id	sid	tid	token	lemma	pos
ejpam-1240	1	1	1_xxx_xiaojiang.dvi	1_xxx_xiaojiang.dvi	NUM
ejpam-1240	1	2	european	european	ADJ
ejpam-1240	1	3	journal	journal	NOUN
ejpam-1240	1	4	of	of	ADP
ejpam-1240	1	5	pure	pure	ADJ
ejpam-1240	1	6	and	and	CCONJ
ejpam-1240	1	7	applied	apply	VERB
ejpam-1240	1	8	mathematics	mathematic	NOUN
ejpam-1240	1	9	vol	vol	NOUN
ejpam-1240	1	10	.	.	PROPN
ejpam-1240	1	11	4	4	NUM
ejpam-1240	1	12	,	,	PUNCT
ejpam-1240	1	13	no	no	INTJ
ejpam-1240	1	14	.	.	NOUN
ejpam-1240	1	15	3	3	NUM
ejpam-1240	1	16	,	,	PUNCT
ejpam-1240	1	17	2011	2011	NUM
ejpam-1240	1	18	,	,	PUNCT
ejpam-1240	1	19	210	210	NUM
ejpam-1240	1	20	-	-	SYM
ejpam-1240	1	21	220	220	NUM
ejpam-1240	1	22	issn	issn	PROPN
ejpam-1240	1	23	1307	1307	NUM
ejpam-1240	1	24	-	-	SYM
ejpam-1240	1	25	5543	5543	NUM
ejpam-1240	1	26	–	–	PUNCT
ejpam-1240	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1240	1	28	naturally	naturally	ADV
ejpam-1240	1	29	ordered	order	VERB
ejpam-1240	1	30	abundant	abundant	ADJ
ejpam-1240	1	31	semigroups	semigroup	NOUN
ejpam-1240	1	32	for	for	ADP
ejpam-1240	1	33	which	which	PRON
ejpam-1240	1	34	each	each	DET
ejpam-1240	1	35	idempotent	idempotent	NOUN
ejpam-1240	1	36	has	have	VERB
ejpam-1240	1	37	a	a	DET
ejpam-1240	1	38	greatest	great	ADJ
ejpam-1240	1	39	inverse	inverse	NOUN
ejpam-1240	1	40	xiaojiang	xiaojiang	PROPN
ejpam-1240	1	41	guo1	guo1	PROPN
ejpam-1240	1	42	,	,	PUNCT
ejpam-1240	1	43	k.p	k.p	PROPN
ejpam-1240	1	44	.	.	PROPN
ejpam-1240	1	45	shum2,∗	shum2,∗	PROPN
ejpam-1240	1	46	1	1	NUM
ejpam-1240	1	47	department	department	NOUN
ejpam-1240	1	48	of	of	ADP
ejpam-1240	1	49	mathematics	mathematic	NOUN
ejpam-1240	1	50	,	,	PUNCT
ejpam-1240	1	51	jiangxi	jiangxi	PROPN
ejpam-1240	1	52	normal	normal	PROPN
ejpam-1240	1	53	university	university	PROPN
ejpam-1240	1	54	,	,	PUNCT
ejpam-1240	1	55	nanchang	nanchang	PROPN
ejpam-1240	1	56	,	,	PUNCT
ejpam-1240	1	57	jiangxi	jiangxi	PROPN
ejpam-1240	1	58	330022	330022	NUM
ejpam-1240	1	59	,	,	PUNCT
ejpam-1240	1	60	people	people	NOUN
ejpam-1240	1	61	’s	’s	PART
ejpam-1240	1	62	republic	republic	NOUN
ejpam-1240	1	63	of	of	ADP
ejpam-1240	1	64	china	china	PROPN
ejpam-1240	1	65	2	2	PROPN
ejpam-1240	1	66	institute	institute	PROPN
ejpam-1240	1	67	of	of	ADP
ejpam-1240	1	68	mathematics	mathematics	PROPN
ejpam-1240	1	69	,	,	PUNCT
ejpam-1240	1	70	yunnan	yunnan	PROPN
ejpam-1240	1	71	university	university	PROPN
ejpam-1240	1	72	,	,	PUNCT
ejpam-1240	1	73	kunming	kunming	PROPN
ejpam-1240	1	74	,	,	PUNCT
ejpam-1240	1	75	yunnan	yunnan	NOUN
ejpam-1240	1	76	650091	650091	NUM
ejpam-1240	1	77	,	,	PUNCT
ejpam-1240	1	78	people	people	NOUN
ejpam-1240	1	79	’s	’s	PART
ejpam-1240	1	80	republic	republic	PROPN
ejpam-1240	1	81	of	of	ADP
ejpam-1240	1	82	china	china	PROPN
ejpam-1240	1	83	abstract	abstract	PROPN
ejpam-1240	1	84	.	.	PUNCT
ejpam-1240	2	1	g	g	NOUN
ejpam-1240	2	2	-	-	PUNCT
ejpam-1240	2	3	regular	regular	ADJ
ejpam-1240	2	4	and	and	CCONJ
ejpam-1240	2	5	reflexive	reflexive	ADJ
ejpam-1240	2	6	naturally	naturally	ADV
ejpam-1240	2	7	ordered	order	VERB
ejpam-1240	2	8	abundant	abundant	ADJ
ejpam-1240	2	9	semigroups	semigroup	NOUN
ejpam-1240	2	10	each	each	PRON
ejpam-1240	2	11	of	of	ADP
ejpam-1240	2	12	whose	whose	DET
ejpam-1240	2	13	idempotents	idempotent	NOUN
ejpam-1240	2	14	has	have	VERB
ejpam-1240	2	15	a	a	DET
ejpam-1240	2	16	greatest	great	ADJ
ejpam-1240	2	17	inverse	inverse	NOUN
ejpam-1240	2	18	are	be	AUX
ejpam-1240	2	19	studied	study	VERB
ejpam-1240	2	20	.	.	PUNCT
ejpam-1240	3	1	in	in	ADP
ejpam-1240	3	2	this	this	DET
ejpam-1240	3	3	paper	paper	NOUN
ejpam-1240	3	4	,	,	PUNCT
ejpam-1240	3	5	we	we	PRON
ejpam-1240	3	6	give	give	VERB
ejpam-1240	3	7	a	a	DET
ejpam-1240	3	8	construction	construction	NOUN
ejpam-1240	3	9	theorem	theorem	NOUN
ejpam-1240	3	10	for	for	ADP
ejpam-1240	3	11	such	such	ADJ
ejpam-1240	3	12	ordered	order	VERB
ejpam-1240	3	13	semigroups	semigroup	NOUN
ejpam-1240	3	14	.	.	PUNCT
ejpam-1240	4	1	our	our	PRON
ejpam-1240	4	2	theorem	theorem	NOUN
ejpam-1240	4	3	extends	extend	VERB
ejpam-1240	4	4	a	a	DET
ejpam-1240	4	5	previous	previous	ADJ
ejpam-1240	4	6	structure	structure	NOUN
ejpam-1240	4	7	theorem	theorem	VERB
ejpam-1240	4	8	on	on	ADP
ejpam-1240	4	9	naturally	naturally	ADV
ejpam-1240	4	10	ordered	order	VERB
ejpam-1240	4	11	abundant	abundant	ADJ
ejpam-1240	4	12	semigroups	semigroup	NOUN
ejpam-1240	4	13	of	of	ADP
ejpam-1240	4	14	x.j	x.j	PROPN
ejpam-1240	4	15	.	.	PROPN
ejpam-1240	4	16	guo	guo	PROPN
ejpam-1240	4	17	and	and	CCONJ
ejpam-1240	4	18	x.y	x.y	PROPN
ejpam-1240	4	19	.	.	PROPN
ejpam-1240	4	20	xie	xie	PROPN
ejpam-1240	5	1	[	[	X
ejpam-1240	5	2	13	13	NUM
ejpam-1240	5	3	]	]	PUNCT
ejpam-1240	5	4	.	.	PUNCT
ejpam-1240	6	1	some	some	DET
ejpam-1240	6	2	other	other	ADJ
ejpam-1240	6	3	results	result	NOUN
ejpam-1240	6	4	related	relate	VERB
ejpam-1240	6	5	to	to	AUX
ejpam-1240	6	6	naturally	naturally	ADV
ejpam-1240	6	7	ordered	order	VERB
ejpam-1240	6	8	regular	regular	ADJ
ejpam-1240	6	9	semigroups	semigroup	NOUN
ejpam-1240	6	10	are	be	AUX
ejpam-1240	6	11	amplified	amplify	VERB
ejpam-1240	6	12	and	and	CCONJ
ejpam-1240	6	13	strengthened	strengthen	VERB
ejpam-1240	6	14	.	.	PUNCT
ejpam-1240	7	1	2000	2000	NUM
ejpam-1240	7	2	mathematics	mathematic	NOUN
ejpam-1240	7	3	subject	subject	NOUN
ejpam-1240	7	4	classifications	classification	NOUN
ejpam-1240	7	5	:	:	PUNCT
ejpam-1240	7	6	20m10	20m10	NUM
ejpam-1240	7	7	key	key	ADJ
ejpam-1240	7	8	words	word	NOUN
ejpam-1240	7	9	and	and	CCONJ
ejpam-1240	7	10	phrases	phrase	NOUN
ejpam-1240	7	11	:	:	PUNCT
ejpam-1240	7	12	naturally	naturally	ADV
ejpam-1240	7	13	ordered	order	VERB
ejpam-1240	7	14	semigroup	semigroup	NOUN
ejpam-1240	7	15	;	;	PUNCT
ejpam-1240	7	16	abundant	abundant	ADJ
ejpam-1240	7	17	semigroup	semigroup	NOUN
ejpam-1240	7	18	;	;	PUNCT
ejpam-1240	7	19	greatest	great	ADJ
ejpam-1240	7	20	inverse	inverse	NOUN
ejpam-1240	7	21	;	;	PUNCT
ejpam-1240	7	22	partial	partial	ADJ
ejpam-1240	7	23	semilattices	semilattice	NOUN
ejpam-1240	7	24	;	;	PUNCT
ejpam-1240	7	25	*	*	PUNCT
ejpam-1240	7	26	-unipotent	-unipotent	NOUN
ejpam-1240	7	27	semigroups	semigroup	NOUN
ejpam-1240	7	28	1	1	X
ejpam-1240	7	29	.	.	X
ejpam-1240	7	30	introduction	introduction	NOUN
ejpam-1240	7	31	let	let	VERB
ejpam-1240	7	32	e	e	PRON
ejpam-1240	7	33	be	be	AUX
ejpam-1240	7	34	the	the	DET
ejpam-1240	7	35	set	set	NOUN
ejpam-1240	7	36	of	of	ADP
ejpam-1240	7	37	idempotents	idempotent	NOUN
ejpam-1240	7	38	of	of	ADP
ejpam-1240	7	39	a	a	DET
ejpam-1240	7	40	semigroup	semigroup	NOUN
ejpam-1240	7	41	s	s	NOUN
ejpam-1240	7	42	,	,	PUNCT
ejpam-1240	7	43	define	define	VERB
ejpam-1240	7	44	a	a	DET
ejpam-1240	7	45	relation	relation	NOUN
ejpam-1240	7	46	“	"	PUNCT
ejpam-1240	7	47	�	�	PROPN
ejpam-1240	7	48	”	"	PUNCT
ejpam-1240	7	49	on	on	ADP
ejpam-1240	7	50	e	e	X
ejpam-1240	7	51	by	by	ADP
ejpam-1240	7	52	e	e	PROPN
ejpam-1240	7	53	�	�	PROPN
ejpam-1240	7	54	f	f	PROPN
ejpam-1240	7	55	⇔	⇔	PROPN
ejpam-1240	7	56	e	e	PROPN
ejpam-1240	7	57	=	=	SYM
ejpam-1240	7	58	e	e	X
ejpam-1240	7	59	f	f	PROPN
ejpam-1240	7	60	=	=	SYM
ejpam-1240	7	61	f	f	PROPN
ejpam-1240	7	62	e.	e.	PROPN
ejpam-1240	7	63	then	then	ADV
ejpam-1240	7	64	,	,	PUNCT
ejpam-1240	7	65	the	the	DET
ejpam-1240	7	66	relation	relation	NOUN
ejpam-1240	7	67	“	"	PUNCT
ejpam-1240	7	68	�	�	PROPN
ejpam-1240	7	69	”	"	PUNCT
ejpam-1240	7	70	is	be	AUX
ejpam-1240	7	71	clearly	clearly	ADV
ejpam-1240	7	72	an	an	DET
ejpam-1240	7	73	order	order	NOUN
ejpam-1240	7	74	on	on	ADP
ejpam-1240	7	75	e	e	ADP
ejpam-1240	7	76	which	which	PRON
ejpam-1240	7	77	is	be	AUX
ejpam-1240	7	78	called	call	VERB
ejpam-1240	7	79	the	the	DET
ejpam-1240	7	80	natural	natural	ADJ
ejpam-1240	7	81	order	order	NOUN
ejpam-1240	7	82	on	on	ADP
ejpam-1240	7	83	e.	e.	PROPN
ejpam-1240	7	84	an	an	DET
ejpam-1240	7	85	ordered	order	VERB
ejpam-1240	7	86	semigroup	semigroup	NOUN
ejpam-1240	7	87	(	(	PUNCT
ejpam-1240	7	88	s,≤	s,≤	NOUN
ejpam-1240	7	89	)	)	PUNCT
ejpam-1240	7	90	endowed	endow	VERB
ejpam-1240	7	91	with	with	ADP
ejpam-1240	7	92	a	a	DET
ejpam-1240	7	93	natural	natural	ADJ
ejpam-1240	7	94	order	order	NOUN
ejpam-1240	7	95	is	be	AUX
ejpam-1240	7	96	said	say	VERB
ejpam-1240	7	97	to	to	PART
ejpam-1240	7	98	be	be	AUX
ejpam-1240	7	99	a	a	DET
ejpam-1240	7	100	naturally	naturally	ADV
ejpam-1240	7	101	ordered	order	VERB
ejpam-1240	7	102	semigroup	semigroup	NOUN
ejpam-1240	7	103	if	if	SCONJ
ejpam-1240	7	104	the	the	DET
ejpam-1240	7	105	order	order	NOUN
ejpam-1240	7	106	≤	≤	X
ejpam-1240	7	107	extends	extend	VERB
ejpam-1240	7	108	the	the	DET
ejpam-1240	7	109	natural	natural	ADJ
ejpam-1240	7	110	order	order	NOUN
ejpam-1240	7	111	�	�	PROPN
ejpam-1240	7	112	on	on	ADP
ejpam-1240	7	113	the	the	DET
ejpam-1240	7	114	idempotents	idempotent	NOUN
ejpam-1240	7	115	,	,	PUNCT
ejpam-1240	7	116	i.e.	i.e.	X
ejpam-1240	7	117	if	if	SCONJ
ejpam-1240	7	118	(	(	PUNCT
ejpam-1240	7	119	∀e	∀e	NOUN
ejpam-1240	7	120	,	,	PUNCT
ejpam-1240	7	121	f	f	PROPN
ejpam-1240	7	122	∈	∈	PROPN
ejpam-1240	7	123	e	e	X
ejpam-1240	7	124	)	)	PUNCT
ejpam-1240	7	125	e	e	PROPN
ejpam-1240	7	126	�	�	PROPN
ejpam-1240	7	127	f	f	PROPN
ejpam-1240	7	128	⇒	⇒	PROPN
ejpam-1240	7	129	e	e	PROPN
ejpam-1240	7	130	≤	≤	ADJ
ejpam-1240	7	131	f	f	X
ejpam-1240	7	132	.	.	PUNCT
ejpam-1240	8	1	in	in	ADP
ejpam-1240	8	2	general	general	ADJ
ejpam-1240	8	3	,	,	PUNCT
ejpam-1240	8	4	in	in	ADP
ejpam-1240	8	5	an	an	DET
ejpam-1240	8	6	ordered	order	VERB
ejpam-1240	8	7	semigroup	semigroup	NOUN
ejpam-1240	8	8	(	(	PUNCT
ejpam-1240	8	9	s,≤	s,≤	NOUN
ejpam-1240	8	10	)	)	PUNCT
ejpam-1240	8	11	the	the	DET
ejpam-1240	8	12	order	order	NOUN
ejpam-1240	8	13	≤	≤	X
ejpam-1240	8	14	does	do	AUX
ejpam-1240	8	15	not	not	PART
ejpam-1240	8	16	give	give	VERB
ejpam-1240	8	17	much	much	ADJ
ejpam-1240	8	18	information	information	NOUN
ejpam-1240	8	19	of	of	ADP
ejpam-1240	8	20	the	the	DET
ejpam-1240	8	21	algebraic	algebraic	ADJ
ejpam-1240	8	22	properties	property	NOUN
ejpam-1240	8	23	of	of	ADP
ejpam-1240	8	24	s.	s.	PROPN
ejpam-1240	8	25	for	for	ADP
ejpam-1240	8	26	instance	instance	NOUN
ejpam-1240	8	27	,	,	PUNCT
ejpam-1240	8	28	this	this	PRON
ejpam-1240	8	29	is	be	AUX
ejpam-1240	8	30	particularly	particularly	ADV
ejpam-1240	8	31	true	true	ADJ
ejpam-1240	8	32	in	in	ADP
ejpam-1240	8	33	the	the	DET
ejpam-1240	8	34	theory	theory	NOUN
ejpam-1240	8	35	of	of	ADP
ejpam-1240	8	36	residuated	residuate	VERB
ejpam-1240	8	37	semigroups	semigroup	NOUN
ejpam-1240	8	38	.	.	PUNCT
ejpam-1240	9	1	nevertheless	nevertheless	ADV
ejpam-1240	9	2	,	,	PUNCT
ejpam-1240	9	3	the	the	DET
ejpam-1240	9	4	semigroups	semigroup	NOUN
ejpam-1240	9	5	which	which	PRON
ejpam-1240	9	6	are	be	AUX
ejpam-1240	9	7	regular	regular	ADJ
ejpam-1240	9	8	and	and	CCONJ
ejpam-1240	9	9	naturally	naturally	ADV
ejpam-1240	9	10	ordered	order	VERB
ejpam-1240	9	11	form	form	NOUN
ejpam-1240	9	12	a	a	DET
ejpam-1240	9	13	∗corresponding	∗corresponding	NOUN
ejpam-1240	9	14	author	author	NOUN
ejpam-1240	9	15	.	.	PUNCT
ejpam-1240	10	1	email	email	NOUN
ejpam-1240	10	2	addresses	address	NOUN
ejpam-1240	10	3	:	:	PUNCT
ejpam-1240	10	4	xjguo�jxnu.edu	xjguo�jxnu.edu	PROPN
ejpam-1240	10	5	.	.	PUNCT
ejpam-1240	11	1	n	n	CCONJ
ejpam-1240	11	2	(	(	PUNCT
ejpam-1240	11	3	x.	x.	NOUN
ejpam-1240	11	4	guo	guo	PROPN
ejpam-1240	11	5	)	)	PUNCT
ejpam-1240	11	6	,	,	PUNCT
ejpam-1240	11	7	kpshum�ynu.edu	kpshum�ynu.edu	PROPN
ejpam-1240	11	8	.	.	PROPN
ejpam-1240	12	1	n	n	PROPN
ejpam-1240	12	2	(	(	PUNCT
ejpam-1240	12	3	k.	k.	NOUN
ejpam-1240	12	4	shum	shum	PROPN
ejpam-1240	12	5	)	)	PUNCT
ejpam-1240	12	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1240	13	1	210	210	NUM
ejpam-1240	14	1	c	c	X
ejpam-1240	14	2	©	©	NOUN
ejpam-1240	14	3	2011	2011	NUM
ejpam-1240	14	4	ejpam	ejpam	VERB
ejpam-1240	14	5	all	all	DET
ejpam-1240	14	6	rights	right	NOUN
ejpam-1240	14	7	reserved	reserve	VERB
ejpam-1240	14	8	.	.	PUNCT
ejpam-1240	15	1	x.	x.	PROPN
ejpam-1240	15	2	guo	guo	PROPN
ejpam-1240	15	3	,	,	PUNCT
ejpam-1240	15	4	k.	k.	PROPN
ejpam-1240	15	5	shum	shum	PROPN
ejpam-1240	15	6	/	/	SYM
ejpam-1240	15	7	eur	eur	PROPN
ejpam-1240	15	8	.	.	PUNCT
ejpam-1240	16	1	j.	j.	PROPN
ejpam-1240	16	2	pure	pure	PROPN
ejpam-1240	16	3	appl	appl	PROPN
ejpam-1240	16	4	.	.	PROPN
ejpam-1240	16	5	math	math	PROPN
ejpam-1240	16	6	,	,	PUNCT
ejpam-1240	16	7	4	4	NUM
ejpam-1240	16	8	(	(	PUNCT
ejpam-1240	16	9	2011	2011	NUM
ejpam-1240	16	10	)	)	PUNCT
ejpam-1240	16	11	,	,	PUNCT
ejpam-1240	16	12	210	210	NUM
ejpam-1240	16	13	-	-	SYM
ejpam-1240	16	14	220	220	NUM
ejpam-1240	16	15	211	211	NUM
ejpam-1240	16	16	large	large	ADJ
ejpam-1240	16	17	class	class	NOUN
ejpam-1240	16	18	which	which	PRON
ejpam-1240	16	19	has	have	AUX
ejpam-1240	16	20	been	be	AUX
ejpam-1240	16	21	investigated	investigate	VERB
ejpam-1240	16	22	by	by	ADP
ejpam-1240	16	23	many	many	ADJ
ejpam-1240	16	24	authors	author	NOUN
ejpam-1240	16	25	.	.	PUNCT
ejpam-1240	17	1	in	in	ADP
ejpam-1240	17	2	particular	particular	ADJ
ejpam-1240	17	3	,	,	PUNCT
ejpam-1240	17	4	the	the	DET
ejpam-1240	17	5	structure	structure	NOUN
ejpam-1240	17	6	of	of	ADP
ejpam-1240	17	7	an	an	DET
ejpam-1240	17	8	naturally	naturally	ADV
ejpam-1240	17	9	ordered	order	VERB
ejpam-1240	17	10	regular	regular	ADJ
ejpam-1240	17	11	semigroups	semigroup	NOUN
ejpam-1240	17	12	with	with	ADP
ejpam-1240	17	13	a	a	DET
ejpam-1240	17	14	greatest	great	ADJ
ejpam-1240	17	15	idempotent	idempotent	NOUN
ejpam-1240	17	16	was	be	AUX
ejpam-1240	17	17	investigated	investigate	VERB
ejpam-1240	17	18	by	by	ADP
ejpam-1240	17	19	t.s	t.s	PROPN
ejpam-1240	17	20	.	.	PROPN
ejpam-1240	17	21	blyth	blyth	PROPN
ejpam-1240	17	22	and	and	CCONJ
ejpam-1240	17	23	r.b	r.b	PROPN
ejpam-1240	17	24	.	.	PROPN
ejpam-1240	17	25	mcfadden	mcfadden	PROPN
ejpam-1240	17	26	in	in	ADP
ejpam-1240	17	27	[	[	X
ejpam-1240	17	28	1	1	NUM
ejpam-1240	17	29	]	]	PUNCT
ejpam-1240	17	30	in	in	ADP
ejpam-1240	17	31	1981	1981	NUM
ejpam-1240	17	32	.	.	PUNCT
ejpam-1240	18	1	in	in	ADP
ejpam-1240	18	2	particular	particular	ADJ
ejpam-1240	18	3	,	,	PUNCT
ejpam-1240	18	4	they	they	PRON
ejpam-1240	18	5	established	establish	VERB
ejpam-1240	18	6	a	a	DET
ejpam-1240	18	7	structure	structure	NOUN
ejpam-1240	18	8	theorem	theorem	NOUN
ejpam-1240	18	9	for	for	ADP
ejpam-1240	18	10	these	these	DET
ejpam-1240	18	11	semigroups	semigroup	NOUN
ejpam-1240	18	12	.	.	PUNCT
ejpam-1240	19	1	they	they	PRON
ejpam-1240	19	2	have	have	AUX
ejpam-1240	19	3	also	also	ADV
ejpam-1240	19	4	shown	show	VERB
ejpam-1240	19	5	that	that	SCONJ
ejpam-1240	19	6	each	each	DET
ejpam-1240	19	7	element	element	NOUN
ejpam-1240	19	8	of	of	ADP
ejpam-1240	19	9	such	such	DET
ejpam-1240	19	10	a	a	DET
ejpam-1240	19	11	naturally	naturally	ADV
ejpam-1240	19	12	ordered	order	VERB
ejpam-1240	19	13	regular	regular	ADJ
ejpam-1240	19	14	semigroup	semigroup	NOUN
ejpam-1240	19	15	has	have	VERB
ejpam-1240	19	16	a	a	DET
ejpam-1240	19	17	greatest	great	ADJ
ejpam-1240	19	18	inverse	inverse	NOUN
ejpam-1240	19	19	.	.	PUNCT
ejpam-1240	20	1	in	in	ADP
ejpam-1240	20	2	[	[	X
ejpam-1240	20	3	2	2	NUM
ejpam-1240	20	4	]	]	PUNCT
ejpam-1240	20	5	,	,	PUNCT
ejpam-1240	20	6	they	they	PRON
ejpam-1240	20	7	extended	extend	VERB
ejpam-1240	20	8	their	their	PRON
ejpam-1240	20	9	results	result	NOUN
ejpam-1240	20	10	more	more	ADV
ejpam-1240	20	11	generally	generally	ADV
ejpam-1240	20	12	to	to	ADP
ejpam-1240	20	13	the	the	DET
ejpam-1240	20	14	naturally	naturally	ADV
ejpam-1240	20	15	ordered	order	VERB
ejpam-1240	20	16	regular	regular	ADJ
ejpam-1240	20	17	semigroups	semigroup	NOUN
ejpam-1240	20	18	for	for	ADP
ejpam-1240	20	19	which	which	PRON
ejpam-1240	20	20	each	each	DET
ejpam-1240	20	21	element	element	NOUN
ejpam-1240	20	22	has	have	VERB
ejpam-1240	20	23	a	a	DET
ejpam-1240	20	24	greatest	great	ADJ
ejpam-1240	20	25	inverse	inverse	NOUN
ejpam-1240	20	26	.	.	PUNCT
ejpam-1240	21	1	after	after	ADP
ejpam-1240	21	2	this	this	DET
ejpam-1240	21	3	interesting	interesting	ADJ
ejpam-1240	21	4	result	result	NOUN
ejpam-1240	21	5	,	,	PUNCT
ejpam-1240	21	6	a	a	DET
ejpam-1240	21	7	series	series	NOUN
ejpam-1240	21	8	of	of	ADP
ejpam-1240	21	9	papers	paper	NOUN
ejpam-1240	21	10	on	on	ADP
ejpam-1240	21	11	this	this	DET
ejpam-1240	21	12	topic	topic	NOUN
ejpam-1240	21	13	have	have	AUX
ejpam-1240	21	14	been	be	AUX
ejpam-1240	21	15	produced	produce	VERB
ejpam-1240	21	16	,	,	PUNCT
ejpam-1240	21	17	for	for	ADP
ejpam-1240	21	18	instance	instance	NOUN
ejpam-1240	21	19	,	,	PUNCT
ejpam-1240	21	20	the	the	DET
ejpam-1240	21	21	reader	reader	NOUN
ejpam-1240	21	22	is	be	AUX
ejpam-1240	21	23	referred	refer	VERB
ejpam-1240	21	24	to	to	ADP
ejpam-1240	21	25	the	the	DET
ejpam-1240	21	26	papers	paper	NOUN
ejpam-1240	21	27	[	[	X
ejpam-1240	21	28	1]-[7	1]-[7	X
ejpam-1240	21	29	]	]	X
ejpam-1240	21	30	,	,	PUNCT
ejpam-1240	21	31	[	[	X
ejpam-1240	21	32	19	19	NUM
ejpam-1240	21	33	]	]	PUNCT
ejpam-1240	21	34	and	and	CCONJ
ejpam-1240	21	35	the	the	DET
ejpam-1240	21	36	references	reference	NOUN
ejpam-1240	21	37	listed	list	VERB
ejpam-1240	21	38	in	in	ADP
ejpam-1240	21	39	[	[	X
ejpam-1240	21	40	18	18	NUM
ejpam-1240	21	41	]	]	PUNCT
ejpam-1240	21	42	.	.	PUNCT
ejpam-1240	22	1	it	it	PRON
ejpam-1240	22	2	is	be	AUX
ejpam-1240	22	3	easy	easy	ADJ
ejpam-1240	22	4	to	to	PART
ejpam-1240	22	5	see	see	VERB
ejpam-1240	22	6	that	that	SCONJ
ejpam-1240	22	7	the	the	DET
ejpam-1240	22	8	relations	relation	NOUN
ejpam-1240	22	9	r∗	r∗	VERB
ejpam-1240	22	10	and	and	CCONJ
ejpam-1240	22	11	l	l	NOUN
ejpam-1240	22	12	∗	∗	NOUN
ejpam-1240	22	13	are	be	AUX
ejpam-1240	22	14	the	the	DET
ejpam-1240	22	15	generalizations	generalization	NOUN
ejpam-1240	22	16	of	of	ADP
ejpam-1240	22	17	the	the	DET
ejpam-1240	22	18	green	green	PROPN
ejpam-1240	22	19	’s	’s	PART
ejpam-1240	22	20	relations	relation	NOUN
ejpam-1240	22	21	r	r	NOUN
ejpam-1240	22	22	and	and	CCONJ
ejpam-1240	22	23	l	l	NOUN
ejpam-1240	22	24	,	,	PUNCT
ejpam-1240	22	25	respectively	respectively	ADV
ejpam-1240	22	26	.	.	PUNCT
ejpam-1240	23	1	for	for	ADP
ejpam-1240	23	2	the	the	DET
ejpam-1240	23	3	elements	element	NOUN
ejpam-1240	23	4	a	a	PRON
ejpam-1240	23	5	,	,	PUNCT
ejpam-1240	23	6	b	b	PROPN
ejpam-1240	23	7	∈	∈	PROPN
ejpam-1240	23	8	s	s	NOUN
ejpam-1240	23	9	,	,	PUNCT
ejpam-1240	23	10	define	define	VERB
ejpam-1240	23	11	ar∗b	ar∗b	ADV
ejpam-1240	23	12	if	if	SCONJ
ejpam-1240	24	1	and	and	CCONJ
ejpam-1240	24	2	only	only	ADV
ejpam-1240	24	3	if	if	SCONJ
ejpam-1240	24	4	they	they	PRON
ejpam-1240	24	5	are	be	AUX
ejpam-1240	24	6	related	relate	VERB
ejpam-1240	24	7	by	by	ADP
ejpam-1240	24	8	r	r	NOUN
ejpam-1240	24	9	in	in	ADP
ejpam-1240	24	10	some	some	DET
ejpam-1240	24	11	oversemigroup	oversemigroup	NOUN
ejpam-1240	24	12	of	of	ADP
ejpam-1240	24	13	s.	s.	PROPN
ejpam-1240	24	14	the	the	DET
ejpam-1240	24	15	relation	relation	NOUN
ejpam-1240	24	16	l	l	PROPN
ejpam-1240	24	17	∗	∗	NOUN
ejpam-1240	24	18	can	can	AUX
ejpam-1240	24	19	be	be	AUX
ejpam-1240	24	20	dually	dually	ADV
ejpam-1240	24	21	defined	define	VERB
ejpam-1240	24	22	.	.	PUNCT
ejpam-1240	25	1	by	by	ADP
ejpam-1240	25	2	an	an	DET
ejpam-1240	25	3	rpp	rpp	PROPN
ejpam-1240	25	4	semigroup	semigroup	PROPN
ejpam-1240	25	5	,	,	PUNCT
ejpam-1240	25	6	we	we	PRON
ejpam-1240	25	7	mean	mean	VERB
ejpam-1240	25	8	a	a	DET
ejpam-1240	25	9	semigroup	semigroup	NOUN
ejpam-1240	25	10	s	s	X
ejpam-1240	25	11	in	in	ADP
ejpam-1240	25	12	which	which	PRON
ejpam-1240	25	13	for	for	ADP
ejpam-1240	25	14	any	any	DET
ejpam-1240	25	15	a	a	DET
ejpam-1240	25	16	∈	∈	ADJ
ejpam-1240	25	17	s	s	NOUN
ejpam-1240	25	18	,	,	PUNCT
ejpam-1240	25	19	the	the	DET
ejpam-1240	25	20	system	system	NOUN
ejpam-1240	25	21	as1	as1	NOUN
ejpam-1240	25	22	,	,	PUNCT
ejpam-1240	25	23	regarded	regard	VERB
ejpam-1240	25	24	as	as	ADP
ejpam-1240	25	25	an	an	DET
ejpam-1240	25	26	s1	s1	NOUN
ejpam-1240	25	27	-	-	PUNCT
ejpam-1240	25	28	system	system	NOUN
ejpam-1240	25	29	,	,	PUNCT
ejpam-1240	25	30	is	be	AUX
ejpam-1240	25	31	projective	projective	ADJ
ejpam-1240	25	32	.	.	PUNCT
ejpam-1240	26	1	in	in	ADP
ejpam-1240	26	2	the	the	DET
ejpam-1240	26	3	literature	literature	NOUN
ejpam-1240	26	4	,	,	PUNCT
ejpam-1240	26	5	fountain	fountain	NOUN
ejpam-1240	26	6	[	[	X
ejpam-1240	26	7	10	10	NUM
ejpam-1240	26	8	]	]	PUNCT
ejpam-1240	26	9	called	call	VERB
ejpam-1240	26	10	such	such	DET
ejpam-1240	26	11	a	a	DET
ejpam-1240	26	12	semigroup	semigroup	NOUN
ejpam-1240	26	13	abundant	abundant	ADJ
ejpam-1240	26	14	if	if	SCONJ
ejpam-1240	26	15	each	each	DET
ejpam-1240	26	16	r∗-class	r∗-class	NOUN
ejpam-1240	26	17	and	and	CCONJ
ejpam-1240	26	18	each	each	DET
ejpam-1240	26	19	l	l	NOUN
ejpam-1240	26	20	∗-class	∗-class	NOUN
ejpam-1240	26	21	contains	contain	VERB
ejpam-1240	26	22	an	an	DET
ejpam-1240	26	23	idempotent	idempotent	NOUN
ejpam-1240	26	24	.	.	PUNCT
ejpam-1240	27	1	in	in	ADP
ejpam-1240	27	2	fact	fact	NOUN
ejpam-1240	27	3	,	,	PUNCT
ejpam-1240	27	4	abundant	abundant	ADJ
ejpam-1240	27	5	semigroups	semigroup	NOUN
ejpam-1240	27	6	are	be	AUX
ejpam-1240	27	7	rpp	rpp	PROPN
ejpam-1240	27	8	and	and	CCONJ
ejpam-1240	27	9	lpp	lpp	PROPN
ejpam-1240	27	10	semigroups	semigroup	NOUN
ejpam-1240	27	11	.	.	PUNCT
ejpam-1240	28	1	it	it	PRON
ejpam-1240	28	2	is	be	AUX
ejpam-1240	28	3	known	know	VERB
ejpam-1240	28	4	that	that	SCONJ
ejpam-1240	28	5	the	the	DET
ejpam-1240	28	6	regular	regular	ADJ
ejpam-1240	28	7	semigroups	semigroup	NOUN
ejpam-1240	28	8	are	be	AUX
ejpam-1240	28	9	abundant	abundant	ADJ
ejpam-1240	28	10	semigroups	semigroup	NOUN
ejpam-1240	28	11	.	.	PUNCT
ejpam-1240	29	1	hence	hence	ADV
ejpam-1240	29	2	,	,	PUNCT
ejpam-1240	29	3	it	it	PRON
ejpam-1240	29	4	is	be	AUX
ejpam-1240	29	5	natural	natural	ADJ
ejpam-1240	29	6	to	to	PART
ejpam-1240	29	7	probe	probe	VERB
ejpam-1240	29	8	the	the	DET
ejpam-1240	29	9	ordered	order	VERB
ejpam-1240	29	10	abundant	abundant	ADJ
ejpam-1240	29	11	semigroups	semigroup	NOUN
ejpam-1240	29	12	.	.	PUNCT
ejpam-1240	30	1	in	in	ADP
ejpam-1240	30	2	this	this	DET
ejpam-1240	30	3	aspect	aspect	NOUN
ejpam-1240	30	4	,	,	PUNCT
ejpam-1240	30	5	the	the	DET
ejpam-1240	30	6	first	first	ADJ
ejpam-1240	30	7	author	author	NOUN
ejpam-1240	30	8	and	and	CCONJ
ejpam-1240	30	9	his	his	PRON
ejpam-1240	30	10	collaborators	collaborator	NOUN
ejpam-1240	30	11	(	(	PUNCT
ejpam-1240	30	12	see	see	VERB
ejpam-1240	30	13	[	[	X
ejpam-1240	30	14	11]-[16	11]-[16	PROPN
ejpam-1240	30	15	]	]	PUNCT
ejpam-1240	30	16	)	)	PUNCT
ejpam-1240	30	17	have	have	AUX
ejpam-1240	30	18	probed	probe	VERB
ejpam-1240	30	19	the	the	DET
ejpam-1240	30	20	structure	structure	NOUN
ejpam-1240	30	21	of	of	ADP
ejpam-1240	30	22	several	several	ADJ
ejpam-1240	30	23	classes	class	NOUN
ejpam-1240	30	24	of	of	ADP
ejpam-1240	30	25	naturally	naturally	ADV
ejpam-1240	30	26	ordered	order	VERB
ejpam-1240	30	27	abundant	abundant	ADJ
ejpam-1240	30	28	semigroups	semigroup	NOUN
ejpam-1240	30	29	.	.	PUNCT
ejpam-1240	31	1	in	in	ADP
ejpam-1240	31	2	this	this	DET
ejpam-1240	31	3	paper	paper	NOUN
ejpam-1240	31	4	,	,	PUNCT
ejpam-1240	31	5	we	we	PRON
ejpam-1240	31	6	will	will	AUX
ejpam-1240	31	7	also	also	ADV
ejpam-1240	31	8	investigated	investigate	VERB
ejpam-1240	31	9	the	the	DET
ejpam-1240	31	10	naturally	naturally	ADV
ejpam-1240	31	11	ordered	order	VERB
ejpam-1240	31	12	abundant	abundant	ADJ
ejpam-1240	31	13	semigroups	semigroup	NOUN
ejpam-1240	31	14	for	for	ADP
ejpam-1240	31	15	which	which	PRON
ejpam-1240	31	16	each	each	DET
ejpam-1240	31	17	idempotent	idempotent	NOUN
ejpam-1240	31	18	has	have	VERB
ejpam-1240	31	19	a	a	DET
ejpam-1240	31	20	greatest	great	ADJ
ejpam-1240	31	21	inverse	inverse	NOUN
ejpam-1240	31	22	.	.	PUNCT
ejpam-1240	32	1	recently	recently	ADV
ejpam-1240	32	2	,	,	PUNCT
ejpam-1240	32	3	ren	ren	PROPN
ejpam-1240	32	4	and	and	CCONJ
ejpam-1240	32	5	the	the	DET
ejpam-1240	32	6	authors	author	NOUN
ejpam-1240	32	7	[	[	X
ejpam-1240	32	8	12	12	NUM
ejpam-1240	32	9	]	]	PUNCT
ejpam-1240	32	10	have	have	AUX
ejpam-1240	32	11	studied	study	VERB
ejpam-1240	32	12	the	the	DET
ejpam-1240	32	13	naturally	naturally	ADV
ejpam-1240	32	14	ordered	order	VERB
ejpam-1240	32	15	rpp	rpp	PROPN
ejpam-1240	32	16	semigroups	semigroup	NOUN
ejpam-1240	32	17	in	in	ADP
ejpam-1240	32	18	which	which	PRON
ejpam-1240	32	19	each	each	DET
ejpam-1240	32	20	idempotent	idempotent	NOUN
ejpam-1240	32	21	has	have	VERB
ejpam-1240	32	22	a	a	DET
ejpam-1240	32	23	greatest	great	ADJ
ejpam-1240	32	24	inverse	inverse	NOUN
ejpam-1240	32	25	and	and	CCONJ
ejpam-1240	32	26	they	they	PRON
ejpam-1240	32	27	obtained	obtain	VERB
ejpam-1240	32	28	a	a	DET
ejpam-1240	32	29	structure	structure	NOUN
ejpam-1240	32	30	theorem	theorem	VERB
ejpam-1240	32	31	for	for	ADP
ejpam-1240	32	32	a	a	DET
ejpam-1240	32	33	special	special	ADJ
ejpam-1240	32	34	class	class	NOUN
ejpam-1240	32	35	of	of	ADP
ejpam-1240	32	36	such	such	ADJ
ejpam-1240	32	37	naturally	naturally	ADV
ejpam-1240	32	38	ordered	order	VERB
ejpam-1240	32	39	semigroups	semigroup	NOUN
ejpam-1240	32	40	.	.	PUNCT
ejpam-1240	33	1	as	as	ADP
ejpam-1240	33	2	a	a	DET
ejpam-1240	33	3	continuation	continuation	NOUN
ejpam-1240	33	4	of	of	ADP
ejpam-1240	33	5	the	the	DET
ejpam-1240	33	6	work	work	NOUN
ejpam-1240	33	7	of	of	ADP
ejpam-1240	33	8	guo	guo	PROPN
ejpam-1240	33	9	and	and	CCONJ
ejpam-1240	33	10	xie	xie	PROPN
ejpam-1240	34	1	[	[	X
ejpam-1240	34	2	13	13	NUM
ejpam-1240	34	3	]	]	PUNCT
ejpam-1240	34	4	,	,	PUNCT
ejpam-1240	34	5	we	we	PRON
ejpam-1240	34	6	further	far	ADV
ejpam-1240	34	7	investigate	investigate	VERB
ejpam-1240	34	8	the	the	DET
ejpam-1240	34	9	structure	structure	NOUN
ejpam-1240	34	10	of	of	ADP
ejpam-1240	34	11	the	the	DET
ejpam-1240	34	12	naturally	naturally	ADV
ejpam-1240	34	13	ordered	order	VERB
ejpam-1240	34	14	abundant	abundant	ADJ
ejpam-1240	34	15	semigroups	semigroup	NOUN
ejpam-1240	34	16	for	for	ADP
ejpam-1240	34	17	which	which	PRON
ejpam-1240	34	18	every	every	DET
ejpam-1240	34	19	idempotent	idempotent	NOUN
ejpam-1240	34	20	has	have	VERB
ejpam-1240	34	21	a	a	DET
ejpam-1240	34	22	greatest	great	ADJ
ejpam-1240	34	23	inverse	inverse	NOUN
ejpam-1240	34	24	.	.	PUNCT
ejpam-1240	35	1	a	a	DET
ejpam-1240	35	2	new	new	ADJ
ejpam-1240	35	3	construction	construction	NOUN
ejpam-1240	35	4	theorem	theorem	NOUN
ejpam-1240	35	5	for	for	ADP
ejpam-1240	35	6	such	such	ADJ
ejpam-1240	35	7	semigroups	semigroup	NOUN
ejpam-1240	35	8	will	will	AUX
ejpam-1240	35	9	be	be	AUX
ejpam-1240	35	10	presented	present	VERB
ejpam-1240	35	11	.	.	PUNCT
ejpam-1240	36	1	it	it	PRON
ejpam-1240	36	2	is	be	AUX
ejpam-1240	36	3	noteworthy	noteworthy	ADJ
ejpam-1240	36	4	that	that	SCONJ
ejpam-1240	36	5	our	our	PRON
ejpam-1240	36	6	construction	construction	NOUN
ejpam-1240	36	7	theorem	theorem	NOUN
ejpam-1240	36	8	is	be	AUX
ejpam-1240	36	9	different	different	ADJ
