id	sid	tid	token	lemma	pos
ejpam-6052	1	1	european	european	PROPN
ejpam-6052	1	2	journal	journal	PROPN
ejpam-6052	1	3	of	of	ADP
ejpam-6052	1	4	pure	pure	ADJ
ejpam-6052	1	5	and	and	CCONJ
ejpam-6052	1	6	applied	applied	ADJ
ejpam-6052	1	7	mathematics	mathematic	NOUN
ejpam-6052	1	8	2025	2025	NUM
ejpam-6052	1	9	,	,	PUNCT
ejpam-6052	1	10	vol	vol	NOUN
ejpam-6052	1	11	.	.	PROPN
ejpam-6052	1	12	18	18	NUM
ejpam-6052	1	13	,	,	PUNCT
ejpam-6052	1	14	issue	issue	NOUN
ejpam-6052	1	15	2	2	NUM
ejpam-6052	1	16	,	,	PUNCT
ejpam-6052	1	17	article	article	NOUN
ejpam-6052	1	18	number	number	NOUN
ejpam-6052	1	19	6052	6052	NUM
ejpam-6052	1	20	issn	issn	VERB
ejpam-6052	1	21	1307	1307	NUM
ejpam-6052	1	22	-	-	SYM
ejpam-6052	1	23	5543	5543	NUM
ejpam-6052	1	24	–	–	PUNCT
ejpam-6052	1	25	ejpam.com	ejpam.com	X
ejpam-6052	1	26	published	publish	VERB
ejpam-6052	1	27	by	by	ADP
ejpam-6052	1	28	new	new	PROPN
ejpam-6052	1	29	york	york	PROPN
ejpam-6052	1	30	business	business	PROPN
ejpam-6052	1	31	global	global	PROPN
ejpam-6052	1	32	on	on	ADP
ejpam-6052	1	33	pseudo	pseudo	NOUN
ejpam-6052	1	34	bn	bn	NOUN
ejpam-6052	1	35	-	-	PUNCT
ejpam-6052	1	36	algebras	algebras	PROPN
ejpam-6052	1	37	irene	irene	PROPN
ejpam-6052	1	38	mae	mae	PROPN
ejpam-6052	1	39	y.	y.	PROPN
ejpam-6052	1	40	antabo1,3,∗	antabo1,3,∗	PROPN
ejpam-6052	1	41	,	,	PUNCT
ejpam-6052	1	42	lyster	lyster	PROPN
ejpam-6052	1	43	rey	rey	PROPN
ejpam-6052	1	44	b.	b.	PROPN
ejpam-6052	1	45	cabardo1,2	cabardo1,2	PROPN
ejpam-6052	1	46	,	,	PUNCT
ejpam-6052	1	47	susan	susan	PROPN
ejpam-6052	1	48	c.	c.	PROPN
ejpam-6052	1	49	dagondon1,2	dagondon1,2	PROPN
ejpam-6052	1	50	,	,	PUNCT
ejpam-6052	1	51	jocelyn	jocelyn	PROPN
ejpam-6052	1	52	p.	p.	PROPN
ejpam-6052	1	53	vilela1,2	vilela1,2	PROPN
ejpam-6052	1	54	1	1	NUM
ejpam-6052	1	55	department	department	NOUN
ejpam-6052	1	56	of	of	ADP
ejpam-6052	1	57	mathematics	mathematic	NOUN
ejpam-6052	1	58	and	and	CCONJ
ejpam-6052	1	59	statistics	statistic	NOUN
ejpam-6052	1	60	,	,	PUNCT
ejpam-6052	1	61	msu	msu	PROPN
ejpam-6052	1	62	-	-	PUNCT
ejpam-6052	1	63	iligan	iligan	PROPN
ejpam-6052	1	64	institute	institute	PROPN
ejpam-6052	1	65	of	of	ADP
ejpam-6052	1	66	technology	technology	PROPN
ejpam-6052	1	67	,	,	PUNCT
ejpam-6052	1	68	9200	9200	NUM
ejpam-6052	1	69	iligan	iligan	ADJ
ejpam-6052	1	70	city	city	NOUN
ejpam-6052	1	71	,	,	PUNCT
ejpam-6052	1	72	philippines	philippine	NOUN
ejpam-6052	1	73	2	2	NUM
ejpam-6052	1	74	center	center	NOUN
ejpam-6052	1	75	for	for	ADP
ejpam-6052	1	76	mathematical	mathematical	ADJ
ejpam-6052	1	77	and	and	CCONJ
ejpam-6052	1	78	theoretical	theoretical	ADJ
ejpam-6052	1	79	physical	physical	ADJ
ejpam-6052	1	80	sciences	science	NOUN
ejpam-6052	1	81	,	,	PUNCT
ejpam-6052	1	82	prism	prism	NOUN
ejpam-6052	1	83	,	,	PUNCT
ejpam-6052	1	84	msu	msu	PROPN
ejpam-6052	1	85	-	-	PUNCT
ejpam-6052	1	86	iligan	iligan	PROPN
ejpam-6052	1	87	institute	institute	PROPN
ejpam-6052	1	88	of	of	ADP
ejpam-6052	1	89	technology	technology	PROPN
ejpam-6052	1	90	,	,	PUNCT
ejpam-6052	1	91	9200	9200	NUM
ejpam-6052	1	92	iligan	iligan	ADJ
ejpam-6052	1	93	city	city	NOUN
ejpam-6052	1	94	,	,	PUNCT
ejpam-6052	1	95	philippines	philippine	VERB
ejpam-6052	1	96	3	3	NUM
ejpam-6052	1	97	math	math	NOUN
ejpam-6052	1	98	and	and	CCONJ
ejpam-6052	1	99	science	science	PROPN
ejpam-6052	1	100	department	department	PROPN
ejpam-6052	1	101	,	,	PUNCT
ejpam-6052	1	102	capitol	capitol	PROPN
ejpam-6052	1	103	university	university	PROPN
ejpam-6052	1	104	,	,	PUNCT
ejpam-6052	1	105	cagayan	cagayan	PROPN
ejpam-6052	1	106	de	de	PROPN
ejpam-6052	1	107	oro	oro	PROPN
ejpam-6052	1	108	city	city	NOUN
ejpam-6052	1	109	,	,	PUNCT
ejpam-6052	1	110	9000	9000	NUM
ejpam-6052	1	111	,	,	PUNCT
ejpam-6052	1	112	philippines	philippine	NOUN
ejpam-6052	1	113	abstract	abstract	ADJ
ejpam-6052	1	114	.	.	PUNCT
ejpam-6052	2	1	in	in	ADP
ejpam-6052	2	2	this	this	DET
ejpam-6052	2	3	paper	paper	NOUN
ejpam-6052	2	4	,	,	PUNCT
ejpam-6052	2	5	we	we	PRON
ejpam-6052	2	6	introduce	introduce	VERB
ejpam-6052	2	7	the	the	DET
ejpam-6052	2	8	notion	notion	NOUN
ejpam-6052	2	9	of	of	ADP
ejpam-6052	2	10	pseudo	pseudo	NOUN
ejpam-6052	2	11	bn	bn	NOUN
ejpam-6052	2	12	-algebras	-algebra	NOUN
ejpam-6052	2	13	and	and	CCONJ
ejpam-6052	2	14	investigate	investigate	VERB
ejpam-6052	2	15	some	some	PRON
ejpam-6052	2	16	of	of	ADP
ejpam-6052	2	17	its	its	PRON
ejpam-6052	2	18	basic	basic	ADJ
ejpam-6052	2	19	properties	property	NOUN
ejpam-6052	2	20	.	.	PUNCT
ejpam-6052	3	1	moreover	moreover	ADV
ejpam-6052	3	2	,	,	PUNCT
ejpam-6052	3	3	its	its	PRON
ejpam-6052	3	4	relationship	relationship	NOUN
ejpam-6052	3	5	with	with	ADP
ejpam-6052	3	6	the	the	DET
ejpam-6052	3	7	already	already	ADV
ejpam-6052	3	8	established	establish	VERB
ejpam-6052	3	9	pseudo	pseudo	NOUN
ejpam-6052	3	10	bf	bf	NOUN
ejpam-6052	3	11	-algebra	-algebra	NOUN
ejpam-6052	3	12	is	be	AUX
ejpam-6052	3	13	investigated	investigate	VERB
ejpam-6052	3	14	.	.	PUNCT
ejpam-6052	4	1	furthermore	furthermore	ADV
ejpam-6052	4	2	,	,	PUNCT
ejpam-6052	4	3	subalgebras	subalgebras	PROPN
ejpam-6052	4	4	,	,	PUNCT
ejpam-6052	4	5	ideals	ideal	NOUN
ejpam-6052	4	6	and	and	CCONJ
ejpam-6052	4	7	pseudo	pseudo	NOUN
ejpam-6052	4	8	-	-	NOUN
ejpam-6052	4	9	normality	normality	NOUN
ejpam-6052	4	10	of	of	ADP
ejpam-6052	4	11	pseudo	pseudo	NOUN
ejpam-6052	4	12	bn	bn	NOUN
ejpam-6052	4	13	-algebras	-algebra	NOUN
ejpam-6052	4	14	are	be	AUX
ejpam-6052	4	15	studied	study	VERB
ejpam-6052	4	16	.	.	PUNCT
ejpam-6052	5	1	illustrations	illustration	NOUN
ejpam-6052	5	2	are	be	AUX
ejpam-6052	5	3	provided	provide	VERB
ejpam-6052	5	4	for	for	ADP
ejpam-6052	5	5	new	new	ADJ
ejpam-6052	5	6	concepts	concept	NOUN
ejpam-6052	5	7	.	.	PUNCT
ejpam-6052	6	1	finally	finally	ADV
ejpam-6052	6	2	,	,	PUNCT
ejpam-6052	6	3	we	we	PRON
ejpam-6052	6	4	establish	establish	VERB
ejpam-6052	6	5	the	the	DET
ejpam-6052	6	6	equivalency	equivalency	NOUN
ejpam-6052	6	7	of	of	ADP
ejpam-6052	6	8	pseudo	pseudo	NOUN
ejpam-6052	6	9	-	-	ADJ
ejpam-6052	6	10	normal	normal	ADJ
ejpam-6052	6	11	subalgebras	subalgebra	NOUN
ejpam-6052	6	12	and	and	CCONJ
ejpam-6052	6	13	pseudo	pseudo	NOUN
ejpam-6052	6	14	-	-	ADJ
ejpam-6052	6	15	normal	normal	ADJ
ejpam-6052	6	16	ideals	ideal	NOUN
ejpam-6052	6	17	.	.	PUNCT
ejpam-6052	7	1	2020	2020	NUM
ejpam-6052	7	2	mathematics	mathematic	NOUN
ejpam-6052	7	3	subject	subject	NOUN
ejpam-6052	7	4	classifications	classification	NOUN
ejpam-6052	7	5	:	:	PUNCT
ejpam-6052	7	6	03g25	03g25	NUM
ejpam-6052	7	7	,	,	PUNCT
ejpam-6052	7	8	08a05	08a05	NUM
ejpam-6052	7	9	,	,	PUNCT
ejpam-6052	7	10	08a30	08a30	VERB
ejpam-6052	7	11	key	key	ADJ
ejpam-6052	7	12	words	word	NOUN
ejpam-6052	7	13	and	and	CCONJ
ejpam-6052	7	14	phrases	phrase	NOUN
ejpam-6052	7	15	:	:	PUNCT
ejpam-6052	7	16	bn	bn	NOUN
ejpam-6052	7	17	-algebra	-algebra	PROPN
ejpam-6052	7	18	,	,	PUNCT
ejpam-6052	7	19	bf	bf	NOUN
ejpam-6052	7	20	-algebra	-algebra	NOUN
ejpam-6052	7	21	,	,	PUNCT
ejpam-6052	7	22	pseudo	pseudo	NOUN
ejpam-6052	7	23	bn	bn	NOUN
ejpam-6052	7	24	-algebra	-algebra	NOUN
ejpam-6052	7	25	,	,	PUNCT
ejpam-6052	7	26	pseudo	pseudo	NOUN
ejpam-6052	7	27	bf	bf	NOUN
ejpam-6052	7	28	-algebra	-algebra	NOUN
ejpam-6052	7	29	1	1	NUM
ejpam-6052	7	30	.	.	PUNCT
ejpam-6052	8	1	introduction	introduction	NOUN
ejpam-6052	8	2	logic	logic	NOUN
ejpam-6052	8	3	algebras	algebras	PROPN
ejpam-6052	8	4	form	form	VERB
ejpam-6052	8	5	the	the	DET
ejpam-6052	8	6	mathematical	mathematical	ADJ
ejpam-6052	8	7	foundation	foundation	NOUN
ejpam-6052	8	8	of	of	ADP
ejpam-6052	8	9	reasoning	reasoning	NOUN
ejpam-6052	8	10	in	in	ADP
ejpam-6052	8	11	artificial	artificial	ADJ
ejpam-6052	8	12	intelligence	intelligence	NOUN
ejpam-6052	8	13	,	,	PUNCT
ejpam-6052	8	14	cybernetics	cybernetic	NOUN
ejpam-6052	8	15	,	,	PUNCT
ejpam-6052	8	16	and	and	CCONJ
ejpam-6052	8	17	computer	computer	NOUN
ejpam-6052	8	18	science	science	NOUN
ejpam-6052	8	19	,	,	PUNCT
ejpam-6052	8	20	offering	offer	VERB
ejpam-6052	8	21	a	a	DET
ejpam-6052	8	22	formal	formal	ADJ
ejpam-6052	8	23	structure	structure	NOUN
ejpam-6052	8	24	for	for	ADP
ejpam-6052	8	25	representing	represent	VERB
ejpam-6052	8	26	and	and	CCONJ
ejpam-6052	8	27	manipulating	manipulate	VERB
ejpam-6052	8	28	logical	logical	ADJ
ejpam-6052	8	29	statements	statement	NOUN
ejpam-6052	8	30	.	.	PUNCT
ejpam-6052	9	1	evolving	evolve	VERB
ejpam-6052	9	2	from	from	ADP
ejpam-6052	9	3	set	set	VERB
ejpam-6052	9	4	theory	theory	NOUN
ejpam-6052	9	5	and	and	CCONJ
ejpam-6052	9	6	non	non	ADJ
ejpam-6052	9	7	-	-	ADJ
ejpam-6052	9	8	classical	classical	ADJ
ejpam-6052	9	9	logic	logic	NOUN
ejpam-6052	9	10	,	,	PUNCT
ejpam-6052	9	11	they	they	PRON
ejpam-6052	9	12	extend	extend	VERB
ejpam-6052	9	13	beyond	beyond	ADP
ejpam-6052	9	14	traditional	traditional	ADJ
ejpam-6052	9	15	boolean	boolean	ADJ
ejpam-6052	9	16	frameworks	framework	NOUN
ejpam-6052	9	17	to	to	PART
ejpam-6052	9	18	support	support	VERB
ejpam-6052	9	19	more	more	ADV
ejpam-6052	9	20	advanced	advanced	ADJ
ejpam-6052	9	21	reasoning	reasoning	NOUN
ejpam-6052	9	22	systems	system	NOUN
ejpam-6052	9	23	.	.	PUNCT
ejpam-6052	10	1	the	the	DET
ejpam-6052	10	2	development	development	NOUN
ejpam-6052	10	3	of	of	ADP
ejpam-6052	10	4	logic	logic	NOUN
ejpam-6052	10	5	algebras	algebras	PROPN
ejpam-6052	10	6	has	have	AUX
ejpam-6052	10	7	led	lead	VERB
ejpam-6052	10	8	to	to	ADP
ejpam-6052	10	9	various	various	ADJ
ejpam-6052	10	10	generalizations	generalization	NOUN
ejpam-6052	10	11	.	.	PUNCT
ejpam-6052	11	1	in	in	ADP
ejpam-6052	11	2	1966	1966	NUM
ejpam-6052	11	3	,	,	PUNCT
ejpam-6052	11	4	imai	imai	PROPN
ejpam-6052	11	5	and	and	CCONJ
ejpam-6052	11	6	iséki	iséki	NUM
ejpam-6052	11	7	introduced	introduce	VERB
ejpam-6052	11	8	bckand	bckand	ADP
ejpam-6052	11	9	bci	bci	NOUN
ejpam-6052	11	10	-	-	PUNCT
ejpam-6052	11	11	algebras	algebras	X
ejpam-6052	12	1	[	[	X
ejpam-6052	12	2	1	1	NUM
ejpam-6052	12	3	,	,	PUNCT
ejpam-6052	12	4	2	2	NUM
ejpam-6052	12	5	]	]	PUNCT
ejpam-6052	12	6	,	,	PUNCT
ejpam-6052	12	7	expanding	expand	VERB
ejpam-6052	12	8	the	the	DET
ejpam-6052	12	9	study	study	NOUN
ejpam-6052	12	10	of	of	ADP
ejpam-6052	12	11	non	non	ADJ
ejpam-6052	12	12	-	-	ADJ
ejpam-6052	12	13	classical	classical	ADJ
ejpam-6052	12	14	logic	logic	NOUN
ejpam-6052	12	15	by	by	ADP
ejpam-6052	12	16	generalizing	generalize	VERB
ejpam-6052	12	17	set	set	VERB
ejpam-6052	12	18	-	-	PUNCT
ejpam-6052	12	19	theoretic	theoretic	NOUN
ejpam-6052	12	20	differences	difference	NOUN
ejpam-6052	12	21	and	and	CCONJ
ejpam-6052	12	22	propositional	propositional	ADJ
ejpam-6052	12	23	calculus	calculus	NOUN
ejpam-6052	12	24	.	.	PUNCT
ejpam-6052	13	1	many	many	ADJ
ejpam-6052	13	2	-	-	PUNCT
ejpam-6052	13	3	valued	value	VERB
ejpam-6052	13	4	logics	logic	NOUN
ejpam-6052	13	5	further	far	ADV
ejpam-6052	13	6	contributed	contribute	VERB
ejpam-6052	13	7	to	to	ADP
ejpam-6052	13	8	this	this	DET
ejpam-6052	13	9	field	field	NOUN
ejpam-6052	13	10	,	,	PUNCT
ejpam-6052	13	11	with	with	ADP
ejpam-6052	13	12	chang	chang	PROPN
ejpam-6052	13	13	introducing	introduce	VERB
ejpam-6052	13	14	mv	mv	PROPN
ejpam-6052	13	15	-	-	PUNCT
ejpam-6052	13	16	algebras	algebras	X
ejpam-6052	14	1	[	[	X
ejpam-6052	14	2	3	3	NUM
ejpam-6052	14	3	]	]	PUNCT
ejpam-6052	14	4	and	and	CCONJ
ejpam-6052	14	5	hájek	hájek	NOUN
ejpam-6052	14	6	extending	extend	VERB
ejpam-6052	14	7	them	they	PRON
ejpam-6052	14	8	to	to	PART
ejpam-6052	14	9	bl	bl	VERB
ejpam-6052	14	10	-	-	PUNCT
ejpam-6052	14	11	algebras	algebras	X
ejpam-6052	15	1	[	[	X
ejpam-6052	15	2	4	4	NUM
ejpam-6052	15	3	]	]	PUNCT
ejpam-6052	15	4	.	.	PUNCT
ejpam-6052	16	1	another	another	DET
ejpam-6052	16	2	significant	significant	ADJ
ejpam-6052	16	3	contribution	contribution	NOUN
ejpam-6052	16	4	is	be	AUX
ejpam-6052	16	5	the	the	DET
ejpam-6052	16	6	bn	bn	ADJ
ejpam-6052	16	7	-algebra	-algebra	NOUN
ejpam-6052	16	8	,	,	PUNCT
ejpam-6052	16	9	introduced	introduce	VERB
ejpam-6052	16	10	by	by	ADP
ejpam-6052	16	11	c.b	c.b	PROPN
ejpam-6052	16	12	.	.	PROPN
ejpam-6052	16	13	kim	kim	PROPN
ejpam-6052	16	14	and	and	CCONJ
ejpam-6052	16	15	h.s	h.s	PROPN
ejpam-6052	16	16	.	.	PROPN
ejpam-6052	16	17	kim	kim	PROPN
ejpam-6052	17	1	[	[	X
ejpam-6052	17	2	5	5	NUM
ejpam-6052	17	3	]	]	PUNCT
ejpam-6052	17	4	,	,	PUNCT
ejpam-6052	17	5	which	which	PRON
ejpam-6052	17	6	is	be	AUX
ejpam-6052	17	7	a	a	DET
ejpam-6052	17	8	subclass	subclass	NOUN
ejpam-6052	17	9	of	of	ADP
ejpam-6052	17	10	bf	bf	NOUN
ejpam-6052	17	11	-	-	PUNCT
ejpam-6052	17	12	algebras	algebras	PROPN
ejpam-6052	17	13	introduced	introduce	VERB
ejpam-6052	17	14	by	by	ADP
ejpam-6052	17	15	walendziak	walendziak	NOUN
ejpam-6052	18	1	[	[	X
ejpam-6052	18	2	6	6	NUM
ejpam-6052	18	3	]	]	PUNCT
ejpam-6052	18	4	.	.	PUNCT
ejpam-6052	19	1	these	these	DET
ejpam-6052	19	2	structures	structure	NOUN
ejpam-6052	19	3	provide	provide	VERB
ejpam-6052	19	4	valuable	valuable	ADJ
ejpam-6052	19	5	insights	insight	NOUN
ejpam-6052	19	6	into	into	ADP
ejpam-6052	19	7	the	the	DET
ejpam-6052	19	8	algebraic	algebraic	ADJ
ejpam-6052	19	9	foundations	foundation	NOUN
ejpam-6052	19	10	of	of	ADP
ejpam-6052	19	11	logic	logic	NOUN
ejpam-6052	19	12	.	.	PUNCT
ejpam-6052	20	1	∗corresponding	∗corresponde	VERB
ejpam-6052	20	2	author	author	NOUN
ejpam-6052	20	3	.	.	PUNCT
ejpam-6052	21	1	doi	doi	NOUN
ejpam-6052	21	2	:	:	PUNCT
ejpam-6052	21	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6052	https://doi.org/10.29020/nybg.ejpam.v18i2.6052	NUM
ejpam-6052	21	4	email	email	NOUN
ejpam-6052	21	5	addresses	address	NOUN
ejpam-6052	21	6	:	:	PUNCT
ejpam-6052	22	1	irenemae.antabo@g.msuiit.edu.ph	irenemae.antabo@g.msuiit.edu.ph	PROPN
ejpam-6052	22	2	(	(	PUNCT
ejpam-6052	22	3	i.m	i.m	PROPN
ejpam-6052	22	4	.	.	PROPN
ejpam-6052	22	5	antabo	antabo	PROPN
ejpam-6052	22	6	)	)	PUNCT
ejpam-6052	22	7	,	,	PUNCT
ejpam-6052	22	8	lysterrey.cabardo@g.msuiit.edu.ph	lysterrey.cabardo@g.msuiit.edu.ph	PROPN
ejpam-6052	22	9	(	(	PUNCT
ejpam-6052	22	10	l.	l.	PROPN
ejpam-6052	22	11	r.	r.	PROPN
ejpam-6052	22	12	cabardo	cabardo	PROPN
ejpam-6052	22	13	)	)	PUNCT
ejpam-6052	22	14	,	,	PUNCT
ejpam-6052	22	15	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-6052	22	16	(	(	PUNCT
ejpam-6052	22	17	s.	s.	PROPN
ejpam-6052	22	18	dagondon	dagondon	PROPN
ejpam-6052	22	19	)	)	PUNCT
ejpam-6052	22	20	,	,	PUNCT
ejpam-6052	22	21	jocelyn.vilela@g.msuiit.edu.ph	jocelyn.vilela@g.msuiit.edu.ph	PROPN
ejpam-6052	22	22	(	(	PUNCT
ejpam-6052	22	23	j.	j.	PROPN
ejpam-6052	22	24	vilela	vilela	PROPN
ejpam-6052	22	25	)	)	PUNCT
ejpam-6052	22	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6052	22	27	1	1	NUM
ejpam-6052	22	28	copyright	copyright	NOUN
ejpam-6052	22	29	:	:	PUNCT
ejpam-6052	22	30	©	©	PROPN
ejpam-6052	22	31	2025	2025	NUM
ejpam-6052	22	32	the	the	DET
ejpam-6052	22	33	author(s	author(s	NOUN
ejpam-6052	22	34	)	)	PUNCT
ejpam-6052	22	35	.	.	PUNCT
ejpam-6052	23	1	(	(	PUNCT
ejpam-6052	23	2	cc	cc	NOUN
ejpam-6052	23	3	by	by	ADP
ejpam-6052	23	4	-	-	PUNCT
ejpam-6052	23	5	nc	nc	PROPN
ejpam-6052	23	6	4.0	4.0	NUM
ejpam-6052	23	7	)	)	PUNCT
ejpam-6052	23	8	i.m	i.m	PROPN
ejpam-6052	23	9	.	.	PUNCT
ejpam-6052	23	10	antabo	antabo	PROPN
ejpam-6052	23	11	et	et	PROPN
ejpam-6052	23	12	al	al	PROPN
ejpam-6052	23	13	.	.	PUNCT
ejpam-6052	23	14	/	/	SYM
ejpam-6052	23	15	eur	eur	PROPN
ejpam-6052	23	16	.	.	PUNCT
ejpam-6052	24	1	j.	j.	PROPN
ejpam-6052	24	2	pure	pure	PROPN
ejpam-6052	24	3	appl	appl	PROPN
ejpam-6052	24	4	.	.	PROPN
ejpam-6052	24	5	math	math	PROPN
ejpam-6052	24	6	,	,	PUNCT
ejpam-6052	24	7	18	18	NUM
ejpam-6052	24	8	(	(	PUNCT
ejpam-6052	24	9	2	2	NUM
ejpam-6052	24	10	)	)	PUNCT
ejpam-6052	24	11	(	(	PUNCT
ejpam-6052	24	12	2025	2025	NUM
ejpam-6052	24	13	)	)	PUNCT
ejpam-6052	24	14	,	,	PUNCT
ejpam-6052	24	15	6052	6052	NUM
ejpam-6052	24	16	2	2	NUM
ejpam-6052	24	17	of	of	ADP
ejpam-6052	24	18	14	14	NUM
ejpam-6052	24	19	a	a	DET
ejpam-6052	24	20	key	key	ADJ
ejpam-6052	24	21	advancement	advancement	NOUN
ejpam-6052	24	22	in	in	ADP
ejpam-6052	24	23	algebraic	algebraic	ADJ
ejpam-6052	24	24	logic	logic	NOUN
ejpam-6052	24	25	is	be	AUX
ejpam-6052	24	26	the	the	DET
ejpam-6052	24	27	introduction	introduction	NOUN
ejpam-6052	24	28	of	of	ADP
