id	sid	tid	token	lemma	pos
ejpam-1977	1	1	european	european	PROPN
ejpam-1977	1	2	journal	journal	PROPN
ejpam-1977	1	3	of	of	ADP
ejpam-1977	1	4	pure	pure	ADJ
ejpam-1977	1	5	and	and	CCONJ
ejpam-1977	1	6	applied	apply	VERB
ejpam-1977	1	7	mathematics	mathematic	NOUN
ejpam-1977	1	8	vol	vol	NOUN
ejpam-1977	1	9	.	.	PUNCT
ejpam-1977	2	1	7	7	NUM
ejpam-1977	2	2	,	,	PUNCT
ejpam-1977	2	3	no	no	INTJ
ejpam-1977	2	4	.	.	NOUN
ejpam-1977	2	5	1	1	NUM
ejpam-1977	2	6	,	,	PUNCT
ejpam-1977	2	7	2014	2014	NUM
ejpam-1977	2	8	,	,	PUNCT
ejpam-1977	2	9	77	77	NUM
ejpam-1977	2	10	-	-	SYM
ejpam-1977	2	11	85	85	NUM
ejpam-1977	2	12	issn	issn	PROPN
ejpam-1977	2	13	1307	1307	NUM
ejpam-1977	2	14	-	-	SYM
ejpam-1977	2	15	5543	5543	NUM
ejpam-1977	2	16	–	–	PUNCT
ejpam-1977	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1977	2	18	the	the	DET
ejpam-1977	2	19	relation	relation	PROPN
ejpam-1977	2	20	b	b	PROPN
ejpam-1977	2	21	and	and	CCONJ
ejpam-1977	2	22	minimal	minimal	ADJ
ejpam-1977	2	23	bi	bi	NOUN
ejpam-1977	2	24	–	–	PUNCT
ejpam-1977	2	25	ideals	ideal	NOUN
ejpam-1977	2	26	in	in	ADP
ejpam-1977	2	27	γ	γ	NOUN
ejpam-1977	2	28	–	–	PUNCT
ejpam-1977	2	29	semigroups	semigroups	X
ejpam-1977	2	30	islam	islam	PROPN
ejpam-1977	2	31	braja1	braja1	PROPN
ejpam-1977	2	32	,	,	PUNCT
ejpam-1977	2	33	petraq	petraq	VERB
ejpam-1977	2	34	petro2,∗	petro2,∗	ADJ
ejpam-1977	2	35	1	1	NUM
ejpam-1977	2	36	department	department	NOUN
ejpam-1977	2	37	of	of	ADP
ejpam-1977	2	38	mathematics	mathematic	NOUN
ejpam-1977	2	39	,	,	PUNCT
ejpam-1977	2	40	faculty	faculty	NOUN
ejpam-1977	2	41	of	of	ADP
ejpam-1977	2	42	natural	natural	ADJ
ejpam-1977	2	43	sciences	science	NOUN
ejpam-1977	2	44	,	,	PUNCT
ejpam-1977	2	45	university	university	NOUN
ejpam-1977	2	46	“	"	PUNCT
ejpam-1977	2	47	a.	a.	PROPN
ejpam-1977	2	48	xhuvani	xhuvani	PROPN
ejpam-1977	2	49	”	"	PUNCT
ejpam-1977	2	50	,	,	PUNCT
ejpam-1977	2	51	elbasan	elbasan	PROPN
ejpam-1977	2	52	,	,	PUNCT
ejpam-1977	2	53	albania	albania	PROPN
ejpam-1977	2	54	2	2	NUM
ejpam-1977	2	55	department	department	NOUN
ejpam-1977	2	56	of	of	ADP
ejpam-1977	2	57	mathematics	mathematic	NOUN
ejpam-1977	2	58	,	,	PUNCT
ejpam-1977	2	59	faculty	faculty	NOUN
ejpam-1977	2	60	of	of	ADP
ejpam-1977	2	61	natural	natural	ADJ
ejpam-1977	2	62	sciences	science	NOUN
ejpam-1977	2	63	,	,	PUNCT
ejpam-1977	2	64	university	university	NOUN
ejpam-1977	2	65	of	of	ADP
ejpam-1977	2	66	tirana	tirana	PROPN
ejpam-1977	2	67	,	,	PUNCT
ejpam-1977	2	68	tirana	tirana	PROPN
ejpam-1977	2	69	,	,	PUNCT
ejpam-1977	2	70	albania	albania	PROPN
ejpam-1977	2	71	abstract	abstract	PROPN
ejpam-1977	2	72	.	.	PUNCT
ejpam-1977	3	1	in	in	ADP
ejpam-1977	3	2	this	this	DET
ejpam-1977	3	3	paper	paper	NOUN
ejpam-1977	3	4	we	we	PRON
ejpam-1977	3	5	introduce	introduce	VERB
ejpam-1977	3	6	the	the	DET
ejpam-1977	3	7	relation	relation	NOUN
ejpam-1977	3	8	b	b	NOUN
ejpam-1977	3	9	“	"	PUNCT
ejpam-1977	3	10	to	to	PART
ejpam-1977	3	11	generate	generate	VERB
ejpam-1977	3	12	the	the	DET
ejpam-1977	3	13	same	same	ADJ
ejpam-1977	3	14	principal	principal	ADJ
ejpam-1977	3	15	bi	bi	NOUN
ejpam-1977	3	16	-	-	ADJ
ejpam-1977	3	17	ideal	ideal	ADJ
ejpam-1977	3	18	”	"	PUNCT
ejpam-1977	3	19	in	in	ADP
ejpam-1977	3	20	γ	γ	NOUN
ejpam-1977	3	21	–	–	PUNCT
ejpam-1977	3	22	semigroups	semigroup	NOUN
ejpam-1977	3	23	.	.	PUNCT
ejpam-1977	4	1	one	one	NUM
ejpam-1977	4	2	of	of	ADP
ejpam-1977	4	3	the	the	DET
ejpam-1977	4	4	main	main	ADJ
ejpam-1977	4	5	results	result	NOUN
ejpam-1977	4	6	that	that	PRON
ejpam-1977	4	7	are	be	AUX
ejpam-1977	4	8	proved	prove	VERB
ejpam-1977	4	9	here	here	ADV
ejpam-1977	4	10	is	be	AUX
ejpam-1977	4	11	the	the	DET
ejpam-1977	4	12	analogue	analogue	NOUN
ejpam-1977	4	13	of	of	ADP
ejpam-1977	4	14	the	the	DET
ejpam-1977	4	15	green	green	PROPN
ejpam-1977	4	16	’s	’s	PART
ejpam-1977	4	17	theorem	theorem	NOUN
ejpam-1977	4	18	for	for	ADP
ejpam-1977	4	19	γ	γ	NOUN
ejpam-1977	4	20	–	–	PUNCT
ejpam-1977	4	21	semigroups	semigroup	NOUN
ejpam-1977	4	22	,	,	PUNCT
ejpam-1977	4	23	which	which	PRON
ejpam-1977	4	24	we	we	PRON
ejpam-1977	4	25	call	call	VERB
ejpam-1977	4	26	the	the	DET
ejpam-1977	4	27	green	green	PROPN
ejpam-1977	4	28	’s	’s	PART
ejpam-1977	4	29	theorem	theorem	NOUN
ejpam-1977	4	30	for	for	ADP
ejpam-1977	4	31	the	the	DET
ejpam-1977	4	32	relation	relation	PROPN
ejpam-1977	4	33	b	b	PROPN
ejpam-1977	4	34	in	in	ADP
ejpam-1977	4	35	γ	γ	NOUN
ejpam-1977	4	36	–	–	PUNCT
ejpam-1977	4	37	semigroups	semigroup	NOUN
ejpam-1977	4	38	.	.	PUNCT
ejpam-1977	5	1	applying	apply	VERB
ejpam-1977	5	2	our	our	PRON
ejpam-1977	5	3	green	green	NOUN
ejpam-1977	5	4	’s	’s	PART
ejpam-1977	5	5	theorem	theorem	NOUN
ejpam-1977	5	6	for	for	ADP
ejpam-1977	5	7	relationb	relationb	ADV
ejpam-1977	5	8	in	in	ADP
ejpam-1977	5	9	γ	γ	NOUN
ejpam-1977	5	10	–	–	PUNCT
ejpam-1977	5	11	semigroups	semigroup	NOUN
ejpam-1977	5	12	,	,	PUNCT
ejpam-1977	5	13	we	we	PRON
ejpam-1977	5	14	prove	prove	VERB
ejpam-1977	5	15	that	that	SCONJ
ejpam-1977	5	16	any	any	DET
ejpam-1977	5	17	bi	bi	NOUN
ejpam-1977	5	18	-	-	NOUN
ejpam-1977	5	19	ideal	ideal	NOUN
ejpam-1977	5	20	of	of	ADP
ejpam-1977	5	21	a	a	DET
ejpam-1977	5	22	γ	γ	X
ejpam-1977	5	23	–	–	PUNCT
ejpam-1977	5	24	semigroup	semigroup	NOUN
ejpam-1977	5	25	without	without	ADP
ejpam-1977	5	26	zero	zero	NUM
ejpam-1977	5	27	is	be	AUX
ejpam-1977	5	28	minimal	minimal	ADJ
ejpam-1977	5	29	if	if	SCONJ
ejpam-1977	5	30	and	and	CCONJ
ejpam-1977	5	31	only	only	ADV
ejpam-1977	5	32	if	if	SCONJ
ejpam-1977	5	33	it	it	PRON
ejpam-1977	5	34	is	be	AUX
ejpam-1977	5	35	a	a	DET
ejpam-1977	5	36	γ	γ	X
ejpam-1977	5	37	–	–	PUNCT
ejpam-1977	5	38	subgroup	subgroup	NOUN
ejpam-1977	5	39	.	.	PUNCT
ejpam-1977	6	1	further	far	ADV
ejpam-1977	6	2	,	,	PUNCT
ejpam-1977	6	3	we	we	PRON
ejpam-1977	6	4	prove	prove	VERB
ejpam-1977	6	5	that	that	SCONJ
ejpam-1977	6	6	,	,	PUNCT
ejpam-1977	6	7	if	if	SCONJ
ejpam-1977	6	8	a	a	DET
ejpam-1977	6	9	γ	γ	X
ejpam-1977	6	10	–	–	PUNCT
ejpam-1977	6	11	semigroup	semigroup	NOUN
ejpam-1977	6	12	m	m	VERB
ejpam-1977	6	13	without	without	ADP
ejpam-1977	6	14	zero	zero	NUM
ejpam-1977	6	15	has	have	VERB
ejpam-1977	6	16	a	a	DET
ejpam-1977	6	17	cancellable	cancellable	ADJ
ejpam-1977	6	18	element	element	NOUN
ejpam-1977	6	19	contained	contain	VERB
ejpam-1977	6	20	in	in	ADP
ejpam-1977	6	21	a	a	DET
ejpam-1977	6	22	minimal	minimal	ADJ
ejpam-1977	6	23	bi	bi	ADJ
ejpam-1977	6	24	-	-	ADJ
ejpam-1977	6	25	ideal	ideal	ADJ
ejpam-1977	6	26	b	b	PROPN
ejpam-1977	6	27	of	of	ADP
ejpam-1977	6	28	m	m	PROPN
ejpam-1977	6	29	,	,	PUNCT
ejpam-1977	6	30	then	then	ADV
ejpam-1977	6	31	m	m	VERB
ejpam-1977	6	32	is	be	AUX
ejpam-1977	6	33	a	a	DET
ejpam-1977	6	34	γ	γ	X
ejpam-1977	6	35	–	–	PUNCT
ejpam-1977	6	36	group	group	NOUN
ejpam-1977	6	37	.	.	PUNCT
ejpam-1977	7	1	finally	finally	ADV
ejpam-1977	7	2	,	,	PUNCT
ejpam-1977	7	3	we	we	PRON
ejpam-1977	7	4	prove	prove	VERB
ejpam-1977	7	5	that	that	SCONJ
ejpam-1977	7	6	,	,	PUNCT
ejpam-1977	7	7	if	if	SCONJ
ejpam-1977	7	8	for	for	ADP
ejpam-1977	7	9	elements	element	NOUN
ejpam-1977	7	10	a	a	PRON
ejpam-1977	7	11	,	,	PUNCT
ejpam-1977	7	12	c	c	NOUN
ejpam-1977	7	13	of	of	ADP
ejpam-1977	7	14	a	a	DET
ejpam-1977	7	15	γ	γ	X
ejpam-1977	7	16	–	–	PUNCT
ejpam-1977	7	17	semigroup	semigroup	NOUN
ejpam-1977	7	18	without	without	ADP
ejpam-1977	7	19	zero	zero	NUM
ejpam-1977	7	20	we	we	PRON
ejpam-1977	7	21	have	have	VERB
ejpam-1977	7	22	adc	adc	NOUN
ejpam-1977	7	23	and	and	CCONJ
ejpam-1977	7	24	the	the	DET
ejpam-1977	7	25	principal	principal	ADJ
ejpam-1977	7	26	bi	bi	NOUN
ejpam-1977	7	27	-	-	NOUN
ejpam-1977	7	28	ideal	ideal	ADJ
ejpam-1977	7	29	(	(	PUNCT
ejpam-1977	7	30	a)b	a)b	ADJ
ejpam-1977	7	31	and	and	CCONJ
ejpam-1977	7	32	principal	principal	ADJ
ejpam-1977	7	33	quasi	quasi	NOUN
ejpam-1977	7	34	-	-	NOUN
ejpam-1977	7	35	ideal	ideal	ADJ
ejpam-1977	7	36	(	(	PUNCT
ejpam-1977	7	37	a)q	a)q	X
ejpam-1977	7	38	are	be	AUX
ejpam-1977	7	39	minimal	minimal	ADJ
ejpam-1977	7	40	,	,	PUNCT
ejpam-1977	7	41	then	then	ADV
ejpam-1977	7	42	(	(	PUNCT
ejpam-1977	7	43	a)b	a)b	X
ejpam-1977	7	44	=	=	SYM
ejpam-1977	7	45	(	(	PUNCT
ejpam-1977	7	46	a)q	a)q	X
ejpam-1977	7	47	and	and	CCONJ
ejpam-1977	7	48	the	the	DET
ejpam-1977	7	49	principal	principal	ADJ
ejpam-1977	7	50	bi	bi	NOUN
ejpam-1977	7	51	-	-	NOUN
ejpam-1977	7	52	ideal	ideal	ADJ
ejpam-1977	7	53	(	(	PUNCT
ejpam-1977	7	54	c)b	c)b	NOUN
ejpam-1977	7	55	and	and	CCONJ
ejpam-1977	7	56	the	the	DET
ejpam-1977	7	57	principal	principal	ADJ
ejpam-1977	7	58	quasi	quasi	NOUN
ejpam-1977	7	59	-	-	NOUN
ejpam-1977	7	60	ideal	ideal	ADJ
ejpam-1977	7	61	(	(	PUNCT
ejpam-1977	7	62	c)q	c)q	NOUN
ejpam-1977	7	63	are	be	AUX
ejpam-1977	7	64	minimal	minimal	ADJ
ejpam-1977	7	65	too	too	ADV
ejpam-1977	7	66	,	,	PUNCT
ejpam-1977	7	67	and	and	CCONJ
ejpam-1977	7	68	(	(	PUNCT
ejpam-1977	7	69	c)b	c)b	NOUN
ejpam-1977	7	70	=	=	SYM
ejpam-1977	7	71	(	(	PUNCT
ejpam-1977	7	72	c)q	c)q	NOUN
ejpam-1977	7	73	.	.	PUNCT
ejpam-1977	8	1	key	key	ADJ
ejpam-1977	8	2	words	word	NOUN
ejpam-1977	8	3	and	and	CCONJ
ejpam-1977	8	4	phrases	phrase	NOUN
ejpam-1977	8	5	:	:	PUNCT
ejpam-1977	8	6	γ	γ	X
ejpam-1977	8	7	–	–	PUNCT
ejpam-1977	8	8	semigroup	semigroup	ADJ
ejpam-1977	8	9	,	,	PUNCT
ejpam-1977	8	10	green	green	PROPN
ejpam-1977	8	11	’s	’s	PART
ejpam-1977	8	12	theorem	theorem	ADJ
ejpam-1977	8	13	,	,	PUNCT
ejpam-1977	8	14	quasi	quasi	ADJ
ejpam-1977	8	15	–	–	PUNCT
ejpam-1977	8	16	ideal	ideal	ADJ
ejpam-1977	8	17	,	,	PUNCT
ejpam-1977	8	18	bi	bi	ADJ
ejpam-1977	8	19	–	–	NOUN
ejpam-1977	8	20	ideal	ideal	ADJ
ejpam-1977	8	21	,	,	PUNCT
ejpam-1977	8	22	γ	γ	X
ejpam-1977	8	23	–	–	PUNCT
ejpam-1977	8	24	group	group	NOUN
ejpam-1977	8	25	.	.	PUNCT
ejpam-1977	9	1	1	1	X
ejpam-1977	9	2	.	.	X
ejpam-1977	9	3	introduction	introduction	NOUN
ejpam-1977	9	4	the	the	DET
ejpam-1977	9	5	notion	notion	NOUN
ejpam-1977	9	6	of	of	ADP
ejpam-1977	9	7	γ	γ	PROPN
ejpam-1977	9	8	–	–	PUNCT
ejpam-1977	9	9	semigroup	semigroup	NOUN
ejpam-1977	9	10	is	be	AUX
ejpam-1977	9	11	introduced	introduce	VERB
ejpam-1977	9	12	by	by	ADP
ejpam-1977	9	13	sen	sen	PROPN
ejpam-1977	9	14	in	in	ADP
ejpam-1977	9	15	[	[	X
ejpam-1977	9	16	8	8	NUM
ejpam-1977	9	17	]	]	PUNCT
ejpam-1977	9	18	.	.	PUNCT
ejpam-1977	10	1	let	let	VERB
ejpam-1977	10	2	m	m	PRON
ejpam-1977	10	3	and	and	CCONJ
ejpam-1977	10	4	γ	γ	PROPN
ejpam-1977	10	5	be	be	AUX
ejpam-1977	10	6	non	non	ADJ
ejpam-1977	10	7	–	–	ADJ
ejpam-1977	10	8	empty	empty	ADJ
ejpam-1977	10	9	sets	set	NOUN
ejpam-1977	10	10	.	.	PUNCT
ejpam-1977	11	1	any	any	DET
ejpam-1977	11	2	map	map	NOUN
ejpam-1977	11	3	from	from	ADP
ejpam-1977	11	4	m	m	PROPN
ejpam-1977	11	5	×γ×m	×γ×m	NOUN
ejpam-1977	11	6	to	to	ADP
ejpam-1977	11	7	m	m	PROPN
ejpam-1977	11	8	will	will	AUX
ejpam-1977	11	9	be	be	AUX
ejpam-1977	11	10	called	call	VERB
ejpam-1977	11	11	a	a	DET
ejpam-1977	11	12	γ	γ	X
ejpam-1977	11	13	–	–	PUNCT
ejpam-1977	11	14	multiplication	multiplication	NOUN
ejpam-1977	11	15	in	in	ADP
ejpam-1977	11	16	m	m	PRON
ejpam-1977	11	17	and	and	CCONJ
ejpam-1977	11	18	is	be	AUX
ejpam-1977	11	19	denoted	denote	VERB
ejpam-1977	11	20	by	by	ADP
ejpam-1977	11	21	(	(	PUNCT
ejpam-1977	11	22	·	·	SYM
ejpam-1977	11	23	)	)	PUNCT
ejpam-1977	11	24	γ	γ	X
ejpam-1977	11	25	.	.	PUNCT
ejpam-1977	12	1	the	the	DET
ejpam-1977	12	2	result	result	NOUN
ejpam-1977	12	3	of	of	ADP
ejpam-1977	12	4	this	this	DET
ejpam-1977	12	5	γ	γ	NOUN
ejpam-1977	12	6	–	–	PUNCT
ejpam-1977	12	7	multiplication	multiplication	NOUN
ejpam-1977	12	8	for	for	ADP
ejpam-1977	12	9	a	a	DET
ejpam-1977	12	10	,	,	PUNCT
ejpam-1977	12	11	b	b	PROPN
ejpam-1977	12	12	∈	∈	NOUN
ejpam-1977	12	13	m	m	NOUN
ejpam-1977	12	14	and	and	CCONJ
ejpam-1977	12	15	γ	γ	PROPN
ejpam-1977	12	16	∈	∈	PROPN
ejpam-1977	12	17	γ	γ	NOUN
ejpam-1977	12	18	is	be	AUX
ejpam-1977	12	19	denoted	denote	VERB
ejpam-1977	12	20	by	by	ADP
ejpam-1977	12	21	aγb	aγb	NOUN
ejpam-1977	12	22	.	.	PUNCT
ejpam-1977	13	1	according	accord	VERB
ejpam-1977	13	2	to	to	ADP
ejpam-1977	13	3	sen	sen	PROPN
ejpam-1977	13	4	and	and	CCONJ
ejpam-1977	13	5	saha	saha	PROPN
ejpam-1977	13	6	[	[	X
ejpam-1977	13	7	9	9	NUM
ejpam-1977	13	8	]	]	PUNCT
ejpam-1977	13	9	,	,	PUNCT
ejpam-1977	13	10	a	a	DET
ejpam-1977	13	11	γ	γ	X
ejpam-1977	13	12	–	–	PUNCT
ejpam-1977	13	13	semigroup	semigroup	NOUN
ejpam-1977	13	14	is	be	AUX
ejpam-1977	13	15	an	an	DET
ejpam-1977	13	16	ordered	order	VERB
ejpam-1977	13	17	pair	pair	NOUN
ejpam-1977	13	18	(	(	PUNCT
ejpam-1977	13	19	m	m	PROPN
ejpam-1977	13	20	,	,	PUNCT
ejpam-1977	13	21	(	(	PUNCT
ejpam-1977	13	22	·	·	PUNCT
ejpam-1977	13	23	)	)	PUNCT
ejpam-1977	13	24	γ	γ	NOUN
ejpam-1977	13	25	)	)	PUNCT
ejpam-1977	13	26	,	,	PUNCT
ejpam-1977	13	27	where	where	SCONJ
ejpam-1977	13	28	m	m	VERB
ejpam-1977	13	29	and	and	CCONJ
ejpam-1977	13	30	γ	γ	NOUN
ejpam-1977	13	31	are	be	AUX
ejpam-1977	13	32	non	non	ADJ
ejpam-1977	13	33	-	-	ADJ
ejpam-1977	13	34	empty	empty	ADJ
ejpam-1977	13	35	sets	set	NOUN
ejpam-1977	13	36	and	and	CCONJ
ejpam-1977	13	37	(	(	PUNCT
ejpam-1977	13	38	·	·	PUNCT
ejpam-1977	13	39	)	)	PUNCT
ejpam-1977	13	40	γ	γ	PROPN
ejpam-1977	13	41	is	be	AUX
ejpam-1977	13	42	a	a	DET
ejpam-1977	13	43	γ	γ	X
ejpam-1977	13	44	–	–	PUNCT
ejpam-1977	13	45	multiplication	multiplication	NOUN
ejpam-1977	13	46	in	in	ADP
ejpam-1977	13	47	m	m	PROPN
ejpam-1977	13	48	for	for	ADP
ejpam-1977	13	49	which	which	PRON
ejpam-1977	13	50	the	the	DET
ejpam-1977	13	51	following	follow	VERB
ejpam-1977	13	52	proposition	proposition	NOUN
ejpam-1977	13	53	:	:	PUNCT
ejpam-1977	13	54	∀(a	∀(a	PROPN
ejpam-1977	13	55	,	,	PUNCT
ejpam-1977	13	56	b	b	PROPN
ejpam-1977	13	57	,	,	PUNCT
ejpam-1977	13	58	c	c	PROPN
ejpam-1977	13	59	,	,	PUNCT
ejpam-1977	13	60	α	α	NOUN
ejpam-1977	13	61	,	,	PUNCT
ejpam-1977	13	62	β	β	NOUN
ejpam-1977	13	63	)	)	PUNCT
ejpam-1977	13	64	∈	∈	PROPN
ejpam-1977	13	65	m3×γ2	m3×γ2	PROPN
ejpam-1977	13	66	,	,	PUNCT
ejpam-1977	13	67	(	(	PUNCT
ejpam-1977	13	68	aαb)β	aαb)β	NOUN
ejpam-1977	13	69	c	c	NOUN
ejpam-1977	13	70	=	=	PUNCT
ejpam-1977	13	71	aα(bβ	aα(bβ	PROPN
ejpam-1977	13	72	c	c	PROPN
ejpam-1977	13	73	)	)	PUNCT
ejpam-1977	13	74	is	be	AUX
ejpam-1977	13	75	true	true	ADJ
ejpam-1977	13	76	.	.	PUNCT
ejpam-1977	14	1	in	in	ADP
ejpam-1977	14	2	the	the	DET
ejpam-1977	14	3	literature	literature	NOUN
ejpam-1977	14	4	there	there	PRON
ejpam-1977	14	5	are	be	VERB
ejpam-1977	14	6	many	many	ADJ
ejpam-1977	14	7	examples	example	NOUN
ejpam-1977	14	8	of	of	ADP
ejpam-1977	14	9	γ	γ	X
ejpam-1977	14	10	–	–	PUNCT
ejpam-1977	14	11	semigroups	semigroup	NOUN
ejpam-1977	14	12	,	,	PUNCT
ejpam-1977	14	13	but	but	CCONJ
ejpam-1977	14	14	the	the	DET
ejpam-1977	14	15	following	follow	VERB
ejpam-1977	14	16	example	example	NOUN
ejpam-1977	14	17	,	,	PUNCT
ejpam-1977	14	18	which	which	PRON
ejpam-1977	14	19	is	be	AUX
ejpam-1977	14	20	inspired	inspire	VERB
ejpam-1977	14	21	from	from	ADP
ejpam-1977	14	22	hestenes	hestene	NOUN
ejpam-1977	14	23	’s	’s	PART
ejpam-1977	14	24	rings	ring	NOUN
ejpam-1977	15	1	[	[	X
ejpam-1977	15	2	3	3	X
ejpam-1977	15	3	]	]	PUNCT
ejpam-1977	15	4	is	be	AUX
ejpam-1977	15	5	the	the	DET
ejpam-1977	15	6	most	most	ADV
ejpam-1977	15	7	well	well	ADV
ejpam-1977	15	8	known	know	VERB
ejpam-1977	15	9	one	one	NUM
ejpam-1977	15	10	.	.	PUNCT
ejpam-1977	16	1	∗corresponding	∗corresponde	VERB
ejpam-1977	16	2	author	author	NOUN
ejpam-1977	16	3	.	.	PUNCT
ejpam-1977	17	1	email	email	NOUN
ejpam-1977	17	2	addresses	address	NOUN
ejpam-1977	17	3	:	:	PUNCT
ejpam-1977	17	4	braja_islam@yahoo.com	braja_islam@yahoo.com	X
ejpam-1977	17	5	(	(	PUNCT
ejpam-1977	17	6	i.	i.	PROPN
ejpam-1977	17	7	braja	braja	PROPN
ejpam-1977	17	8	)	)	PUNCT
ejpam-1977	17	9	,	,	PUNCT
ejpam-1977	17	10	petropetraq@yahoo.com	petropetraq@yahoo.com	X
ejpam-1977	18	1	(	(	PUNCT
ejpam-1977	18	2	p.	p.	NOUN
ejpam-1977	18	3	petro	petro	PROPN
ejpam-1977	18	4	)	)	PUNCT
ejpam-1977	18	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1977	19	1	77	77	NUM
ejpam-1977	20	1	c	c	X
ejpam-1977	20	2	©	©	PROPN
ejpam-1977	20	3	2014	2014	NUM
ejpam-1977	20	4	ejpam	ejpam	NOUN
ejpam-1977	20	5	all	all	DET
ejpam-1977	20	6	rights	right	NOUN
ejpam-1977	20	7	reserved	reserve	VERB
ejpam-1977	20	8	.	.	PUNCT
ejpam-1977	21	1	i.	i.	PROPN
ejpam-1977	21	2	braja	braja	PROPN
ejpam-1977	21	3	,	,	PUNCT
ejpam-1977	21	4	p.	p.	NOUN
ejpam-1977	21	5	petro	petro	PROPN
ejpam-1977	21	6	/	/	PUNCT
ejpam-1977	21	7	eur	eur	PROPN
ejpam-1977	21	8	.	.	PUNCT
ejpam-1977	22	1	j.	j.	PROPN
ejpam-1977	22	2	pure	pure	PROPN
ejpam-1977	22	3	appl	appl	PROPN
ejpam-1977	22	4	.	.	PROPN
ejpam-1977	22	5	math	math	PROPN
ejpam-1977	22	6	,	,	PUNCT
ejpam-1977	22	7	7	7	NUM
ejpam-1977	22	8	(	(	PUNCT
ejpam-1977	22	9	2014	2014	NUM
ejpam-1977	22	10	)	)	PUNCT
ejpam-1977	22	11	,	,	PUNCT
ejpam-1977	22	12	77	77	NUM
ejpam-1977	22	13	-	-	SYM
ejpam-1977	22	14	85	85	NUM
ejpam-1977	22	15	78	78	NUM
ejpam-1977	22	16	example	example	NOUN
ejpam-1977	22	17	1	1	NUM
ejpam-1977	22	18	.	.	PUNCT
ejpam-1977	23	1	the	the	DET
ejpam-1977	23	2	γ	γ	PROPN
ejpam-1977	23	3	–	–	PUNCT
ejpam-1977	23	4	semigroup	semigroup	NOUN
ejpam-1977	23	5	m	m	NOUN
ejpam-1977	23	6	of	of	ADP
ejpam-1977	23	7	all	all	DET
ejpam-1977	23	8	m×n	m×n	ADJ
ejpam-1977	23	9	matrices	matrix	NOUN
ejpam-1977	23	10	with	with	ADP
ejpam-1977	23	11	entries	entry	NOUN
ejpam-1977	23	12	from	from	ADP
ejpam-1977	23	13	a	a	DET
ejpam-1977	23	14	field	field	NOUN
ejpam-1977	23	15	f	f	NOUN
ejpam-1977	23	16	,	,	PUNCT
ejpam-1977	23	17	where	where	SCONJ
ejpam-1977	23	18	γ	γ	PROPN
ejpam-1977	23	19	is	be	AUX
ejpam-1977	23	20	the	the	DET
ejpam-1977	23	21	set	set	NOUN
ejpam-1977	23	22	of	of	ADP
ejpam-1977	23	23	all	all	DET
ejpam-1977	23	24	n×m	n×m	PROPN
ejpam-1977	23	25	matrices	matrix	NOUN
ejpam-1977	23	26	,	,	PUNCT
ejpam-1977	23	27	with	with	ADP
ejpam-1977	23	28	entries	entry	NOUN
ejpam-1977	23	29	from	from	ADP
ejpam-1977	23	30	f.	f.	PROPN
ejpam-1977	23	31	the	the	DET
ejpam-1977	23	32	result	result	NOUN
ejpam-1977	23	33	of	of	ADP
ejpam-1977	23	34	γ	γ	X
ejpam-1977	23	35	–	–	PUNCT
ejpam-1977	23	36	multiplication	multiplication	NOUN
ejpam-1977	23	37	in	in	ADP
ejpam-1977	23	38	m	m	PROPN
ejpam-1977	23	39	for	for	ADP
ejpam-1977	23	40	two	two	NUM
ejpam-1977	23	41	m×	m×	NOUN
ejpam-1977	23	42	n	n	PRON
ejpam-1977	23	43	matrices	matrice	VERB
ejpam-1977	23	44	a	a	DET
ejpam-1977	23	45	,	,	PUNCT
ejpam-1977	23	46	b	b	NOUN
ejpam-1977	23	47	and	and	CCONJ
ejpam-1977	23	48	an	an	DET
ejpam-1977	23	49	n×m	n×m	PROPN
ejpam-1977	23	50	matrix	matrix	NOUN
ejpam-1977	23	51	c	c	NOUN
ejpam-1977	23	52	is	be	AUX
ejpam-1977	23	53	the	the	DET
ejpam-1977	23	54	usual	usual	ADJ
ejpam-1977	23	55	product	product	NOUN
ejpam-1977	23	56	acb	acb	PROPN
ejpam-1977	23	57	.	.	PUNCT
ejpam-1977	24	1	note	note	VERB
ejpam-1977	24	2	that	that	SCONJ
ejpam-1977	24	3	every	every	DET
ejpam-1977	24	4	plain	plain	ADJ
ejpam-1977	24	5	semigroup	semigroup	NOUN
ejpam-1977	24	6	s	s	VERB
ejpam-1977	24	7	can	can	AUX
ejpam-1977	24	8	be	be	AUX
ejpam-1977	24	9	considered	consider	VERB
ejpam-1977	24	10	as	as	ADP
ejpam-1977	24	11	a	a	DET
ejpam-1977	24	12	γ	γ	X
ejpam-1977	24	13	–	–	PUNCT
ejpam-1977	24	14	semigroup	semigroup	NOUN
ejpam-1977	24	15	by	by	ADP
ejpam-1977	24	16	taking	take	VERB
ejpam-1977	24	17	as	as	ADP
ejpam-1977	24	18	γ	γ	X
ejpam-1977	24	19	a	a	DET
ejpam-1977	24	20	singelton	singelton	NOUN
ejpam-1977	24	21	{	{	PUNCT
ejpam-1977	24	22	1	1	NUM
ejpam-1977	24	23	}	}	PUNCT
ejpam-1977	24	24	,	,	PUNCT
ejpam-1977	24	25	where	where	SCONJ