ejpam-1240	36	10	from	from	ADP
ejpam-1240	36	11	the	the	DET
ejpam-1240	36	12	structure	structure	NOUN
ejpam-1240	36	13	theorem	theorem	VERB
ejpam-1240	36	14	previously	previously	ADV
ejpam-1240	36	15	given	give	VERB
ejpam-1240	36	16	by	by	ADP
ejpam-1240	36	17	guo	guo	PROPN
ejpam-1240	36	18	and	and	CCONJ
ejpam-1240	36	19	xie	xie	PROPN
ejpam-1240	36	20	in	in	ADP
ejpam-1240	36	21	[	[	X
ejpam-1240	36	22	13	13	NUM
ejpam-1240	36	23	]	]	PUNCT
ejpam-1240	36	24	.	.	PUNCT
ejpam-1240	37	1	in	in	ADP
ejpam-1240	37	2	fact	fact	NOUN
ejpam-1240	37	3	,	,	PUNCT
ejpam-1240	37	4	our	our	PRON
ejpam-1240	37	5	new	new	ADJ
ejpam-1240	37	6	theorem	theorem	NOUN
ejpam-1240	37	7	generalizes	generalize	VERB
ejpam-1240	37	8	the	the	DET
ejpam-1240	37	9	previous	previous	ADJ
ejpam-1240	37	10	theorem	theorem	NOUN
ejpam-1240	37	11	given	give	VERB
ejpam-1240	37	12	by	by	ADP
ejpam-1240	37	13	guo	guo	PROPN
ejpam-1240	37	14	and	and	CCONJ
ejpam-1240	37	15	xie	xie	PROPN
ejpam-1240	37	16	in	in	ADP
ejpam-1240	37	17	the	the	DET
ejpam-1240	37	18	following	follow	VERB
ejpam-1240	37	19	aspects	aspect	NOUN
ejpam-1240	37	20	:	:	PUNCT
ejpam-1240	37	21	(	(	PUNCT
ejpam-1240	37	22	1	1	X
ejpam-1240	37	23	)	)	PUNCT
ejpam-1240	37	24	in	in	ADP
ejpam-1240	37	25	the	the	DET
ejpam-1240	37	26	previous	previous	ADJ
ejpam-1240	37	27	theorem	theorem	NOUN
ejpam-1240	37	28	of	of	ADP
ejpam-1240	37	29	guo	guo	PROPN
ejpam-1240	37	30	-	-	PUNCT
ejpam-1240	37	31	xie	xie	PROPN
ejpam-1240	37	32	,	,	PUNCT
ejpam-1240	37	33	the	the	DET
ejpam-1240	37	34	authors	author	NOUN
ejpam-1240	37	35	only	only	ADV
ejpam-1240	37	36	considered	consider	VERB
ejpam-1240	37	37	the	the	DET
ejpam-1240	37	38	case	case	NOUN
ejpam-1240	37	39	that	that	SCONJ
ejpam-1240	37	40	s	s	VERB
ejpam-1240	37	41	♭	♭	PROPN
ejpam-1240	37	42	is	be	AUX
ejpam-1240	37	43	an	an	DET
ejpam-1240	37	44	adequate	adequate	ADJ
ejpam-1240	37	45	subsemigroup	subsemigroup	NOUN
ejpam-1240	37	46	of	of	ADP
ejpam-1240	37	47	the	the	DET
ejpam-1240	37	48	semigroup	semigroup	PROPN
ejpam-1240	37	49	s.	s.	PROPN
ejpam-1240	37	50	in	in	ADP
ejpam-1240	37	51	other	other	ADJ
ejpam-1240	37	52	words	word	NOUN
ejpam-1240	37	53	,	,	PUNCT
ejpam-1240	37	54	the	the	DET
ejpam-1240	37	55	ordered	order	VERB
ejpam-1240	37	56	semigroup	semigroup	NOUN
ejpam-1240	37	57	s	s	X
ejpam-1240	37	58	in	in	ADP
ejpam-1240	37	59	[	[	X
ejpam-1240	37	60	13	13	NUM
ejpam-1240	37	61	]	]	PUNCT
ejpam-1240	37	62	is	be	AUX
ejpam-1240	37	63	only	only	ADV
ejpam-1240	37	64	an	an	DET
ejpam-1240	37	65	abundant	abundant	ADJ
ejpam-1240	37	66	semigroup	semigroup	NOUN
ejpam-1240	37	67	with	with	ADP
ejpam-1240	37	68	a	a	DET
ejpam-1240	37	69	quasi	quasi	ADJ
ejpam-1240	37	70	-	-	ADJ
ejpam-1240	37	71	ideal	ideal	ADJ
ejpam-1240	37	72	adequate	adequate	ADJ
ejpam-1240	37	73	transversal	transversal	NOUN
ejpam-1240	37	74	.	.	PUNCT
ejpam-1240	38	1	in	in	ADP
ejpam-1240	38	2	our	our	PRON
ejpam-1240	38	3	new	new	ADJ
ejpam-1240	38	4	theorem	theorem	NOUN
ejpam-1240	38	5	,	,	PUNCT
ejpam-1240	38	6	we	we	PRON
ejpam-1240	38	7	consider	consider	VERB
ejpam-1240	38	8	a	a	DET
ejpam-1240	38	9	more	more	ADV
ejpam-1240	38	10	general	general	ADJ
ejpam-1240	38	11	situation	situation	NOUN
ejpam-1240	38	12	.	.	PUNCT
ejpam-1240	39	1	(	(	PUNCT
ejpam-1240	39	2	2	2	X
ejpam-1240	39	3	)	)	PUNCT
ejpam-1240	39	4	in	in	ADP
ejpam-1240	39	5	the	the	DET
ejpam-1240	39	6	previous	previous	ADJ
ejpam-1240	39	7	theorem	theorem	NOUN
ejpam-1240	39	8	given	give	VERB
ejpam-1240	39	9	by	by	ADP
ejpam-1240	39	10	guo	guo	PROPN
ejpam-1240	39	11	-	-	PUNCT
ejpam-1240	39	12	xie	xie	PROPN
ejpam-1240	39	13	in	in	ADP
ejpam-1240	39	14	[	[	X
ejpam-1240	39	15	13	13	NUM
ejpam-1240	39	16	]	]	PUNCT
ejpam-1240	39	17	,	,	PUNCT
ejpam-1240	39	18	the	the	DET
ejpam-1240	39	19	authors	author	NOUN
ejpam-1240	39	20	only	only	ADV
ejpam-1240	39	21	studied	study	VERB
ejpam-1240	39	22	the	the	DET
ejpam-1240	39	23	naturally	naturally	ADV
ejpam-1240	39	24	ordered	order	VERB
ejpam-1240	39	25	abundant	abundant	ADJ
ejpam-1240	39	26	semigroups	semigroup	NOUN
ejpam-1240	39	27	with	with	ADP
ejpam-1240	39	28	a	a	DET
ejpam-1240	39	29	greatest	great	ADJ
ejpam-1240	39	30	idempotent	idempotent	NOUN
ejpam-1240	39	31	and	and	CCONJ
ejpam-1240	39	32	showed	show	VERB
ejpam-1240	39	33	how	how	SCONJ
ejpam-1240	39	34	to	to	PART
ejpam-1240	39	35	construct	construct	VERB
ejpam-1240	39	36	a	a	DET
ejpam-1240	39	37	kind	kind	NOUN
ejpam-1240	39	38	of	of	ADP
ejpam-1240	39	39	naturally	naturally	ADV
ejpam-1240	39	40	ordered	order	VERB
ejpam-1240	39	41	abundant	abundant	ADJ
ejpam-1240	39	42	semigroups	semigroup	NOUN
ejpam-1240	39	43	each	each	PRON
ejpam-1240	39	44	of	of	ADP
ejpam-1240	39	45	whose	whose	DET
ejpam-1240	39	46	idempotents	idempotent	NOUN
ejpam-1240	39	47	has	have	VERB
ejpam-1240	39	48	a	a	DET
ejpam-1240	39	49	greatest	great	ADJ
ejpam-1240	39	50	inverse	inverse	NOUN
ejpam-1240	39	51	and	and	CCONJ
ejpam-1240	39	52	which	which	PRON
ejpam-1240	39	53	is	be	AUX
ejpam-1240	39	54	g	g	NOUN
ejpam-1240	39	55	-	-	PUNCT
ejpam-1240	39	56	regular	regular	ADJ
ejpam-1240	39	57	and	and	CCONJ
ejpam-1240	39	58	reflexive	reflexive	ADJ
ejpam-1240	39	59	.	.	PUNCT
ejpam-1240	40	1	in	in	ADP
ejpam-1240	40	2	this	this	DET
ejpam-1240	40	3	paper	paper	NOUN
ejpam-1240	40	4	,	,	PUNCT
ejpam-1240	40	5	we	we	PRON
ejpam-1240	40	6	shall	shall	AUX
ejpam-1240	40	7	prove	prove	VERB
ejpam-1240	40	8	that	that	SCONJ
ejpam-1240	40	9	any	any	PRON
ejpam-1240	40	10	naturally	naturally	ADV
ejpam-1240	40	11	ordered	order	VERB
ejpam-1240	40	12	abundant	abundant	ADJ
ejpam-1240	40	13	semigroups	semigroup	NOUN
ejpam-1240	40	14	each	each	PRON
ejpam-1240	40	15	of	of	ADP
ejpam-1240	40	16	whose	whose	DET
ejpam-1240	40	17	idempotents	idempotent	NOUN
ejpam-1240	40	18	has	have	VERB
ejpam-1240	40	19	a	a	DET
ejpam-1240	40	20	greatest	great	ADJ
ejpam-1240	40	21	inverse	inverse	NOUN
ejpam-1240	40	22	and	and	CCONJ
ejpam-1240	40	23	which	which	PRON
ejpam-1240	40	24	is	be	AUX
ejpam-1240	40	25	g	g	NOUN
ejpam-1240	40	26	-	-	PUNCT
ejpam-1240	40	27	regular	regular	ADJ
ejpam-1240	40	28	and	and	CCONJ
ejpam-1240	40	29	reflexive	reflexive	ADJ
ejpam-1240	40	30	is	be	AUX
ejpam-1240	40	31	orderly	orderly	ADV
ejpam-1240	40	32	isomorphic	isomorphic	ADJ
ejpam-1240	40	33	to	to	ADP
ejpam-1240	40	34	some	some	DET
ejpam-1240	40	35	ordered	order	VERB
ejpam-1240	40	36	semigroup	semigroup	NOUN
ejpam-1240	40	37	constructed	construct	VERB
ejpam-1240	40	38	in	in	ADP
ejpam-1240	40	39	[	[	X
ejpam-1240	40	40	13	13	NUM
ejpam-1240	40	41	]	]	PUNCT
ejpam-1240	40	42	.	.	PUNCT
ejpam-1240	41	1	so	so	ADV
ejpam-1240	41	2	,	,	PUNCT
ejpam-1240	41	3	we	we	PRON
ejpam-1240	41	4	give	give	VERB
ejpam-1240	41	5	a	a	DET
ejpam-1240	41	6	construction	construction	NOUN
ejpam-1240	41	7	theorem	theorem	NOUN
ejpam-1240	41	8	of	of	ADP
ejpam-1240	41	9	such	such	ADJ
ejpam-1240	41	10	naturally	naturally	ADV
ejpam-1240	41	11	ordered	order	VERB
ejpam-1240	41	12	semigroups	semigroup	NOUN
ejpam-1240	41	13	.	.	PUNCT
ejpam-1240	42	1	x.	x.	PROPN
ejpam-1240	42	2	guo	guo	PROPN
ejpam-1240	42	3	,	,	PUNCT
ejpam-1240	42	4	k.	k.	PROPN
ejpam-1240	42	5	shum	shum	PROPN
ejpam-1240	42	6	/	/	SYM
ejpam-1240	42	7	eur	eur	PROPN
ejpam-1240	42	8	.	.	PUNCT
ejpam-1240	43	1	j.	j.	PROPN
ejpam-1240	43	2	pure	pure	PROPN
ejpam-1240	43	3	appl	appl	PROPN
ejpam-1240	43	4	.	.	PROPN
ejpam-1240	43	5	math	math	PROPN
ejpam-1240	43	6	,	,	PUNCT
ejpam-1240	43	7	4	4	NUM
ejpam-1240	43	8	(	(	PUNCT
ejpam-1240	43	9	2011	2011	NUM
ejpam-1240	43	10	)	)	PUNCT
ejpam-1240	43	11	,	,	PUNCT
ejpam-1240	43	12	210	210	NUM
ejpam-1240	43	13	-	-	SYM
ejpam-1240	43	14	220	220	NUM
ejpam-1240	43	15	212	212	NUM
ejpam-1240	43	16	2	2	NUM
ejpam-1240	43	17	.	.	PUNCT
ejpam-1240	43	18	main	main	ADJ
ejpam-1240	43	19	result	result	NOUN
ejpam-1240	43	20	throughout	throughout	ADP
ejpam-1240	43	21	this	this	DET
ejpam-1240	43	22	paper	paper	NOUN
ejpam-1240	43	23	,	,	PUNCT
ejpam-1240	43	24	the	the	DET
ejpam-1240	43	25	notations	notation	NOUN
ejpam-1240	43	26	and	and	CCONJ
ejpam-1240	43	27	terminologies	terminology	NOUN
ejpam-1240	43	28	are	be	AUX
ejpam-1240	43	29	taken	take	VERB
ejpam-1240	43	30	from	from	ADP
ejpam-1240	43	31	[	[	X
ejpam-1240	43	32	9]-[12	9]-[12	NOUN
ejpam-1240	43	33	]	]	PUNCT
ejpam-1240	43	34	.	.	PUNCT
ejpam-1240	44	1	for	for	ADP
ejpam-1240	44	2	other	other	ADJ
ejpam-1240	44	3	undefined	undefined	ADJ
ejpam-1240	44	4	terminologies	terminology	NOUN
ejpam-1240	44	5	and	and	CCONJ
ejpam-1240	44	6	definitions	definition	NOUN
ejpam-1240	44	7	,	,	PUNCT
ejpam-1240	44	8	the	the	DET
ejpam-1240	44	9	reader	reader	NOUN
ejpam-1240	44	10	is	be	AUX
ejpam-1240	44	11	referred	refer	VERB
ejpam-1240	44	12	to	to	ADP
ejpam-1240	44	13	the	the	DET
ejpam-1240	44	14	text	text	NOUN
ejpam-1240	44	15	of	of	ADP
ejpam-1240	44	16	howie	howie	NOUN
ejpam-1240	44	17	[	[	X
ejpam-1240	44	18	17	17	NUM
ejpam-1240	44	19	]	]	PUNCT
ejpam-1240	44	20	.	.	PUNCT
ejpam-1240	45	1	we	we	PRON
ejpam-1240	45	2	first	first	ADV
ejpam-1240	45	3	recall	recall	VERB
ejpam-1240	45	4	some	some	DET
ejpam-1240	45	5	known	know	VERB
ejpam-1240	45	6	concepts	concept	NOUN
ejpam-1240	45	7	.	.	PUNCT
ejpam-1240	46	1	a	a	DET
ejpam-1240	46	2	nonempty	nonempty	ADV
ejpam-1240	46	3	set	set	VERB
ejpam-1240	46	4	m	m	VERB
ejpam-1240	46	5	is	be	AUX
ejpam-1240	46	6	called	call	VERB
ejpam-1240	46	7	a	a	DET
ejpam-1240	46	8	groupoid	groupoid	NOUN
ejpam-1240	46	9	if	if	SCONJ
ejpam-1240	46	10	there	there	PRON
ejpam-1240	46	11	is	be	VERB
ejpam-1240	46	12	a	a	DET
ejpam-1240	46	13	partial	partial	ADJ
ejpam-1240	46	14	operation	operation	NOUN
ejpam-1240	46	15	on	on	ADP
ejpam-1240	46	16	m	m	PROPN
ejpam-1240	46	17	.	.	PUNCT
ejpam-1240	47	1	we	we	PRON
ejpam-1240	47	2	call	call	VERB
ejpam-1240	47	3	a	a	DET
ejpam-1240	47	4	groupoid	groupoid	NOUN
ejpam-1240	47	5	(	(	PUNCT
ejpam-1240	47	6	m	m	PROPN
ejpam-1240	47	7	,	,	PUNCT
ejpam-1240	47	8	◦	◦	NOUN
ejpam-1240	47	9	)	)	PUNCT
ejpam-1240	47	10	a	a	DET
ejpam-1240	47	11	partial	partial	ADJ
ejpam-1240	47	12	semigroup	semigroup	NOUN
ejpam-1240	47	13	if	if	SCONJ
ejpam-1240	47	14	for	for	ADP
ejpam-1240	47	15	the	the	DET
ejpam-1240	47	16	elements	element	NOUN
ejpam-1240	47	17	x	x	SYM
ejpam-1240	47	18	,	,	PUNCT
ejpam-1240	47	19	y	y	PROPN
ejpam-1240	47	20	,	,	PUNCT
ejpam-1240	47	21	z	z	PROPN
ejpam-1240	47	22	∈	∈	PROPN
ejpam-1240	47	23	s	s	PART
ejpam-1240	47	24	,	,	PUNCT
ejpam-1240	47	25	(	(	PUNCT
ejpam-1240	47	26	x	x	SYM
ejpam-1240	47	27	y)z	y)z	NOUN
ejpam-1240	47	28	and	and	CCONJ
ejpam-1240	47	29	x(yz	x(yz	NUM
ejpam-1240	47	30	)	)	PUNCT
ejpam-1240	47	31	are	be	AUX
ejpam-1240	47	32	defined	define	VERB
ejpam-1240	47	33	,	,	PUNCT
ejpam-1240	47	34	then	then	ADV
ejpam-1240	47	35	the	the	DET
ejpam-1240	47	36	other	other	ADJ
ejpam-1240	47	37	one	one	NUM
ejpam-1240	47	38	of	of	ADP
ejpam-1240	47	39	(	(	PUNCT
ejpam-1240	47	40	x	x	SYM
ejpam-1240	47	41	y)z	y)z	NOUN
ejpam-1240	47	42	and	and	CCONJ
ejpam-1240	47	43	x(yz	x(yz	NUM
ejpam-1240	47	44	)	)	PUNCT
ejpam-1240	47	45	is	be	AUX
ejpam-1240	47	46	defined	define	VERB
ejpam-1240	47	47	and	and	CCONJ
ejpam-1240	47	48	x(yz	x(yz	NUM
ejpam-1240	47	49	)	)	PUNCT
ejpam-1240	47	50	=	=	SYM
ejpam-1240	48	1	(	(	PUNCT
ejpam-1240	48	2	x	x	X
ejpam-1240	48	3	y)z	y)z	NOUN
ejpam-1240	48	4	.	.	PUNCT
ejpam-1240	49	1	a	a	DET
ejpam-1240	49	2	partial	partial	ADJ
ejpam-1240	49	3	semigroup	semigroup	NOUN
ejpam-1240	49	4	m	m	VERB
ejpam-1240	49	5	with	with	ADP
ejpam-1240	49	6	a	a	DET
ejpam-1240	49	7	partial	partial	ADJ
ejpam-1240	49	8	order	order	NOUN
ejpam-1240	49	9	≤	≤	X
ejpam-1240	49	10	is	be	AUX
ejpam-1240	49	11	called	call	VERB
ejpam-1240	49	12	an	an	DET
ejpam-1240	49	13	ordered	order	VERB
ejpam-1240	49	14	partial	partial	ADJ
ejpam-1240	49	15	semigroup	semigroup	NOUN
ejpam-1240	49	16	provided	provide	VERB
ejpam-1240	49	17	that	that	SCONJ
ejpam-1240	49	18	for	for	SCONJ
ejpam-1240	49	19	all	all	DET
ejpam-1240	49	20	x	x	SYM
ejpam-1240	49	21	,	,	PUNCT
ejpam-1240	49	22	y	y	PROPN
ejpam-1240	49	23	,	,	PUNCT
ejpam-1240	49	24	u	u	NOUN
ejpam-1240	49	25	,	,	PUNCT
ejpam-1240	49	26	v	v	PROPN
ejpam-1240	49	27	∈	∈	NOUN
ejpam-1240	49	28	m	m	NOUN
ejpam-1240	49	29	with	with	ADP
ejpam-1240	49	30	x	x	PROPN
ejpam-1240	49	31	≤	≤	NUM
ejpam-1240	49	32	y	y	NOUN
ejpam-1240	49	33	and	and	CCONJ
ejpam-1240	49	34	u	u	NOUN
ejpam-1240	49	35	≤	≤	PROPN
ejpam-1240	49	36	v	v	NOUN
ejpam-1240	49	37	,	,	PUNCT
ejpam-1240	49	38	if	if	SCONJ
ejpam-1240	49	39	xu	xu	PROPN
ejpam-1240	49	40	and	and	CCONJ
ejpam-1240	49	41	yv	yv	PROPN
ejpam-1240	49	42	are	be	AUX
ejpam-1240	49	43	defined	define	VERB
ejpam-1240	49	44	,	,	PUNCT
ejpam-1240	49	45	then	then	ADV
ejpam-1240	49	46	xu≤	xu≤	PROPN
ejpam-1240	49	47	yv	yv	PROPN
ejpam-1240	49	48	.	.	PUNCT
ejpam-1240	50	1	moreover	moreover	ADV
ejpam-1240	50	2	,	,	PUNCT
ejpam-1240	50	3	an	an	DET
ejpam-1240	50	4	ordered	order	VERB
ejpam-1240	50	5	partial	partial	ADJ
ejpam-1240	50	6	semigroup	semigroup	NOUN
ejpam-1240	50	7	(	(	PUNCT
ejpam-1240	50	8	m	m	PROPN
ejpam-1240	50	9	,	,	PUNCT
ejpam-1240	50	10	≤	≤	NUM
ejpam-1240	50	11	)	)	PUNCT
ejpam-1240	50	12	is	be	AUX
ejpam-1240	50	13	called	call	VERB
ejpam-1240	50	14	naturally	naturally	ADV
ejpam-1240	50	15	ordered	order	VERB
ejpam-1240	50	16	if	if	SCONJ
ejpam-1240	50	17	≤	≤	PROPN
ejpam-1240	50	18	extends	extend	VERB
ejpam-1240	50	19	the	the	DET
ejpam-1240	50	20	natural	natural	ADJ
ejpam-1240	50	21	order	order	NOUN
ejpam-1240	50	22	�	�	PROPN
ejpam-1240	50	23	on	on	ADP
ejpam-1240	50	24	m	m	PROPN
ejpam-1240	50	25	.	.	PUNCT
ejpam-1240	51	1	we	we	PRON
ejpam-1240	51	2	now	now	ADV
ejpam-1240	51	3	assume	assume	VERB
ejpam-1240	51	4	that	that	SCONJ
ejpam-1240	51	5	m	m	PROPN
ejpam-1240	51	6	is	be	AUX
ejpam-1240	51	7	a	a	DET
ejpam-1240	51	8	partial	partial	ADJ
ejpam-1240	51	9	semigroup	semigroup	NOUN
ejpam-1240	51	10	.	.	PUNCT
ejpam-1240	52	1	as	as	ADP
ejpam-1240	52	2	in	in	ADP
ejpam-1240	52	3	[	[	X
ejpam-1240	52	4	12	12	NUM
ejpam-1240	52	5	]	]	PUNCT
ejpam-1240	52	6	,	,	PUNCT
ejpam-1240	52	7	m	m	VERB
ejpam-1240	52	8	is	be	AUX
ejpam-1240	52	9	called	call	VERB
ejpam-1240	52	10	a	a	DET
ejpam-1240	52	11	partial	partial	ADJ
ejpam-1240	52	12	semilattice	semilattice	NOUN
ejpam-1240	52	13	if	if	SCONJ
ejpam-1240	52	14	there	there	PRON
ejpam-1240	52	15	exists	exist	VERB
ejpam-1240	52	16	a	a	DET
ejpam-1240	52	17	unipotent	unipotent	ADJ
ejpam-1240	52	18	semigroup	semigroup	NOUN
ejpam-1240	52	19	s	s	X
ejpam-1240	52	20	(	(	PUNCT
ejpam-1240	52	21	that	that	PRON
ejpam-1240	52	22	is	is	ADV
ejpam-1240	52	23	,	,	PUNCT
ejpam-1240	52	24	a	a	DET
ejpam-1240	52	25	semigroup	semigroup	NOUN
ejpam-1240	52	26	in	in	ADP
ejpam-1240	52	27	which	which	PRON
ejpam-1240	52	28	each	each	DET
ejpam-1240	52	29	l	l	NOUN
ejpam-1240	52	30	-class	-class	PROPN
ejpam-1240	52	31	and	and	CCONJ
ejpam-1240	52	32	each	each	DET
ejpam-1240	52	33	r	r	NOUN
ejpam-1240	52	34	-	-	PUNCT
ejpam-1240	52	35	class	class	NOUN
ejpam-1240	52	36	contains	contain	VERB
ejpam-1240	52	37	at	at	ADP
ejpam-1240	52	38	most	most	ADJ
ejpam-1240	52	39	one	one	NUM
ejpam-1240	52	40	idempotent	idempotent	NOUN
ejpam-1240	52	41	)	)	PUNCT
ejpam-1240	52	42	such	such	ADJ
ejpam-1240	52	43	that	that	SCONJ
ejpam-1240	52	44	e(s	e(s	PROPN
ejpam-1240	52	45	)	)	PUNCT
ejpam-1240	53	1	=	=	PUNCT
ejpam-1240	54	1	m	m	PROPN
ejpam-1240	54	2	.	.	PUNCT
ejpam-1240	55	1	and	and	CCONJ
ejpam-1240	55	2	,	,	PUNCT
ejpam-1240	55	3	m	m	VERB
ejpam-1240	55	4	is	be	AUX
ejpam-1240	55	5	called	call	VERB
ejpam-1240	55	6	a	a	DET
ejpam-1240	55	7	left	left	ADJ
ejpam-1240	55	8	(	(	PUNCT
ejpam-1240	55	9	right	right	ADJ
ejpam-1240	55	10	)	)	PUNCT
ejpam-1240	55	11	regular	regular	ADJ
ejpam-1240	55	12	partial	partial	ADJ
ejpam-1240	55	13	band	band	NOUN
ejpam-1240	55	14	if	if	SCONJ
ejpam-1240	55	15	m	m	NOUN
ejpam-1240	55	16	is	be	AUX
ejpam-1240	55	17	the	the	DET
ejpam-1240	55	18	disjoint	disjoint	PROPN
ejpam-1240	55	19	union	union	NOUN
ejpam-1240	55	20	of	of	ADP
ejpam-1240	55	21	left	left	PROPN
ejpam-1240	55	22	(	(	PUNCT
ejpam-1240	55	23	right	right	ADJ
ejpam-1240	55	24	)	)	PUNCT
ejpam-1240	55	25	zero	zero	NUM
ejpam-1240	55	26	rectangular	rectangular	ADJ
ejpam-1240	55	27	bands	band	NOUN
ejpam-1240	55	28	mα	mα	NOUN
ejpam-1240	55	29	with	with	ADP
ejpam-1240	55	30	α	α	PROPN
ejpam-1240	55	31	∈	∈	PROPN
ejpam-1240	55	32	y	y	PROPN
ejpam-1240	55	33	,	,	PUNCT
ejpam-1240	55	34	where	where	SCONJ
ejpam-1240	55	35	y	y	PROPN
ejpam-1240	55	36	is	be	AUX
ejpam-1240	55	37	a	a	DET
ejpam-1240	55	38	partial	partial	ADJ
ejpam-1240	55	39	semilattice	semilattice	NOUN
ejpam-1240	55	40	,	,	PUNCT
ejpam-1240	55	41	satisfying	satisfy	VERB
ejpam-1240	55	42	the	the	DET
ejpam-1240	55	43	following	follow	VERB
ejpam-1240	55	44	conditions	condition	NOUN
ejpam-1240	55	45	:	:	PUNCT
ejpam-1240	55	46	(	(	PUNCT
ejpam-1240	55	47	pb1	pb1	NOUN
ejpam-1240	55	48	)	)	PUNCT
ejpam-1240	55	49	for	for	ADP
ejpam-1240	55	50	all	all	DET
ejpam-1240	55	51	α	α	NOUN
ejpam-1240	55	52	,	,	PUNCT
ejpam-1240	55	53	β	β	X
ejpam-1240	55	54	∈	∈	PROPN
ejpam-1240	55	55	y	y	PROPN
ejpam-1240	55	56	and	and	CCONJ
ejpam-1240	55	57	x	x	PROPN
ejpam-1240	55	58	∈	∈	PROPN
ejpam-1240	55	59	mα	mα	PROPN
ejpam-1240	55	60	,	,	PUNCT
ejpam-1240	55	61	y	y	PROPN
ejpam-1240	55	62	∈	∈	PROPN
ejpam-1240	56	1	mβ	mβ	INTJ
ejpam-1240	56	2	,	,	PUNCT
ejpam-1240	56	3	if	if	SCONJ
ejpam-1240	56	4	α	α	PRON
ejpam-1240	56	5	�	�	PROPN
ejpam-1240	56	6	β	β	X
ejpam-1240	56	7	,	,	PUNCT
ejpam-1240	56	8	then	then	ADV
ejpam-1240	56	9	x	x	SYM
ejpam-1240	56	10	y	y	PROPN
ejpam-1240	56	11	and	and	CCONJ
ejpam-1240	56	12	y	y	PROPN
ejpam-1240	56	13	x	x	PROPN
ejpam-1240	56	14	are	be	AUX
ejpam-1240	56	15	defined	define	VERB
ejpam-1240	56	16	for	for	ADP
ejpam-1240	56	17	all	all	DET
ejpam-1240	56	18	x	x	SYM
ejpam-1240	56	19	∈	∈	PROPN
ejpam-1240	56	20	mα	mα	PROPN
ejpam-1240	56	21	,	,	PUNCT
ejpam-1240	56	22	y	y	PROPN
ejpam-1240	56	23	∈	∈	PROPN
ejpam-1240	56	24	mβ	mβ	INTJ
ejpam-1240	56	25	.	.	PUNCT
ejpam-1240	57	1	(	(	PUNCT
ejpam-1240	57	2	pb2	pb2	PROPN
ejpam-1240	57	3	)	)	PUNCT
ejpam-1240	57	4	for	for	ADP
ejpam-1240	57	5	all	all	DET
ejpam-1240	57	6	x	x	SYM
ejpam-1240	57	7	∈	∈	PROPN
ejpam-1240	57	8	m	m	NOUN
ejpam-1240	57	9	and	and	CCONJ
ejpam-1240	57	10	y	y	PROPN
ejpam-1240	57	11	∈	∈	PROPN
ejpam-1240	57	12	mα	mα	PROPN
ejpam-1240	57	13	,	,	PUNCT
ejpam-1240	57	14	if	if	SCONJ
ejpam-1240	57	15	x	x	SYM
ejpam-1240	57	16	y	y	PROPN
ejpam-1240	57	17	and	and	CCONJ
ejpam-1240	57	18	y	y	PROPN
ejpam-1240	57	19	x	x	PROPN
ejpam-1240	57	20	are	be	AUX
ejpam-1240	57	21	defined	define	VERB
ejpam-1240	57	22	and	and	CCONJ
ejpam-1240	57	23	such	such	ADJ
ejpam-1240	58	1	that	that	SCONJ
ejpam-1240	58	2	x	x	X
ejpam-1240	58	3	y	y	NOUN
ejpam-1240	58	4	=	=	PUNCT
ejpam-1240	58	5	x	x	PROPN
ejpam-1240	58	6	and	and	CCONJ
ejpam-1240	58	7	y	y	PROPN
ejpam-1240	58	8	x	x	PUNCT
ejpam-1240	58	9	=	=	PUNCT
ejpam-1240	58	10	y	y	PROPN
ejpam-1240	58	11	(	(	PUNCT
ejpam-1240	58	12	x	x	NOUN
ejpam-1240	58	13	y	y	PROPN
ejpam-1240	58	14	=	=	SYM
ejpam-1240	58	15	y	y	PROPN
ejpam-1240	58	16	and	and	CCONJ
ejpam-1240	58	17	y	y	PROPN
ejpam-1240	58	18	x	x	PUNCT
ejpam-1240	58	19	=	=	PUNCT
ejpam-1240	58	20	x	x	X
ejpam-1240	58	21	)	)	PUNCT
ejpam-1240	58	22	,	,	PUNCT
ejpam-1240	58	23	then	then	ADV
ejpam-1240	58	24	x	x	PART
ejpam-1240	58	25	∈	∈	PROPN
ejpam-1240	58	26	mα	mα	PROPN
ejpam-1240	58	27	.	.	PUNCT
ejpam-1240	58	28	in	in	ADP
ejpam-1240	58	29	this	this	DET
ejpam-1240	58	30	case	case	NOUN
ejpam-1240	58	31	,	,	PUNCT
ejpam-1240	58	32	we	we	PRON
ejpam-1240	58	33	call	call	VERB
ejpam-1240	58	34	y	y	NOUN
ejpam-1240	58	35	the	the	DET
ejpam-1240	58	36	structure	structure	NOUN
ejpam-1240	58	37	partial	partial	ADJ
ejpam-1240	58	38	semilattice	semilattice	NOUN
ejpam-1240	58	39	of	of	ADP
ejpam-1240	58	40	the	the	DET
ejpam-1240	58	41	left	left	ADJ
ejpam-1240	58	42	(	(	PUNCT
ejpam-1240	58	43	right	right	ADJ
ejpam-1240	58	44	)	)	PUNCT
ejpam-1240	58	45	regular	regular	ADJ
ejpam-1240	58	46	partial	partial	ADJ
ejpam-1240	58	47	band	band	NOUN
ejpam-1240	58	48	m	m	NOUN
ejpam-1240	58	49	.	.	PUNCT
ejpam-1240	59	1	moreover	moreover	ADV
ejpam-1240	59	2	,	,	PUNCT
ejpam-1240	59	3	a	a	DET
ejpam-1240	59	4	subset	subset	NOUN
ejpam-1240	59	5	n	n	NOUN
ejpam-1240	59	6	of	of	ADP
ejpam-1240	59	7	the	the	DET
ejpam-1240	59	8	left	left	ADJ
ejpam-1240	59	9	(	(	PUNCT
ejpam-1240	59	10	right	right	ADJ
ejpam-1240	59	11	)	)	PUNCT
ejpam-1240	59	12	regular	regular	ADJ
ejpam-1240	59	13	partial	partial	ADJ
ejpam-1240	59	14	band	band	NOUN
ejpam-1240	59	15	(	(	PUNCT
ejpam-1240	59	16	m	m	NOUN
ejpam-1240	59	17	,	,	PUNCT
ejpam-1240	59	18	◦	◦	NOUN
ejpam-1240	59	19	)	)	PUNCT
ejpam-1240	59	20	=	=	SYM
ejpam-1240	59	21	∪α∈y	∪α∈y	PROPN
ejpam-1240	59	22	mα	mα	NOUN
ejpam-1240	59	23	with	with	ADP
ejpam-1240	59	24	a	a	DET
ejpam-1240	59	25	structure	structure	NOUN
ejpam-1240	59	26	partial	partial	ADJ
ejpam-1240	59	27	semilattice	semilattice	NOUN
ejpam-1240	59	28	y	y	PROPN
ejpam-1240	59	29	is	be	AUX
ejpam-1240	59	30	called	call	VERB
ejpam-1240	59	31	a	a	DET
ejpam-1240	59	32	skeleton	skeleton	NOUN
ejpam-1240	59	33	if	if	SCONJ
ejpam-1240	59	34	(	(	PUNCT
ejpam-1240	59	35	n	n	X
ejpam-1240	59	36	,	,	PUNCT
ejpam-1240	59	37	◦	◦	NOUN
ejpam-1240	59	38	)	)	PUNCT
ejpam-1240	59	39	is	be	AUX
ejpam-1240	59	40	partial	partial	ADJ
ejpam-1240	59	41	semilattice	semilattice	NOUN
ejpam-1240	59	42	isomorphic	isomorphic	ADJ
ejpam-1240	59	43	to	to	ADP
ejpam-1240	59	44	y	y	PROPN
ejpam-1240	59	45	and	and	CCONJ
ejpam-1240	59	46	|n	|n	PRON
ejpam-1240	59	47	∩mα|=	∩mα|=	PROPN
ejpam-1240	59	48	1	1	NUM
ejpam-1240	59	49	,	,	PUNCT
ejpam-1240	59	50	for	for	ADP
ejpam-1240	59	51	all	all	PRON
ejpam-1240	59	52	α	α	DET
ejpam-1240	59	53	∈	∈	PROPN
ejpam-1240	59	54	y	y	PROPN
ejpam-1240	59	55	.	.	PUNCT
ejpam-1240	60	1	a	a	DET
ejpam-1240	60	2	semigroup	semigroup	NOUN
ejpam-1240	60	3	is	be	AUX
ejpam-1240	60	4	called	call	VERB
ejpam-1240	60	5	left	leave	VERB
ejpam-1240	60	6	*	*	PUNCT
ejpam-1240	60	7	-unipotent	-unipotent	NOUN
ejpam-1240	60	8	if	if	SCONJ
ejpam-1240	60	9	each	each	DET
ejpam-1240	60	10	l	l	NOUN
ejpam-1240	60	11	∗-class	∗-class	NOUN
ejpam-1240	60	12	contains	contain	VERB
ejpam-1240	60	13	at	at	ADP
ejpam-1240	60	14	most	most	ADJ
ejpam-1240	60	15	one	one	NUM
ejpam-1240	60	16	idempotent	idempotent	NOUN
ejpam-1240	60	17	.	.	PUNCT
ejpam-1240	61	1	right	right	ADJ
ejpam-1240	61	2	∗-unipotent	∗-unipotent	ADJ
ejpam-1240	61	3	semigroups	semigroup	NOUN
ejpam-1240	61	4	can	can	AUX
ejpam-1240	61	5	be	be	AUX
ejpam-1240	61	6	dually	dually	ADV
ejpam-1240	61	7	defined	define	VERB
ejpam-1240	61	8	.	.	PUNCT
ejpam-1240	62	1	and	and	CCONJ
ejpam-1240	62	2	,	,	PUNCT
ejpam-1240	62	3	we	we	PRON
ejpam-1240	62	4	call	call	VERB
ejpam-1240	62	5	a	a	DET
ejpam-1240	62	6	semigroup	semigroup	NOUN
ejpam-1240	62	7	s	s	NOUN
ejpam-1240	62	8	∗-unipotent	∗-unipotent	NOUN
ejpam-1240	62	9	if	if	SCONJ
ejpam-1240	62	10	s	s	NOUN
ejpam-1240	62	11	is	be	AUX
ejpam-1240	62	12	both	both	PRON
ejpam-1240	62	13	left	leave	VERB
ejpam-1240	62	14	∗-unipotent	∗-unipotent	ADJ
ejpam-1240	62	15	and	and	CCONJ
ejpam-1240	62	16	right	right	ADJ
ejpam-1240	62	17	∗-unipotent	∗-unipotent	NOUN
ejpam-1240	62	18	.	.	PUNCT
ejpam-1240	63	1	we	we	PRON
ejpam-1240	63	2	now	now	ADV
ejpam-1240	63	3	introduce	introduce	VERB
ejpam-1240	63	4	the	the	DET
ejpam-1240	63	5	concept	concept	NOUN
ejpam-1240	63	6	of	of	ADP
ejpam-1240	63	7	a	a	DET
ejpam-1240	63	8	gi	gi	NOUN
ejpam-1240	63	9	-	-	PUNCT
ejpam-1240	63	10	system	system	NOUN
ejpam-1240	63	11	.	.	PUNCT
ejpam-1240	64	1	by	by	ADP
ejpam-1240	64	2	a	a	DET
ejpam-1240	64	3	gi	gi	NOUN
ejpam-1240	64	4	-	-	PUNCT
ejpam-1240	64	5	system	system	NOUN
ejpam-1240	64	6	,	,	PUNCT
ejpam-1240	64	7	we	we	PRON
ejpam-1240	64	8	mean	mean	VERB
ejpam-1240	64	9	a	a	DET
ejpam-1240	64	10	quadruple	quadruple	NOUN
ejpam-1240	64	11	(	(	PUNCT
ejpam-1240	64	12	t	t	NOUN
ejpam-1240	64	13	;	;	PUNCT
ejpam-1240	64	14	l	l	X
ejpam-1240	64	15	,	,	PUNCT
ejpam-1240	64	16	r	r	NOUN
ejpam-1240	64	17	;	;	PUNCT
ejpam-1240	65	1	[	[	X
ejpam-1240	65	2	,	,	PUNCT
ejpam-1240	65	3	]	]	X
ejpam-1240	65	4	)	)	PUNCT
ejpam-1240	65	5	,	,	PUNCT
ejpam-1240	65	6	where	where	SCONJ
ejpam-1240	65	7	•	•	NUM
ejpam-1240	65	8	t	t	PROPN
ejpam-1240	65	9	is	be	AUX
ejpam-1240	65	10	a	a	DET
ejpam-1240	65	11	*	*	PUNCT
ejpam-1240	65	12	-unipotent	-unipotent	NOUN
ejpam-1240	65	13	abundant	abundant	ADJ
ejpam-1240	65	14	semigroup	semigroup	NOUN
ejpam-1240	65	15	with	with	ADP
ejpam-1240	65	16	a	a	DET
ejpam-1240	65	17	set	set	NOUN
ejpam-1240	65	18	of	of	ADP
ejpam-1240	65	19	idempotents	idempotent	NOUN
ejpam-1240	65	20	y	y	PROPN
ejpam-1240	65	21	.	.	PUNCT
ejpam-1240	66	1	•	•	NUM
ejpam-1240	66	2	l	l	NOUN
ejpam-1240	66	3	=	=	PUNCT
ejpam-1240	67	1	⋃	⋃	NOUN
ejpam-1240	67	2	α∈y	α∈y	NOUN
ejpam-1240	67	3	lα	lα	NOUN
ejpam-1240	67	4	is	be	AUX
ejpam-1240	67	5	a	a	DET
ejpam-1240	67	6	left	left	ADJ
ejpam-1240	67	7	regular	regular	ADJ
ejpam-1240	67	8	partial	partial	ADJ
ejpam-1240	67	9	band	band	NOUN
ejpam-1240	67	10	with	with	ADP
ejpam-1240	67	11	y	y	PROPN
ejpam-1240	67	12	as	as	ADP
ejpam-1240	67	13	its	its	PRON
ejpam-1240	67	14	skeleton	skeleton	NOUN
ejpam-1240	67	15	.	.	PUNCT
ejpam-1240	68	1	•	•	NUM
ejpam-1240	68	2	r=	r=	ADJ
ejpam-1240	68	3	⋃	⋃	NOUN
ejpam-1240	68	4	α∈y	α∈y	NOUN
ejpam-1240	68	5	rα	rα	ADJ
ejpam-1240	68	6	is	be	AUX
ejpam-1240	68	7	a	a	DET
ejpam-1240	68	8	right	right	ADJ
ejpam-1240	68	9	regular	regular	ADJ
ejpam-1240	68	10	partial	partial	ADJ
ejpam-1240	68	11	band	band	NOUN
ejpam-1240	68	12	with	with	ADP
ejpam-1240	68	13	y	y	PROPN
ejpam-1240	68	14	as	as	ADP
ejpam-1240	68	15	its	its	PRON
ejpam-1240	68	16	skeleton	skeleton	NOUN
ejpam-1240	68	17	.	.	PUNCT
ejpam-1240	69	1	•	•	NUM
ejpam-1240	70	1	[	[	X
ejpam-1240	70	2	,	,	PUNCT
ejpam-1240	70	3	]	]	PUNCT
ejpam-1240	70	4	is	be	AUX
ejpam-1240	70	5	a	a	DET
ejpam-1240	70	6	mapping	mapping	NOUN
ejpam-1240	70	7	from	from	ADP
ejpam-1240	70	8	r×	r×	NOUN
ejpam-1240	70	9	l	l	NOUN
ejpam-1240	70	10	into	into	ADP
ejpam-1240	70	11	t	t	PROPN
ejpam-1240	70	12	,	,	PUNCT
ejpam-1240	70	13	if	if	SCONJ
ejpam-1240	70	14	the	the	DET
ejpam-1240	70	15	following	follow	VERB
ejpam-1240	70	16	conditions	condition	NOUN
ejpam-1240	70	17	hold	hold	VERB
ejpam-1240	70	18	:	:	PUNCT
ejpam-1240	70	19	(	(	PUNCT
ejpam-1240	70	20	gi1	gi1	NOUN
ejpam-1240	70	21	)	)	PUNCT
ejpam-1240	71	1	[	[	X
ejpam-1240	71	2	x	x	X
ejpam-1240	71	3	y	y	PROPN
ejpam-1240	71	4	,	,	PUNCT
ejpam-1240	71	5	uv	uv	NOUN
ejpam-1240	71	6	]	]	X
ejpam-1240	71	7	=	=	PUNCT
ejpam-1240	72	1	[	[	X
ejpam-1240	72	2	x	x	X
ejpam-1240	72	3	,	,	PUNCT
ejpam-1240	72	4	α][y	α][y	NOUN
ejpam-1240	72	5	,	,	PUNCT
ejpam-1240	72	6	uv	uv	NOUN
ejpam-1240	72	7	]	]	X
ejpam-1240	72	8	=	=	PUNCT