ejpam-6052	24	29	pseudo	pseudo	NOUN
ejpam-6052	24	30	-	-	NOUN
ejpam-6052	24	31	algebras	algebra	NOUN
ejpam-6052	24	32	,	,	PUNCT
ejpam-6052	24	33	which	which	PRON
ejpam-6052	24	34	extend	extend	VERB
ejpam-6052	24	35	classical	classical	ADJ
ejpam-6052	24	36	structures	structure	NOUN
ejpam-6052	24	37	by	by	ADP
ejpam-6052	24	38	relaxing	relax	VERB
ejpam-6052	24	39	commutativity	commutativity	NOUN
ejpam-6052	24	40	constraints	constraint	NOUN
ejpam-6052	24	41	.	.	PUNCT
ejpam-6052	25	1	these	these	PRON
ejpam-6052	25	2	include	include	VERB
ejpam-6052	25	3	pseudobck	pseudobck	ADJ
ejpam-6052	25	4	algebras	algebra	NOUN
ejpam-6052	25	5	[	[	X
ejpam-6052	25	6	7	7	NUM
ejpam-6052	25	7	]	]	PUNCT
ejpam-6052	25	8	,	,	PUNCT
ejpam-6052	25	9	pseudo	pseudo	NOUN
ejpam-6052	25	10	-	-	ADJ
ejpam-6052	25	11	bci	bci	ADJ
ejpam-6052	25	12	algebras	algebra	NOUN
ejpam-6052	25	13	[	[	X
ejpam-6052	25	14	8	8	NUM
ejpam-6052	25	15	]	]	PUNCT
ejpam-6052	25	16	,	,	PUNCT
ejpam-6052	25	17	pseudo	pseudo	NOUN
ejpam-6052	25	18	-	-	ADJ
ejpam-6052	25	19	mv	mv	ADJ
ejpam-6052	25	20	algebras	algebras	PROPN
ejpam-6052	26	1	[	[	X
ejpam-6052	26	2	9	9	NUM
ejpam-6052	26	3	]	]	PUNCT
ejpam-6052	26	4	,	,	PUNCT
ejpam-6052	26	5	and	and	CCONJ
ejpam-6052	26	6	pseudo	pseudo	NOUN
ejpam-6052	26	7	-	-	NOUN
ejpam-6052	26	8	bl	bl	NOUN
ejpam-6052	26	9	algebras	algebras	PROPN
ejpam-6052	27	1	[	[	X
ejpam-6052	27	2	10–13	10–13	NUM
ejpam-6052	27	3	]	]	X
ejpam-6052	27	4	.	.	PUNCT
ejpam-6052	28	1	an	an	DET
ejpam-6052	28	2	essential	essential	ADJ
ejpam-6052	28	3	aspect	aspect	NOUN
ejpam-6052	28	4	of	of	ADP
ejpam-6052	28	5	algebraic	algebraic	ADJ
ejpam-6052	28	6	structures	structure	NOUN
ejpam-6052	28	7	is	be	AUX
ejpam-6052	28	8	the	the	DET
ejpam-6052	28	9	study	study	NOUN
ejpam-6052	28	10	of	of	ADP
ejpam-6052	28	11	subalgebras	subalgebras	PROPN
ejpam-6052	28	12	,	,	PUNCT
ejpam-6052	28	13	normality	normality	NOUN
ejpam-6052	28	14	,	,	PUNCT
ejpam-6052	28	15	and	and	CCONJ
ejpam-6052	28	16	ideals	ideal	NOUN
ejpam-6052	28	17	,	,	PUNCT
ejpam-6052	28	18	which	which	PRON
ejpam-6052	28	19	play	play	VERB
ejpam-6052	28	20	a	a	DET
ejpam-6052	28	21	crucial	crucial	ADJ
ejpam-6052	28	22	role	role	NOUN
ejpam-6052	28	23	in	in	ADP
ejpam-6052	28	24	understanding	understand	VERB
ejpam-6052	28	25	the	the	DET
ejpam-6052	28	26	internal	internal	ADJ
ejpam-6052	28	27	organization	organization	NOUN
ejpam-6052	28	28	of	of	ADP
ejpam-6052	28	29	algebraic	algebraic	PROPN
ejpam-6052	28	30	systems	system	NOUN
ejpam-6052	28	31	.	.	PUNCT
ejpam-6052	29	1	subalgebras	subalgebras	PROPN
ejpam-6052	29	2	help	help	AUX
ejpam-6052	29	3	classify	classify	VERB
ejpam-6052	29	4	algebraic	algebraic	ADJ
ejpam-6052	29	5	structures	structure	NOUN
ejpam-6052	29	6	by	by	ADP
ejpam-6052	29	7	identifying	identify	VERB
ejpam-6052	29	8	subsets	subset	NOUN
ejpam-6052	29	9	that	that	PRON
ejpam-6052	29	10	inherit	inherit	VERB
ejpam-6052	29	11	operations	operation	NOUN
ejpam-6052	29	12	from	from	ADP
ejpam-6052	29	13	the	the	DET
ejpam-6052	29	14	parent	parent	NOUN
ejpam-6052	29	15	algebra	algebra	NOUN
ejpam-6052	29	16	,	,	PUNCT
ejpam-6052	29	17	while	while	SCONJ
ejpam-6052	29	18	normality	normality	NOUN
ejpam-6052	29	19	and	and	CCONJ
ejpam-6052	29	20	ideals	ideal	NOUN
ejpam-6052	29	21	are	be	AUX
ejpam-6052	29	22	fundamental	fundamental	ADJ
ejpam-6052	29	23	in	in	ADP
ejpam-6052	29	24	defining	define	VERB
ejpam-6052	29	25	quotient	quotient	NOUN
ejpam-6052	29	26	structures	structure	NOUN
ejpam-6052	29	27	and	and	CCONJ
ejpam-6052	29	28	homomorphic	homomorphic	ADJ
ejpam-6052	29	29	properties	property	NOUN
ejpam-6052	29	30	.	.	PUNCT
ejpam-6052	30	1	investigating	investigate	VERB
ejpam-6052	30	2	these	these	DET
ejpam-6052	30	3	aspects	aspect	NOUN
ejpam-6052	30	4	in	in	ADP
ejpam-6052	30	5	pseudoalgebras	pseudoalgebra	NOUN
ejpam-6052	30	6	provides	provide	VERB
ejpam-6052	30	7	deeper	deep	ADJ
ejpam-6052	30	8	insight	insight	NOUN
ejpam-6052	30	9	into	into	ADP
ejpam-6052	30	10	their	their	PRON
ejpam-6052	30	11	structural	structural	ADJ
ejpam-6052	30	12	behavior	behavior	NOUN
ejpam-6052	30	13	and	and	CCONJ
ejpam-6052	30	14	their	their	PRON
ejpam-6052	30	15	connections	connection	NOUN
ejpam-6052	30	16	to	to	ADP
ejpam-6052	30	17	existing	exist	VERB
ejpam-6052	30	18	logical	logical	ADJ
ejpam-6052	30	19	frameworks	framework	NOUN
ejpam-6052	30	20	.	.	PUNCT
ejpam-6052	31	1	despite	despite	SCONJ
ejpam-6052	31	2	extensive	extensive	ADJ
ejpam-6052	31	3	research	research	NOUN
ejpam-6052	31	4	on	on	ADP
ejpam-6052	31	5	logic	logic	NOUN
ejpam-6052	31	6	algebras	algebra	NOUN
ejpam-6052	31	7	and	and	CCONJ
ejpam-6052	31	8	pseudo	pseudo	NOUN
ejpam-6052	31	9	-	-	NOUN
ejpam-6052	31	10	algebras	algebra	NOUN
ejpam-6052	31	11	,	,	PUNCT
ejpam-6052	31	12	pseudo	pseudo	NOUN
ejpam-6052	31	13	bn	bn	NOUN
ejpam-6052	31	14	-algebras	-algebra	NOUN
ejpam-6052	31	15	have	have	AUX
ejpam-6052	31	16	not	not	PART
ejpam-6052	31	17	yet	yet	ADV
ejpam-6052	31	18	been	be	AUX
ejpam-6052	31	19	formally	formally	ADV
ejpam-6052	31	20	studied	study	VERB
ejpam-6052	31	21	.	.	PUNCT
ejpam-6052	32	1	this	this	DET
ejpam-6052	32	2	paper	paper	NOUN
ejpam-6052	32	3	introduces	introduce	VERB
ejpam-6052	32	4	the	the	DET
ejpam-6052	32	5	pseudo	pseudo	NOUN
ejpam-6052	32	6	-	-	NOUN
ejpam-6052	32	7	variant	variant	NOUN
ejpam-6052	32	8	of	of	ADP
ejpam-6052	32	9	bn	bn	NOUN
ejpam-6052	32	10	algebras	algebra	NOUN
ejpam-6052	32	11	,	,	PUNCT
ejpam-6052	32	12	developed	develop	VERB
ejpam-6052	32	13	in	in	ADP
ejpam-6052	32	14	light	light	NOUN
ejpam-6052	32	15	of	of	ADP
ejpam-6052	32	16	the	the	DET
ejpam-6052	32	17	established	establish	VERB
ejpam-6052	32	18	structural	structural	ADJ
ejpam-6052	32	19	connections	connection	NOUN
ejpam-6052	32	20	between	between	ADP
ejpam-6052	32	21	bn	bn	NOUN
ejpam-6052	32	22	-algebras	-algebras	ADJ
ejpam-6052	32	23	and	and	CCONJ
ejpam-6052	32	24	bf	bf	NOUN
ejpam-6052	32	25	-algebras	-algebras	PROPN
ejpam-6052	32	26	.	.	PUNCT
ejpam-6052	33	1	this	this	DET
ejpam-6052	33	2	study	study	NOUN
ejpam-6052	33	3	aims	aim	VERB
ejpam-6052	33	4	to	to	PART
ejpam-6052	33	5	define	define	VERB
ejpam-6052	33	6	pseudo	pseudo	NOUN
ejpam-6052	33	7	bn	bn	NOUN
ejpam-6052	33	8	-algebras	-algebra	NOUN
ejpam-6052	33	9	,	,	PUNCT
ejpam-6052	33	10	establish	establish	VERB
ejpam-6052	33	11	their	their	PRON
ejpam-6052	33	12	fundamental	fundamental	ADJ
ejpam-6052	33	13	properties	property	NOUN
ejpam-6052	33	14	,	,	PUNCT
ejpam-6052	33	15	explore	explore	VERB
ejpam-6052	33	16	their	their	PRON
ejpam-6052	33	17	subalgebra	subalgebra	NOUN
ejpam-6052	33	18	structures	structure	NOUN
ejpam-6052	33	19	,	,	PUNCT
ejpam-6052	33	20	normality	normality	NOUN
ejpam-6052	33	21	conditions	condition	NOUN
ejpam-6052	33	22	,	,	PUNCT
ejpam-6052	33	23	and	and	CCONJ
ejpam-6052	33	24	ideal	ideal	ADJ
ejpam-6052	33	25	theory	theory	NOUN
ejpam-6052	33	26	and	and	CCONJ
ejpam-6052	33	27	examine	examine	VERB
ejpam-6052	33	28	their	their	PRON
ejpam-6052	33	29	relationships	relationship	NOUN
ejpam-6052	33	30	with	with	ADP
ejpam-6052	33	31	existing	exist	VERB
ejpam-6052	33	32	pseudo	pseudo	NOUN
ejpam-6052	33	33	-	-	ADJ
ejpam-6052	33	34	algebraic	algebraic	ADJ
ejpam-6052	33	35	frameworks	framework	NOUN
ejpam-6052	33	36	.	.	PUNCT
ejpam-6052	34	1	by	by	ADP
ejpam-6052	34	2	doing	do	VERB
ejpam-6052	34	3	so	so	ADV
ejpam-6052	34	4	,	,	PUNCT
ejpam-6052	34	5	it	it	PRON
ejpam-6052	34	6	contributes	contribute	VERB
ejpam-6052	34	7	to	to	ADP
ejpam-6052	34	8	the	the	DET
ejpam-6052	34	9	ongoing	ongoing	ADJ
ejpam-6052	34	10	development	development	NOUN
ejpam-6052	34	11	of	of	ADP
ejpam-6052	34	12	algebraic	algebraic	ADJ
ejpam-6052	34	13	logic	logic	NOUN
ejpam-6052	34	14	and	and	CCONJ
ejpam-6052	34	15	noncommutative	noncommutative	ADJ
ejpam-6052	34	16	reasoning	reasoning	NOUN
ejpam-6052	34	17	frameworks	framework	NOUN
ejpam-6052	34	18	.	.	PUNCT
ejpam-6052	35	1	2	2	X
ejpam-6052	35	2	.	.	X
ejpam-6052	35	3	preliminaries	preliminary	NOUN
ejpam-6052	35	4	some	some	DET
ejpam-6052	35	5	preliminary	preliminary	ADJ
ejpam-6052	35	6	concepts	concept	NOUN
ejpam-6052	35	7	are	be	AUX
ejpam-6052	35	8	given	give	VERB
ejpam-6052	35	9	below	below	ADP
ejpam-6052	35	10	,	,	PUNCT
ejpam-6052	35	11	as	as	ADV
ejpam-6052	35	12	well	well	ADV
ejpam-6052	35	13	as	as	ADP
ejpam-6052	35	14	results	result	NOUN
ejpam-6052	35	15	that	that	PRON
ejpam-6052	35	16	are	be	AUX
ejpam-6052	35	17	needed	need	VERB
ejpam-6052	35	18	in	in	ADP
ejpam-6052	35	19	this	this	DET
ejpam-6052	35	20	study	study	NOUN
ejpam-6052	35	21	.	.	PUNCT
ejpam-6052	36	1	definition	definition	NOUN
ejpam-6052	36	2	1	1	NUM
ejpam-6052	36	3	.	.	PUNCT
ejpam-6052	37	1	[	[	X
ejpam-6052	37	2	5	5	NUM
ejpam-6052	37	3	]	]	PUNCT
ejpam-6052	37	4	a	a	DET
ejpam-6052	37	5	bn	bn	NOUN
ejpam-6052	37	6	-	-	PUNCT
ejpam-6052	37	7	algebra	algebra	NOUN
ejpam-6052	37	8	is	be	AUX
ejpam-6052	37	9	an	an	DET
ejpam-6052	37	10	algebra	algebra	NOUN
ejpam-6052	37	11	(	(	PUNCT
ejpam-6052	37	12	x	x	X
ejpam-6052	37	13	,	,	PUNCT
ejpam-6052	37	14	∗	∗	NOUN
ejpam-6052	37	15	,	,	PUNCT
ejpam-6052	37	16	0	0	NUM
ejpam-6052	37	17	)	)	PUNCT
ejpam-6052	37	18	of	of	ADP
ejpam-6052	37	19	type	type	NOUN
ejpam-6052	37	20	(	(	PUNCT
ejpam-6052	37	21	2	2	NUM
ejpam-6052	37	22	,	,	PUNCT
ejpam-6052	37	23	0	0	NUM
ejpam-6052	37	24	)	)	PUNCT
ejpam-6052	37	25	satisfying	satisfy	VERB
ejpam-6052	37	26	the	the	DET
ejpam-6052	37	27	following	follow	VERB
ejpam-6052	37	28	axioms	axiom	NOUN
ejpam-6052	37	29	:	:	PUNCT
ejpam-6052	37	30	for	for	ADP
ejpam-6052	37	31	any	any	DET
ejpam-6052	37	32	x	x	NOUN
ejpam-6052	37	33	,	,	PUNCT
ejpam-6052	37	34	y	y	PROPN
ejpam-6052	37	35	,	,	PUNCT
ejpam-6052	37	36	z	z	PROPN
ejpam-6052	37	37	∈	∈	PROPN
ejpam-6052	37	38	x	x	X
ejpam-6052	37	39	,	,	PUNCT
ejpam-6052	37	40	(	(	PUNCT
ejpam-6052	37	41	bn1	bn1	PROPN
ejpam-6052	37	42	)	)	PUNCT
ejpam-6052	37	43	x	x	SYM
ejpam-6052	37	44	∗	∗	NOUN
ejpam-6052	37	45	x	x	SYM
ejpam-6052	37	46	=	=	SYM
ejpam-6052	37	47	0	0	NUM
ejpam-6052	37	48	,	,	PUNCT
ejpam-6052	37	49	(	(	PUNCT
ejpam-6052	37	50	bn2	bn2	NOUN
ejpam-6052	37	51	)	)	PUNCT
ejpam-6052	37	52	x	x	SYM
ejpam-6052	37	53	∗	∗	NOUN
ejpam-6052	37	54	0	0	NUM
ejpam-6052	38	1	=	=	SYM
ejpam-6052	38	2	x	x	NOUN
ejpam-6052	38	3	,	,	PUNCT
ejpam-6052	38	4	and	and	CCONJ
ejpam-6052	38	5	(	(	PUNCT
ejpam-6052	38	6	bn3	bn3	PROPN
ejpam-6052	38	7	)	)	PUNCT
ejpam-6052	38	8	(	(	PUNCT
ejpam-6052	38	9	x	x	SYM
ejpam-6052	38	10	∗	∗	PROPN
ejpam-6052	38	11	y	y	NOUN
ejpam-6052	38	12	)	)	PUNCT
ejpam-6052	38	13	∗	∗	NOUN
ejpam-6052	38	14	z	z	NOUN
ejpam-6052	38	15	=	=	SYM
ejpam-6052	38	16	(	(	PUNCT
ejpam-6052	38	17	0	0	NUM
ejpam-6052	38	18	∗	∗	PROPN
ejpam-6052	38	19	z	z	NOUN
ejpam-6052	38	20	)	)	PUNCT
ejpam-6052	38	21	∗	∗	NOUN
ejpam-6052	38	22	(	(	PUNCT
ejpam-6052	38	23	y	y	PROPN
ejpam-6052	38	24	∗	∗	NOUN
ejpam-6052	38	25	x	x	NOUN
ejpam-6052	38	26	)	)	PUNCT
ejpam-6052	38	27	.	.	PUNCT
ejpam-6052	39	1	example	example	NOUN
ejpam-6052	40	1	1	1	NUM
ejpam-6052	40	2	.	.	PUNCT
ejpam-6052	41	1	(	(	PUNCT
ejpam-6052	41	2	[	[	X
ejpam-6052	41	3	5	5	NUM
ejpam-6052	41	4	]	]	PUNCT
ejpam-6052	41	5	,	,	PUNCT
ejpam-6052	41	6	example	example	NOUN
ejpam-6052	41	7	2.26	2.26	NUM
ejpam-6052	41	8	)	)	PUNCT
ejpam-6052	41	9	let	let	VERB
ejpam-6052	41	10	x	x	PUNCT
ejpam-6052	41	11	=	=	PUNCT
ejpam-6052	41	12	{	{	PUNCT
ejpam-6052	41	13	0	0	NUM
ejpam-6052	41	14	,	,	PUNCT
ejpam-6052	41	15	1	1	NUM
ejpam-6052	41	16	,	,	PUNCT
ejpam-6052	41	17	2	2	NUM
ejpam-6052	41	18	,	,	PUNCT
ejpam-6052	41	19	3	3	NUM
ejpam-6052	41	20	}	}	PUNCT
ejpam-6052	41	21	be	be	AUX
ejpam-6052	41	22	a	a	DET
ejpam-6052	41	23	set	set	NOUN
ejpam-6052	41	24	and	and	CCONJ
ejpam-6052	41	25	∗	∗	NOUN
ejpam-6052	41	26	be	be	VERB
ejpam-6052	41	27	a	a	DET
ejpam-6052	41	28	binary	binary	ADJ
ejpam-6052	41	29	operation	operation	NOUN
ejpam-6052	41	30	defined	define	VERB
ejpam-6052	41	31	by	by	ADP
ejpam-6052	41	32	the	the	DET
ejpam-6052	41	33	following	follow	VERB
ejpam-6052	41	34	cayley	cayley	ADJ
ejpam-6052	41	35	table	table	NOUN
ejpam-6052	41	36	.	.	PUNCT
ejpam-6052	42	1	∗	∗	NOUN
ejpam-6052	42	2	0	0	NUM
ejpam-6052	42	3	1	1	NUM
ejpam-6052	42	4	2	2	NUM
ejpam-6052	42	5	3	3	NUM
ejpam-6052	42	6	0	0	NUM
ejpam-6052	42	7	0	0	NUM
ejpam-6052	42	8	1	1	NUM
ejpam-6052	42	9	2	2	NUM
ejpam-6052	42	10	3	3	NUM
ejpam-6052	42	11	1	1	NUM
ejpam-6052	42	12	1	1	NUM
ejpam-6052	42	13	0	0	NUM
ejpam-6052	42	14	1	1	NUM
ejpam-6052	42	15	1	1	NUM
ejpam-6052	42	16	2	2	NUM
ejpam-6052	42	17	2	2	NUM
ejpam-6052	42	18	1	1	NUM
ejpam-6052	42	19	0	0	NUM
ejpam-6052	42	20	1	1	NUM
ejpam-6052	42	21	3	3	NUM
ejpam-6052	42	22	3	3	NUM
ejpam-6052	42	23	1	1	NUM
ejpam-6052	42	24	1	1	NUM
ejpam-6052	42	25	0	0	NUM
ejpam-6052	42	26	then	then	ADV
ejpam-6052	42	27	(	(	PUNCT
ejpam-6052	42	28	x	x	X
ejpam-6052	42	29	,	,	PUNCT
ejpam-6052	42	30	∗	∗	NOUN
ejpam-6052	42	31	,	,	PUNCT
ejpam-6052	42	32	0	0	NUM
ejpam-6052	42	33	)	)	PUNCT
ejpam-6052	42	34	is	be	AUX
ejpam-6052	42	35	a	a	DET
ejpam-6052	42	36	bn	bn	NOUN
ejpam-6052	42	37	-algebra	-algebra	NOUN
ejpam-6052	42	38	.	.	PUNCT
ejpam-6052	43	1	i.m	i.m	PROPN
ejpam-6052	43	2	.	.	PROPN
ejpam-6052	43	3	antabo	antabo	PROPN
ejpam-6052	43	4	et	et	PROPN
ejpam-6052	43	5	al	al	PROPN
ejpam-6052	43	6	.	.	PUNCT
ejpam-6052	43	7	/	/	SYM
ejpam-6052	43	8	eur	eur	PROPN
ejpam-6052	43	9	.	.	PUNCT
ejpam-6052	44	1	j.	j.	PROPN
ejpam-6052	44	2	pure	pure	PROPN
ejpam-6052	44	3	appl	appl	PROPN
ejpam-6052	44	4	.	.	PROPN
ejpam-6052	44	5	math	math	PROPN
ejpam-6052	44	6	,	,	PUNCT
ejpam-6052	44	7	18	18	NUM
ejpam-6052	44	8	(	(	PUNCT
ejpam-6052	44	9	2	2	NUM
ejpam-6052	44	10	)	)	PUNCT
ejpam-6052	44	11	(	(	PUNCT
ejpam-6052	44	12	2025	2025	NUM
ejpam-6052	44	13	)	)	PUNCT
ejpam-6052	44	14	,	,	PUNCT
ejpam-6052	44	15	6052	6052	NUM
ejpam-6052	44	16	3	3	NUM
ejpam-6052	44	17	of	of	ADP
ejpam-6052	44	18	14	14	NUM
ejpam-6052	44	19	example	example	NOUN
ejpam-6052	44	20	2	2	NUM
ejpam-6052	44	21	.	.	PUNCT
ejpam-6052	45	1	(	(	PUNCT
ejpam-6052	45	2	[	[	X
ejpam-6052	45	3	14	14	NUM
ejpam-6052	45	4	]	]	PUNCT
ejpam-6052	45	5	,	,	PUNCT
ejpam-6052	45	6	example	example	NOUN
ejpam-6052	45	7	5	5	NUM
ejpam-6052	45	8	)	)	PUNCT
ejpam-6052	45	9	let	let	VERB
ejpam-6052	45	10	r	r	NOUN
ejpam-6052	45	11	be	be	AUX
ejpam-6052	45	12	the	the	DET
ejpam-6052	45	13	set	set	NOUN
ejpam-6052	45	14	of	of	ADP
ejpam-6052	45	15	real	real	ADJ
ejpam-6052	45	16	numbers	number	NOUN
ejpam-6052	45	17	.	.	PUNCT
ejpam-6052	46	1	define	define	VERB
ejpam-6052	46	2	the	the	DET
ejpam-6052	46	3	operation	operation	NOUN
ejpam-6052	46	4	“	"	PUNCT
ejpam-6052	46	5	∗	∗	NOUN
ejpam-6052	46	6	”	"	PUNCT
ejpam-6052	46	7	on	on	ADP
ejpam-6052	46	8	r	r	NOUN
ejpam-6052	46	9	as	as	SCONJ
ejpam-6052	46	10	follows	follow	VERB
ejpam-6052	46	11	:	:	PUNCT
ejpam-6052	46	12	for	for	ADP
ejpam-6052	46	13	x	x	X
ejpam-6052	46	14	,	,	PUNCT
ejpam-6052	46	15	y	y	PROPN
ejpam-6052	46	16	∈	∈	PROPN
ejpam-6052	46	17	r	r	PROPN
ejpam-6052	46	18	,	,	PUNCT
ejpam-6052	46	19	x	x	X
ejpam-6052	46	20	∗	∗	NOUN
ejpam-6052	46	21	y	y	NOUN
ejpam-6052	46	22	=	=	SYM
ejpam-6052	46	23			PROPN
ejpam-6052	46	24	x	x	X
ejpam-6052	46	25	,	,	PUNCT
ejpam-6052	46	26	if	if	SCONJ
ejpam-6052	46	27	y	y	PROPN
ejpam-6052	46	28	=	=	SYM
ejpam-6052	46	29	0	0	PROPN
ejpam-6052	46	30	,	,	PUNCT
ejpam-6052	46	31	y	y	PROPN
ejpam-6052	46	32	,	,	PUNCT
ejpam-6052	46	33	if	if	SCONJ
ejpam-6052	46	34	x	x	ADP
ejpam-6052	46	35	=	=	SYM
ejpam-6052	46	36	0	0	NUM
ejpam-6052	46	37	,	,	PUNCT
ejpam-6052	46	38	0	0	NUM
ejpam-6052	46	39	,	,	PUNCT
ejpam-6052	46	40	otherwise	otherwise	ADV
ejpam-6052	46	41	.	.	PUNCT
ejpam-6052	47	1	(	(	PUNCT
ejpam-6052	47	2	1	1	X
ejpam-6052	47	3	)	)	PUNCT
ejpam-6052	47	4	then	then	ADV
ejpam-6052	47	5	(	(	PUNCT
ejpam-6052	47	6	r	r	NOUN
ejpam-6052	47	7	,	,	PUNCT
ejpam-6052	47	8	∗	∗	NOUN
ejpam-6052	47	9	,	,	PUNCT
ejpam-6052	47	10	0	0	NUM
ejpam-6052	47	11	)	)	PUNCT
ejpam-6052	47	12	is	be	AUX
ejpam-6052	47	13	a	a	DET
ejpam-6052	47	14	bn	bn	NOUN
ejpam-6052	47	15	-algebra	-algebra	NOUN
ejpam-6052	47	16	.	.	PUNCT
ejpam-6052	47	17	example	example	NOUN
ejpam-6052	48	1	3	3	X
ejpam-6052	48	2	.	.	PUNCT
ejpam-6052	49	1	let	let	VERB
ejpam-6052	49	2	r	r	NOUN
