id	sid	tid	token	lemma	pos
ejpam-3931	1	1	european	european	PROPN
ejpam-3931	1	2	journal	journal	PROPN
ejpam-3931	1	3	of	of	ADP
ejpam-3931	1	4	pure	pure	ADJ
ejpam-3931	1	5	and	and	CCONJ
ejpam-3931	1	6	applied	apply	VERB
ejpam-3931	1	7	mathematics	mathematic	NOUN
ejpam-3931	1	8	vol	vol	NOUN
ejpam-3931	1	9	.	.	PUNCT
ejpam-3931	2	1	14	14	NUM
ejpam-3931	2	2	,	,	PUNCT
ejpam-3931	2	3	no	no	INTJ
ejpam-3931	2	4	.	.	NOUN
ejpam-3931	2	5	4	4	NUM
ejpam-3931	2	6	,	,	PUNCT
ejpam-3931	2	7	2021	2021	NUM
ejpam-3931	2	8	,	,	PUNCT
ejpam-3931	2	9	43	43	NUM
ejpam-3931	2	10	-	-	SYM
ejpam-3931	2	11	52	52	NUM
ejpam-3931	2	12	issn	issn	PROPN
ejpam-3931	2	13	1307	1307	NUM
ejpam-3931	2	14	-	-	SYM
ejpam-3931	2	15	5543	5543	NUM
ejpam-3931	2	16	–	–	PUNCT
ejpam-3931	2	17	ejpam.com	ejpam.com	X
ejpam-3931	2	18	published	publish	VERB
ejpam-3931	2	19	by	by	ADP
ejpam-3931	2	20	new	new	PROPN
ejpam-3931	2	21	york	york	PROPN
ejpam-3931	2	22	business	business	PROPN
ejpam-3931	2	23	global	global	ADJ
ejpam-3931	2	24	bi	bi	ADJ
ejpam-3931	2	25	-	-	ADJ
ejpam-3931	2	26	interior	interior	ADJ
ejpam-3931	2	27	ideal	ideal	ADJ
ejpam-3931	2	28	elements	element	NOUN
ejpam-3931	2	29	in	in	ADP
ejpam-3931	2	30	∧e	∧e	NOUN
ejpam-3931	2	31	-	-	PUNCT
ejpam-3931	2	32	semigroups	semigroup	NOUN
ejpam-3931	2	33	niovi	niovi	ADJ
ejpam-3931	2	34	kehayopulu	kehayopulu	ADJ
ejpam-3931	2	35	abstract	abstract	NOUN
ejpam-3931	2	36	.	.	PUNCT
ejpam-3931	3	1	all	all	DET
ejpam-3931	3	2	the	the	DET
ejpam-3931	3	3	results	result	NOUN
ejpam-3931	3	4	on	on	ADP
ejpam-3931	3	5	semigroups	semigroup	NOUN
ejpam-3931	3	6	obtained	obtain	VERB
ejpam-3931	3	7	using	use	VERB
ejpam-3931	3	8	only	only	ADJ
ejpam-3931	3	9	sets	set	NOUN
ejpam-3931	3	10	,	,	PUNCT
ejpam-3931	3	11	can	can	AUX
ejpam-3931	3	12	be	be	AUX
ejpam-3931	3	13	written	write	VERB
ejpam-3931	3	14	in	in	ADP
ejpam-3931	3	15	an	an	DET
ejpam-3931	3	16	abstract	abstract	ADJ
ejpam-3931	3	17	form	form	NOUN
ejpam-3931	3	18	in	in	ADP
ejpam-3931	3	19	a	a	DET
ejpam-3931	3	20	more	more	ADV
ejpam-3931	3	21	general	general	ADJ
ejpam-3931	3	22	setting	setting	NOUN
ejpam-3931	3	23	.	.	PUNCT
ejpam-3931	4	1	let	let	VERB
ejpam-3931	4	2	us	we	PRON
ejpam-3931	4	3	consider	consider	VERB
ejpam-3931	4	4	a	a	DET
ejpam-3931	4	5	recent	recent	ADJ
ejpam-3931	4	6	paper	paper	NOUN
ejpam-3931	4	7	to	to	PART
ejpam-3931	4	8	justify	justify	VERB
ejpam-3931	4	9	what	what	PRON
ejpam-3931	4	10	we	we	PRON
ejpam-3931	4	11	say	say	VERB
ejpam-3931	4	12	.	.	PUNCT
ejpam-3931	5	1	the	the	DET
ejpam-3931	5	2	biinterior	biinterior	PROPN
ejpam-3931	5	3	ideals	ideal	NOUN
ejpam-3931	5	4	of	of	ADP
ejpam-3931	5	5	semigroups	semigroup	NOUN
ejpam-3931	5	6	introduced	introduce	VERB
ejpam-3931	5	7	and	and	CCONJ
ejpam-3931	5	8	studied	study	VERB
ejpam-3931	5	9	by	by	ADP
ejpam-3931	5	10	m.	m.	NOUN
ejpam-3931	5	11	murali	murali	PROPN
ejpam-3931	5	12	krishna	krishna	PROPN
ejpam-3931	5	13	rao	rao	PROPN
ejpam-3931	5	14	in	in	ADP
ejpam-3931	5	15	discuss	discuss	PROPN
ejpam-3931	5	16	.	.	PUNCT
ejpam-3931	6	1	math	math	NOUN
ejpam-3931	6	2	.	.	PUNCT
ejpam-3931	7	1	gen	gen	PROPN
ejpam-3931	7	2	.	.	PROPN
ejpam-3931	7	3	algebra	algebra	PROPN
ejpam-3931	7	4	appl	appl	PROPN
ejpam-3931	7	5	.	.	PUNCT
ejpam-3931	8	1	in	in	ADP
ejpam-3931	8	2	2018	2018	NUM
ejpam-3931	8	3	,	,	PUNCT
ejpam-3931	8	4	follow	follow	VERB
ejpam-3931	8	5	for	for	ADP
ejpam-3931	8	6	more	more	ADV
ejpam-3931	8	7	general	general	ADJ
ejpam-3931	8	8	statements	statement	NOUN
ejpam-3931	8	9	about	about	ADP
ejpam-3931	8	10	ordered	order	VERB
ejpam-3931	8	11	semigroups	semigroup	NOUN
ejpam-3931	8	12	.	.	PUNCT
ejpam-3931	9	1	the	the	DET
ejpam-3931	9	2	same	same	ADJ
ejpam-3931	9	3	holds	hold	VERB
ejpam-3931	9	4	for	for	ADP
ejpam-3931	9	5	every	every	DET
ejpam-3931	9	6	result	result	NOUN
ejpam-3931	9	7	of	of	ADP
ejpam-3931	9	8	this	this	DET
ejpam-3931	9	9	sort	sort	NOUN
ejpam-3931	9	10	on	on	ADP
ejpam-3931	9	11	semigroups	semigroup	NOUN
ejpam-3931	9	12	based	base	VERB
ejpam-3931	9	13	on	on	ADP
ejpam-3931	9	14	right	right	ADJ
ejpam-3931	9	15	(	(	PUNCT
ejpam-3931	9	16	left	left	ADJ
ejpam-3931	9	17	)	)	PUNCT
ejpam-3931	9	18	ideals	ideal	NOUN
ejpam-3931	9	19	,	,	PUNCT
ejpam-3931	9	20	bi	bi	NOUN
ejpam-3931	9	21	-	-	NOUN
ejpam-3931	9	22	ideals	ideal	NOUN
ejpam-3931	9	23	,	,	PUNCT
ejpam-3931	9	24	quasiideals	quasiideal	NOUN
ejpam-3931	9	25	,	,	PUNCT
ejpam-3931	9	26	interior	interior	ADJ
ejpam-3931	9	27	ideals	ideal	NOUN
ejpam-3931	9	28	etc	etc	X
ejpam-3931	9	29	.	.	X
ejpam-3931	9	30	for	for	ADP
ejpam-3931	9	31	which	which	PRON
ejpam-3931	9	32	we	we	PRON
ejpam-3931	9	33	use	use	VERB
ejpam-3931	9	34	sets	set	NOUN
ejpam-3931	9	35	.	.	PUNCT
ejpam-3931	10	1	as	as	ADP
ejpam-3931	10	2	a	a	DET
ejpam-3931	10	3	result	result	NOUN
ejpam-3931	10	4	,	,	PUNCT
ejpam-3931	10	5	we	we	PRON
ejpam-3931	10	6	have	have	VERB
ejpam-3931	10	7	an	an	DET
ejpam-3931	10	8	abstract	abstract	ADJ
ejpam-3931	10	9	formulation	formulation	NOUN
ejpam-3931	10	10	of	of	ADP
ejpam-3931	10	11	the	the	DET
ejpam-3931	10	12	results	result	NOUN
ejpam-3931	10	13	on	on	ADP
ejpam-3931	10	14	semigroups	semigroup	NOUN
ejpam-3931	10	15	obtained	obtain	VERB
ejpam-3931	10	16	by	by	ADP
ejpam-3931	10	17	sets	set	NOUN
ejpam-3931	10	18	that	that	PRON
ejpam-3931	10	19	is	be	AUX
ejpam-3931	10	20	in	in	ADP
ejpam-3931	10	21	the	the	DET
ejpam-3931	10	22	same	same	ADJ
ejpam-3931	10	23	spirit	spirit	NOUN
ejpam-3931	10	24	with	with	ADP
ejpam-3931	10	25	the	the	DET
ejpam-3931	10	26	abstract	abstract	ADJ
ejpam-3931	10	27	formulation	formulation	NOUN
ejpam-3931	10	28	of	of	ADP
ejpam-3931	10	29	general	general	ADJ
ejpam-3931	10	30	topology	topology	NOUN
ejpam-3931	10	31	(	(	PUNCT
ejpam-3931	10	32	the	the	DET
ejpam-3931	10	33	so	so	ADV
ejpam-3931	10	34	-	-	PUNCT
ejpam-3931	10	35	called	call	VERB
ejpam-3931	10	36	topology	topology	NOUN
ejpam-3931	10	37	without	without	ADP
ejpam-3931	10	38	points	point	NOUN
ejpam-3931	10	39	)	)	PUNCT
ejpam-3931	10	40	initiated	initiate	VERB
ejpam-3931	10	41	by	by	ADP
ejpam-3931	10	42	koutský	koutský	NOUN
ejpam-3931	10	43	,	,	PUNCT
ejpam-3931	10	44	nöbeling	nöbeling	NOUN
ejpam-3931	10	45	and	and	CCONJ
ejpam-3931	10	46	,	,	PUNCT
ejpam-3931	10	47	even	even	ADV
ejpam-3931	10	48	earlier	early	ADV
ejpam-3931	10	49	,	,	PUNCT
ejpam-3931	10	50	by	by	ADP
ejpam-3931	10	51	chittenden	chittenden	PROPN
ejpam-3931	10	52	,	,	PUNCT
ejpam-3931	10	53	terasaka	terasaka	PROPN
ejpam-3931	10	54	,	,	PUNCT
ejpam-3931	10	55	nakamura	nakamura	PROPN
ejpam-3931	10	56	,	,	PUNCT
ejpam-3931	10	57	monteiro	monteiro	PROPN
ejpam-3931	10	58	and	and	CCONJ
ejpam-3931	10	59	ribeiro	ribeiro	PROPN
ejpam-3931	10	60	.	.	PROPN
ejpam-3931	11	1	as	as	ADP
ejpam-3931	11	2	a	a	DET
ejpam-3931	11	3	consequence	consequence	NOUN
ejpam-3931	11	4	,	,	PUNCT
ejpam-3931	11	5	results	result	NOUN
ejpam-3931	11	6	on	on	ADP
ejpam-3931	11	7	ordered	order	VERB
ejpam-3931	11	8	γ	γ	NOUN
ejpam-3931	11	9	-	-	PUNCT
ejpam-3931	11	10	hypersemigroups	hypersemigroup	NOUN
ejpam-3931	11	11	and	and	CCONJ
ejpam-3931	11	12	on	on	ADP
ejpam-3931	11	13	similar	similar	ADJ
ejpam-3931	11	14	simpler	simple	ADJ
ejpam-3931	11	15	structures	structure	NOUN
ejpam-3931	11	16	can	can	AUX
ejpam-3931	11	17	be	be	AUX
ejpam-3931	11	18	obtained	obtain	VERB
ejpam-3931	11	19	.	.	PUNCT
ejpam-3931	12	1	2020	2020	NUM
ejpam-3931	12	2	mathematics	mathematic	NOUN
ejpam-3931	12	3	subject	subject	NOUN
ejpam-3931	12	4	classifications	classification	NOUN
ejpam-3931	12	5	:	:	PUNCT
ejpam-3931	12	6	06f05	06f05	NUM
ejpam-3931	12	7	,	,	PUNCT
ejpam-3931	12	8	20m10	20m10	NUM
ejpam-3931	12	9	key	key	ADJ
ejpam-3931	12	10	words	word	NOUN
ejpam-3931	12	11	and	and	CCONJ
ejpam-3931	12	12	phrases	phrase	NOUN
ejpam-3931	12	13	:	:	PUNCT
ejpam-3931	12	14	∧e	∧e	PROPN
ejpam-3931	12	15	-	-	PUNCT
ejpam-3931	12	16	semigroup	semigroup	PROPN
ejpam-3931	12	17	,	,	PUNCT
ejpam-3931	12	18	right	right	INTJ
ejpam-3931	12	19	(	(	PUNCT
ejpam-3931	12	20	left	left	ADV
ejpam-3931	12	21	)	)	PUNCT
ejpam-3931	12	22	,	,	PUNCT
ejpam-3931	12	23	bi	bi	NOUN
ejpam-3931	12	24	-	-	ADJ
ejpam-3931	12	25	ideal	ideal	ADJ
ejpam-3931	12	26	,	,	PUNCT
ejpam-3931	12	27	quasi	quasi	ADJ
ejpam-3931	12	28	-	-	ADJ
ejpam-3931	12	29	ideal	ideal	ADJ
ejpam-3931	12	30	element	element	NOUN
ejpam-3931	12	31	,	,	PUNCT
ejpam-3931	12	32	bi	bi	ADJ
ejpam-3931	12	33	-	-	ADJ
ejpam-3931	12	34	interior	interior	ADJ
ejpam-3931	12	35	ideal	ideal	ADJ
ejpam-3931	12	36	element	element	NOUN
ejpam-3931	12	37	,	,	PUNCT
ejpam-3931	12	38	left	leave	VERB
ejpam-3931	12	39	simple	simple	ADJ
ejpam-3931	12	40	,	,	PUNCT
ejpam-3931	12	41	simple	simple	ADJ
ejpam-3931	12	42	,	,	PUNCT
ejpam-3931	12	43	bi	bi	ADJ
ejpam-3931	12	44	-	-	ADJ
ejpam-3931	12	45	interior	interior	ADJ
ejpam-3931	12	46	simple	simple	NOUN
ejpam-3931	12	47	,	,	PUNCT
ejpam-3931	12	48	regular	regular	ADJ
ejpam-3931	12	49	1	1	NUM
ejpam-3931	12	50	.	.	PUNCT
ejpam-3931	12	51	introduction	introduction	NOUN
ejpam-3931	12	52	and	and	CCONJ
ejpam-3931	12	53	prerequisites	prerequisite	VERB
ejpam-3931	12	54	the	the	DET
ejpam-3931	12	55	concept	concept	NOUN
ejpam-3931	12	56	of	of	ADP
ejpam-3931	12	57	bi	bi	ADJ
ejpam-3931	12	58	-	-	ADJ
ejpam-3931	12	59	interior	interior	ADJ
ejpam-3931	12	60	ideal	ideal	NOUN
ejpam-3931	12	61	of	of	ADP
ejpam-3931	12	62	semigroup	semigroup	PROPN
ejpam-3931	12	63	has	have	AUX
ejpam-3931	12	64	been	be	AUX
ejpam-3931	12	65	introduced	introduce	VERB
ejpam-3931	12	66	my	my	PRON
ejpam-3931	12	67	m.m	m.m	PROPN
ejpam-3931	12	68	.	.	PROPN
ejpam-3931	12	69	krishna	krishna	PROPN
ejpam-3931	12	70	rao	rao	PROPN
ejpam-3931	13	1	[	[	X
ejpam-3931	13	2	4	4	X
ejpam-3931	13	3	]	]	PUNCT
ejpam-3931	13	4	as	as	SCONJ
ejpam-3931	13	5	follows	follow	VERB
ejpam-3931	13	6	:	:	PUNCT
ejpam-3931	13	7	let	let	VERB
ejpam-3931	13	8	s	s	PRON
ejpam-3931	13	9	be	be	AUX
ejpam-3931	13	10	a	a	DET
ejpam-3931	13	11	semigroup	semigroup	NOUN
ejpam-3931	13	12	and	and	CCONJ
ejpam-3931	13	13	a	a	DET
ejpam-3931	13	14	a	a	DET
ejpam-3931	13	15	nonempty	nonempty	ADJ
ejpam-3931	13	16	subset	subset	NOUN
ejpam-3931	13	17	of	of	ADP
ejpam-3931	13	18	s.	s.	PROPN
ejpam-3931	13	19	then	then	ADV
ejpam-3931	13	20	a	a	PRON
ejpam-3931	13	21	is	be	AUX
ejpam-3931	13	22	called	call	VERB
ejpam-3931	13	23	a	a	DET
ejpam-3931	13	24	bi	bi	ADJ
ejpam-3931	13	25	-	-	ADJ
ejpam-3931	13	26	interior	interior	ADJ
ejpam-3931	13	27	ideal	ideal	NOUN
ejpam-3931	13	28	of	of	ADP
ejpam-3931	13	29	s	s	PRON
ejpam-3931	13	30	if	if	SCONJ
ejpam-3931	13	31	asa	asa	PROPN
ejpam-3931	13	32	∩	∩	NOUN
ejpam-3931	13	33	sas	sas	VERB
ejpam-3931	13	34	⊆	⊆	NUM
ejpam-3931	13	35	a.	a.	NOUN
ejpam-3931	13	36	as	as	SCONJ
ejpam-3931	13	37	one	one	PRON
ejpam-3931	13	38	can	can	AUX
ejpam-3931	13	39	easily	easily	ADV
ejpam-3931	13	40	see	see	VERB
ejpam-3931	13	41	,	,	PUNCT
ejpam-3931	13	42	every	every	DET
ejpam-3931	13	43	bi	bi	NOUN
ejpam-3931	13	44	-	-	NOUN
ejpam-3931	13	45	ideal	ideal	NOUN
ejpam-3931	13	46	a	a	PRON
ejpam-3931	13	47	of	of	ADP
ejpam-3931	13	48	s	s	NOUN
ejpam-3931	13	49	is	be	AUX
ejpam-3931	13	50	a	a	DET
ejpam-3931	13	51	bi	bi	ADJ
ejpam-3931	13	52	-	-	ADJ
ejpam-3931	13	53	interior	interior	ADJ
ejpam-3931	13	54	ideal	ideal	NOUN
ejpam-3931	13	55	of	of	ADP
ejpam-3931	13	56	s	s	PRON
ejpam-3931	13	57	and	and	CCONJ
ejpam-3931	13	58	every	every	DET
ejpam-3931	13	59	interior	interior	ADJ
ejpam-3931	13	60	ideal	ideal	NOUN
ejpam-3931	13	61	of	of	ADP
ejpam-3931	13	62	s	s	PROPN
ejpam-3931	13	63	is	be	AUX
ejpam-3931	13	64	a	a	DET
ejpam-3931	13	65	bi	bi	ADJ
ejpam-3931	13	66	-	-	ADJ
ejpam-3931	13	67	interior	interior	ADJ
ejpam-3931	13	68	ideal	ideal	NOUN
ejpam-3931	13	69	of	of	ADP
ejpam-3931	13	70	s.	s.	PROPN
ejpam-3931	14	1	so	so	SCONJ
ejpam-3931	14	2	the	the	DET
ejpam-3931	14	3	concept	concept	NOUN
ejpam-3931	14	4	of	of	ADP
ejpam-3931	14	5	bi	bi	ADJ
ejpam-3931	14	6	-	-	ADJ
ejpam-3931	14	7	interior	interior	ADJ
ejpam-3931	14	8	ideal	ideal	NOUN
ejpam-3931	14	9	generalizes	generalize	VERB
ejpam-3931	14	10	the	the	DET
ejpam-3931	14	11	concept	concept	NOUN
ejpam-3931	14	12	of	of	ADP
ejpam-3931	14	13	bi	bi	NOUN
ejpam-3931	14	14	-	-	NOUN
ejpam-3931	14	15	ideal	ideal	NOUN
ejpam-3931	14	16	and	and	CCONJ
ejpam-3931	14	17	the	the	DET
ejpam-3931	14	18	concept	concept	NOUN
ejpam-3931	14	19	of	of	ADP
ejpam-3931	14	20	interior	interior	ADJ
ejpam-3931	14	21	ideal	ideal	NOUN
ejpam-3931	14	22	.	.	PUNCT
ejpam-3931	15	1	as	as	ADP
ejpam-3931	15	2	every	every	DET
ejpam-3931	15	3	right	right	NOUN
ejpam-3931	15	4	(	(	PUNCT
ejpam-3931	15	5	resp	resp	NOUN
ejpam-3931	15	6	.	.	PUNCT
ejpam-3931	16	1	left	left	ADJ
ejpam-3931	16	2	)	)	PUNCT
ejpam-3931	16	3	ideal	ideal	NOUN
ejpam-3931	16	4	and	and	CCONJ
ejpam-3931	16	5	every	every	DET
ejpam-3931	16	6	quasi	quasi	NOUN
ejpam-3931	16	7	-	-	NOUN
ejpam-3931	16	8	ideal	ideal	NOUN
ejpam-3931	16	9	of	of	ADP
ejpam-3931	16	10	a	a	DET
ejpam-3931	16	11	semigroup	semigroup	NOUN
ejpam-3931	16	12	s	s	VERB
ejpam-3931	16	13	is	be	AUX
ejpam-3931	16	14	a	a	DET
ejpam-3931	16	15	bi	bi	NOUN
ejpam-3931	16	16	-	-	NOUN
ejpam-3931	16	17	ideal	ideal	NOUN
ejpam-3931	16	18	of	of	ADP
ejpam-3931	16	19	s	s	PROPN
ejpam-3931	16	20	,	,	PUNCT
ejpam-3931	16	21	the	the	DET
ejpam-3931	16	22	concept	concept	NOUN
ejpam-3931	16	23	of	of	ADP
ejpam-3931	16	24	bi	bi	ADJ
ejpam-3931	16	25	-	-	ADJ
ejpam-3931	16	26	interior	interior	ADJ
ejpam-3931	16	27	ideal	ideal	NOUN
ejpam-3931	16	28	generalizes	generalize	VERB
ejpam-3931	16	29	the	the	DET
ejpam-3931	16	30	concepts	concept	NOUN
ejpam-3931	16	31	of	of	ADP
ejpam-3931	16	32	right	right	ADJ
ejpam-3931	16	33	ideal	ideal	NOUN
ejpam-3931	16	34	,	,	PUNCT
ejpam-3931	16	35	left	leave	VERB
ejpam-3931	16	36	ideal	ideal	ADJ
ejpam-3931	16	37	,	,	PUNCT
ejpam-3931	16	38	and	and	CCONJ
ejpam-3931	16	39	the	the	DET
ejpam-3931	16	40	concept	concept	NOUN
ejpam-3931	16	41	of	of	ADP
ejpam-3931	16	42	quasi	quasi	NOUN
ejpam-3931	16	43	-	-	NOUN
ejpam-3931	16	44	ideal	ideal	ADJ
ejpam-3931	16	45	of	of	ADP
ejpam-3931	16	46	a	a	DET
ejpam-3931	16	47	semigroup	semigroup	NOUN
ejpam-3931	16	48	as	as	ADV
ejpam-3931	16	49	well	well	ADV
ejpam-3931	16	50	.	.	PUNCT
ejpam-3931	17	1	m.	m.	PROPN
ejpam-3931	17	2	murali	murali	PROPN
ejpam-3931	17	3	krishna	krishna	PROPN
ejpam-3931	17	4	rao	rao	PROPN
ejpam-3931	17	5	assumes	assume	VERB
ejpam-3931	17	6	that	that	SCONJ
ejpam-3931	17	7	the	the	DET
ejpam-3931	17	8	bi	bi	NOUN
ejpam-3931	17	9	-	-	NOUN
ejpam-3931	17	10	ideals	ideal	NOUN
ejpam-3931	17	11	and	and	CCONJ
ejpam-3931	17	12	the	the	DET
ejpam-3931	17	13	interior	interior	ADJ
ejpam-3931	17	14	ideals	ideal	NOUN
ejpam-3931	17	15	of	of	ADP
ejpam-3931	17	16	a	a	DET
ejpam-3931	17	17	semigroup	semigroup	NOUN
ejpam-3931	17	18	s	s	NOUN
ejpam-3931	17	19	are	be	AUX
ejpam-3931	17	20	subsemigroups	subsemigroup	NOUN
ejpam-3931	17	21	of	of	ADP
ejpam-3931	17	22	s	s	NOUN
ejpam-3931	17	23	but	but	CCONJ
ejpam-3931	17	24	this	this	PRON
ejpam-3931	17	25	does	do	AUX
ejpam-3931	17	26	not	not	PART
ejpam-3931	17	27	make	make	VERB
ejpam-3931	17	28	any	any	DET
ejpam-3931	17	29	difference	difference	NOUN
ejpam-3931	17	30	to	to	ADP
ejpam-3931	17	31	the	the	DET
ejpam-3931	17	32	investigation	investigation	NOUN
ejpam-3931	17	33	.	.	PUNCT
ejpam-3931	18	1	the	the	DET
ejpam-3931	18	2	results	result	NOUN
ejpam-3931	18	3	of	of	ADP
ejpam-3931	18	4	[	[	X
ejpam-3931	18	5	4	4	NUM
ejpam-3931	18	6	]	]	PUNCT
ejpam-3931	18	7	follows	follow	VERB
ejpam-3931	18	8	from	from	ADP
ejpam-3931	18	9	a	a	DET
ejpam-3931	18	10	more	more	ADV
ejpam-3931	18	11	general	general	ADJ
ejpam-3931	18	12	setting	setting	NOUN
ejpam-3931	18	13	of	of	ADP
ejpam-3931	18	14	that	that	PRON
ejpam-3931	18	15	of	of	ADP
ejpam-3931	18	16	ordered	order	VERB
ejpam-3931	18	17	∧e	∧e	PROPN
ejpam-3931	18	18	-	-	PUNCT
ejpam-3931	18	19	semigroups	semigroup	NOUN
ejpam-3931	18	20	.	.	PUNCT
ejpam-3931	19	1	the	the	DET
ejpam-3931	19	2	same	same	ADJ
ejpam-3931	19	3	can	can	AUX
ejpam-3931	19	4	be	be	AUX
ejpam-3931	19	5	said	say	VERB
ejpam-3931	19	6	for	for	ADP
ejpam-3931	19	7	any	any	DET
ejpam-3931	19	8	similar	similar	ADJ
ejpam-3931	19	9	result	result	NOUN
ejpam-3931	19	10	based	base	VERB
ejpam-3931	19	11	on	on	ADP
ejpam-3931	19	12	sets	set	NOUN
ejpam-3931	19	13	.	.	PUNCT
ejpam-3931	20	1	we	we	PRON
ejpam-3931	20	2	casually	casually	ADV
ejpam-3931	20	3	chose	choose	VERB
ejpam-3931	20	4	a	a	DET
ejpam-3931	20	5	recent	recent	ADJ
ejpam-3931	20	6	paper	paper	NOUN
ejpam-3931	20	7	by	by	ADP
ejpam-3931	20	8	m.	m.	NOUN
ejpam-3931	20	9	murali	murali	PROPN
ejpam-3931	20	10	krishna	krishna	PROPN
ejpam-3931	20	11	rao	rao	PROPN
ejpam-3931	20	12	in	in	ADP
ejpam-3931	20	13	discuss	discuss	PROPN
ejpam-3931	20	14	.	.	PUNCT
ejpam-3931	21	1	math	math	NOUN
ejpam-3931	21	2	.	.	PUNCT
ejpam-3931	22	1	gen	gen	PROPN
ejpam-3931	22	2	.	.	PROPN
ejpam-3931	22	3	algebra	algebra	PROPN
ejpam-3931	22	4	appl	appl	PROPN
ejpam-3931	22	5	.	.	PUNCT
ejpam-3931	23	1	in	in	ADP
ejpam-3931	23	2	2018	2018	NUM
ejpam-3931	23	3	as	as	ADP
ejpam-3931	23	4	an	an	DET
ejpam-3931	23	5	example	example	NOUN
ejpam-3931	23	6	to	to	PART
ejpam-3931	23	7	justify	justify	VERB
ejpam-3931	23	8	what	what	PRON
ejpam-3931	23	9	we	we	PRON
ejpam-3931	23	10	say	say	VERB
ejpam-3931	23	11	.	.	PUNCT
ejpam-3931	24	1	this	this	PRON
ejpam-3931	24	2	is	be	AUX
ejpam-3931	24	3	in	in	ADP
ejpam-3931	24	4	the	the	DET
ejpam-3931	24	5	same	same	ADJ
ejpam-3931	24	6	spirit	spirit	NOUN
ejpam-3931	24	7	with	with	ADP
ejpam-3931	24	8	the	the	DET
ejpam-3931	24	9	abstract	abstract	ADJ
ejpam-3931	24	10	formulation	formulation	NOUN
ejpam-3931	24	11	of	of	ADP
ejpam-3931	24	12	general	general	ADJ
ejpam-3931	24	13	doi	doi	PROPN
ejpam-3931	24	14	:	:	PUNCT
ejpam-3931	24	15	https://doi.org/10.29020/nybg.ejpam.v14i4.3931	https://doi.org/10.29020/nybg.ejpam.v14i4.3931	PROPN
ejpam-3931	24	16	email	email	NOUN
ejpam-3931	24	17	address	address	NOUN
ejpam-3931	24	18	:	:	PUNCT
ejpam-3931	24	19	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3931	24	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3931	25	1	43	43	NUM
ejpam-3931	26	1	©	©	PROPN
ejpam-3931	26	2	2021	2021	NUM
ejpam-3931	26	3	ejpam	ejpam	VERB
ejpam-3931	26	4	all	all	DET
ejpam-3931	26	5	rights	right	NOUN
ejpam-3931	26	6	reserved	reserve	VERB
ejpam-3931	26	7	.	.	PUNCT
ejpam-3931	27	1	n.	n.	PROPN
ejpam-3931	27	2	kehayopulu	kehayopulu	PROPN
ejpam-3931	27	3	/	/	SYM
ejpam-3931	27	4	eur	eur	PROPN
ejpam-3931	27	5	.	.	PUNCT
ejpam-3931	28	1	j.	j.	PROPN
ejpam-3931	28	2	pure	pure	PROPN
ejpam-3931	28	3	appl	appl	PROPN
ejpam-3931	28	4	.	.	PROPN
ejpam-3931	28	5	math	math	PROPN
ejpam-3931	28	6	,	,	PUNCT
ejpam-3931	28	7	14	14	NUM
ejpam-3931	28	8	(	(	PUNCT
ejpam-3931	28	9	4	4	NUM
ejpam-3931	28	10	)	)	PUNCT
ejpam-3931	28	11	(	(	PUNCT
ejpam-3931	28	12	2021	2021	NUM
ejpam-3931	28	13	)	)	PUNCT
ejpam-3931	28	14	,	,	PUNCT
ejpam-3931	28	15	43	43	NUM
ejpam-3931	28	16	-	-	SYM
ejpam-3931	28	17	52	52	NUM
ejpam-3931	28	18	44	44	NUM
ejpam-3931	28	19	topology	topology	NOUN
ejpam-3931	28	20	(	(	PUNCT
ejpam-3931	28	21	the	the	DET
ejpam-3931	28	22	so	so	ADV
ejpam-3931	28	23	-	-	PUNCT
ejpam-3931	28	24	called	call	VERB
ejpam-3931	28	25	topology	topology	NOUN
ejpam-3931	28	26	without	without	ADP
ejpam-3931	28	27	points	point	NOUN
ejpam-3931	28	28	)	)	PUNCT
ejpam-3931	28	29	initiated	initiate	VERB
ejpam-3931	28	30	by	by	ADP
ejpam-3931	28	31	koutský	koutský	NOUN
ejpam-3931	28	32	and	and	CCONJ
ejpam-3931	28	33	nóbeling	nóbeling	PROPN
ejpam-3931	29	1	[	[	X
ejpam-3931	29	2	3	3	NUM
ejpam-3931	29	3	,	,	PUNCT
ejpam-3931	29	4	5	5	NUM
ejpam-3931	29	5	]	]	PUNCT
ejpam-3931	29	6	.	.	PUNCT
ejpam-3931	30	1	topology	topology	NOUN
ejpam-3931	30	2	without	without	ADP
ejpam-3931	30	3	points	point	NOUN
ejpam-3931	30	4	has	have	AUX
ejpam-3931	30	5	been	be	AUX
ejpam-3931	30	6	also	also	ADV
ejpam-3931	30	7	studied	study	VERB
ejpam-3931	30	8	much	much	ADV
ejpam-3931	30	9	earlier	early	ADV
ejpam-3931	30	10	by	by	ADP
ejpam-3931	30	11	m.	m.	NOUN
ejpam-3931	30	12	nakamura	nakamura	NOUN
ejpam-3931	31	1	[	[	X
ejpam-3931	31	2	closure	closure	NOUN
ejpam-3931	31	3	in	in	ADP
ejpam-3931	31	4	general	general	ADJ
ejpam-3931	31	5	lattices	lattice	NOUN
ejpam-3931	31	6	.	.	PUNCT
ejpam-3931	32	1	proc	proc	NOUN
ejpam-3931	32	2	.	.	PUNCT
ejpam-3931	33	1	imp	imp	PROPN
ejpam-3931	33	2	.	.	PUNCT
ejpam-3931	33	3	acad	acad	PROPN
ejpam-3931	33	4	.	.	PUNCT
ejpam-3931	34	1	tokyo	tokyo	PROPN
ejpam-3931	34	2	17	17	NUM
ejpam-3931	34	3	,	,	PUNCT
ejpam-3931	34	4	5–6	5–6	NUM
ejpam-3931	34	5	(	(	PUNCT
ejpam-3931	34	6	1941	1941	NUM
ejpam-3931	34	7	)	)	PUNCT
ejpam-3931	34	8	;	;	PUNCT
ejpam-3931	34	9	mr0004225	mr0004225	PROPN
ejpam-3931	34	10	]	]	PUNCT
ejpam-3931	34	11	,	,	PUNCT
ejpam-3931	34	12	a.	a.	PROPN
ejpam-3931	34	13	monteiro	monteiro	PROPN
ejpam-3931	34	14	and	and	CCONJ
ejpam-3931	34	15	h.	h.	PROPN
ejpam-3931	34	16	ribeiro	ribeiro	PROPN
ejpam-3931	35	1	[	[	X
ejpam-3931	35	2	l’operation	l’operation	PROPN
ejpam-3931	35	3	de	de	PROPN
ejpam-3931	35	4	fermeture	fermeture	PROPN
ejpam-3931	35	5	et	et	PROPN
ejpam-3931	35	6	ses	ses	PROPN
ejpam-3931	35	7	invariants	invariant	NOUN
ejpam-3931	35	8	dans	dans	PROPN
ejpam-3931	35	9	les	les	PROPN
ejpam-3931	35	10	systèmes	systèmes	PROPN
ejpam-3931	35	11	partiellement	partiellement	ADJ
ejpam-3931	35	12	ordonnées	ordonnée	NOUN
ejpam-3931	35	13	.	.	PUNCT
ejpam-3931	36	1	portugal	portugal	PROPN
ejpam-3931	36	2	.	.	PUNCT
ejpam-3931	36	3	math	math	PROPN
ejpam-3931	36	4	.	.	PUNCT
ejpam-3931	37	1	3	3	NUM
ejpam-3931	37	2	(	(	PUNCT
ejpam-3931	37	3	1942	1942	NUM
ejpam-3931	37	4	)	)	PUNCT
ejpam-3931	37	5	,	,	PUNCT
ejpam-3931	37	6	171–184	171–184	NUM
ejpam-3931	37	7	;	;	PUNCT
ejpam-3931	37	8	mr0007973	mr0007973	NOUN
ejpam-3931	37	9	]	]	PUNCT
ejpam-3931	37	10	or	or	CCONJ
ejpam-3931	37	11	,	,	PUNCT
ejpam-3931	37	12	even	even	ADV
ejpam-3931	37	13	earlier	early	ADV
ejpam-3931	37	14	,	,	PUNCT
ejpam-3931	37	15	by	by	ADP
ejpam-3931	37	16	e.w	e.w	PROPN
ejpam-3931	37	17	.	.	PROPN
