id	sid	tid	token	lemma	pos
ejpam-23	1	1	european	european	PROPN
ejpam-23	1	2	journal	journal	PROPN
ejpam-23	1	3	of	of	ADP
ejpam-23	1	4	pure	pure	ADJ
ejpam-23	1	5	and	and	CCONJ
ejpam-23	1	6	applied	apply	VERB
ejpam-23	1	7	mathematics	mathematic	NOUN
ejpam-23	1	8	vol	vol	NOUN
ejpam-23	1	9	.	.	PROPN
ejpam-23	2	1	1	1	NUM
ejpam-23	2	2	,	,	PUNCT
ejpam-23	2	3	no	no	INTJ
ejpam-23	2	4	.	.	NOUN
ejpam-23	2	5	1	1	NUM
ejpam-23	2	6	,	,	PUNCT
ejpam-23	2	7	2008	2008	NUM
ejpam-23	2	8	,	,	PUNCT
ejpam-23	2	9	(	(	PUNCT
ejpam-23	2	10	46	46	NUM
ejpam-23	2	11	-	-	SYM
ejpam-23	2	12	59	59	NUM
ejpam-23	2	13	)	)	PUNCT
ejpam-23	2	14	issn	issn	PROPN
ejpam-23	2	15	1307	1307	NUM
ejpam-23	2	16	-	-	SYM
ejpam-23	2	17	5543	5543	NUM
ejpam-23	2	18	–	–	PUNCT
ejpam-23	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-23	2	20	honorary	honorary	PROPN
ejpam-23	2	21	invited	invite	VERB
ejpam-23	2	22	paper	paper	NOUN
ejpam-23	2	23	on	on	ADP
ejpam-23	2	24	the	the	DET
ejpam-23	2	25	structure	structure	NOUN
ejpam-23	2	26	of	of	ADP
ejpam-23	2	27	regular	regular	ADJ
ejpam-23	2	28	h̃-cryptogroups	h̃-cryptogroups	PROPN
ejpam-23	2	29	xiangzhi	xiangzhi	PROPN
ejpam-23	3	1	kong	kong	PROPN
ejpam-23	3	2	1	1	NUM
ejpam-23	3	3	,	,	PUNCT
ejpam-23	3	4	yue	yue	PROPN
ejpam-23	3	5	ding	ding	PROPN
ejpam-23	3	6	,	,	PUNCT
ejpam-23	3	7	k.p	k.p	PROPN
ejpam-23	3	8	.	.	PROPN
ejpam-23	3	9	shum2,∗,†	shum2,∗,†	PROPN
ejpam-23	3	10	1	1	NUM
ejpam-23	3	11	school	school	NOUN
ejpam-23	3	12	of	of	ADP
ejpam-23	3	13	science	science	NOUN
ejpam-23	3	14	,	,	PUNCT
ejpam-23	3	15	jiangnan	jiangnan	PROPN
ejpam-23	3	16	university	university	PROPN
ejpam-23	3	17	,	,	PUNCT
ejpam-23	3	18	wuxi	wuxi	PROPN
ejpam-23	3	19	,	,	PUNCT
ejpam-23	3	20	jiangsu	jiangsu	PROPN
ejpam-23	3	21	,	,	PUNCT
ejpam-23	3	22	214122	214122	NUM
ejpam-23	3	23	,	,	PUNCT
ejpam-23	3	24	china	china	PROPN
ejpam-23	3	25	2	2	NUM
ejpam-23	3	26	department	department	NOUN
ejpam-23	3	27	of	of	ADP
ejpam-23	3	28	mathematics	mathematic	NOUN
ejpam-23	3	29	,	,	PUNCT
ejpam-23	3	30	the	the	DET
ejpam-23	3	31	university	university	NOUN
ejpam-23	3	32	of	of	ADP
ejpam-23	3	33	hong	hong	PROPN
ejpam-23	3	34	kong	kong	PROPN
ejpam-23	3	35	,	,	PUNCT
ejpam-23	3	36	pokfulam	pokfulam	PROPN
ejpam-23	3	37	road	road	PROPN
ejpam-23	3	38	,	,	PUNCT
ejpam-23	3	39	hong	hong	PROPN
ejpam-23	3	40	kong	kong	PROPN
ejpam-23	3	41	(	(	PUNCT
ejpam-23	3	42	sar	sar	PROPN
ejpam-23	3	43	)	)	PUNCT
ejpam-23	3	44	,	,	PUNCT
ejpam-23	3	45	china	china	PROPN
ejpam-23	3	46	abstract	abstract	NOUN
ejpam-23	3	47	.	.	PUNCT
ejpam-23	4	1	we	we	PRON
ejpam-23	4	2	introduce	introduce	VERB
ejpam-23	4	3	the	the	DET
ejpam-23	4	4	concepts	concept	NOUN
ejpam-23	4	5	of	of	ADP
ejpam-23	4	6	green	green	ADJ
ejpam-23	4	7	∼-relations	∼-relation	NOUN
ejpam-23	4	8	on	on	ADP
ejpam-23	4	9	h̃-abundant	h̃-abundant	ADJ
ejpam-23	4	10	semigroups	semigroup	NOUN
ejpam-23	4	11	.	.	PUNCT
ejpam-23	5	1	by	by	ADP
ejpam-23	5	2	using	use	VERB
ejpam-23	5	3	the	the	DET
ejpam-23	5	4	generalized	generalized	ADJ
ejpam-23	5	5	strong	strong	ADJ
ejpam-23	5	6	semilattice	semilattice	NOUN
ejpam-23	5	7	of	of	ADP
ejpam-23	5	8	semigroups	semigroup	NOUN
ejpam-23	5	9	,	,	PUNCT
ejpam-23	5	10	we	we	PRON
ejpam-23	5	11	show	show	VERB
ejpam-23	5	12	that	that	SCONJ
ejpam-23	5	13	an	an	DET
ejpam-23	5	14	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	5	15	is	be	AUX
ejpam-23	5	16	a	a	DET
ejpam-23	5	17	regular	regular	ADJ
ejpam-23	5	18	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	5	19	if	if	SCONJ
ejpam-23	5	20	and	and	CCONJ
ejpam-23	5	21	only	only	ADV
ejpam-23	5	22	if	if	SCONJ
ejpam-23	5	23	it	it	PRON
ejpam-23	5	24	is	be	AUX
ejpam-23	5	25	an	an	DET
ejpam-23	5	26	h̃g	h̃g	ADJ
ejpam-23	5	27	-	-	PUNCT
ejpam-23	5	28	strong	strong	ADJ
ejpam-23	5	29	semilattice	semilattice	NOUN
ejpam-23	5	30	of	of	ADP
ejpam-23	5	31	completely	completely	ADV
ejpam-23	5	32	j̃	j̃	PROPN
ejpam-23	5	33	-simple	-simple	ADJ
ejpam-23	5	34	semigroups	semigroup	NOUN
ejpam-23	5	35	.	.	PUNCT
ejpam-23	6	1	this	this	DET
ejpam-23	6	2	result	result	VERB
ejpam-23	6	3	not	not	PART
ejpam-23	6	4	only	only	ADV
ejpam-23	6	5	extends	extend	VERB
ejpam-23	6	6	a	a	DET
ejpam-23	6	7	known	know	VERB
ejpam-23	6	8	result	result	NOUN
ejpam-23	6	9	of	of	ADP
ejpam-23	6	10	petrich	petrich	NOUN
ejpam-23	6	11	from	from	ADP
ejpam-23	6	12	the	the	DET
ejpam-23	6	13	class	class	NOUN
ejpam-23	6	14	of	of	ADP
ejpam-23	6	15	completely	completely	ADV
ejpam-23	6	16	regular	regular	ADJ
ejpam-23	6	17	semigroups	semigroup	NOUN
ejpam-23	6	18	to	to	ADP
ejpam-23	6	19	the	the	DET
ejpam-23	6	20	class	class	NOUN
ejpam-23	6	21	of	of	ADP
ejpam-23	6	22	semiabundant	semiabundant	ADJ
ejpam-23	6	23	semigroups	semigroup	NOUN
ejpam-23	6	24	but	but	CCONJ
ejpam-23	6	25	also	also	ADV
ejpam-23	6	26	generalizes	generalize	VERB
ejpam-23	6	27	a	a	DET
ejpam-23	6	28	well	well	ADV
ejpam-23	6	29	known	know	VERB
ejpam-23	6	30	result	result	NOUN
ejpam-23	6	31	of	of	ADP
ejpam-23	6	32	fountain	fountain	NOUN
ejpam-23	6	33	on	on	ADP
ejpam-23	6	34	superabundant	superabundant	ADJ
ejpam-23	6	35	semigroups	semigroup	NOUN
ejpam-23	6	36	from	from	ADP
ejpam-23	6	37	the	the	DET
ejpam-23	6	38	class	class	NOUN
ejpam-23	6	39	of	of	ADP
ejpam-23	6	40	abundant	abundant	ADJ
ejpam-23	6	41	semigroups	semigroup	NOUN
ejpam-23	6	42	to	to	ADP
ejpam-23	6	43	the	the	DET
ejpam-23	6	44	class	class	NOUN
ejpam-23	6	45	of	of	ADP
ejpam-23	6	46	semiabundant	semiabundant	PROPN
ejpam-23	6	47	semigroups	semigroup	NOUN
ejpam-23	6	48	.	.	PUNCT
ejpam-23	7	1	ams	am	NOUN
ejpam-23	7	2	subject	subject	ADJ
ejpam-23	7	3	classifications	classification	NOUN
ejpam-23	7	4	:	:	PUNCT
ejpam-23	7	5	20m10	20m10	NUM
ejpam-23	7	6	key	key	ADJ
ejpam-23	7	7	words	word	NOUN
ejpam-23	7	8	:	:	PUNCT
ejpam-23	7	9	the	the	DET
ejpam-23	7	10	green	green	ADJ
ejpam-23	7	11	∼-relations	∼-relation	NOUN
ejpam-23	7	12	;	;	PUNCT
ejpam-23	7	13	homomorphisms	homomorphism	NOUN
ejpam-23	7	14	of	of	ADP
ejpam-23	7	15	h̃-abundant	h̃-abundant	ADJ
ejpam-23	7	16	semigroups	semigroup	NOUN
ejpam-23	7	17	;	;	PUNCT
ejpam-23	7	18	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	7	19	.	.	PUNCT
ejpam-23	8	1	1	1	X
ejpam-23	8	2	.	.	X
ejpam-23	8	3	introduction	introduction	NOUN
ejpam-23	8	4	it	it	PRON
ejpam-23	8	5	was	be	AUX
ejpam-23	8	6	proved	prove	VERB
ejpam-23	8	7	by	by	ADP
ejpam-23	8	8	clifford	clifford	PROPN
ejpam-23	9	1	[	[	X
ejpam-23	9	2	1	1	X
ejpam-23	9	3	]	]	PUNCT
ejpam-23	9	4	that	that	SCONJ
ejpam-23	9	5	a	a	DET
ejpam-23	9	6	regular	regular	ADJ
ejpam-23	9	7	semigroup	semigroup	NOUN
ejpam-23	9	8	is	be	AUX
ejpam-23	9	9	a	a	DET
ejpam-23	9	10	union	union	NOUN
ejpam-23	9	11	of	of	ADP
ejpam-23	9	12	groups	group	NOUN
ejpam-23	9	13	if	if	SCONJ
ejpam-23	9	14	and	and	CCONJ
ejpam-23	9	15	only	only	ADV
ejpam-23	9	16	if	if	SCONJ
ejpam-23	9	17	it	it	PRON
ejpam-23	9	18	is	be	AUX
ejpam-23	9	19	a	a	DET
ejpam-23	9	20	semilattice	semilattice	NOUN
ejpam-23	9	21	of	of	ADP
ejpam-23	9	22	completely	completely	ADV
ejpam-23	9	23	simple	simple	ADJ
ejpam-23	9	24	semigroups	semigroup	NOUN
ejpam-23	9	25	.	.	PUNCT
ejpam-23	10	1	it	it	PRON
ejpam-23	10	2	is	be	AUX
ejpam-23	10	3	also	also	ADV
ejpam-23	10	4	known	know	VERB
ejpam-23	10	5	that	that	SCONJ
ejpam-23	10	6	if	if	SCONJ
ejpam-23	10	7	the	the	DET
ejpam-23	10	8	set	set	NOUN
ejpam-23	10	9	of	of	ADP
ejpam-23	10	10	all	all	DET
ejpam-23	10	11	idempotents	idempotent	NOUN
ejpam-23	10	12	of	of	ADP
ejpam-23	10	13	a	a	DET
ejpam-23	10	14	completely	completely	ADV
ejpam-23	10	15	regular	regular	ADJ
ejpam-23	10	16	semigroup	semigroup	NOUN
ejpam-23	10	17	s	s	PART
ejpam-23	10	18	is	be	AUX
ejpam-23	10	19	the	the	DET
ejpam-23	10	20	center	center	NOUN
ejpam-23	10	21	of	of	ADP
ejpam-23	10	22	s	s	PROPN
ejpam-23	10	23	,	,	PUNCT
ejpam-23	10	24	then	then	ADV
ejpam-23	10	25	s	s	VERB
ejpam-23	10	26	can	can	AUX
ejpam-23	10	27	be	be	AUX
ejpam-23	10	28	expressed	express	VERB
ejpam-23	10	29	by	by	ADP
ejpam-23	10	30	a	a	DET
ejpam-23	10	31	strong	strong	ADJ
ejpam-23	10	32	semilattice	semilattice	NOUN
ejpam-23	10	33	of	of	ADP
ejpam-23	10	34	groups	group	NOUN
ejpam-23	10	35	(	(	PUNCT
ejpam-23	10	36	see	see	VERB
ejpam-23	10	37	[	[	X
ejpam-23	10	38	1	1	NUM
ejpam-23	10	39	]	]	NUM
ejpam-23	10	40	)	)	PUNCT
ejpam-23	10	41	.	.	PUNCT
ejpam-23	11	1	thus	thus	ADV
ejpam-23	11	2	,	,	PUNCT
ejpam-23	11	3	we	we	PRON
ejpam-23	11	4	usually	usually	ADV
ejpam-23	11	5	regard	regard	VERB
ejpam-23	11	6	the	the	DET
ejpam-23	11	7	completely	completely	ADV
ejpam-23	11	8	regular	regular	ADJ
ejpam-23	11	9	semigroups	semigroup	NOUN
ejpam-23	11	10	as	as	ADP
ejpam-23	11	11	generalized	generalized	ADJ
ejpam-23	11	12	groups	group	NOUN
ejpam-23	11	13	.	.	PUNCT
ejpam-23	12	1	moreover	moreover	ADV
ejpam-23	12	2	,	,	PUNCT
ejpam-23	12	3	by	by	ADP
ejpam-23	12	4	petrich	petrich	NOUN
ejpam-23	12	5	and	and	CCONJ
ejpam-23	12	6	reilly	reilly	ADV
ejpam-23	12	7	,	,	PUNCT
ejpam-23	12	8	we	we	PRON
ejpam-23	12	9	call	call	VERB
ejpam-23	12	10	a	a	DET
ejpam-23	12	11	completely	completely	ADV
ejpam-23	12	12	regular	regular	ADJ
ejpam-23	12	13	semigroup	semigroup	NOUN
ejpam-23	12	14	s	s	VERB
ejpam-23	12	15	a	a	DET
ejpam-23	12	16	normal	normal	ADJ
ejpam-23	12	17	cryptogroup	cryptogroup	NOUN
ejpam-23	12	18	if	if	SCONJ
ejpam-23	12	19	the	the	DET
ejpam-23	12	20	green	green	PROPN
ejpam-23	12	21	relation	relation	PROPN
ejpam-23	12	22	h	h	PROPN
ejpam-23	12	23	on	on	ADP
ejpam-23	12	24	s	s	NOUN
ejpam-23	12	25	is	be	AUX
ejpam-23	12	26	a	a	DET
ejpam-23	12	27	normal	normal	ADJ
ejpam-23	12	28	band	band	NOUN
ejpam-23	12	29	congruence	congruence	NOUN
ejpam-23	12	30	on	on	ADP
ejpam-23	12	31	s.	s.	PROPN
ejpam-23	12	32	in	in	ADP
ejpam-23	12	33	particular	particular	ADJ
ejpam-23	12	34	,	,	PUNCT
ejpam-23	13	1	a	a	DET
ejpam-23	13	2	completely	completely	ADV
ejpam-23	13	3	regular	regular	ADJ
ejpam-23	13	4	semigroup	semigroup	NOUN
ejpam-23	13	5	s	s	VERB
ejpam-23	13	6	is	be	AUX
ejpam-23	13	7	a	a	DET
ejpam-23	13	8	normal	normal	ADJ
ejpam-23	13	9	cryptogroup	cryptogroup	NOUN
ejpam-23	13	10	if	if	SCONJ
ejpam-23	13	11	and	and	CCONJ
ejpam-23	13	12	only	only	ADV
ejpam-23	13	13	if	if	SCONJ
ejpam-23	13	14	s	s	NOUN
ejpam-23	13	15	can	can	AUX
ejpam-23	13	16	be	be	AUX
ejpam-23	13	17	expressed	express	VERB
ejpam-23	13	18	by	by	ADP
ejpam-23	13	19	a	a	DET
ejpam-23	13	20	strong	strong	ADJ
ejpam-23	13	21	semilattice	semilattice	NOUN
ejpam-23	13	22	of	of	ADP
ejpam-23	13	23	completely	completely	ADV
ejpam-23	13	24	simple	simple	ADJ
ejpam-23	13	25	semigroups	semigroup	NOUN
ejpam-23	13	26	(	(	PUNCT
ejpam-23	13	27	see	see	VERB
ejpam-23	13	28	[	[	X
ejpam-23	13	29	12	12	NUM
ejpam-23	13	30	]	]	PUNCT
ejpam-23	13	31	and	and	CCONJ
ejpam-23	13	32	[	[	X
ejpam-23	13	33	13	13	NUM
ejpam-23	13	34	]	]	NUM
ejpam-23	13	35	)	)	PUNCT
ejpam-23	13	36	.	.	PUNCT
ejpam-23	14	1	this	this	DET
ejpam-23	14	2	result	result	NOUN
ejpam-23	14	3	was	be	AUX
ejpam-23	14	4	further	far	ADV
ejpam-23	14	5	generalized	generalize	VERB
ejpam-23	14	6	by	by	ADP
ejpam-23	14	7	fountain	fountain	NOUN
ejpam-23	14	8	by	by	ADP
ejpam-23	14	9	proving	prove	VERB
ejpam-23	14	10	that	that	SCONJ
ejpam-23	14	11	an	an	DET
ejpam-23	14	12	abundant	abundant	ADJ
ejpam-23	14	13	semigroup	semigroup	NOUN
ejpam-23	14	14	s	s	PART
ejpam-23	14	15	is	be	AUX
ejpam-23	14	16	a	a	DET
ejpam-23	14	17	superabundant	superabundant	ADJ
ejpam-23	14	18	semigroup	semigroup	NOUN
ejpam-23	14	19	if	if	SCONJ
ejpam-23	14	20	and	and	CCONJ
ejpam-23	14	21	only	only	ADV
ejpam-23	14	22	if	if	SCONJ
ejpam-23	14	23	s	s	NOUN
ejpam-23	14	24	is	be	AUX
ejpam-23	14	25	a	a	DET
ejpam-23	14	26	semilattice	semilattice	NOUN
ejpam-23	14	27	of	of	ADP
ejpam-23	14	28	completely	completely	ADV
ejpam-23	14	29	j	j	PROPN
ejpam-23	14	30	∗	∗	NOUN
ejpam-23	14	31	-simple	-simple	ADJ
ejpam-23	14	32	semigroups	semigroup	NOUN
ejpam-23	14	33	[	[	X
ejpam-23	14	34	4	4	NUM
ejpam-23	14	35	]	]	PUNCT
ejpam-23	14	36	.	.	PUNCT
ejpam-23	15	1	the	the	DET
ejpam-23	15	2	structure	structure	NOUN
ejpam-23	15	3	of	of	ADP
ejpam-23	15	4	superabundant	superabundant	ADJ
ejpam-23	15	5	semigroups	semigroup	NOUN
ejpam-23	15	6	whose	whose	DET
ejpam-23	15	7	set	set	NOUN
ejpam-23	15	8	of	of	ADP
ejpam-23	15	9	idempotents	idempotent	NOUN
ejpam-23	15	10	forms	form	VERB
ejpam-23	15	11	a	a	DET
ejpam-23	15	12	subsemigroup	subsemigroup	NOUN
ejpam-23	15	13	have	have	AUX
ejpam-23	15	14	been	be	AUX
ejpam-23	15	15	recently	recently	ADV
ejpam-23	15	16	extensively	extensively	ADV
ejpam-23	15	17	investigated	investigate	VERB
ejpam-23	15	18	by	by	ADP
ejpam-23	15	19	ren	ren	PROPN
ejpam-23	15	20	and	and	CCONJ
ejpam-23	15	21	shum	shum	ADV
ejpam-23	15	22	in	in	ADP
ejpam-23	15	23	[	[	X
ejpam-23	15	24	15	15	NUM
ejpam-23	15	25	]	]	PUNCT
ejpam-23	15	26	and	and	CCONJ
ejpam-23	15	27	[	[	X
ejpam-23	15	28	16	16	NUM
ejpam-23	15	29	]	]	PUNCT
ejpam-23	15	30	.	.	PUNCT
ejpam-23	16	1	the	the	DET
ejpam-23	16	2	green	green	PROPN
ejpam-23	16	3	∗-relations	∗-relations	PROPN
ejpam-23	16	4	on	on	ADP
ejpam-23	16	5	a	a	DET
ejpam-23	16	6	semigroup	semigroup	NOUN
ejpam-23	16	7	s	s	VERB
ejpam-23	16	8	were	be	AUX
ejpam-23	16	9	first	first	ADV
ejpam-23	16	10	defined	define	VERB
ejpam-23	16	11	by	by	ADP
ejpam-23	16	12	pastijn	pastijn	NOUN
ejpam-23	16	13	[	[	X
ejpam-23	16	14	11	11	NUM
ejpam-23	16	15	]	]	PUNCT
ejpam-23	16	16	which	which	PRON
ejpam-23	16	17	can	can	AUX
ejpam-23	16	18	be	be	AUX
ejpam-23	16	19	regarded	regard	VERB
ejpam-23	16	20	as	as	ADP
ejpam-23	16	21	the	the	DET
ejpam-23	16	22	green	green	ADJ
ejpam-23	16	23	relations	relation	NOUN
ejpam-23	16	24	in	in	ADP
ejpam-23	16	25	some	some	DET
ejpam-23	16	26	oversemigroups	oversemigroup	NOUN
ejpam-23	16	27	of	of	ADP
ejpam-23	16	28	s.	s.	PROPN
ejpam-23	16	29	these	these	DET
ejpam-23	16	30	relations	relation	NOUN
ejpam-23	16	31	were	be	AUX
ejpam-23	16	32	formulated	formulate	VERB
ejpam-23	16	33	by	by	ADP
ejpam-23	16	34	∗corresponding	∗corresponde	VERB
ejpam-23	16	35	author	author	NOUN
ejpam-23	16	36	.	.	PUNCT
ejpam-23	17	1	email	email	NOUN
ejpam-23	17	2	addresses	address	NOUN
ejpam-23	17	3	:	:	PUNCT
ejpam-23	17	4	xiangzhikong@163.com	xiangzhikong@163.com	PROPN
ejpam-23	17	5	(	(	PUNCT
ejpam-23	17	6	x.	x.	PROPN
ejpam-23	17	7	kong	kong	PROPN
ejpam-23	17	8	)	)	PUNCT
ejpam-23	17	9	,	,	PUNCT
ejpam-23	17	10	kpshum@maths.hku.edu.hk	kpshum@maths.hku.edu.hk	PROPN
ejpam-23	17	11	(	(	PUNCT
ejpam-23	17	12	k.p	k.p	PROPN
ejpam-23	17	13	.	.	PROPN
ejpam-23	17	14	shum	shum	PROPN
ejpam-23	17	15	)	)	PUNCT
ejpam-23	17	16	†the	†the	DET
ejpam-23	17	17	research	research	NOUN
ejpam-23	17	18	of	of	ADP
ejpam-23	17	19	k.p	k.p	PROPN
ejpam-23	17	20	.	.	PROPN
ejpam-23	17	21	shum	shum	PROPN
ejpam-23	17	22	is	be	AUX
ejpam-23	17	23	partially	partially	ADV
ejpam-23	17	24	supported	support	VERB
ejpam-23	17	25	by	by	ADP
ejpam-23	17	26	a	a	DET
ejpam-23	17	27	wu	wu	PROPN
ejpam-23	17	28	jiehyee	jiehyee	PROPN
ejpam-23	17	29	charitable	charitable	PROPN
ejpam-23	17	30	foundation	foundation	PROPN
ejpam-23	17	31	grant	grant	VERB
ejpam-23	17	32	no	no	NOUN
ejpam-23	17	33	.	.	PROPN
ejpam-23	17	34	7103084	7103084	NUM
ejpam-23	17	35	,	,	PUNCT
ejpam-23	17	36	2006	2006	NUM
ejpam-23	17	37	-	-	SYM
ejpam-23	17	38	07	07	NUM
ejpam-23	17	39	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-23	17	40	46	46	NUM
ejpam-23	17	41	c	c	X
ejpam-23	17	42	©	©	PROPN
ejpam-23	17	43	2007	2007	NUM
ejpam-23	17	44	ejpam	ejpam	NOUN
ejpam-23	17	45	all	all	DET
ejpam-23	17	46	rights	right	NOUN
ejpam-23	17	47	reserved	reserve	VERB
ejpam-23	17	48	.	.	PUNCT
ejpam-23	18	1	baris	baris	PROPN
ejpam-23	18	2	stamp	stamp	PROPN
ejpam-23	18	3	x.	x.	PROPN
ejpam-23	18	4	kong	kong	PROPN
ejpam-23	18	5	,	,	PUNCT
ejpam-23	18	6	y.ding	y.de	VERB
ejpam-23	18	7	,	,	PUNCT
ejpam-23	18	8	k.p.shum	k.p.shum	ADJ
ejpam-23	18	9	/	/	SYM
ejpam-23	18	10	eur	eur	PROPN
ejpam-23	18	11	.	.	PUNCT
ejpam-23	19	1	j.	j.	PROPN
ejpam-23	19	2	pure	pure	PROPN
ejpam-23	19	3	appl	appl	PROPN
ejpam-23	19	4	.	.	PROPN
ejpam-23	19	5	math	math	PROPN
ejpam-23	19	6	,	,	PUNCT
ejpam-23	19	7	1	1	NUM
ejpam-23	19	8	(	(	PUNCT
ejpam-23	19	9	2008	2008	NUM
ejpam-23	19	10	)	)	PUNCT
ejpam-23	19	11	,	,	PUNCT
ejpam-23	19	12	(	(	PUNCT
ejpam-23	19	13	46	46	NUM
ejpam-23	19	14	-	-	SYM
ejpam-23	19	15	59	59	NUM
ejpam-23	19	16	)	)	PUNCT
ejpam-23	19	17	47	47	NUM
ejpam-23	19	18	fountain	fountain	NOUN
ejpam-23	20	1	[	[	X
ejpam-23	20	2	4	4	NUM
ejpam-23	20	3	]	]	PUNCT
ejpam-23	20	4	as	as	SCONJ
ejpam-23	20	5	follows	follow	VERB
ejpam-23	20	6	:	:	PUNCT
ejpam-23	20	7	l∗	l∗	PROPN
ejpam-23	20	8	=	=	PRON
ejpam-23	20	9	{	{	PUNCT
ejpam-23	20	10	(	(	PUNCT
ejpam-23	20	11	a	a	PRON
ejpam-23	20	12	,	,	PUNCT
ejpam-23	20	13	b	b	NOUN
ejpam-23	20	14	)	)	PUNCT
ejpam-23	20	15	∈	∈	PROPN
ejpam-23	20	16	s	s	PART
ejpam-23	20	17	×	×	NOUN
ejpam-23	20	18	s	s	X
ejpam-23	20	19	:	:	PUNCT
ejpam-23	20	20	(	(	PUNCT
ejpam-23	20	21	∀x	∀x	X
ejpam-23	20	22	,	,	PUNCT
ejpam-23	20	23	y	y	PROPN
ejpam-23	20	24	∈	∈	PROPN
ejpam-23	20	25	s1)ax	s1)ax	PROPN
ejpam-23	20	26	=	=	SYM
ejpam-23	20	27	ay	ay	PROPN
ejpam-23	20	28	⇔	⇔	PROPN
ejpam-23	20	29	bx	bx	PROPN
ejpam-23	20	30	=	=	PUNCT
ejpam-23	20	31	by	by	ADP
ejpam-23	20	32	}	}	PUNCT
ejpam-23	20	33	,	,	PUNCT
ejpam-23	20	34	r∗	r∗	PROPN
ejpam-23	20	35	=	=	SYM
ejpam-23	20	36	{	{	PUNCT
ejpam-23	20	37	(	(	PUNCT
ejpam-23	20	38	a	a	PRON
ejpam-23	20	39	,	,	PUNCT
ejpam-23	20	40	b	b	NOUN
ejpam-23	20	41	)	)	PUNCT
ejpam-23	20	42	∈	∈	PROPN
ejpam-23	20	43	s	s	PART
ejpam-23	20	44	×	×	NOUN
ejpam-23	20	45	s	s	X
ejpam-23	20	46	:	:	PUNCT
ejpam-23	20	47	(	(	PUNCT
ejpam-23	20	48	∀x	∀x	X
ejpam-23	20	49	,	,	PUNCT
ejpam-23	20	50	y	y	PROPN
ejpam-23	20	51	∈	∈	PROPN
ejpam-23	20	52	s1)xa	s1)xa	NOUN
ejpam-23	20	53	=	=	SYM
ejpam-23	20	54	ya	ya	PROPN
ejpam-23	20	55	⇔	⇔	PROPN
ejpam-23	20	56	xb	xb	PROPN
ejpam-23	20	57	=	=	SYM
ejpam-23	20	58	yb	yb	PROPN
ejpam-23	20	59	}	}	PUNCT
ejpam-23	20	60	,	,	PUNCT
ejpam-23	20	61	h∗	h∗	PROPN
ejpam-23	20	62	=	=	PROPN
ejpam-23	20	63	l∗	l∗	PROPN
ejpam-23	20	64	∩r∗	∩r∗	NUM
ejpam-23	20	65	,	,	PUNCT
ejpam-23	20	66	d∗	d∗	PROPN
ejpam-23	20	67	=	=	SYM
ejpam-23	20	68	l∗	l∗	PROPN
ejpam-23	20	69	∨r∗.	∨r∗.	VERB
ejpam-23	20	70	later	later	ADV
ejpam-23	20	71	on	on	ADV
ejpam-23	20	72	,	,	PUNCT
ejpam-23	20	73	el	el	PROPN
ejpam-23	20	74	-	-	PUNCT
ejpam-23	20	75	qallali	qallali	VERB
ejpam-23	20	76	further	far	ADV
ejpam-23	20	77	generalized	generalize	VERB
ejpam-23	20	78	the	the	DET
ejpam-23	20	79	green	green	PROPN
ejpam-23	20	80	∗-relations	∗-relation	NOUN
ejpam-23	20	81	to	to	ADP
ejpam-23	20	82	green	green	ADJ
ejpam-23	20	83	∼-relations	∼-relation	NOUN
ejpam-23	20	84	[	[	X
ejpam-23	20	85	3	3	X
ejpam-23	20	86	]	]	PUNCT
ejpam-23	20	87	as	as	SCONJ
ejpam-23	20	88	follows	follow	VERB
ejpam-23	20	89	:	:	PUNCT
ejpam-23	20	90	l̃	l̃	PROPN
ejpam-23	20	91	=	=	PRON
ejpam-23	20	92	{	{	PUNCT
ejpam-23	20	93	(	(	PUNCT
ejpam-23	20	94	a	a	PRON
ejpam-23	20	95	,	,	PUNCT
ejpam-23	20	96	b	b	NOUN
ejpam-23	20	97	)	)	PUNCT
ejpam-23	20	98	∈	∈	PROPN
ejpam-23	20	99	s	s	PART
ejpam-23	20	100	×	×	NOUN
ejpam-23	20	101	s	s	X
ejpam-23	20	102	:	:	PUNCT
ejpam-23	20	103	(	(	PUNCT
ejpam-23	20	104	∀e	∀e	NOUN
ejpam-23	20	105	∈	∈	NOUN
ejpam-23	20	106	e(s))ae	e(s))ae	VERB
ejpam-23	20	107	=	=	NOUN
ejpam-23	20	108	a	a	DET
ejpam-23	20	109	⇔	⇔	PROPN
ejpam-23	20	110	be	be	NOUN
ejpam-23	20	111	=	=	ADJ
ejpam-23	20	112	b	b	NOUN
ejpam-23	20	113	}	}	PUNCT
ejpam-23	20	114	,	,	PUNCT
ejpam-23	20	115	r̃	r̃	NOUN
ejpam-23	20	116	=	=	SYM
ejpam-23	20	117	{	{	PUNCT
ejpam-23	20	118	(	(	PUNCT
ejpam-23	20	119	a	a	PRON
ejpam-23	20	120	,	,	PUNCT
ejpam-23	20	121	b	b	NOUN
ejpam-23	20	122	)	)	PUNCT
ejpam-23	20	123	∈	∈	PROPN
ejpam-23	20	124	s	s	PART
ejpam-23	20	125	×	×	NOUN
ejpam-23	20	126	s	s	X
ejpam-23	20	127	:	:	PUNCT
ejpam-23	20	128	(	(	PUNCT
ejpam-23	20	129	∀e	∀e	PROPN
ejpam-23	20	130	∈	∈	PROPN
ejpam-23	20	131	e(s))ea	e(s))ea	NOUN
ejpam-23	20	132	=	=	PUNCT
ejpam-23	20	133	a	a	DET
ejpam-23	20	134	⇔	⇔	PROPN
ejpam-23	20	135	eb	eb	PROPN
ejpam-23	20	136	=	=	SYM
ejpam-23	20	137	b	b	PROPN
ejpam-23	20	138	}	}	PUNCT
ejpam-23	20	139	,	,	PUNCT
ejpam-23	20	140	h̃	h̃	PROPN
ejpam-23	20	141	=	=	SYM
ejpam-23	20	142	l̃	l̃	PROPN
ejpam-23	21	1	∩	∩	NOUN
ejpam-23	21	2	r̃	r̃	PROPN
ejpam-23	21	3	,	,	PUNCT
ejpam-23	21	4	d̃	d̃	PROPN
ejpam-23	21	5	=	=	SYM
ejpam-23	21	6	l̃	l̃	PROPN
ejpam-23	21	7	∨	∨	NUM
ejpam-23	21	8	r̃.	r̃.	NOUN
ejpam-23	21	9	we	we	PRON
ejpam-23	21	10	can	can	AUX
ejpam-23	21	11	easily	easily	ADV
ejpam-23	21	12	see	see	VERB
ejpam-23	21	13	that	that	SCONJ
ejpam-23	21	14	l̃	l̃	PROPN
ejpam-23	21	15	and	and	CCONJ
ejpam-23	21	16	r̃	r̃	NOUN
ejpam-23	21	17	are	be	AUX
ejpam-23	21	18	equivalent	equivalent	ADJ
ejpam-23	21	19	relations	relation	NOUN
ejpam-23	21	20	on	on	ADP
ejpam-23	21	21	s	s	NOUN
ejpam-23	21	22	,	,	PUNCT
ejpam-23	21	23	however	however	ADV
ejpam-23	21	24	,	,	PUNCT
ejpam-23	21	25	the	the	DET
ejpam-23	21	26	l̃	l̃	PROPN
ejpam-23	21	27	relation	relation	NOUN
ejpam-23	21	28	is	be	AUX
ejpam-23	21	29	not	not	PART
ejpam-23	21	30	necessary	necessary	ADJ
ejpam-23	21	31	to	to	PART
ejpam-23	21	32	be	be	AUX
ejpam-23	21	33	right	right	ADV
ejpam-23	21	34	compatible	compatible	ADJ
ejpam-23	21	35	with	with	ADP
ejpam-23	21	36	the	the	DET
ejpam-23	21	37	semigroup	semigroup	ADJ
ejpam-23	21	38	multiplication	multiplication	NOUN
ejpam-23	21	39	and	and	CCONJ
ejpam-23	21	40	the	the	DET
ejpam-23	21	41	r̃	r̃	ADJ
ejpam-23	21	42	relation	relation	NOUN
ejpam-23	21	43	is	be	AUX
ejpam-23	21	44	not	not	PART
ejpam-23	21	45	necessary	necessary	ADJ
ejpam-23	21	46	to	to	PART
ejpam-23	21	47	be	be	AUX
ejpam-23	21	48	left	leave	VERB
ejpam-23	21	49	compatible	compatible	ADJ
ejpam-23	21	50	with	with	ADP
ejpam-23	21	51	the	the	DET
ejpam-23	21	52	semigroup	semigroup	ADJ
ejpam-23	21	53	multiplication	multiplication	NOUN
ejpam-23	21	54	.	.	PUNCT
ejpam-23	22	1	we	we	PRON
ejpam-23	22	2	now	now	ADV
ejpam-23	22	3	denote	denote	VERB
ejpam-23	22	4	the	the	DET
ejpam-23	22	5	l̃	l̃	PROPN
ejpam-23	22	6	-class	-class	NOUN
ejpam-23	22	7	containing	contain	VERB
ejpam-23	22	8	the	the	DET
ejpam-23	22	9	element	element	NOUN
ejpam-23	22	10	a	a	PRON
ejpam-23	22	11	of	of	ADP
ejpam-23	22	12	the	the	DET
ejpam-23	22	13	semigroup	semigroup	NOUN
ejpam-23	22	14	s	s	VERB
ejpam-23	22	15	by	by	ADV
ejpam-23	22	16	l̃a	l̃a	NOUN
ejpam-23	23	1	and	and	CCONJ
ejpam-23	23	2	we	we	PRON
ejpam-23	23	3	observe	observe	VERB
ejpam-23	23	4	thatl	thatl	NOUN
ejpam-23	23	5	⊆	⊆	NUM
ejpam-23	23	6	l∗	l∗	PROPN
ejpam-23	23	7	⊆	⊆	NUM
ejpam-23	23	8	l̃.	l̃.	NOUN
ejpam-23	23	9	among	among	ADP
ejpam-23	23	10	the	the	DET
ejpam-23	23	11	usual	usual	ADJ
ejpam-23	23	12	green	green	ADJ
ejpam-23	23	13	relations	relation	NOUN
ejpam-23	23	14	or	or	CCONJ
ejpam-23	23	15	the	the	DET
ejpam-23	23	16	above	above	ADJ
ejpam-23	23	17	relations	relation	NOUN
ejpam-23	23	18	,	,	PUNCT
ejpam-23	23	19	lor	lor	NOUN
ejpam-23	23	20	the	the	DET
ejpam-23	23	21	generalized	generalized	ADJ
ejpam-23	23	22	l	l	NOUN
ejpam-23	23	23	-	-	NOUN
ejpam-23	23	24	relations	relation	NOUN
ejpam-23	23	25	are	be	AUX
ejpam-23	23	26	duals	dual	NOUN
ejpam-23	23	27	of	of	ADP
ejpam-23	23	28	the	the	DET
ejpam-23	23	29	corresponding	correspond	VERB
ejpam-23	23	30	r	r	NOUN
ejpam-23	23	31	-relations	-relation	NOUN
ejpam-23	23	32	or	or	CCONJ
ejpam-23	23	33	generalized	generalize	VERB
ejpam-23	23	34	r	r	NOUN
ejpam-23	23	35	-	-	PUNCT
ejpam-23	23	36	relations	relation	NOUN
ejpam-23	23	37	.	.	PUNCT
ejpam-23	24	1	in	in	ADP
ejpam-23	24	2	what	what	PRON
ejpam-23	24	3	follows	follow	VERB
ejpam-23	24	4	,	,	PUNCT
ejpam-23	24	5	we	we	PRON
ejpam-23	24	6	only	only	ADV
ejpam-23	24	7	discuss	discuss	VERB
ejpam-23	24	8	the	the	DET
ejpam-23	24	9	properties	property	NOUN
ejpam-23	24	10	which	which	PRON
ejpam-23	24	11	are	be	AUX
ejpam-23	24	12	related	relate	VERB
ejpam-23	24	13	to	to	ADP
ejpam-23	24	14	the	the	DET
ejpam-23	24	15	lrelation	lrelation	NOUN
ejpam-23	24	16	and	and	CCONJ
ejpam-23	24	17	the	the	DET
ejpam-23	24	18	generalized	generalized	ADJ
ejpam-23	24	19	l	l	NOUN
ejpam-23	24	20	-	-	NOUN
ejpam-23	24	21	relation	relation	NOUN
ejpam-23	24	22	,	,	PUNCT
ejpam-23	24	23	respectively	respectively	ADV
ejpam-23	24	24	.	.	PUNCT
ejpam-23	25	1	one	one	PRON
ejpam-23	25	2	can	can	AUX
ejpam-23	25	3	easily	easily	ADV
ejpam-23	25	4	see	see	VERB
ejpam-23	25	5	that	that	SCONJ
ejpam-23	25	6	there	there	PRON
ejpam-23	25	7	is	be	VERB
ejpam-23	25	8	at	at	ADP
ejpam-23	25	9	most	most	ADJ
ejpam-23	25	10	one	one	NUM
ejpam-23	25	11	idempotent	idempotent	NOUN
ejpam-23	25	12	of	of	ADP
ejpam-23	25	13	the	the	DET
ejpam-23	25	14	semigroup	semigroup	NOUN
ejpam-23	25	15	s	s	PROPN
ejpam-23	25	16	in	in	ADP
ejpam-23	25	17	each	each	DET
ejpam-23	25	18	h̃	h̃	PROPN
ejpam-23	25	19	-class	-class	NOUN
ejpam-23	25	20	.	.	PUNCT
ejpam-23	26	1	if	if	SCONJ
ejpam-23	26	2	e	e	PROPN
ejpam-23	26	3	∈	∈	PROPN
ejpam-23	26	4	h̃a	h̃a	NOUN
ejpam-23	26	5	∩e(s	∩e(s	PROPN
ejpam-23	26	6	)	)	PUNCT
ejpam-23	26	7	,	,	PUNCT
ejpam-23	26	8	for	for	ADP
ejpam-23	26	9	some	some	PRON
ejpam-23	26	10	a	a	DET
ejpam-23	26	11	∈	∈	ADJ
ejpam-23	26	12	s	s	NOUN
ejpam-23	26	13	,	,	PUNCT
ejpam-23	26	14	then	then	ADV
ejpam-23	26	15	we	we	PRON
ejpam-23	26	16	simply	simply	ADV
ejpam-23	26	17	denote	denote	VERB
ejpam-23	26	18	the	the	DET
ejpam-23	26	19	idempotent	idempotent	ADJ
ejpam-23	26	20	e	e	NOUN
ejpam-23	26	21	by	by	ADP
ejpam-23	26	22	x0	x0	PROPN
ejpam-23	26	23	,	,	PUNCT
ejpam-23	26	24	for	for	ADP
ejpam-23	26	25	any	any	DET
ejpam-23	26	26	x	x	SYM
ejpam-23	26	27	∈	∈	PROPN
ejpam-23	26	28	h̃a	h̃a	NOUN
ejpam-23	26	29	.	.	PUNCT
ejpam-23	27	1	clearly	clearly	ADV
ejpam-23	27	2	,	,	PUNCT
ejpam-23	27	3	for	for	ADP
ejpam-23	27	4	any	any	DET
ejpam-23	27	5	x	x	SYM
ejpam-23	27	6	∈	∈	PROPN
ejpam-23	27	7	h̃a	h̃a	NOUN
ejpam-23	27	8	with	with	ADP
ejpam-23	27	9	a	a	DET
ejpam-23	27	10	∈	∈	PROPN
ejpam-23	27	11	s	s	NOUN
ejpam-23	27	12	,	,	PUNCT
ejpam-23	27	13	we	we	PRON
ejpam-23	27	14	have	have	VERB
ejpam-23	27	15	x	x	X
ejpam-23	27	16	=	=	SYM
ejpam-23	27	17	xx0	xx0	PUNCT
ejpam-23	28	1	=	=	SYM
ejpam-23	28	2	x0x	x0x	PROPN
ejpam-23	28	3	.	.	PUNCT
ejpam-23	29	1	if	if	SCONJ
ejpam-23	29	2	a	a	DET
ejpam-23	29	3	semigroup	semigroup	NOUN
ejpam-23	29	4	s	s	VERB
ejpam-23	29	5	is	be	AUX
ejpam-23	29	6	regular	regular	ADJ
ejpam-23	29	7	,	,	PUNCT
ejpam-23	29	8	then	then	ADV
ejpam-23	29	9	every	every	DET
ejpam-23	29	10	l	l	NOUN
ejpam-23	29	11	-	-	NOUN
ejpam-23	29	12	class	class	NOUN
ejpam-23	29	13	of	of	ADP
ejpam-23	29	14	s	s	NOUN
ejpam-23	29	15	contains	contain	VERB
ejpam-23	29	16	at	at	ADV
ejpam-23	29	17	least	least	ADV
ejpam-23	29	18	one	one	NUM
ejpam-23	29	19	idempotent	idempotent	NOUN
ejpam-23	29	20	,	,	PUNCT
ejpam-23	29	21	and	and	CCONJ
ejpam-23	29	22	so	so	ADV
ejpam-23	29	23	does	do	VERB
ejpam-23	29	24	every	every	DET
ejpam-23	29	25	r	r	NOUN
ejpam-23	29	26	-	-	PUNCT
ejpam-23	29	27	class	class	NOUN
ejpam-23	29	28	of	of	ADP
ejpam-23	29	29	s.	s.	PROPN
ejpam-23	29	30	if	if	SCONJ
ejpam-23	29	31	s	s	PROPN
ejpam-23	29	32	is	be	AUX
ejpam-23	29	33	a	a	DET
ejpam-23	29	34	completely	completely	ADV
ejpam-23	29	35	regular	regular	ADJ
ejpam-23	29	36	semigroup	semigroup	NOUN
ejpam-23	29	37	,	,	PUNCT
ejpam-23	29	38	then	then	ADV
ejpam-23	29	39	every	every	DET
ejpam-23	29	40	h	h	NOUN
ejpam-23	29	41	-	-	PUNCT
ejpam-23	29	42	class	class	NOUN
ejpam-23	29	43	of	of	ADP
ejpam-23	29	44	s	s	PROPN
ejpam-23	29	45	contains	contain	VERB
ejpam-23	29	46	an	an	DET
ejpam-23	29	47	idempotent	idempotent	NOUN
ejpam-23	29	48	.	.	PUNCT
ejpam-23	30	1	according	accord	VERB
ejpam-23	30	2	to	to	ADP
ejpam-23	30	3	fountain	fountain	NOUN
ejpam-23	30	4	[	[	X
ejpam-23	30	5	4	4	NUM
ejpam-23	30	6	]	]	PUNCT
ejpam-23	30	7	,	,	PUNCT
ejpam-23	30	8	a	a	DET
ejpam-23	30	9	semigroup	semigroup	NOUN
ejpam-23	30	10	is	be	AUX
ejpam-23	30	11	abundant	abundant	ADJ
ejpam-23	30	12	if	if	SCONJ
ejpam-23	30	13	every	every	DET
ejpam-23	30	14	l∗and	l∗and	ADJ
ejpam-23	30	15	r∗-class	r∗-class	NOUN
ejpam-23	30	16	of	of	ADP
ejpam-23	30	17	s	s	NOUN
ejpam-23	30	18	contains	contain	VERB
ejpam-23	30	19	some	some	DET
ejpam-23	30	20	idempotents	idempotent	NOUN
ejpam-23	30	21	.	.	PUNCT
ejpam-23	31	1	in	in	ADP
ejpam-23	31	2	other	other	ADJ
ejpam-23	31	3	words	word	NOUN
ejpam-23	31	4	,	,	PUNCT
ejpam-23	31	5	the	the	DET
ejpam-23	31	6	term	term	NOUN
ejpam-23	31	7	“	"	PUNCT
ejpam-23	31	8	abundant	abundant	ADJ
ejpam-23	31	9	”	"	PUNCT
ejpam-23	31	10	means	mean	VERB
ejpam-23	31	11	that	that	SCONJ
ejpam-23	31	12	the	the	DET
ejpam-23	31	13	semigroup	semigroup	NOUN
ejpam-23	31	14	has	have	VERB
ejpam-23	31	15	plenty	plenty	NOUN
ejpam-23	31	16	of	of	ADP
ejpam-23	31	17	idempotents	idempotent	NOUN
ejpam-23	31	18	.	.	PUNCT
ejpam-23	32	1	clearly	clearly	ADV
ejpam-23	32	2	,	,	PUNCT
ejpam-23	32	3	we	we	PRON
ejpam-23	32	4	have	have	VERB
ejpam-23	32	5	l∗	l∗	NOUN
ejpam-23	32	6	=	=	PUNCT
ejpam-23	32	7	l	l	NOUN
ejpam-23	32	8	on	on	ADP
ejpam-23	32	9	the	the	DET
ejpam-23	32	10	set	set	NOUN
ejpam-23	32	11	of	of	ADP
ejpam-23	32	12	all	all	DET
ejpam-23	32	13	regular	regular	ADJ
ejpam-23	32	14	elements	element	NOUN
ejpam-23	32	15	of	of	ADP
ejpam-23	32	16	a	a	DET
ejpam-23	32	17	semigroup	semigroup	NOUN
ejpam-23	32	18	.	.	PUNCT
ejpam-23	33	1	thus	thus	ADV
ejpam-23	33	2	,	,	PUNCT
ejpam-23	33	3	regular	regular	ADJ
ejpam-23	33	4	semigroups	semigroup	NOUN
ejpam-23	33	5	are	be	AUX
ejpam-23	33	6	obviously	obviously	ADV
ejpam-23	33	7	special	special	ADJ
ejpam-23	33	8	abundant	abundant	ADJ
ejpam-23	33	9	semigroups	semigroup	NOUN
ejpam-23	33	10	.	.	PUNCT
ejpam-23	34	1	thus	thus	ADV
ejpam-23	34	2	,	,	PUNCT
ejpam-23	34	3	fountain	fountain	NOUN
ejpam-23	34	4	called	call	VERB
ejpam-23	34	5	such	such	ADJ
ejpam-23	34	6	semigroup	semigroup	ADJ
ejpam-23	34	7	superabundant	superabundant	ADJ
ejpam-23	34	8	[	[	X
ejpam-23	34	9	4	4	X
ejpam-23	34	10	]	]	X
ejpam-23	34	11	if	if	SCONJ
ejpam-23	34	12	its	its	PRON
ejpam-23	34	13	everyh∗-classes	everyh∗-classes	PROPN
ejpam-23	34	14	contains	contain	VERB
ejpam-23	34	15	an	an	DET
ejpam-23	34	16	idempotent	idempotent	NOUN
ejpam-23	34	17	.	.	PUNCT
ejpam-23	35	1	obviously	obviously	ADV
ejpam-23	35	2	,	,	PUNCT
ejpam-23	35	3	completely	completely	ADV
ejpam-23	35	4	regular	regular	ADJ
ejpam-23	35	5	semigroups	semigroup	NOUN
ejpam-23	35	6	are	be	AUX
ejpam-23	35	7	special	special	ADJ
ejpam-23	35	8	superabundant	superabundant	ADJ
ejpam-23	35	9	semigroups	semigroup	NOUN
ejpam-23	35	10	.	.	PUNCT
ejpam-23	36	1	following	follow	VERB
ejpam-23	36	2	elqallali	elqallali	NOUN
ejpam-23	36	3	[	[	X
ejpam-23	36	4	3	3	NUM
ejpam-23	36	5	]	]	PUNCT
ejpam-23	36	6	,	,	PUNCT
ejpam-23	36	7	we	we	PRON
ejpam-23	36	8	call	call	VERB
ejpam-23	36	9	a	a	DET
ejpam-23	36	10	semigroup	semigroup	NOUN
ejpam-23	36	11	s	s	VERB
ejpam-23	36	12	a	a	DET
ejpam-23	36	13	semiabundant	semiabundant	NOUN
ejpam-23	36	14	semigroup	semigroup	NOUN
ejpam-23	36	15	if	if	SCONJ
ejpam-23	36	16	every	every	DET
ejpam-23	36	17	l̃-class	l̃-class	NOUN
ejpam-23	36	18	and	and	CCONJ
ejpam-23	36	19	every	every	DET
ejpam-23	36	20	r̃-class	r̃-class	PROPN
ejpam-23	36	21	of	of	ADP
ejpam-23	36	22	s	s	PRON
ejpam-23	36	23	contain	contain	VERB
ejpam-23	36	24	at	at	ADV
ejpam-23	36	25	least	least	ADJ
ejpam-23	36	26	one	one	NUM
ejpam-23	36	27	idempotent	idempotent	NOUN
ejpam-23	36	28	.	.	PUNCT
ejpam-23	37	1	a	a	DET
ejpam-23	37	2	semigroup	semigroup	NOUN
ejpam-23	37	3	s	s	VERB
ejpam-23	37	4	is	be	AUX
ejpam-23	37	5	called	call	VERB
ejpam-23	37	6	h̃-abundant	h̃-abundant	ADJ
ejpam-23	37	7	if	if	SCONJ
ejpam-23	37	8	every	every	DET
ejpam-23	37	9	h̃-class	h̃-class	PROPN
ejpam-23	37	10	contains	contain	VERB
ejpam-23	37	11	an	an	DET
ejpam-23	37	12	idempotent	idempotent	NOUN
ejpam-23	37	13	of	of	ADP
ejpam-23	37	14	s.	s.	PROPN
ejpam-23	37	15	clearly	clearly	ADV
ejpam-23	37	16	,	,	PUNCT
ejpam-23	37	17	the	the	DET
ejpam-23	37	18	h̃-abundant	h̃-abundant	ADJ
ejpam-23	37	19	semigroups	semigroup	NOUN
ejpam-23	37	20	are	be	AUX
ejpam-23	37	21	generalizations	generalization	NOUN
ejpam-23	37	22	of	of	ADP
ejpam-23	37	23	superabundant	superabundant	ADJ
ejpam-23	37	24	semigroups	semigroup	NOUN
ejpam-23	37	25	in	in	ADP
ejpam-23	37	26	the	the	DET
ejpam-23	37	27	class	class	NOUN
ejpam-23	37	28	of	of	ADP
ejpam-23	37	29	semiabundant	semiabundant	PROPN
ejpam-23	37	30	semigroups	semigroup	NOUN
ejpam-23	37	31	.	.	PUNCT
ejpam-23	38	1	one	one	PRON
ejpam-23	38	2	can	can	AUX
ejpam-23	38	3	easily	easily	ADV
ejpam-23	38	4	see	see	VERB
ejpam-23	38	5	that	that	PRON
ejpam-23	38	6	l̃	l̃	PROPN
ejpam-23	38	7	=	=	PUNCT
ejpam-23	38	8	l	l	NOUN
ejpam-23	38	9	on	on	ADP
ejpam-23	38	10	the	the	DET
ejpam-23	38	11	set	set	NOUN
ejpam-23	38	12	of	of	ADP
ejpam-23	38	13	regular	regular	ADJ
ejpam-23	38	14	elements	element	NOUN
ejpam-23	38	15	in	in	ADP
ejpam-23	38	16	any	any	DET
ejpam-23	38	17	h̃-abundant	h̃-abundant	ADJ
ejpam-23	38	18	semigroup	semigroup	NOUN
ejpam-23	38	19	.	.	PUNCT
ejpam-23	39	1	throughout	throughout	ADP
ejpam-23	39	2	this	this	DET
ejpam-23	39	3	paper	paper	NOUN
ejpam-23	39	4	,	,	PUNCT
ejpam-23	39	5	we	we	PRON
ejpam-23	39	6	call	call	VERB
ejpam-23	39	7	a	a	DET
ejpam-23	39	8	band	band	NOUN
ejpam-23	39	9	b	b	NOUN
ejpam-23	39	10	a	a	DET
ejpam-23	39	11	regular	regular	ADJ
ejpam-23	39	12	band	band	NOUN
ejpam-23	39	13	(	(	PUNCT
ejpam-23	39	14	right	right	ADJ
ejpam-23	39	15	quasi	quasi	X
ejpam-23	39	16	normal	normal	ADJ
ejpam-23	39	17	band	band	NOUN
ejpam-23	39	18	)	)	PUNCT
ejpam-23	39	19	if	if	SCONJ
ejpam-23	39	20	b	b	NOUN
ejpam-23	39	21	satisfies	satisfy	VERB
ejpam-23	39	22	the	the	DET
ejpam-23	39	23	identity	identity	NOUN
ejpam-23	39	24	axya	axya	NOUN
ejpam-23	39	25	=	=	PUNCT
ejpam-23	39	26	axaya(xya	axaya(xya	PROPN
ejpam-23	39	27	=	=	PUNCT
ejpam-23	39	28	xaya	xaya	PROPN
ejpam-23	39	29	)	)	PUNCT
ejpam-23	39	30	.	.	PUNCT
ejpam-23	40	1	according	accord	VERB
ejpam-23	40	2	to	to	ADP
ejpam-23	40	3	petrich	petrich	NOUN
ejpam-23	40	4	and	and	CCONJ
ejpam-23	40	5	reilly	reilly	ADV
ejpam-23	40	6	[	[	X
ejpam-23	40	7	12	12	NUM
ejpam-23	40	8	]	]	X
ejpam-23	40	9	,	,	PUNCT
ejpam-23	40	10	a	a	DET
ejpam-23	40	11	completely	completely	ADV
ejpam-23	40	12	regular	regular	ADJ
ejpam-23	40	13	semigroup	semigroup	NOUN
ejpam-23	40	14	s	s	VERB
ejpam-23	40	15	was	be	AUX
ejpam-23	40	16	called	call	VERB
ejpam-23	40	17	a	a	DET
ejpam-23	40	18	regular	regular	ADJ
ejpam-23	40	19	cryptogroup	cryptogroup	NOUN
ejpam-23	40	20	if	if	SCONJ
ejpam-23	40	21	the	the	DET
ejpam-23	40	22	green	green	PROPN
ejpam-23	40	23	relation	relation	PROPN
ejpam-23	40	24	h	h	PROPN
ejpam-23	40	25	on	on	ADP
ejpam-23	40	26	s	s	NOUN
ejpam-23	40	27	is	be	AUX
ejpam-23	40	28	a	a	DET
ejpam-23	40	29	regular	regular	ADJ
ejpam-23	40	30	band	band	NOUN
ejpam-23	40	31	congruence	congruence	NOUN
ejpam-23	40	32	on	on	ADP
ejpam-23	40	33	s.	s.	PROPN
ejpam-23	40	34	the	the	DET
ejpam-23	40	35	structure	structure	NOUN
ejpam-23	40	36	of	of	ADP
ejpam-23	40	37	regular	regular	ADJ
ejpam-23	40	38	cryptogroup	cryptogroup	NOUN
ejpam-23	40	39	was	be	AUX
ejpam-23	40	40	investigated	investigate	VERB
ejpam-23	40	41	by	by	ADP
ejpam-23	40	42	kong	kong	NOUN
ejpam-23	40	43	-	-	PUNCT
ejpam-23	40	44	shum	shum	NOUN
ejpam-23	40	45	in	in	ADP
ejpam-23	40	46	[	[	X
ejpam-23	40	47	8	8	NUM
ejpam-23	40	48	]	]	PUNCT
ejpam-23	40	49	and	and	CCONJ
ejpam-23	40	50	[	[	X
ejpam-23	40	51	9	9	NUM
ejpam-23	40	52	]	]	PUNCT
ejpam-23	40	53	.	.	PUNCT
ejpam-23	41	1	in	in	ADP
ejpam-23	41	2	the	the	DET
ejpam-23	41	3	class	class	NOUN
ejpam-23	41	4	of	of	ADP
ejpam-23	41	5	abundant	abundant	ADJ
ejpam-23	41	6	semigroups	semigroup	NOUN