ejpam-6052	49	3	be	be	AUX
ejpam-6052	49	4	the	the	DET
ejpam-6052	49	5	set	set	NOUN
ejpam-6052	49	6	of	of	ADP
ejpam-6052	49	7	real	real	ADJ
ejpam-6052	49	8	numbers	number	NOUN
ejpam-6052	49	9	.	.	PUNCT
ejpam-6052	50	1	define	define	VERB
ejpam-6052	50	2	the	the	DET
ejpam-6052	50	3	operation	operation	NOUN
ejpam-6052	50	4	“	"	PUNCT
ejpam-6052	50	5	∗	∗	NOUN
ejpam-6052	50	6	”	"	PUNCT
ejpam-6052	50	7	on	on	ADP
ejpam-6052	50	8	r	r	NOUN
ejpam-6052	50	9	as	as	SCONJ
ejpam-6052	50	10	follows	follow	VERB
ejpam-6052	50	11	:	:	PUNCT
ejpam-6052	50	12	for	for	ADP
ejpam-6052	50	13	x	x	X
ejpam-6052	50	14	,	,	PUNCT
ejpam-6052	50	15	y	y	PROPN
ejpam-6052	50	16	∈	∈	PROPN
ejpam-6052	50	17	r	r	PROPN
ejpam-6052	50	18	,	,	PUNCT
ejpam-6052	50	19	x	x	X
ejpam-6052	50	20	∗	∗	NOUN
ejpam-6052	50	21	y	y	NOUN
ejpam-6052	50	22	=	=	PRON
ejpam-6052	50	23	{	{	PUNCT
ejpam-6052	50	24	x+	x+	PROPN
ejpam-6052	50	25	y	y	NOUN
ejpam-6052	50	26	,	,	PUNCT
ejpam-6052	50	27	if	if	SCONJ
ejpam-6052	50	28	x	x	PROPN
ejpam-6052	50	29	̸=	̸=	PROPN
ejpam-6052	50	30	y	y	PROPN
ejpam-6052	50	31	0	0	NUM
ejpam-6052	50	32	,	,	PUNCT
ejpam-6052	50	33	if	if	SCONJ
ejpam-6052	50	34	x	x	ADP
ejpam-6052	50	35	=	=	SYM
ejpam-6052	50	36	y	y	PROPN
ejpam-6052	50	37	(	(	PUNCT
ejpam-6052	50	38	2	2	NUM
ejpam-6052	50	39	)	)	PUNCT
ejpam-6052	50	40	then	then	ADV
ejpam-6052	50	41	(	(	PUNCT
ejpam-6052	50	42	r	r	NOUN
ejpam-6052	50	43	,	,	PUNCT
ejpam-6052	50	44	∗	∗	NOUN
ejpam-6052	50	45	,	,	PUNCT
ejpam-6052	50	46	0	0	NUM
ejpam-6052	50	47	)	)	PUNCT
ejpam-6052	50	48	is	be	AUX
ejpam-6052	50	49	a	a	DET
ejpam-6052	50	50	bn	bn	NOUN
ejpam-6052	50	51	-algebra	-algebra	NOUN
ejpam-6052	50	52	.	.	PUNCT
ejpam-6052	51	1	theorem	theorem	NOUN
ejpam-6052	51	2	1	1	NUM
ejpam-6052	51	3	.	.	PUNCT
ejpam-6052	52	1	(	(	PUNCT
ejpam-6052	52	2	[	[	X
ejpam-6052	52	3	5	5	NUM
ejpam-6052	52	4	]	]	PUNCT
ejpam-6052	52	5	,	,	PUNCT
ejpam-6052	52	6	theorem	theorem	VERB
ejpam-6052	52	7	2.3	2.3	NUM
ejpam-6052	52	8	)	)	PUNCT
ejpam-6052	52	9	if	if	SCONJ
ejpam-6052	52	10	(	(	PUNCT
ejpam-6052	52	11	x	x	NOUN
ejpam-6052	52	12	,	,	PUNCT
ejpam-6052	52	13	∗	∗	NOUN
ejpam-6052	52	14	,	,	PUNCT
ejpam-6052	52	15	0	0	NUM
ejpam-6052	52	16	)	)	PUNCT
ejpam-6052	52	17	is	be	AUX
ejpam-6052	52	18	a	a	DET
ejpam-6052	52	19	bn	bn	ADJ
ejpam-6052	52	20	-algebra	-algebra	NOUN
ejpam-6052	52	21	,	,	PUNCT
ejpam-6052	52	22	then	then	ADV
ejpam-6052	52	23	(	(	PUNCT
ejpam-6052	52	24	x	x	X
ejpam-6052	52	25	,	,	PUNCT
ejpam-6052	52	26	∗	∗	NOUN
ejpam-6052	52	27	,	,	PUNCT
ejpam-6052	52	28	0	0	NUM
ejpam-6052	52	29	)	)	PUNCT
ejpam-6052	52	30	is	be	AUX
ejpam-6052	52	31	a	a	DET
ejpam-6052	52	32	bf	bf	NOUN
ejpam-6052	52	33	algebra	algebra	NOUN
ejpam-6052	52	34	.	.	PUNCT
ejpam-6052	53	1	remark	remark	NOUN
ejpam-6052	53	2	1	1	NUM
ejpam-6052	53	3	.	.	PUNCT
ejpam-6052	54	1	the	the	DET
ejpam-6052	54	2	converse	converse	NOUN
ejpam-6052	54	3	of	of	ADP
ejpam-6052	54	4	theorem	theorem	NOUN
ejpam-6052	54	5	1	1	NUM
ejpam-6052	54	6	does	do	AUX
ejpam-6052	54	7	not	not	PART
ejpam-6052	54	8	hold	hold	VERB
ejpam-6052	54	9	in	in	ADP
ejpam-6052	54	10	general	general	ADJ
ejpam-6052	54	11	as	as	SCONJ
ejpam-6052	54	12	it	it	PRON
ejpam-6052	54	13	was	be	AUX
ejpam-6052	54	14	shown	show	VERB
ejpam-6052	54	15	in	in	ADP
ejpam-6052	54	16	[	[	X
ejpam-6052	54	17	5	5	NUM
ejpam-6052	54	18	]	]	PUNCT
ejpam-6052	54	19	,	,	PUNCT
ejpam-6052	54	20	example	example	NOUN
ejpam-6052	54	21	2.4	2.4	NUM
ejpam-6052	54	22	.	.	PUNCT
ejpam-6052	55	1	proposition	proposition	NOUN
ejpam-6052	55	2	1	1	NUM
ejpam-6052	55	3	.	.	PUNCT
ejpam-6052	56	1	[	[	X
ejpam-6052	56	2	5	5	X
ejpam-6052	56	3	]	]	PUNCT
ejpam-6052	56	4	if	if	SCONJ
ejpam-6052	56	5	(	(	PUNCT
ejpam-6052	56	6	x	x	NOUN
ejpam-6052	56	7	,	,	PUNCT
ejpam-6052	56	8	∗	∗	NOUN
ejpam-6052	56	9	,	,	PUNCT
ejpam-6052	56	10	0	0	NUM
ejpam-6052	56	11	)	)	PUNCT
ejpam-6052	56	12	is	be	AUX
ejpam-6052	56	13	a	a	DET
ejpam-6052	56	14	bn	bn	ADJ
ejpam-6052	56	15	-algebra	-algebra	NOUN
ejpam-6052	56	16	,	,	PUNCT
ejpam-6052	56	17	then	then	ADV
ejpam-6052	56	18	for	for	ADP
ejpam-6052	56	19	any	any	DET
ejpam-6052	56	20	x	x	NOUN
ejpam-6052	56	21	,	,	PUNCT
ejpam-6052	56	22	y	y	PROPN
ejpam-6052	56	23	,	,	PUNCT
ejpam-6052	56	24	z	z	PROPN
ejpam-6052	56	25	∈	∈	PROPN
ejpam-6052	56	26	x	x	X
ejpam-6052	56	27	,	,	PUNCT
ejpam-6052	56	28	(	(	PUNCT
ejpam-6052	56	29	i	i	NOUN
ejpam-6052	56	30	)	)	PUNCT
ejpam-6052	56	31	0	0	NUM
ejpam-6052	57	1	∗	∗	NOUN
ejpam-6052	57	2	(	(	PUNCT
ejpam-6052	57	3	0	0	NUM
ejpam-6052	57	4	∗	∗	NOUN
ejpam-6052	57	5	x	x	NOUN
ejpam-6052	57	6	)	)	PUNCT
ejpam-6052	57	7	=	=	SYM
ejpam-6052	57	8	x	x	X
ejpam-6052	57	9	;	;	PUNCT
ejpam-6052	57	10	(	(	PUNCT
ejpam-6052	57	11	ii	ii	X
ejpam-6052	57	12	)	)	PUNCT
ejpam-6052	57	13	y	y	PROPN
ejpam-6052	57	14	∗	∗	NOUN
ejpam-6052	57	15	x	x	PUNCT
ejpam-6052	57	16	=	=	SYM
ejpam-6052	57	17	(	(	PUNCT
ejpam-6052	57	18	0	0	NUM
ejpam-6052	57	19	∗	∗	NOUN
ejpam-6052	57	20	x	x	NOUN
ejpam-6052	57	21	)	)	PUNCT
ejpam-6052	57	22	∗	∗	NOUN
ejpam-6052	57	23	(	(	PUNCT
ejpam-6052	57	24	0	0	NUM
ejpam-6052	57	25	∗	∗	NOUN
ejpam-6052	57	26	y	y	PROPN
ejpam-6052	57	27	)	)	PUNCT
ejpam-6052	57	28	;	;	PUNCT
ejpam-6052	57	29	(	(	PUNCT
ejpam-6052	57	30	iii	iii	X
ejpam-6052	57	31	)	)	PUNCT
ejpam-6052	57	32	(	(	PUNCT
ejpam-6052	57	33	0	0	NUM
ejpam-6052	57	34	∗	∗	NOUN
ejpam-6052	57	35	x	x	NOUN
ejpam-6052	57	36	)	)	PUNCT
ejpam-6052	57	37	∗	∗	NOUN
ejpam-6052	57	38	y	y	NOUN
ejpam-6052	57	39	=	=	SYM
ejpam-6052	57	40	(	(	PUNCT
ejpam-6052	57	41	0	0	NUM
ejpam-6052	57	42	∗	∗	PROPN
ejpam-6052	57	43	y	y	NOUN
ejpam-6052	57	44	)	)	PUNCT
ejpam-6052	57	45	∗	∗	NOUN
ejpam-6052	57	46	x	x	SYM
ejpam-6052	57	47	;	;	PUNCT
ejpam-6052	57	48	(	(	PUNCT
ejpam-6052	57	49	iv	iv	X
ejpam-6052	57	50	)	)	PUNCT
ejpam-6052	57	51	x	x	PROPN
ejpam-6052	58	1	∗	∗	NOUN
ejpam-6052	58	2	y	y	NOUN
ejpam-6052	58	3	=	=	SYM
ejpam-6052	58	4	0	0	PUNCT
ejpam-6052	59	1	=	=	NOUN
ejpam-6052	59	2	⇒	⇒	X
ejpam-6052	59	3	y	y	PROPN
ejpam-6052	59	4	∗	∗	NOUN
ejpam-6052	59	5	x	x	PUNCT
ejpam-6052	59	6	=	=	SYM
ejpam-6052	59	7	0	0	NUM
ejpam-6052	59	8	;	;	PUNCT
ejpam-6052	59	9	(	(	PUNCT
ejpam-6052	59	10	v	v	NOUN
ejpam-6052	59	11	)	)	PUNCT
ejpam-6052	59	12	0	0	NUM
ejpam-6052	59	13	∗	∗	NOUN
ejpam-6052	59	14	x	x	X
ejpam-6052	60	1	=	=	SYM
ejpam-6052	60	2	0	0	NUM
ejpam-6052	60	3	∗	∗	NOUN
ejpam-6052	60	4	y	y	NOUN
ejpam-6052	60	5	=	=	NOUN
ejpam-6052	60	6	⇒	⇒	VERB
ejpam-6052	60	7	x	x	PUNCT
ejpam-6052	60	8	=	=	SYM
ejpam-6052	60	9	y	y	PROPN
ejpam-6052	60	10	;	;	PUNCT
ejpam-6052	60	11	(	(	PUNCT
ejpam-6052	60	12	vi	vi	NOUN
ejpam-6052	60	13	)	)	PUNCT
ejpam-6052	60	14	(	(	PUNCT
ejpam-6052	60	15	x	x	SYM
ejpam-6052	60	16	∗	∗	PROPN
ejpam-6052	60	17	z	z	NOUN
ejpam-6052	60	18	)	)	PUNCT
ejpam-6052	60	19	∗	∗	NOUN
ejpam-6052	60	20	(	(	PUNCT
ejpam-6052	60	21	y	y	PROPN
ejpam-6052	60	22	∗	∗	PROPN
ejpam-6052	60	23	z	z	NOUN
ejpam-6052	60	24	)	)	PUNCT
ejpam-6052	60	25	=	=	PUNCT
ejpam-6052	61	1	(	(	PUNCT
ejpam-6052	61	2	z	z	NOUN
ejpam-6052	61	3	∗	∗	PROPN
ejpam-6052	61	4	y	y	PROPN
ejpam-6052	61	5	)	)	PUNCT
ejpam-6052	61	6	∗	∗	NOUN
ejpam-6052	61	7	(	(	PUNCT
ejpam-6052	61	8	z	z	NOUN
ejpam-6052	61	9	∗	∗	NOUN
ejpam-6052	61	10	x	x	NOUN
ejpam-6052	61	11	)	)	PUNCT
ejpam-6052	61	12	.	.	PUNCT
ejpam-6052	62	1	definition	definition	NOUN
ejpam-6052	62	2	2	2	NUM
ejpam-6052	62	3	.	.	PUNCT
ejpam-6052	63	1	(	(	PUNCT
ejpam-6052	63	2	[	[	X
ejpam-6052	63	3	15	15	NUM
ejpam-6052	63	4	]	]	PUNCT
ejpam-6052	63	5	,	,	PUNCT
ejpam-6052	63	6	definition	definition	NOUN
ejpam-6052	63	7	4	4	NUM
ejpam-6052	63	8	)	)	PUNCT
ejpam-6052	63	9	an	an	DET
ejpam-6052	63	10	algebra	algebra	NOUN
ejpam-6052	63	11	(	(	PUNCT
ejpam-6052	63	12	e	e	NOUN
ejpam-6052	63	13	,	,	PUNCT
ejpam-6052	63	14	•	•	NUM
ejpam-6052	63	15	,	,	PUNCT
ejpam-6052	63	16	⋆	⋆	NOUN
ejpam-6052	63	17	,	,	PUNCT
ejpam-6052	63	18	0	0	NUM
ejpam-6052	63	19	)	)	PUNCT
ejpam-6052	63	20	of	of	ADP
ejpam-6052	63	21	type	type	NOUN
ejpam-6052	63	22	(	(	PUNCT
ejpam-6052	63	23	2	2	NUM
ejpam-6052	63	24	,	,	PUNCT
ejpam-6052	63	25	2	2	NUM
ejpam-6052	63	26	,	,	PUNCT
ejpam-6052	63	27	0	0	NUM
ejpam-6052	63	28	)	)	PUNCT
ejpam-6052	63	29	is	be	AUX
ejpam-6052	63	30	said	say	VERB
ejpam-6052	63	31	to	to	PART
ejpam-6052	63	32	be	be	AUX
ejpam-6052	63	33	a	a	DET
ejpam-6052	63	34	pseudo	pseudo	NOUN
ejpam-6052	63	35	-	-	NOUN
ejpam-6052	63	36	bf	bf	NOUN
ejpam-6052	63	37	-algebra	-algebra	NOUN
ejpam-6052	63	38	,	,	PUNCT
ejpam-6052	63	39	if	if	SCONJ
ejpam-6052	63	40	the	the	DET
ejpam-6052	63	41	following	follow	VERB
ejpam-6052	63	42	axioms	axiom	NOUN
ejpam-6052	63	43	are	be	AUX
ejpam-6052	63	44	satisfied	satisfied	ADJ
ejpam-6052	63	45	for	for	ADP
ejpam-6052	63	46	all	all	DET
ejpam-6052	63	47	a	a	PRON
ejpam-6052	63	48	,	,	PUNCT
ejpam-6052	63	49	b	b	X
ejpam-6052	63	50	∈	∈	PROPN
ejpam-6052	63	51	e	e	NOUN
ejpam-6052	63	52	:	:	PUNCT
ejpam-6052	63	53	(	(	PUNCT
ejpam-6052	63	54	pbf1	pbf1	NOUN
ejpam-6052	63	55	):	):	PUNCT
ejpam-6052	63	56	a	a	DET
ejpam-6052	63	57	•	•	NOUN
ejpam-6052	63	58	a	a	DET
ejpam-6052	63	59	=	=	NOUN
ejpam-6052	63	60	0	0	NUM
ejpam-6052	63	61	and	and	CCONJ
ejpam-6052	63	62	a	a	DET
ejpam-6052	63	63	⋆	⋆	NOUN
ejpam-6052	63	64	a	a	PRON
ejpam-6052	63	65	=	=	NOUN
ejpam-6052	63	66	0	0	NUM
ejpam-6052	63	67	,	,	PUNCT
ejpam-6052	63	68	(	(	PUNCT
ejpam-6052	63	69	pbf2	pbf2	NOUN
ejpam-6052	63	70	):	):	PUNCT
ejpam-6052	63	71	a	a	DET
ejpam-6052	63	72	•	•	NOUN
ejpam-6052	63	73	0	0	NUM
ejpam-6052	63	74	=	=	NOUN
ejpam-6052	63	75	a	a	PRON
ejpam-6052	63	76	and	and	CCONJ
ejpam-6052	63	77	a	a	DET
ejpam-6052	63	78	⋆	⋆	NOUN
ejpam-6052	63	79	0	0	X
ejpam-6052	63	80	=	=	SYM
ejpam-6052	63	81	a	a	X
ejpam-6052	63	82	,	,	PUNCT
ejpam-6052	63	83	(	(	PUNCT
ejpam-6052	63	84	pbf3	pbf3	PROPN
ejpam-6052	63	85	):	):	PUNCT
ejpam-6052	63	86	0	0	NUM
ejpam-6052	63	87	•	•	NOUN
ejpam-6052	63	88	(	(	PUNCT
ejpam-6052	63	89	a	a	DET
ejpam-6052	63	90	⋆	⋆	NOUN
ejpam-6052	63	91	b	b	NOUN
ejpam-6052	63	92	)	)	PUNCT
ejpam-6052	63	93	=	=	SYM
ejpam-6052	64	1	b	b	X
ejpam-6052	64	2	⋆	⋆	NOUN
ejpam-6052	64	3	a	a	PRON
ejpam-6052	64	4	and	and	CCONJ
ejpam-6052	64	5	0	0	NUM
ejpam-6052	64	6	⋆	⋆	NOUN
ejpam-6052	64	7	(	(	PUNCT
ejpam-6052	64	8	a	a	DET
ejpam-6052	64	9	•	•	NUM
ejpam-6052	64	10	b	b	NOUN
ejpam-6052	64	11	)	)	PUNCT
ejpam-6052	65	1	=	=	SYM
ejpam-6052	65	2	b	b	NOUN
ejpam-6052	65	3	•	•	NUM
ejpam-6052	65	4	a.	a.	NOUN
ejpam-6052	65	5	example	example	NOUN
ejpam-6052	65	6	4	4	NUM
ejpam-6052	65	7	.	.	PUNCT
ejpam-6052	66	1	[	[	X
ejpam-6052	66	2	15	15	NUM
ejpam-6052	66	3	]	]	PUNCT
ejpam-6052	66	4	consider	consider	VERB
ejpam-6052	66	5	the	the	DET
ejpam-6052	66	6	additive	additive	ADJ
ejpam-6052	66	7	group	group	NOUN
ejpam-6052	66	8	(	(	PUNCT
ejpam-6052	66	9	g,+	g,+	PROPN
ejpam-6052	66	10	,	,	PUNCT
ejpam-6052	66	11	0	0	NUM
ejpam-6052	66	12	)	)	PUNCT
ejpam-6052	66	13	.	.	PUNCT
ejpam-6052	67	1	define	define	VERB
ejpam-6052	67	2	the	the	DET
ejpam-6052	67	3	operations	operation	NOUN
ejpam-6052	67	4	“	"	PUNCT
ejpam-6052	67	5	•	•	NOUN
ejpam-6052	67	6	”	"	PUNCT
ejpam-6052	67	7	and	and	CCONJ
ejpam-6052	67	8	“	"	PUNCT
ejpam-6052	67	9	⋆	⋆	VERB
ejpam-6052	67	10	”	"	PUNCT
ejpam-6052	67	11	on	on	ADP
ejpam-6052	67	12	g	g	NOUN
ejpam-6052	67	13	by	by	ADP
ejpam-6052	67	14	:	:	PUNCT
ejpam-6052	67	15	a	a	DET
ejpam-6052	67	16	•	•	NOUN
ejpam-6052	67	17	b	b	X
ejpam-6052	67	18	=	=	PUNCT
ejpam-6052	67	19	(	(	PUNCT
ejpam-6052	67	20	−b	−b	ADJ
ejpam-6052	67	21	)	)	PUNCT
ejpam-6052	67	22	+	+	CCONJ
ejpam-6052	67	23	a	a	PRON
ejpam-6052	67	24	and	and	CCONJ
ejpam-6052	67	25	a	a	DET
ejpam-6052	67	26	⋆	⋆	NOUN
ejpam-6052	67	27	b	b	NOUN
ejpam-6052	67	28	=	=	PUNCT
ejpam-6052	67	29	(	(	PUNCT
ejpam-6052	67	30	−b	−b	ADJ
ejpam-6052	67	31	)	)	PUNCT
ejpam-6052	68	1	+	+	CCONJ
ejpam-6052	68	2	a	a	PRON
ejpam-6052	68	3	for	for	ADP
ejpam-6052	68	4	all	all	DET
ejpam-6052	68	5	a	a	PRON
ejpam-6052	68	6	,	,	PUNCT
ejpam-6052	68	7	b	b	X
ejpam-6052	68	8	∈	∈	PROPN
ejpam-6052	68	9	g.	g.	NOUN
ejpam-6052	68	10	then	then	ADV
ejpam-6052	68	11	(	(	PUNCT
ejpam-6052	68	12	g	g	NOUN
ejpam-6052	68	13	,	,	PUNCT
ejpam-6052	68	14	•	•	NUM
ejpam-6052	68	15	,	,	PUNCT
ejpam-6052	68	16	⋆	⋆	NOUN
ejpam-6052	68	17	,	,	PUNCT
ejpam-6052	68	18	0	0	NUM
ejpam-6052	68	19	)	)	PUNCT
ejpam-6052	68	20	is	be	AUX
ejpam-6052	68	21	a	a	DET
ejpam-6052	68	22	pseudo	pseudo	NOUN
ejpam-6052	68	23	-	-	NOUN
ejpam-6052	68	24	bf	bf	NOUN
ejpam-6052	68	25	-algebra	-algebra	NOUN
ejpam-6052	68	26	.	.	PUNCT
ejpam-6052	69	1	i.m	i.m	PROPN
ejpam-6052	69	2	.	.	PROPN
ejpam-6052	69	3	antabo	antabo	PROPN
ejpam-6052	69	4	et	et	PROPN
ejpam-6052	69	5	al	al	PROPN
ejpam-6052	69	6	.	.	PUNCT
ejpam-6052	69	7	/	/	SYM
ejpam-6052	69	8	eur	eur	PROPN
ejpam-6052	69	9	.	.	PUNCT
ejpam-6052	70	1	j.	j.	PROPN
ejpam-6052	70	2	pure	pure	PROPN
ejpam-6052	70	3	appl	appl	PROPN
ejpam-6052	70	4	.	.	PROPN
ejpam-6052	70	5	math	math	PROPN
ejpam-6052	70	6	,	,	PUNCT
ejpam-6052	70	7	18	18	NUM
ejpam-6052	70	8	(	(	PUNCT
ejpam-6052	70	9	2	2	NUM
ejpam-6052	70	10	)	)	PUNCT
ejpam-6052	70	11	(	(	PUNCT
ejpam-6052	70	12	2025	2025	NUM
ejpam-6052	70	13	)	)	PUNCT
ejpam-6052	70	14	,	,	PUNCT
ejpam-6052	70	15	6052	6052	NUM
ejpam-6052	70	16	4	4	NUM
ejpam-6052	70	17	of	of	ADP
ejpam-6052	70	18	14	14	NUM
ejpam-6052	70	19	example	example	NOUN
ejpam-6052	70	20	5	5	NUM
ejpam-6052	70	21	.	.	PUNCT
ejpam-6052	71	1	(	(	PUNCT
ejpam-6052	71	2	[	[	X
ejpam-6052	71	3	15	15	NUM
ejpam-6052	71	4	]	]	PUNCT
ejpam-6052	71	5	,	,	PUNCT
ejpam-6052	71	6	example	example	NOUN
ejpam-6052	71	7	2	2	NUM
ejpam-6052	71	8	)	)	PUNCT
ejpam-6052	71	9	define	define	VERB
ejpam-6052	71	10	the	the	DET
ejpam-6052	71	11	operations	operation	NOUN
ejpam-6052	71	12	“	"	PUNCT
ejpam-6052	71	13	•	•	NOUN
ejpam-6052	71	14	”	"	PUNCT
ejpam-6052	71	15	and	and	CCONJ
ejpam-6052	71	16	“	"	PUNCT
ejpam-6052	71	17	⋆	⋆	VERB
ejpam-6052	71	18	”	"	PUNCT
ejpam-6052	71	19	on	on	ADP
ejpam-6052	71	20	e	e	X
ejpam-6052	71	21	=	=	PUNCT
ejpam-6052	71	22	{	{	PUNCT
ejpam-6052	71	23	0	0	NUM
ejpam-6052	71	24	,	,	PUNCT
ejpam-6052	71	25	1	1	NUM
ejpam-6052	71	26	,	,	PUNCT
ejpam-6052	71	27	2	2	NUM
ejpam-6052	71	28	,	,	PUNCT
ejpam-6052	71	29	3	3	NUM
ejpam-6052	71	30	}	}	PUNCT
ejpam-6052	71	31	by	by	ADP
ejpam-6052	71	32	the	the	DET
ejpam-6052	71	33	following	following	ADJ
ejpam-6052	71	34	cayley	cayley	ADJ
ejpam-6052	71	35	tables	table	NOUN
ejpam-6052	71	36	.	.	PUNCT
ejpam-6052	72	1	•	•	NUM
ejpam-6052	72	2	0	0	NUM
ejpam-6052	72	3	1	1	NUM
ejpam-6052	72	4	2	2	NUM
ejpam-6052	72	5	3	3	NUM
ejpam-6052	72	6	0	0	NUM
ejpam-6052	72	7	0	0	NUM
ejpam-6052	72	8	1	1	NUM
ejpam-6052	72	9	2	2	NUM
ejpam-6052	72	10	3	3	NUM
ejpam-6052	72	11	1	1	NUM
ejpam-6052	72	12	1	1	NUM
ejpam-6052	72	13	0	0	NUM
ejpam-6052	72	14	3	3	NUM
ejpam-6052	72	15	0	0	NUM
ejpam-6052	72	16	2	2	NUM
ejpam-6052	72	17	2	2	NUM
ejpam-6052	72	18	3	3	NUM
ejpam-6052	72	19	0	0	NUM
ejpam-6052	72	20	2	2	NUM
ejpam-6052	72	21	3	3	NUM
ejpam-6052	72	22	3	3	NUM
ejpam-6052	72	23	0	0	NUM
ejpam-6052	72	24	2	2	NUM
ejpam-6052	72	25	0	0	NUM
ejpam-6052	72	26	⋆	⋆	VERB
ejpam-6052	72	27	0	0	NUM
ejpam-6052	72	28	1	1	NUM
ejpam-6052	72	29	2	2	NUM
ejpam-6052	72	30	3	3	NUM
ejpam-6052	72	31	0	0	NUM
ejpam-6052	72	32	0	0	NUM
ejpam-6052	72	33	1	1	NUM
ejpam-6052	72	34	2	2	NUM
ejpam-6052	72	35	3	3	NUM
ejpam-6052	72	36	1	1	NUM
ejpam-6052	72	37	1	1	NUM
ejpam-6052	72	38	0	0	NUM
ejpam-6052	72	39	1	1	NUM
ejpam-6052	72	40	1	1	NUM
ejpam-6052	72	41	2	2	NUM
ejpam-6052	72	42	2	2	NUM
ejpam-6052	72	43	1	1	NUM
ejpam-6052	72	44	0	0	NUM
ejpam-6052	72	45	1	1	NUM
ejpam-6052	72	46	3	3	NUM
ejpam-6052	72	47	3	3	NUM
ejpam-6052	72	48	1	1	NUM
ejpam-6052	72	49	1	1	NUM
ejpam-6052	72	50	0	0	NUM
ejpam-6052	72	51	then	then	ADV
ejpam-6052	72	52	(	(	PUNCT
ejpam-6052	72	53	e	e	NOUN
ejpam-6052	72	54	,	,	PUNCT
ejpam-6052	72	55	•	•	NUM
ejpam-6052	72	56	,	,	PUNCT
ejpam-6052	72	57	0	0	NUM
ejpam-6052	72	58	)	)	PUNCT
ejpam-6052	72	59	and	and	CCONJ
ejpam-6052	72	60	(	(	PUNCT
ejpam-6052	72	61	e	e	NOUN
ejpam-6052	72	62	,	,	PUNCT
ejpam-6052	72	63	⋆	⋆	INTJ
ejpam-6052	72	64	,	,	PUNCT
ejpam-6052	72	65	0	0	NUM
ejpam-6052	72	66	)	)	PUNCT
ejpam-6052	72	67	are	be	AUX
ejpam-6052	72	68	bf	bf	NOUN
ejpam-6052	72	69	-algebras	-algebra	NOUN
ejpam-6052	72	70	(	(	PUNCT