ejpam-1240	73	1	[	[	X
ejpam-1240	73	2	x	x	X
ejpam-1240	73	3	y	y	PROPN
ejpam-1240	73	4	,	,	PUNCT
ejpam-1240	73	5	u][β	u][β	NOUN
ejpam-1240	73	6	,	,	PUNCT
ejpam-1240	73	7	v	v	ADP
ejpam-1240	73	8	]	]	PUNCT
ejpam-1240	73	9	for	for	ADP
ejpam-1240	73	10	all	all	DET
ejpam-1240	73	11	x	x	SYM
ejpam-1240	73	12	∈	∈	PROPN
ejpam-1240	73	13	r	r	NOUN
ejpam-1240	73	14	,	,	PUNCT
ejpam-1240	73	15	y	y	PROPN
ejpam-1240	73	16	∈	∈	PROPN
ejpam-1240	73	17	rα	rα	VERB
ejpam-1240	73	18	,	,	PUNCT
ejpam-1240	73	19	u	u	PROPN
ejpam-1240	73	20	∈	∈	NOUN
ejpam-1240	73	21	lβ	lβ	NOUN
ejpam-1240	73	22	and	and	CCONJ
ejpam-1240	73	23	v	v	ADP
ejpam-1240	73	24	∈	∈	PROPN
ejpam-1240	73	25	l.	l.	NOUN
ejpam-1240	73	26	(	(	PUNCT
ejpam-1240	73	27	gi2	gi2	PROPN
ejpam-1240	73	28	)	)	PUNCT
ejpam-1240	74	1	[	[	X
ejpam-1240	74	2	α	α	X
ejpam-1240	74	3	,	,	PUNCT
ejpam-1240	74	4	β	β	X
ejpam-1240	74	5	]	]	X
ejpam-1240	74	6	=	=	SYM
ejpam-1240	74	7	αβ	αβ	INTJ
ejpam-1240	74	8	for	for	ADP
ejpam-1240	74	9	all	all	DET
ejpam-1240	74	10	α	α	NOUN
ejpam-1240	74	11	,	,	PUNCT
ejpam-1240	74	12	β	β	X
ejpam-1240	74	13	∈	∈	PROPN
ejpam-1240	74	14	y	y	PROPN
ejpam-1240	74	15	.	.	PUNCT
ejpam-1240	74	16	x.	x.	PROPN
ejpam-1240	74	17	guo	guo	PROPN
ejpam-1240	74	18	,	,	PUNCT
ejpam-1240	74	19	k.	k.	PROPN
ejpam-1240	74	20	shum	shum	PROPN
ejpam-1240	74	21	/	/	SYM
ejpam-1240	74	22	eur	eur	PROPN
ejpam-1240	74	23	.	.	PUNCT
ejpam-1240	75	1	j.	j.	PROPN
ejpam-1240	75	2	pure	pure	PROPN
ejpam-1240	75	3	appl	appl	PROPN
ejpam-1240	75	4	.	.	PROPN
ejpam-1240	75	5	math	math	PROPN
ejpam-1240	75	6	,	,	PUNCT
ejpam-1240	75	7	4	4	NUM
ejpam-1240	75	8	(	(	PUNCT
ejpam-1240	75	9	2011	2011	NUM
ejpam-1240	75	10	)	)	PUNCT
ejpam-1240	75	11	,	,	PUNCT
ejpam-1240	75	12	210	210	NUM
ejpam-1240	75	13	-	-	SYM
ejpam-1240	75	14	220	220	NUM
ejpam-1240	75	15	213	213	NUM
ejpam-1240	75	16	(	(	PUNCT
ejpam-1240	75	17	gi3	gi3	NOUN
ejpam-1240	75	18	)	)	PUNCT
ejpam-1240	76	1	[	[	X
ejpam-1240	76	2	u	u	NOUN
ejpam-1240	76	3	,	,	PUNCT
ejpam-1240	76	4	α	α	X
ejpam-1240	76	5	]	]	X
ejpam-1240	76	6	=	=	SYM
ejpam-1240	76	7	α=	α=	PROPN
ejpam-1240	77	1	[	[	X
ejpam-1240	77	2	α	α	NOUN
ejpam-1240	77	3	,	,	PUNCT
ejpam-1240	77	4	v	v	NOUN
ejpam-1240	77	5	]	]	PUNCT
ejpam-1240	77	6	for	for	ADP
ejpam-1240	77	7	all	all	DET
ejpam-1240	77	8	u	u	PROPN
ejpam-1240	77	9	∈	∈	NOUN
ejpam-1240	77	10	rα	rα	ADJ
ejpam-1240	77	11	and	and	CCONJ
ejpam-1240	77	12	v	v	ADP
ejpam-1240	77	13	∈	∈	PROPN
ejpam-1240	77	14	lα	lα	NOUN
ejpam-1240	77	15	.	.	PROPN
ejpam-1240	77	16	given	give	VERB
ejpam-1240	77	17	a	a	DET
ejpam-1240	77	18	gi	gi	NOUN
ejpam-1240	77	19	-	-	PUNCT
ejpam-1240	77	20	system	system	NOUN
ejpam-1240	77	21	(	(	PUNCT
ejpam-1240	77	22	t	t	NOUN
ejpam-1240	77	23	;	;	PUNCT
ejpam-1240	77	24	l	l	X
ejpam-1240	77	25	,	,	PUNCT
ejpam-1240	77	26	r	r	NOUN
ejpam-1240	77	27	;	;	PUNCT
ejpam-1240	77	28	[	[	X
ejpam-1240	77	29	,	,	PUNCT
ejpam-1240	77	30	]	]	X
ejpam-1240	77	31	)	)	PUNCT
ejpam-1240	77	32	,	,	PUNCT
ejpam-1240	77	33	we	we	PRON
ejpam-1240	77	34	put	put	VERB
ejpam-1240	77	35	the	the	DET
ejpam-1240	77	36	set	set	NOUN
ejpam-1240	77	37	gi	gi	NOUN
ejpam-1240	77	38	=	=	NOUN
ejpam-1240	77	39	gi(t	gi(t	NOUN
ejpam-1240	77	40	;	;	PUNCT
ejpam-1240	78	1	l	l	X
ejpam-1240	78	2	,	,	PUNCT
ejpam-1240	78	3	r	r	NOUN
ejpam-1240	78	4	;	;	PUNCT
ejpam-1240	78	5	[	[	X
ejpam-1240	78	6	,	,	PUNCT
ejpam-1240	78	7	]	]	X
ejpam-1240	78	8	)	)	PUNCT
ejpam-1240	78	9	=	=	SYM
ejpam-1240	78	10	{	{	PUNCT
ejpam-1240	78	11	(	(	PUNCT
ejpam-1240	78	12	x	x	INTJ
ejpam-1240	78	13	,	,	PUNCT
ejpam-1240	78	14	s	s	PROPN
ejpam-1240	78	15	,	,	PUNCT
ejpam-1240	78	16	u	u	NOUN
ejpam-1240	78	17	)	)	PUNCT
ejpam-1240	78	18	∈	∈	PROPN
ejpam-1240	78	19	l	l	NOUN
ejpam-1240	78	20	×	×	NOUN
ejpam-1240	78	21	t	t	NOUN
ejpam-1240	78	22	×	×	NOUN
ejpam-1240	78	23	r	r	NOUN
ejpam-1240	78	24	:	:	PUNCT
ejpam-1240	78	25	x	x	PUNCT
ejpam-1240	78	26	∈	∈	X
ejpam-1240	78	27	ls†	ls†	ADJ
ejpam-1240	78	28	and	and	CCONJ
ejpam-1240	78	29	rs∗	rs∗	ADJ
ejpam-1240	78	30	}	}	PUNCT
ejpam-1240	78	31	.	.	PUNCT
ejpam-1240	79	1	now	now	ADV
ejpam-1240	79	2	,	,	PUNCT
ejpam-1240	79	3	we	we	PRON
ejpam-1240	79	4	define	define	VERB
ejpam-1240	79	5	(	(	PUNCT
ejpam-1240	79	6	x	x	INTJ
ejpam-1240	79	7	,	,	PUNCT
ejpam-1240	79	8	s	s	PROPN
ejpam-1240	79	9	,	,	PUNCT
ejpam-1240	79	10	u	u	NOUN
ejpam-1240	79	11	)	)	PUNCT
ejpam-1240	79	12	◦	◦	NOUN
ejpam-1240	79	13	(	(	PUNCT
ejpam-1240	79	14	y	y	PROPN
ejpam-1240	79	15	,	,	PUNCT
ejpam-1240	79	16	t	t	PROPN
ejpam-1240	79	17	,	,	PUNCT
ejpam-1240	79	18	v	v	NOUN
ejpam-1240	79	19	)	)	PUNCT
ejpam-1240	79	20	=	=	SYM
ejpam-1240	79	21	(	(	PUNCT
ejpam-1240	79	22	xa†	xa†	PROPN
ejpam-1240	79	23	,	,	PUNCT
ejpam-1240	79	24	a	a	PRON
ejpam-1240	79	25	,	,	PUNCT
ejpam-1240	79	26	a∗v	a∗v	NOUN
ejpam-1240	79	27	)	)	PUNCT
ejpam-1240	79	28	,	,	PUNCT
ejpam-1240	79	29	where	where	SCONJ
ejpam-1240	79	30	a	a	DET
ejpam-1240	79	31	=	=	SYM
ejpam-1240	79	32	s[u	s[u	NOUN
ejpam-1240	79	33	,	,	PUNCT
ejpam-1240	79	34	y]t	y]t	NOUN
ejpam-1240	79	35	.	.	PUNCT
ejpam-1240	80	1	then	then	ADV
ejpam-1240	80	2	,	,	PUNCT
ejpam-1240	80	3	it	it	PRON
ejpam-1240	80	4	is	be	AUX
ejpam-1240	80	5	easy	easy	ADJ
ejpam-1240	80	6	to	to	PART
ejpam-1240	80	7	verify	verify	VERB
ejpam-1240	80	8	that	that	SCONJ
ejpam-1240	80	9	the	the	DET
ejpam-1240	80	10	system	system	NOUN
ejpam-1240	80	11	(	(	PUNCT
ejpam-1240	80	12	gi	gi	INTJ
ejpam-1240	80	13	,	,	PUNCT
ejpam-1240	80	14	◦	◦	NOUN
ejpam-1240	80	15	)	)	PUNCT
ejpam-1240	80	16	forms	form	VERB
ejpam-1240	80	17	an	an	DET
ejpam-1240	80	18	abundant	abundant	ADJ
ejpam-1240	80	19	semigroup	semigroup	NOUN
ejpam-1240	80	20	[	[	X
ejpam-1240	80	21	see	see	VERB
ejpam-1240	80	22	13	13	NUM
ejpam-1240	80	23	]	]	PUNCT
ejpam-1240	80	24	.	.	PUNCT
ejpam-1240	81	1	we	we	PRON
ejpam-1240	81	2	denote	denote	VERB
ejpam-1240	81	3	this	this	DET
ejpam-1240	81	4	semigroup	semigroup	NOUN
ejpam-1240	81	5	by	by	ADP
ejpam-1240	81	6	gi(t	gi(t	NOUN
ejpam-1240	81	7	;	;	PUNCT
ejpam-1240	81	8	l	l	X
ejpam-1240	81	9	,	,	PUNCT
ejpam-1240	81	10	r	r	NOUN
ejpam-1240	81	11	;	;	PUNCT
ejpam-1240	81	12	[	[	X
ejpam-1240	81	13	,	,	PUNCT
ejpam-1240	81	14	]	]	X
ejpam-1240	81	15	)	)	PUNCT
ejpam-1240	81	16	.	.	PUNCT
ejpam-1240	82	1	assume	assume	VERB
ejpam-1240	82	2	that	that	SCONJ
ejpam-1240	82	3	s	s	VERB
ejpam-1240	82	4	is	be	AUX
ejpam-1240	82	5	an	an	DET
ejpam-1240	82	6	ordered	order	VERB
ejpam-1240	82	7	abundant	abundant	ADJ
ejpam-1240	82	8	semigroup	semigroup	NOUN
ejpam-1240	82	9	in	in	ADP
ejpam-1240	82	10	which	which	PRON
ejpam-1240	82	11	each	each	DET
ejpam-1240	82	12	regular	regular	ADJ
ejpam-1240	82	13	element	element	NOUN
ejpam-1240	82	14	has	have	VERB
ejpam-1240	82	15	a	a	DET
ejpam-1240	82	16	maximum	maximum	ADJ
ejpam-1240	82	17	inverse	inverse	NOUN
ejpam-1240	82	18	.	.	PUNCT
ejpam-1240	83	1	throughout	throughout	ADP
ejpam-1240	83	2	this	this	DET
ejpam-1240	83	3	paper	paper	NOUN
ejpam-1240	83	4	,	,	PUNCT
ejpam-1240	83	5	we	we	PRON
ejpam-1240	83	6	use	use	VERB
ejpam-1240	83	7	x	x	VERB
ejpam-1240	83	8	◦	◦	NOUN
ejpam-1240	83	9	to	to	PART
ejpam-1240	83	10	denote	denote	VERB
ejpam-1240	83	11	the	the	DET
ejpam-1240	83	12	greatest	great	ADJ
ejpam-1240	83	13	inverse	inverse	NOUN
ejpam-1240	83	14	of	of	ADP
ejpam-1240	83	15	x	x	SYM
ejpam-1240	83	16	if	if	SCONJ
ejpam-1240	83	17	x	x	PRON
ejpam-1240	83	18	has	have	AUX
ejpam-1240	83	19	the	the	DET
ejpam-1240	83	20	greatest	great	ADJ
ejpam-1240	83	21	inverse	inverse	NOUN
ejpam-1240	83	22	.	.	PUNCT
ejpam-1240	84	1	similar	similar	ADJ
ejpam-1240	84	2	as	as	ADP
ejpam-1240	84	3	in	in	ADP
ejpam-1240	84	4	[	[	PUNCT
ejpam-1240	84	5	13	13	NUM
ejpam-1240	84	6	]	]	PUNCT
ejpam-1240	84	7	,	,	PUNCT
ejpam-1240	84	8	we	we	PRON
ejpam-1240	84	9	call	call	VERB
ejpam-1240	84	10	the	the	DET
ejpam-1240	84	11	semigroup	semigroup	NOUN
ejpam-1240	84	12	s	s	PART
ejpam-1240	84	13	g	g	NOUN
ejpam-1240	84	14	-	-	PUNCT
ejpam-1240	84	15	regular	regular	ADJ
ejpam-1240	84	16	if	if	SCONJ
ejpam-1240	84	17	for	for	ADP
ejpam-1240	84	18	any	any	DET
ejpam-1240	84	19	x	x	NOUN
ejpam-1240	84	20	,	,	PUNCT
ejpam-1240	84	21	y	y	PROPN
ejpam-1240	84	22	∈	∈	PROPN
ejpam-1240	84	23	s	s	PROPN
ejpam-1240	84	24	,	,	PUNCT
ejpam-1240	84	25	x	x	PUNCT
ejpam-1240	84	26	≤	≤	ADJ
ejpam-1240	84	27	y	y	PROPN
ejpam-1240	84	28	implies	imply	VERB
ejpam-1240	84	29	x∗	x∗	PROPN
ejpam-1240	84	30	◦	◦	VERB
ejpam-1240	84	31	x∗	x∗	PROPN
ejpam-1240	84	32	≤	≤	ADV
ejpam-1240	84	33	y∗	y∗	ADV
ejpam-1240	84	34	◦	◦	NOUN
ejpam-1240	84	35	y∗	y∗	ADV
ejpam-1240	84	36	and	and	CCONJ
ejpam-1240	84	37	x†x†	x†x†	PROPN
ejpam-1240	84	38	◦	◦	NOUN
ejpam-1240	84	39	≤	≤	NUM
ejpam-1240	84	40	y†	y†	VERB
ejpam-1240	84	41	y†	y†	ADJ
ejpam-1240	84	42	◦	◦	NOUN
ejpam-1240	84	43	.	.	PUNCT
ejpam-1240	85	1	also	also	ADV
ejpam-1240	85	2	,	,	PUNCT
ejpam-1240	85	3	we	we	PRON
ejpam-1240	85	4	call	call	VERB
ejpam-1240	85	5	s	s	VERB
ejpam-1240	85	6	reflexive	reflexive	ADJ
ejpam-1240	85	7	if	if	SCONJ
ejpam-1240	85	8	for	for	SCONJ
ejpam-1240	85	9	all	all	DET
ejpam-1240	85	10	x	x	SYM
ejpam-1240	85	11	,	,	PUNCT
ejpam-1240	85	12	y	y	PROPN
ejpam-1240	85	13	∈	∈	PROPN
ejpam-1240	85	14	reg	reg	NOUN
ejpam-1240	85	15	s	s	NOUN
ejpam-1240	85	16	,	,	PUNCT
ejpam-1240	85	17	x	x	PUNCT
ejpam-1240	85	18	≤	≤	ADJ
ejpam-1240	85	19	y	y	PROPN
ejpam-1240	85	20	implies	imply	VERB
ejpam-1240	85	21	that	that	SCONJ
ejpam-1240	85	22	x	x	X
ejpam-1240	85	23	◦	◦	VERB
ejpam-1240	85	24	≤	≤	NUM
ejpam-1240	85	25	y	y	NOUN
ejpam-1240	85	26	◦	◦	NOUN
ejpam-1240	85	27	.	.	PUNCT
ejpam-1240	86	1	in	in	ADP
ejpam-1240	86	2	the	the	DET
ejpam-1240	86	3	following	following	NOUN
ejpam-1240	86	4	theorem	theorem	NOUN
ejpam-1240	86	5	,	,	PUNCT
ejpam-1240	86	6	we	we	PRON
ejpam-1240	86	7	establish	establish	VERB
ejpam-1240	86	8	a	a	DET
ejpam-1240	86	9	construction	construction	NOUN
ejpam-1240	86	10	theorem	theorem	NOUN
ejpam-1240	86	11	for	for	ADP
ejpam-1240	86	12	the	the	DET
ejpam-1240	86	13	g	g	NOUN
ejpam-1240	86	14	-	-	PUNCT
ejpam-1240	86	15	regular	regular	ADJ
ejpam-1240	86	16	and	and	CCONJ
ejpam-1240	86	17	reflexive	reflexive	ADJ
ejpam-1240	86	18	naturally	naturally	ADV
ejpam-1240	86	19	ordered	order	VERB
ejpam-1240	86	20	abundant	abundant	ADJ
ejpam-1240	86	21	semigroup	semigroup	NOUN
ejpam-1240	86	22	s	s	X
ejpam-1240	86	23	in	in	ADP
ejpam-1240	86	24	which	which	PRON
ejpam-1240	86	25	each	each	DET
ejpam-1240	86	26	idempotent	idempotent	NOUN
ejpam-1240	86	27	of	of	ADP
ejpam-1240	86	28	s	s	PROPN
ejpam-1240	86	29	has	have	VERB
ejpam-1240	86	30	a	a	DET
ejpam-1240	86	31	greatest	great	ADJ
ejpam-1240	86	32	inverse	inverse	NOUN
ejpam-1240	86	33	.	.	PUNCT
ejpam-1240	87	1	theorem	theorem	NOUN
ejpam-1240	87	2	1	1	NUM
ejpam-1240	87	3	.	.	PUNCT
ejpam-1240	88	1	let	let	VERB
ejpam-1240	88	2	(	(	PUNCT
ejpam-1240	88	3	t	t	NOUN
ejpam-1240	88	4	;	;	PUNCT
ejpam-1240	88	5	l	l	X
ejpam-1240	88	6	,	,	PUNCT
ejpam-1240	88	7	r	r	NOUN
ejpam-1240	88	8	;	;	PUNCT
ejpam-1240	88	9	[	[	X
ejpam-1240	88	10	,	,	PUNCT
ejpam-1240	88	11	]	]	X
ejpam-1240	88	12	)	)	PUNCT
ejpam-1240	88	13	be	be	AUX
ejpam-1240	88	14	a	a	DET
ejpam-1240	88	15	gi	gi	NOUN
ejpam-1240	88	16	-	-	PUNCT
ejpam-1240	88	17	system	system	NOUN
ejpam-1240	88	18	.	.	PUNCT
ejpam-1240	89	1	assume	assume	VERB
ejpam-1240	89	2	that	that	SCONJ
ejpam-1240	89	3	the	the	DET
ejpam-1240	89	4	following	follow	VERB
ejpam-1240	89	5	gi	gi	NOUN
ejpam-1240	89	6	-	-	PUNCT
ejpam-1240	89	7	conditions	condition	NOUN
ejpam-1240	89	8	are	be	AUX
ejpam-1240	89	9	satisfied	satisfied	ADJ
ejpam-1240	89	10	:	:	PUNCT
ejpam-1240	89	11	1	1	X
ejpam-1240	89	12	.	.	X
ejpam-1240	89	13	t	t	PROPN
ejpam-1240	89	14	is	be	AUX
ejpam-1240	89	15	a	a	DET
ejpam-1240	89	16	*	*	PUNCT
ejpam-1240	89	17	-unipotent	-unipotent	NOUN
ejpam-1240	89	18	naturally	naturally	ADV
ejpam-1240	89	19	ordered	order	VERB
ejpam-1240	89	20	abundant	abundant	ADJ
ejpam-1240	89	21	semigroup	semigroup	NOUN
ejpam-1240	89	22	in	in	ADP
ejpam-1240	89	23	which	which	PRON
ejpam-1240	89	24	each	each	DET
ejpam-1240	89	25	idempotent	idempotent	NOUN
ejpam-1240	89	26	has	have	VERB
ejpam-1240	89	27	a	a	DET
ejpam-1240	89	28	greatest	great	ADJ
ejpam-1240	89	29	inverse	inverse	NOUN
ejpam-1240	89	30	and	and	CCONJ
ejpam-1240	89	31	which	which	PRON
ejpam-1240	89	32	is	be	AUX
ejpam-1240	89	33	g	g	NOUN
ejpam-1240	89	34	-	-	PUNCT
ejpam-1240	89	35	regular	regular	ADJ
ejpam-1240	89	36	and	and	CCONJ
ejpam-1240	89	37	reflexive	reflexive	ADJ
ejpam-1240	89	38	.	.	PUNCT
ejpam-1240	90	1	2	2	X
ejpam-1240	90	2	.	.	X
ejpam-1240	90	3	l	l	NOUN
ejpam-1240	90	4	is	be	AUX
ejpam-1240	90	5	a	a	DET
ejpam-1240	90	6	naturally	naturally	ADV
ejpam-1240	90	7	ordered	order	VERB
ejpam-1240	90	8	left	leave	VERB
ejpam-1240	90	9	regular	regular	ADJ
ejpam-1240	90	10	partial	partial	ADJ
ejpam-1240	90	11	band	band	NOUN
ejpam-1240	90	12	in	in	ADP
ejpam-1240	90	13	which	which	PRON
ejpam-1240	90	14	α	α	PRON
ejpam-1240	90	15	is	be	AUX
ejpam-1240	90	16	the	the	DET
ejpam-1240	90	17	greatest	great	ADJ
ejpam-1240	90	18	element	element	NOUN
ejpam-1240	90	19	in	in	ADP
ejpam-1240	90	20	lα	lα	NOUN
ejpam-1240	90	21	for	for	ADP
ejpam-1240	90	22	all	all	DET
ejpam-1240	90	23	α	α	DET
ejpam-1240	90	24	∈	∈	PROPN
ejpam-1240	90	25	y	y	PROPN
ejpam-1240	90	26	.	.	PUNCT
ejpam-1240	91	1	3	3	X
ejpam-1240	91	2	.	.	X
ejpam-1240	91	3	r	r	NOUN
ejpam-1240	91	4	is	be	AUX
ejpam-1240	91	5	a	a	DET
ejpam-1240	91	6	naturally	naturally	ADV
ejpam-1240	91	7	ordered	order	VERB
ejpam-1240	91	8	right	right	ADV
ejpam-1240	91	9	regular	regular	ADJ
ejpam-1240	91	10	partial	partial	ADJ
ejpam-1240	91	11	band	band	NOUN
ejpam-1240	91	12	in	in	ADP
ejpam-1240	91	13	which	which	PRON
ejpam-1240	91	14	β	β	NOUN
ejpam-1240	91	15	is	be	AUX
ejpam-1240	91	16	the	the	DET
ejpam-1240	91	17	greatest	great	ADJ
ejpam-1240	91	18	element	element	NOUN
ejpam-1240	91	19	in	in	ADP
ejpam-1240	91	20	rβ	rβ	NOUN
ejpam-1240	91	21	for	for	ADP
ejpam-1240	91	22	all	all	DET
ejpam-1240	91	23	β	β	X
ejpam-1240	91	24	∈	∈	PROPN
ejpam-1240	91	25	y	y	PROPN
ejpam-1240	91	26	.	.	PUNCT
ejpam-1240	92	1	4	4	X
ejpam-1240	92	2	.	.	X
ejpam-1240	92	3	for	for	ADP
ejpam-1240	92	4	all	all	PRON
ejpam-1240	92	5	x	x	SYM
ejpam-1240	92	6	,	,	PUNCT
ejpam-1240	92	7	y	y	PROPN
ejpam-1240	92	8	∈	∈	PROPN
ejpam-1240	92	9	l	l	NOUN
ejpam-1240	92	10	and	and	CCONJ
ejpam-1240	92	11	u	u	NOUN
ejpam-1240	92	12	,	,	PUNCT
ejpam-1240	92	13	v	v	NOUN
ejpam-1240	92	14	∈	∈	NOUN
ejpam-1240	92	15	r	r	NOUN
ejpam-1240	92	16	,	,	PUNCT
ejpam-1240	92	17	if	if	SCONJ
ejpam-1240	92	18	x	x	ADP
ejpam-1240	92	19	≤	≤	ADJ
ejpam-1240	92	20	y	y	NOUN
ejpam-1240	92	21	and	and	CCONJ
ejpam-1240	92	22	u	u	PROPN
ejpam-1240	92	23	≤	≤	PROPN
ejpam-1240	92	24	v	v	NOUN
ejpam-1240	92	25	,	,	PUNCT
ejpam-1240	92	26	then	then	ADV
ejpam-1240	92	27	[	[	X
ejpam-1240	92	28	u	u	X
ejpam-1240	92	29	,	,	PUNCT
ejpam-1240	92	30	x]≤	x]≤	PROPN
ejpam-1240	93	1	[	[	X
ejpam-1240	93	2	v	v	PROPN
ejpam-1240	93	3	,	,	PUNCT
ejpam-1240	93	4	y	y	PROPN
ejpam-1240	93	5	]	]	X
ejpam-1240	93	6	.	.	PUNCT
ejpam-1240	94	1	5	5	X
ejpam-1240	94	2	.	.	X
ejpam-1240	94	3	for	for	ADP
ejpam-1240	94	4	any	any	PRON
ejpam-1240	94	5	(	(	PUNCT
ejpam-1240	94	6	x	x	PROPN
ejpam-1240	94	7	,	,	PUNCT
ejpam-1240	94	8	t	t	PROPN
ejpam-1240	94	9	,	,	PUNCT
ejpam-1240	94	10	u	u	NOUN
ejpam-1240	94	11	)	)	PUNCT
ejpam-1240	94	12	,	,	PUNCT
ejpam-1240	94	13	(	(	PUNCT
ejpam-1240	94	14	y	y	PROPN
ejpam-1240	94	15	,	,	PUNCT
ejpam-1240	94	16	s	s	PROPN
ejpam-1240	94	17	,	,	PUNCT
ejpam-1240	94	18	v	v	NOUN
ejpam-1240	94	19	)	)	PUNCT
ejpam-1240	94	20	∈	∈	NOUN
ejpam-1240	94	21	lgi	lgi	NOUN
ejpam-1240	94	22	,	,	PUNCT
ejpam-1240	94	23	if	if	SCONJ
ejpam-1240	94	24	(	(	PUNCT
ejpam-1240	94	25	x	x	X
ejpam-1240	94	26	,	,	PUNCT
ejpam-1240	94	27	s	s	PROPN
ejpam-1240	94	28	,	,	PUNCT
ejpam-1240	94	29	v	v	NOUN
ejpam-1240	94	30	)	)	PUNCT
ejpam-1240	94	31	is	be	AUX
ejpam-1240	94	32	an	an	DET
ejpam-1240	94	33	inverse	inverse	NOUN
ejpam-1240	94	34	of	of	ADP
ejpam-1240	94	35	(	(	PUNCT
ejpam-1240	94	36	y	y	PROPN
ejpam-1240	94	37	,	,	PUNCT
ejpam-1240	94	38	t	t	PROPN
ejpam-1240	94	39	,	,	PUNCT
ejpam-1240	94	40	u	u	NOUN
ejpam-1240	94	41	)	)	PUNCT
ejpam-1240	94	42	,	,	PUNCT
ejpam-1240	94	43	then	then	ADV
ejpam-1240	94	44	t	t	PROPN
ejpam-1240	94	45	∈	∈	PROPN
ejpam-1240	94	46	regt	regt	VERB
ejpam-1240	94	47	and	and	CCONJ
ejpam-1240	94	48	s	s	NOUN
ejpam-1240	94	49	≤	≤	NUM
ejpam-1240	94	50	t	t	PROPN
ejpam-1240	94	51	◦	◦	NOUN
ejpam-1240	94	52	.	.	PUNCT
ejpam-1240	95	1	then	then	ADV
ejpam-1240	95	2	,	,	PUNCT
ejpam-1240	95	3	with	with	ADP
ejpam-1240	95	4	respect	respect	NOUN
ejpam-1240	95	5	to	to	ADP
ejpam-1240	95	6	the	the	DET
ejpam-1240	95	7	cartesian	cartesian	ADJ
ejpam-1240	95	8	order	order	NOUN
ejpam-1240	95	9	,	,	PUNCT
ejpam-1240	95	10	gi(t	gi(t	PUNCT
ejpam-1240	95	11	;	;	PUNCT
ejpam-1240	95	12	l	l	X
ejpam-1240	95	13	,	,	PUNCT
ejpam-1240	95	14	r	r	NOUN
ejpam-1240	95	15	;	;	PUNCT
ejpam-1240	95	16	[	[	X
ejpam-1240	95	17	,	,	PUNCT
ejpam-1240	95	18	]	]	X
ejpam-1240	95	19	)	)	PUNCT
ejpam-1240	95	20	forms	form	VERB
ejpam-1240	95	21	a	a	PRON
ejpam-1240	95	22	g	g	NOUN
ejpam-1240	95	23	-	-	PUNCT
ejpam-1240	95	24	regular	regular	ADJ
ejpam-1240	95	25	and	and	CCONJ
ejpam-1240	95	26	reflexive	reflexive	ADJ
ejpam-1240	95	27	naturally	naturally	ADV
ejpam-1240	95	28	ordered	order	VERB
ejpam-1240	95	29	abundant	abundant	ADJ
ejpam-1240	95	30	semigroup	semigroup	NOUN
ejpam-1240	95	31	in	in	ADP
ejpam-1240	95	32	which	which	PRON
ejpam-1240	95	33	each	each	DET
ejpam-1240	95	34	idempotent	idempotent	NOUN
ejpam-1240	95	35	has	have	VERB
ejpam-1240	95	36	a	a	DET
ejpam-1240	95	37	greatest	great	ADJ
ejpam-1240	95	38	inverse	inverse	NOUN
ejpam-1240	95	39	.	.	PUNCT
ejpam-1240	96	1	conversely	conversely	ADV
ejpam-1240	96	2	,	,	PUNCT
ejpam-1240	96	3	any	any	DET
ejpam-1240	96	4	g	g	NOUN
ejpam-1240	96	5	-	-	PUNCT
ejpam-1240	96	6	regular	regular	ADJ
ejpam-1240	96	7	and	and	CCONJ
ejpam-1240	96	8	reflexive	reflexive	ADJ
ejpam-1240	96	9	naturally	naturally	ADV
ejpam-1240	96	10	ordered	order	VERB
ejpam-1240	96	11	abundant	abundant	ADJ
ejpam-1240	96	12	semigroup	semigroup	NOUN
ejpam-1240	96	13	in	in	ADP
ejpam-1240	96	14	which	which	PRON
ejpam-1240	96	15	each	each	DET
ejpam-1240	96	16	idempotent	idempotent	NOUN
ejpam-1240	96	17	has	have	VERB
ejpam-1240	96	18	a	a	DET
ejpam-1240	96	19	greatest	great	ADJ
ejpam-1240	96	20	inverse	inverse	NOUN
ejpam-1240	96	21	can	can	AUX
ejpam-1240	96	22	be	be	AUX
ejpam-1240	96	23	constructed	construct	VERB
ejpam-1240	96	24	in	in	ADP
ejpam-1240	96	25	the	the	DET
ejpam-1240	96	26	above	above	ADJ
ejpam-1240	96	27	manner	manner	NOUN
ejpam-1240	96	28	.	.	PUNCT
ejpam-1240	97	1	3	3	X
ejpam-1240	97	2	.	.	X
ejpam-1240	97	3	proofs	proof	NOUN
ejpam-1240	97	4	in	in	ADP
ejpam-1240	97	5	this	this	DET
ejpam-1240	97	6	section	section	NOUN
ejpam-1240	97	7	,	,	PUNCT
ejpam-1240	97	8	we	we	PRON
ejpam-1240	97	9	give	give	VERB
ejpam-1240	97	10	the	the	DET
ejpam-1240	97	11	proof	proof	NOUN
ejpam-1240	97	12	of	of	ADP
ejpam-1240	97	13	theorem	theorem	NOUN
ejpam-1240	97	14	1	1	NUM
ejpam-1240	97	15	.	.	PUNCT
ejpam-1240	97	16	to	to	PART
ejpam-1240	97	17	begin	begin	VERB
ejpam-1240	97	18	with	with	ADP
ejpam-1240	97	19	the	the	DET
ejpam-1240	97	20	proof	proof	NOUN
ejpam-1240	97	21	,	,	PUNCT
ejpam-1240	97	22	we	we	PRON
ejpam-1240	97	23	list	list	VERB
ejpam-1240	97	24	the	the	DET
ejpam-1240	97	25	following	follow	VERB
ejpam-1240	97	26	known	know	VERB
ejpam-1240	97	27	results	result	NOUN
ejpam-1240	97	28	which	which	PRON
ejpam-1240	97	29	will	will	AUX
ejpam-1240	97	30	be	be	AUX
ejpam-1240	97	31	useful	useful	ADJ
ejpam-1240	97	32	in	in	ADP
ejpam-1240	97	33	the	the	DET
ejpam-1240	97	34	sequel	sequel	NOUN
ejpam-1240	97	35	.	.	PUNCT
ejpam-1240	98	1	x.	x.	PROPN
ejpam-1240	98	2	guo	guo	PROPN
ejpam-1240	98	3	,	,	PUNCT
ejpam-1240	98	4	k.	k.	PROPN
ejpam-1240	98	5	shum	shum	PROPN
ejpam-1240	98	6	/	/	SYM
ejpam-1240	98	7	eur	eur	PROPN
ejpam-1240	98	8	.	.	PUNCT
ejpam-1240	99	1	j.	j.	PROPN
ejpam-1240	99	2	pure	pure	PROPN
ejpam-1240	99	3	appl	appl	PROPN
ejpam-1240	99	4	.	.	PROPN
ejpam-1240	99	5	math	math	PROPN
ejpam-1240	99	6	,	,	PUNCT
ejpam-1240	99	7	4	4	NUM
ejpam-1240	99	8	(	(	PUNCT
ejpam-1240	99	9	2011	2011	NUM
ejpam-1240	99	10	)	)	PUNCT
ejpam-1240	99	11	,	,	PUNCT
ejpam-1240	99	12	210	210	NUM
ejpam-1240	99	13	-	-	SYM
ejpam-1240	99	14	220	220	NUM
ejpam-1240	99	15	214	214	NUM
ejpam-1240	99	16	lemma	lemma	PROPN
ejpam-1240	99	17	1	1	NUM
ejpam-1240	99	18	(	(	PUNCT
ejpam-1240	99	19	13	13	NUM
ejpam-1240	99	20	)	)	PUNCT
ejpam-1240	99	21	.	.	PUNCT
ejpam-1240	100	1	let	let	VERB
ejpam-1240	100	2	s	s	PRON
ejpam-1240	100	3	be	be	AUX
ejpam-1240	100	4	an	an	DET
ejpam-1240	100	5	ordered	order	VERB
ejpam-1240	100	6	semigroup	semigroup	NOUN
ejpam-1240	100	7	.	.	PUNCT
ejpam-1240	101	1	then	then	ADV
ejpam-1240	101	2	the	the	DET
ejpam-1240	101	3	following	follow	VERB
ejpam-1240	101	4	statements	statement	NOUN
ejpam-1240	101	5	are	be	AUX
ejpam-1240	101	6	equivalent	equivalent	ADJ
ejpam-1240	101	7	:	:	PUNCT
ejpam-1240	101	8	1	1	X
ejpam-1240	101	9	.	.	X
ejpam-1240	102	1	every	every	DET
ejpam-1240	102	2	idempotent	idempotent	NOUN
ejpam-1240	102	3	of	of	ADP
ejpam-1240	102	4	s	s	PROPN
ejpam-1240	102	5	has	have	VERB
ejpam-1240	102	6	a	a	DET
ejpam-1240	102	7	greatest	great	ADJ
ejpam-1240	102	8	inverse	inverse	NOUN
ejpam-1240	102	9	.	.	PUNCT
ejpam-1240	103	1	2	2	X
ejpam-1240	103	2	.	.	X
ejpam-1240	103	3	every	every	DET
ejpam-1240	103	4	regular	regular	ADJ
ejpam-1240	103	5	element	element	NOUN
ejpam-1240	103	6	of	of	ADP
ejpam-1240	103	7	s	s	PROPN
ejpam-1240	103	8	has	have	VERB
ejpam-1240	103	9	a	a	DET
ejpam-1240	103	10	greatest	great	ADJ
ejpam-1240	103	11	inverse	inverse	NOUN
ejpam-1240	103	12	.	.	PUNCT
ejpam-1240	104	1	lemma	lemma	PROPN
ejpam-1240	104	2	2	2	NUM
ejpam-1240	104	3	(	(	PUNCT
ejpam-1240	104	4	13	13	NUM
ejpam-1240	104	5	,	,	PUNCT
ejpam-1240	104	6	lemmas	lemma	VERB
ejpam-1240	104	7	3.2	3.2	NUM
ejpam-1240	104	8	and	and	CCONJ
ejpam-1240	104	9	3.3	3.3	NUM
ejpam-1240	104	10	)	)	PUNCT
ejpam-1240	104	11	.	.	PUNCT
ejpam-1240	105	1	let	let	VERB
ejpam-1240	105	2	s	s	PRON
ejpam-1240	105	3	be	be	AUX
ejpam-1240	105	4	an	an	DET
ejpam-1240	105	5	ordered	order	VERB
ejpam-1240	105	6	semigroup	semigroup	NOUN
ejpam-1240	105	7	and	and	CCONJ
ejpam-1240	105	8	e	e	NOUN
ejpam-1240	105	9	,	,	PUNCT
ejpam-1240	105	10	f	f	PROPN
ejpam-1240	105	11	∈	∈	PROPN
ejpam-1240	105	12	e.	e.	PROPN
ejpam-1240	106	1	if	if	SCONJ
ejpam-1240	106	2	any	any	DET
ejpam-1240	106	3	idempotent	idempotent	NOUN
ejpam-1240	106	4	of	of	ADP
ejpam-1240	106	5	s	s	PROPN
ejpam-1240	106	6	has	have	VERB
ejpam-1240	106	7	a	a	DET
ejpam-1240	106	8	greatest	great	ADJ
ejpam-1240	106	9	inverse	inverse	NOUN
ejpam-1240	106	10	,	,	PUNCT
ejpam-1240	106	11	then	then	ADV
ejpam-1240	106	12	1	1	X
ejpam-1240	106	13	.	.	PUNCT
ejpam-1240	107	1	(	(	PUNCT
ejpam-1240	107	2	x	x	X
ejpam-1240	107	3	x	x	NOUN
ejpam-1240	107	4	◦	◦	NOUN
ejpam-1240	107	5	)	)	PUNCT
ejpam-1240	107	6	◦	◦	NOUN
ejpam-1240	107	7	=	=	SYM
ejpam-1240	107	8	(	(	PUNCT
ejpam-1240	107	9	x	x	NOUN
ejpam-1240	107	10	◦	◦	NOUN
ejpam-1240	107	11	)	)	PUNCT
ejpam-1240	107	12	◦	◦	NOUN
ejpam-1240	107	13	x	x	NOUN
ejpam-1240	107	14	◦	◦	NOUN
ejpam-1240	107	15	and	and	CCONJ
ejpam-1240	107	16	(	(	PUNCT
ejpam-1240	107	17	x	x	X
ejpam-1240	107	18	◦	◦	NOUN
ejpam-1240	107	19	x	x	NOUN
ejpam-1240	107	20	)	)	PUNCT
ejpam-1240	107	21	◦	◦	NOUN
ejpam-1240	107	22	=	=	SYM
ejpam-1240	107	23	x	x	SYM
ejpam-1240	107	24	◦	◦	NOUN
ejpam-1240	107	25	(x	(x	NOUN
ejpam-1240	107	26	◦	◦	NOUN
ejpam-1240	107	27	)	)	PUNCT
ejpam-1240	107	28	◦	◦	NOUN
ejpam-1240	107	29	for	for	ADP
ejpam-1240	107	30	all	all	DET
ejpam-1240	107	31	x	x	SYM
ejpam-1240	107	32	∈	∈	PROPN
ejpam-1240	107	33	reg	reg	NOUN
ejpam-1240	107	34	s.	s.	PROPN
ejpam-1240	107	35	2	2	NUM
ejpam-1240	107	36	.	.	PUNCT
ejpam-1240	107	37	x	x	PUNCT
ejpam-1240	108	1	x	x	X
ejpam-1240	108	2	◦	◦	NOUN
ejpam-1240	108	3	[	[	X
ejpam-1240	108	4	resp	resp	NOUN
ejpam-1240	108	5	.	.	PUNCT
ejpam-1240	109	1	x	x	PUNCT
ejpam-1240	109	2	◦	◦	NOUN
ejpam-1240	109	3	x	x	X
ejpam-1240	109	4	]	]	X
ejpam-1240	109	5	is	be	AUX
ejpam-1240	109	6	the	the	DET
ejpam-1240	109	7	greatest	great	ADJ
ejpam-1240	109	8	idempotent	idempotent	NOUN
ejpam-1240	109	9	of	of	ADP
ejpam-1240	109	10	rx	rx	NOUN
ejpam-1240	109	11	[	[	X
ejpam-1240	109	12	resp	resp	NOUN
ejpam-1240	109	13	.	.	PUNCT
ejpam-1240	110	1	lx	lx	NOUN
ejpam-1240	110	2	]	]	PUNCT
ejpam-1240	110	3	for	for	ADP
ejpam-1240	110	4	all	all	DET
ejpam-1240	110	5	x	x	SYM
ejpam-1240	110	6	∈	∈	PROPN
ejpam-1240	110	7	reg	reg	NOUN
ejpam-1240	110	8	s.	s.	PROPN
ejpam-1240	110	9	3	3	NUM
ejpam-1240	110	10	.	.	X
ejpam-1240	111	1	x	x	PUNCT
ejpam-1240	111	2	◦	◦	NOUN
ejpam-1240	111	3	◦	◦	NOUN
ejpam-1240	111	4	◦	◦	NOUN
ejpam-1240	111	5	=	=	SYM
ejpam-1240	111	6	x	x	PART
ejpam-1240	111	7	◦	◦	NOUN
ejpam-1240	111	8	for	for	ADP
ejpam-1240	111	9	all	all	DET
ejpam-1240	111	10	x	x	SYM
ejpam-1240	111	11	∈	∈	NOUN
ejpam-1240	111	12	reg	reg	NOUN
ejpam-1240	111	13	s.	s.	PROPN
ejpam-1240	111	14	let	let	VERB
ejpam-1240	111	15	s	s	PRON
ejpam-1240	111	16	be	be	AUX
ejpam-1240	111	17	an	an	DET
ejpam-1240	111	18	ordered	order	VERB
ejpam-1240	111	19	abundant	abundant	ADJ
ejpam-1240	111	20	semigroup	semigroup	NOUN
ejpam-1240	111	21	in	in	ADP
ejpam-1240	111	22	which	which	PRON
ejpam-1240	111	23	each	each	DET
ejpam-1240	111	24	regular	regular	ADJ
ejpam-1240	111	25	element	element	NOUN
ejpam-1240	111	26	has	have	VERB
ejpam-1240	111	27	a	a	DET
ejpam-1240	111	28	maximum	maximum	ADJ
ejpam-1240	111	29	inverse	inverse	NOUN
ejpam-1240	111	30	.	.	PUNCT
ejpam-1240	112	1	if	if	SCONJ
ejpam-1240	112	2	x	x	PUNCT
ejpam-1240	112	3	∈	∈	PROPN
ejpam-1240	112	4	s	s	PROPN
ejpam-1240	112	5	,	,	PUNCT
ejpam-1240	112	6	the	the	DET
ejpam-1240	112	7	greatest	great	ADJ
ejpam-1240	112	8	idempotent	idempotent	NOUN
ejpam-1240	112	9	of	of	ADP
ejpam-1240	112	10	the	the	DET
ejpam-1240	112	11	l	l	NOUN
ejpam-1240	112	12	-class	-class	NOUN
ejpam-1240	112	13	[	[	X
ejpam-1240	112	14	resp	resp	NOUN
ejpam-1240	112	15	.	.	PUNCT
ejpam-1240	113	1	r	r	X
ejpam-1240	113	2	-	-	PUNCT
ejpam-1240	113	3	class	class	NOUN
ejpam-1240	113	4	]	]	PUNCT
ejpam-1240	113	5	of	of	ADP
ejpam-1240	113	6	s	s	VERB
ejpam-1240	113	7	containing	contain	VERB
ejpam-1240	113	8	the	the	DET
ejpam-1240	113	9	greatest	great	ADJ
ejpam-1240	113	10	idempotent	idempotent	NOUN
ejpam-1240	113	11	of	of	ADP
ejpam-1240	113	12	r∗x	r∗x	NUM
ejpam-1240	114	1	[	[	X
ejpam-1240	114	2	resp	resp	NOUN
ejpam-1240	114	3	.	.	PUNCT
ejpam-1240	115	1	l∗x]is	l∗x]is	NOUN
ejpam-1240	115	2	denoted	denote	VERB
ejpam-1240	115	3	by	by	ADP
ejpam-1240	115	4	ex	ex	PRON
ejpam-1240	116	1	[	[	X