ejpam-23	41	7	,	,	PUNCT
ejpam-23	41	8	guo	guo	NOUN
ejpam-23	41	9	and	and	CCONJ
ejpam-23	41	10	shum	shum	ADJ
ejpam-23	41	11	[	[	X
ejpam-23	41	12	5	5	NUM
ejpam-23	41	13	]	]	PUNCT
ejpam-23	41	14	called	call	VERB
ejpam-23	41	15	an	an	DET
ejpam-23	41	16	abundant	abundant	ADJ
ejpam-23	41	17	semigroup	semigroup	NOUN
ejpam-23	41	18	whose	whose	DET
ejpam-23	41	19	set	set	NOUN
ejpam-23	41	20	of	of	ADP
ejpam-23	41	21	idempotents	idempotent	NOUN
ejpam-23	41	22	forms	form	VERB
ejpam-23	41	23	a	a	DET
ejpam-23	41	24	regular	regular	ADJ
ejpam-23	41	25	band	band	NOUN
ejpam-23	41	26	a	a	DET
ejpam-23	41	27	cyber	cyber	NOUN
ejpam-23	41	28	group	group	NOUN
ejpam-23	41	29	.	.	PUNCT
ejpam-23	42	1	the	the	DET
ejpam-23	42	2	semilattice	semilattice	NOUN
ejpam-23	42	3	structure	structure	NOUN
ejpam-23	42	4	of	of	ADP
ejpam-23	42	5	regular	regular	ADJ
ejpam-23	42	6	cyber	cyber	NOUN
ejpam-23	42	7	groups	group	NOUN
ejpam-23	42	8	have	have	AUX
ejpam-23	42	9	been	be	AUX
ejpam-23	42	10	recently	recently	ADV
ejpam-23	42	11	investigated	investigate	VERB
ejpam-23	42	12	in	in	ADP
ejpam-23	42	13	[	[	X
ejpam-23	42	14	9	9	NUM
ejpam-23	42	15	]	]	PUNCT
ejpam-23	42	16	.	.	PUNCT
ejpam-23	43	1	naturally	naturally	ADV
ejpam-23	43	2	,	,	PUNCT
ejpam-23	43	3	one	one	PRON
ejpam-23	43	4	would	would	AUX
ejpam-23	43	5	ask	ask	VERB
ejpam-23	43	6	:	:	PUNCT
ejpam-23	43	7	can	can	AUX
ejpam-23	43	8	we	we	PRON
ejpam-23	43	9	establish	establish	VERB
ejpam-23	43	10	an	an	DET
ejpam-23	43	11	analogous	analogous	ADJ
ejpam-23	43	12	result	result	NOUN
ejpam-23	43	13	of	of	ADP
ejpam-23	43	14	superabundant	superabundant	ADJ
ejpam-23	43	15	semigroups	semigroup	NOUN
ejpam-23	44	1	[	[	X
ejpam-23	44	2	4	4	X
ejpam-23	44	3	]	]	PUNCT
ejpam-23	44	4	in	in	ADP
ejpam-23	44	5	the	the	DET
ejpam-23	44	6	class	class	NOUN
ejpam-23	44	7	of	of	ADP
ejpam-23	44	8	semiabundant	semiabundant	ADJ
ejpam-23	44	9	semigroups	semigroup	NOUN
ejpam-23	44	10	or	or	CCONJ
ejpam-23	44	11	an	an	DET
ejpam-23	44	12	analogous	analogous	ADJ
ejpam-23	44	13	result	result	NOUN
ejpam-23	44	14	of	of	ADP
ejpam-23	44	15	cryptogroups	cryptogroup	NOUN
ejpam-23	44	16	[	[	X
ejpam-23	44	17	12	12	NUM
ejpam-23	44	18	]	]	PUNCT
ejpam-23	44	19	in	in	ADP
ejpam-23	44	20	the	the	DET
ejpam-23	44	21	x.	x.	PROPN
ejpam-23	44	22	kong	kong	PROPN
ejpam-23	44	23	,	,	PUNCT
ejpam-23	44	24	y.ding	y.de	VERB
ejpam-23	44	25	,	,	PUNCT
ejpam-23	44	26	k.p.shum	k.p.shum	ADJ
ejpam-23	44	27	/	/	SYM
ejpam-23	44	28	eur	eur	PROPN
ejpam-23	44	29	.	.	PUNCT
ejpam-23	45	1	j.	j.	PROPN
ejpam-23	45	2	pure	pure	PROPN
ejpam-23	45	3	appl	appl	PROPN
ejpam-23	45	4	.	.	PROPN
ejpam-23	45	5	math	math	PROPN
ejpam-23	45	6	,	,	PUNCT
ejpam-23	45	7	1	1	NUM
ejpam-23	45	8	(	(	PUNCT
ejpam-23	45	9	2008	2008	NUM
ejpam-23	45	10	)	)	PUNCT
ejpam-23	45	11	,	,	PUNCT
ejpam-23	45	12	(	(	PUNCT
ejpam-23	45	13	46	46	NUM
ejpam-23	45	14	-	-	SYM
ejpam-23	45	15	59	59	NUM
ejpam-23	45	16	)	)	PUNCT
ejpam-23	45	17	48	48	NUM
ejpam-23	45	18	class	class	NOUN
ejpam-23	45	19	of	of	ADP
ejpam-23	45	20	h̃	h̃	PROPN
ejpam-23	45	21	-abundant	-abundant	NOUN
ejpam-23	45	22	semigroups	semigroup	VERB
ejpam-23	45	23	?	?	PUNCT
ejpam-23	46	1	in	in	ADP
ejpam-23	46	2	this	this	DET
ejpam-23	46	3	paper	paper	NOUN
ejpam-23	46	4	,	,	PUNCT
ejpam-23	46	5	we	we	PRON
ejpam-23	46	6	will	will	AUX
ejpam-23	46	7	establish	establish	VERB
ejpam-23	46	8	a	a	DET
ejpam-23	46	9	theorem	theorem	NOUN
ejpam-23	46	10	for	for	ADP
ejpam-23	46	11	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	46	12	by	by	ADP
ejpam-23	46	13	using	use	VERB
ejpam-23	46	14	the	the	DET
ejpam-23	46	15	green∼-relations	green∼-relation	NOUN
ejpam-23	46	16	and	and	CCONJ
ejpam-23	46	17	thekg	thekg	NOUN
ejpam-23	46	18	-	-	PUNCT
ejpam-23	46	19	strong	strong	ADJ
ejpam-23	46	20	semilattice	semilattice	NOUN
ejpam-23	46	21	of	of	ADP
ejpam-23	46	22	semigroups	semigroup	NOUN
ejpam-23	46	23	,	,	PUNCT
ejpam-23	46	24	as	as	SCONJ
ejpam-23	46	25	described	describe	VERB
ejpam-23	46	26	in	in	ADP
ejpam-23	46	27	[	[	X
ejpam-23	46	28	10	10	NUM
ejpam-23	46	29	]	]	PUNCT
ejpam-23	46	30	.	.	PUNCT
ejpam-23	47	1	we	we	PRON
ejpam-23	47	2	will	will	AUX
ejpam-23	47	3	show	show	VERB
ejpam-23	47	4	that	that	SCONJ
ejpam-23	47	5	an	an	DET
ejpam-23	47	6	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	47	7	is	be	AUX
ejpam-23	47	8	a	a	DET
ejpam-23	47	9	regular	regular	ADJ
ejpam-23	47	10	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	47	11	if	if	SCONJ
ejpam-23	47	12	and	and	CCONJ
ejpam-23	47	13	only	only	ADV
ejpam-23	47	14	if	if	SCONJ
ejpam-23	47	15	it	it	PRON
ejpam-23	47	16	is	be	AUX
ejpam-23	47	17	an	an	DET
ejpam-23	47	18	h̃g	h̃g	ADJ
ejpam-23	47	19	-	-	PUNCT
ejpam-23	47	20	strong	strong	ADJ
ejpam-23	47	21	semilattice	semilattice	NOUN
ejpam-23	47	22	of	of	ADP
ejpam-23	47	23	completely	completely	ADV
ejpam-23	47	24	j̃	j̃	PROPN
ejpam-23	47	25	-simple	-simple	ADJ
ejpam-23	47	26	semigroups	semigroup	NOUN
ejpam-23	47	27	.	.	PUNCT
ejpam-23	48	1	our	our	PRON
ejpam-23	48	2	results	result	NOUN
ejpam-23	48	3	in	in	ADP
ejpam-23	48	4	this	this	DET
ejpam-23	48	5	paper	paper	NOUN
ejpam-23	48	6	also	also	ADV
ejpam-23	48	7	generalize	generalize	VERB
ejpam-23	48	8	and	and	CCONJ
ejpam-23	48	9	enrich	enrich	VERB
ejpam-23	48	10	the	the	DET
ejpam-23	48	11	corresponding	corresponding	ADJ
ejpam-23	48	12	results	result	NOUN
ejpam-23	48	13	given	give	VERB
ejpam-23	48	14	in	in	ADP
ejpam-23	48	15	[	[	X
ejpam-23	48	16	1	1	NUM
ejpam-23	48	17	]	]	PUNCT
ejpam-23	48	18	,	,	PUNCT
ejpam-23	48	19	[	[	X
ejpam-23	48	20	4	4	NUM
ejpam-23	48	21	]	]	PUNCT
ejpam-23	48	22	,	,	PUNCT
ejpam-23	48	23	[	[	X
ejpam-23	48	24	7	7	NUM
ejpam-23	48	25	]	]	PUNCT
ejpam-23	48	26	,	,	PUNCT
ejpam-23	48	27	[	[	X
ejpam-23	48	28	8	8	NUM
ejpam-23	48	29	]	]	PUNCT
ejpam-23	48	30	and	and	CCONJ
ejpam-23	48	31	[	[	X
ejpam-23	48	32	13	13	NUM
ejpam-23	48	33	]	]	PUNCT
ejpam-23	48	34	.	.	PUNCT
ejpam-23	49	1	2	2	X
ejpam-23	49	2	.	.	X
ejpam-23	49	3	kg	kg	ADJ
ejpam-23	49	4	-	-	PUNCT
ejpam-23	49	5	strong	strong	ADJ
ejpam-23	49	6	semilattices	semilattice	NOUN
ejpam-23	49	7	we	we	PRON
ejpam-23	49	8	now	now	ADV
ejpam-23	49	9	restate	restate	VERB
ejpam-23	49	10	the	the	DET
ejpam-23	49	11	concept	concept	NOUN
ejpam-23	49	12	of	of	ADP
ejpam-23	49	13	g	g	NOUN
ejpam-23	49	14	-	-	PUNCT
ejpam-23	49	15	strong	strong	ADJ
ejpam-23	49	16	semilattice	semilattice	NOUN
ejpam-23	49	17	decomposition	decomposition	NOUN
ejpam-23	49	18	of	of	ADP
ejpam-23	49	19	semigroup	semigroup	PROPN
ejpam-23	49	20	s	s	AUX
ejpam-23	49	21	given	give	VERB
ejpam-23	49	22	by	by	ADP
ejpam-23	49	23	kong	kong	PROPN
ejpam-23	49	24	and	and	CCONJ
ejpam-23	49	25	shum	shum	ADJ
ejpam-23	49	26	in	in	ADP
ejpam-23	49	27	[	[	X
ejpam-23	49	28	8	8	NUM
ejpam-23	49	29	]	]	PUNCT
ejpam-23	49	30	and	and	CCONJ
ejpam-23	49	31	[	[	X
ejpam-23	49	32	9	9	NUM
ejpam-23	49	33	]	]	PUNCT
ejpam-23	49	34	.	.	PUNCT
ejpam-23	50	1	let	let	VERB
ejpam-23	50	2	s	s	VERB
ejpam-23	50	3	=	=	PUNCT
ejpam-23	50	4	(	(	PUNCT
ejpam-23	50	5	y	y	PROPN
ejpam-23	50	6	;	;	PUNCT
ejpam-23	50	7	sα	sα	X
ejpam-23	50	8	)	)	PUNCT
ejpam-23	50	9	be	be	AUX
ejpam-23	50	10	a	a	DET
ejpam-23	50	11	semilattice	semilattice	NOUN
ejpam-23	50	12	of	of	ADP
ejpam-23	50	13	the	the	DET
ejpam-23	50	14	semigroups	semigroup	NOUN
ejpam-23	50	15	sα	sα	PROPN
ejpam-23	50	16	,	,	PUNCT
ejpam-23	50	17	where	where	SCONJ
ejpam-23	50	18	each	each	DET
ejpam-23	50	19	sα	sα	NOUN
ejpam-23	50	20	is	be	AUX
ejpam-23	50	21	a	a	DET
ejpam-23	50	22	subsemigroup	subsemigroup	NOUN
ejpam-23	50	23	of	of	ADP
ejpam-23	50	24	the	the	DET
ejpam-23	50	25	semigroup	semigroup	PROPN
ejpam-23	50	26	s	s	PROPN
ejpam-23	50	27	and	and	CCONJ
ejpam-23	50	28	y	y	PROPN
ejpam-23	50	29	is	be	AUX
ejpam-23	50	30	a	a	DET
ejpam-23	50	31	semilattice	semilattice	NOUN
ejpam-23	50	32	.	.	PUNCT
ejpam-23	51	1	we	we	PRON
ejpam-23	51	2	define	define	VERB
ejpam-23	51	3	the	the	DET
ejpam-23	51	4	g	g	NOUN
ejpam-23	51	5	-	-	PUNCT
ejpam-23	51	6	strong	strong	ADJ
ejpam-23	51	7	semilattice	semilattice	NOUN
ejpam-23	51	8	of	of	ADP
ejpam-23	51	9	semigroups	semigroup	NOUN
ejpam-23	51	10	by	by	ADP
ejpam-23	51	11	generalizing	generalize	VERB
ejpam-23	51	12	the	the	DET
ejpam-23	51	13	well	well	ADV
ejpam-23	51	14	known	know	VERB
ejpam-23	51	15	strong	strong	ADJ
ejpam-23	51	16	semilattice	semilattice	NOUN
ejpam-23	51	17	of	of	ADP
ejpam-23	51	18	semigroups	semigroup	NOUN
ejpam-23	51	19	(	(	PUNCT
ejpam-23	51	20	see	see	VERB
ejpam-23	51	21	[	[	X
ejpam-23	51	22	9	9	NUM
ejpam-23	51	23	]	]	NUM
ejpam-23	51	24	)	)	PUNCT
ejpam-23	51	25	.	.	PUNCT
ejpam-23	52	1	definition	definition	NOUN
ejpam-23	52	2	2.1	2.1	NUM
ejpam-23	52	3	let	let	VERB
ejpam-23	52	4	s	s	VERB
ejpam-23	52	5	=	=	PUNCT
ejpam-23	52	6	(	(	PUNCT
ejpam-23	52	7	y	y	PROPN
ejpam-23	52	8	;	;	PUNCT
ejpam-23	52	9	sα	sα	AUX
ejpam-23	52	10	)	)	PUNCT
ejpam-23	52	11	be	be	AUX
ejpam-23	52	12	a	a	DET
ejpam-23	52	13	semigroup	semigroup	NOUN
ejpam-23	52	14	.	.	PUNCT
ejpam-23	52	15	suppose	suppose	VERB
ejpam-23	52	16	that	that	SCONJ
ejpam-23	52	17	the	the	DET
ejpam-23	52	18	following	follow	VERB
ejpam-23	52	19	conditions	condition	NOUN
ejpam-23	52	20	s	s	PRON
ejpam-23	52	21	are	be	AUX
ejpam-23	52	22	satisfied	satisfied	ADJ
ejpam-23	52	23	:	:	PUNCT
ejpam-23	52	24	(	(	PUNCT
ejpam-23	52	25	i	i	NOUN
ejpam-23	52	26	)	)	PUNCT
ejpam-23	52	27	(	(	PUNCT
ejpam-23	52	28	∀α	∀α	NOUN
ejpam-23	52	29	,	,	PUNCT
ejpam-23	52	30	β	β	X
ejpam-23	52	31	∈	∈	PROPN
ejpam-23	52	32	y	y	PROPN
ejpam-23	52	33	,	,	PUNCT
ejpam-23	52	34	α	α	X
ejpam-23	52	35	>	>	X
ejpam-23	52	36	β	β	NOUN
ejpam-23	52	37	)	)	PUNCT
ejpam-23	52	38	,	,	PUNCT
ejpam-23	52	39	there	there	PRON
ejpam-23	52	40	exists	exist	VERB
ejpam-23	52	41	a	a	DET
ejpam-23	52	42	family	family	NOUN
ejpam-23	52	43	of	of	ADP
ejpam-23	52	44	homomorphisms	homomorphisms	PROPN
ejpam-23	52	45	ϕd(α	ϕd(α	PROPN
ejpam-23	52	46	,	,	PUNCT
ejpam-23	52	47	β	β	NOUN
ejpam-23	52	48	)	)	PUNCT
ejpam-23	52	49	:	:	PUNCT
ejpam-23	53	1	sα	sα	ADV
ejpam-23	53	2	−→	−→	NOUN
ejpam-23	53	3	sβ	sβ	X
ejpam-23	53	4	,	,	PUNCT
ejpam-23	53	5	where	where	SCONJ
ejpam-23	53	6	d(α	d(α	NOUN
ejpam-23	53	7	,	,	PUNCT
ejpam-23	53	8	β	β	X
ejpam-23	53	9	)	)	PUNCT
ejpam-23	53	10	∈	∈	PROPN
ejpam-23	53	11	d(α	d(α	PROPN
ejpam-23	53	12	,	,	PUNCT
ejpam-23	53	13	β	β	NOUN
ejpam-23	53	14	)	)	PUNCT
ejpam-23	53	15	and	and	CCONJ
ejpam-23	53	16	d(α	d(α	PROPN
ejpam-23	53	17	,	,	PUNCT
ejpam-23	53	18	β	β	NOUN
ejpam-23	53	19	)	)	PUNCT
ejpam-23	53	20	is	be	AUX
ejpam-23	53	21	a	a	DET
ejpam-23	53	22	non	non	ADJ
ejpam-23	53	23	-	-	ADJ
ejpam-23	53	24	empty	empty	ADJ
ejpam-23	53	25	index	index	NOUN
ejpam-23	53	26	set	set	NOUN
ejpam-23	53	27	.	.	PUNCT
ejpam-23	54	1	(	(	PUNCT
ejpam-23	54	2	ii	ii	NOUN
ejpam-23	54	3	)	)	PUNCT
ejpam-23	54	4	(	(	PUNCT
ejpam-23	54	5	∀α	∀α	NOUN
ejpam-23	54	6	∈	∈	PROPN
ejpam-23	54	7	y	y	PROPN
ejpam-23	54	8	)	)	PUNCT
ejpam-23	54	9	,	,	PUNCT
ejpam-23	54	10	d(α	d(α	PROPN
ejpam-23	54	11	,	,	PUNCT
ejpam-23	54	12	α	α	NOUN
ejpam-23	54	13	)	)	PUNCT
ejpam-23	54	14	is	be	AUX
ejpam-23	54	15	a	a	DET
ejpam-23	54	16	singleton	singleton	NOUN
ejpam-23	54	17	.	.	PUNCT
ejpam-23	55	1	denote	denote	VERB
ejpam-23	55	2	the	the	DET
ejpam-23	55	3	element	element	NOUN
ejpam-23	55	4	in	in	ADP
ejpam-23	55	5	d(α	d(α	PROPN
ejpam-23	55	6	,	,	PUNCT
ejpam-23	55	7	α	α	NOUN
ejpam-23	55	8	)	)	PUNCT
ejpam-23	55	9	by	by	ADP
ejpam-23	55	10	d(α	d(α	PROPN
ejpam-23	55	11	,	,	PUNCT
ejpam-23	55	12	α	α	NOUN
ejpam-23	55	13	)	)	PUNCT
ejpam-23	55	14	.	.	PUNCT
ejpam-23	56	1	in	in	ADP
ejpam-23	56	2	this	this	DET
ejpam-23	56	3	case	case	NOUN
ejpam-23	56	4	,	,	PUNCT
ejpam-23	56	5	the	the	DET
ejpam-23	56	6	homomorphism	homomorphism	PROPN
ejpam-23	56	7	ϕd(α	ϕd(α	PROPN
ejpam-23	56	8	,	,	PUNCT
ejpam-23	56	9	α	α	NOUN
ejpam-23	56	10	)	)	PUNCT
ejpam-23	56	11	:	:	PUNCT
ejpam-23	56	12	sα	sα	ADV
ejpam-23	56	13	−→	−→	ADV
ejpam-23	56	14	sα	sα	ADV
ejpam-23	56	15	is	be	AUX
ejpam-23	56	16	the	the	DET
ejpam-23	56	17	identity	identity	NOUN
ejpam-23	56	18	automorphism	automorphism	NOUN
ejpam-23	56	19	of	of	ADP
ejpam-23	56	20	the	the	DET
ejpam-23	56	21	semigroup	semigroup	PROPN
ejpam-23	56	22	sα	sα	PROPN
ejpam-23	56	23	.	.	PUNCT
ejpam-23	56	24	(	(	PUNCT
ejpam-23	56	25	iii	iii	NOUN
ejpam-23	56	26	)	)	PUNCT
ejpam-23	56	27	(	(	PUNCT
ejpam-23	56	28	∀α	∀α	NOUN
ejpam-23	56	29	,	,	PUNCT
ejpam-23	56	30	β	β	X
ejpam-23	56	31	,	,	PUNCT
ejpam-23	56	32	γ	γ	PROPN
ejpam-23	56	33	∈	∈	PROPN
ejpam-23	56	34	y	y	PROPN
ejpam-23	56	35	,	,	PUNCT
ejpam-23	56	36	α	α	X
ejpam-23	56	37	>	>	X
ejpam-23	56	38	β	β	X
ejpam-23	56	39	>	>	X
ejpam-23	56	40	γ	γ	PROPN
ejpam-23	56	41	)	)	PUNCT
ejpam-23	56	42	,	,	PUNCT
ejpam-23	56	43	if	if	SCONJ
ejpam-23	56	44	we	we	PRON
ejpam-23	56	45	write	write	VERB
ejpam-23	56	46	ϕα	ϕα	ADV
ejpam-23	56	47	,	,	PUNCT
ejpam-23	56	48	β	β	X
ejpam-23	56	49	=	=	SYM
ejpam-23	56	50	{	{	PUNCT
ejpam-23	56	51	ϕd(α	ϕd(α	PROPN
ejpam-23	56	52	,	,	PUNCT
ejpam-23	56	53	β	β	NOUN
ejpam-23	56	54	)	)	PUNCT
ejpam-23	56	55	:	:	PUNCT
ejpam-23	57	1	d(α	d(α	NOUN
ejpam-23	57	2	,	,	PUNCT
ejpam-23	57	3	β	β	X
ejpam-23	57	4	)	)	PUNCT
ejpam-23	57	5	∈	∈	PROPN
ejpam-23	57	6	d(α	d(α	PROPN
ejpam-23	57	7	,	,	PUNCT
ejpam-23	57	8	β	β	NOUN
ejpam-23	57	9	)	)	PUNCT
ejpam-23	57	10	}	}	PUNCT
ejpam-23	57	11	then	then	ADV
ejpam-23	57	12	ϕα	ϕα	ADV
ejpam-23	57	13	,	,	PUNCT
ejpam-23	57	14	βϕβ	βϕβ	PROPN
ejpam-23	57	15	,	,	PUNCT
ejpam-23	57	16	γ	γ	X
ejpam-23	57	17	⊆	⊆	NUM
ejpam-23	57	18	ϕα	ϕα	NOUN
ejpam-23	57	19	,	,	PUNCT
ejpam-23	57	20	γ	γ	X
ejpam-23	57	21	,	,	PUNCT
ejpam-23	57	22	where	where	SCONJ
ejpam-23	57	23	ϕα	ϕα	ADV
ejpam-23	57	24	,	,	PUNCT
ejpam-23	57	25	βϕβ	βϕβ	PROPN
ejpam-23	57	26	,	,	PUNCT
ejpam-23	57	27	γ	γ	X
ejpam-23	57	28	=	=	SYM
ejpam-23	57	29	{	{	PUNCT
ejpam-23	57	30	ϕd(α	ϕd(α	PROPN
ejpam-23	57	31	,	,	PUNCT
ejpam-23	57	32	β)ϕd(β	β)ϕd(β	PROPN
ejpam-23	57	33	,	,	PUNCT
ejpam-23	57	34	γ	γ	NOUN
ejpam-23	57	35	)	)	PUNCT
ejpam-23	57	36	:	:	PUNCT
ejpam-23	57	37	∀d(α	∀d(α	PROPN
ejpam-23	57	38	,	,	PUNCT
ejpam-23	57	39	β	β	X
ejpam-23	57	40	)	)	PUNCT
ejpam-23	57	41	∈	∈	PROPN
ejpam-23	57	42	d(α	d(α	PROPN
ejpam-23	57	43	,	,	PUNCT
ejpam-23	57	44	β	β	NOUN
ejpam-23	57	45	)	)	PUNCT
ejpam-23	57	46	,	,	PUNCT
ejpam-23	57	47	d(β	d(β	PROPN
ejpam-23	57	48	,	,	PUNCT
ejpam-23	57	49	γ	γ	NOUN
ejpam-23	57	50	)	)	PUNCT
ejpam-23	57	51	∈	∈	PROPN
ejpam-23	57	52	d(β	d(β	PROPN
ejpam-23	57	53	,	,	PUNCT
ejpam-23	57	54	γ	γ	NOUN
ejpam-23	57	55	)	)	PUNCT
ejpam-23	57	56	}	}	PUNCT
ejpam-23	57	57	.	.	PUNCT
ejpam-23	58	1	(	(	PUNCT
ejpam-23	58	2	iv	iv	X
ejpam-23	58	3	)	)	PUNCT
ejpam-23	58	4	for	for	ADP
ejpam-23	58	5	each	each	DET
ejpam-23	58	6	α	α	NOUN
ejpam-23	58	7	,	,	PUNCT
ejpam-23	58	8	β	β	X
ejpam-23	58	9	∈	∈	PROPN
ejpam-23	58	10	y	y	PROPN
ejpam-23	58	11	,	,	PUNCT
ejpam-23	58	12	there	there	PRON
ejpam-23	58	13	is	be	VERB
ejpam-23	58	14	a	a	DET
ejpam-23	58	15	mapping	mapping	NOUN
ejpam-23	58	16	from	from	ADP
ejpam-23	58	17	sα	sα	ADV
ejpam-23	58	18	into	into	ADP
ejpam-23	58	19	the	the	DET
ejpam-23	58	20	set	set	NOUN
ejpam-23	58	21	ϕβ	ϕβ	PROPN
ejpam-23	58	22	,	,	PUNCT
ejpam-23	58	23	αβ	αβ	CCONJ
ejpam-23	58	24	whose	whose	DET
ejpam-23	58	25	value	value	NOUN
ejpam-23	58	26	at	at	ADP
ejpam-23	58	27	any	any	DET
ejpam-23	58	28	given	give	VERB
ejpam-23	58	29	element	element	NOUN
ejpam-23	58	30	a	a	DET
ejpam-23	58	31	∈	∈	NOUN
ejpam-23	58	32	sα	sα	ADV
ejpam-23	58	33	is	be	AUX
ejpam-23	58	34	denoted	denote	VERB
ejpam-23	58	35	by	by	ADP
ejpam-23	58	36	ϕa	ϕa	PROPN
ejpam-23	58	37	d(β	d(β	PROPN
ejpam-23	58	38	,	,	PUNCT
ejpam-23	58	39	αβ	αβ	INTJ
ejpam-23	58	40	)	)	PUNCT
ejpam-23	58	41	such	such	ADJ
ejpam-23	58	42	that	that	PRON
ejpam-23	58	43	for	for	ADP
ejpam-23	58	44	all	all	DET
ejpam-23	58	45	b	b	PROPN
ejpam-23	58	46	∈	∈	ADJ
ejpam-23	58	47	sβ	sβ	X
ejpam-23	58	48	,	,	PUNCT
ejpam-23	58	49	ab	ab	PROPN
ejpam-23	58	50	=	=	PUNCT
ejpam-23	58	51	(	(	PUNCT
ejpam-23	58	52	aϕb	aϕb	VERB
ejpam-23	58	53	d(α	d(α	PROPN
ejpam-23	58	54	,	,	PUNCT
ejpam-23	58	55	αβ))(bϕ	αβ))(bϕ	PROPN
ejpam-23	58	56	a	a	DET
ejpam-23	58	57	d(β	d(β	PROPN
ejpam-23	58	58	,	,	PUNCT
ejpam-23	58	59	αβ	αβ	NOUN
ejpam-23	58	60	)	)	PUNCT
ejpam-23	58	61	)	)	PUNCT
ejpam-23	58	62	.	.	PUNCT
ejpam-23	59	1	then	then	ADV
ejpam-23	59	2	the	the	DET
ejpam-23	59	3	above	above	ADJ
ejpam-23	59	4	semilatttice	semilatttice	NOUN
ejpam-23	59	5	of	of	ADP
ejpam-23	59	6	semigroups	semigroup	NOUN
ejpam-23	59	7	is	be	AUX
ejpam-23	59	8	called	call	VERB
ejpam-23	59	9	the	the	DET
ejpam-23	59	10	generalized	generalize	VERB
ejpam-23	59	11	strong	strong	ADJ
ejpam-23	59	12	semilattice	semilattice	NOUN
ejpam-23	59	13	of	of	ADP
ejpam-23	59	14	semigroups	semigroup	NOUN
ejpam-23	59	15	sα	sα	ADV
ejpam-23	59	16	and	and	CCONJ
ejpam-23	59	17	in	in	ADP
ejpam-23	59	18	brevity	brevity	NOUN
ejpam-23	59	19	,	,	PUNCT
ejpam-23	59	20	the	the	DET
ejpam-23	59	21	“	"	PUNCT
ejpam-23	59	22	g	g	NOUN
ejpam-23	59	23	-	-	PUNCT
ejpam-23	59	24	strong	strong	ADJ
ejpam-23	59	25	semilattice	semilattice	NOUN
ejpam-23	59	26	”	"	PUNCT
ejpam-23	59	27	of	of	ADP
ejpam-23	59	28	semigroups	semigroup	NOUN
ejpam-23	59	29	sα	sα	ADV
ejpam-23	59	30	and	and	CCONJ
ejpam-23	59	31	denoted	denote	VERB
ejpam-23	59	32	it	it	PRON
ejpam-23	59	33	by	by	ADP
ejpam-23	59	34	s	s	NOUN
ejpam-23	59	35	=	=	X
ejpam-23	59	36	g[y	g[y	PROPN
ejpam-23	59	37	;	;	PUNCT
ejpam-23	59	38	sα	sα	X
ejpam-23	59	39	,	,	PUNCT
ejpam-23	59	40	ϕα	ϕα	ADV
ejpam-23	59	41	,	,	PUNCT
ejpam-23	59	42	β	β	NOUN
ejpam-23	59	43	]	]	X
ejpam-23	59	44	.	.	PUNCT
ejpam-23	60	1	the	the	DET
ejpam-23	60	2	following	follow	VERB
ejpam-23	60	3	definition	definition	NOUN
ejpam-23	60	4	is	be	AUX
ejpam-23	60	5	a	a	DET
ejpam-23	60	6	more	more	ADV
ejpam-23	60	7	general	general	ADJ
ejpam-23	60	8	version	version	NOUN
ejpam-23	60	9	of	of	ADP
ejpam-23	60	10	g	g	NOUN
ejpam-23	60	11	-	-	PUNCT
ejpam-23	60	12	strong	strong	ADJ
ejpam-23	60	13	semilattices	semilattice	NOUN
ejpam-23	60	14	.	.	PUNCT
ejpam-23	61	1	definition	definition	NOUN
ejpam-23	61	2	2.2	2.2	NUM
ejpam-23	61	3	let	let	VERB
ejpam-23	61	4	k	k	PROPN
ejpam-23	61	5	be	be	AUX
ejpam-23	61	6	any	any	DET
ejpam-23	61	7	equivalent	equivalent	ADJ
ejpam-23	61	8	relation	relation	NOUN
ejpam-23	61	9	on	on	ADP
ejpam-23	61	10	a	a	DET
ejpam-23	61	11	g	g	NOUN
ejpam-23	61	12	-	-	PUNCT
ejpam-23	61	13	strong	strong	ADJ
ejpam-23	61	14	semilattice	semilattice	NOUN
ejpam-23	61	15	of	of	ADP
ejpam-23	61	16	semigroups	semigroups	X
ejpam-23	61	17	s	s	PART
ejpam-23	61	18	=	=	X
ejpam-23	61	19	g[y	g[y	NOUN
ejpam-23	61	20	;	;	PUNCT
ejpam-23	61	21	sα	sα	X
ejpam-23	61	22	,	,	PUNCT
ejpam-23	61	23	ϕα	ϕα	ADV
ejpam-23	61	24	,	,	PUNCT
ejpam-23	61	25	β	β	NOUN
ejpam-23	61	26	]	]	X
ejpam-23	61	27	.	.	PUNCT
ejpam-23	62	1	then	then	ADV
ejpam-23	62	2	,	,	PUNCT
ejpam-23	62	3	we	we	PRON
ejpam-23	62	4	call	call	VERB
ejpam-23	62	5	s	s	VERB
ejpam-23	62	6	a	a	DET
ejpam-23	62	7	“	"	PUNCT
ejpam-23	62	8	kg	kg	ADJ
ejpam-23	62	9	-	-	PUNCT
ejpam-23	62	10	strong	strong	ADJ
ejpam-23	62	11	semilattice	semilattice	NOUN
ejpam-23	62	12	of	of	ADP
ejpam-23	62	13	semigroups	semigroups	X
ejpam-23	62	14	sα	sα	PART
ejpam-23	62	15	”	"	PUNCT
ejpam-23	62	16	if	if	SCONJ
ejpam-23	62	17	for	for	ADP
ejpam-23	62	18	every	every	DET
ejpam-23	62	19	α	α	NOUN
ejpam-23	62	20	,	,	PUNCT
ejpam-23	62	21	β	β	PROPN
ejpam-23	62	22	∈	∈	PROPN
ejpam-23	62	23	y	y	PROPN
ejpam-23	62	24	,	,	PUNCT
ejpam-23	62	25	the	the	DET
ejpam-23	62	26	mapping	mapping	NOUN
ejpam-23	62	27	a	a	DET
ejpam-23	62	28	7−→	7−→	NOUN
ejpam-23	62	29	ϕa	ϕa	ADP
ejpam-23	62	30	α(β	α(β	PROPN
ejpam-23	62	31	,	,	PUNCT
ejpam-23	62	32	αβ	αβ	X
ejpam-23	62	33	)	)	PUNCT
ejpam-23	62	34	has	have	VERB
ejpam-23	62	35	the	the	DET
ejpam-23	62	36	property	property	NOUN
ejpam-23	62	37	that	that	PRON
ejpam-23	62	38	ϕa	ϕa	ADP
ejpam-23	62	39	d(β	d(β	PROPN
ejpam-23	62	40	,	,	PUNCT
ejpam-23	62	41	αβ	αβ	INTJ
ejpam-23	62	42	)	)	PUNCT
ejpam-23	62	43	=	=	PRON
ejpam-23	62	44	ϕb	ϕb	ADP
ejpam-23	62	45	d(β	d(β	PROPN
ejpam-23	62	46	,	,	PUNCT
ejpam-23	62	47	αβ	αβ	INTJ
ejpam-23	62	48	)	)	PUNCT
ejpam-23	62	49	whenever	whenever	SCONJ
ejpam-23	62	50	the	the	DET
ejpam-23	62	51	elements	element	NOUN
ejpam-23	62	52	a	a	PRON
ejpam-23	62	53	,	,	PUNCT
ejpam-23	62	54	b	b	X
ejpam-23	62	55	∈	∈	PROPN
ejpam-23	62	56	sα	sα	NOUN
ejpam-23	62	57	are	be	AUX
ejpam-23	62	58	in	in	ADP
ejpam-23	62	59	the	the	DET
ejpam-23	62	60	same	same	ADJ
ejpam-23	62	61	k	k	NOUN
ejpam-23	62	62	-	-	PUNCT
ejpam-23	62	63	class	class	NOUN
ejpam-23	62	64	of	of	ADP
ejpam-23	62	65	s.	s.	PROPN
ejpam-23	62	66	thus	thus	ADV
ejpam-23	62	67	,	,	PUNCT
ejpam-23	62	68	it	it	PRON
ejpam-23	62	69	is	be	AUX
ejpam-23	62	70	clear	clear	ADJ
ejpam-23	62	71	that	that	SCONJ
ejpam-23	62	72	the	the	DET
ejpam-23	62	73	g	g	NOUN
ejpam-23	62	74	-	-	PUNCT
ejpam-23	62	75	strong	strong	ADJ
ejpam-23	62	76	semilattice	semilattice	NOUN
ejpam-23	62	77	of	of	ADP
ejpam-23	62	78	semigroups	semigroups	X
ejpam-23	62	79	s	s	X
ejpam-23	62	80	can	can	AUX
ejpam-23	62	81	be	be	AUX
ejpam-23	62	82	determined	determine	VERB
ejpam-23	62	83	by	by	ADP
ejpam-23	62	84	an	an	DET
ejpam-23	62	85	equivalent	equivalent	ADJ
ejpam-23	62	86	x.	x.	PROPN
ejpam-23	62	87	kong	kong	PROPN
ejpam-23	62	88	,	,	PUNCT
ejpam-23	62	89	y.ding	y.de	VERB
ejpam-23	62	90	,	,	PUNCT
ejpam-23	62	91	k.p.shum	k.p.shum	ADJ
ejpam-23	62	92	/	/	SYM
ejpam-23	62	93	eur	eur	PROPN
ejpam-23	62	94	.	.	PUNCT
ejpam-23	63	1	j.	j.	PROPN
ejpam-23	63	2	pure	pure	PROPN
ejpam-23	63	3	appl	appl	PROPN
ejpam-23	63	4	.	.	PROPN
ejpam-23	63	5	math	math	PROPN
ejpam-23	63	6	,	,	PUNCT
ejpam-23	63	7	1	1	NUM
ejpam-23	63	8	(	(	PUNCT
ejpam-23	63	9	2008	2008	NUM
ejpam-23	63	10	)	)	PUNCT
ejpam-23	63	11	,	,	PUNCT
ejpam-23	63	12	(	(	PUNCT
ejpam-23	63	13	46	46	NUM
ejpam-23	63	14	-	-	SYM
ejpam-23	63	15	59	59	NUM
ejpam-23	63	16	)	)	PUNCT
ejpam-23	63	17	49	49	NUM
ejpam-23	63	18	relation	relation	NOUN
ejpam-23	63	19	k.	k.	PROPN
ejpam-23	64	1	we	we	PRON
ejpam-23	64	2	therefore	therefore	ADV
ejpam-23	64	3	call	call	VERB
ejpam-23	64	4	the	the	DET
ejpam-23	64	5	above	above	ADJ
ejpam-23	64	6	generalized	generalized	ADJ
ejpam-23	64	7	strong	strong	ADJ
ejpam-23	64	8	semilattice	semilattice	NOUN
ejpam-23	64	9	of	of	ADP
ejpam-23	64	10	semigroups	semigroup	NOUN
ejpam-23	64	11	sα	sα	VERB
ejpam-23	64	12	a	a	DET
ejpam-23	64	13	“	"	PUNCT
ejpam-23	64	14	kg	kg	NUM
ejpam-23	64	15	-strong	-strong	ADJ
ejpam-23	64	16	semilattice	semilattice	NOUN
ejpam-23	64	17	of	of	ADP
ejpam-23	64	18	semigroups	semigroups	PROPN
ejpam-23	64	19	sα	sα	VERB
ejpam-23	64	20	”	"	PUNCT
ejpam-23	64	21	and	and	CCONJ
ejpam-23	64	22	is	be	AUX
ejpam-23	64	23	denoted	denote	VERB
ejpam-23	64	24	by	by	ADP
ejpam-23	64	25	s	s	NOUN
ejpam-23	64	26	=	=	SYM
ejpam-23	64	27	kg[y	kg[y	PROPN
ejpam-23	64	28	;	;	PUNCT
ejpam-23	64	29	sα	sα	ADV
ejpam-23	64	30	,	,	PUNCT
ejpam-23	64	31	ϕα	ϕα	ADV
ejpam-23	64	32	,	,	PUNCT
ejpam-23	64	33	β	β	X
ejpam-23	64	34	]	]	X
ejpam-23	64	35	,	,	PUNCT
ejpam-23	64	36	where	where	SCONJ
ejpam-23	64	37	k	k	PROPN
ejpam-23	64	38	is	be	AUX
ejpam-23	64	39	any	any	DET
ejpam-23	64	40	one	one	NUM
ejpam-23	64	41	of	of	ADP
ejpam-23	64	42	the	the	DET
ejpam-23	64	43	green	green	PROPN
ejpam-23	64	44	relations	relations	PROPN
ejpam-23	64	45	l	l	PROPN
ejpam-23	64	46	,	,	PUNCT
ejpam-23	64	47	r	r	NOUN
ejpam-23	64	48	,	,	PUNCT
ejpam-23	64	49	d	d	NOUN
ejpam-23	64	50	and	and	CCONJ
ejpam-23	64	51	h	h	NOUN
ejpam-23	64	52	,	,	PUNCT
ejpam-23	64	53	respectively	respectively	ADV
ejpam-23	64	54	.	.	PUNCT
ejpam-23	65	1	remark	remark	VERB
ejpam-23	65	2	2.3	2.3	NUM
ejpam-23	65	3	it	it	PRON
ejpam-23	65	4	is	be	AUX
ejpam-23	65	5	clear	clear	ADJ
ejpam-23	65	6	that	that	SCONJ
ejpam-23	65	7	the	the	DET
ejpam-23	65	8	kg	kg	ADJ
ejpam-23	65	9	-	-	PUNCT
ejpam-23	65	10	strong	strong	ADJ
ejpam-23	65	11	semilattice	semilattice	NOUN
ejpam-23	65	12	is	be	AUX
ejpam-23	65	13	stronger	strong	ADJ
ejpam-23	65	14	than	than	ADP
ejpam-23	65	15	the	the	DET
ejpam-23	65	16	g	g	NOUN
ejpam-23	65	17	-	-	PUNCT
ejpam-23	65	18	strong	strong	ADJ
ejpam-23	65	19	semilattice	semilattice	NOUN
ejpam-23	66	1	but	but	CCONJ
ejpam-23	66	2	it	it	PRON
ejpam-23	66	3	is	be	AUX
ejpam-23	66	4	weaker	weak	ADJ
ejpam-23	66	5	than	than	ADP
ejpam-23	66	6	the	the	DET
ejpam-23	66	7	usual	usual	ADJ
ejpam-23	66	8	strong	strong	ADJ
ejpam-23	66	9	semilattice	semilattice	NOUN
ejpam-23	66	10	.	.	PUNCT
ejpam-23	67	1	in	in	ADP
ejpam-23	67	2	fact	fact	NOUN
ejpam-23	67	3	,	,	PUNCT
ejpam-23	67	4	if	if	SCONJ
ejpam-23	67	5	ρ	ρ	PROPN
ejpam-23	67	6	and	and	CCONJ
ejpam-23	67	7	δ	δ	PROPN
ejpam-23	67	8	are	be	AUX
ejpam-23	67	9	equivalent	equivalent	ADJ
ejpam-23	67	10	relations	relation	NOUN
ejpam-23	67	11	on	on	ADP
ejpam-23	67	12	the	the	DET
ejpam-23	67	13	semigroup	semigroup	NOUN
ejpam-23	67	14	s	s	PART
ejpam-23	67	15	=	=	PUNCT
ejpam-23	67	16	(	(	PUNCT
ejpam-23	67	17	y	y	PROPN
ejpam-23	67	18	;	;	PUNCT
ejpam-23	67	19	sα	sα	X
ejpam-23	67	20	)	)	PUNCT
ejpam-23	67	21	with	with	ADP
ejpam-23	67	22	ρ	ρ	PROPN
ejpam-23	67	23	⊆	⊆	NUM
ejpam-23	67	24	δ	δ	PROPN
ejpam-23	67	25	,	,	PUNCT
ejpam-23	67	26	then	then	ADV
ejpam-23	67	27	one	one	PRON
ejpam-23	67	28	can	can	AUX
ejpam-23	67	29	observe	observe	VERB
ejpam-23	67	30	that	that	SCONJ
ejpam-23	67	31	δg[y	δg[y	NOUN
ejpam-23	67	32	;	;	PUNCT
ejpam-23	67	33	sα	sα	PROPN
ejpam-23	67	34	,	,	PUNCT
ejpam-23	67	35	ϕα	ϕα	ADV
ejpam-23	67	36	,	,	PUNCT
ejpam-23	67	37	β	β	X
ejpam-23	67	38	]	]	X
ejpam-23	67	39	is	be	AUX
ejpam-23	67	40	“	"	PUNCT
ejpam-23	67	41	stronger	strong	ADJ
ejpam-23	67	42	”	"	PUNCT
ejpam-23	67	43	than	than	ADP
ejpam-23	67	44	ρg[y	ρg[y	PROPN
ejpam-23	67	45	;	;	PUNCT
ejpam-23	67	46	sα	sα	PROPN
ejpam-23	67	47	,	,	PUNCT
ejpam-23	67	48	ϕα	ϕα	ADV
ejpam-23	67	49	,	,	PUNCT
ejpam-23	67	50	β	β	NOUN
ejpam-23	67	51	]	]	X
ejpam-23	67	52	.	.	PUNCT
ejpam-23	68	1	as	as	ADP
ejpam-23	68	2	special	special	ADJ
ejpam-23	68	3	cases	case	NOUN
ejpam-23	68	4	,	,	PUNCT
ejpam-23	68	5	1sg[y	1sg[y	NUM
ejpam-23	68	6	;	;	PUNCT
ejpam-23	68	7	sα	sα	PROPN
ejpam-23	68	8	,	,	PUNCT
ejpam-23	68	9	ϕα	ϕα	ADV
ejpam-23	68	10	,	,	PUNCT
ejpam-23	68	11	β	β	X
ejpam-23	68	12	]	]	X
ejpam-23	68	13	is	be	AUX
ejpam-23	68	14	the	the	DET
ejpam-23	68	15	“	"	PUNCT
ejpam-23	68	16	weakest”kg	weakest”kg	ADJ
ejpam-23	68	17	-	-	PUNCT
ejpam-23	68	18	strong	strong	ADJ
ejpam-23	68	19	semilattice	semilattice	NOUN
ejpam-23	68	20	of	of	ADP
ejpam-23	68	21	semigroups	semigroup	NOUN
ejpam-23	68	22	since	since	SCONJ
ejpam-23	68	23	1s	1s	NUM
ejpam-23	68	24	is	be	AUX
ejpam-23	68	25	the	the	DET
ejpam-23	68	26	“	"	PUNCT
ejpam-23	68	27	smallest	small	ADJ
ejpam-23	68	28	”	"	PUNCT
ejpam-23	68	29	equivalent	equivalent	ADJ
ejpam-23	68	30	relation	relation	NOUN
ejpam-23	68	31	on	on	ADP
ejpam-23	68	32	s	s	PRON
ejpam-23	68	33	and	and	CCONJ
ejpam-23	68	34	also	also	ADV
ejpam-23	68	35	ηg[y	ηg[y	PROPN
ejpam-23	68	36	;	;	PUNCT
ejpam-23	68	37	sα	sα	PROPN
ejpam-23	68	38	,	,	PUNCT
ejpam-23	68	39	ϕα	ϕα	ADV
ejpam-23	68	40	,	,	PUNCT
ejpam-23	68	41	β	β	X
ejpam-23	68	42	]	]	X
ejpam-23	68	43	is	be	AUX
ejpam-23	68	44	the	the	DET
ejpam-23	68	45	strongest	strong	ADJ
ejpam-23	68	46	kg	kg	ADJ
ejpam-23	68	47	-	-	PUNCT
ejpam-23	68	48	strong	strong	ADJ
ejpam-23	68	49	semilattice	semilattice	NOUN
ejpam-23	68	50	of	of	ADP
ejpam-23	68	51	semigroups	semigroup	NOUN
ejpam-23	68	52	since	since	SCONJ
ejpam-23	68	53	η	η	PROPN
ejpam-23	68	54	is	be	AUX
ejpam-23	68	55	the	the	DET
ejpam-23	68	56	“	"	PUNCT
ejpam-23	68	57	greatest	great	ADJ
ejpam-23	68	58	”	"	PUNCT
ejpam-23	68	59	equivalent	equivalent	ADJ
ejpam-23	68	60	relation	relation	NOUN
ejpam-23	68	61	on	on	ADP
ejpam-23	68	62	s	s	NOUN
ejpam-23	68	63	,	,	PUNCT
ejpam-23	68	64	where	where	SCONJ
ejpam-23	68	65	1s	1s	PROPN
ejpam-23	68	66	is	be	AUX
ejpam-23	68	67	the	the	DET
ejpam-23	68	68	identity	identity	NOUN
ejpam-23	68	69	relation	relation	NOUN
ejpam-23	68	70	on	on	ADP
ejpam-23	68	71	s	s	NOUN
ejpam-23	68	72	and	and	CCONJ
ejpam-23	68	73	η	η	PROPN
ejpam-23	68	74	is	be	AUX
ejpam-23	68	75	the	the	DET
ejpam-23	68	76	semilattice	semilattice	NOUN
ejpam-23	68	77	congruence	congruence	NOUN
ejpam-23	68	78	on	on	ADP
ejpam-23	68	79	s	s	PROPN
ejpam-23	68	80	which	which	PRON
ejpam-23	68	81	partitions	partition	VERB
ejpam-23	68	82	the	the	DET
ejpam-23	68	83	semigroup	semigroup	NOUN
ejpam-23	68	84	s	s	PROPN
ejpam-23	68	85	into	into	ADP
ejpam-23	68	86	disjoint	disjoint	NOUN
ejpam-23	68	87	subsemigroups	subsemigroup	NOUN
ejpam-23	68	88	sα(α	sα(α	X
ejpam-23	68	89	∈	∈	PROPN
ejpam-23	68	90	y	y	PROPN
ejpam-23	68	91	)	)	PUNCT
ejpam-23	68	92	of	of	ADP
ejpam-23	68	93	s.	s.	PROPN
ejpam-23	68	94	hence	hence	ADV
ejpam-23	68	95	,	,	PUNCT
ejpam-23	68	96	we	we	PRON
ejpam-23	68	97	can	can	AUX
ejpam-23	68	98	easily	easily	ADV
ejpam-23	68	99	see	see	VERB
ejpam-23	68	100	that	that	SCONJ
ejpam-23	68	101	ηg[y	ηg[y	PROPN
ejpam-23	68	102	;	;	PUNCT
ejpam-23	68	103	sα	sα	PROPN
ejpam-23	68	104	,	,	PUNCT
ejpam-23	68	105	ϕα	ϕα	ADV
ejpam-23	68	106	,	,	PUNCT
ejpam-23	68	107	β	β	X
ejpam-23	68	108	]	]	X
ejpam-23	68	109	is	be	AUX
ejpam-23	68	110	the	the	DET
ejpam-23	68	111	usual	usual	ADJ
ejpam-23	68	112	strong	strong	ADJ
ejpam-23	68	113	semilattice	semilattice	NOUN
ejpam-23	68	114	of	of	ADP
ejpam-23	68	115	semigroups	semigroup	NOUN
ejpam-23	68	116	since	since	SCONJ
ejpam-23	68	117	in	in	ADP
ejpam-23	68	118	this	this	DET
ejpam-23	68	119	case	case	NOUN
ejpam-23	68	120	,	,	PUNCT
ejpam-23	68	121	every	every	DET
ejpam-23	68	122	index	index	NOUN
ejpam-23	68	123	set	set	VERB
ejpam-23	68	124	d(α	d(α	PROPN
ejpam-23	68	125	,	,	PUNCT
ejpam-23	68	126	β	β	NOUN
ejpam-23	68	127	)	)	PUNCT
ejpam-23	68	128	is	be	AUX
ejpam-23	68	129	a	a	DET
ejpam-23	68	130	singleton	singleton	NOUN
ejpam-23	68	131	for	for	ADP
ejpam-23	68	132	α	α	PROPN
ejpam-23	68	133	>	>	X
ejpam-23	68	134	β	β	X
ejpam-23	68	135	on	on	ADP
ejpam-23	68	136	y	y	PROPN
ejpam-23	68	137	and	and	CCONJ
ejpam-23	68	138	hence	hence	ADV
ejpam-23	68	139	there	there	PRON
ejpam-23	68	140	exists	exist	VERB
ejpam-23	68	141	one	one	NUM
ejpam-23	68	142	and	and	CCONJ
ejpam-23	68	143	only	only	ADV
ejpam-23	68	144	one	one	NUM
ejpam-23	68	145	structure	structure	NOUN
ejpam-23	68	146	homomorphism	homomorphism	NOUN
ejpam-23	68	147	in	in	ADP
ejpam-23	68	148	the	the	DET
ejpam-23	68	149	set	set	NOUN
ejpam-23	68	150	of	of	ADP
ejpam-23	68	151	structure	structure	NOUN
ejpam-23	68	152	homomorphisms	homomorphism	NOUN
ejpam-23	68	153	ϕα	ϕα	ADV
ejpam-23	68	154	,	,	PUNCT
ejpam-23	68	155	β	β	X
ejpam-23	68	156	.	.	PUNCT
ejpam-23	69	1	we	we	PRON
ejpam-23	69	2	have	have	AUX
ejpam-23	69	3	already	already	ADV
ejpam-23	69	4	defined	define	VERB
ejpam-23	69	5	the	the	DET
ejpam-23	69	6	green	green	ADJ
ejpam-23	69	7	∼-relations	∼-relation	NOUN
ejpam-23	69	8	l̃	l̃	PROPN
ejpam-23	69	9	,	,	PUNCT
ejpam-23	69	10	r̃	r̃	PROPN
ejpam-23	69	11	,	,	PUNCT
ejpam-23	69	12	h̃	h̃	PROPN
ejpam-23	69	13	and	and	CCONJ
ejpam-23	69	14	d̃	d̃	PROPN
ejpam-23	69	15	on	on	ADP
ejpam-23	69	16	a	a	DET
ejpam-23	69	17	semigroup	semigroup	NOUN
ejpam-23	69	18	s.	s.	PROPN
ejpam-23	69	19	in	in	ADP
ejpam-23	69	20	order	order	NOUN
ejpam-23	69	21	to	to	PART
ejpam-23	69	22	define	define	VERB
ejpam-23	69	23	the	the	DET
ejpam-23	69	24	green	green	ADJ
ejpam-23	69	25	∼-relation	∼-relation	NOUN
ejpam-23	69	26	j̃	j̃	PROPN
ejpam-23	69	27	on	on	ADP
ejpam-23	69	28	s	s	PROPN
ejpam-23	69	29	,	,	PUNCT
ejpam-23	69	30	we	we	PRON
ejpam-23	69	31	consider	consider	VERB
ejpam-23	69	32	the	the	DET
ejpam-23	69	33	left	left	ADJ
ejpam-23	69	34	∼-ideal	∼-ideal	NOUN
ejpam-23	69	35	l	l	NOUN
ejpam-23	69	36	of	of	ADP
ejpam-23	69	37	a	a	DET
ejpam-23	69	38	semigroup	semigroup	PROPN
ejpam-23	69	39	s.	s.	PROPN
ejpam-23	69	40	definition	definition	NOUN
ejpam-23	69	41	2.4	2.4	NUM
ejpam-23	69	42	a	a	DET
ejpam-23	69	43	left	left	ADJ
ejpam-23	69	44	(	(	PUNCT
ejpam-23	69	45	right	right	ADJ
ejpam-23	69	46	)	)	PUNCT
ejpam-23	69	47	ideal	ideal	ADJ
ejpam-23	69	48	l	l	NOUN
ejpam-23	69	49	(	(	PUNCT
ejpam-23	69	50	r	r	NOUN
ejpam-23	69	51	)	)	PUNCT
ejpam-23	69	52	of	of	ADP
ejpam-23	69	53	a	a	DET
ejpam-23	69	54	semigroup	semigroup	NOUN
ejpam-23	69	55	s	s	PART
ejpam-23	69	56	is	be	AUX
ejpam-23	69	57	called	call	VERB
ejpam-23	69	58	a	a	DET
ejpam-23	69	59	left	left	ADJ
ejpam-23	69	60	∼-ideal	∼-ideal	NOUN
ejpam-23	69	61	of	of	ADP
ejpam-23	69	62	s	s	PRON
ejpam-23	69	63	if	if	SCONJ
ejpam-23	69	64	l̃a	l̃a	PROPN
ejpam-23	69	65	⊆	⊆	NUM
ejpam-23	69	66	l(r̃a	l(r̃a	PROPN
ejpam-23	69	67	⊆	⊆	NUM
ejpam-23	69	68	r	r	NOUN
ejpam-23	69	69	)	)	PUNCT
ejpam-23	69	70	holds	hold	NOUN
ejpam-23	69	71	,	,	PUNCT
ejpam-23	69	72	for	for	ADP
ejpam-23	69	73	all	all	DET
ejpam-23	69	74	a	a	DET
ejpam-23	69	75	∈	∈	PROPN
ejpam-23	69	76	l(a	l(a	PROPN
ejpam-23	69	77	∈	∈	PROPN
ejpam-23	69	78	r	r	NOUN
ejpam-23	69	79	)	)	PUNCT
ejpam-23	69	80	.	.	PUNCT
ejpam-23	70	1	we	we	PRON
ejpam-23	70	2	call	call	VERB
ejpam-23	70	3	a	a	DET
ejpam-23	70	4	subset	subset	NOUN
ejpam-23	70	5	i	i	PRON
ejpam-23	70	6	of	of	ADP
ejpam-23	70	7	a	a	DET
ejpam-23	70	8	semigroup	semigroup	NOUN
ejpam-23	70	9	s	s	VERB
ejpam-23	70	10	a	a	DET
ejpam-23	70	11	∼-ideal	∼-ideal	NOUN
ejpam-23	70	12	of	of	ADP
ejpam-23	70	13	s	s	PRON
ejpam-23	70	14	if	if	SCONJ
ejpam-23	70	15	it	it	PRON
ejpam-23	70	16	is	be	AUX
ejpam-23	70	17	both	both	CCONJ
ejpam-23	70	18	a	a	DET
ejpam-23	70	19	left	left	ADJ
ejpam-23	70	20	∼-ideal	∼-ideal	NOUN
ejpam-23	70	21	and	and	CCONJ
ejpam-23	70	22	a	a	DET
ejpam-23	70	23	right	right	ADJ
ejpam-23	70	24	∼-ideal	∼-ideal	NOUN
ejpam-23	70	25	.	.	PUNCT
ejpam-23	71	1	it	it	PRON
ejpam-23	71	2	is	be	AUX
ejpam-23	71	3	noteworthy	noteworthy	ADJ
ejpam-23	71	4	that	that	SCONJ
ejpam-23	71	5	if	if	SCONJ
ejpam-23	71	6	s	s	NOUN
ejpam-23	71	7	is	be	AUX
ejpam-23	71	8	a	a	DET
ejpam-23	71	9	regular	regular	ADJ
ejpam-23	71	10	semigroup	semigroup	NOUN
ejpam-23	71	11	,	,	PUNCT
ejpam-23	71	12	then	then	ADV
ejpam-23	71	13	every	every	DET
ejpam-23	71	14	left	left	ADJ
ejpam-23	71	15	(	(	PUNCT
ejpam-23	71	16	right	right	ADJ
ejpam-23	71	17	,	,	PUNCT
ejpam-23	71	18	two	two	NUM
ejpam-23	71	19	-	-	PUNCT
ejpam-23	71	20	sided	sided	ADJ
ejpam-23	71	21	)	)	PUNCT
ejpam-23	71	22	ideal	ideal	NOUN
ejpam-23	71	23	of	of	ADP
ejpam-23	71	24	s	s	PROPN
ejpam-23	71	25	is	be	AUX
ejpam-23	71	26	a	a	DET
ejpam-23	71	27	left	left	ADJ
ejpam-23	71	28	(	(	PUNCT
ejpam-23	71	29	right	right	ADJ
ejpam-23	71	30	,	,	PUNCT
ejpam-23	71	31	two	two	NUM
ejpam-23	71	32	-	-	PUNCT
ejpam-23	71	33	sided	sided	ADJ
ejpam-23	71	34	)	)	PUNCT
ejpam-23	71	35	∼-ideal	∼-ideal	NOUN
ejpam-23	71	36	.	.	PUNCT
ejpam-23	72	1	we	we	PRON
ejpam-23	72	2	also	also	ADV
ejpam-23	72	3	observe	observe	VERB
ejpam-23	72	4	that	that	SCONJ
ejpam-23	72	5	for	for	ADP
ejpam-23	72	6	any	any	DET
ejpam-23	72	7	idempotent	idempotent	ADJ
ejpam-23	72	8	e	e	NOUN
ejpam-23	72	9	in	in	ADP
ejpam-23	72	10	a	a	DET
ejpam-23	72	11	semigroup	semigroup	NOUN
ejpam-23	72	12	s	s	NOUN
ejpam-23	72	13	,	,	PUNCT
ejpam-23	72	14	the	the	DET
ejpam-23	72	15	left	left	ADJ
ejpam-23	72	16	(	(	PUNCT
ejpam-23	72	17	right	right	ADJ
ejpam-23	72	18	)	)	PUNCT
ejpam-23	72	19	ideal	ideal	NOUN
ejpam-23	72	20	se(es	se(es	PROPN
ejpam-23	72	21	)	)	PUNCT
ejpam-23	72	22	is	be	AUX
ejpam-23	72	23	a	a	DET
ejpam-23	72	24	left(right	left(right	NOUN
ejpam-23	72	25	)	)	PUNCT
ejpam-23	72	26	∼-ideal	∼-ideal	NOUN
ejpam-23	72	27	.	.	PUNCT
ejpam-23	73	1	for	for	ADP
ejpam-23	73	2	if	if	SCONJ
ejpam-23	73	3	a	a	DET
ejpam-23	73	4	∈	∈	PROPN
ejpam-23	73	5	se	se	X
ejpam-23	73	6	,	,	PUNCT
ejpam-23	73	7	then	then	ADV
ejpam-23	73	8	a	a	DET
ejpam-23	73	9	=	=	SYM
