id	sid	tid	token	lemma	pos
ejpam-3527	1	1	european	european	PROPN
ejpam-3527	1	2	journal	journal	PROPN
ejpam-3527	1	3	of	of	ADP
ejpam-3527	1	4	pure	pure	ADJ
ejpam-3527	1	5	and	and	CCONJ
ejpam-3527	1	6	applied	apply	VERB
ejpam-3527	1	7	mathematics	mathematic	NOUN
ejpam-3527	1	8	vol	vol	NOUN
ejpam-3527	1	9	.	.	PROPN
ejpam-3527	2	1	12	12	NUM
ejpam-3527	2	2	,	,	PUNCT
ejpam-3527	2	3	no	no	INTJ
ejpam-3527	2	4	.	.	NOUN
ejpam-3527	2	5	4	4	NUM
ejpam-3527	2	6	,	,	PUNCT
ejpam-3527	2	7	2019	2019	NUM
ejpam-3527	2	8	,	,	PUNCT
ejpam-3527	2	9	1483	1483	NUM
ejpam-3527	2	10	-	-	SYM
ejpam-3527	2	11	1496	1496	NUM
ejpam-3527	2	12	issn	issn	PROPN
ejpam-3527	2	13	1307	1307	NUM
ejpam-3527	2	14	-	-	SYM
ejpam-3527	2	15	5543	5543	NUM
ejpam-3527	2	16	–	–	PUNCT
ejpam-3527	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3527	2	18	published	publish	VERB
ejpam-3527	2	19	by	by	ADP
ejpam-3527	2	20	new	new	PROPN
ejpam-3527	2	21	york	york	PROPN
ejpam-3527	2	22	business	business	PROPN
ejpam-3527	2	23	global	global	VERB
ejpam-3527	2	24	some	some	DET
ejpam-3527	2	25	structural	structural	ADJ
ejpam-3527	2	26	properties	property	NOUN
ejpam-3527	2	27	of	of	ADP
ejpam-3527	2	28	fully	fully	ADV
ejpam-3527	2	29	up	up	ADP
ejpam-3527	2	30	-	-	PUNCT
ejpam-3527	2	31	semigroups	semigroup	NOUN
ejpam-3527	2	32	dianne	dianne	PROPN
ejpam-3527	2	33	p.	p.	PROPN
ejpam-3527	2	34	gomisong1,2,∗	gomisong1,2,∗	PROPN
ejpam-3527	2	35	,	,	PUNCT
ejpam-3527	2	36	rowena	rowena	PROPN
ejpam-3527	2	37	t.	t.	PROPN
ejpam-3527	2	38	isla1,2	isla1,2	PROPN
ejpam-3527	2	39	1	1	NUM
ejpam-3527	2	40	department	department	NOUN
ejpam-3527	2	41	of	of	ADP
ejpam-3527	2	42	mathematics	mathematic	NOUN
ejpam-3527	2	43	and	and	CCONJ
ejpam-3527	2	44	statistics	statistic	NOUN
ejpam-3527	2	45	,	,	PUNCT
ejpam-3527	2	46	college	college	NOUN
ejpam-3527	2	47	of	of	ADP
ejpam-3527	2	48	science	science	NOUN
ejpam-3527	2	49	and	and	CCONJ
ejpam-3527	2	50	mathematics	mathematic	NOUN
ejpam-3527	2	51	,	,	PUNCT
ejpam-3527	2	52	mindanao	mindanao	PROPN
ejpam-3527	2	53	state	state	PROPN
ejpam-3527	2	54	university	university	PROPN
ejpam-3527	2	55	-	-	PUNCT
ejpam-3527	2	56	iligan	iligan	PROPN
ejpam-3527	2	57	institute	institute	PROPN
ejpam-3527	2	58	of	of	ADP
ejpam-3527	2	59	technology	technology	PROPN
ejpam-3527	2	60	,	,	PUNCT
ejpam-3527	2	61	9200	9200	NUM
ejpam-3527	2	62	iligan	iligan	ADJ
ejpam-3527	2	63	city	city	NOUN
ejpam-3527	2	64	,	,	PUNCT
ejpam-3527	2	65	philippines	philippine	NOUN
ejpam-3527	2	66	2	2	NUM
ejpam-3527	2	67	center	center	NOUN
ejpam-3527	2	68	for	for	ADP
ejpam-3527	2	69	graph	graph	NOUN
ejpam-3527	2	70	theory	theory	NOUN
ejpam-3527	2	71	,	,	PUNCT
ejpam-3527	2	72	algebra	algebra	NOUN
ejpam-3527	2	73	and	and	CCONJ
ejpam-3527	2	74	analysis	analysis	NOUN
ejpam-3527	2	75	,	,	PUNCT
ejpam-3527	2	76	premier	premier	PROPN
ejpam-3527	2	77	research	research	PROPN
ejpam-3527	2	78	institute	institute	PROPN
ejpam-3527	2	79	of	of	ADP
ejpam-3527	2	80	science	science	NOUN
ejpam-3527	2	81	and	and	CCONJ
ejpam-3527	2	82	mathematics	mathematic	NOUN
ejpam-3527	2	83	,	,	PUNCT
ejpam-3527	2	84	mindanao	mindanao	PROPN
ejpam-3527	2	85	state	state	PROPN
ejpam-3527	2	86	university	university	PROPN
ejpam-3527	2	87	-	-	PUNCT
ejpam-3527	2	88	iligan	iligan	PROPN
ejpam-3527	2	89	institute	institute	PROPN
ejpam-3527	2	90	of	of	ADP
ejpam-3527	2	91	technology	technology	PROPN
ejpam-3527	2	92	,	,	PUNCT
ejpam-3527	2	93	9200	9200	NUM
ejpam-3527	2	94	iligan	iligan	ADJ
ejpam-3527	2	95	city	city	NOUN
ejpam-3527	2	96	,	,	PUNCT
ejpam-3527	2	97	philippines	philippine	NOUN
ejpam-3527	2	98	abstract	abstract	ADJ
ejpam-3527	2	99	.	.	PUNCT
ejpam-3527	3	1	this	this	DET
ejpam-3527	3	2	paper	paper	NOUN
ejpam-3527	3	3	investigates	investigate	VERB
ejpam-3527	3	4	a	a	DET
ejpam-3527	3	5	new	new	ADJ
ejpam-3527	3	6	class	class	NOUN
ejpam-3527	3	7	of	of	ADP
ejpam-3527	3	8	algebra	algebra	NOUN
ejpam-3527	3	9	related	relate	VERB
ejpam-3527	3	10	to	to	ADP
ejpam-3527	3	11	up	up	ADV
ejpam-3527	3	12	-	-	PUNCT
ejpam-3527	3	13	algebras	algebra	NOUN
ejpam-3527	3	14	and	and	CCONJ
ejpam-3527	3	15	semigroups	semigroup	NOUN
ejpam-3527	3	16	called	call	VERB
ejpam-3527	3	17	fully	fully	ADV
ejpam-3527	3	18	up	up	ADP
ejpam-3527	3	19	-	-	PUNCT
ejpam-3527	3	20	semigroups	semigroup	NOUN
ejpam-3527	3	21	(	(	PUNCT
ejpam-3527	3	22	or	or	CCONJ
ejpam-3527	3	23	f	f	PROPN
ejpam-3527	3	24	-up	-up	NOUN
ejpam-3527	3	25	-	-	PUNCT
ejpam-3527	3	26	semigroups	semigroup	NOUN
ejpam-3527	3	27	)	)	PUNCT
ejpam-3527	3	28	.	.	PUNCT
ejpam-3527	4	1	it	it	PRON
ejpam-3527	4	2	establishes	establish	VERB
ejpam-3527	4	3	some	some	DET
ejpam-3527	4	4	structural	structural	ADJ
ejpam-3527	4	5	properties	property	NOUN
ejpam-3527	4	6	of	of	ADP
ejpam-3527	4	7	f	f	PROPN
ejpam-3527	4	8	up	up	ADP
ejpam-3527	4	9	-	-	PUNCT
ejpam-3527	4	10	semigroups	semigroup	NOUN
ejpam-3527	4	11	.	.	PUNCT
ejpam-3527	5	1	it	it	PRON
ejpam-3527	5	2	also	also	ADV
ejpam-3527	5	3	introduces	introduce	VERB
ejpam-3527	5	4	and	and	CCONJ
ejpam-3527	5	5	examines	examine	VERB
ejpam-3527	5	6	f	f	PROPN
ejpam-3527	5	7	-up	-up	NOUN
ejpam-3527	5	8	-	-	NOUN
ejpam-3527	5	9	fields	field	NOUN
ejpam-3527	5	10	,	,	PUNCT
ejpam-3527	5	11	f	f	PROPN
ejpam-3527	5	12	-up	-up	NOUN
ejpam-3527	5	13	-	-	NOUN
ejpam-3527	5	14	domains	domain	NOUN
ejpam-3527	5	15	,	,	PUNCT
ejpam-3527	5	16	f	f	PROPN
ejpam-3527	5	17	-up	-up	NOUN
ejpam-3527	5	18	-	-	NOUN
ejpam-3527	5	19	ideals	ideal	NOUN
ejpam-3527	5	20	,	,	PUNCT
ejpam-3527	5	21	and	and	CCONJ
ejpam-3527	5	22	quotient	quotient	VERB
ejpam-3527	5	23	f	f	PROPN
ejpam-3527	5	24	-up	-up	NOUN
ejpam-3527	5	25	-	-	PUNCT
ejpam-3527	5	26	semigroups	semigroup	NOUN
ejpam-3527	5	27	.	.	PUNCT
ejpam-3527	6	1	moreover	moreover	ADV
ejpam-3527	6	2	,	,	PUNCT
ejpam-3527	6	3	it	it	PRON
ejpam-3527	6	4	investigates	investigate	VERB
ejpam-3527	6	5	the	the	DET
ejpam-3527	6	6	relationship	relationship	NOUN
ejpam-3527	6	7	between	between	ADP
ejpam-3527	6	8	an	an	DET
ejpam-3527	6	9	f	f	PROPN
ejpam-3527	6	10	-up	-up	NOUN
ejpam-3527	6	11	-	-	PUNCT
ejpam-3527	6	12	field	field	NOUN
ejpam-3527	6	13	and	and	CCONJ
ejpam-3527	6	14	an	an	DET
ejpam-3527	6	15	f	f	NOUN
ejpam-3527	6	16	-up	-up	NOUN
ejpam-3527	6	17	-	-	NOUN
ejpam-3527	6	18	domain	domain	NOUN
ejpam-3527	6	19	.	.	PUNCT
ejpam-3527	7	1	2010	2010	NUM
ejpam-3527	7	2	mathematics	mathematic	NOUN
ejpam-3527	7	3	subject	subject	NOUN
ejpam-3527	7	4	classifications	classification	NOUN
ejpam-3527	7	5	:	:	PUNCT
ejpam-3527	7	6	03g25	03g25	NUM
ejpam-3527	7	7	,	,	PUNCT
ejpam-3527	7	8	08a99	08a99	VERB
ejpam-3527	7	9	key	key	ADJ
ejpam-3527	7	10	words	word	NOUN
ejpam-3527	7	11	and	and	CCONJ
ejpam-3527	7	12	phrases	phrase	NOUN
ejpam-3527	7	13	:	:	PUNCT
ejpam-3527	7	14	up	up	ADP
ejpam-3527	7	15	-	-	PUNCT
ejpam-3527	7	16	algebra	algebra	NOUN
ejpam-3527	7	17	,	,	PUNCT
ejpam-3527	7	18	f	f	PROPN
ejpam-3527	7	19	-up	-up	NOUN
ejpam-3527	7	20	-	-	PUNCT
ejpam-3527	7	21	semigroup	semigroup	PROPN
ejpam-3527	7	22	,	,	PUNCT
ejpam-3527	7	23	f	f	PROPN
ejpam-3527	7	24	-up	-up	NOUN
ejpam-3527	7	25	-	-	PUNCT
ejpam-3527	7	26	field	field	NOUN
ejpam-3527	7	27	,	,	PUNCT
ejpam-3527	7	28	f	f	PROPN
ejpam-3527	7	29	-up	-up	NOUN
ejpam-3527	7	30	-	-	NOUN
ejpam-3527	7	31	domain	domain	NOUN
ejpam-3527	7	32	,	,	PUNCT
ejpam-3527	7	33	f	f	PROPN
ejpam-3527	7	34	-up	-up	NOUN
ejpam-3527	7	35	-	-	PUNCT
ejpam-3527	7	36	ideal	ideal	ADJ
ejpam-3527	7	37	,	,	PUNCT
ejpam-3527	7	38	quotient	quotient	NOUN
ejpam-3527	7	39	f	f	PROPN
ejpam-3527	7	40	-up	-up	PROPN
ejpam-3527	7	41	-	-	PUNCT
ejpam-3527	7	42	semigroup	semigroup	ADJ
ejpam-3527	7	43	1	1	NUM
ejpam-3527	7	44	.	.	PUNCT
ejpam-3527	7	45	introduction	introduction	NOUN
ejpam-3527	7	46	in	in	ADP
ejpam-3527	7	47	1966	1966	NUM
ejpam-3527	7	48	,	,	PUNCT
ejpam-3527	7	49	y.	y.	PROPN
ejpam-3527	7	50	imai	imai	PROPN
ejpam-3527	7	51	and	and	CCONJ
ejpam-3527	7	52	k.	k.	PROPN
ejpam-3527	7	53	iseki	iseki	PROPN
ejpam-3527	8	1	[	[	X
ejpam-3527	8	2	5	5	X
ejpam-3527	8	3	]	]	PUNCT
ejpam-3527	8	4	introduced	introduce	VERB
ejpam-3527	8	5	the	the	DET
ejpam-3527	8	6	idea	idea	NOUN
ejpam-3527	8	7	of	of	ADP
ejpam-3527	8	8	bck	bck	NOUN
ejpam-3527	8	9	-	-	PUNCT
ejpam-3527	8	10	algebra	algebra	NOUN
ejpam-3527	8	11	as	as	ADP
ejpam-3527	8	12	a	a	DET
ejpam-3527	8	13	generalization	generalization	NOUN
ejpam-3527	8	14	of	of	ADP
ejpam-3527	8	15	the	the	DET
ejpam-3527	8	16	concept	concept	NOUN
ejpam-3527	8	17	of	of	ADP
ejpam-3527	8	18	set	set	NOUN
ejpam-3527	8	19	-	-	PUNCT
ejpam-3527	8	20	theoretic	theoretic	NOUN
ejpam-3527	8	21	difference	difference	NOUN
ejpam-3527	8	22	and	and	CCONJ
ejpam-3527	8	23	propositional	propositional	ADJ
ejpam-3527	8	24	calculi	calculi	NOUN
ejpam-3527	8	25	.	.	PUNCT
ejpam-3527	9	1	in	in	ADP
ejpam-3527	9	2	the	the	DET
ejpam-3527	9	3	same	same	ADJ
ejpam-3527	9	4	year	year	NOUN
ejpam-3527	9	5	,	,	PUNCT
ejpam-3527	9	6	k.	k.	PROPN
ejpam-3527	9	7	iseki	iseki	PROPN
ejpam-3527	10	1	[	[	X
ejpam-3527	10	2	6	6	X
ejpam-3527	10	3	]	]	PUNCT
ejpam-3527	10	4	introduced	introduce	VERB
ejpam-3527	10	5	the	the	DET
ejpam-3527	10	6	notion	notion	NOUN
ejpam-3527	10	7	of	of	ADP
ejpam-3527	10	8	bci	bci	NOUN
ejpam-3527	10	9	-	-	NOUN
ejpam-3527	10	10	algebra	algebra	NOUN
ejpam-3527	10	11	as	as	ADP
ejpam-3527	10	12	a	a	DET
ejpam-3527	10	13	generalization	generalization	NOUN
ejpam-3527	10	14	of	of	ADP
ejpam-3527	10	15	bck	bck	NOUN
ejpam-3527	10	16	-	-	PUNCT
ejpam-3527	10	17	algebra	algebra	NOUN
ejpam-3527	10	18	.	.	PUNCT
ejpam-3527	11	1	studies	study	NOUN
ejpam-3527	11	2	on	on	ADP
ejpam-3527	11	3	different	different	ADJ
ejpam-3527	11	4	types	type	NOUN
ejpam-3527	11	5	of	of	ADP
ejpam-3527	11	6	algebraic	algebraic	ADJ
ejpam-3527	11	7	structures	structure	NOUN
ejpam-3527	11	8	followed	follow	VERB
ejpam-3527	11	9	,	,	PUNCT
ejpam-3527	11	10	among	among	ADP
ejpam-3527	11	11	them	they	PRON
ejpam-3527	11	12	b	b	NOUN
ejpam-3527	11	13	-	-	PUNCT
ejpam-3527	11	14	algebras	algebras	PROPN
ejpam-3527	11	15	,	,	PUNCT
ejpam-3527	11	16	galgebras	galgebras	PROPN
ejpam-3527	11	17	,	,	PUNCT
ejpam-3527	11	18	bch	bch	PROPN
ejpam-3527	11	19	-	-	PUNCT
ejpam-3527	11	20	algebras	algebras	PROPN
ejpam-3527	11	21	,	,	PUNCT
ejpam-3527	11	22	be	be	AUX
ejpam-3527	11	23	-	-	PUNCT
ejpam-3527	11	24	algebras	algebras	X
ejpam-3527	11	25	,	,	PUNCT
ejpam-3527	11	26	and	and	CCONJ
ejpam-3527	11	27	su	su	PROPN
ejpam-3527	11	28	-	-	PUNCT
ejpam-3527	11	29	algebras	algebras	PROPN
ejpam-3527	11	30	.	.	PUNCT
ejpam-3527	12	1	in	in	ADP
ejpam-3527	12	2	2009	2009	NUM
ejpam-3527	12	3	,	,	PUNCT
ejpam-3527	12	4	c.	c.	NOUN
ejpam-3527	12	5	prabpayak	prabpayak	NOUN
ejpam-3527	12	6	and	and	CCONJ
ejpam-3527	12	7	u.	u.	NOUN
ejpam-3527	12	8	leerawat	leerawat	NOUN
ejpam-3527	13	1	[	[	X
ejpam-3527	13	2	11	11	NUM
ejpam-3527	13	3	]	]	PUNCT
ejpam-3527	13	4	introduced	introduce	VERB
ejpam-3527	13	5	the	the	DET
ejpam-3527	13	6	notion	notion	NOUN
ejpam-3527	13	7	of	of	ADP
ejpam-3527	13	8	ku	ku	PROPN
ejpam-3527	13	9	-	-	PUNCT
ejpam-3527	13	10	algebra	algebra	PROPN
ejpam-3527	13	11	and	and	CCONJ
ejpam-3527	13	12	investigated	investigate	VERB
ejpam-3527	13	13	some	some	DET
ejpam-3527	13	14	related	relate	VERB
ejpam-3527	13	15	properties	property	NOUN
ejpam-3527	13	16	.	.	PUNCT
ejpam-3527	14	1	in	in	ADP
ejpam-3527	14	2	2017	2017	NUM
ejpam-3527	14	3	,	,	PUNCT
ejpam-3527	14	4	a.	a.	NOUN
ejpam-3527	14	5	iampan	iampan	NOUN
ejpam-3527	14	6	[	[	X
ejpam-3527	14	7	3	3	X
ejpam-3527	14	8	]	]	PUNCT
ejpam-3527	14	9	introduced	introduce	VERB
ejpam-3527	14	10	a	a	DET
ejpam-3527	14	11	class	class	NOUN
ejpam-3527	14	12	of	of	ADP
ejpam-3527	14	13	algebra	algebra	NOUN
ejpam-3527	14	14	called	call	VERB
ejpam-3527	14	15	up	up	ADP
ejpam-3527	14	16	-	-	PUNCT
ejpam-3527	14	17	algebra	algebra	NOUN
ejpam-3527	14	18	(	(	PUNCT
ejpam-3527	14	19	up	up	ADP
ejpam-3527	14	20	means	mean	VERB
ejpam-3527	14	21	the	the	DET
ejpam-3527	14	22	university	university	NOUN
ejpam-3527	14	23	of	of	ADP
ejpam-3527	14	24	phayao	phayao	NOUN
ejpam-3527	14	25	)	)	PUNCT
ejpam-3527	14	26	.	.	PUNCT
ejpam-3527	15	1	he	he	PRON
ejpam-3527	15	2	established	establish	VERB
ejpam-3527	15	3	its	its	PRON
ejpam-3527	15	4	structure	structure	NOUN
ejpam-3527	15	5	and	and	CCONJ
ejpam-3527	15	6	defined	define	VERB
ejpam-3527	15	7	some	some	DET
ejpam-3527	15	8	concepts	concept	NOUN
ejpam-3527	15	9	such	such	ADJ
ejpam-3527	15	10	as	as	ADP
ejpam-3527	15	11	up	up	ADP
ejpam-3527	15	12	-	-	PUNCT
ejpam-3527	15	13	subalgebras	subalgebras	X
ejpam-3527	15	14	,	,	PUNCT
ejpam-3527	15	15	up	up	ADP
ejpam-3527	15	16	-	-	PUNCT
ejpam-3527	15	17	ideals	ideal	NOUN
ejpam-3527	15	18	,	,	PUNCT
ejpam-3527	15	19	congruences	congruence	NOUN
ejpam-3527	15	20	,	,	PUNCT
ejpam-3527	15	21	and	and	CCONJ
ejpam-3527	15	22	up	up	ADP
ejpam-3527	15	23	-	-	PUNCT
ejpam-3527	15	24	homomorphism	homomorphism	NOUN
ejpam-3527	15	25	.	.	PUNCT
ejpam-3527	16	1	he	he	PRON
ejpam-3527	16	2	determined	determine	VERB
ejpam-3527	16	3	some	some	DET
ejpam-3527	16	4	properties	property	NOUN
ejpam-3527	16	5	of	of	ADP
ejpam-3527	16	6	up	up	ADP
ejpam-3527	16	7	-	-	PUNCT
ejpam-3527	16	8	homomorphism	homomorphism	NOUN
ejpam-3527	16	9	,	,	PUNCT
ejpam-3527	16	10	which	which	PRON
ejpam-3527	16	11	led	lead	VERB
ejpam-3527	16	12	to	to	ADP
ejpam-3527	16	13	four	four	NUM
ejpam-3527	16	14	isomorphism	isomorphism	NOUN
ejpam-3527	16	15	theorems	theorem	NOUN
ejpam-3527	16	16	for	for	ADP
ejpam-3527	16	17	up	up	ADV
ejpam-3527	16	18	-	-	PUNCT
ejpam-3527	16	19	algebras	algebras	X
ejpam-3527	16	20	.	.	PUNCT
ejpam-3527	17	1	he	he	PRON
ejpam-3527	17	2	also	also	ADV
ejpam-3527	17	3	presented	present	VERB
ejpam-3527	17	4	some	some	DET
ejpam-3527	17	5	connections	connection	NOUN
ejpam-3527	17	6	between	between	ADP
ejpam-3527	17	7	up	up	ADV
ejpam-3527	17	8	-	-	PUNCT
ejpam-3527	17	9	algebras	algebra	NOUN
ejpam-3527	17	10	and	and	CCONJ
ejpam-3527	17	11	ku	ku	PROPN
ejpam-3527	17	12	-	-	PUNCT
ejpam-3527	17	13	algebras	algebras	PROPN
ejpam-3527	17	14	and	and	CCONJ
ejpam-3527	17	15	showed	show	VERB
ejpam-3527	17	16	that	that	SCONJ
ejpam-3527	17	17	the	the	DET
ejpam-3527	17	18	notion	notion	NOUN
ejpam-3527	17	19	of	of	ADP
ejpam-3527	17	20	up	up	ADP
ejpam-3527	17	21	-	-	PUNCT
ejpam-3527	17	22	algebra	algebra	NOUN
ejpam-3527	17	23	is	be	AUX
ejpam-3527	17	24	a	a	DET
ejpam-3527	17	25	generalization	generalization	NOUN
ejpam-3527	17	26	of	of	ADP
ejpam-3527	17	27	ku	ku	PROPN
ejpam-3527	17	28	-	-	PUNCT
ejpam-3527	17	29	algebra	algebra	PROPN
ejpam-3527	17	30	.	.	PUNCT
ejpam-3527	18	1	∗corresponding	∗corresponde	VERB
ejpam-3527	18	2	author	author	NOUN
ejpam-3527	18	3	.	.	PUNCT
ejpam-3527	19	1	doi	doi	NOUN
ejpam-3527	19	2	:	:	PUNCT
ejpam-3527	19	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3527	https://doi.org/10.29020/nybg.ejpam.v12i4.3527	PROPN
ejpam-3527	19	4	email	email	NOUN
ejpam-3527	19	5	addresses	address	NOUN
ejpam-3527	19	6	:	:	PUNCT
ejpam-3527	20	1	dianne.gomisong@g.msuiit.edu.ph	dianne.gomisong@g.msuiit.edu.ph	PROPN
ejpam-3527	20	2	(	(	PUNCT
ejpam-3527	20	3	d.	d.	PROPN
ejpam-3527	20	4	gomisong	gomisong	PROPN
ejpam-3527	20	5	)	)	PUNCT
ejpam-3527	20	6	,	,	PUNCT
ejpam-3527	20	7	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3527	20	8	(	(	PUNCT
ejpam-3527	20	9	r.	r.	PROPN
ejpam-3527	20	10	isla	isla	PROPN
ejpam-3527	20	11	)	)	PUNCT
ejpam-3527	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3527	20	13	1483	1483	NUM
ejpam-3527	21	1	c	c	X
ejpam-3527	21	2	©	©	PROPN
ejpam-3527	21	3	2019	2019	NUM
ejpam-3527	21	4	ejpam	ejpam	NOUN
ejpam-3527	21	5	all	all	DET
ejpam-3527	21	6	rights	right	NOUN
ejpam-3527	21	7	reserved	reserve	VERB
ejpam-3527	21	8	.	.	PUNCT
ejpam-3527	22	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	22	2	,	,	PUNCT
ejpam-3527	22	3	r.	r.	PROPN
ejpam-3527	22	4	isla	isla	PROPN
ejpam-3527	22	5	/	/	SYM
ejpam-3527	22	6	eur	eur	PROPN
ejpam-3527	22	7	.	.	PUNCT
ejpam-3527	23	1	j.	j.	PROPN
ejpam-3527	23	2	pure	pure	PROPN
ejpam-3527	23	3	appl	appl	PROPN
ejpam-3527	23	4	.	.	PROPN
ejpam-3527	23	5	math	math	PROPN
ejpam-3527	23	6	,	,	PUNCT
ejpam-3527	23	7	12	12	NUM
ejpam-3527	23	8	(	(	PUNCT
ejpam-3527	23	9	4	4	NUM
ejpam-3527	23	10	)	)	PUNCT
ejpam-3527	23	11	(	(	PUNCT
ejpam-3527	23	12	2019	2019	NUM
ejpam-3527	23	13	)	)	PUNCT
ejpam-3527	23	14	,	,	PUNCT
ejpam-3527	23	15	1483	1483	NUM
ejpam-3527	23	16	-	-	SYM
ejpam-3527	23	17	1496	1496	NUM
ejpam-3527	23	18	1484	1484	NUM
ejpam-3527	23	19	in	in	ADP
ejpam-3527	23	20	1993	1993	NUM
ejpam-3527	23	21	,	,	PUNCT
ejpam-3527	23	22	jun	jun	PROPN
ejpam-3527	23	23	,	,	PUNCT
ejpam-3527	23	24	hong	hong	PROPN
ejpam-3527	23	25	,	,	PUNCT
ejpam-3527	23	26	and	and	CCONJ
ejpam-3527	23	27	roh	roh	NOUN
ejpam-3527	24	1	[	[	X
ejpam-3527	24	2	7	7	X
ejpam-3527	24	3	]	]	PUNCT
ejpam-3527	24	4	introduced	introduce	VERB
ejpam-3527	24	5	a	a	DET
ejpam-3527	24	6	class	class	NOUN
ejpam-3527	24	7	of	of	ADP
ejpam-3527	24	8	algebra	algebra	NOUN
ejpam-3527	24	9	related	relate	VERB
ejpam-3527	24	10	to	to	ADP
ejpam-3527	24	11	bci	bci	NOUN
ejpam-3527	24	12	-	-	PUNCT
ejpam-3527	24	13	algebras	algebras	PROPN
ejpam-3527	24	14	and	and	CCONJ
ejpam-3527	24	15	semigroups	semigroup	NOUN
ejpam-3527	24	16	with	with	ADP
ejpam-3527	24	17	distributive	distributive	ADJ
ejpam-3527	24	18	laws	law	NOUN
ejpam-3527	24	19	property	property	NOUN
ejpam-3527	24	20	,	,	PUNCT
ejpam-3527	24	21	called	call	VERB
ejpam-3527	24	22	a	a	DET
ejpam-3527	24	23	bci	bci	PROPN
ejpam-3527	24	24	-	-	PUNCT
ejpam-3527	24	25	semigroup	semigroup	NOUN
ejpam-3527	24	26	.	.	PUNCT
ejpam-3527	25	1	jun	jun	PROPN
ejpam-3527	25	2	et	et	PROPN
ejpam-3527	25	3	al	al	PROPN
ejpam-3527	25	4	.	.	PUNCT
ejpam-3527	26	1	[	[	X
ejpam-3527	26	2	8	8	NUM
ejpam-3527	26	3	,	,	PUNCT
ejpam-3527	26	4	9	9	NUM
ejpam-3527	26	5	]	]	PUNCT
ejpam-3527	26	6	renamed	rename	VERB
ejpam-3527	26	7	the	the	DET
ejpam-3527	26	8	bci	bci	PROPN
ejpam-3527	26	9	-	-	PUNCT
ejpam-3527	26	10	semigroup	semigroup	NOUN
ejpam-3527	26	11	as	as	ADP
ejpam-3527	26	12	the	the	DET
ejpam-3527	26	13	is	is	NOUN
ejpam-3527	26	14	-	-	PUNCT
ejpam-3527	26	15	algebra	algebra	NOUN
ejpam-3527	26	16	and	and	CCONJ
ejpam-3527	26	17	studied	study	VERB
ejpam-3527	26	18	related	related	ADJ
ejpam-3527	26	19	properties	property	NOUN
ejpam-3527	26	20	.	.	PUNCT
ejpam-3527	27	1	in	in	ADP
ejpam-3527	27	2	2018	2018	NUM
ejpam-3527	27	3	,	,	PUNCT
ejpam-3527	27	4	f.	f.	PROPN
ejpam-3527	27	5	kareem	kareem	PROPN
ejpam-3527	27	6	and	and	CCONJ
ejpam-3527	27	7	e.	e.	PROPN
ejpam-3527	27	8	hasan	hasan	PROPN
ejpam-3527	28	1	[	[	X
ejpam-3527	28	2	10	10	NUM
ejpam-3527	28	3	]	]	PUNCT
ejpam-3527	28	4	introduced	introduce	VERB
ejpam-3527	28	5	the	the	DET
ejpam-3527	28	6	concept	concept	NOUN
ejpam-3527	28	7	of	of	ADP
ejpam-3527	28	8	ku	ku	PROPN
ejpam-3527	28	9	-	-	PUNCT
ejpam-3527	28	10	semigroup	semigroup	PROPN
ejpam-3527	28	11	which	which	PRON
ejpam-3527	28	12	is	be	AUX
ejpam-3527	28	13	a	a	DET
ejpam-3527	28	14	combination	combination	NOUN
ejpam-3527	28	15	of	of	ADP
ejpam-3527	28	16	ku	ku	PROPN
ejpam-3527	28	17	-	-	PUNCT
ejpam-3527	28	18	algebra	algebra	PROPN
ejpam-3527	28	19	and	and	CCONJ
ejpam-3527	28	20	semigroup	semigroup	NOUN
ejpam-3527	28	21	.	.	PUNCT
ejpam-3527	29	1	in	in	ADP
ejpam-3527	29	2	the	the	DET
ejpam-3527	29	3	same	same	ADJ
ejpam-3527	29	4	year	year	NOUN
ejpam-3527	29	5	,	,	PUNCT
ejpam-3527	29	6	a.	a.	NOUN
ejpam-3527	29	7	iampan	iampan	NOUN
ejpam-3527	29	8	[	[	X
ejpam-3527	29	9	4	4	X
ejpam-3527	29	10	]	]	PUNCT
ejpam-3527	29	11	introduced	introduce	VERB
ejpam-3527	29	12	a	a	DET
ejpam-3527	29	13	new	new	ADJ
ejpam-3527	29	14	class	class	NOUN
ejpam-3527	29	15	of	of	ADP
ejpam-3527	29	16	algebra	algebra	NOUN
ejpam-3527	29	17	called	call	VERB
ejpam-3527	29	18	a	a	DET
ejpam-3527	29	19	fully	fully	ADV
ejpam-3527	29	20	up	up	ADJ
ejpam-3527	29	21	-	-	PUNCT
ejpam-3527	29	22	semigroup	semigroup	NOUN
ejpam-3527	29	23	(	(	PUNCT
ejpam-3527	29	24	or	or	CCONJ
ejpam-3527	29	25	f	f	PROPN
ejpam-3527	29	26	-up	-up	NOUN
ejpam-3527	29	27	-	-	PUNCT
ejpam-3527	29	28	semigroup	semigroup	NOUN
ejpam-3527	29	29	)	)	PUNCT
ejpam-3527	29	30	which	which	PRON
ejpam-3527	29	31	is	be	AUX
ejpam-3527	29	32	a	a	DET
ejpam-3527	29	33	combination	combination	NOUN
ejpam-3527	29	34	of	of	ADP
ejpam-3527	29	35	up	up	NOUN
ejpam-3527	29	36	-	-	PUNCT
ejpam-3527	29	37	algebra	algebra	NOUN
ejpam-3527	29	38	and	and	CCONJ
ejpam-3527	29	39	semigroup	semigroup	NOUN
ejpam-3527	29	40	.	.	PUNCT
ejpam-3527	30	1	in	in	ADP
ejpam-3527	30	2	this	this	DET
ejpam-3527	30	3	study	study	NOUN
ejpam-3527	30	4	,	,	PUNCT
ejpam-3527	30	5	the	the	DET
ejpam-3527	30	6	notion	notion	NOUN
ejpam-3527	30	7	of	of	ADP
ejpam-3527	30	8	f	f	PROPN
ejpam-3527	30	9	-up	-up	NOUN
ejpam-3527	30	10	-	-	PUNCT
ejpam-3527	30	11	semigroup	semigroup	PROPN
ejpam-3527	30	12	is	be	AUX
ejpam-3527	30	13	investigated	investigate	VERB
ejpam-3527	30	14	and	and	CCONJ
ejpam-3527	30	15	some	some	PRON
ejpam-3527	30	16	of	of	ADP
ejpam-3527	30	17	its	its	PRON
ejpam-3527	30	18	properties	property	NOUN
ejpam-3527	30	19	are	be	AUX
ejpam-3527	30	20	established	establish	VERB
ejpam-3527	30	21	.	.	PUNCT
ejpam-3527	31	1	2	2	X
ejpam-3527	31	2	.	.	NUM
ejpam-3527	31	3	preliminaries	preliminary	NOUN
ejpam-3527	31	4	an	an	DET
ejpam-3527	31	5	algebra	algebra	NOUN
ejpam-3527	31	6	of	of	ADP
ejpam-3527	31	7	type	type	NOUN
ejpam-3527	31	8	(	(	PUNCT
ejpam-3527	31	9	2	2	NUM
ejpam-3527	31	10	,	,	PUNCT
ejpam-3527	31	11	0	0	NUM
ejpam-3527	31	12	)	)	PUNCT
ejpam-3527	31	13	is	be	AUX
ejpam-3527	31	14	an	an	DET
ejpam-3527	31	15	algebra	algebra	NOUN
ejpam-3527	31	16	with	with	ADP
ejpam-3527	31	17	a	a	DET
ejpam-3527	31	18	binary	binary	ADJ
ejpam-3527	31	19	operation	operation	NOUN
ejpam-3527	31	20	and	and	CCONJ
ejpam-3527	31	21	a	a	DET
ejpam-3527	31	22	constant	constant	ADJ
ejpam-3527	31	23	element	element	NOUN
ejpam-3527	31	24	.	.	PUNCT
ejpam-3527	32	1	definition	definition	NOUN
ejpam-3527	32	2	1	1	NUM
ejpam-3527	32	3	.	.	PUNCT
ejpam-3527	33	1	[	[	X
ejpam-3527	33	2	11	11	NUM
ejpam-3527	33	3	]	]	PUNCT
ejpam-3527	33	4	a	a	DET
ejpam-3527	33	5	ku	ku	PROPN
ejpam-3527	33	6	-	-	PUNCT
ejpam-3527	33	7	algebra	algebra	PROPN
ejpam-3527	33	8	is	be	AUX
ejpam-3527	33	9	an	an	DET
ejpam-3527	33	10	algebra	algebra	NOUN
ejpam-3527	33	11	(	(	PUNCT
ejpam-3527	33	12	x	x	NOUN
ejpam-3527	33	13	;	;	PUNCT
ejpam-3527	33	14	∗	∗	NOUN
ejpam-3527	33	15	,	,	PUNCT
ejpam-3527	33	16	0	0	NUM
ejpam-3527	33	17	)	)	PUNCT
ejpam-3527	33	18	of	of	ADP
ejpam-3527	33	19	type	type	NOUN
ejpam-3527	33	20	(	(	PUNCT
ejpam-3527	33	21	2	2	NUM
ejpam-3527	33	22	,	,	PUNCT
ejpam-3527	33	23	0	0	NUM
ejpam-3527	33	24	)	)	PUNCT
ejpam-3527	33	25	satisfying	satisfy	VERB
ejpam-3527	33	26	the	the	DET
ejpam-3527	33	27	following	follow	VERB
ejpam-3527	33	28	axioms	axiom	NOUN
ejpam-3527	33	29	:	:	PUNCT
ejpam-3527	33	30	for	for	ADP
ejpam-3527	33	31	all	all	DET
ejpam-3527	33	32	x	x	NOUN
ejpam-3527	33	33	,	,	PUNCT
ejpam-3527	33	34	y	y	PROPN
ejpam-3527	33	35	,	,	PUNCT
ejpam-3527	33	36	z	z	PROPN
ejpam-3527	33	37	∈	∈	PROPN
ejpam-3527	33	38	x	x	X
ejpam-3527	33	39	,	,	PUNCT
ejpam-3527	33	40	(	(	PUNCT
ejpam-3527	33	41	ku1	ku1	NOUN
ejpam-3527	33	42	)	)	PUNCT
ejpam-3527	33	43	(	(	PUNCT
ejpam-3527	33	44	x	x	SYM
ejpam-3527	33	45	∗	∗	PROPN
ejpam-3527	33	46	y	y	NOUN
ejpam-3527	33	47	)	)	PUNCT
ejpam-3527	33	48	∗	∗	NOUN
ejpam-3527	34	1	[	[	X
ejpam-3527	34	2	(	(	PUNCT
ejpam-3527	34	3	y	y	PROPN
ejpam-3527	34	4	∗	∗	PROPN
ejpam-3527	34	5	z	z	PROPN
ejpam-3527	34	6	)	)	PUNCT
ejpam-3527	34	7	∗	∗	NOUN
ejpam-3527	34	8	(	(	PUNCT
ejpam-3527	34	9	x	x	X
ejpam-3527	34	10	∗	∗	NOUN
ejpam-3527	34	11	z	z	NOUN
ejpam-3527	34	12	)	)	PUNCT
ejpam-3527	34	13	]	]	PUNCT
ejpam-3527	35	1	=	=	PUNCT
ejpam-3527	35	2	0	0	NUM
ejpam-3527	35	3	,	,	PUNCT
ejpam-3527	35	4	(	(	PUNCT
ejpam-3527	35	5	ku2	ku2	NOUN
ejpam-3527	35	6	)	)	PUNCT
ejpam-3527	35	7	0	0	NUM
ejpam-3527	35	8	∗	∗	NOUN
ejpam-3527	35	9	x	x	X
ejpam-3527	36	1	=	=	SYM
ejpam-3527	36	2	x	x	X
ejpam-3527	36	3	,	,	PUNCT
ejpam-3527	36	4	(	(	PUNCT
ejpam-3527	36	5	ku3	ku3	X
ejpam-3527	36	6	)	)	PUNCT
ejpam-3527	36	7	x	x	SYM
ejpam-3527	36	8	∗	∗	NOUN
ejpam-3527	36	9	0	0	NUM
ejpam-3527	37	1	=	=	SYM
ejpam-3527	37	2	0	0	NUM
ejpam-3527	37	3	,	,	PUNCT
ejpam-3527	37	4	(	(	PUNCT
ejpam-3527	37	5	ku4	ku4	NOUN
ejpam-3527	37	6	)	)	PUNCT
ejpam-3527	38	1	x	x	SYM
ejpam-3527	38	2	∗	∗	NOUN
ejpam-3527	38	3	y	y	NOUN
ejpam-3527	38	4	=	=	SYM
ejpam-3527	38	5	y	y	PROPN
ejpam-3527	38	6	∗	∗	NOUN
ejpam-3527	38	7	x	x	PUNCT
ejpam-3527	38	8	=	=	SYM
ejpam-3527	38	9	0	0	NUM
ejpam-3527	38	10	implies	imply	VERB
ejpam-3527	38	11	x	x	PUNCT
ejpam-3527	38	12	=	=	PUNCT
ejpam-3527	38	13	y.	y.	NOUN
ejpam-3527	38	14	example	example	NOUN
ejpam-3527	39	1	1	1	NUM
ejpam-3527	39	2	.	.	PUNCT
ejpam-3527	40	1	[	[	X
ejpam-3527	40	2	11	11	NUM
ejpam-3527	40	3	]	]	PUNCT
ejpam-3527	40	4	let	let	VERB
ejpam-3527	40	5	x	x	PUNCT
ejpam-3527	40	6	=	=	PUNCT
ejpam-3527	40	7	{	{	PUNCT
ejpam-3527	40	8	0	0	NUM
ejpam-3527	40	9	,	,	PUNCT
ejpam-3527	40	10	a	a	PRON
ejpam-3527	40	11	,	,	PUNCT
ejpam-3527	40	12	b	b	NOUN
ejpam-3527	40	13	,	,	PUNCT
ejpam-3527	40	14	c	c	AUX
ejpam-3527	40	15	}	}	PUNCT
ejpam-3527	40	16	be	be	AUX
ejpam-3527	40	17	a	a	DET
ejpam-3527	40	18	set	set	NOUN
ejpam-3527	40	19	with	with	ADP
ejpam-3527	40	20	a	a	DET
ejpam-3527	40	21	binary	binary	ADJ
ejpam-3527	40	22	operation	operation	NOUN
ejpam-3527	40	23	∗	∗	NOUN
ejpam-3527	40	24	defined	define	VERB
ejpam-3527	40	25	by	by	ADP
ejpam-3527	40	26	the	the	DET
ejpam-3527	40	27	following	follow	VERB
ejpam-3527	40	28	cayley	cayley	ADJ
ejpam-3527	40	29	table	table	NOUN
ejpam-3527	40	30	:	:	PUNCT
ejpam-3527	40	31	∗	∗	NOUN
ejpam-3527	40	32	0	0	PUNCT
ejpam-3527	41	1	a	a	DET
ejpam-3527	41	2	b	b	NOUN
ejpam-3527	41	3	c	c	NOUN
ejpam-3527	41	4	0	0	NUM
ejpam-3527	41	5	0	0	NUM
ejpam-3527	41	6	a	a	DET
ejpam-3527	41	7	b	b	NOUN
ejpam-3527	41	8	c	c	NOUN
ejpam-3527	41	9	a	a	DET
ejpam-3527	41	10	0	0	NUM
ejpam-3527	41	11	0	0	NUM
ejpam-3527	41	12	b	b	PROPN
ejpam-3527	41	13	c	c	NOUN
ejpam-3527	41	14	b	b	PROPN
ejpam-3527	41	15	0	0	NUM
ejpam-3527	41	16	a	a	DET
ejpam-3527	41	17	0	0	NUM
ejpam-3527	41	18	c	c	NOUN
ejpam-3527	41	19	c	c	NOUN
ejpam-3527	41	20	0	0	NUM
ejpam-3527	41	21	0	0	NUM
ejpam-3527	41	22	0	0	NUM
ejpam-3527	41	23	0	0	PUNCT
ejpam-3527	41	24	then	then	ADV
ejpam-3527	41	25	,	,	PUNCT
ejpam-3527	41	26	(	(	PUNCT
ejpam-3527	41	27	x	x	X
ejpam-3527	41	28	;	;	PUNCT
ejpam-3527	41	29	∗	∗	NOUN
ejpam-3527	41	30	,	,	PUNCT
ejpam-3527	41	31	0	0	NUM
ejpam-3527	41	32	)	)	PUNCT
ejpam-3527	41	33	is	be	AUX
ejpam-3527	41	34	a	a	DET
ejpam-3527	41	35	ku	ku	NOUN
ejpam-3527	41	36	-	-	PUNCT
ejpam-3527	41	37	algebra	algebra	PROPN
ejpam-3527	41	38	.	.	PUNCT
ejpam-3527	42	1	definition	definition	NOUN
ejpam-3527	42	2	2	2	NUM
ejpam-3527	42	3	.	.	PUNCT
ejpam-3527	43	1	[	[	X
ejpam-3527	43	2	3	3	X
ejpam-3527	43	3	]	]	X
ejpam-3527	43	4	a	a	DET
ejpam-3527	43	5	up	up	ADP
ejpam-3527	43	6	-	-	PUNCT
ejpam-3527	43	7	algebra	algebra	NOUN
ejpam-3527	43	8	is	be	AUX
ejpam-3527	43	9	an	an	DET
ejpam-3527	43	10	algebra	algebra	NOUN
ejpam-3527	43	11	(	(	PUNCT
ejpam-3527	43	12	x	x	NOUN
ejpam-3527	43	13	;	;	PUNCT
ejpam-3527	43	14	∗	∗	NOUN
ejpam-3527	43	15	,	,	PUNCT
ejpam-3527	43	16	0	0	NUM
ejpam-3527	43	17	)	)	PUNCT
ejpam-3527	43	18	of	of	ADP
ejpam-3527	43	19	type	type	NOUN
ejpam-3527	43	20	(	(	PUNCT
ejpam-3527	43	21	2	2	NUM
ejpam-3527	43	22	,	,	PUNCT
ejpam-3527	43	23	0	0	NUM
ejpam-3527	43	24	)	)	PUNCT
ejpam-3527	43	25	satisfying	satisfy	VERB
ejpam-3527	43	26	the	the	DET
ejpam-3527	43	27	following	follow	VERB
ejpam-3527	43	28	axioms	axiom	NOUN
ejpam-3527	43	29	:	:	PUNCT
ejpam-3527	43	30	for	for	ADP
ejpam-3527	43	31	all	all	DET
ejpam-3527	43	32	x	x	NOUN
ejpam-3527	43	33	,	,	PUNCT
ejpam-3527	43	34	y	y	PROPN
ejpam-3527	43	35	,	,	PUNCT
ejpam-3527	43	36	z	z	PROPN
ejpam-3527	43	37	∈	∈	PROPN
ejpam-3527	43	38	x	x	X
ejpam-3527	43	39	,	,	PUNCT
ejpam-3527	43	40	(	(	PUNCT
ejpam-3527	43	41	up1	up1	X
ejpam-3527	43	42	)	)	PUNCT
ejpam-3527	43	43	(	(	PUNCT
ejpam-3527	43	44	y	y	PROPN
ejpam-3527	43	45	∗	∗	PROPN
ejpam-3527	43	46	z	z	PROPN
ejpam-3527	43	47	)	)	PUNCT
ejpam-3527	43	48	∗	∗	NOUN
ejpam-3527	43	49	[	[	X
ejpam-3527	43	50	(	(	PUNCT
ejpam-3527	43	51	x	x	X
ejpam-3527	43	52	∗	∗	PROPN
ejpam-3527	43	53	y	y	NOUN
ejpam-3527	43	54	)	)	PUNCT
ejpam-3527	43	55	∗	∗	NOUN
ejpam-3527	43	56	(	(	PUNCT
ejpam-3527	43	57	x	x	X
ejpam-3527	43	58	∗	∗	NOUN
ejpam-3527	43	59	z	z	NOUN
ejpam-3527	43	60	)	)	PUNCT
ejpam-3527	43	61	]	]	PUNCT
ejpam-3527	44	1	=	=	PUNCT
ejpam-3527	44	2	0	0	NUM
ejpam-3527	44	3	,	,	PUNCT
ejpam-3527	44	4	(	(	PUNCT
ejpam-3527	44	5	up2	up2	NOUN
ejpam-3527	44	6	)	)	PUNCT
ejpam-3527	44	7	0	0	NUM
ejpam-3527	44	8	∗	∗	NOUN
ejpam-3527	44	9	x	x	X
ejpam-3527	45	1	=	=	SYM
ejpam-3527	45	2	x	x	NOUN
ejpam-3527	45	3	,	,	PUNCT
ejpam-3527	45	4	(	(	PUNCT
ejpam-3527	45	5	up3	up3	PROPN
ejpam-3527	45	6	)	)	PUNCT
ejpam-3527	45	7	x	x	SYM
ejpam-3527	45	8	∗	∗	NOUN
ejpam-3527	45	9	0	0	NUM
ejpam-3527	46	1	=	=	SYM
ejpam-3527	46	2	0	0	NUM
ejpam-3527	46	3	,	,	PUNCT
ejpam-3527	46	4	(	(	PUNCT
ejpam-3527	46	5	up4	up4	PROPN
ejpam-3527	46	6	)	)	PUNCT
ejpam-3527	46	7	x	x	PROPN
ejpam-3527	47	1	∗	∗	NOUN
ejpam-3527	47	2	y	y	NOUN
ejpam-3527	47	3	=	=	SYM
ejpam-3527	47	4	y	y	PROPN
ejpam-3527	47	5	∗	∗	NOUN
ejpam-3527	47	6	x	x	PUNCT
ejpam-3527	47	7	=	=	SYM
ejpam-3527	47	8	0	0	NUM
ejpam-3527	47	9	implies	imply	VERB
ejpam-3527	47	10	x	x	PUNCT
ejpam-3527	47	11	=	=	PUNCT
ejpam-3527	47	12	y.	y.	NOUN
ejpam-3527	47	13	example	example	NOUN
ejpam-3527	48	1	2	2	NUM
ejpam-3527	48	2	.	.	PUNCT
ejpam-3527	49	1	[	[	X
ejpam-3527	49	2	3	3	X
ejpam-3527	49	3	]	]	X
ejpam-3527	49	4	let	let	VERB
ejpam-3527	49	5	x	x	PUNCT
ejpam-3527	49	6	=	=	PUNCT
ejpam-3527	49	7	{	{	PUNCT
ejpam-3527	49	8	0	0	NUM
ejpam-3527	49	9	,	,	PUNCT
ejpam-3527	49	10	a	a	DET
ejpam-3527	49	11	,	,	PUNCT
ejpam-3527	49	12	b	b	NOUN
ejpam-3527	49	13	,	,	PUNCT
ejpam-3527	49	14	c	c	AUX
ejpam-3527	49	15	}	}	PUNCT
ejpam-3527	49	16	be	be	AUX
ejpam-3527	49	17	a	a	DET
ejpam-3527	49	18	set	set	NOUN
ejpam-3527	49	19	with	with	ADP
ejpam-3527	49	20	a	a	DET
ejpam-3527	49	21	binary	binary	ADJ
ejpam-3527	49	22	operation	operation	NOUN
ejpam-3527	49	23	∗	∗	NOUN
ejpam-3527	49	24	defined	define	VERB
ejpam-3527	49	25	by	by	ADP
ejpam-3527	49	26	the	the	DET
ejpam-3527	49	27	following	following	ADJ
ejpam-3527	49	28	cayley	cayley	ADJ
ejpam-3527	49	29	table	table	NOUN
ejpam-3527	49	30	:	:	PUNCT
ejpam-3527	49	31	d.gomisong	d.gomisong	PROPN
ejpam-3527	49	32	,	,	PUNCT
ejpam-3527	49	33	r.	r.	PROPN
ejpam-3527	49	34	isla	isla	PROPN
ejpam-3527	49	35	/	/	SYM
ejpam-3527	49	36	eur	eur	PROPN
ejpam-3527	49	37	.	.	PUNCT
ejpam-3527	50	1	j.	j.	PROPN
ejpam-3527	50	2	pure	pure	PROPN
ejpam-3527	50	3	appl	appl	PROPN
ejpam-3527	50	4	.	.	PROPN
ejpam-3527	50	5	math	math	PROPN
ejpam-3527	50	6	,	,	PUNCT
ejpam-3527	50	7	12	12	NUM
ejpam-3527	50	8	(	(	PUNCT
ejpam-3527	50	9	4	4	NUM
ejpam-3527	50	10	)	)	PUNCT
ejpam-3527	50	11	(	(	PUNCT
ejpam-3527	50	12	2019	2019	NUM
ejpam-3527	50	13	)	)	PUNCT
ejpam-3527	50	14	,	,	PUNCT
ejpam-3527	50	15	1483	1483	NUM
ejpam-3527	50	16	-	-	SYM
ejpam-3527	50	17	1496	1496	NUM
ejpam-3527	50	18	1485	1485	NUM
ejpam-3527	50	19	∗	∗	NOUN
ejpam-3527	50	20	0	0	NUM
ejpam-3527	51	1	a	a	DET
ejpam-3527	51	2	b	b	NOUN
ejpam-3527	51	3	c	c	NOUN
ejpam-3527	51	4	0	0	NUM
ejpam-3527	51	5	0	0	NUM
ejpam-3527	51	6	a	a	DET
ejpam-3527	51	7	b	b	NOUN
ejpam-3527	51	8	c	c	NOUN
ejpam-3527	51	9	a	a	PRON
ejpam-3527	51	10	0	0	NUM
ejpam-3527	51	11	0	0	NUM
ejpam-3527	51	12	b	b	PROPN
ejpam-3527	51	13	b	b	PROPN
ejpam-3527	51	14	b	b	PROPN
ejpam-3527	51	15	0	0	NUM