ejpam-3931	37	18	chittenden	chittenden	PROPN
ejpam-3931	38	1	[	[	X
ejpam-3931	38	2	on	on	ADP
ejpam-3931	38	3	general	general	ADJ
ejpam-3931	38	4	topology	topology	NOUN
ejpam-3931	38	5	and	and	CCONJ
ejpam-3931	38	6	the	the	DET
ejpam-3931	38	7	relation	relation	NOUN
ejpam-3931	38	8	of	of	ADP
ejpam-3931	38	9	the	the	DET
ejpam-3931	38	10	properties	property	NOUN
ejpam-3931	38	11	of	of	ADP
ejpam-3931	38	12	the	the	DET
ejpam-3931	38	13	class	class	NOUN
ejpam-3931	38	14	of	of	ADP
ejpam-3931	38	15	all	all	DET
ejpam-3931	38	16	continuous	continuous	ADJ
ejpam-3931	38	17	functions	function	NOUN
ejpam-3931	38	18	to	to	ADP
ejpam-3931	38	19	the	the	DET
ejpam-3931	38	20	properties	property	NOUN
ejpam-3931	38	21	of	of	ADP
ejpam-3931	38	22	space	space	NOUN
ejpam-3931	38	23	.	.	PUNCT
ejpam-3931	39	1	trans	trans	PROPN
ejpam-3931	39	2	.	.	PUNCT
ejpam-3931	40	1	amer	amer	PROPN
ejpam-3931	40	2	.	.	PUNCT
ejpam-3931	40	3	math	math	PROPN
ejpam-3931	40	4	.	.	PUNCT
ejpam-3931	41	1	soc	soc	PROPN
ejpam-3931	41	2	.	.	PUNCT
ejpam-3931	42	1	31	31	NUM
ejpam-3931	42	2	,	,	PUNCT
ejpam-3931	42	3	no	no	INTJ
ejpam-3931	42	4	.	.	NOUN
ejpam-3931	42	5	2	2	NUM
ejpam-3931	42	6	(	(	PUNCT
ejpam-3931	42	7	1929	1929	NUM
ejpam-3931	42	8	)	)	PUNCT
ejpam-3931	42	9	,	,	PUNCT
ejpam-3931	42	10	290–321	290–321	NUM
ejpam-3931	42	11	;	;	PUNCT
ejpam-3931	42	12	mr1501484	mr1501484	NOUN
ejpam-3931	42	13	]	]	PUNCT
ejpam-3931	42	14	and	and	CCONJ
ejpam-3931	42	15	h.	h.	PROPN
ejpam-3931	42	16	terasaka	terasaka	PROPN
ejpam-3931	43	1	[	[	X
ejpam-3931	43	2	die	die	VERB
ejpam-3931	43	3	theorie	theorie	PROPN
ejpam-3931	43	4	der	der	NOUN
ejpam-3931	43	5	topologischen	topologischen	ADV
ejpam-3931	43	6	verbände	verbände	NOUN
ejpam-3931	43	7	.	.	PUNCT
ejpam-3931	44	1	coll	coll	PROPN
ejpam-3931	44	2	.	.	PUNCT
ejpam-3931	45	1	papers	papers	PROPN
ejpam-3931	45	2	fac	fac	PROPN
ejpam-3931	45	3	.	.	PUNCT
ejpam-3931	46	1	sci	sci	PROPN
ejpam-3931	46	2	.	.	PUNCT
ejpam-3931	46	3	osaka	osaka	PROPN
ejpam-3931	46	4	univ	univ	PROPN
ejpam-3931	46	5	.	.	PUNCT
ejpam-3931	47	1	ser	ser	PROPN
ejpam-3931	47	2	.	.	PUNCT
ejpam-3931	48	1	a	a	DET
ejpam-3931	48	2	8	8	NUM
ejpam-3931	48	3	,	,	PUNCT
ejpam-3931	48	4	no	no	INTJ
ejpam-3931	48	5	.	.	NOUN
ejpam-3931	48	6	1	1	NUM
ejpam-3931	48	7	(	(	PUNCT
ejpam-3931	48	8	1940	1940	NUM
ejpam-3931	48	9	)	)	PUNCT
ejpam-3931	48	10	,	,	PUNCT
ejpam-3931	48	11	33	33	NUM
ejpam-3931	48	12	pp	pp	NOUN
ejpam-3931	48	13	.	.	PUNCT
ejpam-3931	48	14	;	;	PUNCT
ejpam-3931	48	15	mr0032581	mr0032581	PROPN
ejpam-3931	48	16	]	]	PUNCT
ejpam-3931	48	17	.	.	PUNCT
ejpam-3931	49	1	the	the	DET
ejpam-3931	49	2	following	follow	VERB
ejpam-3931	49	3	definitions	definition	NOUN
ejpam-3931	49	4	are	be	AUX
ejpam-3931	49	5	well	well	ADV
ejpam-3931	49	6	known	know	VERB
ejpam-3931	49	7	:	:	PUNCT
ejpam-3931	49	8	if	if	SCONJ
ejpam-3931	49	9	s	s	NOUN
ejpam-3931	49	10	is	be	AUX
ejpam-3931	49	11	a	a	DET
ejpam-3931	49	12	semigroup	semigroup	NOUN
ejpam-3931	49	13	,	,	PUNCT
ejpam-3931	49	14	a	a	DET
ejpam-3931	49	15	nonempty	nonempty	NOUN
ejpam-3931	49	16	subset	subset	VERB
ejpam-3931	49	17	a	a	PRON
ejpam-3931	49	18	of	of	ADP
ejpam-3931	49	19	s	s	PRON
ejpam-3931	49	20	is	be	AUX
ejpam-3931	49	21	called	call	VERB
ejpam-3931	49	22	a	a	DET
ejpam-3931	49	23	right	right	NOUN
ejpam-3931	49	24	(	(	PUNCT
ejpam-3931	49	25	resp	resp	NOUN
ejpam-3931	49	26	.	.	PUNCT
ejpam-3931	50	1	left	left	ADJ
ejpam-3931	50	2	)	)	PUNCT
ejpam-3931	50	3	ideal	ideal	NOUN
ejpam-3931	50	4	of	of	ADP
ejpam-3931	50	5	s	s	PRON
ejpam-3931	50	6	if	if	SCONJ
ejpam-3931	50	7	as	as	ADP
ejpam-3931	50	8	⊆	⊆	NUM
ejpam-3931	50	9	a	a	DET
ejpam-3931	50	10	(	(	PUNCT
ejpam-3931	50	11	resp	resp	NOUN
ejpam-3931	50	12	.	.	PUNCT
ejpam-3931	51	1	sa	sa	PROPN
ejpam-3931	51	2	⊆	⊆	NUM
ejpam-3931	51	3	a	a	PRON
ejpam-3931	51	4	)	)	PUNCT
ejpam-3931	51	5	.	.	PUNCT
ejpam-3931	52	1	it	it	PRON
ejpam-3931	52	2	is	be	AUX
ejpam-3931	52	3	called	call	VERB
ejpam-3931	52	4	a	a	DET
ejpam-3931	52	5	bi	bi	NOUN
ejpam-3931	52	6	-	-	NOUN
ejpam-3931	52	7	ideal	ideal	NOUN
ejpam-3931	52	8	of	of	ADP
ejpam-3931	52	9	s	s	PROPN
ejpam-3931	52	10	is	be	AUX
ejpam-3931	52	11	asa	asa	PROPN
ejpam-3931	52	12	⊆	⊆	NUM
ejpam-3931	52	13	a	a	DET
ejpam-3931	52	14	(	(	PUNCT
ejpam-3931	52	15	kehayopulu	kehayopulu	PROPN
ejpam-3931	52	16	)	)	PUNCT
ejpam-3931	52	17	;	;	PUNCT
ejpam-3931	52	18	and	and	CCONJ
ejpam-3931	52	19	quasi	quasi	NOUN
ejpam-3931	52	20	-	-	NOUN
ejpam-3931	52	21	ideal	ideal	NOUN
ejpam-3931	52	22	of	of	ADP
ejpam-3931	52	23	s	s	PRON
ejpam-3931	52	24	if	if	SCONJ
ejpam-3931	52	25	as	as	SCONJ
ejpam-3931	52	26	∩sa	∩sa	NOUN
ejpam-3931	52	27	⊆	⊆	NUM
ejpam-3931	52	28	a.	a.	NOUN
ejpam-3931	52	29	s.	s.	PROPN
ejpam-3931	52	30	lajos	lajos	PROPN
ejpam-3931	52	31	considered	consider	VERB
ejpam-3931	52	32	the	the	DET
ejpam-3931	52	33	bi	bi	NOUN
ejpam-3931	52	34	-	-	NOUN
ejpam-3931	52	35	ideal	ideal	NOUN
ejpam-3931	52	36	of	of	ADP
ejpam-3931	52	37	a	a	DET
ejpam-3931	52	38	semigroup	semigroup	NOUN
ejpam-3931	52	39	s	s	PRON
ejpam-3931	52	40	as	as	ADP
ejpam-3931	52	41	a	a	DET
ejpam-3931	52	42	subsemigroup	subsemigroup	NOUN
ejpam-3931	52	43	of	of	ADP
ejpam-3931	52	44	s	s	PRON
ejpam-3931	52	45	except	except	SCONJ
ejpam-3931	52	46	in	in	ADP
ejpam-3931	52	47	his	his	PRON
ejpam-3931	52	48	last	last	ADJ
ejpam-3931	52	49	publications	publication	NOUN
ejpam-3931	52	50	in	in	ADP
ejpam-3931	52	51	which	which	PRON
ejpam-3931	52	52	he	he	PRON
ejpam-3931	52	53	used	use	VERB
ejpam-3931	52	54	the	the	DET
ejpam-3931	52	55	definition	definition	NOUN
ejpam-3931	52	56	given	give	VERB
ejpam-3931	52	57	above	above	ADV
ejpam-3931	52	58	.	.	PUNCT
ejpam-3931	53	1	it	it	PRON
ejpam-3931	53	2	might	might	AUX
ejpam-3931	53	3	be	be	AUX
ejpam-3931	53	4	mentioned	mention	VERB
ejpam-3931	53	5	that	that	SCONJ
ejpam-3931	53	6	most	most	ADJ
ejpam-3931	53	7	of	of	ADP
ejpam-3931	53	8	the	the	DET
ejpam-3931	53	9	results	result	NOUN
ejpam-3931	53	10	hold	hold	VERB
ejpam-3931	53	11	without	without	ADP
ejpam-3931	53	12	the	the	DET
ejpam-3931	53	13	assumption	assumption	NOUN
ejpam-3931	53	14	that	that	SCONJ
ejpam-3931	53	15	the	the	DET
ejpam-3931	53	16	bi	bi	NOUN
ejpam-3931	53	17	-	-	NOUN
ejpam-3931	53	18	ideal	ideal	NOUN
ejpam-3931	53	19	is	be	AUX
ejpam-3931	53	20	a	a	DET
ejpam-3931	53	21	subsemigroup	subsemigroup	NOUN
ejpam-3931	53	22	;	;	PUNCT
ejpam-3931	53	23	as	as	SCONJ
ejpam-3931	53	24	so	so	ADV
ejpam-3931	53	25	we	we	PRON
ejpam-3931	53	26	do	do	AUX
ejpam-3931	53	27	not	not	PART
ejpam-3931	53	28	have	have	VERB
ejpam-3931	53	29	to	to	PART
ejpam-3931	53	30	use	use	VERB
ejpam-3931	53	31	the	the	DET
ejpam-3931	53	32	term	term	NOUN
ejpam-3931	53	33	“	"	PUNCT
ejpam-3931	53	34	generalized	generalized	ADJ
ejpam-3931	53	35	biideal	biideal	NOUN
ejpam-3931	53	36	”	"	PUNCT
ejpam-3931	53	37	so	so	ADV
ejpam-3931	53	38	often	often	ADV
ejpam-3931	53	39	.	.	PUNCT
ejpam-3931	54	1	a	a	DET
ejpam-3931	54	2	poe	poe	PROPN
ejpam-3931	54	3	-	-	PUNCT
ejpam-3931	54	4	groupoid	groupoid	PROPN
ejpam-3931	54	5	is	be	AUX
ejpam-3931	54	6	a	a	DET
ejpam-3931	54	7	groupoid	groupoid	PROPN
ejpam-3931	54	8	s	s	NOUN
ejpam-3931	54	9	at	at	ADP
ejpam-3931	54	10	the	the	DET
ejpam-3931	54	11	same	same	ADJ
ejpam-3931	54	12	time	time	NOUN
ejpam-3931	54	13	an	an	DET
ejpam-3931	54	14	ordered	order	VERB
ejpam-3931	54	15	set	set	NOUN
ejpam-3931	54	16	having	have	VERB
ejpam-3931	54	17	a	a	DET
ejpam-3931	54	18	greatest	great	ADJ
ejpam-3931	54	19	element	element	NOUN
ejpam-3931	54	20	“	"	PUNCT
ejpam-3931	54	21	e	e	NOUN
ejpam-3931	54	22	”	"	PUNCT
ejpam-3931	54	23	(:	(:	PROPN
ejpam-3931	54	24	e	e	NOUN
ejpam-3931	54	25	≥	≥	NOUN
ejpam-3931	54	26	a	a	PRON
ejpam-3931	54	27	for	for	ADP
ejpam-3931	54	28	every	every	DET
ejpam-3931	54	29	a	a	DET
ejpam-3931	54	30	∈	∈	PROPN
ejpam-3931	54	31	s	s	NOUN
ejpam-3931	54	32	)	)	PUNCT
ejpam-3931	54	33	such	such	ADJ
ejpam-3931	54	34	that	that	SCONJ
ejpam-3931	54	35	a	a	DET
ejpam-3931	54	36	≤	≤	PROPN
ejpam-3931	54	37	b	b	NOUN
ejpam-3931	54	38	implies	imply	VERB
ejpam-3931	54	39	ac	ac	PROPN
ejpam-3931	54	40	≤	≤	PUNCT
ejpam-3931	54	41	bc	bc	PROPN
ejpam-3931	54	42	and	and	CCONJ
ejpam-3931	54	43	ca	can	AUX
ejpam-3931	54	44	≤	≤	NUM
ejpam-3931	54	45	cb	cb	X
ejpam-3931	54	46	for	for	ADP
ejpam-3931	54	47	every	every	DET
ejpam-3931	54	48	c	c	PROPN
ejpam-3931	54	49	∈	∈	PROPN
ejpam-3931	54	50	s.	s.	PROPN
ejpam-3931	54	51	if	if	SCONJ
ejpam-3931	54	52	the	the	DET
ejpam-3931	54	53	multiplication	multiplication	NOUN
ejpam-3931	54	54	on	on	ADP
ejpam-3931	54	55	s	s	NOUN
ejpam-3931	54	56	is	be	AUX
ejpam-3931	54	57	associative	associative	ADJ
ejpam-3931	54	58	,	,	PUNCT
ejpam-3931	54	59	then	then	ADV
ejpam-3931	54	60	s	s	VERB
ejpam-3931	54	61	is	be	AUX
ejpam-3931	54	62	called	call	VERB
ejpam-3931	54	63	poe	poe	PROPN
ejpam-3931	54	64	-	-	PUNCT
ejpam-3931	54	65	semigroup	semigroup	PROPN
ejpam-3931	54	66	.	.	PUNCT
ejpam-3931	55	1	an	an	DET
ejpam-3931	55	2	le	le	PROPN
ejpam-3931	55	3	-	-	PUNCT
ejpam-3931	55	4	semigroup	semigroup	PROPN
ejpam-3931	55	5	is	be	AUX
ejpam-3931	55	6	a	a	DET
ejpam-3931	55	7	semigroup	semigroup	NOUN
ejpam-3931	55	8	s	s	NOUN
ejpam-3931	55	9	at	at	ADP
ejpam-3931	55	10	the	the	DET
ejpam-3931	55	11	same	same	ADJ
ejpam-3931	55	12	time	time	NOUN
ejpam-3931	55	13	a	a	DET
ejpam-3931	55	14	lattice	lattice	NOUN
ejpam-3931	55	15	having	have	VERB
ejpam-3931	55	16	a	a	DET
ejpam-3931	55	17	greatest	great	ADJ
ejpam-3931	55	18	element	element	NOUN
ejpam-3931	55	19	e	e	NOUN
ejpam-3931	55	20	(	(	PUNCT
ejpam-3931	55	21	with	with	ADP
ejpam-3931	55	22	respect	respect	NOUN
ejpam-3931	55	23	to	to	ADP
ejpam-3931	55	24	the	the	DET
ejpam-3931	55	25	order	order	NOUN
ejpam-3931	55	26	)	)	PUNCT
ejpam-3931	55	27	such	such	ADJ
ejpam-3931	55	28	that	that	SCONJ
ejpam-3931	55	29	a(b	a(b	PROPN
ejpam-3931	55	30	∨	∨	NUM
ejpam-3931	55	31	c	c	NOUN
ejpam-3931	55	32	)	)	PUNCT
ejpam-3931	55	33	=	=	SYM
ejpam-3931	55	34	ab	ab	PROPN
ejpam-3931	55	35	∨	∨	NUM
ejpam-3931	55	36	ac	ac	PROPN
ejpam-3931	55	37	and	and	CCONJ
ejpam-3931	55	38	(	(	PUNCT
ejpam-3931	55	39	a	a	DET
ejpam-3931	55	40	∨	∨	NOUN
ejpam-3931	55	41	b)c	b)c	X
ejpam-3931	55	42	=	=	PRON
ejpam-3931	55	43	ac	ac	PROPN
ejpam-3931	55	44	∨	∨	PROPN
ejpam-3931	55	45	bc	bc	PROPN
ejpam-3931	55	46	for	for	ADP
ejpam-3931	55	47	every	every	DET
ejpam-3931	55	48	a	a	PROPN
ejpam-3931	55	49	,	,	PUNCT
ejpam-3931	55	50	b	b	NOUN
ejpam-3931	55	51	,	,	PUNCT
ejpam-3931	55	52	c	c	PROPN
ejpam-3931	55	53	∈	∈	PROPN
ejpam-3931	55	54	s.	s.	PROPN
ejpam-3931	55	55	every	every	DET
ejpam-3931	55	56	le	le	PROPN
ejpam-3931	55	57	-	-	PUNCT
ejpam-3931	55	58	semigroup	semigroup	PROPN
ejpam-3931	55	59	is	be	AUX
ejpam-3931	55	60	a	a	DET
ejpam-3931	55	61	poe	poe	PROPN
ejpam-3931	55	62	-	-	PUNCT
ejpam-3931	55	63	semigroup	semigroup	PROPN
ejpam-3931	55	64	.	.	PUNCT
ejpam-3931	56	1	a	a	DET
ejpam-3931	56	2	∧e	∧e	PROPN
ejpam-3931	56	3	-	-	PUNCT
ejpam-3931	56	4	groupoid	groupoid	PROPN
ejpam-3931	56	5	is	be	AUX
ejpam-3931	56	6	a	a	DET
ejpam-3931	56	7	groupoid	groupoid	PROPN
ejpam-3931	56	8	s	s	NOUN
ejpam-3931	56	9	at	at	ADP
ejpam-3931	56	10	the	the	DET
ejpam-3931	56	11	same	same	ADJ
ejpam-3931	56	12	time	time	NOUN
ejpam-3931	56	13	a	a	DET
ejpam-3931	56	14	semilattice	semilattice	NOUN
ejpam-3931	56	15	under	under	ADP
ejpam-3931	56	16	∧	∧	PROPN
ejpam-3931	56	17	(:	(:	NOUN
ejpam-3931	56	18	∧-semilattice	∧-semilattice	NOUN
ejpam-3931	56	19	)	)	PUNCT
ejpam-3931	56	20	having	have	VERB
ejpam-3931	56	21	a	a	DET
ejpam-3931	56	22	greatest	great	ADJ
ejpam-3931	56	23	element	element	NOUN
ejpam-3931	56	24	“	"	PUNCT
ejpam-3931	56	25	e	e	NOUN
ejpam-3931	56	26	”	"	PUNCT
ejpam-3931	56	27	such	such	ADJ
ejpam-3931	56	28	that	that	SCONJ
ejpam-3931	56	29	a	a	DET
ejpam-3931	56	30	≤	≤	PROPN
ejpam-3931	56	31	b	b	NOUN
ejpam-3931	56	32	implies	imply	VERB
ejpam-3931	56	33	ac	ac	PROPN
ejpam-3931	56	34	≤	≤	PUNCT
ejpam-3931	56	35	bc	bc	PROPN
ejpam-3931	56	36	and	and	CCONJ
ejpam-3931	56	37	ca	can	AUX
ejpam-3931	56	38	≤	≤	NUM
ejpam-3931	56	39	cb	cb	X
ejpam-3931	56	40	for	for	ADP
ejpam-3931	56	41	every	every	DET
ejpam-3931	56	42	c	c	PROPN
ejpam-3931	56	43	∈	∈	PROPN
ejpam-3931	56	44	s	s	PART
ejpam-3931	56	45	;	;	PUNCT
ejpam-3931	56	46	if	if	SCONJ
ejpam-3931	56	47	its	its	PRON
ejpam-3931	56	48	multiplication	multiplication	NOUN
ejpam-3931	56	49	is	be	AUX
ejpam-3931	56	50	associative	associative	ADJ
ejpam-3931	56	51	,	,	PUNCT
ejpam-3931	56	52	then	then	ADV
ejpam-3931	56	53	it	it	PRON
ejpam-3931	56	54	is	be	AUX
ejpam-3931	56	55	called	call	VERB
ejpam-3931	56	56	∧e	∧e	PROPN
ejpam-3931	56	57	-	-	PUNCT
ejpam-3931	56	58	semigroup	semigroup	NOUN
ejpam-3931	56	59	.	.	PUNCT
ejpam-3931	57	1	let	let	VERB
ejpam-3931	57	2	s	s	PRON
ejpam-3931	57	3	be	be	AUX
ejpam-3931	57	4	a	a	DET
ejpam-3931	57	5	poe	poe	PROPN
ejpam-3931	57	6	-	-	NOUN
ejpam-3931	57	7	groupoid	groupoid	PROPN
ejpam-3931	57	8	.	.	PUNCT
ejpam-3931	58	1	an	an	DET
ejpam-3931	58	2	element	element	NOUN
ejpam-3931	58	3	a	a	PRON
ejpam-3931	58	4	of	of	ADP
ejpam-3931	58	5	s	s	PRON
ejpam-3931	58	6	is	be	AUX
ejpam-3931	58	7	called	call	VERB
ejpam-3931	58	8	right	right	ADJ
ejpam-3931	58	9	(	(	PUNCT
ejpam-3931	58	10	left	left	ADJ
ejpam-3931	58	11	)	)	PUNCT
ejpam-3931	58	12	ideal	ideal	ADJ
ejpam-3931	58	13	element	element	NOUN
ejpam-3931	58	14	of	of	ADP
ejpam-3931	58	15	s	s	PRON
ejpam-3931	58	16	if	if	SCONJ
ejpam-3931	58	17	ae	ae	PROPN
ejpam-3931	58	18	≤	≤	VERB
ejpam-3931	58	19	a	a	DET
ejpam-3931	58	20	(	(	PUNCT
ejpam-3931	58	21	resp	resp	NOUN
ejpam-3931	58	22	.	.	PUNCT
ejpam-3931	59	1	ea	ea	NOUN
ejpam-3931	59	2	≤	≤	NUM
ejpam-3931	59	3	a	a	PRON
ejpam-3931	59	4	)	)	PUNCT
ejpam-3931	59	5	.	.	PUNCT
ejpam-3931	60	1	an	an	DET
ejpam-3931	60	2	element	element	NOUN
ejpam-3931	60	3	that	that	PRON
ejpam-3931	60	4	is	be	AUX
ejpam-3931	60	5	both	both	CCONJ
ejpam-3931	60	6	a	a	DET
ejpam-3931	60	7	right	right	NOUN
ejpam-3931	60	8	and	and	CCONJ
ejpam-3931	60	9	a	a	DET
ejpam-3931	60	10	left	left	ADJ
ejpam-3931	60	11	ideal	ideal	ADJ
ejpam-3931	60	12	element	element	NOUN
ejpam-3931	60	13	is	be	AUX
ejpam-3931	60	14	called	call	VERB
ejpam-3931	60	15	ideal	ideal	ADJ
ejpam-3931	60	16	element	element	NOUN
ejpam-3931	60	17	.	.	PUNCT
ejpam-3931	61	1	if	if	SCONJ
ejpam-3931	61	2	s	s	PROPN
ejpam-3931	61	3	is	be	AUX
ejpam-3931	61	4	a	a	DET
ejpam-3931	61	5	∧e	∧e	PROPN
ejpam-3931	61	6	-	-	PUNCT
ejpam-3931	61	7	groupoid	groupoid	NOUN
ejpam-3931	61	8	,	,	PUNCT
ejpam-3931	61	9	then	then	ADV
ejpam-3931	61	10	an	an	DET
ejpam-3931	61	11	element	element	NOUN
ejpam-3931	61	12	a	a	PRON
ejpam-3931	61	13	of	of	ADP
ejpam-3931	61	14	s	s	PRON
ejpam-3931	61	15	called	call	VERB
ejpam-3931	61	16	a	a	DET
ejpam-3931	61	17	quasi	quasi	ADJ
ejpam-3931	61	18	-	-	ADJ
ejpam-3931	61	19	ideal	ideal	ADJ
ejpam-3931	61	20	element	element	NOUN
ejpam-3931	61	21	if	if	SCONJ
ejpam-3931	61	22	ae	ae	PROPN
ejpam-3931	61	23	∧	∧	PROPN
ejpam-3931	61	24	ea	ea	PROPN
ejpam-3931	61	25	≤	≤	NUM
ejpam-3931	61	26	a.	a.	NOUN
ejpam-3931	61	27	an	an	DET
ejpam-3931	61	28	element	element	NOUN
ejpam-3931	61	29	a	a	PRON
ejpam-3931	61	30	of	of	ADP
ejpam-3931	61	31	a	a	DET
ejpam-3931	61	32	poe	poe	PROPN
ejpam-3931	61	33	-	-	PUNCT
ejpam-3931	61	34	semigroup	semigroup	PROPN
ejpam-3931	61	35	is	be	AUX
ejpam-3931	61	36	called	call	VERB
ejpam-3931	61	37	a	a	DET
ejpam-3931	61	38	bi	bi	ADJ
ejpam-3931	61	39	-	-	ADJ
ejpam-3931	61	40	ideal	ideal	ADJ
ejpam-3931	61	41	element	element	NOUN
ejpam-3931	61	42	if	if	SCONJ
ejpam-3931	61	43	aea	aea	PROPN
ejpam-3931	61	44	≤	≤	PROPN
ejpam-3931	61	45	a	a	PRON
ejpam-3931	61	46	and	and	CCONJ
ejpam-3931	61	47	an	an	DET
ejpam-3931	61	48	interior	interior	ADJ
ejpam-3931	61	49	ideal	ideal	NOUN
ejpam-3931	61	50	element	element	NOUN
ejpam-3931	61	51	if	if	SCONJ
ejpam-3931	61	52	eae	eae	PROPN
ejpam-3931	61	53	≤	≤	PROPN
ejpam-3931	61	54	a.	a.	NOUN
ejpam-3931	61	55	denote	denote	NOUN
ejpam-3931	61	56	by	by	ADP
ejpam-3931	61	57	r(a	r(a	PROPN
ejpam-3931	61	58	)	)	PUNCT
ejpam-3931	61	59	(	(	PUNCT
ejpam-3931	61	60	resp	resp	NOUN
ejpam-3931	61	61	.	.	PUNCT
ejpam-3931	61	62	l(a	l(a	PROPN
ejpam-3931	61	63	)	)	PUNCT
ejpam-3931	61	64	)	)	PUNCT
ejpam-3931	62	1	the	the	DET
ejpam-3931	62	2	right	right	NOUN
ejpam-3931	62	3	(	(	PUNCT
ejpam-3931	62	4	resp	resp	NOUN
ejpam-3931	62	5	.	.	PUNCT
ejpam-3931	63	1	left	left	ADJ
ejpam-3931	63	2	)	)	PUNCT
ejpam-3931	63	3	ideal	ideal	NOUN
ejpam-3931	63	4	of	of	ADP
ejpam-3931	63	5	s	s	AUX
ejpam-3931	63	6	generated	generate	VERB
ejpam-3931	63	7	by	by	ADP
ejpam-3931	63	8	a.	a.	NOUN
ejpam-3931	63	9	for	for	ADP
ejpam-3931	63	10	an	an	DET
ejpam-3931	63	11	le	le	X
ejpam-3931	63	12	-	-	NOUN
ejpam-3931	63	13	semigroup	semigroup	PROPN
ejpam-3931	63	14	s	s	PART
ejpam-3931	63	15	,	,	PUNCT
ejpam-3931	63	16	we	we	PRON
ejpam-3931	63	17	have	have	AUX
ejpam-3931	63	18	r(a	r(a	VERB
ejpam-3931	63	19	)	)	PUNCT
ejpam-3931	63	20	=	=	PUNCT
ejpam-3931	63	21	a	a	DET
ejpam-3931	63	22	∨	∨	NUM
ejpam-3931	63	23	ae	ae	PROPN
ejpam-3931	63	24	and	and	CCONJ
ejpam-3931	63	25	l(a	l(a	PROPN
ejpam-3931	63	26	)	)	PUNCT
ejpam-3931	63	27	=	=	PUNCT
ejpam-3931	63	28	a	a	DET
ejpam-3931	63	29	∨	∨	NUM
ejpam-3931	63	30	ea	ea	NOUN
ejpam-3931	63	31	.	.	PUNCT
ejpam-3931	64	1	an	an	DET
ejpam-3931	64	2	element	element	NOUN
ejpam-3931	64	3	a	a	PRON
ejpam-3931	64	4	of	of	ADP
ejpam-3931	64	5	a	a	DET
ejpam-3931	64	6	poe	poe	PROPN
ejpam-3931	64	7	-	-	PUNCT
ejpam-3931	64	8	groupoid	groupoid	PROPN
ejpam-3931	64	9	is	be	AUX
ejpam-3931	64	10	called	call	VERB
ejpam-3931	64	11	subidempotent	subidempotent	NOUN
ejpam-3931	64	12	if	if	SCONJ
ejpam-3931	64	13	a2	a2	PROPN
ejpam-3931	64	14	≤	≤	PROPN
ejpam-3931	64	15	a	a	PRON
ejpam-3931	64	16	;	;	PUNCT
ejpam-3931	64	17	it	it	PRON
ejpam-3931	64	18	is	be	AUX
ejpam-3931	64	19	called	call	VERB
ejpam-3931	64	20	idempotent	idempotent	ADJ
ejpam-3931	64	21	if	if	SCONJ
ejpam-3931	64	22	a2	a2	PROPN
ejpam-3931	64	23	=	=	PUNCT
ejpam-3931	64	24	a	a	PRON
ejpam-3931	64	25	[	[	X
ejpam-3931	64	26	1	1	NUM
ejpam-3931	64	27	]	]	PUNCT
ejpam-3931	64	28	.	.	PUNCT
ejpam-3931	65	1	an	an	DET
ejpam-3931	65	2	element	element	NOUN
ejpam-3931	65	3	e′	e′	PROPN
ejpam-3931	65	4	of	of	ADP
ejpam-3931	65	5	a	a	DET
ejpam-3931	65	6	poe	poe	PROPN
ejpam-3931	65	7	-	-	PROPN
ejpam-3931	65	8	groupoid	groupoid	PROPN
ejpam-3931	65	9	s	s	PART
ejpam-3931	65	10	is	be	AUX
ejpam-3931	65	11	called	call	VERB
ejpam-3931	65	12	an	an	DET
ejpam-3931	65	13	identity	identity	NOUN
ejpam-3931	65	14	(	(	PUNCT
ejpam-3931	65	15	or	or	CCONJ
ejpam-3931	65	16	unity	unity	NOUN
ejpam-3931	65	17	)	)	PUNCT
ejpam-3931	65	18	of	of	ADP
ejpam-3931	65	19	s	s	PROPN
ejpam-3931	65	20	is	be	AUX
ejpam-3931	66	1	ae′	ae′	NUM
ejpam-3931	66	2	=	=	SYM
ejpam-3931	66	3	e′a	e′a	PROPN
ejpam-3931	66	4	=	=	PUNCT
ejpam-3931	66	5	a	a	PRON
ejpam-3931	66	6	for	for	ADP
ejpam-3931	66	7	every	every	DET
ejpam-3931	66	8	a	a	DET
ejpam-3931	66	9	∈	∈	PROPN
ejpam-3931	66	10	s.	s.	NOUN
ejpam-3931	66	11	the	the	DET
ejpam-3931	66	12	study	study	NOUN
ejpam-3931	66	13	of	of	ADP
ejpam-3931	66	14	poe	poe	PROPN
ejpam-3931	66	15	-	-	PUNCT
ejpam-3931	66	16	semigroups	semigroups	PROPN
ejpam-3931	66	17	plays	play	VERB
ejpam-3931	66	18	an	an	DET
ejpam-3931	66	19	essential	essential	ADJ
ejpam-3931	66	20	role	role	NOUN
ejpam-3931	66	21	in	in	ADP
ejpam-3931	66	22	the	the	DET
ejpam-3931	66	23	theory	theory	NOUN
ejpam-3931	66	24	of	of	ADP
ejpam-3931	66	25	ordered	order	VERB
ejpam-3931	66	26	γ	γ	NOUN
ejpam-3931	66	27	-	-	PUNCT
ejpam-3931	66	28	hypersemigroups	hypersemigroup	NOUN
ejpam-3931	66	29	and	and	CCONJ
ejpam-3931	66	30	related	relate	VERB
ejpam-3931	66	31	simpler	simple	ADJ
ejpam-3931	66	32	structures	structure	NOUN
ejpam-3931	66	33	,	,	PUNCT
ejpam-3931	66	34	like	like	ADP
ejpam-3931	66	35	the	the	DET
ejpam-3931	66	36	hypersemigroups	hypersemigroup	NOUN
ejpam-3931	66	37	,	,	PUNCT
ejpam-3931	66	38	for	for	ADP
ejpam-3931	66	39	example	example	NOUN
ejpam-3931	66	40	.	.	PUNCT
ejpam-3931	67	1	2	2	X
ejpam-3931	67	2	.	.	X
ejpam-3931	67	3	bi	bi	ADJ
ejpam-3931	67	4	-	-	ADJ
ejpam-3931	67	5	interior	interior	ADJ
ejpam-3931	67	6	ideal	ideal	ADJ
ejpam-3931	67	7	elements	element	NOUN
ejpam-3931	67	8	in	in	ADP
ejpam-3931	67	9	∧e	∧e	NOUN
ejpam-3931	67	10	-	-	PUNCT
ejpam-3931	67	11	semigroups	semigroup	NOUN
ejpam-3931	67	12	proposition	proposition	NOUN
ejpam-3931	67	13	2.1	2.1	NUM
ejpam-3931	67	14	.	.	PUNCT
ejpam-3931	68	1	if	if	SCONJ
ejpam-3931	68	2	s	s	PROPN
ejpam-3931	68	3	is	be	AUX
ejpam-3931	68	4	a	a	DET
ejpam-3931	68	5	∧e	∧e	PROPN
ejpam-3931	68	6	-	-	PUNCT
ejpam-3931	68	7	groupoid	groupoid	NOUN
ejpam-3931	68	8	,	,	PUNCT
ejpam-3931	68	9	then	then	ADV
ejpam-3931	68	10	every	every	DET
ejpam-3931	68	11	right	right	NOUN
ejpam-3931	68	12	(	(	PUNCT
ejpam-3931	68	13	resp	resp	NOUN
ejpam-3931	68	14	.	.	PUNCT
ejpam-3931	69	1	left	left	ADJ
ejpam-3931	69	2	)	)	PUNCT
ejpam-3931	69	3	ideal	ideal	ADJ
ejpam-3931	69	4	element	element	NOUN
ejpam-3931	69	5	of	of	ADP
ejpam-3931	69	6	s	s	PROPN
ejpam-3931	69	7	is	be	AUX
ejpam-3931	69	8	a	a	DET
ejpam-3931	69	9	quasi	quasi	ADJ
ejpam-3931	69	10	-	-	ADJ
ejpam-3931	69	11	ideal	ideal	ADJ
ejpam-3931	69	12	element	element	NOUN
ejpam-3931	69	13	of	of	ADP
ejpam-3931	69	14	s.	s.	PROPN
ejpam-3931	69	15	if	if	SCONJ
ejpam-3931	69	16	s	s	PROPN
ejpam-3931	69	17	is	be	AUX
ejpam-3931	69	18	a	a	DET
ejpam-3931	69	19	∧e	∧e	PROPN
ejpam-3931	69	20	-	-	PUNCT
ejpam-3931	69	21	semigroup	semigroup	NOUN
ejpam-3931	69	22	,	,	PUNCT
ejpam-3931	69	23	then	then	ADV
ejpam-3931	69	24	every	every	DET
ejpam-3931	69	25	quasi	quasi	ADJ
ejpam-3931	69	26	-	-	ADJ
ejpam-3931	69	27	ideal	ideal	ADJ
ejpam-3931	69	28	element	element	NOUN
ejpam-3931	69	29	of	of	ADP
ejpam-3931	69	30	s	s	PROPN
ejpam-3931	69	31	is	be	AUX
ejpam-3931	69	32	a	a	DET
ejpam-3931	69	33	bi	bi	ADJ
ejpam-3931	69	34	-	-	ADJ
ejpam-3931	69	35	ideal	ideal	ADJ
ejpam-3931	69	36	element	element	NOUN
ejpam-3931	69	37	of	of	ADP
ejpam-3931	69	38	s.	s.	PROPN
ejpam-3931	69	39	proof	proof	PROPN
ejpam-3931	69	40	.	.	PUNCT
