id	sid	tid	token	lemma	pos
ejpam-3274	1	1	european	european	PROPN
ejpam-3274	1	2	journal	journal	PROPN
ejpam-3274	1	3	of	of	ADP
ejpam-3274	1	4	pure	pure	ADJ
ejpam-3274	1	5	and	and	CCONJ
ejpam-3274	1	6	applied	apply	VERB
ejpam-3274	1	7	mathematics	mathematic	NOUN
ejpam-3274	1	8	vol	vol	NOUN
ejpam-3274	1	9	.	.	PUNCT
ejpam-3274	2	1	11	11	NUM
ejpam-3274	2	2	,	,	PUNCT
ejpam-3274	2	3	no	no	INTJ
ejpam-3274	2	4	.	.	NOUN
ejpam-3274	2	5	3	3	NUM
ejpam-3274	2	6	,	,	PUNCT
ejpam-3274	2	7	2018	2018	NUM
ejpam-3274	2	8	,	,	PUNCT
ejpam-3274	2	9	589	589	NUM
ejpam-3274	2	10	-	-	SYM
ejpam-3274	2	11	597	597	NUM
ejpam-3274	2	12	issn	issn	PROPN
ejpam-3274	2	13	1307	1307	NUM
ejpam-3274	2	14	-	-	SYM
ejpam-3274	2	15	5543	5543	NUM
ejpam-3274	2	16	–	–	PUNCT
ejpam-3274	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3274	2	18	published	publish	VERB
ejpam-3274	2	19	by	by	ADP
ejpam-3274	2	20	new	new	PROPN
ejpam-3274	2	21	york	york	PROPN
ejpam-3274	2	22	business	business	PROPN
ejpam-3274	2	23	global	global	PROPN
ejpam-3274	2	24	the	the	DET
ejpam-3274	2	25	strong	strong	ADJ
ejpam-3274	2	26	semilattice	semilattice	NOUN
ejpam-3274	2	27	of	of	ADP
ejpam-3274	2	28	π	π	NOUN
ejpam-3274	2	29	-	-	PUNCT
ejpam-3274	2	30	groups	group	NOUN
ejpam-3274	2	31	jiangang	jiangang	PROPN
ejpam-3274	2	32	zhang1,∗	zhang1,∗	PROPN
ejpam-3274	2	33	,	,	PUNCT
ejpam-3274	2	34	yuhui	yuhui	PROPN
ejpam-3274	2	35	yang2	yang2	PROPN
ejpam-3274	2	36	,	,	PUNCT
ejpam-3274	2	37	ran	run	VERB
ejpam-3274	2	38	shen3	shen3	NOUN
ejpam-3274	2	39	1	1	NUM
ejpam-3274	2	40	department	department	NOUN
ejpam-3274	2	41	of	of	ADP
ejpam-3274	2	42	mathematics	mathematics	PROPN
ejpam-3274	2	43	,	,	PUNCT
ejpam-3274	2	44	shanghai	shanghai	PROPN
ejpam-3274	2	45	normal	normal	ADJ
ejpam-3274	2	46	university	university	PROPN
ejpam-3274	2	47	,	,	PUNCT
ejpam-3274	2	48	shanghai	shanghai	PROPN
ejpam-3274	2	49	,	,	PUNCT
ejpam-3274	2	50	200234	200234	NUM
ejpam-3274	2	51	,	,	PUNCT
ejpam-3274	2	52	china	china	PROPN
ejpam-3274	2	53	2	2	NUM
ejpam-3274	2	54	department	department	NOUN
ejpam-3274	2	55	of	of	ADP
ejpam-3274	2	56	mathematics	mathematics	PROPN
ejpam-3274	2	57	,	,	PUNCT
ejpam-3274	2	58	lvliang	lvliang	PROPN
ejpam-3274	2	59	university	university	PROPN
ejpam-3274	2	60	,	,	PUNCT
ejpam-3274	2	61	shanxi	shanxi	PROPN
ejpam-3274	2	62	lvliang	lvliang	PROPN
ejpam-3274	2	63	,	,	PUNCT
ejpam-3274	2	64	033000	033000	NUM
ejpam-3274	2	65	,	,	PUNCT
ejpam-3274	2	66	china	china	PROPN
ejpam-3274	2	67	3	3	NUM
ejpam-3274	2	68	college	college	PROPN
ejpam-3274	2	69	of	of	ADP
ejpam-3274	2	70	science	science	PROPN
ejpam-3274	2	71	,	,	PUNCT
ejpam-3274	2	72	donghua	donghua	PROPN
ejpam-3274	2	73	university	university	PROPN
ejpam-3274	2	74	,	,	PUNCT
ejpam-3274	2	75	shanghai	shanghai	PROPN
ejpam-3274	2	76	,	,	PUNCT
ejpam-3274	2	77	201620	201620	NUM
ejpam-3274	2	78	,	,	PUNCT
ejpam-3274	2	79	china	china	PROPN
ejpam-3274	2	80	abstract	abstract	PROPN
ejpam-3274	2	81	.	.	PUNCT
ejpam-3274	3	1	a	a	DET
ejpam-3274	3	2	semigroup	semigroup	NOUN
ejpam-3274	3	3	is	be	AUX
ejpam-3274	3	4	called	call	VERB
ejpam-3274	3	5	a	a	DET
ejpam-3274	3	6	gv	gv	NOUN
ejpam-3274	3	7	-	-	ADJ
ejpam-3274	3	8	inverse	inverse	ADJ
ejpam-3274	3	9	semigroup	semigroup	NOUN
ejpam-3274	4	1	if	if	SCONJ
ejpam-3274	4	2	and	and	CCONJ
ejpam-3274	4	3	only	only	ADV
ejpam-3274	4	4	if	if	SCONJ
ejpam-3274	4	5	it	it	PRON
ejpam-3274	4	6	is	be	AUX
ejpam-3274	4	7	isomorphic	isomorphic	ADJ
ejpam-3274	4	8	to	to	ADP
ejpam-3274	4	9	a	a	DET
ejpam-3274	4	10	semilattice	semilattice	NOUN
ejpam-3274	4	11	of	of	ADP
ejpam-3274	4	12	π	π	NOUN
ejpam-3274	4	13	-	-	NOUN
ejpam-3274	4	14	groups	group	NOUN
ejpam-3274	4	15	.	.	PUNCT
ejpam-3274	5	1	in	in	ADP
ejpam-3274	5	2	this	this	DET
ejpam-3274	5	3	paper	paper	NOUN
ejpam-3274	5	4	,	,	PUNCT
ejpam-3274	5	5	we	we	PRON
ejpam-3274	5	6	give	give	VERB
ejpam-3274	5	7	the	the	DET
ejpam-3274	5	8	sufficient	sufficient	ADJ
ejpam-3274	5	9	and	and	CCONJ
ejpam-3274	5	10	necessary	necessary	ADJ
ejpam-3274	5	11	conditions	condition	NOUN
ejpam-3274	5	12	for	for	SCONJ
ejpam-3274	5	13	a	a	DET
ejpam-3274	5	14	gv	gv	NOUN
ejpam-3274	5	15	-	-	ADJ
ejpam-3274	5	16	inverse	inverse	ADJ
ejpam-3274	5	17	semigroup	semigroup	NOUN
ejpam-3274	5	18	to	to	PART
ejpam-3274	5	19	be	be	AUX
ejpam-3274	5	20	a	a	DET
ejpam-3274	5	21	strong	strong	ADJ
ejpam-3274	5	22	semilattice	semilattice	NOUN
ejpam-3274	5	23	of	of	ADP
ejpam-3274	5	24	π	π	NOUN
ejpam-3274	5	25	-	-	NOUN
ejpam-3274	5	26	groups	group	NOUN
ejpam-3274	5	27	.	.	PUNCT
ejpam-3274	6	1	some	some	DET
ejpam-3274	6	2	conclusions	conclusion	NOUN
ejpam-3274	6	3	about	about	ADP
ejpam-3274	6	4	clifford	clifford	PROPN
ejpam-3274	6	5	semigroups	semigroup	NOUN
ejpam-3274	6	6	are	be	AUX
ejpam-3274	6	7	generalized	generalize	VERB
ejpam-3274	6	8	.	.	PUNCT
ejpam-3274	7	1	key	key	ADJ
ejpam-3274	7	2	words	word	NOUN
ejpam-3274	7	3	and	and	CCONJ
ejpam-3274	7	4	phrases	phrase	NOUN
ejpam-3274	7	5	:	:	PUNCT
ejpam-3274	7	6	gv	gv	X
ejpam-3274	7	7	-	-	ADJ
ejpam-3274	7	8	inverse	inverse	ADJ
ejpam-3274	7	9	semigroup	semigroup	NOUN
ejpam-3274	7	10	,	,	PUNCT
ejpam-3274	7	11	π	π	PROPN
ejpam-3274	7	12	-	-	NOUN
ejpam-3274	7	13	group	group	NOUN
ejpam-3274	7	14	,	,	PUNCT
ejpam-3274	7	15	strong	strong	ADJ
ejpam-3274	7	16	semilattice	semilattice	NOUN
ejpam-3274	7	17	,	,	PUNCT
ejpam-3274	7	18	homomorphism	homomorphism	NOUN
ejpam-3274	7	19	1	1	X
ejpam-3274	7	20	.	.	X
ejpam-3274	7	21	introduction	introduction	NOUN
ejpam-3274	7	22	first	first	ADV
ejpam-3274	7	23	of	of	ADP
ejpam-3274	7	24	all	all	PRON
ejpam-3274	7	25	,	,	PUNCT
ejpam-3274	7	26	we	we	PRON
ejpam-3274	7	27	give	give	VERB
ejpam-3274	7	28	the	the	DET
ejpam-3274	7	29	basic	basic	ADJ
ejpam-3274	7	30	definition	definition	NOUN
ejpam-3274	7	31	for	for	ADP
ejpam-3274	7	32	this	this	DET
ejpam-3274	7	33	paper	paper	NOUN
ejpam-3274	7	34	.	.	PUNCT
ejpam-3274	8	1	let	let	VERB
ejpam-3274	8	2	y	y	PRON
ejpam-3274	8	3	be	be	AUX
ejpam-3274	8	4	a	a	DET
ejpam-3274	8	5	semilattice	semilattice	NOUN
ejpam-3274	8	6	.	.	PUNCT
ejpam-3274	9	1	for	for	ADP
ejpam-3274	9	2	each	each	DET
ejpam-3274	9	3	α	α	PROPN
ejpam-3274	9	4	∈	∈	PROPN
ejpam-3274	9	5	y	y	PROPN
ejpam-3274	9	6	,	,	PUNCT
ejpam-3274	9	7	let	let	VERB
ejpam-3274	9	8	sα	sα	ADV
ejpam-3274	9	9	be	be	AUX
ejpam-3274	9	10	a	a	DET
ejpam-3274	9	11	semigroup	semigroup	NOUN
ejpam-3274	9	12	and	and	CCONJ
ejpam-3274	9	13	assume	assume	VERB
ejpam-3274	9	14	that	that	SCONJ
ejpam-3274	9	15	sα	sα	ADV
ejpam-3274	9	16	∩	∩	NOUN
ejpam-3274	9	17	sβ	sβ	NOUN
ejpam-3274	9	18	=	=	VERB
ejpam-3274	9	19	∅	∅	NOUN
ejpam-3274	9	20	if	if	SCONJ
ejpam-3274	9	21	α	α	PROPN
ejpam-3274	9	22	6=	6=	ADP
ejpam-3274	9	23	β	β	X
ejpam-3274	9	24	.	.	PUNCT
ejpam-3274	10	1	for	for	ADP
ejpam-3274	10	2	each	each	DET
ejpam-3274	10	3	pair	pair	NOUN
ejpam-3274	10	4	α	α	NOUN
ejpam-3274	10	5	,	,	PUNCT
ejpam-3274	10	6	β	β	X
ejpam-3274	10	7	∈	∈	X
ejpam-3274	10	8	y	y	PROPN
ejpam-3274	10	9	such	such	ADJ
ejpam-3274	10	10	that	that	SCONJ
ejpam-3274	10	11	α	α	PROPN
ejpam-3274	10	12	≥	≥	NOUN
ejpam-3274	10	13	β	β	NOUN
ejpam-3274	10	14	,	,	PUNCT
ejpam-3274	10	15	there	there	PRON
ejpam-3274	10	16	exists	exist	VERB
ejpam-3274	10	17	a	a	DET
ejpam-3274	10	18	homomorphism	homomorphism	NOUN
ejpam-3274	10	19	φα	φα	ADP
ejpam-3274	10	20	,	,	PUNCT
ejpam-3274	10	21	β	β	X
ejpam-3274	10	22	:	:	PUNCT
ejpam-3274	10	23	sα	sα	X
ejpam-3274	10	24	→	→	SYM
ejpam-3274	10	25	sβ	sβ	NUM
ejpam-3274	10	26	such	such	ADJ
ejpam-3274	10	27	that	that	PRON
ejpam-3274	10	28	:	:	PUNCT
ejpam-3274	10	29	(	(	PUNCT
ejpam-3274	10	30	c1	c1	PROPN
ejpam-3274	10	31	)	)	PUNCT
ejpam-3274	10	32	φα	φα	PROPN
ejpam-3274	10	33	,	,	PUNCT
ejpam-3274	10	34	α	α	NOUN
ejpam-3274	10	35	=	=	SYM
ejpam-3274	10	36	1sα	1sα	NOUN
ejpam-3274	10	37	for	for	ADP
ejpam-3274	10	38	any	any	DET
ejpam-3274	10	39	α	α	NOUN
ejpam-3274	10	40	∈	∈	PROPN
ejpam-3274	10	41	y	y	PROPN
ejpam-3274	10	42	.	.	PUNCT
ejpam-3274	11	1	(	(	PUNCT
ejpam-3274	11	2	c2	c2	PROPN
ejpam-3274	11	3	)	)	PUNCT
ejpam-3274	11	4	for	for	ADP
ejpam-3274	11	5	any	any	DET
ejpam-3274	11	6	α	α	NOUN
ejpam-3274	11	7	,	,	PUNCT
ejpam-3274	11	8	β	β	X
ejpam-3274	11	9	,	,	PUNCT
ejpam-3274	11	10	γ	γ	PROPN
ejpam-3274	11	11	∈	∈	PROPN
ejpam-3274	11	12	y	y	PROPN
ejpam-3274	11	13	with	with	ADP
ejpam-3274	11	14	α	α	PROPN
ejpam-3274	11	15	≥	≥	PROPN
ejpam-3274	11	16	β	β	X
ejpam-3274	11	17	≥	≥	X
ejpam-3274	11	18	γ	γ	PROPN
ejpam-3274	11	19	,	,	PUNCT
ejpam-3274	11	20	φα	φα	ADV
ejpam-3274	11	21	,	,	PUNCT
ejpam-3274	11	22	βφβ	βφβ	NOUN
ejpam-3274	11	23	,	,	PUNCT
ejpam-3274	11	24	γ	γ	X
ejpam-3274	11	25	=	=	SYM
ejpam-3274	11	26	φα	φα	PROPN
ejpam-3274	11	27	,	,	PUNCT
ejpam-3274	11	28	γ	γ	X
ejpam-3274	11	29	.	.	PUNCT
ejpam-3274	12	1	define	define	VERB
ejpam-3274	12	2	a	a	DET
ejpam-3274	12	3	multiplication	multiplication	NOUN
ejpam-3274	12	4	on	on	ADP
ejpam-3274	12	5	s	s	NOUN
ejpam-3274	12	6	=	=	PUNCT
ejpam-3274	12	7	∪α∈y	∪α∈y	PROPN
ejpam-3274	12	8	sα	sα	ADV
ejpam-3274	12	9	,	,	PUNCT
ejpam-3274	12	10	in	in	ADP
ejpam-3274	12	11	terms	term	NOUN
ejpam-3274	12	12	of	of	ADP
ejpam-3274	12	13	the	the	DET
ejpam-3274	12	14	multiplications	multiplication	NOUN
ejpam-3274	12	15	in	in	ADP
ejpam-3274	12	16	the	the	DET
ejpam-3274	12	17	components	component	NOUN
ejpam-3274	12	18	sα	sα	ADV
ejpam-3274	12	19	and	and	CCONJ
ejpam-3274	12	20	the	the	DET
ejpam-3274	12	21	homomorphisms	homomorphism	NOUN
ejpam-3274	12	22	φα	φα	ADP
ejpam-3274	12	23	,	,	PUNCT
ejpam-3274	12	24	β	β	NOUN
ejpam-3274	12	25	,	,	PUNCT
ejpam-3274	12	26	for	for	ADP
ejpam-3274	12	27	each	each	DET
ejpam-3274	12	28	x	x	PUNCT
ejpam-3274	12	29	in	in	ADP
ejpam-3274	12	30	sα	sα	ADV
ejpam-3274	12	31	and	and	CCONJ
ejpam-3274	12	32	y	y	PROPN
ejpam-3274	12	33	in	in	ADP
ejpam-3274	12	34	sβ	sβ	PROPN
ejpam-3274	12	35	,	,	PUNCT
ejpam-3274	12	36	xy	xy	PROPN
ejpam-3274	12	37	=	=	SYM
ejpam-3274	12	38	xφα	xφα	PROPN
ejpam-3274	12	39	,	,	PUNCT
ejpam-3274	12	40	αβyφβ	αβyφβ	ADJ
ejpam-3274	12	41	,	,	PUNCT
ejpam-3274	12	42	αβ	αβ	INTJ
ejpam-3274	12	43	.	.	PUNCT
ejpam-3274	13	1	then	then	ADV
ejpam-3274	13	2	s	s	VERB
ejpam-3274	13	3	with	with	SCONJ
ejpam-3274	13	4	the	the	DET
ejpam-3274	13	5	multiplication	multiplication	NOUN
ejpam-3274	13	6	defined	define	VERB
ejpam-3274	13	7	above	above	ADP
ejpam-3274	13	8	is	be	AUX
ejpam-3274	13	9	a	a	DET
ejpam-3274	13	10	strong	strong	ADJ
ejpam-3274	13	11	semilattice	semilattice	NOUN
ejpam-3274	13	12	y	y	PROPN
ejpam-3274	13	13	of	of	ADP
ejpam-3274	13	14	semigroup	semigroup	PROPN
ejpam-3274	13	15	sα	sα	PROPN
ejpam-3274	13	16	,	,	PUNCT
ejpam-3274	13	17	to	to	PART
ejpam-3274	13	18	be	be	AUX
ejpam-3274	13	19	denoted	denote	VERB
ejpam-3274	13	20	by	by	ADP
ejpam-3274	13	21	s[y	s[y	NUM
ejpam-3274	13	22	;	;	PUNCT
ejpam-3274	13	23	sα	sα	X
ejpam-3274	13	24	,	,	PUNCT
ejpam-3274	13	25	φα	φα	ADP
ejpam-3274	13	26	,	,	PUNCT
ejpam-3274	13	27	β	β	NOUN
ejpam-3274	13	28	]	]	X
ejpam-3274	13	29	.	.	PUNCT
ejpam-3274	14	1	the	the	DET
ejpam-3274	14	2	homomorphisms	homomorphisms	PROPN
ejpam-3274	14	3	φα	φα	PROPN
ejpam-3274	14	4	,	,	PUNCT
ejpam-3274	14	5	β	β	X
ejpam-3274	14	6	are	be	AUX
ejpam-3274	14	7	called	call	VERB
ejpam-3274	14	8	the	the	DET
ejpam-3274	14	9	structure	structure	NOUN
ejpam-3274	14	10	homomorphisms	homomorphism	NOUN
ejpam-3274	14	11	of	of	ADP
ejpam-3274	14	12	s.	s.	PROPN
ejpam-3274	14	13	and	and	CCONJ
ejpam-3274	14	14	if	if	SCONJ
ejpam-3274	14	15	sα	sα	PROPN
ejpam-3274	14	16	∈	∈	PROPN
ejpam-3274	14	17	h	h	NOUN
ejpam-3274	14	18	for	for	ADP
ejpam-3274	14	19	all	all	DET
ejpam-3274	14	20	α	α	PRON
ejpam-3274	14	21	∈	∈	ADJ
ejpam-3274	14	22	y	y	PROPN
ejpam-3274	14	23	and	and	CCONJ
ejpam-3274	14	24	some	some	DET
ejpam-3274	14	25	class	class	NOUN
ejpam-3274	14	26	of	of	ADP
ejpam-3274	14	27	semigroups	semigroup	NOUN
ejpam-3274	14	28	h	h	NOUN
ejpam-3274	14	29	,	,	PUNCT
ejpam-3274	14	30	then	then	ADV
ejpam-3274	14	31	s	s	VERB
ejpam-3274	14	32	is	be	AUX
ejpam-3274	14	33	a	a	DET
ejpam-3274	14	34	strong	strong	ADJ
ejpam-3274	14	35	semilattice	semilattice	NOUN
ejpam-3274	14	36	of	of	ADP
ejpam-3274	14	37	type	type	NOUN
ejpam-3274	14	38	h.	h.	PROPN
ejpam-3274	14	39	as	as	SCONJ
ejpam-3274	14	40	is	be	AUX
ejpam-3274	14	41	well	well	ADV
ejpam-3274	14	42	known	know	VERB
ejpam-3274	14	43	,	,	PUNCT
ejpam-3274	14	44	a	a	DET
ejpam-3274	14	45	semigroup	semigroup	NOUN
ejpam-3274	14	46	is	be	AUX
ejpam-3274	14	47	a	a	DET
ejpam-3274	14	48	clifford	clifford	PROPN
ejpam-3274	14	49	semigroup	semigroup	NOUN
ejpam-3274	14	50	if	if	SCONJ
ejpam-3274	14	51	and	and	CCONJ
ejpam-3274	14	52	only	only	ADV
ejpam-3274	14	53	if	if	SCONJ
ejpam-3274	14	54	it	it	PRON
ejpam-3274	14	55	is	be	AUX
ejpam-3274	14	56	isomorphic	isomorphic	ADJ
ejpam-3274	14	57	to	to	ADP
ejpam-3274	14	58	a	a	DET
ejpam-3274	14	59	strong	strong	ADJ
ejpam-3274	14	60	semilattice	semilattice	NOUN
ejpam-3274	14	61	of	of	ADP
ejpam-3274	14	62	groups	group	NOUN
ejpam-3274	14	63	.	.	PUNCT
ejpam-3274	15	1	a	a	DET
ejpam-3274	15	2	semigroup	semigroup	NOUN
ejpam-3274	15	3	s	s	VERB
ejpam-3274	15	4	is	be	AUX
ejpam-3274	15	5	a	a	DET
ejpam-3274	15	6	π	π	NOUN
ejpam-3274	15	7	-	-	NOUN
ejpam-3274	15	8	group	group	NOUN
ejpam-3274	15	9	if	if	SCONJ
ejpam-3274	15	10	it	it	PRON
ejpam-3274	15	11	is	be	AUX
ejpam-3274	15	12	a	a	DET
ejpam-3274	15	13	nil	nil	ADJ
ejpam-3274	15	14	-	-	PUNCT
ejpam-3274	15	15	extension	extension	NOUN
ejpam-3274	15	16	of	of	ADP
ejpam-3274	15	17	a	a	DET
ejpam-3274	15	18	group	group	NOUN
ejpam-3274	15	19	,	,	PUNCT
ejpam-3274	15	20	which	which	PRON
ejpam-3274	15	21	means	mean	VERB
ejpam-3274	15	22	that	that	SCONJ
ejpam-3274	15	23	there	there	PRON
ejpam-3274	15	24	exists	exist	VERB
ejpam-3274	15	25	a	a	DET
ejpam-3274	15	26	subgroup	subgroup	NOUN
ejpam-3274	15	27	g	g	NOUN
ejpam-3274	15	28	of	of	ADP
ejpam-3274	15	29	s	s	PRON
ejpam-3274	15	30	and	and	CCONJ
ejpam-3274	15	31	g	g	PROPN
ejpam-3274	15	32	is	be	AUX
ejpam-3274	15	33	an	an	DET
ejpam-3274	15	34	ideal	ideal	NOUN
ejpam-3274	15	35	,	,	PUNCT
ejpam-3274	15	36	and	and	CCONJ
ejpam-3274	15	37	for	for	ADP
ejpam-3274	15	38	any	any	DET
ejpam-3274	15	39	a	a	DET
ejpam-3274	15	40	∈	∈	ADJ
ejpam-3274	15	41	s	s	NOUN
ejpam-3274	15	42	,	,	PUNCT
ejpam-3274	15	43	there	there	PRON
ejpam-3274	15	44	exists	exist	VERB
ejpam-3274	15	45	a	a	DET
ejpam-3274	15	46	number	number	NOUN
ejpam-3274	15	47	n	n	NOUN
ejpam-3274	15	48	∈	∈	NOUN
ejpam-3274	15	49	n	n	PRON
ejpam-3274	15	50	such	such	ADJ
ejpam-3274	15	51	that	that	SCONJ
ejpam-3274	15	52	an	an	DET
ejpam-3274	15	53	∈	∈	PROPN
ejpam-3274	15	54	g	g	NOUN
ejpam-3274	15	55	,	,	PUNCT
ejpam-3274	15	56	where	where	SCONJ
ejpam-3274	15	57	n	n	X
ejpam-3274	15	58	is	be	AUX
ejpam-3274	15	59	the	the	DET
ejpam-3274	15	60	natural	natural	ADJ
ejpam-3274	15	61	number	number	NOUN
ejpam-3274	15	62	set	set	NOUN
ejpam-3274	15	63	.	.	PUNCT
ejpam-3274	16	1	a	a	DET
ejpam-3274	16	2	semigroup	semigroup	NOUN
ejpam-3274	16	3	is	be	AUX
ejpam-3274	16	4	called	call	VERB
ejpam-3274	16	5	a	a	DET
ejpam-3274	16	6	gv	gv	NOUN
ejpam-3274	16	7	-	-	ADJ
ejpam-3274	16	8	inverse	inverse	ADJ
ejpam-3274	16	9	semigroup	semigroup	NOUN
ejpam-3274	17	1	if	if	SCONJ
ejpam-3274	17	2	and	and	CCONJ
ejpam-3274	17	3	only	only	ADV
ejpam-3274	17	4	if	if	SCONJ
ejpam-3274	17	5	it	it	PRON
ejpam-3274	17	6	is	be	AUX
ejpam-3274	17	7	isomorphic	isomorphic	ADJ
ejpam-3274	17	8	to	to	ADP
ejpam-3274	17	9	a	a	DET
ejpam-3274	17	10	semilattice	semilattice	NOUN
ejpam-3274	17	11	of	of	ADP
ejpam-3274	17	12	π	π	NOUN
ejpam-3274	17	13	-	-	NOUN
ejpam-3274	17	14	groups	group	NOUN
ejpam-3274	17	15	.	.	PUNCT
ejpam-3274	18	1	it	it	PRON
ejpam-3274	18	2	is	be	AUX
ejpam-3274	18	3	natural	natural	ADJ
ejpam-3274	18	4	to	to	PART
ejpam-3274	18	5	ask	ask	VERB
ejpam-3274	18	6	how	how	SCONJ
ejpam-3274	18	7	about	about	ADP
ejpam-3274	18	8	the	the	DET
ejpam-3274	18	9	strong	strong	ADJ
ejpam-3274	18	10	semilattice	semilattice	NOUN
ejpam-3274	18	11	of	of	ADP
ejpam-3274	18	12	π	π	NOUN
ejpam-3274	18	13	-	-	NOUN
ejpam-3274	18	14	groups	group	NOUN
ejpam-3274	18	15	.	.	PUNCT
ejpam-3274	19	1	in	in	ADP
ejpam-3274	19	2	this	this	DET
ejpam-3274	19	3	paper	paper	NOUN
ejpam-3274	19	4	,	,	PUNCT
ejpam-3274	19	5	we	we	PRON
ejpam-3274	19	6	give	give	VERB
ejpam-3274	19	7	the	the	DET
ejpam-3274	19	8	sufficient	sufficient	ADJ
ejpam-3274	19	9	and	and	CCONJ
ejpam-3274	19	10	necessary	necessary	ADJ
ejpam-3274	19	11	conditions	condition	NOUN
ejpam-3274	19	12	for	for	SCONJ
ejpam-3274	19	13	a	a	DET
ejpam-3274	19	14	gv	gv	NOUN
ejpam-3274	19	15	-	-	ADJ
ejpam-3274	19	16	inverse	inverse	ADJ
ejpam-3274	19	17	semigroup	semigroup	NOUN
ejpam-3274	19	18	to	to	PART
ejpam-3274	19	19	be	be	AUX
ejpam-3274	19	20	a	a	DET
ejpam-3274	19	21	strong	strong	ADJ
ejpam-3274	19	22	semilattice	semilattice	NOUN
ejpam-3274	19	23	of	of	ADP
ejpam-3274	19	24	π	π	NOUN
ejpam-3274	19	25	-	-	NOUN
ejpam-3274	19	26	groups	group	NOUN
ejpam-3274	19	27	.	.	PUNCT
ejpam-3274	20	1	∗corresponding	∗corresponde	VERB
ejpam-3274	20	2	author	author	NOUN
ejpam-3274	20	3	.	.	PUNCT
ejpam-3274	21	1	doi	doi	NOUN
ejpam-3274	21	2	:	:	PUNCT
ejpam-3274	21	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3274	https://doi.org/10.29020/nybg.ejpam.v11i3.3274	NOUN
ejpam-3274	21	4	email	email	NOUN
ejpam-3274	21	5	addresses	address	NOUN
ejpam-3274	21	6	:	:	PUNCT
ejpam-3274	21	7	jgzhang@shnu.edu.cn	jgzhang@shnu.edu.cn	PROPN
ejpam-3274	21	8	(	(	PUNCT
ejpam-3274	21	9	j.	j.	PROPN
ejpam-3274	21	10	zhang	zhang	PROPN
ejpam-3274	21	11	)	)	PUNCT
ejpam-3274	21	12	,	,	PUNCT
ejpam-3274	21	13	ranshen@dhu.edu.cn	ranshen@dhu.edu.cn	PROPN
ejpam-3274	21	14	(	(	PUNCT
ejpam-3274	21	15	r.	r.	PROPN
ejpam-3274	21	16	shen	shen	PROPN
ejpam-3274	21	17	)	)	PUNCT
ejpam-3274	21	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3274	22	1	589	589	NUM
ejpam-3274	22	2	c	c	NOUN
ejpam-3274	22	3	©	©	PROPN
ejpam-3274	22	4	2018	2018	NUM
ejpam-3274	22	5	ejpam	ejpam	VERB
ejpam-3274	22	6	all	all	DET
ejpam-3274	22	7	rights	right	NOUN
ejpam-3274	22	8	reserved	reserve	VERB
ejpam-3274	22	9	.	.	PUNCT
ejpam-3274	23	1	j.	j.	PROPN
ejpam-3274	23	2	zhang	zhang	PROPN
ejpam-3274	23	3	,	,	PUNCT
ejpam-3274	23	4	y.	y.	PROPN
ejpam-3274	23	5	yang	yang	PROPN
ejpam-3274	23	6	,	,	PUNCT
ejpam-3274	23	7	r.	r.	PROPN
ejpam-3274	23	8	shen	shen	PROPN
ejpam-3274	23	9	/	/	SYM
ejpam-3274	23	10	eur	eur	PROPN
ejpam-3274	23	11	.	.	PUNCT
ejpam-3274	24	1	j.	j.	PROPN
ejpam-3274	24	2	pure	pure	PROPN
ejpam-3274	24	3	appl	appl	PROPN
ejpam-3274	24	4	.	.	PROPN
ejpam-3274	24	5	math	math	PROPN
ejpam-3274	24	6	,	,	PUNCT
ejpam-3274	24	7	11	11	NUM
ejpam-3274	24	8	(	(	PUNCT
ejpam-3274	24	9	3	3	NUM
ejpam-3274	24	10	)	)	PUNCT
ejpam-3274	24	11	(	(	PUNCT
ejpam-3274	24	12	2018	2018	NUM
ejpam-3274	24	13	)	)	PUNCT
ejpam-3274	24	14	,	,	PUNCT
ejpam-3274	24	15	589	589	NUM
ejpam-3274	24	16	-	-	SYM
ejpam-3274	24	17	597	597	NUM
ejpam-3274	24	18	590	590	NUM
ejpam-3274	24	19	2	2	NUM
ejpam-3274	24	20	.	.	PUNCT
ejpam-3274	24	21	preliminaries	preliminary	NOUN
ejpam-3274	24	22	the	the	DET
ejpam-3274	24	23	class	class	NOUN
ejpam-3274	24	24	of	of	ADP
ejpam-3274	24	25	π	π	PROPN
ejpam-3274	24	26	-	-	ADJ
ejpam-3274	24	27	regular	regular	ADJ
ejpam-3274	24	28	semigroups	semigroup	NOUN
ejpam-3274	24	29	is	be	AUX
ejpam-3274	24	30	one	one	NUM
ejpam-3274	24	31	of	of	ADP
ejpam-3274	24	32	the	the	DET
ejpam-3274	24	33	important	important	ADJ
ejpam-3274	24	34	classes	class	NOUN
ejpam-3274	24	35	of	of	ADP
ejpam-3274	24	36	non	non	ADJ
ejpam-3274	24	37	-	-	ADJ
ejpam-3274	24	38	regular	regular	ADJ
ejpam-3274	24	39	semigroups	semigroup	NOUN
ejpam-3274	24	40	.	.	PUNCT
ejpam-3274	25	1	recall	recall	VERB
ejpam-3274	25	2	that	that	SCONJ
ejpam-3274	25	3	a	a	DET
ejpam-3274	25	4	semigroup	semigroup	NOUN
ejpam-3274	25	5	s	s	NOUN
ejpam-3274	25	6	is	be	AUX
ejpam-3274	25	7	said	say	VERB
ejpam-3274	25	8	to	to	PART
ejpam-3274	25	9	be	be	AUX
ejpam-3274	25	10	a	a	DET
ejpam-3274	25	11	π	π	ADJ
ejpam-3274	25	12	-	-	ADJ
ejpam-3274	25	13	regular	regular	ADJ
ejpam-3274	25	14	semigroup	semigroup	NOUN
ejpam-3274	25	15	if	if	SCONJ
ejpam-3274	25	16	for	for	ADP