ejpam-1977	24	26	1	1	NUM
ejpam-1977	24	27	is	be	AUX
ejpam-1977	24	28	the	the	DET
ejpam-1977	24	29	identity	identity	NOUN
ejpam-1977	24	30	element	element	NOUN
ejpam-1977	24	31	of	of	ADP
ejpam-1977	24	32	s	s	NOUN
ejpam-1977	24	33	,	,	PUNCT
ejpam-1977	24	34	when	when	SCONJ
ejpam-1977	24	35	s	s	PROPN
ejpam-1977	24	36	has	have	VERB
ejpam-1977	24	37	a	a	DET
ejpam-1977	24	38	such	such	ADJ
ejpam-1977	24	39	element	element	NOUN
ejpam-1977	24	40	,	,	PUNCT
ejpam-1977	24	41	or	or	CCONJ
ejpam-1977	24	42	it	it	PRON
ejpam-1977	24	43	is	be	AUX
ejpam-1977	24	44	a	a	DET
ejpam-1977	24	45	symbol	symbol	NOUN
ejpam-1977	24	46	not	not	PART
ejpam-1977	24	47	representing	represent	VERB
ejpam-1977	24	48	an	an	DET
ejpam-1977	24	49	element	element	NOUN
ejpam-1977	24	50	of	of	ADP
ejpam-1977	24	51	s	s	NOUN
ejpam-1977	24	52	,	,	PUNCT
ejpam-1977	24	53	and	and	CCONJ
ejpam-1977	24	54	the	the	DET
ejpam-1977	24	55	γ	γ	X
ejpam-1977	24	56	–	–	PUNCT
ejpam-1977	24	57	multiplication	multiplication	NOUN
ejpam-1977	24	58	in	in	ADP
ejpam-1977	24	59	s	s	PROPN
ejpam-1977	24	60	is	be	AUX
ejpam-1977	24	61	defined	define	VERB
ejpam-1977	24	62	by	by	ADP
ejpam-1977	24	63	a1b	a1b	NOUN
ejpam-1977	24	64	=	=	SYM
ejpam-1977	24	65	ab	ab	PROPN
ejpam-1977	24	66	,	,	PUNCT
ejpam-1977	24	67	where	where	SCONJ
ejpam-1977	24	68	ab	ab	PROPN
ejpam-1977	24	69	is	be	AUX
ejpam-1977	24	70	the	the	DET
ejpam-1977	24	71	usual	usual	ADJ
ejpam-1977	24	72	product	product	NOUN
ejpam-1977	24	73	in	in	ADP
ejpam-1977	24	74	plain	plain	ADJ
ejpam-1977	24	75	semigroup	semigroup	PROPN
ejpam-1977	24	76	s.	s.	PROPN
ejpam-1977	24	77	similarly	similarly	ADV
ejpam-1977	24	78	to	to	ADP
ejpam-1977	24	79	the	the	DET
ejpam-1977	24	80	definition	definition	NOUN
ejpam-1977	24	81	of	of	ADP
ejpam-1977	24	82	relationsrplain	relationsrplain	NOUN
ejpam-1977	24	83	,	,	PUNCT
ejpam-1977	24	84	lplain	lplain	NOUN
ejpam-1977	24	85	,	,	PUNCT
ejpam-1977	24	86	hplain	hplain	VERB
ejpam-1977	24	87	and	and	CCONJ
ejpam-1977	24	88	dplain	dplain	VERB
ejpam-1977	24	89	in	in	ADP
ejpam-1977	24	90	plain	plain	ADJ
ejpam-1977	24	91	semigroup	semigroup	PROPN
ejpam-1977	24	92	,	,	PUNCT
ejpam-1977	24	93	saha	saha	PROPN
ejpam-1977	24	94	in	in	ADP
ejpam-1977	24	95	[	[	X
ejpam-1977	24	96	7	7	NUM
ejpam-1977	24	97	]	]	PUNCT
ejpam-1977	24	98	has	have	AUX
ejpam-1977	24	99	introduced	introduce	VERB
ejpam-1977	24	100	the	the	DET
ejpam-1977	24	101	analogue	analogue	NOUN
ejpam-1977	24	102	relations	relation	NOUN
ejpam-1977	24	103	r	r	NOUN
ejpam-1977	24	104	,	,	PUNCT
ejpam-1977	24	105	l	l	NOUN
ejpam-1977	24	106	,	,	PUNCT
ejpam-1977	24	107	h	h	NOUN
ejpam-1977	24	108	,	,	PUNCT
ejpam-1977	25	1	d	d	X
ejpam-1977	25	2	in	in	ADP
ejpam-1977	25	3	a	a	DET
ejpam-1977	25	4	γ	γ	X
ejpam-1977	25	5	–	–	PUNCT
ejpam-1977	25	6	semigroup	semigroup	NOUN
ejpam-1977	25	7	m	m	VERB
ejpam-1977	25	8	,	,	PUNCT
ejpam-1977	25	9	which	which	PRON
ejpam-1977	25	10	are	be	AUX
ejpam-1977	25	11	called	call	VERB
ejpam-1977	25	12	the	the	DET
ejpam-1977	25	13	green	green	PROPN
ejpam-1977	25	14	’s	’s	PART
ejpam-1977	25	15	relations	relation	NOUN
ejpam-1977	25	16	in	in	ADP
ejpam-1977	25	17	the	the	DET
ejpam-1977	25	18	γ	γ	X
ejpam-1977	25	19	–	–	PUNCT
ejpam-1977	25	20	semigroup	semigroup	NOUN
ejpam-1977	25	21	m	m	NOUN
ejpam-1977	25	22	.	.	PUNCT
ejpam-1977	26	1	in	in	ADP
ejpam-1977	26	2	this	this	DET
ejpam-1977	26	3	paper	paper	NOUN
ejpam-1977	26	4	we	we	PRON
ejpam-1977	26	5	define	define	VERB
ejpam-1977	26	6	the	the	DET
ejpam-1977	26	7	relation	relation	NOUN
ejpam-1977	26	8	b	b	PROPN
ejpam-1977	26	9	in	in	ADP
ejpam-1977	26	10	a	a	DET
ejpam-1977	26	11	γ	γ	X
ejpam-1977	26	12	–	–	PUNCT
ejpam-1977	26	13	semigroup	semigroup	NOUN
ejpam-1977	26	14	m	m	VERB
ejpam-1977	26	15	such	such	ADJ
ejpam-1977	26	16	that	that	SCONJ
ejpam-1977	26	17	ab	ab	PROPN
ejpam-1977	26	18	c	c	PROPN
ejpam-1977	27	1	if	if	SCONJ
ejpam-1977	27	2	and	and	CCONJ
ejpam-1977	27	3	only	only	ADV
ejpam-1977	27	4	if	if	SCONJ
ejpam-1977	27	5	(	(	PUNCT
ejpam-1977	27	6	a)b	a)b	X
ejpam-1977	27	7	=	=	SYM
ejpam-1977	27	8	(	(	PUNCT
ejpam-1977	27	9	c)b	c)b	NOUN
ejpam-1977	27	10	,	,	PUNCT
ejpam-1977	27	11	where	where	SCONJ
ejpam-1977	27	12	(	(	PUNCT
ejpam-1977	27	13	a)b	a)b	X
ejpam-1977	27	14	and	and	CCONJ
ejpam-1977	27	15	(	(	PUNCT
ejpam-1977	27	16	c)b	c)b	NOUN
ejpam-1977	27	17	are	be	AUX
ejpam-1977	27	18	the	the	DET
ejpam-1977	27	19	principal	principal	ADJ
ejpam-1977	27	20	bi	bi	NOUN
ejpam-1977	27	21	–	–	PUNCT
ejpam-1977	27	22	ideals	ideal	NOUN
ejpam-1977	27	23	generated	generate	VERB
ejpam-1977	27	24	by	by	ADP
ejpam-1977	27	25	elements	element	NOUN
ejpam-1977	27	26	a	a	PRON
ejpam-1977	27	27	,	,	PUNCT
ejpam-1977	27	28	c	c	PROPN
ejpam-1977	27	29	of	of	ADP
ejpam-1977	27	30	m	m	PRON
ejpam-1977	27	31	respectively	respectively	ADV
ejpam-1977	27	32	.	.	PUNCT
ejpam-1977	28	1	the	the	DET
ejpam-1977	28	2	definition	definition	NOUN
ejpam-1977	28	3	of	of	ADP
ejpam-1977	28	4	relation	relation	PROPN
ejpam-1977	28	5	b	b	PROPN
ejpam-1977	28	6	in	in	ADP
ejpam-1977	28	7	γ	γ	NOUN
ejpam-1977	28	8	-	-	PUNCT
ejpam-1977	28	9	semigroups	semigroup	NOUN
ejpam-1977	28	10	mimics	mimic	VERB
ejpam-1977	28	11	the	the	DET
ejpam-1977	28	12	definition	definition	NOUN
ejpam-1977	28	13	of	of	ADP
ejpam-1977	28	14	relation	relation	NOUN
ejpam-1977	28	15	b	b	PROPN
ejpam-1977	28	16	in	in	ADP
ejpam-1977	28	17	plain	plain	ADJ
ejpam-1977	28	18	semigroup	semigroup	NOUN
ejpam-1977	28	19	introduced	introduce	VERB
ejpam-1977	28	20	in	in	ADP
ejpam-1977	28	21	[	[	X
ejpam-1977	28	22	4	4	NUM
ejpam-1977	28	23	]	]	PUNCT
ejpam-1977	28	24	.	.	PUNCT
ejpam-1977	29	1	we	we	PRON
ejpam-1977	29	2	show	show	VERB
ejpam-1977	29	3	that	that	SCONJ
ejpam-1977	29	4	in	in	ADP
ejpam-1977	29	5	γ	γ	NOUN
ejpam-1977	29	6	–	–	PUNCT
ejpam-1977	29	7	semigroups	semigroups	X
ejpam-1977	29	8	the	the	DET
ejpam-1977	29	9	relation	relation	NOUN
ejpam-1977	29	10	b	b	PROPN
ejpam-1977	29	11	is	be	AUX
ejpam-1977	29	12	different	different	ADJ
ejpam-1977	29	13	from	from	ADP
ejpam-1977	29	14	green	green	PROPN
ejpam-1977	29	15	’s	’s	PART
ejpam-1977	29	16	relation	relation	NOUN
ejpam-1977	29	17	h	h	PROPN
ejpam-1977	29	18	.	.	PUNCT
ejpam-1977	30	1	one	one	NUM
ejpam-1977	30	2	of	of	ADP
ejpam-1977	30	3	our	our	PRON
ejpam-1977	30	4	main	main	ADJ
ejpam-1977	30	5	results	result	NOUN
ejpam-1977	30	6	claims	claim	VERB
ejpam-1977	30	7	that	that	SCONJ
ejpam-1977	30	8	the	the	DET
ejpam-1977	30	9	analogue	analogue	NOUN
ejpam-1977	30	10	of	of	ADP
ejpam-1977	30	11	green	green	PROPN
ejpam-1977	30	12	’s	’s	PART
ejpam-1977	30	13	theorem	theorem	NOUN
ejpam-1977	30	14	for	for	ADP
ejpam-1977	30	15	green	green	PROPN
ejpam-1977	30	16	’s	’s	PART
ejpam-1977	30	17	relation	relation	NOUN
ejpam-1977	30	18	hplain	hplain	NOUN
ejpam-1977	30	19	=	=	VERB
ejpam-1977	30	20	rplain	rplain	NOUN
ejpam-1977	30	21	∩lplain	∩lplain	PUNCT
ejpam-1977	30	22	holds	hold	VERB
ejpam-1977	30	23	true	true	ADJ
ejpam-1977	30	24	for	for	ADP
ejpam-1977	30	25	the	the	DET
ejpam-1977	30	26	relationb	relationb	ADJ
ejpam-1977	30	27	in	in	ADP
ejpam-1977	30	28	γ	γ	PROPN
ejpam-1977	30	29	-semigroups	-semigroup	NOUN
ejpam-1977	30	30	.	.	PUNCT
ejpam-1977	31	1	this	this	PRON
ejpam-1977	31	2	theorem	theorem	NOUN
ejpam-1977	31	3	we	we	PRON
ejpam-1977	31	4	call	call	VERB
ejpam-1977	31	5	green	green	PROPN
ejpam-1977	31	6	’s	’s	PART
ejpam-1977	31	7	theorem	theorem	NOUN
ejpam-1977	31	8	for	for	ADP
ejpam-1977	31	9	the	the	DET
ejpam-1977	31	10	relationb	relationb	ADJ
ejpam-1977	31	11	in	in	ADP
ejpam-1977	31	12	γ	γ	NOUN
ejpam-1977	31	13	–	–	PUNCT
ejpam-1977	31	14	semigroups	semigroup	NOUN
ejpam-1977	31	15	.	.	PUNCT
ejpam-1977	32	1	from	from	ADP
ejpam-1977	32	2	this	this	DET
ejpam-1977	32	3	theorem	theorem	NOUN
ejpam-1977	32	4	,	,	PUNCT
ejpam-1977	32	5	as	as	ADP
ejpam-1977	32	6	a	a	DET
ejpam-1977	32	7	particular	particular	ADJ
ejpam-1977	32	8	case	case	NOUN
ejpam-1977	32	9	,	,	PUNCT
ejpam-1977	32	10	we	we	PRON
ejpam-1977	32	11	get	get	VERB
ejpam-1977	32	12	a	a	DET
ejpam-1977	32	13	green	green	NOUN
ejpam-1977	32	14	’s	’s	PART
ejpam-1977	32	15	theorem	theorem	NOUN
ejpam-1977	32	16	for	for	ADP
ejpam-1977	32	17	the	the	DET
ejpam-1977	32	18	relation	relation	NOUN
ejpam-1977	32	19	b	b	PROPN
ejpam-1977	32	20	in	in	ADP
ejpam-1977	32	21	plain	plain	ADJ
ejpam-1977	32	22	semigroups	semigroup	NOUN
ejpam-1977	32	23	.	.	PUNCT
ejpam-1977	33	1	then	then	ADV
ejpam-1977	33	2	we	we	PRON
ejpam-1977	33	3	use	use	VERB
ejpam-1977	33	4	our	our	PRON
ejpam-1977	33	5	theorem	theorem	NOUN
ejpam-1977	33	6	for	for	ADP
ejpam-1977	33	7	the	the	DET
ejpam-1977	33	8	relation	relation	PROPN
ejpam-1977	33	9	b	b	PROPN
ejpam-1977	33	10	in	in	ADP
ejpam-1977	33	11	γ	γ	NOUN
ejpam-1977	33	12	–	–	PUNCT
ejpam-1977	33	13	semigroups	semigroup	NOUN
ejpam-1977	33	14	to	to	PART
ejpam-1977	33	15	prove	prove	VERB
ejpam-1977	33	16	that	that	SCONJ
ejpam-1977	33	17	any	any	DET
ejpam-1977	33	18	bi	bi	NOUN
ejpam-1977	33	19	-	-	NOUN
ejpam-1977	33	20	ideal	ideal	NOUN
ejpam-1977	33	21	of	of	ADP
ejpam-1977	33	22	a	a	DET
ejpam-1977	33	23	γ	γ	X
ejpam-1977	33	24	–	–	PUNCT
ejpam-1977	33	25	semigroup	semigroup	NOUN
ejpam-1977	33	26	without	without	ADP
ejpam-1977	33	27	zero	zero	NUM
ejpam-1977	33	28	is	be	AUX
ejpam-1977	33	29	minimal	minimal	ADJ
ejpam-1977	33	30	if	if	SCONJ
ejpam-1977	33	31	and	and	CCONJ
ejpam-1977	33	32	only	only	ADV
ejpam-1977	33	33	if	if	SCONJ
ejpam-1977	33	34	it	it	PRON
ejpam-1977	33	35	is	be	AUX
ejpam-1977	33	36	a	a	DET
ejpam-1977	33	37	γ	γ	X
ejpam-1977	33	38	–	–	PUNCT
ejpam-1977	33	39	subgroup	subgroup	NOUN
ejpam-1977	33	40	.	.	PUNCT
ejpam-1977	34	1	as	as	ADP
ejpam-1977	34	2	a	a	DET
ejpam-1977	34	3	corollary	corollary	NOUN
ejpam-1977	34	4	of	of	ADP
ejpam-1977	34	5	the	the	DET
ejpam-1977	34	6	above	above	ADJ
ejpam-1977	34	7	result	result	NOUN
ejpam-1977	34	8	we	we	PRON
ejpam-1977	34	9	get	get	VERB
ejpam-1977	34	10	the	the	DET
ejpam-1977	34	11	analogue	analogue	NOUN
ejpam-1977	34	12	of	of	ADP
ejpam-1977	34	13	the	the	DET
ejpam-1977	34	14	result	result	NOUN
ejpam-1977	34	15	for	for	ADP
ejpam-1977	34	16	minimal	minimal	ADJ
ejpam-1977	34	17	quasi	quasi	NOUN
ejpam-1977	34	18	-	-	NOUN
ejpam-1977	34	19	ideal	ideal	ADJ
ejpam-1977	34	20	in	in	ADP
ejpam-1977	34	21	γ	γ	X
ejpam-1977	34	22	–	–	PUNCT
ejpam-1977	34	23	semigroup	semigroup	NOUN
ejpam-1977	35	1	[	[	X
ejpam-1977	35	2	6	6	NUM
ejpam-1977	35	3	]	]	PUNCT
ejpam-1977	35	4	,	,	PUNCT
ejpam-1977	35	5	which	which	PRON
ejpam-1977	35	6	states	state	VERB
ejpam-1977	35	7	that	that	SCONJ
ejpam-1977	35	8	“	"	PUNCT
ejpam-1977	35	9	if	if	SCONJ
ejpam-1977	35	10	a	a	DET
ejpam-1977	35	11	γ	γ	X
ejpam-1977	35	12	–	–	PUNCT
ejpam-1977	35	13	semigroup	semigroup	NOUN
ejpam-1977	35	14	m	m	VERB
ejpam-1977	35	15	without	without	ADP
ejpam-1977	35	16	zero	zero	NUM
ejpam-1977	35	17	has	have	VERB
ejpam-1977	35	18	a	a	DET
ejpam-1977	35	19	cancellable	cancellable	ADJ
ejpam-1977	35	20	element	element	NOUN
ejpam-1977	35	21	contained	contain	VERB
ejpam-1977	35	22	in	in	ADP
ejpam-1977	35	23	a	a	DET
ejpam-1977	35	24	minimal	minimal	ADJ
ejpam-1977	35	25	bi	bi	ADJ
ejpam-1977	35	26	-	-	ADJ
ejpam-1977	35	27	ideal	ideal	ADJ
ejpam-1977	35	28	b	b	PROPN
ejpam-1977	35	29	of	of	ADP
ejpam-1977	35	30	m	m	PROPN
ejpam-1977	35	31	,	,	PUNCT
ejpam-1977	35	32	then	then	ADV
ejpam-1977	35	33	m	m	VERB
ejpam-1977	35	34	is	be	AUX
ejpam-1977	35	35	a	a	DET
ejpam-1977	35	36	γ	γ	X
ejpam-1977	35	37	–	–	PUNCT
ejpam-1977	35	38	group	group	NOUN
ejpam-1977	35	39	”	"	PUNCT
ejpam-1977	35	40	.	.	PUNCT
ejpam-1977	36	1	from	from	ADP
ejpam-1977	36	2	this	this	DET
ejpam-1977	36	3	result	result	NOUN
ejpam-1977	36	4	we	we	PRON
ejpam-1977	36	5	get	get	VERB
ejpam-1977	36	6	the	the	DET
ejpam-1977	36	7	analogue	analogue	NOUN
ejpam-1977	36	8	of	of	ADP
ejpam-1977	36	9	result	result	NOUN
ejpam-1977	36	10	for	for	ADP
ejpam-1977	36	11	plain	plain	ADJ
ejpam-1977	36	12	semigroups	semigroup	NOUN
ejpam-1977	36	13	which	which	PRON
ejpam-1977	36	14	state	state	VERB
ejpam-1977	36	15	that	that	SCONJ
ejpam-1977	36	16	“	"	PUNCT
ejpam-1977	36	17	if	if	SCONJ
ejpam-1977	36	18	a	a	DET
ejpam-1977	36	19	semigroup	semigroup	NOUN
ejpam-1977	36	20	s	s	PRON
ejpam-1977	36	21	without	without	ADP
ejpam-1977	36	22	zero	zero	NUM
ejpam-1977	36	23	has	have	VERB
ejpam-1977	36	24	a	a	DET
ejpam-1977	36	25	cancellable	cancellable	ADJ
ejpam-1977	36	26	element	element	NOUN
ejpam-1977	36	27	contained	contain	VERB
ejpam-1977	36	28	in	in	ADP
ejpam-1977	36	29	a	a	DET
ejpam-1977	36	30	minimal	minimal	ADJ
ejpam-1977	36	31	bi	bi	NOUN
ejpam-1977	36	32	–	–	PUNCT
ejpam-1977	36	33	ideal	ideal	ADJ
ejpam-1977	36	34	,	,	PUNCT
ejpam-1977	36	35	then	then	ADV
ejpam-1977	36	36	s	s	VERB
ejpam-1977	36	37	is	be	AUX
ejpam-1977	36	38	group	group	NOUN
ejpam-1977	36	39	”	"	PUNCT
ejpam-1977	36	40	.	.	PUNCT
ejpam-1977	37	1	at	at	ADP
ejpam-1977	37	2	last	last	ADV
ejpam-1977	37	3	,	,	PUNCT
ejpam-1977	37	4	we	we	PRON
ejpam-1977	37	5	show	show	VERB
ejpam-1977	37	6	that	that	SCONJ
ejpam-1977	37	7	if	if	SCONJ
ejpam-1977	37	8	for	for	ADP
ejpam-1977	37	9	the	the	DET
ejpam-1977	37	10	elements	element	NOUN
ejpam-1977	37	11	a	a	PRON
ejpam-1977	37	12	,	,	PUNCT
ejpam-1977	37	13	c	c	PROPN
ejpam-1977	37	14	of	of	ADP
ejpam-1977	37	15	γ	γ	X
ejpam-1977	37	16	–	–	PUNCT
ejpam-1977	37	17	semigroup	semigroup	NOUN
ejpam-1977	37	18	m	m	VERB
ejpam-1977	37	19	without	without	ADP
ejpam-1977	37	20	zero	zero	NUM
ejpam-1977	37	21	,	,	PUNCT
ejpam-1977	37	22	we	we	PRON
ejpam-1977	37	23	have	have	VERB
ejpam-1977	37	24	adc	adc	NOUN
ejpam-1977	37	25	and	and	CCONJ
ejpam-1977	37	26	principal	principal	ADJ
ejpam-1977	37	27	bi	bi	NOUN
ejpam-1977	37	28	-	-	NOUN
ejpam-1977	37	29	ideal	ideal	ADJ
ejpam-1977	37	30	(	(	PUNCT
ejpam-1977	37	31	a)b	a)b	ADJ
ejpam-1977	37	32	and	and	CCONJ
ejpam-1977	37	33	principal	principal	ADJ
ejpam-1977	37	34	quasi	quasi	NOUN
ejpam-1977	37	35	–	–	PUNCT
ejpam-1977	37	36	ideal	ideal	ADJ
ejpam-1977	37	37	(	(	PUNCT
ejpam-1977	37	38	a)q	a)q	X
ejpam-1977	37	39	are	be	AUX
ejpam-1977	37	40	minimal	minimal	ADJ
ejpam-1977	37	41	,	,	PUNCT
ejpam-1977	37	42	then	then	ADV
ejpam-1977	37	43	(	(	PUNCT
ejpam-1977	37	44	a)b	a)b	X
ejpam-1977	37	45	=	=	SYM
ejpam-1977	37	46	(	(	PUNCT
ejpam-1977	37	47	a)q	a)q	X
ejpam-1977	37	48	and	and	CCONJ
ejpam-1977	37	49	the	the	DET
ejpam-1977	37	50	principal	principal	ADJ
ejpam-1977	37	51	bi	bi	NOUN
ejpam-1977	37	52	-	-	NOUN
ejpam-1977	37	53	ideal	ideal	ADJ
ejpam-1977	37	54	(	(	PUNCT
ejpam-1977	37	55	c)b	c)b	NOUN
ejpam-1977	37	56	and	and	CCONJ
ejpam-1977	37	57	the	the	DET
ejpam-1977	37	58	principal	principal	ADJ
ejpam-1977	37	59	quasi	quasi	NOUN
ejpam-1977	37	60	-	-	NOUN
ejpam-1977	37	61	ideal	ideal	ADJ
ejpam-1977	37	62	(	(	PUNCT
ejpam-1977	37	63	c)q	c)q	NOUN
ejpam-1977	37	64	are	be	AUX
ejpam-1977	37	65	minimal	minimal	ADJ
ejpam-1977	37	66	too	too	ADV
ejpam-1977	37	67	,	,	PUNCT
ejpam-1977	37	68	and	and	CCONJ
ejpam-1977	37	69	(	(	PUNCT
ejpam-1977	37	70	c)b	c)b	NOUN
ejpam-1977	37	71	=	=	SYM
ejpam-1977	37	72	(	(	PUNCT
ejpam-1977	37	73	c)q	c)q	NOUN
ejpam-1977	37	74	.	.	PUNCT
ejpam-1977	38	1	at	at	ADP
ejpam-1977	38	2	the	the	DET
ejpam-1977	38	3	end	end	NOUN
ejpam-1977	38	4	of	of	ADP
ejpam-1977	38	5	this	this	DET
ejpam-1977	38	6	paper	paper	NOUN
ejpam-1977	38	7	we	we	PRON
ejpam-1977	38	8	raise	raise	VERB
ejpam-1977	38	9	an	an	DET
ejpam-1977	38	10	open	open	ADJ
ejpam-1977	38	11	problem	problem	NOUN
ejpam-1977	38	12	.	.	PUNCT
ejpam-1977	39	1	2	2	X
ejpam-1977	39	2	.	.	X
ejpam-1977	39	3	preliminaries	preliminary	NOUN
ejpam-1977	39	4	we	we	PRON
ejpam-1977	39	5	give	give	VERB
ejpam-1977	39	6	some	some	DET
ejpam-1977	39	7	notions	notion	NOUN
ejpam-1977	39	8	and	and	CCONJ
ejpam-1977	39	9	present	present	VERB
ejpam-1977	39	10	some	some	DET
ejpam-1977	39	11	auxiliary	auxiliary	ADJ
ejpam-1977	39	12	results	result	NOUN
ejpam-1977	39	13	that	that	PRON
ejpam-1977	39	14	will	will	AUX
ejpam-1977	39	15	be	be	AUX
ejpam-1977	39	16	used	use	VERB
ejpam-1977	39	17	throughout	throughout	ADP
ejpam-1977	39	18	the	the	DET
ejpam-1977	39	19	paper	paper	NOUN
ejpam-1977	39	20	.	.	PUNCT
ejpam-1977	40	1	let	let	VERB
ejpam-1977	40	2	m	m	PRON
ejpam-1977	40	3	be	be	AUX
ejpam-1977	40	4	a	a	DET
ejpam-1977	40	5	γ	γ	X
ejpam-1977	40	6	–	–	PUNCT
ejpam-1977	40	7	semigroup	semigroup	NOUN
ejpam-1977	40	8	and	and	CCONJ
ejpam-1977	40	9	a	a	DET
ejpam-1977	40	10	,	,	PUNCT
ejpam-1977	40	11	b	b	PROPN
ejpam-1977	40	12	be	be	AUX
ejpam-1977	40	13	subsets	subset	NOUN
ejpam-1977	40	14	of	of	ADP
ejpam-1977	40	15	m	m	PROPN
ejpam-1977	40	16	.	.	PUNCT
ejpam-1977	41	1	we	we	PRON
ejpam-1977	41	2	define	define	VERB
ejpam-1977	41	3	the	the	DET
ejpam-1977	41	4	set	set	NOUN
ejpam-1977	41	5	aγb	aγb	NOUN
ejpam-1977	41	6	=	=	X
ejpam-1977	41	7	{	{	PUNCT
ejpam-1977	41	8	aγb	aγb	NOUN
ejpam-1977	41	9	∈	∈	PROPN
ejpam-1977	41	10	m	m	PRON
ejpam-1977	41	11	|a	|a	VERB
ejpam-1977	41	12	∈	∈	PROPN
ejpam-1977	41	13	a	a	DET
ejpam-1977	41	14	,	,	PUNCT
ejpam-1977	41	15	b	b	PROPN
ejpam-1977	41	16	∈	∈	PROPN
ejpam-1977	41	17	b	b	PROPN
ejpam-1977	41	18	and	and	CCONJ
ejpam-1977	41	19	γ	γ	PROPN
ejpam-1977	41	20	∈	∈	PROPN
ejpam-1977	41	21	γ	γ	X
ejpam-1977	41	22	}	}	PUNCT
ejpam-1977	41	23	.	.	PUNCT
ejpam-1977	42	1	for	for	ADP
ejpam-1977	42	2	simplicity	simplicity	NOUN
ejpam-1977	42	3	we	we	PRON
ejpam-1977	42	4	write	write	VERB
ejpam-1977	42	5	aγb	aγb	NOUN
ejpam-1977	42	6	instead	instead	ADV
ejpam-1977	42	7	of	of	ADP
ejpam-1977	42	8	{	{	PUNCT
ejpam-1977	42	9	a}γb	a}γb	PROPN
ejpam-1977	42	10	,	,	PUNCT
ejpam-1977	42	11	aγb	aγb	NOUN
ejpam-1977	42	12	in	in	ADP
ejpam-1977	42	13	place	place	NOUN
ejpam-1977	42	14	of	of	ADP
ejpam-1977	42	15	aγ{b	aγ{b	PROPN
ejpam-1977	42	16	}	}	PUNCT
ejpam-1977	42	17	,	,	PUNCT
ejpam-1977	42	18	and	and	CCONJ
ejpam-1977	42	19	aγb	aγb	VERB
ejpam-1977	42	20	instead	instead	ADV
ejpam-1977	42	21	of	of	ADP
ejpam-1977	42	22	{	{	PUNCT
ejpam-1977	42	23	a}γ{b	a}γ{b	PROPN
ejpam-1977	42	24	}	}	PUNCT
ejpam-1977	42	25	.	.	PUNCT
ejpam-1977	43	1	analogously	analogously	ADV
ejpam-1977	43	2	with	with	ADP
ejpam-1977	43	3	the	the	DET
ejpam-1977	43	4	definitions	definition	NOUN
ejpam-1977	43	5	in	in	ADP
ejpam-1977	43	6	plain	plain	ADJ
ejpam-1977	43	7	semigroups	semigroup	NOUN
ejpam-1977	43	8	there	there	PRON
ejpam-1977	43	9	are	be	VERB
ejpam-1977	43	10	given	give	VERB
ejpam-1977	43	11	the	the	DET
ejpam-1977	43	12	following	follow	VERB
ejpam-1977	43	13	definitions	definition	NOUN
ejpam-1977	43	14	in	in	ADP
ejpam-1977	43	15	γ	γ	NOUN
ejpam-1977	43	16	–	–	PUNCT
ejpam-1977	43	17	semigroups	semigroup	NOUN
ejpam-1977	43	18	.	.	PUNCT
ejpam-1977	44	1	i.	i.	PROPN
ejpam-1977	44	2	braja	braja	PROPN
ejpam-1977	44	3	,	,	PUNCT
ejpam-1977	44	4	p.	p.	NOUN
ejpam-1977	44	5	petro	petro	PROPN
ejpam-1977	44	6	/	/	PUNCT
ejpam-1977	44	7	eur	eur	PROPN
ejpam-1977	44	8	.	.	PUNCT
ejpam-1977	45	1	j.	j.	PROPN
ejpam-1977	45	2	pure	pure	PROPN
ejpam-1977	45	3	appl	appl	PROPN
ejpam-1977	45	4	.	.	PROPN
ejpam-1977	45	5	math	math	PROPN
ejpam-1977	45	6	,	,	PUNCT
ejpam-1977	45	7	7	7	NUM
ejpam-1977	45	8	(	(	PUNCT
ejpam-1977	45	9	2014	2014	NUM
ejpam-1977	45	10	)	)	PUNCT
ejpam-1977	45	11	,	,	PUNCT
ejpam-1977	45	12	77	77	NUM
ejpam-1977	45	13	-	-	SYM
ejpam-1977	45	14	85	85	NUM
ejpam-1977	45	15	79	79	NUM
ejpam-1977	45	16	definition	definition	NOUN
ejpam-1977	45	17	1	1	NUM
ejpam-1977	45	18	.	.	PUNCT
ejpam-1977	46	1	let	let	VERB