ejpam-3527	51	16	a	a	DET
ejpam-3527	51	17	0	0	NUM
ejpam-3527	51	18	b	b	NOUN
ejpam-3527	51	19	c	c	NOUN
ejpam-3527	51	20	0	0	PUNCT
ejpam-3527	52	1	a	a	DET
ejpam-3527	52	2	0	0	NUM
ejpam-3527	52	3	0	0	NUM
ejpam-3527	53	1	then	then	ADV
ejpam-3527	53	2	,	,	PUNCT
ejpam-3527	53	3	(	(	PUNCT
ejpam-3527	53	4	x	x	X
ejpam-3527	53	5	;	;	PUNCT
ejpam-3527	53	6	∗	∗	NOUN
ejpam-3527	53	7	,	,	PUNCT
ejpam-3527	53	8	0	0	NUM
ejpam-3527	53	9	)	)	PUNCT
ejpam-3527	53	10	is	be	AUX
ejpam-3527	53	11	a	a	DET
ejpam-3527	53	12	up	up	NOUN
ejpam-3527	53	13	-	-	PUNCT
ejpam-3527	53	14	algebra	algebra	NOUN
ejpam-3527	53	15	.	.	PUNCT
ejpam-3527	54	1	definition	definition	NOUN
ejpam-3527	54	2	3	3	NUM
ejpam-3527	54	3	.	.	PUNCT
ejpam-3527	55	1	[	[	X
ejpam-3527	55	2	3	3	X
ejpam-3527	55	3	]	]	X
ejpam-3527	55	4	let	let	VERB
ejpam-3527	55	5	x	x	PRON
ejpam-3527	55	6	be	be	AUX
ejpam-3527	55	7	a	a	DET
ejpam-3527	55	8	up	up	NOUN
ejpam-3527	55	9	-	-	PUNCT
ejpam-3527	55	10	algebra	algebra	NOUN
ejpam-3527	55	11	.	.	PUNCT
ejpam-3527	56	1	a	a	DET
ejpam-3527	56	2	subset	subset	NOUN
ejpam-3527	56	3	s	s	NOUN
ejpam-3527	56	4	of	of	ADP
ejpam-3527	56	5	x	x	PRON
ejpam-3527	56	6	is	be	AUX
ejpam-3527	56	7	called	call	VERB
ejpam-3527	56	8	a	a	DET
ejpam-3527	56	9	up	up	NOUN
ejpam-3527	56	10	-	-	PUNCT
ejpam-3527	56	11	subalgebra	subalgebra	NOUN
ejpam-3527	56	12	of	of	ADP
ejpam-3527	56	13	x	x	PRON
ejpam-3527	56	14	if	if	SCONJ
ejpam-3527	56	15	the	the	DET
ejpam-3527	56	16	constant	constant	ADJ
ejpam-3527	56	17	zero	zero	NUM
ejpam-3527	56	18	of	of	ADP
ejpam-3527	56	19	x	x	PRON
ejpam-3527	56	20	is	be	AUX
ejpam-3527	56	21	in	in	ADP
ejpam-3527	56	22	s	s	PRON
ejpam-3527	56	23	and	and	CCONJ
ejpam-3527	56	24	(	(	PUNCT
ejpam-3527	56	25	s	s	NOUN
ejpam-3527	56	26	;	;	PUNCT
ejpam-3527	56	27	∗	∗	NOUN
ejpam-3527	56	28	,	,	PUNCT
ejpam-3527	56	29	0	0	NUM
ejpam-3527	56	30	)	)	PUNCT
ejpam-3527	56	31	itself	itself	PRON
ejpam-3527	56	32	forms	form	VERB
ejpam-3527	56	33	a	a	DET
ejpam-3527	56	34	up	up	NOUN
ejpam-3527	56	35	-	-	PUNCT
ejpam-3527	56	36	algebra	algebra	NOUN
ejpam-3527	56	37	.	.	PUNCT
ejpam-3527	57	1	definition	definition	NOUN
ejpam-3527	57	2	4	4	NUM
ejpam-3527	57	3	.	.	PUNCT
ejpam-3527	58	1	[	[	X
ejpam-3527	58	2	1	1	X
ejpam-3527	58	3	]	]	PUNCT
ejpam-3527	58	4	define	define	NOUN
ejpam-3527	58	5	x∧y	x∧y	PROPN
ejpam-3527	59	1	=	=	SYM
ejpam-3527	59	2	(	(	PUNCT
ejpam-3527	59	3	y∗x)∗x	y∗x)∗x	PROPN
ejpam-3527	59	4	.	.	PUNCT
ejpam-3527	60	1	then	then	ADV
ejpam-3527	60	2	x	x	X
ejpam-3527	60	3	is	be	AUX
ejpam-3527	60	4	said	say	VERB
ejpam-3527	60	5	to	to	PART
ejpam-3527	60	6	be	be	AUX
ejpam-3527	60	7	a	a	DET
ejpam-3527	60	8	commutative	commutative	ADJ
ejpam-3527	60	9	up	up	NOUN
ejpam-3527	60	10	-	-	PUNCT
ejpam-3527	60	11	algebra	algebra	NOUN
ejpam-3527	60	12	if	if	SCONJ
ejpam-3527	60	13	for	for	ADP
ejpam-3527	60	14	any	any	DET
ejpam-3527	60	15	x	x	NOUN
ejpam-3527	60	16	,	,	PUNCT
ejpam-3527	60	17	y	y	PROPN
ejpam-3527	60	18	∈	∈	PROPN
ejpam-3527	60	19	x	x	X
ejpam-3527	60	20	,	,	PUNCT
ejpam-3527	60	21	(	(	PUNCT
ejpam-3527	60	22	y	y	PROPN
ejpam-3527	60	23	∗	∗	X
ejpam-3527	60	24	x	x	NOUN
ejpam-3527	60	25	)	)	PUNCT
ejpam-3527	60	26	∗	∗	NOUN
ejpam-3527	60	27	x	x	X
ejpam-3527	61	1	=	=	SYM
ejpam-3527	61	2	(	(	PUNCT
ejpam-3527	61	3	x	x	X
ejpam-3527	61	4	∗	∗	PROPN
ejpam-3527	61	5	y	y	NOUN
ejpam-3527	61	6	)	)	PUNCT
ejpam-3527	61	7	∗	∗	PROPN
ejpam-3527	61	8	y	y	PROPN
ejpam-3527	61	9	,	,	PUNCT
ejpam-3527	61	10	that	that	ADV
ejpam-3527	61	11	is	is	ADV
ejpam-3527	61	12	,	,	PUNCT
ejpam-3527	61	13	x	x	PUNCT
ejpam-3527	61	14	∧	∧	NOUN
ejpam-3527	61	15	y	y	PROPN
ejpam-3527	61	16	=	=	SYM
ejpam-3527	61	17	y	y	PROPN
ejpam-3527	61	18	∧	∧	PROPN
ejpam-3527	61	19	x.	x.	NOUN
ejpam-3527	61	20	definition	definition	NOUN
ejpam-3527	61	21	5	5	NUM
ejpam-3527	61	22	.	.	PUNCT
ejpam-3527	62	1	[	[	X
ejpam-3527	62	2	3	3	X
ejpam-3527	62	3	]	]	X
ejpam-3527	62	4	let	let	VERB
ejpam-3527	62	5	x	x	PRON
ejpam-3527	62	6	be	be	AUX
ejpam-3527	62	7	a	a	DET
ejpam-3527	62	8	up	up	NOUN
ejpam-3527	62	9	-	-	PUNCT
ejpam-3527	62	10	algebra	algebra	NOUN
ejpam-3527	62	11	.	.	PUNCT
ejpam-3527	63	1	then	then	ADV
ejpam-3527	63	2	,	,	PUNCT
ejpam-3527	63	3	a	a	DET
ejpam-3527	63	4	subset	subset	NOUN
ejpam-3527	63	5	i	i	PRON
ejpam-3527	63	6	of	of	ADP
ejpam-3527	63	7	x	x	PRON
ejpam-3527	63	8	is	be	AUX
ejpam-3527	63	9	called	call	VERB
ejpam-3527	63	10	a	a	DET
ejpam-3527	63	11	up	up	ADJ
ejpam-3527	63	12	-	-	PUNCT
ejpam-3527	63	13	ideal	ideal	NOUN
ejpam-3527	63	14	of	of	ADP
ejpam-3527	63	15	x	x	PRON
ejpam-3527	63	16	if	if	SCONJ
ejpam-3527	63	17	it	it	PRON
ejpam-3527	63	18	satisfies	satisfy	VERB
ejpam-3527	63	19	:	:	PUNCT
ejpam-3527	63	20	(	(	PUNCT
ejpam-3527	63	21	i	i	NOUN
ejpam-3527	63	22	)	)	PUNCT
ejpam-3527	63	23	the	the	DET
ejpam-3527	63	24	constant	constant	ADJ
ejpam-3527	63	25	zero	zero	NUM
ejpam-3527	63	26	of	of	ADP
ejpam-3527	63	27	x	x	SYM
ejpam-3527	63	28	is	be	AUX
ejpam-3527	63	29	in	in	ADP
ejpam-3527	63	30	i	i	PRON
ejpam-3527	63	31	,	,	PUNCT
ejpam-3527	63	32	and	and	CCONJ
ejpam-3527	63	33	(	(	PUNCT
ejpam-3527	63	34	ii	ii	NOUN
ejpam-3527	63	35	)	)	PUNCT
ejpam-3527	63	36	for	for	ADP
ejpam-3527	63	37	any	any	DET
ejpam-3527	63	38	x	x	NOUN
ejpam-3527	63	39	,	,	PUNCT
ejpam-3527	63	40	y	y	PROPN
ejpam-3527	63	41	,	,	PUNCT
ejpam-3527	63	42	z	z	PROPN
ejpam-3527	63	43	∈	∈	PROPN
ejpam-3527	63	44	x	x	X
ejpam-3527	63	45	,	,	PUNCT
ejpam-3527	63	46	x	x	SYM
ejpam-3527	63	47	∗	∗	NOUN
ejpam-3527	63	48	(	(	PUNCT
ejpam-3527	63	49	y	y	PROPN
ejpam-3527	63	50	∗	∗	PROPN
ejpam-3527	63	51	z	z	NOUN
ejpam-3527	63	52	)	)	PUNCT
ejpam-3527	63	53	∈	∈	PROPN
ejpam-3527	63	54	i	i	PRON
ejpam-3527	63	55	and	and	CCONJ
ejpam-3527	63	56	y	y	PROPN
ejpam-3527	63	57	∈	∈	PROPN
ejpam-3527	64	1	i	i	PRON
ejpam-3527	64	2	imply	imply	VERB
ejpam-3527	64	3	x	x	X
ejpam-3527	64	4	∗	∗	NOUN
ejpam-3527	64	5	z	z	PROPN
ejpam-3527	64	6	∈	∈	PROPN
ejpam-3527	64	7	i.	i.	NOUN
ejpam-3527	64	8	proposition	proposition	NOUN
ejpam-3527	64	9	1	1	NUM
ejpam-3527	64	10	.	.	PUNCT
ejpam-3527	65	1	[	[	X
ejpam-3527	65	2	3	3	X
ejpam-3527	65	3	]	]	PUNCT
ejpam-3527	65	4	in	in	ADP
ejpam-3527	65	5	a	a	DET
ejpam-3527	65	6	up	up	NOUN
ejpam-3527	65	7	-	-	PUNCT
ejpam-3527	65	8	algebra	algebra	NOUN
ejpam-3527	65	9	(	(	PUNCT
ejpam-3527	65	10	x	x	NOUN
ejpam-3527	65	11	;	;	PUNCT
ejpam-3527	65	12	∗	∗	NOUN
ejpam-3527	65	13	,	,	PUNCT
ejpam-3527	65	14	0	0	NUM
ejpam-3527	65	15	)	)	PUNCT
ejpam-3527	65	16	,	,	PUNCT
ejpam-3527	65	17	the	the	DET
ejpam-3527	65	18	following	follow	VERB
ejpam-3527	65	19	properties	property	NOUN
ejpam-3527	65	20	hold	hold	VERB
ejpam-3527	65	21	:	:	PUNCT
ejpam-3527	65	22	for	for	ADP
ejpam-3527	65	23	any	any	DET
ejpam-3527	65	24	x	x	NOUN
ejpam-3527	65	25	,	,	PUNCT
ejpam-3527	65	26	y	y	PROPN
ejpam-3527	65	27	,	,	PUNCT
ejpam-3527	65	28	z	z	PROPN
ejpam-3527	65	29	∈	∈	PROPN
ejpam-3527	65	30	x	x	X
ejpam-3527	65	31	,	,	PUNCT
ejpam-3527	65	32	(	(	PUNCT
ejpam-3527	65	33	i	i	NOUN
ejpam-3527	65	34	)	)	PUNCT
ejpam-3527	65	35	x	x	SYM
ejpam-3527	65	36	∗	∗	NOUN
ejpam-3527	65	37	x	x	SYM
ejpam-3527	66	1	=	=	SYM
ejpam-3527	66	2	0	0	NUM
ejpam-3527	66	3	,	,	PUNCT
ejpam-3527	66	4	(	(	PUNCT
ejpam-3527	66	5	ii	ii	NOUN
ejpam-3527	66	6	)	)	PUNCT
ejpam-3527	66	7	x	x	PROPN
ejpam-3527	67	1	∗	∗	NOUN
ejpam-3527	67	2	y	y	NOUN
ejpam-3527	67	3	=	=	SYM
ejpam-3527	67	4	0	0	PROPN
ejpam-3527	68	1	and	and	CCONJ
ejpam-3527	68	2	y	y	PROPN
ejpam-3527	68	3	∗	∗	NOUN
ejpam-3527	68	4	z	z	NOUN
ejpam-3527	69	1	=	=	SYM
ejpam-3527	69	2	0	0	NUM
ejpam-3527	69	3	imply	imply	VERB
ejpam-3527	69	4	x	x	X
ejpam-3527	69	5	∗	∗	NOUN
ejpam-3527	69	6	z	z	NOUN
ejpam-3527	69	7	=	=	SYM
ejpam-3527	69	8	0	0	NUM
ejpam-3527	69	9	,	,	PUNCT
ejpam-3527	69	10	(	(	PUNCT
ejpam-3527	69	11	iii	iii	NOUN
ejpam-3527	69	12	)	)	PUNCT
ejpam-3527	69	13	x	x	SYM
ejpam-3527	69	14	∗	∗	NOUN
ejpam-3527	69	15	y	y	NOUN
ejpam-3527	69	16	=	=	SYM
ejpam-3527	69	17	0	0	NUM
ejpam-3527	69	18	implies	imply	VERB
ejpam-3527	69	19	(	(	PUNCT
ejpam-3527	69	20	z	z	NOUN
ejpam-3527	69	21	∗	∗	NOUN
ejpam-3527	69	22	x	x	NOUN
ejpam-3527	69	23	)	)	PUNCT
ejpam-3527	69	24	∗	∗	NOUN
ejpam-3527	69	25	(	(	PUNCT
ejpam-3527	69	26	z	z	NOUN
ejpam-3527	69	27	∗	∗	NOUN
ejpam-3527	69	28	y	y	NOUN
ejpam-3527	69	29	)	)	PUNCT
ejpam-3527	69	30	=	=	SYM
ejpam-3527	69	31	0	0	NUM
ejpam-3527	69	32	,	,	PUNCT
ejpam-3527	69	33	(	(	PUNCT
ejpam-3527	69	34	iv	iv	X
ejpam-3527	69	35	)	)	PUNCT
ejpam-3527	69	36	x	x	PROPN
ejpam-3527	69	37	∗	∗	NOUN
ejpam-3527	69	38	y	y	NOUN
ejpam-3527	69	39	=	=	SYM
ejpam-3527	69	40	0	0	NUM
ejpam-3527	69	41	implies	imply	VERB
ejpam-3527	69	42	(	(	PUNCT
ejpam-3527	69	43	y	y	PROPN
ejpam-3527	69	44	∗	∗	PROPN
ejpam-3527	69	45	z	z	PROPN
ejpam-3527	69	46	)	)	PUNCT
ejpam-3527	69	47	∗	∗	NOUN
ejpam-3527	69	48	(	(	PUNCT
ejpam-3527	69	49	x	x	X
ejpam-3527	69	50	∗	∗	PROPN
ejpam-3527	69	51	z	z	NOUN
ejpam-3527	69	52	)	)	PUNCT
ejpam-3527	69	53	=	=	SYM
ejpam-3527	69	54	0	0	NUM
ejpam-3527	69	55	,	,	PUNCT
ejpam-3527	69	56	(	(	PUNCT
ejpam-3527	69	57	v	v	NOUN
ejpam-3527	69	58	)	)	PUNCT
ejpam-3527	69	59	x	x	SYM
ejpam-3527	69	60	∗	∗	NOUN
ejpam-3527	69	61	(	(	PUNCT
ejpam-3527	69	62	y	y	PROPN
ejpam-3527	69	63	∗	∗	NOUN
ejpam-3527	69	64	x	x	NOUN
ejpam-3527	69	65	)	)	PUNCT
ejpam-3527	69	66	=	=	SYM
ejpam-3527	69	67	0	0	NUM
ejpam-3527	69	68	,	,	PUNCT
ejpam-3527	69	69	(	(	PUNCT
ejpam-3527	69	70	vi	vi	NOUN
ejpam-3527	69	71	)	)	PUNCT
ejpam-3527	69	72	(	(	PUNCT
ejpam-3527	69	73	y	y	PROPN
ejpam-3527	69	74	∗	∗	X
ejpam-3527	69	75	x	x	NOUN
ejpam-3527	69	76	)	)	PUNCT
ejpam-3527	69	77	∗	∗	NOUN
ejpam-3527	69	78	x	x	PUNCT
ejpam-3527	69	79	=	=	SYM
ejpam-3527	69	80	0	0	NUM
ejpam-3527	69	81	implies	imply	VERB
ejpam-3527	69	82	x	x	PUNCT
ejpam-3527	69	83	=	=	SYM
ejpam-3527	69	84	y	y	PROPN
ejpam-3527	69	85	∗	∗	NOUN
ejpam-3527	69	86	x	x	PROPN
ejpam-3527	69	87	,	,	PUNCT
ejpam-3527	69	88	and	and	CCONJ
ejpam-3527	69	89	(	(	PUNCT
ejpam-3527	69	90	vii	vii	PROPN
ejpam-3527	69	91	)	)	PUNCT
ejpam-3527	69	92	x	x	PROPN
ejpam-3527	69	93	∗	∗	NOUN
ejpam-3527	69	94	(	(	PUNCT
ejpam-3527	69	95	y	y	PROPN
ejpam-3527	69	96	∗	∗	PROPN
ejpam-3527	69	97	y	y	NOUN
ejpam-3527	69	98	)	)	PUNCT
ejpam-3527	69	99	=	=	SYM
ejpam-3527	70	1	0	0	X
ejpam-3527	70	2	.	.	PUNCT
ejpam-3527	71	1	the	the	DET
ejpam-3527	71	2	next	next	ADJ
ejpam-3527	71	3	result	result	NOUN
ejpam-3527	71	4	gives	give	VERB
ejpam-3527	71	5	a	a	DET
ejpam-3527	71	6	relationship	relationship	NOUN
ejpam-3527	71	7	between	between	ADP
ejpam-3527	71	8	up	up	ADV
ejpam-3527	71	9	-	-	PUNCT
ejpam-3527	71	10	algebras	algebra	NOUN
ejpam-3527	71	11	and	and	CCONJ
ejpam-3527	71	12	ku	ku	PROPN
ejpam-3527	71	13	-	-	PUNCT
ejpam-3527	71	14	algebras	algebras	PROPN
ejpam-3527	71	15	.	.	PUNCT
ejpam-3527	72	1	theorem	theorem	NOUN
ejpam-3527	72	2	1	1	NUM
ejpam-3527	72	3	.	.	PUNCT
ejpam-3527	73	1	[	[	X
ejpam-3527	73	2	3	3	X
ejpam-3527	73	3	]	]	X
ejpam-3527	73	4	any	any	DET
ejpam-3527	73	5	ku	ku	PROPN
ejpam-3527	73	6	-	-	PUNCT
ejpam-3527	73	7	algebra	algebra	PROPN
ejpam-3527	73	8	is	be	AUX
ejpam-3527	73	9	a	a	DET
ejpam-3527	73	10	up	up	NOUN
ejpam-3527	73	11	-	-	PUNCT
ejpam-3527	73	12	algebra	algebra	NOUN
ejpam-3527	73	13	.	.	PUNCT
ejpam-3527	74	1	the	the	DET
ejpam-3527	74	2	converse	converse	NOUN
ejpam-3527	74	3	of	of	ADP
ejpam-3527	74	4	theorem	theorem	NOUN
ejpam-3527	74	5	1	1	NUM
ejpam-3527	74	6	does	do	AUX
ejpam-3527	74	7	not	not	PART
ejpam-3527	74	8	hold	hold	VERB
ejpam-3527	74	9	.	.	PUNCT
ejpam-3527	75	1	to	to	PART
ejpam-3527	75	2	see	see	VERB
ejpam-3527	75	3	this	this	PRON
ejpam-3527	75	4	,	,	PUNCT
ejpam-3527	75	5	consider	consider	VERB
ejpam-3527	75	6	the	the	DET
ejpam-3527	75	7	up	up	NOUN
ejpam-3527	75	8	-	-	PUNCT
ejpam-3527	75	9	algebra	algebra	NOUN
ejpam-3527	75	10	(	(	PUNCT
ejpam-3527	75	11	x	x	NOUN
ejpam-3527	75	12	;	;	PUNCT
ejpam-3527	75	13	∗	∗	NOUN
ejpam-3527	75	14	,	,	PUNCT
ejpam-3527	75	15	0	0	NUM
ejpam-3527	75	16	)	)	PUNCT
ejpam-3527	75	17	in	in	ADP
ejpam-3527	75	18	example	example	NOUN
ejpam-3527	76	1	2	2	X
ejpam-3527	76	2	.	.	PUNCT
ejpam-3527	76	3	let	let	VERB
ejpam-3527	76	4	x	x	SYM
ejpam-3527	76	5	=	=	SYM
ejpam-3527	76	6	0	0	NUM
ejpam-3527	76	7	,	,	PUNCT
ejpam-3527	76	8	y	y	PROPN
ejpam-3527	76	9	=	=	PUNCT
ejpam-3527	76	10	a	a	PROPN
ejpam-3527	76	11	,	,	PUNCT
ejpam-3527	76	12	and	and	CCONJ
ejpam-3527	76	13	z	z	NOUN
ejpam-3527	76	14	=	=	SYM
ejpam-3527	76	15	c.	c.	NOUN
ejpam-3527	76	16	observe	observe	VERB
ejpam-3527	76	17	that	that	SCONJ
ejpam-3527	76	18	(	(	PUNCT
ejpam-3527	76	19	x	x	SYM
ejpam-3527	76	20	∗	∗	PROPN
ejpam-3527	76	21	y	y	NOUN
ejpam-3527	76	22	)	)	PUNCT
ejpam-3527	76	23	∗	∗	NOUN
ejpam-3527	76	24	[	[	X
ejpam-3527	76	25	(	(	PUNCT
ejpam-3527	76	26	y	y	PROPN
ejpam-3527	76	27	∗	∗	PROPN
ejpam-3527	76	28	z	z	PROPN
ejpam-3527	76	29	)	)	PUNCT
ejpam-3527	76	30	∗	∗	NOUN
ejpam-3527	76	31	(	(	PUNCT
ejpam-3527	76	32	x	x	X
ejpam-3527	76	33	∗	∗	NOUN
ejpam-3527	76	34	z	z	NOUN
ejpam-3527	76	35	)	)	PUNCT
ejpam-3527	76	36	]	]	PUNCT
ejpam-3527	77	1	=	=	PUNCT
ejpam-3527	77	2	(	(	PUNCT
ejpam-3527	77	3	0	0	NUM
ejpam-3527	77	4	∗	∗	NOUN
ejpam-3527	77	5	a	a	NOUN
ejpam-3527	77	6	)	)	PUNCT
ejpam-3527	77	7	∗	∗	NOUN
ejpam-3527	78	1	[	[	X
ejpam-3527	78	2	(	(	PUNCT
ejpam-3527	78	3	a	a	DET
ejpam-3527	78	4	∗	∗	NOUN
ejpam-3527	78	5	c	c	NOUN
ejpam-3527	78	6	)	)	PUNCT
ejpam-3527	78	7	∗	∗	NOUN
ejpam-3527	78	8	(	(	PUNCT
ejpam-3527	78	9	0	0	NUM
ejpam-3527	78	10	∗	∗	NOUN
ejpam-3527	78	11	c	c	NOUN
ejpam-3527	78	12	)	)	PUNCT
ejpam-3527	78	13	]	]	PUNCT
ejpam-3527	79	1	=	=	PUNCT
ejpam-3527	79	2	a	a	DET
ejpam-3527	79	3	∗	∗	NOUN
ejpam-3527	79	4	(	(	PUNCT
ejpam-3527	79	5	b	b	NOUN
ejpam-3527	79	6	∗	∗	NOUN
ejpam-3527	79	7	c	c	NOUN
ejpam-3527	79	8	)	)	PUNCT
ejpam-3527	79	9	=	=	PUNCT
ejpam-3527	79	10	a	a	DET
ejpam-3527	79	11	∗	∗	NOUN
ejpam-3527	79	12	b	b	NOUN
ejpam-3527	79	13	=	=	SYM
ejpam-3527	79	14	b	b	PROPN
ejpam-3527	79	15	6=	6=	NUM
ejpam-3527	79	16	0	0	NUM
ejpam-3527	79	17	,	,	PUNCT
ejpam-3527	79	18	so	so	ADV
ejpam-3527	79	19	(	(	PUNCT
ejpam-3527	79	20	ku1	ku1	NOUN
ejpam-3527	79	21	)	)	PUNCT
ejpam-3527	79	22	is	be	AUX
ejpam-3527	79	23	not	not	PART
ejpam-3527	79	24	satisfied	satisfied	ADJ
ejpam-3527	79	25	.	.	PUNCT
ejpam-3527	80	1	thus	thus	ADV
ejpam-3527	80	2	,	,	PUNCT
ejpam-3527	80	3	(	(	PUNCT
ejpam-3527	80	4	x	x	X
ejpam-3527	80	5	;	;	PUNCT
ejpam-3527	80	6	∗	∗	NOUN
ejpam-3527	80	7	,	,	PUNCT
ejpam-3527	80	8	0	0	NUM
ejpam-3527	80	9	)	)	PUNCT
ejpam-3527	80	10	is	be	AUX
ejpam-3527	80	11	not	not	PART
ejpam-3527	80	12	a	a	DET
ejpam-3527	80	13	ku	ku	NOUN
ejpam-3527	80	14	-	-	PUNCT
ejpam-3527	80	15	algebra	algebra	PROPN
ejpam-3527	80	16	.	.	PUNCT
ejpam-3527	81	1	in	in	ADP
ejpam-3527	81	2	view	view	NOUN
ejpam-3527	81	3	of	of	ADP
ejpam-3527	81	4	theorem	theorem	NOUN
ejpam-3527	81	5	1	1	NUM
ejpam-3527	81	6	,	,	PUNCT
ejpam-3527	81	7	the	the	DET
ejpam-3527	81	8	notion	notion	NOUN
ejpam-3527	81	9	of	of	ADP
ejpam-3527	81	10	up	up	ADV
ejpam-3527	81	11	-	-	PUNCT
ejpam-3527	81	12	algebras	algebras	PROPN
ejpam-3527	81	13	is	be	AUX
ejpam-3527	81	14	a	a	DET
ejpam-3527	81	15	generalization	generalization	NOUN
ejpam-3527	81	16	of	of	ADP
ejpam-3527	81	17	ku	ku	PROPN
ejpam-3527	81	18	-	-	PUNCT
ejpam-3527	81	19	algebras	algebras	PROPN
ejpam-3527	81	20	.	.	PUNCT
ejpam-3527	82	1	proposition	proposition	NOUN
ejpam-3527	82	2	2	2	NUM
ejpam-3527	82	3	.	.	PUNCT
ejpam-3527	83	1	[	[	X
ejpam-3527	83	2	3	3	X
ejpam-3527	83	3	]	]	PUNCT
ejpam-3527	83	4	a	a	DET
ejpam-3527	83	5	nonempty	nonempty	NOUN
ejpam-3527	83	6	subset	subset	VERB
ejpam-3527	83	7	s	s	NOUN
ejpam-3527	83	8	of	of	ADP
ejpam-3527	83	9	a	a	DET
ejpam-3527	83	10	up	up	NOUN
ejpam-3527	83	11	-	-	PUNCT
ejpam-3527	83	12	algebra	algebra	NOUN
ejpam-3527	83	13	(	(	PUNCT
ejpam-3527	83	14	x	x	NOUN
ejpam-3527	83	15	;	;	PUNCT
ejpam-3527	83	16	∗	∗	NOUN
ejpam-3527	83	17	,	,	PUNCT
ejpam-3527	83	18	0	0	NUM
ejpam-3527	83	19	)	)	PUNCT
ejpam-3527	83	20	is	be	AUX
ejpam-3527	83	21	a	a	DET
ejpam-3527	83	22	up	up	ADJ
ejpam-3527	83	23	-	-	PUNCT
ejpam-3527	83	24	subalgebra	subalgebra	NOUN
ejpam-3527	83	25	of	of	ADP
ejpam-3527	83	26	x	x	PRON
ejpam-3527	83	27	if	if	SCONJ
ejpam-3527	83	28	and	and	CCONJ
ejpam-3527	83	29	only	only	ADV
ejpam-3527	83	30	if	if	SCONJ
ejpam-3527	83	31	s	s	NOUN
ejpam-3527	83	32	is	be	AUX
ejpam-3527	83	33	closed	close	VERB
ejpam-3527	83	34	under	under	ADP
ejpam-3527	83	35	the	the	DET
ejpam-3527	83	36	∗	∗	NOUN
ejpam-3527	83	37	operation	operation	NOUN
ejpam-3527	83	38	.	.	PUNCT
ejpam-3527	84	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	84	2	,	,	PUNCT
ejpam-3527	84	3	r.	r.	PROPN
ejpam-3527	84	4	isla	isla	PROPN
ejpam-3527	84	5	/	/	SYM
ejpam-3527	84	6	eur	eur	PROPN
ejpam-3527	84	7	.	.	PUNCT
ejpam-3527	85	1	j.	j.	PROPN
ejpam-3527	85	2	pure	pure	PROPN
ejpam-3527	85	3	appl	appl	PROPN
ejpam-3527	85	4	.	.	PROPN
ejpam-3527	85	5	math	math	PROPN
ejpam-3527	85	6	,	,	PUNCT
ejpam-3527	85	7	12	12	NUM
ejpam-3527	85	8	(	(	PUNCT
ejpam-3527	85	9	4	4	NUM
ejpam-3527	85	10	)	)	PUNCT
ejpam-3527	85	11	(	(	PUNCT
ejpam-3527	85	12	2019	2019	NUM
ejpam-3527	85	13	)	)	PUNCT
ejpam-3527	85	14	,	,	PUNCT
ejpam-3527	85	15	1483	1483	NUM
ejpam-3527	85	16	-	-	SYM
ejpam-3527	85	17	1496	1496	NUM
ejpam-3527	85	18	1486	1486	NUM
ejpam-3527	85	19	let	let	VERB
ejpam-3527	85	20	x	x	PRON
ejpam-3527	85	21	be	be	AUX
ejpam-3527	85	22	a	a	DET
ejpam-3527	85	23	up	up	NOUN
ejpam-3527	85	24	-	-	PUNCT
ejpam-3527	85	25	algebra	algebra	NOUN
ejpam-3527	85	26	and	and	CCONJ
ejpam-3527	85	27	a	a	DET
ejpam-3527	85	28	be	be	NOUN
ejpam-3527	85	29	a	a	DET
ejpam-3527	85	30	nonempty	nonempty	ADJ
ejpam-3527	85	31	subset	subset	NOUN
ejpam-3527	85	32	of	of	ADP
ejpam-3527	85	33	x.	x.	NOUN
ejpam-3527	85	34	then	then	ADV
ejpam-3527	85	35	x	x	X
ejpam-3527	85	36	∗	∗	NOUN
ejpam-3527	85	37	a	a	PRON
ejpam-3527	85	38	is	be	AUX
ejpam-3527	85	39	given	give	VERB
ejpam-3527	85	40	by	by	ADP
ejpam-3527	85	41	x	x	X
ejpam-3527	85	42	∗a	∗a	PROPN
ejpam-3527	85	43	=	=	SYM
ejpam-3527	85	44	⋃	⋃	NOUN
ejpam-3527	85	45	x∈x	x∈x	NOUN
ejpam-3527	85	46	,	,	PUNCT
ejpam-3527	85	47	a∈a	a∈a	PROPN
ejpam-3527	85	48	(	(	PUNCT
ejpam-3527	85	49	x	x	SYM
ejpam-3527	85	50	∗	∗	NOUN
ejpam-3527	85	51	a	a	NOUN
ejpam-3527	85	52	)	)	PUNCT
ejpam-3527	85	53	.	.	PUNCT
ejpam-3527	86	1	theorem	theorem	NOUN
ejpam-3527	86	2	2	2	NUM
ejpam-3527	86	3	.	.	PUNCT
ejpam-3527	87	1	[	[	X
ejpam-3527	87	2	3	3	X
ejpam-3527	87	3	]	]	X
ejpam-3527	87	4	let	let	VERB
ejpam-3527	87	5	x	x	PRON
ejpam-3527	87	6	be	be	AUX
ejpam-3527	87	7	a	a	DET
ejpam-3527	87	8	up	up	NOUN
ejpam-3527	87	9	-	-	PUNCT
ejpam-3527	87	10	algebra	algebra	NOUN
ejpam-3527	87	11	and	and	CCONJ
ejpam-3527	87	12	b	b	NOUN
ejpam-3527	87	13	a	a	DET
ejpam-3527	87	14	up	up	ADJ
ejpam-3527	87	15	-	-	PUNCT
ejpam-3527	87	16	ideal	ideal	NOUN
ejpam-3527	87	17	of	of	ADP
ejpam-3527	87	18	x.	x.	NOUN
ejpam-3527	87	19	then	then	ADV
ejpam-3527	87	20	x	x	X
ejpam-3527	87	21	∗	∗	PROPN
ejpam-3527	87	22	b	b	PROPN
ejpam-3527	87	23	⊆	⊆	NUM
ejpam-3527	87	24	b.	b.	NOUN
ejpam-3527	87	25	in	in	ADP
ejpam-3527	87	26	particular	particular	ADJ
ejpam-3527	87	27	,	,	PUNCT
ejpam-3527	87	28	b	b	PROPN
ejpam-3527	87	29	is	be	AUX
ejpam-3527	87	30	a	a	DET
ejpam-3527	87	31	up	up	ADJ
ejpam-3527	87	32	-	-	PUNCT
ejpam-3527	87	33	subalgebra	subalgebra	NOUN
ejpam-3527	87	34	of	of	ADP
ejpam-3527	87	35	x.	x.	NOUN
ejpam-3527	87	36	let	let	VERB
ejpam-3527	87	37	(	(	PUNCT
ejpam-3527	87	38	x	x	X
ejpam-3527	87	39	;	;	PUNCT
ejpam-3527	87	40	∗	∗	NOUN
ejpam-3527	87	41	,	,	PUNCT
ejpam-3527	87	42	0	0	NUM
ejpam-3527	87	43	)	)	PUNCT
ejpam-3527	87	44	be	be	AUX
ejpam-3527	87	45	a	a	DET
ejpam-3527	87	46	up	up	NOUN
ejpam-3527	87	47	-	-	PUNCT
ejpam-3527	87	48	algebra	algebra	NOUN
ejpam-3527	87	49	and	and	CCONJ
ejpam-3527	87	50	b	b	NOUN
ejpam-3527	87	51	be	be	AUX
ejpam-3527	87	52	a	a	DET
ejpam-3527	87	53	up	up	ADJ
ejpam-3527	87	54	-	-	PUNCT
ejpam-3527	87	55	ideal	ideal	NOUN
ejpam-3527	87	56	of	of	ADP
ejpam-3527	87	57	x.	x.	NOUN
ejpam-3527	87	58	define	define	VERB
ejpam-3527	87	59	the	the	DET
ejpam-3527	87	60	binary	binary	PROPN
ejpam-3527	87	61	relation	relation	NOUN
ejpam-3527	87	62	∼b	∼b	PROPN
ejpam-3527	87	63	on	on	ADP
ejpam-3527	87	64	x	x	PUNCT
ejpam-3527	87	65	as	as	SCONJ
ejpam-3527	87	66	follows	follow	VERB
ejpam-3527	87	67	:	:	PUNCT
ejpam-3527	87	68	for	for	ADP
ejpam-3527	87	69	all	all	DET
ejpam-3527	87	70	x	x	NOUN
ejpam-3527	87	71	,	,	PUNCT
ejpam-3527	87	72	y	y	PROPN
ejpam-3527	87	73	∈	∈	PROPN
ejpam-3527	87	74	x	x	X
ejpam-3527	87	75	,	,	PUNCT
ejpam-3527	87	76	x	x	PROPN
ejpam-3527	87	77	∼b	∼b	PROPN
ejpam-3527	87	78	y	y	PROPN
ejpam-3527	87	79	if	if	SCONJ
ejpam-3527	87	80	and	and	CCONJ
ejpam-3527	87	81	only	only	ADV
ejpam-3527	87	82	if	if	SCONJ
ejpam-3527	87	83	x	x	X
ejpam-3527	87	84	∗	∗	VERB
ejpam-3527	87	85	y	y	PROPN
ejpam-3527	87	86	∈	∈	PROPN
ejpam-3527	87	87	b	b	PROPN
ejpam-3527	87	88	and	and	CCONJ
ejpam-3527	87	89	y	y	PROPN
ejpam-3527	87	90	∗	∗	NOUN
ejpam-3527	87	91	x	x	PUNCT
ejpam-3527	87	92	∈	∈	PROPN
ejpam-3527	87	93	b.	b.	NOUN
ejpam-3527	87	94	an	an	DET
ejpam-3527	87	95	equivalence	equivalence	NOUN
ejpam-3527	87	96	relation	relation	NOUN
ejpam-3527	87	97	ρ	ρ	NOUN
ejpam-3527	87	98	on	on	ADP
ejpam-3527	87	99	x	x	AUX
ejpam-3527	87	100	is	be	AUX
ejpam-3527	87	101	called	call	VERB
ejpam-3527	87	102	a	a	DET
ejpam-3527	87	103	congruence	congruence	NOUN
ejpam-3527	87	104	if	if	SCONJ
ejpam-3527	87	105	for	for	ADP
ejpam-3527	87	106	any	any	DET
ejpam-3527	87	107	x	x	NOUN
ejpam-3527	87	108	,	,	PUNCT
ejpam-3527	87	109	y	y	PROPN
ejpam-3527	87	110	,	,	PUNCT
ejpam-3527	87	111	z	z	PROPN
ejpam-3527	87	112	∈	∈	PROPN
ejpam-3527	88	1	x	x	X
ejpam-3527	88	2	,	,	PUNCT
ejpam-3527	88	3	xρy	xρy	PROPN
ejpam-3527	88	4	implies	imply	VERB
ejpam-3527	88	5	(	(	PUNCT
ejpam-3527	88	6	x	x	SYM
ejpam-3527	88	7	∗	∗	PROPN
ejpam-3527	88	8	z)ρ(y	z)ρ(y	PROPN
ejpam-3527	88	9	∗	∗	PROPN
ejpam-3527	88	10	z	z	PROPN
ejpam-3527	88	11	)	)	PUNCT
ejpam-3527	88	12	and	and	CCONJ
ejpam-3527	88	13	(	(	PUNCT
ejpam-3527	88	14	z	z	NOUN
ejpam-3527	88	15	∗	∗	PROPN
ejpam-3527	88	16	x)ρ(z	x)ρ(z	PROPN
ejpam-3527	88	17	∗	∗	PROPN
ejpam-3527	88	18	y	y	PROPN
ejpam-3527	88	19	)	)	PUNCT
ejpam-3527	88	20	.	.	PUNCT
ejpam-3527	89	1	if	if	SCONJ
ejpam-3527	89	2	x	x	SYM
ejpam-3527	89	3	∈	∈	PROPN
ejpam-3527	89	4	x	x	NOUN
ejpam-3527	89	5	,	,	PUNCT
ejpam-3527	89	6	then	then	ADV
ejpam-3527	89	7	the	the	DET
ejpam-3527	89	8	ρ	ρ	NOUN
ejpam-3527	89	9	-	-	PUNCT
ejpam-3527	89	10	class	class	NOUN
ejpam-3527	89	11	of	of	ADP
ejpam-3527	89	12	x	x	SYM
ejpam-3527	89	13	is	be	AUX
ejpam-3527	89	14	[	[	PUNCT
ejpam-3527	89	15	x]ρ	x]ρ	ADV
ejpam-3527	89	16	defined	define	VERB
ejpam-3527	89	17	as	as	ADP
ejpam-3527	89	18	[	[	X
ejpam-3527	89	19	x]ρ	x]ρ	NOUN
ejpam-3527	89	20	=	=	SYM
ejpam-3527	89	21	{	{	PUNCT
ejpam-3527	89	22	y	y	PROPN
ejpam-3527	89	23	∈	∈	PROPN
ejpam-3527	89	24	x	x	X
ejpam-3527	89	25	:	:	PUNCT
ejpam-3527	89	26	yρx	yρx	NOUN
ejpam-3527	89	27	}	}	PUNCT
ejpam-3527	89	28	.	.	PUNCT
ejpam-3527	90	1	the	the	DET
ejpam-3527	90	2	set	set	NOUN
ejpam-3527	90	3	of	of	ADP
ejpam-3527	90	4	all	all	DET
ejpam-3527	90	5	ρ	ρ	NOUN
ejpam-3527	90	6	-	-	PUNCT
ejpam-3527	90	7	classes	class	NOUN
ejpam-3527	90	8	is	be	AUX
ejpam-3527	90	9	called	call	VERB
ejpam-3527	90	10	the	the	DET
ejpam-3527	90	11	quotient	quotient	NOUN
ejpam-3527	90	12	set	set	VERB
ejpam-3527	90	13	of	of	ADP
ejpam-3527	90	14	x	x	PUNCT
ejpam-3527	90	15	by	by	ADP
ejpam-3527	90	16	ρ	ρ	NUM
ejpam-3527	90	17	,	,	PUNCT
ejpam-3527	90	18	and	and	CCONJ
ejpam-3527	90	19	is	be	AUX
ejpam-3527	90	20	denoted	denote	VERB
ejpam-3527	90	21	by	by	ADP
ejpam-3527	90	22	x	x	X
ejpam-3527	90	23	/	/	SYM
ejpam-3527	90	24	ρ	ρ	PROPN
ejpam-3527	90	25	.	.	PUNCT
ejpam-3527	91	1	that	that	PRON
ejpam-3527	91	2	is	be	AUX
ejpam-3527	91	3	,	,	PUNCT
ejpam-3527	91	4	x	x	X
ejpam-3527	91	5	/	/	SYM
ejpam-3527	91	6	ρ	ρ	NOUN
ejpam-3527	91	7	=	=	SYM
ejpam-3527	91	8	{	{	PUNCT
ejpam-3527	92	1	[	[	X
ejpam-3527	92	2	x]ρ	x]ρ	NOUN
ejpam-3527	92	3	:	:	PUNCT
ejpam-3527	92	4	x	x	SYM
ejpam-3527	92	5	∈	∈	NOUN
ejpam-3527	92	6	x	x	X
ejpam-3527	92	7	}	}	PUNCT
ejpam-3527	92	8	.	.	PUNCT
ejpam-3527	93	1	theorem	theorem	NOUN
ejpam-3527	93	2	3	3	NUM
ejpam-3527	93	3	.	.	PUNCT
ejpam-3527	94	1	[	[	X
ejpam-3527	94	2	3	3	X
ejpam-3527	94	3	]	]	X
ejpam-3527	94	4	let	let	VERB
ejpam-3527	94	5	(	(	PUNCT
ejpam-3527	94	6	x	x	NOUN
ejpam-3527	94	7	;	;	PUNCT
ejpam-3527	94	8	∗	∗	NOUN
ejpam-3527	94	9	,	,	PUNCT
ejpam-3527	94	10	0	0	NUM
ejpam-3527	94	11	)	)	PUNCT
ejpam-3527	94	12	be	be	AUX
ejpam-3527	94	13	a	a	DET
ejpam-3527	94	14	up	up	NOUN
ejpam-3527	94	15	-	-	PUNCT
ejpam-3527	94	16	algebra	algebra	NOUN
ejpam-3527	94	17	and	and	CCONJ
ejpam-3527	94	18	b	b	NOUN
ejpam-3527	94	19	a	a	DET
ejpam-3527	94	20	up	up	ADJ
ejpam-3527	94	21	-	-	PUNCT
ejpam-3527	94	22	ideal	ideal	NOUN
ejpam-3527	94	23	of	of	ADP
ejpam-3527	94	24	x.	x.	NOUN
ejpam-3527	94	25	then	then	ADV
ejpam-3527	94	26	the	the	DET
ejpam-3527	94	27	following	follow	VERB
ejpam-3527	94	28	hold	hold	NOUN
ejpam-3527	94	29	:	:	PUNCT
ejpam-3527	94	30	(	(	PUNCT
ejpam-3527	94	31	i	i	NOUN
ejpam-3527	94	32	)	)	PUNCT
ejpam-3527	94	33	the	the	DET
ejpam-3527	94	34	∼b	∼b	PROPN
ejpam-3527	94	35	-	-	PUNCT
ejpam-3527	94	36	class	class	NOUN
ejpam-3527	94	37	[	[	X
ejpam-3527	94	38	0]∼b	0]∼b	X
ejpam-3527	94	39	is	be	AUX
ejpam-3527	94	40	a	a	DET
ejpam-3527	94	41	up	up	ADJ
ejpam-3527	94	42	-	-	PUNCT
ejpam-3527	94	43	ideal	ideal	NOUN
ejpam-3527	94	44	and	and	CCONJ
ejpam-3527	94	45	a	a	DET
ejpam-3527	94	46	up	up	NOUN
ejpam-3527	94	47	-	-	PUNCT
ejpam-3527	94	48	subalgebra	subalgebra	NOUN
ejpam-3527	94	49	of	of	ADP
ejpam-3527	94	50	x	x	PRON
ejpam-3527	94	51	,	,	PUNCT
ejpam-3527	94	52	(	(	PUNCT
ejpam-3527	94	53	ii	ii	NOUN
ejpam-3527	94	54	)	)	PUNCT
ejpam-3527	94	55	a	a	DET
ejpam-3527	94	56	∼b	∼b	PROPN
ejpam-3527	94	57	-	-	PUNCT
ejpam-3527	94	58	class	class	NOUN
ejpam-3527	95	1	[	[	X
ejpam-3527	95	2	x]∼b	x]∼b	NOUN
ejpam-3527	95	3	is	be	AUX
ejpam-3527	95	4	a	a	DET
ejpam-3527	95	5	up	up	ADJ
ejpam-3527	95	6	-	-	PUNCT
ejpam-3527	95	7	ideal	ideal	NOUN
ejpam-3527	95	8	of	of	ADP
ejpam-3527	95	9	x	x	SYM
ejpam-3527	95	10	if	if	SCONJ
ejpam-3527	95	11	and	and	CCONJ
ejpam-3527	95	12	only	only	ADV
ejpam-3527	95	13	if	if	SCONJ
ejpam-3527	95	14	x	x	PROPN
ejpam-3527	95	15	∈	∈	PROPN
ejpam-3527	95	16	b	b	PROPN
ejpam-3527	95	17	,	,	PUNCT
ejpam-3527	95	18	(	(	PUNCT
ejpam-3527	95	19	iii	iii	NOUN
ejpam-3527	95	20	)	)	PUNCT
ejpam-3527	95	21	a	a	DET
ejpam-3527	95	22	∼b	∼b	PROPN
ejpam-3527	95	23	-	-	PUNCT
ejpam-3527	95	24	class	class	NOUN
ejpam-3527	96	1	[	[	X
ejpam-3527	96	2	x]∼b	x]∼b	NOUN
ejpam-3527	96	3	is	be	AUX
ejpam-3527	96	4	a	a	DET
ejpam-3527	96	5	up	up	ADJ
ejpam-3527	96	6	-	-	PUNCT
ejpam-3527	96	7	subalgebra	subalgebra	NOUN
ejpam-3527	96	8	of	of	ADP
ejpam-3527	96	9	x	x	PRON
ejpam-3527	96	10	if	if	SCONJ
ejpam-3527	96	11	and	and	CCONJ
ejpam-3527	96	12	only	only	ADV
ejpam-3527	96	13	if	if	SCONJ
ejpam-3527	96	14	x	x	PROPN
ejpam-3527	96	15	∈	∈	PROPN
ejpam-3527	96	16	b	b	PROPN
ejpam-3527	96	17	,	,	PUNCT
ejpam-3527	96	18	and	and	CCONJ
ejpam-3527	96	19	(	(	PUNCT
ejpam-3527	96	20	iv	iv	X
ejpam-3527	96	21	)	)	PUNCT
ejpam-3527	96	22	(	(	PUNCT
ejpam-3527	96	23	x/	x/	PROPN
ejpam-3527	96	24	∼b	∼b	PROPN
ejpam-3527	96	25	;	;	PUNCT
ejpam-3527	96	26	∗	∗	NOUN
ejpam-3527	96	27	,	,	PUNCT
ejpam-3527	96	28	[	[	X
ejpam-3527	96	29	0]∼b	0]∼b	X
ejpam-3527	96	30	)	)	PUNCT
ejpam-3527	96	31	is	be	AUX
ejpam-3527	96	32	a	a	DET
ejpam-3527	96	33	up	up	NOUN
ejpam-3527	96	34	-	-	PUNCT
ejpam-3527	96	35	algebra	algebra	NOUN
ejpam-3527	96	36	under	under	ADP
ejpam-3527	96	37	the	the	DET
ejpam-3527	96	38	operation	operation	NOUN
ejpam-3527	96	39	∗	∗	NOUN
ejpam-3527	96	40	defined	define	VERB
ejpam-3527	96	41	by	by	ADP
ejpam-3527	96	42	[	[	X
ejpam-3527	96	43	x]∼b∗[y]∼b	x]∼b∗[y]∼b	NOUN
ejpam-3527	96	44	=	=	PUNCT
ejpam-3527	97	1	[	[	X
ejpam-3527	97	2	x∗	x∗	X
ejpam-3527	97	3	y]∼b	y]∼b	VERB
ejpam-3527	97	4	for	for	ADP
ejpam-3527	97	5	all	all	DET
ejpam-3527	97	6	x	x	NOUN
ejpam-3527	97	7	,	,	PUNCT
ejpam-3527	97	8	y	y	PROPN
ejpam-3527	97	9	∈	∈	PROPN
ejpam-3527	97	10	x	x	PROPN
ejpam-3527	97	11	,	,	PUNCT
ejpam-3527	97	12	called	call	VERB
ejpam-3527	97	13	the	the	DET
ejpam-3527	97	14	quotient	quotient	NOUN
ejpam-3527	97	15	up	up	ADP
ejpam-3527	97	16	-	-	PUNCT
ejpam-3527	97	17	algebra	algebra	NOUN
ejpam-3527	97	18	of	of	ADP
ejpam-3527	97	19	x	x	PUNCT
ejpam-3527	97	20	induced	induce	VERB
ejpam-3527	97	21	by	by	ADP
ejpam-3527	97	22	the	the	DET
ejpam-3527	97	23	congruence	congruence	PROPN
ejpam-3527	97	24	∼b	∼b	PROPN
ejpam-3527	97	25	.	.	PROPN
ejpam-3527	97	26	definition	definition	NOUN
ejpam-3527	97	27	6	6	NUM
ejpam-3527	97	28	.	.	PUNCT
ejpam-3527	98	1	[	[	X
ejpam-3527	98	2	10	10	NUM
ejpam-3527	98	3	]	]	X
ejpam-3527	98	4	a	a	DET
ejpam-3527	98	5	ku	ku	PROPN
ejpam-3527	98	6	-	-	PUNCT
ejpam-3527	98	7	semigroup	semigroup	PROPN
ejpam-3527	98	8	is	be	AUX
ejpam-3527	98	9	a	a	DET
ejpam-3527	98	10	nonempty	nonempty	ADV
ejpam-3527	98	11	set	set	VERB
ejpam-3527	98	12	x	x	PUNCT
ejpam-3527	98	13	together	together	ADV
ejpam-3527	98	14	with	with	ADP
ejpam-3527	98	15	two	two	NUM
ejpam-3527	98	16	binary	binary	ADJ
ejpam-3527	98	17	operations	operation	NOUN
ejpam-3527	98	18	∗	∗	NOUN
ejpam-3527	98	19	and	and	CCONJ
ejpam-3527	98	20	·	·	PUNCT
ejpam-3527	98	21	and	and	CCONJ
ejpam-3527	98	22	a	a	DET
ejpam-3527	98	23	constant	constant	ADJ
ejpam-3527	98	24	0	0	NUM
ejpam-3527	98	25	satisfying	satisfy	VERB
ejpam-3527	98	26	the	the	DET
ejpam-3527	98	27	following	following	NOUN
ejpam-3527	98	28	:	:	PUNCT
ejpam-3527	98	29	(	(	PUNCT
ejpam-3527	98	30	kus1	kus1	PROPN
ejpam-3527	98	31	)	)	PUNCT
ejpam-3527	98	32	(	(	PUNCT
ejpam-3527	98	33	x	x	X
ejpam-3527	98	34	;	;	PUNCT
ejpam-3527	98	35	∗	∗	NOUN
ejpam-3527	98	36	,	,	PUNCT
ejpam-3527	98	37	0	0	NUM
ejpam-3527	98	38	)	)	PUNCT
ejpam-3527	98	39	is	be	AUX
ejpam-3527	98	40	a	a	DET
ejpam-3527	98	41	ku	ku	NOUN
ejpam-3527	98	42	-	-	PUNCT
ejpam-3527	98	43	algebra	algebra	PROPN
ejpam-3527	98	44	;	;	PUNCT
ejpam-3527	98	45	(	(	PUNCT
ejpam-3527	98	46	kus2	kus2	PROPN
ejpam-3527	98	47	)	)	PUNCT
ejpam-3527	98	48	(	(	PUNCT
ejpam-3527	98	49	x	x	X
ejpam-3527	98	50	,	,	PUNCT
ejpam-3527	98	51	·	·	PUNCT
ejpam-3527	98	52	)	)	PUNCT
ejpam-3527	98	53	is	be	AUX
ejpam-3527	98	54	a	a	DET
ejpam-3527	98	55	semigroup	semigroup	NOUN
ejpam-3527	98	56	;	;	PUNCT
ejpam-3527	98	57	and	and	CCONJ
ejpam-3527	98	58	(	(	PUNCT
ejpam-3527	98	59	kus3	kus3	PROPN
ejpam-3527	98	60	)	)	PUNCT
ejpam-3527	98	61	the	the	DET
ejpam-3527	98	62	operation	operation	NOUN
ejpam-3527	98	63	·	·	PUNCT
ejpam-3527	98	64	is	be	AUX
ejpam-3527	98	65	left	leave	VERB
ejpam-3527	98	66	and	and	CCONJ
ejpam-3527	98	67	right	right	ADV
ejpam-3527	98	68	distributive	distributive	ADJ
ejpam-3527	98	69	over	over	ADP
ejpam-3527	98	70	the	the	DET
ejpam-3527	98	71	operation	operation	NOUN
ejpam-3527	98	72	∗	∗	NOUN
ejpam-3527	98	73	,	,	PUNCT
ejpam-3527	98	74	that	that	ADV
ejpam-3527	98	75	is	is	ADV
ejpam-3527	98	76	,	,	PUNCT
ejpam-3527	98	77	x	x	X
ejpam-3527	98	78	·	·	PUNCT
ejpam-3527	98	79	(	(	PUNCT
ejpam-3527	98	80	y	y	PROPN
ejpam-3527	98	81	∗	∗	PROPN
ejpam-3527	98	82	z	z	NOUN
ejpam-3527	98	83	)	)	PUNCT
ejpam-3527	98	84	=	=	SYM
ejpam-3527	98	85	(	(	PUNCT
ejpam-3527	98	86	x	x	X
ejpam-3527	98	87	·	·	PUNCT
ejpam-3527	98	88	y	y	X
ejpam-3527	98	89	)	)	PUNCT
ejpam-3527	98	90	∗	∗	NOUN
ejpam-3527	98	91	(	(	PUNCT
ejpam-3527	98	92	x	x	SYM
ejpam-3527	98	93	·	·	PUNCT
ejpam-3527	98	94	z	z	X
ejpam-3527	98	95	)	)	PUNCT
ejpam-3527	98	96	and	and	CCONJ
ejpam-3527	98	97	(	(	PUNCT
ejpam-3527	98	98	x	x	PROPN
ejpam-3527	98	99	∗	∗	PROPN
ejpam-3527	98	100	y	y	PROPN
ejpam-3527	98	101	)	)	PUNCT
