′	aαa′)γa′′	NOUN
ejpam-2696	171	4	=	=	SYM
ejpam-2696	171	5	(	(	PUNCT
ejpam-2696	171	6	f(a)αa′)γa′′	f(a)αa′)γa′′	NOUN
ejpam-2696	171	7	=	=	SYM
ejpam-2696	171	8	f(f(a)αa′)γa′′	f(f(a)αa′)γa′′	NOUN
ejpam-2696	171	9	=	=	SYM
ejpam-2696	171	10	(	(	PUNCT
ejpam-2696	171	11	f(a)αf(a′))γa′′	f(a)αf(a′))γa′′	NOUN
ejpam-2696	171	12	=	=	SYM
ejpam-2696	171	13	f(a)α(f(a′)γa′′	f(a)α(f(a′)γa′′	PROPN
ejpam-2696	171	14	)	)	PUNCT
ejpam-2696	171	15	=	=	SYM
ejpam-2696	171	16	aα(f(a′)γa′′	aα(f(a′)γa′′	NOUN
ejpam-2696	171	17	)	)	PUNCT
ejpam-2696	171	18	=	=	SYM
ejpam-2696	171	19	aα(a′γa′′	aα(a′γa′′	NOUN
ejpam-2696	171	20	)	)	PUNCT
ejpam-2696	171	21	.	.	PUNCT
ejpam-2696	172	1	theorem	theorem	ADJ
ejpam-2696	172	2	2	2	NUM
ejpam-2696	172	3	(	(	PUNCT
ejpam-2696	172	4	homomorphism	homomorphism	NOUN
ejpam-2696	172	5	theorem	theorem	VERB
ejpam-2696	172	6	for	for	ADP
ejpam-2696	172	7	γ	γ	NOUN
ejpam-2696	172	8	-	-	PUNCT
ejpam-2696	172	9	acts	act	NOUN
ejpam-2696	172	10	)	)	PUNCT
ejpam-2696	172	11	.	.	PUNCT
ejpam-2696	173	1	let	let	VERB
ejpam-2696	173	2	f	f	NOUN
ejpam-2696	173	3	:	:	PUNCT
ejpam-2696	173	4	γa→	γa→	PROPN
ejpam-2696	173	5	γb	γb	AUX
ejpam-2696	173	6	be	be	AUX
ejpam-2696	173	7	a	a	DET
ejpam-2696	173	8	γ	γ	NOUN
ejpam-2696	173	9	-	-	PUNCT
ejpam-2696	173	10	homomorphism	homomorphism	NOUN
ejpam-2696	173	11	and	and	CCONJ
ejpam-2696	173	12	ρ	ρ	PROPN
ejpam-2696	173	13	be	be	AUX
ejpam-2696	173	14	a	a	DET
ejpam-2696	173	15	γ	γ	NOUN
ejpam-2696	173	16	-	-	NOUN
ejpam-2696	173	17	congruence	congruence	NOUN
ejpam-2696	173	18	on	on	ADP
ejpam-2696	173	19	γa	γa	PRON
ejpam-2696	173	20	such	such	ADJ
ejpam-2696	173	21	that	that	SCONJ
ejpam-2696	173	22	aρa′	aρa′	PROPN
ejpam-2696	173	23	implies	imply	VERB
ejpam-2696	173	24	f(a	f(a	X
ejpam-2696	173	25	)	)	PUNCT
ejpam-2696	173	26	=	=	SYM
ejpam-2696	173	27	f(a′	f(a′	PROPN
ejpam-2696	173	28	)	)	PUNCT
ejpam-2696	173	29	,	,	PUNCT
ejpam-2696	173	30	i.e.	i.e.	X
ejpam-2696	173	31	ρ	ρ	NOUN
ejpam-2696	173	32	≤	≤	NOUN
ejpam-2696	173	33	kerf	kerf	NOUN
ejpam-2696	173	34	.	.	PUNCT
ejpam-2696	174	1	then	then	ADV
ejpam-2696	174	2	f	f	PROPN
ejpam-2696	175	1	′	′	NUM
ejpam-2696	175	2	:	:	PUNCT
ejpam-2696	175	3	γa	γa	PROPN
ejpam-2696	175	4	ρ	ρ	PROPN
ejpam-2696	175	5	→	→	SYM
ejpam-2696	175	6	γb	γb	NOUN
ejpam-2696	175	7	with	with	ADP
ejpam-2696	175	8	f	f	PROPN
ejpam-2696	175	9	′([a]ρ	′([a]ρ	NUM
ejpam-2696	175	10	)	)	PUNCT
ejpam-2696	175	11	:	:	PUNCT
ejpam-2696	175	12	=	=	SYM
ejpam-2696	175	13	f(a	f(a	NOUN
ejpam-2696	175	14	)	)	PUNCT
ejpam-2696	175	15	,	,	PUNCT
ejpam-2696	175	16	a	a	DET
ejpam-2696	175	17	∈	∈	PROPN
ejpam-2696	175	18	γa	γa	NOUN
ejpam-2696	175	19	,	,	PUNCT
ejpam-2696	175	20	is	be	AUX
ejpam-2696	175	21	the	the	DET
ejpam-2696	175	22	unique	unique	ADJ
ejpam-2696	175	23	γ	γ	NOUN
ejpam-2696	175	24	-	-	NOUN
ejpam-2696	175	25	homomorphism	homomorphism	NOUN
ejpam-2696	175	26	such	such	ADJ
ejpam-2696	175	27	that	that	SCONJ
ejpam-2696	175	28	f	f	PROPN
ejpam-2696	175	29	′πρ	′πρ	NOUN
ejpam-2696	175	30	=	=	SYM
ejpam-2696	175	31	f	f	PROPN
ejpam-2696	175	32	.	.	PUNCT
ejpam-2696	176	1	if	if	SCONJ
ejpam-2696	176	2	ρ	ρ	NOUN
ejpam-2696	176	3	=	=	NOUN
ejpam-2696	176	4	kerf	kerf	NOUN
ejpam-2696	176	5	,	,	PUNCT
ejpam-2696	176	6	then	then	ADV
ejpam-2696	176	7	f	f	PROPN
ejpam-2696	176	8	′	′	PROPN
ejpam-2696	176	9	is	be	AUX
ejpam-2696	176	10	injective	injective	ADJ
ejpam-2696	176	11	.	.	PUNCT
ejpam-2696	177	1	also	also	ADV
ejpam-2696	177	2	if	if	SCONJ
ejpam-2696	177	3	f	f	PROPN
ejpam-2696	177	4	is	be	AUX
ejpam-2696	177	5	surjective	surjective	ADJ
ejpam-2696	177	6	,	,	PUNCT
ejpam-2696	177	7	then	then	ADV
ejpam-2696	177	8	so	so	ADV
ejpam-2696	177	9	is	be	AUX
ejpam-2696	177	10	f	f	PROPN
ejpam-2696	177	11	′.	′.	NOUN
ejpam-2696	177	12	proof	proof	NOUN
ejpam-2696	177	13	.	.	PUNCT
ejpam-2696	178	1	the	the	DET
ejpam-2696	178	2	mapping	mapping	NOUN
ejpam-2696	178	3	f	f	NOUN
ejpam-2696	178	4	′	′	NUM
ejpam-2696	178	5	is	be	AUX
ejpam-2696	178	6	well	well	ADV
ejpam-2696	178	7	-	-	PUNCT
ejpam-2696	178	8	defined	define	VERB
ejpam-2696	178	9	,	,	PUNCT
ejpam-2696	178	10	because	because	SCONJ
ejpam-2696	178	11	for	for	ADP
ejpam-2696	178	12	every	every	DET
ejpam-2696	178	13	[	[	X
ejpam-2696	178	14	a]ρ	a]ρ	NOUN
ejpam-2696	178	15	,	,	PUNCT
ejpam-2696	178	16	[	[	X
ejpam-2696	178	17	a	a	DET
ejpam-2696	178	18	′]ρ	′]ρ	INTJ
ejpam-2696	178	19	∈	∈	NOUN
ejpam-2696	178	20	γa	γa	NOUN
ejpam-2696	178	21	ρ	ρ	X
ejpam-2696	178	22	,	,	PUNCT
ejpam-2696	179	1	[	[	X
ejpam-2696	179	2	a]ρ	a]ρ	NOUN
ejpam-2696	179	3	=	=	PUNCT
ejpam-2696	180	1	[	[	X
ejpam-2696	180	2	a′]ρ	a′]ρ	X
ejpam-2696	180	3	⇔	⇔	X
ejpam-2696	180	4	aρa′	aρa′	ADJ
ejpam-2696	180	5	⇒	⇒	PROPN
ejpam-2696	180	6	f(a	f(a	PROPN
ejpam-2696	180	7	)	)	PUNCT
ejpam-2696	180	8	=	=	PUNCT
ejpam-2696	181	1	f(a′)⇒	f(a′)⇒	NUM
ejpam-2696	181	2	f	f	NUM
ejpam-2696	181	3	′([a]ρ	′([a]ρ	NUM
ejpam-2696	181	4	)	)	PUNCT
ejpam-2696	182	1	=	=	SYM
ejpam-2696	182	2	f	f	X
ejpam-2696	182	3	′([a′]ρ	′([a′]ρ	NOUN
ejpam-2696	182	4	)	)	PUNCT
ejpam-2696	182	5	.	.	PUNCT
ejpam-2696	183	1	for	for	ADP
ejpam-2696	183	2	every	every	DET
ejpam-2696	183	3	s	s	PROPN
ejpam-2696	183	4	∈	∈	PROPN
ejpam-2696	183	5	s	s	NOUN
ejpam-2696	183	6	,	,	PUNCT
ejpam-2696	183	7	γ	γ	PROPN
ejpam-2696	183	8	∈	∈	PROPN
ejpam-2696	183	9	γ	γ	NOUN
ejpam-2696	183	10	and	and	CCONJ
ejpam-2696	183	11	a	a	DET
ejpam-2696	183	12	∈	∈	PROPN
ejpam-2696	183	13	a	a	PRON
ejpam-2696	183	14	,	,	PUNCT
ejpam-2696	183	15	f	f	PROPN
ejpam-2696	183	16	′(sγ[a]ρ	′(sγ[a]ρ	PROPN
ejpam-2696	183	17	)	)	PUNCT
ejpam-2696	184	1	=	=	SYM
ejpam-2696	184	2	f	f	PROPN
ejpam-2696	184	3	′([sγa]ρ	′([sγa]ρ	PROPN
ejpam-2696	184	4	)	)	PUNCT
ejpam-2696	184	5	=	=	SYM
ejpam-2696	184	6	f(sγa	f(sγa	NOUN
ejpam-2696	184	7	)	)	PUNCT
ejpam-2696	184	8	=	=	SYM
ejpam-2696	184	9	sγf(a	sγf(a	PROPN
ejpam-2696	184	10	)	)	PUNCT
ejpam-2696	184	11	=	=	PRON
ejpam-2696	184	12	sγf	sγf	NOUN
ejpam-2696	184	13	′([a]ρ	′([a]ρ	NOUN
ejpam-2696	184	14	)	)	PUNCT
ejpam-2696	184	15	.	.	PUNCT
ejpam-2696	185	1	hence	hence	ADV
ejpam-2696	185	2	,	,	PUNCT
ejpam-2696	185	3	f	f	PROPN
ejpam-2696	185	4	′	′	NOUN
ejpam-2696	185	5	is	be	AUX
ejpam-2696	185	6	a	a	DET
ejpam-2696	185	7	γ	γ	NOUN
ejpam-2696	185	8	-	-	PUNCT
ejpam-2696	185	9	homomorphism	homomorphism	NOUN
ejpam-2696	185	10	.	.	PUNCT
ejpam-2696	186	1	also	also	ADV
ejpam-2696	186	2	for	for	ADP
ejpam-2696	186	3	every	every	DET
ejpam-2696	186	4	a	a	DET
ejpam-2696	186	5	∈	∈	PROPN
ejpam-2696	186	6	γa	γa	NOUN
ejpam-2696	186	7	,	,	PUNCT
ejpam-2696	186	8	(	(	PUNCT
ejpam-2696	186	9	f	f	PROPN
ejpam-2696	186	10	′πρ)(a	′πρ)(a	PROPN
ejpam-2696	186	11	)	)	PUNCT
ejpam-2696	187	1	=	=	PUNCT
ejpam-2696	187	2	f	f	NOUN
ejpam-2696	187	3	′(πρ(a	′(πρ(a	NOUN
ejpam-2696	187	4	)	)	PUNCT
ejpam-2696	187	5	)	)	PUNCT
ejpam-2696	188	1	=	=	SYM
ejpam-2696	188	2	f	f	PROPN
ejpam-2696	188	3	′([a]ρ	′([a]ρ	ADJ
ejpam-2696	188	4	)	)	PUNCT
ejpam-2696	189	1	=	=	SYM
ejpam-2696	189	2	f(a	f(a	PROPN
ejpam-2696	189	3	)	)	PUNCT
ejpam-2696	189	4	.	.	PUNCT
ejpam-2696	190	1	now	now	ADV
ejpam-2696	190	2	we	we	PRON
ejpam-2696	190	3	show	show	VERB
ejpam-2696	190	4	that	that	SCONJ
ejpam-2696	190	5	f	f	PROPN
ejpam-2696	190	6	′	′	NOUN
ejpam-2696	190	7	is	be	AUX
ejpam-2696	190	8	unique	unique	ADJ
ejpam-2696	190	9	.	.	PUNCT
ejpam-2696	191	1	suppose	suppose	VERB
ejpam-2696	191	2	there	there	PRON
ejpam-2696	191	3	exists	exist	VERB
ejpam-2696	191	4	f	f	PROPN
ejpam-2696	191	5	′′	′′	PROPN
ejpam-2696	191	6	:	:	PUNCT
ejpam-2696	191	7	γa	γa	PROPN
ejpam-2696	191	8	ρ	ρ	PROPN
ejpam-2696	191	9	→	→	SYM
ejpam-2696	191	10	γb	γb	NOUN
ejpam-2696	191	11	such	such	ADJ
ejpam-2696	191	12	that	that	SCONJ
ejpam-2696	191	13	f	f	PROPN
ejpam-2696	192	1	′′πρ	′′πρ	PROPN
ejpam-2696	192	2	=	=	SYM
ejpam-2696	192	3	f	f	PROPN
ejpam-2696	192	4	.	.	PUNCT
ejpam-2696	193	1	this	this	PRON
ejpam-2696	193	2	implies	imply	VERB
ejpam-2696	193	3	that	that	SCONJ
ejpam-2696	193	4	f	f	PROPN
ejpam-2696	193	5	′′πρ	′′πρ	PROPN
ejpam-2696	193	6	=	=	SYM
ejpam-2696	193	7	f	f	PROPN
ejpam-2696	193	8	′πρ	′πρ	NOUN
ejpam-2696	193	9	.	.	PUNCT
ejpam-2696	194	1	since	since	SCONJ
ejpam-2696	194	2	πρ	πρ	INTJ
ejpam-2696	194	3	is	be	AUX
ejpam-2696	194	4	an	an	DET
ejpam-2696	194	5	epimorphism	epimorphism	NOUN
ejpam-2696	194	6	,	,	PUNCT
ejpam-2696	194	7	f	f	PROPN
ejpam-2696	194	8	′′	′′	PROPN
ejpam-2696	194	9	=	=	SYM
ejpam-2696	194	10	f	f	PROPN
ejpam-2696	194	11	′.	′.	NOUN
ejpam-2696	194	12	the	the	DET
ejpam-2696	194	13	remainder	remainder	NOUN
ejpam-2696	194	14	is	be	AUX
ejpam-2696	194	15	an	an	DET
ejpam-2696	194	16	easy	easy	ADJ
ejpam-2696	194	17	verification	verification	NOUN
ejpam-2696	194	18	.	.	PUNCT
ejpam-2696	195	1	corollary	corollary	ADJ
ejpam-2696	195	2	1	1	NUM
ejpam-2696	195	3	.	.	PUNCT
ejpam-2696	196	1	let	let	VERB
ejpam-2696	196	2	f	f	NOUN
ejpam-2696	196	3	:	:	PUNCT
ejpam-2696	196	4	γa→	γa→	PROPN
ejpam-2696	196	5	γb	γb	AUX
ejpam-2696	196	6	be	be	AUX
ejpam-2696	196	7	a	a	DET
ejpam-2696	196	8	γ	γ	NOUN
ejpam-2696	196	9	-	-	PUNCT
ejpam-2696	196	10	epimorphism	epimorphism	NOUN
ejpam-2696	196	11	.	.	PUNCT
ejpam-2696	197	1	then	then	ADV
ejpam-2696	197	2	γa	γa	AUX
ejpam-2696	197	3	kerf	kerf	NOUN
ejpam-2696	197	4	∼=	∼=	PROPN
ejpam-2696	197	5	γb	γb	NOUN
ejpam-2696	197	6	.	.	NOUN
ejpam-2696	198	1	3	3	X
ejpam-2696	198	2	.	.	X
ejpam-2696	198	3	cyclic	cyclic	ADJ
ejpam-2696	198	4	,	,	PUNCT
ejpam-2696	198	5	indecomposable	indecomposable	ADJ
ejpam-2696	198	6	and	and	CCONJ
ejpam-2696	198	7	free	free	ADJ
ejpam-2696	198	8	γ	γ	PROPN
ejpam-2696	198	9	-	-	PUNCT
ejpam-2696	198	10	s	s	NOUN
ejpam-2696	198	11	-	-	PUNCT
ejpam-2696	198	12	acts	act	NOUN
ejpam-2696	198	13	in	in	ADP
ejpam-2696	198	14	this	this	DET
ejpam-2696	198	15	section	section	NOUN
ejpam-2696	198	16	we	we	PRON
ejpam-2696	198	17	study	study	VERB
ejpam-2696	198	18	the	the	DET
ejpam-2696	198	19	notions	notion	NOUN
ejpam-2696	198	20	of	of	ADP
ejpam-2696	198	21	cyclic	cyclic	ADJ
ejpam-2696	198	22	,	,	PUNCT
ejpam-2696	198	23	free	free	ADJ
ejpam-2696	198	24	and	and	CCONJ
ejpam-2696	198	25	indecomposable	indecomposable	ADJ
ejpam-2696	198	26	γ	γ	PROPN
ejpam-2696	198	27	-	-	PUNCT
ejpam-2696	198	28	s	s	NOUN
ejpam-2696	198	29	-	-	PUNCT
ejpam-2696	198	30	acts	act	NOUN
ejpam-2696	198	31	and	and	CCONJ
ejpam-2696	198	32	investigate	investigate	VERB
ejpam-2696	198	33	their	their	PRON
ejpam-2696	198	34	properties	property	NOUN
ejpam-2696	198	35	.	.	PUNCT
ejpam-2696	199	1	for	for	ADP
ejpam-2696	199	2	each	each	DET
ejpam-2696	199	3	γ	γ	PROPN
ejpam-2696	199	4	-	-	PUNCT
ejpam-2696	199	5	act	act	NOUN
ejpam-2696	199	6	,	,	PUNCT
ejpam-2696	199	7	a	a	DET
ejpam-2696	199	8	unique	unique	ADJ
ejpam-2696	199	9	decomposition	decomposition	NOUN
ejpam-2696	199	10	into	into	ADP
ejpam-2696	199	11	indecomposable	indecomposable	ADJ