ejpam-3931	70	1	let	let	VERB
ejpam-3931	70	2	a	a	PRON
ejpam-3931	70	3	be	be	AUX
ejpam-3931	70	4	a	a	DET
ejpam-3931	70	5	right	right	ADJ
ejpam-3931	70	6	ideal	ideal	ADJ
ejpam-3931	70	7	element	element	NOUN
ejpam-3931	70	8	of	of	ADP
ejpam-3931	70	9	s.	s.	PROPN
ejpam-3931	70	10	then	then	ADV
ejpam-3931	71	1	ae∧ea	ae∧ea	NUM
ejpam-3931	71	2	≤	≤	PUNCT
ejpam-3931	71	3	ae	ae	PROPN
ejpam-3931	71	4	≤	≤	PROPN
ejpam-3931	71	5	a	a	PRON
ejpam-3931	72	1	and	and	CCONJ
ejpam-3931	72	2	so	so	ADV
ejpam-3931	72	3	a	a	PRON
ejpam-3931	72	4	is	be	AUX
ejpam-3931	72	5	a	a	DET
ejpam-3931	72	6	quasi	quasi	ADJ
ejpam-3931	72	7	-	-	ADJ
ejpam-3931	72	8	ideal	ideal	ADJ
ejpam-3931	72	9	n.	n.	NOUN
ejpam-3931	72	10	kehayopulu	kehayopulu	PROPN
ejpam-3931	72	11	/	/	SYM
ejpam-3931	72	12	eur	eur	PROPN
ejpam-3931	72	13	.	.	PUNCT
ejpam-3931	73	1	j.	j.	PROPN
ejpam-3931	73	2	pure	pure	PROPN
ejpam-3931	73	3	appl	appl	PROPN
ejpam-3931	73	4	.	.	PROPN
ejpam-3931	73	5	math	math	PROPN
ejpam-3931	73	6	,	,	PUNCT
ejpam-3931	73	7	14	14	NUM
ejpam-3931	73	8	(	(	PUNCT
ejpam-3931	73	9	4	4	NUM
ejpam-3931	73	10	)	)	PUNCT
ejpam-3931	73	11	(	(	PUNCT
ejpam-3931	73	12	2021	2021	NUM
ejpam-3931	73	13	)	)	PUNCT
ejpam-3931	73	14	,	,	PUNCT
ejpam-3931	73	15	43	43	NUM
ejpam-3931	73	16	-	-	SYM
ejpam-3931	73	17	52	52	NUM
ejpam-3931	73	18	45	45	NUM
ejpam-3931	73	19	element	element	NOUN
ejpam-3931	73	20	of	of	ADP
ejpam-3931	73	21	s.	s.	PROPN
ejpam-3931	73	22	if	if	SCONJ
ejpam-3931	73	23	a	a	PRON
ejpam-3931	73	24	is	be	AUX
ejpam-3931	73	25	a	a	DET
ejpam-3931	73	26	quasi	quasi	ADJ
ejpam-3931	73	27	-	-	ADJ
ejpam-3931	73	28	ideal	ideal	ADJ
ejpam-3931	73	29	element	element	NOUN
ejpam-3931	73	30	of	of	ADP
ejpam-3931	73	31	s	s	PROPN
ejpam-3931	73	32	,	,	PUNCT
ejpam-3931	73	33	then	then	ADV
ejpam-3931	73	34	aea	aea	PROPN
ejpam-3931	73	35	≤	≤	PROPN
ejpam-3931	74	1	ae	ae	PROPN
ejpam-3931	74	2	∧	∧	PROPN
ejpam-3931	74	3	ea	ea	PROPN
ejpam-3931	74	4	≤	≤	NOUN
ejpam-3931	74	5	a	a	PRON
ejpam-3931	75	1	and	and	CCONJ
ejpam-3931	75	2	so	so	ADV
ejpam-3931	75	3	a	a	PRON
ejpam-3931	75	4	is	be	AUX
ejpam-3931	75	5	a	a	DET
ejpam-3931	75	6	bi	bi	ADJ
ejpam-3931	75	7	-	-	ADJ
ejpam-3931	75	8	ideal	ideal	ADJ
ejpam-3931	75	9	element	element	NOUN
ejpam-3931	75	10	of	of	ADP
ejpam-3931	75	11	s.	s.	PROPN
ejpam-3931	75	12	□	□	PUNCT
ejpam-3931	75	13	definition	definition	NOUN
ejpam-3931	75	14	2.2	2.2	NUM
ejpam-3931	75	15	.	.	PUNCT
ejpam-3931	76	1	an	an	DET
ejpam-3931	76	2	element	element	NOUN
ejpam-3931	76	3	b	b	PROPN
ejpam-3931	76	4	of	of	ADP
ejpam-3931	76	5	a	a	DET
ejpam-3931	76	6	∧e	∧e	PROPN
ejpam-3931	76	7	-	-	PUNCT
ejpam-3931	76	8	semigroup	semigroup	PROPN
ejpam-3931	76	9	s	s	VERB
ejpam-3931	76	10	is	be	AUX
ejpam-3931	76	11	called	call	VERB
ejpam-3931	76	12	a	a	DET
ejpam-3931	76	13	bi	bi	ADJ
ejpam-3931	76	14	-	-	ADJ
ejpam-3931	76	15	interior	interior	ADJ
ejpam-3931	76	16	ideal	ideal	ADJ
ejpam-3931	76	17	element	element	NOUN
ejpam-3931	76	18	if	if	SCONJ
ejpam-3931	76	19	beb	beb	PROPN
ejpam-3931	76	20	∧	∧	PROPN
ejpam-3931	76	21	ebe	ebe	PROPN
ejpam-3931	76	22	≤	≤	PROPN
ejpam-3931	76	23	b.	b.	PROPN
ejpam-3931	76	24	proposition	proposition	NOUN
ejpam-3931	76	25	2.3	2.3	NUM
ejpam-3931	76	26	.	.	PUNCT
ejpam-3931	77	1	let	let	VERB
ejpam-3931	77	2	s	s	PRON
ejpam-3931	77	3	be	be	AUX
ejpam-3931	77	4	a	a	DET
ejpam-3931	77	5	∧e	∧e	PROPN
ejpam-3931	77	6	-	-	PUNCT
ejpam-3931	77	7	semigroup	semigroup	NOUN
ejpam-3931	77	8	.	.	PUNCT
ejpam-3931	78	1	then	then	ADV
ejpam-3931	78	2	we	we	PRON
ejpam-3931	78	3	have	have	VERB
ejpam-3931	78	4	the	the	DET
ejpam-3931	78	5	following	following	NOUN
ejpam-3931	78	6	:	:	PUNCT
ejpam-3931	78	7	(	(	PUNCT
ejpam-3931	78	8	1	1	X
ejpam-3931	78	9	)	)	PUNCT
ejpam-3931	78	10	every	every	DET
ejpam-3931	78	11	right	right	NOUN
ejpam-3931	78	12	(	(	PUNCT
ejpam-3931	78	13	resp	resp	NOUN
ejpam-3931	78	14	.	.	PUNCT
ejpam-3931	79	1	left	left	ADJ
ejpam-3931	79	2	)	)	PUNCT
ejpam-3931	79	3	ideal	ideal	ADJ
ejpam-3931	79	4	element	element	NOUN
ejpam-3931	79	5	of	of	ADP
ejpam-3931	79	6	s	s	PROPN
ejpam-3931	79	7	is	be	AUX
ejpam-3931	79	8	a	a	DET
ejpam-3931	79	9	bi	bi	ADJ
ejpam-3931	79	10	-	-	ADJ
ejpam-3931	79	11	interior	interior	ADJ
ejpam-3931	79	12	ideal	ideal	ADJ
ejpam-3931	79	13	element	element	NOUN
ejpam-3931	79	14	of	of	ADP
ejpam-3931	79	15	s.	s.	PROPN
ejpam-3931	79	16	(	(	PUNCT
ejpam-3931	79	17	2	2	X
ejpam-3931	79	18	)	)	PUNCT
ejpam-3931	79	19	every	every	DET
ejpam-3931	79	20	quasi	quasi	ADJ
ejpam-3931	79	21	-	-	ADJ
ejpam-3931	79	22	ideal	ideal	ADJ
ejpam-3931	79	23	element	element	NOUN
ejpam-3931	79	24	of	of	ADP
ejpam-3931	79	25	s	s	PROPN
ejpam-3931	79	26	is	be	AUX
ejpam-3931	79	27	a	a	DET
ejpam-3931	79	28	bi	bi	ADJ
ejpam-3931	79	29	-	-	ADJ
ejpam-3931	79	30	interior	interior	ADJ
ejpam-3931	79	31	ideal	ideal	ADJ
ejpam-3931	79	32	element	element	NOUN
ejpam-3931	79	33	of	of	ADP
ejpam-3931	79	34	s.	s.	PROPN
ejpam-3931	79	35	(	(	PUNCT
ejpam-3931	79	36	3	3	X
ejpam-3931	79	37	)	)	PUNCT
ejpam-3931	79	38	every	every	DET
ejpam-3931	79	39	bi	bi	ADJ
ejpam-3931	79	40	-	-	ADJ
ejpam-3931	79	41	ideal	ideal	ADJ
ejpam-3931	79	42	element	element	NOUN
ejpam-3931	79	43	of	of	ADP
ejpam-3931	79	44	s	s	PROPN
ejpam-3931	79	45	is	be	AUX
ejpam-3931	79	46	a	a	DET
ejpam-3931	79	47	bi	bi	ADJ
ejpam-3931	79	48	-	-	ADJ
ejpam-3931	79	49	interior	interior	ADJ
ejpam-3931	79	50	ideal	ideal	ADJ
ejpam-3931	79	51	element	element	NOUN
ejpam-3931	79	52	of	of	ADP
ejpam-3931	79	53	s.	s.	PROPN
ejpam-3931	79	54	(	(	PUNCT
ejpam-3931	79	55	4	4	X
ejpam-3931	79	56	)	)	PUNCT
ejpam-3931	79	57	every	every	DET
ejpam-3931	79	58	interior	interior	ADJ
ejpam-3931	79	59	ideal	ideal	ADJ
ejpam-3931	79	60	element	element	NOUN
ejpam-3931	79	61	of	of	ADP
ejpam-3931	79	62	s	s	PROPN
ejpam-3931	79	63	is	be	AUX
ejpam-3931	79	64	a	a	DET
ejpam-3931	79	65	bi	bi	ADJ
ejpam-3931	79	66	-	-	ADJ
ejpam-3931	79	67	interior	interior	ADJ
ejpam-3931	79	68	ideal	ideal	ADJ
ejpam-3931	79	69	element	element	NOUN
ejpam-3931	79	70	of	of	ADP
ejpam-3931	79	71	s.	s.	PROPN
ejpam-3931	79	72	proof	proof	PROPN
ejpam-3931	79	73	.	.	PUNCT
ejpam-3931	80	1	(	(	PUNCT
ejpam-3931	80	2	3	3	X
ejpam-3931	80	3	)	)	PUNCT
ejpam-3931	80	4	if	if	SCONJ
ejpam-3931	80	5	b	b	X
ejpam-3931	80	6	be	be	AUX
ejpam-3931	80	7	a	a	DET
ejpam-3931	80	8	bi	bi	ADJ
ejpam-3931	80	9	-	-	ADJ
ejpam-3931	80	10	ideal	ideal	ADJ
ejpam-3931	80	11	element	element	NOUN
ejpam-3931	80	12	of	of	ADP
ejpam-3931	80	13	s	s	PROPN
ejpam-3931	80	14	,	,	PUNCT
ejpam-3931	80	15	then	then	ADV
ejpam-3931	80	16	beb	beb	PROPN
ejpam-3931	80	17	∧	∧	PROPN
ejpam-3931	80	18	ebe	ebe	PROPN
ejpam-3931	80	19	≤	≤	PROPN
ejpam-3931	80	20	beb	beb	PROPN
ejpam-3931	80	21	≤	≤	PROPN
ejpam-3931	80	22	b	b	PROPN
ejpam-3931	80	23	,	,	PUNCT
ejpam-3931	80	24	so	so	CCONJ
ejpam-3931	80	25	b	b	PROPN
ejpam-3931	80	26	is	be	AUX
ejpam-3931	80	27	a	a	DET
ejpam-3931	80	28	bi	bi	ADJ
ejpam-3931	80	29	-	-	ADJ
ejpam-3931	80	30	interior	interior	ADJ
ejpam-3931	80	31	ideal	ideal	ADJ
ejpam-3931	80	32	element	element	NOUN
ejpam-3931	80	33	of	of	ADP
ejpam-3931	80	34	s.	s.	PROPN
ejpam-3931	80	35	(	(	PUNCT
ejpam-3931	80	36	4	4	X
ejpam-3931	80	37	)	)	PUNCT
ejpam-3931	80	38	if	if	SCONJ
ejpam-3931	80	39	b	b	PROPN
ejpam-3931	80	40	is	be	AUX
ejpam-3931	80	41	an	an	DET
ejpam-3931	80	42	interior	interior	ADJ
ejpam-3931	80	43	ideal	ideal	ADJ
ejpam-3931	80	44	element	element	NOUN
ejpam-3931	80	45	of	of	ADP
ejpam-3931	80	46	s	s	PROPN
ejpam-3931	80	47	,	,	PUNCT
ejpam-3931	80	48	then	then	ADV
ejpam-3931	80	49	beb	beb	PROPN
ejpam-3931	80	50	∧	∧	PROPN
ejpam-3931	80	51	ebe	ebe	PROPN
ejpam-3931	80	52	≤	≤	PUNCT
ejpam-3931	80	53	ebe	ebe	PROPN
ejpam-3931	80	54	≤	≤	PROPN
ejpam-3931	80	55	b	b	PROPN
ejpam-3931	80	56	,	,	PUNCT
ejpam-3931	80	57	so	so	CCONJ
ejpam-3931	80	58	b	b	PROPN
ejpam-3931	80	59	is	be	AUX
ejpam-3931	80	60	a	a	DET
ejpam-3931	80	61	bi	bi	ADJ
ejpam-3931	80	62	-	-	ADJ
ejpam-3931	80	63	interior	interior	ADJ
ejpam-3931	80	64	ideal	ideal	ADJ
ejpam-3931	80	65	element	element	NOUN
ejpam-3931	80	66	of	of	ADP
ejpam-3931	80	67	s.	s.	PROPN
ejpam-3931	80	68	(	(	PUNCT
ejpam-3931	80	69	2	2	X
ejpam-3931	80	70	)	)	PUNCT
ejpam-3931	80	71	if	if	SCONJ
ejpam-3931	80	72	q	q	NOUN
ejpam-3931	80	73	is	be	AUX
ejpam-3931	80	74	a	a	DET
ejpam-3931	80	75	quasi	quasi	ADJ
ejpam-3931	80	76	-	-	ADJ
ejpam-3931	80	77	ideal	ideal	ADJ
ejpam-3931	80	78	element	element	NOUN
ejpam-3931	80	79	of	of	ADP
ejpam-3931	80	80	s	s	PRON
ejpam-3931	80	81	then	then	ADV
ejpam-3931	80	82	,	,	PUNCT
ejpam-3931	80	83	by	by	ADP
ejpam-3931	80	84	proposition	proposition	NOUN
ejpam-3931	80	85	2.1	2.1	NUM
ejpam-3931	80	86	,	,	PUNCT
ejpam-3931	80	87	q	q	PUNCT
ejpam-3931	80	88	is	be	AUX
ejpam-3931	80	89	a	a	DET
ejpam-3931	80	90	bi	bi	ADJ
ejpam-3931	80	91	-	-	ADJ
ejpam-3931	80	92	ideal	ideal	ADJ
ejpam-3931	80	93	element	element	NOUN
ejpam-3931	80	94	of	of	ADP
ejpam-3931	80	95	s	s	PRON
ejpam-3931	80	96	so	so	ADV
ejpam-3931	80	97	,	,	PUNCT
ejpam-3931	80	98	by	by	ADP
ejpam-3931	80	99	(	(	PUNCT
ejpam-3931	80	100	3	3	NUM
ejpam-3931	80	101	)	)	PUNCT
ejpam-3931	80	102	,	,	PUNCT
ejpam-3931	80	103	q	q	PROPN
ejpam-3931	80	104	is	be	AUX
ejpam-3931	80	105	a	a	DET
ejpam-3931	80	106	bi	bi	ADJ
ejpam-3931	80	107	-	-	ADJ
ejpam-3931	80	108	interior	interior	ADJ
ejpam-3931	80	109	ideal	ideal	ADJ
ejpam-3931	80	110	element	element	NOUN
ejpam-3931	80	111	of	of	ADP
ejpam-3931	80	112	s.	s.	PROPN
ejpam-3931	80	113	independently	independently	ADV
ejpam-3931	80	114	,	,	PUNCT
ejpam-3931	80	115	if	if	SCONJ
ejpam-3931	80	116	q	q	NOUN
ejpam-3931	80	117	is	be	AUX
ejpam-3931	80	118	a	a	DET
ejpam-3931	80	119	quasi	quasi	ADJ
ejpam-3931	80	120	-	-	ADJ
ejpam-3931	80	121	ideal	ideal	ADJ
ejpam-3931	80	122	element	element	NOUN
ejpam-3931	80	123	of	of	ADP
ejpam-3931	80	124	s	s	PROPN
ejpam-3931	80	125	,	,	PUNCT
ejpam-3931	80	126	then	then	ADV
ejpam-3931	80	127	qeq	qeq	PROPN
ejpam-3931	80	128	∧	∧	PROPN
ejpam-3931	80	129	eqe	eqe	VERB
ejpam-3931	80	130	≤	≤	NUM
ejpam-3931	80	131	qeq	qeq	NOUN
ejpam-3931	80	132	≤	≤	NUM
ejpam-3931	80	133	qe	qe	PROPN
ejpam-3931	80	134	∧	∧	PROPN
ejpam-3931	80	135	eq	eq	ADP
ejpam-3931	80	136	≤	≤	PROPN
ejpam-3931	80	137	q	q	NOUN
ejpam-3931	80	138	,	,	PUNCT
ejpam-3931	80	139	so	so	ADV
ejpam-3931	80	140	q	q	NOUN
ejpam-3931	80	141	is	be	AUX
ejpam-3931	80	142	a	a	DET
ejpam-3931	80	143	bi	bi	ADJ
ejpam-3931	80	144	-	-	ADJ
ejpam-3931	80	145	interior	interior	ADJ
ejpam-3931	80	146	ideal	ideal	ADJ
ejpam-3931	80	147	element	element	NOUN
ejpam-3931	80	148	of	of	ADP
ejpam-3931	80	149	s.	s.	PROPN
ejpam-3931	80	150	(	(	PUNCT
ejpam-3931	80	151	1	1	X
ejpam-3931	80	152	)	)	PUNCT
ejpam-3931	80	153	if	if	SCONJ
ejpam-3931	80	154	a	a	PRON
ejpam-3931	80	155	is	be	AUX
ejpam-3931	80	156	a	a	DET
ejpam-3931	80	157	right	right	ADJ
ejpam-3931	80	158	(	(	PUNCT
ejpam-3931	80	159	resp	resp	NOUN
ejpam-3931	80	160	.	.	PUNCT
ejpam-3931	81	1	left	left	ADJ
ejpam-3931	81	2	)	)	PUNCT
ejpam-3931	81	3	ideal	ideal	ADJ
ejpam-3931	81	4	element	element	NOUN
ejpam-3931	81	5	of	of	ADP
ejpam-3931	81	6	s	s	PRON
ejpam-3931	81	7	then	then	ADV
ejpam-3931	81	8	,	,	PUNCT
ejpam-3931	81	9	by	by	ADP
ejpam-3931	81	10	proposition	proposition	NOUN
ejpam-3931	81	11	2.1	2.1	NUM
ejpam-3931	81	12	,	,	PUNCT
ejpam-3931	81	13	a	a	PRON
ejpam-3931	81	14	is	be	AUX
ejpam-3931	81	15	a	a	DET
ejpam-3931	81	16	quasi	quasi	ADJ
ejpam-3931	81	17	-	-	ADJ
ejpam-3931	81	18	ideal	ideal	ADJ
ejpam-3931	81	19	element	element	NOUN
ejpam-3931	81	20	of	of	ADP
ejpam-3931	81	21	s	s	PRON
ejpam-3931	81	22	so	so	ADV
ejpam-3931	81	23	,	,	PUNCT
ejpam-3931	81	24	by	by	ADP
ejpam-3931	81	25	(	(	PUNCT
ejpam-3931	81	26	2	2	NUM
ejpam-3931	81	27	)	)	PUNCT
ejpam-3931	81	28	,	,	PUNCT
ejpam-3931	81	29	a	a	PRON
ejpam-3931	81	30	is	be	AUX
ejpam-3931	81	31	a	a	DET
ejpam-3931	81	32	bi	bi	ADJ
ejpam-3931	81	33	-	-	ADJ
ejpam-3931	81	34	interior	interior	ADJ
ejpam-3931	81	35	ideal	ideal	ADJ
ejpam-3931	81	36	element	element	NOUN
ejpam-3931	81	37	of	of	ADP
ejpam-3931	81	38	s.	s.	PROPN
ejpam-3931	81	39	□	□	PUNCT
ejpam-3931	81	40	proposition	proposition	NOUN
ejpam-3931	81	41	2.4	2.4	NUM
ejpam-3931	81	42	.	.	PUNCT
ejpam-3931	82	1	let	let	VERB
ejpam-3931	82	2	s	s	PRON
ejpam-3931	82	3	be	be	AUX
ejpam-3931	82	4	a	a	DET
ejpam-3931	82	5	∧e	∧e	PROPN
ejpam-3931	82	6	-	-	PUNCT
ejpam-3931	82	7	semigroup	semigroup	NOUN
ejpam-3931	82	8	.	.	PUNCT
ejpam-3931	83	1	then	then	ADV
ejpam-3931	83	2	we	we	PRON
ejpam-3931	83	3	have	have	VERB
ejpam-3931	83	4	the	the	DET
ejpam-3931	83	5	following	following	NOUN
ejpam-3931	83	6	:	:	PUNCT
ejpam-3931	83	7	(	(	PUNCT
ejpam-3931	83	8	1	1	X
ejpam-3931	83	9	)	)	PUNCT
ejpam-3931	83	10	if	if	SCONJ
ejpam-3931	83	11	a	a	PRON
ejpam-3931	83	12	and	and	CCONJ
ejpam-3931	83	13	b	b	NOUN
ejpam-3931	83	14	are	be	AUX
ejpam-3931	83	15	bi	bi	ADJ
ejpam-3931	83	16	-	-	ADJ
ejpam-3931	83	17	interior	interior	ADJ
ejpam-3931	83	18	ideal	ideal	ADJ
ejpam-3931	83	19	elements	element	NOUN
ejpam-3931	83	20	of	of	ADP
ejpam-3931	83	21	s	s	NOUN
ejpam-3931	83	22	,	,	PUNCT
ejpam-3931	83	23	then	then	ADV
ejpam-3931	83	24	a∧	a∧	PROPN
ejpam-3931	83	25	b	b	PROPN
ejpam-3931	83	26	is	be	AUX
ejpam-3931	83	27	a	a	DET
ejpam-3931	83	28	bi	bi	ADJ
ejpam-3931	83	29	-	-	ADJ
ejpam-3931	83	30	interior	interior	ADJ
ejpam-3931	83	31	ideal	ideal	ADJ
ejpam-3931	83	32	element	element	NOUN
ejpam-3931	83	33	of	of	ADP
ejpam-3931	83	34	s.	s.	PROPN
ejpam-3931	83	35	(	(	PUNCT
ejpam-3931	83	36	2	2	X
ejpam-3931	83	37	)	)	PUNCT
ejpam-3931	83	38	if	if	SCONJ
ejpam-3931	83	39	a	a	PRON
ejpam-3931	83	40	is	be	AUX
ejpam-3931	83	41	a	a	DET
ejpam-3931	83	42	right	right	ADJ
ejpam-3931	83	43	ideal	ideal	ADJ
ejpam-3931	83	44	element	element	NOUN
ejpam-3931	83	45	and	and	CCONJ
ejpam-3931	83	46	b	b	NOUN
ejpam-3931	83	47	is	be	AUX
ejpam-3931	83	48	a	a	DET
ejpam-3931	83	49	left	left	ADJ
ejpam-3931	83	50	ideal	ideal	ADJ
ejpam-3931	83	51	element	element	NOUN
ejpam-3931	83	52	of	of	ADP
ejpam-3931	83	53	s	s	PROPN
ejpam-3931	83	54	,	,	PUNCT
ejpam-3931	83	55	then	then	ADV
ejpam-3931	83	56	a∧b	a∧b	VERB
ejpam-3931	83	57	is	be	AUX
ejpam-3931	83	58	a	a	DET
ejpam-3931	83	59	bi	bi	ADJ
ejpam-3931	83	60	-	-	ADJ
ejpam-3931	83	61	interior	interior	ADJ
ejpam-3931	83	62	ideal	ideal	ADJ
ejpam-3931	83	63	element	element	NOUN
ejpam-3931	83	64	of	of	ADP
ejpam-3931	83	65	s.	s.	PROPN
ejpam-3931	83	66	(	(	PUNCT
ejpam-3931	83	67	3	3	X
ejpam-3931	83	68	)	)	PUNCT
ejpam-3931	83	69	if	if	SCONJ
ejpam-3931	83	70	b	b	PROPN
ejpam-3931	83	71	is	be	AUX
ejpam-3931	83	72	a	a	DET
ejpam-3931	83	73	bi	bi	ADJ
ejpam-3931	83	74	-	-	ADJ
ejpam-3931	83	75	interior	interior	ADJ
ejpam-3931	83	76	ideal	ideal	ADJ
ejpam-3931	83	77	element	element	NOUN
ejpam-3931	83	78	and	and	CCONJ
ejpam-3931	83	79	t	t	PROPN
ejpam-3931	83	80	is	be	AUX
ejpam-3931	83	81	an	an	DET
ejpam-3931	83	82	interior	interior	ADJ
ejpam-3931	83	83	ideal	ideal	ADJ
ejpam-3931	83	84	element	element	NOUN
ejpam-3931	83	85	of	of	ADP
ejpam-3931	83	86	s	s	PROPN
ejpam-3931	83	87	,	,	PUNCT
ejpam-3931	83	88	then	then	ADV
ejpam-3931	83	89	b	b	PROPN
ejpam-3931	83	90	∧	∧	PROPN
ejpam-3931	83	91	t	t	PROPN
ejpam-3931	83	92	is	be	AUX
ejpam-3931	83	93	a	a	DET
ejpam-3931	83	94	bi	bi	ADJ
ejpam-3931	83	95	-	-	ADJ
ejpam-3931	83	96	interior	interior	ADJ
ejpam-3931	83	97	ideal	ideal	ADJ
ejpam-3931	83	98	element	element	NOUN
ejpam-3931	83	99	of	of	ADP
ejpam-3931	83	100	s.	s.	PROPN
ejpam-3931	83	101	proof	proof	PROPN
ejpam-3931	83	102	.	.	PUNCT
ejpam-3931	84	1	(	(	PUNCT
ejpam-3931	84	2	1	1	X
ejpam-3931	84	3	)	)	PUNCT
ejpam-3931	84	4	let	let	VERB
ejpam-3931	84	5	a	a	PRON
ejpam-3931	84	6	and	and	CCONJ
ejpam-3931	84	7	b	b	NOUN
ejpam-3931	84	8	be	be	AUX
ejpam-3931	84	9	bi	bi	ADJ
ejpam-3931	84	10	-	-	ADJ
ejpam-3931	84	11	interior	interior	ADJ
ejpam-3931	84	12	ideal	ideal	ADJ
ejpam-3931	84	13	elements	element	NOUN
ejpam-3931	84	14	of	of	ADP
ejpam-3931	84	15	s.	s.	PROPN
ejpam-3931	84	16	then	then	ADV
ejpam-3931	84	17	aea∧eae	aea∧eae	VERB
ejpam-3931	84	18	≤	≤	NOUN
ejpam-3931	84	19	a	a	PRON
ejpam-3931	84	20	and	and	CCONJ
ejpam-3931	84	21	beb∧ebe	beb∧ebe	VERB
ejpam-3931	84	22	≤	≤	NUM
ejpam-3931	84	23	b	b	NOUN
ejpam-3931	84	24	,	,	PUNCT
ejpam-3931	84	25	then	then	ADV
ejpam-3931	84	26	(	(	PUNCT
ejpam-3931	84	27	a	a	DET
ejpam-3931	84	28	∧	∧	PROPN
ejpam-3931	84	29	b)e(a	b)e(a	PROPN
ejpam-3931	84	30	∧	∧	PROPN
ejpam-3931	84	31	b	b	PROPN
ejpam-3931	84	32	)	)	PUNCT
ejpam-3931	84	33	∧	∧	PROPN
ejpam-3931	84	34	e(a	e(a	PROPN
ejpam-3931	84	35	∧	∧	PROPN
ejpam-3931	84	36	b)e	b)e	PUNCT
ejpam-3931	84	37	≤	≤	PROPN
ejpam-3931	84	38	aea	aea	PROPN
ejpam-3931	84	39	∧	∧	PROPN
ejpam-3931	84	40	eae	eae	PROPN
ejpam-3931	84	41	≤	≤	NOUN
ejpam-3931	85	1	a	a	DET
ejpam-3931	85	2	and	and	CCONJ
ejpam-3931	85	3	(	(	PUNCT
ejpam-3931	85	4	a	a	DET
ejpam-3931	85	5	∧	∧	PROPN
ejpam-3931	85	6	b)e(a	b)e(a	PROPN
ejpam-3931	85	7	∧	∧	PROPN
ejpam-3931	85	8	b	b	PROPN
ejpam-3931	85	9	)	)	PUNCT
ejpam-3931	85	10	∧	∧	PROPN
ejpam-3931	85	11	e(a	e(a	PROPN
ejpam-3931	85	12	∧	∧	PROPN
ejpam-3931	85	13	b)e	b)e	PUNCT
ejpam-3931	85	14	≤	≤	PUNCT
ejpam-3931	85	15	beb	beb	PROPN
ejpam-3931	85	16	∧	∧	PROPN
ejpam-3931	85	17	ebe	ebe	PROPN
ejpam-3931	85	18	≤	≤	PROPN
ejpam-3931	85	19	b.	b.	PROPN
ejpam-3931	86	1	thus	thus	ADV
ejpam-3931	86	2	we	we	PRON
ejpam-3931	86	3	have	have	VERB
ejpam-3931	86	4	(	(	PUNCT
ejpam-3931	86	5	a	a	DET
ejpam-3931	86	6	∧	∧	PROPN
ejpam-3931	86	7	b)e(a	b)e(a	PROPN
ejpam-3931	86	8	∧	∧	PROPN
ejpam-3931	86	9	b	b	PROPN
ejpam-3931	86	10	)	)	PUNCT
ejpam-3931	86	11	∧	∧	PROPN
ejpam-3931	86	12	e(a	e(a	PROPN
ejpam-3931	86	13	∧	∧	PROPN
ejpam-3931	86	14	b)e	b)e	PUNCT
ejpam-3931	86	15	≤	≤	VERB
ejpam-3931	86	16	a	a	DET
ejpam-3931	86	17	∧	∧	PROPN
ejpam-3931	86	18	b	b	PROPN
ejpam-3931	86	19	n.	n.	NOUN
ejpam-3931	86	20	kehayopulu	kehayopulu	PROPN
ejpam-3931	86	21	/	/	SYM
ejpam-3931	86	22	eur	eur	PROPN
ejpam-3931	86	23	.	.	PUNCT
ejpam-3931	87	1	j.	j.	PROPN
ejpam-3931	87	2	pure	pure	PROPN
ejpam-3931	87	3	appl	appl	PROPN
ejpam-3931	87	4	.	.	PROPN
ejpam-3931	87	5	math	math	PROPN
ejpam-3931	87	6	,	,	PUNCT
ejpam-3931	87	7	14	14	NUM
ejpam-3931	87	8	(	(	PUNCT
ejpam-3931	87	9	4	4	NUM
ejpam-3931	87	10	)	)	PUNCT
ejpam-3931	87	11	(	(	PUNCT
ejpam-3931	87	12	2021	2021	NUM
ejpam-3931	87	13	)	)	PUNCT
ejpam-3931	87	14	,	,	PUNCT
ejpam-3931	87	15	43	43	NUM
ejpam-3931	87	16	-	-	SYM
ejpam-3931	87	17	52	52	NUM
ejpam-3931	87	18	46	46	NUM
ejpam-3931	87	19	and	and	CCONJ
ejpam-3931	87	20	so	so	ADV
ejpam-3931	87	21	a	a	DET
ejpam-3931	87	22	∧	∧	PROPN
ejpam-3931	87	23	b	b	PROPN
ejpam-3931	87	24	is	be	AUX
ejpam-3931	87	25	a	a	DET
ejpam-3931	87	26	bi	bi	ADJ
ejpam-3931	87	27	-	-	ADJ
ejpam-3931	87	28	interior	interior	ADJ
ejpam-3931	87	29	ideal	ideal	ADJ
ejpam-3931	87	30	element	element	NOUN
ejpam-3931	87	31	of	of	ADP
ejpam-3931	87	32	s.	s.	PROPN
ejpam-3931	87	33	(	(	PUNCT
ejpam-3931	87	34	2	2	X
ejpam-3931	87	35	)	)	PUNCT
ejpam-3931	87	36	if	if	SCONJ
ejpam-3931	87	37	a	a	PRON
ejpam-3931	87	38	is	be	AUX
ejpam-3931	87	39	a	a	DET
ejpam-3931	87	40	right	right	ADJ
ejpam-3931	87	41	ideal	ideal	ADJ
ejpam-3931	87	42	element	element	NOUN
ejpam-3931	87	43	of	of	ADP
ejpam-3931	87	44	s	s	PRON
ejpam-3931	87	45	and	and	CCONJ
ejpam-3931	87	46	b	b	NOUN
ejpam-3931	87	47	is	be	AUX
ejpam-3931	87	48	a	a	DET
ejpam-3931	87	49	left	left	ADJ
ejpam-3931	87	50	ideal	ideal	ADJ
ejpam-3931	87	51	element	element	NOUN
ejpam-3931	87	52	of	of	ADP
ejpam-3931	87	53	s	s	PRON
ejpam-3931	87	54	then	then	ADV
ejpam-3931	87	55	,	,	PUNCT
ejpam-3931	87	56	by	by	ADP
ejpam-3931	87	57	proposition	proposition	NOUN
ejpam-3931	87	58	2.3(1	2.3(1	NUM
ejpam-3931	87	59	)	)	PUNCT
ejpam-3931	87	60	,	,	PUNCT
ejpam-3931	87	61	a	a	PRON
ejpam-3931	87	62	and	and	CCONJ
ejpam-3931	87	63	b	b	NOUN
ejpam-3931	87	64	are	be	AUX
ejpam-3931	87	65	bi	bi	ADJ
ejpam-3931	87	66	-	-	ADJ
ejpam-3931	87	67	interior	interior	ADJ
ejpam-3931	87	68	ideal	ideal	ADJ
ejpam-3931	87	69	elements	element	NOUN
ejpam-3931	87	70	of	of	ADP
ejpam-3931	87	71	s	s	PRON
ejpam-3931	87	72	and	and	CCONJ
ejpam-3931	87	73	then	then	ADV
ejpam-3931	87	74	,	,	PUNCT
ejpam-3931	87	75	by	by	ADP
ejpam-3931	87	76	property	property	NOUN
ejpam-3931	87	77	(	(	PUNCT
ejpam-3931	87	78	1	1	NUM
ejpam-3931	87	79	)	)	PUNCT
ejpam-3931	87	80	,	,	PUNCT
ejpam-3931	87	81	a	a	DET
ejpam-3931	87	82	∧	∧	PROPN
ejpam-3931	87	83	b	b	PROPN
ejpam-3931	87	84	is	be	AUX
ejpam-3931	87	85	a	a	DET
ejpam-3931	87	86	bi	bi	ADJ
ejpam-3931	87	87	-	-	ADJ
ejpam-3931	87	88	interior	interior	ADJ
ejpam-3931	87	89	ideal	ideal	ADJ
ejpam-3931	87	90	element	element	NOUN
ejpam-3931	87	91	of	of	ADP
ejpam-3931	87	92	s.	s.	PROPN
ejpam-3931	87	93	(	(	PUNCT
ejpam-3931	87	94	3	3	X
ejpam-3931	87	95	)	)	PUNCT
ejpam-3931	87	96	if	if	SCONJ
ejpam-3931	87	97	b	b	PROPN
ejpam-3931	87	98	is	be	AUX
ejpam-3931	87	99	a	a	DET
ejpam-3931	87	100	bi	bi	ADJ
ejpam-3931	87	101	-	-	ADJ
ejpam-3931	87	102	interior	interior	ADJ
ejpam-3931	87	103	ideal	ideal	ADJ
ejpam-3931	87	104	element	element	NOUN
ejpam-3931	87	105	and	and	CCONJ
ejpam-3931	87	106	t	t	PROPN
ejpam-3931	87	107	is	be	AUX
ejpam-3931	87	108	an	an	DET
ejpam-3931	87	109	interior	interior	ADJ
ejpam-3931	87	110	ideal	ideal	ADJ
ejpam-3931	87	111	element	element	NOUN
ejpam-3931	87	112	of	of	ADP
ejpam-3931	87	113	s	s	PRON
ejpam-3931	87	114	then	then	ADV
ejpam-3931	87	115	,	,	PUNCT
ejpam-3931	87	116	by	by	ADP
ejpam-3931	87	117	proposition	proposition	NOUN
ejpam-3931	87	118	2.3(4	2.3(4	NUM
ejpam-3931	87	119	)	)	PUNCT
ejpam-3931	87	120	,	,	PUNCT
ejpam-3931	87	121	a	a	PRON
ejpam-3931	87	122	and	and	CCONJ
ejpam-3931	87	123	b	b	NOUN
ejpam-3931	87	124	are	be	AUX
ejpam-3931	87	125	bi	bi	ADJ
ejpam-3931	87	126	-	-	ADJ
ejpam-3931	87	127	interior	interior	ADJ
ejpam-3931	87	128	ideal	ideal	ADJ
ejpam-3931	87	129	elements	element	NOUN
ejpam-3931	87	130	of	of	ADP
ejpam-3931	87	131	s	s	PRON
ejpam-3931	87	132	so	so	ADV
ejpam-3931	87	133	,	,	PUNCT
ejpam-3931	87	134	by	by	ADP
ejpam-3931	87	135	(	(	PUNCT
ejpam-3931	87	136	1	1	NUM
ejpam-3931	87	137	)	)	PUNCT