ejpam-1240	116	2	resp	resp	NOUN
ejpam-1240	116	3	.	.	PUNCT
ejpam-1240	117	1	fx	fx	NOUN
ejpam-1240	117	2	]	]	PUNCT
ejpam-1240	117	3	.	.	PUNCT
ejpam-1240	118	1	clearly	clearly	ADV
ejpam-1240	118	2	,	,	PUNCT
ejpam-1240	118	3	ex	ex	X
ejpam-1240	118	4	=	=	PUNCT
ejpam-1240	118	5	ex†	ex†	PROPN
ejpam-1240	118	6	and	and	CCONJ
ejpam-1240	118	7	fx	fx	NOUN
ejpam-1240	118	8	=	=	PUNCT
ejpam-1240	118	9	fx∗	fx∗	PROPN
ejpam-1240	118	10	.	.	PUNCT
ejpam-1240	119	1	by	by	ADP
ejpam-1240	119	2	lemma	lemma	PROPN
ejpam-1240	119	3	1	1	NUM
ejpam-1240	119	4	,	,	PUNCT
ejpam-1240	119	5	we	we	PRON
ejpam-1240	119	6	have	have	VERB
ejpam-1240	119	7	ex	ex	ADJ
ejpam-1240	119	8	=	=	SYM
ejpam-1240	119	9	(	(	PUNCT
ejpam-1240	119	10	x	x	NOUN
ejpam-1240	119	11	†x†	†x†	NOUN
ejpam-1240	119	12	◦	◦	NOUN
ejpam-1240	119	13	)	)	PUNCT
ejpam-1240	119	14	◦	◦	NOUN
ejpam-1240	119	15	(x†x†	(x†x†	NOUN
ejpam-1240	119	16	◦	◦	NOUN
ejpam-1240	119	17	)	)	PUNCT
ejpam-1240	119	18	and	and	CCONJ
ejpam-1240	119	19	fx	fx	NOUN
ejpam-1240	119	20	=	=	SYM
ejpam-1240	119	21	(	(	PUNCT
ejpam-1240	119	22	x	x	NOUN
ejpam-1240	119	23	∗	∗	NOUN
ejpam-1240	119	24	◦	◦	NOUN
ejpam-1240	119	25	x∗)(x∗	x∗)(x∗	PROPN
ejpam-1240	119	26	◦	◦	PROPN
ejpam-1240	119	27	x∗)	x∗)	PROPN
ejpam-1240	119	28	◦	◦	NOUN
ejpam-1240	119	29	.	.	PUNCT
ejpam-1240	120	1	putting	put	VERB
ejpam-1240	120	2	x	x	PUNCT
ejpam-1240	120	3	♭	♭	PROPN
ejpam-1240	120	4	=	=	PUNCT
ejpam-1240	120	5	ex	ex	X
ejpam-1240	120	6	x	x	NOUN
ejpam-1240	120	7	fx	fx	PROPN
ejpam-1240	120	8	.	.	PUNCT
ejpam-1240	121	1	then	then	ADV
ejpam-1240	121	2	,	,	PUNCT
ejpam-1240	121	3	it	it	PRON
ejpam-1240	121	4	is	be	AUX
ejpam-1240	121	5	easy	easy	ADJ
ejpam-1240	121	6	to	to	PART
ejpam-1240	121	7	see	see	VERB
ejpam-1240	121	8	that	that	SCONJ
ejpam-1240	121	9	x	x	PUNCT
ejpam-1240	121	10	♭	♭	PROPN
ejpam-1240	121	11	is	be	AUX
ejpam-1240	121	12	the	the	DET
ejpam-1240	121	13	greatest	great	ADJ
ejpam-1240	121	14	element	element	NOUN
ejpam-1240	121	15	of	of	ADP
ejpam-1240	121	16	the	the	DET
ejpam-1240	121	17	set	set	NOUN
ejpam-1240	121	18	{	{	PUNCT
ejpam-1240	121	19	ex	ex	ADJ
ejpam-1240	121	20	f	f	NOUN
ejpam-1240	121	21	:	:	PUNCT
ejpam-1240	121	22	e	e	X
ejpam-1240	121	23	,	,	PUNCT
ejpam-1240	121	24	f	f	PROPN
ejpam-1240	121	25	∈	∈	PROPN
ejpam-1240	121	26	e(s	e(s	PROPN
ejpam-1240	121	27	)	)	PUNCT
ejpam-1240	122	1	such	such	ADJ
ejpam-1240	122	2	that	that	SCONJ
ejpam-1240	122	3	el	el	PROPN
ejpam-1240	122	4	x†	x†	PROPN
ejpam-1240	122	5	x†	x†	VERB
ejpam-1240	122	6	◦	◦	NOUN
ejpam-1240	122	7	and	and	CCONJ
ejpam-1240	122	8	fr	fr	PROPN
ejpam-1240	122	9	x∗	x∗	PROPN
ejpam-1240	122	10	◦	◦	VERB
ejpam-1240	122	11	x∗	x∗	PROPN
ejpam-1240	122	12	}	}	PUNCT
ejpam-1240	122	13	.	.	PUNCT
ejpam-1240	123	1	in	in	ADP
ejpam-1240	123	2	what	what	PRON
ejpam-1240	123	3	follows	follow	VERB
ejpam-1240	123	4	,	,	PUNCT
ejpam-1240	123	5	we	we	PRON
ejpam-1240	123	6	use	use	VERB
ejpam-1240	123	7	the	the	DET
ejpam-1240	123	8	set	set	NOUN
ejpam-1240	123	9	s	s	NOUN
ejpam-1240	123	10	♭	♭	PROPN
ejpam-1240	123	11	to	to	PART
ejpam-1240	123	12	denote	denote	VERB
ejpam-1240	123	13	the	the	DET
ejpam-1240	123	14	set	set	NOUN
ejpam-1240	123	15	{	{	PUNCT
ejpam-1240	123	16	x	x	PUNCT
ejpam-1240	123	17	♭	♭	INTJ
ejpam-1240	123	18	:	:	PUNCT
ejpam-1240	123	19	x	x	PUNCT
ejpam-1240	123	20	∈	∈	NOUN
ejpam-1240	123	21	s	s	PART
ejpam-1240	123	22	}	}	PUNCT
ejpam-1240	123	23	.	.	PUNCT
ejpam-1240	124	1	an	an	DET
ejpam-1240	124	2	abundant	abundant	ADJ
ejpam-1240	124	3	subsemigroup	subsemigroup	NOUN
ejpam-1240	124	4	u	u	NOUN
ejpam-1240	124	5	of	of	ADP
ejpam-1240	124	6	s	s	PROPN
ejpam-1240	124	7	is	be	AUX
ejpam-1240	124	8	said	say	VERB
ejpam-1240	124	9	to	to	PART
ejpam-1240	124	10	be	be	AUX
ejpam-1240	124	11	a	a	DET
ejpam-1240	124	12	left	left	NOUN
ejpam-1240	125	1	[	[	X
ejpam-1240	125	2	right	right	X
ejpam-1240	125	3	]	]	X
ejpam-1240	125	4	*	*	PUNCT
ejpam-1240	125	5	-subsemigroup[8	-subsemigroup[8	NOUN
ejpam-1240	125	6	]	]	PUNCT
ejpam-1240	125	7	of	of	ADP
ejpam-1240	125	8	s	s	PRON
ejpam-1240	125	9	if	if	SCONJ
ejpam-1240	125	10	for	for	ADP
ejpam-1240	125	11	all	all	DET
ejpam-1240	125	12	a	a	DET
ejpam-1240	125	13	∈	∈	PROPN
ejpam-1240	125	14	u	u	NOUN
ejpam-1240	125	15	,	,	PUNCT
ejpam-1240	125	16	there	there	PRON
ejpam-1240	125	17	exists	exist	VERB
ejpam-1240	126	1	e	e	X
ejpam-1240	126	2	∈	∈	PROPN
ejpam-1240	126	3	u	u	NOUN
ejpam-1240	126	4	⋂	⋂	PROPN
ejpam-1240	126	5	e	e	PROPN
ejpam-1240	126	6	such	such	ADJ
ejpam-1240	126	7	that	that	SCONJ
ejpam-1240	126	8	al	al	PROPN
ejpam-1240	126	9	∗(s)e	∗(s)e	PROPN
ejpam-1240	127	1	[	[	X
ejpam-1240	127	2	ar∗(s)e	ar∗(s)e	NOUN
ejpam-1240	127	3	]	]	PUNCT
ejpam-1240	127	4	.	.	PUNCT
ejpam-1240	128	1	furthermore	furthermore	ADV
ejpam-1240	128	2	,	,	PUNCT
ejpam-1240	128	3	if	if	SCONJ
ejpam-1240	128	4	u	u	NOUN
ejpam-1240	128	5	is	be	AUX
ejpam-1240	128	6	both	both	CCONJ
ejpam-1240	128	7	a	a	DET
ejpam-1240	128	8	left	left	ADJ
ejpam-1240	128	9	*	*	NOUN
ejpam-1240	128	10	-subsemigroup	-subsemigroup	NOUN
ejpam-1240	128	11	and	and	CCONJ
ejpam-1240	128	12	a	a	DET
ejpam-1240	128	13	right	right	NOUN
ejpam-1240	128	14	*	*	ADJ
ejpam-1240	128	15	-subsemigroup	-subsemigroup	NOUN
ejpam-1240	128	16	,	,	PUNCT
ejpam-1240	128	17	then	then	ADV
ejpam-1240	128	18	we	we	PRON
ejpam-1240	128	19	call	call	VERB
ejpam-1240	128	20	u	u	PRON
ejpam-1240	128	21	a	a	DET
ejpam-1240	128	22	*	*	PROPN
ejpam-1240	128	23	-subsemigroup	-subsemigroup	NOUN
ejpam-1240	128	24	.	.	PUNCT
ejpam-1240	129	1	lemma	lemma	PROPN
ejpam-1240	129	2	3	3	X
ejpam-1240	129	3	.	.	PUNCT
ejpam-1240	130	1	let	let	VERB
ejpam-1240	130	2	s	s	PRON
ejpam-1240	130	3	be	be	AUX
ejpam-1240	130	4	an	an	DET
ejpam-1240	130	5	ordered	order	VERB
ejpam-1240	130	6	abundant	abundant	ADJ
ejpam-1240	130	7	semigroup	semigroup	NOUN
ejpam-1240	130	8	in	in	ADP
ejpam-1240	130	9	which	which	PRON
ejpam-1240	130	10	each	each	DET
ejpam-1240	130	11	idempotent	idempotent	NOUN
ejpam-1240	130	12	has	have	VERB
ejpam-1240	130	13	a	a	DET
ejpam-1240	130	14	greatest	great	ADJ
ejpam-1240	130	15	idempotent	idempotent	NOUN
ejpam-1240	130	16	.	.	PUNCT
ejpam-1240	131	1	1	1	X
ejpam-1240	131	2	.	.	PUNCT
ejpam-1240	132	1	[	[	X
ejpam-1240	132	2	13	13	NUM
ejpam-1240	132	3	,	,	PUNCT
ejpam-1240	132	4	lemma	lemma	PROPN
ejpam-1240	132	5	3.4	3.4	NUM
ejpam-1240	132	6	]	]	PUNCT
ejpam-1240	132	7	if	if	SCONJ
ejpam-1240	132	8	x	x	PROPN
ejpam-1240	132	9	∈	∈	PROPN
ejpam-1240	132	10	regs	reg	NOUN
ejpam-1240	132	11	,	,	PUNCT
ejpam-1240	132	12	then	then	ADV
ejpam-1240	132	13	x	x	X
ejpam-1240	132	14	♭	♭	PROPN
ejpam-1240	132	15	=	=	PUNCT
ejpam-1240	132	16	x	x	SYM
ejpam-1240	132	17	◦	◦	NOUN
ejpam-1240	132	18	◦	◦	NOUN
ejpam-1240	132	19	.	.	NOUN
ejpam-1240	132	20	2	2	NUM
ejpam-1240	132	21	.	.	PUNCT
ejpam-1240	133	1	[	[	X
ejpam-1240	133	2	13	13	NUM
ejpam-1240	133	3	,	,	PUNCT
ejpam-1240	133	4	theorem	theorem	VERB
ejpam-1240	133	5	3.6	3.6	NUM
ejpam-1240	133	6	]	]	PUNCT
ejpam-1240	133	7	s	s	X
ejpam-1240	133	8	♭	♭	PROPN
ejpam-1240	133	9	is	be	AUX
ejpam-1240	133	10	a	a	DET
ejpam-1240	133	11	∗-subsemigroup	∗-subsemigroup	NOUN
ejpam-1240	133	12	of	of	ADP
ejpam-1240	133	13	s	s	PROPN
ejpam-1240	133	14	,	,	PUNCT
ejpam-1240	133	15	which	which	PRON
ejpam-1240	133	16	is	be	AUX
ejpam-1240	133	17	∗-unipotent	∗-unipotent	ADJ
ejpam-1240	133	18	,	,	PUNCT
ejpam-1240	133	19	and	and	CCONJ
ejpam-1240	133	20	is	be	AUX
ejpam-1240	133	21	a	a	DET
ejpam-1240	133	22	quasi	quasi	NOUN
ejpam-1240	133	23	-	-	NOUN
ejpam-1240	133	24	ideal	ideal	NOUN
ejpam-1240	133	25	of	of	ADP
ejpam-1240	133	26	s.	s.	PROPN
ejpam-1240	133	27	3	3	NUM
ejpam-1240	133	28	.	.	PUNCT
ejpam-1240	134	1	[	[	X
ejpam-1240	134	2	13	13	NUM
ejpam-1240	134	3	,	,	PUNCT
ejpam-1240	134	4	lemma	lemma	PROPN
ejpam-1240	134	5	5.1	5.1	NUM
ejpam-1240	134	6	]	]	X
ejpam-1240	134	7	m	m	VERB
ejpam-1240	134	8	=	=	SYM
ejpam-1240	134	9	{	{	PUNCT
ejpam-1240	134	10	e	e	NOUN
ejpam-1240	134	11	∈	∈	PROPN
ejpam-1240	134	12	e(s	e(s	PROPN
ejpam-1240	134	13	)	)	PUNCT
ejpam-1240	134	14	:	:	PUNCT
ejpam-1240	135	1	elα	elα	ADV
ejpam-1240	135	2	,	,	PUNCT
ejpam-1240	135	3	α	α	PROPN
ejpam-1240	135	4	∈	∈	PROPN
ejpam-1240	135	5	e(s	e(s	PROPN
ejpam-1240	135	6	♭	♭	PRON
ejpam-1240	135	7	)	)	PUNCT
ejpam-1240	135	8	}	}	PUNCT
ejpam-1240	135	9	is	be	AUX
ejpam-1240	135	10	a	a	DET
ejpam-1240	135	11	left	left	ADJ
ejpam-1240	135	12	regular	regular	ADJ
ejpam-1240	135	13	partial	partial	ADJ
ejpam-1240	135	14	band	band	NOUN
ejpam-1240	135	15	with	with	ADP
ejpam-1240	135	16	skeleton	skeleton	NOUN
ejpam-1240	135	17	e(s	e(s	PROPN
ejpam-1240	135	18	♭	♭	PRON
ejpam-1240	135	19	)	)	PUNCT
ejpam-1240	135	20	while	while	SCONJ
ejpam-1240	135	21	n	n	PRON
ejpam-1240	135	22	=	=	SYM
ejpam-1240	135	23	{	{	PUNCT
ejpam-1240	135	24	e	e	NOUN
ejpam-1240	135	25	∈	∈	PROPN
ejpam-1240	135	26	e(s	e(s	PROPN
ejpam-1240	135	27	)	)	PUNCT
ejpam-1240	135	28	:	:	PUNCT
ejpam-1240	136	1	erβ	erβ	ADV
ejpam-1240	136	2	,	,	PUNCT
ejpam-1240	136	3	β	β	PROPN
ejpam-1240	136	4	∈	∈	PROPN
ejpam-1240	136	5	e(s	e(s	PROPN
ejpam-1240	136	6	♭	♭	PRON
ejpam-1240	136	7	)	)	PUNCT
ejpam-1240	136	8	}	}	PUNCT
ejpam-1240	136	9	is	be	AUX
ejpam-1240	136	10	a	a	DET
ejpam-1240	136	11	right	right	ADJ
ejpam-1240	136	12	regular	regular	ADJ
ejpam-1240	136	13	partial	partial	ADJ
ejpam-1240	136	14	band	band	NOUN
ejpam-1240	136	15	with	with	ADP
ejpam-1240	136	16	skeleton	skeleton	NOUN
ejpam-1240	136	17	e(s	e(s	PROPN
ejpam-1240	136	18	♭	♭	PROPN
ejpam-1240	136	19	)	)	PUNCT
ejpam-1240	136	20	.	.	PUNCT
ejpam-1240	137	1	we	we	PRON
ejpam-1240	137	2	now	now	ADV
ejpam-1240	137	3	state	state	VERB
ejpam-1240	137	4	a	a	DET
ejpam-1240	137	5	lemma	lemma	PROPN
ejpam-1240	137	6	related	relate	VERB
ejpam-1240	137	7	to	to	ADP
ejpam-1240	137	8	the	the	DET
ejpam-1240	137	9	*	*	PUNCT
ejpam-1240	137	10	-subsemigroup	-subsemigroup	NOUN
ejpam-1240	137	11	of	of	ADP
ejpam-1240	137	12	an	an	DET
ejpam-1240	137	13	abundant	abundant	ADJ
ejpam-1240	137	14	semigroup	semigroup	NOUN
ejpam-1240	137	15	s.	s.	PROPN
ejpam-1240	137	16	lemma	lemma	PROPN
ejpam-1240	137	17	4	4	NUM
ejpam-1240	137	18	(	(	PUNCT
ejpam-1240	137	19	8)	8)	NUM
ejpam-1240	137	20	.	.	PUNCT
ejpam-1240	138	1	let	let	VERB
ejpam-1240	138	2	s	s	PRON
ejpam-1240	138	3	be	be	AUX
ejpam-1240	138	4	an	an	DET
ejpam-1240	138	5	abundant	abundant	ADJ
ejpam-1240	138	6	semigroup	semigroup	NOUN
ejpam-1240	138	7	and	and	CCONJ
ejpam-1240	138	8	t	t	X
ejpam-1240	138	9	a	a	DET
ejpam-1240	138	10	*	*	PUNCT
ejpam-1240	138	11	-subsemigroup	-subsemigroup	NOUN
ejpam-1240	138	12	of	of	ADP
ejpam-1240	138	13	s.	s.	PROPN
ejpam-1240	138	14	if	if	SCONJ
ejpam-1240	138	15	x	x	PROPN
ejpam-1240	138	16	∈	∈	PROPN
ejpam-1240	138	17	s	s	X
ejpam-1240	138	18	and	and	CCONJ
ejpam-1240	138	19	a	a	DET
ejpam-1240	138	20	∈	∈	PROPN
ejpam-1240	138	21	t	t	NOUN
ejpam-1240	138	22	such	such	ADJ
ejpam-1240	138	23	that	that	PRON
ejpam-1240	138	24	x	x	X
ejpam-1240	138	25	=	=	PUNCT
ejpam-1240	138	26	ea	ea	NUM
ejpam-1240	138	27	f	f	PROPN
ejpam-1240	138	28	with	with	ADP
ejpam-1240	138	29	e	e	PROPN
ejpam-1240	138	30	,	,	PUNCT
ejpam-1240	138	31	f	f	PROPN
ejpam-1240	138	32	∈	∈	PROPN
ejpam-1240	138	33	e(s	e(s	PROPN
ejpam-1240	138	34	)	)	PUNCT
ejpam-1240	138	35	,	,	PUNCT
ejpam-1240	138	36	el	el	PROPN
ejpam-1240	138	37	a†	a†	PROPN
ejpam-1240	138	38	,	,	PUNCT
ejpam-1240	138	39	fra∗	fra∗	PROPN
ejpam-1240	138	40	for	for	ADP
ejpam-1240	138	41	a†	a†	NOUN
ejpam-1240	138	42	,	,	PUNCT
ejpam-1240	138	43	a∗	a∗	PROPN
ejpam-1240	138	44	∈	∈	PROPN
ejpam-1240	138	45	t	t	PROPN
ejpam-1240	138	46	,	,	PUNCT
ejpam-1240	138	47	then	then	ADV
ejpam-1240	138	48	er∗xl	er∗xl	PROPN
ejpam-1240	138	49	∗	∗	NOUN
ejpam-1240	138	50	f	f	PROPN
ejpam-1240	138	51	.	.	PUNCT
ejpam-1240	139	1	lemma	lemma	PROPN
ejpam-1240	139	2	5	5	X
ejpam-1240	139	3	.	.	PUNCT
ejpam-1240	140	1	let	let	VERB
ejpam-1240	140	2	s	s	PRON
ejpam-1240	140	3	be	be	AUX
ejpam-1240	140	4	a	a	DET
ejpam-1240	140	5	naturally	naturally	ADV
ejpam-1240	140	6	ordered	order	VERB
ejpam-1240	140	7	abundant	abundant	ADJ
ejpam-1240	140	8	semigroup	semigroup	NOUN
ejpam-1240	140	9	in	in	ADP
ejpam-1240	140	10	which	which	PRON
ejpam-1240	140	11	each	each	DET
ejpam-1240	140	12	idempotent	idempotent	NOUN
ejpam-1240	140	13	has	have	VERB
ejpam-1240	140	14	a	a	DET
ejpam-1240	140	15	greatest	great	ADJ
ejpam-1240	140	16	inverse	inverse	NOUN
ejpam-1240	140	17	and	and	CCONJ
ejpam-1240	140	18	which	which	PRON
ejpam-1240	140	19	is	be	AUX
ejpam-1240	140	20	both	both	PRON
ejpam-1240	140	21	g	g	NOUN
ejpam-1240	140	22	-	-	PUNCT
ejpam-1240	140	23	regular	regular	ADJ
ejpam-1240	140	24	and	and	CCONJ
ejpam-1240	140	25	reflexive	reflexive	ADJ
ejpam-1240	140	26	.	.	PUNCT
ejpam-1240	141	1	then	then	ADV
ejpam-1240	141	2	,	,	PUNCT
ejpam-1240	141	3	the	the	DET
ejpam-1240	141	4	following	follow	VERB
ejpam-1240	141	5	properties	property	NOUN
ejpam-1240	141	6	hold	hold	VERB
ejpam-1240	141	7	:	:	PUNCT
ejpam-1240	141	8	1	1	X
ejpam-1240	141	9	.	.	X
ejpam-1240	142	1	for	for	ADP
ejpam-1240	142	2	every	every	DET
ejpam-1240	142	3	s	s	PROPN
ejpam-1240	142	4	∈	∈	PROPN
ejpam-1240	142	5	s	s	PROPN
ejpam-1240	142	6	,	,	PUNCT
ejpam-1240	142	7	s	s	PART
ejpam-1240	142	8	◦	◦	NOUN
ejpam-1240	142	9	♭	♭	PROPN
ejpam-1240	142	10	is	be	AUX
ejpam-1240	142	11	an	an	DET
ejpam-1240	142	12	inverse	inverse	NOUN
ejpam-1240	142	13	of	of	ADP
ejpam-1240	142	14	s	s	NOUN
ejpam-1240	142	15	♭	♭	X
ejpam-1240	142	16	satisfying	satisfying	ADJ
ejpam-1240	143	1	t	t	PROPN
ejpam-1240	143	2	♭	♭	PROPN
ejpam-1240	143	3	≤	≤	NUM
ejpam-1240	143	4	s	s	PART
ejpam-1240	143	5	◦	◦	NOUN
ejpam-1240	143	6	♭	♭	NOUN
ejpam-1240	143	7	for	for	ADP
ejpam-1240	143	8	all	all	DET
ejpam-1240	143	9	inverse	inverse	NOUN
ejpam-1240	143	10	t	t	PROPN
ejpam-1240	143	11	of	of	ADP
ejpam-1240	143	12	s.	s.	PROPN
ejpam-1240	143	13	x.	x.	PROPN
ejpam-1240	143	14	guo	guo	PROPN
ejpam-1240	143	15	,	,	PUNCT
ejpam-1240	143	16	k.	k.	PROPN
ejpam-1240	143	17	shum	shum	PROPN
ejpam-1240	143	18	/	/	SYM
ejpam-1240	143	19	eur	eur	PROPN
ejpam-1240	143	20	.	.	PUNCT
ejpam-1240	144	1	j.	j.	PROPN
ejpam-1240	144	2	pure	pure	PROPN
ejpam-1240	144	3	appl	appl	PROPN
ejpam-1240	144	4	.	.	PROPN
ejpam-1240	144	5	math	math	PROPN
ejpam-1240	144	6	,	,	PUNCT
ejpam-1240	144	7	4	4	NUM
ejpam-1240	144	8	(	(	PUNCT
ejpam-1240	144	9	2011	2011	NUM
ejpam-1240	144	10	)	)	PUNCT
ejpam-1240	144	11	,	,	PUNCT
ejpam-1240	144	12	210	210	NUM
ejpam-1240	144	13	-	-	SYM
ejpam-1240	144	14	220	220	NUM
ejpam-1240	144	15	215	215	NUM
ejpam-1240	144	16	2	2	NUM
ejpam-1240	144	17	.	.	PUNCT
ejpam-1240	145	1	for	for	ADP
ejpam-1240	145	2	any	any	DET
ejpam-1240	145	3	x	x	SYM
ejpam-1240	145	4	∈	∈	PROPN
ejpam-1240	145	5	s	s	NOUN
ejpam-1240	145	6	,	,	PUNCT
ejpam-1240	145	7	there	there	PRON
ejpam-1240	145	8	exists	exist	VERB
ejpam-1240	145	9	a	a	DET
ejpam-1240	145	10	unique	unique	ADJ
ejpam-1240	145	11	b	b	X
ejpam-1240	145	12	∈	∈	NOUN
ejpam-1240	145	13	s	s	VERB
ejpam-1240	145	14	♭	♭	NOUN
ejpam-1240	145	15	such	such	ADJ
ejpam-1240	145	16	that	that	PRON
ejpam-1240	145	17	x	x	X
ejpam-1240	145	18	=	=	PUNCT
ejpam-1240	145	19	eb	eb	PROPN
ejpam-1240	145	20	f	f	PROPN
ejpam-1240	145	21	,	,	PUNCT
ejpam-1240	145	22	where	where	SCONJ
ejpam-1240	145	23	e	e	X
ejpam-1240	145	24	,	,	PUNCT
ejpam-1240	145	25	f	f	PROPN
ejpam-1240	145	26	∈	∈	PROPN
ejpam-1240	145	27	e	e	NOUN
ejpam-1240	145	28	,	,	PUNCT
ejpam-1240	145	29	fr	fr	ADV
ejpam-1240	145	30	b∗	b∗	ADJ
ejpam-1240	145	31	and	and	CCONJ
ejpam-1240	145	32	el	el	PROPN
ejpam-1240	145	33	b†	b†	PROPN
ejpam-1240	145	34	for	for	ADP
ejpam-1240	145	35	b†	b†	ADJ
ejpam-1240	145	36	,	,	PUNCT
ejpam-1240	145	37	b∗	b∗	PROPN
ejpam-1240	145	38	∈	∈	PROPN
ejpam-1240	145	39	e(s	e(s	PROPN
ejpam-1240	145	40	♭	♭	PRON
ejpam-1240	145	41	)	)	PUNCT
ejpam-1240	145	42	.	.	PUNCT
ejpam-1240	146	1	proof	proof	NOUN
ejpam-1240	146	2	.	.	PUNCT
ejpam-1240	147	1	1	1	X
ejpam-1240	147	2	.	.	X
ejpam-1240	147	3	by	by	ADP
ejpam-1240	147	4	lemma	lemma	PROPN
ejpam-1240	147	5	3	3	NUM
ejpam-1240	147	6	,	,	PUNCT
ejpam-1240	147	7	s	s	NOUN
ejpam-1240	147	8	♭	♭	X
ejpam-1240	147	9	=	=	SYM
ejpam-1240	147	10	s	s	PROPN
ejpam-1240	147	11	◦	◦	NOUN
ejpam-1240	147	12	◦	◦	NOUN
ejpam-1240	147	13	and	and	CCONJ
ejpam-1240	147	14	by	by	ADP
ejpam-1240	147	15	lemma	lemma	PROPN
ejpam-1240	147	16	2	2	NUM
ejpam-1240	147	17	,	,	PUNCT
ejpam-1240	147	18	we	we	PRON
ejpam-1240	147	19	obtain	obtain	VERB
ejpam-1240	147	20	the	the	DET
ejpam-1240	147	21	following	follow	VERB
ejpam-1240	147	22	equalities	equality	NOUN
ejpam-1240	147	23	:	:	PUNCT
ejpam-1240	147	24	s	s	X
ejpam-1240	147	25	◦	◦	NOUN
ejpam-1240	147	26	♭	♭	X
ejpam-1240	147	27	=	=	SYM
ejpam-1240	147	28	(	(	PUNCT
ejpam-1240	147	29	s	s	NUM
ejpam-1240	147	30	◦	◦	NOUN
ejpam-1240	147	31	s	s	NOUN
ejpam-1240	147	32	◦	◦	NOUN
ejpam-1240	147	33	◦	◦	NOUN
ejpam-1240	147	34	)	)	PUNCT
ejpam-1240	147	35	◦	◦	NOUN
ejpam-1240	147	36	(s	(s	PROPN
ejpam-1240	147	37	◦	◦	NOUN
ejpam-1240	147	38	s	s	NOUN
ejpam-1240	147	39	◦	◦	NOUN
ejpam-1240	147	40	◦	◦	NOUN
ejpam-1240	147	41	)s	)s	NOUN
ejpam-1240	147	42	◦	◦	NOUN
ejpam-1240	147	43	(s	(s	NOUN
ejpam-1240	147	44	◦	◦	NOUN
ejpam-1240	147	45	◦	◦	NOUN
ejpam-1240	147	46	s	s	NOUN
ejpam-1240	147	47	◦	◦	ADJ
ejpam-1240	147	48	)(s	)(s	ADJ
ejpam-1240	147	49	◦	◦	NOUN
ejpam-1240	147	50	◦	◦	NOUN
ejpam-1240	147	51	s	s	NOUN
ejpam-1240	147	52	◦	◦	NOUN
ejpam-1240	147	53	)	)	PUNCT
ejpam-1240	147	54	◦	◦	NOUN
ejpam-1240	147	55	=	=	SYM
ejpam-1240	147	56	(	(	PUNCT
ejpam-1240	147	57	s	s	NOUN
ejpam-1240	147	58	◦	◦	NOUN
ejpam-1240	147	59	◦	◦	NOUN
ejpam-1240	147	60	◦	◦	NOUN
ejpam-1240	147	61	s	s	NOUN
ejpam-1240	147	62	◦	◦	NOUN
ejpam-1240	147	63	◦	◦	NOUN
ejpam-1240	147	64	)(s	)(s	ADJ
ejpam-1240	147	65	◦	◦	NOUN
ejpam-1240	147	66	s	s	NOUN
ejpam-1240	147	67	◦	◦	NOUN
ejpam-1240	147	68	◦	◦	NOUN
ejpam-1240	147	69	)s	)s	NOUN
ejpam-1240	147	70	◦	◦	NOUN
ejpam-1240	147	71	(s	(s	NOUN
ejpam-1240	147	72	◦	◦	NOUN
ejpam-1240	147	73	◦	◦	NOUN
ejpam-1240	147	74	s	s	NOUN
ejpam-1240	147	75	◦	◦	ADJ
ejpam-1240	147	76	)(s	)(s	ADJ
ejpam-1240	147	77	◦	◦	NOUN
ejpam-1240	147	78	◦	◦	NOUN
ejpam-1240	147	79	s	s	NOUN
ejpam-1240	147	80	◦	◦	NOUN
ejpam-1240	147	81	◦	◦	NOUN
ejpam-1240	147	82	◦	◦	NOUN
ejpam-1240	147	83	)	)	PUNCT
ejpam-1240	148	1	=	=	SYM
ejpam-1240	148	2	s	s	X
ejpam-1240	148	3	◦	◦	NOUN
ejpam-1240	148	4	s	s	NOUN
ejpam-1240	148	5	◦	◦	NOUN
ejpam-1240	148	6	◦	◦	NOUN
ejpam-1240	148	7	s	s	NOUN
ejpam-1240	148	8	◦	◦	NOUN
ejpam-1240	148	9	s	s	NOUN
ejpam-1240	148	10	◦	◦	NOUN
ejpam-1240	148	11	◦	◦	NOUN
ejpam-1240	148	12	s	s	NOUN
ejpam-1240	148	13	◦	◦	NOUN
ejpam-1240	148	14	s	s	NOUN
ejpam-1240	148	15	◦	◦	NOUN
ejpam-1240	148	16	◦	◦	NOUN
ejpam-1240	148	17	s	s	NOUN
ejpam-1240	148	18	◦	◦	NOUN
ejpam-1240	148	19	=	=	SYM
ejpam-1240	148	20	s	s	X
ejpam-1240	148	21	◦	◦	NOUN
ejpam-1240	148	22	s	s	NOUN
ejpam-1240	148	23	◦	◦	NOUN
ejpam-1240	148	24	◦	◦	NOUN
ejpam-1240	148	25	s	s	NOUN
ejpam-1240	148	26	◦	◦	NOUN
ejpam-1240	148	27	=	=	SYM
ejpam-1240	148	28	s	s	NOUN
ejpam-1240	148	29	◦	◦	NOUN
ejpam-1240	148	30	,	,	PUNCT
ejpam-1240	148	31	hence	hence	ADV
ejpam-1240	148	32	,	,	PUNCT
ejpam-1240	148	33	s	s	NOUN
ejpam-1240	148	34	♭	♭	PRON
ejpam-1240	148	35	s	s	NOUN
ejpam-1240	148	36	◦	◦	NOUN
ejpam-1240	148	37	♭	♭	SYM
ejpam-1240	148	38	s	s	X
ejpam-1240	148	39	♭	♭	X
ejpam-1240	148	40	=	=	SYM
ejpam-1240	148	41	s	s	PROPN
ejpam-1240	148	42	◦	◦	NOUN
ejpam-1240	148	43	◦	◦	NOUN
ejpam-1240	148	44	s	s	NOUN
ejpam-1240	148	45	◦	◦	NOUN
ejpam-1240	148	46	s	s	NOUN
ejpam-1240	148	47	◦	◦	NOUN
ejpam-1240	148	48	◦	◦	NOUN
ejpam-1240	148	49	=	=	SYM
ejpam-1240	148	50	s	s	NOUN
ejpam-1240	148	51	◦	◦	NOUN
ejpam-1240	148	52	◦	◦	NOUN
ejpam-1240	148	53	=	=	SYM
ejpam-1240	148	54	s	s	X
ejpam-1240	148	55	♭	♭	PROPN
ejpam-1240	148	56	and	and	CCONJ
ejpam-1240	148	57	s	s	NOUN
ejpam-1240	148	58	◦	◦	NOUN
ejpam-1240	148	59	♭	♭	NUM
ejpam-1240	148	60	s	s	NOUN
ejpam-1240	148	61	♭	♭	NOUN
ejpam-1240	148	62	s	s	NOUN
ejpam-1240	148	63	◦	◦	NOUN
ejpam-1240	148	64	♭	♭	NOUN
ejpam-1240	148	65	=	=	SYM
ejpam-1240	148	66	s	s	PROPN
ejpam-1240	148	67	◦	◦	NOUN
ejpam-1240	148	68	s	s	NOUN
ejpam-1240	148	69	◦	◦	NOUN
ejpam-1240	148	70	◦	◦	NOUN
ejpam-1240	148	71	s	s	NOUN
ejpam-1240	148	72	◦	◦	NOUN
ejpam-1240	148	73	=	=	SYM
ejpam-1240	148	74	s	s	AUX
ejpam-1240	148	75	◦	◦	NOUN
ejpam-1240	148	76	=	=	SYM
ejpam-1240	148	77	s	s	X
ejpam-1240	148	78	◦	◦	NOUN
ejpam-1240	148	79	♭	♭	PROPN
ejpam-1240	148	80	,	,	PUNCT
ejpam-1240	148	81	whence	whence	NOUN
ejpam-1240	148	82	s	s	NOUN
ejpam-1240	148	83	◦	◦	NOUN
ejpam-1240	148	84	♭	♭	PROPN
ejpam-1240	148	85	is	be	AUX
ejpam-1240	148	86	an	an	DET
ejpam-1240	148	87	inverse	inverse	NOUN
ejpam-1240	148	88	of	of	ADP
ejpam-1240	148	89	s	s	NOUN
ejpam-1240	148	90	♭	♭	PROPN
ejpam-1240	148	91	.	.	PUNCT
ejpam-1240	149	1	on	on	ADP
ejpam-1240	149	2	the	the	DET
ejpam-1240	149	3	other	other	ADJ
ejpam-1240	149	4	hand	hand	NOUN
ejpam-1240	149	5	,	,	PUNCT
ejpam-1240	149	6	since	since	SCONJ
ejpam-1240	149	7	s	s	NOUN
ejpam-1240	149	8	is	be	AUX
ejpam-1240	149	9	g	g	NOUN
ejpam-1240	149	10	-	-	PUNCT
ejpam-1240	149	11	reflexive	reflexive	ADJ
ejpam-1240	149	12	,	,	PUNCT
ejpam-1240	149	13	et	et	PROPN
ejpam-1240	149	14	≤	≤	NOUN
ejpam-1240	149	15	es	es	ADP
ejpam-1240	149	16	◦	◦	NOUN
ejpam-1240	149	17	and	and	CCONJ
ejpam-1240	149	18	ft	ft	NOUN
ejpam-1240	149	19	≤	≤	NUM
ejpam-1240	149	20	fs	fs	ADP
ejpam-1240	149	21	◦	◦	NOUN
ejpam-1240	149	22	for	for	ADP
ejpam-1240	149	23	any	any	DET
ejpam-1240	149	24	inverse	inverse	NOUN
ejpam-1240	149	25	t	t	NOUN
ejpam-1240	149	26	of	of	ADP
ejpam-1240	149	27	s.	s.	PROPN
ejpam-1240	149	28	this	this	PRON
ejpam-1240	149	29	shows	show	VERB
ejpam-1240	149	30	that	that	SCONJ
ejpam-1240	149	31	t	t	PROPN
ejpam-1240	149	32	♭	♭	PROPN
ejpam-1240	149	33	=	=	PUNCT
ejpam-1240	149	34	et	et	PROPN
ejpam-1240	149	35	t	t	NOUN
ejpam-1240	149	36	ft	ft	PROPN
ejpam-1240	149	37	≤	≤	NUM
ejpam-1240	149	38	es	es	ADP
ejpam-1240	149	39	◦	◦	NOUN
ejpam-1240	149	40	s	s	NOUN
ejpam-1240	149	41	◦	◦	NOUN
ejpam-1240	149	42	fs	fs	ADP
ejpam-1240	149	43	◦	◦	NOUN
ejpam-1240	149	44	=	=	SYM
ejpam-1240	149	45	s	s	X
ejpam-1240	149	46	◦	◦	NOUN
ejpam-1240	149	47	♭	♭	PROPN
ejpam-1240	149	48	,	,	PUNCT
ejpam-1240	149	49	as	as	SCONJ
ejpam-1240	149	50	required	require	VERB
ejpam-1240	149	51	.	.	PUNCT
ejpam-1240	150	1	2	2	X
ejpam-1240	150	2	.	.	X
ejpam-1240	150	3	for	for	ADP
ejpam-1240	150	4	all	all	DET
ejpam-1240	150	5	x	x	SYM
ejpam-1240	150	6	∈	∈	PROPN
ejpam-1240	150	7	s	s	X
ejpam-1240	150	8	,	,	PUNCT
ejpam-1240	150	9	we	we	PRON
ejpam-1240	150	10	have	have	VERB
ejpam-1240	150	11	x	x	X
ejpam-1240	150	12	=	=	SYM
ejpam-1240	150	13	(	(	PUNCT
ejpam-1240	150	14	x†x†	x†x†	PROPN
ejpam-1240	150	15	◦	◦	NOUN
ejpam-1240	150	16	)[(x†x†	)[(x†x†	NOUN
ejpam-1240	150	17	◦	◦	NOUN
ejpam-1240	150	18	)	)	PUNCT
ejpam-1240	150	19	◦	◦	NOUN
ejpam-1240	150	20	(x†x†	(x†x†	NOUN
ejpam-1240	150	21	◦	◦	NOUN
ejpam-1240	150	22	)]x[(x∗	)]x[(x∗	NOUN
ejpam-1240	150	23	◦	◦	NOUN
ejpam-1240	150	24	x∗)(x∗	x∗)(x∗	PROPN
ejpam-1240	150	25	◦	◦	PROPN
ejpam-1240	150	26	x∗)	x∗)	PROPN
ejpam-1240	150	27	◦	◦	NOUN
ejpam-1240	150	28	](x∗	](x∗	X
ejpam-1240	150	29	◦	◦	NOUN
ejpam-1240	150	30	x∗	x∗	NOUN
ejpam-1240	150	31	)	)	PUNCT
ejpam-1240	150	32	,	,	PUNCT
ejpam-1240	150	33	that	that	ADV
ejpam-1240	150	34	is	be	AUX
ejpam-1240	150	35	,	,	PUNCT
ejpam-1240	150	36	x	x	SYM
ejpam-1240	150	37	=	=	SYM
ejpam-1240	150	38	(	(	PUNCT
ejpam-1240	150	39	x†x†	x†x†	PROPN
ejpam-1240	150	40	◦	◦	NOUN
ejpam-1240	150	41	)x	)x	X
ejpam-1240	151	1	♭	♭	PROPN
ejpam-1240	151	2	(	(	PUNCT
ejpam-1240	151	3	x∗	x∗	X
ejpam-1240	151	4	◦	◦	VERB
ejpam-1240	151	5	x∗	x∗	PROPN
ejpam-1240	151	6	)	)	PUNCT
ejpam-1240	151	7	.	.	PUNCT
ejpam-1240	152	1	it	it	PRON
ejpam-1240	152	2	is	be	AUX
ejpam-1240	152	3	easy	easy	ADJ
ejpam-1240	152	4	to	to	PART
ejpam-1240	152	5	see	see	VERB
ejpam-1240	152	6	that	that	DET
ejpam-1240	152	7	x†x†	x†x†	PROPN
ejpam-1240	152	8	◦	◦	NOUN
ejpam-1240	152	9	l	l	NOUN
ejpam-1240	152	10	ex	ex	X
ejpam-1240	152	11	and	and	CCONJ
ejpam-1240	152	12	x∗	x∗	PROPN
ejpam-1240	152	13	◦	◦	VERB
ejpam-1240	152	14	x∗r	x∗r	NUM
ejpam-1240	152	15	fx	fx	NOUN
ejpam-1240	152	16	.	.	PUNCT
ejpam-1240	153	1	now	now	ADV
ejpam-1240	153	2	let	let	VERB
ejpam-1240	153	3	x	x	SYM
ejpam-1240	153	4	=	=	PUNCT
ejpam-1240	153	5	g	g	PROPN
ejpam-1240	153	6	bh	bh	NOUN
ejpam-1240	153	7	with	with	ADP
ejpam-1240	153	8	g	g	PROPN
ejpam-1240	153	9	,	,	PUNCT
ejpam-1240	153	10	h	h	NOUN
ejpam-1240	153	11	∈	∈	PROPN
ejpam-1240	153	12	e(s	e(s	PROPN
ejpam-1240	153	13	)	)	PUNCT
ejpam-1240	153	14	,	,	PUNCT
ejpam-1240	153	15	gl	gl	PROPN
ejpam-1240	153	16	b†	b†	PROPN
ejpam-1240	153	17	and	and	CCONJ
ejpam-1240	153	18	hr	hr	NOUN
ejpam-1240	153	19	b∗	b∗	ADJ
ejpam-1240	153	20	for	for	ADP
ejpam-1240	153	21	b†	b†	ADJ
ejpam-1240	153	22	,	,	PUNCT
ejpam-1240	153	23	b∗	b∗	PROPN
ejpam-1240	153	24	∈	∈	PROPN
ejpam-1240	153	25	e(s	e(s	PROPN
ejpam-1240	153	26	♭	♭	PROPN
ejpam-1240	153	27	)	)	PUNCT
ejpam-1240	153	28	.	.	PUNCT
ejpam-1240	154	1	denote	denote	PROPN
ejpam-1240	154	2	b	b	PROPN
ejpam-1240	155	1	=	=	SYM
ejpam-1240	155	2	y	y	PROPN
ejpam-1240	155	3	♭	♭	PROPN
ejpam-1240	155	4	.	.	PUNCT
ejpam-1240	156	1	then	then	ADV
ejpam-1240	156	2	,	,	PUNCT
ejpam-1240	156	3	by	by	ADP
ejpam-1240	156	4	lemma	lemma	PROPN
ejpam-1240	156	5	4	4	NUM
ejpam-1240	156	6	,	,	PUNCT
ejpam-1240	156	7	eyr	eyr	NOUN
ejpam-1240	156	8	∗	∗	PROPN
ejpam-1240	156	9	y	y	PROPN
ejpam-1240	156	10	♭	♭	PROPN
ejpam-1240	156	11	and	and	CCONJ
ejpam-1240	156	12	,	,	PUNCT
ejpam-1240	156	13	by	by	ADP
ejpam-1240	156	14	[	[	PUNCT
ejpam-1240	156	15	13	13	NUM
ejpam-1240	156	16	,	,	PUNCT
ejpam-1240	156	17	lemma	lemma	PROPN
ejpam-1240	156	18	3.5(3	3.5(3	NUM
ejpam-1240	156	19	)	)	PUNCT
ejpam-1240	156	20	]	]	PUNCT
ejpam-1240	156	21	,	,	PUNCT
ejpam-1240	156	22	ey	ey	PROPN
ejpam-1240	156	23	∈	∈	PROPN
ejpam-1240	156	24	s	s	NOUN
ejpam-1240	156	25	♭	♭	PROPN
ejpam-1240	156	26	.	.	PUNCT
ejpam-1240	157	1	furthermore	furthermore	ADV
ejpam-1240	157	2	,	,	PUNCT
ejpam-1240	157	3	by	by	ADP
ejpam-1240	157	4	[	[	PUNCT
ejpam-1240	157	5	13	13	NUM
ejpam-1240	157	6	,	,	PUNCT
ejpam-1240	157	7	lemma	lemma	PROPN
ejpam-1240	157	8	3.5(4	3.5(4	NUM
ejpam-1240	157	9	)	)	PUNCT
ejpam-1240	157	10	]	]	PUNCT
ejpam-1240	157	11	,	,	PUNCT
ejpam-1240	157	12	we	we	PRON
ejpam-1240	157	13	have	have	VERB
ejpam-1240	157	14	ey	ey	PRON
ejpam-1240	157	15	♭	♭	PROPN
ejpam-1240	157	16	=	=	PUNCT
ejpam-1240	157	17	ey	ey	PROPN
ejpam-1240	157	18	=	=	SYM
ejpam-1240	157	19	y	y	PROPN
ejpam-1240	157	20	♭	♭	PROPN
ejpam-1240	157	21	†	†	X
ejpam-1240	157	22	=	=	PUNCT
ejpam-1240	157	23	b†	b†	PROPN
ejpam-1240	157	24	and	and	CCONJ
ejpam-1240	157	25	f	f	PROPN
ejpam-1240	158	1	y	y	X
ejpam-1240	158	2	♭	♭	PROPN
ejpam-1240	158	3	=	=	PUNCT