ejpam-2696	199	12	γ	γ	NOUN
ejpam-2696	199	13	-	-	PUNCT
ejpam-2696	199	14	subacts	subact	NOUN
ejpam-2696	199	15	is	be	AUX
ejpam-2696	199	16	obtained	obtain	VERB
ejpam-2696	199	17	.	.	PUNCT
ejpam-2696	200	1	it	it	PRON
ejpam-2696	200	2	is	be	AUX
ejpam-2696	200	3	also	also	ADV
ejpam-2696	200	4	proved	prove	VERB
ejpam-2696	200	5	that	that	SCONJ
ejpam-2696	200	6	if	if	SCONJ
ejpam-2696	200	7	a	a	DET
ejpam-2696	200	8	γ	γ	NOUN
ejpam-2696	200	9	-	-	PUNCT
ejpam-2696	200	10	act	act	NOUN
ejpam-2696	200	11	is	be	AUX
ejpam-2696	200	12	free	free	ADJ
ejpam-2696	200	13	,	,	PUNCT
ejpam-2696	200	14	then	then	ADV
ejpam-2696	200	15	γ	γ	PROPN
ejpam-2696	200	16	is	be	AUX
ejpam-2696	200	17	a	a	DET
ejpam-2696	200	18	singleton	singleton	NOUN
ejpam-2696	200	19	.	.	PUNCT
ejpam-2696	201	1	h.	h.	PROPN
ejpam-2696	201	2	rasouli	rasouli	PROPN
ejpam-2696	201	3	,	,	PUNCT
ejpam-2696	201	4	a.r	a.r	PROPN
ejpam-2696	201	5	.	.	PROPN
ejpam-2696	201	6	shabani	shabani	PROPN
ejpam-2696	201	7	/	/	SYM
ejpam-2696	201	8	eur	eur	PROPN
ejpam-2696	201	9	.	.	PUNCT
ejpam-2696	202	1	j.	j.	PROPN
ejpam-2696	202	2	pure	pure	PROPN
ejpam-2696	202	3	appl	appl	PROPN
ejpam-2696	202	4	.	.	PROPN
ejpam-2696	202	5	math	math	PROPN
ejpam-2696	202	6	,	,	PUNCT
ejpam-2696	202	7	10	10	NUM
ejpam-2696	202	8	(	(	PUNCT
ejpam-2696	202	9	4	4	NUM
ejpam-2696	202	10	)	)	PUNCT
ejpam-2696	202	11	(	(	PUNCT
ejpam-2696	202	12	2017	2017	NUM
ejpam-2696	202	13	)	)	PUNCT
ejpam-2696	202	14	,	,	PUNCT
ejpam-2696	202	15	739	739	NUM
ejpam-2696	202	16	-	-	SYM
ejpam-2696	202	17	748	748	NUM
ejpam-2696	202	18	745	745	NUM
ejpam-2696	202	19	definition	definition	NOUN
ejpam-2696	202	20	2	2	NUM
ejpam-2696	202	21	.	.	PUNCT
ejpam-2696	202	22	a	a	DET
ejpam-2696	202	23	subset	subset	ADJ
ejpam-2696	202	24	u	u	PROPN
ejpam-2696	202	25	6=	6=	NOUN
ejpam-2696	202	26	∅	∅	NOUN
ejpam-2696	202	27	of	of	ADP
ejpam-2696	202	28	a	a	DET
ejpam-2696	202	29	γ	γ	PROPN
ejpam-2696	202	30	-	-	PUNCT
ejpam-2696	202	31	s	s	NOUN
ejpam-2696	202	32	-	-	PUNCT
ejpam-2696	202	33	act	act	NOUN
ejpam-2696	202	34	γa	γa	PROPN
ejpam-2696	202	35	is	be	AUX
ejpam-2696	202	36	said	say	VERB
ejpam-2696	202	37	to	to	PART
ejpam-2696	202	38	be	be	AUX
ejpam-2696	202	39	a	a	DET
ejpam-2696	202	40	generating	generate	VERB
ejpam-2696	202	41	set	set	NOUN
ejpam-2696	202	42	of	of	ADP
ejpam-2696	202	43	γa	γa	PRON
ejpam-2696	202	44	if	if	SCONJ
ejpam-2696	202	45	every	every	DET
ejpam-2696	202	46	element	element	NOUN
ejpam-2696	202	47	a	a	DET
ejpam-2696	202	48	∈	∈	NOUN
ejpam-2696	202	49	a	a	PRON
ejpam-2696	202	50	can	can	AUX
ejpam-2696	202	51	be	be	AUX
ejpam-2696	202	52	presented	present	VERB
ejpam-2696	202	53	as	as	ADP
ejpam-2696	202	54	a	a	DET
ejpam-2696	202	55	=	=	PUNCT
ejpam-2696	202	56	sγu	sγu	NOUN
ejpam-2696	202	57	for	for	ADP
ejpam-2696	202	58	some	some	DET
ejpam-2696	202	59	s	s	PART
ejpam-2696	202	60	∈	∈	PROPN
ejpam-2696	202	61	s	s	PROPN
ejpam-2696	202	62	,	,	PUNCT
ejpam-2696	202	63	u	u	PROPN
ejpam-2696	202	64	∈	∈	PROPN
ejpam-2696	202	65	u	u	NOUN
ejpam-2696	202	66	and	and	CCONJ
ejpam-2696	202	67	γ	γ	PROPN
ejpam-2696	202	68	∈	∈	PROPN
ejpam-2696	202	69	γ	γ	X
ejpam-2696	202	70	.	.	PUNCT
ejpam-2696	203	1	in	in	ADP
ejpam-2696	203	2	this	this	DET
ejpam-2696	203	3	case	case	NOUN
ejpam-2696	203	4	,	,	PUNCT
ejpam-2696	203	5	we	we	PRON
ejpam-2696	203	6	write	write	VERB
ejpam-2696	203	7	γa	γa	PROPN
ejpam-2696	203	8	=	=	SYM
ejpam-2696	204	1	〈	〈	PROPN
ejpam-2696	204	2	u	u	NOUN
ejpam-2696	204	3	〉	〉	NOUN
ejpam-2696	204	4	(	(	PUNCT
ejpam-2696	204	5	or	or	CCONJ
ejpam-2696	204	6	sγu	sγu	ADJ
ejpam-2696	204	7	)	)	PUNCT
ejpam-2696	204	8	,	,	PUNCT
ejpam-2696	204	9	where	where	SCONJ
ejpam-2696	204	10	sγu	sγu	NOUN
ejpam-2696	204	11	=	=	SYM
ejpam-2696	204	12	{	{	PUNCT
ejpam-2696	204	13	sγu	sγu	NOUN
ejpam-2696	204	14	:	:	PUNCT
ejpam-2696	204	15	s	s	VERB
ejpam-2696	204	16	∈	∈	PROPN
ejpam-2696	204	17	s	s	PROPN
ejpam-2696	204	18	,	,	PUNCT
ejpam-2696	204	19	γ	γ	PROPN
ejpam-2696	204	20	∈	∈	PROPN
ejpam-2696	204	21	γ	γ	X
ejpam-2696	204	22	,	,	PUNCT
ejpam-2696	204	23	u	u	PROPN
ejpam-2696	204	24	∈	∈	PROPN
ejpam-2696	204	25	u	u	NOUN
ejpam-2696	204	26	}	}	PUNCT
ejpam-2696	204	27	.	.	PUNCT
ejpam-2696	205	1	for	for	ADP
ejpam-2696	205	2	simplicity	simplicity	NOUN
ejpam-2696	205	3	,	,	PUNCT
ejpam-2696	205	4	we	we	PRON
ejpam-2696	205	5	use	use	VERB
ejpam-2696	205	6	the	the	DET
ejpam-2696	205	7	notations	notation	NOUN
ejpam-2696	205	8	sγu	sγu	NOUN
ejpam-2696	205	9	and	and	CCONJ
ejpam-2696	205	10	sγu	sγu	NOUN
ejpam-2696	205	11	for	for	ADP
ejpam-2696	205	12	s{γ}u	s{γ}u	PROPN
ejpam-2696	205	13	and	and	CCONJ
ejpam-2696	205	14	sγ{u	sγ{u	PROPN
ejpam-2696	205	15	}	}	PUNCT
ejpam-2696	205	16	,	,	PUNCT
ejpam-2696	205	17	respectively	respectively	ADV
ejpam-2696	205	18	.	.	PUNCT
ejpam-2696	206	1	also	also	ADV
ejpam-2696	206	2	a	a	PRON
ejpam-2696	206	3	is	be	AUX
ejpam-2696	206	4	finitely	finitely	ADV
ejpam-2696	206	5	generated	generate	VERB
ejpam-2696	206	6	if	if	SCONJ
ejpam-2696	206	7	it	it	PRON
ejpam-2696	206	8	has	have	VERB
ejpam-2696	206	9	a	a	DET
ejpam-2696	206	10	finite	finite	NOUN
ejpam-2696	206	11	generating	generate	VERB
ejpam-2696	206	12	set	set	NOUN
ejpam-2696	206	13	of	of	ADP
ejpam-2696	206	14	elements	element	NOUN
ejpam-2696	206	15	.	.	PUNCT
ejpam-2696	207	1	we	we	PRON
ejpam-2696	207	2	call	call	VERB
ejpam-2696	207	3	γa	γa	PRON
ejpam-2696	207	4	a	a	DET
ejpam-2696	207	5	cyclic	cyclic	ADJ
ejpam-2696	207	6	γ	γ	X
ejpam-2696	207	7	-	-	PUNCT
ejpam-2696	207	8	s	s	NOUN
ejpam-2696	207	9	-	-	PUNCT
ejpam-2696	207	10	act	act	NOUN
ejpam-2696	207	11	if	if	SCONJ
ejpam-2696	207	12	γa	γa	PROPN
ejpam-2696	207	13	=	=	PUNCT
ejpam-2696	207	14	〈	〈	PROPN
ejpam-2696	207	15	a	a	PRON
ejpam-2696	207	16	〉	〉	PROPN
ejpam-2696	207	17	(=	(=	SYM
ejpam-2696	207	18	sγa	sγa	PROPN
ejpam-2696	207	19	)	)	PUNCT
ejpam-2696	207	20	for	for	ADP
ejpam-2696	207	21	some	some	PRON
ejpam-2696	207	22	a	a	DET
ejpam-2696	207	23	∈	∈	PROPN
ejpam-2696	207	24	γa	γa	NOUN
ejpam-2696	207	25	.	.	PUNCT
ejpam-2696	208	1	not	not	PART
ejpam-2696	208	2	that	that	SCONJ
ejpam-2696	208	3	γa	γa	NOUN
ejpam-2696	208	4	=	=	PUNCT
ejpam-2696	208	5	〈	〈	PROPN
ejpam-2696	208	6	a	a	DET
ejpam-2696	208	7	〉	〉	NOUN
ejpam-2696	208	8	,	,	PUNCT
ejpam-2696	208	9	i.e.	i.e.	X
ejpam-2696	208	10	γa	γa	PROPN
ejpam-2696	208	11	is	be	AUX
ejpam-2696	208	12	always	always	ADV
ejpam-2696	208	13	a	a	DET
ejpam-2696	208	14	generating	generate	VERB
ejpam-2696	208	15	set	set	NOUN
ejpam-2696	208	16	of	of	ADP
ejpam-2696	208	17	itself	itself	PRON
ejpam-2696	208	18	.	.	PUNCT
ejpam-2696	209	1	lemma	lemma	PROPN
ejpam-2696	209	2	3	3	X
ejpam-2696	209	3	.	.	PUNCT
ejpam-2696	210	1	let	let	VERB
ejpam-2696	210	2	u	u	PRON
ejpam-2696	210	3	be	be	AUX
ejpam-2696	210	4	a	a	DET
ejpam-2696	210	5	non	non	ADJ
ejpam-2696	210	6	-	-	ADJ
ejpam-2696	210	7	empty	empty	ADJ
ejpam-2696	210	8	subset	subset	NOUN
ejpam-2696	210	9	of	of	ADP
ejpam-2696	210	10	a	a	DET
ejpam-2696	210	11	γ	γ	NOUN
ejpam-2696	210	12	-	-	PUNCT
ejpam-2696	210	13	act	act	NOUN
ejpam-2696	210	14	γa	γa	PROPN
ejpam-2696	210	15	and	and	CCONJ
ejpam-2696	210	16	a	a	DET
ejpam-2696	210	17	∈	∈	PROPN
ejpam-2696	210	18	γa	γa	NOUN
ejpam-2696	210	19	.	.	PUNCT
ejpam-2696	211	1	then	then	ADV
ejpam-2696	211	2	the	the	DET
ejpam-2696	211	3	following	follow	VERB
ejpam-2696	211	4	assertions	assertion	NOUN
ejpam-2696	211	5	hold	hold	VERB
ejpam-2696	211	6	:	:	PUNCT
ejpam-2696	211	7	(	(	PUNCT
ejpam-2696	211	8	i	i	NOUN
ejpam-2696	211	9	)	)	PUNCT
ejpam-2696	211	10	sγa	sγa	PROPN
ejpam-2696	212	1	=	=	PUNCT
ejpam-2696	212	2	sγa	sγa	PROPN
ejpam-2696	212	3	for	for	ADP
ejpam-2696	212	4	every	every	DET
ejpam-2696	212	5	γ	γ	PROPN
ejpam-2696	212	6	∈	∈	PROPN
ejpam-2696	212	7	γ	γ	X
ejpam-2696	212	8	.	.	PROPN
ejpam-2696	212	9	(	(	PUNCT
ejpam-2696	212	10	ii	ii	NOUN
ejpam-2696	212	11	)	)	PUNCT
ejpam-2696	212	12	sγa	sγa	NOUN
ejpam-2696	212	13	=	=	PUNCT
ejpam-2696	212	14	sβa	sβa	PROPN
ejpam-2696	212	15	for	for	ADP
ejpam-2696	212	16	every	every	DET
ejpam-2696	212	17	γ	γ	PROPN
ejpam-2696	212	18	,	,	PUNCT
ejpam-2696	212	19	β	β	PROPN
ejpam-2696	212	20	∈	∈	PROPN
ejpam-2696	212	21	γ	γ	X
ejpam-2696	212	22	.	.	PUNCT
ejpam-2696	212	23	(	(	PUNCT
ejpam-2696	212	24	iii	iii	X
ejpam-2696	212	25	)	)	PUNCT
ejpam-2696	212	26	sγu	sγu	NOUN
ejpam-2696	212	27	=	=	NOUN
ejpam-2696	212	28	sγu	sγu	NOUN
ejpam-2696	212	29	for	for	ADP
ejpam-2696	212	30	every	every	DET
ejpam-2696	212	31	γ	γ	PROPN
ejpam-2696	212	32	∈	∈	PROPN
ejpam-2696	212	33	γ	γ	X
ejpam-2696	212	34	.	.	PUNCT
ejpam-2696	212	35	proof	proof	NOUN
ejpam-2696	212	36	.	.	PUNCT
ejpam-2696	213	1	(	(	PUNCT
ejpam-2696	213	2	i	i	NOUN
ejpam-2696	213	3	)	)	PUNCT
ejpam-2696	213	4	let	let	VERB
ejpam-2696	213	5	γ	γ	X
ejpam-2696	213	6	∈	∈	PROPN
ejpam-2696	213	7	γ	γ	NOUN
ejpam-2696	213	8	and	and	CCONJ
ejpam-2696	213	9	a	a	DET
ejpam-2696	213	10	∈	∈	PROPN
ejpam-2696	213	11	γa	γa	NOUN
ejpam-2696	213	12	.	.	PUNCT
ejpam-2696	214	1	clearly	clearly	ADV
ejpam-2696	214	2	,	,	PUNCT
ejpam-2696	214	3	sγa	sγa	ADJ
ejpam-2696	214	4	⊆	⊆	NUM
ejpam-2696	214	5	sγa	sγa	NOUN
ejpam-2696	214	6	.	.	PUNCT
ejpam-2696	215	1	for	for	ADP
ejpam-2696	215	2	the	the	DET
ejpam-2696	215	3	reverse	reverse	ADJ
ejpam-2696	215	4	inclusion	inclusion	NOUN
ejpam-2696	215	5	,	,	PUNCT
ejpam-2696	215	6	take	take	VERB
ejpam-2696	215	7	any	any	DET
ejpam-2696	215	8	β	β	NOUN
ejpam-2696	215	9	∈	∈	PROPN
ejpam-2696	215	10	γ	γ	X
ejpam-2696	215	11	and	and	CCONJ
ejpam-2696	215	12	s	s	PROPN
ejpam-2696	215	13	∈	∈	PROPN
ejpam-2696	215	14	s.	s.	PROPN
ejpam-2696	215	15	then	then	ADV
ejpam-2696	215	16	sβa	sβa	PROPN
ejpam-2696	215	17	=	=	SYM
ejpam-2696	215	18	sβ(eγa	sβ(eγa	PROPN
ejpam-2696	215	19	)	)	PUNCT
ejpam-2696	215	20	=	=	PUNCT
ejpam-2696	216	1	(	(	PUNCT
ejpam-2696	216	2	sβe)γa	sβe)γa	NOUN
ejpam-2696	216	3	∈	∈	PROPN
ejpam-2696	216	4	sγa	sγa	NOUN
ejpam-2696	216	5	which	which	PRON
ejpam-2696	216	6	implies	imply	VERB
ejpam-2696	216	7	that	that	SCONJ
ejpam-2696	216	8	sγa	sγa	PROPN
ejpam-2696	216	9	=	=	SYM
ejpam-2696	216	10	sγa	sγa	NOUN
ejpam-2696	216	11	.	.	PUNCT
ejpam-2696	216	12	(	(	PUNCT
ejpam-2696	216	13	ii	ii	NOUN
ejpam-2696	216	14	)	)	PUNCT
ejpam-2696	216	15	let	let	VERB
ejpam-2696	216	16	γ	γ	X
ejpam-2696	216	17	,	,	PUNCT
ejpam-2696	216	18	β	β	PROPN
ejpam-2696	216	19	∈	∈	PROPN
ejpam-2696	216	20	γ	γ	X
ejpam-2696	216	21	.	.	PUNCT
ejpam-2696	217	1	using	use	VERB
ejpam-2696	217	2	(	(	PUNCT
ejpam-2696	217	3	i	i	NOUN
ejpam-2696	217	4	)	)	PUNCT
ejpam-2696	217	5	,	,	PUNCT
ejpam-2696	217	6	we	we	PRON
ejpam-2696	217	7	get	get	VERB
ejpam-2696	217	8	sγa	sγa	ADJ
ejpam-2696	217	9	=	=	SYM
ejpam-2696	217	10	sγa	sγa	NOUN
ejpam-2696	217	11	and	and	CCONJ
ejpam-2696	217	12	sβa	sβa	PROPN
ejpam-2696	217	13	=	=	SYM
ejpam-2696	217	14	sγa	sγa	PROPN
ejpam-2696	217	15	.	.	PUNCT