ejpam-1977	46	2	m	m	PRON
ejpam-1977	46	3	be	be	AUX
ejpam-1977	46	4	a	a	DET
ejpam-1977	46	5	γ	γ	X
ejpam-1977	46	6	–	–	PUNCT
ejpam-1977	46	7	semigroup	semigroup	NOUN
ejpam-1977	46	8	.	.	PUNCT
ejpam-1977	47	1	a	a	DET
ejpam-1977	47	2	non	non	ADJ
ejpam-1977	47	3	–	–	ADJ
ejpam-1977	47	4	empty	empty	ADJ
ejpam-1977	47	5	subset	subset	ADJ
ejpam-1977	47	6	m1	m1	NOUN
ejpam-1977	47	7	of	of	ADP
ejpam-1977	47	8	m	m	PROPN
ejpam-1977	47	9	is	be	AUX
ejpam-1977	47	10	said	say	VERB
ejpam-1977	47	11	to	to	PART
ejpam-1977	47	12	be	be	AUX
ejpam-1977	47	13	a	a	DET
ejpam-1977	47	14	γ	γ	X
ejpam-1977	47	15	–	–	PUNCT
ejpam-1977	47	16	subsemigroup	subsemigroup	NOUN
ejpam-1977	47	17	of	of	ADP
ejpam-1977	47	18	m	m	PROPN
ejpam-1977	47	19	if	if	SCONJ
ejpam-1977	47	20	m1γm1	m1γm1	NOUN
ejpam-1977	47	21	⊆	⊆	NUM
ejpam-1977	47	22	m1	m1	NOUN
ejpam-1977	47	23	.	.	PUNCT
ejpam-1977	48	1	definition	definition	NOUN
ejpam-1977	48	2	2	2	NUM
ejpam-1977	48	3	.	.	PUNCT
ejpam-1977	49	1	a	a	DET
ejpam-1977	49	2	right	right	NOUN
ejpam-1977	50	1	[	[	X
ejpam-1977	50	2	left	left	ADJ
ejpam-1977	50	3	]	]	X
ejpam-1977	50	4	ideal	ideal	NOUN
ejpam-1977	50	5	of	of	ADP
ejpam-1977	50	6	a	a	DET
ejpam-1977	50	7	γ	γ	X
ejpam-1977	50	8	–	–	PUNCT
ejpam-1977	50	9	semigroup	semigroup	ADJ
ejpam-1977	50	10	m	m	VERB
ejpam-1977	50	11	is	be	AUX
ejpam-1977	50	12	a	a	DET
ejpam-1977	50	13	non	non	ADJ
ejpam-1977	50	14	–	–	ADJ
ejpam-1977	50	15	empty	empty	ADJ
ejpam-1977	50	16	subset	subset	NOUN
ejpam-1977	51	1	r	r	NOUN
ejpam-1977	52	1	[	[	X
ejpam-1977	52	2	l	l	X
ejpam-1977	52	3	]	]	X
ejpam-1977	52	4	of	of	ADP
ejpam-1977	52	5	m	m	PRON
ejpam-1977	52	6	such	such	ADJ
ejpam-1977	52	7	that	that	DET
ejpam-1977	52	8	rγm	rγm	NOUN
ejpam-1977	52	9	⊆	⊆	NUM
ejpam-1977	52	10	r	r	NOUN
ejpam-1977	52	11	,	,	PUNCT
ejpam-1977	53	1	[	[	X
ejpam-1977	53	2	mγl	mγl	NOUN
ejpam-1977	53	3	⊆	⊆	NUM
ejpam-1977	53	4	l	l	NOUN
ejpam-1977	53	5	]	]	PUNCT
ejpam-1977	53	6	.	.	PUNCT
ejpam-1977	54	1	definition	definition	NOUN
ejpam-1977	54	2	3	3	NUM
ejpam-1977	54	3	.	.	PUNCT
ejpam-1977	55	1	a	a	DET
ejpam-1977	55	2	quasi	quasi	NOUN
ejpam-1977	55	3	–	–	PUNCT
ejpam-1977	55	4	ideal	ideal	NOUN
ejpam-1977	55	5	of	of	ADP
ejpam-1977	55	6	a	a	DET
ejpam-1977	55	7	γ	γ	X
ejpam-1977	55	8	–	–	PUNCT
ejpam-1977	55	9	semigroup	semigroup	ADJ
ejpam-1977	55	10	m	m	VERB
ejpam-1977	55	11	is	be	AUX
ejpam-1977	55	12	a	a	DET
ejpam-1977	55	13	non	non	ADJ
ejpam-1977	55	14	–	–	ADJ
ejpam-1977	55	15	empty	empty	ADJ
ejpam-1977	55	16	subset	subset	NOUN
ejpam-1977	55	17	q	q	NOUN
ejpam-1977	55	18	of	of	ADP
ejpam-1977	55	19	m	m	PRON
ejpam-1977	55	20	such	such	ADJ
ejpam-1977	55	21	that	that	DET
ejpam-1977	55	22	qγm	qγm	NOUN
ejpam-1977	55	23	∩mγq	∩mγq	PROPN
ejpam-1977	55	24	⊆q	⊆q	NOUN
ejpam-1977	55	25	.	.	PUNCT
ejpam-1977	56	1	definition	definition	NOUN
ejpam-1977	56	2	4	4	NUM
ejpam-1977	56	3	.	.	PUNCT
ejpam-1977	57	1	a	a	DET
ejpam-1977	57	2	bi	bi	NOUN
ejpam-1977	57	3	–	–	PUNCT
ejpam-1977	57	4	ideal	ideal	NOUN
ejpam-1977	57	5	of	of	ADP
ejpam-1977	57	6	a	a	DET
ejpam-1977	57	7	γ	γ	X
ejpam-1977	57	8	–	–	PUNCT
ejpam-1977	57	9	semigroup	semigroup	ADJ
ejpam-1977	57	10	m	m	VERB
ejpam-1977	57	11	is	be	AUX
ejpam-1977	57	12	a	a	DET
ejpam-1977	57	13	γ	γ	X
ejpam-1977	57	14	–	–	PUNCT
ejpam-1977	57	15	subsemigroup	subsemigroup	NOUN
ejpam-1977	57	16	b	b	PROPN
ejpam-1977	57	17	of	of	ADP
ejpam-1977	57	18	m	m	PRON
ejpam-1977	57	19	such	such	ADJ
ejpam-1977	57	20	that	that	SCONJ
ejpam-1977	57	21	bγmγb	bγmγb	VERB
ejpam-1977	57	22	⊆	⊆	NUM
ejpam-1977	57	23	b.	b.	NOUN
ejpam-1977	57	24	similarly	similarly	ADV
ejpam-1977	57	25	to	to	ADP
ejpam-1977	57	26	the	the	DET
ejpam-1977	57	27	plain	plain	ADJ
ejpam-1977	57	28	semigroups	semigroup	NOUN
ejpam-1977	57	29	,	,	PUNCT
ejpam-1977	57	30	it	it	PRON
ejpam-1977	57	31	is	be	AUX
ejpam-1977	57	32	easy	easy	ADJ
ejpam-1977	57	33	to	to	PART
ejpam-1977	57	34	prove	prove	VERB
ejpam-1977	57	35	the	the	DET
ejpam-1977	57	36	following	follow	VERB
ejpam-1977	57	37	two	two	NUM
ejpam-1977	57	38	propositions	proposition	NOUN
ejpam-1977	57	39	:	:	PUNCT
ejpam-1977	57	40	proposition	proposition	NOUN
ejpam-1977	57	41	1	1	NUM
ejpam-1977	57	42	.	.	PUNCT
ejpam-1977	58	1	every	every	DET
ejpam-1977	58	2	quasi	quasi	NOUN
ejpam-1977	58	3	–	–	PUNCT
ejpam-1977	58	4	ideal	ideal	NOUN
ejpam-1977	58	5	of	of	ADP
ejpam-1977	58	6	a	a	DET
ejpam-1977	58	7	γ	γ	X
ejpam-1977	58	8	–	–	PUNCT
ejpam-1977	58	9	semigroup	semigroup	ADJ
ejpam-1977	58	10	m	m	VERB
ejpam-1977	58	11	is	be	AUX
ejpam-1977	58	12	a	a	DET
ejpam-1977	58	13	bi	bi	NOUN
ejpam-1977	58	14	–	–	PUNCT
ejpam-1977	58	15	ideal	ideal	NOUN
ejpam-1977	58	16	of	of	ADP
ejpam-1977	58	17	m.	m.	NOUN
ejpam-1977	58	18	proposition	proposition	NOUN
ejpam-1977	58	19	2	2	NUM
ejpam-1977	58	20	.	.	PUNCT
ejpam-1977	59	1	the	the	DET
ejpam-1977	59	2	intersection	intersection	NOUN
ejpam-1977	59	3	of	of	ADP
ejpam-1977	59	4	any	any	DET
ejpam-1977	59	5	set	set	NOUN
ejpam-1977	59	6	of	of	ADP
ejpam-1977	59	7	bi	bi	NOUN
ejpam-1977	59	8	-	-	NOUN
ejpam-1977	59	9	ideals	ideal	NOUN
ejpam-1977	59	10	of	of	ADP
ejpam-1977	59	11	a	a	DET
ejpam-1977	59	12	γ	γ	X
ejpam-1977	59	13	–	–	PUNCT
ejpam-1977	59	14	semigroup	semigroup	ADJ
ejpam-1977	59	15	m	m	VERB
ejpam-1977	59	16	is	be	AUX
ejpam-1977	59	17	an	an	DET
ejpam-1977	59	18	empty	empty	ADJ
ejpam-1977	59	19	set	set	NOUN
ejpam-1977	59	20	or	or	CCONJ
ejpam-1977	59	21	is	be	AUX
ejpam-1977	59	22	a	a	DET
ejpam-1977	59	23	bi	bi	NOUN
ejpam-1977	59	24	-	-	NOUN
ejpam-1977	59	25	ideal	ideal	NOUN
ejpam-1977	59	26	of	of	ADP
ejpam-1977	59	27	m.	m.	NOUN
ejpam-1977	59	28	theorem	theorem	NOUN
ejpam-1977	59	29	1	1	NUM
ejpam-1977	59	30	(	(	PUNCT
ejpam-1977	59	31	[	[	X
ejpam-1977	59	32	1	1	NUM
ejpam-1977	59	33	]	]	PUNCT
ejpam-1977	59	34	)	)	PUNCT
ejpam-1977	59	35	.	.	PUNCT
ejpam-1977	60	1	let	let	VERB
ejpam-1977	60	2	a	a	PRON
ejpam-1977	60	3	be	be	AUX
ejpam-1977	60	4	a	a	DET
ejpam-1977	60	5	nonempty	nonempty	ADJ
ejpam-1977	60	6	subset	subset	NOUN
ejpam-1977	60	7	of	of	ADP
ejpam-1977	60	8	a	a	DET
ejpam-1977	60	9	γ	γ	X
ejpam-1977	60	10	–	–	PUNCT
ejpam-1977	60	11	semigroup	semigroup	ADJ
ejpam-1977	60	12	m.	m.	NOUN
ejpam-1977	60	13	then	then	ADV
ejpam-1977	60	14	(	(	PUNCT
ejpam-1977	60	15	a)b	a)b	X
ejpam-1977	61	1	=	=	SYM
ejpam-1977	61	2	a∪	a∪	PROPN
ejpam-1977	61	3	aγa∪	aγa∪	PROPN
ejpam-1977	61	4	aγmγa	aγmγa	PROPN
ejpam-1977	61	5	,	,	PUNCT
ejpam-1977	61	6	where	where	SCONJ
ejpam-1977	61	7	(	(	PUNCT
ejpam-1977	61	8	a)b	a)b	X
ejpam-1977	61	9	is	be	AUX
ejpam-1977	61	10	the	the	DET
ejpam-1977	61	11	smallest	small	ADJ
ejpam-1977	61	12	bi	bi	NOUN
ejpam-1977	61	13	–	–	PUNCT
ejpam-1977	61	14	ideal	ideal	NOUN
ejpam-1977	61	15	of	of	ADP
ejpam-1977	61	16	m	m	AUX
ejpam-1977	61	17	containing	contain	VERB
ejpam-1977	61	18	a	a	DET
ejpam-1977	61	19	,	,	PUNCT
ejpam-1977	61	20	i.e.	i.e.	X
ejpam-1977	61	21	the	the	DET
ejpam-1977	61	22	intersection	intersection	NOUN
ejpam-1977	61	23	of	of	ADP
ejpam-1977	61	24	bi	bi	NOUN
ejpam-1977	61	25	–	–	PUNCT
ejpam-1977	61	26	ideals	ideal	NOUN
ejpam-1977	61	27	of	of	ADP
ejpam-1977	61	28	m	m	AUX
ejpam-1977	61	29	containing	contain	VERB
ejpam-1977	61	30	a.	a.	NOUN
ejpam-1977	61	31	let	let	VERB
ejpam-1977	61	32	m	m	PRON
ejpam-1977	61	33	be	be	AUX
ejpam-1977	61	34	a	a	DET
ejpam-1977	61	35	γ	γ	X
ejpam-1977	61	36	–	–	PUNCT
ejpam-1977	61	37	semigroup	semigroup	NOUN
ejpam-1977	61	38	and	and	CCONJ
ejpam-1977	61	39	γ	γ	PROPN
ejpam-1977	61	40	∈	∈	PROPN
ejpam-1977	61	41	γ	γ	X
ejpam-1977	61	42	is	be	AUX
ejpam-1977	61	43	a	a	DET
ejpam-1977	61	44	fixed	fix	VERB
ejpam-1977	61	45	element	element	NOUN
ejpam-1977	61	46	.	.	PUNCT
ejpam-1977	62	1	as	as	ADP
ejpam-1977	62	2	in	in	ADP
ejpam-1977	62	3	[	[	X
ejpam-1977	62	4	9	9	NUM
ejpam-1977	62	5	]	]	PUNCT
ejpam-1977	62	6	,	,	PUNCT
ejpam-1977	62	7	we	we	PRON
ejpam-1977	62	8	define	define	VERB
ejpam-1977	62	9	the	the	DET
ejpam-1977	62	10	multiplication	multiplication	NOUN
ejpam-1977	62	11	◦	◦	NOUN
ejpam-1977	62	12	in	in	ADP
ejpam-1977	62	13	m	m	NOUN
ejpam-1977	62	14	by	by	ADP
ejpam-1977	62	15	a	a	DET
ejpam-1977	62	16	◦	◦	NOUN
ejpam-1977	62	17	b	b	NOUN
ejpam-1977	62	18	=	=	NOUN
ejpam-1977	62	19	aγb	aγb	NOUN
ejpam-1977	62	20	.	.	PUNCT
ejpam-1977	63	1	it	it	PRON
ejpam-1977	63	2	is	be	AUX
ejpam-1977	63	3	obvious	obvious	ADJ
ejpam-1977	63	4	that	that	SCONJ
ejpam-1977	63	5	◦	◦	NOUN
ejpam-1977	63	6	is	be	AUX
ejpam-1977	63	7	associative	associative	ADJ
ejpam-1977	63	8	,	,	PUNCT
ejpam-1977	63	9	hence	hence	ADV
ejpam-1977	63	10	we	we	PRON
ejpam-1977	63	11	obtain	obtain	VERB
ejpam-1977	63	12	a	a	DET
ejpam-1977	63	13	semigroup	semigroup	NOUN
ejpam-1977	63	14	(	(	PUNCT
ejpam-1977	63	15	m	m	PROPN
ejpam-1977	63	16	,	,	PUNCT
ejpam-1977	63	17	◦	◦	NOUN
ejpam-1977	63	18	)	)	PUNCT
ejpam-1977	63	19	which	which	PRON
ejpam-1977	63	20	is	be	AUX
ejpam-1977	63	21	shortly	shortly	ADV
ejpam-1977	63	22	denoted	denote	VERB
ejpam-1977	63	23	by	by	ADP
ejpam-1977	63	24	mγ	mγ	X
ejpam-1977	63	25	.	.	PUNCT
ejpam-1977	64	1	a	a	DET
ejpam-1977	64	2	zero	zero	NUM
ejpam-1977	64	3	of	of	ADP
ejpam-1977	64	4	a	a	DET
ejpam-1977	64	5	γ	γ	X
ejpam-1977	64	6	–	–	PUNCT
ejpam-1977	64	7	semigroup	semigroup	ADJ
ejpam-1977	64	8	m	m	VERB
ejpam-1977	64	9	is	be	AUX
ejpam-1977	64	10	an	an	DET
ejpam-1977	64	11	element	element	NOUN
ejpam-1977	64	12	0	0	NUM
ejpam-1977	64	13	of	of	ADP
ejpam-1977	64	14	m	m	PRON
ejpam-1977	64	15	such	such	ADJ
ejpam-1977	64	16	that	that	SCONJ
ejpam-1977	64	17	for	for	ADP
ejpam-1977	64	18	all	all	DET
ejpam-1977	64	19	a	a	DET
ejpam-1977	64	20	∈	∈	NOUN
ejpam-1977	64	21	m	m	NOUN
ejpam-1977	64	22	and	and	CCONJ
ejpam-1977	64	23	γ	γ	PROPN
ejpam-1977	64	24	∈	∈	PROPN
ejpam-1977	64	25	γ	γ	NOUN
ejpam-1977	64	26	we	we	PRON
ejpam-1977	64	27	have	have	VERB
ejpam-1977	64	28	aγ0=	aγ0=	PROPN
ejpam-1977	64	29	0γa	0γa	NOUN
ejpam-1977	65	1	=	=	SYM
ejpam-1977	65	2	0	0	X
ejpam-1977	65	3	.	.	PUNCT
ejpam-1977	65	4	theorem	theorem	ADJ
ejpam-1977	65	5	2	2	NUM
ejpam-1977	65	6	(	(	PUNCT
ejpam-1977	65	7	[	[	X
ejpam-1977	65	8	6	6	NUM
ejpam-1977	65	9	]	]	PUNCT
ejpam-1977	65	10	)	)	PUNCT
ejpam-1977	65	11	.	.	PUNCT
ejpam-1977	66	1	let	let	VERB
ejpam-1977	66	2	m	m	PRON
ejpam-1977	66	3	be	be	AUX
ejpam-1977	66	4	any	any	DET
ejpam-1977	66	5	γ	γ	X
ejpam-1977	66	6	–	–	PUNCT
ejpam-1977	66	7	semigroup	semigroup	NOUN
ejpam-1977	66	8	without	without	ADP
ejpam-1977	66	9	zero	zero	NUM
ejpam-1977	66	10	and	and	CCONJ
ejpam-1977	66	11	γ	γ	X
ejpam-1977	66	12	∈	∈	PROPN
ejpam-1977	66	13	γ	γ	X
ejpam-1977	66	14	a	a	DET
ejpam-1977	66	15	fixed	fix	VERB
ejpam-1977	66	16	element	element	NOUN
ejpam-1977	66	17	.	.	PUNCT
ejpam-1977	67	1	then	then	ADV
ejpam-1977	67	2	sγ	sγ	PROPN
ejpam-1977	67	3	is	be	AUX
ejpam-1977	67	4	a	a	DET
ejpam-1977	67	5	group	group	NOUN
ejpam-1977	67	6	if	if	SCONJ
ejpam-1977	68	1	and	and	CCONJ
ejpam-1977	68	2	only	only	ADV
ejpam-1977	68	3	if	if	SCONJ
ejpam-1977	68	4	s	s	NOUN
ejpam-1977	68	5	has	have	VERB
ejpam-1977	68	6	not	not	PART
ejpam-1977	68	7	proper	proper	ADJ
ejpam-1977	68	8	quasi	quasi	NOUN
ejpam-1977	68	9	-	-	NOUN
ejpam-1977	68	10	ideals	ideal	NOUN
ejpam-1977	68	11	.	.	PUNCT
ejpam-1977	69	1	from	from	ADP
ejpam-1977	69	2	this	this	DET
ejpam-1977	69	3	theorem	theorem	NOUN
ejpam-1977	69	4	we	we	PRON
ejpam-1977	69	5	give	give	VERB
ejpam-1977	69	6	:	:	PUNCT
ejpam-1977	69	7	theorem	theorem	ADJ
ejpam-1977	69	8	3	3	NUM
ejpam-1977	69	9	(	(	PUNCT
ejpam-1977	69	10	citesensaha	citesensaha	NOUN
ejpam-1977	69	11	)	)	PUNCT
ejpam-1977	69	12	.	.	PUNCT
ejpam-1977	70	1	let	let	VERB
ejpam-1977	70	2	m	m	PRON
ejpam-1977	70	3	be	be	AUX
ejpam-1977	70	4	a	a	DET
ejpam-1977	70	5	γ	γ	X
ejpam-1977	70	6	–	–	PUNCT
ejpam-1977	70	7	semigroup	semigroup	NOUN
ejpam-1977	70	8	without	without	ADP
ejpam-1977	70	9	zero	zero	NUM
ejpam-1977	70	10	.	.	PUNCT
ejpam-1977	71	1	if	if	SCONJ
ejpam-1977	71	2	mγ	mγ	PRON
ejpam-1977	71	3	is	be	AUX
ejpam-1977	71	4	a	a	DET
ejpam-1977	71	5	group	group	NOUN
ejpam-1977	71	6	for	for	ADP
ejpam-1977	71	7	some	some	DET
ejpam-1977	71	8	γ	γ	PROPN
ejpam-1977	71	9	∈	∈	PROPN
ejpam-1977	71	10	γ	γ	X
ejpam-1977	71	11	,	,	PUNCT
ejpam-1977	71	12	then	then	ADV
ejpam-1977	71	13	it	it	PRON
ejpam-1977	71	14	is	be	AUX
ejpam-1977	71	15	a	a	DET
ejpam-1977	71	16	group	group	NOUN
ejpam-1977	71	17	for	for	ADP
ejpam-1977	71	18	all	all	DET
ejpam-1977	71	19	γ	γ	PROPN
ejpam-1977	71	20	∈	∈	PROPN
ejpam-1977	71	21	γ	γ	X
ejpam-1977	71	22	.	.	PROPN
ejpam-1977	71	23	definition	definition	NOUN
ejpam-1977	71	24	5	5	NUM
ejpam-1977	71	25	(	(	PUNCT
ejpam-1977	71	26	[	[	X
ejpam-1977	71	27	9	9	NUM
ejpam-1977	71	28	]	]	NUM
ejpam-1977	71	29	)	)	PUNCT
ejpam-1977	71	30	.	.	PUNCT
ejpam-1977	72	1	a	a	DET
ejpam-1977	72	2	γ	γ	X
ejpam-1977	72	3	–	–	PUNCT
ejpam-1977	72	4	semigroup	semigroup	ADJ
ejpam-1977	72	5	m	m	VERB
ejpam-1977	72	6	is	be	AUX
ejpam-1977	72	7	called	call	VERB
ejpam-1977	72	8	a	a	DET
ejpam-1977	72	9	γ	γ	X
ejpam-1977	72	10	–	–	PUNCT
ejpam-1977	72	11	group	group	NOUN
ejpam-1977	72	12	if	if	SCONJ
ejpam-1977	72	13	mγ	mγ	PRON
ejpam-1977	72	14	is	be	AUX
ejpam-1977	72	15	a	a	DET
ejpam-1977	72	16	group	group	NOUN
ejpam-1977	72	17	for	for	ADP
ejpam-1977	72	18	some	some	PRON
ejpam-1977	72	19	(	(	PUNCT
ejpam-1977	72	20	hence	hence	ADV
ejpam-1977	72	21	for	for	ADP
ejpam-1977	72	22	all	all	PRON
ejpam-1977	72	23	)	)	PUNCT
ejpam-1977	72	24	γ	γ	PROPN
ejpam-1977	72	25	∈	∈	PROPN
ejpam-1977	72	26	γ	γ	X
ejpam-1977	72	27	.	.	PUNCT
ejpam-1977	73	1	let	let	VERB
ejpam-1977	73	2	m	m	PRON
ejpam-1977	73	3	be	be	AUX
ejpam-1977	73	4	a	a	DET
ejpam-1977	73	5	γ	γ	X
ejpam-1977	73	6	–	–	PUNCT
ejpam-1977	73	7	subsemigroup	subsemigroup	NOUN
ejpam-1977	73	8	of	of	ADP
ejpam-1977	73	9	a	a	DET
ejpam-1977	73	10	γ	γ	X
ejpam-1977	73	11	–	–	PUNCT
ejpam-1977	73	12	semigroup	semigroup	NOUN
ejpam-1977	73	13	m	m	NOUN
ejpam-1977	73	14	.	.	PUNCT
ejpam-1977	74	1	in	in	ADP
ejpam-1977	74	2	the	the	DET
ejpam-1977	74	3	set	set	NOUN
ejpam-1977	74	4	m	m	VERB
ejpam-1977	74	5	we	we	PRON
ejpam-1977	74	6	have	have	VERB
ejpam-1977	74	7	a	a	DET
ejpam-1977	74	8	γ	γ	X
ejpam-1977	74	9	–	–	PUNCT
ejpam-1977	74	10	multiplication	multiplication	NOUN
ejpam-1977	74	11	induced	induce	VERB
ejpam-1977	74	12	by	by	ADP
ejpam-1977	74	13	the	the	DET
ejpam-1977	74	14	γ	γ	X
ejpam-1977	74	15	–	–	PUNCT
ejpam-1977	74	16	multiplication	multiplication	NOUN
ejpam-1977	74	17	of	of	ADP
ejpam-1977	74	18	γ	γ	X
ejpam-1977	74	19	–	–	PUNCT
ejpam-1977	74	20	semigroup	semigroup	NOUN
ejpam-1977	74	21	m	m	VERB
ejpam-1977	74	22	,	,	PUNCT
ejpam-1977	74	23	(	(	PUNCT
ejpam-1977	74	24	·	·	PUNCT
ejpam-1977	74	25	)	)	PUNCT
ejpam-1977	74	26	γ	γ	X
ejpam-1977	74	27	,	,	PUNCT
ejpam-1977	74	28	denoting	denote	VERB
ejpam-1977	74	29	it	it	PRON
ejpam-1977	74	30	with	with	ADP
ejpam-1977	74	31	the	the	DET
ejpam-1977	74	32	same	same	ADJ
ejpam-1977	74	33	symbol	symbol	NOUN
ejpam-1977	74	34	.	.	PUNCT
ejpam-1977	75	1	it	it	PRON
ejpam-1977	75	2	is	be	AUX
ejpam-1977	75	3	clear	clear	ADJ
ejpam-1977	75	4	that	that	SCONJ
ejpam-1977	75	5	the	the	DET
ejpam-1977	75	6	ordered	order	VERB
ejpam-1977	75	7	pair	pair	NOUN
ejpam-1977	75	8	(	(	PUNCT
ejpam-1977	75	9	m	m	PROPN
ejpam-1977	75	10	,	,	PUNCT
ejpam-1977	75	11	(	(	PUNCT
ejpam-1977	75	12	·	·	PUNCT
ejpam-1977	75	13	)	)	PUNCT
ejpam-1977	75	14	γ	γ	X
ejpam-1977	75	15	)	)	PUNCT
ejpam-1977	75	16	is	be	AUX
ejpam-1977	75	17	a	a	DET
ejpam-1977	75	18	γ	γ	X
ejpam-1977	75	19	–	–	PUNCT
ejpam-1977	75	20	semigroup	semigroup	NOUN
ejpam-1977	75	21	.	.	PUNCT
ejpam-1977	76	1	from	from	ADP
ejpam-1977	76	2	theorem	theorem	ADJ
ejpam-1977	76	3	3	3	NUM
ejpam-1977	76	4	,	,	PUNCT
ejpam-1977	76	5	if	if	SCONJ
ejpam-1977	76	6	mγ	mγ	PRON
ejpam-1977	76	7	is	be	AUX
ejpam-1977	76	8	a	a	DET
ejpam-1977	76	9	group	group	NOUN
ejpam-1977	76	10	for	for	ADP
ejpam-1977	76	11	some	some	DET
ejpam-1977	76	12	γ	γ	PROPN
ejpam-1977	76	13	∈	∈	PROPN
ejpam-1977	76	14	γ	γ	X
ejpam-1977	76	15	,	,	PUNCT
ejpam-1977	76	16	then	then	ADV
ejpam-1977	76	17	it	it	PRON
ejpam-1977	76	18	is	be	AUX
ejpam-1977	76	19	group	group	NOUN
ejpam-1977	76	20	for	for	ADP
ejpam-1977	76	21	all	all	DET
ejpam-1977	76	22	γ	γ	PROPN
ejpam-1977	76	23	∈	∈	PROPN
ejpam-1977	76	24	γ	γ	NOUN
ejpam-1977	76	25	and	and	CCONJ
ejpam-1977	76	26	so	so	ADV
ejpam-1977	76	27	it	it	PRON
ejpam-1977	76	28	is	be	AUX
ejpam-1977	76	29	a	a	DET
ejpam-1977	76	30	γ	γ	X
ejpam-1977	76	31	–	–	PUNCT
ejpam-1977	76	32	group	group	NOUN
ejpam-1977	76	33	.	.	PUNCT
ejpam-1977	77	1	in	in	ADP
ejpam-1977	77	2	this	this	DET
ejpam-1977	77	3	case	case	NOUN
ejpam-1977	77	4	,	,	PUNCT
ejpam-1977	77	5	we	we	PRON
ejpam-1977	77	6	will	will	AUX
ejpam-1977	77	7	call	call	VERB
ejpam-1977	77	8	m	m	PROPN
ejpam-1977	77	9	a	a	DET
ejpam-1977	77	10	γ	γ	X
ejpam-1977	77	11	–	–	PUNCT
ejpam-1977	77	12	subgroup	subgroup	NOUN
ejpam-1977	77	13	of	of	ADP
ejpam-1977	77	14	the	the	DET
ejpam-1977	77	15	γ	γ	X
ejpam-1977	77	16	–	–	PUNCT
ejpam-1977	77	17	semigroup	semigroup	PROPN
ejpam-1977	77	18	m	m	PROPN
ejpam-1977	77	19	.	.	PUNCT
ejpam-1977	77	20	i.	i.	PROPN
ejpam-1977	77	21	braja	braja	PROPN
ejpam-1977	77	22	,	,	PUNCT
ejpam-1977	77	23	p.	p.	NOUN
ejpam-1977	77	24	petro	petro	PROPN
ejpam-1977	77	25	/	/	PUNCT
ejpam-1977	77	26	eur	eur	PROPN
ejpam-1977	77	27	.	.	PUNCT
ejpam-1977	78	1	j.	j.	PROPN
ejpam-1977	78	2	pure	pure	PROPN
ejpam-1977	78	3	appl	appl	PROPN
ejpam-1977	78	4	.	.	PROPN
ejpam-1977	78	5	math	math	PROPN
ejpam-1977	78	6	,	,	PUNCT
ejpam-1977	78	7	7	7	NUM
ejpam-1977	78	8	(	(	PUNCT
ejpam-1977	78	9	2014	2014	NUM
ejpam-1977	78	10	)	)	PUNCT
ejpam-1977	78	11	,	,	PUNCT
ejpam-1977	78	12	77	77	NUM
ejpam-1977	78	13	-	-	SYM
ejpam-1977	78	14	85	85	NUM
ejpam-1977	78	15	80	80	NUM
ejpam-1977	78	16	saha	saha	NOUN
ejpam-1977	78	17	has	have	AUX
ejpam-1977	78	18	defined	define	VERB
ejpam-1977	78	19	in	in	ADP
ejpam-1977	78	20	[	[	X
ejpam-1977	78	21	7	7	X
ejpam-1977	78	22	]	]	PUNCT
ejpam-1977	78	23	the	the	DET
ejpam-1977	78	24	green	green	PROPN
ejpam-1977	78	25	’s	’s	PART
ejpam-1977	78	26	relations	relation	NOUN
ejpam-1977	78	27	r	r	NOUN
ejpam-1977	78	28	,	,	PUNCT
ejpam-1977	78	29	l	l	NOUN
ejpam-1977	78	30	,	,	PUNCT
ejpam-1977	78	31	h	h	NOUN
ejpam-1977	78	32	in	in	ADP
ejpam-1977	78	33	a	a	DET
ejpam-1977	78	34	γ	γ	X
ejpam-1977	78	35	–	–	PUNCT
ejpam-1977	78	36	semigroup	semigroup	NOUN
ejpam-1977	78	37	m	m	NOUN
ejpam-1977	78	38	as	as	SCONJ
ejpam-1977	78	39	follows	follow	VERB
ejpam-1977	78	40	:	:	PUNCT
ejpam-1977	78	41	∀(a	∀(a	NUM
ejpam-1977	78	42	,	,	PUNCT
ejpam-1977	78	43	b	b	NOUN
ejpam-1977	78	44	)	)	PUNCT
ejpam-1977	78	45	∈m2	∈m2	NOUN
ejpam-1977	78	46	,	,	PUNCT
ejpam-1977	78	47	ar	ar	NOUN
ejpam-1977	78	48	b⇔	b⇔	PROPN
ejpam-1977	78	49	(	(	PUNCT
ejpam-1977	78	50	a)r	a)r	X
ejpam-1977	78	51	=	=	SYM
ejpam-1977	78	52	(	(	PUNCT
ejpam-1977	78	53	b)r	b)r	NOUN
ejpam-1977	78	54	,	,	PUNCT
ejpam-1977	78	55	∀(a	∀(a	PROPN
ejpam-1977	78	56	,	,	PUNCT
ejpam-1977	78	57	b	b	NOUN
ejpam-1977	78	58	)	)	PUNCT
ejpam-1977	78	59	∈m2	∈m2	NOUN
ejpam-1977	78	60	,	,	PUNCT
ejpam-1977	78	61	al	al	PROPN
ejpam-1977	78	62	b⇔	b⇔	PROPN
ejpam-1977	78	63	(	(	PUNCT
ejpam-1977	78	64	a)l	a)l	NOUN
ejpam-1977	78	65	=	=	SYM
ejpam-1977	78	66	(	(	PUNCT
ejpam-1977	78	67	b)l	b)l	X
ejpam-1977	78	68	,	,	PUNCT
ejpam-1977	78	69	∀(a	∀(a	PROPN
ejpam-1977	78	70	,	,	PUNCT
ejpam-1977	78	71	b	b	NOUN
ejpam-1977	78	72	)	)	PUNCT
ejpam-1977	78	73	∈m2	∈m2	NOUN
ejpam-1977	78	74	,	,	PUNCT
ejpam-1977	78	75	ah	ah	INTJ
ejpam-1977	78	76	b⇔	b⇔	PROPN
