id	sid	tid	token	lemma	pos
ejpam-3010	1	1	european	european	PROPN
ejpam-3010	1	2	journal	journal	PROPN
ejpam-3010	1	3	of	of	ADP
ejpam-3010	1	4	pure	pure	ADJ
ejpam-3010	1	5	and	and	CCONJ
ejpam-3010	1	6	applied	apply	VERB
ejpam-3010	1	7	mathematics	mathematic	NOUN
ejpam-3010	1	8	vol	vol	NOUN
ejpam-3010	1	9	.	.	PROPN
ejpam-3010	2	1	10	10	NUM
ejpam-3010	2	2	,	,	PUNCT
ejpam-3010	2	3	no	no	INTJ
ejpam-3010	2	4	.	.	NOUN
ejpam-3010	2	5	4	4	NUM
ejpam-3010	2	6	,	,	PUNCT
ejpam-3010	2	7	2017	2017	NUM
ejpam-3010	2	8	,	,	PUNCT
ejpam-3010	2	9	620	620	NUM
ejpam-3010	2	10	-	-	SYM
ejpam-3010	2	11	630	630	NUM
ejpam-3010	2	12	issn	issn	PROPN
ejpam-3010	2	13	1307	1307	NUM
ejpam-3010	2	14	-	-	SYM
ejpam-3010	2	15	5543	5543	NUM
ejpam-3010	2	16	–	–	PUNCT
ejpam-3010	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3010	2	18	published	publish	VERB
ejpam-3010	2	19	by	by	ADP
ejpam-3010	2	20	new	new	PROPN
ejpam-3010	2	21	york	york	PROPN
ejpam-3010	2	22	business	business	PROPN
ejpam-3010	2	23	global	global	PROPN
ejpam-3010	2	24	on	on	ADP
ejpam-3010	2	25	intra	intra	ADJ
ejpam-3010	2	26	-	-	ADJ
ejpam-3010	2	27	regular	regular	ADJ
ejpam-3010	2	28	ordered	order	VERB
ejpam-3010	2	29	γ	γ	NOUN
ejpam-3010	2	30	-	-	PUNCT
ejpam-3010	2	31	semigroups	semigroup	NOUN
ejpam-3010	2	32	niovi	niovi	PROPN
ejpam-3010	2	33	kehayopulu	kehayopulu	PROPN
ejpam-3010	2	34	university	university	PROPN
ejpam-3010	2	35	of	of	ADP
ejpam-3010	2	36	athens	athens	PROPN
ejpam-3010	2	37	,	,	PUNCT
ejpam-3010	2	38	department	department	NOUN
ejpam-3010	2	39	of	of	ADP
ejpam-3010	2	40	mathematics	mathematics	PROPN
ejpam-3010	2	41	,	,	PUNCT
ejpam-3010	2	42	panepistimiopolis	panepistimiopolis	PROPN
ejpam-3010	2	43	,	,	PUNCT
ejpam-3010	2	44	greece	greece	PROPN
ejpam-3010	2	45	abstract	abstract	PROPN
ejpam-3010	2	46	.	.	PUNCT
ejpam-3010	3	1	we	we	PRON
ejpam-3010	3	2	use	use	VERB
ejpam-3010	3	3	the	the	DET
ejpam-3010	3	4	definition	definition	NOUN
ejpam-3010	3	5	of	of	ADP
ejpam-3010	3	6	intra	intra	ADJ
ejpam-3010	3	7	-	-	ADJ
ejpam-3010	3	8	regularity	regularity	ADJ
ejpam-3010	3	9	(	(	PUNCT
ejpam-3010	3	10	left	leave	VERB
ejpam-3010	3	11	regularity	regularity	NOUN
ejpam-3010	3	12	)	)	PUNCT
ejpam-3010	3	13	of	of	ADP
ejpam-3010	3	14	po	po	NOUN
ejpam-3010	3	15	-	-	PUNCT
ejpam-3010	3	16	γ	γ	NOUN
ejpam-3010	3	17	-	-	PUNCT
ejpam-3010	3	18	semigroups	semigroup	NOUN
ejpam-3010	3	19	introduced	introduce	VERB
ejpam-3010	3	20	in	in	ADP
ejpam-3010	3	21	2016	2016	NUM
ejpam-3010	3	22	in	in	ADP
ejpam-3010	3	23	armenian	armenian	ADJ
ejpam-3010	3	24	journal	journal	NOUN
ejpam-3010	3	25	of	of	ADP
ejpam-3010	3	26	mathematics	mathematic	NOUN
ejpam-3010	3	27	.	.	PUNCT
ejpam-3010	4	1	being	be	AUX
ejpam-3010	4	2	able	able	ADJ
ejpam-3010	4	3	to	to	PART
ejpam-3010	4	4	describe	describe	VERB
ejpam-3010	4	5	the	the	DET
ejpam-3010	4	6	form	form	NOUN
ejpam-3010	4	7	of	of	ADP
ejpam-3010	4	8	the	the	DET
ejpam-3010	4	9	elements	element	NOUN
ejpam-3010	4	10	of	of	ADP
ejpam-3010	4	11	the	the	DET
ejpam-3010	4	12	principal	principal	ADJ
ejpam-3010	4	13	filter	filter	NOUN
ejpam-3010	4	14	by	by	ADP
ejpam-3010	4	15	using	use	VERB
ejpam-3010	4	16	this	this	DET
ejpam-3010	4	17	definition	definition	NOUN
ejpam-3010	4	18	,	,	PUNCT
ejpam-3010	4	19	we	we	PRON
ejpam-3010	4	20	study	study	VERB
ejpam-3010	4	21	the	the	DET
ejpam-3010	4	22	decomposition	decomposition	NOUN
ejpam-3010	4	23	of	of	ADP
ejpam-3010	4	24	an	an	DET
ejpam-3010	4	25	intra	intra	ADJ
ejpam-3010	4	26	-	-	ADJ
ejpam-3010	4	27	regular	regular	ADJ
ejpam-3010	4	28	poγ	poγ	NOUN
ejpam-3010	4	29	-	-	PUNCT
ejpam-3010	4	30	semigroup	semigroup	NOUN
ejpam-3010	4	31	into	into	ADP
ejpam-3010	4	32	simple	simple	ADJ
ejpam-3010	4	33	components	component	NOUN
ejpam-3010	4	34	.	.	PUNCT
ejpam-3010	5	1	then	then	ADV
ejpam-3010	5	2	we	we	PRON
ejpam-3010	5	3	prove	prove	VERB
ejpam-3010	5	4	that	that	SCONJ
ejpam-3010	5	5	a	a	DET
ejpam-3010	5	6	po	po	NOUN
ejpam-3010	5	7	-	-	PUNCT
ejpam-3010	5	8	γ	γ	NOUN
ejpam-3010	5	9	-	-	PUNCT
ejpam-3010	5	10	semigroup	semigroup	NOUN
ejpam-3010	5	11	m	m	VERB
ejpam-3010	5	12	is	be	AUX
ejpam-3010	5	13	intra	intra	ADJ
ejpam-3010	5	14	-	-	ADJ
ejpam-3010	5	15	regular	regular	ADJ
ejpam-3010	5	16	and	and	CCONJ
ejpam-3010	5	17	the	the	DET
ejpam-3010	5	18	ideals	ideal	NOUN
ejpam-3010	5	19	of	of	ADP
ejpam-3010	5	20	m	m	PROPN
ejpam-3010	5	21	form	form	VERB
ejpam-3010	5	22	a	a	DET
ejpam-3010	5	23	chain	chain	NOUN
ejpam-3010	5	24	if	if	SCONJ
ejpam-3010	5	25	and	and	CCONJ
ejpam-3010	5	26	only	only	ADV
ejpam-3010	5	27	if	if	SCONJ
ejpam-3010	5	28	m	m	NOUN
ejpam-3010	5	29	is	be	AUX
ejpam-3010	5	30	a	a	DET
ejpam-3010	5	31	chain	chain	NOUN
ejpam-3010	5	32	of	of	ADP
ejpam-3010	5	33	simple	simple	ADJ
ejpam-3010	5	34	semigroups	semigroup	NOUN
ejpam-3010	5	35	.	.	PUNCT
ejpam-3010	6	1	moreover	moreover	ADV
ejpam-3010	6	2	,	,	PUNCT
ejpam-3010	6	3	a	a	DET
ejpam-3010	6	4	po	po	NOUN
ejpam-3010	6	5	-	-	PUNCT
ejpam-3010	6	6	γ	γ	NOUN
ejpam-3010	6	7	-	-	PUNCT
ejpam-3010	6	8	semigroup	semigroup	NOUN
ejpam-3010	6	9	m	m	VERB
ejpam-3010	6	10	is	be	AUX
ejpam-3010	6	11	intra	intra	ADJ
ejpam-3010	6	12	-	-	ADJ
ejpam-3010	6	13	regular	regular	ADJ
ejpam-3010	6	14	and	and	CCONJ
ejpam-3010	6	15	the	the	DET
ejpam-3010	6	16	ideals	ideal	NOUN
ejpam-3010	6	17	of	of	ADP
ejpam-3010	6	18	m	m	PROPN
ejpam-3010	6	19	form	form	VERB
ejpam-3010	6	20	a	a	DET
ejpam-3010	6	21	chain	chain	NOUN
ejpam-3010	6	22	if	if	SCONJ
ejpam-3010	6	23	and	and	CCONJ
ejpam-3010	6	24	only	only	ADV
ejpam-3010	6	25	if	if	SCONJ
ejpam-3010	6	26	the	the	DET
ejpam-3010	6	27	ideals	ideal	NOUN
ejpam-3010	6	28	of	of	ADP
ejpam-3010	6	29	m	m	NOUN
ejpam-3010	6	30	are	be	AUX
ejpam-3010	6	31	prime	prime	ADJ
ejpam-3010	6	32	.	.	PUNCT
ejpam-3010	7	1	finally	finally	ADV
ejpam-3010	7	2	,	,	PUNCT
ejpam-3010	7	3	for	for	ADP
ejpam-3010	7	4	an	an	DET
ejpam-3010	7	5	intra	intra	ADJ
ejpam-3010	7	6	-	-	ADJ
ejpam-3010	7	7	regular	regular	ADJ
ejpam-3010	7	8	po	po	NOUN
ejpam-3010	7	9	-	-	PUNCT
ejpam-3010	7	10	γ	γ	NOUN
ejpam-3010	7	11	-	-	PUNCT
ejpam-3010	7	12	semigroup	semigroup	NOUN
ejpam-3010	7	13	m	m	NOUN
ejpam-3010	7	14	,	,	PUNCT
ejpam-3010	7	15	the	the	DET
ejpam-3010	7	16	set	set	NOUN
ejpam-3010	7	17	{	{	PUNCT
ejpam-3010	7	18	(	(	PUNCT
ejpam-3010	7	19	x)n	x)n	PUNCT
ejpam-3010	7	20	|	|	ADV
ejpam-3010	7	21	x	x	SYM
ejpam-3010	7	22	∈	∈	PROPN
ejpam-3010	7	23	m	m	PRON
ejpam-3010	7	24	}	}	PUNCT
ejpam-3010	7	25	coincides	coincide	NOUN
ejpam-3010	7	26	with	with	ADP
ejpam-3010	7	27	the	the	DET
ejpam-3010	7	28	set	set	NOUN
ejpam-3010	7	29	of	of	ADP
ejpam-3010	7	30	all	all	DET
ejpam-3010	7	31	maximal	maximal	ADJ
ejpam-3010	7	32	simple	simple	ADJ
ejpam-3010	7	33	subsemigroups	subsemigroup	NOUN
ejpam-3010	7	34	of	of	ADP
ejpam-3010	7	35	m	m	PROPN
ejpam-3010	7	36	.	.	PUNCT
ejpam-3010	8	1	a	a	DET
ejpam-3010	8	2	decomposition	decomposition	NOUN
ejpam-3010	8	3	of	of	ADP
ejpam-3010	8	4	some	some	DET
ejpam-3010	8	5	left	leave	VERB
ejpam-3010	8	6	regular	regular	ADJ
ejpam-3010	8	7	po	po	NOUN
ejpam-3010	8	8	-	-	PUNCT
ejpam-3010	8	9	γ	γ	NOUN
ejpam-3010	8	10	-	-	PUNCT
ejpam-3010	8	11	semigroups	semigroup	NOUN
ejpam-3010	8	12	into	into	ADP
ejpam-3010	8	13	their	their	PRON
ejpam-3010	8	14	left	left	ADJ
ejpam-3010	8	15	simple	simple	ADJ
ejpam-3010	8	16	components	component	NOUN
ejpam-3010	8	17	is	be	AUX
ejpam-3010	8	18	also	also	ADV
ejpam-3010	8	19	given	give	VERB
ejpam-3010	8	20	.	.	PUNCT
ejpam-3010	9	1	2010	2010	NUM
ejpam-3010	9	2	mathematics	mathematic	NOUN
ejpam-3010	9	3	subject	subject	NOUN
ejpam-3010	9	4	classifications	classification	NOUN
ejpam-3010	9	5	:	:	PUNCT
ejpam-3010	9	6	ams	am	NOUN
ejpam-3010	9	7	20m99	20m99	NUM
ejpam-3010	9	8	key	key	ADJ
ejpam-3010	9	9	words	word	NOUN
ejpam-3010	9	10	and	and	CCONJ
ejpam-3010	9	11	phrases	phrase	NOUN
ejpam-3010	9	12	:	:	PUNCT
ejpam-3010	9	13	po	po	NOUN
ejpam-3010	9	14	-	-	PUNCT
ejpam-3010	9	15	γ	γ	NOUN
ejpam-3010	9	16	-	-	PUNCT
ejpam-3010	9	17	semigroup	semigroup	NOUN
ejpam-3010	9	18	,	,	PUNCT
ejpam-3010	9	19	intra	intra	ADJ
ejpam-3010	9	20	-	-	ADJ
ejpam-3010	9	21	regular	regular	ADJ
ejpam-3010	9	22	,	,	PUNCT
ejpam-3010	9	23	ideal	ideal	ADJ
ejpam-3010	9	24	,	,	PUNCT
ejpam-3010	9	25	prime	prime	ADJ
ejpam-3010	9	26	ideal	ideal	NOUN
ejpam-3010	9	27	,	,	PUNCT
ejpam-3010	9	28	semilattice	semilattice	NOUN
ejpam-3010	9	29	(	(	PUNCT
ejpam-3010	9	30	chains	chain	NOUN
ejpam-3010	9	31	)	)	PUNCT
ejpam-3010	9	32	of	of	ADP
ejpam-3010	9	33	simple	simple	ADJ
ejpam-3010	9	34	semigroups	semigroup	NOUN
ejpam-3010	9	35	1	1	NUM
ejpam-3010	9	36	.	.	X
ejpam-3010	9	37	introduction	introduction	NOUN
ejpam-3010	9	38	and	and	CCONJ
ejpam-3010	9	39	prerequisites	prerequisite	VERB
ejpam-3010	9	40	the	the	DET
ejpam-3010	9	41	notion	notion	NOUN
ejpam-3010	9	42	of	of	ADP
ejpam-3010	9	43	a	a	DET
ejpam-3010	9	44	γ	γ	NOUN
ejpam-3010	9	45	-	-	NOUN
ejpam-3010	9	46	ring	ring	NOUN
ejpam-3010	9	47	,	,	PUNCT
ejpam-3010	9	48	a	a	DET
ejpam-3010	9	49	generalization	generalization	NOUN
ejpam-3010	9	50	of	of	ADP
ejpam-3010	9	51	the	the	DET
ejpam-3010	9	52	concept	concept	NOUN
ejpam-3010	9	53	of	of	ADP
ejpam-3010	9	54	associative	associative	ADJ
ejpam-3010	9	55	rings	ring	NOUN
ejpam-3010	9	56	,	,	PUNCT
ejpam-3010	9	57	has	have	AUX
ejpam-3010	9	58	been	be	AUX
ejpam-3010	9	59	introduced	introduce	VERB
ejpam-3010	9	60	and	and	CCONJ
ejpam-3010	9	61	studied	study	VERB
ejpam-3010	9	62	by	by	ADP
ejpam-3010	9	63	nobusawa	nobusawa	PROPN
ejpam-3010	9	64	in	in	ADP
ejpam-3010	9	65	[	[	X
ejpam-3010	9	66	11	11	NUM
ejpam-3010	9	67	]	]	PUNCT
ejpam-3010	9	68	.	.	PUNCT
ejpam-3010	10	1	γ	γ	NOUN
ejpam-3010	10	2	-	-	PUNCT
ejpam-3010	10	3	rings	ring	NOUN
ejpam-3010	10	4	have	have	AUX
ejpam-3010	10	5	been	be	AUX
ejpam-3010	10	6	also	also	ADV
ejpam-3010	10	7	studied	study	VERB
ejpam-3010	10	8	by	by	ADP
ejpam-3010	10	9	barnes	barne	NOUN
ejpam-3010	10	10	in	in	ADP
ejpam-3010	10	11	[	[	X
ejpam-3010	10	12	1	1	NUM
ejpam-3010	10	13	]	]	PUNCT
ejpam-3010	10	14	.	.	PUNCT
ejpam-3010	11	1	luh	luh	PROPN
ejpam-3010	11	2	studied	study	VERB
ejpam-3010	11	3	many	many	ADJ
ejpam-3010	11	4	properties	property	NOUN
ejpam-3010	11	5	of	of	ADP
ejpam-3010	11	6	simple	simple	ADJ
ejpam-3010	11	7	γ	γ	NOUN
ejpam-3010	11	8	-	-	PUNCT
ejpam-3010	11	9	rings	ring	NOUN
ejpam-3010	11	10	and	and	CCONJ
ejpam-3010	11	11	primitive	primitive	ADJ
ejpam-3010	11	12	γ	γ	NOUN
ejpam-3010	11	13	-	-	PUNCT
ejpam-3010	11	14	rings	ring	NOUN
ejpam-3010	11	15	in	in	ADP
ejpam-3010	11	16	[	[	X
ejpam-3010	11	17	10	10	NUM
ejpam-3010	11	18	]	]	PUNCT
ejpam-3010	11	19	.	.	PUNCT
ejpam-3010	12	1	the	the	DET
ejpam-3010	12	2	concept	concept	NOUN
ejpam-3010	12	3	of	of	ADP
ejpam-3010	12	4	a	a	DET
ejpam-3010	12	5	γ	γ	PROPN
ejpam-3010	12	6	-	-	PUNCT
ejpam-3010	12	7	semigroup	semigroup	NOUN
ejpam-3010	12	8	has	have	AUX
ejpam-3010	12	9	been	be	AUX
ejpam-3010	12	10	introduced	introduce	VERB
ejpam-3010	12	11	by	by	ADP
ejpam-3010	12	12	sen	sen	PROPN
ejpam-3010	12	13	in	in	ADP
ejpam-3010	12	14	1981	1981	NUM
ejpam-3010	12	15	as	as	SCONJ
ejpam-3010	12	16	follows	follow	VERB
ejpam-3010	12	17	:	:	PUNCT
ejpam-3010	12	18	given	give	VERB
ejpam-3010	12	19	two	two	NUM
ejpam-3010	12	20	nonempty	nonempty	ADJ
ejpam-3010	12	21	sets	set	NOUN
ejpam-3010	12	22	s	s	PART
ejpam-3010	12	23	and	and	CCONJ
ejpam-3010	12	24	γ	γ	X
ejpam-3010	12	25	,	,	PUNCT
ejpam-3010	12	26	s	s	PART
ejpam-3010	12	27	is	be	AUX
ejpam-3010	12	28	called	call	VERB
ejpam-3010	12	29	a	a	DET
ejpam-3010	12	30	γ	γ	NOUN
ejpam-3010	12	31	-	-	PUNCT
ejpam-3010	12	32	semigroup	semigroup	NOUN
ejpam-3010	12	33	if	if	SCONJ
ejpam-3010	12	34	the	the	DET
ejpam-3010	12	35	following	follow	VERB
ejpam-3010	12	36	assertions	assertion	NOUN
ejpam-3010	12	37	are	be	AUX
ejpam-3010	12	38	satisfied	satisfied	ADJ
ejpam-3010	12	39	:	:	PUNCT
ejpam-3010	12	40	(	(	PUNCT
ejpam-3010	12	41	1	1	X
ejpam-3010	12	42	)	)	PUNCT
ejpam-3010	12	43	aαb	aαb	NOUN
ejpam-3010	12	44	∈	∈	PROPN
ejpam-3010	12	45	s	s	PART
ejpam-3010	12	46	and	and	CCONJ
ejpam-3010	12	47	αaβ	αaβ	NOUN
ejpam-3010	12	48	∈	∈	PROPN
ejpam-3010	12	49	γ	γ	X
ejpam-3010	12	50	and	and	CCONJ
ejpam-3010	12	51	(	(	PUNCT
ejpam-3010	12	52	2	2	NUM
ejpam-3010	12	53	)	)	PUNCT
ejpam-3010	12	54	(	(	PUNCT
ejpam-3010	12	55	aαb)βc	aαb)βc	NOUN
ejpam-3010	12	56	=	=	SYM
ejpam-3010	12	57	a(αbβ)c	a(αbβ)c	NOUN
ejpam-3010	12	58	=	=	SYM
ejpam-3010	12	59	aα(bβc	aα(bβc	PROPN
ejpam-3010	12	60	)	)	PUNCT
ejpam-3010	12	61	for	for	ADP
ejpam-3010	12	62	all	all	DET
ejpam-3010	12	63	a	a	DET
ejpam-3010	12	64	,	,	PUNCT
ejpam-3010	12	65	b	b	NOUN
ejpam-3010	12	66	,	,	PUNCT
ejpam-3010	12	67	c	c	PROPN
ejpam-3010	12	68	∈	∈	PROPN
ejpam-3010	12	69	s	s	X
ejpam-3010	12	70	and	and	CCONJ
ejpam-3010	12	71	all	all	DET
ejpam-3010	12	72	α	α	NOUN
ejpam-3010	12	73	,	,	PUNCT
ejpam-3010	12	74	β	β	X
ejpam-3010	12	75	∈	∈	PROPN
ejpam-3010	12	76	γ	γ	X
ejpam-3010	12	77	[	[	X
ejpam-3010	12	78	13	13	NUM
ejpam-3010	12	79	]	]	PUNCT
ejpam-3010	12	80	.	.	PUNCT
ejpam-3010	13	1	in	in	ADP
ejpam-3010	13	2	1986	1986	NUM
ejpam-3010	13	3	sen	sen	PROPN
ejpam-3010	13	4	and	and	CCONJ
ejpam-3010	13	5	saha	saha	PROPN
ejpam-3010	13	6	gave	give	VERB
ejpam-3010	13	7	a	a	DET
ejpam-3010	13	8	second	second	ADJ
ejpam-3010	13	9	definition	definition	NOUN
ejpam-3010	13	10	of	of	ADP
ejpam-3010	13	11	γ	γ	NOUN
ejpam-3010	13	12	-	-	PUNCT
ejpam-3010	13	13	semigroups	semigroup	NOUN
ejpam-3010	13	14	as	as	SCONJ
ejpam-3010	13	15	follows	follow	VERB
ejpam-3010	13	16	:	:	PUNCT
ejpam-3010	13	17	let	let	VERB
ejpam-3010	13	18	s	s	VERB
ejpam-3010	13	19	=	=	X
ejpam-3010	13	20	{	{	PUNCT
ejpam-3010	13	21	a	a	PRON
ejpam-3010	13	22	,	,	PUNCT
ejpam-3010	13	23	b	b	NOUN
ejpam-3010	13	24	,	,	PUNCT
ejpam-3010	13	25	c	c	NOUN
ejpam-3010	13	26	,	,	PUNCT
ejpam-3010	13	27	......	......	PUNCT
ejpam-3010	13	28	}	}	PUNCT
ejpam-3010	13	29	and	and	CCONJ
ejpam-3010	13	30	γ	γ	X
ejpam-3010	13	31	=	=	SYM
ejpam-3010	13	32	{	{	PUNCT
ejpam-3010	13	33	α	α	PROPN
ejpam-3010	13	34	,	,	PUNCT
ejpam-3010	13	35	β	β	X
ejpam-3010	13	36	,	,	PUNCT
ejpam-3010	13	37	γ	γ	X
ejpam-3010	13	38	,	,	PUNCT
ejpam-3010	13	39	......	......	PUNCT
ejpam-3010	13	40	}	}	PUNCT
ejpam-3010	13	41	be	be	AUX
ejpam-3010	13	42	two	two	NUM
ejpam-3010	13	43	nonempty	nonempty	ADJ
ejpam-3010	13	44	sets	set	NOUN
ejpam-3010	13	45	.	.	PUNCT
ejpam-3010	14	1	then	then	ADV
ejpam-3010	14	2	s	s	VERB
ejpam-3010	14	3	is	be	AUX
ejpam-3010	14	4	called	call	VERB
ejpam-3010	14	5	a	a	DET
ejpam-3010	14	6	γ	γ	NOUN
ejpam-3010	14	7	-	-	PUNCT
ejpam-3010	14	8	semigroup	semigroup	NOUN
ejpam-3010	14	9	if	if	SCONJ
ejpam-3010	14	10	(	(	PUNCT
ejpam-3010	14	11	1	1	X
ejpam-3010	14	12	)	)	PUNCT
ejpam-3010	14	13	aαb	aαb	NOUN
ejpam-3010	14	14	∈	∈	PROPN
ejpam-3010	14	15	s	s	PART
ejpam-3010	14	16	and	and	CCONJ
ejpam-3010	14	17	(	(	PUNCT
ejpam-3010	14	18	2	2	NUM
ejpam-3010	14	19	)	)	PUNCT
ejpam-3010	14	20	(	(	PUNCT
ejpam-3010	14	21	aαb)βc	aαb)βc	NOUN
ejpam-3010	14	22	=	=	SYM
ejpam-3010	14	23	aα(bβc	aα(bβc	PROPN
ejpam-3010	14	24	)	)	PUNCT
ejpam-3010	14	25	for	for	ADP
ejpam-3010	14	26	all	all	DET
ejpam-3010	14	27	a	a	DET
ejpam-3010	14	28	,	,	PUNCT
ejpam-3010	14	29	b	b	NOUN
ejpam-3010	14	30	,	,	PUNCT
ejpam-3010	14	31	c	c	PROPN
ejpam-3010	14	32	∈	∈	PROPN
ejpam-3010	14	33	s	s	X
ejpam-3010	14	34	and	and	CCONJ
ejpam-3010	14	35	all	all	DET
ejpam-3010	14	36	α	α	NOUN
ejpam-3010	14	37	,	,	PUNCT
ejpam-3010	14	38	β	β	X
ejpam-3010	14	39	∈	∈	PROPN
ejpam-3010	14	40	γ	γ	X
ejpam-3010	14	41	[	[	X
ejpam-3010	14	42	14	14	NUM
ejpam-3010	14	43	]	]	PUNCT
ejpam-3010	14	44	(	(	PUNCT
ejpam-3010	14	45	the	the	DET
ejpam-3010	14	46	sets	set	NOUN
ejpam-3010	14	47	s	s	PART
ejpam-3010	14	48	and	and	CCONJ
ejpam-3010	14	49	γ	γ	NOUN
ejpam-3010	14	50	should	should	AUX
ejpam-3010	14	51	not	not	PART
ejpam-3010	14	52	be	be	AUX
ejpam-3010	14	53	denumerable	denumerable	ADJ
ejpam-3010	14	54	)	)	PUNCT
ejpam-3010	14	55	.	.	PUNCT
ejpam-3010	15	1	one	one	PRON
ejpam-3010	15	2	can	can	AUX
ejpam-3010	15	3	find	find	VERB
ejpam-3010	15	4	this	this	DET
ejpam-3010	15	5	definition	definition	NOUN
ejpam-3010	15	6	of	of	ADP
ejpam-3010	15	7	γ	γ	NOUN
ejpam-3010	15	8	-	-	PUNCT
ejpam-3010	15	9	semigroups	semigroup	NOUN
ejpam-3010	15	10	in	in	ADP
ejpam-3010	15	11	[	[	X
ejpam-3010	15	12	17	17	NUM
ejpam-3010	15	13	]	]	PUNCT
ejpam-3010	15	14	where	where	SCONJ
ejpam-3010	15	15	the	the	DET
ejpam-3010	15	16	notion	notion	NOUN
ejpam-3010	15	17	of	of	ADP
ejpam-3010	15	18	a	a	DET
ejpam-3010	15	19	radical	radical	ADJ
ejpam-3010	15	20	in	in	ADP
ejpam-3010	15	21	γsemigroups	γsemigroup	NOUN
ejpam-3010	15	22	and	and	CCONJ
ejpam-3010	15	23	the	the	DET
ejpam-3010	15	24	notion	notion	NOUN
ejpam-3010	15	25	of	of	ADP
ejpam-3010	15	26	γs	γs	NOUN
ejpam-3010	15	27	-	-	PUNCT
ejpam-3010	15	28	act	act	NOUN
ejpam-3010	15	29	over	over	ADP
ejpam-3010	15	30	a	a	DET
ejpam-3010	15	31	γ	γ	PROPN
ejpam-3010	15	32	-	-	PUNCT
ejpam-3010	15	33	semigroup	semigroup	NOUN
ejpam-3010	15	34	have	have	AUX
ejpam-3010	15	35	been	be	AUX
ejpam-3010	15	36	introduced	introduce	VERB
ejpam-3010	15	37	and	and	CCONJ
ejpam-3010	15	38	in	in	ADP
ejpam-3010	15	39	[	[	X
ejpam-3010	15	40	15	15	NUM
ejpam-3010	15	41	]	]	PUNCT
ejpam-3010	15	42	email	email	NOUN
ejpam-3010	15	43	address	address	NOUN
ejpam-3010	15	44	:	:	PUNCT
ejpam-3010	15	45	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3010	15	46	(	(	PUNCT
ejpam-3010	15	47	n.	n.	PROPN
ejpam-3010	15	48	kehayopulu	kehayopulu	PROPN
ejpam-3010	15	49	)	)	PUNCT
ejpam-3010	15	50	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3010	16	1	620	620	NUM
ejpam-3010	17	1	c	c	X
ejpam-3010	17	2	©	©	PROPN
ejpam-3010	17	3	2017	2017	NUM
ejpam-3010	17	4	ejpam	ejpam	NOUN
ejpam-3010	17	5	all	all	DET
ejpam-3010	17	6	rights	right	NOUN
ejpam-3010	17	7	reserved	reserve	VERB
ejpam-3010	17	8	.	.	PUNCT
ejpam-3010	18	1	n.	n.	PROPN
ejpam-3010	18	2	kehayopulu	kehayopulu	PROPN
ejpam-3010	18	3	/	/	SYM
ejpam-3010	18	4	eur	eur	PROPN
ejpam-3010	18	5	.	.	PUNCT
ejpam-3010	19	1	j.	j.	PROPN
ejpam-3010	19	2	pure	pure	PROPN
ejpam-3010	19	3	appl	appl	PROPN
ejpam-3010	19	4	.	.	PROPN
ejpam-3010	19	5	math	math	PROPN
ejpam-3010	19	6	,	,	PUNCT
ejpam-3010	19	7	10	10	NUM
ejpam-3010	19	8	(	(	PUNCT
ejpam-3010	19	9	4	4	NUM
ejpam-3010	19	10	)	)	PUNCT
ejpam-3010	19	11	(	(	PUNCT
ejpam-3010	19	12	2017	2017	NUM
ejpam-3010	19	13	)	)	PUNCT
ejpam-3010	19	14	,	,	PUNCT
ejpam-3010	19	15	620	620	NUM
ejpam-3010	19	16	-	-	SYM
ejpam-3010	19	17	630	630	NUM
ejpam-3010	19	18	621	621	NUM
ejpam-3010	19	19	and	and	CCONJ
ejpam-3010	19	20	[	[	X
ejpam-3010	19	21	16	16	NUM
ejpam-3010	19	22	]	]	PUNCT
ejpam-3010	19	23	where	where	SCONJ
ejpam-3010	19	24	the	the	DET
ejpam-3010	19	25	notions	notion	NOUN
ejpam-3010	19	26	of	of	ADP
ejpam-3010	19	27	regular	regular	ADJ
ejpam-3010	19	28	and	and	CCONJ
ejpam-3010	19	29	orthodox	orthodox	ADJ
ejpam-3010	19	30	γ	γ	NOUN
ejpam-3010	19	31	-	-	PUNCT
ejpam-3010	19	32	semigroups	semigroup	NOUN
ejpam-3010	19	33	have	have	AUX
ejpam-3010	19	34	been	be	AUX
ejpam-3010	19	35	introduced	introduce	VERB
ejpam-3010	19	36	and	and	CCONJ
ejpam-3010	19	37	studied	study	VERB
ejpam-3010	19	38	.	.	PUNCT
ejpam-3010	20	1	but	but	CCONJ
ejpam-3010	20	2	still	still	ADV
ejpam-3010	20	3	we	we	PRON
ejpam-3010	20	4	can	can	AUX
ejpam-3010	20	5	not	not	PART
ejpam-3010	20	6	say	say	VERB
ejpam-3010	20	7	that	that	SCONJ
ejpam-3010	20	8	γ	γ	PROPN
ejpam-3010	20	9	is	be	AUX
ejpam-3010	20	10	a	a	DET
ejpam-3010	20	11	set	set	NOUN
ejpam-3010	20	12	of	of	ADP
ejpam-3010	20	13	binary	binary	ADJ
ejpam-3010	20	14	operations	operation	NOUN
ejpam-3010	20	15	on	on	ADP
ejpam-3010	20	16	the	the	DET
ejpam-3010	20	17	set	set	NOUN
ejpam-3010	20	18	m	m	NOUN
ejpam-3010	20	19	.	.	PUNCT
ejpam-3010	21	1	probably	probably	ADV
ejpam-3010	21	2	this	this	PRON
ejpam-3010	21	3	is	be	AUX
ejpam-3010	21	4	why	why	SCONJ
ejpam-3010	21	5	saha	saha	PROPN
ejpam-3010	21	6	defines	define	VERB
ejpam-3010	21	7	in	in	ADP
ejpam-3010	21	8	[	[	X
ejpam-3010	21	9	12	12	NUM
ejpam-3010	21	10	]	]	PUNCT
ejpam-3010	22	1	the	the	DET
ejpam-3010	22	2	γ	γ	PROPN
ejpam-3010	22	3	-	-	PUNCT
ejpam-3010	22	4	semigroup	semigroup	NOUN
ejpam-3010	22	5	as	as	SCONJ
ejpam-3010	22	6	follows	follow	VERB
ejpam-3010	22	7	:	:	PUNCT
ejpam-3010	22	8	given	give	VERB
ejpam-3010	22	9	two	two	NUM
ejpam-3010	22	10	nonempty	nonempty	ADJ
ejpam-3010	22	11	sets	set	NOUN
ejpam-3010	22	12	s	s	PART
ejpam-3010	22	13	and	and	CCONJ
ejpam-3010	22	14	γ	γ	X
ejpam-3010	22	15	,	,	PUNCT
ejpam-3010	22	16	s	s	PART
ejpam-3010	22	17	is	be	AUX
ejpam-3010	22	18	called	call	VERB
ejpam-3010	22	19	a	a	DET
ejpam-3010	22	20	γ	γ	NOUN
ejpam-3010	22	21	-	-	PUNCT
ejpam-3010	22	22	semigroup	semigroup	NOUN
ejpam-3010	22	23	if	if	SCONJ
ejpam-3010	22	24	there	there	PRON
ejpam-3010	22	25	exists	exist	VERB
ejpam-3010	22	26	a	a	DET
ejpam-3010	22	27	mapping	mapping	NOUN
ejpam-3010	22	28	s	s	PART
ejpam-3010	22	29	×	×	NOUN
ejpam-3010	23	1	γ×	γ×	PROPN
ejpam-3010	23	2	s	s	PROPN
ejpam-3010	23	3	→	→	SYM
ejpam-3010	23	4	s	s	PART
ejpam-3010	23	5	|	|	ADV
ejpam-3010	23	6	(	(	PUNCT
ejpam-3010	23	7	a	a	PRON
ejpam-3010	23	8	,	,	PUNCT
ejpam-3010	23	9	γ	γ	X
ejpam-3010	23	10	,	,	PUNCT
ejpam-3010	23	11	b)→	b)→	VERB
ejpam-3010	23	12	aγb	aγb	NOUN
ejpam-3010	23	13	such	such	ADJ
ejpam-3010	23	14	that	that	SCONJ
ejpam-3010	23	15	(	(	PUNCT
ejpam-3010	23	16	aαb)βc	aαb)βc	NOUN
ejpam-3010	23	17	=	=	SYM
ejpam-3010	23	18	aα(bβc	aα(bβc	PROPN
ejpam-3010	23	19	)	)	PUNCT
ejpam-3010	23	20	for	for	ADP
ejpam-3010	23	21	all	all	DET
ejpam-3010	23	22	a	a	DET
ejpam-3010	23	23	,	,	PUNCT
ejpam-3010	23	24	b	b	NOUN
ejpam-3010	23	25	,	,	PUNCT
ejpam-3010	23	26	c	c	PROPN
ejpam-3010	23	27	∈	∈	PROPN
ejpam-3010	23	28	s	s	X
ejpam-3010	23	29	and	and	CCONJ
ejpam-3010	23	30	all	all	DET
ejpam-3010	23	31	α	α	NOUN
ejpam-3010	23	32	,	,	PUNCT
ejpam-3010	23	33	β	β	X
ejpam-3010	23	34	∈	∈	PROPN
ejpam-3010	23	35	γ	γ	NOUN
ejpam-3010	23	36	and	and	CCONJ
ejpam-3010	23	37	remarks	remark	VERB
ejpam-3010	23	38	that	that	SCONJ
ejpam-3010	23	39	most	most	ADJ
ejpam-3010	23	40	usual	usual	ADJ
ejpam-3010	23	41	semigroup	semigroup	ADJ
ejpam-3010	23	42	concepts	concept	NOUN
ejpam-3010	23	43	,	,	PUNCT
ejpam-3010	23	44	in	in	ADP
ejpam-3010	23	45	particular	particular	ADJ
ejpam-3010	23	46	regular	regular	ADJ
ejpam-3010	23	47	and	and	CCONJ
ejpam-3010	23	48	inverse	inverse	NOUN
ejpam-3010	23	49	semigroups	semigroup	NOUN
ejpam-3010	23	50	,	,	PUNCT
ejpam-3010	23	51	have	have	AUX
ejpam-3010	23	52	their	their	PRON
ejpam-3010	23	53	analogous	analogous	ADJ
ejpam-3010	23	54	for	for	ADP
ejpam-3010	23	55	γ	γ	NOUN
ejpam-3010	23	56	-	-	PUNCT
ejpam-3010	23	57	semigroups	semigroup	NOUN
ejpam-3010	23	58	.	.	PUNCT
ejpam-3010	24	1	defining	define	VERB
ejpam-3010	24	2	the	the	DET
ejpam-3010	24	3	γ	γ	NOUN
ejpam-3010	24	4	-	-	PUNCT
ejpam-3010	24	5	semigroup	semigroup	NOUN
ejpam-3010	24	6	via	via	ADP
ejpam-3010	24	7	mappings	mapping	NOUN
ejpam-3010	24	8	,	,	PUNCT
ejpam-3010	24	9	in	in	ADP
ejpam-3010	24	10	an	an	DET
ejpam-3010	24	11	expression	expression	NOUN
ejpam-3010	24	12	of	of	ADP
ejpam-3010	24	13	the	the	DET
ejpam-3010	24	14	form	form	NOUN
ejpam-3010	24	15	a1γ1a2γ2a3	a1γ1a2γ2a3	NUM
ejpam-3010	24	16	....	....	PUNCT
ejpam-3010	25	1	anγn	anγn	NOUN
ejpam-3010	25	2	,	,	PUNCT
ejpam-3010	25	3	we	we	PRON
ejpam-3010	25	4	can	can	AUX
ejpam-3010	25	5	put	put	VERB
ejpam-3010	25	6	parentheses	parenthesis	NOUN
ejpam-3010	25	7	in	in	ADP
ejpam-3010	25	8	any	any	DET
ejpam-3010	25	9	place	place	NOUN
ejpam-3010	25	10	beginning	begin	VERB
ejpam-3010	25	11	with	with	ADP
ejpam-3010	25	12	some	some	DET
ejpam-3010	25	13	ai	ai	NOUN
ejpam-3010	25	14	and	and	CCONJ
ejpam-3010	25	15	ending	end	VERB
ejpam-3010	25	16	in	in	ADP
ejpam-3010	25	17	some	some	DET
ejpam-3010	25	18	aj	aj	PROPN
ejpam-3010	25	19	.	.	PUNCT
ejpam-3010	26	1	the	the	DET
ejpam-3010	26	2	ordered	order	VERB
ejpam-3010	26	3	γ	γ	NOUN
ejpam-3010	26	4	-	-	PUNCT
ejpam-3010	26	5	semigroups	semigroup	NOUN
ejpam-3010	26	6	have	have	AUX
ejpam-3010	26	7	been	be	AUX
ejpam-3010	26	8	first	first	ADV
ejpam-3010	26	9	considered	consider	VERB
ejpam-3010	26	10	by	by	ADP
ejpam-3010	26	11	sen	sen	PROPN
ejpam-3010	26	12	and	and	CCONJ
ejpam-3010	26	13	seth	seth	PROPN
ejpam-3010	26	14	in	in	ADP
ejpam-3010	26	15	[	[	X
ejpam-3010	26	16	18	18	NUM
ejpam-3010	26	17	]	]	PUNCT
ejpam-3010	26	18	.	.	PUNCT
ejpam-3010	27	1	let	let	VERB
ejpam-3010	27	2	m	m	PRON
ejpam-3010	27	3	and	and	CCONJ
ejpam-3010	27	4	γ	γ	NOUN
ejpam-3010	27	5	be	be	AUX
ejpam-3010	27	6	two	two	NUM
ejpam-3010	27	7	nonempty	nonempty	ADJ
ejpam-3010	27	8	sets	set	NOUN
ejpam-3010	27	9	.	.	PUNCT
ejpam-3010	28	1	denote	denote	VERB
ejpam-3010	28	2	by	by	ADP
ejpam-3010	28	3	mγm	mγm	NOUN
ejpam-3010	28	4	the	the	DET
ejpam-3010	28	5	set	set	NOUN
ejpam-3010	28	6	of	of	ADP
ejpam-3010	28	7	(	(	PUNCT
ejpam-3010	28	8	all	all	PRON
ejpam-3010	28	9	)	)	PUNCT
ejpam-3010	28	10	elements	element	NOUN
ejpam-3010	28	11	of	of	ADP
ejpam-3010	28	12	the	the	DET
ejpam-3010	28	13	form	form	NOUN
ejpam-3010	28	14	aγb	aγb	VERB
ejpam-3010	28	15	,	,	PUNCT
ejpam-3010	28	16	where	where	SCONJ
ejpam-3010	28	17	a	a	DET
ejpam-3010	28	18	,	,	PUNCT
ejpam-3010	28	19	b	b	NOUN
ejpam-3010	28	20	∈m	∈m	NOUN
ejpam-3010	28	21	and	and	CCONJ
ejpam-3010	28	22	γ	γ	PROPN
ejpam-3010	28	23	∈	∈	PROPN
ejpam-3010	28	24	γ	γ	X
ejpam-3010	28	25	.	.	PROPN
ejpam-3010	29	1	that	that	PRON
ejpam-3010	29	2	is	is	ADV
ejpam-3010	29	3	,	,	PUNCT
ejpam-3010	29	4	mγm	mγm	INTJ
ejpam-3010	29	5	:	:	PUNCT
ejpam-3010	29	6	=	=	SYM
ejpam-3010	29	7	{	{	PUNCT
ejpam-3010	29	8	aγb	aγb	NOUN
ejpam-3010	29	9	|	|	ADV
ejpam-3010	29	10	a	a	PRON
ejpam-3010	29	11	,	,	PUNCT
ejpam-3010	29	12	b	b	NOUN
ejpam-3010	29	13	∈m	∈m	NOUN
ejpam-3010	29	14	,	,	PUNCT
ejpam-3010	29	15	γ	γ	PROPN
ejpam-3010	29	16	∈	∈	NOUN
ejpam-3010	29	17	γ	γ	X
ejpam-3010	29	18	}	}	PUNCT
ejpam-3010	29	19	.	.	PUNCT
ejpam-3010	30	1	then	then	ADV
ejpam-3010	30	2	m	m	PROPN
ejpam-3010	30	3	is	be	AUX
ejpam-3010	30	4	called	call	VERB
ejpam-3010	30	5	a	a	DET
ejpam-3010	30	6	γ	γ	NOUN
ejpam-3010	30	7	-	-	PUNCT
ejpam-3010	30	8	semigroup	semigroup	NOUN
ejpam-3010	30	9	[	[	X
ejpam-3010	30	10	5	5	NUM
ejpam-3010	30	11	,	,	PUNCT
ejpam-3010	30	12	6	6	NUM
ejpam-3010	30	13	]	]	PUNCT
ejpam-3010	30	14	if	if	SCONJ
ejpam-3010	30	15	the	the	DET
ejpam-3010	30	16	following	follow	VERB
ejpam-3010	30	17	assertions	assertion	NOUN
ejpam-3010	30	18	are	be	AUX
ejpam-3010	30	19	satisfied	satisfied	ADJ
ejpam-3010	30	20	:	:	PUNCT
ejpam-3010	30	21	(	(	PUNCT
ejpam-3010	30	22	1	1	X
ejpam-3010	30	23	)	)	PUNCT
ejpam-3010	30	24	mγm	mγm	NOUN
ejpam-3010	30	25	⊆m	⊆m	NOUN
ejpam-3010	30	26	;	;	PUNCT
ejpam-3010	30	27	(	(	PUNCT
ejpam-3010	30	28	2	2	X
ejpam-3010	30	29	)	)	PUNCT
ejpam-3010	30	30	if	if	SCONJ
ejpam-3010	30	31	a	a	DET
ejpam-3010	30	32	,	,	PUNCT
ejpam-3010	30	33	b	b	NOUN
ejpam-3010	30	34	,	,	PUNCT
ejpam-3010	30	35	c	c	NOUN
ejpam-3010	30	36	,	,	PUNCT
ejpam-3010	30	37	d	d	PRON
ejpam-3010	30	38	∈m	∈m	NOUN
ejpam-3010	30	39	,	,	PUNCT
ejpam-3010	30	40	γ	γ	X
ejpam-3010	30	41	,	,	PUNCT
ejpam-3010	30	42	µ	µ	PRON
ejpam-3010	30	43	∈	∈	PROPN
ejpam-3010	30	44	γ	γ	X
ejpam-3010	30	45	,	,	PUNCT
ejpam-3010	30	46	a	a	DET
ejpam-3010	30	47	=	=	SYM
ejpam-3010	30	48	b	b	NOUN
ejpam-3010	30	49	,	,	PUNCT
ejpam-3010	30	50	γ	γ	PROPN
ejpam-3010	30	51	=	=	SYM
ejpam-3010	30	52	µ	µ	PROPN
ejpam-3010	30	53	and	and	CCONJ
ejpam-3010	30	54	c	c	NOUN
ejpam-3010	30	55	=	=	SYM
ejpam-3010	30	56	d	d	PROPN
ejpam-3010	30	57	,	,	PUNCT
ejpam-3010	30	58	then	then	ADV
ejpam-3010	30	59	aγc	aγc	NOUN
ejpam-3010	30	60	=	=	PUNCT
ejpam-3010	30	61	bµd	bµd	NOUN
ejpam-3010	30	62	;	;	PUNCT
ejpam-3010	30	63	(	(	PUNCT
ejpam-3010	30	64	3	3	X
ejpam-3010	30	65	)	)	PUNCT
ejpam-3010	30	66	aγ(bµc	aγ(bµc	NOUN
ejpam-3010	30	67	)	)	PUNCT
ejpam-3010	30	68	=	=	PUNCT
ejpam-3010	31	1	(	(	PUNCT
ejpam-3010	31	2	aγb)µc	aγb)µc	NOUN
ejpam-3010	31	3	∀	∀	X
ejpam-3010	31	4	a	a	PRON
ejpam-3010	31	5	,	,	PUNCT
ejpam-3010	31	6	b	b	NOUN
ejpam-3010	31	7	,	,	PUNCT
ejpam-3010	31	8	c	c	PROPN
ejpam-3010	31	9	∈m	∈m	NOUN
ejpam-3010	31	10	∀	∀	X
ejpam-3010	31	11	γ	γ	X
ejpam-3010	31	12	,	,	PUNCT
ejpam-3010	31	13	µ	µ	PRON
ejpam-3010	31	14	∈	∈	PROPN
ejpam-3010	31	15	γ	γ	X
ejpam-3010	31	16	.	.	PROPN
ejpam-3010	31	17	in	in	ADP
ejpam-3010	31	18	other	other	ADJ
ejpam-3010	31	19	words	word	NOUN
ejpam-3010	31	20	,	,	PUNCT
ejpam-3010	31	21	γ	γ	X
ejpam-3010	31	22	is	be	AUX