ejpam-3527	98	102	·	·	PUNCT
ejpam-3527	99	1	z	z	X
ejpam-3527	99	2	=	=	SYM
ejpam-3527	99	3	(	(	PUNCT
ejpam-3527	99	4	x	x	SYM
ejpam-3527	99	5	·	·	PUNCT
ejpam-3527	99	6	z	z	X
ejpam-3527	99	7	)	)	PUNCT
ejpam-3527	99	8	∗	∗	NOUN
ejpam-3527	99	9	(	(	PUNCT
ejpam-3527	99	10	y	y	PROPN
ejpam-3527	99	11	·	·	PUNCT
ejpam-3527	99	12	z	z	X
ejpam-3527	99	13	)	)	PUNCT
ejpam-3527	99	14	.	.	PUNCT
ejpam-3527	100	1	example	example	NOUN
ejpam-3527	101	1	3	3	NUM
ejpam-3527	101	2	.	.	PUNCT
ejpam-3527	102	1	[	[	X
ejpam-3527	102	2	10	10	NUM
ejpam-3527	102	3	]	]	PUNCT
ejpam-3527	102	4	let	let	VERB
ejpam-3527	102	5	x	x	PUNCT
ejpam-3527	102	6	=	=	PUNCT
ejpam-3527	102	7	{	{	PUNCT
ejpam-3527	102	8	0	0	NUM
ejpam-3527	102	9	,	,	PUNCT
ejpam-3527	102	10	a	a	PRON
ejpam-3527	102	11	,	,	PUNCT
ejpam-3527	102	12	b	b	NOUN
ejpam-3527	102	13	,	,	PUNCT
ejpam-3527	102	14	c	c	AUX
ejpam-3527	102	15	}	}	PUNCT
ejpam-3527	102	16	be	be	AUX
ejpam-3527	102	17	a	a	DET
ejpam-3527	102	18	set	set	NOUN
ejpam-3527	102	19	with	with	ADP
ejpam-3527	102	20	the	the	DET
ejpam-3527	102	21	binary	binary	ADJ
ejpam-3527	102	22	operations	operation	NOUN
ejpam-3527	102	23	∗	∗	NOUN
ejpam-3527	102	24	and	and	CCONJ
ejpam-3527	102	25	·	·	PUNCT
ejpam-3527	102	26	defined	define	VERB
ejpam-3527	102	27	by	by	ADP
ejpam-3527	102	28	the	the	DET
ejpam-3527	102	29	following	following	ADJ
ejpam-3527	102	30	cayley	cayley	ADJ
ejpam-3527	102	31	tables	table	NOUN
ejpam-3527	102	32	:	:	PUNCT
ejpam-3527	102	33	∗	∗	NOUN
ejpam-3527	102	34	0	0	NUM
ejpam-3527	103	1	a	a	DET
ejpam-3527	103	2	b	b	NOUN
ejpam-3527	103	3	c	c	NOUN
ejpam-3527	103	4	0	0	NUM
ejpam-3527	103	5	0	0	NUM
ejpam-3527	103	6	a	a	DET
ejpam-3527	103	7	b	b	NOUN
ejpam-3527	103	8	c	c	NOUN
ejpam-3527	103	9	a	a	DET
ejpam-3527	103	10	0	0	NUM
ejpam-3527	103	11	0	0	NUM
ejpam-3527	103	12	b	b	PROPN
ejpam-3527	103	13	c	c	NOUN
ejpam-3527	103	14	b	b	PROPN
ejpam-3527	103	15	0	0	NUM
ejpam-3527	103	16	a	a	DET
ejpam-3527	103	17	0	0	NUM
ejpam-3527	103	18	c	c	NOUN
ejpam-3527	103	19	c	c	NOUN
ejpam-3527	103	20	0	0	NUM
ejpam-3527	103	21	0	0	NUM
ejpam-3527	103	22	0	0	NUM
ejpam-3527	103	23	0	0	NUM
ejpam-3527	103	24	·	·	PUNCT
ejpam-3527	103	25	0	0	PUNCT
ejpam-3527	104	1	a	a	DET
ejpam-3527	104	2	b	b	X
ejpam-3527	104	3	c	c	NOUN
ejpam-3527	104	4	0	0	NUM
ejpam-3527	104	5	0	0	NUM
ejpam-3527	104	6	0	0	NUM
ejpam-3527	104	7	0	0	NUM
ejpam-3527	104	8	0	0	NUM
ejpam-3527	104	9	a	a	DET
ejpam-3527	104	10	0	0	NUM
ejpam-3527	104	11	0	0	NUM
ejpam-3527	104	12	0	0	NUM
ejpam-3527	104	13	0	0	NUM
ejpam-3527	104	14	b	b	X
ejpam-3527	104	15	0	0	NUM
ejpam-3527	104	16	0	0	NUM
ejpam-3527	104	17	0	0	NUM
ejpam-3527	104	18	b	b	X
ejpam-3527	104	19	c	c	NOUN
ejpam-3527	104	20	0	0	NUM
ejpam-3527	104	21	0	0	NUM
ejpam-3527	104	22	b	b	PROPN
ejpam-3527	104	23	c	c	NOUN
ejpam-3527	104	24	d.gomisong	d.gomisong	PROPN
ejpam-3527	104	25	,	,	PUNCT
ejpam-3527	104	26	r.	r.	PROPN
ejpam-3527	104	27	isla	isla	PROPN
ejpam-3527	104	28	/	/	SYM
ejpam-3527	104	29	eur	eur	PROPN
ejpam-3527	104	30	.	.	PUNCT
ejpam-3527	105	1	j.	j.	PROPN
ejpam-3527	105	2	pure	pure	PROPN
ejpam-3527	105	3	appl	appl	PROPN
ejpam-3527	105	4	.	.	PROPN
ejpam-3527	105	5	math	math	PROPN
ejpam-3527	105	6	,	,	PUNCT
ejpam-3527	105	7	12	12	NUM
ejpam-3527	105	8	(	(	PUNCT
ejpam-3527	105	9	4	4	NUM
ejpam-3527	105	10	)	)	PUNCT
ejpam-3527	105	11	(	(	PUNCT
ejpam-3527	105	12	2019	2019	NUM
ejpam-3527	105	13	)	)	PUNCT
ejpam-3527	105	14	,	,	PUNCT
ejpam-3527	105	15	1483	1483	NUM
ejpam-3527	105	16	-	-	SYM
ejpam-3527	105	17	1496	1496	NUM
ejpam-3527	105	18	1487	1487	NUM
ejpam-3527	105	19	then	then	ADV
ejpam-3527	105	20	,	,	PUNCT
ejpam-3527	105	21	(	(	PUNCT
ejpam-3527	105	22	x	x	X
ejpam-3527	105	23	;	;	PUNCT
ejpam-3527	105	24	∗	∗	NOUN
ejpam-3527	105	25	,	,	PUNCT
ejpam-3527	105	26	·	·	PUNCT
ejpam-3527	105	27	,	,	PUNCT
ejpam-3527	105	28	0	0	NUM
ejpam-3527	105	29	)	)	PUNCT
ejpam-3527	105	30	is	be	AUX
ejpam-3527	105	31	a	a	DET
ejpam-3527	105	32	ku	ku	PROPN
ejpam-3527	105	33	-	-	PUNCT
ejpam-3527	105	34	semigroup	semigroup	PROPN
ejpam-3527	105	35	.	.	PUNCT
ejpam-3527	106	1	definition	definition	NOUN
ejpam-3527	106	2	7	7	NUM
ejpam-3527	106	3	.	.	PUNCT
ejpam-3527	107	1	[	[	X
ejpam-3527	107	2	4	4	X
ejpam-3527	107	3	]	]	X
ejpam-3527	107	4	a	a	DET
ejpam-3527	107	5	fully	fully	ADV
ejpam-3527	107	6	up	up	ADJ
ejpam-3527	107	7	-	-	PUNCT
ejpam-3527	107	8	semigroup	semigroup	NOUN
ejpam-3527	107	9	(	(	PUNCT
ejpam-3527	107	10	or	or	CCONJ
ejpam-3527	107	11	f	f	PROPN
ejpam-3527	107	12	-up	-up	NOUN
ejpam-3527	107	13	-	-	PUNCT
ejpam-3527	107	14	semigroup	semigroup	NOUN
ejpam-3527	107	15	)	)	PUNCT
ejpam-3527	107	16	is	be	AUX
ejpam-3527	107	17	a	a	DET
ejpam-3527	107	18	nonempty	nonempty	ADV
ejpam-3527	107	19	set	set	VERB
ejpam-3527	107	20	x	x	PUNCT
ejpam-3527	107	21	together	together	ADV
ejpam-3527	107	22	with	with	ADP
ejpam-3527	107	23	two	two	NUM
ejpam-3527	107	24	binary	binary	ADJ
ejpam-3527	107	25	operations	operation	NOUN
ejpam-3527	107	26	∗	∗	NOUN
ejpam-3527	107	27	and	and	CCONJ
ejpam-3527	107	28	·	·	PUNCT
ejpam-3527	107	29	and	and	CCONJ
ejpam-3527	107	30	a	a	DET
ejpam-3527	107	31	constant	constant	ADJ
ejpam-3527	107	32	0	0	NUM
ejpam-3527	107	33	satisfying	satisfy	VERB
ejpam-3527	107	34	the	the	DET
ejpam-3527	107	35	following	following	NOUN
ejpam-3527	107	36	:	:	PUNCT
ejpam-3527	107	37	(	(	PUNCT
ejpam-3527	107	38	fup1	fup1	PROPN
ejpam-3527	107	39	)	)	PUNCT
ejpam-3527	107	40	(	(	PUNCT
ejpam-3527	107	41	x	x	X
ejpam-3527	107	42	;	;	PUNCT
ejpam-3527	107	43	∗	∗	NOUN
ejpam-3527	107	44	,	,	PUNCT
ejpam-3527	107	45	0	0	NUM
ejpam-3527	107	46	)	)	PUNCT
ejpam-3527	107	47	is	be	AUX
ejpam-3527	107	48	a	a	DET
ejpam-3527	107	49	up	up	NOUN
ejpam-3527	107	50	-	-	PUNCT
ejpam-3527	107	51	algebra	algebra	NOUN
ejpam-3527	107	52	;	;	PUNCT
ejpam-3527	107	53	(	(	PUNCT
ejpam-3527	107	54	fup2	fup2	ADJ
ejpam-3527	107	55	)	)	PUNCT
ejpam-3527	107	56	(	(	PUNCT
ejpam-3527	107	57	x	x	X
ejpam-3527	107	58	,	,	PUNCT
ejpam-3527	107	59	·	·	PUNCT
ejpam-3527	107	60	)	)	PUNCT
ejpam-3527	107	61	is	be	AUX
ejpam-3527	107	62	a	a	DET
ejpam-3527	107	63	semigroup	semigroup	NOUN
ejpam-3527	107	64	;	;	PUNCT
ejpam-3527	107	65	and	and	CCONJ
ejpam-3527	107	66	(	(	PUNCT
ejpam-3527	107	67	fup3	fup3	PROPN
ejpam-3527	107	68	)	)	PUNCT
ejpam-3527	107	69	the	the	DET
ejpam-3527	107	70	operation	operation	NOUN
ejpam-3527	107	71	·	·	PUNCT
ejpam-3527	107	72	is	be	AUX
ejpam-3527	107	73	left	leave	VERB
ejpam-3527	107	74	and	and	CCONJ
ejpam-3527	107	75	right	right	ADV
ejpam-3527	107	76	distributive	distributive	ADJ
ejpam-3527	107	77	over	over	ADP
ejpam-3527	107	78	the	the	DET
ejpam-3527	107	79	operation	operation	NOUN
ejpam-3527	107	80	∗.	∗.	PROPN
ejpam-3527	107	81	a.	a.	NOUN
ejpam-3527	107	82	iampan	iampan	NOUN
ejpam-3527	108	1	[	[	X
ejpam-3527	108	2	4	4	X
ejpam-3527	108	3	]	]	PUNCT
ejpam-3527	108	4	analogously	analogously	ADV
ejpam-3527	108	5	introduced	introduce	VERB
ejpam-3527	108	6	a	a	DET
ejpam-3527	108	7	left	left	NOUN
ejpam-3527	108	8	[	[	X
ejpam-3527	108	9	resp	resp	NOUN
ejpam-3527	108	10	.	.	PUNCT
ejpam-3527	109	1	,	,	PUNCT
ejpam-3527	109	2	right	right	ADV
ejpam-3527	109	3	]	]	PUNCT
ejpam-3527	109	4	up	up	ADP
ejpam-3527	109	5	-	-	PUNCT
ejpam-3527	109	6	semigroup	semigroup	NOUN
ejpam-3527	109	7	as	as	ADP
ejpam-3527	109	8	a	a	DET
ejpam-3527	109	9	nonempty	nonempty	ADV
ejpam-3527	109	10	set	set	VERB
ejpam-3527	109	11	x	x	PUNCT
ejpam-3527	109	12	together	together	ADV
ejpam-3527	109	13	with	with	ADP
ejpam-3527	109	14	two	two	NUM
ejpam-3527	109	15	binary	binary	ADJ
ejpam-3527	109	16	operations	operation	NOUN
ejpam-3527	109	17	∗	∗	NOUN
ejpam-3527	109	18	and	and	CCONJ
ejpam-3527	109	19	·	·	PUNCT
ejpam-3527	109	20	and	and	CCONJ
ejpam-3527	109	21	a	a	DET
ejpam-3527	109	22	constant	constant	ADJ
ejpam-3527	109	23	0	0	NUM
ejpam-3527	109	24	satisfying	satisfy	VERB
ejpam-3527	109	25	(	(	PUNCT
ejpam-3527	109	26	fup1	fup1	PROPN
ejpam-3527	109	27	)	)	PUNCT
ejpam-3527	109	28	,	,	PUNCT
ejpam-3527	109	29	(	(	PUNCT
ejpam-3527	109	30	fup2	fup2	ADJ
ejpam-3527	109	31	)	)	PUNCT
ejpam-3527	109	32	,	,	PUNCT
ejpam-3527	109	33	and	and	CCONJ
ejpam-3527	109	34	the	the	DET
ejpam-3527	109	35	operation	operation	NOUN
ejpam-3527	109	36	·	·	PUNCT
ejpam-3527	109	37	is	be	AUX
ejpam-3527	109	38	left	leave	VERB
ejpam-3527	110	1	[	[	X
ejpam-3527	110	2	resp	resp	NOUN
ejpam-3527	110	3	.	.	PUNCT
ejpam-3527	111	1	right	right	ADJ
ejpam-3527	111	2	]	]	PUNCT
ejpam-3527	112	1	distributive	distributive	ADJ
ejpam-3527	112	2	over	over	ADP
ejpam-3527	112	3	the	the	DET
ejpam-3527	112	4	operation	operation	NOUN
ejpam-3527	112	5	∗.	∗.	PROPN
ejpam-3527	112	6	thus	thus	ADV
ejpam-3527	112	7	,	,	PUNCT
ejpam-3527	112	8	an	an	DET
ejpam-3527	112	9	f	f	PROPN
ejpam-3527	112	10	-up	-up	NOUN
ejpam-3527	112	11	-	-	PUNCT
ejpam-3527	112	12	semigroup	semigroup	PROPN
ejpam-3527	112	13	is	be	AUX
ejpam-3527	112	14	both	both	PRON
ejpam-3527	112	15	a	a	DET
ejpam-3527	112	16	left	left	NOUN
ejpam-3527	112	17	and	and	CCONJ
ejpam-3527	112	18	a	a	DET
ejpam-3527	112	19	right	right	ADJ
ejpam-3527	112	20	up	up	ADJ
ejpam-3527	112	21	-	-	PUNCT
ejpam-3527	112	22	semigroup	semigroup	NOUN
ejpam-3527	112	23	.	.	PUNCT
ejpam-3527	112	24	example	example	NOUN
ejpam-3527	113	1	4	4	NUM
ejpam-3527	113	2	.	.	PUNCT
ejpam-3527	114	1	[	[	X
ejpam-3527	114	2	4	4	X
ejpam-3527	114	3	]	]	PUNCT
ejpam-3527	114	4	let	let	VERB
ejpam-3527	114	5	x	x	PUNCT
ejpam-3527	114	6	=	=	PUNCT
ejpam-3527	114	7	{	{	PUNCT
ejpam-3527	114	8	0	0	NUM
ejpam-3527	114	9	,	,	PUNCT
ejpam-3527	114	10	a	a	DET
ejpam-3527	114	11	,	,	PUNCT
ejpam-3527	114	12	b	b	NOUN
ejpam-3527	114	13	,	,	PUNCT
ejpam-3527	114	14	c	c	AUX
ejpam-3527	114	15	}	}	PUNCT
ejpam-3527	114	16	be	be	AUX
ejpam-3527	114	17	a	a	DET
ejpam-3527	114	18	set	set	NOUN
ejpam-3527	114	19	with	with	ADP
ejpam-3527	114	20	the	the	DET
ejpam-3527	114	21	binary	binary	ADJ
ejpam-3527	114	22	operations	operation	NOUN
ejpam-3527	114	23	∗	∗	NOUN
ejpam-3527	114	24	and	and	CCONJ
ejpam-3527	114	25	·	·	PUNCT
ejpam-3527	114	26	defined	define	VERB
ejpam-3527	114	27	by	by	ADP
ejpam-3527	114	28	the	the	DET
ejpam-3527	114	29	following	following	ADJ
ejpam-3527	114	30	cayley	cayley	ADJ
ejpam-3527	114	31	tables	table	NOUN
ejpam-3527	114	32	:	:	PUNCT
ejpam-3527	114	33	∗	∗	NOUN
ejpam-3527	114	34	0	0	NUM
ejpam-3527	115	1	a	a	DET
ejpam-3527	115	2	b	b	NOUN
ejpam-3527	115	3	c	c	NOUN
ejpam-3527	115	4	0	0	NUM
ejpam-3527	115	5	0	0	NUM
ejpam-3527	115	6	a	a	DET
ejpam-3527	115	7	b	b	NOUN
ejpam-3527	115	8	c	c	NOUN
ejpam-3527	115	9	a	a	DET
ejpam-3527	115	10	0	0	NUM
ejpam-3527	115	11	0	0	NUM
ejpam-3527	115	12	b	b	PROPN
ejpam-3527	115	13	c	c	NOUN
ejpam-3527	115	14	b	b	PROPN
ejpam-3527	115	15	0	0	NUM
ejpam-3527	115	16	a	a	DET
ejpam-3527	115	17	0	0	NUM
ejpam-3527	115	18	c	c	NOUN
ejpam-3527	115	19	c	c	NOUN
ejpam-3527	115	20	0	0	PUNCT
ejpam-3527	116	1	a	a	DET
ejpam-3527	116	2	b	b	PROPN
ejpam-3527	116	3	0	0	NUM
ejpam-3527	116	4	·	·	SYM
ejpam-3527	116	5	0	0	PUNCT
ejpam-3527	117	1	a	a	DET
ejpam-3527	117	2	b	b	X
ejpam-3527	117	3	c	c	NOUN
ejpam-3527	117	4	0	0	NUM
ejpam-3527	117	5	0	0	NUM
ejpam-3527	117	6	0	0	NUM
ejpam-3527	117	7	0	0	NUM
ejpam-3527	117	8	0	0	NUM
ejpam-3527	117	9	a	a	DET
ejpam-3527	117	10	0	0	NUM
ejpam-3527	117	11	0	0	NUM
ejpam-3527	117	12	0	0	NUM
ejpam-3527	117	13	0	0	NUM
ejpam-3527	117	14	b	b	X
ejpam-3527	117	15	0	0	NUM
ejpam-3527	117	16	0	0	NUM
ejpam-3527	117	17	0	0	NUM
ejpam-3527	117	18	a	a	DET
ejpam-3527	117	19	c	c	NOUN
ejpam-3527	117	20	0	0	NUM
ejpam-3527	117	21	0	0	NUM
ejpam-3527	117	22	a	a	DET
ejpam-3527	117	23	0	0	NUM
ejpam-3527	117	24	then	then	ADV
ejpam-3527	117	25	,	,	PUNCT
ejpam-3527	117	26	(	(	PUNCT
ejpam-3527	117	27	x	x	X
ejpam-3527	117	28	;	;	PUNCT
ejpam-3527	117	29	∗	∗	NOUN
ejpam-3527	117	30	,	,	PUNCT
ejpam-3527	117	31	·	·	PUNCT
ejpam-3527	117	32	,	,	PUNCT
ejpam-3527	117	33	0	0	NUM
ejpam-3527	117	34	)	)	PUNCT
ejpam-3527	117	35	is	be	AUX
ejpam-3527	117	36	an	an	DET
ejpam-3527	117	37	f	f	PROPN
ejpam-3527	117	38	-up	-up	NOUN
ejpam-3527	117	39	-	-	PUNCT
ejpam-3527	117	40	semigroup	semigroup	NOUN
ejpam-3527	117	41	.	.	PUNCT
ejpam-3527	117	42	example	example	NOUN
ejpam-3527	118	1	5	5	NUM
ejpam-3527	118	2	.	.	PUNCT
ejpam-3527	119	1	let	let	VERB
ejpam-3527	119	2	x	x	PUNCT
ejpam-3527	119	3	=	=	PUNCT
ejpam-3527	119	4	{	{	PUNCT
ejpam-3527	119	5	0	0	NUM
ejpam-3527	119	6	,	,	PUNCT
ejpam-3527	119	7	a	a	DET
ejpam-3527	119	8	,	,	PUNCT
ejpam-3527	119	9	b	b	NOUN
ejpam-3527	119	10	,	,	PUNCT
ejpam-3527	119	11	c	c	AUX
ejpam-3527	119	12	}	}	PUNCT
ejpam-3527	119	13	be	be	AUX
ejpam-3527	119	14	a	a	DET
ejpam-3527	119	15	set	set	NOUN
ejpam-3527	119	16	with	with	ADP
ejpam-3527	119	17	the	the	DET
ejpam-3527	119	18	binary	binary	ADJ
ejpam-3527	119	19	operations	operation	NOUN
ejpam-3527	119	20	∗	∗	NOUN
ejpam-3527	119	21	and	and	CCONJ
ejpam-3527	119	22	·	·	PUNCT
ejpam-3527	119	23	defined	define	VERB
ejpam-3527	119	24	by	by	ADP
ejpam-3527	119	25	the	the	DET
ejpam-3527	119	26	following	following	ADJ
ejpam-3527	119	27	cayley	cayley	ADJ
ejpam-3527	119	28	tables	table	NOUN
ejpam-3527	119	29	:	:	PUNCT
ejpam-3527	119	30	∗	∗	NOUN
ejpam-3527	119	31	0	0	NUM
ejpam-3527	120	1	a	a	DET
ejpam-3527	120	2	b	b	NOUN
ejpam-3527	120	3	c	c	NOUN
ejpam-3527	120	4	0	0	NUM
ejpam-3527	120	5	0	0	NUM
ejpam-3527	120	6	a	a	DET
ejpam-3527	120	7	b	b	NOUN
ejpam-3527	120	8	c	c	NOUN
ejpam-3527	120	9	a	a	DET
ejpam-3527	120	10	0	0	NUM
ejpam-3527	120	11	0	0	NUM
ejpam-3527	120	12	b	b	PROPN
ejpam-3527	120	13	c	c	NOUN
ejpam-3527	120	14	b	b	PROPN
ejpam-3527	120	15	0	0	NUM
ejpam-3527	120	16	a	a	DET
ejpam-3527	120	17	0	0	NUM
ejpam-3527	120	18	c	c	NOUN
ejpam-3527	120	19	c	c	NOUN
ejpam-3527	120	20	0	0	NUM
ejpam-3527	120	21	0	0	NUM
ejpam-3527	120	22	0	0	NUM
ejpam-3527	120	23	0	0	NUM
ejpam-3527	120	24	·	·	PUNCT
ejpam-3527	120	25	0	0	PUNCT
ejpam-3527	121	1	a	a	DET
ejpam-3527	121	2	b	b	X
ejpam-3527	121	3	c	c	NOUN
ejpam-3527	121	4	0	0	NUM
ejpam-3527	121	5	0	0	NUM
ejpam-3527	121	6	0	0	NUM
ejpam-3527	121	7	0	0	NUM
ejpam-3527	121	8	0	0	NUM
ejpam-3527	121	9	a	a	DET
ejpam-3527	121	10	0	0	NUM
ejpam-3527	121	11	0	0	NUM
ejpam-3527	121	12	0	0	NUM
ejpam-3527	121	13	0	0	NUM
ejpam-3527	121	14	b	b	X
ejpam-3527	121	15	0	0	NUM
ejpam-3527	121	16	0	0	NUM
ejpam-3527	121	17	0	0	NUM
ejpam-3527	121	18	0	0	NUM
ejpam-3527	122	1	c	c	NOUN
ejpam-3527	122	2	0	0	NUM
ejpam-3527	123	1	a	a	DET
ejpam-3527	123	2	b	b	X
ejpam-3527	123	3	c	c	NOUN
ejpam-3527	123	4	then	then	ADV
ejpam-3527	123	5	,	,	PUNCT
ejpam-3527	123	6	routine	routine	ADJ
ejpam-3527	123	7	calculations	calculation	NOUN
ejpam-3527	123	8	show	show	VERB
ejpam-3527	123	9	that	that	SCONJ
ejpam-3527	123	10	(	(	PUNCT
ejpam-3527	123	11	x	x	X
ejpam-3527	123	12	;	;	PUNCT
ejpam-3527	123	13	∗	∗	NOUN
ejpam-3527	123	14	,	,	PUNCT
ejpam-3527	123	15	·	·	PUNCT
ejpam-3527	123	16	,	,	PUNCT
ejpam-3527	123	17	0	0	NUM
ejpam-3527	123	18	)	)	PUNCT
ejpam-3527	123	19	is	be	AUX
ejpam-3527	123	20	an	an	DET
ejpam-3527	123	21	f	f	PROPN
ejpam-3527	123	22	-up	-up	NOUN
ejpam-3527	123	23	-	-	PUNCT
ejpam-3527	123	24	semigroup	semigroup	NOUN
ejpam-3527	123	25	.	.	PUNCT
ejpam-3527	123	26	example	example	NOUN
ejpam-3527	124	1	6	6	NUM
ejpam-3527	124	2	.	.	PUNCT
ejpam-3527	125	1	let	let	VERB
ejpam-3527	125	2	x	x	PUNCT
ejpam-3527	125	3	=	=	PUNCT
ejpam-3527	125	4	{	{	PUNCT
ejpam-3527	125	5	0	0	NUM
ejpam-3527	125	6	,	,	PUNCT
ejpam-3527	125	7	a	a	DET
ejpam-3527	125	8	,	,	PUNCT
ejpam-3527	125	9	b	b	NOUN
ejpam-3527	125	10	,	,	PUNCT
ejpam-3527	125	11	c	c	NOUN
ejpam-3527	125	12	,	,	PUNCT
ejpam-3527	125	13	d	d	AUX
ejpam-3527	125	14	}	}	PUNCT
ejpam-3527	125	15	be	be	AUX
ejpam-3527	125	16	a	a	DET
ejpam-3527	125	17	set	set	NOUN
ejpam-3527	125	18	with	with	ADP
ejpam-3527	125	19	the	the	DET
ejpam-3527	125	20	binary	binary	ADJ
ejpam-3527	125	21	operations	operation	NOUN
ejpam-3527	125	22	∗	∗	NOUN
ejpam-3527	125	23	and	and	CCONJ
ejpam-3527	125	24	·	·	PUNCT
ejpam-3527	125	25	defined	define	VERB
ejpam-3527	125	26	by	by	ADP
ejpam-3527	125	27	the	the	DET
ejpam-3527	125	28	following	following	ADJ
ejpam-3527	125	29	cayley	cayley	ADJ
ejpam-3527	125	30	tables	table	NOUN
ejpam-3527	125	31	:	:	PUNCT
ejpam-3527	125	32	∗	∗	NOUN
ejpam-3527	125	33	0	0	NUM
ejpam-3527	126	1	a	a	DET
ejpam-3527	126	2	b	b	NOUN
ejpam-3527	126	3	c	c	NOUN
ejpam-3527	126	4	0	0	NUM
ejpam-3527	126	5	0	0	NUM
ejpam-3527	126	6	a	a	DET
ejpam-3527	126	7	b	b	NOUN
ejpam-3527	126	8	c	c	NOUN
ejpam-3527	126	9	a	a	DET
ejpam-3527	126	10	0	0	NUM
ejpam-3527	126	11	0	0	NUM
ejpam-3527	126	12	b	b	PROPN
ejpam-3527	126	13	c	c	NOUN
ejpam-3527	126	14	b	b	PROPN
ejpam-3527	126	15	0	0	NUM
ejpam-3527	126	16	a	a	DET
ejpam-3527	126	17	0	0	NUM
ejpam-3527	126	18	c	c	NOUN
ejpam-3527	126	19	c	c	NOUN
ejpam-3527	126	20	0	0	PUNCT
ejpam-3527	127	1	a	a	DET
ejpam-3527	127	2	b	b	PROPN
ejpam-3527	127	3	0	0	NUM
ejpam-3527	127	4	·	·	SYM
ejpam-3527	127	5	0	0	PUNCT
ejpam-3527	128	1	a	a	DET
ejpam-3527	128	2	b	b	X
ejpam-3527	128	3	c	c	NOUN
ejpam-3527	128	4	0	0	NUM
ejpam-3527	128	5	0	0	NUM
ejpam-3527	128	6	0	0	NUM
ejpam-3527	128	7	0	0	NUM
ejpam-3527	128	8	0	0	NUM
ejpam-3527	128	9	a	a	DET
ejpam-3527	128	10	0	0	NUM
ejpam-3527	128	11	a	a	DET
ejpam-3527	128	12	b	b	NOUN
ejpam-3527	128	13	c	c	NOUN
ejpam-3527	128	14	b	b	PROPN
ejpam-3527	128	15	0	0	NUM
ejpam-3527	128	16	b	b	PROPN
ejpam-3527	128	17	c	c	PROPN
ejpam-3527	128	18	a	a	DET
ejpam-3527	128	19	c	c	NOUN
ejpam-3527	128	20	0	0	PUNCT
ejpam-3527	128	21	c	c	PROPN
ejpam-3527	128	22	a	a	DET
ejpam-3527	128	23	b	b	NOUN
ejpam-3527	128	24	d.gomisong	d.gomisong	PROPN
ejpam-3527	128	25	,	,	PUNCT
ejpam-3527	128	26	r.	r.	PROPN
ejpam-3527	128	27	isla	isla	PROPN
ejpam-3527	128	28	/	/	SYM
ejpam-3527	128	29	eur	eur	PROPN
ejpam-3527	128	30	.	.	PUNCT
ejpam-3527	129	1	j.	j.	PROPN
ejpam-3527	129	2	pure	pure	PROPN
ejpam-3527	129	3	appl	appl	PROPN
ejpam-3527	129	4	.	.	PROPN
ejpam-3527	129	5	math	math	PROPN
ejpam-3527	129	6	,	,	PUNCT
ejpam-3527	129	7	12	12	NUM
ejpam-3527	129	8	(	(	PUNCT
ejpam-3527	129	9	4	4	NUM
ejpam-3527	129	10	)	)	PUNCT
ejpam-3527	129	11	(	(	PUNCT
ejpam-3527	129	12	2019	2019	NUM
ejpam-3527	129	13	)	)	PUNCT
ejpam-3527	129	14	,	,	PUNCT
ejpam-3527	129	15	1483	1483	NUM
ejpam-3527	129	16	-	-	SYM
ejpam-3527	129	17	1496	1496	NUM
ejpam-3527	129	18	1488	1488	NUM
ejpam-3527	129	19	then	then	ADV
ejpam-3527	129	20	,	,	PUNCT
ejpam-3527	129	21	routine	routine	ADJ
ejpam-3527	129	22	calculations	calculation	NOUN
ejpam-3527	129	23	show	show	VERB
ejpam-3527	129	24	that	that	SCONJ
ejpam-3527	129	25	(	(	PUNCT
ejpam-3527	129	26	x	x	X
ejpam-3527	129	27	;	;	PUNCT
ejpam-3527	129	28	∗	∗	NOUN
ejpam-3527	129	29	,	,	PUNCT
ejpam-3527	129	30	·	·	PUNCT
ejpam-3527	129	31	,	,	PUNCT
ejpam-3527	129	32	0	0	NUM
ejpam-3527	129	33	)	)	PUNCT
ejpam-3527	129	34	is	be	AUX
ejpam-3527	129	35	an	an	DET
ejpam-3527	129	36	f	f	PROPN
ejpam-3527	129	37	-up	-up	NOUN
ejpam-3527	129	38	-	-	PUNCT
ejpam-3527	129	39	semigroup	semigroup	NOUN
ejpam-3527	129	40	.	.	PUNCT
ejpam-3527	130	1	hereinafter	hereinafter	NOUN
ejpam-3527	130	2	,	,	PUNCT
ejpam-3527	130	3	let	let	VERB
ejpam-3527	130	4	x	x	PRON
ejpam-3527	130	5	denote	denote	VERB
ejpam-3527	130	6	the	the	DET
ejpam-3527	130	7	f	f	PROPN
ejpam-3527	130	8	-up	-up	NOUN
ejpam-3527	130	9	-	-	NOUN
ejpam-3527	130	10	semigroup	semigroup	NOUN
ejpam-3527	130	11	(	(	PUNCT
ejpam-3527	130	12	x	x	NOUN
ejpam-3527	130	13	;	;	PUNCT
ejpam-3527	130	14	∗	∗	NOUN
ejpam-3527	130	15	,	,	PUNCT
ejpam-3527	130	16	·	·	PUNCT
ejpam-3527	130	17	,	,	PUNCT
ejpam-3527	130	18	0	0	NUM
ejpam-3527	130	19	)	)	PUNCT
ejpam-3527	130	20	,	,	PUNCT
ejpam-3527	130	21	unless	unless	SCONJ
ejpam-3527	130	22	otherwise	otherwise	ADV
ejpam-3527	130	23	indicated	indicate	VERB
ejpam-3527	130	24	.	.	PUNCT
ejpam-3527	131	1	definition	definition	NOUN
ejpam-3527	131	2	8	8	NUM
ejpam-3527	131	3	.	.	PUNCT
ejpam-3527	132	1	a	a	DET
ejpam-3527	132	2	nonempty	nonempty	ADJ
ejpam-3527	132	3	subset	subset	VERB
ejpam-3527	132	4	s	s	NOUN
ejpam-3527	132	5	of	of	ADP
ejpam-3527	132	6	an	an	DET
ejpam-3527	132	7	f	f	PROPN
ejpam-3527	132	8	-up	-up	NOUN
ejpam-3527	132	9	-	-	PUNCT
ejpam-3527	132	10	semigroupx	semigroupx	NOUN
ejpam-3527	132	11	is	be	AUX
ejpam-3527	132	12	called	call	VERB
ejpam-3527	132	13	an	an	DET
ejpam-3527	132	14	f	f	PROPN
ejpam-3527	132	15	-up	-up	PROPN
ejpam-3527	132	16	-	-	PROPN
ejpam-3527	132	17	subsemigroup	subsemigroup	NOUN
ejpam-3527	132	18	of	of	ADP
ejpam-3527	132	19	x	x	PRON
ejpam-3527	132	20	if	if	SCONJ
ejpam-3527	132	21	the	the	DET
ejpam-3527	132	22	constant	constant	ADJ
ejpam-3527	132	23	0	0	NUM
ejpam-3527	132	24	of	of	ADP
ejpam-3527	132	25	x	x	PRON
ejpam-3527	132	26	is	be	AUX
ejpam-3527	132	27	in	in	ADP
ejpam-3527	132	28	s	s	PRON
ejpam-3527	132	29	and	and	CCONJ
ejpam-3527	132	30	(	(	PUNCT
ejpam-3527	132	31	s	s	NOUN
ejpam-3527	132	32	;	;	PUNCT
ejpam-3527	132	33	∗	∗	NOUN
ejpam-3527	132	34	,	,	PUNCT
ejpam-3527	132	35	·	·	PUNCT
ejpam-3527	132	36	,	,	PUNCT
ejpam-3527	132	37	0	0	NUM
ejpam-3527	132	38	)	)	PUNCT
ejpam-3527	132	39	itself	itself	PRON
ejpam-3527	132	40	forms	form	VERB
ejpam-3527	132	41	an	an	DET
ejpam-3527	132	42	f	f	PROPN
ejpam-3527	132	43	-up	-up	NOUN
ejpam-3527	132	44	-	-	PUNCT
ejpam-3527	132	45	semigroup	semigroup	NOUN
ejpam-3527	132	46	.	.	PUNCT
ejpam-3527	133	1	obviously	obviously	ADV
ejpam-3527	133	2	,	,	PUNCT
ejpam-3527	133	3	{	{	PUNCT
ejpam-3527	133	4	0	0	NUM
ejpam-3527	133	5	}	}	PUNCT
ejpam-3527	133	6	and	and	CCONJ
ejpam-3527	133	7	x	x	AUX
ejpam-3527	133	8	are	be	AUX
ejpam-3527	133	9	f	f	PROPN
ejpam-3527	133	10	-up	-up	NOUN
ejpam-3527	133	11	-	-	PUNCT
ejpam-3527	133	12	subsemigroups	subsemigroup	NOUN
ejpam-3527	133	13	of	of	ADP
ejpam-3527	133	14	x.	x.	NOUN
ejpam-3527	133	15	in	in	ADP
ejpam-3527	133	16	example	example	NOUN
ejpam-3527	133	17	4	4	NUM
ejpam-3527	133	18	,	,	PUNCT
ejpam-3527	133	19	the	the	DET
ejpam-3527	133	20	set	set	NOUN
ejpam-3527	133	21	s1	s1	NOUN
ejpam-3527	133	22	=	=	PUNCT
ejpam-3527	133	23	{	{	PUNCT
ejpam-3527	133	24	0	0	NUM
ejpam-3527	133	25	,	,	PUNCT
ejpam-3527	133	26	b	b	NOUN
ejpam-3527	133	27	}	}	PUNCT
ejpam-3527	133	28	is	be	AUX
ejpam-3527	133	29	an	an	DET
ejpam-3527	133	30	f	f	PROPN
ejpam-3527	133	31	-up	-up	NOUN
ejpam-3527	133	32	-	-	PROPN
ejpam-3527	133	33	subsemigroup	subsemigroup	NOUN
ejpam-3527	133	34	of	of	ADP
ejpam-3527	133	35	x	x	PRON
ejpam-3527	133	36	,	,	PUNCT
ejpam-3527	133	37	while	while	SCONJ
ejpam-3527	133	38	the	the	DET
ejpam-3527	133	39	set	set	VERB
ejpam-3527	133	40	s2	s2	NOUN
ejpam-3527	133	41	=	=	PUNCT
ejpam-3527	133	42	{	{	PUNCT
ejpam-3527	133	43	0	0	NUM
ejpam-3527	133	44	,	,	PUNCT
ejpam-3527	133	45	b	b	NOUN
ejpam-3527	133	46	,	,	PUNCT
ejpam-3527	133	47	c	c	NOUN
ejpam-3527	133	48	}	}	PUNCT
ejpam-3527	133	49	is	be	AUX
ejpam-3527	133	50	not	not	PART
ejpam-3527	133	51	an	an	DET
ejpam-3527	133	52	f	f	PROPN
ejpam-3527	133	53	-up	-up	NOUN
ejpam-3527	133	54	-	-	PROPN
ejpam-3527	133	55	subsemigroup	subsemigroup	NOUN
ejpam-3527	133	56	since	since	SCONJ
ejpam-3527	133	57	b	b	PROPN
ejpam-3527	133	58	·	·	PUNCT
ejpam-3527	133	59	c	c	X
ejpam-3527	133	60	=	=	PUNCT
ejpam-3527	133	61	a	a	DET
ejpam-3527	133	62	/∈	/∈	NOUN
ejpam-3527	133	63	s2	s2	PROPN
ejpam-3527	133	64	.	.	PUNCT
ejpam-3527	134	1	the	the	DET
ejpam-3527	134	2	following	follow	VERB
ejpam-3527	134	3	remark	remark	NOUN
ejpam-3527	134	4	immediately	immediately	ADV
ejpam-3527	134	5	follows	follow	VERB
ejpam-3527	134	6	from	from	ADP
ejpam-3527	134	7	definitions	definition	NOUN
ejpam-3527	134	8	8	8	NUM
ejpam-3527	134	9	,	,	PUNCT
ejpam-3527	134	10	7	7	NUM
ejpam-3527	134	11	,	,	PUNCT
ejpam-3527	134	12	and	and	CCONJ
ejpam-3527	134	13	3	3	X
ejpam-3527	134	14	.	.	NOUN
ejpam-3527	134	15	remark	remark	NOUN
ejpam-3527	134	16	1	1	NUM
ejpam-3527	134	17	.	.	PUNCT
ejpam-3527	135	1	every	every	DET
ejpam-3527	135	2	f	f	PROPN
ejpam-3527	135	3	-up	-up	NOUN
ejpam-3527	135	4	-	-	NOUN
ejpam-3527	135	5	subsemigroup	subsemigroup	NOUN
ejpam-3527	135	6	of	of	ADP
ejpam-3527	135	7	(	(	PUNCT
ejpam-3527	135	8	x	x	NOUN
ejpam-3527	135	9	;	;	PUNCT
ejpam-3527	135	10	∗	∗	NOUN
ejpam-3527	135	11	,	,	PUNCT
ejpam-3527	135	12	·	·	PUNCT
ejpam-3527	135	13	,	,	PUNCT
ejpam-3527	135	14	0	0	NUM
ejpam-3527	135	15	)	)	PUNCT
ejpam-3527	135	16	is	be	AUX
ejpam-3527	135	17	a	a	DET
ejpam-3527	135	18	up	up	ADJ
ejpam-3527	135	19	-	-	PUNCT
ejpam-3527	135	20	subalgebra	subalgebra	NOUN
ejpam-3527	135	21	of	of	ADP
ejpam-3527	135	22	x	x	PUNCT
ejpam-3527	135	23	with	with	ADP
ejpam-3527	135	24	respect	respect	NOUN
ejpam-3527	135	25	to	to	ADP
ejpam-3527	135	26	∗.	∗.	PROPN
ejpam-3527	135	27	the	the	DET
ejpam-3527	135	28	converse	converse	NOUN
ejpam-3527	135	29	of	of	ADP
ejpam-3527	135	30	remark	remark	NOUN
ejpam-3527	135	31	1	1	NUM
ejpam-3527	135	32	does	do	AUX
ejpam-3527	135	33	not	not	PART
ejpam-3527	135	34	hold	hold	VERB
ejpam-3527	135	35	.	.	PUNCT
ejpam-3527	136	1	to	to	PART
ejpam-3527	136	2	see	see	VERB
ejpam-3527	136	3	this	this	PRON
ejpam-3527	136	4	,	,	PUNCT
ejpam-3527	136	5	consider	consider	VERB
ejpam-3527	136	6	example	example	NOUN
ejpam-3527	136	7	4	4	NUM
ejpam-3527	136	8	.	.	PUNCT
ejpam-3527	137	1	it	it	PRON
ejpam-3527	137	2	can	can	AUX
ejpam-3527	137	3	be	be	AUX
ejpam-3527	137	4	easily	easily	ADV
ejpam-3527	137	5	verified	verify	VERB
ejpam-3527	137	6	that	that	SCONJ
ejpam-3527	137	7	s	s	VERB
ejpam-3527	137	8	=	=	X
ejpam-3527	137	9	{	{	PUNCT
ejpam-3527	137	10	0	0	NUM
ejpam-3527	137	11	,	,	PUNCT
ejpam-3527	137	12	b	b	NOUN
ejpam-3527	137	13	,	,	PUNCT
ejpam-3527	137	14	c	c	NOUN
ejpam-3527	137	15	}	}	PUNCT
ejpam-3527	137	16	is	be	AUX
ejpam-3527	137	17	a	a	DET
ejpam-3527	137	18	up	up	ADJ
ejpam-3527	137	19	-	-	PUNCT
ejpam-3527	137	20	subalgebra	subalgebra	NOUN
ejpam-3527	137	21	of	of	ADP
ejpam-3527	137	22	(	(	PUNCT
ejpam-3527	137	23	x	x	NOUN
ejpam-3527	137	24	;	;	PUNCT
ejpam-3527	137	25	∗	∗	NOUN
ejpam-3527	137	26	,	,	PUNCT
ejpam-3527	137	27	0	0	NUM
ejpam-3527	137	28	)	)	PUNCT
ejpam-3527	137	29	but	but	CCONJ
ejpam-3527	137	30	s	s	NOUN
ejpam-3527	137	31	is	be	AUX
ejpam-3527	137	32	not	not	PART
ejpam-3527	137	33	an	an	DET
ejpam-3527	137	34	f	f	PROPN
ejpam-3527	137	35	-upsubsemigroup	-upsubsemigroup	NOUN
ejpam-3527	137	36	of	of	ADP
ejpam-3527	137	37	(	(	PUNCT
ejpam-3527	137	38	x	x	NOUN
ejpam-3527	137	39	;	;	PUNCT
ejpam-3527	137	40	∗	∗	NOUN
ejpam-3527	137	41	,	,	PUNCT
ejpam-3527	137	42	·	·	PUNCT
ejpam-3527	137	43	,	,	PUNCT
ejpam-3527	137	44	0	0	NUM
ejpam-3527	137	45	)	)	PUNCT
ejpam-3527	137	46	since	since	SCONJ
ejpam-3527	137	47	b	b	PROPN
ejpam-3527	137	48	·	·	PUNCT
ejpam-3527	137	49	c	c	X
ejpam-3527	137	50	=	=	PUNCT
ejpam-3527	137	51	a	a	PROPN
ejpam-3527	137	52	/∈	/∈	PUNCT
ejpam-3527	137	53	s.	s.	PROPN
ejpam-3527	137	54	definition	definition	NOUN
ejpam-3527	137	55	9	9	NUM
ejpam-3527	137	56	.	.	PUNCT
ejpam-3527	138	1	an	an	DET
ejpam-3527	138	2	f	f	PROPN
ejpam-3527	138	3	-up	-up	NOUN
ejpam-3527	138	4	-	-	NOUN
ejpam-3527	138	5	semigroup	semigroup	NOUN
ejpam-3527	138	6	x	x	VERB
ejpam-3527	138	7	is	be	AUX
ejpam-3527	138	8	said	say	VERB
ejpam-3527	138	9	to	to	PART
ejpam-3527	138	10	be	be	AUX
ejpam-3527	138	11	commutative	commutative	ADJ
ejpam-3527	139	1	if	if	SCONJ
ejpam-3527	139	2	a	a	DET
ejpam-3527	139	3	·	·	SYM
ejpam-3527	139	4	b	b	X
ejpam-3527	139	5	=	=	SYM
ejpam-3527	139	6	b	b	PROPN
ejpam-3527	139	7	·	·	PUNCT
ejpam-3527	139	8	a	a	PRON
ejpam-3527	139	9	for	for	ADP
ejpam-3527	139	10	all	all	DET
ejpam-3527	139	11	a	a	DET
ejpam-3527	139	12	,	,	PUNCT
ejpam-3527	139	13	b	b	X
ejpam-3527	139	14	∈	∈	PROPN
ejpam-3527	139	15	x.	x.	NOUN
ejpam-3527	140	1	if	if	SCONJ
ejpam-3527	140	2	x	x	PRON
ejpam-3527	140	3	is	be	AUX
ejpam-3527	140	4	not	not	PART
ejpam-3527	140	5	commutative	commutative	ADJ
ejpam-3527	140	6	,	,	PUNCT
ejpam-3527	140	7	then	then	ADV
ejpam-3527	140	8	it	it	PRON
ejpam-3527	140	9	is	be	AUX
ejpam-3527	140	10	called	call	VERB
ejpam-3527	140	11	a	a	DET
ejpam-3527	140	12	noncommutative	noncommutative	ADJ
ejpam-3527	140	13	f	f	PROPN
ejpam-3527	140	14	-up	-up	NOUN
ejpam-3527	140	15	-	-	PUNCT
ejpam-3527	140	16	semigroup	semigroup	NOUN
ejpam-3527	140	17	.	.	PUNCT
ejpam-3527	141	1	routine	routine	ADJ
ejpam-3527	141	2	calculations	calculation	NOUN
ejpam-3527	141	3	show	show	VERB
ejpam-3527	141	4	that	that	SCONJ
ejpam-3527	141	5	the	the	DET
ejpam-3527	141	6	f	f	PROPN
ejpam-3527	141	7	-up	-up	NOUN
ejpam-3527	141	8	-	-	PUNCT
ejpam-3527	141	9	semigroups	semigroup	NOUN
ejpam-3527	141	10	in	in	ADP
ejpam-3527	141	11	examples	example	NOUN
ejpam-3527	141	12	4	4	NUM
ejpam-3527	141	13	and	and	CCONJ
ejpam-3527	141	14	6	6	NUM
ejpam-3527	141	15	are	be	AUX
ejpam-3527	141	16	commutative	commutative	ADJ
ejpam-3527	141	17	while	while	SCONJ
ejpam-3527	141	18	the	the	DET
ejpam-3527	141	19	f	f	PROPN
ejpam-3527	141	20	-up	-up	NOUN
ejpam-3527	141	21	-	-	PUNCT
ejpam-3527	141	22	semigroup	semigroup	NOUN
ejpam-3527	141	23	in	in	ADP
ejpam-3527	141	24	example	example	NOUN
ejpam-3527	141	25	5	5	NUM
ejpam-3527	141	26	is	be	AUX
ejpam-3527	141	27	noncommutative	noncommutative	ADJ
ejpam-3527	141	28	since	since	SCONJ
ejpam-3527	141	29	a·c	a·c	NOUN
ejpam-3527	141	30	=	=	SYM
ejpam-3527	141	31	0	0	PUNCT
ejpam-3527	141	32	6=	6=	ADP
ejpam-3527	141	33	a	a	DET
ejpam-3527	141	34	=	=	NOUN
ejpam-3527	141	35	c·a	c·a	NOUN
ejpam-3527	141	36	.	.	PUNCT
ejpam-3527	142	1	definition	definition	NOUN
ejpam-3527	142	2	10	10	NUM
ejpam-3527	142	3	.	.	PUNCT
ejpam-3527	143	1	let	let	VERB
ejpam-3527	143	2	x	x	PRON
ejpam-3527	143	3	be	be	AUX
ejpam-3527	143	4	an	an	DET
ejpam-3527	143	5	f	f	PROPN
ejpam-3527	143	6	-up	-up	NOUN
ejpam-3527	143	7	-	-	PUNCT
ejpam-3527	143	8	semigroup	semigroup	NOUN
ejpam-3527	143	9	.	.	PUNCT
ejpam-3527	144	1	an	an	DET
ejpam-3527	144	2	element	element	NOUN
ejpam-3527	144	3	e	e	X
ejpam-3527	144	4	∈	∈	PROPN
ejpam-3527	144	5	x	x	PUNCT
ejpam-3527	144	6	is	be	AUX
ejpam-3527	144	7	called	call	VERB
ejpam-3527	144	8	a	a	DET
ejpam-3527	144	9	unity	unity	NOUN
ejpam-3527	144	10	in	in	ADP
ejpam-3527	144	11	x	x	PUNCT
ejpam-3527	144	12	if	if	SCONJ
ejpam-3527	144	13	x	x	X
ejpam-3527	144	14	·	·	PUNCT
ejpam-3527	144	15	e	e	X
ejpam-3527	144	16	=	=	PUNCT
ejpam-3527	144	17	x	x	SYM
ejpam-3527	144	18	=	=	PUNCT
ejpam-3527	144	19	e	e	X
ejpam-3527	144	20	·	·	PUNCT
ejpam-3527	144	21	x	x	PUNCT
ejpam-3527	144	22	for	for	ADP
ejpam-3527	144	23	all	all	DET
ejpam-3527	144	24	x	x	SYM
ejpam-3527	144	25	∈	∈	NOUN
ejpam-3527	144	26	x.	x.	NOUN
ejpam-3527	144	27	proposition	proposition	NOUN
ejpam-3527	144	28	3	3	NUM
ejpam-3527	144	29	.	.	PUNCT
ejpam-3527	145	1	let	let	VERB
ejpam-3527	145	2	x	x	PRON
ejpam-3527	145	3	be	be	AUX
ejpam-3527	145	4	an	an	DET
ejpam-3527	145	5	f	f	PROPN
ejpam-3527	145	6	-up	-up	NOUN
ejpam-3527	145	7	-	-	PUNCT
ejpam-3527	145	8	semigroup	semigroup	NOUN
ejpam-3527	145	9	.	.	PUNCT
ejpam-3527	146	1	if	if	SCONJ
ejpam-3527	146	2	the	the	DET
ejpam-3527	146	3	unity	unity	NOUN
ejpam-3527	146	4	of	of	ADP
ejpam-3527	146	5	x	x	PRON
ejpam-3527	146	6	exists	exist	NOUN
ejpam-3527	146	7	,	,	PUNCT
ejpam-3527	146	8	then	then	ADV
ejpam-3527	146	9	it	it	PRON
ejpam-3527	146	10	is	be	AUX
ejpam-3527	146	11	unique	unique	ADJ
ejpam-3527	146	12	.	.	PUNCT
ejpam-3527	147	1	proof	proof	NOUN
ejpam-3527	147	2	.	.	PUNCT
ejpam-3527	148	1	let	let	VERB
ejpam-3527	148	2	x	x	PRON
ejpam-3527	148	3	be	be	AUX
ejpam-3527	148	4	an	an	DET
ejpam-3527	148	5	f	f	PROPN
ejpam-3527	148	6	-up	-up	NOUN
ejpam-3527	148	7	-	-	NOUN
ejpam-3527	148	8	semigroup	semigroup	NOUN
ejpam-3527	148	9	with	with	ADP
ejpam-3527	148	10	unity	unity	NOUN
ejpam-3527	148	11	.	.	PUNCT
ejpam-3527	149	1	suppose	suppose	VERB
ejpam-3527	149	2	1	1	NUM
ejpam-3527	149	3	,	,	PUNCT