ejpam-1977	78	77	(	(	PUNCT
ejpam-1977	78	78	a)r	a)r	NOUN
ejpam-1977	78	79	=	=	SYM
ejpam-1977	78	80	(	(	PUNCT
ejpam-1977	78	81	b)r	b)r	NOUN
ejpam-1977	78	82	and	and	CCONJ
ejpam-1977	78	83	(	(	PUNCT
ejpam-1977	78	84	a)l	a)l	NOUN
ejpam-1977	78	85	=	=	SYM
ejpam-1977	78	86	(	(	PUNCT
ejpam-1977	78	87	b)l	b)l	NOUN
ejpam-1977	78	88	,	,	PUNCT
ejpam-1977	78	89	where	where	SCONJ
ejpam-1977	78	90	(	(	PUNCT
ejpam-1977	78	91	a)r	a)r	NOUN
ejpam-1977	78	92	=	=	PUNCT
ejpam-1977	78	93	a∪	a∪	PROPN
ejpam-1977	78	94	aγm	aγm	NOUN
ejpam-1977	78	95	,	,	PUNCT
ejpam-1977	78	96	(	(	PUNCT
ejpam-1977	78	97	b)r	b)r	NOUN
ejpam-1977	78	98	=	=	SYM
ejpam-1977	78	99	b∪	b∪	ADJ
ejpam-1977	78	100	bγm	bγm	NOUN
ejpam-1977	78	101	,	,	PUNCT
ejpam-1977	78	102	(	(	PUNCT
ejpam-1977	78	103	a)l	a)l	NOUN
ejpam-1977	78	104	=	=	SYM
ejpam-1977	78	105	a∪mγa	a∪mγa	PROPN
ejpam-1977	78	106	,	,	PUNCT
ejpam-1977	78	107	(	(	PUNCT
ejpam-1977	78	108	b)l	b)l	X
ejpam-1977	78	109	=	=	SYM
ejpam-1977	78	110	b∪mγb	b∪mγb	NOUN
ejpam-1977	78	111	,	,	PUNCT
ejpam-1977	78	112	are	be	AUX
ejpam-1977	78	113	respectively	respectively	ADV
ejpam-1977	78	114	the	the	DET
ejpam-1977	78	115	principal	principal	ADJ
ejpam-1977	78	116	right	right	ADJ
ejpam-1977	78	117	ideal	ideal	NOUN
ejpam-1977	78	118	generated	generate	VERB
ejpam-1977	78	119	by	by	ADP
ejpam-1977	78	120	a	a	PRON
ejpam-1977	78	121	,	,	PUNCT
ejpam-1977	78	122	the	the	DET
ejpam-1977	78	123	principal	principal	ADJ
ejpam-1977	78	124	right	right	ADJ
ejpam-1977	78	125	ideal	ideal	NOUN
ejpam-1977	78	126	generated	generate	VERB
ejpam-1977	78	127	by	by	ADP
ejpam-1977	78	128	b	b	PROPN
ejpam-1977	78	129	,	,	PUNCT
ejpam-1977	78	130	the	the	DET
ejpam-1977	78	131	principal	principal	NOUN
ejpam-1977	78	132	left	leave	VERB
ejpam-1977	78	133	ideal	ideal	NOUN
ejpam-1977	78	134	generated	generate	VERB
ejpam-1977	78	135	by	by	ADP
ejpam-1977	78	136	a	a	PRON
ejpam-1977	78	137	,	,	PUNCT
ejpam-1977	78	138	and	and	CCONJ
ejpam-1977	78	139	the	the	DET
ejpam-1977	78	140	principal	principal	NOUN
ejpam-1977	78	141	left	leave	VERB
ejpam-1977	78	142	ideal	ideal	NOUN
ejpam-1977	78	143	generated	generate	VERB
ejpam-1977	78	144	by	by	ADP
ejpam-1977	78	145	b	b	PROPN
ejpam-1977	78	146	in	in	ADP
ejpam-1977	78	147	γ	γ	X
ejpam-1977	78	148	–	–	PUNCT
ejpam-1977	78	149	semigroup	semigroup	ADJ
ejpam-1977	78	150	m	m	NOUN
ejpam-1977	78	151	.	.	PUNCT
ejpam-1977	79	1	it	it	PRON
ejpam-1977	79	2	turns	turn	VERB
ejpam-1977	79	3	out	out	ADP
ejpam-1977	79	4	that	that	SCONJ
ejpam-1977	79	5	r	r	NOUN
ejpam-1977	79	6	,	,	PUNCT
ejpam-1977	79	7	l	l	NOUN
ejpam-1977	79	8	,	,	PUNCT
ejpam-1977	79	9	h	h	NOUN
ejpam-1977	79	10	are	be	AUX
ejpam-1977	79	11	equivalent	equivalent	ADJ
ejpam-1977	79	12	relations	relation	NOUN
ejpam-1977	79	13	.	.	PUNCT
ejpam-1977	80	1	the	the	DET
ejpam-1977	80	2	respective	respective	ADJ
ejpam-1977	80	3	equivalence	equivalence	NOUN
ejpam-1977	80	4	classes	class	NOUN
ejpam-1977	80	5	of	of	ADP
ejpam-1977	80	6	a	a	DET
ejpam-1977	80	7	∈	∈	NOUN
ejpam-1977	80	8	m	m	VERB
ejpam-1977	80	9	are	be	AUX
ejpam-1977	80	10	denoted	denote	VERB
ejpam-1977	80	11	by	by	ADP
ejpam-1977	80	12	ra	ra	PROPN
ejpam-1977	80	13	,	,	PUNCT
ejpam-1977	80	14	la	la	PROPN
ejpam-1977	80	15	,	,	PUNCT
ejpam-1977	80	16	ha	ha	INTJ
ejpam-1977	80	17	.	.	PUNCT
ejpam-1977	80	18	proposition	proposition	NOUN
ejpam-1977	80	19	3	3	NUM
ejpam-1977	80	20	(	(	PUNCT
ejpam-1977	80	21	[	[	X
ejpam-1977	80	22	7	7	NUM
ejpam-1977	80	23	]	]	NUM
ejpam-1977	80	24	)	)	PUNCT
ejpam-1977	80	25	.	.	PUNCT
ejpam-1977	81	1	let	let	VERB
ejpam-1977	81	2	m	m	PRON
ejpam-1977	81	3	be	be	AUX
ejpam-1977	81	4	a	a	DET
ejpam-1977	81	5	γ	γ	X
ejpam-1977	81	6	–	–	PUNCT
ejpam-1977	81	7	semigroup	semigroup	NOUN
ejpam-1977	81	8	.	.	PUNCT
ejpam-1977	82	1	then	then	ADV
ejpam-1977	82	2	we	we	PRON
ejpam-1977	82	3	have	have	VERB
ejpam-1977	82	4	:	:	PUNCT
ejpam-1977	82	5	(	(	PUNCT
ejpam-1977	82	6	i	i	NOUN
ejpam-1977	82	7	)	)	PUNCT
ejpam-1977	82	8	for	for	ADP
ejpam-1977	82	9	every	every	DET
ejpam-1977	82	10	three	three	NUM
ejpam-1977	82	11	elements	element	NOUN
ejpam-1977	82	12	a	a	DET
ejpam-1977	82	13	,	,	PUNCT
ejpam-1977	82	14	b	b	NOUN
ejpam-1977	82	15	,	,	PUNCT
ejpam-1977	82	16	c	c	PROPN
ejpam-1977	82	17	of	of	ADP
ejpam-1977	82	18	m	m	PROPN
ejpam-1977	82	19	and	and	CCONJ
ejpam-1977	82	20	for	for	ADP
ejpam-1977	82	21	every	every	DET
ejpam-1977	82	22	γ	γ	PROPN
ejpam-1977	82	23	∈	∈	PROPN
ejpam-1977	82	24	γ	γ	PROPN
ejpam-1977	82	25	ar	ar	PROPN
ejpam-1977	82	26	b⇒	b⇒	PROPN
ejpam-1977	82	27	cγarcγb	cγarcγb	PROPN
ejpam-1977	82	28	and	and	CCONJ
ejpam-1977	82	29	al	al	PROPN
ejpam-1977	82	30	b⇒	b⇒	PROPN
ejpam-1977	82	31	aγcl	aγcl	PROPN
ejpam-1977	82	32	aγb	aγb	PROPN
ejpam-1977	82	33	.	.	PUNCT
ejpam-1977	83	1	(	(	PUNCT
ejpam-1977	83	2	ii	ii	NOUN
ejpam-1977	83	3	)	)	PUNCT
ejpam-1977	83	4	for	for	ADP
ejpam-1977	83	5	every	every	DET
ejpam-1977	83	6	two	two	NUM
ejpam-1977	83	7	elements	element	NOUN
ejpam-1977	83	8	a	a	PRON
ejpam-1977	83	9	,	,	PUNCT
ejpam-1977	83	10	b	b	PROPN
ejpam-1977	83	11	∈	∈	PROPN
ejpam-1977	83	12	m	m	PROPN
ejpam-1977	83	13	,	,	PUNCT
ejpam-1977	83	14	ar	ar	PROPN
ejpam-1977	83	15	b	b	PROPN
ejpam-1977	84	1	if	if	SCONJ
ejpam-1977	85	1	and	and	CCONJ
ejpam-1977	85	2	only	only	ADV
ejpam-1977	85	3	if	if	SCONJ
ejpam-1977	85	4	either	either	CCONJ
ejpam-1977	85	5	a	a	DET
ejpam-1977	85	6	=	=	SYM
ejpam-1977	85	7	b	b	NOUN
ejpam-1977	85	8	or	or	CCONJ
ejpam-1977	85	9	there	there	ADV
ejpam-1977	85	10	exist	exist	VERB
ejpam-1977	85	11	α	α	PRON
ejpam-1977	85	12	,	,	PUNCT
ejpam-1977	85	13	β	β	X
ejpam-1977	85	14	∈	∈	PROPN
ejpam-1977	85	15	γ	γ	NOUN
ejpam-1977	85	16	and	and	CCONJ
ejpam-1977	85	17	c	c	NOUN
ejpam-1977	85	18	,	,	PUNCT
ejpam-1977	85	19	d	d	PROPN
ejpam-1977	85	20	∈	∈	PROPN
ejpam-1977	85	21	m	m	VERB
ejpam-1977	85	22	such	such	ADJ
ejpam-1977	85	23	that	that	SCONJ
ejpam-1977	85	24	a	a	DET
ejpam-1977	85	25	=	=	PUNCT
ejpam-1977	85	26	bαc	bαc	NOUN
ejpam-1977	85	27	and	and	CCONJ
ejpam-1977	85	28	b	b	NOUN
ejpam-1977	85	29	=	=	SYM
ejpam-1977	85	30	αβd	αβd	PROPN
ejpam-1977	85	31	.	.	PUNCT
ejpam-1977	86	1	(	(	PUNCT
ejpam-1977	86	2	iii	iii	NOUN
ejpam-1977	86	3	)	)	PUNCT
ejpam-1977	86	4	for	for	ADP
ejpam-1977	86	5	every	every	DET
ejpam-1977	86	6	two	two	NUM
ejpam-1977	86	7	elements	element	NOUN
ejpam-1977	86	8	a	a	PRON
ejpam-1977	86	9	,	,	PUNCT
ejpam-1977	86	10	b	b	PROPN
ejpam-1977	86	11	∈	∈	PROPN
ejpam-1977	86	12	m	m	PROPN
ejpam-1977	86	13	,	,	PUNCT
ejpam-1977	86	14	al	al	PROPN
ejpam-1977	86	15	b	b	PROPN
ejpam-1977	87	1	if	if	SCONJ
ejpam-1977	87	2	and	and	CCONJ
ejpam-1977	87	3	only	only	ADV
ejpam-1977	87	4	if	if	SCONJ
ejpam-1977	87	5	either	either	CCONJ
ejpam-1977	87	6	a	a	DET
ejpam-1977	87	7	=	=	SYM
ejpam-1977	87	8	b	b	NOUN
ejpam-1977	87	9	or	or	CCONJ
ejpam-1977	87	10	there	there	ADV
ejpam-1977	87	11	exist	exist	VERB
ejpam-1977	87	12	α	α	PRON
ejpam-1977	87	13	,	,	PUNCT
ejpam-1977	87	14	β	β	X
ejpam-1977	87	15	∈	∈	PROPN
ejpam-1977	87	16	γ	γ	NOUN
ejpam-1977	87	17	and	and	CCONJ
ejpam-1977	87	18	c	c	NOUN
ejpam-1977	87	19	,	,	PUNCT
ejpam-1977	87	20	d	d	PROPN
ejpam-1977	87	21	∈	∈	PROPN
ejpam-1977	87	22	m	m	VERB
ejpam-1977	87	23	such	such	ADJ
ejpam-1977	87	24	that	that	SCONJ
ejpam-1977	87	25	a	a	DET
ejpam-1977	87	26	=	=	X
ejpam-1977	87	27	cαb	cαb	NOUN
ejpam-1977	87	28	and	and	CCONJ
ejpam-1977	87	29	b	b	X
ejpam-1977	87	30	=	=	SYM
ejpam-1977	87	31	dβα	dβα	PROPN
ejpam-1977	87	32	.	.	PUNCT
ejpam-1977	88	1	(	(	PUNCT
ejpam-1977	88	2	iv	iv	X
ejpam-1977	88	3	)	)	PUNCT
ejpam-1977	88	4	r	r	NOUN
ejpam-1977	88	5	and	and	CCONJ
ejpam-1977	88	6	l	l	NOUN
ejpam-1977	88	7	commute	commute	NOUN
ejpam-1977	88	8	,	,	PUNCT
ejpam-1977	88	9	that	that	PRON
ejpam-1977	88	10	is	is	ADV
ejpam-1977	88	11	r	r	NOUN
ejpam-1977	88	12	◦	◦	NOUN
ejpam-1977	88	13	l	l	NOUN
ejpam-1977	88	14	=	=	SYM
ejpam-1977	88	15	l	l	NOUN
ejpam-1977	88	16	◦	◦	NOUN
ejpam-1977	88	17	r	r	NOUN
ejpam-1977	88	18	.	.	PUNCT
ejpam-1977	89	1	so	so	ADV
ejpam-1977	89	2	,	,	PUNCT
ejpam-1977	89	3	one	one	PRON
ejpam-1977	89	4	can	can	AUX
ejpam-1977	89	5	define	define	VERB
ejpam-1977	89	6	a	a	DET
ejpam-1977	89	7	fourth	fourth	ADJ
ejpam-1977	89	8	green	green	NOUN
ejpam-1977	89	9	’s	’s	PART
ejpam-1977	89	10	relation	relation	NOUN
ejpam-1977	89	11	in	in	ADP
ejpam-1977	89	12	m	m	PROPN
ejpam-1977	89	13	which	which	PRON
ejpam-1977	89	14	is	be	AUX
ejpam-1977	89	15	d	d	X
ejpam-1977	89	16	=	=	NOUN
ejpam-1977	89	17	r	r	NOUN
ejpam-1977	89	18	◦	◦	NOUN
ejpam-1977	89	19	l	l	NOUN
ejpam-1977	89	20	=	=	NOUN
ejpam-1977	89	21	l	l	NOUN
ejpam-1977	89	22	◦	◦	NOUN
ejpam-1977	89	23	r	r	NOUN
ejpam-1977	89	24	.	.	PUNCT
ejpam-1977	90	1	the	the	DET
ejpam-1977	90	2	equivalence	equivalence	NOUN
ejpam-1977	90	3	class	class	NOUN
ejpam-1977	90	4	of	of	ADP
ejpam-1977	90	5	a	a	DET
ejpam-1977	90	6	∈	∈	NOUN
ejpam-1977	90	7	m	m	VERB
ejpam-1977	90	8	from	from	ADP
ejpam-1977	90	9	d	d	PROPN
ejpam-1977	90	10	is	be	AUX
ejpam-1977	90	11	denoted	denote	VERB
ejpam-1977	90	12	by	by	ADP
ejpam-1977	90	13	da	da	PROPN
ejpam-1977	90	14	.	.	PUNCT
ejpam-1977	91	1	in	in	ADP
ejpam-1977	91	2	[	[	X
ejpam-1977	91	3	6	6	NUM
ejpam-1977	91	4	]	]	PUNCT
ejpam-1977	91	5	,	,	PUNCT
ejpam-1977	91	6	it	it	PRON
ejpam-1977	91	7	is	be	AUX
ejpam-1977	91	8	defined	define	VERB
ejpam-1977	91	9	the	the	DET
ejpam-1977	91	10	relation	relation	NOUN
ejpam-1977	91	11	q	q	PUNCT
ejpam-1977	91	12	in	in	ADP
ejpam-1977	91	13	a	a	DET
ejpam-1977	91	14	γ	γ	X
ejpam-1977	91	15	–	–	PUNCT
ejpam-1977	91	16	semigroup	semigroup	NOUN
ejpam-1977	91	17	m	m	VERB
ejpam-1977	91	18	as	as	SCONJ
ejpam-1977	91	19	follows	follow	VERB
ejpam-1977	91	20	∀(a	∀(a	PROPN
ejpam-1977	91	21	,	,	PUNCT
ejpam-1977	91	22	b	b	NOUN
ejpam-1977	91	23	)	)	PUNCT
ejpam-1977	91	24	∈	∈	PROPN
ejpam-1977	91	25	m2	m2	PROPN
ejpam-1977	91	26	,	,	PUNCT
ejpam-1977	91	27	aqb⇔	aqb⇔	NOUN
ejpam-1977	91	28	(	(	PUNCT
ejpam-1977	91	29	a)q	a)q	NOUN
ejpam-1977	91	30	=	=	SYM
ejpam-1977	91	31	(	(	PUNCT
ejpam-1977	91	32	b)q	b)q	X
ejpam-1977	91	33	,	,	PUNCT
ejpam-1977	91	34	where	where	SCONJ
ejpam-1977	91	35	(	(	PUNCT
ejpam-1977	91	36	a)q	a)q	NOUN
ejpam-1977	91	37	=	=	SYM
ejpam-1977	91	38	a	a	DET
ejpam-1977	91	39	∪	∪	X
ejpam-1977	91	40	(	(	PUNCT
ejpam-1977	91	41	aγm	aγm	NOUN
ejpam-1977	91	42	∩	∩	NOUN
ejpam-1977	91	43	mγa	mγa	PROPN
ejpam-1977	91	44	)	)	PUNCT
ejpam-1977	91	45	,	,	PUNCT
ejpam-1977	91	46	(	(	PUNCT
ejpam-1977	91	47	b)q	b)q	PUNCT
ejpam-1977	91	48	=	=	SYM
ejpam-1977	91	49	b	b	X
ejpam-1977	91	50	∪	∪	X
ejpam-1977	91	51	(	(	PUNCT
ejpam-1977	91	52	bγm	bγm	PROPN
ejpam-1977	91	53	∩	∩	NOUN
ejpam-1977	91	54	mγb	mγb	VERB
ejpam-1977	91	55	)	)	PUNCT
ejpam-1977	91	56	,	,	PUNCT
ejpam-1977	91	57	are	be	AUX
ejpam-1977	91	58	the	the	DET
ejpam-1977	91	59	principal	principal	ADJ
ejpam-1977	91	60	quasi	quasi	ADJ
ejpam-1977	91	61	-	-	ADJ
ejpam-1977	91	62	ideal	ideal	ADJ
ejpam-1977	91	63	generated	generate	VERB
ejpam-1977	91	64	by	by	ADP
ejpam-1977	91	65	a	a	PRON
ejpam-1977	91	66	and	and	CCONJ
ejpam-1977	91	67	the	the	DET
ejpam-1977	91	68	principal	principal	ADJ
ejpam-1977	91	69	quasi	quasi	NOUN
ejpam-1977	91	70	-	-	ADJ
ejpam-1977	91	71	ideal	ideal	ADJ
ejpam-1977	91	72	generated	generate	VERB
ejpam-1977	91	73	by	by	ADP
ejpam-1977	91	74	b	b	PROPN
ejpam-1977	91	75	in	in	ADP
ejpam-1977	91	76	γ	γ	X
ejpam-1977	91	77	–	–	PUNCT
ejpam-1977	91	78	semigroup	semigroup	PROPN
ejpam-1977	91	79	m	m	NOUN
ejpam-1977	91	80	,	,	PUNCT
ejpam-1977	91	81	respectively	respectively	ADV
ejpam-1977	91	82	.	.	PUNCT
ejpam-1977	92	1	the	the	DET
ejpam-1977	92	2	relation	relation	NOUN
ejpam-1977	92	3	q	q	PUNCT
ejpam-1977	92	4	is	be	AUX
ejpam-1977	92	5	an	an	DET
ejpam-1977	92	6	equivalence	equivalence	NOUN
ejpam-1977	92	7	relation	relation	NOUN
ejpam-1977	92	8	and	and	CCONJ
ejpam-1977	92	9	moreover	moreover	ADV
ejpam-1977	92	10	we	we	PRON
ejpam-1977	92	11	have	have	VERB
ejpam-1977	92	12	proposition	proposition	NOUN
ejpam-1977	92	13	4	4	NUM
ejpam-1977	92	14	(	(	PUNCT
ejpam-1977	92	15	[	[	X
ejpam-1977	92	16	6	6	NUM
ejpam-1977	92	17	]	]	NUM
ejpam-1977	92	18	)	)	PUNCT
ejpam-1977	92	19	.	.	PUNCT
ejpam-1977	93	1	the	the	DET
ejpam-1977	93	2	relationsh	relationsh	NOUN
ejpam-1977	93	3	and	and	CCONJ
ejpam-1977	93	4	q	q	NOUN
ejpam-1977	93	5	coincide	coincide	NOUN
ejpam-1977	93	6	in	in	ADP
ejpam-1977	93	7	every	every	DET
ejpam-1977	93	8	γ	γ	PROPN
ejpam-1977	93	9	–	–	PUNCT
ejpam-1977	93	10	semigroup	semigroup	ADJ
ejpam-1977	93	11	m.	m.	NOUN
ejpam-1977	93	12	for	for	ADP
ejpam-1977	93	13	the	the	DET
ejpam-1977	93	14	relationh	relationh	NOUN
ejpam-1977	93	15	,	,	PUNCT
ejpam-1977	93	16	consequently	consequently	ADV
ejpam-1977	93	17	for	for	ADP
ejpam-1977	93	18	relation	relation	NOUN
ejpam-1977	93	19	q	q	PROPN
ejpam-1977	93	20	,	,	PUNCT
ejpam-1977	93	21	has	have	VERB
ejpam-1977	93	22	an	an	DET
ejpam-1977	93	23	analogue	analogue	NOUN
ejpam-1977	93	24	of	of	ADP
ejpam-1977	93	25	green	green	PROPN
ejpam-1977	93	26	’s	’s	PART
ejpam-1977	93	27	theorem	theorem	NOUN
ejpam-1977	93	28	for	for	ADP
ejpam-1977	93	29	plain	plain	ADJ
ejpam-1977	93	30	semigroups	semigroup	NOUN
ejpam-1977	93	31	,	,	PUNCT
ejpam-1977	93	32	which	which	PRON
ejpam-1977	93	33	is	be	AUX
ejpam-1977	93	34	called	call	VERB
ejpam-1977	93	35	green	green	PROPN
ejpam-1977	93	36	’s	’s	PART
ejpam-1977	93	37	theorem	theorem	NOUN
ejpam-1977	93	38	for	for	ADP
ejpam-1977	93	39	γ	γ	NOUN
ejpam-1977	93	40	–	–	PUNCT
ejpam-1977	93	41	semigroups	semigroup	NOUN
ejpam-1977	93	42	.	.	PUNCT
ejpam-1977	94	1	theorem	theorem	NOUN
ejpam-1977	94	2	4	4	NUM
ejpam-1977	94	3	(	(	PUNCT
ejpam-1977	94	4	[	[	X
ejpam-1977	94	5	6	6	NUM
ejpam-1977	94	6	]	]	X
ejpam-1977	94	7	green	green	PROPN
ejpam-1977	94	8	’s	’s	PART
ejpam-1977	94	9	theorem	theorem	NOUN
ejpam-1977	94	10	for	for	ADP
ejpam-1977	94	11	γ	γ	NOUN
ejpam-1977	94	12	–	–	PUNCT
ejpam-1977	94	13	semigroups	semigroup	NOUN
ejpam-1977	94	14	)	)	PUNCT
ejpam-1977	94	15	.	.	PUNCT
ejpam-1977	95	1	if	if	SCONJ
ejpam-1977	95	2	the	the	DET
ejpam-1977	95	3	elements	element	NOUN
ejpam-1977	95	4	a	a	DET
ejpam-1977	95	5	,	,	PUNCT
ejpam-1977	95	6	b	b	NOUN
ejpam-1977	95	7	,	,	PUNCT
ejpam-1977	95	8	aγb	aγb	NOUN
ejpam-1977	95	9	of	of	ADP
ejpam-1977	95	10	a	a	DET
ejpam-1977	95	11	γ	γ	X
ejpam-1977	95	12	–	–	PUNCT
ejpam-1977	95	13	semigroup	semigroup	ADJ
ejpam-1977	95	14	m	m	VERB
ejpam-1977	95	15	all	all	PRON
ejpam-1977	95	16	belong	belong	VERB
ejpam-1977	95	17	to	to	ADP
ejpam-1977	95	18	the	the	DET
ejpam-1977	95	19	sameh	sameh	NOUN
ejpam-1977	95	20	–	–	PUNCT
ejpam-1977	95	21	class	class	NOUN
ejpam-1977	95	22	h	h	NOUN
ejpam-1977	95	23	of	of	ADP
ejpam-1977	95	24	m	m	PROPN
ejpam-1977	95	25	,	,	PUNCT
ejpam-1977	95	26	then	then	ADV
ejpam-1977	95	27	h	h	NOUN
ejpam-1977	95	28	is	be	AUX
ejpam-1977	95	29	a	a	DET
ejpam-1977	95	30	subgroup	subgroup	NOUN
ejpam-1977	95	31	of	of	ADP
ejpam-1977	95	32	the	the	DET
ejpam-1977	95	33	semigroup	semigroup	PROPN
ejpam-1977	95	34	mγ	mγ	PROPN
ejpam-1977	95	35	.	.	PUNCT
ejpam-1977	96	1	moreover	moreover	ADV
ejpam-1977	96	2	,	,	PUNCT
ejpam-1977	96	3	for	for	ADP
ejpam-1977	96	4	any	any	DET
ejpam-1977	96	5	two	two	NUM
ejpam-1977	96	6	element	element	NOUN
ejpam-1977	96	7	h1	h1	NOUN
ejpam-1977	96	8	,	,	PUNCT
ejpam-1977	96	9	h2	h2	PROPN
ejpam-1977	96	10	∈	∈	PROPN
ejpam-1977	96	11	h	h	NOUN
ejpam-1977	96	12	,	,	PUNCT
ejpam-1977	96	13	the	the	DET
ejpam-1977	96	14	element	element	NOUN
ejpam-1977	96	15	h1γh2	h1γh2	NOUN
ejpam-1977	96	16	belongs	belong	VERB
ejpam-1977	96	17	to	to	ADP
ejpam-1977	96	18	h.	h.	PROPN
ejpam-1977	96	19	i.	i.	PROPN
ejpam-1977	96	20	braja	braja	PROPN
ejpam-1977	96	21	,	,	PUNCT
ejpam-1977	96	22	p.	p.	NOUN
ejpam-1977	96	23	petro	petro	PROPN
ejpam-1977	96	24	/	/	PUNCT
ejpam-1977	96	25	eur	eur	PROPN
ejpam-1977	96	26	.	.	PUNCT
ejpam-1977	97	1	j.	j.	PROPN
ejpam-1977	97	2	pure	pure	PROPN
ejpam-1977	97	3	appl	appl	PROPN
ejpam-1977	97	4	.	.	PROPN
ejpam-1977	97	5	math	math	PROPN
ejpam-1977	97	6	,	,	PUNCT
ejpam-1977	97	7	7	7	NUM
ejpam-1977	97	8	(	(	PUNCT
ejpam-1977	97	9	2014	2014	NUM
ejpam-1977	97	10	)	)	PUNCT
ejpam-1977	97	11	,	,	PUNCT
ejpam-1977	97	12	77	77	NUM
ejpam-1977	97	13	-	-	SYM
ejpam-1977	97	14	85	85	NUM
ejpam-1977	97	15	81	81	NUM
ejpam-1977	97	16	theorem	theorem	NOUN
ejpam-1977	97	17	5	5	NUM
ejpam-1977	97	18	(	(	PUNCT
ejpam-1977	97	19	[	[	X
ejpam-1977	97	20	6	6	NUM
ejpam-1977	97	21	]	]	NUM
ejpam-1977	97	22	)	)	PUNCT
ejpam-1977	97	23	.	.	PUNCT
ejpam-1977	98	1	a	a	DET
ejpam-1977	98	2	quasi	quasi	ADJ
ejpam-1977	98	3	–	–	PUNCT
ejpam-1977	98	4	ideal	ideal	ADJ
ejpam-1977	98	5	q	q	NOUN
ejpam-1977	98	6	of	of	ADP
ejpam-1977	98	7	a	a	DET
ejpam-1977	98	8	γ	γ	X
ejpam-1977	98	9	–	–	PUNCT
ejpam-1977	98	10	semigroup	semigroup	NOUN
ejpam-1977	98	11	s	s	NOUN
ejpam-1977	98	12	without	without	ADP
ejpam-1977	98	13	zero	zero	NUM
ejpam-1977	98	14	is	be	AUX
ejpam-1977	98	15	minimal	minimal	ADJ
ejpam-1977	98	16	if	if	SCONJ
ejpam-1977	98	17	and	and	CCONJ
ejpam-1977	98	18	only	only	ADV
ejpam-1977	98	19	if	if	SCONJ
ejpam-1977	98	20	q	q	NOUN
ejpam-1977	98	21	is	be	AUX
ejpam-1977	98	22	anh	anh	NOUN
ejpam-1977	98	23	–	–	PUNCT
ejpam-1977	98	24	class	class	NOUN
ejpam-1977	98	25	.	.	PUNCT
ejpam-1977	99	1	theorem	theorem	NOUN
ejpam-1977	99	2	6	6	NUM
ejpam-1977	99	3	(	(	PUNCT
ejpam-1977	99	4	[	[	X
ejpam-1977	99	5	6	6	NUM
ejpam-1977	99	6	]	]	NUM
ejpam-1977	99	7	)	)	PUNCT
ejpam-1977	99	8	.	.	PUNCT
ejpam-1977	100	1	a	a	DET
ejpam-1977	100	2	quasi	quasi	ADJ
ejpam-1977	100	3	–	–	PUNCT
ejpam-1977	100	4	ideal	ideal	ADJ
ejpam-1977	100	5	q	q	NOUN
ejpam-1977	100	6	of	of	ADP
ejpam-1977	100	7	a	a	DET
ejpam-1977	100	8	γ	γ	X
ejpam-1977	100	9	–	–	PUNCT
ejpam-1977	100	10	semigroup	semigroup	NOUN
ejpam-1977	100	11	s	s	NOUN
ejpam-1977	100	12	without	without	ADP
ejpam-1977	100	13	zero	zero	NUM
ejpam-1977	100	14	is	be	AUX
ejpam-1977	100	15	minimal	minimal	ADJ
ejpam-1977	100	16	if	if	SCONJ
ejpam-1977	100	17	and	and	CCONJ
ejpam-1977	100	18	only	only	ADV
ejpam-1977	100	19	if	if	SCONJ
ejpam-1977	100	20	q	q	NOUN
ejpam-1977	100	21	is	be	AUX
ejpam-1977	100	22	a	a	DET
ejpam-1977	100	23	γ	γ	X
ejpam-1977	100	24	–	–	PUNCT
ejpam-1977	100	25	subgroup	subgroup	NOUN
ejpam-1977	100	26	of	of	ADP
ejpam-1977	100	27	s.	s.	PROPN
ejpam-1977	100	28	theorem	theorem	VERB
ejpam-1977	100	29	7	7	NUM
ejpam-1977	100	30	(	(	PUNCT
ejpam-1977	100	31	[	[	X
ejpam-1977	100	32	6	6	NUM
ejpam-1977	100	33	]	]	PUNCT
ejpam-1977	100	34	)	)	PUNCT
ejpam-1977	100	35	.	.	PUNCT
ejpam-1977	101	1	let	let	VERB
ejpam-1977	101	2	a	a	DET
ejpam-1977	101	3	,	,	PUNCT
ejpam-1977	101	4	b	b	NOUN
ejpam-1977	101	5	be	be	AUX
ejpam-1977	101	6	two	two	NUM
ejpam-1977	101	7	elements	element	NOUN
ejpam-1977	101	8	of	of	ADP
ejpam-1977	101	9	a	a	DET
ejpam-1977	101	10	γ	γ	X
ejpam-1977	101	11	–	–	PUNCT
ejpam-1977	101	12	semigroup	semigroup	NOUN
ejpam-1977	101	13	s	s	NOUN
ejpam-1977	101	14	without	without	ADP
ejpam-1977	101	15	zero	zero	NUM
ejpam-1977	101	16	such	such	ADJ
ejpam-1977	101	17	that	that	DET
ejpam-1977	101	18	adb	adb	NOUN
ejpam-1977	101	19	.	.	PUNCT
ejpam-1977	102	1	then	then	ADV
ejpam-1977	102	2	the	the	DET
ejpam-1977	102	3	principal	principal	ADJ
ejpam-1977	102	4	quasi	quasi	NOUN
ejpam-1977	102	5	–	–	PUNCT
ejpam-1977	102	6	ideal	ideal	ADJ
ejpam-1977	102	7	(	(	PUNCT
ejpam-1977	102	8	a)q	a)q	X
ejpam-1977	102	9	is	be	AUX
ejpam-1977	102	10	minimal	minimal	ADJ
ejpam-1977	102	11	if	if	SCONJ
ejpam-1977	102	12	and	and	CCONJ