ejpam-3010	31	23	a	a	DET
ejpam-3010	31	24	set	set	NOUN
ejpam-3010	31	25	of	of	ADP
ejpam-3010	31	26	binary	binary	ADJ
ejpam-3010	31	27	operations	operation	NOUN
ejpam-3010	31	28	on	on	ADP
ejpam-3010	31	29	m	m	NOUN
ejpam-3010	31	30	and	and	CCONJ
ejpam-3010	31	31	the	the	DET
ejpam-3010	31	32	following	follow	VERB
ejpam-3010	31	33	condition	condition	NOUN
ejpam-3010	31	34	is	be	AUX
ejpam-3010	31	35	satisfied	satisfied	ADJ
ejpam-3010	31	36	:	:	PUNCT
ejpam-3010	31	37	aγ(bµc	aγ(bµc	NOUN
ejpam-3010	31	38	)	)	PUNCT
ejpam-3010	31	39	=	=	PUNCT
ejpam-3010	32	1	(	(	PUNCT
ejpam-3010	32	2	aγb)µc	aγb)µc	NOUN
ejpam-3010	32	3	∀	∀	X
ejpam-3010	32	4	a	a	PRON
ejpam-3010	32	5	,	,	PUNCT
ejpam-3010	32	6	b	b	NOUN
ejpam-3010	32	7	,	,	PUNCT
ejpam-3010	32	8	c	c	PROPN
ejpam-3010	32	9	∈m	∈m	NOUN
ejpam-3010	32	10	∀	∀	X
ejpam-3010	32	11	γ	γ	X
ejpam-3010	32	12	,	,	PUNCT
ejpam-3010	32	13	µ	µ	PRON
ejpam-3010	32	14	∈	∈	PROPN
ejpam-3010	32	15	γ	γ	X
ejpam-3010	32	16	.	.	PUNCT
ejpam-3010	32	17	a	a	DET
ejpam-3010	32	18	γ	γ	PROPN
ejpam-3010	32	19	-	-	PUNCT
ejpam-3010	32	20	semigroup	semigroup	NOUN
ejpam-3010	32	21	endowed	endow	VERB
ejpam-3010	32	22	with	with	ADP
ejpam-3010	32	23	an	an	DET
ejpam-3010	32	24	order	order	NOUN
ejpam-3010	32	25	relation	relation	NOUN
ejpam-3010	32	26	“	"	PUNCT
ejpam-3010	32	27	≤	≤	NUM
ejpam-3010	32	28	”	"	PUNCT
ejpam-3010	32	29	such	such	ADJ
ejpam-3010	32	30	that	that	SCONJ
ejpam-3010	32	31	a	a	DET
ejpam-3010	32	32	≤	≤	PROPN
ejpam-3010	32	33	b	b	NOUN
ejpam-3010	32	34	implies	imply	VERB
ejpam-3010	32	35	aγc	aγc	PROPN
ejpam-3010	32	36	≤	≤	PROPN
ejpam-3010	32	37	bγc	bγc	NOUN
ejpam-3010	32	38	and	and	CCONJ
ejpam-3010	32	39	cγa	cγa	PROPN
ejpam-3010	32	40	≤	≤	NUM
ejpam-3010	32	41	cγb	cγb	NOUN
ejpam-3010	32	42	for	for	ADP
ejpam-3010	32	43	every	every	DET
ejpam-3010	32	44	c	c	NOUN
ejpam-3010	32	45	∈m	∈m	NOUN
ejpam-3010	32	46	and	and	CCONJ
ejpam-3010	32	47	every	every	DET
ejpam-3010	32	48	γ	γ	PROPN
ejpam-3010	32	49	∈	∈	PROPN
ejpam-3010	32	50	γ	γ	NOUN
ejpam-3010	32	51	is	be	AUX
ejpam-3010	32	52	called	call	VERB
ejpam-3010	32	53	an	an	DET
ejpam-3010	32	54	ordered	order	VERB
ejpam-3010	32	55	γ	γ	NOUN
ejpam-3010	32	56	-	-	PUNCT
ejpam-3010	32	57	semigroup	semigroup	NOUN
ejpam-3010	32	58	(	(	PUNCT
ejpam-3010	32	59	shortly	shortly	ADV
ejpam-3010	32	60	,	,	PUNCT
ejpam-3010	32	61	po	po	NOUN
ejpam-3010	32	62	-	-	PUNCT
ejpam-3010	32	63	γ	γ	NOUN
ejpam-3010	32	64	-	-	PUNCT
ejpam-3010	32	65	semigroup	semigroup	NOUN
ejpam-3010	32	66	)	)	PUNCT
ejpam-3010	32	67	.	.	PUNCT
ejpam-3010	33	1	for	for	ADP
ejpam-3010	33	2	a	a	DET
ejpam-3010	33	3	po	po	NOUN
ejpam-3010	33	4	-	-	PUNCT
ejpam-3010	33	5	γ	γ	NOUN
ejpam-3010	33	6	-	-	PUNCT
ejpam-3010	33	7	semigroup	semigroup	NOUN
ejpam-3010	33	8	m	m	NOUN
ejpam-3010	33	9	and	and	CCONJ
ejpam-3010	33	10	a	a	DET
ejpam-3010	33	11	subset	subset	ADJ
ejpam-3010	33	12	h	h	NOUN
ejpam-3010	33	13	of	of	ADP
ejpam-3010	33	14	m	m	VERB
ejpam-3010	33	15	we	we	PRON
ejpam-3010	33	16	denote	denote	VERB
ejpam-3010	33	17	by	by	ADP
ejpam-3010	33	18	(	(	PUNCT
ejpam-3010	33	19	h	h	X
ejpam-3010	33	20	]	]	X
ejpam-3010	33	21	the	the	DET
ejpam-3010	33	22	subset	subset	NOUN
ejpam-3010	33	23	of	of	ADP
ejpam-3010	33	24	m	m	PRON
ejpam-3010	33	25	defined	define	VERB
ejpam-3010	33	26	by	by	ADP
ejpam-3010	33	27	(	(	PUNCT
ejpam-3010	33	28	h	h	X
ejpam-3010	33	29	]	]	X
ejpam-3010	33	30	=	=	X
ejpam-3010	33	31	{	{	PUNCT
ejpam-3010	33	32	t	t	NOUN
ejpam-3010	33	33	∈	∈	PROPN
ejpam-3010	34	1	m	m	VERB
ejpam-3010	34	2	|	|	ADV
ejpam-3010	34	3	t	t	X
ejpam-3010	34	4	≤	≤	NOUN
ejpam-3010	34	5	a	a	PRON
ejpam-3010	34	6	for	for	ADP
ejpam-3010	34	7	some	some	PRON
ejpam-3010	34	8	a	a	DET
ejpam-3010	34	9	∈	∈	PROPN
ejpam-3010	34	10	h	h	NOUN
ejpam-3010	34	11	}	}	PUNCT
ejpam-3010	34	12	.	.	PUNCT
ejpam-3010	35	1	we	we	PRON
ejpam-3010	35	2	have	have	VERB
ejpam-3010	35	3	m	m	VERB
ejpam-3010	35	4	=	=	PUNCT
ejpam-3010	35	5	(	(	PUNCT
ejpam-3010	35	6	m	m	X
ejpam-3010	35	7	]	]	X
ejpam-3010	35	8	,	,	PUNCT
ejpam-3010	35	9	and	and	CCONJ
ejpam-3010	35	10	for	for	ADP
ejpam-3010	35	11	any	any	DET
ejpam-3010	35	12	two	two	NUM
ejpam-3010	35	13	subsets	subset	NOUN
ejpam-3010	35	14	a	a	PRON
ejpam-3010	35	15	,	,	PUNCT
ejpam-3010	35	16	b	b	PROPN
ejpam-3010	35	17	of	of	ADP
ejpam-3010	35	18	m	m	PROPN
ejpam-3010	35	19	,	,	PUNCT
ejpam-3010	35	20	we	we	PRON
ejpam-3010	35	21	have	have	VERB
ejpam-3010	35	22	a	a	DET
ejpam-3010	35	23	⊆	⊆	NUM
ejpam-3010	35	24	(	(	PUNCT
ejpam-3010	35	25	a	a	NOUN
ejpam-3010	35	26	]	]	X
ejpam-3010	35	27	;	;	PUNCT
ejpam-3010	35	28	if	if	SCONJ
ejpam-3010	35	29	a	a	PRON
ejpam-3010	35	30	is	be	AUX
ejpam-3010	35	31	a	a	DET
ejpam-3010	35	32	right	right	NOUN
ejpam-3010	35	33	(	(	PUNCT
ejpam-3010	35	34	or	or	CCONJ
ejpam-3010	35	35	left	left	ADJ
ejpam-3010	35	36	)	)	PUNCT
ejpam-3010	35	37	ideal	ideal	NOUN
ejpam-3010	35	38	of	of	ADP
ejpam-3010	35	39	m	m	PROPN
ejpam-3010	35	40	,	,	PUNCT
ejpam-3010	35	41	then	then	ADV
ejpam-3010	35	42	a	a	PRON
ejpam-3010	35	43	=	=	X
ejpam-3010	35	44	(	(	PUNCT
ejpam-3010	35	45	a	a	X
ejpam-3010	35	46	]	]	X
ejpam-3010	35	47	;	;	PUNCT
ejpam-3010	35	48	(	(	PUNCT
ejpam-3010	35	49	a]γ(b	a]γ(b	ADP
ejpam-3010	35	50	]	]	X
ejpam-3010	35	51	⊆	⊆	NUM
ejpam-3010	35	52	(	(	PUNCT
ejpam-3010	35	53	aγb	aγb	NOUN
ejpam-3010	35	54	]	]	X
ejpam-3010	35	55	;	;	PUNCT
ejpam-3010	35	56	if	if	SCONJ
ejpam-3010	35	57	a	a	DET
ejpam-3010	35	58	⊆	⊆	NUM
ejpam-3010	35	59	b	b	NOUN
ejpam-3010	35	60	,	,	PUNCT
ejpam-3010	35	61	then	then	ADV
ejpam-3010	35	62	(	(	PUNCT
ejpam-3010	35	63	a	a	X
ejpam-3010	35	64	]	]	X
ejpam-3010	35	65	⊆	⊆	NUM
ejpam-3010	35	66	(	(	PUNCT
ejpam-3010	35	67	b	b	NOUN
ejpam-3010	35	68	]	]	X
ejpam-3010	35	69	;	;	PUNCT
ejpam-3010	35	70	(	(	PUNCT
ejpam-3010	35	71	(	(	PUNCT
ejpam-3010	35	72	a	a	X
ejpam-3010	35	73	]	]	X
ejpam-3010	35	74	]	]	X
ejpam-3010	35	75	=	=	X
ejpam-3010	35	76	(	(	PUNCT
ejpam-3010	35	77	a	a	PRON
ejpam-3010	35	78	]	]	X
ejpam-3010	35	79	.	.	PUNCT
ejpam-3010	36	1	let	let	VERB
ejpam-3010	36	2	m	m	PRON
ejpam-3010	36	3	be	be	AUX
ejpam-3010	36	4	a	a	DET
ejpam-3010	36	5	po	po	NOUN
ejpam-3010	36	6	-	-	PUNCT
ejpam-3010	36	7	γ	γ	NOUN
ejpam-3010	36	8	-	-	PUNCT
ejpam-3010	36	9	semigroup	semigroup	NOUN
ejpam-3010	36	10	.	.	PUNCT
ejpam-3010	37	1	a	a	DET
ejpam-3010	37	2	nonempty	nonempty	NOUN
ejpam-3010	37	3	subset	subset	VERB
ejpam-3010	37	4	a	a	PRON
ejpam-3010	37	5	of	of	ADP
ejpam-3010	37	6	m	m	PROPN
ejpam-3010	37	7	is	be	AUX
ejpam-3010	37	8	called	call	VERB
ejpam-3010	37	9	a	a	DET
ejpam-3010	37	10	subsemigroup	subsemigroup	NOUN
ejpam-3010	37	11	of	of	ADP
ejpam-3010	37	12	m	m	PROPN
ejpam-3010	37	13	if	if	SCONJ
ejpam-3010	37	14	for	for	ADP
ejpam-3010	37	15	every	every	DET
ejpam-3010	37	16	a	a	PROPN
ejpam-3010	37	17	,	,	PUNCT
ejpam-3010	37	18	b	b	PROPN
ejpam-3010	37	19	∈	∈	PROPN
ejpam-3010	37	20	a	a	PRON
ejpam-3010	37	21	and	and	CCONJ
ejpam-3010	37	22	every	every	DET
ejpam-3010	37	23	γ	γ	PROPN
ejpam-3010	37	24	∈	∈	PROPN
ejpam-3010	37	25	γ	γ	NOUN
ejpam-3010	37	26	we	we	PRON
ejpam-3010	37	27	have	have	VERB
ejpam-3010	37	28	aγb	aγb	NOUN
ejpam-3010	37	29	∈	∈	PROPN
ejpam-3010	37	30	a	a	PRON
ejpam-3010	37	31	,	,	PUNCT
ejpam-3010	37	32	that	that	ADV
ejpam-3010	37	33	is	is	ADV
ejpam-3010	37	34	,	,	PUNCT
ejpam-3010	37	35	if	if	SCONJ
ejpam-3010	37	36	aγa	aγa	VERB
ejpam-3010	37	37	⊆	⊆	NUM
ejpam-3010	37	38	a.	a.	NOUN
ejpam-3010	37	39	a	a	DET
ejpam-3010	37	40	nonempty	nonempty	NOUN
ejpam-3010	37	41	subset	subset	VERB
ejpam-3010	37	42	a	a	PRON
ejpam-3010	37	43	of	of	ADP
ejpam-3010	37	44	m	m	PROPN
ejpam-3010	37	45	is	be	AUX
ejpam-3010	37	46	called	call	VERB
ejpam-3010	37	47	a	a	DET
ejpam-3010	37	48	left	left	ADJ
ejpam-3010	37	49	(	(	PUNCT
ejpam-3010	37	50	resp	resp	NOUN
ejpam-3010	37	51	.	.	PUNCT
ejpam-3010	38	1	right	right	ADJ
ejpam-3010	38	2	)	)	PUNCT
ejpam-3010	38	3	ideal	ideal	NOUN
ejpam-3010	38	4	of	of	ADP
ejpam-3010	38	5	m	m	PRON
ejpam-3010	38	6	if	if	SCONJ
ejpam-3010	38	7	(	(	PUNCT
ejpam-3010	38	8	1	1	X
ejpam-3010	38	9	)	)	PUNCT
ejpam-3010	38	10	mγa	mγa	NOUN
ejpam-3010	38	11	⊆	⊆	NUM
ejpam-3010	38	12	a	a	PRON
ejpam-3010	38	13	and	and	CCONJ
ejpam-3010	38	14	(	(	PUNCT
ejpam-3010	38	15	2	2	NUM
ejpam-3010	38	16	)	)	PUNCT
ejpam-3010	38	17	if	if	SCONJ
ejpam-3010	38	18	a	a	DET
ejpam-3010	38	19	∈	∈	PROPN
ejpam-3010	38	20	a	a	PRON
ejpam-3010	38	21	and	and	CCONJ
ejpam-3010	38	22	m	m	PROPN
ejpam-3010	38	23	3	3	NUM
ejpam-3010	38	24	b	b	X
ejpam-3010	38	25	≤	≤	NUM
ejpam-3010	38	26	a	a	PRON
ejpam-3010	38	27	,	,	PUNCT
ejpam-3010	38	28	then	then	ADV
ejpam-3010	38	29	b	b	X
ejpam-3010	38	30	∈	∈	PROPN
ejpam-3010	38	31	a.	a.	NOUN
ejpam-3010	38	32	it	it	PRON
ejpam-3010	38	33	is	be	AUX
ejpam-3010	38	34	called	call	VERB
ejpam-3010	38	35	an	an	DET
ejpam-3010	38	36	ideal	ideal	NOUN
ejpam-3010	38	37	of	of	ADP
ejpam-3010	38	38	m	m	PRON
ejpam-3010	38	39	if	if	SCONJ
ejpam-3010	38	40	it	it	PRON
ejpam-3010	38	41	is	be	AUX
ejpam-3010	38	42	both	both	CCONJ
ejpam-3010	38	43	a	a	DET
ejpam-3010	38	44	left	left	ADJ
ejpam-3010	38	45	ideal	ideal	NOUN
ejpam-3010	38	46	and	and	CCONJ
ejpam-3010	38	47	a	a	DET
ejpam-3010	38	48	right	right	ADJ
ejpam-3010	38	49	ideal	ideal	NOUN
ejpam-3010	38	50	of	of	ADP
ejpam-3010	38	51	m	m	PROPN
ejpam-3010	38	52	.	.	PUNCT
ejpam-3010	39	1	clearly	clearly	ADV
ejpam-3010	39	2	,	,	PUNCT
ejpam-3010	39	3	every	every	DET
ejpam-3010	39	4	left	left	ADJ
ejpam-3010	39	5	(	(	PUNCT
ejpam-3010	39	6	resp	resp	NOUN
ejpam-3010	39	7	.	.	PUNCT
ejpam-3010	40	1	right	right	ADJ
ejpam-3010	40	2	)	)	PUNCT
ejpam-3010	40	3	ideal	ideal	NOUN
ejpam-3010	40	4	of	of	ADP
ejpam-3010	40	5	m	m	PROPN
ejpam-3010	40	6	is	be	AUX
ejpam-3010	40	7	a	a	DET
ejpam-3010	40	8	subsemigroup	subsemigroup	NOUN
ejpam-3010	40	9	of	of	ADP
ejpam-3010	40	10	m	m	PROPN
ejpam-3010	40	11	.	.	PUNCT
ejpam-3010	41	1	for	for	ADP
ejpam-3010	41	2	an	an	DET
ejpam-3010	41	3	element	element	NOUN
ejpam-3010	41	4	a	a	PRON
ejpam-3010	41	5	of	of	ADP
ejpam-3010	41	6	m	m	PROPN
ejpam-3010	41	7	,	,	PUNCT
ejpam-3010	41	8	we	we	PRON
ejpam-3010	41	9	denote	denote	VERB
ejpam-3010	41	10	by	by	ADP
ejpam-3010	41	11	l(a	l(a	PROPN
ejpam-3010	41	12	)	)	PUNCT
ejpam-3010	41	13	,	,	PUNCT
ejpam-3010	41	14	r(a	r(a	PROPN
ejpam-3010	41	15	)	)	PUNCT
ejpam-3010	41	16	and	and	CCONJ
ejpam-3010	41	17	i(a	i(a	NOUN
ejpam-3010	41	18	)	)	PUNCT
ejpam-3010	41	19	the	the	DET
ejpam-3010	41	20	left	left	ADJ
ejpam-3010	41	21	ideal	ideal	NOUN
ejpam-3010	41	22	,	,	PUNCT
ejpam-3010	41	23	the	the	DET
ejpam-3010	41	24	right	right	ADJ
ejpam-3010	41	25	ideal	ideal	NOUN
ejpam-3010	41	26	and	and	CCONJ
ejpam-3010	41	27	the	the	DET
ejpam-3010	41	28	ideal	ideal	NOUN
ejpam-3010	41	29	of	of	ADP
ejpam-3010	41	30	m	m	PROPN
ejpam-3010	41	31	,	,	PUNCT
ejpam-3010	41	32	respectively	respectively	ADV
ejpam-3010	41	33	,	,	PUNCT
ejpam-3010	41	34	generated	generate	VERB
ejpam-3010	41	35	by	by	ADP
ejpam-3010	41	36	a	a	PRON
ejpam-3010	41	37	,	,	PUNCT
ejpam-3010	41	38	and	and	CCONJ
ejpam-3010	41	39	we	we	PRON
ejpam-3010	41	40	have	have	VERB
ejpam-3010	41	41	l(a	l(a	PROPN
ejpam-3010	41	42	)	)	PUNCT
ejpam-3010	42	1	=	=	PUNCT
ejpam-3010	42	2	(	(	PUNCT
ejpam-3010	42	3	a	a	DET
ejpam-3010	42	4	∪mγa	∪mγa	PROPN
ejpam-3010	42	5	]	]	PUNCT
ejpam-3010	42	6	,	,	PUNCT
ejpam-3010	42	7	r(a	r(a	PROPN
ejpam-3010	42	8	)	)	PUNCT
ejpam-3010	42	9	=	=	SYM
ejpam-3010	43	1	(	(	PUNCT
ejpam-3010	43	2	a	a	DET
ejpam-3010	43	3	∪	∪	ADJ
ejpam-3010	43	4	aγm	aγm	NOUN
ejpam-3010	43	5	]	]	X
ejpam-3010	43	6	,	,	PUNCT
ejpam-3010	43	7	and	and	CCONJ
ejpam-3010	43	8	i(a	i(a	X
ejpam-3010	43	9	)	)	PUNCT
ejpam-3010	43	10	=	=	PUNCT
ejpam-3010	44	1	(	(	PUNCT
ejpam-3010	44	2	a	a	DET
ejpam-3010	44	3	∪mγa	∪mγa	X
ejpam-3010	44	4	∪	∪	X
ejpam-3010	44	5	aγm	aγm	NOUN
ejpam-3010	44	6	∪mγaγm	∪mγaγm	X
ejpam-3010	44	7	]	]	X
ejpam-3010	44	8	.	.	PUNCT
ejpam-3010	45	1	we	we	PRON
ejpam-3010	45	2	denote	denote	VERB
ejpam-3010	45	3	by	by	ADP
ejpam-3010	45	4	l	l	PROPN
ejpam-3010	45	5	the	the	DET
ejpam-3010	45	6	equivalence	equivalence	NOUN
ejpam-3010	45	7	relation	relation	NOUN
ejpam-3010	45	8	on	on	ADP
ejpam-3010	45	9	m	m	VERB
ejpam-3010	45	10	defined	define	VERB
ejpam-3010	45	11	by	by	ADP
ejpam-3010	45	12	alb	alb	PROPN
ejpam-3010	45	13	if	if	SCONJ
ejpam-3010	46	1	and	and	CCONJ
ejpam-3010	46	2	only	only	ADV
ejpam-3010	46	3	if	if	SCONJ
ejpam-3010	46	4	l(a	l(a	PROPN
ejpam-3010	46	5	)	)	PUNCT
ejpam-3010	46	6	=	=	SYM
ejpam-3010	46	7	l(b	l(b	PROPN
ejpam-3010	46	8	)	)	PUNCT
ejpam-3010	46	9	,	,	PUNCT
ejpam-3010	46	10	by	by	ADP
ejpam-3010	46	11	r	r	NOUN
ejpam-3010	46	12	the	the	DET
ejpam-3010	46	13	equivalence	equivalence	NOUN
ejpam-3010	46	14	relation	relation	NOUN
ejpam-3010	46	15	on	on	ADP
ejpam-3010	46	16	m	m	VERB
ejpam-3010	46	17	defined	define	VERB
ejpam-3010	46	18	by	by	ADP
ejpam-3010	46	19	arb	arb	PROPN
ejpam-3010	46	20	if	if	SCONJ
ejpam-3010	46	21	and	and	CCONJ
ejpam-3010	46	22	only	only	ADV
ejpam-3010	46	23	if	if	SCONJ
ejpam-3010	46	24	r(a	r(a	PROPN
ejpam-3010	46	25	)	)	PUNCT
ejpam-3010	46	26	=	=	SYM
ejpam-3010	46	27	r(b	r(b	PROPN
ejpam-3010	46	28	)	)	PUNCT
ejpam-3010	46	29	and	and	CCONJ
ejpam-3010	46	30	by	by	ADP
ejpam-3010	46	31	i	i	PRON
ejpam-3010	46	32	the	the	DET
ejpam-3010	46	33	equivalence	equivalence	NOUN
ejpam-3010	46	34	relation	relation	NOUN
ejpam-3010	46	35	on	on	ADP
ejpam-3010	46	36	m	m	VERB
ejpam-3010	46	37	defined	define	VERB
ejpam-3010	46	38	by	by	ADP
ejpam-3010	46	39	aib	aib	PROPN
ejpam-3010	46	40	if	if	SCONJ
ejpam-3010	46	41	and	and	CCONJ
ejpam-3010	46	42	only	only	ADV
ejpam-3010	46	43	if	if	SCONJ
ejpam-3010	46	44	i(a	i(a	NOUN
ejpam-3010	46	45	)	)	PUNCT
ejpam-3010	46	46	=	=	SYM
ejpam-3010	46	47	i(b	i(b	NOUN
ejpam-3010	46	48	)	)	PUNCT
ejpam-3010	46	49	.	.	PUNCT
ejpam-3010	47	1	a	a	DET
ejpam-3010	47	2	subsemigroup	subsemigroup	NOUN
ejpam-3010	47	3	f	f	PROPN
ejpam-3010	47	4	of	of	ADP
ejpam-3010	47	5	m	m	PROPN
ejpam-3010	47	6	is	be	AUX
ejpam-3010	47	7	called	call	VERB
ejpam-3010	47	8	a	a	DET
ejpam-3010	47	9	filter	filter	NOUN
ejpam-3010	47	10	of	of	ADP
ejpam-3010	47	11	m	m	NOUN
ejpam-3010	47	12	if	if	SCONJ
ejpam-3010	47	13	(	(	PUNCT
ejpam-3010	47	14	1	1	X
ejpam-3010	47	15	)	)	PUNCT
ejpam-3010	47	16	a	a	PRON
ejpam-3010	47	17	,	,	PUNCT
ejpam-3010	47	18	b	b	X
ejpam-3010	47	19	∈	∈	PROPN
ejpam-3010	47	20	f	f	PROPN
ejpam-3010	47	21	and	and	CCONJ
ejpam-3010	47	22	γ	γ	PROPN
ejpam-3010	47	23	∈	∈	PROPN
ejpam-3010	47	24	γ	γ	NOUN
ejpam-3010	47	25	such	such	ADJ
ejpam-3010	47	26	that	that	SCONJ
ejpam-3010	47	27	aγb	aγb	VERB
ejpam-3010	47	28	∈	∈	PROPN
ejpam-3010	47	29	f	f	PROPN
ejpam-3010	47	30	implies	imply	VERB
ejpam-3010	47	31	a	a	DET
ejpam-3010	47	32	∈	∈	PROPN
ejpam-3010	47	33	f	f	NOUN
ejpam-3010	47	34	and	and	CCONJ
ejpam-3010	47	35	b	b	PROPN
ejpam-3010	47	36	∈	∈	PROPN
ejpam-3010	47	37	f	f	X
ejpam-3010	47	38	and	and	CCONJ
ejpam-3010	47	39	(	(	PUNCT
ejpam-3010	47	40	2	2	X
ejpam-3010	47	41	)	)	PUNCT
ejpam-3010	47	42	if	if	SCONJ
ejpam-3010	47	43	a	a	DET
ejpam-3010	47	44	∈	∈	PROPN
ejpam-3010	47	45	f	f	X
ejpam-3010	47	46	and	and	CCONJ
ejpam-3010	47	47	m	m	PROPN
ejpam-3010	48	1	3	3	NUM
ejpam-3010	48	2	c	c	NOUN
ejpam-3010	48	3	≥	≥	NOUN
ejpam-3010	48	4	a	a	NOUN
ejpam-3010	48	5	,	,	PUNCT
ejpam-3010	48	6	then	then	ADV
ejpam-3010	48	7	c	c	PROPN
ejpam-3010	48	8	∈	∈	PROPN
ejpam-3010	48	9	f	f	X
ejpam-3010	48	10	.	.	PUNCT
ejpam-3010	49	1	an	an	DET
ejpam-3010	49	2	equivalence	equivalence	NOUN
ejpam-3010	49	3	relation	relation	NOUN
ejpam-3010	49	4	σ	σ	NOUN
ejpam-3010	49	5	on	on	ADP
ejpam-3010	49	6	m	m	PROPN
ejpam-3010	49	7	is	be	AUX
ejpam-3010	49	8	called	call	VERB
ejpam-3010	49	9	congruence	congruence	NOUN
ejpam-3010	49	10	if	if	SCONJ
ejpam-3010	49	11	(	(	PUNCT
ejpam-3010	49	12	a	a	DET
ejpam-3010	49	13	,	,	PUNCT
ejpam-3010	49	14	b	b	NOUN
ejpam-3010	49	15	)	)	PUNCT
ejpam-3010	49	16	∈	∈	PROPN
ejpam-3010	49	17	σ	σ	NOUN
ejpam-3010	49	18	implies	imply	VERB
ejpam-3010	49	19	(	(	PUNCT
ejpam-3010	49	20	aγc	aγc	PROPN
ejpam-3010	49	21	,	,	PUNCT
ejpam-3010	49	22	bγc	bγc	NOUN
ejpam-3010	49	23	)	)	PUNCT
ejpam-3010	49	24	∈	∈	PROPN
ejpam-3010	49	25	σ	σ	PROPN
ejpam-3010	49	26	and	and	CCONJ
ejpam-3010	49	27	(	(	PUNCT
ejpam-3010	49	28	cγa	cγa	PROPN
ejpam-3010	49	29	,	,	PUNCT
ejpam-3010	49	30	cγb	cγb	NOUN
ejpam-3010	49	31	)	)	PUNCT
ejpam-3010	49	32	∈	∈	PROPN
ejpam-3010	49	33	σ	σ	NOUN
ejpam-3010	49	34	for	for	ADP
ejpam-3010	49	35	any	any	DET
ejpam-3010	49	36	c	c	PROPN
ejpam-3010	49	37	∈	∈	PROPN
ejpam-3010	49	38	m	m	NOUN
ejpam-3010	49	39	and	and	CCONJ
ejpam-3010	49	40	any	any	DET
ejpam-3010	49	41	γ	γ	PROPN
ejpam-3010	49	42	∈	∈	PROPN
ejpam-3010	49	43	γ	γ	X
ejpam-3010	49	44	.	.	PROPN
ejpam-3010	49	45	a	a	DET
ejpam-3010	49	46	congruence	congruence	NOUN
ejpam-3010	49	47	σ	σ	NOUN
ejpam-3010	49	48	on	on	ADP
ejpam-3010	49	49	m	m	PROPN
ejpam-3010	49	50	n.	n.	PROPN
ejpam-3010	49	51	kehayopulu	kehayopulu	PROPN
ejpam-3010	49	52	/	/	SYM
ejpam-3010	49	53	eur	eur	PROPN
ejpam-3010	49	54	.	.	PUNCT
ejpam-3010	50	1	j.	j.	PROPN
ejpam-3010	50	2	pure	pure	PROPN
ejpam-3010	50	3	appl	appl	PROPN
ejpam-3010	50	4	.	.	PROPN
ejpam-3010	50	5	math	math	PROPN
ejpam-3010	50	6	,	,	PUNCT
ejpam-3010	50	7	10	10	NUM
ejpam-3010	50	8	(	(	PUNCT
ejpam-3010	50	9	4	4	NUM
ejpam-3010	50	10	)	)	PUNCT
ejpam-3010	50	11	(	(	PUNCT
ejpam-3010	50	12	2017	2017	NUM
ejpam-3010	50	13	)	)	PUNCT
ejpam-3010	50	14	,	,	PUNCT
ejpam-3010	50	15	620	620	NUM
ejpam-3010	50	16	-	-	SYM
ejpam-3010	50	17	630	630	NUM
ejpam-3010	50	18	622	622	NUM
ejpam-3010	50	19	is	be	AUX
ejpam-3010	50	20	called	call	VERB
ejpam-3010	50	21	semilattice	semilattice	NOUN
ejpam-3010	50	22	congruence	congruence	NOUN
ejpam-3010	50	23	if	if	SCONJ
ejpam-3010	50	24	(	(	PUNCT
ejpam-3010	50	25	aγb	aγb	NOUN
ejpam-3010	50	26	,	,	PUNCT
ejpam-3010	50	27	bγa	bγa	ADJ
ejpam-3010	50	28	)	)	PUNCT
ejpam-3010	50	29	∈	∈	PROPN
ejpam-3010	50	30	σ	σ	PROPN
ejpam-3010	50	31	and	and	CCONJ
ejpam-3010	50	32	(	(	PUNCT
ejpam-3010	50	33	aγa	aγa	PROPN
ejpam-3010	50	34	,	,	PUNCT
ejpam-3010	50	35	a	a	PRON
ejpam-3010	50	36	)	)	PUNCT
ejpam-3010	50	37	∈	∈	PROPN
ejpam-3010	50	38	σ	σ	NOUN
ejpam-3010	50	39	for	for	ADP
ejpam-3010	50	40	every	every	DET
ejpam-3010	50	41	a	a	PROPN
ejpam-3010	50	42	,	,	PUNCT
ejpam-3010	50	43	b	b	X
ejpam-3010	50	44	∈	∈	NOUN
ejpam-3010	50	45	m	m	NOUN
ejpam-3010	50	46	and	and	CCONJ
ejpam-3010	50	47	every	every	DET
ejpam-3010	50	48	γ	γ	PROPN
ejpam-3010	50	49	∈	∈	PROPN
ejpam-3010	50	50	γ	γ	X
ejpam-3010	50	51	.	.	PROPN
ejpam-3010	51	1	if	if	SCONJ
ejpam-3010	51	2	σ	σ	PROPN
ejpam-3010	51	3	is	be	AUX
ejpam-3010	51	4	a	a	DET
ejpam-3010	51	5	semilattice	semilattice	NOUN
ejpam-3010	51	6	congruence	congruence	NOUN
ejpam-3010	51	7	on	on	ADP
ejpam-3010	51	8	m	m	PROPN
ejpam-3010	51	9	,	,	PUNCT
ejpam-3010	51	10	then	then	ADV
ejpam-3010	51	11	the	the	DET
ejpam-3010	51	12	σ	σ	NOUN
ejpam-3010	51	13	-	-	PUNCT
ejpam-3010	51	14	class	class	NOUN
ejpam-3010	51	15	(	(	PUNCT
ejpam-3010	51	16	a)σ	a)σ	X
ejpam-3010	51	17	of	of	ADP
ejpam-3010	51	18	m	m	AUX
ejpam-3010	51	19	containing	contain	VERB
ejpam-3010	51	20	a	a	PRON
ejpam-3010	51	21	is	be	AUX
ejpam-3010	51	22	a	a	DET
ejpam-3010	51	23	subsemigroup	subsemigroup	NOUN
ejpam-3010	51	24	of	of	ADP
ejpam-3010	51	25	m	m	PROPN
ejpam-3010	51	26	for	for	ADP
ejpam-3010	51	27	every	every	DET
ejpam-3010	51	28	a	a	DET
ejpam-3010	51	29	∈	∈	NOUN
ejpam-3010	51	30	m	m	NOUN
ejpam-3010	51	31	.	.	PUNCT
ejpam-3010	52	1	a	a	DET
ejpam-3010	52	2	semilattice	semilattice	NOUN
ejpam-3010	52	3	congruence	congruence	PROPN
ejpam-3010	52	4	σ	σ	PROPN
ejpam-3010	52	5	on	on	ADP
ejpam-3010	52	6	m	m	PROPN
ejpam-3010	52	7	is	be	AUX
ejpam-3010	52	8	called	call	VERB
ejpam-3010	52	9	complete	complete	ADJ
ejpam-3010	52	10	if	if	SCONJ
ejpam-3010	52	11	a	a	DET
ejpam-3010	52	12	≤	≤	NUM
ejpam-3010	52	13	b	b	NOUN
ejpam-3010	52	14	implies	imply	VERB
ejpam-3010	52	15	(	(	PUNCT
ejpam-3010	52	16	a	a	DET
ejpam-3010	52	17	,	,	PUNCT
ejpam-3010	52	18	aγb	aγb	NOUN
ejpam-3010	52	19	)	)	PUNCT
ejpam-3010	52	20	∈	∈	PROPN
ejpam-3010	52	21	σ	σ	NOUN
ejpam-3010	52	22	for	for	ADP
ejpam-3010	52	23	every	every	DET
ejpam-3010	52	24	γ	γ	PROPN
ejpam-3010	52	25	∈	∈	PROPN
ejpam-3010	52	26	γ	γ	X
ejpam-3010	52	27	.	.	PUNCT
ejpam-3010	53	1	we	we	PRON
ejpam-3010	53	2	denote	denote	VERB
ejpam-3010	53	3	by	by	ADP
ejpam-3010	53	4	n	n	PRON
ejpam-3010	53	5	the	the	DET
ejpam-3010	53	6	relation	relation	NOUN
ejpam-3010	53	7	on	on	ADP
ejpam-3010	53	8	m	m	VERB
ejpam-3010	53	9	defined	define	VERB
ejpam-3010	53	10	by	by	ADP
ejpam-3010	53	11	an	an	DET
ejpam-3010	53	12	b	b	NOUN
ejpam-3010	53	13	if	if	SCONJ
ejpam-3010	54	1	and	and	CCONJ
ejpam-3010	54	2	only	only	ADV
ejpam-3010	54	3	if	if	SCONJ
ejpam-3010	54	4	the	the	DET
ejpam-3010	54	5	filters	filter	NOUN
ejpam-3010	54	6	of	of	ADP
ejpam-3010	54	7	m	m	AUX
ejpam-3010	54	8	generated	generate	VERB
ejpam-3010	54	9	by	by	ADP
ejpam-3010	54	10	the	the	DET
ejpam-3010	54	11	elements	element	NOUN
ejpam-3010	54	12	a	a	DET
ejpam-3010	54	13	and	and	CCONJ
ejpam-3010	54	14	b	b	PROPN
ejpam-3010	54	15	of	of	ADP
ejpam-3010	54	16	m	m	PROPN
ejpam-3010	54	17	coincide	coincide	NOUN
ejpam-3010	54	18	.	.	PUNCT
ejpam-3010	55	1	as	as	ADP
ejpam-3010	55	2	in	in	ADP
ejpam-3010	55	3	semigroups	semigroup	NOUN
ejpam-3010	55	4	,	,	PUNCT
ejpam-3010	55	5	the	the	DET
ejpam-3010	55	6	relation	relation	NOUN
ejpam-3010	55	7	n	n	PART
ejpam-3010	55	8	is	be	AUX
ejpam-3010	55	9	a	a	DET
ejpam-3010	55	10	semilattice	semilattice	NOUN
ejpam-3010	55	11	congruence	congruence	NOUN
ejpam-3010	55	12	on	on	ADP
ejpam-3010	55	13	m	m	PROPN
ejpam-3010	55	14	.	.	PUNCT
ejpam-3010	56	1	so	so	ADV
ejpam-3010	56	2	,	,	PUNCT
ejpam-3010	56	3	if	if	SCONJ
ejpam-3010	56	4	z	z	PROPN
ejpam-3010	56	5	∈	∈	PROPN
ejpam-3010	56	6	m	m	NOUN
ejpam-3010	56	7	and	and	CCONJ
ejpam-3010	56	8	γ	γ	PROPN
ejpam-3010	56	9	∈	∈	PROPN
ejpam-3010	56	10	γ	γ	X
ejpam-3010	56	11	,	,	PUNCT
ejpam-3010	56	12	then	then	ADV
ejpam-3010	56	13	we	we	PRON
ejpam-3010	56	14	have	have	VERB
ejpam-3010	56	15	(	(	PUNCT
ejpam-3010	56	16	zγz	zγz	NOUN
ejpam-3010	56	17	,	,	PUNCT
ejpam-3010	56	18	z	z	NOUN
ejpam-3010	56	19	)	)	PUNCT
ejpam-3010	56	20	∈	∈	PROPN
ejpam-3010	56	21	n	n	NOUN
ejpam-3010	56	22	,	,	PUNCT
ejpam-3010	56	23	(	(	PUNCT
ejpam-3010	56	24	zγzγz	zγzγz	NOUN
ejpam-3010	56	25	,	,	PUNCT
ejpam-3010	56	26	zγz	zγz	NOUN
ejpam-3010	56	27	)	)	PUNCT
ejpam-3010	56	28	∈	∈	PROPN
ejpam-3010	56	29	n	n	NOUN
ejpam-3010	56	30	,	,	PUNCT
ejpam-3010	56	31	(	(	PUNCT
ejpam-3010	56	32	zγzγzγz	zγzγzγz	PROPN
ejpam-3010	56	33	,	,	PUNCT
ejpam-3010	56	34	zγzγz	zγzγz	NOUN
ejpam-3010	56	35	)	)	PUNCT
ejpam-3010	56	36	∈	∈	PROPN
ejpam-3010	56	37	n	n	CCONJ
ejpam-3010	56	38	and	and	CCONJ
ejpam-3010	56	39	so	so	ADV
ejpam-3010	56	40	on	on	ADV
ejpam-3010	56	41	.	.	PUNCT
ejpam-3010	57	1	in	in	ADP
ejpam-3010	57	2	particular	particular	ADJ
ejpam-3010	57	3	,	,	PUNCT
ejpam-3010	57	4	exactly	exactly	ADV
ejpam-3010	57	5	as	as	ADP
ejpam-3010	57	6	in	in	ADP
ejpam-3010	57	7	ordered	order	VERB
ejpam-3010	57	8	semigroups	semigroup	NOUN
ejpam-3010	57	9	,	,	PUNCT
ejpam-3010	57	10	the	the	DET
ejpam-3010	57	11	relation	relation	NOUN
ejpam-3010	57	12	n	n	PART
ejpam-3010	57	13	is	be	AUX
ejpam-3010	57	14	a	a	DET
ejpam-3010	57	15	complete	complete	ADJ
ejpam-3010	57	16	semilattice	semilattice	NOUN
ejpam-3010	57	17	congruence	congruence	NOUN
ejpam-3010	57	18	on	on	ADP
ejpam-3010	57	19	m	m	PROPN
ejpam-3010	57	20	.	.	PUNCT
ejpam-3010	58	1	a	a	DET
ejpam-3010	58	2	subsemigroup	subsemigroup	NOUN
ejpam-3010	58	3	t	t	PROPN
ejpam-3010	58	4	of	of	ADP
ejpam-3010	58	5	a	a	DET
ejpam-3010	58	6	po	po	NOUN
ejpam-3010	58	7	-	-	PUNCT
ejpam-3010	58	8	γ	γ	NOUN
ejpam-3010	58	9	-	-	PUNCT
ejpam-3010	58	10	semigroup	semigroup	NOUN
ejpam-3010	58	11	m	m	VERB
ejpam-3010	58	12	is	be	AUX
ejpam-3010	58	13	called	call	VERB
ejpam-3010	58	14	left	left	ADJ
ejpam-3010	58	15	(	(	PUNCT
ejpam-3010	58	16	resp	resp	NOUN
ejpam-3010	58	17	.	.	PUNCT
ejpam-3010	59	1	right	right	ADJ
ejpam-3010	59	2	)	)	PUNCT
ejpam-3010	59	3	simple	simple	ADJ
ejpam-3010	59	4	if	if	SCONJ
ejpam-3010	59	5	for	for	ADP
ejpam-3010	59	6	every	every	DET
ejpam-3010	59	7	left	left	NOUN
ejpam-3010	59	8	(	(	PUNCT
ejpam-3010	59	9	resp	resp	NOUN
ejpam-3010	59	10	.	.	PUNCT
ejpam-3010	60	1	right	right	ADJ
ejpam-3010	60	2	)	)	PUNCT
ejpam-3010	60	3	ideal	ideal	NOUN
ejpam-3010	60	4	a	a	PRON
ejpam-3010	60	5	of	of	ADP
ejpam-3010	60	6	t	t	NOUN
ejpam-3010	60	7	we	we	PRON
ejpam-3010	60	8	have	have	VERB
ejpam-3010	60	9	a	a	DET
ejpam-3010	60	10	=	=	SYM
ejpam-3010	60	11	t	t	NOUN
ejpam-3010	60	12	,	,	PUNCT
ejpam-3010	60	13	that	that	PRON
ejpam-3010	60	14	is	be	AUX
ejpam-3010	60	15	if	if	SCONJ
ejpam-3010	60	16	t	t	PROPN
ejpam-3010	60	17	is	be	AUX
ejpam-3010	60	18	the	the	DET
ejpam-3010	60	19	only	only	ADJ
ejpam-3010	60	20	left	leave	VERB
ejpam-3010	60	21	(	(	PUNCT
ejpam-3010	60	22	resp	resp	NOUN
ejpam-3010	60	23	.	.	PUNCT
ejpam-3010	61	1	right	right	ADJ
ejpam-3010	61	2	)	)	PUNCT
ejpam-3010	61	3	ideal	ideal	NOUN
ejpam-3010	61	4	of	of	ADP
ejpam-3010	61	5	t	t	PROPN
ejpam-3010	61	6	.	.	PUNCT
ejpam-3010	62	1	it	it	PRON
ejpam-3010	62	2	is	be	AUX
ejpam-3010	62	3	called	call	VERB
ejpam-3010	62	4	simple	simple	ADJ
ejpam-3010	62	5	if	if	SCONJ
ejpam-3010	62	6	it	it	PRON
ejpam-3010	62	7	is	be	AUX
ejpam-3010	62	8	both	both	PRON
ejpam-3010	62	9	left	left	ADJ
ejpam-3010	62	10	and	and	CCONJ
ejpam-3010	62	11	right	right	ADJ
ejpam-3010	62	12	simple	simple	NOUN
ejpam-3010	62	13	.	.	PUNCT
ejpam-3010	63	1	a	a	DET
ejpam-3010	63	2	subsemigroup	subsemigroup	NOUN
ejpam-3010	63	3	t	t	PROPN
ejpam-3010	63	4	of	of	ADP
ejpam-3010	63	5	a	a	DET
ejpam-3010	63	6	po	po	NOUN
ejpam-3010	63	7	-	-	PUNCT
ejpam-3010	63	8	γ	γ	NOUN
ejpam-3010	63	9	-	-	PUNCT
ejpam-3010	63	10	semigroup	semigroup	NOUN
ejpam-3010	63	11	m	m	VERB
ejpam-3010	63	12	is	be	AUX
ejpam-3010	63	13	called	call	VERB
ejpam-3010	63	14	maximal	maximal	ADJ
ejpam-3010	63	15	simple	simple	ADJ
ejpam-3010	63	16	if	if	SCONJ
ejpam-3010	63	17	for	for	ADP
ejpam-3010	63	18	any	any	DET
ejpam-3010	63	19	simple	simple	ADJ
ejpam-3010	63	20	subsemigroup	subsemigroup	NOUN
ejpam-3010	63	21	a	a	PRON
ejpam-3010	63	22	of	of	ADP
ejpam-3010	63	23	m	m	PRON
ejpam-3010	63	24	such	such	ADJ
ejpam-3010	63	25	that	that	SCONJ
ejpam-3010	63	26	a	a	DET
ejpam-3010	63	27	⊇	⊇	PROPN
ejpam-3010	63	28	t	t	PROPN
ejpam-3010	63	29	,	,	PUNCT
ejpam-3010	63	30	we	we	PRON
ejpam-3010	63	31	have	have	VERB
ejpam-3010	63	32	a	a	DET
ejpam-3010	63	33	=	=	PROPN
ejpam-3010	63	34	t	t	PROPN
ejpam-3010	63	35	.	.	PUNCT
ejpam-3010	64	1	a	a	DET
ejpam-3010	64	2	po	po	VERB
ejpam-3010	64	3	-	-	PUNCT
ejpam-3010	64	4	γ	γ	NOUN
ejpam-3010	64	5	-	-	PUNCT
ejpam-3010	64	6	semigroup	semigroup	NOUN
ejpam-3010	64	7	m	m	VERB
ejpam-3010	64	8	is	be	AUX
ejpam-3010	64	9	said	say	VERB
ejpam-3010	64	10	to	to	PART
ejpam-3010	64	11	be	be	AUX
ejpam-3010	64	12	a	a	DET
ejpam-3010	64	13	semilattice	semilattice	NOUN
ejpam-3010	64	14	of	of	ADP
ejpam-3010	64	15	simple	simple	ADJ
ejpam-3010	64	16	(	(	PUNCT
ejpam-3010	64	17	resp	resp	NOUN
ejpam-3010	64	18	.	.	PUNCT
ejpam-3010	65	1	left	leave	VERB
ejpam-3010	65	2	simple	simple	NOUN
ejpam-3010	65	3	)	)	PUNCT
ejpam-3010	65	4	semigroups	semigroup	NOUN
ejpam-3010	65	5	if	if	SCONJ
ejpam-3010	65	6	there	there	PRON
ejpam-3010	65	7	exists	exist	VERB
ejpam-3010	65	8	a	a	DET
ejpam-3010	65	9	semilattice	semilattice	NOUN
ejpam-3010	65	10	congruence	congruence	PROPN
ejpam-3010	65	11	σ	σ	PROPN
ejpam-3010	65	12	on	on	ADP
ejpam-3010	65	13	m	m	PRON
ejpam-3010	65	14	such	such	ADJ
ejpam-3010	65	15	that	that	SCONJ
ejpam-3010	65	16	the	the	DET
ejpam-3010	65	17	σ	σ	NOUN
ejpam-3010	65	18	-	-	PUNCT
ejpam-3010	65	19	class	class	NOUN
ejpam-3010	65	20	(	(	PUNCT
ejpam-3010	65	21	x)σ	x)σ	X
ejpam-3010	65	22	of	of	ADP
ejpam-3010	65	23	m	m	AUX
ejpam-3010	65	24	containing	contain	VERB
ejpam-3010	65	25	x	x	PUNCT
ejpam-3010	65	26	is	be	AUX
ejpam-3010	65	27	a	a	DET
ejpam-3010	65	28	simple	simple	ADJ
ejpam-3010	65	29	(	(	PUNCT
ejpam-3010	65	30	resp	resp	NOUN
ejpam-3010	65	31	.	.	PUNCT
ejpam-3010	66	1	left	leave	VERB
ejpam-3010	66	2	simple	simple	ADJ
ejpam-3010	66	3	)	)	PUNCT
ejpam-3010	66	4	subsemigroup	subsemigroup	NOUN
ejpam-3010	66	5	of	of	ADP
ejpam-3010	66	6	m	m	PROPN
ejpam-3010	66	7	for	for	ADP
ejpam-3010	66	8	every	every	DET
ejpam-3010	66	9	x	x	SYM
ejpam-3010	66	10	∈	∈	PROPN
ejpam-3010	66	11	m	m	NOUN
ejpam-3010	66	12	.	.	PUNCT