ejpam-3931	87	138	,	,	PUNCT
ejpam-3931	87	139	b∧t	b∧t	PROPN
ejpam-3931	87	140	is	be	AUX
ejpam-3931	87	141	a	a	DET
ejpam-3931	87	142	bi	bi	ADJ
ejpam-3931	87	143	-	-	ADJ
ejpam-3931	87	144	interior	interior	ADJ
ejpam-3931	87	145	ideal	ideal	ADJ
ejpam-3931	87	146	element	element	NOUN
ejpam-3931	87	147	of	of	ADP
ejpam-3931	87	148	s.	s.	PROPN
ejpam-3931	87	149	□	□	PUNCT
ejpam-3931	87	150	proposition	proposition	NOUN
ejpam-3931	87	151	2.5	2.5	NUM
ejpam-3931	87	152	.	.	PUNCT
ejpam-3931	88	1	let	let	VERB
ejpam-3931	88	2	s	s	PRON
ejpam-3931	88	3	be	be	AUX
ejpam-3931	88	4	a	a	DET
ejpam-3931	88	5	∧e	∧e	PROPN
ejpam-3931	88	6	-	-	PUNCT
ejpam-3931	88	7	semigroup	semigroup	NOUN
ejpam-3931	88	8	.	.	PUNCT
ejpam-3931	89	1	then	then	ADV
ejpam-3931	89	2	we	we	PRON
ejpam-3931	89	3	have	have	VERB
ejpam-3931	89	4	the	the	DET
ejpam-3931	89	5	following	following	NOUN
ejpam-3931	89	6	:	:	PUNCT
ejpam-3931	89	7	(	(	PUNCT
ejpam-3931	89	8	1	1	X
ejpam-3931	89	9	)	)	PUNCT
ejpam-3931	89	10	if	if	SCONJ
ejpam-3931	89	11	b	b	NOUN
ejpam-3931	89	12	is	be	AUX
ejpam-3931	89	13	a	a	DET
ejpam-3931	89	14	bi	bi	ADJ
ejpam-3931	89	15	-	-	ADJ
ejpam-3931	89	16	interior	interior	ADJ
ejpam-3931	89	17	ideal	ideal	ADJ
ejpam-3931	89	18	element	element	NOUN
ejpam-3931	89	19	of	of	ADP
ejpam-3931	89	20	s	s	PROPN
ejpam-3931	89	21	,	,	PUNCT
ejpam-3931	89	22	then	then	ADV
ejpam-3931	89	23	the	the	DET
ejpam-3931	89	24	elements	element	NOUN
ejpam-3931	89	25	be	be	VERB
ejpam-3931	89	26	and	and	CCONJ
ejpam-3931	89	27	eb	eb	PROPN
ejpam-3931	89	28	are	be	AUX
ejpam-3931	89	29	bi	bi	ADJ
ejpam-3931	89	30	-	-	ADJ
ejpam-3931	89	31	interior	interior	ADJ
ejpam-3931	89	32	ideal	ideal	ADJ
ejpam-3931	89	33	elements	element	NOUN
ejpam-3931	89	34	of	of	ADP
ejpam-3931	89	35	s	s	PRON
ejpam-3931	89	36	as	as	ADV
ejpam-3931	89	37	well	well	ADV
ejpam-3931	89	38	.	.	PUNCT
ejpam-3931	90	1	(	(	PUNCT
ejpam-3931	90	2	2	2	X
ejpam-3931	90	3	)	)	PUNCT
ejpam-3931	90	4	if	if	SCONJ
ejpam-3931	90	5	b	b	NOUN
ejpam-3931	90	6	is	be	AUX
ejpam-3931	90	7	a	a	DET
ejpam-3931	90	8	bi	bi	ADJ
ejpam-3931	90	9	-	-	ADJ
ejpam-3931	90	10	interior	interior	ADJ
ejpam-3931	90	11	ideal	ideal	ADJ
ejpam-3931	90	12	element	element	NOUN
ejpam-3931	90	13	of	of	ADP
ejpam-3931	90	14	s	s	PROPN
ejpam-3931	90	15	,	,	PUNCT
ejpam-3931	90	16	b	b	PROPN
ejpam-3931	90	17	≤	≤	X
ejpam-3931	90	18	be	be	VERB
ejpam-3931	90	19	or	or	CCONJ
ejpam-3931	90	20	b	b	PROPN
ejpam-3931	90	21	≤	≤	PROPN
ejpam-3931	90	22	eb	eb	PROPN
ejpam-3931	90	23	,	,	PUNCT
ejpam-3931	90	24	then	then	ADV
ejpam-3931	90	25	b	b	PROPN
ejpam-3931	90	26	is	be	AUX
ejpam-3931	90	27	a	a	DET
ejpam-3931	90	28	subidempotent	subidempotent	NOUN
ejpam-3931	90	29	element	element	NOUN
ejpam-3931	90	30	of	of	ADP
ejpam-3931	90	31	s.	s.	PROPN
ejpam-3931	90	32	(	(	PUNCT
ejpam-3931	90	33	3	3	X
ejpam-3931	90	34	)	)	PUNCT
ejpam-3931	90	35	if	if	SCONJ
ejpam-3931	90	36	b	b	PROPN
ejpam-3931	90	37	is	be	AUX
ejpam-3931	90	38	a	a	DET
ejpam-3931	90	39	bi	bi	ADJ
ejpam-3931	90	40	-	-	ADJ
ejpam-3931	90	41	interior	interior	ADJ
ejpam-3931	90	42	ideal	ideal	ADJ
ejpam-3931	90	43	element	element	NOUN
ejpam-3931	90	44	of	of	ADP
ejpam-3931	90	45	s	s	PRON
ejpam-3931	90	46	and	and	CCONJ
ejpam-3931	90	47	(	(	PUNCT
ejpam-3931	90	48	the	the	DET
ejpam-3931	90	49	greatest	great	ADJ
ejpam-3931	90	50	element	element	NOUN
ejpam-3931	90	51	)	)	PUNCT
ejpam-3931	91	1	e	e	NOUN
ejpam-3931	91	2	is	be	AUX
ejpam-3931	91	3	at	at	ADP
ejpam-3931	91	4	the	the	DET
ejpam-3931	91	5	same	same	ADJ
ejpam-3931	91	6	time	time	NOUN
ejpam-3931	91	7	the	the	DET
ejpam-3931	91	8	identity	identity	NOUN
ejpam-3931	91	9	of	of	ADP
ejpam-3931	91	10	s	s	PROPN
ejpam-3931	91	11	,	,	PUNCT
ejpam-3931	91	12	then	then	ADV
ejpam-3931	91	13	b	b	PROPN
ejpam-3931	91	14	is	be	AUX
ejpam-3931	91	15	a	a	DET
ejpam-3931	91	16	subidempotent	subidempotent	NOUN
ejpam-3931	91	17	element	element	NOUN
ejpam-3931	91	18	of	of	ADP
ejpam-3931	91	19	s.	s.	PROPN
ejpam-3931	91	20	proof	proof	PROPN
ejpam-3931	91	21	.	.	PUNCT
ejpam-3931	92	1	(	(	PUNCT
ejpam-3931	92	2	1	1	X
ejpam-3931	92	3	)	)	PUNCT
ejpam-3931	92	4	let	let	VERB
ejpam-3931	92	5	b	b	X
ejpam-3931	92	6	be	be	AUX
ejpam-3931	92	7	a	a	DET
ejpam-3931	92	8	bi	bi	ADJ
ejpam-3931	92	9	-	-	ADJ
ejpam-3931	92	10	interior	interior	ADJ
ejpam-3931	92	11	ideal	ideal	ADJ
ejpam-3931	92	12	element	element	NOUN
ejpam-3931	92	13	of	of	ADP
ejpam-3931	92	14	s.	s.	PROPN
ejpam-3931	92	15	then	then	ADV
ejpam-3931	92	16	(	(	PUNCT
ejpam-3931	92	17	be)e(be	be)e(be	NOUN
ejpam-3931	92	18	)	)	PUNCT
ejpam-3931	92	19	∧	∧	NOUN
ejpam-3931	92	20	e(be)e	e(be)e	VERB
ejpam-3931	92	21	≤	≤	NUM
ejpam-3931	92	22	(	(	PUNCT
ejpam-3931	92	23	be)e(be	be)e(be	NOUN
ejpam-3931	92	24	)	)	PUNCT
ejpam-3931	92	25	≤	≤	NOUN
ejpam-3931	92	26	be	be	VERB
ejpam-3931	92	27	and	and	CCONJ
ejpam-3931	92	28	(	(	PUNCT
ejpam-3931	92	29	eb)e(eb	eb)e(eb	NOUN
ejpam-3931	92	30	)	)	PUNCT
ejpam-3931	92	31	∧	∧	NOUN
ejpam-3931	92	32	e(eb)e	e(eb)e	ADJ
ejpam-3931	92	33	≤	≤	NOUN
ejpam-3931	92	34	(	(	PUNCT
ejpam-3931	92	35	eb)e(eb	eb)e(eb	NOUN
ejpam-3931	92	36	)	)	PUNCT
ejpam-3931	92	37	≤	≤	PROPN
ejpam-3931	92	38	eb	eb	PROPN
ejpam-3931	92	39	,	,	PUNCT
ejpam-3931	92	40	so	so	ADV
ejpam-3931	92	41	be	be	AUX
ejpam-3931	92	42	and	and	CCONJ
ejpam-3931	92	43	eb	eb	PROPN
ejpam-3931	92	44	are	be	AUX
ejpam-3931	92	45	bi	bi	ADJ
ejpam-3931	92	46	-	-	ADJ
ejpam-3931	92	47	interior	interior	ADJ
ejpam-3931	92	48	ideal	ideal	ADJ
ejpam-3931	92	49	elements	element	NOUN
ejpam-3931	92	50	of	of	ADP
ejpam-3931	92	51	s.	s.	PROPN
ejpam-3931	92	52	(	(	PUNCT
ejpam-3931	92	53	2	2	X
ejpam-3931	92	54	)	)	PUNCT
ejpam-3931	92	55	let	let	VERB
ejpam-3931	92	56	b	b	X
ejpam-3931	92	57	be	be	AUX
ejpam-3931	92	58	a	a	DET
ejpam-3931	92	59	bi	bi	ADJ
ejpam-3931	92	60	-	-	ADJ
ejpam-3931	92	61	interior	interior	ADJ
ejpam-3931	92	62	ideal	ideal	ADJ
ejpam-3931	92	63	element	element	NOUN
ejpam-3931	92	64	of	of	ADP
ejpam-3931	92	65	s	s	PRON
ejpam-3931	92	66	such	such	ADJ
ejpam-3931	92	67	that	that	SCONJ
ejpam-3931	92	68	b	b	PROPN
ejpam-3931	92	69	≤	≤	NUM
ejpam-3931	92	70	be	be	VERB
ejpam-3931	92	71	.	.	PUNCT
ejpam-3931	93	1	then	then	ADV
ejpam-3931	93	2	we	we	PRON
ejpam-3931	93	3	have	have	AUX
ejpam-3931	93	4	b2	b2	VERB
ejpam-3931	93	5	≤	≤	NOUN
ejpam-3931	93	6	(	(	PUNCT
ejpam-3931	93	7	be)b	be)b	NOUN
ejpam-3931	93	8	and	and	CCONJ
ejpam-3931	93	9	b2	b2	NOUN
ejpam-3931	93	10	≤	≤	NOUN
ejpam-3931	93	11	b(be	b(be	NOUN
ejpam-3931	93	12	)	)	PUNCT
ejpam-3931	93	13	≤	≤	NUM
ejpam-3931	93	14	ebe	ebe	NOUN
ejpam-3931	93	15	,	,	PUNCT
ejpam-3931	93	16	thus	thus	ADV
ejpam-3931	93	17	we	we	PRON
ejpam-3931	93	18	have	have	AUX
ejpam-3931	93	19	b2	b2	VERB
ejpam-3931	93	20	≤	≤	NOUN
ejpam-3931	93	21	beb∧ebe	beb∧ebe	VERB
ejpam-3931	93	22	≤	≤	NUM
ejpam-3931	93	23	b	b	PROPN
ejpam-3931	93	24	and	and	CCONJ
ejpam-3931	93	25	so	so	ADV
ejpam-3931	93	26	b	b	PROPN
ejpam-3931	93	27	is	be	AUX
ejpam-3931	93	28	subidempotent	subidempotent	NOUN
ejpam-3931	93	29	.	.	PUNCT
ejpam-3931	94	1	if	if	SCONJ
ejpam-3931	94	2	b	b	PROPN
ejpam-3931	94	3	≤	≤	PROPN
ejpam-3931	94	4	eb	eb	PROPN
ejpam-3931	94	5	,	,	PUNCT
ejpam-3931	94	6	then	then	ADV
ejpam-3931	94	7	b2	b2	VERB
ejpam-3931	94	8	≤	≤	ADJ
ejpam-3931	94	9	b(eb	b(eb	NOUN
ejpam-3931	94	10	)	)	PUNCT
ejpam-3931	94	11	and	and	CCONJ
ejpam-3931	94	12	b2	b2	NOUN
ejpam-3931	94	13	≤	≤	NOUN
ejpam-3931	94	14	(	(	PUNCT
ejpam-3931	94	15	eb)b	eb)b	PROPN
ejpam-3931	94	16	≤	≤	NUM
ejpam-3931	94	17	ebe	ebe	NOUN
ejpam-3931	94	18	,	,	PUNCT
ejpam-3931	94	19	then	then	ADV
ejpam-3931	94	20	b2	b2	VERB
ejpam-3931	94	21	≤	≤	ADJ
ejpam-3931	94	22	beb	beb	PROPN
ejpam-3931	94	23	∧	∧	PROPN
ejpam-3931	94	24	ebe	ebe	PROPN
ejpam-3931	94	25	≤	≤	PROPN
ejpam-3931	94	26	b	b	PROPN
ejpam-3931	95	1	and	and	CCONJ
ejpam-3931	96	1	so	so	ADV
ejpam-3931	96	2	b	b	PROPN
ejpam-3931	96	3	is	be	AUX
ejpam-3931	96	4	subidempotent	subidempotent	NOUN
ejpam-3931	96	5	.	.	PUNCT
ejpam-3931	97	1	(	(	PUNCT
ejpam-3931	97	2	3	3	X
ejpam-3931	97	3	)	)	PUNCT
ejpam-3931	97	4	since	since	SCONJ
ejpam-3931	97	5	b	b	NOUN
ejpam-3931	97	6	=	=	PRON
ejpam-3931	97	7	be	be	AUX
ejpam-3931	97	8	=	=	SYM
ejpam-3931	97	9	eb	eb	PROPN
ejpam-3931	97	10	,	,	PUNCT
ejpam-3931	97	11	the	the	DET
ejpam-3931	97	12	proof	proof	NOUN
ejpam-3931	97	13	follows	follow	VERB
ejpam-3931	97	14	from	from	ADP
ejpam-3931	97	15	(	(	PUNCT
ejpam-3931	97	16	2	2	NUM
ejpam-3931	97	17	)	)	PUNCT
ejpam-3931	97	18	.	.	PUNCT
ejpam-3931	98	1	□	□	PUNCT
ejpam-3931	98	2	propositions	proposition	NOUN
ejpam-3931	98	3	2.3	2.3	NUM
ejpam-3931	98	4	,	,	PUNCT
ejpam-3931	98	5	2.4	2.4	NUM
ejpam-3931	98	6	and	and	CCONJ
ejpam-3931	98	7	2.5	2.5	NUM
ejpam-3931	98	8	generalize	generalize	VERB
ejpam-3931	98	9	the	the	DET
ejpam-3931	98	10	theorem	theorem	NOUN
ejpam-3931	98	11	3.3	3.3	NUM
ejpam-3931	98	12	in	in	ADP
ejpam-3931	98	13	[	[	X
ejpam-3931	98	14	4	4	NUM
ejpam-3931	98	15	]	]	PUNCT
ejpam-3931	98	16	.	.	PUNCT
ejpam-3931	99	1	proposition	proposition	NOUN
ejpam-3931	99	2	2.6	2.6	NUM
ejpam-3931	99	3	.	.	PUNCT
ejpam-3931	100	1	let	let	VERB
ejpam-3931	100	2	s	s	PRON
ejpam-3931	100	3	be	be	AUX
ejpam-3931	100	4	a	a	DET
ejpam-3931	100	5	∧e	∧e	PROPN
ejpam-3931	100	6	-	-	PUNCT
ejpam-3931	100	7	semigroup	semigroup	NOUN
ejpam-3931	100	8	.	.	PUNCT
ejpam-3931	101	1	then	then	ADV
ejpam-3931	101	2	we	we	PRON
ejpam-3931	101	3	have	have	VERB
ejpam-3931	101	4	the	the	DET
ejpam-3931	101	5	following	following	NOUN
ejpam-3931	101	6	:	:	PUNCT
ejpam-3931	101	7	(	(	PUNCT
ejpam-3931	101	8	1	1	X
ejpam-3931	101	9	)	)	PUNCT
ejpam-3931	101	10	if	if	SCONJ
ejpam-3931	101	11	a	a	PRON
ejpam-3931	101	12	is	be	AUX
ejpam-3931	101	13	a	a	DET
ejpam-3931	101	14	right	right	ADJ
ejpam-3931	101	15	ideal	ideal	ADJ
ejpam-3931	101	16	element	element	NOUN
ejpam-3931	101	17	of	of	ADP
ejpam-3931	101	18	s	s	PRON
ejpam-3931	101	19	then	then	ADV
ejpam-3931	101	20	,	,	PUNCT
ejpam-3931	101	21	for	for	ADP
ejpam-3931	101	22	any	any	DET
ejpam-3931	101	23	b	b	PROPN
ejpam-3931	101	24	∈	∈	PROPN
ejpam-3931	101	25	s	s	PROPN
ejpam-3931	101	26	,	,	PUNCT
ejpam-3931	101	27	the	the	DET
ejpam-3931	101	28	element	element	NOUN
ejpam-3931	101	29	ab	ab	PROPN
ejpam-3931	101	30	is	be	AUX
ejpam-3931	101	31	a	a	DET
ejpam-3931	101	32	bi	bi	ADJ
ejpam-3931	101	33	-	-	ADJ
ejpam-3931	101	34	interior	interior	ADJ
ejpam-3931	101	35	ideal	ideal	ADJ
ejpam-3931	101	36	element	element	NOUN
ejpam-3931	101	37	of	of	ADP
ejpam-3931	101	38	s.	s.	PROPN
ejpam-3931	101	39	(	(	PUNCT
ejpam-3931	101	40	2	2	X
ejpam-3931	101	41	)	)	PUNCT
ejpam-3931	101	42	if	if	SCONJ
ejpam-3931	101	43	a	a	PRON
ejpam-3931	101	44	is	be	AUX
ejpam-3931	101	45	a	a	DET
ejpam-3931	101	46	left	left	ADJ
ejpam-3931	101	47	ideal	ideal	ADJ
ejpam-3931	101	48	element	element	NOUN
ejpam-3931	101	49	of	of	ADP
ejpam-3931	101	50	s	s	PRON
ejpam-3931	101	51	then	then	ADV
ejpam-3931	101	52	,	,	PUNCT
ejpam-3931	101	53	for	for	ADP
ejpam-3931	101	54	any	any	DET
ejpam-3931	101	55	b	b	PROPN
ejpam-3931	101	56	∈	∈	PROPN
ejpam-3931	101	57	s	s	PROPN
ejpam-3931	101	58	,	,	PUNCT
ejpam-3931	101	59	the	the	DET
ejpam-3931	101	60	element	element	NOUN
ejpam-3931	101	61	ba	ba	PROPN
ejpam-3931	101	62	is	be	AUX
ejpam-3931	101	63	a	a	DET
ejpam-3931	101	64	bi	bi	ADJ
ejpam-3931	101	65	-	-	ADJ
ejpam-3931	101	66	interior	interior	ADJ
ejpam-3931	101	67	ideal	ideal	ADJ
ejpam-3931	101	68	element	element	NOUN
ejpam-3931	101	69	of	of	ADP
ejpam-3931	101	70	s.	s.	PROPN
ejpam-3931	101	71	(	(	PUNCT
ejpam-3931	101	72	3	3	NUM
ejpam-3931	101	73	)	)	PUNCT
ejpam-3931	101	74	for	for	ADP
ejpam-3931	101	75	any	any	DET
ejpam-3931	101	76	a	a	PRON
ejpam-3931	101	77	,	,	PUNCT
ejpam-3931	101	78	b	b	PROPN
ejpam-3931	101	79	∈	∈	PROPN
ejpam-3931	101	80	s	s	PROPN
ejpam-3931	101	81	,	,	PUNCT
ejpam-3931	101	82	the	the	DET
ejpam-3931	101	83	element	element	NOUN
ejpam-3931	101	84	aeb	aeb	NOUN
ejpam-3931	101	85	is	be	AUX
ejpam-3931	101	86	a	a	DET
ejpam-3931	101	87	bi	bi	ADJ
ejpam-3931	101	88	-	-	ADJ
ejpam-3931	101	89	interior	interior	ADJ
ejpam-3931	101	90	ideal	ideal	ADJ
ejpam-3931	101	91	element	element	NOUN
ejpam-3931	101	92	of	of	ADP
ejpam-3931	101	93	s.	s.	PROPN
ejpam-3931	101	94	n.	n.	PROPN
ejpam-3931	102	1	kehayopulu	kehayopulu	PROPN
ejpam-3931	102	2	/	/	SYM
ejpam-3931	102	3	eur	eur	PROPN
ejpam-3931	102	4	.	.	PUNCT
ejpam-3931	103	1	j.	j.	PROPN
ejpam-3931	103	2	pure	pure	PROPN
ejpam-3931	103	3	appl	appl	PROPN
ejpam-3931	103	4	.	.	PROPN
ejpam-3931	103	5	math	math	PROPN
ejpam-3931	103	6	,	,	PUNCT
ejpam-3931	103	7	14	14	NUM
ejpam-3931	103	8	(	(	PUNCT
ejpam-3931	103	9	4	4	NUM
ejpam-3931	103	10	)	)	PUNCT
ejpam-3931	103	11	(	(	PUNCT
ejpam-3931	103	12	2021	2021	NUM
ejpam-3931	103	13	)	)	PUNCT
ejpam-3931	103	14	,	,	PUNCT
ejpam-3931	103	15	43	43	NUM
ejpam-3931	103	16	-	-	SYM
ejpam-3931	103	17	52	52	NUM
ejpam-3931	103	18	47	47	NUM
ejpam-3931	103	19	proof	proof	NOUN
ejpam-3931	103	20	.	.	PUNCT
ejpam-3931	104	1	(	(	PUNCT
ejpam-3931	104	2	1	1	X
ejpam-3931	104	3	)	)	PUNCT
ejpam-3931	104	4	let	let	VERB
ejpam-3931	104	5	a	a	PRON
ejpam-3931	104	6	be	be	AUX
ejpam-3931	104	7	a	a	DET
ejpam-3931	104	8	right	right	ADJ
ejpam-3931	104	9	ideal	ideal	ADJ
ejpam-3931	104	10	element	element	NOUN
ejpam-3931	104	11	of	of	ADP
ejpam-3931	104	12	s	s	PROPN
ejpam-3931	104	13	and	and	CCONJ
ejpam-3931	105	1	b	b	PROPN
ejpam-3931	105	2	∈	∈	PROPN
ejpam-3931	105	3	s.	s.	PROPN
ejpam-3931	105	4	then	then	ADV
ejpam-3931	105	5	(	(	PUNCT
ejpam-3931	105	6	ab)e(ab	ab)e(ab	PROPN
ejpam-3931	105	7	)	)	PUNCT
ejpam-3931	105	8	∧	∧	PROPN
ejpam-3931	105	9	e(ab)e	e(ab)e	ADJ
ejpam-3931	105	10	≤	≤	NOUN
ejpam-3931	105	11	(	(	PUNCT
ejpam-3931	105	12	ab)e(ab	ab)e(ab	PROPN
ejpam-3931	105	13	)	)	PUNCT
ejpam-3931	105	14	≤	≤	NOUN
ejpam-3931	105	15	(	(	PUNCT
ejpam-3931	105	16	ae)b	ae)b	PROPN
ejpam-3931	105	17	≤	≤	PROPN
ejpam-3931	105	18	ab	ab	PROPN
ejpam-3931	105	19	.	.	PUNCT
ejpam-3931	106	1	(	(	PUNCT
ejpam-3931	106	2	2	2	X
ejpam-3931	106	3	)	)	PUNCT
ejpam-3931	106	4	let	let	VERB
ejpam-3931	106	5	a	a	PRON
ejpam-3931	106	6	be	be	AUX
ejpam-3931	106	7	a	a	DET
ejpam-3931	106	8	left	left	ADJ
ejpam-3931	106	9	ideal	ideal	ADJ
ejpam-3931	106	10	element	element	NOUN
ejpam-3931	106	11	of	of	ADP
ejpam-3931	106	12	s	s	PROPN
ejpam-3931	106	13	and	and	CCONJ
ejpam-3931	107	1	b	b	PROPN
ejpam-3931	107	2	∈	∈	PROPN
ejpam-3931	107	3	s.	s.	PROPN
ejpam-3931	107	4	then	then	ADV
ejpam-3931	107	5	(	(	PUNCT
ejpam-3931	107	6	ba)e(ba	ba)e(ba	X
ejpam-3931	107	7	)	)	PUNCT
ejpam-3931	107	8	∧	∧	NOUN
ejpam-3931	107	9	e(ba)e	e(ba)e	NOUN
ejpam-3931	107	10	≤	≤	NOUN
ejpam-3931	107	11	(	(	PUNCT
ejpam-3931	107	12	ba)e(ba	ba)e(ba	NOUN
ejpam-3931	107	13	)	)	PUNCT
ejpam-3931	107	14	≤	≤	NOUN
ejpam-3931	107	15	b(ea	b(ea	NOUN
ejpam-3931	107	16	)	)	PUNCT
ejpam-3931	107	17	≤	≤	NUM
ejpam-3931	107	18	ba	ba	PROPN
ejpam-3931	107	19	.	.	PUNCT
ejpam-3931	108	1	(	(	PUNCT
ejpam-3931	108	2	3	3	X
ejpam-3931	108	3	)	)	PUNCT
ejpam-3931	108	4	let	let	VERB
ejpam-3931	108	5	a	a	DET
ejpam-3931	108	6	,	,	PUNCT
ejpam-3931	108	7	b	b	X
ejpam-3931	108	8	∈	∈	PROPN
ejpam-3931	108	9	s.	s.	PROPN
ejpam-3931	108	10	the	the	DET
ejpam-3931	108	11	element	element	NOUN
ejpam-3931	108	12	aeb	aeb	NOUN
ejpam-3931	108	13	is	be	AUX
ejpam-3931	108	14	a	a	DET
ejpam-3931	108	15	bi	bi	ADJ
ejpam-3931	108	16	-	-	ADJ
ejpam-3931	108	17	ideal	ideal	ADJ
ejpam-3931	108	18	element	element	NOUN
ejpam-3931	108	19	of	of	ADP
ejpam-3931	108	20	s.	s.	PROPN
ejpam-3931	108	21	in	in	ADP
ejpam-3931	108	22	fact	fact	NOUN
ejpam-3931	108	23	,	,	PUNCT
ejpam-3931	108	24	(	(	PUNCT
ejpam-3931	108	25	aeb)e(aeb	aeb)e(aeb	NOUN
ejpam-3931	108	26	)	)	PUNCT
ejpam-3931	109	1	≤	≤	NOUN
ejpam-3931	109	2	aeb	aeb	NOUN
ejpam-3931	109	3	.	.	PUNCT
ejpam-3931	110	1	then	then	ADV
ejpam-3931	110	2	,	,	PUNCT
ejpam-3931	110	3	by	by	ADP
ejpam-3931	110	4	proposition	proposition	NOUN
ejpam-3931	110	5	2.3(3	2.3(3	NUM
ejpam-3931	110	6	)	)	PUNCT
ejpam-3931	110	7	,	,	PUNCT
ejpam-3931	110	8	aeb	aeb	NOUN
ejpam-3931	110	9	is	be	AUX
ejpam-3931	110	10	a	a	DET
ejpam-3931	110	11	bi	bi	ADJ
ejpam-3931	110	12	-	-	ADJ
ejpam-3931	110	13	interior	interior	ADJ
ejpam-3931	110	14	ideal	ideal	ADJ
ejpam-3931	110	15	element	element	NOUN
ejpam-3931	110	16	of	of	ADP
ejpam-3931	110	17	s.	s.	PROPN
ejpam-3931	110	18	□	□	PUNCT
ejpam-3931	110	19	proposition	proposition	NOUN
ejpam-3931	110	20	2.7	2.7	NUM
ejpam-3931	110	21	.	.	PUNCT
ejpam-3931	111	1	the	the	DET
ejpam-3931	111	2	following	follow	VERB
ejpam-3931	111	3	assertions	assertion	NOUN
ejpam-3931	111	4	are	be	AUX
ejpam-3931	111	5	satisfied	satisfied	ADJ
ejpam-3931	111	6	:	:	PUNCT
ejpam-3931	111	7	(	(	PUNCT
ejpam-3931	111	8	1	1	X
ejpam-3931	111	9	)	)	PUNCT
ejpam-3931	111	10	if	if	SCONJ
ejpam-3931	111	11	s	s	VERB
ejpam-3931	111	12	is	be	AUX
ejpam-3931	111	13	a	a	DET
ejpam-3931	111	14	∧e	∧e	PROPN
ejpam-3931	111	15	-	-	PUNCT
ejpam-3931	111	16	semigroup	semigroup	PROPN
ejpam-3931	111	17	and	and	CCONJ
ejpam-3931	111	18	b	b	NOUN
ejpam-3931	111	19	,	,	PUNCT
ejpam-3931	111	20	t	t	PROPN
ejpam-3931	111	21	∈	∈	PROPN
ejpam-3931	111	22	s	s	VERB
ejpam-3931	111	23	such	such	ADJ
ejpam-3931	111	24	that	that	SCONJ
ejpam-3931	111	25	tet∧	tet∧	ADV
ejpam-3931	111	26	ete	ete	VERB
ejpam-3931	111	27	≤	≤	NUM
ejpam-3931	111	28	b	b	PROPN
ejpam-3931	111	29	≤	≤	NUM
ejpam-3931	111	30	t	t	PROPN
ejpam-3931	111	31	,	,	PUNCT
ejpam-3931	111	32	then	then	ADV
ejpam-3931	111	33	b	b	PROPN
ejpam-3931	111	34	is	be	AUX
ejpam-3931	111	35	a	a	DET
ejpam-3931	111	36	bi	bi	ADJ
ejpam-3931	111	37	-	-	ADJ
ejpam-3931	111	38	interior	interior	ADJ
ejpam-3931	111	39	ideal	ideal	ADJ
ejpam-3931	111	40	element	element	NOUN
ejpam-3931	111	41	of	of	ADP
ejpam-3931	111	42	s.	s.	PROPN
ejpam-3931	111	43	(	(	PUNCT
ejpam-3931	111	44	2	2	X
ejpam-3931	111	45	)	)	PUNCT
ejpam-3931	111	46	if	if	SCONJ
ejpam-3931	111	47	s	s	NOUN
ejpam-3931	111	48	is	be	AUX
ejpam-3931	111	49	an	an	DET
ejpam-3931	111	50	∧e	∧e	PROPN
ejpam-3931	111	51	-	-	PUNCT
ejpam-3931	111	52	semigroup	semigroup	NOUN
ejpam-3931	111	53	and	and	CCONJ
ejpam-3931	111	54	semilattice	semilattice	NOUN
ejpam-3931	111	55	under	under	ADP
ejpam-3931	111	56	∨	∨	NUM
ejpam-3931	111	57	at	at	ADP
ejpam-3931	111	58	the	the	DET
ejpam-3931	111	59	same	same	ADJ
ejpam-3931	111	60	time	time	NOUN
ejpam-3931	111	61	and	and	CCONJ
ejpam-3931	111	62	b	b	NOUN
ejpam-3931	111	63	,	,	PUNCT
ejpam-3931	111	64	t	t	PROPN
ejpam-3931	111	65	∈	∈	PROPN
ejpam-3931	111	66	s	s	VERB
ejpam-3931	111	67	such	such	ADJ
ejpam-3931	111	68	that	that	DET
ejpam-3931	111	69	tet	tet	NOUN
ejpam-3931	111	70	∨	∨	NOUN
ejpam-3931	111	71	ete	ete	PROPN
ejpam-3931	111	72	≤	≤	PROPN
ejpam-3931	111	73	b	b	PROPN
ejpam-3931	111	74	≤	≤	NUM
ejpam-3931	111	75	t	t	PROPN
ejpam-3931	111	76	,	,	PUNCT
ejpam-3931	111	77	then	then	ADV
ejpam-3931	111	78	b	b	PROPN
ejpam-3931	111	79	is	be	AUX
ejpam-3931	111	80	a	a	DET
ejpam-3931	111	81	bi	bi	ADJ
ejpam-3931	111	82	-	-	ADJ
ejpam-3931	111	83	interior	interior	ADJ
ejpam-3931	111	84	ideal	ideal	ADJ
ejpam-3931	111	85	element	element	NOUN
ejpam-3931	111	86	of	of	ADP
ejpam-3931	111	87	s.	s.	PROPN
ejpam-3931	111	88	proof	proof	PROPN
ejpam-3931	111	89	.	.	PUNCT
ejpam-3931	112	1	(	(	PUNCT
ejpam-3931	112	2	1	1	X
ejpam-3931	112	3	)	)	PUNCT
ejpam-3931	112	4	we	we	PRON
ejpam-3931	112	5	have	have	VERB
ejpam-3931	112	6	beb	beb	PROPN
ejpam-3931	112	7	∧	∧	PROPN
ejpam-3931	112	8	ebe	ebe	PROPN
ejpam-3931	112	9	≤	≤	PROPN
ejpam-3931	112	10	tet	tet	NOUN
ejpam-3931	112	11	∧	∧	PROPN
ejpam-3931	112	12	ete	ete	NOUN
ejpam-3931	112	13	≤	≤	PROPN
ejpam-3931	112	14	b	b	NOUN
ejpam-3931	112	15	,	,	PUNCT
ejpam-3931	112	16	so	so	CCONJ
ejpam-3931	112	17	b	b	PROPN
ejpam-3931	112	18	is	be	AUX
ejpam-3931	112	19	a	a	DET
ejpam-3931	112	20	bi	bi	ADJ
ejpam-3931	112	21	-	-	ADJ
ejpam-3931	112	22	interior	interior	ADJ
ejpam-3931	112	23	ideal	ideal	ADJ
ejpam-3931	112	24	element	element	NOUN
ejpam-3931	112	25	of	of	ADP
ejpam-3931	112	26	s.	s.	PROPN
ejpam-3931	112	27	(	(	PUNCT
ejpam-3931	112	28	2	2	X
ejpam-3931	112	29	)	)	PUNCT
ejpam-3931	112	30	we	we	PRON
ejpam-3931	112	31	have	have	VERB
ejpam-3931	112	32	beb	beb	PROPN
ejpam-3931	112	33	≤	≤	PROPN
ejpam-3931	112	34	tet	tet	NOUN
ejpam-3931	112	35	≤	≤	PROPN
ejpam-3931	112	36	tet	tet	NOUN
ejpam-3931	112	37	∨	∨	NOUN
ejpam-3931	112	38	ete	ete	PROPN
ejpam-3931	112	39	≤	≤	PROPN
ejpam-3931	112	40	b	b	PROPN
ejpam-3931	112	41	and	and	CCONJ
ejpam-3931	112	42	ebe	ebe	PROPN
ejpam-3931	112	43	≤	≤	PROPN
ejpam-3931	112	44	ete	ete	NOUN
ejpam-3931	112	45	≤	≤	PROPN
ejpam-3931	112	46	tet	tet	NOUN
ejpam-3931	112	47	∨	∨	NOUN
ejpam-3931	112	48	ete	ete	PROPN
ejpam-3931	112	49	≤	≤	PROPN
ejpam-3931	112	50	b	b	NOUN
ejpam-3931	112	51	;	;	PUNCT
ejpam-3931	112	52	thus	thus	ADV
ejpam-3931	112	53	we	we	PRON
ejpam-3931	112	54	have	have	VERB
ejpam-3931	112	55	beb	beb	PROPN
ejpam-3931	112	56	∧	∧	PROPN
ejpam-3931	112	57	ebe	ebe	PROPN
ejpam-3931	112	58	≤	≤	PROPN
ejpam-3931	112	59	b	b	PROPN
ejpam-3931	112	60	and	and	CCONJ
ejpam-3931	112	61	so	so	ADV
ejpam-3931	112	62	b	b	PROPN
ejpam-3931	112	63	is	be	AUX
ejpam-3931	112	64	a	a	DET
ejpam-3931	112	65	bi	bi	ADJ
ejpam-3931	112	66	-	-	ADJ
ejpam-3931	112	67	interior	interior	ADJ
ejpam-3931	112	68	ideal	ideal	ADJ
ejpam-3931	112	69	element	element	NOUN
ejpam-3931	112	70	of	of	ADP
ejpam-3931	112	71	s.	s.	PROPN
ejpam-3931	112	72	□	□	PUNCT
ejpam-3931	112	73	proposition	proposition	NOUN
ejpam-3931	112	74	2.8	2.8	NUM
ejpam-3931	112	75	.	.	PUNCT
ejpam-3931	113	1	let	let	VERB
ejpam-3931	113	2	s	s	PRON
ejpam-3931	113	3	be	be	AUX
ejpam-3931	113	4	a	a	DET
ejpam-3931	113	5	∧e	∧e	PROPN
ejpam-3931	113	6	-	-	PUNCT
ejpam-3931	113	7	semigroup	semigroup	NOUN
ejpam-3931	113	8	.	.	PUNCT
ejpam-3931	114	1	if	if	SCONJ
ejpam-3931	114	2	b	b	PROPN
ejpam-3931	114	3	is	be	AUX
ejpam-3931	114	4	a	a	DET
ejpam-3931	114	5	bi	bi	ADJ
ejpam-3931	114	6	-	-	ADJ
ejpam-3931	114	7	interior	interior	ADJ
ejpam-3931	114	8	ideal	ideal	ADJ
ejpam-3931	114	9	element	element	NOUN
ejpam-3931	114	10	of	of	ADP
ejpam-3931	114	11	s	s	PRON
ejpam-3931	114	12	and	and	CCONJ