ejpam-1977	102	13	only	only	ADV
ejpam-1977	102	14	if	if	SCONJ
ejpam-1977	102	15	the	the	DET
ejpam-1977	102	16	same	same	ADJ
ejpam-1977	102	17	holds	hold	VERB
ejpam-1977	102	18	for	for	ADP
ejpam-1977	102	19	(	(	PUNCT
ejpam-1977	102	20	b)q	b)q	X
ejpam-1977	102	21	.	.	PUNCT
ejpam-1977	103	1	3	3	X
ejpam-1977	103	2	.	.	X
ejpam-1977	103	3	main	main	ADJ
ejpam-1977	103	4	results	result	NOUN
ejpam-1977	103	5	for	for	ADP
ejpam-1977	103	6	every	every	DET
ejpam-1977	103	7	element	element	NOUN
ejpam-1977	103	8	a	a	PRON
ejpam-1977	103	9	of	of	ADP
ejpam-1977	103	10	a	a	DET
ejpam-1977	103	11	γ	γ	X
ejpam-1977	103	12	–	–	PUNCT
ejpam-1977	103	13	semigroup	semigroup	ADJ
ejpam-1977	103	14	m	m	VERB
ejpam-1977	103	15	we	we	PRON
ejpam-1977	103	16	denote	denote	VERB
ejpam-1977	103	17	by	by	ADP
ejpam-1977	103	18	(	(	PUNCT
ejpam-1977	103	19	a)b	a)b	X
ejpam-1977	103	20	the	the	DET
ejpam-1977	103	21	intersection	intersection	NOUN
ejpam-1977	103	22	of	of	ADP
ejpam-1977	103	23	all	all	DET
ejpam-1977	103	24	bi	bi	NOUN
ejpam-1977	103	25	-	-	NOUN
ejpam-1977	103	26	ideals	ideal	NOUN
ejpam-1977	103	27	of	of	ADP
ejpam-1977	103	28	m	m	PRON
ejpam-1977	103	29	that	that	PRON
ejpam-1977	103	30	contain	contain	VERB
ejpam-1977	103	31	a.	a.	NOUN
ejpam-1977	103	32	this	this	DET
ejpam-1977	103	33	bi	bi	NOUN
ejpam-1977	103	34	–	–	PUNCT
ejpam-1977	103	35	ideal	ideal	ADJ
ejpam-1977	103	36	,	,	PUNCT
ejpam-1977	103	37	that	that	ADV
ejpam-1977	103	38	is	is	ADV
ejpam-1977	103	39	,	,	PUNCT
ejpam-1977	103	40	the	the	DET
ejpam-1977	103	41	smallest	small	ADJ
ejpam-1977	103	42	bi	bi	NOUN
ejpam-1977	103	43	–	–	PUNCT
ejpam-1977	103	44	ideal	ideal	NOUN
ejpam-1977	103	45	of	of	ADP
ejpam-1977	103	46	m	m	AUX
ejpam-1977	103	47	containing	contain	VERB
ejpam-1977	103	48	a	a	PRON
ejpam-1977	103	49	,	,	PUNCT
ejpam-1977	103	50	is	be	AUX
ejpam-1977	103	51	called	call	VERB
ejpam-1977	103	52	principal	principal	ADJ
ejpam-1977	103	53	bi	bi	NOUN
ejpam-1977	103	54	-	-	NOUN
ejpam-1977	103	55	ideal	ideal	NOUN
ejpam-1977	103	56	of	of	ADP
ejpam-1977	103	57	m	m	AUX
ejpam-1977	103	58	generated	generate	VERB
ejpam-1977	103	59	by	by	ADP
ejpam-1977	103	60	a.	a.	NOUN
ejpam-1977	103	61	from	from	ADP
ejpam-1977	103	62	the	the	DET
ejpam-1977	103	63	theorem	theorem	NOUN
ejpam-1977	103	64	1	1	NUM
ejpam-1977	103	65	we	we	PRON
ejpam-1977	103	66	have	have	VERB
ejpam-1977	103	67	(	(	PUNCT
ejpam-1977	103	68	a)b	a)b	X
ejpam-1977	103	69	=	=	PUNCT
ejpam-1977	103	70	a	a	DET
ejpam-1977	103	71	∪	∪	ADJ
ejpam-1977	103	72	aγa	aγa	X
ejpam-1977	103	73	∪	∪	ADJ
ejpam-1977	103	74	aγmγa	aγmγa	NOUN
ejpam-1977	103	75	.	.	PUNCT
ejpam-1977	104	1	now	now	ADV
ejpam-1977	104	2	,	,	PUNCT
ejpam-1977	104	3	similarly	similarly	ADV
ejpam-1977	104	4	with	with	ADP
ejpam-1977	104	5	the	the	DET
ejpam-1977	104	6	definition	definition	NOUN
ejpam-1977	104	7	of	of	ADP
ejpam-1977	104	8	the	the	DET
ejpam-1977	104	9	relation	relation	NOUN
ejpam-1977	104	10	b	b	PROPN
ejpam-1977	104	11	in	in	ADP
ejpam-1977	104	12	plain	plain	ADJ
ejpam-1977	104	13	semigroups	semigroup	NOUN
ejpam-1977	104	14	[	[	X
ejpam-1977	104	15	4	4	NUM
ejpam-1977	104	16	]	]	PUNCT
ejpam-1977	104	17	,	,	PUNCT
ejpam-1977	104	18	we	we	PRON
ejpam-1977	104	19	define	define	VERB
ejpam-1977	104	20	the	the	DET
ejpam-1977	104	21	relationb	relationb	ADJ
ejpam-1977	104	22	in	in	ADP
ejpam-1977	104	23	γ	γ	X
ejpam-1977	104	24	–	–	PUNCT
ejpam-1977	104	25	semigroup	semigroup	NOUN
ejpam-1977	104	26	m	m	VERB
ejpam-1977	104	27	by	by	ADP
ejpam-1977	104	28	∀(a	∀(a	PROPN
ejpam-1977	104	29	,	,	PUNCT
ejpam-1977	104	30	c	c	NOUN
ejpam-1977	104	31	)	)	PUNCT
ejpam-1977	104	32	∈	∈	PROPN
ejpam-1977	104	33	m2	m2	PROPN
ejpam-1977	104	34	,	,	PUNCT
ejpam-1977	104	35	ab	ab	PROPN
ejpam-1977	104	36	c⇔	c⇔	PROPN
ejpam-1977	104	37	(	(	PUNCT
ejpam-1977	104	38	a)b	a)b	X
ejpam-1977	104	39	=	=	SYM
ejpam-1977	104	40	(	(	PUNCT
ejpam-1977	104	41	c)b	c)b	NOUN
ejpam-1977	104	42	.	.	PUNCT
ejpam-1977	105	1	so	so	ADV
ejpam-1977	105	2	,	,	PUNCT
ejpam-1977	105	3	for	for	ADP
ejpam-1977	105	4	every	every	DET
ejpam-1977	105	5	two	two	NUM
ejpam-1977	105	6	elements	element	NOUN
ejpam-1977	105	7	a	a	PRON
ejpam-1977	105	8	,	,	PUNCT
ejpam-1977	105	9	c	c	PROPN
ejpam-1977	105	10	of	of	ADP
ejpam-1977	105	11	γ	γ	X
ejpam-1977	105	12	–	–	PUNCT
ejpam-1977	105	13	semigroups	semigroup	NOUN
ejpam-1977	105	14	we	we	PRON
ejpam-1977	105	15	have	have	VERB
ejpam-1977	105	16	ab	ab	PROPN
ejpam-1977	105	17	c⇔	c⇔	VERB
ejpam-1977	105	18	a	a	DET
ejpam-1977	105	19	∪	∪	NOUN
ejpam-1977	105	20	aγa	aγa	X
ejpam-1977	105	21	∪	∪	ADJ
ejpam-1977	105	22	aγmγa	aγmγa	NOUN
ejpam-1977	105	23	=	=	SYM
ejpam-1977	105	24	c	c	PROPN
ejpam-1977	105	25	∪	∪	ADP
ejpam-1977	105	26	cγc	cγc	NOUN
ejpam-1977	105	27	∪	∪	PROPN
ejpam-1977	105	28	cγmγc	cγmγc	PROPN
ejpam-1977	105	29	.	.	PUNCT
ejpam-1977	106	1	clearly	clearly	ADV
ejpam-1977	106	2	b	b	X
ejpam-1977	106	3	is	be	AUX
ejpam-1977	106	4	an	an	DET
ejpam-1977	106	5	equivalence	equivalence	NOUN
ejpam-1977	106	6	relation	relation	NOUN
ejpam-1977	106	7	on	on	ADP
ejpam-1977	106	8	m	m	PROPN
ejpam-1977	106	9	.	.	PUNCT
ejpam-1977	107	1	the	the	DET
ejpam-1977	107	2	equivalence	equivalence	NOUN
ejpam-1977	107	3	class	class	NOUN
ejpam-1977	107	4	of	of	ADP
ejpam-1977	107	5	m	m	PROPN
ejpam-1977	107	6	modb	modb	NOUN
ejpam-1977	107	7	containing	contain	VERB
ejpam-1977	107	8	the	the	DET
ejpam-1977	107	9	element	element	NOUN
ejpam-1977	107	10	a	a	DET
ejpam-1977	107	11	∈	∈	NOUN
ejpam-1977	107	12	m	m	VERB
ejpam-1977	107	13	is	be	AUX
ejpam-1977	107	14	denoted	denote	VERB
ejpam-1977	107	15	by	by	ADP
ejpam-1977	107	16	ba	ba	PROPN
ejpam-1977	107	17	.	.	PUNCT
ejpam-1977	108	1	from	from	ADP
ejpam-1977	108	2	proposition	proposition	NOUN
ejpam-1977	108	3	3	3	NUM
ejpam-1977	108	4	,	,	PUNCT
ejpam-1977	108	5	it	it	PRON
ejpam-1977	108	6	is	be	AUX
ejpam-1977	108	7	clear	clear	ADJ
ejpam-1977	108	8	that	that	SCONJ
ejpam-1977	108	9	b	b	PROPN
ejpam-1977	108	10	⊆h	⊆h	ADJ
ejpam-1977	108	11	.	.	PUNCT
ejpam-1977	109	1	the	the	DET
ejpam-1977	109	2	following	follow	VERB
ejpam-1977	109	3	example	example	NOUN
ejpam-1977	109	4	shows	show	VERB
ejpam-1977	109	5	that	that	SCONJ
ejpam-1977	109	6	the	the	DET
ejpam-1977	109	7	inclusion	inclusion	NOUN
ejpam-1977	109	8	may	may	AUX
ejpam-1977	109	9	be	be	AUX
ejpam-1977	109	10	strict	strict	ADJ
ejpam-1977	109	11	.	.	PUNCT
ejpam-1977	109	12	example	example	NOUN
ejpam-1977	110	1	2	2	NUM
ejpam-1977	110	2	.	.	X
ejpam-1977	110	3	consider	consider	VERB
ejpam-1977	110	4	the	the	DET
ejpam-1977	110	5	set	set	NOUN
ejpam-1977	110	6	of	of	ADP
ejpam-1977	110	7	integers	integer	NOUN
ejpam-1977	110	8	modulo	modulo	VERB
ejpam-1977	110	9	8	8	NUM
ejpam-1977	110	10	,	,	PUNCT
ejpam-1977	110	11	z/8z=	z/8z=	NUM
ejpam-1977	110	12	{	{	PUNCT
ejpam-1977	110	13	0	0	NUM
ejpam-1977	110	14	,	,	PUNCT
ejpam-1977	110	15	1	1	NUM
ejpam-1977	110	16	,	,	PUNCT
ejpam-1977	110	17	2	2	NUM
ejpam-1977	110	18	,	,	PUNCT
ejpam-1977	110	19	3	3	NUM
ejpam-1977	110	20	,	,	PUNCT
ejpam-1977	110	21	4	4	NUM
ejpam-1977	110	22	,	,	PUNCT
ejpam-1977	110	23	5	5	NUM
ejpam-1977	110	24	,	,	PUNCT
ejpam-1977	110	25	6	6	NUM
ejpam-1977	110	26	,	,	PUNCT
ejpam-1977	110	27	7	7	NUM
ejpam-1977	110	28	}	}	PUNCT
ejpam-1977	110	29	,	,	PUNCT
ejpam-1977	110	30	and	and	CCONJ
ejpam-1977	110	31	γ	γ	X
ejpam-1977	110	32	=	=	SYM
ejpam-1977	110	33	{	{	PUNCT
ejpam-1977	110	34	0,1	0,1	NUM
ejpam-1977	110	35	,	,	PUNCT
ejpam-1977	110	36	2	2	NUM
ejpam-1977	110	37	}	}	SYM
ejpam-1977	110	38	⊆	⊆	NUM
ejpam-1977	110	39	n∪	n∪	X
ejpam-1977	110	40	{	{	PUNCT
ejpam-1977	110	41	0	0	NUM
ejpam-1977	110	42	}	}	PUNCT
ejpam-1977	110	43	.	.	PUNCT
ejpam-1977	111	1	the	the	DET
ejpam-1977	111	2	result	result	NOUN
ejpam-1977	111	3	of	of	ADP
ejpam-1977	111	4	γ	γ	X
ejpam-1977	111	5	–	–	PUNCT
ejpam-1977	111	6	multiplication	multiplication	NOUN
ejpam-1977	111	7	in	in	ADP
ejpam-1977	111	8	m	m	NOUN
ejpam-1977	111	9	=	=	NOUN
ejpam-1977	111	10	z/8z	z/8z	NUM
ejpam-1977	111	11	for	for	ADP
ejpam-1977	111	12	two	two	NUM
ejpam-1977	111	13	any	any	DET
ejpam-1977	111	14	elements	element	NOUN
ejpam-1977	111	15	a	a	DET
ejpam-1977	111	16	,	,	PUNCT
ejpam-1977	111	17	b	b	PROPN
ejpam-1977	111	18	of	of	ADP
ejpam-1977	111	19	m	m	PRON
ejpam-1977	111	20	and	and	CCONJ
ejpam-1977	111	21	every	every	DET
ejpam-1977	111	22	element	element	NOUN
ejpam-1977	111	23	γ	γ	PROPN
ejpam-1977	111	24	∈	∈	PROPN
ejpam-1977	111	25	γ	γ	NOUN
ejpam-1977	111	26	is	be	AUX
ejpam-1977	111	27	the	the	DET
ejpam-1977	111	28	usual	usual	ADJ
ejpam-1977	111	29	product	product	NOUN
ejpam-1977	111	30	aγb	aγb	NOUN
ejpam-1977	111	31	of	of	ADP
ejpam-1977	111	32	integers	integer	NOUN
ejpam-1977	111	33	modulo	modulo	VERB
ejpam-1977	111	34	8	8	NUM
ejpam-1977	111	35	,	,	PUNCT
ejpam-1977	111	36	a	a	DET
ejpam-1977	111	37	,	,	PUNCT
ejpam-1977	111	38	γ	γ	PROPN
ejpam-1977	111	39	,	,	PUNCT
ejpam-1977	111	40	b	b	NOUN
ejpam-1977	111	41	.	.	PUNCT
ejpam-1977	112	1	it	it	PRON
ejpam-1977	112	2	is	be	AUX
ejpam-1977	112	3	clear	clear	ADJ
ejpam-1977	112	4	that	that	SCONJ
ejpam-1977	112	5	(	(	PUNCT
ejpam-1977	112	6	m	m	NOUN
ejpam-1977	112	7	=	=	SYM
ejpam-1977	112	8	z/8z	z/8z	NUM
ejpam-1977	112	9	,	,	PUNCT
ejpam-1977	112	10	(	(	PUNCT
ejpam-1977	112	11	·	·	PUNCT
ejpam-1977	112	12	)	)	PUNCT
ejpam-1977	112	13	γ	γ	X
ejpam-1977	112	14	)	)	PUNCT
ejpam-1977	112	15	is	be	AUX
ejpam-1977	112	16	a	a	DET
ejpam-1977	112	17	γ	γ	X
ejpam-1977	112	18	–	–	PUNCT
ejpam-1977	112	19	semigroup	semigroup	NOUN
ejpam-1977	112	20	.	.	PUNCT
ejpam-1977	113	1	the	the	DET
ejpam-1977	113	2	elements	element	NOUN
ejpam-1977	113	3	2	2	NUM
ejpam-1977	113	4	and	and	CCONJ
ejpam-1977	113	5	6	6	NUM
ejpam-1977	113	6	are	be	AUX
ejpam-1977	113	7	l	l	NOUN
ejpam-1977	113	8	equivalent	equivalent	ADJ
ejpam-1977	113	9	since	since	SCONJ
ejpam-1977	113	10	:	:	PUNCT
ejpam-1977	113	11	(	(	PUNCT
ejpam-1977	113	12	2)l	2)l	X
ejpam-1977	113	13	=	=	VERB
ejpam-1977	113	14	2∪z/8zγ2=	2∪z/8zγ2=	NUM
ejpam-1977	113	15	{	{	PUNCT
ejpam-1977	113	16	0	0	NUM
ejpam-1977	113	17	,	,	PUNCT
ejpam-1977	113	18	2	2	NUM
ejpam-1977	113	19	,	,	PUNCT
ejpam-1977	113	20	4	4	NUM
ejpam-1977	113	21	,	,	PUNCT
ejpam-1977	113	22	6	6	NUM
ejpam-1977	113	23	}	}	PUNCT
ejpam-1977	113	24	,	,	PUNCT
ejpam-1977	113	25	(	(	PUNCT
ejpam-1977	113	26	6)l	6)l	NOUN
ejpam-1977	113	27	=	=	NOUN
ejpam-1977	113	28	6∪z/8zγ6=	6∪z/8zγ6=	NUM
ejpam-1977	113	29	{	{	PUNCT
ejpam-1977	113	30	0	0	NUM
ejpam-1977	113	31	,	,	PUNCT
ejpam-1977	113	32	2	2	NUM
ejpam-1977	113	33	,	,	PUNCT
ejpam-1977	113	34	4	4	NUM
ejpam-1977	113	35	,	,	PUNCT
ejpam-1977	113	36	6	6	NUM
ejpam-1977	113	37	}	}	PUNCT
ejpam-1977	113	38	.	.	PUNCT
ejpam-1977	114	1	in	in	ADP
ejpam-1977	114	2	the	the	DET
ejpam-1977	114	3	γ	γ	X
ejpam-1977	114	4	–	–	PUNCT
ejpam-1977	114	5	semigroup	semigroup	NOUN
ejpam-1977	114	6	(	(	PUNCT
ejpam-1977	114	7	m	m	PROPN
ejpam-1977	114	8	=	=	SYM
ejpam-1977	114	9	z/8z	z/8z	NUM
ejpam-1977	114	10	,	,	PUNCT
ejpam-1977	114	11	(	(	PUNCT
ejpam-1977	114	12	·	·	PUNCT
ejpam-1977	114	13	)	)	PUNCT
ejpam-1977	114	14	γ	γ	PROPN
ejpam-1977	114	15	)	)	PUNCT
ejpam-1977	114	16	the	the	DET
ejpam-1977	114	17	green	green	PROPN
ejpam-1977	114	18	’s	’s	PART
ejpam-1977	114	19	relations	relation	NOUN
ejpam-1977	114	20	l	l	PROPN
ejpam-1977	114	21	and	and	CCONJ
ejpam-1977	114	22	r	r	NOUN
ejpam-1977	114	23	coincide	coincide	NOUN
ejpam-1977	115	1	and	and	CCONJ
ejpam-1977	115	2	so	so	ADV
ejpam-1977	115	3	we	we	PRON
ejpam-1977	115	4	have	have	VERB
ejpam-1977	115	5	2h	2h	NUM
ejpam-1977	115	6	6	6	NUM
ejpam-1977	115	7	.	.	PUNCT
ejpam-1977	115	8	i.	i.	PROPN
ejpam-1977	115	9	braja	braja	PROPN
ejpam-1977	115	10	,	,	PUNCT
ejpam-1977	115	11	p.	p.	NOUN
ejpam-1977	115	12	petro	petro	PROPN
ejpam-1977	115	13	/	/	PUNCT
ejpam-1977	115	14	eur	eur	PROPN
ejpam-1977	115	15	.	.	PUNCT
ejpam-1977	116	1	j.	j.	PROPN
ejpam-1977	116	2	pure	pure	PROPN
ejpam-1977	116	3	appl	appl	PROPN
ejpam-1977	116	4	.	.	PROPN
ejpam-1977	116	5	math	math	PROPN
ejpam-1977	116	6	,	,	PUNCT
ejpam-1977	116	7	7	7	NUM
ejpam-1977	116	8	(	(	PUNCT
ejpam-1977	116	9	2014	2014	NUM
ejpam-1977	116	10	)	)	PUNCT
ejpam-1977	116	11	,	,	PUNCT
ejpam-1977	116	12	77	77	NUM
ejpam-1977	116	13	-	-	SYM
ejpam-1977	116	14	85	85	NUM
ejpam-1977	116	15	82	82	NUM
ejpam-1977	116	16	the	the	DET
ejpam-1977	116	17	elements	element	NOUN
ejpam-1977	116	18	2	2	NUM
ejpam-1977	116	19	,	,	PUNCT
ejpam-1977	116	20	6	6	NUM
ejpam-1977	116	21	of	of	ADP
ejpam-1977	116	22	γ	γ	X
ejpam-1977	116	23	–	–	PUNCT
ejpam-1977	116	24	semigroup	semigroup	NOUN
ejpam-1977	116	25	m	m	NOUN
ejpam-1977	116	26	=	=	NOUN
ejpam-1977	116	27	z/8z	z/8z	NUM
ejpam-1977	116	28	are	be	AUX
ejpam-1977	116	29	notb	notb	NOUN
ejpam-1977	116	30	–	–	PUNCT
ejpam-1977	116	31	equivalent	equivalent	ADJ
ejpam-1977	116	32	since	since	SCONJ
ejpam-1977	116	33	:	:	PUNCT
ejpam-1977	116	34	(	(	PUNCT
ejpam-1977	116	35	2)b	2)b	NOUN
ejpam-1977	116	36	=	=	NOUN
ejpam-1977	116	37	2∪	2∪	NUM
ejpam-1977	116	38	2γ2∪	2γ2∪	NUM
ejpam-1977	116	39	2γmγ2=	2γmγ2=	NUM
ejpam-1977	116	40	{	{	PUNCT
ejpam-1977	116	41	0	0	NUM
ejpam-1977	116	42	,	,	PUNCT
ejpam-1977	116	43	2	2	NUM
ejpam-1977	116	44	,	,	PUNCT
ejpam-1977	116	45	4	4	NUM
ejpam-1977	116	46	}	}	PUNCT
ejpam-1977	116	47	,	,	PUNCT
ejpam-1977	116	48	(	(	PUNCT
ejpam-1977	116	49	6)b	6)b	NUM
ejpam-1977	116	50	=	=	SYM
ejpam-1977	116	51	6∪	6∪	NUM
ejpam-1977	116	52	6γ6∪	6γ6∪	NUM
ejpam-1977	116	53	6γmγ6=	6γmγ6=	NUM
ejpam-1977	116	54	{	{	PUNCT
ejpam-1977	116	55	0	0	NUM
ejpam-1977	116	56	,	,	PUNCT
ejpam-1977	116	57	4	4	NUM
ejpam-1977	116	58	,	,	PUNCT
ejpam-1977	116	59	6	6	NUM
ejpam-1977	116	60	}	}	PUNCT
ejpam-1977	116	61	,	,	PUNCT
ejpam-1977	116	62	and	and	CCONJ
ejpam-1977	116	63	soh	soh	NOUN
ejpam-1977	116	64	6	6	NUM
ejpam-1977	116	65	=	=	SYM
ejpam-1977	116	66	b	b	PROPN
ejpam-1977	116	67	.	.	PUNCT
ejpam-1977	117	1	for	for	ADP
ejpam-1977	117	2	the	the	DET
ejpam-1977	117	3	equivalence	equivalence	NOUN
ejpam-1977	117	4	relation	relation	NOUN
ejpam-1977	117	5	b	b	PROPN
ejpam-1977	117	6	in	in	ADP
ejpam-1977	117	7	γ	γ	X
ejpam-1977	117	8	–	–	PUNCT
ejpam-1977	117	9	semigroup	semigroup	NOUN
ejpam-1977	117	10	it	it	PRON
ejpam-1977	117	11	is	be	AUX
ejpam-1977	117	12	true	true	ADJ
ejpam-1977	117	13	the	the	DET
ejpam-1977	117	14	following	follow	VERB
ejpam-1977	117	15	theorem	theorem	VERB
ejpam-1977	117	16	,	,	PUNCT
ejpam-1977	117	17	which	which	PRON
ejpam-1977	117	18	resembles	resemble	VERB
ejpam-1977	117	19	the	the	DET
ejpam-1977	117	20	green	green	PROPN
ejpam-1977	117	21	’s	’s	PART
ejpam-1977	117	22	theorem	theorem	NOUN
ejpam-1977	117	23	for	for	ADP
ejpam-1977	117	24	plain	plain	ADJ
ejpam-1977	117	25	semigroups	semigroup	NOUN
ejpam-1977	117	26	[	[	X
ejpam-1977	117	27	10	10	NUM
ejpam-1977	117	28	]	]	PUNCT
ejpam-1977	117	29	,	,	PUNCT
ejpam-1977	117	30	the	the	DET
ejpam-1977	117	31	green	green	PROPN
ejpam-1977	117	32	’s	’s	PART
ejpam-1977	117	33	theorem	theorem	NOUN
ejpam-1977	117	34	for	for	ADP
ejpam-1977	117	35	rings	ring	NOUN
ejpam-1977	117	36	[	[	X
ejpam-1977	117	37	5	5	NUM
ejpam-1977	117	38	]	]	PUNCT
ejpam-1977	117	39	,	,	PUNCT
ejpam-1977	117	40	the	the	DET
ejpam-1977	117	41	green	green	PROPN
ejpam-1977	117	42	’s	’s	PART
ejpam-1977	117	43	theorem	theorem	NOUN
ejpam-1977	117	44	for	for	ADP
ejpam-1977	117	45	semirings	semiring	NOUN
ejpam-1977	117	46	[	[	X
ejpam-1977	117	47	2	2	NUM
ejpam-1977	117	48	]	]	PUNCT
ejpam-1977	117	49	,	,	PUNCT
ejpam-1977	117	50	and	and	CCONJ
ejpam-1977	117	51	green	green	PROPN
ejpam-1977	117	52	’s	’s	PART
ejpam-1977	117	53	theorem	theorem	NOUN
ejpam-1977	117	54	for	for	ADP
ejpam-1977	117	55	γ	γ	X
ejpam-1977	117	56	–	–	PUNCT
ejpam-1977	117	57	semigroup	semigroup	NOUN
ejpam-1977	118	1	[	[	X
ejpam-1977	118	2	6	6	NUM
ejpam-1977	118	3	]	]	PUNCT
ejpam-1977	118	4	.	.	PUNCT
ejpam-1977	119	1	we	we	PRON
ejpam-1977	119	2	will	will	AUX
ejpam-1977	119	3	call	call	VERB
ejpam-1977	119	4	this	this	PRON
ejpam-1977	119	5	theorem	theorem	NOUN
ejpam-1977	119	6	the	the	DET
ejpam-1977	119	7	green	green	PROPN
ejpam-1977	119	8	’s	’s	PART
ejpam-1977	119	9	theorem	theorem	NOUN
ejpam-1977	119	10	for	for	ADP
ejpam-1977	119	11	the	the	DET
ejpam-1977	119	12	relationb	relationb	ADJ
ejpam-1977	119	13	in	in	ADP
ejpam-1977	119	14	γ	γ	NOUN
ejpam-1977	119	15	–	–	PUNCT
ejpam-1977	119	16	semigroups	semigroup	NOUN
ejpam-1977	119	17	.	.	PUNCT
ejpam-1977	120	1	theorem	theorem	VERB
ejpam-1977	120	2	8	8	NUM
ejpam-1977	120	3	.	.	PUNCT
ejpam-1977	121	1	if	if	SCONJ
ejpam-1977	121	2	the	the	DET
ejpam-1977	121	3	elements	element	NOUN
ejpam-1977	121	4	a	a	DET
ejpam-1977	121	5	,	,	PUNCT
ejpam-1977	121	6	b	b	NOUN
ejpam-1977	121	7	,	,	PUNCT
ejpam-1977	121	8	aγb	aγb	NOUN
ejpam-1977	121	9	of	of	ADP
ejpam-1977	121	10	a	a	DET
ejpam-1977	121	11	γ	γ	X
ejpam-1977	121	12	–	–	PUNCT
ejpam-1977	121	13	semigroup	semigroup	NOUN
ejpam-1977	121	14	(	(	PUNCT
ejpam-1977	121	15	m	m	PROPN
ejpam-1977	121	16	,	,	PUNCT
ejpam-1977	121	17	(	(	PUNCT
ejpam-1977	121	18	·	·	PUNCT
ejpam-1977	121	19	)	)	PUNCT
ejpam-1977	121	20	γ	γ	NOUN
ejpam-1977	121	21	)	)	PUNCT
ejpam-1977	121	22	all	all	PRON
ejpam-1977	121	23	belong	belong	VERB
ejpam-1977	121	24	to	to	ADP
ejpam-1977	121	25	the	the	DET
ejpam-1977	121	26	sameb	sameb	NOUN
ejpam-1977	121	27	-	-	PUNCT
ejpam-1977	121	28	class	class	NOUN
ejpam-1977	121	29	b	b	NOUN
ejpam-1977	121	30	,	,	PUNCT
ejpam-1977	121	31	then	then	ADV
ejpam-1977	121	32	b	b	PROPN
ejpam-1977	121	33	is	be	AUX
ejpam-1977	121	34	a	a	DET
ejpam-1977	121	35	γ	γ	X
ejpam-1977	121	36	–	–	PUNCT
ejpam-1977	121	37	subgroup	subgroup	NOUN
ejpam-1977	121	38	of	of	ADP
ejpam-1977	121	39	semigroup	semigroup	PROPN
ejpam-1977	121	40	mγ	mγ	PROPN
ejpam-1977	121	41	.	.	PUNCT
ejpam-1977	122	1	proof	proof	NOUN
ejpam-1977	122	2	.	.	PUNCT
ejpam-1977	123	1	since	since	SCONJ
ejpam-1977	123	2	the	the	DET
ejpam-1977	123	3	relationb	relationb	NOUN
ejpam-1977	123	4	is	be	AUX
ejpam-1977	123	5	included	include	VERB
ejpam-1977	123	6	in	in	ADP
ejpam-1977	123	7	the	the	DET
ejpam-1977	123	8	relationh	relationh	NOUN
ejpam-1977	123	9	,	,	PUNCT
ejpam-1977	123	10	we	we	PRON
ejpam-1977	123	11	have	have	VERB
ejpam-1977	123	12	b	b	NOUN
ejpam-1977	123	13	=	=	SYM
ejpam-1977	123	14	ba	ba	PROPN
ejpam-1977	123	15	⊆	⊆	NUM
ejpam-1977	123	16	ha	ha	INTJ
ejpam-1977	123	17	.	.	PUNCT
ejpam-1977	124	1	thus	thus	ADV
ejpam-1977	124	2	the	the	DET
ejpam-1977	124	3	elements	element	NOUN
ejpam-1977	124	4	a	a	DET
ejpam-1977	124	5	,	,	PUNCT
ejpam-1977	124	6	b	b	NOUN
ejpam-1977	124	7	,	,	PUNCT
ejpam-1977	124	8	aγb	aγb	NOUN
ejpam-1977	124	9	belong	belong	VERB
ejpam-1977	124	10	to	to	ADP
ejpam-1977	124	11	theh	theh	VERB
ejpam-1977	124	12	–	–	PUNCT
ejpam-1977	124	13	class	class	NOUN
ejpam-1977	124	14	ha	ha	INTJ
ejpam-1977	124	15	of	of	ADP
ejpam-1977	124	16	γ	γ	X
ejpam-1977	124	17	–	–	PUNCT
ejpam-1977	124	18	semigroup	semigroup	PROPN
ejpam-1977	124	19	m	m	NOUN
ejpam-1977	124	20	.	.	PUNCT
ejpam-1977	125	1	so	so	ADV
ejpam-1977	125	2	,	,	PUNCT
ejpam-1977	125	3	by	by	ADP
ejpam-1977	125	4	theorem	theorem	NOUN
ejpam-1977	125	5	3	3	NUM
ejpam-1977	125	6	,	,	PUNCT
ejpam-1977	125	7	ha	ha	INTJ
ejpam-1977	125	8	is	be	AUX
ejpam-1977	125	9	a	a	DET
ejpam-1977	125	10	subgroup	subgroup	NOUN
ejpam-1977	125	11	of	of	ADP
ejpam-1977	125	12	semigroup	semigroup	PROPN
ejpam-1977	125	13	mγ	mγ	PROPN
ejpam-1977	125	14	and	and	CCONJ
ejpam-1977	125	15	therefore	therefore	ADV