ejpam-23	73	10	ae	ae	PROPN
ejpam-23	73	11	,	,	PUNCT
ejpam-23	73	12	and	and	CCONJ
ejpam-23	73	13	hence	hence	ADV
ejpam-23	73	14	for	for	ADP
ejpam-23	73	15	any	any	DET
ejpam-23	73	16	element	element	NOUN
ejpam-23	73	17	b	b	PROPN
ejpam-23	73	18	in	in	ADP
ejpam-23	73	19	l̃a	l̃a	PROPN
ejpam-23	73	20	,	,	PUNCT
ejpam-23	73	21	we	we	PRON
ejpam-23	73	22	have	have	VERB
ejpam-23	73	23	b	b	NOUN
ejpam-23	73	24	=	=	PRON
ejpam-23	73	25	be	be	AUX
ejpam-23	73	26	∈	∈	PROPN
ejpam-23	73	27	se	se	X
ejpam-23	73	28	.	.	PUNCT
ejpam-23	74	1	by	by	ADP
ejpam-23	74	2	definition	definition	NOUN
ejpam-23	74	3	2.4	2.4	NUM
ejpam-23	74	4	,	,	PUNCT
ejpam-23	74	5	we	we	PRON
ejpam-23	74	6	see	see	VERB
ejpam-23	74	7	that	that	SCONJ
ejpam-23	74	8	the	the	DET
ejpam-23	74	9	semigroup	semigroup	NOUN
ejpam-23	74	10	s	s	VERB
ejpam-23	74	11	is	be	AUX
ejpam-23	74	12	always	always	ADV
ejpam-23	74	13	a∼-ideal	a∼-ideal	ADJ
ejpam-23	74	14	of	of	ADP
ejpam-23	74	15	itself	itself	PRON
ejpam-23	74	16	,	,	PUNCT
ejpam-23	74	17	and	and	CCONJ
ejpam-23	74	18	we	we	PRON
ejpam-23	74	19	denote	denote	VERB
ejpam-23	74	20	the	the	DET
ejpam-23	74	21	smallest	small	ADJ
ejpam-23	74	22	∼-ideal	∼-ideal	NOUN
ejpam-23	74	23	containing	contain	VERB
ejpam-23	74	24	the	the	DET
ejpam-23	74	25	element	element	NOUN
ejpam-23	74	26	a	a	PRON
ejpam-23	74	27	of	of	ADP
ejpam-23	74	28	s	s	PRON
ejpam-23	74	29	by	by	ADP
ejpam-23	74	30	j̃(a	j̃(a	PROPN
ejpam-23	74	31	)	)	PUNCT
ejpam-23	74	32	.	.	PUNCT
ejpam-23	75	1	now	now	ADV
ejpam-23	75	2	,	,	PUNCT
ejpam-23	75	3	we	we	PRON
ejpam-23	75	4	define	define	VERB
ejpam-23	75	5	j̃	j̃	PROPN
ejpam-23	75	6	=	=	PUNCT
ejpam-23	75	7	{	{	PUNCT
ejpam-23	75	8	(	(	PUNCT
ejpam-23	75	9	a	a	PRON
ejpam-23	75	10	,	,	PUNCT
ejpam-23	75	11	b	b	NOUN
ejpam-23	75	12	)	)	PUNCT
ejpam-23	75	13	∈	∈	PROPN
ejpam-23	75	14	s	s	PART
ejpam-23	75	15	×	×	NOUN
ejpam-23	75	16	s	s	X
ejpam-23	75	17	:	:	PUNCT
ejpam-23	75	18	j̃(a	j̃(a	PROPN
ejpam-23	75	19	)	)	PUNCT
ejpam-23	75	20	=	=	SYM
ejpam-23	75	21	j̃(b	j̃(b	NOUN
ejpam-23	75	22	)	)	PUNCT
ejpam-23	75	23	}	}	PUNCT
ejpam-23	75	24	.	.	PUNCT
ejpam-23	76	1	definition	definition	NOUN
ejpam-23	76	2	2.5	2.5	NUM
ejpam-23	76	3	an	an	DET
ejpam-23	76	4	h̃-abundant	h̃-abundant	ADJ
ejpam-23	76	5	semigroup	semigroup	NOUN
ejpam-23	76	6	s	s	VERB
ejpam-23	76	7	is	be	AUX
ejpam-23	76	8	called	call	VERB
ejpam-23	76	9	completely	completely	ADV
ejpam-23	76	10	j̃	j̃	PROPN
ejpam-23	76	11	-simple	-simple	NOUN
ejpam-23	76	12	if	if	SCONJ
ejpam-23	76	13	s	s	PRON
ejpam-23	76	14	does	do	AUX
ejpam-23	76	15	not	not	PART
ejpam-23	76	16	contain	contain	VERB
ejpam-23	76	17	any	any	DET
ejpam-23	76	18	non	non	ADJ
ejpam-23	76	19	-	-	ADJ
ejpam-23	76	20	trivial	trivial	ADJ
ejpam-23	76	21	proper	proper	ADJ
ejpam-23	76	22	∼-ideal	∼-ideal	NOUN
ejpam-23	76	23	of	of	ADP
ejpam-23	76	24	s.	s.	PROPN
ejpam-23	76	25	we	we	PRON
ejpam-23	76	26	now	now	ADV
ejpam-23	76	27	give	give	VERB
ejpam-23	76	28	some	some	DET
ejpam-23	76	29	properties	property	NOUN
ejpam-23	76	30	of	of	ADP
ejpam-23	76	31	the	the	DET
ejpam-23	76	32	h̃-abundant	h̃-abundant	ADJ
ejpam-23	76	33	semigroups	semigroup	NOUN
ejpam-23	76	34	.	.	PUNCT
ejpam-23	77	1	some	some	PRON
ejpam-23	77	2	of	of	ADP
ejpam-23	77	3	the	the	DET
ejpam-23	77	4	properties	property	NOUN
ejpam-23	77	5	may	may	AUX
ejpam-23	77	6	have	have	AUX
ejpam-23	77	7	already	already	ADV
ejpam-23	77	8	been	be	AUX
ejpam-23	77	9	known	know	VERB
ejpam-23	77	10	or	or	CCONJ
ejpam-23	77	11	can	can	AUX
ejpam-23	77	12	be	be	AUX
ejpam-23	77	13	easily	easily	ADV
ejpam-23	77	14	derived	derive	VERB
ejpam-23	77	15	,	,	PUNCT
ejpam-23	77	16	however	however	ADV
ejpam-23	77	17	,	,	PUNCT
ejpam-23	77	18	for	for	ADP
ejpam-23	77	19	the	the	DET
ejpam-23	77	20	sake	sake	NOUN
ejpam-23	77	21	of	of	ADP
ejpam-23	77	22	completeness	completeness	NOUN
ejpam-23	77	23	,	,	PUNCT
ejpam-23	77	24	we	we	PRON
ejpam-23	77	25	provide	provide	VERB
ejpam-23	77	26	here	here	ADV
ejpam-23	77	27	the	the	DET
ejpam-23	77	28	proofs	proof	NOUN
ejpam-23	77	29	.	.	PUNCT
ejpam-23	78	1	lemma	lemma	PROPN
ejpam-23	78	2	2.6	2.6	NUM
ejpam-23	78	3	let	let	VERB
ejpam-23	78	4	s	s	PRON
ejpam-23	78	5	be	be	AUX
ejpam-23	78	6	an	an	DET
ejpam-23	78	7	h̃-abundant	h̃-abundant	ADJ
ejpam-23	78	8	semigroup	semigroup	NOUN
ejpam-23	78	9	.	.	PUNCT
ejpam-23	79	1	then	then	ADV
ejpam-23	79	2	the	the	DET
ejpam-23	79	3	following	follow	VERB
ejpam-23	79	4	properties	property	NOUN
ejpam-23	79	5	hold	hold	VERB
ejpam-23	79	6	:	:	PUNCT
ejpam-23	79	7	(	(	PUNCT
ejpam-23	79	8	i	i	NOUN
ejpam-23	79	9	)	)	PUNCT
ejpam-23	79	10	the	the	DET
ejpam-23	79	11	green	green	ADJ
ejpam-23	79	12	∼-relation	∼-relation	NOUN
ejpam-23	80	1	h̃	h̃	PROPN
ejpam-23	80	2	is	be	AUX
ejpam-23	80	3	a	a	DET
ejpam-23	80	4	congruence	congruence	NOUN
ejpam-23	80	5	on	on	ADP
ejpam-23	80	6	s	s	PRON
ejpam-23	80	7	if	if	SCONJ
ejpam-23	80	8	and	and	CCONJ
ejpam-23	80	9	only	only	ADV
ejpam-23	80	10	if	if	SCONJ
ejpam-23	80	11	for	for	ADP
ejpam-23	80	12	any	any	DET
ejpam-23	80	13	a	a	NOUN
ejpam-23	80	14	,	,	PUNCT
ejpam-23	80	15	b	b	PROPN
ejpam-23	80	16	∈	∈	PROPN
ejpam-23	80	17	s	s	PART
ejpam-23	80	18	,	,	PUNCT
ejpam-23	80	19	(	(	PUNCT
ejpam-23	80	20	ab)0	ab)0	PROPN
ejpam-23	80	21	=	=	PRON
ejpam-23	80	22	(	(	PUNCT
ejpam-23	80	23	a0b0)0	a0b0)0	NOUN
ejpam-23	80	24	.	.	PUNCT
ejpam-23	81	1	(	(	PUNCT
ejpam-23	81	2	ii	ii	NOUN
ejpam-23	81	3	)	)	PUNCT
ejpam-23	81	4	if	if	SCONJ
ejpam-23	81	5	e	e	X
ejpam-23	81	6	,	,	PUNCT
ejpam-23	81	7	f	f	PROPN
ejpam-23	81	8	are	be	AUX
ejpam-23	81	9	d̃-related	d̃-relate	VERB
ejpam-23	81	10	idempotents	idempotent	NOUN
ejpam-23	81	11	of	of	ADP
ejpam-23	81	12	s	s	PROPN
ejpam-23	81	13	,	,	PUNCT
ejpam-23	81	14	then	then	ADV
ejpam-23	81	15	edf	edf	PROPN
ejpam-23	81	16	.	.	PROPN
ejpam-23	82	1	(	(	PUNCT
ejpam-23	82	2	iii	iii	X
ejpam-23	82	3	)	)	PUNCT
ejpam-23	82	4	d̃	d̃	PROPN
ejpam-23	82	5	=	=	SYM
ejpam-23	82	6	l̃	l̃	PROPN
ejpam-23	82	7	◦	◦	NOUN
ejpam-23	82	8	r̃	r̃	NOUN
ejpam-23	82	9	=	=	SYM
ejpam-23	82	10	r̃	r̃	NOUN
ejpam-23	82	11	◦	◦	NOUN
ejpam-23	82	12	l̃.	l̃.	PROPN
ejpam-23	82	13	x.	x.	PROPN
ejpam-23	82	14	kong	kong	PROPN
ejpam-23	82	15	,	,	PUNCT
ejpam-23	82	16	y.ding	y.de	VERB
ejpam-23	82	17	,	,	PUNCT
ejpam-23	82	18	k.p.shum	k.p.shum	ADJ
ejpam-23	82	19	/	/	SYM
ejpam-23	82	20	eur	eur	PROPN
ejpam-23	82	21	.	.	PUNCT
ejpam-23	83	1	j.	j.	PROPN
ejpam-23	83	2	pure	pure	PROPN
ejpam-23	83	3	appl	appl	PROPN
ejpam-23	83	4	.	.	PROPN
ejpam-23	83	5	math	math	PROPN
ejpam-23	83	6	,	,	PUNCT
ejpam-23	83	7	1	1	NUM
ejpam-23	83	8	(	(	PUNCT
ejpam-23	83	9	2008	2008	NUM
ejpam-23	83	10	)	)	PUNCT
ejpam-23	83	11	,	,	PUNCT
ejpam-23	83	12	(	(	PUNCT
ejpam-23	83	13	46	46	NUM
ejpam-23	83	14	-	-	SYM
ejpam-23	83	15	59	59	NUM
ejpam-23	83	16	)	)	PUNCT
ejpam-23	83	17	50	50	NUM
ejpam-23	83	18	(	(	PUNCT
ejpam-23	83	19	iv	iv	X
ejpam-23	83	20	)	)	PUNCT
ejpam-23	83	21	if	if	SCONJ
ejpam-23	83	22	e	e	X
ejpam-23	83	23	,	,	PUNCT
ejpam-23	83	24	f	f	PROPN
ejpam-23	83	25	are	be	AUX
ejpam-23	83	26	idempotents	idempotent	NOUN
ejpam-23	83	27	in	in	ADP
ejpam-23	83	28	s	s	PRON
ejpam-23	83	29	such	such	ADJ
ejpam-23	83	30	that	that	SCONJ
ejpam-23	83	31	ej	ej	PROPN
ejpam-23	83	32	f	f	PROPN
ejpam-23	83	33	,	,	PUNCT
ejpam-23	83	34	then	then	ADV
ejpam-23	83	35	edf	edf	PROPN
ejpam-23	83	36	.	.	PUNCT
ejpam-23	84	1	proof	proof	NOUN
ejpam-23	84	2	.	.	PUNCT
ejpam-23	85	1	(	(	PUNCT
ejpam-23	85	2	i	i	NOUN
ejpam-23	85	3	)	)	PUNCT
ejpam-23	85	4	(	(	PUNCT
ejpam-23	85	5	necessity	necessity	NOUN
ejpam-23	85	6	)	)	PUNCT
ejpam-23	85	7	.	.	PUNCT
ejpam-23	86	1	for	for	ADP
ejpam-23	86	2	any	any	DET
ejpam-23	86	3	a	a	PRON
ejpam-23	86	4	,	,	PUNCT
ejpam-23	86	5	b	b	PROPN
ejpam-23	86	6	∈	∈	PROPN
ejpam-23	86	7	s	s	X
ejpam-23	86	8	,	,	PUNCT
ejpam-23	86	9	we	we	PRON
ejpam-23	86	10	have	have	VERB
ejpam-23	86	11	ah̃a0	ah̃a0	PROPN
ejpam-23	86	12	and	and	CCONJ
ejpam-23	86	13	bh̃b0	bh̃b0	PROPN
ejpam-23	86	14	.	.	PUNCT
ejpam-23	87	1	since	since	SCONJ
ejpam-23	87	2	h̃	h̃	PROPN
ejpam-23	87	3	is	be	AUX
ejpam-23	87	4	a	a	DET
ejpam-23	87	5	congruence	congruence	NOUN
ejpam-23	87	6	on	on	ADP
ejpam-23	87	7	s	s	PROPN
ejpam-23	87	8	,	,	PUNCT
ejpam-23	87	9	abh̃a0b0	abh̃a0b0	ADJ
ejpam-23	87	10	.	.	PUNCT
ejpam-23	88	1	but	but	CCONJ
ejpam-23	88	2	abh̃(ab)0	abh̃(ab)0	ADJ
ejpam-23	88	3	,	,	PUNCT
ejpam-23	88	4	and	and	CCONJ
ejpam-23	88	5	so	so	ADV
ejpam-23	88	6	(	(	PUNCT
ejpam-23	88	7	ab)0	ab)0	PROPN
ejpam-23	88	8	=	=	PRON
ejpam-23	89	1	(	(	PUNCT
ejpam-23	89	2	a0b0)0	a0b0)0	NOUN
ejpam-23	89	3	since	since	SCONJ
ejpam-23	89	4	every	every	DET
ejpam-23	89	5	h̃-class	h̃-class	PROPN
ejpam-23	89	6	contains	contain	VERB
ejpam-23	89	7	a	a	DET
ejpam-23	89	8	unique	unique	ADJ
ejpam-23	89	9	idempotent	idempotent	NOUN
ejpam-23	89	10	.	.	PUNCT
ejpam-23	90	1	(	(	PUNCT
ejpam-23	90	2	sufficiency	sufficiency	NOUN
ejpam-23	90	3	)	)	PUNCT
ejpam-23	90	4	.	.	PUNCT
ejpam-23	91	1	we	we	PRON
ejpam-23	91	2	only	only	ADV
ejpam-23	91	3	need	need	VERB
ejpam-23	91	4	to	to	PART
ejpam-23	91	5	show	show	VERB
ejpam-23	91	6	that	that	SCONJ
ejpam-23	91	7	h̃	h̃	PROPN
ejpam-23	91	8	is	be	AUX
ejpam-23	91	9	compatible	compatible	ADJ
ejpam-23	91	10	with	with	ADP
ejpam-23	91	11	the	the	DET
ejpam-23	91	12	semigroup	semigroup	ADJ
ejpam-23	91	13	multiplication	multiplication	NOUN
ejpam-23	91	14	of	of	ADP
ejpam-23	91	15	s	s	PRON
ejpam-23	91	16	since	since	SCONJ
ejpam-23	91	17	h̃	h̃	PROPN
ejpam-23	91	18	is	be	AUX
ejpam-23	91	19	an	an	DET
ejpam-23	91	20	equivalent	equivalent	ADJ
ejpam-23	91	21	relation	relation	NOUN
ejpam-23	91	22	on	on	ADP
ejpam-23	91	23	s.	s.	PROPN
ejpam-23	91	24	let	let	VERB
ejpam-23	91	25	(	(	PUNCT
ejpam-23	91	26	a	a	PRON
ejpam-23	91	27	,	,	PUNCT
ejpam-23	91	28	b	b	NOUN
ejpam-23	91	29	)	)	PUNCT
ejpam-23	91	30	∈	∈	PROPN
ejpam-23	91	31	h̃	h̃	PROPN
ejpam-23	91	32	and	and	CCONJ
ejpam-23	91	33	c	c	PROPN
ejpam-23	91	34	∈	∈	PROPN
ejpam-23	91	35	s.	s.	PROPN
ejpam-23	92	1	then	then	ADV
ejpam-23	92	2	(	(	PUNCT
ejpam-23	92	3	ca)0	ca)0	NOUN
ejpam-23	92	4	=	=	SYM
ejpam-23	92	5	(	(	PUNCT
ejpam-23	92	6	c0a0)0	c0a0)0	NOUN
ejpam-23	92	7	=	=	PUNCT
ejpam-23	92	8	(	(	PUNCT
ejpam-23	92	9	c0b0)0	c0b0)0	NOUN
ejpam-23	92	10	=	=	PUNCT
ejpam-23	92	11	(	(	PUNCT
ejpam-23	92	12	cb)0	cb)0	NOUN
ejpam-23	92	13	and	and	CCONJ
ejpam-23	92	14	hence	hence	ADV
ejpam-23	92	15	,	,	PUNCT
ejpam-23	92	16	h̃	h̃	PROPN
ejpam-23	92	17	is	be	AUX
ejpam-23	92	18	left	leave	VERB
ejpam-23	92	19	compatible	compatible	ADJ
ejpam-23	92	20	to	to	ADP
ejpam-23	92	21	the	the	DET
ejpam-23	92	22	semigroup	semigroup	ADJ
ejpam-23	92	23	multiplication	multiplication	NOUN
ejpam-23	92	24	.	.	PUNCT
ejpam-23	93	1	dually	dually	PROPN
ejpam-23	93	2	,	,	PUNCT
ejpam-23	93	3	h̃	h̃	PROPN
ejpam-23	93	4	is	be	AUX
ejpam-23	93	5	right	right	ADV
ejpam-23	93	6	compatible	compatible	ADJ
ejpam-23	93	7	with	with	ADP
ejpam-23	93	8	the	the	DET
ejpam-23	93	9	semigroup	semigroup	ADJ
ejpam-23	93	10	multiplication	multiplication	NOUN
ejpam-23	93	11	and	and	CCONJ
ejpam-23	93	12	thus	thus	ADV
ejpam-23	93	13	h̃	h̃	PROPN
ejpam-23	93	14	is	be	AUX
ejpam-23	93	15	a	a	DET
ejpam-23	93	16	congruence	congruence	NOUN
ejpam-23	93	17	on	on	ADP
ejpam-23	93	18	s.	s.	PROPN
ejpam-23	93	19	(	(	PUNCT
ejpam-23	93	20	ii	ii	PROPN
ejpam-23	93	21	)	)	PUNCT
ejpam-23	93	22	since	since	SCONJ
ejpam-23	93	23	ed̃f	ed̃f	NOUN
ejpam-23	93	24	,	,	PUNCT
ejpam-23	93	25	there	there	PRON
ejpam-23	93	26	exist	exist	VERB
ejpam-23	93	27	elements	element	NOUN
ejpam-23	93	28	a1	a1	NOUN
ejpam-23	93	29	,	,	PUNCT
ejpam-23	93	30	·	·	PUNCT
ejpam-23	93	31	·	·	PUNCT
ejpam-23	93	32	·	·	PUNCT
ejpam-23	93	33	,	,	PUNCT
ejpam-23	93	34	ak	ak	PROPN
ejpam-23	93	35	of	of	ADP
ejpam-23	93	36	s	s	PRON
ejpam-23	93	37	such	such	ADJ
ejpam-23	93	38	that	that	SCONJ
ejpam-23	93	39	el̃a1r̃a2	el̃a1r̃a2	PROPN
ejpam-23	93	40	·	·	PUNCT
ejpam-23	93	41	·	·	PUNCT
ejpam-23	93	42	·	·	PUNCT
ejpam-23	93	43	ak	ak	PROPN
ejpam-23	93	44	l̃	l̃	PROPN
ejpam-23	93	45	f	f	PROPN
ejpam-23	93	46	.	.	PUNCT
ejpam-23	94	1	since	since	SCONJ
ejpam-23	94	2	s	s	PROPN
ejpam-23	94	3	is	be	AUX
ejpam-23	94	4	an	an	DET
ejpam-23	94	5	h̃-abundant	h̃-abundant	ADJ
ejpam-23	94	6	semigroup	semigroup	NOUN
ejpam-23	94	7	,	,	PUNCT
ejpam-23	94	8	ela0	ela0	PROPN
ejpam-23	94	9	1ra0	1ra0	NUM
ejpam-23	94	10	2	2	NUM
ejpam-23	94	11	·	·	PUNCT
ejpam-23	94	12	·	·	PUNCT
ejpam-23	94	13	·	·	PUNCT
ejpam-23	94	14	a0	a0	PROPN
ejpam-23	94	15	klf	klf	PROPN
ejpam-23	94	16	.	.	PUNCT
ejpam-23	95	1	thus	thus	ADV
ejpam-23	95	2	edf	edf	X
ejpam-23	95	3	.	.	PUNCT
ejpam-23	96	1	(	(	PUNCT
ejpam-23	96	2	iii	iii	X
ejpam-23	96	3	)	)	PUNCT
ejpam-23	96	4	if	if	SCONJ
ejpam-23	96	5	a	a	DET
ejpam-23	96	6	,	,	PUNCT
ejpam-23	96	7	b	b	PROPN
ejpam-23	96	8	∈	∈	PROPN
ejpam-23	96	9	s	s	NOUN
ejpam-23	96	10	and	and	CCONJ
ejpam-23	96	11	ad̃b	ad̃b	PROPN
ejpam-23	96	12	,	,	PUNCT
ejpam-23	96	13	then	then	ADV
ejpam-23	96	14	by	by	ADP
ejpam-23	96	15	(	(	PUNCT
ejpam-23	96	16	ii	ii	NOUN
ejpam-23	96	17	)	)	PUNCT
ejpam-23	96	18	,	,	PUNCT
ejpam-23	96	19	a0db0	a0db0	PROPN
ejpam-23	96	20	.	.	PUNCT
ejpam-23	97	1	hence	hence	ADV
ejpam-23	97	2	there	there	PRON
ejpam-23	97	3	exist	exist	VERB
ejpam-23	97	4	elements	element	NOUN
ejpam-23	97	5	c	c	NOUN
ejpam-23	97	6	,	,	PUNCT
ejpam-23	97	7	d	d	X
ejpam-23	97	8	in	in	ADP
ejpam-23	97	9	s	s	PRON
ejpam-23	97	10	with	with	ADP
ejpam-23	97	11	a0lcrb0	a0lcrb0	PROPN
ejpam-23	97	12	and	and	CCONJ
ejpam-23	97	13	a0rdlb0	a0rdlb0	PROPN
ejpam-23	97	14	,	,	PUNCT
ejpam-23	97	15	and	and	CCONJ
ejpam-23	97	16	consequently	consequently	ADV
ejpam-23	97	17	,	,	PUNCT
ejpam-23	97	18	al̃cr̃b	al̃cr̃b	PROPN
ejpam-23	97	19	and	and	CCONJ
ejpam-23	97	20	ar̃dl̃b	ar̃dl̃b	ADJ
ejpam-23	97	21	.	.	PUNCT
ejpam-23	98	1	thus	thus	ADV
ejpam-23	98	2	the	the	DET
ejpam-23	98	3	result	result	NOUN
ejpam-23	98	4	is	be	AUX
ejpam-23	98	5	proved	prove	VERB
ejpam-23	98	6	.	.	PUNCT
ejpam-23	99	1	(	(	PUNCT
ejpam-23	99	2	iv	iv	X
ejpam-23	99	3	)	)	PUNCT
ejpam-23	99	4	since	since	SCONJ
ejpam-23	99	5	ses	se	NOUN
ejpam-23	99	6	=	=	SYM
ejpam-23	99	7	sfs	sfs	PROPN
ejpam-23	99	8	,	,	PUNCT
ejpam-23	99	9	there	there	PRON
ejpam-23	99	10	exist	exist	VERB
ejpam-23	99	11	elements	element	NOUN
ejpam-23	99	12	x	x	X
ejpam-23	99	13	,	,	PUNCT
ejpam-23	99	14	y	y	PROPN
ejpam-23	99	15	,	,	PUNCT
ejpam-23	99	16	s	s	PROPN
ejpam-23	99	17	,	,	PUNCT
ejpam-23	99	18	t	t	PROPN
ejpam-23	99	19	in	in	ADP
ejpam-23	99	20	s	s	PRON
ejpam-23	100	1	such	such	ADJ
ejpam-23	100	2	that	that	SCONJ
ejpam-23	100	3	f	f	PROPN
ejpam-23	100	4	=	=	PUNCT
ejpam-23	100	5	set	set	NOUN
ejpam-23	100	6	and	and	CCONJ
ejpam-23	100	7	e	e	NOUN
ejpam-23	100	8	=	=	PROPN
ejpam-23	100	9	xfy	xfy	PROPN
ejpam-23	100	10	.	.	PUNCT
ejpam-23	101	1	let	let	VERB
ejpam-23	101	2	h	h	NOUN
ejpam-23	101	3	=	=	PUNCT
ejpam-23	101	4	(	(	PUNCT
ejpam-23	101	5	fy)0	fy)0	NOUN
ejpam-23	101	6	and	and	CCONJ
ejpam-23	101	7	k	k	PROPN
ejpam-23	102	1	=	=	PROPN
ejpam-23	102	2	(	(	PUNCT
ejpam-23	102	3	se)0	se)0	PROPN
ejpam-23	102	4	.	.	PUNCT
ejpam-23	103	1	then	then	ADV
ejpam-23	103	2	hfy	hfy	NOUN
ejpam-23	103	3	=	=	SYM
ejpam-23	103	4	fy	fy	PROPN
ejpam-23	103	5	=	=	SYM
ejpam-23	103	6	ffy	ffy	PROPN
ejpam-23	104	1	and	and	CCONJ
ejpam-23	104	2	so	so	ADV
ejpam-23	104	3	h	h	NOUN
ejpam-23	104	4	=	=	SYM
ejpam-23	104	5	h2	h2	PROPN
ejpam-23	104	6	=	=	SYM
ejpam-23	104	7	fh	fh	PROPN
ejpam-23	104	8	and	and	CCONJ
ejpam-23	104	9	sek	sek	PROPN
ejpam-23	104	10	=	=	SYM
ejpam-23	104	11	se	se	X
ejpam-23	105	1	=	=	PRON
ejpam-23	105	2	see	see	VERB
ejpam-23	105	3	,	,	PUNCT
ejpam-23	105	4	and	and	CCONJ
ejpam-23	105	5	thereby	thereby	ADV
ejpam-23	105	6	,	,	PUNCT
ejpam-23	105	7	k	k	PROPN
ejpam-23	105	8	=	=	SYM
ejpam-23	105	9	k2	k2	PROPN
ejpam-23	105	10	=	=	PROPN
ejpam-23	105	11	ke	ke	PROPN
ejpam-23	105	12	.	.	PUNCT
ejpam-23	106	1	hence	hence	ADV
ejpam-23	106	2	,	,	PUNCT
ejpam-23	106	3	hf	hf	INTJ
ejpam-23	106	4	,	,	PUNCT
ejpam-23	106	5	ek	ek	PROPN
ejpam-23	106	6	are	be	AUX
ejpam-23	106	7	the	the	DET
ejpam-23	106	8	idempotents	idempotent	NOUN
ejpam-23	106	9	satisfying	satisfy	VERB
ejpam-23	106	10	the	the	DET
ejpam-23	106	11	relations	relation	NOUN
ejpam-23	106	12	hfrh	hfrh	NOUN
ejpam-23	106	13	and	and	CCONJ
ejpam-23	106	14	eklk	eklk	ADJ
ejpam-23	106	15	.	.	PUNCT
ejpam-23	107	1	these	these	PRON
ejpam-23	107	2	imply	imply	VERB
ejpam-23	107	3	that	that	SCONJ
ejpam-23	107	4	ehfreh	ehfreh	NOUN
ejpam-23	107	5	and	and	CCONJ
ejpam-23	107	6	ekflkf	ekflkf	NOUN
ejpam-23	107	7	.	.	PUNCT
ejpam-23	108	1	now	now	ADV
ejpam-23	108	2	by	by	ADP
ejpam-23	108	3	eh	eh	INTJ
ejpam-23	108	4	=	=	SYM
ejpam-23	108	5	xfyh	xfyh	PROPN
ejpam-23	109	1	=	=	PUNCT
ejpam-23	109	2	xfy	xfy	PROPN
ejpam-23	110	1	=	=	PUNCT
ejpam-23	110	2	e	e	PROPN
ejpam-23	110	3	and	and	CCONJ
ejpam-23	110	4	kf	kf	PROPN
ejpam-23	110	5	=	=	PUNCT
ejpam-23	110	6	kset	kset	NOUN
ejpam-23	110	7	=	=	PUNCT
ejpam-23	110	8	set	set	NOUN
ejpam-23	110	9	=	=	PUNCT
ejpam-23	110	10	f	f	PROPN
ejpam-23	110	11	,	,	PUNCT
ejpam-23	110	12	we	we	PRON
ejpam-23	110	13	have	have	AUX
ejpam-23	110	14	ereflf	ereflf	NOUN
ejpam-23	110	15	.	.	PUNCT
ejpam-23	111	1	this	this	PRON
ejpam-23	111	2	shows	show	VERB
ejpam-23	111	3	that	that	SCONJ
ejpam-23	111	4	edf	edf	PROPN
ejpam-23	111	5	.	.	PUNCT
ejpam-23	112	1	similar	similar	ADJ
ejpam-23	112	2	to	to	ADP
ejpam-23	112	3	the	the	DET
ejpam-23	112	4	definition	definition	NOUN
ejpam-23	112	5	of	of	ADP
ejpam-23	112	6	cyber	cyber	PROPN
ejpam-23	112	7	group	group	NOUN
ejpam-23	112	8	given	give	VERB
ejpam-23	112	9	by	by	ADP
ejpam-23	112	10	guo	guo	PROPN
ejpam-23	112	11	and	and	CCONJ
ejpam-23	112	12	shum	shum	ADJ
ejpam-23	112	13	[	[	X
ejpam-23	112	14	5	5	NUM
ejpam-23	112	15	]	]	PUNCT
ejpam-23	112	16	,	,	PUNCT
ejpam-23	112	17	we	we	PRON
ejpam-23	112	18	formulate	formulate	VERB
ejpam-23	112	19	the	the	DET
ejpam-23	112	20	following	follow	VERB
ejpam-23	112	21	definition	definition	NOUN
ejpam-23	112	22	.	.	PUNCT
ejpam-23	113	1	definition	definition	NOUN
ejpam-23	113	2	2.7	2.7	NUM
ejpam-23	113	3	an	an	DET
ejpam-23	113	4	h̃-abundant	h̃-abundant	ADJ
ejpam-23	113	5	semigroup	semigroup	NOUN
ejpam-23	113	6	s	s	PART
ejpam-23	113	7	is	be	AUX
ejpam-23	113	8	called	call	VERB
ejpam-23	113	9	an	an	DET
ejpam-23	113	10	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	113	11	if	if	SCONJ
ejpam-23	113	12	the	the	DET
ejpam-23	113	13	green	green	ADJ
ejpam-23	113	14	∼-relation	∼-relation	NOUN
ejpam-23	113	15	h̃	h̃	PROPN
ejpam-23	113	16	is	be	AUX
ejpam-23	113	17	a	a	DET
ejpam-23	113	18	congruence	congruence	NOUN
ejpam-23	113	19	on	on	ADP
ejpam-23	113	20	s.	s.	PROPN
ejpam-23	113	21	also	also	ADV
ejpam-23	113	22	,	,	PUNCT
ejpam-23	113	23	we	we	PRON
ejpam-23	113	24	call	call	VERB
ejpam-23	113	25	an	an	DET
ejpam-23	113	26	h̃-abundant	h̃-abundant	ADJ
ejpam-23	113	27	semigroup	semigroup	NOUN
ejpam-23	113	28	s	s	VERB
ejpam-23	113	29	a	a	DET
ejpam-23	113	30	regular	regular	ADJ
ejpam-23	113	31	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	113	32	if	if	SCONJ
ejpam-23	113	33	h̃	h̃	PROPN
ejpam-23	113	34	is	be	AUX
ejpam-23	113	35	a	a	DET
ejpam-23	113	36	congruence	congruence	NOUN
ejpam-23	113	37	on	on	ADP
ejpam-23	113	38	s	s	PRON
ejpam-23	113	39	such	such	ADJ
ejpam-23	113	40	that	that	PRON
ejpam-23	113	41	s	s	PROPN
ejpam-23	113	42	/	/	SYM
ejpam-23	113	43	h̃	h̃	PROPN
ejpam-23	113	44	is	be	AUX
ejpam-23	113	45	a	a	DET
ejpam-23	113	46	regular	regular	ADJ
ejpam-23	113	47	band	band	NOUN
ejpam-23	113	48	.	.	PUNCT
ejpam-23	114	1	thus	thus	ADV
ejpam-23	114	2	,	,	PUNCT
ejpam-23	114	3	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	114	4	are	be	AUX
ejpam-23	114	5	analogy	analogy	NOUN
ejpam-23	114	6	of	of	ADP
ejpam-23	114	7	cryptogroups	cryptogroup	NOUN
ejpam-23	114	8	in	in	ADP
ejpam-23	114	9	the	the	DET
ejpam-23	114	10	class	class	NOUN
ejpam-23	114	11	of	of	ADP
ejpam-23	114	12	h̃-abundant	h̃-abundant	ADJ
ejpam-23	114	13	semigroups	semigroup	NOUN
ejpam-23	114	14	.	.	PUNCT
ejpam-23	115	1	also	also	ADV
ejpam-23	115	2	,	,	PUNCT
ejpam-23	115	3	we	we	PRON
ejpam-23	115	4	see	see	VERB
ejpam-23	115	5	in	in	ADP
ejpam-23	115	6	[	[	X
ejpam-23	115	7	5	5	NUM
ejpam-23	115	8	]	]	PUNCT
ejpam-23	115	9	that	that	SCONJ
ejpam-23	115	10	an	an	DET
ejpam-23	115	11	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	115	12	is	be	AUX
ejpam-23	115	13	a	a	DET
ejpam-23	115	14	generalized	generalized	ADJ
ejpam-23	115	15	cyber	cyber	NOUN
ejpam-23	115	16	groups	group	NOUN
ejpam-23	115	17	.	.	PUNCT
ejpam-23	116	1	the	the	DET
ejpam-23	116	2	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	116	3	s	s	PART
ejpam-23	116	4	has	have	VERB
ejpam-23	116	5	the	the	DET
ejpam-23	116	6	following	follow	VERB
ejpam-23	116	7	properties	property	NOUN
ejpam-23	116	8	:	:	PUNCT
ejpam-23	116	9	lemma	lemma	PROPN
ejpam-23	116	10	2.8	2.8	NUM
ejpam-23	116	11	(	(	PUNCT
ejpam-23	116	12	i	i	NOUN
ejpam-23	116	13	)	)	PUNCT
ejpam-23	116	14	for	for	ADP
ejpam-23	116	15	any	any	DET
ejpam-23	116	16	element	element	NOUN
ejpam-23	116	17	a	a	PRON
ejpam-23	116	18	of	of	ADP
ejpam-23	116	19	the	the	DET
ejpam-23	116	20	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	116	21	s	s	PART
ejpam-23	116	22	,	,	PUNCT
ejpam-23	116	23	j̃(a	j̃(a	PROPN
ejpam-23	116	24	)	)	PUNCT
ejpam-23	116	25	=	=	SYM
ejpam-23	116	26	sa0s	sa0s	PROPN
ejpam-23	116	27	.	.	PUNCT
ejpam-23	117	1	(	(	PUNCT
ejpam-23	117	2	ii	ii	NOUN
ejpam-23	117	3	)	)	PUNCT
ejpam-23	117	4	for	for	ADP
ejpam-23	117	5	the	the	DET
ejpam-23	117	6	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	117	7	s	s	PART
ejpam-23	117	8	,	,	PUNCT
ejpam-23	117	9	j̃	j̃	PROPN
ejpam-23	117	10	=	=	PUNCT
ejpam-23	117	11	d̃.	d̃.	PROPN
ejpam-23	117	12	(	(	PUNCT
ejpam-23	117	13	iii	iii	NOUN
ejpam-23	117	14	)	)	PUNCT
ejpam-23	117	15	if	if	SCONJ
ejpam-23	117	16	the	the	DET
ejpam-23	117	17	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	117	18	s	s	VERB
ejpam-23	117	19	is	be	AUX
ejpam-23	117	20	completely	completely	ADV
ejpam-23	117	21	j̃	j̃	PROPN
ejpam-23	117	22	-simple	-simple	NUM
ejpam-23	117	23	,	,	PUNCT
ejpam-23	117	24	then	then	ADV
ejpam-23	117	25	the	the	DET
ejpam-23	117	26	idempotents	idempotent	NOUN
ejpam-23	117	27	of	of	ADP
ejpam-23	117	28	s	s	NOUN
ejpam-23	117	29	are	be	AUX
ejpam-23	117	30	primitive	primitive	ADJ
ejpam-23	117	31	.	.	PUNCT
ejpam-23	118	1	x.	x.	PROPN
ejpam-23	118	2	kong	kong	PROPN
ejpam-23	118	3	,	,	PUNCT
ejpam-23	118	4	y.ding	y.de	VERB
ejpam-23	118	5	,	,	PUNCT
ejpam-23	118	6	k.p.shum	k.p.shum	ADJ
ejpam-23	118	7	/	/	SYM
ejpam-23	118	8	eur	eur	PROPN
ejpam-23	118	9	.	.	PUNCT
ejpam-23	119	1	j.	j.	PROPN
ejpam-23	119	2	pure	pure	PROPN
ejpam-23	119	3	appl	appl	PROPN
ejpam-23	119	4	.	.	PROPN
ejpam-23	119	5	math	math	PROPN
ejpam-23	119	6	,	,	PUNCT
ejpam-23	119	7	1	1	NUM
ejpam-23	119	8	(	(	PUNCT
ejpam-23	119	9	2008	2008	NUM
ejpam-23	119	10	)	)	PUNCT
ejpam-23	119	11	,	,	PUNCT
ejpam-23	119	12	(	(	PUNCT
ejpam-23	119	13	46	46	NUM
ejpam-23	119	14	-	-	SYM
ejpam-23	119	15	59	59	NUM
ejpam-23	119	16	)	)	PUNCT
ejpam-23	119	17	51	51	NUM
ejpam-23	119	18	(	(	PUNCT
ejpam-23	119	19	iv	iv	X
ejpam-23	119	20	)	)	PUNCT
ejpam-23	119	21	if	if	SCONJ
ejpam-23	119	22	the	the	DET
ejpam-23	119	23	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	119	24	s	s	VERB
ejpam-23	119	25	is	be	AUX
ejpam-23	119	26	completely	completely	ADV
ejpam-23	119	27	j̃	j̃	PROPN
ejpam-23	119	28	-simple	-simple	NUM
ejpam-23	119	29	,	,	PUNCT
ejpam-23	119	30	then	then	ADV
ejpam-23	119	31	the	the	DET
ejpam-23	119	32	regular	regular	ADJ
ejpam-23	119	33	elements	element	NOUN
ejpam-23	119	34	of	of	ADP
ejpam-23	119	35	s	s	PRON
ejpam-23	119	36	generate	generate	VERB
ejpam-23	119	37	a	a	DET
ejpam-23	119	38	regular	regular	ADJ
ejpam-23	119	39	subsemigroup	subsemigroup	NOUN
ejpam-23	119	40	of	of	ADP
ejpam-23	119	41	s.	s.	PROPN
ejpam-23	119	42	proof	proof	PROPN
ejpam-23	119	43	.	.	PUNCT
ejpam-23	120	1	(	(	PUNCT
ejpam-23	120	2	i	i	NOUN
ejpam-23	120	3	)	)	PUNCT
ejpam-23	120	4	obviously	obviously	ADV
ejpam-23	120	5	,	,	PUNCT
ejpam-23	120	6	we	we	PRON
ejpam-23	120	7	have	have	VERB
ejpam-23	120	8	a0	a0	PROPN
ejpam-23	120	9	∈	∈	PROPN
ejpam-23	120	10	j̃(a	j̃(a	PROPN
ejpam-23	120	11	)	)	PUNCT
ejpam-23	120	12	and	and	CCONJ
ejpam-23	120	13	so	so	ADV
ejpam-23	120	14	sa0s	sa0s	PROPN
ejpam-23	120	15	⊆	⊆	NUM
ejpam-23	120	16	j̃(a	j̃(a	PROPN
ejpam-23	120	17	)	)	PUNCT
ejpam-23	120	18	.	.	PUNCT
ejpam-23	121	1	we	we	PRON
ejpam-23	121	2	need	need	VERB
ejpam-23	121	3	to	to	PART
ejpam-23	121	4	show	show	VERB
ejpam-23	121	5	that	that	SCONJ
ejpam-23	121	6	the	the	DET
ejpam-23	121	7	ideal	ideal	ADJ
ejpam-23	121	8	sa0s	sa0s	PROPN
ejpam-23	121	9	is	be	AUX
ejpam-23	121	10	in	in	ADP
ejpam-23	121	11	fact	fact	NOUN
ejpam-23	121	12	a	a	DET
ejpam-23	121	13	∼-ideal	∼-ideal	NOUN
ejpam-23	121	14	and	and	CCONJ
ejpam-23	121	15	since	since	SCONJ
ejpam-23	121	16	a	a	DET
ejpam-23	121	17	=	=	SYM
ejpam-23	121	18	aa0a0	aa0a0	PROPN
ejpam-23	121	19	∈	∈	PROPN
ejpam-23	121	20	sa0s	sa0s	PROPN
ejpam-23	121	21	,	,	PUNCT
ejpam-23	121	22	j̃(a	j̃(a	PROPN
ejpam-23	121	23	)	)	PUNCT
ejpam-23	121	24	⊆	⊆	NUM
ejpam-23	121	25	sa0s	sa0s	PROPN
ejpam-23	121	26	.	.	PUNCT
ejpam-23	122	1	let	let	VERB
ejpam-23	122	2	b	b	NOUN
ejpam-23	122	3	=	=	SYM
ejpam-23	122	4	xa0y	xa0y	PROPN
ejpam-23	122	5	∈	∈	PROPN
ejpam-23	122	6	sa0s(x	sa0s(x	PROPN
ejpam-23	122	7	,	,	PUNCT
ejpam-23	122	8	y	y	PROPN
ejpam-23	122	9	∈	∈	PROPN
ejpam-23	122	10	s	s	PART
ejpam-23	122	11	)	)	PUNCT
ejpam-23	122	12	and	and	CCONJ
ejpam-23	122	13	k	k	PROPN
ejpam-23	122	14	=	=	SYM
ejpam-23	122	15	(	(	PUNCT
ejpam-23	122	16	a0y)0	a0y)0	PROPN
ejpam-23	122	17	.	.	PROPN
ejpam-23	122	18	then	then	ADV
ejpam-23	122	19	a0a0y	a0a0y	PUNCT
ejpam-23	123	1	=	=	SYM
ejpam-23	123	2	a0y	a0y	PROPN
ejpam-23	123	3	=	=	PROPN
ejpam-23	123	4	ka0y	ka0y	PROPN
ejpam-23	123	5	so	so	SCONJ
ejpam-23	123	6	that	that	SCONJ
ejpam-23	123	7	a0(a0y)0	a0(a0y)0	NOUN
ejpam-23	123	8	=	=	PUNCT
ejpam-23	123	9	k2	k2	PROPN
ejpam-23	123	10	=	=	SYM
ejpam-23	123	11	k.	k.	PROPN
ejpam-23	123	12	also	also	ADV
ejpam-23	123	13	since	since	SCONJ
ejpam-23	123	14	h̃	h̃	PROPN
ejpam-23	123	15	is	be	AUX
ejpam-23	123	16	a	a	DET
ejpam-23	123	17	congruence	congruence	NOUN
ejpam-23	123	18	,	,	PUNCT
ejpam-23	123	19	xa0yh̃xk	xa0yh̃xk	PROPN
ejpam-23	123	20	.	.	PUNCT
ejpam-23	124	1	now	now	ADV
ejpam-23	124	2	let	let	VERB
ejpam-23	124	3	h	h	NOUN
ejpam-23	124	4	=	=	SYM
ejpam-23	124	5	(	(	PUNCT
ejpam-23	124	6	xk)0	xk)0	PROPN
ejpam-23	124	7	=	=	SYM
ejpam-23	124	8	(	(	PUNCT
ejpam-23	124	9	xa0y)0	xa0y)0	PROPN
ejpam-23	124	10	.	.	PUNCT
ejpam-23	125	1	then	then	ADV
ejpam-23	125	2	xkh	xkh	PUNCT
ejpam-23	126	1	=	=	SYM
ejpam-23	126	2	xk	xk	PROPN
ejpam-23	126	3	=	=	SYM
ejpam-23	126	4	xkk	xkk	PROPN
ejpam-23	127	1	so	so	SCONJ
ejpam-23	127	2	that	that	SCONJ
ejpam-23	127	3	h	h	NOUN
ejpam-23	127	4	=	=	SYM
ejpam-23	127	5	h2	h2	NOUN
ejpam-23	127	6	=	=	SYM
ejpam-23	128	1	hk	hk	PROPN
ejpam-23	129	1	=	=	PUNCT
ejpam-23	129	2	ha0k	ha0k	PROPN
ejpam-23	129	3	∈	∈	PROPN
ejpam-23	129	4	sa0s	sa0s	PROPN
ejpam-23	129	5	.	.	PUNCT
ejpam-23	130	1	hence	hence	ADV
ejpam-23	130	2	if	if	SCONJ
ejpam-23	130	3	c	c	PROPN
ejpam-23	130	4	∈	∈	PROPN
ejpam-23	130	5	l̃b	l̃b	ADV
ejpam-23	130	6	,	,	PUNCT
ejpam-23	130	7	d	d	PROPN
ejpam-23	130	8	∈	∈	PROPN
ejpam-23	130	9	r̃b	r̃b	PROPN
ejpam-23	130	10	,	,	PUNCT
ejpam-23	130	11	then	then	ADV
ejpam-23	130	12	c	c	PROPN
ejpam-23	130	13	=	=	SYM
ejpam-23	130	14	ch	ch	PROPN
ejpam-23	130	15	,	,	PUNCT
ejpam-23	130	16	d	d	PROPN
ejpam-23	130	17	=	=	SYM
ejpam-23	130	18	hd	hd	PROPN
ejpam-23	130	19	∈	∈	PROPN
ejpam-23	130	20	sa0s	sa0s	PROPN
ejpam-23	130	21	and	and	CCONJ
ejpam-23	130	22	hence	hence	ADV
ejpam-23	130	23	,	,	PUNCT
ejpam-23	130	24	sa0s	sa0s	PROPN
ejpam-23	130	25	is	be	AUX
ejpam-23	130	26	a	a	DET
ejpam-23	130	27	∼-ideal	∼-ideal	NOUN
ejpam-23	130	28	,	,	PUNCT
ejpam-23	130	29	as	as	SCONJ
ejpam-23	130	30	required	require	VERB
ejpam-23	130	31	.	.	PUNCT
ejpam-23	131	1	(	(	PUNCT
ejpam-23	131	2	ii	ii	NOUN
ejpam-23	131	3	)	)	PUNCT
ejpam-23	131	4	suppose	suppose	VERB
ejpam-23	131	5	that	that	SCONJ
ejpam-23	131	6	(	(	PUNCT
ejpam-23	131	7	a	a	PRON
ejpam-23	131	8	,	,	PUNCT
ejpam-23	131	9	b	b	NOUN
ejpam-23	131	10	)	)	PUNCT
ejpam-23	131	11	∈	∈	PROPN
ejpam-23	131	12	s	s	PART
ejpam-23	131	13	with	with	ADP
ejpam-23	131	14	aj̃	aj̃	PROPN
ejpam-23	131	15	b.	b.	PROPN
ejpam-23	131	16	then	then	ADV
ejpam-23	131	17	by	by	ADP
ejpam-23	131	18	(	(	PUNCT
ejpam-23	131	19	i	i	NOUN
ejpam-23	131	20	)	)	PUNCT
ejpam-23	131	21	,	,	PUNCT
ejpam-23	131	22	we	we	PRON
ejpam-23	131	23	have	have	VERB
ejpam-23	131	24	sa0s	sa0s	PROPN
ejpam-23	131	25	=	=	PUNCT
ejpam-23	131	26	sb0s	sb0s	PROPN
ejpam-23	131	27	.	.	PUNCT
ejpam-23	132	1	now	now	ADV
ejpam-23	132	2	,	,	PUNCT
ejpam-23	132	3	by	by	ADP
ejpam-23	132	4	lemma	lemma	PROPN
ejpam-23	132	5	2.6	2.6	NUM
ejpam-23	132	6	(	(	PUNCT
ejpam-23	132	7	iv	iv	NUM
ejpam-23	132	8	)	)	PUNCT
ejpam-23	132	9	,	,	PUNCT
ejpam-23	132	10	a0db0	a0db0	NOUN
ejpam-23	132	11	and	and	CCONJ
ejpam-23	132	12	so	so	ADV
ejpam-23	132	13	ah̃a0db0h̃b	ah̃a0db0h̃b	PROPN
ejpam-23	132	14	.	.	PUNCT
ejpam-23	133	1	this	this	PRON
ejpam-23	133	2	implies	imply	VERB
ejpam-23	133	3	that	that	DET
ejpam-23	133	4	ad̃b	ad̃b	PROPN
ejpam-23	133	5	and	and	CCONJ
ejpam-23	133	6	hence	hence	ADV
ejpam-23	133	7	j̃	j̃	PROPN
ejpam-23	133	8	⊆	⊆	NUM
ejpam-23	133	9	d̃.	d̃.	PROPN
ejpam-23	133	10	conversely	conversely	ADV
ejpam-23	133	11	,	,	PUNCT
ejpam-23	133	12	let	let	VERB
ejpam-23	133	13	a	a	DET
ejpam-23	133	14	,	,	PUNCT
ejpam-23	133	15	b	b	X
ejpam-23	133	16	∈	∈	NOUN
ejpam-23	133	17	s	s	VERB
ejpam-23	133	18	with	with	ADP
ejpam-23	133	19	ad̃b	ad̃b	PROPN
ejpam-23	133	20	.	.	PUNCT
ejpam-23	134	1	then	then	ADV
ejpam-23	134	2	by	by	ADP
ejpam-23	134	3	lemma	lemma	PROPN
ejpam-23	134	4	2.6	2.6	NUM
ejpam-23	134	5	(	(	PUNCT
ejpam-23	134	6	iii	iii	NOUN
ejpam-23	134	7	)	)	PUNCT
ejpam-23	134	8	,	,	PUNCT
ejpam-23	134	9	there	there	PRON
ejpam-23	134	10	exists	exist	VERB
ejpam-23	134	11	an	an	DET
ejpam-23	134	12	element	element	NOUN
ejpam-23	134	13	c	c	PROPN
ejpam-23	134	14	∈	∈	NOUN
ejpam-23	134	15	s	s	VERB
ejpam-23	134	16	such	such	ADJ
ejpam-23	134	17	that	that	SCONJ
ejpam-23	134	18	al̃cr̃b	al̃cr̃b	PROPN
ejpam-23	134	19	.	.	PUNCT
ejpam-23	135	1	this	this	PRON
ejpam-23	135	2	leads	lead	VERB
ejpam-23	135	3	to	to	ADP
ejpam-23	135	4	a0lc0rb0	a0lc0rb0	PROPN
ejpam-23	135	5	and	and	CCONJ
ejpam-23	135	6	so	so	ADV
ejpam-23	135	7	sa0s	sa0s	PROPN
ejpam-23	135	8	=	=	SYM
ejpam-23	135	9	sc0s	sc0s	NUM
ejpam-23	135	10	=	=	SYM
ejpam-23	135	11	sb0s	sb0	NOUN
ejpam-23	135	12	.	.	PUNCT
ejpam-23	136	1	now	now	ADV
ejpam-23	136	2	,	,	PUNCT
ejpam-23	136	3	by	by	ADP
ejpam-23	136	4	(	(	PUNCT
ejpam-23	136	5	i	i	NOUN
ejpam-23	136	6	)	)	PUNCT
ejpam-23	136	7	,	,	PUNCT
ejpam-23	136	8	(	(	PUNCT
ejpam-23	136	9	a	a	PRON
ejpam-23	136	10	,	,	PUNCT
ejpam-23	136	11	b	b	NOUN
ejpam-23	136	12	)	)	PUNCT
ejpam-23	136	13	∈	∈	PROPN
ejpam-23	136	14	j̃	j̃	PROPN
ejpam-23	136	15	and	and	CCONJ
ejpam-23	136	16	hence	hence	ADV
ejpam-23	136	17	d̃	d̃	PROPN
ejpam-23	136	18	⊆	⊆	NUM
ejpam-23	136	19	j̃	j̃	PROPN
ejpam-23	136	20	.	.	PUNCT
ejpam-23	137	1	therefore	therefore	ADV
ejpam-23	137	2	,	,	PUNCT
ejpam-23	137	3	j̃	j̃	PROPN
ejpam-23	137	4	=	=	PUNCT
ejpam-23	137	5	d̃.	d̃.	PROPN
ejpam-23	137	6	(	(	PUNCT
ejpam-23	137	7	iii	iii	NOUN
ejpam-23	137	8	)	)	PUNCT
ejpam-23	137	9	let	let	VERB
ejpam-23	137	10	e	e	NOUN
ejpam-23	137	11	,	,	PUNCT
ejpam-23	137	12	f	f	PROPN
ejpam-23	137	13	be	be	VERB
ejpam-23	137	14	idempotents	idempotent	NOUN
ejpam-23	137	15	in	in	ADP
ejpam-23	137	16	s	s	PRON
ejpam-23	137	17	with	with	ADP
ejpam-23	137	18	e	e	PROPN
ejpam-23	137	19	6	6	NUM
ejpam-23	137	20	f	f	NOUN
ejpam-23	137	21	.	.	PUNCT
ejpam-23	138	1	since	since	SCONJ
ejpam-23	138	2	s	s	NOUN
ejpam-23	138	3	is	be	AUX
ejpam-23	138	4	completely	completely	ADV
ejpam-23	138	5	j̃	j̃	PROPN
ejpam-23	138	6	-simple	-simple	NUM
ejpam-23	138	7	,	,	PUNCT
ejpam-23	138	8	f	f	PROPN
ejpam-23	138	9	∈	∈	PROPN
ejpam-23	138	10	ses	se	NOUN
ejpam-23	138	11	.	.	PUNCT
ejpam-23	139	1	now	now	ADV
ejpam-23	139	2	by	by	ADP
ejpam-23	139	3	the	the	DET
ejpam-23	139	4	first	first	ADJ
ejpam-23	139	5	part	part	NOUN
ejpam-23	139	6	of	of	ADP
ejpam-23	139	7	exercise	exercise	NOUN
ejpam-23	139	8	3	3	NUM
ejpam-23	139	9	in	in	ADP
ejpam-23	139	10	[	[	X
ejpam-23	139	11	14][§8.4	14][§8.4	NOUN
ejpam-23	139	12	]	]	PUNCT
ejpam-23	139	13	,	,	PUNCT
ejpam-23	139	14	there	there	PRON
ejpam-23	139	15	exists	exist	VERB
ejpam-23	139	16	an	an	DET
ejpam-23	139	17	idempotent	idempotent	ADJ
ejpam-23	139	18	g	g	NOUN
ejpam-23	139	19	of	of	ADP
ejpam-23	139	20	s	s	PRON
ejpam-23	139	21	such	such	ADJ
ejpam-23	139	22	that	that	SCONJ
ejpam-23	139	23	fdg	fdg	PROPN
ejpam-23	139	24	and	and	CCONJ
ejpam-23	139	25	g	g	PROPN
ejpam-23	139	26	6	6	NUM
ejpam-23	139	27	e.	e.	PROPN
ejpam-23	139	28	let	let	VERB
ejpam-23	139	29	a	a	DET
ejpam-23	139	30	∈	∈	NOUN
ejpam-23	139	31	s	s	AUX
ejpam-23	139	32	be	be	AUX
ejpam-23	139	33	such	such	ADJ
ejpam-23	139	34	that	that	DET
ejpam-23	139	35	flarg	flarg	NOUN
ejpam-23	139	36	.	.	PUNCT
ejpam-23	140	1	then	then	ADV
ejpam-23	140	2	fla0rg	fla0rg	VERB
ejpam-23	140	3	and	and	CCONJ
ejpam-23	140	4	since	since	SCONJ
ejpam-23	140	5	g	g	PROPN
ejpam-23	140	6	6	6	NUM
ejpam-23	140	7	f	f	NOUN
ejpam-23	140	8	,	,	PUNCT
ejpam-23	140	9	we	we	PRON
ejpam-23	140	10	have	have	VERB
ejpam-23	141	1	a0	a0	NOUN
ejpam-23	141	2	=	=	SYM
ejpam-23	141	3	ga0(gf)a0	ga0(gf)a0	PROPN
ejpam-23	141	4	=	=	SYM
ejpam-23	141	5	g(fa0	g(fa0	NOUN
ejpam-23	141	6	)	)	PUNCT
ejpam-23	141	7	=	=	PUNCT
ejpam-23	141	8	gf	gf	NOUN
ejpam-23	141	9	=	=	PUNCT
ejpam-23	141	10	g.	g.	PROPN
ejpam-23	141	11	now	now	ADV
ejpam-23	141	12	by	by	ADP
ejpam-23	141	13	noting	note	VERB
ejpam-23	141	14	that	that	SCONJ
ejpam-23	141	15	g	g	PROPN
ejpam-23	141	16	6	6	NUM
ejpam-23	141	17	f	f	NOUN
ejpam-23	141	18	and	and	CCONJ
ejpam-23	141	19	glf	glf	PROPN
ejpam-23	141	20	,	,	PUNCT
ejpam-23	141	21	we	we	PRON
ejpam-23	141	22	have	have	VERB
ejpam-23	141	23	f	f	NOUN
ejpam-23	141	24	=	=	SYM
ejpam-23	141	25	fg	fg	PROPN
ejpam-23	141	26	=	=	PROPN
ejpam-23	141	27	g.	g.	PROPN
ejpam-23	141	28	however	however	ADV
ejpam-23	141	29	,	,	PUNCT
ejpam-23	141	30	since	since	SCONJ
ejpam-23	141	31	g	g	PROPN
ejpam-23	141	32	6	6	NUM
ejpam-23	141	33	e	e	NOUN
ejpam-23	141	34	,	,	PUNCT
ejpam-23	141	35	we	we	PRON
ejpam-23	141	36	obtain	obtain	VERB
ejpam-23	141	37	e	e	X
ejpam-23	141	38	=	=	SYM
ejpam-23	141	39	f	f	PROPN
ejpam-23	141	40	and	and	CCONJ
ejpam-23	141	41	hence	hence	ADV
ejpam-23	141	42	all	all	DET
ejpam-23	141	43	idempotents	idempotent	NOUN
ejpam-23	141	44	of	of	ADP
ejpam-23	141	45	s	s	NOUN
ejpam-23	141	46	are	be	AUX
ejpam-23	141	47	primitive	primitive	ADJ
ejpam-23	141	48	.	.	PUNCT
ejpam-23	142	1	(	(	PUNCT
ejpam-23	142	2	iv	iv	X
ejpam-23	142	3	)	)	PUNCT
ejpam-23	142	4	let	let	VERB
ejpam-23	142	5	a	a	DET
ejpam-23	142	6	,	,	PUNCT
ejpam-23	142	7	b	b	PROPN
ejpam-23	142	8	be	be	AUX
ejpam-23	142	9	regular	regular	ADJ
ejpam-23	142	10	elements	element	NOUN
ejpam-23	142	11	of	of	ADP
ejpam-23	142	12	s.	s.	PROPN
ejpam-23	142	13	since	since	SCONJ
ejpam-23	142	14	s	s	PRON
ejpam-23	142	15	consists	consist	VERB
ejpam-23	142	16	of	of	ADP
ejpam-23	142	17	a	a	DET
ejpam-23	142	18	single	single	ADJ
ejpam-23	142	19	d̃-class	d̃-class	NOUN
ejpam-23	142	20	,	,	PUNCT
ejpam-23	142	21	by	by	ADP
ejpam-23	142	22	(	(	PUNCT
ejpam-23	142	23	ii	ii	NOUN
ejpam-23	142	24	)	)	PUNCT
ejpam-23	142	25	and	and	CCONJ
ejpam-23	142	26	by	by	ADP
ejpam-23	142	27	lemma	lemma	PROPN
ejpam-23	142	28	2.6	2.6	NUM