ejpam-3527	149	4	1′	1′	NUM
ejpam-3527	149	5	∈	∈	NOUN
ejpam-3527	149	6	x	x	PUNCT
ejpam-3527	149	7	both	both	PRON
ejpam-3527	149	8	satisfy	satisfy	VERB
ejpam-3527	149	9	the	the	DET
ejpam-3527	149	10	properties	property	NOUN
ejpam-3527	149	11	of	of	ADP
ejpam-3527	149	12	being	be	AUX
ejpam-3527	149	13	a	a	DET
ejpam-3527	149	14	unity	unity	NOUN
ejpam-3527	149	15	.	.	PUNCT
ejpam-3527	150	1	then	then	ADV
ejpam-3527	150	2	,	,	PUNCT
ejpam-3527	150	3	for	for	ADP
ejpam-3527	150	4	all	all	DET
ejpam-3527	150	5	x	x	SYM
ejpam-3527	150	6	∈	∈	PROPN
ejpam-3527	150	7	x	x	X
ejpam-3527	150	8	,	,	PUNCT
ejpam-3527	150	9	x	x	X
ejpam-3527	150	10	·	·	PUNCT
ejpam-3527	150	11	1	1	NUM
ejpam-3527	150	12	=	=	SYM
ejpam-3527	150	13	1	1	NUM
ejpam-3527	150	14	·	·	PUNCT
ejpam-3527	150	15	x	x	SYM
ejpam-3527	150	16	=	=	PUNCT
ejpam-3527	150	17	x	x	X
ejpam-3527	150	18	and	and	CCONJ
ejpam-3527	150	19	x	x	SYM
ejpam-3527	150	20	·	·	PUNCT
ejpam-3527	150	21	1′	1′	NUM
ejpam-3527	150	22	=	=	SYM
ejpam-3527	150	23	1′	1′	NUM
ejpam-3527	150	24	·	·	PUNCT
ejpam-3527	150	25	x	x	PUNCT
ejpam-3527	151	1	=	=	PUNCT
ejpam-3527	151	2	x.	x.	NOUN
ejpam-3527	151	3	if	if	SCONJ
ejpam-3527	151	4	x	x	SYM
ejpam-3527	151	5	=	=	SYM
ejpam-3527	151	6	1	1	NUM
ejpam-3527	151	7	,	,	PUNCT
ejpam-3527	151	8	we	we	PRON
ejpam-3527	151	9	have	have	VERB
ejpam-3527	151	10	1	1	NUM
ejpam-3527	151	11	·	·	SYM
ejpam-3527	151	12	1′	1′	NUM
ejpam-3527	152	1	=	=	SYM
ejpam-3527	152	2	1	1	X
ejpam-3527	152	3	.	.	PUNCT
ejpam-3527	153	1	if	if	SCONJ
ejpam-3527	153	2	x	x	PROPN
ejpam-3527	153	3	=	=	SYM
ejpam-3527	153	4	1′	1′	NUM
ejpam-3527	153	5	,	,	PUNCT
ejpam-3527	153	6	we	we	PRON
ejpam-3527	153	7	have	have	VERB
ejpam-3527	153	8	1	1	NUM
ejpam-3527	153	9	·	·	SYM
ejpam-3527	153	10	1′	1′	NUM
ejpam-3527	153	11	=	=	SYM
ejpam-3527	153	12	1′.	1′.	NOUN
ejpam-3527	153	13	therefore	therefore	ADV
ejpam-3527	153	14	,	,	PUNCT
ejpam-3527	153	15	1	1	NUM
ejpam-3527	153	16	=	=	SYM
ejpam-3527	153	17	1′.	1′.	NUM
ejpam-3527	153	18	if	if	SCONJ
ejpam-3527	153	19	an	an	DET
ejpam-3527	153	20	f	f	PROPN
ejpam-3527	153	21	-up	-up	NOUN
ejpam-3527	153	22	-	-	NOUN
ejpam-3527	153	23	semigroup	semigroup	ADJ
ejpam-3527	153	24	x	x	PUNCT
ejpam-3527	153	25	has	have	VERB
ejpam-3527	153	26	unity	unity	NOUN
ejpam-3527	153	27	,	,	PUNCT
ejpam-3527	153	28	it	it	PRON
ejpam-3527	153	29	shall	shall	AUX
ejpam-3527	153	30	be	be	AUX
ejpam-3527	153	31	denoted	denote	VERB
ejpam-3527	153	32	by	by	ADP
ejpam-3527	153	33	1	1	NUM
ejpam-3527	153	34	.	.	PUNCT
ejpam-3527	153	35	definition	definition	NOUN
ejpam-3527	153	36	11	11	NUM
ejpam-3527	153	37	.	.	PUNCT
ejpam-3527	154	1	let	let	VERB
ejpam-3527	154	2	x	x	PRON
ejpam-3527	154	3	be	be	AUX
ejpam-3527	154	4	an	an	DET
ejpam-3527	154	5	f	f	PROPN
ejpam-3527	154	6	-up	-up	NOUN
ejpam-3527	154	7	-	-	NOUN
ejpam-3527	154	8	semigroup	semigroup	NOUN
ejpam-3527	154	9	with	with	ADP
ejpam-3527	154	10	unity	unity	NOUN
ejpam-3527	154	11	1	1	NUM
ejpam-3527	154	12	.	.	PUNCT
ejpam-3527	155	1	an	an	DET
ejpam-3527	155	2	element	element	NOUN
ejpam-3527	155	3	a	a	PRON
ejpam-3527	155	4	of	of	ADP
ejpam-3527	155	5	x	x	PRON
ejpam-3527	155	6	is	be	AUX
ejpam-3527	155	7	called	call	VERB
ejpam-3527	155	8	1	1	NUM
ejpam-3527	155	9	-	-	PUNCT
ejpam-3527	155	10	invertible	invertible	ADJ
ejpam-3527	155	11	if	if	SCONJ
ejpam-3527	155	12	there	there	PRON
ejpam-3527	155	13	exists	exist	VERB
ejpam-3527	155	14	b	b	PROPN
ejpam-3527	155	15	∈	∈	PROPN
ejpam-3527	155	16	x	x	PUNCT
ejpam-3527	155	17	such	such	ADJ
ejpam-3527	155	18	that	that	SCONJ
ejpam-3527	155	19	a	a	DET
ejpam-3527	155	20	·	·	SYM
ejpam-3527	155	21	b	b	X
ejpam-3527	155	22	=	=	SYM
ejpam-3527	155	23	1	1	NUM
ejpam-3527	155	24	=	=	SYM
ejpam-3527	155	25	b	b	PROPN
ejpam-3527	155	26	·	·	PUNCT
ejpam-3527	155	27	a.	a.	NOUN
ejpam-3527	156	1	we	we	PRON
ejpam-3527	156	2	next	next	ADV
ejpam-3527	156	3	introduce	introduce	VERB
ejpam-3527	156	4	the	the	DET
ejpam-3527	156	5	concepts	concept	NOUN
ejpam-3527	156	6	of	of	ADP
ejpam-3527	156	7	f	f	PROPN
ejpam-3527	156	8	-up	-up	NOUN
ejpam-3527	156	9	-	-	PUNCT
ejpam-3527	156	10	field	field	NOUN
ejpam-3527	156	11	and	and	CCONJ
ejpam-3527	156	12	f	f	PROPN
ejpam-3527	156	13	-up	-up	NOUN
ejpam-3527	156	14	-	-	NOUN
ejpam-3527	156	15	domain	domain	NOUN
ejpam-3527	156	16	analogous	analogous	NOUN
ejpam-3527	156	17	to	to	ADP
ejpam-3527	156	18	the	the	DET
ejpam-3527	156	19	definitions	definition	NOUN
ejpam-3527	156	20	of	of	ADP
ejpam-3527	156	21	jb	jb	NOUN
ejpam-3527	156	22	-	-	PUNCT
ejpam-3527	156	23	field	field	NOUN
ejpam-3527	156	24	and	and	CCONJ
ejpam-3527	156	25	jb	jb	NOUN
ejpam-3527	156	26	-	-	PUNCT
ejpam-3527	156	27	domain	domain	NOUN
ejpam-3527	156	28	given	give	VERB
ejpam-3527	156	29	by	by	ADP
ejpam-3527	156	30	j.	j.	PROPN
ejpam-3527	156	31	endam	endam	PROPN
ejpam-3527	156	32	and	and	CCONJ
ejpam-3527	156	33	j.	j.	PROPN
ejpam-3527	156	34	vilela	vilela	PROPN
ejpam-3527	157	1	[	[	X
ejpam-3527	157	2	2	2	NUM
ejpam-3527	157	3	]	]	PUNCT
ejpam-3527	157	4	.	.	PUNCT
ejpam-3527	158	1	definition	definition	NOUN
ejpam-3527	158	2	12	12	NUM
ejpam-3527	158	3	.	.	PUNCT
ejpam-3527	159	1	let	let	VERB
ejpam-3527	159	2	x	x	PRON
ejpam-3527	159	3	be	be	AUX
ejpam-3527	159	4	an	an	DET
ejpam-3527	159	5	f	f	PROPN
ejpam-3527	159	6	-up	-up	NOUN
ejpam-3527	159	7	-	-	NOUN
ejpam-3527	159	8	semigroup	semigroup	NOUN
ejpam-3527	159	9	with	with	ADP
ejpam-3527	159	10	unity	unity	NOUN
ejpam-3527	159	11	1	1	NUM
ejpam-3527	159	12	.	.	PUNCT
ejpam-3527	160	1	then	then	ADV
ejpam-3527	160	2	x	x	VERB
ejpam-3527	160	3	is	be	AUX
ejpam-3527	160	4	called	call	VERB
ejpam-3527	160	5	an	an	DET
ejpam-3527	160	6	f	f	PROPN
ejpam-3527	160	7	-up	-up	NOUN
ejpam-3527	160	8	-	-	PUNCT
ejpam-3527	160	9	field	field	NOUN
ejpam-3527	160	10	if	if	SCONJ
ejpam-3527	160	11	the	the	DET
ejpam-3527	160	12	following	follow	VERB
ejpam-3527	160	13	hold	hold	NOUN
ejpam-3527	160	14	:	:	PUNCT
ejpam-3527	160	15	(	(	PUNCT
ejpam-3527	160	16	i	i	NOUN
ejpam-3527	160	17	)	)	PUNCT
ejpam-3527	160	18	the	the	DET
ejpam-3527	160	19	semigroup	semigroup	NOUN
ejpam-3527	160	20	(	(	PUNCT
ejpam-3527	160	21	x	x	X
ejpam-3527	160	22	,	,	PUNCT
ejpam-3527	160	23	·	·	PUNCT
ejpam-3527	160	24	)	)	PUNCT
ejpam-3527	160	25	is	be	AUX
ejpam-3527	160	26	commutative	commutative	ADJ
ejpam-3527	160	27	;	;	PUNCT
ejpam-3527	160	28	and	and	CCONJ
ejpam-3527	160	29	(	(	PUNCT
ejpam-3527	160	30	ii	ii	NOUN
ejpam-3527	160	31	)	)	PUNCT
ejpam-3527	160	32	every	every	DET
ejpam-3527	160	33	0	0	NUM
ejpam-3527	160	34	6=	6=	ADP
ejpam-3527	160	35	a	a	DET
ejpam-3527	160	36	∈	∈	NOUN
ejpam-3527	160	37	x	x	X
ejpam-3527	160	38	is	be	AUX
ejpam-3527	160	39	1	1	NUM
ejpam-3527	160	40	-	-	PUNCT
ejpam-3527	160	41	invertible	invertible	ADJ
ejpam-3527	160	42	.	.	PUNCT
ejpam-3527	161	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	161	2	,	,	PUNCT
ejpam-3527	161	3	r.	r.	PROPN
ejpam-3527	161	4	isla	isla	PROPN
ejpam-3527	161	5	/	/	SYM
ejpam-3527	161	6	eur	eur	PROPN
ejpam-3527	161	7	.	.	PUNCT
ejpam-3527	162	1	j.	j.	PROPN
ejpam-3527	162	2	pure	pure	PROPN
ejpam-3527	162	3	appl	appl	PROPN
ejpam-3527	162	4	.	.	PROPN
ejpam-3527	162	5	math	math	PROPN
ejpam-3527	162	6	,	,	PUNCT
ejpam-3527	162	7	12	12	NUM
ejpam-3527	162	8	(	(	PUNCT
ejpam-3527	162	9	4	4	NUM
ejpam-3527	162	10	)	)	PUNCT
ejpam-3527	162	11	(	(	PUNCT
ejpam-3527	162	12	2019	2019	NUM
ejpam-3527	162	13	)	)	PUNCT
ejpam-3527	162	14	,	,	PUNCT
ejpam-3527	162	15	1483	1483	NUM
ejpam-3527	162	16	-	-	SYM
ejpam-3527	162	17	1496	1496	NUM
ejpam-3527	162	18	1489	1489	NUM
ejpam-3527	162	19	definition	definition	NOUN
ejpam-3527	162	20	13	13	NUM
ejpam-3527	162	21	.	.	PUNCT
ejpam-3527	163	1	a	a	DET
ejpam-3527	163	2	nonzero	nonzero	PROPN
ejpam-3527	163	3	element	element	NOUN
ejpam-3527	163	4	a	a	PRON
ejpam-3527	163	5	of	of	ADP
ejpam-3527	163	6	an	an	DET
ejpam-3527	163	7	f	f	PROPN
ejpam-3527	163	8	-up	-up	NOUN
ejpam-3527	163	9	-	-	NOUN
ejpam-3527	163	10	semigroup	semigroup	NOUN
ejpam-3527	163	11	x	x	VERB
ejpam-3527	163	12	is	be	AUX
ejpam-3527	163	13	called	call	VERB
ejpam-3527	163	14	a	a	DET
ejpam-3527	163	15	0	0	NUM
ejpam-3527	163	16	-	-	PUNCT
ejpam-3527	163	17	divisor	divisor	NOUN
ejpam-3527	163	18	if	if	SCONJ
ejpam-3527	163	19	there	there	PRON
ejpam-3527	163	20	exists	exist	VERB
ejpam-3527	163	21	b	b	PROPN
ejpam-3527	163	22	∈	∈	PROPN
ejpam-3527	163	23	x	x	PUNCT
ejpam-3527	163	24	such	such	ADJ
ejpam-3527	163	25	that	that	DET
ejpam-3527	163	26	b	b	NOUN
ejpam-3527	163	27	6=	6=	ADP
ejpam-3527	163	28	0	0	NUM
ejpam-3527	163	29	and	and	CCONJ
ejpam-3527	163	30	either	either	CCONJ
ejpam-3527	163	31	a	a	DET
ejpam-3527	163	32	·	·	PUNCT
ejpam-3527	163	33	b	b	X
ejpam-3527	163	34	=	=	SYM
ejpam-3527	163	35	0	0	NUM
ejpam-3527	163	36	or	or	CCONJ
ejpam-3527	163	37	b	b	X
ejpam-3527	163	38	·	·	PUNCT
ejpam-3527	163	39	a	a	PRON
ejpam-3527	163	40	=	=	NOUN
ejpam-3527	163	41	0	0	X
ejpam-3527	163	42	.	.	PUNCT
ejpam-3527	164	1	note	note	VERB
ejpam-3527	164	2	that	that	SCONJ
ejpam-3527	164	3	0	0	NUM
ejpam-3527	164	4	is	be	AUX
ejpam-3527	164	5	not	not	PART
ejpam-3527	164	6	a	a	DET
ejpam-3527	164	7	0	0	NUM
ejpam-3527	164	8	-	-	PUNCT
ejpam-3527	164	9	divisor	divisor	NOUN
ejpam-3527	164	10	.	.	PUNCT
ejpam-3527	165	1	remark	remark	PROPN
ejpam-3527	165	2	2	2	NUM
ejpam-3527	165	3	.	.	PUNCT
ejpam-3527	166	1	an	an	DET
ejpam-3527	166	2	element	element	NOUN
ejpam-3527	166	3	can	can	AUX
ejpam-3527	166	4	not	not	PART
ejpam-3527	166	5	be	be	AUX
ejpam-3527	166	6	1	1	NUM
ejpam-3527	166	7	-	-	PUNCT
ejpam-3527	166	8	invertible	invertible	ADJ
ejpam-3527	166	9	and	and	CCONJ
ejpam-3527	166	10	a	a	DET
ejpam-3527	166	11	0	0	NUM
ejpam-3527	166	12	-	-	PUNCT
ejpam-3527	166	13	divisor	divisor	NOUN
ejpam-3527	166	14	at	at	ADP
ejpam-3527	166	15	the	the	DET
ejpam-3527	166	16	same	same	ADJ
ejpam-3527	166	17	time	time	NOUN
ejpam-3527	166	18	.	.	PUNCT
ejpam-3527	167	1	thus	thus	ADV
ejpam-3527	167	2	,	,	PUNCT
ejpam-3527	167	3	an	an	PRON
ejpam-3527	167	4	f	f	PROPN
ejpam-3527	167	5	-up	-up	NOUN
ejpam-3527	167	6	-	-	PUNCT
ejpam-3527	167	7	field	field	NOUN
ejpam-3527	167	8	has	have	VERB
ejpam-3527	167	9	no	no	DET
ejpam-3527	167	10	0	0	NUM
ejpam-3527	167	11	-	-	PUNCT
ejpam-3527	167	12	divisors	divisor	NOUN
ejpam-3527	167	13	.	.	PUNCT
ejpam-3527	168	1	definition	definition	NOUN
ejpam-3527	168	2	14	14	NUM
ejpam-3527	168	3	.	.	PUNCT
ejpam-3527	169	1	let	let	VERB
ejpam-3527	169	2	x	x	PRON
ejpam-3527	169	3	be	be	AUX
ejpam-3527	169	4	an	an	DET
ejpam-3527	169	5	f	f	PROPN
ejpam-3527	169	6	-up	-up	NOUN
ejpam-3527	169	7	-	-	NOUN
ejpam-3527	169	8	semigroup	semigroup	NOUN
ejpam-3527	169	9	with	with	ADP
ejpam-3527	169	10	unity	unity	NOUN
ejpam-3527	169	11	1	1	NUM
ejpam-3527	169	12	.	.	PUNCT
ejpam-3527	170	1	then	then	ADV
ejpam-3527	170	2	x	x	VERB
ejpam-3527	170	3	is	be	AUX
ejpam-3527	170	4	called	call	VERB
ejpam-3527	170	5	an	an	DET
ejpam-3527	170	6	f	f	NOUN
ejpam-3527	170	7	-updomain	-updomain	PROPN
ejpam-3527	170	8	if	if	SCONJ
ejpam-3527	170	9	the	the	DET
ejpam-3527	170	10	following	follow	VERB
ejpam-3527	170	11	hold	hold	NOUN
ejpam-3527	170	12	:	:	PUNCT
ejpam-3527	170	13	(	(	PUNCT
ejpam-3527	170	14	i	i	NOUN
ejpam-3527	170	15	)	)	PUNCT
ejpam-3527	170	16	the	the	DET
ejpam-3527	170	17	semigroup	semigroup	NOUN
ejpam-3527	170	18	(	(	PUNCT
ejpam-3527	170	19	x	x	X
ejpam-3527	170	20	,	,	PUNCT
ejpam-3527	170	21	·	·	PUNCT
ejpam-3527	170	22	)	)	PUNCT
ejpam-3527	170	23	is	be	AUX
ejpam-3527	170	24	commutative	commutative	ADJ
ejpam-3527	170	25	;	;	PUNCT
ejpam-3527	170	26	and	and	CCONJ
ejpam-3527	170	27	(	(	PUNCT
ejpam-3527	170	28	ii	ii	NOUN
ejpam-3527	170	29	)	)	PUNCT
ejpam-3527	170	30	x	x	PUNCT
ejpam-3527	170	31	has	have	VERB
ejpam-3527	170	32	no	no	DET
ejpam-3527	170	33	0	0	NUM
ejpam-3527	170	34	-	-	PUNCT
ejpam-3527	170	35	divisors	divisor	NOUN
ejpam-3527	170	36	.	.	PUNCT
ejpam-3527	171	1	the	the	DET
ejpam-3527	171	2	f	f	PROPN
ejpam-3527	171	3	-up	-up	NOUN
ejpam-3527	171	4	-	-	PUNCT
ejpam-3527	171	5	semigroup	semigroup	NOUN
ejpam-3527	171	6	in	in	ADP
ejpam-3527	171	7	example	example	NOUN
ejpam-3527	172	1	6	6	NUM
ejpam-3527	172	2	is	be	AUX
ejpam-3527	172	3	an	an	DET
ejpam-3527	172	4	f	f	PROPN
ejpam-3527	172	5	-up	-up	NOUN
ejpam-3527	172	6	-	-	NOUN
ejpam-3527	172	7	domain	domain	NOUN
ejpam-3527	172	8	.	.	PUNCT
ejpam-3527	173	1	remark	remark	NOUN
ejpam-3527	173	2	3	3	NUM
ejpam-3527	173	3	.	.	PUNCT
ejpam-3527	174	1	every	every	PRON
ejpam-3527	174	2	f	f	PROPN
ejpam-3527	174	3	-up	-up	NOUN
ejpam-3527	174	4	-	-	PUNCT
ejpam-3527	174	5	field	field	NOUN
ejpam-3527	174	6	is	be	AUX
ejpam-3527	174	7	an	an	DET
ejpam-3527	174	8	f	f	PROPN
ejpam-3527	174	9	-up	-up	NOUN
ejpam-3527	174	10	-	-	NOUN
ejpam-3527	174	11	domain	domain	NOUN
ejpam-3527	174	12	.	.	PUNCT
ejpam-3527	175	1	3	3	X
ejpam-3527	175	2	.	.	X
ejpam-3527	175	3	elementary	elementary	ADJ
ejpam-3527	175	4	properties	property	NOUN
ejpam-3527	175	5	of	of	ADP
ejpam-3527	175	6	f	f	PROPN
ejpam-3527	175	7	-	-	PUNCT
ejpam-3527	175	8	up	up	NOUN
ejpam-3527	175	9	-	-	PUNCT
ejpam-3527	175	10	semigroups	semigroup	NOUN
ejpam-3527	175	11	this	this	DET
ejpam-3527	175	12	section	section	NOUN
ejpam-3527	175	13	presents	present	VERB
ejpam-3527	175	14	some	some	DET
ejpam-3527	175	15	elementary	elementary	ADJ
ejpam-3527	175	16	properties	property	NOUN
ejpam-3527	175	17	of	of	ADP
ejpam-3527	175	18	f	f	PROPN
ejpam-3527	175	19	-up	-up	NOUN
ejpam-3527	175	20	-	-	PUNCT
ejpam-3527	175	21	semigroups	semigroup	NOUN
ejpam-3527	175	22	.	.	PUNCT
ejpam-3527	176	1	throughout	throughout	ADP
ejpam-3527	176	2	this	this	DET
ejpam-3527	176	3	section	section	NOUN
ejpam-3527	176	4	,	,	PUNCT
ejpam-3527	176	5	x	x	PRON
ejpam-3527	176	6	means	mean	VERB
ejpam-3527	176	7	an	an	DET
ejpam-3527	176	8	f	f	PROPN
ejpam-3527	176	9	-up	-up	NOUN
ejpam-3527	176	10	-	-	NOUN
ejpam-3527	176	11	semigroup	semigroup	NOUN
ejpam-3527	176	12	(	(	PUNCT
ejpam-3527	176	13	x	x	NOUN
ejpam-3527	176	14	;	;	PUNCT
ejpam-3527	176	15	∗	∗	NOUN
ejpam-3527	176	16	,	,	PUNCT
ejpam-3527	176	17	·	·	PUNCT
ejpam-3527	176	18	,	,	PUNCT
ejpam-3527	176	19	0	0	NUM
ejpam-3527	176	20	)	)	PUNCT
ejpam-3527	176	21	.	.	PUNCT
ejpam-3527	177	1	theorem	theorem	ADJ
ejpam-3527	177	2	4	4	NUM
ejpam-3527	177	3	.	.	PUNCT
ejpam-3527	178	1	let	let	VERB
ejpam-3527	178	2	a	a	DET
ejpam-3527	178	3	,	,	PUNCT
ejpam-3527	178	4	b	b	NOUN
ejpam-3527	179	1	,	,	PUNCT
ejpam-3527	179	2	c	c	PROPN
ejpam-3527	179	3	∈	∈	PROPN
ejpam-3527	179	4	x.	x.	NOUN
ejpam-3527	179	5	then	then	ADV
ejpam-3527	179	6	the	the	DET
ejpam-3527	179	7	following	follow	VERB
ejpam-3527	179	8	properties	property	NOUN
ejpam-3527	179	9	hold	hold	VERB
ejpam-3527	179	10	:	:	PUNCT
ejpam-3527	179	11	(	(	PUNCT
ejpam-3527	179	12	i	i	NOUN
ejpam-3527	179	13	)	)	PUNCT
ejpam-3527	179	14	a	a	PRON
ejpam-3527	179	15	·	·	PUNCT
ejpam-3527	179	16	0	0	NUM
ejpam-3527	180	1	=	=	SYM
ejpam-3527	180	2	0	0	PUNCT
ejpam-3527	180	3	·	·	PUNCT
ejpam-3527	180	4	a	a	X
ejpam-3527	180	5	=	=	SYM
ejpam-3527	180	6	0	0	NUM
ejpam-3527	180	7	,	,	PUNCT
ejpam-3527	180	8	(	(	PUNCT
ejpam-3527	180	9	ii	ii	NOUN
ejpam-3527	180	10	)	)	PUNCT
ejpam-3527	180	11	a	a	DET
ejpam-3527	180	12	·	·	PUNCT
ejpam-3527	180	13	(	(	PUNCT
ejpam-3527	180	14	0	0	NUM
ejpam-3527	180	15	∗	∗	NUM
ejpam-3527	180	16	b	b	NOUN
ejpam-3527	180	17	)	)	PUNCT
ejpam-3527	180	18	=	=	SYM
ejpam-3527	180	19	(	(	PUNCT
ejpam-3527	180	20	0	0	NUM
ejpam-3527	180	21	∗	∗	NOUN
ejpam-3527	180	22	a	a	NOUN
ejpam-3527	180	23	)	)	PUNCT
ejpam-3527	180	24	·	·	PUNCT
ejpam-3527	181	1	b	b	X
ejpam-3527	181	2	=	=	PUNCT
ejpam-3527	181	3	a	a	DET
ejpam-3527	181	4	·	·	SYM
ejpam-3527	181	5	b	b	NOUN
ejpam-3527	181	6	,	,	PUNCT
ejpam-3527	181	7	(	(	PUNCT
ejpam-3527	181	8	iii	iii	NOUN
ejpam-3527	181	9	)	)	PUNCT
ejpam-3527	181	10	a	a	DET
ejpam-3527	181	11	·	·	PUNCT
ejpam-3527	181	12	(	(	PUNCT
ejpam-3527	181	13	b	b	NOUN
ejpam-3527	181	14	∗	∗	NOUN
ejpam-3527	181	15	(	(	PUNCT
ejpam-3527	181	16	0	0	NUM
ejpam-3527	181	17	∗	∗	NOUN
ejpam-3527	181	18	c	c	NOUN
ejpam-3527	181	19	)	)	PUNCT
ejpam-3527	181	20	)	)	PUNCT
ejpam-3527	182	1	=	=	PRON
ejpam-3527	182	2	(	(	PUNCT
ejpam-3527	182	3	a	a	PRON
ejpam-3527	182	4	·	·	SYM
ejpam-3527	182	5	b	b	X
ejpam-3527	182	6	)	)	PUNCT
ejpam-3527	182	7	∗	∗	NOUN
ejpam-3527	182	8	(	(	PUNCT
ejpam-3527	182	9	a	a	DET
ejpam-3527	182	10	·	·	PUNCT
ejpam-3527	182	11	c	c	X
ejpam-3527	182	12	)	)	PUNCT
ejpam-3527	182	13	and	and	CCONJ
ejpam-3527	182	14	(	(	PUNCT
ejpam-3527	182	15	b	b	NOUN
ejpam-3527	182	16	∗	∗	NOUN
ejpam-3527	182	17	(	(	PUNCT
ejpam-3527	182	18	0	0	NUM
ejpam-3527	182	19	∗	∗	NOUN
ejpam-3527	182	20	c	c	NOUN
ejpam-3527	182	21	)	)	PUNCT
ejpam-3527	182	22	)	)	PUNCT
ejpam-3527	182	23	·	·	PUNCT
ejpam-3527	183	1	a	a	DET
ejpam-3527	183	2	=	=	SYM
ejpam-3527	183	3	(	(	PUNCT
ejpam-3527	183	4	b	b	PROPN
ejpam-3527	183	5	·	·	PUNCT
ejpam-3527	183	6	a	a	X
ejpam-3527	183	7	)	)	PUNCT
ejpam-3527	183	8	∗	∗	NOUN
ejpam-3527	183	9	(	(	PUNCT
ejpam-3527	183	10	c	c	X
ejpam-3527	183	11	·	·	PUNCT
ejpam-3527	183	12	a	a	X
ejpam-3527	183	13	)	)	PUNCT
ejpam-3527	183	14	,	,	PUNCT
ejpam-3527	183	15	(	(	PUNCT
ejpam-3527	183	16	iv	iv	X
ejpam-3527	183	17	)	)	PUNCT
ejpam-3527	183	18	a	a	PRON
ejpam-3527	183	19	·	·	PUNCT
ejpam-3527	183	20	(	(	PUNCT
ejpam-3527	183	21	b	b	X
ejpam-3527	183	22	∧	∧	NOUN
ejpam-3527	183	23	c	c	NOUN
ejpam-3527	183	24	)	)	PUNCT
ejpam-3527	183	25	=	=	SYM
ejpam-3527	183	26	(	(	PUNCT
ejpam-3527	183	27	a	a	DET
ejpam-3527	183	28	·	·	SYM
ejpam-3527	183	29	b	b	X
ejpam-3527	183	30	)	)	PUNCT
ejpam-3527	183	31	∧	∧	NOUN
ejpam-3527	183	32	(	(	PUNCT
ejpam-3527	183	33	a	a	DET
ejpam-3527	183	34	·	·	PUNCT
ejpam-3527	183	35	c	c	X
ejpam-3527	183	36	)	)	PUNCT
ejpam-3527	183	37	and	and	CCONJ
ejpam-3527	183	38	(	(	PUNCT
ejpam-3527	183	39	a	a	DET
ejpam-3527	183	40	∧	∧	PROPN
ejpam-3527	183	41	b	b	NOUN
ejpam-3527	183	42	)	)	PUNCT
ejpam-3527	183	43	·	·	PUNCT
ejpam-3527	183	44	c	c	X
ejpam-3527	184	1	=	=	SYM
ejpam-3527	184	2	(	(	PUNCT
ejpam-3527	184	3	a	a	PRON
ejpam-3527	184	4	·	·	PUNCT
ejpam-3527	184	5	c	c	X
ejpam-3527	184	6	)	)	PUNCT
ejpam-3527	184	7	∧	∧	NOUN
ejpam-3527	184	8	(	(	PUNCT
ejpam-3527	184	9	b	b	PROPN
ejpam-3527	184	10	·	·	PUNCT
ejpam-3527	184	11	c	c	X
ejpam-3527	184	12	)	)	PUNCT
ejpam-3527	184	13	,	,	PUNCT
ejpam-3527	184	14	(	(	PUNCT
ejpam-3527	184	15	v	v	NOUN
ejpam-3527	184	16	)	)	PUNCT
ejpam-3527	184	17	if	if	SCONJ
ejpam-3527	184	18	a	a	DET
ejpam-3527	184	19	·	·	SYM
ejpam-3527	184	20	b	b	X
ejpam-3527	184	21	=	=	SYM
ejpam-3527	184	22	0	0	PROPN
ejpam-3527	184	23	,	,	PUNCT
ejpam-3527	184	24	then	then	ADV
ejpam-3527	184	25	a	a	PRON
ejpam-3527	184	26	·	·	PUNCT
ejpam-3527	184	27	(	(	PUNCT
ejpam-3527	184	28	b	b	NOUN
ejpam-3527	184	29	∗	∗	NOUN
ejpam-3527	184	30	c	c	NOUN
ejpam-3527	184	31	)	)	PUNCT
ejpam-3527	184	32	=	=	SYM
ejpam-3527	184	33	a	a	DET
ejpam-3527	184	34	·	·	PUNCT
ejpam-3527	184	35	c	c	X
ejpam-3527	184	36	,	,	PUNCT
ejpam-3527	184	37	(	(	PUNCT
ejpam-3527	184	38	vi	vi	NOUN
ejpam-3527	184	39	)	)	PUNCT
ejpam-3527	184	40	if	if	SCONJ
ejpam-3527	184	41	a	a	PRON
ejpam-3527	184	42	·	·	PUNCT
ejpam-3527	184	43	c	c	NOUN
ejpam-3527	184	44	=	=	SYM
ejpam-3527	184	45	0	0	NUM
ejpam-3527	184	46	,	,	PUNCT
ejpam-3527	184	47	then	then	ADV
ejpam-3527	184	48	(	(	PUNCT
ejpam-3527	184	49	a	a	DET
ejpam-3527	184	50	∗	∗	NOUN
ejpam-3527	184	51	b	b	NOUN
ejpam-3527	184	52	)	)	PUNCT
ejpam-3527	184	53	·	·	PUNCT
ejpam-3527	184	54	c	c	X
ejpam-3527	184	55	=	=	SYM
ejpam-3527	184	56	b	b	PROPN
ejpam-3527	184	57	·	·	PUNCT
ejpam-3527	184	58	c.	c.	NOUN
ejpam-3527	184	59	proof	proof	NOUN
ejpam-3527	184	60	.	.	PUNCT
ejpam-3527	185	1	let	let	VERB
ejpam-3527	185	2	a	a	DET
ejpam-3527	185	3	,	,	PUNCT
ejpam-3527	185	4	b	b	NOUN
ejpam-3527	185	5	,	,	PUNCT
ejpam-3527	185	6	c	c	PROPN
ejpam-3527	185	7	∈	∈	PROPN
ejpam-3527	185	8	x.	x.	NOUN
ejpam-3527	185	9	(	(	PUNCT
ejpam-3527	185	10	i	i	NOUN
ejpam-3527	185	11	)	)	PUNCT
ejpam-3527	185	12	by	by	ADP
ejpam-3527	185	13	proposition	proposition	NOUN
ejpam-3527	185	14	1(i	1(i	NUM
ejpam-3527	185	15	)	)	PUNCT
ejpam-3527	185	16	and	and	CCONJ
ejpam-3527	185	17	(	(	PUNCT
ejpam-3527	185	18	fup3	fup3	PROPN
ejpam-3527	185	19	)	)	PUNCT
ejpam-3527	185	20	,	,	PUNCT
ejpam-3527	185	21	a	a	PRON
ejpam-3527	185	22	·	·	SYM
ejpam-3527	185	23	0	0	NUM
ejpam-3527	186	1	=	=	PUNCT
ejpam-3527	186	2	a	a	DET
ejpam-3527	186	3	·	·	PUNCT
ejpam-3527	186	4	(	(	PUNCT
ejpam-3527	186	5	0	0	NUM
ejpam-3527	186	6	∗	∗	NOUN
ejpam-3527	186	7	0	0	NUM
ejpam-3527	186	8	)	)	PUNCT
ejpam-3527	186	9	=	=	NOUN
ejpam-3527	186	10	(	(	PUNCT
ejpam-3527	186	11	a	a	PRON
ejpam-3527	186	12	·	·	SYM
ejpam-3527	186	13	0	0	NUM
ejpam-3527	186	14	)	)	PUNCT
ejpam-3527	186	15	∗	∗	NOUN
ejpam-3527	186	16	(	(	PUNCT
ejpam-3527	186	17	a	a	PRON
ejpam-3527	186	18	·	·	PUNCT
ejpam-3527	186	19	0	0	NUM
ejpam-3527	186	20	)	)	PUNCT
ejpam-3527	186	21	=	=	SYM
ejpam-3527	186	22	0	0	X
ejpam-3527	186	23	.	.	PUNCT
ejpam-3527	187	1	similarly	similarly	ADV
ejpam-3527	187	2	,	,	PUNCT
ejpam-3527	187	3	0	0	NUM
ejpam-3527	187	4	·	·	PUNCT
ejpam-3527	187	5	a	a	X
ejpam-3527	187	6	=	=	NOUN
ejpam-3527	187	7	0	0	NUM
ejpam-3527	187	8	.	.	PUNCT
ejpam-3527	187	9	(	(	PUNCT
ejpam-3527	187	10	ii	ii	NOUN
ejpam-3527	187	11	)	)	PUNCT
ejpam-3527	187	12	by	by	ADP
ejpam-3527	187	13	(	(	PUNCT
ejpam-3527	187	14	up2	up2	PROPN
ejpam-3527	187	15	)	)	PUNCT
ejpam-3527	187	16	,	,	PUNCT
ejpam-3527	187	17	a	a	DET
ejpam-3527	187	18	·	·	PUNCT
ejpam-3527	187	19	(	(	PUNCT
ejpam-3527	187	20	0	0	NUM
ejpam-3527	187	21	∗	∗	NUM
ejpam-3527	187	22	b	b	NOUN
ejpam-3527	187	23	)	)	PUNCT
ejpam-3527	187	24	=	=	SYM
ejpam-3527	187	25	a	a	DET
ejpam-3527	187	26	·	·	PUNCT
ejpam-3527	187	27	b	b	X
ejpam-3527	187	28	=	=	SYM
ejpam-3527	187	29	(	(	PUNCT
ejpam-3527	187	30	0	0	NUM
ejpam-3527	187	31	∗	∗	NOUN
ejpam-3527	187	32	a	a	NOUN
ejpam-3527	187	33	)	)	PUNCT
ejpam-3527	187	34	·	·	PUNCT
ejpam-3527	187	35	b.	b.	PROPN
ejpam-3527	187	36	(	(	PUNCT
ejpam-3527	187	37	iii	iii	NOUN
ejpam-3527	187	38	)	)	PUNCT
ejpam-3527	187	39	by	by	ADP
ejpam-3527	187	40	(	(	PUNCT
ejpam-3527	187	41	up2	up2	PROPN
ejpam-3527	187	42	)	)	PUNCT
ejpam-3527	187	43	and	and	CCONJ
ejpam-3527	187	44	(	(	PUNCT
ejpam-3527	187	45	fup3	fup3	PROPN
ejpam-3527	187	46	)	)	PUNCT
ejpam-3527	187	47	,	,	PUNCT
ejpam-3527	187	48	a	a	DET
ejpam-3527	187	49	·	·	PUNCT
ejpam-3527	187	50	(	(	PUNCT
ejpam-3527	187	51	b	b	NOUN
ejpam-3527	187	52	∗	∗	NOUN
ejpam-3527	187	53	(	(	PUNCT
ejpam-3527	187	54	0	0	NUM
ejpam-3527	187	55	∗	∗	NOUN
ejpam-3527	187	56	c	c	NOUN
ejpam-3527	187	57	)	)	PUNCT
ejpam-3527	187	58	)	)	PUNCT
ejpam-3527	188	1	=	=	SYM
ejpam-3527	188	2	a	a	PRON
ejpam-3527	188	3	·	·	PUNCT
ejpam-3527	188	4	(	(	PUNCT
ejpam-3527	188	5	b	b	NOUN
ejpam-3527	188	6	∗	∗	NOUN
ejpam-3527	188	7	c	c	NOUN
ejpam-3527	188	8	)	)	PUNCT
ejpam-3527	188	9	=	=	SYM
ejpam-3527	188	10	(	(	PUNCT
ejpam-3527	188	11	a	a	DET
ejpam-3527	188	12	·	·	SYM
ejpam-3527	188	13	b	b	X
ejpam-3527	188	14	)	)	PUNCT
ejpam-3527	188	15	∗	∗	NOUN
ejpam-3527	188	16	(	(	PUNCT
ejpam-3527	188	17	a	a	DET
ejpam-3527	188	18	·	·	PUNCT
ejpam-3527	188	19	c	c	NOUN
ejpam-3527	188	20	)	)	PUNCT
ejpam-3527	188	21	.	.	PUNCT
ejpam-3527	189	1	similarly	similarly	ADV
ejpam-3527	189	2	,	,	PUNCT
ejpam-3527	189	3	(	(	PUNCT
ejpam-3527	189	4	b	b	NOUN
ejpam-3527	189	5	∗	∗	NOUN
ejpam-3527	189	6	(	(	PUNCT
ejpam-3527	189	7	0	0	NUM
ejpam-3527	189	8	∗	∗	NOUN
ejpam-3527	189	9	c	c	NOUN
ejpam-3527	189	10	)	)	PUNCT
ejpam-3527	189	11	)	)	PUNCT
ejpam-3527	189	12	·	·	PUNCT
ejpam-3527	190	1	a	a	X
ejpam-3527	190	2	=	=	SYM
ejpam-3527	190	3	(	(	PUNCT
ejpam-3527	190	4	b	b	NOUN
ejpam-3527	190	5	∗	∗	NOUN
ejpam-3527	190	6	c	c	NOUN
ejpam-3527	190	7	)	)	PUNCT
ejpam-3527	190	8	·	·	PUNCT
ejpam-3527	190	9	a	a	X
ejpam-3527	190	10	=	=	SYM
ejpam-3527	190	11	(	(	PUNCT
ejpam-3527	190	12	b	b	PROPN
ejpam-3527	190	13	·	·	PUNCT
ejpam-3527	190	14	a	a	X
ejpam-3527	190	15	)	)	PUNCT
ejpam-3527	190	16	∗	∗	NOUN
ejpam-3527	190	17	(	(	PUNCT
ejpam-3527	190	18	c	c	X
ejpam-3527	190	19	·	·	PUNCT
ejpam-3527	190	20	a	a	X
ejpam-3527	190	21	)	)	PUNCT
ejpam-3527	190	22	.	.	PUNCT
ejpam-3527	191	1	(	(	PUNCT
ejpam-3527	191	2	iv	iv	X
ejpam-3527	191	3	)	)	PUNCT
ejpam-3527	191	4	by	by	ADP
ejpam-3527	191	5	definition	definition	NOUN
ejpam-3527	191	6	4	4	NUM
ejpam-3527	191	7	and	and	CCONJ
ejpam-3527	191	8	(	(	PUNCT
ejpam-3527	191	9	fup3	fup3	PROPN
ejpam-3527	191	10	)	)	PUNCT
ejpam-3527	191	11	,	,	PUNCT
ejpam-3527	191	12	a	a	DET
ejpam-3527	191	13	·	·	PUNCT
ejpam-3527	191	14	(	(	PUNCT
ejpam-3527	191	15	b	b	X
ejpam-3527	191	16	∧	∧	NOUN
ejpam-3527	191	17	c	c	NOUN
ejpam-3527	191	18	)	)	PUNCT
ejpam-3527	191	19	=	=	SYM
ejpam-3527	192	1	a	a	PRON
ejpam-3527	192	2	·	·	PUNCT
ejpam-3527	193	1	[	[	X
ejpam-3527	193	2	(	(	PUNCT
ejpam-3527	193	3	c	c	NOUN
ejpam-3527	193	4	∗	∗	X
ejpam-3527	193	5	b	b	NOUN
ejpam-3527	193	6	)	)	PUNCT
ejpam-3527	193	7	∗	∗	NOUN
ejpam-3527	193	8	b	b	NOUN
ejpam-3527	193	9	]	]	X
ejpam-3527	193	10	=	=	PUNCT
ejpam-3527	194	1	[	[	X
ejpam-3527	194	2	a	a	X
ejpam-3527	194	3	·	·	PUNCT
ejpam-3527	194	4	(	(	PUNCT
ejpam-3527	194	5	c	c	NOUN
ejpam-3527	194	6	∗	∗	X
ejpam-3527	194	7	b	b	NOUN
ejpam-3527	194	8	)	)	PUNCT
ejpam-3527	194	9	]	]	PUNCT
ejpam-3527	194	10	∗	∗	NOUN
ejpam-3527	194	11	(	(	PUNCT
ejpam-3527	194	12	a	a	DET
ejpam-3527	194	13	·	·	SYM
ejpam-3527	194	14	b	b	X
ejpam-3527	194	15	)	)	PUNCT
ejpam-3527	194	16	=	=	SYM
ejpam-3527	195	1	[	[	X
ejpam-3527	195	2	(	(	PUNCT
ejpam-3527	195	3	a	a	DET
ejpam-3527	195	4	·	·	PUNCT
ejpam-3527	195	5	c)∗(a	c)∗(a	NOUN
ejpam-3527	195	6	·	·	PUNCT
ejpam-3527	195	7	b)]∗(a	b)]∗(a	X
ejpam-3527	195	8	·	·	SYM
ejpam-3527	195	9	b	b	NOUN
ejpam-3527	195	10	)	)	PUNCT
ejpam-3527	195	11	=	=	SYM
ejpam-3527	195	12	(	(	PUNCT
ejpam-3527	195	13	a	a	DET
ejpam-3527	195	14	·	·	PUNCT
ejpam-3527	195	15	b)∧(a	b)∧(a	X
ejpam-3527	195	16	·	·	SYM
ejpam-3527	195	17	c	c	X
ejpam-3527	195	18	)	)	PUNCT
ejpam-3527	195	19	and	and	CCONJ
ejpam-3527	195	20	(	(	PUNCT
ejpam-3527	195	21	a∧b	a∧b	PROPN
ejpam-3527	195	22	)	)	PUNCT
ejpam-3527	195	23	·	·	PUNCT
ejpam-3527	195	24	c	c	X
ejpam-3527	195	25	=	=	SYM
ejpam-3527	196	1	[	[	X
ejpam-3527	196	2	(	(	PUNCT
ejpam-3527	196	3	b∗a)∗a	b∗a)∗a	NOUN
ejpam-3527	196	4	]	]	PUNCT
ejpam-3527	196	5	·	·	PUNCT
ejpam-3527	196	6	c	c	X
ejpam-3527	196	7	=	=	SYM
ejpam-3527	197	1	[	[	X
ejpam-3527	197	2	(	(	PUNCT
ejpam-3527	197	3	b∗a	b∗a	X
ejpam-3527	197	4	)	)	PUNCT
ejpam-3527	197	5	·	·	PUNCT
ejpam-3527	197	6	c]∗(a	c]∗(a	NOUN
ejpam-3527	197	7	·	·	SYM
ejpam-3527	197	8	c	c	NOUN
ejpam-3527	197	9	)	)	PUNCT
ejpam-3527	197	10	=	=	PUNCT
ejpam-3527	198	1	[	[	X
ejpam-3527	198	2	(	(	PUNCT
ejpam-3527	198	3	b	b	PROPN
ejpam-3527	198	4	·	·	PUNCT
ejpam-3527	198	5	c	c	X
ejpam-3527	198	6	)	)	PUNCT
ejpam-3527	198	7	∗	∗	NOUN
ejpam-3527	198	8	(	(	PUNCT
ejpam-3527	198	9	a	a	DET
ejpam-3527	198	10	·	·	PUNCT
ejpam-3527	198	11	c	c	NOUN
ejpam-3527	198	12	)	)	PUNCT
ejpam-3527	198	13	]	]	PUNCT
ejpam-3527	198	14	∗	∗	NOUN
ejpam-3527	198	15	(	(	PUNCT
ejpam-3527	198	16	a	a	DET
ejpam-3527	198	17	·	·	PUNCT
ejpam-3527	198	18	c	c	X
ejpam-3527	198	19	)	)	PUNCT
ejpam-3527	198	20	=	=	SYM
ejpam-3527	198	21	(	(	PUNCT
ejpam-3527	198	22	a	a	PRON
ejpam-3527	198	23	·	·	PUNCT
ejpam-3527	198	24	c	c	X
ejpam-3527	198	25	)	)	PUNCT
ejpam-3527	198	26	∧	∧	NOUN
ejpam-3527	198	27	(	(	PUNCT
ejpam-3527	198	28	b	b	PROPN
ejpam-3527	198	29	·	·	PUNCT
ejpam-3527	198	30	c	c	X
ejpam-3527	198	31	)	)	PUNCT
ejpam-3527	198	32	.	.	PUNCT
ejpam-3527	199	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	199	2	,	,	PUNCT
ejpam-3527	199	3	r.	r.	PROPN
ejpam-3527	199	4	isla	isla	PROPN
ejpam-3527	199	5	/	/	SYM
ejpam-3527	199	6	eur	eur	PROPN
ejpam-3527	199	7	.	.	PUNCT
ejpam-3527	200	1	j.	j.	PROPN
ejpam-3527	200	2	pure	pure	PROPN
ejpam-3527	200	3	appl	appl	PROPN
ejpam-3527	200	4	.	.	PROPN
ejpam-3527	200	5	math	math	PROPN
ejpam-3527	200	6	,	,	PUNCT
ejpam-3527	200	7	12	12	NUM
ejpam-3527	200	8	(	(	PUNCT
ejpam-3527	200	9	4	4	NUM
ejpam-3527	200	10	)	)	PUNCT
ejpam-3527	200	11	(	(	PUNCT
ejpam-3527	200	12	2019	2019	NUM
ejpam-3527	200	13	)	)	PUNCT
ejpam-3527	200	14	,	,	PUNCT
ejpam-3527	200	15	1483	1483	NUM
ejpam-3527	200	16	-	-	SYM
ejpam-3527	200	17	1496	1496	NUM
ejpam-3527	200	18	1490	1490	NUM
ejpam-3527	200	19	(	(	PUNCT
ejpam-3527	200	20	v	v	NOUN
ejpam-3527	200	21	)	)	PUNCT
ejpam-3527	200	22	suppose	suppose	VERB
ejpam-3527	200	23	a·b	a·b	NOUN
ejpam-3527	200	24	=	=	SYM
ejpam-3527	200	25	0	0	X
ejpam-3527	200	26	.	.	PUNCT
ejpam-3527	201	1	then	then	ADV
ejpam-3527	201	2	by	by	ADP
ejpam-3527	201	3	(	(	PUNCT
ejpam-3527	201	4	fup3	fup3	PROPN
ejpam-3527	201	5	)	)	PUNCT
ejpam-3527	201	6	and	and	CCONJ
ejpam-3527	201	7	(	(	PUNCT
ejpam-3527	201	8	up2	up2	NOUN
ejpam-3527	201	9	)	)	PUNCT
ejpam-3527	201	10	,	,	PUNCT
ejpam-3527	201	11	a·(b∗c	a·(b∗c	PUNCT
ejpam-3527	201	12	)	)	PUNCT
ejpam-3527	201	13	=	=	SYM
ejpam-3527	201	14	(	(	PUNCT
ejpam-3527	201	15	a·b)∗(a·c	a·b)∗(a·c	NOUN
ejpam-3527	201	16	)	)	PUNCT
ejpam-3527	201	17	=	=	NUM
ejpam-3527	201	18	0∗(a·c	0∗(a·c	NOUN
ejpam-3527	201	19	)	)	PUNCT
ejpam-3527	201	20	=	=	SYM
ejpam-3527	201	21	a·c	a·c	NOUN
ejpam-3527	201	22	.	.	PUNCT
ejpam-3527	202	1	(	(	PUNCT
ejpam-3527	202	2	vi	vi	X
ejpam-3527	202	3	)	)	PUNCT
ejpam-3527	202	4	if	if	SCONJ
ejpam-3527	202	5	a	a	DET
ejpam-3527	202	6	·	·	SYM
ejpam-3527	202	7	c	c	NOUN
ejpam-3527	202	8	=	=	SYM
ejpam-3527	202	9	0	0	NUM
ejpam-3527	202	10	,	,	PUNCT
ejpam-3527	202	11	then	then	ADV
ejpam-3527	202	12	by	by	ADP
ejpam-3527	202	13	(	(	PUNCT
ejpam-3527	202	14	fup3	fup3	PROPN
ejpam-3527	202	15	)	)	PUNCT
ejpam-3527	202	16	and	and	CCONJ
ejpam-3527	202	17	(	(	PUNCT
ejpam-3527	202	18	up2	up2	NOUN
ejpam-3527	202	19	)	)	PUNCT
ejpam-3527	202	20	,	,	PUNCT
ejpam-3527	202	21	(	(	PUNCT
ejpam-3527	202	22	a∗b	a∗b	NUM
ejpam-3527	202	23	)	)	PUNCT
ejpam-3527	202	24	·	·	PUNCT
ejpam-3527	202	25	c	c	X
ejpam-3527	202	26	=	=	SYM
ejpam-3527	202	27	(	(	PUNCT
ejpam-3527	202	28	a	a	DET
ejpam-3527	202	29	·	·	SYM
ejpam-3527	202	30	c)∗(b	c)∗(b	PROPN
ejpam-3527	202	31	·	·	SYM
ejpam-3527	202	32	c	c	X
ejpam-3527	202	33	)	)	PUNCT
ejpam-3527	203	1	=	=	PUNCT
ejpam-3527	204	1	0∗(b	0∗(b	PUNCT
ejpam-3527	204	2	·	·	PUNCT
ejpam-3527	204	3	c	c	X
ejpam-3527	204	4	)	)	PUNCT
ejpam-3527	204	5	=	=	SYM
ejpam-3527	204	6	b	b	X
ejpam-3527	204	7	·	·	PUNCT
ejpam-3527	204	8	c.	c.	NOUN
ejpam-3527	204	9	the	the	DET
ejpam-3527	204	10	following	follow	VERB
ejpam-3527	204	11	theorem	theorem	NOUN
ejpam-3527	204	12	gives	give	VERB
ejpam-3527	204	13	a	a	DET
ejpam-3527	204	14	necessary	necessary	ADJ
ejpam-3527	204	15	and	and	CCONJ
ejpam-3527	204	16	sufficient	sufficient	ADJ
ejpam-3527	204	17	condition	condition	NOUN
ejpam-3527	204	18	for	for	ADP
ejpam-3527	204	19	a	a	DET
ejpam-3527	204	20	subset	subset	NOUN
ejpam-3527	204	21	of	of	ADP
ejpam-3527	204	22	an	an	DET
ejpam-3527	204	23	f	f	PROPN
ejpam-3527	204	24	-up	-up	NOUN
ejpam-3527	204	25	-	-	PUNCT
ejpam-3527	204	26	semigroup	semigroup	NOUN
ejpam-3527	204	27	to	to	PART
ejpam-3527	204	28	be	be	AUX
ejpam-3527	204	29	an	an	DET
ejpam-3527	204	30	f	f	PROPN
ejpam-3527	204	31	-up	-up	NOUN
ejpam-3527	204	32	-	-	NOUN
ejpam-3527	204	33	subsemigroup	subsemigroup	NOUN
ejpam-3527	204	34	.	.	PUNCT
ejpam-3527	205	1	theorem	theorem	ADJ
ejpam-3527	205	2	5	5	NUM
ejpam-3527	205	3	.	.	PUNCT
ejpam-3527	206	1	a	a	DET
ejpam-3527	206	2	nonempty	nonempty	ADJ
ejpam-3527	206	3	subset	subset	VERB
ejpam-3527	206	4	s	s	NOUN
ejpam-3527	206	5	of	of	ADP
ejpam-3527	206	6	an	an	DET
ejpam-3527	206	7	f	f	PROPN
ejpam-3527	206	8	-up	-up	NOUN
ejpam-3527	206	9	-	-	NOUN
ejpam-3527	206	10	semigroup	semigroup	NOUN
ejpam-3527	206	11	(	(	PUNCT
ejpam-3527	206	12	x	x	NOUN
ejpam-3527	206	13	;	;	PUNCT