ejpam-3274	25	17	any	any	DET
ejpam-3274	25	18	a	a	DET
ejpam-3274	25	19	∈	∈	ADJ
ejpam-3274	25	20	s	s	NOUN
ejpam-3274	25	21	,	,	PUNCT
ejpam-3274	25	22	there	there	PRON
ejpam-3274	25	23	exists	exist	VERB
ejpam-3274	25	24	a	a	DET
ejpam-3274	25	25	positive	positive	ADJ
ejpam-3274	25	26	integer	integer	NOUN
ejpam-3274	25	27	m	m	VERB
ejpam-3274	25	28	such	such	ADJ
ejpam-3274	25	29	that	that	PRON
ejpam-3274	25	30	am	be	AUX
ejpam-3274	25	31	∈	∈	PROPN
ejpam-3274	25	32	amsam	amsam	NOUN
ejpam-3274	25	33	.	.	PUNCT
ejpam-3274	26	1	denote	denote	PROPN
ejpam-3274	26	2	r(a	r(a	PROPN
ejpam-3274	26	3	)	)	PUNCT
ejpam-3274	27	1	=	=	SYM
ejpam-3274	27	2	min{m	min{m	PROPN
ejpam-3274	27	3	∈	∈	PROPN
ejpam-3274	27	4	n	n	AUX
ejpam-3274	27	5	:	:	PUNCT
ejpam-3274	27	6	am	be	AUX
ejpam-3274	27	7	∈	∈	PROPN
ejpam-3274	27	8	amsam	amsam	NOUN
ejpam-3274	27	9	}	}	PUNCT
ejpam-3274	27	10	and	and	CCONJ
ejpam-3274	27	11	call	call	VERB
ejpam-3274	27	12	it	it	PRON
ejpam-3274	27	13	the	the	DET
ejpam-3274	27	14	least	least	ADJ
ejpam-3274	27	15	regular	regular	ADJ
ejpam-3274	27	16	index	index	NOUN
ejpam-3274	27	17	of	of	ADP
ejpam-3274	27	18	a.	a.	NOUN
ejpam-3274	27	19	a	a	DET
ejpam-3274	27	20	π	π	ADJ
ejpam-3274	27	21	-	-	ADJ
ejpam-3274	27	22	regular	regular	ADJ
ejpam-3274	27	23	semigroup	semigroup	NOUN
ejpam-3274	27	24	is	be	AUX
ejpam-3274	27	25	called	call	VERB
ejpam-3274	27	26	a	a	DET
ejpam-3274	27	27	gvsemigroup	gvsemigroup	NOUN
ejpam-3274	27	28	if	if	SCONJ
ejpam-3274	27	29	every	every	DET
ejpam-3274	27	30	regular	regular	ADJ
ejpam-3274	27	31	element	element	NOUN
ejpam-3274	27	32	is	be	AUX
ejpam-3274	27	33	completely	completely	ADV
ejpam-3274	27	34	regular	regular	ADJ
ejpam-3274	27	35	.	.	PUNCT
ejpam-3274	28	1	furthermore	furthermore	ADV
ejpam-3274	28	2	,	,	PUNCT
ejpam-3274	28	3	a	a	DET
ejpam-3274	28	4	gv	gv	NOUN
ejpam-3274	28	5	-	-	NOUN
ejpam-3274	28	6	semigroup	semigroup	NOUN
ejpam-3274	28	7	s	s	VERB
ejpam-3274	28	8	is	be	AUX
ejpam-3274	28	9	called	call	VERB
ejpam-3274	28	10	a	a	DET
ejpam-3274	28	11	gv	gv	NOUN
ejpam-3274	28	12	-	-	ADJ
ejpam-3274	28	13	inverse	inverse	ADJ
ejpam-3274	28	14	semigroup	semigroup	NOUN
ejpam-3274	28	15	if	if	SCONJ
ejpam-3274	28	16	every	every	DET
ejpam-3274	28	17	regular	regular	ADJ
ejpam-3274	28	18	element	element	NOUN
ejpam-3274	28	19	of	of	ADP
ejpam-3274	28	20	s	s	PRON
ejpam-3274	28	21	possesses	possess	VERB
ejpam-3274	28	22	a	a	DET
ejpam-3274	28	23	unique	unique	ADJ
ejpam-3274	28	24	inverse	inverse	NOUN
ejpam-3274	28	25	.	.	PUNCT
ejpam-3274	29	1	gv	gv	VERB
ejpam-3274	29	2	-	-	PUNCT
ejpam-3274	29	3	semigroups	semigroup	NOUN
ejpam-3274	29	4	and	and	CCONJ
ejpam-3274	29	5	gv	gv	NOUN
ejpam-3274	29	6	-	-	PUNCT
ejpam-3274	29	7	inverse	inverse	ADJ
ejpam-3274	29	8	semigroups	semigroup	NOUN
ejpam-3274	29	9	are	be	AUX
ejpam-3274	29	10	the	the	DET
ejpam-3274	29	11	generalizations	generalization	NOUN
ejpam-3274	29	12	of	of	ADP
ejpam-3274	29	13	completely	completely	ADV
ejpam-3274	29	14	regular	regular	ADJ
ejpam-3274	29	15	semigroups	semigroup	NOUN
ejpam-3274	29	16	and	and	CCONJ
ejpam-3274	29	17	clifford	clifford	PROPN
ejpam-3274	29	18	semigroups	semigroup	NOUN
ejpam-3274	29	19	in	in	ADP
ejpam-3274	29	20	the	the	DET
ejpam-3274	29	21	range	range	NOUN
ejpam-3274	29	22	of	of	ADP
ejpam-3274	29	23	π	π	PROPN
ejpam-3274	29	24	-	-	ADJ
ejpam-3274	29	25	regular	regular	ADJ
ejpam-3274	29	26	semigroups	semigroup	NOUN
ejpam-3274	29	27	respectively	respectively	ADV
ejpam-3274	29	28	.	.	PUNCT
ejpam-3274	30	1	throughout	throughout	ADP
ejpam-3274	30	2	this	this	DET
ejpam-3274	30	3	paper	paper	NOUN
ejpam-3274	30	4	,	,	PUNCT
ejpam-3274	30	5	we	we	PRON
ejpam-3274	30	6	denote	denote	VERB
ejpam-3274	30	7	the	the	DET
ejpam-3274	30	8	set	set	NOUN
ejpam-3274	30	9	of	of	ADP
ejpam-3274	30	10	all	all	DET
ejpam-3274	30	11	regular	regular	ADJ
ejpam-3274	30	12	elements	element	NOUN
ejpam-3274	30	13	of	of	ADP
ejpam-3274	30	14	a	a	DET
ejpam-3274	30	15	π	π	ADJ
ejpam-3274	30	16	-	-	ADJ
ejpam-3274	30	17	regular	regular	ADJ
ejpam-3274	30	18	semigroup	semigroup	NOUN
ejpam-3274	30	19	s	s	NOUN
ejpam-3274	30	20	by	by	ADP
ejpam-3274	30	21	regs	reg	NOUN
ejpam-3274	30	22	.	.	PUNCT
ejpam-3274	31	1	we	we	PRON
ejpam-3274	31	2	will	will	AUX
ejpam-3274	31	3	write	write	VERB
ejpam-3274	31	4	maps	map	NOUN
ejpam-3274	31	5	on	on	ADP
ejpam-3274	31	6	the	the	DET
ejpam-3274	31	7	right	right	NOUN
ejpam-3274	31	8	of	of	ADP
ejpam-3274	31	9	the	the	DET
ejpam-3274	31	10	objects	object	NOUN
ejpam-3274	31	11	on	on	ADP
ejpam-3274	31	12	which	which	PRON
ejpam-3274	31	13	they	they	PRON
ejpam-3274	31	14	act	act	VERB
ejpam-3274	31	15	.	.	PUNCT
ejpam-3274	32	1	let	let	VERB
ejpam-3274	32	2	s	s	PRON
ejpam-3274	32	3	be	be	AUX
ejpam-3274	32	4	a	a	DET
ejpam-3274	32	5	π	π	ADJ
ejpam-3274	32	6	-	-	ADJ
ejpam-3274	32	7	regular	regular	ADJ
ejpam-3274	32	8	semigroup	semigroup	NOUN
ejpam-3274	32	9	.	.	PUNCT
ejpam-3274	33	1	generalized	generalize	VERB
ejpam-3274	33	2	green	green	PROPN
ejpam-3274	33	3	’s	’s	PART
ejpam-3274	33	4	equivalences	equivalence	NOUN
ejpam-3274	33	5	were	be	AUX
ejpam-3274	33	6	defined	define	VERB
ejpam-3274	33	7	by	by	ADP
ejpam-3274	33	8	:	:	PUNCT
ejpam-3274	33	9	al∗b⇔	al∗b⇔	PROPN
ejpam-3274	33	10	s1ar(a	s1ar(a	PROPN
ejpam-3274	33	11	)	)	PUNCT
ejpam-3274	33	12	=	=	SYM
ejpam-3274	33	13	s1br(b	s1br(b	PROPN
ejpam-3274	33	14	)	)	PUNCT
ejpam-3274	33	15	,	,	PUNCT
ejpam-3274	33	16	ar∗b⇔	ar∗b⇔	PROPN
ejpam-3274	33	17	ar(a)s1	ar(a)s1	NOUN
ejpam-3274	33	18	=	=	SYM
ejpam-3274	33	19	br(b)s1	br(b)s1	PROPN
ejpam-3274	33	20	,	,	PUNCT
ejpam-3274	33	21	aj	aj	PROPN
ejpam-3274	33	22	∗b⇔	∗b⇔	PROPN
ejpam-3274	33	23	s1ar(a)s1	s1ar(a)s1	PROPN
ejpam-3274	33	24	=	=	SYM
ejpam-3274	33	25	s1br(b)s1	s1br(b)s1	PROPN
ejpam-3274	33	26	h∗	h∗	NOUN
ejpam-3274	33	27	=	=	PROPN
ejpam-3274	33	28	l∗	l∗	PROPN
ejpam-3274	33	29	∩r∗	∩r∗	NUM
ejpam-3274	33	30	,	,	PUNCT
ejpam-3274	33	31	d∗	d∗	PROPN
ejpam-3274	33	32	=	=	SYM
ejpam-3274	33	33	l∗	l∗	PROPN
ejpam-3274	33	34	∨r∗.	∨r∗.	VERB
ejpam-3274	34	1	if	if	SCONJ
ejpam-3274	34	2	s	s	VERB
ejpam-3274	34	3	is	be	AUX
ejpam-3274	34	4	a	a	DET
ejpam-3274	34	5	regular	regular	ADJ
ejpam-3274	34	6	semigroup	semigroup	NOUN
ejpam-3274	34	7	,	,	PUNCT
ejpam-3274	34	8	then	then	ADV
ejpam-3274	34	9	k	k	PROPN
ejpam-3274	34	10	=	=	SYM
ejpam-3274	34	11	k∗	k∗	VERB
ejpam-3274	34	12	on	on	ADP
ejpam-3274	34	13	s	s	PRON
ejpam-3274	34	14	for	for	ADP
ejpam-3274	34	15	any	any	DET
ejpam-3274	34	16	k	k	PROPN
ejpam-3274	34	17	∈	∈	PROPN
ejpam-3274	34	18	{	{	PUNCT
ejpam-3274	34	19	h	h	NOUN
ejpam-3274	34	20	,	,	PUNCT
ejpam-3274	34	21	l	l	NOUN
ejpam-3274	34	22	,	,	PUNCT
ejpam-3274	34	23	r	r	NOUN
ejpam-3274	34	24	,	,	PUNCT
ejpam-3274	34	25	d	d	PROPN
ejpam-3274	34	26	,	,	PUNCT
ejpam-3274	34	27	j	j	PROPN
ejpam-3274	34	28	}	}	PUNCT
ejpam-3274	34	29	.	.	PUNCT
ejpam-3274	35	1	the	the	DET
ejpam-3274	35	2	class	class	NOUN
ejpam-3274	35	3	of	of	ADP
ejpam-3274	35	4	π	π	PROPN
ejpam-3274	35	5	-	-	ADJ
ejpam-3274	35	6	regular	regular	ADJ
ejpam-3274	35	7	semigroups	semigroup	NOUN
ejpam-3274	35	8	and	and	CCONJ
ejpam-3274	35	9	some	some	PRON
ejpam-3274	35	10	of	of	ADP
ejpam-3274	35	11	its	its	PRON
ejpam-3274	35	12	subclasses	subclass	NOUN
ejpam-3274	35	13	have	have	AUX
ejpam-3274	35	14	been	be	AUX
ejpam-3274	35	15	studied	study	VERB
ejpam-3274	35	16	in	in	ADP
ejpam-3274	35	17	in	in	ADP
ejpam-3274	35	18	[	[	X
ejpam-3274	35	19	1	1	NUM
ejpam-3274	35	20	]	]	PUNCT
ejpam-3274	35	21	,	,	PUNCT
ejpam-3274	35	22	[	[	X
ejpam-3274	35	23	2	2	NUM
ejpam-3274	35	24	]	]	PUNCT
ejpam-3274	35	25	,	,	PUNCT
ejpam-3274	35	26	[	[	X
ejpam-3274	35	27	4	4	NUM
ejpam-3274	35	28	]	]	PUNCT
ejpam-3274	35	29	,	,	PUNCT
ejpam-3274	35	30	[	[	X
ejpam-3274	35	31	5	5	NUM
ejpam-3274	35	32	]	]	PUNCT
ejpam-3274	35	33	,	,	PUNCT
ejpam-3274	35	34	[	[	X
ejpam-3274	35	35	6	6	NUM
ejpam-3274	35	36	]	]	PUNCT
ejpam-3274	35	37	.	.	PUNCT
ejpam-3274	36	1	for	for	ADP
ejpam-3274	36	2	notations	notation	NOUN
ejpam-3274	36	3	and	and	CCONJ
ejpam-3274	36	4	terminologies	terminology	NOUN
ejpam-3274	36	5	not	not	PART
ejpam-3274	36	6	mentioned	mention	VERB
ejpam-3274	36	7	here	here	ADV
ejpam-3274	36	8	,	,	PUNCT
ejpam-3274	36	9	the	the	DET
ejpam-3274	36	10	reader	reader	NOUN
ejpam-3274	36	11	is	be	AUX
ejpam-3274	36	12	referred	refer	VERB
ejpam-3274	36	13	to	to	ADP
ejpam-3274	36	14	[	[	X
ejpam-3274	36	15	1	1	NUM
ejpam-3274	36	16	]	]	PUNCT
ejpam-3274	36	17	and	and	CCONJ
ejpam-3274	36	18	[	[	X
ejpam-3274	36	19	3	3	NUM
ejpam-3274	36	20	]	]	PUNCT
ejpam-3274	36	21	.	.	PUNCT
ejpam-3274	37	1	3	3	X
ejpam-3274	37	2	.	.	X
ejpam-3274	37	3	strong	strong	ADJ
ejpam-3274	37	4	semilattice	semilattice	NOUN
ejpam-3274	37	5	of	of	ADP
ejpam-3274	37	6	π	π	NOUN
ejpam-3274	37	7	-	-	NOUN
ejpam-3274	37	8	groups	group	NOUN
ejpam-3274	37	9	in	in	ADP
ejpam-3274	37	10	this	this	DET
ejpam-3274	37	11	section	section	NOUN
ejpam-3274	37	12	,	,	PUNCT
ejpam-3274	37	13	we	we	PRON
ejpam-3274	37	14	characterize	characterize	VERB
ejpam-3274	37	15	the	the	DET
ejpam-3274	37	16	strong	strong	ADJ
ejpam-3274	37	17	semilattice	semilattice	NOUN
ejpam-3274	37	18	of	of	ADP
ejpam-3274	37	19	π	π	NOUN
ejpam-3274	37	20	-	-	NOUN
ejpam-3274	37	21	groups	group	NOUN
ejpam-3274	37	22	.	.	PUNCT
ejpam-3274	38	1	at	at	ADP
ejpam-3274	38	2	first	first	ADV
ejpam-3274	38	3	,	,	PUNCT
ejpam-3274	38	4	we	we	PRON
ejpam-3274	38	5	give	give	VERB
ejpam-3274	38	6	some	some	DET
ejpam-3274	38	7	characterizations	characterization	NOUN
ejpam-3274	38	8	of	of	ADP
ejpam-3274	38	9	gv	gv	NOUN
ejpam-3274	38	10	-	-	ADJ
ejpam-3274	38	11	inverse	inverse	ADJ
ejpam-3274	38	12	semigroups	semigroup	NOUN
ejpam-3274	38	13	.	.	PUNCT
ejpam-3274	39	1	lemma	lemma	PROPN
ejpam-3274	39	2	1	1	NUM
ejpam-3274	39	3	.	.	PUNCT
ejpam-3274	40	1	(	(	PUNCT
ejpam-3274	40	2	[	[	X
ejpam-3274	40	3	1	1	NUM
ejpam-3274	40	4	]	]	PUNCT
ejpam-3274	40	5	)	)	PUNCT
ejpam-3274	40	6	let	let	VERB
ejpam-3274	40	7	s	s	PRON
ejpam-3274	40	8	be	be	AUX
ejpam-3274	40	9	a	a	DET
ejpam-3274	40	10	semigroup	semigroup	NOUN
ejpam-3274	40	11	and	and	CCONJ
ejpam-3274	40	12	x	x	ADJ
ejpam-3274	40	13	be	be	AUX
ejpam-3274	40	14	an	an	DET
ejpam-3274	40	15	element	element	NOUN
ejpam-3274	40	16	of	of	ADP
ejpam-3274	40	17	s	s	PRON
ejpam-3274	40	18	such	such	ADJ
ejpam-3274	40	19	that	that	SCONJ
ejpam-3274	40	20	xn	xn	PROPN
ejpam-3274	40	21	lies	lie	VERB
ejpam-3274	40	22	in	in	ADP
ejpam-3274	40	23	a	a	DET
ejpam-3274	40	24	subgroup	subgroup	NOUN
ejpam-3274	40	25	g	g	NOUN
ejpam-3274	40	26	of	of	ADP
ejpam-3274	40	27	s	s	PRON
ejpam-3274	40	28	for	for	ADP
ejpam-3274	40	29	some	some	DET
ejpam-3274	40	30	positive	positive	ADJ
ejpam-3274	40	31	integer	integer	NOUN
ejpam-3274	40	32	n.	n.	NOUN
ejpam-3274	40	33	if	if	SCONJ
ejpam-3274	40	34	e	e	NOUN
ejpam-3274	40	35	is	be	AUX
ejpam-3274	40	36	the	the	DET
ejpam-3274	40	37	identity	identity	NOUN
ejpam-3274	40	38	of	of	ADP
ejpam-3274	40	39	g	g	NOUN
ejpam-3274	40	40	,	,	PUNCT
ejpam-3274	40	41	then	then	ADV
ejpam-3274	40	42	(	(	PUNCT
ejpam-3274	40	43	i	i	NOUN
ejpam-3274	40	44	)	)	PUNCT
ejpam-3274	40	45	ex	ex	X
ejpam-3274	41	1	=	=	PUNCT
ejpam-3274	41	2	xe	xe	PROPN
ejpam-3274	41	3	∈	∈	PROPN
ejpam-3274	41	4	g.	g.	PROPN
ejpam-3274	41	5	(	(	PUNCT
ejpam-3274	41	6	ii	ii	PROPN
ejpam-3274	41	7	)	)	PUNCT
ejpam-3274	41	8	xm	xm	PROPN
ejpam-3274	41	9	∈	∈	PROPN
ejpam-3274	41	10	g	g	PROPN
ejpam-3274	41	11	for	for	ADP
ejpam-3274	41	12	every	every	DET
ejpam-3274	41	13	m	m	NOUN
ejpam-3274	41	14	≥	≥	NOUN
ejpam-3274	41	15	n	n	NOUN
ejpam-3274	41	16	and	and	CCONJ
ejpam-3274	41	17	m	m	PROPN
ejpam-3274	41	18	∈	∈	PROPN
ejpam-3274	41	19	n	n	NOUN
ejpam-3274	41	20	.	.	PUNCT
ejpam-3274	42	1	lemma	lemma	PROPN
ejpam-3274	42	2	2	2	NUM
ejpam-3274	42	3	.	.	PUNCT
ejpam-3274	43	1	(	(	PUNCT
ejpam-3274	43	2	[	[	X
ejpam-3274	43	3	1	1	NUM
ejpam-3274	43	4	]	]	PUNCT
ejpam-3274	43	5	)	)	PUNCT
ejpam-3274	43	6	let	let	VERB
ejpam-3274	43	7	s	s	PRON
ejpam-3274	43	8	be	be	AUX
ejpam-3274	43	9	a	a	DET
ejpam-3274	43	10	semigroup	semigroup	NOUN
ejpam-3274	43	11	.	.	PUNCT
ejpam-3274	44	1	then	then	ADV
ejpam-3274	44	2	the	the	DET
ejpam-3274	44	3	following	follow	VERB
ejpam-3274	44	4	conditions	condition	NOUN
ejpam-3274	44	5	are	be	AUX
ejpam-3274	44	6	equivalent	equivalent	ADJ
ejpam-3274	44	7	:	:	PUNCT
ejpam-3274	44	8	(	(	PUNCT
ejpam-3274	44	9	i	i	NOUN
ejpam-3274	44	10	)	)	PUNCT
ejpam-3274	44	11	s	s	VERB
ejpam-3274	44	12	is	be	AUX
ejpam-3274	44	13	a	a	DET
ejpam-3274	44	14	gv	gv	NOUN
ejpam-3274	44	15	-	-	ADJ
ejpam-3274	44	16	inverse	inverse	ADJ
ejpam-3274	44	17	semigroup	semigroup	NOUN
ejpam-3274	44	18	.	.	PUNCT
ejpam-3274	45	1	(	(	PUNCT
ejpam-3274	45	2	ii	ii	NOUN
ejpam-3274	45	3	)	)	PUNCT
ejpam-3274	45	4	s	s	VERB
ejpam-3274	45	5	is	be	AUX
ejpam-3274	45	6	π	π	NOUN
ejpam-3274	45	7	-	-	ADJ
ejpam-3274	45	8	regular	regular	ADJ
ejpam-3274	45	9	,	,	PUNCT
ejpam-3274	45	10	and	and	CCONJ
ejpam-3274	45	11	a	a	DET
ejpam-3274	45	12	=	=	X
ejpam-3274	45	13	axa	axa	NOUN
ejpam-3274	45	14	implies	imply	VERB
ejpam-3274	45	15	that	that	SCONJ
ejpam-3274	45	16	ax	ax	NOUN
ejpam-3274	45	17	=	=	SYM
ejpam-3274	45	18	xa	xa	PROPN
ejpam-3274	45	19	.	.	PUNCT
ejpam-3274	45	20	(	(	PUNCT
ejpam-3274	45	21	iii	iii	X
ejpam-3274	45	22	)	)	PUNCT
ejpam-3274	45	23	s	s	VERB
ejpam-3274	45	24	is	be	AUX
ejpam-3274	45	25	a	a	DET
ejpam-3274	45	26	semilattice	semilattice	NOUN
ejpam-3274	45	27	of	of	ADP
ejpam-3274	45	28	π	π	NOUN
ejpam-3274	45	29	-	-	NOUN
ejpam-3274	45	30	groups	group	NOUN
ejpam-3274	45	31	.	.	PUNCT
ejpam-3274	46	1	for	for	ADP
ejpam-3274	46	2	convenience	convenience	NOUN
ejpam-3274	46	3	,	,	PUNCT
ejpam-3274	46	4	we	we	PRON
ejpam-3274	46	5	always	always	ADV
ejpam-3274	46	6	denote	denote	VERB
ejpam-3274	46	7	a	a	DET
ejpam-3274	46	8	gv	gv	NOUN
ejpam-3274	46	9	-	-	ADJ
ejpam-3274	46	10	inverse	inverse	ADJ
ejpam-3274	46	11	semigroup	semigroup	NOUN
ejpam-3274	46	12	by	by	ADP
ejpam-3274	46	13	s	s	NOUN
ejpam-3274	46	14	=	=	X
ejpam-3274	46	15	∪α∈y	∪α∈y	PROPN
ejpam-3274	46	16	sα	sα	ADV
ejpam-3274	46	17	in	in	ADP
ejpam-3274	46	18	this	this	DET
ejpam-3274	46	19	section	section	NOUN
ejpam-3274	46	20	,	,	PUNCT
ejpam-3274	46	21	where	where	SCONJ
ejpam-3274	46	22	y	y	PROPN
ejpam-3274	46	23	is	be	AUX
ejpam-3274	46	24	a	a	DET
ejpam-3274	46	25	semilattice	semilattice	NOUN
ejpam-3274	46	26	,	,	PUNCT
ejpam-3274	46	27	sα	sα	ADV
ejpam-3274	46	28	is	be	AUX
ejpam-3274	46	29	a	a	DET
ejpam-3274	46	30	π	π	NOUN
ejpam-3274	46	31	-	-	NOUN
ejpam-3274	46	32	group	group	NOUN
ejpam-3274	46	33	for	for	ADP
ejpam-3274	46	34	each	each	DET
ejpam-3274	46	35	α	α	NOUN
ejpam-3274	46	36	∈	∈	PROPN
ejpam-3274	46	37	y	y	PROPN
ejpam-3274	46	38	by	by	ADP
ejpam-3274	46	39	lemma	lemma	PROPN
ejpam-3274	46	40	2	2	NUM
ejpam-3274	46	41	.	.	PUNCT
ejpam-3274	46	42	further	far	ADV
ejpam-3274	46	43	,	,	PUNCT
ejpam-3274	46	44	we	we	PRON
ejpam-3274	46	45	write	write	VERB
ejpam-3274	46	46	sα	sα	ADV
ejpam-3274	46	47	=	=	VERB
ejpam-3274	46	48	gα	gα	ADP
ejpam-3274	46	49	∪	∪	ADJ
ejpam-3274	46	50	qα	qα	PROPN
ejpam-3274	46	51	,	,	PUNCT
ejpam-3274	46	52	where	where	SCONJ
ejpam-3274	46	53	gα	gα	NOUN
ejpam-3274	46	54	is	be	AUX
ejpam-3274	46	55	the	the	DET
ejpam-3274	46	56	group	group	NOUN
ejpam-3274	46	57	kernel	kernel	NOUN
ejpam-3274	46	58	of	of	ADP
ejpam-3274	46	59	sα	sα	PROPN
ejpam-3274	46	60	,	,	PUNCT
ejpam-3274	46	61	and	and	CCONJ
ejpam-3274	46	62	the	the	DET
ejpam-3274	46	63	identity	identity	NOUN
ejpam-3274	46	64	of	of	ADP
ejpam-3274	46	65	gα	gα	NOUN
ejpam-3274	46	66	is	be	AUX
ejpam-3274	46	67	denoted	denote	VERB
ejpam-3274	46	68	by	by	ADP
ejpam-3274	46	69	eα	eα	PRON
ejpam-3274	46	70	for	for	ADP
ejpam-3274	46	71	any	any	DET
ejpam-3274	46	72	α	α	NOUN
ejpam-3274	46	73	∈	∈	PROPN
ejpam-3274	46	74	y	y	PROPN
ejpam-3274	46	75	.	.	PUNCT
ejpam-3274	47	1	and	and	CCONJ
ejpam-3274	47	2	qα	qα	PROPN
ejpam-3274	47	3	=	=	SYM
ejpam-3274	47	4	sα\gα	sα\gα	PROPN
ejpam-3274	47	5	is	be	AUX
ejpam-3274	47	6	the	the	DET
ejpam-3274	47	7	set	set	NOUN
ejpam-3274	47	8	of	of	ADP
ejpam-3274	47	9	non	non	ADJ
ejpam-3274	47	10	-	-	ADJ
ejpam-3274	47	11	regular	regular	ADJ
ejpam-3274	47	12	elements	element	NOUN
ejpam-3274	47	13	of	of	ADP
ejpam-3274	47	14	sα	sα	ADJ
ejpam-3274	47	15	and	and	CCONJ
ejpam-3274	47	16	it	it	PRON
ejpam-3274	47	17	is	be	AUX
ejpam-3274	47	18	a	a	DET
ejpam-3274	47	19	partial	partial	ADJ
ejpam-3274	47	20	semigroup	semigroup	NOUN
ejpam-3274	47	21	by	by	ADP
ejpam-3274	47	22	the	the	DET
ejpam-3274	47	23	definition	definition	NOUN
ejpam-3274	47	24	of	of	ADP
ejpam-3274	47	25	π	π	PROPN
ejpam-3274	47	26	-	-	NOUN
ejpam-3274	47	27	group	group	NOUN
ejpam-3274	47	28	.	.	PUNCT
ejpam-3274	48	1	certainly	certainly	ADV
ejpam-3274	48	2	,	,	PUNCT
ejpam-3274	48	3	if	if	SCONJ
ejpam-3274	48	4	sα	sα	ADV
ejpam-3274	48	5	is	be	AUX
ejpam-3274	48	6	just	just	ADV
ejpam-3274	48	7	a	a	DET
ejpam-3274	48	8	group	group	NOUN
ejpam-3274	48	9	,	,	PUNCT
ejpam-3274	48	10	then	then	ADV
ejpam-3274	48	11	qα	qα	PROPN
ejpam-3274	48	12	is	be	AUX
ejpam-3274	48	13	an	an	DET
ejpam-3274	48	14	empty	empty	ADJ
ejpam-3274	48	15	set	set	NOUN
ejpam-3274	48	16	.	.	PUNCT
ejpam-3274	49	1	according	accord	VERB
ejpam-3274	49	2	to	to	ADP
ejpam-3274	49	3	the	the	DET
ejpam-3274	49	4	results	result	NOUN
ejpam-3274	49	5	in	in	ADP
ejpam-3274	49	6	[	[	X
ejpam-3274	49	7	1	1	NUM
ejpam-3274	49	8	]	]	PUNCT
ejpam-3274	49	9	,	,	PUNCT
ejpam-3274	49	10	we	we	PRON
ejpam-3274	49	11	know	know	VERB
ejpam-3274	49	12	that	that	PRON
ejpam-3274	49	13	h∗	h∗	PROPN
ejpam-3274	49	14	=	=	NOUN
ejpam-3274	49	15	l∗	l∗	PROPN
ejpam-3274	49	16	=	=	SYM
ejpam-3274	49	17	r∗	r∗	PROPN
ejpam-3274	49	18	=	=	PUNCT
ejpam-3274	49	19	d∗	d∗	PROPN
ejpam-3274	49	20	=	=	SYM
ejpam-3274	49	21	j	j	PROPN
ejpam-3274	49	22	∗	∗	VERB
ejpam-3274	49	23	on	on	ADP
ejpam-3274	49	24	a	a	DET
ejpam-3274	49	25	gv	gv	NOUN
ejpam-3274	49	26	-	-	ADJ
ejpam-3274	49	27	inverse	inverse	ADJ
ejpam-3274	49	28	semigroup	semigroup	NOUN
ejpam-3274	49	29	.	.	PUNCT
ejpam-3274	50	1	on	on	ADP
ejpam-3274	50	2	the	the	DET
ejpam-3274	50	3	other	other	ADJ
ejpam-3274	50	4	hand	hand	NOUN
ejpam-3274	50	5	,	,	PUNCT
ejpam-3274	50	6	we	we	PRON
ejpam-3274	50	7	have	have	VERB
ejpam-3274	50	8	the	the	DET
ejpam-3274	50	9	following	follow	VERB
ejpam-3274	50	10	results	result	NOUN
ejpam-3274	50	11	.	.	PUNCT
ejpam-3274	51	1	j.	j.	PROPN
ejpam-3274	51	2	zhang	zhang	PROPN
ejpam-3274	51	3	,	,	PUNCT
ejpam-3274	51	4	y.	y.	PROPN
ejpam-3274	51	5	yang	yang	PROPN
ejpam-3274	51	6	,	,	PUNCT
ejpam-3274	51	7	r.	r.	PROPN
ejpam-3274	51	8	shen	shen	PROPN
ejpam-3274	51	9	/	/	SYM
ejpam-3274	51	10	eur	eur	PROPN
ejpam-3274	51	11	.	.	PUNCT
ejpam-3274	52	1	j.	j.	PROPN
ejpam-3274	52	2	pure	pure	PROPN
ejpam-3274	52	3	appl	appl	PROPN
ejpam-3274	52	4	.	.	PROPN
ejpam-3274	52	5	math	math	PROPN
ejpam-3274	52	6	,	,	PUNCT
ejpam-3274	52	7	11	11	NUM
ejpam-3274	52	8	(	(	PUNCT
ejpam-3274	52	9	3	3	NUM
ejpam-3274	52	10	)	)	PUNCT
ejpam-3274	52	11	(	(	PUNCT
ejpam-3274	52	12	2018	2018	NUM
ejpam-3274	52	13	)	)	PUNCT
ejpam-3274	52	14	,	,	PUNCT
ejpam-3274	52	15	589	589	NUM
ejpam-3274	52	16	-	-	SYM
ejpam-3274	52	17	597	597	NUM
ejpam-3274	52	18	591	591	NUM
ejpam-3274	52	19	lemma	lemma	PROPN
ejpam-3274	52	20	3	3	NUM
ejpam-3274	52	21	.	.	PUNCT
ejpam-3274	53	1	[	[	X
ejpam-3274	53	2	5	5	X
ejpam-3274	53	3	]	]	PUNCT
ejpam-3274	53	4	let	let	VERB
ejpam-3274	53	5	s	s	PRON
ejpam-3274	53	6	be	be	AUX
ejpam-3274	53	7	a	a	DET
ejpam-3274	53	8	gv	gv	NOUN
ejpam-3274	53	9	-	-	ADJ
ejpam-3274	53	10	inverse	inverse	ADJ
ejpam-3274	53	11	semigroup	semigroup	NOUN
ejpam-3274	53	12	.	.	PUNCT
ejpam-3274	54	1	then	then	ADV
ejpam-3274	54	2	for	for	ADP
ejpam-3274	54	3	any	any	DET
ejpam-3274	54	4	k	k	PROPN
ejpam-3274	54	5	∈	∈	PROPN
ejpam-3274	54	6	{	{	PUNCT
ejpam-3274	54	7	h	h	NOUN
ejpam-3274	54	8	,	,	PUNCT
ejpam-3274	54	9	l	l	NOUN
ejpam-3274	54	10	,	,	PUNCT
ejpam-3274	54	11	r	r	NOUN
ejpam-3274	54	12	,	,	PUNCT
ejpam-3274	54	13	d	d	PROPN
ejpam-3274	54	14	,	,	PUNCT
ejpam-3274	54	15	j	j	PROPN
ejpam-3274	54	16	}	}	PUNCT
ejpam-3274	54	17	,	,	PUNCT
ejpam-3274	54	18	k	k	PROPN
ejpam-3274	54	19	⊆	⊆	NUM