ejpam-23	142	29	(	(	PUNCT
ejpam-23	142	30	iii	iii	NOUN
ejpam-23	142	31	)	)	PUNCT
ejpam-23	142	32	,	,	PUNCT
ejpam-23	142	33	there	there	PRON
ejpam-23	142	34	exists	exist	VERB
ejpam-23	142	35	an	an	DET
ejpam-23	142	36	element	element	NOUN
ejpam-23	142	37	c	c	PROPN
ejpam-23	142	38	∈	∈	NOUN
ejpam-23	142	39	s	s	VERB
ejpam-23	142	40	such	such	ADJ
ejpam-23	142	41	that	that	SCONJ
ejpam-23	142	42	al̃cr̃b	al̃cr̃b	PROPN
ejpam-23	142	43	.	.	PUNCT
ejpam-23	143	1	hence	hence	ADV
ejpam-23	143	2	al̃c0r̃b	al̃c0r̃b	PROPN
ejpam-23	143	3	.	.	PUNCT
ejpam-23	144	1	this	this	PRON
ejpam-23	144	2	leads	lead	VERB
ejpam-23	144	3	to	to	ADP
ejpam-23	144	4	c0b	c0b	PROPN
ejpam-23	144	5	=	=	SYM
ejpam-23	144	6	b	b	PROPN
ejpam-23	144	7	and	and	CCONJ
ejpam-23	144	8	alc0	alc0	NOUN
ejpam-23	144	9	since	since	SCONJ
ejpam-23	144	10	a	a	PRON
ejpam-23	144	11	is	be	AUX
ejpam-23	144	12	regular	regular	ADJ
ejpam-23	144	13	.	.	PUNCT
ejpam-23	145	1	now	now	ADV
ejpam-23	145	2	we	we	PRON
ejpam-23	145	3	have	have	VERB
ejpam-23	145	4	ablb	ablb	VERB
ejpam-23	146	1	and	and	CCONJ
ejpam-23	146	2	so	so	ADV
ejpam-23	146	3	the	the	DET
ejpam-23	146	4	regularity	regularity	NOUN
ejpam-23	146	5	of	of	ADP
ejpam-23	146	6	ab	ab	PROPN
ejpam-23	146	7	follows	follow	VERB
ejpam-23	146	8	from	from	ADP
ejpam-23	146	9	the	the	DET
ejpam-23	146	10	regularity	regularity	NOUN
ejpam-23	146	11	of	of	ADP
ejpam-23	146	12	b.	b.	PROPN
ejpam-23	146	13	we	we	PRON
ejpam-23	146	14	now	now	ADV
ejpam-23	146	15	establish	establish	VERB
ejpam-23	146	16	the	the	DET
ejpam-23	146	17	following	follow	VERB
ejpam-23	146	18	theorem	theorem	NOUN
ejpam-23	146	19	for	for	ADP
ejpam-23	146	20	h̃	h̃	PROPN
ejpam-23	146	21	-cryptogroups	-cryptogroup	NOUN
ejpam-23	146	22	.	.	PUNCT
ejpam-23	147	1	theorem	theorem	VERB
ejpam-23	147	2	2.9	2.9	NUM
ejpam-23	147	3	let	let	VERB
ejpam-23	147	4	s	s	PRON
ejpam-23	147	5	be	be	AUX
ejpam-23	147	6	an	an	DET
ejpam-23	147	7	h̃	h̃	PROPN
ejpam-23	147	8	-cryptogroup	-cryptogroup	NOUN
ejpam-23	147	9	.	.	PUNCT
ejpam-23	148	1	then	then	ADV
ejpam-23	148	2	s	s	VERB
ejpam-23	148	3	is	be	AUX
ejpam-23	148	4	a	a	DET
ejpam-23	148	5	semilattice	semilattice	NOUN
ejpam-23	148	6	y	y	NOUN
ejpam-23	148	7	of	of	ADP
ejpam-23	148	8	completely	completely	ADV
ejpam-23	148	9	j̃	j̃	PROPN
ejpam-23	148	10	-simple	-simple	ADJ
ejpam-23	148	11	semigroups	semigroup	NOUN
ejpam-23	148	12	sα(α	sα(α	X
ejpam-23	148	13	∈	∈	PROPN
ejpam-23	148	14	y	y	PROPN
ejpam-23	148	15	)	)	PUNCT
ejpam-23	148	16	such	such	ADJ
ejpam-23	148	17	that	that	PRON
ejpam-23	148	18	for	for	ADP
ejpam-23	148	19	every	every	DET
ejpam-23	148	20	α	α	PROPN
ejpam-23	148	21	∈	∈	PROPN
ejpam-23	148	22	y	y	PROPN
ejpam-23	148	23	and	and	CCONJ
ejpam-23	148	24	a	a	DET
ejpam-23	148	25	∈	∈	NOUN
ejpam-23	148	26	sα	sα	ADV
ejpam-23	148	27	,	,	PUNCT
ejpam-23	148	28	we	we	PRON
ejpam-23	148	29	have	have	VERB
ejpam-23	148	30	l̃a(s	l̃a(s	PROPN
ejpam-23	148	31	)	)	PUNCT
ejpam-23	148	32	=	=	SYM
ejpam-23	148	33	l̃a(sα	l̃a(sα	X
ejpam-23	148	34	)	)	PUNCT
ejpam-23	148	35	and	and	CCONJ
ejpam-23	148	36	r̃a(s	r̃a(	NOUN
ejpam-23	148	37	)	)	PUNCT
ejpam-23	148	38	=	=	SYM
ejpam-23	148	39	l̃a(sα	l̃a(sα	X
ejpam-23	148	40	)	)	PUNCT
ejpam-23	148	41	.	.	PUNCT
ejpam-23	149	1	proof	proof	NOUN
ejpam-23	149	2	.	.	PUNCT
ejpam-23	150	1	if	if	SCONJ
ejpam-23	150	2	a	a	DET
ejpam-23	150	3	∈	∈	PROPN
ejpam-23	150	4	s	s	NOUN
ejpam-23	150	5	,	,	PUNCT
ejpam-23	150	6	then	then	ADV
ejpam-23	150	7	ah̃a2	ah̃a2	PUNCT
ejpam-23	150	8	and	and	CCONJ
ejpam-23	150	9	so	so	ADV
ejpam-23	150	10	,	,	PUNCT
ejpam-23	150	11	j̃(a	j̃(a	PROPN
ejpam-23	150	12	)	)	PUNCT
ejpam-23	150	13	=	=	SYM
ejpam-23	150	14	j̃(a2	j̃(a2	PROPN
ejpam-23	150	15	)	)	PUNCT
ejpam-23	150	16	.	.	PUNCT
ejpam-23	151	1	now	now	ADV
ejpam-23	151	2	for	for	ADP
ejpam-23	151	3	a	a	DET
ejpam-23	151	4	,	,	PUNCT
ejpam-23	151	5	b	b	PROPN
ejpam-23	151	6	∈	∈	PROPN
ejpam-23	151	7	s	s	X
ejpam-23	151	8	,	,	PUNCT
ejpam-23	151	9	we	we	PRON
ejpam-23	151	10	have	have	VERB
ejpam-23	151	11	(	(	PUNCT
ejpam-23	151	12	ab)2	ab)2	PROPN
ejpam-23	151	13	∈	∈	PROPN
ejpam-23	151	14	sbas	sbas	NOUN
ejpam-23	151	15	,	,	PUNCT
ejpam-23	151	16	and	and	CCONJ
ejpam-23	151	17	hence	hence	ADV
ejpam-23	151	18	,	,	PUNCT
ejpam-23	151	19	it	it	PRON
ejpam-23	151	20	follows	follow	VERB
ejpam-23	151	21	that	that	SCONJ
ejpam-23	151	22	j̃(ab	j̃(ab	NOUN
ejpam-23	151	23	)	)	PUNCT
ejpam-23	152	1	=	=	SYM
ejpam-23	152	2	j̃((ab)2	j̃((ab)2	ADJ
ejpam-23	152	3	)	)	PUNCT
ejpam-23	152	4	⊆	⊆	NUM
ejpam-23	152	5	j̃(ba	j̃(ba	NOUN
ejpam-23	152	6	)	)	PUNCT
ejpam-23	152	7	.	.	PUNCT
ejpam-23	153	1	now	now	ADV
ejpam-23	153	2	,	,	PUNCT
ejpam-23	153	3	by	by	ADP
ejpam-23	153	4	symmetry	symmetry	NOUN
ejpam-23	153	5	,	,	PUNCT
ejpam-23	153	6	we	we	PRON
ejpam-23	153	7	obtain	obtain	VERB
ejpam-23	153	8	j̃(ab	j̃(ab	ADV
ejpam-23	153	9	)	)	PUNCT
ejpam-23	153	10	=	=	SYM
ejpam-23	153	11	j̃(ba	j̃(ba	NOUN
ejpam-23	153	12	)	)	PUNCT
ejpam-23	153	13	.	.	PUNCT
ejpam-23	154	1	since	since	SCONJ
ejpam-23	154	2	,	,	PUNCT
ejpam-23	154	3	by	by	ADP
ejpam-23	154	4	lemma	lemma	PROPN
ejpam-23	154	5	2.8	2.8	NUM
ejpam-23	154	6	(	(	PUNCT
ejpam-23	154	7	i	i	NOUN
ejpam-23	154	8	)	)	PUNCT
ejpam-23	154	9	,	,	PUNCT
ejpam-23	154	10	we	we	PRON
ejpam-23	154	11	have	have	VERB
ejpam-23	154	12	j̃(a	j̃(a	NOUN
ejpam-23	154	13	)	)	PUNCT
ejpam-23	155	1	=	=	SYM
ejpam-23	155	2	sa0s	sa0s	NOUN
ejpam-23	155	3	and	and	CCONJ
ejpam-23	155	4	j̃(b	j̃(b	PROPN
ejpam-23	155	5	)	)	PUNCT
ejpam-23	156	1	=	=	PUNCT
ejpam-23	156	2	sb0s	sb0	VERB
ejpam-23	156	3	so	so	SCONJ
ejpam-23	156	4	that	that	SCONJ
ejpam-23	156	5	if	if	SCONJ
ejpam-23	156	6	c	c	PROPN
ejpam-23	156	7	∈	∈	PROPN
ejpam-23	156	8	j̃(a	j̃(a	PROPN
ejpam-23	156	9	)	)	PUNCT
ejpam-23	156	10	∩	∩	NOUN
ejpam-23	156	11	j̃(b	j̃(b	PROPN
ejpam-23	156	12	)	)	PUNCT
ejpam-23	156	13	,	,	PUNCT
ejpam-23	156	14	then	then	ADV
ejpam-23	156	15	c	c	X
ejpam-23	156	16	=	=	SYM
ejpam-23	156	17	xa0y	xa0y	PROPN
ejpam-23	156	18	=	=	SYM
ejpam-23	157	1	zb0	zb0	PROPN
ejpam-23	157	2	t	t	NOUN
ejpam-23	157	3	for	for	ADP
ejpam-23	157	4	some	some	DET
ejpam-23	157	5	x	x	NOUN
ejpam-23	157	6	,	,	PUNCT
ejpam-23	157	7	y	y	PROPN
ejpam-23	157	8	,	,	PUNCT
ejpam-23	157	9	z	z	PROPN
ejpam-23	157	10	,	,	PUNCT
ejpam-23	157	11	t	t	PROPN
ejpam-23	157	12	∈	∈	PROPN
ejpam-23	157	13	s.	s.	PROPN
ejpam-23	157	14	now	now	ADV
ejpam-23	157	15	c2	c2	PROPN
ejpam-23	157	16	=	=	SYM
ejpam-23	157	17	zb0txa0y	zb0txa0y	PROPN
ejpam-23	157	18	∈	∈	PROPN
ejpam-23	157	19	sb0txa0s	sb0txa0s	PROPN
ejpam-23	157	20	⊆	⊆	NUM
ejpam-23	157	21	j̃(b0txa0	j̃(b0txa0	NOUN
ejpam-23	157	22	)	)	PUNCT
ejpam-23	157	23	and	and	CCONJ
ejpam-23	157	24	hence	hence	ADV
ejpam-23	157	25	,	,	PUNCT
ejpam-23	157	26	j̃(b0txa0	j̃(b0txa0	NOUN
ejpam-23	157	27	)	)	PUNCT
ejpam-23	157	28	=	=	SYM
ejpam-23	157	29	j̃(a0b0tx	j̃(a0b0tx	PROPN
ejpam-23	157	30	)	)	PUNCT
ejpam-23	157	31	by	by	ADP
ejpam-23	157	32	using	use	VERB
ejpam-23	157	33	previous	previous	ADJ
ejpam-23	157	34	arguments	argument	NOUN
ejpam-23	157	35	.	.	PUNCT
ejpam-23	158	1	thus	thus	ADV
ejpam-23	158	2	,	,	PUNCT
ejpam-23	158	3	c2	c2	PROPN
ejpam-23	158	4	∈	∈	PROPN
ejpam-23	158	5	j̃(a0b0	j̃(a0b0	PROPN
ejpam-23	158	6	)	)	PUNCT
ejpam-23	158	7	and	and	CCONJ
ejpam-23	158	8	since	since	SCONJ
ejpam-23	158	9	ch̃c2	ch̃c2	PROPN
ejpam-23	158	10	,	,	PUNCT
ejpam-23	158	11	we	we	PRON
ejpam-23	158	12	have	have	VERB
ejpam-23	158	13	c	c	NOUN
ejpam-23	158	14	∈	∈	NOUN
ejpam-23	158	15	j̃(a0b0	j̃(a0b0	PROPN
ejpam-23	158	16	)	)	PUNCT
ejpam-23	158	17	.	.	PUNCT
ejpam-23	159	1	since	since	SCONJ
ejpam-23	159	2	ah̃a0	ah̃a0	PROPN
ejpam-23	159	3	,	,	PUNCT
ejpam-23	159	4	x.	x.	PROPN
ejpam-23	159	5	kong	kong	PROPN
ejpam-23	159	6	,	,	PUNCT
ejpam-23	159	7	y.ding	y.de	VERB
ejpam-23	159	8	,	,	PUNCT
ejpam-23	159	9	k.p.shum	k.p.shum	ADJ
ejpam-23	159	10	/	/	SYM
ejpam-23	159	11	eur	eur	PROPN
ejpam-23	159	12	.	.	PUNCT
ejpam-23	160	1	j.	j.	PROPN
ejpam-23	160	2	pure	pure	PROPN
ejpam-23	160	3	appl	appl	PROPN
ejpam-23	160	4	.	.	PROPN
ejpam-23	160	5	math	math	PROPN
ejpam-23	160	6	,	,	PUNCT
ejpam-23	160	7	1	1	NUM
ejpam-23	160	8	(	(	PUNCT
ejpam-23	160	9	2008	2008	NUM
ejpam-23	160	10	)	)	PUNCT
ejpam-23	160	11	,	,	PUNCT
ejpam-23	160	12	(	(	PUNCT
ejpam-23	160	13	46	46	NUM
ejpam-23	160	14	-	-	SYM
ejpam-23	160	15	59	59	NUM
ejpam-23	160	16	)	)	PUNCT
ejpam-23	160	17	52	52	NUM
ejpam-23	160	18	bh̃b0	bh̃b0	NOUN
ejpam-23	160	19	and	and	CCONJ
ejpam-23	160	20	h̃	h̃	PROPN
ejpam-23	160	21	is	be	AUX
ejpam-23	160	22	a	a	DET
ejpam-23	160	23	congruence	congruence	NOUN
ejpam-23	160	24	on	on	ADP
ejpam-23	160	25	s	s	PROPN
ejpam-23	160	26	,	,	PUNCT
ejpam-23	160	27	we	we	PRON
ejpam-23	160	28	have	have	VERB
ejpam-23	160	29	abh̃a0b0	abh̃a0b0	INTJ
ejpam-23	160	30	.	.	PUNCT
ejpam-23	161	1	consequently	consequently	ADV
ejpam-23	161	2	,	,	PUNCT
ejpam-23	161	3	c	c	PROPN
ejpam-23	161	4	∈	∈	PROPN
ejpam-23	161	5	j̃(ab	j̃(ab	NOUN
ejpam-23	161	6	)	)	PUNCT
ejpam-23	161	7	,	,	PUNCT
ejpam-23	161	8	and	and	CCONJ
ejpam-23	161	9	thereby	thereby	ADV
ejpam-23	161	10	j̃(a	j̃(a	PROPN
ejpam-23	161	11	)	)	PUNCT
ejpam-23	161	12	∩	∩	NOUN
ejpam-23	161	13	j̃(b	j̃(b	NOUN
ejpam-23	161	14	)	)	PUNCT
ejpam-23	161	15	⊆	⊆	NUM
ejpam-23	161	16	j̃(ab	j̃(ab	NOUN
ejpam-23	161	17	)	)	PUNCT
ejpam-23	161	18	.	.	PUNCT
ejpam-23	162	1	the	the	DET
ejpam-23	162	2	converse	converse	NOUN
ejpam-23	162	3	containment	containment	NOUN
ejpam-23	162	4	is	be	AUX
ejpam-23	162	5	clear	clear	ADJ
ejpam-23	162	6	so	so	SCONJ
ejpam-23	162	7	that	that	SCONJ
ejpam-23	162	8	j̃(a	j̃(a	PROPN
ejpam-23	162	9	)	)	PUNCT
ejpam-23	162	10	∩	∩	NOUN
ejpam-23	162	11	j̃(b	j̃(b	ADJ
ejpam-23	162	12	)	)	PUNCT
ejpam-23	162	13	=	=	SYM
ejpam-23	162	14	j̃(ab	j̃(ab	NOUN
ejpam-23	162	15	)	)	PUNCT
ejpam-23	162	16	.	.	PUNCT
ejpam-23	163	1	we	we	PRON
ejpam-23	163	2	can	can	AUX
ejpam-23	163	3	easily	easily	ADV
ejpam-23	163	4	see	see	VERB
ejpam-23	163	5	that	that	SCONJ
ejpam-23	163	6	the	the	DET
ejpam-23	163	7	set	set	NOUN
ejpam-23	163	8	y	y	PROPN
ejpam-23	163	9	of	of	ADP
ejpam-23	163	10	all∼-ideals	all∼-ideal	NOUN
ejpam-23	163	11	j̃(a)(a	j̃(a)(a	PROPN
ejpam-23	163	12	∈	∈	PROPN
ejpam-23	163	13	s	s	PART
ejpam-23	163	14	)	)	PUNCT
ejpam-23	163	15	forms	form	VERB
ejpam-23	163	16	a	a	DET
ejpam-23	163	17	semilattice	semilattice	NOUN
ejpam-23	163	18	under	under	ADP
ejpam-23	163	19	set	set	VERB
ejpam-23	163	20	intersection	intersection	NOUN
ejpam-23	163	21	and	and	CCONJ
ejpam-23	163	22	that	that	SCONJ
ejpam-23	163	23	the	the	DET
ejpam-23	163	24	mapping	mapping	NOUN
ejpam-23	163	25	a	a	DET
ejpam-23	163	26	7→	7→	NUM
ejpam-23	163	27	j̃(a	j̃(a	PROPN
ejpam-23	163	28	)	)	PUNCT
ejpam-23	163	29	is	be	AUX
ejpam-23	163	30	a	a	DET
ejpam-23	163	31	homomorphism	homomorphism	NOUN
ejpam-23	163	32	from	from	ADP
ejpam-23	163	33	s	s	PRON
ejpam-23	163	34	onto	onto	ADP
ejpam-23	163	35	y	y	PROPN
ejpam-23	163	36	.	.	PUNCT
ejpam-23	164	1	the	the	DET
ejpam-23	164	2	inverse	inverse	ADJ
ejpam-23	164	3	image	image	NOUN
ejpam-23	164	4	of	of	ADP
ejpam-23	164	5	j̃(a	j̃(a	PROPN
ejpam-23	164	6	)	)	PUNCT
ejpam-23	164	7	is	be	AUX
ejpam-23	164	8	just	just	ADV
ejpam-23	164	9	the	the	DET
ejpam-23	164	10	j̃	j̃	PROPN
ejpam-23	164	11	-class	-class	PROPN
ejpam-23	164	12	j̃a	j̃a	NOUN
ejpam-23	164	13	which	which	PRON
ejpam-23	164	14	is	be	AUX
ejpam-23	164	15	a	a	DET
ejpam-23	164	16	subsemigroup	subsemigroup	NOUN
ejpam-23	164	17	of	of	ADP
ejpam-23	164	18	s.	s.	PROPN
ejpam-23	164	19	hence	hence	ADV
ejpam-23	164	20	s	s	VERB
ejpam-23	164	21	is	be	AUX
ejpam-23	164	22	a	a	DET
ejpam-23	164	23	semilattice	semilattice	NOUN
ejpam-23	164	24	y	y	PROPN
ejpam-23	164	25	of	of	ADP
ejpam-23	164	26	the	the	DET
ejpam-23	164	27	semigroups	semigroup	NOUN
ejpam-23	164	28	j̃a	j̃a	PROPN
ejpam-23	164	29	.	.	PUNCT
ejpam-23	165	1	now	now	ADV
ejpam-23	165	2	let	let	VERB
ejpam-23	165	3	a	a	DET
ejpam-23	165	4	,	,	PUNCT
ejpam-23	165	5	b	b	NOUN
ejpam-23	165	6	be	be	AUX
ejpam-23	165	7	elements	element	NOUN
ejpam-23	165	8	of	of	ADP
ejpam-23	165	9	j̃	j̃	PROPN
ejpam-23	165	10	-class	-class	PROPN
ejpam-23	165	11	j̃	j̃	PROPN
ejpam-23	165	12	and	and	CCONJ
ejpam-23	165	13	suppose	suppose	VERB
ejpam-23	165	14	that	that	SCONJ
ejpam-23	165	15	(	(	PUNCT
ejpam-23	165	16	a	a	PRON
ejpam-23	165	17	,	,	PUNCT
ejpam-23	165	18	b	b	NOUN
ejpam-23	165	19	)	)	PUNCT
ejpam-23	165	20	∈	∈	PROPN
ejpam-23	165	21	l̃(j̃	l̃(j̃	NOUN
ejpam-23	165	22	)	)	PUNCT
ejpam-23	165	23	.	.	PUNCT
ejpam-23	166	1	then	then	ADV
ejpam-23	166	2	,	,	PUNCT
ejpam-23	166	3	a0	a0	PROPN
ejpam-23	166	4	,	,	PUNCT
ejpam-23	166	5	b0	b0	NOUN
ejpam-23	166	6	∈	∈	PRON
ejpam-23	166	7	j̃	j̃	PROPN
ejpam-23	167	1	so	so	SCONJ
ejpam-23	167	2	that	that	SCONJ
ejpam-23	167	3	(	(	PUNCT
ejpam-23	167	4	a0	a0	NOUN
ejpam-23	167	5	,	,	PUNCT
ejpam-23	167	6	b0	b0	NOUN
ejpam-23	167	7	)	)	PUNCT
ejpam-23	167	8	∈	∈	PROPN
ejpam-23	167	9	l̃(j̃	l̃(j̃	NOUN
ejpam-23	167	10	)	)	PUNCT
ejpam-23	167	11	,	,	PUNCT
ejpam-23	167	12	that	that	ADV
ejpam-23	167	13	is	is	ADV
ejpam-23	167	14	,	,	PUNCT
ejpam-23	167	15	a0b0	a0b0	PROPN
ejpam-23	167	16	=	=	SYM
ejpam-23	167	17	a0	a0	PROPN
ejpam-23	167	18	,	,	PUNCT
ejpam-23	167	19	b0a0	b0a0	PROPN
ejpam-23	167	20	=	=	SYM
ejpam-23	167	21	b0	b0	PROPN
ejpam-23	167	22	and	and	CCONJ
ejpam-23	167	23	(	(	PUNCT
ejpam-23	167	24	a0	a0	NOUN
ejpam-23	167	25	,	,	PUNCT
ejpam-23	167	26	b0	b0	NOUN
ejpam-23	167	27	)	)	PUNCT
ejpam-23	167	28	∈	∈	PROPN
ejpam-23	167	29	l̃(s	l̃(s	PROPN
ejpam-23	167	30	)	)	PUNCT
ejpam-23	167	31	.	.	PUNCT
ejpam-23	168	1	it	it	PRON
ejpam-23	168	2	follows	follow	VERB
ejpam-23	168	3	that	that	SCONJ
ejpam-23	168	4	(	(	PUNCT
ejpam-23	168	5	a	a	PRON
ejpam-23	168	6	,	,	PUNCT
ejpam-23	168	7	b	b	NOUN
ejpam-23	168	8	)	)	PUNCT
ejpam-23	168	9	∈	∈	PROPN
ejpam-23	168	10	l̃(s	l̃(s	PROPN
ejpam-23	168	11	)	)	PUNCT
ejpam-23	168	12	and	and	CCONJ
ejpam-23	168	13	consequently	consequently	ADV
ejpam-23	168	14	,	,	PUNCT
ejpam-23	168	15	by	by	ADP
ejpam-23	168	16	l̃a(s	l̃a(	NOUN
ejpam-23	168	17	)	)	PUNCT
ejpam-23	168	18	⊆	⊆	NUM
ejpam-23	168	19	j̃	j̃	PROPN
ejpam-23	168	20	,	,	PUNCT
ejpam-23	168	21	we	we	PRON
ejpam-23	168	22	have	have	VERB
ejpam-23	168	23	l̃a(s	l̃a(	NOUN
ejpam-23	168	24	)	)	PUNCT
ejpam-23	168	25	=	=	PUNCT
ejpam-23	169	1	l̃a(j̃	l̃a(j̃	PROPN
ejpam-23	169	2	)	)	PUNCT
ejpam-23	169	3	.	.	PUNCT
ejpam-23	170	1	by	by	ADP
ejpam-23	170	2	using	use	VERB
ejpam-23	170	3	a	a	DET
ejpam-23	170	4	similar	similar	ADJ
ejpam-23	170	5	argument	argument	NOUN
ejpam-23	170	6	,	,	PUNCT
ejpam-23	170	7	we	we	PRON
ejpam-23	170	8	can	can	AUX
ejpam-23	170	9	show	show	VERB
ejpam-23	170	10	that	that	SCONJ
ejpam-23	170	11	r̃a(s	r̃a(	NOUN
ejpam-23	170	12	)	)	PUNCT
ejpam-23	170	13	=	=	SYM
ejpam-23	170	14	r̃a(j̃	r̃a(j̃	PROPN
ejpam-23	170	15	)	)	PUNCT
ejpam-23	170	16	.	.	PUNCT
ejpam-23	171	1	from	from	ADP
ejpam-23	171	2	the	the	DET
ejpam-23	171	3	above	above	ADJ
ejpam-23	171	4	discussion	discussion	NOUN
ejpam-23	171	5	,	,	PUNCT
ejpam-23	171	6	we	we	PRON
ejpam-23	171	7	can	can	AUX
ejpam-23	171	8	deduce	deduce	VERB
ejpam-23	171	9	that	that	DET
ejpam-23	171	10	h̃a(j̃	h̃a(j̃	NOUN
ejpam-23	171	11	)	)	PUNCT
ejpam-23	171	12	=	=	SYM
ejpam-23	172	1	h̃a(s	h̃a(s	PROPN
ejpam-23	172	2	)	)	PUNCT
ejpam-23	172	3	and	and	CCONJ
ejpam-23	172	4	so	so	ADV
ejpam-23	172	5	j̃	j̃	PROPN
ejpam-23	172	6	is	be	AUX
ejpam-23	172	7	indeed	indeed	ADV
ejpam-23	172	8	an	an	DET
ejpam-23	172	9	h̃-abundant	h̃-abundant	ADJ
ejpam-23	172	10	semigroup	semigroup	NOUN
ejpam-23	172	11	.	.	PUNCT
ejpam-23	173	1	furthermore	furthermore	ADV
ejpam-23	173	2	,	,	PUNCT
ejpam-23	173	3	if	if	SCONJ
ejpam-23	173	4	a	a	DET
ejpam-23	173	5	,	,	PUNCT
ejpam-23	173	6	b	b	X
ejpam-23	173	7	∈	∈	PROPN
ejpam-23	173	8	j̃	j̃	PROPN
ejpam-23	173	9	,	,	PUNCT
ejpam-23	173	10	then	then	ADV
ejpam-23	173	11	by	by	ADP
ejpam-23	173	12	lemma	lemma	PROPN
ejpam-23	173	13	2.8	2.8	NUM
ejpam-23	173	14	(	(	PUNCT
ejpam-23	173	15	i	i	NOUN
ejpam-23	173	16	)	)	PUNCT
ejpam-23	173	17	,	,	PUNCT
ejpam-23	173	18	(	(	PUNCT
ejpam-23	173	19	a	a	PRON
ejpam-23	173	20	,	,	PUNCT
ejpam-23	173	21	b	b	NOUN
ejpam-23	173	22	)	)	PUNCT
ejpam-23	173	23	∈	∈	PROPN
ejpam-23	173	24	d̃(s	d̃(s	PROPN
ejpam-23	173	25	)	)	PUNCT
ejpam-23	173	26	and	and	CCONJ
ejpam-23	173	27	hence	hence	ADV
ejpam-23	173	28	,	,	PUNCT
ejpam-23	173	29	by	by	ADP
ejpam-23	173	30	lemma	lemma	PROPN
ejpam-23	173	31	2.6	2.6	NUM
ejpam-23	173	32	(	(	PUNCT
ejpam-23	173	33	iii	iii	NOUN
ejpam-23	173	34	)	)	PUNCT
ejpam-23	173	35	,	,	PUNCT
ejpam-23	173	36	there	there	PRON
ejpam-23	173	37	exists	exist	VERB
ejpam-23	173	38	an	an	DET
ejpam-23	173	39	element	element	NOUN
ejpam-23	173	40	c	c	PROPN
ejpam-23	173	41	in	in	ADP
ejpam-23	173	42	l̃a(s	l̃a(s	PROPN
ejpam-23	173	43	)	)	PUNCT
ejpam-23	173	44	∩	∩	ADJ
ejpam-23	173	45	r̃b(s	r̃b(	NOUN
ejpam-23	173	46	)	)	PUNCT
ejpam-23	174	1	=	=	SYM
ejpam-23	174	2	l̃a(j̃	l̃a(j̃	PROPN
ejpam-23	174	3	)	)	PUNCT
ejpam-23	174	4	∩	∩	NOUN
ejpam-23	174	5	r̃b(j̃	r̃b(j̃	NOUN
ejpam-23	174	6	)	)	PUNCT
ejpam-23	174	7	.	.	PUNCT
ejpam-23	175	1	thus	thus	ADV
ejpam-23	175	2	a	a	DET
ejpam-23	175	3	,	,	PUNCT
ejpam-23	175	4	b	b	NOUN
ejpam-23	175	5	are	be	AUX
ejpam-23	175	6	d̃-related	d̃-relate	VERB
ejpam-23	175	7	in	in	ADP
ejpam-23	175	8	j̃	j̃	PROPN
ejpam-23	175	9	and	and	CCONJ
ejpam-23	175	10	so	so	ADV
ejpam-23	175	11	j̃	j̃	PROPN
ejpam-23	175	12	is	be	AUX
ejpam-23	175	13	j̃	j̃	PROPN
ejpam-23	175	14	-simple	-simple	NUM
ejpam-23	175	15	.	.	PUNCT
ejpam-23	176	1	for	for	ADP
ejpam-23	176	2	the	the	DET
ejpam-23	176	3	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	176	4	,	,	PUNCT
ejpam-23	176	5	we	we	PRON
ejpam-23	176	6	have	have	VERB
ejpam-23	176	7	the	the	DET
ejpam-23	176	8	following	follow	VERB
ejpam-23	176	9	theorem	theorem	NOUN
ejpam-23	176	10	.	.	PUNCT
ejpam-23	176	11	theorem	theorem	VERB
ejpam-23	176	12	2.10	2.10	NUM
ejpam-23	176	13	let	let	VERB
ejpam-23	176	14	s	s	PRON
ejpam-23	176	15	be	be	AUX
ejpam-23	176	16	an	an	DET
ejpam-23	176	17	h̃	h̃	PROPN
ejpam-23	176	18	-cryptogroup	-cryptogroup	NOUN
ejpam-23	176	19	which	which	PRON
ejpam-23	176	20	is	be	AUX
ejpam-23	176	21	expressed	express	VERB
ejpam-23	176	22	by	by	ADP
ejpam-23	176	23	the	the	DET
ejpam-23	176	24	semilattice	semilattice	NOUN
ejpam-23	176	25	of	of	ADP
ejpam-23	176	26	semigroups	semigroups	X
ejpam-23	176	27	s	s	PART
ejpam-23	176	28	=	=	PUNCT
ejpam-23	176	29	(	(	PUNCT
ejpam-23	176	30	y	y	PROPN
ejpam-23	176	31	;	;	PUNCT
ejpam-23	176	32	sα	sα	X
ejpam-23	176	33	)	)	PUNCT
ejpam-23	176	34	.	.	PUNCT
ejpam-23	177	1	then	then	ADV
ejpam-23	177	2	the	the	DET
ejpam-23	177	3	following	following	ADJ
ejpam-23	177	4	statements	statement	NOUN
ejpam-23	177	5	hold	hold	VERB
ejpam-23	177	6	:	:	PUNCT
ejpam-23	177	7	(	(	PUNCT
ejpam-23	177	8	i	i	NOUN
ejpam-23	177	9	)	)	PUNCT
ejpam-23	177	10	for	for	ADP
ejpam-23	177	11	α	α	NOUN
ejpam-23	177	12	,	,	PUNCT
ejpam-23	177	13	and	and	CCONJ
ejpam-23	177	14	β	β	X
ejpam-23	177	15	in	in	ADP
ejpam-23	177	16	the	the	DET
ejpam-23	177	17	semilattice	semilattice	NOUN
ejpam-23	177	18	y	y	PROPN
ejpam-23	177	19	with	with	ADP
ejpam-23	177	20	α	α	PROPN
ejpam-23	177	21	>	>	X
ejpam-23	177	22	β	β	X
ejpam-23	177	23	,	,	PUNCT
ejpam-23	177	24	if	if	SCONJ
ejpam-23	177	25	a	a	DET
ejpam-23	177	26	∈	∈	NOUN
ejpam-23	177	27	sα	sα	ADV
ejpam-23	177	28	then	then	ADV
ejpam-23	177	29	there	there	PRON
ejpam-23	177	30	exists	exist	VERB
ejpam-23	177	31	b	b	PROPN
ejpam-23	177	32	∈	∈	PROPN
ejpam-23	177	33	sβ	sβ	NOUN
ejpam-23	177	34	with	with	ADP
ejpam-23	177	35	a	a	DET
ejpam-23	177	36	>	>	X
ejpam-23	177	37	b	b	NOUN
ejpam-23	177	38	;	;	PUNCT
ejpam-23	177	39	(	(	PUNCT
ejpam-23	177	40	ii	ii	NOUN
ejpam-23	177	41	)	)	PUNCT
ejpam-23	177	42	for	for	ADP
ejpam-23	177	43	a	a	DET
ejpam-23	177	44	,	,	PUNCT
ejpam-23	177	45	b	b	NOUN
ejpam-23	177	46	,	,	PUNCT
ejpam-23	177	47	c	c	PROPN
ejpam-23	177	48	∈	∈	PROPN
ejpam-23	177	49	s	s	PART
ejpam-23	177	50	with	with	ADP
ejpam-23	177	51	bh̃c	bh̃c	PROPN
ejpam-23	177	52	,	,	PUNCT
ejpam-23	177	53	if	if	SCONJ
ejpam-23	177	54	a	a	DET
ejpam-23	177	55	>	>	X
ejpam-23	177	56	b	b	PROPN
ejpam-23	177	57	,	,	PUNCT
ejpam-23	177	58	a	a	PRON
ejpam-23	177	59	>	>	X
ejpam-23	177	60	c	c	X
ejpam-23	178	1	then	then	ADV
ejpam-23	178	2	b	b	X
ejpam-23	178	3	=	=	SYM
ejpam-23	178	4	c	c	X
ejpam-23	178	5	;	;	PUNCT
ejpam-23	178	6	(	(	PUNCT
ejpam-23	178	7	iii	iii	NOUN
ejpam-23	178	8	)	)	PUNCT
ejpam-23	178	9	for	for	ADP
ejpam-23	178	10	a	a	DET
ejpam-23	178	11	∈	∈	PROPN
ejpam-23	178	12	e(s	e(s	PROPN
ejpam-23	178	13	)	)	PUNCT
ejpam-23	178	14	and	and	CCONJ
ejpam-23	178	15	b	b	X
ejpam-23	178	16	∈	∈	NOUN
ejpam-23	178	17	s	s	VERB
ejpam-23	178	18	,	,	PUNCT
ejpam-23	178	19	if	if	SCONJ
ejpam-23	178	20	a	a	PRON
ejpam-23	178	21	>	>	X
ejpam-23	178	22	b	b	NOUN
ejpam-23	178	23	then	then	ADV
ejpam-23	178	24	b	b	PROPN
ejpam-23	178	25	∈	∈	PROPN
ejpam-23	178	26	e(s	e(s	PROPN
ejpam-23	178	27	)	)	PUNCT
ejpam-23	178	28	.	.	PUNCT
ejpam-23	179	1	proof	proof	NOUN
ejpam-23	179	2	.	.	PUNCT
ejpam-23	180	1	(	(	PUNCT
ejpam-23	180	2	i	i	NOUN
ejpam-23	180	3	)	)	PUNCT
ejpam-23	180	4	let	let	VERB
ejpam-23	180	5	c	c	PROPN
ejpam-23	180	6	∈	∈	PROPN
ejpam-23	180	7	sβ	sβ	VERB
ejpam-23	180	8	.	.	PUNCT
ejpam-23	181	1	then	then	ADV
ejpam-23	181	2	,	,	PUNCT
ejpam-23	181	3	by	by	ADP
ejpam-23	181	4	lemma	lemma	PROPN
ejpam-23	181	5	2.6	2.6	NUM
ejpam-23	181	6	(	(	PUNCT
ejpam-23	181	7	i	i	PROPN
ejpam-23	181	8	)	)	PUNCT
ejpam-23	181	9	,	,	PUNCT
ejpam-23	181	10	we	we	PRON
ejpam-23	181	11	see	see	VERB
ejpam-23	181	12	that	that	SCONJ
ejpam-23	181	13	a(aca)0	a(aca)0	PRON
ejpam-23	181	14	,	,	PUNCT
ejpam-23	181	15	(	(	PUNCT
ejpam-23	181	16	aca)0a	aca)0a	ADJ
ejpam-23	181	17	and	and	CCONJ
ejpam-23	181	18	(	(	PUNCT
ejpam-23	181	19	aca)0	aca)0	NOUN
ejpam-23	181	20	are	be	AUX
ejpam-23	181	21	all	all	PRON
ejpam-23	181	22	in	in	ADP
ejpam-23	181	23	the	the	DET
ejpam-23	181	24	same	same	ADJ
ejpam-23	181	25	h̃-class	h̃-class	NOUN
ejpam-23	181	26	of	of	ADP
ejpam-23	181	27	the	the	DET
ejpam-23	181	28	semigroup	semigroup	PROPN
ejpam-23	181	29	s	s	PROPN
ejpam-23	181	30	and	and	CCONJ
ejpam-23	181	31	hence	hence	ADV
ejpam-23	181	32	,	,	PUNCT
ejpam-23	181	33	a(aca)0	a(aca)0	PROPN
ejpam-23	181	34	=	=	SYM
ejpam-23	181	35	(	(	PUNCT
ejpam-23	181	36	aca)0a(aca)0	aca)0a(aca)0	PROPN
ejpam-23	181	37	=	=	SYM
ejpam-23	181	38	(	(	PUNCT
ejpam-23	181	39	aca)0a	aca)0a	NOUN
ejpam-23	181	40	.	.	PUNCT
ejpam-23	182	1	write	write	PROPN
ejpam-23	182	2	b	b	PROPN
ejpam-23	182	3	=	=	SYM
ejpam-23	182	4	a(aca)0	a(aca)0	PROPN
ejpam-23	182	5	.	.	PUNCT
ejpam-23	183	1	then	then	ADV
ejpam-23	183	2	b	b	X
ejpam-23	183	3	∈	∈	ADJ
ejpam-23	183	4	sβ	sβ	X
ejpam-23	183	5	and	and	CCONJ
ejpam-23	183	6	a	a	DET
ejpam-23	183	7	>	>	X
ejpam-23	183	8	b.	b.	PROPN
ejpam-23	183	9	(	(	PUNCT
ejpam-23	183	10	ii	ii	PROPN
ejpam-23	183	11	)	)	PUNCT
ejpam-23	183	12	by	by	ADP
ejpam-23	183	13	the	the	DET
ejpam-23	183	14	definition	definition	NOUN
ejpam-23	183	15	of	of	ADP
ejpam-23	183	16	“	"	PUNCT
ejpam-23	183	17	>	>	PUNCT
ejpam-23	183	18	”	"	PUNCT
ejpam-23	183	19	,	,	PUNCT
ejpam-23	183	20	there	there	PRON
ejpam-23	183	21	exist	exist	VERB
ejpam-23	183	22	e	e	NOUN
ejpam-23	183	23	,	,	PUNCT
ejpam-23	183	24	f	f	X
ejpam-23	183	25	,	,	PUNCT
ejpam-23	183	26	g	g	PROPN
ejpam-23	183	27	,	,	PUNCT
ejpam-23	183	28	h	h	NOUN
ejpam-23	183	29	∈	∈	PROPN
ejpam-23	183	30	e(s	e(s	PROPN
ejpam-23	183	31	)	)	PUNCT
ejpam-23	184	1	such	such	ADJ
ejpam-23	184	2	that	that	DET
ejpam-23	184	3	b	b	NOUN
ejpam-23	184	4	=	=	SYM
ejpam-23	184	5	ea	ea	PROPN
ejpam-23	185	1	=	=	VERB
ejpam-23	186	1	af	af	PROPN
ejpam-23	186	2	,	,	PUNCT
ejpam-23	186	3	c	c	PROPN
ejpam-23	186	4	=	=	SYM
ejpam-23	186	5	ga	ga	PROPN
ejpam-23	186	6	=	=	NOUN
ejpam-23	186	7	ah	ah	INTJ
ejpam-23	186	8	.	.	PUNCT
ejpam-23	187	1	from	from	ADP
ejpam-23	187	2	eb	eb	PROPN
ejpam-23	187	3	=	=	SYM
ejpam-23	187	4	b	b	PROPN
ejpam-23	187	5	and	and	CCONJ
ejpam-23	187	6	bh̃b0	bh̃b0	PROPN
ejpam-23	187	7	,	,	PUNCT
ejpam-23	187	8	we	we	PRON
ejpam-23	187	9	have	have	VERB
ejpam-23	187	10	eb0	eb0	NOUN
ejpam-23	187	11	=	=	SYM
ejpam-23	187	12	b0	b0	NOUN
ejpam-23	187	13	.	.	PUNCT
ejpam-23	188	1	similarly	similarly	ADV
ejpam-23	188	2	,	,	PUNCT
ejpam-23	188	3	c0h	c0h	X
ejpam-23	188	4	=	=	SYM
ejpam-23	188	5	c0	c0	NOUN
ejpam-23	188	6	.	.	PUNCT
ejpam-23	189	1	thus	thus	ADV
ejpam-23	189	2	ec	ec	PROPN
ejpam-23	189	3	=	=	PUNCT
ejpam-23	189	4	ec0c	ec0c	PROPN
ejpam-23	190	1	=	=	SYM
ejpam-23	190	2	eb0c	eb0c	NOUN
ejpam-23	190	3	=	=	SYM
ejpam-23	190	4	b0c	b0c	PROPN
ejpam-23	190	5	=	=	PROPN
ejpam-23	190	6	c.	c.	NOUN
ejpam-23	190	7	by	by	ADP
ejpam-23	190	8	using	use	VERB
ejpam-23	190	9	similar	similar	ADJ
ejpam-23	190	10	arguments	argument	NOUN
ejpam-23	190	11	,	,	PUNCT
ejpam-23	190	12	we	we	PRON
ejpam-23	190	13	have	have	VERB
ejpam-23	190	14	bh	bh	NOUN
ejpam-23	190	15	=	=	PROPN
ejpam-23	190	16	b	b	PROPN
ejpam-23	190	17	and	and	CCONJ
ejpam-23	190	18	so	so	ADV
ejpam-23	190	19	,	,	PUNCT
ejpam-23	190	20	b	b	X
ejpam-23	190	21	=	=	SYM
ejpam-23	190	22	bh	bh	NOUN
ejpam-23	190	23	=	=	PROPN
ejpam-23	190	24	eah	eah	PROPN
ejpam-23	190	25	=	=	PROPN
ejpam-23	190	26	ec	ec	PROPN
ejpam-23	190	27	=	=	PUNCT
ejpam-23	190	28	c	c	X
ejpam-23	190	29	,	,	PUNCT
ejpam-23	190	30	as	as	SCONJ
ejpam-23	190	31	required	require	VERB
ejpam-23	190	32	.	.	PUNCT
ejpam-23	191	1	(	(	PUNCT
ejpam-23	191	2	iii	iii	X
ejpam-23	191	3	)	)	PUNCT
ejpam-23	191	4	we	we	PRON
ejpam-23	191	5	have	have	VERB
ejpam-23	191	6	b	b	NOUN
ejpam-23	191	7	=	=	SYM
ejpam-23	191	8	ea	ea	PROPN
ejpam-23	191	9	=	=	NOUN
ejpam-23	191	10	af	af	VERB
ejpam-23	191	11	for	for	ADP
ejpam-23	191	12	some	some	DET
ejpam-23	191	13	e	e	NOUN
ejpam-23	191	14	,	,	PUNCT
ejpam-23	191	15	f	f	PROPN
ejpam-23	191	16	∈	∈	PROPN
ejpam-23	191	17	e(s	e(s	PROPN
ejpam-23	191	18	)	)	PUNCT
ejpam-23	191	19	,	,	PUNCT
ejpam-23	191	20	and	and	CCONJ
ejpam-23	191	21	whence	whence	NOUN
ejpam-23	191	22	b2	b2	NOUN
ejpam-23	191	23	=	=	SYM
ejpam-23	191	24	(	(	PUNCT
ejpam-23	191	25	ea)(af	ea)(af	X
ejpam-23	191	26	)	)	PUNCT
ejpam-23	192	1	=	=	SYM
ejpam-23	192	2	ea2f	ea2f	PROPN
ejpam-23	192	3	=	=	SYM
ejpam-23	192	4	b.	b.	PROPN
ejpam-23	193	1	the	the	DET
ejpam-23	193	2	following	follow	VERB
ejpam-23	193	3	fact	fact	NOUN
ejpam-23	193	4	can	can	AUX
ejpam-23	193	5	be	be	AUX
ejpam-23	193	6	easily	easily	ADV
ejpam-23	193	7	observed	observe	VERB
ejpam-23	193	8	:	:	PUNCT
ejpam-23	193	9	fact	fact	NOUN
ejpam-23	193	10	2.11	2.11	NUM
ejpam-23	193	11	let	let	VERB
ejpam-23	193	12	ϕ	ϕ	NOUN
ejpam-23	193	13	be	be	AUX
ejpam-23	193	14	a	a	DET
ejpam-23	193	15	homomorphism	homomorphism	NOUN
ejpam-23	193	16	which	which	PRON
ejpam-23	193	17	maps	map	VERB
ejpam-23	193	18	an	an	DET
ejpam-23	193	19	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	193	20	s	s	VERB
ejpam-23	193	21	into	into	ADP
ejpam-23	193	22	another	another	DET
ejpam-23	193	23	h̃	h̃	PROPN
ejpam-23	193	24	-cryptogroup	-cryptogroup	PROPN
ejpam-23	193	25	t	t	PROPN
ejpam-23	193	26	.	.	PUNCT
ejpam-23	194	1	then	then	ADV
ejpam-23	194	2	(	(	PUNCT
ejpam-23	194	3	aϕ)0	aϕ)0	NOUN
ejpam-23	194	4	=	=	PUNCT
ejpam-23	194	5	a0ϕ.	a0ϕ.	NOUN
ejpam-23	194	6	3	3	NUM
ejpam-23	194	7	.	.	PUNCT
ejpam-23	195	1	properties	property	NOUN
ejpam-23	195	2	of	of	ADP
ejpam-23	195	3	regular	regular	ADJ
ejpam-23	195	4	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	195	5	lemma	lemma	PROPN
ejpam-23	195	6	3.1	3.1	NUM
ejpam-23	195	7	let	let	VERB
ejpam-23	195	8	s	s	PRON
ejpam-23	195	9	be	be	AUX
ejpam-23	195	10	a	a	DET
ejpam-23	195	11	regular	regular	ADJ
ejpam-23	195	12	h̃	h̃	PROPN
ejpam-23	195	13	-cryptogroup(that	-cryptogroup(that	PUNCT
ejpam-23	195	14	is	be	AUX
ejpam-23	195	15	,	,	PUNCT
ejpam-23	195	16	h̃	h̃	PROPN
ejpam-23	195	17	is	be	AUX
ejpam-23	195	18	a	a	DET
ejpam-23	195	19	congruence	congruence	NOUN
ejpam-23	195	20	on	on	ADP
ejpam-23	195	21	the	the	DET
ejpam-23	195	22	h̃-abundant	h̃-abundant	ADJ
ejpam-23	195	23	semigroup	semigroup	NOUN
ejpam-23	195	24	s	s	VERB
ejpam-23	195	25	such	such	ADJ
ejpam-23	195	26	that	that	SCONJ
ejpam-23	195	27	s	s	PROPN
ejpam-23	195	28	/	/	SYM
ejpam-23	195	29	h̃	h̃	PROPN
ejpam-23	195	30	is	be	AUX
ejpam-23	195	31	a	a	DET
ejpam-23	195	32	regular	regular	ADJ
ejpam-23	195	33	band	band	NOUN
ejpam-23	195	34	)	)	PUNCT
ejpam-23	195	35	.	.	PUNCT
ejpam-23	196	1	for	for	ADP
ejpam-23	196	2	every	every	DET
ejpam-23	196	3	a	a	DET
ejpam-23	196	4	∈	∈	PROPN
ejpam-23	196	5	s	s	NOUN
ejpam-23	196	6	,	,	PUNCT
ejpam-23	196	7	we	we	PRON
ejpam-23	196	8	define	define	VERB
ejpam-23	196	9	a	a	DET
ejpam-23	196	10	relation	relation	NOUN
ejpam-23	196	11	ρa	ρa	PRON
ejpam-23	196	12	on	on	ADP
ejpam-23	196	13	s	s	PRON
ejpam-23	196	14	by	by	X
ejpam-23	196	15	(	(	PUNCT
ejpam-23	196	16	b1	b1	NOUN
ejpam-23	196	17	,	,	PUNCT
ejpam-23	196	18	b2	b2	NOUN
ejpam-23	196	19	)	)	PUNCT
ejpam-23	196	20	∈	∈	NOUN
ejpam-23	197	1	ρa	ρa	PRON
ejpam-23	198	1	if	if	SCONJ
ejpam-23	198	2	and	and	CCONJ
ejpam-23	198	3	only	only	ADV
ejpam-23	198	4	if	if	SCONJ
ejpam-23	198	5	(	(	PUNCT
ejpam-23	198	6	ab1a)0	ab1a)0	NOUN
ejpam-23	198	7	=	=	SYM
ejpam-23	198	8	(	(	PUNCT
ejpam-23	198	9	ab2a)0	ab2a)0	PROPN
ejpam-23	198	10	,	,	PUNCT
ejpam-23	198	11	(	(	PUNCT
ejpam-23	198	12	b1	b1	NOUN
ejpam-23	198	13	,	,	PUNCT
ejpam-23	198	14	b2	b2	NOUN
ejpam-23	198	15	∈	∈	PROPN
ejpam-23	198	16	s	s	PART
ejpam-23	198	17	)	)	PUNCT
ejpam-23	198	18	.	.	PUNCT
ejpam-23	199	1	then	then	ADV
ejpam-23	199	2	the	the	DET
ejpam-23	199	3	following	follow	VERB
ejpam-23	199	4	properties	property	NOUN
ejpam-23	199	5	hold	hold	VERB
ejpam-23	199	6	on	on	ADP
ejpam-23	199	7	s	s	PROPN
ejpam-23	199	8	:	:	PUNCT
ejpam-23	199	9	x.	x.	PROPN
ejpam-23	199	10	kong	kong	PROPN
ejpam-23	199	11	,	,	PUNCT
ejpam-23	199	12	y.ding	y.de	VERB
ejpam-23	199	13	,	,	PUNCT
ejpam-23	199	14	k.p.shum	k.p.shum	ADJ
ejpam-23	199	15	/	/	SYM
ejpam-23	199	16	eur	eur	PROPN
ejpam-23	199	17	.	.	PUNCT
ejpam-23	200	1	j.	j.	PROPN
ejpam-23	200	2	pure	pure	PROPN
ejpam-23	200	3	appl	appl	PROPN
ejpam-23	200	4	.	.	PROPN
ejpam-23	200	5	math	math	PROPN
ejpam-23	200	6	,	,	PUNCT
ejpam-23	200	7	1	1	NUM
ejpam-23	200	8	(	(	PUNCT
ejpam-23	200	9	2008	2008	NUM
ejpam-23	200	10	)	)	PUNCT
ejpam-23	200	11	,	,	PUNCT
ejpam-23	200	12	(	(	PUNCT
ejpam-23	200	13	46	46	NUM
ejpam-23	200	14	-	-	SYM
ejpam-23	200	15	59	59	NUM
ejpam-23	200	16	)	)	PUNCT
ejpam-23	200	17	53	53	NUM
ejpam-23	200	18	(	(	PUNCT
ejpam-23	200	19	i	i	NOUN
ejpam-23	200	20	)	)	PUNCT
ejpam-23	200	21	ρa	ρa	PRON
ejpam-23	200	22	is	be	AUX
ejpam-23	200	23	a	a	DET
ejpam-23	200	24	band	band	NOUN
ejpam-23	200	25	congruence	congruence	NOUN
ejpam-23	200	26	on	on	ADP
ejpam-23	200	27	s	s	PROPN
ejpam-23	200	28	;	;	PUNCT
ejpam-23	200	29	(	(	PUNCT
ejpam-23	200	30	ii	ii	NOUN
ejpam-23	200	31	)	)	PUNCT
ejpam-23	200	32	(	(	PUNCT
ejpam-23	200	33	∀a	∀a	NOUN
ejpam-23	200	34	,	,	PUNCT
ejpam-23	200	35	a1	a1	PROPN
ejpam-23	200	36	∈	∈	PROPN
ejpam-23	200	37	sα	sα	NOUN
ejpam-23	200	38	)	)	PUNCT
ejpam-23	200	39	,	,	PUNCT
ejpam-23	200	40	ρa	ρa	ADP
ejpam-23	201	1	=	=	PUNCT
ejpam-23	201	2	ρa1	ρa1	NUM
ejpam-23	201	3	,	,	PUNCT
ejpam-23	201	4	that	that	ADV
ejpam-23	201	5	is	is	ADV
ejpam-23	201	6	,	,	PUNCT
ejpam-23	201	7	ρa	ρa	PRON
ejpam-23	201	8	depends	depend	VERB
ejpam-23	201	9	only	only	ADV
ejpam-23	201	10	on	on	ADP
ejpam-23	201	11	the	the	DET
ejpam-23	201	12	component	component	NOUN
ejpam-23	201	13	sα	sα	ADV
ejpam-23	201	14	containing	contain	VERB
ejpam-23	201	15	the	the	DET
ejpam-23	201	16	element	element	NOUN
ejpam-23	201	17	a	a	PRON
ejpam-23	201	18	rather	rather	ADV
ejpam-23	201	19	than	than	ADP
ejpam-23	201	20	on	on	ADP
ejpam-23	201	21	the	the	DET
ejpam-23	201	22	element	element	NOUN
ejpam-23	201	23	itself	itself	PRON
ejpam-23	201	24	,	,	PUNCT
ejpam-23	201	25	hence	hence	ADV
ejpam-23	201	26	we	we	PRON
ejpam-23	201	27	can	can	AUX
ejpam-23	201	28	write	write	VERB
ejpam-23	201	29	ρα	ρα	PROPN
ejpam-23	201	30	=	=	SYM
ejpam-23	201	31	ρa	ρa	PROPN
ejpam-23	201	32	,	,	PUNCT
ejpam-23	201	33	for	for	ADP
ejpam-23	201	34	all	all	DET
ejpam-23	201	35	a	a	DET
ejpam-23	201	36	∈	∈	NOUN
ejpam-23	201	37	sα	sα	NOUN
ejpam-23	201	38	.	.	PUNCT
ejpam-23	202	1	(	(	PUNCT
ejpam-23	202	2	iii	iii	NOUN
ejpam-23	202	3	)	)	PUNCT
ejpam-23	202	4	(	(	PUNCT
ejpam-23	202	5	∀α	∀α	NOUN
ejpam-23	202	6	,	,	PUNCT
ejpam-23	202	7	β	β	X
ejpam-23	202	8	∈	∈	PROPN
ejpam-23	202	9	y	y	PROPN
ejpam-23	202	10	with	with	ADP
ejpam-23	202	11	α	α	PROPN
ejpam-23	202	12	>	>	X
ejpam-23	202	13	β	β	PROPN
ejpam-23	202	14	)	)	PUNCT
ejpam-23	202	15	,	,	PUNCT
ejpam-23	202	16	ρα	ρα	PRON
ejpam-23	202	17	⊆	⊆	NUM
ejpam-23	202	18	ρβ	ρβ	PROPN
ejpam-23	202	19	and	and	CCONJ
ejpam-23	202	20	ρβ|sα	ρβ|sα	X
ejpam-23	202	21	=	=	X
ejpam-23	203	1	ωsα	ωsα	ADV
ejpam-23	203	2	,	,	PUNCT
ejpam-23	203	3	where	where	SCONJ
ejpam-23	203	4	ωsα	ωsα	ADV
ejpam-23	203	5	is	be	AUX
ejpam-23	203	6	the	the	DET
ejpam-23	203	7	universal	universal	ADJ
ejpam-23	203	8	relation	relation	NOUN
ejpam-23	203	9	on	on	ADP
ejpam-23	203	10	sα	sα	PROPN
ejpam-23	203	11	.	.	PROPN
ejpam-23	203	12	proof	proof	NOUN
ejpam-23	203	13	.	.	PUNCT
ejpam-23	204	1	(	(	PUNCT
ejpam-23	204	2	i	i	NOUN
ejpam-23	204	3	)	)	PUNCT
ejpam-23	204	4	it	it	PRON
ejpam-23	204	5	is	be	AUX
ejpam-23	204	6	easy	easy	ADJ
ejpam-23	204	7	to	to	PART
ejpam-23	204	8	see	see	VERB
ejpam-23	204	9	that	that	PRON
ejpam-23	204	10	ρa	ρa	PRON
ejpam-23	204	11	is	be	AUX
ejpam-23	204	12	an	an	DET
ejpam-23	204	13	equivalent	equivalent	ADJ
ejpam-23	204	14	relation	relation	NOUN
ejpam-23	204	15	on	on	ADP
ejpam-23	204	16	s	s	NOUN
ejpam-23	204	17	,	,	PUNCT
ejpam-23	204	18	for	for	ADP
ejpam-23	204	19	all	all	DET
ejpam-23	204	20	a	a	DET
ejpam-23	204	21	∈	∈	NOUN
ejpam-23	204	22	s.	s.	NOUN
ejpam-23	204	23	we	we	PRON
ejpam-23	204	24	now	now	ADV
ejpam-23	204	25	prove	prove	VERB
ejpam-23	204	26	that	that	SCONJ
ejpam-23	204	27	ρa	ρa	PRON
ejpam-23	204	28	is	be	AUX
ejpam-23	204	29	left	leave	VERB
ejpam-23	204	30	compatible	compatible	ADJ
ejpam-23	204	31	with	with	ADP
ejpam-23	204	32	the	the	DET
ejpam-23	204	33	semigroup	semigroup	ADJ
ejpam-23	204	34	multiplication	multiplication	NOUN
ejpam-23	204	35	.	.	PUNCT
ejpam-23	205	1	for	for	ADP
ejpam-23	205	2	this	this	DET
ejpam-23	205	3	purpose	purpose	NOUN
ejpam-23	205	4	,	,	PUNCT
ejpam-23	205	5	we	we	PRON
ejpam-23	205	6	let	let	VERB
ejpam-23	205	7	(	(	PUNCT
ejpam-23	205	8	x	x	NOUN
ejpam-23	205	9	,	,	PUNCT
ejpam-23	205	10	y	y	NOUN
ejpam-23	205	11	)	)	PUNCT
ejpam-23	205	12	∈	∈	PROPN
ejpam-23	205	13	ρa	ρa	PROPN
ejpam-23	205	14	and	and	CCONJ
ejpam-23	205	15	c	c	PROPN
ejpam-23	205	16	∈	∈	PROPN
ejpam-23	205	17	s.	s.	PROPN
ejpam-23	205	18	then	then	ADV
ejpam-23	205	19	,	,	PUNCT
ejpam-23	205	20	by	by	ADP
ejpam-23	205	21	the	the	DET
ejpam-23	205	22	definition	definition	NOUN
ejpam-23	205	23	of	of	ADP
ejpam-23	205	24	ρa	ρa	ADP
ejpam-23	205	25	,	,	PUNCT
ejpam-23	205	26	we	we	PRON
ejpam-23	205	27	have	have	VERB
ejpam-23	205	28	(	(	PUNCT
ejpam-23	205	29	axa)0	axa)0	PROPN
ejpam-23	205	30	=	=	SYM
ejpam-23	205	31	(	(	PUNCT
ejpam-23	205	32	aya)0	aya)0	PROPN
ejpam-23	205	33	.	.	PUNCT
ejpam-23	206	1	since	since	SCONJ
ejpam-23	206	2	s	s	PROPN
ejpam-23	206	3	is	be	AUX
ejpam-23	206	4	a	a	DET
ejpam-23	206	5	regular	regular	ADJ
ejpam-23	206	6	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	206	7	,	,	PUNCT
ejpam-23	206	8	by	by	ADP
ejpam-23	206	9	lemma	lemma	PROPN
ejpam-23	206	10	2.6	2.6	NUM
ejpam-23	206	11	(	(	PUNCT
ejpam-23	206	12	i	i	NOUN
ejpam-23	206	13	)	)	PUNCT
ejpam-23	206	14	and	and	CCONJ
ejpam-23	206	15	the	the	DET
ejpam-23	206	16	regularity	regularity	NOUN
ejpam-23	206	17	of	of	ADP