ejpam-1977	125	16	there	there	PRON
ejpam-1977	125	17	exists	exist	VERB
ejpam-1977	125	18	the	the	DET
ejpam-1977	125	19	identity	identity	NOUN
ejpam-1977	125	20	e	e	PROPN
ejpam-1977	125	21	of	of	ADP
ejpam-1977	125	22	subgroup	subgroup	NOUN
ejpam-1977	125	23	ha	ha	INTJ
ejpam-1977	125	24	and	and	CCONJ
ejpam-1977	125	25	the	the	DET
ejpam-1977	125	26	following	follow	VERB
ejpam-1977	125	27	equalities	equality	NOUN
ejpam-1977	125	28	are	be	AUX
ejpam-1977	125	29	true	true	ADJ
ejpam-1977	125	30	:	:	PUNCT
ejpam-1977	125	31	a	a	DET
ejpam-1977	125	32	=	=	NOUN
ejpam-1977	125	33	eγaγe	eγaγe	NOUN
ejpam-1977	125	34	,	,	PUNCT
ejpam-1977	125	35	e	e	NOUN
ejpam-1977	125	36	=	=	SYM
ejpam-1977	125	37	aγa−1γa−1γa	aγa−1γa−1γa	PROPN
ejpam-1977	125	38	,	,	PUNCT
ejpam-1977	125	39	where	where	SCONJ
ejpam-1977	125	40	a−1	a−1	PROPN
ejpam-1977	125	41	is	be	AUX
ejpam-1977	125	42	the	the	DET
ejpam-1977	125	43	inverse	inverse	ADJ
ejpam-1977	125	44	element	element	NOUN
ejpam-1977	125	45	of	of	ADP
ejpam-1977	125	46	a	a	PRON
ejpam-1977	125	47	in	in	ADP
ejpam-1977	125	48	the	the	DET
ejpam-1977	125	49	subgroup	subgroup	NOUN
ejpam-1977	125	50	ha	ha	INTJ
ejpam-1977	125	51	of	of	ADP
ejpam-1977	125	52	semigroup	semigroup	PROPN
ejpam-1977	125	53	mγ	mγ	PROPN
ejpam-1977	125	54	.	.	PUNCT
ejpam-1977	126	1	these	these	DET
ejpam-1977	126	2	equalities	equality	NOUN
ejpam-1977	126	3	show	show	VERB
ejpam-1977	126	4	that	that	SCONJ
ejpam-1977	126	5	the	the	DET
ejpam-1977	126	6	principal	principal	ADJ
ejpam-1977	126	7	bi	bi	NOUN
ejpam-1977	126	8	–	–	PUNCT
ejpam-1977	126	9	ideals	ideal	NOUN
ejpam-1977	126	10	generated	generate	VERB
ejpam-1977	126	11	by	by	ADP
ejpam-1977	126	12	elements	element	NOUN
ejpam-1977	126	13	a	a	PRON
ejpam-1977	126	14	and	and	CCONJ
ejpam-1977	126	15	e	e	NOUN
ejpam-1977	126	16	are	be	AUX
ejpam-1977	126	17	the	the	DET
ejpam-1977	126	18	same	same	ADJ
ejpam-1977	126	19	.	.	PUNCT
ejpam-1977	127	1	thus	thus	ADV
ejpam-1977	127	2	,	,	PUNCT
ejpam-1977	127	3	the	the	DET
ejpam-1977	127	4	element	element	NOUN
ejpam-1977	127	5	e	e	PROPN
ejpam-1977	127	6	belongs	belong	VERB
ejpam-1977	127	7	to	to	ADP
ejpam-1977	127	8	the	the	DET
ejpam-1977	127	9	class	class	NOUN
ejpam-1977	127	10	ba	ba	PROPN
ejpam-1977	127	11	=	=	PROPN
ejpam-1977	127	12	b.	b.	PROPN
ejpam-1977	127	13	now	now	ADV
ejpam-1977	127	14	,	,	PUNCT
ejpam-1977	127	15	let	let	VERB
ejpam-1977	127	16	x	x	PRON
ejpam-1977	127	17	be	be	AUX
ejpam-1977	127	18	any	any	DET
ejpam-1977	127	19	element	element	NOUN
ejpam-1977	127	20	of	of	ADP
ejpam-1977	127	21	subgroup	subgroup	PROPN
ejpam-1977	127	22	ha	ha	INTJ
ejpam-1977	127	23	.	.	PUNCT
ejpam-1977	128	1	we	we	PRON
ejpam-1977	128	2	have	have	VERB
ejpam-1977	128	3	the	the	DET
ejpam-1977	128	4	following	follow	VERB
ejpam-1977	128	5	equalities	equality	NOUN
ejpam-1977	128	6	:	:	PUNCT
ejpam-1977	128	7	x	x	SYM
ejpam-1977	128	8	=	=	SYM
ejpam-1977	128	9	eγxγe	eγxγe	ADJ
ejpam-1977	128	10	,	,	PUNCT
ejpam-1977	128	11	e	e	X
ejpam-1977	128	12	=	=	PUNCT
ejpam-1977	128	13	xγx−1γx−1γx	xγx−1γx−1γx	PROPN
ejpam-1977	128	14	,	,	PUNCT
ejpam-1977	128	15	where	where	SCONJ
ejpam-1977	128	16	x−1	x−1	PROPN
ejpam-1977	128	17	is	be	AUX
ejpam-1977	128	18	the	the	DET
ejpam-1977	128	19	inverse	inverse	ADJ
ejpam-1977	128	20	element	element	NOUN
ejpam-1977	128	21	of	of	ADP
ejpam-1977	128	22	the	the	DET
ejpam-1977	128	23	element	element	NOUN
ejpam-1977	128	24	x	x	PROPN
ejpam-1977	128	25	of	of	ADP
ejpam-1977	128	26	subgroup	subgroup	NOUN
ejpam-1977	128	27	ha	ha	INTJ
ejpam-1977	128	28	of	of	ADP
ejpam-1977	128	29	semigroup	semigroup	PROPN
ejpam-1977	128	30	mγ	mγ	PROPN
ejpam-1977	128	31	.	.	PUNCT
ejpam-1977	129	1	these	these	DET
ejpam-1977	129	2	equalities	equality	NOUN
ejpam-1977	129	3	show	show	VERB
ejpam-1977	129	4	that	that	SCONJ
ejpam-1977	129	5	(	(	PUNCT
ejpam-1977	129	6	x)b	x)b	SYM
ejpam-1977	129	7	=	=	SYM
ejpam-1977	129	8	(	(	PUNCT
ejpam-1977	129	9	e)b	e)b	NOUN
ejpam-1977	129	10	.	.	PUNCT
ejpam-1977	130	1	so	so	ADV
ejpam-1977	130	2	,	,	PUNCT
ejpam-1977	130	3	since	since	SCONJ
ejpam-1977	130	4	e	e	PROPN
ejpam-1977	130	5	∈	∈	PROPN
ejpam-1977	130	6	ba	ba	PROPN
ejpam-1977	130	7	,	,	PUNCT
ejpam-1977	130	8	the	the	DET
ejpam-1977	130	9	element	element	NOUN
ejpam-1977	130	10	x	x	PUNCT
ejpam-1977	130	11	belongs	belong	VERB
ejpam-1977	130	12	to	to	ADP
ejpam-1977	130	13	ba	ba	PROPN
ejpam-1977	130	14	.	.	PUNCT
ejpam-1977	131	1	thus	thus	ADV
ejpam-1977	131	2	,	,	PUNCT
ejpam-1977	131	3	we	we	PRON
ejpam-1977	131	4	have	have	VERB
ejpam-1977	131	5	b	b	NOUN
ejpam-1977	131	6	=	=	SYM
ejpam-1977	131	7	ba	ba	NOUN
ejpam-1977	131	8	=	=	SYM
ejpam-1977	131	9	ha	ha	INTJ
ejpam-1977	131	10	,	,	PUNCT
ejpam-1977	131	11	and	and	CCONJ
ejpam-1977	131	12	consequentlyb	consequentlyb	NOUN
ejpam-1977	131	13	-	-	PUNCT
ejpam-1977	131	14	class	class	NOUN
ejpam-1977	131	15	b	b	NOUN
ejpam-1977	131	16	is	be	AUX
ejpam-1977	131	17	a	a	DET
ejpam-1977	131	18	subgroup	subgroup	NOUN
ejpam-1977	131	19	of	of	ADP
ejpam-1977	131	20	γ	γ	PROPN
ejpam-1977	131	21	–	–	PUNCT
ejpam-1977	131	22	semigroup	semigroup	PROPN
ejpam-1977	131	23	mγ	mγ	NOUN
ejpam-1977	131	24	.	.	PUNCT
ejpam-1977	132	1	a	a	DET
ejpam-1977	132	2	element	element	NOUN
ejpam-1977	132	3	e	e	NOUN
ejpam-1977	132	4	of	of	ADP
ejpam-1977	132	5	a	a	DET
ejpam-1977	132	6	γ	γ	PROPN
ejpam-1977	132	7	-	-	PUNCT
ejpam-1977	132	8	semigroup	semigroup	NOUN
ejpam-1977	132	9	m	m	VERB
ejpam-1977	132	10	is	be	AUX
ejpam-1977	132	11	called	call	VERB
ejpam-1977	132	12	idempotent	idempotent	ADJ
ejpam-1977	132	13	if	if	SCONJ
ejpam-1977	132	14	there	there	PRON
ejpam-1977	132	15	exists	exist	VERB
ejpam-1977	132	16	γ	γ	PROPN
ejpam-1977	132	17	∈	∈	PROPN
ejpam-1977	132	18	γ	γ	NOUN
ejpam-1977	132	19	such	such	ADJ
ejpam-1977	132	20	that	that	SCONJ
ejpam-1977	132	21	e	e	NOUN
ejpam-1977	132	22	=	=	PUNCT
ejpam-1977	132	23	eγe	eγe	PROPN
ejpam-1977	132	24	.	.	PUNCT
ejpam-1977	133	1	from	from	ADP
ejpam-1977	133	2	the	the	DET
ejpam-1977	133	3	theorem	theorem	NOUN
ejpam-1977	133	4	8	8	NUM
ejpam-1977	133	5	we	we	PRON
ejpam-1977	133	6	get	get	VERB
ejpam-1977	133	7	immediately	immediately	ADV
ejpam-1977	133	8	the	the	DET
ejpam-1977	133	9	following	follow	VERB
ejpam-1977	133	10	:	:	PUNCT
ejpam-1977	133	11	corollary	corollary	ADJ
ejpam-1977	133	12	1	1	NUM
ejpam-1977	133	13	.	.	PUNCT
ejpam-1977	134	1	if	if	SCONJ
ejpam-1977	134	2	ab	ab	PROPN
ejpam-1977	134	3	–	–	PUNCT
ejpam-1977	134	4	class	class	NOUN
ejpam-1977	134	5	b	b	PROPN
ejpam-1977	134	6	of	of	ADP
ejpam-1977	134	7	a	a	DET
ejpam-1977	134	8	γ	γ	X
ejpam-1977	134	9	–	–	PUNCT
ejpam-1977	134	10	semigroup	semigroup	NOUN
ejpam-1977	134	11	m	m	VERB
ejpam-1977	134	12	contains	contain	VERB
ejpam-1977	134	13	an	an	DET
ejpam-1977	134	14	idempotent	idempotent	NOUN
ejpam-1977	134	15	e	e	NOUN
ejpam-1977	134	16	=	=	SYM
ejpam-1977	134	17	eγe	eγe	NOUN
ejpam-1977	134	18	,	,	PUNCT
ejpam-1977	134	19	γ	γ	PROPN
ejpam-1977	134	20	∈	∈	PROPN
ejpam-1977	134	21	γ	γ	X
ejpam-1977	134	22	,	,	PUNCT
ejpam-1977	134	23	then	then	ADV
ejpam-1977	134	24	b	b	PROPN
ejpam-1977	134	25	is	be	AUX
ejpam-1977	134	26	a	a	DET
ejpam-1977	134	27	subgroup	subgroup	NOUN
ejpam-1977	134	28	of	of	ADP
ejpam-1977	134	29	semigroup	semigroup	PROPN
ejpam-1977	134	30	mγ	mγ	PROPN
ejpam-1977	134	31	.	.	PUNCT
ejpam-1977	135	1	since	since	ADV
ejpam-1977	135	2	,	,	PUNCT
ejpam-1977	135	3	every	every	DET
ejpam-1977	135	4	plain	plain	ADJ
ejpam-1977	135	5	semigroup	semigroup	NOUN
ejpam-1977	135	6	s	s	VERB
ejpam-1977	135	7	can	can	AUX
ejpam-1977	135	8	be	be	AUX
ejpam-1977	135	9	considered	consider	VERB
ejpam-1977	135	10	as	as	ADP
ejpam-1977	135	11	a	a	DET
ejpam-1977	135	12	γ	γ	X
ejpam-1977	135	13	–	–	PUNCT
ejpam-1977	135	14	semigroup	semigroup	NOUN
ejpam-1977	135	15	,	,	PUNCT
ejpam-1977	135	16	from	from	ADP
ejpam-1977	135	17	the	the	DET
ejpam-1977	135	18	theorem	theorem	NOUN
ejpam-1977	135	19	8	8	NUM
ejpam-1977	135	20	and	and	CCONJ
ejpam-1977	135	21	the	the	DET
ejpam-1977	135	22	corollary	corollary	ADJ
ejpam-1977	135	23	1	1	NUM
ejpam-1977	135	24	,	,	PUNCT
ejpam-1977	135	25	we	we	PRON
ejpam-1977	135	26	get	get	VERB
ejpam-1977	135	27	the	the	DET
ejpam-1977	135	28	following	following	ADJ
ejpam-1977	135	29	theorem	theorem	NOUN
ejpam-1977	135	30	and	and	CCONJ
ejpam-1977	135	31	corollary	corollary	ADJ
ejpam-1977	135	32	to	to	ADP
ejpam-1977	135	33	plain	plain	ADJ
ejpam-1977	135	34	semigroups	semigroup	NOUN
ejpam-1977	135	35	:	:	PUNCT
ejpam-1977	135	36	theorem	theorem	NOUN
ejpam-1977	135	37	9	9	NUM
ejpam-1977	135	38	.	.	PUNCT
ejpam-1977	136	1	if	if	SCONJ
ejpam-1977	136	2	the	the	DET
ejpam-1977	136	3	elements	element	NOUN
ejpam-1977	136	4	a	a	DET
ejpam-1977	136	5	,	,	PUNCT
ejpam-1977	136	6	b	b	PROPN
ejpam-1977	136	7	,	,	PUNCT
ejpam-1977	136	8	ab	ab	PROPN
ejpam-1977	136	9	of	of	ADP
ejpam-1977	136	10	a	a	DET
ejpam-1977	136	11	semigroup	semigroup	NOUN
ejpam-1977	136	12	s	s	PRON
ejpam-1977	136	13	all	all	PRON
ejpam-1977	136	14	belong	belong	VERB
ejpam-1977	136	15	to	to	ADP
ejpam-1977	136	16	the	the	DET
ejpam-1977	136	17	same	same	ADJ
ejpam-1977	136	18	b	b	NOUN
ejpam-1977	136	19	–	–	PUNCT
ejpam-1977	136	20	class	class	NOUN
ejpam-1977	136	21	b	b	NOUN
ejpam-1977	136	22	,	,	PUNCT
ejpam-1977	136	23	then	then	ADV
ejpam-1977	136	24	b	b	PROPN
ejpam-1977	136	25	is	be	AUX
ejpam-1977	136	26	a	a	DET
ejpam-1977	136	27	subgroup	subgroup	NOUN
ejpam-1977	136	28	of	of	ADP
ejpam-1977	136	29	semigroup	semigroup	PROPN
ejpam-1977	136	30	s.	s.	PROPN
ejpam-1977	136	31	i.	i.	PROPN
ejpam-1977	136	32	braja	braja	PROPN
ejpam-1977	136	33	,	,	PUNCT
ejpam-1977	136	34	p.	p.	NOUN
ejpam-1977	136	35	petro	petro	PROPN
ejpam-1977	136	36	/	/	PUNCT
ejpam-1977	136	37	eur	eur	PROPN
ejpam-1977	136	38	.	.	PUNCT
ejpam-1977	137	1	j.	j.	PROPN
ejpam-1977	137	2	pure	pure	PROPN
ejpam-1977	137	3	appl	appl	PROPN
ejpam-1977	137	4	.	.	PROPN
ejpam-1977	137	5	math	math	PROPN
ejpam-1977	137	6	,	,	PUNCT
ejpam-1977	137	7	7	7	NUM
ejpam-1977	137	8	(	(	PUNCT
ejpam-1977	137	9	2014	2014	NUM
ejpam-1977	137	10	)	)	PUNCT
ejpam-1977	137	11	,	,	PUNCT
ejpam-1977	137	12	77	77	NUM
ejpam-1977	137	13	-	-	SYM
ejpam-1977	137	14	85	85	NUM
ejpam-1977	137	15	83	83	NUM
ejpam-1977	137	16	corollary	corollary	ADJ
ejpam-1977	137	17	2	2	NUM
ejpam-1977	137	18	.	.	PUNCT
ejpam-1977	138	1	if	if	SCONJ
ejpam-1977	138	2	an	an	DET
ejpam-1977	138	3	b	b	NOUN
ejpam-1977	138	4	–	–	PUNCT
ejpam-1977	138	5	class	class	NOUN
ejpam-1977	138	6	b	b	NOUN
ejpam-1977	138	7	of	of	ADP
ejpam-1977	138	8	a	a	DET
ejpam-1977	138	9	semigroup	semigroup	NOUN
ejpam-1977	138	10	s	s	NOUN
ejpam-1977	138	11	contains	contain	VERB
ejpam-1977	138	12	an	an	DET
ejpam-1977	138	13	idempotent	idempotent	ADJ
ejpam-1977	138	14	e	e	NOUN
ejpam-1977	138	15	,	,	PUNCT
ejpam-1977	138	16	then	then	ADV
ejpam-1977	138	17	b	b	PROPN
ejpam-1977	138	18	is	be	AUX
ejpam-1977	138	19	a	a	DET
ejpam-1977	138	20	subgroup	subgroup	NOUN
ejpam-1977	138	21	of	of	ADP
ejpam-1977	138	22	semigroup	semigroup	PROPN
ejpam-1977	138	23	s.	s.	PROPN
ejpam-1977	138	24	we	we	PRON
ejpam-1977	138	25	can	can	AUX
ejpam-1977	138	26	call	call	VERB
ejpam-1977	138	27	the	the	DET
ejpam-1977	138	28	theorem	theorem	NOUN
ejpam-1977	138	29	9	9	NUM
ejpam-1977	138	30	the	the	DET
ejpam-1977	138	31	green	green	PROPN
ejpam-1977	138	32	’s	’s	PART
ejpam-1977	138	33	theorem	theorem	NOUN
ejpam-1977	138	34	for	for	ADP
ejpam-1977	138	35	the	the	DET
ejpam-1977	138	36	relationb	relationb	ADJ
ejpam-1977	138	37	in	in	ADP
ejpam-1977	138	38	plain	plain	ADJ
ejpam-1977	138	39	semigroups	semigroup	NOUN
ejpam-1977	138	40	.	.	PUNCT
ejpam-1977	139	1	proposition	proposition	NOUN
ejpam-1977	139	2	5	5	NUM
ejpam-1977	139	3	.	.	PUNCT
ejpam-1977	140	1	let	let	VERB
ejpam-1977	140	2	m	m	PRON
ejpam-1977	140	3	be	be	AUX
ejpam-1977	140	4	an	an	DET
ejpam-1977	140	5	arbitrary	arbitrary	ADJ
ejpam-1977	140	6	γ	γ	X
ejpam-1977	140	7	–	–	PUNCT
ejpam-1977	140	8	semigroup	semigroup	NOUN
ejpam-1977	140	9	.	.	PUNCT
ejpam-1977	141	1	if	if	SCONJ
ejpam-1977	141	2	the	the	DET
ejpam-1977	141	3	idempotent	idempotent	NOUN
ejpam-1977	141	4	e	e	NOUN
ejpam-1977	141	5	=	=	SYM
ejpam-1977	141	6	eγe	eγe	NOUN
ejpam-1977	141	7	,	,	PUNCT
ejpam-1977	141	8	γ	γ	PROPN
ejpam-1977	141	9	∈	∈	PROPN
ejpam-1977	141	10	γ	γ	X
ejpam-1977	141	11	together	together	ADV
ejpam-1977	141	12	with	with	ADP
ejpam-1977	141	13	a	a	PRON
ejpam-1977	141	14	,	,	PUNCT
ejpam-1977	141	15	b	b	X
ejpam-1977	141	16	∈	∈	PROPN
ejpam-1977	141	17	m	m	VERB
ejpam-1977	141	18	all	all	PRON
ejpam-1977	141	19	belong	belong	VERB
ejpam-1977	141	20	to	to	ADP
ejpam-1977	141	21	the	the	DET
ejpam-1977	141	22	sameb	sameb	NOUN
ejpam-1977	141	23	-	-	PUNCT
ejpam-1977	141	24	class	class	NOUN
ejpam-1977	141	25	b	b	NOUN
ejpam-1977	141	26	,	,	PUNCT
ejpam-1977	141	27	then	then	ADV
ejpam-1977	141	28	eγa	eγa	NOUN
ejpam-1977	141	29	=	=	PUNCT
ejpam-1977	141	30	aγe	aγe	PROPN
ejpam-1977	141	31	=	=	SYM
ejpam-1977	141	32	a	a	PROPN
ejpam-1977	141	33	and	and	CCONJ
ejpam-1977	141	34	aγb	aγb	NOUN
ejpam-1977	141	35	∈	∈	PROPN
ejpam-1977	141	36	b.	b.	PROPN
ejpam-1977	141	37	proof	proof	NOUN
ejpam-1977	141	38	.	.	PUNCT
ejpam-1977	142	1	since	since	SCONJ
ejpam-1977	142	2	b	b	NOUN
ejpam-1977	142	3	contains	contain	VERB
ejpam-1977	142	4	an	an	DET
ejpam-1977	142	5	idempotent	idempotent	NOUN
ejpam-1977	142	6	e	e	NOUN
ejpam-1977	142	7	=	=	SYM
ejpam-1977	142	8	eγe	eγe	NOUN
ejpam-1977	142	9	,	,	PUNCT
ejpam-1977	142	10	γ	γ	PROPN
ejpam-1977	142	11	∈	∈	PROPN
ejpam-1977	142	12	γ	γ	X
ejpam-1977	142	13	,	,	PUNCT
ejpam-1977	142	14	then	then	ADV
ejpam-1977	142	15	the	the	DET
ejpam-1977	142	16	corollary	corollary	ADJ
ejpam-1977	142	17	1	1	NUM
ejpam-1977	142	18	implies	imply	VERB
ejpam-1977	142	19	that	that	SCONJ
ejpam-1977	142	20	b	b	NOUN
ejpam-1977	142	21	is	be	AUX
ejpam-1977	142	22	a	a	DET
ejpam-1977	142	23	subgroup	subgroup	NOUN
ejpam-1977	142	24	of	of	ADP
ejpam-1977	142	25	mγ	mγ	PROPN
ejpam-1977	142	26	.	.	PUNCT
ejpam-1977	143	1	the	the	DET
ejpam-1977	143	2	identity	identity	NOUN
ejpam-1977	143	3	of	of	ADP
ejpam-1977	143	4	b	b	NOUN
ejpam-1977	143	5	is	be	AUX
ejpam-1977	143	6	e	e	NOUN
ejpam-1977	143	7	because	because	SCONJ
ejpam-1977	143	8	e	e	PROPN
ejpam-1977	143	9	◦	◦	NOUN
ejpam-1977	143	10	e	e	X
ejpam-1977	143	11	=	=	NOUN
ejpam-1977	143	12	eγe	eγe	PROPN
ejpam-1977	143	13	=	=	SYM
ejpam-1977	143	14	e.	e.	PROPN
ejpam-1977	143	15	since	since	SCONJ
ejpam-1977	143	16	a	a	DET
ejpam-1977	143	17	◦	◦	NOUN
ejpam-1977	143	18	e	e	X
ejpam-1977	143	19	=	=	SYM
ejpam-1977	143	20	e	e	AUX
ejpam-1977	143	21	◦	◦	VERB
ejpam-1977	143	22	a	a	DET
ejpam-1977	143	23	=	=	SYM
ejpam-1977	143	24	e	e	NOUN
ejpam-1977	143	25	,	,	PUNCT
ejpam-1977	143	26	we	we	PRON
ejpam-1977	143	27	have	have	VERB
ejpam-1977	143	28	aγe	aγe	NOUN
ejpam-1977	143	29	=	=	SYM
ejpam-1977	143	30	a	a	PRON
ejpam-1977	143	31	=	=	PUNCT
ejpam-1977	143	32	aγe	aγe	NOUN
ejpam-1977	143	33	.	.	PUNCT
ejpam-1977	144	1	the	the	DET
ejpam-1977	144	2	element	element	NOUN
ejpam-1977	144	3	a	a	PRON
ejpam-1977	144	4	,	,	PUNCT
ejpam-1977	144	5	b	b	NOUN
ejpam-1977	144	6	belongs	belong	VERB
ejpam-1977	144	7	to	to	ADP
ejpam-1977	144	8	b	b	NOUN
ejpam-1977	144	9	,	,	PUNCT
ejpam-1977	144	10	therefore	therefore	ADV
ejpam-1977	144	11	aγb	aγb	VERB
ejpam-1977	144	12	=	=	SYM
ejpam-1977	144	13	a	a	DET
ejpam-1977	144	14	◦	◦	NOUN
ejpam-1977	144	15	b	b	PROPN
ejpam-1977	144	16	∈	∈	PROPN
ejpam-1977	144	17	b.	b.	PROPN
ejpam-1977	145	1	a	a	DET
ejpam-1977	145	2	bi	bi	PROPN
ejpam-1977	145	3	–	–	PUNCT
ejpam-1977	145	4	ideal	ideal	ADJ
ejpam-1977	145	5	b	b	PROPN
ejpam-1977	145	6	of	of	ADP
ejpam-1977	145	7	a	a	DET
ejpam-1977	145	8	γ	γ	X
ejpam-1977	145	9	–	–	PUNCT
ejpam-1977	145	10	semigroup	semigroup	NOUN
ejpam-1977	145	11	m	m	NOUN
ejpam-1977	145	12	without	without	ADP
ejpam-1977	145	13	zero	zero	NUM
ejpam-1977	145	14	is	be	AUX
ejpam-1977	145	15	called	call	VERB
ejpam-1977	145	16	minimal	minimal	ADJ
ejpam-1977	145	17	if	if	SCONJ
ejpam-1977	145	18	b	b	NOUN
ejpam-1977	145	19	does	do	AUX
ejpam-1977	145	20	not	not	PART
ejpam-1977	145	21	properly	properly	ADV
ejpam-1977	145	22	contain	contain	VERB
ejpam-1977	145	23	any	any	DET
ejpam-1977	145	24	bi	bi	NOUN
ejpam-1977	145	25	–	–	PUNCT
ejpam-1977	145	26	ideal	ideal	NOUN
ejpam-1977	145	27	of	of	ADP
ejpam-1977	145	28	m	m	PROPN
ejpam-1977	145	29	.	.	PUNCT
ejpam-1977	146	1	one	one	PRON
ejpam-1977	146	2	can	can	AUX
ejpam-1977	146	3	prove	prove	VERB
ejpam-1977	146	4	easily	easily	ADV
ejpam-1977	146	5	that	that	SCONJ
ejpam-1977	146	6	:	:	PUNCT
ejpam-1977	146	7	lemma	lemma	PROPN
ejpam-1977	146	8	1	1	X
ejpam-1977	146	9	.	.	PUNCT
ejpam-1977	147	1	a	a	DET
ejpam-1977	147	2	bi	bi	ADJ
ejpam-1977	147	3	–	–	PUNCT
ejpam-1977	147	4	ideal	ideal	ADJ
ejpam-1977	147	5	b	b	PROPN
ejpam-1977	147	6	of	of	ADP
ejpam-1977	147	7	a	a	DET
ejpam-1977	147	8	γ	γ	X
ejpam-1977	147	9	–	–	PUNCT
ejpam-1977	147	10	semigroup	semigroup	NOUN
ejpam-1977	147	11	m	m	VERB
ejpam-1977	147	12	without	without	ADP
ejpam-1977	147	13	zero	zero	NUM
ejpam-1977	147	14	is	be	AUX
ejpam-1977	147	15	minimal	minimal	ADJ
ejpam-1977	147	16	if	if	SCONJ
ejpam-1977	147	17	and	and	CCONJ
ejpam-1977	147	18	only	only	ADV
ejpam-1977	147	19	if	if	SCONJ
ejpam-1977	147	20	b	b	NOUN
ejpam-1977	147	21	is	be	AUX
ejpam-1977	147	22	an	an	DET
ejpam-1977	147	23	b	b	NOUN
ejpam-1977	147	24	–	–	PUNCT
ejpam-1977	147	25	class	class	NOUN
ejpam-1977	147	26	.	.	PUNCT
ejpam-1977	148	1	now	now	ADV
ejpam-1977	148	2	we	we	PRON
ejpam-1977	148	3	will	will	AUX
ejpam-1977	148	4	use	use	VERB
ejpam-1977	148	5	the	the	DET
ejpam-1977	148	6	green	green	PROPN
ejpam-1977	148	7	’s	’s	PART
ejpam-1977	148	8	theorem	theorem	NOUN
ejpam-1977	148	9	for	for	ADP
ejpam-1977	148	10	the	the	DET
ejpam-1977	148	11	relation	relation	PROPN
ejpam-1977	148	12	b	b	PROPN
ejpam-1977	148	13	in	in	ADP
ejpam-1977	148	14	γ	γ	X
ejpam-1977	148	15	–	–	PUNCT
ejpam-1977	148	16	semigroup	semigroup	NOUN
ejpam-1977	148	17	(	(	PUNCT
ejpam-1977	148	18	theorem	theorem	NOUN
ejpam-1977	148	19	8)	8)	NUM
ejpam-1977	148	20	to	to	PART
ejpam-1977	148	21	prove	prove	VERB
ejpam-1977	148	22	a	a	DET
ejpam-1977	148	23	theorem	theorem	NOUN
ejpam-1977	148	24	concerning	concern	VERB
ejpam-1977	148	25	minimal	minimal	ADJ
ejpam-1977	148	26	bi	bi	NOUN
ejpam-1977	148	27	–	–	PUNCT
ejpam-1977	148	28	ideals	ideal	NOUN
ejpam-1977	148	29	in	in	ADP
ejpam-1977	148	30	γ	γ	X
ejpam-1977	148	31	–	–	PUNCT
ejpam-1977	148	32	semigroup	semigroup	NOUN
ejpam-1977	148	33	m	m	NOUN
ejpam-1977	148	34	without	without	ADP
ejpam-1977	148	35	zero	zero	NUM
ejpam-1977	148	36	.	.	PUNCT
ejpam-1977	149	1	theorem	theorem	VERB
ejpam-1977	149	2	10	10	NUM
ejpam-1977	149	3	.	.	PUNCT
ejpam-1977	150	1	a	a	DET
ejpam-1977	150	2	bi	bi	ADJ
ejpam-1977	150	3	–	–	PUNCT
ejpam-1977	150	4	ideal	ideal	ADJ
ejpam-1977	150	5	b	b	PROPN
ejpam-1977	150	6	of	of	ADP
ejpam-1977	150	7	a	a	DET
ejpam-1977	150	8	γ	γ	X
ejpam-1977	150	9	–	–	PUNCT
ejpam-1977	150	10	semigroup	semigroup	NOUN
ejpam-1977	150	11	m	m	VERB
ejpam-1977	150	12	without	without	ADP
ejpam-1977	150	13	zero	zero	NUM
ejpam-1977	150	14	is	be	AUX
ejpam-1977	150	15	minimal	minimal	ADJ
ejpam-1977	150	16	if	if	SCONJ
ejpam-1977	150	17	and	and	CCONJ
ejpam-1977	150	18	only	only	ADV
ejpam-1977	150	19	if	if	SCONJ
ejpam-1977	150	20	b	b	NOUN
ejpam-1977	150	21	is	be	AUX
ejpam-1977	150	22	a	a	DET
ejpam-1977	150	23	γ	γ	X
ejpam-1977	150	24	–	–	PUNCT