ejpam-2696	218	1	then	then	ADV
ejpam-2696	218	2	sγa	sγa	PROPN
ejpam-2696	218	3	=	=	SYM
ejpam-2696	218	4	sβa	sβa	PROPN
ejpam-2696	218	5	.	.	PUNCT
ejpam-2696	219	1	(	(	PUNCT
ejpam-2696	219	2	iii	iii	X
ejpam-2696	219	3	)	)	PUNCT
ejpam-2696	219	4	let	let	VERB
ejpam-2696	219	5	γ	γ	X
ejpam-2696	219	6	∈	∈	PROPN
ejpam-2696	219	7	γ	γ	X
ejpam-2696	219	8	.	.	PUNCT
ejpam-2696	220	1	it	it	PRON
ejpam-2696	220	2	follows	follow	VERB
ejpam-2696	220	3	from	from	ADP
ejpam-2696	220	4	(	(	PUNCT
ejpam-2696	220	5	i	i	NOUN
ejpam-2696	220	6	)	)	PUNCT
ejpam-2696	220	7	that	that	PRON
ejpam-2696	220	8	sγu	sγu	VERB
ejpam-2696	220	9	=	=	SYM
ejpam-2696	220	10	⋃	⋃	NOUN
ejpam-2696	220	11	u∈u	u∈u	ADJ
ejpam-2696	220	12	sγu	sγu	NOUN
ejpam-2696	220	13	=	=	SYM
ejpam-2696	220	14	⋃	⋃	NOUN
ejpam-2696	220	15	u∈u	u∈u	ADJ
ejpam-2696	220	16	sγu	sγu	NOUN
ejpam-2696	220	17	=	=	NOUN
ejpam-2696	220	18	sγu	sγu	NOUN
ejpam-2696	220	19	.	.	PUNCT
ejpam-2696	221	1	the	the	DET
ejpam-2696	221	2	above	above	ADJ
ejpam-2696	221	3	lemma	lemma	PROPN
ejpam-2696	221	4	presents	present	VERB
ejpam-2696	221	5	a	a	DET
ejpam-2696	221	6	simple	simple	ADJ
ejpam-2696	221	7	characterization	characterization	NOUN
ejpam-2696	221	8	for	for	ADP
ejpam-2696	221	9	generating	generate	VERB
ejpam-2696	221	10	subsets	subset	NOUN
ejpam-2696	221	11	of	of	ADP
ejpam-2696	221	12	a	a	DET
ejpam-2696	221	13	γ	γ	NOUN
ejpam-2696	221	14	-	-	NOUN
ejpam-2696	221	15	act	act	NOUN
ejpam-2696	221	16	.	.	PUNCT
ejpam-2696	222	1	in	in	ADP
ejpam-2696	222	2	particular	particular	ADJ
ejpam-2696	222	3	,	,	PUNCT
ejpam-2696	222	4	one	one	PRON
ejpam-2696	222	5	can	can	AUX
ejpam-2696	222	6	consider	consider	VERB
ejpam-2696	222	7	a	a	DET
ejpam-2696	222	8	cyclic	cyclic	ADJ
ejpam-2696	222	9	γ	γ	X
ejpam-2696	222	10	-	-	PUNCT
ejpam-2696	222	11	act	act	NOUN
ejpam-2696	222	12	γa	γa	NOUN
ejpam-2696	222	13	=	=	PUNCT
ejpam-2696	222	14	〈	〈	PROPN
ejpam-2696	222	15	a	a	DET
ejpam-2696	222	16	〉	〉	NOUN
ejpam-2696	222	17	as	as	ADP
ejpam-2696	222	18	sγa	sγa	NOUN
ejpam-2696	222	19	for	for	ADP
ejpam-2696	222	20	any	any	DET
ejpam-2696	222	21	γ	γ	PROPN
ejpam-2696	222	22	∈	∈	PROPN
ejpam-2696	222	23	γ	γ	X
ejpam-2696	222	24	.	.	PROPN
ejpam-2696	222	25	in	in	ADP
ejpam-2696	222	26	the	the	DET
ejpam-2696	222	27	following	following	NOUN
ejpam-2696	222	28	,	,	PUNCT
ejpam-2696	222	29	we	we	PRON
ejpam-2696	222	30	characterize	characterize	VERB
ejpam-2696	222	31	cyclic	cyclic	ADJ
ejpam-2696	222	32	γ	γ	NOUN
ejpam-2696	222	33	-	-	PUNCT
ejpam-2696	222	34	acts	act	NOUN
ejpam-2696	222	35	in	in	ADP
ejpam-2696	222	36	terms	term	NOUN
ejpam-2696	222	37	of	of	ADP
ejpam-2696	222	38	the	the	DET
ejpam-2696	222	39	factor	factor	NOUN
ejpam-2696	222	40	γ	γ	NOUN
ejpam-2696	222	41	-	-	PUNCT
ejpam-2696	222	42	acts	act	NOUN
ejpam-2696	222	43	of	of	ADP
ejpam-2696	222	44	γs	γs	NOUN
ejpam-2696	222	45	.	.	PUNCT
ejpam-2696	222	46	theorem	theorem	NOUN
ejpam-2696	222	47	4	4	NUM
ejpam-2696	222	48	.	.	PUNCT
ejpam-2696	223	1	if	if	SCONJ
ejpam-2696	223	2	a	a	DET
ejpam-2696	223	3	γ	γ	NOUN
ejpam-2696	223	4	-	-	PUNCT
ejpam-2696	223	5	act	act	NOUN
ejpam-2696	223	6	γa	γa	NOUN
ejpam-2696	223	7	is	be	AUX
ejpam-2696	223	8	cyclic	cyclic	ADJ
ejpam-2696	223	9	,	,	PUNCT
ejpam-2696	223	10	then	then	ADV
ejpam-2696	223	11	there	there	PRON
ejpam-2696	223	12	exists	exist	VERB
ejpam-2696	223	13	a	a	DET
ejpam-2696	223	14	γ	γ	NOUN
ejpam-2696	223	15	-	-	ADJ
ejpam-2696	223	16	congruence	congruence	ADJ
ejpam-2696	223	17	ρ	ρ	NOUN
ejpam-2696	223	18	on	on	ADP
ejpam-2696	223	19	γs	γs	ADP
ejpam-2696	223	20	such	such	ADJ
ejpam-2696	223	21	that	that	SCONJ
ejpam-2696	223	22	γa	γa	PROPN
ejpam-2696	223	23	∼=	∼=	ADV
ejpam-2696	223	24	γs	γ	VERB
ejpam-2696	223	25	ρ	ρ	NOUN
ejpam-2696	223	26	.	.	PUNCT
ejpam-2696	224	1	the	the	DET
ejpam-2696	224	2	converse	converse	NOUN
ejpam-2696	224	3	also	also	ADV
ejpam-2696	224	4	holds	hold	VERB
ejpam-2696	224	5	provided	provide	VERB
ejpam-2696	224	6	s	s	PROPN
ejpam-2696	224	7	is	be	AUX
ejpam-2696	224	8	a	a	DET
ejpam-2696	224	9	γ	γ	X
ejpam-2696	224	10	-	-	PUNCT
ejpam-2696	224	11	monoid	monoid	NOUN
ejpam-2696	224	12	.	.	PUNCT
ejpam-2696	225	1	proof	proof	NOUN
ejpam-2696	225	2	.	.	PUNCT
ejpam-2696	226	1	let	let	VERB
ejpam-2696	226	2	γa	γa	NOUN
ejpam-2696	226	3	=	=	PUNCT
ejpam-2696	226	4	sγa	sγa	PROPN
ejpam-2696	226	5	for	for	ADP
ejpam-2696	226	6	some	some	DET
ejpam-2696	226	7	a	a	DET
ejpam-2696	226	8	∈	∈	PROPN
ejpam-2696	226	9	γa	γa	NOUN
ejpam-2696	226	10	and	and	CCONJ
ejpam-2696	226	11	γ	γ	PROPN
ejpam-2696	226	12	∈	∈	PROPN
ejpam-2696	226	13	γ	γ	X
ejpam-2696	226	14	.	.	PROPN
ejpam-2696	227	1	then	then	ADV
ejpam-2696	227	2	the	the	DET
ejpam-2696	227	3	γ	γ	PROPN
ejpam-2696	227	4	-	-	ADJ
ejpam-2696	227	5	homomorphism	homomorphism	ADJ
ejpam-2696	227	6	λa	λa	PROPN
ejpam-2696	227	7	,	,	PUNCT
ejpam-2696	227	8	γ	γ	X
ejpam-2696	227	9	:	:	PUNCT
ejpam-2696	227	10	γs	γs	ADP
ejpam-2696	227	11	→	→	SYM
ejpam-2696	227	12	γa	γa	PROPN
ejpam-2696	227	13	is	be	AUX
ejpam-2696	227	14	obviously	obviously	ADV
ejpam-2696	227	15	a	a	DET
ejpam-2696	227	16	γ	γ	NOUN
ejpam-2696	227	17	-	-	PUNCT
ejpam-2696	227	18	epimorphism	epimorphism	NOUN
ejpam-2696	227	19	.	.	PUNCT
ejpam-2696	228	1	using	use	VERB
ejpam-2696	228	2	corollary	corollary	ADJ
ejpam-2696	228	3	1	1	NUM
ejpam-2696	228	4	,	,	PUNCT
ejpam-2696	228	5	we	we	PRON
ejpam-2696	228	6	get	get	VERB
ejpam-2696	228	7	γa	γa	NOUN
ejpam-2696	228	8	∼=	∼=	PROPN
ejpam-2696	228	9	γs	γ	VERB
ejpam-2696	228	10	kerλa	kerλa	NOUN
ejpam-2696	228	11	,	,	PUNCT
ejpam-2696	228	12	γ	γ	X
ejpam-2696	228	13	.	.	PUNCT
ejpam-2696	229	1	then	then	ADV
ejpam-2696	229	2	setting	set	VERB
ejpam-2696	229	3	ρ	ρ	NOUN
ejpam-2696	229	4	=	=	SYM
ejpam-2696	229	5	kerλa	kerλa	NOUN
ejpam-2696	229	6	,	,	PUNCT
ejpam-2696	229	7	γ	γ	X
ejpam-2696	229	8	we	we	PRON
ejpam-2696	229	9	get	get	VERB
ejpam-2696	229	10	the	the	DET
ejpam-2696	229	11	result	result	NOUN
ejpam-2696	229	12	.	.	PUNCT
ejpam-2696	230	1	conversely	conversely	ADV
ejpam-2696	230	2	,	,	PUNCT
ejpam-2696	230	3	if	if	SCONJ
ejpam-2696	230	4	ρ	ρ	PROPN
ejpam-2696	230	5	is	be	AUX
ejpam-2696	230	6	a	a	DET
ejpam-2696	230	7	γ	γ	NOUN
ejpam-2696	230	8	-	-	NOUN
ejpam-2696	230	9	congruence	congruence	NOUN
ejpam-2696	230	10	on	on	ADP
ejpam-2696	230	11	a	a	DET
ejpam-2696	230	12	γmonoid	γmonoid	NOUN
ejpam-2696	230	13	γs	γs	NOUN
ejpam-2696	230	14	with	with	ADP
ejpam-2696	230	15	identity	identity	NOUN
ejpam-2696	230	16	1	1	NUM
ejpam-2696	230	17	,	,	PUNCT
ejpam-2696	230	18	then	then	ADV
ejpam-2696	230	19	for	for	ADP
ejpam-2696	230	20	every	every	DET
ejpam-2696	230	21	[	[	X
ejpam-2696	230	22	s]ρ	s]ρ	NOUN
ejpam-2696	230	23	∈	∈	NOUN
ejpam-2696	230	24	γs	γ	VERB
ejpam-2696	230	25	ρ	ρ	PROPN
ejpam-2696	230	26	and	and	CCONJ
ejpam-2696	230	27	γ	γ	PROPN
ejpam-2696	230	28	∈	∈	PROPN
ejpam-2696	230	29	γ	γ	X
ejpam-2696	230	30	,	,	PUNCT
ejpam-2696	230	31	[	[	X
ejpam-2696	230	32	s]ρ	s]ρ	NOUN
ejpam-2696	231	1	=	=	PUNCT
ejpam-2696	232	1	[	[	X
ejpam-2696	232	2	sγ1]ρ	sγ1]ρ	NOUN
ejpam-2696	232	3	=	=	PUNCT
ejpam-2696	232	4	sγ[1]ρ	sγ[1]ρ	NOUN
ejpam-2696	232	5	which	which	PRON
ejpam-2696	232	6	shows	show	VERB
ejpam-2696	232	7	that	that	PRON
ejpam-2696	232	8	γs	γs	ADP
ejpam-2696	232	9	ρ	ρ	NOUN
ejpam-2696	232	10	=	=	SYM
ejpam-2696	232	11	〈	〈	PROPN
ejpam-2696	232	12	[	[	X
ejpam-2696	232	13	1]ρ	1]ρ	PROPN
ejpam-2696	232	14	〉	〉	NUM
ejpam-2696	232	15	.	.	PUNCT
ejpam-2696	233	1	a	a	DET
ejpam-2696	233	2	γ	γ	NOUN
ejpam-2696	233	3	-	-	PUNCT
ejpam-2696	233	4	act	act	NOUN
ejpam-2696	233	5	is	be	AUX
ejpam-2696	233	6	called	call	VERB
ejpam-2696	233	7	simple	simple	ADJ
ejpam-2696	233	8	if	if	SCONJ
ejpam-2696	233	9	it	it	PRON
ejpam-2696	233	10	contains	contain	VERB
ejpam-2696	233	11	no	no	DET
ejpam-2696	233	12	proper	proper	ADJ
ejpam-2696	233	13	γ	γ	NOUN
ejpam-2696	233	14	-	-	PUNCT
ejpam-2696	233	15	subacts	subact	NOUN
ejpam-2696	233	16	.	.	PUNCT
ejpam-2696	234	1	it	it	PRON
ejpam-2696	234	2	is	be	AUX
ejpam-2696	234	3	clear	clear	ADJ
ejpam-2696	234	4	that	that	SCONJ
ejpam-2696	234	5	a	a	DET
ejpam-2696	234	6	simple	simple	ADJ
ejpam-2696	234	7	act	act	NOUN
ejpam-2696	234	8	must	must	AUX
ejpam-2696	234	9	be	be	AUX
ejpam-2696	234	10	cyclic	cyclic	ADJ
ejpam-2696	234	11	.	.	PUNCT
ejpam-2696	235	1	now	now	ADV
ejpam-2696	235	2	we	we	PRON
ejpam-2696	235	3	give	give	VERB
ejpam-2696	235	4	conditions	condition	NOUN
ejpam-2696	235	5	under	under	ADP
ejpam-2696	235	6	which	which	PRON
ejpam-2696	235	7	cyclic	cyclic	ADJ
ejpam-2696	235	8	γ	γ	NOUN
ejpam-2696	235	9	-	-	PUNCT
ejpam-2696	235	10	acts	act	NOUN
ejpam-2696	235	11	,	,	PUNCT
ejpam-2696	235	12	principal	principal	NOUN
ejpam-2696	235	13	left	leave	VERB
ejpam-2696	235	14	γ	γ	NOUN
ejpam-2696	235	15	-	-	PUNCT
ejpam-2696	235	16	ideals	ideal	NOUN
ejpam-2696	235	17	and	and	CCONJ
ejpam-2696	235	18	rees	ree	NOUN
ejpam-2696	235	19	factor	factor	NOUN
ejpam-2696	235	20	γ	γ	NOUN
ejpam-2696	235	21	-	-	PUNCT
ejpam-2696	235	22	acts	act	NOUN
ejpam-2696	235	23	of	of	ADP
ejpam-2696	235	24	a	a	DET
ejpam-2696	235	25	γ	γ	X
ejpam-2696	235	26	-	-	NOUN
ejpam-2696	235	27	monoid	monoid	NOUN
ejpam-2696	235	28	by	by	ADP
ejpam-2696	235	29	left	leave	VERB
ejpam-2696	235	30	γ	γ	NOUN
ejpam-2696	235	31	-	-	PUNCT
ejpam-2696	235	32	ideals	ideal	NOUN
ejpam-2696	235	33	are	be	AUX
ejpam-2696	235	34	simple	simple	ADJ
ejpam-2696	235	35	.	.	PUNCT
ejpam-2696	236	1	proposition	proposition	NOUN
ejpam-2696	236	2	3	3	NUM
ejpam-2696	236	3	.	.	PUNCT
ejpam-2696	237	1	let	let	VERB
ejpam-2696	237	2	ρ	ρ	NOUN
ejpam-2696	237	3	be	be	AUX
ejpam-2696	237	4	a	a	DET
ejpam-2696	237	5	left	left	ADJ
ejpam-2696	237	6	γ	γ	NOUN
ejpam-2696	237	7	-	-	NOUN
ejpam-2696	237	8	congruence	congruence	NOUN
ejpam-2696	237	9	on	on	ADP
ejpam-2696	237	10	a	a	DET
ejpam-2696	237	11	γ	γ	X
ejpam-2696	237	12	-	-	PUNCT
ejpam-2696	237	13	monoid	monoid	NOUN
ejpam-2696	237	14	γs	γs	NOUN
ejpam-2696	237	15	.	.	PUNCT
ejpam-2696	238	1	the	the	DET
ejpam-2696	238	2	cyclic	cyclic	ADJ
ejpam-2696	238	3	γ	γ	PROPN
ejpam-2696	238	4	-	-	PUNCT
ejpam-2696	238	5	act	act	NOUN
ejpam-2696	238	6	γs	γ	VERB
ejpam-2696	238	7	ρ	ρ	PROPN
ejpam-2696	238	8	is	be	AUX
ejpam-2696	238	9	simple	simple	ADJ
ejpam-2696	238	10	if	if	SCONJ
ejpam-2696	239	1	and	and	CCONJ
ejpam-2696	239	2	only	only	ADV
ejpam-2696	239	3	if	if	SCONJ
ejpam-2696	239	4	[	[	X
ejpam-2696	239	5	1]ρ	1]ρ	NUM
ejpam-2696	239	6	∩	∩	ADJ
ejpam-2696	239	7	sγt	sγt	VERB
ejpam-2696	239	8	6=	6=	NOUN
ejpam-2696	239	9	∅	∅	NOUN
ejpam-2696	239	10	for	for	ADP
ejpam-2696	239	11	any	any	DET
ejpam-2696	239	12	t	t	NOUN
ejpam-2696	239	13	∈	∈	PROPN
ejpam-2696	239	14	s	s	PART
ejpam-2696	239	15	and	and	CCONJ
ejpam-2696	239	16	γ	γ	PROPN
ejpam-2696	239	17	∈	∈	PROPN
ejpam-2696	239	18	γ	γ	X
ejpam-2696	239	19	.	.	PUNCT
ejpam-2696	239	20	proof	proof	NOUN