ejpam-3010	67	1	a	a	DET
ejpam-3010	67	2	po	po	VERB
ejpam-3010	67	3	-	-	PUNCT
ejpam-3010	67	4	γ	γ	NOUN
ejpam-3010	67	5	-	-	PUNCT
ejpam-3010	67	6	semigroup	semigroup	NOUN
ejpam-3010	67	7	m	m	VERB
ejpam-3010	67	8	is	be	AUX
ejpam-3010	67	9	called	call	VERB
ejpam-3010	67	10	a	a	DET
ejpam-3010	67	11	chain	chain	NOUN
ejpam-3010	67	12	of	of	ADP
ejpam-3010	67	13	simple	simple	ADJ
ejpam-3010	67	14	semigroups	semigroup	NOUN
ejpam-3010	67	15	if	if	SCONJ
ejpam-3010	67	16	there	there	PRON
ejpam-3010	67	17	exists	exist	VERB
ejpam-3010	67	18	a	a	DET
ejpam-3010	67	19	semilattice	semilattice	NOUN
ejpam-3010	67	20	congruence	congruence	PROPN
ejpam-3010	67	21	σ	σ	PROPN
ejpam-3010	67	22	on	on	ADP
ejpam-3010	67	23	m	m	PRON
ejpam-3010	67	24	such	such	ADJ
ejpam-3010	67	25	that	that	SCONJ
ejpam-3010	67	26	(	(	PUNCT
ejpam-3010	67	27	x)σ	x)σ	X
ejpam-3010	67	28	is	be	AUX
ejpam-3010	67	29	a	a	DET
ejpam-3010	67	30	simple	simple	ADJ
ejpam-3010	67	31	subsemigroup	subsemigroup	NOUN
ejpam-3010	67	32	of	of	ADP
ejpam-3010	67	33	m	m	PROPN
ejpam-3010	67	34	for	for	ADP
ejpam-3010	67	35	every	every	DET
ejpam-3010	67	36	x	x	SYM
ejpam-3010	67	37	∈m	∈m	NOUN
ejpam-3010	67	38	and	and	CCONJ
ejpam-3010	67	39	the	the	DET
ejpam-3010	67	40	set	set	NOUN
ejpam-3010	67	41	m	m	PROPN
ejpam-3010	67	42	/	/	SYM
ejpam-3010	67	43	σ	σ	PROPN
ejpam-3010	67	44	of	of	ADP
ejpam-3010	67	45	all	all	DET
ejpam-3010	67	46	σ	σ	NOUN
ejpam-3010	67	47	-	-	PUNCT
ejpam-3010	67	48	classes	class	NOUN
ejpam-3010	67	49	of	of	ADP
ejpam-3010	67	50	m	m	PROPN
ejpam-3010	67	51	endowed	endow	VERB
ejpam-3010	67	52	with	with	ADP
ejpam-3010	67	53	the	the	DET
ejpam-3010	67	54	order	order	NOUN
ejpam-3010	67	55	relation	relation	NOUN
ejpam-3010	67	56	(	(	PUNCT
ejpam-3010	67	57	x)σ	x)σ	X
ejpam-3010	67	58	�	�	PROPN
ejpam-3010	67	59	(	(	PUNCT
ejpam-3010	67	60	y)σ	y)σ	X
ejpam-3010	67	61	⇔	⇔	X
ejpam-3010	67	62	(	(	PUNCT
ejpam-3010	67	63	x)σ	x)σ	X
ejpam-3010	67	64	=	=	SYM
ejpam-3010	67	65	(	(	PUNCT
ejpam-3010	67	66	xγy)σ	xγy)σ	PROPN
ejpam-3010	67	67	∀	∀	X
ejpam-3010	67	68	γ	γ	X
ejpam-3010	67	69	∈	∈	PROPN
ejpam-3010	67	70	γ	γ	X
ejpam-3010	67	71	is	be	AUX
ejpam-3010	67	72	a	a	DET
ejpam-3010	67	73	chain	chain	NOUN
ejpam-3010	67	74	.	.	PUNCT
ejpam-3010	68	1	many	many	ADJ
ejpam-3010	68	2	results	result	NOUN
ejpam-3010	68	3	on	on	ADP
ejpam-3010	68	4	γ	γ	NOUN
ejpam-3010	68	5	-	-	PUNCT
ejpam-3010	68	6	semigroups	semigroup	NOUN
ejpam-3010	68	7	(	(	PUNCT
ejpam-3010	68	8	or	or	CCONJ
ejpam-3010	68	9	po	po	NOUN
ejpam-3010	68	10	-	-	PUNCT
ejpam-3010	68	11	γ	γ	NOUN
ejpam-3010	68	12	-	-	PUNCT
ejpam-3010	68	13	semigroups	semigroup	NOUN
ejpam-3010	68	14	)	)	PUNCT
ejpam-3010	68	15	can	can	AUX
ejpam-3010	68	16	be	be	AUX
ejpam-3010	68	17	obtained	obtain	VERB
ejpam-3010	68	18	from	from	ADP
ejpam-3010	68	19	semigroups	semigroup	NOUN
ejpam-3010	68	20	(	(	PUNCT
ejpam-3010	68	21	ordered	order	VERB
ejpam-3010	68	22	semigroups	semigroup	NOUN
ejpam-3010	68	23	)	)	PUNCT
ejpam-3010	68	24	just	just	ADV
ejpam-3010	68	25	putting	put	VERB
ejpam-3010	68	26	a	a	DET
ejpam-3010	68	27	“	"	PUNCT
ejpam-3010	68	28	gamma	gamma	NOUN
ejpam-3010	68	29	”	"	PUNCT
ejpam-3010	68	30	in	in	ADP
ejpam-3010	68	31	the	the	DET
ejpam-3010	68	32	appropriate	appropriate	ADJ
ejpam-3010	68	33	place	place	NOUN
ejpam-3010	68	34	.	.	PUNCT
ejpam-3010	69	1	but	but	CCONJ
ejpam-3010	69	2	there	there	PRON
ejpam-3010	69	3	are	be	VERB
ejpam-3010	69	4	also	also	ADV
ejpam-3010	69	5	results	result	NOUN
ejpam-3010	69	6	for	for	ADP
ejpam-3010	69	7	which	which	PRON
ejpam-3010	69	8	the	the	DET
ejpam-3010	69	9	transfer	transfer	NOUN
ejpam-3010	69	10	is	be	AUX
ejpam-3010	69	11	not	not	PART
ejpam-3010	69	12	so	so	ADV
ejpam-3010	69	13	easy	easy	ADJ
ejpam-3010	69	14	.	.	PUNCT
ejpam-3010	70	1	both	both	PRON
ejpam-3010	70	2	for	for	ADP
ejpam-3010	70	3	a	a	DET
ejpam-3010	70	4	γ	γ	NOUN
ejpam-3010	70	5	-	-	PUNCT
ejpam-3010	70	6	semigroup	semigroup	NOUN
ejpam-3010	70	7	or	or	CCONJ
ejpam-3010	70	8	po	po	NOUN
ejpam-3010	70	9	-	-	PUNCT
ejpam-3010	70	10	γ	γ	NOUN
ejpam-3010	70	11	-	-	PUNCT
ejpam-3010	70	12	semigroup	semigroup	NOUN
ejpam-3010	70	13	m	m	VERB
ejpam-3010	70	14	the	the	DET
ejpam-3010	70	15	filter	filter	NOUN
ejpam-3010	70	16	of	of	ADP
ejpam-3010	70	17	m	m	AUX
ejpam-3010	70	18	generated	generate	VERB
ejpam-3010	70	19	by	by	ADP
ejpam-3010	70	20	an	an	DET
ejpam-3010	70	21	element	element	NOUN
ejpam-3010	70	22	a	a	PRON
ejpam-3010	70	23	of	of	ADP
ejpam-3010	70	24	m	m	PROPN
ejpam-3010	70	25	plays	play	VERB
ejpam-3010	70	26	an	an	DET
ejpam-3010	70	27	essential	essential	ADJ
ejpam-3010	70	28	role	role	NOUN
ejpam-3010	70	29	in	in	ADP
ejpam-3010	70	30	the	the	DET
ejpam-3010	70	31	structure	structure	NOUN
ejpam-3010	70	32	,	,	PUNCT
ejpam-3010	70	33	in	in	ADP
ejpam-3010	70	34	particular	particular	ADJ
ejpam-3010	70	35	,	,	PUNCT
ejpam-3010	70	36	in	in	ADP
ejpam-3010	70	37	the	the	DET
ejpam-3010	70	38	decomposition	decomposition	NOUN
ejpam-3010	70	39	of	of	ADP
ejpam-3010	70	40	m	m	PROPN
ejpam-3010	70	41	.	.	PUNCT
ejpam-3010	71	1	so	so	ADV
ejpam-3010	71	2	it	it	PRON
ejpam-3010	71	3	is	be	AUX
ejpam-3010	71	4	important	important	ADJ
ejpam-3010	71	5	to	to	PART
ejpam-3010	71	6	get	get	VERB
ejpam-3010	71	7	the	the	DET
ejpam-3010	71	8	form	form	NOUN
ejpam-3010	71	9	of	of	ADP
ejpam-3010	71	10	its	its	PRON
ejpam-3010	71	11	elements	element	NOUN
ejpam-3010	71	12	.	.	PUNCT
ejpam-3010	72	1	the	the	DET
ejpam-3010	72	2	definition	definition	NOUN
ejpam-3010	72	3	of	of	ADP
ejpam-3010	72	4	intra	intra	ADJ
ejpam-3010	72	5	-	-	NOUN
ejpam-3010	72	6	regularity	regularity	NOUN
ejpam-3010	72	7	of	of	ADP
ejpam-3010	72	8	a	a	DET
ejpam-3010	72	9	po	po	NOUN
ejpam-3010	72	10	-	-	PUNCT
ejpam-3010	72	11	γ	γ	NOUN
ejpam-3010	72	12	-	-	PUNCT
ejpam-3010	72	13	semigroup	semigroup	NOUN
ejpam-3010	72	14	in	in	ADP
ejpam-3010	72	15	the	the	DET
ejpam-3010	72	16	bibliography	bibliography	NOUN
ejpam-3010	72	17	was	be	AUX
ejpam-3010	72	18	as	as	SCONJ
ejpam-3010	72	19	follows	follow	VERB
ejpam-3010	72	20	:	:	PUNCT
ejpam-3010	72	21	a	a	DET
ejpam-3010	72	22	po	po	VERB
ejpam-3010	72	23	-	-	PUNCT
ejpam-3010	72	24	γ	γ	NOUN
ejpam-3010	72	25	-	-	PUNCT
ejpam-3010	72	26	semigroup	semigroup	NOUN
ejpam-3010	72	27	m	m	VERB
ejpam-3010	72	28	is	be	AUX
ejpam-3010	72	29	intra	intra	ADJ
ejpam-3010	72	30	-	-	ADJ
ejpam-3010	72	31	regular	regular	ADJ
ejpam-3010	72	32	if	if	SCONJ
ejpam-3010	72	33	a	a	DET
ejpam-3010	72	34	∈	∈	NOUN
ejpam-3010	72	35	(	(	PUNCT
ejpam-3010	72	36	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	72	37	]	]	PUNCT
ejpam-3010	72	38	for	for	ADP
ejpam-3010	72	39	every	every	DET
ejpam-3010	72	40	a	a	DET
ejpam-3010	72	41	∈	∈	NOUN
ejpam-3010	72	42	m	m	NOUN
ejpam-3010	72	43	.	.	PUNCT
ejpam-3010	73	1	with	with	ADP
ejpam-3010	73	2	this	this	DET
ejpam-3010	73	3	definition	definition	NOUN
ejpam-3010	73	4	is	be	AUX
ejpam-3010	73	5	not	not	PART
ejpam-3010	73	6	possible	possible	ADJ
ejpam-3010	73	7	to	to	PART
ejpam-3010	73	8	describe	describe	VERB
ejpam-3010	73	9	the	the	DET
ejpam-3010	73	10	form	form	NOUN
ejpam-3010	73	11	of	of	ADP
ejpam-3010	73	12	the	the	DET
ejpam-3010	73	13	elements	element	NOUN
ejpam-3010	73	14	of	of	ADP
ejpam-3010	73	15	the	the	DET
ejpam-3010	73	16	n(x	n(x	NOUN
ejpam-3010	73	17	)	)	PUNCT
ejpam-3010	73	18	(	(	PUNCT
ejpam-3010	73	19	x	x	PUNCT
ejpam-3010	73	20	∈	∈	PROPN
ejpam-3010	73	21	s	s	PART
ejpam-3010	73	22	)	)	PUNCT
ejpam-3010	73	23	.	.	PUNCT
ejpam-3010	74	1	to	to	PART
ejpam-3010	74	2	overcome	overcome	VERB
ejpam-3010	74	3	this	this	DET
ejpam-3010	74	4	difficulty	difficulty	NOUN
ejpam-3010	74	5	,	,	PUNCT
ejpam-3010	74	6	the	the	DET
ejpam-3010	74	7	following	follow	VERB
ejpam-3010	74	8	new	new	ADJ
ejpam-3010	74	9	concept	concept	NOUN
ejpam-3010	74	10	of	of	ADP
ejpam-3010	74	11	intra	intra	ADJ
ejpam-3010	74	12	-	-	ADJ
ejpam-3010	74	13	regularity	regularity	NOUN
ejpam-3010	74	14	has	have	AUX
ejpam-3010	74	15	been	be	AUX
ejpam-3010	74	16	introduced	introduce	VERB
ejpam-3010	74	17	in	in	ADP
ejpam-3010	74	18	[	[	X
ejpam-3010	74	19	9	9	NUM
ejpam-3010	74	20	]	]	PUNCT
ejpam-3010	74	21	:	:	PUNCT
ejpam-3010	74	22	we	we	PRON
ejpam-3010	74	23	say	say	VERB
ejpam-3010	74	24	that	that	SCONJ
ejpam-3010	74	25	a	a	DET
ejpam-3010	74	26	po	po	NOUN
ejpam-3010	74	27	-	-	PUNCT
ejpam-3010	74	28	γ	γ	NOUN
ejpam-3010	74	29	-	-	PUNCT
ejpam-3010	74	30	semigroup	semigroup	NOUN
ejpam-3010	74	31	m	m	VERB
ejpam-3010	74	32	is	be	AUX
ejpam-3010	74	33	intra	intra	ADJ
ejpam-3010	74	34	-	-	ADJ
ejpam-3010	74	35	regular	regular	ADJ
ejpam-3010	74	36	if	if	SCONJ
ejpam-3010	74	37	a	a	DET
ejpam-3010	74	38	∈	∈	NOUN
ejpam-3010	74	39	(	(	PUNCT
ejpam-3010	74	40	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	74	41	]	]	PUNCT
ejpam-3010	74	42	for	for	ADP
ejpam-3010	74	43	every	every	DET
ejpam-3010	74	44	a	a	DET
ejpam-3010	74	45	∈	∈	NOUN
ejpam-3010	74	46	m	m	NOUN
ejpam-3010	74	47	and	and	CCONJ
ejpam-3010	74	48	every	every	DET
ejpam-3010	74	49	γ	γ	PROPN
ejpam-3010	74	50	∈	∈	PROPN
ejpam-3010	74	51	γ	γ	X
ejpam-3010	74	52	.	.	PUNCT
ejpam-3010	74	53	using	use	VERB
ejpam-3010	74	54	this	this	DET
ejpam-3010	74	55	definition	definition	NOUN
ejpam-3010	74	56	,	,	PUNCT
ejpam-3010	74	57	we	we	PRON
ejpam-3010	74	58	first	first	ADV
ejpam-3010	74	59	give	give	VERB
ejpam-3010	74	60	a	a	DET
ejpam-3010	74	61	structure	structure	NOUN
ejpam-3010	74	62	theorem	theorem	NOUN
ejpam-3010	74	63	referring	refer	VERB
ejpam-3010	74	64	to	to	ADP
ejpam-3010	74	65	the	the	DET
ejpam-3010	74	66	decomposition	decomposition	NOUN
ejpam-3010	74	67	of	of	ADP
ejpam-3010	74	68	a	a	DET
ejpam-3010	74	69	po	po	NOUN
ejpam-3010	74	70	-	-	PUNCT
ejpam-3010	74	71	γ	γ	NOUN
ejpam-3010	74	72	-	-	PUNCT
ejpam-3010	74	73	semigroup	semigroup	NOUN
ejpam-3010	74	74	into	into	ADP
ejpam-3010	74	75	simple	simple	ADJ
ejpam-3010	74	76	components	component	NOUN
ejpam-3010	74	77	.	.	PUNCT
ejpam-3010	75	1	then	then	ADV
ejpam-3010	75	2	,	,	PUNCT
ejpam-3010	75	3	for	for	ADP
ejpam-3010	75	4	a	a	DET
ejpam-3010	75	5	po	po	NOUN
ejpam-3010	75	6	-	-	PUNCT
ejpam-3010	75	7	γsemigroup	γsemigroup	NOUN
ejpam-3010	75	8	m	m	VERB
ejpam-3010	75	9	,	,	PUNCT
ejpam-3010	75	10	we	we	PRON
ejpam-3010	75	11	prove	prove	VERB
ejpam-3010	75	12	the	the	DET
ejpam-3010	75	13	following	following	NOUN
ejpam-3010	75	14	:	:	PUNCT
ejpam-3010	75	15	the	the	DET
ejpam-3010	75	16	ideals	ideal	NOUN
ejpam-3010	75	17	of	of	ADP
ejpam-3010	75	18	m	m	NOUN
ejpam-3010	75	19	are	be	AUX
ejpam-3010	75	20	weakly	weakly	ADV
ejpam-3010	75	21	prime	prime	ADJ
ejpam-3010	75	22	if	if	SCONJ
ejpam-3010	76	1	and	and	CCONJ
ejpam-3010	76	2	only	only	ADV
ejpam-3010	76	3	if	if	SCONJ
ejpam-3010	76	4	they	they	PRON
ejpam-3010	76	5	are	be	AUX
ejpam-3010	76	6	idempotent	idempotent	ADJ
ejpam-3010	76	7	and	and	CCONJ
ejpam-3010	76	8	they	they	PRON
ejpam-3010	76	9	form	form	VERB
ejpam-3010	76	10	a	a	DET
ejpam-3010	76	11	chain	chain	NOUN
ejpam-3010	76	12	.	.	PUNCT
ejpam-3010	77	1	the	the	DET
ejpam-3010	77	2	ideals	ideal	NOUN
ejpam-3010	77	3	of	of	ADP
ejpam-3010	77	4	m	m	NOUN
ejpam-3010	77	5	are	be	AUX
ejpam-3010	77	6	prime	prime	ADJ
ejpam-3010	77	7	if	if	SCONJ
ejpam-3010	78	1	and	and	CCONJ
ejpam-3010	78	2	only	only	ADV
ejpam-3010	78	3	if	if	SCONJ
ejpam-3010	78	4	they	they	PRON
ejpam-3010	78	5	form	form	VERB
ejpam-3010	78	6	a	a	DET
ejpam-3010	78	7	chain	chain	NOUN
ejpam-3010	78	8	and	and	CCONJ
ejpam-3010	78	9	m	m	NOUN
ejpam-3010	78	10	is	be	AUX
ejpam-3010	78	11	intra	intra	ADJ
ejpam-3010	78	12	-	-	ADJ
ejpam-3010	78	13	regular	regular	ADJ
ejpam-3010	78	14	.	.	PUNCT
ejpam-3010	79	1	m	m	PROPN
ejpam-3010	79	2	is	be	AUX
ejpam-3010	79	3	intra	intra	ADJ
ejpam-3010	79	4	-	-	ADJ
ejpam-3010	79	5	regular	regular	ADJ
ejpam-3010	79	6	and	and	CCONJ
ejpam-3010	79	7	the	the	DET
ejpam-3010	79	8	ideals	ideal	NOUN
ejpam-3010	79	9	of	of	ADP
ejpam-3010	79	10	m	m	PROPN
ejpam-3010	79	11	form	form	VERB
ejpam-3010	79	12	a	a	DET
ejpam-3010	79	13	chain	chain	NOUN
ejpam-3010	79	14	if	if	SCONJ
ejpam-3010	79	15	and	and	CCONJ
ejpam-3010	79	16	only	only	ADV
ejpam-3010	79	17	if	if	SCONJ
ejpam-3010	79	18	m	m	NOUN
ejpam-3010	79	19	is	be	AUX
ejpam-3010	79	20	a	a	DET
ejpam-3010	79	21	chain	chain	NOUN
ejpam-3010	79	22	of	of	ADP
ejpam-3010	79	23	simple	simple	ADJ
ejpam-3010	79	24	semigroups	semigroup	NOUN
ejpam-3010	79	25	.	.	PUNCT
ejpam-3010	80	1	for	for	ADP
ejpam-3010	80	2	an	an	DET
ejpam-3010	80	3	intra	intra	ADJ
ejpam-3010	80	4	-	-	ADJ
ejpam-3010	80	5	regular	regular	ADJ
ejpam-3010	80	6	po	po	NOUN
ejpam-3010	80	7	-	-	PUNCT
ejpam-3010	80	8	γ	γ	NOUN
ejpam-3010	80	9	-	-	PUNCT
ejpam-3010	80	10	semigroup	semigroup	NOUN
ejpam-3010	80	11	m	m	VERB
ejpam-3010	80	12	the	the	DET
ejpam-3010	80	13	set	set	NOUN
ejpam-3010	80	14	{	{	PUNCT
ejpam-3010	80	15	(	(	PUNCT
ejpam-3010	80	16	x)n	x)n	PUNCT
ejpam-3010	80	17	|	|	ADV
ejpam-3010	80	18	x	x	SYM
ejpam-3010	80	19	∈	∈	PROPN
ejpam-3010	80	20	m	m	PRON
ejpam-3010	80	21	}	}	PUNCT
ejpam-3010	80	22	coincides	coincide	NOUN
ejpam-3010	80	23	with	with	ADP
ejpam-3010	80	24	the	the	DET
ejpam-3010	80	25	set	set	NOUN
ejpam-3010	80	26	of	of	ADP
ejpam-3010	80	27	all	all	DET
ejpam-3010	80	28	maximal	maximal	ADJ
ejpam-3010	80	29	simple	simple	ADJ
ejpam-3010	80	30	subsemigroups	subsemigroup	NOUN
ejpam-3010	80	31	of	of	ADP
ejpam-3010	80	32	m	m	PROPN
ejpam-3010	80	33	.	.	PUNCT
ejpam-3010	81	1	keeping	keep	VERB
ejpam-3010	81	2	the	the	DET
ejpam-3010	81	3	new	new	ADJ
ejpam-3010	81	4	definition	definition	NOUN
ejpam-3010	81	5	of	of	ADP
ejpam-3010	81	6	left	left	ADJ
ejpam-3010	81	7	(	(	PUNCT
ejpam-3010	81	8	right	right	ADJ
ejpam-3010	81	9	)	)	PUNCT
ejpam-3010	81	10	regularity	regularity	NOUN
ejpam-3010	81	11	of	of	ADP
ejpam-3010	81	12	po	po	NOUN
ejpam-3010	81	13	-	-	PUNCT
ejpam-3010	81	14	γ	γ	NOUN
ejpam-3010	81	15	-	-	PUNCT
ejpam-3010	81	16	semigroups	semigroup	NOUN
ejpam-3010	81	17	introduced	introduce	VERB
ejpam-3010	81	18	in	in	ADP
ejpam-3010	81	19	[	[	X
ejpam-3010	81	20	9	9	NUM
ejpam-3010	81	21	]	]	PUNCT
ejpam-3010	81	22	,	,	PUNCT
ejpam-3010	81	23	we	we	PRON
ejpam-3010	81	24	also	also	ADV
ejpam-3010	81	25	give	give	VERB
ejpam-3010	81	26	a	a	DET
ejpam-3010	81	27	structure	structure	NOUN
ejpam-3010	81	28	theorem	theorem	VERB
ejpam-3010	81	29	related	relate	VERB
ejpam-3010	81	30	to	to	ADP
ejpam-3010	81	31	the	the	DET
ejpam-3010	81	32	decomposition	decomposition	NOUN
ejpam-3010	81	33	of	of	ADP
ejpam-3010	81	34	a	a	DET
ejpam-3010	81	35	po	po	NOUN
ejpam-3010	81	36	-	-	PUNCT
ejpam-3010	81	37	γ	γ	NOUN
ejpam-3010	81	38	-	-	PUNCT
ejpam-3010	81	39	semigroup	semigroup	NOUN
ejpam-3010	81	40	m	m	VERB
ejpam-3010	81	41	which	which	PRON
ejpam-3010	81	42	is	be	AUX
ejpam-3010	81	43	left	leave	VERB
ejpam-3010	81	44	regular	regular	ADV
ejpam-3010	81	45	and	and	CCONJ
ejpam-3010	81	46	satisfies	satisfy	VERB
ejpam-3010	81	47	the	the	DET
ejpam-3010	81	48	relation	relation	NOUN
ejpam-3010	81	49	(	(	PUNCT
ejpam-3010	81	50	xγm	xγm	PROPN
ejpam-3010	81	51	]	]	PUNCT
ejpam-3010	81	52	⊆	⊆	X
ejpam-3010	81	53	(	(	PUNCT
ejpam-3010	81	54	mγx	mγx	NOUN
ejpam-3010	81	55	]	]	PUNCT
ejpam-3010	81	56	for	for	ADP
ejpam-3010	81	57	every	every	DET
ejpam-3010	81	58	x	x	SYM
ejpam-3010	81	59	∈	∈	PROPN
ejpam-3010	81	60	m	m	VERB
ejpam-3010	81	61	into	into	ADP
ejpam-3010	81	62	left	left	ADJ
ejpam-3010	81	63	simple	simple	ADJ
ejpam-3010	81	64	components	component	NOUN
ejpam-3010	81	65	.	.	PUNCT
ejpam-3010	82	1	the	the	DET
ejpam-3010	82	2	results	result	NOUN
ejpam-3010	82	3	of	of	ADP
ejpam-3010	82	4	this	this	DET
ejpam-3010	82	5	paper	paper	NOUN
ejpam-3010	82	6	are	be	AUX
ejpam-3010	82	7	based	base	VERB
ejpam-3010	82	8	on	on	ADP
ejpam-3010	82	9	the	the	DET
ejpam-3010	82	10	corresponding	corresponding	ADJ
ejpam-3010	82	11	results	result	NOUN
ejpam-3010	82	12	on	on	ADP
ejpam-3010	82	13	ordered	order	VERB
ejpam-3010	82	14	semigroups	semigroup	NOUN
ejpam-3010	82	15	considered	consider	VERB
ejpam-3010	82	16	in	in	ADP
ejpam-3010	82	17	[	[	X
ejpam-3010	82	18	3	3	NUM
ejpam-3010	82	19	]	]	PUNCT
ejpam-3010	82	20	and	and	CCONJ
ejpam-3010	82	21	[	[	X
ejpam-3010	82	22	4	4	NUM
ejpam-3010	82	23	]	]	PUNCT
ejpam-3010	82	24	,	,	PUNCT
ejpam-3010	82	25	and	and	CCONJ
ejpam-3010	82	26	the	the	DET
ejpam-3010	82	27	aim	aim	NOUN
ejpam-3010	82	28	of	of	ADP
ejpam-3010	82	29	writing	write	VERB
ejpam-3010	82	30	this	this	DET
ejpam-3010	82	31	paper	paper	NOUN
ejpam-3010	82	32	is	be	AUX
ejpam-3010	82	33	to	to	PART
ejpam-3010	82	34	show	show	VERB
ejpam-3010	82	35	the	the	DET
ejpam-3010	82	36	importance	importance	NOUN
ejpam-3010	82	37	of	of	ADP
ejpam-3010	82	38	these	these	DET
ejpam-3010	82	39	new	new	ADJ
ejpam-3010	82	40	concepts	concept	NOUN
ejpam-3010	82	41	of	of	ADP
ejpam-3010	82	42	intra	intra	ADJ
ejpam-3010	82	43	-	-	ADJ
ejpam-3010	82	44	regularity	regularity	NOUN
ejpam-3010	82	45	and	and	CCONJ
ejpam-3010	82	46	left	leave	VERB
ejpam-3010	82	47	(	(	PUNCT
ejpam-3010	82	48	right	right	ADJ
ejpam-3010	82	49	)	)	PUNCT
ejpam-3010	82	50	regularity	regularity	NOUN
ejpam-3010	82	51	in	in	ADP
ejpam-3010	82	52	the	the	DET
ejpam-3010	82	53	investigation	investigation	NOUN
ejpam-3010	82	54	.	.	PUNCT
ejpam-3010	83	1	n.	n.	PROPN
ejpam-3010	83	2	kehayopulu	kehayopulu	PROPN
ejpam-3010	83	3	/	/	SYM
ejpam-3010	83	4	eur	eur	PROPN
ejpam-3010	83	5	.	.	PUNCT
ejpam-3010	84	1	j.	j.	PROPN
ejpam-3010	84	2	pure	pure	PROPN
ejpam-3010	84	3	appl	appl	PROPN
ejpam-3010	84	4	.	.	PROPN
ejpam-3010	84	5	math	math	PROPN
ejpam-3010	84	6	,	,	PUNCT
ejpam-3010	84	7	10	10	NUM
ejpam-3010	84	8	(	(	PUNCT
ejpam-3010	84	9	4	4	NUM
ejpam-3010	84	10	)	)	PUNCT
ejpam-3010	84	11	(	(	PUNCT
ejpam-3010	84	12	2017	2017	NUM
ejpam-3010	84	13	)	)	PUNCT
ejpam-3010	84	14	,	,	PUNCT
ejpam-3010	84	15	620	620	NUM
ejpam-3010	84	16	-	-	SYM
ejpam-3010	84	17	630	630	NUM
ejpam-3010	84	18	623	623	NUM
ejpam-3010	84	19	2	2	NUM
ejpam-3010	84	20	.	.	PUNCT
ejpam-3010	84	21	main	main	ADJ
ejpam-3010	84	22	results	result	NOUN
ejpam-3010	84	23	let	let	VERB
ejpam-3010	84	24	m	m	PRON
ejpam-3010	84	25	be	be	AUX
ejpam-3010	84	26	a	a	DET
ejpam-3010	84	27	po	po	NOUN
ejpam-3010	84	28	-	-	PUNCT
ejpam-3010	84	29	γ	γ	NOUN
ejpam-3010	84	30	-	-	PUNCT
ejpam-3010	84	31	semigroup	semigroup	NOUN
ejpam-3010	84	32	.	.	PUNCT
ejpam-3010	85	1	a	a	DET
ejpam-3010	85	2	subset	subset	NOUN
ejpam-3010	85	3	a	a	PRON
ejpam-3010	85	4	of	of	ADP
ejpam-3010	85	5	m	m	PROPN
ejpam-3010	85	6	is	be	AUX
ejpam-3010	85	7	called	call	VERB
ejpam-3010	85	8	idempotent	idempotent	ADJ
ejpam-3010	85	9	,	,	PUNCT
ejpam-3010	85	10	if	if	SCONJ
ejpam-3010	85	11	a	a	PRON
ejpam-3010	85	12	=	=	X
ejpam-3010	85	13	(	(	PUNCT
ejpam-3010	85	14	aγa	aγa	ADP
ejpam-3010	85	15	]	]	PUNCT
ejpam-3010	85	16	.	.	PUNCT
ejpam-3010	86	1	a	a	DET
ejpam-3010	86	2	subset	subset	NOUN
ejpam-3010	86	3	t	t	NOUN
ejpam-3010	86	4	of	of	ADP
ejpam-3010	86	5	m	m	PROPN
ejpam-3010	86	6	is	be	AUX
ejpam-3010	86	7	called	call	VERB
ejpam-3010	86	8	prime	prime	ADJ
ejpam-3010	86	9	if	if	SCONJ
ejpam-3010	86	10	a	a	PRON
ejpam-3010	86	11	,	,	PUNCT
ejpam-3010	86	12	b	b	X
ejpam-3010	86	13	∈	∈	NOUN
ejpam-3010	86	14	m	m	NOUN
ejpam-3010	86	15	and	and	CCONJ
ejpam-3010	86	16	γ	γ	PROPN
ejpam-3010	86	17	∈	∈	PROPN
ejpam-3010	86	18	γ	γ	NOUN
ejpam-3010	86	19	such	such	ADJ
ejpam-3010	86	20	that	that	SCONJ
ejpam-3010	86	21	aγb	aγb	NOUN
ejpam-3010	86	22	∈	∈	PROPN
ejpam-3010	86	23	t	t	PROPN
ejpam-3010	86	24	implies	imply	VERB
ejpam-3010	86	25	a	a	DET
ejpam-3010	86	26	∈	∈	PROPN
ejpam-3010	86	27	t	t	NOUN
ejpam-3010	86	28	or	or	CCONJ
ejpam-3010	86	29	b	b	PROPN
ejpam-3010	86	30	∈	∈	PROPN
ejpam-3010	86	31	t	t	NOUN
ejpam-3010	86	32	.	.	PUNCT
ejpam-3010	87	1	the	the	DET
ejpam-3010	87	2	set	set	PROPN
ejpam-3010	87	3	t	t	PROPN
ejpam-3010	87	4	is	be	AUX
ejpam-3010	87	5	called	call	VERB
ejpam-3010	87	6	semiprime	semiprime	NOUN
ejpam-3010	87	7	if	if	SCONJ
ejpam-3010	87	8	a	a	DET
ejpam-3010	87	9	∈m	∈m	NOUN
ejpam-3010	87	10	and	and	CCONJ
ejpam-3010	87	11	γ	γ	NOUN
ejpam-3010	87	12	∈	∈	PROPN
ejpam-3010	87	13	γ	γ	NOUN
ejpam-3010	87	14	such	such	ADJ
ejpam-3010	87	15	that	that	SCONJ
ejpam-3010	87	16	aγa	aγa	PROPN
ejpam-3010	87	17	∈	∈	PROPN
ejpam-3010	87	18	t	t	PROPN
ejpam-3010	87	19	implies	imply	VERB
ejpam-3010	87	20	a	a	DET
ejpam-3010	87	21	∈	∈	PROPN
ejpam-3010	87	22	t	t	NOUN
ejpam-3010	88	1	[	[	X
ejpam-3010	88	2	9	9	NUM
ejpam-3010	88	3	]	]	PUNCT
ejpam-3010	88	4	.	.	PUNCT
ejpam-3010	89	1	a	a	DET
ejpam-3010	89	2	subset	subset	NOUN
ejpam-3010	89	3	t	t	NOUN
ejpam-3010	89	4	of	of	ADP
ejpam-3010	89	5	m	m	PROPN
ejpam-3010	89	6	is	be	AUX
ejpam-3010	89	7	called	call	VERB
ejpam-3010	89	8	weakly	weakly	ADJ
ejpam-3010	89	9	prime	prime	NOUN
ejpam-3010	89	10	if	if	SCONJ
ejpam-3010	89	11	the	the	DET
ejpam-3010	89	12	following	follow	VERB
ejpam-3010	89	13	assertion	assertion	NOUN
ejpam-3010	89	14	is	be	AUX
ejpam-3010	89	15	satisfied	satisfied	ADJ
ejpam-3010	89	16	:	:	PUNCT
ejpam-3010	89	17	if	if	SCONJ
ejpam-3010	89	18	a	a	PRON
ejpam-3010	89	19	,	,	PUNCT
ejpam-3010	89	20	b	b	NOUN
ejpam-3010	89	21	are	be	AUX
ejpam-3010	89	22	ideals	ideal	NOUN
ejpam-3010	89	23	of	of	ADP
ejpam-3010	89	24	m	m	NOUN
ejpam-3010	89	25	such	such	ADJ
ejpam-3010	89	26	that	that	SCONJ
ejpam-3010	89	27	aγb	aγb	ADV
ejpam-3010	89	28	⊆	⊆	NUM
ejpam-3010	89	29	t	t	NOUN
ejpam-3010	89	30	,	,	PUNCT
ejpam-3010	89	31	then	then	ADV
ejpam-3010	89	32	a	a	DET
ejpam-3010	89	33	⊆	⊆	NUM
ejpam-3010	89	34	t	t	NOUN
ejpam-3010	89	35	or	or	CCONJ
ejpam-3010	89	36	b	b	NOUN
ejpam-3010	89	37	⊆	⊆	NUM
ejpam-3010	89	38	t	t	NOUN
ejpam-3010	89	39	.	.	PUNCT
ejpam-3010	90	1	for	for	ADP
ejpam-3010	90	2	a	a	DET
ejpam-3010	90	3	subset	subset	NOUN
ejpam-3010	90	4	t	t	NOUN
ejpam-3010	90	5	of	of	ADP
ejpam-3010	90	6	m	m	PROPN
ejpam-3010	90	7	,	,	PUNCT
ejpam-3010	90	8	we	we	PRON
ejpam-3010	90	9	consider	consider	VERB
ejpam-3010	90	10	the	the	DET
ejpam-3010	90	11	statements	statement	NOUN
ejpam-3010	90	12	:	:	PUNCT
ejpam-3010	90	13	(	(	PUNCT
ejpam-3010	90	14	1	1	X
ejpam-3010	90	15	)	)	PUNCT
ejpam-3010	90	16	a	a	DET
ejpam-3010	90	17	,	,	PUNCT
ejpam-3010	90	18	b	b	NOUN
ejpam-3010	90	19	∈m	∈m	NOUN
ejpam-3010	90	20	,	,	PUNCT
ejpam-3010	90	21	γ	γ	PROPN
ejpam-3010	90	22	∈	∈	PROPN
ejpam-3010	90	23	γ	γ	X
ejpam-3010	90	24	,	,	PUNCT
ejpam-3010	90	25	aγb	aγb	NOUN
ejpam-3010	90	26	∈	∈	PROPN
ejpam-3010	90	27	t	t	NOUN
ejpam-3010	90	28	=	=	PRON
ejpam-3010	90	29	⇒	⇒	VERB
ejpam-3010	90	30	a	a	DET
ejpam-3010	90	31	∈	∈	PROPN
ejpam-3010	90	32	t	t	NOUN
ejpam-3010	90	33	or	or	CCONJ
ejpam-3010	90	34	b	b	PROPN
ejpam-3010	90	35	∈	∈	PROPN
ejpam-3010	90	36	t	t	NOUN
ejpam-3010	90	37	.	.	PUNCT
ejpam-3010	91	1	(	(	PUNCT
ejpam-3010	91	2	2	2	X
ejpam-3010	91	3	)	)	PUNCT
ejpam-3010	91	4	a	a	DET
ejpam-3010	91	5	,	,	PUNCT
ejpam-3010	91	6	b	b	NOUN
ejpam-3010	91	7	⊆m	⊆m	NOUN
ejpam-3010	91	8	,	,	PUNCT
ejpam-3010	91	9	aγb	aγb	ADV
ejpam-3010	91	10	⊆	⊆	NUM
ejpam-3010	91	11	t	t	NOUN
ejpam-3010	91	12	=	=	PRON
ejpam-3010	91	13	⇒	⇒	VERB
ejpam-3010	91	14	a	a	DET
ejpam-3010	91	15	⊆	⊆	NUM
ejpam-3010	91	16	t	t	NOUN
ejpam-3010	91	17	or	or	CCONJ
ejpam-3010	91	18	b	b	NOUN
ejpam-3010	91	19	⊆	⊆	NUM
ejpam-3010	91	20	t	t	NOUN
ejpam-3010	91	21	.	.	PUNCT
ejpam-3010	92	1	then	then	ADV
ejpam-3010	92	2	(	(	PUNCT
ejpam-3010	92	3	1	1	X
ejpam-3010	92	4	)	)	PUNCT
ejpam-3010	92	5	⇒	⇒	NOUN
ejpam-3010	92	6	(	(	PUNCT
ejpam-3010	92	7	2	2	NUM
ejpam-3010	92	8	)	)	PUNCT
ejpam-3010	92	9	.	.	PUNCT
ejpam-3010	93	1	in	in	ADP
ejpam-3010	93	2	fact	fact	NOUN
ejpam-3010	93	3	:	:	PUNCT
ejpam-3010	93	4	let	let	VERB
ejpam-3010	93	5	a	a	DET
ejpam-3010	93	6	,	,	PUNCT
ejpam-3010	93	7	b	b	PROPN
ejpam-3010	93	8	⊆	⊆	NUM
ejpam-3010	93	9	m	m	NOUN
ejpam-3010	93	10	,	,	PUNCT
ejpam-3010	93	11	aγb	aγb	ADV
ejpam-3010	93	12	⊆	⊆	NUM
ejpam-3010	93	13	t	t	NOUN
ejpam-3010	93	14	,	,	PUNCT
ejpam-3010	93	15	a	a	DET
ejpam-3010	93	16	*	*	X
ejpam-3010	93	17	t	t	PROPN
ejpam-3010	93	18	and	and	CCONJ
ejpam-3010	93	19	b	b	PROPN
ejpam-3010	93	20	∈	∈	PROPN
ejpam-3010	93	21	b.	b.	PROPN
ejpam-3010	93	22	take	take	VERB
ejpam-3010	93	23	an	an	DET
ejpam-3010	93	24	element	element	NOUN
ejpam-3010	93	25	a	a	DET
ejpam-3010	93	26	∈	∈	PROPN
ejpam-3010	93	27	a	a	DET
ejpam-3010	93	28	such	such	ADJ
ejpam-3010	93	29	that	that	SCONJ
ejpam-3010	93	30	a	a	DET
ejpam-3010	93	31	6∈	6∈	PROPN
ejpam-3010	93	32	t	t	NOUN
ejpam-3010	93	33	and	and	CCONJ
ejpam-3010	93	34	an	an	DET
ejpam-3010	93	35	element	element	NOUN
ejpam-3010	93	36	γ	γ	X
ejpam-3010	93	37	∈	∈	PROPN
ejpam-3010	93	38	γ	γ	X
ejpam-3010	93	39	(	(	PUNCT
ejpam-3010	93	40	γ	γ	PROPN
ejpam-3010	93	41	6=	6=	NOUN
ejpam-3010	93	42	∅	∅	NOUN
ejpam-3010	93	43	)	)	PUNCT
ejpam-3010	93	44	.	.	PUNCT
ejpam-3010	94	1	since	since	SCONJ
ejpam-3010	94	2	aγb	aγb	NOUN
ejpam-3010	94	3	∈	∈	PROPN
ejpam-3010	94	4	aγb	aγb	NOUN
ejpam-3010	94	5	⊆	⊆	NUM
ejpam-3010	94	6	t	t	NOUN
ejpam-3010	94	7	,	,	PUNCT
ejpam-3010	94	8	by	by	ADP
ejpam-3010	94	9	(	(	PUNCT
ejpam-3010	94	10	1	1	NUM
ejpam-3010	94	11	)	)	PUNCT
ejpam-3010	94	12	,	,	PUNCT
ejpam-3010	94	13	we	we	PRON
ejpam-3010	94	14	have	have	VERB
ejpam-3010	94	15	a	a	DET
ejpam-3010	94	16	∈	∈	PROPN
ejpam-3010	94	17	t	t	NOUN
ejpam-3010	94	18	or	or	CCONJ
ejpam-3010	94	19	b	b	PROPN
ejpam-3010	94	20	∈	∈	PROPN
ejpam-3010	94	21	t	t	NOUN
ejpam-3010	94	22	.	.	PUNCT
ejpam-3010	95	1	since	since	SCONJ
ejpam-3010	95	2	a	a	DET
ejpam-3010	95	3	6∈	6∈	PROPN
ejpam-3010	95	4	t	t	NOUN
ejpam-3010	95	5	,	,	PUNCT
ejpam-3010	95	6	we	we	PRON
ejpam-3010	95	7	get	get	VERB
ejpam-3010	95	8	b	b	PROPN
ejpam-3010	95	9	∈	∈	PROPN
ejpam-3010	95	10	t	t	NOUN
ejpam-3010	95	11	.	.	PUNCT
ejpam-3010	96	1	we	we	PRON
ejpam-3010	96	2	have	have	VERB
ejpam-3010	96	3	the	the	DET
ejpam-3010	96	4	following	following	NOUN
ejpam-3010	96	5	:	:	PUNCT
ejpam-3010	96	6	(	(	PUNCT
ejpam-3010	96	7	a	a	X
ejpam-3010	96	8	)	)	PUNCT
ejpam-3010	96	9	if	if	SCONJ
ejpam-3010	96	10	t	t	PROPN
ejpam-3010	96	11	is	be	AUX
ejpam-3010	96	12	a	a	DET
ejpam-3010	96	13	prime	prime	ADJ
ejpam-3010	96	14	subset	subset	NOUN
ejpam-3010	96	15	of	of	ADP
ejpam-3010	96	16	m	m	PROPN
ejpam-3010	96	17	,	,	PUNCT
ejpam-3010	96	18	then	then	ADV
ejpam-3010	96	19	t	t	PROPN
ejpam-3010	96	20	is	be	AUX
ejpam-3010	96	21	a	a	DET
ejpam-3010	96	22	semiprime	semiprime	NOUN
ejpam-3010	96	23	subset	subset	NOUN
ejpam-3010	96	24	of	of	ADP
ejpam-3010	96	25	m	m	PROPN
ejpam-3010	96	26	.	.	PUNCT
ejpam-3010	97	1	(	(	PUNCT
ejpam-3010	97	2	b	b	X
ejpam-3010	97	3	)	)	PUNCT
ejpam-3010	97	4	if	if	SCONJ
ejpam-3010	97	5	t	t	PROPN
ejpam-3010	97	6	is	be	AUX
ejpam-3010	97	7	a	a	DET
ejpam-3010	97	8	prime	prime	ADJ
ejpam-3010	97	9	subset	subset	NOUN
ejpam-3010	97	10	of	of	ADP
ejpam-3010	97	11	m	m	PROPN
ejpam-3010	97	12	,	,	PUNCT
ejpam-3010	97	13	then	then	ADV
ejpam-3010	97	14	t	t	PROPN
ejpam-3010	97	15	is	be	AUX
ejpam-3010	97	16	a	a	DET
ejpam-3010	97	17	weakly	weakly	ADJ
ejpam-3010	97	18	prime	prime	ADJ
ejpam-3010	97	19	subset	subset	NOUN
ejpam-3010	97	20	of	of	ADP
ejpam-3010	97	21	m	m	PROPN
ejpam-3010	97	22	.	.	PUNCT
ejpam-3010	98	1	definition	definition	NOUN
ejpam-3010	98	2	1	1	NUM
ejpam-3010	98	3	.	.	PUNCT
ejpam-3010	99	1	[	[	X
ejpam-3010	99	2	9	9	NUM
ejpam-3010	99	3	]	]	PUNCT
ejpam-3010	99	4	a	a	DET
ejpam-3010	99	5	po	po	NOUN
ejpam-3010	99	6	-	-	PUNCT
ejpam-3010	99	7	γ	γ	NOUN
ejpam-3010	99	8	-	-	PUNCT
ejpam-3010	99	9	semigroup	semigroup	NOUN
ejpam-3010	99	10	m	m	VERB
ejpam-3010	99	11	is	be	AUX
ejpam-3010	99	12	called	call	VERB
ejpam-3010	99	13	intra	intra	ADJ
ejpam-3010	99	14	-	-	ADJ
ejpam-3010	99	15	regular	regular	ADJ
ejpam-3010	99	16	if	if	SCONJ
ejpam-3010	99	17	x	x	SYM
ejpam-3010	99	18	∈	∈	PROPN
ejpam-3010	99	19	(	(	PUNCT
ejpam-3010	99	20	mγxγxγm	mγxγxγm	NOUN
ejpam-3010	99	21	]	]	PUNCT
ejpam-3010	99	22	for	for	ADP
ejpam-3010	99	23	every	every	DET
ejpam-3010	99	24	x	x	SYM
ejpam-3010	99	25	∈m	∈m	NOUN
ejpam-3010	99	26	and	and	CCONJ
ejpam-3010	99	27	every	every	DET
ejpam-3010	99	28	γ	γ	PROPN
ejpam-3010	99	29	∈	∈	PROPN
ejpam-3010	99	30	γ	γ	X
ejpam-3010	99	31	.	.	PROPN
ejpam-3010	99	32	proposition	proposition	NOUN
ejpam-3010	99	33	2	2	NUM
ejpam-3010	99	34	.	.	PUNCT
ejpam-3010	100	1	if	if	SCONJ
ejpam-3010	100	2	m	m	NOUN
ejpam-3010	100	3	is	be	AUX
ejpam-3010	100	4	an	an	DET
ejpam-3010	100	5	intra	intra	ADJ
ejpam-3010	100	6	-	-	ADJ
ejpam-3010	100	7	regular	regular	ADJ
ejpam-3010	100	8	po	po	NOUN
ejpam-3010	100	9	-	-	PUNCT
ejpam-3010	100	10	γ	γ	NOUN
ejpam-3010	100	11	-	-	PUNCT
ejpam-3010	100	12	semigroup	semigroup	NOUN