ejpam-1240	158	4	f	f	PROPN
ejpam-1240	158	5	y	y	PROPN
ejpam-1240	158	6	=	=	PUNCT
ejpam-1240	158	7	b∗.	b∗.	NOUN
ejpam-1240	158	8	by	by	ADP
ejpam-1240	158	9	x	x	SYM
ejpam-1240	158	10	=	=	PUNCT
ejpam-1240	158	11	g	g	PROPN
ejpam-1240	158	12	y	y	PROPN
ejpam-1240	158	13	♭	♭	PROPN
ejpam-1240	158	14	h	h	PROPN
ejpam-1240	158	15	,	,	PUNCT
ejpam-1240	158	16	we	we	PRON
ejpam-1240	158	17	have	have	VERB
ejpam-1240	158	18	x	x	NOUN
ejpam-1240	158	19	≤	≤	NUM
ejpam-1240	158	20	y	y	PROPN
ejpam-1240	158	21	♭	♭	PROPN
ejpam-1240	158	22	♭	♭	X
ejpam-1240	159	1	=	=	PUNCT
ejpam-1240	159	2	y	y	PROPN
ejpam-1240	159	3	♭	♭	PROPN
ejpam-1240	159	4	,	,	PUNCT
ejpam-1240	159	5	and	and	CCONJ
ejpam-1240	160	1	so	so	ADV
ejpam-1240	160	2	x	x	SYM
ejpam-1240	161	1	♭	♭	INTJ
ejpam-1240	161	2	≤	≤	NUM
ejpam-1240	162	1	y	y	PUNCT
ejpam-1240	162	2	♭	♭	PROPN
ejpam-1240	162	3	♭	♭	X
ejpam-1240	163	1	=	=	PUNCT
ejpam-1240	163	2	y	y	SYM
ejpam-1240	163	3	♭	♭	PROPN
ejpam-1240	163	4	,	,	PUNCT
ejpam-1240	163	5	that	that	ADV
ejpam-1240	163	6	is	is	ADV
ejpam-1240	163	7	,	,	PUNCT
ejpam-1240	163	8	x	x	PROPN
ejpam-1240	163	9	♭	♭	PROPN
ejpam-1240	163	10	≤	≤	PUNCT
ejpam-1240	163	11	b.	b.	PROPN
ejpam-1240	163	12	by	by	ADP
ejpam-1240	163	13	lemma	lemma	PROPN
ejpam-1240	163	14	2	2	NUM
ejpam-1240	163	15	(	(	PUNCT
ejpam-1240	163	16	2	2	NUM
ejpam-1240	163	17	)	)	PUNCT
ejpam-1240	163	18	,	,	PUNCT
ejpam-1240	163	19	g	g	NOUN
ejpam-1240	163	20	≤	≤	PROPN
ejpam-1240	163	21	g	g	ADP
ejpam-1240	163	22	g	g	ADP
ejpam-1240	163	23	◦	◦	NOUN
ejpam-1240	163	24	,	,	PUNCT
ejpam-1240	163	25	hence	hence	ADV
ejpam-1240	163	26	g	g	ADP
ejpam-1240	163	27	◦	◦	NOUN
ejpam-1240	163	28	≤	≤	NUM
ejpam-1240	163	29	(	(	PUNCT
ejpam-1240	163	30	g	g	NOUN
ejpam-1240	163	31	g	g	PROPN
ejpam-1240	163	32	◦	◦	NOUN
ejpam-1240	163	33	)	)	PUNCT
ejpam-1240	163	34	◦	◦	NOUN
ejpam-1240	163	35	.	.	PUNCT
ejpam-1240	164	1	thus	thus	ADV
ejpam-1240	164	2	,	,	PUNCT
ejpam-1240	164	3	g	g	ADP
ejpam-1240	164	4	◦	◦	NOUN
ejpam-1240	164	5	g	g	NOUN
ejpam-1240	164	6	≤	≤	NOUN
ejpam-1240	164	7	(	(	PUNCT
ejpam-1240	164	8	g	g	NOUN
ejpam-1240	164	9	g	g	PROPN
ejpam-1240	164	10	◦	◦	NOUN
ejpam-1240	164	11	)(g	)(g	NOUN
ejpam-1240	164	12	g	g	NOUN
ejpam-1240	164	13	◦	◦	NOUN
ejpam-1240	164	14	)	)	PUNCT
ejpam-1240	164	15	◦	◦	NOUN
ejpam-1240	164	16	.	.	NOUN
ejpam-1240	164	17	again	again	ADV
ejpam-1240	164	18	,	,	PUNCT
ejpam-1240	164	19	by	by	ADP
ejpam-1240	164	20	lemma	lemma	PROPN
ejpam-1240	164	21	2	2	NUM
ejpam-1240	164	22	(	(	PUNCT
ejpam-1240	164	23	2	2	NUM
ejpam-1240	164	24	)	)	PUNCT
ejpam-1240	164	25	,	,	PUNCT
ejpam-1240	164	26	we	we	PRON
ejpam-1240	164	27	know	know	VERB
ejpam-1240	164	28	that	that	SCONJ
ejpam-1240	164	29	g	g	NOUN
ejpam-1240	164	30	◦	◦	NOUN
ejpam-1240	164	31	g	g	NOUN
ejpam-1240	164	32	is	be	AUX
ejpam-1240	164	33	the	the	DET
ejpam-1240	164	34	greatest	great	ADJ
ejpam-1240	164	35	idempotent	idempotent	NOUN
ejpam-1240	164	36	in	in	ADP
ejpam-1240	164	37	lg	lg	NOUN
ejpam-1240	164	38	=	=	NOUN
ejpam-1240	164	39	lb†	lb†	NOUN
ejpam-1240	164	40	.	.	PUNCT
ejpam-1240	165	1	this	this	PRON
ejpam-1240	165	2	shows	show	VERB
ejpam-1240	165	3	that	that	SCONJ
ejpam-1240	165	4	b†	b†	ADJ
ejpam-1240	165	5	≤	≤	NOUN
ejpam-1240	165	6	g	g	ADP
ejpam-1240	165	7	◦	◦	NOUN
ejpam-1240	165	8	g	g	NOUN
ejpam-1240	165	9	(	(	PUNCT
ejpam-1240	165	10	≤	≤	X
ejpam-1240	165	11	(	(	PUNCT
ejpam-1240	165	12	g	g	NOUN
ejpam-1240	165	13	g	g	PROPN
ejpam-1240	165	14	◦	◦	NOUN
ejpam-1240	165	15	)(g	)(g	NOUN
ejpam-1240	165	16	g	g	NOUN
ejpam-1240	165	17	◦	◦	NOUN
ejpam-1240	165	18	)	)	PUNCT
ejpam-1240	165	19	◦	◦	NOUN
ejpam-1240	165	20	)	)	PUNCT
ejpam-1240	165	21	.	.	PUNCT
ejpam-1240	166	1	therefore	therefore	ADV
ejpam-1240	166	2	,	,	PUNCT
ejpam-1240	166	3	b†	b†	ADJ
ejpam-1240	166	4	≤	≤	X
ejpam-1240	166	5	(	(	PUNCT
ejpam-1240	166	6	x†x†	x†x†	NOUN
ejpam-1240	166	7	◦	◦	NOUN
ejpam-1240	166	8	)	)	PUNCT
ejpam-1240	166	9	◦	◦	NOUN
ejpam-1240	166	10	(x†x†	(x†x†	NOUN
ejpam-1240	166	11	◦	◦	NOUN
ejpam-1240	166	12	)	)	PUNCT
ejpam-1240	166	13	,	,	PUNCT
ejpam-1240	166	14	that	that	ADV
ejpam-1240	166	15	is	is	ADV
ejpam-1240	166	16	,	,	PUNCT
ejpam-1240	166	17	b†	b†	ADJ
ejpam-1240	166	18	≤	≤	X
ejpam-1240	166	19	ex	ex	X
ejpam-1240	166	20	.dually	.dually	PROPN
ejpam-1240	166	21	,	,	PUNCT
ejpam-1240	166	22	b∗	b∗	ADJ
ejpam-1240	166	23	≤	≤	ADJ
ejpam-1240	166	24	fx	fx	NOUN
ejpam-1240	166	25	.	.	PUNCT
ejpam-1240	167	1	thus	thus	ADV
ejpam-1240	167	2	,	,	PUNCT
ejpam-1240	167	3	b	b	X
ejpam-1240	167	4	=	=	SYM
ejpam-1240	167	5	b†	b†	ADJ
ejpam-1240	167	6	bb∗	bb∗	NOUN
ejpam-1240	167	7	=	=	SYM
ejpam-1240	167	8	(	(	PUNCT
ejpam-1240	167	9	b†g)b(hb∗	b†g)b(hb∗	NUM
ejpam-1240	167	10	)	)	PUNCT
ejpam-1240	167	11	=	=	SYM
ejpam-1240	167	12	b†	b†	ADJ
ejpam-1240	167	13	x	x	SYM
ejpam-1240	167	14	b∗	b∗	ADJ
ejpam-1240	167	15	≤	≤	X
ejpam-1240	168	1	ex	ex	PRON
ejpam-1240	168	2	x	x	PUNCT
ejpam-1240	168	3	fx	fx	NOUN
ejpam-1240	168	4	=	=	PUNCT
ejpam-1240	168	5	x	x	SYM
ejpam-1240	168	6	♭	♭	INTJ
ejpam-1240	168	7	.	.	PUNCT
ejpam-1240	169	1	we	we	PRON
ejpam-1240	169	2	have	have	AUX
ejpam-1240	169	3	now	now	ADV
ejpam-1240	169	4	proved	prove	VERB
ejpam-1240	169	5	that	that	PRON
ejpam-1240	169	6	b	b	X
ejpam-1240	170	1	=	=	PUNCT
ejpam-1240	170	2	x	x	SYM
ejpam-1240	170	3	♭	♭	INTJ
ejpam-1240	170	4	.	.	PUNCT
ejpam-1240	170	5	proof	proof	NOUN
ejpam-1240	170	6	.	.	PUNCT
ejpam-1240	171	1	[	[	X
ejpam-1240	171	2	theorem	theorem	NOUN
ejpam-1240	171	3	1	1	NUM
ejpam-1240	171	4	]	]	PUNCT
ejpam-1240	171	5	(	(	PUNCT
ejpam-1240	171	6	⇒	⇒	NOUN
ejpam-1240	171	7	)	)	PUNCT
ejpam-1240	171	8	assume	assume	VERB
ejpam-1240	171	9	that	that	SCONJ
ejpam-1240	171	10	(	(	PUNCT
ejpam-1240	171	11	t	t	NOUN
ejpam-1240	171	12	;	;	PUNCT
ejpam-1240	171	13	l	l	X
ejpam-1240	171	14	,	,	PUNCT
ejpam-1240	171	15	r	r	NOUN
ejpam-1240	171	16	;	;	PUNCT
ejpam-1240	171	17	[	[	X
ejpam-1240	171	18	,	,	PUNCT
ejpam-1240	171	19	]	]	X
ejpam-1240	171	20	)	)	PUNCT
ejpam-1240	171	21	is	be	AUX
ejpam-1240	171	22	a	a	DET
ejpam-1240	171	23	gi	gi	NOUN
ejpam-1240	171	24	-	-	PUNCT
ejpam-1240	171	25	system	system	NOUN
ejpam-1240	171	26	satisfying	satisfy	VERB
ejpam-1240	171	27	the	the	DET
ejpam-1240	171	28	conditions	condition	NOUN
ejpam-1240	171	29	in	in	ADP
ejpam-1240	171	30	theorem	theorem	NOUN
ejpam-1240	171	31	1	1	NUM
ejpam-1240	171	32	.	.	PUNCT
ejpam-1240	171	33	by	by	ADP
ejpam-1240	171	34	[	[	X
ejpam-1240	171	35	13	13	NUM
ejpam-1240	171	36	,	,	PUNCT
ejpam-1240	171	37	theorem	theorem	VERB
ejpam-1240	171	38	4.7	4.7	NUM
ejpam-1240	171	39	]	]	PUNCT
ejpam-1240	171	40	,	,	PUNCT
ejpam-1240	171	41	gi	gi	NOUN
ejpam-1240	171	42	=	=	SYM
ejpam-1240	171	43	gi(t	gi(t	NOUN
ejpam-1240	171	44	;	;	PUNCT
ejpam-1240	171	45	l	l	X
ejpam-1240	171	46	,	,	PUNCT
ejpam-1240	171	47	r	r	NOUN
ejpam-1240	171	48	;	;	PUNCT
ejpam-1240	171	49	[	[	X
ejpam-1240	171	50	,	,	PUNCT
ejpam-1240	171	51	]	]	X
ejpam-1240	171	52	)	)	PUNCT
ejpam-1240	171	53	is	be	AUX
ejpam-1240	171	54	a	a	DET
ejpam-1240	171	55	naturally	naturally	ADV
ejpam-1240	171	56	ordered	order	VERB
ejpam-1240	171	57	abundant	abundant	ADJ
ejpam-1240	171	58	semigroup	semigroup	NOUN
ejpam-1240	171	59	.	.	PUNCT
ejpam-1240	172	1	now	now	ADV
ejpam-1240	172	2	let	let	VERB
ejpam-1240	172	3	(	(	PUNCT
ejpam-1240	172	4	x	x	X
ejpam-1240	172	5	,	,	PUNCT
ejpam-1240	172	6	s	s	PROPN
ejpam-1240	172	7	,	,	PUNCT
ejpam-1240	172	8	u	u	NOUN
ejpam-1240	172	9	)	)	PUNCT
ejpam-1240	172	10	be	be	VERB
ejpam-1240	172	11	a	a	DET
ejpam-1240	172	12	regular	regular	ADJ
ejpam-1240	172	13	element	element	NOUN
ejpam-1240	172	14	of	of	ADP
ejpam-1240	172	15	gi	gi	NOUN
ejpam-1240	172	16	.	.	PUNCT
ejpam-1240	173	1	then	then	ADV
ejpam-1240	173	2	,	,	PUNCT
ejpam-1240	173	3	there	there	PRON
ejpam-1240	173	4	exists	exist	VERB
ejpam-1240	173	5	(	(	PUNCT
ejpam-1240	173	6	y	y	PROPN
ejpam-1240	173	7	,	,	PUNCT
ejpam-1240	173	8	t	t	PROPN
ejpam-1240	173	9	,	,	PUNCT
ejpam-1240	173	10	v	v	NOUN
ejpam-1240	173	11	)	)	PUNCT
ejpam-1240	173	12	∈	∈	NOUN
ejpam-1240	173	13	gi	gi	VERB
ejpam-1240	173	14	such	such	ADJ
ejpam-1240	173	15	that	that	PRON
ejpam-1240	173	16	(	(	PUNCT
ejpam-1240	173	17	x	x	X
ejpam-1240	173	18	,	,	PUNCT
ejpam-1240	173	19	s	s	PROPN
ejpam-1240	173	20	,	,	PUNCT
ejpam-1240	173	21	u	u	NOUN
ejpam-1240	173	22	)	)	PUNCT
ejpam-1240	173	23	=	=	SYM
ejpam-1240	174	1	(	(	PUNCT
ejpam-1240	174	2	x	x	INTJ
ejpam-1240	174	3	,	,	PUNCT
ejpam-1240	174	4	s	s	PROPN
ejpam-1240	174	5	,	,	PUNCT
ejpam-1240	174	6	u)(y	u)(y	PROPN
ejpam-1240	174	7	,	,	PUNCT
ejpam-1240	174	8	t	t	PROPN
ejpam-1240	174	9	,	,	PUNCT
ejpam-1240	174	10	v)(x	v)(x	NOUN
ejpam-1240	174	11	,	,	PUNCT
ejpam-1240	174	12	s	s	X
ejpam-1240	174	13	,	,	PUNCT
ejpam-1240	174	14	u	u	NOUN
ejpam-1240	174	15	)	)	PUNCT
ejpam-1240	174	16	.	.	PUNCT
ejpam-1240	175	1	by	by	ADP
ejpam-1240	175	2	comparing	compare	VERB
ejpam-1240	175	3	components	component	NOUN
ejpam-1240	175	4	,	,	PUNCT
ejpam-1240	175	5	s	s	PART
ejpam-1240	175	6	=	=	NOUN
ejpam-1240	175	7	s[u	s[u	PROPN
ejpam-1240	175	8	,	,	PUNCT
ejpam-1240	175	9	y]t[(s[u	y]t[(s[u	PROPN
ejpam-1240	175	10	,	,	PUNCT
ejpam-1240	175	11	y]t)∗	y]t)∗	NOUN
ejpam-1240	175	12	v	v	NOUN
ejpam-1240	175	13	,	,	PUNCT
ejpam-1240	175	14	x]s	x]s	PROPN
ejpam-1240	175	15	x.	x.	PROPN
ejpam-1240	175	16	guo	guo	PROPN
ejpam-1240	175	17	,	,	PUNCT
ejpam-1240	175	18	k.	k.	PROPN
ejpam-1240	175	19	shum	shum	PROPN
ejpam-1240	175	20	/	/	SYM
ejpam-1240	175	21	eur	eur	PROPN
ejpam-1240	175	22	.	.	PUNCT
ejpam-1240	176	1	j.	j.	PROPN
ejpam-1240	176	2	pure	pure	PROPN
ejpam-1240	176	3	appl	appl	PROPN
ejpam-1240	176	4	.	.	PROPN
ejpam-1240	176	5	math	math	PROPN
ejpam-1240	176	6	,	,	PUNCT
ejpam-1240	176	7	4	4	NUM
ejpam-1240	176	8	(	(	PUNCT
ejpam-1240	176	9	2011	2011	NUM
ejpam-1240	176	10	)	)	PUNCT
ejpam-1240	176	11	,	,	PUNCT
ejpam-1240	176	12	210	210	NUM
ejpam-1240	176	13	-	-	SYM
ejpam-1240	176	14	220	220	NUM
ejpam-1240	176	15	216	216	NUM
ejpam-1240	176	16	and	and	CCONJ
ejpam-1240	176	17	s	s	NOUN
ejpam-1240	176	18	is	be	AUX
ejpam-1240	176	19	a	a	DET
ejpam-1240	176	20	regular	regular	ADJ
ejpam-1240	176	21	element	element	NOUN
ejpam-1240	176	22	of	of	ADP
ejpam-1240	176	23	t	t	PROPN
ejpam-1240	176	24	.	.	PUNCT
ejpam-1240	177	1	note	note	VERB
ejpam-1240	177	2	that	that	SCONJ
ejpam-1240	177	3	s[u	s[u	NOUN
ejpam-1240	177	4	,	,	PUNCT
ejpam-1240	177	5	s	s	PART
ejpam-1240	177	6	◦	◦	NOUN
ejpam-1240	177	7	s]s	s]s	NOUN
ejpam-1240	177	8	◦	◦	NOUN
ejpam-1240	177	9	[ss	[ss	X
ejpam-1240	177	10	◦	◦	NOUN
ejpam-1240	177	11	,	,	PUNCT
ejpam-1240	177	12	x]s	x]s	PUNCT
ejpam-1240	178	1	=	=	SYM
ejpam-1240	178	2	ss	ss	PROPN
ejpam-1240	178	3	◦	◦	NOUN
ejpam-1240	178	4	ss	ss	NOUN
ejpam-1240	178	5	◦	◦	NOUN
ejpam-1240	178	6	ss	ss	NOUN
ejpam-1240	178	7	◦	◦	NOUN
ejpam-1240	178	8	s	s	NOUN
ejpam-1240	178	9	=	=	X
ejpam-1240	178	10	ss	ss	PROPN
ejpam-1240	178	11	◦	◦	NOUN
ejpam-1240	178	12	s	s	NOUN
ejpam-1240	178	13	=	=	SYM
ejpam-1240	178	14	s	s	PROPN
ejpam-1240	178	15	,	,	PUNCT
ejpam-1240	178	16	we	we	PRON
ejpam-1240	178	17	have	have	AUX
ejpam-1240	178	18	,	,	PUNCT
ejpam-1240	178	19	(	(	PUNCT
ejpam-1240	178	20	x	x	X
ejpam-1240	178	21	,	,	PUNCT
ejpam-1240	178	22	s	s	X
ejpam-1240	178	23	,	,	PUNCT
ejpam-1240	178	24	u)(s	u)(s	PROPN
ejpam-1240	178	25	◦	◦	NOUN
ejpam-1240	178	26	s	s	SYM
ejpam-1240	178	27	,	,	PUNCT
ejpam-1240	178	28	s	s	NOUN
ejpam-1240	178	29	◦	◦	NOUN
ejpam-1240	178	30	,	,	PUNCT
ejpam-1240	178	31	ss	ss	NOUN
ejpam-1240	178	32	◦	◦	NOUN
ejpam-1240	178	33	)(x	)(x	NOUN
ejpam-1240	178	34	,	,	PUNCT
ejpam-1240	178	35	s	s	X
ejpam-1240	178	36	,	,	PUNCT
ejpam-1240	178	37	u	u	NOUN
ejpam-1240	178	38	)	)	PUNCT
ejpam-1240	178	39	=	=	SYM
ejpam-1240	178	40	�	�	PROPN
ejpam-1240	178	41	x(s[u	x(s[u	X
ejpam-1240	178	42	,	,	PUNCT
ejpam-1240	178	43	s	s	PART
ejpam-1240	178	44	◦	◦	NOUN
ejpam-1240	178	45	s]s	s]s	NOUN
ejpam-1240	178	46	◦	◦	NOUN
ejpam-1240	178	47	[ss	[ss	X
ejpam-1240	178	48	◦	◦	NOUN
ejpam-1240	178	49	,	,	PUNCT
ejpam-1240	178	50	x]s)†	x]s)†	PROPN
ejpam-1240	178	51	,	,	PUNCT
ejpam-1240	178	52	s[u	s[u	PROPN
ejpam-1240	178	53	,	,	PUNCT
ejpam-1240	178	54	s	s	PART
ejpam-1240	178	55	◦	◦	NOUN
ejpam-1240	178	56	s]s	s]s	NOUN
ejpam-1240	178	57	◦	◦	NOUN
ejpam-1240	178	58	[ss	[ss	X
ejpam-1240	178	59	◦	◦	NOUN
ejpam-1240	178	60	,	,	PUNCT
ejpam-1240	178	61	x]s	x]s	PROPN
ejpam-1240	178	62	,	,	PUNCT
ejpam-1240	178	63	(	(	PUNCT
ejpam-1240	178	64	s[u	s[u	ADJ
ejpam-1240	178	65	,	,	PUNCT
ejpam-1240	178	66	s	s	PART
ejpam-1240	178	67	◦	◦	NOUN
ejpam-1240	178	68	s]s	s]s	NOUN
ejpam-1240	178	69	◦	◦	NOUN
ejpam-1240	178	70	[ss	[ss	X
ejpam-1240	178	71	◦	◦	NOUN
ejpam-1240	178	72	,	,	PUNCT
ejpam-1240	178	73	x]s)∗u	x]s)∗u	ADJ
ejpam-1240	178	74	�	�	PROPN
ejpam-1240	178	75	=	=	SYM
ejpam-1240	178	76	(	(	PUNCT
ejpam-1240	178	77	xs†	xs†	PROPN
ejpam-1240	178	78	,	,	PUNCT
ejpam-1240	178	79	s	s	X
ejpam-1240	178	80	,	,	PUNCT
ejpam-1240	178	81	s∗u	s∗u	NUM
ejpam-1240	178	82	)	)	PUNCT
ejpam-1240	178	83	=	=	SYM
ejpam-1240	178	84	(	(	PUNCT
ejpam-1240	178	85	x	x	INTJ
ejpam-1240	178	86	,	,	PUNCT
ejpam-1240	178	87	s	s	PROPN
ejpam-1240	178	88	,	,	PUNCT
ejpam-1240	178	89	u	u	NOUN
ejpam-1240	178	90	)	)	PUNCT
ejpam-1240	178	91	and	and	CCONJ
ejpam-1240	178	92	similarly	similarly	ADV
ejpam-1240	178	93	,	,	PUNCT
ejpam-1240	178	94	(	(	PUNCT
ejpam-1240	178	95	s	s	X
ejpam-1240	178	96	◦	◦	NOUN
ejpam-1240	178	97	s	s	NOUN
ejpam-1240	178	98	,	,	PUNCT
ejpam-1240	178	99	s	s	NOUN
ejpam-1240	178	100	◦	◦	NOUN
ejpam-1240	178	101	,	,	PUNCT
ejpam-1240	178	102	ss	ss	NOUN
ejpam-1240	178	103	◦	◦	NOUN
ejpam-1240	178	104	)(x	)(x	NOUN
ejpam-1240	178	105	,	,	PUNCT
ejpam-1240	178	106	s	s	X
ejpam-1240	178	107	,	,	PUNCT
ejpam-1240	178	108	u)(s	u)(s	PRON
ejpam-1240	178	109	◦	◦	NOUN
ejpam-1240	178	110	s	s	SYM
ejpam-1240	178	111	,	,	PUNCT
ejpam-1240	178	112	s	s	NOUN
ejpam-1240	178	113	◦	◦	NOUN
ejpam-1240	178	114	,	,	PUNCT
ejpam-1240	178	115	ss	ss	NOUN
ejpam-1240	178	116	◦	◦	NOUN
ejpam-1240	178	117	)	)	PUNCT
ejpam-1240	178	118	=	=	PUNCT
ejpam-1240	178	119	(	(	PUNCT
ejpam-1240	178	120	s	s	X
ejpam-1240	178	121	◦	◦	NOUN
ejpam-1240	178	122	s	s	NOUN
ejpam-1240	178	123	,	,	PUNCT
ejpam-1240	178	124	s	s	NOUN
ejpam-1240	178	125	◦	◦	NOUN
ejpam-1240	178	126	,	,	PUNCT
ejpam-1240	178	127	ss	ss	NOUN
ejpam-1240	178	128	◦	◦	NOUN
ejpam-1240	178	129	)	)	PUNCT
ejpam-1240	178	130	.	.	PUNCT
ejpam-1240	179	1	hence	hence	ADV
ejpam-1240	179	2	,	,	PUNCT
ejpam-1240	179	3	(	(	PUNCT
ejpam-1240	179	4	s	s	X
ejpam-1240	179	5	◦	◦	NOUN
ejpam-1240	179	6	s	s	NOUN
ejpam-1240	179	7	,	,	PUNCT
ejpam-1240	179	8	s	s	NOUN
ejpam-1240	179	9	◦	◦	NOUN
ejpam-1240	179	10	,	,	PUNCT
ejpam-1240	179	11	ss	ss	NOUN
ejpam-1240	179	12	◦	◦	NOUN
ejpam-1240	179	13	)	)	PUNCT
ejpam-1240	179	14	is	be	AUX
ejpam-1240	179	15	an	an	DET
ejpam-1240	179	16	inverse	inverse	NOUN
ejpam-1240	179	17	of	of	ADP
ejpam-1240	179	18	(	(	PUNCT
ejpam-1240	179	19	x	x	INTJ
ejpam-1240	179	20	,	,	PUNCT
ejpam-1240	179	21	s	s	PROPN
ejpam-1240	179	22	,	,	PUNCT
ejpam-1240	179	23	u	u	NOUN
ejpam-1240	179	24	)	)	PUNCT
ejpam-1240	179	25	.	.	PUNCT
ejpam-1240	180	1	if	if	SCONJ
ejpam-1240	180	2	(	(	PUNCT
ejpam-1240	180	3	z	z	NOUN
ejpam-1240	180	4	,	,	PUNCT
ejpam-1240	180	5	p	p	X
ejpam-1240	180	6	,	,	PUNCT
ejpam-1240	180	7	w	w	NOUN
ejpam-1240	180	8	)	)	PUNCT
ejpam-1240	180	9	is	be	AUX
ejpam-1240	180	10	an	an	DET
ejpam-1240	180	11	inverse	inverse	NOUN
ejpam-1240	180	12	of	of	ADP
ejpam-1240	180	13	(	(	PUNCT
ejpam-1240	180	14	x	x	INTJ
ejpam-1240	180	15	,	,	PUNCT
ejpam-1240	180	16	s	s	PROPN
ejpam-1240	180	17	,	,	PUNCT
ejpam-1240	180	18	u	u	NOUN
ejpam-1240	180	19	)	)	PUNCT
ejpam-1240	180	20	,	,	PUNCT
ejpam-1240	180	21	then	then	ADV
ejpam-1240	180	22	by	by	ADP
ejpam-1240	180	23	the	the	DET
ejpam-1240	180	24	condition	condition	NOUN
ejpam-1240	180	25	(	(	PUNCT
ejpam-1240	180	26	5	5	NUM
ejpam-1240	180	27	)	)	PUNCT
ejpam-1240	180	28	,	,	PUNCT
ejpam-1240	180	29	p	p	NOUN
ejpam-1240	180	30	≤	≤	NUM
ejpam-1240	180	31	s	s	PART
ejpam-1240	180	32	◦	◦	NOUN
ejpam-1240	180	33	and	and	CCONJ
ejpam-1240	180	34	(	(	PUNCT
ejpam-1240	180	35	z	z	NOUN
ejpam-1240	180	36	,	,	PUNCT
ejpam-1240	180	37	p	p	X
ejpam-1240	180	38	,	,	PUNCT
ejpam-1240	180	39	w	w	NOUN
ejpam-1240	180	40	)	)	PUNCT
ejpam-1240	180	41	≤	≤	NOUN
ejpam-1240	180	42	(	(	PUNCT
ejpam-1240	180	43	s	s	X
ejpam-1240	180	44	◦	◦	NOUN
ejpam-1240	180	45	s	s	NOUN
ejpam-1240	180	46	,	,	PUNCT
ejpam-1240	180	47	s	s	NOUN
ejpam-1240	180	48	◦	◦	NOUN
ejpam-1240	180	49	,	,	PUNCT
ejpam-1240	180	50	ss	ss	NOUN
ejpam-1240	180	51	◦	◦	NOUN
ejpam-1240	180	52	)	)	PUNCT
ejpam-1240	180	53	.	.	PUNCT
ejpam-1240	181	1	this	this	PRON
ejpam-1240	181	2	means	mean	VERB
ejpam-1240	181	3	that	that	SCONJ
ejpam-1240	181	4	(	(	PUNCT
ejpam-1240	181	5	s	s	X
ejpam-1240	181	6	◦	◦	NOUN
ejpam-1240	181	7	s	s	NOUN
ejpam-1240	181	8	,	,	PUNCT
ejpam-1240	181	9	s	s	NOUN
ejpam-1240	181	10	◦	◦	NOUN
ejpam-1240	181	11	,	,	PUNCT
ejpam-1240	181	12	ss	ss	NOUN
ejpam-1240	181	13	◦	◦	NOUN
ejpam-1240	181	14	)	)	PUNCT
ejpam-1240	181	15	is	be	AUX
ejpam-1240	181	16	a	a	DET
ejpam-1240	181	17	greatest	great	ADJ
ejpam-1240	181	18	inverse	inverse	NOUN
ejpam-1240	181	19	of	of	ADP
ejpam-1240	181	20	(	(	PUNCT
ejpam-1240	181	21	x	x	INTJ
ejpam-1240	181	22	,	,	PUNCT
ejpam-1240	181	23	s	s	PROPN
ejpam-1240	181	24	,	,	PUNCT
ejpam-1240	181	25	u	u	NOUN
ejpam-1240	181	26	)	)	PUNCT
ejpam-1240	181	27	.	.	PUNCT
ejpam-1240	182	1	thus	thus	ADV
ejpam-1240	182	2	,	,	PUNCT
ejpam-1240	182	3	gi	gi	NOUN
ejpam-1240	182	4	becomes	become	VERB
ejpam-1240	182	5	a	a	DET
ejpam-1240	182	6	naturally	naturally	ADV
ejpam-1240	182	7	ordered	order	VERB
ejpam-1240	182	8	abundant	abundant	ADJ
ejpam-1240	182	9	semigroup	semigroup	NOUN
ejpam-1240	182	10	in	in	ADP
ejpam-1240	182	11	which	which	PRON
ejpam-1240	182	12	each	each	DET
ejpam-1240	182	13	idempotent	idempotent	NOUN
ejpam-1240	182	14	has	have	VERB
ejpam-1240	182	15	a	a	DET
ejpam-1240	182	16	greatest	great	ADJ
ejpam-1240	182	17	inverse	inverse	NOUN
ejpam-1240	182	18	.	.	PUNCT
ejpam-1240	183	1	if	if	SCONJ
ejpam-1240	183	2	(	(	PUNCT
ejpam-1240	183	3	x	x	X
ejpam-1240	183	4	,	,	PUNCT
ejpam-1240	183	5	s	s	PROPN
ejpam-1240	183	6	,	,	PUNCT
ejpam-1240	183	7	u	u	NOUN
ejpam-1240	183	8	)	)	PUNCT
ejpam-1240	183	9	,	,	PUNCT
ejpam-1240	183	10	(	(	PUNCT
ejpam-1240	183	11	y	y	PROPN
ejpam-1240	183	12	,	,	PUNCT
ejpam-1240	183	13	t	t	PROPN
ejpam-1240	183	14	,	,	PUNCT
ejpam-1240	183	15	v	v	NOUN
ejpam-1240	183	16	)	)	PUNCT
ejpam-1240	183	17	∈	∈	NOUN
ejpam-1240	183	18	gi	gi	NOUN
ejpam-1240	183	19	and	and	CCONJ
ejpam-1240	183	20	(	(	PUNCT
ejpam-1240	183	21	x	x	INTJ
ejpam-1240	183	22	,	,	PUNCT
ejpam-1240	183	23	s	s	PROPN
ejpam-1240	183	24	,	,	PUNCT
ejpam-1240	183	25	u	u	NOUN
ejpam-1240	183	26	)	)	PUNCT
ejpam-1240	183	27	≤	≤	NOUN
ejpam-1240	183	28	(	(	PUNCT
ejpam-1240	183	29	y	y	PROPN
ejpam-1240	183	30	,	,	PUNCT
ejpam-1240	183	31	t	t	PROPN
ejpam-1240	183	32	,	,	PUNCT
ejpam-1240	183	33	v	v	NOUN
ejpam-1240	183	34	)	)	PUNCT
ejpam-1240	183	35	,	,	PUNCT
ejpam-1240	183	36	then	then	ADV
ejpam-1240	183	37	s	s	VERB
ejpam-1240	183	38	≤	≤	ADJ
ejpam-1240	183	39	t.	t.	NOUN
ejpam-1240	183	40	hence	hence	ADV
ejpam-1240	183	41	,	,	PUNCT
ejpam-1240	183	42	s	s	X
ejpam-1240	183	43	◦	◦	NOUN
ejpam-1240	183	44	≤	≤	X
ejpam-1240	183	45	t	t	NOUN
ejpam-1240	183	46	◦	◦	NOUN
ejpam-1240	183	47	,	,	PUNCT
ejpam-1240	183	48	so	so	SCONJ
ejpam-1240	183	49	that	that	SCONJ
ejpam-1240	183	50	ss	ss	ADP
ejpam-1240	183	51	◦	◦	NOUN
ejpam-1240	183	52	≤	≤	NUM
ejpam-1240	183	53	t	t	PROPN
ejpam-1240	183	54	t	t	NOUN
ejpam-1240	183	55	◦	◦	NOUN
ejpam-1240	183	56	and	and	CCONJ
ejpam-1240	183	57	s	s	NOUN
ejpam-1240	183	58	◦	◦	NOUN
ejpam-1240	183	59	s	s	PART
ejpam-1240	183	60	≤	≤	NUM
ejpam-1240	183	61	t	t	PROPN
ejpam-1240	183	62	◦	◦	NOUN
ejpam-1240	183	63	t.	t.	NOUN
ejpam-1240	183	64	thus	thus	ADV
ejpam-1240	183	65	,	,	PUNCT
ejpam-1240	183	66	(	(	PUNCT
ejpam-1240	183	67	s	s	X
ejpam-1240	183	68	◦	◦	NOUN
ejpam-1240	183	69	s	s	NOUN
ejpam-1240	183	70	,	,	PUNCT
ejpam-1240	183	71	s	s	NOUN
ejpam-1240	183	72	◦	◦	NOUN
ejpam-1240	183	73	,	,	PUNCT
ejpam-1240	183	74	ss	ss	NOUN
ejpam-1240	183	75	◦	◦	NOUN
ejpam-1240	183	76	)	)	PUNCT
ejpam-1240	183	77	≤	≤	NOUN
ejpam-1240	183	78	(	(	PUNCT
ejpam-1240	183	79	t	t	PROPN
ejpam-1240	183	80	◦	◦	NOUN
ejpam-1240	183	81	t	t	PROPN
ejpam-1240	183	82	,	,	PUNCT
ejpam-1240	183	83	t	t	PROPN
ejpam-1240	183	84	◦	◦	NOUN
ejpam-1240	183	85	,	,	PUNCT
ejpam-1240	183	86	t	t	PROPN
ejpam-1240	183	87	t	t	PROPN
ejpam-1240	183	88	◦	◦	NOUN
ejpam-1240	183	89	)	)	PUNCT
ejpam-1240	183	90	,	,	PUNCT
ejpam-1240	183	91	that	that	ADV
ejpam-1240	183	92	is	is	ADV
ejpam-1240	183	93	,	,	PUNCT
ejpam-1240	183	94	(	(	PUNCT
ejpam-1240	183	95	x	x	X
ejpam-1240	183	96	,	,	PUNCT
ejpam-1240	183	97	s	s	PROPN
ejpam-1240	183	98	,	,	PUNCT
ejpam-1240	183	99	u	u	NOUN
ejpam-1240	183	100	)	)	PUNCT
ejpam-1240	183	101	◦	◦	VERB
ejpam-1240	183	102	≤	≤	NUM
ejpam-1240	183	103	(	(	PUNCT
ejpam-1240	183	104	y	y	PROPN
ejpam-1240	183	105	,	,	PUNCT
ejpam-1240	183	106	t	t	PROPN
ejpam-1240	183	107	,	,	PUNCT
ejpam-1240	183	108	v)	v)	NUM
ejpam-1240	183	109	◦	◦	NOUN
ejpam-1240	183	110	.	.	PUNCT
ejpam-1240	184	1	therefore	therefore	ADV
ejpam-1240	184	2	,	,	PUNCT
ejpam-1240	184	3	gi	gi	X
ejpam-1240	184	4	is	be	AUX
ejpam-1240	184	5	reflexive	reflexive	ADJ
ejpam-1240	184	6	and	and	CCONJ
ejpam-1240	184	7	(	(	PUNCT
ejpam-1240	184	8	x	x	INTJ
ejpam-1240	184	9	,	,	PUNCT
ejpam-1240	184	10	s	s	X
ejpam-1240	184	11	,	,	PUNCT
ejpam-1240	184	12	u)(s	u)(s	PROPN
ejpam-1240	184	13	◦	◦	NOUN
ejpam-1240	184	14	s	s	SYM
ejpam-1240	184	15	,	,	PUNCT
ejpam-1240	184	16	s	s	NOUN
ejpam-1240	184	17	◦	◦	NOUN
ejpam-1240	184	18	,	,	PUNCT
ejpam-1240	184	19	ss	ss	NOUN
ejpam-1240	184	20	◦	◦	NOUN
ejpam-1240	184	21	)≤	)≤	PUNCT
ejpam-1240	184	22	(	(	PUNCT
ejpam-1240	184	23	y	y	PROPN
ejpam-1240	184	24	,	,	PUNCT
ejpam-1240	184	25	t	t	PROPN
ejpam-1240	184	26	,	,	PUNCT
ejpam-1240	184	27	v)(t	v)(t	ADJ
ejpam-1240	184	28	◦	◦	NOUN
ejpam-1240	184	29	t	t	PROPN
ejpam-1240	184	30	,	,	PUNCT
ejpam-1240	184	31	t	t	PROPN
ejpam-1240	184	32	◦	◦	NOUN
ejpam-1240	184	33	,	,	PUNCT
ejpam-1240	184	34	t	t	PROPN
ejpam-1240	184	35	t	t	PROPN
ejpam-1240	184	36	◦	◦	NOUN
ejpam-1240	184	37	)	)	PUNCT
ejpam-1240	184	38	.	.	PUNCT
ejpam-1240	185	1	from	from	ADP
ejpam-1240	185	2	this	this	DET
ejpam-1240	185	3	result	result	NOUN
ejpam-1240	185	4	and	and	CCONJ
ejpam-1240	185	5	its	its	PRON
ejpam-1240	185	6	dual	dual	ADJ
ejpam-1240	185	7	,	,	PUNCT
ejpam-1240	185	8	one	one	PRON
ejpam-1240	185	9	can	can	AUX
ejpam-1240	185	10	see	see	VERB
ejpam-1240	185	11	immediately	immediately	ADV
ejpam-1240	185	12	that	that	SCONJ
ejpam-1240	185	13	gi	gi	INTJ
ejpam-1240	185	14	is	be	AUX
ejpam-1240	185	15	a	a	DET
ejpam-1240	185	16	g	g	NOUN
ejpam-1240	185	17	-	-	PUNCT
ejpam-1240	185	18	regular	regular	ADJ
ejpam-1240	185	19	semigroup	semigroup	NOUN
ejpam-1240	185	20	.	.	PUNCT
ejpam-1240	186	1	(	(	PUNCT
ejpam-1240	186	2	⇐	⇐	NOUN
ejpam-1240	186	3	)	)	PUNCT
ejpam-1240	186	4	suppose	suppose	VERB
ejpam-1240	186	5	that	that	SCONJ
ejpam-1240	186	6	s	s	VERB
ejpam-1240	186	7	is	be	AUX
ejpam-1240	186	8	a	a	DET
ejpam-1240	186	9	naturally	naturally	ADV
ejpam-1240	186	10	ordered	order	VERB
ejpam-1240	186	11	abundant	abundant	ADJ
ejpam-1240	186	12	semigroup	semigroup	NOUN
ejpam-1240	186	13	in	in	ADP
ejpam-1240	186	14	which	which	PRON
ejpam-1240	186	15	each	each	DET
ejpam-1240	186	16	idempotent	idempotent	NOUN
ejpam-1240	186	17	has	have	VERB
ejpam-1240	186	18	a	a	DET
ejpam-1240	186	19	greatest	great	ADJ
ejpam-1240	186	20	inverse	inverse	NOUN
ejpam-1240	186	21	which	which	PRON
ejpam-1240	186	22	is	be	AUX
ejpam-1240	186	23	both	both	DET
ejpam-1240	186	24	g	g	NOUN
ejpam-1240	186	25	-	-	PUNCT
ejpam-1240	186	26	regular	regular	ADJ
ejpam-1240	186	27	and	and	CCONJ
ejpam-1240	186	28	reflexive	reflexive	ADJ
ejpam-1240	186	29	.	.	PUNCT
ejpam-1240	187	1	let	let	VERB
ejpam-1240	187	2	m	m	PRON
ejpam-1240	187	3	,	,	PUNCT
ejpam-1240	187	4	n	n	PROPN
ejpam-1240	187	5	and	and	CCONJ
ejpam-1240	187	6	s	s	X
ejpam-1240	187	7	♭	♭	PROPN
ejpam-1240	187	8	have	have	VERB
ejpam-1240	187	9	the	the	DET
ejpam-1240	187	10	same	same	ADJ
ejpam-1240	187	11	meanings	meaning	NOUN
ejpam-1240	187	12	as	as	SCONJ
ejpam-1240	187	13	lemma	lemma	PROPN
ejpam-1240	187	14	3	3	X
ejpam-1240	187	15	.	.	PUNCT
ejpam-1240	187	16	define	define	VERB
ejpam-1240	187	17	a	a	DET
ejpam-1240	187	18	mapping	mapping	NOUN
ejpam-1240	187	19	〈	〈	NOUN
ejpam-1240	187	20	,	,	PUNCT
ejpam-1240	187	21	〉	〉	NOUN
ejpam-1240	187	22	:	:	PUNCT
ejpam-1240	188	1	n	n	PRON
ejpam-1240	188	2	×m	×m	NOUN
ejpam-1240	188	3	→	→	SYM
ejpam-1240	188	4	s	s	X
ejpam-1240	188	5	♭	♭	INTJ
ejpam-1240	188	6	;	;	PUNCT
ejpam-1240	188	7	(	(	PUNCT
ejpam-1240	188	8	u	u	NOUN
ejpam-1240	188	9	,	,	PUNCT
ejpam-1240	188	10	x	x	NOUN
ejpam-1240	188	11	)	)	PUNCT
ejpam-1240	188	12	7→	7→	NUM
ejpam-1240	188	13	〈	〈	PROPN
ejpam-1240	188	14	u	u	NOUN
ejpam-1240	188	15	,	,	PUNCT
ejpam-1240	188	16	x	x	SYM
ejpam-1240	188	17	〉	〉	NOUN
ejpam-1240	188	18	=	=	SYM
ejpam-1240	188	19	ux	ux	NOUN
ejpam-1240	188	20	.	.	PUNCT
ejpam-1240	189	1	by	by	ADP
ejpam-1240	189	2	routine	routine	ADJ
ejpam-1240	189	3	checking	checking	NOUN
ejpam-1240	189	4	,	,	PUNCT
ejpam-1240	189	5	we	we	PRON
ejpam-1240	189	6	can	can	AUX
ejpam-1240	189	7	see	see	VERB
ejpam-1240	189	8	that	that	PRON
ejpam-1240	189	9	(	(	PUNCT
ejpam-1240	189	10	s	s	NOUN
ejpam-1240	189	11	♭	♭	INTJ
ejpam-1240	189	12	;	;	PUNCT
ejpam-1240	189	13	m	m	PROPN
ejpam-1240	189	14	,	,	PUNCT
ejpam-1240	189	15	n	n	CCONJ
ejpam-1240	189	16	;	;	PUNCT
ejpam-1240	189	17	〈	〈	PROPN
ejpam-1240	189	18	,	,	PUNCT
ejpam-1240	189	19	〉	〉	NOUN
ejpam-1240	189	20	)	)	PUNCT
ejpam-1240	189	21	is	be	AUX
ejpam-1240	189	22	a	a	DET
ejpam-1240	189	23	gi	gi	NOUN
ejpam-1240	189	24	-	-	PUNCT
ejpam-1240	189	25	system	system	NOUN
ejpam-1240	189	26	.	.	PUNCT
ejpam-1240	190	1	we	we	PRON
ejpam-1240	190	2	next	next	ADV
ejpam-1240	190	3	prove	prove	VERB
ejpam-1240	190	4	that	that	SCONJ
ejpam-1240	190	5	the	the	DET
ejpam-1240	190	6	mapping	mapping	NOUN
ejpam-1240	190	7	θ	θ	NOUN
ejpam-1240	190	8	:	:	PUNCT
ejpam-1240	190	9	s→	s→	X
ejpam-1240	190	10	gi(s	gi(s	NOUN
ejpam-1240	190	11	♭	♭	PROPN
ejpam-1240	190	12	;	;	PUNCT
ejpam-1240	190	13	m	m	PROPN
ejpam-1240	190	14	,	,	PUNCT
ejpam-1240	190	15	n	n	CCONJ
ejpam-1240	190	16	;	;	PUNCT
ejpam-1240	190	17	〈	〈	PROPN
ejpam-1240	190	18	,	,	PUNCT
ejpam-1240	190	19	〉	〉	NOUN
ejpam-1240	190	20	)	)	PUNCT
ejpam-1240	190	21	;	;	PUNCT
ejpam-1240	190	22	s	s	VERB
ejpam-1240	190	23	7→	7→	NUM
ejpam-1240	190	24	(	(	PUNCT
ejpam-1240	190	25	s†s†	s†s†	NOUN
ejpam-1240	190	26	◦	◦	NOUN
ejpam-1240	190	27	,	,	PUNCT
ejpam-1240	190	28	s	s	PROPN
ejpam-1240	190	29	♭	♭	PROPN
ejpam-1240	190	30	,	,	PUNCT