ejpam-3931	114	13	t	t	PROPN
ejpam-3931	114	14	∈	∈	PROPN
ejpam-3931	114	15	s	s	VERB
ejpam-3931	114	16	such	such	ADJ
ejpam-3931	114	17	that	that	SCONJ
ejpam-3931	114	18	t	t	PROPN
ejpam-3931	114	19	≤	≤	NUM
ejpam-3931	114	20	b	b	X
ejpam-3931	114	21	≤	≤	NOUN
ejpam-3931	114	22	bt	bt	PROPN
ejpam-3931	114	23	,	,	PUNCT
ejpam-3931	114	24	then	then	ADV
ejpam-3931	114	25	bt	bt	PROPN
ejpam-3931	114	26	is	be	AUX
ejpam-3931	114	27	a	a	DET
ejpam-3931	114	28	bi	bi	ADJ
ejpam-3931	114	29	-	-	ADJ
ejpam-3931	114	30	interior	interior	ADJ
ejpam-3931	114	31	ideal	ideal	ADJ
ejpam-3931	114	32	element	element	NOUN
ejpam-3931	114	33	of	of	ADP
ejpam-3931	114	34	s.	s.	PROPN
ejpam-3931	114	35	proof	proof	PROPN
ejpam-3931	114	36	.	.	PUNCT
ejpam-3931	115	1	let	let	VERB
ejpam-3931	115	2	b	b	X
ejpam-3931	115	3	be	be	AUX
ejpam-3931	115	4	a	a	DET
ejpam-3931	115	5	bi	bi	ADJ
ejpam-3931	115	6	-	-	ADJ
ejpam-3931	115	7	interior	interior	ADJ
ejpam-3931	115	8	ideal	ideal	ADJ
ejpam-3931	115	9	element	element	NOUN
ejpam-3931	115	10	of	of	ADP
ejpam-3931	115	11	s	s	PRON
ejpam-3931	115	12	and	and	CCONJ
ejpam-3931	115	13	t	t	X
ejpam-3931	115	14	≤	≤	NUM
ejpam-3931	115	15	b	b	X
ejpam-3931	115	16	≤	≤	NUM
ejpam-3931	115	17	bt	bt	PROPN
ejpam-3931	115	18	.	.	PUNCT
ejpam-3931	116	1	then	then	ADV
ejpam-3931	116	2	we	we	PRON
ejpam-3931	116	3	have	have	VERB
ejpam-3931	116	4	(	(	PUNCT
ejpam-3931	116	5	bt)e(bt	bt)e(bt	NOUN
ejpam-3931	116	6	)	)	PUNCT
ejpam-3931	116	7	∧	∧	NOUN
ejpam-3931	116	8	e(bt)e	e(bt)e	PROPN
ejpam-3931	116	9	≤	≤	NUM
ejpam-3931	116	10	bet	bet	NOUN
ejpam-3931	117	1	∧	∧	PROPN
ejpam-3931	117	2	ebe	ebe	PROPN
ejpam-3931	117	3	≤	≤	PUNCT
ejpam-3931	117	4	beb	beb	PROPN
ejpam-3931	117	5	∧	∧	PROPN
ejpam-3931	117	6	ebe	ebe	PROPN
ejpam-3931	117	7	≤	≤	PROPN
ejpam-3931	117	8	b	b	PROPN
ejpam-3931	117	9	≤	≤	NOUN
ejpam-3931	117	10	bt	bt	PROPN
ejpam-3931	117	11	,	,	PUNCT
ejpam-3931	117	12	thus	thus	ADV
ejpam-3931	117	13	bt	bt	NOUN
ejpam-3931	117	14	is	be	AUX
ejpam-3931	117	15	a	a	DET
ejpam-3931	117	16	bi	bi	ADJ
ejpam-3931	117	17	-	-	ADJ
ejpam-3931	117	18	interior	interior	ADJ
ejpam-3931	117	19	ideal	ideal	ADJ
ejpam-3931	117	20	element	element	NOUN
ejpam-3931	117	21	of	of	ADP
ejpam-3931	117	22	s.	s.	PROPN
ejpam-3931	117	23	□	□	PUNCT
ejpam-3931	117	24	theorem	theorem	VERB
ejpam-3931	117	25	2.9	2.9	NUM
ejpam-3931	117	26	.	.	PUNCT
ejpam-3931	118	1	let	let	VERB
ejpam-3931	118	2	s	s	PRON
ejpam-3931	118	3	be	be	AUX
ejpam-3931	118	4	a	a	DET
ejpam-3931	118	5	∧e	∧e	PROPN
ejpam-3931	118	6	-	-	PUNCT
ejpam-3931	118	7	semigroup	semigroup	NOUN
ejpam-3931	118	8	such	such	ADJ
ejpam-3931	118	9	that	that	SCONJ
ejpam-3931	118	10	x	x	X
ejpam-3931	118	11	≤	≤	PROPN
ejpam-3931	118	12	xe	xe	PROPN
ejpam-3931	118	13	for	for	ADP
ejpam-3931	118	14	every	every	DET
ejpam-3931	118	15	x	x	PROPN
ejpam-3931	118	16	∈	∈	PROPN
ejpam-3931	118	17	s.	s.	PROPN
ejpam-3931	118	18	let	let	VERB
ejpam-3931	118	19	a	a	PRON
ejpam-3931	118	20	be	be	AUX
ejpam-3931	118	21	a	a	DET
ejpam-3931	118	22	minimal	minimal	ADJ
ejpam-3931	118	23	right	right	ADJ
ejpam-3931	118	24	ideal	ideal	ADJ
ejpam-3931	118	25	element	element	NOUN
ejpam-3931	118	26	and	and	CCONJ
ejpam-3931	118	27	b	b	NOUN
ejpam-3931	118	28	a	a	DET
ejpam-3931	118	29	minimal	minimal	ADJ
ejpam-3931	118	30	left	leave	VERB
ejpam-3931	118	31	ideal	ideal	ADJ
ejpam-3931	118	32	element	element	NOUN
ejpam-3931	118	33	of	of	ADP
ejpam-3931	118	34	s.	s.	PROPN
ejpam-3931	118	35	then	then	ADV
ejpam-3931	118	36	ab	ab	PROPN
ejpam-3931	118	37	is	be	AUX
ejpam-3931	118	38	a	a	DET
ejpam-3931	118	39	minimal	minimal	ADJ
ejpam-3931	118	40	bi	bi	ADJ
ejpam-3931	118	41	-	-	ADJ
ejpam-3931	118	42	interior	interior	ADJ
ejpam-3931	118	43	ideal	ideal	ADJ
ejpam-3931	118	44	element	element	NOUN
ejpam-3931	118	45	of	of	ADP
ejpam-3931	118	46	s.	s.	PROPN
ejpam-3931	118	47	proof	proof	PROPN
ejpam-3931	118	48	.	.	PUNCT
ejpam-3931	119	1	since	since	SCONJ
ejpam-3931	119	2	a	a	PRON
ejpam-3931	119	3	is	be	AUX
ejpam-3931	119	4	a	a	DET
ejpam-3931	119	5	right	right	ADJ
ejpam-3931	119	6	ideal	ideal	ADJ
ejpam-3931	119	7	element	element	NOUN
ejpam-3931	119	8	of	of	ADP
ejpam-3931	119	9	s	s	PROPN
ejpam-3931	119	10	,	,	PUNCT
ejpam-3931	119	11	we	we	PRON
ejpam-3931	119	12	have	have	VERB
ejpam-3931	119	13	(	(	PUNCT
ejpam-3931	119	14	ab)e(ab	ab)e(ab	ADV
ejpam-3931	119	15	)	)	PUNCT
ejpam-3931	119	16	≤	≤	NOUN
ejpam-3931	119	17	(	(	PUNCT
ejpam-3931	119	18	ae)b	ae)b	PROPN
ejpam-3931	119	19	≤	≤	PROPN
ejpam-3931	119	20	ab	ab	PROPN
ejpam-3931	119	21	,	,	PUNCT
ejpam-3931	119	22	then	then	ADV
ejpam-3931	119	23	ab	ab	PROPN
ejpam-3931	119	24	is	be	AUX
ejpam-3931	119	25	a	a	DET
ejpam-3931	119	26	bi	bi	ADJ
ejpam-3931	119	27	-	-	ADJ
ejpam-3931	119	28	ideal	ideal	ADJ
ejpam-3931	119	29	element	element	NOUN
ejpam-3931	119	30	of	of	ADP
ejpam-3931	119	31	s	s	PRON
ejpam-3931	119	32	and	and	CCONJ
ejpam-3931	119	33	so	so	ADV
ejpam-3931	119	34	ab	ab	PROPN
ejpam-3931	119	35	is	be	AUX
ejpam-3931	119	36	a	a	DET
ejpam-3931	119	37	bi	bi	ADJ
ejpam-3931	119	38	-	-	ADJ
ejpam-3931	119	39	interior	interior	ADJ
ejpam-3931	119	40	ideal	ideal	ADJ
ejpam-3931	119	41	element	element	NOUN
ejpam-3931	119	42	of	of	ADP
ejpam-3931	119	43	s	s	PROPN
ejpam-3931	119	44	(	(	PUNCT
ejpam-3931	119	45	by	by	ADP
ejpam-3931	119	46	prop	prop	NOUN
ejpam-3931	119	47	.	.	PUNCT
ejpam-3931	120	1	2.3(3	2.3(3	NUM
ejpam-3931	120	2	)	)	PUNCT
ejpam-3931	120	3	)	)	PUNCT
ejpam-3931	120	4	.	.	PUNCT
ejpam-3931	121	1	let	let	VERB
ejpam-3931	121	2	now	now	ADV
ejpam-3931	121	3	z	z	AUX
ejpam-3931	121	4	be	be	AUX
ejpam-3931	121	5	a	a	DET
ejpam-3931	121	6	bi	bi	ADJ
ejpam-3931	121	7	-	-	ADJ
ejpam-3931	121	8	interior	interior	ADJ
ejpam-3931	121	9	ideal	ideal	ADJ
ejpam-3931	121	10	element	element	NOUN
ejpam-3931	121	11	of	of	ADP
ejpam-3931	121	12	s	s	PRON
ejpam-3931	121	13	such	such	ADJ
ejpam-3931	121	14	that	that	SCONJ
ejpam-3931	121	15	z	z	PROPN
ejpam-3931	121	16	≤	≤	PROPN
ejpam-3931	122	1	ab	ab	PROPN
ejpam-3931	122	2	.	.	PUNCT
ejpam-3931	123	1	then	then	ADV
ejpam-3931	123	2	ez	ez	PROPN
ejpam-3931	123	3	≤	≤	PROPN
ejpam-3931	123	4	e(ab	e(ab	PROPN
ejpam-3931	123	5	)	)	PUNCT
ejpam-3931	123	6	≤	≤	NUM
ejpam-3931	123	7	eb	eb	PROPN
ejpam-3931	123	8	≤	≤	PROPN
ejpam-3931	123	9	b	b	PROPN
ejpam-3931	123	10	and	and	CCONJ
ejpam-3931	123	11	ze	ze	PROPN
ejpam-3931	123	12	≤	≤	NOUN
ejpam-3931	123	13	(	(	PUNCT
ejpam-3931	123	14	ab)e	ab)e	PROPN
ejpam-3931	123	15	≤	≤	NUM
ejpam-3931	123	16	ae	ae	PROPN
ejpam-3931	123	17	≤	≤	PROPN
ejpam-3931	123	18	a.	a.	NOUN
ejpam-3931	123	19	since	since	SCONJ
ejpam-3931	123	20	ez	ez	PROPN
ejpam-3931	123	21	is	be	AUX
ejpam-3931	123	22	a	a	DET
ejpam-3931	123	23	left	left	ADJ
ejpam-3931	123	24	ideal	ideal	ADJ
ejpam-3931	123	25	element	element	NOUN
ejpam-3931	123	26	of	of	ADP
ejpam-3931	123	27	s	s	PROPN
ejpam-3931	123	28	,	,	PUNCT
ejpam-3931	123	29	ez	ez	PROPN
ejpam-3931	123	30	≤	≤	PROPN
ejpam-3931	123	31	b	b	PROPN
ejpam-3931	123	32	,	,	PUNCT
ejpam-3931	123	33	and	and	CCONJ
ejpam-3931	123	34	b	b	NOUN
ejpam-3931	123	35	is	be	AUX
ejpam-3931	123	36	a	a	DET
ejpam-3931	123	37	minimal	minimal	ADJ
ejpam-3931	123	38	left	leave	VERB
ejpam-3931	123	39	ideal	ideal	ADJ
ejpam-3931	123	40	element	element	NOUN
ejpam-3931	123	41	of	of	ADP
ejpam-3931	123	42	s	s	PROPN
ejpam-3931	123	43	,	,	PUNCT
ejpam-3931	123	44	we	we	PRON
ejpam-3931	123	45	have	have	VERB
ejpam-3931	123	46	ez	ez	PROPN
ejpam-3931	123	47	=	=	PROPN
ejpam-3931	123	48	b.	b.	PROPN
ejpam-3931	123	49	since	since	SCONJ
ejpam-3931	123	50	ze	ze	PROPN
ejpam-3931	123	51	is	be	AUX
ejpam-3931	123	52	a	a	DET
ejpam-3931	123	53	right	right	ADJ
ejpam-3931	123	54	ideal	ideal	ADJ
ejpam-3931	123	55	element	element	NOUN
ejpam-3931	123	56	of	of	ADP
ejpam-3931	123	57	s	s	PROPN
ejpam-3931	123	58	,	,	PUNCT
ejpam-3931	123	59	ze	ze	PROPN
ejpam-3931	123	60	≤	≤	PROPN
ejpam-3931	123	61	a	a	PRON
ejpam-3931	123	62	,	,	PUNCT
ejpam-3931	123	63	and	and	CCONJ
ejpam-3931	123	64	a	a	PRON
ejpam-3931	123	65	is	be	AUX
ejpam-3931	123	66	a	a	DET
ejpam-3931	123	67	minimal	minimal	ADJ
ejpam-3931	123	68	right	right	ADJ
ejpam-3931	123	69	ideal	ideal	ADJ
ejpam-3931	123	70	element	element	NOUN
ejpam-3931	123	71	of	of	ADP
ejpam-3931	123	72	s	s	PROPN
ejpam-3931	123	73	,	,	PUNCT
ejpam-3931	123	74	we	we	PRON
ejpam-3931	123	75	have	have	VERB
ejpam-3931	123	76	ze	ze	NOUN
ejpam-3931	123	77	=	=	NOUN
ejpam-3931	123	78	a.	a.	NOUN
ejpam-3931	124	1	then	then	ADV
ejpam-3931	124	2	we	we	PRON
ejpam-3931	124	3	have	have	VERB
ejpam-3931	124	4	ab	ab	PROPN
ejpam-3931	124	5	=	=	SYM
ejpam-3931	124	6	(	(	PUNCT
ejpam-3931	124	7	ze)(ez	ze)(ez	PROPN
ejpam-3931	124	8	)	)	PUNCT
ejpam-3931	124	9	≤	≤	NUM
ejpam-3931	124	10	zez	zez	NOUN
ejpam-3931	124	11	.	.	PUNCT
ejpam-3931	125	1	by	by	ADP
ejpam-3931	125	2	hypothesis	hypothesis	NOUN
ejpam-3931	125	3	,	,	PUNCT
ejpam-3931	125	4	we	we	PRON
ejpam-3931	125	5	have	have	VERB
ejpam-3931	125	6	ab	ab	PROPN
ejpam-3931	125	7	≤	≤	NUM
ejpam-3931	125	8	(	(	PUNCT
ejpam-3931	125	9	ab)e	ab)e	PROPN
ejpam-3931	125	10	=	=	SYM
ejpam-3931	125	11	abe	abe	PROPN
ejpam-3931	125	12	=	=	SYM
ejpam-3931	125	13	(	(	PUNCT
ejpam-3931	125	14	ze)(ez)e	ze)(ez)e	NOUN
ejpam-3931	125	15	≤	≤	NUM
ejpam-3931	125	16	eze	eze	NOUN
ejpam-3931	125	17	.	.	PUNCT
ejpam-3931	126	1	thus	thus	ADV
ejpam-3931	126	2	we	we	PRON
ejpam-3931	126	3	have	have	VERB
ejpam-3931	126	4	ab	ab	PROPN
ejpam-3931	126	5	≤	≤	NUM
ejpam-3931	126	6	zez∧eze	zez∧eze	PROPN
ejpam-3931	126	7	≤	≤	PROPN
ejpam-3931	126	8	z.	z.	PROPN
ejpam-3931	127	1	then	then	ADV
ejpam-3931	127	2	we	we	PRON
ejpam-3931	127	3	obtain	obtain	VERB
ejpam-3931	127	4	z	z	NOUN
ejpam-3931	127	5	=	=	SYM
ejpam-3931	127	6	ab	ab	PROPN
ejpam-3931	127	7	and	and	CCONJ
ejpam-3931	127	8	the	the	DET
ejpam-3931	127	9	proof	proof	NOUN
ejpam-3931	127	10	is	be	AUX
ejpam-3931	127	11	complete	complete	ADJ
ejpam-3931	127	12	.	.	PUNCT
ejpam-3931	128	1	□	□	PUNCT
ejpam-3931	128	2	.	.	PUNCT
ejpam-3931	128	3	corollary	corollary	ADJ
ejpam-3931	128	4	2.10	2.10	NUM
ejpam-3931	128	5	.	.	PUNCT
ejpam-3931	129	1	(	(	PUNCT
ejpam-3931	129	2	cf	cf	NOUN
ejpam-3931	129	3	.	.	PUNCT
ejpam-3931	130	1	also	also	ADV
ejpam-3931	130	2	[	[	X
ejpam-3931	130	3	4	4	NUM
ejpam-3931	130	4	;	;	PUNCT
ejpam-3931	130	5	theorem	theorem	VERB
ejpam-3931	130	6	3.10	3.10	NUM
ejpam-3931	130	7	]	]	PUNCT
ejpam-3931	130	8	)	)	PUNCT
ejpam-3931	130	9	let	let	VERB
ejpam-3931	130	10	s	s	PRON
ejpam-3931	130	11	be	be	AUX
ejpam-3931	130	12	a	a	DET
ejpam-3931	130	13	semigroup	semigroup	NOUN
ejpam-3931	130	14	such	such	ADJ
ejpam-3931	130	15	that	that	SCONJ
ejpam-3931	130	16	a	a	DET
ejpam-3931	130	17	⊆	⊆	NUM
ejpam-3931	130	18	as	as	ADP
ejpam-3931	130	19	for	for	ADP
ejpam-3931	130	20	every	every	DET
ejpam-3931	130	21	a	a	DET
ejpam-3931	130	22	⊆	⊆	NUM
ejpam-3931	130	23	s.	s.	NOUN
ejpam-3931	130	24	if	if	SCONJ
ejpam-3931	130	25	a	a	PRON
ejpam-3931	130	26	is	be	AUX
ejpam-3931	130	27	a	a	DET
ejpam-3931	130	28	minimal	minimal	ADJ
ejpam-3931	130	29	right	right	ADJ
ejpam-3931	130	30	ideal	ideal	NOUN
ejpam-3931	130	31	and	and	CCONJ
ejpam-3931	130	32	b	b	NOUN
ejpam-3931	130	33	is	be	AUX
ejpam-3931	130	34	a	a	DET
ejpam-3931	130	35	minimal	minimal	ADJ
ejpam-3931	130	36	left	left	ADJ
ejpam-3931	130	37	ideal	ideal	NOUN
ejpam-3931	130	38	of	of	ADP
ejpam-3931	130	39	s	s	PROPN
ejpam-3931	130	40	,	,	PUNCT
ejpam-3931	130	41	then	then	ADV
ejpam-3931	130	42	the	the	DET
ejpam-3931	130	43	product	product	NOUN
ejpam-3931	130	44	ab	ab	PROPN
ejpam-3931	130	45	is	be	AUX
ejpam-3931	130	46	a	a	DET
ejpam-3931	130	47	minimal	minimal	ADJ
ejpam-3931	130	48	bi	bi	ADJ
ejpam-3931	130	49	-	-	ADJ
ejpam-3931	130	50	interior	interior	ADJ
ejpam-3931	130	51	ideal	ideal	NOUN
ejpam-3931	130	52	of	of	ADP
ejpam-3931	130	53	s.	s.	PROPN
ejpam-3931	130	54	n.	n.	PROPN
ejpam-3931	130	55	kehayopulu	kehayopulu	PROPN
ejpam-3931	130	56	/	/	SYM
ejpam-3931	130	57	eur	eur	PROPN
ejpam-3931	130	58	.	.	PUNCT
ejpam-3931	131	1	j.	j.	PROPN
ejpam-3931	131	2	pure	pure	PROPN
ejpam-3931	131	3	appl	appl	PROPN
ejpam-3931	131	4	.	.	PROPN
ejpam-3931	131	5	math	math	PROPN
ejpam-3931	131	6	,	,	PUNCT
ejpam-3931	131	7	14	14	NUM
ejpam-3931	131	8	(	(	PUNCT
ejpam-3931	131	9	4	4	NUM
ejpam-3931	131	10	)	)	PUNCT
ejpam-3931	131	11	(	(	PUNCT
ejpam-3931	131	12	2021	2021	NUM
ejpam-3931	131	13	)	)	PUNCT
ejpam-3931	131	14	,	,	PUNCT
ejpam-3931	131	15	43	43	NUM
ejpam-3931	131	16	-	-	SYM
ejpam-3931	131	17	52	52	NUM
ejpam-3931	131	18	48	48	NUM
ejpam-3931	131	19	3	3	NUM
ejpam-3931	131	20	.	.	PUNCT
ejpam-3931	132	1	bi	bi	ADJ
ejpam-3931	132	2	-	-	ADJ
ejpam-3931	132	3	interior	interior	ADJ
ejpam-3931	132	4	ideal	ideal	ADJ
ejpam-3931	132	5	elements	element	NOUN
ejpam-3931	132	6	in	in	ADP
ejpam-3931	132	7	left	left	ADJ
ejpam-3931	132	8	simple	simple	ADJ
ejpam-3931	132	9	,	,	PUNCT
ejpam-3931	132	10	simple	simple	ADJ
ejpam-3931	132	11	and	and	CCONJ
ejpam-3931	132	12	bi	bi	ADJ
ejpam-3931	132	13	-	-	ADJ
ejpam-3931	132	14	interior	interior	ADJ
ejpam-3931	132	15	simple	simple	ADJ
ejpam-3931	132	16	∧e	∧e	PROPN
ejpam-3931	132	17	-	-	PUNCT
ejpam-3931	132	18	semigroups	semigroup	NOUN
ejpam-3931	132	19	definition	definition	NOUN
ejpam-3931	132	20	3.1	3.1	NUM
ejpam-3931	132	21	.	.	PUNCT
ejpam-3931	133	1	a	a	DET
ejpam-3931	133	2	poe	poe	PROPN
ejpam-3931	133	3	-	-	PUNCT
ejpam-3931	133	4	groupoid	groupoid	PROPN
ejpam-3931	133	5	s	s	PART
ejpam-3931	133	6	is	be	AUX
ejpam-3931	133	7	said	say	VERB
ejpam-3931	133	8	to	to	PART
ejpam-3931	133	9	be	be	AUX
ejpam-3931	133	10	left	leave	VERB
ejpam-3931	133	11	(	(	PUNCT
ejpam-3931	133	12	resp	resp	NOUN
ejpam-3931	133	13	.	.	PUNCT
ejpam-3931	134	1	right	right	ADJ
ejpam-3931	134	2	)	)	PUNCT
ejpam-3931	134	3	simple	simple	ADJ
ejpam-3931	134	4	if	if	SCONJ
ejpam-3931	134	5	for	for	ADP
ejpam-3931	134	6	every	every	DET
ejpam-3931	134	7	left	left	NOUN
ejpam-3931	134	8	(	(	PUNCT
ejpam-3931	134	9	resp	resp	NOUN
ejpam-3931	134	10	.	.	PUNCT
ejpam-3931	135	1	right	right	ADJ
ejpam-3931	135	2	)	)	PUNCT
ejpam-3931	135	3	ideal	ideal	PROPN
ejpam-3931	135	4	element	element	NOUN
ejpam-3931	135	5	a	a	PRON
ejpam-3931	135	6	of	of	ADP
ejpam-3931	135	7	s	s	PRON
ejpam-3931	135	8	we	we	PRON
ejpam-3931	135	9	have	have	VERB
ejpam-3931	135	10	a	a	DET
ejpam-3931	135	11	=	=	PUNCT
ejpam-3931	135	12	e.	e.	PROPN
ejpam-3931	135	13	that	that	PRON
ejpam-3931	135	14	is	be	AUX
ejpam-3931	135	15	,	,	PUNCT
ejpam-3931	135	16	if	if	SCONJ
ejpam-3931	135	17	e	e	NOUN
ejpam-3931	135	18	is	be	AUX
ejpam-3931	135	19	the	the	DET
ejpam-3931	135	20	only	only	ADJ
ejpam-3931	135	21	left	leave	VERB
ejpam-3931	135	22	(	(	PUNCT
ejpam-3931	135	23	resp	resp	NOUN
ejpam-3931	135	24	.	.	PUNCT
ejpam-3931	136	1	right	right	ADJ
ejpam-3931	136	2	)	)	PUNCT
ejpam-3931	136	3	ideal	ideal	ADJ
ejpam-3931	136	4	element	element	NOUN
ejpam-3931	136	5	of	of	ADP
ejpam-3931	136	6	s.	s.	PROPN
ejpam-3931	136	7	it	it	PRON
ejpam-3931	136	8	is	be	AUX
ejpam-3931	136	9	called	call	VERB
ejpam-3931	136	10	simple	simple	ADJ
ejpam-3931	136	11	if	if	SCONJ
ejpam-3931	136	12	for	for	ADP
ejpam-3931	136	13	every	every	DET
ejpam-3931	136	14	ideal	ideal	ADJ
ejpam-3931	136	15	element	element	NOUN
ejpam-3931	136	16	a	a	PRON
ejpam-3931	136	17	of	of	ADP
ejpam-3931	136	18	s	s	PRON
ejpam-3931	136	19	we	we	PRON
ejpam-3931	136	20	have	have	VERB
ejpam-3931	136	21	a	a	DET
ejpam-3931	136	22	=	=	SYM
ejpam-3931	136	23	e	e	NOUN
ejpam-3931	136	24	;	;	PUNCT
ejpam-3931	136	25	that	that	PRON
ejpam-3931	136	26	is	is	ADV
ejpam-3931	136	27	,	,	PUNCT
ejpam-3931	136	28	if	if	SCONJ
ejpam-3931	136	29	e	e	NOUN
ejpam-3931	136	30	is	be	AUX
ejpam-3931	136	31	the	the	DET
ejpam-3931	136	32	only	only	ADJ
ejpam-3931	136	33	ideal	ideal	ADJ
ejpam-3931	136	34	element	element	NOUN
ejpam-3931	136	35	of	of	ADP
ejpam-3931	136	36	s.	s.	PROPN
ejpam-3931	136	37	if	if	SCONJ
ejpam-3931	136	38	s	s	PROPN
ejpam-3931	136	39	is	be	AUX
ejpam-3931	136	40	left	leave	VERB
ejpam-3931	136	41	(	(	PUNCT
ejpam-3931	136	42	or	or	CCONJ
ejpam-3931	136	43	right	right	ADJ
ejpam-3931	136	44	)	)	PUNCT
ejpam-3931	136	45	simple	simple	NOUN
ejpam-3931	136	46	,	,	PUNCT
ejpam-3931	136	47	then	then	ADV
ejpam-3931	136	48	it	it	PRON
ejpam-3931	136	49	is	be	AUX
ejpam-3931	136	50	simple	simple	ADJ
ejpam-3931	136	51	.	.	PUNCT
ejpam-3931	137	1	proposition	proposition	NOUN
ejpam-3931	137	2	3.2	3.2	NUM
ejpam-3931	137	3	.	.	PUNCT
ejpam-3931	138	1	if	if	SCONJ
ejpam-3931	138	2	s	s	NOUN
ejpam-3931	138	3	is	be	AUX
ejpam-3931	138	4	a	a	DET
ejpam-3931	138	5	left	left	ADJ
ejpam-3931	138	6	(	(	PUNCT
ejpam-3931	138	7	resp	resp	NOUN
ejpam-3931	138	8	.	.	PUNCT
ejpam-3931	139	1	right	right	ADJ
ejpam-3931	139	2	)	)	PUNCT
ejpam-3931	139	3	simple	simple	ADJ
ejpam-3931	139	4	∧e	∧e	PROPN
ejpam-3931	139	5	-	-	PUNCT
ejpam-3931	139	6	semigroup	semigroup	PROPN
ejpam-3931	139	7	and	and	CCONJ
ejpam-3931	139	8	b	b	NOUN
ejpam-3931	139	9	is	be	AUX
ejpam-3931	139	10	a	a	DET
ejpam-3931	139	11	bi	bi	ADJ
ejpam-3931	139	12	-	-	ADJ
ejpam-3931	139	13	interior	interior	ADJ
ejpam-3931	139	14	ideal	ideal	ADJ
ejpam-3931	139	15	element	element	NOUN
ejpam-3931	139	16	of	of	ADP
ejpam-3931	139	17	s	s	PROPN
ejpam-3931	139	18	,	,	PUNCT
ejpam-3931	139	19	then	then	ADV
ejpam-3931	139	20	b	b	PROPN
ejpam-3931	139	21	is	be	AUX
ejpam-3931	139	22	a	a	DET
ejpam-3931	139	23	right	right	ADJ
ejpam-3931	139	24	(	(	PUNCT
ejpam-3931	139	25	resp	resp	NOUN
ejpam-3931	139	26	.	.	PUNCT
ejpam-3931	140	1	left	left	ADJ
ejpam-3931	140	2	)	)	PUNCT
ejpam-3931	140	3	ideal	ideal	ADJ
ejpam-3931	140	4	element	element	NOUN
ejpam-3931	140	5	of	of	ADP
ejpam-3931	140	6	s.	s.	PROPN
ejpam-3931	140	7	proof	proof	PROPN
ejpam-3931	140	8	.	.	PUNCT
ejpam-3931	141	1	let	let	VERB
ejpam-3931	141	2	s	s	PRON
ejpam-3931	141	3	be	be	AUX
ejpam-3931	141	4	left	leave	VERB
ejpam-3931	141	5	simple	simple	ADJ
ejpam-3931	141	6	and	and	CCONJ
ejpam-3931	141	7	b	b	DET
ejpam-3931	141	8	a	a	DET
ejpam-3931	141	9	bi	bi	ADJ
ejpam-3931	141	10	-	-	ADJ
ejpam-3931	141	11	interior	interior	ADJ
ejpam-3931	141	12	ideal	ideal	ADJ
ejpam-3931	141	13	element	element	NOUN
ejpam-3931	141	14	of	of	ADP
ejpam-3931	141	15	s.	s.	PROPN
ejpam-3931	141	16	since	since	SCONJ
ejpam-3931	141	17	eb	eb	PROPN
ejpam-3931	141	18	is	be	AUX
ejpam-3931	141	19	a	a	DET
ejpam-3931	141	20	left	left	ADJ
ejpam-3931	141	21	ideal	ideal	ADJ
ejpam-3931	141	22	element	element	NOUN
ejpam-3931	141	23	of	of	ADP
ejpam-3931	141	24	s	s	PRON
ejpam-3931	141	25	and	and	CCONJ
ejpam-3931	141	26	s	s	VERB
ejpam-3931	141	27	is	be	AUX
ejpam-3931	141	28	left	leave	VERB
ejpam-3931	141	29	simple	simple	ADJ
ejpam-3931	141	30	,	,	PUNCT
ejpam-3931	141	31	we	we	PRON
ejpam-3931	141	32	have	have	VERB
ejpam-3931	141	33	eb	eb	PROPN
ejpam-3931	141	34	=	=	PROPN
ejpam-3931	141	35	e.	e.	PROPN
ejpam-3931	141	36	since	since	SCONJ
ejpam-3931	141	37	beb	beb	PROPN
ejpam-3931	141	38	∧	∧	PROPN
ejpam-3931	141	39	ebe	ebe	PROPN
ejpam-3931	141	40	≤	≤	PROPN
ejpam-3931	141	41	b	b	PROPN
ejpam-3931	141	42	,	,	PUNCT
ejpam-3931	141	43	we	we	PRON
ejpam-3931	141	44	get	get	AUX
ejpam-3931	141	45	be	be	AUX
ejpam-3931	141	46	∧	∧	PROPN
ejpam-3931	141	47	e2	e2	PROPN
ejpam-3931	141	48	≤	≤	PROPN
ejpam-3931	141	49	b.	b.	PROPN
ejpam-3931	141	50	since	since	SCONJ
ejpam-3931	141	51	e2	e2	PROPN
ejpam-3931	141	52	is	be	AUX
ejpam-3931	141	53	a	a	DET
ejpam-3931	141	54	left	left	ADJ
ejpam-3931	141	55	ideal	ideal	ADJ
ejpam-3931	141	56	element	element	NOUN
ejpam-3931	141	57	of	of	ADP
ejpam-3931	141	58	s	s	PRON
ejpam-3931	141	59	and	and	CCONJ
ejpam-3931	141	60	s	s	VERB
ejpam-3931	141	61	is	be	AUX
ejpam-3931	141	62	left	leave	VERB
ejpam-3931	141	63	simple	simple	ADJ
ejpam-3931	141	64	,	,	PUNCT
ejpam-3931	141	65	we	we	PRON
ejpam-3931	141	66	have	have	VERB
ejpam-3931	141	67	e2	e2	PROPN
ejpam-3931	141	68	=	=	SYM
ejpam-3931	141	69	e.	e.	PROPN
ejpam-3931	142	1	then	then	ADV
ejpam-3931	142	2	we	we	PRON
ejpam-3931	142	3	have	have	AUX
ejpam-3931	142	4	be	be	VERB
ejpam-3931	142	5	=	=	PRON
ejpam-3931	142	6	be	be	AUX
ejpam-3931	142	7	∧	∧	PROPN
ejpam-3931	142	8	e	e	NOUN
ejpam-3931	142	9	≤	≤	NOUN
ejpam-3931	142	10	b	b	NUM
ejpam-3931	142	11	,	,	PUNCT
ejpam-3931	142	12	then	then	ADV
ejpam-3931	142	13	be	be	AUX
ejpam-3931	142	14	≤	≤	NUM
ejpam-3931	142	15	b	b	NOUN
ejpam-3931	143	1	and	and	CCONJ
ejpam-3931	143	2	so	so	ADV
ejpam-3931	143	3	b	b	PROPN
ejpam-3931	143	4	is	be	AUX
ejpam-3931	143	5	a	a	DET
ejpam-3931	143	6	right	right	ADJ
ejpam-3931	143	7	ideal	ideal	ADJ
ejpam-3931	143	8	element	element	NOUN
ejpam-3931	143	9	of	of	ADP
ejpam-3931	143	10	s.	s.	PROPN
ejpam-3931	143	11	□	□	PUNCT
ejpam-3931	143	12	since	since	SCONJ
ejpam-3931	143	13	every	every	DET
ejpam-3931	143	14	bi	bi	ADJ
ejpam-3931	143	15	-	-	ADJ
ejpam-3931	143	16	ideal	ideal	ADJ
ejpam-3931	143	17	element	element	NOUN
ejpam-3931	143	18	of	of	ADP
ejpam-3931	143	19	s	s	PROPN
ejpam-3931	143	20	is	be	AUX
ejpam-3931	143	21	a	a	DET
ejpam-3931	143	22	bi	bi	ADJ
ejpam-3931	143	23	-	-	ADJ
ejpam-3931	143	24	interior	interior	ADJ
ejpam-3931	143	25	ideal	ideal	ADJ
ejpam-3931	143	26	element	element	NOUN
ejpam-3931	143	27	of	of	ADP
ejpam-3931	143	28	s	s	PROPN
ejpam-3931	143	29	(	(	PUNCT
ejpam-3931	143	30	prop	prop	NOUN
ejpam-3931	143	31	.	.	PUNCT
ejpam-3931	143	32	2.3(3	2.3(3	NUM
ejpam-3931	143	33	)	)	PUNCT
ejpam-3931	143	34	)	)	PUNCT
ejpam-3931	143	35	,	,	PUNCT
ejpam-3931	143	36	by	by	ADP
ejpam-3931	143	37	proposition	proposition	NOUN
ejpam-3931	143	38	3.2	3.2	NUM
ejpam-3931	143	39	we	we	PRON
ejpam-3931	143	40	have	have	VERB
ejpam-3931	143	41	the	the	DET
ejpam-3931	143	42	following	following	NOUN
ejpam-3931	143	43	.	.	PUNCT
ejpam-3931	144	1	corollary	corollary	ADJ
ejpam-3931	144	2	3.3	3.3	NUM
ejpam-3931	144	3	.	.	PUNCT
ejpam-3931	145	1	if	if	SCONJ
ejpam-3931	145	2	s	s	NOUN
ejpam-3931	145	3	is	be	AUX
ejpam-3931	145	4	a	a	DET
ejpam-3931	145	5	left	left	ADJ
ejpam-3931	145	6	(	(	PUNCT
ejpam-3931	145	7	resp	resp	NOUN
ejpam-3931	145	8	.	.	PUNCT
ejpam-3931	146	1	right	right	ADJ
ejpam-3931	146	2	)	)	PUNCT
ejpam-3931	146	3	simple	simple	ADJ