ejpam-3527	206	14	∗	∗	NOUN
ejpam-3527	206	15	,	,	PUNCT
ejpam-3527	206	16	·	·	PUNCT
ejpam-3527	206	17	,	,	PUNCT
ejpam-3527	206	18	0	0	NUM
ejpam-3527	206	19	)	)	PUNCT
ejpam-3527	206	20	is	be	AUX
ejpam-3527	206	21	an	an	DET
ejpam-3527	206	22	f	f	PROPN
ejpam-3527	206	23	-up	-up	NOUN
ejpam-3527	206	24	-	-	PROPN
ejpam-3527	206	25	subsemigroup	subsemigroup	NOUN
ejpam-3527	206	26	of	of	ADP
ejpam-3527	206	27	x	x	SYM
ejpam-3527	206	28	if	if	SCONJ
ejpam-3527	207	1	and	and	CCONJ
ejpam-3527	207	2	only	only	ADV
ejpam-3527	207	3	if	if	SCONJ
ejpam-3527	207	4	x	x	X
ejpam-3527	207	5	∗	∗	VERB
ejpam-3527	207	6	y	y	PROPN
ejpam-3527	207	7	,	,	PUNCT
ejpam-3527	207	8	x	x	X
ejpam-3527	207	9	·	·	PUNCT
ejpam-3527	207	10	y	y	X
ejpam-3527	207	11	∈	∈	PROPN
ejpam-3527	207	12	s	s	X
ejpam-3527	207	13	for	for	ADP
ejpam-3527	207	14	all	all	DET
ejpam-3527	207	15	x	x	NOUN
ejpam-3527	207	16	,	,	PUNCT
ejpam-3527	207	17	y	y	PROPN
ejpam-3527	207	18	∈	∈	PROPN
ejpam-3527	207	19	s.	s.	PROPN
ejpam-3527	207	20	proof	proof	PROPN
ejpam-3527	207	21	.	.	PUNCT
ejpam-3527	208	1	let	let	VERB
ejpam-3527	208	2	∅	∅	NOUN
ejpam-3527	208	3	6=	6=	ADP
ejpam-3527	208	4	s	s	NOUN
ejpam-3527	208	5	⊆	⊆	NUM
ejpam-3527	208	6	x.	x.	NOUN
ejpam-3527	208	7	suppose	suppose	VERB
ejpam-3527	208	8	s	s	NOUN
ejpam-3527	208	9	is	be	AUX
ejpam-3527	208	10	an	an	DET
ejpam-3527	208	11	f	f	PROPN
ejpam-3527	208	12	-up	-up	NOUN
ejpam-3527	208	13	-	-	PROPN
ejpam-3527	208	14	subsemigroup	subsemigroup	NOUN
ejpam-3527	208	15	of	of	ADP
ejpam-3527	208	16	x.	x.	NOUN
ejpam-3527	208	17	then	then	ADV
ejpam-3527	208	18	by	by	ADP
ejpam-3527	208	19	definition	definition	NOUN
ejpam-3527	208	20	8	8	NUM
ejpam-3527	208	21	,	,	PUNCT
ejpam-3527	208	22	(	(	PUNCT
ejpam-3527	208	23	s	s	X
ejpam-3527	208	24	;	;	PUNCT
ejpam-3527	208	25	∗	∗	NOUN
ejpam-3527	208	26	,	,	PUNCT
ejpam-3527	208	27	·	·	PUNCT
ejpam-3527	208	28	,	,	PUNCT
ejpam-3527	208	29	0	0	NUM
ejpam-3527	208	30	)	)	PUNCT
ejpam-3527	208	31	is	be	AUX
ejpam-3527	208	32	an	an	DET
ejpam-3527	208	33	f	f	PROPN
ejpam-3527	208	34	-up	-up	NOUN
ejpam-3527	208	35	-	-	PUNCT
ejpam-3527	208	36	semigroup	semigroup	NOUN
ejpam-3527	208	37	.	.	PUNCT
ejpam-3527	209	1	thus	thus	ADV
ejpam-3527	209	2	,	,	PUNCT
ejpam-3527	209	3	the	the	DET
ejpam-3527	209	4	binary	binary	ADJ
ejpam-3527	209	5	operations	operation	NOUN
ejpam-3527	209	6	∗	∗	NOUN
ejpam-3527	209	7	and	and	CCONJ
ejpam-3527	209	8	·	·	PUNCT
ejpam-3527	209	9	are	be	AUX
ejpam-3527	209	10	closed	close	VERB
ejpam-3527	209	11	in	in	ADP
ejpam-3527	209	12	s	s	PROPN
ejpam-3527	209	13	,	,	PUNCT
ejpam-3527	209	14	that	that	ADV
ejpam-3527	209	15	is	is	ADV
ejpam-3527	209	16	,	,	PUNCT
ejpam-3527	209	17	x∗y	x∗y	X
ejpam-3527	209	18	,	,	PUNCT
ejpam-3527	209	19	x	x	X
ejpam-3527	209	20	·	·	PUNCT
ejpam-3527	209	21	y	y	PROPN
ejpam-3527	209	22	∈	∈	PROPN
ejpam-3527	209	23	s	s	X
ejpam-3527	209	24	for	for	ADP
ejpam-3527	209	25	all	all	DET
ejpam-3527	209	26	x	x	NOUN
ejpam-3527	209	27	,	,	PUNCT
ejpam-3527	209	28	y	y	PROPN
ejpam-3527	209	29	∈	∈	PROPN
ejpam-3527	209	30	s.	s.	PROPN
ejpam-3527	209	31	conversely	conversely	ADV
ejpam-3527	209	32	,	,	PUNCT
ejpam-3527	209	33	suppose	suppose	VERB
ejpam-3527	209	34	x∗y	x∗y	X
ejpam-3527	209	35	,	,	PUNCT
ejpam-3527	209	36	x	x	X
ejpam-3527	209	37	·	·	PUNCT
ejpam-3527	209	38	y	y	PROPN
ejpam-3527	209	39	∈	∈	PROPN
ejpam-3527	209	40	s	s	X
ejpam-3527	209	41	for	for	ADP
ejpam-3527	209	42	all	all	DET
ejpam-3527	209	43	x	x	NOUN
ejpam-3527	209	44	,	,	PUNCT
ejpam-3527	209	45	y	y	PROPN
ejpam-3527	209	46	∈	∈	PROPN
ejpam-3527	209	47	s.	s.	PROPN
ejpam-3527	209	48	then	then	ADV
ejpam-3527	209	49	0	0	NUM
ejpam-3527	210	1	=	=	SYM
ejpam-3527	210	2	x	x	SYM
ejpam-3527	210	3	∗	∗	NOUN
ejpam-3527	210	4	x	x	SYM
ejpam-3527	210	5	∈	∈	PROPN
ejpam-3527	210	6	s.	s.	PROPN
ejpam-3527	210	7	by	by	ADP
ejpam-3527	210	8	proposition	proposition	NOUN
ejpam-3527	210	9	2	2	NUM
ejpam-3527	210	10	,	,	PUNCT
ejpam-3527	210	11	(	(	PUNCT
ejpam-3527	210	12	s	s	X
ejpam-3527	210	13	;	;	PUNCT
ejpam-3527	210	14	∗	∗	NOUN
ejpam-3527	210	15	,	,	PUNCT
ejpam-3527	210	16	0	0	NUM
ejpam-3527	210	17	)	)	PUNCT
ejpam-3527	210	18	is	be	AUX
ejpam-3527	210	19	a	a	DET
ejpam-3527	210	20	up	up	ADJ
ejpam-3527	210	21	-	-	PUNCT
ejpam-3527	210	22	subalgebra	subalgebra	NOUN
ejpam-3527	210	23	of	of	ADP
ejpam-3527	210	24	x	x	PRON
ejpam-3527	210	25	,	,	PUNCT
ejpam-3527	210	26	hence	hence	ADV
ejpam-3527	210	27	(	(	PUNCT
ejpam-3527	210	28	fup1	fup1	PROPN
ejpam-3527	210	29	)	)	PUNCT
ejpam-3527	210	30	holds	hold	VERB
ejpam-3527	210	31	.	.	PUNCT
ejpam-3527	211	1	let	let	VERB
ejpam-3527	211	2	x	x	PRON
ejpam-3527	211	3	,	,	PUNCT
ejpam-3527	211	4	y	y	PROPN
ejpam-3527	211	5	,	,	PUNCT
ejpam-3527	211	6	z	z	PROPN
ejpam-3527	211	7	∈	∈	PROPN
ejpam-3527	211	8	s	s	PART
ejpam-3527	211	9	⊆	⊆	NUM
ejpam-3527	211	10	x.	x.	NOUN
ejpam-3527	211	11	then	then	ADV
ejpam-3527	211	12	x	x	X
ejpam-3527	211	13	·	·	PUNCT
ejpam-3527	211	14	y	y	X
ejpam-3527	211	15	∈	∈	PROPN
ejpam-3527	211	16	s	s	VERB
ejpam-3527	211	17	by	by	ADP
ejpam-3527	211	18	our	our	PRON
ejpam-3527	211	19	assumption	assumption	NOUN
ejpam-3527	211	20	and	and	CCONJ
ejpam-3527	212	1	x	x	SYM
ejpam-3527	212	2	·	·	PUNCT
ejpam-3527	212	3	(	(	PUNCT
ejpam-3527	212	4	y	y	PROPN
ejpam-3527	212	5	·	·	PUNCT
ejpam-3527	212	6	z	z	X
ejpam-3527	212	7	)	)	PUNCT
ejpam-3527	212	8	=	=	SYM
ejpam-3527	212	9	(	(	PUNCT
ejpam-3527	212	10	x	x	X
ejpam-3527	212	11	·	·	PUNCT
ejpam-3527	212	12	y	y	X
ejpam-3527	212	13	)	)	PUNCT
ejpam-3527	212	14	·	·	PUNCT
ejpam-3527	212	15	z	z	NOUN
ejpam-3527	212	16	by	by	ADP
ejpam-3527	212	17	associativity	associativity	NOUN
ejpam-3527	212	18	in	in	ADP
ejpam-3527	212	19	x.	x.	PROPN
ejpam-3527	212	20	hence	hence	ADV
ejpam-3527	212	21	,	,	PUNCT
ejpam-3527	212	22	(	(	PUNCT
ejpam-3527	212	23	s	s	X
ejpam-3527	212	24	,	,	PUNCT
ejpam-3527	212	25	·	·	PUNCT
ejpam-3527	212	26	)	)	PUNCT
ejpam-3527	212	27	is	be	AUX
ejpam-3527	212	28	a	a	DET
ejpam-3527	212	29	semigroup	semigroup	NOUN
ejpam-3527	212	30	and	and	CCONJ
ejpam-3527	212	31	(	(	PUNCT
ejpam-3527	212	32	fup2	fup2	ADJ
ejpam-3527	212	33	)	)	PUNCT
ejpam-3527	212	34	is	be	AUX
ejpam-3527	212	35	satisfied	satisfied	ADJ
ejpam-3527	212	36	.	.	PUNCT
ejpam-3527	213	1	moreover	moreover	ADV
ejpam-3527	213	2	,	,	PUNCT
ejpam-3527	213	3	(	(	PUNCT
ejpam-3527	213	4	fup3	fup3	PROPN
ejpam-3527	213	5	)	)	PUNCT
ejpam-3527	213	6	holds	hold	VERB
ejpam-3527	213	7	for	for	ADP
ejpam-3527	213	8	all	all	DET
ejpam-3527	213	9	x	x	NOUN
ejpam-3527	213	10	,	,	PUNCT
ejpam-3527	213	11	y	y	PROPN
ejpam-3527	213	12	,	,	PUNCT
ejpam-3527	213	13	z	z	PROPN
ejpam-3527	213	14	∈	∈	PROPN
ejpam-3527	213	15	s	s	PART
ejpam-3527	213	16	⊆	⊆	NUM
ejpam-3527	213	17	x.	x.	NOUN
ejpam-3527	213	18	thus	thus	ADV
ejpam-3527	213	19	,	,	PUNCT
ejpam-3527	213	20	s	s	VERB
ejpam-3527	213	21	is	be	AUX
ejpam-3527	213	22	an	an	DET
ejpam-3527	213	23	f	f	PROPN
ejpam-3527	213	24	-up	-up	NOUN
ejpam-3527	213	25	-	-	PROPN
ejpam-3527	213	26	subsemigroup	subsemigroup	NOUN
ejpam-3527	213	27	of	of	ADP
ejpam-3527	213	28	x.	x.	PROPN
ejpam-3527	213	29	theorem	theorem	VERB
ejpam-3527	213	30	6	6	NUM
ejpam-3527	213	31	.	.	PUNCT
ejpam-3527	214	1	let	let	VERB
ejpam-3527	214	2	x	x	PRON
ejpam-3527	214	3	be	be	AUX
ejpam-3527	214	4	an	an	DET
ejpam-3527	214	5	f	f	PROPN
ejpam-3527	214	6	-up	-up	NOUN
ejpam-3527	214	7	-	-	PUNCT
ejpam-3527	214	8	semigroup	semigroup	NOUN
ejpam-3527	214	9	and	and	CCONJ
ejpam-3527	214	10	{	{	PUNCT
ejpam-3527	214	11	ai	ai	INTJ
ejpam-3527	214	12	:	:	PUNCT
ejpam-3527	214	13	i	i	PRON
ejpam-3527	214	14	∈	∈	VERB
ejpam-3527	215	1	i	i	PRON
ejpam-3527	215	2	}	}	PUNCT
ejpam-3527	215	3	a	a	DET
ejpam-3527	215	4	family	family	NOUN
ejpam-3527	215	5	of	of	ADP
ejpam-3527	215	6	f	f	PROPN
ejpam-3527	215	7	-up	-up	NOUN
ejpam-3527	215	8	-	-	PUNCT
ejpam-3527	215	9	subsemigroups	subsemigroup	NOUN
ejpam-3527	215	10	of	of	ADP
ejpam-3527	215	11	x.	x.	NOUN
ejpam-3527	216	1	then	then	ADV
ejpam-3527	216	2	⋂	⋂	PROPN
ejpam-3527	216	3	i∈i	i∈i	NOUN
ejpam-3527	216	4	ai	ai	VERB
ejpam-3527	216	5	is	be	AUX
ejpam-3527	216	6	an	an	DET
ejpam-3527	216	7	f	f	PROPN
ejpam-3527	216	8	-up	-up	NOUN
ejpam-3527	216	9	-	-	PROPN
ejpam-3527	216	10	subsemigroup	subsemigroup	NOUN
ejpam-3527	216	11	of	of	ADP
ejpam-3527	216	12	x.	x.	NOUN
ejpam-3527	216	13	proof	proof	NOUN
ejpam-3527	216	14	.	.	PUNCT
ejpam-3527	217	1	since	since	SCONJ
ejpam-3527	217	2	ai	ai	NOUN
ejpam-3527	217	3	is	be	AUX
ejpam-3527	217	4	an	an	DET
ejpam-3527	217	5	f	f	PROPN
ejpam-3527	217	6	-up	-up	NOUN
ejpam-3527	217	7	-	-	PROPN
ejpam-3527	217	8	subsemigroup	subsemigroup	NOUN
ejpam-3527	217	9	of	of	ADP
ejpam-3527	217	10	x	x	PROPN
ejpam-3527	217	11	,	,	PUNCT
ejpam-3527	217	12	0	0	NUM
ejpam-3527	217	13	∈	∈	NOUN
ejpam-3527	217	14	ai	ai	VERB
ejpam-3527	217	15	for	for	ADP
ejpam-3527	217	16	all	all	PRON
ejpam-3527	217	17	i	i	PRON
ejpam-3527	217	18	∈	∈	PROPN
ejpam-3527	217	19	i.	i.	NOUN
ejpam-3527	217	20	thus	thus	ADV
ejpam-3527	217	21	,	,	PUNCT
ejpam-3527	217	22	0	0	NUM
ejpam-3527	217	23	∈	∈	PROPN
ejpam-3527	217	24	⋂	⋂	PROPN
ejpam-3527	217	25	i∈i	i∈i	ADJ
ejpam-3527	217	26	ai	ai	VERB
ejpam-3527	217	27	and	and	CCONJ
ejpam-3527	217	28	⋂	⋂	PROPN
ejpam-3527	217	29	i∈i	i∈i	ADJ
ejpam-3527	217	30	ai	ai	VERB
ejpam-3527	217	31	6=	6=	ADP
ejpam-3527	217	32	∅.	∅.	AUX
ejpam-3527	217	33	let	let	VERB
ejpam-3527	217	34	x	x	PRON
ejpam-3527	217	35	,	,	PUNCT
ejpam-3527	217	36	y	y	PROPN
ejpam-3527	217	37	∈	∈	PROPN
ejpam-3527	217	38	⋂	⋂	PROPN
ejpam-3527	217	39	i∈i	i∈i	ADJ
ejpam-3527	217	40	ai	ai	VERB
ejpam-3527	217	41	.	.	PUNCT
ejpam-3527	218	1	then	then	ADV
ejpam-3527	218	2	for	for	ADP
ejpam-3527	218	3	all	all	PRON
ejpam-3527	218	4	i	i	PRON
ejpam-3527	218	5	∈	∈	PROPN
ejpam-3527	219	1	i	i	PRON
ejpam-3527	219	2	,	,	PUNCT
ejpam-3527	219	3	x	x	PROPN
ejpam-3527	219	4	,	,	PUNCT
ejpam-3527	219	5	y	y	PROPN
ejpam-3527	219	6	∈	∈	PROPN
ejpam-3527	219	7	ai	ai	VERB
ejpam-3527	219	8	and	and	CCONJ
ejpam-3527	219	9	by	by	ADP
ejpam-3527	219	10	theorem	theorem	NOUN
ejpam-3527	219	11	5	5	NUM
ejpam-3527	219	12	,	,	PUNCT
ejpam-3527	219	13	x	x	X
ejpam-3527	219	14	∗	∗	NOUN
ejpam-3527	219	15	y	y	PROPN
ejpam-3527	219	16	,	,	PUNCT
ejpam-3527	219	17	x	x	X
ejpam-3527	219	18	·	·	PUNCT
ejpam-3527	219	19	y	y	X
ejpam-3527	219	20	∈	∈	PROPN
ejpam-3527	219	21	ai	ai	VERB
ejpam-3527	219	22	.	.	PUNCT
ejpam-3527	220	1	hence	hence	ADV
ejpam-3527	220	2	,	,	PUNCT
ejpam-3527	220	3	x	x	PROPN
ejpam-3527	220	4	∗	∗	NOUN
ejpam-3527	220	5	y	y	PROPN
ejpam-3527	220	6	,	,	PUNCT
ejpam-3527	220	7	x	x	X
ejpam-3527	220	8	·	·	PUNCT
ejpam-3527	220	9	y	y	PROPN
ejpam-3527	220	10	∈	∈	PROPN
ejpam-3527	220	11	⋂	⋂	PROPN
ejpam-3527	220	12	i∈i	i∈i	ADJ
ejpam-3527	220	13	ai	ai	VERB
ejpam-3527	220	14	.	.	PUNCT
ejpam-3527	221	1	therefore	therefore	ADV
ejpam-3527	221	2	,	,	PUNCT
ejpam-3527	221	3	⋂	⋂	PROPN
ejpam-3527	221	4	i∈i	i∈i	ADJ
ejpam-3527	221	5	ai	ai	VERB
ejpam-3527	221	6	is	be	AUX
ejpam-3527	221	7	an	an	DET
ejpam-3527	221	8	f	f	PROPN
ejpam-3527	221	9	-up	-up	NOUN
ejpam-3527	221	10	-	-	PROPN
ejpam-3527	221	11	subsemigroup	subsemigroup	NOUN
ejpam-3527	221	12	of	of	ADP
ejpam-3527	221	13	x.	x.	NOUN
ejpam-3527	222	1	the	the	DET
ejpam-3527	222	2	next	next	ADJ
ejpam-3527	222	3	result	result	NOUN
ejpam-3527	222	4	shows	show	VERB
ejpam-3527	222	5	a	a	DET
ejpam-3527	222	6	relationship	relationship	NOUN
ejpam-3527	222	7	between	between	ADP
ejpam-3527	222	8	ku	ku	PROPN
ejpam-3527	222	9	-	-	PUNCT
ejpam-3527	222	10	semigroups	semigroup	NOUN
ejpam-3527	222	11	and	and	CCONJ
ejpam-3527	222	12	f	f	PROPN
ejpam-3527	222	13	-up	-up	NOUN
ejpam-3527	222	14	-	-	PUNCT
ejpam-3527	222	15	semigroups	semigroup	NOUN
ejpam-3527	222	16	.	.	PUNCT
ejpam-3527	223	1	theorem	theorem	NOUN
ejpam-3527	223	2	7	7	NUM
ejpam-3527	223	3	.	.	PUNCT
ejpam-3527	224	1	any	any	DET
ejpam-3527	224	2	ku	ku	PROPN
ejpam-3527	224	3	-	-	PUNCT
ejpam-3527	224	4	semigroup	semigroup	PROPN
ejpam-3527	224	5	is	be	AUX
ejpam-3527	224	6	an	an	DET
ejpam-3527	224	7	f	f	PROPN
ejpam-3527	224	8	-up	-up	NOUN
ejpam-3527	224	9	-	-	PUNCT
ejpam-3527	224	10	semigroup	semigroup	NOUN
ejpam-3527	224	11	.	.	PUNCT
ejpam-3527	225	1	proof	proof	NOUN
ejpam-3527	225	2	.	.	PUNCT
ejpam-3527	226	1	let	let	VERB
ejpam-3527	226	2	x	x	PUNCT
ejpam-3527	226	3	=	=	SYM
ejpam-3527	226	4	(	(	PUNCT
ejpam-3527	226	5	x	x	NOUN
ejpam-3527	226	6	;	;	PUNCT
ejpam-3527	226	7	∗	∗	NOUN
ejpam-3527	226	8	,	,	PUNCT
ejpam-3527	226	9	·	·	PUNCT
ejpam-3527	226	10	,	,	PUNCT
ejpam-3527	226	11	0	0	NUM
ejpam-3527	226	12	)	)	PUNCT
ejpam-3527	226	13	be	be	AUX
ejpam-3527	226	14	a	a	DET
ejpam-3527	226	15	ku	ku	PROPN
ejpam-3527	226	16	-	-	PUNCT
ejpam-3527	226	17	semigroup	semigroup	NOUN
ejpam-3527	226	18	.	.	PUNCT
ejpam-3527	227	1	by	by	ADP
ejpam-3527	227	2	theorem	theorem	NOUN
ejpam-3527	227	3	1	1	NUM
ejpam-3527	227	4	,	,	PUNCT
ejpam-3527	227	5	(	(	PUNCT
ejpam-3527	227	6	x	x	X
ejpam-3527	227	7	;	;	PUNCT
ejpam-3527	227	8	∗	∗	NOUN
ejpam-3527	227	9	,	,	PUNCT
ejpam-3527	227	10	0	0	NUM
ejpam-3527	227	11	)	)	PUNCT
ejpam-3527	227	12	is	be	AUX
ejpam-3527	227	13	a	a	DET
ejpam-3527	227	14	upalgebra	upalgebra	NOUN
ejpam-3527	227	15	.	.	PUNCT
ejpam-3527	228	1	by	by	ADP
ejpam-3527	228	2	definition	definition	NOUN
ejpam-3527	228	3	6	6	NUM
ejpam-3527	228	4	,	,	PUNCT
ejpam-3527	228	5	(	(	PUNCT
ejpam-3527	228	6	x	x	X
ejpam-3527	228	7	,	,	PUNCT
ejpam-3527	228	8	·	·	PUNCT
ejpam-3527	228	9	)	)	PUNCT
ejpam-3527	228	10	is	be	AUX
ejpam-3527	228	11	a	a	DET
ejpam-3527	228	12	semigroup	semigroup	NOUN
ejpam-3527	228	13	and	and	CCONJ
ejpam-3527	228	14	left	leave	VERB
ejpam-3527	228	15	and	and	CCONJ
ejpam-3527	228	16	right	right	ADJ
ejpam-3527	228	17	distributivity	distributivity	NOUN
ejpam-3527	228	18	hold	hold	NOUN
ejpam-3527	228	19	for	for	ADP
ejpam-3527	228	20	·	·	PUNCT
ejpam-3527	228	21	over	over	ADP
ejpam-3527	228	22	∗	∗	NOUN
ejpam-3527	228	23	,	,	PUNCT
ejpam-3527	228	24	thus	thus	ADV
ejpam-3527	228	25	x	x	PRON
ejpam-3527	228	26	is	be	AUX
ejpam-3527	228	27	an	an	DET
ejpam-3527	228	28	f	f	PROPN
ejpam-3527	228	29	-up	-up	NOUN
ejpam-3527	228	30	-	-	PUNCT
ejpam-3527	228	31	semigroup	semigroup	NOUN
ejpam-3527	228	32	.	.	PUNCT
ejpam-3527	229	1	remark	remark	PROPN
ejpam-3527	229	2	4	4	NUM
ejpam-3527	229	3	.	.	PUNCT
ejpam-3527	230	1	the	the	DET
ejpam-3527	230	2	converse	converse	NOUN
ejpam-3527	230	3	of	of	ADP
ejpam-3527	230	4	theorem	theorem	NOUN
ejpam-3527	230	5	7	7	NUM
ejpam-3527	230	6	does	do	AUX
ejpam-3527	230	7	not	not	PART
ejpam-3527	230	8	hold	hold	VERB
ejpam-3527	230	9	.	.	PUNCT
ejpam-3527	231	1	to	to	PART
ejpam-3527	231	2	see	see	VERB
ejpam-3527	231	3	this	this	PRON
ejpam-3527	231	4	,	,	PUNCT
ejpam-3527	231	5	let	let	VERB
ejpam-3527	231	6	x	x	PUNCT
ejpam-3527	231	7	=	=	PUNCT
ejpam-3527	231	8	{	{	PUNCT
ejpam-3527	231	9	0	0	NUM
ejpam-3527	231	10	,	,	PUNCT
ejpam-3527	231	11	a	a	DET
ejpam-3527	231	12	,	,	PUNCT
ejpam-3527	231	13	b	b	NOUN
ejpam-3527	231	14	,	,	PUNCT
ejpam-3527	231	15	c	c	NOUN
ejpam-3527	231	16	,	,	PUNCT
ejpam-3527	231	17	d	d	AUX
ejpam-3527	231	18	}	}	PUNCT
ejpam-3527	231	19	be	be	AUX
ejpam-3527	231	20	a	a	DET
ejpam-3527	231	21	set	set	NOUN
ejpam-3527	231	22	with	with	ADP
ejpam-3527	231	23	the	the	DET
ejpam-3527	231	24	binary	binary	ADJ
ejpam-3527	231	25	operations	operation	NOUN
ejpam-3527	231	26	∗	∗	NOUN
ejpam-3527	231	27	and	and	CCONJ
ejpam-3527	231	28	·	·	PUNCT
ejpam-3527	231	29	defined	define	VERB
ejpam-3527	231	30	by	by	ADP
ejpam-3527	231	31	the	the	DET
ejpam-3527	231	32	following	following	ADJ
ejpam-3527	231	33	cayley	cayley	ADJ
ejpam-3527	231	34	tables	table	NOUN
ejpam-3527	231	35	:	:	PUNCT
ejpam-3527	231	36	∗	∗	NOUN
ejpam-3527	231	37	0	0	NUM
ejpam-3527	232	1	a	a	DET
ejpam-3527	232	2	b	b	NOUN
ejpam-3527	232	3	c	c	NOUN
ejpam-3527	232	4	d	d	NOUN
ejpam-3527	232	5	0	0	NUM
ejpam-3527	232	6	0	0	NUM
ejpam-3527	233	1	a	a	DET
ejpam-3527	233	2	b	b	NOUN
ejpam-3527	233	3	c	c	NOUN
ejpam-3527	233	4	d	d	NOUN
ejpam-3527	233	5	a	a	PRON
ejpam-3527	233	6	0	0	NUM
ejpam-3527	233	7	0	0	NUM
ejpam-3527	233	8	0	0	NUM
ejpam-3527	233	9	0	0	NUM
ejpam-3527	233	10	0	0	NUM
ejpam-3527	233	11	b	b	X
ejpam-3527	233	12	0	0	NUM
ejpam-3527	233	13	b	b	NOUN
ejpam-3527	233	14	0	0	NUM
ejpam-3527	233	15	0	0	NUM
ejpam-3527	233	16	0	0	NUM
ejpam-3527	234	1	c	c	NOUN
ejpam-3527	234	2	0	0	NUM
ejpam-3527	235	1	b	b	PROPN
ejpam-3527	235	2	b	b	PROPN
ejpam-3527	235	3	0	0	NUM
ejpam-3527	235	4	0	0	NUM
ejpam-3527	236	1	d	d	NOUN
ejpam-3527	236	2	0	0	NUM
ejpam-3527	236	3	b	b	X
ejpam-3527	236	4	b	b	PROPN
ejpam-3527	236	5	d	d	NOUN
ejpam-3527	236	6	0	0	NUM
ejpam-3527	236	7	·	·	SYM
ejpam-3527	236	8	0	0	PUNCT
ejpam-3527	237	1	a	a	DET
ejpam-3527	237	2	b	b	NOUN
ejpam-3527	237	3	c	c	NOUN
ejpam-3527	237	4	d	d	NOUN
ejpam-3527	237	5	0	0	NUM
ejpam-3527	237	6	0	0	NUM
ejpam-3527	237	7	0	0	NUM
ejpam-3527	237	8	0	0	NUM
ejpam-3527	237	9	0	0	NUM
ejpam-3527	237	10	0	0	NUM
ejpam-3527	238	1	a	a	DET
ejpam-3527	238	2	0	0	NUM
ejpam-3527	238	3	0	0	NUM
ejpam-3527	238	4	0	0	NUM
ejpam-3527	238	5	0	0	NUM
ejpam-3527	238	6	0	0	NUM
ejpam-3527	238	7	b	b	X
ejpam-3527	238	8	0	0	NUM
ejpam-3527	238	9	0	0	NUM
ejpam-3527	238	10	0	0	NUM
ejpam-3527	238	11	0	0	NUM
ejpam-3527	238	12	0	0	NUM
ejpam-3527	238	13	c	c	NOUN
ejpam-3527	238	14	0	0	NUM
ejpam-3527	238	15	0	0	NUM
ejpam-3527	238	16	0	0	NUM
ejpam-3527	238	17	0	0	NUM
ejpam-3527	238	18	0	0	NUM
ejpam-3527	239	1	d	d	NOUN
ejpam-3527	239	2	0	0	NUM
ejpam-3527	239	3	0	0	NUM
ejpam-3527	239	4	0	0	NUM
ejpam-3527	239	5	0	0	NUM
ejpam-3527	239	6	0	0	NUM
ejpam-3527	239	7	d.gomisong	d.gomisong	PROPN
ejpam-3527	239	8	,	,	PUNCT
ejpam-3527	239	9	r.	r.	PROPN
ejpam-3527	239	10	isla	isla	PROPN
ejpam-3527	239	11	/	/	SYM
ejpam-3527	239	12	eur	eur	PROPN
ejpam-3527	239	13	.	.	PUNCT
ejpam-3527	240	1	j.	j.	PROPN
ejpam-3527	240	2	pure	pure	PROPN
ejpam-3527	240	3	appl	appl	PROPN
ejpam-3527	240	4	.	.	PROPN
ejpam-3527	240	5	math	math	PROPN
ejpam-3527	240	6	,	,	PUNCT
ejpam-3527	240	7	12	12	NUM
ejpam-3527	240	8	(	(	PUNCT
ejpam-3527	240	9	4	4	NUM
ejpam-3527	240	10	)	)	PUNCT
ejpam-3527	240	11	(	(	PUNCT
ejpam-3527	240	12	2019	2019	NUM
ejpam-3527	240	13	)	)	PUNCT
ejpam-3527	240	14	,	,	PUNCT
ejpam-3527	240	15	1483	1483	NUM
ejpam-3527	240	16	-	-	SYM
ejpam-3527	240	17	1496	1496	NUM
ejpam-3527	240	18	1491	1491	NUM
ejpam-3527	240	19	then	then	ADV
ejpam-3527	240	20	by	by	ADP
ejpam-3527	240	21	routine	routine	ADJ
ejpam-3527	240	22	calculations	calculation	NOUN
ejpam-3527	240	23	,	,	PUNCT
ejpam-3527	240	24	(	(	PUNCT
ejpam-3527	240	25	x	x	NOUN
ejpam-3527	240	26	;	;	PUNCT
ejpam-3527	240	27	∗	∗	NOUN
ejpam-3527	240	28	,	,	PUNCT
ejpam-3527	240	29	·	·	PUNCT
ejpam-3527	240	30	,	,	PUNCT
ejpam-3527	240	31	0	0	NUM
ejpam-3527	240	32	)	)	PUNCT
ejpam-3527	240	33	is	be	AUX
ejpam-3527	240	34	an	an	DET
ejpam-3527	240	35	f	f	PROPN
ejpam-3527	240	36	-up	-up	NOUN
ejpam-3527	240	37	-	-	PUNCT
ejpam-3527	240	38	semigroup	semigroup	NOUN
ejpam-3527	240	39	.	.	PUNCT
ejpam-3527	241	1	let	let	VERB
ejpam-3527	241	2	x	x	SYM
ejpam-3527	241	3	=	=	SYM
ejpam-3527	241	4	0	0	NUM
ejpam-3527	241	5	,	,	PUNCT
ejpam-3527	241	6	y	y	PROPN
ejpam-3527	241	7	=	=	SYM
ejpam-3527	241	8	c	c	NOUN
ejpam-3527	241	9	,	,	PUNCT
ejpam-3527	241	10	and	and	CCONJ
ejpam-3527	241	11	z	z	NOUN
ejpam-3527	241	12	=	=	NOUN
ejpam-3527	241	13	a.	a.	NOUN
ejpam-3527	241	14	observe	observe	VERB
ejpam-3527	241	15	that	that	SCONJ
ejpam-3527	241	16	(	(	PUNCT
ejpam-3527	241	17	x∗y)∗	x∗y)∗	PROPN
ejpam-3527	242	1	[	[	X
ejpam-3527	242	2	(	(	PUNCT
ejpam-3527	242	3	y∗z)∗(x∗z	y∗z)∗(x∗z	NOUN
ejpam-3527	242	4	)	)	PUNCT
ejpam-3527	242	5	]	]	PUNCT
ejpam-3527	243	1	=	=	PUNCT
ejpam-3527	243	2	(	(	PUNCT
ejpam-3527	243	3	0∗c)∗	0∗c)∗	NUM
ejpam-3527	244	1	[	[	X
ejpam-3527	244	2	(	(	PUNCT
ejpam-3527	244	3	c∗a)∗(0∗a	c∗a)∗(0∗a	NUM
ejpam-3527	244	4	)	)	PUNCT
ejpam-3527	244	5	]	]	PUNCT
ejpam-3527	245	1	=	=	SYM
ejpam-3527	245	2	c∗(b∗a	c∗(b∗a	PROPN
ejpam-3527	245	3	)	)	PUNCT
ejpam-3527	245	4	=	=	PUNCT
ejpam-3527	246	1	c∗b	c∗b	PROPN
ejpam-3527	246	2	=	=	SYM
ejpam-3527	246	3	b	b	NOUN
ejpam-3527	246	4	,	,	PUNCT
ejpam-3527	246	5	so	so	CCONJ
ejpam-3527	246	6	(	(	PUNCT
ejpam-3527	246	7	ku1	ku1	NOUN
ejpam-3527	246	8	)	)	PUNCT
ejpam-3527	246	9	is	be	AUX
ejpam-3527	246	10	not	not	PART
ejpam-3527	246	11	satisfied	satisfied	ADJ
ejpam-3527	246	12	.	.	PUNCT
ejpam-3527	247	1	thus	thus	ADV
ejpam-3527	247	2	,	,	PUNCT
ejpam-3527	247	3	(	(	PUNCT
ejpam-3527	247	4	x	x	X
ejpam-3527	247	5	;	;	PUNCT
ejpam-3527	247	6	∗	∗	NOUN
ejpam-3527	247	7	,	,	PUNCT
ejpam-3527	247	8	·	·	PUNCT
ejpam-3527	247	9	,	,	PUNCT
ejpam-3527	247	10	0	0	NUM
ejpam-3527	247	11	)	)	PUNCT
ejpam-3527	247	12	is	be	AUX
ejpam-3527	247	13	not	not	PART
ejpam-3527	247	14	a	a	DET
ejpam-3527	247	15	ku	ku	PROPN
ejpam-3527	247	16	-	-	PUNCT
ejpam-3527	247	17	semigroup	semigroup	PROPN
ejpam-3527	247	18	.	.	PUNCT
ejpam-3527	248	1	theorem	theorem	NOUN
ejpam-3527	248	2	8	8	NUM
ejpam-3527	248	3	.	.	PUNCT
ejpam-3527	249	1	let	let	VERB
ejpam-3527	249	2	x	x	PRON
ejpam-3527	249	3	be	be	AUX
ejpam-3527	249	4	an	an	DET
ejpam-3527	249	5	f	f	PROPN
ejpam-3527	249	6	-up	-up	NOUN
ejpam-3527	249	7	-	-	NOUN
ejpam-3527	249	8	semigroup	semigroup	NOUN
ejpam-3527	249	9	with	with	ADP
ejpam-3527	249	10	unity	unity	NOUN
ejpam-3527	249	11	1	1	NUM
ejpam-3527	249	12	and	and	CCONJ
ejpam-3527	249	13	let	let	VERB
ejpam-3527	249	14	t	t	PROPN
ejpam-3527	249	15	be	be	AUX
ejpam-3527	249	16	the	the	DET
ejpam-3527	249	17	set	set	NOUN
ejpam-3527	249	18	of	of	ADP
ejpam-3527	249	19	all	all	DET
ejpam-3527	249	20	1invertible	1invertible	NUM
ejpam-3527	249	21	elements	element	NOUN
ejpam-3527	249	22	of	of	ADP
ejpam-3527	249	23	x.	x.	NOUN
ejpam-3527	249	24	then	then	ADV
ejpam-3527	249	25	(	(	PUNCT
ejpam-3527	249	26	i	i	NOUN
ejpam-3527	249	27	)	)	PUNCT
ejpam-3527	249	28	1	1	NUM
ejpam-3527	249	29	∈	∈	PROPN
ejpam-3527	249	30	t	t	NOUN
ejpam-3527	249	31	,	,	PUNCT
ejpam-3527	249	32	(	(	PUNCT
ejpam-3527	249	33	ii	ii	NOUN
ejpam-3527	249	34	)	)	PUNCT
ejpam-3527	249	35	0	0	NUM
ejpam-3527	250	1	/∈	/∈	PROPN
ejpam-3527	251	1	t	t	NOUN
ejpam-3527	251	2	,	,	PUNCT
ejpam-3527	251	3	and	and	CCONJ
ejpam-3527	251	4	(	(	PUNCT
ejpam-3527	251	5	iii	iii	X
ejpam-3527	251	6	)	)	PUNCT
ejpam-3527	251	7	a	a	DET
ejpam-3527	251	8	·	·	PUNCT
ejpam-3527	251	9	b	b	X
ejpam-3527	251	10	∈	∈	PROPN
ejpam-3527	251	11	t	t	PROPN
ejpam-3527	251	12	for	for	ADP
ejpam-3527	251	13	all	all	DET
ejpam-3527	251	14	a	a	PRON
ejpam-3527	251	15	,	,	PUNCT
ejpam-3527	251	16	b	b	PROPN
ejpam-3527	251	17	∈	∈	PROPN
ejpam-3527	251	18	t	t	NOUN
ejpam-3527	251	19	.	.	PUNCT
ejpam-3527	252	1	proof	proof	NOUN
ejpam-3527	252	2	.	.	PUNCT
ejpam-3527	253	1	let	let	VERB
ejpam-3527	253	2	t	t	NOUN
ejpam-3527	253	3	be	be	AUX
ejpam-3527	253	4	the	the	DET
ejpam-3527	253	5	set	set	NOUN
ejpam-3527	253	6	of	of	ADP
ejpam-3527	253	7	all	all	DET
ejpam-3527	253	8	1	1	NUM
ejpam-3527	253	9	-	-	PUNCT
ejpam-3527	253	10	invertible	invertible	ADJ
ejpam-3527	253	11	elements	element	NOUN
ejpam-3527	253	12	of	of	ADP
ejpam-3527	253	13	x.	x.	PROPN
ejpam-3527	253	14	(	(	PUNCT
ejpam-3527	253	15	i	i	NOUN
ejpam-3527	253	16	)	)	PUNCT
ejpam-3527	253	17	since	since	SCONJ
ejpam-3527	253	18	1	1	NUM
ejpam-3527	253	19	·	·	SYM
ejpam-3527	253	20	1	1	NUM
ejpam-3527	253	21	=	=	SYM
ejpam-3527	253	22	1	1	NUM
ejpam-3527	253	23	,	,	PUNCT
ejpam-3527	253	24	1	1	NUM
ejpam-3527	253	25	∈	∈	PROPN
ejpam-3527	253	26	t	t	NOUN
ejpam-3527	253	27	.	.	PUNCT
ejpam-3527	254	1	thus	thus	ADV
ejpam-3527	254	2	,	,	PUNCT
ejpam-3527	254	3	t	t	PROPN
ejpam-3527	254	4	6=	6=	ADP
ejpam-3527	254	5	∅.	∅.	PROPN
ejpam-3527	254	6	(	(	PUNCT
ejpam-3527	254	7	ii	ii	NOUN
ejpam-3527	254	8	)	)	PUNCT
ejpam-3527	254	9	suppose	suppose	VERB
ejpam-3527	254	10	0	0	NUM
ejpam-3527	254	11	∈	∈	PROPN
ejpam-3527	254	12	t	t	NOUN
ejpam-3527	254	13	.	.	PUNCT
ejpam-3527	255	1	then	then	ADV
ejpam-3527	255	2	there	there	PRON
ejpam-3527	255	3	exists	exist	VERB
ejpam-3527	255	4	b	b	PROPN
ejpam-3527	255	5	∈	∈	PROPN
ejpam-3527	255	6	x	x	PUNCT
ejpam-3527	256	1	such	such	ADJ
ejpam-3527	256	2	that	that	DET
ejpam-3527	256	3	0	0	NUM
ejpam-3527	256	4	·	·	PUNCT
ejpam-3527	256	5	b	b	X
ejpam-3527	256	6	=	=	SYM
ejpam-3527	256	7	1	1	NUM
ejpam-3527	256	8	=	=	SYM
ejpam-3527	256	9	b	b	PROPN
ejpam-3527	256	10	·	·	PUNCT
ejpam-3527	256	11	0	0	X
ejpam-3527	256	12	.	.	PUNCT
ejpam-3527	257	1	but	but	CCONJ
ejpam-3527	257	2	0	0	NUM
ejpam-3527	257	3	·	·	PUNCT
ejpam-3527	257	4	b	b	X
ejpam-3527	257	5	=	=	SYM
ejpam-3527	257	6	0	0	NUM
ejpam-3527	257	7	and	and	CCONJ
ejpam-3527	257	8	so	so	ADV
ejpam-3527	257	9	,	,	PUNCT
ejpam-3527	257	10	0	0	NUM
ejpam-3527	257	11	=	=	SYM
ejpam-3527	257	12	1	1	NUM
ejpam-3527	257	13	,	,	PUNCT
ejpam-3527	257	14	a	a	DET
ejpam-3527	257	15	contradiction	contradiction	NOUN
ejpam-3527	257	16	.	.	PUNCT
ejpam-3527	258	1	thus	thus	ADV
ejpam-3527	258	2	,	,	PUNCT
ejpam-3527	258	3	0	0	NUM
ejpam-3527	258	4	/∈	/∈	PROPN
ejpam-3527	258	5	t	t	PROPN
ejpam-3527	258	6	.	.	PUNCT
ejpam-3527	259	1	(	(	PUNCT
ejpam-3527	259	2	iii	iii	X
ejpam-3527	259	3	)	)	PUNCT
ejpam-3527	259	4	let	let	VERB
ejpam-3527	259	5	a	a	DET
ejpam-3527	259	6	,	,	PUNCT
ejpam-3527	259	7	b	b	PROPN
ejpam-3527	259	8	∈	∈	PROPN
ejpam-3527	259	9	t	t	NOUN
ejpam-3527	259	10	.	.	PUNCT
ejpam-3527	260	1	then	then	ADV
ejpam-3527	260	2	there	there	PRON
ejpam-3527	260	3	exist	exist	VERB
ejpam-3527	260	4	c	c	NOUN
ejpam-3527	260	5	,	,	PUNCT
ejpam-3527	260	6	d	d	PROPN
ejpam-3527	260	7	∈	∈	PROPN
ejpam-3527	260	8	x	x	PUNCT
ejpam-3527	260	9	such	such	ADJ
ejpam-3527	260	10	that	that	SCONJ
ejpam-3527	260	11	a	a	DET
ejpam-3527	260	12	·	·	PUNCT
ejpam-3527	260	13	c	c	NOUN
ejpam-3527	260	14	=	=	SYM
ejpam-3527	260	15	1	1	NUM
ejpam-3527	260	16	=	=	SYM
ejpam-3527	260	17	c	c	X
ejpam-3527	260	18	·	·	PUNCT
ejpam-3527	260	19	a	a	PRON
ejpam-3527	260	20	and	and	CCONJ
ejpam-3527	260	21	b	b	NOUN
ejpam-3527	260	22	·	·	PUNCT
ejpam-3527	260	23	d	d	X
ejpam-3527	260	24	=	=	SYM
ejpam-3527	260	25	1	1	NUM
ejpam-3527	260	26	=	=	SYM
ejpam-3527	260	27	d	d	PROPN
ejpam-3527	260	28	·	·	PUNCT
ejpam-3527	260	29	b.	b.	PROPN
ejpam-3527	261	1	moreover	moreover	ADV
ejpam-3527	261	2	,	,	PUNCT
ejpam-3527	261	3	d	d	PROPN
ejpam-3527	261	4	·	·	PUNCT
ejpam-3527	261	5	c	c	X
ejpam-3527	261	6	∈	∈	PROPN
ejpam-3527	261	7	x.	x.	NOUN
ejpam-3527	261	8	by	by	ADP
ejpam-3527	261	9	(	(	PUNCT
ejpam-3527	261	10	fup2	fup2	ADJ
ejpam-3527	261	11	)	)	PUNCT
ejpam-3527	261	12	,	,	PUNCT
ejpam-3527	261	13	(	(	PUNCT
ejpam-3527	261	14	a	a	DET
ejpam-3527	261	15	·	·	SYM
ejpam-3527	261	16	b	b	NOUN
ejpam-3527	261	17	)	)	PUNCT
ejpam-3527	261	18	·	·	PUNCT
ejpam-3527	262	1	(	(	PUNCT
ejpam-3527	262	2	d	d	X
ejpam-3527	262	3	·	·	PUNCT
ejpam-3527	262	4	c	c	X
ejpam-3527	262	5	)	)	PUNCT
ejpam-3527	262	6	=	=	SYM
ejpam-3527	262	7	(	(	PUNCT
ejpam-3527	262	8	(	(	PUNCT
ejpam-3527	262	9	a	a	DET
ejpam-3527	262	10	·	·	SYM
ejpam-3527	262	11	b	b	NOUN
ejpam-3527	262	12	)	)	PUNCT
ejpam-3527	262	13	·	·	PUNCT
ejpam-3527	263	1	d	d	X
ejpam-3527	263	2	)	)	PUNCT
ejpam-3527	263	3	·	·	PUNCT
ejpam-3527	263	4	c	c	X
ejpam-3527	263	5	=	=	SYM
ejpam-3527	263	6	(	(	PUNCT
ejpam-3527	263	7	a	a	PRON
ejpam-3527	263	8	·	·	PUNCT
ejpam-3527	263	9	(	(	PUNCT
ejpam-3527	263	10	b	b	X
ejpam-3527	263	11	·	·	PUNCT
ejpam-3527	263	12	d	d	NOUN
ejpam-3527	263	13	)	)	PUNCT
ejpam-3527	263	14	)	)	PUNCT
ejpam-3527	263	15	·	·	PUNCT
ejpam-3527	264	1	c	c	X
ejpam-3527	264	2	=	=	SYM
ejpam-3527	264	3	(	(	PUNCT
ejpam-3527	264	4	a	a	DET
ejpam-3527	264	5	·	·	SYM
ejpam-3527	264	6	1	1	NUM
ejpam-3527	264	7	)	)	PUNCT
ejpam-3527	264	8	·	·	PUNCT
ejpam-3527	264	9	c	c	X
ejpam-3527	264	10	=	=	SYM
ejpam-3527	264	11	a	a	DET
ejpam-3527	264	12	·	·	SYM
ejpam-3527	264	13	c	c	NOUN
ejpam-3527	264	14	=	=	SYM
ejpam-3527	264	15	1	1	NUM
ejpam-3527	264	16	and	and	CCONJ
ejpam-3527	264	17	(	(	PUNCT
ejpam-3527	264	18	d	d	PROPN
ejpam-3527	264	19	·	·	SYM
ejpam-3527	264	20	c	c	NOUN
ejpam-3527	264	21	)	)	PUNCT
ejpam-3527	264	22	·	·	PUNCT
ejpam-3527	264	23	(	(	PUNCT
ejpam-3527	264	24	a	a	DET
ejpam-3527	264	25	·	·	SYM
ejpam-3527	264	26	b	b	NOUN
ejpam-3527	264	27	)	)	PUNCT
ejpam-3527	264	28	=	=	SYM
ejpam-3527	264	29	(	(	PUNCT
ejpam-3527	264	30	(	(	PUNCT
ejpam-3527	264	31	d	d	NOUN
ejpam-3527	264	32	·	·	SYM
ejpam-3527	264	33	c	c	NOUN
ejpam-3527	264	34	)	)	PUNCT
ejpam-3527	264	35	·	·	PUNCT
ejpam-3527	264	36	a	a	X
ejpam-3527	264	37	)	)	PUNCT
ejpam-3527	264	38	·	·	PUNCT
ejpam-3527	264	39	b	b	X
ejpam-3527	264	40	=	=	SYM
ejpam-3527	264	41	(	(	PUNCT
ejpam-3527	264	42	d	d	PROPN
ejpam-3527	264	43	·	·	PUNCT
ejpam-3527	264	44	(	(	PUNCT
ejpam-3527	264	45	c	c	NOUN
ejpam-3527	264	46	·	·	SYM
ejpam-3527	264	47	a	a	NOUN
ejpam-3527	264	48	)	)	PUNCT
ejpam-3527	264	49	)	)	PUNCT
ejpam-3527	264	50	·	·	PUNCT
ejpam-3527	264	51	b	b	X
ejpam-3527	264	52	=	=	SYM
ejpam-3527	264	53	(	(	PUNCT
ejpam-3527	264	54	d	d	X
ejpam-3527	264	55	·	·	PUNCT
ejpam-3527	264	56	1	1	NUM
ejpam-3527	264	57	)	)	PUNCT
ejpam-3527	264	58	·	·	PUNCT
ejpam-3527	264	59	b	b	X
ejpam-3527	264	60	=	=	SYM
ejpam-3527	264	61	d	d	PROPN
ejpam-3527	264	62	·	·	SYM
ejpam-3527	264	63	b	b	NOUN
ejpam-3527	264	64	=	=	SYM
ejpam-3527	264	65	1	1	NUM
ejpam-3527	264	66	.	.	PUNCT
ejpam-3527	265	1	hence	hence	ADV
ejpam-3527	265	2	,	,	PUNCT
ejpam-3527	265	3	a	a	DET
ejpam-3527	265	4	·	·	PUNCT
ejpam-3527	265	5	b	b	X
ejpam-3527	265	6	∈	∈	PROPN
ejpam-3527	265	7	t	t	PROPN
ejpam-3527	265	8	.	.	PUNCT
ejpam-3527	266	1	the	the	DET
ejpam-3527	266	2	next	next	ADJ
ejpam-3527	266	3	result	result	NOUN
ejpam-3527	266	4	establishes	establish	VERB
ejpam-3527	266	5	a	a	DET
ejpam-3527	266	6	relation	relation	NOUN
ejpam-3527	266	7	between	between	ADP
ejpam-3527	266	8	0	0	NOUN
ejpam-3527	266	9	-	-	PUNCT
ejpam-3527	266	10	divisors	divisor	NOUN
ejpam-3527	266	11	and	and	CCONJ
ejpam-3527	266	12	the	the	DET
ejpam-3527	266	13	cancellation	cancellation	NOUN
ejpam-3527	266	14	property	property	NOUN
ejpam-3527	266	15	of	of	ADP
ejpam-3527	266	16	an	an	DET
ejpam-3527	266	17	f	f	PROPN
ejpam-3527	266	18	-up	-up	NOUN
ejpam-3527	266	19	-	-	PUNCT
ejpam-3527	266	20	semigroup	semigroup	NOUN
ejpam-3527	266	21	.	.	PUNCT
ejpam-3527	267	1	theorem	theorem	NOUN
ejpam-3527	267	2	9	9	NUM
ejpam-3527	267	3	.	.	PUNCT
ejpam-3527	268	1	if	if	SCONJ
ejpam-3527	268	2	an	an	DET
ejpam-3527	268	3	f	f	PROPN
ejpam-3527	268	4	-up	-up	NOUN
ejpam-3527	268	5	-	-	NOUN
ejpam-3527	268	6	semigroup	semigroup	NOUN
ejpam-3527	268	7	x	x	PUNCT
ejpam-3527	268	8	has	have	VERB
ejpam-3527	268	9	no	no	DET
ejpam-3527	268	10	0	0	NUM
ejpam-3527	268	11	-	-	PUNCT
ejpam-3527	268	12	divisors	divisor	NOUN
ejpam-3527	268	13	,	,	PUNCT
ejpam-3527	268	14	then	then	ADV
ejpam-3527	268	15	left	leave	VERB
ejpam-3527	268	16	and	and	CCONJ
ejpam-3527	268	17	right	right	ADJ
ejpam-3527	268	18	cancellation	cancellation	NOUN
ejpam-3527	268	19	laws	law	NOUN
ejpam-3527	268	20	hold	hold	VERB
ejpam-3527	268	21	,	,	PUNCT
ejpam-3527	268	22	that	that	ADV
ejpam-3527	268	23	is	is	ADV
ejpam-3527	268	24	,	,	PUNCT
ejpam-3527	268	25	for	for	ADP
ejpam-3527	268	26	all	all	DET
ejpam-3527	268	27	a	a	DET
ejpam-3527	268	28	,	,	PUNCT
ejpam-3527	268	29	b	b	NOUN
ejpam-3527	268	30	,	,	PUNCT
ejpam-3527	268	31	c	c	PROPN
ejpam-3527	268	32	∈	∈	PROPN
ejpam-3527	268	33	x	x	SYM
ejpam-3527	268	34	,	,	PUNCT
ejpam-3527	268	35	a	a	DET
ejpam-3527	268	36	6=	6=	NUM
ejpam-3527	268	37	0	0	NUM
ejpam-3527	268	38	,	,	PUNCT
ejpam-3527	268	39	a	a	PRON
ejpam-3527	268	40	·	·	SYM
ejpam-3527	268	41	b	b	X
ejpam-3527	268	42	=	=	SYM
ejpam-3527	268	43	a	a	PRON
ejpam-3527	268	44	·	·	PUNCT
ejpam-3527	268	45	c	c	NOUN
ejpam-3527	268	46	implies	imply	VERB
ejpam-3527	268	47	b	b	X
ejpam-3527	268	48	=	=	SYM
ejpam-3527	268	49	c	c	PROPN
ejpam-3527	268	50	(	(	PUNCT