ejpam-1240	190	31	s∗	s∗	PROPN
ejpam-1240	190	32	◦	◦	PROPN
ejpam-1240	190	33	s∗	s∗	PROPN
ejpam-1240	190	34	)	)	PUNCT
ejpam-1240	190	35	is	be	AUX
ejpam-1240	190	36	a	a	DET
ejpam-1240	190	37	semigroup	semigroup	ADJ
ejpam-1240	190	38	isomorphism	isomorphism	NOUN
ejpam-1240	190	39	.	.	PUNCT
ejpam-1240	191	1	by	by	ADP
ejpam-1240	191	2	lemma	lemma	PROPN
ejpam-1240	191	3	4	4	NUM
ejpam-1240	191	4	,	,	PUNCT
ejpam-1240	191	5	we	we	PRON
ejpam-1240	191	6	have	have	VERB
ejpam-1240	191	7	s	s	NUM
ejpam-1240	191	8	♭	♭	X
ejpam-1240	191	9	†	†	X
ejpam-1240	191	10	=	=	PUNCT
ejpam-1240	191	11	es	es	PROPN
ejpam-1240	191	12	=	=	SYM
ejpam-1240	191	13	(	(	PUNCT
ejpam-1240	191	14	s	s	PROPN
ejpam-1240	191	15	†s†	†s†	PROPN
ejpam-1240	191	16	◦	◦	NOUN
ejpam-1240	191	17	)	)	PUNCT
ejpam-1240	191	18	◦	◦	NOUN
ejpam-1240	191	19	(s†s†	(s†s†	NOUN
ejpam-1240	191	20	◦	◦	NOUN
ejpam-1240	191	21	)	)	PUNCT
ejpam-1240	191	22	and	and	CCONJ
ejpam-1240	191	23	clearly	clearly	ADV
ejpam-1240	191	24	s	s	X
ejpam-1240	191	25	♭	♭	X
ejpam-1240	191	26	†	†	PROPN
ejpam-1240	191	27	l	l	PROPN
ejpam-1240	191	28	s†s†	s†s†	PROPN
ejpam-1240	191	29	◦	◦	NOUN
ejpam-1240	191	30	.	.	PUNCT
ejpam-1240	192	1	dually	dually	PROPN
ejpam-1240	192	2	,	,	PUNCT
ejpam-1240	192	3	s	s	AUX
ejpam-1240	192	4	♭	♭	PROPN
ejpam-1240	192	5	∗	∗	X
ejpam-1240	192	6	rs∗	rs∗	ADJ
ejpam-1240	192	7	◦	◦	NOUN
ejpam-1240	192	8	s∗.	s∗.	ADJ
ejpam-1240	192	9	this	this	PRON
ejpam-1240	192	10	means	mean	VERB
ejpam-1240	192	11	that	that	SCONJ
ejpam-1240	192	12	(	(	PUNCT
ejpam-1240	192	13	s†s†	s†s†	PROPN
ejpam-1240	192	14	◦	◦	NOUN
ejpam-1240	192	15	,	,	PUNCT
ejpam-1240	192	16	s	s	PROPN
ejpam-1240	192	17	♭	♭	PROPN
ejpam-1240	192	18	,	,	PUNCT
ejpam-1240	192	19	s∗	s∗	PROPN
ejpam-1240	192	20	◦	◦	PROPN
ejpam-1240	192	21	s∗	s∗	PROPN
ejpam-1240	192	22	)	)	PUNCT
ejpam-1240	192	23	∈	∈	PROPN
ejpam-1240	192	24	gi	gi	NOUN
ejpam-1240	192	25	.	.	PUNCT
ejpam-1240	193	1	in	in	ADP
ejpam-1240	193	2	other	other	ADJ
ejpam-1240	193	3	words	word	NOUN
ejpam-1240	193	4	,	,	PUNCT
ejpam-1240	193	5	θ	θ	PROPN
ejpam-1240	193	6	is	be	AUX
ejpam-1240	193	7	well	well	ADV
ejpam-1240	193	8	defined	define	VERB
ejpam-1240	193	9	.	.	PUNCT
ejpam-1240	194	1	•	•	INTJ
ejpam-1240	194	2	let	let	VERB
ejpam-1240	194	3	(	(	PUNCT
ejpam-1240	194	4	x	x	X
ejpam-1240	194	5	,	,	PUNCT
ejpam-1240	194	6	t	t	PROPN
ejpam-1240	194	7	,	,	PUNCT
ejpam-1240	194	8	u	u	NOUN
ejpam-1240	194	9	)	)	PUNCT
ejpam-1240	194	10	∈	∈	PROPN
ejpam-1240	194	11	gi(s	gi(s	NOUN
ejpam-1240	194	12	♭	♭	PROPN
ejpam-1240	194	13	;	;	PUNCT
ejpam-1240	194	14	m	m	PROPN
ejpam-1240	194	15	,	,	PUNCT
ejpam-1240	194	16	n	n	CCONJ
ejpam-1240	194	17	;	;	PUNCT
ejpam-1240	194	18	〈	〈	PROPN
ejpam-1240	194	19	,	,	PUNCT
ejpam-1240	194	20	〉	〉	NOUN
ejpam-1240	194	21	)	)	PUNCT
ejpam-1240	194	22	.	.	PUNCT
ejpam-1240	195	1	then	then	ADV
ejpam-1240	195	2	,	,	PUNCT
ejpam-1240	195	3	by	by	ADP
ejpam-1240	195	4	lemma	lemma	PROPN
ejpam-1240	195	5	4	4	NUM
ejpam-1240	195	6	,	,	PUNCT
ejpam-1240	195	7	xr∗x	xr∗x	PROPN
ejpam-1240	195	8	tul	tul	PROPN
ejpam-1240	195	9	∗u	∗u	PROPN
ejpam-1240	195	10	.	.	PUNCT
ejpam-1240	196	1	put	put	VERB
ejpam-1240	196	2	a	a	DET
ejpam-1240	196	3	=	=	NOUN
ejpam-1240	196	4	x	x	SYM
ejpam-1240	196	5	tu	tu	PROPN
ejpam-1240	196	6	.	.	PROPN
ejpam-1240	196	7	again	again	ADV
ejpam-1240	196	8	,	,	PUNCT
ejpam-1240	196	9	by	by	ADP
ejpam-1240	196	10	lemma	lemma	PROPN
ejpam-1240	196	11	5(2	5(2	NUM
ejpam-1240	196	12	)	)	PUNCT
ejpam-1240	196	13	,	,	PUNCT
ejpam-1240	196	14	a	a	DET
ejpam-1240	196	15	♭	♭	PROPN
ejpam-1240	196	16	=	=	SYM
ejpam-1240	196	17	t	t	PROPN
ejpam-1240	196	18	,	,	PUNCT
ejpam-1240	196	19	a†a†	a†a†	NOUN
ejpam-1240	196	20	◦	◦	NOUN
ejpam-1240	196	21	=	=	SYM
ejpam-1240	197	1	x	x	X
ejpam-1240	197	2	and	and	CCONJ
ejpam-1240	197	3	a∗	a∗	PROPN
ejpam-1240	197	4	◦	◦	NOUN
ejpam-1240	197	5	a∗	a∗	NOUN
ejpam-1240	197	6	=	=	SYM
ejpam-1240	197	7	u.	u.	NOUN
ejpam-1240	197	8	hence	hence	ADV
ejpam-1240	197	9	,	,	PUNCT
ejpam-1240	197	10	aθ	aθ	NOUN
ejpam-1240	197	11	=	=	SYM
ejpam-1240	197	12	(	(	PUNCT
ejpam-1240	197	13	x	x	INTJ
ejpam-1240	197	14	,	,	PUNCT
ejpam-1240	197	15	t	t	PROPN
ejpam-1240	197	16	,	,	PUNCT
ejpam-1240	197	17	u	u	NOUN
ejpam-1240	197	18	)	)	PUNCT
ejpam-1240	197	19	and	and	CCONJ
ejpam-1240	197	20	θ	θ	PROPN
ejpam-1240	197	21	is	be	AUX
ejpam-1240	197	22	a	a	DET
ejpam-1240	197	23	surjective	surjective	ADJ
ejpam-1240	197	24	mapping	mapping	NOUN
ejpam-1240	197	25	.	.	PUNCT
ejpam-1240	198	1	•	•	NUM
ejpam-1240	198	2	by	by	ADP
ejpam-1240	198	3	lemma	lemma	PROPN
ejpam-1240	198	4	5(2	5(2	NUM
ejpam-1240	198	5	)	)	PUNCT
ejpam-1240	198	6	,	,	PUNCT
ejpam-1240	198	7	we	we	PRON
ejpam-1240	198	8	can	can	AUX
ejpam-1240	198	9	easily	easily	ADV
ejpam-1240	198	10	see	see	VERB
ejpam-1240	198	11	that	that	SCONJ
ejpam-1240	198	12	θ	θ	PROPN
ejpam-1240	198	13	is	be	AUX
ejpam-1240	198	14	an	an	DET
ejpam-1240	198	15	injective	injective	ADJ
ejpam-1240	198	16	mapping	mapping	NOUN
ejpam-1240	198	17	.	.	PUNCT
ejpam-1240	199	1	x.	x.	PROPN
ejpam-1240	199	2	guo	guo	PROPN
ejpam-1240	199	3	,	,	PUNCT
ejpam-1240	199	4	k.	k.	PROPN
ejpam-1240	199	5	shum	shum	PROPN
ejpam-1240	199	6	/	/	SYM
ejpam-1240	199	7	eur	eur	PROPN
ejpam-1240	199	8	.	.	PUNCT
ejpam-1240	200	1	j.	j.	PROPN
ejpam-1240	200	2	pure	pure	PROPN
ejpam-1240	200	3	appl	appl	PROPN
ejpam-1240	200	4	.	.	PROPN
ejpam-1240	200	5	math	math	PROPN
ejpam-1240	200	6	,	,	PUNCT
ejpam-1240	200	7	4	4	NUM
ejpam-1240	200	8	(	(	PUNCT
ejpam-1240	200	9	2011	2011	NUM
ejpam-1240	200	10	)	)	PUNCT
ejpam-1240	200	11	,	,	PUNCT
ejpam-1240	200	12	210	210	NUM
ejpam-1240	200	13	-	-	SYM
ejpam-1240	200	14	220	220	NUM
ejpam-1240	200	15	217	217	NUM
ejpam-1240	200	16	•	•	NOUN
ejpam-1240	200	17	if	if	SCONJ
ejpam-1240	200	18	a	a	PRON
ejpam-1240	200	19	,	,	PUNCT
ejpam-1240	200	20	b	b	PROPN
ejpam-1240	200	21	∈	∈	PROPN
ejpam-1240	200	22	s	s	NOUN
ejpam-1240	200	23	,	,	PUNCT
ejpam-1240	200	24	then	then	ADV
ejpam-1240	200	25	a	a	PRON
ejpam-1240	200	26	=	=	PUNCT
ejpam-1240	200	27	(	(	PUNCT
ejpam-1240	200	28	a†a†	a†a†	PROPN
ejpam-1240	200	29	◦	◦	NOUN
ejpam-1240	200	30	)a	)a	NOUN
ejpam-1240	200	31	♭	♭	PROPN
ejpam-1240	200	32	(a∗	(a∗	PROPN
ejpam-1240	200	33	◦	◦	NOUN
ejpam-1240	200	34	a∗	a∗	NOUN
ejpam-1240	200	35	)	)	PUNCT
ejpam-1240	200	36	and	and	CCONJ
ejpam-1240	200	37	b	b	X
ejpam-1240	200	38	=	=	SYM
ejpam-1240	200	39	(	(	PUNCT
ejpam-1240	200	40	b†b†	b†b†	NOUN
ejpam-1240	200	41	◦	◦	NOUN
ejpam-1240	200	42	)b	)b	PUNCT
ejpam-1240	200	43	♭	♭	PROPN
ejpam-1240	200	44	(b∗	(b∗	PROPN
ejpam-1240	200	45	◦	◦	NOUN
ejpam-1240	200	46	b∗	b∗	ADJ
ejpam-1240	200	47	)	)	PUNCT
ejpam-1240	200	48	,	,	PUNCT
ejpam-1240	200	49	which	which	PRON
ejpam-1240	200	50	imply	imply	VERB
ejpam-1240	200	51	that	that	SCONJ
ejpam-1240	200	52	ab	ab	PROPN
ejpam-1240	200	53	=	=	PRON
ejpam-1240	200	54	(	(	PUNCT
ejpam-1240	200	55	a†a†	a†a†	PROPN
ejpam-1240	200	56	◦	◦	NOUN
ejpam-1240	200	57	)a	)a	NOUN
ejpam-1240	200	58	♭	♭	PROPN
ejpam-1240	200	59	(a∗	(a∗	PROPN
ejpam-1240	200	60	◦	◦	PROPN
ejpam-1240	200	61	a∗)(b†b†	a∗)(b†b†	NOUN
ejpam-1240	200	62	◦	◦	NOUN
ejpam-1240	200	63	)b	)b	PUNCT
ejpam-1240	200	64	♭	♭	PROPN
ejpam-1240	200	65	(b∗	(b∗	PROPN
ejpam-1240	200	66	◦	◦	NOUN
ejpam-1240	200	67	b∗	b∗	ADJ
ejpam-1240	200	68	)	)	PUNCT
ejpam-1240	200	69	=	=	SYM
ejpam-1240	200	70	(	(	PUNCT
ejpam-1240	200	71	a†a†	a†a†	PROPN
ejpam-1240	200	72	◦	◦	NOUN
ejpam-1240	200	73	)a	)a	NOUN
ejpam-1240	200	74	♭	♭	PROPN
ejpam-1240	201	1	〈(a∗	〈(a∗	NOUN
ejpam-1240	201	2	◦	◦	NOUN
ejpam-1240	201	3	a∗	a∗	ADJ
ejpam-1240	201	4	)	)	PUNCT
ejpam-1240	201	5	,	,	PUNCT
ejpam-1240	201	6	(	(	PUNCT
ejpam-1240	201	7	b†	b†	X
ejpam-1240	201	8	b†	b†	X
ejpam-1240	201	9	◦	◦	NOUN
ejpam-1240	201	10	)〉b	)〉b	SYM
ejpam-1240	201	11	♭	♭	PROPN
ejpam-1240	201	12	(b∗	(b∗	PROPN
ejpam-1240	201	13	◦	◦	NOUN
ejpam-1240	201	14	b∗	b∗	ADJ
ejpam-1240	201	15	)	)	PUNCT
ejpam-1240	202	1	=	=	PUNCT
ejpam-1240	202	2	(	(	PUNCT
ejpam-1240	202	3	a†a†	a†a†	PROPN
ejpam-1240	202	4	◦	◦	NOUN
ejpam-1240	202	5	)ess	)ess	PUNCT
ejpam-1240	202	6	fs(b	fs(b	NOUN
ejpam-1240	202	7	∗	∗	NOUN
ejpam-1240	202	8	◦	◦	NOUN
ejpam-1240	202	9	b∗	b∗	ADJ
ejpam-1240	202	10	)	)	PUNCT
ejpam-1240	202	11	,	,	PUNCT
ejpam-1240	202	12	where	where	SCONJ
ejpam-1240	202	13	s	s	VERB
ejpam-1240	202	14	=	=	PUNCT
ejpam-1240	202	15	a	a	DET
ejpam-1240	202	16	♭	♭	INTJ
ejpam-1240	202	17	〈(a∗	〈(a∗	PROPN
ejpam-1240	202	18	◦	◦	NOUN
ejpam-1240	202	19	a∗	a∗	ADJ
ejpam-1240	202	20	)	)	PUNCT
ejpam-1240	202	21	,	,	PUNCT
ejpam-1240	202	22	(	(	PUNCT
ejpam-1240	202	23	b†	b†	X
ejpam-1240	202	24	b†	b†	X
ejpam-1240	202	25	◦	◦	NOUN
ejpam-1240	202	26	)〉b	)〉b	NOUN
ejpam-1240	202	27	♭	♭	PROPN
ejpam-1240	202	28	.	.	PUNCT
ejpam-1240	203	1	on	on	ADP
ejpam-1240	203	2	the	the	DET
ejpam-1240	203	3	other	other	ADJ
ejpam-1240	203	4	hand	hand	NOUN
ejpam-1240	203	5	,	,	PUNCT
ejpam-1240	203	6	by	by	ADP
ejpam-1240	203	7	lemma	lemma	PROPN
ejpam-1240	203	8	4	4	NUM
ejpam-1240	203	9	,	,	PUNCT
ejpam-1240	203	10	ear	ear	VERB
ejpam-1240	203	11	∗a	∗a	PROPN
ejpam-1240	203	12	♭	♭	PROPN
ejpam-1240	203	13	and	and	CCONJ
ejpam-1240	203	14	eas	eas	PROPN
ejpam-1240	203	15	=	=	SYM
ejpam-1240	203	16	s.	s.	PROPN
ejpam-1240	203	17	hence	hence	ADV
ejpam-1240	203	18	eas†	eas†	PROPN
ejpam-1240	203	19	=	=	SYM
ejpam-1240	203	20	s†	s†	NOUN
ejpam-1240	203	21	,	,	PUNCT
ejpam-1240	203	22	that	that	ADV
ejpam-1240	203	23	is	is	ADV
ejpam-1240	203	24	,	,	PUNCT
ejpam-1240	203	25	(	(	PUNCT
ejpam-1240	203	26	a†a†	a†a†	PROPN
ejpam-1240	203	27	◦	◦	NOUN
ejpam-1240	203	28	)	)	PUNCT
ejpam-1240	203	29	◦	◦	NOUN
ejpam-1240	203	30	a†a†	a†a†	NOUN
ejpam-1240	203	31	◦	◦	NOUN
ejpam-1240	203	32	s†	s†	NOUN
ejpam-1240	203	33	=	=	PUNCT
ejpam-1240	203	34	s†	s†	NOUN
ejpam-1240	203	35	and	and	CCONJ
ejpam-1240	203	36	a†a†	a†a†	PROPN
ejpam-1240	203	37	◦	◦	NOUN
ejpam-1240	203	38	s†l	s†l	NUM
ejpam-1240	203	39	s†	s†	NOUN
ejpam-1240	203	40	and	and	CCONJ
ejpam-1240	203	41	dually	dually	ADV
ejpam-1240	203	42	s∗b∗	s∗b∗	NOUN
ejpam-1240	203	43	◦	◦	NOUN
ejpam-1240	203	44	b∗rs∗.	b∗rs∗.	NOUN
ejpam-1240	203	45	thus	thus	ADV
ejpam-1240	203	46	,	,	PUNCT
ejpam-1240	203	47	by	by	ADP
ejpam-1240	203	48	lemma	lemma	PROPN
ejpam-1240	203	49	5(2	5(2	NUM
ejpam-1240	203	50	)	)	PUNCT
ejpam-1240	203	51	,	,	PUNCT
ejpam-1240	203	52	(	(	PUNCT
ejpam-1240	203	53	ab	ab	X
ejpam-1240	203	54	)	)	PUNCT
ejpam-1240	203	55	♭	♭	PROPN
ejpam-1240	203	56	=	=	SYM
ejpam-1240	203	57	s	s	PROPN
ejpam-1240	203	58	,	,	PUNCT
ejpam-1240	203	59	(	(	PUNCT
ejpam-1240	203	60	ab)†(ab)†	ab)†(ab)†	NOUN
ejpam-1240	203	61	◦	◦	NOUN
ejpam-1240	203	62	=	=	SYM
ejpam-1240	203	63	a†a†	a†a†	NOUN
ejpam-1240	203	64	◦	◦	NOUN
ejpam-1240	203	65	es	es	NOUN
ejpam-1240	203	66	and	and	CCONJ
ejpam-1240	203	67	(	(	PUNCT
ejpam-1240	203	68	ab)∗	ab)∗	PROPN
ejpam-1240	203	69	◦	◦	NOUN
ejpam-1240	203	70	(	(	PUNCT
ejpam-1240	203	71	ab)∗	ab)∗	NOUN
ejpam-1240	203	72	=	=	SYM
ejpam-1240	203	73	fs	fs	ADP
ejpam-1240	203	74	b∗	b∗	ADJ
ejpam-1240	203	75	◦	◦	NOUN
ejpam-1240	203	76	b∗.	b∗.	NOUN
ejpam-1240	203	77	this	this	PRON
ejpam-1240	203	78	proves	prove	VERB
ejpam-1240	203	79	that	that	SCONJ
ejpam-1240	203	80	(	(	PUNCT
ejpam-1240	203	81	ab)θ	ab)θ	X
ejpam-1240	203	82	=	=	PRON
ejpam-1240	203	83	(	(	PUNCT
ejpam-1240	203	84	a†a†	a†a†	PROPN
ejpam-1240	203	85	◦	◦	NOUN
ejpam-1240	203	86	es	es	NOUN
ejpam-1240	203	87	,	,	PUNCT
ejpam-1240	203	88	(	(	PUNCT
ejpam-1240	203	89	ab	ab	X
ejpam-1240	203	90	)	)	PUNCT
ejpam-1240	203	91	♭	♭	PROPN
ejpam-1240	203	92	,	,	PUNCT
ejpam-1240	203	93	fs	fs	ADP
ejpam-1240	203	94	b∗	b∗	ADJ
ejpam-1240	203	95	◦	◦	NOUN
ejpam-1240	203	96	b∗	b∗	ADJ
ejpam-1240	203	97	)	)	PUNCT
ejpam-1240	203	98	=	=	SYM
ejpam-1240	203	99	(	(	PUNCT
ejpam-1240	203	100	a†a†	a†a†	PROPN
ejpam-1240	203	101	◦	◦	NOUN
ejpam-1240	203	102	,	,	PUNCT
ejpam-1240	203	103	a	a	DET
ejpam-1240	203	104	♭	♭	PROPN
ejpam-1240	203	105	,	,	PUNCT
ejpam-1240	203	106	a∗	a∗	PROPN
ejpam-1240	203	107	◦	◦	PROPN
ejpam-1240	203	108	a∗)(b†b†	a∗)(b†b†	PROPN
ejpam-1240	203	109	◦	◦	PROPN
ejpam-1240	203	110	,	,	PUNCT
ejpam-1240	203	111	b	b	NOUN
ejpam-1240	203	112	♭	♭	PROPN
ejpam-1240	203	113	,	,	PUNCT
ejpam-1240	203	114	b∗	b∗	ADJ
ejpam-1240	203	115	◦	◦	NOUN
ejpam-1240	203	116	b∗	b∗	ADJ
ejpam-1240	203	117	)	)	PUNCT
ejpam-1240	203	118	=	=	SYM
ejpam-1240	203	119	(	(	PUNCT
ejpam-1240	203	120	aθ)(bθ	aθ)(bθ	PROPN
ejpam-1240	203	121	)	)	PUNCT
ejpam-1240	203	122	.	.	PUNCT
ejpam-1240	204	1	thus	thus	ADV
ejpam-1240	204	2	,	,	PUNCT
ejpam-1240	204	3	we	we	PRON
ejpam-1240	204	4	have	have	AUX
ejpam-1240	204	5	proved	prove	VERB
ejpam-1240	204	6	that	that	SCONJ
ejpam-1240	204	7	θ	θ	PROPN
ejpam-1240	204	8	is	be	AUX
ejpam-1240	204	9	a	a	DET
ejpam-1240	204	10	semigroup	semigroup	ADJ
ejpam-1240	204	11	isomorphism	isomorphism	NOUN
ejpam-1240	204	12	,	,	PUNCT
ejpam-1240	204	13	as	as	SCONJ
ejpam-1240	204	14	required	require	VERB
ejpam-1240	204	15	.	.	PUNCT
ejpam-1240	205	1	it	it	PRON
ejpam-1240	205	2	remains	remain	VERB
ejpam-1240	205	3	to	to	PART
ejpam-1240	205	4	show	show	VERB
ejpam-1240	205	5	that	that	SCONJ
ejpam-1240	205	6	(	(	PUNCT
ejpam-1240	205	7	s	s	AUX
ejpam-1240	205	8	♭	♭	INTJ
ejpam-1240	205	9	;	;	PUNCT
ejpam-1240	205	10	m	m	PROPN
ejpam-1240	205	11	,	,	PUNCT
ejpam-1240	205	12	n	n	CCONJ
ejpam-1240	205	13	;	;	PUNCT
ejpam-1240	205	14	〈	〈	PROPN
ejpam-1240	205	15	,	,	PUNCT
ejpam-1240	205	16	〉	〉	NOUN
ejpam-1240	205	17	)	)	PUNCT
ejpam-1240	205	18	satisfying	satisfy	VERB
ejpam-1240	205	19	the	the	DET
ejpam-1240	205	20	condition	condition	NOUN
ejpam-1240	205	21	(	(	PUNCT
ejpam-1240	205	22	e	e	NOUN
ejpam-1240	205	23	)	)	PUNCT
ejpam-1240	205	24	in	in	ADP
ejpam-1240	205	25	theorem	theorem	NOUN
ejpam-1240	205	26	1	1	NUM
ejpam-1240	205	27	.	.	PUNCT
ejpam-1240	206	1	for	for	ADP
ejpam-1240	206	2	this	this	DET
ejpam-1240	206	3	purpose	purpose	NOUN
ejpam-1240	206	4	,	,	PUNCT
ejpam-1240	206	5	we	we	PRON
ejpam-1240	206	6	need	need	AUX
ejpam-1240	206	7	only	only	ADV
ejpam-1240	206	8	verify	verify	VERB
ejpam-1240	206	9	that	that	SCONJ
ejpam-1240	206	10	for	for	ADP
ejpam-1240	206	11	any	any	DET
ejpam-1240	206	12	s	s	X
ejpam-1240	206	13	∈	∈	NOUN
ejpam-1240	206	14	s	s	NOUN
ejpam-1240	206	15	and	and	CCONJ
ejpam-1240	206	16	for	for	ADP
ejpam-1240	206	17	all	all	DET
ejpam-1240	206	18	inverse	inverse	NOUN
ejpam-1240	206	19	t	t	PROPN
ejpam-1240	206	20	of	of	ADP
ejpam-1240	206	21	s	s	PROPN
ejpam-1240	206	22	,	,	PUNCT
ejpam-1240	206	23	t	t	PROPN
ejpam-1240	206	24	♭	♭	PROPN
ejpam-1240	206	25	≤	≤	NUM
ejpam-1240	206	26	s	s	X
ejpam-1240	206	27	♭	♭	PROPN
ejpam-1240	206	28	◦	◦	NOUN
ejpam-1240	206	29	(	(	PUNCT
ejpam-1240	206	30	since	since	SCONJ
ejpam-1240	206	31	θ	θ	PROPN
ejpam-1240	206	32	is	be	AUX
ejpam-1240	206	33	an	an	DET
ejpam-1240	206	34	order	order	NOUN
ejpam-1240	206	35	isomorphism	isomorphism	NOUN
ejpam-1240	206	36	)	)	PUNCT
ejpam-1240	206	37	.	.	PUNCT
ejpam-1240	207	1	in	in	ADP
ejpam-1240	207	2	fact	fact	NOUN
ejpam-1240	207	3	,	,	PUNCT
ejpam-1240	207	4	by	by	ADP
ejpam-1240	207	5	lemma	lemma	PROPN
ejpam-1240	207	6	5(1	5(1	NUM
ejpam-1240	207	7	)	)	PUNCT
ejpam-1240	207	8	,	,	PUNCT
ejpam-1240	207	9	s	s	X
ejpam-1240	207	10	◦	◦	NOUN
ejpam-1240	207	11	♭	♭	PROPN
ejpam-1240	207	12	is	be	AUX
ejpam-1240	207	13	an	an	DET
ejpam-1240	207	14	inverse	inverse	NOUN
ejpam-1240	207	15	of	of	ADP
ejpam-1240	207	16	s	s	NOUN
ejpam-1240	207	17	♭	♭	X
ejpam-1240	207	18	satisfying	satisfy	VERB
ejpam-1240	207	19	that	that	SCONJ
ejpam-1240	207	20	t	t	PROPN
ejpam-1240	207	21	♭	♭	X
ejpam-1240	207	22	≤	≤	NUM
ejpam-1240	207	23	s	s	PART
ejpam-1240	207	24	◦	◦	NOUN
ejpam-1240	207	25	♭	♭	NOUN
ejpam-1240	207	26	for	for	ADP
ejpam-1240	207	27	all	all	DET
ejpam-1240	207	28	inverse	inverse	NOUN
ejpam-1240	207	29	t	t	PROPN
ejpam-1240	207	30	of	of	ADP
ejpam-1240	207	31	s.	s.	PROPN
ejpam-1240	207	32	but	but	CCONJ
ejpam-1240	207	33	clearly	clearly	ADV
ejpam-1240	207	34	,	,	PUNCT
ejpam-1240	207	35	s	s	X
ejpam-1240	207	36	◦	◦	NOUN
ejpam-1240	207	37	♭	♭	X
ejpam-1240	207	38	≤	≤	NUM
ejpam-1240	207	39	s	s	X
ejpam-1240	207	40	♭	♭	PROPN
ejpam-1240	207	41	◦	◦	NOUN
ejpam-1240	207	42	.	.	PUNCT
ejpam-1240	208	1	now	now	ADV
ejpam-1240	208	2	,	,	PUNCT
ejpam-1240	208	3	we	we	PRON
ejpam-1240	208	4	have	have	VERB
ejpam-1240	208	5	t	t	PROPN
ejpam-1240	208	6	♭	♭	X
ejpam-1240	208	7	≤	≤	NUM
ejpam-1240	208	8	s	s	X
ejpam-1240	208	9	♭	♭	PROPN
ejpam-1240	208	10	◦	◦	NOUN
ejpam-1240	208	11	,	,	PUNCT
ejpam-1240	208	12	as	as	SCONJ
ejpam-1240	208	13	required	require	VERB
ejpam-1240	208	14	.	.	PUNCT
ejpam-1240	209	1	thus	thus	ADV
ejpam-1240	209	2	,	,	PUNCT
ejpam-1240	209	3	the	the	DET
ejpam-1240	209	4	proof	proof	NOUN
ejpam-1240	209	5	is	be	AUX
ejpam-1240	209	6	completed	complete	VERB
ejpam-1240	209	7	.	.	PUNCT
ejpam-1240	210	1	4	4	X
ejpam-1240	210	2	.	.	X
ejpam-1240	210	3	examples	example	NOUN
ejpam-1240	210	4	in	in	ADP
ejpam-1240	210	5	this	this	DET
ejpam-1240	210	6	section	section	NOUN
ejpam-1240	210	7	,	,	PUNCT
ejpam-1240	210	8	we	we	PRON
ejpam-1240	210	9	give	give	VERB
ejpam-1240	210	10	some	some	DET
ejpam-1240	210	11	examples	example	NOUN
ejpam-1240	210	12	of	of	ADP
ejpam-1240	210	13	a	a	DET
ejpam-1240	210	14	*	*	PUNCT
ejpam-1240	210	15	-unipotent	-unipotent	NOUN
ejpam-1240	210	16	naturally	naturally	ADV
ejpam-1240	210	17	ordered	order	VERB
ejpam-1240	210	18	abundant	abundant	ADJ
ejpam-1240	210	19	semigroup	semigroup	NOUN
ejpam-1240	210	20	in	in	ADP
ejpam-1240	210	21	which	which	PRON
ejpam-1240	210	22	each	each	DET
ejpam-1240	210	23	idempotent	idempotent	NOUN
ejpam-1240	210	24	has	have	VERB
ejpam-1240	210	25	a	a	DET
ejpam-1240	210	26	greatest	great	ADJ
ejpam-1240	210	27	inverse	inverse	NOUN
ejpam-1240	210	28	and	and	CCONJ
ejpam-1240	210	29	the	the	DET
ejpam-1240	210	30	semigroup	semigroup	NOUN
ejpam-1240	210	31	is	be	AUX
ejpam-1240	210	32	g	g	NOUN
ejpam-1240	210	33	-	-	PUNCT
ejpam-1240	210	34	regular	regular	ADJ
ejpam-1240	210	35	and	and	CCONJ
ejpam-1240	210	36	reflexive	reflexive	ADJ
ejpam-1240	210	37	.	.	PUNCT
ejpam-1240	211	1	example	example	NOUN
ejpam-1240	211	2	1	1	NUM
ejpam-1240	211	3	(	(	PUNCT
ejpam-1240	211	4	9	9	NUM
ejpam-1240	211	5	,	,	PUNCT
ejpam-1240	211	6	example	example	NOUN
ejpam-1240	211	7	1.4	1.4	NUM
ejpam-1240	211	8	)	)	PUNCT
ejpam-1240	211	9	.	.	PUNCT
ejpam-1240	212	1	let	let	VERB
ejpam-1240	212	2	a=	a=	VERB
ejpam-1240	212	3	�	�	PROPN
ejpam-1240	212	4	1	1	NUM
ejpam-1240	212	5	0	0	NUM
ejpam-1240	212	6	0	0	NUM
ejpam-1240	212	7	0	0	NUM
ejpam-1240	212	8	�	�	PROPN
ejpam-1240	212	9	,	,	PUNCT
ejpam-1240	212	10	b	b	X
ejpam-1240	212	11	=	=	SYM
ejpam-1240	212	12	�	�	PROPN
ejpam-1240	212	13	1	1	NUM
ejpam-1240	212	14	0	0	NUM
ejpam-1240	212	15	1	1	NUM
ejpam-1240	212	16	0	0	NUM
ejpam-1240	212	17	�	�	PROPN
ejpam-1240	212	18	,	,	PUNCT
ejpam-1240	212	19	c	c	NOUN
ejpam-1240	212	20	=	=	SYM
ejpam-1240	212	21	�	�	PROPN
ejpam-1240	212	22	1	1	NUM
ejpam-1240	212	23	1	1	NUM
ejpam-1240	212	24	0	0	NUM
ejpam-1240	212	25	0	0	NUM
ejpam-1240	212	26	�	�	PROPN
ejpam-1240	212	27	,	,	PUNCT
ejpam-1240	212	28	d	d	X
ejpam-1240	212	29	=	=	SYM
ejpam-1240	212	30	�	�	PROPN
ejpam-1240	212	31	1	1	NUM
ejpam-1240	212	32	1	1	NUM
ejpam-1240	212	33	1	1	NUM
ejpam-1240	212	34	1	1	NUM
ejpam-1240	212	35	�	�	NOUN
ejpam-1240	212	36	and	and	CCONJ
ejpam-1240	212	37	put	put	VERB
ejpam-1240	212	38	t	t	NOUN
ejpam-1240	212	39	=	=	SYM
ejpam-1240	212	40	{	{	PUNCT
ejpam-1240	212	41	2ma	2ma	NOUN
ejpam-1240	212	42	,	,	PUNCT
ejpam-1240	212	43	2nb	2nb	PROPN
ejpam-1240	212	44	,	,	PUNCT
ejpam-1240	212	45	2nc	2nc	NOUN
ejpam-1240	212	46	,	,	PUNCT
ejpam-1240	212	47	2nd	2nd	NOUN
ejpam-1240	212	48	:	:	PUNCT
ejpam-1240	213	1	m≥	m≥	NOUN
ejpam-1240	213	2	1	1	NUM
ejpam-1240	213	3	,	,	PUNCT
ejpam-1240	213	4	n≥	n≥	NOUN
ejpam-1240	213	5	0	0	NUM
ejpam-1240	213	6	}	}	PUNCT
ejpam-1240	213	7	.	.	PUNCT
ejpam-1240	214	1	it	it	PRON
ejpam-1240	214	2	is	be	AUX
ejpam-1240	214	3	easy	easy	ADJ
ejpam-1240	214	4	to	to	PART
ejpam-1240	214	5	see	see	VERB
ejpam-1240	214	6	that	that	PRON
ejpam-1240	214	7	t	t	PROPN
ejpam-1240	214	8	is	be	AUX
ejpam-1240	214	9	a	a	DET
ejpam-1240	214	10	semigroup	semigroup	NOUN
ejpam-1240	214	11	under	under	ADP
ejpam-1240	214	12	matrix	matrix	NOUN
ejpam-1240	214	13	multiplication	multiplication	NOUN
ejpam-1240	214	14	.	.	PUNCT
ejpam-1240	215	1	further	far	ADV
ejpam-1240	215	2	,	,	PUNCT
ejpam-1240	215	3	t	t	PROPN
ejpam-1240	215	4	is	be	AUX
ejpam-1240	215	5	generated	generate	VERB
ejpam-1240	215	6	by	by	ADP
ejpam-1240	215	7	b	b	PROPN
ejpam-1240	215	8	and	and	CCONJ
ejpam-1240	215	9	c	c	PROPN
ejpam-1240	215	10	and	and	CCONJ
ejpam-1240	215	11	these	these	DET
ejpam-1240	215	12	elements	element	NOUN
ejpam-1240	215	13	are	be	AUX
ejpam-1240	215	14	the	the	DET
ejpam-1240	215	15	only	only	ADJ
ejpam-1240	215	16	idempotents	idempotent	NOUN
ejpam-1240	215	17	in	in	ADP
ejpam-1240	215	18	t	t	PROPN
ejpam-1240	215	19	.	.	PUNCT
ejpam-1240	216	1	it	it	PRON
ejpam-1240	216	2	is	be	AUX
ejpam-1240	216	3	routine	routine	ADJ
ejpam-1240	216	4	to	to	PART
ejpam-1240	216	5	check	check	VERB
ejpam-1240	216	6	that	that	PRON
ejpam-1240	216	7	thel	thel	PROPN
ejpam-1240	216	8	∗-classes	∗-classes	PROPN
ejpam-1240	216	9	of	of	ADP
ejpam-1240	216	10	t	t	PROPN
ejpam-1240	216	11	are	be	AUX
ejpam-1240	216	12	{	{	PUNCT
ejpam-1240	216	13	2ma	2ma	NOUN
ejpam-1240	216	14	,	,	PUNCT
ejpam-1240	216	15	2nb	2nb	PROPN
ejpam-1240	216	16	:	:	PUNCT
ejpam-1240	216	17	m	m	VERB
ejpam-1240	216	18	≥	≥	NOUN
ejpam-1240	216	19	1	1	NUM
ejpam-1240	216	20	,	,	PUNCT
ejpam-1240	216	21	n≥	n≥	NOUN
ejpam-1240	216	22	0	0	NUM
ejpam-1240	216	23	}	}	PUNCT
ejpam-1240	216	24	,	,	PUNCT
ejpam-1240	216	25	{	{	PUNCT
ejpam-1240	216	26	2nc	2nc	NOUN
ejpam-1240	216	27	,	,	PUNCT
ejpam-1240	216	28	2nd	2nd	NOUN
ejpam-1240	216	29	:	:	PUNCT
ejpam-1240	216	30	n≥	n≥	NOUN
ejpam-1240	216	31	0	0	NUM
ejpam-1240	216	32	}	}	PUNCT
ejpam-1240	216	33	and	and	CCONJ
ejpam-1240	216	34	that	that	SCONJ
ejpam-1240	216	35	the	the	DET
ejpam-1240	216	36	r∗-classes	r∗-classes	PROPN
ejpam-1240	216	37	of	of	ADP
ejpam-1240	216	38	t	t	PROPN
ejpam-1240	216	39	are	be	AUX
ejpam-1240	216	40	{	{	PUNCT
ejpam-1240	216	41	2ma	2ma	NOUN
ejpam-1240	216	42	,	,	PUNCT
ejpam-1240	216	43	2nc	2nc	NOUN
ejpam-1240	216	44	:	:	PUNCT
ejpam-1240	216	45	m	m	VERB
ejpam-1240	216	46	≥	≥	NOUN
ejpam-1240	216	47	1	1	NUM
ejpam-1240	216	48	,	,	PUNCT
ejpam-1240	216	49	n≥	n≥	NOUN
ejpam-1240	216	50	0	0	NUM
ejpam-1240	216	51	}	}	PUNCT
ejpam-1240	216	52	,	,	PUNCT
ejpam-1240	216	53	{	{	PUNCT
ejpam-1240	216	54	2nb	2nb	ADJ
ejpam-1240	216	55	,	,	PUNCT
ejpam-1240	216	56	2nd	2nd	NOUN
ejpam-1240	216	57	:	:	PUNCT
ejpam-1240	216	58	n≥	n≥	NOUN
ejpam-1240	216	59	0	0	NUM
ejpam-1240	216	60	}	}	PUNCT
ejpam-1240	216	61	.	.	PUNCT
ejpam-1240	217	1	thus	thus	ADV
ejpam-1240	217	2	,	,	PUNCT
ejpam-1240	217	3	each	each	DET
ejpam-1240	217	4	l	l	NOUN
ejpam-1240	217	5	∗-class	∗-class	NOUN
ejpam-1240	217	6	and	and	CCONJ
ejpam-1240	217	7	each	each	DET
ejpam-1240	217	8	r∗-class	r∗-class	NOUN
ejpam-1240	217	9	of	of	ADP
ejpam-1240	217	10	t	t	PROPN
ejpam-1240	217	11	contains	contain	VERB
ejpam-1240	217	12	a	a	DET
ejpam-1240	217	13	unique	unique	ADJ
ejpam-1240	217	14	idempotent	idempotent	NOUN
ejpam-1240	217	15	but	but	CCONJ
ejpam-1240	217	16	t	t	NOUN
ejpam-1240	217	17	is	be	AUX
ejpam-1240	217	18	not	not	PART
ejpam-1240	217	19	adequate	adequate	ADJ
ejpam-1240	217	20	since	since	SCONJ
ejpam-1240	217	21	bc	bc	PROPN
ejpam-1240	217	22	6=	6=	PROPN
ejpam-1240	217	23	cb	cb	PROPN
ejpam-1240	217	24	.	.	PROPN
ejpam-1240	218	1	on	on	ADP
ejpam-1240	218	2	the	the	DET
ejpam-1240	218	3	other	other	ADJ
ejpam-1240	218	4	hand	hand	NOUN
ejpam-1240	218	5	,	,	PUNCT
ejpam-1240	218	6	reg(t	reg(t	PROPN
ejpam-1240	218	7	)	)	PUNCT
ejpam-1240	218	8	=	=	PUNCT
ejpam-1240	219	1	{	{	PUNCT
ejpam-1240	219	2	b	b	NOUN
ejpam-1240	219	3	,	,	PUNCT
ejpam-1240	219	4	c	c	NOUN
ejpam-1240	219	5	}	}	PUNCT
ejpam-1240	219	6	and	and	CCONJ
ejpam-1240	219	7	obviously	obviously	ADV
ejpam-1240	219	8	,	,	PUNCT
ejpam-1240	219	9	with	with	ADP
ejpam-1240	219	10	respective	respective	ADJ
ejpam-1240	219	11	to	to	ADP
ejpam-1240	219	12	the	the	DET
ejpam-1240	219	13	trivial	trivial	ADJ
ejpam-1240	219	14	order	order	NOUN
ejpam-1240	219	15	,	,	PUNCT
ejpam-1240	219	16	t	t	PROPN
ejpam-1240	219	17	is	be	AUX
ejpam-1240	219	18	a	a	DET
ejpam-1240	219	19	*	*	PUNCT
ejpam-1240	219	20	-unipotent	-unipotent	NOUN
ejpam-1240	219	21	naturally	naturally	ADV
ejpam-1240	219	22	ordered	order	VERB
ejpam-1240	219	23	abundant	abundant	ADJ
ejpam-1240	219	24	semigroup	semigroup	NOUN
ejpam-1240	219	25	in	in	ADP
ejpam-1240	219	26	which	which	PRON
ejpam-1240	219	27	each	each	DET
ejpam-1240	219	28	idempotent	idempotent	NOUN
ejpam-1240	219	29	has	have	VERB
ejpam-1240	219	30	a	a	DET
ejpam-1240	219	31	greatest	great	ADJ
ejpam-1240	219	32	inverse	inverse	NOUN
ejpam-1240	219	33	and	and	CCONJ
ejpam-1240	219	34	which	which	PRON
ejpam-1240	219	35	is	be	AUX
ejpam-1240	219	36	g	g	NOUN
ejpam-1240	219	37	-	-	PUNCT
ejpam-1240	219	38	regular	regular	ADJ
ejpam-1240	219	39	and	and	CCONJ
ejpam-1240	219	40	reflexive	reflexive	ADJ
ejpam-1240	219	41	.	.	PUNCT
ejpam-1240	220	1	and	and	CCONJ
ejpam-1240	220	2	e(t	e(t	PROPN
ejpam-1240	220	3	)	)	PUNCT
ejpam-1240	221	1	=	=	PUNCT
ejpam-1240	221	2	{	{	PUNCT
ejpam-1240	221	3	b	b	NOUN
ejpam-1240	221	4	,	,	PUNCT
ejpam-1240	221	5	c	c	NOUN
ejpam-1240	221	6	}	}	PUNCT
ejpam-1240	221	7	is	be	AUX
ejpam-1240	221	8	a	a	DET
ejpam-1240	221	9	partial	partial	ADJ
ejpam-1240	221	10	semilattice	semilattice	NOUN
ejpam-1240	221	11	.	.	PUNCT
ejpam-1240	222	1	x.	x.	PROPN
ejpam-1240	222	2	guo	guo	PROPN
ejpam-1240	222	3	,	,	PUNCT
ejpam-1240	222	4	k.	k.	PROPN
ejpam-1240	222	5	shum	shum	PROPN
ejpam-1240	222	6	/	/	SYM
ejpam-1240	222	7	eur	eur	PROPN
ejpam-1240	222	8	.	.	PUNCT
ejpam-1240	223	1	j.	j.	PROPN
ejpam-1240	223	2	pure	pure	PROPN
ejpam-1240	223	3	appl	appl	PROPN
ejpam-1240	223	4	.	.	PROPN
ejpam-1240	223	5	math	math	PROPN
ejpam-1240	223	6	,	,	PUNCT
ejpam-1240	223	7	4	4	NUM
ejpam-1240	223	8	(	(	PUNCT
ejpam-1240	223	9	2011	2011	NUM
ejpam-1240	223	10	)	)	PUNCT
ejpam-1240	223	11	,	,	PUNCT
ejpam-1240	223	12	210	210	NUM
ejpam-1240	223	13	-	-	SYM
ejpam-1240	223	14	220	220	NUM
ejpam-1240	223	15	218	218	NUM
ejpam-1240	223	16	example	example	NOUN
ejpam-1240	223	17	1	1	NUM
ejpam-1240	223	18	shows	show	VERB
ejpam-1240	223	19	that	that	PRON
ejpam-1240	223	20	theorem	theorem	NOUN
ejpam-1240	223	21	1	1	NUM
ejpam-1240	223	22	is	be	AUX
ejpam-1240	223	23	an	an	DET
ejpam-1240	223	24	extension	extension	NOUN
ejpam-1240	223	25	of	of	ADP
ejpam-1240	223	26	the	the	DET
ejpam-1240	223	27	construction	construction	NOUN
ejpam-1240	223	28	theorem	theorem	NOUN
ejpam-1240	223	29	previously	previously	ADV