ejpam-3931	146	4	∧e	∧e	PROPN
ejpam-3931	146	5	-	-	PUNCT
ejpam-3931	146	6	semigroup	semigroup	PROPN
ejpam-3931	146	7	and	and	CCONJ
ejpam-3931	146	8	b	b	NOUN
ejpam-3931	146	9	is	be	AUX
ejpam-3931	146	10	a	a	DET
ejpam-3931	146	11	bi	bi	ADJ
ejpam-3931	146	12	-	-	ADJ
ejpam-3931	146	13	ideal	ideal	ADJ
ejpam-3931	146	14	element	element	NOUN
ejpam-3931	146	15	of	of	ADP
ejpam-3931	146	16	s	s	PROPN
ejpam-3931	146	17	,	,	PUNCT
ejpam-3931	146	18	then	then	ADV
ejpam-3931	146	19	b	b	PROPN
ejpam-3931	146	20	is	be	AUX
ejpam-3931	146	21	a	a	DET
ejpam-3931	146	22	right	right	ADJ
ejpam-3931	146	23	(	(	PUNCT
ejpam-3931	146	24	resp	resp	NOUN
ejpam-3931	146	25	.	.	PUNCT
ejpam-3931	147	1	left	left	ADJ
ejpam-3931	147	2	)	)	PUNCT
ejpam-3931	147	3	ideal	ideal	ADJ
ejpam-3931	147	4	element	element	NOUN
ejpam-3931	147	5	of	of	ADP
ejpam-3931	147	6	s.	s.	PROPN
ejpam-3931	147	7	proposition	proposition	PROPN
ejpam-3931	147	8	3.4	3.4	NUM
ejpam-3931	147	9	.	.	PUNCT
ejpam-3931	148	1	if	if	SCONJ
ejpam-3931	148	2	s	s	PROPN
ejpam-3931	148	3	is	be	AUX
ejpam-3931	148	4	a	a	DET
ejpam-3931	148	5	simple	simple	ADJ
ejpam-3931	148	6	∧e	∧e	PROPN
ejpam-3931	148	7	-	-	PUNCT
ejpam-3931	148	8	semigroup	semigroup	NOUN
ejpam-3931	148	9	,	,	PUNCT
ejpam-3931	148	10	then	then	ADV
ejpam-3931	148	11	every	every	DET
ejpam-3931	148	12	bi	bi	ADJ
ejpam-3931	148	13	-	-	ADJ
ejpam-3931	148	14	interior	interior	ADJ
ejpam-3931	148	15	ideal	ideal	ADJ
ejpam-3931	148	16	element	element	NOUN
ejpam-3931	148	17	of	of	ADP
ejpam-3931	148	18	s	s	PROPN
ejpam-3931	148	19	is	be	AUX
ejpam-3931	148	20	a	a	DET
ejpam-3931	148	21	bi	bi	ADJ
ejpam-3931	148	22	-	-	ADJ
ejpam-3931	148	23	ideal	ideal	ADJ
ejpam-3931	148	24	element	element	NOUN
ejpam-3931	148	25	of	of	ADP
ejpam-3931	148	26	s.	s.	PROPN
ejpam-3931	148	27	proof	proof	PROPN
ejpam-3931	148	28	.	.	PUNCT
ejpam-3931	149	1	let	let	VERB
ejpam-3931	149	2	b	b	X
ejpam-3931	149	3	be	be	AUX
ejpam-3931	149	4	a	a	DET
ejpam-3931	149	5	bi	bi	ADJ
ejpam-3931	149	6	-	-	ADJ
ejpam-3931	149	7	interior	interior	ADJ
ejpam-3931	149	8	ideal	ideal	ADJ
ejpam-3931	149	9	element	element	NOUN
ejpam-3931	149	10	of	of	ADP
ejpam-3931	149	11	s.	s.	PROPN
ejpam-3931	149	12	then	then	ADV
ejpam-3931	149	13	beb∧	beb∧	PROPN
ejpam-3931	149	14	ebe	ebe	PROPN
ejpam-3931	149	15	≤	≤	PROPN
ejpam-3931	149	16	b.	b.	PROPN
ejpam-3931	149	17	since	since	SCONJ
ejpam-3931	149	18	ebe	ebe	PROPN
ejpam-3931	149	19	is	be	AUX
ejpam-3931	149	20	an	an	DET
ejpam-3931	149	21	ideal	ideal	ADJ
ejpam-3931	149	22	element	element	NOUN
ejpam-3931	149	23	of	of	ADP
ejpam-3931	149	24	s	s	PRON
ejpam-3931	149	25	and	and	CCONJ
ejpam-3931	149	26	s	s	VERB
ejpam-3931	149	27	is	be	AUX
ejpam-3931	149	28	simple	simple	ADJ
ejpam-3931	149	29	,	,	PUNCT
ejpam-3931	149	30	we	we	PRON
ejpam-3931	149	31	have	have	VERB
ejpam-3931	149	32	ebe	ebe	PROPN
ejpam-3931	149	33	=	=	PROPN
ejpam-3931	149	34	e.	e.	PROPN
ejpam-3931	150	1	then	then	ADV
ejpam-3931	150	2	beb	beb	PROPN
ejpam-3931	150	3	∧	∧	PROPN
ejpam-3931	150	4	e	e	PROPN
ejpam-3931	150	5	≤	≤	NOUN
ejpam-3931	150	6	b	b	PROPN
ejpam-3931	151	1	and	and	CCONJ
ejpam-3931	151	2	so	so	ADV
ejpam-3931	151	3	beb	beb	PROPN
ejpam-3931	151	4	≤	≤	PROPN
ejpam-3931	151	5	b.	b.	PROPN
ejpam-3931	151	6	□	□	PUNCT
ejpam-3931	151	7	following	follow	VERB
ejpam-3931	151	8	m.	m.	PROPN
ejpam-3931	151	9	murali	murali	PROPN
ejpam-3931	151	10	krishna	krishna	PROPN
ejpam-3931	151	11	rao	rao	PROPN
ejpam-3931	151	12	,	,	PUNCT
ejpam-3931	151	13	we	we	PRON
ejpam-3931	151	14	give	give	VERB
ejpam-3931	151	15	the	the	DET
ejpam-3931	151	16	following	follow	VERB
ejpam-3931	151	17	definition	definition	NOUN
ejpam-3931	151	18	.	.	PUNCT
ejpam-3931	152	1	definition	definition	NOUN
ejpam-3931	152	2	3.5	3.5	NUM
ejpam-3931	152	3	.	.	PUNCT
ejpam-3931	153	1	a	a	DET
ejpam-3931	153	2	∧e	∧e	PROPN
ejpam-3931	153	3	-	-	PUNCT
ejpam-3931	153	4	semigroup	semigroup	PROPN
ejpam-3931	153	5	s	s	VERB
ejpam-3931	153	6	is	be	AUX
ejpam-3931	153	7	said	say	VERB
ejpam-3931	153	8	to	to	PART
ejpam-3931	153	9	be	be	AUX
ejpam-3931	153	10	bi	bi	ADJ
ejpam-3931	153	11	-	-	ADJ
ejpam-3931	153	12	interior	interior	ADJ
ejpam-3931	153	13	simple	simple	NOUN
ejpam-3931	153	14	if	if	SCONJ
ejpam-3931	153	15	,	,	PUNCT
ejpam-3931	153	16	for	for	ADP
ejpam-3931	153	17	every	every	DET
ejpam-3931	153	18	bi	bi	ADJ
ejpam-3931	153	19	-	-	ADJ
ejpam-3931	153	20	interior	interior	ADJ
ejpam-3931	153	21	ideal	ideal	ADJ
ejpam-3931	153	22	element	element	PROPN
ejpam-3931	153	23	b	b	PROPN
ejpam-3931	153	24	of	of	ADP
ejpam-3931	153	25	s	s	PROPN
ejpam-3931	153	26	,	,	PUNCT
ejpam-3931	153	27	we	we	PRON
ejpam-3931	153	28	have	have	VERB
ejpam-3931	153	29	b	b	NOUN
ejpam-3931	153	30	=	=	SYM
ejpam-3931	153	31	e.	e.	PROPN
ejpam-3931	153	32	proposition	proposition	PROPN
ejpam-3931	153	33	3.6	3.6	NUM
ejpam-3931	153	34	.	.	PUNCT
ejpam-3931	154	1	let	let	VERB
ejpam-3931	154	2	s	s	PRON
ejpam-3931	154	3	be	be	AUX
ejpam-3931	154	4	a	a	DET
ejpam-3931	154	5	∧e	∧e	PROPN
ejpam-3931	154	6	-	-	PUNCT
ejpam-3931	154	7	semigroup	semigroup	NOUN
ejpam-3931	154	8	.	.	PUNCT
ejpam-3931	155	1	then	then	ADV
ejpam-3931	155	2	s	s	VERB
ejpam-3931	155	3	is	be	AUX
ejpam-3931	155	4	bi	bi	ADJ
ejpam-3931	155	5	-	-	ADJ
ejpam-3931	155	6	interior	interior	ADJ
ejpam-3931	155	7	simple	simple	NOUN
ejpam-3931	155	8	if	if	SCONJ
ejpam-3931	155	9	and	and	CCONJ
ejpam-3931	155	10	only	only	ADV
ejpam-3931	155	11	if	if	SCONJ
ejpam-3931	155	12	,	,	PUNCT
ejpam-3931	155	13	for	for	ADP
ejpam-3931	155	14	every	every	DET
ejpam-3931	155	15	a	a	DET
ejpam-3931	155	16	∈	∈	PROPN
ejpam-3931	155	17	s	s	NOUN
ejpam-3931	155	18	,	,	PUNCT
ejpam-3931	155	19	we	we	PRON
ejpam-3931	155	20	have	have	VERB
ejpam-3931	155	21	aea	aea	PROPN
ejpam-3931	155	22	∧	∧	PROPN
ejpam-3931	155	23	eae	eae	PROPN
ejpam-3931	155	24	=	=	PROPN
ejpam-3931	155	25	e.	e.	PROPN
ejpam-3931	155	26	proof	proof	NOUN
ejpam-3931	155	27	.	.	PUNCT
ejpam-3931	156	1	=	=	NOUN
ejpam-3931	156	2	⇒.	⇒.	NOUN
ejpam-3931	156	3	let	let	VERB
ejpam-3931	156	4	a	a	DET
ejpam-3931	156	5	∈	∈	NOUN
ejpam-3931	156	6	s.	s.	PROPN
ejpam-3931	156	7	the	the	DET
ejpam-3931	156	8	element	element	PROPN
ejpam-3931	156	9	aea∧	aea∧	PROPN
ejpam-3931	156	10	eae	eae	PROPN
ejpam-3931	156	11	is	be	AUX
ejpam-3931	156	12	a	a	DET
ejpam-3931	156	13	bi	bi	ADJ
ejpam-3931	156	14	-	-	ADJ
ejpam-3931	156	15	interior	interior	ADJ
ejpam-3931	156	16	ideal	ideal	ADJ
ejpam-3931	156	17	element	element	NOUN
ejpam-3931	156	18	of	of	ADP
ejpam-3931	156	19	s.	s.	PROPN
ejpam-3931	156	20	indeed	indeed	ADV
ejpam-3931	156	21	,	,	PUNCT
ejpam-3931	156	22	(	(	PUNCT
ejpam-3931	156	23	aea	aea	PROPN
ejpam-3931	156	24	∧	∧	PROPN
ejpam-3931	156	25	eae)e(aea	eae)e(aea	PROPN
ejpam-3931	156	26	∧	∧	PROPN
ejpam-3931	156	27	eae	eae	PROPN
ejpam-3931	156	28	)	)	PUNCT
ejpam-3931	156	29	∧	∧	NOUN
ejpam-3931	156	30	e(aea	e(aea	NOUN
ejpam-3931	156	31	∧	∧	PROPN
ejpam-3931	156	32	eae)e	eae)e	PROPN
ejpam-3931	156	33	≤	≤	NUM
ejpam-3931	156	34	aeaeaea	aeaeaea	NOUN
ejpam-3931	156	35	∧	∧	PROPN
ejpam-3931	156	36	eaeae	eaeae	PROPN
ejpam-3931	156	37	≤	≤	PROPN
ejpam-3931	156	38	aea	aea	PROPN
ejpam-3931	156	39	∧	∧	PROPN
ejpam-3931	156	40	eae	eae	PROPN
ejpam-3931	156	41	.	.	PUNCT
ejpam-3931	157	1	since	since	SCONJ
ejpam-3931	157	2	s	s	PROPN
ejpam-3931	157	3	is	be	AUX
ejpam-3931	157	4	bi	bi	ADJ
ejpam-3931	157	5	-	-	ADJ
ejpam-3931	157	6	interior	interior	ADJ
ejpam-3931	157	7	simple	simple	NOUN
ejpam-3931	157	8	,	,	PUNCT
ejpam-3931	157	9	we	we	PRON
ejpam-3931	157	10	have	have	VERB
ejpam-3931	157	11	aea	aea	PROPN
ejpam-3931	157	12	∧	∧	PROPN
ejpam-3931	157	13	eae	eae	PROPN
ejpam-3931	157	14	=	=	PROPN
ejpam-3931	157	15	e.	e.	PROPN
ejpam-3931	157	16	⇐	⇐	PROPN
ejpam-3931	157	17	=	=	PROPN
ejpam-3931	157	18	.	.	PUNCT
ejpam-3931	158	1	let	let	VERB
ejpam-3931	158	2	b	b	X
ejpam-3931	158	3	be	be	AUX
ejpam-3931	158	4	a	a	DET
ejpam-3931	158	5	bi	bi	ADJ
ejpam-3931	158	6	-	-	ADJ
ejpam-3931	158	7	interior	interior	ADJ
ejpam-3931	158	8	ideal	ideal	ADJ
ejpam-3931	158	9	element	element	NOUN
ejpam-3931	158	10	of	of	ADP
ejpam-3931	158	11	s.	s.	PROPN
ejpam-3931	158	12	by	by	ADP
ejpam-3931	158	13	hypothesis	hypothesis	NOUN
ejpam-3931	158	14	,	,	PUNCT
ejpam-3931	158	15	we	we	PRON
ejpam-3931	158	16	have	have	VERB
ejpam-3931	158	17	e	e	NOUN
ejpam-3931	158	18	=	=	SYM
ejpam-3931	158	19	beb	beb	PROPN
ejpam-3931	158	20	∧	∧	PROPN
ejpam-3931	158	21	ebe	ebe	PROPN
ejpam-3931	158	22	≤	≤	PROPN
ejpam-3931	158	23	b.	b.	PROPN
ejpam-3931	159	1	then	then	ADV
ejpam-3931	159	2	b	b	X
ejpam-3931	159	3	=	=	SYM
ejpam-3931	159	4	e	e	PROPN
ejpam-3931	159	5	and	and	CCONJ
ejpam-3931	159	6	so	so	ADV
ejpam-3931	159	7	s	s	VERB
ejpam-3931	159	8	is	be	AUX
ejpam-3931	159	9	bi	bi	ADJ
ejpam-3931	159	10	-	-	ADJ
ejpam-3931	159	11	interior	interior	ADJ
ejpam-3931	159	12	simple	simple	NOUN
ejpam-3931	159	13	.	.	PUNCT
ejpam-3931	160	1	□	□	PUNCT
ejpam-3931	160	2	corollary	corollary	ADJ
ejpam-3931	160	3	3.7	3.7	NUM
ejpam-3931	160	4	.	.	PUNCT
ejpam-3931	161	1	[	[	X
ejpam-3931	161	2	4	4	NUM
ejpam-3931	161	3	;	;	PUNCT
ejpam-3931	161	4	theorem	theorem	VERB
ejpam-3931	161	5	3.5	3.5	NUM
ejpam-3931	161	6	]	]	PUNCT
ejpam-3931	161	7	a	a	DET
ejpam-3931	161	8	semigroup	semigroup	NOUN
ejpam-3931	161	9	m	m	VERB
ejpam-3931	161	10	is	be	AUX
ejpam-3931	161	11	bi	bi	ADJ
ejpam-3931	161	12	-	-	ADJ
ejpam-3931	161	13	interior	interior	ADJ
ejpam-3931	161	14	simple	simple	NOUN
ejpam-3931	161	15	if	if	SCONJ
ejpam-3931	161	16	and	and	CCONJ
ejpam-3931	161	17	only	only	ADV
ejpam-3931	161	18	if	if	SCONJ
ejpam-3931	161	19	mam	mam	PROPN
ejpam-3931	161	20	∩	∩	X
ejpam-3931	161	21	ama	ama	NOUN
ejpam-3931	161	22	=	=	SYM
ejpam-3931	161	23	m	m	VERB
ejpam-3931	161	24	for	for	ADP
ejpam-3931	161	25	every	every	DET
ejpam-3931	161	26	a	a	DET
ejpam-3931	161	27	∈	∈	NOUN
ejpam-3931	161	28	m	m	NOUN
ejpam-3931	161	29	.	.	PUNCT
ejpam-3931	162	1	n.	n.	PROPN
ejpam-3931	162	2	kehayopulu	kehayopulu	PROPN
ejpam-3931	162	3	/	/	SYM
ejpam-3931	162	4	eur	eur	PROPN
ejpam-3931	162	5	.	.	PUNCT
ejpam-3931	163	1	j.	j.	PROPN
ejpam-3931	163	2	pure	pure	PROPN
ejpam-3931	163	3	appl	appl	PROPN
ejpam-3931	163	4	.	.	PROPN
ejpam-3931	163	5	math	math	PROPN
ejpam-3931	163	6	,	,	PUNCT
ejpam-3931	163	7	14	14	NUM
ejpam-3931	163	8	(	(	PUNCT
ejpam-3931	163	9	4	4	NUM
ejpam-3931	163	10	)	)	PUNCT
ejpam-3931	163	11	(	(	PUNCT
ejpam-3931	163	12	2021	2021	NUM
ejpam-3931	163	13	)	)	PUNCT
ejpam-3931	163	14	,	,	PUNCT
ejpam-3931	163	15	43	43	NUM
ejpam-3931	163	16	-	-	SYM
ejpam-3931	163	17	52	52	NUM
ejpam-3931	163	18	49	49	NUM
ejpam-3931	163	19	4	4	NUM
ejpam-3931	163	20	.	.	PUNCT
ejpam-3931	164	1	bi	bi	ADJ
ejpam-3931	164	2	-	-	ADJ
ejpam-3931	164	3	interior	interior	ADJ
ejpam-3931	164	4	ideal	ideal	ADJ
ejpam-3931	164	5	elements	element	NOUN
ejpam-3931	164	6	in	in	ADP
ejpam-3931	164	7	regular	regular	ADJ
ejpam-3931	164	8	∧e	∧e	NOUN
ejpam-3931	164	9	-	-	PUNCT
ejpam-3931	164	10	semigroups	semigroup	NOUN
ejpam-3931	164	11	a	a	DET
ejpam-3931	164	12	poe	poe	PROPN
ejpam-3931	164	13	-	-	PUNCT
ejpam-3931	164	14	semigroup	semigroup	PROPN
ejpam-3931	164	15	s	s	VERB
ejpam-3931	164	16	is	be	AUX
ejpam-3931	164	17	said	say	VERB
ejpam-3931	164	18	to	to	PART
ejpam-3931	164	19	be	be	AUX
ejpam-3931	164	20	regular	regular	ADJ
ejpam-3931	164	21	if	if	SCONJ
ejpam-3931	164	22	,	,	PUNCT
ejpam-3931	164	23	for	for	ADP
ejpam-3931	164	24	every	every	DET
ejpam-3931	164	25	x	x	SYM
ejpam-3931	164	26	∈	∈	PROPN
ejpam-3931	164	27	s	s	PART
ejpam-3931	164	28	,	,	PUNCT
ejpam-3931	164	29	we	we	PRON
ejpam-3931	164	30	have	have	VERB
ejpam-3931	164	31	x	x	NOUN
ejpam-3931	164	32	≤	≤	X
ejpam-3931	164	33	xex	xex	PROPN
ejpam-3931	165	1	[	[	X
ejpam-3931	165	2	1	1	NUM
ejpam-3931	165	3	]	]	PUNCT
ejpam-3931	165	4	.	.	PUNCT
ejpam-3931	166	1	theorem	theorem	VERB
ejpam-3931	166	2	4.1	4.1	NUM
ejpam-3931	166	3	.	.	PUNCT
ejpam-3931	167	1	let	let	VERB
ejpam-3931	167	2	s	s	PRON
ejpam-3931	167	3	be	be	AUX
ejpam-3931	167	4	a	a	DET
ejpam-3931	167	5	∧e	∧e	PROPN
ejpam-3931	167	6	-	-	PUNCT
ejpam-3931	167	7	semigroup	semigroup	NOUN
ejpam-3931	167	8	.	.	PUNCT
ejpam-3931	168	1	if	if	SCONJ
ejpam-3931	168	2	s	s	VERB
ejpam-3931	168	3	is	be	AUX
ejpam-3931	168	4	regular	regular	ADJ
ejpam-3931	168	5	then	then	ADV
ejpam-3931	168	6	,	,	PUNCT
ejpam-3931	168	7	for	for	ADP
ejpam-3931	168	8	every	every	DET
ejpam-3931	168	9	bi	bi	ADJ
ejpam-3931	168	10	-	-	ADJ
ejpam-3931	168	11	interior	interior	ADJ
ejpam-3931	168	12	ideal	ideal	ADJ
ejpam-3931	168	13	element	element	PROPN
ejpam-3931	168	14	b	b	PROPN
ejpam-3931	168	15	of	of	ADP
ejpam-3931	168	16	s	s	PROPN
ejpam-3931	168	17	,	,	PUNCT
ejpam-3931	168	18	we	we	PRON
ejpam-3931	168	19	have	have	VERB
ejpam-3931	168	20	beb	beb	NOUN
ejpam-3931	168	21	∧	∧	PROPN
ejpam-3931	168	22	ebe	ebe	PROPN
ejpam-3931	168	23	=	=	PROPN
ejpam-3931	168	24	b.	b.	PROPN
ejpam-3931	168	25	in	in	ADP
ejpam-3931	168	26	particular	particular	ADJ
ejpam-3931	168	27	,	,	PUNCT
ejpam-3931	168	28	if	if	SCONJ
ejpam-3931	168	29	s	s	VERB
ejpam-3931	168	30	is	be	AUX
ejpam-3931	168	31	an	an	DET
ejpam-3931	168	32	le	le	NOUN
ejpam-3931	168	33	-	-	PUNCT
ejpam-3931	168	34	semigroup	semigroup	PROPN
ejpam-3931	168	35	,	,	PUNCT
ejpam-3931	168	36	then	then	ADV
ejpam-3931	168	37	s	s	VERB
ejpam-3931	168	38	is	be	AUX
ejpam-3931	168	39	regular	regular	ADJ
ejpam-3931	168	40	if	if	SCONJ
ejpam-3931	168	41	and	and	CCONJ
ejpam-3931	168	42	only	only	ADV
ejpam-3931	168	43	if	if	SCONJ
ejpam-3931	168	44	for	for	ADP
ejpam-3931	168	45	every	every	DET
ejpam-3931	168	46	bi	bi	ADJ
ejpam-3931	168	47	-	-	ADJ
ejpam-3931	168	48	interior	interior	ADJ
ejpam-3931	168	49	ideal	ideal	ADJ
ejpam-3931	168	50	element	element	PROPN
ejpam-3931	168	51	b	b	PROPN
ejpam-3931	168	52	of	of	ADP
ejpam-3931	168	53	s	s	PROPN
ejpam-3931	168	54	,	,	PUNCT
ejpam-3931	168	55	we	we	PRON
ejpam-3931	168	56	have	have	VERB
ejpam-3931	168	57	beb	beb	NOUN
ejpam-3931	168	58	∧	∧	PROPN
ejpam-3931	168	59	ebe	ebe	PROPN
ejpam-3931	168	60	=	=	PROPN
ejpam-3931	168	61	b.	b.	PROPN
ejpam-3931	168	62	proof	proof	NOUN
ejpam-3931	168	63	.	.	PUNCT
ejpam-3931	169	1	=	=	NOUN
ejpam-3931	169	2	⇒.	⇒.	NOUN
ejpam-3931	169	3	let	let	VERB
ejpam-3931	169	4	b	b	X
ejpam-3931	169	5	be	be	AUX
ejpam-3931	169	6	a	a	DET
ejpam-3931	169	7	bi	bi	ADJ
ejpam-3931	169	8	-	-	ADJ
ejpam-3931	169	9	interior	interior	ADJ
ejpam-3931	169	10	ideal	ideal	ADJ
ejpam-3931	169	11	element	element	NOUN
ejpam-3931	169	12	of	of	ADP
ejpam-3931	169	13	s.	s.	PROPN
ejpam-3931	169	14	then	then	ADV
ejpam-3931	169	15	beb	beb	PROPN
ejpam-3931	169	16	∧	∧	PROPN
ejpam-3931	169	17	ebe	ebe	PROPN
ejpam-3931	169	18	≤	≤	PROPN
ejpam-3931	169	19	b.	b.	PROPN
ejpam-3931	169	20	since	since	SCONJ
ejpam-3931	169	21	s	s	PROPN
ejpam-3931	169	22	is	be	AUX
ejpam-3931	169	23	regular	regular	ADJ
ejpam-3931	169	24	,	,	PUNCT
ejpam-3931	169	25	we	we	PRON
ejpam-3931	169	26	have	have	VERB
ejpam-3931	169	27	b	b	NOUN
ejpam-3931	169	28	≤	≤	X
ejpam-3931	169	29	beb	beb	PROPN
ejpam-3931	169	30	≤	≤	PROPN
ejpam-3931	169	31	(	(	PUNCT
ejpam-3931	169	32	beb)e(beb	beb)e(beb	NOUN
ejpam-3931	169	33	)	)	PUNCT
ejpam-3931	169	34	≤	≤	NOUN
ejpam-3931	169	35	beb	beb	PROPN
ejpam-3931	169	36	∧	∧	PROPN
ejpam-3931	169	37	ebe	ebe	NOUN
ejpam-3931	169	38	.	.	PUNCT
ejpam-3931	170	1	thus	thus	ADV
ejpam-3931	170	2	beb	beb	PROPN
ejpam-3931	170	3	∧	∧	PROPN
ejpam-3931	170	4	ebe	ebe	PROPN
ejpam-3931	170	5	=	=	PROPN
ejpam-3931	170	6	b.	b.	PROPN
ejpam-3931	170	7	⇐	⇐	PROPN
ejpam-3931	170	8	=	=	PRON
ejpam-3931	170	9	.	.	PUNCT
ejpam-3931	170	10	let	let	VERB
ejpam-3931	170	11	a	a	PRON
ejpam-3931	170	12	be	be	AUX
ejpam-3931	170	13	a	a	DET
ejpam-3931	170	14	right	right	ADJ
ejpam-3931	170	15	ideal	ideal	ADJ
ejpam-3931	170	16	element	element	NOUN
ejpam-3931	170	17	and	and	CCONJ
ejpam-3931	170	18	and	and	CCONJ
ejpam-3931	170	19	b	b	ADP
ejpam-3931	170	20	a	a	DET
ejpam-3931	170	21	left	left	ADJ
ejpam-3931	170	22	ideal	ideal	ADJ
ejpam-3931	170	23	element	element	NOUN
ejpam-3931	170	24	of	of	ADP
ejpam-3931	170	25	s.	s.	PROPN
ejpam-3931	170	26	by	by	ADP
ejpam-3931	170	27	proposition	proposition	NOUN
ejpam-3931	170	28	2.4(2	2.4(2	NUM
ejpam-3931	170	29	)	)	PUNCT
ejpam-3931	170	30	,	,	PUNCT
ejpam-3931	170	31	a∧b	a∧b	PROPN
ejpam-3931	170	32	is	be	AUX
ejpam-3931	170	33	a	a	DET
ejpam-3931	170	34	bi	bi	ADJ
ejpam-3931	170	35	-	-	ADJ
ejpam-3931	170	36	interior	interior	ADJ
ejpam-3931	170	37	element	element	NOUN
ejpam-3931	170	38	of	of	ADP
ejpam-3931	170	39	s.	s.	PROPN
ejpam-3931	170	40	by	by	ADP
ejpam-3931	170	41	hypothesis	hypothesis	NOUN
ejpam-3931	170	42	,	,	PUNCT
ejpam-3931	170	43	we	we	PRON
ejpam-3931	170	44	have	have	VERB
ejpam-3931	170	45	(	(	PUNCT
ejpam-3931	170	46	a∧b)e(a∧b)∧e(a∧b)e	a∧b)e(a∧b)∧e(a∧b)e	NOUN
ejpam-3931	170	47	=	=	PUNCT
ejpam-3931	170	48	a	a	DET
ejpam-3931	170	49	∧	∧	PROPN
ejpam-3931	170	50	b.	b.	PROPN
ejpam-3931	171	1	then	then	ADV
ejpam-3931	171	2	we	we	PRON
ejpam-3931	171	3	have	have	VERB
ejpam-3931	171	4	a	a	DET
ejpam-3931	171	5	∧	∧	PROPN
ejpam-3931	171	6	b	b	PROPN
ejpam-3931	171	7	≤	≤	NOUN
ejpam-3931	171	8	(	(	PUNCT
ejpam-3931	171	9	a	a	DET
ejpam-3931	171	10	∧	∧	PROPN
ejpam-3931	171	11	b)e(a	b)e(a	PROPN
ejpam-3931	171	12	∧	∧	PROPN
ejpam-3931	171	13	b	b	PROPN
ejpam-3931	171	14	)	)	PUNCT
ejpam-3931	171	15	≤	≤	NOUN
ejpam-3931	171	16	(	(	PUNCT
ejpam-3931	171	17	ae)b	ae)b	PROPN
ejpam-3931	171	18	≤	≤	PROPN
ejpam-3931	171	19	ab	ab	PROPN
ejpam-3931	171	20	≤	≤	PROPN
ejpam-3931	171	21	ae	ae	PROPN
ejpam-3931	171	22	∧	∧	PROPN
ejpam-3931	171	23	eb	eb	PROPN
ejpam-3931	171	24	≤	≤	PROPN
ejpam-3931	171	25	a	a	DET
ejpam-3931	171	26	∧	∧	PROPN
ejpam-3931	171	27	b.	b.	PROPN
ejpam-3931	171	28	then	then	ADV
ejpam-3931	171	29	a	a	DET
ejpam-3931	171	30	∧	∧	PROPN
ejpam-3931	171	31	b	b	PROPN
ejpam-3931	171	32	=	=	SYM
ejpam-3931	171	33	ab	ab	PROPN
ejpam-3931	171	34	.	.	PUNCT
ejpam-3931	172	1	thus	thus	ADV
ejpam-3931	172	2	,	,	PUNCT
ejpam-3931	172	3	for	for	ADP
ejpam-3931	172	4	any	any	DET
ejpam-3931	172	5	x	x	SYM
ejpam-3931	172	6	∈	∈	PROPN
ejpam-3931	172	7	s	s	PART
ejpam-3931	172	8	,	,	PUNCT
ejpam-3931	172	9	we	we	PRON
ejpam-3931	172	10	have	have	VERB
ejpam-3931	172	11	x	x	NOUN
ejpam-3931	172	12	≤	≤	PROPN
ejpam-3931	172	13	r(x	r(x	NOUN
ejpam-3931	172	14	)	)	PUNCT
ejpam-3931	172	15	∧	∧	PROPN
ejpam-3931	172	16	l(x	l(x	PROPN
ejpam-3931	172	17	)	)	PUNCT
ejpam-3931	172	18	=	=	SYM
ejpam-3931	172	19	r(x)l(x	r(x)l(x	NOUN
ejpam-3931	172	20	)	)	PUNCT
ejpam-3931	172	21	=	=	PRON
ejpam-3931	173	1	(	(	PUNCT
ejpam-3931	173	2	x	x	PROPN
ejpam-3931	173	3	∨	∨	NUM
ejpam-3931	173	4	xe)(x	xe)(x	PROPN
ejpam-3931	173	5	∨	∨	NUM
ejpam-3931	173	6	ex	ex	NOUN
ejpam-3931	173	7	)	)	PUNCT
ejpam-3931	174	1	=	=	SYM
ejpam-3931	174	2	x2	x2	PROPN
ejpam-3931	174	3	∨	∨	PROPN
ejpam-3931	174	4	xex	xex	PROPN
ejpam-3931	174	5	,	,	PUNCT
ejpam-3931	174	6	then	then	ADV
ejpam-3931	174	7	x2	x2	PROPN
ejpam-3931	174	8	≤	≤	PROPN
ejpam-3931	174	9	x3	x3	PROPN
ejpam-3931	174	10	∨	∨	PROPN
ejpam-3931	174	11	xex2	xex2	PROPN
ejpam-3931	174	12	≤	≤	PROPN
ejpam-3931	174	13	xex	xex	PROPN
ejpam-3931	174	14	,	,	PUNCT
ejpam-3931	174	15	then	then	ADV
ejpam-3931	174	16	x	x	SYM
ejpam-3931	174	17	≤	≤	X
ejpam-3931	174	18	xex	xex	PROPN
ejpam-3931	174	19	and	and	CCONJ
ejpam-3931	174	20	so	so	ADV
ejpam-3931	174	21	s	s	VERB
ejpam-3931	174	22	is	be	AUX
ejpam-3931	174	23	regular	regular	ADJ
ejpam-3931	174	24	.	.	PUNCT
ejpam-3931	175	1	□	□	PUNCT
ejpam-3931	175	2	theorem	theorem	VERB
ejpam-3931	175	3	4.2	4.2	NUM
ejpam-3931	175	4	.	.	PUNCT
ejpam-3931	176	1	let	let	VERB
ejpam-3931	176	2	s	s	PRON
ejpam-3931	176	3	be	be	AUX
ejpam-3931	176	4	a	a	DET
ejpam-3931	176	5	∧e	∧e	PROPN
ejpam-3931	176	6	-	-	PUNCT
ejpam-3931	176	7	semigroup	semigroup	NOUN
ejpam-3931	176	8	.	.	PUNCT
ejpam-3931	177	1	if	if	SCONJ
ejpam-3931	177	2	s	s	NOUN
ejpam-3931	177	3	is	be	AUX
ejpam-3931	177	4	regular	regular	ADJ
ejpam-3931	177	5	,	,	PUNCT
ejpam-3931	177	6	then	then	ADV
ejpam-3931	177	7	every	every	DET
ejpam-3931	177	8	bi	bi	ADJ
ejpam-3931	177	9	-	-	ADJ
ejpam-3931	177	10	interior	interior	ADJ
ejpam-3931	177	11	ideal	ideal	ADJ
ejpam-3931	177	12	element	element	NOUN
ejpam-3931	177	13	of	of	ADP
ejpam-3931	177	14	s	s	PROPN
ejpam-3931	177	15	is	be	AUX
ejpam-3931	177	16	subidempotent	subidempotent	NOUN
ejpam-3931	177	17	.	.	PUNCT
ejpam-3931	178	1	“	"	PUNCT
ejpam-3931	178	2	conversely	conversely	ADV
ejpam-3931	178	3	”	"	PUNCT
ejpam-3931	178	4	,	,	PUNCT
ejpam-3931	178	5	if	if	SCONJ
ejpam-3931	178	6	s	s	NOUN
ejpam-3931	178	7	is	be	AUX
ejpam-3931	178	8	an	an	DET
ejpam-3931	178	9	le	le	NOUN
ejpam-3931	178	10	-	-	PUNCT
ejpam-3931	178	11	semigroup	semigroup	PROPN
ejpam-3931	178	12	,	,	PUNCT
ejpam-3931	178	13	then	then	ADV
ejpam-3931	178	14	s	s	VERB
ejpam-3931	178	15	is	be	AUX
ejpam-3931	178	16	regular	regular	ADJ
ejpam-3931	178	17	if	if	SCONJ
ejpam-3931	178	18	and	and	CCONJ
ejpam-3931	178	19	only	only	ADV
ejpam-3931	178	20	if	if	SCONJ
ejpam-3931	178	21	every	every	DET
ejpam-3931	178	22	bi	bi	ADJ
ejpam-3931	178	23	-	-	ADJ
ejpam-3931	178	24	interior	interior	ADJ
ejpam-3931	178	25	ideal	ideal	ADJ
ejpam-3931	178	26	element	element	NOUN
ejpam-3931	178	27	of	of	ADP
ejpam-3931	178	28	s	s	PROPN
ejpam-3931	178	29	is	be	AUX
ejpam-3931	178	30	idempotent	idempotent	ADJ
ejpam-3931	178	31	.	.	PUNCT
ejpam-3931	179	1	proof	proof	NOUN
ejpam-3931	179	2	.	.	PUNCT
ejpam-3931	180	1	=	=	NOUN
ejpam-3931	180	2	⇒.	⇒.	NOUN
ejpam-3931	180	3	let	let	VERB
ejpam-3931	180	4	b	b	X
ejpam-3931	180	5	be	be	AUX
ejpam-3931	180	6	a	a	DET
ejpam-3931	180	7	bi	bi	ADJ
ejpam-3931	180	8	-	-	ADJ
ejpam-3931	180	9	interior	interior	ADJ
ejpam-3931	180	10	ideal	ideal	ADJ
ejpam-3931	180	11	element	element	NOUN
ejpam-3931	180	12	of	of	ADP
ejpam-3931	180	13	s.	s.	PROPN
ejpam-3931	180	14	since	since	SCONJ
ejpam-3931	180	15	s	s	PROPN
ejpam-3931	180	16	is	be	AUX
ejpam-3931	180	17	regular	regular	ADJ
ejpam-3931	180	18	,	,	PUNCT
ejpam-3931	180	19	we	we	PRON
ejpam-3931	180	20	have	have	VERB
ejpam-3931	180	21	b	b	PROPN
ejpam-3931	180	22	≤	≤	X