ejpam-3274	54	20	k∗	k∗	NOUN
ejpam-3274	54	21	on	on	ADP
ejpam-3274	54	22	s.	s.	PROPN
ejpam-3274	54	23	lemma	lemma	PROPN
ejpam-3274	54	24	4	4	X
ejpam-3274	54	25	.	.	PUNCT
ejpam-3274	55	1	let	let	VERB
ejpam-3274	55	2	s	s	PRON
ejpam-3274	55	3	be	be	AUX
ejpam-3274	55	4	a	a	DET
ejpam-3274	55	5	gv	gv	NOUN
ejpam-3274	55	6	-	-	ADJ
ejpam-3274	55	7	inverse	inverse	ADJ
ejpam-3274	55	8	semigroup	semigroup	NOUN
ejpam-3274	55	9	and	and	CCONJ
ejpam-3274	55	10	regs	reg	NOUN
ejpam-3274	55	11	be	be	AUX
ejpam-3274	55	12	an	an	DET
ejpam-3274	55	13	ideal	ideal	NOUN
ejpam-3274	55	14	of	of	ADP
ejpam-3274	55	15	s.	s.	PROPN
ejpam-3274	55	16	for	for	ADP
ejpam-3274	55	17	any	any	DET
ejpam-3274	55	18	α	α	PROPN
ejpam-3274	55	19	∈	∈	PROPN
ejpam-3274	55	20	y	y	PROPN
ejpam-3274	55	21	,	,	PUNCT
ejpam-3274	55	22	if	if	SCONJ
ejpam-3274	55	23	a	a	DET
ejpam-3274	55	24	∈	∈	PROPN
ejpam-3274	55	25	gα	gα	NOUN
ejpam-3274	55	26	,	,	PUNCT
ejpam-3274	55	27	then	then	ADV
ejpam-3274	55	28	ha	ha	INTJ
ejpam-3274	55	29	=	=	SYM
ejpam-3274	55	30	la	la	PROPN
ejpam-3274	55	31	=	=	PROPN
ejpam-3274	55	32	ra	ra	PROPN
ejpam-3274	55	33	=	=	SYM
ejpam-3274	55	34	ja	ja	PROPN
ejpam-3274	55	35	=	=	PUNCT
ejpam-3274	56	1	gα	gα	NOUN
ejpam-3274	56	2	;	;	PUNCT
ejpam-3274	56	3	if	if	SCONJ
ejpam-3274	56	4	a	a	DET
ejpam-3274	56	5	∈	∈	PROPN
ejpam-3274	56	6	qα	qα	PROPN
ejpam-3274	56	7	,	,	PUNCT
ejpam-3274	56	8	then	then	ADV
ejpam-3274	56	9	ja	ja	PROPN
ejpam-3274	56	10	=	=	PUNCT
ejpam-3274	56	11	{	{	PUNCT
ejpam-3274	56	12	a	a	X
ejpam-3274	56	13	}	}	PUNCT
ejpam-3274	56	14	.	.	PUNCT
ejpam-3274	57	1	proof	proof	NOUN
ejpam-3274	57	2	.	.	PUNCT
ejpam-3274	58	1	for	for	ADP
ejpam-3274	58	2	any	any	DET
ejpam-3274	58	3	α	α	PROPN
ejpam-3274	58	4	∈	∈	PROPN
ejpam-3274	58	5	y	y	PROPN
ejpam-3274	58	6	,	,	PUNCT
ejpam-3274	58	7	let	let	VERB
ejpam-3274	58	8	a	a	DET
ejpam-3274	58	9	,	,	PUNCT
ejpam-3274	58	10	b	b	PROPN
ejpam-3274	58	11	∈	∈	PROPN
ejpam-3274	58	12	qα	qα	PROPN
ejpam-3274	58	13	.	.	PROPN
ejpam-3274	58	14	suppose	suppose	VERB
ejpam-3274	58	15	that	that	SCONJ
ejpam-3274	58	16	arb	arb	PROPN
ejpam-3274	58	17	.	.	PUNCT
ejpam-3274	59	1	then	then	ADV
ejpam-3274	59	2	there	there	PRON
ejpam-3274	59	3	exist	exist	VERB
ejpam-3274	59	4	s	s	X
ejpam-3274	59	5	∈	∈	NOUN
ejpam-3274	59	6	sβ	sβ	NOUN
ejpam-3274	59	7	and	and	CCONJ
ejpam-3274	59	8	t	t	PROPN
ejpam-3274	59	9	∈	∈	PROPN
ejpam-3274	59	10	sγ	sγ	VERB
ejpam-3274	59	11	such	such	DET
ejpam-3274	59	12	that	that	SCONJ
ejpam-3274	59	13	a	a	DET
ejpam-3274	59	14	=	=	NOUN
ejpam-3274	59	15	bs	bs	NOUN
ejpam-3274	59	16	,	,	PUNCT
ejpam-3274	59	17	b	b	NOUN
ejpam-3274	59	18	=	=	PUNCT
ejpam-3274	59	19	at	at	ADP
ejpam-3274	59	20	for	for	ADP
ejpam-3274	59	21	some	some	DET
ejpam-3274	59	22	β	β	NOUN
ejpam-3274	59	23	,	,	PUNCT
ejpam-3274	59	24	γ	γ	PROPN
ejpam-3274	59	25	∈	∈	PROPN
ejpam-3274	59	26	y	y	PROPN
ejpam-3274	59	27	with	with	ADP
ejpam-3274	59	28	β	β	PROPN
ejpam-3274	59	29	,	,	PUNCT
ejpam-3274	59	30	γ	γ	PROPN
ejpam-3274	59	31	≥	≥	NUM
ejpam-3274	59	32	α	α	X
ejpam-3274	59	33	.	.	PUNCT
ejpam-3274	60	1	further	far	ADV
ejpam-3274	60	2	,	,	PUNCT
ejpam-3274	60	3	a	a	DET
ejpam-3274	60	4	=	=	NOUN
ejpam-3274	60	5	bs	bs	NOUN
ejpam-3274	60	6	=	=	PUNCT
ejpam-3274	60	7	ats	ats	PROPN
ejpam-3274	60	8	=	=	PUNCT
ejpam-3274	60	9	a(ts)2	a(ts)2	PUNCT
ejpam-3274	60	10	=	=	PUNCT
ejpam-3274	60	11	·	·	PUNCT
ejpam-3274	60	12	·	·	PUNCT
ejpam-3274	60	13	·	·	PUNCT
ejpam-3274	61	1	=	=	SYM
ejpam-3274	61	2	a(ts)m	a(ts)m	PROPN
ejpam-3274	61	3	,	,	PUNCT
ejpam-3274	61	4	b	b	NOUN
ejpam-3274	61	5	=	=	PUNCT
ejpam-3274	61	6	at	at	ADP
ejpam-3274	61	7	=	=	PROPN
ejpam-3274	61	8	bst	bst	PROPN
ejpam-3274	61	9	=	=	SYM
ejpam-3274	61	10	b(st)2	b(st)2	PROPN
ejpam-3274	61	11	=	=	SYM
ejpam-3274	61	12	·	·	PUNCT
ejpam-3274	61	13	·	·	PUNCT
ejpam-3274	61	14	·	·	PUNCT
ejpam-3274	62	1	=	=	PUNCT
ejpam-3274	62	2	b(st)m	b(st)m	ADV
ejpam-3274	62	3	where	where	SCONJ
ejpam-3274	62	4	m	m	PROPN
ejpam-3274	62	5	≥	≥	PROPN
ejpam-3274	62	6	max{r(st	max{r(st	PROPN
ejpam-3274	62	7	)	)	PUNCT
ejpam-3274	62	8	,	,	PUNCT
ejpam-3274	62	9	r(ts	r(ts	PROPN
ejpam-3274	62	10	)	)	PUNCT
ejpam-3274	62	11	}	}	PUNCT
ejpam-3274	62	12	.	.	PUNCT
ejpam-3274	63	1	by	by	ADP
ejpam-3274	63	2	lemma	lemma	PROPN
ejpam-3274	63	3	1	1	NUM
ejpam-3274	63	4	,	,	PUNCT
ejpam-3274	63	5	(	(	PUNCT
ejpam-3274	63	6	ts)m	ts)m	NUM
ejpam-3274	63	7	,	,	PUNCT
ejpam-3274	63	8	(	(	PUNCT
ejpam-3274	63	9	st)m	st)m	PROPN
ejpam-3274	63	10	∈	∈	PROPN
ejpam-3274	63	11	gβγ	gβγ	VERB
ejpam-3274	63	12	⊆	⊆	NUM
ejpam-3274	63	13	regs	reg	NOUN
ejpam-3274	63	14	.	.	PUNCT
ejpam-3274	64	1	since	since	SCONJ
ejpam-3274	64	2	regs	reg	NOUN
ejpam-3274	64	3	is	be	AUX
ejpam-3274	64	4	an	an	DET
ejpam-3274	64	5	ideal	ideal	NOUN
ejpam-3274	64	6	of	of	ADP
ejpam-3274	64	7	s	s	PROPN
ejpam-3274	64	8	,	,	PUNCT
ejpam-3274	64	9	we	we	PRON
ejpam-3274	64	10	get	get	VERB
ejpam-3274	64	11	that	that	PRON
ejpam-3274	64	12	s	s	PART
ejpam-3274	64	13	=	=	X
ejpam-3274	64	14	t	t	NOUN
ejpam-3274	64	15	=	=	SYM
ejpam-3274	64	16	1	1	NUM
ejpam-3274	64	17	and	and	CCONJ
ejpam-3274	64	18	a	a	DET
ejpam-3274	64	19	=	=	SYM
ejpam-3274	64	20	b	b	NOUN
ejpam-3274	64	21	,	,	PUNCT
ejpam-3274	64	22	so	so	ADV
ejpam-3274	64	23	ra	ra	PROPN
ejpam-3274	64	24	=	=	PUNCT
ejpam-3274	64	25	{	{	PUNCT
ejpam-3274	64	26	a	a	NOUN
ejpam-3274	64	27	}	}	PUNCT
ejpam-3274	64	28	.	.	PUNCT
ejpam-3274	65	1	similarly	similarly	ADV
ejpam-3274	65	2	,	,	PUNCT
ejpam-3274	65	3	ka	ka	PROPN
ejpam-3274	65	4	=	=	X
ejpam-3274	65	5	{	{	PUNCT
ejpam-3274	65	6	a	a	NOUN
ejpam-3274	65	7	}	}	PUNCT
ejpam-3274	65	8	for	for	ADP
ejpam-3274	65	9	any	any	DET
ejpam-3274	65	10	k	k	PROPN
ejpam-3274	65	11	∈	∈	PROPN
ejpam-3274	65	12	{	{	PUNCT
ejpam-3274	65	13	h	h	NOUN
ejpam-3274	65	14	,	,	PUNCT
ejpam-3274	65	15	l	l	NOUN
ejpam-3274	65	16	,	,	PUNCT
ejpam-3274	65	17	r	r	NOUN
ejpam-3274	65	18	,	,	PUNCT
ejpam-3274	65	19	d	d	PROPN
ejpam-3274	65	20	,	,	PUNCT
ejpam-3274	65	21	j	j	PROPN
ejpam-3274	65	22	}	}	PUNCT
ejpam-3274	65	23	,	,	PUNCT
ejpam-3274	65	24	a	a	DET
ejpam-3274	65	25	∈	∈	PROPN
ejpam-3274	65	26	qα	qα	PROPN
ejpam-3274	65	27	.	.	PUNCT
ejpam-3274	66	1	(	(	PUNCT
ejpam-3274	66	2	1	1	X
ejpam-3274	66	3	)	)	PUNCT
ejpam-3274	66	4	on	on	ADP
ejpam-3274	66	5	the	the	DET
ejpam-3274	66	6	other	other	ADJ
ejpam-3274	66	7	hand	hand	NOUN
ejpam-3274	66	8	,	,	PUNCT
ejpam-3274	66	9	by	by	ADP
ejpam-3274	66	10	lemma	lemma	PROPN
ejpam-3274	66	11	2	2	NUM
ejpam-3274	66	12	,	,	PUNCT
ejpam-3274	66	13	it	it	PRON
ejpam-3274	66	14	is	be	AUX
ejpam-3274	66	15	easy	easy	ADJ
ejpam-3274	66	16	to	to	PART
ejpam-3274	66	17	see	see	VERB
ejpam-3274	66	18	that	that	SCONJ
ejpam-3274	66	19	if	if	SCONJ
ejpam-3274	66	20	a	a	DET
ejpam-3274	66	21	∈	∈	PROPN
ejpam-3274	66	22	gα	gα	NOUN
ejpam-3274	66	23	,	,	PUNCT
ejpam-3274	66	24	ha	ha	INTJ
ejpam-3274	66	25	=	=	PUNCT
ejpam-3274	66	26	la	la	PROPN
ejpam-3274	66	27	=	=	PROPN
ejpam-3274	67	1	ra	ra	PROPN
ejpam-3274	67	2	=	=	SYM
ejpam-3274	67	3	ja	ja	PROPN
ejpam-3274	67	4	=	=	PUNCT
ejpam-3274	67	5	gα	gα	PROPN
ejpam-3274	67	6	.	.	PUNCT
ejpam-3274	68	1	(	(	PUNCT
ejpam-3274	68	2	2	2	X
ejpam-3274	68	3	)	)	PUNCT
ejpam-3274	68	4	let	let	VERB
ejpam-3274	68	5	s	s	PRON
ejpam-3274	68	6	be	be	AUX
ejpam-3274	68	7	a	a	DET
ejpam-3274	68	8	gv	gv	NOUN
ejpam-3274	68	9	-	-	ADJ
ejpam-3274	68	10	inverse	inverse	ADJ
ejpam-3274	68	11	semigroup	semigroup	NOUN
ejpam-3274	68	12	.	.	PUNCT
ejpam-3274	69	1	define	define	VERB
ejpam-3274	69	2	a	a	DET
ejpam-3274	69	3	mapping	mapping	NOUN
ejpam-3274	69	4	ψ	ψ	NOUN
ejpam-3274	69	5	from	from	ADP
ejpam-3274	69	6	s	s	PRON
ejpam-3274	69	7	into	into	ADP
ejpam-3274	69	8	regs	reg	NOUN
ejpam-3274	69	9	as	as	SCONJ
ejpam-3274	69	10	follows	follow	VERB
ejpam-3274	69	11	:	:	PUNCT
ejpam-3274	69	12	for	for	ADP
ejpam-3274	69	13	any	any	DET
ejpam-3274	69	14	a	a	DET
ejpam-3274	69	15	∈	∈	ADJ
ejpam-3274	69	16	s	s	NOUN
ejpam-3274	69	17	,	,	PUNCT
ejpam-3274	69	18	ψ	ψ	X
ejpam-3274	69	19	:	:	PUNCT
ejpam-3274	69	20	s	s	X
ejpam-3274	69	21	→	→	SYM
ejpam-3274	69	22	regs	reg	NOUN
ejpam-3274	69	23	;	;	PUNCT
ejpam-3274	69	24	a	a	DET
ejpam-3274	69	25	7→	7→	NUM
ejpam-3274	69	26	aeα	aeα	NOUN
ejpam-3274	69	27	,	,	PUNCT
ejpam-3274	69	28	if	if	SCONJ
ejpam-3274	69	29	a	a	DET
ejpam-3274	69	30	∈	∈	NOUN
ejpam-3274	69	31	sα	sα	VERB
ejpam-3274	69	32	where	where	SCONJ
ejpam-3274	69	33	eα	eα	NOUN
ejpam-3274	69	34	is	be	AUX
ejpam-3274	69	35	the	the	DET
ejpam-3274	69	36	unique	unique	ADJ
ejpam-3274	69	37	idempotent	idempotent	NOUN
ejpam-3274	69	38	of	of	ADP
ejpam-3274	69	39	π	π	PROPN
ejpam-3274	69	40	-	-	NOUN
ejpam-3274	69	41	group	group	NOUN
ejpam-3274	69	42	sα	sα	PROPN
ejpam-3274	69	43	.	.	PUNCT
ejpam-3274	70	1	then	then	ADV
ejpam-3274	70	2	it	it	PRON
ejpam-3274	70	3	is	be	AUX
ejpam-3274	70	4	obvious	obvious	ADJ
ejpam-3274	70	5	that	that	SCONJ
ejpam-3274	70	6	ψ|gα	ψ|gα	PUNCT
ejpam-3274	70	7	=	=	SYM
ejpam-3274	70	8	1gα	1gα	NOUN
ejpam-3274	70	9	.	.	PUNCT
ejpam-3274	71	1	for	for	ADP
ejpam-3274	71	2	any	any	DET
ejpam-3274	71	3	a	a	PRON
ejpam-3274	71	4	,	,	PUNCT
ejpam-3274	71	5	b	b	PROPN
ejpam-3274	71	6	∈	∈	PROPN
ejpam-3274	71	7	s	s	NOUN
ejpam-3274	71	8	,	,	PUNCT
ejpam-3274	71	9	define	define	VERB
ejpam-3274	71	10	the	the	DET
ejpam-3274	71	11	following	follow	VERB
ejpam-3274	71	12	relation	relation	NOUN
ejpam-3274	71	13	:	:	PUNCT
ejpam-3274	71	14	aψ̃b	aψ̃b	NOUN
ejpam-3274	72	1	if	if	SCONJ
ejpam-3274	72	2	and	and	CCONJ
ejpam-3274	72	3	only	only	ADV
ejpam-3274	72	4	if	if	SCONJ
ejpam-3274	72	5	aψ	aψ	NUM
ejpam-3274	72	6	=	=	NOUN
ejpam-3274	72	7	bψ	bψ	NOUN
ejpam-3274	72	8	.	.	PUNCT
ejpam-3274	73	1	then	then	ADV
ejpam-3274	73	2	it	it	PRON
ejpam-3274	73	3	is	be	AUX
ejpam-3274	73	4	clear	clear	ADJ
ejpam-3274	73	5	that	that	SCONJ
ejpam-3274	73	6	ψ̃	ψ̃	PROPN
ejpam-3274	73	7	is	be	AUX
ejpam-3274	73	8	an	an	DET
ejpam-3274	73	9	equivalence	equivalence	NOUN
ejpam-3274	73	10	on	on	ADP
ejpam-3274	73	11	s	s	PRON
ejpam-3274	73	12	and	and	CCONJ
ejpam-3274	73	13	ψ̃	ψ̃	PROPN
ejpam-3274	73	14	|regs=	|regs=	PART
ejpam-3274	73	15	ε	ε	PROPN
ejpam-3274	73	16	,	,	PUNCT
ejpam-3274	73	17	where	where	SCONJ
ejpam-3274	73	18	ε	ε	PROPN
ejpam-3274	73	19	is	be	AUX
ejpam-3274	73	20	the	the	DET
ejpam-3274	73	21	equality	equality	NOUN
ejpam-3274	73	22	relation	relation	NOUN
ejpam-3274	73	23	.	.	PUNCT
ejpam-3274	74	1	since	since	SCONJ
ejpam-3274	74	2	aψ̃aeα	aψ̃aeα	PROPN
ejpam-3274	74	3	for	for	ADP
ejpam-3274	74	4	any	any	DET
ejpam-3274	74	5	a	a	DET
ejpam-3274	74	6	∈	∈	ADJ
ejpam-3274	74	7	sα	sα	ADV
ejpam-3274	74	8	,	,	PUNCT
ejpam-3274	74	9	ψ̃	ψ̃	PROPN
ejpam-3274	74	10	|s=	|s=	NOUN
ejpam-3274	74	11	ε	ε	PROPN
ejpam-3274	75	1	if	if	SCONJ
ejpam-3274	75	2	and	and	CCONJ
ejpam-3274	75	3	only	only	ADV
ejpam-3274	75	4	if	if	SCONJ
ejpam-3274	75	5	s	s	NOUN
ejpam-3274	75	6	is	be	AUX
ejpam-3274	75	7	a	a	DET
ejpam-3274	75	8	clifford	clifford	PROPN
ejpam-3274	75	9	semigroup	semigroup	PROPN
ejpam-3274	75	10	.	.	PUNCT
ejpam-3274	76	1	in	in	ADP
ejpam-3274	76	2	general	general	ADJ
ejpam-3274	76	3	,	,	PUNCT
ejpam-3274	76	4	ψ̃	ψ̃	PROPN
ejpam-3274	76	5	|s\regs	|s\reg	NOUN
ejpam-3274	76	6	is	be	AUX
ejpam-3274	76	7	not	not	PART
ejpam-3274	76	8	necessary	necessary	ADJ
ejpam-3274	76	9	the	the	DET
ejpam-3274	76	10	equality	equality	NOUN
ejpam-3274	76	11	relation	relation	NOUN
ejpam-3274	76	12	.	.	PUNCT
ejpam-3274	77	1	next	next	ADV
ejpam-3274	77	2	,	,	PUNCT
ejpam-3274	77	3	we	we	PRON
ejpam-3274	77	4	give	give	VERB
ejpam-3274	77	5	an	an	DET
ejpam-3274	77	6	example	example	NOUN
ejpam-3274	77	7	.	.	PUNCT
ejpam-3274	78	1	example	example	NOUN
ejpam-3274	79	1	1	1	NUM
ejpam-3274	79	2	.	.	PUNCT
ejpam-3274	79	3	let	let	VERB
ejpam-3274	79	4	s	s	VERB
ejpam-3274	79	5	=	=	PUNCT
ejpam-3274	79	6	{	{	PUNCT
ejpam-3274	79	7	e	e	NOUN
ejpam-3274	79	8	,	,	PUNCT
ejpam-3274	79	9	a	a	DET
ejpam-3274	79	10	,	,	PUNCT
ejpam-3274	79	11	b	b	NOUN
ejpam-3274	79	12	}	}	PUNCT
ejpam-3274	79	13	with	with	ADP
ejpam-3274	79	14	the	the	DET
ejpam-3274	79	15	following	follow	VERB
ejpam-3274	79	16	cayley	cayley	ADJ
ejpam-3274	79	17	table	table	NOUN
ejpam-3274	79	18	a	a	DET
ejpam-3274	79	19	b	b	NOUN
ejpam-3274	79	20	e	e	NOUN
ejpam-3274	79	21	a	a	DET
ejpam-3274	79	22	b	b	X
ejpam-3274	79	23	e	e	ADP
ejpam-3274	79	24	e	e	X
ejpam-3274	79	25	b	b	PROPN
ejpam-3274	79	26	e	e	X
ejpam-3274	79	27	e	e	X
ejpam-3274	79	28	e	e	X
ejpam-3274	79	29	e	e	X
ejpam-3274	79	30	e	e	X
ejpam-3274	79	31	e	e	X
ejpam-3274	79	32	e	e	X
ejpam-3274	79	33	it	it	PRON
ejpam-3274	79	34	is	be	AUX
ejpam-3274	79	35	clear	clear	ADJ
ejpam-3274	79	36	that	that	SCONJ
ejpam-3274	79	37	s	s	VERB
ejpam-3274	79	38	is	be	AUX
ejpam-3274	79	39	a	a	DET
ejpam-3274	79	40	π	π	PROPN
ejpam-3274	79	41	-	-	NOUN
ejpam-3274	79	42	group	group	NOUN
ejpam-3274	79	43	and	and	CCONJ
ejpam-3274	79	44	regs	reg	NOUN
ejpam-3274	79	45	=	=	PUNCT
ejpam-3274	79	46	{	{	PUNCT
ejpam-3274	79	47	e	e	NOUN
ejpam-3274	79	48	}	}	PUNCT
ejpam-3274	79	49	and	and	CCONJ
ejpam-3274	79	50	aψ	aψ	NUM
ejpam-3274	79	51	=	=	SYM
ejpam-3274	79	52	ae	ae	PROPN
ejpam-3274	79	53	=	=	SYM
ejpam-3274	79	54	e	e	X
ejpam-3274	79	55	=	=	PRON
ejpam-3274	79	56	be	be	AUX
ejpam-3274	79	57	=	=	PUNCT
ejpam-3274	79	58	bψ	bψ	NOUN
ejpam-3274	79	59	,	,	PUNCT
ejpam-3274	79	60	but	but	CCONJ
ejpam-3274	79	61	a	a	DET
ejpam-3274	79	62	6=	6=	PROPN
ejpam-3274	79	63	b.	b.	PROPN
ejpam-3274	79	64	lemma	lemma	PROPN
ejpam-3274	79	65	5	5	X
ejpam-3274	79	66	.	.	PUNCT
ejpam-3274	80	1	let	let	VERB
ejpam-3274	80	2	s	s	PRON
ejpam-3274	80	3	be	be	AUX
ejpam-3274	80	4	a	a	DET
ejpam-3274	80	5	gv	gv	NOUN
ejpam-3274	80	6	-	-	ADJ
ejpam-3274	80	7	inverse	inverse	ADJ
ejpam-3274	80	8	semigroup	semigroup	NOUN
ejpam-3274	80	9	.	.	PUNCT
ejpam-3274	81	1	for	for	ADP
ejpam-3274	81	2	any	any	DET
ejpam-3274	81	3	a	a	PRON
ejpam-3274	81	4	,	,	PUNCT
ejpam-3274	81	5	b	b	X
ejpam-3274	81	6	∈	∈	PROPN
ejpam-3274	81	7	sα	sα	ADV
ejpam-3274	81	8	,	,	PUNCT
ejpam-3274	81	9	if	if	SCONJ
ejpam-3274	81	10	aψ	aψ	NUM
ejpam-3274	81	11	=	=	NOUN
ejpam-3274	81	12	bψ	bψ	NOUN
ejpam-3274	81	13	,	,	PUNCT
ejpam-3274	81	14	then	then	ADV
ejpam-3274	81	15	there	there	PRON
ejpam-3274	81	16	exists	exist	VERB
ejpam-3274	81	17	m	m	VERB
ejpam-3274	81	18	∈	∈	PROPN
ejpam-3274	81	19	n	n	PRON
ejpam-3274	81	20	such	such	ADJ
ejpam-3274	81	21	that	that	PRON
ejpam-3274	81	22	am	be	AUX
ejpam-3274	81	23	=	=	X
ejpam-3274	81	24	bm	bm	PROPN
ejpam-3274	81	25	for	for	ADP
ejpam-3274	81	26	any	any	DET
ejpam-3274	81	27	m	m	NOUN
ejpam-3274	81	28	∈	∈	NOUN
ejpam-3274	81	29	n	n	NOUN
ejpam-3274	81	30	with	with	ADP
ejpam-3274	81	31	m	m	PROPN
ejpam-3274	81	32	≥	≥	NOUN
ejpam-3274	81	33	m	m	PROPN
ejpam-3274	81	34	.	.	PUNCT
ejpam-3274	82	1	in	in	ADP
ejpam-3274	82	2	particular	particular	ADJ
ejpam-3274	82	3	,	,	PUNCT
ejpam-3274	82	4	(	(	PUNCT
ejpam-3274	82	5	aψ)r(a	aψ)r(a	VERB
ejpam-3274	82	6	)	)	PUNCT
ejpam-3274	82	7	=	=	PUNCT
ejpam-3274	82	8	ar(a	ar(a	X
ejpam-3274	82	9	)	)	PUNCT
ejpam-3274	82	10	.	.	PUNCT
ejpam-3274	83	1	and	and	CCONJ
ejpam-3274	83	2	if	if	SCONJ
ejpam-3274	83	3	aψ	aψ	X
ejpam-3274	83	4	=	=	PUNCT
ejpam-3274	83	5	ar(a	ar(a	PROPN
ejpam-3274	83	6	)	)	PUNCT
ejpam-3274	83	7	,	,	PUNCT
ejpam-3274	83	8	then	then	ADV
ejpam-3274	83	9	ar(a	ar(a	PUNCT
ejpam-3274	83	10	)	)	PUNCT
ejpam-3274	84	1	2−r(a	2−r(a	NUM
ejpam-3274	84	2	)	)	PUNCT
ejpam-3274	84	3	=	=	SYM
ejpam-3274	84	4	eα	eα	X
ejpam-3274	84	5	.	.	NOUN
ejpam-3274	84	6	proof	proof	NOUN
ejpam-3274	84	7	.	.	PUNCT
ejpam-3274	85	1	let	let	VERB
ejpam-3274	85	2	a	a	DET
ejpam-3274	85	3	,	,	PUNCT
ejpam-3274	85	4	b	b	X
ejpam-3274	85	5	∈	∈	NOUN
ejpam-3274	85	6	sα	sα	VERB
ejpam-3274	85	7	.	.	PUNCT
ejpam-3274	86	1	if	if	SCONJ
ejpam-3274	86	2	aψ	aψ	NUM
ejpam-3274	86	3	=	=	NOUN
ejpam-3274	86	4	bψ	bψ	NOUN
ejpam-3274	86	5	,	,	PUNCT
ejpam-3274	86	6	then	then	ADV
ejpam-3274	86	7	aeα	aeα	NOUN
ejpam-3274	86	8	=	=	SYM
ejpam-3274	86	9	beα	beα	PROPN
ejpam-3274	86	10	,	,	PUNCT
ejpam-3274	86	11	and	and	CCONJ
ejpam-3274	86	12	(	(	PUNCT
ejpam-3274	86	13	aeα)n	aeα)n	PROPN
ejpam-3274	86	14	=	=	SYM
ejpam-3274	86	15	(	(	PUNCT
ejpam-3274	86	16	beα)n	beα)n	VERB
ejpam-3274	86	17	for	for	ADP
ejpam-3274	86	18	any	any	DET
ejpam-3274	86	19	n	n	PRON
ejpam-3274	86	20	∈	∈	PROPN
ejpam-3274	86	21	n	n	NOUN
ejpam-3274	86	22	.	.	PUNCT
ejpam-3274	87	1	by	by	ADP
ejpam-3274	87	2	lemma	lemma	PROPN
ejpam-3274	87	3	1	1	NUM
ejpam-3274	87	4	,	,	PUNCT
ejpam-3274	87	5	aneα	aneα	NOUN
ejpam-3274	87	6	=	=	PUNCT
ejpam-3274	87	7	bneα	bneα	PROPN
ejpam-3274	87	8	.	.	PUNCT
ejpam-3274	88	1	take	take	VERB
ejpam-3274	88	2	m	m	NOUN
ejpam-3274	88	3	=	=	PUNCT
ejpam-3274	88	4	max{r(a	max{r(a	PROPN
ejpam-3274	88	5	)	)	PUNCT
ejpam-3274	88	6	,	,	PUNCT
ejpam-3274	88	7	r(b	r(b	PROPN
ejpam-3274	88	8	)	)	PUNCT
ejpam-3274	88	9	}	}	PUNCT
ejpam-3274	88	10	,	,	PUNCT
ejpam-3274	88	11	then	then	ADV
ejpam-3274	88	12	for	for	ADP
ejpam-3274	88	13	any	any	DET
ejpam-3274	88	14	m	m	NOUN
ejpam-3274	88	15	∈	∈	NOUN
ejpam-3274	88	16	n	n	NOUN
ejpam-3274	88	17	with	with	ADP
ejpam-3274	88	18	m	m	PROPN
ejpam-3274	88	19	≥m	≥m	NOUN
ejpam-3274	88	20	,	,	PUNCT
ejpam-3274	88	21	am	be	AUX
ejpam-3274	88	22	,	,	PUNCT
ejpam-3274	88	23	bm	bm	PROPN
ejpam-3274	88	24	∈	∈	PROPN
ejpam-3274	88	25	regs	reg	NOUN
ejpam-3274	88	26	and	and	CCONJ
ejpam-3274	88	27	am	be	AUX
ejpam-3274	88	28	=	=	ADJ
ejpam-3274	88	29	bm	bm	PROPN
ejpam-3274	88	30	.	.	PUNCT
ejpam-3274	89	1	in	in	ADP
ejpam-3274	89	2	particular	particular	ADJ
ejpam-3274	89	3	,	,	PUNCT
ejpam-3274	89	4	(	(	PUNCT
ejpam-3274	89	5	aψ)r(a	aψ)r(a	VERB
ejpam-3274	89	6	)	)	PUNCT
ejpam-3274	89	7	=	=	SYM
ejpam-3274	90	1	ar(a)eα	ar(a)eα	NOUN
ejpam-3274	90	2	=	=	PUNCT
ejpam-3274	90	3	ar(a	ar(a	X
ejpam-3274	90	4	)	)	PUNCT
ejpam-3274	90	5	.	.	PUNCT
ejpam-3274	91	1	if	if	SCONJ
ejpam-3274	91	2	aψ	aψ	X
ejpam-3274	91	3	=	=	PUNCT
ejpam-3274	91	4	ar(a	ar(a	PROPN
ejpam-3274	91	5	)	)	PUNCT
ejpam-3274	91	6	,	,	PUNCT
ejpam-3274	91	7	then	then	ADV
ejpam-3274	91	8	aψ	aψ	X
ejpam-3274	91	9	=	=	PUNCT
ejpam-3274	91	10	(	(	PUNCT
ejpam-3274	91	11	aψ)r(a	aψ)r(a	VERB
ejpam-3274	91	12	)	)	PUNCT
ejpam-3274	91	13	and	and	CCONJ
ejpam-3274	91	14	(	(	PUNCT
ejpam-3274	91	15	aψ)r(a)−1	aψ)r(a)−1	NOUN
ejpam-3274	91	16	=	=	SYM
ejpam-3274	91	17	eα	eα	NOUN
ejpam-3274	91	18	,	,	PUNCT
ejpam-3274	91	19	and	and	CCONJ
ejpam-3274	91	20	hence	hence	ADV
ejpam-3274	91	21	ar(a	ar(a	NUM
ejpam-3274	91	22	)	)	PUNCT
ejpam-3274	91	23	2−r(a	2−r(a	NUM
ejpam-3274	91	24	)	)	PUNCT
ejpam-3274	91	25	=	=	SYM
ejpam-3274	91	26	eα	eα	PROPN
ejpam-3274	91	27	.	.	PROPN
ejpam-3274	91	28	j.	j.	PROPN
ejpam-3274	91	29	zhang	zhang	PROPN
ejpam-3274	91	30	,	,	PUNCT
ejpam-3274	91	31	y.	y.	PROPN
ejpam-3274	91	32	yang	yang	PROPN
ejpam-3274	91	33	,	,	PUNCT
ejpam-3274	91	34	r.	r.	PROPN
ejpam-3274	91	35	shen	shen	PROPN
ejpam-3274	91	36	/	/	SYM
ejpam-3274	91	37	eur	eur	PROPN
ejpam-3274	91	38	.	.	PUNCT
ejpam-3274	92	1	j.	j.	PROPN
ejpam-3274	92	2	pure	pure	PROPN
ejpam-3274	92	3	appl	appl	PROPN
ejpam-3274	92	4	.	.	PROPN
ejpam-3274	92	5	math	math	PROPN
ejpam-3274	92	6	,	,	PUNCT
ejpam-3274	92	7	11	11	NUM
ejpam-3274	92	8	(	(	PUNCT
ejpam-3274	92	9	3	3	NUM
ejpam-3274	92	10	)	)	PUNCT
ejpam-3274	92	11	(	(	PUNCT
ejpam-3274	92	12	2018	2018	NUM
ejpam-3274	92	13	)	)	PUNCT
ejpam-3274	92	14	,	,	PUNCT
ejpam-3274	92	15	589	589	NUM
ejpam-3274	92	16	-	-	SYM
ejpam-3274	92	17	597	597	NUM
ejpam-3274	92	18	592	592	NUM
ejpam-3274	92	19	lemma	lemma	PROPN
ejpam-3274	92	20	6	6	NUM
ejpam-3274	92	21	.	.	PUNCT
ejpam-3274	93	1	let	let	VERB
ejpam-3274	93	2	s	s	PRON
ejpam-3274	93	3	be	be	AUX
ejpam-3274	93	4	a	a	DET
ejpam-3274	93	5	gv	gv	NOUN
ejpam-3274	93	6	-	-	ADJ
ejpam-3274	93	7	inverse	inverse	ADJ
ejpam-3274	93	8	semigroup	semigroup	NOUN
ejpam-3274	93	9	and	and	CCONJ
ejpam-3274	93	10	regs	reg	NOUN
ejpam-3274	93	11	be	be	AUX
ejpam-3274	93	12	an	an	DET
ejpam-3274	93	13	ideal	ideal	NOUN
ejpam-3274	93	14	of	of	ADP
ejpam-3274	93	15	s.	s.	PROPN
ejpam-3274	93	16	then	then	ADV
ejpam-3274	93	17	for	for	ADP
ejpam-3274	93	18	any	any	DET
ejpam-3274	93	19	α	α	NOUN
ejpam-3274	93	20	,	,	PUNCT
ejpam-3274	93	21	β	β	X
ejpam-3274	93	22	∈	∈	PROPN
ejpam-3274	93	23	y	y	PROPN