ejpam-1240	223	30	given	give	VERB
ejpam-1240	223	31	by	by	ADP
ejpam-1240	223	32	guo	guo	PROPN
ejpam-1240	223	33	and	and	CCONJ
ejpam-1240	223	34	xie	xie	PROPN
ejpam-1240	223	35	in	in	ADP
ejpam-1240	223	36	[	[	X
ejpam-1240	223	37	13	13	NUM
ejpam-1240	223	38	]	]	PUNCT
ejpam-1240	223	39	on	on	ADP
ejpam-1240	223	40	naturally	naturally	ADV
ejpam-1240	223	41	ordered	order	VERB
ejpam-1240	223	42	abundant	abundant	ADJ
ejpam-1240	223	43	semigroups	semigroup	NOUN
ejpam-1240	223	44	in	in	ADP
ejpam-1240	223	45	which	which	PRON
ejpam-1240	223	46	every	every	DET
ejpam-1240	223	47	idempotent	idempotent	NOUN
ejpam-1240	223	48	has	have	VERB
ejpam-1240	223	49	a	a	DET
ejpam-1240	223	50	greatest	great	ADJ
ejpam-1240	223	51	inverse	inverse	NOUN
ejpam-1240	223	52	.	.	PUNCT
ejpam-1240	224	1	obviously	obviously	ADV
ejpam-1240	224	2	,	,	PUNCT
ejpam-1240	224	3	the	the	DET
ejpam-1240	224	4	left	left	ADJ
ejpam-1240	224	5	regular	regular	ADJ
ejpam-1240	224	6	bands	band	NOUN
ejpam-1240	224	7	are	be	AUX
ejpam-1240	224	8	left	leave	VERB
ejpam-1240	224	9	regular	regular	ADJ
ejpam-1240	224	10	partial	partial	ADJ
ejpam-1240	224	11	bands	band	NOUN
ejpam-1240	224	12	and	and	CCONJ
ejpam-1240	224	13	right	right	ADJ
ejpam-1240	224	14	regular	regular	ADJ
ejpam-1240	224	15	bands	band	NOUN
ejpam-1240	224	16	are	be	AUX
ejpam-1240	224	17	right	right	ADV
ejpam-1240	224	18	regular	regular	ADJ
ejpam-1240	224	19	partial	partial	ADJ
ejpam-1240	224	20	bands	band	NOUN
ejpam-1240	224	21	.	.	PUNCT
ejpam-1240	225	1	the	the	DET
ejpam-1240	225	2	following	follow	VERB
ejpam-1240	225	3	example	example	NOUN
ejpam-1240	225	4	illustrates	illustrate	VERB
ejpam-1240	225	5	that	that	SCONJ
ejpam-1240	225	6	there	there	PRON
ejpam-1240	225	7	exist	exist	VERB
ejpam-1240	225	8	left	left	ADJ
ejpam-1240	225	9	(	(	PUNCT
ejpam-1240	225	10	right	right	ADJ
ejpam-1240	225	11	)	)	PUNCT
ejpam-1240	225	12	regular	regular	ADJ
ejpam-1240	225	13	partial	partial	ADJ
ejpam-1240	225	14	bands	band	NOUN
ejpam-1240	225	15	being	be	AUX
ejpam-1240	225	16	not	not	PART
ejpam-1240	225	17	left	leave	VERB
ejpam-1240	225	18	(	(	PUNCT
ejpam-1240	225	19	right	right	ADJ
ejpam-1240	225	20	)	)	PUNCT
ejpam-1240	225	21	regular	regular	ADJ
ejpam-1240	225	22	bands	band	NOUN
ejpam-1240	225	23	and	and	CCONJ
ejpam-1240	225	24	that	that	SCONJ
ejpam-1240	225	25	there	there	PRON
ejpam-1240	225	26	exist	exist	VERB
ejpam-1240	225	27	left	left	ADJ
ejpam-1240	225	28	(	(	PUNCT
ejpam-1240	225	29	right	right	ADJ
ejpam-1240	225	30	)	)	PUNCT
ejpam-1240	225	31	regular	regular	ADJ
ejpam-1240	225	32	partial	partial	ADJ
ejpam-1240	225	33	bands	band	NOUN
ejpam-1240	225	34	being	be	AUX
ejpam-1240	225	35	also	also	ADV
ejpam-1240	225	36	right	right	ADJ
ejpam-1240	225	37	(	(	PUNCT
ejpam-1240	225	38	left	left	ADJ
ejpam-1240	225	39	)	)	PUNCT
ejpam-1240	225	40	regular	regular	ADJ
ejpam-1240	225	41	partial	partial	ADJ
ejpam-1240	225	42	bands	band	NOUN
ejpam-1240	225	43	.	.	PUNCT
ejpam-1240	225	44	example	example	NOUN
ejpam-1240	226	1	2	2	NUM
ejpam-1240	226	2	.	.	PUNCT
ejpam-1240	226	3	with	with	ADP
ejpam-1240	226	4	the	the	DET
ejpam-1240	226	5	notations	notation	NOUN
ejpam-1240	226	6	of	of	ADP
ejpam-1240	226	7	example	example	NOUN
ejpam-1240	226	8	1	1	NUM
ejpam-1240	226	9	,	,	PUNCT
ejpam-1240	226	10	it	it	PRON
ejpam-1240	226	11	is	be	AUX
ejpam-1240	226	12	easy	easy	ADJ
ejpam-1240	226	13	to	to	PART
ejpam-1240	226	14	see	see	VERB
ejpam-1240	226	15	that	that	SCONJ
ejpam-1240	226	16	the	the	DET
ejpam-1240	226	17	set	set	NOUN
ejpam-1240	226	18	x	x	X
ejpam-1240	226	19	=	=	X
ejpam-1240	226	20	{	{	PUNCT
ejpam-1240	226	21	a	a	PRON
ejpam-1240	226	22	,	,	PUNCT
ejpam-1240	226	23	b	b	NOUN
ejpam-1240	226	24	,	,	PUNCT
ejpam-1240	226	25	c	c	NOUN
ejpam-1240	226	26	}	}	PUNCT
ejpam-1240	226	27	forms	form	VERB
ejpam-1240	226	28	a	a	DET
ejpam-1240	226	29	partial	partial	ADJ
ejpam-1240	226	30	semigroup	semigroup	NOUN
ejpam-1240	226	31	under	under	ADP
ejpam-1240	226	32	the	the	DET
ejpam-1240	226	33	matrix	matrix	NOUN
ejpam-1240	226	34	multiplication	multiplication	NOUN
ejpam-1240	226	35	.	.	PUNCT
ejpam-1240	227	1	putting	put	VERB
ejpam-1240	227	2	lb	lb	X
ejpam-1240	227	3	=	=	PUNCT
ejpam-1240	227	4	{	{	PUNCT
ejpam-1240	227	5	a	a	PROPN
ejpam-1240	227	6	,	,	PUNCT
ejpam-1240	227	7	b	b	NOUN
ejpam-1240	227	8	}	}	PUNCT
ejpam-1240	227	9	and	and	CCONJ
ejpam-1240	227	10	lc	lc	NOUN
ejpam-1240	227	11	=	=	PUNCT
ejpam-1240	227	12	{	{	PUNCT
ejpam-1240	227	13	c	c	NOUN
ejpam-1240	227	14	}	}	PUNCT
ejpam-1240	227	15	.	.	PUNCT
ejpam-1240	228	1	then	then	ADV
ejpam-1240	228	2	,	,	PUNCT
ejpam-1240	228	3	lb	lb	X
ejpam-1240	228	4	and	and	CCONJ
ejpam-1240	228	5	lc	lc	NOUN
ejpam-1240	228	6	are	be	AUX
ejpam-1240	228	7	both	both	PRON
ejpam-1240	228	8	left	leave	VERB
ejpam-1240	228	9	zero	zero	NUM
ejpam-1240	228	10	rectangular	rectangular	ADJ
ejpam-1240	228	11	bands	band	NOUN
ejpam-1240	228	12	.	.	PUNCT
ejpam-1240	229	1	since	since	SCONJ
ejpam-1240	229	2	on	on	ADP
ejpam-1240	229	3	the	the	DET
ejpam-1240	229	4	set	set	NOUN
ejpam-1240	229	5	e(t	e(t	PROPN
ejpam-1240	229	6	)	)	PUNCT
ejpam-1240	229	7	,	,	PUNCT
ejpam-1240	229	8	�	�	PROPN
ejpam-1240	229	9	is	be	AUX
ejpam-1240	229	10	the	the	DET
ejpam-1240	229	11	identity	identity	NOUN
ejpam-1240	229	12	relation	relation	NOUN
ejpam-1240	229	13	.	.	PUNCT
ejpam-1240	230	1	thus	thus	ADV
ejpam-1240	230	2	,	,	PUNCT
ejpam-1240	230	3	we	we	PRON
ejpam-1240	230	4	can	can	AUX
ejpam-1240	230	5	easily	easily	ADV
ejpam-1240	230	6	see	see	VERB
ejpam-1240	230	7	that	that	SCONJ
ejpam-1240	230	8	x	x	PRON
ejpam-1240	230	9	satisfies	satisfy	VERB
ejpam-1240	230	10	the	the	DET
ejpam-1240	230	11	condition	condition	NOUN
ejpam-1240	230	12	(	(	PUNCT
ejpam-1240	230	13	pb1	pb1	NOUN
ejpam-1240	230	14	)	)	PUNCT
ejpam-1240	230	15	.	.	PUNCT
ejpam-1240	231	1	note	note	VERB
ejpam-1240	231	2	that	that	SCONJ
ejpam-1240	231	3	in	in	ADP
ejpam-1240	231	4	l	l	PROPN
ejpam-1240	231	5	,	,	PUNCT
ejpam-1240	231	6	ab	ab	PROPN
ejpam-1240	231	7	=	=	PUNCT
ejpam-1240	231	8	a	a	PROPN
ejpam-1240	231	9	,	,	PUNCT
ejpam-1240	231	10	ba	ba	PROPN
ejpam-1240	231	11	=	=	SYM
ejpam-1240	231	12	b	b	PROPN
ejpam-1240	231	13	,	,	PUNCT
ejpam-1240	231	14	ac	ac	PROPN
ejpam-1240	231	15	=	=	SYM
ejpam-1240	231	16	c	c	PROPN
ejpam-1240	231	17	but	but	CCONJ
ejpam-1240	231	18	ca=	ca=	PROPN
ejpam-1240	231	19	a.	a.	NOUN
ejpam-1240	231	20	we	we	PRON
ejpam-1240	231	21	observe	observe	VERB
ejpam-1240	231	22	that	that	SCONJ
ejpam-1240	231	23	x	x	X
ejpam-1240	231	24	=	=	NOUN
ejpam-1240	231	25	lb	lb	ADP
ejpam-1240	231	26	∪	∪	PROPN
ejpam-1240	231	27	lc	lc	NOUN
ejpam-1240	231	28	also	also	ADV
ejpam-1240	231	29	satisfies	satisfy	VERB
ejpam-1240	231	30	the	the	DET
ejpam-1240	231	31	condition	condition	NOUN
ejpam-1240	231	32	(	(	PUNCT
ejpam-1240	231	33	pb2	pb2	PROPN
ejpam-1240	231	34	)	)	PUNCT
ejpam-1240	231	35	.	.	PUNCT
ejpam-1240	232	1	thus	thus	ADV
ejpam-1240	232	2	,	,	PUNCT
ejpam-1240	232	3	the	the	DET
ejpam-1240	232	4	band	band	NOUN
ejpam-1240	232	5	x	x	PUNCT
ejpam-1240	232	6	is	be	AUX
ejpam-1240	232	7	a	a	DET
ejpam-1240	232	8	left	left	ADJ
ejpam-1240	232	9	regular	regular	ADJ
ejpam-1240	232	10	partial	partial	ADJ
ejpam-1240	232	11	band	band	NOUN
ejpam-1240	232	12	.	.	PUNCT
ejpam-1240	233	1	also	also	ADV
ejpam-1240	233	2	,	,	PUNCT
ejpam-1240	233	3	e(t	e(t	PROPN
ejpam-1240	233	4	)	)	PUNCT
ejpam-1240	233	5	is	be	AUX
ejpam-1240	233	6	a	a	DET
ejpam-1240	233	7	skeleton	skeleton	NOUN
ejpam-1240	233	8	of	of	ADP
ejpam-1240	233	9	the	the	DET
ejpam-1240	233	10	left	left	ADJ
ejpam-1240	233	11	regular	regular	ADJ
ejpam-1240	233	12	partial	partial	ADJ
ejpam-1240	233	13	band	band	NOUN
ejpam-1240	233	14	x	x	X
ejpam-1240	233	15	.	.	PUNCT
ejpam-1240	234	1	if	if	SCONJ
ejpam-1240	234	2	rb	rb	X
ejpam-1240	234	3	=	=	SYM
ejpam-1240	234	4	{	{	PUNCT
ejpam-1240	234	5	b	b	NOUN
ejpam-1240	234	6	}	}	PUNCT
ejpam-1240	234	7	and	and	CCONJ
ejpam-1240	234	8	rc	rc	PROPN
ejpam-1240	234	9	=	=	PUNCT
ejpam-1240	234	10	{	{	PUNCT
ejpam-1240	234	11	a	a	X
ejpam-1240	234	12	,	,	PUNCT
ejpam-1240	234	13	c	c	NOUN
ejpam-1240	234	14	}	}	PUNCT
ejpam-1240	234	15	,	,	PUNCT
ejpam-1240	234	16	then	then	ADV
ejpam-1240	234	17	by	by	ADP
ejpam-1240	234	18	applying	apply	VERB
ejpam-1240	234	19	the	the	DET
ejpam-1240	234	20	arguments	argument	NOUN
ejpam-1240	234	21	similar	similar	ADJ
ejpam-1240	234	22	to	to	ADP
ejpam-1240	234	23	the	the	DET
ejpam-1240	234	24	above	above	NOUN
ejpam-1240	234	25	,	,	PUNCT
ejpam-1240	234	26	we	we	PRON
ejpam-1240	234	27	know	know	VERB
ejpam-1240	234	28	the	the	DET
ejpam-1240	234	29	set	set	NOUN
ejpam-1240	234	30	x	x	X
ejpam-1240	234	31	=	=	SYM
ejpam-1240	234	32	rb	rb	PROPN
ejpam-1240	234	33	∪	∪	X
ejpam-1240	234	34	rc	rc	PROPN
ejpam-1240	234	35	is	be	AUX
ejpam-1240	234	36	a	a	DET
ejpam-1240	234	37	right	right	ADJ
ejpam-1240	234	38	regular	regular	ADJ
ejpam-1240	234	39	partial	partial	ADJ
ejpam-1240	234	40	band	band	NOUN
ejpam-1240	234	41	with	with	ADP
ejpam-1240	234	42	e(t	e(t	PROPN
ejpam-1240	234	43	)	)	PUNCT
ejpam-1240	234	44	as	as	ADP
ejpam-1240	234	45	its	its	PRON
ejpam-1240	234	46	skeleton	skeleton	NOUN
ejpam-1240	234	47	.	.	PUNCT
ejpam-1240	235	1	example	example	NOUN
ejpam-1240	236	1	3	3	X
ejpam-1240	236	2	.	.	PUNCT
ejpam-1240	236	3	let	let	VERB
ejpam-1240	236	4	f	f	PROPN
ejpam-1240	236	5	=	=	SYM
ejpam-1240	236	6	�	�	PROPN
ejpam-1240	236	7	0	0	NUM
ejpam-1240	236	8	1	1	NUM
ejpam-1240	236	9	0	0	NUM
ejpam-1240	236	10	1	1	NUM
ejpam-1240	236	11	�	�	PROPN
ejpam-1240	236	12	and	and	CCONJ
ejpam-1240	236	13	denote	denote	VERB
ejpam-1240	236	14	r	r	NOUN
ejpam-1240	236	15	=	=	SYM
ejpam-1240	236	16	{	{	PUNCT
ejpam-1240	236	17	b	b	NOUN
ejpam-1240	236	18	,	,	PUNCT
ejpam-1240	236	19	c	c	NOUN
ejpam-1240	236	20	,	,	PUNCT
ejpam-1240	236	21	f	f	X
ejpam-1240	236	22	}	}	PUNCT
ejpam-1240	236	23	.	.	PUNCT
ejpam-1240	237	1	then	then	ADV
ejpam-1240	237	2	r	r	NOUN
ejpam-1240	237	3	forms	form	VERB
ejpam-1240	237	4	a	a	DET
ejpam-1240	237	5	partial	partial	ADJ
ejpam-1240	237	6	semigroup	semigroup	NOUN
ejpam-1240	237	7	under	under	ADP
ejpam-1240	237	8	matrix	matrix	NOUN
ejpam-1240	237	9	multiplication	multiplication	NOUN
ejpam-1240	237	10	.	.	PUNCT
ejpam-1240	238	1	set	set	VERB
ejpam-1240	238	2	rb	rb	NOUN
ejpam-1240	238	3	=	=	PUNCT
ejpam-1240	238	4	{	{	PUNCT
ejpam-1240	238	5	b	b	PROPN
ejpam-1240	238	6	,	,	PUNCT
ejpam-1240	238	7	f	f	NOUN
ejpam-1240	238	8	}	}	PUNCT
ejpam-1240	238	9	and	and	CCONJ
ejpam-1240	238	10	rc	rc	PROPN
ejpam-1240	238	11	=	=	PUNCT
ejpam-1240	238	12	{	{	PUNCT
ejpam-1240	238	13	c	c	NOUN
ejpam-1240	238	14	}	}	PUNCT
ejpam-1240	238	15	.	.	PUNCT
ejpam-1240	239	1	now	now	ADV
ejpam-1240	239	2	,	,	PUNCT
ejpam-1240	239	3	by	by	ADP
ejpam-1240	239	4	computation	computation	NOUN
ejpam-1240	239	5	,	,	PUNCT
ejpam-1240	239	6	we	we	PRON
ejpam-1240	239	7	see	see	VERB
ejpam-1240	239	8	that	that	DET
ejpam-1240	239	9	rb	rb	NOUN
ejpam-1240	239	10	and	and	CCONJ
ejpam-1240	239	11	rc	rc	PROPN
ejpam-1240	239	12	are	be	AUX
ejpam-1240	239	13	both	both	ADV
ejpam-1240	239	14	right	right	ADJ
ejpam-1240	239	15	zero	zero	NUM
ejpam-1240	239	16	rectangular	rectangular	ADJ
ejpam-1240	239	17	bands	band	NOUN
ejpam-1240	239	18	.	.	PUNCT
ejpam-1240	240	1	note	note	VERB
ejpam-1240	240	2	that	that	SCONJ
ejpam-1240	240	3	in	in	ADP
ejpam-1240	240	4	r	r	NOUN
ejpam-1240	240	5	,	,	PUNCT
ejpam-1240	240	6	only	only	ADV
ejpam-1240	240	7	b	b	PROPN
ejpam-1240	240	8	and	and	CCONJ
ejpam-1240	240	9	f	f	NOUN
ejpam-1240	240	10	,	,	PUNCT
ejpam-1240	240	11	and	and	CCONJ
ejpam-1240	240	12	f	f	PROPN
ejpam-1240	240	13	and	and	CCONJ
ejpam-1240	240	14	b	b	PROPN
ejpam-1240	240	15	are	be	AUX
ejpam-1240	240	16	defined	define	VERB
ejpam-1240	240	17	.	.	PUNCT
ejpam-1240	241	1	it	it	PRON
ejpam-1240	241	2	is	be	AUX
ejpam-1240	241	3	easy	easy	ADJ
ejpam-1240	241	4	to	to	PART
ejpam-1240	241	5	see	see	VERB
ejpam-1240	241	6	that	that	SCONJ
ejpam-1240	241	7	r	r	NOUN
ejpam-1240	241	8	satisfies	satisfy	VERB
ejpam-1240	241	9	the	the	DET
ejpam-1240	241	10	conditions	condition	NOUN
ejpam-1240	241	11	(	(	PUNCT
ejpam-1240	241	12	pb1	pb1	NOUN
ejpam-1240	241	13	)	)	PUNCT
ejpam-1240	241	14	and	and	CCONJ
ejpam-1240	241	15	(	(	PUNCT
ejpam-1240	241	16	pb2	pb2	PROPN
ejpam-1240	241	17	)	)	PUNCT
ejpam-1240	241	18	.	.	PUNCT
ejpam-1240	242	1	this	this	PRON
ejpam-1240	242	2	shows	show	VERB
ejpam-1240	242	3	that	that	SCONJ
ejpam-1240	242	4	r	r	NOUN
ejpam-1240	242	5	is	be	AUX
ejpam-1240	242	6	a	a	DET
ejpam-1240	242	7	right	right	ADJ
ejpam-1240	242	8	regular	regular	ADJ
ejpam-1240	242	9	partial	partial	ADJ
ejpam-1240	242	10	band	band	NOUN
ejpam-1240	242	11	.	.	PUNCT
ejpam-1240	243	1	on	on	ADP
ejpam-1240	243	2	the	the	DET
ejpam-1240	243	3	other	other	ADJ
ejpam-1240	243	4	hand	hand	NOUN
ejpam-1240	243	5	,	,	PUNCT
ejpam-1240	243	6	it	it	PRON
ejpam-1240	243	7	is	be	AUX
ejpam-1240	243	8	obvious	obvious	ADJ
ejpam-1240	243	9	that	that	SCONJ
ejpam-1240	243	10	r	r	NOUN
ejpam-1240	243	11	is	be	AUX
ejpam-1240	243	12	not	not	PART
ejpam-1240	243	13	a	a	DET
ejpam-1240	243	14	left	left	ADJ
ejpam-1240	243	15	regular	regular	ADJ
ejpam-1240	243	16	partial	partial	ADJ
ejpam-1240	243	17	band	band	NOUN
ejpam-1240	243	18	.	.	PUNCT
ejpam-1240	244	1	define	define	VERB
ejpam-1240	244	2	[	[	X
ejpam-1240	244	3	,	,	PUNCT
ejpam-1240	244	4	]	]	X
ejpam-1240	244	5	:	:	PUNCT
ejpam-1240	244	6	r×	r×	NOUN
ejpam-1240	244	7	e(t	e(t	NOUN
ejpam-1240	244	8	)	)	PUNCT
ejpam-1240	244	9	→	→	SYM
ejpam-1240	244	10	t	t	NOUN
ejpam-1240	244	11	by	by	ADP
ejpam-1240	244	12	the	the	DET
ejpam-1240	244	13	rule	rule	NOUN
ejpam-1240	244	14	that	that	SCONJ
ejpam-1240	244	15	[	[	X
ejpam-1240	244	16	f	f	X
ejpam-1240	244	17	,	,	PUNCT
ejpam-1240	244	18	b	b	NOUN
ejpam-1240	244	19	]	]	X
ejpam-1240	244	20	=	=	SYM
ejpam-1240	244	21	b	b	X
ejpam-1240	244	22	,	,	PUNCT
ejpam-1240	244	23	[	[	X
ejpam-1240	244	24	f	f	X
ejpam-1240	244	25	,	,	PUNCT
ejpam-1240	244	26	c	c	NOUN
ejpam-1240	244	27	]	]	X
ejpam-1240	244	28	=	=	SYM
ejpam-1240	244	29	bc	bc	PROPN
ejpam-1240	244	30	,	,	PUNCT
ejpam-1240	244	31	[	[	X
ejpam-1240	244	32	b	b	X
ejpam-1240	244	33	,	,	PUNCT
ejpam-1240	244	34	b	b	NOUN
ejpam-1240	244	35	]	]	X
ejpam-1240	244	36	=	=	SYM
ejpam-1240	244	37	b	b	NOUN
ejpam-1240	244	38	,	,	PUNCT
ejpam-1240	244	39	[	[	X
ejpam-1240	244	40	b	b	X
ejpam-1240	244	41	,	,	PUNCT
ejpam-1240	244	42	c	c	NOUN
ejpam-1240	244	43	]	]	X
ejpam-1240	244	44	=	=	SYM
ejpam-1240	244	45	bc	bc	PROPN
ejpam-1240	244	46	,	,	PUNCT
ejpam-1240	244	47	[	[	X
ejpam-1240	244	48	c	c	X
ejpam-1240	244	49	,	,	PUNCT
ejpam-1240	244	50	b	b	X
ejpam-1240	244	51	]	]	X
ejpam-1240	244	52	=	=	SYM
ejpam-1240	244	53	cb	cb	PROPN
ejpam-1240	244	54	,	,	PUNCT
ejpam-1240	244	55	[	[	X
ejpam-1240	244	56	c	c	X
ejpam-1240	244	57	,	,	PUNCT
ejpam-1240	244	58	c	c	X
ejpam-1240	244	59	]	]	X
ejpam-1240	244	60	=	=	SYM
ejpam-1240	244	61	c	c	NOUN
ejpam-1240	244	62	.	.	PUNCT
ejpam-1240	245	1	then	then	ADV
ejpam-1240	245	2	,	,	PUNCT
ejpam-1240	245	3	it	it	PRON
ejpam-1240	245	4	is	be	AUX
ejpam-1240	245	5	trivial	trivial	ADJ
ejpam-1240	245	6	to	to	PART
ejpam-1240	245	7	see	see	VERB
ejpam-1240	245	8	that	that	PRON
ejpam-1240	245	9	[	[	X
ejpam-1240	245	10	,	,	PUNCT
ejpam-1240	245	11	]	]	PUNCT
ejpam-1240	245	12	satisfies	satisfy	VERB
ejpam-1240	245	13	the	the	DET
ejpam-1240	245	14	conditions	condition	NOUN
ejpam-1240	245	15	(	(	PUNCT
ejpam-1240	245	16	gi2	gi2	NOUN
ejpam-1240	245	17	)	)	PUNCT
ejpam-1240	245	18	and	and	CCONJ
ejpam-1240	245	19	(	(	PUNCT
ejpam-1240	245	20	gi3	gi3	PROPN
ejpam-1240	245	21	)	)	PUNCT
ejpam-1240	245	22	.	.	PUNCT
ejpam-1240	246	1	compute	compute	PROPN
ejpam-1240	247	1	[	[	X
ejpam-1240	247	2	fb	fb	INTJ
ejpam-1240	247	3	,	,	PUNCT
ejpam-1240	247	4	b	b	NOUN
ejpam-1240	247	5	]	]	X
ejpam-1240	247	6	=	=	PUNCT
ejpam-1240	248	1	[	[	X
ejpam-1240	248	2	b	b	X
ejpam-1240	248	3	,	,	PUNCT
ejpam-1240	248	4	b	b	NOUN
ejpam-1240	248	5	]	]	X
ejpam-1240	248	6	=	=	SYM
ejpam-1240	248	7	b	b	X
ejpam-1240	248	8	=	=	PUNCT
ejpam-1240	248	9	bb	bb	NOUN
ejpam-1240	248	10	=	=	PUNCT
ejpam-1240	249	1	[	[	X
ejpam-1240	249	2	f	f	X
ejpam-1240	249	3	,	,	PUNCT
ejpam-1240	249	4	b][b	b][b	PROPN
ejpam-1240	249	5	,	,	PUNCT
ejpam-1240	249	6	b	b	X
ejpam-1240	249	7	]	]	X
ejpam-1240	249	8	,	,	PUNCT
ejpam-1240	249	9	[	[	X
ejpam-1240	249	10	fb	fb	INTJ
ejpam-1240	249	11	,	,	PUNCT
ejpam-1240	249	12	c	c	X
ejpam-1240	249	13	]	]	PUNCT
ejpam-1240	249	14	=	=	PUNCT
ejpam-1240	250	1	[	[	X
ejpam-1240	250	2	b	b	X
ejpam-1240	250	3	,	,	PUNCT
ejpam-1240	250	4	c	c	NOUN
ejpam-1240	250	5	]	]	X
ejpam-1240	250	6	=	=	PUNCT
ejpam-1240	250	7	bc	bc	PROPN
ejpam-1240	251	1	=	=	PUNCT
ejpam-1240	252	1	[	[	X
ejpam-1240	252	2	f	f	X
ejpam-1240	252	3	,	,	PUNCT
ejpam-1240	252	4	b][f	b][f	NOUN
ejpam-1240	252	5	,	,	PUNCT
ejpam-1240	252	6	c	c	X
ejpam-1240	252	7	]	]	PUNCT
ejpam-1240	252	8	,	,	PUNCT
ejpam-1240	252	9	[	[	X
ejpam-1240	252	10	bf	bf	ADP
ejpam-1240	252	11	,	,	PUNCT
ejpam-1240	252	12	b	b	NOUN
ejpam-1240	252	13	]	]	X
ejpam-1240	252	14	=	=	PUNCT
ejpam-1240	253	1	[	[	X
ejpam-1240	253	2	f	f	X
ejpam-1240	253	3	,	,	PUNCT
ejpam-1240	253	4	b	b	NOUN
ejpam-1240	253	5	]	]	X
ejpam-1240	253	6	=	=	SYM
ejpam-1240	253	7	b	b	X
ejpam-1240	253	8	=	=	PUNCT
ejpam-1240	254	1	[	[	X
ejpam-1240	254	2	b	b	X
ejpam-1240	254	3	,	,	PUNCT
ejpam-1240	254	4	b][f	b][f	NOUN
ejpam-1240	254	5	,	,	PUNCT
ejpam-1240	254	6	b	b	NOUN
ejpam-1240	254	7	]	]	X
ejpam-1240	254	8	,	,	PUNCT
ejpam-1240	254	9	[	[	X
ejpam-1240	254	10	bf	bf	NOUN
ejpam-1240	254	11	,	,	PUNCT
ejpam-1240	254	12	c	c	NOUN
ejpam-1240	254	13	]	]	PUNCT
ejpam-1240	254	14	=	=	PUNCT
ejpam-1240	255	1	[	[	X
ejpam-1240	255	2	f	f	X
ejpam-1240	255	3	,	,	PUNCT
ejpam-1240	255	4	c	c	NOUN
ejpam-1240	255	5	]	]	X
ejpam-1240	255	6	=	=	PUNCT
ejpam-1240	255	7	bc	bc	PROPN
ejpam-1240	255	8	=	=	PUNCT
ejpam-1240	256	1	[	[	X
ejpam-1240	256	2	b	b	X
ejpam-1240	256	3	,	,	PUNCT
ejpam-1240	256	4	b][f	b][f	NOUN
ejpam-1240	256	5	,	,	PUNCT
ejpam-1240	256	6	c	c	NOUN
ejpam-1240	256	7	]	]	PUNCT
ejpam-1240	256	8	.	.	PUNCT
ejpam-1240	257	1	but	but	CCONJ
ejpam-1240	257	2	in	in	ADP
ejpam-1240	257	3	r	r	NOUN
ejpam-1240	257	4	,	,	PUNCT
ejpam-1240	257	5	only	only	ADV
ejpam-1240	257	6	b	b	PROPN
ejpam-1240	257	7	and	and	CCONJ
ejpam-1240	257	8	f	f	PROPN
ejpam-1240	257	9	,	,	PUNCT
ejpam-1240	257	10	and	and	CCONJ
ejpam-1240	257	11	f	f	PROPN
ejpam-1240	257	12	and	and	CCONJ
ejpam-1240	257	13	b	b	PROPN
ejpam-1240	257	14	are	be	AUX
ejpam-1240	257	15	defined	define	VERB
ejpam-1240	257	16	.	.	PUNCT
ejpam-1240	258	1	thus	thus	ADV
ejpam-1240	258	2	,	,	PUNCT
ejpam-1240	258	3	[	[	X
ejpam-1240	258	4	,	,	PUNCT
ejpam-1240	258	5	]	]	PUNCT
ejpam-1240	258	6	satisfies	satisfy	VERB
ejpam-1240	258	7	the	the	DET
ejpam-1240	258	8	conditions	condition	NOUN
ejpam-1240	258	9	(	(	PUNCT
ejpam-1240	258	10	gi1	gi1	NOUN
ejpam-1240	258	11	)	)	PUNCT
ejpam-1240	258	12	.	.	PUNCT
ejpam-1240	259	1	therefore	therefore	ADV
ejpam-1240	259	2	,	,	PUNCT
ejpam-1240	259	3	(	(	PUNCT
ejpam-1240	259	4	t	t	PROPN
ejpam-1240	259	5	;	;	PUNCT
ejpam-1240	259	6	e(t	e(t	PROPN
ejpam-1240	259	7	)	)	PUNCT
ejpam-1240	259	8	,	,	PUNCT
ejpam-1240	259	9	r	r	NOUN
ejpam-1240	259	10	;	;	PUNCT
ejpam-1240	259	11	[	[	X
ejpam-1240	259	12	,	,	PUNCT
ejpam-1240	259	13	]	]	X
ejpam-1240	259	14	)	)	PUNCT
ejpam-1240	259	15	is	be	AUX
ejpam-1240	259	16	indeed	indeed	ADV
ejpam-1240	259	17	a	a	DET
ejpam-1240	259	18	gi	gi	NOUN
ejpam-1240	259	19	-	-	PUNCT
ejpam-1240	259	20	system	system	NOUN
ejpam-1240	259	21	.	.	PUNCT
ejpam-1240	260	1	now	now	ADV
ejpam-1240	260	2	,	,	PUNCT
ejpam-1240	260	3	define	define	VERB
ejpam-1240	260	4	an	an	DET
ejpam-1240	260	5	order	order	NOUN
ejpam-1240	260	6	on	on	ADP
ejpam-1240	260	7	r	r	NOUN
ejpam-1240	260	8	by	by	ADP
ejpam-1240	260	9	the	the	DET
ejpam-1240	260	10	rule	rule	NOUN
ejpam-1240	260	11	that	that	SCONJ
ejpam-1240	260	12	b	b	X
ejpam-1240	260	13	≤	≤	NUM
ejpam-1240	260	14	b	b	NOUN
ejpam-1240	260	15	,	,	PUNCT
ejpam-1240	260	16	c	c	PROPN
ejpam-1240	260	17	≤	≤	PROPN
ejpam-1240	260	18	c	c	NOUN
ejpam-1240	260	19	,	,	PUNCT
ejpam-1240	260	20	f	f	PROPN
ejpam-1240	260	21	≤	≤	PROPN
ejpam-1240	260	22	f	f	PROPN
ejpam-1240	260	23	and	and	CCONJ
ejpam-1240	260	24	f	f	PROPN
ejpam-1240	260	25	≤	≤	PROPN
ejpam-1240	260	26	b.	b.	PROPN
ejpam-1240	260	27	evidently	evidently	ADV
ejpam-1240	260	28	,	,	PUNCT
ejpam-1240	260	29	≤	≤	NUM
ejpam-1240	260	30	is	be	AUX
ejpam-1240	260	31	well	well	ADV
ejpam-1240	260	32	defined	define	VERB
ejpam-1240	260	33	,	,	PUNCT
ejpam-1240	260	34	and	and	CCONJ
ejpam-1240	260	35	(	(	PUNCT
ejpam-1240	260	36	r,≤	r,≤	PROPN
ejpam-1240	260	37	)	)	PUNCT
ejpam-1240	260	38	is	be	AUX
ejpam-1240	260	39	a	a	DET
ejpam-1240	260	40	naturally	naturally	ADV
ejpam-1240	260	41	ordered	order	VERB
ejpam-1240	260	42	right	right	ADV
ejpam-1240	260	43	regular	regular	ADJ
ejpam-1240	260	44	partial	partial	ADJ
ejpam-1240	260	45	band	band	NOUN
ejpam-1240	260	46	satisfying	satisfy	VERB
ejpam-1240	260	47	condition	condition	NOUN
ejpam-1240	260	48	(	(	PUNCT
ejpam-1240	260	49	c	c	NOUN
ejpam-1240	260	50	)	)	PUNCT
ejpam-1240	260	51	in	in	ADP
ejpam-1240	260	52	theorem	theorem	NOUN
ejpam-1240	260	53	1	1	NUM
ejpam-1240	260	54	.	.	PUNCT
ejpam-1240	260	55	references	reference	NOUN
ejpam-1240	260	56	219	219	NUM
ejpam-1240	260	57	proposition	proposition	NOUN
ejpam-1240	260	58	1	1	NUM
ejpam-1240	260	59	.	.	PUNCT
ejpam-1240	261	1	if	if	SCONJ
ejpam-1240	261	2	we	we	PRON
ejpam-1240	261	3	endow	endow	VERB
ejpam-1240	261	4	t	t	PROPN
ejpam-1240	261	5	with	with	ADP
ejpam-1240	261	6	the	the	DET
ejpam-1240	261	7	trivial	trivial	ADJ
ejpam-1240	261	8	order	order	NOUN
ejpam-1240	261	9	,	,	PUNCT
ejpam-1240	261	10	then	then	ADV
ejpam-1240	261	11	gi(t	gi(t	PUNCT
ejpam-1240	261	12	;	;	PUNCT
ejpam-1240	261	13	e(t	e(t	PROPN
ejpam-1240	261	14	)	)	PUNCT
ejpam-1240	261	15	,	,	PUNCT
ejpam-1240	261	16	r	r	NOUN
ejpam-1240	261	17	;	;	PUNCT
ejpam-1240	261	18	[	[	X
ejpam-1240	261	19	,	,	PUNCT
ejpam-1240	261	20	]	]	X
ejpam-1240	261	21	)	)	PUNCT
ejpam-1240	261	22	forms	form	VERB
ejpam-1240	261	23	a	a	DET
ejpam-1240	261	24	naturally	naturally	ADV
ejpam-1240	261	25	ordered	order	VERB
ejpam-1240	261	26	abundant	abundant	ADJ
ejpam-1240	261	27	semigroup	semigroup	NOUN
ejpam-1240	261	28	in	in	ADP
ejpam-1240	261	29	which	which	PRON
ejpam-1240	261	30	each	each	DET
ejpam-1240	261	31	idempotent	idempotent	NOUN
ejpam-1240	261	32	has	have	VERB
ejpam-1240	261	33	a	a	DET
ejpam-1240	261	34	greatest	great	ADJ
ejpam-1240	261	35	inverse	inverse	NOUN
ejpam-1240	261	36	and	and	CCONJ
ejpam-1240	261	37	which	which	PRON
ejpam-1240	261	38	is	be	AUX
ejpam-1240	261	39	gregular	gregular	ADJ
ejpam-1240	261	40	and	and	CCONJ
ejpam-1240	261	41	reflexive	reflexive	ADJ
ejpam-1240	261	42	.	.	PUNCT
ejpam-1240	262	1	proof	proof	NOUN
ejpam-1240	262	2	.	.	PUNCT
ejpam-1240	263	1	obviously	obviously	ADV
ejpam-1240	263	2	,	,	PUNCT
ejpam-1240	263	3	e(t	e(t	PROPN
ejpam-1240	263	4	)	)	PUNCT
ejpam-1240	263	5	satisfies	satisfy	VERB
ejpam-1240	263	6	the	the	DET
ejpam-1240	263	7	condition	condition	NOUN
ejpam-1240	263	8	(	(	PUNCT
ejpam-1240	263	9	b	b	NOUN
ejpam-1240	263	10	)	)	PUNCT
ejpam-1240	263	11	in	in	ADP
ejpam-1240	263	12	theorem	theorem	NOUN
ejpam-1240	263	13	1	1	NUM
ejpam-1240	263	14	,	,	PUNCT
ejpam-1240	263	15	under	under	ADP
ejpam-1240	263	16	the	the	DET
ejpam-1240	263	17	trivial	trivial	ADJ
ejpam-1240	263	18	order	order	NOUN
ejpam-1240	263	19	.	.	PUNCT
ejpam-1240	264	1	since	since	SCONJ
ejpam-1240	264	2	[	[	X
ejpam-1240	264	3	f	f	X
ejpam-1240	264	4	,	,	PUNCT
ejpam-1240	264	5	b	b	NOUN
ejpam-1240	264	6	]	]	X
ejpam-1240	264	7	=	=	SYM
ejpam-1240	264	8	b	b	X
ejpam-1240	264	9	=	=	PUNCT
ejpam-1240	265	1	[	[	X
ejpam-1240	265	2	b	b	X
ejpam-1240	265	3	,	,	PUNCT
ejpam-1240	265	4	b	b	NOUN
ejpam-1240	265	5	]	]	PUNCT
ejpam-1240	265	6	and	and	CCONJ
ejpam-1240	265	7	[	[	X
ejpam-1240	265	8	f	f	X
ejpam-1240	265	9	,	,	PUNCT
ejpam-1240	265	10	c	c	NOUN
ejpam-1240	265	11	]	]	X
ejpam-1240	265	12	=	=	PUNCT
ejpam-1240	265	13	bc	bc	PROPN
ejpam-1240	265	14	=	=	PUNCT
ejpam-1240	266	1	[	[	X
ejpam-1240	266	2	b	b	X
ejpam-1240	266	3	,	,	PUNCT
ejpam-1240	266	4	c	c	NOUN
ejpam-1240	266	5	]	]	X
ejpam-1240	266	6	,	,	PUNCT
ejpam-1240	266	7	(	(	PUNCT
ejpam-1240	266	8	t	t	PROPN
ejpam-1240	266	9	;	;	PUNCT
ejpam-1240	266	10	e(t	e(t	PROPN
ejpam-1240	266	11	)	)	PUNCT
ejpam-1240	266	12	,	,	PUNCT
ejpam-1240	266	13	r	r	NOUN
ejpam-1240	266	14	;	;	PUNCT
ejpam-1240	266	15	[	[	X
ejpam-1240	266	16	,	,	PUNCT
ejpam-1240	266	17	]	]	X
ejpam-1240	266	18	)	)	PUNCT
ejpam-1240	266	19	satisfies	satisfy	VERB
ejpam-1240	266	20	the	the	DET
ejpam-1240	266	21	condition	condition	NOUN
ejpam-1240	266	22	(	(	PUNCT
ejpam-1240	266	23	d	d	NOUN
ejpam-1240	266	24	)	)	PUNCT
ejpam-1240	266	25	in	in	ADP
ejpam-1240	266	26	theorem	theorem	NOUN
ejpam-1240	266	27	1	1	NUM
ejpam-1240	266	28	.	.	PUNCT
ejpam-1240	267	1	on	on	ADP
ejpam-1240	267	2	the	the	DET
ejpam-1240	267	3	other	other	ADJ
ejpam-1240	267	4	hand	hand	NOUN
ejpam-1240	267	5	,	,	PUNCT
ejpam-1240	267	6	if	if	SCONJ
ejpam-1240	267	7	(	(	PUNCT
ejpam-1240	267	8	u	u	NOUN
ejpam-1240	267	9	,	,	PUNCT
ejpam-1240	267	10	x	x	PROPN
ejpam-1240	267	11	,	,	PUNCT
ejpam-1240	267	12	v	v	NOUN
ejpam-1240	267	13	)	)	PUNCT
ejpam-1240	267	14	∈	∈	PROPN
ejpam-1240	267	15	gi(t	gi(t	NOUN
ejpam-1240	267	16	;	;	PUNCT
ejpam-1240	267	17	e(t	e(t	PROPN
ejpam-1240	267	18	)	)	PUNCT
ejpam-1240	267	19	,	,	PUNCT
ejpam-1240	267	20	r	r	NOUN
ejpam-1240	267	21	;	;	PUNCT
ejpam-1240	267	22	[	[	X
ejpam-1240	267	23	,	,	PUNCT
ejpam-1240	267	24	]	]	X
ejpam-1240	267	25	)	)	PUNCT
ejpam-1240	267	26	is	be	AUX
ejpam-1240	267	27	regular	regular	ADJ
ejpam-1240	267	28	and	and	CCONJ
ejpam-1240	267	29	(	(	PUNCT
ejpam-1240	267	30	m	m	PROPN
ejpam-1240	267	31	,	,	PUNCT
ejpam-1240	267	32	y	y	PROPN
ejpam-1240	267	33	,	,	PUNCT
ejpam-1240	267	34	n	n	CCONJ
ejpam-1240	267	35	)	)	PUNCT
ejpam-1240	267	36	is	be	AUX
ejpam-1240	267	37	an	an	DET
ejpam-1240	267	38	inverse	inverse	NOUN
ejpam-1240	267	39	of	of	ADP
ejpam-1240	267	40	(	(	PUNCT
ejpam-1240	267	41	u	u	NOUN
ejpam-1240	267	42	,	,	PUNCT
ejpam-1240	267	43	x	x	PROPN
ejpam-1240	267	44	,	,	PUNCT
ejpam-1240	267	45	v	v	NOUN
ejpam-1240	267	46	)	)	PUNCT
ejpam-1240	267	47	,	,	PUNCT
ejpam-1240	267	48	then	then	ADV
ejpam-1240	267	49	(	(	PUNCT
ejpam-1240	267	50	u	u	INTJ
ejpam-1240	267	51	,	,	PUNCT
ejpam-1240	267	52	x	x	PROPN
ejpam-1240	267	53	,	,	PUNCT
ejpam-1240	267	54	v	v	NOUN
ejpam-1240	267	55	)	)	PUNCT
ejpam-1240	267	56	(	(	PUNCT
ejpam-1240	267	57	m	m	PROPN
ejpam-1240	267	58	,	,	PUNCT
ejpam-1240	267	59	y	y	PROPN
ejpam-1240	267	60	,	,	PUNCT
ejpam-1240	267	61	n)(u	n)(u	ADJ
ejpam-1240	267	62	,	,	PUNCT
ejpam-1240	267	63	x	x	SYM