ejpam-6052	72	71	shown	show	VERB
ejpam-6052	72	72	in	in	ADP
ejpam-6052	72	73	[	[	X
ejpam-6052	72	74	6	6	NUM
ejpam-6052	72	75	]	]	PUNCT
ejpam-6052	72	76	)	)	PUNCT
ejpam-6052	72	77	.	.	PUNCT
ejpam-6052	73	1	it	it	PRON
ejpam-6052	73	2	can	can	AUX
ejpam-6052	73	3	also	also	ADV
ejpam-6052	73	4	be	be	AUX
ejpam-6052	73	5	verified	verify	VERB
ejpam-6052	73	6	that	that	SCONJ
ejpam-6052	73	7	(	(	PUNCT
ejpam-6052	73	8	e	e	NOUN
ejpam-6052	73	9	,	,	PUNCT
ejpam-6052	73	10	•	•	NUM
ejpam-6052	73	11	,	,	PUNCT
ejpam-6052	73	12	⋆	⋆	NOUN
ejpam-6052	73	13	,	,	PUNCT
ejpam-6052	73	14	0	0	NUM
ejpam-6052	73	15	)	)	PUNCT
ejpam-6052	73	16	is	be	AUX
ejpam-6052	73	17	a	a	DET
ejpam-6052	73	18	pseudo	pseudo	NOUN
ejpam-6052	73	19	-	-	NOUN
ejpam-6052	73	20	bf	bf	NOUN
ejpam-6052	73	21	-algebra	-algebra	NOUN
ejpam-6052	73	22	.	.	PUNCT
ejpam-6052	74	1	3	3	X
ejpam-6052	74	2	.	.	X
ejpam-6052	74	3	results	result	VERB
ejpam-6052	74	4	this	this	DET
ejpam-6052	74	5	section	section	NOUN
ejpam-6052	74	6	explores	explore	VERB
ejpam-6052	74	7	key	key	ADJ
ejpam-6052	74	8	properties	property	NOUN
ejpam-6052	74	9	of	of	ADP
ejpam-6052	74	10	pseudo	pseudo	NOUN
ejpam-6052	74	11	bn	bn	X
ejpam-6052	74	12	-algebras	-algebra	NOUN
ejpam-6052	74	13	,	,	PUNCT
ejpam-6052	74	14	distinguishing	distinguish	VERB
ejpam-6052	74	15	them	they	PRON
ejpam-6052	74	16	from	from	ADP
ejpam-6052	74	17	classical	classical	ADJ
ejpam-6052	74	18	bn	bn	ADJ
ejpam-6052	74	19	-algebras	-algebra	NOUN
ejpam-6052	74	20	and	and	CCONJ
ejpam-6052	74	21	establishing	establish	VERB
ejpam-6052	74	22	their	their	PRON
ejpam-6052	74	23	structural	structural	ADJ
ejpam-6052	74	24	foundations	foundation	NOUN
ejpam-6052	74	25	.	.	PUNCT
ejpam-6052	75	1	3.1	3.1	NUM
ejpam-6052	75	2	.	.	PUNCT
ejpam-6052	76	1	some	some	DET
ejpam-6052	76	2	properties	property	NOUN
ejpam-6052	76	3	of	of	ADP
ejpam-6052	76	4	pseudo	pseudo	NOUN
ejpam-6052	76	5	bn	bn	NOUN
ejpam-6052	76	6	-	-	PUNCT
ejpam-6052	76	7	algebras	algebra	VERB
ejpam-6052	76	8	the	the	DET
ejpam-6052	76	9	results	result	NOUN
ejpam-6052	76	10	in	in	ADP
ejpam-6052	76	11	this	this	DET
ejpam-6052	76	12	section	section	NOUN
ejpam-6052	76	13	provide	provide	VERB
ejpam-6052	76	14	insights	insight	NOUN
ejpam-6052	76	15	into	into	ADP
ejpam-6052	76	16	the	the	DET
ejpam-6052	76	17	algebraic	algebraic	ADJ
ejpam-6052	76	18	nature	nature	NOUN
ejpam-6052	76	19	of	of	ADP
ejpam-6052	76	20	pseudo	pseudo	NOUN
ejpam-6052	76	21	bn	bn	NOUN
ejpam-6052	76	22	algebras	algebra	NOUN
ejpam-6052	76	23	,	,	PUNCT
ejpam-6052	76	24	setting	set	VERB
ejpam-6052	76	25	the	the	DET
ejpam-6052	76	26	stage	stage	NOUN
ejpam-6052	76	27	for	for	ADP
ejpam-6052	76	28	further	further	ADJ
ejpam-6052	76	29	exploration	exploration	NOUN
ejpam-6052	76	30	of	of	ADP
ejpam-6052	76	31	their	their	PRON
ejpam-6052	76	32	operations	operation	NOUN
ejpam-6052	76	33	and	and	CCONJ
ejpam-6052	76	34	applications	application	NOUN
ejpam-6052	76	35	.	.	PUNCT
ejpam-6052	77	1	definition	definition	NOUN
ejpam-6052	77	2	3	3	NUM
ejpam-6052	77	3	.	.	PUNCT
ejpam-6052	78	1	a	a	DET
ejpam-6052	78	2	pseudo	pseudo	NOUN
ejpam-6052	78	3	bn	bn	NOUN
ejpam-6052	78	4	-algebra	-algebra	NOUN
ejpam-6052	78	5	is	be	AUX
ejpam-6052	78	6	a	a	DET
ejpam-6052	78	7	structure	structure	NOUN
ejpam-6052	78	8	x	x	PUNCT
ejpam-6052	78	9	=	=	SYM
ejpam-6052	78	10	(	(	PUNCT
ejpam-6052	78	11	x	x	X
ejpam-6052	78	12	,	,	PUNCT
ejpam-6052	78	13	∗	∗	NOUN
ejpam-6052	78	14	,	,	PUNCT
ejpam-6052	78	15	◦	◦	NOUN
ejpam-6052	78	16	,	,	PUNCT
ejpam-6052	78	17	0	0	NUM
ejpam-6052	78	18	)	)	PUNCT
ejpam-6052	78	19	,	,	PUNCT
ejpam-6052	78	20	where	where	SCONJ
ejpam-6052	78	21	x	x	PRON
ejpam-6052	78	22	is	be	AUX
ejpam-6052	78	23	a	a	DET
ejpam-6052	78	24	set	set	NOUN
ejpam-6052	78	25	,	,	PUNCT
ejpam-6052	78	26	“	"	PUNCT
ejpam-6052	78	27	∗	∗	NOUN
ejpam-6052	78	28	”	"	PUNCT
ejpam-6052	78	29	and	and	CCONJ
ejpam-6052	78	30	“	"	PUNCT
ejpam-6052	78	31	◦	◦	NOUN
ejpam-6052	78	32	”	"	PUNCT
ejpam-6052	78	33	are	be	AUX
ejpam-6052	78	34	binary	binary	ADJ
ejpam-6052	78	35	operations	operation	NOUN
ejpam-6052	78	36	on	on	ADP
ejpam-6052	78	37	x	x	NOUN
ejpam-6052	78	38	,	,	PUNCT
ejpam-6052	78	39	and	and	CCONJ
ejpam-6052	78	40	“	"	PUNCT
ejpam-6052	78	41	0	0	NUM
ejpam-6052	78	42	”	"	PUNCT
ejpam-6052	78	43	is	be	AUX
ejpam-6052	78	44	a	a	DET
ejpam-6052	78	45	distinguished	distinguished	ADJ
ejpam-6052	78	46	element	element	NOUN
ejpam-6052	78	47	called	call	VERB
ejpam-6052	78	48	the	the	DET
ejpam-6052	78	49	zero	zero	NUM
ejpam-6052	78	50	element	element	NOUN
ejpam-6052	78	51	,	,	PUNCT
ejpam-6052	78	52	satisfying	satisfy	VERB
ejpam-6052	78	53	:	:	PUNCT
ejpam-6052	78	54	for	for	ADP
ejpam-6052	78	55	all	all	DET
ejpam-6052	78	56	x	x	NOUN
ejpam-6052	78	57	,	,	PUNCT
ejpam-6052	78	58	y	y	PROPN
ejpam-6052	78	59	,	,	PUNCT
ejpam-6052	78	60	z	z	PROPN
ejpam-6052	78	61	∈	∈	PROPN
ejpam-6052	78	62	x	x	X
ejpam-6052	78	63	,	,	PUNCT
ejpam-6052	78	64	(	(	PUNCT
ejpam-6052	78	65	pbn1	pbn1	NOUN
ejpam-6052	78	66	)	)	PUNCT
ejpam-6052	78	67	:	:	PUNCT
ejpam-6052	79	1	x	x	X
ejpam-6052	79	2	∗	∗	NOUN
ejpam-6052	79	3	x	x	X
ejpam-6052	79	4	=	=	SYM
ejpam-6052	79	5	0	0	NUM
ejpam-6052	79	6	and	and	CCONJ
ejpam-6052	79	7	x	x	PART
ejpam-6052	79	8	◦	◦	NOUN
ejpam-6052	79	9	x	x	SYM
ejpam-6052	79	10	=	=	SYM
ejpam-6052	79	11	0	0	NUM
ejpam-6052	79	12	,	,	PUNCT
ejpam-6052	79	13	(	(	PUNCT
ejpam-6052	79	14	pbn2	pbn2	NOUN
ejpam-6052	79	15	)	)	PUNCT
ejpam-6052	79	16	:	:	PUNCT
ejpam-6052	80	1	x	x	X
ejpam-6052	80	2	∗	∗	NOUN
ejpam-6052	80	3	0	0	NUM
ejpam-6052	81	1	=	=	SYM
ejpam-6052	81	2	x	x	X
ejpam-6052	81	3	and	and	CCONJ
ejpam-6052	81	4	x	x	PART
ejpam-6052	81	5	◦	◦	NOUN
ejpam-6052	81	6	0	0	NUM
ejpam-6052	81	7	=	=	SYM
ejpam-6052	81	8	x	x	NOUN
ejpam-6052	81	9	,	,	PUNCT
ejpam-6052	81	10	(	(	PUNCT
ejpam-6052	81	11	pbn3	pbn3	PROPN
ejpam-6052	81	12	)	)	PUNCT
ejpam-6052	81	13	:	:	PUNCT
ejpam-6052	81	14	(	(	PUNCT
ejpam-6052	81	15	x	x	X
ejpam-6052	81	16	∗	∗	PROPN
ejpam-6052	81	17	y	y	NOUN
ejpam-6052	81	18	)	)	PUNCT
ejpam-6052	81	19	◦	◦	NOUN
ejpam-6052	81	20	z	z	NOUN
ejpam-6052	81	21	=	=	SYM
ejpam-6052	81	22	(	(	PUNCT
ejpam-6052	81	23	0	0	NUM
ejpam-6052	81	24	∗	∗	PROPN
ejpam-6052	81	25	z	z	NOUN
ejpam-6052	81	26	)	)	PUNCT
ejpam-6052	81	27	◦	◦	NOUN
ejpam-6052	81	28	(	(	PUNCT
ejpam-6052	81	29	y	y	PROPN
ejpam-6052	81	30	∗	∗	NOUN
ejpam-6052	81	31	x	x	NOUN
ejpam-6052	81	32	)	)	PUNCT
ejpam-6052	81	33	and	and	CCONJ
ejpam-6052	81	34	(	(	PUNCT
ejpam-6052	81	35	x	x	X
ejpam-6052	81	36	◦	◦	VERB
ejpam-6052	81	37	y	y	NOUN
ejpam-6052	81	38	)	)	PUNCT
ejpam-6052	81	39	∗	∗	NOUN
ejpam-6052	81	40	z	z	NOUN
ejpam-6052	81	41	=	=	SYM
ejpam-6052	81	42	(	(	PUNCT
ejpam-6052	81	43	0	0	NUM
ejpam-6052	81	44	◦	◦	NOUN
ejpam-6052	81	45	z	z	NOUN
ejpam-6052	81	46	)	)	PUNCT
ejpam-6052	81	47	∗	∗	NOUN
ejpam-6052	81	48	(	(	PUNCT
ejpam-6052	81	49	y	y	PROPN
ejpam-6052	81	50	◦	◦	NOUN
ejpam-6052	81	51	x	x	X
ejpam-6052	81	52	)	)	PUNCT
ejpam-6052	81	53	.	.	PUNCT
ejpam-6052	82	1	example	example	NOUN
ejpam-6052	83	1	6	6	NUM
ejpam-6052	83	2	.	.	PUNCT
ejpam-6052	83	3	define	define	VERB
ejpam-6052	83	4	the	the	DET
ejpam-6052	83	5	binary	binary	ADJ
ejpam-6052	83	6	operations	operation	NOUN
ejpam-6052	83	7	“	"	PUNCT
ejpam-6052	83	8	∗	∗	NOUN
ejpam-6052	83	9	”	"	PUNCT
ejpam-6052	83	10	and	and	CCONJ
ejpam-6052	83	11	“	"	PUNCT
ejpam-6052	83	12	◦	◦	NOUN
ejpam-6052	83	13	”	"	PUNCT
ejpam-6052	83	14	on	on	ADP
ejpam-6052	83	15	x	x	X
ejpam-6052	83	16	=	=	SYM
ejpam-6052	83	17	{	{	PUNCT
ejpam-6052	83	18	0	0	NUM
ejpam-6052	83	19	,	,	PUNCT
ejpam-6052	83	20	1	1	NUM
ejpam-6052	83	21	,	,	PUNCT
ejpam-6052	83	22	2	2	NUM
ejpam-6052	83	23	,	,	PUNCT
ejpam-6052	83	24	3	3	NUM
ejpam-6052	83	25	}	}	PUNCT
ejpam-6052	83	26	by	by	ADP
ejpam-6052	83	27	the	the	DET
ejpam-6052	83	28	following	following	ADJ
ejpam-6052	83	29	cayley	cayley	ADJ
ejpam-6052	83	30	tables	table	NOUN
ejpam-6052	83	31	:	:	PUNCT
ejpam-6052	83	32	∗	∗	NOUN
ejpam-6052	83	33	0	0	NUM
ejpam-6052	83	34	1	1	NUM
ejpam-6052	83	35	2	2	NUM
ejpam-6052	83	36	3	3	NUM
ejpam-6052	83	37	0	0	NUM
ejpam-6052	83	38	0	0	NUM
ejpam-6052	83	39	1	1	NUM
ejpam-6052	83	40	2	2	NUM
ejpam-6052	83	41	3	3	NUM
ejpam-6052	83	42	1	1	NUM
ejpam-6052	83	43	1	1	NUM
ejpam-6052	83	44	0	0	NUM
ejpam-6052	83	45	1	1	NUM
ejpam-6052	83	46	1	1	NUM
ejpam-6052	83	47	2	2	NUM
ejpam-6052	83	48	2	2	NUM
ejpam-6052	83	49	1	1	NUM
ejpam-6052	83	50	0	0	NUM
ejpam-6052	83	51	1	1	NUM
ejpam-6052	83	52	3	3	NUM
ejpam-6052	83	53	3	3	NUM
ejpam-6052	83	54	1	1	NUM
ejpam-6052	83	55	1	1	NUM
ejpam-6052	83	56	0	0	NUM
ejpam-6052	83	57	◦	◦	NOUN
ejpam-6052	83	58	0	0	NUM
ejpam-6052	83	59	1	1	NUM
ejpam-6052	83	60	2	2	NUM
ejpam-6052	83	61	3	3	NUM
ejpam-6052	83	62	0	0	NUM
ejpam-6052	83	63	0	0	NUM
ejpam-6052	83	64	1	1	NUM
ejpam-6052	83	65	2	2	NUM
ejpam-6052	83	66	3	3	NUM
ejpam-6052	83	67	1	1	NUM
ejpam-6052	83	68	1	1	NUM
ejpam-6052	83	69	0	0	NUM
ejpam-6052	83	70	3	3	NUM
ejpam-6052	83	71	0	0	NUM
ejpam-6052	83	72	2	2	NUM
ejpam-6052	83	73	2	2	NUM
ejpam-6052	83	74	3	3	NUM
ejpam-6052	83	75	0	0	NUM
ejpam-6052	83	76	2	2	NUM
ejpam-6052	83	77	3	3	NUM
ejpam-6052	83	78	3	3	NUM
ejpam-6052	83	79	0	0	NUM
ejpam-6052	83	80	2	2	NUM
ejpam-6052	83	81	0	0	NUM
ejpam-6052	84	1	it	it	PRON
ejpam-6052	84	2	can	can	AUX
ejpam-6052	84	3	be	be	AUX
ejpam-6052	84	4	verified	verify	VERB
ejpam-6052	84	5	that	that	SCONJ
ejpam-6052	84	6	both	both	DET
ejpam-6052	84	7	(	(	PUNCT
ejpam-6052	84	8	x	x	NOUN
ejpam-6052	84	9	,	,	PUNCT
ejpam-6052	84	10	∗	∗	NOUN
ejpam-6052	84	11	,	,	PUNCT
ejpam-6052	84	12	0	0	NUM
ejpam-6052	84	13	)	)	PUNCT
ejpam-6052	84	14	and	and	CCONJ
ejpam-6052	84	15	(	(	PUNCT
ejpam-6052	84	16	x	x	X
ejpam-6052	84	17	,	,	PUNCT
ejpam-6052	84	18	◦	◦	NOUN
ejpam-6052	84	19	,	,	PUNCT
ejpam-6052	84	20	0	0	NUM
ejpam-6052	84	21	)	)	PUNCT
ejpam-6052	84	22	satisfy	satisfy	VERB
ejpam-6052	84	23	the	the	DET
ejpam-6052	84	24	axioms	axiom	NOUN
ejpam-6052	84	25	of	of	ADP
ejpam-6052	84	26	a	a	DET
ejpam-6052	84	27	bn	bn	NOUN
ejpam-6052	84	28	-algebra	-algebra	NOUN
ejpam-6052	84	29	.	.	PUNCT
ejpam-6052	85	1	it	it	PRON
ejpam-6052	85	2	can	can	AUX
ejpam-6052	85	3	also	also	ADV
ejpam-6052	85	4	be	be	AUX
ejpam-6052	85	5	verified	verify	VERB
ejpam-6052	85	6	that	that	SCONJ
ejpam-6052	85	7	(	(	PUNCT
ejpam-6052	85	8	x	x	X
ejpam-6052	85	9	,	,	PUNCT
ejpam-6052	85	10	∗	∗	NOUN
ejpam-6052	85	11	,	,	PUNCT
ejpam-6052	85	12	◦	◦	NOUN
ejpam-6052	85	13	,	,	PUNCT
ejpam-6052	85	14	0	0	NUM
ejpam-6052	85	15	)	)	PUNCT
ejpam-6052	85	16	is	be	AUX
ejpam-6052	85	17	a	a	DET
ejpam-6052	85	18	pseudo	pseudo	NOUN
ejpam-6052	85	19	bn	bn	NOUN
ejpam-6052	85	20	-algebra	-algebra	NOUN
ejpam-6052	85	21	.	.	PUNCT
ejpam-6052	86	1	observe	observe	VERB
ejpam-6052	86	2	that	that	SCONJ
ejpam-6052	86	3	if	if	SCONJ
ejpam-6052	86	4	(	(	PUNCT
ejpam-6052	86	5	x	x	NOUN
ejpam-6052	86	6	,	,	PUNCT
ejpam-6052	86	7	∗	∗	NOUN
ejpam-6052	86	8	,	,	PUNCT
ejpam-6052	86	9	0	0	NUM
ejpam-6052	86	10	)	)	PUNCT
ejpam-6052	86	11	is	be	AUX
ejpam-6052	86	12	a	a	DET
ejpam-6052	86	13	bn	bn	ADJ
ejpam-6052	86	14	-algebra	-algebra	NOUN
ejpam-6052	86	15	,	,	PUNCT
ejpam-6052	86	16	defining	define	VERB
ejpam-6052	86	17	x	x	X
ejpam-6052	86	18	∗	∗	NOUN
ejpam-6052	86	19	y	y	NOUN
ejpam-6052	86	20	=	=	PUNCT
ejpam-6052	86	21	x	x	PUNCT
ejpam-6052	86	22	◦	◦	NOUN
ejpam-6052	86	23	y	y	NOUN
ejpam-6052	86	24	yields	yield	VERB
ejpam-6052	86	25	a	a	DET
ejpam-6052	86	26	pseudo	pseudo	NOUN
ejpam-6052	86	27	bn	bn	NOUN
ejpam-6052	86	28	algebra	algebra	NOUN
ejpam-6052	86	29	(	(	PUNCT
ejpam-6052	86	30	x	x	X
ejpam-6052	86	31	,	,	PUNCT
ejpam-6052	86	32	∗	∗	NOUN
ejpam-6052	86	33	,	,	PUNCT
ejpam-6052	86	34	◦	◦	NOUN
ejpam-6052	86	35	,	,	PUNCT
ejpam-6052	86	36	0	0	NUM
ejpam-6052	86	37	)	)	PUNCT
ejpam-6052	86	38	.	.	PUNCT
ejpam-6052	87	1	thus	thus	ADV
ejpam-6052	87	2	,	,	PUNCT
ejpam-6052	87	3	every	every	DET
ejpam-6052	87	4	bn	bn	NOUN
ejpam-6052	87	5	-algebra	-algebra	NOUN
ejpam-6052	87	6	is	be	AUX
ejpam-6052	87	7	a	a	DET
ejpam-6052	87	8	special	special	ADJ
ejpam-6052	87	9	case	case	NOUN
ejpam-6052	87	10	of	of	ADP
ejpam-6052	87	11	a	a	DET
ejpam-6052	87	12	pseudo	pseudo	NOUN
ejpam-6052	87	13	bn	bn	NOUN
ejpam-6052	87	14	-algebra	-algebra	NOUN
ejpam-6052	87	15	where	where	SCONJ
ejpam-6052	87	16	◦	◦	NOUN
ejpam-6052	87	17	coincides	coincide	VERB
ejpam-6052	87	18	with	with	ADP
ejpam-6052	87	19	∗	∗	NOUN
ejpam-6052	87	20	,	,	PUNCT
ejpam-6052	87	21	inherently	inherently	ADV
ejpam-6052	87	22	satisfying	satisfy	VERB
ejpam-6052	87	23	its	its	PRON
ejpam-6052	87	24	structure	structure	NOUN
ejpam-6052	87	25	.	.	PUNCT
ejpam-6052	88	1	i.m	i.m	PROPN
ejpam-6052	88	2	.	.	PROPN
ejpam-6052	88	3	antabo	antabo	PROPN
ejpam-6052	88	4	et	et	PROPN
ejpam-6052	88	5	al	al	PROPN
ejpam-6052	88	6	.	.	PUNCT
ejpam-6052	88	7	/	/	SYM
ejpam-6052	88	8	eur	eur	PROPN
ejpam-6052	88	9	.	.	PUNCT
ejpam-6052	89	1	j.	j.	PROPN
ejpam-6052	89	2	pure	pure	PROPN
ejpam-6052	89	3	appl	appl	PROPN
ejpam-6052	89	4	.	.	PROPN
ejpam-6052	89	5	math	math	PROPN
ejpam-6052	89	6	,	,	PUNCT
ejpam-6052	89	7	18	18	NUM
ejpam-6052	89	8	(	(	PUNCT
ejpam-6052	89	9	2	2	NUM
ejpam-6052	89	10	)	)	PUNCT
ejpam-6052	89	11	(	(	PUNCT
ejpam-6052	89	12	2025	2025	NUM
ejpam-6052	89	13	)	)	PUNCT
ejpam-6052	89	14	,	,	PUNCT
ejpam-6052	89	15	6052	6052	NUM
ejpam-6052	89	16	5	5	NUM
ejpam-6052	89	17	of	of	ADP
ejpam-6052	89	18	14	14	NUM
ejpam-6052	89	19	example	example	NOUN
ejpam-6052	89	20	7	7	NUM
ejpam-6052	89	21	.	.	X
ejpam-6052	89	22	consider	consider	VERB
ejpam-6052	89	23	the	the	DET
ejpam-6052	89	24	set	set	NOUN
ejpam-6052	89	25	r	r	NOUN
ejpam-6052	89	26	of	of	ADP
ejpam-6052	89	27	real	real	ADJ
ejpam-6052	89	28	numbers	number	NOUN
ejpam-6052	89	29	,	,	PUNCT
ejpam-6052	89	30	and	and	CCONJ
ejpam-6052	89	31	define	define	VERB
ejpam-6052	89	32	the	the	DET
ejpam-6052	89	33	binary	binary	ADJ
ejpam-6052	89	34	operations	operation	NOUN
ejpam-6052	89	35	“	"	PUNCT
ejpam-6052	89	36	∗	∗	NOUN
ejpam-6052	89	37	”	"	PUNCT
ejpam-6052	89	38	and	and	CCONJ
ejpam-6052	89	39	“	"	PUNCT
ejpam-6052	89	40	◦	◦	NOUN
ejpam-6052	89	41	”	"	PUNCT
ejpam-6052	89	42	on	on	ADP
ejpam-6052	89	43	r	r	NOUN
ejpam-6052	89	44	as	as	SCONJ
ejpam-6052	89	45	follows	follow	VERB
ejpam-6052	89	46	:	:	PUNCT
ejpam-6052	89	47	x	x	SYM
ejpam-6052	89	48	∗	∗	NOUN
ejpam-6052	89	49	y	y	NOUN
ejpam-6052	89	50	=	=	SYM
ejpam-6052	89	51			PROPN
ejpam-6052	89	52	x	x	X
ejpam-6052	89	53	,	,	PUNCT
ejpam-6052	89	54	if	if	SCONJ
ejpam-6052	89	55	y	y	PROPN
ejpam-6052	89	56	=	=	SYM
ejpam-6052	89	57	0	0	PROPN
ejpam-6052	90	1	y	y	NOUN
ejpam-6052	90	2	,	,	PUNCT
ejpam-6052	90	3	if	if	SCONJ
ejpam-6052	90	4	x	x	ADP
ejpam-6052	90	5	=	=	SYM
ejpam-6052	90	6	0	0	NUM
ejpam-6052	90	7	0	0	NUM
ejpam-6052	90	8	,	,	PUNCT
ejpam-6052	90	9	otherwise	otherwise	ADV
ejpam-6052	90	10	x	x	VERB
ejpam-6052	90	11	◦	◦	NOUN
ejpam-6052	90	12	y	y	NOUN
ejpam-6052	90	13	=	=	PRON
ejpam-6052	90	14	{	{	PUNCT
ejpam-6052	90	15	x+	x+	PROPN
ejpam-6052	90	16	y	y	NOUN
ejpam-6052	90	17	,	,	PUNCT
ejpam-6052	90	18	if	if	SCONJ
ejpam-6052	90	19	x	x	PROPN
ejpam-6052	90	20	̸=	̸=	PROPN
ejpam-6052	90	21	y	y	PROPN
ejpam-6052	90	22	0	0	NUM
ejpam-6052	90	23	,	,	PUNCT
ejpam-6052	90	24	if	if	SCONJ
ejpam-6052	90	25	x	x	ADP
ejpam-6052	90	26	=	=	SYM
ejpam-6052	90	27	y	y	PROPN
ejpam-6052	90	28	then	then	ADV
ejpam-6052	90	29	it	it	PRON
ejpam-6052	90	30	can	can	AUX
ejpam-6052	90	31	be	be	AUX
ejpam-6052	90	32	shown	show	VERB
ejpam-6052	90	33	that	that	SCONJ
ejpam-6052	90	34	(	(	PUNCT
ejpam-6052	90	35	r	r	NOUN
ejpam-6052	90	36	,	,	PUNCT
ejpam-6052	90	37	∗	∗	NOUN
ejpam-6052	90	38	,	,	PUNCT
ejpam-6052	90	39	◦	◦	NOUN
ejpam-6052	90	40	,	,	PUNCT
ejpam-6052	90	41	0	0	NUM
ejpam-6052	90	42	)	)	PUNCT
ejpam-6052	90	43	is	be	AUX
ejpam-6052	90	44	a	a	DET
ejpam-6052	90	45	pseudo	pseudo	NOUN
ejpam-6052	90	46	bn	bn	NOUN
ejpam-6052	90	47	-algebra	-algebra	NOUN
ejpam-6052	90	48	.	.	PUNCT
ejpam-6052	91	1	the	the	DET
ejpam-6052	91	2	same	same	ADJ
ejpam-6052	91	3	holds	hold	VERB
ejpam-6052	91	4	for	for	ADP
ejpam-6052	91	5	when	when	SCONJ
ejpam-6052	91	6	r	r	NOUN
ejpam-6052	91	7	is	be	AUX
ejpam-6052	91	8	replaced	replace	VERB
ejpam-6052	91	9	by	by	ADP
ejpam-6052	91	10	z	z	PROPN
ejpam-6052	91	11	and	and	CCONJ
ejpam-6052	91	12	q.	q.	PROPN