ejpam-3010	100	13	then	then	ADV
ejpam-3010	100	14	,	,	PUNCT
ejpam-3010	100	15	for	for	SCONJ
ejpam-3010	100	16	every	every	DET
ejpam-3010	100	17	x	x	NOUN
ejpam-3010	100	18	,	,	PUNCT
ejpam-3010	100	19	y	y	PROPN
ejpam-3010	100	20	∈	∈	PROPN
ejpam-3010	100	21	m	m	PROPN
ejpam-3010	100	22	and	and	CCONJ
ejpam-3010	100	23	every	every	DET
ejpam-3010	100	24	γ	γ	PROPN
ejpam-3010	100	25	∈	∈	PROPN
ejpam-3010	100	26	γ	γ	X
ejpam-3010	100	27	,	,	PUNCT
ejpam-3010	100	28	we	we	PRON
ejpam-3010	100	29	have	have	VERB
ejpam-3010	100	30	(	(	PUNCT
ejpam-3010	100	31	mγxγyγm	mγxγyγm	X
ejpam-3010	100	32	]	]	X
ejpam-3010	100	33	=	=	PUNCT
ejpam-3010	100	34	(	(	PUNCT
ejpam-3010	100	35	mγyγxγm	mγyγxγm	X
ejpam-3010	100	36	]	]	PUNCT
ejpam-3010	100	37	.	.	PUNCT
ejpam-3010	101	1	proof	proof	NOUN
ejpam-3010	101	2	.	.	PUNCT
ejpam-3010	102	1	let	let	VERB
ejpam-3010	102	2	x	x	PRON
ejpam-3010	102	3	,	,	PUNCT
ejpam-3010	102	4	y	y	PROPN
ejpam-3010	102	5	∈m	∈m	NOUN
ejpam-3010	102	6	and	and	CCONJ
ejpam-3010	102	7	γ	γ	PROPN
ejpam-3010	102	8	∈	∈	PROPN
ejpam-3010	102	9	γ	γ	X
ejpam-3010	102	10	.	.	PUNCT
ejpam-3010	103	1	since	since	SCONJ
ejpam-3010	103	2	xγy	xγy	PROPN
ejpam-3010	103	3	∈mγm	∈mγm	NOUN
ejpam-3010	103	4	⊆m	⊆m	NOUN
ejpam-3010	103	5	and	and	CCONJ
ejpam-3010	103	6	m	m	PROPN
ejpam-3010	103	7	is	be	AUX
ejpam-3010	103	8	intra	intra	ADJ
ejpam-3010	103	9	-	-	ADJ
ejpam-3010	103	10	regular	regular	ADJ
ejpam-3010	103	11	,	,	PUNCT
ejpam-3010	103	12	we	we	PRON
ejpam-3010	103	13	have	have	VERB
ejpam-3010	103	14	xγy	xγy	PROPN
ejpam-3010	103	15	∈	∈	PROPN
ejpam-3010	103	16	(	(	PUNCT
ejpam-3010	103	17	mγ(xγy)γ(xγy)γm	mγ(xγy)γ(xγy)γm	X
ejpam-3010	103	18	]	]	PUNCT
ejpam-3010	103	19	⊆	⊆	NUM
ejpam-3010	103	20	(	(	PUNCT
ejpam-3010	103	21	(	(	PUNCT
ejpam-3010	103	22	mγm)γ(yγx)γ(mγm	mγm)γ(yγx)γ(mγm	NUM
ejpam-3010	103	23	)	)	PUNCT
ejpam-3010	103	24	]	]	PUNCT
ejpam-3010	104	1	⊆	⊆	X
ejpam-3010	104	2	(	(	PUNCT
ejpam-3010	104	3	mγyγxγm	mγyγxγm	X
ejpam-3010	104	4	]	]	X
ejpam-3010	104	5	.	.	PUNCT
ejpam-3010	105	1	then	then	ADV
ejpam-3010	105	2	we	we	PRON
ejpam-3010	105	3	have	have	VERB
ejpam-3010	105	4	mγ(xγy)γm	mγ(xγy)γm	NOUN
ejpam-3010	105	5	⊆	⊆	NUM
ejpam-3010	105	6	(	(	PUNCT
ejpam-3010	105	7	m	m	PROPN
ejpam-3010	105	8	]	]	X
ejpam-3010	105	9	γ(mγyγxγm	γ(mγyγxγm	NOUN
ejpam-3010	105	10	]	]	X
ejpam-3010	105	11	γ(m	γ(m	X
ejpam-3010	105	12	]	]	PUNCT
ejpam-3010	105	13	⊆	⊆	NUM
ejpam-3010	105	14	(	(	PUNCT
ejpam-3010	105	15	mγmγyγxγmγm	mγmγyγxγmγm	NOUN
ejpam-3010	105	16	]	]	PUNCT
ejpam-3010	105	17	⊆	⊆	NUM
ejpam-3010	105	18	(	(	PUNCT
ejpam-3010	105	19	mγyγxγm	mγyγxγm	X
ejpam-3010	105	20	]	]	X
ejpam-3010	105	21	,	,	PUNCT
ejpam-3010	105	22	from	from	ADP
ejpam-3010	105	23	which	which	PRON
ejpam-3010	105	24	(	(	PUNCT
ejpam-3010	105	25	mγ(xγy)γm	mγ(xγy)γm	NOUN
ejpam-3010	105	26	]	]	PUNCT
ejpam-3010	106	1	⊆	⊆	X
ejpam-3010	106	2	(	(	PUNCT
ejpam-3010	106	3	(	(	PUNCT
ejpam-3010	106	4	mγyγxγm	mγyγxγm	VERB
ejpam-3010	106	5	]	]	X
ejpam-3010	106	6	]	]	PUNCT
ejpam-3010	107	1	=	=	PUNCT
ejpam-3010	107	2	(	(	PUNCT
ejpam-3010	107	3	mγyγxγm	mγyγxγm	VERB
ejpam-3010	107	4	]	]	X
ejpam-3010	107	5	.	.	PUNCT
ejpam-3010	108	1	since	since	SCONJ
ejpam-3010	108	2	m	m	PROPN
ejpam-3010	108	3	is	be	AUX
ejpam-3010	108	4	intra	intra	ADJ
ejpam-3010	108	5	-	-	ADJ
ejpam-3010	108	6	regular	regular	ADJ
ejpam-3010	108	7	and	and	CCONJ
ejpam-3010	108	8	yγx	yγx	NOUN
ejpam-3010	108	9	∈m	∈m	NOUN
ejpam-3010	108	10	,	,	PUNCT
ejpam-3010	108	11	by	by	ADP
ejpam-3010	108	12	symmetry	symmetry	NOUN
ejpam-3010	108	13	,	,	PUNCT
ejpam-3010	108	14	we	we	PRON
ejpam-3010	108	15	get	get	VERB
ejpam-3010	108	16	(	(	PUNCT
ejpam-3010	108	17	mγyγxγm	mγyγxγm	VERB
ejpam-3010	108	18	]	]	X
ejpam-3010	109	1	⊆	⊆	X
ejpam-3010	109	2	(	(	PUNCT
ejpam-3010	109	3	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	109	4	]	]	X
ejpam-3010	109	5	,	,	PUNCT
ejpam-3010	109	6	thus	thus	ADV
ejpam-3010	109	7	we	we	PRON
ejpam-3010	109	8	have	have	VERB
ejpam-3010	109	9	(	(	PUNCT
ejpam-3010	109	10	mγxγyγm	mγxγyγm	X
ejpam-3010	109	11	]	]	X
ejpam-3010	109	12	=	=	PUNCT
ejpam-3010	109	13	(	(	PUNCT
ejpam-3010	109	14	mγyγxγm	mγyγxγm	VERB
ejpam-3010	109	15	]	]	PUNCT
ejpam-3010	109	16	.	.	PUNCT
ejpam-3010	110	1	�	�	PROPN
ejpam-3010	110	2	lemma	lemma	PROPN
ejpam-3010	110	3	3	3	X
ejpam-3010	110	4	.	.	PUNCT
ejpam-3010	111	1	[	[	X
ejpam-3010	111	2	9	9	NUM
ejpam-3010	111	3	]	]	PUNCT
ejpam-3010	111	4	a	a	DET
ejpam-3010	111	5	po	po	NOUN
ejpam-3010	111	6	-	-	PUNCT
ejpam-3010	111	7	γ	γ	NOUN
ejpam-3010	111	8	-	-	PUNCT
ejpam-3010	111	9	semigroup	semigroup	NOUN
ejpam-3010	111	10	m	m	VERB
ejpam-3010	111	11	is	be	AUX
ejpam-3010	111	12	intra	intra	ADJ
ejpam-3010	111	13	-	-	ADJ
ejpam-3010	111	14	regular	regular	ADJ
ejpam-3010	111	15	if	if	SCONJ
ejpam-3010	111	16	and	and	CCONJ
ejpam-3010	111	17	only	only	ADV
ejpam-3010	111	18	if	if	SCONJ
ejpam-3010	111	19	,	,	PUNCT
ejpam-3010	111	20	for	for	ADP
ejpam-3010	111	21	every	every	DET
ejpam-3010	111	22	x	x	SYM
ejpam-3010	111	23	∈	∈	PROPN
ejpam-3010	111	24	m	m	VERB
ejpam-3010	111	25	,	,	PUNCT
ejpam-3010	111	26	we	we	PRON
ejpam-3010	111	27	have	have	VERB
ejpam-3010	111	28	n(x	n(x	NOUN
ejpam-3010	111	29	)	)	PUNCT
ejpam-3010	111	30	=	=	SYM
ejpam-3010	111	31	{	{	PUNCT
ejpam-3010	111	32	y	y	NOUN
ejpam-3010	111	33	∈m	∈m	NOUN
ejpam-3010	111	34	|	|	ADV
ejpam-3010	111	35	x	x	SYM
ejpam-3010	111	36	∈	∈	PROPN
ejpam-3010	111	37	(	(	PUNCT
ejpam-3010	111	38	mγyγm	mγyγm	NOUN
ejpam-3010	111	39	]	]	PUNCT
ejpam-3010	111	40	}	}	PUNCT
ejpam-3010	111	41	.	.	PUNCT
ejpam-3010	112	1	in	in	ADP
ejpam-3010	112	2	a	a	DET
ejpam-3010	112	3	similar	similar	ADJ
ejpam-3010	112	4	way	way	NOUN
ejpam-3010	112	5	as	as	ADP
ejpam-3010	112	6	in	in	ADP
ejpam-3010	112	7	[	[	X
ejpam-3010	112	8	2	2	NUM
ejpam-3010	112	9	]	]	PUNCT
ejpam-3010	112	10	and	and	CCONJ
ejpam-3010	112	11	[	[	X
ejpam-3010	112	12	7	7	NUM
ejpam-3010	112	13	]	]	PUNCT
ejpam-3010	112	14	,	,	PUNCT
ejpam-3010	112	15	we	we	PRON
ejpam-3010	112	16	can	can	AUX
ejpam-3010	112	17	prove	prove	VERB
ejpam-3010	112	18	the	the	DET
ejpam-3010	112	19	following	follow	VERB
ejpam-3010	112	20	lemma	lemma	PROPN
ejpam-3010	112	21	.	.	PUNCT
ejpam-3010	113	1	lemma	lemma	PROPN
ejpam-3010	113	2	4	4	X
ejpam-3010	113	3	.	.	PUNCT
ejpam-3010	114	1	if	if	SCONJ
ejpam-3010	114	2	m	m	NOUN
ejpam-3010	114	3	is	be	AUX
ejpam-3010	114	4	a	a	DET
ejpam-3010	114	5	po	po	NOUN
ejpam-3010	114	6	-	-	PUNCT
ejpam-3010	114	7	γ	γ	NOUN
ejpam-3010	114	8	-	-	PUNCT
ejpam-3010	114	9	semigroup	semigroup	NOUN
ejpam-3010	114	10	,	,	PUNCT
ejpam-3010	114	11	then	then	ADV
ejpam-3010	114	12	i	i	PRON
ejpam-3010	114	13	⊆	⊆	PROPN
ejpam-3010	114	14	n	n	NOUN
ejpam-3010	114	15	and	and	CCONJ
ejpam-3010	114	16	i	i	PRON
ejpam-3010	114	17	⊆	⊆	NUM
ejpam-3010	114	18	l.	l.	PROPN
ejpam-3010	114	19	n.	n.	PROPN
ejpam-3010	114	20	kehayopulu	kehayopulu	PROPN
ejpam-3010	114	21	/	/	SYM
ejpam-3010	114	22	eur	eur	PROPN
ejpam-3010	114	23	.	.	PUNCT
ejpam-3010	115	1	j.	j.	PROPN
ejpam-3010	115	2	pure	pure	PROPN
ejpam-3010	115	3	appl	appl	PROPN
ejpam-3010	115	4	.	.	PROPN
ejpam-3010	115	5	math	math	PROPN
ejpam-3010	115	6	,	,	PUNCT
ejpam-3010	115	7	10	10	NUM
ejpam-3010	115	8	(	(	PUNCT
ejpam-3010	115	9	4	4	NUM
ejpam-3010	115	10	)	)	PUNCT
ejpam-3010	115	11	(	(	PUNCT
ejpam-3010	115	12	2017	2017	NUM
ejpam-3010	115	13	)	)	PUNCT
ejpam-3010	115	14	,	,	PUNCT
ejpam-3010	115	15	620	620	NUM
ejpam-3010	115	16	-	-	SYM
ejpam-3010	115	17	630	630	NUM
ejpam-3010	115	18	624	624	NUM
ejpam-3010	115	19	lemma	lemma	PROPN
ejpam-3010	115	20	5	5	NUM
ejpam-3010	115	21	.	.	PUNCT
ejpam-3010	116	1	[	[	X
ejpam-3010	116	2	9	9	NUM
ejpam-3010	116	3	]	]	PUNCT
ejpam-3010	116	4	a	a	DET
ejpam-3010	116	5	po	po	NOUN
ejpam-3010	116	6	-	-	PUNCT
ejpam-3010	116	7	γ	γ	NOUN
ejpam-3010	116	8	-	-	PUNCT
ejpam-3010	116	9	semigroup	semigroup	NOUN
ejpam-3010	116	10	m	m	VERB
ejpam-3010	116	11	is	be	AUX
ejpam-3010	116	12	intra	intra	ADJ
ejpam-3010	116	13	-	-	ADJ
ejpam-3010	116	14	regular	regular	ADJ
ejpam-3010	116	15	if	if	SCONJ
ejpam-3010	116	16	and	and	CCONJ
ejpam-3010	116	17	only	only	ADV
ejpam-3010	116	18	if	if	SCONJ
ejpam-3010	116	19	the	the	DET
ejpam-3010	116	20	ideals	ideal	NOUN
ejpam-3010	116	21	of	of	ADP
ejpam-3010	116	22	m	m	NOUN
ejpam-3010	116	23	are	be	AUX
ejpam-3010	116	24	semiprime	semiprime	ADJ
ejpam-3010	116	25	.	.	PUNCT
ejpam-3010	117	1	the	the	DET
ejpam-3010	117	2	proof	proof	NOUN
ejpam-3010	117	3	of	of	ADP
ejpam-3010	117	4	the	the	DET
ejpam-3010	117	5	following	follow	VERB
ejpam-3010	117	6	lemma	lemma	PROPN
ejpam-3010	117	7	is	be	AUX
ejpam-3010	117	8	easy	easy	ADJ
ejpam-3010	117	9	.	.	PUNCT
ejpam-3010	118	1	lemma	lemma	PROPN
ejpam-3010	118	2	6	6	NUM
ejpam-3010	118	3	.	.	PUNCT
ejpam-3010	119	1	if	if	SCONJ
ejpam-3010	119	2	m	m	NOUN
ejpam-3010	119	3	is	be	AUX
ejpam-3010	119	4	a	a	DET
ejpam-3010	119	5	po	po	NOUN
ejpam-3010	119	6	-	-	PUNCT
ejpam-3010	119	7	γ	γ	NOUN
ejpam-3010	119	8	-	-	PUNCT
ejpam-3010	119	9	semigroup	semigroup	NOUN
ejpam-3010	119	10	,	,	PUNCT
ejpam-3010	119	11	then	then	ADV
ejpam-3010	119	12	the	the	DET
ejpam-3010	119	13	set	set	NOUN
ejpam-3010	119	14	(	(	PUNCT
ejpam-3010	119	15	mγaγm	mγaγm	NOUN
ejpam-3010	119	16	]	]	PUNCT
ejpam-3010	119	17	(	(	PUNCT
ejpam-3010	119	18	resp	resp	NOUN
ejpam-3010	119	19	.	.	PUNCT
ejpam-3010	120	1	(	(	PUNCT
ejpam-3010	120	2	mγa	mγa	PROPN
ejpam-3010	120	3	]	]	PUNCT
ejpam-3010	120	4	)	)	PUNCT
ejpam-3010	120	5	is	be	AUX
ejpam-3010	120	6	an	an	DET
ejpam-3010	120	7	ideal	ideal	ADJ
ejpam-3010	120	8	(	(	PUNCT
ejpam-3010	120	9	resp	resp	NOUN
ejpam-3010	120	10	.	.	PUNCT
ejpam-3010	121	1	left	leave	VERB
ejpam-3010	121	2	ideal	ideal	NOUN
ejpam-3010	121	3	)	)	PUNCT
ejpam-3010	121	4	of	of	ADP
ejpam-3010	121	5	m	m	PROPN
ejpam-3010	121	6	,	,	PUNCT
ejpam-3010	121	7	and	and	CCONJ
ejpam-3010	121	8	the	the	DET
ejpam-3010	121	9	set	set	NOUN
ejpam-3010	121	10	(	(	PUNCT
ejpam-3010	121	11	aγm	aγm	NOUN
ejpam-3010	121	12	]	]	PUNCT
ejpam-3010	121	13	is	be	AUX
ejpam-3010	121	14	a	a	DET
ejpam-3010	121	15	right	right	ADJ
ejpam-3010	121	16	ideal	ideal	NOUN
ejpam-3010	121	17	of	of	ADP
ejpam-3010	121	18	m	m	PRON
ejpam-3010	121	19	for	for	ADP
ejpam-3010	121	20	every	every	DET
ejpam-3010	121	21	a	a	DET
ejpam-3010	121	22	∈m	∈m	NOUN
ejpam-3010	121	23	.	.	PUNCT
ejpam-3010	122	1	definition	definition	NOUN
ejpam-3010	122	2	7	7	NUM
ejpam-3010	122	3	.	.	PUNCT
ejpam-3010	123	1	a	a	DET
ejpam-3010	123	2	po	po	NOUN
ejpam-3010	123	3	-	-	PUNCT
ejpam-3010	123	4	γ	γ	NOUN
ejpam-3010	123	5	-	-	PUNCT
ejpam-3010	123	6	semigroup	semigroup	NOUN
ejpam-3010	123	7	s	s	VERB
ejpam-3010	123	8	is	be	AUX
ejpam-3010	123	9	said	say	VERB
ejpam-3010	123	10	to	to	PART
ejpam-3010	123	11	be	be	AUX
ejpam-3010	123	12	a	a	DET
ejpam-3010	123	13	semilattice	semilattice	NOUN
ejpam-3010	123	14	of	of	ADP
ejpam-3010	123	15	simple	simple	ADJ
ejpam-3010	123	16	(	(	PUNCT
ejpam-3010	123	17	resp	resp	NOUN
ejpam-3010	123	18	.	.	PUNCT
ejpam-3010	124	1	left	leave	VERB
ejpam-3010	124	2	simple	simple	NOUN
ejpam-3010	124	3	)	)	PUNCT
ejpam-3010	124	4	semigroups	semigroup	NOUN
ejpam-3010	124	5	if	if	SCONJ
ejpam-3010	124	6	there	there	PRON
ejpam-3010	124	7	exists	exist	VERB
ejpam-3010	124	8	a	a	DET
ejpam-3010	124	9	semilattice	semilattice	NOUN
ejpam-3010	124	10	congruence	congruence	PROPN
ejpam-3010	124	11	σ	σ	PROPN
ejpam-3010	124	12	on	on	ADP
ejpam-3010	124	13	m	m	PRON
ejpam-3010	124	14	such	such	ADJ
ejpam-3010	124	15	that	that	SCONJ
ejpam-3010	124	16	the	the	DET
ejpam-3010	124	17	σ	σ	NOUN
ejpam-3010	124	18	-	-	PUNCT
ejpam-3010	124	19	class	class	NOUN
ejpam-3010	124	20	(	(	PUNCT
ejpam-3010	124	21	x)σ	x)σ	X
ejpam-3010	124	22	of	of	ADP
ejpam-3010	124	23	m	m	AUX
ejpam-3010	124	24	containing	contain	VERB
ejpam-3010	124	25	x	x	PUNCT
ejpam-3010	124	26	is	be	AUX
ejpam-3010	124	27	a	a	DET
ejpam-3010	124	28	simple	simple	ADJ
ejpam-3010	124	29	(	(	PUNCT
ejpam-3010	124	30	resp	resp	NOUN
ejpam-3010	124	31	.	.	PUNCT
ejpam-3010	125	1	left	leave	VERB
ejpam-3010	125	2	simple	simple	ADJ
ejpam-3010	125	3	)	)	PUNCT
ejpam-3010	125	4	subsemigroup	subsemigroup	NOUN
ejpam-3010	125	5	of	of	ADP
ejpam-3010	125	6	m	m	PROPN
ejpam-3010	125	7	for	for	ADP
ejpam-3010	125	8	every	every	DET
ejpam-3010	125	9	x	x	SYM
ejpam-3010	125	10	∈m	∈m	NOUN
ejpam-3010	125	11	.	.	PUNCT
ejpam-3010	126	1	theorem	theorem	ADJ
ejpam-3010	126	2	8	8	NUM
ejpam-3010	126	3	.	.	PUNCT
ejpam-3010	127	1	let	let	VERB
ejpam-3010	127	2	m	m	PRON
ejpam-3010	127	3	be	be	AUX
ejpam-3010	127	4	a	a	DET
ejpam-3010	127	5	po	po	NOUN
ejpam-3010	127	6	-	-	PUNCT
ejpam-3010	127	7	γ	γ	NOUN
ejpam-3010	127	8	-	-	PUNCT
ejpam-3010	127	9	semigroup	semigroup	NOUN
ejpam-3010	127	10	.	.	PUNCT
ejpam-3010	128	1	the	the	DET
ejpam-3010	128	2	following	follow	VERB
ejpam-3010	128	3	are	be	AUX
ejpam-3010	128	4	equivalent	equivalent	ADJ
ejpam-3010	128	5	:	:	PUNCT
ejpam-3010	128	6	(	(	PUNCT
ejpam-3010	128	7	1	1	X
ejpam-3010	128	8	)	)	PUNCT
ejpam-3010	128	9	m	m	VERB
ejpam-3010	128	10	is	be	AUX
ejpam-3010	128	11	intra	intra	ADJ
ejpam-3010	128	12	-	-	ADJ
ejpam-3010	128	13	regular	regular	ADJ
ejpam-3010	128	14	.	.	PUNCT
ejpam-3010	129	1	(	(	PUNCT
ejpam-3010	129	2	2	2	X
ejpam-3010	129	3	)	)	PUNCT
ejpam-3010	129	4	n(x	n(x	X
ejpam-3010	129	5	)	)	PUNCT
ejpam-3010	129	6	=	=	SYM
ejpam-3010	129	7	{	{	PUNCT
ejpam-3010	129	8	y	y	NOUN
ejpam-3010	129	9	∈m	∈m	NOUN
ejpam-3010	129	10	|	|	ADV
ejpam-3010	129	11	x	x	SYM
ejpam-3010	129	12	∈	∈	PROPN
ejpam-3010	129	13	(	(	PUNCT
ejpam-3010	129	14	mγyγm	mγyγm	NOUN
ejpam-3010	129	15	]	]	PUNCT
ejpam-3010	129	16	}	}	PUNCT
ejpam-3010	129	17	for	for	ADP
ejpam-3010	129	18	every	every	DET
ejpam-3010	129	19	x	x	SYM
ejpam-3010	129	20	∈m	∈m	NOUN
ejpam-3010	129	21	.	.	PUNCT
ejpam-3010	130	1	(	(	PUNCT
ejpam-3010	130	2	3	3	X
ejpam-3010	130	3	)	)	PUNCT
ejpam-3010	130	4	n	n	NOUN
ejpam-3010	130	5	=	=	PROPN
ejpam-3010	130	6	i.	i.	NOUN
ejpam-3010	130	7	(	(	PUNCT
ejpam-3010	130	8	4	4	NUM
ejpam-3010	130	9	)	)	PUNCT
ejpam-3010	130	10	for	for	ADP
ejpam-3010	130	11	every	every	DET
ejpam-3010	130	12	ideal	ideal	NOUN
ejpam-3010	130	13	i	i	PRON
ejpam-3010	130	14	of	of	ADP
ejpam-3010	130	15	m	m	PROPN
ejpam-3010	130	16	,	,	PUNCT
ejpam-3010	130	17	we	we	PRON
ejpam-3010	130	18	have	have	VERB
ejpam-3010	130	19	i	i	NOUN
ejpam-3010	130	20	=	=	SYM
ejpam-3010	130	21	⋃	⋃	NOUN
ejpam-3010	130	22	x∈i	x∈i	NOUN
ejpam-3010	130	23	(	(	PUNCT
ejpam-3010	130	24	x)n	x)n	PROPN
ejpam-3010	130	25	.	.	PUNCT
ejpam-3010	131	1	(	(	PUNCT
ejpam-3010	131	2	5	5	NUM
ejpam-3010	131	3	)	)	PUNCT
ejpam-3010	131	4	(	(	PUNCT
ejpam-3010	131	5	x)n	x)n	X
ejpam-3010	131	6	is	be	AUX
ejpam-3010	131	7	a	a	DET
ejpam-3010	131	8	simple	simple	ADJ
ejpam-3010	131	9	subsemigroup	subsemigroup	NOUN
ejpam-3010	131	10	of	of	ADP
ejpam-3010	131	11	m	m	PROPN
ejpam-3010	131	12	for	for	ADP
ejpam-3010	131	13	every	every	DET
ejpam-3010	131	14	x	x	SYM
ejpam-3010	131	15	∈m	∈m	NOUN
ejpam-3010	131	16	.	.	PUNCT
ejpam-3010	132	1	(	(	PUNCT
ejpam-3010	132	2	6	6	X
ejpam-3010	132	3	)	)	PUNCT
ejpam-3010	132	4	m	m	VERB
ejpam-3010	132	5	is	be	AUX
ejpam-3010	132	6	a	a	DET
ejpam-3010	132	7	semilattice	semilattice	NOUN
ejpam-3010	132	8	of	of	ADP
ejpam-3010	132	9	simple	simple	ADJ
ejpam-3010	132	10	semigroups	semigroup	NOUN
ejpam-3010	132	11	.	.	PUNCT
ejpam-3010	133	1	(	(	PUNCT
ejpam-3010	133	2	7	7	X
ejpam-3010	133	3	)	)	PUNCT
ejpam-3010	133	4	every	every	DET
ejpam-3010	133	5	ideal	ideal	NOUN
ejpam-3010	133	6	of	of	ADP
ejpam-3010	133	7	m	m	PROPN
ejpam-3010	133	8	is	be	AUX
ejpam-3010	133	9	semiprime	semiprime	ADJ
ejpam-3010	133	10	.	.	PUNCT
ejpam-3010	134	1	proof	proof	NOUN
ejpam-3010	134	2	.	.	PUNCT
ejpam-3010	135	1	the	the	DET
ejpam-3010	135	2	implication	implication	NOUN
ejpam-3010	135	3	(	(	PUNCT
ejpam-3010	135	4	1)⇒	1)⇒	NUM
ejpam-3010	135	5	(	(	PUNCT
ejpam-3010	135	6	2	2	NUM
ejpam-3010	135	7	)	)	PUNCT
ejpam-3010	135	8	follows	follow	VERB
ejpam-3010	135	9	from	from	ADP
ejpam-3010	135	10	lemma	lemma	PROPN
ejpam-3010	135	11	3	3	NUM
ejpam-3010	135	12	,	,	PUNCT
ejpam-3010	135	13	the	the	DET
ejpam-3010	135	14	proof	proof	NOUN
ejpam-3010	135	15	of	of	ADP
ejpam-3010	135	16	(	(	PUNCT
ejpam-3010	135	17	3)⇒	3)⇒	NUM
ejpam-3010	135	18	(	(	PUNCT
ejpam-3010	135	19	4	4	NUM
ejpam-3010	135	20	)	)	PUNCT
ejpam-3010	135	21	is	be	AUX
ejpam-3010	135	22	similar	similar	ADJ
ejpam-3010	135	23	with	with	ADP
ejpam-3010	135	24	the	the	DET
ejpam-3010	135	25	corresponding	corresponding	ADJ
ejpam-3010	135	26	result	result	NOUN
ejpam-3010	135	27	for	for	ADP
ejpam-3010	135	28	semigroups	semigroup	NOUN
ejpam-3010	135	29	without	without	ADP
ejpam-3010	135	30	order	order	NOUN
ejpam-3010	135	31	in	in	ADP
ejpam-3010	135	32	[	[	X
ejpam-3010	135	33	8	8	NUM
ejpam-3010	135	34	]	]	PUNCT
ejpam-3010	135	35	,	,	PUNCT
ejpam-3010	135	36	(	(	PUNCT
ejpam-3010	135	37	5)⇒	5)⇒	NUM
ejpam-3010	135	38	(	(	PUNCT
ejpam-3010	135	39	6	6	NUM
ejpam-3010	135	40	)	)	PUNCT
ejpam-3010	135	41	since	since	SCONJ
ejpam-3010	135	42	n	n	NUM
ejpam-3010	135	43	is	be	AUX
ejpam-3010	135	44	a	a	DET
ejpam-3010	135	45	semilattice	semilattice	NOUN
ejpam-3010	135	46	congruence	congruence	NOUN
ejpam-3010	135	47	on	on	ADP
ejpam-3010	135	48	m	m	PRON
ejpam-3010	135	49	and	and	CCONJ
ejpam-3010	135	50	(	(	PUNCT
ejpam-3010	135	51	7)⇒	7)⇒	NUM
ejpam-3010	135	52	(	(	PUNCT
ejpam-3010	135	53	1	1	NUM
ejpam-3010	135	54	)	)	PUNCT
ejpam-3010	135	55	by	by	ADP
ejpam-3010	135	56	lemma	lemma	PROPN
ejpam-3010	135	57	5	5	NUM
ejpam-3010	135	58	.	.	PUNCT
ejpam-3010	136	1	(	(	PUNCT
ejpam-3010	136	2	2	2	X
ejpam-3010	136	3	)	)	PUNCT
ejpam-3010	136	4	=	=	NOUN
ejpam-3010	136	5	⇒	⇒	NOUN
ejpam-3010	136	6	(	(	PUNCT
ejpam-3010	136	7	3	3	NUM
ejpam-3010	136	8	)	)	PUNCT
ejpam-3010	136	9	.	.	PUNCT
ejpam-3010	137	1	let	let	VERB
ejpam-3010	137	2	(	(	PUNCT
ejpam-3010	137	3	a	a	PRON
ejpam-3010	137	4	,	,	PUNCT
ejpam-3010	137	5	b	b	NOUN
ejpam-3010	137	6	)	)	PUNCT
ejpam-3010	137	7	∈	∈	PROPN
ejpam-3010	137	8	n	n	NOUN
ejpam-3010	137	9	.	.	PUNCT
ejpam-3010	138	1	since	since	SCONJ
ejpam-3010	138	2	a	a	DET
ejpam-3010	138	3	∈	∈	PROPN
ejpam-3010	138	4	n(a	n(a	PROPN
ejpam-3010	138	5	)	)	PUNCT
ejpam-3010	138	6	=	=	SYM
ejpam-3010	138	7	n(b	n(b	NOUN
ejpam-3010	138	8	)	)	PUNCT
ejpam-3010	138	9	,	,	PUNCT
ejpam-3010	138	10	by	by	ADP
ejpam-3010	138	11	(	(	PUNCT
ejpam-3010	138	12	2	2	NUM
ejpam-3010	138	13	)	)	PUNCT
ejpam-3010	138	14	,	,	PUNCT
ejpam-3010	138	15	we	we	PRON
ejpam-3010	138	16	have	have	VERB
ejpam-3010	138	17	b	b	PROPN
ejpam-3010	138	18	∈	∈	NOUN
ejpam-3010	138	19	(	(	PUNCT
ejpam-3010	138	20	mγaγm	mγaγm	NOUN
ejpam-3010	138	21	]	]	PUNCT
ejpam-3010	138	22	⊆	⊆	NUM
ejpam-3010	138	23	(	(	PUNCT
ejpam-3010	138	24	a∪mγa∪aγm	a∪mγa∪aγm	NOUN
ejpam-3010	138	25	∪mγaγm	∪mγaγm	X
ejpam-3010	138	26	]	]	X
ejpam-3010	138	27	=	=	SYM
ejpam-3010	138	28	i(a	i(a	PROPN
ejpam-3010	138	29	)	)	PUNCT
ejpam-3010	138	30	,	,	PUNCT
ejpam-3010	138	31	so	so	SCONJ
ejpam-3010	138	32	i(b	i(b	NOUN
ejpam-3010	138	33	)	)	PUNCT
ejpam-3010	138	34	⊆	⊆	NUM
ejpam-3010	138	35	i(a	i(a	NOUN
ejpam-3010	138	36	)	)	PUNCT
ejpam-3010	138	37	.	.	PUNCT
ejpam-3010	139	1	since	since	SCONJ
ejpam-3010	139	2	b	b	PROPN
ejpam-3010	139	3	∈	∈	PROPN
ejpam-3010	139	4	n(a	n(a	PROPN
ejpam-3010	139	5	)	)	PUNCT
ejpam-3010	139	6	,	,	PUNCT
ejpam-3010	139	7	by	by	ADP
ejpam-3010	139	8	symmetry	symmetry	NOUN
ejpam-3010	139	9	,	,	PUNCT
ejpam-3010	139	10	we	we	PRON
ejpam-3010	139	11	get	get	VERB
ejpam-3010	139	12	i(a	i(a	NUM
ejpam-3010	139	13	)	)	PUNCT
ejpam-3010	139	14	⊆	⊆	NUM
ejpam-3010	139	15	i(b	i(b	NOUN
ejpam-3010	139	16	)	)	PUNCT
ejpam-3010	139	17	,	,	PUNCT
ejpam-3010	139	18	so	so	ADV
ejpam-3010	139	19	i(a	i(a	PROPN
ejpam-3010	139	20	)	)	PUNCT
ejpam-3010	139	21	=	=	SYM
ejpam-3010	139	22	i(b	i(b	NOUN
ejpam-3010	139	23	)	)	PUNCT
ejpam-3010	139	24	,	,	PUNCT
ejpam-3010	139	25	and	and	CCONJ
ejpam-3010	139	26	(	(	PUNCT
ejpam-3010	139	27	a	a	PRON
ejpam-3010	139	28	,	,	PUNCT
ejpam-3010	139	29	b	b	NOUN
ejpam-3010	139	30	)	)	PUNCT
ejpam-3010	139	31	∈	∈	PROPN
ejpam-3010	139	32	i.	i.	NOUN
ejpam-3010	139	33	then	then	ADV
ejpam-3010	139	34	n	n	PROPN
ejpam-3010	139	35	⊆	⊆	NUM
ejpam-3010	139	36	i	i	PRON
ejpam-3010	139	37	,	,	PUNCT
ejpam-3010	139	38	on	on	ADP
ejpam-3010	139	39	the	the	DET
ejpam-3010	139	40	other	other	ADJ
ejpam-3010	139	41	hand	hand	NOUN
ejpam-3010	139	42	by	by	ADP
ejpam-3010	139	43	lemma	lemma	PROPN
ejpam-3010	139	44	4	4	NUM
ejpam-3010	139	45	,	,	PUNCT
ejpam-3010	139	46	we	we	PRON
ejpam-3010	139	47	have	have	VERB
ejpam-3010	139	48	i	i	PRON
ejpam-3010	139	49	⊆	⊆	NUM
ejpam-3010	139	50	n	n	NOUN
ejpam-3010	139	51	,	,	PUNCT
ejpam-3010	139	52	thus	thus	ADV
ejpam-3010	139	53	i	i	PRON
ejpam-3010	139	54	=	=	SYM
ejpam-3010	139	55	n	n	X
ejpam-3010	139	56	.	.	PUNCT
ejpam-3010	140	1	(	(	PUNCT
ejpam-3010	140	2	4	4	X
ejpam-3010	140	3	)	)	PUNCT
ejpam-3010	140	4	=	=	NOUN
ejpam-3010	140	5	⇒	⇒	NOUN
ejpam-3010	140	6	(	(	PUNCT
ejpam-3010	140	7	5	5	NUM
ejpam-3010	140	8	)	)	PUNCT
ejpam-3010	140	9	.	.	PUNCT
ejpam-3010	141	1	let	let	VERB
ejpam-3010	141	2	x	x	PRON
ejpam-3010	141	3	∈m	∈m	NOUN
ejpam-3010	141	4	.	.	PUNCT
ejpam-3010	142	1	sincen	sincen	NOUN
ejpam-3010	142	2	is	be	AUX
ejpam-3010	142	3	a	a	DET
ejpam-3010	142	4	semilattice	semilattice	NOUN
ejpam-3010	142	5	congruence	congruence	NOUN
ejpam-3010	142	6	on	on	ADP
ejpam-3010	142	7	m	m	PRON
ejpam-3010	142	8	,	,	PUNCT
ejpam-3010	142	9	(	(	PUNCT
ejpam-3010	142	10	x)n	x)n	X
ejpam-3010	142	11	is	be	AUX
ejpam-3010	142	12	a	a	DET
ejpam-3010	142	13	subsemigroup	subsemigroup	NOUN
ejpam-3010	142	14	of	of	ADP
ejpam-3010	142	15	m	m	PROPN
ejpam-3010	142	16	.	.	PUNCT
ejpam-3010	143	1	let	let	VERB
ejpam-3010	143	2	i	i	PRON
ejpam-3010	143	3	be	be	AUX
ejpam-3010	143	4	an	an	DET
ejpam-3010	143	5	ideal	ideal	NOUN
ejpam-3010	143	6	of	of	ADP
ejpam-3010	143	7	(	(	PUNCT
ejpam-3010	143	8	x)n	x)n	PROPN
ejpam-3010	143	9	.	.	PUNCT
ejpam-3010	144	1	then	then	ADV
ejpam-3010	144	2	i	i	PRON
ejpam-3010	144	3	=	=	PUNCT
ejpam-3010	144	4	(	(	PUNCT
ejpam-3010	144	5	x)n	x)n	PROPN
ejpam-3010	144	6	.	.	PUNCT
ejpam-3010	145	1	indeed	indeed	ADV
ejpam-3010	145	2	:	:	PUNCT
ejpam-3010	145	3	let	let	VERB
ejpam-3010	145	4	y	y	PROPN
ejpam-3010	145	5	∈	∈	PROPN
ejpam-3010	145	6	(	(	PUNCT
ejpam-3010	145	7	x)n	x)n	PROPN
ejpam-3010	145	8	.	.	PUNCT
ejpam-3010	146	1	take	take	VERB
ejpam-3010	146	2	an	an	DET
ejpam-3010	146	3	element	element	NOUN
ejpam-3010	146	4	z	z	NOUN
ejpam-3010	146	5	∈	∈	PROPN
ejpam-3010	147	1	i	i	PRON
ejpam-3010	147	2	and	and	CCONJ
ejpam-3010	147	3	an	an	DET
ejpam-3010	147	4	element	element	NOUN
ejpam-3010	147	5	γ	γ	X
ejpam-3010	147	6	∈	∈	PROPN
ejpam-3010	147	7	γ	γ	X
ejpam-3010	147	8	(	(	PUNCT
ejpam-3010	147	9	i	i	PROPN
ejpam-3010	147	10	,	,	PUNCT
ejpam-3010	147	11	γ	γ	PROPN
ejpam-3010	147	12	6=	6=	NOUN
ejpam-3010	147	13	∅	∅	NOUN
ejpam-3010	147	14	)	)	PUNCT
ejpam-3010	147	15	.	.	PUNCT
ejpam-3010	148	1	since	since	SCONJ
ejpam-3010	148	2	zγzγz	zγzγz	NOUN
ejpam-3010	148	3	∈	∈	PROPN
ejpam-3010	148	4	(	(	PUNCT
ejpam-3010	148	5	mγm)γm	mγm)γm	NOUN
ejpam-3010	148	6	⊆	⊆	NUM
ejpam-3010	148	7	mγm	mγm	NOUN
ejpam-3010	148	8	⊆	⊆	NUM
ejpam-3010	148	9	m	m	NOUN
ejpam-3010	148	10	,	,	PUNCT
ejpam-3010	148	11	by	by	ADP
ejpam-3010	148	12	lemma	lemma	PROPN
ejpam-3010	148	13	6	6	NUM
ejpam-3010	148	14	,	,	PUNCT
ejpam-3010	148	15	(	(	PUNCT
ejpam-3010	148	16	mγzγzγzγm	mγzγzγzγm	NOUN
ejpam-3010	148	17	]	]	PUNCT
ejpam-3010	148	18	is	be	AUX
ejpam-3010	148	19	an	an	DET
ejpam-3010	148	20	ideal	ideal	NOUN
ejpam-3010	148	21	of	of	ADP
ejpam-3010	148	22	m	m	PRON
ejpam-3010	148	23	.	.	PUNCT
ejpam-3010	149	1	by	by	ADP
ejpam-3010	149	2	hypothesis	hypothesis	NOUN
ejpam-3010	149	3	,	,	PUNCT
ejpam-3010	149	4	we	we	PRON
ejpam-3010	149	5	have	have	VERB
ejpam-3010	149	6	(	(	PUNCT
ejpam-3010	149	7	mγzγzγzγm	mγzγzγzγm	VERB
ejpam-3010	149	8	]	]	PUNCT
ejpam-3010	149	9	=	=	PUNCT
ejpam-3010	149	10	⋃	⋃	VERB
ejpam-3010	149	11	t∈(mγzγzγzγm	t∈(mγzγzγzγm	NOUN
ejpam-3010	149	12	]	]	X
ejpam-3010	149	13	(	(	PUNCT
ejpam-3010	149	14	t)n	t)n	NOUN
ejpam-3010	149	15	.	.	PUNCT
ejpam-3010	150	1	since	since	SCONJ
ejpam-3010	150	2	z	z	PROPN
ejpam-3010	150	3	∈	∈	PROPN
ejpam-3010	150	4	i	i	PRON
ejpam-3010	150	5	⊆	⊆	NUM
ejpam-3010	150	6	(	(	PUNCT
ejpam-3010	150	7	x)n	x)n	PUNCT
ejpam-3010	150	8	,	,	PUNCT
ejpam-3010	150	9	we	we	PRON
ejpam-3010	150	10	have	have	AUX
ejpam-3010	150	11	(	(	PUNCT
ejpam-3010	150	12	x)n	x)n	PUNCT
ejpam-3010	150	13	=	=	SYM
ejpam-3010	150	14	(	(	PUNCT
ejpam-3010	150	15	z)n	z)n	X
ejpam-3010	150	16	.	.	PUNCT
ejpam-3010	151	1	since	since	SCONJ
ejpam-3010	151	2	y	y	PROPN
ejpam-3010	151	3	∈	∈	PROPN
ejpam-3010	151	4	(	(	PUNCT
ejpam-3010	151	5	x)n	x)n	PUNCT
ejpam-3010	151	6	=	=	SYM
ejpam-3010	151	7	(	(	PUNCT
ejpam-3010	151	8	z)n	z)n	X
ejpam-3010	151	9	=	=	SYM
ejpam-3010	151	10	(	(	PUNCT
ejpam-3010	151	11	zγzγzγzγz)n	zγzγzγzγz)n	NUM
ejpam-3010	151	12	⊆	⊆	NUM
ejpam-3010	151	13	(	(	PUNCT
ejpam-3010	151	14	mγzγzγzγm	mγzγzγzγm	NOUN
ejpam-3010	151	15	]	]	PUNCT
ejpam-3010	151	16	,	,	PUNCT
ejpam-3010	151	17	we	we	PRON
ejpam-3010	151	18	have	have	VERB
ejpam-3010	151	19	y	y	NOUN
ejpam-3010	151	20	≤	≤	NOUN
ejpam-3010	151	21	aδzγzγzξb	aδzγzγzξb	NOUN
ejpam-3010	151	22	=	=	SYM
ejpam-3010	151	23	(	(	PUNCT
ejpam-3010	151	24	aδz)γzγ(zξb	aδz)γzγ(zξb	NOUN
ejpam-3010	151	25	)	)	PUNCT
ejpam-3010	151	26	for	for	ADP
ejpam-3010	151	27	some	some	PRON
ejpam-3010	151	28	a	a	DET
ejpam-3010	151	29	,	,	PUNCT
ejpam-3010	151	30	b	b	NOUN
ejpam-3010	151	31	∈m	∈m	NOUN
ejpam-3010	151	32	,	,	PUNCT
ejpam-3010	151	33	δ	δ	PROPN
ejpam-3010	151	34	,	,	PUNCT
ejpam-3010	151	35	ξ	ξ	PROPN
ejpam-3010	151	36	∈	∈	PROPN
ejpam-3010	151	37	γ	γ	X
ejpam-3010	151	38	.	.	PUNCT
ejpam-3010	151	39	using	use	VERB
ejpam-3010	151	40	the	the	DET
ejpam-3010	151	41	fact	fact	NOUN
ejpam-3010	151	42	that	that	SCONJ
ejpam-3010	151	43	n	n	PRON
ejpam-3010	151	44	is	be	AUX
ejpam-3010	151	45	a	a	DET
ejpam-3010	151	46	complete	complete	ADJ
ejpam-3010	151	47	semilattice	semilattice	NOUN
ejpam-3010	151	48	congruence	congruence	NOUN
ejpam-3010	151	49	on	on	ADP
ejpam-3010	151	50	m	m	PROPN
ejpam-3010	151	51	,	,	PUNCT
ejpam-3010	151	52	in	in	ADP
ejpam-3010	151	53	a	a	DET
ejpam-3010	151	54	similar	similar	ADJ
ejpam-3010	151	55	way	way	NOUN
ejpam-3010	151	56	as	as	ADP
ejpam-3010	151	57	in	in	ADP
ejpam-3010	151	58	[	[	X
ejpam-3010	151	59	8	8	NUM
ejpam-3010	151	60	]	]	PUNCT
ejpam-3010	151	61	,	,	PUNCT
ejpam-3010	151	62	we	we	PRON
ejpam-3010	151	63	prove	prove	VERB
ejpam-3010	151	64	that	that	SCONJ
ejpam-3010	151	65	aδz	aδz	PROPN
ejpam-3010	151	66	∈	∈	PROPN
ejpam-3010	151	67	(	(	PUNCT
ejpam-3010	151	68	x)n	x)n	PUNCT
ejpam-3010	151	69	and	and	CCONJ
ejpam-3010	151	70	zξb	zξb	X
ejpam-3010	151	71	∈	∈	PROPN
ejpam-3010	151	72	(	(	PUNCT
ejpam-3010	151	73	x)n	x)n	PROPN
ejpam-3010	151	74	.	.	PUNCT
ejpam-3010	152	1	then	then	ADV
ejpam-3010	152	2	,	,	PUNCT
ejpam-3010	152	3	since	since	SCONJ
ejpam-3010	152	4	i	i	PRON
ejpam-3010	152	5	is	be	AUX
ejpam-3010	152	6	an	an	DET
ejpam-3010	152	7	ideal	ideal	NOUN
ejpam-3010	152	8	of	of	ADP
ejpam-3010	152	9	(	(	PUNCT
ejpam-3010	152	10	x)n	x)n	PUNCT
ejpam-3010	152	11	and	and	CCONJ
ejpam-3010	152	12	z	z	NOUN
ejpam-3010	152	13	∈	∈	PROPN
ejpam-3010	153	1	i	i	PRON
ejpam-3010	153	2	,	,	PUNCT
ejpam-3010	153	3	we	we	PRON
ejpam-3010	153	4	have	have	VERB
ejpam-3010	153	5	we	we	PRON
ejpam-3010	153	6	have	have	VERB
ejpam-3010	153	7	(	(	PUNCT
ejpam-3010	154	1	aδz)γzγ(zξb	aδz)γzγ(zξb	NOUN
ejpam-3010	154	2	)	)	PUNCT
ejpam-3010	154	3	∈	∈	PROPN
ejpam-3010	154	4	(	(	PUNCT
ejpam-3010	154	5	x)nγiγ(x)n	x)nγiγ(x)n	NOUN
ejpam-3010	154	6	⊆	⊆	NUM
ejpam-3010	154	7	i	i	PRON
ejpam-3010	154	8	,	,	PUNCT
ejpam-3010	154	9	and	and	CCONJ
ejpam-3010	154	10	y	y	PROPN
ejpam-3010	154	11	∈	∈	PROPN
ejpam-3010	154	12	i.	i.	NOUN
ejpam-3010	154	13	hence	hence	ADV
ejpam-3010	154	14	(	(	PUNCT
ejpam-3010	154	15	x)n	x)n	PUNCT
ejpam-3010	154	16	⊆	⊆	X
ejpam-3010	154	17	i	i	PRON
ejpam-3010	154	18	,	,	PUNCT
ejpam-3010	154	19	and	and	CCONJ
ejpam-3010	154	20	so	so	ADV
ejpam-3010	154	21	i	i	PRON
ejpam-3010	154	22	=	=	SYM
ejpam-3010	154	23	(	(	PUNCT
ejpam-3010	154	24	x)n	x)n	PROPN
ejpam-3010	154	25	.	.	PUNCT
ejpam-3010	155	1	(	(	PUNCT
ejpam-3010	155	2	6	6	X
ejpam-3010	155	3	)	)	PUNCT
ejpam-3010	155	4	=	=	NOUN
ejpam-3010	155	5	⇒	⇒	NOUN
ejpam-3010	155	6	(	(	PUNCT
ejpam-3010	155	7	7	7	NUM
ejpam-3010	155	8	)	)	PUNCT
ejpam-3010	155	9	.	.	PUNCT