ejpam-2696	239	21	.	.	PUNCT
ejpam-2696	240	1	for	for	ADP
ejpam-2696	240	2	a	a	DET
ejpam-2696	240	3	left	left	ADJ
ejpam-2696	240	4	γ	γ	PROPN
ejpam-2696	240	5	-	-	ADJ
ejpam-2696	240	6	congruence	congruence	ADJ
ejpam-2696	240	7	ρ	ρ	PROPN
ejpam-2696	240	8	on	on	ADP
ejpam-2696	240	9	γs	γs	NOUN
ejpam-2696	240	10	,	,	PUNCT
ejpam-2696	240	11	consider	consider	VERB
ejpam-2696	240	12	the	the	DET
ejpam-2696	240	13	canonical	canonical	ADJ
ejpam-2696	240	14	γ	γ	X
ejpam-2696	240	15	-	-	PUNCT
ejpam-2696	240	16	epimorphism	epimorphism	NOUN
ejpam-2696	240	17	π	π	NOUN
ejpam-2696	240	18	:	:	PUNCT
ejpam-2696	240	19	γs	γs	PART
ejpam-2696	240	20	→	→	SYM
ejpam-2696	240	21	γs	γs	ADP
ejpam-2696	240	22	ρ	ρ	PROPN
ejpam-2696	240	23	.	.	PUNCT
ejpam-2696	241	1	let	let	VERB
ejpam-2696	241	2	γs	γs	AUX
ejpam-2696	241	3	ρ	ρ	NOUN
ejpam-2696	241	4	be	be	AUX
ejpam-2696	241	5	simple	simple	ADJ
ejpam-2696	241	6	and	and	CCONJ
ejpam-2696	241	7	t	t	NOUN
ejpam-2696	241	8	∈	∈	PROPN
ejpam-2696	241	9	s	s	PROPN
ejpam-2696	241	10	,	,	PUNCT
ejpam-2696	241	11	γ	γ	PROPN
ejpam-2696	241	12	∈	∈	PROPN
ejpam-2696	241	13	γ	γ	X
ejpam-2696	241	14	.	.	PROPN
ejpam-2696	241	15	since	since	SCONJ
ejpam-2696	241	16	π(sγt	π(sγt	PROPN
ejpam-2696	241	17	)	)	PUNCT
ejpam-2696	241	18	is	be	AUX
ejpam-2696	241	19	a	a	DET
ejpam-2696	241	20	γ	γ	NOUN
ejpam-2696	241	21	-	-	NOUN
ejpam-2696	241	22	subact	subact	NOUN
ejpam-2696	241	23	of	of	ADP
ejpam-2696	241	24	γs	γs	ADP
ejpam-2696	241	25	ρ	ρ	PROPN
ejpam-2696	241	26	and	and	CCONJ
ejpam-2696	241	27	γs	γ	VERB
ejpam-2696	241	28	ρ	ρ	PROPN
ejpam-2696	241	29	is	be	AUX
ejpam-2696	241	30	simple	simple	ADJ
ejpam-2696	241	31	,	,	PUNCT
ejpam-2696	241	32	π(sγt	π(sγt	NOUN
ejpam-2696	241	33	)	)	PUNCT
ejpam-2696	241	34	=	=	PUNCT
ejpam-2696	241	35	γs	γ	VERB
ejpam-2696	241	36	ρ	ρ	PROPN
ejpam-2696	241	37	.	.	PUNCT
ejpam-2696	242	1	hence	hence	ADV
ejpam-2696	242	2	,	,	PUNCT
ejpam-2696	242	3	there	there	PRON
ejpam-2696	242	4	exists	exist	VERB
ejpam-2696	242	5	u	u	PROPN
ejpam-2696	242	6	∈	∈	PROPN
ejpam-2696	242	7	sγt	sγt	VERB
ejpam-2696	242	8	such	such	ADJ
ejpam-2696	242	9	that	that	PRON
ejpam-2696	242	10	π(u	π(u	PROPN
ejpam-2696	242	11	)	)	PUNCT
ejpam-2696	242	12	=	=	PUNCT
ejpam-2696	243	1	[	[	X
ejpam-2696	243	2	1]ρ	1]ρ	NUM
ejpam-2696	243	3	.	.	PUNCT
ejpam-2696	244	1	thus	thus	ADV
ejpam-2696	244	2	u	u	X
ejpam-2696	244	3	∈	∈	PROPN
ejpam-2696	245	1	[	[	X
ejpam-2696	245	2	1]ρ	1]ρ	X
ejpam-2696	245	3	and	and	CCONJ
ejpam-2696	245	4	then	then	ADV
ejpam-2696	245	5	[	[	X
ejpam-2696	245	6	1]ρ	1]ρ	NUM
ejpam-2696	245	7	∩	∩	ADJ
ejpam-2696	245	8	sγt	sγt	VERB
ejpam-2696	245	9	6=	6=	ADP
ejpam-2696	245	10	∅.	∅.	VERB
ejpam-2696	245	11	conversely	conversely	ADV
ejpam-2696	245	12	,	,	PUNCT
ejpam-2696	245	13	let	let	VERB
ejpam-2696	245	14	γa	γa	PRON
ejpam-2696	245	15	be	be	AUX
ejpam-2696	245	16	a	a	DET
ejpam-2696	245	17	γ	γ	NOUN
ejpam-2696	245	18	-	-	NOUN
ejpam-2696	245	19	subact	subact	NOUN
ejpam-2696	245	20	of	of	ADP
ejpam-2696	245	21	γs	γs	ADP
ejpam-2696	245	22	ρ	ρ	PROPN
ejpam-2696	245	23	.	.	PUNCT
ejpam-2696	246	1	take	take	VERB
ejpam-2696	246	2	any	any	DET
ejpam-2696	246	3	t	t	NOUN
ejpam-2696	246	4	∈	∈	PROPN
ejpam-2696	246	5	π−1(a	π−1(a	PROPN
ejpam-2696	246	6	)	)	PUNCT
ejpam-2696	246	7	and	and	CCONJ
ejpam-2696	246	8	γ	γ	PROPN
ejpam-2696	246	9	∈	∈	PROPN
ejpam-2696	246	10	γ	γ	X
ejpam-2696	246	11	.	.	PUNCT
ejpam-2696	246	12	using	use	VERB
ejpam-2696	246	13	the	the	DET
ejpam-2696	246	14	assumption	assumption	NOUN
ejpam-2696	246	15	,	,	PUNCT
ejpam-2696	246	16	there	there	PRON
ejpam-2696	246	17	exists	exist	VERB
ejpam-2696	246	18	s	s	PROPN
ejpam-2696	246	19	∈	∈	PROPN
ejpam-2696	246	20	s	s	VERB
ejpam-2696	246	21	such	such	ADJ
ejpam-2696	246	22	that	that	DET
ejpam-2696	246	23	sγt	sγt	NOUN
ejpam-2696	246	24	∈	∈	PROPN
ejpam-2696	247	1	[	[	X
ejpam-2696	247	2	1]ρ	1]ρ	NUM
ejpam-2696	247	3	.	.	PUNCT
ejpam-2696	248	1	now	now	ADV
ejpam-2696	248	2	[	[	X
ejpam-2696	248	3	1]ρ	1]ρ	X
ejpam-2696	248	4	=	=	SYM
ejpam-2696	248	5	π(sγt	π(sγt	NOUN
ejpam-2696	248	6	)	)	PUNCT
ejpam-2696	248	7	=	=	SYM
ejpam-2696	248	8	sγπ(t	sγπ(t	PROPN
ejpam-2696	248	9	)	)	PUNCT
ejpam-2696	248	10	∈	∈	PROPN
ejpam-2696	248	11	γa	γa	NOUN
ejpam-2696	248	12	.	.	PUNCT
ejpam-2696	249	1	this	this	PRON
ejpam-2696	249	2	implies	imply	VERB
ejpam-2696	249	3	that	that	SCONJ
ejpam-2696	249	4	γa	γa	PROPN
ejpam-2696	249	5	=	=	PUNCT
ejpam-2696	249	6	γs	γ	VERB
ejpam-2696	249	7	ρ	ρ	PROPN
ejpam-2696	249	8	and	and	CCONJ
ejpam-2696	249	9	hence	hence	ADV
ejpam-2696	249	10	γs	γ	VERB
ejpam-2696	249	11	ρ	ρ	PROPN
ejpam-2696	249	12	is	be	AUX
ejpam-2696	249	13	simple	simple	ADJ
ejpam-2696	249	14	.	.	PUNCT
ejpam-2696	250	1	h.	h.	PROPN
ejpam-2696	250	2	rasouli	rasouli	PROPN
ejpam-2696	250	3	,	,	PUNCT
ejpam-2696	250	4	a.r	a.r	PROPN
ejpam-2696	250	5	.	.	PROPN
ejpam-2696	250	6	shabani	shabani	PROPN
ejpam-2696	250	7	/	/	SYM
ejpam-2696	250	8	eur	eur	PROPN
ejpam-2696	250	9	.	.	PUNCT
ejpam-2696	251	1	j.	j.	PROPN
ejpam-2696	251	2	pure	pure	PROPN
ejpam-2696	251	3	appl	appl	PROPN
ejpam-2696	251	4	.	.	PROPN
ejpam-2696	251	5	math	math	PROPN
ejpam-2696	251	6	,	,	PUNCT
ejpam-2696	251	7	10	10	NUM
ejpam-2696	251	8	(	(	PUNCT
ejpam-2696	251	9	4	4	NUM
ejpam-2696	251	10	)	)	PUNCT
ejpam-2696	251	11	(	(	PUNCT
ejpam-2696	251	12	2017	2017	NUM
ejpam-2696	251	13	)	)	PUNCT
ejpam-2696	251	14	,	,	PUNCT
ejpam-2696	251	15	739	739	NUM
ejpam-2696	251	16	-	-	SYM
ejpam-2696	251	17	748	748	NUM
ejpam-2696	251	18	746	746	NUM
ejpam-2696	251	19	the	the	DET
ejpam-2696	251	20	following	follow	VERB
ejpam-2696	251	21	two	two	NUM
ejpam-2696	251	22	statements	statement	NOUN
ejpam-2696	251	23	are	be	AUX
ejpam-2696	251	24	corollaries	corollary	NOUN
ejpam-2696	251	25	of	of	ADP
ejpam-2696	251	26	the	the	DET
ejpam-2696	251	27	previous	previous	ADJ
ejpam-2696	251	28	proposition	proposition	NOUN
ejpam-2696	251	29	.	.	PUNCT
ejpam-2696	252	1	they	they	PRON
ejpam-2696	252	2	can	can	AUX
ejpam-2696	252	3	also	also	ADV
ejpam-2696	252	4	be	be	AUX
ejpam-2696	252	5	obtained	obtain	VERB
ejpam-2696	252	6	straightforward	straightforward	ADJ
ejpam-2696	252	7	from	from	ADP
ejpam-2696	252	8	the	the	DET
ejpam-2696	252	9	definition	definition	NOUN
ejpam-2696	252	10	of	of	ADP
ejpam-2696	252	11	a	a	DET
ejpam-2696	252	12	simple	simple	ADJ
ejpam-2696	252	13	γ	γ	NOUN
ejpam-2696	252	14	-	-	PUNCT
ejpam-2696	252	15	act	act	NOUN
ejpam-2696	252	16	.	.	PUNCT
ejpam-2696	253	1	corollary	corollary	ADJ
ejpam-2696	253	2	2	2	NUM
ejpam-2696	253	3	.	.	PUNCT
ejpam-2696	254	1	a	a	DET
ejpam-2696	254	2	principal	principal	NOUN
ejpam-2696	254	3	left	leave	VERB
ejpam-2696	254	4	γ	γ	PROPN
ejpam-2696	254	5	-	-	PUNCT
ejpam-2696	254	6	ideal	ideal	ADJ
ejpam-2696	254	7	sγz	sγz	NOUN
ejpam-2696	254	8	,	,	PUNCT
ejpam-2696	254	9	z	z	PROPN
ejpam-2696	254	10	∈	∈	PROPN
ejpam-2696	254	11	s	s	PART
ejpam-2696	254	12	,	,	PUNCT
ejpam-2696	254	13	γ	γ	PROPN
ejpam-2696	254	14	∈	∈	PROPN
ejpam-2696	254	15	γ	γ	NOUN
ejpam-2696	254	16	is	be	AUX
ejpam-2696	254	17	a	a	DET
ejpam-2696	254	18	simple	simple	ADJ
ejpam-2696	254	19	γ	γ	NOUN
ejpam-2696	254	20	-	-	NOUN
ejpam-2696	254	21	act	act	NOUN
ejpam-2696	254	22	if	if	SCONJ
ejpam-2696	254	23	and	and	CCONJ
ejpam-2696	254	24	only	only	ADV
ejpam-2696	254	25	if	if	SCONJ
ejpam-2696	254	26	z	z	PROPN
ejpam-2696	254	27	∈	∈	PROPN
ejpam-2696	254	28	sβtγz	sβtγz	ADV
ejpam-2696	254	29	for	for	ADP
ejpam-2696	254	30	all	all	DET
ejpam-2696	254	31	t	t	NOUN
ejpam-2696	254	32	∈	∈	PROPN
ejpam-2696	254	33	s	s	PROPN
ejpam-2696	254	34	,	,	PUNCT
ejpam-2696	254	35	β	β	PROPN
ejpam-2696	254	36	∈	∈	PROPN
ejpam-2696	254	37	γ	γ	X
ejpam-2696	254	38	.	.	PROPN
ejpam-2696	254	39	corollary	corollary	ADJ
ejpam-2696	254	40	3	3	X
ejpam-2696	254	41	.	.	PUNCT
ejpam-2696	255	1	let	let	VERB
ejpam-2696	255	2	i	i	PRON
ejpam-2696	255	3	be	be	AUX
ejpam-2696	255	4	a	a	DET
ejpam-2696	255	5	left	left	ADJ
ejpam-2696	255	6	γ	γ	NOUN
ejpam-2696	255	7	-	-	NOUN
ejpam-2696	255	8	ideal	ideal	NOUN
ejpam-2696	255	9	of	of	ADP
ejpam-2696	255	10	s.	s.	PROPN
ejpam-2696	255	11	the	the	DET
ejpam-2696	255	12	rees	rees	PROPN
ejpam-2696	255	13	factor	factor	NOUN
ejpam-2696	255	14	γ	γ	PROPN
ejpam-2696	255	15	-	-	PUNCT
ejpam-2696	255	16	act	act	NOUN
ejpam-2696	255	17	γs	γ	VERB
ejpam-2696	255	18	i	i	PRON
ejpam-2696	255	19	is	be	AUX
ejpam-2696	255	20	simple	simple	ADJ
ejpam-2696	255	21	if	if	SCONJ
ejpam-2696	256	1	and	and	CCONJ
ejpam-2696	256	2	only	only	ADV
ejpam-2696	256	3	if	if	SCONJ
ejpam-2696	256	4	i	i	PRON
ejpam-2696	256	5	=	=	PUNCT
ejpam-2696	256	6	s.	s.	PROPN
ejpam-2696	256	7	definition	definition	NOUN
ejpam-2696	256	8	3	3	NUM
ejpam-2696	256	9	.	.	PUNCT
ejpam-2696	257	1	a	a	DET
ejpam-2696	257	2	γ	γ	PROPN
ejpam-2696	257	3	-	-	PUNCT
ejpam-2696	257	4	act	act	NOUN
ejpam-2696	257	5	γa	γa	PROPN
ejpam-2696	257	6	is	be	AUX
ejpam-2696	257	7	called	call	VERB
ejpam-2696	257	8	decomposable	decomposable	ADJ
ejpam-2696	257	9	if	if	SCONJ
ejpam-2696	257	10	there	there	PRON
ejpam-2696	257	11	exist	exist	VERB
ejpam-2696	257	12	two	two	NUM
ejpam-2696	257	13	γ	γ	NOUN
ejpam-2696	257	14	-	-	PUNCT
ejpam-2696	257	15	subacts	subact	NOUN
ejpam-2696	257	16	γb	γb	NOUN
ejpam-2696	257	17	and	and	CCONJ
ejpam-2696	257	18	γc	γc	PROPN
ejpam-2696	257	19	of	of	ADP
ejpam-2696	257	20	γa	γa	PRON
ejpam-2696	258	1	such	such	ADJ
ejpam-2696	258	2	that	that	SCONJ
ejpam-2696	258	3	γa	γa	NOUN
ejpam-2696	258	4	=	=	PUNCT
ejpam-2696	258	5	γb∪	γb∪	X
ejpam-2696	258	6	γc	γc	VERB
ejpam-2696	258	7	and	and	CCONJ
ejpam-2696	258	8	γb∩	γb∩	X
ejpam-2696	258	9	γc	γc	X
ejpam-2696	259	1	=	=	PUNCT
ejpam-2696	259	2	∅.	∅.	NOUN
ejpam-2696	259	3	in	in	ADP
ejpam-2696	259	4	this	this	DET
ejpam-2696	259	5	case	case	NOUN
ejpam-2696	259	6	,	,	PUNCT
ejpam-2696	259	7	the	the	DET
ejpam-2696	259	8	disjoint	disjoint	PROPN
ejpam-2696	259	9	union	union	PROPN
ejpam-2696	259	10	γb	γb	PROPN
ejpam-2696	259	11	∪̇	∪̇	PROPN
ejpam-2696	259	12	γc	γc	PROPN
ejpam-2696	259	13	is	be	AUX
ejpam-2696	259	14	called	call	VERB
ejpam-2696	259	15	a	a	DET
ejpam-2696	259	16	decomposition	decomposition	NOUN
ejpam-2696	259	17	of	of	ADP
ejpam-2696	259	18	γa	γa	PROPN
ejpam-2696	259	19	.	.	PUNCT
ejpam-2696	260	1	otherwise	otherwise	ADV
ejpam-2696	260	2	,	,	PUNCT
ejpam-2696	260	3	γa	γa	PROPN
ejpam-2696	260	4	is	be	AUX
ejpam-2696	260	5	called	call	VERB
ejpam-2696	260	6	indecomposable	indecomposable	ADJ
ejpam-2696	260	7	.	.	PUNCT
ejpam-2696	261	1	if	if	SCONJ
ejpam-2696	261	2	we	we	PRON
ejpam-2696	261	3	consider	consider	VERB
ejpam-2696	261	4	γ	γ	X
ejpam-2696	261	5	-	-	PUNCT
ejpam-2696	261	6	s	s	NOUN
ejpam-2696	261	7	-	-	PUNCT
ejpam-2696	261	8	acts	act	NOUN
ejpam-2696	261	9	with	with	ADP
ejpam-2696	261	10	unique	unique	ADJ
ejpam-2696	261	11	zero	zero	NUM
ejpam-2696	261	12	θ	θ	NOUN
ejpam-2696	261	13	,	,	PUNCT