ejpam-1240	267	64	,	,	PUNCT
ejpam-1240	267	65	v	v	NOUN
ejpam-1240	267	66	)	)	PUNCT
ejpam-1240	267	67	=	=	SYM
ejpam-1240	267	68	(	(	PUNCT
ejpam-1240	267	69	u	u	NOUN
ejpam-1240	267	70	,	,	PUNCT
ejpam-1240	267	71	x	x	PROPN
ejpam-1240	267	72	,	,	PUNCT
ejpam-1240	267	73	v	v	NOUN
ejpam-1240	267	74	)	)	PUNCT
ejpam-1240	267	75	,	,	PUNCT
ejpam-1240	267	76	and	and	CCONJ
ejpam-1240	267	77	by	by	ADP
ejpam-1240	267	78	comparing	compare	VERB
ejpam-1240	267	79	the	the	DET
ejpam-1240	267	80	components	component	NOUN
ejpam-1240	267	81	,	,	PUNCT
ejpam-1240	267	82	we	we	PRON
ejpam-1240	267	83	have	have	VERB
ejpam-1240	267	84	x[v	x[v	PROPN
ejpam-1240	267	85	,	,	PUNCT
ejpam-1240	267	86	m]y[w	m]y[w	NOUN
ejpam-1240	267	87	,	,	PUNCT
ejpam-1240	267	88	u]x	u]x	ADJ
ejpam-1240	267	89	=	=	PUNCT
ejpam-1240	267	90	x	x	X
ejpam-1240	267	91	,	,	PUNCT
ejpam-1240	267	92	where	where	SCONJ
ejpam-1240	267	93	w	w	NOUN
ejpam-1240	267	94	=	=	SYM
ejpam-1240	267	95	(	(	PUNCT
ejpam-1240	267	96	x[v	x[v	PROPN
ejpam-1240	267	97	,	,	PUNCT
ejpam-1240	267	98	m]y)∗n	m]y)∗n	NOUN
ejpam-1240	267	99	so	so	SCONJ
ejpam-1240	267	100	that	that	SCONJ
ejpam-1240	267	101	x	x	X
ejpam-1240	268	1	=	=	PUNCT
ejpam-1240	268	2	y	y	NOUN
ejpam-1240	268	3	=	=	PUNCT
ejpam-1240	269	1	[	[	X
ejpam-1240	269	2	v	v	NOUN
ejpam-1240	269	3	,	,	PUNCT
ejpam-1240	269	4	m	m	VERB
ejpam-1240	269	5	]	]	X
ejpam-1240	269	6	=	=	PUNCT
ejpam-1240	270	1	[	[	X
ejpam-1240	270	2	w	w	X
ejpam-1240	270	3	,	,	PUNCT
ejpam-1240	270	4	u	u	NOUN
ejpam-1240	270	5	]	]	X
ejpam-1240	270	6	∈	∈	PROPN
ejpam-1240	270	7	e(t	e(t	PROPN
ejpam-1240	270	8	)	)	PUNCT
ejpam-1240	270	9	since	since	SCONJ
ejpam-1240	270	10	reg(t	reg(t	PROPN
ejpam-1240	270	11	)	)	PUNCT
ejpam-1240	271	1	=	=	PUNCT
ejpam-1240	271	2	{	{	PUNCT
ejpam-1240	271	3	b	b	NOUN
ejpam-1240	271	4	,	,	PUNCT
ejpam-1240	271	5	c	c	NOUN
ejpam-1240	271	6	}	}	PUNCT
ejpam-1240	271	7	.	.	PUNCT
ejpam-1240	272	1	by	by	ADP
ejpam-1240	272	2	using	use	VERB
ejpam-1240	272	3	these	these	DET
ejpam-1240	272	4	equalities	equality	NOUN
ejpam-1240	272	5	,	,	PUNCT
ejpam-1240	272	6	we	we	PRON
ejpam-1240	272	7	can	can	AUX
ejpam-1240	272	8	derive	derive	VERB
ejpam-1240	272	9	that	that	SCONJ
ejpam-1240	272	10	u	u	NOUN
ejpam-1240	272	11	=	=	NOUN
ejpam-1240	272	12	x	x	X
ejpam-1240	272	13	,	,	PUNCT
ejpam-1240	272	14	m	m	VERB
ejpam-1240	272	15	=	=	SYM
ejpam-1240	272	16	y	y	PROPN
ejpam-1240	272	17	and	and	CCONJ
ejpam-1240	272	18	n	n	PROPN
ejpam-1240	272	19	,	,	PUNCT
ejpam-1240	272	20	v	v	X
ejpam-1240	272	21	∈	∈	NOUN
ejpam-1240	272	22	rx	rx	NOUN
ejpam-1240	272	23	,	,	PUNCT
ejpam-1240	272	24	and	and	CCONJ
ejpam-1240	272	25	whence	whence	NOUN
ejpam-1240	272	26	(	(	PUNCT
ejpam-1240	272	27	t	t	PROPN
ejpam-1240	272	28	;	;	PUNCT
ejpam-1240	272	29	e(t	e(t	PROPN
ejpam-1240	272	30	)	)	PUNCT
ejpam-1240	272	31	,	,	PUNCT
ejpam-1240	273	1	r	r	NOUN
ejpam-1240	273	2	;	;	PUNCT
ejpam-1240	273	3	[	[	X
ejpam-1240	273	4	,	,	PUNCT
ejpam-1240	273	5	]	]	X
ejpam-1240	273	6	)	)	PUNCT
ejpam-1240	273	7	satisfies	satisfy	VERB
ejpam-1240	273	8	the	the	DET
ejpam-1240	273	9	condition	condition	NOUN
ejpam-1240	273	10	(	(	PUNCT
ejpam-1240	273	11	e	e	NOUN
ejpam-1240	273	12	)	)	PUNCT
ejpam-1240	273	13	in	in	ADP
ejpam-1240	273	14	theorem	theorem	NOUN
ejpam-1240	273	15	1	1	NUM
ejpam-1240	273	16	.	.	PUNCT
ejpam-1240	273	17	consequently	consequently	ADV
ejpam-1240	273	18	,	,	PUNCT
ejpam-1240	273	19	the	the	DET
ejpam-1240	273	20	system	system	NOUN
ejpam-1240	273	21	gi(t	gi(t	NOUN
ejpam-1240	273	22	;	;	PUNCT
ejpam-1240	273	23	e(t	e(t	PROPN
ejpam-1240	273	24	)	)	PUNCT
ejpam-1240	273	25	,	,	PUNCT
ejpam-1240	273	26	r	r	NOUN
ejpam-1240	273	27	;	;	PUNCT
ejpam-1240	273	28	[	[	X
ejpam-1240	273	29	,	,	PUNCT
ejpam-1240	273	30	]	]	X
ejpam-1240	273	31	)	)	PUNCT
ejpam-1240	273	32	forms	form	VERB
ejpam-1240	273	33	a	a	DET
ejpam-1240	273	34	naturally	naturally	ADV
ejpam-1240	273	35	ordered	order	VERB
ejpam-1240	273	36	abundant	abundant	ADJ
ejpam-1240	273	37	semigroup	semigroup	NOUN
ejpam-1240	273	38	which	which	PRON
ejpam-1240	273	39	is	be	AUX
ejpam-1240	273	40	g	g	NOUN
ejpam-1240	273	41	-	-	PUNCT
ejpam-1240	273	42	regular	regular	ADJ
ejpam-1240	273	43	and	and	CCONJ
ejpam-1240	273	44	reflexive	reflexive	ADJ
ejpam-1240	273	45	,	,	PUNCT
ejpam-1240	273	46	for	for	ADP
ejpam-1240	273	47	which	which	PRON
ejpam-1240	273	48	,	,	PUNCT
ejpam-1240	273	49	each	each	DET
ejpam-1240	273	50	idempotent	idempotent	NOUN
ejpam-1240	273	51	has	have	VERB
ejpam-1240	273	52	a	a	DET
ejpam-1240	273	53	greatest	great	ADJ
ejpam-1240	273	54	inverse	inverse	NOUN
ejpam-1240	273	55	.	.	PUNCT
ejpam-1240	274	1	this	this	PRON
ejpam-1240	274	2	completes	complete	VERB
ejpam-1240	274	3	the	the	DET
ejpam-1240	274	4	proof	proof	NOUN
ejpam-1240	274	5	.	.	PUNCT
ejpam-1240	275	1	acknowledgements	acknowledgement	VERB
ejpam-1240	275	2	the	the	DET
ejpam-1240	275	3	research	research	NOUN
ejpam-1240	275	4	of	of	ADP
ejpam-1240	275	5	xiaojiang	xiaojiang	PROPN
ejpam-1240	275	6	guo	guo	PROPN
ejpam-1240	275	7	is	be	AUX
ejpam-1240	275	8	supported	support	VERB
ejpam-1240	275	9	by	by	ADP
ejpam-1240	275	10	an	an	DET
ejpam-1240	275	11	nnsf	nnsf	PROPN
ejpam-1240	275	12	grant	grant	NOUN
ejpam-1240	275	13	of	of	ADP
ejpam-1240	275	14	china	china	PROPN
ejpam-1240	275	15	(	(	PUNCT
ejpam-1240	275	16	grant	grant	VERB
ejpam-1240	275	17	#	#	NOUN
ejpam-1240	275	18	:	:	PUNCT
ejpam-1240	275	19	10961014	10961014	NUM
ejpam-1240	275	20	)	)	PUNCT
ejpam-1240	275	21	;	;	PUNCT
ejpam-1240	275	22	the	the	DET
ejpam-1240	275	23	nsf	nsf	PROPN
ejpam-1240	275	24	of	of	ADP
ejpam-1240	275	25	jiangxi	jiangxi	PROPN
ejpam-1240	275	26	province	province	PROPN
ejpam-1240	275	27	;	;	PUNCT
ejpam-1240	275	28	the	the	DET
ejpam-1240	275	29	sf	sf	PROPN
ejpam-1240	275	30	of	of	ADP
ejpam-1240	275	31	education	education	PROPN
ejpam-1240	275	32	department	department	PROPN
ejpam-1240	275	33	of	of	ADP
ejpam-1240	275	34	jiangxi	jiangxi	PROPN
ejpam-1240	275	35	province	province	PROPN
ejpam-1240	275	36	and	and	CCONJ
ejpam-1240	275	37	a	a	DET
ejpam-1240	275	38	grant	grant	NOUN
ejpam-1240	275	39	of	of	ADP
ejpam-1240	275	40	the	the	DET
ejpam-1240	275	41	sf	sf	PROPN
ejpam-1240	275	42	of	of	ADP
ejpam-1240	275	43	jiangxi	jiangxi	PROPN
ejpam-1240	275	44	normal	normal	ADJ
ejpam-1240	275	45	university	university	NOUN
ejpam-1240	275	46	.	.	PUNCT
ejpam-1240	276	1	and	and	CCONJ
ejpam-1240	276	2	the	the	DET
ejpam-1240	276	3	research	research	NOUN
ejpam-1240	276	4	of	of	ADP
ejpam-1240	276	5	k.p	k.p	PROPN
ejpam-1240	276	6	.	.	PROPN
ejpam-1240	276	7	shum	shum	PROPN
ejpam-1240	276	8	is	be	AUX
ejpam-1240	276	9	partially	partially	ADV
ejpam-1240	276	10	supported	support	VERB
ejpam-1240	276	11	by	by	ADP
ejpam-1240	276	12	a	a	DET
ejpam-1240	276	13	rgc	rgc	PROPN
ejpam-1240	276	14	direct	direct	ADJ
ejpam-1240	276	15	grant	grant	NOUN
ejpam-1240	276	16	(	(	PUNCT
ejpam-1240	276	17	#	#	SYM
ejpam-1240	276	18	216097/05	216097/05	NUM
ejpam-1240	276	19	-	-	SYM
ejpam-1240	276	20	07	07	NUM
ejpam-1240	276	21	)	)	PUNCT
ejpam-1240	276	22	.	.	PUNCT
ejpam-1240	277	1	references	reference	NOUN
ejpam-1240	277	2	[	[	X
ejpam-1240	277	3	1	1	NUM
ejpam-1240	277	4	]	]	X
ejpam-1240	277	5	t.s	t.s	PROPN
ejpam-1240	277	6	.	.	PROPN
ejpam-1240	277	7	blyth	blyth	PROPN
ejpam-1240	277	8	and	and	CCONJ
ejpam-1240	277	9	r.b	r.b	PROPN
ejpam-1240	277	10	.	.	PROPN
ejpam-1240	277	11	mcfadden	mcfadden	PROPN
ejpam-1240	277	12	,	,	PUNCT
ejpam-1240	277	13	naturally	naturally	ADV
ejpam-1240	277	14	ordered	order	VERB
ejpam-1240	277	15	regular	regular	ADJ
ejpam-1240	277	16	semigroups	semigroup	NOUN
ejpam-1240	277	17	with	with	ADP
ejpam-1240	277	18	a	a	DET
ejpam-1240	277	19	greatest	great	ADJ
ejpam-1240	277	20	idempotnt	idempotnt	NOUN
ejpam-1240	277	21	,	,	PUNCT
ejpam-1240	277	22	proc	proc	NOUN
ejpam-1240	277	23	.	.	PUNCT
ejpam-1240	278	1	roy	roy	PROPN
ejpam-1240	278	2	.	.	PROPN
ejpam-1240	278	3	soc	soc	PROPN
ejpam-1240	278	4	.	.	PUNCT
ejpam-1240	279	1	edinb	edinb	PROPN
ejpam-1240	279	2	.	.	PUNCT
ejpam-1240	279	3	,	,	PUNCT
ejpam-1240	279	4	91a	91a	NOUN
ejpam-1240	279	5	,	,	PUNCT
ejpam-1240	279	6	107	107	NUM
ejpam-1240	279	7	-	-	SYM
ejpam-1240	279	8	122	122	NUM
ejpam-1240	279	9	.	.	PUNCT
ejpam-1240	279	10	1981	1981	NUM
ejpam-1240	279	11	.	.	PUNCT
ejpam-1240	280	1	[	[	X
ejpam-1240	280	2	2	2	NUM
ejpam-1240	280	3	]	]	X
ejpam-1240	280	4	t.s	t.s	PROPN
ejpam-1240	280	5	.	.	PROPN
ejpam-1240	280	6	blyth	blyth	PROPN
ejpam-1240	280	7	and	and	CCONJ
ejpam-1240	280	8	r.b	r.b	PROPN
ejpam-1240	280	9	.	.	PROPN
ejpam-1240	280	10	mcfadden	mcfadden	PROPN
ejpam-1240	280	11	,	,	PUNCT
ejpam-1240	280	12	regular	regular	ADJ
ejpam-1240	280	13	semigroups	semigroup	NOUN
ejpam-1240	280	14	with	with	ADP
ejpam-1240	280	15	multiplicative	multiplicative	ADJ
ejpam-1240	280	16	inverse	inverse	NOUN
ejpam-1240	280	17	transversals	transversal	NOUN
ejpam-1240	280	18	,	,	PUNCT
ejpam-1240	280	19	proc	proc	PROPN
ejpam-1240	280	20	.	.	PUNCT
ejpam-1240	281	1	roy	roy	PROPN
ejpam-1240	281	2	.	.	PROPN
ejpam-1240	281	3	soc	soc	PROPN
ejpam-1240	281	4	.	.	PUNCT
ejpam-1240	282	1	edinb	edinb	PROPN
ejpam-1240	282	2	.	.	PUNCT
ejpam-1240	282	3	,	,	PUNCT
ejpam-1240	282	4	92a	92a	NUM
ejpam-1240	282	5	,	,	PUNCT
ejpam-1240	282	6	253	253	NUM
ejpam-1240	282	7	-	-	SYM
ejpam-1240	282	8	270	270	NUM
ejpam-1240	282	9	.	.	PUNCT
ejpam-1240	282	10	1981	1981	NUM
ejpam-1240	282	11	.	.	PUNCT
ejpam-1240	283	1	[	[	X
ejpam-1240	283	2	3	3	X
ejpam-1240	283	3	]	]	X
ejpam-1240	283	4	t.s	t.s	PROPN
ejpam-1240	283	5	.	.	PROPN
ejpam-1240	283	6	blyth	blyth	PROPN
ejpam-1240	283	7	and	and	CCONJ
ejpam-1240	283	8	r.b	r.b	PROPN
ejpam-1240	283	9	.	.	PROPN
ejpam-1240	283	10	mcfadden	mcfadden	PROPN
ejpam-1240	283	11	,	,	PUNCT
ejpam-1240	283	12	maximum	maximum	ADJ
ejpam-1240	283	13	idempotents	idempotent	NOUN
ejpam-1240	283	14	in	in	ADP
ejpam-1240	283	15	naturally	naturally	ADV
ejpam-1240	283	16	ordered	order	VERB
ejpam-1240	283	17	regular	regular	ADJ
ejpam-1240	283	18	semigroups	semigroup	NOUN
ejpam-1240	283	19	,	,	PUNCT
ejpam-1240	283	20	proc	proc	NOUN
ejpam-1240	283	21	.	.	PUNCT
ejpam-1240	284	1	edinb	edinb	PROPN
ejpam-1240	284	2	.	.	PUNCT
ejpam-1240	285	1	math	math	NOUN
ejpam-1240	285	2	.	.	PUNCT
ejpam-1240	286	1	soc	soc	PROPN
ejpam-1240	286	2	.	.	PROPN
ejpam-1240	286	3	,	,	PUNCT
ejpam-1240	286	4	26	26	NUM
ejpam-1240	286	5	,	,	PUNCT
ejpam-1240	286	6	213	213	NUM
ejpam-1240	286	7	-	-	SYM
ejpam-1240	286	8	220	220	NUM
ejpam-1240	286	9	.	.	PUNCT
ejpam-1240	286	10	1983	1983	NUM
ejpam-1240	286	11	.	.	PUNCT
ejpam-1240	287	1	[	[	X
ejpam-1240	287	2	4	4	NUM
ejpam-1240	287	3	]	]	X
ejpam-1240	287	4	t.s	t.s	PROPN
ejpam-1240	287	5	.	.	PROPN
ejpam-1240	287	6	blyth	blyth	PROPN
ejpam-1240	287	7	and	and	CCONJ
ejpam-1240	287	8	g.a.p	g.a.p	PROPN
ejpam-1240	287	9	.	.	PUNCT
ejpam-1240	287	10	pinto	pinto	NOUN
ejpam-1240	287	11	,	,	PUNCT
ejpam-1240	287	12	on	on	ADP
ejpam-1240	287	13	naturally	naturally	ADV
ejpam-1240	287	14	ordered	order	VERB
ejpam-1240	287	15	regular	regular	ADJ
ejpam-1240	287	16	semigroups	semigroup	NOUN
ejpam-1240	287	17	with	with	ADP
ejpam-1240	287	18	biggest	big	ADJ
ejpam-1240	287	19	inverses	inverse	NOUN
ejpam-1240	287	20	,	,	PUNCT
ejpam-1240	287	21	semigroup	semigroup	PROPN
ejpam-1240	287	22	forum	forum	PROPN
ejpam-1240	287	23	,	,	PUNCT
ejpam-1240	287	24	54	54	NUM
ejpam-1240	287	25	,	,	PUNCT
ejpam-1240	287	26	154	154	NUM
ejpam-1240	287	27	-	-	SYM
ejpam-1240	287	28	165	165	NUM
ejpam-1240	287	29	.	.	PUNCT
ejpam-1240	287	30	1997	1997	NUM
ejpam-1240	287	31	.	.	PUNCT
ejpam-1240	288	1	[	[	X
ejpam-1240	288	2	5	5	NUM
ejpam-1240	288	3	]	]	X
ejpam-1240	288	4	t.s	t.s	PROPN
ejpam-1240	288	5	.	.	PROPN
ejpam-1240	288	6	blyth	blyth	PROPN
ejpam-1240	288	7	and	and	CCONJ
ejpam-1240	288	8	m.h	m.h	PROPN
ejpam-1240	288	9	.	.	PROPN
ejpam-1240	288	10	almeida	almeida	PROPN
ejpam-1240	288	11	santos	santos	PROPN
ejpam-1240	288	12	,	,	PUNCT
ejpam-1240	288	13	on	on	ADP
ejpam-1240	288	14	naturally	naturally	ADV
ejpam-1240	288	15	ordered	order	VERB
ejpam-1240	288	16	regular	regular	ADJ
ejpam-1240	288	17	semigroups	semigroup	NOUN
ejpam-1240	288	18	with	with	ADP
ejpam-1240	288	19	biggest	big	ADJ
ejpam-1240	288	20	idempotents	idempotent	NOUN
ejpam-1240	288	21	,	,	PUNCT
ejpam-1240	288	22	comm	comm	NOUN
ejpam-1240	288	23	.	.	PUNCT
ejpam-1240	289	1	algebra	algebra	NOUN
ejpam-1240	289	2	,	,	PUNCT
ejpam-1240	289	3	21	21	NUM
ejpam-1240	289	4	,	,	PUNCT
ejpam-1240	289	5	1761	1761	NUM
ejpam-1240	289	6	-	-	SYM
ejpam-1240	289	7	1771	1771	NUM
ejpam-1240	289	8	.	.	PUNCT
ejpam-1240	290	1	1993	1993	NUM
ejpam-1240	291	1	[	[	X
ejpam-1240	291	2	6	6	NUM
ejpam-1240	291	3	]	]	X
ejpam-1240	291	4	t.s	t.s	PROPN
ejpam-1240	291	5	.	.	PROPN
ejpam-1240	291	6	blyth	blyth	PROPN
ejpam-1240	291	7	and	and	CCONJ
ejpam-1240	291	8	m.h	m.h	PROPN
ejpam-1240	291	9	.	.	PROPN
ejpam-1240	291	10	alemeida	alemeida	PROPN
ejpam-1240	291	11	santos	santos	PROPN
ejpam-1240	291	12	,	,	PUNCT
ejpam-1240	291	13	naturally	naturally	ADV
ejpam-1240	291	14	ordered	order	VERB
ejpam-1240	291	15	orthodox	orthodox	NOUN
ejpam-1240	291	16	dubreil	dubreil	NOUN
ejpam-1240	291	17	-	-	PUNCT
ejpam-1240	291	18	jacotin	jacotin	NOUN
ejpam-1240	291	19	semigroups	semigroup	NOUN
ejpam-1240	291	20	,	,	PUNCT
ejpam-1240	291	21	comm	comm	NOUN
ejpam-1240	291	22	.	.	PUNCT
ejpam-1240	292	1	algebra	algebra	NOUN
ejpam-1240	292	2	,	,	PUNCT
ejpam-1240	292	3	20	20	NUM
ejpam-1240	292	4	,	,	PUNCT
ejpam-1240	292	5	1167	1167	NUM
ejpam-1240	292	6	-	-	SYM
ejpam-1240	292	7	1199	1199	NUM
ejpam-1240	292	8	.	.	PUNCT
ejpam-1240	292	9	1992	1992	NUM
ejpam-1240	292	10	.	.	PUNCT
ejpam-1240	293	1	[	[	X
ejpam-1240	293	2	7	7	X
ejpam-1240	293	3	]	]	X
ejpam-1240	293	4	t.s	t.s	PROPN
ejpam-1240	293	5	.	.	PROPN
ejpam-1240	293	6	blyth	blyth	PROPN
ejpam-1240	293	7	and	and	CCONJ
ejpam-1240	293	8	m.h	m.h	PROPN
ejpam-1240	293	9	.	.	PROPN
ejpam-1240	293	10	alemeida	alemeida	PROPN
ejpam-1240	293	11	santos	santos	PROPN
ejpam-1240	293	12	,	,	PUNCT
ejpam-1240	293	13	naturally	naturally	ADV
ejpam-1240	293	14	ordered	order	VERB
ejpam-1240	293	15	regular	regular	ADJ
ejpam-1240	293	16	semigroups	semigroup	NOUN
ejpam-1240	293	17	with	with	ADP
ejpam-1240	293	18	an	an	DET
ejpam-1240	293	19	inverse	inverse	NOUN
ejpam-1240	293	20	monoid	monoid	NOUN
ejpam-1240	293	21	transversal	transversal	NOUN
ejpam-1240	293	22	,	,	PUNCT
ejpam-1240	293	23	semigroup	semigroup	PROPN
ejpam-1240	293	24	forum	forum	PROPN
ejpam-1240	293	25	,	,	PUNCT
ejpam-1240	293	26	76	76	NUM
ejpam-1240	293	27	,	,	PUNCT
ejpam-1240	293	28	71	71	NUM
ejpam-1240	293	29	-	-	SYM
ejpam-1240	293	30	86	86	NUM
ejpam-1240	293	31	.	.	PUNCT
ejpam-1240	293	32	2008	2008	NUM
ejpam-1240	293	33	.	.	PUNCT
ejpam-1240	294	1	references	reference	NOUN
ejpam-1240	294	2	220	220	NUM
ejpam-1240	295	1	[	[	NOUN
ejpam-1240	295	2	8	8	NUM
ejpam-1240	295	3	]	]	X
ejpam-1240	295	4	a.	a.	PROPN
ejpam-1240	295	5	el	el	PROPN
ejpam-1240	295	6	-	-	PUNCT
ejpam-1240	295	7	qallali	qallali	PROPN
ejpam-1240	295	8	,	,	PUNCT
ejpam-1240	295	9	abundant	abundant	ADJ
ejpam-1240	295	10	semigroups	semigroup	NOUN
ejpam-1240	295	11	with	with	ADP
ejpam-1240	295	12	a	a	DET
ejpam-1240	295	13	multiplicative	multiplicative	ADJ
ejpam-1240	295	14	type	type	NOUN
ejpam-1240	295	15	-	-	PUNCT
ejpam-1240	295	16	a	a	DET
ejpam-1240	295	17	transversal	transversal	NOUN
ejpam-1240	295	18	,	,	PUNCT
ejpam-1240	295	19	semigroup	semigroup	PROPN
ejpam-1240	295	20	forum	forum	PROPN
ejpam-1240	295	21	,	,	PUNCT
ejpam-1240	295	22	47	47	NUM
ejpam-1240	295	23	,	,	PUNCT
ejpam-1240	295	24	327	327	NUM
ejpam-1240	295	25	-	-	SYM
ejpam-1240	295	26	340	340	NUM
ejpam-1240	295	27	.	.	PUNCT
ejpam-1240	296	1	1993	1993	NUM
ejpam-1240	297	1	[	[	X
ejpam-1240	297	2	9	9	NUM
ejpam-1240	297	3	]	]	X
ejpam-1240	297	4	j.b	j.b	PROPN
ejpam-1240	297	5	.	.	PROPN
ejpam-1240	297	6	fountain	fountain	NOUN
ejpam-1240	297	7	,	,	PUNCT
ejpam-1240	297	8	adequate	adequate	ADJ
ejpam-1240	297	9	semigroups	semigroup	NOUN
ejpam-1240	297	10	,	,	PUNCT
ejpam-1240	297	11	proc	proc	NOUN
ejpam-1240	297	12	.	.	PUNCT
ejpam-1240	298	1	edinb	edinb	PROPN
ejpam-1240	298	2	.	.	PUNCT
ejpam-1240	299	1	math	math	NOUN
ejpam-1240	299	2	.	.	PUNCT
ejpam-1240	300	1	soc	soc	PROPN
ejpam-1240	300	2	.	.	PUNCT
ejpam-1240	301	1	22	22	NUM
ejpam-1240	301	2	,	,	PUNCT
ejpam-1240	301	3	113	113	NUM
ejpam-1240	301	4	-	-	SYM
ejpam-1240	301	5	125	125	NUM
ejpam-1240	301	6	.	.	PUNCT
ejpam-1240	302	1	1979	1979	NUM
ejpam-1240	302	2	.	.	PUNCT
ejpam-1240	303	1	[	[	X
ejpam-1240	303	2	10	10	NUM
ejpam-1240	303	3	]	]	X
ejpam-1240	303	4	j.b	j.b	PROPN
ejpam-1240	303	5	.	.	PROPN
ejpam-1240	303	6	fountain	fountain	NOUN
ejpam-1240	303	7	,	,	PUNCT
ejpam-1240	303	8	abundant	abundant	ADJ
ejpam-1240	303	9	semigroups	semigroup	NOUN
ejpam-1240	303	10	,	,	PUNCT
ejpam-1240	303	11	proc	proc	NOUN
ejpam-1240	303	12	.	.	PUNCT
ejpam-1240	304	1	london	london	PROPN
ejpam-1240	304	2	math	math	PROPN
ejpam-1240	304	3	.	.	PUNCT
ejpam-1240	305	1	soc	soc	PROPN
ejpam-1240	305	2	.	.	PUNCT
ejpam-1240	306	1	44	44	NUM
ejpam-1240	306	2	,	,	PUNCT
ejpam-1240	306	3	103	103	NUM
ejpam-1240	306	4	-	-	SYM
ejpam-1240	306	5	129	129	NUM
ejpam-1240	306	6	.	.	PUNCT
ejpam-1240	307	1	1982	1982	NUM
ejpam-1240	307	2	.	.	PUNCT
ejpam-1240	308	1	[	[	X
ejpam-1240	308	2	11	11	NUM
ejpam-1240	308	3	]	]	X
ejpam-1240	308	4	x.j	x.j	PROPN
ejpam-1240	308	5	.	.	PUNCT
ejpam-1240	308	6	guo	guo	PROPN
ejpam-1240	308	7	,	,	PUNCT
ejpam-1240	308	8	amenably	amenably	ADV
ejpam-1240	308	9	natural	natural	ADJ
ejpam-1240	308	10	order	order	NOUN
ejpam-1240	308	11	abundant	abundant	ADJ
ejpam-1240	308	12	semigroups	semigroup	NOUN
ejpam-1240	308	13	,	,	PUNCT
ejpam-1240	308	14	adv	adv	PROPN
ejpam-1240	308	15	.	.	PUNCT
ejpam-1240	308	16	math	math	PROPN
ejpam-1240	308	17	.	.	PUNCT
ejpam-1240	309	1	(	(	PUNCT
ejpam-1240	309	2	china	china	PROPN
ejpam-1240	309	3	)	)	PUNCT
ejpam-1240	309	4	,	,	PUNCT
ejpam-1240	309	5	30,683690	30,683690	NUM
ejpam-1240	309	6	.	.	PUNCT
ejpam-1240	309	7	2001	2001	NUM
ejpam-1240	309	8	.	.	PUNCT
ejpam-1240	310	1	[	[	X
ejpam-1240	310	2	12	12	NUM
ejpam-1240	310	3	]	]	X
ejpam-1240	310	4	x.j	x.j	PROPN
ejpam-1240	310	5	.	.	PUNCT
ejpam-1240	310	6	guo	guo	PROPN
ejpam-1240	310	7	,	,	PUNCT
ejpam-1240	310	8	c.c	c.c	PROPN
ejpam-1240	310	9	.	.	PROPN
ejpam-1240	310	10	ren	ren	PROPN
ejpam-1240	310	11	and	and	CCONJ
ejpam-1240	310	12	k.p	k.p	PROPN
ejpam-1240	310	13	.	.	PROPN
ejpam-1240	310	14	shum	shum	PROPN
ejpam-1240	310	15	,	,	PUNCT
ejpam-1240	310	16	a	a	DET
ejpam-1240	310	17	structure	structure	NOUN
ejpam-1240	310	18	theorem	theorem	NOUN
ejpam-1240	310	19	of	of	ADP
ejpam-1240	310	20	an	an	DET
ejpam-1240	310	21	ordered	order	VERB
ejpam-1240	310	22	rpp	rpp	NOUN
ejpam-1240	310	23	semigroups	semigroup	NOUN
ejpam-1240	310	24	with	with	ADP
ejpam-1240	310	25	max	max	PROPN
ejpam-1240	310	26	-	-	PUNCT
ejpam-1240	310	27	idempotents	idempotent	NOUN
ejpam-1240	310	28	.	.	PUNCT
ejpam-1240	311	1	to	to	PART
ejpam-1240	311	2	appear	appear	VERB
ejpam-1240	311	3	in	in	ADP
ejpam-1240	311	4	algebra	algebra	NOUN
ejpam-1240	311	5	colloqium	colloqium	NOUN
ejpam-1240	311	6	.	.	PUNCT
ejpam-1240	312	1	[	[	X
ejpam-1240	312	2	13	13	NUM
ejpam-1240	312	3	]	]	SYM
ejpam-1240	312	4	x.j	x.j	PROPN
ejpam-1240	312	5	.	.	PROPN
ejpam-1240	312	6	guo	guo	PROPN
ejpam-1240	312	7	and	and	CCONJ
ejpam-1240	312	8	x.y	x.y	PROPN
ejpam-1240	312	9	.	.	PROPN
ejpam-1240	312	10	xie	xie	PROPN
ejpam-1240	312	11	,	,	PUNCT
ejpam-1240	312	12	naturally	naturally	ADV
ejpam-1240	312	13	ordered	order	VERB
ejpam-1240	312	14	semigroups	semigroup	NOUN
ejpam-1240	312	15	in	in	ADP
ejpam-1240	312	16	which	which	PRON
ejpam-1240	312	17	each	each	DET
ejpam-1240	312	18	idempotent	idempotent	NOUN
ejpam-1240	312	19	has	have	VERB
ejpam-1240	312	20	a	a	DET
ejpam-1240	312	21	greatest	great	ADJ
ejpam-1240	312	22	inverse	inverse	NOUN
ejpam-1240	312	23	,	,	PUNCT
ejpam-1240	312	24	commun	commun	PROPN
ejpam-1240	312	25	.	.	PUNCT
ejpam-1240	313	1	algebra	algebra	PROPN
ejpam-1240	313	2	35	35	NUM
ejpam-1240	313	3	,	,	PUNCT
ejpam-1240	313	4	2324	2324	NUM
ejpam-1240	313	5	-	-	SYM
ejpam-1240	313	6	2339	2339	NUM
ejpam-1240	313	7	.	.	PUNCT
ejpam-1240	314	1	2007	2007	NUM
ejpam-1240	314	2	.	.	PUNCT
ejpam-1240	315	1	[	[	X
ejpam-1240	315	2	14	14	NUM
ejpam-1240	315	3	]	]	X
ejpam-1240	315	4	x.j	x.j	PROPN
ejpam-1240	315	5	.	.	PUNCT
ejpam-1240	315	6	guo	guo	PROPN
ejpam-1240	315	7	,	,	PUNCT
ejpam-1240	315	8	r.h	r.h	PROPN
ejpam-1240	315	9	.	.	PROPN
ejpam-1240	315	10	zhang	zhang	PROPN
ejpam-1240	315	11	and	and	CCONJ
ejpam-1240	315	12	x.n	x.n	PROPN
ejpam-1240	315	13	.	.	PUNCT
ejpam-1240	315	14	li	li	PROPN
ejpam-1240	315	15	,	,	PUNCT
ejpam-1240	315	16	natural	natural	ADJ
ejpam-1240	315	17	dubreil	dubreil	NOUN
ejpam-1240	315	18	-	-	PUNCT
ejpam-1240	315	19	jacotin	jacotin	NOUN
ejpam-1240	315	20	abundant	abundant	ADJ
ejpam-1240	315	21	semigroups	semigroup	NOUN
ejpam-1240	315	22	,	,	PUNCT
ejpam-1240	315	23	j.	j.	PROPN
ejpam-1240	315	24	math	math	PROPN
ejpam-1240	315	25	.	.	PUNCT
ejpam-1240	316	1	(	(	PUNCT
ejpam-1240	316	2	china),29	china),29	NOUN
ejpam-1240	316	3	,	,	PUNCT
ejpam-1240	316	4	329	329	NUM
ejpam-1240	316	5	-	-	SYM
ejpam-1240	316	6	334	334	NUM
ejpam-1240	316	7	.	.	PUNCT
ejpam-1240	316	8	2000	2000	NUM
ejpam-1240	317	1	[	[	X
ejpam-1240	317	2	15	15	NUM
ejpam-1240	317	3	]	]	X
ejpam-1240	317	4	x.j	x.j	PROPN
ejpam-1240	317	5	.	.	PUNCT
ejpam-1240	317	6	guo	guo	PROPN
ejpam-1240	317	7	,	,	PUNCT
ejpam-1240	317	8	w.	w.	PROPN
ejpam-1240	317	9	chen	chen	PROPN
ejpam-1240	317	10	and	and	CCONJ
ejpam-1240	317	11	k.p	k.p	PROPN
ejpam-1240	317	12	.	.	PROPN
ejpam-1240	317	13	shum	shum	PROPN
ejpam-1240	317	14	,	,	PUNCT
ejpam-1240	317	15	on	on	ADP
ejpam-1240	317	16	left	left	ADJ
ejpam-1240	317	17	negatively	negatively	ADV
ejpam-1240	317	18	ordered	order	VERB
ejpam-1240	317	19	rpp	rpp	PROPN
ejpam-1240	317	20	semigroups	semigroup	NOUN
ejpam-1240	317	21	,	,	PUNCT
ejpam-1240	317	22	inter	inter	PROPN
ejpam-1240	317	23	.	.	PUNCT
ejpam-1240	318	1	j.	j.	PROPN
ejpam-1240	318	2	pure	pure	PROPN
ejpam-1240	318	3	appl	appl	PROPN
ejpam-1240	318	4	.	.	PUNCT
ejpam-1240	318	5	math	math	PROPN
ejpam-1240	318	6	.	.	PUNCT
ejpam-1240	318	7	,	,	PUNCT
ejpam-1240	318	8	32	32	NUM
ejpam-1240	318	9	,	,	PUNCT
ejpam-1240	318	10	105	105	NUM
ejpam-1240	318	11	-	-	SYM
ejpam-1240	318	12	116	116	NUM
ejpam-1240	318	13	.	.	PUNCT
ejpam-1240	319	1	2006	2006	NUM
ejpam-1240	319	2	.	.	PUNCT
ejpam-1240	320	1	[	[	X
ejpam-1240	320	2	16	16	NUM
ejpam-1240	320	3	]	]	X
ejpam-1240	320	4	x.j	x.j	PROPN
ejpam-1240	320	5	.	.	PROPN
ejpam-1240	320	6	guo	guo	PROPN
ejpam-1240	320	7	and	and	CCONJ
ejpam-1240	320	8	k.p	k.p	PROPN
ejpam-1240	320	9	.	.	PROPN
ejpam-1240	320	10	shum	shum	PROPN
ejpam-1240	320	11	,	,	PUNCT
ejpam-1240	320	12	the	the	DET
ejpam-1240	320	13	lawson	lawson	PROPN
ejpam-1240	320	14	partial	partial	ADJ
ejpam-1240	320	15	orders	order	NOUN
ejpam-1240	320	16	on	on	ADP
ejpam-1240	320	17	rpp	rpp	PROPN
ejpam-1240	320	18	semigroups	semigroup	NOUN
ejpam-1240	320	19	,	,	PUNCT
ejpam-1240	320	20	inter	inter	PROPN
ejpam-1240	320	21	.	.	PUNCT
ejpam-1240	321	1	j.	j.	PROPN
ejpam-1240	321	2	pure	pure	PROPN
ejpam-1240	321	3	appl	appl	PROPN
ejpam-1240	321	4	.	.	PUNCT
ejpam-1240	321	5	math	math	PROPN
ejpam-1240	321	6	.	.	PUNCT
ejpam-1240	321	7	,	,	PUNCT
ejpam-1240	321	8	29	29	NUM
ejpam-1240	321	9	,	,	PUNCT
ejpam-1240	321	10	415	415	NUM
ejpam-1240	321	11	-	-	SYM
ejpam-1240	321	12	423	423	NUM
ejpam-1240	321	13	.	.	PUNCT
ejpam-1240	322	1	2006	2006	NUM
ejpam-1240	322	2	.	.	PUNCT
ejpam-1240	323	1	[	[	X
ejpam-1240	323	2	17	17	NUM
ejpam-1240	323	3	]	]	X
ejpam-1240	323	4	j.m	j.m	PROPN
ejpam-1240	323	5	.	.	PROPN
ejpam-1240	323	6	howie	howie	PROPN
ejpam-1240	323	7	,	,	PUNCT
ejpam-1240	323	8	an	an	DET
ejpam-1240	323	9	introduction	introduction	NOUN
ejpam-1240	323	10	to	to	ADP
ejpam-1240	323	11	semigroup	semigroup	PROPN
ejpam-1240	323	12	theory	theory	NOUN
ejpam-1240	323	13	,	,	PUNCT
ejpam-1240	323	14	academic	academic	ADJ
ejpam-1240	323	15	press	press	NOUN
ejpam-1240	323	16	,	,	PUNCT
ejpam-1240	323	17	london	london	PROPN
ejpam-1240	323	18	,	,	PUNCT
ejpam-1240	323	19	1976	1976	NUM
ejpam-1240	323	20	.	.	PUNCT
ejpam-1240	324	1	[	[	X
ejpam-1240	324	2	18	18	NUM
ejpam-1240	324	3	]	]	X
ejpam-1240	324	4	k.p	k.p	PROPN
ejpam-1240	324	5	.	.	PROPN
ejpam-1240	324	6	shum	shum	PROPN
ejpam-1240	324	7	and	and	CCONJ
ejpam-1240	324	8	x.m	x.m	PROPN
ejpam-1240	324	9	.	.	PROPN
ejpam-1240	324	10	ren	ren	PROPN
ejpam-1240	324	11	,	,	PUNCT
ejpam-1240	324	12	abundant	abundant	ADJ
ejpam-1240	324	13	semigroups	semigroup	NOUN
ejpam-1240	324	14	and	and	CCONJ
ejpam-1240	324	15	their	their	PRON
ejpam-1240	324	16	special	special	ADJ
ejpam-1240	324	17	subclasses	subclass	NOUN
ejpam-1240	324	18	,	,	PUNCT
ejpam-1240	324	19	proceedings	proceeding	NOUN
ejpam-1240	324	20	of	of	ADP
ejpam-1240	324	21	international	international	ADJ
ejpam-1240	324	22	conference	conference	NOUN
ejpam-1240	324	23	on	on	ADP
ejpam-1240	324	24	algebra	algebra	NOUN
ejpam-1240	324	25	and	and	CCONJ
ejpam-1240	324	26	its	its	PRON
ejpam-1240	324	27	applicatons	applicaton	NOUN
ejpam-1240	324	28	(	(	PUNCT
ejpam-1240	324	29	icaa	icaa	NOUN
ejpam-1240	324	30	2002	2002	NUM
ejpam-1240	324	31	)	)	PUNCT
ejpam-1240	324	32	,	,	PUNCT
ejpam-1240	324	33	chulalongkorn	chulalongkorn	PROPN
ejpam-1240	324	34	univ	univ	PROPN
ejpam-1240	324	35	.	.	PROPN
ejpam-1240	324	36	,	,	PUNCT
ejpam-1240	324	37	bangkok	bangkok	PROPN
ejpam-1240	324	38	,	,	PUNCT
ejpam-1240	324	39	p.	p.	NOUN
ejpam-1240	324	40	66	66	NUM
ejpam-1240	324	41	-	-	SYM
ejpam-1240	324	42	86	86	NUM
ejpam-1240	324	43	.	.	PUNCT
ejpam-1240	324	44	2002	2002	NUM
ejpam-1240	324	45	.	.	PUNCT
ejpam-1240	325	1	[	[	X
ejpam-1240	325	2	19	19	NUM
ejpam-1240	325	3	]	]	PUNCT
ejpam-1240	325	4	t.	t.	PROPN
ejpam-1240	325	5	saito	saito	PROPN
ejpam-1240	325	6	,	,	PUNCT
ejpam-1240	325	7	natually	natually	ADV
ejpam-1240	325	8	ordered	order	VERB
ejpam-1240	325	9	regular	regular	ADJ
ejpam-1240	325	10	semigroups	semigroup	NOUN
ejpam-1240	325	11	with	with	ADP
ejpam-1240	325	12	maximum	maximum	ADJ
ejpam-1240	325	13	inverses	inverse	NOUN
ejpam-1240	325	14	,	,	PUNCT
ejpam-1240	325	15	proc	proc	NOUN
ejpam-1240	325	16	.	.	PUNCT
ejpam-1240	326	1	edinb	edinb	PROPN
ejpam-1240	326	2	.	.	PUNCT
ejpam-1240	327	1	math	math	NOUN
ejpam-1240	327	2	.	.	PUNCT
ejpam-1240	328	1	soc	soc	PROPN
ejpam-1240	328	2	.	.	PUNCT
ejpam-1240	329	1	32	32	NUM
ejpam-1240	329	2	,	,	PUNCT
ejpam-1240	329	3	33	33	NUM
ejpam-1240	329	4	-	-	SYM
ejpam-1240	329	5	39	39	NUM
ejpam-1240	329	6	.	.	PUNCT
ejpam-1240	330	1	1989	1989	NUM
ejpam-1240	330	2	.	.	PUNCT