ejpam-3010	156	1	let	let	VERB
ejpam-3010	156	2	σ	σ	NOUN
ejpam-3010	156	3	be	be	AUX
ejpam-3010	156	4	a	a	DET
ejpam-3010	156	5	semilattice	semilattice	NOUN
ejpam-3010	156	6	congruence	congruence	NOUN
ejpam-3010	156	7	on	on	ADP
ejpam-3010	156	8	m	m	PRON
ejpam-3010	156	9	such	such	ADJ
ejpam-3010	156	10	that	that	SCONJ
ejpam-3010	156	11	(	(	PUNCT
ejpam-3010	156	12	x)σ	x)σ	X
ejpam-3010	156	13	is	be	AUX
ejpam-3010	156	14	a	a	DET
ejpam-3010	156	15	simple	simple	ADJ
ejpam-3010	156	16	subsemigroup	subsemigroup	NOUN
ejpam-3010	156	17	of	of	ADP
ejpam-3010	156	18	m	m	PROPN
ejpam-3010	156	19	for	for	ADP
ejpam-3010	156	20	every	every	DET
ejpam-3010	156	21	x	x	SYM
ejpam-3010	156	22	∈	∈	PROPN
ejpam-3010	156	23	m	m	VERB
ejpam-3010	156	24	.	.	PUNCT
ejpam-3010	157	1	let	let	VERB
ejpam-3010	157	2	i	i	PRON
ejpam-3010	157	3	be	be	AUX
ejpam-3010	157	4	an	an	DET
ejpam-3010	157	5	ideal	ideal	NOUN
ejpam-3010	157	6	of	of	ADP
ejpam-3010	157	7	m	m	PRON
ejpam-3010	157	8	,	,	PUNCT
ejpam-3010	157	9	x	x	PUNCT
ejpam-3010	157	10	∈	∈	PROPN
ejpam-3010	157	11	m	m	NOUN
ejpam-3010	157	12	and	and	CCONJ
ejpam-3010	157	13	γ	γ	PROPN
ejpam-3010	157	14	∈	∈	PROPN
ejpam-3010	157	15	γ	γ	NOUN
ejpam-3010	157	16	such	such	ADJ
ejpam-3010	157	17	that	that	DET
ejpam-3010	157	18	xγx	xγx	NOUN
ejpam-3010	157	19	∈	∈	PROPN
ejpam-3010	157	20	i.	i.	NOUN
ejpam-3010	157	21	the	the	DET
ejpam-3010	157	22	set	set	NOUN
ejpam-3010	157	23	i	i	PRON
ejpam-3010	157	24	∩	∩	NOUN
ejpam-3010	157	25	(	(	PUNCT
ejpam-3010	157	26	x)σ	x)σ	X
ejpam-3010	157	27	is	be	AUX
ejpam-3010	157	28	an	an	DET
ejpam-3010	157	29	ideal	ideal	NOUN
ejpam-3010	157	30	of	of	ADP
ejpam-3010	157	31	(	(	PUNCT
ejpam-3010	157	32	x)σ	x)σ	PROPN
ejpam-3010	157	33	.	.	PUNCT
ejpam-3010	158	1	indeed	indeed	ADV
ejpam-3010	158	2	:	:	PUNCT
ejpam-3010	158	3	taking	take	VERB
ejpam-3010	158	4	into	into	ADP
ejpam-3010	158	5	account	account	NOUN
ejpam-3010	158	6	the	the	DET
ejpam-3010	158	7	proof	proof	NOUN
ejpam-3010	158	8	of	of	ADP
ejpam-3010	158	9	the	the	DET
ejpam-3010	158	10	implication	implication	NOUN
ejpam-3010	158	11	(	(	PUNCT
ejpam-3010	158	12	6)⇒	6)⇒	NUM
ejpam-3010	158	13	(	(	PUNCT
ejpam-3010	158	14	7	7	NUM
ejpam-3010	158	15	)	)	PUNCT
ejpam-3010	158	16	in	in	ADP
ejpam-3010	158	17	[	[	X
ejpam-3010	158	18	8	8	NUM
ejpam-3010	158	19	]	]	PUNCT
ejpam-3010	158	20	,	,	PUNCT
ejpam-3010	158	21	it	it	PRON
ejpam-3010	158	22	is	be	AUX
ejpam-3010	158	23	enough	enough	ADJ
ejpam-3010	158	24	to	to	PART
ejpam-3010	158	25	prove	prove	VERB
ejpam-3010	158	26	the	the	DET
ejpam-3010	158	27	following	following	NOUN
ejpam-3010	158	28	:	:	PUNCT
ejpam-3010	158	29	let	let	VERB
ejpam-3010	158	30	a	a	DET
ejpam-3010	158	31	∈	∈	NOUN
ejpam-3010	158	32	i	i	PRON
ejpam-3010	158	33	∩	∩	NOUN
ejpam-3010	158	34	(	(	PUNCT
ejpam-3010	158	35	x)σ	x)σ	PUNCT
ejpam-3010	158	36	and	and	CCONJ
ejpam-3010	158	37	n.	n.	PROPN
ejpam-3010	158	38	kehayopulu	kehayopulu	PROPN
ejpam-3010	158	39	/	/	SYM
ejpam-3010	158	40	eur	eur	PROPN
ejpam-3010	158	41	.	.	PUNCT
ejpam-3010	159	1	j.	j.	PROPN
ejpam-3010	159	2	pure	pure	PROPN
ejpam-3010	159	3	appl	appl	PROPN
ejpam-3010	159	4	.	.	PROPN
ejpam-3010	159	5	math	math	PROPN
ejpam-3010	159	6	,	,	PUNCT
ejpam-3010	159	7	10	10	NUM
ejpam-3010	159	8	(	(	PUNCT
ejpam-3010	159	9	4	4	NUM
ejpam-3010	159	10	)	)	PUNCT
ejpam-3010	159	11	(	(	PUNCT
ejpam-3010	159	12	2017	2017	NUM
ejpam-3010	159	13	)	)	PUNCT
ejpam-3010	159	14	,	,	PUNCT
ejpam-3010	159	15	620	620	NUM
ejpam-3010	159	16	-	-	SYM
ejpam-3010	159	17	630	630	NUM
ejpam-3010	159	18	625	625	NUM
ejpam-3010	159	19	(	(	PUNCT
ejpam-3010	159	20	x)σ	x)σ	PROPN
ejpam-3010	159	21	3	3	NUM
ejpam-3010	159	22	b	b	X
ejpam-3010	159	23	≤	≤	NUM
ejpam-3010	159	24	a	a	PRON
ejpam-3010	159	25	,	,	PUNCT
ejpam-3010	159	26	then	then	ADV
ejpam-3010	159	27	b	b	PROPN
ejpam-3010	159	28	∈	∈	PROPN
ejpam-3010	159	29	i∩(x)σ	i∩(x)σ	PROPN
ejpam-3010	159	30	.	.	PUNCT
ejpam-3010	160	1	since	since	SCONJ
ejpam-3010	160	2	m	m	PROPN
ejpam-3010	160	3	∈	∈	PROPN
ejpam-3010	160	4	b	b	PROPN
ejpam-3010	160	5	≤	≤	NOUN
ejpam-3010	160	6	a	a	DET
ejpam-3010	160	7	∈	∈	NOUN
ejpam-3010	161	1	i	i	PRON
ejpam-3010	161	2	and	and	CCONJ
ejpam-3010	161	3	i	i	PRON
ejpam-3010	161	4	is	be	AUX
ejpam-3010	161	5	an	an	DET
ejpam-3010	161	6	ideal	ideal	NOUN
ejpam-3010	161	7	of	of	ADP
ejpam-3010	161	8	m	m	PROPN
ejpam-3010	161	9	,	,	PUNCT
ejpam-3010	161	10	we	we	PRON
ejpam-3010	161	11	have	have	VERB
ejpam-3010	161	12	b	b	NUM
ejpam-3010	161	13	∈	∈	PROPN
ejpam-3010	161	14	i	i	PRON
ejpam-3010	161	15	,	,	PUNCT
ejpam-3010	161	16	then	then	ADV
ejpam-3010	161	17	b	b	X
ejpam-3010	161	18	∈	∈	PROPN
ejpam-3010	161	19	i	i	PRON
ejpam-3010	161	20	∩	∩	NOUN
ejpam-3010	161	21	(	(	PUNCT
ejpam-3010	161	22	x)σ	x)σ	PROPN
ejpam-3010	161	23	.	.	PUNCT
ejpam-3010	162	1	since	since	SCONJ
ejpam-3010	162	2	(	(	PUNCT
ejpam-3010	162	3	x)σ	x)σ	X
ejpam-3010	162	4	is	be	AUX
ejpam-3010	162	5	a	a	DET
ejpam-3010	162	6	simple	simple	ADJ
ejpam-3010	162	7	subsemigroup	subsemigroup	NOUN
ejpam-3010	162	8	of	of	ADP
ejpam-3010	162	9	m	m	PROPN
ejpam-3010	162	10	,	,	PUNCT
ejpam-3010	162	11	we	we	PRON
ejpam-3010	162	12	have	have	VERB
ejpam-3010	162	13	i	i	PRON
ejpam-3010	162	14	∩	∩	NOUN
ejpam-3010	162	15	(	(	PUNCT
ejpam-3010	162	16	x)σ	x)σ	X
ejpam-3010	162	17	=	=	SYM
ejpam-3010	162	18	(	(	PUNCT
ejpam-3010	162	19	x)σ	x)σ	ADJ
ejpam-3010	162	20	,	,	PUNCT
ejpam-3010	162	21	then	then	ADV
ejpam-3010	162	22	x	x	PART
ejpam-3010	162	23	∈	∈	PROPN
ejpam-3010	162	24	i.	i.	NOUN
ejpam-3010	162	25	thus	thus	ADV
ejpam-3010	162	26	m	m	VERB
ejpam-3010	162	27	is	be	AUX
ejpam-3010	162	28	semiprime	semiprime	NOUN
ejpam-3010	162	29	.	.	PUNCT
ejpam-3010	163	1	�	�	PROPN
ejpam-3010	163	2	lemma	lemma	PROPN
ejpam-3010	163	3	9	9	X
ejpam-3010	163	4	.	.	PUNCT
ejpam-3010	164	1	let	let	VERB
ejpam-3010	164	2	m	m	PRON
ejpam-3010	164	3	be	be	AUX
ejpam-3010	164	4	a	a	DET
ejpam-3010	164	5	po	po	NOUN
ejpam-3010	164	6	-	-	PUNCT
ejpam-3010	164	7	γ	γ	NOUN
ejpam-3010	164	8	-	-	PUNCT
ejpam-3010	164	9	semigroup	semigroup	NOUN
ejpam-3010	164	10	.	.	PUNCT
ejpam-3010	165	1	the	the	DET
ejpam-3010	165	2	ideals	ideal	NOUN
ejpam-3010	165	3	of	of	ADP
ejpam-3010	165	4	m	m	NOUN
ejpam-3010	165	5	are	be	AUX
ejpam-3010	165	6	idempotent	idempotent	ADJ
ejpam-3010	165	7	if	if	SCONJ
ejpam-3010	165	8	and	and	CCONJ
ejpam-3010	165	9	only	only	ADV
ejpam-3010	165	10	if	if	SCONJ
ejpam-3010	165	11	for	for	ADP
ejpam-3010	165	12	any	any	DET
ejpam-3010	165	13	ideals	ideal	NOUN
ejpam-3010	165	14	a	a	DET
ejpam-3010	165	15	,	,	PUNCT
ejpam-3010	165	16	b	b	PROPN
ejpam-3010	165	17	of	of	ADP
ejpam-3010	165	18	m	m	PROPN
ejpam-3010	165	19	,	,	PUNCT
ejpam-3010	165	20	we	we	PRON
ejpam-3010	165	21	have	have	VERB
ejpam-3010	165	22	a	a	DET
ejpam-3010	165	23	∩b	∩b	NOUN
ejpam-3010	165	24	=	=	PUNCT
ejpam-3010	165	25	(	(	PUNCT
ejpam-3010	165	26	aγb	aγb	NOUN
ejpam-3010	165	27	]	]	PUNCT
ejpam-3010	165	28	.	.	PUNCT
ejpam-3010	166	1	proof	proof	NOUN
ejpam-3010	166	2	.	.	PUNCT
ejpam-3010	167	1	=	=	NOUN
ejpam-3010	167	2	⇒.	⇒.	NOUN
ejpam-3010	167	3	let	let	VERB
ejpam-3010	167	4	a	a	DET
ejpam-3010	167	5	,	,	PUNCT
ejpam-3010	167	6	b	b	NOUN
ejpam-3010	167	7	be	be	AUX
ejpam-3010	167	8	ideals	ideal	NOUN
ejpam-3010	167	9	of	of	ADP
ejpam-3010	167	10	m	m	PROPN
ejpam-3010	167	11	.	.	PUNCT
ejpam-3010	168	1	then	then	ADV
ejpam-3010	168	2	(	(	PUNCT
ejpam-3010	168	3	aγb	aγb	NOUN
ejpam-3010	168	4	]	]	X
ejpam-3010	168	5	⊆	⊆	NUM
ejpam-3010	168	6	(	(	PUNCT
ejpam-3010	168	7	aγm	aγm	NOUN
ejpam-3010	168	8	]	]	PUNCT
ejpam-3010	168	9	⊆	⊆	NUM
ejpam-3010	168	10	(	(	PUNCT
ejpam-3010	168	11	a	a	X
ejpam-3010	168	12	]	]	X
ejpam-3010	168	13	=	=	PUNCT
ejpam-3010	168	14	a	a	PROPN
ejpam-3010	168	15	and	and	CCONJ
ejpam-3010	168	16	(	(	PUNCT
ejpam-3010	168	17	aγb	aγb	NOUN
ejpam-3010	168	18	]	]	X
ejpam-3010	168	19	⊆	⊆	NUM
ejpam-3010	168	20	(	(	PUNCT
ejpam-3010	168	21	mγb	mγb	VERB
ejpam-3010	168	22	]	]	X
ejpam-3010	168	23	⊆	⊆	NUM
ejpam-3010	168	24	(	(	PUNCT
ejpam-3010	168	25	b	b	NOUN
ejpam-3010	168	26	]	]	X
ejpam-3010	168	27	=	=	SYM
ejpam-3010	168	28	b	b	NOUN
ejpam-3010	168	29	,	,	PUNCT
ejpam-3010	168	30	thus	thus	ADV
ejpam-3010	168	31	(	(	PUNCT
ejpam-3010	168	32	aγb	aγb	NOUN
ejpam-3010	168	33	]	]	X
ejpam-3010	168	34	⊆	⊆	NUM
ejpam-3010	168	35	a	a	DET
ejpam-3010	168	36	∩	∩	ADJ
ejpam-3010	168	37	b.	b.	NOUN
ejpam-3010	168	38	on	on	ADP
ejpam-3010	168	39	the	the	DET
ejpam-3010	168	40	other	other	ADJ
ejpam-3010	168	41	hand	hand	NOUN
ejpam-3010	168	42	,	,	PUNCT
ejpam-3010	168	43	a	a	DET
ejpam-3010	168	44	∩	∩	ADJ
ejpam-3010	168	45	b	b	NOUN
ejpam-3010	168	46	is	be	AUX
ejpam-3010	168	47	an	an	DET
ejpam-3010	168	48	ideal	ideal	NOUN
ejpam-3010	168	49	of	of	ADP
ejpam-3010	168	50	m	m	PROPN
ejpam-3010	168	51	.	.	PUNCT
ejpam-3010	169	1	indeed	indeed	ADV
ejpam-3010	169	2	:	:	PUNCT
ejpam-3010	169	3	take	take	VERB
ejpam-3010	169	4	an	an	DET
ejpam-3010	169	5	element	element	NOUN
ejpam-3010	169	6	a	a	DET
ejpam-3010	169	7	∈	∈	PROPN
ejpam-3010	169	8	a	a	PRON
ejpam-3010	169	9	,	,	PUNCT
ejpam-3010	169	10	an	an	DET
ejpam-3010	169	11	element	element	NOUN
ejpam-3010	169	12	b	b	PROPN
ejpam-3010	169	13	∈	∈	PROPN
ejpam-3010	169	14	b	b	PROPN
ejpam-3010	169	15	and	and	CCONJ
ejpam-3010	169	16	an	an	DET
ejpam-3010	169	17	element	element	NOUN
ejpam-3010	169	18	γ	γ	X
ejpam-3010	169	19	∈	∈	PROPN
ejpam-3010	169	20	γ	γ	X
ejpam-3010	169	21	(	(	PUNCT
ejpam-3010	169	22	a	a	PROPN
ejpam-3010	169	23	,	,	PUNCT
ejpam-3010	169	24	b	b	NOUN
ejpam-3010	169	25	,	,	PUNCT
ejpam-3010	169	26	γ	γ	NOUN
ejpam-3010	169	27	6=	6=	NOUN
ejpam-3010	169	28	∅	∅	NOUN
ejpam-3010	169	29	)	)	PUNCT
ejpam-3010	169	30	.	.	PUNCT
ejpam-3010	170	1	then	then	ADV
ejpam-3010	170	2	aγb	aγb	ADV
ejpam-3010	170	3	∈	∈	PROPN
ejpam-3010	170	4	aγb	aγb	VERB
ejpam-3010	170	5	⊆	⊆	NUM
ejpam-3010	170	6	aγm	aγm	NOUN
ejpam-3010	170	7	⊆	⊆	NUM
ejpam-3010	170	8	a	a	PRON
ejpam-3010	170	9	and	and	CCONJ
ejpam-3010	170	10	aγb	aγb	NOUN
ejpam-3010	170	11	∈	∈	PROPN
ejpam-3010	170	12	aγb	aγb	VERB
ejpam-3010	170	13	⊆mγb	⊆mγb	NUM
ejpam-3010	170	14	⊆	⊆	NUM
ejpam-3010	170	15	b	b	NOUN
ejpam-3010	170	16	,	,	PUNCT
ejpam-3010	170	17	so	so	SCONJ
ejpam-3010	170	18	aγb	aγb	NOUN
ejpam-3010	170	19	∈	∈	PROPN
ejpam-3010	170	20	a∩b	a∩b	PROPN
ejpam-3010	170	21	,	,	PUNCT
ejpam-3010	170	22	so	so	ADV
ejpam-3010	170	23	a∩b	a∩b	PROPN
ejpam-3010	170	24	is	be	AUX
ejpam-3010	170	25	a	a	DET
ejpam-3010	170	26	nonempty	nonempty	ADJ
ejpam-3010	170	27	subset	subset	NOUN
ejpam-3010	170	28	of	of	ADP
ejpam-3010	170	29	m	m	PROPN
ejpam-3010	170	30	.	.	PUNCT
ejpam-3010	171	1	we	we	PRON
ejpam-3010	171	2	also	also	ADV
ejpam-3010	171	3	have	have	VERB
ejpam-3010	171	4	(	(	PUNCT
ejpam-3010	171	5	a∩b)γm	a∩b)γm	NOUN
ejpam-3010	171	6	⊆	⊆	NUM
ejpam-3010	171	7	aγm	aγm	NOUN
ejpam-3010	171	8	⊆	⊆	NUM
ejpam-3010	171	9	a	a	DET
ejpam-3010	171	10	,	,	PUNCT
ejpam-3010	171	11	mγ(a∩b	mγ(a∩b	NOUN
ejpam-3010	171	12	)	)	PUNCT
ejpam-3010	171	13	⊆mγb	⊆mγb	NOUN
ejpam-3010	171	14	⊆	⊆	NUM
ejpam-3010	171	15	b	b	NOUN
ejpam-3010	171	16	,	,	PUNCT
ejpam-3010	171	17	and	and	CCONJ
ejpam-3010	171	18	if	if	SCONJ
ejpam-3010	171	19	x	x	SYM
ejpam-3010	171	20	∈	∈	PROPN
ejpam-3010	171	21	a	a	DET
ejpam-3010	171	22	∩	∩	ADJ
ejpam-3010	171	23	b	b	PROPN
ejpam-3010	171	24	and	and	CCONJ
ejpam-3010	171	25	m	m	PROPN
ejpam-3010	171	26	3	3	NUM
ejpam-3010	171	27	y	y	NOUN
ejpam-3010	171	28	≤	≤	NUM
ejpam-3010	171	29	x	x	PUNCT
ejpam-3010	171	30	then	then	ADV
ejpam-3010	171	31	,	,	PUNCT
ejpam-3010	171	32	since	since	SCONJ
ejpam-3010	171	33	x	x	PROPN
ejpam-3010	171	34	∈	∈	PROPN
ejpam-3010	171	35	a	a	PRON
ejpam-3010	171	36	we	we	PRON
ejpam-3010	171	37	have	have	VERB
ejpam-3010	171	38	y	y	PROPN
ejpam-3010	171	39	∈	∈	PROPN
ejpam-3010	171	40	a	a	PRON
ejpam-3010	171	41	and	and	CCONJ
ejpam-3010	171	42	since	since	SCONJ
ejpam-3010	171	43	x	x	PROPN
ejpam-3010	171	44	∈	∈	PROPN
ejpam-3010	171	45	b	b	NOUN
ejpam-3010	171	46	we	we	PRON
ejpam-3010	171	47	have	have	VERB
ejpam-3010	171	48	y	y	PROPN
ejpam-3010	171	49	∈	∈	PROPN
ejpam-3010	171	50	b	b	PROPN
ejpam-3010	171	51	,	,	PUNCT
ejpam-3010	171	52	so	so	ADV
ejpam-3010	171	53	y	y	PROPN
ejpam-3010	171	54	∈	∈	PROPN
ejpam-3010	171	55	a	a	DET
ejpam-3010	171	56	∩	∩	X
ejpam-3010	171	57	b.	b.	NOUN
ejpam-3010	171	58	since	since	SCONJ
ejpam-3010	171	59	a	a	DET
ejpam-3010	171	60	∩	∩	ADJ
ejpam-3010	171	61	b	b	NOUN
ejpam-3010	171	62	is	be	AUX
ejpam-3010	171	63	an	an	DET
ejpam-3010	171	64	ideal	ideal	NOUN
ejpam-3010	171	65	of	of	ADP
ejpam-3010	171	66	m	m	PRON
ejpam-3010	171	67	,	,	PUNCT
ejpam-3010	171	68	by	by	ADP
ejpam-3010	171	69	hypothesis	hypothesis	NOUN
ejpam-3010	171	70	,	,	PUNCT
ejpam-3010	171	71	we	we	PRON
ejpam-3010	171	72	have	have	VERB
ejpam-3010	171	73	a	a	DET
ejpam-3010	171	74	∩b	∩b	NOUN
ejpam-3010	171	75	=	=	SYM
ejpam-3010	171	76	(	(	PUNCT
ejpam-3010	171	77	(	(	PUNCT
ejpam-3010	171	78	a	a	DET
ejpam-3010	171	79	∩b)γ(a	∩b)γ(a	ADJ
ejpam-3010	171	80	∩b	∩b	NOUN
ejpam-3010	171	81	)	)	PUNCT
ejpam-3010	171	82	]	]	PUNCT
ejpam-3010	172	1	⊆	⊆	X
ejpam-3010	172	2	(	(	PUNCT
ejpam-3010	172	3	aγb	aγb	NOUN
ejpam-3010	172	4	]	]	PUNCT
ejpam-3010	172	5	.	.	PUNCT
ejpam-3010	173	1	hence	hence	ADV
ejpam-3010	173	2	we	we	PRON
ejpam-3010	173	3	have	have	VERB
ejpam-3010	173	4	a	a	DET
ejpam-3010	173	5	∩b	∩b	NOUN
ejpam-3010	173	6	=	=	PUNCT
ejpam-3010	173	7	(	(	PUNCT
ejpam-3010	173	8	aγb	aγb	NOUN
ejpam-3010	173	9	]	]	PUNCT
ejpam-3010	173	10	.	.	PUNCT
ejpam-3010	174	1	⇐	⇐	PROPN
ejpam-3010	174	2	=	=	PRON
ejpam-3010	174	3	.	.	PUNCT
ejpam-3010	175	1	let	let	VERB
ejpam-3010	175	2	a	a	PRON
ejpam-3010	175	3	be	be	AUX
ejpam-3010	175	4	an	an	DET
ejpam-3010	175	5	ideal	ideal	NOUN
ejpam-3010	175	6	of	of	ADP
ejpam-3010	175	7	m	m	PRON
ejpam-3010	175	8	.	.	PUNCT
ejpam-3010	176	1	by	by	ADP
ejpam-3010	176	2	hypothesis	hypothesis	NOUN
ejpam-3010	176	3	,	,	PUNCT
ejpam-3010	176	4	we	we	PRON
ejpam-3010	176	5	have	have	VERB
ejpam-3010	176	6	a	a	DET
ejpam-3010	176	7	=	=	X
ejpam-3010	176	8	(	(	PUNCT
ejpam-3010	176	9	aγa	aγa	NOUN
ejpam-3010	176	10	]	]	PUNCT
ejpam-3010	176	11	,	,	PUNCT
ejpam-3010	176	12	so	so	CCONJ
ejpam-3010	176	13	a	a	PRON
ejpam-3010	176	14	is	be	AUX
ejpam-3010	176	15	idempotent	idempotent	ADJ
ejpam-3010	176	16	.	.	PUNCT
ejpam-3010	177	1	�	�	PROPN
ejpam-3010	177	2	theorem	theorem	VERB
ejpam-3010	177	3	10	10	NUM
ejpam-3010	177	4	.	.	PUNCT
ejpam-3010	178	1	let	let	VERB
ejpam-3010	178	2	m	m	PRON
ejpam-3010	178	3	be	be	AUX
ejpam-3010	178	4	a	a	DET
ejpam-3010	178	5	po	po	NOUN
ejpam-3010	178	6	-	-	PUNCT
ejpam-3010	178	7	γ	γ	NOUN
ejpam-3010	178	8	-	-	PUNCT
ejpam-3010	178	9	semigroup	semigroup	NOUN
ejpam-3010	178	10	.	.	PUNCT
ejpam-3010	179	1	the	the	DET
ejpam-3010	179	2	ideals	ideal	NOUN
ejpam-3010	179	3	of	of	ADP
ejpam-3010	179	4	m	m	NOUN
ejpam-3010	179	5	are	be	AUX
ejpam-3010	179	6	weakly	weakly	ADV
ejpam-3010	179	7	prime	prime	ADJ
ejpam-3010	179	8	if	if	SCONJ
ejpam-3010	180	1	and	and	CCONJ
ejpam-3010	180	2	only	only	ADV
ejpam-3010	180	3	if	if	SCONJ
ejpam-3010	180	4	they	they	PRON
ejpam-3010	180	5	are	be	AUX
ejpam-3010	180	6	idempotent	idempotent	ADJ
ejpam-3010	180	7	and	and	CCONJ
ejpam-3010	180	8	they	they	PRON
ejpam-3010	180	9	form	form	VERB
ejpam-3010	180	10	a	a	DET
ejpam-3010	180	11	chain	chain	NOUN
ejpam-3010	180	12	.	.	PUNCT
ejpam-3010	181	1	proof	proof	NOUN
ejpam-3010	181	2	.	.	PUNCT
ejpam-3010	182	1	=	=	NOUN
ejpam-3010	182	2	⇒.	⇒.	NOUN
ejpam-3010	182	3	let	let	VERB
ejpam-3010	182	4	a	a	DET
ejpam-3010	182	5	,	,	PUNCT
ejpam-3010	182	6	b	b	NOUN
ejpam-3010	182	7	be	be	AUX
ejpam-3010	182	8	ideals	ideal	NOUN
ejpam-3010	182	9	of	of	ADP
ejpam-3010	182	10	m	m	PROPN
ejpam-3010	182	11	.	.	PUNCT
ejpam-3010	183	1	one	one	PRON
ejpam-3010	183	2	can	can	AUX
ejpam-3010	183	3	easily	easily	ADV
ejpam-3010	183	4	prove	prove	VERB
ejpam-3010	183	5	that	that	SCONJ
ejpam-3010	183	6	(	(	PUNCT
ejpam-3010	183	7	aγb	aγb	NOUN
ejpam-3010	183	8	]	]	X
ejpam-3010	183	9	is	be	AUX
ejpam-3010	183	10	an	an	DET
ejpam-3010	183	11	ideal	ideal	NOUN
ejpam-3010	183	12	of	of	ADP
ejpam-3010	183	13	m	m	PROPN
ejpam-3010	183	14	.	.	PUNCT
ejpam-3010	184	1	since	since	SCONJ
ejpam-3010	184	2	a	a	DET
ejpam-3010	184	3	,	,	PUNCT
ejpam-3010	184	4	b	b	NOUN
ejpam-3010	184	5	,	,	PUNCT
ejpam-3010	184	6	(	(	PUNCT
ejpam-3010	184	7	aγb	aγb	NOUN
ejpam-3010	184	8	]	]	X
ejpam-3010	184	9	are	be	AUX
ejpam-3010	184	10	ideals	ideal	NOUN
ejpam-3010	184	11	of	of	ADP
ejpam-3010	184	12	m	m	PROPN
ejpam-3010	184	13	,	,	PUNCT
ejpam-3010	184	14	aγb	aγb	ADV
ejpam-3010	184	15	⊆	⊆	NUM
ejpam-3010	184	16	(	(	PUNCT
ejpam-3010	184	17	aγb	aγb	NOUN
ejpam-3010	184	18	]	]	X
ejpam-3010	184	19	and	and	CCONJ
ejpam-3010	184	20	(	(	PUNCT
ejpam-3010	184	21	aγb	aγb	NOUN
ejpam-3010	184	22	]	]	X
ejpam-3010	184	23	is	be	AUX
ejpam-3010	184	24	weakly	weakly	ADV
ejpam-3010	184	25	prime	prime	ADJ
ejpam-3010	184	26	,	,	PUNCT
ejpam-3010	184	27	we	we	PRON
ejpam-3010	184	28	have	have	VERB
ejpam-3010	184	29	a	a	DET
ejpam-3010	184	30	⊆	⊆	NUM
ejpam-3010	184	31	(	(	PUNCT
ejpam-3010	184	32	aγb	aγb	NOUN
ejpam-3010	184	33	]	]	X
ejpam-3010	184	34	⊆	⊆	NUM
ejpam-3010	184	35	(	(	PUNCT
ejpam-3010	184	36	mγb	mγb	VERB
ejpam-3010	184	37	]	]	X
ejpam-3010	184	38	⊆	⊆	NUM
ejpam-3010	184	39	(	(	PUNCT
ejpam-3010	184	40	b	b	NOUN
ejpam-3010	184	41	]	]	X
ejpam-3010	184	42	=	=	SYM
ejpam-3010	184	43	b	b	PROPN
ejpam-3010	184	44	or	or	CCONJ
ejpam-3010	184	45	b	b	NOUN
ejpam-3010	184	46	⊆	⊆	NUM
ejpam-3010	184	47	(	(	PUNCT
ejpam-3010	184	48	aγb	aγb	NOUN
ejpam-3010	184	49	]	]	X
ejpam-3010	184	50	⊆	⊆	NUM
ejpam-3010	184	51	(	(	PUNCT
ejpam-3010	184	52	aγm	aγm	NOUN
ejpam-3010	184	53	]	]	PUNCT
ejpam-3010	184	54	⊆	⊆	NUM
ejpam-3010	184	55	(	(	PUNCT
ejpam-3010	184	56	a	a	X
ejpam-3010	184	57	]	]	X
ejpam-3010	184	58	=	=	SYM
ejpam-3010	184	59	a	a	X
ejpam-3010	184	60	,	,	PUNCT
ejpam-3010	184	61	thus	thus	ADV
ejpam-3010	184	62	the	the	DET
ejpam-3010	184	63	ideals	ideal	NOUN
ejpam-3010	184	64	of	of	ADP
ejpam-3010	184	65	m	m	PROPN
ejpam-3010	184	66	form	form	VERB
ejpam-3010	184	67	a	a	DET
ejpam-3010	184	68	chain	chain	NOUN
ejpam-3010	184	69	.	.	PUNCT
ejpam-3010	185	1	furthermore	furthermore	ADV
ejpam-3010	185	2	,	,	PUNCT
ejpam-3010	185	3	since	since	SCONJ
ejpam-3010	185	4	a	a	PRON
ejpam-3010	185	5	and	and	CCONJ
ejpam-3010	185	6	(	(	PUNCT
ejpam-3010	185	7	aγa	aγa	PROPN
ejpam-3010	185	8	]	]	X
ejpam-3010	185	9	are	be	AUX
ejpam-3010	185	10	ideals	ideal	NOUN
ejpam-3010	185	11	of	of	ADP
ejpam-3010	185	12	m	m	PRON
ejpam-3010	185	13	,	,	PUNCT
ejpam-3010	185	14	aγa	aγa	VERB
ejpam-3010	185	15	⊆	⊆	NUM
ejpam-3010	185	16	(	(	PUNCT
ejpam-3010	185	17	aγa	aγa	NOUN
ejpam-3010	185	18	]	]	PUNCT
ejpam-3010	185	19	and	and	CCONJ
ejpam-3010	185	20	(	(	PUNCT
ejpam-3010	185	21	aγa	aγa	PROPN
ejpam-3010	185	22	]	]	X
ejpam-3010	185	23	is	be	AUX
ejpam-3010	185	24	weakly	weakly	ADV
ejpam-3010	185	25	prime	prime	ADJ
ejpam-3010	185	26	,	,	PUNCT
ejpam-3010	185	27	we	we	PRON
ejpam-3010	185	28	have	have	VERB
ejpam-3010	185	29	a	a	DET
ejpam-3010	185	30	⊆	⊆	NUM
ejpam-3010	185	31	(	(	PUNCT
ejpam-3010	185	32	aγa	aγa	NOUN
ejpam-3010	185	33	]	]	X
ejpam-3010	185	34	⊆	⊆	NUM
ejpam-3010	185	35	(	(	PUNCT
ejpam-3010	185	36	mγa	mγa	PROPN
ejpam-3010	185	37	]	]	PUNCT
ejpam-3010	185	38	⊆	⊆	NUM
ejpam-3010	185	39	(	(	PUNCT
ejpam-3010	185	40	a	a	X
ejpam-3010	185	41	]	]	X
ejpam-3010	185	42	=	=	SYM
ejpam-3010	185	43	a	a	NOUN
ejpam-3010	185	44	,	,	PUNCT
ejpam-3010	185	45	thus	thus	ADV
ejpam-3010	185	46	we	we	PRON
ejpam-3010	185	47	get	get	VERB
ejpam-3010	185	48	a	a	DET
ejpam-3010	185	49	=	=	X
ejpam-3010	185	50	(	(	PUNCT
ejpam-3010	185	51	aγa	aγa	NOUN
ejpam-3010	185	52	]	]	X
ejpam-3010	185	53	,	,	PUNCT
ejpam-3010	185	54	and	and	CCONJ
ejpam-3010	185	55	a	a	PRON
ejpam-3010	185	56	is	be	AUX
ejpam-3010	185	57	idempotent	idempotent	ADJ
ejpam-3010	185	58	.	.	PUNCT
ejpam-3010	186	1	⇐	⇐	PROPN
ejpam-3010	186	2	=	=	PRON
ejpam-3010	186	3	.	.	PUNCT
ejpam-3010	187	1	let	let	VERB
ejpam-3010	187	2	a	a	DET
ejpam-3010	187	3	,	,	PUNCT
ejpam-3010	187	4	b	b	NOUN
ejpam-3010	187	5	,	,	PUNCT
ejpam-3010	187	6	t	t	PROPN
ejpam-3010	187	7	be	be	AUX
ejpam-3010	187	8	ideals	ideal	NOUN
ejpam-3010	187	9	of	of	ADP
ejpam-3010	187	10	m	m	NOUN
ejpam-3010	187	11	such	such	ADJ
ejpam-3010	187	12	that	that	SCONJ
ejpam-3010	187	13	aγb	aγb	ADV
ejpam-3010	187	14	⊆	⊆	NUM
ejpam-3010	187	15	t	t	NOUN
ejpam-3010	187	16	.	.	PUNCT
ejpam-3010	188	1	by	by	ADP
ejpam-3010	188	2	hypothesis	hypothesis	NOUN
ejpam-3010	188	3	,	,	PUNCT
ejpam-3010	188	4	we	we	PRON
ejpam-3010	188	5	have	have	VERB
ejpam-3010	188	6	a	a	DET
ejpam-3010	188	7	⊆	⊆	NUM
ejpam-3010	188	8	b	b	NOUN
ejpam-3010	188	9	or	or	CCONJ
ejpam-3010	188	10	b	b	NOUN
ejpam-3010	188	11	⊆	⊆	NUM
ejpam-3010	188	12	a.	a.	NOUN
ejpam-3010	188	13	if	if	SCONJ
ejpam-3010	188	14	a	a	DET
ejpam-3010	188	15	⊆	⊆	NUM
ejpam-3010	188	16	b	b	NOUN
ejpam-3010	188	17	then	then	ADV
ejpam-3010	188	18	,	,	PUNCT
ejpam-3010	188	19	by	by	ADP
ejpam-3010	188	20	lemma	lemma	PROPN
ejpam-3010	188	21	9	9	NUM
ejpam-3010	188	22	,	,	PUNCT
ejpam-3010	188	23	a	a	DET
ejpam-3010	188	24	=	=	X
ejpam-3010	188	25	a	a	DET
ejpam-3010	188	26	∩	∩	ADJ
ejpam-3010	188	27	b	b	NOUN
ejpam-3010	188	28	=	=	SYM
ejpam-3010	188	29	(	(	PUNCT
ejpam-3010	188	30	aγb	aγb	NOUN
ejpam-3010	188	31	]	]	X
ejpam-3010	188	32	⊆	⊆	NUM
ejpam-3010	188	33	(	(	PUNCT
ejpam-3010	188	34	t	t	NOUN
ejpam-3010	188	35	]	]	PUNCT
ejpam-3010	188	36	=	=	PUNCT
ejpam-3010	188	37	t	t	PROPN
ejpam-3010	188	38	.	.	PUNCT
ejpam-3010	189	1	if	if	SCONJ
ejpam-3010	189	2	b	b	PROPN
ejpam-3010	189	3	⊆	⊆	SYM
ejpam-3010	189	4	a	a	PRON
ejpam-3010	189	5	,	,	PUNCT
ejpam-3010	189	6	then	then	ADV
ejpam-3010	189	7	b	b	X
ejpam-3010	189	8	=	=	PUNCT
ejpam-3010	189	9	a	a	DET
ejpam-3010	189	10	∩b	∩b	NOUN
ejpam-3010	189	11	=	=	PUNCT
ejpam-3010	189	12	(	(	PUNCT
ejpam-3010	189	13	aγb	aγb	NOUN
ejpam-3010	189	14	]	]	X
ejpam-3010	189	15	⊆	⊆	NUM
ejpam-3010	189	16	(	(	PUNCT
ejpam-3010	189	17	t	t	NOUN
ejpam-3010	189	18	]	]	PUNCT
ejpam-3010	189	19	=	=	SYM
ejpam-3010	189	20	t	t	PROPN
ejpam-3010	189	21	,	,	PUNCT
ejpam-3010	189	22	thus	thus	ADV
ejpam-3010	189	23	m	m	NOUN
ejpam-3010	189	24	is	be	AUX
ejpam-3010	189	25	weakly	weakly	ADV
ejpam-3010	189	26	prime	prime	ADJ
ejpam-3010	189	27	.	.	PUNCT
ejpam-3010	190	1	�	�	PROPN
ejpam-3010	190	2	lemma	lemma	PROPN
ejpam-3010	190	3	11	11	NUM
ejpam-3010	190	4	.	.	PUNCT
ejpam-3010	191	1	let	let	VERB
ejpam-3010	191	2	m	m	PRON
ejpam-3010	191	3	be	be	AUX
ejpam-3010	191	4	a	a	DET
ejpam-3010	191	5	po	po	NOUN
ejpam-3010	191	6	-	-	PUNCT
ejpam-3010	191	7	γ	γ	NOUN
ejpam-3010	191	8	-	-	PUNCT
ejpam-3010	191	9	semigroup	semigroup	NOUN
ejpam-3010	191	10	.	.	PUNCT
ejpam-3010	192	1	if	if	SCONJ
ejpam-3010	192	2	m	m	NOUN
ejpam-3010	192	3	is	be	AUX
ejpam-3010	192	4	intra	intra	ADJ
ejpam-3010	192	5	-	-	ADJ
ejpam-3010	192	6	regular	regular	ADJ
ejpam-3010	192	7	,	,	PUNCT
ejpam-3010	192	8	then	then	ADV
ejpam-3010	192	9	i(x	i(x	NOUN
ejpam-3010	192	10	)	)	PUNCT
ejpam-3010	193	1	=	=	PUNCT
ejpam-3010	193	2	(	(	PUNCT
ejpam-3010	193	3	mγxγm	mγxγm	VERB
ejpam-3010	193	4	]	]	PUNCT
ejpam-3010	193	5	for	for	ADP
ejpam-3010	193	6	every	every	DET
ejpam-3010	193	7	x	x	SYM
ejpam-3010	193	8	∈m	∈m	NOUN
ejpam-3010	193	9	.	.	PUNCT
ejpam-3010	194	1	proof	proof	NOUN
ejpam-3010	194	2	.	.	PUNCT
ejpam-3010	195	1	let	let	VERB
ejpam-3010	195	2	x	x	PRON
ejpam-3010	195	3	∈m	∈m	VERB
ejpam-3010	195	4	.	.	PUNCT
ejpam-3010	196	1	since	since	SCONJ
ejpam-3010	196	2	(	(	PUNCT
ejpam-3010	196	3	mγxγm	mγxγm	NOUN
ejpam-3010	196	4	]	]	PUNCT
ejpam-3010	196	5	is	be	AUX
ejpam-3010	196	6	an	an	DET
ejpam-3010	196	7	ideal	ideal	NOUN
ejpam-3010	196	8	of	of	ADP
ejpam-3010	196	9	m	m	PRON
ejpam-3010	196	10	,	,	PUNCT
ejpam-3010	196	11	by	by	ADP
ejpam-3010	196	12	lemma	lemma	PROPN
ejpam-3010	196	13	5	5	NUM
ejpam-3010	196	14	,	,	PUNCT
ejpam-3010	196	15	it	it	PRON
ejpam-3010	196	16	is	be	AUX
ejpam-3010	196	17	semiprime	semiprime	NOUN
ejpam-3010	196	18	.	.	PUNCT
ejpam-3010	197	1	take	take	VERB
ejpam-3010	197	2	an	an	DET
ejpam-3010	197	3	element	element	NOUN
ejpam-3010	197	4	γ	γ	NOUN
ejpam-3010	197	5	∈	∈	PROPN
ejpam-3010	197	6	γ	γ	X
ejpam-3010	197	7	(	(	PUNCT
ejpam-3010	197	8	γ	γ	PROPN
ejpam-3010	197	9	6=	6=	NOUN
ejpam-3010	197	10	∅	∅	NOUN
ejpam-3010	197	11	)	)	PUNCT
ejpam-3010	197	12	.	.	PUNCT
ejpam-3010	198	1	since	since	SCONJ
ejpam-3010	198	2	xγx	xγx	PROPN
ejpam-3010	198	3	∈	∈	PROPN
ejpam-3010	198	4	m	m	PRON
ejpam-3010	198	5	,	,	PUNCT
ejpam-3010	198	6	(	(	PUNCT
ejpam-3010	198	7	xγx)γ(xγx	xγx)γ(xγx	X
ejpam-3010	198	8	)	)	PUNCT
ejpam-3010	198	9	∈	∈	PROPN
ejpam-3010	198	10	(	(	PUNCT
ejpam-3010	198	11	mγxγx	mγxγx	ADJ
ejpam-3010	198	12	]	]	PUNCT
ejpam-3010	198	13	and	and	CCONJ
ejpam-3010	198	14	(	(	PUNCT
ejpam-3010	198	15	mγxγm	mγxγm	NOUN
ejpam-3010	198	16	]	]	PUNCT
ejpam-3010	198	17	is	be	AUX
ejpam-3010	198	18	a	a	DET
ejpam-3010	198	19	semiprime	semiprime	NOUN
ejpam-3010	198	20	subset	subset	NOUN
ejpam-3010	198	21	of	of	ADP
ejpam-3010	198	22	m	m	PROPN
ejpam-3010	198	23	,	,	PUNCT
ejpam-3010	198	24	we	we	PRON
ejpam-3010	198	25	have	have	AUX
ejpam-3010	198	26	xγx	xγx	VERB
ejpam-3010	198	27	∈	∈	PROPN
ejpam-3010	198	28	(	(	PUNCT
ejpam-3010	198	29	mγxγx	mγxγx	ADJ
ejpam-3010	198	30	]	]	PUNCT
ejpam-3010	198	31	,	,	PUNCT
ejpam-3010	198	32	then	then	ADV
ejpam-3010	198	33	x	x	SYM
ejpam-3010	198	34	∈	∈	PROPN
ejpam-3010	198	35	(	(	PUNCT
ejpam-3010	198	36	mγxγx	mγxγx	ADJ
ejpam-3010	198	37	]	]	PUNCT
ejpam-3010	198	38	,	,	PUNCT
ejpam-3010	198	39	and	and	CCONJ
ejpam-3010	198	40	i(x	i(x	PROPN
ejpam-3010	198	41	)	)	PUNCT
ejpam-3010	199	1	⊆	⊆	NUM
ejpam-3010	199	2	(	(	PUNCT
ejpam-3010	199	3	mγxγx	mγxγx	ADJ
ejpam-3010	199	4	]	]	PUNCT
ejpam-3010	199	5	.	.	PUNCT
ejpam-3010	200	1	on	on	ADP
ejpam-3010	200	2	the	the	DET
ejpam-3010	200	3	other	other	ADJ
ejpam-3010	200	4	hand	hand	NOUN
ejpam-3010	200	5	,	,	PUNCT
ejpam-3010	200	6	(	(	PUNCT
ejpam-3010	200	7	mγxγx	mγxγx	VERB
ejpam-3010	200	8	]	]	X
ejpam-3010	200	9	⊆	⊆	NUM
ejpam-3010	200	10	i(x	i(x	NOUN
ejpam-3010	200	11	)	)	PUNCT
ejpam-3010	200	12	,	,	PUNCT
ejpam-3010	200	13	thus	thus	ADV
ejpam-3010	200	14	we	we	PRON
ejpam-3010	200	15	get	get	VERB
ejpam-3010	200	16	i(x	i(x	NOUN
ejpam-3010	200	17	)	)	PUNCT
ejpam-3010	201	1	=	=	PUNCT
ejpam-3010	201	2	(	(	PUNCT
ejpam-3010	201	3	mγxγm	mγxγm	VERB
ejpam-3010	201	4	]	]	PUNCT
ejpam-3010	201	5	.	.	PUNCT
ejpam-3010	202	1	�	�	PROPN
ejpam-3010	202	2	lemma	lemma	PROPN
ejpam-3010	202	3	12	12	NUM
ejpam-3010	202	4	.	.	PUNCT
ejpam-3010	203	1	if	if	SCONJ
ejpam-3010	203	2	m	m	NOUN
ejpam-3010	203	3	is	be	AUX
ejpam-3010	203	4	a	a	DET
ejpam-3010	203	5	po	po	NOUN
ejpam-3010	203	6	-	-	PUNCT
ejpam-3010	203	7	γ	γ	NOUN
ejpam-3010	203	8	-	-	PUNCT
ejpam-3010	203	9	semigroup	semigroup	NOUN
ejpam-3010	203	10	,	,	PUNCT
ejpam-3010	203	11	x	x	NOUN
ejpam-3010	203	12	,	,	PUNCT
ejpam-3010	203	13	y	y	PROPN
ejpam-3010	203	14	∈m	∈m	NOUN
ejpam-3010	203	15	and	and	CCONJ
ejpam-3010	203	16	γ	γ	PROPN
ejpam-3010	203	17	∈	∈	PROPN
ejpam-3010	203	18	γ	γ	X
ejpam-3010	203	19	,	,	PUNCT
ejpam-3010	203	20	then	then	ADV
ejpam-3010	203	21	i(xγy	i(xγy	PROPN
ejpam-3010	203	22	)	)	PUNCT
ejpam-3010	203	23	⊆	⊆	NUM
ejpam-3010	203	24	i(x	i(x	NOUN
ejpam-3010	203	25	)	)	PUNCT
ejpam-3010	203	26	∩	∩	NOUN
ejpam-3010	203	27	i(y	i(y	NOUN
ejpam-3010	203	28	)	)	PUNCT
ejpam-3010	203	29	.	.	PUNCT
ejpam-3010	204	1	in	in	ADP
ejpam-3010	204	2	particular	particular	ADJ
ejpam-3010	204	3	,	,	PUNCT
ejpam-3010	204	4	if	if	SCONJ
ejpam-3010	204	5	m	m	NOUN
ejpam-3010	204	6	is	be	AUX
ejpam-3010	204	7	intra	intra	ADJ
ejpam-3010	204	8	-	-	ADJ
ejpam-3010	204	9	regular	regular	ADJ
ejpam-3010	204	10	,	,	PUNCT
ejpam-3010	204	11	then	then	ADV
ejpam-3010	204	12	i(xγy	i(xγy	ADJ
ejpam-3010	204	13	)	)	PUNCT
ejpam-3010	205	1	=	=	SYM
ejpam-3010	205	2	i(x	i(x	NOUN
ejpam-3010	205	3	)	)	PUNCT
ejpam-3010	205	4	∩	∩	NOUN
ejpam-3010	205	5	i(y	i(y	NOUN
ejpam-3010	205	6	)	)	PUNCT
ejpam-3010	205	7	.	.	PUNCT
ejpam-3010	206	1	proof	proof	NOUN
ejpam-3010	206	2	.	.	PUNCT
ejpam-3010	207	1	let	let	VERB
ejpam-3010	207	2	x	x	PRON
ejpam-3010	207	3	,	,	PUNCT
ejpam-3010	207	4	y	y	PROPN
ejpam-3010	207	5	∈m	∈m	NOUN
ejpam-3010	207	6	and	and	CCONJ
ejpam-3010	207	7	γ	γ	PROPN
ejpam-3010	207	8	∈	∈	PROPN
ejpam-3010	207	9	γ	γ	X
ejpam-3010	207	10	.	.	PROPN
ejpam-3010	207	11	since	since	SCONJ
ejpam-3010	207	12	i(x	i(x	PROPN
ejpam-3010	207	13	)	)	PUNCT
ejpam-3010	207	14	is	be	AUX