ejpam-2696	261	14	then	then	ADV
ejpam-2696	261	15	we	we	PRON
ejpam-2696	261	16	have	have	VERB
ejpam-2696	261	17	to	to	PART
ejpam-2696	261	18	replace	replace	VERB
ejpam-2696	261	19	∅	∅	NOUN
ejpam-2696	261	20	by	by	ADP
ejpam-2696	261	21	{	{	PUNCT
ejpam-2696	261	22	θ	θ	NOUN
ejpam-2696	261	23	}	}	PUNCT
ejpam-2696	261	24	to	to	PART
ejpam-2696	261	25	define	define	VERB
ejpam-2696	261	26	decomposable	decomposable	ADJ
ejpam-2696	261	27	and	and	CCONJ
ejpam-2696	261	28	indecomposable	indecomposable	ADJ
ejpam-2696	261	29	γ	γ	NOUN
ejpam-2696	261	30	-	-	PUNCT
ejpam-2696	261	31	acts	act	NOUN
ejpam-2696	261	32	with	with	ADP
ejpam-2696	261	33	unique	unique	ADJ
ejpam-2696	261	34	zero	zero	NUM
ejpam-2696	261	35	.	.	PUNCT
ejpam-2696	262	1	recall	recall	VERB
ejpam-2696	262	2	that	that	SCONJ
ejpam-2696	262	3	every	every	DET
ejpam-2696	262	4	s	s	NOUN
ejpam-2696	262	5	-	-	PUNCT
ejpam-2696	262	6	act	act	NOUN
ejpam-2696	262	7	has	have	VERB
ejpam-2696	262	8	a	a	DET
ejpam-2696	262	9	unique	unique	ADJ
ejpam-2696	262	10	decomposition	decomposition	NOUN
ejpam-2696	262	11	into	into	ADP
ejpam-2696	262	12	indecomposable	indecomposable	ADJ
ejpam-2696	262	13	subacts	subact	NOUN
ejpam-2696	262	14	(	(	PUNCT
ejpam-2696	262	15	see	see	VERB
ejpam-2696	262	16	[	[	X
ejpam-2696	262	17	9	9	NUM
ejpam-2696	262	18	,	,	PUNCT
ejpam-2696	262	19	i.5.10	i.5.10	PROPN
ejpam-2696	262	20	]	]	PUNCT
ejpam-2696	262	21	)	)	PUNCT
ejpam-2696	262	22	.	.	PUNCT
ejpam-2696	263	1	in	in	ADP
ejpam-2696	263	2	the	the	DET
ejpam-2696	263	3	following	following	NOUN
ejpam-2696	263	4	,	,	PUNCT
ejpam-2696	263	5	an	an	DET
ejpam-2696	263	6	analogous	analogous	ADJ
ejpam-2696	263	7	result	result	NOUN
ejpam-2696	263	8	is	be	AUX
ejpam-2696	263	9	obtained	obtain	VERB
ejpam-2696	263	10	for	for	ADP
ejpam-2696	263	11	the	the	DET
ejpam-2696	263	12	decomposition	decomposition	NOUN
ejpam-2696	263	13	of	of	ADP
ejpam-2696	263	14	γ	γ	NOUN
ejpam-2696	263	15	-	-	NOUN
ejpam-2696	263	16	acts	act	NOUN
ejpam-2696	263	17	.	.	PUNCT
ejpam-2696	264	1	to	to	ADP
ejpam-2696	264	2	this	this	DET
ejpam-2696	264	3	end	end	NOUN
ejpam-2696	264	4	,	,	PUNCT
ejpam-2696	264	5	first	first	ADV
ejpam-2696	264	6	note	note	VERB
ejpam-2696	264	7	the	the	DET
ejpam-2696	264	8	following	following	NOUN
ejpam-2696	264	9	:	:	PUNCT
ejpam-2696	264	10	proposition	proposition	NOUN
ejpam-2696	264	11	4	4	NUM
ejpam-2696	264	12	.	.	PUNCT
ejpam-2696	265	1	every	every	DET
ejpam-2696	265	2	cyclic	cyclic	ADJ
ejpam-2696	265	3	γ	γ	NOUN
ejpam-2696	265	4	-	-	PUNCT
ejpam-2696	265	5	act	act	NOUN
ejpam-2696	265	6	is	be	AUX
ejpam-2696	265	7	indecomposable	indecomposable	ADJ
ejpam-2696	265	8	.	.	PUNCT
ejpam-2696	266	1	proof	proof	NOUN
ejpam-2696	266	2	.	.	PUNCT
ejpam-2696	267	1	suppose	suppose	VERB
ejpam-2696	267	2	γa	γa	PROPN
ejpam-2696	267	3	=	=	SYM
ejpam-2696	267	4	sγa	sγa	PROPN
ejpam-2696	267	5	,	,	PUNCT
ejpam-2696	267	6	γ	γ	PROPN
ejpam-2696	267	7	∈	∈	PROPN
ejpam-2696	267	8	γ	γ	X
ejpam-2696	267	9	,	,	PUNCT
ejpam-2696	267	10	a	a	DET
ejpam-2696	267	11	∈	∈	PROPN
ejpam-2696	267	12	a	a	PRON
ejpam-2696	267	13	,	,	PUNCT
ejpam-2696	267	14	is	be	AUX
ejpam-2696	267	15	cyclic	cyclic	ADJ
ejpam-2696	267	16	and	and	CCONJ
ejpam-2696	267	17	a	a	DET
ejpam-2696	267	18	=	=	NOUN
ejpam-2696	267	19	γb	γb	X
ejpam-2696	267	20	∪̇	∪̇	X
ejpam-2696	267	21	γc	γc	VERB
ejpam-2696	267	22	for	for	SCONJ
ejpam-2696	267	23	some	some	DET
ejpam-2696	267	24	γsubacts	γsubact	NOUN
ejpam-2696	267	25	γb	γb	VERB
ejpam-2696	267	26	and	and	CCONJ
ejpam-2696	267	27	γc	γc	PROPN
ejpam-2696	267	28	of	of	ADP
ejpam-2696	267	29	γa	γa	PROPN
ejpam-2696	267	30	.	.	PUNCT
ejpam-2696	268	1	then	then	ADV
ejpam-2696	268	2	a	a	DET
ejpam-2696	268	3	=	=	PUNCT
ejpam-2696	268	4	eγa	eγa	NOUN
ejpam-2696	268	5	∈	∈	PROPN
ejpam-2696	268	6	γb	γb	NOUN
ejpam-2696	268	7	,	,	PUNCT
ejpam-2696	268	8	say	say	VERB
ejpam-2696	268	9	,	,	PUNCT
ejpam-2696	268	10	and	and	CCONJ
ejpam-2696	268	11	then	then	ADV
ejpam-2696	268	12	γa	γa	PROPN
ejpam-2696	268	13	=	=	PUNCT
ejpam-2696	268	14	sγa	sγa	PROPN
ejpam-2696	268	15	⊆	⊆	NUM
ejpam-2696	268	16	γb	γb	NOUN
ejpam-2696	268	17	which	which	PRON
ejpam-2696	268	18	is	be	AUX
ejpam-2696	268	19	a	a	DET
ejpam-2696	268	20	contradiction	contradiction	NOUN
ejpam-2696	268	21	.	.	PUNCT
ejpam-2696	269	1	lemma	lemma	PROPN
ejpam-2696	269	2	5	5	X
ejpam-2696	269	3	.	.	PUNCT
ejpam-2696	270	1	let	let	AUX
ejpam-2696	270	2	ai	ai	VERB
ejpam-2696	270	3	⊆	⊆	NUM
ejpam-2696	270	4	γa	γa	NOUN
ejpam-2696	270	5	,	,	PUNCT
ejpam-2696	270	6	i	i	PRON
ejpam-2696	270	7	∈	∈	VERB
ejpam-2696	270	8	i	i	PRON
ejpam-2696	270	9	,	,	PUNCT
ejpam-2696	270	10	be	be	AUX
ejpam-2696	270	11	indecomposable	indecomposable	ADJ
ejpam-2696	270	12	γ	γ	NOUN
ejpam-2696	270	13	-	-	PUNCT
ejpam-2696	270	14	subacts	subact	NOUN
ejpam-2696	270	15	of	of	ADP
ejpam-2696	270	16	an	an	DET
ejpam-2696	270	17	γ	γ	NOUN
ejpam-2696	270	18	-	-	PUNCT
ejpam-2696	270	19	act	act	NOUN
ejpam-2696	270	20	γa	γa	NOUN
ejpam-2696	270	21	such	such	ADJ
ejpam-2696	270	22	that	that	SCONJ
ejpam-2696	270	23	∩i∈iai	∩i∈iai	PROPN
ejpam-2696	270	24	6=	6=	ADP
ejpam-2696	270	25	∅.	∅.	VERB
ejpam-2696	270	26	then	then	ADV
ejpam-2696	270	27	∪i∈iai	∪i∈iai	PROPN
ejpam-2696	270	28	is	be	AUX
ejpam-2696	270	29	an	an	DET
ejpam-2696	270	30	indecomposable	indecomposable	ADJ
ejpam-2696	270	31	γ	γ	NOUN
ejpam-2696	270	32	-	-	NOUN
ejpam-2696	270	33	subact	subact	NOUN
ejpam-2696	270	34	of	of	ADP
ejpam-2696	270	35	γa	γa	NOUN
ejpam-2696	270	36	.	.	PUNCT
ejpam-2696	271	1	proof	proof	NOUN
ejpam-2696	271	2	.	.	PUNCT
ejpam-2696	272	1	first	first	ADV
ejpam-2696	272	2	note	note	VERB
ejpam-2696	272	3	that	that	SCONJ
ejpam-2696	272	4	∪i∈iai	∪i∈iai	PROPN
ejpam-2696	272	5	is	be	AUX
ejpam-2696	272	6	a	a	DET
ejpam-2696	272	7	γ	γ	NOUN
ejpam-2696	272	8	-	-	NOUN
ejpam-2696	272	9	subact	subact	NOUN
ejpam-2696	272	10	of	of	ADP
ejpam-2696	272	11	γa	γa	PROPN
ejpam-2696	272	12	.	.	PUNCT
ejpam-2696	273	1	indeed	indeed	ADV
ejpam-2696	273	2	,	,	PUNCT
ejpam-2696	273	3	sγai	sγai	NOUN
ejpam-2696	273	4	⊆	⊆	NUM
ejpam-2696	273	5	ai	ai	VERB
ejpam-2696	273	6	for	for	ADP
ejpam-2696	273	7	every	every	DET
ejpam-2696	273	8	i	i	NOUN
ejpam-2696	273	9	∈	∈	PROPN
ejpam-2696	274	1	i	i	PRON
ejpam-2696	274	2	whence	whence	NOUN
ejpam-2696	274	3	sγ(∪i∈iai	sγ(∪i∈iai	PROPN
ejpam-2696	274	4	)	)	PUNCT
ejpam-2696	274	5	=	=	SYM
ejpam-2696	274	6	∪i∈i(sγai	∪i∈i(sγai	X
ejpam-2696	274	7	)	)	PUNCT
ejpam-2696	274	8	⊆	⊆	NUM
ejpam-2696	274	9	∪i∈iai	∪i∈iai	ADJ
ejpam-2696	274	10	.	.	PUNCT
ejpam-2696	275	1	suppose	suppose	VERB
ejpam-2696	275	2	there	there	PRON
ejpam-2696	275	3	exists	exist	VERB
ejpam-2696	275	4	a	a	DET
ejpam-2696	275	5	decomposition	decomposition	NOUN
ejpam-2696	275	6	∪i∈iai	∪i∈iai	NOUN
ejpam-2696	275	7	=	=	SYM
ejpam-2696	275	8	γb	γb	AUX
ejpam-2696	275	9	∪̇	∪̇	X
ejpam-2696	275	10	γc	γc	PROPN
ejpam-2696	275	11	.	.	PUNCT
ejpam-2696	275	12	take	take	VERB
ejpam-2696	275	13	x	x	PUNCT
ejpam-2696	275	14	∈	∈	PROPN
ejpam-2696	275	15	∩i∈iai	∩i∈iai	NOUN
ejpam-2696	275	16	with	with	ADP
ejpam-2696	275	17	x	x	PROPN
ejpam-2696	275	18	∈	∈	PROPN
ejpam-2696	275	19	γb	γb	NOUN
ejpam-2696	275	20	,	,	PUNCT
ejpam-2696	275	21	say	say	VERB
ejpam-2696	275	22	.	.	PUNCT
ejpam-2696	276	1	then	then	ADV
ejpam-2696	276	2	x	x	X
ejpam-2696	276	3	∈	∈	PROPN
ejpam-2696	276	4	ai	ai	VERB
ejpam-2696	276	5	∩	∩	ADJ
ejpam-2696	276	6	γb	γb	VERB
ejpam-2696	276	7	for	for	ADP
ejpam-2696	276	8	all	all	PRON
ejpam-2696	276	9	i	i	PRON
ejpam-2696	276	10	∈	∈	PROPN
ejpam-2696	276	11	i.	i.	NOUN
ejpam-2696	276	12	since	since	SCONJ
ejpam-2696	276	13	ai	ai	PROPN
ejpam-2696	276	14	=	=	PUNCT
ejpam-2696	276	15	ai	ai	PROPN
ejpam-2696	276	16	∩	∩	NOUN
ejpam-2696	276	17	(	(	PUNCT
ejpam-2696	276	18	γb	γb	PROPN
ejpam-2696	276	19	∪̇	∪̇	X
ejpam-2696	276	20	γc	γc	PROPN
ejpam-2696	276	21	)	)	PUNCT
ejpam-2696	276	22	=	=	SYM
ejpam-2696	276	23	(	(	PUNCT
ejpam-2696	276	24	ai	ai	PROPN
ejpam-2696	276	25	∩	∩	ADJ
ejpam-2696	276	26	γb	γb	NOUN
ejpam-2696	276	27	)	)	PUNCT
ejpam-2696	276	28	∪̇	∪̇	X
ejpam-2696	276	29	(	(	PUNCT
ejpam-2696	276	30	ai	ai	VERB
ejpam-2696	276	31	∩	∩	NOUN
ejpam-2696	276	32	γc	γc	NOUN
ejpam-2696	276	33	)	)	PUNCT
ejpam-2696	276	34	and	and	CCONJ
ejpam-2696	276	35	ai	ai	INTJ
ejpam-2696	276	36	is	be	AUX
ejpam-2696	276	37	indecomposable	indecomposable	ADJ
ejpam-2696	276	38	,	,	PUNCT
ejpam-2696	276	39	ai	ai	VERB
ejpam-2696	276	40	∩	∩	NOUN
ejpam-2696	276	41	γc	γc	NOUN
ejpam-2696	276	42	=	=	SYM
ejpam-2696	276	43	∅	∅	NOUN
ejpam-2696	276	44	for	for	ADP
ejpam-2696	276	45	every	every	DET
ejpam-2696	276	46	i	i	PROPN
ejpam-2696	276	47	∈	∈	PROPN
ejpam-2696	276	48	i.	i.	NOUN
ejpam-2696	276	49	thus	thus	ADV
ejpam-2696	276	50	∪i∈iai	∪i∈iai	ADJ
ejpam-2696	276	51	=	=	SYM
ejpam-2696	276	52	γb	γb	INTJ
ejpam-2696	276	53	which	which	PRON
ejpam-2696	276	54	is	be	AUX
ejpam-2696	276	55	a	a	DET
ejpam-2696	276	56	contradiction	contradiction	NOUN
ejpam-2696	276	57	.	.	PUNCT
ejpam-2696	277	1	theorem	theorem	ADJ
ejpam-2696	277	2	6	6	NUM
ejpam-2696	277	3	.	.	PUNCT
ejpam-2696	278	1	every	every	DET
ejpam-2696	278	2	γ	γ	PROPN
ejpam-2696	278	3	-	-	PUNCT
ejpam-2696	278	4	s	s	NOUN
ejpam-2696	278	5	-	-	PUNCT
ejpam-2696	278	6	act	act	NOUN
ejpam-2696	278	7	γa	γa	PROPN
ejpam-2696	278	8	has	have	VERB
ejpam-2696	278	9	a	a	DET
ejpam-2696	278	10	unique	unique	ADJ
ejpam-2696	278	11	decomposition	decomposition	NOUN
ejpam-2696	278	12	into	into	ADP
ejpam-2696	278	13	indecomposable	indecomposable	ADJ
ejpam-2696	278	14	γ	γ	NOUN
ejpam-2696	278	15	-	-	PUNCT
ejpam-2696	278	16	subacts	subact	NOUN
ejpam-2696	278	17	.	.	PUNCT
ejpam-2696	279	1	proof	proof	NOUN
ejpam-2696	279	2	.	.	PUNCT
ejpam-2696	280	1	take	take	VERB
ejpam-2696	280	2	x	x	PUNCT
ejpam-2696	280	3	∈	∈	PROPN
ejpam-2696	280	4	γa	γa	NOUN
ejpam-2696	280	5	.	.	PUNCT
ejpam-2696	281	1	then	then	ADV
ejpam-2696	281	2	sγx	sγx	PROPN
ejpam-2696	281	3	,	,	PUNCT
ejpam-2696	281	4	γ	γ	PROPN
ejpam-2696	281	5	∈	∈	PROPN
ejpam-2696	281	6	γ	γ	NOUN
ejpam-2696	281	7	,	,	PUNCT
ejpam-2696	281	8	is	be	AUX
ejpam-2696	281	9	indecomposable	indecomposable	ADJ
ejpam-2696	281	10	by	by	ADP
ejpam-2696	281	11	proposition	proposition	NOUN
ejpam-2696	281	12	4	4	NUM
ejpam-2696	281	13	.	.	PUNCT
ejpam-2696	281	14	using	use	VERB
ejpam-2696	281	15	lemma	lemma	PROPN
ejpam-2696	281	16	5	5	NUM
ejpam-2696	281	17	,	,	PUNCT
ejpam-2696	281	18	we	we	PRON
ejpam-2696	281	19	get	get	VERB
ejpam-2696	281	20	ux	ux	NOUN
ejpam-2696	281	21	=	=	SYM
ejpam-2696	281	22	⋃	⋃	NOUN
ejpam-2696	281	23	{	{	PUNCT
ejpam-2696	281	24	γu	γu	NOUN
ejpam-2696	281	25	⊆	⊆	NUM
ejpam-2696	281	26	γa	γa	NOUN
ejpam-2696	281	27	:	:	PUNCT
ejpam-2696	281	28	γu	γu	INTJ
ejpam-2696	281	29	is	be	AUX
ejpam-2696	281	30	indecomposable	indecomposable	ADJ
ejpam-2696	281	31	and	and	CCONJ
ejpam-2696	281	32	x	x	SYM