ejpam-23	206	18	the	the	DET
ejpam-23	206	19	band	band	NOUN
ejpam-23	206	20	s	s	NOUN
ejpam-23	206	21	/	/	SYM
ejpam-23	206	22	h̃	h̃	PROPN
ejpam-23	206	23	,	,	PUNCT
ejpam-23	206	24	we	we	PRON
ejpam-23	206	25	obtain	obtain	VERB
ejpam-23	206	26	that	that	DET
ejpam-23	206	27	(	(	PUNCT
ejpam-23	206	28	acxa)0	acxa)0	NOUN
ejpam-23	206	29	=	=	SYM
ejpam-23	206	30	(	(	PUNCT
ejpam-23	206	31	ac(axa))0	ac(axa))0	X
ejpam-23	206	32	=	=	SYM
ejpam-23	206	33	(	(	PUNCT
ejpam-23	206	34	(	(	PUNCT
ejpam-23	206	35	ac)0(axa)0)0	ac)0(axa)0)0	SYM
ejpam-23	206	36	=	=	SYM
ejpam-23	206	37	(	(	PUNCT
ejpam-23	206	38	(	(	PUNCT
ejpam-23	206	39	ac)0(aya)0)0	ac)0(aya)0)0	PROPN
ejpam-23	206	40	=	=	SYM
ejpam-23	206	41	(	(	PUNCT
ejpam-23	206	42	acya)0	acya)0	PROPN
ejpam-23	206	43	.	.	PUNCT
ejpam-23	207	1	hence	hence	ADV
ejpam-23	207	2	,	,	PUNCT
ejpam-23	207	3	(	(	PUNCT
ejpam-23	207	4	cx	cx	NOUN
ejpam-23	207	5	,	,	PUNCT
ejpam-23	207	6	cy	cy	PROPN
ejpam-23	207	7	)	)	PUNCT
ejpam-23	207	8	∈	∈	PROPN
ejpam-23	207	9	ρa	ρa	PROPN
ejpam-23	207	10	.	.	PUNCT
ejpam-23	207	11	dually	dually	PROPN
ejpam-23	207	12	,	,	PUNCT
ejpam-23	207	13	we	we	PRON
ejpam-23	207	14	can	can	AUX
ejpam-23	207	15	prove	prove	VERB
ejpam-23	207	16	that	that	SCONJ
ejpam-23	207	17	ρa	ρa	PRON
ejpam-23	207	18	is	be	AUX
ejpam-23	207	19	right	right	ADV
ejpam-23	207	20	compatible	compatible	ADJ
ejpam-23	207	21	with	with	ADP
ejpam-23	207	22	the	the	DET
ejpam-23	207	23	semigroup	semigroup	ADJ
ejpam-23	207	24	multiplication	multiplication	NOUN
ejpam-23	207	25	.	.	PUNCT
ejpam-23	208	1	thus	thus	ADV
ejpam-23	208	2	ρa	ρa	PRON
ejpam-23	208	3	is	be	AUX
ejpam-23	208	4	a	a	DET
ejpam-23	208	5	congruence	congruence	NOUN
ejpam-23	208	6	on	on	ADP
ejpam-23	208	7	s.	s.	PROPN
ejpam-23	208	8	obviously	obviously	ADV
ejpam-23	208	9	,	,	PUNCT
ejpam-23	208	10	h̃	h̃	PROPN
ejpam-23	208	11	⊆	⊆	NUM
ejpam-23	208	12	ρa	ρa	ADV
ejpam-23	209	1	and	and	CCONJ
ejpam-23	209	2	so	so	ADV
ejpam-23	209	3	ρa	ρa	PRON
ejpam-23	209	4	is	be	AUX
ejpam-23	209	5	a	a	DET
ejpam-23	209	6	band	band	NOUN
ejpam-23	209	7	congruence	congruence	NOUN
ejpam-23	209	8	on	on	ADP
ejpam-23	209	9	s.	s.	PROPN
ejpam-23	209	10	(	(	PUNCT
ejpam-23	209	11	ii	ii	PROPN
ejpam-23	209	12	)	)	PUNCT
ejpam-23	209	13	let	let	VERB
ejpam-23	209	14	(	(	PUNCT
ejpam-23	209	15	x	x	NOUN
ejpam-23	209	16	,	,	PUNCT
ejpam-23	209	17	y	y	NOUN
ejpam-23	209	18	)	)	PUNCT
ejpam-23	209	19	∈	∈	PROPN
ejpam-23	210	1	ρa	ρa	PROPN
ejpam-23	210	2	.	.	PUNCT
ejpam-23	211	1	then	then	ADV
ejpam-23	211	2	,	,	PUNCT
ejpam-23	211	3	by	by	ADP
ejpam-23	211	4	the	the	DET
ejpam-23	211	5	definition	definition	NOUN
ejpam-23	211	6	of	of	ADP
ejpam-23	211	7	ρa	ρa	ADP
ejpam-23	211	8	,	,	PUNCT
ejpam-23	211	9	we	we	PRON
ejpam-23	211	10	have	have	VERB
ejpam-23	211	11	(	(	PUNCT
ejpam-23	211	12	axa)0	axa)0	PROPN
ejpam-23	211	13	=	=	SYM
ejpam-23	211	14	(	(	PUNCT
ejpam-23	211	15	aya)0	aya)0	PROPN
ejpam-23	211	16	and	and	CCONJ
ejpam-23	211	17	so	so	ADV
ejpam-23	211	18	a0	a0	PROPN
ejpam-23	211	19	1(axa)0a0	1(axa)0a0	NUM
ejpam-23	211	20	1	1	NUM
ejpam-23	211	21	=	=	SYM
ejpam-23	211	22	a0	a0	NOUN
ejpam-23	211	23	1(aya)0a0	1(aya)0a0	NUM
ejpam-23	211	24	1	1	NUM
ejpam-23	211	25	.	.	PUNCT
ejpam-23	212	1	this	this	PRON
ejpam-23	212	2	leads	lead	VERB
ejpam-23	212	3	to	to	ADP
ejpam-23	212	4	(	(	PUNCT
ejpam-23	212	5	a0	a0	NOUN
ejpam-23	212	6	1(axa)0a0	1(axa)0a0	PROPN
ejpam-23	212	7	1	1	NUM
ejpam-23	212	8	)	)	PUNCT
ejpam-23	212	9	0	0	NUM
ejpam-23	213	1	=	=	SYM
ejpam-23	213	2	(	(	PUNCT
ejpam-23	213	3	a0	a0	NOUN
ejpam-23	213	4	1(aya)0a0	1(aya)0a0	NUM
ejpam-23	213	5	1	1	NUM
ejpam-23	213	6	)	)	PUNCT
ejpam-23	213	7	0	0	NUM
ejpam-23	213	8	.	.	PUNCT
ejpam-23	214	1	since	since	SCONJ
ejpam-23	214	2	s	s	PROPN
ejpam-23	214	3	/	/	SYM
ejpam-23	214	4	h̃	h̃	PROPN
ejpam-23	214	5	=	=	PUNCT
ejpam-23	214	6	(	(	PUNCT
ejpam-23	214	7	y	y	PROPN
ejpam-23	214	8	;	;	PUNCT
ejpam-23	214	9	sα	sα	PROPN
ejpam-23	214	10	/	/	SYM
ejpam-23	214	11	h̃	h̃	PROPN
ejpam-23	214	12	)	)	PUNCT
ejpam-23	214	13	is	be	AUX
ejpam-23	214	14	a	a	DET
ejpam-23	214	15	regular	regular	ADJ
ejpam-23	214	16	band	band	NOUN
ejpam-23	214	17	and	and	CCONJ
ejpam-23	214	18	by	by	ADP
ejpam-23	214	19	lemma	lemma	PROPN
ejpam-23	214	20	2.6	2.6	NUM
ejpam-23	214	21	(	(	PUNCT
ejpam-23	214	22	i	i	PROPN
ejpam-23	214	23	)	)	PUNCT
ejpam-23	214	24	,	,	PUNCT
ejpam-23	214	25	we	we	PRON
ejpam-23	214	26	obtain	obtain	VERB
ejpam-23	214	27	(	(	PUNCT
ejpam-23	214	28	a1aa1xa1aa1)0	a1aa1xa1aa1)0	NOUN
ejpam-23	214	29	=	=	SYM
ejpam-23	214	30	(	(	PUNCT
ejpam-23	214	31	a1aa1ya1aa1)0	a1aa1ya1aa1)0	NOUN
ejpam-23	214	32	.	.	PUNCT
ejpam-23	215	1	however	however	ADV
ejpam-23	215	2	,	,	PUNCT
ejpam-23	215	3	since	since	SCONJ
ejpam-23	215	4	a	a	PRON
ejpam-23	215	5	,	,	PUNCT
ejpam-23	215	6	a1	a1	NOUN
ejpam-23	215	7	are	be	AUX
ejpam-23	215	8	elements	element	NOUN
ejpam-23	215	9	of	of	ADP
ejpam-23	215	10	the	the	DET
ejpam-23	215	11	completely	completely	ADV
ejpam-23	215	12	j̃	j̃	PROPN
ejpam-23	215	13	-simple	-simple	NOUN
ejpam-23	215	14	semigroup	semigroup	VERB
ejpam-23	215	15	sα	sα	ADV
ejpam-23	215	16	,	,	PUNCT
ejpam-23	215	17	(	(	PUNCT
ejpam-23	215	18	a1aa1)0	a1aa1)0	NOUN
ejpam-23	215	19	=	=	SYM
ejpam-23	215	20	a0	a0	PROPN
ejpam-23	215	21	1	1	NUM
ejpam-23	215	22	.	.	PUNCT
ejpam-23	215	23	thereby	thereby	ADV
ejpam-23	215	24	,	,	PUNCT
ejpam-23	215	25	by	by	ADP
ejpam-23	215	26	lemma	lemma	PROPN
ejpam-23	215	27	2.6	2.6	NUM
ejpam-23	215	28	(	(	PUNCT
ejpam-23	215	29	i	i	NOUN
ejpam-23	215	30	)	)	PUNCT
ejpam-23	215	31	again	again	ADV
ejpam-23	215	32	,	,	PUNCT
ejpam-23	215	33	we	we	PRON
ejpam-23	215	34	have	have	VERB
ejpam-23	215	35	(	(	PUNCT
ejpam-23	215	36	a1xa1)0	a1xa1)0	NUM
ejpam-23	215	37	=	=	SYM
ejpam-23	215	38	(	(	PUNCT
ejpam-23	215	39	a1ya1)0	a1ya1)0	PROPN
ejpam-23	215	40	,	,	PUNCT
ejpam-23	215	41	that	that	ADV
ejpam-23	215	42	is	is	ADV
ejpam-23	215	43	,	,	PUNCT
ejpam-23	215	44	(	(	PUNCT
ejpam-23	215	45	x	x	NOUN
ejpam-23	215	46	,	,	PUNCT
ejpam-23	215	47	y	y	NOUN
ejpam-23	215	48	)	)	PUNCT
ejpam-23	215	49	∈	∈	PROPN
ejpam-23	216	1	ρa1	ρa1	NOUN
ejpam-23	216	2	.	.	PUNCT
ejpam-23	217	1	this	this	PRON
ejpam-23	217	2	shows	show	VERB
ejpam-23	217	3	that	that	SCONJ
ejpam-23	217	4	ρa	ρa	ADV
ejpam-23	217	5	⊆	⊆	NUM
ejpam-23	217	6	ρa1	ρa1	NUM
ejpam-23	217	7	.	.	PUNCT
ejpam-23	218	1	similarly	similarly	ADV
ejpam-23	218	2	,	,	PUNCT
ejpam-23	218	3	we	we	PRON
ejpam-23	218	4	also	also	ADV
ejpam-23	218	5	have	have	VERB
ejpam-23	218	6	ρa1	ρa1	NUM
ejpam-23	218	7	⊆	⊆	NUM
ejpam-23	218	8	ρa	ρa	NOUN
ejpam-23	218	9	.	.	PUNCT
ejpam-23	219	1	thus	thus	ADV
ejpam-23	219	2	,	,	PUNCT
ejpam-23	219	3	ρa	ρa	PRON
ejpam-23	219	4	=	=	PUNCT
ejpam-23	220	1	ρa1	ρa1	NUM
ejpam-23	220	2	.	.	PUNCT
ejpam-23	221	1	since	since	SCONJ
ejpam-23	221	2	this	this	DET
ejpam-23	221	3	relation	relation	NOUN
ejpam-23	221	4	holds	hold	VERB
ejpam-23	221	5	for	for	SCONJ
ejpam-23	221	6	all	all	DET
ejpam-23	221	7	a	a	DET
ejpam-23	221	8	∈	∈	NOUN
ejpam-23	221	9	sα	sα	ADV
ejpam-23	221	10	,	,	PUNCT
ejpam-23	221	11	we	we	PRON
ejpam-23	221	12	usually	usually	ADV
ejpam-23	221	13	write	write	VERB
ejpam-23	221	14	ρa	ρa	PRON
ejpam-23	222	1	=	=	PUNCT
ejpam-23	222	2	ρα	ρα	PROPN
ejpam-23	222	3	.	.	PUNCT
ejpam-23	223	1	(	(	PUNCT
ejpam-23	223	2	iii	iii	X
ejpam-23	223	3	)	)	PUNCT
ejpam-23	223	4	let	let	VERB
ejpam-23	223	5	a	a	DET
ejpam-23	223	6	∈	∈	NOUN
ejpam-23	223	7	sα	sα	NOUN
ejpam-23	223	8	,	,	PUNCT
ejpam-23	223	9	b	b	X
ejpam-23	223	10	∈	∈	ADJ
ejpam-23	223	11	sβ	sβ	NOUN
ejpam-23	223	12	and	and	CCONJ
ejpam-23	223	13	α	α	X
ejpam-23	223	14	>	>	X
ejpam-23	223	15	β	β	X
ejpam-23	223	16	.	.	PUNCT
ejpam-23	224	1	we	we	PRON
ejpam-23	224	2	need	need	VERB
ejpam-23	224	3	to	to	PART
ejpam-23	224	4	prove	prove	VERB
ejpam-23	224	5	that	that	SCONJ
ejpam-23	224	6	ρα	ρα	PRON
ejpam-23	224	7	⊆	⊆	NUM
ejpam-23	224	8	ρβ	ρβ	PROPN
ejpam-23	224	9	.	.	PUNCT
ejpam-23	225	1	for	for	ADP
ejpam-23	225	2	this	this	DET
ejpam-23	225	3	purpose	purpose	NOUN
ejpam-23	225	4	,	,	PUNCT
ejpam-23	225	5	we	we	PRON
ejpam-23	225	6	let	let	VERB
ejpam-23	225	7	(	(	PUNCT
ejpam-23	225	8	x	x	NOUN
ejpam-23	225	9	,	,	PUNCT
ejpam-23	225	10	y	y	NOUN
ejpam-23	225	11	)	)	PUNCT
ejpam-23	225	12	∈	∈	PROPN
ejpam-23	226	1	ρα	ρα	NOUN
ejpam-23	226	2	=	=	SYM
ejpam-23	226	3	ρa	ρa	PROPN
ejpam-23	226	4	,	,	PUNCT
ejpam-23	226	5	by	by	ADP
ejpam-23	226	6	(	(	PUNCT
ejpam-23	226	7	ii	ii	NOUN
ejpam-23	226	8	)	)	PUNCT
ejpam-23	226	9	.	.	PUNCT
ejpam-23	227	1	then	then	ADV
ejpam-23	227	2	,	,	PUNCT
ejpam-23	227	3	by	by	ADP
ejpam-23	227	4	the	the	DET
ejpam-23	227	5	definition	definition	NOUN
ejpam-23	227	6	of	of	ADP
ejpam-23	227	7	ρa	ρa	ADP
ejpam-23	227	8	,	,	PUNCT
ejpam-23	227	9	we	we	PRON
ejpam-23	227	10	have	have	VERB
ejpam-23	227	11	(	(	PUNCT
ejpam-23	227	12	axa)0	axa)0	PROPN
ejpam-23	227	13	=	=	SYM
ejpam-23	227	14	(	(	PUNCT
ejpam-23	227	15	aya)0	aya)0	PROPN
ejpam-23	227	16	and	and	CCONJ
ejpam-23	227	17	hence	hence	ADV
ejpam-23	227	18	b(axa)0b	b(axa)0b	PROPN
ejpam-23	227	19	=	=	SYM
ejpam-23	227	20	b(aya)0b	b(aya)0b	PROPN
ejpam-23	227	21	.	.	PUNCT
ejpam-23	228	1	by	by	ADP
ejpam-23	228	2	lemma	lemma	PROPN
ejpam-23	228	3	2.6	2.6	NUM
ejpam-23	228	4	(	(	PUNCT
ejpam-23	228	5	i	i	NOUN
ejpam-23	228	6	)	)	PUNCT
ejpam-23	228	7	and	and	CCONJ
ejpam-23	228	8	the	the	DET
ejpam-23	228	9	regularity	regularity	NOUN
ejpam-23	228	10	of	of	ADP
ejpam-23	228	11	the	the	DET
ejpam-23	228	12	band	band	NOUN
ejpam-23	228	13	,	,	PUNCT
ejpam-23	228	14	we	we	PRON
ejpam-23	228	15	have	have	VERB
ejpam-23	228	16	(	(	PUNCT
ejpam-23	228	17	babxbab)0	babxbab)0	X
ejpam-23	228	18	=	=	SYM
ejpam-23	228	19	(	(	PUNCT
ejpam-23	228	20	babybab)0	babybab)0	PROPN
ejpam-23	228	21	.	.	PUNCT
ejpam-23	229	1	since	since	SCONJ
ejpam-23	229	2	α	α	X
ejpam-23	229	3	>	>	X
ejpam-23	229	4	β	β	X
ejpam-23	229	5	in	in	ADP
ejpam-23	229	6	y	y	PROPN
ejpam-23	229	7	and	and	CCONJ
ejpam-23	229	8	a	a	DET
ejpam-23	229	9	∈	∈	PROPN
ejpam-23	229	10	sα	sα	NOUN
ejpam-23	229	11	,	,	PUNCT
ejpam-23	229	12	b	b	X
ejpam-23	229	13	∈	∈	ADJ
ejpam-23	229	14	sβ	sβ	INTJ
ejpam-23	229	15	,	,	PUNCT
ejpam-23	229	16	we	we	PRON
ejpam-23	229	17	have	have	VERB
ejpam-23	229	18	(	(	PUNCT
ejpam-23	229	19	bab)0	bab)0	NOUN
ejpam-23	229	20	=	=	SYM
ejpam-23	229	21	b0	b0	NOUN
ejpam-23	229	22	.	.	PUNCT
ejpam-23	230	1	by	by	ADP
ejpam-23	230	2	using	use	VERB
ejpam-23	230	3	lemma	lemma	PROPN
ejpam-23	230	4	2.6	2.6	NUM
ejpam-23	230	5	(	(	PUNCT
ejpam-23	230	6	i	i	NOUN
ejpam-23	230	7	)	)	PUNCT
ejpam-23	230	8	again	again	ADV
ejpam-23	230	9	,	,	PUNCT
ejpam-23	230	10	we	we	PRON
ejpam-23	230	11	can	can	AUX
ejpam-23	230	12	show	show	VERB
ejpam-23	230	13	that	that	SCONJ
ejpam-23	230	14	(	(	PUNCT
ejpam-23	230	15	bxb)0	bxb)0	PROPN
ejpam-23	230	16	=	=	SYM
ejpam-23	230	17	(	(	PUNCT
ejpam-23	230	18	byb)0	byb)0	PROPN
ejpam-23	230	19	,	,	PUNCT
ejpam-23	230	20	that	that	ADV
ejpam-23	230	21	is	is	ADV
ejpam-23	230	22	,	,	PUNCT
ejpam-23	230	23	(	(	PUNCT
ejpam-23	230	24	x	x	NOUN
ejpam-23	230	25	,	,	PUNCT
ejpam-23	230	26	y	y	NOUN
ejpam-23	230	27	)	)	PUNCT
ejpam-23	230	28	∈	∈	NOUN
ejpam-23	230	29	ρb	ρb	X
ejpam-23	230	30	=	=	SYM
ejpam-23	230	31	ρβ	ρβ	PROPN
ejpam-23	230	32	.	.	PUNCT
ejpam-23	231	1	thus	thus	ADV
ejpam-23	231	2	,	,	PUNCT
ejpam-23	231	3	ρα	ρα	PRON
ejpam-23	231	4	⊆	⊆	NUM
ejpam-23	231	5	ρβ	ρβ	PROPN
ejpam-23	231	6	as	as	SCONJ
ejpam-23	231	7	required	require	VERB
ejpam-23	231	8	.	.	PUNCT
ejpam-23	232	1	furthermore	furthermore	ADV
ejpam-23	232	2	,	,	PUNCT
ejpam-23	232	3	it	it	PRON
ejpam-23	232	4	is	be	AUX
ejpam-23	232	5	trivial	trivial	ADJ
ejpam-23	232	6	that	that	SCONJ
ejpam-23	232	7	ρβ|sα	ρβ|sα	PUNCT
ejpam-23	233	1	=	=	X
ejpam-23	233	2	ωsα	ωsα	ADV
ejpam-23	233	3	,	,	PUNCT
ejpam-23	233	4	which	which	PRON
ejpam-23	233	5	is	be	AUX
ejpam-23	233	6	the	the	DET
ejpam-23	233	7	universal	universal	ADJ
ejpam-23	233	8	relation	relation	NOUN
ejpam-23	233	9	on	on	ADP
ejpam-23	233	10	the	the	DET
ejpam-23	233	11	semigroup	semigroup	PROPN
ejpam-23	233	12	sα	sα	PROPN
ejpam-23	233	13	.	.	PUNCT
ejpam-23	234	1	we	we	PRON
ejpam-23	234	2	now	now	ADV
ejpam-23	234	3	use	use	VERB
ejpam-23	234	4	the	the	DET
ejpam-23	234	5	band	band	NOUN
ejpam-23	234	6	congruence	congruence	NOUN
ejpam-23	234	7	ρα	ρα	PROPN
ejpam-23	234	8	defined	define	VERB
ejpam-23	234	9	in	in	ADP
ejpam-23	234	10	lemma	lemma	PROPN
ejpam-23	234	11	3.1	3.1	NUM
ejpam-23	234	12	to	to	PART
ejpam-23	234	13	describe	describe	VERB
ejpam-23	234	14	the	the	DET
ejpam-23	234	15	structural	structural	ADJ
ejpam-23	234	16	homomorphisms	homomorphism	NOUN
ejpam-23	234	17	for	for	ADP
ejpam-23	234	18	the	the	DET
ejpam-23	234	19	h̃	h̃	PROPN
ejpam-23	234	20	-cryptogroup	-cryptogroup	PROPN
ejpam-23	234	21	s	s	PART
ejpam-23	234	22	=	=	PUNCT
ejpam-23	234	23	(	(	PUNCT
ejpam-23	234	24	y	y	PROPN
ejpam-23	234	25	;	;	PUNCT
ejpam-23	234	26	sα	sα	X
ejpam-23	234	27	)	)	PUNCT
ejpam-23	234	28	,	,	PUNCT
ejpam-23	234	29	where	where	SCONJ
ejpam-23	234	30	each	each	DET
ejpam-23	234	31	sα	sα	NOUN
ejpam-23	234	32	is	be	AUX
ejpam-23	234	33	a	a	DET
ejpam-23	234	34	completely	completely	ADV
ejpam-23	234	35	j̃	j̃	PROPN
ejpam-23	234	36	-simple	-simple	NUM
ejpam-23	234	37	semigroup	semigroup	ADJ
ejpam-23	234	38	.	.	PUNCT
ejpam-23	235	1	we	we	PRON
ejpam-23	235	2	first	first	ADV
ejpam-23	235	3	consider	consider	VERB
ejpam-23	235	4	the	the	DET
ejpam-23	235	5	congruence	congruence	NOUN
ejpam-23	235	6	ρα	ρα	PROPN
ejpam-23	235	7	,	,	PUNCT
ejpam-23	235	8	β	β	X
ejpam-23	235	9	=	=	PUNCT
ejpam-23	235	10	ρα|sβ	ρα|sβ	PROPN
ejpam-23	235	11	for	for	ADP
ejpam-23	235	12	α	α	NOUN
ejpam-23	235	13	,	,	PUNCT
ejpam-23	235	14	β	β	X
ejpam-23	235	15	∈	∈	PROPN
ejpam-23	235	16	y	y	PROPN
ejpam-23	235	17	,	,	PUNCT
ejpam-23	235	18	which	which	PRON
ejpam-23	235	19	is	be	AUX
ejpam-23	235	20	a	a	DET
ejpam-23	235	21	band	band	NOUN
ejpam-23	235	22	congruence	congruence	NOUN
ejpam-23	235	23	on	on	ADP
ejpam-23	235	24	the	the	DET
ejpam-23	235	25	semigroup	semigroup	NOUN
ejpam-23	235	26	sβ	sβ	NOUN
ejpam-23	235	27	.	.	PUNCT
ejpam-23	236	1	now	now	ADV
ejpam-23	236	2	,	,	PUNCT
ejpam-23	236	3	we	we	PRON
ejpam-23	236	4	denote	denote	VERB
ejpam-23	236	5	all	all	DET
ejpam-23	236	6	the	the	DET
ejpam-23	236	7	ρα	ρα	PROPN
ejpam-23	236	8	,	,	PUNCT
ejpam-23	236	9	β	β	NOUN
ejpam-23	236	10	-	-	PUNCT
ejpam-23	236	11	classes	class	NOUN
ejpam-23	236	12	of	of	ADP
ejpam-23	236	13	sβ	sβ	NUM
ejpam-23	236	14	by	by	ADP
ejpam-23	236	15	{	{	PUNCT
ejpam-23	236	16	sd(α	sd(α	PROPN
ejpam-23	236	17	,	,	PUNCT
ejpam-23	236	18	β	β	NOUN
ejpam-23	236	19	)	)	PUNCT
ejpam-23	236	20	:	:	PUNCT
ejpam-23	237	1	d(α	d(α	NOUN
ejpam-23	237	2	,	,	PUNCT
ejpam-23	237	3	β	β	X
ejpam-23	237	4	)	)	PUNCT
ejpam-23	237	5	∈	∈	PROPN
ejpam-23	237	6	d(α	d(α	PROPN
ejpam-23	237	7	,	,	PUNCT
ejpam-23	237	8	β	β	NOUN
ejpam-23	237	9	)	)	PUNCT
ejpam-23	237	10	}	}	PUNCT
ejpam-23	237	11	,	,	PUNCT
ejpam-23	237	12	where	where	SCONJ
ejpam-23	237	13	d(α	d(α	NOUN
ejpam-23	237	14	,	,	PUNCT
ejpam-23	237	15	β	β	NOUN
ejpam-23	237	16	)	)	PUNCT
ejpam-23	237	17	is	be	AUX
ejpam-23	237	18	a	a	DET
ejpam-23	237	19	non	non	ADJ
ejpam-23	237	20	-	-	ADJ
ejpam-23	237	21	empty	empty	ADJ
ejpam-23	237	22	index	index	NOUN
ejpam-23	237	23	set	set	NOUN
ejpam-23	237	24	.	.	PUNCT
ejpam-23	238	1	in	in	ADP
ejpam-23	238	2	particular	particular	ADJ
ejpam-23	238	3	,	,	PUNCT
ejpam-23	238	4	the	the	DET
ejpam-23	238	5	set	set	NOUN
ejpam-23	238	6	d(α	d(α	PROPN
ejpam-23	238	7	,	,	PUNCT
ejpam-23	238	8	α	α	X
ejpam-23	238	9	)	)	PUNCT
ejpam-23	238	10	is	be	AUX
ejpam-23	238	11	a	a	DET
ejpam-23	238	12	singleton	singleton	NOUN
ejpam-23	238	13	and	and	CCONJ
ejpam-23	238	14	we	we	PRON
ejpam-23	238	15	can	can	AUX
ejpam-23	238	16	therefore	therefore	ADV
ejpam-23	238	17	write	write	VERB
ejpam-23	238	18	d(α	d(α	PROPN
ejpam-23	238	19	,	,	PUNCT
ejpam-23	238	20	α	α	NOUN
ejpam-23	238	21	)	)	PUNCT
ejpam-23	238	22	=	=	PUNCT
ejpam-23	239	1	d(α	d(α	NOUN
ejpam-23	239	2	,	,	PUNCT
ejpam-23	239	3	α	α	NOUN
ejpam-23	239	4	)	)	PUNCT
ejpam-23	239	5	.	.	PUNCT
ejpam-23	240	1	we	we	PRON
ejpam-23	240	2	have	have	VERB
ejpam-23	240	3	the	the	DET
ejpam-23	240	4	following	follow	VERB
ejpam-23	240	5	lemma	lemma	PROPN
ejpam-23	240	6	.	.	PUNCT
ejpam-23	241	1	lemma	lemma	PROPN
ejpam-23	241	2	3.2	3.2	NUM
ejpam-23	241	3	let	let	VERB
ejpam-23	241	4	s	s	VERB
ejpam-23	241	5	=	=	PUNCT
ejpam-23	241	6	(	(	PUNCT
ejpam-23	241	7	y	y	PROPN
ejpam-23	241	8	;	;	PUNCT
ejpam-23	241	9	sα	sα	X
ejpam-23	241	10	)	)	PUNCT
ejpam-23	241	11	be	be	AUX
ejpam-23	241	12	a	a	DET
ejpam-23	241	13	regular	regular	ADJ
ejpam-23	241	14	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	241	15	.	.	PUNCT
ejpam-23	242	1	then	then	ADV
ejpam-23	242	2	,	,	PUNCT
ejpam-23	242	3	for	for	ADP
ejpam-23	242	4	all	all	DET
ejpam-23	242	5	α	α	NOUN
ejpam-23	242	6	,	,	PUNCT
ejpam-23	242	7	β	β	X
ejpam-23	242	8	∈	∈	PROPN
ejpam-23	242	9	y	y	PROPN
ejpam-23	242	10	with	with	ADP
ejpam-23	242	11	α	α	PROPN
ejpam-23	242	12	>	>	X
ejpam-23	242	13	β	β	X
ejpam-23	242	14	,	,	PUNCT
ejpam-23	242	15	the	the	DET
ejpam-23	242	16	following	follow	VERB
ejpam-23	242	17	statements	statement	NOUN
ejpam-23	242	18	hold	hold	VERB
ejpam-23	242	19	for	for	ADP
ejpam-23	242	20	all	all	DET
ejpam-23	242	21	d(α	d(α	NOUN
ejpam-23	242	22	,	,	PUNCT
ejpam-23	242	23	β	β	X
ejpam-23	242	24	)	)	PUNCT
ejpam-23	242	25	∈	∈	PROPN
ejpam-23	242	26	d(α	d(α	PROPN
ejpam-23	242	27	,	,	PUNCT
ejpam-23	242	28	β	β	NOUN
ejpam-23	242	29	)	)	PUNCT
ejpam-23	242	30	.	.	PUNCT
ejpam-23	243	1	(	(	PUNCT
ejpam-23	243	2	i	i	NOUN
ejpam-23	243	3	)	)	PUNCT
ejpam-23	243	4	for	for	ADP
ejpam-23	243	5	all	all	DET
ejpam-23	243	6	a	a	DET
ejpam-23	243	7	∈	∈	NOUN
ejpam-23	243	8	sα	sα	ADP
ejpam-23	243	9	,	,	PUNCT
ejpam-23	243	10	there	there	PRON
ejpam-23	243	11	exists	exist	VERB
ejpam-23	243	12	a	a	DET
ejpam-23	243	13	unique	unique	ADJ
ejpam-23	243	14	ad(α	ad(α	NOUN
ejpam-23	243	15	,	,	PUNCT
ejpam-23	243	16	β	β	X
ejpam-23	243	17	)	)	PUNCT
ejpam-23	243	18	∈	∈	PROPN
ejpam-23	243	19	sd(α	sd(α	NOUN
ejpam-23	243	20	,	,	PUNCT
ejpam-23	243	21	β	β	X
ejpam-23	243	22	)	)	PUNCT
ejpam-23	243	23	satisfying	satisfy	VERB
ejpam-23	243	24	a	a	DET
ejpam-23	243	25	>	>	X
ejpam-23	243	26	ad(α	ad(α	NOUN
ejpam-23	243	27	,	,	PUNCT
ejpam-23	243	28	β	β	NOUN
ejpam-23	243	29	)	)	PUNCT
ejpam-23	243	30	;	;	PUNCT
ejpam-23	243	31	(	(	PUNCT
ejpam-23	243	32	ii	ii	NOUN
ejpam-23	243	33	)	)	PUNCT
ejpam-23	243	34	for	for	ADP
ejpam-23	243	35	all	all	DET
ejpam-23	243	36	a	a	DET
ejpam-23	243	37	∈	∈	NOUN
ejpam-23	243	38	sα	sα	ADV
ejpam-23	243	39	and	and	CCONJ
ejpam-23	243	40	x	x	SYM
ejpam-23	243	41	∈	∈	PROPN
ejpam-23	243	42	sd(α	sd(α	NOUN
ejpam-23	243	43	,	,	PUNCT
ejpam-23	243	44	β	β	NOUN
ejpam-23	243	45	)	)	PUNCT
ejpam-23	243	46	,	,	PUNCT
ejpam-23	243	47	if	if	SCONJ
ejpam-23	243	48	a0	a0	PROPN
ejpam-23	243	49	>	>	X
ejpam-23	243	50	e	e	PROPN
ejpam-23	243	51	for	for	ADP
ejpam-23	243	52	some	some	DET
ejpam-23	243	53	idempotent	idempotent	ADJ
ejpam-23	243	54	e	e	NOUN
ejpam-23	243	55	∈	∈	PROPN
ejpam-23	243	56	sd(α	sd(α	NOUN
ejpam-23	243	57	,	,	PUNCT
ejpam-23	243	58	β	β	NOUN
ejpam-23	243	59	)	)	PUNCT
ejpam-23	243	60	then	then	ADV
ejpam-23	243	61	eax	eax	NOUN
ejpam-23	243	62	=	=	NOUN
ejpam-23	243	63	ax	ax	NOUN
ejpam-23	243	64	,	,	PUNCT
ejpam-23	243	65	xae	xae	PROPN
ejpam-23	243	66	=	=	SYM
ejpam-23	243	67	xa	xa	PROPN
ejpam-23	243	68	,	,	PUNCT
ejpam-23	243	69	ea	ea	X
ejpam-23	244	1	=	=	SYM
ejpam-23	244	2	ae	ae	PROPN
ejpam-23	244	3	and	and	CCONJ
ejpam-23	244	4	(	(	PUNCT
ejpam-23	244	5	ea)0	ea)0	PROPN
ejpam-23	244	6	=	=	SYM
ejpam-23	244	7	e	e	NOUN
ejpam-23	244	8	;	;	PUNCT
ejpam-23	244	9	x.	x.	PROPN
ejpam-23	244	10	kong	kong	PROPN
ejpam-23	244	11	,	,	PUNCT
ejpam-23	244	12	y.ding	y.de	VERB
ejpam-23	244	13	,	,	PUNCT
ejpam-23	244	14	k.p.shum	k.p.shum	ADJ
ejpam-23	244	15	/	/	SYM
ejpam-23	244	16	eur	eur	PROPN
ejpam-23	244	17	.	.	PUNCT
ejpam-23	245	1	j.	j.	PROPN
ejpam-23	245	2	pure	pure	PROPN
ejpam-23	245	3	appl	appl	PROPN
ejpam-23	245	4	.	.	PROPN
ejpam-23	245	5	math	math	PROPN
ejpam-23	245	6	,	,	PUNCT
ejpam-23	245	7	1	1	NUM
ejpam-23	245	8	(	(	PUNCT
ejpam-23	245	9	2008	2008	NUM
ejpam-23	245	10	)	)	PUNCT
ejpam-23	245	11	,	,	PUNCT
ejpam-23	245	12	(	(	PUNCT
ejpam-23	245	13	46	46	NUM
ejpam-23	245	14	-	-	SYM
ejpam-23	245	15	59	59	NUM
ejpam-23	245	16	)	)	PUNCT
ejpam-23	245	17	54	54	NUM
ejpam-23	245	18	(	(	PUNCT
ejpam-23	245	19	iii	iii	NOUN
ejpam-23	245	20	)	)	PUNCT
ejpam-23	245	21	let	let	VERB
ejpam-23	245	22	a	a	DET
ejpam-23	245	23	∈	∈	ADJ
ejpam-23	245	24	sα	sα	PROPN
ejpam-23	245	25	.	.	PROPN
ejpam-23	245	26	define	define	VERB
ejpam-23	245	27	ϕd(α	ϕd(α	NOUN
ejpam-23	245	28	,	,	PUNCT
ejpam-23	245	29	β	β	NOUN
ejpam-23	245	30	)	)	PUNCT
ejpam-23	245	31	:	:	PUNCT
ejpam-23	245	32	sα	sα	ADV
ejpam-23	245	33	−→	−→	NOUN
ejpam-23	245	34	sd(α	sd(α	NOUN
ejpam-23	245	35	,	,	PUNCT
ejpam-23	245	36	β	β	X
ejpam-23	245	37	)	)	PUNCT
ejpam-23	245	38	by	by	ADP
ejpam-23	245	39	aϕd(α	aϕd(α	NOUN
ejpam-23	245	40	,	,	PUNCT
ejpam-23	245	41	β	β	X
ejpam-23	245	42	)	)	PUNCT
ejpam-23	245	43	=	=	SYM
ejpam-23	245	44	ad(α	ad(α	NOUN
ejpam-23	245	45	,	,	PUNCT
ejpam-23	245	46	β	β	NOUN
ejpam-23	245	47	)	)	PUNCT
ejpam-23	245	48	,	,	PUNCT
ejpam-23	245	49	where	where	SCONJ
ejpam-23	245	50	ad(α	ad(α	NOUN
ejpam-23	245	51	,	,	PUNCT
ejpam-23	245	52	β	β	X
ejpam-23	245	53	)	)	PUNCT
ejpam-23	245	54	∈	∈	PROPN
ejpam-23	245	55	sd(α	sd(α	NOUN
ejpam-23	245	56	,	,	PUNCT
ejpam-23	245	57	β	β	NOUN
ejpam-23	245	58	)	)	PUNCT
ejpam-23	245	59	and	and	CCONJ
ejpam-23	245	60	a	a	DET
ejpam-23	245	61	>	>	X
ejpam-23	245	62	ad(α	ad(α	NOUN
ejpam-23	245	63	,	,	PUNCT
ejpam-23	245	64	β	β	NOUN
ejpam-23	245	65	)	)	PUNCT
ejpam-23	245	66	.	.	PUNCT
ejpam-23	246	1	then	then	ADV
ejpam-23	246	2	ϕd(α	ϕd(α	PUNCT
ejpam-23	246	3	,	,	PUNCT
ejpam-23	246	4	β	β	X
ejpam-23	246	5	)	)	PUNCT
ejpam-23	246	6	is	be	AUX
ejpam-23	246	7	a	a	DET
ejpam-23	246	8	homomorphism	homomorphism	NOUN
ejpam-23	246	9	and	and	CCONJ
ejpam-23	246	10	ad(α	ad(α	NOUN
ejpam-23	246	11	,	,	PUNCT
ejpam-23	246	12	β	β	X
ejpam-23	246	13	)	)	PUNCT
ejpam-23	246	14	=	=	PUNCT
ejpam-23	247	1	a(aba)0	a(aba)0	NOUN
ejpam-23	248	1	=	=	SYM
ejpam-23	249	1	(	(	PUNCT
ejpam-23	249	2	aba)0a	aba)0a	NOUN
ejpam-23	249	3	for	for	ADP
ejpam-23	249	4	any	any	DET
ejpam-23	249	5	b	b	PROPN
ejpam-23	249	6	∈	∈	PROPN
ejpam-23	249	7	sd(α	sd(α	NOUN
ejpam-23	249	8	,	,	PUNCT
ejpam-23	249	9	β	β	NOUN
ejpam-23	249	10	)	)	PUNCT
ejpam-23	249	11	.	.	PUNCT
ejpam-23	250	1	proof	proof	NOUN
ejpam-23	250	2	.	.	PUNCT
ejpam-23	251	1	(	(	PUNCT
ejpam-23	251	2	i	i	NOUN
ejpam-23	251	3	)	)	PUNCT
ejpam-23	251	4	we	we	PRON
ejpam-23	251	5	first	first	ADV
ejpam-23	251	6	show	show	VERB
ejpam-23	251	7	that	that	SCONJ
ejpam-23	251	8	for	for	ADP
ejpam-23	251	9	any	any	DET
ejpam-23	251	10	a	a	DET
ejpam-23	251	11	∈	∈	NOUN
ejpam-23	251	12	sα	sα	NOUN
ejpam-23	251	13	and	and	CCONJ
ejpam-23	251	14	b	b	X
ejpam-23	251	15	∈	∈	PROPN
ejpam-23	251	16	sd(α	sd(α	AUX
ejpam-23	251	17	,	,	PUNCT
ejpam-23	251	18	β	β	NOUN
ejpam-23	251	19	)	)	PUNCT
ejpam-23	251	20	,	,	PUNCT
ejpam-23	251	21	we	we	PRON
ejpam-23	251	22	have	have	VERB
ejpam-23	251	23	ab	ab	PROPN
ejpam-23	251	24	∈	∈	PROPN
ejpam-23	251	25	sd(α	sd(α	PROPN
ejpam-23	251	26	,	,	PUNCT
ejpam-23	251	27	β	β	NOUN
ejpam-23	251	28	)	)	PUNCT
ejpam-23	251	29	,	,	PUNCT
ejpam-23	251	30	that	that	ADV
ejpam-23	251	31	is	is	ADV
ejpam-23	251	32	,	,	PUNCT
ejpam-23	251	33	(	(	PUNCT
ejpam-23	251	34	ab	ab	PROPN
ejpam-23	251	35	,	,	PUNCT
ejpam-23	251	36	b	b	NOUN
ejpam-23	251	37	)	)	PUNCT
ejpam-23	251	38	∈	∈	PROPN
ejpam-23	251	39	ρα	ρα	PROPN
ejpam-23	251	40	,	,	PUNCT
ejpam-23	251	41	β	β	X
ejpam-23	251	42	.	.	PUNCT
ejpam-23	252	1	in	in	ADP
ejpam-23	252	2	fact	fact	NOUN
ejpam-23	252	3	,	,	PUNCT
ejpam-23	252	4	since	since	SCONJ
ejpam-23	252	5	s	s	PART
ejpam-23	252	6	=	=	SYM
ejpam-23	252	7	(	(	PUNCT
ejpam-23	252	8	y	y	PROPN
ejpam-23	252	9	,	,	PUNCT
ejpam-23	252	10	sα	sα	ADV
ejpam-23	252	11	)	)	PUNCT
ejpam-23	252	12	is	be	AUX
ejpam-23	252	13	an	an	DET
ejpam-23	252	14	h̃	h̃	PROPN
ejpam-23	252	15	-cryptogroup	-cryptogroup	NOUN
ejpam-23	252	16	,	,	PUNCT
ejpam-23	252	17	each	each	PRON
ejpam-23	252	18	sα	sα	NOUN
ejpam-23	252	19	is	be	AUX
ejpam-23	252	20	a	a	DET
ejpam-23	252	21	completely	completely	ADV
ejpam-23	252	22	j̃	j̃	PROPN
ejpam-23	252	23	-simple	-simple	NUM
ejpam-23	252	24	semigroup	semigroup	ADJ
ejpam-23	252	25	.	.	PUNCT
ejpam-23	253	1	hence	hence	ADV
ejpam-23	253	2	,	,	PUNCT
ejpam-23	253	3	we	we	PRON
ejpam-23	253	4	have	have	VERB
ejpam-23	253	5	(	(	PUNCT
ejpam-23	253	6	xax)0	xax)0	PROPN
ejpam-23	253	7	=	=	PUNCT
ejpam-23	253	8	x0	x0	PROPN
ejpam-23	253	9	,	,	PUNCT
ejpam-23	253	10	for	for	ADP
ejpam-23	253	11	all	all	DET
ejpam-23	253	12	x	x	SYM
ejpam-23	253	13	∈	∈	NOUN
ejpam-23	253	14	sα	sα	NOUN
ejpam-23	253	15	.	.	PUNCT
ejpam-23	254	1	this	this	PRON
ejpam-23	254	2	leads	lead	VERB
ejpam-23	254	3	to	to	ADP
ejpam-23	254	4	(	(	PUNCT
ejpam-23	254	5	xabx)0	xabx)0	PROPN
ejpam-23	254	6	=	=	SYM
ejpam-23	254	7	(	(	PUNCT
ejpam-23	254	8	xaxbx)0	xaxbx)0	NUM
ejpam-23	254	9	=	=	SYM
ejpam-23	254	10	(	(	PUNCT
ejpam-23	254	11	xbx)0	xbx)0	PROPN
ejpam-23	254	12	by	by	ADP
ejpam-23	254	13	the	the	DET
ejpam-23	254	14	regularity	regularity	NOUN
ejpam-23	254	15	of	of	ADP
ejpam-23	254	16	the	the	DET
ejpam-23	254	17	band	band	NOUN
ejpam-23	254	18	s	s	PROPN
ejpam-23	254	19	/	/	SYM
ejpam-23	254	20	h̃	h̃	PROPN
ejpam-23	254	21	and	and	CCONJ
ejpam-23	254	22	lemma	lemma	PROPN
ejpam-23	254	23	2.6	2.6	NUM
ejpam-23	254	24	(	(	PUNCT
ejpam-23	254	25	i	i	NOUN
ejpam-23	254	26	)	)	PUNCT
ejpam-23	254	27	.	.	PUNCT
ejpam-23	255	1	thereby	thereby	ADV
ejpam-23	255	2	,	,	PUNCT
ejpam-23	255	3	(	(	PUNCT
ejpam-23	255	4	ab	ab	PROPN
ejpam-23	255	5	,	,	PUNCT
ejpam-23	255	6	b	b	NOUN
ejpam-23	255	7	)	)	PUNCT
ejpam-23	255	8	∈	∈	PROPN
ejpam-23	255	9	ρα	ρα	PROPN
ejpam-23	255	10	,	,	PUNCT
ejpam-23	255	11	β	β	X
ejpam-23	255	12	.	.	PUNCT
ejpam-23	256	1	similarly	similarly	ADV
ejpam-23	256	2	,	,	PUNCT
ejpam-23	256	3	we	we	PRON
ejpam-23	256	4	also	also	ADV
ejpam-23	256	5	have	have	VERB
ejpam-23	256	6	ba	ba	PROPN
ejpam-23	256	7	∈	∈	PROPN
ejpam-23	256	8	sd(α	sd(α	NOUN
ejpam-23	256	9	,	,	PUNCT
ejpam-23	256	10	β	β	NOUN
ejpam-23	256	11	)	)	PUNCT
ejpam-23	256	12	.	.	PUNCT
ejpam-23	257	1	invoking	invoke	VERB
ejpam-23	257	2	the	the	DET
ejpam-23	257	3	above	above	ADJ
ejpam-23	257	4	results	result	NOUN
ejpam-23	257	5	,	,	PUNCT
ejpam-23	257	6	we	we	PRON
ejpam-23	257	7	have	have	VERB
ejpam-23	257	8	aba	aba	PROPN
ejpam-23	257	9	∈	∈	PROPN
ejpam-23	257	10	sd(α	sd(α	PROPN
ejpam-23	257	11	,	,	PUNCT
ejpam-23	257	12	β	β	NOUN
ejpam-23	257	13	)	)	PUNCT
ejpam-23	257	14	for	for	ADP
ejpam-23	257	15	any	any	DET
ejpam-23	257	16	b	b	PROPN
ejpam-23	257	17	∈	∈	PROPN
ejpam-23	257	18	sd(α	sd(α	NOUN
ejpam-23	257	19	,	,	PUNCT
ejpam-23	257	20	β	β	NOUN
ejpam-23	257	21	)	)	PUNCT
ejpam-23	257	22	.	.	PUNCT
ejpam-23	258	1	since	since	SCONJ
ejpam-23	258	2	h̃	h̃	PROPN
ejpam-23	258	3	is	be	AUX
ejpam-23	258	4	a	a	DET
ejpam-23	258	5	band	band	NOUN
ejpam-23	258	6	congruence	congruence	NOUN
ejpam-23	258	7	on	on	ADP
ejpam-23	258	8	s	s	PROPN
ejpam-23	258	9	,	,	PUNCT
ejpam-23	258	10	by	by	ADP
ejpam-23	258	11	lemma	lemma	PROPN
ejpam-23	258	12	2.6	2.6	NUM
ejpam-23	258	13	(	(	PUNCT
ejpam-23	258	14	i	i	NOUN
ejpam-23	258	15	)	)	PUNCT
ejpam-23	258	16	again	again	ADV
ejpam-23	258	17	,	,	PUNCT
ejpam-23	258	18	we	we	PRON
ejpam-23	258	19	see	see	VERB
ejpam-23	258	20	that	that	PRON
ejpam-23	258	21	a(aba)0	a(aba)0	NOUN
ejpam-23	258	22	,	,	PUNCT
ejpam-23	258	23	(	(	PUNCT
ejpam-23	258	24	aba)0	aba)0	PROPN
ejpam-23	258	25	and	and	CCONJ
ejpam-23	258	26	(	(	PUNCT
ejpam-23	258	27	aba)0a	aba)0a	NOUN
ejpam-23	258	28	are	be	AUX
ejpam-23	258	29	in	in	ADP
ejpam-23	258	30	the	the	DET
ejpam-23	258	31	same	same	ADJ
ejpam-23	258	32	h̃-class	h̃-class	NOUN
ejpam-23	258	33	of	of	ADP
ejpam-23	258	34	s	s	PRON
ejpam-23	258	35	so	so	SCONJ
ejpam-23	258	36	that	that	SCONJ
ejpam-23	258	37	a(aba)0	a(aba)0	NOUN
ejpam-23	259	1	=	=	PUNCT
ejpam-23	260	1	(	(	PUNCT
ejpam-23	260	2	aba)0a(aba)0	aba)0a(aba)0	PROPN
ejpam-23	260	3	=	=	SYM
ejpam-23	260	4	(	(	PUNCT
ejpam-23	260	5	aba)0a	aba)0a	PROPN
ejpam-23	260	6	.	.	PUNCT
ejpam-23	260	7	let	let	VERB
ejpam-23	260	8	a(aba)0	a(aba)0	NOUN
ejpam-23	260	9	=	=	PUNCT
ejpam-23	260	10	ad(α	ad(α	NOUN
ejpam-23	260	11	,	,	PUNCT
ejpam-23	260	12	β	β	NOUN
ejpam-23	260	13	)	)	PUNCT
ejpam-23	260	14	.	.	PUNCT
ejpam-23	261	1	then	then	ADV
ejpam-23	261	2	by	by	ADP
ejpam-23	261	3	the	the	DET
ejpam-23	261	4	natural	natural	ADJ
ejpam-23	261	5	partial	partial	ADJ
ejpam-23	261	6	order	order	NOUN
ejpam-23	261	7	imposed	impose	VERB
ejpam-23	261	8	on	on	ADP
ejpam-23	261	9	s	s	PROPN
ejpam-23	261	10	,	,	PUNCT
ejpam-23	261	11	we	we	PRON
ejpam-23	261	12	have	have	VERB
ejpam-23	261	13	a	a	DET
ejpam-23	261	14	>	>	X
ejpam-23	261	15	ad(α	ad(α	NOUN
ejpam-23	261	16	,	,	PUNCT
ejpam-23	261	17	β	β	NOUN
ejpam-23	261	18	)	)	PUNCT
ejpam-23	261	19	.	.	PUNCT
ejpam-23	262	1	in	in	ADP
ejpam-23	262	2	order	order	NOUN
ejpam-23	262	3	to	to	PART
ejpam-23	262	4	show	show	VERB
ejpam-23	262	5	the	the	DET
ejpam-23	262	6	uniqueness	uniqueness	NOUN
ejpam-23	262	7	of	of	ADP
ejpam-23	262	8	ad(α	ad(α	PROPN
ejpam-23	262	9	,	,	PUNCT
ejpam-23	262	10	β	β	NOUN
ejpam-23	262	11	)	)	PUNCT
ejpam-23	262	12	,	,	PUNCT
ejpam-23	262	13	we	we	PRON
ejpam-23	262	14	assume	assume	VERB
ejpam-23	262	15	that	that	SCONJ
ejpam-23	262	16	there	there	PRON
ejpam-23	262	17	is	be	VERB
ejpam-23	262	18	another	another	DET
ejpam-23	262	19	a∗d(α	a∗d(α	PROPN
ejpam-23	262	20	,	,	PUNCT
ejpam-23	262	21	β	β	X
ejpam-23	262	22	)	)	PUNCT
ejpam-23	262	23	∈	∈	PROPN
ejpam-23	262	24	sd(α	sd(α	NOUN
ejpam-23	262	25	,	,	PUNCT
ejpam-23	262	26	β	β	X
ejpam-23	262	27	)	)	PUNCT
ejpam-23	262	28	satisfying	satisfy	VERB
ejpam-23	262	29	a	a	DET
ejpam-23	262	30	>	>	X
ejpam-23	262	31	a∗d(α	a∗d(α	PROPN
ejpam-23	262	32	,	,	PUNCT
ejpam-23	262	33	β	β	NOUN
ejpam-23	262	34	)	)	PUNCT
ejpam-23	262	35	.	.	PUNCT
ejpam-23	263	1	then	then	ADV
ejpam-23	263	2	,	,	PUNCT
ejpam-23	263	3	by	by	ADP
ejpam-23	263	4	the	the	DET
ejpam-23	263	5	definition	definition	NOUN
ejpam-23	263	6	of	of	ADP
ejpam-23	263	7	“	"	PUNCT
ejpam-23	263	8	6	6	NUM
ejpam-23	263	9	”	"	PUNCT
ejpam-23	263	10	,	,	PUNCT
ejpam-23	263	11	we	we	PRON
ejpam-23	263	12	can	can	AUX
ejpam-23	263	13	write	write	VERB
ejpam-23	263	14	a∗d(α	a∗d(α	PROPN
ejpam-23	263	15	,	,	PUNCT
ejpam-23	263	16	β	β	NOUN
ejpam-23	263	17	)	)	PUNCT
ejpam-23	263	18	=	=	SYM
ejpam-23	263	19	ea	ea	X
ejpam-23	263	20	=	=	PUNCT
ejpam-23	263	21	af	af	VERB
ejpam-23	263	22	for	for	ADP
ejpam-23	263	23	some	some	DET
ejpam-23	263	24	e	e	NOUN
ejpam-23	263	25	,	,	PUNCT
ejpam-23	263	26	f	f	PROPN
ejpam-23	263	27	∈	∈	PROPN
ejpam-23	263	28	e(s	e(s	PROPN
ejpam-23	263	29	)	)	PUNCT
ejpam-23	263	30	and	and	CCONJ
ejpam-23	263	31	so	so	ADV
ejpam-23	263	32	a∗d(α	a∗d(α	NOUN
ejpam-23	263	33	,	,	PUNCT
ejpam-23	263	34	β)a	β)a	PUNCT
ejpam-23	263	35	0	0	X
ejpam-23	264	1	=	=	SYM
ejpam-23	264	2	a∗d(α	a∗d(α	PROPN
ejpam-23	264	3	,	,	PUNCT
ejpam-23	264	4	β	β	NOUN
ejpam-23	264	5	)	)	PUNCT
ejpam-23	264	6	=	=	SYM
ejpam-23	264	7	a0a∗d(α	a0a∗d(α	PROPN
ejpam-23	264	8	,	,	PUNCT
ejpam-23	264	9	β	β	NOUN
ejpam-23	264	10	)	)	PUNCT
ejpam-23	264	11	.	.	PUNCT
ejpam-23	265	1	by	by	ADP
ejpam-23	265	2	the	the	DET
ejpam-23	265	3	fact	fact	NOUN
ejpam-23	265	4	a∗d(α	a∗d(α	NOUN
ejpam-23	265	5	,	,	PUNCT
ejpam-23	265	6	β)h̃a0	β)h̃a0	PROPN
ejpam-23	265	7	,	,	PUNCT
ejpam-23	265	8	we	we	PRON
ejpam-23	265	9	have	have	VERB
ejpam-23	265	10	(	(	PUNCT
ejpam-23	265	11	a∗d(α	a∗d(α	PROPN
ejpam-23	265	12	,	,	PUNCT
ejpam-23	265	13	β	β	NOUN
ejpam-23	265	14	)	)	PUNCT
ejpam-23	265	15	)	)	PUNCT
ejpam-23	265	16	0a0	0a0	X
ejpam-23	266	1	=	=	SYM
ejpam-23	266	2	(	(	PUNCT
ejpam-23	266	3	a∗d(α	a∗d(α	PROPN
ejpam-23	266	4	,	,	PUNCT
ejpam-23	266	5	β	β	NOUN
ejpam-23	266	6	)	)	PUNCT
ejpam-23	266	7	)	)	PUNCT
ejpam-23	266	8	0	0	NUM
ejpam-23	266	9	and	and	CCONJ
ejpam-23	266	10	a0(a∗d(α	a0(a∗d(α	NOUN
ejpam-23	266	11	,	,	PUNCT
ejpam-23	266	12	β	β	NOUN
ejpam-23	266	13	)	)	PUNCT
ejpam-23	266	14	)	)	PUNCT
ejpam-23	266	15	0	0	NUM
ejpam-23	267	1	=	=	SYM
ejpam-23	267	2	(	(	PUNCT
ejpam-23	267	3	a∗d(α	a∗d(α	PROPN
ejpam-23	267	4	,	,	PUNCT
ejpam-23	267	5	β	β	NOUN
ejpam-23	267	6	)	)	PUNCT
ejpam-23	267	7	)	)	PUNCT
ejpam-23	267	8	0	0	X
ejpam-23	267	9	.	.	PUNCT
ejpam-23	268	1	consequently	consequently	ADV
ejpam-23	268	2	,	,	PUNCT
ejpam-23	268	3	by	by	ADP
ejpam-23	268	4	the	the	DET
ejpam-23	268	5	definition	definition	NOUN
ejpam-23	268	6	of	of	ADP
ejpam-23	268	7	“	"	PUNCT
ejpam-23	268	8	6	6	NUM
ejpam-23	268	9	”	"	PUNCT
ejpam-23	268	10	,	,	PUNCT
ejpam-23	268	11	we	we	PRON
ejpam-23	268	12	have	have	VERB
ejpam-23	268	13	a0	a0	PROPN
ejpam-23	268	14	>	>	X
ejpam-23	268	15	(	(	PUNCT
ejpam-23	268	16	a∗d(α	a∗d(α	PROPN
ejpam-23	268	17	,	,	PUNCT
ejpam-23	268	18	β	β	NOUN
ejpam-23	268	19	)	)	PUNCT
ejpam-23	268	20	)	)	PUNCT
ejpam-23	268	21	0	0	X
ejpam-23	268	22	.	.	PUNCT
ejpam-23	269	1	by	by	ADP
ejpam-23	269	2	lemma	lemma	PROPN
ejpam-23	269	3	2.6	2.6	NUM
ejpam-23	269	4	(	(	PUNCT
ejpam-23	269	5	i	i	NOUN
ejpam-23	269	6	)	)	PUNCT
ejpam-23	269	7	again	again	ADV
ejpam-23	269	8	,	,	PUNCT
ejpam-23	269	9	we	we	PRON
ejpam-23	269	10	deduce	deduce	VERB
ejpam-23	269	11	that	that	PRON
ejpam-23	269	12	(	(	PUNCT
ejpam-23	269	13	a∗d(α	a∗d(α	PROPN
ejpam-23	269	14	,	,	PUNCT
ejpam-23	269	15	β	β	NOUN
ejpam-23	269	16	)	)	PUNCT
ejpam-23	269	17	)	)	PUNCT
ejpam-23	269	18	0	0	NUM
ejpam-23	270	1	=	=	SYM
ejpam-23	270	2	(	(	PUNCT
ejpam-23	270	3	a0(a∗d(α	a0(a∗d(α	NOUN
ejpam-23	270	4	,	,	PUNCT
ejpam-23	270	5	β	β	NOUN
ejpam-23	270	6	)	)	PUNCT
ejpam-23	270	7	)	)	PUNCT
ejpam-23	271	1	0a0)0	0a0)0	PROPN
ejpam-23	271	2	=	=	SYM
ejpam-23	271	3	(	(	PUNCT
ejpam-23	271	4	aa∗d(α	aa∗d(α	PROPN
ejpam-23	271	5	,	,	PUNCT
ejpam-23	271	6	β)a)0	β)a)0	ADJ
ejpam-23	271	7	=	=	SYM
ejpam-23	271	8	(	(	PUNCT
ejpam-23	271	9	aba)0	aba)0	PROPN
ejpam-23	271	10	.	.	PUNCT
ejpam-23	272	1	hence	hence	ADV
ejpam-23	272	2	,	,	PUNCT
ejpam-23	272	3	(	(	PUNCT
ejpam-23	272	4	a∗d(α	a∗d(α	PROPN
ejpam-23	272	5	,	,	PUNCT
ejpam-23	272	6	β	β	NOUN
ejpam-23	272	7	)	)	PUNCT
ejpam-23	272	8	,	,	PUNCT
ejpam-23	272	9	ad(α	ad(α	PROPN
ejpam-23	272	10	,	,	PUNCT
ejpam-23	272	11	β	β	NOUN
ejpam-23	272	12	)	)	PUNCT
ejpam-23	272	13	)	)	PUNCT
ejpam-23	273	1	∈	∈	PROPN
ejpam-23	273	2	h̃	h̃	PROPN
ejpam-23	273	3	,	,	PUNCT
ejpam-23	273	4	and	and	CCONJ
ejpam-23	273	5	consequently	consequently	ADV
ejpam-23	273	6	,	,	PUNCT
ejpam-23	273	7	by	by	ADP
ejpam-23	273	8	theorem	theorem	ADJ
ejpam-23	273	9	2.10	2.10	NUM
ejpam-23	273	10	(	(	PUNCT
ejpam-23	273	11	ii	ii	NOUN
ejpam-23	273	12	)	)	PUNCT
ejpam-23	273	13	,	,	PUNCT
ejpam-23	273	14	a∗d(α	a∗d(α	PROPN
ejpam-23	273	15	,	,	PUNCT
ejpam-23	273	16	β	β	NOUN
ejpam-23	273	17	)	)	PUNCT
ejpam-23	273	18	=	=	SYM
ejpam-23	273	19	ad(α	ad(α	NOUN
ejpam-23	273	20	,	,	PUNCT
ejpam-23	273	21	β	β	NOUN
ejpam-23	273	22	)	)	PUNCT
ejpam-23	273	23	.	.	PUNCT
ejpam-23	274	1	this	this	PRON
ejpam-23	274	2	shows	show	VERB
ejpam-23	274	3	the	the	DET
ejpam-23	274	4	uniqueness	uniqueness	NOUN
ejpam-23	274	5	of	of	ADP
ejpam-23	274	6	ad(α	ad(α	PROPN
ejpam-23	274	7	,	,	PUNCT
ejpam-23	274	8	β	β	NOUN
ejpam-23	274	9	)	)	PUNCT
ejpam-23	274	10	.	.	PUNCT
ejpam-23	275	1	(	(	PUNCT
ejpam-23	275	2	ii	ii	X
ejpam-23	275	3	)	)	PUNCT
ejpam-23	275	4	it	it	PRON
ejpam-23	275	5	is	be	AUX
ejpam-23	275	6	easy	easy	ADJ
ejpam-23	275	7	to	to	PART
ejpam-23	275	8	see	see	VERB
ejpam-23	275	9	that	that	PRON
ejpam-23	275	10	,	,	PUNCT