ejpam-6052	91	13	remark	remark	NOUN
ejpam-6052	91	14	2	2	NUM
ejpam-6052	91	15	.	.	PUNCT
ejpam-6052	92	1	the	the	DET
ejpam-6052	92	2	zero	zero	NUM
ejpam-6052	92	3	element	element	NOUN
ejpam-6052	92	4	“	"	PUNCT
ejpam-6052	92	5	0	0	NUM
ejpam-6052	92	6	”	"	PUNCT
ejpam-6052	92	7	in	in	ADP
ejpam-6052	92	8	definition	definition	NOUN
ejpam-6052	92	9	3	3	NUM
ejpam-6052	92	10	is	be	AUX
ejpam-6052	92	11	unique	unique	ADJ
ejpam-6052	92	12	such	such	ADJ
ejpam-6052	92	13	that	that	SCONJ
ejpam-6052	92	14	it	it	PRON
ejpam-6052	92	15	is	be	AUX
ejpam-6052	92	16	the	the	DET
ejpam-6052	92	17	only	only	ADJ
ejpam-6052	92	18	element	element	NOUN
ejpam-6052	92	19	that	that	PRON
ejpam-6052	92	20	satisfies	satisfy	VERB
ejpam-6052	92	21	properties	property	NOUN
ejpam-6052	92	22	pbn1	pbn1	PROPN
ejpam-6052	92	23	,	,	PUNCT
ejpam-6052	92	24	pbn2	pbn2	NOUN
ejpam-6052	92	25	and	and	CCONJ
ejpam-6052	92	26	pbn3	pbn3	PROPN
ejpam-6052	92	27	.	.	PUNCT
ejpam-6052	93	1	remark	remark	PROPN
ejpam-6052	93	2	3	3	NUM
ejpam-6052	93	3	.	.	PUNCT
ejpam-6052	94	1	if	if	SCONJ
ejpam-6052	94	2	(	(	PUNCT
ejpam-6052	94	3	x	x	X
ejpam-6052	94	4	,	,	PUNCT
ejpam-6052	94	5	∗	∗	NOUN
ejpam-6052	94	6	,	,	PUNCT
ejpam-6052	94	7	0	0	NUM
ejpam-6052	94	8	)	)	PUNCT
ejpam-6052	94	9	and	and	CCONJ
ejpam-6052	94	10	(	(	PUNCT
ejpam-6052	94	11	x	x	X
ejpam-6052	94	12	,	,	PUNCT
ejpam-6052	94	13	◦	◦	NOUN
ejpam-6052	94	14	,	,	PUNCT
ejpam-6052	94	15	0	0	NUM
ejpam-6052	94	16	)	)	PUNCT
ejpam-6052	94	17	are	be	AUX
ejpam-6052	94	18	bn	bn	X
ejpam-6052	94	19	-algebras	-algebra	NOUN
ejpam-6052	94	20	,	,	PUNCT
ejpam-6052	94	21	then	then	ADV
ejpam-6052	94	22	(	(	PUNCT
ejpam-6052	94	23	x	x	X
ejpam-6052	94	24	,	,	PUNCT
ejpam-6052	94	25	∗	∗	NOUN
ejpam-6052	94	26	,	,	PUNCT
ejpam-6052	94	27	◦	◦	NOUN
ejpam-6052	94	28	,	,	PUNCT
ejpam-6052	94	29	0	0	NUM
ejpam-6052	94	30	)	)	PUNCT
ejpam-6052	94	31	is	be	AUX
ejpam-6052	94	32	not	not	PART
ejpam-6052	94	33	necessarily	necessarily	ADV
ejpam-6052	94	34	a	a	DET
ejpam-6052	94	35	pseudo	pseudo	NOUN
ejpam-6052	94	36	bn	bn	NOUN
ejpam-6052	94	37	-algebra	-algebra	NOUN
ejpam-6052	94	38	as	as	SCONJ
ejpam-6052	94	39	shown	show	VERB
ejpam-6052	94	40	in	in	ADP
ejpam-6052	94	41	the	the	DET
ejpam-6052	94	42	following	follow	VERB
ejpam-6052	94	43	example	example	NOUN
ejpam-6052	94	44	:	:	PUNCT
ejpam-6052	94	45	example	example	NOUN
ejpam-6052	94	46	8	8	NUM
ejpam-6052	94	47	.	.	PUNCT
ejpam-6052	94	48	define	define	VERB
ejpam-6052	94	49	the	the	DET
ejpam-6052	94	50	operations	operation	NOUN
ejpam-6052	94	51	“	"	PUNCT
ejpam-6052	94	52	∗	∗	NOUN
ejpam-6052	94	53	”	"	PUNCT
ejpam-6052	94	54	and	and	CCONJ
ejpam-6052	94	55	“	"	PUNCT
ejpam-6052	94	56	◦	◦	NOUN
ejpam-6052	94	57	”	"	PUNCT
ejpam-6052	94	58	on	on	ADP
ejpam-6052	94	59	x	x	X
ejpam-6052	94	60	=	=	SYM
ejpam-6052	94	61	{	{	PUNCT
ejpam-6052	94	62	0	0	NUM
ejpam-6052	94	63	,	,	PUNCT
ejpam-6052	94	64	1	1	NUM
ejpam-6052	94	65	,	,	PUNCT
ejpam-6052	94	66	2	2	NUM
ejpam-6052	94	67	}	}	PUNCT
ejpam-6052	94	68	,	,	PUNCT
ejpam-6052	94	69	by	by	ADP
ejpam-6052	94	70	the	the	DET
ejpam-6052	94	71	following	following	ADJ
ejpam-6052	94	72	cayley	cayley	ADJ
ejpam-6052	94	73	tables	table	NOUN
ejpam-6052	94	74	:	:	PUNCT
ejpam-6052	94	75	∗	∗	NOUN
ejpam-6052	94	76	0	0	NUM
ejpam-6052	94	77	1	1	NUM
ejpam-6052	94	78	2	2	NUM
ejpam-6052	94	79	0	0	NUM
ejpam-6052	94	80	0	0	NUM
ejpam-6052	94	81	1	1	NUM
ejpam-6052	94	82	2	2	NUM
ejpam-6052	94	83	1	1	NUM
ejpam-6052	94	84	1	1	NUM
ejpam-6052	94	85	0	0	NUM
ejpam-6052	94	86	1	1	NUM
ejpam-6052	94	87	2	2	NUM
ejpam-6052	94	88	2	2	NUM
ejpam-6052	94	89	1	1	NUM
ejpam-6052	94	90	0	0	NUM
ejpam-6052	94	91	◦	◦	NOUN
ejpam-6052	94	92	0	0	NUM
ejpam-6052	94	93	1	1	NUM
ejpam-6052	94	94	2	2	NUM
ejpam-6052	94	95	0	0	NUM
ejpam-6052	94	96	0	0	NUM
ejpam-6052	94	97	2	2	NUM
ejpam-6052	94	98	1	1	NUM
ejpam-6052	94	99	1	1	NUM
ejpam-6052	94	100	1	1	NUM
ejpam-6052	94	101	0	0	NUM
ejpam-6052	94	102	2	2	NUM
ejpam-6052	94	103	2	2	NUM
ejpam-6052	94	104	2	2	NUM
ejpam-6052	94	105	1	1	NUM
ejpam-6052	94	106	0	0	NUM
ejpam-6052	94	107	both	both	PRON
ejpam-6052	94	108	(	(	PUNCT
ejpam-6052	94	109	x	x	NOUN
ejpam-6052	94	110	,	,	PUNCT
ejpam-6052	94	111	∗	∗	NOUN
ejpam-6052	94	112	,	,	PUNCT
ejpam-6052	94	113	0	0	NUM
ejpam-6052	94	114	)	)	PUNCT
ejpam-6052	94	115	and	and	CCONJ
ejpam-6052	94	116	(	(	PUNCT
ejpam-6052	94	117	x	x	X
ejpam-6052	94	118	,	,	PUNCT
ejpam-6052	94	119	◦	◦	NOUN
ejpam-6052	94	120	,	,	PUNCT
ejpam-6052	94	121	0	0	NUM
ejpam-6052	94	122	)	)	PUNCT
ejpam-6052	94	123	are	be	AUX
ejpam-6052	94	124	bn	bn	X
ejpam-6052	94	125	-algebras	-algebra	NOUN
ejpam-6052	94	126	.	.	PUNCT
ejpam-6052	95	1	but	but	CCONJ
ejpam-6052	95	2	(	(	PUNCT
ejpam-6052	95	3	x	x	X
ejpam-6052	95	4	,	,	PUNCT
ejpam-6052	95	5	∗	∗	NOUN
ejpam-6052	95	6	,	,	PUNCT
ejpam-6052	95	7	◦	◦	NOUN
ejpam-6052	95	8	,	,	PUNCT
ejpam-6052	95	9	0	0	NUM
ejpam-6052	95	10	)	)	PUNCT
ejpam-6052	95	11	is	be	AUX
ejpam-6052	95	12	not	not	PART
ejpam-6052	95	13	a	a	DET
ejpam-6052	95	14	pseudo	pseudo	NOUN
ejpam-6052	95	15	bn	bn	NOUN
ejpam-6052	95	16	-algebra	-algebra	NOUN
ejpam-6052	95	17	since	since	SCONJ
ejpam-6052	95	18	(	(	PUNCT
ejpam-6052	95	19	0	0	NUM
ejpam-6052	95	20	∗	∗	NOUN
ejpam-6052	95	21	1	1	NUM
ejpam-6052	95	22	)	)	PUNCT
ejpam-6052	95	23	◦	◦	NOUN
ejpam-6052	95	24	2	2	NUM
ejpam-6052	95	25	=	=	SYM
ejpam-6052	95	26	2	2	NUM
ejpam-6052	95	27	̸=	̸=	PROPN
ejpam-6052	95	28	1	1	NUM
ejpam-6052	95	29	=	=	SYM
ejpam-6052	95	30	(	(	PUNCT
ejpam-6052	95	31	0	0	NUM
ejpam-6052	95	32	∗	∗	NOUN
ejpam-6052	95	33	2	2	NUM
ejpam-6052	95	34	)	)	PUNCT
ejpam-6052	95	35	◦	◦	NOUN
ejpam-6052	95	36	(	(	PUNCT
ejpam-6052	95	37	1	1	NUM
ejpam-6052	95	38	∗	∗	NOUN
ejpam-6052	95	39	0	0	NUM
ejpam-6052	95	40	)	)	PUNCT
ejpam-6052	95	41	.	.	PUNCT
ejpam-6052	96	1	theorem	theorem	NOUN
ejpam-6052	96	2	2	2	NUM
ejpam-6052	96	3	.	.	PUNCT
ejpam-6052	97	1	if	if	SCONJ
ejpam-6052	97	2	(	(	PUNCT
ejpam-6052	97	3	x	x	X
ejpam-6052	97	4	,	,	PUNCT
ejpam-6052	97	5	∗	∗	NOUN
ejpam-6052	97	6	,	,	PUNCT
ejpam-6052	97	7	◦	◦	NOUN
ejpam-6052	97	8	,	,	PUNCT
ejpam-6052	97	9	0	0	NUM
ejpam-6052	97	10	)	)	PUNCT
ejpam-6052	97	11	is	be	AUX
ejpam-6052	97	12	a	a	DET
ejpam-6052	97	13	pseudo	pseudo	NOUN
ejpam-6052	97	14	bn	bn	NOUN
ejpam-6052	97	15	-algebra	-algebra	NOUN
ejpam-6052	97	16	,	,	PUNCT
ejpam-6052	97	17	then	then	ADV
ejpam-6052	97	18	(	(	PUNCT
ejpam-6052	97	19	x	x	X
ejpam-6052	97	20	,	,	PUNCT
ejpam-6052	97	21	∗	∗	NOUN
ejpam-6052	97	22	,	,	PUNCT
ejpam-6052	97	23	◦	◦	NOUN
ejpam-6052	97	24	,	,	PUNCT
ejpam-6052	97	25	0	0	NUM
ejpam-6052	97	26	)	)	PUNCT
ejpam-6052	97	27	is	be	AUX
ejpam-6052	97	28	a	a	DET
ejpam-6052	97	29	pseudo	pseudo	NOUN
ejpam-6052	97	30	bf	bf	NOUN
ejpam-6052	97	31	algebra	algebra	NOUN
ejpam-6052	97	32	.	.	PUNCT
ejpam-6052	98	1	proof	proof	NOUN
ejpam-6052	98	2	.	.	PUNCT
ejpam-6052	99	1	if	if	SCONJ
ejpam-6052	99	2	we	we	PRON
ejpam-6052	99	3	let	let	VERB
ejpam-6052	99	4	z	z	NOUN
ejpam-6052	99	5	=	=	SYM
ejpam-6052	99	6	0	0	NUM
ejpam-6052	99	7	in	in	ADP
ejpam-6052	99	8	(	(	PUNCT
ejpam-6052	99	9	pbn3	pbn3	PROPN
ejpam-6052	99	10	)	)	PUNCT
ejpam-6052	99	11	,	,	PUNCT
ejpam-6052	99	12	we	we	PRON
ejpam-6052	99	13	obtain	obtain	VERB
ejpam-6052	99	14	x	x	PUNCT
ejpam-6052	99	15	∗	∗	NOUN
ejpam-6052	99	16	y	y	NOUN
ejpam-6052	99	17	=	=	SYM
ejpam-6052	99	18	(	(	PUNCT
ejpam-6052	99	19	x	x	X
ejpam-6052	99	20	∗	∗	PROPN
ejpam-6052	99	21	y	y	NOUN
ejpam-6052	99	22	)	)	PUNCT
ejpam-6052	99	23	◦	◦	NOUN
ejpam-6052	99	24	0	0	NUM
ejpam-6052	100	1	=	=	SYM
ejpam-6052	100	2	(	(	PUNCT
ejpam-6052	100	3	0	0	NUM
ejpam-6052	100	4	∗	∗	NOUN
ejpam-6052	100	5	0	0	NUM
ejpam-6052	100	6	)	)	PUNCT
ejpam-6052	100	7	◦	◦	NOUN
ejpam-6052	100	8	(	(	PUNCT
ejpam-6052	100	9	y	y	PROPN
ejpam-6052	100	10	∗	∗	NOUN
ejpam-6052	100	11	x	x	NOUN
ejpam-6052	100	12	)	)	PUNCT
ejpam-6052	100	13	=	=	SYM
ejpam-6052	100	14	0	0	NUM
ejpam-6052	100	15	◦	◦	NOUN
ejpam-6052	100	16	(	(	PUNCT
ejpam-6052	100	17	y	y	PROPN
ejpam-6052	100	18	∗	∗	NOUN
ejpam-6052	100	19	x	x	NOUN
ejpam-6052	100	20	)	)	PUNCT
ejpam-6052	100	21	and	and	CCONJ
ejpam-6052	100	22	x	x	PUNCT
ejpam-6052	100	23	◦	◦	NOUN
ejpam-6052	100	24	y	y	NOUN
ejpam-6052	100	25	=	=	SYM
ejpam-6052	100	26	(	(	PUNCT
ejpam-6052	100	27	x	x	SYM
ejpam-6052	100	28	◦	◦	VERB
ejpam-6052	100	29	y	y	NOUN
ejpam-6052	100	30	)	)	PUNCT
ejpam-6052	100	31	∗	∗	NOUN
ejpam-6052	100	32	0	0	NUM
ejpam-6052	101	1	=	=	SYM
ejpam-6052	101	2	(	(	PUNCT
ejpam-6052	101	3	0	0	NUM
ejpam-6052	101	4	◦	◦	NOUN
ejpam-6052	101	5	0	0	NUM
ejpam-6052	101	6	)	)	PUNCT
ejpam-6052	101	7	∗	∗	NOUN
ejpam-6052	101	8	(	(	PUNCT
ejpam-6052	101	9	y	y	PROPN
ejpam-6052	101	10	◦	◦	NOUN
ejpam-6052	101	11	x	x	X
ejpam-6052	101	12	)	)	PUNCT
ejpam-6052	101	13	=	=	SYM
ejpam-6052	101	14	0	0	NUM
ejpam-6052	101	15	∗	∗	NOUN
ejpam-6052	101	16	(	(	PUNCT
ejpam-6052	101	17	y	y	PROPN
ejpam-6052	101	18	◦	◦	NOUN
ejpam-6052	101	19	x	x	SYM
ejpam-6052	101	20	)	)	PUNCT
ejpam-6052	101	21	hence	hence	ADV
ejpam-6052	101	22	,	,	PUNCT
ejpam-6052	101	23	(	(	PUNCT
ejpam-6052	101	24	x	x	X
ejpam-6052	101	25	,	,	PUNCT
ejpam-6052	101	26	∗	∗	NOUN
ejpam-6052	101	27	,	,	PUNCT
ejpam-6052	101	28	◦	◦	NOUN
ejpam-6052	101	29	,	,	PUNCT
ejpam-6052	101	30	0	0	NUM
ejpam-6052	101	31	)	)	PUNCT
ejpam-6052	101	32	is	be	AUX
ejpam-6052	101	33	a	a	DET
ejpam-6052	101	34	pseudo	pseudo	NOUN
ejpam-6052	101	35	bf	bf	NOUN
ejpam-6052	101	36	-algebra	-algebra	PROPN
ejpam-6052	101	37	.	.	PUNCT
ejpam-6052	102	1	remark	remark	PROPN
ejpam-6052	102	2	4	4	NUM
ejpam-6052	102	3	.	.	PUNCT
ejpam-6052	103	1	the	the	DET
ejpam-6052	103	2	converse	converse	NOUN
ejpam-6052	103	3	of	of	ADP
ejpam-6052	103	4	theorem	theorem	NOUN
ejpam-6052	103	5	2	2	NUM
ejpam-6052	103	6	does	do	AUX
ejpam-6052	103	7	not	not	PART
ejpam-6052	103	8	hold	hold	VERB
ejpam-6052	103	9	in	in	ADP
ejpam-6052	103	10	general	general	ADJ
ejpam-6052	103	11	as	as	SCONJ
ejpam-6052	103	12	shown	show	VERB
ejpam-6052	103	13	in	in	ADP
ejpam-6052	103	14	the	the	DET
ejpam-6052	103	15	following	follow	VERB
ejpam-6052	103	16	example	example	NOUN
ejpam-6052	103	17	:	:	PUNCT
ejpam-6052	103	18	example	example	NOUN
ejpam-6052	103	19	9	9	NUM
ejpam-6052	103	20	.	.	X
ejpam-6052	103	21	consider	consider	VERB
ejpam-6052	103	22	the	the	DET
ejpam-6052	103	23	set	set	NOUN
ejpam-6052	103	24	r	r	NOUN
ejpam-6052	103	25	of	of	ADP
ejpam-6052	103	26	real	real	ADJ
ejpam-6052	103	27	numbers	number	NOUN
ejpam-6052	103	28	,	,	PUNCT
ejpam-6052	103	29	and	and	CCONJ
ejpam-6052	103	30	define	define	VERB
ejpam-6052	103	31	the	the	DET
ejpam-6052	103	32	binary	binary	ADJ
ejpam-6052	103	33	operations	operation	NOUN
ejpam-6052	103	34	“	"	PUNCT
ejpam-6052	103	35	∗	∗	NOUN
ejpam-6052	103	36	”	"	PUNCT
ejpam-6052	103	37	and	and	CCONJ
ejpam-6052	103	38	“	"	PUNCT
ejpam-6052	103	39	◦	◦	NOUN
ejpam-6052	103	40	”	"	PUNCT
ejpam-6052	103	41	on	on	ADP
ejpam-6052	103	42	r	r	NOUN
ejpam-6052	103	43	as	as	SCONJ
ejpam-6052	103	44	follows	follow	VERB
ejpam-6052	103	45	:	:	PUNCT
ejpam-6052	103	46	x	x	SYM
ejpam-6052	103	47	∗	∗	NOUN
ejpam-6052	103	48	y	y	NOUN
ejpam-6052	103	49	=	=	SYM
ejpam-6052	103	50			PROPN
ejpam-6052	103	51	x	x	X
ejpam-6052	103	52	,	,	PUNCT
ejpam-6052	103	53	if	if	SCONJ
ejpam-6052	103	54	y	y	PROPN
ejpam-6052	103	55	=	=	SYM
ejpam-6052	103	56	0	0	PROPN
ejpam-6052	104	1	y	y	NOUN
ejpam-6052	104	2	,	,	PUNCT
ejpam-6052	104	3	if	if	SCONJ
ejpam-6052	104	4	x	x	ADP
ejpam-6052	104	5	=	=	SYM
ejpam-6052	104	6	0	0	NUM
ejpam-6052	104	7	0	0	NUM
ejpam-6052	104	8	,	,	PUNCT
ejpam-6052	104	9	otherwise	otherwise	ADV
ejpam-6052	104	10	x	x	VERB
ejpam-6052	104	11	◦	◦	NOUN
ejpam-6052	104	12	y	y	NOUN
ejpam-6052	104	13	=	=	SYM
ejpam-6052	104	14			NOUN
ejpam-6052	104	15	x	x	X
ejpam-6052	104	16	,	,	PUNCT
ejpam-6052	104	17	if	if	SCONJ
ejpam-6052	104	18	y	y	PROPN
ejpam-6052	104	19	=	=	SYM
ejpam-6052	104	20	0	0	NUM
ejpam-6052	104	21	0	0	NUM
ejpam-6052	104	22	,	,	PUNCT
ejpam-6052	104	23	if	if	SCONJ
ejpam-6052	104	24	x	x	ADP
ejpam-6052	104	25	=	=	SYM
ejpam-6052	104	26	0	0	NUM
ejpam-6052	104	27	or	or	CCONJ
ejpam-6052	104	28	x	x	SYM
ejpam-6052	105	1	=	=	VERB
ejpam-6052	105	2	y	y	PROPN
ejpam-6052	105	3	y	y	PROPN
ejpam-6052	105	4	◦	◦	NOUN
ejpam-6052	105	5	x	x	PUNCT
ejpam-6052	105	6	otherwise	otherwise	ADV
ejpam-6052	105	7	then	then	ADV
ejpam-6052	105	8	(	(	PUNCT
ejpam-6052	105	9	r	r	NOUN
ejpam-6052	105	10	,	,	PUNCT
ejpam-6052	105	11	∗	∗	NOUN
ejpam-6052	105	12	,	,	PUNCT
ejpam-6052	105	13	◦	◦	NOUN
ejpam-6052	105	14	,	,	PUNCT
ejpam-6052	105	15	0	0	NUM
ejpam-6052	105	16	)	)	PUNCT
ejpam-6052	105	17	is	be	AUX
ejpam-6052	105	18	a	a	DET
ejpam-6052	105	19	pseudo	pseudo	NOUN
ejpam-6052	105	20	bf	bf	NOUN
ejpam-6052	105	21	-algebra	-algebra	NOUN
ejpam-6052	105	22	.	.	PUNCT
ejpam-6052	106	1	but	but	CCONJ
ejpam-6052	106	2	it	it	PRON
ejpam-6052	106	3	is	be	AUX
ejpam-6052	106	4	not	not	PART
ejpam-6052	106	5	a	a	DET
ejpam-6052	106	6	pseudo	pseudo	NOUN
ejpam-6052	106	7	bn	bn	NOUN
ejpam-6052	106	8	-algebra	-algebra	NOUN
ejpam-6052	106	9	since	since	SCONJ
ejpam-6052	106	10	if	if	SCONJ
ejpam-6052	106	11	we	we	PRON
ejpam-6052	106	12	let	let	VERB
ejpam-6052	106	13	x	x	PUNCT
ejpam-6052	106	14	=	=	PUNCT
ejpam-6052	106	15	y	y	PROPN
ejpam-6052	106	16	=	=	PUNCT
ejpam-6052	107	1	z	z	NOUN
ejpam-6052	107	2	we	we	PRON
ejpam-6052	107	3	have	have	VERB
ejpam-6052	107	4	(	(	PUNCT
ejpam-6052	107	5	x	x	SYM
ejpam-6052	107	6	∗	∗	PROPN
ejpam-6052	107	7	y	y	NOUN
ejpam-6052	107	8	)	)	PUNCT
ejpam-6052	107	9	◦	◦	NOUN
ejpam-6052	107	10	z	z	NOUN
ejpam-6052	107	11	=	=	SYM
ejpam-6052	107	12	0	0	NUM
ejpam-6052	108	1	◦	◦	NOUN
ejpam-6052	108	2	z	z	NOUN
ejpam-6052	108	3	=	=	SYM
ejpam-6052	108	4	0	0	PUNCT
ejpam-6052	109	1	̸=	̸=	PROPN
ejpam-6052	109	2	z	z	NOUN
ejpam-6052	109	3	=	=	SYM
ejpam-6052	109	4	z	z	NOUN
ejpam-6052	109	5	◦	◦	NOUN
ejpam-6052	109	6	0	0	NUM
ejpam-6052	110	1	=	=	SYM
ejpam-6052	110	2	(	(	PUNCT
ejpam-6052	110	3	0	0	NUM
ejpam-6052	110	4	∗	∗	PROPN
ejpam-6052	110	5	z	z	NOUN
ejpam-6052	110	6	)	)	PUNCT
ejpam-6052	110	7	◦	◦	NOUN
ejpam-6052	110	8	(	(	PUNCT
ejpam-6052	110	9	y	y	PROPN
ejpam-6052	110	10	∗	∗	NOUN
ejpam-6052	110	11	x	x	NOUN
ejpam-6052	110	12	)	)	PUNCT
ejpam-6052	110	13	.	.	PUNCT
ejpam-6052	111	1	i.m	i.m	PROPN
ejpam-6052	111	2	.	.	PROPN
ejpam-6052	111	3	antabo	antabo	PROPN
ejpam-6052	111	4	et	et	PROPN
ejpam-6052	111	5	al	al	PROPN
ejpam-6052	111	6	.	.	PUNCT
ejpam-6052	111	7	/	/	SYM
ejpam-6052	111	8	eur	eur	PROPN
ejpam-6052	111	9	.	.	PUNCT
ejpam-6052	112	1	j.	j.	PROPN
ejpam-6052	112	2	pure	pure	PROPN
ejpam-6052	112	3	appl	appl	PROPN
ejpam-6052	112	4	.	.	PROPN
ejpam-6052	112	5	math	math	PROPN
ejpam-6052	112	6	,	,	PUNCT
ejpam-6052	112	7	18	18	NUM
ejpam-6052	112	8	(	(	PUNCT
ejpam-6052	112	9	2	2	NUM
ejpam-6052	112	10	)	)	PUNCT
ejpam-6052	112	11	(	(	PUNCT
ejpam-6052	112	12	2025	2025	NUM
ejpam-6052	112	13	)	)	PUNCT
ejpam-6052	112	14	,	,	PUNCT
ejpam-6052	112	15	6052	6052	NUM
ejpam-6052	112	16	6	6	NUM
ejpam-6052	112	17	of	of	ADP
ejpam-6052	112	18	14	14	NUM
ejpam-6052	112	19	the	the	DET
ejpam-6052	112	20	following	follow	VERB
ejpam-6052	112	21	proposition	proposition	NOUN
ejpam-6052	112	22	gives	give	VERB
ejpam-6052	112	23	the	the	DET
ejpam-6052	112	24	routinary	routinary	ADJ
ejpam-6052	112	25	properties	property	NOUN
ejpam-6052	112	26	of	of	ADP
ejpam-6052	112	27	pseudo	pseudo	NOUN
ejpam-6052	112	28	bn	bn	NOUN
ejpam-6052	112	29	-algebras	-algebra	NOUN
ejpam-6052	112	30	.	.	PUNCT
ejpam-6052	113	1	proposition	proposition	NOUN
ejpam-6052	113	2	2	2	NUM
ejpam-6052	113	3	.	.	PUNCT
ejpam-6052	114	1	if	if	SCONJ
ejpam-6052	114	2	(	(	PUNCT
ejpam-6052	114	3	x	x	X
ejpam-6052	114	4	,	,	PUNCT
ejpam-6052	114	5	∗	∗	NOUN
ejpam-6052	114	6	,	,	PUNCT
ejpam-6052	114	7	◦	◦	NOUN
ejpam-6052	114	8	,	,	PUNCT
ejpam-6052	114	9	0	0	NUM
ejpam-6052	114	10	)	)	PUNCT
ejpam-6052	114	11	is	be	AUX
ejpam-6052	114	12	a	a	DET
ejpam-6052	114	13	pseudo	pseudo	NOUN
ejpam-6052	114	14	bn	bn	NOUN
ejpam-6052	114	15	-algebra	-algebra	NOUN
ejpam-6052	114	16	for	for	ADP
ejpam-6052	114	17	all	all	DET
ejpam-6052	114	18	x	x	NOUN
ejpam-6052	114	19	,	,	PUNCT
ejpam-6052	114	20	y	y	PROPN
ejpam-6052	114	21	,	,	PUNCT
ejpam-6052	114	22	z	z	NOUN
ejpam-6052	114	23	∈	∈	PROPN