ejpam-3010	207	15	an	an	DET
ejpam-3010	207	16	ideal	ideal	NOUN
ejpam-3010	207	17	of	of	ADP
ejpam-3010	207	18	m	m	PROPN
ejpam-3010	207	19	,	,	PUNCT
ejpam-3010	207	20	we	we	PRON
ejpam-3010	207	21	have	have	VERB
ejpam-3010	207	22	xγy	xγy	PROPN
ejpam-3010	207	23	∈	∈	PROPN
ejpam-3010	207	24	i(x)γm	i(x)γm	PART
ejpam-3010	207	25	⊆	⊆	NUM
ejpam-3010	207	26	i(x	i(x	NOUN
ejpam-3010	207	27	)	)	PUNCT
ejpam-3010	207	28	and	and	CCONJ
ejpam-3010	207	29	xγy	xγy	NOUN
ejpam-3010	207	30	∈mγi(y	∈mγi(y	ADJ
ejpam-3010	207	31	)	)	PUNCT
ejpam-3010	207	32	⊆	⊆	NUM
ejpam-3010	207	33	i(y	i(y	NOUN
ejpam-3010	207	34	)	)	PUNCT
ejpam-3010	207	35	.	.	PUNCT
ejpam-3010	208	1	thus	thus	ADV
ejpam-3010	208	2	we	we	PRON
ejpam-3010	208	3	have	have	VERB
ejpam-3010	208	4	i(xγy	i(xγy	NOUN
ejpam-3010	208	5	)	)	PUNCT
ejpam-3010	208	6	⊆	⊆	NUM
ejpam-3010	208	7	i(x	i(x	NOUN
ejpam-3010	208	8	)	)	PUNCT
ejpam-3010	208	9	∩	∩	NOUN
ejpam-3010	208	10	i(y	i(y	NOUN
ejpam-3010	208	11	)	)	PUNCT
ejpam-3010	208	12	.	.	PUNCT
ejpam-3010	209	1	n.	n.	PROPN
ejpam-3010	209	2	kehayopulu	kehayopulu	PROPN
ejpam-3010	209	3	/	/	SYM
ejpam-3010	209	4	eur	eur	PROPN
ejpam-3010	209	5	.	.	PUNCT
ejpam-3010	210	1	j.	j.	PROPN
ejpam-3010	210	2	pure	pure	PROPN
ejpam-3010	210	3	appl	appl	PROPN
ejpam-3010	210	4	.	.	PROPN
ejpam-3010	210	5	math	math	PROPN
ejpam-3010	210	6	,	,	PUNCT
ejpam-3010	210	7	10	10	NUM
ejpam-3010	210	8	(	(	PUNCT
ejpam-3010	210	9	4	4	NUM
ejpam-3010	210	10	)	)	PUNCT
ejpam-3010	210	11	(	(	PUNCT
ejpam-3010	210	12	2017	2017	NUM
ejpam-3010	210	13	)	)	PUNCT
ejpam-3010	210	14	,	,	PUNCT
ejpam-3010	210	15	620	620	NUM
ejpam-3010	210	16	-	-	SYM
ejpam-3010	210	17	630	630	NUM
ejpam-3010	210	18	626	626	NUM
ejpam-3010	210	19	let	let	VERB
ejpam-3010	210	20	now	now	ADV
ejpam-3010	210	21	m	m	AUX
ejpam-3010	210	22	be	be	AUX
ejpam-3010	210	23	intra	intra	ADJ
ejpam-3010	210	24	-	-	ADJ
ejpam-3010	210	25	regular	regular	ADJ
ejpam-3010	210	26	and	and	CCONJ
ejpam-3010	210	27	t	t	NOUN
ejpam-3010	210	28	∈	∈	PROPN
ejpam-3010	210	29	i(x	i(x	PROPN
ejpam-3010	210	30	)	)	PUNCT
ejpam-3010	210	31	∩	∩	NOUN
ejpam-3010	210	32	i(y	i(y	NOUN
ejpam-3010	210	33	)	)	PUNCT
ejpam-3010	210	34	.	.	PUNCT
ejpam-3010	211	1	then	then	ADV
ejpam-3010	211	2	,	,	PUNCT
ejpam-3010	211	3	by	by	ADP
ejpam-3010	211	4	lemma	lemma	PROPN
ejpam-3010	211	5	11	11	NUM
ejpam-3010	211	6	,	,	PUNCT
ejpam-3010	211	7	we	we	PRON
ejpam-3010	211	8	have	have	VERB
ejpam-3010	211	9	t	t	PROPN
ejpam-3010	211	10	∈	∈	PROPN
ejpam-3010	211	11	(	(	PUNCT
ejpam-3010	211	12	mγxγm	mγxγm	VERB
ejpam-3010	211	13	]	]	PUNCT
ejpam-3010	211	14	and	and	CCONJ
ejpam-3010	211	15	t	t	PROPN
ejpam-3010	211	16	∈	∈	PROPN
ejpam-3010	211	17	(	(	PUNCT
ejpam-3010	211	18	mγyγm	mγyγm	NOUN
ejpam-3010	211	19	]	]	PUNCT
ejpam-3010	211	20	.	.	PUNCT
ejpam-3010	212	1	thus	thus	ADV
ejpam-3010	212	2	we	we	PRON
ejpam-3010	212	3	have	have	VERB
ejpam-3010	212	4	t	t	NOUN
ejpam-3010	212	5	≤	≤	NUM
ejpam-3010	212	6	aµxρb	aµxρb	NOUN
ejpam-3010	212	7	and	and	CCONJ
ejpam-3010	212	8	t	t	NOUN
ejpam-3010	212	9	≤	≤	NOUN
ejpam-3010	212	10	cξyζd	cξyζd	ADJ
ejpam-3010	212	11	for	for	ADP
ejpam-3010	212	12	some	some	PRON
ejpam-3010	212	13	a	a	DET
ejpam-3010	212	14	,	,	PUNCT
ejpam-3010	212	15	b	b	NOUN
ejpam-3010	212	16	,	,	PUNCT
ejpam-3010	212	17	c	c	NOUN
ejpam-3010	212	18	,	,	PUNCT
ejpam-3010	212	19	d	d	NOUN
ejpam-3010	212	20	∈m	∈m	NOUN
ejpam-3010	212	21	,	,	PUNCT
ejpam-3010	212	22	µ	µ	NOUN
ejpam-3010	212	23	,	,	PUNCT
ejpam-3010	212	24	ρ	ρ	PROPN
ejpam-3010	212	25	,	,	PUNCT
ejpam-3010	212	26	ξ	ξ	PROPN
ejpam-3010	212	27	,	,	PUNCT
ejpam-3010	212	28	ζ	ζ	PROPN
ejpam-3010	212	29	∈	∈	PROPN
ejpam-3010	212	30	γ	γ	X
ejpam-3010	212	31	.	.	PROPN
ejpam-3010	212	32	then	then	ADV
ejpam-3010	212	33	tγt	tγt	VERB
ejpam-3010	212	34	≤	≤	X
ejpam-3010	212	35	(	(	PUNCT
ejpam-3010	212	36	cξyζd)γ(aµxρb	cξyζd)γ(aµxρb	NOUN
ejpam-3010	212	37	)	)	PUNCT
ejpam-3010	212	38	=	=	SYM
ejpam-3010	212	39	cξ(yζdγaµx)ρb	cξ(yζdγaµx)ρb	PROPN
ejpam-3010	212	40	.	.	PUNCT
ejpam-3010	213	1	in	in	ADP
ejpam-3010	213	2	addition	addition	NOUN
ejpam-3010	213	3	,	,	PUNCT
ejpam-3010	213	4	we	we	PRON
ejpam-3010	213	5	have	have	VERB
ejpam-3010	213	6	yζdγaµx	yζdγaµx	VERB
ejpam-3010	213	7	∈	∈	PROPN
ejpam-3010	213	8	i(xγy	i(xγy	NOUN
ejpam-3010	213	9	)	)	PUNCT
ejpam-3010	213	10	.	.	PUNCT
ejpam-3010	214	1	indeed	indeed	ADV
ejpam-3010	214	2	,	,	PUNCT
ejpam-3010	214	3	by	by	ADP
ejpam-3010	214	4	lemma	lemma	PROPN
ejpam-3010	214	5	11	11	NUM
ejpam-3010	214	6	,	,	PUNCT
ejpam-3010	214	7	(	(	PUNCT
ejpam-3010	214	8	yζdγaµx)γ(yζdγaµx	yζdγaµx)γ(yζdγaµx	NOUN
ejpam-3010	214	9	)	)	PUNCT
ejpam-3010	214	10	∈mγ(xγy)γm	∈mγ(xγy)γm	NOUN
ejpam-3010	214	11	⊆	⊆	NUM
ejpam-3010	214	12	(	(	PUNCT
ejpam-3010	214	13	mγ(xγy)γm	mγ(xγy)γm	NOUN
ejpam-3010	214	14	]	]	PUNCT
ejpam-3010	214	15	=	=	SYM
ejpam-3010	214	16	i(xγy	i(xγy	NOUN
ejpam-3010	214	17	)	)	PUNCT
ejpam-3010	214	18	.	.	PUNCT
ejpam-3010	215	1	since	since	SCONJ
ejpam-3010	215	2	m	m	PROPN
ejpam-3010	215	3	is	be	AUX
ejpam-3010	215	4	intra	intra	ADJ
ejpam-3010	215	5	-	-	ADJ
ejpam-3010	215	6	regular	regular	ADJ
ejpam-3010	215	7	and	and	CCONJ
ejpam-3010	215	8	i(xγy	i(xγy	NOUN
ejpam-3010	215	9	)	)	PUNCT
ejpam-3010	215	10	is	be	AUX
ejpam-3010	215	11	an	an	DET
ejpam-3010	215	12	ideal	ideal	NOUN
ejpam-3010	215	13	of	of	ADP
ejpam-3010	215	14	m	m	PRON
ejpam-3010	215	15	,	,	PUNCT
ejpam-3010	215	16	by	by	ADP
ejpam-3010	215	17	lemma	lemma	PROPN
ejpam-3010	215	18	5	5	NUM
ejpam-3010	215	19	,	,	PUNCT
ejpam-3010	215	20	i(xγy	i(xγy	NOUN
ejpam-3010	215	21	)	)	PUNCT
ejpam-3010	215	22	is	be	AUX
ejpam-3010	215	23	semiprime	semiprime	NOUN
ejpam-3010	215	24	.	.	PUNCT
ejpam-3010	216	1	so	so	ADV
ejpam-3010	216	2	we	we	PRON
ejpam-3010	216	3	get	get	VERB
ejpam-3010	216	4	yζdγaµx	yζdγaµx	NOUN
ejpam-3010	216	5	∈	∈	PROPN
ejpam-3010	216	6	i(xγy	i(xγy	NOUN
ejpam-3010	216	7	)	)	PUNCT
ejpam-3010	216	8	.	.	PUNCT
ejpam-3010	217	1	since	since	SCONJ
ejpam-3010	217	2	i(xγy	i(xγy	NUM
ejpam-3010	217	3	)	)	PUNCT
ejpam-3010	217	4	is	be	AUX
ejpam-3010	217	5	an	an	DET
ejpam-3010	217	6	ideal	ideal	NOUN
ejpam-3010	217	7	of	of	ADP
ejpam-3010	217	8	m	m	PROPN
ejpam-3010	217	9	,	,	PUNCT
ejpam-3010	217	10	we	we	PRON
ejpam-3010	217	11	have	have	VERB
ejpam-3010	217	12	cξ(yζdγaµx)ρb	cξ(yζdγaµx)ρb	PROPN
ejpam-3010	217	13	∈	∈	NOUN
ejpam-3010	217	14	mγi(xγy)γm	mγi(xγy)γm	NOUN
ejpam-3010	217	15	⊆	⊆	NUM
ejpam-3010	217	16	i(xγy)γm	i(xγy)γm	NUM
ejpam-3010	217	17	⊆	⊆	NUM
ejpam-3010	217	18	i(xγy	i(xγy	NOUN
ejpam-3010	217	19	)	)	PUNCT
ejpam-3010	217	20	,	,	PUNCT
ejpam-3010	217	21	then	then	ADV
ejpam-3010	217	22	tγt	tγt	VERB
ejpam-3010	217	23	∈	∈	PROPN
ejpam-3010	217	24	i(xγy	i(xγy	NOUN
ejpam-3010	217	25	)	)	PUNCT
ejpam-3010	217	26	.	.	PUNCT
ejpam-3010	218	1	since	since	SCONJ
ejpam-3010	218	2	i(xγy	i(xγy	NUM
ejpam-3010	218	3	)	)	PUNCT
ejpam-3010	218	4	is	be	AUX
ejpam-3010	218	5	semiprime	semiprime	NOUN
ejpam-3010	218	6	,	,	PUNCT
ejpam-3010	218	7	we	we	PRON
ejpam-3010	218	8	have	have	VERB
ejpam-3010	218	9	t	t	PROPN
ejpam-3010	218	10	∈	∈	PROPN
ejpam-3010	218	11	i(xγy	i(xγy	NOUN
ejpam-3010	218	12	)	)	PUNCT
ejpam-3010	218	13	.	.	PUNCT
ejpam-3010	219	1	thus	thus	ADV
ejpam-3010	219	2	we	we	PRON
ejpam-3010	219	3	get	get	VERB
ejpam-3010	219	4	i(x	i(x	NOUN
ejpam-3010	219	5	)	)	PUNCT
ejpam-3010	219	6	∩	∩	NOUN
ejpam-3010	219	7	i(y	i(y	NOUN
ejpam-3010	219	8	)	)	PUNCT
ejpam-3010	219	9	⊆	⊆	NUM
ejpam-3010	219	10	i(xγy	i(xγy	NOUN
ejpam-3010	219	11	)	)	PUNCT
ejpam-3010	219	12	and	and	CCONJ
ejpam-3010	219	13	so	so	ADV
ejpam-3010	219	14	i(xγy	i(xγy	ADJ
ejpam-3010	219	15	)	)	PUNCT
ejpam-3010	220	1	=	=	SYM
ejpam-3010	220	2	i(x	i(x	NOUN
ejpam-3010	220	3	)	)	PUNCT
ejpam-3010	220	4	∩	∩	NOUN
ejpam-3010	220	5	i(y	i(y	NOUN
ejpam-3010	220	6	)	)	PUNCT
ejpam-3010	220	7	.	.	PUNCT
ejpam-3010	221	1	�	�	PROPN
ejpam-3010	221	2	theorem	theorem	VERB
ejpam-3010	221	3	13	13	NUM
ejpam-3010	221	4	.	.	PUNCT
ejpam-3010	222	1	let	let	VERB
ejpam-3010	222	2	m	m	PRON
ejpam-3010	222	3	be	be	AUX
ejpam-3010	222	4	a	a	DET
ejpam-3010	222	5	po	po	NOUN
ejpam-3010	222	6	-	-	PUNCT
ejpam-3010	222	7	γ	γ	NOUN
ejpam-3010	222	8	-	-	PUNCT
ejpam-3010	222	9	semigroup	semigroup	NOUN
ejpam-3010	222	10	.	.	PUNCT
ejpam-3010	223	1	the	the	DET
ejpam-3010	223	2	ideals	ideal	NOUN
ejpam-3010	223	3	of	of	ADP
ejpam-3010	223	4	m	m	NOUN
ejpam-3010	223	5	are	be	AUX
ejpam-3010	223	6	prime	prime	ADJ
ejpam-3010	223	7	if	if	SCONJ
ejpam-3010	224	1	and	and	CCONJ
ejpam-3010	224	2	only	only	ADV
ejpam-3010	224	3	if	if	SCONJ
ejpam-3010	224	4	they	they	PRON
ejpam-3010	224	5	form	form	VERB
ejpam-3010	224	6	a	a	DET
ejpam-3010	224	7	chain	chain	NOUN
ejpam-3010	224	8	and	and	CCONJ
ejpam-3010	224	9	m	m	NOUN
ejpam-3010	224	10	is	be	AUX
ejpam-3010	224	11	intra	intra	ADJ
ejpam-3010	224	12	-	-	ADJ
ejpam-3010	224	13	regular	regular	ADJ
ejpam-3010	224	14	.	.	PUNCT
ejpam-3010	225	1	proof	proof	NOUN
ejpam-3010	225	2	.	.	PUNCT
ejpam-3010	226	1	=	=	NOUN
ejpam-3010	226	2	⇒.	⇒.	ADP
ejpam-3010	226	3	the	the	DET
ejpam-3010	226	4	ideals	ideal	NOUN
ejpam-3010	226	5	of	of	ADP
ejpam-3010	226	6	m	m	NOUN
ejpam-3010	226	7	are	be	AUX
ejpam-3010	226	8	prime	prime	ADJ
ejpam-3010	226	9	,	,	PUNCT
ejpam-3010	226	10	so	so	SCONJ
ejpam-3010	226	11	they	they	PRON
ejpam-3010	226	12	are	be	AUX
ejpam-3010	226	13	weakly	weakly	ADV
ejpam-3010	226	14	prime	prime	ADJ
ejpam-3010	226	15	and	and	CCONJ
ejpam-3010	226	16	semiprime	semiprime	NOUN
ejpam-3010	226	17	.	.	PUNCT
ejpam-3010	227	1	since	since	SCONJ
ejpam-3010	227	2	they	they	PRON
ejpam-3010	227	3	are	be	AUX
ejpam-3010	227	4	weakly	weakly	ADV
ejpam-3010	227	5	prime	prime	ADJ
ejpam-3010	227	6	,	,	PUNCT
ejpam-3010	227	7	by	by	ADP
ejpam-3010	227	8	theorem	theorem	NOUN
ejpam-3010	227	9	10	10	NUM
ejpam-3010	227	10	,	,	PUNCT
ejpam-3010	227	11	they	they	PRON
ejpam-3010	227	12	form	form	VERB
ejpam-3010	227	13	a	a	DET
ejpam-3010	227	14	chain	chain	NOUN
ejpam-3010	227	15	.	.	PUNCT
ejpam-3010	228	1	let	let	VERB
ejpam-3010	228	2	now	now	ADV
ejpam-3010	228	3	a	a	DET
ejpam-3010	228	4	∈	∈	NOUN
ejpam-3010	228	5	m	m	NOUN
ejpam-3010	228	6	and	and	CCONJ
ejpam-3010	228	7	γ	γ	PROPN
ejpam-3010	228	8	∈	∈	PROPN
ejpam-3010	228	9	γ	γ	X
ejpam-3010	228	10	.	.	PUNCT
ejpam-3010	229	1	since	since	SCONJ
ejpam-3010	229	2	(	(	PUNCT
ejpam-3010	229	3	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	229	4	]	]	PUNCT
ejpam-3010	229	5	is	be	AUX
ejpam-3010	229	6	an	an	DET
ejpam-3010	229	7	ideal	ideal	NOUN
ejpam-3010	229	8	of	of	ADP
ejpam-3010	229	9	m	m	PRON
ejpam-3010	229	10	,	,	PUNCT
ejpam-3010	229	11	(	(	PUNCT
ejpam-3010	229	12	aγa)γ(aγa	aγa)γ(aγa	PROPN
ejpam-3010	229	13	)	)	PUNCT
ejpam-3010	229	14	∈	∈	PROPN
ejpam-3010	229	15	(	(	PUNCT
ejpam-3010	229	16	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	229	17	]	]	PUNCT
ejpam-3010	229	18	and	and	CCONJ
ejpam-3010	229	19	(	(	PUNCT
ejpam-3010	229	20	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	229	21	]	]	PUNCT
ejpam-3010	229	22	is	be	AUX
ejpam-3010	229	23	semiprime	semiprime	NOUN
ejpam-3010	229	24	,	,	PUNCT
ejpam-3010	229	25	we	we	PRON
ejpam-3010	229	26	have	have	VERB
ejpam-3010	229	27	aγa	aγa	ADJ
ejpam-3010	229	28	∈	∈	NOUN
ejpam-3010	229	29	(	(	PUNCT
ejpam-3010	229	30	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	229	31	]	]	PUNCT
ejpam-3010	229	32	,	,	PUNCT
ejpam-3010	229	33	then	then	ADV
ejpam-3010	229	34	a	a	DET
ejpam-3010	229	35	∈	∈	NOUN
ejpam-3010	229	36	(	(	PUNCT
ejpam-3010	229	37	mγaγaγm	mγaγaγm	NOUN
ejpam-3010	229	38	]	]	PUNCT
ejpam-3010	229	39	,	,	PUNCT
ejpam-3010	229	40	thus	thus	ADV
ejpam-3010	229	41	m	m	NOUN
ejpam-3010	229	42	is	be	AUX
ejpam-3010	229	43	intra	intra	ADJ
ejpam-3010	229	44	-	-	ADJ
ejpam-3010	229	45	regular	regular	ADJ
ejpam-3010	229	46	.	.	PUNCT
ejpam-3010	230	1	⇐	⇐	PROPN
ejpam-3010	230	2	=	=	PRON
ejpam-3010	230	3	.	.	PROPN
ejpam-3010	230	4	suppose	suppose	VERB
ejpam-3010	230	5	m	m	NOUN
ejpam-3010	230	6	is	be	AUX
ejpam-3010	230	7	intra	intra	ADJ
ejpam-3010	230	8	-	-	ADJ
ejpam-3010	230	9	regular	regular	ADJ
ejpam-3010	230	10	and	and	CCONJ
ejpam-3010	230	11	the	the	DET
ejpam-3010	230	12	ideals	ideal	NOUN
ejpam-3010	230	13	of	of	ADP
ejpam-3010	230	14	m	m	PROPN
ejpam-3010	230	15	form	form	VERB
ejpam-3010	230	16	a	a	DET
ejpam-3010	230	17	chain	chain	NOUN
ejpam-3010	230	18	.	.	PUNCT
ejpam-3010	231	1	let	let	VERB
ejpam-3010	231	2	now	now	ADV
ejpam-3010	231	3	t	t	AUX
ejpam-3010	231	4	be	be	AUX
ejpam-3010	231	5	an	an	DET
ejpam-3010	231	6	ideal	ideal	NOUN
ejpam-3010	231	7	of	of	ADP
ejpam-3010	231	8	m	m	PROPN
ejpam-3010	231	9	,	,	PUNCT
ejpam-3010	231	10	a	a	PRON
ejpam-3010	231	11	,	,	PUNCT
ejpam-3010	231	12	b	b	X
ejpam-3010	231	13	∈	∈	NOUN
ejpam-3010	231	14	m	m	NOUN
ejpam-3010	231	15	and	and	CCONJ
ejpam-3010	231	16	γ	γ	PROPN
ejpam-3010	231	17	∈	∈	PROPN
ejpam-3010	231	18	γ	γ	NOUN
ejpam-3010	231	19	such	such	ADJ
ejpam-3010	231	20	that	that	SCONJ
ejpam-3010	231	21	aγb	aγb	NOUN
ejpam-3010	231	22	∈	∈	PROPN
ejpam-3010	231	23	t	t	PROPN
ejpam-3010	231	24	.	.	PUNCT
ejpam-3010	232	1	we	we	PRON
ejpam-3010	232	2	have	have	VERB
ejpam-3010	232	3	i(a	i(a	PROPN
ejpam-3010	232	4	)	)	PUNCT
ejpam-3010	232	5	⊆	⊆	NUM
ejpam-3010	232	6	i(b	i(b	NOUN
ejpam-3010	232	7	)	)	PUNCT
ejpam-3010	232	8	or	or	CCONJ
ejpam-3010	232	9	i(b	i(b	PROPN
ejpam-3010	232	10	)	)	PUNCT
ejpam-3010	232	11	⊆	⊆	NUM
ejpam-3010	232	12	i(a	i(a	NOUN
ejpam-3010	232	13	)	)	PUNCT
ejpam-3010	232	14	.	.	PUNCT
ejpam-3010	233	1	if	if	SCONJ
ejpam-3010	233	2	i(a	i(a	NOUN
ejpam-3010	233	3	)	)	PUNCT
ejpam-3010	233	4	⊆	⊆	NUM
ejpam-3010	233	5	i(b	i(b	NOUN
ejpam-3010	233	6	)	)	PUNCT
ejpam-3010	233	7	then	then	ADV
ejpam-3010	233	8	,	,	PUNCT
ejpam-3010	233	9	by	by	ADP
ejpam-3010	233	10	lemma	lemma	PROPN
ejpam-3010	233	11	12	12	NUM
ejpam-3010	233	12	,	,	PUNCT
ejpam-3010	233	13	we	we	PRON
ejpam-3010	233	14	have	have	VERB
ejpam-3010	233	15	a	a	DET
ejpam-3010	233	16	∈	∈	PROPN
ejpam-3010	233	17	i(a	i(a	PROPN
ejpam-3010	233	18	)	)	PUNCT
ejpam-3010	233	19	=	=	SYM
ejpam-3010	233	20	i(a	i(a	PROPN
ejpam-3010	233	21	)	)	PUNCT
ejpam-3010	233	22	∩	∩	NOUN
ejpam-3010	233	23	i(b	i(b	NOUN
ejpam-3010	233	24	)	)	PUNCT
ejpam-3010	233	25	=	=	SYM
ejpam-3010	234	1	i(aγb	i(aγb	PROPN
ejpam-3010	234	2	)	)	PUNCT
ejpam-3010	234	3	⊆	⊆	NUM
ejpam-3010	234	4	i(t	i(t	NOUN
ejpam-3010	234	5	)	)	PUNCT
ejpam-3010	234	6	=	=	SYM
ejpam-3010	235	1	t	t	NOUN
ejpam-3010	235	2	.	.	PUNCT
ejpam-3010	236	1	if	if	SCONJ
ejpam-3010	236	2	i(b	i(b	PROPN
ejpam-3010	236	3	)	)	PUNCT
ejpam-3010	236	4	⊆	⊆	NUM
ejpam-3010	236	5	i(a	i(a	NOUN
ejpam-3010	236	6	)	)	PUNCT
ejpam-3010	236	7	,	,	PUNCT
ejpam-3010	236	8	then	then	ADV
ejpam-3010	236	9	b	b	PROPN
ejpam-3010	236	10	∈	∈	PROPN
ejpam-3010	236	11	i(b	i(b	PROPN
ejpam-3010	236	12	)	)	PUNCT
ejpam-3010	236	13	=	=	PUNCT
ejpam-3010	236	14	i(a)∩	i(a)∩	PROPN
ejpam-3010	236	15	i(b	i(b	NOUN
ejpam-3010	236	16	)	)	PUNCT
ejpam-3010	236	17	=	=	SYM
ejpam-3010	236	18	i(aγb	i(aγb	NOUN
ejpam-3010	236	19	)	)	PUNCT
ejpam-3010	236	20	⊆	⊆	NUM
ejpam-3010	236	21	t	t	NOUN
ejpam-3010	236	22	.	.	PUNCT
ejpam-3010	237	1	thus	thus	ADV
ejpam-3010	237	2	the	the	DET
ejpam-3010	237	3	ideals	ideal	NOUN
ejpam-3010	237	4	of	of	ADP
ejpam-3010	237	5	m	m	NOUN
ejpam-3010	237	6	are	be	AUX
ejpam-3010	237	7	prime	prime	ADJ
ejpam-3010	237	8	.	.	PUNCT
ejpam-3010	238	1	�	�	PROPN
ejpam-3010	238	2	proposition	proposition	NOUN
ejpam-3010	238	3	14	14	NUM
ejpam-3010	238	4	.	.	PUNCT
ejpam-3010	239	1	let	let	VERB
ejpam-3010	239	2	m	m	PRON
ejpam-3010	239	3	be	be	AUX
ejpam-3010	239	4	an	an	DET
ejpam-3010	239	5	intra	intra	ADJ
ejpam-3010	239	6	-	-	ADJ
ejpam-3010	239	7	regular	regular	ADJ
ejpam-3010	239	8	po	po	NOUN
ejpam-3010	239	9	-	-	PUNCT
ejpam-3010	239	10	γ	γ	NOUN
ejpam-3010	239	11	-	-	PUNCT
ejpam-3010	239	12	semigroup	semigroup	NOUN
ejpam-3010	239	13	such	such	ADJ
ejpam-3010	239	14	that	that	SCONJ
ejpam-3010	239	15	the	the	DET
ejpam-3010	239	16	ideals	ideal	NOUN
ejpam-3010	239	17	of	of	ADP
ejpam-3010	239	18	m	m	PROPN
ejpam-3010	239	19	form	form	VERB
ejpam-3010	239	20	a	a	DET
ejpam-3010	239	21	chain	chain	NOUN
ejpam-3010	239	22	.	.	PUNCT
ejpam-3010	240	1	then	then	ADV
ejpam-3010	240	2	,	,	PUNCT
ejpam-3010	240	3	for	for	ADP
ejpam-3010	240	4	every	every	DET
ejpam-3010	240	5	x	x	NOUN
ejpam-3010	240	6	,	,	PUNCT
ejpam-3010	240	7	y	y	PROPN
ejpam-3010	240	8	∈m	∈m	NOUN
ejpam-3010	240	9	and	and	CCONJ
ejpam-3010	240	10	every	every	DET
ejpam-3010	240	11	γ	γ	PROPN
ejpam-3010	240	12	∈	∈	PROPN
ejpam-3010	240	13	γ	γ	X
ejpam-3010	240	14	,	,	PUNCT
ejpam-3010	240	15	we	we	PRON
ejpam-3010	240	16	have	have	VERB
ejpam-3010	240	17	x	x	SYM
ejpam-3010	240	18	∈	∈	PROPN
ejpam-3010	240	19	(	(	PUNCT
ejpam-3010	240	20	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	240	21	]	]	PUNCT
ejpam-3010	240	22	or	or	CCONJ
ejpam-3010	240	23	y	y	PROPN
ejpam-3010	240	24	∈	∈	PROPN
ejpam-3010	240	25	(	(	PUNCT
ejpam-3010	240	26	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	240	27	]	]	PUNCT
ejpam-3010	240	28	.	.	PUNCT
ejpam-3010	241	1	proof	proof	NOUN
ejpam-3010	241	2	.	.	PUNCT
ejpam-3010	242	1	let	let	VERB
ejpam-3010	242	2	x	x	PRON
ejpam-3010	242	3	,	,	PUNCT
ejpam-3010	242	4	y	y	PROPN
ejpam-3010	242	5	∈	∈	PROPN
ejpam-3010	242	6	m	m	VERB
ejpam-3010	242	7	and	and	CCONJ
ejpam-3010	242	8	γ	γ	PROPN
ejpam-3010	242	9	∈	∈	PROPN
ejpam-3010	242	10	γ	γ	X
ejpam-3010	242	11	.	.	PROPN
ejpam-3010	243	1	since	since	SCONJ
ejpam-3010	243	2	m	m	PROPN
ejpam-3010	243	3	is	be	AUX
ejpam-3010	243	4	intra	intra	ADJ
ejpam-3010	243	5	-	-	ADJ
ejpam-3010	243	6	regular	regular	ADJ
ejpam-3010	243	7	and	and	CCONJ
ejpam-3010	243	8	the	the	DET
ejpam-3010	243	9	ideals	ideal	NOUN
ejpam-3010	243	10	of	of	ADP
ejpam-3010	243	11	m	m	PROPN
ejpam-3010	243	12	form	form	VERB
ejpam-3010	243	13	a	a	DET
ejpam-3010	243	14	chain	chain	NOUN
ejpam-3010	243	15	,	,	PUNCT
ejpam-3010	243	16	by	by	ADP
ejpam-3010	243	17	theorem	theorem	NOUN
ejpam-3010	243	18	13	13	NUM
ejpam-3010	243	19	,	,	PUNCT
ejpam-3010	243	20	the	the	DET
ejpam-3010	243	21	ideals	ideal	NOUN
ejpam-3010	243	22	of	of	ADP
ejpam-3010	243	23	m	m	NOUN
ejpam-3010	243	24	are	be	AUX
ejpam-3010	243	25	prime	prime	ADJ
ejpam-3010	243	26	.	.	PUNCT
ejpam-3010	244	1	since	since	SCONJ
ejpam-3010	244	2	(	(	PUNCT
ejpam-3010	244	3	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	244	4	]	]	PUNCT
ejpam-3010	244	5	is	be	AUX
ejpam-3010	244	6	an	an	DET
ejpam-3010	244	7	ideal	ideal	NOUN
ejpam-3010	244	8	of	of	ADP
ejpam-3010	244	9	m	m	PRON
ejpam-3010	244	10	,	,	PUNCT
ejpam-3010	244	11	(	(	PUNCT
ejpam-3010	244	12	mγxγyγm	mγxγyγm	X
ejpam-3010	244	13	]	]	PUNCT
ejpam-3010	244	14	is	be	AUX
ejpam-3010	244	15	prime	prime	ADJ
ejpam-3010	244	16	.	.	PUNCT
ejpam-3010	245	1	since	since	SCONJ
ejpam-3010	245	2	(	(	PUNCT
ejpam-3010	245	3	xγx)γ(yγy	xγx)γ(yγy	PROPN
ejpam-3010	245	4	)	)	PUNCT
ejpam-3010	245	5	∈	∈	PROPN
ejpam-3010	245	6	(	(	PUNCT
ejpam-3010	245	7	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	245	8	]	]	PUNCT
ejpam-3010	245	9	,	,	PUNCT
ejpam-3010	245	10	we	we	PRON
ejpam-3010	245	11	have	have	AUX
ejpam-3010	245	12	xγx	xγx	VERB
ejpam-3010	245	13	∈	∈	PROPN
ejpam-3010	245	14	(	(	PUNCT
ejpam-3010	245	15	mγxγyγm	mγxγyγm	NOUN
ejpam-3010	245	16	]	]	PUNCT
ejpam-3010	245	17	or	or	CCONJ
ejpam-3010	245	18	yγy	yγy	PROPN
ejpam-3010	245	19	∈	∈	PROPN
ejpam-3010	245	20	(	(	PUNCT
ejpam-3010	245	21	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	245	22	]	]	X
ejpam-3010	245	23	.	.	PUNCT
ejpam-3010	246	1	if	if	SCONJ
ejpam-3010	246	2	xγx	xγx	PROPN
ejpam-3010	246	3	∈	∈	PROPN
ejpam-3010	246	4	(	(	PUNCT
ejpam-3010	246	5	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	246	6	]	]	PUNCT
ejpam-3010	246	7	then	then	ADV
ejpam-3010	246	8	,	,	PUNCT
ejpam-3010	246	9	since	since	SCONJ
ejpam-3010	246	10	(	(	PUNCT
ejpam-3010	246	11	mγxγyγm	mγxγyγm	X
ejpam-3010	246	12	]	]	PUNCT
ejpam-3010	246	13	is	be	AUX
ejpam-3010	246	14	prime	prime	ADJ
ejpam-3010	246	15	,	,	PUNCT
ejpam-3010	246	16	we	we	PRON
ejpam-3010	246	17	have	have	VERB
ejpam-3010	246	18	x	x	SYM
ejpam-3010	246	19	∈	∈	PROPN
ejpam-3010	246	20	(	(	PUNCT
ejpam-3010	246	21	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	246	22	]	]	X
ejpam-3010	246	23	.	.	PUNCT
ejpam-3010	247	1	if	if	SCONJ
ejpam-3010	247	2	yγy	yγy	PROPN
ejpam-3010	247	3	∈	∈	PROPN
ejpam-3010	247	4	(	(	PUNCT
ejpam-3010	247	5	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	247	6	]	]	X
ejpam-3010	247	7	,	,	PUNCT
ejpam-3010	247	8	then	then	ADV
ejpam-3010	247	9	y	y	PROPN
ejpam-3010	247	10	∈	∈	PROPN
ejpam-3010	247	11	(	(	PUNCT
ejpam-3010	247	12	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	247	13	]	]	PUNCT
ejpam-3010	247	14	.	.	PUNCT
ejpam-3010	248	1	�	�	PROPN
ejpam-3010	248	2	definition	definition	NOUN
ejpam-3010	248	3	15	15	NUM
ejpam-3010	248	4	.	.	PUNCT
ejpam-3010	249	1	a	a	DET
ejpam-3010	249	2	po	po	NOUN
ejpam-3010	249	3	-	-	PUNCT
ejpam-3010	249	4	γ	γ	NOUN
ejpam-3010	249	5	-	-	PUNCT
ejpam-3010	249	6	semigroup	semigroup	NOUN
ejpam-3010	249	7	m	m	VERB
ejpam-3010	249	8	is	be	AUX
ejpam-3010	249	9	called	call	VERB
ejpam-3010	249	10	a	a	DET
ejpam-3010	249	11	chain	chain	NOUN
ejpam-3010	249	12	of	of	ADP
ejpam-3010	249	13	simple	simple	ADJ
ejpam-3010	249	14	semigroups	semigroup	NOUN
ejpam-3010	249	15	if	if	SCONJ
ejpam-3010	249	16	there	there	PRON
ejpam-3010	249	17	exists	exist	VERB
ejpam-3010	249	18	a	a	DET
ejpam-3010	249	19	semilattice	semilattice	NOUN
ejpam-3010	249	20	congruence	congruence	PROPN
ejpam-3010	249	21	σ	σ	PROPN
ejpam-3010	249	22	on	on	ADP
ejpam-3010	249	23	m	m	PRON
ejpam-3010	249	24	such	such	ADJ
ejpam-3010	249	25	that	that	SCONJ
ejpam-3010	249	26	(	(	PUNCT
ejpam-3010	249	27	x)σ	x)σ	X
ejpam-3010	249	28	is	be	AUX
ejpam-3010	249	29	a	a	DET
ejpam-3010	249	30	simple	simple	ADJ
ejpam-3010	249	31	subsemigroup	subsemigroup	NOUN
ejpam-3010	249	32	of	of	ADP
ejpam-3010	249	33	m	m	PROPN
ejpam-3010	249	34	for	for	ADP
ejpam-3010	249	35	every	every	DET
ejpam-3010	249	36	x	x	SYM
ejpam-3010	249	37	∈m	∈m	NOUN
ejpam-3010	249	38	and	and	CCONJ
ejpam-3010	249	39	the	the	DET
ejpam-3010	249	40	set	set	NOUN
ejpam-3010	249	41	m	m	PROPN
ejpam-3010	249	42	/	/	SYM
ejpam-3010	249	43	σ	σ	PROPN
ejpam-3010	249	44	of	of	ADP
ejpam-3010	249	45	all	all	DET
ejpam-3010	249	46	σ	σ	NOUN
ejpam-3010	249	47	-	-	PUNCT
ejpam-3010	249	48	classes	class	NOUN
ejpam-3010	249	49	of	of	ADP
ejpam-3010	249	50	m	m	PROPN
ejpam-3010	249	51	endowed	endow	VERB
ejpam-3010	249	52	with	with	ADP
ejpam-3010	249	53	the	the	DET
ejpam-3010	249	54	order	order	NOUN
ejpam-3010	249	55	relation	relation	NOUN
ejpam-3010	249	56	(	(	PUNCT
ejpam-3010	249	57	x)σ	x)σ	X
ejpam-3010	249	58	�	�	PROPN
ejpam-3010	249	59	(	(	PUNCT
ejpam-3010	249	60	y)σ	y)σ	X
ejpam-3010	249	61	⇔	⇔	X
ejpam-3010	249	62	(	(	PUNCT
ejpam-3010	249	63	x)σ	x)σ	X
ejpam-3010	249	64	=	=	SYM
ejpam-3010	249	65	(	(	PUNCT
ejpam-3010	249	66	xγy)σ	xγy)σ	PROPN
ejpam-3010	249	67	∀	∀	X
ejpam-3010	249	68	γ	γ	X
ejpam-3010	249	69	∈	∈	PROPN
ejpam-3010	249	70	γ	γ	X
ejpam-3010	249	71	is	be	AUX
ejpam-3010	249	72	a	a	DET
ejpam-3010	249	73	chain	chain	NOUN
ejpam-3010	249	74	.	.	PUNCT
ejpam-3010	250	1	in	in	ADP
ejpam-3010	250	2	other	other	ADJ
ejpam-3010	250	3	words	word	NOUN
ejpam-3010	250	4	,	,	PUNCT
ejpam-3010	250	5	for	for	ADP
ejpam-3010	250	6	any	any	DET
ejpam-3010	250	7	x	x	NOUN
ejpam-3010	250	8	,	,	PUNCT
ejpam-3010	250	9	y	y	PROPN
ejpam-3010	250	10	∈m	∈m	NOUN
ejpam-3010	250	11	and	and	CCONJ
ejpam-3010	250	12	any	any	DET
ejpam-3010	250	13	γ	γ	PROPN
ejpam-3010	250	14	∈	∈	PROPN
ejpam-3010	250	15	γ	γ	NOUN
ejpam-3010	250	16	we	we	PRON
ejpam-3010	250	17	have	have	VERB
ejpam-3010	250	18	(	(	PUNCT
ejpam-3010	250	19	x)σ	x)σ	NOUN
ejpam-3010	250	20	=	=	SYM
ejpam-3010	250	21	(	(	PUNCT
ejpam-3010	250	22	xγy)σ	xγy)σ	PROPN
ejpam-3010	250	23	or	or	CCONJ
ejpam-3010	250	24	(	(	PUNCT
ejpam-3010	250	25	y)σ	y)σ	X
ejpam-3010	250	26	=	=	SYM
ejpam-3010	250	27	(	(	PUNCT
ejpam-3010	250	28	xγy)σ	xγy)σ	PROPN
ejpam-3010	250	29	.	.	PUNCT
ejpam-3010	251	1	n.	n.	PROPN
ejpam-3010	251	2	kehayopulu	kehayopulu	PROPN
ejpam-3010	251	3	/	/	SYM
ejpam-3010	251	4	eur	eur	PROPN
ejpam-3010	251	5	.	.	PUNCT
ejpam-3010	252	1	j.	j.	PROPN
ejpam-3010	252	2	pure	pure	PROPN
ejpam-3010	252	3	appl	appl	PROPN
ejpam-3010	252	4	.	.	PROPN
ejpam-3010	252	5	math	math	PROPN
ejpam-3010	252	6	,	,	PUNCT
ejpam-3010	252	7	10	10	NUM
ejpam-3010	252	8	(	(	PUNCT
ejpam-3010	252	9	4	4	NUM
ejpam-3010	252	10	)	)	PUNCT
ejpam-3010	252	11	(	(	PUNCT
ejpam-3010	252	12	2017	2017	NUM
ejpam-3010	252	13	)	)	PUNCT
ejpam-3010	252	14	,	,	PUNCT
ejpam-3010	252	15	620	620	NUM
ejpam-3010	252	16	-	-	SYM
ejpam-3010	252	17	630	630	NUM
ejpam-3010	252	18	627	627	NUM
ejpam-3010	252	19	theorem	theorem	NOUN
ejpam-3010	252	20	16	16	NUM
ejpam-3010	252	21	.	.	PUNCT
ejpam-3010	253	1	a	a	DET
ejpam-3010	253	2	po	po	VERB
ejpam-3010	253	3	-	-	PUNCT
ejpam-3010	253	4	γ	γ	NOUN
ejpam-3010	253	5	-	-	PUNCT
ejpam-3010	253	6	semigroup	semigroup	NOUN
ejpam-3010	253	7	m	m	VERB
ejpam-3010	253	8	is	be	AUX
ejpam-3010	253	9	intra	intra	ADJ
ejpam-3010	253	10	-	-	ADJ
ejpam-3010	253	11	regular	regular	ADJ
ejpam-3010	253	12	and	and	CCONJ
ejpam-3010	253	13	the	the	DET
ejpam-3010	253	14	ideals	ideal	NOUN
ejpam-3010	253	15	of	of	ADP
ejpam-3010	253	16	m	m	PROPN
ejpam-3010	253	17	form	form	VERB
ejpam-3010	253	18	a	a	DET
ejpam-3010	253	19	chain	chain	NOUN
ejpam-3010	254	1	if	if	SCONJ
ejpam-3010	254	2	and	and	CCONJ
ejpam-3010	254	3	only	only	ADV
ejpam-3010	254	4	if	if	SCONJ
ejpam-3010	254	5	m	m	NOUN
ejpam-3010	254	6	is	be	AUX
ejpam-3010	254	7	chain	chain	NOUN
ejpam-3010	254	8	of	of	ADP
ejpam-3010	254	9	simple	simple	ADJ
ejpam-3010	254	10	semigroups	semigroup	NOUN
ejpam-3010	254	11	.	.	PUNCT
ejpam-3010	255	1	proof	proof	NOUN
ejpam-3010	255	2	.	.	PUNCT
ejpam-3010	256	1	=	=	NOUN
ejpam-3010	256	2	⇒.	⇒.	NOUN
ejpam-3010	256	3	since	since	SCONJ
ejpam-3010	256	4	m	m	PROPN
ejpam-3010	256	5	is	be	AUX
ejpam-3010	256	6	intra	intra	ADJ
ejpam-3010	256	7	-	-	ADJ
ejpam-3010	256	8	regular	regular	ADJ
ejpam-3010	256	9	and	and	CCONJ
ejpam-3010	256	10	n	n	PRON
ejpam-3010	256	11	is	be	AUX
ejpam-3010	256	12	a	a	DET
ejpam-3010	256	13	semilattice	semilattice	NOUN
ejpam-3010	256	14	congruence	congruence	NOUN
ejpam-3010	256	15	on	on	ADP
ejpam-3010	256	16	m	m	PROPN
ejpam-3010	256	17	,	,	PUNCT
ejpam-3010	256	18	by	by	ADP
ejpam-3010	256	19	theorem	theorem	ADJ
ejpam-3010	256	20	8(1)⇒	8(1)⇒	NOUN
ejpam-3010	256	21	(	(	PUNCT
ejpam-3010	256	22	5	5	NUM
ejpam-3010	256	23	)	)	PUNCT
ejpam-3010	256	24	,	,	PUNCT
ejpam-3010	256	25	(	(	PUNCT
ejpam-3010	256	26	x)n	x)n	X
ejpam-3010	256	27	is	be	AUX
ejpam-3010	256	28	a	a	DET
ejpam-3010	256	29	simple	simple	ADJ
ejpam-3010	256	30	subsemigroup	subsemigroup	NOUN
ejpam-3010	256	31	of	of	ADP
ejpam-3010	256	32	m	m	PROPN
ejpam-3010	256	33	for	for	ADP
ejpam-3010	256	34	every	every	DET
ejpam-3010	256	35	x	x	SYM
ejpam-3010	256	36	∈m	∈m	NOUN
ejpam-3010	256	37	,	,	PUNCT
ejpam-3010	256	38	so	so	ADV
ejpam-3010	256	39	m	m	NOUN
ejpam-3010	256	40	is	be	AUX
ejpam-3010	256	41	a	a	DET
ejpam-3010	256	42	semilattice	semilattice	NOUN
ejpam-3010	256	43	of	of	ADP
ejpam-3010	256	44	simple	simple	ADJ
ejpam-3010	256	45	semigroups	semigroup	NOUN
ejpam-3010	256	46	.	.	PUNCT
ejpam-3010	257	1	let	let	VERB
ejpam-3010	257	2	now	now	ADV
ejpam-3010	257	3	x	x	NOUN
ejpam-3010	257	4	,	,	PUNCT
ejpam-3010	257	5	y	y	PROPN
ejpam-3010	257	6	∈m	∈m	NOUN
ejpam-3010	257	7	and	and	CCONJ
ejpam-3010	257	8	γ	γ	PROPN
ejpam-3010	257	9	∈	∈	PROPN
ejpam-3010	257	10	γ	γ	X
ejpam-3010	257	11	.	.	PROPN
ejpam-3010	257	12	then	then	ADV
ejpam-3010	257	13	(	(	PUNCT
ejpam-3010	257	14	x)n	x)n	PUNCT
ejpam-3010	257	15	=	=	SYM
ejpam-3010	257	16	(	(	PUNCT
ejpam-3010	257	17	xγy)n	xγy)n	PROPN
ejpam-3010	257	18	or	or	CCONJ
ejpam-3010	257	19	(	(	PUNCT
ejpam-3010	257	20	y)n	y)n	PROPN
ejpam-3010	257	21	=	=	SYM
ejpam-3010	257	22	(	(	PUNCT
ejpam-3010	257	23	xγy)n	xγy)n	PROPN
ejpam-3010	257	24	.	.	PUNCT
ejpam-3010	258	1	in	in	ADP
ejpam-3010	258	2	fact	fact	NOUN
ejpam-3010	258	3	:	:	PUNCT
ejpam-3010	258	4	since	since	SCONJ
ejpam-3010	258	5	m	m	PROPN
ejpam-3010	258	6	is	be	AUX
ejpam-3010	258	7	intra	intra	ADJ
ejpam-3010	258	8	-	-	ADJ
ejpam-3010	258	9	regular	regular	ADJ
ejpam-3010	258	10	and	and	CCONJ
ejpam-3010	258	11	the	the	DET
ejpam-3010	258	12	ideals	ideal	NOUN
ejpam-3010	258	13	of	of	ADP
ejpam-3010	258	14	m	m	PROPN
ejpam-3010	258	15	form	form	VERB