ejpam-23	275	11	by	by	ADP
ejpam-23	275	12	the	the	DET
ejpam-23	275	13	definition	definition	NOUN
ejpam-23	275	14	of	of	ADP
ejpam-23	275	15	“	"	PUNCT
ejpam-23	275	16	6	6	NUM
ejpam-23	275	17	”	"	PUNCT
ejpam-23	275	18	,	,	PUNCT
ejpam-23	275	19	a0	a0	PROPN
ejpam-23	275	20	>	>	X
ejpam-23	275	21	(	(	PUNCT
ejpam-23	275	22	a0(ax)0a0)0	a0(ax)0a0)0	PROPN
ejpam-23	275	23	.	.	PUNCT
ejpam-23	276	1	also	also	ADV
ejpam-23	276	2	,	,	PUNCT
ejpam-23	276	3	since	since	SCONJ
ejpam-23	276	4	a	a	DET
ejpam-23	276	5	∈	∈	NOUN
ejpam-23	276	6	sα	sα	ADV
ejpam-23	276	7	and	and	CCONJ
ejpam-23	276	8	x	x	SYM
ejpam-23	276	9	∈	∈	PROPN
ejpam-23	276	10	sd(α	sd(α	NOUN
ejpam-23	276	11	,	,	PUNCT
ejpam-23	276	12	β	β	NOUN
ejpam-23	276	13	)	)	PUNCT
ejpam-23	276	14	,	,	PUNCT
ejpam-23	276	15	we	we	PRON
ejpam-23	276	16	have	have	VERB
ejpam-23	276	17	ax	ax	NOUN
ejpam-23	276	18	∈	∈	PROPN
ejpam-23	276	19	sd(α	sd(α	X
ejpam-23	276	20	,	,	PUNCT
ejpam-23	276	21	β	β	NOUN
ejpam-23	276	22	)	)	PUNCT
ejpam-23	276	23	by	by	ADP
ejpam-23	276	24	(	(	PUNCT
ejpam-23	276	25	i	i	NOUN
ejpam-23	276	26	)	)	PUNCT
ejpam-23	276	27	.	.	PUNCT
ejpam-23	277	1	moreover	moreover	ADV
ejpam-23	277	2	,	,	PUNCT
ejpam-23	277	3	since	since	SCONJ
ejpam-23	277	4	sd(α	sd(α	NOUN
ejpam-23	277	5	,	,	PUNCT
ejpam-23	277	6	β	β	X
ejpam-23	277	7	)	)	PUNCT
ejpam-23	277	8	is	be	AUX
ejpam-23	277	9	a	a	DET
ejpam-23	277	10	ρα	ρα	PROPN
ejpam-23	277	11	,	,	PUNCT
ejpam-23	277	12	β	β	NOUN
ejpam-23	277	13	-congruence	-congruence	NOUN
ejpam-23	277	14	class	class	NOUN
ejpam-23	277	15	,	,	PUNCT
ejpam-23	277	16	(	(	PUNCT
ejpam-23	277	17	ax)0	ax)0	PROPN
ejpam-23	277	18	∈	∈	PROPN
ejpam-23	277	19	sd(α	sd(α	NOUN
ejpam-23	277	20	,	,	PUNCT
ejpam-23	277	21	β	β	NOUN
ejpam-23	277	22	)	)	PUNCT
ejpam-23	277	23	.	.	PUNCT
ejpam-23	278	1	thus	thus	ADV
ejpam-23	278	2	,	,	PUNCT
ejpam-23	278	3	by	by	ADP
ejpam-23	278	4	(	(	PUNCT
ejpam-23	278	5	i	i	NOUN
ejpam-23	278	6	)	)	PUNCT
ejpam-23	278	7	again	again	ADV
ejpam-23	278	8	,	,	PUNCT
ejpam-23	278	9	we	we	PRON
ejpam-23	278	10	have	have	VERB
ejpam-23	278	11	(	(	PUNCT
ejpam-23	278	12	a0(ax)0a0)0	a0(ax)0a0)0	PROPN
ejpam-23	278	13	∈	∈	PROPN
ejpam-23	278	14	sd(α	sd(α	NOUN
ejpam-23	278	15	,	,	PUNCT
ejpam-23	278	16	β	β	NOUN
ejpam-23	278	17	)	)	PUNCT
ejpam-23	278	18	and	and	CCONJ
ejpam-23	278	19	e	e	X
ejpam-23	278	20	=	=	SYM
ejpam-23	278	21	(	(	PUNCT
ejpam-23	278	22	a0(ax)0a0)0	a0(ax)0a0)0	PROPN
ejpam-23	278	23	.	.	PUNCT
ejpam-23	279	1	thereby	thereby	ADV
ejpam-23	279	2	,	,	PUNCT
ejpam-23	279	3	we	we	PRON
ejpam-23	279	4	have	have	VERB
ejpam-23	279	5	eax	eax	NOUN
ejpam-23	279	6	=	=	SYM
ejpam-23	279	7	(	(	PUNCT
ejpam-23	279	8	a0(ax)0a0)0a0(ax)0a0ax	a0(ax)0a0)0a0(ax)0a0ax	X
ejpam-23	279	9	=	=	NOUN
ejpam-23	279	10	ax	ax	NOUN
ejpam-23	279	11	.	.	PUNCT
ejpam-23	280	1	similarly	similarly	ADV
ejpam-23	280	2	,	,	PUNCT
ejpam-23	280	3	we	we	PRON
ejpam-23	280	4	have	have	VERB
ejpam-23	280	5	xae	xae	PROPN
ejpam-23	280	6	=	=	SYM
ejpam-23	280	7	xa	xa	PROPN
ejpam-23	280	8	.	.	PUNCT
ejpam-23	281	1	since	since	SCONJ
ejpam-23	281	2	x	x	PRON
ejpam-23	281	3	is	be	AUX
ejpam-23	281	4	arbitrarily	arbitrarily	ADV
ejpam-23	281	5	chosen	choose	VERB
ejpam-23	281	6	element	element	NOUN
ejpam-23	281	7	in	in	ADP
ejpam-23	281	8	sd(α	sd(α	PROPN
ejpam-23	281	9	,	,	PUNCT
ejpam-23	281	10	β	β	NOUN
ejpam-23	281	11	)	)	PUNCT
ejpam-23	281	12	,	,	PUNCT
ejpam-23	281	13	we	we	PRON
ejpam-23	281	14	can	can	AUX
ejpam-23	281	15	particularly	particularly	ADV
ejpam-23	281	16	choose	choose	VERB
ejpam-23	281	17	x	x	X
ejpam-23	281	18	=	=	SYM
ejpam-23	281	19	e.	e.	PROPN
ejpam-23	281	20	in	in	ADP
ejpam-23	281	21	this	this	DET
ejpam-23	281	22	way	way	NOUN
ejpam-23	281	23	,	,	PUNCT
ejpam-23	281	24	we	we	PRON
ejpam-23	281	25	obtain	obtain	VERB
ejpam-23	281	26	ea	ea	X
ejpam-23	282	1	=	=	SYM
ejpam-23	282	2	ae	ae	PROPN
ejpam-23	282	3	and	and	CCONJ
ejpam-23	282	4	consequently	consequently	ADV
ejpam-23	282	5	,	,	PUNCT
ejpam-23	282	6	by	by	ADP
ejpam-23	282	7	lemma	lemma	PROPN
ejpam-23	282	8	2.6	2.6	NUM
ejpam-23	282	9	(	(	PUNCT
ejpam-23	282	10	i	i	PROPN
ejpam-23	282	11	)	)	PUNCT
ejpam-23	282	12	,	,	PUNCT
ejpam-23	282	13	we	we	PRON
ejpam-23	282	14	have	have	VERB
ejpam-23	282	15	(	(	PUNCT
ejpam-23	283	1	ea)0	ea)0	PROPN
ejpam-23	283	2	=	=	SYM
ejpam-23	283	3	(	(	PUNCT
ejpam-23	283	4	ea0)0	ea0)0	PROPN
ejpam-23	283	5	=	=	SYM
ejpam-23	283	6	e.	e.	PROPN
ejpam-23	283	7	(	(	PUNCT
ejpam-23	283	8	iii	iii	PROPN
ejpam-23	283	9	)	)	PUNCT
ejpam-23	283	10	by	by	ADP
ejpam-23	283	11	using	use	VERB
ejpam-23	283	12	the	the	DET
ejpam-23	283	13	result	result	NOUN
ejpam-23	283	14	in	in	ADP
ejpam-23	283	15	(	(	PUNCT
ejpam-23	283	16	i	i	NOUN
ejpam-23	283	17	)	)	PUNCT
ejpam-23	283	18	,	,	PUNCT
ejpam-23	283	19	we	we	PRON
ejpam-23	283	20	can	can	AUX
ejpam-23	283	21	define	define	VERB
ejpam-23	283	22	ϕd(α	ϕd(α	NOUN
ejpam-23	283	23	,	,	PUNCT
ejpam-23	283	24	β	β	NOUN
ejpam-23	283	25	)	)	PUNCT
ejpam-23	283	26	:	:	PUNCT
ejpam-23	283	27	sα	sα	ADV
ejpam-23	283	28	−→	−→	NOUN
ejpam-23	283	29	sd(α	sd(α	NOUN
ejpam-23	283	30	,	,	PUNCT
ejpam-23	283	31	β	β	X
ejpam-23	283	32	)	)	PUNCT
ejpam-23	283	33	by	by	ADP
ejpam-23	283	34	aϕd(α	aϕd(α	NOUN
ejpam-23	283	35	,	,	PUNCT
ejpam-23	283	36	β	β	X
ejpam-23	283	37	)	)	PUNCT
ejpam-23	283	38	=	=	SYM
ejpam-23	283	39	ad(α	ad(α	NOUN
ejpam-23	283	40	,	,	PUNCT
ejpam-23	283	41	β	β	X
ejpam-23	283	42	)	)	PUNCT
ejpam-23	283	43	=	=	SYM
ejpam-23	284	1	a(aca)0	a(aca)0	X
ejpam-23	284	2	=	=	PUNCT
ejpam-23	284	3	(	(	PUNCT
ejpam-23	284	4	aca)0a	aca)0a	NOUN
ejpam-23	284	5	,	,	PUNCT
ejpam-23	284	6	for	for	ADP
ejpam-23	284	7	any	any	DET
ejpam-23	284	8	a	a	DET
ejpam-23	284	9	∈	∈	NOUN
ejpam-23	284	10	sα	sα	ADV
ejpam-23	284	11	and	and	CCONJ
ejpam-23	284	12	c	c	NOUN
ejpam-23	284	13	∈	∈	PROPN
ejpam-23	284	14	sd(α	sd(α	PROPN
ejpam-23	284	15	,	,	PUNCT
ejpam-23	284	16	β	β	NOUN
ejpam-23	284	17	)	)	PUNCT
ejpam-23	284	18	.	.	PUNCT
ejpam-23	285	1	then	then	ADV
ejpam-23	285	2	,	,	PUNCT
ejpam-23	285	3	for	for	ADP
ejpam-23	285	4	any	any	DET
ejpam-23	285	5	a	a	PRON
ejpam-23	285	6	,	,	PUNCT
ejpam-23	285	7	b	b	X
ejpam-23	285	8	∈	∈	PROPN
ejpam-23	285	9	sα	sα	ADV
ejpam-23	285	10	,	,	PUNCT
ejpam-23	285	11	we	we	PRON
ejpam-23	285	12	have	have	AUX
ejpam-23	285	13	,	,	PUNCT
ejpam-23	285	14	by	by	ADP
ejpam-23	285	15	(	(	PUNCT
ejpam-23	285	16	ii	ii	NOUN
ejpam-23	285	17	)	)	PUNCT
ejpam-23	285	18	,	,	PUNCT
ejpam-23	285	19	(	(	PUNCT
ejpam-23	285	20	aϕd(α	aϕd(α	PROPN
ejpam-23	285	21	,	,	PUNCT
ejpam-23	285	22	β))(bϕd(α	β))(bϕd(α	PROPN
ejpam-23	285	23	,	,	PUNCT
ejpam-23	285	24	β	β	NOUN
ejpam-23	285	25	)	)	PUNCT
ejpam-23	285	26	)	)	PUNCT
ejpam-23	286	1	=	=	PUNCT
ejpam-23	286	2	ad(α	ad(α	NOUN
ejpam-23	286	3	,	,	PUNCT
ejpam-23	286	4	β)bd(α	β)bd(α	NOUN
ejpam-23	286	5	,	,	PUNCT
ejpam-23	286	6	β	β	X
ejpam-23	286	7	)	)	PUNCT
ejpam-23	286	8	=	=	SYM
ejpam-23	286	9	(	(	PUNCT
ejpam-23	286	10	aca)0ab(bcb)0	aca)0ab(bcb)0	PROPN
ejpam-23	286	11	=	=	PRON
ejpam-23	286	12	(	(	PUNCT
ejpam-23	286	13	aca)0(ab(bcb)0	aca)0(ab(bcb)0	NUM
ejpam-23	286	14	)	)	PUNCT
ejpam-23	286	15	=	=	SYM
ejpam-23	286	16	ab(bcb)0	ab(bcb)0	PROPN
ejpam-23	286	17	.	.	PUNCT
ejpam-23	287	1	similarly	similarly	ADV
ejpam-23	287	2	,	,	PUNCT
ejpam-23	287	3	we	we	PRON
ejpam-23	287	4	can	can	AUX
ejpam-23	287	5	show	show	VERB
ejpam-23	287	6	that	that	SCONJ
ejpam-23	287	7	(	(	PUNCT
ejpam-23	287	8	aϕd(α	aϕd(α	PROPN
ejpam-23	287	9	,	,	PUNCT
ejpam-23	287	10	β))(bϕd(α	β))(bϕd(α	PROPN
ejpam-23	287	11	,	,	PUNCT
ejpam-23	287	12	β	β	NOUN
ejpam-23	287	13	)	)	PUNCT
ejpam-23	287	14	)	)	PUNCT
ejpam-23	288	1	=	=	SYM
ejpam-23	288	2	(	(	PUNCT
ejpam-23	288	3	aca)0ab	aca)0ab	NOUN
ejpam-23	288	4	.	.	PUNCT
ejpam-23	289	1	hence	hence	ADV
ejpam-23	289	2	,	,	PUNCT
ejpam-23	289	3	ab	ab	PROPN
ejpam-23	289	4	>	>	X
ejpam-23	289	5	(	(	PUNCT
ejpam-23	289	6	aϕd(α	aϕd(α	PROPN
ejpam-23	289	7	,	,	PUNCT
ejpam-23	289	8	β))(bϕd(α	β))(bϕd(α	PROPN
ejpam-23	289	9	,	,	PUNCT
ejpam-23	289	10	β	β	NOUN
ejpam-23	289	11	)	)	PUNCT
ejpam-23	289	12	)	)	PUNCT
ejpam-23	289	13	.	.	PUNCT
ejpam-23	290	1	thus	thus	ADV
ejpam-23	290	2	(	(	PUNCT
ejpam-23	290	3	ab)ϕd(α	ab)ϕd(α	PROPN
ejpam-23	290	4	,	,	PUNCT
ejpam-23	290	5	β	β	NOUN
ejpam-23	290	6	)	)	PUNCT
ejpam-23	290	7	=	=	SYM
ejpam-23	290	8	(	(	PUNCT
ejpam-23	290	9	aϕd(α	aϕd(α	PROPN
ejpam-23	290	10	,	,	PUNCT
ejpam-23	290	11	β))(bϕd(α	β))(bϕd(α	PROPN
ejpam-23	290	12	,	,	PUNCT
ejpam-23	290	13	β	β	NOUN
ejpam-23	290	14	)	)	PUNCT
ejpam-23	290	15	)	)	PUNCT
ejpam-23	290	16	,	,	PUNCT
ejpam-23	290	17	by	by	ADP
ejpam-23	290	18	the	the	DET
ejpam-23	290	19	definition	definition	NOUN
ejpam-23	290	20	of	of	ADP
ejpam-23	290	21	ϕd(α	ϕd(α	PROPN
ejpam-23	290	22	,	,	PUNCT
ejpam-23	290	23	β	β	NOUN
ejpam-23	290	24	)	)	PUNCT
ejpam-23	290	25	.	.	PUNCT
ejpam-23	291	1	this	this	PRON
ejpam-23	291	2	shows	show	VERB
ejpam-23	291	3	that	that	SCONJ
ejpam-23	291	4	ϕd(α	ϕd(α	ADV
ejpam-23	291	5	,	,	PUNCT
ejpam-23	291	6	β	β	X
ejpam-23	291	7	)	)	PUNCT
ejpam-23	291	8	is	be	AUX
ejpam-23	291	9	indeed	indeed	ADV
ejpam-23	291	10	a	a	DET
ejpam-23	291	11	homomorphism	homomorphism	NOUN
ejpam-23	291	12	.	.	PUNCT
ejpam-23	292	1	we	we	PRON
ejpam-23	292	2	now	now	ADV
ejpam-23	292	3	proceed	proceed	VERB
ejpam-23	292	4	to	to	PART
ejpam-23	292	5	show	show	VERB
ejpam-23	292	6	that	that	SCONJ
ejpam-23	292	7	the	the	DET
ejpam-23	292	8	homomorphisms	homomorphism	NOUN
ejpam-23	292	9	given	give	VERB
ejpam-23	292	10	in	in	ADP
ejpam-23	292	11	lemma	lemma	PROPN
ejpam-23	292	12	3.2	3.2	NUM
ejpam-23	292	13	(	(	PUNCT
ejpam-23	292	14	iii	iii	NOUN
ejpam-23	292	15	)	)	PUNCT
ejpam-23	292	16	are	be	AUX
ejpam-23	292	17	the	the	DET
ejpam-23	292	18	structural	structural	ADJ
ejpam-23	292	19	homomorphisms	homomorphism	NOUN
ejpam-23	292	20	for	for	ADP
ejpam-23	292	21	the	the	DET
ejpam-23	292	22	g	g	NOUN
ejpam-23	292	23	-	-	PUNCT
ejpam-23	292	24	strong	strong	ADJ
ejpam-23	292	25	semilattice	semilattice	NOUN
ejpam-23	292	26	g[y	g[y	NOUN
ejpam-23	292	27	;	;	PUNCT
ejpam-23	292	28	sα	sα	ADV
ejpam-23	292	29	,	,	PUNCT
ejpam-23	292	30	ϕα	ϕα	ADV
ejpam-23	292	31	,	,	PUNCT
ejpam-23	292	32	β	β	X
ejpam-23	292	33	]	]	PUNCT
ejpam-23	292	34	induced	induce	VERB
ejpam-23	292	35	by	by	ADP
ejpam-23	292	36	the	the	DET
ejpam-23	292	37	semigroup	semigroup	NOUN
ejpam-23	292	38	s	s	PART
ejpam-23	292	39	=	=	PUNCT
ejpam-23	292	40	(	(	PUNCT
ejpam-23	292	41	y	y	PROPN
ejpam-23	292	42	;	;	PUNCT
ejpam-23	292	43	sα	sα	X
ejpam-23	292	44	)	)	PUNCT
ejpam-23	292	45	under	under	ADP
ejpam-23	292	46	the	the	DET
ejpam-23	292	47	band	band	NOUN
ejpam-23	292	48	congruence	congruence	NOUN
ejpam-23	292	49	ρα	ρα	PROPN
ejpam-23	292	50	on	on	ADP
ejpam-23	292	51	the	the	DET
ejpam-23	292	52	semigroup	semigroup	PROPN
ejpam-23	292	53	sα	sα	PROPN
ejpam-23	292	54	.	.	PROPN
ejpam-23	292	55	x.	x.	PROPN
ejpam-23	292	56	kong	kong	PROPN
ejpam-23	292	57	,	,	PUNCT
ejpam-23	292	58	y.ding	y.de	VERB
ejpam-23	292	59	,	,	PUNCT
ejpam-23	292	60	k.p.shum	k.p.shum	ADJ
ejpam-23	292	61	/	/	SYM
ejpam-23	292	62	eur	eur	PROPN
ejpam-23	292	63	.	.	PUNCT
ejpam-23	293	1	j.	j.	PROPN
ejpam-23	293	2	pure	pure	PROPN
ejpam-23	293	3	appl	appl	PROPN
ejpam-23	293	4	.	.	PROPN
ejpam-23	293	5	math	math	PROPN
ejpam-23	293	6	,	,	PUNCT
ejpam-23	293	7	1	1	NUM
ejpam-23	293	8	(	(	PUNCT
ejpam-23	293	9	2008	2008	NUM
ejpam-23	293	10	)	)	PUNCT
ejpam-23	293	11	,	,	PUNCT
ejpam-23	293	12	(	(	PUNCT
ejpam-23	293	13	46	46	NUM
ejpam-23	293	14	-	-	SYM
ejpam-23	293	15	59	59	NUM
ejpam-23	293	16	)	)	PUNCT
ejpam-23	293	17	55	55	NUM
ejpam-23	293	18	lemma	lemma	PROPN
ejpam-23	293	19	3.3	3.3	NUM
ejpam-23	293	20	let	let	VERB
ejpam-23	293	21	s	s	VERB
ejpam-23	293	22	=	=	PUNCT
ejpam-23	293	23	(	(	PUNCT
ejpam-23	293	24	y	y	PROPN
ejpam-23	293	25	;	;	PUNCT
ejpam-23	293	26	sα	sα	X
ejpam-23	293	27	)	)	PUNCT
ejpam-23	293	28	be	be	AUX
ejpam-23	293	29	an	an	DET
ejpam-23	293	30	h̃	h̃	PROPN
ejpam-23	293	31	-cryptogroup	-cryptogroup	PROPN
ejpam-23	293	32	and	and	CCONJ
ejpam-23	293	33	ϕα	ϕα	ADV
ejpam-23	293	34	,	,	PUNCT
ejpam-23	293	35	β	β	X
ejpam-23	293	36	=	=	SYM
ejpam-23	293	37	{	{	PUNCT
ejpam-23	293	38	ϕd(α	ϕd(α	PROPN
ejpam-23	293	39	,	,	PUNCT
ejpam-23	293	40	β	β	NOUN
ejpam-23	293	41	)	)	PUNCT
ejpam-23	294	1	|	|	ADV
ejpam-23	294	2	d(α	d(α	PROPN
ejpam-23	294	3	,	,	PUNCT
ejpam-23	294	4	β	β	X
ejpam-23	294	5	)	)	PUNCT
ejpam-23	294	6	∈	∈	PROPN
ejpam-23	294	7	d(α	d(α	PROPN
ejpam-23	294	8	,	,	PUNCT
ejpam-23	294	9	β	β	NOUN
ejpam-23	294	10	)	)	PUNCT
ejpam-23	294	11	}	}	PUNCT
ejpam-23	294	12	for	for	ADP
ejpam-23	294	13	α	α	X
ejpam-23	294	14	>	>	X
ejpam-23	294	15	β	β	X
ejpam-23	294	16	on	on	ADP
ejpam-23	294	17	y	y	PROPN
ejpam-23	294	18	,	,	PUNCT
ejpam-23	294	19	where	where	SCONJ
ejpam-23	294	20	d(α	d(α	NOUN
ejpam-23	294	21	,	,	PUNCT
ejpam-23	294	22	β	β	NOUN
ejpam-23	294	23	)	)	PUNCT
ejpam-23	294	24	is	be	AUX
ejpam-23	294	25	a	a	DET
ejpam-23	294	26	non	non	ADJ
ejpam-23	294	27	-	-	ADJ
ejpam-23	294	28	empty	empty	ADJ
ejpam-23	294	29	index	index	NOUN
ejpam-23	294	30	set	set	NOUN
ejpam-23	294	31	.	.	PUNCT
ejpam-23	295	1	then	then	ADV
ejpam-23	295	2	(	(	PUNCT
ejpam-23	295	3	i	i	NOUN
ejpam-23	295	4	)	)	PUNCT
ejpam-23	295	5	ϕα	ϕα	ADV
ejpam-23	295	6	,	,	PUNCT
ejpam-23	295	7	βϕβ	βϕβ	PROPN
ejpam-23	295	8	,	,	PUNCT
ejpam-23	295	9	γ	γ	X
ejpam-23	295	10	⊆	⊆	NUM
ejpam-23	295	11	ϕα	ϕα	ADV
ejpam-23	295	12	,	,	PUNCT
ejpam-23	295	13	γ	γ	NOUN
ejpam-23	295	14	for	for	ADP
ejpam-23	295	15	α	α	PROPN
ejpam-23	295	16	>	>	X
ejpam-23	295	17	β	β	X
ejpam-23	295	18	>	>	X
ejpam-23	295	19	γ	γ	X
ejpam-23	295	20	on	on	ADP
ejpam-23	295	21	y	y	PROPN
ejpam-23	295	22	.	.	PUNCT
ejpam-23	296	1	(	(	PUNCT
ejpam-23	296	2	ii	ii	NOUN
ejpam-23	296	3	)	)	PUNCT
ejpam-23	296	4	for	for	ADP
ejpam-23	296	5	a	a	DET
ejpam-23	296	6	∈	∈	PROPN
ejpam-23	296	7	sα	sα	ADV
ejpam-23	296	8	and	and	CCONJ
ejpam-23	296	9	β	β	X
ejpam-23	296	10	∈	∈	PROPN
ejpam-23	296	11	y	y	PROPN
ejpam-23	296	12	,	,	PUNCT
ejpam-23	296	13	aϕα	aϕα	PROPN
ejpam-23	296	14	,	,	PUNCT
ejpam-23	296	15	αβ	αβ	NOUN
ejpam-23	296	16	=	=	PRON
ejpam-23	296	17	{	{	PUNCT
ejpam-23	296	18	aϕd(α	aϕd(α	PROPN
ejpam-23	296	19	,	,	PUNCT
ejpam-23	296	20	αβ)|∀d(α	αβ)|∀d(α	NOUN
ejpam-23	296	21	,	,	PUNCT
ejpam-23	296	22	αβ	αβ	INTJ
ejpam-23	297	1	)	)	PUNCT
ejpam-23	297	2	∈	∈	PROPN
ejpam-23	297	3	d(α	d(α	PROPN
ejpam-23	297	4	,	,	PUNCT
ejpam-23	297	5	αβ	αβ	INTJ
ejpam-23	297	6	)	)	PUNCT
ejpam-23	297	7	}	}	PUNCT
ejpam-23	297	8	⊆	⊆	NUM
ejpam-23	297	9	sd(β	sd(β	NOUN
ejpam-23	297	10	,	,	PUNCT
ejpam-23	297	11	αβ	αβ	NOUN
ejpam-23	297	12	)	)	PUNCT
ejpam-23	297	13	,	,	PUNCT
ejpam-23	297	14	for	for	ADP
ejpam-23	297	15	some	some	DET
ejpam-23	297	16	ρβ	ρβ	PROPN
ejpam-23	297	17	,	,	PUNCT
ejpam-23	297	18	αβ	αβ	NOUN
ejpam-23	297	19	-	-	PUNCT
ejpam-23	297	20	class	class	NOUN
ejpam-23	297	21	sd(β	sd(β	NOUN
ejpam-23	297	22	,	,	PUNCT
ejpam-23	297	23	αβ	αβ	X
ejpam-23	297	24	)	)	PUNCT
ejpam-23	297	25	.	.	PUNCT
ejpam-23	298	1	proof	proof	NOUN
ejpam-23	298	2	.	.	PUNCT
ejpam-23	299	1	(	(	PUNCT
ejpam-23	299	2	i	i	NOUN
ejpam-23	299	3	)	)	PUNCT
ejpam-23	299	4	clearly	clearly	ADV
ejpam-23	299	5	,	,	PUNCT
ejpam-23	299	6	ϕd(α	ϕd(α	PROPN
ejpam-23	299	7	,	,	PUNCT
ejpam-23	299	8	α	α	X
ejpam-23	299	9	)	)	PUNCT
ejpam-23	299	10	is	be	AUX
ejpam-23	299	11	an	an	DET
ejpam-23	299	12	identity	identity	NOUN
ejpam-23	299	13	automorphism	automorphism	NOUN
ejpam-23	299	14	of	of	ADP
ejpam-23	299	15	sα	sα	PROPN
ejpam-23	299	16	.	.	PUNCT
ejpam-23	300	1	we	we	PRON
ejpam-23	300	2	now	now	ADV
ejpam-23	300	3	prove	prove	VERB
ejpam-23	300	4	that	that	SCONJ
ejpam-23	300	5	ϕα	ϕα	ADV
ejpam-23	300	6	,	,	PUNCT
ejpam-23	300	7	βϕβ	βϕβ	PROPN
ejpam-23	300	8	,	,	PUNCT
ejpam-23	300	9	γ	γ	X
ejpam-23	300	10	⊆	⊆	NUM
ejpam-23	300	11	ϕα	ϕα	ADV
ejpam-23	300	12	,	,	PUNCT
ejpam-23	300	13	γ	γ	NOUN
ejpam-23	300	14	for	for	ADP
ejpam-23	300	15	α	α	PROPN
ejpam-23	300	16	>	>	X
ejpam-23	300	17	β	β	X
ejpam-23	300	18	>	>	X
ejpam-23	300	19	γ	γ	X
ejpam-23	300	20	on	on	ADP
ejpam-23	300	21	y	y	PROPN
ejpam-23	300	22	.	.	PUNCT
ejpam-23	301	1	pick	pick	VERB
ejpam-23	301	2	ϕd(α	ϕd(α	PROPN
ejpam-23	301	3	,	,	PUNCT
ejpam-23	301	4	β	β	NOUN
ejpam-23	301	5	)	)	PUNCT
ejpam-23	301	6	:	:	PUNCT
ejpam-23	301	7	sα	sα	ADV
ejpam-23	301	8	−→	−→	NOUN
ejpam-23	301	9	sd(α	sd(α	NOUN
ejpam-23	301	10	,	,	PUNCT
ejpam-23	301	11	β	β	X
ejpam-23	301	12	)	)	PUNCT
ejpam-23	301	13	⊆	⊆	NUM
ejpam-23	301	14	sβ	sβ	NOUN
ejpam-23	301	15	and	and	CCONJ
ejpam-23	301	16	ϕd(β	ϕd(β	NOUN
ejpam-23	301	17	,	,	PUNCT
ejpam-23	301	18	γ	γ	NOUN
ejpam-23	301	19	)	)	PUNCT
ejpam-23	301	20	:	:	PUNCT
ejpam-23	301	21	sβ	sβ	NUM
ejpam-23	301	22	−→	−→	PROPN
ejpam-23	301	23	sd(β	sd(β	NOUN
ejpam-23	301	24	,	,	PUNCT
ejpam-23	301	25	γ	γ	X
ejpam-23	301	26	)	)	PUNCT
ejpam-23	301	27	⊆	⊆	NUM
ejpam-23	301	28	sγ	sγ	NOUN
ejpam-23	301	29	.	.	PUNCT
ejpam-23	302	1	we	we	PRON
ejpam-23	302	2	show	show	VERB
ejpam-23	302	3	that	that	SCONJ
ejpam-23	302	4	ϕd(α	ϕd(α	ADV
ejpam-23	302	5	,	,	PUNCT
ejpam-23	302	6	β)ϕd(β	β)ϕd(β	PROPN
ejpam-23	302	7	,	,	PUNCT
ejpam-23	302	8	γ	γ	NOUN
ejpam-23	302	9	)	)	PUNCT
ejpam-23	302	10	=	=	SYM
ejpam-23	302	11	ϕd(α	ϕd(α	PROPN
ejpam-23	302	12	,	,	PUNCT
ejpam-23	302	13	γ	γ	NOUN
ejpam-23	302	14	)	)	PUNCT
ejpam-23	302	15	for	for	ADP
ejpam-23	302	16	some	some	DET
ejpam-23	302	17	ϕd(α	ϕd(α	NOUN
ejpam-23	302	18	,	,	PUNCT
ejpam-23	302	19	γ	γ	X
ejpam-23	302	20	)	)	PUNCT
ejpam-23	302	21	:	:	PUNCT
ejpam-23	302	22	sα	sα	ADV
ejpam-23	302	23	−→	−→	NOUN
ejpam-23	302	24	sd(α	sd(α	NOUN
ejpam-23	302	25	,	,	PUNCT
ejpam-23	302	26	γ	γ	X
ejpam-23	302	27	)	)	PUNCT
ejpam-23	302	28	⊆	⊆	NUM
ejpam-23	302	29	sγ	sγ	NOUN
ejpam-23	302	30	.	.	PUNCT
ejpam-23	303	1	for	for	ADP
ejpam-23	303	2	this	this	DET
ejpam-23	303	3	purpose	purpose	NOUN
ejpam-23	303	4	,	,	PUNCT
ejpam-23	303	5	we	we	PRON
ejpam-23	303	6	let	let	VERB
ejpam-23	303	7	a	a	DET
ejpam-23	303	8	∈	∈	PROPN
ejpam-23	303	9	sα	sα	NOUN
ejpam-23	303	10	,	,	PUNCT
ejpam-23	303	11	b1	b1	NOUN
ejpam-23	303	12	,	,	PUNCT
ejpam-23	303	13	b2	b2	NOUN
ejpam-23	303	14	∈	∈	PROPN
ejpam-23	303	15	sd(α	sd(α	NOUN
ejpam-23	303	16	,	,	PUNCT
ejpam-23	303	17	β	β	NOUN
ejpam-23	303	18	)	)	PUNCT
ejpam-23	303	19	and	and	CCONJ
ejpam-23	303	20	c	c	PROPN
ejpam-23	303	21	∈	∈	PROPN
ejpam-23	303	22	sd(β	sd(β	NOUN
ejpam-23	303	23	,	,	PUNCT
ejpam-23	303	24	γ	γ	NOUN
ejpam-23	303	25	)	)	PUNCT
ejpam-23	303	26	.	.	PUNCT
ejpam-23	304	1	then	then	ADV
ejpam-23	304	2	,	,	PUNCT
ejpam-23	304	3	because	because	SCONJ
ejpam-23	304	4	s	s	PROPN
ejpam-23	304	5	/	/	SYM
ejpam-23	304	6	h̃	h̃	PROPN
ejpam-23	304	7	is	be	AUX
ejpam-23	304	8	a	a	DET
ejpam-23	304	9	band	band	NOUN
ejpam-23	304	10	,	,	PUNCT
ejpam-23	304	11	by	by	ADP
ejpam-23	304	12	lemma	lemma	PROPN
ejpam-23	304	13	3.2	3.2	NUM
ejpam-23	304	14	,	,	PUNCT
ejpam-23	304	15	we	we	PRON
ejpam-23	304	16	have	have	VERB
ejpam-23	304	17	b1ϕd(β	b1ϕd(β	PROPN
ejpam-23	304	18	,	,	PUNCT
ejpam-23	304	19	γ	γ	NOUN
ejpam-23	304	20	)	)	PUNCT
ejpam-23	304	21	=	=	SYM
ejpam-23	304	22	b1(b1cb1)0	b1(b1cb1)0	PROPN
ejpam-23	304	23	,	,	PUNCT
ejpam-23	304	24	b2ϕd(β	b2ϕd(β	PROPN
ejpam-23	304	25	,	,	PUNCT
ejpam-23	304	26	γ	γ	NOUN
ejpam-23	304	27	)	)	PUNCT
ejpam-23	304	28	=	=	SYM
ejpam-23	304	29	b2(b2cb2)0	b2(b2cb2)0	PROPN
ejpam-23	304	30	.	.	PUNCT
ejpam-23	305	1	since	since	SCONJ
ejpam-23	305	2	b1	b1	NOUN
ejpam-23	305	3	,	,	PUNCT
ejpam-23	305	4	b2	b2	NOUN
ejpam-23	305	5	∈	∈	PROPN
ejpam-23	305	6	sd(α	sd(α	NOUN
ejpam-23	305	7	,	,	PUNCT
ejpam-23	305	8	β	β	NOUN
ejpam-23	305	9	)	)	PUNCT
ejpam-23	305	10	,	,	PUNCT
ejpam-23	305	11	by	by	ADP
ejpam-23	305	12	the	the	DET
ejpam-23	305	13	definition	definition	NOUN
ejpam-23	305	14	of	of	ADP
ejpam-23	305	15	ρα	ρα	PROPN
ejpam-23	305	16	,	,	PUNCT
ejpam-23	305	17	β	β	X
ejpam-23	305	18	,	,	PUNCT
ejpam-23	305	19	(	(	PUNCT
ejpam-23	305	20	b1	b1	NOUN
ejpam-23	305	21	,	,	PUNCT
ejpam-23	305	22	b2	b2	NOUN
ejpam-23	305	23	)	)	PUNCT
ejpam-23	305	24	∈	∈	PROPN
ejpam-23	305	25	ρα	ρα	PROPN
ejpam-23	305	26	,	,	PUNCT
ejpam-23	305	27	β	β	X
ejpam-23	305	28	.	.	PUNCT
ejpam-23	306	1	this	this	PRON
ejpam-23	306	2	leads	lead	VERB
ejpam-23	306	3	to	to	ADP
ejpam-23	306	4	(	(	PUNCT
ejpam-23	306	5	ab1a)0	ab1a)0	NOUN
ejpam-23	306	6	=	=	PUNCT
ejpam-23	306	7	(	(	PUNCT
ejpam-23	306	8	ab2a)0	ab2a)0	NOUN
ejpam-23	306	9	.	.	PUNCT
ejpam-23	307	1	now	now	ADV
ejpam-23	307	2	,	,	PUNCT
ejpam-23	307	3	by	by	ADP
ejpam-23	307	4	the	the	DET
ejpam-23	307	5	regularity	regularity	NOUN
ejpam-23	307	6	of	of	ADP
ejpam-23	307	7	the	the	DET
ejpam-23	307	8	band	band	NOUN
ejpam-23	307	9	s	s	NOUN
ejpam-23	307	10	/	/	SYM
ejpam-23	307	11	h̃	h̃	PROPN
ejpam-23	307	12	,	,	PUNCT
ejpam-23	307	13	we	we	PRON
ejpam-23	307	14	can	can	AUX
ejpam-23	307	15	easily	easily	ADV
ejpam-23	307	16	deduce	deduce	VERB
ejpam-23	307	17	that	that	PRON
ejpam-23	307	18	(	(	PUNCT
ejpam-23	307	19	a(b1ϕd(β	a(b1ϕd(β	PROPN
ejpam-23	307	20	,	,	PUNCT
ejpam-23	307	21	γ))a)0	γ))a)0	PROPN
ejpam-23	307	22	=	=	SYM
ejpam-23	307	23	(	(	PUNCT
ejpam-23	307	24	ab1(b1cb1)0a)0	ab1(b1cb1)0a)0	NUM
ejpam-23	307	25	=	=	SYM
ejpam-23	307	26	(	(	PUNCT
ejpam-23	307	27	(	(	PUNCT
ejpam-23	307	28	ab1a)0c(ab1a)0)0	ab1a)0c(ab1a)0)0	X
ejpam-23	307	29	=	=	SYM
ejpam-23	307	30	(	(	PUNCT
ejpam-23	307	31	(	(	PUNCT
ejpam-23	307	32	ab2a)0c(ab2a)0)0	ab2a)0c(ab2a)0)0	X
ejpam-23	307	33	=	=	SYM
ejpam-23	307	34	(	(	PUNCT
ejpam-23	307	35	a(b2(b2cb2)0)a)0	a(b2(b2cb2)0)a)0	NOUN
ejpam-23	307	36	=	=	SYM
ejpam-23	307	37	(	(	PUNCT
ejpam-23	307	38	a(b2ϕd(β	a(b2ϕd(β	PROPN
ejpam-23	307	39	,	,	PUNCT
ejpam-23	307	40	γ))a)0	γ))a)0	NUM
ejpam-23	307	41	.	.	PUNCT
ejpam-23	308	1	thus	thus	ADV
ejpam-23	308	2	,	,	PUNCT
ejpam-23	308	3	by	by	ADP
ejpam-23	308	4	the	the	DET
ejpam-23	308	5	definition	definition	NOUN
ejpam-23	308	6	of	of	ADP
ejpam-23	308	7	ρα	ρα	PROPN
ejpam-23	308	8	,	,	PUNCT
ejpam-23	308	9	γ	γ	X
ejpam-23	308	10	,	,	PUNCT
ejpam-23	308	11	we	we	PRON
ejpam-23	308	12	have	have	VERB
ejpam-23	308	13	(	(	PUNCT
ejpam-23	308	14	b1ϕd(β	b1ϕd(β	PROPN
ejpam-23	308	15	,	,	PUNCT
ejpam-23	308	16	γ	γ	NOUN
ejpam-23	308	17	)	)	PUNCT
ejpam-23	308	18	,	,	PUNCT
ejpam-23	308	19	b2ϕd(β	b2ϕd(β	PROPN
ejpam-23	308	20	,	,	PUNCT
ejpam-23	308	21	γ	γ	NOUN
ejpam-23	308	22	)	)	PUNCT
ejpam-23	308	23	)	)	PUNCT
ejpam-23	309	1	∈	∈	PROPN
ejpam-23	309	2	ρα	ρα	PROPN
ejpam-23	309	3	,	,	PUNCT
ejpam-23	309	4	γ	γ	X
ejpam-23	309	5	.	.	PUNCT
ejpam-23	310	1	in	in	ADP
ejpam-23	310	2	other	other	ADJ
ejpam-23	310	3	words	word	NOUN
ejpam-23	310	4	,	,	PUNCT
ejpam-23	310	5	there	there	PRON
ejpam-23	310	6	exists	exist	VERB
ejpam-23	310	7	a	a	DET
ejpam-23	310	8	ρα	ρα	PROPN
ejpam-23	310	9	,	,	PUNCT
ejpam-23	310	10	γ	γ	NOUN
ejpam-23	310	11	-	-	PUNCT
ejpam-23	310	12	class	class	NOUN
ejpam-23	310	13	sd(α	sd(α	PROPN
ejpam-23	310	14	,	,	PUNCT
ejpam-23	310	15	γ	γ	X
ejpam-23	310	16	)	)	PUNCT
ejpam-23	310	17	satisfying	satisfy	VERB
ejpam-23	310	18	sd(α	sd(α	NOUN
ejpam-23	310	19	,	,	PUNCT
ejpam-23	310	20	β)ϕd(β	β)ϕd(β	PROPN
ejpam-23	310	21	,	,	PUNCT
ejpam-23	310	22	γ	γ	NOUN
ejpam-23	310	23	)	)	PUNCT
ejpam-23	310	24	⊆	⊆	NUM
ejpam-23	310	25	sd(α	sd(α	PROPN
ejpam-23	310	26	,	,	PUNCT
ejpam-23	310	27	γ	γ	NOUN
ejpam-23	310	28	)	)	PUNCT
ejpam-23	310	29	.	.	PUNCT
ejpam-23	311	1	also	also	ADV
ejpam-23	311	2	,	,	PUNCT
ejpam-23	311	3	ϕd(α	ϕd(α	ADV
ejpam-23	311	4	,	,	PUNCT
ejpam-23	311	5	β)ϕd(β	β)ϕd(β	PROPN
ejpam-23	311	6	,	,	PUNCT
ejpam-23	311	7	γ	γ	NOUN
ejpam-23	311	8	)	)	PUNCT
ejpam-23	311	9	clearly	clearly	ADV
ejpam-23	311	10	maps	map	VERB
ejpam-23	311	11	sα	sα	ADV
ejpam-23	311	12	into	into	ADP
ejpam-23	311	13	sd(α	sd(α	PROPN
ejpam-23	311	14	,	,	PUNCT
ejpam-23	311	15	γ	γ	X
ejpam-23	311	16	)	)	PUNCT
ejpam-23	311	17	by	by	ADP
ejpam-23	311	18	the	the	DET
ejpam-23	311	19	transitivity	transitivity	NOUN
ejpam-23	311	20	of	of	ADP
ejpam-23	311	21	“	"	PUNCT
ejpam-23	311	22	6	6	NUM
ejpam-23	311	23	”	"	PUNCT
ejpam-23	311	24	,	,	PUNCT
ejpam-23	311	25	and	and	CCONJ
ejpam-23	311	26	hence	hence	ADV
ejpam-23	311	27	ϕd(α	ϕd(α	PUNCT
ejpam-23	311	28	,	,	PUNCT
ejpam-23	311	29	β)ϕd(β	β)ϕd(β	PROPN
ejpam-23	311	30	,	,	PUNCT
ejpam-23	311	31	γ	γ	NOUN
ejpam-23	311	32	)	)	PUNCT
ejpam-23	311	33	=	=	SYM
ejpam-23	311	34	ϕd(α	ϕd(α	PROPN
ejpam-23	311	35	,	,	PUNCT
ejpam-23	311	36	γ	γ	X
ejpam-23	311	37	)	)	PUNCT
ejpam-23	311	38	.	.	PUNCT
ejpam-23	312	1	this	this	PRON
ejpam-23	312	2	proves	prove	VERB
ejpam-23	312	3	that	that	SCONJ
ejpam-23	312	4	ϕα	ϕα	ADV
ejpam-23	312	5	,	,	PUNCT
ejpam-23	312	6	βϕβ	βϕβ	PROPN
ejpam-23	312	7	,	,	PUNCT
ejpam-23	312	8	γ	γ	X
ejpam-23	312	9	⊆	⊆	NUM
ejpam-23	312	10	ϕα	ϕα	NOUN
ejpam-23	312	11	,	,	PUNCT
ejpam-23	312	12	γ	γ	X
ejpam-23	312	13	.	.	PUNCT
ejpam-23	313	1	(	(	PUNCT
ejpam-23	313	2	ii	ii	X
ejpam-23	313	3	)	)	PUNCT
ejpam-23	313	4	it	it	PRON
ejpam-23	313	5	suffices	suffice	VERB
ejpam-23	313	6	to	to	PART
ejpam-23	313	7	show	show	VERB
ejpam-23	313	8	that	that	SCONJ
ejpam-23	313	9	for	for	ADP
ejpam-23	313	10	any	any	PRON
ejpam-23	313	11	ϕd(α	ϕd(α	NOUN
ejpam-23	313	12	,	,	PUNCT
ejpam-23	313	13	αβ	αβ	INTJ
ejpam-23	313	14	)	)	PUNCT
ejpam-23	313	15	and	and	CCONJ
ejpam-23	313	16	ϕd′(α	ϕd′(α	PROPN
ejpam-23	313	17	,	,	PUNCT
ejpam-23	313	18	αβ	αβ	INTJ
ejpam-23	313	19	)	)	PUNCT
ejpam-23	313	20	∈	∈	PROPN
ejpam-23	313	21	ϕα	ϕα	ADV
ejpam-23	313	22	,	,	PUNCT
ejpam-23	313	23	αβ	αβ	INTJ
ejpam-23	313	24	,	,	PUNCT
ejpam-23	313	25	we	we	PRON
ejpam-23	313	26	have	have	VERB
ejpam-23	313	27	(	(	PUNCT
ejpam-23	313	28	aϕd(α	aϕd(α	PROPN
ejpam-23	313	29	,	,	PUNCT
ejpam-23	313	30	αβ	αβ	NOUN
ejpam-23	313	31	)	)	PUNCT
ejpam-23	313	32	,	,	PUNCT
ejpam-23	313	33	aϕd′(α	aϕd′(α	NOUN
ejpam-23	313	34	,	,	PUNCT
ejpam-23	313	35	αβ	αβ	NOUN
ejpam-23	313	36	)	)	PUNCT
ejpam-23	313	37	)	)	PUNCT
ejpam-23	314	1	∈	∈	PROPN
ejpam-23	314	2	ρβ	ρβ	VERB
ejpam-23	314	3	,	,	PUNCT
ejpam-23	314	4	αβ	αβ	INTJ
ejpam-23	314	5	.	.	PUNCT
ejpam-23	315	1	for	for	ADP
ejpam-23	315	2	this	this	DET
ejpam-23	315	3	purpose	purpose	NOUN
ejpam-23	315	4	,	,	PUNCT
ejpam-23	315	5	we	we	PRON
ejpam-23	315	6	let	let	VERB
ejpam-23	315	7	x	x	X
ejpam-23	315	8	∈	∈	PROPN
ejpam-23	315	9	sd(α	sd(α	NOUN
ejpam-23	315	10	,	,	PUNCT
ejpam-23	315	11	αβ	αβ	INTJ
ejpam-23	315	12	)	)	PUNCT
ejpam-23	315	13	and	and	CCONJ
ejpam-23	315	14	x′	x′	PROPN
ejpam-23	315	15	∈	∈	PROPN
ejpam-23	315	16	sd′(α	sd′(α	PROPN
ejpam-23	315	17	,	,	PUNCT
ejpam-23	315	18	αβ	αβ	NOUN
ejpam-23	315	19	)	)	PUNCT
ejpam-23	315	20	.	.	PUNCT
ejpam-23	316	1	then	then	ADV
ejpam-23	316	2	,	,	PUNCT
ejpam-23	316	3	by	by	ADP
ejpam-23	316	4	lemma	lemma	PROPN
ejpam-23	316	5	3.2	3.2	NUM
ejpam-23	316	6	(	(	PUNCT
ejpam-23	316	7	iii	iii	NOUN
ejpam-23	316	8	)	)	PUNCT
ejpam-23	316	9	,	,	PUNCT
ejpam-23	316	10	we	we	PRON
ejpam-23	316	11	have	have	VERB
ejpam-23	316	12	aϕd(α	aϕd(α	NOUN
ejpam-23	316	13	,	,	PUNCT
ejpam-23	316	14	αβ	αβ	INTJ
ejpam-23	316	15	)	)	PUNCT
ejpam-23	316	16	=	=	SYM
ejpam-23	316	17	a(axa)0	a(axa)0	PROPN
ejpam-23	316	18	and	and	CCONJ
ejpam-23	316	19	aϕd′(α	aϕd′(α	NOUN
ejpam-23	316	20	,	,	PUNCT
ejpam-23	316	21	αβ	αβ	X
ejpam-23	316	22	)	)	PUNCT
ejpam-23	316	23	=	=	SYM
ejpam-23	317	1	a(ax′0	a(ax′0	NOUN
ejpam-23	317	2	.	.	PUNCT
ejpam-23	318	1	let	let	VERB
ejpam-23	318	2	b	b	X
ejpam-23	318	3	∈	∈	PROPN
ejpam-23	318	4	sβ	sβ	VERB
ejpam-23	318	5	.	.	PUNCT
ejpam-23	319	1	since	since	SCONJ
ejpam-23	319	2	sαβ	sαβ	PROPN
ejpam-23	319	3	is	be	AUX
ejpam-23	319	4	a	a	DET
ejpam-23	319	5	completely	completely	ADV
ejpam-23	319	6	j̃	j̃	PROPN
ejpam-23	319	7	-simple	-simple	NUM
ejpam-23	319	8	semigroup	semigroup	ADJ
ejpam-23	319	9	,	,	PUNCT
ejpam-23	319	10	and	and	CCONJ
ejpam-23	319	11	bab	bab	PROPN
ejpam-23	319	12	,	,	PUNCT
ejpam-23	319	13	aϕd(α	aϕd(α	PROPN
ejpam-23	319	14	,	,	PUNCT
ejpam-23	319	15	αβ	αβ	NOUN
ejpam-23	319	16	)	)	PUNCT
ejpam-23	319	17	,	,	PUNCT
ejpam-23	319	18	aϕd′(α	aϕd′(α	NOUN
ejpam-23	319	19	,	,	PUNCT
ejpam-23	319	20	αβ	αβ	PRON
ejpam-23	319	21	)	)	PUNCT
ejpam-23	319	22	are	be	AUX
ejpam-23	319	23	elements	element	NOUN
ejpam-23	319	24	in	in	ADP
ejpam-23	319	25	sαβ	sαβ	NOUN
ejpam-23	319	26	,	,	PUNCT
ejpam-23	319	27	we	we	PRON
ejpam-23	319	28	obtain	obtain	VERB
ejpam-23	319	29	that	that	PRON
ejpam-23	319	30	(	(	PUNCT
ejpam-23	319	31	bab	bab	PROPN
ejpam-23	319	32	,	,	PUNCT
ejpam-23	319	33	(	(	PUNCT
ejpam-23	319	34	bab)(aϕd(α	bab)(aϕd(α	ADP
ejpam-23	319	35	,	,	PUNCT
ejpam-23	319	36	αβ))(bab	αβ))(bab	PROPN
ejpam-23	319	37	)	)	PUNCT
ejpam-23	319	38	)	)	PUNCT
ejpam-23	320	1	∈	∈	PROPN
ejpam-23	320	2	h̃	h̃	PROPN
ejpam-23	320	3	and	and	CCONJ
ejpam-23	320	4	(	(	PUNCT
ejpam-23	320	5	bab	bab	PROPN
ejpam-23	320	6	,	,	PUNCT
ejpam-23	320	7	(	(	PUNCT
ejpam-23	320	8	bab)(aϕd′(α	bab)(aϕd′(α	PROPN
ejpam-23	320	9	,	,	PUNCT
ejpam-23	320	10	αβ))(bab	αβ))(bab	PROPN
ejpam-23	320	11	)	)	PUNCT
ejpam-23	320	12	)	)	PUNCT
ejpam-23	321	1	∈	∈	PROPN
ejpam-23	321	2	h̃.	h̃.	PROPN
ejpam-23	321	3	since	since	SCONJ
ejpam-23	321	4	every	every	DET
ejpam-23	321	5	h̃-class	h̃-class	NOUN
ejpam-23	321	6	of	of	ADP
ejpam-23	321	7	sαβ	sαβ	PROPN
ejpam-23	321	8	contains	contain	VERB
ejpam-23	321	9	a	a	DET
ejpam-23	321	10	unique	unique	ADJ
ejpam-23	321	11	idempotent	idempotent	NOUN
ejpam-23	321	12	,	,	PUNCT
ejpam-23	321	13	(	(	PUNCT
ejpam-23	321	14	(	(	PUNCT
ejpam-23	321	15	bab)(aϕd(α	bab)(aϕd(α	ADP
ejpam-23	321	16	,	,	PUNCT
ejpam-23	321	17	αβ))(bab))0	αβ))(bab))0	NOUN
ejpam-23	321	18	=	=	SYM
ejpam-23	321	19	(	(	PUNCT
ejpam-23	321	20	(	(	PUNCT
ejpam-23	321	21	bab)(aϕd′(α	bab)(aϕd′(α	NOUN
ejpam-23	321	22	,	,	PUNCT
ejpam-23	321	23	αβ))(bab))0	αβ))(bab))0	ADJ
ejpam-23	321	24	.	.	PUNCT
ejpam-23	322	1	in	in	ADP
ejpam-23	322	2	other	other	ADJ
ejpam-23	322	3	words	word	NOUN
ejpam-23	322	4	,	,	PUNCT
ejpam-23	322	5	we	we	PRON
ejpam-23	322	6	have	have	AUX
ejpam-23	322	7	(	(	PUNCT
ejpam-23	322	8	(	(	PUNCT
ejpam-23	322	9	bab)(a(axa)0)(bab))0	bab)(a(axa)0)(bab))0	PROPN
ejpam-23	322	10	=	=	SYM
ejpam-23	322	11	(	(	PUNCT
ejpam-23	322	12	(	(	PUNCT
ejpam-23	322	13	bab)(a(ax′0)(bab))0	bab)(a(ax′0)(bab))0	X
ejpam-23	322	14	.	.	PUNCT
ejpam-23	322	15	thus	thus	ADV
ejpam-23	322	16	,	,	PUNCT
ejpam-23	322	17	by	by	ADP
ejpam-23	322	18	the	the	DET
ejpam-23	322	19	regularity	regularity	NOUN
ejpam-23	322	20	of	of	ADP
ejpam-23	322	21	the	the	DET
ejpam-23	322	22	band	band	NOUN
ejpam-23	322	23	s	s	NOUN
ejpam-23	322	24	/	/	SYM
ejpam-23	322	25	h̃	h̃	PROPN
ejpam-23	322	26	,	,	PUNCT
ejpam-23	322	27	we	we	PRON
ejpam-23	322	28	can	can	AUX
ejpam-23	322	29	further	far	ADV
ejpam-23	322	30	simplify	simplify	VERB
ejpam-23	322	31	the	the	DET
ejpam-23	322	32	above	above	ADJ
ejpam-23	322	33	equality	equality	NOUN
ejpam-23	322	34	to	to	ADP
ejpam-23	322	35	(	(	PUNCT
ejpam-23	322	36	b(a(axa)0)b)0	b(a(axa)0)b)0	X
ejpam-23	322	37	=	=	SYM
ejpam-23	322	38	(	(	PUNCT
ejpam-23	322	39	b(a(ax′0)b)0	b(a(ax′0)b)0	PROPN
ejpam-23	322	40	,	,	PUNCT
ejpam-23	322	41	that	that	ADV
ejpam-23	322	42	is	is	ADV
ejpam-23	322	43	,	,	PUNCT
ejpam-23	322	44	(	(	PUNCT
ejpam-23	322	45	b(aϕd(α	b(aϕd(α	NOUN
ejpam-23	322	46	,	,	PUNCT
ejpam-23	322	47	αβ))b)0	αβ))b)0	PROPN
ejpam-23	322	48	=	=	SYM
ejpam-23	322	49	(	(	PUNCT
ejpam-23	322	50	b(aϕd′(α	b(aϕd′(α	PROPN
ejpam-23	322	51	,	,	PUNCT
ejpam-23	322	52	αβ))b)0	αβ))b)0	PROPN
ejpam-23	322	53	.	.	PUNCT
ejpam-23	323	1	by	by	ADP
ejpam-23	323	2	the	the	DET
ejpam-23	323	3	definition	definition	NOUN
ejpam-23	323	4	of	of	ADP
ejpam-23	323	5	ρβ	ρβ	PROPN
ejpam-23	323	6	,	,	PUNCT
ejpam-23	323	7	αβ	αβ	INTJ
ejpam-23	323	8	,	,	PUNCT
ejpam-23	323	9	we	we	PRON
ejpam-23	323	10	see	see	VERB
ejpam-23	323	11	that	that	SCONJ
ejpam-23	323	12	(	(	PUNCT
ejpam-23	323	13	aϕd(α	aϕd(α	PROPN
ejpam-23	323	14	,	,	PUNCT
ejpam-23	323	15	αβ	αβ	NOUN
ejpam-23	323	16	)	)	PUNCT
ejpam-23	323	17	,	,	PUNCT
ejpam-23	323	18	aϕd′(α	aϕd′(α	NOUN
ejpam-23	323	19	,	,	PUNCT
ejpam-23	323	20	αβ	αβ	NOUN
ejpam-23	323	21	)	)	PUNCT
ejpam-23	323	22	)	)	PUNCT
ejpam-23	324	1	∈	∈	PROPN
ejpam-23	324	2	ρβ	ρβ	PROPN
ejpam-23	324	3	,	,	PUNCT
ejpam-23	324	4	αβ	αβ	INTJ
ejpam-23	324	5	.	.	PUNCT
ejpam-23	325	1	finally	finally	ADV
ejpam-23	325	2	we	we	PRON
ejpam-23	325	3	show	show	VERB
ejpam-23	325	4	that	that	SCONJ
ejpam-23	325	5	s	s	VERB
ejpam-23	325	6	=	=	PUNCT
ejpam-23	325	7	(	(	PUNCT
ejpam-23	325	8	y	y	PROPN
ejpam-23	325	9	;	;	PUNCT
ejpam-23	325	10	sα	sα	X
ejpam-23	325	11	)	)	PUNCT
ejpam-23	325	12	equipped	equip	VERB
ejpam-23	325	13	with	with	ADP
ejpam-23	325	14	the	the	DET
ejpam-23	325	15	above	above	ADJ
ejpam-23	325	16	structural	structural	ADJ
ejpam-23	325	17	homomorphisms	homomorphism	NOUN
ejpam-23	325	18	acting	act	VERB
ejpam-23	325	19	on	on	ADP
ejpam-23	325	20	the	the	DET
ejpam-23	325	21	ρα	ρα	PROPN
ejpam-23	325	22	,	,	PUNCT
ejpam-23	325	23	β	β	NOUN
ejpam-23	325	24	-	-	PUNCT
ejpam-23	325	25	equivalence	equivalence	NOUN
ejpam-23	325	26	class	class	NOUN
ejpam-23	325	27	of	of	ADP
ejpam-23	325	28	s	s	PROPN
ejpam-23	325	29	forms	form	NOUN
ejpam-23	325	30	a	a	DET
ejpam-23	325	31	g	g	NOUN
ejpam-23	325	32	-	-	PUNCT
ejpam-23	325	33	strong	strong	ADJ
ejpam-23	325	34	semilattice	semilattice	NOUN
ejpam-23	325	35	of	of	ADP
ejpam-23	325	36	semigroups	semigroups	X
ejpam-23	325	37	sα	sα	VERB
ejpam-23	325	38	.	.	PUNCT
ejpam-23	326	1	we	we	PRON
ejpam-23	326	2	need	need	VERB
ejpam-23	326	3	the	the	DET
ejpam-23	326	4	following	follow	VERB
ejpam-23	326	5	lemma	lemma	PROPN
ejpam-23	326	6	.	.	PUNCT
ejpam-23	327	1	lemma	lemma	PROPN
ejpam-23	327	2	3.4	3.4	NUM
ejpam-23	327	3	let	let	VERB
ejpam-23	327	4	s	s	VERB
ejpam-23	327	5	=	=	PUNCT
ejpam-23	327	6	(	(	PUNCT
ejpam-23	327	7	y	y	PROPN
ejpam-23	327	8	;	;	PUNCT
ejpam-23	327	9	sα	sα	X
ejpam-23	327	10	)	)	PUNCT
ejpam-23	327	11	be	be	AUX
ejpam-23	327	12	a	a	DET
ejpam-23	327	13	regular	regular	ADJ
ejpam-23	327	14	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	327	15	.	.	PUNCT
ejpam-23	328	1	for	for	ADP
ejpam-23	328	2	any	any	DET
ejpam-23	328	3	a	a	DET
ejpam-23	328	4	∈	∈	PROPN
ejpam-23	328	5	sα	sα	NOUN
ejpam-23	328	6	,	,	PUNCT
ejpam-23	328	7	b	b	PROPN
ejpam-23	328	8	∈	∈	PROPN
ejpam-23	328	9	sβ	sβ	NOUN
ejpam-23	328	10	,	,	PUNCT
ejpam-23	328	11	suppose	suppose	VERB
ejpam-23	328	12	that	that	SCONJ
ejpam-23	328	13	aϕα	aϕα	NOUN
ejpam-23	328	14	,	,	PUNCT
ejpam-23	328	15	αβ	αβ	PRON
ejpam-23	328	16	⊆	⊆	NUM
ejpam-23	328	17	sd(β	sd(β	NOUN
ejpam-23	328	18	,	,	PUNCT
ejpam-23	328	19	αβ	αβ	X
ejpam-23	328	20	)	)	PUNCT
ejpam-23	328	21	,	,	PUNCT
ejpam-23	328	22	bϕβ	bϕβ	ADJ
ejpam-23	328	23	,	,	PUNCT
ejpam-23	328	24	αβ	αβ	PRON
ejpam-23	328	25	⊆	⊆	NUM
ejpam-23	328	26	sd(α	sd(α	X
ejpam-23	328	27	,	,	PUNCT
ejpam-23	328	28	αβ	αβ	X
ejpam-23	328	29	)	)	PUNCT
ejpam-23	328	30	,	,	PUNCT
ejpam-23	328	31	where	where	SCONJ
ejpam-23	328	32	ϕα	ϕα	ADV
ejpam-23	328	33	,	,	PUNCT
ejpam-23	328	34	αβ	αβ	INTJ
ejpam-23	328	35	and	and	CCONJ
ejpam-23	328	36	ϕβ	ϕβ	PROPN
ejpam-23	328	37	,	,	PUNCT
ejpam-23	328	38	αβ	αβ	PRON
ejpam-23	328	39	are	be	AUX
ejpam-23	328	40	the	the	DET
ejpam-23	328	41	structural	structural	ADJ
ejpam-23	328	42	homomorphisms	homomorphism	NOUN
ejpam-23	328	43	defined	define	VERB
ejpam-23	328	44	in	in	ADP
ejpam-23	328	45	lemma	lemma	PROPN
ejpam-23	328	46	3.3	3.3	NUM
ejpam-23	328	47	.	.	PUNCT
ejpam-23	329	1	then	then	ADV
ejpam-23	329	2	we	we	PRON
ejpam-23	329	3	have	have	VERB
ejpam-23	329	4	ab	ab	PROPN
ejpam-23	329	5	=	=	SYM
ejpam-23	329	6	(	(	PUNCT
ejpam-23	329	7	aϕd(α	aϕd(α	PROPN
ejpam-23	329	8	,	,	PUNCT
ejpam-23	329	9	αβ))(bϕd(β	αβ))(bϕd(β	PROPN
ejpam-23	329	10	,	,	PUNCT
ejpam-23	329	11	αβ	αβ	NOUN
ejpam-23	329	12	)	)	PUNCT
ejpam-23	329	13	)	)	PUNCT
ejpam-23	329	14	.	.	PUNCT
ejpam-23	330	1	x.	x.	PROPN
ejpam-23	330	2	kong	kong	PROPN
ejpam-23	330	3	,	,	PUNCT
ejpam-23	330	4	y.ding	y.de	VERB