ejpam-3274	93	24	and	and	CCONJ
ejpam-3274	93	25	a	a	DET
ejpam-3274	93	26	∈	∈	PROPN
ejpam-3274	93	27	sα	sα	ADV
ejpam-3274	93	28	,	,	PUNCT
ejpam-3274	93	29	eβ	eβ	PROPN
ejpam-3274	93	30	∈	∈	PROPN
ejpam-3274	93	31	sβ	sβ	NOUN
ejpam-3274	93	32	,	,	PUNCT
ejpam-3274	93	33	aeβ	aeβ	PROPN
ejpam-3274	93	34	=	=	SYM
ejpam-3274	93	35	eβa	eβa	PROPN
ejpam-3274	93	36	,	,	PUNCT
ejpam-3274	93	37	which	which	PRON
ejpam-3274	93	38	means	mean	VERB
ejpam-3274	93	39	that	that	SCONJ
ejpam-3274	93	40	e(s	e(s	PROPN
ejpam-3274	93	41	)	)	PUNCT
ejpam-3274	93	42	⊆	⊆	NUM
ejpam-3274	93	43	c(s	c(	NOUN
ejpam-3274	93	44	)	)	PUNCT
ejpam-3274	93	45	,	,	PUNCT
ejpam-3274	93	46	where	where	SCONJ
ejpam-3274	93	47	c(s	c(	NOUN
ejpam-3274	93	48	)	)	PUNCT
ejpam-3274	93	49	is	be	AUX
ejpam-3274	93	50	the	the	DET
ejpam-3274	93	51	center	center	NOUN
ejpam-3274	93	52	of	of	ADP
ejpam-3274	93	53	s.	s.	PROPN
ejpam-3274	93	54	proof	proof	PROPN
ejpam-3274	93	55	.	.	PUNCT
ejpam-3274	94	1	by	by	ADP
ejpam-3274	94	2	lemma	lemma	PROPN
ejpam-3274	94	3	2	2	NUM
ejpam-3274	94	4	,	,	PUNCT
ejpam-3274	94	5	regs	regs	PROPN
ejpam-3274	94	6	is	be	AUX
ejpam-3274	94	7	a	a	DET
ejpam-3274	94	8	clifford	clifford	PROPN
ejpam-3274	94	9	subsemigroup	subsemigroup	NOUN
ejpam-3274	94	10	of	of	ADP
ejpam-3274	94	11	s	s	PROPN
ejpam-3274	94	12	,	,	PUNCT
ejpam-3274	94	13	then	then	ADV
ejpam-3274	94	14	aeβ	aeβ	PROPN
ejpam-3274	94	15	,	,	PUNCT
ejpam-3274	94	16	eβa	eβa	PROPN
ejpam-3274	94	17	∈	∈	PROPN
ejpam-3274	94	18	gαβ	gαβ	PROPN
ejpam-3274	94	19	.	.	PUNCT
ejpam-3274	95	1	and	and	CCONJ
ejpam-3274	95	2	hence	hence	ADV
ejpam-3274	95	3	aeβ	aeβ	NOUN
ejpam-3274	95	4	=	=	SYM
ejpam-3274	95	5	eαβ(aeβ)eαβ	eαβ(aeβ)eαβ	NOUN
ejpam-3274	95	6	=	=	SYM
ejpam-3274	95	7	(	(	PUNCT
ejpam-3274	95	8	eαβa)eαβ	eαβa)eαβ	X
ejpam-3274	95	9	=	=	SYM
ejpam-3274	95	10	eαβ(eβa)eαβ	eαβ(eβa)eαβ	NOUN
ejpam-3274	95	11	=	=	SYM
ejpam-3274	95	12	eβa	eβa	PROPN
ejpam-3274	95	13	.	.	PUNCT
ejpam-3274	96	1	lemma	lemma	PROPN
ejpam-3274	96	2	7	7	X
ejpam-3274	96	3	.	.	PUNCT
ejpam-3274	97	1	let	let	VERB
ejpam-3274	97	2	s	s	PRON
ejpam-3274	97	3	be	be	AUX
ejpam-3274	97	4	a	a	DET
ejpam-3274	97	5	gv	gv	NOUN
ejpam-3274	97	6	-	-	ADJ
ejpam-3274	97	7	inverse	inverse	ADJ
ejpam-3274	97	8	semigroup	semigroup	NOUN
ejpam-3274	97	9	and	and	CCONJ
ejpam-3274	97	10	regs	reg	NOUN
ejpam-3274	97	11	be	be	AUX
ejpam-3274	97	12	an	an	DET
ejpam-3274	97	13	ideal	ideal	NOUN
ejpam-3274	97	14	of	of	ADP
ejpam-3274	97	15	s.	s.	PROPN
ejpam-3274	97	16	then	then	ADV
ejpam-3274	97	17	ψ	ψ	X
ejpam-3274	97	18	is	be	AUX
ejpam-3274	97	19	a	a	DET
ejpam-3274	97	20	homomorphism	homomorphism	NOUN
ejpam-3274	97	21	and	and	CCONJ
ejpam-3274	97	22	ψ̃	ψ̃	PROPN
ejpam-3274	97	23	is	be	AUX
ejpam-3274	97	24	the	the	DET
ejpam-3274	97	25	least	least	ADJ
ejpam-3274	97	26	clifford	clifford	PROPN
ejpam-3274	97	27	congruence	congruence	NOUN
ejpam-3274	97	28	on	on	ADP
ejpam-3274	97	29	s.	s.	PROPN
ejpam-3274	97	30	proof	proof	PROPN
ejpam-3274	97	31	.	.	PUNCT
ejpam-3274	98	1	let	let	VERB
ejpam-3274	98	2	a	a	DET
ejpam-3274	98	3	,	,	PUNCT
ejpam-3274	98	4	b	b	PROPN
ejpam-3274	98	5	∈	∈	PROPN
ejpam-3274	98	6	s	s	X
ejpam-3274	98	7	and	and	CCONJ
ejpam-3274	98	8	a	a	DET
ejpam-3274	98	9	∈	∈	PROPN
ejpam-3274	98	10	sα	sα	NOUN
ejpam-3274	98	11	,	,	PUNCT
ejpam-3274	98	12	b	b	PROPN
ejpam-3274	98	13	∈	∈	PROPN
ejpam-3274	98	14	sβ	sβ	PROPN
ejpam-3274	98	15	.	.	PUNCT
ejpam-3274	99	1	then	then	ADV
ejpam-3274	99	2	aψ	aψ	X
ejpam-3274	99	3	=	=	NOUN
ejpam-3274	99	4	aeα	aeα	NOUN
ejpam-3274	99	5	and	and	CCONJ
ejpam-3274	99	6	bψ	bψ	NOUN
ejpam-3274	99	7	=	=	PUNCT
ejpam-3274	99	8	beβ	beβ	NOUN
ejpam-3274	99	9	.	.	PUNCT
ejpam-3274	100	1	by	by	ADP
ejpam-3274	100	2	lemma	lemma	PROPN
ejpam-3274	100	3	6	6	NUM
ejpam-3274	100	4	,	,	PUNCT
ejpam-3274	100	5	we	we	PRON
ejpam-3274	100	6	can	can	AUX
ejpam-3274	100	7	get	get	VERB
ejpam-3274	100	8	that	that	DET
ejpam-3274	100	9	aψbψ	aψbψ	NOUN
ejpam-3274	100	10	=	=	SYM
ejpam-3274	100	11	aeαbeβ	aeαbeβ	ADV
ejpam-3274	100	12	=	=	SYM
ejpam-3274	100	13	aeαeβb	aeαeβb	NOUN
ejpam-3274	100	14	=	=	NOUN
ejpam-3274	100	15	aeαβb	aeαβb	NOUN
ejpam-3274	100	16	=	=	SYM
ejpam-3274	100	17	abeαβ	abeαβ	NOUN
ejpam-3274	100	18	=	=	SYM
ejpam-3274	100	19	(	(	PUNCT
ejpam-3274	100	20	ab)ψ	ab)ψ	PROPN
ejpam-3274	100	21	.	.	PUNCT
ejpam-3274	101	1	so	so	ADV
ejpam-3274	101	2	ψ	ψ	NOUN
ejpam-3274	101	3	is	be	AUX
ejpam-3274	101	4	a	a	DET
ejpam-3274	101	5	homomorphism	homomorphism	NOUN
ejpam-3274	101	6	and	and	CCONJ
ejpam-3274	101	7	it	it	PRON
ejpam-3274	101	8	is	be	AUX
ejpam-3274	101	9	easy	easy	ADJ
ejpam-3274	101	10	to	to	PART
ejpam-3274	101	11	understand	understand	VERB
ejpam-3274	101	12	that	that	SCONJ
ejpam-3274	101	13	ψ̃	ψ̃	PROPN
ejpam-3274	101	14	is	be	AUX
ejpam-3274	101	15	a	a	DET
ejpam-3274	101	16	congruence	congruence	NOUN
ejpam-3274	101	17	on	on	ADP
ejpam-3274	101	18	s.	s.	PROPN
ejpam-3274	101	19	for	for	ADP
ejpam-3274	101	20	any	any	DET
ejpam-3274	101	21	a	a	DET
ejpam-3274	101	22	∈	∈	ADJ
ejpam-3274	101	23	s	s	PART
ejpam-3274	101	24	,	,	PUNCT
ejpam-3274	101	25	it	it	PRON
ejpam-3274	101	26	is	be	AUX
ejpam-3274	101	27	easy	easy	ADJ
ejpam-3274	101	28	to	to	PART
ejpam-3274	101	29	see	see	VERB
ejpam-3274	101	30	that	that	PRON
ejpam-3274	101	31	aψ̃aψ(∈	aψ̃aψ(∈	NOUN
ejpam-3274	101	32	regs	reg	NOUN
ejpam-3274	101	33	)	)	PUNCT
ejpam-3274	101	34	and	and	CCONJ
ejpam-3274	101	35	so	so	ADV
ejpam-3274	101	36	ψ̃	ψ̃	PROPN
ejpam-3274	101	37	is	be	AUX
ejpam-3274	101	38	a	a	DET
ejpam-3274	101	39	regular	regular	ADJ
ejpam-3274	101	40	congruence	congruence	NOUN
ejpam-3274	101	41	.	.	PUNCT
ejpam-3274	102	1	further	far	ADV
ejpam-3274	102	2	,	,	PUNCT
ejpam-3274	102	3	since	since	SCONJ
ejpam-3274	102	4	aψ̃b	aψ̃b	PROPN
ejpam-3274	102	5	if	if	SCONJ
ejpam-3274	102	6	and	and	CCONJ
ejpam-3274	102	7	only	only	ADV
ejpam-3274	102	8	if	if	SCONJ
ejpam-3274	102	9	a	a	DET
ejpam-3274	102	10	=	=	SYM
ejpam-3274	102	11	b	b	NOUN
ejpam-3274	102	12	for	for	ADP
ejpam-3274	102	13	any	any	DET
ejpam-3274	102	14	a	a	PRON
ejpam-3274	102	15	,	,	PUNCT
ejpam-3274	102	16	b	b	PROPN
ejpam-3274	102	17	∈	∈	PROPN
ejpam-3274	102	18	regs	reg	NOUN
ejpam-3274	102	19	,	,	PUNCT
ejpam-3274	102	20	ψ̃	ψ̃	PROPN
ejpam-3274	102	21	is	be	AUX
ejpam-3274	102	22	the	the	DET
ejpam-3274	102	23	least	least	ADJ
ejpam-3274	102	24	clifford	clifford	PROPN
ejpam-3274	102	25	congruence	congruence	NOUN
ejpam-3274	102	26	on	on	ADP
ejpam-3274	102	27	s.	s.	PROPN
ejpam-3274	102	28	definition	definition	NOUN
ejpam-3274	102	29	1	1	X
ejpam-3274	102	30	.	.	PUNCT
ejpam-3274	103	1	let	let	VERB
ejpam-3274	103	2	s	s	PRON
ejpam-3274	103	3	be	be	AUX
ejpam-3274	103	4	a	a	DET
ejpam-3274	103	5	partial	partial	ADJ
ejpam-3274	103	6	semigroup	semigroup	NOUN
ejpam-3274	103	7	and	and	CCONJ
ejpam-3274	103	8	t	t	PROPN
ejpam-3274	103	9	be	be	AUX
ejpam-3274	103	10	a	a	DET
ejpam-3274	103	11	semigroup	semigroup	NOUN
ejpam-3274	103	12	.	.	PUNCT
ejpam-3274	104	1	a	a	DET
ejpam-3274	104	2	mapping	mapping	NOUN
ejpam-3274	104	3	f	f	X
ejpam-3274	104	4	:	:	PUNCT
ejpam-3274	104	5	s	s	X
ejpam-3274	104	6	→	→	SYM
ejpam-3274	104	7	t	t	PROPN
ejpam-3274	104	8	is	be	AUX
ejpam-3274	104	9	called	call	VERB
ejpam-3274	104	10	a	a	DET
ejpam-3274	104	11	partial	partial	ADJ
ejpam-3274	104	12	semigroup	semigroup	NOUN
ejpam-3274	104	13	homomorphism	homomorphism	NOUN
ejpam-3274	104	14	if	if	SCONJ
ejpam-3274	104	15	(	(	PUNCT
ejpam-3274	104	16	ab)f	ab)f	PROPN
ejpam-3274	104	17	=	=	SYM
ejpam-3274	104	18	(	(	PUNCT
ejpam-3274	104	19	af)(bf	af)(bf	NOUN
ejpam-3274	104	20	)	)	PUNCT
ejpam-3274	104	21	for	for	ADP
ejpam-3274	104	22	any	any	DET
ejpam-3274	104	23	a	a	PRON
ejpam-3274	104	24	,	,	PUNCT
ejpam-3274	104	25	b	b	PROPN
ejpam-3274	104	26	∈	∈	PROPN
ejpam-3274	104	27	s	s	X
ejpam-3274	104	28	and	and	CCONJ
ejpam-3274	104	29	ab	ab	PROPN
ejpam-3274	104	30	∈	∈	PROPN
ejpam-3274	104	31	s.	s.	PROPN
ejpam-3274	104	32	now	now	ADV
ejpam-3274	104	33	we	we	PRON
ejpam-3274	104	34	give	give	VERB
ejpam-3274	104	35	the	the	DET
ejpam-3274	104	36	main	main	ADJ
ejpam-3274	104	37	result	result	NOUN
ejpam-3274	104	38	of	of	ADP
ejpam-3274	104	39	this	this	DET
ejpam-3274	104	40	paper	paper	NOUN
ejpam-3274	104	41	.	.	PUNCT
ejpam-3274	105	1	theorem	theorem	NOUN
ejpam-3274	105	2	1	1	NUM
ejpam-3274	105	3	.	.	PUNCT
ejpam-3274	106	1	let	let	VERB
ejpam-3274	106	2	s	s	PRON
ejpam-3274	106	3	=	=	VERB
ejpam-3274	106	4	∪α∈y	∪α∈y	AUX
ejpam-3274	106	5	sα	sα	ADV
ejpam-3274	106	6	be	be	AUX
ejpam-3274	106	7	a	a	DET
ejpam-3274	106	8	gv	gv	NOUN
ejpam-3274	106	9	-	-	ADJ
ejpam-3274	106	10	inverse	inverse	ADJ
ejpam-3274	106	11	semigroup	semigroup	NOUN
ejpam-3274	106	12	.	.	PUNCT
ejpam-3274	107	1	if	if	SCONJ
ejpam-3274	107	2	the	the	DET
ejpam-3274	107	3	following	follow	VERB
ejpam-3274	107	4	conditions	condition	NOUN
ejpam-3274	107	5	are	be	AUX
ejpam-3274	107	6	satisfied	satisfied	ADJ
ejpam-3274	107	7	:	:	PUNCT
ejpam-3274	107	8	(	(	PUNCT
ejpam-3274	107	9	i	i	NOUN
ejpam-3274	107	10	)	)	PUNCT
ejpam-3274	107	11	regs	reg	NOUN
ejpam-3274	107	12	=	=	SYM
ejpam-3274	107	13	∪α∈ygα	∪α∈ygα	PROPN
ejpam-3274	107	14	is	be	AUX
ejpam-3274	107	15	a	a	DET
ejpam-3274	107	16	clifford	clifford	PROPN
ejpam-3274	107	17	subsemigroup	subsemigroup	NOUN
ejpam-3274	107	18	of	of	ADP
ejpam-3274	107	19	s	s	PROPN
ejpam-3274	107	20	,	,	PUNCT
ejpam-3274	107	21	denoted	denote	VERB
ejpam-3274	107	22	by	by	ADP
ejpam-3274	107	23	g[y	g[y	PROPN
ejpam-3274	107	24	;	;	PUNCT
ejpam-3274	107	25	gα	gα	NOUN
ejpam-3274	107	26	,	,	PUNCT
ejpam-3274	107	27	θα	θα	NOUN
ejpam-3274	107	28	,	,	PUNCT
ejpam-3274	107	29	β	β	NOUN
ejpam-3274	107	30	]	]	X
ejpam-3274	107	31	,	,	PUNCT
ejpam-3274	107	32	and	and	CCONJ
ejpam-3274	107	33	it	it	PRON
ejpam-3274	107	34	is	be	AUX
ejpam-3274	107	35	an	an	DET
ejpam-3274	107	36	ideal	ideal	NOUN
ejpam-3274	107	37	of	of	ADP
ejpam-3274	107	38	s	s	PROPN
ejpam-3274	107	39	,	,	PUNCT
ejpam-3274	107	40	which	which	PRON
ejpam-3274	107	41	means	mean	VERB
ejpam-3274	107	42	that	that	SCONJ
ejpam-3274	107	43	s	s	VERB
ejpam-3274	107	44	is	be	AUX
ejpam-3274	107	45	a	a	DET
ejpam-3274	107	46	nil	nil	ADJ
ejpam-3274	107	47	-	-	PUNCT
ejpam-3274	107	48	extension	extension	NOUN
ejpam-3274	107	49	of	of	ADP
ejpam-3274	107	50	a	a	DET
ejpam-3274	107	51	clifford	clifford	PROPN
ejpam-3274	107	52	semigroup	semigroup	PROPN
ejpam-3274	107	53	.	.	PUNCT
ejpam-3274	108	1	(	(	PUNCT
ejpam-3274	108	2	ii	ii	NOUN
ejpam-3274	108	3	)	)	PUNCT
ejpam-3274	108	4	for	for	ADP
ejpam-3274	108	5	any	any	DET
ejpam-3274	108	6	α	α	NOUN
ejpam-3274	108	7	,	,	PUNCT
ejpam-3274	108	8	β	β	X
ejpam-3274	108	9	∈	∈	PROPN
ejpam-3274	108	10	y	y	PROPN
ejpam-3274	108	11	with	with	ADP
ejpam-3274	108	12	α	α	PROPN
ejpam-3274	108	13	≥	≥	NOUN
ejpam-3274	108	14	β	β	NOUN
ejpam-3274	108	15	,	,	PUNCT
ejpam-3274	108	16	if	if	SCONJ
ejpam-3274	108	17	qα	qα	PROPN
ejpam-3274	108	18	6=	6=	PROPN
ejpam-3274	108	19	∅	∅	NOUN
ejpam-3274	108	20	,	,	PUNCT
ejpam-3274	108	21	there	there	PRON
ejpam-3274	108	22	is	be	VERB
ejpam-3274	108	23	a	a	DET
ejpam-3274	108	24	partial	partial	ADJ
ejpam-3274	108	25	semigroup	semigroup	NOUN
ejpam-3274	108	26	homomorphism	homomorphism	NOUN
ejpam-3274	108	27	ϕα	ϕα	ADV
ejpam-3274	108	28	,	,	PUNCT
ejpam-3274	108	29	β	β	X
ejpam-3274	108	30	:	:	PUNCT
ejpam-3274	108	31	qα	qα	PROPN
ejpam-3274	108	32	→	→	SYM
ejpam-3274	108	33	sβ	sβ	NUM
ejpam-3274	108	34	such	such	ADJ
ejpam-3274	108	35	that	that	SCONJ
ejpam-3274	108	36	(	(	PUNCT
ejpam-3274	108	37	1	1	X
ejpam-3274	108	38	)	)	PUNCT
ejpam-3274	108	39	ϕα	ϕα	ADV
ejpam-3274	108	40	,	,	PUNCT
ejpam-3274	108	41	α	α	NOUN
ejpam-3274	108	42	=	=	SYM
ejpam-3274	108	43	1qα	1qα	NOUN
ejpam-3274	108	44	for	for	ADP
ejpam-3274	108	45	any	any	DET
ejpam-3274	108	46	α	α	NOUN
ejpam-3274	108	47	∈	∈	PROPN
ejpam-3274	108	48	y	y	PROPN
ejpam-3274	108	49	.	.	PUNCT
ejpam-3274	109	1	(	(	PUNCT
ejpam-3274	109	2	2	2	X
ejpam-3274	109	3	)	)	PUNCT
ejpam-3274	109	4	for	for	ADP
ejpam-3274	109	5	any	any	DET
ejpam-3274	109	6	α	α	NOUN
ejpam-3274	109	7	,	,	PUNCT
ejpam-3274	109	8	β	β	X
ejpam-3274	109	9	,	,	PUNCT
ejpam-3274	109	10	γ	γ	PROPN
ejpam-3274	109	11	∈	∈	PROPN
ejpam-3274	109	12	y	y	PROPN
ejpam-3274	109	13	with	with	ADP
ejpam-3274	109	14	γ	γ	NOUN
ejpam-3274	109	15	≤	≤	NUM
ejpam-3274	110	1	αβ	αβ	INTJ
ejpam-3274	110	2	and	and	CCONJ
ejpam-3274	110	3	a	a	DET
ejpam-3274	110	4	∈	∈	PROPN
ejpam-3274	110	5	qα	qα	PROPN
ejpam-3274	110	6	,	,	PUNCT
ejpam-3274	110	7	b	b	PROPN
ejpam-3274	110	8	∈	∈	PROPN
ejpam-3274	111	1	qβ	qβ	NOUN
ejpam-3274	111	2	,	,	PUNCT
ejpam-3274	111	3	if	if	SCONJ
ejpam-3274	111	4	ab	ab	PROPN
ejpam-3274	111	5	/∈	/∈	PUNCT
ejpam-3274	111	6	qαβ	qαβ	PROPN
ejpam-3274	111	7	,	,	PUNCT
ejpam-3274	111	8	then	then	ADV
ejpam-3274	111	9	(	(	PUNCT
ejpam-3274	111	10	aϕα	aϕα	PROPN
ejpam-3274	111	11	,	,	PUNCT
ejpam-3274	111	12	γ)(bϕβ	γ)(bϕβ	NOUN
ejpam-3274	111	13	,	,	PUNCT
ejpam-3274	111	14	γ	γ	NOUN
ejpam-3274	111	15	)	)	PUNCT
ejpam-3274	111	16	/∈	/∈	PUNCT
ejpam-3274	112	1	qγ	qγ	NOUN
ejpam-3274	112	2	.	.	PUNCT
ejpam-3274	113	1	(	(	PUNCT
ejpam-3274	113	2	3	3	X
ejpam-3274	113	3	)	)	PUNCT
ejpam-3274	113	4	for	for	ADP
ejpam-3274	113	5	any	any	DET
ejpam-3274	113	6	α	α	NOUN
ejpam-3274	113	7	,	,	PUNCT
ejpam-3274	113	8	β	β	X
ejpam-3274	113	9	,	,	PUNCT
ejpam-3274	113	10	γ	γ	PROPN
ejpam-3274	113	11	∈	∈	PROPN
ejpam-3274	113	12	y	y	PROPN
ejpam-3274	113	13	with	with	ADP
ejpam-3274	113	14	α	α	PROPN
ejpam-3274	113	15	≥	≥	PROPN
ejpam-3274	113	16	β	β	X
ejpam-3274	113	17	≥	≥	PROPN
ejpam-3274	113	18	γ	γ	PROPN
ejpam-3274	113	19	and	and	CCONJ
ejpam-3274	113	20	a	a	DET
ejpam-3274	113	21	∈	∈	ADJ
ejpam-3274	113	22	qα	qα	NOUN
ejpam-3274	113	23	,	,	PUNCT
ejpam-3274	113	24	if	if	SCONJ
ejpam-3274	113	25	aϕα	aϕα	NOUN
ejpam-3274	113	26	,	,	PUNCT
ejpam-3274	113	27	β	β	X
ejpam-3274	113	28	∈	∈	PROPN
ejpam-3274	113	29	qβ	qβ	PROPN
ejpam-3274	113	30	,	,	PUNCT
ejpam-3274	113	31	then	then	ADV
ejpam-3274	113	32	aϕα	aϕα	PROPN
ejpam-3274	113	33	,	,	PUNCT
ejpam-3274	113	34	βϕβ	βϕβ	PROPN
ejpam-3274	113	35	,	,	PUNCT
ejpam-3274	113	36	γ	γ	PROPN
ejpam-3274	113	37	=	=	SYM
ejpam-3274	113	38	aϕα	aϕα	PROPN
ejpam-3274	113	39	,	,	PUNCT
ejpam-3274	113	40	γ	γ	X
ejpam-3274	113	41	.	.	PROPN
ejpam-3274	114	1	if	if	SCONJ
ejpam-3274	114	2	aϕα	aϕα	PROPN
ejpam-3274	114	3	,	,	PUNCT
ejpam-3274	114	4	β	β	X
ejpam-3274	114	5	/∈	/∈	PUNCT
ejpam-3274	115	1	qβ	qβ	PROPN
ejpam-3274	115	2	,	,	PUNCT
ejpam-3274	115	3	then	then	ADV
ejpam-3274	115	4	aϕα	aϕα	PROPN
ejpam-3274	115	5	,	,	PUNCT
ejpam-3274	115	6	γ	γ	X
ejpam-3274	115	7	/∈	/∈	NOUN
ejpam-3274	115	8	qγ	qγ	PROPN
ejpam-3274	115	9	.	.	PUNCT
ejpam-3274	116	1	(	(	PUNCT
ejpam-3274	116	2	4	4	NUM
ejpam-3274	116	3	)	)	PUNCT
ejpam-3274	116	4	for	for	ADP
ejpam-3274	116	5	any	any	DET
ejpam-3274	116	6	α	α	NOUN
ejpam-3274	116	7	,	,	PUNCT
ejpam-3274	116	8	β	β	X
ejpam-3274	116	9	∈	∈	PROPN
ejpam-3274	116	10	y	y	PROPN
ejpam-3274	116	11	and	and	CCONJ
ejpam-3274	116	12	a	a	DET
ejpam-3274	116	13	∈	∈	PROPN
ejpam-3274	116	14	qα	qα	PROPN
ejpam-3274	116	15	,	,	PUNCT
ejpam-3274	116	16	b	b	PROPN
ejpam-3274	116	17	∈	∈	PROPN
ejpam-3274	117	1	qβ	qβ	NOUN
ejpam-3274	117	2	,	,	PUNCT
ejpam-3274	117	3	if	if	SCONJ
ejpam-3274	117	4	ab	ab	PROPN
ejpam-3274	117	5	∈	∈	PROPN
ejpam-3274	117	6	qαβ	qαβ	PROPN
ejpam-3274	117	7	,	,	PUNCT
ejpam-3274	117	8	then	then	ADV
ejpam-3274	117	9	ab	ab	PROPN
ejpam-3274	117	10	=	=	SYM
ejpam-3274	117	11	(	(	PUNCT
ejpam-3274	117	12	aϕα	aϕα	PROPN
ejpam-3274	117	13	,	,	PUNCT
ejpam-3274	117	14	αβ)(bϕβ	αβ)(bϕβ	NUM
ejpam-3274	117	15	,	,	PUNCT
ejpam-3274	117	16	αβ	αβ	NOUN
ejpam-3274	117	17	)	)	PUNCT
ejpam-3274	117	18	.	.	PUNCT
ejpam-3274	118	1	(	(	PUNCT
ejpam-3274	118	2	iii	iii	X
ejpam-3274	118	3	)	)	PUNCT
ejpam-3274	118	4	for	for	ADP
ejpam-3274	118	5	any	any	DET
ejpam-3274	118	6	α	α	NOUN
ejpam-3274	118	7	,	,	PUNCT
ejpam-3274	118	8	β	β	X
ejpam-3274	118	9	∈	∈	PROPN
ejpam-3274	118	10	y	y	PROPN
ejpam-3274	118	11	with	with	ADP
ejpam-3274	118	12	α	α	PROPN
ejpam-3274	118	13	≥	≥	NOUN
ejpam-3274	118	14	β	β	X
ejpam-3274	118	15	,	,	PUNCT
ejpam-3274	118	16	ϕα	ϕα	ADV
ejpam-3274	118	17	,	,	PUNCT
ejpam-3274	118	18	βψ	βψ	X
ejpam-3274	118	19	=	=	SYM
ejpam-3274	118	20	ψθα	ψθα	NOUN
ejpam-3274	118	21	,	,	PUNCT
ejpam-3274	118	22	β	β	NOUN
ejpam-3274	118	23	,	,	PUNCT
ejpam-3274	118	24	where	where	SCONJ
ejpam-3274	118	25	ψ	ψ	NOUN
ejpam-3274	118	26	is	be	AUX
ejpam-3274	118	27	the	the	DET
ejpam-3274	118	28	homomorphism	homomorphism	NOUN
ejpam-3274	118	29	in	in	ADP
ejpam-3274	118	30	lemma	lemma	PROPN
ejpam-3274	118	31	7	7	NUM
ejpam-3274	118	32	.	.	PUNCT
ejpam-3274	118	33	define	define	VERB
ejpam-3274	118	34	a	a	DET
ejpam-3274	118	35	mapping	mapping	NOUN
ejpam-3274	118	36	φα	φα	ADP
ejpam-3274	118	37	,	,	PUNCT
ejpam-3274	118	38	β	β	X
ejpam-3274	118	39	:	:	PUNCT
ejpam-3274	118	40	sα	sα	PROPN
ejpam-3274	118	41	→	→	SYM
ejpam-3274	118	42	sβ	sβ	NOUN
ejpam-3274	118	43	for	for	ADP
ejpam-3274	118	44	any	any	DET
ejpam-3274	118	45	α	α	NOUN
ejpam-3274	118	46	,	,	PUNCT
ejpam-3274	118	47	β	β	X
ejpam-3274	118	48	∈	∈	PROPN
ejpam-3274	118	49	y	y	PROPN
ejpam-3274	118	50	with	with	ADP
ejpam-3274	118	51	α	α	PROPN
ejpam-3274	118	52	≥	≥	NUM
ejpam-3274	118	53	β	β	NOUN
ejpam-3274	118	54	and	and	CCONJ
ejpam-3274	118	55	a	a	DET
ejpam-3274	118	56	∈	∈	PROPN
ejpam-3274	118	57	sα	sα	PROPN
ejpam-3274	118	58	,	,	PUNCT
ejpam-3274	118	59	aφα	aφα	PROPN
ejpam-3274	118	60	,	,	PUNCT
ejpam-3274	118	61	β	β	X
ejpam-3274	118	62	=	=	SYM
ejpam-3274	118	63	{	{	PUNCT
ejpam-3274	118	64	aθα	aθα	NOUN
ejpam-3274	118	65	,	,	PUNCT
ejpam-3274	118	66	β	β	NOUN
ejpam-3274	118	67	,	,	PUNCT
ejpam-3274	118	68	a	a	DET
ejpam-3274	118	69	∈	∈	PROPN
ejpam-3274	118	70	gα	gα	NOUN
ejpam-3274	118	71	,	,	PUNCT
ejpam-3274	118	72	aϕα	aϕα	PROPN
ejpam-3274	118	73	,	,	PUNCT
ejpam-3274	118	74	β	β	NOUN
ejpam-3274	118	75	,	,	PUNCT
ejpam-3274	118	76	a	a	DET
ejpam-3274	118	77	∈	∈	PROPN
ejpam-3274	118	78	qα	qα	PROPN
ejpam-3274	118	79	.	.	PUNCT
ejpam-3274	119	1	then	then	ADV
ejpam-3274	119	2	s	s	VERB
ejpam-3274	119	3	is	be	AUX
ejpam-3274	119	4	a	a	DET
ejpam-3274	119	5	strong	strong	ADJ
ejpam-3274	119	6	semilattice	semilattice	NOUN
ejpam-3274	119	7	of	of	ADP
ejpam-3274	119	8	π	π	NOUN
ejpam-3274	119	9	-	-	NOUN
ejpam-3274	119	10	groups	group	NOUN
ejpam-3274	119	11	,	,	PUNCT
ejpam-3274	119	12	denoted	denote	VERB
ejpam-3274	119	13	by	by	ADP
ejpam-3274	119	14	s[y	s[y	NUM
ejpam-3274	119	15	;	;	PUNCT
ejpam-3274	119	16	sα	sα	X
ejpam-3274	119	17	,	,	PUNCT
ejpam-3274	119	18	φα	φα	ADP
ejpam-3274	119	19	,	,	PUNCT
ejpam-3274	119	20	β	β	NOUN
ejpam-3274	119	21	]	]	X
ejpam-3274	119	22	.	.	PUNCT
ejpam-3274	120	1	conversely	conversely	ADV
ejpam-3274	120	2	,	,	PUNCT
ejpam-3274	120	3	every	every	DET
ejpam-3274	120	4	strong	strong	ADJ
ejpam-3274	120	5	semilattice	semilattice	NOUN
ejpam-3274	120	6	of	of	ADP
ejpam-3274	120	7	π	π	NOUN
ejpam-3274	120	8	-	-	NOUN
ejpam-3274	120	9	groups	group	NOUN
ejpam-3274	120	10	can	can	AUX
ejpam-3274	120	11	be	be	AUX
ejpam-3274	120	12	so	so	ADV
ejpam-3274	120	13	obtained	obtain	VERB
ejpam-3274	120	14	.	.	PUNCT
ejpam-3274	121	1	j.	j.	PROPN
ejpam-3274	121	2	zhang	zhang	PROPN
ejpam-3274	121	3	,	,	PUNCT
ejpam-3274	121	4	y.	y.	PROPN
ejpam-3274	121	5	yang	yang	PROPN
ejpam-3274	121	6	,	,	PUNCT
ejpam-3274	121	7	r.	r.	PROPN
ejpam-3274	121	8	shen	shen	PROPN
ejpam-3274	121	9	/	/	SYM
ejpam-3274	121	10	eur	eur	PROPN
ejpam-3274	121	11	.	.	PUNCT
ejpam-3274	122	1	j.	j.	PROPN
ejpam-3274	122	2	pure	pure	PROPN
ejpam-3274	122	3	appl	appl	PROPN
ejpam-3274	122	4	.	.	PROPN
ejpam-3274	122	5	math	math	PROPN
ejpam-3274	122	6	,	,	PUNCT
ejpam-3274	122	7	11	11	NUM
ejpam-3274	122	8	(	(	PUNCT
ejpam-3274	122	9	3	3	NUM
ejpam-3274	122	10	)	)	PUNCT
ejpam-3274	122	11	(	(	PUNCT
ejpam-3274	122	12	2018	2018	NUM
ejpam-3274	122	13	)	)	PUNCT
ejpam-3274	122	14	,	,	PUNCT
ejpam-3274	122	15	589	589	NUM
ejpam-3274	122	16	-	-	SYM
ejpam-3274	122	17	597	597	NUM
ejpam-3274	122	18	593	593	NUM
ejpam-3274	122	19	proof	proof	NOUN
ejpam-3274	122	20	.	.	PUNCT
ejpam-3274	123	1	let	let	VERB
ejpam-3274	123	2	s	s	PRON
ejpam-3274	123	3	be	be	AUX
ejpam-3274	123	4	a	a	DET
ejpam-3274	123	5	gv	gv	NOUN