ejpam-1977	150	25	subgroup	subgroup	NOUN
ejpam-1977	150	26	of	of	ADP
ejpam-1977	150	27	m.	m.	NOUN
ejpam-1977	150	28	proof	proof	NOUN
ejpam-1977	150	29	.	.	PUNCT
ejpam-1977	151	1	if	if	SCONJ
ejpam-1977	151	2	b	b	PROPN
ejpam-1977	151	3	is	be	AUX
ejpam-1977	151	4	a	a	DET
ejpam-1977	151	5	minimal	minimal	ADJ
ejpam-1977	151	6	bi	bi	NOUN
ejpam-1977	151	7	–	–	PUNCT
ejpam-1977	151	8	ideal	ideal	NOUN
ejpam-1977	151	9	of	of	ADP
ejpam-1977	151	10	the	the	DET
ejpam-1977	151	11	γ	γ	X
ejpam-1977	151	12	–	–	PUNCT
ejpam-1977	151	13	semigroup	semigroup	NOUN
ejpam-1977	151	14	m	m	VERB
ejpam-1977	151	15	,	,	PUNCT
ejpam-1977	151	16	then	then	ADV
ejpam-1977	151	17	by	by	ADP
ejpam-1977	151	18	lemma	lemma	PROPN
ejpam-1977	151	19	1	1	NUM
ejpam-1977	151	20	all	all	DET
ejpam-1977	151	21	elements	element	NOUN
ejpam-1977	151	22	of	of	ADP
ejpam-1977	151	23	b	b	NOUN
ejpam-1977	151	24	are	be	AUX
ejpam-1977	151	25	b	b	NOUN
ejpam-1977	151	26	–	–	PUNCT
ejpam-1977	151	27	equivalent	equivalent	ADJ
ejpam-1977	151	28	.	.	PUNCT
ejpam-1977	152	1	thus	thus	ADV
ejpam-1977	152	2	for	for	ADP
ejpam-1977	152	3	two	two	NUM
ejpam-1977	152	4	elements	element	NOUN
ejpam-1977	152	5	a	a	DET
ejpam-1977	152	6	,	,	PUNCT
ejpam-1977	152	7	b	b	PROPN
ejpam-1977	152	8	of	of	ADP
ejpam-1977	152	9	b	b	PROPN
ejpam-1977	152	10	and	and	CCONJ
ejpam-1977	152	11	every	every	DET
ejpam-1977	152	12	γ	γ	PROPN
ejpam-1977	152	13	∈	∈	PROPN
ejpam-1977	152	14	γ	γ	X
ejpam-1977	152	15	the	the	DET
ejpam-1977	152	16	elements	element	NOUN
ejpam-1977	152	17	a	a	DET
ejpam-1977	152	18	,	,	PUNCT
ejpam-1977	152	19	b	b	NOUN
ejpam-1977	152	20	,	,	PUNCT
ejpam-1977	152	21	aγb	aγb	ADV
ejpam-1977	152	22	all	all	PRON
ejpam-1977	152	23	belong	belong	VERB
ejpam-1977	152	24	to	to	ADP
ejpam-1977	152	25	the	the	DET
ejpam-1977	152	26	same	same	ADJ
ejpam-1977	152	27	b	b	NOUN
ejpam-1977	152	28	–	–	PUNCT
ejpam-1977	152	29	class	class	NOUN
ejpam-1977	152	30	of	of	ADP
ejpam-1977	152	31	m	m	PROPN
ejpam-1977	152	32	.	.	PUNCT
ejpam-1977	153	1	now	now	ADV
ejpam-1977	153	2	applying	apply	VERB
ejpam-1977	153	3	the	the	DET
ejpam-1977	153	4	green	green	NOUN
ejpam-1977	153	5	’s	’s	PART
ejpam-1977	153	6	theorem	theorem	NOUN
ejpam-1977	153	7	for	for	ADP
ejpam-1977	153	8	the	the	DET
ejpam-1977	153	9	relation	relation	PROPN
ejpam-1977	153	10	b	b	PROPN
ejpam-1977	153	11	in	in	ADP
ejpam-1977	153	12	γ	γ	X
ejpam-1977	153	13	–	–	PUNCT
ejpam-1977	153	14	semigroup	semigroup	NOUN
ejpam-1977	153	15	(	(	PUNCT
ejpam-1977	153	16	theorem	theorem	NOUN
ejpam-1977	153	17	8)	8)	NUM
ejpam-1977	153	18	the	the	DET
ejpam-1977	153	19	b	b	PROPN
ejpam-1977	153	20	–	–	PUNCT
ejpam-1977	153	21	class	class	NOUN
ejpam-1977	153	22	b	b	NOUN
ejpam-1977	153	23	is	be	AUX
ejpam-1977	153	24	a	a	DET
ejpam-1977	153	25	subgroup	subgroup	NOUN
ejpam-1977	153	26	of	of	ADP
ejpam-1977	153	27	semigroup	semigroup	PROPN
ejpam-1977	153	28	mγ	mγ	PROPN
ejpam-1977	153	29	for	for	ADP
ejpam-1977	153	30	every	every	DET
ejpam-1977	153	31	γ	γ	PROPN
ejpam-1977	153	32	∈	∈	PROPN
ejpam-1977	153	33	γ	γ	X
ejpam-1977	153	34	.	.	PUNCT
ejpam-1977	154	1	so	so	ADV
ejpam-1977	154	2	,	,	PUNCT
ejpam-1977	154	3	b	b	PROPN
ejpam-1977	154	4	is	be	AUX
ejpam-1977	154	5	a	a	DET
ejpam-1977	154	6	γ	γ	X
ejpam-1977	154	7	–	–	PUNCT
ejpam-1977	154	8	subsemigroup	subsemigroup	NOUN
ejpam-1977	154	9	such	such	ADJ
ejpam-1977	154	10	that	that	PRON
ejpam-1977	154	11	for	for	ADP
ejpam-1977	154	12	every	every	DET
ejpam-1977	154	13	γ	γ	PROPN
ejpam-1977	154	14	∈	∈	PROPN
ejpam-1977	154	15	γ	γ	X
ejpam-1977	154	16	,	,	PUNCT
ejpam-1977	154	17	bγ	bγ	NOUN
ejpam-1977	154	18	=	=	PUNCT
ejpam-1977	154	19	(	(	PUNCT
ejpam-1977	154	20	b	b	NOUN
ejpam-1977	154	21	,	,	PUNCT
ejpam-1977	154	22	◦	◦	NOUN
ejpam-1977	154	23	)	)	PUNCT
ejpam-1977	154	24	is	be	AUX
ejpam-1977	154	25	a	a	DET
ejpam-1977	154	26	group	group	NOUN
ejpam-1977	154	27	.	.	PUNCT
ejpam-1977	155	1	thus	thus	ADV
ejpam-1977	155	2	b	b	X
ejpam-1977	155	3	is	be	AUX
ejpam-1977	155	4	a	a	DET
ejpam-1977	155	5	γ	γ	X
ejpam-1977	155	6	–	–	PUNCT
ejpam-1977	155	7	subgroup	subgroup	NOUN
ejpam-1977	155	8	of	of	ADP
ejpam-1977	155	9	γ	γ	PROPN
ejpam-1977	155	10	–	–	PUNCT
ejpam-1977	155	11	semigroup	semigroup	NOUN
ejpam-1977	155	12	m	m	NOUN
ejpam-1977	155	13	and	and	CCONJ
ejpam-1977	155	14	it	it	PRON
ejpam-1977	155	15	is	be	AUX
ejpam-1977	155	16	ah	ah	INTJ
ejpam-1977	155	17	–	–	PUNCT
ejpam-1977	155	18	class	class	NOUN
ejpam-1977	155	19	.	.	PUNCT
ejpam-1977	156	1	conversely	conversely	ADV
ejpam-1977	156	2	,	,	PUNCT
ejpam-1977	156	3	let	let	VERB
ejpam-1977	156	4	the	the	DET
ejpam-1977	156	5	bi	bi	NOUN
ejpam-1977	156	6	–	–	PUNCT
ejpam-1977	156	7	ideal	ideal	ADJ
ejpam-1977	156	8	b	b	AUX
ejpam-1977	156	9	be	be	AUX
ejpam-1977	156	10	a	a	DET
ejpam-1977	156	11	γ	γ	X
ejpam-1977	156	12	–	–	PUNCT
ejpam-1977	156	13	subgroup	subgroup	NOUN
ejpam-1977	156	14	of	of	ADP
ejpam-1977	156	15	m	m	PROPN
ejpam-1977	156	16	.	.	PUNCT
ejpam-1977	157	1	if	if	SCONJ
ejpam-1977	157	2	b′	b′	NOUN
ejpam-1977	157	3	is	be	AUX
ejpam-1977	157	4	a	a	DET
ejpam-1977	157	5	bi	bi	NOUN
ejpam-1977	157	6	–	–	PUNCT
ejpam-1977	157	7	ideal	ideal	NOUN
ejpam-1977	157	8	of	of	ADP
ejpam-1977	157	9	m	m	VERB
ejpam-1977	157	10	contain	contain	VERB
ejpam-1977	157	11	in	in	ADP
ejpam-1977	157	12	b	b	NOUN
ejpam-1977	157	13	,	,	PUNCT
ejpam-1977	157	14	then	then	ADV
ejpam-1977	157	15	b′γbγb′	b′γbγb′	NOUN
ejpam-1977	157	16	⊆	⊆	NUM
ejpam-1977	157	17	b′γmγb′	b′γmγb′	NOUN
ejpam-1977	157	18	⊆	⊆	NUM
ejpam-1977	157	19	b′	b′	NOUN
ejpam-1977	157	20	,	,	PUNCT
ejpam-1977	157	21	that	that	ADV
ejpam-1977	157	22	is	is	ADV
ejpam-1977	157	23	,	,	PUNCT
ejpam-1977	157	24	b′	b′	NOUN
ejpam-1977	157	25	is	be	AUX
ejpam-1977	157	26	a	a	DET
ejpam-1977	157	27	bi	bi	NOUN
ejpam-1977	157	28	–	–	PUNCT
ejpam-1977	157	29	ideal	ideal	NOUN
ejpam-1977	157	30	of	of	ADP
ejpam-1977	157	31	b	b	NOUN
ejpam-1977	157	32	,	,	PUNCT
ejpam-1977	157	33	too	too	ADV
ejpam-1977	157	34	.	.	PUNCT
ejpam-1977	158	1	let	let	VERB
ejpam-1977	158	2	a	a	PRON
ejpam-1977	158	3	be	be	AUX
ejpam-1977	158	4	an	an	DET
ejpam-1977	158	5	element	element	NOUN
ejpam-1977	158	6	of	of	ADP
ejpam-1977	158	7	b′	b′	NUM
ejpam-1977	158	8	and	and	CCONJ
ejpam-1977	158	9	γ	γ	X
ejpam-1977	158	10	an	an	DET
ejpam-1977	158	11	element	element	NOUN
ejpam-1977	158	12	of	of	ADP
ejpam-1977	158	13	γ	γ	PROPN
ejpam-1977	158	14	.	.	PROPN
ejpam-1977	159	1	then	then	ADV
ejpam-1977	159	2	,	,	PUNCT
ejpam-1977	159	3	since	since	SCONJ
ejpam-1977	159	4	the	the	DET
ejpam-1977	159	5	semigroup	semigroup	NOUN
ejpam-1977	159	6	bγ	bγ	ADV
ejpam-1977	159	7	=	=	PUNCT
ejpam-1977	159	8	(	(	PUNCT
ejpam-1977	159	9	b	b	NOUN
ejpam-1977	159	10	,	,	PUNCT
ejpam-1977	159	11	◦	◦	NOUN
ejpam-1977	159	12	)	)	PUNCT
ejpam-1977	159	13	is	be	AUX
ejpam-1977	159	14	a	a	DET
ejpam-1977	159	15	group	group	NOUN
ejpam-1977	159	16	,	,	PUNCT
ejpam-1977	159	17	we	we	PRON
ejpam-1977	159	18	have	have	VERB
ejpam-1977	159	19	b	b	NOUN
ejpam-1977	159	20	=	=	SYM
ejpam-1977	159	21	a	a	DET
ejpam-1977	159	22	◦	◦	NOUN
ejpam-1977	159	23	b	b	X
ejpam-1977	159	24	◦	◦	NOUN
ejpam-1977	159	25	a	a	DET
ejpam-1977	159	26	=	=	SYM
ejpam-1977	159	27	aγbγa	aγbγa	ADP
ejpam-1977	159	28	⊆	⊆	NUM
ejpam-1977	159	29	b′	b′	NUM
ejpam-1977	159	30	,	,	PUNCT
ejpam-1977	159	31	whence	whence	NOUN
ejpam-1977	159	32	b	b	X
ejpam-1977	159	33	=	=	X
ejpam-1977	159	34	b′.	b′.	PROPN
ejpam-1977	159	35	this	this	PRON
ejpam-1977	159	36	means	mean	VERB
ejpam-1977	159	37	that	that	SCONJ
ejpam-1977	159	38	b	b	NOUN
ejpam-1977	159	39	is	be	AUX
ejpam-1977	159	40	a	a	DET
ejpam-1977	159	41	minimal	minimal	ADJ
ejpam-1977	159	42	bi	bi	NOUN
ejpam-1977	159	43	–	–	PUNCT
ejpam-1977	159	44	ideal	ideal	NOUN
ejpam-1977	159	45	of	of	ADP
ejpam-1977	159	46	γ	γ	X
ejpam-1977	159	47	–	–	PUNCT
ejpam-1977	159	48	semigroup	semigroup	NOUN
ejpam-1977	159	49	m	m	NOUN
ejpam-1977	159	50	.	.	PUNCT
ejpam-1977	160	1	as	as	ADP
ejpam-1977	160	2	a	a	DET
ejpam-1977	160	3	particular	particular	ADJ
ejpam-1977	160	4	case	case	NOUN
ejpam-1977	160	5	we	we	PRON
ejpam-1977	160	6	get	get	VERB
ejpam-1977	160	7	the	the	DET
ejpam-1977	160	8	following	following	NOUN
ejpam-1977	160	9	theorem	theorem	NOUN
ejpam-1977	160	10	for	for	ADP
ejpam-1977	160	11	plain	plain	ADJ
ejpam-1977	160	12	semigroups	semigroup	NOUN
ejpam-1977	160	13	:	:	PUNCT
ejpam-1977	160	14	theorem	theorem	NOUN
ejpam-1977	160	15	11	11	NUM
ejpam-1977	160	16	.	.	PUNCT
ejpam-1977	161	1	a	a	DET
ejpam-1977	161	2	bi	bi	ADJ
ejpam-1977	161	3	–	–	PUNCT
ejpam-1977	161	4	ideal	ideal	ADJ
ejpam-1977	161	5	b	b	PROPN
ejpam-1977	161	6	of	of	ADP
ejpam-1977	161	7	a	a	DET
ejpam-1977	161	8	plain	plain	ADJ
ejpam-1977	161	9	semigroup	semigroup	NOUN
ejpam-1977	161	10	s	s	PRON
ejpam-1977	161	11	without	without	ADP
ejpam-1977	161	12	zero	zero	NUM
ejpam-1977	161	13	is	be	AUX
ejpam-1977	161	14	minimal	minimal	ADJ
ejpam-1977	161	15	if	if	SCONJ
ejpam-1977	161	16	and	and	CCONJ
ejpam-1977	161	17	only	only	ADV
ejpam-1977	161	18	if	if	SCONJ
ejpam-1977	161	19	b	b	NOUN
ejpam-1977	161	20	is	be	AUX
ejpam-1977	161	21	a	a	DET
ejpam-1977	161	22	subgroup	subgroup	NOUN
ejpam-1977	161	23	of	of	ADP
ejpam-1977	161	24	s.	s.	PROPN
ejpam-1977	161	25	this	this	DET
ejpam-1977	161	26	theorem	theorem	NOUN
ejpam-1977	161	27	is	be	AUX
ejpam-1977	161	28	proved	prove	VERB
ejpam-1977	161	29	in	in	ADP
ejpam-1977	161	30	[	[	X
ejpam-1977	161	31	4	4	X
ejpam-1977	161	32	]	]	PUNCT
ejpam-1977	161	33	by	by	ADP
ejpam-1977	161	34	a	a	DET
ejpam-1977	161	35	direct	direct	ADJ
ejpam-1977	161	36	method	method	NOUN
ejpam-1977	161	37	.	.	PUNCT
ejpam-1977	162	1	i.	i.	PROPN
ejpam-1977	162	2	braja	braja	PROPN
ejpam-1977	162	3	,	,	PUNCT
ejpam-1977	162	4	p.	p.	NOUN
ejpam-1977	162	5	petro	petro	PROPN
ejpam-1977	162	6	/	/	PUNCT
ejpam-1977	162	7	eur	eur	PROPN
ejpam-1977	162	8	.	.	PUNCT
ejpam-1977	163	1	j.	j.	PROPN
ejpam-1977	163	2	pure	pure	PROPN
ejpam-1977	163	3	appl	appl	PROPN
ejpam-1977	163	4	.	.	PROPN
ejpam-1977	163	5	math	math	PROPN
ejpam-1977	163	6	,	,	PUNCT
ejpam-1977	163	7	7	7	NUM
ejpam-1977	163	8	(	(	PUNCT
ejpam-1977	163	9	2014	2014	NUM
ejpam-1977	163	10	)	)	PUNCT
ejpam-1977	163	11	,	,	PUNCT
ejpam-1977	163	12	77	77	NUM
ejpam-1977	163	13	-	-	SYM
ejpam-1977	163	14	85	85	NUM
ejpam-1977	163	15	84	84	NUM
ejpam-1977	163	16	definition	definition	NOUN
ejpam-1977	163	17	6	6	NUM
ejpam-1977	163	18	.	.	PUNCT
ejpam-1977	164	1	an	an	DET
ejpam-1977	164	2	element	element	NOUN
ejpam-1977	164	3	a	a	PRON
ejpam-1977	164	4	of	of	ADP
ejpam-1977	164	5	a	a	DET
ejpam-1977	164	6	γ	γ	X
ejpam-1977	164	7	–	–	PUNCT
ejpam-1977	164	8	semigroup	semigroup	ADJ
ejpam-1977	164	9	m	m	VERB
ejpam-1977	164	10	is	be	AUX
ejpam-1977	164	11	called	call	VERB
ejpam-1977	164	12	cancellable	cancellable	ADJ
ejpam-1977	164	13	if	if	SCONJ
ejpam-1977	164	14	for	for	ADP
ejpam-1977	164	15	two	two	NUM
ejpam-1977	164	16	elements	element	NOUN
ejpam-1977	164	17	b	b	NOUN
ejpam-1977	164	18	,	,	PUNCT
ejpam-1977	164	19	c	c	PROPN
ejpam-1977	164	20	∈	∈	PROPN
ejpam-1977	164	21	m	m	NOUN
ejpam-1977	164	22	and	and	CCONJ
ejpam-1977	164	23	every	every	DET
ejpam-1977	164	24	γ	γ	PROPN
ejpam-1977	164	25	∈	∈	PROPN
ejpam-1977	164	26	γ	γ	NOUN
ejpam-1977	164	27	we	we	PRON
ejpam-1977	164	28	have	have	VERB
ejpam-1977	164	29	(	(	PUNCT
ejpam-1977	164	30	aγb	aγb	NOUN
ejpam-1977	164	31	=	=	SYM
ejpam-1977	164	32	aγc⇒	aγc⇒	PROPN
ejpam-1977	164	33	b	b	PROPN
ejpam-1977	164	34	=	=	SYM
ejpam-1977	164	35	c)∧	c)∧	PROPN
ejpam-1977	164	36	(	(	PUNCT
ejpam-1977	164	37	bγa	bγa	PROPN
ejpam-1977	164	38	=	=	SYM
ejpam-1977	164	39	cγa⇒	cγa⇒	PROPN
ejpam-1977	164	40	b	b	X
ejpam-1977	164	41	=	=	SYM
ejpam-1977	164	42	c	c	NOUN
ejpam-1977	164	43	)	)	PUNCT
ejpam-1977	164	44	.	.	PUNCT
ejpam-1977	165	1	theorem	theorem	NOUN
ejpam-1977	165	2	12	12	NUM
ejpam-1977	165	3	.	.	PUNCT
ejpam-1977	166	1	if	if	SCONJ
ejpam-1977	166	2	a	a	DET
ejpam-1977	166	3	γ	γ	X
ejpam-1977	166	4	–	–	PUNCT
ejpam-1977	166	5	semigroup	semigroup	NOUN
ejpam-1977	166	6	m	m	VERB
ejpam-1977	166	7	without	without	ADP
ejpam-1977	166	8	zero	zero	NUM
ejpam-1977	166	9	has	have	VERB
ejpam-1977	166	10	a	a	DET
ejpam-1977	166	11	cancellable	cancellable	ADJ
ejpam-1977	166	12	element	element	NOUN
ejpam-1977	166	13	contained	contain	VERB
ejpam-1977	166	14	in	in	ADP
ejpam-1977	166	15	a	a	DET
ejpam-1977	166	16	minimal	minimal	ADJ
ejpam-1977	166	17	bi	bi	ADJ
ejpam-1977	166	18	–	–	PUNCT
ejpam-1977	166	19	ideal	ideal	ADJ
ejpam-1977	166	20	b	b	PROPN
ejpam-1977	166	21	of	of	ADP
ejpam-1977	166	22	m	m	PROPN
ejpam-1977	166	23	,	,	PUNCT
ejpam-1977	166	24	then	then	ADV
ejpam-1977	166	25	m	m	VERB
ejpam-1977	166	26	is	be	AUX
ejpam-1977	166	27	a	a	DET
ejpam-1977	166	28	γ	γ	X
ejpam-1977	166	29	–	–	PUNCT
ejpam-1977	166	30	group	group	NOUN
ejpam-1977	166	31	.	.	PUNCT
ejpam-1977	167	1	proof	proof	NOUN
ejpam-1977	167	2	.	.	PUNCT
ejpam-1977	168	1	by	by	ADP
ejpam-1977	168	2	the	the	DET
ejpam-1977	168	3	theorem	theorem	NOUN
ejpam-1977	168	4	10	10	NUM
ejpam-1977	168	5	,	,	PUNCT
ejpam-1977	168	6	the	the	DET
ejpam-1977	168	7	minimal	minimal	ADJ
ejpam-1977	168	8	bi	bi	NOUN
ejpam-1977	168	9	–	–	PUNCT
ejpam-1977	168	10	ideal	ideal	ADJ
ejpam-1977	168	11	b	b	NOUN
ejpam-1977	168	12	is	be	AUX
ejpam-1977	168	13	a	a	DET
ejpam-1977	168	14	γ	γ	X
ejpam-1977	168	15	–	–	PUNCT
ejpam-1977	168	16	subgroup	subgroup	NOUN
ejpam-1977	168	17	of	of	ADP
ejpam-1977	168	18	m	m	PROPN
ejpam-1977	168	19	.	.	PUNCT
ejpam-1977	169	1	let	let	VERB
ejpam-1977	169	2	e	e	PRON
ejpam-1977	169	3	be	be	AUX
ejpam-1977	169	4	the	the	DET
ejpam-1977	169	5	identity	identity	NOUN
ejpam-1977	169	6	of	of	ADP
ejpam-1977	169	7	the	the	DET
ejpam-1977	169	8	group	group	NOUN
ejpam-1977	169	9	bγ	bγ	ADV
ejpam-1977	169	10	=	=	PUNCT
ejpam-1977	169	11	(	(	PUNCT
ejpam-1977	169	12	b	b	NOUN
ejpam-1977	169	13	,	,	PUNCT
ejpam-1977	169	14	◦	◦	NOUN
ejpam-1977	169	15	)	)	PUNCT
ejpam-1977	169	16	for	for	ADP
ejpam-1977	169	17	a	a	DET
ejpam-1977	169	18	fixed	fix	VERB
ejpam-1977	169	19	γ	γ	NOUN
ejpam-1977	169	20	∈	∈	PROPN
ejpam-1977	169	21	γ	γ	NOUN
ejpam-1977	169	22	and	and	CCONJ
ejpam-1977	169	23	let	let	VERB
ejpam-1977	169	24	a	a	PRON
ejpam-1977	169	25	be	be	AUX
ejpam-1977	169	26	a	a	DET
ejpam-1977	169	27	cancellable	cancellable	ADJ
ejpam-1977	169	28	element	element	NOUN
ejpam-1977	169	29	of	of	ADP
ejpam-1977	169	30	m	m	PROPN
ejpam-1977	169	31	contained	contain	VERB
ejpam-1977	169	32	in	in	ADP
ejpam-1977	169	33	b.	b.	PROPN
ejpam-1977	169	34	then	then	ADV
ejpam-1977	169	35	multiplying	multiply	VERB
ejpam-1977	169	36	both	both	DET
ejpam-1977	169	37	side	side	NOUN
ejpam-1977	169	38	of	of	ADP
ejpam-1977	169	39	the	the	DET
ejpam-1977	169	40	equality	equality	NOUN
ejpam-1977	169	41	eγa	eγa	NOUN
ejpam-1977	169	42	=	=	PUNCT
ejpam-1977	169	43	a	a	NOUN
ejpam-1977	169	44	by	by	ADP
ejpam-1977	169	45	any	any	DET
ejpam-1977	169	46	element	element	NOUN
ejpam-1977	169	47	b	b	PROPN
ejpam-1977	169	48	of	of	ADP
ejpam-1977	169	49	m	m	PROPN
ejpam-1977	169	50	,	,	PUNCT
ejpam-1977	169	51	we	we	PRON
ejpam-1977	169	52	have	have	VERB
ejpam-1977	169	53	bγeγa	bγeγa	NOUN
ejpam-1977	169	54	=	=	SYM
ejpam-1977	169	55	bγa	bγa	PROPN
ejpam-1977	169	56	,	,	PUNCT
ejpam-1977	169	57	hence	hence	ADV
ejpam-1977	169	58	bγe	bγe	PROPN
ejpam-1977	169	59	=	=	SYM
ejpam-1977	169	60	b.	b.	PROPN
ejpam-1977	169	61	dually	dually	PROPN
ejpam-1977	169	62	we	we	PRON
ejpam-1977	169	63	obtain	obtain	VERB
ejpam-1977	169	64	eγb	eγb	NOUN
ejpam-1977	169	65	=	=	SYM
ejpam-1977	169	66	b	b	NOUN
ejpam-1977	169	67	for	for	ADP
ejpam-1977	169	68	every	every	DET
ejpam-1977	169	69	b	b	PROPN
ejpam-1977	169	70	∈	∈	ADV
ejpam-1977	169	71	m	m	NOUN
ejpam-1977	169	72	.	.	PUNCT
ejpam-1977	170	1	thus	thus	ADV
ejpam-1977	170	2	e	e	X
ejpam-1977	170	3	is	be	AUX
ejpam-1977	170	4	the	the	DET
ejpam-1977	170	5	identity	identity	NOUN
ejpam-1977	170	6	element	element	NOUN
ejpam-1977	170	7	of	of	ADP
ejpam-1977	170	8	the	the	DET
ejpam-1977	170	9	semigroup	semigroup	PROPN
ejpam-1977	170	10	mγ	mγ	NOUN
ejpam-1977	170	11	=	=	SYM
ejpam-1977	170	12	(	(	PUNCT
ejpam-1977	170	13	m	m	PROPN
ejpam-1977	170	14	,	,	PUNCT
ejpam-1977	170	15	◦	◦	NOUN
ejpam-1977	170	16	)	)	PUNCT
ejpam-1977	170	17	.	.	PUNCT
ejpam-1977	171	1	since	since	SCONJ
ejpam-1977	171	2	e	e	PROPN
ejpam-1977	171	3	∈	∈	PROPN
ejpam-1977	171	4	b	b	PROPN
ejpam-1977	171	5	,	,	PUNCT
ejpam-1977	171	6	for	for	ADP
ejpam-1977	171	7	any	any	DET
ejpam-1977	171	8	b	b	PROPN
ejpam-1977	171	9	∈	∈	NOUN
ejpam-1977	171	10	m	m	VERB
ejpam-1977	171	11	we	we	PRON
ejpam-1977	171	12	have	have	VERB
ejpam-1977	171	13	b	b	NOUN
ejpam-1977	171	14	=	=	PUNCT
ejpam-1977	171	15	eγbγe	eγbγe	PROPN
ejpam-1977	171	16	∈	∈	PROPN
ejpam-1977	171	17	b.	b.	PROPN
ejpam-1977	172	1	so	so	ADV
ejpam-1977	172	2	,	,	PUNCT
ejpam-1977	172	3	m	m	VERB
ejpam-1977	172	4	=	=	SYM
ejpam-1977	172	5	b	b	PROPN
ejpam-1977	172	6	and	and	CCONJ
ejpam-1977	172	7	consequently	consequently	ADV
ejpam-1977	172	8	m	m	VERB
ejpam-1977	172	9	is	be	AUX
ejpam-1977	172	10	a	a	DET
ejpam-1977	172	11	γ	γ	X
ejpam-1977	172	12	–	–	PUNCT
ejpam-1977	172	13	group	group	NOUN
ejpam-1977	172	14	with	with	ADP
ejpam-1977	172	15	zero	zero	NUM
ejpam-1977	172	16	.	.	PUNCT
ejpam-1977	173	1	since	since	SCONJ
ejpam-1977	173	2	every	every	DET
ejpam-1977	173	3	plain	plain	ADJ
ejpam-1977	173	4	groups	group	NOUN
ejpam-1977	173	5	is	be	AUX
ejpam-1977	173	6	a	a	DET
ejpam-1977	173	7	minimal	minimal	ADJ
ejpam-1977	173	8	bi	bi	NOUN
ejpam-1977	173	9	–	–	PUNCT
ejpam-1977	173	10	ideal	ideal	ADJ
ejpam-1977	173	11	and	and	CCONJ
ejpam-1977	173	12	has	have	VERB
ejpam-1977	173	13	a	a	DET
ejpam-1977	173	14	cancellable	cancellable	ADJ
ejpam-1977	173	15	element	element	NOUN
ejpam-1977	173	16	(	(	PUNCT
ejpam-1977	173	17	this	this	PRON
ejpam-1977	173	18	is	be	AUX
ejpam-1977	173	19	the	the	DET
ejpam-1977	173	20	identity	identity	NOUN
ejpam-1977	173	21	element	element	NOUN
ejpam-1977	173	22	of	of	ADP
ejpam-1977	173	23	the	the	DET
ejpam-1977	173	24	group	group	NOUN
ejpam-1977	173	25	)	)	PUNCT
ejpam-1977	173	26	,	,	PUNCT
ejpam-1977	173	27	therefore	therefore	ADV
ejpam-1977	173	28	from	from	ADP
ejpam-1977	173	29	the	the	DET
ejpam-1977	173	30	theorem	theorem	NOUN
ejpam-1977	173	31	12	12	NUM
ejpam-1977	173	32	,	,	PUNCT
ejpam-1977	173	33	we	we	PRON
ejpam-1977	173	34	get	get	VERB
ejpam-1977	173	35	the	the	DET
ejpam-1977	173	36	following	following	NOUN
ejpam-1977	173	37	:	:	PUNCT
ejpam-1977	173	38	theorem	theorem	VERB
ejpam-1977	173	39	13	13	NUM
ejpam-1977	173	40	.	.	PUNCT
ejpam-1977	174	1	a	a	DET
ejpam-1977	174	2	semigroup	semigroup	NOUN
ejpam-1977	174	3	s	s	PRON
ejpam-1977	174	4	without	without	ADP
ejpam-1977	174	5	zero	zero	NUM
ejpam-1977	174	6	is	be	AUX
ejpam-1977	174	7	a	a	DET
ejpam-1977	174	8	group	group	NOUN
ejpam-1977	174	9	if	if	SCONJ
ejpam-1977	175	1	and	and	CCONJ
ejpam-1977	175	2	only	only	ADV
ejpam-1977	175	3	if	if	SCONJ
ejpam-1977	175	4	it	it	PRON
ejpam-1977	175	5	has	have	VERB
ejpam-1977	175	6	a	a	DET
ejpam-1977	175	7	cancellable	cancellable	ADJ
ejpam-1977	175	8	element	element	NOUN
ejpam-1977	175	9	contained	contain	VERB
ejpam-1977	175	10	in	in	ADP
ejpam-1977	175	11	a	a	DET
ejpam-1977	175	12	minimal	minimal	ADJ
ejpam-1977	175	13	bi	bi	ADJ
ejpam-1977	175	14	–	–	PUNCT
ejpam-1977	175	15	ideal	ideal	ADJ
ejpam-1977	175	16	b	b	PROPN
ejpam-1977	175	17	of	of	ADP
ejpam-1977	175	18	s.	s.	PROPN
ejpam-1977	175	19	theorem	theorem	VERB
ejpam-1977	175	20	14	14	NUM