ejpam-3010	258	16	a	a	DET
ejpam-3010	258	17	chain	chain	NOUN
ejpam-3010	258	18	,	,	PUNCT
ejpam-3010	258	19	by	by	ADP
ejpam-3010	258	20	proposition	proposition	NOUN
ejpam-3010	258	21	14	14	NUM
ejpam-3010	258	22	,	,	PUNCT
ejpam-3010	258	23	we	we	PRON
ejpam-3010	258	24	have	have	VERB
ejpam-3010	258	25	x	x	PROPN
ejpam-3010	258	26	∈	∈	PROPN
ejpam-3010	258	27	(	(	PUNCT
ejpam-3010	258	28	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	258	29	]	]	PUNCT
ejpam-3010	258	30	or	or	CCONJ
ejpam-3010	258	31	y	y	PROPN
ejpam-3010	258	32	∈	∈	PROPN
ejpam-3010	258	33	(	(	PUNCT
ejpam-3010	258	34	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	258	35	]	]	X
ejpam-3010	258	36	.	.	PUNCT
ejpam-3010	259	1	if	if	SCONJ
ejpam-3010	259	2	x	x	SYM
ejpam-3010	259	3	∈	∈	PROPN
ejpam-3010	259	4	(	(	PUNCT
ejpam-3010	259	5	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	259	6	]	]	X
ejpam-3010	259	7	,	,	PUNCT
ejpam-3010	259	8	then	then	ADV
ejpam-3010	259	9	n(x	n(x	X
ejpam-3010	259	10	)	)	PUNCT
ejpam-3010	259	11	3	3	NUM
ejpam-3010	259	12	x	x	SYM
ejpam-3010	259	13	≤	≤	ADV
ejpam-3010	259	14	aµ(xγy)ρb	aµ(xγy)ρb	PROPN
ejpam-3010	259	15	for	for	ADP
ejpam-3010	259	16	some	some	PRON
ejpam-3010	259	17	a	a	PRON
ejpam-3010	259	18	,	,	PUNCT
ejpam-3010	259	19	b	b	NOUN
ejpam-3010	259	20	∈m	∈m	NOUN
ejpam-3010	259	21	,	,	PUNCT
ejpam-3010	259	22	µ	µ	NUM
ejpam-3010	259	23	,	,	PUNCT
ejpam-3010	259	24	ρ	ρ	PROPN
ejpam-3010	259	25	∈	∈	PROPN
ejpam-3010	259	26	γ	γ	X
ejpam-3010	259	27	.	.	PROPN
ejpam-3010	259	28	since	since	SCONJ
ejpam-3010	259	29	n(x	n(x	PROPN
ejpam-3010	259	30	)	)	PUNCT
ejpam-3010	259	31	is	be	AUX
ejpam-3010	259	32	a	a	DET
ejpam-3010	259	33	filter	filter	NOUN
ejpam-3010	259	34	of	of	ADP
ejpam-3010	259	35	m	m	PROPN
ejpam-3010	259	36	,	,	PUNCT
ejpam-3010	259	37	we	we	PRON
ejpam-3010	259	38	have	have	VERB
ejpam-3010	259	39	aµ(xγy)ρb	aµ(xγy)ρb	PROPN
ejpam-3010	259	40	∈	∈	PROPN
ejpam-3010	259	41	n(x	n(x	PROPN
ejpam-3010	259	42	)	)	PUNCT
ejpam-3010	259	43	,	,	PUNCT
ejpam-3010	259	44	then	then	ADV
ejpam-3010	259	45	(	(	PUNCT
ejpam-3010	259	46	xγy)ρb	xγy)ρb	NOUN
ejpam-3010	259	47	∈	∈	PROPN
ejpam-3010	259	48	n(x	n(x	PROPN
ejpam-3010	259	49	)	)	PUNCT
ejpam-3010	259	50	,	,	PUNCT
ejpam-3010	259	51	xγy	xγy	NOUN
ejpam-3010	259	52	∈	∈	PROPN
ejpam-3010	259	53	n(x	n(x	PROPN
ejpam-3010	259	54	)	)	PUNCT
ejpam-3010	259	55	and	and	CCONJ
ejpam-3010	259	56	n(xγy	n(xγy	NOUN
ejpam-3010	259	57	)	)	PUNCT
ejpam-3010	260	1	⊆	⊆	NUM
ejpam-3010	260	2	n(x	n(x	NOUN
ejpam-3010	260	3	)	)	PUNCT
ejpam-3010	260	4	.	.	PUNCT
ejpam-3010	261	1	if	if	SCONJ
ejpam-3010	261	2	y	y	PROPN
ejpam-3010	261	3	∈	∈	PROPN
ejpam-3010	261	4	(	(	PUNCT
ejpam-3010	261	5	mγxγyγm	mγxγyγm	PROPN
ejpam-3010	261	6	]	]	X
ejpam-3010	261	7	,	,	PUNCT
ejpam-3010	261	8	then	then	ADV
ejpam-3010	261	9	n(y	n(y	ADJ
ejpam-3010	261	10	)	)	PUNCT
ejpam-3010	261	11	3	3	NUM
ejpam-3010	261	12	y	y	PROPN
ejpam-3010	261	13	≤	≤	NOUN
ejpam-3010	261	14	cξ(xγy)ζd	cξ(xγy)ζd	NOUN
ejpam-3010	261	15	for	for	ADP
ejpam-3010	261	16	some	some	DET
ejpam-3010	261	17	c	c	NOUN
ejpam-3010	261	18	,	,	PUNCT
ejpam-3010	261	19	d	d	NOUN
ejpam-3010	261	20	∈m	∈m	NOUN
ejpam-3010	261	21	,	,	PUNCT
ejpam-3010	261	22	ξ	ξ	PROPN
ejpam-3010	261	23	,	,	PUNCT
ejpam-3010	261	24	ζ	ζ	PROPN
ejpam-3010	261	25	∈	∈	PROPN
ejpam-3010	261	26	γ	γ	NOUN
ejpam-3010	261	27	,	,	PUNCT
ejpam-3010	261	28	then	then	ADV
ejpam-3010	261	29	cξ(xγy)ζd	cξ(xγy)ζd	PROPN
ejpam-3010	261	30	∈	∈	PROPN
ejpam-3010	261	31	n(y	n(y	PROPN
ejpam-3010	261	32	)	)	PUNCT
ejpam-3010	261	33	,	,	PUNCT
ejpam-3010	261	34	xγy	xγy	PROPN
ejpam-3010	261	35	∈	∈	PROPN
ejpam-3010	261	36	n(y	n(y	PROPN
ejpam-3010	261	37	)	)	PUNCT
ejpam-3010	261	38	,	,	PUNCT
ejpam-3010	261	39	and	and	CCONJ
ejpam-3010	261	40	n(xγy	n(xγy	PROPN
ejpam-3010	261	41	)	)	PUNCT
ejpam-3010	261	42	⊆	⊆	NUM
ejpam-3010	261	43	n(y	n(y	NUM
ejpam-3010	261	44	)	)	PUNCT
ejpam-3010	261	45	.	.	PUNCT
ejpam-3010	262	1	on	on	ADP
ejpam-3010	262	2	the	the	DET
ejpam-3010	262	3	other	other	ADJ
ejpam-3010	262	4	hand	hand	NOUN
ejpam-3010	262	5	,	,	PUNCT
ejpam-3010	262	6	since	since	SCONJ
ejpam-3010	262	7	xγy	xγy	PROPN
ejpam-3010	262	8	∈	∈	PROPN
ejpam-3010	262	9	n(xγy	n(xγy	PROPN
ejpam-3010	262	10	)	)	PUNCT
ejpam-3010	262	11	,	,	PUNCT
ejpam-3010	262	12	we	we	PRON
ejpam-3010	262	13	have	have	VERB
ejpam-3010	262	14	x	x	X
ejpam-3010	262	15	∈	∈	PROPN
ejpam-3010	262	16	n(xγy	n(xγy	PROPN
ejpam-3010	262	17	)	)	PUNCT
ejpam-3010	262	18	and	and	CCONJ
ejpam-3010	262	19	y	y	PROPN
ejpam-3010	262	20	∈	∈	PROPN
ejpam-3010	262	21	n(xγy	n(xγy	PROPN
ejpam-3010	262	22	)	)	PUNCT
ejpam-3010	262	23	,	,	PUNCT
ejpam-3010	262	24	so	so	ADV
ejpam-3010	262	25	n(x	n(x	NOUN
ejpam-3010	262	26	)	)	PUNCT
ejpam-3010	262	27	⊆	⊆	NUM
ejpam-3010	262	28	n(xγy	n(xγy	NOUN
ejpam-3010	262	29	)	)	PUNCT
ejpam-3010	262	30	and	and	CCONJ
ejpam-3010	262	31	n(y	n(y	NUM
ejpam-3010	262	32	)	)	PUNCT
ejpam-3010	262	33	⊆	⊆	NUM
ejpam-3010	262	34	n(xγy	n(xγy	NOUN
ejpam-3010	262	35	)	)	PUNCT
ejpam-3010	262	36	.	.	PUNCT
ejpam-3010	263	1	thus	thus	ADV
ejpam-3010	263	2	we	we	PRON
ejpam-3010	263	3	get	get	VERB
ejpam-3010	263	4	n(x	n(x	PRON
ejpam-3010	263	5	)	)	PUNCT
ejpam-3010	263	6	=	=	PUNCT
ejpam-3010	263	7	n(xγy	n(xγy	PROPN
ejpam-3010	263	8	)	)	PUNCT
ejpam-3010	263	9	or	or	CCONJ
ejpam-3010	263	10	n(y	n(y	NUM
ejpam-3010	263	11	)	)	PUNCT
ejpam-3010	263	12	=	=	SYM
ejpam-3010	263	13	n(xγy	n(xγy	PROPN
ejpam-3010	263	14	)	)	PUNCT
ejpam-3010	263	15	,	,	PUNCT
ejpam-3010	263	16	then	then	ADV
ejpam-3010	263	17	(	(	PUNCT
ejpam-3010	263	18	x)n	x)n	PUNCT
ejpam-3010	263	19	=	=	SYM
ejpam-3010	263	20	(	(	PUNCT
ejpam-3010	263	21	xγy)n	xγy)n	PROPN
ejpam-3010	263	22	or	or	CCONJ
ejpam-3010	263	23	(	(	PUNCT
ejpam-3010	263	24	y)n	y)n	PROPN
ejpam-3010	263	25	=	=	SYM
ejpam-3010	263	26	(	(	PUNCT
ejpam-3010	263	27	xγy)n	xγy)n	PROPN
ejpam-3010	263	28	.	.	PUNCT
ejpam-3010	264	1	therefore	therefore	ADV
ejpam-3010	264	2	m	m	PROPN
ejpam-3010	264	3	is	be	AUX
ejpam-3010	264	4	a	a	DET
ejpam-3010	264	5	chain	chain	NOUN
ejpam-3010	264	6	of	of	ADP
ejpam-3010	264	7	simple	simple	ADJ
ejpam-3010	264	8	semigroups	semigroup	NOUN
ejpam-3010	264	9	.	.	PUNCT
ejpam-3010	265	1	⇐	⇐	PROPN
ejpam-3010	265	2	=	=	PRON
ejpam-3010	265	3	.	.	PUNCT
ejpam-3010	266	1	let	let	VERB
ejpam-3010	266	2	σ	σ	NOUN
ejpam-3010	266	3	be	be	AUX
ejpam-3010	266	4	a	a	DET
ejpam-3010	266	5	semilattice	semilattice	NOUN
ejpam-3010	266	6	congruence	congruence	NOUN
ejpam-3010	266	7	on	on	ADP
ejpam-3010	266	8	m	m	PRON
ejpam-3010	266	9	such	such	ADJ
ejpam-3010	266	10	that	that	SCONJ
ejpam-3010	266	11	(	(	PUNCT
ejpam-3010	266	12	x)σ	x)σ	X
ejpam-3010	266	13	is	be	AUX
ejpam-3010	266	14	a	a	DET
ejpam-3010	266	15	simple	simple	ADJ
ejpam-3010	266	16	subsemigroup	subsemigroup	NOUN
ejpam-3010	266	17	of	of	ADP
ejpam-3010	266	18	m	m	PROPN
ejpam-3010	266	19	for	for	ADP
ejpam-3010	266	20	every	every	DET
ejpam-3010	266	21	x	x	SYM
ejpam-3010	266	22	∈	∈	PROPN
ejpam-3010	266	23	m	m	NOUN
ejpam-3010	266	24	and	and	CCONJ
ejpam-3010	266	25	(	(	PUNCT
ejpam-3010	266	26	m	m	PROPN
ejpam-3010	266	27	/	/	SYM
ejpam-3010	266	28	σ	σ	PROPN
ejpam-3010	266	29	,	,	PUNCT
ejpam-3010	266	30	�	�	PROPN
ejpam-3010	266	31	)	)	PUNCT
ejpam-3010	266	32	is	be	AUX
ejpam-3010	266	33	a	a	DET
ejpam-3010	266	34	chain	chain	NOUN
ejpam-3010	266	35	.	.	PUNCT
ejpam-3010	267	1	by	by	ADP
ejpam-3010	267	2	theorem	theorem	NOUN
ejpam-3010	267	3	13	13	NUM
ejpam-3010	267	4	it	it	PRON
ejpam-3010	267	5	is	be	AUX
ejpam-3010	267	6	enough	enough	ADJ
ejpam-3010	267	7	to	to	PART
ejpam-3010	267	8	prove	prove	VERB
ejpam-3010	267	9	that	that	SCONJ
ejpam-3010	267	10	the	the	DET
ejpam-3010	267	11	ideals	ideal	NOUN
ejpam-3010	267	12	of	of	ADP
ejpam-3010	267	13	m	m	NOUN
ejpam-3010	267	14	are	be	AUX
ejpam-3010	267	15	prime	prime	ADJ
ejpam-3010	267	16	.	.	PUNCT
ejpam-3010	268	1	so	so	ADV
ejpam-3010	268	2	,	,	PUNCT
ejpam-3010	268	3	let	let	VERB
ejpam-3010	268	4	i	i	PRON
ejpam-3010	268	5	be	be	AUX
ejpam-3010	268	6	an	an	DET
ejpam-3010	268	7	ideal	ideal	NOUN
ejpam-3010	268	8	of	of	ADP
ejpam-3010	268	9	m	m	PROPN
ejpam-3010	268	10	,	,	PUNCT
ejpam-3010	268	11	a	a	PRON
ejpam-3010	268	12	,	,	PUNCT
ejpam-3010	268	13	b	b	X
ejpam-3010	268	14	∈	∈	NOUN
ejpam-3010	268	15	m	m	NOUN
ejpam-3010	268	16	and	and	CCONJ
ejpam-3010	268	17	γ	γ	PROPN
ejpam-3010	268	18	∈	∈	PROPN
ejpam-3010	268	19	γ	γ	NOUN
ejpam-3010	268	20	such	such	ADJ
ejpam-3010	268	21	that	that	SCONJ
ejpam-3010	268	22	aγb	aγb	VERB
ejpam-3010	268	23	∈	∈	PROPN
ejpam-3010	268	24	i.	i.	NOUN
ejpam-3010	268	25	the	the	DET
ejpam-3010	268	26	set	set	NOUN
ejpam-3010	268	27	(	(	PUNCT
ejpam-3010	268	28	aγb)σ	aγb)σ	PROPN
ejpam-3010	268	29	∩	∩	NOUN
ejpam-3010	268	30	i	i	PRON
ejpam-3010	268	31	is	be	AUX
ejpam-3010	268	32	an	an	DET
ejpam-3010	268	33	ideal	ideal	NOUN
ejpam-3010	268	34	of	of	ADP
ejpam-3010	268	35	(	(	PUNCT
ejpam-3010	268	36	aγb)σ	aγb)σ	PROPN
ejpam-3010	268	37	.	.	PROPN
ejpam-3010	269	1	indeed	indeed	ADV
ejpam-3010	269	2	:	:	PUNCT
ejpam-3010	269	3	∅	∅	NOUN
ejpam-3010	269	4	6=	6=	NUM
ejpam-3010	269	5	(	(	PUNCT
ejpam-3010	269	6	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	7	∩	∩	NOUN
ejpam-3010	269	8	i	i	PRON
ejpam-3010	269	9	⊆	⊆	NUM
ejpam-3010	269	10	(	(	PUNCT
ejpam-3010	269	11	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	12	(	(	PUNCT
ejpam-3010	269	13	aγb	aγb	NOUN
ejpam-3010	269	14	∈	∈	PROPN
ejpam-3010	269	15	(	(	PUNCT
ejpam-3010	269	16	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	17	,	,	PUNCT
ejpam-3010	269	18	aγb	aγb	NOUN
ejpam-3010	269	19	∈	∈	PROPN
ejpam-3010	269	20	i	i	PROPN
ejpam-3010	269	21	)	)	PUNCT
ejpam-3010	269	22	,	,	PUNCT
ejpam-3010	269	23	(	(	PUNCT
ejpam-3010	269	24	(	(	PUNCT
ejpam-3010	269	25	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	26	∩	∩	ADJ
ejpam-3010	269	27	i	i	NOUN
ejpam-3010	269	28	)	)	PUNCT
ejpam-3010	269	29	γ(aγb)σ	γ(aγb)σ	NOUN
ejpam-3010	269	30	⊆	⊆	NUM
ejpam-3010	269	31	(	(	PUNCT
ejpam-3010	269	32	aγb)σγ(aγb)σ	aγb)σγ(aγb)σ	NOUN
ejpam-3010	269	33	∩	∩	NOUN
ejpam-3010	269	34	iγ(aγb)σ	iγ(aγb)σ	X
ejpam-3010	269	35	⊆	⊆	NUM
ejpam-3010	269	36	(	(	PUNCT
ejpam-3010	269	37	aγb)σ	aγb)σ	NOUN
ejpam-3010	269	38	∩	∩	NOUN
ejpam-3010	269	39	iγ(aγb)σ	iγ(aγb)σ	X
ejpam-3010	269	40	⊆	⊆	NUM
ejpam-3010	269	41	(	(	PUNCT
ejpam-3010	269	42	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	43	∩	∩	NOUN
ejpam-3010	269	44	iγm	iγm	ADJ
ejpam-3010	269	45	⊆	⊆	NUM
ejpam-3010	269	46	(	(	PUNCT
ejpam-3010	269	47	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	48	∩	∩	NOUN
ejpam-3010	269	49	i	i	PRON
ejpam-3010	269	50	,	,	PUNCT
ejpam-3010	269	51	(	(	PUNCT
ejpam-3010	269	52	aγb)σγ	aγb)σγ	INTJ
ejpam-3010	269	53	(	(	PUNCT
ejpam-3010	269	54	(	(	PUNCT
ejpam-3010	269	55	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	56	∩	∩	NOUN
ejpam-3010	269	57	i	i	NOUN
ejpam-3010	269	58	)	)	PUNCT
ejpam-3010	269	59	⊆	⊆	X
ejpam-3010	269	60	(	(	PUNCT
ejpam-3010	269	61	aγb)σγ(aγb)σ	aγb)σγ(aγb)σ	PROPN
ejpam-3010	269	62	∩	∩	NOUN
ejpam-3010	269	63	(	(	PUNCT
ejpam-3010	269	64	aγb)σγi	aγb)σγi	VERB
ejpam-3010	269	65	⊆	⊆	NUM
ejpam-3010	269	66	(	(	PUNCT
ejpam-3010	269	67	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	68	∩mγi	∩mγi	PROPN
ejpam-3010	269	69	⊆	⊆	NUM
ejpam-3010	269	70	(	(	PUNCT
ejpam-3010	269	71	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	72	∩	∩	ADJ
ejpam-3010	269	73	i.	i.	NOUN
ejpam-3010	269	74	let	let	VERB
ejpam-3010	269	75	x	x	X
ejpam-3010	269	76	∈	∈	PROPN
ejpam-3010	269	77	(	(	PUNCT
ejpam-3010	269	78	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	79	∩	∩	NOUN
ejpam-3010	269	80	i	i	PRON
ejpam-3010	269	81	and	and	CCONJ
ejpam-3010	269	82	(	(	PUNCT
ejpam-3010	269	83	aγb)σ	aγb)σ	PROPN
ejpam-3010	269	84	3	3	NUM
ejpam-3010	269	85	y	y	PROPN
ejpam-3010	269	86	≤	≤	NUM
ejpam-3010	269	87	x.	x.	NOUN
ejpam-3010	270	1	since	since	SCONJ
ejpam-3010	270	2	m	m	PROPN
ejpam-3010	270	3	3	3	NUM
ejpam-3010	270	4	y	y	PROPN
ejpam-3010	270	5	≤	≤	NUM
ejpam-3010	270	6	x	x	PUNCT
ejpam-3010	270	7	∈	∈	PROPN
ejpam-3010	271	1	i	i	PRON
ejpam-3010	271	2	and	and	CCONJ
ejpam-3010	271	3	i	i	PRON
ejpam-3010	271	4	is	be	AUX
ejpam-3010	271	5	an	an	DET
ejpam-3010	271	6	ideal	ideal	NOUN
ejpam-3010	271	7	of	of	ADP
ejpam-3010	271	8	m	m	PROPN
ejpam-3010	271	9	,	,	PUNCT
ejpam-3010	271	10	we	we	PRON
ejpam-3010	271	11	have	have	VERB
ejpam-3010	271	12	y	y	PROPN
ejpam-3010	271	13	∈	∈	PROPN
ejpam-3010	272	1	i	i	PRON
ejpam-3010	272	2	,	,	PUNCT
ejpam-3010	272	3	then	then	ADV
ejpam-3010	272	4	y	y	PROPN
ejpam-3010	272	5	∈	∈	PROPN
ejpam-3010	272	6	(	(	PUNCT
ejpam-3010	272	7	aγb)σ	aγb)σ	PROPN
ejpam-3010	272	8	∩	∩	ADJ
ejpam-3010	272	9	i.	i.	NOUN
ejpam-3010	272	10	since	since	SCONJ
ejpam-3010	272	11	(	(	PUNCT
ejpam-3010	272	12	aγb)σ	aγb)σ	PROPN
ejpam-3010	272	13	is	be	AUX
ejpam-3010	272	14	simple	simple	ADJ
ejpam-3010	272	15	,	,	PUNCT
ejpam-3010	272	16	we	we	PRON
ejpam-3010	272	17	have	have	VERB
ejpam-3010	272	18	(	(	PUNCT
ejpam-3010	272	19	aγb)σ	aγb)σ	VERB
ejpam-3010	272	20	∩	∩	NOUN
ejpam-3010	272	21	i	i	PRON
ejpam-3010	272	22	=	=	SYM
ejpam-3010	272	23	(	(	PUNCT
ejpam-3010	272	24	aγb)σ	aγb)σ	PROPN
ejpam-3010	272	25	.	.	PROPN
ejpam-3010	272	26	by	by	ADP
ejpam-3010	272	27	hypothesis	hypothesis	NOUN
ejpam-3010	272	28	,	,	PUNCT
ejpam-3010	272	29	(	(	PUNCT
ejpam-3010	272	30	a)σ	a)σ	X
ejpam-3010	272	31	=	=	SYM
ejpam-3010	272	32	(	(	PUNCT
ejpam-3010	272	33	aγb)σ	aγb)σ	PROPN
ejpam-3010	272	34	or	or	CCONJ
ejpam-3010	272	35	(	(	PUNCT
ejpam-3010	272	36	b)σ	b)σ	PUNCT
ejpam-3010	272	37	=	=	SYM
ejpam-3010	272	38	(	(	PUNCT
ejpam-3010	272	39	aγb)σ	aγb)σ	PROPN
ejpam-3010	272	40	.	.	PROPN
ejpam-3010	273	1	then	then	ADV
ejpam-3010	273	2	we	we	PRON
ejpam-3010	273	3	have	have	VERB
ejpam-3010	273	4	a	a	DET
ejpam-3010	273	5	∈	∈	ADJ
ejpam-3010	273	6	i	i	PRON
ejpam-3010	273	7	or	or	CCONJ
ejpam-3010	273	8	b	b	X
ejpam-3010	273	9	∈	∈	PROPN
ejpam-3010	274	1	i	i	PRON
ejpam-3010	274	2	,	,	PUNCT
ejpam-3010	274	3	thus	thus	ADV
ejpam-3010	274	4	i	i	PRON
ejpam-3010	274	5	is	be	AUX
ejpam-3010	274	6	a	a	DET
ejpam-3010	274	7	prime	prime	NOUN
ejpam-3010	274	8	.	.	PUNCT
ejpam-3010	275	1	�	�	PROPN
ejpam-3010	275	2	lemma	lemma	PROPN
ejpam-3010	275	3	17	17	NUM
ejpam-3010	275	4	.	.	PUNCT
ejpam-3010	276	1	let	let	VERB
ejpam-3010	276	2	m	m	PRON
ejpam-3010	276	3	be	be	AUX
ejpam-3010	276	4	a	a	DET
ejpam-3010	276	5	po	po	NOUN
ejpam-3010	276	6	-	-	PUNCT
ejpam-3010	276	7	γ	γ	NOUN
ejpam-3010	276	8	-	-	PUNCT
ejpam-3010	276	9	semigroup	semigroup	NOUN
ejpam-3010	276	10	,	,	PUNCT
ejpam-3010	276	11	t	t	PROPN
ejpam-3010	276	12	a	a	DET
ejpam-3010	276	13	subsemigroup	subsemigroup	NOUN
ejpam-3010	276	14	of	of	ADP
ejpam-3010	276	15	m	m	PROPN
ejpam-3010	276	16	and	and	CCONJ
ejpam-3010	276	17	x	x	PROPN
ejpam-3010	276	18	∈	∈	PROPN
ejpam-3010	276	19	t	t	NOUN
ejpam-3010	276	20	.	.	PUNCT
ejpam-3010	277	1	then	then	ADV
ejpam-3010	277	2	the	the	DET
ejpam-3010	277	3	set	set	NOUN
ejpam-3010	277	4	(	(	PUNCT
ejpam-3010	277	5	mγxγm	mγxγm	VERB
ejpam-3010	277	6	]	]	PUNCT
ejpam-3010	277	7	∩	∩	PROPN
ejpam-3010	277	8	t	t	PROPN
ejpam-3010	277	9	is	be	AUX
ejpam-3010	277	10	an	an	DET
ejpam-3010	277	11	ideal	ideal	NOUN
ejpam-3010	277	12	of	of	ADP
ejpam-3010	277	13	t.	t.	NOUN
ejpam-3010	277	14	proof	proof	NOUN
ejpam-3010	277	15	.	.	PUNCT
ejpam-3010	278	1	first	first	ADV
ejpam-3010	278	2	of	of	ADP
ejpam-3010	278	3	all	all	PRON
ejpam-3010	278	4	,	,	PUNCT
ejpam-3010	278	5	the	the	DET
ejpam-3010	278	6	set	set	NOUN
ejpam-3010	278	7	(	(	PUNCT
ejpam-3010	278	8	mγxγm	mγxγm	VERB
ejpam-3010	278	9	]	]	PUNCT
ejpam-3010	278	10	∩	∩	PROPN
ejpam-3010	278	11	t	t	PROPN
ejpam-3010	278	12	is	be	AUX
ejpam-3010	278	13	a	a	DET
ejpam-3010	278	14	nonempty	nonempty	ADJ
ejpam-3010	278	15	subset	subset	NOUN
ejpam-3010	278	16	of	of	ADP
ejpam-3010	278	17	t	t	PROPN
ejpam-3010	278	18	.	.	PUNCT
ejpam-3010	279	1	indeed	indeed	ADV
ejpam-3010	279	2	:	:	PUNCT
ejpam-3010	279	3	take	take	VERB
ejpam-3010	279	4	an	an	DET
ejpam-3010	279	5	element	element	NOUN
ejpam-3010	279	6	γ	γ	NOUN
ejpam-3010	279	7	∈	∈	PROPN
ejpam-3010	279	8	γ	γ	X
ejpam-3010	279	9	(	(	PUNCT
ejpam-3010	279	10	γ	γ	PROPN
ejpam-3010	279	11	6=	6=	NOUN
ejpam-3010	279	12	∅	∅	NOUN
ejpam-3010	279	13	)	)	PUNCT
ejpam-3010	279	14	.	.	PUNCT
ejpam-3010	280	1	then	then	ADV
ejpam-3010	280	2	we	we	PRON
ejpam-3010	280	3	have	have	VERB
ejpam-3010	280	4	xγxγx	xγxγx	PROPN
ejpam-3010	280	5	∈	∈	PROPN
ejpam-3010	280	6	mγxγm	mγxγm	NOUN
ejpam-3010	280	7	and	and	CCONJ
ejpam-3010	280	8	xγxγx	xγxγx	PROPN
ejpam-3010	280	9	∈	∈	PROPN
ejpam-3010	280	10	(	(	PUNCT
ejpam-3010	280	11	tγt	tγt	NOUN
ejpam-3010	280	12	)	)	PUNCT
ejpam-3010	280	13	γt	γt	NOUN
ejpam-3010	280	14	⊆	⊆	NUM
ejpam-3010	280	15	tγt	tγt	NOUN
ejpam-3010	280	16	⊆	⊆	NUM
ejpam-3010	280	17	t	t	NOUN
ejpam-3010	280	18	.	.	PUNCT
ejpam-3010	281	1	moreover	moreover	ADV
ejpam-3010	281	2	,	,	PUNCT
ejpam-3010	281	3	(	(	PUNCT
ejpam-3010	281	4	(	(	PUNCT
ejpam-3010	281	5	mγxγm	mγxγm	VERB
ejpam-3010	281	6	]	]	PUNCT
ejpam-3010	281	7	∩	∩	PROPN
ejpam-3010	281	8	t	t	NOUN
ejpam-3010	281	9	)	)	PUNCT
ejpam-3010	281	10	γt	γt	ADP
ejpam-3010	281	11	⊆	⊆	NUM
ejpam-3010	281	12	(	(	PUNCT
ejpam-3010	281	13	mγxγm	mγxγm	NOUN
ejpam-3010	281	14	]	]	PUNCT
ejpam-3010	281	15	γt	γt	NOUN
ejpam-3010	281	16	∩	∩	NOUN
ejpam-3010	281	17	tγt	tγt	VERB
ejpam-3010	281	18	⊆	⊆	NUM
ejpam-3010	281	19	(	(	PUNCT
ejpam-3010	281	20	mγxγm	mγxγm	NOUN
ejpam-3010	281	21	]	]	PUNCT
ejpam-3010	281	22	γ(m	γ(m	PROPN
ejpam-3010	281	23	]	]	PUNCT
ejpam-3010	281	24	∩	∩	PROPN
ejpam-3010	281	25	t	t	PROPN
ejpam-3010	281	26	n.	n.	PROPN
ejpam-3010	281	27	kehayopulu	kehayopulu	PROPN
ejpam-3010	281	28	/	/	SYM
ejpam-3010	281	29	eur	eur	PROPN
ejpam-3010	281	30	.	.	PUNCT
ejpam-3010	282	1	j.	j.	PROPN
ejpam-3010	282	2	pure	pure	PROPN
ejpam-3010	282	3	appl	appl	PROPN
ejpam-3010	282	4	.	.	PROPN
ejpam-3010	282	5	math	math	PROPN
ejpam-3010	282	6	,	,	PUNCT
ejpam-3010	282	7	10	10	NUM
ejpam-3010	282	8	(	(	PUNCT
ejpam-3010	282	9	4	4	NUM
ejpam-3010	282	10	)	)	PUNCT
ejpam-3010	282	11	(	(	PUNCT
ejpam-3010	282	12	2017	2017	NUM
ejpam-3010	282	13	)	)	PUNCT
ejpam-3010	282	14	,	,	PUNCT
ejpam-3010	282	15	620	620	NUM
ejpam-3010	282	16	-	-	SYM
ejpam-3010	282	17	630	630	NUM
ejpam-3010	282	18	628	628	NUM
ejpam-3010	282	19	⊆	⊆	NUM
ejpam-3010	282	20	(	(	PUNCT
ejpam-3010	282	21	mγxγ(mγm	mγxγ(mγm	PROPN
ejpam-3010	282	22	)	)	PUNCT
ejpam-3010	282	23	]	]	PUNCT
ejpam-3010	283	1	∩	∩	PROPN
ejpam-3010	283	2	t	t	PROPN
ejpam-3010	283	3	⊆	⊆	NUM
ejpam-3010	283	4	(	(	PUNCT
ejpam-3010	283	5	mγxγm	mγxγm	NOUN
ejpam-3010	283	6	]	]	PUNCT
ejpam-3010	283	7	∩	∩	PROPN
ejpam-3010	283	8	t.	t.	NOUN
ejpam-3010	283	9	in	in	ADP
ejpam-3010	283	10	a	a	DET
ejpam-3010	283	11	similar	similar	ADJ
ejpam-3010	283	12	way	way	NOUN
ejpam-3010	283	13	,	,	PUNCT
ejpam-3010	283	14	we	we	PRON
ejpam-3010	283	15	have	have	VERB
ejpam-3010	283	16	tγ	tγ	VERB
ejpam-3010	283	17	(	(	PUNCT
ejpam-3010	283	18	(	(	PUNCT
ejpam-3010	283	19	mγxγm	mγxγm	VERB
ejpam-3010	283	20	]	]	PUNCT
ejpam-3010	283	21	∩t	∩t	NOUN
ejpam-3010	283	22	)	)	PUNCT
ejpam-3010	284	1	⊆	⊆	X
ejpam-3010	284	2	(	(	PUNCT
ejpam-3010	284	3	mγxγm	mγxγm	NOUN
ejpam-3010	284	4	]	]	PUNCT
ejpam-3010	284	5	∩t	∩t	NOUN
ejpam-3010	284	6	.	.	PUNCT
ejpam-3010	285	1	let	let	VERB
ejpam-3010	285	2	now	now	ADV
ejpam-3010	285	3	a	a	DET
ejpam-3010	285	4	∈	∈	NOUN
ejpam-3010	285	5	(	(	PUNCT
ejpam-3010	285	6	mγxγm	mγxγm	NOUN
ejpam-3010	285	7	]	]	PUNCT
ejpam-3010	285	8	∩t	∩t	PROPN
ejpam-3010	285	9	and	and	CCONJ
ejpam-3010	285	10	t	t	PROPN
ejpam-3010	285	11	3	3	NUM
ejpam-3010	285	12	b	b	PROPN
ejpam-3010	285	13	≤	≤	NUM
ejpam-3010	285	14	a.	a.	NOUN
ejpam-3010	285	15	since	since	SCONJ
ejpam-3010	285	16	a	a	DET
ejpam-3010	285	17	∈	∈	PROPN
ejpam-3010	285	18	(	(	PUNCT
ejpam-3010	285	19	mγxγm	mγxγm	PROPN
ejpam-3010	285	20	]	]	PUNCT
ejpam-3010	285	21	,	,	PUNCT
ejpam-3010	285	22	there	there	PRON
ejpam-3010	285	23	exist	exist	VERB
ejpam-3010	285	24	u	u	NOUN
ejpam-3010	285	25	,	,	PUNCT
ejpam-3010	285	26	v	v	NOUN
ejpam-3010	285	27	∈	∈	NOUN
ejpam-3010	285	28	m	m	NOUN
ejpam-3010	285	29	and	and	CCONJ
ejpam-3010	285	30	ξ	ξ	PROPN
ejpam-3010	285	31	,	,	PUNCT
ejpam-3010	285	32	ζ	ζ	PROPN
ejpam-3010	285	33	∈	∈	PROPN
ejpam-3010	285	34	γ	γ	NOUN
ejpam-3010	285	35	such	such	ADJ
ejpam-3010	285	36	that	that	SCONJ
ejpam-3010	285	37	a	a	DET
ejpam-3010	285	38	≤	≤	ADJ
ejpam-3010	285	39	uξxζv	uξxζv	NOUN
ejpam-3010	285	40	.	.	PUNCT
ejpam-3010	286	1	then	then	ADV
ejpam-3010	286	2	we	we	PRON
ejpam-3010	286	3	have	have	VERB
ejpam-3010	286	4	b	b	NUM
ejpam-3010	286	5	≤	≤	ADJ
ejpam-3010	286	6	uξxζv	uξxζv	PROPN
ejpam-3010	286	7	∈mγxγm	∈mγxγm	PROPN
ejpam-3010	286	8	,	,	PUNCT
ejpam-3010	286	9	and	and	CCONJ
ejpam-3010	286	10	b	b	X
ejpam-3010	286	11	∈	∈	PROPN
ejpam-3010	286	12	(	(	PUNCT
ejpam-3010	286	13	mγxγm	mγxγm	PROPN
ejpam-3010	286	14	]	]	PUNCT
ejpam-3010	286	15	,	,	PUNCT
ejpam-3010	286	16	thus	thus	ADV
ejpam-3010	286	17	b	b	X
ejpam-3010	286	18	∈	∈	PROPN
ejpam-3010	286	19	(	(	PUNCT
ejpam-3010	286	20	mγxγm	mγxγm	NOUN
ejpam-3010	286	21	]	]	PUNCT
ejpam-3010	286	22	∩t	∩t	PROPN
ejpam-3010	286	23	.	.	PUNCT
ejpam-3010	287	1	�	�	PROPN
ejpam-3010	287	2	theorem	theorem	VERB
ejpam-3010	287	3	18	18	NUM
ejpam-3010	287	4	.	.	PUNCT
ejpam-3010	288	1	let	let	VERB
ejpam-3010	288	2	m	m	PRON
ejpam-3010	288	3	be	be	AUX
ejpam-3010	288	4	an	an	DET
ejpam-3010	288	5	intra	intra	ADJ
ejpam-3010	288	6	-	-	ADJ
ejpam-3010	288	7	regular	regular	ADJ
ejpam-3010	288	8	po	po	NOUN
ejpam-3010	288	9	-	-	PUNCT
ejpam-3010	288	10	γ	γ	NOUN
ejpam-3010	288	11	-	-	PUNCT
ejpam-3010	288	12	semigroup	semigroup	NOUN
ejpam-3010	288	13	.	.	PUNCT
ejpam-3010	289	1	then	then	ADV
ejpam-3010	289	2	the	the	DET
ejpam-3010	289	3	set	set	NOUN
ejpam-3010	289	4	(	(	PUNCT
ejpam-3010	289	5	x)n	x)n	X
ejpam-3010	289	6	is	be	AUX
ejpam-3010	289	7	a	a	DET
ejpam-3010	289	8	maximal	maximal	ADJ
ejpam-3010	289	9	simple	simple	ADJ
ejpam-3010	289	10	subsemigroup	subsemigroup	NOUN
ejpam-3010	289	11	of	of	ADP
ejpam-3010	289	12	m	m	PROPN
ejpam-3010	289	13	for	for	ADP
ejpam-3010	289	14	every	every	DET
ejpam-3010	289	15	x	x	SYM
ejpam-3010	289	16	∈	∈	PROPN
ejpam-3010	289	17	m	m	NOUN
ejpam-3010	289	18	.	.	PUNCT
ejpam-3010	290	1	moreover	moreover	ADV
ejpam-3010	290	2	,	,	PUNCT
ejpam-3010	290	3	if	if	SCONJ
ejpam-3010	290	4	t	t	PROPN
ejpam-3010	290	5	is	be	AUX
ejpam-3010	290	6	a	a	DET
ejpam-3010	290	7	maximal	maximal	ADJ
ejpam-3010	290	8	simple	simple	ADJ
ejpam-3010	290	9	subsemigroup	subsemigroup	NOUN
ejpam-3010	290	10	of	of	ADP
ejpam-3010	290	11	m	m	PROPN
ejpam-3010	290	12	,	,	PUNCT
ejpam-3010	290	13	then	then	ADV
ejpam-3010	290	14	there	there	PRON
ejpam-3010	290	15	exists	exist	VERB
ejpam-3010	290	16	x	x	X
ejpam-3010	290	17	∈m	∈m	NOUN
ejpam-3010	290	18	such	such	ADJ
ejpam-3010	290	19	that	that	DET
ejpam-3010	290	20	t	t	NOUN
ejpam-3010	290	21	=	=	SYM
ejpam-3010	290	22	(	(	PUNCT
ejpam-3010	290	23	x)n	x)n	X
ejpam-3010	290	24	.	.	PUNCT
ejpam-3010	291	1	proof	proof	NOUN
ejpam-3010	291	2	.	.	PUNCT
ejpam-3010	292	1	let	let	VERB
ejpam-3010	292	2	x	x	SYM
ejpam-3010	292	3	∈	∈	PROPN
ejpam-3010	292	4	m	m	VERB
ejpam-3010	292	5	.	.	PUNCT
ejpam-3010	293	1	by	by	ADP
ejpam-3010	293	2	the	the	DET
ejpam-3010	293	3	theorem	theorem	ADJ
ejpam-3010	293	4	8(1)⇒	8(1)⇒	PROPN
ejpam-3010	293	5	(	(	PUNCT
ejpam-3010	293	6	5	5	NUM
ejpam-3010	293	7	)	)	PUNCT
ejpam-3010	293	8	,	,	PUNCT
ejpam-3010	293	9	the	the	DET
ejpam-3010	293	10	set	set	NOUN
ejpam-3010	293	11	(	(	PUNCT
ejpam-3010	293	12	x)n	x)n	X
ejpam-3010	293	13	is	be	AUX
ejpam-3010	293	14	a	a	DET
ejpam-3010	293	15	simple	simple	ADJ
ejpam-3010	293	16	subsemigroup	subsemigroup	NOUN
ejpam-3010	293	17	of	of	ADP
ejpam-3010	293	18	m	m	PROPN
ejpam-3010	293	19	.	.	PUNCT
ejpam-3010	294	1	let	let	VERB
ejpam-3010	294	2	now	now	ADV
ejpam-3010	294	3	t	t	AUX
ejpam-3010	294	4	be	be	AUX
ejpam-3010	294	5	a	a	DET
ejpam-3010	294	6	simple	simple	ADJ
ejpam-3010	294	7	subsemigroup	subsemigroup	NOUN
ejpam-3010	294	8	of	of	ADP
ejpam-3010	294	9	m	m	NOUN
ejpam-3010	294	10	such	such	ADJ
ejpam-3010	294	11	that	that	SCONJ
ejpam-3010	294	12	t	t	PROPN
ejpam-3010	294	13	⊇	⊇	PROPN
ejpam-3010	294	14	(	(	PUNCT
ejpam-3010	294	15	x)n	x)n	PROPN
ejpam-3010	294	16	.	.	PUNCT
ejpam-3010	295	1	then	then	ADV
ejpam-3010	295	2	t	t	PROPN
ejpam-3010	295	3	=	=	SYM
ejpam-3010	295	4	(	(	PUNCT
ejpam-3010	295	5	x)n	x)n	PROPN
ejpam-3010	295	6	.	.	PUNCT
ejpam-3010	296	1	indeed	indeed	ADV
ejpam-3010	296	2	:	:	PUNCT
ejpam-3010	296	3	let	let	VERB
ejpam-3010	296	4	y	y	PROPN
ejpam-3010	296	5	∈	∈	PROPN
ejpam-3010	296	6	t	t	PROPN
ejpam-3010	296	7	.	.	PUNCT
ejpam-3010	297	1	since	since	SCONJ
ejpam-3010	297	2	x	x	PROPN
ejpam-3010	297	3	∈	∈	PROPN
ejpam-3010	297	4	t	t	PROPN
ejpam-3010	297	5	and	and	CCONJ
ejpam-3010	297	6	t	t	PROPN
ejpam-3010	297	7	is	be	AUX
ejpam-3010	297	8	a	a	DET
ejpam-3010	297	9	subsemigroup	subsemigroup	NOUN
ejpam-3010	297	10	of	of	ADP
ejpam-3010	297	11	m	m	PRON
ejpam-3010	297	12	,	,	PUNCT
ejpam-3010	297	13	by	by	ADP
ejpam-3010	297	14	lemma	lemma	PROPN
ejpam-3010	297	15	17	17	NUM
ejpam-3010	297	16	,	,	PUNCT
ejpam-3010	297	17	the	the	DET
ejpam-3010	297	18	set	set	NOUN
ejpam-3010	297	19	(	(	PUNCT
ejpam-3010	297	20	mγxγm	mγxγm	VERB
ejpam-3010	297	21	]	]	PUNCT
ejpam-3010	297	22	∩	∩	PROPN
ejpam-3010	297	23	t	t	PROPN
ejpam-3010	297	24	is	be	AUX
ejpam-3010	297	25	an	an	DET
ejpam-3010	297	26	ideal	ideal	NOUN
ejpam-3010	297	27	of	of	ADP
ejpam-3010	297	28	t	t	PROPN
ejpam-3010	297	29	.	.	PUNCT
ejpam-3010	298	1	since	since	SCONJ
ejpam-3010	298	2	t	t	PROPN
ejpam-3010	298	3	is	be	AUX
ejpam-3010	298	4	a	a	DET
ejpam-3010	298	5	simple	simple	ADJ
ejpam-3010	298	6	subsemigroup	subsemigroup	NOUN
ejpam-3010	298	7	of	of	ADP
ejpam-3010	298	8	m	m	PROPN
ejpam-3010	298	9	,	,	PUNCT
ejpam-3010	298	10	we	we	PRON
ejpam-3010	298	11	have	have	AUX
ejpam-3010	298	12	(	(	PUNCT
ejpam-3010	298	13	mγxγm	mγxγm	VERB
ejpam-3010	298	14	]	]	PUNCT
ejpam-3010	298	15	∩	∩	ADJ
ejpam-3010	298	16	t	t	NOUN
ejpam-3010	298	17	=	=	SYM
ejpam-3010	298	18	t	t	PROPN
ejpam-3010	298	19	,	,	PUNCT
ejpam-3010	298	20	then	then	ADV
ejpam-3010	298	21	y	y	PROPN
ejpam-3010	298	22	∈	∈	PROPN
ejpam-3010	298	23	(	(	PUNCT
ejpam-3010	298	24	mγxγm	mγxγm	VERB
ejpam-3010	298	25	]	]	PUNCT
ejpam-3010	298	26	.	.	PUNCT
ejpam-3010	299	1	since	since	SCONJ
ejpam-3010	299	2	m	m	PROPN
ejpam-3010	299	3	is	be	AUX
ejpam-3010	299	4	intra	intra	ADJ
ejpam-3010	299	5	-	-	ADJ
ejpam-3010	299	6	regular	regular	ADJ
ejpam-3010	299	7	,	,	PUNCT
ejpam-3010	299	8	by	by	ADP
ejpam-3010	299	9	lemma	lemma	PROPN
ejpam-3010	299	10	3	3	NUM
ejpam-3010	299	11	,	,	PUNCT
ejpam-3010	299	12	we	we	PRON
ejpam-3010	299	13	have	have	VERB
ejpam-3010	299	14	x	x	PROPN
ejpam-3010	299	15	∈	∈	PROPN
ejpam-3010	299	16	n(y	n(y	PROPN
ejpam-3010	299	17	)	)	PUNCT
ejpam-3010	299	18	,	,	PUNCT
ejpam-3010	299	19	then	then	ADV
ejpam-3010	299	20	n(x	n(x	PROPN
ejpam-3010	299	21	)	)	PUNCT
ejpam-3010	299	22	⊆	⊆	NUM
ejpam-3010	299	23	n(y	n(y	NUM
ejpam-3010	299	24	)	)	PUNCT
ejpam-3010	299	25	.	.	PUNCT
ejpam-3010	300	1	on	on	ADP
ejpam-3010	300	2	the	the	DET
ejpam-3010	300	3	other	other	ADJ
ejpam-3010	300	4	hand	hand	NOUN
ejpam-3010	300	5	,	,	PUNCT
ejpam-3010	300	6	since	since	SCONJ
ejpam-3010	300	7	y	y	PROPN
ejpam-3010	300	8	∈	∈	PROPN
ejpam-3010	300	9	t	t	PROPN
ejpam-3010	300	10	and	and	CCONJ
ejpam-3010	300	11	t	t	PROPN
ejpam-3010	300	12	is	be	AUX
ejpam-3010	300	13	a	a	DET
ejpam-3010	300	14	subsemigroup	subsemigroup	NOUN
ejpam-3010	300	15	of	of	ADP
ejpam-3010	300	16	m	m	PRON
ejpam-3010	300	17	,	,	PUNCT
ejpam-3010	300	18	by	by	ADP
ejpam-3010	300	19	lemma	lemma	PROPN
ejpam-3010	300	20	17	17	NUM
ejpam-3010	300	21	,	,	PUNCT
ejpam-3010	300	22	the	the	DET
ejpam-3010	300	23	set	set	NOUN
ejpam-3010	300	24	(	(	PUNCT
ejpam-3010	300	25	mγyγm	mγyγm	X
ejpam-3010	300	26	]	]	PUNCT
ejpam-3010	300	27	∩	∩	NOUN
ejpam-3010	300	28	t	t	PROPN
ejpam-3010	300	29	is	be	AUX
ejpam-3010	300	30	an	an	DET
ejpam-3010	300	31	ideal	ideal	NOUN
ejpam-3010	300	32	of	of	ADP
ejpam-3010	300	33	t	t	PROPN
ejpam-3010	300	34	.	.	PUNCT
ejpam-3010	301	1	so	so	ADV
ejpam-3010	301	2	(	(	PUNCT
ejpam-3010	301	3	mγyγm	mγyγm	X
ejpam-3010	301	4	]	]	PUNCT
ejpam-3010	301	5	∩	∩	NOUN
ejpam-3010	301	6	t	t	PROPN
ejpam-3010	301	7	=	=	SYM
ejpam-3010	301	8	t	t	PROPN
ejpam-3010	301	9	,	,	PUNCT
ejpam-3010	301	10	x	x	PUNCT
ejpam-3010	301	11	∈	∈	PROPN