ejpam-3274	123	6	-	-	ADJ
ejpam-3274	123	7	inverse	inverse	ADJ
ejpam-3274	123	8	semigroup	semigroup	NOUN
ejpam-3274	123	9	and	and	CCONJ
ejpam-3274	123	10	the	the	DET
ejpam-3274	123	11	given	give	VERB
ejpam-3274	123	12	conditions	condition	NOUN
ejpam-3274	123	13	are	be	AUX
ejpam-3274	123	14	satisfied	satisfied	ADJ
ejpam-3274	123	15	.	.	PUNCT
ejpam-3274	124	1	in	in	ADP
ejpam-3274	124	2	order	order	NOUN
ejpam-3274	124	3	to	to	PART
ejpam-3274	124	4	prove	prove	VERB
ejpam-3274	124	5	that	that	SCONJ
ejpam-3274	124	6	s	s	VERB
ejpam-3274	124	7	is	be	AUX
ejpam-3274	124	8	a	a	DET
ejpam-3274	124	9	strong	strong	ADJ
ejpam-3274	124	10	semilattice	semilattice	NOUN
ejpam-3274	124	11	of	of	ADP
ejpam-3274	124	12	π	π	NOUN
ejpam-3274	124	13	-	-	NOUN
ejpam-3274	124	14	groups	group	NOUN
ejpam-3274	124	15	,	,	PUNCT
ejpam-3274	124	16	we	we	PRON
ejpam-3274	124	17	firstly	firstly	ADV
ejpam-3274	124	18	show	show	VERB
ejpam-3274	124	19	that	that	SCONJ
ejpam-3274	124	20	the	the	DET
ejpam-3274	124	21	mapping	mapping	NOUN
ejpam-3274	124	22	φα	φα	PROPN
ejpam-3274	124	23	,	,	PUNCT
ejpam-3274	124	24	β	β	X
ejpam-3274	124	25	defined	define	VERB
ejpam-3274	124	26	is	be	AUX
ejpam-3274	124	27	a	a	DET
ejpam-3274	124	28	homomorphism	homomorphism	NOUN
ejpam-3274	124	29	from	from	ADP
ejpam-3274	124	30	sα	sα	ADV
ejpam-3274	124	31	to	to	ADP
ejpam-3274	124	32	sβ	sβ	PROPN
ejpam-3274	124	33	.	.	PUNCT
ejpam-3274	125	1	for	for	ADP
ejpam-3274	125	2	any	any	DET
ejpam-3274	125	3	α	α	NOUN
ejpam-3274	125	4	,	,	PUNCT
ejpam-3274	125	5	β	β	X
ejpam-3274	125	6	∈	∈	PROPN
ejpam-3274	125	7	y	y	PROPN
ejpam-3274	125	8	with	with	ADP
ejpam-3274	125	9	α	α	PROPN
ejpam-3274	125	10	≥	≥	X
ejpam-3274	125	11	β	β	X
ejpam-3274	125	12	,	,	PUNCT
ejpam-3274	125	13	suppose	suppose	VERB
ejpam-3274	125	14	that	that	SCONJ
ejpam-3274	125	15	a	a	DET
ejpam-3274	125	16	,	,	PUNCT
ejpam-3274	125	17	b	b	X
ejpam-3274	125	18	∈	∈	NUM
ejpam-3274	125	19	sα	sα	PROPN
ejpam-3274	125	20	.	.	PUNCT
ejpam-3274	125	21	case	case	NOUN
ejpam-3274	125	22	1	1	NUM
ejpam-3274	125	23	:	:	PUNCT
ejpam-3274	125	24	if	if	SCONJ
ejpam-3274	125	25	a	a	DET
ejpam-3274	125	26	∈	∈	PROPN
ejpam-3274	125	27	qα	qα	PROPN
ejpam-3274	125	28	,	,	PUNCT
ejpam-3274	125	29	b	b	PROPN
ejpam-3274	125	30	∈	∈	PROPN
ejpam-3274	125	31	qα	qα	PROPN
ejpam-3274	125	32	and	and	CCONJ
ejpam-3274	125	33	ab	ab	PROPN
ejpam-3274	125	34	∈	∈	PROPN
ejpam-3274	126	1	qα	qα	PROPN
ejpam-3274	126	2	,	,	PUNCT
ejpam-3274	126	3	since	since	SCONJ
ejpam-3274	126	4	ϕα	ϕα	ADV
ejpam-3274	126	5	,	,	PUNCT
ejpam-3274	126	6	β	β	X
ejpam-3274	126	7	is	be	AUX
ejpam-3274	126	8	a	a	DET
ejpam-3274	126	9	partial	partial	ADJ
ejpam-3274	126	10	semigroup	semigroup	NOUN
ejpam-3274	126	11	homomorphism	homomorphism	NOUN
ejpam-3274	126	12	,	,	PUNCT
ejpam-3274	126	13	(	(	PUNCT
ejpam-3274	126	14	ab)φα	ab)φα	PROPN
ejpam-3274	126	15	,	,	PUNCT
ejpam-3274	126	16	β	β	X
ejpam-3274	126	17	=	=	SYM
ejpam-3274	126	18	(	(	PUNCT
ejpam-3274	126	19	ab)ϕα	ab)ϕα	PROPN
ejpam-3274	126	20	,	,	PUNCT
ejpam-3274	126	21	β	β	X
ejpam-3274	126	22	=	=	SYM
ejpam-3274	126	23	(	(	PUNCT
ejpam-3274	126	24	aϕα	aϕα	PROPN
ejpam-3274	126	25	,	,	PUNCT
ejpam-3274	126	26	β)(bϕα	β)(bϕα	NUM
ejpam-3274	126	27	,	,	PUNCT
ejpam-3274	126	28	β	β	X
ejpam-3274	126	29	)	)	PUNCT
ejpam-3274	126	30	=	=	SYM
ejpam-3274	126	31	(	(	PUNCT
ejpam-3274	126	32	aφα	aφα	PROPN
ejpam-3274	126	33	,	,	PUNCT
ejpam-3274	126	34	β)(bφα	β)(bφα	PROPN
ejpam-3274	126	35	,	,	PUNCT
ejpam-3274	126	36	β	β	NOUN
ejpam-3274	126	37	)	)	PUNCT
ejpam-3274	126	38	.	.	PUNCT
ejpam-3274	127	1	case	case	NOUN
ejpam-3274	127	2	2	2	NUM
ejpam-3274	127	3	:	:	PUNCT
ejpam-3274	127	4	if	if	SCONJ
ejpam-3274	127	5	a	a	DET
ejpam-3274	127	6	∈	∈	PROPN
ejpam-3274	127	7	qα	qα	PROPN
ejpam-3274	127	8	,	,	PUNCT
ejpam-3274	127	9	b	b	PROPN
ejpam-3274	127	10	∈	∈	PROPN
ejpam-3274	127	11	qα	qα	PROPN
ejpam-3274	127	12	and	and	CCONJ
ejpam-3274	127	13	ab	ab	PROPN
ejpam-3274	127	14	∈	∈	PROPN
ejpam-3274	127	15	gα	gα	NOUN
ejpam-3274	127	16	,	,	PUNCT
ejpam-3274	127	17	since	since	SCONJ
ejpam-3274	127	18	gα	gα	NOUN
ejpam-3274	127	19	is	be	AUX
ejpam-3274	127	20	the	the	DET
ejpam-3274	127	21	group	group	NOUN
ejpam-3274	127	22	kernel	kernel	NOUN
ejpam-3274	127	23	of	of	ADP
ejpam-3274	127	24	sα	sα	PROPN
ejpam-3274	127	25	,	,	PUNCT
ejpam-3274	127	26	(	(	PUNCT
ejpam-3274	127	27	ab)φα	ab)φα	PROPN
ejpam-3274	127	28	,	,	PUNCT
ejpam-3274	127	29	β	β	X
ejpam-3274	127	30	=	=	SYM
ejpam-3274	127	31	(	(	PUNCT
ejpam-3274	127	32	abeα)φα	abeα)φα	PROPN
ejpam-3274	127	33	,	,	PUNCT
ejpam-3274	127	34	β	β	X
ejpam-3274	127	35	=	=	SYM
ejpam-3274	127	36	(	(	PUNCT
ejpam-3274	127	37	(	(	PUNCT
ejpam-3274	127	38	aeα)(beα))θα	aeα)(beα))θα	ADV
ejpam-3274	127	39	,	,	PUNCT
ejpam-3274	127	40	β	β	X
ejpam-3274	127	41	=	=	SYM
ejpam-3274	127	42	(	(	PUNCT
ejpam-3274	127	43	aeα)θα	aeα)θα	ADV
ejpam-3274	127	44	,	,	PUNCT
ejpam-3274	127	45	β(beα)θα	β(beα)θα	NUM
ejpam-3274	127	46	,	,	PUNCT
ejpam-3274	127	47	β	β	X
ejpam-3274	127	48	=	=	SYM
ejpam-3274	127	49	(	(	PUNCT
ejpam-3274	127	50	aψθα	aψθα	NOUN
ejpam-3274	127	51	,	,	PUNCT
ejpam-3274	127	52	β)(bψθα	β)(bψθα	NUM
ejpam-3274	127	53	,	,	PUNCT
ejpam-3274	127	54	β	β	NOUN
ejpam-3274	127	55	)	)	PUNCT
ejpam-3274	127	56	=	=	SYM
ejpam-3274	127	57	(	(	PUNCT
ejpam-3274	127	58	aϕα	aϕα	PROPN
ejpam-3274	127	59	,	,	PUNCT
ejpam-3274	127	60	βψ)(bϕα	βψ)(bϕα	PUNCT
ejpam-3274	127	61	,	,	PUNCT
ejpam-3274	127	62	βψ)(by	βψ)(by	PUNCT
ejpam-3274	127	63	condition	condition	NOUN
ejpam-3274	127	64	(	(	PUNCT
ejpam-3274	127	65	iii	iii	NOUN
ejpam-3274	127	66	)	)	PUNCT
ejpam-3274	127	67	)	)	PUNCT
ejpam-3274	128	1	=	=	SYM
ejpam-3274	128	2	(	(	PUNCT
ejpam-3274	128	3	aϕα	aϕα	PROPN
ejpam-3274	128	4	,	,	PUNCT
ejpam-3274	128	5	βeβ)(bϕα	βeβ)(bϕα	NOUN
ejpam-3274	128	6	,	,	PUNCT
ejpam-3274	128	7	βeβ	βeβ	NOUN
ejpam-3274	128	8	)	)	PUNCT
ejpam-3274	128	9	=	=	SYM
ejpam-3274	128	10	aϕα	aϕα	PROPN
ejpam-3274	128	11	,	,	PUNCT
ejpam-3274	128	12	βbϕα	βbϕα	ADJ
ejpam-3274	128	13	,	,	PUNCT
ejpam-3274	128	14	βeβ	βeβ	NOUN
ejpam-3274	128	15	=	=	SYM
ejpam-3274	128	16	aϕα	aϕα	PROPN
ejpam-3274	128	17	,	,	PUNCT
ejpam-3274	128	18	βbϕα	βbϕα	VERB
ejpam-3274	128	19	,	,	PUNCT
ejpam-3274	128	20	β	β	X
ejpam-3274	128	21	=	=	PUNCT
ejpam-3274	128	22	aφα	aφα	PROPN
ejpam-3274	128	23	,	,	PUNCT
ejpam-3274	128	24	βbφα	βbφα	PROPN
ejpam-3274	128	25	,	,	PUNCT
ejpam-3274	128	26	β	β	X
ejpam-3274	128	27	(	(	PUNCT
ejpam-3274	128	28	by	by	ADP
ejpam-3274	128	29	condition	condition	NOUN
ejpam-3274	128	30	(	(	PUNCT
ejpam-3274	128	31	ii)(2	ii)(2	NOUN
ejpam-3274	128	32	)	)	PUNCT
ejpam-3274	128	33	)	)	PUNCT
ejpam-3274	128	34	.	.	PUNCT
ejpam-3274	129	1	case	case	NOUN
ejpam-3274	129	2	3	3	NUM
ejpam-3274	129	3	:	:	PUNCT
ejpam-3274	129	4	if	if	SCONJ
ejpam-3274	129	5	a	a	DET
ejpam-3274	129	6	∈	∈	PROPN
ejpam-3274	129	7	qα	qα	PROPN
ejpam-3274	129	8	,	,	PUNCT
ejpam-3274	129	9	b	b	PROPN
ejpam-3274	129	10	∈	∈	PROPN
ejpam-3274	129	11	gα	gα	NOUN
ejpam-3274	129	12	,	,	PUNCT
ejpam-3274	129	13	then	then	ADV
ejpam-3274	129	14	ab	ab	PROPN
ejpam-3274	129	15	∈	∈	PROPN
ejpam-3274	129	16	gα	gα	ADV
ejpam-3274	129	17	since	since	SCONJ
ejpam-3274	129	18	gα	gα	NOUN
ejpam-3274	129	19	is	be	AUX
ejpam-3274	129	20	the	the	DET
ejpam-3274	129	21	group	group	NOUN
ejpam-3274	129	22	kernel	kernel	NOUN
ejpam-3274	129	23	of	of	ADP
ejpam-3274	129	24	sα	sα	PROPN
ejpam-3274	129	25	,	,	PUNCT
ejpam-3274	129	26	(	(	PUNCT
ejpam-3274	129	27	ab)φα	ab)φα	PROPN
ejpam-3274	129	28	,	,	PUNCT
ejpam-3274	129	29	β	β	X
ejpam-3274	129	30	=	=	SYM
ejpam-3274	129	31	(	(	PUNCT
ejpam-3274	129	32	ab)θα	ab)θα	PROPN
ejpam-3274	129	33	,	,	PUNCT
ejpam-3274	129	34	β	β	X
ejpam-3274	129	35	=	=	SYM
ejpam-3274	129	36	(	(	PUNCT
ejpam-3274	129	37	a(eαb))θα	a(eαb))θα	PROPN
ejpam-3274	129	38	,	,	PUNCT
ejpam-3274	129	39	β	β	X
ejpam-3274	129	40	=	=	SYM
ejpam-3274	129	41	(	(	PUNCT
ejpam-3274	129	42	(	(	PUNCT
ejpam-3274	129	43	aeα)b)θα	aeα)b)θα	PROPN
ejpam-3274	129	44	,	,	PUNCT
ejpam-3274	129	45	β	β	X
ejpam-3274	129	46	=	=	SYM
ejpam-3274	129	47	(	(	PUNCT
ejpam-3274	129	48	aeα)θα	aeα)θα	ADV
ejpam-3274	129	49	,	,	PUNCT
ejpam-3274	129	50	βbθα	βbθα	ADP
ejpam-3274	129	51	,	,	PUNCT
ejpam-3274	129	52	β	β	X
ejpam-3274	129	53	=	=	SYM
ejpam-3274	129	54	(	(	PUNCT
ejpam-3274	129	55	aψθα	aψθα	NOUN
ejpam-3274	129	56	,	,	PUNCT
ejpam-3274	129	57	β)bθα	β)bθα	NUM
ejpam-3274	129	58	,	,	PUNCT
ejpam-3274	129	59	β	β	X
ejpam-3274	129	60	=	=	SYM
ejpam-3274	129	61	(	(	PUNCT
ejpam-3274	129	62	aϕα	aϕα	PROPN
ejpam-3274	129	63	,	,	PUNCT
ejpam-3274	129	64	βeβ)(bθα	βeβ)(bθα	NOUN
ejpam-3274	129	65	,	,	PUNCT
ejpam-3274	129	66	β	β	NOUN
ejpam-3274	129	67	)	)	PUNCT
ejpam-3274	129	68	(	(	PUNCT
ejpam-3274	129	69	by	by	ADP
ejpam-3274	129	70	condition	condition	NOUN
ejpam-3274	129	71	(	(	PUNCT
ejpam-3274	129	72	iii	iii	NOUN
ejpam-3274	129	73	)	)	PUNCT
ejpam-3274	129	74	)	)	PUNCT
ejpam-3274	130	1	=	=	SYM
ejpam-3274	130	2	(	(	PUNCT
ejpam-3274	130	3	aϕα	aϕα	PROPN
ejpam-3274	130	4	,	,	PUNCT
ejpam-3274	130	5	β)(eβbθα	β)(eβbθα	NUM
ejpam-3274	130	6	,	,	PUNCT
ejpam-3274	130	7	β	β	X
ejpam-3274	130	8	)	)	PUNCT
ejpam-3274	130	9	=	=	SYM
ejpam-3274	130	10	aϕα	aϕα	NOUN
ejpam-3274	130	11	,	,	PUNCT
ejpam-3274	130	12	βbθα	βbθα	NOUN
ejpam-3274	130	13	,	,	PUNCT
ejpam-3274	130	14	β	β	X
ejpam-3274	130	15	=	=	PUNCT
ejpam-3274	130	16	aφα	aφα	PROPN
ejpam-3274	130	17	,	,	PUNCT
ejpam-3274	130	18	βbφα	βbφα	PROPN
ejpam-3274	130	19	,	,	PUNCT
ejpam-3274	130	20	β	β	X
ejpam-3274	130	21	.	.	PUNCT
ejpam-3274	130	22	case	case	NOUN
ejpam-3274	130	23	4	4	NUM
ejpam-3274	130	24	:	:	PUNCT
ejpam-3274	130	25	if	if	SCONJ
ejpam-3274	130	26	a	a	DET
ejpam-3274	130	27	∈	∈	PROPN
ejpam-3274	130	28	gα	gα	NOUN
ejpam-3274	130	29	,	,	PUNCT
ejpam-3274	130	30	b	b	PROPN
ejpam-3274	130	31	∈	∈	PROPN
ejpam-3274	130	32	qα	qα	PROPN
ejpam-3274	130	33	,	,	PUNCT
ejpam-3274	130	34	then	then	ADV
ejpam-3274	130	35	ab	ab	PROPN
ejpam-3274	130	36	∈	∈	PROPN
ejpam-3274	130	37	gα	gα	NOUN
ejpam-3274	130	38	,	,	PUNCT
ejpam-3274	130	39	similar	similar	ADJ
ejpam-3274	130	40	to	to	ADP
ejpam-3274	130	41	the	the	DET
ejpam-3274	130	42	above	above	ADJ
ejpam-3274	130	43	case	case	NOUN
ejpam-3274	130	44	,	,	PUNCT
ejpam-3274	130	45	(	(	PUNCT
ejpam-3274	130	46	ab)φα	ab)φα	PROPN
ejpam-3274	130	47	,	,	PUNCT
ejpam-3274	130	48	β	β	X
ejpam-3274	130	49	=	=	SYM
ejpam-3274	130	50	(	(	PUNCT
ejpam-3274	130	51	ab)θα	ab)θα	PROPN
ejpam-3274	130	52	,	,	PUNCT
ejpam-3274	130	53	β	β	X
ejpam-3274	130	54	=	=	SYM
ejpam-3274	130	55	(	(	PUNCT
ejpam-3274	130	56	(	(	PUNCT
ejpam-3274	130	57	aeα)b)θα	aeα)b)θα	PROPN
ejpam-3274	130	58	,	,	PUNCT
ejpam-3274	130	59	β	β	X
ejpam-3274	130	60	=	=	SYM
ejpam-3274	130	61	(	(	PUNCT
ejpam-3274	130	62	a(eαb))θα	a(eαb))θα	PROPN
ejpam-3274	130	63	,	,	PUNCT
ejpam-3274	130	64	β	β	X
ejpam-3274	130	65	=	=	SYM
ejpam-3274	130	66	aθα	aθα	PROPN
ejpam-3274	130	67	,	,	PUNCT
ejpam-3274	130	68	β(eαb)θα	β(eαb)θα	VERB
ejpam-3274	130	69	,	,	PUNCT
ejpam-3274	130	70	β	β	X
ejpam-3274	130	71	=	=	SYM
ejpam-3274	130	72	aθα	aθα	PROPN
ejpam-3274	130	73	,	,	PUNCT
ejpam-3274	130	74	β(beα)θα	β(beα)θα	NUM
ejpam-3274	130	75	,	,	PUNCT
ejpam-3274	130	76	β	β	X
ejpam-3274	130	77	(	(	PUNCT
ejpam-3274	130	78	by	by	ADP
ejpam-3274	130	79	lemma	lemma	PROPN
ejpam-3274	130	80	1	1	NUM
ejpam-3274	130	81	)	)	PUNCT
ejpam-3274	130	82	=	=	VERB
ejpam-3274	130	83	aθα	aθα	NOUN
ejpam-3274	130	84	,	,	PUNCT
ejpam-3274	130	85	βbϕα	βbϕα	ADJ
ejpam-3274	130	86	,	,	PUNCT
ejpam-3274	130	87	βeβ	βeβ	NOUN
ejpam-3274	130	88	=	=	PUNCT
ejpam-3274	130	89	aθα	aθα	PROPN
ejpam-3274	130	90	,	,	PUNCT
ejpam-3274	130	91	βbϕα	βbϕα	ADJ
ejpam-3274	130	92	,	,	PUNCT
ejpam-3274	130	93	β	β	X
ejpam-3274	130	94	(	(	PUNCT
ejpam-3274	130	95	by	by	ADP
ejpam-3274	130	96	condition	condition	NOUN
ejpam-3274	130	97	(	(	PUNCT
ejpam-3274	130	98	iii	iii	NOUN
ejpam-3274	130	99	)	)	PUNCT
ejpam-3274	130	100	)	)	PUNCT
ejpam-3274	131	1	=	=	SYM
ejpam-3274	131	2	aφα	aφα	PROPN
ejpam-3274	131	3	,	,	PUNCT
ejpam-3274	131	4	βbφα	βbφα	PROPN
ejpam-3274	131	5	,	,	PUNCT
ejpam-3274	131	6	β	β	X
ejpam-3274	131	7	.	.	PUNCT
ejpam-3274	131	8	case	case	NOUN
ejpam-3274	131	9	5	5	NUM
ejpam-3274	131	10	:	:	PUNCT
ejpam-3274	131	11	if	if	SCONJ
ejpam-3274	131	12	a	a	DET
ejpam-3274	131	13	∈	∈	PROPN
ejpam-3274	131	14	gα	gα	NOUN
ejpam-3274	131	15	,	,	PUNCT
ejpam-3274	131	16	b	b	PROPN
ejpam-3274	131	17	∈	∈	PROPN
ejpam-3274	131	18	gα	gα	NOUN
ejpam-3274	131	19	,	,	PUNCT
ejpam-3274	131	20	then	then	ADV
ejpam-3274	131	21	ab	ab	PROPN
ejpam-3274	131	22	∈	∈	PROPN
ejpam-3274	131	23	gα	gα	NOUN
ejpam-3274	131	24	,	,	PUNCT
ejpam-3274	131	25	by	by	ADP
ejpam-3274	131	26	condition	condition	NOUN
ejpam-3274	131	27	(	(	PUNCT
ejpam-3274	131	28	i	i	NOUN
ejpam-3274	131	29	)	)	PUNCT
ejpam-3274	131	30	,	,	PUNCT
ejpam-3274	131	31	(	(	PUNCT
ejpam-3274	131	32	ab)φα	ab)φα	PROPN
ejpam-3274	131	33	,	,	PUNCT
ejpam-3274	131	34	β	β	X
ejpam-3274	131	35	=	=	SYM
ejpam-3274	131	36	(	(	PUNCT
ejpam-3274	131	37	ab)θα	ab)θα	PROPN
ejpam-3274	131	38	,	,	PUNCT
ejpam-3274	131	39	β	β	X
ejpam-3274	131	40	=	=	SYM
ejpam-3274	131	41	aθα	aθα	PROPN
ejpam-3274	131	42	,	,	PUNCT
ejpam-3274	131	43	βbθα	βbθα	ADP
ejpam-3274	131	44	,	,	PUNCT
ejpam-3274	131	45	β	β	X
ejpam-3274	131	46	=	=	PUNCT
ejpam-3274	131	47	aφα	aφα	PROPN
ejpam-3274	131	48	,	,	PUNCT
ejpam-3274	131	49	βbφα	βbφα	PROPN
ejpam-3274	131	50	,	,	PUNCT
ejpam-3274	131	51	β	β	X
ejpam-3274	131	52	.	.	PUNCT
ejpam-3274	132	1	and	and	CCONJ
ejpam-3274	132	2	so	so	ADV
ejpam-3274	132	3	the	the	DET
ejpam-3274	132	4	mapping	mapping	NOUN
ejpam-3274	132	5	φα	φα	PROPN
ejpam-3274	132	6	,	,	PUNCT
ejpam-3274	132	7	β	β	X
ejpam-3274	132	8	defined	define	VERB
ejpam-3274	132	9	is	be	AUX
ejpam-3274	132	10	a	a	DET
ejpam-3274	132	11	homomorphism	homomorphism	NOUN
ejpam-3274	132	12	from	from	ADP
ejpam-3274	132	13	sα	sα	ADV
ejpam-3274	132	14	to	to	ADP
ejpam-3274	132	15	sβ	sβ	PROPN
ejpam-3274	132	16	.	.	PUNCT
ejpam-3274	133	1	by	by	ADP
ejpam-3274	133	2	condition	condition	NOUN
ejpam-3274	133	3	(	(	PUNCT
ejpam-3274	133	4	i	i	NOUN
ejpam-3274	133	5	)	)	PUNCT
ejpam-3274	133	6	,	,	PUNCT
ejpam-3274	133	7	(	(	PUNCT
ejpam-3274	133	8	ii)(1	ii)(1	NOUN
ejpam-3274	133	9	)	)	PUNCT
ejpam-3274	133	10	and	and	CCONJ
ejpam-3274	133	11	the	the	DET
ejpam-3274	133	12	definition	definition	NOUN
ejpam-3274	133	13	of	of	ADP
ejpam-3274	133	14	φα	φα	PROPN
ejpam-3274	133	15	,	,	PUNCT
ejpam-3274	133	16	β	β	PROPN
ejpam-3274	133	17	,	,	PUNCT
ejpam-3274	133	18	it	it	PRON
ejpam-3274	133	19	is	be	AUX
ejpam-3274	133	20	clear	clear	ADJ
ejpam-3274	133	21	that	that	SCONJ
ejpam-3274	133	22	φα	φα	PROPN
ejpam-3274	133	23	,	,	PUNCT
ejpam-3274	133	24	α	α	NOUN
ejpam-3274	133	25	=	=	SYM
ejpam-3274	133	26	1sα	1sα	NOUN
ejpam-3274	133	27	.	.	PUNCT
ejpam-3274	134	1	for	for	ADP
ejpam-3274	134	2	any	any	DET
ejpam-3274	134	3	α	α	NOUN
ejpam-3274	134	4	,	,	PUNCT
ejpam-3274	134	5	β	β	X
ejpam-3274	134	6	,	,	PUNCT
ejpam-3274	134	7	γ	γ	PROPN
ejpam-3274	134	8	∈	∈	PROPN
ejpam-3274	134	9	y	y	PROPN
ejpam-3274	134	10	with	with	ADP
ejpam-3274	134	11	α	α	PROPN
ejpam-3274	134	12	≥	≥	PROPN
ejpam-3274	134	13	β	β	X
ejpam-3274	134	14	≥	≥	PROPN
ejpam-3274	134	15	γ	γ	X
ejpam-3274	134	16	,	,	PUNCT
ejpam-3274	134	17	let	let	VERB
ejpam-3274	134	18	a	a	DET
ejpam-3274	134	19	∈	∈	ADJ
ejpam-3274	134	20	qα	qα	PROPN
ejpam-3274	134	21	.	.	PUNCT
ejpam-3274	135	1	if	if	SCONJ
ejpam-3274	135	2	aϕα	aϕα	PROPN
ejpam-3274	135	3	,	,	PUNCT
ejpam-3274	135	4	β	β	X
ejpam-3274	135	5	∈	∈	PROPN
ejpam-3274	135	6	qβ	qβ	X
ejpam-3274	135	7	,	,	PUNCT
ejpam-3274	135	8	by	by	ADP
ejpam-3274	135	9	condition	condition	NOUN
ejpam-3274	135	10	(	(	PUNCT
ejpam-3274	135	11	ii)(3	ii)(3	NOUN
ejpam-3274	135	12	)	)	PUNCT
ejpam-3274	135	13	,	,	PUNCT
ejpam-3274	135	14	aφα	aφα	PROPN
ejpam-3274	135	15	,	,	PUNCT
ejpam-3274	135	16	βφβ	βφβ	NOUN
ejpam-3274	135	17	,	,	PUNCT
ejpam-3274	135	18	γ	γ	NOUN
ejpam-3274	135	19	=	=	SYM
ejpam-3274	135	20	aϕα	aϕα	PROPN
ejpam-3274	135	21	,	,	PUNCT
ejpam-3274	135	22	βφβ	βφβ	NOUN
ejpam-3274	135	23	,	,	PUNCT
ejpam-3274	135	24	γ	γ	NOUN
ejpam-3274	135	25	=	=	SYM
ejpam-3274	135	26	aϕα	aϕα	PROPN
ejpam-3274	135	27	,	,	PUNCT
ejpam-3274	135	28	βϕβ	βϕβ	PROPN
ejpam-3274	135	29	,	,	PUNCT
ejpam-3274	135	30	γ	γ	PROPN
ejpam-3274	135	31	=	=	SYM
ejpam-3274	135	32	aϕα	aϕα	PROPN
ejpam-3274	135	33	,	,	PUNCT
ejpam-3274	135	34	γ	γ	PROPN
ejpam-3274	135	35	=	=	SYM
ejpam-3274	135	36	aφα	aφα	PROPN
ejpam-3274	135	37	,	,	PUNCT
ejpam-3274	135	38	γ	γ	X
ejpam-3274	135	39	.	.	PUNCT
ejpam-3274	136	1	if	if	SCONJ
ejpam-3274	136	2	a	a	DET
ejpam-3274	136	3	∈	∈	PROPN
ejpam-3274	136	4	qα	qα	PROPN
ejpam-3274	136	5	and	and	CCONJ
ejpam-3274	136	6	aϕα	aϕα	PROPN
ejpam-3274	136	7	,	,	PUNCT
ejpam-3274	136	8	β	β	X
ejpam-3274	136	9	/∈	/∈	PUNCT
ejpam-3274	137	1	qβ	qβ	PROPN
ejpam-3274	137	2	,	,	PUNCT
ejpam-3274	137	3	then	then	ADV
ejpam-3274	137	4	aϕα	aϕα	PROPN
ejpam-3274	137	5	,	,	PUNCT
ejpam-3274	137	6	γ	γ	X
ejpam-3274	137	7	/∈	/∈	PROPN
ejpam-3274	137	8	qγ	qγ	NOUN
ejpam-3274	137	9	by	by	ADP
ejpam-3274	137	10	condition	condition	NOUN
ejpam-3274	137	11	(	(	PUNCT
ejpam-3274	137	12	ii)(3	ii)(3	NOUN
ejpam-3274	137	13	)	)	PUNCT
ejpam-3274	137	14	,	,	PUNCT
ejpam-3274	137	15	aφα	aφα	PROPN
ejpam-3274	137	16	,	,	PUNCT
ejpam-3274	137	17	βφβ	βφβ	NOUN
ejpam-3274	137	18	,	,	PUNCT
ejpam-3274	137	19	γ	γ	NOUN
ejpam-3274	137	20	=	=	SYM
ejpam-3274	137	21	aϕα	aϕα	PROPN
ejpam-3274	137	22	,	,	PUNCT
ejpam-3274	137	23	βθβ	βθβ	NOUN
ejpam-3274	137	24	,	,	PUNCT
ejpam-3274	137	25	γ	γ	X
ejpam-3274	137	26	=	=	SYM
ejpam-3274	137	27	(	(	PUNCT
ejpam-3274	137	28	aϕα	aϕα	PROPN
ejpam-3274	137	29	,	,	PUNCT
ejpam-3274	137	30	βeβ)θβ	βeβ)θβ	NOUN
ejpam-3274	137	31	,	,	PUNCT
ejpam-3274	137	32	γ	γ	X
ejpam-3274	137	33	=	=	SYM
ejpam-3274	137	34	(	(	PUNCT
ejpam-3274	137	35	aψθα	aψθα	NOUN
ejpam-3274	137	36	,	,	PUNCT
ejpam-3274	137	37	β)θβ	β)θβ	PROPN
ejpam-3274	137	38	,	,	PUNCT
ejpam-3274	137	39	γ	γ	NOUN
ejpam-3274	137	40	=	=	X
ejpam-3274	137	41	(	(	PUNCT
ejpam-3274	137	42	aeα)θα	aeα)θα	ADV
ejpam-3274	137	43	,	,	PUNCT
ejpam-3274	137	44	βθβ	βθβ	NOUN
ejpam-3274	137	45	,	,	PUNCT
ejpam-3274	137	46	γ	γ	X
ejpam-3274	137	47	(	(	PUNCT
ejpam-3274	137	48	by	by	ADP
ejpam-3274	137	49	condition	condition	NOUN
ejpam-3274	137	50	(	(	PUNCT
ejpam-3274	137	51	iii	iii	NOUN
ejpam-3274	137	52	)	)	PUNCT
ejpam-3274	137	53	)	)	PUNCT
ejpam-3274	138	1	=	=	PRON
ejpam-3274	138	2	(	(	PUNCT
ejpam-3274	138	3	aeα)θα	aeα)θα	ADV
ejpam-3274	138	4	,	,	PUNCT
ejpam-3274	138	5	γ	γ	X
ejpam-3274	138	6	=	=	SYM
ejpam-3274	138	7	(	(	PUNCT
ejpam-3274	138	8	aψ)θα	aψ)θα	PROPN
ejpam-3274	138	9	,	,	PUNCT
ejpam-3274	138	10	γ	γ	NOUN
ejpam-3274	138	11	=	=	SYM
ejpam-3274	138	12	aϕα	aϕα	PROPN
ejpam-3274	138	13	,	,	PUNCT
ejpam-3274	138	14	γψ	γψ	ADV
ejpam-3274	138	15	(	(	PUNCT
ejpam-3274	138	16	by	by	ADP
ejpam-3274	138	17	condition	condition	NOUN
ejpam-3274	138	18	(	(	PUNCT
ejpam-3274	138	19	i	i	NOUN
ejpam-3274	138	20	)	)	PUNCT
ejpam-3274	138	21	,	,	PUNCT
ejpam-3274	138	22	(	(	PUNCT
ejpam-3274	138	23	iii	iii	NOUN
ejpam-3274	138	24	)	)	PUNCT
ejpam-3274	138	25	)	)	PUNCT
ejpam-3274	138	26	=	=	SYM
ejpam-3274	138	27	aϕα	aϕα	PROPN
ejpam-3274	138	28	,	,	PUNCT
ejpam-3274	138	29	γeγ	γeγ	NOUN
ejpam-3274	138	30	=	=	SYM
ejpam-3274	138	31	aϕα	aϕα	PROPN
ejpam-3274	138	32	,	,	PUNCT
ejpam-3274	138	33	γ	γ	PROPN
ejpam-3274	138	34	=	=	SYM
ejpam-3274	138	35	aφα	aφα	PROPN
ejpam-3274	138	36	,	,	PUNCT
ejpam-3274	138	37	γ	γ	X
ejpam-3274	138	38	.	.	PUNCT
ejpam-3274	139	1	j.	j.	PROPN
ejpam-3274	139	2	zhang	zhang	PROPN
ejpam-3274	139	3	,	,	PUNCT
ejpam-3274	139	4	y.	y.	PROPN
ejpam-3274	139	5	yang	yang	PROPN
ejpam-3274	139	6	,	,	PUNCT
ejpam-3274	139	7	r.	r.	PROPN
ejpam-3274	139	8	shen	shen	PROPN
ejpam-3274	139	9	/	/	SYM
ejpam-3274	139	10	eur	eur	PROPN
ejpam-3274	139	11	.	.	PUNCT
ejpam-3274	140	1	j.	j.	PROPN
ejpam-3274	140	2	pure	pure	PROPN
ejpam-3274	140	3	appl	appl	PROPN
ejpam-3274	140	4	.	.	PROPN
ejpam-3274	140	5	math	math	PROPN
ejpam-3274	140	6	,	,	PUNCT
ejpam-3274	140	7	11	11	NUM
ejpam-3274	140	8	(	(	PUNCT
ejpam-3274	140	9	3	3	NUM
ejpam-3274	140	10	)	)	PUNCT