ejpam-23	330	5	,	,	PUNCT
ejpam-23	330	6	k.p.shum	k.p.shum	ADJ
ejpam-23	330	7	/	/	SYM
ejpam-23	330	8	eur	eur	PROPN
ejpam-23	330	9	.	.	PUNCT
ejpam-23	331	1	j.	j.	PROPN
ejpam-23	331	2	pure	pure	PROPN
ejpam-23	331	3	appl	appl	PROPN
ejpam-23	331	4	.	.	PROPN
ejpam-23	331	5	math	math	PROPN
ejpam-23	331	6	,	,	PUNCT
ejpam-23	331	7	1	1	NUM
ejpam-23	331	8	(	(	PUNCT
ejpam-23	331	9	2008	2008	NUM
ejpam-23	331	10	)	)	PUNCT
ejpam-23	331	11	,	,	PUNCT
ejpam-23	331	12	(	(	PUNCT
ejpam-23	331	13	46	46	NUM
ejpam-23	331	14	-	-	SYM
ejpam-23	331	15	59	59	NUM
ejpam-23	331	16	)	)	PUNCT
ejpam-23	331	17	56	56	NUM
ejpam-23	331	18	proof	proof	NOUN
ejpam-23	331	19	.	.	PUNCT
ejpam-23	332	1	let	let	VERB
ejpam-23	332	2	c1	c1	PROPN
ejpam-23	332	3	∈	∈	PROPN
ejpam-23	332	4	sd(α	sd(α	PROPN
ejpam-23	332	5	,	,	PUNCT
ejpam-23	332	6	αβ	αβ	X
ejpam-23	332	7	)	)	PUNCT
ejpam-23	332	8	,	,	PUNCT
ejpam-23	332	9	c2	c2	PROPN
ejpam-23	332	10	∈	∈	PROPN
ejpam-23	332	11	sd(β	sd(β	NOUN
ejpam-23	332	12	,	,	PUNCT
ejpam-23	332	13	αβ	αβ	X
ejpam-23	332	14	)	)	PUNCT
ejpam-23	332	15	.	.	PUNCT
ejpam-23	333	1	then	then	ADV
ejpam-23	333	2	(	(	PUNCT
ejpam-23	333	3	ac1a)0	ac1a)0	PROPN
ejpam-23	333	4	∈	∈	NOUN
ejpam-23	333	5	sd(α	sd(α	NOUN
ejpam-23	333	6	,	,	PUNCT
ejpam-23	333	7	αβ	αβ	INTJ
ejpam-23	333	8	)	)	PUNCT
ejpam-23	333	9	because	because	SCONJ
ejpam-23	333	10	sd(α	sd(α	NOUN
ejpam-23	333	11	,	,	PUNCT
ejpam-23	333	12	αβ	αβ	PRON
ejpam-23	333	13	)	)	PUNCT
ejpam-23	333	14	is	be	AUX
ejpam-23	333	15	a	a	DET
ejpam-23	333	16	ρα	ρα	PROPN
ejpam-23	333	17	,	,	PUNCT
ejpam-23	333	18	αβequivalence	αβequivalence	NOUN
ejpam-23	333	19	class	class	NOUN
ejpam-23	333	20	of	of	ADP
ejpam-23	333	21	sαβ	sαβ	PROPN
ejpam-23	333	22	.	.	PUNCT
ejpam-23	334	1	now	now	ADV
ejpam-23	334	2	,	,	PUNCT
ejpam-23	334	3	by	by	ADP
ejpam-23	334	4	lemma	lemma	PROPN
ejpam-23	334	5	3.2	3.2	NUM
ejpam-23	334	6	,	,	PUNCT
ejpam-23	334	7	aϕd(α	aϕd(α	PROPN
ejpam-23	334	8	,	,	PUNCT
ejpam-23	334	9	αβ	αβ	INTJ
ejpam-23	334	10	)	)	PUNCT
ejpam-23	334	11	=	=	SYM
ejpam-23	334	12	(	(	PUNCT
ejpam-23	334	13	ac1a)0a	ac1a)0a	PROPN
ejpam-23	334	14	and	and	CCONJ
ejpam-23	334	15	bϕd(β	bϕd(β	PROPN
ejpam-23	334	16	,	,	PUNCT
ejpam-23	334	17	αβ	αβ	INTJ
ejpam-23	334	18	)	)	PUNCT
ejpam-23	334	19	=	=	SYM
ejpam-23	334	20	b(bc2b)0	b(bc2b)0	PROPN
ejpam-23	334	21	for	for	ADP
ejpam-23	334	22	ϕd(α	ϕd(α	NOUN
ejpam-23	334	23	,	,	PUNCT
ejpam-23	334	24	αβ	αβ	INTJ
ejpam-23	334	25	)	)	PUNCT
ejpam-23	334	26	∈	∈	PROPN
ejpam-23	335	1	ϕα	ϕα	ADV
ejpam-23	335	2	,	,	PUNCT
ejpam-23	335	3	αβ	αβ	INTJ
ejpam-23	335	4	and	and	CCONJ
ejpam-23	335	5	ϕd(β	ϕd(β	NOUN
ejpam-23	335	6	,	,	PUNCT
ejpam-23	335	7	αβ	αβ	INTJ
ejpam-23	335	8	)	)	PUNCT
ejpam-23	335	9	∈	∈	PROPN
ejpam-23	335	10	ϕβ	ϕβ	PROPN
ejpam-23	335	11	,	,	PUNCT
ejpam-23	335	12	αβ	αβ	INTJ
ejpam-23	335	13	.	.	PUNCT
ejpam-23	336	1	since	since	SCONJ
ejpam-23	336	2	we	we	PRON
ejpam-23	336	3	assume	assume	VERB
ejpam-23	336	4	that	that	SCONJ
ejpam-23	336	5	aϕα	aϕα	NOUN
ejpam-23	336	6	,	,	PUNCT
ejpam-23	336	7	αβ	αβ	PRON
ejpam-23	336	8	⊆	⊆	NUM
ejpam-23	336	9	sd(β	sd(β	NOUN
ejpam-23	336	10	,	,	PUNCT
ejpam-23	336	11	αβ	αβ	X
ejpam-23	336	12	)	)	PUNCT
ejpam-23	336	13	,	,	PUNCT
ejpam-23	336	14	we	we	PRON
ejpam-23	336	15	have	have	VERB
ejpam-23	336	16	aϕd(α	aϕd(α	NOUN
ejpam-23	336	17	,	,	PUNCT
ejpam-23	336	18	αβ	αβ	INTJ
ejpam-23	336	19	)	)	PUNCT
ejpam-23	337	1	=	=	SYM
ejpam-23	337	2	(	(	PUNCT
ejpam-23	337	3	ac1a)0a	ac1a)0a	PROPN
ejpam-23	337	4	∈	∈	PROPN
ejpam-23	337	5	sd(β	sd(β	NOUN
ejpam-23	337	6	,	,	PUNCT
ejpam-23	337	7	αβ	αβ	X
ejpam-23	337	8	)	)	PUNCT
ejpam-23	337	9	.	.	PUNCT
ejpam-23	338	1	similarly	similarly	ADV
ejpam-23	338	2	,	,	PUNCT
ejpam-23	338	3	we	we	PRON
ejpam-23	338	4	have	have	VERB
ejpam-23	338	5	bϕd(β	bϕd(β	PROPN
ejpam-23	338	6	,	,	PUNCT
ejpam-23	338	7	αβ	αβ	INTJ
ejpam-23	338	8	)	)	PUNCT
ejpam-23	338	9	∈	∈	PROPN
ejpam-23	338	10	sd(α	sd(α	NOUN
ejpam-23	338	11	,	,	PUNCT
ejpam-23	338	12	αβ	αβ	INTJ
ejpam-23	338	13	)	)	PUNCT
ejpam-23	338	14	∩	∩	NOUN
ejpam-23	338	15	sd(β	sd(β	NOUN
ejpam-23	338	16	,	,	PUNCT
ejpam-23	338	17	αβ	αβ	X
ejpam-23	338	18	)	)	PUNCT
ejpam-23	338	19	.	.	PUNCT
ejpam-23	339	1	thus	thus	ADV
ejpam-23	339	2	,	,	PUNCT
ejpam-23	339	3	by	by	ADP
ejpam-23	339	4	lemma	lemma	PROPN
ejpam-23	339	5	3.2	3.2	NUM
ejpam-23	339	6	(	(	PUNCT
ejpam-23	339	7	ii	ii	NOUN
ejpam-23	339	8	)	)	PUNCT
ejpam-23	339	9	,	,	PUNCT
ejpam-23	339	10	we	we	PRON
ejpam-23	339	11	have	have	VERB
ejpam-23	339	12	(	(	PUNCT
ejpam-23	339	13	aϕd(α	aϕd(α	PROPN
ejpam-23	339	14	,	,	PUNCT
ejpam-23	339	15	αβ))(bϕd(β	αβ))(bϕd(β	PROPN
ejpam-23	339	16	,	,	PUNCT
ejpam-23	339	17	αβ	αβ	NOUN
ejpam-23	339	18	)	)	PUNCT
ejpam-23	339	19	)	)	PUNCT
ejpam-23	340	1	=	=	SYM
ejpam-23	340	2	(	(	PUNCT
ejpam-23	340	3	ac1a)0(ab(bc2b)0	ac1a)0(ab(bc2b)0	PROPN
ejpam-23	340	4	)	)	PUNCT
ejpam-23	340	5	=	=	NOUN
ejpam-23	340	6	ab(bc2b)0	ab(bc2b)0	NOUN
ejpam-23	340	7	and	and	CCONJ
ejpam-23	340	8	also	also	ADV
ejpam-23	340	9	(	(	PUNCT
ejpam-23	340	10	aϕd(α	aϕd(α	PROPN
ejpam-23	340	11	,	,	PUNCT
ejpam-23	340	12	αβ))(bϕd(β	αβ))(bϕd(β	PROPN
ejpam-23	340	13	,	,	PUNCT
ejpam-23	340	14	αβ	αβ	NOUN
ejpam-23	340	15	)	)	PUNCT
ejpam-23	340	16	)	)	PUNCT
ejpam-23	341	1	=	=	SYM
ejpam-23	341	2	(	(	PUNCT
ejpam-23	341	3	(	(	PUNCT
ejpam-23	341	4	ac1a)0ab)(bc2b)0	ac1a)0ab)(bc2b)0	PROPN
ejpam-23	341	5	=	=	SYM
ejpam-23	341	6	(	(	PUNCT
ejpam-23	341	7	ac1a)0ab	ac1a)0ab	PROPN
ejpam-23	341	8	.	.	PUNCT
ejpam-23	342	1	however	however	ADV
ejpam-23	342	2	,	,	PUNCT
ejpam-23	342	3	by	by	ADP
ejpam-23	342	4	the	the	DET
ejpam-23	342	5	definition	definition	NOUN
ejpam-23	342	6	of	of	ADP
ejpam-23	342	7	the	the	DET
ejpam-23	342	8	natural	natural	ADJ
ejpam-23	342	9	partial	partial	ADJ
ejpam-23	342	10	order	order	NOUN
ejpam-23	342	11	“	"	PUNCT
ejpam-23	342	12	6	6	NUM
ejpam-23	342	13	”	"	PUNCT
ejpam-23	342	14	,	,	PUNCT
ejpam-23	342	15	we	we	PRON
ejpam-23	342	16	have	have	VERB
ejpam-23	342	17	ab	ab	PROPN
ejpam-23	342	18	>	>	X
ejpam-23	342	19	(	(	PUNCT
ejpam-23	342	20	aϕd(α	aϕd(α	PROPN
ejpam-23	342	21	,	,	PUNCT
ejpam-23	342	22	αβ))(bϕd(β	αβ))(bϕd(β	PROPN
ejpam-23	342	23	,	,	PUNCT
ejpam-23	342	24	αβ	αβ	NOUN
ejpam-23	342	25	)	)	PUNCT
ejpam-23	342	26	)	)	PUNCT
ejpam-23	342	27	.	.	PUNCT
ejpam-23	343	1	on	on	ADP
ejpam-23	343	2	the	the	DET
ejpam-23	343	3	other	other	ADJ
ejpam-23	343	4	hands	hand	NOUN
ejpam-23	343	5	,	,	PUNCT
ejpam-23	343	6	since	since	SCONJ
ejpam-23	343	7	every	every	DET
ejpam-23	343	8	semigroup	semigroup	PROPN
ejpam-23	343	9	sαβ	sαβ	PROPN
ejpam-23	343	10	is	be	AUX
ejpam-23	343	11	primitive	primitive	ADJ
ejpam-23	343	12	,	,	PUNCT
ejpam-23	343	13	we	we	PRON
ejpam-23	343	14	obtain	obtain	VERB
ejpam-23	343	15	ab	ab	NOUN
ejpam-23	343	16	=	=	PUNCT
ejpam-23	343	17	(	(	PUNCT
ejpam-23	343	18	aϕd(α	aϕd(α	PROPN
ejpam-23	343	19	,	,	PUNCT
ejpam-23	343	20	αβ))(bϕd(β	αβ))(bϕd(β	PROPN
ejpam-23	343	21	,	,	PUNCT
ejpam-23	343	22	αβ	αβ	NOUN
ejpam-23	343	23	)	)	PUNCT
ejpam-23	343	24	)	)	PUNCT
ejpam-23	343	25	.	.	PUNCT
ejpam-23	344	1	4	4	X
ejpam-23	344	2	.	.	X
ejpam-23	344	3	structure	structure	NOUN
ejpam-23	344	4	of	of	ADP
ejpam-23	344	5	regular	regular	ADJ
ejpam-23	344	6	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	344	7	in	in	ADP
ejpam-23	344	8	this	this	DET
ejpam-23	344	9	section	section	NOUN
ejpam-23	344	10	,	,	PUNCT
ejpam-23	344	11	we	we	PRON
ejpam-23	344	12	use	use	VERB
ejpam-23	344	13	the	the	DET
ejpam-23	344	14	kg	kg	NOUN
ejpam-23	344	15	-	-	PUNCT
ejpam-23	344	16	strong	strong	ADJ
ejpam-23	344	17	semilattice	semilattice	NOUN
ejpam-23	344	18	to	to	PART
ejpam-23	344	19	characterize	characterize	VERB
ejpam-23	344	20	regular	regular	ADJ
ejpam-23	344	21	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	344	22	.	.	PUNCT
ejpam-23	345	1	also	also	ADV
ejpam-23	345	2	,	,	PUNCT
ejpam-23	345	3	we	we	PRON
ejpam-23	345	4	consider	consider	VERB
ejpam-23	345	5	the	the	DET
ejpam-23	345	6	question	question	NOUN
ejpam-23	345	7	when	when	SCONJ
ejpam-23	345	8	will	will	AUX
ejpam-23	345	9	the	the	DET
ejpam-23	345	10	green	green	ADJ
ejpam-23	345	11	∼-relation	∼-relation	NOUN
ejpam-23	345	12	h̃	h̃	PROPN
ejpam-23	345	13	to	to	PART
ejpam-23	345	14	be	be	AUX
ejpam-23	345	15	a	a	DET
ejpam-23	345	16	right	right	ADJ
ejpam-23	345	17	quasi	quasi	ADJ
ejpam-23	345	18	-	-	ADJ
ejpam-23	345	19	normal	normal	ADJ
ejpam-23	345	20	band	band	NOUN
ejpam-23	345	21	congruence	congruence	NOUN
ejpam-23	345	22	?	?	PUNCT
ejpam-23	346	1	by	by	ADP
ejpam-23	346	2	using	use	VERB
ejpam-23	346	3	the	the	DET
ejpam-23	346	4	kg	kg	ADJ
ejpam-23	346	5	-	-	PUNCT
ejpam-23	346	6	strong	strong	ADJ
ejpam-23	346	7	semilattice	semilattice	NOUN
ejpam-23	346	8	,	,	PUNCT
ejpam-23	346	9	we	we	PRON
ejpam-23	346	10	are	be	AUX
ejpam-23	346	11	able	able	ADJ
ejpam-23	346	12	to	to	PART
ejpam-23	346	13	give	give	VERB
ejpam-23	346	14	a	a	DET
ejpam-23	346	15	description	description	NOUN
ejpam-23	346	16	for	for	ADP
ejpam-23	346	17	the	the	DET
ejpam-23	346	18	normal	normal	ADJ
ejpam-23	346	19	h̃	h̃	PROPN
ejpam-23	346	20	-cryptogroups	-cryptogroup	NOUN
ejpam-23	346	21	.	.	PUNCT
ejpam-23	347	1	we	we	PRON
ejpam-23	347	2	note	note	VERB
ejpam-23	347	3	here	here	ADV
ejpam-23	347	4	that	that	SCONJ
ejpam-23	347	5	the	the	DET
ejpam-23	347	6	orthodox	orthodox	NOUN
ejpam-23	347	7	regular	regular	ADJ
ejpam-23	347	8	h̃	h̃	PROPN
ejpam-23	347	9	-cryptogroups	-cryptogroup	NOUN
ejpam-23	347	10	with	with	ADP
ejpam-23	347	11	kg	kg	ADJ
ejpam-23	347	12	-	-	PUNCT
ejpam-23	347	13	strong	strong	ADJ
ejpam-23	347	14	semilattices	semilattice	NOUN
ejpam-23	347	15	have	have	AUX
ejpam-23	347	16	been	be	AUX
ejpam-23	347	17	studies	study	NOUN
ejpam-23	347	18	in	in	ADP
ejpam-23	347	19	[	[	X
ejpam-23	347	20	10	10	NUM
ejpam-23	347	21	]	]	PUNCT
ejpam-23	347	22	.	.	PUNCT
ejpam-23	348	1	a	a	DET
ejpam-23	348	2	construction	construction	NOUN
ejpam-23	348	3	theorem	theorem	NOUN
ejpam-23	348	4	of	of	ADP
ejpam-23	348	5	orthodox	orthodox	NOUN
ejpam-23	348	6	regular	regular	ADJ
ejpam-23	348	7	h̃	h̃	PROPN
ejpam-23	348	8	-cryptogroups	-cryptogroup	NOUN
ejpam-23	348	9	was	be	AUX
ejpam-23	348	10	also	also	ADV
ejpam-23	348	11	given	give	VERB
ejpam-23	348	12	in	in	ADP
ejpam-23	348	13	[	[	NOUN
ejpam-23	348	14	8	8	NUM
ejpam-23	348	15	]	]	PUNCT
ejpam-23	348	16	.	.	PUNCT
ejpam-23	349	1	theorem	theorem	VERB
ejpam-23	349	2	4.1	4.1	NUM
ejpam-23	349	3	an	an	DET
ejpam-23	349	4	h̃-cryptogroup	h̃-cryptogroup	PROPN
ejpam-23	349	5	s	s	PART
ejpam-23	349	6	is	be	AUX
ejpam-23	349	7	a	a	DET
ejpam-23	349	8	regular	regular	ADJ
ejpam-23	349	9	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	349	10	if	if	SCONJ
ejpam-23	349	11	and	and	CCONJ
ejpam-23	349	12	only	only	ADV
ejpam-23	349	13	if	if	SCONJ
ejpam-23	349	14	s	s	NOUN
ejpam-23	349	15	is	be	AUX
ejpam-23	349	16	an	an	DET
ejpam-23	349	17	h̃g	h̃g	ADJ
ejpam-23	349	18	-	-	PUNCT
ejpam-23	349	19	strong	strong	ADJ
ejpam-23	349	20	semilattice	semilattice	NOUN
ejpam-23	349	21	of	of	ADP
ejpam-23	349	22	completely	completely	ADV
ejpam-23	349	23	j̃	j̃	PROPN
ejpam-23	349	24	-simple	-simple	ADJ
ejpam-23	349	25	semigroups	semigroup	NOUN
ejpam-23	349	26	,	,	PUNCT
ejpam-23	349	27	that	that	ADV
ejpam-23	349	28	is	be	AUX
ejpam-23	349	29	,	,	PUNCT
ejpam-23	349	30	s	s	PART
ejpam-23	349	31	=	=	X
ejpam-23	349	32	h̃g[y	h̃g[y	NOUN
ejpam-23	349	33	;	;	PUNCT
ejpam-23	349	34	sα	sα	ADV
ejpam-23	349	35	,	,	PUNCT
ejpam-23	349	36	ϕα	ϕα	ADV
ejpam-23	349	37	,	,	PUNCT
ejpam-23	349	38	β	β	NOUN
ejpam-23	349	39	]	]	PUNCT
ejpam-23	349	40	.	.	PUNCT
ejpam-23	350	1	proof	proof	NOUN
ejpam-23	350	2	.	.	PUNCT
ejpam-23	351	1	by	by	ADP
ejpam-23	351	2	the	the	DET
ejpam-23	351	3	definition	definition	NOUN
ejpam-23	351	4	of	of	ADP
ejpam-23	351	5	the	the	DET
ejpam-23	351	6	kg	kg	NOUN
ejpam-23	351	7	-	-	PUNCT
ejpam-23	351	8	strong	strong	ADJ
ejpam-23	351	9	semilattice	semilattice	NOUN
ejpam-23	351	10	and	and	CCONJ
ejpam-23	351	11	the	the	DET
ejpam-23	351	12	results	result	NOUN
ejpam-23	351	13	obtained	obtain	VERB
ejpam-23	351	14	in	in	ADP
ejpam-23	351	15	§	§	PROPN
ejpam-23	351	16	3	3	NUM
ejpam-23	351	17	,	,	PUNCT
ejpam-23	351	18	we	we	PRON
ejpam-23	351	19	have	have	AUX
ejpam-23	351	20	already	already	ADV
ejpam-23	351	21	proved	prove	VERB
ejpam-23	351	22	the	the	DET
ejpam-23	351	23	necessity	necessity	NOUN
ejpam-23	351	24	part	part	NOUN
ejpam-23	351	25	of	of	ADP
ejpam-23	351	26	theorem	theorem	NOUN
ejpam-23	351	27	4.1	4.1	NUM
ejpam-23	351	28	since	since	SCONJ
ejpam-23	351	29	it	it	PRON
ejpam-23	351	30	is	be	AUX
ejpam-23	351	31	obvious	obvious	ADJ
ejpam-23	351	32	that	that	SCONJ
ejpam-23	351	33	h̃|sβ	h̃|sβ	PROPN
ejpam-23	351	34	⊆	⊆	NUM
ejpam-23	351	35	ρα	ρα	PROPN
ejpam-23	351	36	,	,	PUNCT
ejpam-23	351	37	β	β	X
ejpam-23	351	38	for	for	ADP
ejpam-23	351	39	α	α	PROPN
ejpam-23	351	40	>	>	X
ejpam-23	351	41	β	β	X
ejpam-23	351	42	on	on	ADP
ejpam-23	351	43	y	y	PROPN
ejpam-23	351	44	.	.	PUNCT
ejpam-23	352	1	we	we	PRON
ejpam-23	352	2	now	now	ADV
ejpam-23	352	3	prove	prove	VERB
ejpam-23	352	4	the	the	DET
ejpam-23	352	5	sufficiency	sufficiency	NOUN
ejpam-23	352	6	part	part	NOUN
ejpam-23	352	7	of	of	ADP
ejpam-23	352	8	the	the	DET
ejpam-23	352	9	theorem	theorem	NOUN
ejpam-23	352	10	.	.	PROPN
ejpam-23	352	11	to	to	PART
ejpam-23	352	12	prove	prove	VERB
ejpam-23	352	13	that	that	SCONJ
ejpam-23	352	14	s	s	PROPN
ejpam-23	352	15	/	/	SYM
ejpam-23	352	16	h̃	h̃	PROPN
ejpam-23	352	17	is	be	AUX
ejpam-23	352	18	a	a	DET
ejpam-23	352	19	regular	regular	ADJ
ejpam-23	352	20	band	band	NOUN
ejpam-23	352	21	,	,	PUNCT
ejpam-23	352	22	we	we	PRON
ejpam-23	352	23	use	use	VERB
ejpam-23	352	24	a	a	DET
ejpam-23	352	25	result	result	NOUN
ejpam-23	352	26	in	in	ADP
ejpam-23	352	27	[	[	X
ejpam-23	352	28	14	14	NUM
ejpam-23	352	29	]	]	PUNCT
ejpam-23	352	30	.	.	PUNCT
ejpam-23	353	1	what	what	PRON
ejpam-23	353	2	we	we	PRON
ejpam-23	353	3	need	need	VERB
ejpam-23	353	4	is	be	AUX
ejpam-23	353	5	to	to	PART
ejpam-23	353	6	prove	prove	VERB
ejpam-23	353	7	that	that	SCONJ
ejpam-23	353	8	the	the	DET
ejpam-23	353	9	usual	usual	ADJ
ejpam-23	353	10	green	green	ADJ
ejpam-23	353	11	relations	relation	NOUN
ejpam-23	353	12	l	l	NOUN
ejpam-23	353	13	and	and	CCONJ
ejpam-23	353	14	r	r	NOUN
ejpam-23	353	15	are	be	AUX
ejpam-23	353	16	congruences	congruence	NOUN
ejpam-23	353	17	on	on	ADP
ejpam-23	353	18	s	s	NOUN
ejpam-23	353	19	/	/	SYM
ejpam-23	353	20	h̃.	h̃.	PROPN
ejpam-23	353	21	in	in	ADP
ejpam-23	353	22	fact	fact	NOUN
ejpam-23	353	23	,	,	PUNCT
ejpam-23	353	24	we	we	PRON
ejpam-23	353	25	only	only	ADV
ejpam-23	353	26	need	need	VERB
ejpam-23	353	27	to	to	PART
ejpam-23	353	28	verify	verify	VERB
ejpam-23	353	29	that	that	SCONJ
ejpam-23	353	30	l	l	NOUN
ejpam-23	353	31	is	be	AUX
ejpam-23	353	32	a	a	DET
ejpam-23	353	33	left	left	ADJ
ejpam-23	353	34	congruence	congruence	NOUN
ejpam-23	353	35	on	on	ADP
ejpam-23	353	36	s	s	PROPN
ejpam-23	353	37	/	/	SYM
ejpam-23	353	38	h̃	h̃	PROPN
ejpam-23	353	39	since	since	SCONJ
ejpam-23	353	40	r	r	NOUN
ejpam-23	353	41	is	be	AUX
ejpam-23	353	42	a	a	DET
ejpam-23	353	43	right	right	ADJ
ejpam-23	353	44	congruence	congruence	NOUN
ejpam-23	353	45	on	on	ADP
ejpam-23	353	46	s	s	PROPN
ejpam-23	353	47	/	/	SYM
ejpam-23	353	48	h̃	h̃	PROPN
ejpam-23	353	49	can	can	AUX
ejpam-23	353	50	be	be	AUX
ejpam-23	353	51	proved	prove	VERB
ejpam-23	353	52	in	in	ADP
ejpam-23	353	53	a	a	DET
ejpam-23	353	54	similar	similar	ADJ
ejpam-23	353	55	fashion	fashion	NOUN
ejpam-23	353	56	.	.	PUNCT
ejpam-23	354	1	since	since	SCONJ
ejpam-23	354	2	s	s	PART
ejpam-23	354	3	=	=	PUNCT
ejpam-23	354	4	(	(	PUNCT
ejpam-23	354	5	y	y	PROPN
ejpam-23	354	6	;	;	PUNCT
ejpam-23	354	7	sα	sα	X
ejpam-23	354	8	)	)	PUNCT
ejpam-23	354	9	is	be	AUX
ejpam-23	354	10	an	an	DET
ejpam-23	354	11	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	354	12	,	,	PUNCT
ejpam-23	354	13	we	we	PRON
ejpam-23	354	14	can	can	AUX
ejpam-23	354	15	let	let	VERB
ejpam-23	354	16	eh̃	eh̃	NOUN
ejpam-23	354	17	,	,	PUNCT
ejpam-23	354	18	fh̃	fh̃	NUM
ejpam-23	354	19	and	and	CCONJ
ejpam-23	354	20	gh̃	gh̃	ADP
ejpam-23	354	21	∈	∈	PROPN
ejpam-23	354	22	s	s	PROPN
ejpam-23	354	23	/	/	SYM
ejpam-23	354	24	h̃	h̃	PROPN
ejpam-23	354	25	,	,	PUNCT
ejpam-23	354	26	where	where	SCONJ
ejpam-23	354	27	e	e	NOUN
ejpam-23	354	28	,	,	PUNCT
ejpam-23	354	29	f	f	PROPN
ejpam-23	354	30	∈	∈	PROPN
ejpam-23	354	31	sα	sα	NOUN
ejpam-23	354	32	∩	∩	ADJ
ejpam-23	354	33	e(s	e(s	PROPN
ejpam-23	354	34	)	)	PUNCT
ejpam-23	354	35	,	,	PUNCT
ejpam-23	354	36	g	g	PROPN
ejpam-23	354	37	∈	∈	PROPN
ejpam-23	354	38	sβ	sβ	NUM
ejpam-23	354	39	∩	∩	NOUN
ejpam-23	354	40	e(s	e(s	PROPN
ejpam-23	354	41	)	)	PUNCT
ejpam-23	354	42	with	with	ADP
ejpam-23	354	43	(	(	PUNCT
ejpam-23	354	44	e	e	NOUN
ejpam-23	354	45	,	,	PUNCT
ejpam-23	354	46	f	f	X
ejpam-23	354	47	)	)	PUNCT
ejpam-23	354	48	∈	∈	PROPN
ejpam-23	355	1	l̃.	l̃.	ADV
ejpam-23	355	2	then	then	ADV
ejpam-23	355	3	,	,	PUNCT
ejpam-23	355	4	we	we	PRON
ejpam-23	355	5	have	have	VERB
ejpam-23	355	6	ef	ef	NOUN
ejpam-23	355	7	=	=	SYM
ejpam-23	355	8	e	e	PROPN
ejpam-23	355	9	and	and	CCONJ
ejpam-23	355	10	fe	fe	X
ejpam-23	355	11	=	=	SYM
ejpam-23	355	12	f	f	PROPN
ejpam-23	355	13	.	.	PUNCT
ejpam-23	356	1	by	by	ADP
ejpam-23	356	2	the	the	DET
ejpam-23	356	3	definition	definition	NOUN
ejpam-23	356	4	of	of	ADP
ejpam-23	356	5	h̃g	h̃g	ADJ
ejpam-23	356	6	-	-	PUNCT
ejpam-23	356	7	strong	strong	ADJ
ejpam-23	356	8	semilattice	semilattice	NOUN
ejpam-23	356	9	h̃g[y	h̃g[y	NOUN
ejpam-23	356	10	;	;	PUNCT
ejpam-23	356	11	sα	sα	X
ejpam-23	356	12	,	,	PUNCT
ejpam-23	356	13	ϕα	ϕα	ADV
ejpam-23	356	14	,	,	PUNCT
ejpam-23	356	15	β	β	X
ejpam-23	356	16	]	]	X
ejpam-23	356	17	,	,	PUNCT
ejpam-23	356	18	we	we	PRON
ejpam-23	356	19	can	can	AUX
ejpam-23	356	20	find	find	VERB
ejpam-23	356	21	the	the	DET
ejpam-23	356	22	homomorphisms	homomorphism	NOUN
ejpam-23	356	23	ϕef	ϕef	ADP
ejpam-23	356	24	d(β	d(β	PROPN
ejpam-23	356	25	,	,	PUNCT
ejpam-23	356	26	αβ	αβ	INTJ
ejpam-23	356	27	)	)	PUNCT
ejpam-23	356	28	and	and	CCONJ
ejpam-23	356	29	ϕf	ϕf	PROPN
ejpam-23	356	30	d(β	d(β	PROPN
ejpam-23	356	31	,	,	PUNCT
ejpam-23	356	32	αβ	αβ	INTJ
ejpam-23	356	33	)	)	PUNCT
ejpam-23	356	34	∈	∈	PROPN
ejpam-23	356	35	ϕβ	ϕβ	PROPN
ejpam-23	356	36	,	,	PUNCT
ejpam-23	356	37	αβ	αβ	INTJ
ejpam-23	356	38	,	,	PUNCT
ejpam-23	356	39	ϕg	ϕg	PROPN
ejpam-23	356	40	d(α	d(α	PROPN
ejpam-23	356	41	,	,	PUNCT
ejpam-23	356	42	αβ	αβ	INTJ
ejpam-23	356	43	)	)	PUNCT
ejpam-23	356	44	∈	∈	PROPN
ejpam-23	356	45	ϕα	ϕα	ADV
ejpam-23	356	46	,	,	PUNCT
ejpam-23	356	47	αβ	αβ	INTJ
ejpam-23	356	48	such	such	ADJ
ejpam-23	356	49	that	that	PRON
ejpam-23	356	50	(	(	PUNCT
ejpam-23	356	51	gegf)h̃	gegf)h̃	NOUN
ejpam-23	356	52	=	=	PUNCT
ejpam-23	356	53	{	{	PUNCT
ejpam-23	357	1	[	[	X
ejpam-23	357	2	g(ef)](gf)}h̃	g(ef)](gf)}h̃	VERB
ejpam-23	357	3	=	=	PUNCT
ejpam-23	357	4	{	{	PUNCT
ejpam-23	357	5	[	[	X
ejpam-23	357	6	(	(	PUNCT
ejpam-23	357	7	gϕef	gϕef	PROPN
ejpam-23	357	8	d(β	d(β	PROPN
ejpam-23	357	9	,	,	PUNCT
ejpam-23	357	10	αβ))((ef)ϕg	αβ))((ef)ϕg	PROPN
ejpam-23	357	11	d(α	d(α	PROPN
ejpam-23	357	12	,	,	PUNCT
ejpam-23	357	13	αβ))][(gϕf	αβ))][(gϕf	NUM
ejpam-23	357	14	d(β	d(β	PROPN
ejpam-23	357	15	,	,	PUNCT
ejpam-23	357	16	αβ))(fϕg	αβ))(fϕg	NOUN
ejpam-23	357	17	d(α	d(α	NOUN
ejpam-23	357	18	,	,	PUNCT
ejpam-23	357	19	αβ))]}h̃	αβ))]}h̃	NUM
ejpam-23	357	20	=	=	SYM
ejpam-23	357	21	[	[	X
ejpam-23	357	22	(	(	PUNCT
ejpam-23	357	23	gϕef	gϕef	PROPN
ejpam-23	357	24	d(β	d(β	PROPN
ejpam-23	357	25	,	,	PUNCT
ejpam-23	357	26	αβ))(fϕg	αβ))(fϕg	NOUN
ejpam-23	357	27	d(α	d(α	NOUN
ejpam-23	357	28	,	,	PUNCT
ejpam-23	357	29	αβ))]h̃	αβ))]h̃	PROPN
ejpam-23	357	30	x.	x.	PROPN
ejpam-23	357	31	kong	kong	PROPN
ejpam-23	357	32	,	,	PUNCT
ejpam-23	357	33	y.ding	y.de	VERB
ejpam-23	357	34	,	,	PUNCT
ejpam-23	357	35	k.p.shum	k.p.shum	ADJ
ejpam-23	357	36	/	/	SYM
ejpam-23	357	37	eur	eur	PROPN
ejpam-23	357	38	.	.	PUNCT
ejpam-23	358	1	j.	j.	PROPN
ejpam-23	358	2	pure	pure	PROPN
ejpam-23	358	3	appl	appl	PROPN
ejpam-23	358	4	.	.	PROPN
ejpam-23	358	5	math	math	PROPN
ejpam-23	358	6	,	,	PUNCT
ejpam-23	358	7	1	1	NUM
ejpam-23	358	8	(	(	PUNCT
ejpam-23	358	9	2008	2008	NUM
ejpam-23	358	10	)	)	PUNCT
ejpam-23	358	11	,	,	PUNCT
ejpam-23	358	12	(	(	PUNCT
ejpam-23	358	13	46	46	NUM
ejpam-23	358	14	-	-	SYM
ejpam-23	358	15	59	59	NUM
ejpam-23	358	16	)	)	PUNCT
ejpam-23	358	17	57	57	NUM
ejpam-23	358	18	and	and	CCONJ
ejpam-23	358	19	(	(	PUNCT
ejpam-23	358	20	ge)h̃	ge)h̃	NOUN
ejpam-23	358	21	=	=	PUNCT
ejpam-23	359	1	[	[	X
ejpam-23	359	2	g(ef)]h̃	g(ef)]h̃	X
ejpam-23	359	3	=	=	PUNCT
ejpam-23	360	1	[	[	X
ejpam-23	360	2	(	(	PUNCT
ejpam-23	360	3	gϕef	gϕef	PROPN
ejpam-23	360	4	d(β	d(β	PROPN
ejpam-23	360	5	,	,	PUNCT
ejpam-23	360	6	αβ))((ef)ϕg	αβ))((ef)ϕg	PROPN
ejpam-23	360	7	d(α	d(α	PROPN
ejpam-23	360	8	,	,	PUNCT
ejpam-23	360	9	αβ))]h̃	αβ))]h̃	NOUN
ejpam-23	360	10	=	=	SYM
ejpam-23	361	1	[	[	X
ejpam-23	361	2	(	(	PUNCT
ejpam-23	361	3	gϕef	gϕef	PROPN
ejpam-23	361	4	d(β	d(β	PROPN
ejpam-23	361	5	,	,	PUNCT
ejpam-23	361	6	αβ))(fϕg	αβ))(fϕg	NOUN
ejpam-23	361	7	d(α	d(α	NOUN
ejpam-23	361	8	,	,	PUNCT
ejpam-23	361	9	αβ))]h̃.	αβ))]h̃.	NOUN
ejpam-23	361	10	thereby	thereby	ADV
ejpam-23	361	11	,	,	PUNCT
ejpam-23	361	12	(	(	PUNCT
ejpam-23	361	13	gegf)h̃	gegf)h̃	NOUN
ejpam-23	361	14	=	=	PUNCT
ejpam-23	361	15	(	(	PUNCT
ejpam-23	361	16	ge)h̃.	ge)h̃.	NOUN
ejpam-23	361	17	analogously	analogously	ADV
ejpam-23	361	18	,	,	PUNCT
ejpam-23	361	19	we	we	PRON
ejpam-23	361	20	can	can	AUX
ejpam-23	361	21	also	also	ADV
ejpam-23	361	22	prove	prove	VERB
ejpam-23	361	23	that	that	SCONJ
ejpam-23	361	24	(	(	PUNCT
ejpam-23	361	25	gfge)h̃	gfge)h̃	NOUN
ejpam-23	361	26	=	=	SYM
ejpam-23	361	27	(	(	PUNCT
ejpam-23	361	28	gf)h̃	gf)h̃	NOUN
ejpam-23	361	29	.	.	PUNCT
ejpam-23	362	1	this	this	PRON
ejpam-23	362	2	proves	prove	VERB
ejpam-23	362	3	that	that	SCONJ
ejpam-23	362	4	l	l	NOUN
ejpam-23	362	5	is	be	AUX
ejpam-23	362	6	left	leave	VERB
ejpam-23	362	7	compatible	compatible	ADJ
ejpam-23	362	8	with	with	ADP
ejpam-23	362	9	the	the	DET
ejpam-23	362	10	multiplication	multiplication	NOUN
ejpam-23	362	11	of	of	ADP
ejpam-23	362	12	s	s	NOUN
ejpam-23	362	13	/	/	SYM
ejpam-23	362	14	h̃.	h̃.	PROPN
ejpam-23	362	15	since	since	SCONJ
ejpam-23	362	16	l	l	NOUN
ejpam-23	362	17	is	be	AUX
ejpam-23	362	18	always	always	ADV
ejpam-23	362	19	right	right	ADJ
ejpam-23	362	20	congruence	congruence	NOUN
ejpam-23	362	21	,	,	PUNCT
ejpam-23	362	22	l	l	NOUN
ejpam-23	362	23	is	be	AUX
ejpam-23	362	24	a	a	DET
ejpam-23	362	25	congruence	congruence	NOUN
ejpam-23	362	26	on	on	ADP
ejpam-23	362	27	s	s	PROPN
ejpam-23	362	28	/	/	SYM
ejpam-23	362	29	h̃	h̃	PROPN
ejpam-23	362	30	,	,	PUNCT
ejpam-23	362	31	as	as	SCONJ
ejpam-23	362	32	required	require	VERB
ejpam-23	362	33	.	.	PUNCT
ejpam-23	363	1	dually	dually	PROPN
ejpam-23	363	2	,	,	PUNCT
ejpam-23	363	3	r	r	NOUN
ejpam-23	363	4	is	be	AUX
ejpam-23	363	5	also	also	ADV
ejpam-23	363	6	a	a	DET
ejpam-23	363	7	congruence	congruence	NOUN
ejpam-23	363	8	on	on	ADP
ejpam-23	363	9	s	s	NOUN
ejpam-23	363	10	/	/	SYM
ejpam-23	363	11	h̃.	h̃.	PROPN
ejpam-23	363	12	thus	thus	ADV
ejpam-23	363	13	by	by	ADP
ejpam-23	363	14	[	[	X
ejpam-23	363	15	14	14	NUM
ejpam-23	363	16	]	]	PUNCT
ejpam-23	363	17	(	(	PUNCT
ejpam-23	363	18	see	see	VERB
ejpam-23	363	19	ii	ii	PROPN
ejpam-23	363	20	.	.	PROPN
ejpam-23	363	21	3.6	3.6	NUM
ejpam-23	363	22	proposition	proposition	NOUN
ejpam-23	363	23	)	)	PUNCT
ejpam-23	363	24	,	,	PUNCT
ejpam-23	363	25	s	s	X
ejpam-23	363	26	/	/	SYM
ejpam-23	363	27	h̃	h̃	PROPN
ejpam-23	363	28	forms	form	VERB
ejpam-23	363	29	a	a	DET
ejpam-23	363	30	regular	regular	ADJ
ejpam-23	363	31	band	band	NOUN
ejpam-23	363	32	and	and	CCONJ
ejpam-23	363	33	hence	hence	ADV
ejpam-23	363	34	s	s	VERB
ejpam-23	363	35	is	be	AUX
ejpam-23	363	36	indeed	indeed	ADV
ejpam-23	363	37	a	a	DET
ejpam-23	363	38	regular	regular	ADJ
ejpam-23	363	39	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	363	40	.	.	PUNCT
ejpam-23	364	1	our	our	PRON
ejpam-23	364	2	proof	proof	NOUN
ejpam-23	364	3	is	be	AUX
ejpam-23	364	4	completed	complete	VERB
ejpam-23	364	5	.	.	PUNCT
ejpam-23	365	1	recall	recall	VERB
ejpam-23	365	2	that	that	SCONJ
ejpam-23	365	3	a	a	DET
ejpam-23	365	4	right	right	ADJ
ejpam-23	365	5	quasi	quasi	ADJ
ejpam-23	365	6	-	-	ADJ
ejpam-23	365	7	normal	normal	ADJ
ejpam-23	365	8	band	band	NOUN
ejpam-23	365	9	is	be	AUX
ejpam-23	365	10	a	a	DET
ejpam-23	365	11	band	band	NOUN
ejpam-23	365	12	satisfying	satisfy	VERB
ejpam-23	365	13	the	the	DET
ejpam-23	365	14	identity	identity	NOUN
ejpam-23	365	15	yxa	yxa	NOUN
ejpam-23	365	16	=	=	PUNCT
ejpam-23	365	17	yaxa	yaxa	NOUN
ejpam-23	366	1	[	[	X
ejpam-23	366	2	6	6	NUM
ejpam-23	366	3	]	]	PUNCT
ejpam-23	366	4	.	.	PUNCT
ejpam-23	367	1	also	also	ADV
ejpam-23	367	2	,	,	PUNCT
ejpam-23	367	3	a	a	DET
ejpam-23	367	4	left	left	ADJ
ejpam-23	367	5	quasi	quasi	ADJ
ejpam-23	367	6	-	-	ADJ
ejpam-23	367	7	normal	normal	ADJ
ejpam-23	367	8	band	band	NOUN
ejpam-23	367	9	is	be	AUX
ejpam-23	367	10	a	a	DET
ejpam-23	367	11	band	band	NOUN
ejpam-23	367	12	satisfying	satisfy	VERB
ejpam-23	367	13	the	the	DET
ejpam-23	367	14	identity	identity	NOUN
ejpam-23	367	15	axy	axy	NOUN
ejpam-23	367	16	=	=	SYM
ejpam-23	367	17	axay	axay	PROPN
ejpam-23	367	18	.	.	PUNCT
ejpam-23	368	1	thus	thus	ADV
ejpam-23	368	2	,	,	PUNCT
ejpam-23	368	3	we	we	PRON
ejpam-23	368	4	can	can	AUX
ejpam-23	368	5	easily	easily	ADV
ejpam-23	368	6	observe	observe	VERB
ejpam-23	368	7	that	that	SCONJ
ejpam-23	368	8	both	both	CCONJ
ejpam-23	368	9	the	the	DET
ejpam-23	368	10	right	right	ADJ
ejpam-23	368	11	quasi	quasi	ADJ
ejpam-23	368	12	-	-	ADJ
ejpam-23	368	13	normal	normal	ADJ
ejpam-23	368	14	bands	band	NOUN
ejpam-23	368	15	and	and	CCONJ
ejpam-23	368	16	the	the	DET
ejpam-23	368	17	left	left	ADJ
ejpam-23	368	18	quasi	quasi	ADJ
ejpam-23	368	19	-	-	ADJ
ejpam-23	368	20	normal	normal	ADJ
ejpam-23	368	21	bands	band	NOUN
ejpam-23	368	22	are	be	AUX
ejpam-23	368	23	special	special	ADJ
ejpam-23	368	24	cases	case	NOUN
ejpam-23	368	25	of	of	ADP
ejpam-23	368	26	the	the	DET
ejpam-23	368	27	regular	regular	ADJ
ejpam-23	368	28	bands	band	NOUN
ejpam-23	368	29	.	.	PUNCT
ejpam-23	369	1	also	also	ADV
ejpam-23	369	2	,	,	PUNCT
ejpam-23	369	3	a	a	DET
ejpam-23	369	4	normal	normal	ADJ
ejpam-23	369	5	band	band	NOUN
ejpam-23	369	6	(	(	PUNCT
ejpam-23	369	7	that	that	ADV
ejpam-23	369	8	is	is	ADV
ejpam-23	369	9	,	,	PUNCT
ejpam-23	369	10	a	a	DET
ejpam-23	369	11	band	band	NOUN
ejpam-23	369	12	satisfies	satisfy	VERB
ejpam-23	369	13	the	the	DET
ejpam-23	369	14	identity	identity	NOUN
ejpam-23	369	15	axya	axya	NOUN
ejpam-23	369	16	=	=	SYM
ejpam-23	369	17	ayxa	ayxa	NOUN
ejpam-23	369	18	)	)	PUNCT
ejpam-23	369	19	is	be	AUX
ejpam-23	369	20	a	a	DET
ejpam-23	369	21	special	special	ADJ
ejpam-23	369	22	right	right	NOUN
ejpam-23	369	23	quasi	quasi	ADJ
ejpam-23	369	24	-	-	ADJ
ejpam-23	369	25	normal	normal	ADJ
ejpam-23	369	26	band	band	NOUN
ejpam-23	369	27	and	and	CCONJ
ejpam-23	369	28	a	a	DET
ejpam-23	369	29	left	left	ADJ
ejpam-23	369	30	quasi	quasi	ADJ
ejpam-23	369	31	-	-	ADJ
ejpam-23	369	32	normal	normal	ADJ
ejpam-23	369	33	band	band	NOUN
ejpam-23	369	34	.	.	PUNCT
ejpam-23	370	1	based	base	VERB
ejpam-23	370	2	on	on	ADP
ejpam-23	370	3	the	the	DET
ejpam-23	370	4	above	above	ADJ
ejpam-23	370	5	observation	observation	NOUN
ejpam-23	370	6	,	,	PUNCT
ejpam-23	370	7	we	we	PRON
ejpam-23	370	8	are	be	AUX
ejpam-23	370	9	able	able	ADJ
ejpam-23	370	10	to	to	PART
ejpam-23	370	11	establish	establish	VERB
ejpam-23	370	12	the	the	DET
ejpam-23	370	13	following	follow	VERB
ejpam-23	370	14	theorem	theorem	NOUN
ejpam-23	370	15	for	for	ADP
ejpam-23	370	16	right	right	ADJ
ejpam-23	370	17	quasi	quasi	ADJ
ejpam-23	370	18	-	-	ADJ
ejpam-23	370	19	normal	normal	ADJ
ejpam-23	370	20	h̃-cryptogroups	h̃-cryptogroup	NOUN
ejpam-23	370	21	.	.	PUNCT
ejpam-23	371	1	theorem	theorem	VERB
ejpam-23	371	2	4.2	4.2	NUM
ejpam-23	371	3	an	an	DET
ejpam-23	371	4	h̃-abundant	h̃-abundant	ADJ
ejpam-23	371	5	semigroup	semigroup	NOUN
ejpam-23	371	6	s	s	VERB
ejpam-23	371	7	is	be	AUX
ejpam-23	371	8	a	a	DET
ejpam-23	371	9	right	right	ADJ
ejpam-23	371	10	quasi	quasi	ADJ
ejpam-23	371	11	-	-	ADJ
ejpam-23	371	12	normal	normal	ADJ
ejpam-23	371	13	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	372	1	if	if	SCONJ
ejpam-23	372	2	and	and	CCONJ
ejpam-23	372	3	only	only	ADV
ejpam-23	372	4	if	if	SCONJ
ejpam-23	372	5	s	s	NOUN
ejpam-23	372	6	is	be	AUX
ejpam-23	372	7	an	an	DET
ejpam-23	372	8	l̃g	l̃g	ADJ
ejpam-23	372	9	-	-	ADJ
ejpam-23	372	10	strong	strong	ADJ
ejpam-23	372	11	semilattice	semilattice	NOUN
ejpam-23	372	12	of	of	ADP
ejpam-23	372	13	completely	completely	ADV
ejpam-23	372	14	j̃	j̃	PROPN
ejpam-23	372	15	-simple	-simple	ADJ
ejpam-23	372	16	semigroups	semigroup	NOUN
ejpam-23	372	17	,	,	PUNCT
ejpam-23	372	18	that	that	ADV
ejpam-23	372	19	is	be	AUX
ejpam-23	372	20	,	,	PUNCT
ejpam-23	372	21	s	s	PART
ejpam-23	372	22	=	=	PUNCT
ejpam-23	372	23	l̃g[y	l̃g[y	PROPN
ejpam-23	372	24	;	;	PUNCT
ejpam-23	372	25	sα	sα	ADJ
ejpam-23	372	26	,	,	PUNCT
ejpam-23	372	27	ϕα	ϕα	ADV
ejpam-23	372	28	,	,	PUNCT
ejpam-23	372	29	β	β	NOUN
ejpam-23	372	30	]	]	PUNCT
ejpam-23	372	31	.	.	PUNCT
ejpam-23	373	1	proof	proof	NOUN
ejpam-23	373	2	.	.	PUNCT
ejpam-23	374	1	(	(	PUNCT
ejpam-23	374	2	necessity	necessity	NOUN
ejpam-23	374	3	)	)	PUNCT
ejpam-23	374	4	let	let	VERB
ejpam-23	374	5	s	s	PRON
ejpam-23	374	6	be	be	AUX
ejpam-23	374	7	a	a	DET
ejpam-23	374	8	right	right	ADJ
ejpam-23	374	9	quasi	quasi	ADJ
ejpam-23	374	10	-	-	ADJ
ejpam-23	374	11	normal	normal	ADJ
ejpam-23	374	12	h̃	h̃	PROPN
ejpam-23	374	13	-cryptogroup	-cryptogroup	NOUN
ejpam-23	374	14	.	.	PUNCT
ejpam-23	375	1	then	then	ADV
ejpam-23	375	2	s	s	X
ejpam-23	375	3	/	/	SYM
ejpam-23	375	4	h̃	h̃	PROPN
ejpam-23	375	5	is	be	AUX
ejpam-23	375	6	a	a	DET
ejpam-23	375	7	right	right	ADJ
ejpam-23	375	8	quasi	quasi	ADJ
ejpam-23	375	9	-	-	ADJ
ejpam-23	375	10	normal	normal	ADJ
ejpam-23	375	11	band	band	NOUN
ejpam-23	375	12	.	.	PUNCT
ejpam-23	376	1	to	to	PART
ejpam-23	376	2	show	show	VERB
ejpam-23	376	3	that	that	SCONJ
ejpam-23	376	4	s	s	VERB
ejpam-23	376	5	is	be	AUX
ejpam-23	376	6	an	an	DET
ejpam-23	376	7	l̃g	l̃g	ADJ
ejpam-23	376	8	-	-	ADJ
ejpam-23	376	9	strong	strong	ADJ
ejpam-23	376	10	semilattice	semilattice	NOUN
ejpam-23	376	11	,	,	PUNCT
ejpam-23	376	12	by	by	ADP
ejpam-23	376	13	invoking	invoke	VERB
ejpam-23	376	14	lemma	lemma	PROPN
ejpam-23	376	15	3.3	3.3	NUM
ejpam-23	376	16	and	and	CCONJ
ejpam-23	376	17	its	its	PRON
ejpam-23	376	18	proof	proof	NOUN
ejpam-23	376	19	,	,	PUNCT
ejpam-23	376	20	we	we	PRON
ejpam-23	376	21	only	only	ADV
ejpam-23	376	22	need	need	VERB
ejpam-23	376	23	to	to	PART
ejpam-23	376	24	show	show	VERB
ejpam-23	376	25	that	that	SCONJ
ejpam-23	376	26	for	for	ADP
ejpam-23	376	27	any	any	DET
ejpam-23	376	28	δ	δ	PROPN
ejpam-23	376	29	>	>	X
ejpam-23	376	30	γ	γ	X
ejpam-23	376	31	on	on	ADP
ejpam-23	376	32	y	y	PROPN
ejpam-23	376	33	,	,	PUNCT
ejpam-23	376	34	l̃|sγ	l̃|sγ	PROPN
ejpam-23	376	35	⊆	⊆	NUM
ejpam-23	376	36	ρδ	ρδ	NOUN
ejpam-23	376	37	,	,	PUNCT
ejpam-23	376	38	γ	γ	X
ejpam-23	376	39	.	.	PUNCT
ejpam-23	377	1	in	in	ADP
ejpam-23	377	2	fact	fact	NOUN
ejpam-23	377	3	,	,	PUNCT
ejpam-23	377	4	for	for	ADP
ejpam-23	377	5	a	a	DET
ejpam-23	377	6	∈	∈	PROPN
ejpam-23	377	7	sδ	sδ	NOUN
ejpam-23	377	8	,	,	PUNCT
ejpam-23	377	9	x	x	AUX
ejpam-23	377	10	,	,	PUNCT
ejpam-23	377	11	y	y	PROPN
ejpam-23	377	12	∈	∈	PROPN
ejpam-23	377	13	sγ	sγ	VERB
ejpam-23	377	14	with	with	ADP
ejpam-23	377	15	(	(	PUNCT
ejpam-23	377	16	x	x	NOUN
ejpam-23	377	17	,	,	PUNCT
ejpam-23	377	18	y	y	NOUN
ejpam-23	377	19	)	)	PUNCT
ejpam-23	377	20	∈	∈	PROPN
ejpam-23	377	21	l̃	l̃	PROPN
ejpam-23	377	22	,	,	PUNCT
ejpam-23	377	23	we	we	PRON
ejpam-23	377	24	have	have	VERB
ejpam-23	377	25	(	(	PUNCT
ejpam-23	377	26	axa)h̃	axa)h̃	NUM
ejpam-23	377	27	=	=	PUNCT
ejpam-23	377	28	(	(	PUNCT
ejpam-23	377	29	(	(	PUNCT
ejpam-23	377	30	axy)a)h̃	axy)a)h̃	NOUN
ejpam-23	377	31	=	=	PRON
ejpam-23	377	32	(	(	PUNCT
ejpam-23	377	33	ayxya)h̃	ayxya)h̃	NOUN
ejpam-23	377	34	=	=	PUNCT
ejpam-23	377	35	(	(	PUNCT
ejpam-23	377	36	aya)h̃	aya)h̃	ADV
ejpam-23	377	37	by	by	ADP
ejpam-23	377	38	the	the	DET
ejpam-23	377	39	right	right	ADJ
ejpam-23	377	40	quasi	quasi	NOUN
ejpam-23	377	41	-	-	NOUN
ejpam-23	377	42	normality	normality	NOUN
ejpam-23	377	43	of	of	ADP
ejpam-23	377	44	the	the	DET
ejpam-23	377	45	band	band	NOUN
ejpam-23	377	46	s	s	PART
ejpam-23	377	47	/	/	SYM
ejpam-23	377	48	h̃.	h̃.	PROPN
ejpam-23	377	49	thus	thus	ADV
ejpam-23	377	50	,	,	PUNCT
ejpam-23	377	51	by	by	ADP
ejpam-23	377	52	the	the	DET
ejpam-23	377	53	definition	definition	NOUN
ejpam-23	377	54	of	of	ADP
ejpam-23	377	55	ρδ	ρδ	NOUN
ejpam-23	377	56	,	,	PUNCT
ejpam-23	377	57	γ	γ	X
ejpam-23	377	58	,	,	PUNCT
ejpam-23	377	59	we	we	PRON
ejpam-23	377	60	have	have	VERB
ejpam-23	377	61	l̃|sγ	l̃|sγ	ADJ
ejpam-23	377	62	⊆	⊆	NUM
ejpam-23	377	63	ρδ	ρδ	NOUN
ejpam-23	377	64	,	,	PUNCT
ejpam-23	377	65	γ	γ	X
ejpam-23	377	66	as	as	SCONJ
ejpam-23	377	67	required	require	VERB
ejpam-23	377	68	.	.	PUNCT
ejpam-23	378	1	this	this	PRON
ejpam-23	378	2	shows	show	VERB
ejpam-23	378	3	that	that	SCONJ
ejpam-23	378	4	s	s	VERB
ejpam-23	378	5	=	=	PUNCT
ejpam-23	378	6	l̃g[y	l̃g[y	PROPN
ejpam-23	378	7	;	;	PUNCT
ejpam-23	378	8	sα	sα	ADV
ejpam-23	378	9	,	,	PUNCT
ejpam-23	378	10	ϕα	ϕα	ADV
ejpam-23	378	11	,	,	PUNCT
ejpam-23	378	12	β	β	NOUN
ejpam-23	378	13	]	]	X
ejpam-23	378	14	.	.	PUNCT
ejpam-23	379	1	(	(	PUNCT
ejpam-23	379	2	sufficiency	sufficiency	NOUN
ejpam-23	379	3	)	)	PUNCT
ejpam-23	379	4	let	let	VERB
ejpam-23	379	5	a	a	DET
ejpam-23	379	6	∈	∈	NOUN
ejpam-23	379	7	sα	sα	NOUN
ejpam-23	379	8	,	,	PUNCT
ejpam-23	379	9	x	x	PROPN
ejpam-23	379	10	∈	∈	PROPN
ejpam-23	379	11	sβ	sβ	X
ejpam-23	379	12	,	,	PUNCT
ejpam-23	379	13	and	and	CCONJ
ejpam-23	379	14	y	y	PROPN
ejpam-23	379	15	∈	∈	PROPN
ejpam-23	379	16	sγ	sγ	INTJ
ejpam-23	379	17	.	.	PUNCT
ejpam-23	380	1	then	then	ADV
ejpam-23	380	2	,	,	PUNCT
ejpam-23	380	3	since	since	SCONJ
ejpam-23	380	4	s	s	PART
ejpam-23	380	5	=	=	VERB
ejpam-23	380	6	l̃g[y	l̃g[y	PROPN
ejpam-23	380	7	;	;	PUNCT
ejpam-23	380	8	sα	sα	ADJ
ejpam-23	380	9	,	,	PUNCT
ejpam-23	380	10	ϕα	ϕα	ADV
ejpam-23	380	11	,	,	PUNCT
ejpam-23	380	12	β	β	X
ejpam-23	380	13	]	]	X
ejpam-23	380	14	is	be	AUX
ejpam-23	380	15	an	an	DET
ejpam-23	380	16	h̃g	h̃g	ADJ
ejpam-23	380	17	-	-	PUNCT
ejpam-23	380	18	strong	strong	ADJ
ejpam-23	380	19	semilattice	semilattice	NOUN
ejpam-23	380	20	of	of	ADP
ejpam-23	380	21	sα	sα	ADV
ejpam-23	380	22	and	and	CCONJ
ejpam-23	380	23	by	by	ADP
ejpam-23	380	24	theorem	theorem	NOUN
ejpam-23	380	25	4.1	4.1	NUM
ejpam-23	380	26	,	,	PUNCT
ejpam-23	380	27	h̃	h̃	PROPN
ejpam-23	380	28	is	be	AUX
ejpam-23	380	29	a	a	DET
ejpam-23	380	30	congruence	congruence	NOUN
ejpam-23	380	31	on	on	ADP
ejpam-23	380	32	s.	s.	PROPN
ejpam-23	380	33	moreover	moreover	ADV
ejpam-23	380	34	,	,	PUNCT
ejpam-23	380	35	we	we	PRON
ejpam-23	380	36	have	have	VERB
ejpam-23	380	37	xa	xa	PROPN
ejpam-23	380	38	=	=	PRON
ejpam-23	380	39	(	(	PUNCT
ejpam-23	380	40	xϕa	xϕa	PROPN
ejpam-23	380	41	d(β	d(β	PROPN
ejpam-23	380	42	,	,	PUNCT
ejpam-23	380	43	αβ))(aϕx	αβ))(aϕx	PROPN
ejpam-23	380	44	d(α	d(α	NOUN
ejpam-23	380	45	,	,	PUNCT
ejpam-23	380	46	αβ	αβ	NOUN
ejpam-23	380	47	)	)	PUNCT
ejpam-23	380	48	)	)	PUNCT
ejpam-23	380	49	and	and	CCONJ
ejpam-23	380	50	thereby	thereby	ADV
ejpam-23	380	51	,	,	PUNCT
ejpam-23	380	52	axa	axa	NOUN
ejpam-23	380	53	=	=	PUNCT
ejpam-23	380	54	(	(	PUNCT
ejpam-23	380	55	aϕx	aϕx	PROPN
ejpam-23	380	56	d(α	d(α	PROPN