ejpam-6052	114	24	x	x	X
ejpam-6052	114	25	then	then	ADV
ejpam-6052	114	26	(	(	PUNCT
ejpam-6052	114	27	i	i	NOUN
ejpam-6052	114	28	)	)	PUNCT
ejpam-6052	114	29	0	0	NUM
ejpam-6052	114	30	∗	∗	NOUN
ejpam-6052	114	31	(	(	PUNCT
ejpam-6052	114	32	0	0	NUM
ejpam-6052	114	33	∗	∗	NOUN
ejpam-6052	114	34	x	x	NOUN
ejpam-6052	114	35	)	)	PUNCT
ejpam-6052	115	1	=	=	SYM
ejpam-6052	115	2	x	x	PROPN
ejpam-6052	115	3	and	and	CCONJ
ejpam-6052	115	4	0	0	NUM
ejpam-6052	115	5	◦	◦	NOUN
ejpam-6052	115	6	(	(	PUNCT
ejpam-6052	115	7	0	0	NUM
ejpam-6052	115	8	◦	◦	NOUN
ejpam-6052	115	9	x	x	NOUN
ejpam-6052	115	10	)	)	PUNCT
ejpam-6052	115	11	=	=	SYM
ejpam-6052	116	1	x	x	X
ejpam-6052	116	2	,	,	PUNCT
ejpam-6052	116	3	(	(	PUNCT
ejpam-6052	116	4	ii	ii	NOUN
ejpam-6052	116	5	)	)	PUNCT
ejpam-6052	116	6	0	0	NUM
ejpam-6052	116	7	∗	∗	NOUN
ejpam-6052	116	8	(	(	PUNCT
ejpam-6052	116	9	0	0	NUM
ejpam-6052	116	10	◦	◦	NOUN
ejpam-6052	116	11	x	x	NOUN
ejpam-6052	116	12	)	)	PUNCT
ejpam-6052	116	13	=	=	SYM
ejpam-6052	117	1	x	x	PROPN
ejpam-6052	117	2	and	and	CCONJ
ejpam-6052	117	3	0	0	NUM
ejpam-6052	117	4	◦	◦	NOUN
ejpam-6052	117	5	(	(	PUNCT
ejpam-6052	117	6	0	0	NUM
ejpam-6052	117	7	∗	∗	NOUN
ejpam-6052	117	8	x	x	NOUN
ejpam-6052	117	9	)	)	PUNCT
ejpam-6052	118	1	=	=	SYM
ejpam-6052	118	2	x	x	X
ejpam-6052	118	3	,	,	PUNCT
ejpam-6052	118	4	(	(	PUNCT
ejpam-6052	118	5	iii	iii	X
ejpam-6052	118	6	)	)	PUNCT
ejpam-6052	118	7	y	y	NOUN
ejpam-6052	118	8	∗	∗	NOUN
ejpam-6052	118	9	x	x	PUNCT
ejpam-6052	118	10	=	=	SYM
ejpam-6052	118	11	(	(	PUNCT
ejpam-6052	118	12	0	0	NUM
ejpam-6052	118	13	◦	◦	NOUN
ejpam-6052	118	14	x	x	SYM
ejpam-6052	118	15	)	)	PUNCT
ejpam-6052	118	16	∗	∗	NOUN
ejpam-6052	118	17	(	(	PUNCT
ejpam-6052	118	18	0	0	NUM
ejpam-6052	118	19	◦	◦	NOUN
ejpam-6052	118	20	y	y	PROPN
ejpam-6052	118	21	)	)	PUNCT
ejpam-6052	118	22	and	and	CCONJ
ejpam-6052	118	23	y	y	PROPN
ejpam-6052	118	24	◦	◦	NOUN
ejpam-6052	118	25	x	x	X
ejpam-6052	118	26	=	=	SYM
ejpam-6052	118	27	(	(	PUNCT
ejpam-6052	118	28	0	0	NUM
ejpam-6052	118	29	∗	∗	NOUN
ejpam-6052	118	30	x	x	NOUN
ejpam-6052	118	31	)	)	PUNCT
ejpam-6052	118	32	◦	◦	NOUN
ejpam-6052	118	33	(	(	PUNCT
ejpam-6052	118	34	0	0	NUM
ejpam-6052	118	35	∗	∗	PROPN
ejpam-6052	118	36	y	y	PROPN
ejpam-6052	118	37	)	)	PUNCT
ejpam-6052	118	38	,	,	PUNCT
ejpam-6052	118	39	(	(	PUNCT
ejpam-6052	118	40	iv	iv	X
ejpam-6052	118	41	)	)	PUNCT
ejpam-6052	118	42	(	(	PUNCT
ejpam-6052	118	43	0	0	NUM
ejpam-6052	118	44	∗	∗	NOUN
ejpam-6052	118	45	x	x	NOUN
ejpam-6052	118	46	)	)	PUNCT
ejpam-6052	118	47	◦	◦	NOUN
ejpam-6052	118	48	y	y	NOUN
ejpam-6052	118	49	=	=	SYM
ejpam-6052	118	50	(	(	PUNCT
ejpam-6052	118	51	0	0	NUM
ejpam-6052	118	52	∗	∗	PROPN
ejpam-6052	118	53	y	y	NOUN
ejpam-6052	118	54	)	)	PUNCT
ejpam-6052	118	55	◦	◦	NOUN
ejpam-6052	118	56	x	x	SYM
ejpam-6052	118	57	and	and	CCONJ
ejpam-6052	118	58	(	(	PUNCT
ejpam-6052	118	59	0	0	NUM
ejpam-6052	118	60	◦	◦	NOUN
ejpam-6052	118	61	x	x	SYM
ejpam-6052	118	62	)	)	PUNCT
ejpam-6052	118	63	∗	∗	NOUN
ejpam-6052	118	64	y	y	NOUN
ejpam-6052	118	65	=	=	SYM
ejpam-6052	118	66	(	(	PUNCT
ejpam-6052	118	67	0	0	NUM
ejpam-6052	118	68	◦	◦	NOUN
ejpam-6052	118	69	y	y	NOUN
ejpam-6052	118	70	)	)	PUNCT
ejpam-6052	118	71	∗	∗	NOUN
ejpam-6052	118	72	x	x	SYM
ejpam-6052	118	73	,	,	PUNCT
ejpam-6052	118	74	(	(	PUNCT
ejpam-6052	118	75	v	v	NOUN
ejpam-6052	118	76	)	)	PUNCT
ejpam-6052	118	77	0	0	NUM
ejpam-6052	118	78	∗	∗	NOUN
ejpam-6052	118	79	x	x	X
ejpam-6052	118	80	=	=	SYM
ejpam-6052	118	81	0	0	NUM
ejpam-6052	118	82	◦	◦	NOUN
ejpam-6052	118	83	y	y	NOUN
ejpam-6052	118	84	=	=	NOUN
ejpam-6052	118	85	⇒	⇒	VERB
ejpam-6052	118	86	x	x	PUNCT
ejpam-6052	118	87	=	=	SYM
ejpam-6052	118	88	y	y	PROPN
ejpam-6052	118	89	,	,	PUNCT
ejpam-6052	118	90	(	(	PUNCT
ejpam-6052	118	91	vi	vi	NOUN
ejpam-6052	118	92	)	)	PUNCT
ejpam-6052	118	93	x	x	X
ejpam-6052	118	94	∗	∗	NOUN
ejpam-6052	118	95	y	y	NOUN
ejpam-6052	118	96	=	=	SYM
ejpam-6052	118	97	0	0	NUM
ejpam-6052	118	98	implies	imply	VERB
ejpam-6052	118	99	y	y	PROPN
ejpam-6052	118	100	∗	∗	NOUN
ejpam-6052	118	101	x	x	PUNCT
ejpam-6052	119	1	=	=	SYM
ejpam-6052	119	2	0	0	NUM
ejpam-6052	119	3	and	and	CCONJ
ejpam-6052	119	4	x	x	PART
ejpam-6052	119	5	◦	◦	NOUN
ejpam-6052	119	6	y	y	NOUN
ejpam-6052	119	7	=	=	SYM
ejpam-6052	119	8	0	0	NUM
ejpam-6052	119	9	implies	imply	VERB
ejpam-6052	119	10	y	y	PROPN
ejpam-6052	119	11	◦	◦	VERB
ejpam-6052	119	12	x	x	X
ejpam-6052	120	1	=	=	SYM
ejpam-6052	120	2	0	0	NUM
ejpam-6052	120	3	,	,	PUNCT
ejpam-6052	120	4	(	(	PUNCT
ejpam-6052	120	5	vii	vii	PROPN
ejpam-6052	120	6	)	)	PUNCT
ejpam-6052	120	7	(	(	PUNCT
ejpam-6052	120	8	x	x	SYM
ejpam-6052	120	9	∗	∗	PROPN
ejpam-6052	120	10	z	z	NOUN
ejpam-6052	120	11	)	)	PUNCT
ejpam-6052	120	12	◦	◦	NOUN
ejpam-6052	120	13	(	(	PUNCT
ejpam-6052	120	14	y	y	PROPN
ejpam-6052	120	15	∗	∗	PROPN
ejpam-6052	120	16	z	z	NOUN
ejpam-6052	120	17	)	)	PUNCT
ejpam-6052	121	1	=	=	PUNCT
ejpam-6052	121	2	(	(	PUNCT
ejpam-6052	121	3	z	z	NOUN
ejpam-6052	121	4	∗	∗	PROPN
ejpam-6052	121	5	y	y	PROPN
ejpam-6052	121	6	)	)	PUNCT
ejpam-6052	121	7	◦	◦	NOUN
ejpam-6052	121	8	(	(	PUNCT
ejpam-6052	121	9	z	z	NOUN
ejpam-6052	121	10	∗	∗	NOUN
ejpam-6052	121	11	x	x	NOUN
ejpam-6052	121	12	)	)	PUNCT
ejpam-6052	121	13	and	and	CCONJ
ejpam-6052	121	14	(	(	PUNCT
ejpam-6052	121	15	x	x	PART
ejpam-6052	121	16	◦	◦	NOUN
ejpam-6052	121	17	z	z	NOUN
ejpam-6052	121	18	)	)	PUNCT
ejpam-6052	121	19	∗	∗	NOUN
ejpam-6052	121	20	(	(	PUNCT
ejpam-6052	121	21	y	y	PROPN
ejpam-6052	121	22	◦	◦	PROPN
ejpam-6052	121	23	z	z	PROPN
ejpam-6052	121	24	)	)	PUNCT
ejpam-6052	121	25	=	=	PUNCT
ejpam-6052	122	1	(	(	PUNCT
ejpam-6052	122	2	z	z	NOUN
ejpam-6052	122	3	◦	◦	NOUN
ejpam-6052	122	4	y	y	NOUN
ejpam-6052	122	5	)	)	PUNCT
ejpam-6052	122	6	∗	∗	NOUN
ejpam-6052	122	7	(	(	PUNCT
ejpam-6052	122	8	z	z	NOUN
ejpam-6052	122	9	◦	◦	NOUN
ejpam-6052	122	10	x	x	NOUN
ejpam-6052	122	11	)	)	PUNCT
ejpam-6052	122	12	.	.	PUNCT
ejpam-6052	123	1	proof	proof	NOUN
ejpam-6052	123	2	.	.	PUNCT
ejpam-6052	124	1	(	(	PUNCT
ejpam-6052	124	2	i	i	NOUN
ejpam-6052	124	3	)	)	PUNCT
ejpam-6052	124	4	for	for	ADP
ejpam-6052	124	5	any	any	DET
ejpam-6052	124	6	x	x	SYM
ejpam-6052	124	7	∈	∈	PROPN
ejpam-6052	124	8	x	x	NOUN
ejpam-6052	124	9	,	,	PUNCT
ejpam-6052	124	10	applying	apply	VERB
ejpam-6052	124	11	(	(	PUNCT
ejpam-6052	124	12	pbn2	pbn2	NOUN
ejpam-6052	124	13	)	)	PUNCT
ejpam-6052	124	14	and	and	CCONJ
ejpam-6052	124	15	theorem	theorem	VERB
ejpam-6052	124	16	2	2	NUM
ejpam-6052	124	17	,	,	PUNCT
ejpam-6052	124	18	we	we	PRON
ejpam-6052	124	19	get	get	VERB
ejpam-6052	124	20	0	0	NUM
ejpam-6052	124	21	∗	∗	NOUN
ejpam-6052	124	22	(	(	PUNCT
ejpam-6052	124	23	0	0	NUM
ejpam-6052	124	24	∗	∗	NOUN
ejpam-6052	124	25	x	x	NOUN
ejpam-6052	124	26	)	)	PUNCT
ejpam-6052	124	27	=	=	SYM
ejpam-6052	124	28	0	0	NUM
ejpam-6052	124	29	∗	∗	NOUN
ejpam-6052	124	30	[	[	X
ejpam-6052	124	31	0	0	NUM
ejpam-6052	124	32	◦	◦	NOUN
ejpam-6052	124	33	(	(	PUNCT
ejpam-6052	124	34	x	x	X
ejpam-6052	124	35	∗	∗	NOUN
ejpam-6052	124	36	0	0	NUM
ejpam-6052	124	37	)	)	PUNCT
ejpam-6052	124	38	]	]	PUNCT
ejpam-6052	125	1	=	=	SYM
ejpam-6052	125	2	0	0	NUM
ejpam-6052	125	3	∗	∗	NOUN
ejpam-6052	125	4	(	(	PUNCT
ejpam-6052	125	5	0	0	NUM
ejpam-6052	125	6	◦	◦	NOUN
ejpam-6052	125	7	x	x	NOUN
ejpam-6052	125	8	)	)	PUNCT
ejpam-6052	125	9	=	=	SYM
ejpam-6052	125	10	x	x	PUNCT
ejpam-6052	125	11	◦	◦	NOUN
ejpam-6052	125	12	0	0	NUM
ejpam-6052	126	1	=	=	SYM
ejpam-6052	126	2	x	x	X
ejpam-6052	126	3	and	and	CCONJ
ejpam-6052	126	4	similarly	similarly	ADV
ejpam-6052	126	5	,	,	PUNCT
ejpam-6052	126	6	0	0	NUM
ejpam-6052	126	7	◦	◦	NOUN
ejpam-6052	126	8	(	(	PUNCT
ejpam-6052	126	9	0	0	NUM
ejpam-6052	126	10	◦	◦	NOUN
ejpam-6052	126	11	x	x	NOUN
ejpam-6052	126	12	)	)	PUNCT
ejpam-6052	126	13	=	=	SYM
ejpam-6052	126	14	0	0	PUNCT
ejpam-6052	127	1	◦	◦	NOUN
ejpam-6052	127	2	[	[	X
ejpam-6052	127	3	0	0	NUM
ejpam-6052	127	4	∗	∗	NOUN
ejpam-6052	127	5	(	(	PUNCT
ejpam-6052	127	6	x	x	SYM
ejpam-6052	127	7	◦	◦	NOUN
ejpam-6052	127	8	0	0	NUM
ejpam-6052	127	9	)	)	PUNCT
ejpam-6052	127	10	]	]	PUNCT
ejpam-6052	128	1	=	=	SYM
ejpam-6052	128	2	0	0	NUM
ejpam-6052	128	3	◦	◦	NOUN
ejpam-6052	128	4	(	(	PUNCT
ejpam-6052	128	5	0	0	NUM
ejpam-6052	128	6	∗	∗	NOUN
ejpam-6052	128	7	x	x	NOUN
ejpam-6052	128	8	)	)	PUNCT
ejpam-6052	128	9	=	=	PUNCT
ejpam-6052	129	1	x	x	X
ejpam-6052	129	2	∗	∗	NOUN
ejpam-6052	129	3	0	0	NUM
ejpam-6052	130	1	=	=	SYM
ejpam-6052	130	2	x.	x.	NOUN
ejpam-6052	130	3	(	(	PUNCT
ejpam-6052	130	4	ii	ii	NOUN
ejpam-6052	130	5	)	)	PUNCT
ejpam-6052	130	6	setting	set	VERB
ejpam-6052	130	7	y	y	PROPN
ejpam-6052	130	8	=	=	PUNCT
ejpam-6052	130	9	0	0	PROPN
ejpam-6052	130	10	and	and	CCONJ
ejpam-6052	130	11	z	z	NOUN
ejpam-6052	130	12	=	=	SYM
ejpam-6052	130	13	0	0	NUM
ejpam-6052	130	14	in	in	ADP
ejpam-6052	130	15	(	(	PUNCT
ejpam-6052	130	16	pbn3	pbn3	PROPN
ejpam-6052	130	17	)	)	PUNCT
ejpam-6052	130	18	,	,	PUNCT
ejpam-6052	130	19	we	we	PRON
ejpam-6052	130	20	obtain	obtain	VERB
ejpam-6052	130	21	(	(	PUNCT
ejpam-6052	130	22	x	x	NOUN
ejpam-6052	130	23	∗	∗	NOUN
ejpam-6052	130	24	0	0	NUM
ejpam-6052	130	25	)	)	PUNCT
ejpam-6052	130	26	◦	◦	NOUN
ejpam-6052	130	27	0	0	NUM
ejpam-6052	131	1	=	=	SYM
ejpam-6052	131	2	(	(	PUNCT
ejpam-6052	131	3	0	0	NUM
ejpam-6052	131	4	∗	∗	NOUN
ejpam-6052	131	5	0	0	NUM
ejpam-6052	131	6	)	)	PUNCT
ejpam-6052	131	7	◦	◦	NOUN
ejpam-6052	131	8	(	(	PUNCT
ejpam-6052	131	9	x	x	X
ejpam-6052	131	10	∗	∗	NOUN
ejpam-6052	131	11	0	0	NUM
ejpam-6052	131	12	)	)	PUNCT
ejpam-6052	131	13	.	.	PUNCT
ejpam-6052	132	1	using	use	VERB
ejpam-6052	132	2	(	(	PUNCT
ejpam-6052	132	3	pbn1	pbn1	NOUN
ejpam-6052	132	4	)	)	PUNCT
ejpam-6052	132	5	and	and	CCONJ
ejpam-6052	132	6	(	(	PUNCT
ejpam-6052	132	7	pbn2	pbn2	PROPN
ejpam-6052	132	8	)	)	PUNCT
ejpam-6052	132	9	,	,	PUNCT
ejpam-6052	132	10	we	we	PRON
ejpam-6052	132	11	conclude	conclude	VERB
ejpam-6052	132	12	x	x	PUNCT
ejpam-6052	132	13	=	=	SYM
ejpam-6052	132	14	0	0	NUM
ejpam-6052	132	15	◦	◦	NOUN
ejpam-6052	132	16	(	(	PUNCT
ejpam-6052	132	17	0	0	NUM
ejpam-6052	132	18	∗	∗	NOUN
ejpam-6052	132	19	x	x	NOUN
ejpam-6052	132	20	)	)	PUNCT
ejpam-6052	132	21	.	.	PUNCT
ejpam-6052	133	1	by	by	ADP
ejpam-6052	133	2	a	a	DET
ejpam-6052	133	3	similar	similar	ADJ
ejpam-6052	133	4	argument	argument	NOUN
ejpam-6052	133	5	,	,	PUNCT
ejpam-6052	133	6	x	x	X
ejpam-6052	133	7	=	=	PUNCT
ejpam-6052	133	8	x	x	SYM
ejpam-6052	133	9	∗	∗	NOUN
ejpam-6052	133	10	0	0	NUM
ejpam-6052	134	1	=	=	SYM
ejpam-6052	134	2	(	(	PUNCT
ejpam-6052	134	3	x	x	PART
ejpam-6052	134	4	◦	◦	NOUN
ejpam-6052	134	5	0	0	NUM
ejpam-6052	134	6	)	)	PUNCT
ejpam-6052	134	7	∗	∗	NOUN
ejpam-6052	134	8	0	0	NUM
ejpam-6052	134	9	=	=	SYM
ejpam-6052	134	10	0	0	NUM
ejpam-6052	134	11	∗	∗	NOUN
ejpam-6052	134	12	(	(	PUNCT
ejpam-6052	134	13	0	0	NUM
ejpam-6052	134	14	◦	◦	NOUN
ejpam-6052	134	15	x	x	NOUN
ejpam-6052	134	16	)	)	PUNCT
ejpam-6052	134	17	.	.	PUNCT
ejpam-6052	135	1	(	(	PUNCT
ejpam-6052	135	2	iii	iii	X
ejpam-6052	135	3	)	)	PUNCT
ejpam-6052	135	4	applying	apply	VERB
ejpam-6052	135	5	(	(	PUNCT
ejpam-6052	135	6	pbn3	pbn3	PROPN
ejpam-6052	135	7	)	)	PUNCT
ejpam-6052	135	8	and	and	CCONJ
ejpam-6052	135	9	(	(	PUNCT
ejpam-6052	135	10	pbn2	pbn2	PROPN
ejpam-6052	135	11	)	)	PUNCT
ejpam-6052	135	12	,	,	PUNCT
ejpam-6052	135	13	we	we	PRON
ejpam-6052	135	14	derive	derive	VERB
ejpam-6052	135	15	y	y	PROPN
ejpam-6052	135	16	∗	∗	NOUN
ejpam-6052	135	17	x	x	PUNCT
ejpam-6052	135	18	=	=	SYM
ejpam-6052	135	19	(	(	PUNCT
ejpam-6052	135	20	0	0	NUM
ejpam-6052	135	21	◦	◦	NOUN
ejpam-6052	135	22	x	x	SYM
ejpam-6052	135	23	)	)	PUNCT
ejpam-6052	135	24	∗	∗	NOUN
ejpam-6052	135	25	(	(	PUNCT
ejpam-6052	135	26	0	0	NUM
ejpam-6052	135	27	◦	◦	NOUN
ejpam-6052	135	28	y	y	PROPN
ejpam-6052	135	29	)	)	PUNCT
ejpam-6052	135	30	,	,	PUNCT
ejpam-6052	135	31	y	y	PROPN
ejpam-6052	135	32	◦	◦	NOUN
ejpam-6052	135	33	x	x	X
ejpam-6052	135	34	=	=	SYM
ejpam-6052	135	35	(	(	PUNCT
ejpam-6052	135	36	0	0	NUM
ejpam-6052	135	37	∗	∗	NOUN
ejpam-6052	135	38	x	x	NOUN
ejpam-6052	135	39	)	)	PUNCT
ejpam-6052	135	40	◦	◦	NOUN
ejpam-6052	135	41	(	(	PUNCT
ejpam-6052	135	42	0	0	NUM
ejpam-6052	135	43	∗	∗	PROPN
ejpam-6052	135	44	y	y	PROPN
ejpam-6052	135	45	)	)	PUNCT
ejpam-6052	135	46	.	.	PUNCT
ejpam-6052	136	1	(	(	PUNCT
ejpam-6052	136	2	iv	iv	X
ejpam-6052	136	3	)	)	PUNCT
ejpam-6052	136	4	from	from	ADP
ejpam-6052	136	5	(	(	PUNCT
ejpam-6052	136	6	pbn3	pbn3	PROPN
ejpam-6052	136	7	)	)	PUNCT
ejpam-6052	136	8	and	and	CCONJ
ejpam-6052	136	9	(	(	PUNCT
ejpam-6052	136	10	pbn2	pbn2	PROPN
ejpam-6052	136	11	)	)	PUNCT
ejpam-6052	136	12	,	,	PUNCT
ejpam-6052	136	13	we	we	PRON
ejpam-6052	136	14	get	get	VERB
ejpam-6052	136	15	(	(	PUNCT
ejpam-6052	136	16	0	0	NUM
ejpam-6052	136	17	∗	∗	NOUN
ejpam-6052	136	18	x	x	NOUN
ejpam-6052	136	19	)	)	PUNCT
ejpam-6052	137	1	◦	◦	NOUN
ejpam-6052	137	2	y	y	NOUN
ejpam-6052	137	3	=	=	SYM
ejpam-6052	137	4	(	(	PUNCT
ejpam-6052	137	5	0	0	NUM
ejpam-6052	137	6	∗	∗	PROPN
ejpam-6052	137	7	y	y	NOUN
ejpam-6052	137	8	)	)	PUNCT
ejpam-6052	138	1	◦	◦	NOUN
ejpam-6052	138	2	x.	x.	NOUN
ejpam-6052	138	3	(	(	PUNCT
ejpam-6052	138	4	v	v	NOUN
ejpam-6052	138	5	)	)	PUNCT
ejpam-6052	138	6	if	if	SCONJ
ejpam-6052	138	7	x	x	PROPN
ejpam-6052	138	8	∗	∗	NOUN
ejpam-6052	138	9	0	0	NUM
ejpam-6052	139	1	=	=	SYM
ejpam-6052	139	2	y	y	PROPN
ejpam-6052	139	3	◦	◦	NOUN
ejpam-6052	139	4	0	0	NUM
ejpam-6052	139	5	,	,	PUNCT
ejpam-6052	139	6	then	then	ADV
ejpam-6052	139	7	by	by	ADP
ejpam-6052	139	8	proposition	proposition	NOUN
ejpam-6052	139	9	2(i	2(i	NUM
ejpam-6052	139	10	)	)	PUNCT
ejpam-6052	139	11	,	,	PUNCT
ejpam-6052	139	12	x	x	PUNCT
ejpam-6052	139	13	=	=	SYM
ejpam-6052	139	14	0	0	NUM
ejpam-6052	139	15	∗	∗	NOUN
ejpam-6052	139	16	(	(	PUNCT
ejpam-6052	139	17	0	0	NUM
ejpam-6052	139	18	∗	∗	NOUN
ejpam-6052	139	19	x	x	NOUN
ejpam-6052	139	20	)	)	PUNCT
ejpam-6052	139	21	=	=	SYM
ejpam-6052	139	22	0	0	NUM
ejpam-6052	139	23	∗	∗	NOUN
ejpam-6052	139	24	(	(	PUNCT
ejpam-6052	139	25	0	0	NUM
ejpam-6052	139	26	◦	◦	NOUN
ejpam-6052	139	27	y	y	NOUN
ejpam-6052	139	28	)	)	PUNCT
ejpam-6052	140	1	=	=	PUNCT
ejpam-6052	140	2	y.	y.	PROPN
ejpam-6052	140	3	i.m	i.m	PROPN
ejpam-6052	140	4	.	.	PUNCT
ejpam-6052	141	1	antabo	antabo	PROPN
ejpam-6052	141	2	et	et	PROPN
ejpam-6052	141	3	al	al	PROPN
ejpam-6052	141	4	.	.	PUNCT
ejpam-6052	141	5	/	/	SYM
ejpam-6052	141	6	eur	eur	PROPN
ejpam-6052	141	7	.	.	PUNCT
ejpam-6052	142	1	j.	j.	PROPN
ejpam-6052	142	2	pure	pure	PROPN
ejpam-6052	142	3	appl	appl	PROPN
ejpam-6052	142	4	.	.	PROPN
ejpam-6052	142	5	math	math	PROPN
ejpam-6052	142	6	,	,	PUNCT
ejpam-6052	142	7	18	18	NUM
ejpam-6052	142	8	(	(	PUNCT
ejpam-6052	142	9	2	2	NUM
ejpam-6052	142	10	)	)	PUNCT
ejpam-6052	142	11	(	(	PUNCT
ejpam-6052	142	12	2025	2025	NUM
ejpam-6052	142	13	)	)	PUNCT
ejpam-6052	142	14	,	,	PUNCT
ejpam-6052	142	15	6052	6052	NUM
ejpam-6052	142	16	7	7	NUM
ejpam-6052	142	17	of	of	ADP
ejpam-6052	142	18	14	14	NUM
ejpam-6052	142	19	(	(	PUNCT
ejpam-6052	142	20	vi	vi	NOUN
ejpam-6052	142	21	)	)	PUNCT
ejpam-6052	142	22	suppose	suppose	VERB
ejpam-6052	142	23	x	x	X
ejpam-6052	142	24	∗	∗	NOUN
ejpam-6052	142	25	y	y	NOUN
ejpam-6052	143	1	=	=	SYM
ejpam-6052	143	2	0	0	PROPN
ejpam-6052	143	3	.	.	PUNCT
ejpam-6052	144	1	then	then	ADV
ejpam-6052	144	2	by	by	ADP
ejpam-6052	144	3	(	(	PUNCT
ejpam-6052	144	4	pbn2	pbn2	PROPN
ejpam-6052	144	5	)	)	PUNCT
ejpam-6052	144	6	and	and	CCONJ
ejpam-6052	144	7	theorem	theorem	VERB
ejpam-6052	144	8	2	2	NUM
ejpam-6052	144	9	,	,	PUNCT
ejpam-6052	144	10	0	0	NUM
ejpam-6052	144	11	=	=	SYM
ejpam-6052	144	12	0	0	NUM
ejpam-6052	144	13	◦	◦	NOUN
ejpam-6052	144	14	0	0	NUM
ejpam-6052	144	15	=	=	SYM
ejpam-6052	144	16	0	0	NUM
ejpam-6052	144	17	◦	◦	NOUN
ejpam-6052	144	18	(	(	PUNCT
ejpam-6052	144	19	x	x	X
ejpam-6052	144	20	∗	∗	NUM
ejpam-6052	144	21	y	y	NOUN
ejpam-6052	144	22	)	)	PUNCT
ejpam-6052	144	23	=	=	SYM
ejpam-6052	144	24	y	y	PROPN
ejpam-6052	144	25	∗	∗	NOUN
ejpam-6052	144	26	x.	x.	NOUN
ejpam-6052	145	1	hence	hence	ADV
ejpam-6052	145	2	,	,	PUNCT
ejpam-6052	145	3	y	y	PROPN
ejpam-6052	145	4	∗	∗	NOUN
ejpam-6052	145	5	x	x	PUNCT
ejpam-6052	146	1	=	=	SYM
ejpam-6052	146	2	0	0	X
ejpam-6052	146	3	.	.	PUNCT
ejpam-6052	147	1	similarly	similarly	ADV
ejpam-6052	147	2	,	,	PUNCT
ejpam-6052	147	3	if	if	SCONJ