ejpam-1977	175	21	.	.	PUNCT
ejpam-1977	176	1	let	let	VERB
ejpam-1977	176	2	a	a	PRON
ejpam-1977	176	3	,	,	PUNCT
ejpam-1977	176	4	c	c	PROPN
ejpam-1977	176	5	are	be	AUX
ejpam-1977	176	6	two	two	NUM
ejpam-1977	176	7	elements	element	NOUN
ejpam-1977	176	8	of	of	ADP
ejpam-1977	176	9	a	a	DET
ejpam-1977	176	10	γ	γ	X
ejpam-1977	176	11	–	–	PUNCT
ejpam-1977	176	12	semigroup	semigroup	NOUN
ejpam-1977	176	13	without	without	ADP
ejpam-1977	176	14	zero	zero	NUM
ejpam-1977	176	15	such	such	ADJ
ejpam-1977	176	16	that	that	DET
ejpam-1977	176	17	adc	adc	PROPN
ejpam-1977	176	18	.	.	PUNCT
ejpam-1977	177	1	if	if	SCONJ
ejpam-1977	177	2	the	the	DET
ejpam-1977	177	3	principal	principal	ADJ
ejpam-1977	177	4	bi	bi	NOUN
ejpam-1977	177	5	–	–	PUNCT
ejpam-1977	177	6	ideal	ideal	ADJ
ejpam-1977	177	7	(	(	PUNCT
ejpam-1977	177	8	a)b	a)b	ADJ
ejpam-1977	177	9	and	and	CCONJ
ejpam-1977	177	10	the	the	DET
ejpam-1977	177	11	principal	principal	ADJ
ejpam-1977	177	12	quasi	quasi	NOUN
ejpam-1977	177	13	–	–	PUNCT
ejpam-1977	177	14	ideal	ideal	ADJ
ejpam-1977	177	15	(	(	PUNCT
ejpam-1977	177	16	a)q	a)q	X
ejpam-1977	177	17	are	be	AUX
ejpam-1977	177	18	minimal	minimal	ADJ
ejpam-1977	177	19	,	,	PUNCT
ejpam-1977	177	20	then	then	ADV
ejpam-1977	177	21	(	(	PUNCT
ejpam-1977	177	22	a)b	a)b	X
ejpam-1977	177	23	=	=	SYM
ejpam-1977	177	24	(	(	PUNCT
ejpam-1977	177	25	a)q	a)q	X
ejpam-1977	177	26	and	and	CCONJ
ejpam-1977	177	27	the	the	DET
ejpam-1977	177	28	principal	principal	ADJ
ejpam-1977	177	29	bi	bi	NOUN
ejpam-1977	177	30	–	–	PUNCT
ejpam-1977	177	31	ideal	ideal	ADJ
ejpam-1977	177	32	(	(	PUNCT
ejpam-1977	177	33	c)b	c)b	NOUN
ejpam-1977	177	34	and	and	CCONJ
ejpam-1977	177	35	the	the	DET
ejpam-1977	177	36	principal	principal	ADJ
ejpam-1977	177	37	quasi	quasi	NOUN
ejpam-1977	177	38	–	–	PUNCT
ejpam-1977	177	39	ideal	ideal	ADJ
ejpam-1977	177	40	(	(	PUNCT
ejpam-1977	177	41	c)q	c)q	NOUN
ejpam-1977	177	42	are	be	AUX
ejpam-1977	177	43	minimal	minimal	ADJ
ejpam-1977	177	44	and	and	CCONJ
ejpam-1977	177	45	(	(	PUNCT
ejpam-1977	177	46	c)b	c)b	NOUN
ejpam-1977	177	47	=	=	SYM
ejpam-1977	177	48	(	(	PUNCT
ejpam-1977	177	49	c)q	c)q	NOUN
ejpam-1977	177	50	.	.	PUNCT
ejpam-1977	178	1	proof	proof	NOUN
ejpam-1977	178	2	.	.	PUNCT
ejpam-1977	179	1	assume	assume	VERB
ejpam-1977	179	2	that	that	SCONJ
ejpam-1977	179	3	bi	bi	NOUN
ejpam-1977	179	4	–	–	PUNCT
ejpam-1977	179	5	ideal	ideal	ADJ
ejpam-1977	179	6	(	(	PUNCT
ejpam-1977	179	7	a)b	a)b	ADJ
ejpam-1977	179	8	and	and	CCONJ
ejpam-1977	179	9	quasi	quasi	ADJ
ejpam-1977	179	10	–	–	PUNCT
ejpam-1977	179	11	ideal	ideal	ADJ
ejpam-1977	179	12	(	(	PUNCT
ejpam-1977	179	13	a)q	a)q	X
ejpam-1977	179	14	are	be	AUX
ejpam-1977	179	15	minimal	minimal	ADJ
ejpam-1977	179	16	.	.	PUNCT
ejpam-1977	180	1	firstly	firstly	ADV
ejpam-1977	180	2	we	we	PRON
ejpam-1977	180	3	prove	prove	VERB
ejpam-1977	180	4	that	that	SCONJ
ejpam-1977	180	5	(	(	PUNCT
ejpam-1977	180	6	a)b	a)b	X
ejpam-1977	180	7	=	=	SYM
ejpam-1977	180	8	(	(	PUNCT
ejpam-1977	180	9	a)q	a)q	ADV
ejpam-1977	180	10	.	.	PUNCT
ejpam-1977	181	1	it	it	PRON
ejpam-1977	181	2	is	be	AUX
ejpam-1977	181	3	clear	clear	ADJ
ejpam-1977	181	4	the	the	DET
ejpam-1977	181	5	inclusion	inclusion	NOUN
ejpam-1977	181	6	(	(	PUNCT
ejpam-1977	181	7	a)b	a)b	NOUN
ejpam-1977	181	8	⊆	⊆	NUM
ejpam-1977	181	9	(	(	PUNCT
ejpam-1977	181	10	a)q	a)q	ADV
ejpam-1977	181	11	.	.	PUNCT
ejpam-1977	182	1	since	since	SCONJ
ejpam-1977	182	2	(	(	PUNCT
ejpam-1977	182	3	a)q	a)q	X
ejpam-1977	182	4	is	be	AUX
ejpam-1977	182	5	a	a	DET
ejpam-1977	182	6	minimal	minimal	ADJ
ejpam-1977	182	7	quasi	quasi	NOUN
ejpam-1977	182	8	–	–	PUNCT
ejpam-1977	182	9	ideal	ideal	ADJ
ejpam-1977	182	10	,	,	PUNCT
ejpam-1977	182	11	then	then	ADV
ejpam-1977	182	12	theorem	theorem	VERB
ejpam-1977	182	13	5	5	NUM
ejpam-1977	182	14	implies	imply	VERB
ejpam-1977	182	15	that	that	SCONJ
ejpam-1977	182	16	(	(	PUNCT
ejpam-1977	182	17	a)q	a)q	X
ejpam-1977	182	18	=	=	SYM
ejpam-1977	182	19	ha	ha	INTJ
ejpam-1977	182	20	.	.	PUNCT
ejpam-1977	183	1	so	so	ADV
ejpam-1977	183	2	,	,	PUNCT
ejpam-1977	183	3	we	we	PRON
ejpam-1977	183	4	have	have	VERB
ejpam-1977	183	5	ba	ba	NOUN
ejpam-1977	183	6	=	=	SYM
ejpam-1977	183	7	(	(	PUNCT
ejpam-1977	183	8	a)b	a)b	X
ejpam-1977	183	9	⊆	⊆	NUM
ejpam-1977	183	10	(	(	PUNCT
ejpam-1977	183	11	a)q	a)q	NOUN
ejpam-1977	183	12	⊆	⊆	NUM
ejpam-1977	183	13	ha	ha	INTJ
ejpam-1977	183	14	.	.	PUNCT
ejpam-1977	184	1	by	by	ADP
ejpam-1977	184	2	theorem	theorem	NOUN
ejpam-1977	184	3	4	4	NUM
ejpam-1977	184	4	,	,	PUNCT
ejpam-1977	184	5	ha	ha	INTJ
ejpam-1977	184	6	is	be	AUX
ejpam-1977	184	7	a	a	DET
ejpam-1977	184	8	γ	γ	X
ejpam-1977	184	9	–	–	PUNCT
ejpam-1977	184	10	subgroup	subgroup	NOUN
ejpam-1977	184	11	,	,	PUNCT
ejpam-1977	184	12	therefore	therefore	ADV
ejpam-1977	184	13	ha	ha	X
ejpam-1977	184	14	⊆	⊆	NUM
ejpam-1977	184	15	ba	ba	PROPN
ejpam-1977	184	16	and	and	CCONJ
ejpam-1977	184	17	consequently	consequently	ADV
ejpam-1977	184	18	(	(	PUNCT
ejpam-1977	184	19	a)b	a)b	X
ejpam-1977	184	20	=	=	SYM
ejpam-1977	184	21	(	(	PUNCT
ejpam-1977	184	22	a)q	a)q	ADV
ejpam-1977	184	23	.	.	PUNCT
ejpam-1977	185	1	since	since	SCONJ
ejpam-1977	185	2	the	the	DET
ejpam-1977	185	3	principal	principal	ADJ
ejpam-1977	185	4	quasi	quasi	NOUN
ejpam-1977	185	5	–	–	PUNCT
ejpam-1977	185	6	ideal	ideal	ADJ
ejpam-1977	185	7	(	(	PUNCT
ejpam-1977	185	8	a)q	a)q	X
ejpam-1977	185	9	is	be	AUX
ejpam-1977	185	10	minimal	minimal	ADJ
ejpam-1977	185	11	,	,	PUNCT
ejpam-1977	185	12	then	then	ADV
ejpam-1977	185	13	the	the	DET
ejpam-1977	185	14	theorem	theorem	ADJ
ejpam-1977	185	15	7	7	NUM
ejpam-1977	185	16	implies	imply	VERB
ejpam-1977	185	17	that	that	SCONJ
ejpam-1977	185	18	the	the	DET
ejpam-1977	185	19	principal	principal	ADJ
ejpam-1977	185	20	quasi	quasi	NOUN
ejpam-1977	185	21	–	–	PUNCT
ejpam-1977	185	22	ideal	ideal	ADJ
ejpam-1977	185	23	(	(	PUNCT
ejpam-1977	185	24	c)q	c)q	NOUN
ejpam-1977	185	25	is	be	AUX
ejpam-1977	185	26	minimal	minimal	ADJ
ejpam-1977	185	27	.	.	PUNCT
ejpam-1977	186	1	now	now	ADV
ejpam-1977	186	2	from	from	ADP
ejpam-1977	186	3	the	the	DET
ejpam-1977	186	4	theorem	theorem	NOUN
ejpam-1977	186	5	5	5	NUM
ejpam-1977	186	6	we	we	PRON
ejpam-1977	186	7	have	have	AUX
ejpam-1977	186	8	bc	bc	PROPN
ejpam-1977	186	9	⊆	⊆	NUM
ejpam-1977	186	10	(	(	PUNCT
ejpam-1977	186	11	c)b	c)b	NOUN
ejpam-1977	186	12	⊆	⊆	NUM
ejpam-1977	186	13	(	(	PUNCT
ejpam-1977	186	14	c)q	c)q	NOUN
ejpam-1977	186	15	=	=	SYM
ejpam-1977	186	16	hc	hc	PROPN
ejpam-1977	186	17	.	.	PUNCT
ejpam-1977	187	1	by	by	ADP
ejpam-1977	187	2	the	the	DET
ejpam-1977	187	3	theorem	theorem	NOUN
ejpam-1977	187	4	4	4	NUM
ejpam-1977	187	5	,	,	PUNCT
ejpam-1977	187	6	hc	hc	PROPN
ejpam-1977	187	7	is	be	AUX
ejpam-1977	187	8	a	a	DET
ejpam-1977	187	9	γ	γ	X
ejpam-1977	187	10	–	–	PUNCT
ejpam-1977	187	11	group	group	NOUN
ejpam-1977	187	12	,	,	PUNCT
ejpam-1977	187	13	therefore	therefore	ADV
ejpam-1977	187	14	hc	hc	PROPN
ejpam-1977	187	15	⊆	⊆	NUM
ejpam-1977	187	16	bc	bc	PROPN
ejpam-1977	187	17	and	and	CCONJ
ejpam-1977	187	18	consequently	consequently	ADV
ejpam-1977	187	19	there	there	PRON
ejpam-1977	187	20	are	be	VERB
ejpam-1977	187	21	true	true	ADJ
ejpam-1977	187	22	the	the	DET
ejpam-1977	187	23	equalities	equality	NOUN
ejpam-1977	187	24	bc	bc	PROPN
ejpam-1977	187	25	=	=	SYM
ejpam-1977	187	26	(	(	PUNCT
ejpam-1977	187	27	c)b	c)b	X
ejpam-1977	187	28	=	=	SYM
ejpam-1977	187	29	(	(	PUNCT
ejpam-1977	187	30	c)q	c)q	NOUN
ejpam-1977	187	31	=	=	SYM
ejpam-1977	187	32	hc	hc	PROPN
ejpam-1977	187	33	.	.	PUNCT
ejpam-1977	188	1	so	so	ADV
ejpam-1977	188	2	,	,	PUNCT
ejpam-1977	188	3	(	(	PUNCT
ejpam-1977	188	4	c)b	c)b	X
ejpam-1977	188	5	=	=	SYM
ejpam-1977	188	6	(	(	PUNCT
ejpam-1977	188	7	c)q	c)q	NOUN
ejpam-1977	188	8	.	.	PUNCT
ejpam-1977	189	1	at	at	ADP
ejpam-1977	189	2	the	the	DET
ejpam-1977	189	3	end	end	NOUN
ejpam-1977	189	4	of	of	ADP
ejpam-1977	189	5	this	this	DET
ejpam-1977	189	6	paper	paper	NOUN
ejpam-1977	189	7	,	,	PUNCT
ejpam-1977	189	8	we	we	PRON
ejpam-1977	189	9	raise	raise	VERB
ejpam-1977	189	10	the	the	DET
ejpam-1977	189	11	following	follow	VERB
ejpam-1977	189	12	open	open	ADJ
ejpam-1977	189	13	problem	problem	NOUN
ejpam-1977	189	14	:	:	PUNCT
ejpam-1977	189	15	problem	problem	NOUN
ejpam-1977	189	16	.	.	PUNCT
ejpam-1977	190	1	if	if	SCONJ
ejpam-1977	190	2	the	the	DET
ejpam-1977	190	3	element	element	NOUN
ejpam-1977	190	4	a	a	PROPN
ejpam-1977	190	5	,	,	PUNCT
ejpam-1977	190	6	c	c	NOUN
ejpam-1977	190	7	of	of	ADP
ejpam-1977	190	8	a	a	DET
ejpam-1977	190	9	γ	γ	X
ejpam-1977	190	10	–	–	PUNCT
ejpam-1977	190	11	semigroup	semigroup	NOUN
ejpam-1977	190	12	m	m	NOUN
ejpam-1977	190	13	without	without	ADP
ejpam-1977	190	14	zero	zero	NUM
ejpam-1977	190	15	are	be	AUX
ejpam-1977	190	16	such	such	ADJ
ejpam-1977	190	17	that	that	DET
ejpam-1977	190	18	adc	adc	PROPN
ejpam-1977	190	19	,	,	PUNCT
ejpam-1977	190	20	then	then	ADV
ejpam-1977	190	21	is	be	AUX
ejpam-1977	190	22	it	it	PRON
ejpam-1977	190	23	the	the	DET
ejpam-1977	190	24	principal	principal	ADJ
ejpam-1977	190	25	bi	bi	NOUN
ejpam-1977	190	26	–	–	PUNCT
ejpam-1977	190	27	ideal	ideal	ADJ
ejpam-1977	190	28	(	(	PUNCT
ejpam-1977	190	29	a)b	a)b	X
ejpam-1977	190	30	minimal	minimal	ADJ
ejpam-1977	190	31	if	if	SCONJ
ejpam-1977	190	32	and	and	CCONJ
ejpam-1977	190	33	only	only	ADV
ejpam-1977	190	34	if	if	SCONJ
ejpam-1977	190	35	the	the	DET
ejpam-1977	190	36	same	same	ADJ
ejpam-1977	190	37	holds	hold	VERB
ejpam-1977	190	38	for	for	ADP
ejpam-1977	190	39	(	(	PUNCT
ejpam-1977	190	40	c)b	c)b	NOUN
ejpam-1977	190	41	?	?	PUNCT
ejpam-1977	191	1	references	reference	NOUN
ejpam-1977	191	2	85	85	NUM
ejpam-1977	191	3	references	reference	NOUN
ejpam-1977	191	4	[	[	X
ejpam-1977	191	5	1	1	NUM
ejpam-1977	191	6	]	]	PUNCT
ejpam-1977	191	7	r.	r.	PROPN
ejpam-1977	191	8	chinram	chinram	PROPN
ejpam-1977	191	9	and	and	CCONJ
ejpam-1977	191	10	ch	ch	PROPN
ejpam-1977	191	11	.	.	PROPN
ejpam-1977	191	12	jirojkul	jirojkul	PROPN
ejpam-1977	191	13	.	.	PUNCT
ejpam-1977	192	1	on	on	ADP
ejpam-1977	192	2	bi	bi	PROPN
ejpam-1977	192	3	–	–	PUNCT
ejpam-1977	192	4	γ	γ	X
ejpam-1977	192	5	–	–	PUNCT
ejpam-1977	192	6	ideals	ideal	NOUN
ejpam-1977	192	7	in	in	ADP
ejpam-1977	192	8	γ	γ	NOUN
ejpam-1977	192	9	–	–	PUNCT
ejpam-1977	192	10	semigroups	semigroup	NOUN
ejpam-1977	192	11	,	,	PUNCT
ejpam-1977	192	12	songklanakarin	songklanakarin	NOUN
ejpam-1977	192	13	journal	journal	NOUN
ejpam-1977	192	14	of	of	ADP
ejpam-1977	192	15	science	science	NOUN
ejpam-1977	192	16	and	and	CCONJ
ejpam-1977	192	17	technology	technology	NOUN
ejpam-1977	192	18	,	,	PUNCT
ejpam-1977	192	19	29	29	NUM
ejpam-1977	192	20	no	no	NOUN
ejpam-1977	192	21	.	.	NOUN
ejpam-1977	192	22	1	1	NUM
ejpam-1977	192	23	,	,	PUNCT
ejpam-1977	192	24	231–234	231–234	NUM
ejpam-1977	192	25	.	.	NOUN
ejpam-1977	192	26	2007	2007	NUM
ejpam-1977	192	27	.	.	PUNCT
ejpam-1977	193	1	[	[	X
ejpam-1977	193	2	2	2	NUM
ejpam-1977	193	3	]	]	X
ejpam-1977	193	4	m.p	m.p	PROPN
ejpam-1977	193	5	.	.	PROPN
ejpam-1977	193	6	grillet	grillet	PROPN
ejpam-1977	193	7	.	.	PUNCT
ejpam-1977	194	1	green	green	PROPN
ejpam-1977	194	2	’s	’s	PART
ejpam-1977	194	3	relations	relation	NOUN
ejpam-1977	194	4	in	in	ADP
ejpam-1977	194	5	a	a	DET
ejpam-1977	194	6	semiring	semiring	NOUN
ejpam-1977	194	7	,	,	PUNCT
ejpam-1977	194	8	portugaliae	portugaliae	PROPN
ejpam-1977	194	9	mathematical	mathematical	PROPN
ejpam-1977	194	10	,	,	PUNCT
ejpam-1977	194	11	29	29	NUM
ejpam-1977	194	12	,	,	PUNCT
ejpam-1977	194	13	181–195	181–195	NUM
ejpam-1977	194	14	.	.	NOUN
ejpam-1977	194	15	1970	1970	NUM
ejpam-1977	194	16	.	.	PUNCT
ejpam-1977	195	1	[	[	X
ejpam-1977	195	2	3	3	X
ejpam-1977	195	3	]	]	X
ejpam-1977	195	4	m.r	m.r	PROPN
ejpam-1977	195	5	.	.	PROPN
ejpam-1977	195	6	hestenes	hestene	NOUN
ejpam-1977	195	7	.	.	PUNCT
ejpam-1977	196	1	a	a	DET
ejpam-1977	196	2	ternary	ternary	ADJ
ejpam-1977	196	3	algebra	algebra	NOUN
ejpam-1977	196	4	with	with	ADP
ejpam-1977	196	5	applications	application	NOUN
ejpam-1977	196	6	to	to	ADP
ejpam-1977	196	7	matrices	matrix	NOUN
ejpam-1977	196	8	and	and	CCONJ
ejpam-1977	196	9	linear	linear	ADJ
ejpam-1977	196	10	transformations	transformation	NOUN
ejpam-1977	196	11	.	.	PUNCT
ejpam-1977	197	1	archive	archive	NOUN
ejpam-1977	197	2	for	for	ADP
ejpam-1977	197	3	rational	rational	ADJ
ejpam-1977	197	4	mechanics	mechanic	NOUN
ejpam-1977	197	5	and	and	CCONJ
ejpam-1977	197	6	analysis	analysis	NOUN
ejpam-1977	197	7	,	,	PUNCT
ejpam-1977	197	8	11	11	NUM
ejpam-1977	197	9	,	,	PUNCT
ejpam-1977	197	10	138–194	138–194	NUM
ejpam-1977	197	11	.	.	PUNCT
ejpam-1977	197	12	1962	1962	NUM
ejpam-1977	197	13	.	.	PUNCT
ejpam-1977	198	1	[	[	X
ejpam-1977	198	2	4	4	NUM
ejpam-1977	198	3	]	]	X
ejpam-1977	198	4	k.m	k.m	PROPN
ejpam-1977	198	5	.	.	PROPN
ejpam-1977	198	6	kapp	kapp	PROPN
ejpam-1977	198	7	.	.	PUNCT
ejpam-1977	199	1	on	on	ADP
ejpam-1977	199	2	bi	bi	ADJ
ejpam-1977	199	3	–	–	PUNCT
ejpam-1977	199	4	ideals	ideal	NOUN
ejpam-1977	199	5	and	and	CCONJ
ejpam-1977	199	6	quasi	quasi	ADJ
ejpam-1977	199	7	–	–	PUNCT
ejpam-1977	199	8	ideals	ideal	NOUN
ejpam-1977	199	9	in	in	ADP
ejpam-1977	199	10	semigroups	semigroup	NOUN
ejpam-1977	199	11	,	,	PUNCT
ejpam-1977	199	12	publicationes	publicatione	NOUN
ejpam-1977	199	13	mathematicae	mathematicae	PROPN
ejpam-1977	199	14	debrecen	debrecen	PROPN
ejpam-1977	199	15	,	,	PUNCT
ejpam-1977	199	16	16	16	NUM
ejpam-1977	199	17	,	,	PUNCT
ejpam-1977	199	18	179–185	179–185	NUM
ejpam-1977	199	19	.	.	PUNCT
ejpam-1977	199	20	1969	1969	NUM
ejpam-1977	199	21	.	.	PUNCT
ejpam-1977	200	1	[	[	X
ejpam-1977	200	2	5	5	X
ejpam-1977	200	3	]	]	PUNCT
ejpam-1977	200	4	p.	p.	NOUN
ejpam-1977	200	5	petro	petro	PROPN
ejpam-1977	200	6	.	.	PUNCT
ejpam-1977	201	1	green	green	PROPN
ejpam-1977	201	2	’s	’s	PART
ejpam-1977	201	3	relations	relation	NOUN
ejpam-1977	201	4	and	and	CCONJ
ejpam-1977	201	5	minimal	minimal	ADJ
ejpam-1977	201	6	quasi	quasi	NOUN
ejpam-1977	201	7	–	–	PUNCT
ejpam-1977	201	8	ideals	ideal	NOUN
ejpam-1977	201	9	in	in	ADP
ejpam-1977	201	10	rings	ring	NOUN
ejpam-1977	201	11	,	,	PUNCT
ejpam-1977	201	12	communications	communication	NOUN
ejpam-1977	201	13	in	in	ADP
ejpam-1977	201	14	algebra	algebra	NOUN
ejpam-1977	201	15	,	,	PUNCT
ejpam-1977	201	16	30	30	NUM
ejpam-1977	201	17	,	,	PUNCT
ejpam-1977	201	18	no	no	NOUN
ejpam-1977	201	19	.	.	NOUN
ejpam-1977	201	20	10	10	NUM
ejpam-1977	201	21	,	,	PUNCT
ejpam-1977	201	22	4677–4688	4677–4688	NUM
ejpam-1977	201	23	.	.	PUNCT
ejpam-1977	201	24	2002	2002	NUM
ejpam-1977	201	25	.	.	PUNCT
ejpam-1977	202	1	[	[	X
ejpam-1977	202	2	6	6	NUM
ejpam-1977	202	3	]	]	PUNCT
ejpam-1977	202	4	p.	p.	NOUN
ejpam-1977	202	5	petro	petro	NOUN
ejpam-1977	202	6	and	and	CCONJ
ejpam-1977	202	7	th	th	NOUN
ejpam-1977	202	8	.	.	PUNCT
ejpam-1977	203	1	xhillari	xhillari	PROPN
ejpam-1977	203	2	.	.	PUNCT
ejpam-1977	204	1	green	green	PROPN
ejpam-1977	204	2	’s	’s	PART
ejpam-1977	204	3	theorem	theorem	NOUN
ejpam-1977	204	4	and	and	CCONJ
ejpam-1977	204	5	minimal	minimal	ADJ
ejpam-1977	204	6	quasi	quasi	NOUN
ejpam-1977	204	7	–	–	PUNCT
ejpam-1977	204	8	ideals	ideal	NOUN
ejpam-1977	204	9	in	in	ADP
ejpam-1977	204	10	γ	γ	NOUN
ejpam-1977	204	11	–	–	PUNCT
ejpam-1977	204	12	semigroups	semigroup	NOUN
ejpam-1977	204	13	,	,	PUNCT
ejpam-1977	204	14	international	international	ADJ
ejpam-1977	204	15	journal	journal	NOUN
ejpam-1977	204	16	of	of	ADP
ejpam-1977	204	17	algebra	algebra	PROPN
ejpam-1977	204	18	,	,	PUNCT
ejpam-1977	204	19	5	5	NUM
ejpam-1977	204	20	,	,	PUNCT
ejpam-1977	204	21	no	no	NOUN
ejpam-1977	204	22	.	.	NOUN
ejpam-1977	204	23	10	10	NUM
ejpam-1977	204	24	,	,	PUNCT
ejpam-1977	204	25	461–470	461–470	NUM
ejpam-1977	204	26	.	.	PUNCT
ejpam-1977	205	1	2011	2011	NUM
ejpam-1977	205	2	.	.	PUNCT
ejpam-1977	206	1	[	[	X
ejpam-1977	206	2	7	7	X
ejpam-1977	206	3	]	]	X
ejpam-1977	206	4	n.k	n.k	PROPN
ejpam-1977	206	5	.	.	PROPN
ejpam-1977	206	6	saha	saha	PROPN
ejpam-1977	206	7	.	.	PUNCT
ejpam-1977	207	1	on	on	ADP
ejpam-1977	207	2	γ	γ	X
ejpam-1977	207	3	–	–	PUNCT
ejpam-1977	207	4	semigroups	semigroup	NOUN
ejpam-1977	207	5	,	,	PUNCT
ejpam-1977	207	6	bulletin	bulletin	NOUN
ejpam-1977	207	7	of	of	ADP
ejpam-1977	207	8	calcutta	calcutta	PROPN
ejpam-1977	207	9	mathematical	mathematical	ADJ
ejpam-1977	207	10	society	society	NOUN
ejpam-1977	207	11	,	,	PUNCT
ejpam-1977	207	12	79	79	NUM
ejpam-1977	207	13	,	,	PUNCT
ejpam-1977	207	14	331–335	331–335	NUM
ejpam-1977	207	15	.	.	NOUN
ejpam-1977	207	16	1987	1987	NUM
ejpam-1977	207	17	.	.	PUNCT
ejpam-1977	208	1	[	[	X
ejpam-1977	208	2	8	8	NUM
ejpam-1977	208	3	]	]	X
ejpam-1977	208	4	m.k	m.k	PROPN
ejpam-1977	208	5	.	.	PUNCT
ejpam-1977	208	6	sen	sen	PROPN
ejpam-1977	208	7	.	.	PROPN
ejpam-1977	208	8	on	on	ADP
ejpam-1977	208	9	γ	γ	X
ejpam-1977	208	10	–	–	PUNCT
ejpam-1977	208	11	semigroup	semigroup	NOUN
ejpam-1977	208	12	,	,	PUNCT
ejpam-1977	208	13	algebra	algebra	NOUN
ejpam-1977	208	14	and	and	CCONJ
ejpam-1977	208	15	its	its	PRON
ejpam-1977	208	16	application	application	NOUN
ejpam-1977	208	17	(	(	PUNCT
ejpam-1977	208	18	new	new	ADJ
ejpam-1977	208	19	delhi	delhi	PROPN
ejpam-1977	208	20	,	,	PUNCT
ejpam-1977	208	21	1981	1981	NUM
ejpam-1977	208	22	)	)	PUNCT
ejpam-1977	208	23	,	,	PUNCT
ejpam-1977	208	24	301–308	301–308	NUM
ejpam-1977	208	25	,	,	PUNCT
ejpam-1977	208	26	lectures	lecture	NOUN
ejpam-1977	208	27	in	in	ADP
ejpam-1977	208	28	pure	pure	ADJ
ejpam-1977	208	29	and	and	CCONJ
ejpam-1977	208	30	applied	applied	ADJ
ejpam-1977	208	31	mathematics	mathematic	NOUN
ejpam-1977	208	32	,	,	PUNCT
ejpam-1977	208	33	91	91	NUM
ejpam-1977	208	34	,	,	PUNCT
ejpam-1977	208	35	dekker	dekker	NOUN
ejpam-1977	208	36	,	,	PUNCT
ejpam-1977	208	37	new	new	PROPN
ejpam-1977	208	38	york	york	PROPN
ejpam-1977	208	39	,	,	PUNCT
ejpam-1977	208	40	1984	1984	NUM
ejpam-1977	208	41	.	.	PUNCT
ejpam-1977	209	1	[	[	X
ejpam-1977	209	2	9	9	NUM
ejpam-1977	209	3	]	]	X
ejpam-1977	209	4	m.k	m.k	PROPN
ejpam-1977	209	5	.	.	PUNCT
ejpam-1977	209	6	sen	sen	PROPN
ejpam-1977	209	7	and	and	CCONJ
ejpam-1977	209	8	n.k	n.k	PROPN
ejpam-1977	209	9	.	.	PROPN
ejpam-1977	209	10	saha	saha	PROPN
ejpam-1977	209	11	.	.	PUNCT
ejpam-1977	210	1	on	on	ADP
ejpam-1977	210	2	γ	γ	NOUN
ejpam-1977	210	3	–	–	PUNCT
ejpam-1977	210	4	semigroups	semigroups	X
ejpam-1977	210	5	i	i	PRON
ejpam-1977	210	6	,	,	PUNCT
ejpam-1977	210	7	bulletin	bulletin	NOUN
ejpam-1977	210	8	of	of	ADP
ejpam-1977	210	9	calcutta	calcutta	PROPN
ejpam-1977	210	10	mathematical	mathematical	ADJ
ejpam-1977	210	11	society	society	NOUN
ejpam-1977	210	12	,	,	PUNCT
ejpam-1977	210	13	78	78	NUM
ejpam-1977	210	14	,	,	PUNCT
ejpam-1977	210	15	180–186	180–186	NUM
ejpam-1977	210	16	.	.	PUNCT
ejpam-1977	210	17	1986	1986	NUM
ejpam-1977	210	18	.	.	PUNCT
ejpam-1977	211	1	[	[	X
ejpam-1977	211	2	10	10	NUM
ejpam-1977	211	3	]	]	X
ejpam-1977	211	4	o.	o.	PROPN
ejpam-1977	211	5	steinfeld	steinfeld	PROPN
ejpam-1977	211	6	.	.	PUNCT
ejpam-1977	212	1	quasi	quasi	ADJ
ejpam-1977	212	2	–	–	PUNCT
ejpam-1977	212	3	ideals	ideal	NOUN
ejpam-1977	212	4	in	in	ADP
ejpam-1977	212	5	semigroups	semigroup	NOUN
ejpam-1977	212	6	and	and	CCONJ
ejpam-1977	212	7	rings	ring	NOUN
ejpam-1977	212	8	,	,	PUNCT
ejpam-1977	212	9	akademia	akademia	ADJ
ejpam-1977	212	10	kiado	kiado	PROPN
ejpam-1977	212	11	,	,	PUNCT
ejpam-1977	212	12	budapest	budapest	NOUN
ejpam-1977	212	13	,	,	PUNCT
ejpam-1977	212	14	1978	1978	NUM
ejpam-1977	212	15	.	.	PUNCT