ejpam-23	380	57	,	,	PUNCT
ejpam-23	380	58	αβ))(xϕa	αβ))(xϕa	PROPN
ejpam-23	380	59	d(β	d(β	PROPN
ejpam-23	380	60	,	,	PUNCT
ejpam-23	380	61	αβ))(aϕx	αβ))(aϕx	PROPN
ejpam-23	380	62	d(α	d(α	NOUN
ejpam-23	380	63	,	,	PUNCT
ejpam-23	380	64	αβ	αβ	NOUN
ejpam-23	380	65	)	)	PUNCT
ejpam-23	380	66	)	)	PUNCT
ejpam-23	380	67	.	.	PUNCT
ejpam-23	381	1	by	by	ADP
ejpam-23	381	2	the	the	DET
ejpam-23	381	3	fact	fact	NOUN
ejpam-23	381	4	(	(	PUNCT
ejpam-23	381	5	(	(	PUNCT
ejpam-23	381	6	xa)0	xa)0	PROPN
ejpam-23	381	7	,	,	PUNCT
ejpam-23	381	8	(	(	PUNCT
ejpam-23	381	9	axa)0	axa)0	PROPN
ejpam-23	381	10	)	)	PUNCT
ejpam-23	381	11	∈	∈	PROPN
ejpam-23	381	12	l	l	NOUN
ejpam-23	381	13	,	,	PUNCT
ejpam-23	381	14	we	we	PRON
ejpam-23	381	15	can	can	AUX
ejpam-23	381	16	easily	easily	ADV
ejpam-23	381	17	see	see	VERB
ejpam-23	381	18	that	that	SCONJ
ejpam-23	381	19	(	(	PUNCT
ejpam-23	381	20	xa	xa	PROPN
ejpam-23	381	21	,	,	PUNCT
ejpam-23	381	22	axa	axa	PROPN
ejpam-23	381	23	)	)	PUNCT
ejpam-23	381	24	∈	∈	PROPN
ejpam-23	381	25	l̃|sαβ	l̃|sαβ	PROPN
ejpam-23	381	26	,	,	PUNCT
ejpam-23	381	27	and	and	CCONJ
ejpam-23	381	28	so	so	ADV
ejpam-23	381	29	,	,	PUNCT
ejpam-23	381	30	by	by	ADP
ejpam-23	381	31	our	our	PRON
ejpam-23	381	32	hypothesis	hypothesis	NOUN
ejpam-23	381	33	,	,	PUNCT
ejpam-23	381	34	s	s	PART
ejpam-23	381	35	=	=	PUNCT
ejpam-23	381	36	l̃g[y	l̃g[y	PROPN
ejpam-23	381	37	;	;	PUNCT
ejpam-23	381	38	sα	sα	ADJ
ejpam-23	381	39	,	,	PUNCT
ejpam-23	381	40	ϕα	ϕα	ADV
ejpam-23	381	41	,	,	PUNCT
ejpam-23	381	42	β	β	NOUN
ejpam-23	381	43	]	]	X
ejpam-23	381	44	.	.	PUNCT
ejpam-23	382	1	this	this	PRON
ejpam-23	382	2	implies	imply	VERB
ejpam-23	382	3	that	that	SCONJ
ejpam-23	382	4	there	there	PRON
ejpam-23	382	5	exist	exist	VERB
ejpam-23	382	6	some	some	DET
ejpam-23	382	7	homomorphisms	homomorphism	NOUN
ejpam-23	382	8	ϕ	ϕ	PROPN
ejpam-23	382	9	el	el	PROPN
ejpam-23	382	10	d(αβ	d(αβ	PROPN
ejpam-23	382	11	,	,	PUNCT
ejpam-23	382	12	αβγ	αβγ	NOUN
ejpam-23	382	13	)	)	PUNCT
ejpam-23	382	14	∈	∈	PROPN
ejpam-23	382	15	ϕαβ	ϕαβ	NOUN
ejpam-23	382	16	,	,	PUNCT
ejpam-23	382	17	αβγ	αβγ	NOUN
ejpam-23	382	18	and	and	CCONJ
ejpam-23	382	19	ϕ	ϕ	X
ejpam-23	382	20	el	el	PROPN
ejpam-23	382	21	d(γ	d(γ	PROPN
ejpam-23	382	22	,	,	PUNCT
ejpam-23	382	23	αβγ	αβγ	NOUN
ejpam-23	382	24	)	)	PUNCT
ejpam-23	382	25	∈	∈	PROPN
ejpam-23	382	26	ϕγ	ϕγ	PROPN
ejpam-23	382	27	,	,	PUNCT
ejpam-23	382	28	αβγ	αβγ	NOUN
ejpam-23	382	29	satisfying	satisfy	VERB
ejpam-23	382	30	the	the	DET
ejpam-23	382	31	conditions	condition	NOUN
ejpam-23	382	32	y(xa	y(xa	NUM
ejpam-23	382	33	)	)	PUNCT
ejpam-23	382	34	=	=	PUNCT
ejpam-23	383	1	(	(	PUNCT
ejpam-23	383	2	yϕ	yϕ	INTJ
ejpam-23	383	3	el	el	PROPN
ejpam-23	383	4	d(γ	d(γ	PROPN
ejpam-23	383	5	,	,	PUNCT
ejpam-23	383	6	αβγ))((xa)ϕ	αβγ))((xa)ϕ	NOUN
ejpam-23	383	7	eld(αβ	eld(αβ	NOUN
ejpam-23	383	8	,	,	PUNCT
ejpam-23	383	9	αβγ	αβγ	NOUN
ejpam-23	383	10	)	)	PUNCT
ejpam-23	383	11	)	)	PUNCT
ejpam-23	383	12	and	and	CCONJ
ejpam-23	383	13	y(axa	y(axa	NOUN
ejpam-23	383	14	)	)	PUNCT
ejpam-23	383	15	=	=	PUNCT
ejpam-23	384	1	(	(	PUNCT
ejpam-23	384	2	yϕ	yϕ	INTJ
ejpam-23	384	3	el	el	PROPN
ejpam-23	384	4	d(γ	d(γ	PROPN
ejpam-23	384	5	,	,	PUNCT
ejpam-23	384	6	αβγ))((axa)ϕ	αβγ))((axa)ϕ	PRON
ejpam-23	384	7	eld(αβ	eld(αβ	NOUN
ejpam-23	384	8	,	,	PUNCT
ejpam-23	384	9	αβγ	αβγ	NOUN
ejpam-23	384	10	)	)	PUNCT
ejpam-23	384	11	)	)	PUNCT
ejpam-23	384	12	.	.	PUNCT
ejpam-23	385	1	hence	hence	ADV
ejpam-23	385	2	,	,	PUNCT
ejpam-23	385	3	it	it	PRON
ejpam-23	385	4	follows	follow	VERB
ejpam-23	385	5	that	that	PRON
ejpam-23	385	6	(	(	PUNCT
ejpam-23	385	7	y(xa))h̃	y(xa))h̃	NOUN
ejpam-23	385	8	=	=	PUNCT
ejpam-23	386	1	[	[	X
ejpam-23	386	2	(	(	PUNCT
ejpam-23	386	3	yϕ	yϕ	INTJ
ejpam-23	386	4	el	el	PROPN
ejpam-23	386	5	d(γ	d(γ	PROPN
ejpam-23	386	6	,	,	PUNCT
ejpam-23	386	7	αβγ))((xa)ϕ	αβγ))((xa)ϕ	NOUN
ejpam-23	386	8	eld(αβ	eld(αβ	NOUN
ejpam-23	386	9	,	,	PUNCT
ejpam-23	386	10	αβγ))]h̃	αβγ))]h̃	NOUN
ejpam-23	386	11	=	=	NOUN
ejpam-23	386	12	{	{	PUNCT
ejpam-23	386	13	(	(	PUNCT
ejpam-23	386	14	yϕ	yϕ	INTJ
ejpam-23	386	15	el	el	PROPN
ejpam-23	386	16	d(γ	d(γ	PROPN
ejpam-23	386	17	,	,	PUNCT
ejpam-23	386	18	αβγ)){[(xϕa	αβγ)){[(xϕa	PROPN
ejpam-23	386	19	d(β	d(β	PROPN
ejpam-23	386	20	,	,	PUNCT
ejpam-23	386	21	αβ))(aϕx	αβ))(aϕx	PROPN
ejpam-23	386	22	d(α	d(α	NOUN
ejpam-23	386	23	,	,	PUNCT
ejpam-23	386	24	αβ))]ϕ	αβ))]ϕ	X
ejpam-23	386	25	el	el	NOUN
ejpam-23	386	26	d(αβ	d(αβ	NOUN
ejpam-23	386	27	,	,	PUNCT
ejpam-23	386	28	αβγ)}}h̃	αβγ)}}h̃	ADV
ejpam-23	386	29	=[	=[	NOUN
ejpam-23	386	30	(	(	PUNCT
ejpam-23	386	31	yϕ	yϕ	PROPN
ejpam-23	386	32	el	el	PROPN
ejpam-23	386	33	d(γ	d(γ	PROPN
ejpam-23	386	34	,	,	PUNCT
ejpam-23	386	35	αβγ))((aϕx	αβγ))((aϕx	ADJ
ejpam-23	386	36	d(α	d(α	NOUN
ejpam-23	386	37	,	,	PUNCT
ejpam-23	386	38	αβ))ϕ	αβ))ϕ	PROPN
ejpam-23	386	39	el	el	PROPN
ejpam-23	386	40	d(αβ	d(αβ	NOUN
ejpam-23	386	41	,	,	PUNCT
ejpam-23	386	42	αβγ))]h̃	αβγ))]h̃	ADJ
ejpam-23	386	43	references	reference	NOUN
ejpam-23	386	44	58	58	NUM
ejpam-23	386	45	and	and	CCONJ
ejpam-23	386	46	(	(	PUNCT
ejpam-23	386	47	y(axa))h̃	y(axa))h̃	NUM
ejpam-23	386	48	=	=	PRON
ejpam-23	386	49	{	{	PUNCT
ejpam-23	386	50	(	(	PUNCT
ejpam-23	386	51	yϕ	yϕ	INTJ
ejpam-23	386	52	el	el	PROPN
ejpam-23	386	53	d(γ	d(γ	PROPN
ejpam-23	386	54	,	,	PUNCT
ejpam-23	386	55	αβγ)){[(aϕx	αβγ)){[(aϕx	ADJ
ejpam-23	386	56	d(α	d(α	NOUN
ejpam-23	386	57	,	,	PUNCT
ejpam-23	386	58	αβ))(xϕa	αβ))(xϕa	PROPN
ejpam-23	386	59	d(β	d(β	PROPN
ejpam-23	386	60	,	,	PUNCT
ejpam-23	386	61	αβ))(aϕx	αβ))(aϕx	PROPN
ejpam-23	386	62	d(α	d(α	NOUN
ejpam-23	386	63	,	,	PUNCT
ejpam-23	386	64	αβ))]ϕ	αβ))]ϕ	X
ejpam-23	386	65	el	el	NOUN
ejpam-23	386	66	d(αβ	d(αβ	NOUN
ejpam-23	386	67	,	,	PUNCT
ejpam-23	386	68	αβγ)}}h̃	αβγ)}}h̃	ADV
ejpam-23	386	69	=	=	PUNCT
ejpam-23	387	1	[	[	X
ejpam-23	387	2	(	(	PUNCT
ejpam-23	387	3	yϕ	yϕ	INTJ
ejpam-23	387	4	el	el	PROPN
ejpam-23	387	5	d(γ	d(γ	PROPN
ejpam-23	387	6	,	,	PUNCT
ejpam-23	387	7	αβγ))((aϕx	αβγ))((aϕx	ADJ
ejpam-23	387	8	d(α	d(α	NOUN
ejpam-23	387	9	,	,	PUNCT
ejpam-23	387	10	αβ))ϕ	αβ))ϕ	PROPN
ejpam-23	387	11	el	el	PROPN
ejpam-23	387	12	d(αβ	d(αβ	PROPN
ejpam-23	387	13	,	,	PUNCT
ejpam-23	387	14	αβγ))]h̃.	αβγ))]h̃.	NUM
ejpam-23	387	15	this	this	PRON
ejpam-23	387	16	leads	lead	VERB
ejpam-23	387	17	to	to	ADP
ejpam-23	387	18	(	(	PUNCT
ejpam-23	387	19	yxa)h̃	yxa)h̃	NOUN
ejpam-23	387	20	=	=	SYM
ejpam-23	387	21	(	(	PUNCT
ejpam-23	387	22	yaxa)h̃	yaxa)h̃	NOUN
ejpam-23	387	23	and	and	CCONJ
ejpam-23	387	24	so	so	ADV
ejpam-23	387	25	s	s	PROPN
ejpam-23	387	26	/	/	SYM
ejpam-23	387	27	h̃	h̃	PROPN
ejpam-23	387	28	is	be	AUX
ejpam-23	387	29	a	a	DET
ejpam-23	387	30	right	right	ADJ
ejpam-23	387	31	quasi	quasi	ADJ
ejpam-23	387	32	-	-	ADJ
ejpam-23	387	33	normal	normal	ADJ
ejpam-23	387	34	band	band	NOUN
ejpam-23	387	35	.	.	PUNCT
ejpam-23	388	1	thus	thus	ADV
ejpam-23	388	2	,	,	PUNCT
ejpam-23	388	3	s	s	VERB
ejpam-23	388	4	is	be	AUX
ejpam-23	388	5	indeed	indeed	ADV
ejpam-23	388	6	a	a	DET
ejpam-23	388	7	right	right	ADJ
ejpam-23	388	8	quasi	quasi	ADJ
ejpam-23	388	9	-	-	ADJ
ejpam-23	388	10	normal	normal	ADJ
ejpam-23	388	11	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	388	12	.	.	PUNCT
ejpam-23	389	1	since	since	SCONJ
ejpam-23	389	2	we	we	PRON
ejpam-23	389	3	have	have	AUX
ejpam-23	389	4	already	already	ADV
ejpam-23	389	5	mentioned	mention	VERB
ejpam-23	389	6	that	that	SCONJ
ejpam-23	389	7	a	a	DET
ejpam-23	389	8	band	band	NOUN
ejpam-23	389	9	b	b	NOUN
ejpam-23	389	10	is	be	AUX
ejpam-23	389	11	a	a	DET
ejpam-23	389	12	normal	normal	ADJ
ejpam-23	389	13	band	band	NOUN
ejpam-23	389	14	if	if	SCONJ
ejpam-23	389	15	for	for	ADP
ejpam-23	389	16	all	all	DET
ejpam-23	389	17	elements	element	NOUN
ejpam-23	389	18	e	e	NOUN
ejpam-23	389	19	,	,	PUNCT
ejpam-23	389	20	f	f	PROPN
ejpam-23	389	21	,	,	PUNCT
ejpam-23	389	22	g	g	PROPN
ejpam-23	389	23	in	in	ADP
ejpam-23	389	24	b	b	PROPN
ejpam-23	389	25	,	,	PUNCT
ejpam-23	389	26	the	the	DET
ejpam-23	389	27	identity	identity	NOUN
ejpam-23	389	28	efge	efge	NOUN
ejpam-23	389	29	=	=	PUNCT
ejpam-23	389	30	egfe	egfe	NOUN
ejpam-23	389	31	holds	hold	VERB
ejpam-23	389	32	in	in	ADP
ejpam-23	389	33	b	b	PROPN
ejpam-23	389	34	(	(	PUNCT
ejpam-23	389	35	see	see	VERB
ejpam-23	389	36	[	[	X
ejpam-23	389	37	6	6	NUM
ejpam-23	389	38	]	]	NUM
ejpam-23	389	39	)	)	PUNCT
ejpam-23	389	40	.	.	PUNCT
ejpam-23	390	1	in	in	ADP
ejpam-23	390	2	closing	close	VERB
ejpam-23	390	3	this	this	DET
ejpam-23	390	4	paper	paper	NOUN
ejpam-23	390	5	,	,	PUNCT
ejpam-23	390	6	we	we	PRON
ejpam-23	390	7	characterize	characterize	VERB
ejpam-23	390	8	the	the	DET
ejpam-23	390	9	normal	normal	ADJ
ejpam-23	390	10	h̃	h̃	PROPN
ejpam-23	390	11	-cryptogroups	-cryptogroup	NOUN
ejpam-23	390	12	.	.	PUNCT
ejpam-23	391	1	in	in	ADP
ejpam-23	391	2	fact	fact	NOUN
ejpam-23	391	3	,	,	PUNCT
ejpam-23	391	4	this	this	DET
ejpam-23	391	5	result	result	NOUN
ejpam-23	391	6	gives	give	VERB
ejpam-23	391	7	a	a	DET
ejpam-23	391	8	modified	modify	VERB
ejpam-23	391	9	version	version	NOUN
ejpam-23	391	10	of	of	ADP
ejpam-23	391	11	the	the	DET
ejpam-23	391	12	theorem	theorem	NOUN
ejpam-23	391	13	of	of	ADP
ejpam-23	391	14	petrich	petrich	NOUN
ejpam-23	391	15	and	and	CCONJ
ejpam-23	391	16	reilly	reilly	ADV
ejpam-23	391	17	in	in	ADP
ejpam-23	391	18	[	[	X
ejpam-23	391	19	11	11	NUM
ejpam-23	391	20	]	]	PUNCT
ejpam-23	391	21	on	on	ADP
ejpam-23	391	22	normal	normal	ADJ
ejpam-23	391	23	cryptogroups	cryptogroup	NOUN
ejpam-23	391	24	,	,	PUNCT
ejpam-23	391	25	in	in	ADP
ejpam-23	391	26	particular	particular	ADJ
ejpam-23	391	27	,	,	PUNCT
ejpam-23	391	28	the	the	DET
ejpam-23	391	29	theorem	theorem	NOUN
ejpam-23	391	30	on	on	ADP
ejpam-23	391	31	normal	normal	ADJ
ejpam-23	391	32	cryptogroups	cryptogroup	NOUN
ejpam-23	391	33	in	in	ADP
ejpam-23	391	34	[	[	X
ejpam-23	391	35	11	11	NUM
ejpam-23	391	36	]	]	PUNCT
ejpam-23	391	37	and	and	CCONJ
ejpam-23	391	38	also	also	ADV
ejpam-23	391	39	the	the	DET
ejpam-23	391	40	theorem	theorem	NOUN
ejpam-23	391	41	of	of	ADP
ejpam-23	391	42	fountain	fountain	NOUN
ejpam-23	391	43	on	on	ADP
ejpam-23	391	44	superabundant	superabundant	ADJ
ejpam-23	391	45	semigroups	semigroup	NOUN
ejpam-23	391	46	in	in	ADP
ejpam-23	391	47	[	[	X
ejpam-23	391	48	4	4	X
ejpam-23	391	49	]	]	PUNCT
ejpam-23	391	50	is	be	AUX
ejpam-23	391	51	now	now	ADV
ejpam-23	391	52	refined	refine	VERB
ejpam-23	391	53	and	and	CCONJ
ejpam-23	391	54	amplified	amplify	VERB
ejpam-23	391	55	in	in	ADP
ejpam-23	391	56	the	the	DET
ejpam-23	391	57	class	class	NOUN
ejpam-23	391	58	of	of	ADP
ejpam-23	391	59	quasiabundant	quasiabundant	ADJ
ejpam-23	391	60	semigroups	semigroup	NOUN
ejpam-23	391	61	.	.	PUNCT
ejpam-23	392	1	theorem	theorem	VERB
ejpam-23	392	2	4.3	4.3	NUM
ejpam-23	392	3	an	an	DET
ejpam-23	392	4	h̃-abundant	h̃-abundant	ADJ
ejpam-23	392	5	semigroup	semigroup	NOUN
ejpam-23	392	6	s	s	VERB
ejpam-23	392	7	is	be	AUX
ejpam-23	392	8	a	a	DET
ejpam-23	392	9	normal	normal	ADJ
ejpam-23	392	10	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	392	11	if	if	SCONJ
ejpam-23	392	12	and	and	CCONJ
ejpam-23	392	13	only	only	ADV
ejpam-23	392	14	if	if	SCONJ
ejpam-23	392	15	s	s	NOUN
ejpam-23	392	16	is	be	AUX
ejpam-23	392	17	a	a	DET
ejpam-23	392	18	d̃gstrong	d̃gstrong	ADJ
ejpam-23	392	19	semilattice	semilattice	NOUN
ejpam-23	392	20	of	of	ADP
ejpam-23	392	21	completely	completely	ADV
ejpam-23	392	22	j̃	j̃	PROPN
ejpam-23	392	23	-simple	-simple	ADJ
ejpam-23	392	24	semigroups	semigroup	NOUN
ejpam-23	392	25	,	,	PUNCT
ejpam-23	392	26	that	that	ADV
ejpam-23	392	27	is	be	AUX
ejpam-23	392	28	,	,	PUNCT
ejpam-23	392	29	s	s	PART
ejpam-23	392	30	=	=	X
ejpam-23	392	31	d̃g[y	d̃g[y	NOUN
ejpam-23	392	32	;	;	PUNCT
ejpam-23	392	33	sα	sα	ADV
ejpam-23	392	34	,	,	PUNCT
ejpam-23	392	35	ϕα	ϕα	ADV
ejpam-23	392	36	,	,	PUNCT
ejpam-23	392	37	β	β	NOUN
ejpam-23	392	38	]	]	PUNCT
ejpam-23	392	39	.	.	PUNCT
ejpam-23	393	1	proof	proof	NOUN
ejpam-23	393	2	.	.	PUNCT
ejpam-23	394	1	(	(	PUNCT
ejpam-23	394	2	necessity	necessity	NOUN
ejpam-23	394	3	)	)	PUNCT
ejpam-23	394	4	the	the	DET
ejpam-23	394	5	proof	proof	NOUN
ejpam-23	394	6	is	be	AUX
ejpam-23	394	7	similar	similar	ADJ
ejpam-23	394	8	to	to	ADP
ejpam-23	394	9	the	the	DET
ejpam-23	394	10	necessity	necessity	NOUN
ejpam-23	394	11	part	part	NOUN
ejpam-23	394	12	given	give	VERB
ejpam-23	394	13	in	in	ADP
ejpam-23	394	14	theorem	theorem	ADJ
ejpam-23	394	15	4.2	4.2	NUM
ejpam-23	394	16	,	,	PUNCT
ejpam-23	394	17	that	that	ADV
ejpam-23	394	18	is	is	ADV
ejpam-23	394	19	,	,	PUNCT
ejpam-23	394	20	we	we	PRON
ejpam-23	394	21	only	only	ADV
ejpam-23	394	22	need	need	VERB
ejpam-23	394	23	to	to	PART
ejpam-23	394	24	prove	prove	VERB
ejpam-23	394	25	that	that	SCONJ
ejpam-23	394	26	d̃|sβ	d̃|sβ	PROPN
ejpam-23	394	27	⊆	⊆	NUM
ejpam-23	394	28	ρα	ρα	PROPN
ejpam-23	394	29	,	,	PUNCT
ejpam-23	394	30	β	β	X
ejpam-23	394	31	for	for	ADP
ejpam-23	394	32	all	all	DET
ejpam-23	394	33	α	α	NOUN
ejpam-23	394	34	,	,	PUNCT
ejpam-23	394	35	β	β	X
ejpam-23	394	36	∈	∈	PROPN
ejpam-23	394	37	y	y	PROPN
ejpam-23	394	38	with	with	ADP
ejpam-23	394	39	α	α	PROPN
ejpam-23	394	40	>	>	X
ejpam-23	394	41	β	β	PROPN
ejpam-23	394	42	.	.	PUNCT
ejpam-23	395	1	since	since	SCONJ
ejpam-23	395	2	every	every	DET
ejpam-23	395	3	semigroup	semigroup	NOUN
ejpam-23	395	4	sα	sα	PROPN
ejpam-23	395	5	can	can	AUX
ejpam-23	395	6	be	be	AUX
ejpam-23	395	7	regarded	regard	VERB
ejpam-23	395	8	as	as	ADP
ejpam-23	395	9	a	a	DET
ejpam-23	395	10	d̃-class	d̃-class	NOUN
ejpam-23	395	11	of	of	ADP
ejpam-23	395	12	s	s	PROPN
ejpam-23	395	13	,	,	PUNCT
ejpam-23	395	14	we	we	PRON
ejpam-23	395	15	can	can	AUX
ejpam-23	395	16	just	just	ADV
ejpam-23	395	17	let	let	VERB
ejpam-23	395	18	a	a	DET
ejpam-23	395	19	∈	∈	NOUN
ejpam-23	395	20	sα	sα	NOUN
ejpam-23	395	21	,	,	PUNCT
ejpam-23	395	22	x	x	PRON
ejpam-23	395	23	,	,	PUNCT
ejpam-23	395	24	y	y	PROPN
ejpam-23	395	25	∈	∈	PROPN
ejpam-23	395	26	sβ	sβ	VERB
ejpam-23	395	27	.	.	PUNCT
ejpam-23	396	1	recall	recall	VERB
ejpam-23	396	2	that	that	PRON
ejpam-23	396	3	s	s	VERB
ejpam-23	396	4	=	=	PUNCT
ejpam-23	396	5	(	(	PUNCT
ejpam-23	396	6	y	y	PROPN
ejpam-23	396	7	;	;	PUNCT
ejpam-23	396	8	sα	sα	X
ejpam-23	396	9	)	)	PUNCT
ejpam-23	396	10	is	be	AUX
ejpam-23	396	11	a	a	DET
ejpam-23	396	12	normal	normal	ADJ
ejpam-23	396	13	h̃-cryptogroup	h̃-cryptogroup	NOUN
ejpam-23	396	14	,	,	PUNCT
ejpam-23	396	15	s	s	PROPN
ejpam-23	396	16	/	/	SYM
ejpam-23	396	17	h̃	h̃	PROPN
ejpam-23	396	18	is	be	AUX
ejpam-23	396	19	a	a	DET
ejpam-23	396	20	normal	normal	ADJ
ejpam-23	396	21	band	band	NOUN
ejpam-23	396	22	.	.	PUNCT
ejpam-23	397	1	now	now	ADV
ejpam-23	397	2	,	,	PUNCT
ejpam-23	397	3	by	by	ADP
ejpam-23	397	4	the	the	DET
ejpam-23	397	5	normality	normality	NOUN
ejpam-23	397	6	of	of	ADP
ejpam-23	397	7	the	the	DET
ejpam-23	397	8	band	band	NOUN
ejpam-23	397	9	s	s	NOUN
ejpam-23	397	10	/	/	SYM
ejpam-23	397	11	h̃	h̃	PROPN
ejpam-23	397	12	,	,	PUNCT
ejpam-23	397	13	we	we	PRON
ejpam-23	397	14	have	have	VERB
ejpam-23	397	15	(	(	PUNCT
ejpam-23	397	16	axa)h̃	axa)h̃	NUM
ejpam-23	397	17	=	=	PUNCT
ejpam-23	397	18	(	(	PUNCT
ejpam-23	397	19	a(xyx)a)h̃	a(xyx)a)h̃	NOUN
ejpam-23	397	20	=	=	PUNCT
ejpam-23	397	21	(	(	PUNCT
ejpam-23	397	22	ayxya)h̃	ayxya)h̃	PROPN
ejpam-23	397	23	=	=	SYM
ejpam-23	397	24	(	(	PUNCT
ejpam-23	397	25	aya)h̃.	aya)h̃.	NOUN
ejpam-23	397	26	thus	thus	ADV
ejpam-23	397	27	,	,	PUNCT
ejpam-23	397	28	by	by	ADP
ejpam-23	397	29	lemma	lemma	PROPN
ejpam-23	397	30	3.1	3.1	NUM
ejpam-23	397	31	,	,	PUNCT
ejpam-23	397	32	we	we	PRON
ejpam-23	397	33	see	see	VERB
ejpam-23	397	34	that	that	SCONJ
ejpam-23	397	35	(	(	PUNCT
ejpam-23	397	36	x	x	X
ejpam-23	397	37	,	,	PUNCT
ejpam-23	397	38	y	y	PROPN
ejpam-23	397	39	)	)	PUNCT
ejpam-23	397	40	∈	∈	PROPN
ejpam-23	397	41	ρα	ρα	PROPN
ejpam-23	397	42	,	,	PUNCT
ejpam-23	397	43	β	β	PROPN
ejpam-23	397	44	and	and	CCONJ
ejpam-23	397	45	whence	whence	ADV
ejpam-23	397	46	d̃|sβ	d̃|sβ	PROPN
ejpam-23	397	47	⊆	⊆	NUM
ejpam-23	397	48	ρα	ρα	PROPN
ejpam-23	397	49	,	,	PUNCT
ejpam-23	397	50	β	β	X
ejpam-23	397	51	.	.	PUNCT
ejpam-23	398	1	this	this	PRON
ejpam-23	398	2	proves	prove	VERB
ejpam-23	398	3	that	that	PRON
ejpam-23	398	4	s	s	VERB
ejpam-23	398	5	=	=	X
ejpam-23	398	6	d̃g[y	d̃g[y	NOUN
ejpam-23	398	7	;	;	PUNCT
ejpam-23	398	8	sα	sα	X
ejpam-23	398	9	,	,	PUNCT
ejpam-23	398	10	ϕα	ϕα	ADV
ejpam-23	398	11	,	,	PUNCT
ejpam-23	398	12	β	β	NOUN
ejpam-23	398	13	]	]	PUNCT
ejpam-23	398	14	.	.	PUNCT
ejpam-23	399	1	(	(	PUNCT
ejpam-23	399	2	sufficency	sufficency	NOUN
ejpam-23	399	3	)	)	PUNCT
ejpam-23	399	4	let	let	VERB
ejpam-23	399	5	s	s	NOUN
ejpam-23	399	6	=	=	X
ejpam-23	399	7	d̃g[y	d̃g[y	NOUN
ejpam-23	399	8	;	;	PUNCT
ejpam-23	399	9	sα	sα	ADV
ejpam-23	399	10	,	,	PUNCT
ejpam-23	399	11	ϕα	ϕα	ADV
ejpam-23	399	12	,	,	PUNCT
ejpam-23	399	13	β	β	X
ejpam-23	399	14	]	]	X
ejpam-23	399	15	,	,	PUNCT
ejpam-23	399	16	where	where	SCONJ
ejpam-23	399	17	each	each	DET
ejpam-23	399	18	sα	sα	NOUN
ejpam-23	399	19	is	be	AUX
ejpam-23	399	20	a	a	DET
ejpam-23	399	21	completely	completely	ADV
ejpam-23	399	22	j̃	j̃	PROPN
ejpam-23	399	23	simple	simple	ADJ
ejpam-23	399	24	semigroup	semigroup	NOUN
ejpam-23	399	25	,	,	PUNCT
ejpam-23	399	26	for	for	ADP
ejpam-23	399	27	all	all	DET
ejpam-23	399	28	α	α	DET
ejpam-23	399	29	∈	∈	PROPN
ejpam-23	399	30	y	y	PROPN
ejpam-23	399	31	.	.	PUNCT
ejpam-23	400	1	then	then	ADV
ejpam-23	400	2	by	by	ADP
ejpam-23	400	3	definition	definition	NOUN
ejpam-23	400	4	,	,	PUNCT
ejpam-23	400	5	s	s	PART
ejpam-23	400	6	is	be	AUX
ejpam-23	400	7	an	an	DET
ejpam-23	400	8	l̃g	l̃g	ADJ
ejpam-23	400	9	-	-	ADJ
ejpam-23	400	10	strong	strong	ADJ
ejpam-23	400	11	semilattice	semilattice	NOUN
ejpam-23	400	12	of	of	ADP
ejpam-23	400	13	semigroups	semigroup	NOUN
ejpam-23	400	14	sα	sα	ADV
ejpam-23	401	1	and	and	CCONJ
ejpam-23	401	2	also	also	ADV
ejpam-23	401	3	s	s	VERB
ejpam-23	401	4	is	be	AUX
ejpam-23	401	5	an	an	DET
ejpam-23	401	6	r̃g	r̃g	ADJ
ejpam-23	401	7	-	-	PUNCT
ejpam-23	401	8	strong	strong	ADJ
ejpam-23	401	9	semilattice	semilattice	NOUN
ejpam-23	401	10	of	of	ADP
ejpam-23	401	11	semigroups	semigroup	NOUN
ejpam-23	401	12	sα	sα	ADV
ejpam-23	401	13	.	.	PUNCT
ejpam-23	402	1	by	by	ADP
ejpam-23	402	2	applying	apply	VERB
ejpam-23	402	3	theorem	theorem	ADJ
ejpam-23	402	4	4.2	4.2	NUM
ejpam-23	402	5	and	and	CCONJ
ejpam-23	402	6	its	its	PRON
ejpam-23	402	7	dual	dual	ADJ
ejpam-23	402	8	,	,	PUNCT
ejpam-23	402	9	we	we	PRON
ejpam-23	402	10	immediately	immediately	ADV
ejpam-23	402	11	deduce	deduce	VERB
ejpam-23	402	12	that	that	SCONJ
ejpam-23	402	13	h̃	h̃	PROPN
ejpam-23	402	14	is	be	AUX
ejpam-23	402	15	a	a	DET
ejpam-23	402	16	congruence	congruence	NOUN
ejpam-23	402	17	on	on	ADP
ejpam-23	402	18	s	s	PRON
ejpam-23	402	19	and	and	CCONJ
ejpam-23	402	20	for	for	ADP
ejpam-23	402	21	all	all	DET
ejpam-23	402	22	a	a	PRON
ejpam-23	402	23	,	,	PUNCT
ejpam-23	402	24	x	x	PRON
ejpam-23	402	25	,	,	PUNCT
ejpam-23	402	26	y	y	PROPN
ejpam-23	402	27	∈	∈	PROPN
ejpam-23	402	28	s	s	PART
ejpam-23	402	29	,	,	PUNCT
ejpam-23	402	30	we	we	PRON
ejpam-23	402	31	have	have	VERB
ejpam-23	402	32	[	[	X
ejpam-23	402	33	(	(	PUNCT
ejpam-23	402	34	axy)a]h̃	axy)a]h̃	NOUN
ejpam-23	402	35	=	=	PUNCT
ejpam-23	403	1	[	[	X
ejpam-23	403	2	ay(xya)]h̃	ay(xya)]h̃	NOUN
ejpam-23	403	3	=	=	PUNCT
ejpam-23	403	4	(	(	PUNCT
ejpam-23	403	5	ayxyxa)h̃	ayxyxa)h̃	PROPN
ejpam-23	403	6	=	=	SYM
ejpam-23	403	7	(	(	PUNCT
ejpam-23	403	8	ayxa)h̃.	ayxa)h̃.	AUX
ejpam-23	403	9	this	this	PRON
ejpam-23	403	10	shows	show	VERB
ejpam-23	403	11	that	that	SCONJ
ejpam-23	403	12	s	s	PROPN
ejpam-23	403	13	/	/	SYM
ejpam-23	403	14	h̃	h̃	PROPN
ejpam-23	403	15	is	be	AUX
ejpam-23	403	16	a	a	DET
ejpam-23	403	17	normal	normal	ADJ
ejpam-23	403	18	band	band	NOUN
ejpam-23	403	19	.	.	PUNCT
ejpam-23	404	1	moreover	moreover	ADV
ejpam-23	404	2	,	,	PUNCT
ejpam-23	404	3	since	since	SCONJ
ejpam-23	404	4	each	each	DET
ejpam-23	404	5	sα	sα	NOUN
ejpam-23	404	6	is	be	AUX
ejpam-23	404	7	a	a	DET
ejpam-23	404	8	d̃-class	d̃-class	NOUN
ejpam-23	404	9	of	of	ADP
ejpam-23	404	10	s	s	NOUN
ejpam-23	404	11	,	,	PUNCT
ejpam-23	404	12	for	for	ADP
ejpam-23	404	13	every	every	DET
ejpam-23	404	14	α	α	NOUN
ejpam-23	404	15	,	,	PUNCT
ejpam-23	404	16	β	β	X
ejpam-23	404	17	∈	∈	PROPN
ejpam-23	404	18	y	y	PROPN
ejpam-23	404	19	with	with	ADP
ejpam-23	404	20	α	α	PROPN
ejpam-23	404	21	>	>	X
ejpam-23	404	22	β	β	X
ejpam-23	404	23	,	,	PUNCT
ejpam-23	404	24	the	the	DET
ejpam-23	404	25	set	set	NOUN
ejpam-23	404	26	d(α	d(α	PROPN
ejpam-23	404	27	,	,	PUNCT
ejpam-23	404	28	β	β	NOUN
ejpam-23	404	29	)	)	PUNCT
ejpam-23	404	30	is	be	AUX
ejpam-23	404	31	just	just	ADV
ejpam-23	404	32	a	a	DET
ejpam-23	404	33	singleton	singleton	NOUN
ejpam-23	404	34	.	.	PUNCT
ejpam-23	405	1	this	this	PRON
ejpam-23	405	2	means	mean	VERB
ejpam-23	405	3	that	that	SCONJ
ejpam-23	405	4	s	s	VERB
ejpam-23	405	5	is	be	AUX
ejpam-23	405	6	a	a	DET
ejpam-23	405	7	strong	strong	ADJ
ejpam-23	405	8	semilattice	semilattice	NOUN
ejpam-23	405	9	of	of	ADP
ejpam-23	405	10	completely	completely	ADV
ejpam-23	405	11	j̃	j̃	PROPN
ejpam-23	405	12	-simple	-simple	ADJ
ejpam-23	405	13	semigroups	semigroup	VERB
ejpam-23	405	14	sα	sα	VERB
ejpam-23	405	15	.	.	PUNCT
ejpam-23	406	1	our	our	PRON
ejpam-23	406	2	proof	proof	NOUN
ejpam-23	406	3	is	be	AUX
ejpam-23	406	4	completed	complete	VERB
ejpam-23	406	5	.	.	PUNCT
ejpam-23	407	1	references	reference	NOUN
ejpam-23	407	2	[	[	X
ejpam-23	407	3	1	1	NUM
ejpam-23	407	4	]	]	PUNCT
ejpam-23	407	5	a.	a.	NOUN
ejpam-23	407	6	h.	h.	PROPN
ejpam-23	407	7	clifford	clifford	PROPN
ejpam-23	407	8	,	,	PUNCT
ejpam-23	407	9	semigroups	semigroup	NOUN
ejpam-23	407	10	admitting	admit	VERB
ejpam-23	407	11	relative	relative	ADJ
ejpam-23	407	12	inverses	inverse	NOUN
ejpam-23	407	13	,	,	PUNCT
ejpam-23	407	14	ann	ann	PROPN
ejpam-23	407	15	of	of	ADP
ejpam-23	407	16	math	math	NOUN
ejpam-23	407	17	.	.	PUNCT
ejpam-23	408	1	42	42	NUM
ejpam-23	408	2	,	,	PUNCT
ejpam-23	408	3	1037	1037	NUM
ejpam-23	408	4	-	-	SYM
ejpam-23	408	5	1049	1049	NUM
ejpam-23	408	6	,	,	PUNCT
ejpam-23	408	7	(	(	PUNCT
ejpam-23	408	8	1941	1941	NUM
ejpam-23	408	9	)	)	PUNCT
ejpam-23	409	1	[	[	X
ejpam-23	409	2	2	2	NUM
ejpam-23	409	3	]	]	PUNCT
ejpam-23	409	4	a.	a.	NOUN
ejpam-23	409	5	h.	h.	PROPN
ejpam-23	409	6	clifford	clifford	PROPN
ejpam-23	409	7	and	and	CCONJ
ejpam-23	409	8	g.	g.	PROPN
ejpam-23	409	9	b.	b.	PROPN
ejpam-23	409	10	preston	preston	PROPN
ejpam-23	409	11	,	,	PUNCT
ejpam-23	409	12	the	the	DET
ejpam-23	409	13	algebraic	algebraic	ADJ
ejpam-23	409	14	theory	theory	NOUN
ejpam-23	409	15	of	of	ADP
ejpam-23	409	16	semigroups	semigroup	NOUN
ejpam-23	409	17	,	,	PUNCT
ejpam-23	409	18	mathematical	mathematical	ADJ
ejpam-23	409	19	surveys	survey	NOUN
ejpam-23	409	20	7	7	NUM
ejpam-23	409	21	,	,	PUNCT
ejpam-23	409	22	vols	vol	NOUN
ejpam-23	409	23	1	1	NUM
ejpam-23	409	24	and	and	CCONJ
ejpam-23	409	25	2	2	NUM
ejpam-23	409	26	,	,	PUNCT
ejpam-23	409	27	american	american	PROPN
ejpam-23	409	28	mathematical	mathematical	ADJ
ejpam-23	409	29	society	society	NOUN
ejpam-23	409	30	,	,	PUNCT
ejpam-23	409	31	providence	providence	NOUN
ejpam-23	409	32	,	,	PUNCT
ejpam-23	409	33	r.i	r.i	PROPN
ejpam-23	409	34	.	.	PROPN
ejpam-23	409	35	,	,	PUNCT
ejpam-23	409	36	(	(	PUNCT
ejpam-23	409	37	1967	1967	NUM
ejpam-23	409	38	)	)	PUNCT
ejpam-23	410	1	[	[	X
ejpam-23	410	2	3	3	NUM
ejpam-23	410	3	]	]	X
ejpam-23	410	4	a.	a.	PROPN
ejpam-23	410	5	el	el	PROPN
ejpam-23	410	6	-	-	PROPN
ejpam-23	410	7	qallali	qallali	ADJ
ejpam-23	410	8	,	,	PUNCT
ejpam-23	410	9	structure	structure	NOUN
ejpam-23	410	10	theory	theory	NOUN
ejpam-23	410	11	for	for	ADP
ejpam-23	410	12	abundant	abundant	ADJ
ejpam-23	410	13	and	and	CCONJ
ejpam-23	410	14	related	related	ADJ
ejpam-23	410	15	semigroups	semigroup	NOUN
ejpam-23	410	16	,	,	PUNCT
ejpam-23	410	17	phd	phd	NOUN
ejpam-23	410	18	thesis	thesis	PROPN
ejpam-23	410	19	,	,	PUNCT
ejpam-23	410	20	york	york	PROPN
ejpam-23	410	21	university	university	PROPN
ejpam-23	410	22	,	,	PUNCT
ejpam-23	410	23	england	england	PROPN
ejpam-23	410	24	,	,	PUNCT
ejpam-23	410	25	(	(	PUNCT
ejpam-23	410	26	1980	1980	NUM
ejpam-23	410	27	)	)	PUNCT
ejpam-23	410	28	references	reference	NOUN
ejpam-23	410	29	59	59	NUM
ejpam-23	410	30	[	[	X
ejpam-23	410	31	4	4	NUM
ejpam-23	410	32	]	]	PUNCT
ejpam-23	410	33	j.	j.	PROPN
ejpam-23	410	34	b.	b.	PROPN
ejpam-23	410	35	fountain	fountain	PROPN
ejpam-23	410	36	,	,	PUNCT
ejpam-23	410	37	abundant	abundant	ADJ
ejpam-23	410	38	semigroups	semigroup	NOUN
ejpam-23	410	39	,	,	PUNCT
ejpam-23	410	40	proc	proc	PROPN
ejpam-23	410	41	london	london	PROPN
ejpam-23	410	42	math	math	NOUN
ejpam-23	410	43	soc	soc	NOUN
ejpam-23	410	44	43	43	NUM
ejpam-23	410	45	(	(	PUNCT
ejpam-23	410	46	3	3	NUM
ejpam-23	410	47	)	)	PUNCT
ejpam-23	410	48	103	103	NUM
ejpam-23	410	49	-	-	SYM
ejpam-23	410	50	129	129	NUM
ejpam-23	410	51	,	,	PUNCT
ejpam-23	410	52	(	(	PUNCT
ejpam-23	410	53	1982	1982	NUM
ejpam-23	410	54	)	)	PUNCT
ejpam-23	411	1	[	[	X
ejpam-23	411	2	5	5	NUM
ejpam-23	411	3	]	]	PUNCT
ejpam-23	411	4	x.	x.	NOUN
ejpam-23	411	5	j.	j.	PROPN
ejpam-23	411	6	guo	guo	PROPN
ejpam-23	411	7	and	and	CCONJ
ejpam-23	411	8	k.	k.	PROPN
ejpam-23	411	9	p.	p.	PROPN
ejpam-23	411	10	shum	shum	PROPN
ejpam-23	411	11	,	,	PUNCT
ejpam-23	411	12	on	on	ADP
ejpam-23	411	13	left	leave	VERB
ejpam-23	411	14	cyber	cyber	NOUN
ejpam-23	411	15	groups	group	NOUN
ejpam-23	411	16	.	.	PUNCT
ejpam-23	412	1	int	int	NOUN
ejpam-23	412	2	.	.	PUNCT
ejpam-23	413	1	math	math	NOUN
ejpam-23	413	2	.	.	PUNCT
ejpam-23	414	1	j	j	NOUN
ejpam-23	414	2	,	,	PUNCT
ejpam-23	414	3	5	5	NUM
ejpam-23	414	4	705–717	705–717	NUM
ejpam-23	414	5	,	,	PUNCT
ejpam-23	414	6	(	(	PUNCT
ejpam-23	414	7	2004	2004	NUM
ejpam-23	414	8	)	)	PUNCT
ejpam-23	415	1	[	[	X
ejpam-23	415	2	6	6	X
ejpam-23	415	3	]	]	PUNCT
ejpam-23	415	4	j.	j.	PROPN
ejpam-23	415	5	m.	m.	PROPN
ejpam-23	415	6	howie	howie	PROPN
ejpam-23	415	7	,	,	PUNCT
ejpam-23	415	8	fundamental	fundamental	ADJ
ejpam-23	415	9	of	of	ADP
ejpam-23	415	10	semigroup	semigroup	PROPN
ejpam-23	415	11	theory	theory	NOUN
ejpam-23	415	12	,	,	PUNCT
ejpam-23	415	13	clarendon	clarendon	PROPN
ejpam-23	415	14	press	press	PROPN
ejpam-23	415	15	,	,	PUNCT
ejpam-23	415	16	oxford	oxford	PROPN
ejpam-23	415	17	,	,	PUNCT
ejpam-23	415	18	(	(	PUNCT
ejpam-23	415	19	1995	1995	NUM
ejpam-23	415	20	)	)	PUNCT
ejpam-23	416	1	[	[	X
ejpam-23	416	2	7	7	X
ejpam-23	416	3	]	]	PUNCT
ejpam-23	416	4	x.	x.	NOUN
ejpam-23	416	5	z.	z.	PROPN
ejpam-23	416	6	kong	kong	PROPN
ejpam-23	416	7	and	and	CCONJ
ejpam-23	416	8	k.	k.	PROPN
ejpam-23	416	9	p.	p.	PROPN
ejpam-23	416	10	shum	shum	PROPN
ejpam-23	416	11	,	,	PUNCT
ejpam-23	416	12	completely	completely	ADV
ejpam-23	416	13	regular	regular	ADJ
ejpam-23	416	14	semigroups	semigroup	NOUN
ejpam-23	416	15	with	with	ADP
ejpam-23	416	16	generalized	generalized	ADJ
ejpam-23	416	17	strong	strong	ADJ
ejpam-23	416	18	semilattice	semilattice	NOUN
ejpam-23	416	19	decompositions	decomposition	NOUN
ejpam-23	416	20	,	,	PUNCT
ejpam-23	416	21	algebra	algebra	NOUN
ejpam-23	416	22	colloqium	colloqium	NOUN
ejpam-23	416	23	,	,	PUNCT
ejpam-23	416	24	12	12	NUM
ejpam-23	416	25	(	(	PUNCT
ejpam-23	416	26	2	2	NUM
ejpam-23	416	27	)	)	PUNCT
ejpam-23	416	28	269	269	NUM
ejpam-23	416	29	-	-	SYM
ejpam-23	416	30	280	280	NUM
ejpam-23	416	31	,	,	PUNCT
ejpam-23	416	32	(	(	PUNCT
ejpam-23	416	33	2005	2005	NUM
ejpam-23	416	34	)	)	PUNCT
ejpam-23	417	1	[	[	X
ejpam-23	417	2	8	8	NUM
ejpam-23	417	3	]	]	PUNCT
ejpam-23	417	4	x.	x.	NOUN
ejpam-23	417	5	z.	z.	PROPN
ejpam-23	417	6	kong	kong	PROPN
ejpam-23	417	7	and	and	CCONJ
ejpam-23	417	8	k.	k.	PROPN
ejpam-23	417	9	p.	p.	PROPN
ejpam-23	417	10	shum	shum	PROPN
ejpam-23	417	11	,	,	PUNCT
ejpam-23	417	12	on	on	ADP
ejpam-23	417	13	the	the	DET
ejpam-23	417	14	structure	structure	NOUN
ejpam-23	417	15	of	of	ADP
ejpam-23	417	16	regular	regular	ADJ
ejpam-23	417	17	crypto	crypto	NOUN
ejpam-23	417	18	semigroups	semigroup	NOUN
ejpam-23	417	19	,	,	PUNCT
ejpam-23	417	20	comm	comm	NOUN
ejpam-23	417	21	.	.	PUNCT
ejpam-23	418	1	in	in	ADP
ejpam-23	418	2	algebra	algebra	NOUN
ejpam-23	418	3	,	,	PUNCT
ejpam-23	418	4	29	29	NUM
ejpam-23	418	5	(	(	PUNCT
ejpam-23	418	6	6	6	NUM
ejpam-23	418	7	)	)	PUNCT
ejpam-23	418	8	,	,	PUNCT
ejpam-23	418	9	2461	2461	NUM
ejpam-23	418	10	-	-	SYM
ejpam-23	418	11	2479	2479	NUM
ejpam-23	418	12	,	,	PUNCT
ejpam-23	418	13	(	(	PUNCT
ejpam-23	418	14	2001	2001	NUM
ejpam-23	418	15	)	)	PUNCT
ejpam-23	419	1	[	[	X
ejpam-23	419	2	9	9	NUM
ejpam-23	419	3	]	]	PUNCT
ejpam-23	419	4	x.	x.	NOUN
ejpam-23	419	5	z.	z.	PROPN
ejpam-23	419	6	kong	kong	PROPN
ejpam-23	419	7	and	and	CCONJ
ejpam-23	419	8	k.	k.	PROPN
ejpam-23	419	9	p.	p.	PROPN
ejpam-23	419	10	shum	shum	PROPN
ejpam-23	419	11	,	,	PUNCT
ejpam-23	419	12	semilattice	semilattice	NOUN
ejpam-23	419	13	structure	structure	NOUN
ejpam-23	419	14	of	of	ADP
ejpam-23	419	15	regular	regular	ADJ
ejpam-23	419	16	cyber	cyber	ADJ
ejpam-23	419	17	groups	group	NOUN
ejpam-23	419	18	,	,	PUNCT
ejpam-23	419	19	pragmatic	pragmatic	ADJ
ejpam-23	419	20	algebra	algebra	NOUN
ejpam-23	419	21	,	,	PUNCT
ejpam-23	419	22	1	1	NUM
ejpam-23	419	23	1	1	NUM
ejpam-23	419	24	-	-	SYM
ejpam-23	419	25	12	12	NUM
ejpam-23	419	26	,	,	PUNCT
ejpam-23	419	27	(	(	PUNCT
ejpam-23	419	28	2006	2006	NUM
ejpam-23	419	29	)	)	PUNCT
ejpam-23	420	1	[	[	X
ejpam-23	420	2	10	10	NUM
ejpam-23	420	3	]	]	PUNCT
ejpam-23	420	4	x.	x.	NOUN
ejpam-23	420	5	z.	z.	PROPN
ejpam-23	420	6	kong	kong	PROPN
ejpam-23	420	7	and	and	CCONJ
ejpam-23	420	8	z.	z.	PROPN
ejpam-23	420	9	l.	l.	PROPN
ejpam-23	420	10	yuan	yuan	PROPN
ejpam-23	420	11	,	,	PUNCT
ejpam-23	420	12	kg	kg	ADJ
ejpam-23	420	13	-	-	PUNCT
ejpam-23	420	14	strong	strong	ADJ
ejpam-23	420	15	semilattice	semilattice	NOUN
ejpam-23	420	16	decomposition	decomposition	NOUN
ejpam-23	420	17	of	of	ADP
ejpam-23	420	18	regular	regular	ADJ
ejpam-23	420	19	orthocryptosemigroups	orthocryptosemigroup	NOUN
ejpam-23	420	20	,	,	PUNCT
ejpam-23	420	21	semigroup	semigroup	PROPN
ejpam-23	420	22	forum	forum	PROPN
ejpam-23	420	23	,	,	PUNCT
ejpam-23	420	24	73	73	NUM
ejpam-23	420	25	,	,	PUNCT
ejpam-23	420	26	95	95	NUM
ejpam-23	420	27	-	-	SYM
ejpam-23	420	28	108	108	NUM
ejpam-23	420	29	,	,	PUNCT
ejpam-23	420	30	(	(	PUNCT
ejpam-23	420	31	2006	2006	NUM
ejpam-23	420	32	)	)	PUNCT
ejpam-23	421	1	[	[	X
ejpam-23	421	2	11	11	NUM
ejpam-23	421	3	]	]	X
ejpam-23	421	4	f.	f.	NOUN
ejpam-23	421	5	pastijn	pastijn	PROPN
ejpam-23	421	6	,	,	PUNCT
ejpam-23	421	7	a	a	DET
ejpam-23	421	8	representation	representation	NOUN
ejpam-23	421	9	of	of	ADP
ejpam-23	421	10	a	a	DET
ejpam-23	421	11	semigroup	semigroup	NOUN
ejpam-23	421	12	by	by	ADP
ejpam-23	421	13	a	a	DET
ejpam-23	421	14	semigroup	semigroup	NOUN
ejpam-23	421	15	of	of	ADP
ejpam-23	421	16	matrices	matrix	NOUN
ejpam-23	421	17	over	over	ADP
ejpam-23	421	18	a	a	DET
ejpam-23	421	19	group	group	NOUN
ejpam-23	421	20	with	with	ADP
ejpam-23	421	21	zero	zero	NUM
ejpam-23	421	22	,	,	PUNCT
ejpam-23	421	23	semigroup	semigroup	PROPN
ejpam-23	421	24	forum	forum	PROPN
ejpam-23	421	25	,	,	PUNCT
ejpam-23	421	26	10	10	NUM
ejpam-23	421	27	,	,	PUNCT
ejpam-23	421	28	238	238	NUM
ejpam-23	421	29	-	-	SYM
ejpam-23	421	30	249,(1975	249,(1975	NUM
ejpam-23	421	31	)	)	PUNCT
ejpam-23	422	1	[	[	X
ejpam-23	422	2	12	12	NUM
ejpam-23	422	3	]	]	PUNCT
ejpam-23	422	4	m.	m.	NOUN
ejpam-23	422	5	petrich	petrich	PROPN
ejpam-23	422	6	and	and	CCONJ
ejpam-23	422	7	n.	n.	PROPN
ejpam-23	422	8	r.	r.	PROPN
ejpam-23	422	9	reilly	reilly	PROPN
ejpam-23	422	10	,	,	PUNCT
ejpam-23	422	11	completely	completely	ADV
ejpam-23	422	12	regular	regular	ADJ
ejpam-23	422	13	semigroups	semigroup	NOUN
ejpam-23	422	14	,	,	PUNCT
ejpam-23	422	15	john	john	PROPN
ejpam-23	422	16	wiley	wiley	PROPN
ejpam-23	422	17	&	&	CCONJ
ejpam-23	422	18	sons	son	NOUN
ejpam-23	422	19	,	,	PUNCT
ejpam-23	422	20	162	162	NUM
ejpam-23	422	21	-	-	SYM
ejpam-23	422	22	242	242	NUM
ejpam-23	422	23	,	,	PUNCT
ejpam-23	422	24	(	(	PUNCT
ejpam-23	422	25	1999	1999	NUM
ejpam-23	422	26	)	)	PUNCT
ejpam-23	423	1	[	[	X
ejpam-23	423	2	13	13	NUM
ejpam-23	423	3	]	]	PUNCT
ejpam-23	423	4	m.	m.	NOUN
ejpam-23	423	5	petrich	petrich	PROPN
ejpam-23	423	6	,	,	PUNCT
ejpam-23	423	7	the	the	DET
ejpam-23	423	8	structure	structure	NOUN
ejpam-23	423	9	of	of	ADP
ejpam-23	423	10	completely	completely	ADV
ejpam-23	423	11	regular	regular	ADJ
ejpam-23	423	12	semigroups	semigroup	NOUN
ejpam-23	423	13	,	,	PUNCT
ejpam-23	423	14	trans	trans	PROPN
ejpam-23	423	15	amer	amer	PROPN
ejpam-23	423	16	math	math	PROPN
ejpam-23	423	17	soc	soc	PROPN
ejpam-23	423	18	,	,	PUNCT
ejpam-23	423	19	189	189	NUM
ejpam-23	423	20	,	,	PUNCT
ejpam-23	423	21	211	211	NUM
ejpam-23	423	22	-	-	SYM
ejpam-23	423	23	236	236	NUM
ejpam-23	423	24	,	,	PUNCT
ejpam-23	423	25	(	(	PUNCT
ejpam-23	423	26	1974	1974	NUM
ejpam-23	423	27	)	)	PUNCT
ejpam-23	424	1	[	[	X
ejpam-23	424	2	14	14	NUM
ejpam-23	424	3	]	]	PUNCT
ejpam-23	424	4	m.	m.	NOUN
ejpam-23	424	5	petrich	petrich	PROPN
ejpam-23	424	6	,	,	PUNCT
ejpam-23	424	7	lectures	lecture	NOUN
ejpam-23	424	8	in	in	ADP
ejpam-23	424	9	semigroups	semigroup	NOUN
ejpam-23	424	10	,	,	PUNCT
ejpam-23	424	11	wiley	wiley	PROPN
ejpam-23	424	12	&	&	CCONJ
ejpam-23	424	13	sons	sons	PROPN
ejpam-23	424	14	inc	inc	PROPN
ejpam-23	424	15	.	.	PROPN
ejpam-23	424	16	london	london	PROPN
ejpam-23	424	17	,	,	PUNCT
ejpam-23	424	18	(	(	PUNCT
ejpam-23	424	19	1976	1976	NUM
ejpam-23	424	20	)	)	PUNCT
ejpam-23	425	1	[	[	X
ejpam-23	425	2	15	15	NUM
ejpam-23	425	3	]	]	X
ejpam-23	425	4	x.	x.	NOUN
ejpam-23	425	5	m.	m.	PROPN
ejpam-23	425	6	ren	ren	PROPN
ejpam-23	425	7	and	and	CCONJ
ejpam-23	425	8	k.	k.	PROPN
ejpam-23	425	9	p.	p.	PROPN
ejpam-23	425	10	shum	shum	PROPN
ejpam-23	425	11	,	,	PUNCT
ejpam-23	425	12	the	the	DET
ejpam-23	425	13	structure	structure	NOUN
ejpam-23	425	14	of	of	ADP
ejpam-23	425	15	superabundant	superabundant	ADJ
ejpam-23	425	16	semigroups	semigroup	NOUN
ejpam-23	425	17	,	,	PUNCT
ejpam-23	425	18	sci	sci	PROPN
ejpam-23	425	19	in	in	ADP
ejpam-23	425	20	china	china	PROPN
ejpam-23	425	21	,	,	PUNCT
ejpam-23	425	22	ser	ser	PROPN
ejpam-23	425	23	.	.	PUNCT
ejpam-23	426	1	a	a	DET
ejpam-23	426	2	,	,	PUNCT
ejpam-23	426	3	47	47	NUM
ejpam-23	426	4	(	(	PUNCT
ejpam-23	426	5	5	5	NUM
ejpam-23	426	6	)	)	PUNCT
ejpam-23	426	7	,	,	PUNCT
ejpam-23	426	8	756	756	NUM
ejpam-23	426	9	-	-	SYM
ejpam-23	426	10	771	771	NUM
ejpam-23	426	11	,	,	PUNCT
ejpam-23	426	12	(	(	PUNCT
ejpam-23	426	13	2004	2004	NUM
ejpam-23	426	14	)	)	PUNCT
ejpam-23	427	1	[	[	X
ejpam-23	427	2	16	16	NUM
ejpam-23	427	3	]	]	PUNCT
ejpam-23	427	4	x.	x.	NOUN
ejpam-23	427	5	m.	m.	NOUN
ejpam-23	427	6	and	and	CCONJ
ejpam-23	427	7	k.	k.	PROPN
ejpam-23	427	8	p.	p.	PROPN
ejpam-23	427	9	shum	shum	PROPN
ejpam-23	427	10	,	,	PUNCT
ejpam-23	427	11	on	on	ADP
ejpam-23	427	12	superabundant	superabundant	ADJ
ejpam-23	427	13	semigroups	semigroup	NOUN
ejpam-23	427	14	whose	whose	DET
ejpam-23	427	15	set	set	NOUN
ejpam-23	427	16	of	of	ADP
ejpam-23	427	17	idempotnets	idempotnet	NOUN
ejpam-23	427	18	forms	form	VERB
ejpam-23	427	19	a	a	DET
ejpam-23	427	20	subsemigroup	subsemigroup	NOUN
ejpam-23	427	21	,	,	PUNCT
ejpam-23	427	22	algebra	algebra	NOUN
ejpam-23	427	23	colloqium	colloqium	NOUN
ejpam-23	427	24	,	,	PUNCT
ejpam-23	427	25	14	14	NUM
ejpam-23	427	26	(	(	PUNCT
ejpam-23	427	27	2	2	NUM
ejpam-23	427	28	)	)	PUNCT
ejpam-23	427	29	,	,	PUNCT
ejpam-23	427	30	215	215	NUM
ejpam-23	427	31	-	-	SYM
ejpam-23	427	32	228	228	NUM
ejpam-23	427	33	,	,	PUNCT
ejpam-23	427	34	(	(	PUNCT
ejpam-23	427	35	2007	2007	NUM
ejpam-23	427	36	)	)	PUNCT