ejpam-6052	147	4	x	x	PART
ejpam-6052	147	5	◦	◦	VERB
ejpam-6052	147	6	y	y	NOUN
ejpam-6052	147	7	=	=	PUNCT
ejpam-6052	147	8	0	0	PUNCT
ejpam-6052	148	1	then	then	ADV
ejpam-6052	148	2	y	y	PROPN
ejpam-6052	148	3	◦	◦	NOUN
ejpam-6052	148	4	x	x	X
ejpam-6052	149	1	=	=	NOUN
ejpam-6052	149	2	0	0	X
ejpam-6052	149	3	.	.	PUNCT
ejpam-6052	149	4	(	(	PUNCT
ejpam-6052	149	5	vii	vii	PROPN
ejpam-6052	149	6	)	)	PUNCT
ejpam-6052	149	7	using	use	VERB
ejpam-6052	149	8	(	(	PUNCT
ejpam-6052	149	9	pbn3	pbn3	PROPN
ejpam-6052	149	10	)	)	PUNCT
ejpam-6052	149	11	and	and	CCONJ
ejpam-6052	149	12	theorem	theorem	VERB
ejpam-6052	149	13	2	2	NUM
ejpam-6052	149	14	,	,	PUNCT
ejpam-6052	149	15	we	we	PRON
ejpam-6052	149	16	obtain	obtain	VERB
ejpam-6052	149	17	(	(	PUNCT
ejpam-6052	149	18	x	x	NOUN
ejpam-6052	149	19	∗	∗	PROPN
ejpam-6052	149	20	z	z	NOUN
ejpam-6052	149	21	)	)	PUNCT
ejpam-6052	149	22	◦	◦	NOUN
ejpam-6052	149	23	(	(	PUNCT
ejpam-6052	149	24	y	y	PROPN
ejpam-6052	149	25	∗	∗	PROPN
ejpam-6052	149	26	z	z	NOUN
ejpam-6052	149	27	)	)	PUNCT
ejpam-6052	150	1	=	=	PUNCT
ejpam-6052	150	2	(	(	PUNCT
ejpam-6052	150	3	z	z	NOUN
ejpam-6052	150	4	∗	∗	PROPN
ejpam-6052	150	5	y	y	PROPN
ejpam-6052	150	6	)	)	PUNCT
ejpam-6052	150	7	◦	◦	NOUN
ejpam-6052	150	8	(	(	PUNCT
ejpam-6052	150	9	z	z	NOUN
ejpam-6052	150	10	∗	∗	NOUN
ejpam-6052	150	11	x	x	NOUN
ejpam-6052	150	12	)	)	PUNCT
ejpam-6052	150	13	,	,	PUNCT
ejpam-6052	150	14	(	(	PUNCT
ejpam-6052	150	15	x	x	X
ejpam-6052	150	16	◦	◦	NOUN
ejpam-6052	150	17	z	z	NOUN
ejpam-6052	150	18	)	)	PUNCT
ejpam-6052	150	19	∗	∗	NOUN
ejpam-6052	150	20	(	(	PUNCT
ejpam-6052	150	21	y	y	PROPN
ejpam-6052	150	22	◦	◦	PROPN
ejpam-6052	150	23	z	z	PROPN
ejpam-6052	150	24	)	)	PUNCT
ejpam-6052	150	25	=	=	PUNCT
ejpam-6052	151	1	(	(	PUNCT
ejpam-6052	151	2	z	z	NOUN
ejpam-6052	151	3	◦	◦	NOUN
ejpam-6052	151	4	y	y	NOUN
ejpam-6052	151	5	)	)	PUNCT
ejpam-6052	151	6	∗	∗	NOUN
ejpam-6052	151	7	(	(	PUNCT
ejpam-6052	151	8	z	z	NOUN
ejpam-6052	151	9	◦	◦	NOUN
ejpam-6052	151	10	x	x	NOUN
ejpam-6052	151	11	)	)	PUNCT
ejpam-6052	151	12	.	.	PUNCT
ejpam-6052	152	1	definition	definition	NOUN
ejpam-6052	152	2	4	4	NUM
ejpam-6052	152	3	.	.	PUNCT
ejpam-6052	153	1	an	an	DET
ejpam-6052	153	2	algebra	algebra	NOUN
ejpam-6052	153	3	(	(	PUNCT
ejpam-6052	153	4	x	x	X
ejpam-6052	153	5	,	,	PUNCT
ejpam-6052	153	6	∗	∗	NOUN
ejpam-6052	153	7	,	,	PUNCT
ejpam-6052	153	8	◦	◦	NOUN
ejpam-6052	153	9	,	,	PUNCT
ejpam-6052	153	10	0	0	NUM
ejpam-6052	153	11	)	)	PUNCT
ejpam-6052	153	12	is	be	AUX
ejpam-6052	153	13	said	say	VERB
ejpam-6052	153	14	to	to	PART
ejpam-6052	153	15	be	be	AUX
ejpam-6052	153	16	0	0	NUM
ejpam-6052	153	17	-	-	PUNCT
ejpam-6052	153	18	commutative	commutative	ADJ
ejpam-6052	153	19	if	if	SCONJ
ejpam-6052	153	20	for	for	ADP
ejpam-6052	153	21	all	all	DET
ejpam-6052	153	22	x	x	NOUN
ejpam-6052	153	23	,	,	PUNCT
ejpam-6052	153	24	y	y	PROPN
ejpam-6052	153	25	∈	∈	PROPN
ejpam-6052	153	26	x	x	X
ejpam-6052	153	27	,	,	PUNCT
ejpam-6052	153	28	x	x	SYM
ejpam-6052	153	29	∗	∗	NOUN
ejpam-6052	153	30	(	(	PUNCT
ejpam-6052	153	31	0	0	NUM
ejpam-6052	153	32	∗	∗	NUM
ejpam-6052	153	33	y	y	NOUN
ejpam-6052	153	34	)	)	PUNCT
ejpam-6052	154	1	=	=	SYM
ejpam-6052	154	2	y	y	PROPN
ejpam-6052	154	3	∗	∗	NOUN
ejpam-6052	154	4	(	(	PUNCT
ejpam-6052	154	5	0	0	NUM
ejpam-6052	154	6	∗	∗	NOUN
ejpam-6052	154	7	x	x	NOUN
ejpam-6052	154	8	)	)	PUNCT
ejpam-6052	154	9	and	and	CCONJ
ejpam-6052	154	10	x	x	PART
ejpam-6052	154	11	◦	◦	NOUN
ejpam-6052	154	12	(	(	PUNCT
ejpam-6052	154	13	0	0	NUM
ejpam-6052	154	14	◦	◦	NOUN
ejpam-6052	154	15	y	y	NOUN
ejpam-6052	154	16	)	)	PUNCT
ejpam-6052	155	1	=	=	SYM
ejpam-6052	155	2	y	y	PROPN
ejpam-6052	155	3	◦	◦	NOUN
ejpam-6052	155	4	(	(	PUNCT
ejpam-6052	155	5	0	0	NUM
ejpam-6052	155	6	◦	◦	NOUN
ejpam-6052	155	7	x	x	NOUN
ejpam-6052	155	8	)	)	PUNCT
ejpam-6052	155	9	.	.	PUNCT
ejpam-6052	156	1	example	example	NOUN
ejpam-6052	157	1	10	10	NUM
ejpam-6052	157	2	.	.	PUNCT
ejpam-6052	158	1	consider	consider	VERB
ejpam-6052	158	2	the	the	DET
ejpam-6052	158	3	cayley	cayley	ADJ
ejpam-6052	158	4	table	table	NOUN
ejpam-6052	158	5	in	in	ADP
ejpam-6052	158	6	example	example	NOUN
ejpam-6052	158	7	6	6	NUM
ejpam-6052	158	8	.	.	PUNCT
ejpam-6052	159	1	since	since	SCONJ
ejpam-6052	159	2	all	all	DET
ejpam-6052	159	3	conditions	condition	NOUN
ejpam-6052	159	4	are	be	AUX
ejpam-6052	159	5	satisfied	satisfied	ADJ
ejpam-6052	159	6	for	for	ADP
ejpam-6052	159	7	both	both	DET
ejpam-6052	159	8	operations	operation	NOUN
ejpam-6052	159	9	∗	∗	NOUN
ejpam-6052	159	10	and	and	CCONJ
ejpam-6052	159	11	◦	◦	NOUN
ejpam-6052	159	12	,	,	PUNCT
ejpam-6052	159	13	the	the	DET
ejpam-6052	159	14	algebra	algebra	NOUN
ejpam-6052	159	15	is	be	AUX
ejpam-6052	159	16	a	a	DET
ejpam-6052	159	17	0	0	NUM
ejpam-6052	159	18	-	-	PUNCT
ejpam-6052	159	19	commutative	commutative	ADJ
ejpam-6052	159	20	.	.	PUNCT
ejpam-6052	160	1	definition	definition	NOUN
ejpam-6052	160	2	5	5	NUM
ejpam-6052	160	3	.	.	PUNCT
ejpam-6052	161	1	an	an	DET
ejpam-6052	161	2	algebra	algebra	NOUN
ejpam-6052	161	3	(	(	PUNCT
ejpam-6052	161	4	x	x	X
ejpam-6052	161	5	,	,	PUNCT
ejpam-6052	161	6	∗	∗	NOUN
ejpam-6052	161	7	,	,	PUNCT
ejpam-6052	161	8	◦	◦	NOUN
ejpam-6052	161	9	,	,	PUNCT
ejpam-6052	161	10	0	0	NUM
ejpam-6052	161	11	)	)	PUNCT
ejpam-6052	161	12	is	be	AUX
ejpam-6052	161	13	said	say	VERB
ejpam-6052	161	14	to	to	PART
ejpam-6052	161	15	be	be	AUX
ejpam-6052	161	16	pseudo	pseudo	NOUN
ejpam-6052	161	17	0	0	NOUN
ejpam-6052	161	18	-	-	PUNCT
ejpam-6052	161	19	commutative	commutative	ADJ
ejpam-6052	161	20	if	if	SCONJ
ejpam-6052	161	21	x	x	ADP
ejpam-6052	161	22	∗	∗	NOUN
ejpam-6052	161	23	(	(	PUNCT
ejpam-6052	161	24	0	0	NUM
ejpam-6052	161	25	◦	◦	NOUN
ejpam-6052	161	26	y	y	NOUN
ejpam-6052	161	27	)	)	PUNCT
ejpam-6052	162	1	=	=	SYM
ejpam-6052	162	2	y	y	PROPN
ejpam-6052	162	3	∗	∗	NOUN
ejpam-6052	162	4	(	(	PUNCT
ejpam-6052	162	5	0	0	NUM
ejpam-6052	162	6	◦	◦	NOUN
ejpam-6052	162	7	x	x	SYM
ejpam-6052	162	8	)	)	PUNCT
ejpam-6052	162	9	and	and	CCONJ
ejpam-6052	162	10	x	x	PART
ejpam-6052	162	11	◦	◦	NOUN
ejpam-6052	162	12	(	(	PUNCT
ejpam-6052	162	13	0	0	NUM
ejpam-6052	162	14	∗	∗	NUM
ejpam-6052	162	15	y	y	NOUN
ejpam-6052	162	16	)	)	PUNCT
ejpam-6052	163	1	=	=	SYM
ejpam-6052	163	2	y	y	PROPN
ejpam-6052	163	3	◦	◦	NOUN
ejpam-6052	163	4	(	(	PUNCT
ejpam-6052	163	5	0	0	NUM
ejpam-6052	163	6	∗	∗	NOUN
ejpam-6052	163	7	x	x	NOUN
ejpam-6052	163	8	)	)	PUNCT
ejpam-6052	163	9	for	for	ADP
ejpam-6052	163	10	all	all	DET
ejpam-6052	163	11	x	x	NOUN
ejpam-6052	163	12	,	,	PUNCT
ejpam-6052	163	13	y	y	PROPN
ejpam-6052	163	14	∈	∈	PROPN
ejpam-6052	163	15	x.	x.	NOUN
ejpam-6052	163	16	example	example	NOUN
ejpam-6052	163	17	11	11	NUM
ejpam-6052	163	18	.	.	PUNCT
ejpam-6052	164	1	using	use	VERB
ejpam-6052	164	2	the	the	DET
ejpam-6052	164	3	cayley	cayley	ADJ
ejpam-6052	164	4	table	table	NOUN
ejpam-6052	164	5	in	in	ADP
ejpam-6052	164	6	example	example	NOUN
ejpam-6052	164	7	6	6	NUM
ejpam-6052	164	8	,	,	PUNCT
ejpam-6052	164	9	all	all	DET
ejpam-6052	164	10	conditions	condition	NOUN
ejpam-6052	164	11	are	be	AUX
ejpam-6052	164	12	satisfied	satisfied	ADJ
ejpam-6052	164	13	for	for	ADP
ejpam-6052	164	14	both	both	PRON
ejpam-6052	164	15	operations	operation	NOUN
ejpam-6052	164	16	∗	∗	NOUN
ejpam-6052	164	17	and	and	CCONJ
ejpam-6052	164	18	◦	◦	NOUN
ejpam-6052	164	19	.	.	PUNCT
ejpam-6052	165	1	hence	hence	ADV
ejpam-6052	165	2	,	,	PUNCT
ejpam-6052	165	3	the	the	DET
ejpam-6052	165	4	algebra	algebra	NOUN
ejpam-6052	165	5	is	be	AUX
ejpam-6052	165	6	pseudo	pseudo	NOUN
ejpam-6052	165	7	0	0	NUM
ejpam-6052	165	8	-	-	PUNCT
ejpam-6052	165	9	commutative	commutative	ADJ
ejpam-6052	165	10	pseudo	pseudo	NOUN
ejpam-6052	165	11	bn	bn	NOUN
ejpam-6052	165	12	-algebra	-algebra	NOUN
ejpam-6052	165	13	.	.	PUNCT
ejpam-6052	166	1	proposition	proposition	NOUN
ejpam-6052	166	2	3	3	NUM
ejpam-6052	166	3	.	.	PUNCT
ejpam-6052	167	1	if	if	SCONJ
ejpam-6052	167	2	(	(	PUNCT
ejpam-6052	167	3	x	x	X
ejpam-6052	167	4	,	,	PUNCT
ejpam-6052	167	5	∗	∗	NOUN
ejpam-6052	167	6	,	,	PUNCT
ejpam-6052	167	7	◦	◦	NOUN
ejpam-6052	167	8	,	,	PUNCT
ejpam-6052	167	9	0	0	NUM
ejpam-6052	167	10	)	)	PUNCT
ejpam-6052	167	11	is	be	AUX
ejpam-6052	167	12	a	a	DET
ejpam-6052	167	13	pseudo	pseudo	NOUN
ejpam-6052	167	14	bn	bn	NOUN
ejpam-6052	167	15	-algebra	-algebra	NOUN
ejpam-6052	167	16	,	,	PUNCT
ejpam-6052	167	17	then	then	ADV
ejpam-6052	167	18	it	it	PRON
ejpam-6052	167	19	is	be	AUX
ejpam-6052	167	20	0	0	NUM
ejpam-6052	167	21	-	-	PUNCT
ejpam-6052	167	22	commutative	commutative	ADJ
ejpam-6052	167	23	and	and	CCONJ
ejpam-6052	167	24	pseudo	pseudo	NOUN
ejpam-6052	167	25	0	0	NOUN
ejpam-6052	167	26	-	-	PUNCT
ejpam-6052	167	27	commutative	commutative	ADJ
ejpam-6052	167	28	.	.	PUNCT
ejpam-6052	168	1	proof	proof	NOUN
ejpam-6052	168	2	.	.	PUNCT
ejpam-6052	169	1	let	let	VERB
ejpam-6052	169	2	x	x	PRON
ejpam-6052	169	3	,	,	PUNCT
ejpam-6052	169	4	y	y	PROPN
ejpam-6052	169	5	∈	∈	PROPN
ejpam-6052	169	6	x.	x.	NOUN
ejpam-6052	169	7	using	use	VERB
ejpam-6052	169	8	theorem	theorem	ADJ
ejpam-6052	169	9	2(ii	2(ii	NUM
ejpam-6052	169	10	)	)	PUNCT
ejpam-6052	169	11	,	,	PUNCT
ejpam-6052	169	12	(	(	PUNCT
ejpam-6052	169	13	pbn3	pbn3	PROPN
ejpam-6052	169	14	)	)	PUNCT
ejpam-6052	169	15	,	,	PUNCT
ejpam-6052	169	16	and	and	CCONJ
ejpam-6052	169	17	(	(	PUNCT
ejpam-6052	169	18	pbn2	pbn2	PROPN
ejpam-6052	169	19	)	)	PUNCT
ejpam-6052	169	20	,	,	PUNCT
ejpam-6052	169	21	we	we	PRON
ejpam-6052	169	22	derive	derive	VERB
ejpam-6052	169	23	:	:	PUNCT
ejpam-6052	169	24	x	x	SYM
ejpam-6052	169	25	∗	∗	NOUN
ejpam-6052	169	26	(	(	PUNCT
ejpam-6052	169	27	0	0	NUM
ejpam-6052	169	28	∗	∗	NUM
ejpam-6052	169	29	y	y	NOUN
ejpam-6052	169	30	)	)	PUNCT
ejpam-6052	169	31	=	=	PUNCT
ejpam-6052	170	1	[	[	X
ejpam-6052	170	2	0	0	NUM
ejpam-6052	170	3	◦	◦	NOUN
ejpam-6052	170	4	(	(	PUNCT
ejpam-6052	170	5	0	0	NUM
ejpam-6052	170	6	∗	∗	NUM
ejpam-6052	170	7	y	y	PROPN
ejpam-6052	170	8	)	)	PUNCT
ejpam-6052	170	9	]	]	PUNCT
ejpam-6052	171	1	∗	∗	NOUN
ejpam-6052	171	2	[	[	X
ejpam-6052	171	3	(	(	PUNCT
ejpam-6052	171	4	0	0	NUM
ejpam-6052	171	5	∗	∗	NOUN
ejpam-6052	171	6	x	x	NOUN
ejpam-6052	171	7	)	)	PUNCT
ejpam-6052	171	8	◦	◦	NOUN
ejpam-6052	171	9	0	0	NUM
ejpam-6052	171	10	]	]	PUNCT
ejpam-6052	171	11	=	=	SYM
ejpam-6052	171	12	y	y	PROPN
ejpam-6052	171	13	∗	∗	NOUN
ejpam-6052	171	14	(	(	PUNCT
ejpam-6052	171	15	0	0	NUM
ejpam-6052	171	16	∗	∗	NOUN
ejpam-6052	171	17	x	x	NOUN
ejpam-6052	171	18	)	)	PUNCT
ejpam-6052	171	19	.	.	PUNCT
ejpam-6052	172	1	similarly	similarly	ADV
ejpam-6052	172	2	,	,	PUNCT
ejpam-6052	172	3	x	x	PUNCT
ejpam-6052	172	4	◦	◦	NOUN
ejpam-6052	172	5	(	(	PUNCT
ejpam-6052	172	6	0	0	NUM
ejpam-6052	172	7	◦	◦	NOUN
ejpam-6052	172	8	y	y	NOUN
ejpam-6052	172	9	)	)	PUNCT
ejpam-6052	172	10	=	=	PUNCT
ejpam-6052	173	1	[	[	X
ejpam-6052	173	2	0	0	NUM
ejpam-6052	173	3	∗	∗	NOUN
ejpam-6052	173	4	(	(	PUNCT
ejpam-6052	173	5	0	0	NUM
ejpam-6052	173	6	◦	◦	NOUN
ejpam-6052	173	7	y	y	PROPN
ejpam-6052	173	8	)	)	PUNCT
ejpam-6052	173	9	]	]	PUNCT
ejpam-6052	174	1	◦	◦	NOUN
ejpam-6052	174	2	[	[	X
ejpam-6052	174	3	(	(	PUNCT
ejpam-6052	174	4	0	0	NUM
ejpam-6052	174	5	◦	◦	NOUN
ejpam-6052	174	6	x	x	SYM
ejpam-6052	174	7	)	)	PUNCT
ejpam-6052	174	8	∗	∗	NOUN
ejpam-6052	174	9	0	0	NUM
ejpam-6052	174	10	]	]	PUNCT
ejpam-6052	174	11	=	=	SYM
ejpam-6052	174	12	y	y	PROPN
ejpam-6052	174	13	◦	◦	NOUN
ejpam-6052	174	14	(	(	PUNCT
ejpam-6052	174	15	0	0	NUM
ejpam-6052	174	16	◦	◦	NOUN
ejpam-6052	174	17	x	x	NOUN
ejpam-6052	174	18	)	)	PUNCT
ejpam-6052	174	19	.	.	PUNCT
ejpam-6052	175	1	applying	apply	VERB
ejpam-6052	175	2	proposition	proposition	NOUN
ejpam-6052	175	3	2(i	2(i	NUM
ejpam-6052	175	4	)	)	PUNCT
ejpam-6052	175	5	,	,	PUNCT
ejpam-6052	175	6	(	(	PUNCT
ejpam-6052	175	7	pbn3	pbn3	PROPN
ejpam-6052	175	8	)	)	PUNCT
ejpam-6052	175	9	,	,	PUNCT
ejpam-6052	175	10	and	and	CCONJ
ejpam-6052	175	11	(	(	PUNCT
ejpam-6052	175	12	pbn2	pbn2	PROPN
ejpam-6052	175	13	)	)	PUNCT
ejpam-6052	175	14	,	,	PUNCT
ejpam-6052	175	15	we	we	PRON
ejpam-6052	175	16	also	also	ADV
ejpam-6052	175	17	obtain	obtain	VERB
ejpam-6052	175	18	:	:	PUNCT
ejpam-6052	175	19	x	x	X
ejpam-6052	175	20	∗	∗	NOUN
ejpam-6052	175	21	(	(	PUNCT
ejpam-6052	175	22	0	0	NUM
ejpam-6052	175	23	◦	◦	NOUN
ejpam-6052	175	24	y	y	NOUN
ejpam-6052	175	25	)	)	PUNCT
ejpam-6052	175	26	=	=	PUNCT
ejpam-6052	176	1	[	[	X
ejpam-6052	176	2	0	0	NUM
ejpam-6052	176	3	◦	◦	NOUN
ejpam-6052	176	4	(	(	PUNCT
ejpam-6052	176	5	0	0	NUM
ejpam-6052	176	6	◦	◦	NOUN
ejpam-6052	176	7	y	y	PROPN
ejpam-6052	176	8	)	)	PUNCT
ejpam-6052	176	9	]	]	PUNCT
ejpam-6052	177	1	∗	∗	NOUN
ejpam-6052	177	2	[	[	X
ejpam-6052	177	3	(	(	PUNCT
ejpam-6052	177	4	0	0	NUM
ejpam-6052	177	5	◦	◦	NOUN
ejpam-6052	177	6	x	x	NOUN
ejpam-6052	177	7	)	)	PUNCT
ejpam-6052	177	8	◦	◦	NOUN
ejpam-6052	177	9	0	0	NUM
ejpam-6052	177	10	]	]	PUNCT
ejpam-6052	177	11	=	=	SYM
ejpam-6052	177	12	y	y	PROPN
ejpam-6052	177	13	∗	∗	NOUN
ejpam-6052	177	14	(	(	PUNCT
ejpam-6052	177	15	0	0	NUM
ejpam-6052	177	16	◦	◦	NOUN
ejpam-6052	177	17	x	x	NOUN
ejpam-6052	177	18	)	)	PUNCT
ejpam-6052	177	19	,	,	PUNCT
ejpam-6052	177	20	and	and	CCONJ
ejpam-6052	177	21	x	x	PART
ejpam-6052	177	22	◦	◦	NOUN
ejpam-6052	177	23	(	(	PUNCT
ejpam-6052	177	24	0	0	NUM
ejpam-6052	177	25	∗	∗	NUM
ejpam-6052	177	26	y	y	NOUN
ejpam-6052	177	27	)	)	PUNCT
ejpam-6052	178	1	=	=	PUNCT
ejpam-6052	179	1	[	[	X
ejpam-6052	179	2	0	0	NUM
ejpam-6052	179	3	∗	∗	NOUN
ejpam-6052	179	4	(	(	PUNCT
ejpam-6052	179	5	0	0	NUM
ejpam-6052	179	6	∗	∗	NOUN
ejpam-6052	179	7	y	y	PROPN
ejpam-6052	179	8	)	)	PUNCT
ejpam-6052	179	9	]	]	PUNCT
ejpam-6052	180	1	◦	◦	NOUN
ejpam-6052	180	2	[	[	X
ejpam-6052	180	3	(	(	PUNCT
ejpam-6052	180	4	0	0	NUM
ejpam-6052	180	5	∗	∗	NOUN
ejpam-6052	180	6	x	x	NOUN
ejpam-6052	180	7	)	)	PUNCT
ejpam-6052	180	8	∗	∗	NOUN
ejpam-6052	180	9	0	0	NUM
ejpam-6052	180	10	]	]	PUNCT
ejpam-6052	180	11	=	=	SYM
ejpam-6052	180	12	y	y	PROPN
ejpam-6052	180	13	◦	◦	NOUN
ejpam-6052	180	14	(	(	PUNCT
ejpam-6052	180	15	0	0	NUM
ejpam-6052	180	16	∗	∗	NOUN
ejpam-6052	180	17	x	x	NOUN
ejpam-6052	180	18	)	)	PUNCT
ejpam-6052	180	19	.	.	PUNCT
ejpam-6052	181	1	thus	thus	ADV
ejpam-6052	181	2	,	,	PUNCT
ejpam-6052	181	3	the	the	DET
ejpam-6052	181	4	result	result	NOUN
ejpam-6052	181	5	follows	follow	VERB
ejpam-6052	181	6	.	.	PUNCT
ejpam-6052	182	1	theorem	theorem	NOUN
ejpam-6052	182	2	3	3	X
ejpam-6052	182	3	.	.	PUNCT
ejpam-6052	183	1	let	let	VERB
ejpam-6052	183	2	(	(	PUNCT
ejpam-6052	183	3	x	x	X
ejpam-6052	183	4	,	,	PUNCT
ejpam-6052	183	5	∗	∗	NOUN
ejpam-6052	183	6	,	,	PUNCT
ejpam-6052	183	7	◦	◦	NOUN
ejpam-6052	183	8	,	,	PUNCT
ejpam-6052	183	9	0	0	NUM
ejpam-6052	183	10	)	)	PUNCT
ejpam-6052	183	11	be	be	AUX
ejpam-6052	183	12	a	a	DET
ejpam-6052	183	13	pseudo	pseudo	NOUN
ejpam-6052	183	14	bn	bn	NOUN
ejpam-6052	183	15	-algebra	-algebra	NOUN
ejpam-6052	183	16	.	.	PUNCT
ejpam-6052	184	1	then	then	ADV
ejpam-6052	184	2	(	(	PUNCT
ejpam-6052	184	3	x	x	X
ejpam-6052	184	4	,	,	PUNCT
ejpam-6052	184	5	∗	∗	NOUN
ejpam-6052	184	6	,	,	PUNCT
ejpam-6052	184	7	◦	◦	NOUN
ejpam-6052	184	8	,	,	PUNCT
ejpam-6052	184	9	0	0	NUM
ejpam-6052	184	10	)	)	PUNCT
ejpam-6052	184	11	is	be	AUX
ejpam-6052	184	12	0	0	NUM
ejpam-6052	184	13	-	-	PUNCT
ejpam-6052	184	14	commutative	commutative	ADJ
ejpam-6052	184	15	if	if	SCONJ
ejpam-6052	184	16	and	and	CCONJ
ejpam-6052	184	17	only	only	ADV
ejpam-6052	184	18	if	if	SCONJ
ejpam-6052	184	19	it	it	PRON
ejpam-6052	184	20	is	be	AUX
ejpam-6052	184	21	pseudo	pseudo	NOUN
ejpam-6052	184	22	0	0	NOUN
ejpam-6052	184	23	-	-	PUNCT
ejpam-6052	184	24	commutative	commutative	ADJ
ejpam-6052	184	25	.	.	PUNCT
ejpam-6052	185	1	i.m	i.m	PROPN
ejpam-6052	185	2	.	.	PROPN
ejpam-6052	185	3	antabo	antabo	PROPN
ejpam-6052	185	4	et	et	PROPN
ejpam-6052	185	5	al	al	PROPN
ejpam-6052	185	6	.	.	PUNCT
ejpam-6052	185	7	/	/	SYM
ejpam-6052	185	8	eur	eur	PROPN
ejpam-6052	185	9	.	.	PUNCT
ejpam-6052	186	1	j.	j.	PROPN
ejpam-6052	186	2	pure	pure	PROPN
ejpam-6052	186	3	appl	appl	PROPN
ejpam-6052	186	4	.	.	PROPN
ejpam-6052	186	5	math	math	PROPN
ejpam-6052	186	6	,	,	PUNCT
ejpam-6052	186	7	18	18	NUM
ejpam-6052	186	8	(	(	PUNCT
ejpam-6052	186	9	2	2	NUM
ejpam-6052	186	10	)	)	PUNCT
ejpam-6052	186	11	(	(	PUNCT
ejpam-6052	186	12	2025	2025	NUM