ejpam-3527	268	51	left	leave	VERB
ejpam-3527	268	52	cancellation	cancellation	NOUN
ejpam-3527	268	53	)	)	PUNCT
ejpam-3527	268	54	and	and	CCONJ
ejpam-3527	268	55	b	b	X
ejpam-3527	268	56	·	·	PUNCT
ejpam-3527	268	57	a	a	X
ejpam-3527	268	58	=	=	SYM
ejpam-3527	268	59	c	c	NOUN
ejpam-3527	268	60	·	·	PUNCT
ejpam-3527	268	61	a	a	DET
ejpam-3527	268	62	implies	imply	VERB
ejpam-3527	268	63	b	b	X
ejpam-3527	268	64	=	=	SYM
ejpam-3527	268	65	c	c	X
ejpam-3527	268	66	(	(	PUNCT
ejpam-3527	268	67	right	right	ADJ
ejpam-3527	268	68	cancellation	cancellation	NOUN
ejpam-3527	268	69	)	)	PUNCT
ejpam-3527	268	70	.	.	PUNCT
ejpam-3527	269	1	if	if	SCONJ
ejpam-3527	269	2	either	either	CCONJ
ejpam-3527	269	3	left	left	ADJ
ejpam-3527	269	4	or	or	CCONJ
ejpam-3527	269	5	right	right	ADJ
ejpam-3527	269	6	cancellation	cancellation	NOUN
ejpam-3527	269	7	law	law	NOUN
ejpam-3527	269	8	holds	hold	VERB
ejpam-3527	269	9	,	,	PUNCT
ejpam-3527	269	10	then	then	ADV
ejpam-3527	269	11	x	x	PUNCT
ejpam-3527	269	12	has	have	VERB
ejpam-3527	269	13	no	no	DET
ejpam-3527	269	14	0	0	NUM
ejpam-3527	269	15	-	-	PUNCT
ejpam-3527	269	16	divisors	divisor	NOUN
ejpam-3527	269	17	.	.	PUNCT
ejpam-3527	270	1	proof	proof	NOUN
ejpam-3527	270	2	.	.	PUNCT
ejpam-3527	271	1	let	let	VERB
ejpam-3527	271	2	a	a	DET
ejpam-3527	271	3	,	,	PUNCT
ejpam-3527	271	4	b	b	NOUN
ejpam-3527	271	5	,	,	PUNCT
ejpam-3527	271	6	c	c	PROPN
ejpam-3527	271	7	∈	∈	PROPN
ejpam-3527	271	8	x	x	PUNCT
ejpam-3527	271	9	such	such	ADJ
ejpam-3527	271	10	that	that	SCONJ
ejpam-3527	271	11	a	a	DET
ejpam-3527	271	12	·	·	SYM
ejpam-3527	271	13	b	b	X
ejpam-3527	271	14	=	=	SYM
ejpam-3527	271	15	a	a	DET
ejpam-3527	271	16	·	·	PUNCT
ejpam-3527	271	17	c	c	NOUN
ejpam-3527	271	18	and	and	CCONJ
ejpam-3527	271	19	a	a	DET
ejpam-3527	271	20	6=	6=	NUM
ejpam-3527	271	21	0	0	NUM
ejpam-3527	271	22	.	.	PUNCT
ejpam-3527	272	1	then	then	ADV
ejpam-3527	272	2	a	a	DET
ejpam-3527	272	3	·	·	PUNCT
ejpam-3527	272	4	(	(	PUNCT
ejpam-3527	272	5	b∗c	b∗c	PROPN
ejpam-3527	272	6	)	)	PUNCT
ejpam-3527	272	7	=	=	SYM
ejpam-3527	272	8	(	(	PUNCT
ejpam-3527	272	9	a	a	DET
ejpam-3527	272	10	·	·	PUNCT
ejpam-3527	272	11	b)∗(a	b)∗(a	NOUN
ejpam-3527	272	12	·	·	SYM
ejpam-3527	272	13	c	c	NOUN
ejpam-3527	272	14	)	)	PUNCT
ejpam-3527	273	1	=	=	SYM
ejpam-3527	273	2	0	0	NUM
ejpam-3527	273	3	by	by	ADP
ejpam-3527	273	4	proposition	proposition	NOUN
ejpam-3527	273	5	1(i	1(i	NUM
ejpam-3527	273	6	)	)	PUNCT
ejpam-3527	273	7	.	.	PUNCT
ejpam-3527	274	1	since	since	SCONJ
ejpam-3527	274	2	x	x	PRON
ejpam-3527	274	3	has	have	VERB
ejpam-3527	274	4	no	no	DET
ejpam-3527	274	5	0	0	NUM
ejpam-3527	274	6	-	-	PUNCT
ejpam-3527	274	7	divisors	divisor	NOUN
ejpam-3527	274	8	and	and	CCONJ
ejpam-3527	274	9	a	a	DET
ejpam-3527	274	10	6=	6=	NUM
ejpam-3527	274	11	0	0	NUM
ejpam-3527	274	12	,	,	PUNCT
ejpam-3527	274	13	we	we	PRON
ejpam-3527	274	14	have	have	VERB
ejpam-3527	274	15	b∗c	b∗c	VERB
ejpam-3527	275	1	=	=	SYM
ejpam-3527	275	2	0	0	X
ejpam-3527	275	3	.	.	PUNCT
ejpam-3527	275	4	since	since	SCONJ
ejpam-3527	275	5	a·b	a·b	NOUN
ejpam-3527	275	6	=	=	SYM
ejpam-3527	275	7	a·c	a·c	NOUN
ejpam-3527	275	8	,	,	PUNCT
ejpam-3527	275	9	we	we	PRON
ejpam-3527	275	10	have	have	VERB
ejpam-3527	275	11	0	0	NUM
ejpam-3527	275	12	=	=	SYM
ejpam-3527	275	13	a	a	PRON
ejpam-3527	275	14	·	·	PUNCT
ejpam-3527	275	15	(	(	PUNCT
ejpam-3527	275	16	b	b	NOUN
ejpam-3527	275	17	∗	∗	NOUN
ejpam-3527	275	18	c	c	NOUN
ejpam-3527	275	19	)	)	PUNCT
ejpam-3527	275	20	=	=	SYM
ejpam-3527	275	21	(	(	PUNCT
ejpam-3527	275	22	a	a	DET
ejpam-3527	275	23	·	·	SYM
ejpam-3527	275	24	b	b	X
ejpam-3527	275	25	)	)	PUNCT
ejpam-3527	275	26	∗	∗	NOUN
ejpam-3527	275	27	(	(	PUNCT
ejpam-3527	275	28	a	a	DET
ejpam-3527	275	29	·	·	PUNCT
ejpam-3527	275	30	c	c	X
ejpam-3527	275	31	)	)	PUNCT
ejpam-3527	276	1	=	=	SYM
ejpam-3527	276	2	(	(	PUNCT
ejpam-3527	276	3	a	a	PRON
ejpam-3527	276	4	·	·	PUNCT
ejpam-3527	276	5	c	c	X
ejpam-3527	276	6	)	)	PUNCT
ejpam-3527	276	7	∗	∗	NOUN
ejpam-3527	276	8	(	(	PUNCT
ejpam-3527	276	9	a	a	DET
ejpam-3527	276	10	·	·	SYM
ejpam-3527	276	11	b	b	X
ejpam-3527	276	12	)	)	PUNCT
ejpam-3527	276	13	=	=	SYM
ejpam-3527	276	14	a	a	DET
ejpam-3527	276	15	·	·	PUNCT
ejpam-3527	276	16	(	(	PUNCT
ejpam-3527	276	17	c	c	NOUN
ejpam-3527	276	18	∗	∗	X
ejpam-3527	276	19	b	b	NOUN
ejpam-3527	276	20	)	)	PUNCT
ejpam-3527	276	21	and	and	CCONJ
ejpam-3527	276	22	so	so	ADV
ejpam-3527	276	23	,	,	PUNCT
ejpam-3527	276	24	c	c	PROPN
ejpam-3527	276	25	∗	∗	X
ejpam-3527	276	26	b	b	NOUN
ejpam-3527	276	27	=	=	SYM
ejpam-3527	276	28	0	0	NUM
ejpam-3527	276	29	.	.	PUNCT
ejpam-3527	277	1	by	by	ADP
ejpam-3527	277	2	(	(	PUNCT
ejpam-3527	277	3	up4	up4	PROPN
ejpam-3527	277	4	)	)	PUNCT
ejpam-3527	277	5	,	,	PUNCT
ejpam-3527	277	6	b	b	X
ejpam-3527	277	7	=	=	SYM
ejpam-3527	277	8	c.	c.	PROPN
ejpam-3527	277	9	hence	hence	ADV
ejpam-3527	277	10	,	,	PUNCT
ejpam-3527	277	11	the	the	DET
ejpam-3527	277	12	left	left	ADJ
ejpam-3527	277	13	cancellation	cancellation	NOUN
ejpam-3527	277	14	law	law	NOUN
ejpam-3527	277	15	holds	hold	VERB
ejpam-3527	277	16	.	.	PUNCT
ejpam-3527	278	1	similarly	similarly	ADV
ejpam-3527	278	2	,	,	PUNCT
ejpam-3527	278	3	the	the	DET
ejpam-3527	278	4	right	right	ADJ
ejpam-3527	278	5	cancellation	cancellation	NOUN
ejpam-3527	278	6	law	law	NOUN
ejpam-3527	278	7	holds	hold	VERB
ejpam-3527	278	8	.	.	PUNCT
ejpam-3527	279	1	conversely	conversely	ADV
ejpam-3527	279	2	,	,	PUNCT
ejpam-3527	279	3	suppose	suppose	VERB
ejpam-3527	279	4	one	one	NUM
ejpam-3527	279	5	of	of	ADP
ejpam-3527	279	6	the	the	DET
ejpam-3527	279	7	cancellation	cancellation	NOUN
ejpam-3527	279	8	laws	law	NOUN
ejpam-3527	279	9	holds	hold	VERB
ejpam-3527	279	10	,	,	PUNCT
ejpam-3527	279	11	say	say	INTJ
ejpam-3527	279	12	,	,	PUNCT
ejpam-3527	279	13	the	the	DET
ejpam-3527	279	14	left	left	ADJ
ejpam-3527	279	15	cancellation	cancellation	NOUN
ejpam-3527	279	16	.	.	PUNCT
ejpam-3527	280	1	let	let	VERB
ejpam-3527	280	2	a	a	PRON
ejpam-3527	280	3	be	be	AUX
ejpam-3527	280	4	a	a	DET
ejpam-3527	280	5	nonzero	nonzero	ADJ
ejpam-3527	280	6	element	element	NOUN
ejpam-3527	280	7	of	of	ADP
ejpam-3527	280	8	x	x	PROPN
ejpam-3527	280	9	and	and	CCONJ
ejpam-3527	280	10	b	b	PROPN
ejpam-3527	280	11	∈	∈	PROPN
ejpam-3527	280	12	x.	x.	NOUN
ejpam-3527	280	13	suppose	suppose	VERB
ejpam-3527	280	14	a	a	DET
ejpam-3527	280	15	·	·	SYM
ejpam-3527	280	16	b	b	NOUN
ejpam-3527	280	17	=	=	SYM
ejpam-3527	280	18	0	0	PROPN
ejpam-3527	280	19	.	.	PUNCT
ejpam-3527	281	1	then	then	ADV
ejpam-3527	281	2	by	by	ADP
ejpam-3527	281	3	theorem	theorem	NOUN
ejpam-3527	281	4	4(i	4(i	NUM
ejpam-3527	281	5	)	)	PUNCT
ejpam-3527	281	6	,	,	PUNCT
ejpam-3527	281	7	a	a	DET
ejpam-3527	281	8	·	·	SYM
ejpam-3527	281	9	b	b	X
ejpam-3527	281	10	=	=	SYM
ejpam-3527	281	11	a	a	DET
ejpam-3527	281	12	·	·	SYM
ejpam-3527	281	13	0	0	NUM
ejpam-3527	281	14	and	and	CCONJ
ejpam-3527	281	15	so	so	ADV
ejpam-3527	281	16	by	by	ADP
ejpam-3527	281	17	left	left	ADJ
ejpam-3527	281	18	cancellation	cancellation	NOUN
ejpam-3527	281	19	,	,	PUNCT
ejpam-3527	281	20	b	b	NOUN
ejpam-3527	281	21	=	=	SYM
ejpam-3527	281	22	0	0	X
ejpam-3527	281	23	.	.	PUNCT
ejpam-3527	281	24	suppose	suppose	VERB
ejpam-3527	281	25	b	b	X
ejpam-3527	281	26	·	·	PUNCT
ejpam-3527	281	27	a	a	DET
ejpam-3527	281	28	=	=	SYM
ejpam-3527	281	29	0	0	NUM
ejpam-3527	281	30	and	and	CCONJ
ejpam-3527	281	31	b	b	NOUN
ejpam-3527	281	32	6=	6=	NUM
ejpam-3527	281	33	0	0	NUM
ejpam-3527	281	34	.	.	PUNCT
ejpam-3527	282	1	then	then	ADV
ejpam-3527	282	2	by	by	ADP
ejpam-3527	282	3	theorem	theorem	NOUN
ejpam-3527	282	4	4(i	4(i	NUM
ejpam-3527	282	5	)	)	PUNCT
ejpam-3527	282	6	,	,	PUNCT
ejpam-3527	282	7	b	b	X
ejpam-3527	282	8	·	·	PUNCT
ejpam-3527	282	9	a	a	DET
ejpam-3527	282	10	=	=	SYM
ejpam-3527	282	11	b	b	PROPN
ejpam-3527	282	12	·	·	PUNCT
ejpam-3527	282	13	0	0	NUM
ejpam-3527	282	14	and	and	CCONJ
ejpam-3527	282	15	so	so	ADV
ejpam-3527	282	16	by	by	ADP
ejpam-3527	282	17	left	left	ADJ
ejpam-3527	282	18	cancellation	cancellation	NOUN
ejpam-3527	282	19	,	,	PUNCT
ejpam-3527	282	20	a	a	DET
ejpam-3527	282	21	=	=	SYM
ejpam-3527	282	22	0	0	NUM
ejpam-3527	282	23	,	,	PUNCT
ejpam-3527	282	24	a	a	DET
ejpam-3527	282	25	contradiction	contradiction	NOUN
ejpam-3527	282	26	.	.	PUNCT
ejpam-3527	283	1	therefore	therefore	ADV
ejpam-3527	283	2	,	,	PUNCT
ejpam-3527	283	3	b	b	X
ejpam-3527	283	4	=	=	SYM
ejpam-3527	283	5	0	0	PROPN
ejpam-3527	283	6	and	and	CCONJ
ejpam-3527	283	7	x	x	PRON
ejpam-3527	283	8	has	have	VERB
ejpam-3527	283	9	no	no	DET
ejpam-3527	283	10	0	0	NUM
ejpam-3527	283	11	-	-	PUNCT
ejpam-3527	283	12	divisors	divisor	NOUN
ejpam-3527	283	13	.	.	PUNCT
ejpam-3527	284	1	similarly	similarly	ADV
ejpam-3527	284	2	,	,	PUNCT
ejpam-3527	284	3	the	the	DET
ejpam-3527	284	4	right	right	ADJ
ejpam-3527	284	5	cancellation	cancellation	NOUN
ejpam-3527	284	6	law	law	NOUN
ejpam-3527	284	7	implies	imply	VERB
ejpam-3527	284	8	that	that	SCONJ
ejpam-3527	284	9	x	x	PRON
ejpam-3527	284	10	has	have	VERB
ejpam-3527	284	11	no	no	DET
ejpam-3527	284	12	0	0	NUM
ejpam-3527	284	13	-	-	PUNCT
ejpam-3527	284	14	divisors	divisor	NOUN
ejpam-3527	284	15	.	.	PUNCT
ejpam-3527	285	1	theorem	theorem	VERB
ejpam-3527	285	2	10	10	NUM
ejpam-3527	285	3	.	.	PUNCT
ejpam-3527	286	1	a	a	DET
ejpam-3527	286	2	finite	finite	PROPN
ejpam-3527	286	3	commutative	commutative	PROPN
ejpam-3527	286	4	f	f	PROPN
ejpam-3527	286	5	-up	-up	NOUN
ejpam-3527	286	6	-	-	PUNCT
ejpam-3527	286	7	semigroup	semigroup	NOUN
ejpam-3527	286	8	x	x	PUNCT
ejpam-3527	286	9	with	with	ADP
ejpam-3527	286	10	more	more	ADJ
ejpam-3527	286	11	than	than	ADP
ejpam-3527	286	12	one	one	NUM
ejpam-3527	286	13	element	element	NOUN
ejpam-3527	286	14	and	and	CCONJ
ejpam-3527	286	15	without	without	ADP
ejpam-3527	286	16	0	0	NOUN
ejpam-3527	286	17	-	-	PUNCT
ejpam-3527	286	18	divisors	divisor	NOUN
ejpam-3527	286	19	is	be	AUX
ejpam-3527	286	20	an	an	DET
ejpam-3527	286	21	f	f	PROPN
ejpam-3527	286	22	-up	-up	NOUN
ejpam-3527	286	23	-	-	NOUN
ejpam-3527	286	24	field	field	NOUN
ejpam-3527	286	25	.	.	PUNCT
ejpam-3527	287	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	287	2	,	,	PUNCT
ejpam-3527	287	3	r.	r.	PROPN
ejpam-3527	287	4	isla	isla	PROPN
ejpam-3527	287	5	/	/	SYM
ejpam-3527	287	6	eur	eur	PROPN
ejpam-3527	287	7	.	.	PUNCT
ejpam-3527	288	1	j.	j.	PROPN
ejpam-3527	288	2	pure	pure	PROPN
ejpam-3527	288	3	appl	appl	PROPN
ejpam-3527	288	4	.	.	PROPN
ejpam-3527	288	5	math	math	PROPN
ejpam-3527	288	6	,	,	PUNCT
ejpam-3527	288	7	12	12	NUM
ejpam-3527	288	8	(	(	PUNCT
ejpam-3527	288	9	4	4	NUM
ejpam-3527	288	10	)	)	PUNCT
ejpam-3527	288	11	(	(	PUNCT
ejpam-3527	288	12	2019	2019	NUM
ejpam-3527	288	13	)	)	PUNCT
ejpam-3527	288	14	,	,	PUNCT
ejpam-3527	288	15	1483	1483	NUM
ejpam-3527	288	16	-	-	SYM
ejpam-3527	288	17	1496	1496	NUM
ejpam-3527	288	18	1492	1492	NUM
ejpam-3527	288	19	proof	proof	NOUN
ejpam-3527	288	20	.	.	PUNCT
ejpam-3527	289	1	let	let	VERB
ejpam-3527	289	2	a1	a1	NOUN
ejpam-3527	289	3	,	,	PUNCT
ejpam-3527	289	4	a2	a2	PROPN
ejpam-3527	289	5	,	,	PUNCT
ejpam-3527	289	6	.	.	PUNCT
ejpam-3527	289	7	.	.	PUNCT
ejpam-3527	290	1	.	.	PUNCT
ejpam-3527	291	1	,	,	PUNCT
ejpam-3527	291	2	an	an	DET
ejpam-3527	291	3	be	be	AUX
ejpam-3527	291	4	the	the	DET
ejpam-3527	291	5	distinct	distinct	ADJ
ejpam-3527	291	6	elements	element	NOUN
ejpam-3527	291	7	of	of	ADP
ejpam-3527	291	8	x.	x.	NOUN
ejpam-3527	291	9	let	let	VERB
ejpam-3527	291	10	a	a	DET
ejpam-3527	291	11	∈	∈	NOUN
ejpam-3527	291	12	x	x	PUNCT
ejpam-3527	291	13	with	with	ADP
ejpam-3527	291	14	a	a	DET
ejpam-3527	291	15	6=	6=	NUM
ejpam-3527	291	16	0	0	NUM
ejpam-3527	291	17	.	.	PUNCT
ejpam-3527	292	1	now	now	ADV
ejpam-3527	292	2	,	,	PUNCT
ejpam-3527	292	3	a	a	DET
ejpam-3527	292	4	·	·	PUNCT
ejpam-3527	292	5	ai	ai	VERB
ejpam-3527	292	6	∈	∈	PROPN
ejpam-3527	292	7	x	x	PUNCT
ejpam-3527	292	8	for	for	ADP
ejpam-3527	292	9	all	all	DET
ejpam-3527	292	10	i	i	PRON
ejpam-3527	292	11	=	=	NOUN
ejpam-3527	292	12	1	1	NUM
ejpam-3527	292	13	,	,	PUNCT
ejpam-3527	292	14	2	2	NUM
ejpam-3527	292	15	,	,	PUNCT
ejpam-3527	292	16	.	.	PUNCT
ejpam-3527	292	17	.	.	PUNCT
ejpam-3527	292	18	.	.	PUNCT
ejpam-3527	293	1	,	,	PUNCT
ejpam-3527	294	1	n	n	CCONJ
ejpam-3527	294	2	and	and	CCONJ
ejpam-3527	294	3	so	so	ADV
ejpam-3527	294	4	{	{	PUNCT
ejpam-3527	294	5	a	a	PRON
ejpam-3527	294	6	·	·	PUNCT
ejpam-3527	294	7	a1	a1	NOUN
ejpam-3527	294	8	,	,	PUNCT
ejpam-3527	294	9	a	a	DET
ejpam-3527	294	10	·	·	PUNCT
ejpam-3527	294	11	a2	a2	PROPN
ejpam-3527	294	12	,	,	PUNCT
ejpam-3527	294	13	.	.	PUNCT
ejpam-3527	294	14	.	.	PUNCT
ejpam-3527	295	1	.	.	PUNCT
ejpam-3527	296	1	,	,	PUNCT
ejpam-3527	296	2	a	a	DET
ejpam-3527	296	3	·	·	SYM
ejpam-3527	296	4	an	an	PRON
ejpam-3527	296	5	}	}	PUNCT
ejpam-3527	296	6	⊆	⊆	NUM
ejpam-3527	296	7	x.	x.	NOUN
ejpam-3527	296	8	if	if	SCONJ
ejpam-3527	296	9	a	a	DET
ejpam-3527	296	10	·	·	PUNCT
ejpam-3527	296	11	ai	ai	NOUN
ejpam-3527	296	12	=	=	PUNCT
ejpam-3527	296	13	a	a	DET
ejpam-3527	296	14	·	·	PUNCT
ejpam-3527	296	15	aj	aj	PROPN
ejpam-3527	296	16	,	,	PUNCT
ejpam-3527	296	17	then	then	ADV
ejpam-3527	296	18	by	by	ADP
ejpam-3527	296	19	theorem	theorem	NOUN
ejpam-3527	296	20	9	9	NUM
ejpam-3527	296	21	,	,	PUNCT
ejpam-3527	296	22	ai	ai	VERB
ejpam-3527	296	23	=	=	PROPN
ejpam-3527	296	24	aj	aj	PROPN
ejpam-3527	296	25	.	.	PUNCT
ejpam-3527	297	1	thus	thus	ADV
ejpam-3527	297	2	,	,	PUNCT
ejpam-3527	297	3	the	the	DET
ejpam-3527	297	4	elements	element	NOUN
ejpam-3527	297	5	a	a	DET
ejpam-3527	297	6	·	·	PUNCT
ejpam-3527	297	7	a1	a1	NOUN
ejpam-3527	297	8	,	,	PUNCT
ejpam-3527	297	9	a	a	DET
ejpam-3527	297	10	·	·	PUNCT
ejpam-3527	297	11	a2	a2	PROPN
ejpam-3527	297	12	,	,	PUNCT
ejpam-3527	297	13	.	.	PUNCT
ejpam-3527	297	14	.	.	PUNCT
ejpam-3527	298	1	.	.	PUNCT
ejpam-3527	299	1	,	,	PUNCT
ejpam-3527	299	2	a	a	PRON
ejpam-3527	299	3	·	·	PUNCT
ejpam-3527	299	4	an	an	PRON
ejpam-3527	299	5	are	be	AUX
ejpam-3527	299	6	distinct	distinct	ADJ
ejpam-3527	299	7	and	and	CCONJ
ejpam-3527	299	8	so	so	ADV
ejpam-3527	299	9	x	x	SYM
ejpam-3527	300	1	=	=	X
ejpam-3527	300	2	{	{	PUNCT
ejpam-3527	300	3	a	a	DET
ejpam-3527	300	4	·	·	PUNCT
ejpam-3527	300	5	a1	a1	NOUN
ejpam-3527	300	6	,	,	PUNCT
ejpam-3527	300	7	a	a	DET
ejpam-3527	300	8	·	·	PUNCT
ejpam-3527	300	9	a2	a2	PROPN
ejpam-3527	300	10	,	,	PUNCT
ejpam-3527	300	11	.	.	PUNCT
ejpam-3527	300	12	.	.	PUNCT
ejpam-3527	301	1	.	.	PUNCT
ejpam-3527	302	1	,	,	PUNCT
ejpam-3527	302	2	a	a	DET
ejpam-3527	302	3	·	·	PUNCT
ejpam-3527	302	4	an	an	PRON
ejpam-3527	302	5	}	}	PUNCT
ejpam-3527	302	6	.	.	PUNCT
ejpam-3527	303	1	hence	hence	ADV
ejpam-3527	303	2	,	,	PUNCT
ejpam-3527	303	3	one	one	NUM
ejpam-3527	303	4	of	of	ADP
ejpam-3527	303	5	the	the	DET
ejpam-3527	303	6	elements	element	NOUN
ejpam-3527	303	7	,	,	PUNCT
ejpam-3527	303	8	say	say	VERB
ejpam-3527	303	9	a	a	DET
ejpam-3527	303	10	·	·	PUNCT
ejpam-3527	303	11	ai	ai	VERB
ejpam-3527	303	12	,	,	PUNCT
ejpam-3527	303	13	must	must	AUX
ejpam-3527	303	14	be	be	AUX
ejpam-3527	303	15	equal	equal	ADJ
ejpam-3527	303	16	to	to	ADP
ejpam-3527	303	17	a.	a.	NOUN
ejpam-3527	303	18	since	since	SCONJ
ejpam-3527	303	19	x	x	PROPN
ejpam-3527	303	20	is	be	AUX
ejpam-3527	303	21	commutative	commutative	ADJ
ejpam-3527	303	22	,	,	PUNCT
ejpam-3527	303	23	ai	ai	VERB
ejpam-3527	303	24	·	·	PUNCT
ejpam-3527	303	25	a	a	PRON
ejpam-3527	303	26	=	=	X
ejpam-3527	303	27	a	a	DET
ejpam-3527	303	28	·	·	SYM
ejpam-3527	303	29	ai	ai	NOUN
ejpam-3527	303	30	=	=	NOUN
ejpam-3527	303	31	a.	a.	NOUN
ejpam-3527	303	32	let	let	VERB
ejpam-3527	304	1	b	b	PROPN
ejpam-3527	304	2	∈	∈	PROPN
ejpam-3527	304	3	x.	x.	NOUN
ejpam-3527	304	4	then	then	ADV
ejpam-3527	304	5	there	there	PRON
ejpam-3527	304	6	exists	exist	VERB
ejpam-3527	304	7	aj	aj	PROPN
ejpam-3527	304	8	∈	∈	PROPN
ejpam-3527	304	9	x	x	PUNCT
ejpam-3527	305	1	such	such	ADJ
ejpam-3527	305	2	that	that	PRON
ejpam-3527	305	3	b	b	X
ejpam-3527	305	4	=	=	SYM
ejpam-3527	305	5	a	a	DET
ejpam-3527	305	6	·	·	PUNCT
ejpam-3527	305	7	aj	aj	PROPN
ejpam-3527	305	8	.	.	PUNCT
ejpam-3527	306	1	thus	thus	ADV
ejpam-3527	306	2	,	,	PUNCT
ejpam-3527	306	3	b	b	X
ejpam-3527	306	4	·	·	SYM
ejpam-3527	306	5	ai	ai	NOUN
ejpam-3527	306	6	=	=	NOUN
ejpam-3527	306	7	ai	ai	PROPN
ejpam-3527	306	8	·	·	PUNCT
ejpam-3527	306	9	b	b	X
ejpam-3527	306	10	=	=	PRON
ejpam-3527	306	11	ai	ai	VERB
ejpam-3527	306	12	·	·	PUNCT
ejpam-3527	306	13	(	(	PUNCT
ejpam-3527	306	14	a	a	PRON
ejpam-3527	306	15	·	·	SYM
ejpam-3527	306	16	aj	aj	ADJ
ejpam-3527	306	17	)	)	PUNCT
ejpam-3527	307	1	=	=	PRON
ejpam-3527	307	2	(	(	PUNCT
ejpam-3527	307	3	ai	ai	PROPN
ejpam-3527	307	4	·	·	SYM
ejpam-3527	307	5	a	a	NOUN
ejpam-3527	307	6	)	)	PUNCT
ejpam-3527	307	7	·	·	PUNCT
ejpam-3527	307	8	aj	aj	PROPN
ejpam-3527	307	9	=	=	PROPN
ejpam-3527	307	10	a	a	DET
ejpam-3527	307	11	·	·	PUNCT
ejpam-3527	307	12	aj	aj	PROPN
ejpam-3527	307	13	=	=	PROPN
ejpam-3527	307	14	b.	b.	PROPN
ejpam-3527	308	1	this	this	PRON
ejpam-3527	308	2	implies	imply	VERB
ejpam-3527	308	3	that	that	SCONJ
ejpam-3527	308	4	ai	ai	VERB
ejpam-3527	308	5	is	be	AUX
ejpam-3527	308	6	the	the	DET
ejpam-3527	308	7	unity	unity	NOUN
ejpam-3527	308	8	of	of	ADP
ejpam-3527	308	9	x.	x.	NOUN
ejpam-3527	308	10	we	we	PRON
ejpam-3527	308	11	denote	denote	VERB
ejpam-3527	308	12	the	the	DET
ejpam-3527	308	13	unity	unity	NOUN
ejpam-3527	308	14	of	of	ADP
ejpam-3527	308	15	x	x	PUNCT
ejpam-3527	308	16	by	by	ADP
ejpam-3527	308	17	1	1	NUM
ejpam-3527	308	18	.	.	PUNCT
ejpam-3527	309	1	now	now	ADV
ejpam-3527	309	2	,	,	PUNCT
ejpam-3527	309	3	1	1	NUM
ejpam-3527	309	4	∈	∈	NOUN
ejpam-3527	309	5	x	x	SYM
ejpam-3527	309	6	=	=	NOUN
ejpam-3527	309	7	{	{	PUNCT
ejpam-3527	309	8	a	a	DET
ejpam-3527	309	9	·	·	SYM
ejpam-3527	309	10	a1	a1	NOUN
ejpam-3527	309	11	,	,	PUNCT
ejpam-3527	309	12	a	a	DET
ejpam-3527	309	13	·	·	SYM
ejpam-3527	309	14	a2	a2	PROPN
ejpam-3527	309	15	,	,	PUNCT
ejpam-3527	309	16	.	.	PUNCT
ejpam-3527	309	17	.	.	PUNCT
ejpam-3527	309	18	.	.	PUNCT
ejpam-3527	310	1	,	,	PUNCT
ejpam-3527	310	2	a	a	DET
ejpam-3527	310	3	·	·	SYM
ejpam-3527	310	4	an	an	NOUN
ejpam-3527	310	5	}	}	PUNCT
ejpam-3527	310	6	and	and	CCONJ
ejpam-3527	310	7	so	so	ADV
ejpam-3527	310	8	one	one	NUM
ejpam-3527	310	9	of	of	ADP
ejpam-3527	310	10	the	the	DET
ejpam-3527	310	11	elements	element	NOUN
ejpam-3527	310	12	,	,	PUNCT
ejpam-3527	310	13	say	say	VERB
ejpam-3527	310	14	a	a	DET
ejpam-3527	310	15	·	·	SYM
ejpam-3527	310	16	ak	ak	NOUN
ejpam-3527	310	17	,	,	PUNCT
ejpam-3527	310	18	must	must	AUX
ejpam-3527	310	19	be	be	AUX
ejpam-3527	310	20	equal	equal	ADJ
ejpam-3527	310	21	to	to	ADP
ejpam-3527	310	22	1	1	NUM
ejpam-3527	310	23	.	.	PUNCT
ejpam-3527	310	24	by	by	ADP
ejpam-3527	310	25	commutativity	commutativity	NOUN
ejpam-3527	310	26	,	,	PUNCT
ejpam-3527	310	27	ak	ak	PROPN
ejpam-3527	310	28	·	·	PUNCT
ejpam-3527	310	29	a	a	PRON
ejpam-3527	310	30	=	=	X
ejpam-3527	310	31	a	a	DET
ejpam-3527	310	32	·	·	SYM
ejpam-3527	310	33	ak	ak	X
ejpam-3527	310	34	=	=	ADJ
ejpam-3527	310	35	1	1	NUM
ejpam-3527	310	36	.	.	PUNCT
ejpam-3527	311	1	hence	hence	ADV
ejpam-3527	311	2	,	,	PUNCT
ejpam-3527	311	3	every	every	DET
ejpam-3527	311	4	nonzero	nonzero	NOUN
ejpam-3527	311	5	element	element	NOUN
ejpam-3527	311	6	of	of	ADP
ejpam-3527	311	7	x	x	PUNCT
ejpam-3527	311	8	is	be	AUX
ejpam-3527	311	9	1	1	NUM
ejpam-3527	311	10	-	-	PUNCT
ejpam-3527	311	11	invertible	invertible	ADJ
ejpam-3527	311	12	.	.	PUNCT
ejpam-3527	312	1	therefore	therefore	ADV
ejpam-3527	312	2	,	,	PUNCT
ejpam-3527	312	3	x	x	X
ejpam-3527	312	4	is	be	AUX
ejpam-3527	312	5	an	an	DET
ejpam-3527	312	6	f	f	PROPN
ejpam-3527	312	7	-up	-up	NOUN
ejpam-3527	312	8	-	-	NOUN
ejpam-3527	312	9	field	field	NOUN
ejpam-3527	312	10	.	.	PUNCT
ejpam-3527	313	1	as	as	ADP
ejpam-3527	313	2	a	a	DET
ejpam-3527	313	3	consequence	consequence	NOUN
ejpam-3527	313	4	of	of	ADP
ejpam-3527	313	5	theorem	theorem	NOUN
ejpam-3527	313	6	10	10	NUM
ejpam-3527	313	7	,	,	PUNCT
ejpam-3527	313	8	the	the	DET
ejpam-3527	313	9	following	follow	VERB
ejpam-3527	313	10	corollary	corollary	ADJ
ejpam-3527	313	11	holds	hold	NOUN
ejpam-3527	313	12	.	.	PUNCT
ejpam-3527	314	1	corollary	corollary	ADJ
ejpam-3527	314	2	1	1	NUM
ejpam-3527	314	3	.	.	PUNCT
ejpam-3527	315	1	every	every	DET
ejpam-3527	315	2	finite	finite	NOUN
ejpam-3527	315	3	f	f	PROPN
ejpam-3527	315	4	-up	-up	NOUN
ejpam-3527	315	5	-	-	NOUN
ejpam-3527	315	6	domain	domain	NOUN
ejpam-3527	315	7	is	be	AUX
ejpam-3527	315	8	an	an	DET
ejpam-3527	315	9	f	f	PROPN
ejpam-3527	315	10	-up	-up	NOUN
ejpam-3527	315	11	-	-	NOUN
ejpam-3527	315	12	field	field	NOUN
ejpam-3527	315	13	.	.	PUNCT
ejpam-3527	316	1	4	4	X
ejpam-3527	316	2	.	.	X
ejpam-3527	316	3	f	f	X
ejpam-3527	316	4	-	-	PUNCT
ejpam-3527	316	5	up	up	ADP
ejpam-3527	316	6	-	-	PUNCT
ejpam-3527	316	7	ideal	ideal	NOUN
ejpam-3527	316	8	and	and	CCONJ
ejpam-3527	316	9	the	the	DET
ejpam-3527	316	10	quotient	quotient	NOUN
ejpam-3527	316	11	f	f	NOUN
ejpam-3527	316	12	-	-	PUNCT
ejpam-3527	316	13	up	up	ADP
ejpam-3527	316	14	-	-	PUNCT
ejpam-3527	316	15	semigroup	semigroup	NOUN
ejpam-3527	316	16	definition	definition	NOUN
ejpam-3527	316	17	15	15	NUM
ejpam-3527	316	18	.	.	PUNCT
ejpam-3527	317	1	a	a	DET
ejpam-3527	317	2	nonempty	nonempty	NOUN
ejpam-3527	317	3	subset	subset	VERB
ejpam-3527	317	4	i	i	PRON
ejpam-3527	317	5	of	of	ADP
ejpam-3527	317	6	an	an	DET
ejpam-3527	317	7	f	f	PROPN
ejpam-3527	317	8	-up	-up	NOUN
ejpam-3527	317	9	-	-	NOUN
ejpam-3527	317	10	semigroup	semigroup	NOUN
ejpam-3527	317	11	x	x	VERB
ejpam-3527	317	12	is	be	AUX
ejpam-3527	317	13	called	call	VERB
ejpam-3527	317	14	an	an	DET
ejpam-3527	317	15	f	f	PROPN
ejpam-3527	317	16	-up	-up	NOUN
ejpam-3527	317	17	-	-	PUNCT
ejpam-3527	317	18	ideal	ideal	NOUN
ejpam-3527	317	19	of	of	ADP
ejpam-3527	317	20	x	x	PRON
ejpam-3527	317	21	if	if	SCONJ
ejpam-3527	317	22	the	the	DET
ejpam-3527	317	23	following	follow	VERB
ejpam-3527	317	24	hold	hold	NOUN
ejpam-3527	317	25	:	:	PUNCT
ejpam-3527	317	26	(	(	PUNCT
ejpam-3527	317	27	fupi1	fupi1	NOUN
ejpam-3527	317	28	)	)	PUNCT
ejpam-3527	317	29	the	the	DET
ejpam-3527	317	30	constant	constant	ADJ
ejpam-3527	317	31	0	0	NUM
ejpam-3527	317	32	of	of	ADP
ejpam-3527	317	33	x	x	PRON
ejpam-3527	317	34	is	be	AUX
ejpam-3527	317	35	in	in	ADP
ejpam-3527	317	36	i	i	PRON
ejpam-3527	317	37	,	,	PUNCT
ejpam-3527	317	38	(	(	PUNCT
ejpam-3527	317	39	fupi2	fupi2	PROPN
ejpam-3527	317	40	)	)	PUNCT
ejpam-3527	317	41	for	for	ADP
ejpam-3527	317	42	any	any	DET
ejpam-3527	317	43	x	x	NOUN
ejpam-3527	317	44	,	,	PUNCT
ejpam-3527	317	45	y	y	PROPN
ejpam-3527	317	46	,	,	PUNCT
ejpam-3527	317	47	z	z	PROPN
ejpam-3527	317	48	∈	∈	PROPN
ejpam-3527	318	1	x	x	X
ejpam-3527	318	2	,	,	PUNCT
ejpam-3527	318	3	x	x	SYM
ejpam-3527	318	4	∗	∗	NOUN
ejpam-3527	318	5	(	(	PUNCT
ejpam-3527	318	6	y	y	PROPN
ejpam-3527	318	7	∗	∗	PROPN
ejpam-3527	318	8	z	z	NOUN
ejpam-3527	318	9	)	)	PUNCT
ejpam-3527	318	10	∈	∈	PROPN
ejpam-3527	319	1	i	i	PRON
ejpam-3527	319	2	and	and	CCONJ
ejpam-3527	319	3	y	y	PROPN
ejpam-3527	319	4	∈	∈	PROPN
ejpam-3527	320	1	i	i	PRON
ejpam-3527	320	2	imply	imply	VERB
ejpam-3527	320	3	x	x	X
ejpam-3527	320	4	∗	∗	NOUN
ejpam-3527	320	5	z	z	NOUN
ejpam-3527	320	6	∈	∈	PROPN
ejpam-3527	321	1	i	i	PRON
ejpam-3527	321	2	,	,	PUNCT
ejpam-3527	321	3	and	and	CCONJ
ejpam-3527	321	4	(	(	PUNCT
ejpam-3527	321	5	fupi3	fupi3	NOUN
ejpam-3527	321	6	)	)	PUNCT
ejpam-3527	321	7	for	for	ADP
ejpam-3527	321	8	any	any	PRON
ejpam-3527	321	9	a	a	DET
ejpam-3527	321	10	∈	∈	NOUN
ejpam-3527	322	1	i	i	NOUN
ejpam-3527	322	2	,	,	PUNCT
ejpam-3527	322	3	x	x	PUNCT
ejpam-3527	322	4	∈	∈	PROPN
ejpam-3527	322	5	x	x	NOUN
ejpam-3527	322	6	,	,	PUNCT
ejpam-3527	322	7	a	a	PRON
ejpam-3527	322	8	·	·	PUNCT
ejpam-3527	322	9	x	x	NOUN
ejpam-3527	322	10	,	,	PUNCT
ejpam-3527	322	11	x	x	X
ejpam-3527	322	12	·	·	PUNCT
ejpam-3527	322	13	a	a	DET
ejpam-3527	322	14	∈	∈	PROPN
ejpam-3527	322	15	i.	i.	NOUN
ejpam-3527	322	16	obviously	obviously	ADV
ejpam-3527	322	17	,	,	PUNCT
ejpam-3527	322	18	the	the	DET
ejpam-3527	322	19	subsets	subset	NOUN
ejpam-3527	322	20	{	{	PUNCT
ejpam-3527	322	21	0	0	NUM
ejpam-3527	322	22	}	}	PUNCT
ejpam-3527	322	23	and	and	CCONJ
ejpam-3527	322	24	x	x	AUX
ejpam-3527	322	25	are	be	AUX
ejpam-3527	322	26	f	f	PROPN
ejpam-3527	322	27	-up	-up	NOUN
ejpam-3527	322	28	-	-	NOUN
ejpam-3527	322	29	ideals	ideal	NOUN
ejpam-3527	322	30	of	of	ADP
ejpam-3527	322	31	x.	x.	NOUN
ejpam-3527	322	32	consider	consider	VERB
ejpam-3527	322	33	the	the	DET
ejpam-3527	322	34	f	f	PROPN
ejpam-3527	322	35	-up	-up	NOUN
ejpam-3527	322	36	-	-	PUNCT
ejpam-3527	322	37	semigroup	semigroup	NOUN
ejpam-3527	322	38	in	in	ADP
ejpam-3527	322	39	example	example	NOUN
ejpam-3527	322	40	4	4	NUM
ejpam-3527	322	41	.	.	PUNCT
ejpam-3527	322	42	routine	routine	ADJ
ejpam-3527	322	43	calculations	calculation	NOUN
ejpam-3527	322	44	show	show	VERB
ejpam-3527	322	45	that	that	SCONJ
ejpam-3527	322	46	the	the	DET
ejpam-3527	322	47	set	set	NOUN
ejpam-3527	322	48	i1	i1	PROPN
ejpam-3527	322	49	=	=	PUNCT
ejpam-3527	322	50	{	{	PUNCT
ejpam-3527	322	51	0	0	NUM
ejpam-3527	322	52	,	,	PUNCT
ejpam-3527	322	53	a	a	DET
ejpam-3527	322	54	,	,	PUNCT
ejpam-3527	322	55	b	b	NOUN
ejpam-3527	322	56	}	}	PUNCT
ejpam-3527	322	57	is	be	AUX
ejpam-3527	322	58	an	an	DET
ejpam-3527	322	59	f	f	PROPN
ejpam-3527	322	60	-up	-up	NOUN
ejpam-3527	322	61	-	-	PUNCT
ejpam-3527	322	62	ideal	ideal	NOUN
ejpam-3527	322	63	of	of	ADP
ejpam-3527	322	64	x	x	PART
ejpam-3527	322	65	while	while	SCONJ
ejpam-3527	322	66	the	the	DET
ejpam-3527	322	67	set	set	NOUN
ejpam-3527	322	68	i2	i2	PROPN
ejpam-3527	322	69	=	=	PUNCT
ejpam-3527	322	70	{	{	PUNCT
ejpam-3527	322	71	0	0	NUM
ejpam-3527	322	72	,	,	PUNCT
ejpam-3527	322	73	b	b	NOUN
ejpam-3527	322	74	,	,	PUNCT
ejpam-3527	322	75	c	c	NOUN
ejpam-3527	322	76	}	}	PUNCT
ejpam-3527	322	77	is	be	AUX
ejpam-3527	322	78	not	not	PART
ejpam-3527	322	79	an	an	DET
ejpam-3527	322	80	f	f	PROPN
ejpam-3527	322	81	-up	-up	NOUN
ejpam-3527	322	82	-	-	PUNCT
ejpam-3527	322	83	ideal	ideal	NOUN
ejpam-3527	322	84	of	of	ADP
ejpam-3527	322	85	x	x	PRON
ejpam-3527	322	86	since	since	SCONJ
ejpam-3527	322	87	b	b	PROPN
ejpam-3527	322	88	·	·	PUNCT
ejpam-3527	322	89	c	c	X
ejpam-3527	322	90	=	=	PUNCT
ejpam-3527	322	91	a	a	DET
ejpam-3527	322	92	/∈	/∈	PROPN
ejpam-3527	322	93	i2	i2	PROPN
ejpam-3527	322	94	.	.	PUNCT
ejpam-3527	323	1	theorem	theorem	VERB
ejpam-3527	323	2	11	11	NUM
ejpam-3527	323	3	.	.	PUNCT
ejpam-3527	324	1	let	let	AUX
ejpam-3527	324	2	(	(	PUNCT
ejpam-3527	324	3	x	x	X
ejpam-3527	324	4	;	;	PUNCT
ejpam-3527	324	5	∗	∗	NOUN
ejpam-3527	324	6	,	,	PUNCT
ejpam-3527	324	7	·	·	PUNCT
ejpam-3527	324	8	,	,	PUNCT
ejpam-3527	324	9	0	0	NUM
ejpam-3527	324	10	)	)	PUNCT
ejpam-3527	324	11	be	be	AUX
ejpam-3527	324	12	an	an	DET
ejpam-3527	324	13	f	f	PROPN
ejpam-3527	324	14	-up	-up	NOUN
ejpam-3527	324	15	-	-	PUNCT
ejpam-3527	324	16	semigroup	semigroup	NOUN
ejpam-3527	325	1	and	and	CCONJ
ejpam-3527	325	2	i	i	PRON
ejpam-3527	325	3	an	an	DET
ejpam-3527	325	4	f	f	PROPN
ejpam-3527	325	5	-up	-up	NOUN
ejpam-3527	325	6	-	-	NOUN
ejpam-3527	325	7	ideal	ideal	NOUN
ejpam-3527	325	8	of	of	ADP
ejpam-3527	325	9	x.	x.	NOUN
ejpam-3527	325	10	then	then	ADV
ejpam-3527	325	11	i	i	PRON
ejpam-3527	325	12	is	be	AUX
ejpam-3527	325	13	an	an	DET
ejpam-3527	325	14	f	f	PROPN
ejpam-3527	325	15	-up	-up	NOUN
ejpam-3527	325	16	-	-	PROPN
ejpam-3527	325	17	subsemigroup	subsemigroup	NOUN
ejpam-3527	325	18	of	of	ADP
ejpam-3527	325	19	x.	x.	NOUN
ejpam-3527	325	20	proof	proof	NOUN
ejpam-3527	325	21	.	.	PUNCT
ejpam-3527	326	1	by	by	ADP
ejpam-3527	326	2	(	(	PUNCT
ejpam-3527	326	3	fup1	fup1	PROPN
ejpam-3527	326	4	)	)	PUNCT
ejpam-3527	326	5	,	,	PUNCT
ejpam-3527	326	6	(	(	PUNCT
ejpam-3527	326	7	x	x	X
ejpam-3527	326	8	;	;	PUNCT
ejpam-3527	326	9	∗	∗	NOUN
ejpam-3527	326	10	,	,	PUNCT
ejpam-3527	326	11	0	0	NUM
ejpam-3527	326	12	)	)	PUNCT
ejpam-3527	326	13	is	be	AUX
ejpam-3527	326	14	a	a	DET
ejpam-3527	326	15	up	up	NOUN
ejpam-3527	326	16	-	-	PUNCT
ejpam-3527	326	17	algebra	algebra	NOUN
ejpam-3527	326	18	and	and	CCONJ
ejpam-3527	326	19	by	by	ADP
ejpam-3527	326	20	definition	definition	NOUN
ejpam-3527	326	21	,	,	PUNCT
ejpam-3527	326	22	i	i	PRON
ejpam-3527	326	23	is	be	AUX
ejpam-3527	326	24	a	a	DET
ejpam-3527	326	25	up	up	ADJ
ejpam-3527	326	26	-	-	PUNCT
ejpam-3527	326	27	ideal	ideal	NOUN
ejpam-3527	326	28	of	of	ADP
ejpam-3527	326	29	the	the	DET
ejpam-3527	326	30	up	up	NOUN
ejpam-3527	326	31	-	-	PUNCT
ejpam-3527	326	32	algebra	algebra	NOUN
ejpam-3527	326	33	x.	x.	NOUN
ejpam-3527	326	34	by	by	ADP
ejpam-3527	326	35	theorem	theorem	NOUN
ejpam-3527	326	36	2	2	NUM
ejpam-3527	326	37	,	,	PUNCT
ejpam-3527	326	38	i	i	PRON
ejpam-3527	326	39	is	be	AUX
ejpam-3527	326	40	a	a	DET
ejpam-3527	326	41	up	up	ADJ
ejpam-3527	326	42	-	-	PUNCT
ejpam-3527	326	43	subalgebra	subalgebra	NOUN
ejpam-3527	326	44	of	of	ADP
ejpam-3527	326	45	x.	x.	NOUN
ejpam-3527	326	46	let	let	VERB
ejpam-3527	326	47	x	x	PRON
ejpam-3527	326	48	,	,	PUNCT
ejpam-3527	326	49	y	y	PROPN
ejpam-3527	326	50	∈	∈	PROPN
ejpam-3527	326	51	i	i	PRON
ejpam-3527	326	52	⊆	⊆	NUM
ejpam-3527	326	53	x.	x.	NOUN
ejpam-3527	326	54	then	then	ADV
ejpam-3527	326	55	by	by	ADP
ejpam-3527	326	56	proposition	proposition	NOUN
ejpam-3527	326	57	2	2	NUM
ejpam-3527	326	58	,	,	PUNCT
ejpam-3527	327	1	x	x	PUNCT
ejpam-3527	327	2	∗	∗	NOUN
ejpam-3527	327	3	y	y	PROPN
ejpam-3527	327	4	∈	∈	PROPN
ejpam-3527	327	5	i.	i.	NOUN
ejpam-3527	327	6	since	since	SCONJ
ejpam-3527	327	7	i	i	PRON
ejpam-3527	327	8	is	be	AUX
ejpam-3527	327	9	an	an	DET
ejpam-3527	327	10	f	f	PROPN
ejpam-3527	327	11	-up	-up	NOUN
ejpam-3527	327	12	-	-	NOUN
ejpam-3527	327	13	ideal	ideal	NOUN
ejpam-3527	327	14	of	of	ADP
ejpam-3527	327	15	the	the	DET
ejpam-3527	327	16	f	f	PROPN
ejpam-3527	327	17	-up	-up	PROPN
ejpam-3527	327	18	-	-	PUNCT
ejpam-3527	327	19	semigroup	semigroup	NOUN
ejpam-3527	327	20	x	x	NOUN
ejpam-3527	327	21	,	,	PUNCT
ejpam-3527	327	22	x	x	X
ejpam-3527	327	23	·	·	PUNCT
ejpam-3527	327	24	y	y	X
ejpam-3527	327	25	∈	∈	PROPN
ejpam-3527	328	1	i	i	PRON
ejpam-3527	328	2	by	by	ADP
ejpam-3527	328	3	(	(	PUNCT
ejpam-3527	328	4	fupi3	fupi3	NOUN
ejpam-3527	328	5	)	)	PUNCT
ejpam-3527	328	6	.	.	PUNCT
ejpam-3527	329	1	thus	thus	ADV
ejpam-3527	329	2	,	,	PUNCT
ejpam-3527	329	3	i	i	PRON
ejpam-3527	329	4	is	be	AUX
ejpam-3527	329	5	an	an	DET
ejpam-3527	329	6	f	f	PROPN
ejpam-3527	329	7	-up	-up	NOUN
ejpam-3527	329	8	-	-	PROPN
ejpam-3527	329	9	subsemigroup	subsemigroup	NOUN
ejpam-3527	329	10	of	of	ADP
ejpam-3527	329	11	x	x	PUNCT
ejpam-3527	329	12	by	by	ADP
ejpam-3527	329	13	theorem	theorem	NOUN
ejpam-3527	329	14	5	5	NUM
ejpam-3527	329	15	.	.	PUNCT
ejpam-3527	329	16	theorem	theorem	NOUN
ejpam-3527	329	17	12	12	NUM
ejpam-3527	329	18	.	.	PUNCT
ejpam-3527	330	1	let	let	VERB
ejpam-3527	330	2	x	x	PRON
ejpam-3527	330	3	be	be	AUX
ejpam-3527	330	4	an	an	DET
ejpam-3527	330	5	f	f	PROPN
ejpam-3527	330	6	-up	-up	NOUN
ejpam-3527	330	7	-	-	PUNCT
ejpam-3527	330	8	semigroup	semigroup	NOUN
ejpam-3527	330	9	and	and	CCONJ
ejpam-3527	330	10	{	{	PUNCT
ejpam-3527	330	11	ai	ai	INTJ
ejpam-3527	330	12	:	:	PUNCT
ejpam-3527	330	13	i	i	PRON
ejpam-3527	330	14	∈	∈	VERB
ejpam-3527	330	15	i	i	PRON
ejpam-3527	330	16	}	}	PUNCT
ejpam-3527	330	17	be	be	VERB
ejpam-3527	330	18	a	a	DET
ejpam-3527	330	19	nonempty	nonempty	ADJ
ejpam-3527	330	20	collection	collection	NOUN
ejpam-3527	330	21	of	of	ADP
ejpam-3527	330	22	f	f	PROPN
ejpam-3527	330	23	-up	-up	NOUN
ejpam-3527	330	24	-	-	NOUN
ejpam-3527	330	25	ideals	ideal	NOUN
ejpam-3527	330	26	of	of	ADP
ejpam-3527	330	27	x.	x.	NOUN
ejpam-3527	330	28	then	then	ADV
ejpam-3527	330	29	⋂	⋂	PROPN
ejpam-3527	330	30	i∈i	i∈i	NOUN
ejpam-3527	330	31	ai	ai	VERB