ejpam-2696	281	33	∈	∈	PROPN
ejpam-2696	281	34	γu	γu	PROPN
ejpam-2696	281	35	}	}	PUNCT
ejpam-2696	281	36	is	be	AUX
ejpam-2696	281	37	an	an	DET
ejpam-2696	281	38	indecomposable	indecomposable	ADJ
ejpam-2696	281	39	γ	γ	NOUN
ejpam-2696	281	40	-	-	NOUN
ejpam-2696	281	41	subact	subact	NOUN
ejpam-2696	281	42	of	of	ADP
ejpam-2696	281	43	γa	γa	NOUN
ejpam-2696	281	44	.	.	PUNCT
ejpam-2696	282	1	for	for	ADP
ejpam-2696	282	2	x	x	X
ejpam-2696	282	3	,	,	PUNCT
ejpam-2696	282	4	y	y	PROPN
ejpam-2696	282	5	∈	∈	PROPN
ejpam-2696	282	6	γa	γa	PROPN
ejpam-2696	282	7	,	,	PUNCT
ejpam-2696	282	8	ux	ux	PROPN
ejpam-2696	282	9	=	=	PUNCT
ejpam-2696	282	10	uy	uy	PROPN
ejpam-2696	282	11	or	or	CCONJ
ejpam-2696	282	12	ux	ux	PROPN
ejpam-2696	282	13	∩	∩	NOUN
ejpam-2696	282	14	uy	uy	NOUN
ejpam-2696	282	15	=	=	PUNCT
ejpam-2696	282	16	∅.	∅.	VERB
ejpam-2696	282	17	indeed	indeed	ADV
ejpam-2696	282	18	,	,	PUNCT
ejpam-2696	282	19	z	z	PROPN
ejpam-2696	282	20	∈	∈	PROPN
ejpam-2696	282	21	ux	ux	PROPN
ejpam-2696	282	22	∩	∩	NOUN
ejpam-2696	282	23	uy	uy	PROPN
ejpam-2696	282	24	implies	imply	VERB
ejpam-2696	282	25	ux	ux	PROPN
ejpam-2696	282	26	,	,	PUNCT
ejpam-2696	282	27	uy	uy	PROPN
ejpam-2696	282	28	⊆	⊆	NUM
ejpam-2696	282	29	uz	uz	NOUN
ejpam-2696	282	30	.	.	PUNCT
ejpam-2696	283	1	thus	thus	ADV
ejpam-2696	283	2	x	x	SYM
ejpam-2696	283	3	∈	∈	NOUN
ejpam-2696	283	4	ux	ux	PROPN
ejpam-2696	283	5	⊆	⊆	NUM
ejpam-2696	283	6	uz	uz	NOUN
ejpam-2696	283	7	,	,	PUNCT
ejpam-2696	283	8	y	y	PROPN
ejpam-2696	283	9	∈	∈	PROPN
ejpam-2696	283	10	uy	uy	PROPN
ejpam-2696	283	11	⊆	⊆	NUM
ejpam-2696	283	12	uz	uz	NOUN
ejpam-2696	283	13	,	,	PUNCT
ejpam-2696	283	14	i.e.	i.e.	X
ejpam-2696	283	15	uz	uz	PROPN
ejpam-2696	283	16	⊆	⊆	NUM
ejpam-2696	283	17	ux	ux	PROPN
ejpam-2696	283	18	∩	∩	PROPN
ejpam-2696	283	19	uy	uy	PROPN
ejpam-2696	283	20	.	.	PUNCT
ejpam-2696	284	1	therefore	therefore	ADV
ejpam-2696	284	2	,	,	PUNCT
ejpam-2696	284	3	ux	ux	PROPN
ejpam-2696	284	4	=	=	PUNCT
ejpam-2696	284	5	uy	uy	PROPN
ejpam-2696	284	6	=	=	SYM
ejpam-2696	284	7	uz	uz	PROPN
ejpam-2696	284	8	.	.	PROPN
ejpam-2696	284	9	denote	denote	VERB
ejpam-2696	284	10	by	by	ADP
ejpam-2696	284	11	a′	a′	PROPN
ejpam-2696	284	12	a	a	DET
ejpam-2696	284	13	representative	representative	ADJ
ejpam-2696	284	14	subset	subset	NOUN
ejpam-2696	284	15	of	of	ADP
ejpam-2696	284	16	elements	element	NOUN
ejpam-2696	284	17	x	x	SYM
ejpam-2696	284	18	∈	∈	PROPN
ejpam-2696	284	19	γa	γa	NOUN
ejpam-2696	284	20	with	with	ADP
ejpam-2696	284	21	respect	respect	NOUN
ejpam-2696	284	22	to	to	ADP
ejpam-2696	284	23	the	the	DET
ejpam-2696	284	24	equivalence	equivalence	NOUN
ejpam-2696	284	25	relation	relation	NOUN
ejpam-2696	284	26	∼	∼	NOUN
ejpam-2696	284	27	defined	define	VERB
ejpam-2696	284	28	by	by	ADP
ejpam-2696	284	29	x	x	X
ejpam-2696	284	30	∼	∼	NOUN
ejpam-2696	284	31	y	y	NOUN
ejpam-2696	284	32	if	if	SCONJ
ejpam-2696	285	1	and	and	CCONJ
ejpam-2696	285	2	only	only	ADV
ejpam-2696	285	3	if	if	SCONJ
ejpam-2696	285	4	ux	ux	PROPN
ejpam-2696	285	5	=	=	NOUN
ejpam-2696	285	6	uy	uy	PROPN
ejpam-2696	285	7	.	.	PUNCT
ejpam-2696	286	1	then	then	ADV
ejpam-2696	286	2	γa	γa	PROPN
ejpam-2696	286	3	=	=	SYM
ejpam-2696	286	4	⋃	⋃	PROPN
ejpam-2696	286	5	x∈a′	x∈a′	PROPN
ejpam-2696	286	6	ux	ux	PROPN
ejpam-2696	286	7	is	be	AUX
ejpam-2696	286	8	the	the	DET
ejpam-2696	286	9	unique	unique	ADJ
ejpam-2696	286	10	decomposition	decomposition	NOUN
ejpam-2696	286	11	of	of	ADP
ejpam-2696	286	12	γa	γa	PRON
ejpam-2696	286	13	into	into	ADP
ejpam-2696	286	14	indecomposable	indecomposable	ADJ
ejpam-2696	286	15	subacts	subact	NOUN
ejpam-2696	286	16	.	.	PUNCT
ejpam-2696	287	1	definition	definition	NOUN
ejpam-2696	287	2	4	4	NUM
ejpam-2696	287	3	.	.	PUNCT
ejpam-2696	288	1	a	a	DET
ejpam-2696	288	2	set	set	ADJ
ejpam-2696	288	3	u	u	NOUN
ejpam-2696	288	4	of	of	ADP
ejpam-2696	288	5	generating	generate	VERB
ejpam-2696	288	6	elements	element	NOUN
ejpam-2696	288	7	of	of	ADP
ejpam-2696	288	8	a	a	DET
ejpam-2696	288	9	γ	γ	PROPN
ejpam-2696	288	10	-	-	PUNCT
ejpam-2696	288	11	s	s	NOUN
ejpam-2696	288	12	-	-	PUNCT
ejpam-2696	288	13	act	act	NOUN
ejpam-2696	288	14	γa	γa	PROPN
ejpam-2696	288	15	is	be	AUX
ejpam-2696	288	16	said	say	VERB
ejpam-2696	288	17	to	to	PART
ejpam-2696	288	18	be	be	AUX
ejpam-2696	288	19	a	a	DET
ejpam-2696	288	20	basis	basis	NOUN
ejpam-2696	288	21	of	of	ADP
ejpam-2696	288	22	γa	γa	PRON
ejpam-2696	288	23	if	if	SCONJ
ejpam-2696	288	24	every	every	DET
ejpam-2696	288	25	element	element	NOUN
ejpam-2696	288	26	a	a	DET
ejpam-2696	288	27	∈	∈	NOUN
ejpam-2696	288	28	γa	γa	NOUN
ejpam-2696	288	29	can	can	AUX
ejpam-2696	288	30	be	be	AUX
ejpam-2696	288	31	uniquely	uniquely	ADV
ejpam-2696	288	32	presented	present	VERB
ejpam-2696	288	33	in	in	ADP
ejpam-2696	288	34	the	the	PRON
ejpam-2696	288	35	from	from	ADP
ejpam-2696	288	36	a	a	DET
ejpam-2696	288	37	=	=	NOUN
ejpam-2696	288	38	sγu	sγu	NOUN
ejpam-2696	288	39	for	for	ADP
ejpam-2696	288	40	some	some	DET
ejpam-2696	288	41	s	s	PART
ejpam-2696	288	42	∈	∈	PROPN
ejpam-2696	288	43	s	s	PROPN
ejpam-2696	288	44	,	,	PUNCT
ejpam-2696	288	45	u	u	PROPN
ejpam-2696	288	46	∈	∈	PROPN
ejpam-2696	288	47	u	u	NOUN
ejpam-2696	288	48	and	and	CCONJ
ejpam-2696	288	49	γ	γ	PROPN
ejpam-2696	288	50	∈	∈	PROPN
ejpam-2696	288	51	γ	γ	X
ejpam-2696	288	52	,	,	PUNCT
ejpam-2696	288	53	i.e.	i.e.	X
ejpam-2696	288	54	if	if	SCONJ
ejpam-2696	288	55	a	a	PRON
ejpam-2696	288	56	=	=	X
ejpam-2696	288	57	sγu	sγu	NOUN
ejpam-2696	288	58	=	=	PUNCT
ejpam-2696	288	59	s′γ′u′	s′γ′u′	NOUN
ejpam-2696	288	60	for	for	ADP
ejpam-2696	288	61	s	s	PROPN
ejpam-2696	288	62	,	,	PUNCT
ejpam-2696	288	63	s′	s′	ADJ
ejpam-2696	288	64	∈	∈	PROPN
ejpam-2696	288	65	s	s	PROPN
ejpam-2696	288	66	,	,	PUNCT
ejpam-2696	288	67	u	u	NOUN
ejpam-2696	288	68	,	,	PUNCT
ejpam-2696	288	69	u′	u′	PROPN
ejpam-2696	288	70	∈	∈	PROPN
ejpam-2696	288	71	u	u	NOUN
ejpam-2696	288	72	and	and	CCONJ
ejpam-2696	288	73	γ	γ	X
ejpam-2696	288	74	,	,	PUNCT
ejpam-2696	288	75	γ′	γ′	PROPN
ejpam-2696	288	76	∈	∈	PROPN
ejpam-2696	288	77	γ	γ	X
ejpam-2696	288	78	,	,	PUNCT
ejpam-2696	288	79	then	then	ADV
ejpam-2696	288	80	s	s	PART
ejpam-2696	288	81	=	=	SYM
ejpam-2696	288	82	s′	s′	X
ejpam-2696	288	83	,	,	PUNCT
ejpam-2696	288	84	u	u	NOUN
ejpam-2696	288	85	=	=	PUNCT
ejpam-2696	288	86	u′	u′	PROPN
ejpam-2696	288	87	and	and	CCONJ
ejpam-2696	288	88	γ	γ	X
ejpam-2696	288	89	=	=	PUNCT
ejpam-2696	288	90	γ′.	γ′.	VERB
ejpam-2696	288	91	if	if	SCONJ
ejpam-2696	288	92	a	a	DET
ejpam-2696	288	93	γ	γ	NOUN
ejpam-2696	288	94	-	-	PUNCT
ejpam-2696	288	95	act	act	NOUN
ejpam-2696	288	96	γa	γa	PROPN
ejpam-2696	288	97	has	have	VERB
ejpam-2696	288	98	a	a	DET
ejpam-2696	288	99	basis	basis	NOUN
ejpam-2696	288	100	u	u	NOUN
ejpam-2696	288	101	,	,	PUNCT
ejpam-2696	288	102	then	then	ADV
ejpam-2696	288	103	it	it	PRON
ejpam-2696	288	104	is	be	AUX
ejpam-2696	288	105	called	call	VERB
ejpam-2696	288	106	a	a	DET
ejpam-2696	288	107	free	free	ADJ
ejpam-2696	288	108	γ	γ	NOUN
ejpam-2696	288	109	-	-	NOUN
ejpam-2696	288	110	act	act	NOUN
ejpam-2696	288	111	.	.	PUNCT
ejpam-2696	289	1	references	reference	NOUN
ejpam-2696	289	2	747	747	NUM
ejpam-2696	289	3	proposition	proposition	NOUN
ejpam-2696	289	4	5	5	NUM
ejpam-2696	289	5	.	.	PUNCT
ejpam-2696	290	1	let	let	VERB
ejpam-2696	290	2	f	f	NOUN
ejpam-2696	290	3	:	:	PUNCT
ejpam-2696	290	4	γa→	γa→	PROPN
ejpam-2696	290	5	γb	γb	AUX
ejpam-2696	290	6	be	be	AUX
ejpam-2696	290	7	a	a	DET
ejpam-2696	290	8	γ	γ	NOUN
ejpam-2696	290	9	-	-	PUNCT
ejpam-2696	290	10	homomorphism	homomorphism	NOUN
ejpam-2696	290	11	.	.	PUNCT
ejpam-2696	291	1	(	(	PUNCT
ejpam-2696	291	2	i	i	NOUN
ejpam-2696	291	3	)	)	PUNCT
ejpam-2696	291	4	if	if	SCONJ
ejpam-2696	291	5	γa	γa	PRON
ejpam-2696	291	6	if	if	SCONJ
ejpam-2696	291	7	finitely	finitely	ADV
ejpam-2696	291	8	generated	generate	VERB
ejpam-2696	291	9	then	then	ADV
ejpam-2696	291	10	so	so	ADV
ejpam-2696	291	11	is	be	AUX
ejpam-2696	291	12	f(γa	f(γa	PROPN
ejpam-2696	291	13	)	)	PUNCT
ejpam-2696	291	14	.	.	PUNCT
ejpam-2696	292	1	(	(	PUNCT
ejpam-2696	292	2	ii	ii	NOUN
ejpam-2696	292	3	)	)	PUNCT
ejpam-2696	292	4	if	if	SCONJ
ejpam-2696	292	5	γa	γa	NOUN
ejpam-2696	292	6	=	=	PUNCT
ejpam-2696	292	7	〈	〈	PROPN
ejpam-2696	292	8	u	u	NOUN
ejpam-2696	292	9	〉	〉	NOUN
ejpam-2696	292	10	and	and	CCONJ
ejpam-2696	292	11	g	g	NOUN
ejpam-2696	292	12	:	:	PUNCT
ejpam-2696	292	13	γa	γa	PROPN
ejpam-2696	292	14	→	→	SYM
ejpam-2696	292	15	γb	γb	PROPN
ejpam-2696	292	16	is	be	AUX
ejpam-2696	292	17	a	a	DET
ejpam-2696	292	18	γ	γ	NOUN
ejpam-2696	292	19	-	-	PUNCT
ejpam-2696	292	20	homomorphism	homomorphism	NOUN
ejpam-2696	292	21	,	,	PUNCT
ejpam-2696	292	22	then	then	ADV
ejpam-2696	292	23	f(u	f(u	PROPN
ejpam-2696	292	24	)	)	PUNCT
ejpam-2696	293	1	=	=	SYM
ejpam-2696	293	2	g(u	g(u	PROPN
ejpam-2696	293	3	)	)	PUNCT
ejpam-2696	293	4	for	for	ADP
ejpam-2696	293	5	every	every	DET
ejpam-2696	293	6	u	u	PROPN
ejpam-2696	293	7	∈	∈	PROPN
ejpam-2696	293	8	u	u	NOUN
ejpam-2696	293	9	implies	imply	VERB
ejpam-2696	293	10	f	f	PROPN
ejpam-2696	293	11	=	=	PUNCT
ejpam-2696	293	12	g.	g.	PROPN
ejpam-2696	293	13	(	(	PUNCT
ejpam-2696	293	14	iii	iii	NOUN
ejpam-2696	293	15	)	)	PUNCT
ejpam-2696	293	16	if	if	SCONJ
ejpam-2696	293	17	f	f	PROPN
ejpam-2696	293	18	is	be	AUX
ejpam-2696	293	19	a	a	DET
ejpam-2696	293	20	γ	γ	NOUN
ejpam-2696	293	21	-	-	PUNCT
ejpam-2696	293	22	epimorphism	epimorphism	NOUN
ejpam-2696	293	23	and	and	CCONJ
ejpam-2696	293	24	γa	γa	PROPN
ejpam-2696	293	25	=	=	SYM
ejpam-2696	293	26	〈	〈	PROPN
ejpam-2696	293	27	u	u	NOUN
ejpam-2696	293	28	〉	〉	PROPN
ejpam-2696	293	29	,	,	PUNCT
ejpam-2696	293	30	then	then	ADV
ejpam-2696	293	31	γb	γb	VERB
ejpam-2696	293	32	=	=	SYM
ejpam-2696	293	33	〈	〈	PROPN
ejpam-2696	293	34	f(u	f(u	PROPN
ejpam-2696	293	35	)	)	PUNCT
ejpam-2696	293	36	〉	〉	PROPN
ejpam-2696	293	37	.	.	PUNCT
ejpam-2696	294	1	(	(	PUNCT
ejpam-2696	294	2	iv	iv	X
ejpam-2696	294	3	)	)	PUNCT
ejpam-2696	294	4	if	if	SCONJ
ejpam-2696	294	5	is	be	AUX
ejpam-2696	294	6	a	a	DET
ejpam-2696	294	7	γ	γ	NOUN
ejpam-2696	294	8	-	-	PUNCT
ejpam-2696	294	9	isomorphism	isomorphism	NOUN
ejpam-2696	294	10	and	and	CCONJ
ejpam-2696	294	11	γa	γa	NOUN
ejpam-2696	294	12	is	be	AUX
ejpam-2696	294	13	a	a	DET
ejpam-2696	294	14	free	free	ADJ
ejpam-2696	294	15	γ	γ	NOUN
ejpam-2696	294	16	-	-	NOUN
ejpam-2696	294	17	act	act	NOUN
ejpam-2696	294	18	,	,	PUNCT
ejpam-2696	294	19	then	then	ADV
ejpam-2696	294	20	so	so	ADV
ejpam-2696	294	21	is	be	AUX
ejpam-2696	294	22	γb	γb	NOUN
ejpam-2696	294	23	.	.	PUNCT
ejpam-2696	294	24	proof	proof	NOUN
ejpam-2696	294	25	.	.	PUNCT
ejpam-2696	295	1	it	it	PRON
ejpam-2696	295	2	is	be	AUX
ejpam-2696	295	3	straightforward	straightforward	ADJ
ejpam-2696	295	4	.	.	PUNCT
ejpam-2696	296	1	the	the	DET
ejpam-2696	296	2	following	follow	VERB
ejpam-2696	296	3	result	result	NOUN