ejpam-3931	180	23	beb	beb	PROPN
ejpam-3931	180	24	.	.	PUNCT
ejpam-3931	181	1	then	then	ADV
ejpam-3931	181	2	we	we	PRON
ejpam-3931	181	3	have	have	AUX
ejpam-3931	181	4	b2	b2	VERB
ejpam-3931	181	5	≤	≤	NOUN
ejpam-3931	181	6	(	(	PUNCT
ejpam-3931	181	7	beb)b	beb)b	PROPN
ejpam-3931	181	8	≤	≤	NUM
ejpam-3931	181	9	beb	beb	PROPN
ejpam-3931	181	10	∧	∧	PROPN
ejpam-3931	181	11	ebe	ebe	PROPN
ejpam-3931	181	12	=	=	SYM
ejpam-3931	181	13	b	b	PROPN
ejpam-3931	181	14	,	,	PUNCT
ejpam-3931	181	15	thus	thus	ADV
ejpam-3931	181	16	b	b	NOUN
ejpam-3931	181	17	is	be	AUX
ejpam-3931	181	18	subidempotent	subidempotent	NOUN
ejpam-3931	181	19	.	.	PUNCT
ejpam-3931	182	1	⇐	⇐	PROPN
ejpam-3931	182	2	=	=	PRON
ejpam-3931	182	3	.	.	PUNCT
ejpam-3931	183	1	let	let	VERB
ejpam-3931	183	2	a	a	PRON
ejpam-3931	183	3	be	be	AUX
ejpam-3931	183	4	a	a	DET
ejpam-3931	183	5	right	right	ADJ
ejpam-3931	183	6	ideal	ideal	ADJ
ejpam-3931	183	7	element	element	NOUN
ejpam-3931	183	8	and	and	CCONJ
ejpam-3931	183	9	b	b	ADP
ejpam-3931	183	10	a	a	DET
ejpam-3931	183	11	left	left	ADJ
ejpam-3931	183	12	ideal	ideal	ADJ
ejpam-3931	183	13	element	element	NOUN
ejpam-3931	183	14	of	of	ADP
ejpam-3931	183	15	s.	s.	PROPN
ejpam-3931	183	16	by	by	ADP
ejpam-3931	183	17	proposition	proposition	NOUN
ejpam-3931	183	18	2.4(2	2.4(2	NUM
ejpam-3931	183	19	)	)	PUNCT
ejpam-3931	183	20	,	,	PUNCT
ejpam-3931	183	21	a	a	DET
ejpam-3931	183	22	∧	∧	PROPN
ejpam-3931	183	23	b	b	PROPN
ejpam-3931	183	24	is	be	AUX
ejpam-3931	183	25	a	a	DET
ejpam-3931	183	26	bi	bi	ADJ
ejpam-3931	183	27	-	-	ADJ
ejpam-3931	183	28	interior	interior	ADJ
ejpam-3931	183	29	ideal	ideal	ADJ
ejpam-3931	183	30	element	element	NOUN
ejpam-3931	183	31	of	of	ADP
ejpam-3931	183	32	s.	s.	PROPN
ejpam-3931	183	33	by	by	ADP
ejpam-3931	183	34	hypothesis	hypothesis	NOUN
ejpam-3931	183	35	,	,	PUNCT
ejpam-3931	183	36	we	we	PRON
ejpam-3931	183	37	have	have	VERB
ejpam-3931	183	38	a	a	DET
ejpam-3931	183	39	∧	∧	PROPN
ejpam-3931	183	40	b	b	NOUN
ejpam-3931	183	41	=	=	PUNCT
ejpam-3931	183	42	(	(	PUNCT
ejpam-3931	183	43	a	a	DET
ejpam-3931	183	44	∧	∧	PROPN
ejpam-3931	183	45	b)2	b)2	ADJ
ejpam-3931	183	46	=	=	PUNCT
ejpam-3931	183	47	(	(	PUNCT
ejpam-3931	183	48	a	a	DET
ejpam-3931	183	49	∧	∧	PROPN
ejpam-3931	183	50	b)(a	b)(a	ADP
ejpam-3931	183	51	∧	∧	PROPN
ejpam-3931	183	52	b	b	PROPN
ejpam-3931	183	53	)	)	PUNCT
ejpam-3931	183	54	≤	≤	NOUN
ejpam-3931	183	55	ab	ab	PROPN
ejpam-3931	183	56	≤	≤	PROPN
ejpam-3931	183	57	ae	ae	PROPN
ejpam-3931	183	58	∧	∧	PROPN
ejpam-3931	183	59	eb	eb	PROPN
ejpam-3931	183	60	≤	≤	PROPN
ejpam-3931	183	61	a	a	DET
ejpam-3931	183	62	∧	∧	PROPN
ejpam-3931	183	63	b	b	PROPN
ejpam-3931	183	64	,	,	PUNCT
ejpam-3931	183	65	thus	thus	ADV
ejpam-3931	183	66	a	a	DET
ejpam-3931	183	67	∧	∧	PROPN
ejpam-3931	183	68	b	b	PROPN
ejpam-3931	183	69	=	=	SYM
ejpam-3931	183	70	ab	ab	PROPN
ejpam-3931	183	71	,	,	PUNCT
ejpam-3931	183	72	and	and	CCONJ
ejpam-3931	183	73	s	s	VERB
ejpam-3931	183	74	is	be	AUX
ejpam-3931	183	75	regular	regular	ADJ
ejpam-3931	183	76	(	(	PUNCT
ejpam-3931	183	77	see	see	VERB
ejpam-3931	183	78	the	the	DET
ejpam-3931	183	79	proof	proof	NOUN
ejpam-3931	183	80	of	of	ADP
ejpam-3931	183	81	theorem	theorem	NOUN
ejpam-3931	183	82	4.1	4.1	NUM
ejpam-3931	183	83	)	)	PUNCT
ejpam-3931	183	84	.	.	PUNCT
ejpam-3931	184	1	□	□	PUNCT
ejpam-3931	184	2	proposition	proposition	NOUN
ejpam-3931	184	3	4.3	4.3	NUM
ejpam-3931	184	4	.	.	PUNCT
ejpam-3931	185	1	let	let	VERB
ejpam-3931	185	2	s	s	PRON
ejpam-3931	185	3	be	be	AUX
ejpam-3931	185	4	a	a	DET
ejpam-3931	185	5	regular	regular	ADJ
ejpam-3931	185	6	∧e	∧e	PROPN
ejpam-3931	185	7	-	-	PUNCT
ejpam-3931	185	8	semigroup	semigroup	NOUN
ejpam-3931	185	9	.	.	PUNCT
ejpam-3931	186	1	then	then	ADV
ejpam-3931	186	2	b	b	PROPN
ejpam-3931	186	3	is	be	AUX
ejpam-3931	186	4	a	a	DET
ejpam-3931	186	5	bi	bi	ADJ
ejpam-3931	186	6	-	-	ADJ
ejpam-3931	186	7	interior	interior	ADJ
ejpam-3931	186	8	ideal	ideal	ADJ
ejpam-3931	186	9	element	element	NOUN
ejpam-3931	186	10	of	of	ADP
ejpam-3931	186	11	s	s	PRON
ejpam-3931	186	12	if	if	SCONJ
ejpam-3931	186	13	and	and	CCONJ
ejpam-3931	186	14	only	only	ADV
ejpam-3931	186	15	if	if	SCONJ
ejpam-3931	186	16	b	b	NOUN
ejpam-3931	186	17	is	be	AUX
ejpam-3931	186	18	a	a	DET
ejpam-3931	186	19	bi	bi	ADJ
ejpam-3931	186	20	-	-	ADJ
ejpam-3931	186	21	ideal	ideal	ADJ
ejpam-3931	186	22	element	element	NOUN
ejpam-3931	186	23	of	of	ADP
ejpam-3931	186	24	s.	s.	PROPN
ejpam-3931	186	25	proof	proof	PROPN
ejpam-3931	186	26	.	.	PUNCT
ejpam-3931	187	1	=	=	NOUN
ejpam-3931	187	2	⇒.	⇒.	NOUN
ejpam-3931	187	3	let	let	VERB
ejpam-3931	187	4	b	b	X
ejpam-3931	187	5	be	be	AUX
ejpam-3931	187	6	a	a	DET
ejpam-3931	187	7	bi	bi	ADJ
ejpam-3931	187	8	-	-	ADJ
ejpam-3931	187	9	interior	interior	ADJ
ejpam-3931	187	10	element	element	NOUN
ejpam-3931	187	11	of	of	ADP
ejpam-3931	187	12	s.	s.	PROPN
ejpam-3931	187	13	since	since	SCONJ
ejpam-3931	187	14	s	s	PROPN
ejpam-3931	187	15	is	be	AUX
ejpam-3931	187	16	regular	regular	ADJ
ejpam-3931	187	17	,	,	PUNCT
ejpam-3931	187	18	we	we	PRON
ejpam-3931	187	19	have	have	VERB
ejpam-3931	187	20	b	b	NOUN
ejpam-3931	187	21	≤	≤	X
ejpam-3931	187	22	beb	beb	PROPN
ejpam-3931	187	23	≤	≤	PROPN
ejpam-3931	187	24	(	(	PUNCT
ejpam-3931	187	25	beb)e(beb	beb)e(beb	NOUN
ejpam-3931	187	26	)	)	PUNCT
ejpam-3931	187	27	≤	≤	NOUN
ejpam-3931	187	28	(	(	PUNCT
ejpam-3931	187	29	beb	beb	PROPN
ejpam-3931	187	30	)	)	PUNCT
ejpam-3931	187	31	∧	∧	PROPN
ejpam-3931	187	32	(	(	PUNCT
ejpam-3931	187	33	ebe	ebe	PROPN
ejpam-3931	187	34	)	)	PUNCT
ejpam-3931	187	35	≤	≤	PROPN
ejpam-3931	187	36	b.	b.	PROPN
ejpam-3931	188	1	thus	thus	ADV
ejpam-3931	188	2	we	we	PRON
ejpam-3931	188	3	have	have	VERB
ejpam-3931	188	4	b	b	PROPN
ejpam-3931	188	5	=	=	SYM
ejpam-3931	188	6	beb	beb	PROPN
ejpam-3931	188	7	,	,	PUNCT
ejpam-3931	188	8	and	and	CCONJ
ejpam-3931	188	9	b	b	NOUN
ejpam-3931	188	10	is	be	AUX
ejpam-3931	188	11	a	a	DET
ejpam-3931	188	12	bi	bi	ADJ
ejpam-3931	188	13	-	-	ADJ
ejpam-3931	188	14	ideal	ideal	ADJ
ejpam-3931	188	15	element	element	NOUN
ejpam-3931	188	16	of	of	ADP
ejpam-3931	188	17	s.	s.	PROPN
ejpam-3931	188	18	the	the	DET
ejpam-3931	188	19	⇐	⇐	PROPN
ejpam-3931	188	20	-part	-part	PROPN
ejpam-3931	188	21	follows	follow	VERB
ejpam-3931	188	22	from	from	ADP
ejpam-3931	188	23	proposition	proposition	NOUN
ejpam-3931	188	24	2.3(3	2.3(3	NUM
ejpam-3931	188	25	)	)	PUNCT
ejpam-3931	188	26	,	,	PUNCT
ejpam-3931	188	27	and	and	CCONJ
ejpam-3931	188	28	it	it	PRON
ejpam-3931	188	29	holds	hold	VERB
ejpam-3931	188	30	for	for	ADP
ejpam-3931	188	31	∧e	∧e	NOUN
ejpam-3931	188	32	-	-	PUNCT
ejpam-3931	188	33	semigroups	semigroup	NOUN
ejpam-3931	188	34	in	in	ADP
ejpam-3931	188	35	general	general	ADJ
ejpam-3931	188	36	.	.	PUNCT
ejpam-3931	189	1	□	□	PUNCT
ejpam-3931	189	2	theorem	theorem	VERB
ejpam-3931	189	3	4.4	4.4	NUM
ejpam-3931	189	4	.	.	PUNCT
ejpam-3931	190	1	let	let	VERB
ejpam-3931	190	2	s	s	PRON
ejpam-3931	190	3	be	be	AUX
ejpam-3931	190	4	a	a	DET
ejpam-3931	190	5	regular	regular	ADJ
ejpam-3931	190	6	∧e	∧e	PROPN
ejpam-3931	190	7	-	-	PUNCT
ejpam-3931	190	8	semigroup	semigroup	NOUN
ejpam-3931	190	9	.	.	PUNCT
ejpam-3931	191	1	then	then	ADV
ejpam-3931	191	2	b	b	PROPN
ejpam-3931	191	3	is	be	AUX
ejpam-3931	191	4	a	a	DET
ejpam-3931	191	5	bi	bi	ADJ
ejpam-3931	191	6	-	-	ADJ
ejpam-3931	191	7	interior	interior	ADJ
ejpam-3931	191	8	ideal	ideal	ADJ
ejpam-3931	191	9	element	element	NOUN
ejpam-3931	191	10	of	of	ADP
ejpam-3931	191	11	s	s	PRON
ejpam-3931	191	12	if	if	SCONJ
ejpam-3931	191	13	and	and	CCONJ
ejpam-3931	191	14	only	only	ADV
ejpam-3931	191	15	if	if	SCONJ
ejpam-3931	191	16	there	there	PRON
ejpam-3931	191	17	exists	exist	VERB
ejpam-3931	191	18	a	a	DET
ejpam-3931	191	19	right	right	ADJ
ejpam-3931	191	20	ideal	ideal	ADJ
ejpam-3931	191	21	element	element	NOUN
ejpam-3931	191	22	r	r	NOUN
ejpam-3931	191	23	and	and	CCONJ
ejpam-3931	191	24	a	a	DET
ejpam-3931	191	25	left	left	ADJ
ejpam-3931	191	26	ideal	ideal	ADJ
ejpam-3931	191	27	element	element	NOUN
ejpam-3931	191	28	l	l	NOUN
ejpam-3931	191	29	of	of	ADP
ejpam-3931	191	30	s	s	PRON
ejpam-3931	192	1	such	such	ADJ
ejpam-3931	192	2	that	that	DET
ejpam-3931	192	3	b	b	X
ejpam-3931	192	4	=	=	SYM
ejpam-3931	192	5	rl	rl	PROPN
ejpam-3931	192	6	.	.	PUNCT
ejpam-3931	192	7	n.	n.	PROPN
ejpam-3931	192	8	kehayopulu	kehayopulu	PROPN
ejpam-3931	192	9	/	/	SYM
ejpam-3931	192	10	eur	eur	PROPN
ejpam-3931	192	11	.	.	PUNCT
ejpam-3931	193	1	j.	j.	PROPN
ejpam-3931	193	2	pure	pure	PROPN
ejpam-3931	193	3	appl	appl	PROPN
ejpam-3931	193	4	.	.	PROPN
ejpam-3931	193	5	math	math	PROPN
ejpam-3931	193	6	,	,	PUNCT
ejpam-3931	193	7	14	14	NUM
ejpam-3931	193	8	(	(	PUNCT
ejpam-3931	193	9	4	4	NUM
ejpam-3931	193	10	)	)	PUNCT
ejpam-3931	193	11	(	(	PUNCT
ejpam-3931	193	12	2021	2021	NUM
ejpam-3931	193	13	)	)	PUNCT
ejpam-3931	193	14	,	,	PUNCT
ejpam-3931	193	15	43	43	NUM
ejpam-3931	193	16	-	-	SYM
ejpam-3931	193	17	52	52	NUM
ejpam-3931	193	18	50	50	NUM
ejpam-3931	193	19	proof	proof	NOUN
ejpam-3931	193	20	.	.	PUNCT
ejpam-3931	194	1	=	=	NOUN
ejpam-3931	194	2	⇒.	⇒.	NOUN
ejpam-3931	194	3	let	let	VERB
ejpam-3931	194	4	b	b	X
ejpam-3931	194	5	be	be	AUX
ejpam-3931	194	6	a	a	DET
ejpam-3931	194	7	bi	bi	ADJ
ejpam-3931	194	8	-	-	ADJ
ejpam-3931	194	9	interior	interior	ADJ
ejpam-3931	194	10	ideal	ideal	ADJ
ejpam-3931	194	11	element	element	NOUN
ejpam-3931	194	12	of	of	ADP
ejpam-3931	194	13	s.	s.	PROPN
ejpam-3931	194	14	since	since	SCONJ
ejpam-3931	194	15	s	s	PROPN
ejpam-3931	194	16	is	be	AUX
ejpam-3931	194	17	regular	regular	ADJ
ejpam-3931	194	18	,	,	PUNCT
ejpam-3931	194	19	by	by	ADP
ejpam-3931	194	20	theorem	theorem	NOUN
ejpam-3931	194	21	4.1	4.1	NUM
ejpam-3931	194	22	,	,	PUNCT
ejpam-3931	194	23	we	we	PRON
ejpam-3931	194	24	have	have	VERB
ejpam-3931	194	25	beb	beb	NOUN
ejpam-3931	194	26	∧	∧	PROPN
ejpam-3931	194	27	ebe	ebe	PROPN
ejpam-3931	194	28	=	=	PROPN
ejpam-3931	194	29	b.	b.	PROPN
ejpam-3931	195	1	the	the	DET
ejpam-3931	195	2	element	element	NOUN
ejpam-3931	195	3	be	be	AUX
ejpam-3931	195	4	and	and	CCONJ
ejpam-3931	195	5	eb	eb	PROPN
ejpam-3931	195	6	are	be	AUX
ejpam-3931	195	7	right	right	ADJ
ejpam-3931	195	8	and	and	CCONJ
ejpam-3931	195	9	left	leave	VERB
ejpam-3931	195	10	ideal	ideal	ADJ
ejpam-3931	195	11	elements	element	NOUN
ejpam-3931	195	12	of	of	ADP
ejpam-3931	195	13	s	s	NOUN
ejpam-3931	195	14	,	,	PUNCT
ejpam-3931	195	15	respectively	respectively	ADV
ejpam-3931	195	16	.	.	PUNCT
ejpam-3931	196	1	it	it	PRON
ejpam-3931	196	2	is	be	AUX
ejpam-3931	196	3	enough	enough	ADJ
ejpam-3931	196	4	to	to	PART
ejpam-3931	196	5	prove	prove	VERB
ejpam-3931	196	6	that	that	DET
ejpam-3931	196	7	b	b	NOUN
ejpam-3931	196	8	=	=	SYM
ejpam-3931	196	9	(	(	PUNCT
ejpam-3931	196	10	be)(eb	be)(eb	NOUN
ejpam-3931	196	11	)	)	PUNCT
ejpam-3931	196	12	.	.	PUNCT
ejpam-3931	197	1	since	since	SCONJ
ejpam-3931	197	2	s	s	PROPN
ejpam-3931	197	3	is	be	AUX
ejpam-3931	197	4	regular	regular	ADJ
ejpam-3931	197	5	,	,	PUNCT
ejpam-3931	197	6	we	we	PRON
ejpam-3931	197	7	have	have	VERB
ejpam-3931	197	8	b	b	PROPN
ejpam-3931	197	9	≤	≤	X
ejpam-3931	197	10	beb	beb	NOUN
ejpam-3931	197	11	.	.	PUNCT
ejpam-3931	198	1	thus	thus	ADV
ejpam-3931	198	2	we	we	PRON
ejpam-3931	198	3	have	have	VERB
ejpam-3931	198	4	(	(	PUNCT
ejpam-3931	198	5	be)(eb	be)(eb	NOUN
ejpam-3931	198	6	)	)	PUNCT
ejpam-3931	198	7	≤	≤	NOUN
ejpam-3931	198	8	(	(	PUNCT
ejpam-3931	198	9	beb)e(beb	beb)e(beb	NOUN
ejpam-3931	198	10	)	)	PUNCT
ejpam-3931	198	11	≤	≤	NOUN
ejpam-3931	198	12	(	(	PUNCT
ejpam-3931	198	13	beb	beb	PROPN
ejpam-3931	198	14	)	)	PUNCT
ejpam-3931	198	15	∧	∧	PROPN
ejpam-3931	198	16	(	(	PUNCT
ejpam-3931	198	17	ebe	ebe	PROPN
ejpam-3931	198	18	)	)	PUNCT
ejpam-3931	198	19	=	=	PUNCT
ejpam-3931	199	1	b.	b.	NOUN
ejpam-3931	199	2	we	we	PRON
ejpam-3931	199	3	also	also	ADV
ejpam-3931	199	4	have	have	VERB
ejpam-3931	199	5	b	b	NUM
ejpam-3931	199	6	≤	≤	NUM
ejpam-3931	199	7	beb	beb	PROPN
ejpam-3931	199	8	≤	≤	PROPN
ejpam-3931	199	9	(	(	PUNCT
ejpam-3931	199	10	beb)e(beb	beb)e(beb	NOUN
ejpam-3931	199	11	)	)	PUNCT
ejpam-3931	199	12	≤	≤	NOUN
ejpam-3931	199	13	(	(	PUNCT
ejpam-3931	199	14	be)(eb	be)(eb	NOUN
ejpam-3931	199	15	)	)	PUNCT
ejpam-3931	199	16	and	and	CCONJ
ejpam-3931	199	17	so	so	ADV
ejpam-3931	199	18	b	b	X
ejpam-3931	199	19	=	=	SYM
ejpam-3931	199	20	(	(	PUNCT
ejpam-3931	199	21	be)(eb	be)(eb	NOUN
ejpam-3931	199	22	)	)	PUNCT
ejpam-3931	199	23	.	.	PUNCT
ejpam-3931	200	1	the	the	DET
ejpam-3931	200	2	“	"	PUNCT
ejpam-3931	200	3	⇐	⇐	ADJ
ejpam-3931	200	4	-part	-part	PROPN
ejpam-3931	200	5	follows	follow	VERB
ejpam-3931	200	6	by	by	ADP
ejpam-3931	200	7	proposition	proposition	NOUN
ejpam-3931	200	8	2.6(1	2.6(1	NUM
ejpam-3931	200	9	)	)	PUNCT
ejpam-3931	200	10	(	(	PUNCT
ejpam-3931	200	11	or	or	CCONJ
ejpam-3931	200	12	2.6(2	2.6(2	NUM
ejpam-3931	200	13	)	)	PUNCT
ejpam-3931	200	14	)	)	PUNCT
ejpam-3931	201	1	and	and	CCONJ
ejpam-3931	201	2	it	it	PRON
ejpam-3931	201	3	holds	hold	VERB
ejpam-3931	201	4	for	for	ADP
ejpam-3931	201	5	∧e	∧e	NOUN
ejpam-3931	201	6	-	-	PUNCT
ejpam-3931	201	7	semigroups	semigroup	NOUN
ejpam-3931	201	8	in	in	ADP
ejpam-3931	201	9	general	general	ADJ
ejpam-3931	201	10	.	.	PUNCT
ejpam-3931	202	1	□	□	PUNCT
ejpam-3931	202	2	corollary	corollary	ADJ
ejpam-3931	202	3	4.5	4.5	NUM
ejpam-3931	202	4	.	.	PUNCT
ejpam-3931	203	1	(	(	PUNCT
ejpam-3931	203	2	cf	cf	NOUN
ejpam-3931	203	3	.	.	PUNCT
ejpam-3931	204	1	also	also	ADV
ejpam-3931	204	2	[	[	X
ejpam-3931	204	3	4	4	NUM
ejpam-3931	204	4	;	;	PUNCT
ejpam-3931	204	5	theorem	theorem	VERB
ejpam-3931	204	6	3.28	3.28	NUM
ejpam-3931	204	7	]	]	PUNCT
ejpam-3931	204	8	)	)	PUNCT
ejpam-3931	204	9	let	let	VERB
ejpam-3931	204	10	m	m	PRON
ejpam-3931	204	11	be	be	AUX
ejpam-3931	204	12	a	a	DET
ejpam-3931	204	13	regular	regular	ADJ
ejpam-3931	204	14	semigroup	semigroup	NOUN
ejpam-3931	204	15	.	.	PUNCT
ejpam-3931	205	1	then	then	ADV
ejpam-3931	205	2	b	b	PROPN
ejpam-3931	205	3	is	be	AUX
ejpam-3931	205	4	a	a	DET
ejpam-3931	205	5	bi	bi	ADJ
ejpam-3931	205	6	-	-	ADJ
ejpam-3931	205	7	interior	interior	ADJ
ejpam-3931	205	8	ideal	ideal	NOUN
ejpam-3931	205	9	of	of	ADP
ejpam-3931	205	10	m	m	PRON
ejpam-3931	205	11	if	if	SCONJ
ejpam-3931	206	1	and	and	CCONJ
ejpam-3931	206	2	only	only	ADV
ejpam-3931	206	3	if	if	SCONJ
ejpam-3931	206	4	there	there	PRON
ejpam-3931	206	5	exists	exist	VERB
ejpam-3931	206	6	a	a	DET
ejpam-3931	206	7	right	right	ADJ
ejpam-3931	206	8	ideal	ideal	ADJ
ejpam-3931	206	9	r	r	NOUN
ejpam-3931	206	10	and	and	CCONJ
ejpam-3931	206	11	a	a	DET
ejpam-3931	206	12	left	left	ADJ
ejpam-3931	206	13	ideal	ideal	NOUN
ejpam-3931	206	14	l	l	NOUN
ejpam-3931	206	15	of	of	ADP
ejpam-3931	206	16	m	m	PRON
ejpam-3931	206	17	such	such	ADJ
ejpam-3931	206	18	that	that	PRON
ejpam-3931	206	19	b	b	X
ejpam-3931	206	20	=	=	SYM
ejpam-3931	206	21	rl	rl	PROPN
ejpam-3931	206	22	.	.	PUNCT
ejpam-3931	206	23	proposition	proposition	NOUN
ejpam-3931	206	24	4.6	4.6	NUM
ejpam-3931	206	25	.	.	PUNCT
ejpam-3931	207	1	let	let	VERB
ejpam-3931	207	2	s	s	PRON
ejpam-3931	207	3	be	be	AUX
ejpam-3931	207	4	a	a	DET
ejpam-3931	207	5	poe	poe	PROPN
ejpam-3931	207	6	-	-	PUNCT
ejpam-3931	207	7	semigroup	semigroup	PROPN
ejpam-3931	207	8	,	,	PUNCT
ejpam-3931	207	9	b	b	PROPN
ejpam-3931	207	10	a	a	DET
ejpam-3931	207	11	subidempotent	subidempotent	NOUN
ejpam-3931	207	12	bi	bi	ADJ
ejpam-3931	207	13	-	-	ADJ
ejpam-3931	207	14	ideal	ideal	ADJ
ejpam-3931	207	15	element	element	NOUN
ejpam-3931	207	16	of	of	ADP
ejpam-3931	207	17	s	s	PRON
ejpam-3931	207	18	and	and	CCONJ
ejpam-3931	207	19	a	a	DET
ejpam-3931	207	20	∈	∈	NOUN
ejpam-3931	207	21	s	s	VERB
ejpam-3931	207	22	such	such	ADJ
ejpam-3931	207	23	that	that	SCONJ
ejpam-3931	207	24	a	a	DET
ejpam-3931	207	25	≤	≤	PROPN
ejpam-3931	207	26	b	b	NOUN
ejpam-3931	207	27	and	and	CCONJ
ejpam-3931	207	28	a	a	DET
ejpam-3931	207	29	=	=	X
ejpam-3931	207	30	aba	aba	PROPN
ejpam-3931	207	31	.	.	PUNCT
ejpam-3931	208	1	then	then	ADV
ejpam-3931	208	2	a	a	PRON
ejpam-3931	208	3	is	be	AUX
ejpam-3931	208	4	a	a	DET
ejpam-3931	208	5	bi	bi	ADJ
ejpam-3931	208	6	-	-	ADJ
ejpam-3931	208	7	interior	interior	ADJ
ejpam-3931	208	8	ideal	ideal	ADJ
ejpam-3931	208	9	element	element	NOUN
ejpam-3931	208	10	of	of	ADP
ejpam-3931	208	11	s.	s.	PROPN
ejpam-3931	208	12	proof	proof	PROPN
ejpam-3931	208	13	.	.	PUNCT
ejpam-3931	209	1	since	since	SCONJ
ejpam-3931	209	2	a	a	DET
ejpam-3931	209	3	≤	≤	NUM
ejpam-3931	209	4	b	b	NOUN
ejpam-3931	209	5	,	,	PUNCT
ejpam-3931	209	6	we	we	PRON
ejpam-3931	209	7	have	have	VERB
ejpam-3931	209	8	ba	ba	PROPN
ejpam-3931	209	9	≤	≤	NUM
ejpam-3931	209	10	b2	b2	NOUN
ejpam-3931	209	11	≤	≤	NUM
ejpam-3931	209	12	b	b	PROPN
ejpam-3931	209	13	and	and	CCONJ
ejpam-3931	209	14	ab	ab	PROPN
ejpam-3931	209	15	≤	≤	PROPN
ejpam-3931	209	16	b2	b2	PROPN
ejpam-3931	209	17	≤	≤	PROPN
ejpam-3931	209	18	b.	b.	PROPN
ejpam-3931	209	19	then	then	ADV
ejpam-3931	209	20	a	a	DET
ejpam-3931	209	21	=	=	SYM
ejpam-3931	209	22	a(ba	a(ba	NOUN
ejpam-3931	209	23	)	)	PUNCT
ejpam-3931	209	24	≤	≤	PUNCT
ejpam-3931	209	25	ab	ab	PROPN
ejpam-3931	209	26	and	and	CCONJ
ejpam-3931	209	27	a	a	PRON
ejpam-3931	209	28	=	=	X
ejpam-3931	209	29	(	(	PUNCT
ejpam-3931	209	30	ab)a	ab)a	PROPN
ejpam-3931	209	31	≤	≤	PROPN
ejpam-3931	209	32	ba	ba	PROPN
ejpam-3931	209	33	.	.	PUNCT
ejpam-3931	210	1	then	then	ADV
ejpam-3931	210	2	aea	aea	PROPN
ejpam-3931	210	3	≤	≤	PROPN
ejpam-3931	210	4	(	(	PUNCT
ejpam-3931	210	5	ab)e(ba	ab)e(ba	X
ejpam-3931	210	6	)	)	PUNCT
ejpam-3931	210	7	=	=	PUNCT
ejpam-3931	211	1	a(beb)a	a(beb)a	ADP
ejpam-3931	211	2	≤	≤	PUNCT
ejpam-3931	212	1	aba	aba	PROPN
ejpam-3931	213	1	=	=	PUNCT
ejpam-3931	214	1	a	a	PROPN
ejpam-3931	215	1	and	and	CCONJ
ejpam-3931	215	2	so	so	ADV
ejpam-3931	215	3	a	a	PRON
ejpam-3931	215	4	is	be	AUX
ejpam-3931	215	5	a	a	DET
ejpam-3931	215	6	bi	bi	ADJ
ejpam-3931	215	7	-	-	ADJ
ejpam-3931	215	8	ideal	ideal	ADJ
ejpam-3931	215	9	element	element	NOUN
ejpam-3931	215	10	of	of	ADP
ejpam-3931	215	11	s.	s.	PROPN
ejpam-3931	215	12	then	then	ADV
ejpam-3931	215	13	,	,	PUNCT
ejpam-3931	215	14	by	by	ADP
ejpam-3931	215	15	proposition	proposition	NOUN
ejpam-3931	215	16	2.3(3	2.3(3	NUM
ejpam-3931	215	17	)	)	PUNCT
ejpam-3931	215	18	,	,	PUNCT
ejpam-3931	215	19	it	it	PRON
ejpam-3931	215	20	is	be	AUX
ejpam-3931	215	21	a	a	DET
ejpam-3931	215	22	bi	bi	ADJ
ejpam-3931	215	23	-	-	ADJ
ejpam-3931	215	24	interior	interior	ADJ
ejpam-3931	215	25	ideal	ideal	ADJ
ejpam-3931	215	26	element	element	NOUN
ejpam-3931	215	27	of	of	ADP
ejpam-3931	215	28	s	s	PRON
ejpam-3931	215	29	as	as	ADV
ejpam-3931	215	30	well	well	ADV
ejpam-3931	215	31	.	.	PUNCT
ejpam-3931	216	1	□	□	PUNCT
ejpam-3931	216	2	theorem	theorem	VERB
ejpam-3931	216	3	4.7	4.7	NUM
ejpam-3931	216	4	.	.	PUNCT
ejpam-3931	217	1	a	a	DET
ejpam-3931	217	2	∧e	∧e	PROPN
ejpam-3931	217	3	-	-	PUNCT
ejpam-3931	217	4	semigroup	semigroup	PROPN
ejpam-3931	217	5	s	s	AUX
ejpam-3931	217	6	is	be	AUX
ejpam-3931	217	7	regular	regular	ADJ
ejpam-3931	217	8	if	if	SCONJ
ejpam-3931	217	9	and	and	CCONJ
ejpam-3931	217	10	only	only	ADV
ejpam-3931	217	11	if	if	SCONJ
ejpam-3931	217	12	for	for	ADP
ejpam-3931	217	13	every	every	DET
ejpam-3931	217	14	bi	bi	ADJ
ejpam-3931	217	15	-	-	ADJ
ejpam-3931	217	16	interior	interior	ADJ
ejpam-3931	217	17	ideal	ideal	ADJ
ejpam-3931	217	18	element	element	PROPN
ejpam-3931	217	19	b	b	PROPN
ejpam-3931	217	20	,	,	PUNCT
ejpam-3931	217	21	every	every	DET
ejpam-3931	217	22	ideal	ideal	ADJ
ejpam-3931	217	23	element	element	NOUN
ejpam-3931	217	24	i	i	PRON
ejpam-3931	217	25	and	and	CCONJ
ejpam-3931	217	26	every	every	DET
ejpam-3931	217	27	left	leave	VERB
ejpam-3931	217	28	ideal	ideal	ADJ
ejpam-3931	217	29	element	element	PROPN
ejpam-3931	217	30	l	l	NOUN
ejpam-3931	217	31	of	of	ADP
ejpam-3931	217	32	s	s	PROPN
ejpam-3931	217	33	,	,	PUNCT
ejpam-3931	217	34	we	we	PRON
ejpam-3931	217	35	have	have	VERB
ejpam-3931	217	36	b∧	b∧	ADJ
ejpam-3931	217	37	i∧	i∧	PROPN
ejpam-3931	217	38	l	l	NOUN
ejpam-3931	217	39	≤	≤	NUM
ejpam-3931	217	40	bil	bil	NUM
ejpam-3931	217	41	.	.	PUNCT
ejpam-3931	218	1	proof	proof	NOUN
ejpam-3931	218	2	.	.	PUNCT
ejpam-3931	219	1	=	=	NOUN
ejpam-3931	219	2	⇒.	⇒.	NOUN
ejpam-3931	219	3	let	let	VERB
ejpam-3931	219	4	b	b	X
ejpam-3931	219	5	be	be	AUX
ejpam-3931	219	6	a	a	DET
ejpam-3931	219	7	bi	bi	ADJ
ejpam-3931	219	8	-	-	ADJ
ejpam-3931	219	9	interior	interior	ADJ
ejpam-3931	219	10	ideal	ideal	ADJ
ejpam-3931	219	11	element	element	NOUN
ejpam-3931	219	12	,	,	PUNCT
ejpam-3931	219	13	i	i	PRON
ejpam-3931	219	14	an	an	DET
ejpam-3931	219	15	ideal	ideal	ADJ
ejpam-3931	219	16	element	element	NOUN
ejpam-3931	219	17	and	and	CCONJ
ejpam-3931	219	18	l	l	NOUN
ejpam-3931	219	19	a	a	DET
ejpam-3931	219	20	left	left	ADJ
ejpam-3931	219	21	ideal	ideal	ADJ
ejpam-3931	219	22	element	element	NOUN
ejpam-3931	219	23	of	of	ADP
ejpam-3931	219	24	s.	s.	PROPN
ejpam-3931	219	25	since	since	SCONJ
ejpam-3931	219	26	s	s	PROPN
ejpam-3931	219	27	is	be	AUX
ejpam-3931	219	28	regular	regular	ADJ
ejpam-3931	219	29	,	,	PUNCT
ejpam-3931	219	30	we	we	PRON
ejpam-3931	219	31	have	have	VERB
ejpam-3931	219	32	b	b	NUM
ejpam-3931	219	33	∧	∧	PROPN
ejpam-3931	219	34	i	i	PRON
ejpam-3931	219	35	∧	∧	PROPN
ejpam-3931	219	36	l	l	NOUN
ejpam-3931	219	37	≤	≤	X
ejpam-3931	220	1	(	(	PUNCT
ejpam-3931	220	2	b	b	X
ejpam-3931	220	3	∧	∧	NOUN
ejpam-3931	220	4	i	i	PRON
ejpam-3931	220	5	∧	∧	PROPN
ejpam-3931	220	6	l)e(b	l)e(b	VERB
ejpam-3931	220	7	∧	∧	NOUN
ejpam-3931	221	1	i	i	NOUN
ejpam-3931	221	2	∧	∧	PROPN
ejpam-3931	221	3	l	l	NOUN
ejpam-3931	221	4	)	)	PUNCT
ejpam-3931	221	5	≤	≤	NOUN
ejpam-3931	221	6	(	(	PUNCT
ejpam-3931	221	7	(	(	PUNCT
ejpam-3931	221	8	b	b	X
ejpam-3931	221	9	∧	∧	NOUN
ejpam-3931	222	1	i	i	PRON
ejpam-3931	222	2	∧	∧	PROPN
ejpam-3931	222	3	l)e(b	l)e(b	VERB
ejpam-3931	222	4	∧	∧	NOUN
ejpam-3931	223	1	i	i	PRON
ejpam-3931	223	2	∧	∧	PROPN
ejpam-3931	223	3	l)e(b	l)e(b	VERB
ejpam-3931	223	4	∧	∧	NOUN
ejpam-3931	223	5	i	i	NOUN
ejpam-3931	223	6	∧	∧	PROPN
ejpam-3931	223	7	l	l	NOUN
ejpam-3931	223	8	)	)	PUNCT
ejpam-3931	223	9	)	)	PUNCT
ejpam-3931	224	1	(	(	PUNCT