ejpam-3527	330	32	is	be	AUX
ejpam-3527	330	33	an	an	DET
ejpam-3527	330	34	f	f	PROPN
ejpam-3527	330	35	-up	-up	NOUN
ejpam-3527	330	36	-	-	NOUN
ejpam-3527	330	37	ideal	ideal	NOUN
ejpam-3527	330	38	of	of	ADP
ejpam-3527	330	39	x.	x.	NOUN
ejpam-3527	330	40	proof	proof	NOUN
ejpam-3527	330	41	.	.	PUNCT
ejpam-3527	331	1	suppose	suppose	VERB
ejpam-3527	331	2	{	{	PUNCT
ejpam-3527	331	3	ai	ai	VERB
ejpam-3527	331	4	:	:	PUNCT
ejpam-3527	331	5	i	i	PRON
ejpam-3527	331	6	∈	∈	VERB
ejpam-3527	331	7	i	i	PRON
ejpam-3527	331	8	}	}	PUNCT
ejpam-3527	331	9	is	be	AUX
ejpam-3527	331	10	a	a	DET
ejpam-3527	331	11	nonempty	nonempty	ADJ
ejpam-3527	331	12	collection	collection	NOUN
ejpam-3527	331	13	of	of	ADP
ejpam-3527	331	14	f	f	PROPN
ejpam-3527	331	15	-up	-up	NOUN
ejpam-3527	331	16	-	-	NOUN
ejpam-3527	331	17	ideals	ideal	NOUN
ejpam-3527	331	18	of	of	ADP
ejpam-3527	331	19	x.	x.	NOUN
ejpam-3527	331	20	since	since	SCONJ
ejpam-3527	331	21	0	0	NUM
ejpam-3527	331	22	∈	∈	PROPN
ejpam-3527	331	23	ai	ai	VERB
ejpam-3527	331	24	for	for	ADP
ejpam-3527	331	25	all	all	PRON
ejpam-3527	331	26	i	i	PRON
ejpam-3527	331	27	∈	∈	VERB
ejpam-3527	332	1	i	i	PRON
ejpam-3527	332	2	,	,	PUNCT
ejpam-3527	332	3	0	0	NUM
ejpam-3527	332	4	∈	∈	PROPN
ejpam-3527	332	5	⋂	⋂	PROPN
ejpam-3527	332	6	i∈i	i∈i	ADJ
ejpam-3527	332	7	ai	ai	VERB
ejpam-3527	333	1	and	and	CCONJ
ejpam-3527	333	2	so	so	ADV
ejpam-3527	333	3	⋂	⋂	PROPN
ejpam-3527	333	4	i∈i	i∈i	ADJ
ejpam-3527	333	5	ai	ai	VERB
ejpam-3527	333	6	6=	6=	ADP
ejpam-3527	333	7	∅.	∅.	AUX
ejpam-3527	333	8	suppose	suppose	VERB
ejpam-3527	333	9	x	x	PRON
ejpam-3527	333	10	,	,	PUNCT
ejpam-3527	333	11	y	y	PROPN
ejpam-3527	333	12	,	,	PUNCT
ejpam-3527	333	13	z	z	NOUN
ejpam-3527	333	14	∈	∈	PROPN
ejpam-3527	333	15	x	x	PUNCT
ejpam-3527	333	16	such	such	ADJ
ejpam-3527	333	17	that	that	SCONJ
ejpam-3527	333	18	x	x	SYM
ejpam-3527	333	19	∗	∗	NOUN
ejpam-3527	333	20	(	(	PUNCT
ejpam-3527	333	21	y	y	PROPN
ejpam-3527	333	22	∗	∗	PROPN
ejpam-3527	333	23	z	z	NOUN
ejpam-3527	333	24	)	)	PUNCT
ejpam-3527	333	25	∈	∈	PROPN
ejpam-3527	333	26	⋂	⋂	PROPN
ejpam-3527	333	27	i∈i	i∈i	ADJ
ejpam-3527	333	28	ai	ai	VERB
ejpam-3527	333	29	and	and	CCONJ
ejpam-3527	333	30	y	y	PROPN
ejpam-3527	333	31	∈	∈	PROPN
ejpam-3527	334	1	⋂	⋂	PROPN
ejpam-3527	334	2	i∈i	i∈i	ADJ
ejpam-3527	334	3	ai	ai	VERB
ejpam-3527	334	4	.	.	PUNCT
ejpam-3527	335	1	then	then	ADV
ejpam-3527	335	2	x	x	X
ejpam-3527	335	3	∗	∗	NOUN
ejpam-3527	335	4	(	(	PUNCT
ejpam-3527	335	5	y	y	PROPN
ejpam-3527	335	6	∗	∗	PROPN
ejpam-3527	335	7	z	z	PROPN
ejpam-3527	335	8	)	)	PUNCT
ejpam-3527	335	9	∈	∈	PROPN
ejpam-3527	335	10	ai	ai	VERB
ejpam-3527	335	11	and	and	CCONJ
ejpam-3527	335	12	y	y	PROPN
ejpam-3527	335	13	∈	∈	PROPN
ejpam-3527	335	14	ai	ai	VERB
ejpam-3527	335	15	for	for	ADP
ejpam-3527	335	16	all	all	PRON
ejpam-3527	335	17	i	i	PRON
ejpam-3527	335	18	∈	∈	PROPN
ejpam-3527	336	1	i	i	PRON
ejpam-3527	336	2	.	.	PUNCT
ejpam-3527	337	1	since	since	SCONJ
ejpam-3527	337	2	d.gomisong	d.gomisong	PROPN
ejpam-3527	337	3	,	,	PUNCT
ejpam-3527	337	4	r.	r.	PROPN
ejpam-3527	337	5	isla	isla	PROPN
ejpam-3527	337	6	/	/	SYM
ejpam-3527	337	7	eur	eur	PROPN
ejpam-3527	337	8	.	.	PUNCT
ejpam-3527	338	1	j.	j.	PROPN
ejpam-3527	338	2	pure	pure	PROPN
ejpam-3527	338	3	appl	appl	PROPN
ejpam-3527	338	4	.	.	PROPN
ejpam-3527	338	5	math	math	PROPN
ejpam-3527	338	6	,	,	PUNCT
ejpam-3527	338	7	12	12	NUM
ejpam-3527	338	8	(	(	PUNCT
ejpam-3527	338	9	4	4	NUM
ejpam-3527	338	10	)	)	PUNCT
ejpam-3527	338	11	(	(	PUNCT
ejpam-3527	338	12	2019	2019	NUM
ejpam-3527	338	13	)	)	PUNCT
ejpam-3527	338	14	,	,	PUNCT
ejpam-3527	338	15	1483	1483	NUM
ejpam-3527	338	16	-	-	SYM
ejpam-3527	338	17	1496	1496	NUM
ejpam-3527	338	18	1493	1493	NUM
ejpam-3527	338	19	each	each	PRON
ejpam-3527	338	20	ai	ai	VERB
ejpam-3527	338	21	is	be	AUX
ejpam-3527	338	22	an	an	DET
ejpam-3527	338	23	f	f	PROPN
ejpam-3527	338	24	-up	-up	NOUN
ejpam-3527	338	25	-	-	NOUN
ejpam-3527	338	26	ideal	ideal	NOUN
ejpam-3527	338	27	for	for	ADP
ejpam-3527	338	28	all	all	PRON
ejpam-3527	338	29	i	i	PRON
ejpam-3527	338	30	∈	∈	PROPN
ejpam-3527	339	1	i	i	PRON
ejpam-3527	339	2	,	,	PUNCT
ejpam-3527	339	3	it	it	PRON
ejpam-3527	339	4	follows	follow	VERB
ejpam-3527	339	5	that	that	SCONJ
ejpam-3527	339	6	x	x	NOUN
ejpam-3527	339	7	∗	∗	NOUN
ejpam-3527	339	8	z	z	NOUN
ejpam-3527	339	9	∈	∈	PROPN
ejpam-3527	339	10	ai	ai	VERB
ejpam-3527	339	11	for	for	ADP
ejpam-3527	339	12	all	all	PRON
ejpam-3527	339	13	i	i	PRON
ejpam-3527	339	14	∈	∈	VERB
ejpam-3527	340	1	i	i	PRON
ejpam-3527	340	2	.	.	PUNCT
ejpam-3527	341	1	hence	hence	ADV
ejpam-3527	341	2	,	,	PUNCT
ejpam-3527	341	3	x	x	X
ejpam-3527	341	4	∗	∗	NOUN
ejpam-3527	341	5	z	z	PROPN
ejpam-3527	341	6	∈	∈	PROPN
ejpam-3527	341	7	⋂	⋂	PROPN
ejpam-3527	341	8	i∈i	i∈i	ADJ
ejpam-3527	341	9	ai	ai	VERB
ejpam-3527	341	10	.	.	PUNCT
ejpam-3527	342	1	let	let	VERB
ejpam-3527	342	2	a	a	DET
ejpam-3527	342	3	∈	∈	PROPN
ejpam-3527	342	4	⋂	⋂	PROPN
ejpam-3527	342	5	i∈i	i∈i	ADJ
ejpam-3527	342	6	ai	ai	VERB
ejpam-3527	343	1	and	and	CCONJ
ejpam-3527	343	2	x	x	PUNCT
ejpam-3527	343	3	∈	∈	PROPN
ejpam-3527	343	4	x.	x.	NOUN
ejpam-3527	343	5	then	then	ADV
ejpam-3527	343	6	a	a	DET
ejpam-3527	343	7	∈	∈	NOUN
ejpam-3527	343	8	ai	ai	VERB
ejpam-3527	343	9	for	for	ADP
ejpam-3527	343	10	all	all	PRON
ejpam-3527	343	11	i	i	PRON
ejpam-3527	343	12	∈	∈	PROPN
ejpam-3527	344	1	i	i	PRON
ejpam-3527	344	2	.	.	PUNCT
ejpam-3527	345	1	since	since	SCONJ
ejpam-3527	345	2	each	each	DET
ejpam-3527	345	3	ai	ai	VERB
ejpam-3527	345	4	is	be	AUX
ejpam-3527	345	5	an	an	DET
ejpam-3527	345	6	f	f	PROPN
ejpam-3527	345	7	-up	-up	NOUN
ejpam-3527	345	8	-	-	NOUN
ejpam-3527	345	9	ideal	ideal	NOUN
ejpam-3527	345	10	for	for	ADP
ejpam-3527	345	11	all	all	PRON
ejpam-3527	345	12	i	i	PRON
ejpam-3527	345	13	∈	∈	PROPN
ejpam-3527	346	1	i	i	PRON
ejpam-3527	346	2	,	,	PUNCT
ejpam-3527	346	3	a	a	PRON
ejpam-3527	346	4	·	·	PUNCT
ejpam-3527	346	5	x	x	NOUN
ejpam-3527	346	6	,	,	PUNCT
ejpam-3527	346	7	x	x	X
ejpam-3527	346	8	·	·	PUNCT
ejpam-3527	346	9	a	a	DET
ejpam-3527	346	10	∈	∈	NOUN
ejpam-3527	346	11	ai	ai	VERB
ejpam-3527	346	12	for	for	ADP
ejpam-3527	346	13	all	all	PRON
ejpam-3527	346	14	i	i	PRON
ejpam-3527	346	15	∈	∈	VERB
ejpam-3527	347	1	i	i	PRON
ejpam-3527	347	2	.	.	PUNCT
ejpam-3527	348	1	hence	hence	ADV
ejpam-3527	348	2	,	,	PUNCT
ejpam-3527	348	3	a	a	DET
ejpam-3527	348	4	·	·	PUNCT
ejpam-3527	348	5	x	x	NOUN
ejpam-3527	348	6	,	,	PUNCT
ejpam-3527	348	7	x	x	X
ejpam-3527	348	8	·	·	PUNCT
ejpam-3527	348	9	a	a	DET
ejpam-3527	348	10	∈	∈	PROPN
ejpam-3527	348	11	⋂	⋂	PROPN
ejpam-3527	348	12	i∈i	i∈i	ADJ
ejpam-3527	348	13	ai	ai	VERB
ejpam-3527	348	14	.	.	PUNCT
ejpam-3527	349	1	therefore	therefore	ADV
ejpam-3527	349	2	,	,	PUNCT
ejpam-3527	349	3	⋂	⋂	PROPN
ejpam-3527	349	4	i∈i	i∈i	ADJ
ejpam-3527	349	5	ai	ai	VERB
ejpam-3527	349	6	is	be	AUX
ejpam-3527	349	7	an	an	DET
ejpam-3527	349	8	f	f	PROPN
ejpam-3527	349	9	-up	-up	NOUN
ejpam-3527	349	10	-	-	NOUN
ejpam-3527	349	11	ideal	ideal	NOUN
ejpam-3527	349	12	of	of	ADP
ejpam-3527	349	13	x.	x.	NOUN
ejpam-3527	349	14	let	let	VERB
ejpam-3527	349	15	(	(	PUNCT
ejpam-3527	349	16	x	x	X
ejpam-3527	349	17	;	;	PUNCT
ejpam-3527	349	18	∗	∗	NOUN
ejpam-3527	349	19	,	,	PUNCT
ejpam-3527	349	20	·	·	PUNCT
ejpam-3527	349	21	,	,	PUNCT
ejpam-3527	349	22	0	0	NUM
ejpam-3527	349	23	)	)	PUNCT
ejpam-3527	349	24	be	be	AUX
ejpam-3527	349	25	an	an	DET
ejpam-3527	349	26	f	f	PROPN
ejpam-3527	349	27	-up	-up	NOUN
ejpam-3527	349	28	-	-	PUNCT
ejpam-3527	349	29	semigroup	semigroup	NOUN
ejpam-3527	350	1	and	and	CCONJ
ejpam-3527	350	2	i	i	PRON
ejpam-3527	350	3	be	be	VERB
ejpam-3527	350	4	an	an	DET
ejpam-3527	350	5	f	f	PROPN
ejpam-3527	350	6	-up	-up	NOUN
ejpam-3527	350	7	-	-	NOUN
ejpam-3527	350	8	ideal	ideal	NOUN
ejpam-3527	350	9	of	of	ADP
ejpam-3527	350	10	x.	x.	NOUN
ejpam-3527	350	11	define	define	VERB
ejpam-3527	350	12	the	the	DET
ejpam-3527	350	13	binary	binary	PROPN
ejpam-3527	350	14	relation	relation	PROPN
ejpam-3527	350	15	∼i	∼i	PROPN
ejpam-3527	350	16	on	on	ADP
ejpam-3527	350	17	x	x	PUNCT
ejpam-3527	350	18	as	as	SCONJ
ejpam-3527	350	19	follows	follow	VERB
ejpam-3527	350	20	:	:	PUNCT
ejpam-3527	350	21	for	for	ADP
ejpam-3527	350	22	all	all	DET
ejpam-3527	350	23	x	x	NOUN
ejpam-3527	350	24	,	,	PUNCT
ejpam-3527	350	25	y	y	PROPN
ejpam-3527	350	26	∈	∈	PROPN
ejpam-3527	350	27	x	x	X
ejpam-3527	350	28	,	,	PUNCT
ejpam-3527	350	29	x	x	PROPN
ejpam-3527	350	30	∼i	∼i	PROPN
ejpam-3527	350	31	y	y	PROPN
ejpam-3527	351	1	if	if	SCONJ
ejpam-3527	351	2	and	and	CCONJ
ejpam-3527	351	3	only	only	ADV
ejpam-3527	351	4	if	if	SCONJ
ejpam-3527	351	5	x	x	X
ejpam-3527	351	6	∗	∗	VERB
ejpam-3527	351	7	y	y	NOUN
ejpam-3527	351	8	∈	∈	PROPN
ejpam-3527	352	1	i	i	PRON
ejpam-3527	352	2	and	and	CCONJ
ejpam-3527	352	3	y	y	PROPN
ejpam-3527	352	4	∗	∗	NOUN
ejpam-3527	352	5	x	x	PUNCT
ejpam-3527	352	6	∈	∈	PROPN
ejpam-3527	352	7	i.	i.	NOUN
ejpam-3527	352	8	denote	denote	VERB
ejpam-3527	352	9	[	[	X
ejpam-3527	352	10	x]i	x]i	NOUN
ejpam-3527	352	11	as	as	ADP
ejpam-3527	352	12	the	the	DET
ejpam-3527	352	13	equivalence	equivalence	NOUN
ejpam-3527	352	14	class	class	NOUN
ejpam-3527	352	15	containing	contain	VERB
ejpam-3527	352	16	x	x	SYM
ejpam-3527	352	17	∈	∈	PROPN
ejpam-3527	352	18	x	x	X
ejpam-3527	352	19	and	and	CCONJ
ejpam-3527	352	20	x	x	X
ejpam-3527	352	21	/	/	SYM
ejpam-3527	352	22	i	i	PRON
ejpam-3527	352	23	as	as	ADP
ejpam-3527	352	24	the	the	DET
ejpam-3527	352	25	set	set	NOUN
ejpam-3527	352	26	of	of	ADP
ejpam-3527	352	27	all	all	DET
ejpam-3527	352	28	equivalence	equivalence	NOUN
ejpam-3527	352	29	classes	class	NOUN
ejpam-3527	352	30	of	of	ADP
ejpam-3527	352	31	x	x	PUNCT
ejpam-3527	352	32	with	with	ADP
ejpam-3527	352	33	respect	respect	NOUN
ejpam-3527	352	34	to	to	ADP
ejpam-3527	352	35	“	"	PUNCT
ejpam-3527	352	36	∼i	∼i	PROPN
ejpam-3527	352	37	”	"	PUNCT
ejpam-3527	352	38	,	,	PUNCT
ejpam-3527	352	39	that	that	ADV
ejpam-3527	352	40	is	is	ADV
ejpam-3527	352	41	,	,	PUNCT
ejpam-3527	352	42	[	[	X
ejpam-3527	352	43	x]i	x]i	X
ejpam-3527	352	44	=	=	SYM
ejpam-3527	352	45	{	{	PUNCT
ejpam-3527	352	46	y	y	PROPN
ejpam-3527	352	47	∈	∈	PROPN
ejpam-3527	352	48	x	x	X
ejpam-3527	352	49	:	:	PUNCT
ejpam-3527	352	50	x	x	PUNCT
ejpam-3527	352	51	∼i	∼i	PROPN
ejpam-3527	352	52	y	y	PROPN
ejpam-3527	352	53	}	}	PUNCT
ejpam-3527	352	54	and	and	CCONJ
ejpam-3527	352	55	x	x	X
ejpam-3527	352	56	/	/	SYM
ejpam-3527	352	57	i	i	PRON
ejpam-3527	352	58	=	=	PUNCT
ejpam-3527	352	59	{	{	PUNCT
ejpam-3527	353	1	[	[	X
ejpam-3527	353	2	x]i	x]i	NOUN
ejpam-3527	353	3	:	:	PUNCT
ejpam-3527	353	4	x	x	SYM
ejpam-3527	353	5	∈	∈	NOUN
ejpam-3527	353	6	x	x	X
ejpam-3527	353	7	}	}	PUNCT
ejpam-3527	353	8	.	.	PUNCT
ejpam-3527	354	1	remark	remark	NOUN
ejpam-3527	354	2	5	5	NUM
ejpam-3527	354	3	.	.	PUNCT
ejpam-3527	355	1	let	let	VERB
ejpam-3527	355	2	x	x	PRON
ejpam-3527	355	3	be	be	AUX
ejpam-3527	355	4	an	an	DET
ejpam-3527	355	5	f	f	PROPN
ejpam-3527	355	6	-up	-up	NOUN
ejpam-3527	355	7	-	-	PUNCT
ejpam-3527	355	8	semigroup	semigroup	NOUN
ejpam-3527	356	1	and	and	CCONJ
ejpam-3527	356	2	i	i	PRON
ejpam-3527	356	3	be	be	VERB
ejpam-3527	356	4	an	an	DET
ejpam-3527	356	5	f	f	PROPN
ejpam-3527	356	6	-up	-up	NOUN
ejpam-3527	356	7	-	-	NOUN
ejpam-3527	356	8	ideal	ideal	NOUN
ejpam-3527	356	9	of	of	ADP
ejpam-3527	356	10	x.	x.	NOUN
ejpam-3527	356	11	then	then	ADV
ejpam-3527	356	12	x	x	SYM
ejpam-3527	356	13	∈	∈	PROPN
ejpam-3527	357	1	[	[	X
ejpam-3527	357	2	x]i	x]i	NOUN
ejpam-3527	357	3	for	for	ADP
ejpam-3527	357	4	all	all	DET
ejpam-3527	357	5	x	x	SYM
ejpam-3527	357	6	∈	∈	PROPN
ejpam-3527	357	7	x.	x.	NOUN
ejpam-3527	357	8	lemma	lemma	PROPN
ejpam-3527	357	9	1	1	X
ejpam-3527	357	10	.	.	PUNCT
ejpam-3527	358	1	let	let	VERB
ejpam-3527	358	2	x	x	PRON
ejpam-3527	358	3	be	be	AUX
ejpam-3527	358	4	an	an	DET
ejpam-3527	358	5	f	f	PROPN
ejpam-3527	358	6	-up	-up	NOUN
ejpam-3527	358	7	-	-	PUNCT
ejpam-3527	358	8	semigroup	semigroup	NOUN
ejpam-3527	359	1	and	and	CCONJ
ejpam-3527	359	2	i	i	PRON
ejpam-3527	359	3	be	be	VERB
ejpam-3527	359	4	an	an	DET
ejpam-3527	359	5	f	f	PROPN
ejpam-3527	359	6	-up	-up	NOUN
ejpam-3527	359	7	-	-	NOUN
ejpam-3527	359	8	ideal	ideal	NOUN
ejpam-3527	359	9	of	of	ADP
ejpam-3527	359	10	x.	x.	NOUN
ejpam-3527	360	1	then	then	ADV
ejpam-3527	361	1	[	[	X
ejpam-3527	361	2	x]i	x]i	X
ejpam-3527	361	3	=	=	PUNCT
ejpam-3527	362	1	[	[	X
ejpam-3527	362	2	y]i	y]i	ADJ
ejpam-3527	362	3	if	if	SCONJ
ejpam-3527	362	4	and	and	CCONJ
ejpam-3527	362	5	only	only	ADV
ejpam-3527	362	6	if	if	SCONJ
ejpam-3527	362	7	x	x	X
ejpam-3527	362	8	∼i	∼i	PROPN
ejpam-3527	362	9	y.	y.	PROPN
ejpam-3527	362	10	proof	proof	PROPN
ejpam-3527	362	11	.	.	PUNCT
ejpam-3527	362	12	suppose	suppose	VERB
ejpam-3527	363	1	[	[	X
ejpam-3527	363	2	x]i	x]i	X
ejpam-3527	363	3	=	=	SYM
ejpam-3527	363	4	[	[	X
ejpam-3527	363	5	y]i	y]i	NOUN
ejpam-3527	363	6	.	.	PUNCT
ejpam-3527	364	1	since	since	SCONJ
ejpam-3527	364	2	y	y	PROPN
ejpam-3527	364	3	∈	∈	PROPN
ejpam-3527	365	1	[	[	X
ejpam-3527	365	2	y]i	y]i	NOUN
ejpam-3527	365	3	=	=	SYM
ejpam-3527	366	1	[	[	X
ejpam-3527	366	2	x]i	x]i	X
ejpam-3527	366	3	,	,	PUNCT
ejpam-3527	366	4	we	we	PRON
ejpam-3527	366	5	have	have	VERB
ejpam-3527	366	6	x	x	PROPN
ejpam-3527	366	7	∼i	∼i	PROPN
ejpam-3527	366	8	y.	y.	PROPN
ejpam-3527	366	9	conversely	conversely	ADV
ejpam-3527	366	10	,	,	PUNCT
ejpam-3527	366	11	suppose	suppose	VERB
ejpam-3527	366	12	x	x	X
ejpam-3527	366	13	∼i	∼i	PROPN
ejpam-3527	366	14	y.	y.	PROPN
ejpam-3527	366	15	let	let	VERB
ejpam-3527	366	16	z	z	NOUN
ejpam-3527	366	17	∈	∈	PROPN
ejpam-3527	367	1	[	[	X
ejpam-3527	367	2	x]i	x]i	X
ejpam-3527	367	3	.	.	PUNCT
ejpam-3527	368	1	then	then	ADV
ejpam-3527	368	2	x	x	X
ejpam-3527	368	3	∼i	∼i	PROPN
ejpam-3527	368	4	z.	z.	PROPN
ejpam-3527	368	5	by	by	ADP
ejpam-3527	368	6	symmetric	symmetric	ADJ
ejpam-3527	368	7	property	property	NOUN
ejpam-3527	368	8	,	,	PUNCT
ejpam-3527	368	9	z	z	NOUN
ejpam-3527	368	10	∼i	∼i	PROPN
ejpam-3527	368	11	x.	x.	VERB
ejpam-3527	368	12	by	by	ADP
ejpam-3527	368	13	transitivity	transitivity	NOUN
ejpam-3527	368	14	,	,	PUNCT
ejpam-3527	368	15	z	z	PROPN
ejpam-3527	368	16	∼i	∼i	PROPN
ejpam-3527	368	17	y	y	PROPN
ejpam-3527	368	18	and	and	CCONJ
ejpam-3527	368	19	by	by	ADP
ejpam-3527	368	20	symmetric	symmetric	ADJ
ejpam-3527	368	21	property	property	NOUN
ejpam-3527	368	22	,	,	PUNCT
ejpam-3527	368	23	y	y	PROPN
ejpam-3527	368	24	∼i	∼i	PROPN
ejpam-3527	368	25	z	z	PROPN
ejpam-3527	369	1	and	and	CCONJ
ejpam-3527	369	2	so	so	ADV
ejpam-3527	369	3	,	,	PUNCT
ejpam-3527	369	4	z	z	NOUN
ejpam-3527	369	5	∈	∈	PROPN
ejpam-3527	370	1	[	[	X
ejpam-3527	370	2	y]i	y]i	NOUN
ejpam-3527	370	3	.	.	PUNCT
ejpam-3527	371	1	thus	thus	ADV
ejpam-3527	371	2	,	,	PUNCT
ejpam-3527	371	3	[	[	X
ejpam-3527	371	4	x]i	x]i	X
ejpam-3527	371	5	⊆	⊆	NUM
ejpam-3527	371	6	[	[	X
ejpam-3527	371	7	y]i	y]i	ADJ
ejpam-3527	371	8	.	.	PUNCT
ejpam-3527	372	1	let	let	VERB
ejpam-3527	372	2	z	z	NOUN
ejpam-3527	372	3	∈	∈	PROPN
ejpam-3527	373	1	[	[	X
ejpam-3527	373	2	y]i	y]i	NOUN
ejpam-3527	373	3	.	.	PUNCT
ejpam-3527	374	1	then	then	ADV
ejpam-3527	374	2	y	y	PROPN
ejpam-3527	374	3	∼i	∼i	PROPN
ejpam-3527	374	4	z.	z.	PROPN
ejpam-3527	374	5	by	by	ADP
ejpam-3527	374	6	transitivity	transitivity	NOUN
ejpam-3527	374	7	,	,	PUNCT
ejpam-3527	374	8	x	x	PROPN
ejpam-3527	374	9	∼i	∼i	PROPN
ejpam-3527	374	10	z	z	PROPN
ejpam-3527	374	11	,	,	PUNCT
ejpam-3527	374	12	that	that	ADV
ejpam-3527	374	13	is	is	ADV
ejpam-3527	374	14	,	,	PUNCT
ejpam-3527	374	15	z	z	NOUN
ejpam-3527	374	16	∈	∈	PROPN
ejpam-3527	375	1	[	[	X
ejpam-3527	375	2	x]i	x]i	X
ejpam-3527	375	3	.	.	PUNCT
ejpam-3527	376	1	thus	thus	ADV
ejpam-3527	376	2	,	,	PUNCT
ejpam-3527	376	3	[	[	X
ejpam-3527	376	4	y]i	y]i	ADJ
ejpam-3527	376	5	⊆	⊆	NUM
ejpam-3527	376	6	[	[	X
ejpam-3527	376	7	x]i	x]i	X
ejpam-3527	376	8	.	.	PUNCT
ejpam-3527	377	1	hence	hence	ADV
ejpam-3527	377	2	,	,	PUNCT
ejpam-3527	377	3	[	[	X
ejpam-3527	377	4	x]i	x]i	X
ejpam-3527	377	5	=	=	SYM
ejpam-3527	378	1	[	[	X
ejpam-3527	378	2	y]i	y]i	NOUN
ejpam-3527	378	3	.	.	PUNCT
ejpam-3527	379	1	proposition	proposition	NOUN
ejpam-3527	379	2	4	4	NUM
ejpam-3527	379	3	.	.	PUNCT
ejpam-3527	380	1	let	let	VERB
ejpam-3527	380	2	x	x	PRON
ejpam-3527	380	3	be	be	AUX
ejpam-3527	380	4	an	an	DET
ejpam-3527	380	5	f	f	PROPN
ejpam-3527	380	6	-up	-up	NOUN
ejpam-3527	380	7	-	-	PUNCT
ejpam-3527	380	8	semigroup	semigroup	NOUN
ejpam-3527	381	1	and	and	CCONJ
ejpam-3527	381	2	i	i	PRON
ejpam-3527	381	3	be	be	VERB
ejpam-3527	381	4	an	an	DET
ejpam-3527	381	5	f	f	PROPN
ejpam-3527	381	6	-up	-up	NOUN
ejpam-3527	381	7	-	-	NOUN
ejpam-3527	381	8	ideal	ideal	NOUN
ejpam-3527	381	9	of	of	ADP
ejpam-3527	381	10	x.	x.	NOUN
ejpam-3527	381	11	then	then	ADV
ejpam-3527	381	12	(	(	PUNCT
ejpam-3527	381	13	i	i	NOUN
ejpam-3527	381	14	)	)	PUNCT
ejpam-3527	382	1	[	[	X
ejpam-3527	382	2	0]i	0]i	X
ejpam-3527	382	3	=	=	SYM
ejpam-3527	382	4	i	i	PROPN
ejpam-3527	382	5	,	,	PUNCT
ejpam-3527	382	6	(	(	PUNCT
ejpam-3527	382	7	ii	ii	NOUN
ejpam-3527	382	8	)	)	PUNCT
ejpam-3527	383	1	[	[	X
ejpam-3527	383	2	x]i	x]i	X
ejpam-3527	384	1	=	=	PUNCT
ejpam-3527	384	2	i	i	PRON
ejpam-3527	384	3	if	if	SCONJ
ejpam-3527	385	1	and	and	CCONJ
ejpam-3527	385	2	only	only	ADV
ejpam-3527	385	3	if	if	SCONJ
ejpam-3527	385	4	x	x	SYM
ejpam-3527	385	5	∈	∈	PROPN
ejpam-3527	385	6	i	i	PRON
ejpam-3527	385	7	,	,	PUNCT
ejpam-3527	385	8	for	for	ADP
ejpam-3527	385	9	all	all	DET
ejpam-3527	385	10	x	x	SYM
ejpam-3527	385	11	∈	∈	PROPN
ejpam-3527	385	12	i	i	PRON
ejpam-3527	385	13	,	,	PUNCT
ejpam-3527	385	14	and	and	CCONJ
ejpam-3527	385	15	(	(	PUNCT
ejpam-3527	385	16	iii	iii	X
ejpam-3527	385	17	)	)	PUNCT
ejpam-3527	385	18	i	i	PRON
ejpam-3527	385	19	∗	∗	VERB
ejpam-3527	386	1	[	[	X
ejpam-3527	386	2	x]i	x]i	X
ejpam-3527	386	3	=	=	SYM
ejpam-3527	387	1	[	[	X
ejpam-3527	387	2	x]i	x]i	NOUN
ejpam-3527	387	3	for	for	ADP
ejpam-3527	387	4	all	all	DET
ejpam-3527	387	5	x	x	SYM
ejpam-3527	387	6	∈	∈	ADJ
ejpam-3527	387	7	x.	x.	NOUN
ejpam-3527	387	8	proof	proof	NOUN
ejpam-3527	387	9	.	.	PUNCT
ejpam-3527	388	1	let	let	VERB
ejpam-3527	388	2	i	i	PRON
ejpam-3527	388	3	be	be	AUX
ejpam-3527	388	4	an	an	DET
ejpam-3527	388	5	f	f	PROPN
ejpam-3527	388	6	-up	-up	NOUN
ejpam-3527	388	7	-	-	NOUN
ejpam-3527	388	8	ideal	ideal	NOUN
ejpam-3527	388	9	of	of	ADP
ejpam-3527	388	10	x.	x.	PROPN
ejpam-3527	388	11	(	(	PUNCT
ejpam-3527	388	12	i	i	NOUN
ejpam-3527	388	13	)	)	PUNCT
ejpam-3527	389	1	if	if	SCONJ
ejpam-3527	389	2	x	x	PUNCT
ejpam-3527	389	3	∈	∈	PROPN
ejpam-3527	389	4	[	[	X
ejpam-3527	389	5	0]i	0]i	NOUN
ejpam-3527	389	6	,	,	PUNCT
ejpam-3527	389	7	then	then	ADV
ejpam-3527	389	8	by	by	ADP
ejpam-3527	389	9	definition	definition	NOUN
ejpam-3527	389	10	,	,	PUNCT
ejpam-3527	389	11	0	0	NUM
ejpam-3527	389	12	∼i	∼i	PROPN
ejpam-3527	389	13	x	x	PUNCT
ejpam-3527	389	14	and	and	CCONJ
ejpam-3527	389	15	by	by	ADP
ejpam-3527	389	16	(	(	PUNCT
ejpam-3527	389	17	up2	up2	NOUN
ejpam-3527	389	18	)	)	PUNCT
ejpam-3527	389	19	,	,	PUNCT
ejpam-3527	389	20	x	x	PUNCT
ejpam-3527	389	21	=	=	SYM
ejpam-3527	389	22	0	0	NUM
ejpam-3527	389	23	∗	∗	NOUN
ejpam-3527	389	24	x	x	SYM
ejpam-3527	389	25	∈	∈	PROPN
ejpam-3527	389	26	i.	i.	NOUN
ejpam-3527	389	27	thus	thus	ADV
ejpam-3527	389	28	,	,	PUNCT
ejpam-3527	389	29	[	[	X
ejpam-3527	389	30	0]i	0]i	NOUN
ejpam-3527	389	31	⊆	⊆	NUM
ejpam-3527	389	32	i.	i.	NOUN
ejpam-3527	389	33	let	let	VERB
ejpam-3527	389	34	x	x	X
ejpam-3527	389	35	∈	∈	PROPN
ejpam-3527	389	36	i.	i.	NOUN
ejpam-3527	389	37	by	by	ADP
ejpam-3527	389	38	(	(	PUNCT
ejpam-3527	389	39	up2	up2	PROPN
ejpam-3527	389	40	)	)	PUNCT
ejpam-3527	389	41	,	,	PUNCT
ejpam-3527	389	42	0	0	NUM
ejpam-3527	389	43	∗	∗	NOUN
ejpam-3527	389	44	x	x	X
ejpam-3527	390	1	=	=	SYM
ejpam-3527	390	2	x	x	SYM
ejpam-3527	390	3	∈	∈	PROPN
ejpam-3527	390	4	i.	i.	NOUN
ejpam-3527	390	5	by	by	ADP
ejpam-3527	390	6	(	(	PUNCT
ejpam-3527	390	7	up3	up3	PROPN
ejpam-3527	390	8	)	)	PUNCT
ejpam-3527	390	9	and	and	CCONJ
ejpam-3527	390	10	(	(	PUNCT
ejpam-3527	390	11	fupi1	fupi1	PROPN
ejpam-3527	390	12	)	)	PUNCT
ejpam-3527	390	13	,	,	PUNCT
ejpam-3527	390	14	x	x	X
ejpam-3527	390	15	∗	∗	NOUN
ejpam-3527	390	16	0	0	NUM
ejpam-3527	390	17	=	=	SYM
ejpam-3527	390	18	0	0	NUM
ejpam-3527	390	19	∈	∈	PROPN
ejpam-3527	390	20	i.	i.	NOUN
ejpam-3527	390	21	thus	thus	ADV
ejpam-3527	390	22	,	,	PUNCT
ejpam-3527	390	23	0	0	NUM
ejpam-3527	390	24	∼i	∼i	PROPN
ejpam-3527	390	25	x	x	PUNCT
ejpam-3527	390	26	and	and	CCONJ
ejpam-3527	390	27	so	so	ADV
ejpam-3527	390	28	,	,	PUNCT
ejpam-3527	390	29	x	x	PUNCT
ejpam-3527	390	30	∈	∈	PROPN
ejpam-3527	391	1	[	[	X
ejpam-3527	391	2	0]i	0]i	NUM
ejpam-3527	391	3	.	.	PUNCT
ejpam-3527	392	1	hence	hence	ADV
ejpam-3527	392	2	,	,	PUNCT
ejpam-3527	392	3	i	i	PRON
ejpam-3527	392	4	⊆	⊆	NUM
ejpam-3527	393	1	[	[	X
ejpam-3527	393	2	0]i	0]i	NUM
ejpam-3527	393	3	.	.	PUNCT
ejpam-3527	394	1	therefore	therefore	ADV
ejpam-3527	394	2	,	,	PUNCT
ejpam-3527	394	3	[	[	X
ejpam-3527	394	4	0]i	0]i	X
ejpam-3527	394	5	=	=	SYM
ejpam-3527	394	6	i.	i.	PROPN
ejpam-3527	394	7	(	(	PUNCT
ejpam-3527	394	8	ii	ii	PROPN
ejpam-3527	394	9	)	)	PUNCT
ejpam-3527	394	10	suppose	suppose	VERB
ejpam-3527	394	11	[	[	X
ejpam-3527	394	12	x]i	x]i	X
ejpam-3527	394	13	=	=	SYM
ejpam-3527	394	14	i.	i.	NOUN
ejpam-3527	394	15	then	then	ADV
ejpam-3527	394	16	by	by	ADP
ejpam-3527	394	17	remark	remark	NOUN
ejpam-3527	394	18	5	5	NUM
ejpam-3527	394	19	,	,	PUNCT
ejpam-3527	394	20	x	x	SYM
ejpam-3527	394	21	∈	∈	PROPN
ejpam-3527	394	22	i.	i.	NOUN
ejpam-3527	394	23	conversely	conversely	ADV
ejpam-3527	394	24	,	,	PUNCT
ejpam-3527	394	25	let	let	VERB
ejpam-3527	394	26	x	x	X
ejpam-3527	394	27	∈	∈	PROPN
ejpam-3527	394	28	i.	i.	NOUN
ejpam-3527	394	29	by	by	ADP
ejpam-3527	394	30	(	(	PUNCT
ejpam-3527	394	31	up2	up2	PROPN
ejpam-3527	394	32	)	)	PUNCT
ejpam-3527	394	33	,	,	PUNCT
ejpam-3527	394	34	0∗x	0∗x	X
ejpam-3527	395	1	=	=	PUNCT
ejpam-3527	395	2	x	x	SYM
ejpam-3527	395	3	∈	∈	PROPN
ejpam-3527	395	4	i.	i.	NOUN
ejpam-3527	395	5	by	by	ADP
ejpam-3527	395	6	(	(	PUNCT
ejpam-3527	395	7	up3	up3	PROPN
ejpam-3527	395	8	)	)	PUNCT
ejpam-3527	395	9	and	and	CCONJ
ejpam-3527	395	10	(	(	PUNCT
ejpam-3527	395	11	fupi1	fupi1	PROPN
ejpam-3527	395	12	)	)	PUNCT
ejpam-3527	395	13	,	,	PUNCT
ejpam-3527	395	14	x∗0	x∗0	NOUN
ejpam-3527	395	15	=	=	SYM
ejpam-3527	395	16	0	0	NUM
ejpam-3527	395	17	∈	∈	PROPN
ejpam-3527	395	18	i.	i.	NOUN
ejpam-3527	395	19	thus	thus	ADV
ejpam-3527	395	20	,	,	PUNCT
ejpam-3527	395	21	0	0	NUM
ejpam-3527	395	22	∼i	∼i	PROPN
ejpam-3527	395	23	x	x	NOUN
ejpam-3527	395	24	,	,	PUNCT
ejpam-3527	395	25	and	and	CCONJ
ejpam-3527	395	26	by	by	ADP
ejpam-3527	395	27	lemma	lemma	PROPN
ejpam-3527	395	28	1	1	NUM
ejpam-3527	395	29	,	,	PUNCT
ejpam-3527	395	30	[	[	X
ejpam-3527	395	31	0]i	0]i	PUNCT
ejpam-3527	395	32	=	=	PUNCT
ejpam-3527	396	1	[	[	X
ejpam-3527	396	2	x]i	x]i	X
ejpam-3527	396	3	.	.	PUNCT
ejpam-3527	397	1	by	by	ADP
ejpam-3527	397	2	(	(	PUNCT
ejpam-3527	397	3	i	i	NOUN
ejpam-3527	397	4	)	)	PUNCT
ejpam-3527	397	5	,	,	PUNCT
ejpam-3527	397	6	i	i	PRON
ejpam-3527	397	7	=	=	PUNCT
ejpam-3527	398	1	[	[	X
ejpam-3527	398	2	x]i	x]i	X
ejpam-3527	398	3	.	.	PUNCT
ejpam-3527	399	1	(	(	PUNCT
ejpam-3527	399	2	iii	iii	NOUN
ejpam-3527	399	3	)	)	PUNCT
ejpam-3527	399	4	for	for	ADP
ejpam-3527	399	5	all	all	DET
ejpam-3527	399	6	x	x	SYM
ejpam-3527	399	7	∈	∈	PROPN
ejpam-3527	399	8	x	x	X
ejpam-3527	399	9	,	,	PUNCT
ejpam-3527	399	10	[	[	X
ejpam-3527	399	11	x]i	x]i	X
ejpam-3527	399	12	=	=	SYM
ejpam-3527	400	1	[	[	X
ejpam-3527	400	2	0	0	NUM
ejpam-3527	400	3	∗	∗	NOUN
ejpam-3527	400	4	x]i	x]i	PUNCT
ejpam-3527	401	1	=	=	SYM
ejpam-3527	402	1	[	[	X
ejpam-3527	402	2	0]i	0]i	NUM
ejpam-3527	402	3	∗	∗	NOUN
ejpam-3527	402	4	[	[	X
ejpam-3527	402	5	x]i	x]i	NOUN
ejpam-3527	402	6	as	as	SCONJ
ejpam-3527	402	7	defined	define	VERB
ejpam-3527	402	8	in	in	ADP
ejpam-3527	402	9	theorem	theorem	NOUN
ejpam-3527	402	10	3(iv	3(iv	NUM
ejpam-3527	402	11	)	)	PUNCT
ejpam-3527	402	12	.	.	PUNCT
ejpam-3527	403	1	by	by	ADP
ejpam-3527	403	2	(	(	PUNCT
ejpam-3527	403	3	i	i	NOUN
ejpam-3527	403	4	)	)	PUNCT
ejpam-3527	403	5	,	,	PUNCT
ejpam-3527	403	6	[	[	X
ejpam-3527	403	7	x]i	x]i	X
ejpam-3527	403	8	=	=	VERB
ejpam-3527	403	9	i	i	PRON
ejpam-3527	403	10	∗	∗	VERB
ejpam-3527	403	11	[	[	X
ejpam-3527	403	12	x]i	x]i	X
ejpam-3527	403	13	.	.	PUNCT
ejpam-3527	404	1	d.gomisong	d.gomisong	PROPN
ejpam-3527	404	2	,	,	PUNCT
ejpam-3527	404	3	r.	r.	PROPN
ejpam-3527	404	4	isla	isla	PROPN
ejpam-3527	404	5	/	/	SYM
ejpam-3527	404	6	eur	eur	PROPN
ejpam-3527	404	7	.	.	PUNCT
ejpam-3527	405	1	j.	j.	PROPN
ejpam-3527	405	2	pure	pure	PROPN
ejpam-3527	405	3	appl	appl	PROPN
ejpam-3527	405	4	.	.	PROPN
ejpam-3527	405	5	math	math	PROPN
ejpam-3527	405	6	,	,	PUNCT
ejpam-3527	405	7	12	12	NUM
ejpam-3527	405	8	(	(	PUNCT
ejpam-3527	405	9	4	4	NUM
ejpam-3527	405	10	)	)	PUNCT
ejpam-3527	405	11	(	(	PUNCT
ejpam-3527	405	12	2019	2019	NUM
ejpam-3527	405	13	)	)	PUNCT
ejpam-3527	405	14	,	,	PUNCT
ejpam-3527	405	15	1483	1483	NUM
ejpam-3527	405	16	-	-	SYM
ejpam-3527	405	17	1496	1496	NUM
ejpam-3527	405	18	1494	1494	NUM
ejpam-3527	405	19	theorem	theorem	VERB
ejpam-3527	405	20	13	13	NUM
ejpam-3527	405	21	.	.	PUNCT
ejpam-3527	406	1	if	if	SCONJ
ejpam-3527	406	2	x	x	PRON
ejpam-3527	406	3	is	be	AUX
ejpam-3527	406	4	an	an	DET
ejpam-3527	406	5	f	f	PROPN
ejpam-3527	406	6	-up	-up	NOUN
ejpam-3527	406	7	-	-	PUNCT
ejpam-3527	406	8	semigroup	semigroup	NOUN
ejpam-3527	406	9	and	and	CCONJ
ejpam-3527	406	10	i	i	PRON
ejpam-3527	406	11	an	an	DET
ejpam-3527	406	12	f	f	PROPN
ejpam-3527	406	13	-up	-up	NOUN
ejpam-3527	406	14	-	-	PUNCT
ejpam-3527	406	15	ideal	ideal	NOUN
ejpam-3527	406	16	of	of	ADP
ejpam-3527	406	17	x	x	PRON
ejpam-3527	406	18	,	,	PUNCT
ejpam-3527	406	19	then	then	ADV
ejpam-3527	406	20	(	(	PUNCT
ejpam-3527	406	21	x	x	X
ejpam-3527	406	22	/	/	SYM
ejpam-3527	406	23	i	i	PROPN
ejpam-3527	406	24	;	;	PUNCT
ejpam-3527	406	25	∗	∗	NOUN
ejpam-3527	406	26	,	,	PUNCT
ejpam-3527	406	27	·	·	PUNCT
ejpam-3527	406	28	,	,	PUNCT
ejpam-3527	406	29	[	[	X
ejpam-3527	406	30	0]i	0]i	NUM
ejpam-3527	406	31	)	)	PUNCT
ejpam-3527	406	32	is	be	AUX
ejpam-3527	406	33	an	an	DET
ejpam-3527	406	34	f	f	PROPN
ejpam-3527	406	35	-up	-up	NOUN
ejpam-3527	406	36	-	-	PUNCT
ejpam-3527	406	37	semigroup	semigroup	NOUN
ejpam-3527	406	38	,	,	PUNCT
ejpam-3527	406	39	where	where	SCONJ
ejpam-3527	406	40	∗	∗	NOUN
ejpam-3527	406	41	and	and	CCONJ
ejpam-3527	406	42	·	·	PUNCT
ejpam-3527	406	43	are	be	AUX
ejpam-3527	406	44	defined	define	VERB
ejpam-3527	406	45	by	by	ADP
ejpam-3527	406	46	[	[	X
ejpam-3527	406	47	x]i∗[y]i	x]i∗[y]i	PROPN
ejpam-3527	406	48	=	=	PUNCT
ejpam-3527	407	1	[	[	X
ejpam-3527	407	2	x∗y]i	x∗y]i	NOUN
ejpam-3527	407	3	and	and	CCONJ
ejpam-3527	407	4	[	[	X
ejpam-3527	407	5	x]i	x]i	X
ejpam-3527	407	6	·	·	PUNCT
ejpam-3527	407	7	[	[	X
ejpam-3527	407	8	y]i	y]i	NOUN
ejpam-3527	407	9	=	=	SYM
ejpam-3527	408	1	[	[	X
ejpam-3527	408	2	x·y]i	x·y]i	X
ejpam-3527	408	3	,	,	PUNCT
ejpam-3527	408	4	respectively	respectively	ADV
ejpam-3527	408	5	.	.	PUNCT
ejpam-3527	409	1	if	if	SCONJ
ejpam-3527	409	2	x	x	PRON
ejpam-3527	409	3	is	be	AUX
ejpam-3527	409	4	commutative	commutative	ADJ
ejpam-3527	409	5	,	,	PUNCT
ejpam-3527	409	6	then	then	ADV
ejpam-3527	409	7	x	x	X
ejpam-3527	409	8	/	/	SYM
ejpam-3527	409	9	i	i	PRON
ejpam-3527	409	10	is	be	AUX
ejpam-3527	409	11	commutative	commutative	ADJ
ejpam-3527	409	12	and	and	CCONJ
ejpam-3527	409	13	if	if	SCONJ
ejpam-3527	409	14	x	x	PRON
ejpam-3527	409	15	has	have	VERB
ejpam-3527	409	16	unity	unity	NOUN
ejpam-3527	409	17	,	,	PUNCT
ejpam-3527	409	18	then	then	ADV
ejpam-3527	409	19	x	x	X
ejpam-3527	409	20	/	/	SYM
ejpam-3527	410	1	i	i	PRON
ejpam-3527	410	2	has	have	VERB
ejpam-3527	410	3	unity	unity	NOUN
ejpam-3527	410	4	.	.	PUNCT
ejpam-3527	411	1	proof	proof	NOUN
ejpam-3527	411	2	.	.	PUNCT
ejpam-3527	412	1	let	let	VERB
ejpam-3527	412	2	i	i	PRON
ejpam-3527	412	3	be	be	AUX
ejpam-3527	412	4	an	an	DET
ejpam-3527	412	5	f	f	PROPN
ejpam-3527	412	6	-up	-up	NOUN
ejpam-3527	412	7	-	-	NOUN
ejpam-3527	412	8	ideal	ideal	NOUN
ejpam-3527	412	9	of	of	ADP
ejpam-3527	412	10	x.	x.	NOUN
ejpam-3527	412	11	then	then	ADV
ejpam-3527	412	12	i	i	PRON
ejpam-3527	412	13	is	be	AUX
ejpam-3527	412	14	a	a	DET
ejpam-3527	412	15	up	up	ADJ
ejpam-3527	412	16	-	-	PUNCT
ejpam-3527	412	17	ideal	ideal	NOUN
ejpam-3527	412	18	of	of	ADP
ejpam-3527	412	19	the	the	DET
ejpam-3527	412	20	up	up	NOUN
ejpam-3527	412	21	-	-	PUNCT
ejpam-3527	412	22	algebra	algebra	NOUN
ejpam-3527	412	23	(	(	PUNCT
ejpam-3527	412	24	x	x	NOUN
ejpam-3527	412	25	;	;	PUNCT
ejpam-3527	412	26	∗	∗	NOUN
ejpam-3527	412	27	,	,	PUNCT
ejpam-3527	412	28	0	0	NUM
ejpam-3527	412	29	)	)	PUNCT
ejpam-3527	412	30	.	.	PUNCT
ejpam-3527	413	1	by	by	ADP
ejpam-3527	413	2	theorem	theorem	NOUN
ejpam-3527	413	3	3	3	NUM
ejpam-3527	413	4	,	,	PUNCT
ejpam-3527	413	5	(	(	PUNCT
ejpam-3527	413	6	x	x	X
ejpam-3527	413	7	/	/	SYM
ejpam-3527	413	8	i	i	PROPN
ejpam-3527	413	9	;	;	PUNCT
ejpam-3527	413	10	∗	∗	NOUN
ejpam-3527	413	11	,	,	PUNCT
ejpam-3527	413	12	[	[	X
ejpam-3527	413	13	0]i	0]i	NUM
ejpam-3527	413	14	)	)	PUNCT
ejpam-3527	413	15	is	be	AUX
ejpam-3527	413	16	a	a	DET
ejpam-3527	413	17	up	up	NOUN
ejpam-3527	413	18	-	-	PUNCT
ejpam-3527	413	19	algebra	algebra	NOUN
ejpam-3527	413	20	,	,	PUNCT
ejpam-3527	413	21	where	where	SCONJ
ejpam-3527	413	22	∗	∗	NOUN
ejpam-3527	413	23	is	be	AUX
ejpam-3527	413	24	defined	define	VERB
ejpam-3527	413	25	by	by	ADP
ejpam-3527	413	26	[	[	X
ejpam-3527	413	27	x]i	x]i	PROPN
ejpam-3527	413	28	∗	∗	NOUN
ejpam-3527	413	29	[	[	X
ejpam-3527	413	30	y]i	y]i	NOUN
ejpam-3527	413	31	=	=	PUNCT
ejpam-3527	414	1	[	[	X
ejpam-3527	414	2	x∗y]i	x∗y]i	PROPN
ejpam-3527	414	3	.	.	PUNCT
ejpam-3527	415	1	we	we	PRON
ejpam-3527	415	2	show	show	VERB
ejpam-3527	415	3	that	that	SCONJ
ejpam-3527	415	4	the	the	DET
ejpam-3527	415	5	binary	binary	PROPN
ejpam-3527	415	6	operation	operation	NOUN
ejpam-3527	415	7	·	·	PUNCT
ejpam-3527	415	8	on	on	ADP
ejpam-3527	415	9	x	x	SYM
ejpam-3527	415	10	/	/	SYM
ejpam-3527	415	11	i	i	PRON
ejpam-3527	415	12	is	be	AUX
ejpam-3527	415	13	well	well	ADV
ejpam-3527	415	14	-	-	PUNCT
ejpam-3527	415	15	defined	define	VERB
ejpam-3527	415	16	.	.	PUNCT
ejpam-3527	416	1	let	let	VERB
ejpam-3527	417	1	[	[	X
ejpam-3527	417	2	x]i	x]i	X
ejpam-3527	417	3	=	=	PUNCT
ejpam-3527	418	1	[	[	X
ejpam-3527	418	2	x′]i	x′]i	X
ejpam-3527	418	3	and	and	CCONJ
ejpam-3527	418	4	[	[	X
ejpam-3527	418	5	y]i	y]i	NOUN
ejpam-3527	418	6	=	=	SYM
ejpam-3527	419	1	[	[	X
ejpam-3527	419	2	y′]i	y′]i	NUM
ejpam-3527	419	3	.	.	PUNCT
ejpam-3527	420	1	then	then	ADV
ejpam-3527	420	2	x	x	X
ejpam-3527	420	3	∼i	∼i	PROPN
ejpam-3527	420	4	x′	x′	PROPN
ejpam-3527	420	5	and	and	CCONJ
ejpam-3527	420	6	y	y	PROPN
ejpam-3527	420	7	∼i	∼i	PROPN
ejpam-3527	420	8	y′	y′	NOUN
ejpam-3527	420	9	which	which	PRON
ejpam-3527	420	10	imply	imply	VERB
ejpam-3527	420	11	x	x	X
ejpam-3527	420	12	∗	∗	NOUN
ejpam-3527	420	13	x′	x′	NUM
ejpam-3527	420	14	,	,	PUNCT
ejpam-3527	420	15	x′	x′	PROPN
ejpam-3527	420	16	∗	∗	NOUN
ejpam-3527	420	17	x	x	PROPN
ejpam-3527	420	18	,	,	PUNCT
ejpam-3527	420	19	y	y	PROPN
ejpam-3527	420	20	∗	∗	NOUN
ejpam-3527	420	21	y′	y′	NUM
ejpam-3527	420	22	,	,	PUNCT
ejpam-3527	420	23	y′	y′	NOUN
ejpam-3527	420	24	∗	∗	NOUN
ejpam-3527	420	25	y	y	PROPN
ejpam-3527	420	26	∈	∈	PROPN
ejpam-3527	420	27	i.	i.	NOUN
ejpam-3527	420	28	by	by	ADP
ejpam-3527	420	29	theorem	theorem	ADJ
ejpam-3527	420	30	4(iii	4(iii	NUM
ejpam-3527	420	31	)	)	PUNCT
ejpam-3527	420	32	,	,	PUNCT
ejpam-3527	420	33	(	(	PUNCT
ejpam-3527	420	34	up2	up2	NOUN
ejpam-3527	420	35	)	)	PUNCT
ejpam-3527	420	36	,	,	PUNCT
ejpam-3527	420	37	and	and	CCONJ
ejpam-3527	420	38	(	(	PUNCT