ejpam-3274	140	11	(	(	PUNCT
ejpam-3274	140	12	2018	2018	NUM
ejpam-3274	140	13	)	)	PUNCT
ejpam-3274	140	14	,	,	PUNCT
ejpam-3274	140	15	589	589	NUM
ejpam-3274	140	16	-	-	SYM
ejpam-3274	140	17	597	597	NUM
ejpam-3274	140	18	594	594	NUM
ejpam-3274	140	19	let	let	VERB
ejpam-3274	140	20	a	a	DET
ejpam-3274	140	21	∈	∈	PROPN
ejpam-3274	141	1	gα	gα	PROPN
ejpam-3274	141	2	.	.	PUNCT
ejpam-3274	141	3	aφα	aφα	PROPN
ejpam-3274	141	4	,	,	PUNCT
ejpam-3274	141	5	βφβ	βφβ	NOUN
ejpam-3274	141	6	,	,	PUNCT
ejpam-3274	141	7	γ	γ	NOUN
ejpam-3274	141	8	=	=	SYM
ejpam-3274	141	9	aθα	aθα	PROPN
ejpam-3274	141	10	,	,	PUNCT
ejpam-3274	141	11	βφβ	βφβ	NOUN
ejpam-3274	141	12	,	,	PUNCT
ejpam-3274	141	13	γ	γ	NOUN
ejpam-3274	141	14	=	=	SYM
ejpam-3274	141	15	aθα	aθα	PROPN
ejpam-3274	141	16	,	,	PUNCT
ejpam-3274	141	17	βθβ	βθβ	NOUN
ejpam-3274	141	18	,	,	PUNCT
ejpam-3274	141	19	γ	γ	PROPN
ejpam-3274	141	20	=	=	SYM
ejpam-3274	141	21	aθα	aθα	PROPN
ejpam-3274	141	22	,	,	PUNCT
ejpam-3274	141	23	γ	γ	PROPN
ejpam-3274	141	24	=	=	SYM
ejpam-3274	141	25	aφα	aφα	PROPN
ejpam-3274	141	26	,	,	PUNCT
ejpam-3274	141	27	γ	γ	X
ejpam-3274	141	28	.	.	PUNCT
ejpam-3274	142	1	now	now	ADV
ejpam-3274	142	2	we	we	PRON
ejpam-3274	142	3	consider	consider	VERB
ejpam-3274	142	4	the	the	DET
ejpam-3274	142	5	multiplication	multiplication	NOUN
ejpam-3274	142	6	on	on	ADP
ejpam-3274	142	7	s.	s.	PROPN
ejpam-3274	142	8	for	for	ADP
ejpam-3274	142	9	any	any	DET
ejpam-3274	142	10	α	α	NOUN
ejpam-3274	142	11	,	,	PUNCT
ejpam-3274	142	12	β	β	X
ejpam-3274	142	13	∈	∈	PROPN
ejpam-3274	142	14	y	y	PROPN
ejpam-3274	142	15	,	,	PUNCT
ejpam-3274	142	16	suppose	suppose	VERB
ejpam-3274	142	17	that	that	SCONJ
ejpam-3274	142	18	a	a	DET
ejpam-3274	142	19	∈	∈	PROPN
ejpam-3274	142	20	sα	sα	NOUN
ejpam-3274	142	21	and	and	CCONJ
ejpam-3274	142	22	b	b	X
ejpam-3274	142	23	∈	∈	PROPN
ejpam-3274	142	24	sβ	sβ	PROPN
ejpam-3274	142	25	.	.	PUNCT
ejpam-3274	142	26	case	case	NOUN
ejpam-3274	143	1	i	i	PRON
ejpam-3274	143	2	:	:	PUNCT
ejpam-3274	143	3	if	if	SCONJ
ejpam-3274	143	4	a	a	DET
ejpam-3274	143	5	∈	∈	PROPN
ejpam-3274	143	6	qα	qα	PROPN
ejpam-3274	143	7	,	,	PUNCT
ejpam-3274	143	8	b	b	PROPN
ejpam-3274	143	9	∈	∈	PROPN
ejpam-3274	143	10	qβ	qβ	X
ejpam-3274	143	11	,	,	PUNCT
ejpam-3274	143	12	and	and	CCONJ
ejpam-3274	143	13	ab	ab	PROPN
ejpam-3274	143	14	∈	∈	PROPN
ejpam-3274	143	15	qαβ	qαβ	PROPN
ejpam-3274	143	16	,	,	PUNCT
ejpam-3274	143	17	then	then	ADV
ejpam-3274	143	18	by	by	ADP
ejpam-3274	143	19	condition	condition	NOUN
ejpam-3274	143	20	(	(	PUNCT
ejpam-3274	143	21	ii)(4	ii)(4	NOUN
ejpam-3274	143	22	)	)	PUNCT
ejpam-3274	143	23	,	,	PUNCT
ejpam-3274	143	24	ab	ab	PROPN
ejpam-3274	143	25	=	=	PROPN
ejpam-3274	143	26	aϕα	aϕα	PROPN
ejpam-3274	143	27	,	,	PUNCT
ejpam-3274	143	28	αβbϕβ	αβbϕβ	NOUN
ejpam-3274	143	29	,	,	PUNCT
ejpam-3274	143	30	αβ	αβ	PROPN
ejpam-3274	143	31	=	=	X
ejpam-3274	143	32	aφα	aφα	PROPN
ejpam-3274	143	33	,	,	PUNCT
ejpam-3274	143	34	αβbφβ	αβbφβ	NOUN
ejpam-3274	143	35	,	,	PUNCT
ejpam-3274	143	36	αβ	αβ	INTJ
ejpam-3274	143	37	.	.	PUNCT
ejpam-3274	144	1	case	case	NOUN
ejpam-3274	144	2	ii	ii	NOUN
ejpam-3274	144	3	:	:	PUNCT
ejpam-3274	144	4	if	if	SCONJ
ejpam-3274	144	5	a	a	DET
ejpam-3274	144	6	∈	∈	PROPN
ejpam-3274	144	7	qα	qα	PROPN
ejpam-3274	144	8	,	,	PUNCT
ejpam-3274	144	9	b	b	PROPN
ejpam-3274	144	10	∈	∈	PROPN
ejpam-3274	144	11	qβ	qβ	X
ejpam-3274	144	12	,	,	PUNCT
ejpam-3274	144	13	and	and	CCONJ
ejpam-3274	144	14	ab	ab	PROPN
ejpam-3274	144	15	∈	∈	PROPN
ejpam-3274	144	16	gαβ	gαβ	PROPN
ejpam-3274	144	17	,	,	PUNCT
ejpam-3274	144	18	then	then	ADV
ejpam-3274	144	19	ab	ab	PROPN
ejpam-3274	144	20	=	=	PUNCT
ejpam-3274	144	21	(	(	PUNCT
ejpam-3274	144	22	ab)eαβ	ab)eαβ	X
ejpam-3274	144	23	=	=	SYM
ejpam-3274	144	24	a(beαβ	a(beαβ	PROPN
ejpam-3274	144	25	)	)	PUNCT
ejpam-3274	144	26	=	=	SYM
ejpam-3274	144	27	aeαβ(beαβ	aeαβ(beαβ	PROPN
ejpam-3274	144	28	)	)	PUNCT
ejpam-3274	144	29	(	(	PUNCT
ejpam-3274	144	30	since	since	SCONJ
ejpam-3274	144	31	regs	reg	NOUN
ejpam-3274	144	32	is	be	AUX
ejpam-3274	144	33	an	an	DET
ejpam-3274	144	34	ideal	ideal	NOUN
ejpam-3274	144	35	of	of	ADP
ejpam-3274	144	36	s	s	NOUN
ejpam-3274	144	37	)	)	PUNCT
ejpam-3274	145	1	=	=	NOUN
ejpam-3274	145	2	aeαeαβbeβeαβ	aeαeαβbeβeαβ	NOUN
ejpam-3274	145	3	=	=	SYM
ejpam-3274	145	4	(	(	PUNCT
ejpam-3274	145	5	aeα)eαβ(beβ)eαβ	aeα)eαβ(beβ)eαβ	NOUN
ejpam-3274	145	6	=	=	SYM
ejpam-3274	145	7	(	(	PUNCT
ejpam-3274	145	8	aeα)θα	aeα)θα	ADV
ejpam-3274	145	9	,	,	PUNCT
ejpam-3274	145	10	αβ(beβ)θβ	αβ(beβ)θβ	PROPN
ejpam-3274	145	11	,	,	PUNCT
ejpam-3274	145	12	αβ	αβ	PRON
ejpam-3274	145	13	(	(	PUNCT
ejpam-3274	145	14	since	since	SCONJ
ejpam-3274	145	15	regs	reg	NOUN
ejpam-3274	145	16	is	be	AUX
ejpam-3274	145	17	a	a	DET
ejpam-3274	145	18	clifford	clifford	PROPN
ejpam-3274	145	19	subsemigroup	subsemigroup	NOUN
ejpam-3274	145	20	)	)	PUNCT
ejpam-3274	146	1	=	=	PRON
ejpam-3274	146	2	(	(	PUNCT
ejpam-3274	146	3	aψθα	aψθα	NOUN
ejpam-3274	146	4	,	,	PUNCT
ejpam-3274	146	5	αβ)(bψθβ	αβ)(bψθβ	NOUN
ejpam-3274	146	6	,	,	PUNCT
ejpam-3274	146	7	αβ	αβ	X
ejpam-3274	146	8	)	)	PUNCT
ejpam-3274	146	9	=	=	SYM
ejpam-3274	146	10	(	(	PUNCT
ejpam-3274	146	11	aϕα	aϕα	PROPN
ejpam-3274	146	12	,	,	PUNCT
ejpam-3274	146	13	αβeαβ)(bϕβ	αβeαβ)(bϕβ	NUM
ejpam-3274	146	14	,	,	PUNCT
ejpam-3274	146	15	αβeαβ	αβeαβ	NOUN
ejpam-3274	146	16	)	)	PUNCT
ejpam-3274	146	17	(	(	PUNCT
ejpam-3274	146	18	by	by	ADP
ejpam-3274	146	19	condition	condition	NOUN
ejpam-3274	146	20	(	(	PUNCT
ejpam-3274	146	21	iii	iii	NOUN
ejpam-3274	146	22	)	)	PUNCT
ejpam-3274	146	23	)	)	PUNCT
ejpam-3274	147	1	=	=	SYM
ejpam-3274	147	2	aϕα	aϕα	PROPN
ejpam-3274	147	3	,	,	PUNCT
ejpam-3274	147	4	αβ(eαβbϕβ	αβ(eαβbϕβ	NOUN
ejpam-3274	147	5	,	,	PUNCT
ejpam-3274	147	6	αβeαβ	αβeαβ	NOUN
ejpam-3274	147	7	)	)	PUNCT
ejpam-3274	147	8	=	=	SYM
ejpam-3274	147	9	aϕα	aϕα	PROPN
ejpam-3274	147	10	,	,	PUNCT
ejpam-3274	147	11	αβbϕβ	αβbϕβ	NOUN
ejpam-3274	147	12	,	,	PUNCT
ejpam-3274	147	13	αβeαβ	αβeαβ	NOUN
ejpam-3274	147	14	=	=	SYM
ejpam-3274	147	15	aϕα	aϕα	PROPN
ejpam-3274	147	16	,	,	PUNCT
ejpam-3274	147	17	αβbϕβ	αβbϕβ	NOUN
ejpam-3274	147	18	,	,	PUNCT
ejpam-3274	147	19	αβ	αβ	INTJ
ejpam-3274	147	20	(	(	PUNCT
ejpam-3274	147	21	by	by	ADP
ejpam-3274	147	22	condition	condition	NOUN
ejpam-3274	147	23	(	(	PUNCT
ejpam-3274	147	24	ii)(2	ii)(2	NOUN
ejpam-3274	147	25	)	)	PUNCT
ejpam-3274	147	26	)	)	PUNCT
ejpam-3274	147	27	=	=	PUNCT
ejpam-3274	147	28	aφα	aφα	PROPN
ejpam-3274	147	29	,	,	PUNCT
ejpam-3274	147	30	αβbφβ	αβbφβ	NOUN
ejpam-3274	147	31	,	,	PUNCT
ejpam-3274	147	32	αβ	αβ	INTJ
ejpam-3274	147	33	.	.	PUNCT
ejpam-3274	148	1	case	case	NOUN
ejpam-3274	148	2	iii	iii	X
ejpam-3274	148	3	:	:	PUNCT
ejpam-3274	148	4	if	if	SCONJ
ejpam-3274	148	5	a	a	DET
ejpam-3274	148	6	∈	∈	PROPN
ejpam-3274	148	7	qα	qα	PROPN
ejpam-3274	148	8	,	,	PUNCT
ejpam-3274	148	9	b	b	X
ejpam-3274	148	10	∈	∈	PROPN
ejpam-3274	148	11	gβ	gβ	NOUN
ejpam-3274	148	12	,	,	PUNCT
ejpam-3274	148	13	then	then	ADV
ejpam-3274	148	14	ab	ab	PROPN
ejpam-3274	148	15	∈	∈	PROPN
ejpam-3274	148	16	gαβ	gαβ	PROPN
ejpam-3274	148	17	by	by	ADP
ejpam-3274	148	18	condition	condition	NOUN
ejpam-3274	148	19	(	(	PUNCT
ejpam-3274	148	20	i	i	NOUN
ejpam-3274	148	21	)	)	PUNCT
ejpam-3274	148	22	,	,	PUNCT
ejpam-3274	148	23	and	and	CCONJ
ejpam-3274	148	24	ab	ab	PROPN
ejpam-3274	148	25	=	=	SYM
ejpam-3274	148	26	(	(	PUNCT
ejpam-3274	148	27	ab)eαβ	ab)eαβ	X
ejpam-3274	148	28	=	=	SYM
ejpam-3274	148	29	aeαβ(beαβ	aeαβ(beαβ	PROPN
ejpam-3274	148	30	)	)	PUNCT
ejpam-3274	148	31	=	=	PRON
ejpam-3274	148	32	(	(	PUNCT
ejpam-3274	148	33	aeαeαβ)beαβ	aeαeαβ)beαβ	X
ejpam-3274	148	34	=	=	SYM
ejpam-3274	148	35	(	(	PUNCT
ejpam-3274	148	36	aeα)θα	aeα)θα	ADV
ejpam-3274	148	37	,	,	PUNCT
ejpam-3274	148	38	αβbθβ	αβbθβ	ADV
ejpam-3274	148	39	,	,	PUNCT
ejpam-3274	148	40	αβ	αβ	INTJ
ejpam-3274	148	41	=	=	SYM
ejpam-3274	148	42	(	(	PUNCT
ejpam-3274	148	43	aψθα	aψθα	NOUN
ejpam-3274	148	44	,	,	PUNCT
ejpam-3274	148	45	αβ)bθβ	αβ)bθβ	NOUN
ejpam-3274	148	46	,	,	PUNCT
ejpam-3274	148	47	αβ	αβ	NOUN
ejpam-3274	148	48	=	=	SYM
ejpam-3274	148	49	(	(	PUNCT
ejpam-3274	148	50	aϕα	aϕα	PROPN
ejpam-3274	148	51	,	,	PUNCT
ejpam-3274	148	52	αβψ)bθβ	αβψ)bθβ	NOUN
ejpam-3274	148	53	,	,	PUNCT
ejpam-3274	148	54	αβ	αβ	NOUN
ejpam-3274	148	55	=	=	SYM
ejpam-3274	148	56	aϕα	aϕα	PROPN
ejpam-3274	148	57	,	,	PUNCT
ejpam-3274	148	58	αβeαβbθβ	αβeαβbθβ	NOUN
ejpam-3274	148	59	,	,	PUNCT
ejpam-3274	148	60	αβ	αβ	INTJ
ejpam-3274	148	61	(	(	PUNCT
ejpam-3274	148	62	by	by	ADP
ejpam-3274	148	63	condition	condition	NOUN
ejpam-3274	148	64	(	(	PUNCT
ejpam-3274	148	65	iii	iii	NOUN
ejpam-3274	148	66	)	)	PUNCT
ejpam-3274	148	67	)	)	PUNCT
ejpam-3274	149	1	=	=	SYM
ejpam-3274	149	2	aϕα	aϕα	NOUN
ejpam-3274	149	3	,	,	PUNCT
ejpam-3274	149	4	αβbθβ	αβbθβ	ADV
ejpam-3274	149	5	,	,	PUNCT
ejpam-3274	149	6	αβ	αβ	PROPN
ejpam-3274	149	7	=	=	PUNCT
ejpam-3274	149	8	aφα	aφα	PROPN
ejpam-3274	149	9	,	,	PUNCT
ejpam-3274	149	10	αβbφβ	αβbφβ	NOUN
ejpam-3274	149	11	,	,	PUNCT
ejpam-3274	149	12	αβ	αβ	INTJ
ejpam-3274	149	13	.	.	PUNCT
ejpam-3274	150	1	case	case	NOUN
ejpam-3274	150	2	iv	iv	ADP
ejpam-3274	150	3	:	:	PUNCT
ejpam-3274	150	4	if	if	SCONJ
ejpam-3274	150	5	a	a	DET
ejpam-3274	150	6	∈	∈	PROPN
ejpam-3274	150	7	gα	gα	NOUN
ejpam-3274	150	8	,	,	PUNCT
ejpam-3274	150	9	b	b	PROPN
ejpam-3274	150	10	∈	∈	PROPN
ejpam-3274	150	11	qβ	qβ	PROPN
ejpam-3274	150	12	,	,	PUNCT
ejpam-3274	150	13	ab	ab	PROPN
ejpam-3274	150	14	∈	∈	PROPN
ejpam-3274	150	15	gαβ	gαβ	PROPN
ejpam-3274	150	16	,	,	PUNCT
ejpam-3274	150	17	then	then	ADV
ejpam-3274	150	18	similar	similar	ADJ
ejpam-3274	150	19	to	to	ADP
ejpam-3274	150	20	the	the	DET
ejpam-3274	150	21	above	above	ADJ
ejpam-3274	150	22	case	case	NOUN
ejpam-3274	150	23	ab	ab	X
ejpam-3274	150	24	=	=	SYM
ejpam-3274	150	25	(	(	PUNCT
ejpam-3274	150	26	ab)eαβ	ab)eαβ	X
ejpam-3274	150	27	=	=	SYM
ejpam-3274	150	28	aeαβ(beαβ	aeαβ(beαβ	PROPN
ejpam-3274	150	29	)	)	PUNCT
ejpam-3274	150	30	=	=	PRON
ejpam-3274	150	31	aeαβbeβeαβ	aeαβbeβeαβ	NOUN
ejpam-3274	150	32	=	=	SYM
ejpam-3274	150	33	aθα	aθα	NOUN
ejpam-3274	150	34	,	,	PUNCT
ejpam-3274	150	35	αβ(beβ)θβ	αβ(beβ)θβ	PROPN
ejpam-3274	150	36	,	,	PUNCT
ejpam-3274	150	37	αβ	αβ	NOUN
ejpam-3274	150	38	=	=	NOUN
ejpam-3274	150	39	aθα	aθα	PROPN
ejpam-3274	150	40	,	,	PUNCT
ejpam-3274	150	41	αβ(bψθβ	αβ(bψθβ	PROPN
ejpam-3274	150	42	,	,	PUNCT
ejpam-3274	150	43	αβ	αβ	X
ejpam-3274	150	44	)	)	PUNCT
ejpam-3274	150	45	=	=	SYM
ejpam-3274	150	46	aθα	aθα	NOUN
ejpam-3274	150	47	,	,	PUNCT
ejpam-3274	150	48	αβ(bϕβ	αβ(bϕβ	NOUN
ejpam-3274	150	49	,	,	PUNCT
ejpam-3274	150	50	αβψ	αβψ	NOUN
ejpam-3274	150	51	)	)	PUNCT
ejpam-3274	150	52	=	=	SYM
ejpam-3274	150	53	aθα	aθα	NOUN
ejpam-3274	150	54	,	,	PUNCT
ejpam-3274	150	55	αβbϕβ	αβbϕβ	NOUN
ejpam-3274	150	56	,	,	PUNCT
ejpam-3274	150	57	αβeαβ	αβeαβ	NOUN
ejpam-3274	150	58	(	(	PUNCT
ejpam-3274	150	59	by	by	ADP
ejpam-3274	150	60	condition	condition	NOUN
ejpam-3274	150	61	(	(	PUNCT
ejpam-3274	150	62	iii	iii	NOUN
ejpam-3274	150	63	)	)	PUNCT
ejpam-3274	150	64	)	)	PUNCT
ejpam-3274	150	65	=	=	SYM
ejpam-3274	150	66	aθα	aθα	PROPN
ejpam-3274	150	67	,	,	PUNCT
ejpam-3274	150	68	αβbϕβ	αβbϕβ	NOUN
ejpam-3274	150	69	,	,	PUNCT
ejpam-3274	150	70	αβ	αβ	PROPN
ejpam-3274	150	71	=	=	X
ejpam-3274	150	72	aφα	aφα	PROPN
ejpam-3274	150	73	,	,	PUNCT
ejpam-3274	150	74	αβbφβ	αβbφβ	NOUN
ejpam-3274	150	75	,	,	PUNCT
ejpam-3274	150	76	αβ	αβ	INTJ
ejpam-3274	150	77	.	.	PUNCT
ejpam-3274	151	1	case	case	NOUN
ejpam-3274	151	2	v	v	ADP
ejpam-3274	151	3	:	:	PUNCT
ejpam-3274	151	4	if	if	SCONJ
ejpam-3274	151	5	a	a	DET
ejpam-3274	151	6	∈	∈	PROPN
ejpam-3274	151	7	gα	gα	NOUN
ejpam-3274	151	8	,	,	PUNCT
ejpam-3274	151	9	b	b	PROPN
ejpam-3274	151	10	∈	∈	PROPN
ejpam-3274	151	11	gβ	gβ	NOUN
ejpam-3274	151	12	,	,	PUNCT
ejpam-3274	151	13	then	then	ADV
ejpam-3274	151	14	ab	ab	PROPN
ejpam-3274	151	15	∈	∈	PROPN
ejpam-3274	151	16	gαβ	gαβ	PROPN
ejpam-3274	151	17	,	,	PUNCT
ejpam-3274	151	18	since	since	SCONJ
ejpam-3274	151	19	regs	reg	NOUN
ejpam-3274	151	20	is	be	AUX
ejpam-3274	151	21	a	a	DET
ejpam-3274	151	22	clifford	clifford	PROPN
ejpam-3274	151	23	subsemigroup	subsemigroup	NOUN
ejpam-3274	151	24	of	of	ADP
ejpam-3274	151	25	s	s	PROPN
ejpam-3274	151	26	,	,	PUNCT
ejpam-3274	151	27	ab	ab	PROPN
ejpam-3274	151	28	=	=	PUNCT
ejpam-3274	151	29	aθα	aθα	PROPN
ejpam-3274	151	30	,	,	PUNCT
ejpam-3274	151	31	αβbθβ	αβbθβ	ADV
ejpam-3274	151	32	,	,	PUNCT
ejpam-3274	151	33	αβ	αβ	PROPN
ejpam-3274	151	34	=	=	PUNCT
ejpam-3274	151	35	aφα	aφα	PROPN
ejpam-3274	151	36	,	,	PUNCT
ejpam-3274	151	37	αβbφβ	αβbφβ	NOUN
ejpam-3274	151	38	,	,	PUNCT
ejpam-3274	151	39	αβ	αβ	INTJ
ejpam-3274	151	40	.	.	PUNCT
ejpam-3274	152	1	by	by	ADP
ejpam-3274	152	2	now	now	ADV
ejpam-3274	152	3	we	we	PRON
ejpam-3274	152	4	have	have	AUX
ejpam-3274	152	5	proved	prove	VERB
ejpam-3274	152	6	that	that	SCONJ
ejpam-3274	152	7	gv	gv	NOUN
ejpam-3274	152	8	-	-	ADJ
ejpam-3274	152	9	inverse	inverse	ADJ
ejpam-3274	152	10	semigroup	semigroup	NOUN
ejpam-3274	152	11	s	s	PART
ejpam-3274	152	12	is	be	AUX
ejpam-3274	152	13	a	a	DET
ejpam-3274	152	14	strong	strong	ADJ
ejpam-3274	152	15	semilattice	semilattice	NOUN
ejpam-3274	152	16	of	of	ADP
ejpam-3274	152	17	π	π	NOUN
ejpam-3274	152	18	-	-	NOUN
ejpam-3274	152	19	groups	group	NOUN
ejpam-3274	152	20	if	if	SCONJ
ejpam-3274	152	21	it	it	PRON
ejpam-3274	152	22	satisfies	satisfy	VERB
ejpam-3274	152	23	the	the	DET
ejpam-3274	152	24	conditions	condition	NOUN
ejpam-3274	152	25	.	.	PUNCT
ejpam-3274	153	1	conversely	conversely	ADV
ejpam-3274	153	2	,	,	PUNCT
ejpam-3274	153	3	suppose	suppose	VERB
ejpam-3274	153	4	that	that	SCONJ
ejpam-3274	153	5	gv	gv	NOUN
ejpam-3274	153	6	-	-	ADJ
ejpam-3274	153	7	inverse	inverse	ADJ
ejpam-3274	153	8	semigroup	semigroup	NOUN
ejpam-3274	153	9	s	s	PART
ejpam-3274	153	10	is	be	AUX
ejpam-3274	153	11	a	a	DET
ejpam-3274	153	12	strong	strong	ADJ
ejpam-3274	153	13	semilattice	semilattice	NOUN
ejpam-3274	153	14	of	of	ADP
ejpam-3274	153	15	π	π	NOUN
ejpam-3274	153	16	-	-	NOUN
ejpam-3274	153	17	groups	group	NOUN
ejpam-3274	153	18	,	,	PUNCT
ejpam-3274	153	19	denoted	denote	VERB
ejpam-3274	153	20	by	by	ADP
ejpam-3274	153	21	s[y	s[y	NUM
ejpam-3274	153	22	;	;	PUNCT
ejpam-3274	153	23	sα	sα	X
ejpam-3274	153	24	,	,	PUNCT
ejpam-3274	153	25	φα	φα	ADP
ejpam-3274	153	26	,	,	PUNCT
ejpam-3274	153	27	β	β	NOUN
ejpam-3274	153	28	]	]	X
ejpam-3274	153	29	.	.	PUNCT
ejpam-3274	154	1	for	for	ADP
ejpam-3274	154	2	any	any	DET
ejpam-3274	154	3	α	α	NOUN
ejpam-3274	154	4	,	,	PUNCT
ejpam-3274	154	5	β	β	X
ejpam-3274	154	6	∈	∈	PROPN
ejpam-3274	154	7	y	y	PROPN
ejpam-3274	154	8	and	and	CCONJ
ejpam-3274	154	9	a	a	DET
ejpam-3274	154	10	∈	∈	PROPN
ejpam-3274	154	11	sα	sα	NOUN
ejpam-3274	154	12	,	,	PUNCT
ejpam-3274	154	13	b	b	X
ejpam-3274	154	14	∈	∈	VERB
ejpam-3274	154	15	gβ	gβ	VERB
ejpam-3274	154	16	⊆	⊆	NUM
ejpam-3274	154	17	regs	reg	NOUN
ejpam-3274	154	18	,	,	PUNCT
ejpam-3274	154	19	ab	ab	PROPN
ejpam-3274	154	20	=	=	PUNCT
ejpam-3274	154	21	aφα	aφα	PROPN
ejpam-3274	154	22	,	,	PUNCT
ejpam-3274	154	23	αβbφβ	αβbφβ	NOUN
ejpam-3274	154	24	,	,	PUNCT
ejpam-3274	154	25	αβ	αβ	INTJ
ejpam-3274	154	26	.	.	PUNCT
ejpam-3274	155	1	because	because	SCONJ
ejpam-3274	155	2	the	the	DET
ejpam-3274	155	3	structure	structure	NOUN
ejpam-3274	155	4	homomorphisms	homomorphism	VERB
ejpam-3274	155	5	φα	φα	PROPN
ejpam-3274	155	6	,	,	PUNCT
ejpam-3274	155	7	β	β	PRON
ejpam-3274	155	8	preserve	preserve	VERB
ejpam-3274	155	9	the	the	DET
ejpam-3274	155	10	green	green	NOUN
ejpam-3274	155	11	’s	’s	PART
ejpam-3274	155	12	relations	relation	NOUN
ejpam-3274	155	13	on	on	ADP
ejpam-3274	155	14	s	s	PROPN
ejpam-3274	155	15	,	,	PUNCT
ejpam-3274	155	16	bφβ	bφβ	NOUN
ejpam-3274	155	17	,	,	PUNCT
ejpam-3274	155	18	αβ	αβ	INTJ
ejpam-3274	155	19	∈	∈	PROPN
ejpam-3274	155	20	gαβ	gαβ	PROPN
ejpam-3274	155	21	by	by	ADP
ejpam-3274	155	22	lemma	lemma	PROPN
ejpam-3274	155	23	4	4	NUM
ejpam-3274	155	24	.	.	PUNCT
ejpam-3274	156	1	on	on	ADP
ejpam-3274	156	2	the	the	DET
ejpam-3274	156	3	other	other	ADJ
ejpam-3274	156	4	hand	hand	NOUN
ejpam-3274	156	5	,	,	PUNCT
ejpam-3274	156	6	gαβ	gαβ	PROPN
ejpam-3274	156	7	is	be	AUX
ejpam-3274	156	8	an	an	DET
ejpam-3274	156	9	ideal	ideal	NOUN
ejpam-3274	156	10	of	of	ADP
ejpam-3274	156	11	sαβ	sαβ	PROPN
ejpam-3274	156	12	,	,	PUNCT
ejpam-3274	156	13	and	and	CCONJ
ejpam-3274	156	14	so	so	ADV
ejpam-3274	156	15	ab	ab	PROPN
ejpam-3274	156	16	∈	∈	PROPN
ejpam-3274	156	17	gαβ	gαβ	PROPN
ejpam-3274	156	18	⊆	⊆	NUM
ejpam-3274	156	19	regs	reg	NOUN
ejpam-3274	156	20	.	.	PUNCT
ejpam-3274	157	1	similarly	similarly	ADV
ejpam-3274	157	2	,	,	PUNCT
ejpam-3274	157	3	we	we	PRON
ejpam-3274	157	4	can	can	AUX
ejpam-3274	157	5	prove	prove	VERB
ejpam-3274	157	6	that	that	SCONJ
ejpam-3274	157	7	ab	ab	PROPN
ejpam-3274	157	8	∈	∈	PROPN
ejpam-3274	157	9	regs	reg	NOUN
ejpam-3274	157	10	for	for	ADP
ejpam-3274	157	11	any	any	DET
ejpam-3274	157	12	a	a	DET
ejpam-3274	157	13	∈	∈	NOUN
ejpam-3274	157	14	regs	reg	NOUN
ejpam-3274	157	15	,	,	PUNCT
ejpam-3274	157	16	b	b	PROPN
ejpam-3274	157	17	∈	∈	PROPN
ejpam-3274	157	18	s.	s.	PROPN
ejpam-3274	157	19	and	and	CCONJ
ejpam-3274	157	20	so	so	ADV
ejpam-3274	157	21	regs	regs	PROPN
ejpam-3274	157	22	is	be	AUX
ejpam-3274	157	23	an	an	DET
ejpam-3274	157	24	ideal	ideal	NOUN
ejpam-3274	157	25	of	of	ADP
ejpam-3274	157	26	s.	s.	PROPN
ejpam-3274	157	27	since	since	SCONJ
ejpam-3274	157	28	regs	regs	PROPN
ejpam-3274	157	29	=	=	PROPN
ejpam-3274	157	30	∪α∈ygα	∪α∈ygα	PROPN
ejpam-3274	157	31	,	,	PUNCT
ejpam-3274	157	32	it	it	PRON
ejpam-3274	157	33	is	be	AUX
ejpam-3274	157	34	clear	clear	ADJ
ejpam-3274	157	35	that	that	SCONJ
ejpam-3274	157	36	regs	reg	NOUN
ejpam-3274	157	37	is	be	AUX
ejpam-3274	157	38	a	a	DET
ejpam-3274	157	39	clifford	clifford	PROPN
ejpam-3274	157	40	subsemigroup	subsemigroup	NOUN
ejpam-3274	157	41	of	of	ADP
ejpam-3274	157	42	s.	s.	PROPN
ejpam-3274	157	43	denote	denote	VERB
ejpam-3274	157	44	φα	φα	PROPN
ejpam-3274	157	45	,	,	PUNCT
ejpam-3274	157	46	β|gα	β|gα	VERB
ejpam-3274	157	47	by	by	ADP
ejpam-3274	157	48	θα	θα	NOUN
ejpam-3274	157	49	,	,	PUNCT
ejpam-3274	157	50	β	β	NOUN
ejpam-3274	157	51	,	,	PUNCT
ejpam-3274	157	52	then	then	ADV
ejpam-3274	157	53	regs	reg	VERB
ejpam-3274	157	54	=	=	SYM
ejpam-3274	157	55	g[y	g[y	PROPN
ejpam-3274	157	56	;	;	PUNCT
ejpam-3274	157	57	gα	gα	NOUN
ejpam-3274	157	58	,	,	PUNCT
ejpam-3274	157	59	θα	θα	NOUN
ejpam-3274	157	60	,	,	PUNCT
ejpam-3274	157	61	β	β	NOUN
ejpam-3274	157	62	]	]	PUNCT
ejpam-3274	157	63	.	.	PUNCT
ejpam-3274	158	1	j.	j.	PROPN
ejpam-3274	158	2	zhang	zhang	PROPN
ejpam-3274	158	3	,	,	PUNCT
ejpam-3274	158	4	y.	y.	PROPN
ejpam-3274	158	5	yang	yang	PROPN
ejpam-3274	158	6	,	,	PUNCT
ejpam-3274	158	7	r.	r.	PROPN
ejpam-3274	158	8	shen	shen	PROPN
ejpam-3274	158	9	/	/	SYM
ejpam-3274	158	10	eur	eur	PROPN
ejpam-3274	158	11	.	.	PUNCT
ejpam-3274	159	1	j.	j.	PROPN
ejpam-3274	159	2	pure	pure	PROPN
ejpam-3274	159	3	appl	appl	PROPN
ejpam-3274	159	4	.	.	PROPN
ejpam-3274	159	5	math	math	PROPN
ejpam-3274	159	6	,	,	PUNCT
ejpam-3274	159	7	11	11	NUM
ejpam-3274	159	8	(	(	PUNCT
ejpam-3274	159	9	3	3	NUM
ejpam-3274	159	10	)	)	PUNCT
ejpam-3274	159	11	(	(	PUNCT
ejpam-3274	159	12	2018	2018	NUM
ejpam-3274	159	13	)	)	PUNCT
ejpam-3274	159	14	,	,	PUNCT
ejpam-3274	159	15	589	589	NUM
ejpam-3274	159	16	-	-	SYM
ejpam-3274	159	17	597	597	NUM
ejpam-3274	159	18	595	595	NUM
ejpam-3274	159	19	by	by	ADP
ejpam-3274	159	20	lemma	lemma	PROPN
ejpam-3274	159	21	2	2	NUM
ejpam-3274	159	22	,	,	PUNCT
ejpam-3274	159	23	qα	qα	PROPN
ejpam-3274	159	24	is	be	AUX
ejpam-3274	159	25	a	a	DET
ejpam-3274	159	26	partial	partial	ADJ
ejpam-3274	159	27	semigroup	semigroup	NOUN
ejpam-3274	159	28	for	for	ADP
ejpam-3274	159	29	any	any	DET
ejpam-3274	159	30	α	α	NOUN
ejpam-3274	159	31	∈	∈	PROPN
ejpam-3274	159	32	y	y	PROPN
ejpam-3274	159	33	.	.	PUNCT
ejpam-3274	160	1	denote	denote	VERB
ejpam-3274	160	2	φα	φα	PROPN
ejpam-3274	160	3	,	,	PUNCT
ejpam-3274	160	4	β|qα	β|qα	PUNCT
ejpam-3274	160	5	by	by	ADP
ejpam-3274	160	6	ϕα	ϕα	ADV
ejpam-3274	160	7	,	,	PUNCT
ejpam-3274	160	8	β	β	X
ejpam-3274	160	9	,	,	PUNCT