ejpam-3010	301	12	(	(	PUNCT
ejpam-3010	301	13	mγyγm	mγyγm	PROPN
ejpam-3010	301	14	]	]	PUNCT
ejpam-3010	301	15	,	,	PUNCT
ejpam-3010	301	16	y	y	PROPN
ejpam-3010	301	17	∈	∈	PROPN
ejpam-3010	301	18	n(x	n(x	PROPN
ejpam-3010	301	19	)	)	PUNCT
ejpam-3010	301	20	,	,	PUNCT
ejpam-3010	301	21	and	and	CCONJ
ejpam-3010	301	22	n(y	n(y	NUM
ejpam-3010	301	23	)	)	PUNCT
ejpam-3010	301	24	⊆	⊆	NUM
ejpam-3010	301	25	n(x	n(x	PROPN
ejpam-3010	301	26	)	)	PUNCT
ejpam-3010	301	27	.	.	PUNCT
ejpam-3010	302	1	therefore	therefore	ADV
ejpam-3010	302	2	we	we	PRON
ejpam-3010	302	3	have	have	VERB
ejpam-3010	302	4	n(x	n(x	NOUN
ejpam-3010	302	5	)	)	PUNCT
ejpam-3010	302	6	=	=	SYM
ejpam-3010	302	7	n(y	n(y	PROPN
ejpam-3010	302	8	)	)	PUNCT
ejpam-3010	302	9	,	,	PUNCT
ejpam-3010	302	10	then	then	ADV
ejpam-3010	302	11	y	y	PROPN
ejpam-3010	302	12	∈	∈	PROPN
ejpam-3010	302	13	(	(	PUNCT
ejpam-3010	302	14	x)n	x)n	PUNCT
ejpam-3010	302	15	,	,	PUNCT
ejpam-3010	302	16	and	and	CCONJ
ejpam-3010	302	17	t	t	PROPN
ejpam-3010	302	18	⊆	⊆	NUM
ejpam-3010	302	19	(	(	PUNCT
ejpam-3010	302	20	x)n	x)n	X
ejpam-3010	302	21	.	.	PUNCT
ejpam-3010	303	1	then	then	ADV
ejpam-3010	303	2	we	we	PRON
ejpam-3010	303	3	have	have	VERB
ejpam-3010	303	4	t	t	NOUN
ejpam-3010	303	5	=	=	SYM
ejpam-3010	303	6	(	(	PUNCT
ejpam-3010	303	7	x)n	x)n	PUNCT
ejpam-3010	303	8	,	,	PUNCT
ejpam-3010	303	9	thus	thus	ADV
ejpam-3010	303	10	the	the	DET
ejpam-3010	303	11	class	class	NOUN
ejpam-3010	303	12	(	(	PUNCT
ejpam-3010	303	13	x)n	x)n	X
ejpam-3010	303	14	is	be	AUX
ejpam-3010	303	15	a	a	DET
ejpam-3010	303	16	maximal	maximal	ADJ
ejpam-3010	303	17	simple	simple	ADJ
ejpam-3010	303	18	subsemigroup	subsemigroup	NOUN
ejpam-3010	303	19	of	of	ADP
ejpam-3010	303	20	m	m	PROPN
ejpam-3010	303	21	.	.	PUNCT
ejpam-3010	304	1	let	let	VERB
ejpam-3010	304	2	now	now	ADV
ejpam-3010	304	3	t	t	AUX
ejpam-3010	304	4	be	be	AUX
ejpam-3010	304	5	a	a	DET
ejpam-3010	304	6	maximal	maximal	ADJ
ejpam-3010	304	7	simple	simple	ADJ
ejpam-3010	304	8	subsemigroup	subsemigroup	NOUN
ejpam-3010	304	9	of	of	ADP
ejpam-3010	304	10	m	m	PROPN
ejpam-3010	304	11	.	.	PUNCT
ejpam-3010	305	1	take	take	VERB
ejpam-3010	305	2	an	an	DET
ejpam-3010	305	3	element	element	NOUN
ejpam-3010	305	4	x	x	SYM
ejpam-3010	305	5	∈	∈	PROPN
ejpam-3010	305	6	t	t	PROPN
ejpam-3010	305	7	(	(	PUNCT
ejpam-3010	305	8	t	t	PROPN
ejpam-3010	305	9	6=	6=	NUM
ejpam-3010	305	10	∅	∅	NOUN
ejpam-3010	305	11	)	)	PUNCT
ejpam-3010	305	12	.	.	PUNCT
ejpam-3010	306	1	exactly	exactly	ADV
ejpam-3010	306	2	as	as	ADP
ejpam-3010	306	3	in	in	ADP
ejpam-3010	306	4	the	the	DET
ejpam-3010	306	5	proof	proof	NOUN
ejpam-3010	306	6	of	of	ADP
ejpam-3010	306	7	the	the	DET
ejpam-3010	306	8	“	"	PUNCT
ejpam-3010	306	9	⇒”-part	⇒”-part	PROPN
ejpam-3010	306	10	of	of	ADP
ejpam-3010	306	11	the	the	DET
ejpam-3010	306	12	theorem	theorem	NOUN
ejpam-3010	306	13	given	give	VERB
ejpam-3010	306	14	above	above	ADV
ejpam-3010	306	15	,	,	PUNCT
ejpam-3010	306	16	we	we	PRON
ejpam-3010	306	17	prove	prove	VERB
ejpam-3010	306	18	that	that	SCONJ
ejpam-3010	306	19	t	t	PROPN
ejpam-3010	306	20	⊆	⊆	NUM
ejpam-3010	306	21	(	(	PUNCT
ejpam-3010	306	22	x)n	x)n	X
ejpam-3010	306	23	.	.	PUNCT
ejpam-3010	307	1	since	since	SCONJ
ejpam-3010	307	2	m	m	PROPN
ejpam-3010	307	3	is	be	AUX
ejpam-3010	307	4	intra	intra	ADJ
ejpam-3010	307	5	-	-	ADJ
ejpam-3010	307	6	regular	regular	ADJ
ejpam-3010	307	7	,	,	PUNCT
ejpam-3010	307	8	by	by	ADP
ejpam-3010	307	9	theorem	theorem	ADJ
ejpam-3010	307	10	8(1)⇒	8(1)⇒	NOUN
ejpam-3010	307	11	(	(	PUNCT
ejpam-3010	307	12	5	5	NUM
ejpam-3010	307	13	)	)	PUNCT
ejpam-3010	307	14	,	,	PUNCT
ejpam-3010	307	15	(	(	PUNCT
ejpam-3010	307	16	x)n	x)n	X
ejpam-3010	307	17	is	be	AUX
ejpam-3010	307	18	a	a	DET
ejpam-3010	307	19	simple	simple	ADJ
ejpam-3010	307	20	subsemigroup	subsemigroup	NOUN
ejpam-3010	307	21	of	of	ADP
ejpam-3010	307	22	m	m	PROPN
ejpam-3010	307	23	.	.	PUNCT
ejpam-3010	308	1	since	since	SCONJ
ejpam-3010	308	2	t	t	PROPN
ejpam-3010	308	3	⊆	⊆	NUM
ejpam-3010	308	4	(	(	PUNCT
ejpam-3010	308	5	x)n	x)n	PUNCT
ejpam-3010	308	6	and	and	CCONJ
ejpam-3010	308	7	t	t	PROPN
ejpam-3010	308	8	is	be	AUX
ejpam-3010	308	9	a	a	DET
ejpam-3010	308	10	maximal	maximal	ADJ
ejpam-3010	308	11	simple	simple	ADJ
ejpam-3010	308	12	subsemigroup	subsemigroup	NOUN
ejpam-3010	308	13	of	of	ADP
ejpam-3010	308	14	m	m	PROPN
ejpam-3010	308	15	,	,	PUNCT
ejpam-3010	308	16	we	we	PRON
ejpam-3010	308	17	have	have	VERB
ejpam-3010	308	18	t	t	NOUN
ejpam-3010	308	19	=	=	SYM
ejpam-3010	308	20	(	(	PUNCT
ejpam-3010	308	21	x)n	x)n	PROPN
ejpam-3010	308	22	.	.	PUNCT
ejpam-3010	309	1	�	�	PROPN
ejpam-3010	309	2	corollary	corollary	PROPN
ejpam-3010	309	3	19	19	NUM
ejpam-3010	309	4	.	.	PUNCT
ejpam-3010	310	1	for	for	ADP
ejpam-3010	310	2	an	an	DET
ejpam-3010	310	3	intra	intra	ADJ
ejpam-3010	310	4	-	-	ADJ
ejpam-3010	310	5	regular	regular	ADJ
ejpam-3010	310	6	po	po	NOUN
ejpam-3010	310	7	-	-	PUNCT
ejpam-3010	310	8	γ	γ	NOUN
ejpam-3010	310	9	-	-	PUNCT
ejpam-3010	310	10	semigroup	semigroup	NOUN
ejpam-3010	310	11	m	m	PROPN
ejpam-3010	310	12	,	,	PUNCT
ejpam-3010	310	13	the	the	DET
ejpam-3010	310	14	set	set	NOUN
ejpam-3010	310	15	{	{	PUNCT
ejpam-3010	310	16	(	(	PUNCT
ejpam-3010	310	17	x)n	x)n	PUNCT
ejpam-3010	310	18	|	|	ADV
ejpam-3010	310	19	x	x	SYM
ejpam-3010	310	20	∈m	∈m	NOUN
ejpam-3010	310	21	}	}	PUNCT
ejpam-3010	310	22	coincides	coincide	NOUN
ejpam-3010	310	23	with	with	ADP
ejpam-3010	310	24	the	the	DET
ejpam-3010	310	25	set	set	NOUN
ejpam-3010	310	26	of	of	ADP
ejpam-3010	310	27	all	all	DET
ejpam-3010	310	28	maximal	maximal	ADJ
ejpam-3010	310	29	simple	simple	ADJ
ejpam-3010	310	30	subsemigroup	subsemigroup	NOUN
ejpam-3010	310	31	of	of	ADP
ejpam-3010	310	32	m.	m.	NOUN
ejpam-3010	310	33	definition	definition	NOUN
ejpam-3010	310	34	20	20	NUM
ejpam-3010	310	35	.	.	PUNCT
ejpam-3010	311	1	[	[	X
ejpam-3010	311	2	9	9	NUM
ejpam-3010	311	3	]	]	PUNCT
ejpam-3010	311	4	a	a	DET
ejpam-3010	311	5	γ	γ	PROPN
ejpam-3010	311	6	-	-	PUNCT
ejpam-3010	311	7	semigroup	semigroup	NOUN
ejpam-3010	311	8	m	m	VERB
ejpam-3010	311	9	is	be	AUX
ejpam-3010	311	10	called	call	VERB
ejpam-3010	311	11	left	left	ADJ
ejpam-3010	311	12	(	(	PUNCT
ejpam-3010	311	13	resp	resp	NOUN
ejpam-3010	311	14	.	.	PUNCT
ejpam-3010	312	1	right	right	ADJ
ejpam-3010	312	2	)	)	PUNCT
ejpam-3010	313	1	regular	regular	ADJ
ejpam-3010	313	2	if	if	SCONJ
ejpam-3010	313	3	x	x	SYM
ejpam-3010	313	4	∈	∈	PROPN
ejpam-3010	313	5	(	(	PUNCT
ejpam-3010	313	6	mγxγx	mγxγx	ADJ
ejpam-3010	313	7	]	]	X
ejpam-3010	313	8	(	(	PUNCT
ejpam-3010	313	9	resp	resp	NOUN
ejpam-3010	313	10	.	.	PUNCT
ejpam-3010	314	1	x	x	X
ejpam-3010	314	2	∈	∈	PROPN
ejpam-3010	314	3	(	(	PUNCT
ejpam-3010	314	4	xγxγm	xγxγm	PROPN
ejpam-3010	314	5	]	]	X
ejpam-3010	314	6	)	)	PUNCT
ejpam-3010	314	7	for	for	ADP
ejpam-3010	314	8	every	every	DET
ejpam-3010	314	9	x	x	SYM
ejpam-3010	314	10	∈m	∈m	NOUN
ejpam-3010	314	11	and	and	CCONJ
ejpam-3010	314	12	every	every	DET
ejpam-3010	314	13	γ	γ	PROPN
ejpam-3010	314	14	∈	∈	PROPN
ejpam-3010	314	15	γ	γ	X
ejpam-3010	314	16	.	.	PUNCT
ejpam-3010	314	17	taking	take	VERB
ejpam-3010	314	18	into	into	ADP
ejpam-3010	314	19	account	account	NOUN
ejpam-3010	314	20	the	the	DET
ejpam-3010	314	21	theorem	theorem	NOUN
ejpam-3010	314	22	6	6	NUM
ejpam-3010	314	23	in	in	ADP
ejpam-3010	314	24	[	[	X
ejpam-3010	314	25	8	8	NUM
ejpam-3010	314	26	]	]	PUNCT
ejpam-3010	314	27	,	,	PUNCT
ejpam-3010	314	28	in	in	ADP
ejpam-3010	314	29	a	a	DET
ejpam-3010	314	30	similar	similar	ADJ
ejpam-3010	314	31	way	way	NOUN
ejpam-3010	314	32	as	as	ADP
ejpam-3010	314	33	in	in	ADP
ejpam-3010	314	34	the	the	DET
ejpam-3010	314	35	theorem	theorem	NOUN
ejpam-3010	314	36	8	8	NUM
ejpam-3010	314	37	above	above	ADV
ejpam-3010	314	38	,	,	PUNCT
ejpam-3010	314	39	we	we	PRON
ejpam-3010	314	40	can	can	AUX
ejpam-3010	314	41	prove	prove	VERB
ejpam-3010	314	42	the	the	DET
ejpam-3010	314	43	following	follow	VERB
ejpam-3010	314	44	theorem	theorem	NOUN
ejpam-3010	314	45	theorem	theorem	NOUN
ejpam-3010	314	46	21	21	NUM
ejpam-3010	314	47	.	.	PUNCT
ejpam-3010	315	1	let	let	VERB
ejpam-3010	315	2	m	m	PRON
ejpam-3010	315	3	be	be	AUX
ejpam-3010	315	4	a	a	DET
ejpam-3010	315	5	po	po	NOUN
ejpam-3010	315	6	-	-	PUNCT
ejpam-3010	315	7	γ	γ	NOUN
ejpam-3010	315	8	-	-	PUNCT
ejpam-3010	315	9	semigroup	semigroup	NOUN
ejpam-3010	315	10	.	.	PUNCT
ejpam-3010	316	1	the	the	DET
ejpam-3010	316	2	following	follow	VERB
ejpam-3010	316	3	are	be	AUX
ejpam-3010	316	4	equivalent	equivalent	ADJ
ejpam-3010	316	5	:	:	PUNCT
ejpam-3010	316	6	(	(	PUNCT
ejpam-3010	316	7	1	1	X
ejpam-3010	316	8	)	)	PUNCT
ejpam-3010	316	9	m	m	VERB
ejpam-3010	316	10	is	be	AUX
ejpam-3010	316	11	left	leave	VERB
ejpam-3010	316	12	regular	regular	ADV
ejpam-3010	316	13	and	and	CCONJ
ejpam-3010	316	14	(	(	PUNCT
ejpam-3010	316	15	xγm	xγm	NOUN
ejpam-3010	316	16	]	]	PUNCT
ejpam-3010	316	17	⊆	⊆	X
ejpam-3010	316	18	(	(	PUNCT
ejpam-3010	316	19	mγx	mγx	NOUN
ejpam-3010	316	20	]	]	PUNCT
ejpam-3010	316	21	for	for	ADP
ejpam-3010	316	22	every	every	DET
ejpam-3010	316	23	x	x	SYM
ejpam-3010	316	24	∈m	∈m	NOUN
ejpam-3010	316	25	.	.	PUNCT
ejpam-3010	317	1	(	(	PUNCT
ejpam-3010	317	2	2	2	X
ejpam-3010	317	3	)	)	PUNCT
ejpam-3010	317	4	n(x	n(x	X
ejpam-3010	317	5	)	)	PUNCT
ejpam-3010	317	6	=	=	SYM
ejpam-3010	317	7	{	{	PUNCT
ejpam-3010	317	8	y	y	NOUN
ejpam-3010	317	9	∈m	∈m	NOUN
ejpam-3010	317	10	|	|	ADV
ejpam-3010	317	11	x	x	SYM
ejpam-3010	317	12	∈	∈	PROPN
ejpam-3010	317	13	(	(	PUNCT
ejpam-3010	317	14	mγy	mγy	NOUN
ejpam-3010	317	15	]	]	X
ejpam-3010	317	16	}	}	PUNCT
ejpam-3010	317	17	for	for	ADP
ejpam-3010	317	18	every	every	DET
ejpam-3010	317	19	x	x	SYM
ejpam-3010	317	20	∈m	∈m	NOUN
ejpam-3010	317	21	.	.	PUNCT
ejpam-3010	318	1	(	(	PUNCT
ejpam-3010	318	2	3	3	X
ejpam-3010	318	3	)	)	PUNCT
ejpam-3010	318	4	n	n	PROPN
ejpam-3010	318	5	=	=	SYM
ejpam-3010	318	6	l.	l.	PROPN
ejpam-3010	318	7	(	(	PUNCT
ejpam-3010	318	8	4	4	NUM
ejpam-3010	318	9	)	)	PUNCT
ejpam-3010	318	10	for	for	ADP
ejpam-3010	318	11	every	every	DET
ejpam-3010	318	12	left	leave	VERB
ejpam-3010	318	13	ideal	ideal	ADJ
ejpam-3010	318	14	l	l	PROPN
ejpam-3010	318	15	of	of	ADP
ejpam-3010	318	16	m	m	PROPN
ejpam-3010	318	17	,	,	PUNCT
ejpam-3010	318	18	we	we	PRON
ejpam-3010	318	19	have	have	VERB
ejpam-3010	318	20	l	l	NOUN
ejpam-3010	318	21	=	=	PUNCT
ejpam-3010	318	22	⋃	⋃	PROPN
ejpam-3010	318	23	x∈l	x∈l	NUM
ejpam-3010	318	24	(	(	PUNCT
ejpam-3010	318	25	x)n	x)n	X
ejpam-3010	318	26	.	.	PUNCT
ejpam-3010	319	1	(	(	PUNCT
ejpam-3010	319	2	5	5	NUM
ejpam-3010	319	3	)	)	PUNCT
ejpam-3010	319	4	(	(	PUNCT
ejpam-3010	319	5	x)n	x)n	X
ejpam-3010	319	6	is	be	AUX
ejpam-3010	319	7	a	a	DET
ejpam-3010	319	8	left	left	ADJ
ejpam-3010	319	9	simple	simple	ADJ
ejpam-3010	319	10	subsemigroup	subsemigroup	NOUN
ejpam-3010	319	11	of	of	ADP
ejpam-3010	319	12	m	m	PROPN
ejpam-3010	319	13	for	for	ADP
ejpam-3010	319	14	every	every	DET
ejpam-3010	319	15	x	x	SYM
ejpam-3010	319	16	∈m	∈m	NOUN
ejpam-3010	319	17	.	.	PUNCT
ejpam-3010	320	1	(	(	PUNCT
ejpam-3010	320	2	6	6	X
ejpam-3010	320	3	)	)	PUNCT
ejpam-3010	320	4	m	m	VERB
ejpam-3010	320	5	is	be	AUX
ejpam-3010	320	6	a	a	DET
ejpam-3010	320	7	semilattice	semilattice	NOUN
ejpam-3010	320	8	of	of	ADP
ejpam-3010	320	9	left	left	ADJ
ejpam-3010	320	10	simple	simple	ADJ
ejpam-3010	320	11	semigroups	semigroup	NOUN
ejpam-3010	320	12	.	.	PUNCT
ejpam-3010	321	1	references	reference	NOUN
ejpam-3010	321	2	629	629	NUM
ejpam-3010	321	3	(	(	PUNCT
ejpam-3010	321	4	7	7	NUM
ejpam-3010	321	5	)	)	PUNCT
ejpam-3010	321	6	every	every	DET
ejpam-3010	321	7	left	leave	VERB
ejpam-3010	321	8	ideal	ideal	NOUN
ejpam-3010	321	9	of	of	ADP
ejpam-3010	321	10	m	m	PROPN
ejpam-3010	321	11	is	be	AUX
ejpam-3010	321	12	semiprime	semiprime	NOUN
ejpam-3010	321	13	and	and	CCONJ
ejpam-3010	321	14	two	two	NUM
ejpam-3010	321	15	-	-	PUNCT
ejpam-3010	321	16	sided	sided	ADJ
ejpam-3010	321	17	.	.	PUNCT
ejpam-3010	322	1	the	the	DET
ejpam-3010	322	2	right	right	ADJ
ejpam-3010	322	3	analogue	analogue	NOUN
ejpam-3010	322	4	of	of	ADP
ejpam-3010	322	5	the	the	DET
ejpam-3010	322	6	above	above	ADJ
ejpam-3010	322	7	theorem	theorem	NOUN
ejpam-3010	322	8	also	also	ADV
ejpam-3010	322	9	holds	hold	VERB
ejpam-3010	322	10	.	.	PUNCT
ejpam-3010	323	1	with	with	ADP
ejpam-3010	323	2	my	my	PRON
ejpam-3010	323	3	best	good	ADJ
ejpam-3010	323	4	thanks	thank	NOUN
ejpam-3010	323	5	to	to	ADP
ejpam-3010	323	6	the	the	DET
ejpam-3010	323	7	referee	referee	NOUN
ejpam-3010	323	8	for	for	ADP
ejpam-3010	323	9	reading	read	VERB
ejpam-3010	323	10	the	the	DET
ejpam-3010	323	11	paper	paper	NOUN
ejpam-3010	323	12	carefully	carefully	ADV
ejpam-3010	323	13	,	,	PUNCT
ejpam-3010	323	14	and	and	CCONJ
ejpam-3010	323	15	his	his	PRON
ejpam-3010	323	16	prompt	prompt	ADJ
ejpam-3010	323	17	reply	reply	NOUN
ejpam-3010	323	18	.	.	PUNCT
ejpam-3010	324	1	references	reference	NOUN
ejpam-3010	324	2	[	[	X
ejpam-3010	324	3	1	1	NUM
ejpam-3010	324	4	]	]	X
ejpam-3010	324	5	w.e	w.e	PROPN
ejpam-3010	324	6	.	.	PROPN
ejpam-3010	324	7	barnes	barnes	PROPN
ejpam-3010	324	8	.	.	PUNCT
ejpam-3010	325	1	on	on	ADP
ejpam-3010	325	2	the	the	DET
ejpam-3010	325	3	γ	γ	NOUN
ejpam-3010	325	4	-	-	PUNCT
ejpam-3010	325	5	rings	ring	NOUN
ejpam-3010	325	6	of	of	ADP
ejpam-3010	325	7	nobusawa	nobusawa	PROPN
ejpam-3010	325	8	.	.	PUNCT
ejpam-3010	326	1	pacific	pacific	PROPN
ejpam-3010	326	2	j.	j.	PROPN
ejpam-3010	326	3	math	math	PROPN
ejpam-3010	326	4	.	.	PUNCT
ejpam-3010	327	1	18:411–422	18:411–422	NUM
ejpam-3010	327	2	,	,	PUNCT
ejpam-3010	327	3	1966	1966	NUM
ejpam-3010	327	4	.	.	PUNCT
ejpam-3010	328	1	[	[	X
ejpam-3010	328	2	2	2	NUM
ejpam-3010	328	3	]	]	PUNCT
ejpam-3010	328	4	n.	n.	NOUN
ejpam-3010	328	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	328	6	.	.	PUNCT
ejpam-3010	329	1	note	note	NOUN
ejpam-3010	329	2	on	on	ADP
ejpam-3010	329	3	green	green	PROPN
ejpam-3010	329	4	’s	’s	PART
ejpam-3010	329	5	relations	relation	NOUN
ejpam-3010	329	6	in	in	ADP
ejpam-3010	329	7	ordered	order	VERB
ejpam-3010	329	8	semigroups	semigroup	NOUN
ejpam-3010	329	9	.	.	PUNCT
ejpam-3010	330	1	math	math	NOUN
ejpam-3010	330	2	.	.	PUNCT
ejpam-3010	331	1	japon	japon	PROPN
ejpam-3010	331	2	.	.	PUNCT
ejpam-3010	332	1	36(2):211–214	36(2):211–214	ADJ
ejpam-3010	332	2	,	,	PUNCT
ejpam-3010	332	3	1991	1991	NUM
ejpam-3010	332	4	.	.	PUNCT
ejpam-3010	333	1	[	[	X
ejpam-3010	333	2	3	3	X
ejpam-3010	333	3	]	]	X
ejpam-3010	333	4	n.	n.	NOUN
ejpam-3010	333	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	333	6	.	.	PUNCT
ejpam-3010	334	1	on	on	ADP
ejpam-3010	334	2	prime	prime	ADJ
ejpam-3010	334	3	,	,	PUNCT
ejpam-3010	334	4	weakly	weakly	ADJ
ejpam-3010	334	5	prime	prime	ADJ
ejpam-3010	334	6	ideals	ideal	NOUN
ejpam-3010	334	7	in	in	ADP
ejpam-3010	334	8	ordered	order	VERB
ejpam-3010	334	9	semigroups	semigroup	NOUN
ejpam-3010	334	10	.	.	PUNCT
ejpam-3010	335	1	semigroup	semigroup	PROPN
ejpam-3010	335	2	forum	forum	PROPN
ejpam-3010	335	3	44(3):341–346	44(3):341–346	PROPN
ejpam-3010	335	4	,	,	PUNCT
ejpam-3010	335	5	1992	1992	NUM
ejpam-3010	335	6	.	.	PUNCT
ejpam-3010	336	1	[	[	X
ejpam-3010	336	2	4	4	X
ejpam-3010	336	3	]	]	X
ejpam-3010	336	4	n.	n.	NOUN
ejpam-3010	336	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	336	6	.	.	PUNCT
ejpam-3010	337	1	on	on	ADP
ejpam-3010	337	2	intra	intra	ADJ
ejpam-3010	337	3	-	-	ADJ
ejpam-3010	337	4	regular	regular	ADJ
ejpam-3010	337	5	ordered	order	VERB
ejpam-3010	337	6	semigroups	semigroup	NOUN
ejpam-3010	337	7	.	.	PUNCT
ejpam-3010	338	1	semigroup	semigroup	PROPN
ejpam-3010	338	2	forum	forum	PROPN
ejpam-3010	338	3	46(3):271	46(3):271	NOUN
ejpam-3010	338	4	–	–	PUNCT
ejpam-3010	338	5	278	278	NUM
ejpam-3010	338	6	,	,	PUNCT
ejpam-3010	338	7	1993	1993	NUM
ejpam-3010	338	8	.	.	PUNCT
ejpam-3010	339	1	[	[	X
ejpam-3010	339	2	5	5	NUM
ejpam-3010	339	3	]	]	PUNCT
ejpam-3010	339	4	n.	n.	NOUN
ejpam-3010	339	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	339	6	.	.	PUNCT
ejpam-3010	340	1	on	on	ADP
ejpam-3010	340	2	prime	prime	ADJ
ejpam-3010	340	3	,	,	PUNCT
ejpam-3010	340	4	weakly	weakly	ADJ
ejpam-3010	340	5	prime	prime	ADJ
ejpam-3010	340	6	ideals	ideal	NOUN
ejpam-3010	340	7	in	in	ADP
ejpam-3010	340	8	po	po	NOUN
ejpam-3010	340	9	-	-	PUNCT
ejpam-3010	340	10	γ	γ	NOUN
ejpam-3010	340	11	-	-	PUNCT
ejpam-3010	340	12	semigroups	semigroup	NOUN
ejpam-3010	340	13	.	.	PUNCT
ejpam-3010	341	1	lobachevskii	lobachevskii	PROPN
ejpam-3010	341	2	j.	j.	PROPN
ejpam-3010	341	3	math	math	PROPN
ejpam-3010	341	4	.	.	PUNCT
ejpam-3010	342	1	30(4):257–262	30(4):257–262	NUM
ejpam-3010	342	2	,	,	PUNCT
ejpam-3010	342	3	2009	2009	NUM
ejpam-3010	342	4	.	.	PUNCT
ejpam-3010	343	1	[	[	X
ejpam-3010	343	2	6	6	NUM
ejpam-3010	343	3	]	]	X
ejpam-3010	343	4	n.	n.	NOUN
ejpam-3010	343	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	343	6	.	.	PUNCT
ejpam-3010	344	1	on	on	ADP
ejpam-3010	344	2	ordered	order	VERB
ejpam-3010	344	3	γ	γ	NOUN
ejpam-3010	344	4	-	-	PUNCT
ejpam-3010	344	5	semigroups	semigroup	NOUN
ejpam-3010	344	6	.	.	PUNCT
ejpam-3010	345	1	sci	sci	PROPN
ejpam-3010	345	2	.	.	PROPN
ejpam-3010	345	3	math	math	PROPN
ejpam-3010	345	4	.	.	PUNCT
ejpam-3010	346	1	jpn	jpn	PROPN
ejpam-3010	346	2	.	.	PUNCT
ejpam-3010	347	1	71(2):179–185	71(2):179–185	NUM
ejpam-3010	347	2	,	,	PUNCT
ejpam-3010	347	3	2010	2010	NUM
ejpam-3010	347	4	.	.	PUNCT
ejpam-3010	348	1	[	[	X
ejpam-3010	348	2	7	7	X
ejpam-3010	348	3	]	]	X
ejpam-3010	348	4	n.	n.	NOUN
ejpam-3010	348	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	348	6	.	.	PUNCT
ejpam-3010	349	1	green	green	PROPN
ejpam-3010	349	2	’s	’s	PART
ejpam-3010	349	3	relations	relation	NOUN
ejpam-3010	349	4	and	and	CCONJ
ejpam-3010	349	5	the	the	DET
ejpam-3010	349	6	relation	relation	NOUN
ejpam-3010	349	7	n	n	CCONJ
ejpam-3010	349	8	in	in	ADP
ejpam-3010	349	9	γ	γ	NOUN
ejpam-3010	349	10	-	-	PUNCT
ejpam-3010	349	11	semigroups	semigroup	NOUN
ejpam-3010	349	12	.	.	PUNCT
ejpam-3010	350	1	quasigroups	quasigroup	NOUN
ejpam-3010	350	2	related	related	ADJ
ejpam-3010	350	3	systems	system	NOUN
ejpam-3010	350	4	22(1):89–96	22(1):89–96	NUM
ejpam-3010	350	5	,	,	PUNCT
ejpam-3010	350	6	2014	2014	NUM
ejpam-3010	350	7	.	.	PUNCT
ejpam-3010	351	1	[	[	X
ejpam-3010	351	2	8	8	NUM
ejpam-3010	351	3	]	]	X
ejpam-3010	351	4	n.	n.	NOUN
ejpam-3010	351	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	351	6	,	,	PUNCT
ejpam-3010	351	7	m.	m.	NOUN
ejpam-3010	351	8	tsingelis	tsingelis	PROPN
ejpam-3010	351	9	.	.	PUNCT
ejpam-3010	352	1	on	on	ADP
ejpam-3010	352	2	intra	intra	ADJ
ejpam-3010	352	3	-	-	ADJ
ejpam-3010	352	4	regular	regular	ADJ
ejpam-3010	352	5	and	and	CCONJ
ejpam-3010	352	6	some	some	PRON
ejpam-3010	352	7	left	leave	VERB
ejpam-3010	352	8	regular	regular	ADJ
ejpam-3010	352	9	γ	γ	NOUN
ejpam-3010	352	10	-	-	PUNCT
ejpam-3010	352	11	semigroups	semigroup	NOUN
ejpam-3010	352	12	.	.	PUNCT
ejpam-3010	353	1	quasigroups	quasigroups	PROPN
ejpam-3010	353	2	related	relate	VERB
ejpam-3010	353	3	systems	system	NOUN
ejpam-3010	353	4	23(2):263–270	23(2):263–270	NUM
ejpam-3010	353	5	,	,	PUNCT
ejpam-3010	353	6	2015	2015	NUM
ejpam-3010	353	7	.	.	PUNCT
ejpam-3010	354	1	[	[	X
ejpam-3010	354	2	9	9	NUM
ejpam-3010	354	3	]	]	X
ejpam-3010	354	4	n.	n.	NOUN
ejpam-3010	354	5	kehayopulu	kehayopulu	PROPN
ejpam-3010	354	6	,	,	PUNCT
ejpam-3010	354	7	m.	m.	NOUN
ejpam-3010	354	8	tsingelis	tsingelis	PROPN
ejpam-3010	354	9	.	.	PUNCT
ejpam-3010	355	1	principal	principal	ADJ
ejpam-3010	355	2	filters	filter	NOUN
ejpam-3010	355	3	of	of	ADP
ejpam-3010	355	4	some	some	PRON
ejpam-3010	355	5	ordered	order	VERB
ejpam-3010	355	6	γ	γ	NOUN
ejpam-3010	355	7	-	-	PUNCT
ejpam-3010	355	8	semigroups	semigroup	NOUN
ejpam-3010	355	9	.	.	PUNCT
ejpam-3010	356	1	armen	armen	PROPN
ejpam-3010	356	2	.	.	PUNCT
ejpam-3010	357	1	j.	j.	PROPN
ejpam-3010	357	2	math	math	PROPN
ejpam-3010	357	3	.	.	PUNCT
ejpam-3010	358	1	8(2):96–103	8(2):96–103	NUM
ejpam-3010	358	2	,	,	PUNCT
ejpam-3010	358	3	2016	2016	NUM
ejpam-3010	358	4	.	.	PUNCT
ejpam-3010	359	1	[	[	X
ejpam-3010	359	2	10	10	NUM
ejpam-3010	359	3	]	]	X
ejpam-3010	359	4	jiang	jiang	PROPN
ejpam-3010	359	5	luh	luh	PROPN
ejpam-3010	359	6	.	.	PUNCT
ejpam-3010	360	1	on	on	ADP
ejpam-3010	360	2	the	the	DET
ejpam-3010	360	3	theory	theory	NOUN
ejpam-3010	360	4	of	of	ADP
ejpam-3010	360	5	simple	simple	ADJ
ejpam-3010	360	6	γ	γ	NOUN
ejpam-3010	360	7	-	-	PUNCT
ejpam-3010	360	8	rings	ring	NOUN
ejpam-3010	360	9	.	.	PUNCT
ejpam-3010	361	1	michigan	michigan	PROPN
ejpam-3010	361	2	math	math	PROPN
ejpam-3010	361	3	.	.	PUNCT
ejpam-3010	362	1	j.	j.	PROPN
ejpam-3010	362	2	16:65–75	16:65–75	PROPN
ejpam-3010	362	3	,	,	PUNCT
ejpam-3010	362	4	1969	1969	NUM
ejpam-3010	362	5	.	.	PUNCT
ejpam-3010	363	1	[	[	X
ejpam-3010	363	2	11	11	NUM
ejpam-3010	363	3	]	]	X
ejpam-3010	363	4	n.	n.	PROPN
ejpam-3010	363	5	nobusawa	nobusawa	PROPN
ejpam-3010	363	6	.	.	PUNCT
ejpam-3010	364	1	on	on	ADP
ejpam-3010	364	2	a	a	DET
ejpam-3010	364	3	generalization	generalization	NOUN
ejpam-3010	364	4	of	of	ADP
ejpam-3010	364	5	the	the	DET
ejpam-3010	364	6	ring	ring	NOUN
ejpam-3010	364	7	theory	theory	NOUN
ejpam-3010	364	8	.	.	PUNCT
ejpam-3010	365	1	osaka	osaka	PROPN
ejpam-3010	365	2	j.	j.	PROPN
ejpam-3010	365	3	math	math	PROPN
ejpam-3010	365	4	.	.	PUNCT
ejpam-3010	366	1	1:81–89	1:81–89	NUM
ejpam-3010	366	2	,	,	PUNCT
ejpam-3010	366	3	1964	1964	NUM
ejpam-3010	366	4	.	.	PUNCT
ejpam-3010	367	1	[	[	X
ejpam-3010	367	2	12	12	NUM
ejpam-3010	367	3	]	]	X
ejpam-3010	367	4	n.k	n.k	PROPN
ejpam-3010	367	5	.	.	PROPN
ejpam-3010	367	6	saha	saha	PROPN
ejpam-3010	367	7	.	.	PUNCT
ejpam-3010	368	1	the	the	DET
ejpam-3010	368	2	maximum	maximum	ADJ
ejpam-3010	368	3	idempotent	idempotent	NOUN
ejpam-3010	368	4	-	-	PUNCT
ejpam-3010	368	5	separating	separate	VERB
ejpam-3010	368	6	congruence	congruence	NOUN
ejpam-3010	368	7	on	on	ADP
ejpam-3010	368	8	an	an	DET
ejpam-3010	368	9	inverse	inverse	NOUN
ejpam-3010	368	10	γsemigroup	γsemigroup	NOUN
ejpam-3010	368	11	.	.	PUNCT
ejpam-3010	369	1	kyungpook	kyungpook	PROPN
ejpam-3010	369	2	math	math	PROPN
ejpam-3010	369	3	.	.	PUNCT
ejpam-3010	370	1	j.	j.	PROPN
ejpam-3010	370	2	34(1):59–66	34(1):59–66	NUM
ejpam-3010	370	3	,	,	PUNCT
ejpam-3010	370	4	1994	1994	NUM
ejpam-3010	370	5	.	.	PUNCT
ejpam-3010	371	1	[	[	X
ejpam-3010	371	2	13	13	NUM
ejpam-3010	371	3	]	]	X
ejpam-3010	371	4	m.k	m.k	PROPN
ejpam-3010	371	5	.	.	PUNCT
ejpam-3010	371	6	sen	sen	PROPN
ejpam-3010	371	7	.	.	PROPN
ejpam-3010	371	8	on	on	ADP
ejpam-3010	371	9	γ	γ	PROPN
ejpam-3010	371	10	-	-	PUNCT
ejpam-3010	371	11	semigroup	semigroup	NOUN
ejpam-3010	371	12	.	.	PUNCT
ejpam-3010	372	1	in	in	ADP
ejpam-3010	372	2	:	:	PUNCT
ejpam-3010	372	3	algebra	algebra	NOUN
ejpam-3010	372	4	and	and	CCONJ
ejpam-3010	372	5	its	its	PRON
ejpam-3010	372	6	applications	application	NOUN
ejpam-3010	372	7	,	,	PUNCT
ejpam-3010	372	8	int	int	NOUN
ejpam-3010	372	9	.	.	PUNCT
ejpam-3010	373	1	symp	symp	PROPN
ejpam-3010	373	2	.	.	PUNCT
ejpam-3010	374	1	new	new	ADJ
ejpam-3010	374	2	delhi	delhi	PROPN
ejpam-3010	374	3	,	,	PUNCT
ejpam-3010	374	4	1981	1981	NUM
ejpam-3010	374	5	.	.	PUNCT
ejpam-3010	375	1	lecture	lecture	NOUN
ejpam-3010	375	2	notes	note	NOUN
ejpam-3010	375	3	in	in	ADP
ejpam-3010	375	4	pure	pure	ADJ
ejpam-3010	375	5	and	and	CCONJ
ejpam-3010	375	6	appl	appl	NOUN
ejpam-3010	375	7	.	.	PROPN
ejpam-3010	375	8	math	math	NOUN
ejpam-3010	375	9	.	.	PUNCT
ejpam-3010	376	1	91	91	NUM
ejpam-3010	376	2	,	,	PUNCT
ejpam-3010	376	3	dekker	dekker	NOUN
ejpam-3010	376	4	,	,	PUNCT
ejpam-3010	376	5	new	new	PROPN
ejpam-3010	376	6	york	york	PROPN
ejpam-3010	376	7	,	,	PUNCT
ejpam-3010	376	8	1984	1984	NUM
ejpam-3010	376	9	,	,	PUNCT
ejpam-3010	376	10	pp	pp	ADV
ejpam-3010	376	11	.	.	PUNCT
ejpam-3010	377	1	301	301	NUM
ejpam-3010	377	2	–	–	PUNCT
ejpam-3010	377	3	308	308	NUM
ejpam-3010	377	4	.	.	PUNCT
ejpam-3010	378	1	[	[	X
ejpam-3010	378	2	14	14	NUM
ejpam-3010	378	3	]	]	X
ejpam-3010	378	4	m.k	m.k	PROPN
ejpam-3010	378	5	.	.	PUNCT
ejpam-3010	378	6	sen	sen	PROPN
ejpam-3010	378	7	,	,	PUNCT
ejpam-3010	378	8	n.k	n.k	PROPN
ejpam-3010	378	9	.	.	PROPN
ejpam-3010	378	10	saha	saha	PROPN
ejpam-3010	378	11	.	.	PUNCT
ejpam-3010	379	1	on	on	ADP
ejpam-3010	379	2	γ	γ	PROPN
ejpam-3010	379	3	-	-	PUNCT
ejpam-3010	379	4	semigroup	semigroup	PROPN
ejpam-3010	379	5	i.	i.	PROPN
ejpam-3010	379	6	bull	bull	PROPN
ejpam-3010	379	7	.	.	PUNCT
ejpam-3010	380	1	calcutta	calcutta	PROPN
ejpam-3010	380	2	math	math	PROPN
ejpam-3010	380	3	.	.	PUNCT
ejpam-3010	381	1	soc	soc	PROPN
ejpam-3010	381	2	.	.	PUNCT
ejpam-3010	382	1	78(3):180–186	78(3):180–186	PROPN
ejpam-3010	382	2	,	,	PUNCT
ejpam-3010	382	3	1986	1986	NUM
ejpam-3010	382	4	.	.	PUNCT
ejpam-3010	383	1	references	reference	NOUN
ejpam-3010	383	2	630	630	NUM
ejpam-3010	384	1	[	[	X
ejpam-3010	384	2	15	15	NUM
ejpam-3010	384	3	]	]	X
ejpam-3010	384	4	m.k	m.k	PROPN
ejpam-3010	384	5	.	.	PUNCT
ejpam-3010	384	6	sen	sen	PROPN
ejpam-3010	384	7	,	,	PUNCT
ejpam-3010	384	8	n.k	n.k	PROPN
ejpam-3010	384	9	.	.	PROPN
ejpam-3010	384	10	saha	saha	PROPN
ejpam-3010	384	11	.	.	PUNCT
ejpam-3010	385	1	the	the	DET
ejpam-3010	385	2	maximum	maximum	ADJ
ejpam-3010	385	3	idempotent	idempotent	NOUN
ejpam-3010	385	4	-	-	PUNCT
ejpam-3010	385	5	separating	separate	VERB
ejpam-3010	385	6	congruence	congruence	NOUN
ejpam-3010	385	7	on	on	ADP
ejpam-3010	385	8	an	an	DET
ejpam-3010	385	9	orthodox	orthodox	ADJ
ejpam-3010	385	10	γ	γ	X
ejpam-3010	385	11	-	-	PUNCT
ejpam-3010	385	12	semigroup	semigroup	NOUN
ejpam-3010	385	13	.	.	PUNCT
ejpam-3010	386	1	j.	j.	PROPN
ejpam-3010	386	2	pure	pure	PROPN
ejpam-3010	386	3	math	math	PROPN
ejpam-3010	386	4	.	.	PUNCT
ejpam-3010	387	1	7:39–47	7:39–47	X
ejpam-3010	387	2	,	,	PUNCT
ejpam-3010	387	3	1990	1990	NUM
ejpam-3010	387	4	.	.	PUNCT
ejpam-3010	388	1	[	[	X
ejpam-3010	388	2	16	16	NUM
ejpam-3010	388	3	]	]	X
ejpam-3010	388	4	m.k	m.k	PROPN
ejpam-3010	388	5	.	.	PUNCT
ejpam-3010	388	6	sen	sen	PROPN
ejpam-3010	388	7	,	,	PUNCT
ejpam-3010	388	8	n.k	n.k	PROPN
ejpam-3010	388	9	.	.	PROPN
ejpam-3010	388	10	saha	saha	PROPN
ejpam-3010	388	11	.	.	PUNCT
ejpam-3010	389	1	orthodox	orthodox	PROPN
ejpam-3010	389	2	γ	γ	PROPN
ejpam-3010	389	3	-	-	PUNCT
ejpam-3010	389	4	semigroups	semigroup	NOUN
ejpam-3010	389	5	.	.	PUNCT
ejpam-3010	390	1	internat	internat	PROPN
ejpam-3010	390	2	.	.	PUNCT
ejpam-3010	391	1	j.	j.	PROPN
ejpam-3010	391	2	math	math	PROPN
ejpam-3010	391	3	.	.	PUNCT
ejpam-3010	392	1	math	math	NOUN
ejpam-3010	392	2	.	.	PUNCT
ejpam-3010	393	1	sci	sci	PROPN
ejpam-3010	393	2	.	.	PUNCT
ejpam-3010	394	1	13(3):527–534	13(3):527–534	NUM
ejpam-3010	394	2	,	,	PUNCT
ejpam-3010	394	3	1990	1990	NUM
ejpam-3010	394	4	.	.	PUNCT
ejpam-3010	395	1	[	[	X
ejpam-3010	395	2	17	17	NUM
ejpam-3010	395	3	]	]	X
ejpam-3010	395	4	m.k	m.k	PROPN
ejpam-3010	395	5	.	.	PUNCT
ejpam-3010	395	6	sen	sen	PROPN
ejpam-3010	395	7	,	,	PUNCT
ejpam-3010	395	8	a.	a.	PROPN
ejpam-3010	395	9	seth	seth	PROPN
ejpam-3010	395	10	.	.	PUNCT
ejpam-3010	396	1	radical	radical	PROPN
ejpam-3010	396	2	of	of	ADP
ejpam-3010	396	3	γ	γ	PROPN
ejpam-3010	396	4	-	-	PUNCT
ejpam-3010	396	5	semigroup	semigroup	NOUN
ejpam-3010	396	6	.	.	PUNCT
ejpam-3010	397	1	bull	bull	PROPN
ejpam-3010	397	2	.	.	PUNCT
ejpam-3010	398	1	calcutta	calcutta	PROPN
ejpam-3010	398	2	math	math	PROPN
ejpam-3010	398	3	.	.	PUNCT
ejpam-3010	399	1	soc	soc	PROPN
ejpam-3010	399	2	.	.	PUNCT
ejpam-3010	400	1	80(3):189–196	80(3):189–196	PROPN
ejpam-3010	400	2	,	,	PUNCT
ejpam-3010	400	3	1988	1988	NUM
ejpam-3010	400	4	.	.	PUNCT
ejpam-3010	401	1	[	[	X
ejpam-3010	401	2	18	18	NUM
ejpam-3010	401	3	]	]	X
ejpam-3010	401	4	m.k	m.k	PROPN
ejpam-3010	401	5	.	.	PUNCT
ejpam-3010	401	6	sen	sen	PROPN
ejpam-3010	401	7	,	,	PUNCT
ejpam-3010	401	8	a.	a.	PROPN
ejpam-3010	401	9	seth	seth	PROPN
ejpam-3010	401	10	.	.	PUNCT
ejpam-3010	402	1	on	on	ADP
ejpam-3010	402	2	po	po	NOUN
ejpam-3010	402	3	-	-	PUNCT
ejpam-3010	402	4	γ	γ	NOUN
ejpam-3010	402	5	-	-	PUNCT
ejpam-3010	402	6	semigroups	semigroup	NOUN
ejpam-3010	402	7	.	.	PUNCT
ejpam-3010	403	1	bull	bull	NOUN
ejpam-3010	403	2	.	.	PUNCT
ejpam-3010	404	1	calcutta	calcutta	PROPN
ejpam-3010	404	2	math	math	PROPN
ejpam-3010	404	3	.	.	PUNCT
ejpam-3010	405	1	soc	soc	PROPN
ejpam-3010	405	2	.	.	PUNCT
ejpam-3010	406	1	85(5):445–450	85(5):445–450	NUM
ejpam-3010	406	2	,	,	PUNCT
ejpam-3010	406	3	1993	1993	NUM
ejpam-3010	406	4	.	.	PUNCT