ejpam-3931	224	2	e(b	e(b	PROPN
ejpam-3931	224	3	∧	∧	PROPN
ejpam-3931	224	4	i	i	PRON
ejpam-3931	224	5	∧	∧	PROPN
ejpam-3931	224	6	l)e(b	l)e(b	VERB
ejpam-3931	224	7	∧	∧	NOUN
ejpam-3931	224	8	i	i	NOUN
ejpam-3931	224	9	∧	∧	PROPN
ejpam-3931	224	10	l	l	NOUN
ejpam-3931	224	11	)	)	PUNCT
ejpam-3931	224	12	)	)	PUNCT
ejpam-3931	225	1	e(b	e(b	PROPN
ejpam-3931	225	2	∧	∧	PROPN
ejpam-3931	225	3	i	i	NOUN
ejpam-3931	225	4	∧	∧	PROPN
ejpam-3931	225	5	l	l	NOUN
ejpam-3931	225	6	)	)	PUNCT
ejpam-3931	225	7	.	.	PUNCT
ejpam-3931	226	1	we	we	PRON
ejpam-3931	226	2	have	have	VERB
ejpam-3931	226	3	b	b	NUM
ejpam-3931	226	4	∧	∧	PROPN
ejpam-3931	226	5	i	i	PRON
ejpam-3931	226	6	∧	∧	PROPN
ejpam-3931	226	7	l	l	NOUN
ejpam-3931	226	8	≤	≤	PROPN
ejpam-3931	226	9	b	b	NUM
ejpam-3931	226	10	,	,	PUNCT
ejpam-3931	226	11	e(b	e(b	PROPN
ejpam-3931	226	12	∧	∧	PROPN
ejpam-3931	226	13	i	i	PRON
ejpam-3931	226	14	∧	∧	PROPN
ejpam-3931	226	15	l)e	l)e	VERB
ejpam-3931	226	16	≤	≤	NUM
ejpam-3931	226	17	e	e	NOUN
ejpam-3931	226	18	,	,	PUNCT
ejpam-3931	226	19	(	(	PUNCT
ejpam-3931	226	20	b	b	X
ejpam-3931	226	21	∧	∧	NOUN
ejpam-3931	226	22	i	i	PRON
ejpam-3931	226	23	∧	∧	PROPN
ejpam-3931	226	24	l	l	NOUN
ejpam-3931	226	25	)	)	PUNCT
ejpam-3931	226	26	≤	≤	NUM
ejpam-3931	226	27	b	b	NOUN
ejpam-3931	226	28	and	and	CCONJ
ejpam-3931	226	29	so	so	ADV
ejpam-3931	226	30	(	(	PUNCT
ejpam-3931	226	31	b	b	X
ejpam-3931	226	32	∧	∧	NOUN
ejpam-3931	226	33	i	i	PRON
ejpam-3931	226	34	∧	∧	PROPN
ejpam-3931	226	35	l)e(b	l)e(b	VERB
ejpam-3931	226	36	∧	∧	NOUN
ejpam-3931	227	1	i	i	PRON
ejpam-3931	227	2	∧	∧	PROPN
ejpam-3931	227	3	l)e(b	l)e(b	VERB
ejpam-3931	227	4	∧	∧	NOUN
ejpam-3931	227	5	i	i	NOUN
ejpam-3931	227	6	∧	∧	PROPN
ejpam-3931	227	7	l	l	NOUN
ejpam-3931	227	8	)	)	PUNCT
ejpam-3931	227	9	≤	≤	PROPN
ejpam-3931	227	10	beb	beb	PROPN
ejpam-3931	227	11	.	.	PUNCT
ejpam-3931	228	1	(	(	PUNCT
ejpam-3931	228	2	b	b	X
ejpam-3931	228	3	∧	∧	NOUN
ejpam-3931	228	4	i	i	PRON
ejpam-3931	228	5	∧	∧	PROPN
ejpam-3931	228	6	l)e	l)e	VERB
ejpam-3931	228	7	≤	≤	NUM
ejpam-3931	228	8	e	e	NOUN
ejpam-3931	228	9	,	,	PUNCT
ejpam-3931	228	10	b	b	PROPN
ejpam-3931	228	11	∧	∧	NOUN
ejpam-3931	228	12	i	i	PRON
ejpam-3931	228	13	∧	∧	PROPN
ejpam-3931	228	14	l	l	NOUN
ejpam-3931	228	15	≤	≤	PROPN
ejpam-3931	228	16	b	b	NUM
ejpam-3931	228	17	,	,	PUNCT
ejpam-3931	228	18	e(b	e(b	PROPN
ejpam-3931	228	19	∧	∧	PROPN
ejpam-3931	228	20	i	i	NOUN
ejpam-3931	228	21	∧	∧	PROPN
ejpam-3931	228	22	l	l	NOUN
ejpam-3931	228	23	)	)	PUNCT
ejpam-3931	228	24	≤	≤	NOUN
ejpam-3931	228	25	e	e	NOUN
ejpam-3931	228	26	and	and	CCONJ
ejpam-3931	228	27	so	so	ADV
ejpam-3931	228	28	(	(	PUNCT
ejpam-3931	228	29	b	b	X
ejpam-3931	228	30	∧	∧	NOUN
ejpam-3931	228	31	i	i	PRON
ejpam-3931	228	32	∧	∧	PROPN
ejpam-3931	228	33	l)e(b	l)e(b	VERB
ejpam-3931	228	34	∧	∧	NOUN
ejpam-3931	229	1	i	i	PRON
ejpam-3931	229	2	∧	∧	PROPN
ejpam-3931	229	3	l)e(b	l)e(b	VERB
ejpam-3931	229	4	∧	∧	NOUN
ejpam-3931	230	1	i	i	NOUN
ejpam-3931	230	2	∧	∧	PROPN
ejpam-3931	230	3	l	l	NOUN
ejpam-3931	230	4	)	)	PUNCT
ejpam-3931	230	5	≤	≤	NOUN
ejpam-3931	230	6	ebe	ebe	NOUN
ejpam-3931	230	7	.	.	PUNCT
ejpam-3931	231	1	thus	thus	ADV
ejpam-3931	231	2	we	we	PRON
ejpam-3931	231	3	have	have	VERB
ejpam-3931	231	4	(	(	PUNCT
ejpam-3931	231	5	b	b	X
ejpam-3931	231	6	∧	∧	NOUN
ejpam-3931	231	7	i	i	PRON
ejpam-3931	231	8	∧	∧	PROPN
ejpam-3931	231	9	l)e(b	l)e(b	VERB
ejpam-3931	231	10	∧	∧	NOUN
ejpam-3931	232	1	i	i	PRON
ejpam-3931	232	2	∧	∧	PROPN
ejpam-3931	232	3	l)e(b	l)e(b	VERB
ejpam-3931	232	4	∧	∧	NOUN
ejpam-3931	232	5	i	i	NOUN
ejpam-3931	232	6	∧	∧	PROPN
ejpam-3931	232	7	l	l	NOUN
ejpam-3931	232	8	)	)	PUNCT
ejpam-3931	232	9	≤	≤	NOUN
ejpam-3931	232	10	beb	beb	PROPN
ejpam-3931	232	11	∧	∧	PROPN
ejpam-3931	232	12	ebe	ebe	PROPN
ejpam-3931	232	13	≤	≤	PROPN
ejpam-3931	232	14	b.	b.	PROPN
ejpam-3931	233	1	moreover	moreover	ADV
ejpam-3931	233	2	,	,	PUNCT
ejpam-3931	233	3	e(b	e(b	PROPN
ejpam-3931	233	4	∧	∧	PROPN
ejpam-3931	233	5	i	i	PRON
ejpam-3931	233	6	∧	∧	PROPN
ejpam-3931	233	7	l)e(b	l)e(b	VERB
ejpam-3931	233	8	∧	∧	NOUN
ejpam-3931	234	1	i	i	NOUN
ejpam-3931	234	2	∧	∧	PROPN
ejpam-3931	234	3	l	l	NOUN
ejpam-3931	234	4	)	)	PUNCT
ejpam-3931	234	5	≤	≤	PUNCT
ejpam-3931	234	6	eiei	eiei	PROPN
ejpam-3931	234	7	≤	≤	PUNCT
ejpam-3931	235	1	i	i	PRON
ejpam-3931	235	2	and	and	CCONJ
ejpam-3931	235	3	e(b	e(b	VERB
ejpam-3931	235	4	∧	∧	PROPN
ejpam-3931	235	5	i	i	NOUN
ejpam-3931	235	6	∧	∧	PROPN
ejpam-3931	235	7	l	l	NOUN
ejpam-3931	235	8	)	)	PUNCT
ejpam-3931	235	9	≤	≤	PROPN
ejpam-3931	235	10	el	el	PROPN
ejpam-3931	235	11	≤	≤	PROPN
ejpam-3931	235	12	l.	l.	NOUN
ejpam-3931	235	13	hence	hence	ADV
ejpam-3931	235	14	we	we	PRON
ejpam-3931	235	15	obtain	obtain	VERB
ejpam-3931	235	16	b	b	PRON
ejpam-3931	235	17	∧	∧	NOUN
ejpam-3931	235	18	i	i	PRON
ejpam-3931	235	19	∧	∧	PROPN
ejpam-3931	235	20	l	l	NOUN
ejpam-3931	235	21	≤	≤	PROPN
ejpam-3931	235	22	bil	bil	NUM
ejpam-3931	235	23	.	.	PUNCT
ejpam-3931	236	1	⇐	⇐	PROPN
ejpam-3931	236	2	=	=	PRON
ejpam-3931	236	3	.	.	PUNCT
ejpam-3931	236	4	let	let	VERB
ejpam-3931	236	5	a	a	PRON
ejpam-3931	236	6	be	be	AUX
ejpam-3931	236	7	a	a	DET
ejpam-3931	236	8	right	right	ADJ
ejpam-3931	236	9	ideal	ideal	ADJ
ejpam-3931	236	10	element	element	NOUN
ejpam-3931	236	11	and	and	CCONJ
ejpam-3931	236	12	b	b	ADP
ejpam-3931	236	13	a	a	DET
ejpam-3931	236	14	left	left	ADJ
ejpam-3931	236	15	ideal	ideal	ADJ
ejpam-3931	236	16	element	element	NOUN
ejpam-3931	236	17	of	of	ADP
ejpam-3931	236	18	s.	s.	PROPN
ejpam-3931	236	19	since	since	SCONJ
ejpam-3931	236	20	a	a	PRON
ejpam-3931	236	21	is	be	AUX
ejpam-3931	236	22	a	a	DET
ejpam-3931	236	23	bi	bi	ADJ
ejpam-3931	236	24	-	-	ADJ
ejpam-3931	236	25	interior	interior	ADJ
ejpam-3931	236	26	ideal	ideal	ADJ
ejpam-3931	236	27	element	element	NOUN
ejpam-3931	236	28	,	,	PUNCT
ejpam-3931	236	29	e	e	X
ejpam-3931	236	30	an	an	DET
ejpam-3931	236	31	ideal	ideal	ADJ
ejpam-3931	236	32	element	element	NOUN
ejpam-3931	236	33	and	and	CCONJ
ejpam-3931	236	34	b	b	ADP
ejpam-3931	236	35	a	a	DET
ejpam-3931	236	36	left	left	ADJ
ejpam-3931	236	37	ideal	ideal	ADJ
ejpam-3931	236	38	element	element	NOUN
ejpam-3931	236	39	of	of	ADP
ejpam-3931	236	40	s	s	PROPN
ejpam-3931	236	41	,	,	PUNCT
ejpam-3931	236	42	by	by	ADP
ejpam-3931	236	43	hypothesis	hypothesis	NOUN
ejpam-3931	236	44	,	,	PUNCT
ejpam-3931	236	45	we	we	PRON
ejpam-3931	236	46	have	have	VERB
ejpam-3931	236	47	a	a	DET
ejpam-3931	236	48	∧	∧	PROPN
ejpam-3931	236	49	b	b	NOUN
ejpam-3931	236	50	=	=	PUNCT
ejpam-3931	236	51	a	a	DET
ejpam-3931	236	52	∧	∧	PROPN
ejpam-3931	236	53	e	e	PROPN
ejpam-3931	236	54	∧	∧	PROPN
ejpam-3931	236	55	b	b	PROPN
ejpam-3931	236	56	≤	≤	PROPN
ejpam-3931	236	57	aeb	aeb	NOUN
ejpam-3931	236	58	≤	≤	NUM
ejpam-3931	237	1	ab	ab	PROPN
ejpam-3931	237	2	≤	≤	PROPN
ejpam-3931	237	3	ae	ae	PROPN
ejpam-3931	237	4	∧	∧	PROPN
ejpam-3931	237	5	eb	eb	PROPN
ejpam-3931	237	6	≤	≤	PROPN
ejpam-3931	237	7	ab	ab	PROPN
ejpam-3931	237	8	,	,	PUNCT
ejpam-3931	237	9	then	then	ADV
ejpam-3931	237	10	a	a	DET
ejpam-3931	237	11	∧	∧	PROPN
ejpam-3931	237	12	b	b	PROPN
ejpam-3931	237	13	=	=	PUNCT
ejpam-3931	237	14	ab	ab	PROPN
ejpam-3931	238	1	and	and	CCONJ
ejpam-3931	238	2	so	so	ADV
ejpam-3931	238	3	s	s	VERB
ejpam-3931	238	4	is	be	AUX
ejpam-3931	238	5	regular	regular	ADJ
ejpam-3931	238	6	.	.	PUNCT
ejpam-3931	239	1	□	□	PUNCT
ejpam-3931	239	2	example	example	NOUN
ejpam-3931	239	3	4.8	4.8	NUM
ejpam-3931	239	4	.	.	PUNCT
ejpam-3931	240	1	we	we	PRON
ejpam-3931	240	2	consider	consider	VERB
ejpam-3931	240	3	the	the	DET
ejpam-3931	240	4	∧e	∧e	PROPN
ejpam-3931	240	5	-	-	PUNCT
ejpam-3931	240	6	semigroup	semigroup	NOUN
ejpam-3931	240	7	s	s	PART
ejpam-3931	240	8	=	=	PUNCT
ejpam-3931	240	9	{	{	PUNCT
ejpam-3931	240	10	a	a	PRON
ejpam-3931	240	11	,	,	PUNCT
ejpam-3931	240	12	b	b	NOUN
ejpam-3931	240	13	,	,	PUNCT
ejpam-3931	240	14	c	c	NOUN
ejpam-3931	240	15	,	,	PUNCT
ejpam-3931	240	16	d	d	NOUN
ejpam-3931	240	17	,	,	PUNCT
ejpam-3931	240	18	e	e	NOUN
ejpam-3931	240	19	}	}	PUNCT
ejpam-3931	240	20	given	give	VERB
ejpam-3931	240	21	by	by	ADP
ejpam-3931	240	22	table	table	NOUN
ejpam-3931	240	23	1	1	NUM
ejpam-3931	240	24	and	and	CCONJ
ejpam-3931	240	25	figure	figure	VERB
ejpam-3931	240	26	1	1	NUM
ejpam-3931	240	27	.	.	PUNCT
ejpam-3931	241	1	this	this	PRON
ejpam-3931	241	2	is	be	AUX
ejpam-3931	241	3	an	an	DET
ejpam-3931	241	4	le	le	NOUN
ejpam-3931	241	5	-	-	NOUN
ejpam-3931	241	6	semigroup	semigroup	NOUN
ejpam-3931	241	7	at	at	ADP
ejpam-3931	241	8	the	the	DET
ejpam-3931	241	9	same	same	ADJ
ejpam-3931	241	10	time	time	NOUN
ejpam-3931	241	11	.	.	PUNCT
ejpam-3931	242	1	n.	n.	PROPN
ejpam-3931	242	2	kehayopulu	kehayopulu	PROPN
ejpam-3931	242	3	/	/	SYM
ejpam-3931	242	4	eur	eur	PROPN
ejpam-3931	242	5	.	.	PUNCT
ejpam-3931	243	1	j.	j.	PROPN
ejpam-3931	243	2	pure	pure	PROPN
ejpam-3931	243	3	appl	appl	PROPN
ejpam-3931	243	4	.	.	PROPN
ejpam-3931	243	5	math	math	PROPN
ejpam-3931	243	6	,	,	PUNCT
ejpam-3931	243	7	14	14	NUM
ejpam-3931	243	8	(	(	PUNCT
ejpam-3931	243	9	4	4	NUM
ejpam-3931	243	10	)	)	PUNCT
ejpam-3931	243	11	(	(	PUNCT
ejpam-3931	243	12	2021	2021	NUM
ejpam-3931	243	13	)	)	PUNCT
ejpam-3931	243	14	,	,	PUNCT
ejpam-3931	243	15	43	43	NUM
ejpam-3931	243	16	-	-	SYM
ejpam-3931	243	17	52	52	NUM
ejpam-3931	243	18	51	51	NUM
ejpam-3931	243	19	·	·	PUNCT
ejpam-3931	244	1	a	a	DET
ejpam-3931	244	2	b	b	X
ejpam-3931	244	3	c	c	NOUN
ejpam-3931	244	4	d	d	X
ejpam-3931	244	5	e	e	X
ejpam-3931	244	6	a	a	DET
ejpam-3931	244	7	e	e	X
ejpam-3931	244	8	b	b	PROPN
ejpam-3931	244	9	a	a	PRON
ejpam-3931	244	10	d	d	X
ejpam-3931	244	11	e	e	PROPN
ejpam-3931	244	12	b	b	PROPN
ejpam-3931	244	13	b	b	PROPN
ejpam-3931	244	14	b	b	PROPN
ejpam-3931	244	15	b	b	PROPN
ejpam-3931	244	16	b	b	PROPN
ejpam-3931	244	17	b	b	PROPN
ejpam-3931	244	18	c	c	PROPN
ejpam-3931	244	19	a	a	DET
ejpam-3931	244	20	b	b	NOUN
ejpam-3931	244	21	c	c	NOUN
ejpam-3931	244	22	d	d	X
ejpam-3931	244	23	e	e	PROPN
ejpam-3931	244	24	d	d	PROPN
ejpam-3931	244	25	d	d	PROPN
ejpam-3931	244	26	b	b	PROPN
ejpam-3931	244	27	d	d	X
ejpam-3931	244	28	d	d	PROPN
ejpam-3931	244	29	d	d	X
ejpam-3931	244	30	e	e	X
ejpam-3931	244	31	e	e	X
ejpam-3931	244	32	b	b	PROPN
ejpam-3931	244	33	e	e	X
ejpam-3931	244	34	d	d	X
ejpam-3931	244	35	e	e	PROPN
ejpam-3931	244	36	table	table	NOUN
ejpam-3931	244	37	1	1	NUM
ejpam-3931	244	38	b	b	PROPN
ejpam-3931	244	39	cd	cd	PROPN
ejpam-3931	244	40	e	e	PROPN
ejpam-3931	244	41	a	a	DET
ejpam-3931	244	42	figure	figure	NOUN
ejpam-3931	244	43	1	1	NUM
ejpam-3931	244	44	this	this	PRON
ejpam-3931	244	45	is	be	AUX
ejpam-3931	244	46	regular	regular	ADJ
ejpam-3931	244	47	as	as	SCONJ
ejpam-3931	244	48	x	x	PROPN
ejpam-3931	244	49	≤	≤	X
ejpam-3931	244	50	xex	xex	VERB
ejpam-3931	244	51	for	for	ADP
ejpam-3931	244	52	every	every	DET
ejpam-3931	244	53	x	x	PROPN
ejpam-3931	244	54	∈	∈	PROPN
ejpam-3931	244	55	s.	s.	PROPN
ejpam-3931	244	56	the	the	DET
ejpam-3931	244	57	bi	bi	ADJ
ejpam-3931	244	58	-	-	ADJ
ejpam-3931	244	59	interior	interior	ADJ
ejpam-3931	244	60	ideal	ideal	ADJ
ejpam-3931	244	61	elements	element	NOUN
ejpam-3931	244	62	of	of	ADP
ejpam-3931	244	63	s	s	NOUN
ejpam-3931	244	64	are	be	AUX
ejpam-3931	244	65	the	the	DET
ejpam-3931	244	66	sets	set	NOUN
ejpam-3931	244	67	b	b	PROPN
ejpam-3931	244	68	,	,	PUNCT
ejpam-3931	244	69	d	d	PROPN
ejpam-3931	244	70	and	and	CCONJ
ejpam-3931	244	71	e.	e.	PROPN
ejpam-3931	245	1	the	the	DET
ejpam-3931	245	2	results	result	NOUN
ejpam-3931	245	3	of	of	ADP
ejpam-3931	245	4	sections	section	NOUN
ejpam-3931	245	5	2	2	NUM
ejpam-3931	245	6	and	and	CCONJ
ejpam-3931	245	7	4	4	NUM
ejpam-3931	245	8	can	can	AUX
ejpam-3931	245	9	be	be	AUX
ejpam-3931	245	10	applied	apply	VERB
ejpam-3931	245	11	.	.	PUNCT
ejpam-3931	246	1	this	this	PRON
ejpam-3931	246	2	is	be	AUX
ejpam-3931	246	3	not	not	PART
ejpam-3931	246	4	left	leave	VERB
ejpam-3931	246	5	simple	simple	ADJ
ejpam-3931	246	6	,	,	PUNCT
ejpam-3931	246	7	right	right	ADJ
ejpam-3931	246	8	simple	simple	ADJ
ejpam-3931	246	9	,	,	PUNCT
ejpam-3931	246	10	simple	simple	ADJ
ejpam-3931	246	11	or	or	CCONJ
ejpam-3931	246	12	bi	bi	ADJ
ejpam-3931	246	13	-	-	ADJ
ejpam-3931	246	14	interior	interior	ADJ
ejpam-3931	246	15	simple	simple	NOUN
ejpam-3931	246	16	.	.	PUNCT
ejpam-3931	247	1	note	note	NOUN
ejpam-3931	247	2	.	.	PUNCT
ejpam-3931	248	1	we	we	PRON
ejpam-3931	248	2	do	do	AUX
ejpam-3931	248	3	not	not	PART
ejpam-3931	248	4	have	have	VERB
ejpam-3931	248	5	to	to	PART
ejpam-3931	248	6	assume	assume	VERB
ejpam-3931	248	7	that	that	SCONJ
ejpam-3931	248	8	all	all	DET
ejpam-3931	248	9	semigroups	semigroup	NOUN
ejpam-3931	248	10	in	in	ADP
ejpam-3931	248	11	[	[	X
ejpam-3931	248	12	4	4	X
ejpam-3931	248	13	]	]	PUNCT
ejpam-3931	248	14	have	have	VERB
ejpam-3931	248	15	unity	unity	NOUN
ejpam-3931	248	16	.	.	PUNCT
ejpam-3931	249	1	in	in	ADP
ejpam-3931	249	2	case	case	NOUN
ejpam-3931	249	3	we	we	PRON
ejpam-3931	249	4	need	need	VERB
ejpam-3931	249	5	it	it	PRON
ejpam-3931	249	6	,	,	PUNCT
ejpam-3931	249	7	the	the	DET
ejpam-3931	249	8	assumption	assumption	NOUN
ejpam-3931	249	9	a	a	DET
ejpam-3931	249	10	⊆	⊆	NUM
ejpam-3931	249	11	am	am	NOUN
ejpam-3931	249	12	and	and	CCONJ
ejpam-3931	249	13	a	a	DET
ejpam-3931	249	14	⊆	⊆	NUM
ejpam-3931	249	15	ma	ma	NOUN
ejpam-3931	249	16	for	for	ADP
ejpam-3931	249	17	every	every	DET
ejpam-3931	249	18	nonempty	nonempty	NOUN
ejpam-3931	249	19	subset	subset	VERB
ejpam-3931	249	20	a	a	PRON
ejpam-3931	249	21	of	of	ADP
ejpam-3931	249	22	s	s	PRON
ejpam-3931	249	23	provides	provide	VERB
ejpam-3931	249	24	a	a	DET
ejpam-3931	249	25	more	more	ADV
ejpam-3931	249	26	general	general	ADJ
ejpam-3931	249	27	situation	situation	NOUN
ejpam-3931	249	28	.	.	PUNCT
ejpam-3931	250	1	it	it	PRON
ejpam-3931	250	2	is	be	AUX
ejpam-3931	250	3	not	not	PART
ejpam-3931	250	4	known	know	VERB
ejpam-3931	250	5	if	if	SCONJ
ejpam-3931	250	6	the	the	DET
ejpam-3931	250	7	theorem	theorem	NOUN
ejpam-3931	250	8	3.33	3.33	NUM
ejpam-3931	250	9	in	in	ADP
ejpam-3931	250	10	[	[	X
ejpam-3931	250	11	4	4	X
ejpam-3931	250	12	]	]	PUNCT
ejpam-3931	250	13	holds	hold	VERB
ejpam-3931	250	14	since	since	SCONJ
ejpam-3931	250	15	its	its	PRON
ejpam-3931	250	16	proof	proof	NOUN
ejpam-3931	250	17	is	be	AUX
ejpam-3931	250	18	wrong	wrong	ADJ
ejpam-3931	250	19	.	.	PUNCT
ejpam-3931	251	1	the	the	DET
ejpam-3931	251	2	proof	proof	NOUN
ejpam-3931	251	3	of	of	ADP
ejpam-3931	251	4	the	the	DET
ejpam-3931	251	5	“	"	PUNCT
ejpam-3931	251	6	⇒”-part	⇒”-part	PROPN
ejpam-3931	251	7	of	of	ADP
ejpam-3931	251	8	theorem	theorem	NOUN
ejpam-3931	251	9	3.14	3.14	NUM
ejpam-3931	251	10	in	in	ADP
ejpam-3931	251	11	[	[	X
ejpam-3931	251	12	4	4	NUM
ejpam-3931	251	13	]	]	PUNCT
ejpam-3931	251	14	is	be	AUX
ejpam-3931	251	15	wrong	wrong	ADJ
ejpam-3931	251	16	;	;	PUNCT
ejpam-3931	251	17	however	however	ADV
ejpam-3931	251	18	the	the	DET
ejpam-3931	251	19	above	above	ADJ
ejpam-3931	251	20	theorem	theorem	VERB
ejpam-3931	251	21	4.7	4.7	NUM
ejpam-3931	251	22	shows	show	VERB
ejpam-3931	251	23	that	that	SCONJ
ejpam-3931	251	24	it	it	PRON
ejpam-3931	251	25	can	can	AUX
ejpam-3931	251	26	be	be	AUX
ejpam-3931	251	27	proved	prove	VERB
ejpam-3931	251	28	and	and	CCONJ
ejpam-3931	251	29	the	the	DET
ejpam-3931	251	30	theorem	theorem	NOUN
ejpam-3931	251	31	3.14	3.14	NUM
ejpam-3931	251	32	in	in	ADP
ejpam-3931	251	33	[	[	X
ejpam-3931	251	34	4	4	NUM
ejpam-3931	251	35	]	]	PUNCT
ejpam-3931	251	36	holds	hold	VERB
ejpam-3931	251	37	.	.	PUNCT
ejpam-3931	252	1	5	5	X
ejpam-3931	252	2	.	.	X
ejpam-3931	252	3	conclusion	conclusion	NOUN
ejpam-3931	252	4	the	the	DET
ejpam-3931	252	5	results	result	NOUN
ejpam-3931	252	6	of	of	ADP
ejpam-3931	252	7	the	the	DET
ejpam-3931	252	8	present	present	ADJ
ejpam-3931	252	9	paper	paper	NOUN
ejpam-3931	252	10	generalize	generalize	VERB
ejpam-3931	252	11	corresponding	corresponding	ADJ
ejpam-3931	252	12	results	result	NOUN
ejpam-3931	252	13	by	by	ADP
ejpam-3931	252	14	m.m	m.m	PROPN
ejpam-3931	252	15	.	.	PROPN
ejpam-3931	252	16	krishna	krishna	PROPN
ejpam-3931	252	17	rao	rao	PROPN
ejpam-3931	252	18	in	in	ADP
ejpam-3931	252	19	discuss	discuss	PROPN
ejpam-3931	252	20	.	.	PUNCT
ejpam-3931	253	1	math	math	NOUN
ejpam-3931	253	2	.	.	PUNCT
ejpam-3931	254	1	gen	gen	PROPN
ejpam-3931	254	2	.	.	PROPN
ejpam-3931	254	3	algebra	algebra	PROPN
ejpam-3931	254	4	appl	appl	PROPN
ejpam-3931	254	5	.	.	PUNCT
ejpam-3931	255	1	in	in	ADP
ejpam-3931	255	2	a	a	DET
ejpam-3931	255	3	similar	similar	ADJ
ejpam-3931	255	4	way	way	NOUN
ejpam-3931	255	5	all	all	DET
ejpam-3931	255	6	the	the	DET
ejpam-3931	255	7	results	result	NOUN
ejpam-3931	255	8	on	on	ADP
ejpam-3931	255	9	semigroups	semigroup	NOUN
ejpam-3931	255	10	based	base	VERB
ejpam-3931	255	11	on	on	ADP
ejpam-3931	255	12	sets	set	NOUN
ejpam-3931	255	13	can	can	AUX
ejpam-3931	255	14	be	be	AUX
ejpam-3931	255	15	written	write	VERB
ejpam-3931	255	16	in	in	ADP
ejpam-3931	255	17	an	an	DET
ejpam-3931	255	18	abstract	abstract	ADJ
ejpam-3931	255	19	form	form	NOUN
ejpam-3931	255	20	using	use	VERB
ejpam-3931	255	21	elements	element	NOUN
ejpam-3931	255	22	(	(	PUNCT
ejpam-3931	255	23	instead	instead	ADV
ejpam-3931	255	24	of	of	ADP
ejpam-3931	255	25	sets	set	NOUN
ejpam-3931	255	26	)	)	PUNCT
ejpam-3931	255	27	.	.	PUNCT
ejpam-3931	256	1	references	reference	NOUN
ejpam-3931	256	2	52	52	NUM
ejpam-3931	256	3	references	reference	NOUN
ejpam-3931	256	4	[	[	X
ejpam-3931	256	5	1	1	NUM
ejpam-3931	256	6	]	]	PUNCT
ejpam-3931	256	7	n.	n.	NOUN
ejpam-3931	256	8	kehayopulu	kehayopulu	PROPN
ejpam-3931	256	9	.	.	PUNCT
ejpam-3931	257	1	on	on	ADP
ejpam-3931	257	2	intra	intra	ADJ
ejpam-3931	257	3	-	-	ADJ
ejpam-3931	257	4	regular	regular	ADJ
ejpam-3931	257	5	∨e	∨e	NOUN
ejpam-3931	257	6	-	-	PUNCT
ejpam-3931	257	7	semigroups	semigroup	NOUN
ejpam-3931	257	8	.	.	PUNCT
ejpam-3931	258	1	semigroup	semigroup	PROPN
ejpam-3931	258	2	forum	forum	PROPN
ejpam-3931	258	3	19(2):111–121	19(2):111–121	PROPN
ejpam-3931	258	4	,	,	PUNCT
ejpam-3931	258	5	1980	1980	NUM
ejpam-3931	258	6	.	.	PUNCT
ejpam-3931	259	1	[	[	X
ejpam-3931	259	2	2	2	NUM
ejpam-3931	259	3	]	]	PUNCT
ejpam-3931	259	4	n.	n.	NOUN
ejpam-3931	259	5	kehayopulu	kehayopulu	PROPN
ejpam-3931	259	6	.	.	PUNCT
ejpam-3931	260	1	note	note	NOUN
ejpam-3931	260	2	on	on	ADP
ejpam-3931	260	3	interior	interior	ADJ
ejpam-3931	260	4	ideals	ideal	NOUN
ejpam-3931	260	5	,	,	PUNCT
ejpam-3931	260	6	ideal	ideal	ADJ
ejpam-3931	260	7	elements	element	NOUN
ejpam-3931	260	8	in	in	ADP
ejpam-3931	260	9	ordered	order	VERB
ejpam-3931	260	10	semigroups	semigroup	NOUN
ejpam-3931	260	11	.	.	PUNCT
ejpam-3931	261	1	sci	sci	PROPN
ejpam-3931	261	2	.	.	PUNCT
ejpam-3931	261	3	math	math	PROPN
ejpam-3931	261	4	.	.	PUNCT
ejpam-3931	262	1	2(3):407–409	2(3):407–409	NUM
ejpam-3931	262	2	,	,	PUNCT
ejpam-3931	262	3	1999	1999	NUM
ejpam-3931	262	4	.	.	PUNCT
ejpam-3931	263	1	[	[	X
ejpam-3931	263	2	3	3	X
ejpam-3931	263	3	]	]	PUNCT
ejpam-3931	263	4	k.	k.	PROPN
ejpam-3931	264	1	koutský.	koutský.	PROPN
ejpam-3931	264	2	théory	théory	PROPN
ejpam-3931	264	3	the	the	DET
ejpam-3931	264	4	lattices	lattice	NOUN
ejpam-3931	264	5	topologiques	topologique	NOUN
ejpam-3931	264	6	.	.	PUNCT
ejpam-3931	265	1	publ	publ	PROPN
ejpam-3931	265	2	.	.	PUNCT
ejpam-3931	266	1	fac	fac	PROPN
ejpam-3931	266	2	.	.	PUNCT
ejpam-3931	266	3	sci	sci	PROPN
ejpam-3931	266	4	.	.	PROPN
ejpam-3931	266	5	univ	univ	PROPN
ejpam-3931	266	6	.	.	PUNCT
ejpam-3931	267	1	masaryk	masaryk	PROPN
ejpam-3931	267	2	95:133	95:133	NUM
ejpam-3931	267	3	–	–	PUNCT
ejpam-3931	267	4	171	171	NUM
ejpam-3931	267	5	,	,	PUNCT
ejpam-3931	267	6	1952	1952	NUM
ejpam-3931	267	7	.	.	PUNCT
ejpam-3931	268	1	[	[	X
ejpam-3931	268	2	4	4	NUM
ejpam-3931	268	3	]	]	X
ejpam-3931	268	4	m.m	m.m	PROPN
ejpam-3931	268	5	.	.	PROPN
ejpam-3931	268	6	krishna	krishna	PROPN
ejpam-3931	268	7	rao	rao	PROPN
ejpam-3931	268	8	.	.	PUNCT
ejpam-3931	269	1	bi	bi	ADJ
ejpam-3931	269	2	-	-	ADJ
ejpam-3931	269	3	interior	interior	ADJ
ejpam-3931	269	4	ideals	ideal	NOUN
ejpam-3931	269	5	of	of	ADP
ejpam-3931	269	6	semigroups	semigroup	NOUN
ejpam-3931	269	7	.	.	PUNCT
ejpam-3931	270	1	discuss	discuss	PROPN
ejpam-3931	270	2	.	.	PUNCT
ejpam-3931	270	3	math	math	NOUN
ejpam-3931	270	4	.	.	PUNCT
ejpam-3931	271	1	gen	gen	PROPN
ejpam-3931	271	2	.	.	PROPN
ejpam-3931	271	3	algebra	algebra	PROPN
ejpam-3931	271	4	appl	appl	PROPN
ejpam-3931	271	5	.	.	PUNCT
ejpam-3931	272	1	38(1):69–78	38(1):69–78	NUM
ejpam-3931	272	2	,	,	PUNCT
ejpam-3931	272	3	2018	2018	NUM
ejpam-3931	272	4	.	.	PUNCT
ejpam-3931	273	1	[	[	X
ejpam-3931	273	2	5	5	X
ejpam-3931	273	3	]	]	X
ejpam-3931	273	4	g.	g.	PROPN
ejpam-3931	273	5	nöbeling	nöbeling	PROPN
ejpam-3931	273	6	,	,	PUNCT
ejpam-3931	273	7	grundlagen	grundlagen	X
ejpam-3931	273	8	der	der	NOUN
ejpam-3931	273	9	analytischen	analytischen	PROPN
ejpam-3931	273	10	topologie	topologie	PROPN
ejpam-3931	273	11	.	.	PUNCT
ejpam-3931	274	1	die	die	PROPN
ejpam-3931	274	2	grundlehren	grundlehren	PROPN
ejpam-3931	274	3	der	der	PROPN
ejpam-3931	274	4	mathematischen	mathematischen	PROPN
ejpam-3931	274	5	wissenschaften	wissenschaften	VERB
ejpam-3931	274	6	in	in	ADP
ejpam-3931	274	7	einzeldarstellungen	einzeldarstellungen	PROPN
ejpam-3931	274	8	mit	mit	PROPN
ejpam-3931	274	9	besonderer	besonderer	PROPN
ejpam-3931	274	10	berucksichtigung	berucksichtigung	PROPN
ejpam-3931	274	11	der	der	NOUN
ejpam-3931	274	12	anwendungsgebiete	anwendungsgebiete	NOUN
ejpam-3931	274	13	,	,	PUNCT
ejpam-3931	274	14	bd	bd	PROPN
ejpam-3931	274	15	.	.	PROPN
ejpam-3931	274	16	lxxii	lxxii	PROPN
ejpam-3931	274	17	.	.	PUNCT
ejpam-3931	275	1	springer	springer	NOUN
ejpam-3931	275	2	-	-	PUNCT
ejpam-3931	275	3	verlag	verlag	PROPN
ejpam-3931	275	4	,	,	PUNCT
ejpam-3931	275	5	berlin	berlin	PROPN
ejpam-3931	275	6	-	-	PUNCT
ejpam-3931	275	7	gottingen	gottingen	NOUN
ejpam-3931	275	8	-	-	PUNCT
ejpam-3931	275	9	heidelberg	heidelberg	NOUN
ejpam-3931	275	10	,	,	PUNCT
ejpam-3931	275	11	1954	1954	NUM
ejpam-3931	275	12	.	.	PUNCT
ejpam-3931	276	1	x+221	x+221	PROPN
ejpam-3931	277	1	pp	pp	X
ejpam-3931	277	2	.	.	PUNCT