ejpam-3274	160	10	then	then	ADV
ejpam-3274	160	11	it	it	PRON
ejpam-3274	160	12	is	be	AUX
ejpam-3274	160	13	easy	easy	ADJ
ejpam-3274	160	14	to	to	PART
ejpam-3274	160	15	understand	understand	VERB
ejpam-3274	160	16	that	that	SCONJ
ejpam-3274	160	17	ϕα	ϕα	ADV
ejpam-3274	160	18	,	,	PUNCT
ejpam-3274	160	19	β	β	X
ejpam-3274	160	20	is	be	AUX
ejpam-3274	160	21	a	a	DET
ejpam-3274	160	22	partial	partial	ADJ
ejpam-3274	160	23	semigroup	semigroup	NOUN
ejpam-3274	160	24	homomorphism	homomorphism	NOUN
ejpam-3274	160	25	from	from	ADP
ejpam-3274	160	26	qα	qα	PROPN
ejpam-3274	160	27	to	to	ADP
ejpam-3274	160	28	sβ	sβ	NUM
ejpam-3274	160	29	such	such	ADJ
ejpam-3274	160	30	that	that	DET
ejpam-3274	160	31	condition	condition	NOUN
ejpam-3274	160	32	(	(	PUNCT
ejpam-3274	160	33	ii	ii	NOUN
ejpam-3274	160	34	)	)	PUNCT
ejpam-3274	160	35	and	and	CCONJ
ejpam-3274	160	36	(	(	PUNCT
ejpam-3274	160	37	iii	iii	X
ejpam-3274	160	38	)	)	PUNCT
ejpam-3274	160	39	are	be	AUX
ejpam-3274	160	40	satisfied	satisfied	ADJ
ejpam-3274	160	41	.	.	PUNCT
ejpam-3274	161	1	in	in	ADP
ejpam-3274	161	2	fact	fact	NOUN
ejpam-3274	161	3	,	,	PUNCT
ejpam-3274	161	4	for	for	ADP
ejpam-3274	161	5	any	any	DET
ejpam-3274	161	6	α	α	NOUN
ejpam-3274	161	7	,	,	PUNCT
ejpam-3274	161	8	β	β	X
ejpam-3274	161	9	,	,	PUNCT
ejpam-3274	161	10	γ	γ	PROPN
ejpam-3274	161	11	∈	∈	PROPN
ejpam-3274	161	12	y	y	PROPN
ejpam-3274	161	13	with	with	ADP
ejpam-3274	161	14	γ	γ	NOUN
ejpam-3274	161	15	≤	≤	NUM
ejpam-3274	161	16	αβ	αβ	INTJ
ejpam-3274	161	17	and	and	CCONJ
ejpam-3274	161	18	a	a	DET
ejpam-3274	161	19	∈	∈	PROPN
ejpam-3274	161	20	qα	qα	PROPN
ejpam-3274	161	21	,	,	PUNCT
ejpam-3274	161	22	b	b	PROPN
ejpam-3274	161	23	∈	∈	PROPN
ejpam-3274	162	1	qβ	qβ	X
ejpam-3274	162	2	,	,	PUNCT
ejpam-3274	162	3	since	since	SCONJ
ejpam-3274	162	4	(	(	PUNCT
ejpam-3274	162	5	aϕα	aϕα	PROPN
ejpam-3274	162	6	,	,	PUNCT
ejpam-3274	162	7	γ)(bϕβ	γ)(bϕβ	NOUN
ejpam-3274	162	8	,	,	PUNCT
ejpam-3274	162	9	γ	γ	NOUN
ejpam-3274	162	10	)	)	PUNCT
ejpam-3274	162	11	=	=	SYM
ejpam-3274	162	12	(	(	PUNCT
ejpam-3274	162	13	aφα	aφα	PROPN
ejpam-3274	162	14	,	,	PUNCT
ejpam-3274	162	15	γ)(bφβ	γ)(bφβ	PROPN
ejpam-3274	162	16	,	,	PUNCT
ejpam-3274	162	17	γ	γ	NOUN
ejpam-3274	162	18	)	)	PUNCT
ejpam-3274	162	19	=	=	SYM
ejpam-3274	162	20	(	(	PUNCT
ejpam-3274	162	21	aφα	aφα	PROPN
ejpam-3274	162	22	,	,	PUNCT
ejpam-3274	162	23	αβφαβ	αβφαβ	NOUN
ejpam-3274	162	24	,	,	PUNCT
ejpam-3274	162	25	γ)(bφβ	γ)(bφβ	PROPN
ejpam-3274	162	26	,	,	PUNCT
ejpam-3274	162	27	αβφαβ	αβφαβ	NOUN
ejpam-3274	162	28	,	,	PUNCT
ejpam-3274	162	29	γ	γ	NOUN
ejpam-3274	162	30	)	)	PUNCT
ejpam-3274	162	31	=	=	SYM
ejpam-3274	162	32	(	(	PUNCT
ejpam-3274	162	33	aφα	aφα	PROPN
ejpam-3274	162	34	,	,	PUNCT
ejpam-3274	162	35	αβbφβ	αβbφβ	NOUN
ejpam-3274	162	36	,	,	PUNCT
ejpam-3274	162	37	αβ)φαβ	αβ)φαβ	PROPN
ejpam-3274	162	38	,	,	PUNCT
ejpam-3274	162	39	γ	γ	X
ejpam-3274	162	40	=	=	SYM
ejpam-3274	162	41	(	(	PUNCT
ejpam-3274	162	42	ab)φαβ	ab)φαβ	PROPN
ejpam-3274	162	43	,	,	PUNCT
ejpam-3274	162	44	γ	γ	X
ejpam-3274	162	45	.	.	PUNCT
ejpam-3274	163	1	if	if	SCONJ
ejpam-3274	163	2	ab	ab	PROPN
ejpam-3274	163	3	/∈	/∈	PUNCT
ejpam-3274	163	4	qαβ	qαβ	PROPN
ejpam-3274	163	5	,	,	PUNCT
ejpam-3274	163	6	then	then	ADV
ejpam-3274	163	7	(	(	PUNCT
ejpam-3274	163	8	aϕα	aϕα	PROPN
ejpam-3274	163	9	,	,	PUNCT
ejpam-3274	163	10	γ)(bϕβ	γ)(bϕβ	NOUN
ejpam-3274	163	11	,	,	PUNCT
ejpam-3274	163	12	γ	γ	NOUN
ejpam-3274	163	13	)	)	PUNCT
ejpam-3274	163	14	=	=	SYM
ejpam-3274	163	15	(	(	PUNCT
ejpam-3274	163	16	ab)φαβ	ab)φαβ	PROPN
ejpam-3274	163	17	,	,	PUNCT
ejpam-3274	163	18	γ	γ	X
ejpam-3274	163	19	/∈	/∈	PUNCT
ejpam-3274	163	20	qγ	qγ	NOUN
ejpam-3274	163	21	.	.	PUNCT
ejpam-3274	164	1	so	so	ADV
ejpam-3274	164	2	condition	condition	NOUN
ejpam-3274	164	3	(	(	PUNCT
ejpam-3274	164	4	ii)(2	ii)(2	NOUN
ejpam-3274	164	5	)	)	PUNCT
ejpam-3274	164	6	holds	hold	NOUN
ejpam-3274	164	7	.	.	PUNCT
ejpam-3274	165	1	and	and	CCONJ
ejpam-3274	165	2	it	it	PRON
ejpam-3274	165	3	is	be	AUX
ejpam-3274	165	4	easy	easy	ADJ
ejpam-3274	165	5	to	to	PART
ejpam-3274	165	6	see	see	VERB
ejpam-3274	165	7	that	that	DET
ejpam-3274	165	8	condition	condition	NOUN
ejpam-3274	165	9	(	(	PUNCT
ejpam-3274	165	10	ii)(1),(3),(4	ii)(1),(3),(4	NOUN
ejpam-3274	165	11	)	)	PUNCT
ejpam-3274	165	12	hold	hold	NOUN
ejpam-3274	165	13	by	by	ADP
ejpam-3274	165	14	the	the	DET
ejpam-3274	165	15	definition	definition	NOUN
ejpam-3274	165	16	of	of	ADP
ejpam-3274	165	17	strong	strong	ADJ
ejpam-3274	165	18	semilattice	semilattice	NOUN
ejpam-3274	165	19	.	.	PUNCT
ejpam-3274	166	1	further	far	ADV
ejpam-3274	166	2	,	,	PUNCT
ejpam-3274	166	3	for	for	ADP
ejpam-3274	166	4	any	any	DET
ejpam-3274	166	5	α	α	NOUN
ejpam-3274	166	6	,	,	PUNCT
ejpam-3274	166	7	β	β	X
ejpam-3274	166	8	∈	∈	PROPN
ejpam-3274	166	9	y	y	PROPN
ejpam-3274	166	10	with	with	ADP
ejpam-3274	166	11	α	α	PROPN
ejpam-3274	166	12	≥	≥	NUM
ejpam-3274	166	13	β	β	NOUN
ejpam-3274	166	14	and	and	CCONJ
ejpam-3274	166	15	a	a	DET
ejpam-3274	166	16	∈	∈	ADJ
ejpam-3274	166	17	qα	qα	NOUN
ejpam-3274	166	18	,	,	PUNCT
ejpam-3274	166	19	since	since	SCONJ
ejpam-3274	166	20	aeα	aeα	NOUN
ejpam-3274	166	21	is	be	AUX
ejpam-3274	166	22	regular	regular	ADJ
ejpam-3274	166	23	,	,	PUNCT
ejpam-3274	166	24	aψθα	aψθα	NOUN
ejpam-3274	166	25	,	,	PUNCT
ejpam-3274	166	26	β	β	X
ejpam-3274	166	27	=	=	SYM
ejpam-3274	166	28	(	(	PUNCT
ejpam-3274	166	29	aeα)θα	aeα)θα	ADV
ejpam-3274	166	30	,	,	PUNCT
ejpam-3274	166	31	β	β	X
ejpam-3274	166	32	=	=	SYM
ejpam-3274	166	33	(	(	PUNCT
ejpam-3274	166	34	aeα)φα	aeα)φα	VERB
ejpam-3274	166	35	,	,	PUNCT
ejpam-3274	166	36	β	β	X
ejpam-3274	166	37	=	=	SYM
ejpam-3274	166	38	(	(	PUNCT
ejpam-3274	166	39	aφα	aφα	PROPN
ejpam-3274	166	40	,	,	PUNCT
ejpam-3274	166	41	β)(eαφα	β)(eαφα	NUM
ejpam-3274	166	42	,	,	PUNCT
ejpam-3274	166	43	β	β	X
ejpam-3274	166	44	)	)	PUNCT
ejpam-3274	166	45	=	=	SYM
ejpam-3274	166	46	aϕα	aϕα	NOUN
ejpam-3274	166	47	,	,	PUNCT
ejpam-3274	166	48	βeβ	βeβ	NOUN
ejpam-3274	166	49	=	=	SYM
ejpam-3274	166	50	aϕα	aϕα	PROPN
ejpam-3274	166	51	,	,	PUNCT
ejpam-3274	166	52	βψ	βψ	NOUN
ejpam-3274	166	53	.	.	PUNCT
ejpam-3274	167	1	so	so	ADV
ejpam-3274	167	2	each	each	DET
ejpam-3274	167	3	strong	strong	ADJ
ejpam-3274	167	4	semilattice	semilattice	NOUN
ejpam-3274	167	5	of	of	ADP
ejpam-3274	167	6	π	π	NOUN
ejpam-3274	167	7	-	-	NOUN
ejpam-3274	167	8	groups	group	NOUN
ejpam-3274	167	9	satisfies	satisfy	VERB
ejpam-3274	167	10	the	the	DET
ejpam-3274	167	11	conditions	condition	NOUN
ejpam-3274	167	12	.	.	PUNCT
ejpam-3274	168	1	the	the	DET
ejpam-3274	168	2	proof	proof	NOUN
ejpam-3274	168	3	is	be	AUX
ejpam-3274	168	4	completed	complete	VERB
ejpam-3274	168	5	.	.	PUNCT
ejpam-3274	169	1	at	at	ADP
ejpam-3274	169	2	last	last	ADV
ejpam-3274	169	3	,	,	PUNCT
ejpam-3274	169	4	we	we	PRON
ejpam-3274	169	5	consider	consider	VERB
ejpam-3274	169	6	the	the	DET
ejpam-3274	169	7	homomorphisms	homomorphism	NOUN
ejpam-3274	169	8	between	between	ADP
ejpam-3274	169	9	two	two	NUM
ejpam-3274	169	10	strong	strong	ADJ
ejpam-3274	169	11	semilattices	semilattice	NOUN
ejpam-3274	169	12	of	of	ADP
ejpam-3274	169	13	π	π	NOUN
ejpam-3274	169	14	-	-	NOUN
ejpam-3274	169	15	groups	group	NOUN
ejpam-3274	169	16	.	.	PUNCT
ejpam-3274	170	1	let	let	VERB
ejpam-3274	170	2	s[y	s[y	NUM
ejpam-3274	170	3	;	;	PUNCT
ejpam-3274	170	4	sα	sα	X
ejpam-3274	170	5	,	,	PUNCT
ejpam-3274	170	6	φα	φα	ADP
ejpam-3274	170	7	,	,	PUNCT
ejpam-3274	170	8	β	β	NOUN
ejpam-3274	170	9	]	]	PUNCT
ejpam-3274	170	10	and	and	CCONJ
ejpam-3274	170	11	t	t	X
ejpam-3274	171	1	[	[	X
ejpam-3274	171	2	m	m	X
ejpam-3274	171	3	;	;	PUNCT
ejpam-3274	171	4	tα	tα	PROPN
ejpam-3274	171	5	,	,	PUNCT
ejpam-3274	171	6	ωα	ωα	PROPN
ejpam-3274	171	7	,	,	PUNCT
ejpam-3274	171	8	β	β	NOUN
ejpam-3274	171	9	]	]	X
ejpam-3274	171	10	be	be	VERB
ejpam-3274	171	11	two	two	NUM
ejpam-3274	171	12	strong	strong	ADJ
ejpam-3274	171	13	semilattices	semilattice	NOUN
ejpam-3274	171	14	of	of	ADP
ejpam-3274	171	15	π	π	NOUN
ejpam-3274	171	16	-	-	NOUN
ejpam-3274	171	17	groups	group	NOUN
ejpam-3274	171	18	.	.	PUNCT
ejpam-3274	172	1	denote	denote	VERB
ejpam-3274	172	2	the	the	DET
ejpam-3274	172	3	set	set	NOUN
ejpam-3274	172	4	of	of	ADP
ejpam-3274	172	5	non	non	ADJ
ejpam-3274	172	6	-	-	ADJ
ejpam-3274	172	7	regular	regular	ADJ
ejpam-3274	172	8	elements	element	NOUN
ejpam-3274	172	9	of	of	ADP
ejpam-3274	172	10	s	s	PRON
ejpam-3274	172	11	and	and	CCONJ
ejpam-3274	172	12	t	t	PROPN
ejpam-3274	172	13	by	by	ADP
ejpam-3274	172	14	qs	qs	NOUN
ejpam-3274	172	15	and	and	CCONJ
ejpam-3274	172	16	qt	qt	NOUN
ejpam-3274	172	17	respectively	respectively	ADV
ejpam-3274	172	18	.	.	PUNCT
ejpam-3274	173	1	every	every	DET
ejpam-3274	173	2	homomorphism	homomorphism	PROPN
ejpam-3274	173	3	f	f	X
ejpam-3274	173	4	from	from	ADP
ejpam-3274	173	5	s	s	PRON
ejpam-3274	173	6	to	to	ADP
ejpam-3274	173	7	t	t	PROPN
ejpam-3274	173	8	induces	induce	VERB
ejpam-3274	173	9	a	a	DET
ejpam-3274	173	10	homomorphism	homomorphism	NOUN
ejpam-3274	173	11	from	from	ADP
ejpam-3274	173	12	y	y	PROPN
ejpam-3274	173	13	to	to	ADP
ejpam-3274	173	14	m	m	PRON
ejpam-3274	173	15	,	,	PUNCT
ejpam-3274	173	16	we	we	PRON
ejpam-3274	173	17	denoted	denote	VERB
ejpam-3274	173	18	this	this	DET
ejpam-3274	173	19	semilattice	semilattice	NOUN
ejpam-3274	173	20	homomorphism	homomorphism	PROPN
ejpam-3274	173	21	by	by	ADP
ejpam-3274	173	22	fl	fl	PROPN
ejpam-3274	173	23	,	,	PUNCT
ejpam-3274	173	24	and	and	CCONJ
ejpam-3274	173	25	it	it	PRON
ejpam-3274	173	26	is	be	AUX
ejpam-3274	173	27	obvious	obvious	ADJ
ejpam-3274	173	28	that	that	SCONJ
ejpam-3274	173	29	eαf	eαf	NOUN
ejpam-3274	173	30	=	=	PUNCT
ejpam-3274	173	31	eαfl	eαfl	PROPN
ejpam-3274	173	32	for	for	ADP
ejpam-3274	173	33	any	any	DET
ejpam-3274	173	34	α	α	NOUN
ejpam-3274	173	35	∈	∈	PROPN
ejpam-3274	173	36	y	y	PROPN
ejpam-3274	173	37	.	.	PUNCT
ejpam-3274	174	1	on	on	ADP
ejpam-3274	174	2	the	the	DET
ejpam-3274	174	3	other	other	ADJ
ejpam-3274	174	4	hand	hand	NOUN
ejpam-3274	174	5	,	,	PUNCT
ejpam-3274	174	6	since	since	SCONJ
ejpam-3274	174	7	f	f	PROPN
ejpam-3274	174	8	|sα∈	|sα∈	PROPN
ejpam-3274	174	9	hom(sα	hom(sα	PROPN
ejpam-3274	174	10	,	,	PUNCT
ejpam-3274	174	11	tαfl	tαfl	NOUN
ejpam-3274	174	12	)	)	PUNCT
ejpam-3274	174	13	,	,	PUNCT
ejpam-3274	174	14	we	we	PRON
ejpam-3274	174	15	can	can	AUX
ejpam-3274	174	16	get	get	VERB
ejpam-3274	174	17	a	a	DET
ejpam-3274	174	18	family	family	NOUN
ejpam-3274	174	19	of	of	ADP
ejpam-3274	174	20	π	π	PROPN
ejpam-3274	174	21	-	-	NOUN
ejpam-3274	174	22	group	group	NOUN
ejpam-3274	174	23	homomorphisms	homomorphism	NOUN
ejpam-3274	174	24	denoted	denote	VERB
ejpam-3274	174	25	by	by	ADP
ejpam-3274	174	26	{	{	PUNCT
ejpam-3274	174	27	fα	fα	ADP
ejpam-3274	174	28	:	:	PUNCT
ejpam-3274	174	29	α	α	PROPN
ejpam-3274	174	30	∈	∈	PROPN
ejpam-3274	174	31	y	y	PROPN
ejpam-3274	174	32	}	}	PUNCT
ejpam-3274	174	33	.	.	PUNCT
ejpam-3274	175	1	theorem	theorem	NOUN
ejpam-3274	175	2	2	2	NUM
ejpam-3274	175	3	.	.	PUNCT
ejpam-3274	176	1	let	let	AUX
ejpam-3274	176	2	s	s	PRON
ejpam-3274	176	3	and	and	CCONJ
ejpam-3274	176	4	t	t	PROPN
ejpam-3274	176	5	be	be	AUX
ejpam-3274	176	6	be	be	AUX
ejpam-3274	176	7	two	two	NUM
ejpam-3274	176	8	strong	strong	ADJ
ejpam-3274	176	9	semilattices	semilattice	NOUN
ejpam-3274	176	10	of	of	ADP
ejpam-3274	176	11	π	π	NOUN
ejpam-3274	176	12	-	-	NOUN
ejpam-3274	176	13	groups	group	NOUN
ejpam-3274	176	14	as	as	SCONJ
ejpam-3274	176	15	defined	define	VERB
ejpam-3274	176	16	above	above	ADV
ejpam-3274	176	17	.	.	PUNCT
ejpam-3274	177	1	given	give	VERB
ejpam-3274	177	2	a	a	DET
ejpam-3274	177	3	semilattice	semilattice	NOUN
ejpam-3274	177	4	homomorphism	homomorphism	NOUN
ejpam-3274	177	5	fl	fl	X
ejpam-3274	177	6	:	:	PUNCT
ejpam-3274	177	7	y	y	PROPN
ejpam-3274	177	8	→m	→m	PUNCT
ejpam-3274	177	9	and	and	CCONJ
ejpam-3274	177	10	a	a	DET
ejpam-3274	177	11	family	family	NOUN
ejpam-3274	177	12	of	of	ADP
ejpam-3274	177	13	π	π	PROPN
ejpam-3274	177	14	-	-	NOUN
ejpam-3274	177	15	group	group	NOUN
ejpam-3274	177	16	homomorphisms	homomorphism	NOUN
ejpam-3274	177	17	{	{	PUNCT
ejpam-3274	177	18	fα	fα	ADP
ejpam-3274	177	19	:	:	PUNCT
ejpam-3274	177	20	α	α	PROPN
ejpam-3274	177	21	∈	∈	PROPN
ejpam-3274	177	22	y	y	PROPN
ejpam-3274	177	23	}	}	PUNCT
ejpam-3274	177	24	,	,	PUNCT
ejpam-3274	177	25	where	where	SCONJ
ejpam-3274	177	26	fα	fα	ADP
ejpam-3274	177	27	∈	∈	PROPN
ejpam-3274	177	28	hom(sα	hom(sα	NOUN
ejpam-3274	177	29	,	,	PUNCT
ejpam-3274	177	30	tαfl	tαfl	NOUN
ejpam-3274	177	31	)	)	PUNCT
ejpam-3274	177	32	.	.	PUNCT
ejpam-3274	178	1	define	define	VERB
ejpam-3274	178	2	f	f	X
ejpam-3274	178	3	:	:	PUNCT
ejpam-3274	178	4	s	s	X
ejpam-3274	178	5	→	→	SYM
ejpam-3274	178	6	t	t	NOUN
ejpam-3274	178	7	by	by	ADP
ejpam-3274	178	8	sf	sf	PROPN
ejpam-3274	178	9	=	=	PUNCT
ejpam-3274	178	10	sfα	sfα	NOUN
ejpam-3274	178	11	for	for	ADP
ejpam-3274	178	12	any	any	DET
ejpam-3274	178	13	α	α	NOUN
ejpam-3274	178	14	∈	∈	PROPN
ejpam-3274	178	15	y	y	PROPN
ejpam-3274	178	16	,	,	PUNCT
ejpam-3274	178	17	s	s	PART
ejpam-3274	178	18	∈	∈	NOUN
ejpam-3274	178	19	sα	sα	NOUN
ejpam-3274	178	20	.	.	PUNCT
ejpam-3274	179	1	and	and	CCONJ
ejpam-3274	179	2	the	the	DET
ejpam-3274	179	3	follwing	follwe	VERB
ejpam-3274	179	4	conditions	condition	NOUN
ejpam-3274	179	5	are	be	AUX
ejpam-3274	179	6	satisfied	satisfied	ADJ
ejpam-3274	179	7	.	.	PUNCT
ejpam-3274	180	1	(	(	PUNCT
ejpam-3274	180	2	1	1	X
ejpam-3274	180	3	)	)	PUNCT
ejpam-3274	180	4	f	f	NOUN
ejpam-3274	181	1	|qs	|qs	NOUN
ejpam-3274	181	2	is	be	AUX
ejpam-3274	181	3	a	a	DET
ejpam-3274	181	4	partial	partial	ADJ
ejpam-3274	181	5	semigroup	semigroup	NOUN
ejpam-3274	181	6	homomorphism	homomorphism	NOUN
ejpam-3274	181	7	from	from	ADP
ejpam-3274	181	8	qs	qs	PROPN
ejpam-3274	181	9	to	to	ADP
ejpam-3274	181	10	t	t	PROPN
ejpam-3274	181	11	.	.	PUNCT
ejpam-3274	182	1	and	and	CCONJ
ejpam-3274	182	2	for	for	ADP
ejpam-3274	182	3	any	any	DET
ejpam-3274	182	4	a	a	DET
ejpam-3274	182	5	,	,	PUNCT
ejpam-3274	182	6	b	b	X
ejpam-3274	182	7	∈	∈	NOUN
ejpam-3274	182	8	qs	qs	NOUN
ejpam-3274	182	9	,	,	PUNCT
ejpam-3274	182	10	if	if	SCONJ
ejpam-3274	182	11	ab	ab	PROPN
ejpam-3274	182	12	/∈	/∈	PUNCT
ejpam-3274	182	13	qs	qs	PROPN
ejpam-3274	182	14	,	,	PUNCT
ejpam-3274	182	15	then	then	ADV
ejpam-3274	182	16	(	(	PUNCT
ejpam-3274	182	17	af)(bf	af)(bf	NOUN
ejpam-3274	182	18	)	)	PUNCT
ejpam-3274	182	19	/∈	/∈	PUNCT
ejpam-3274	182	20	qt	qt	NOUN
ejpam-3274	182	21	.	.	PUNCT
ejpam-3274	183	1	(	(	PUNCT
ejpam-3274	183	2	2	2	X
ejpam-3274	183	3	)	)	PUNCT
ejpam-3274	183	4	φα	φα	PROPN
ejpam-3274	183	5	,	,	PUNCT
ejpam-3274	183	6	βfβψ	βfβψ	NOUN
ejpam-3274	183	7	=	=	SYM
ejpam-3274	183	8	fαωαfl	fαωαfl	NOUN
ejpam-3274	183	9	,	,	PUNCT
ejpam-3274	183	10	βflψ	βflψ	NOUN
ejpam-3274	183	11	for	for	ADP
ejpam-3274	183	12	any	any	DET
ejpam-3274	183	13	α	α	NOUN
ejpam-3274	183	14	,	,	PUNCT
ejpam-3274	183	15	β	β	X
ejpam-3274	183	16	∈	∈	PROPN
ejpam-3274	183	17	y	y	PROPN
ejpam-3274	183	18	with	with	ADP
ejpam-3274	183	19	α	α	PROPN
ejpam-3274	183	20	≥	≥	X
ejpam-3274	183	21	β	β	X
ejpam-3274	183	22	.	.	PUNCT
ejpam-3274	184	1	then	then	ADV
ejpam-3274	184	2	f	f	PROPN
ejpam-3274	184	3	is	be	AUX
ejpam-3274	184	4	a	a	DET
ejpam-3274	184	5	homomorphism	homomorphism	NOUN
ejpam-3274	184	6	.	.	PUNCT
ejpam-3274	185	1	conversely	conversely	ADV
ejpam-3274	185	2	,	,	PUNCT
ejpam-3274	185	3	every	every	DET
ejpam-3274	185	4	homomorphism	homomorphism	NOUN
ejpam-3274	185	5	between	between	ADP
ejpam-3274	185	6	two	two	NUM
ejpam-3274	185	7	strong	strong	ADJ
ejpam-3274	185	8	semilattices	semilattice	NOUN
ejpam-3274	185	9	of	of	ADP
ejpam-3274	185	10	π	π	NOUN
ejpam-3274	185	11	-	-	NOUN
ejpam-3274	185	12	groups	group	NOUN
ejpam-3274	185	13	satisfies	satisfy	VERB
ejpam-3274	185	14	the	the	DET
ejpam-3274	185	15	conditions	condition	NOUN
ejpam-3274	185	16	.	.	PUNCT
ejpam-3274	186	1	proof	proof	NOUN
ejpam-3274	186	2	.	.	PUNCT
ejpam-3274	187	1	it	it	PRON
ejpam-3274	187	2	is	be	AUX
ejpam-3274	187	3	obvious	obvious	ADJ
ejpam-3274	187	4	that	that	SCONJ
ejpam-3274	187	5	f	f	PROPN
ejpam-3274	187	6	is	be	AUX
ejpam-3274	187	7	a	a	DET
ejpam-3274	187	8	map	map	NOUN
ejpam-3274	187	9	from	from	ADP
ejpam-3274	187	10	s	s	PRON
ejpam-3274	187	11	to	to	ADP
ejpam-3274	187	12	t	t	PROPN
ejpam-3274	187	13	.	.	PUNCT
ejpam-3274	188	1	we	we	PRON
ejpam-3274	188	2	only	only	ADV
ejpam-3274	188	3	need	need	VERB
ejpam-3274	188	4	to	to	PART
ejpam-3274	188	5	prove	prove	VERB
ejpam-3274	188	6	that	that	SCONJ
ejpam-3274	188	7	f	f	PROPN
ejpam-3274	188	8	is	be	AUX
ejpam-3274	188	9	a	a	DET
ejpam-3274	188	10	homomorphism	homomorphism	NOUN
ejpam-3274	188	11	.	.	PUNCT
ejpam-3274	189	1	let	let	VERB
ejpam-3274	189	2	a	a	DET
ejpam-3274	189	3	∈	∈	NOUN
ejpam-3274	189	4	sα	sα	NOUN
ejpam-3274	189	5	and	and	CCONJ
ejpam-3274	189	6	b	b	X
ejpam-3274	189	7	∈	∈	PROPN
ejpam-3274	189	8	sβ	sβ	PROPN
ejpam-3274	189	9	.	.	PUNCT
ejpam-3274	189	10	case	case	NOUN
ejpam-3274	189	11	1	1	NUM
ejpam-3274	189	12	:	:	PUNCT
ejpam-3274	189	13	if	if	SCONJ
ejpam-3274	189	14	ab	ab	PROPN
ejpam-3274	189	15	∈	∈	PROPN
ejpam-3274	189	16	qαβ	qαβ	PROPN
ejpam-3274	189	17	,	,	PUNCT
ejpam-3274	189	18	then	then	ADV
ejpam-3274	189	19	a	a	DET
ejpam-3274	189	20	∈	∈	PROPN
ejpam-3274	189	21	qα	qα	PROPN
ejpam-3274	189	22	,	,	PUNCT
ejpam-3274	189	23	b	b	PROPN
ejpam-3274	189	24	∈	∈	PROPN
ejpam-3274	189	25	qβ	qβ	NOUN
ejpam-3274	189	26	,	,	PUNCT
ejpam-3274	189	27	then	then	ADV
ejpam-3274	189	28	by	by	ADP
ejpam-3274	189	29	condition	condition	NOUN
ejpam-3274	189	30	(	(	PUNCT
ejpam-3274	189	31	1	1	NUM
ejpam-3274	189	32	)	)	PUNCT
ejpam-3274	189	33	,	,	PUNCT
ejpam-3274	189	34	afbf	afbf	NOUN
ejpam-3274	189	35	=	=	SYM
ejpam-3274	189	36	(	(	PUNCT
ejpam-3274	189	37	ab)f	ab)f	PROPN
ejpam-3274	189	38	.	.	PUNCT
ejpam-3274	189	39	case	case	NOUN
ejpam-3274	189	40	2	2	NUM
ejpam-3274	189	41	:	:	PUNCT
ejpam-3274	190	1	if	if	SCONJ
ejpam-3274	190	2	ab	ab	PROPN
ejpam-3274	190	3	/∈	/∈	PUNCT
ejpam-3274	190	4	qαβ	qαβ	PROPN
ejpam-3274	190	5	,	,	PUNCT
ejpam-3274	190	6	then	then	ADV
ejpam-3274	190	7	(	(	PUNCT
ejpam-3274	190	8	ab)f	ab)f	PROPN
ejpam-3274	190	9	/∈	/∈	PUNCT
ejpam-3274	190	10	qt	qt	NOUN
ejpam-3274	190	11	,	,	PUNCT
ejpam-3274	190	12	(	(	PUNCT
ejpam-3274	190	13	ab)f	ab)f	PROPN
ejpam-3274	190	14	=	=	SYM
ejpam-3274	190	15	(	(	PUNCT
ejpam-3274	190	16	ab)fαβ	ab)fαβ	PROPN
ejpam-3274	190	17	=	=	SYM
ejpam-3274	190	18	(	(	PUNCT
ejpam-3274	190	19	aφα	aφα	PROPN
ejpam-3274	190	20	,	,	PUNCT
ejpam-3274	190	21	αβbφβ	αβbφβ	NOUN
ejpam-3274	190	22	,	,	PUNCT
ejpam-3274	190	23	αβ)fαβ	αβ)fαβ	PROPN
ejpam-3274	190	24	=	=	SYM
ejpam-3274	190	25	(	(	PUNCT
ejpam-3274	190	26	aφα	aφα	PROPN
ejpam-3274	190	27	,	,	PUNCT
ejpam-3274	190	28	αβfαβ)(bφβ	αβfαβ)(bφβ	PROPN
ejpam-3274	190	29	,	,	PUNCT
ejpam-3274	190	30	αβfαβ)e(αβ)fl	αβfαβ)e(αβ)fl	X
ejpam-3274	190	31	=	=	SYM
ejpam-3274	190	32	(	(	PUNCT
ejpam-3274	190	33	aφα	aφα	PROPN
ejpam-3274	190	34	,	,	PUNCT
ejpam-3274	190	35	αβfαβe(αβ)fl)(bφβ	αβfαβe(αβ)fl)(bφβ	NOUN
ejpam-3274	190	36	,	,	PUNCT
ejpam-3274	190	37	αβfαβe(αβ)fl	αβfαβe(αβ)fl	NUM
ejpam-3274	190	38	)	)	PUNCT
ejpam-3274	190	39	=	=	PRON
ejpam-3274	190	40	(	(	PUNCT
ejpam-3274	190	41	aφα	aφα	PROPN
ejpam-3274	190	42	,	,	PUNCT
ejpam-3274	190	43	αβfαβψ)(bφβ	αβfαβψ)(bφβ	PROPN
ejpam-3274	190	44	,	,	PUNCT
ejpam-3274	190	45	αβfαβψ	αβfαβψ	NOUN
ejpam-3274	190	46	)	)	PUNCT
ejpam-3274	190	47	.	.	PUNCT
ejpam-3274	191	1	on	on	ADP
ejpam-3274	191	2	the	the	DET
ejpam-3274	191	3	other	other	ADJ
ejpam-3274	191	4	hand	hand	NOUN
ejpam-3274	191	5	,	,	PUNCT
ejpam-3274	191	6	afbf	afbf	NOUN
ejpam-3274	191	7	=	=	SYM
ejpam-3274	191	8	(	(	PUNCT
ejpam-3274	191	9	afα)(bfβ	afα)(bfβ	NOUN
ejpam-3274	191	10	)	)	PUNCT
ejpam-3274	191	11	=	=	SYM
ejpam-3274	191	12	(	(	PUNCT
ejpam-3274	191	13	afαωαfl,(αβ)fl)(bfβωβfl,(αβ)fl	afαωαfl,(αβ)fl)(bfβωβfl,(αβ)fl	NUM
ejpam-3274	191	14	)	)	PUNCT
ejpam-3274	191	15	=	=	PUNCT
ejpam-3274	191	16	(	(	PUNCT
ejpam-3274	191	17	afαωαfl,(αβ)fle(αβ)fl)(bfβωβfl,(αβ)fle(αβ)fl	afαωαfl,(αβ)fle(αβ)fl)(bfβωβfl,(αβ)fle(αβ)fl	PROPN
ejpam-3274	191	18	)	)	PUNCT