ejpam-2696	296	4	shows	show	VERB
ejpam-2696	296	5	that	that	SCONJ
ejpam-2696	296	6	there	there	PRON
ejpam-2696	296	7	is	be	VERB
ejpam-2696	296	8	no	no	DET
ejpam-2696	296	9	free	free	ADJ
ejpam-2696	296	10	γ	γ	NOUN
ejpam-2696	296	11	-	-	NOUN
ejpam-2696	296	12	act	act	NOUN
ejpam-2696	296	13	whenever	whenever	SCONJ
ejpam-2696	296	14	|γ|	|γ|	PROPN
ejpam-2696	296	15	>	>	X
ejpam-2696	296	16	1	1	X
ejpam-2696	296	17	.	.	PUNCT
ejpam-2696	296	18	theorem	theorem	NOUN
ejpam-2696	296	19	7	7	NUM
ejpam-2696	296	20	.	.	PUNCT
ejpam-2696	297	1	if	if	SCONJ
ejpam-2696	297	2	γa	γa	PROPN
ejpam-2696	297	3	is	be	AUX
ejpam-2696	297	4	a	a	DET
ejpam-2696	297	5	free	free	ADJ
ejpam-2696	297	6	γ	γ	NOUN
ejpam-2696	297	7	-	-	NOUN
ejpam-2696	297	8	act	act	NOUN
ejpam-2696	297	9	,	,	PUNCT
ejpam-2696	297	10	then	then	ADV
ejpam-2696	297	11	|γ|	|γ|	ADV
ejpam-2696	297	12	=	=	SYM
ejpam-2696	297	13	1	1	X
ejpam-2696	297	14	.	.	PUNCT
ejpam-2696	297	15	proof	proof	NOUN
ejpam-2696	297	16	.	.	PUNCT
ejpam-2696	298	1	suppose	suppose	VERB
ejpam-2696	298	2	γa	γa	PRON
ejpam-2696	298	3	is	be	AUX
ejpam-2696	298	4	a	a	DET
ejpam-2696	298	5	free	free	ADJ
ejpam-2696	298	6	γ	γ	NOUN
ejpam-2696	298	7	-	-	NOUN
ejpam-2696	298	8	act	act	NOUN
ejpam-2696	298	9	with	with	ADP
ejpam-2696	298	10	a	a	DET
ejpam-2696	298	11	basis	basis	NOUN
ejpam-2696	298	12	u	u	NOUN
ejpam-2696	298	13	.	.	PUNCT
ejpam-2696	298	14	consider	consider	VERB
ejpam-2696	298	15	γ	γ	NOUN
ejpam-2696	298	16	,	,	PUNCT
ejpam-2696	298	17	γ′	γ′	PROPN
ejpam-2696	298	18	∈	∈	PROPN
ejpam-2696	298	19	γ	γ	X
ejpam-2696	298	20	,	,	PUNCT
ejpam-2696	298	21	s	s	PART
ejpam-2696	298	22	∈	∈	PROPN
ejpam-2696	298	23	s	s	PART
ejpam-2696	298	24	and	and	CCONJ
ejpam-2696	298	25	u	u	PROPN
ejpam-2696	298	26	∈	∈	PROPN
ejpam-2696	298	27	u	u	NOUN
ejpam-2696	298	28	.	.	PUNCT
ejpam-2696	299	1	using	use	VERB
ejpam-2696	299	2	lemma	lemma	PROPN
ejpam-2696	299	3	3(ii	3(ii	NUM
ejpam-2696	299	4	)	)	PUNCT
ejpam-2696	299	5	,	,	PUNCT
ejpam-2696	299	6	sγu	sγu	NOUN
ejpam-2696	299	7	∈	∈	PROPN
ejpam-2696	299	8	sγu	sγu	NOUN
ejpam-2696	299	9	=	=	NOUN
ejpam-2696	299	10	sγ′u	sγ′u	NOUN
ejpam-2696	299	11	and	and	CCONJ
ejpam-2696	299	12	then	then	ADV
ejpam-2696	299	13	sγu	sγu	VERB
ejpam-2696	299	14	=	=	PUNCT
ejpam-2696	299	15	s′γ′u′	s′γ′u′	NOUN
ejpam-2696	299	16	for	for	ADP
ejpam-2696	299	17	some	some	DET
ejpam-2696	299	18	s	s	NOUN
ejpam-2696	299	19	,	,	PUNCT
ejpam-2696	299	20	s′	s′	ADJ
ejpam-2696	299	21	∈	∈	PROPN
ejpam-2696	299	22	s	s	NOUN
ejpam-2696	299	23	and	and	CCONJ
ejpam-2696	299	24	u	u	NOUN
ejpam-2696	299	25	,	,	PUNCT
ejpam-2696	299	26	u′	u′	PROPN
ejpam-2696	299	27	∈	∈	PROPN
ejpam-2696	299	28	u	u	NOUN
ejpam-2696	299	29	.	.	PUNCT
ejpam-2696	300	1	since	since	SCONJ
ejpam-2696	300	2	u	u	NOUN
ejpam-2696	300	3	is	be	AUX
ejpam-2696	300	4	a	a	DET
ejpam-2696	300	5	basis	basis	NOUN
ejpam-2696	300	6	,	,	PUNCT
ejpam-2696	300	7	γ	γ	X
ejpam-2696	300	8	=	=	SYM
ejpam-2696	300	9	γ′.	γ′.	VERB
ejpam-2696	300	10	remark	remark	NOUN
ejpam-2696	300	11	3	3	X
ejpam-2696	300	12	.	.	PUNCT
ejpam-2696	300	13	let	let	VERB
ejpam-2696	300	14	|γ|	|γ|	PRON
ejpam-2696	300	15	=	=	NOUN
ejpam-2696	300	16	1	1	X
ejpam-2696	300	17	.	.	X
ejpam-2696	300	18	using	use	VERB
ejpam-2696	300	19	remark	remark	NOUN
ejpam-2696	300	20	1(i	1(i	NUM
ejpam-2696	300	21	)	)	PUNCT
ejpam-2696	300	22	,	,	PUNCT
ejpam-2696	300	23	the	the	DET
ejpam-2696	300	24	category	category	NOUN
ejpam-2696	300	25	γ	γ	PROPN
ejpam-2696	300	26	-	-	PUNCT
ejpam-2696	300	27	s	s	NOUN
ejpam-2696	300	28	-	-	PUNCT
ejpam-2696	300	29	act	act	NOUN
ejpam-2696	300	30	is	be	AUX
ejpam-2696	300	31	equivalent	equivalent	ADJ
ejpam-2696	300	32	to	to	ADP
ejpam-2696	300	33	the	the	DET
ejpam-2696	300	34	category	category	NOUN
ejpam-2696	300	35	of	of	ADP
ejpam-2696	300	36	all	all	DET
ejpam-2696	300	37	acts	act	NOUN
ejpam-2696	300	38	over	over	ADP
ejpam-2696	300	39	the	the	DET
ejpam-2696	300	40	induced	induced	ADJ
ejpam-2696	300	41	semigroup	semigroup	NOUN
ejpam-2696	300	42	s	s	X
ejpam-2696	300	43	(	(	PUNCT
ejpam-2696	300	44	containing	contain	VERB
ejpam-2696	300	45	a	a	DET
ejpam-2696	300	46	left	left	ADJ
ejpam-2696	300	47	identity	identity	NOUN
ejpam-2696	300	48	)	)	PUNCT
ejpam-2696	300	49	.	.	PUNCT
ejpam-2696	301	1	therefore	therefore	ADV
ejpam-2696	301	2	,	,	PUNCT
ejpam-2696	301	3	any	any	DET
ejpam-2696	301	4	categorical	categorical	ADJ
ejpam-2696	301	5	property	property	NOUN
ejpam-2696	301	6	of	of	ADP
ejpam-2696	301	7	such	such	ADJ
ejpam-2696	301	8	γ	γ	NOUN
ejpam-2696	301	9	-	-	PUNCT
ejpam-2696	301	10	acts	act	NOUN
ejpam-2696	301	11	coincides	coincide	VERB
ejpam-2696	301	12	with	with	ADP
ejpam-2696	301	13	the	the	DET
ejpam-2696	301	14	analogous	analogous	ADJ
ejpam-2696	301	15	property	property	NOUN
ejpam-2696	301	16	of	of	ADP
ejpam-2696	301	17	their	their	PRON
ejpam-2696	301	18	corresponding	correspond	VERB
ejpam-2696	301	19	acts	act	NOUN
ejpam-2696	301	20	.	.	PUNCT
ejpam-2696	302	1	for	for	ADP
ejpam-2696	302	2	a	a	DET
ejpam-2696	302	3	γ	γ	X
ejpam-2696	302	4	=	=	SYM
ejpam-2696	302	5	{	{	PUNCT
ejpam-2696	302	6	γ	γ	X
ejpam-2696	302	7	}	}	PUNCT
ejpam-2696	302	8	and	and	CCONJ
ejpam-2696	302	9	a	a	DET
ejpam-2696	302	10	γ	γ	NOUN
ejpam-2696	302	11	-	-	PUNCT
ejpam-2696	302	12	semigroup	semigroup	NOUN
ejpam-2696	302	13	s	s	NOUN
ejpam-2696	302	14	with	with	ADP
ejpam-2696	302	15	a	a	DET
ejpam-2696	302	16	left	left	ADJ
ejpam-2696	302	17	identity	identity	NOUN
ejpam-2696	302	18	,	,	PUNCT
ejpam-2696	302	19	in	in	ADP
ejpam-2696	302	20	view	view	NOUN
ejpam-2696	302	21	of	of	ADP
ejpam-2696	302	22	the	the	DET
ejpam-2696	302	23	constructing	construct	VERB
ejpam-2696	302	24	free	free	ADJ
ejpam-2696	302	25	acts	act	NOUN
ejpam-2696	302	26	over	over	ADP
ejpam-2696	302	27	monoids	monoid	NOUN
ejpam-2696	302	28	as	as	ADP
ejpam-2696	302	29	in	in	ADP
ejpam-2696	302	30	[	[	PUNCT
ejpam-2696	302	31	9	9	NUM
ejpam-2696	302	32	,	,	PUNCT
ejpam-2696	302	33	construction	construction	NOUN
ejpam-2696	302	34	i.5.14	i.5.14	NOUN
ejpam-2696	302	35	]	]	PUNCT
ejpam-2696	302	36	,	,	PUNCT
ejpam-2696	302	37	a	a	DET
ejpam-2696	302	38	free	free	ADJ
ejpam-2696	302	39	γ	γ	PROPN
ejpam-2696	302	40	-	-	PUNCT
ejpam-2696	302	41	s	s	NOUN
ejpam-2696	302	42	-	-	PUNCT
ejpam-2696	302	43	act	act	NOUN
ejpam-2696	302	44	with	with	ADP
ejpam-2696	302	45	a	a	DET
ejpam-2696	302	46	basis	basis	NOUN
ejpam-2696	302	47	x	x	SYM
ejpam-2696	302	48	6=	6=	NOUN
ejpam-2696	302	49	∅	∅	NOUN
ejpam-2696	302	50	is	be	AUX
ejpam-2696	302	51	isomorphic	isomorphic	ADJ
ejpam-2696	302	52	to	to	ADP
ejpam-2696	302	53	s	s	PRON
ejpam-2696	302	54	×	×	PROPN
ejpam-2696	302	55	γ	γ	X
ejpam-2696	302	56	×x	×x	VERB
ejpam-2696	302	57	with	with	ADP
ejpam-2696	302	58	the	the	DET
ejpam-2696	302	59	action	action	NOUN
ejpam-2696	302	60	sγ(t	sγ(t	NOUN
ejpam-2696	302	61	,	,	PUNCT
ejpam-2696	302	62	γ	γ	X
ejpam-2696	302	63	,	,	PUNCT
ejpam-2696	302	64	x	x	NOUN
ejpam-2696	302	65	)	)	PUNCT
ejpam-2696	302	66	:	:	PUNCT
ejpam-2696	303	1	=	=	SYM
ejpam-2696	303	2	(	(	PUNCT
ejpam-2696	303	3	sγt	sγt	PROPN
ejpam-2696	303	4	,	,	PUNCT
ejpam-2696	303	5	γ	γ	X
ejpam-2696	303	6	,	,	PUNCT
ejpam-2696	303	7	x	x	NOUN
ejpam-2696	303	8	)	)	PUNCT
ejpam-2696	303	9	for	for	ADP
ejpam-2696	303	10	all	all	DET
ejpam-2696	303	11	s	s	PROPN
ejpam-2696	303	12	,	,	PUNCT
ejpam-2696	303	13	t	t	PROPN
ejpam-2696	303	14	∈	∈	PROPN
ejpam-2696	303	15	s	s	PART
ejpam-2696	303	16	and	and	CCONJ
ejpam-2696	303	17	x	x	SYM
ejpam-2696	303	18	∈	∈	PROPN
ejpam-2696	303	19	x.	x.	NOUN
ejpam-2696	303	20	furthermore	furthermore	ADV
ejpam-2696	303	21	,	,	PUNCT
ejpam-2696	303	22	any	any	DET
ejpam-2696	303	23	free	free	ADJ
ejpam-2696	303	24	γ	γ	NOUN
ejpam-2696	303	25	-	-	PUNCT
ejpam-2696	303	26	act	act	NOUN
ejpam-2696	303	27	is	be	AUX
ejpam-2696	303	28	invariant	invariant	ADJ
ejpam-2696	303	29	under	under	ADP
ejpam-2696	303	30	the	the	DET
ejpam-2696	303	31	cardinality	cardinality	NOUN
ejpam-2696	303	32	of	of	ADP
ejpam-2696	303	33	its	its	PRON
ejpam-2696	303	34	bases	basis	NOUN
ejpam-2696	303	35	and	and	CCONJ
ejpam-2696	303	36	the	the	DET
ejpam-2696	303	37	universal	universal	ADJ
ejpam-2696	303	38	property	property	NOUN
ejpam-2696	303	39	of	of	ADP
ejpam-2696	303	40	freeness	freeness	PROPN
ejpam-2696	303	41	holds	hold	VERB
ejpam-2696	303	42	for	for	ADP
ejpam-2696	303	43	free	free	ADJ
ejpam-2696	303	44	γ	γ	NOUN
ejpam-2696	303	45	-	-	NOUN
ejpam-2696	303	46	acts	act	NOUN
ejpam-2696	303	47	.	.	PUNCT
ejpam-2696	304	1	hence	hence	ADV
ejpam-2696	304	2	,	,	PUNCT
ejpam-2696	304	3	every	every	DET
ejpam-2696	304	4	γ	γ	PROPN
ejpam-2696	304	5	-	-	PUNCT
ejpam-2696	304	6	act	act	NOUN
ejpam-2696	304	7	is	be	AUX
ejpam-2696	304	8	a	a	DET
ejpam-2696	304	9	factor	factor	NOUN
ejpam-2696	304	10	γ	γ	NOUN
ejpam-2696	304	11	-	-	NOUN
ejpam-2696	304	12	act	act	NOUN
ejpam-2696	304	13	of	of	ADP
ejpam-2696	304	14	a	a	DET
ejpam-2696	304	15	free	free	ADJ
ejpam-2696	304	16	γ	γ	NOUN
ejpam-2696	304	17	-	-	NOUN
ejpam-2696	304	18	act	act	NOUN
ejpam-2696	304	19	(	(	PUNCT
ejpam-2696	304	20	see	see	VERB
ejpam-2696	304	21	[	[	X
ejpam-2696	304	22	9	9	NUM
ejpam-2696	304	23	,	,	PUNCT
ejpam-2696	304	24	theorem	theorem	VERB
ejpam-2696	304	25	i.5.15	i.5.15	NOUN
ejpam-2696	304	26	,	,	PUNCT
ejpam-2696	304	27	proposition	proposition	NOUN
ejpam-2696	304	28	i.5.16	i.5.16	PRON
ejpam-2696	304	29	]	]	PUNCT
ejpam-2696	304	30	)	)	PUNCT
ejpam-2696	304	31	.	.	PUNCT
ejpam-2696	305	1	acknowledgements	acknowledgement	VERB
ejpam-2696	305	2	the	the	DET
ejpam-2696	305	3	authors	author	NOUN
ejpam-2696	305	4	thank	thank	VERB
ejpam-2696	305	5	the	the	DET
ejpam-2696	305	6	referee	referee	NOUN
ejpam-2696	305	7	for	for	ADP
ejpam-2696	305	8	carefully	carefully	ADV
ejpam-2696	305	9	reading	read	VERB
ejpam-2696	305	10	the	the	DET
ejpam-2696	305	11	paper	paper	NOUN
ejpam-2696	305	12	.	.	PUNCT
ejpam-2696	306	1	references	reference	NOUN
ejpam-2696	306	2	[	[	X
ejpam-2696	306	3	1	1	NUM
ejpam-2696	306	4	]	]	X
ejpam-2696	306	5	r	r	NOUN
ejpam-2696	306	6	ameri	ameri	PROPN
ejpam-2696	306	7	and	and	CCONJ
ejpam-2696	306	8	r	r	PROPN
ejpam-2696	306	9	sadeghi	sadeghi	PROPN
ejpam-2696	306	10	.	.	PUNCT
ejpam-2696	307	1	gamma	gamma	NOUN
ejpam-2696	307	2	modules	module	NOUN
ejpam-2696	307	3	.	.	PUNCT
ejpam-2696	308	1	ratio	ratio	PROPN
ejpam-2696	308	2	mathematica	mathematica	PROPN
ejpam-2696	308	3	,	,	PUNCT
ejpam-2696	308	4	20:127–147	20:127–147	PROPN
ejpam-2696	308	5	,	,	PUNCT
ejpam-2696	308	6	2010	2010	NUM
ejpam-2696	308	7	.	.	PUNCT
ejpam-2696	309	1	[	[	X
ejpam-2696	309	2	2	2	NUM
ejpam-2696	309	3	]	]	PUNCT
ejpam-2696	309	4	w	w	PROPN
ejpam-2696	309	5	e	e	NOUN
ejpam-2696	309	6	barnes	barne	NOUN
ejpam-2696	309	7	.	.	PUNCT
ejpam-2696	310	1	on	on	ADP
ejpam-2696	310	2	the	the	DET
ejpam-2696	310	3	γ	γ	NOUN