ejpam-3527	420	39	fupi3	fupi3	NOUN
ejpam-3527	420	40	)	)	PUNCT
ejpam-3527	420	41	,	,	PUNCT
ejpam-3527	420	42	(	(	PUNCT
ejpam-3527	420	43	x	x	X
ejpam-3527	420	44	·	·	PUNCT
ejpam-3527	420	45	y)∗	y)∗	NOUN
ejpam-3527	420	46	(	(	PUNCT
ejpam-3527	420	47	x	x	X
ejpam-3527	420	48	·	·	PUNCT
ejpam-3527	420	49	y′	y′	NUM
ejpam-3527	420	50	)	)	PUNCT
ejpam-3527	421	1	=	=	SYM
ejpam-3527	421	2	x	x	SYM
ejpam-3527	421	3	·	·	PUNCT
ejpam-3527	421	4	(	(	PUNCT
ejpam-3527	421	5	y	y	NOUN
ejpam-3527	421	6	∗	∗	X
ejpam-3527	421	7	(	(	PUNCT
ejpam-3527	421	8	0∗y′	0∗y′	PROPN
ejpam-3527	421	9	)	)	PUNCT
ejpam-3527	421	10	)	)	PUNCT
ejpam-3527	422	1	=	=	PUNCT
ejpam-3527	422	2	x	x	PUNCT
ejpam-3527	422	3	·	·	PUNCT
ejpam-3527	422	4	(	(	PUNCT
ejpam-3527	422	5	y	y	NOUN
ejpam-3527	422	6	∗y′	∗y′	PROPN
ejpam-3527	422	7	)	)	PUNCT
ejpam-3527	422	8	∈	∈	PROPN
ejpam-3527	423	1	i	i	PRON
ejpam-3527	423	2	and	and	CCONJ
ejpam-3527	423	3	(	(	PUNCT
ejpam-3527	423	4	x	x	X
ejpam-3527	423	5	·	·	PUNCT
ejpam-3527	423	6	y′)∗	y′)∗	NOUN
ejpam-3527	423	7	(	(	PUNCT
ejpam-3527	423	8	x	x	PROPN
ejpam-3527	423	9	·	·	PUNCT
ejpam-3527	423	10	y	y	X
ejpam-3527	423	11	)	)	PUNCT
ejpam-3527	423	12	=	=	SYM
ejpam-3527	423	13	x·(y′∗(0∗y	x·(y′∗(0∗y	PROPN
ejpam-3527	423	14	)	)	PUNCT
ejpam-3527	423	15	)	)	PUNCT
ejpam-3527	424	1	=	=	PUNCT
ejpam-3527	424	2	x·(y′∗y	x·(y′∗y	X
ejpam-3527	424	3	)	)	PUNCT
ejpam-3527	424	4	∈	∈	PROPN
ejpam-3527	424	5	i.	i.	NOUN
ejpam-3527	424	6	thus	thus	ADV
ejpam-3527	424	7	,	,	PUNCT
ejpam-3527	424	8	x·y	x·y	PROPN
ejpam-3527	424	9	∼i	∼i	PROPN
ejpam-3527	424	10	x·y′.	x·y′.	PROPN
ejpam-3527	425	1	similarly	similarly	ADV
ejpam-3527	425	2	,	,	PUNCT
ejpam-3527	425	3	(	(	PUNCT
ejpam-3527	425	4	x·y′)∗(x′·y′	x·y′)∗(x′·y′	NUM
ejpam-3527	425	5	)	)	PUNCT
ejpam-3527	425	6	=	=	PUNCT
ejpam-3527	426	1	(	(	PUNCT
ejpam-3527	426	2	x∗(0∗x′))·y′	x∗(0∗x′))·y′	PROPN
ejpam-3527	426	3	=	=	SYM
ejpam-3527	426	4	(	(	PUNCT
ejpam-3527	426	5	x∗x′	x∗x′	PROPN
ejpam-3527	426	6	)	)	PUNCT
ejpam-3527	426	7	·	·	PUNCT
ejpam-3527	426	8	y′	y′	NOUN
ejpam-3527	427	1	∈	∈	PROPN
ejpam-3527	427	2	i	i	PRON
ejpam-3527	427	3	and	and	CCONJ
ejpam-3527	427	4	(	(	PUNCT
ejpam-3527	427	5	x′	x′	PROPN
ejpam-3527	427	6	·	·	SYM
ejpam-3527	427	7	y′)∗	y′)∗	NOUN
ejpam-3527	427	8	(	(	PUNCT
ejpam-3527	427	9	x	x	X
ejpam-3527	427	10	·	·	PUNCT
ejpam-3527	427	11	y′	y′	NUM
ejpam-3527	427	12	)	)	PUNCT
ejpam-3527	427	13	=	=	SYM
ejpam-3527	427	14	(	(	PUNCT
ejpam-3527	427	15	x′	x′	PROPN
ejpam-3527	427	16	∗	∗	NOUN
ejpam-3527	427	17	(	(	PUNCT
ejpam-3527	427	18	0∗x	0∗x	NOUN
ejpam-3527	427	19	)	)	PUNCT
ejpam-3527	427	20	)	)	PUNCT
ejpam-3527	427	21	·	·	PUNCT
ejpam-3527	427	22	y′	y′	X
ejpam-3527	427	23	=	=	SYM
ejpam-3527	427	24	(	(	PUNCT
ejpam-3527	427	25	x′	x′	PROPN
ejpam-3527	427	26	∗x	∗x	X
ejpam-3527	427	27	)	)	PUNCT
ejpam-3527	427	28	·	·	PUNCT
ejpam-3527	427	29	y′	y′	NOUN
ejpam-3527	427	30	∈	∈	PROPN
ejpam-3527	427	31	i.	i.	NOUN
ejpam-3527	427	32	thus	thus	ADV
ejpam-3527	427	33	,	,	PUNCT
ejpam-3527	427	34	x	x	X
ejpam-3527	427	35	·	·	PUNCT
ejpam-3527	427	36	y′	y′	NOUN
ejpam-3527	427	37	∼i	∼i	PROPN
ejpam-3527	427	38	x′	x′	PROPN
ejpam-3527	427	39	·	·	PUNCT
ejpam-3527	427	40	y′.	y′.	NOUN
ejpam-3527	427	41	by	by	ADP
ejpam-3527	427	42	transitivity	transitivity	NOUN
ejpam-3527	427	43	,	,	PUNCT
ejpam-3527	427	44	x	x	X
ejpam-3527	427	45	·	·	PUNCT
ejpam-3527	427	46	y	y	X
ejpam-3527	427	47	∼i	∼i	PROPN
ejpam-3527	427	48	x′	x′	PROPN
ejpam-3527	427	49	·	·	PUNCT
ejpam-3527	428	1	y′.	y′.	X
ejpam-3527	428	2	by	by	ADP
ejpam-3527	428	3	lemma	lemma	PROPN
ejpam-3527	428	4	1	1	NUM
ejpam-3527	428	5	,	,	PUNCT
ejpam-3527	428	6	[	[	X
ejpam-3527	428	7	x]i	x]i	X
ejpam-3527	428	8	·	·	PUNCT
ejpam-3527	429	1	[	[	X
ejpam-3527	429	2	y]i	y]i	NOUN
ejpam-3527	429	3	=	=	PUNCT
ejpam-3527	429	4	[	[	X
ejpam-3527	429	5	x	x	X
ejpam-3527	429	6	·	·	PUNCT
ejpam-3527	429	7	y]i	y]i	NOUN
ejpam-3527	429	8	=	=	PUNCT
ejpam-3527	430	1	[	[	X
ejpam-3527	430	2	x′	x′	X
ejpam-3527	430	3	·	·	PUNCT
ejpam-3527	430	4	y′]i	y′]i	NUM
ejpam-3527	430	5	=	=	PUNCT
ejpam-3527	431	1	[	[	X
ejpam-3527	431	2	x′]i	x′]i	X
ejpam-3527	431	3	·	·	PUNCT
ejpam-3527	431	4	[	[	X
ejpam-3527	431	5	y′]i	y′]i	X
ejpam-3527	431	6	.	.	PUNCT
ejpam-3527	432	1	let	let	VERB
ejpam-3527	432	2	[	[	X
ejpam-3527	432	3	x]i	x]i	X
ejpam-3527	432	4	,	,	PUNCT
ejpam-3527	432	5	[	[	X
ejpam-3527	432	6	y]i	y]i	ADJ
ejpam-3527	432	7	,	,	PUNCT
ejpam-3527	432	8	[	[	X
ejpam-3527	432	9	z]i	z]i	NOUN
ejpam-3527	432	10	∈	∈	ADJ
ejpam-3527	432	11	x	x	X
ejpam-3527	432	12	/	/	SYM
ejpam-3527	432	13	i.	i.	NOUN
ejpam-3527	432	14	since	since	SCONJ
ejpam-3527	432	15	(	(	PUNCT
ejpam-3527	432	16	x	x	X
ejpam-3527	432	17	,	,	PUNCT
ejpam-3527	432	18	·	·	PUNCT
ejpam-3527	432	19	)	)	PUNCT
ejpam-3527	432	20	is	be	AUX
ejpam-3527	432	21	a	a	DET
ejpam-3527	432	22	semigroup	semigroup	NOUN
ejpam-3527	432	23	,	,	PUNCT
ejpam-3527	432	24	then	then	ADV
ejpam-3527	432	25	[	[	X
ejpam-3527	432	26	x]i	x]i	X
ejpam-3527	432	27	·	·	PUNCT
ejpam-3527	432	28	(	(	PUNCT
ejpam-3527	432	29	[	[	X
ejpam-3527	432	30	y]i	y]i	ADJ
ejpam-3527	432	31	·	·	PUNCT
ejpam-3527	433	1	[	[	X
ejpam-3527	433	2	z]i	z]i	NOUN
ejpam-3527	433	3	)	)	PUNCT
ejpam-3527	433	4	=	=	PUNCT
ejpam-3527	434	1	[	[	X
ejpam-3527	434	2	x]i	x]i	X
ejpam-3527	434	3	·	·	PUNCT
ejpam-3527	435	1	[	[	X
ejpam-3527	435	2	y	y	X
ejpam-3527	435	3	·	·	PUNCT
ejpam-3527	435	4	z]i	z]i	PROPN
ejpam-3527	435	5	=	=	PUNCT
ejpam-3527	436	1	[	[	X
ejpam-3527	436	2	x	x	X
ejpam-3527	436	3	·	·	PUNCT
ejpam-3527	436	4	(	(	PUNCT
ejpam-3527	436	5	y	y	PROPN
ejpam-3527	436	6	·	·	PUNCT
ejpam-3527	436	7	z)]i	z)]i	NOUN
ejpam-3527	436	8	=	=	PUNCT
ejpam-3527	437	1	[	[	X
ejpam-3527	437	2	(	(	PUNCT
ejpam-3527	437	3	x	x	SYM
ejpam-3527	437	4	·	·	PUNCT
ejpam-3527	437	5	y	y	X
ejpam-3527	437	6	)	)	PUNCT
ejpam-3527	437	7	·	·	PUNCT
ejpam-3527	437	8	z]i	z]i	NOUN
ejpam-3527	437	9	=	=	PUNCT
ejpam-3527	438	1	[	[	X
ejpam-3527	438	2	x	x	X
ejpam-3527	438	3	·	·	PUNCT
ejpam-3527	438	4	y]i	y]i	ADJ
ejpam-3527	438	5	·	·	PUNCT
ejpam-3527	439	1	[	[	X
ejpam-3527	439	2	z]i	z]i	NOUN
ejpam-3527	439	3	=	=	X
ejpam-3527	439	4	(	(	PUNCT
ejpam-3527	439	5	[	[	X
ejpam-3527	439	6	x]i	x]i	X
ejpam-3527	439	7	·	·	PUNCT
ejpam-3527	439	8	[	[	X
ejpam-3527	439	9	y]i	y]i	ADV
ejpam-3527	439	10	)	)	PUNCT
ejpam-3527	439	11	·	·	PUNCT
ejpam-3527	440	1	[	[	X
ejpam-3527	440	2	z]i	z]i	NOUN
ejpam-3527	440	3	.	.	PUNCT
ejpam-3527	441	1	hence	hence	ADV
ejpam-3527	441	2	,	,	PUNCT
ejpam-3527	441	3	(	(	PUNCT
ejpam-3527	441	4	x	x	X
ejpam-3527	441	5	/	/	SYM
ejpam-3527	441	6	i	i	PROPN
ejpam-3527	441	7	,	,	PUNCT
ejpam-3527	441	8	·	·	PUNCT
ejpam-3527	441	9	)	)	PUNCT
ejpam-3527	441	10	is	be	AUX
ejpam-3527	441	11	semigroup	semigroup	PROPN
ejpam-3527	441	12	.	.	PUNCT
ejpam-3527	442	1	moreover	moreover	ADV
ejpam-3527	442	2	,	,	PUNCT
ejpam-3527	442	3	by	by	ADP
ejpam-3527	442	4	distributive	distributive	ADJ
ejpam-3527	442	5	property	property	NOUN
ejpam-3527	442	6	on	on	ADP
ejpam-3527	442	7	x	x	X
ejpam-3527	442	8	,	,	PUNCT
ejpam-3527	442	9	[	[	X
ejpam-3527	442	10	x]i	x]i	X
ejpam-3527	442	11	·	·	PUNCT
ejpam-3527	442	12	(	(	PUNCT
ejpam-3527	442	13	[	[	X
ejpam-3527	442	14	y]i	y]i	ADJ
ejpam-3527	442	15	∗	∗	NOUN
ejpam-3527	442	16	[	[	X
ejpam-3527	442	17	z]i	z]i	NOUN
ejpam-3527	442	18	)	)	PUNCT
ejpam-3527	442	19	=	=	PUNCT
ejpam-3527	443	1	[	[	X
ejpam-3527	443	2	x]i	x]i	X
ejpam-3527	443	3	·	·	PUNCT
ejpam-3527	444	1	[	[	X
ejpam-3527	444	2	y	y	NOUN
ejpam-3527	444	3	∗	∗	NOUN
ejpam-3527	444	4	z]i	z]i	PROPN
ejpam-3527	444	5	=	=	PUNCT
ejpam-3527	445	1	[	[	X
ejpam-3527	445	2	x	x	X
ejpam-3527	445	3	·	·	PUNCT
ejpam-3527	445	4	(	(	PUNCT
ejpam-3527	445	5	y	y	NOUN
ejpam-3527	445	6	∗	∗	NOUN
ejpam-3527	445	7	z)]i	z)]i	NOUN
ejpam-3527	445	8	=	=	PUNCT
ejpam-3527	446	1	[	[	X
ejpam-3527	446	2	(	(	PUNCT
ejpam-3527	446	3	x	x	SYM
ejpam-3527	446	4	·	·	PUNCT
ejpam-3527	446	5	y	y	X
ejpam-3527	446	6	)	)	PUNCT
ejpam-3527	446	7	∗	∗	NOUN
ejpam-3527	446	8	(	(	PUNCT
ejpam-3527	446	9	x	x	X
ejpam-3527	446	10	·	·	PUNCT
ejpam-3527	446	11	z)]i	z)]i	NOUN
ejpam-3527	446	12	=	=	PUNCT
ejpam-3527	447	1	[	[	X
ejpam-3527	447	2	x	x	X
ejpam-3527	447	3	·	·	PUNCT
ejpam-3527	447	4	y]i	y]i	ADJ
ejpam-3527	447	5	∗	∗	NOUN
ejpam-3527	448	1	[	[	X
ejpam-3527	448	2	x	x	X
ejpam-3527	448	3	·	·	PUNCT
ejpam-3527	448	4	z]i	z]i	NOUN
ejpam-3527	448	5	=	=	SYM
ejpam-3527	448	6	(	(	PUNCT
ejpam-3527	448	7	[	[	X
ejpam-3527	448	8	x]i	x]i	X
ejpam-3527	448	9	·	·	PUNCT
ejpam-3527	449	1	[	[	X
ejpam-3527	449	2	y]i	y]i	ADJ
ejpam-3527	449	3	)	)	PUNCT
ejpam-3527	449	4	∗	∗	NOUN
ejpam-3527	449	5	(	(	PUNCT
ejpam-3527	449	6	[	[	X
ejpam-3527	449	7	x]i	x]i	X
ejpam-3527	449	8	·	·	PUNCT
ejpam-3527	450	1	[	[	X
ejpam-3527	450	2	z]i	z]i	NOUN
ejpam-3527	450	3	)	)	PUNCT
ejpam-3527	450	4	and	and	CCONJ
ejpam-3527	450	5	(	(	PUNCT
ejpam-3527	450	6	[	[	X
ejpam-3527	450	7	x]i	x]i	X
ejpam-3527	450	8	∗	∗	NOUN
ejpam-3527	450	9	[	[	X
ejpam-3527	450	10	y]i	y]i	ADJ
ejpam-3527	450	11	)	)	PUNCT
ejpam-3527	450	12	·	·	PUNCT
ejpam-3527	451	1	[	[	X
ejpam-3527	451	2	z]i	z]i	NOUN
ejpam-3527	451	3	=	=	PUNCT
ejpam-3527	452	1	[	[	X
ejpam-3527	452	2	x	x	X
ejpam-3527	452	3	∗	∗	NOUN
ejpam-3527	452	4	y]i	y]i	NOUN
ejpam-3527	452	5	·	·	PUNCT
ejpam-3527	453	1	[	[	X
ejpam-3527	453	2	z]i	z]i	NOUN
ejpam-3527	453	3	=	=	PUNCT
ejpam-3527	454	1	[	[	X
ejpam-3527	454	2	(	(	PUNCT
ejpam-3527	454	3	x	x	X
ejpam-3527	454	4	∗	∗	PROPN
ejpam-3527	454	5	y	y	PROPN
ejpam-3527	454	6	)	)	PUNCT
ejpam-3527	454	7	·	·	PUNCT
ejpam-3527	454	8	z]i	z]i	NOUN
ejpam-3527	454	9	=	=	PUNCT
ejpam-3527	455	1	[	[	X
ejpam-3527	455	2	(	(	PUNCT
ejpam-3527	455	3	x	x	SYM
ejpam-3527	455	4	·	·	PUNCT
ejpam-3527	455	5	z	z	X
ejpam-3527	455	6	)	)	PUNCT
ejpam-3527	455	7	∗	∗	NOUN
ejpam-3527	455	8	(	(	PUNCT
ejpam-3527	455	9	y	y	PROPN
ejpam-3527	455	10	·	·	PUNCT
ejpam-3527	455	11	z)]i	z)]i	NOUN
ejpam-3527	455	12	=	=	PUNCT
ejpam-3527	456	1	[	[	X
ejpam-3527	456	2	x	x	X
ejpam-3527	456	3	·	·	PUNCT
ejpam-3527	456	4	z]i	z]i	NOUN
ejpam-3527	456	5	∗	∗	NOUN
ejpam-3527	456	6	[	[	X
ejpam-3527	456	7	y	y	X
ejpam-3527	456	8	·	·	PUNCT
ejpam-3527	456	9	z]i	z]i	PROPN
ejpam-3527	456	10	=	=	SYM
ejpam-3527	456	11	(	(	PUNCT
ejpam-3527	456	12	[	[	X
ejpam-3527	456	13	x]i	x]i	X
ejpam-3527	456	14	·	·	PUNCT
ejpam-3527	457	1	[	[	X
ejpam-3527	457	2	z]i	z]i	NOUN
ejpam-3527	457	3	)	)	PUNCT
ejpam-3527	457	4	∗	∗	NOUN
ejpam-3527	457	5	(	(	PUNCT
ejpam-3527	457	6	[	[	X
ejpam-3527	457	7	y]i	y]i	ADJ
ejpam-3527	457	8	·	·	PUNCT
ejpam-3527	458	1	[	[	X
ejpam-3527	458	2	z]i	z]i	NOUN
ejpam-3527	458	3	)	)	PUNCT
ejpam-3527	458	4	.	.	PUNCT
ejpam-3527	459	1	thus	thus	ADV
ejpam-3527	459	2	,	,	PUNCT
ejpam-3527	459	3	the	the	DET
ejpam-3527	459	4	distributive	distributive	ADJ
ejpam-3527	459	5	property	property	NOUN
ejpam-3527	459	6	holds	hold	VERB
ejpam-3527	459	7	on	on	ADP
ejpam-3527	459	8	x	x	X
ejpam-3527	459	9	/	/	SYM
ejpam-3527	459	10	i.	i.	NOUN
ejpam-3527	459	11	therefore	therefore	ADV
ejpam-3527	459	12	,	,	PUNCT
ejpam-3527	459	13	(	(	PUNCT
ejpam-3527	459	14	x	x	X
ejpam-3527	459	15	/	/	SYM
ejpam-3527	459	16	i	i	PROPN
ejpam-3527	459	17	;	;	PUNCT
ejpam-3527	459	18	∗	∗	NOUN
ejpam-3527	459	19	,	,	PUNCT
ejpam-3527	459	20	·	·	PUNCT
ejpam-3527	459	21	,	,	PUNCT
ejpam-3527	459	22	[	[	X
ejpam-3527	459	23	0]i	0]i	NUM
ejpam-3527	459	24	)	)	PUNCT
ejpam-3527	459	25	is	be	AUX
ejpam-3527	459	26	an	an	DET
ejpam-3527	459	27	f	f	PROPN
ejpam-3527	459	28	-upsemigroup	-upsemigroup	PROPN
ejpam-3527	459	29	.	.	PUNCT
ejpam-3527	460	1	suppose	suppose	VERB
ejpam-3527	460	2	x	x	PRON
ejpam-3527	460	3	is	be	AUX
ejpam-3527	460	4	commutative	commutative	ADJ
ejpam-3527	460	5	.	.	PUNCT
ejpam-3527	461	1	then	then	ADV
ejpam-3527	461	2	x	x	X
ejpam-3527	461	3	·	·	PUNCT
ejpam-3527	461	4	y	y	X
ejpam-3527	461	5	=	=	SYM
ejpam-3527	461	6	y	y	PROPN
ejpam-3527	461	7	·	·	PUNCT
ejpam-3527	461	8	x	x	PUNCT
ejpam-3527	461	9	for	for	ADP
ejpam-3527	461	10	all	all	DET
ejpam-3527	461	11	x	x	NOUN
ejpam-3527	461	12	,	,	PUNCT
ejpam-3527	461	13	y	y	PROPN
ejpam-3527	461	14	∈	∈	PROPN
ejpam-3527	461	15	x.	x.	NOUN
ejpam-3527	461	16	let	let	VERB
ejpam-3527	461	17	[	[	X
ejpam-3527	461	18	x]i	x]i	X
ejpam-3527	461	19	,	,	PUNCT
ejpam-3527	461	20	[	[	X
ejpam-3527	461	21	y]i	y]i	ADJ
ejpam-3527	461	22	∈	∈	ADJ
ejpam-3527	461	23	x	x	X
ejpam-3527	461	24	/	/	SYM
ejpam-3527	461	25	i.	i.	NOUN
ejpam-3527	461	26	then	then	ADV
ejpam-3527	462	1	[	[	X
ejpam-3527	462	2	x]i	x]i	X
ejpam-3527	462	3	·	·	PUNCT
ejpam-3527	463	1	[	[	X
ejpam-3527	463	2	y]i	y]i	NOUN
ejpam-3527	463	3	=	=	PUNCT
ejpam-3527	463	4	[	[	X
ejpam-3527	463	5	x	x	X
ejpam-3527	463	6	·	·	PUNCT
ejpam-3527	463	7	y]i	y]i	NOUN
ejpam-3527	463	8	=	=	PUNCT
ejpam-3527	464	1	[	[	X
ejpam-3527	464	2	y	y	PROPN
ejpam-3527	464	3	·	·	PUNCT
ejpam-3527	464	4	x]i	x]i	PROPN
ejpam-3527	465	1	=	=	PUNCT
ejpam-3527	466	1	[	[	X
ejpam-3527	466	2	y]i	y]i	NOUN
ejpam-3527	466	3	·	·	PUNCT
ejpam-3527	467	1	[	[	X
ejpam-3527	467	2	x]i	x]i	X
ejpam-3527	467	3	.	.	PUNCT
ejpam-3527	468	1	hence	hence	ADV
ejpam-3527	468	2	,	,	PUNCT
ejpam-3527	468	3	x	x	X
ejpam-3527	468	4	/	/	SYM
ejpam-3527	468	5	i	i	PRON
ejpam-3527	468	6	is	be	AUX
ejpam-3527	468	7	commutative	commutative	ADJ
ejpam-3527	468	8	.	.	PUNCT
ejpam-3527	469	1	if	if	SCONJ
ejpam-3527	469	2	x	x	PRON
ejpam-3527	469	3	has	have	VERB
ejpam-3527	469	4	unity	unity	NOUN
ejpam-3527	469	5	1	1	NUM
ejpam-3527	469	6	,	,	PUNCT
ejpam-3527	469	7	then	then	ADV
ejpam-3527	469	8	x	x	X
ejpam-3527	469	9	/	/	SYM
ejpam-3527	469	10	i	i	PRON
ejpam-3527	469	11	has	have	VERB
ejpam-3527	469	12	unity	unity	NOUN
ejpam-3527	469	13	[	[	X
ejpam-3527	469	14	1]i	1]i	NUM
ejpam-3527	469	15	since	since	SCONJ
ejpam-3527	469	16	[	[	X
ejpam-3527	469	17	x]i	x]i	X
ejpam-3527	469	18	·	·	PUNCT
ejpam-3527	470	1	[	[	X
ejpam-3527	470	2	1]i	1]i	NUM
ejpam-3527	470	3	=	=	SYM
ejpam-3527	470	4	[	[	X
ejpam-3527	470	5	x	x	X
ejpam-3527	470	6	·	·	SYM
ejpam-3527	470	7	1]i	1]i	NUM
ejpam-3527	470	8	=	=	SYM
ejpam-3527	471	1	[	[	X
ejpam-3527	471	2	x]i	x]i	X
ejpam-3527	471	3	and	and	CCONJ
ejpam-3527	471	4	[	[	X
ejpam-3527	471	5	1]i	1]i	NUM
ejpam-3527	471	6	·	·	PUNCT
ejpam-3527	472	1	[	[	X
ejpam-3527	472	2	x]i	x]i	X
ejpam-3527	472	3	=	=	PUNCT
ejpam-3527	473	1	[	[	PUNCT
ejpam-3527	473	2	1	1	NUM
ejpam-3527	473	3	·	·	SYM
ejpam-3527	473	4	x]i	x]i	PUNCT
ejpam-3527	473	5	=	=	PUNCT
ejpam-3527	474	1	[	[	X
ejpam-3527	474	2	x]i	x]i	NOUN
ejpam-3527	474	3	for	for	ADP
ejpam-3527	474	4	any	any	DET
ejpam-3527	474	5	x	x	SYM
ejpam-3527	474	6	∈	∈	PROPN
ejpam-3527	474	7	x.	x.	NOUN
ejpam-3527	475	1	the	the	DET
ejpam-3527	475	2	f	f	PROPN
ejpam-3527	475	3	-up	-up	NOUN
ejpam-3527	475	4	-	-	PUNCT
ejpam-3527	475	5	semigroup	semigroup	NOUN
ejpam-3527	475	6	(	(	PUNCT
ejpam-3527	475	7	x	x	X
ejpam-3527	475	8	/	/	SYM
ejpam-3527	475	9	i	i	PROPN
ejpam-3527	475	10	;	;	PUNCT
ejpam-3527	475	11	∗	∗	NOUN
ejpam-3527	475	12	,	,	PUNCT
ejpam-3527	475	13	·	·	PUNCT
ejpam-3527	475	14	,	,	PUNCT
ejpam-3527	475	15	[	[	X
ejpam-3527	475	16	0]i	0]i	NUM
ejpam-3527	475	17	)	)	PUNCT
ejpam-3527	475	18	in	in	ADP
ejpam-3527	475	19	theorem	theorem	NOUN
ejpam-3527	475	20	13	13	NUM
ejpam-3527	475	21	is	be	AUX
ejpam-3527	475	22	called	call	VERB
ejpam-3527	475	23	the	the	DET
ejpam-3527	475	24	quotient	quotient	NOUN
ejpam-3527	475	25	f	f	PROPN
ejpam-3527	475	26	-up	-up	NOUN
ejpam-3527	475	27	-	-	PUNCT
ejpam-3527	475	28	semigroup	semigroup	NOUN
ejpam-3527	475	29	of	of	ADP
ejpam-3527	475	30	x	x	PUNCT
ejpam-3527	475	31	by	by	ADP
ejpam-3527	475	32	i.	i.	PROPN
ejpam-3527	475	33	references	reference	NOUN
ejpam-3527	475	34	1495	1495	NUM
ejpam-3527	475	35	5	5	NUM
ejpam-3527	475	36	.	.	PUNCT
ejpam-3527	476	1	conclusion	conclusion	NOUN
ejpam-3527	476	2	this	this	DET
ejpam-3527	476	3	paper	paper	NOUN
ejpam-3527	476	4	investigated	investigate	VERB
ejpam-3527	476	5	fully	fully	ADV
ejpam-3527	476	6	up	up	ADP
ejpam-3527	476	7	-	-	PUNCT
ejpam-3527	476	8	semigroups	semigroup	NOUN
ejpam-3527	476	9	,	,	PUNCT
ejpam-3527	476	10	a	a	DET
ejpam-3527	476	11	new	new	ADJ
ejpam-3527	476	12	class	class	NOUN
ejpam-3527	476	13	of	of	ADP
ejpam-3527	476	14	algebra	algebra	NOUN
ejpam-3527	476	15	related	relate	VERB
ejpam-3527	476	16	to	to	ADP
ejpam-3527	476	17	upalgebras	upalgebra	NOUN
ejpam-3527	476	18	and	and	CCONJ
ejpam-3527	476	19	semigroups	semigroup	NOUN
ejpam-3527	476	20	,	,	PUNCT
ejpam-3527	476	21	which	which	PRON
ejpam-3527	476	22	was	be	AUX
ejpam-3527	476	23	introduced	introduce	VERB
ejpam-3527	476	24	by	by	ADP
ejpam-3527	476	25	a.	a.	NOUN
ejpam-3527	476	26	iampan	iampan	NOUN
ejpam-3527	477	1	[	[	X
ejpam-3527	477	2	4	4	X
ejpam-3527	477	3	]	]	PUNCT
ejpam-3527	477	4	in	in	ADP
ejpam-3527	477	5	2018	2018	NUM
ejpam-3527	477	6	.	.	PUNCT
ejpam-3527	478	1	it	it	PRON
ejpam-3527	478	2	established	establish	VERB
ejpam-3527	478	3	some	some	DET
ejpam-3527	478	4	structural	structural	ADJ
ejpam-3527	478	5	properties	property	NOUN
ejpam-3527	478	6	of	of	ADP
ejpam-3527	478	7	f	f	PROPN
ejpam-3527	478	8	-up	-up	NOUN
ejpam-3527	478	9	-	-	PUNCT
ejpam-3527	478	10	semigroups	semigroup	NOUN
ejpam-3527	478	11	.	.	PUNCT
ejpam-3527	479	1	it	it	PRON
ejpam-3527	479	2	also	also	ADV
ejpam-3527	479	3	introduced	introduce	VERB
ejpam-3527	479	4	and	and	CCONJ
ejpam-3527	479	5	examined	examine	VERB
ejpam-3527	479	6	f	f	PROPN
ejpam-3527	479	7	-upfields	-upfield	NOUN
ejpam-3527	479	8	,	,	PUNCT
ejpam-3527	479	9	f	f	PROPN
ejpam-3527	479	10	-up	-up	NOUN
ejpam-3527	479	11	-	-	NOUN
ejpam-3527	479	12	domains	domain	NOUN
ejpam-3527	479	13	,	,	PUNCT
ejpam-3527	479	14	f	f	PROPN
ejpam-3527	479	15	-up	-up	NOUN
ejpam-3527	479	16	-	-	NOUN
ejpam-3527	479	17	ideals	ideal	NOUN
ejpam-3527	479	18	,	,	PUNCT
ejpam-3527	479	19	and	and	CCONJ
ejpam-3527	479	20	quotient	quotient	VERB
ejpam-3527	479	21	f	f	PROPN
ejpam-3527	479	22	-up	-up	NOUN
ejpam-3527	479	23	-	-	PUNCT
ejpam-3527	479	24	semigroups	semigroup	NOUN
ejpam-3527	479	25	.	.	PUNCT
ejpam-3527	480	1	moreover	moreover	ADV
ejpam-3527	480	2	,	,	PUNCT
ejpam-3527	480	3	the	the	DET
ejpam-3527	480	4	relationship	relationship	NOUN
ejpam-3527	480	5	between	between	ADP
ejpam-3527	480	6	an	an	DET
ejpam-3527	480	7	f	f	PROPN
ejpam-3527	480	8	-up	-up	NOUN
ejpam-3527	480	9	-	-	PUNCT
ejpam-3527	480	10	field	field	NOUN
ejpam-3527	480	11	and	and	CCONJ
ejpam-3527	480	12	an	an	DET
ejpam-3527	480	13	f	f	PROPN
ejpam-3527	480	14	-up	-up	NOUN
ejpam-3527	480	15	-	-	NOUN
ejpam-3527	480	16	domain	domain	NOUN
ejpam-3527	480	17	is	be	AUX
ejpam-3527	480	18	determined	determine	VERB
ejpam-3527	480	19	.	.	PUNCT
ejpam-3527	481	1	in	in	ADP
ejpam-3527	481	2	the	the	DET
ejpam-3527	481	3	subsequent	subsequent	ADJ
ejpam-3527	481	4	study	study	NOUN
ejpam-3527	481	5	,	,	PUNCT
ejpam-3527	481	6	we	we	PRON
ejpam-3527	481	7	introduce	introduce	VERB
ejpam-3527	481	8	and	and	CCONJ
ejpam-3527	481	9	investigate	investigate	VERB
ejpam-3527	481	10	homomorphisms	homomorphism	NOUN
ejpam-3527	481	11	on	on	ADP
ejpam-3527	481	12	f	f	PROPN
ejpam-3527	481	13	-up	-up	NOUN
ejpam-3527	481	14	-	-	PUNCT
ejpam-3527	481	15	semigroups	semigroup	NOUN
ejpam-3527	481	16	,	,	PUNCT
ejpam-3527	481	17	which	which	PRON
ejpam-3527	481	18	lead	lead	VERB
ejpam-3527	481	19	to	to	ADP
ejpam-3527	481	20	the	the	DET
ejpam-3527	481	21	isomorphism	isomorphism	NOUN
ejpam-3527	481	22	theorems	theorem	NOUN
ejpam-3527	481	23	on	on	ADP
ejpam-3527	481	24	f	f	PROPN
ejpam-3527	481	25	-up	-up	NOUN
ejpam-3527	481	26	-	-	PUNCT
ejpam-3527	481	27	semigroups	semigroup	NOUN
ejpam-3527	481	28	.	.	PUNCT
ejpam-3527	482	1	acknowledgements	acknowledgement	NOUN
ejpam-3527	482	2	this	this	DET
ejpam-3527	482	3	research	research	NOUN
ejpam-3527	482	4	is	be	AUX
ejpam-3527	482	5	funded	fund	VERB
ejpam-3527	482	6	by	by	ADP
ejpam-3527	482	7	the	the	DET
ejpam-3527	482	8	philippine	philippine	PROPN
ejpam-3527	482	9	department	department	PROPN
ejpam-3527	482	10	of	of	ADP
ejpam-3527	482	11	science	science	NOUN
ejpam-3527	482	12	and	and	CCONJ
ejpam-3527	482	13	technologyaccelerated	technologyaccelerated	ADJ
ejpam-3527	482	14	science	science	NOUN
ejpam-3527	482	15	and	and	CCONJ
ejpam-3527	482	16	technology	technology	NOUN
ejpam-3527	482	17	human	human	ADJ
ejpam-3527	482	18	resource	resource	NOUN
ejpam-3527	482	19	development	development	NOUN
ejpam-3527	482	20	program	program	NOUN
ejpam-3527	482	21	(	(	PUNCT
ejpam-3527	482	22	dostasthrdp	dostasthrdp	PROPN
ejpam-3527	482	23	)	)	PUNCT
ejpam-3527	482	24	and	and	CCONJ
ejpam-3527	482	25	the	the	DET
ejpam-3527	482	26	mindanao	mindanao	PROPN
ejpam-3527	482	27	state	state	PROPN
ejpam-3527	482	28	university	university	PROPN
ejpam-3527	482	29	-	-	PUNCT
ejpam-3527	482	30	iligan	iligan	PROPN
ejpam-3527	482	31	institute	institute	PROPN
ejpam-3527	482	32	of	of	ADP
ejpam-3527	482	33	technology	technology	PROPN
ejpam-3527	482	34	.	.	PUNCT
ejpam-3527	483	1	the	the	DET
ejpam-3527	483	2	authors	author	NOUN
ejpam-3527	483	3	wish	wish	VERB
ejpam-3527	483	4	to	to	PART
ejpam-3527	483	5	express	express	VERB
ejpam-3527	483	6	their	their	PRON
ejpam-3527	483	7	sincere	sincere	ADJ
ejpam-3527	483	8	thanks	thank	NOUN
ejpam-3527	483	9	to	to	ADP
ejpam-3527	483	10	the	the	DET
ejpam-3527	483	11	referees	referee	NOUN
ejpam-3527	483	12	for	for	ADP
ejpam-3527	483	13	their	their	PRON
ejpam-3527	483	14	valuable	valuable	ADJ
ejpam-3527	483	15	suggestions	suggestion	NOUN
ejpam-3527	483	16	for	for	ADP
ejpam-3527	483	17	the	the	DET
ejpam-3527	483	18	improvement	improvement	NOUN
ejpam-3527	483	19	of	of	ADP
ejpam-3527	483	20	this	this	DET
ejpam-3527	483	21	paper	paper	NOUN
ejpam-3527	483	22	.	.	PUNCT
ejpam-3527	484	1	references	reference	NOUN
ejpam-3527	484	2	[	[	X
ejpam-3527	484	3	1	1	NUM
ejpam-3527	484	4	]	]	PUNCT
ejpam-3527	484	5	m.	m.	NOUN
ejpam-3527	484	6	ansari	ansari	PROPN
ejpam-3527	484	7	a.	a.	PROPN
ejpam-3527	484	8	haidar	haidar	PROPN
ejpam-3527	484	9	and	and	CCONJ
ejpam-3527	484	10	a.	a.	PROPN
ejpam-3527	484	11	koam	koam	PROPN
ejpam-3527	484	12	.	.	PUNCT
ejpam-3527	485	1	on	on	ADP
ejpam-3527	485	2	a	a	DET
ejpam-3527	485	3	graph	graph	NOUN
ejpam-3527	485	4	associated	associate	VERB
ejpam-3527	485	5	to	to	ADP
ejpam-3527	485	6	up	up	ADV
ejpam-3527	485	7	-	-	PUNCT
ejpam-3527	485	8	algebras	algebras	X
ejpam-3527	485	9	.	.	PUNCT
ejpam-3527	485	10	mathematical	mathematical	ADJ
ejpam-3527	485	11	and	and	CCONJ
ejpam-3527	485	12	computational	computational	ADJ
ejpam-3527	485	13	applications	application	NOUN
ejpam-3527	485	14	,	,	PUNCT
ejpam-3527	485	15	23(61	23(61	ADV
ejpam-3527	485	16	)	)	PUNCT
ejpam-3527	485	17	,	,	PUNCT
ejpam-3527	485	18	2018	2018	NUM
ejpam-3527	485	19	.	.	PUNCT
ejpam-3527	486	1	[	[	X
ejpam-3527	486	2	2	2	X
ejpam-3527	486	3	]	]	PUNCT
ejpam-3527	486	4	j.	j.	PROPN
ejpam-3527	486	5	endam	endam	PROPN
ejpam-3527	486	6	and	and	CCONJ
ejpam-3527	486	7	j.	j.	PROPN
ejpam-3527	486	8	vilela	vilela	PROPN
ejpam-3527	486	9	.	.	PUNCT
ejpam-3527	487	1	on	on	ADP
ejpam-3527	487	2	jb	jb	PROPN
ejpam-3527	487	3	-	-	PUNCT
ejpam-3527	487	4	semigroups	semigroup	NOUN
ejpam-3527	487	5	.	.	PUNCT
ejpam-3527	488	1	applied	apply	VERB
ejpam-3527	488	2	mathematical	mathematical	ADJ
ejpam-3527	488	3	sciences	science	NOUN
ejpam-3527	488	4	,	,	PUNCT
ejpam-3527	488	5	9(59	9(59	NUM
ejpam-3527	488	6	):	):	PUNCT
ejpam-3527	488	7	2901	2901	NUM
ejpam-3527	488	8	-	-	SYM
ejpam-3527	488	9	2911	2911	NUM
ejpam-3527	488	10	,	,	PUNCT
ejpam-3527	488	11	2015	2015	NUM
ejpam-3527	488	12	.	.	PUNCT
ejpam-3527	489	1	[	[	X
ejpam-3527	489	2	3	3	NUM
ejpam-3527	489	3	]	]	PUNCT
ejpam-3527	489	4	a.	a.	NOUN
ejpam-3527	489	5	iampan	iampan	PROPN
ejpam-3527	489	6	.	.	PUNCT
ejpam-3527	490	1	a	a	DET
ejpam-3527	490	2	new	new	ADJ
ejpam-3527	490	3	branch	branch	NOUN
ejpam-3527	490	4	of	of	ADP
ejpam-3527	490	5	the	the	DET
ejpam-3527	490	6	logical	logical	ADJ
ejpam-3527	490	7	algebra	algebra	NOUN
ejpam-3527	490	8	:	:	PUNCT
ejpam-3527	490	9	up	up	ADP
ejpam-3527	490	10	-	-	PUNCT
ejpam-3527	490	11	algebras	algebras	X
ejpam-3527	490	12	.	.	PUNCT
ejpam-3527	490	13	journal	journal	PROPN
ejpam-3527	490	14	of	of	ADP
ejpam-3527	490	15	algebra	algebra	PROPN
ejpam-3527	490	16	and	and	CCONJ
ejpam-3527	490	17	related	related	ADJ
ejpam-3527	490	18	topics	topic	NOUN
ejpam-3527	490	19	,	,	PUNCT
ejpam-3527	490	20	5(1):35	5(1):35	NUM
ejpam-3527	490	21	-	-	SYM
ejpam-3527	490	22	54	54	NUM
ejpam-3527	490	23	,	,	PUNCT
ejpam-3527	490	24	2017	2017	NUM
ejpam-3527	490	25	.	.	PUNCT
ejpam-3527	491	1	[	[	X
ejpam-3527	491	2	4	4	NUM
ejpam-3527	491	3	]	]	PUNCT
ejpam-3527	491	4	a.	a.	NOUN
ejpam-3527	491	5	iampan	iampan	PROPN
ejpam-3527	491	6	.	.	PUNCT
ejpam-3527	492	1	introducing	introduce	VERB
ejpam-3527	492	2	fully	fully	ADV
ejpam-3527	492	3	up	up	ADP
ejpam-3527	492	4	-	-	PUNCT
ejpam-3527	492	5	semigroups	semigroup	NOUN
ejpam-3527	492	6	.	.	PUNCT
ejpam-3527	493	1	discussiones	discussione	NOUN
ejpam-3527	493	2	mathematicae	mathematicae	VERB
ejpam-3527	493	3	,	,	PUNCT
ejpam-3527	493	4	general	general	ADJ
ejpam-3527	493	5	algebra	algebra	NOUN
ejpam-3527	493	6	and	and	CCONJ
ejpam-3527	493	7	applications	application	NOUN
ejpam-3527	493	8	,	,	PUNCT
ejpam-3527	493	9	38:297	38:297	NUM
ejpam-3527	493	10	-	-	SYM
ejpam-3527	493	11	306	306	NUM
ejpam-3527	493	12	,	,	PUNCT
ejpam-3527	493	13	2018	2018	NUM
ejpam-3527	493	14	.	.	PUNCT
ejpam-3527	494	1	[	[	X
ejpam-3527	494	2	5	5	NUM
ejpam-3527	494	3	]	]	X
ejpam-3527	494	4	y.	y.	PROPN
ejpam-3527	494	5	imai	imai	PROPN
ejpam-3527	494	6	and	and	CCONJ
ejpam-3527	494	7	k.	k.	PROPN
ejpam-3527	494	8	iseki	iseki	PROPN
ejpam-3527	494	9	.	.	PUNCT
ejpam-3527	495	1	on	on	ADP
ejpam-3527	495	2	axiom	axiom	NOUN
ejpam-3527	495	3	systems	system	NOUN
ejpam-3527	495	4	of	of	ADP
ejpam-3527	495	5	propositional	propositional	ADJ
ejpam-3527	495	6	calculi	calculi	PROPN
ejpam-3527	495	7	xiv	xiv	PROPN
ejpam-3527	495	8	.	.	PUNCT
ejpam-3527	496	1	proc	proc	PROPN
ejpam-3527	496	2	.	.	PUNCT
ejpam-3527	497	1	japan	japan	PROPN
ejpam-3527	497	2	academy	academy	PROPN
ejpam-3527	497	3	,	,	PUNCT
ejpam-3527	497	4	42:19	42:19	NUM
ejpam-3527	497	5	-	-	SYM
ejpam-3527	497	6	22	22	NUM
ejpam-3527	497	7	,	,	PUNCT
ejpam-3527	497	8	1996	1996	NUM
ejpam-3527	497	9	.	.	PUNCT
ejpam-3527	498	1	[	[	X
ejpam-3527	498	2	6	6	NUM
ejpam-3527	498	3	]	]	PUNCT
ejpam-3527	498	4	k.	k.	PROPN
ejpam-3527	498	5	iseki	iseki	PROPN
ejpam-3527	498	6	.	.	PUNCT
ejpam-3527	499	1	algebra	algebra	NOUN
ejpam-3527	499	2	related	relate	VERB
ejpam-3527	499	3	with	with	ADP
ejpam-3527	499	4	a	a	DET
ejpam-3527	499	5	propositional	propositional	ADJ
ejpam-3527	499	6	calculus	calculus	NOUN
ejpam-3527	499	7	.	.	PUNCT
ejpam-3527	500	1	proc	proc	PROPN
ejpam-3527	500	2	.	.	PUNCT
ejpam-3527	501	1	japan	japan	PROPN
ejpam-3527	501	2	academy	academy	PROPN
ejpam-3527	501	3	,	,	PUNCT
ejpam-3527	501	4	42:351	42:351	NOUN
ejpam-3527	501	5	-	-	SYM
ejpam-3527	501	6	366	366	NUM
ejpam-3527	501	7	,	,	PUNCT
ejpam-3527	501	8	1966	1966	NUM
ejpam-3527	501	9	.	.	PUNCT
ejpam-3527	502	1	[	[	X
ejpam-3527	502	2	7	7	X
ejpam-3527	502	3	]	]	X
ejpam-3527	502	4	y.	y.	PROPN
ejpam-3527	502	5	jun	jun	PROPN
ejpam-3527	502	6	s.	s.	PROPN
ejpam-3527	502	7	hong	hong	PROPN
ejpam-3527	502	8	and	and	CCONJ
ejpam-3527	502	9	e.roh	e.roh	PROPN
ejpam-3527	502	10	.	.	PUNCT
ejpam-3527	503	1	bci	bci	NOUN
ejpam-3527	503	2	-	-	PUNCT
ejpam-3527	503	3	semigroups	semigroup	NOUN
ejpam-3527	503	4	.	.	PUNCT
ejpam-3527	504	1	honam	honam	PROPN
ejpam-3527	504	2	math	math	PROPN
ejpam-3527	504	3	.	.	PUNCT
ejpam-3527	504	4	,	,	PUNCT
ejpam-3527	504	5	15(1):59	15(1):59	NUM
ejpam-3527	504	6	-	-	SYM
ejpam-3527	504	7	64	64	NUM
ejpam-3527	504	8	,	,	PUNCT
ejpam-3527	504	9	1993	1993	NUM
ejpam-3527	504	10	.	.	PUNCT
ejpam-3527	505	1	[	[	X
ejpam-3527	505	2	8	8	NUM
ejpam-3527	505	3	]	]	X
ejpam-3527	505	4	y.	y.	PROPN
ejpam-3527	505	5	jun	jun	PROPN
ejpam-3527	505	6	e.	e.	PROPN
ejpam-3527	505	7	roh	roh	PROPN
ejpam-3527	505	8	and	and	CCONJ
ejpam-3527	505	9	x.	x.	NOUN
ejpam-3527	505	10	xin	xin	PROPN
ejpam-3527	505	11	.	.	PUNCT
ejpam-3527	506	1	a	a	DET
ejpam-3527	506	2	class	class	NOUN
ejpam-3527	506	3	of	of	ADP
ejpam-3527	506	4	algebras	algebras	PROPN
ejpam-3527	506	5	related	relate	VERB
ejpam-3527	506	6	to	to	ADP
ejpam-3527	506	7	bci	bci	NOUN
ejpam-3527	506	8	-	-	PUNCT
ejpam-3527	506	9	algebras	algebra	NOUN
ejpam-3527	506	10	and	and	CCONJ
ejpam-3527	506	11	semigroups	semigroup	NOUN
ejpam-3527	506	12	.	.	PUNCT
ejpam-3527	507	1	soochow	soochow	PROPN
ejpam-3527	507	2	j.	j.	PROPN
ejpam-3527	507	3	math	math	PROPN
ejpam-3527	507	4	.	.	PUNCT
ejpam-3527	507	5	,	,	PUNCT
ejpam-3527	507	6	4	4	NUM
ejpam-3527	507	7	(	(	PUNCT
ejpam-3527	507	8	24):309	24):309	NUM
ejpam-3527	507	9	-	-	SYM
ejpam-3527	507	10	321	321	NUM
ejpam-3527	507	11	.	.	PUNCT
ejpam-3527	508	1	[	[	X
ejpam-3527	508	2	9	9	NUM
ejpam-3527	508	3	]	]	X
ejpam-3527	508	4	y.	y.	PROPN
ejpam-3527	508	5	jun	jun	PROPN
ejpam-3527	508	6	e.	e.	PROPN
ejpam-3527	508	7	roh	roh	PROPN
ejpam-3527	508	8	and	and	CCONJ
ejpam-3527	508	9	x.	x.	NOUN
ejpam-3527	508	10	xin	xin	PROPN
ejpam-3527	508	11	.	.	PUNCT
ejpam-3527	509	1	i	i	PRON
ejpam-3527	509	2	-	-	PUNCT
ejpam-3527	509	3	ideals	ideal	NOUN
ejpam-3527	509	4	generated	generate	VERB
ejpam-3527	509	5	by	by	ADP
ejpam-3527	509	6	a	a	DET
ejpam-3527	509	7	set	set	NOUN
ejpam-3527	509	8	in	in	ADP
ejpam-3527	509	9	is	be	AUX
ejpam-3527	509	10	-	-	PUNCT
ejpam-3527	509	11	algebras	algebras	X
ejpam-3527	509	12	.	.	PUNCT
ejpam-3527	510	1	bull	bull	PROPN
ejpam-3527	510	2	kcrean	kcrean	PROPN
ejpam-3527	510	3	math	math	PROPN
ejpam-3527	510	4	.	.	PUNCT
ejpam-3527	511	1	soc	soc	PROPN
ejpam-3527	511	2	.	.	PUNCT
ejpam-3527	511	3	,	,	PUNCT
ejpam-3527	511	4	35	35	NUM
ejpam-3527	511	5	:	:	PUNCT
ejpam-3527	511	6	615	615	NUM
ejpam-3527	511	7	-	-	SYM
ejpam-3527	511	8	624	624	NUM
ejpam-3527	511	9	,	,	PUNCT
ejpam-3527	511	10	1998	1998	NUM
ejpam-3527	511	11	.	.	PUNCT
ejpam-3527	512	1	references	reference	NOUN
ejpam-3527	512	2	1496	1496	NUM
ejpam-3527	513	1	[	[	X
ejpam-3527	513	2	10	10	NUM
ejpam-3527	513	3	]	]	X
ejpam-3527	513	4	f.	f.	PROPN
ejpam-3527	513	5	kareem	kareem	PROPN
ejpam-3527	513	6	and	and	CCONJ
ejpam-3527	513	7	e.	e.	PROPN
ejpam-3527	513	8	hasan	hasan	PROPN
ejpam-3527	513	9	.	.	PUNCT
ejpam-3527	514	1	on	on	ADP
ejpam-3527	514	2	ku	ku	PROPN
ejpam-3527	514	3	-	-	PUNCT
ejpam-3527	514	4	semigroups	semigroup	NOUN
ejpam-3527	514	5	.	.	PUNCT
ejpam-3527	515	1	international	international	ADJ
ejpam-3527	515	2	journal	journal	PROPN
ejpam-3527	515	3	of	of	ADP
ejpam-3527	515	4	science	science	NOUN
ejpam-3527	515	5	and	and	CCONJ
ejpam-3527	515	6	nature	nature	NOUN
ejpam-3527	515	7	,	,	PUNCT
ejpam-3527	515	8	9(1):79	9(1):79	NUM
ejpam-3527	515	9	-	-	SYM
ejpam-3527	515	10	84	84	NUM
ejpam-3527	515	11	,	,	PUNCT
ejpam-3527	515	12	2018	2018	NUM
ejpam-3527	515	13	.	.	PUNCT
ejpam-3527	516	1	[	[	X
ejpam-3527	516	2	11	11	NUM
ejpam-3527	516	3	]	]	X
ejpam-3527	516	4	c.	c.	NOUN
ejpam-3527	516	5	prabpayak	prabpayak	NOUN
ejpam-3527	516	6	and	and	CCONJ
ejpam-3527	516	7	u.	u.	NOUN
ejpam-3527	516	8	leerawat	leerawat	PROPN
ejpam-3527	516	9	.	.	PUNCT
ejpam-3527	517	1	on	on	ADP
ejpam-3527	517	2	ideals	ideal	NOUN
ejpam-3527	517	3	and	and	CCONJ
ejpam-3527	517	4	congruence	congruence	NOUN
ejpam-3527	517	5	in	in	ADP
ejpam-3527	517	6	ku	ku	PROPN
ejpam-3527	517	7	-	-	PUNCT
ejpam-3527	517	8	algebras	algebras	PROPN
ejpam-3527	517	9	.	.	PUNCT
ejpam-3527	518	1	scientia	scientia	PROPN
ejpam-3527	518	2	magna	magna	PROPN
ejpam-3527	518	3	journal	journal	PROPN
ejpam-3527	518	4	,	,	PUNCT
ejpam-3527	518	5	5(1):54	5(1):54	PROPN
ejpam-3527	518	6	-	-	SYM
ejpam-3527	518	7	57	57	NUM
ejpam-3527	518	8	,	,	PUNCT
ejpam-3527	518	9	2009	2009	NUM
ejpam-3527	518	10	.	.	PUNCT