ejpam-3274	191	19	(	(	PUNCT
ejpam-3274	191	20	by	by	ADP
ejpam-3274	191	21	condition	condition	NOUN
ejpam-3274	191	22	(	(	PUNCT
ejpam-3274	191	23	1	1	NUM
ejpam-3274	191	24	)	)	PUNCT
ejpam-3274	191	25	)	)	PUNCT
ejpam-3274	192	1	=	=	SYM
ejpam-3274	192	2	(	(	PUNCT
ejpam-3274	192	3	afαωαfl,(αβ)flψ)(bfβωβfl,(αβ)flψ	afαωαfl,(αβ)flψ)(bfβωβfl,(αβ)flψ	NOUN
ejpam-3274	192	4	)	)	PUNCT
ejpam-3274	192	5	.	.	PUNCT
ejpam-3274	193	1	j.	j.	PROPN
ejpam-3274	193	2	zhang	zhang	PROPN
ejpam-3274	193	3	,	,	PUNCT
ejpam-3274	193	4	y.	y.	PROPN
ejpam-3274	193	5	yang	yang	PROPN
ejpam-3274	193	6	,	,	PUNCT
ejpam-3274	193	7	r.	r.	PROPN
ejpam-3274	193	8	shen	shen	PROPN
ejpam-3274	193	9	/	/	SYM
ejpam-3274	193	10	eur	eur	PROPN
ejpam-3274	193	11	.	.	PUNCT
ejpam-3274	194	1	j.	j.	PROPN
ejpam-3274	194	2	pure	pure	PROPN
ejpam-3274	194	3	appl	appl	PROPN
ejpam-3274	194	4	.	.	PROPN
ejpam-3274	194	5	math	math	PROPN
ejpam-3274	194	6	,	,	PUNCT
ejpam-3274	194	7	11	11	NUM
ejpam-3274	194	8	(	(	PUNCT
ejpam-3274	194	9	3	3	NUM
ejpam-3274	194	10	)	)	PUNCT
ejpam-3274	194	11	(	(	PUNCT
ejpam-3274	194	12	2018	2018	NUM
ejpam-3274	194	13	)	)	PUNCT
ejpam-3274	194	14	,	,	PUNCT
ejpam-3274	194	15	589	589	NUM
ejpam-3274	194	16	-	-	SYM
ejpam-3274	194	17	597	597	NUM
ejpam-3274	194	18	596	596	NUM
ejpam-3274	194	19	by	by	ADP
ejpam-3274	194	20	condition	condition	NOUN
ejpam-3274	194	21	(	(	PUNCT
ejpam-3274	194	22	2	2	NUM
ejpam-3274	194	23	)	)	PUNCT
ejpam-3274	194	24	,	,	PUNCT
ejpam-3274	194	25	we	we	PRON
ejpam-3274	194	26	get	get	VERB
ejpam-3274	194	27	afbf	afbf	ADJ
ejpam-3274	194	28	=	=	SYM
ejpam-3274	194	29	(	(	PUNCT
ejpam-3274	194	30	ab)f	ab)f	PROPN
ejpam-3274	194	31	.	.	PUNCT
ejpam-3274	195	1	conversely	conversely	ADV
ejpam-3274	195	2	,	,	PUNCT
ejpam-3274	195	3	let	let	VERB
ejpam-3274	195	4	f	f	PRON
ejpam-3274	195	5	be	be	AUX
ejpam-3274	195	6	a	a	DET
ejpam-3274	195	7	homomorphism	homomorphism	NOUN
ejpam-3274	195	8	from	from	ADP
ejpam-3274	195	9	s	s	PRON
ejpam-3274	195	10	to	to	ADP
ejpam-3274	195	11	t	t	PROPN
ejpam-3274	195	12	,	,	PUNCT
ejpam-3274	195	13	fl	fl	PROPN
ejpam-3274	195	14	and	and	CCONJ
ejpam-3274	195	15	{	{	PUNCT
ejpam-3274	195	16	fα	fα	PART
ejpam-3274	195	17	:	:	PUNCT
ejpam-3274	196	1	α	α	PROPN
ejpam-3274	196	2	∈	∈	PROPN
ejpam-3274	196	3	y	y	PROPN
ejpam-3274	196	4	}	}	PUNCT
ejpam-3274	196	5	be	be	AUX
ejpam-3274	196	6	the	the	DET
ejpam-3274	196	7	corresponding	corresponding	ADJ
ejpam-3274	196	8	semilattice	semilattice	NOUN
ejpam-3274	196	9	homomorphism	homomorphism	NOUN
ejpam-3274	196	10	and	and	CCONJ
ejpam-3274	196	11	the	the	DET
ejpam-3274	196	12	family	family	NOUN
ejpam-3274	196	13	of	of	ADP
ejpam-3274	196	14	π	π	PROPN
ejpam-3274	196	15	-	-	NOUN
ejpam-3274	196	16	group	group	NOUN
ejpam-3274	196	17	homomorphisms	homomorphism	NOUN
ejpam-3274	196	18	as	as	SCONJ
ejpam-3274	196	19	considered	consider	VERB
ejpam-3274	196	20	above	above	ADP
ejpam-3274	196	21	this	this	DET
ejpam-3274	196	22	theorem	theorem	NOUN
ejpam-3274	196	23	.	.	PUNCT
ejpam-3274	197	1	that	that	DET
ejpam-3274	197	2	condition	condition	NOUN
ejpam-3274	197	3	(	(	PUNCT
ejpam-3274	197	4	1	1	X
ejpam-3274	197	5	)	)	PUNCT
ejpam-3274	197	6	holds	hold	VERB
ejpam-3274	197	7	is	be	AUX
ejpam-3274	197	8	clear	clear	ADJ
ejpam-3274	197	9	.	.	PUNCT
ejpam-3274	198	1	we	we	PRON
ejpam-3274	198	2	only	only	ADV
ejpam-3274	198	3	need	need	VERB
ejpam-3274	198	4	to	to	PART
ejpam-3274	198	5	prove	prove	VERB
ejpam-3274	198	6	the	the	DET
ejpam-3274	198	7	equation	equation	NOUN
ejpam-3274	198	8	holds	hold	VERB
ejpam-3274	198	9	in	in	ADP
ejpam-3274	198	10	condition	condition	NOUN
ejpam-3274	198	11	(	(	PUNCT
ejpam-3274	198	12	2	2	NUM
ejpam-3274	198	13	)	)	PUNCT
ejpam-3274	198	14	.	.	PUNCT
ejpam-3274	199	1	at	at	ADP
ejpam-3274	199	2	first	first	ADV
ejpam-3274	199	3	,	,	PUNCT
ejpam-3274	199	4	we	we	PRON
ejpam-3274	199	5	give	give	VERB
ejpam-3274	199	6	the	the	DET
ejpam-3274	199	7	following	follow	VERB
ejpam-3274	199	8	fact	fact	NOUN
ejpam-3274	199	9	.	.	PUNCT
ejpam-3274	200	1	let	let	VERB
ejpam-3274	200	2	r[z;rα	r[z;rα	NOUN
ejpam-3274	200	3	,	,	PUNCT
ejpam-3274	200	4	χα	χα	NOUN
ejpam-3274	200	5	,	,	PUNCT
ejpam-3274	200	6	β	β	NOUN
ejpam-3274	200	7	]	]	X
ejpam-3274	200	8	be	be	VERB
ejpam-3274	200	9	a	a	DET
ejpam-3274	200	10	strong	strong	ADJ
ejpam-3274	200	11	semilattices	semilattice	NOUN
ejpam-3274	200	12	of	of	ADP
ejpam-3274	200	13	π	π	NOUN
ejpam-3274	200	14	-	-	NOUN
ejpam-3274	200	15	groups	group	NOUN
ejpam-3274	200	16	.	.	PUNCT
ejpam-3274	201	1	for	for	ADP
ejpam-3274	201	2	any	any	DET
ejpam-3274	201	3	α	α	NOUN
ejpam-3274	201	4	,	,	PUNCT
ejpam-3274	201	5	β	β	X
ejpam-3274	201	6	∈	∈	PROPN
ejpam-3274	201	7	z	z	PROPN
ejpam-3274	201	8	with	with	ADP
ejpam-3274	201	9	α	α	PROPN
ejpam-3274	201	10	≥	≥	NUM
ejpam-3274	201	11	β	β	NOUN
ejpam-3274	201	12	and	and	CCONJ
ejpam-3274	201	13	for	for	ADP
ejpam-3274	201	14	any	any	DET
ejpam-3274	201	15	a	a	DET
ejpam-3274	201	16	∈	∈	ADJ
ejpam-3274	201	17	rα	rα	ADJ
ejpam-3274	201	18	,	,	PUNCT
ejpam-3274	201	19	a(ψχα	a(ψχα	ADJ
ejpam-3274	201	20	,	,	PUNCT
ejpam-3274	201	21	β	β	NOUN
ejpam-3274	201	22	)	)	PUNCT
ejpam-3274	201	23	=	=	SYM
ejpam-3274	201	24	(	(	PUNCT
ejpam-3274	201	25	aeα)χα	aeα)χα	ADJ
ejpam-3274	201	26	,	,	PUNCT
ejpam-3274	201	27	β	β	PROPN
ejpam-3274	201	28	=	=	PUNCT
ejpam-3274	201	29	aχα	aχα	PROPN
ejpam-3274	201	30	,	,	PUNCT
ejpam-3274	201	31	βeαχα	βeαχα	NOUN
ejpam-3274	201	32	,	,	PUNCT
ejpam-3274	201	33	β	β	X
ejpam-3274	201	34	=	=	PUNCT
ejpam-3274	201	35	aχα	aχα	ADJ
ejpam-3274	201	36	,	,	PUNCT
ejpam-3274	201	37	βeβ	βeβ	NOUN
ejpam-3274	202	1	=	=	SYM
ejpam-3274	202	2	a(χα	a(χα	PROPN
ejpam-3274	202	3	,	,	PUNCT
ejpam-3274	202	4	βψ	βψ	NUM
ejpam-3274	202	5	)	)	PUNCT
ejpam-3274	202	6	.	.	PUNCT
ejpam-3274	203	1	and	and	CCONJ
ejpam-3274	203	2	so	so	ADV
ejpam-3274	203	3	ψχα	ψχα	PROPN
ejpam-3274	203	4	,	,	PUNCT
ejpam-3274	203	5	β	β	X
ejpam-3274	203	6	=	=	PUNCT
ejpam-3274	203	7	χα	χα	NOUN
ejpam-3274	203	8	,	,	PUNCT
ejpam-3274	203	9	βψ	βψ	X
ejpam-3274	203	10	.	.	PUNCT
ejpam-3274	204	1	(	(	PUNCT
ejpam-3274	204	2	3	3	X
ejpam-3274	204	3	)	)	PUNCT
ejpam-3274	204	4	now	now	ADV
ejpam-3274	204	5	we	we	PRON
ejpam-3274	204	6	return	return	VERB
ejpam-3274	204	7	to	to	ADP
ejpam-3274	204	8	the	the	DET
ejpam-3274	204	9	proof	proof	NOUN
ejpam-3274	204	10	.	.	PUNCT
ejpam-3274	205	1	for	for	ADP
ejpam-3274	205	2	any	any	DET
ejpam-3274	205	3	α	α	NOUN
ejpam-3274	205	4	,	,	PUNCT
ejpam-3274	205	5	β	β	X
ejpam-3274	205	6	∈	∈	PROPN
ejpam-3274	205	7	y	y	PROPN
ejpam-3274	205	8	with	with	ADP
ejpam-3274	205	9	α	α	PROPN
ejpam-3274	205	10	≥	≥	NUM
ejpam-3274	205	11	β	β	NOUN
ejpam-3274	205	12	and	and	CCONJ
ejpam-3274	205	13	for	for	ADP
ejpam-3274	205	14	any	any	DET
ejpam-3274	205	15	a	a	DET
ejpam-3274	205	16	∈	∈	NOUN
ejpam-3274	205	17	sα	sα	NOUN
ejpam-3274	205	18	,	,	PUNCT
ejpam-3274	205	19	(	(	PUNCT
ejpam-3274	205	20	aeβ)f	aeβ)f	PROPN
ejpam-3274	205	21	=	=	SYM
ejpam-3274	205	22	(	(	PUNCT
ejpam-3274	205	23	aeαeβ)f	aeαeβ)f	NOUN
ejpam-3274	205	24	=	=	SYM
ejpam-3274	205	25	a(ψφα	a(ψφα	PROPN
ejpam-3274	205	26	,	,	PUNCT
ejpam-3274	205	27	βfβ	βfβ	NOUN
ejpam-3274	205	28	)	)	PUNCT
ejpam-3274	205	29	,	,	PUNCT
ejpam-3274	205	30	(	(	PUNCT
ejpam-3274	205	31	af)(eβf	af)(eβf	NOUN
ejpam-3274	205	32	)	)	PUNCT
ejpam-3274	205	33	=	=	SYM
ejpam-3274	205	34	(	(	PUNCT
ejpam-3274	205	35	afα)(eβfl	afα)(eβfl	X
ejpam-3274	205	36	)	)	PUNCT
ejpam-3274	205	37	=	=	SYM
ejpam-3274	205	38	(	(	PUNCT
ejpam-3274	205	39	afα)(eαfl)(eβfl	afα)(eαfl)(eβfl	PROPN
ejpam-3274	205	40	)	)	PUNCT
ejpam-3274	205	41	=	=	PUNCT
ejpam-3274	205	42	a(fαψωαfl	a(fαψωαfl	PROPN
ejpam-3274	205	43	,	,	PUNCT
ejpam-3274	205	44	βfl	βfl	NOUN
ejpam-3274	205	45	)	)	PUNCT
ejpam-3274	205	46	.	.	PUNCT
ejpam-3274	206	1	and	and	CCONJ
ejpam-3274	206	2	hence	hence	ADV
ejpam-3274	206	3	,	,	PUNCT
ejpam-3274	206	4	ψφα	ψφα	NOUN
ejpam-3274	206	5	,	,	PUNCT
ejpam-3274	206	6	βfβ	βfβ	NOUN
ejpam-3274	206	7	=	=	SYM
ejpam-3274	206	8	fαψωαfl	fαψωαfl	ADJ
ejpam-3274	206	9	,	,	PUNCT
ejpam-3274	206	10	βfl	βfl	X
ejpam-3274	206	11	.	.	PUNCT
ejpam-3274	207	1	(	(	PUNCT
ejpam-3274	207	2	4	4	X
ejpam-3274	207	3	)	)	PUNCT
ejpam-3274	207	4	specially	specially	ADV
ejpam-3274	207	5	,	,	PUNCT
ejpam-3274	207	6	for	for	ADP
ejpam-3274	207	7	any	any	DET
ejpam-3274	207	8	α	α	NOUN
ejpam-3274	207	9	∈	∈	PROPN
ejpam-3274	207	10	y	y	PROPN
ejpam-3274	207	11	and	and	CCONJ
ejpam-3274	207	12	a	a	DET
ejpam-3274	207	13	∈	∈	PROPN
ejpam-3274	207	14	sα	sα	ADP
ejpam-3274	207	15	,	,	PUNCT
ejpam-3274	207	16	a(ψfα	a(ψfα	PROPN
ejpam-3274	207	17	)	)	PUNCT
ejpam-3274	207	18	=	=	SYM
ejpam-3274	207	19	(	(	PUNCT
ejpam-3274	207	20	aeα)fα	aeα)fα	NOUN
ejpam-3274	207	21	=	=	SYM
ejpam-3274	207	22	afαeαfl	afαeαfl	PROPN
ejpam-3274	207	23	=	=	PUNCT
ejpam-3274	207	24	a(fαψ	a(fαψ	PROPN
ejpam-3274	207	25	)	)	PUNCT
ejpam-3274	207	26	.	.	PUNCT
ejpam-3274	208	1	which	which	PRON
ejpam-3274	208	2	means	mean	VERB
ejpam-3274	208	3	that	that	DET
ejpam-3274	208	4	ψfα	ψfα	NOUN
ejpam-3274	208	5	=	=	SYM
ejpam-3274	208	6	fαψ	fαψ	ADJ
ejpam-3274	208	7	.	.	PUNCT
ejpam-3274	209	1	(	(	PUNCT
ejpam-3274	209	2	5	5	NUM
ejpam-3274	209	3	)	)	PUNCT
ejpam-3274	209	4	by	by	ADP
ejpam-3274	209	5	the	the	DET
ejpam-3274	209	6	equations	equation	NOUN
ejpam-3274	209	7	(	(	PUNCT
ejpam-3274	209	8	3	3	NUM
ejpam-3274	209	9	)	)	PUNCT
ejpam-3274	209	10	,	,	PUNCT
ejpam-3274	209	11	(	(	PUNCT
ejpam-3274	209	12	4	4	NUM
ejpam-3274	209	13	)	)	PUNCT
ejpam-3274	209	14	and	and	CCONJ
ejpam-3274	209	15	(	(	PUNCT
ejpam-3274	209	16	5	5	NUM
ejpam-3274	209	17	)	)	PUNCT
ejpam-3274	209	18	,	,	PUNCT
ejpam-3274	209	19	it	it	PRON
ejpam-3274	209	20	is	be	AUX
ejpam-3274	209	21	easy	easy	ADJ
ejpam-3274	209	22	to	to	PART
ejpam-3274	209	23	understand	understand	VERB
ejpam-3274	209	24	that	that	PRON
ejpam-3274	209	25	φα	φα	PROPN
ejpam-3274	209	26	,	,	PUNCT
ejpam-3274	209	27	βfβψ	βfβψ	NOUN
ejpam-3274	209	28	=	=	SYM
ejpam-3274	209	29	ψφα	ψφα	NOUN
ejpam-3274	209	30	,	,	PUNCT
ejpam-3274	209	31	βfβ	βfβ	NOUN
ejpam-3274	209	32	=	=	SYM
ejpam-3274	209	33	fαψωαfl	fαψωαfl	ADJ
ejpam-3274	209	34	,	,	PUNCT
ejpam-3274	209	35	βfl	βfl	VERB
ejpam-3274	210	1	=	=	SYM
ejpam-3274	210	2	fαωαfl	fαωαfl	NOUN
ejpam-3274	210	3	,	,	PUNCT
ejpam-3274	210	4	βflψ	βflψ	NOUN
ejpam-3274	210	5	.	.	PUNCT
ejpam-3274	211	1	(	(	PUNCT
ejpam-3274	211	2	6	6	X
ejpam-3274	211	3	)	)	PUNCT
ejpam-3274	211	4	the	the	DET
ejpam-3274	211	5	proof	proof	NOUN
ejpam-3274	211	6	is	be	AUX
ejpam-3274	211	7	completed	complete	VERB
ejpam-3274	211	8	.	.	PUNCT
ejpam-3274	212	1	corollary	corollary	ADJ
ejpam-3274	212	2	1	1	NUM
ejpam-3274	212	3	.	.	PUNCT
ejpam-3274	213	1	let	let	VERB
ejpam-3274	213	2	g1[y1;gα	g1[y1;gα	NOUN
ejpam-3274	213	3	,	,	PUNCT
ejpam-3274	213	4	φα	φα	ADP
ejpam-3274	213	5	,	,	PUNCT
ejpam-3274	213	6	β	β	NOUN
ejpam-3274	213	7	]	]	PUNCT
ejpam-3274	213	8	and	and	CCONJ
ejpam-3274	213	9	g2[y2;gα	g2[y2;gα	PROPN
ejpam-3274	213	10	,	,	PUNCT
ejpam-3274	213	11	ωα	ωα	PROPN
ejpam-3274	213	12	,	,	PUNCT
ejpam-3274	213	13	β	β	NOUN
ejpam-3274	213	14	]	]	X
ejpam-3274	213	15	be	be	VERB
ejpam-3274	213	16	two	two	NUM
ejpam-3274	213	17	clifford	clifford	PROPN
ejpam-3274	213	18	semigroups	semigroup	NOUN
ejpam-3274	213	19	.	.	PUNCT
ejpam-3274	214	1	given	give	VERB
ejpam-3274	214	2	a	a	DET
ejpam-3274	214	3	semilattice	semilattice	NOUN
ejpam-3274	214	4	homomorphism	homomorphism	NOUN
ejpam-3274	214	5	fl	fl	X
ejpam-3274	214	6	:	:	PUNCT
ejpam-3274	214	7	y1	y1	INTJ
ejpam-3274	214	8	→	→	PUNCT
ejpam-3274	214	9	y2	y2	PROPN
ejpam-3274	214	10	and	and	CCONJ
ejpam-3274	214	11	a	a	DET
ejpam-3274	214	12	family	family	NOUN
ejpam-3274	214	13	of	of	ADP
ejpam-3274	214	14	group	group	NOUN
ejpam-3274	214	15	homomorphisms	homomorphism	NOUN
ejpam-3274	214	16	{	{	PUNCT
ejpam-3274	214	17	fα	fα	ADP
ejpam-3274	214	18	:	:	PUNCT
ejpam-3274	214	19	α	α	PROPN
ejpam-3274	214	20	∈	∈	PROPN
ejpam-3274	214	21	y1	y1	PROPN
ejpam-3274	214	22	}	}	PUNCT
ejpam-3274	214	23	,	,	PUNCT
ejpam-3274	214	24	where	where	SCONJ
ejpam-3274	214	25	fα	fα	ADP
ejpam-3274	214	26	∈	∈	PROPN
ejpam-3274	214	27	hom(gα	hom(gα	NOUN
ejpam-3274	214	28	,	,	PUNCT
ejpam-3274	214	29	gαfl	gαfl	PROPN
ejpam-3274	214	30	)	)	PUNCT
ejpam-3274	214	31	.	.	PUNCT
ejpam-3274	215	1	define	define	VERB
ejpam-3274	215	2	f	f	PROPN
ejpam-3274	215	3	:	:	PUNCT
ejpam-3274	215	4	g1	g1	PROPN
ejpam-3274	215	5	→	→	PUNCT
ejpam-3274	215	6	g2	g2	PROPN
ejpam-3274	215	7	by	by	ADP
ejpam-3274	215	8	sf	sf	PROPN
ejpam-3274	215	9	=	=	PUNCT
ejpam-3274	215	10	sfα	sfα	NOUN
ejpam-3274	215	11	for	for	ADP
ejpam-3274	215	12	any	any	DET
ejpam-3274	215	13	s	s	X
ejpam-3274	215	14	∈	∈	NOUN
ejpam-3274	215	15	gα	gα	NOUN
ejpam-3274	215	16	.	.	PUNCT
ejpam-3274	216	1	and	and	CCONJ
ejpam-3274	216	2	for	for	ADP
ejpam-3274	216	3	any	any	DET
ejpam-3274	216	4	α	α	NOUN
ejpam-3274	216	5	,	,	PUNCT
ejpam-3274	216	6	β	β	X
ejpam-3274	216	7	∈	∈	PROPN
ejpam-3274	216	8	y	y	PROPN
ejpam-3274	216	9	with	with	ADP
ejpam-3274	216	10	α	α	PROPN
ejpam-3274	216	11	≥	≥	PROPN
ejpam-3274	216	12	β	β	X
ejpam-3274	216	13	,	,	PUNCT
ejpam-3274	216	14	the	the	DET
ejpam-3274	216	15	follwing	follwe	VERB
ejpam-3274	216	16	equation	equation	NOUN
ejpam-3274	216	17	is	be	AUX
ejpam-3274	216	18	satisfied	satisfied	ADJ
ejpam-3274	216	19	.	.	PUNCT
ejpam-3274	217	1	φα	φα	X
ejpam-3274	217	2	,	,	PUNCT
ejpam-3274	217	3	βfβ	βfβ	NOUN
ejpam-3274	217	4	=	=	SYM
ejpam-3274	217	5	fαωαfl	fαωαfl	NOUN
ejpam-3274	217	6	,	,	PUNCT
ejpam-3274	217	7	βfl	βfl	X
ejpam-3274	217	8	.	.	PUNCT
ejpam-3274	218	1	then	then	ADV
ejpam-3274	218	2	f	f	PROPN
ejpam-3274	218	3	is	be	AUX
ejpam-3274	218	4	a	a	DET
ejpam-3274	218	5	homomorphism	homomorphism	NOUN
ejpam-3274	218	6	.	.	PUNCT
ejpam-3274	219	1	conversely	conversely	ADV
ejpam-3274	219	2	,	,	PUNCT
ejpam-3274	219	3	every	every	DET
ejpam-3274	219	4	homomorphism	homomorphism	NOUN
ejpam-3274	219	5	between	between	ADP
ejpam-3274	219	6	this	this	DET
ejpam-3274	219	7	two	two	NUM
ejpam-3274	219	8	clifford	clifford	PROPN
ejpam-3274	219	9	semigroups	semigroup	NOUN
ejpam-3274	219	10	satisfies	satisfy	VERB
ejpam-3274	219	11	the	the	DET
ejpam-3274	219	12	conditions	condition	NOUN
ejpam-3274	219	13	.	.	PUNCT
ejpam-3274	220	1	references	reference	NOUN
ejpam-3274	220	2	597	597	NUM
ejpam-3274	220	3	references	reference	NOUN
ejpam-3274	220	4	[	[	X
ejpam-3274	220	5	1	1	NUM
ejpam-3274	220	6	]	]	PUNCT
ejpam-3274	220	7	s.	s.	PROPN
ejpam-3274	220	8	bogdanović.	bogdanović.	PROPN
ejpam-3274	220	9	semigroups	semigroup	VERB
ejpam-3274	220	10	with	with	ADP
ejpam-3274	220	11	a	a	DET
ejpam-3274	220	12	system	system	NOUN
ejpam-3274	220	13	of	of	ADP
ejpam-3274	220	14	subsemigroups	subsemigroup	NOUN
ejpam-3274	220	15	.	.	PUNCT
ejpam-3274	221	1	institute	institute	PROPN
ejpam-3274	221	2	of	of	ADP
ejpam-3274	221	3	mathematics	mathematics	PROPN
ejpam-3274	221	4	,	,	PUNCT
ejpam-3274	221	5	novi	novi	PROPN
ejpam-3274	221	6	sad	sad	PROPN
ejpam-3274	221	7	,	,	PUNCT
ejpam-3274	221	8	yugoslavia	yugoslavia	PROPN
ejpam-3274	221	9	,	,	PUNCT
ejpam-3274	221	10	1985	1985	NUM
ejpam-3274	221	11	.	.	PUNCT
ejpam-3274	222	1	[	[	X
ejpam-3274	222	2	2	2	X
ejpam-3274	222	3	]	]	PUNCT
ejpam-3274	222	4	j.	j.	PROPN
ejpam-3274	222	5	l.	l.	PROPN
ejpam-3274	222	6	galbiati	galbiati	PROPN
ejpam-3274	222	7	,	,	PUNCT
ejpam-3274	222	8	m.	m.	PROPN
ejpam-3274	222	9	l.	l.	PROPN
ejpam-3274	222	10	veronesi	veronesi	PROPN
ejpam-3274	222	11	,	,	PUNCT
ejpam-3274	222	12	on	on	ADP
ejpam-3274	222	13	quasi	quasi	ADJ
ejpam-3274	222	14	-	-	ADJ
ejpam-3274	222	15	completely	completely	ADV
ejpam-3274	222	16	regular	regular	ADJ
ejpam-3274	222	17	semigroups	semigroup	NOUN
ejpam-3274	222	18	,	,	PUNCT
ejpam-3274	222	19	semigroup	semigroup	PROPN
ejpam-3274	222	20	forum	forum	PROPN
ejpam-3274	222	21	,	,	PUNCT
ejpam-3274	222	22	29(1	29(1	NUM
ejpam-3274	222	23	):	):	PUNCT
ejpam-3274	222	24	271	271	NUM
ejpam-3274	222	25	-	-	SYM
ejpam-3274	222	26	275	275	NUM
ejpam-3274	222	27	,	,	PUNCT
ejpam-3274	222	28	1984	1984	NUM
ejpam-3274	222	29	.	.	PUNCT
ejpam-3274	223	1	[	[	X
ejpam-3274	223	2	3	3	X
ejpam-3274	223	3	]	]	X
ejpam-3274	223	4	j.	j.	PROPN
ejpam-3274	223	5	m.	m.	PROPN
ejpam-3274	223	6	howie	howie	PROPN
ejpam-3274	223	7	,	,	PUNCT
ejpam-3274	223	8	fundamental	fundamental	ADJ
ejpam-3274	223	9	of	of	ADP
ejpam-3274	223	10	semigroup	semigroup	PROPN
ejpam-3274	223	11	theory	theory	NOUN
ejpam-3274	223	12	,	,	PUNCT
ejpam-3274	223	13	oxford	oxford	PROPN
ejpam-3274	223	14	,	,	PUNCT
ejpam-3274	223	15	clarendon	clarendon	PROPN
ejpam-3274	223	16	press	press	NOUN
ejpam-3274	223	17	,	,	PUNCT
ejpam-3274	223	18	1995	1995	NUM
ejpam-3274	223	19	.	.	PUNCT
ejpam-3274	224	1	[	[	X
ejpam-3274	224	2	4	4	X
ejpam-3274	224	3	]	]	PUNCT
ejpam-3274	224	4	k.	k.	PROPN
ejpam-3274	224	5	p.	p.	PROPN
ejpam-3274	224	6	shum	shum	PROPN
ejpam-3274	224	7	,	,	PUNCT
ejpam-3274	224	8	x.	x.	PROPN
ejpam-3274	224	9	m.	m.	PROPN
ejpam-3274	224	10	ren	ren	PROPN
ejpam-3274	224	11	,	,	PUNCT
ejpam-3274	224	12	y.	y.	PROPN
ejpam-3274	224	13	q.	q.	PROPN
ejpam-3274	224	14	guo	guo	PROPN
ejpam-3274	224	15	,	,	PUNCT
ejpam-3274	224	16	on	on	ADP
ejpam-3274	224	17	c∗-quasiregular	c∗-quasiregular	ADJ
ejpam-3274	224	18	semigroups	semigroup	NOUN
ejpam-3274	224	19	,	,	PUNCT
ejpam-3274	224	20	communications	communication	NOUN
ejpam-3274	224	21	in	in	ADP
ejpam-3274	224	22	algebra	algebra	NOUN
ejpam-3274	224	23	,	,	PUNCT
ejpam-3274	224	24	27(9	27(9	NOUN
ejpam-3274	224	25	):	):	PUNCT
ejpam-3274	224	26	4251	4251	NUM
ejpam-3274	224	27	-	-	SYM
ejpam-3274	224	28	4274	4274	NUM
ejpam-3274	224	29	,	,	PUNCT
ejpam-3274	224	30	1999	1999	NUM
ejpam-3274	224	31	.	.	PUNCT
ejpam-3274	225	1	[	[	X
ejpam-3274	225	2	5	5	X
ejpam-3274	225	3	]	]	PUNCT
ejpam-3274	225	4	j.	j.	PROPN
ejpam-3274	225	5	g.	g.	PROPN
ejpam-3274	225	6	zhang	zhang	PROPN
ejpam-3274	225	7	,	,	PUNCT
ejpam-3274	225	8	r.	r.	PROPN
ejpam-3274	225	9	shen	shen	PROPN
ejpam-3274	225	10	,	,	PUNCT
ejpam-3274	225	11	(	(	PUNCT
ejpam-3274	225	12	generalized	generalized	ADJ
ejpam-3274	225	13	)	)	PUNCT
ejpam-3274	225	14	green	green	PROPN
ejpam-3274	225	15	’s	’s	PART
ejpam-3274	225	16	relations	relation	NOUN
ejpam-3274	225	17	of	of	ADP
ejpam-3274	225	18	gv	gv	NOUN
ejpam-3274	225	19	-	-	PUNCT
ejpam-3274	225	20	semigroups	semigroup	NOUN
ejpam-3274	225	21	,	,	PUNCT
ejpam-3274	225	22	j.	j.	PROPN
ejpam-3274	225	23	of	of	ADP
ejpam-3274	225	24	donghua	donghua	PROPN
ejpam-3274	225	25	univ.(eng	univ.(eng	PROPN
ejpam-3274	225	26	.	.	PUNCT
ejpam-3274	226	1	ed	ed	NOUN
ejpam-3274	226	2	.	.	PUNCT
ejpam-3274	226	3	)	)	PUNCT
ejpam-3274	226	4	,	,	PUNCT
ejpam-3274	226	5	29(2	29(2	NUM
ejpam-3274	226	6	):	):	PUNCT
ejpam-3274	226	7	175	175	NUM
ejpam-3274	226	8	-	-	SYM
ejpam-3274	226	9	177	177	NUM
ejpam-3274	226	10	,	,	PUNCT
ejpam-3274	226	11	2012	2012	NUM
ejpam-3274	226	12	.	.	PUNCT
ejpam-3274	227	1	[	[	X
ejpam-3274	227	2	6	6	NUM
ejpam-3274	227	3	]	]	X
ejpam-3274	227	4	y.h	y.h	PROPN
ejpam-3274	227	5	.	.	PROPN
ejpam-3274	227	6	yang	yang	PROPN
ejpam-3274	227	7	,	,	PUNCT
ejpam-3274	227	8	j.g	j.g	PROPN
ejpam-3274	227	9	.	.	PROPN
ejpam-3274	227	10	zhang	zhang	PROPN
ejpam-3274	227	11	,	,	PUNCT
ejpam-3274	227	12	bitranslations	bitranslation	NOUN
ejpam-3274	227	13	of	of	ADP
ejpam-3274	227	14	completely	completely	ADV
ejpam-3274	227	15	simple	simple	ADJ
ejpam-3274	227	16	semigroups	semigroup	NOUN
ejpam-3274	227	17	and	and	CCONJ
ejpam-3274	227	18	some	some	DET
ejpam-3274	227	19	applications	application	NOUN
ejpam-3274	227	20	,	,	PUNCT
ejpam-3274	227	21	j.	j.	PROPN
ejpam-3274	227	22	of	of	ADP
ejpam-3274	227	23	shanghai	shanghai	PROPN
ejpam-3274	227	24	normal	normal	PROPN
ejpam-3274	227	25	univ	univ	PROPN
ejpam-3274	227	26	.	.	PUNCT
ejpam-3274	228	1	(	(	PUNCT
ejpam-3274	228	2	natural	natural	ADJ
ejpam-3274	228	3	sciences	science	NOUN
ejpam-3274	228	4	)	)	PUNCT
ejpam-3274	228	5	,	,	PUNCT
ejpam-3274	228	6	41(2	41(2	NUM
ejpam-3274	228	7	):	):	PUNCT
ejpam-3274	228	8	111	111	NUM
ejpam-3274	228	9	-	-	SYM
ejpam-3274	228	10	119	119	NUM
ejpam-3274	228	11	,	,	PUNCT
ejpam-3274	228	12	2013	2013	NUM
ejpam-3274	228	13	.	.	PUNCT