ejpam-2696	310	4	-	-	PUNCT
ejpam-2696	310	5	rings	ring	NOUN
ejpam-2696	310	6	of	of	ADP
ejpam-2696	310	7	nobusawa	nobusawa	PROPN
ejpam-2696	310	8	.	.	PUNCT
ejpam-2696	311	1	pacific	pacific	PROPN
ejpam-2696	311	2	j.	j.	PROPN
ejpam-2696	311	3	math	math	PROPN
ejpam-2696	311	4	.	.	PUNCT
ejpam-2696	311	5	,	,	PUNCT
ejpam-2696	312	1	18(3):411–422	18(3):411–422	NUM
ejpam-2696	312	2	,	,	PUNCT
ejpam-2696	312	3	1966	1966	NUM
ejpam-2696	312	4	.	.	PUNCT
ejpam-2696	313	1	[	[	X
ejpam-2696	313	2	3	3	NUM
ejpam-2696	313	3	]	]	X
ejpam-2696	313	4	s	s	VERB
ejpam-2696	313	5	chattopadhyay	chattopadhyay	NOUN
ejpam-2696	313	6	.	.	PUNCT
ejpam-2696	314	1	right	right	ADJ
ejpam-2696	314	2	orthodox	orthodox	PROPN
ejpam-2696	314	3	γ	γ	PROPN
ejpam-2696	314	4	-	-	PUNCT
ejpam-2696	314	5	semigroup	semigroup	NOUN
ejpam-2696	314	6	.	.	PUNCT
ejpam-2696	315	1	southeast	southeast	ADJ
ejpam-2696	315	2	asian	asian	ADJ
ejpam-2696	315	3	bull	bull	PROPN
ejpam-2696	315	4	.	.	PUNCT
ejpam-2696	316	1	math	math	NOUN
ejpam-2696	316	2	.	.	PUNCT
ejpam-2696	317	1	,	,	PUNCT
ejpam-2696	317	2	29:23	29:23	NUM
ejpam-2696	317	3	–	–	PUNCT
ejpam-2696	317	4	30	30	NUM
ejpam-2696	317	5	,	,	PUNCT
ejpam-2696	317	6	2005	2005	NUM
ejpam-2696	317	7	.	.	PUNCT
ejpam-2696	318	1	[	[	X
ejpam-2696	318	2	4	4	NUM
ejpam-2696	318	3	]	]	SYM
ejpam-2696	318	4	r	r	NOUN
ejpam-2696	318	5	chinram	chinram	NOUN
ejpam-2696	318	6	and	and	CCONJ
ejpam-2696	318	7	p	p	PRON
ejpam-2696	318	8	siammai	siammai	VERB
ejpam-2696	318	9	.	.	PUNCT
ejpam-2696	319	1	on	on	ADP
ejpam-2696	319	2	green	green	PROPN
ejpam-2696	319	3	’s	’s	PART
ejpam-2696	319	4	relations	relation	NOUN
ejpam-2696	319	5	for	for	ADP
ejpam-2696	319	6	γ	γ	NOUN
ejpam-2696	319	7	-	-	PUNCT
ejpam-2696	319	8	semigroups	semigroup	NOUN
ejpam-2696	319	9	and	and	CCONJ
ejpam-2696	319	10	redutive	redutive	ADJ
ejpam-2696	319	11	γ	γ	NOUN
ejpam-2696	319	12	-	-	PUNCT
ejpam-2696	319	13	semigroups	semigroup	NOUN
ejpam-2696	319	14	.	.	PUNCT
ejpam-2696	320	1	int	int	NOUN
ejpam-2696	320	2	.	.	PUNCT
ejpam-2696	321	1	j.	j.	PROPN
ejpam-2696	321	2	algebra	algebra	PROPN
ejpam-2696	321	3	,	,	PUNCT
ejpam-2696	321	4	2:187–195	2:187–195	NUM
ejpam-2696	321	5	,	,	PUNCT
ejpam-2696	321	6	2008	2008	NUM
ejpam-2696	321	7	.	.	PUNCT
ejpam-2696	322	1	[	[	X
ejpam-2696	322	2	5	5	NUM
ejpam-2696	322	3	]	]	SYM
ejpam-2696	322	4	r	r	NOUN
ejpam-2696	322	5	chinram	chinram	NOUN
ejpam-2696	322	6	and	and	CCONJ
ejpam-2696	322	7	k	k	PROPN
ejpam-2696	322	8	tinpun	tinpun	VERB
ejpam-2696	322	9	.	.	PUNCT
ejpam-2696	323	1	isomorphism	isomorphism	NOUN
ejpam-2696	323	2	theorems	theorem	NOUN
ejpam-2696	323	3	for	for	ADP
ejpam-2696	323	4	γ	γ	NOUN
ejpam-2696	323	5	-	-	PUNCT
ejpam-2696	323	6	semigroup	semigroup	NOUN
ejpam-2696	323	7	and	and	CCONJ
ejpam-2696	323	8	ordered	order	VERB
ejpam-2696	323	9	γsemigroup	γsemigroup	NOUN
ejpam-2696	323	10	.	.	PUNCT
ejpam-2696	324	1	thai	thai	PROPN
ejpam-2696	324	2	j.	j.	PROPN
ejpam-2696	324	3	math	math	PROPN
ejpam-2696	324	4	.	.	PUNCT
ejpam-2696	324	5	,	,	PUNCT
ejpam-2696	325	1	7(2):231–241	7(2):231–241	X
ejpam-2696	325	2	,	,	PUNCT
ejpam-2696	325	3	2009	2009	NUM
ejpam-2696	325	4	.	.	PUNCT
ejpam-2696	326	1	[	[	X
ejpam-2696	326	2	6	6	NUM
ejpam-2696	326	3	]	]	PUNCT
ejpam-2696	326	4	h	h	NOUN
ejpam-2696	326	5	j	j	PROPN
ejpam-2696	326	6	hoehnke	hoehnke	PROPN
ejpam-2696	326	7	.	.	PUNCT
ejpam-2696	327	1	structure	structure	NOUN
ejpam-2696	327	2	theorie	theorie	PROPN
ejpam-2696	327	3	der	der	PROPN
ejpam-2696	327	4	halgrouppen	halgrouppen	PROPN
ejpam-2696	327	5	.	.	PUNCT
ejpam-2696	328	1	math	math	NOUN
ejpam-2696	328	2	.	.	PUNCT
ejpam-2696	329	1	nachr	nachr	PROPN
ejpam-2696	329	2	.	.	PROPN
ejpam-2696	329	3	,	,	PUNCT
ejpam-2696	329	4	26:1–13	26:1–13	NUM
ejpam-2696	329	5	,	,	PUNCT
ejpam-2696	329	6	1963	1963	NUM
ejpam-2696	329	7	.	.	PUNCT
ejpam-2696	330	1	references	reference	NOUN
ejpam-2696	330	2	748	748	NUM
ejpam-2696	331	1	[	[	X
ejpam-2696	331	2	7	7	NUM
ejpam-2696	331	3	]	]	SYM
ejpam-2696	331	4	h	h	NOUN
ejpam-2696	331	5	j	j	PROPN
ejpam-2696	331	6	hoehnke	hoehnke	PROPN
ejpam-2696	331	7	.	.	PUNCT
ejpam-2696	332	1	structure	structure	NOUN
ejpam-2696	332	2	of	of	ADP
ejpam-2696	332	3	semigroups	semigroup	NOUN
ejpam-2696	332	4	.	.	PUNCT
ejpam-2696	333	1	canada	canada	PROPN
ejpam-2696	333	2	.	.	PUNCT
ejpam-2696	334	1	j.	j.	PROPN
ejpam-2696	334	2	math	math	PROPN
ejpam-2696	334	3	.	.	PUNCT
ejpam-2696	334	4	,	,	PUNCT
ejpam-2696	334	5	18:449–491	18:449–491	NUM
ejpam-2696	334	6	,	,	PUNCT
ejpam-2696	334	7	1966	1966	NUM
ejpam-2696	334	8	.	.	PUNCT
ejpam-2696	335	1	[	[	X
ejpam-2696	335	2	8	8	NUM
ejpam-2696	335	3	]	]	X
ejpam-2696	335	4	j	j	PROPN
ejpam-2696	335	5	m	m	PROPN
ejpam-2696	335	6	howie	howie	PROPN
ejpam-2696	335	7	.	.	PUNCT
ejpam-2696	335	8	automata	automata	NOUN
ejpam-2696	335	9	and	and	CCONJ
ejpam-2696	335	10	languages	language	NOUN
ejpam-2696	335	11	.	.	PUNCT
ejpam-2696	336	1	oxford	oxford	PROPN
ejpam-2696	336	2	university	university	PROPN
ejpam-2696	336	3	press	press	NOUN
ejpam-2696	336	4	,	,	PUNCT
ejpam-2696	336	5	oxford	oxford	NOUN
ejpam-2696	336	6	,	,	PUNCT
ejpam-2696	336	7	1991	1991	NUM
ejpam-2696	336	8	.	.	PUNCT
ejpam-2696	337	1	[	[	X
ejpam-2696	337	2	9	9	NUM
ejpam-2696	337	3	]	]	SYM
ejpam-2696	337	4	u	u	NOUN
ejpam-2696	337	5	knauer	knauer	PROPN
ejpam-2696	337	6	m	m	PROPN
ejpam-2696	337	7	kilp	kilp	PROPN
ejpam-2696	337	8	and	and	CCONJ
ejpam-2696	337	9	a	a	DET
ejpam-2696	337	10	v	v	NOUN
ejpam-2696	337	11	mikhalev	mikhalev	NOUN
ejpam-2696	337	12	.	.	PUNCT
ejpam-2696	338	1	monoids	monoids	PROPN
ejpam-2696	338	2	,	,	PUNCT
ejpam-2696	338	3	acts	act	NOUN
ejpam-2696	338	4	and	and	CCONJ
ejpam-2696	338	5	categories	category	NOUN
ejpam-2696	338	6	.	.	PUNCT
ejpam-2696	339	1	de	de	PROPN
ejpam-2696	339	2	gruyer	gruyer	PROPN
ejpam-2696	339	3	,	,	PUNCT
ejpam-2696	339	4	berlin	berlin	PROPN
ejpam-2696	339	5	,	,	PUNCT
ejpam-2696	339	6	2000	2000	NUM
ejpam-2696	339	7	.	.	PUNCT
ejpam-2696	340	1	[	[	X
ejpam-2696	340	2	10	10	NUM
ejpam-2696	340	3	]	]	X
ejpam-2696	340	4	n	n	DET
ejpam-2696	340	5	nobusawa	nobusawa	NOUN
ejpam-2696	340	6	.	.	PUNCT
ejpam-2696	341	1	on	on	ADP
ejpam-2696	341	2	a	a	DET
ejpam-2696	341	3	generalization	generalization	NOUN
ejpam-2696	341	4	of	of	ADP
ejpam-2696	341	5	the	the	DET
ejpam-2696	341	6	ring	ring	NOUN
ejpam-2696	341	7	theory	theory	NOUN
ejpam-2696	341	8	.	.	PUNCT
ejpam-2696	342	1	osaka	osaka	PROPN
ejpam-2696	342	2	j.	j.	PROPN
ejpam-2696	342	3	math	math	PROPN
ejpam-2696	342	4	.	.	PUNCT
ejpam-2696	342	5	,	,	PUNCT
ejpam-2696	342	6	1:81–89	1:81–89	NUM
ejpam-2696	342	7	,	,	PUNCT
ejpam-2696	342	8	1964	1964	NUM
ejpam-2696	342	9	.	.	PUNCT
ejpam-2696	343	1	[	[	X
ejpam-2696	343	2	11	11	NUM
ejpam-2696	343	3	]	]	PUNCT
ejpam-2696	343	4	n	n	PROPN
ejpam-2696	343	5	k	k	PROPN
ejpam-2696	343	6	saha	saha	PROPN
ejpam-2696	343	7	.	.	PUNCT
ejpam-2696	344	1	the	the	DET
ejpam-2696	344	2	maximum	maximum	ADJ
ejpam-2696	344	3	idempotent	idempotent	NOUN
ejpam-2696	344	4	separating	separate	VERB
ejpam-2696	344	5	congruence	congruence	NOUN
ejpam-2696	344	6	on	on	ADP
ejpam-2696	344	7	an	an	DET
ejpam-2696	344	8	inverse	inverse	NOUN
ejpam-2696	344	9	γsemigroup	γsemigroup	NOUN
ejpam-2696	344	10	.	.	PUNCT
ejpam-2696	345	1	kyungpook	kyungpook	PROPN
ejpam-2696	345	2	math	math	PROPN
ejpam-2696	345	3	.	.	PUNCT
ejpam-2696	346	1	j.	j.	PROPN
ejpam-2696	346	2	,	,	PUNCT
ejpam-2696	346	3	34(1):59–66	34(1):59–66	NUM
ejpam-2696	346	4	,	,	PUNCT
ejpam-2696	346	5	1994	1994	NUM
ejpam-2696	346	6	.	.	PUNCT
ejpam-2696	347	1	[	[	X
ejpam-2696	347	2	12	12	NUM
ejpam-2696	347	3	]	]	X
ejpam-2696	347	4	m	m	VERB
ejpam-2696	347	5	k	k	PROPN
ejpam-2696	347	6	sen	sen	PROPN
ejpam-2696	347	7	.	.	PROPN
ejpam-2696	347	8	on	on	ADP
ejpam-2696	347	9	γ	γ	NOUN
ejpam-2696	347	10	-	-	PUNCT
ejpam-2696	347	11	semigroups	semigroup	NOUN
ejpam-2696	347	12	.	.	PUNCT
ejpam-2696	348	1	in	in	ADP
ejpam-2696	348	2	algebra	algebra	NOUN
ejpam-2696	348	3	and	and	CCONJ
ejpam-2696	348	4	its	its	PRON
ejpam-2696	348	5	applications	application	NOUN
ejpam-2696	348	6	(	(	PUNCT
ejpam-2696	348	7	new	new	ADJ
ejpam-2696	348	8	delhi	delhi	PROPN
ejpam-2696	348	9	,	,	PUNCT
ejpam-2696	348	10	1981	1981	NUM
ejpam-2696	348	11	)	)	PUNCT
ejpam-2696	348	12	,	,	PUNCT
ejpam-2696	348	13	301	301	NUM
ejpam-2696	348	14	-	-	SYM
ejpam-2696	348	15	308	308	NUM
ejpam-2696	348	16	.	.	PUNCT
ejpam-2696	348	17	,	,	PUNCT
ejpam-2696	348	18	lecture	lecture	NOUN
ejpam-2696	348	19	notes	note	NOUN
ejpam-2696	348	20	in	in	ADP
ejpam-2696	348	21	pure	pure	ADJ
ejpam-2696	348	22	and	and	CCONJ
ejpam-2696	348	23	appl	appl	NOUN
ejpam-2696	348	24	.	.	PROPN
ejpam-2696	348	25	math	math	PROPN
ejpam-2696	348	26	.	.	PUNCT
ejpam-2696	348	27	,	,	PUNCT
ejpam-2696	348	28	volume	volume	NOUN
ejpam-2696	348	29	91	91	NUM
ejpam-2696	348	30	.	.	PUNCT
ejpam-2696	349	1	dekker	dekker	PROPN
ejpam-2696	349	2	,	,	PUNCT
ejpam-2696	349	3	new	new	PROPN
ejpam-2696	349	4	york	york	PROPN
ejpam-2696	349	5	,	,	PUNCT
ejpam-2696	349	6	1984	1984	NUM
ejpam-2696	349	7	.	.	PUNCT
ejpam-2696	350	1	[	[	X
ejpam-2696	350	2	13	13	NUM
ejpam-2696	350	3	]	]	SYM
ejpam-2696	350	4	m	m	VERB
ejpam-2696	350	5	k	k	PROPN
ejpam-2696	350	6	sen	sen	PROPN
ejpam-2696	350	7	and	and	CCONJ
ejpam-2696	350	8	n	n	PROPN
ejpam-2696	350	9	k	k	PROPN
ejpam-2696	350	10	saha	saha	PROPN
ejpam-2696	350	11	.	.	PUNCT
ejpam-2696	351	1	on	on	ADP
ejpam-2696	351	2	γ	γ	PROPN
ejpam-2696	351	3	-	-	PUNCT
ejpam-2696	351	4	semigroup	semigroup	PROPN
ejpam-2696	351	5	i.	i.	PROPN
ejpam-2696	351	6	bull	bull	PROPN
ejpam-2696	351	7	.	.	PUNCT
ejpam-2696	352	1	calcutta	calcutta	PROPN
ejpam-2696	352	2	math	math	PROPN
ejpam-2696	352	3	.	.	PUNCT
ejpam-2696	353	1	soc	soc	PROPN
ejpam-2696	353	2	.	.	PUNCT
ejpam-2696	353	3	,	,	PUNCT
ejpam-2696	354	1	78:180–186	78:180–186	NUM
ejpam-2696	354	2	,	,	PUNCT
ejpam-2696	354	3	1986	1986	NUM
ejpam-2696	354	4	.	.	PUNCT
ejpam-2696	355	1	[	[	X
ejpam-2696	355	2	14	14	NUM
ejpam-2696	355	3	]	]	X
ejpam-2696	355	4	m	m	VERB
ejpam-2696	355	5	k	k	PROPN
ejpam-2696	355	6	sen	sen	PROPN
ejpam-2696	355	7	and	and	CCONJ
ejpam-2696	355	8	a	a	DET
ejpam-2696	355	9	seth	seth	PROPN
ejpam-2696	355	10	.	.	PUNCT
ejpam-2696	356	1	radical	radical	PROPN
ejpam-2696	356	2	of	of	ADP
ejpam-2696	356	3	γ	γ	PROPN
ejpam-2696	356	4	-	-	PUNCT
ejpam-2696	356	5	semigroup	semigroup	NOUN
ejpam-2696	356	6	.	.	PUNCT
ejpam-2696	357	1	bull	bull	PROPN
ejpam-2696	357	2	.	.	PUNCT
ejpam-2696	358	1	calcutta	calcutta	PROPN
ejpam-2696	358	2	math	math	PROPN
ejpam-2696	358	3	.	.	PUNCT
ejpam-2696	359	1	soc	soc	PROPN
ejpam-2696	359	2	.	.	PUNCT
ejpam-2696	360	1	,	,	PUNCT
ejpam-2696	360	2	80(3):189	80(3):189	NUM
ejpam-2696	360	3	–	–	PUNCT
ejpam-2696	360	4	196	196	NUM
ejpam-2696	360	5	,	,	PUNCT
ejpam-2696	360	6	1988	1988	NUM
ejpam-2696	360	7	.	.	PUNCT