ejpam-6052	186	13	)	)	PUNCT
ejpam-6052	186	14	,	,	PUNCT
ejpam-6052	186	15	6052	6052	NUM
ejpam-6052	186	16	8	8	NUM
ejpam-6052	186	17	of	of	ADP
ejpam-6052	186	18	14	14	NUM
ejpam-6052	186	19	proof	proof	NOUN
ejpam-6052	186	20	.	.	PUNCT
ejpam-6052	187	1	suppose	suppose	VERB
ejpam-6052	187	2	(	(	PUNCT
ejpam-6052	187	3	x	x	X
ejpam-6052	187	4	,	,	PUNCT
ejpam-6052	187	5	∗	∗	NOUN
ejpam-6052	187	6	,	,	PUNCT
ejpam-6052	187	7	◦	◦	NOUN
ejpam-6052	187	8	,	,	PUNCT
ejpam-6052	187	9	0	0	NUM
ejpam-6052	187	10	)	)	PUNCT
ejpam-6052	187	11	satisfies	satisfy	VERB
ejpam-6052	187	12	0	0	NUM
ejpam-6052	187	13	-	-	PUNCT
ejpam-6052	187	14	commutativity	commutativity	NOUN
ejpam-6052	187	15	:	:	PUNCT
ejpam-6052	187	16	x	x	SYM
ejpam-6052	187	17	∗	∗	NOUN
ejpam-6052	187	18	(	(	PUNCT
ejpam-6052	187	19	0	0	NUM
ejpam-6052	187	20	∗	∗	NUM
ejpam-6052	187	21	y	y	NOUN
ejpam-6052	187	22	)	)	PUNCT
ejpam-6052	188	1	=	=	SYM
ejpam-6052	188	2	y	y	PROPN
ejpam-6052	188	3	∗	∗	NOUN
ejpam-6052	188	4	(	(	PUNCT
ejpam-6052	188	5	0	0	NUM
ejpam-6052	188	6	∗	∗	NOUN
ejpam-6052	188	7	x	x	NOUN
ejpam-6052	188	8	)	)	PUNCT
ejpam-6052	188	9	,	,	PUNCT
ejpam-6052	188	10	x	x	PUNCT
ejpam-6052	188	11	◦	◦	NOUN
ejpam-6052	188	12	(	(	PUNCT
ejpam-6052	188	13	0	0	NUM
ejpam-6052	188	14	◦	◦	NOUN
ejpam-6052	188	15	y	y	NOUN
ejpam-6052	188	16	)	)	PUNCT
ejpam-6052	189	1	=	=	SYM
ejpam-6052	189	2	y	y	PROPN
ejpam-6052	189	3	◦	◦	NOUN
ejpam-6052	189	4	(	(	PUNCT
ejpam-6052	189	5	0	0	NUM
ejpam-6052	189	6	◦	◦	NOUN
ejpam-6052	189	7	x	x	NOUN
ejpam-6052	189	8	)	)	PUNCT
ejpam-6052	189	9	.	.	PUNCT
ejpam-6052	190	1	we	we	PRON
ejpam-6052	190	2	show	show	VERB
ejpam-6052	190	3	it	it	PRON
ejpam-6052	190	4	satisfies	satisfy	VERB
ejpam-6052	190	5	pseudo-0	pseudo-0	NOUN
ejpam-6052	190	6	-	-	PUNCT
ejpam-6052	190	7	commutativity	commutativity	NOUN
ejpam-6052	190	8	:	:	PUNCT
ejpam-6052	190	9	x	x	SYM
ejpam-6052	190	10	∗	∗	NOUN
ejpam-6052	190	11	(	(	PUNCT
ejpam-6052	190	12	0	0	NUM
ejpam-6052	190	13	◦	◦	NOUN
ejpam-6052	190	14	y	y	NOUN
ejpam-6052	190	15	)	)	PUNCT
ejpam-6052	191	1	=	=	SYM
ejpam-6052	191	2	y	y	PROPN
ejpam-6052	191	3	∗	∗	NOUN
ejpam-6052	191	4	(	(	PUNCT
ejpam-6052	191	5	0	0	NUM
ejpam-6052	191	6	◦	◦	NOUN
ejpam-6052	191	7	x	x	NOUN
ejpam-6052	191	8	)	)	PUNCT
ejpam-6052	191	9	,	,	PUNCT
ejpam-6052	191	10	x	x	PUNCT
ejpam-6052	191	11	◦	◦	NOUN
ejpam-6052	191	12	(	(	PUNCT
ejpam-6052	191	13	0	0	NUM
ejpam-6052	191	14	∗	∗	NUM
ejpam-6052	191	15	y	y	NOUN
ejpam-6052	191	16	)	)	PUNCT
ejpam-6052	192	1	=	=	SYM
ejpam-6052	192	2	y	y	PROPN
ejpam-6052	192	3	◦	◦	NOUN
ejpam-6052	192	4	(	(	PUNCT
ejpam-6052	192	5	0	0	NUM
ejpam-6052	192	6	∗	∗	NOUN
ejpam-6052	192	7	x	x	NOUN
ejpam-6052	192	8	)	)	PUNCT
ejpam-6052	192	9	.	.	PUNCT
ejpam-6052	193	1	for	for	ADP
ejpam-6052	193	2	the	the	DET
ejpam-6052	193	3	first	first	ADJ
ejpam-6052	193	4	identity	identity	NOUN
ejpam-6052	193	5	,	,	PUNCT
ejpam-6052	193	6	using	use	VERB
ejpam-6052	193	7	0	0	NOUN
ejpam-6052	193	8	-	-	PUNCT
ejpam-6052	193	9	commutativity	commutativity	NOUN
ejpam-6052	193	10	:	:	PUNCT
ejpam-6052	193	11	x	x	SYM
ejpam-6052	193	12	∗	∗	NOUN
ejpam-6052	193	13	(	(	PUNCT
ejpam-6052	193	14	0	0	NUM
ejpam-6052	193	15	◦	◦	NOUN
ejpam-6052	193	16	y	y	NOUN
ejpam-6052	193	17	)	)	PUNCT
ejpam-6052	193	18	=	=	PUNCT
ejpam-6052	193	19	x	x	X
ejpam-6052	193	20	∗	∗	NOUN
ejpam-6052	193	21	[	[	X
ejpam-6052	193	22	(	(	PUNCT
ejpam-6052	193	23	0	0	NUM
ejpam-6052	193	24	∗	∗	PROPN
ejpam-6052	193	25	y	y	NOUN
ejpam-6052	193	26	)	)	PUNCT
ejpam-6052	193	27	◦	◦	NOUN
ejpam-6052	193	28	0	0	NUM
ejpam-6052	193	29	]	]	PUNCT
ejpam-6052	193	30	=	=	SYM
ejpam-6052	193	31	x	x	SYM
ejpam-6052	193	32	∗	∗	NOUN
ejpam-6052	193	33	(	(	PUNCT
ejpam-6052	193	34	0	0	NUM
ejpam-6052	193	35	∗	∗	NUM
ejpam-6052	193	36	y	y	NOUN
ejpam-6052	193	37	)	)	PUNCT
ejpam-6052	194	1	=	=	SYM
ejpam-6052	194	2	y	y	PROPN
ejpam-6052	194	3	∗	∗	NOUN
ejpam-6052	194	4	(	(	PUNCT
ejpam-6052	194	5	0	0	NUM
ejpam-6052	194	6	∗	∗	NOUN
ejpam-6052	194	7	x	x	NOUN
ejpam-6052	194	8	)	)	PUNCT
ejpam-6052	195	1	=	=	SYM
ejpam-6052	195	2	y	y	PROPN
ejpam-6052	195	3	∗	∗	NOUN
ejpam-6052	195	4	[	[	X
ejpam-6052	195	5	(	(	PUNCT
ejpam-6052	195	6	0	0	NUM
ejpam-6052	195	7	∗	∗	NOUN
ejpam-6052	195	8	x	x	NOUN
ejpam-6052	195	9	)	)	PUNCT
ejpam-6052	195	10	◦	◦	NOUN
ejpam-6052	195	11	0	0	NUM
ejpam-6052	195	12	]	]	PUNCT
ejpam-6052	195	13	=	=	SYM
ejpam-6052	195	14	y	y	PROPN
ejpam-6052	195	15	∗	∗	NOUN
ejpam-6052	195	16	(	(	PUNCT
ejpam-6052	195	17	0	0	NUM
ejpam-6052	195	18	◦	◦	NOUN
ejpam-6052	195	19	x	x	NOUN
ejpam-6052	195	20	)	)	PUNCT
ejpam-6052	195	21	.	.	PUNCT
ejpam-6052	196	1	for	for	ADP
ejpam-6052	196	2	the	the	DET
ejpam-6052	196	3	second	second	ADJ
ejpam-6052	196	4	identity	identity	NOUN
ejpam-6052	196	5	,	,	PUNCT
ejpam-6052	196	6	again	again	ADV
ejpam-6052	196	7	by	by	ADP
ejpam-6052	196	8	0	0	NOUN
ejpam-6052	196	9	-	-	PUNCT
ejpam-6052	196	10	commutativity	commutativity	NOUN
ejpam-6052	196	11	:	:	PUNCT
ejpam-6052	196	12	x	x	SYM
ejpam-6052	196	13	◦	◦	NOUN
ejpam-6052	196	14	(	(	PUNCT
ejpam-6052	196	15	0	0	NUM
ejpam-6052	196	16	∗	∗	NUM
ejpam-6052	196	17	y	y	NOUN
ejpam-6052	196	18	)	)	PUNCT
ejpam-6052	196	19	=	=	PUNCT
ejpam-6052	197	1	x	x	PUNCT
ejpam-6052	197	2	◦	◦	NOUN
ejpam-6052	197	3	[	[	X
ejpam-6052	197	4	(	(	PUNCT
ejpam-6052	197	5	0	0	NUM
ejpam-6052	197	6	◦	◦	NOUN
ejpam-6052	197	7	y	y	NOUN
ejpam-6052	197	8	)	)	PUNCT
ejpam-6052	197	9	∗	∗	NOUN
ejpam-6052	197	10	0	0	NUM
ejpam-6052	197	11	]	]	PUNCT
ejpam-6052	198	1	=	=	SYM
ejpam-6052	198	2	x	x	PUNCT
ejpam-6052	198	3	◦	◦	NOUN
ejpam-6052	198	4	(	(	PUNCT
ejpam-6052	198	5	0	0	NUM
ejpam-6052	198	6	◦	◦	NOUN
ejpam-6052	198	7	y	y	NOUN
ejpam-6052	198	8	)	)	PUNCT
ejpam-6052	199	1	=	=	SYM
ejpam-6052	199	2	y	y	PROPN
ejpam-6052	199	3	◦	◦	NOUN
ejpam-6052	199	4	(	(	PUNCT
ejpam-6052	199	5	0	0	NUM
ejpam-6052	199	6	◦	◦	NOUN
ejpam-6052	199	7	x	x	SYM
ejpam-6052	199	8	)	)	PUNCT
ejpam-6052	200	1	=	=	SYM
ejpam-6052	200	2	y	y	PROPN
ejpam-6052	200	3	◦	◦	NOUN
ejpam-6052	200	4	[	[	X
ejpam-6052	200	5	(	(	PUNCT
ejpam-6052	200	6	0	0	NUM
ejpam-6052	200	7	◦	◦	NOUN
ejpam-6052	200	8	x	x	SYM
ejpam-6052	200	9	)	)	PUNCT
ejpam-6052	200	10	∗	∗	NOUN
ejpam-6052	200	11	0	0	NUM
ejpam-6052	200	12	]	]	PUNCT
ejpam-6052	200	13	=	=	SYM
ejpam-6052	200	14	y	y	PROPN
ejpam-6052	200	15	◦	◦	NOUN
ejpam-6052	200	16	(	(	PUNCT
ejpam-6052	200	17	0	0	NUM
ejpam-6052	200	18	∗	∗	NOUN
ejpam-6052	200	19	x	x	NOUN
ejpam-6052	200	20	)	)	PUNCT
ejpam-6052	200	21	.	.	PUNCT
ejpam-6052	201	1	conversely	conversely	ADV
ejpam-6052	201	2	,	,	PUNCT
ejpam-6052	201	3	assume	assume	VERB
ejpam-6052	201	4	pseudo-0	pseudo-0	NOUN
ejpam-6052	201	5	-	-	PUNCT
ejpam-6052	201	6	commutativity	commutativity	NOUN
ejpam-6052	201	7	holds	hold	VERB
ejpam-6052	201	8	.	.	PUNCT
ejpam-6052	202	1	we	we	PRON
ejpam-6052	202	2	show	show	VERB
ejpam-6052	202	3	that	that	SCONJ
ejpam-6052	202	4	0	0	NUM
ejpam-6052	202	5	-	-	PUNCT
ejpam-6052	202	6	commutativity	commutativity	NOUN
ejpam-6052	202	7	follows	follow	VERB
ejpam-6052	202	8	:	:	PUNCT
ejpam-6052	202	9	x	x	SYM
ejpam-6052	202	10	∗	∗	NOUN
ejpam-6052	202	11	(	(	PUNCT
ejpam-6052	202	12	0	0	NUM
ejpam-6052	202	13	∗	∗	NUM
ejpam-6052	202	14	y	y	NOUN
ejpam-6052	202	15	)	)	PUNCT
ejpam-6052	202	16	=	=	PUNCT
ejpam-6052	203	1	x	x	X
ejpam-6052	203	2	∗	∗	NOUN
ejpam-6052	203	3	[	[	X
ejpam-6052	203	4	(	(	PUNCT
ejpam-6052	203	5	0	0	NUM
ejpam-6052	203	6	◦	◦	NOUN
ejpam-6052	203	7	y	y	NOUN
ejpam-6052	203	8	)	)	PUNCT
ejpam-6052	203	9	∗	∗	NOUN
ejpam-6052	203	10	0	0	NUM
ejpam-6052	203	11	]	]	PUNCT
ejpam-6052	203	12	=	=	SYM
ejpam-6052	203	13	x	x	SYM
ejpam-6052	203	14	∗	∗	NOUN
ejpam-6052	203	15	(	(	PUNCT
ejpam-6052	203	16	0	0	NUM
ejpam-6052	203	17	◦	◦	NOUN
ejpam-6052	203	18	y	y	NOUN
ejpam-6052	203	19	)	)	PUNCT
ejpam-6052	204	1	=	=	SYM
ejpam-6052	204	2	y	y	PROPN
ejpam-6052	204	3	∗	∗	NOUN
ejpam-6052	204	4	(	(	PUNCT
ejpam-6052	204	5	0	0	NUM
ejpam-6052	204	6	◦	◦	NOUN
ejpam-6052	204	7	x	x	NOUN
ejpam-6052	204	8	)	)	PUNCT
ejpam-6052	205	1	=	=	SYM
ejpam-6052	205	2	y	y	PROPN
ejpam-6052	205	3	∗	∗	NOUN
ejpam-6052	205	4	[	[	X
ejpam-6052	205	5	(	(	PUNCT
ejpam-6052	205	6	0	0	NUM
ejpam-6052	205	7	◦	◦	NOUN
ejpam-6052	205	8	x	x	SYM
ejpam-6052	205	9	)	)	PUNCT
ejpam-6052	205	10	∗	∗	NOUN
ejpam-6052	205	11	0	0	NUM
ejpam-6052	205	12	]	]	PUNCT
ejpam-6052	205	13	=	=	SYM
ejpam-6052	205	14	y	y	PROPN
ejpam-6052	205	15	∗	∗	NOUN
ejpam-6052	205	16	(	(	PUNCT
ejpam-6052	205	17	0	0	NUM
ejpam-6052	205	18	∗	∗	NOUN
ejpam-6052	205	19	x	x	NOUN
ejpam-6052	205	20	)	)	PUNCT
ejpam-6052	205	21	.	.	PUNCT
ejpam-6052	206	1	similarly	similarly	ADV
ejpam-6052	206	2	,	,	PUNCT
ejpam-6052	206	3	x	x	PUNCT
ejpam-6052	206	4	◦	◦	NOUN
ejpam-6052	206	5	(	(	PUNCT
ejpam-6052	206	6	0	0	NUM
ejpam-6052	206	7	◦	◦	NOUN
ejpam-6052	206	8	y	y	NOUN
ejpam-6052	206	9	)	)	PUNCT
ejpam-6052	206	10	=	=	PUNCT
ejpam-6052	207	1	x	x	PUNCT
ejpam-6052	207	2	◦	◦	NOUN
ejpam-6052	208	1	[	[	X
ejpam-6052	208	2	(	(	PUNCT
ejpam-6052	208	3	0	0	NUM
ejpam-6052	208	4	∗	∗	PROPN
ejpam-6052	208	5	y	y	NOUN
ejpam-6052	208	6	)	)	PUNCT
ejpam-6052	208	7	◦	◦	NOUN
ejpam-6052	208	8	0	0	NUM
ejpam-6052	208	9	]	]	X
ejpam-6052	208	10	=	=	SYM
ejpam-6052	208	11	x	x	PUNCT
ejpam-6052	208	12	◦	◦	NOUN
ejpam-6052	208	13	(	(	PUNCT
ejpam-6052	208	14	0	0	NUM
ejpam-6052	208	15	∗	∗	NUM
ejpam-6052	208	16	y	y	NOUN
ejpam-6052	208	17	)	)	PUNCT
ejpam-6052	209	1	=	=	SYM
ejpam-6052	209	2	y	y	PROPN
ejpam-6052	209	3	◦	◦	NOUN
ejpam-6052	209	4	(	(	PUNCT
ejpam-6052	209	5	0	0	NUM
ejpam-6052	209	6	∗	∗	NOUN
ejpam-6052	209	7	x	x	NOUN
ejpam-6052	209	8	)	)	PUNCT
ejpam-6052	210	1	=	=	SYM
ejpam-6052	210	2	y	y	PROPN
ejpam-6052	210	3	◦	◦	NOUN
ejpam-6052	211	1	[	[	X
ejpam-6052	211	2	(	(	PUNCT
ejpam-6052	211	3	0	0	NUM
ejpam-6052	211	4	∗	∗	NOUN
ejpam-6052	211	5	x	x	NOUN
ejpam-6052	211	6	)	)	PUNCT
ejpam-6052	211	7	◦	◦	NOUN
ejpam-6052	211	8	0	0	NUM
ejpam-6052	211	9	]	]	PUNCT
ejpam-6052	211	10	=	=	SYM
ejpam-6052	211	11	y	y	PROPN
ejpam-6052	211	12	◦	◦	NOUN
ejpam-6052	211	13	(	(	PUNCT
ejpam-6052	211	14	0	0	NUM
ejpam-6052	211	15	◦	◦	NOUN
ejpam-6052	211	16	x	x	NOUN
ejpam-6052	211	17	)	)	PUNCT
ejpam-6052	211	18	.	.	PUNCT
ejpam-6052	212	1	example	example	NOUN
ejpam-6052	212	2	12	12	NUM
ejpam-6052	212	3	.	.	PUNCT
ejpam-6052	213	1	define	define	VERB
ejpam-6052	213	2	the	the	DET
ejpam-6052	213	3	operations	operation	NOUN
ejpam-6052	213	4	“	"	PUNCT
ejpam-6052	213	5	∗	∗	NOUN
ejpam-6052	213	6	”	"	PUNCT
ejpam-6052	213	7	and	and	CCONJ
ejpam-6052	213	8	“	"	PUNCT
ejpam-6052	213	9	◦	◦	NOUN
ejpam-6052	213	10	”	"	PUNCT
ejpam-6052	213	11	on	on	ADP
ejpam-6052	213	12	e	e	X
ejpam-6052	213	13	=	=	PUNCT
ejpam-6052	213	14	{	{	PUNCT
ejpam-6052	213	15	0	0	NUM
ejpam-6052	213	16	,	,	PUNCT
ejpam-6052	213	17	1	1	NUM
ejpam-6052	213	18	,	,	PUNCT
ejpam-6052	213	19	2	2	NUM
ejpam-6052	213	20	,	,	PUNCT
ejpam-6052	213	21	3	3	NUM
ejpam-6052	213	22	}	}	PUNCT
ejpam-6052	213	23	,	,	PUNCT
ejpam-6052	213	24	by	by	ADP
ejpam-6052	213	25	the	the	DET
ejpam-6052	213	26	following	following	ADJ
ejpam-6052	213	27	cayley	cayley	ADJ
ejpam-6052	213	28	tables	table	NOUN
ejpam-6052	213	29	:	:	PUNCT
ejpam-6052	213	30	∗	∗	NOUN
ejpam-6052	213	31	0	0	NUM
ejpam-6052	213	32	1	1	NUM
ejpam-6052	213	33	2	2	NUM
ejpam-6052	213	34	3	3	NUM
ejpam-6052	213	35	0	0	NUM
ejpam-6052	213	36	0	0	NUM
ejpam-6052	213	37	1	1	NUM
ejpam-6052	213	38	2	2	NUM
ejpam-6052	213	39	3	3	NUM
ejpam-6052	213	40	1	1	NUM
ejpam-6052	213	41	1	1	NUM
ejpam-6052	213	42	0	0	NUM
ejpam-6052	213	43	3	3	NUM
ejpam-6052	213	44	0	0	NUM
ejpam-6052	213	45	2	2	NUM
ejpam-6052	213	46	2	2	NUM
ejpam-6052	213	47	3	3	NUM
ejpam-6052	213	48	0	0	NUM
ejpam-6052	213	49	2	2	NUM
ejpam-6052	213	50	3	3	NUM
ejpam-6052	213	51	3	3	NUM
ejpam-6052	213	52	0	0	NUM
ejpam-6052	213	53	2	2	NUM
ejpam-6052	213	54	0	0	NUM
ejpam-6052	213	55	◦	◦	NOUN
ejpam-6052	213	56	0	0	NUM
ejpam-6052	213	57	1	1	NUM
ejpam-6052	213	58	2	2	NUM
ejpam-6052	213	59	3	3	NUM
ejpam-6052	213	60	0	0	NUM
ejpam-6052	213	61	0	0	NUM
ejpam-6052	213	62	1	1	NUM
ejpam-6052	213	63	2	2	NUM
ejpam-6052	213	64	3	3	NUM
ejpam-6052	213	65	1	1	NUM
ejpam-6052	213	66	1	1	NUM
ejpam-6052	213	67	0	0	NUM
ejpam-6052	213	68	1	1	NUM
ejpam-6052	213	69	1	1	NUM
ejpam-6052	213	70	2	2	NUM
ejpam-6052	213	71	2	2	NUM
ejpam-6052	213	72	1	1	NUM
ejpam-6052	213	73	0	0	NUM
ejpam-6052	213	74	1	1	NUM
ejpam-6052	213	75	3	3	NUM
ejpam-6052	213	76	3	3	NUM
ejpam-6052	213	77	1	1	NUM
ejpam-6052	213	78	1	1	NUM
ejpam-6052	213	79	0	0	NUM
ejpam-6052	213	80	then	then	ADV
ejpam-6052	213	81	(	(	PUNCT
ejpam-6052	213	82	e	e	NOUN
ejpam-6052	213	83	,	,	PUNCT
ejpam-6052	213	84	∗	∗	NOUN
ejpam-6052	213	85	,	,	PUNCT
ejpam-6052	213	86	◦	◦	NOUN
ejpam-6052	213	87	,	,	PUNCT
ejpam-6052	213	88	0	0	NUM
ejpam-6052	213	89	)	)	PUNCT
ejpam-6052	213	90	is	be	AUX
ejpam-6052	213	91	a	a	DET
ejpam-6052	213	92	0	0	NUM
ejpam-6052	213	93	-	-	PUNCT
ejpam-6052	213	94	commutative	commutative	ADJ
ejpam-6052	213	95	pseudo	pseudo	NOUN
ejpam-6052	213	96	bf	bf	NOUN
ejpam-6052	213	97	-algebra	-algebra	NOUN
ejpam-6052	213	98	.	.	PUNCT
ejpam-6052	214	1	futhermore	futhermore	NOUN
ejpam-6052	214	2	,	,	PUNCT
ejpam-6052	214	3	it	it	PRON
ejpam-6052	214	4	can	can	AUX
ejpam-6052	214	5	be	be	AUX
ejpam-6052	214	6	shown	show	VERB
ejpam-6052	214	7	that	that	SCONJ
ejpam-6052	214	8	(	(	PUNCT
ejpam-6052	214	9	e	e	NOUN
ejpam-6052	214	10	,	,	PUNCT
ejpam-6052	214	11	∗	∗	NOUN
ejpam-6052	214	12	,	,	PUNCT
ejpam-6052	214	13	◦	◦	NOUN
ejpam-6052	214	14	,	,	PUNCT
ejpam-6052	214	15	0	0	X
ejpam-6052	214	16	)	)	PUNCT
ejpam-6052	214	17	pseudo	pseudo	NOUN
ejpam-6052	214	18	bn	bn	NOUN
ejpam-6052	214	19	-algebra	-algebra	NOUN
ejpam-6052	214	20	.	.	PUNCT
ejpam-6052	215	1	for	for	ADP
ejpam-6052	215	2	0	0	NUM
ejpam-6052	215	3	-	-	PUNCT
ejpam-6052	215	4	commutative	commutative	ADJ
ejpam-6052	215	5	pseudo	pseudo	NOUN
ejpam-6052	215	6	bf	bf	NOUN
ejpam-6052	215	7	-algebras	-algebra	NOUN
ejpam-6052	215	8	,	,	PUNCT
ejpam-6052	215	9	the	the	DET
ejpam-6052	215	10	converse	converse	NOUN
ejpam-6052	215	11	of	of	ADP
ejpam-6052	215	12	theorem	theorem	ADJ
ejpam-6052	215	13	2	2	NUM
ejpam-6052	215	14	holds	hold	NOUN
ejpam-6052	215	15	.	.	PUNCT
ejpam-6052	216	1	proposition	proposition	NOUN
ejpam-6052	216	2	4	4	NUM
ejpam-6052	216	3	.	.	PUNCT
ejpam-6052	217	1	if	if	SCONJ
ejpam-6052	217	2	(	(	PUNCT
ejpam-6052	217	3	x	x	X
ejpam-6052	217	4	,	,	PUNCT
ejpam-6052	217	5	∗	∗	NOUN
ejpam-6052	217	6	,	,	PUNCT
ejpam-6052	217	7	◦	◦	NOUN
ejpam-6052	217	8	,	,	PUNCT
ejpam-6052	217	9	0	0	NUM
ejpam-6052	217	10	)	)	PUNCT
ejpam-6052	217	11	is	be	AUX
ejpam-6052	217	12	a	a	DET
ejpam-6052	217	13	0	0	NUM
ejpam-6052	217	14	-	-	PUNCT
ejpam-6052	217	15	commutative	commutative	ADJ
ejpam-6052	217	16	pseudo	pseudo	NOUN
ejpam-6052	217	17	bf	bf	NOUN
ejpam-6052	217	18	-algebra	-algebra	NOUN
ejpam-6052	217	19	,	,	PUNCT
ejpam-6052	217	20	then	then	ADV
ejpam-6052	217	21	it	it	PRON
ejpam-6052	217	22	is	be	AUX
ejpam-6052	217	23	a	a	DET
ejpam-6052	217	24	pseudo	pseudo	NOUN
ejpam-6052	217	25	bn	bn	NOUN
ejpam-6052	217	26	-algebra	-algebra	NOUN
ejpam-6052	217	27	.	.	PUNCT
ejpam-6052	218	1	i.m	i.m	PROPN
ejpam-6052	218	2	.	.	PROPN
ejpam-6052	218	3	antabo	antabo	PROPN
ejpam-6052	218	4	et	et	PROPN
ejpam-6052	218	5	al	al	PROPN
ejpam-6052	218	6	.	.	PUNCT
ejpam-6052	218	7	/	/	SYM
ejpam-6052	218	8	eur	eur	PROPN
ejpam-6052	218	9	.	.	PUNCT
ejpam-6052	219	1	j.	j.	PROPN
ejpam-6052	219	2	pure	pure	PROPN
ejpam-6052	219	3	appl	appl	PROPN
ejpam-6052	219	4	.	.	PROPN
ejpam-6052	219	5	math	math	PROPN
ejpam-6052	219	6	,	,	PUNCT
ejpam-6052	219	7	18	18	NUM
ejpam-6052	219	8	(	(	PUNCT
ejpam-6052	219	9	2	2	NUM
ejpam-6052	219	10	)	)	PUNCT
ejpam-6052	219	11	(	(	PUNCT
ejpam-6052	219	12	2025	2025	NUM
ejpam-6052	219	13	)	)	PUNCT
ejpam-6052	219	14	,	,	PUNCT
ejpam-6052	219	15	6052	6052	NUM
ejpam-6052	219	16	9	9	NUM
ejpam-6052	219	17	of	of	ADP
ejpam-6052	219	18	14	14	NUM
ejpam-6052	219	19	proof	proof	NOUN
ejpam-6052	219	20	.	.	PUNCT
ejpam-6052	220	1	let	let	VERB
ejpam-6052	220	2	x	x	PRON
ejpam-6052	220	3	,	,	PUNCT
ejpam-6052	220	4	y	y	PROPN
ejpam-6052	220	5	,	,	PUNCT
ejpam-6052	220	6	z	z	NOUN
ejpam-6052	220	7	∈	∈	NOUN
ejpam-6052	220	8	x.	x.	NOUN
ejpam-6052	220	9	using	use	VERB
ejpam-6052	220	10	(	(	PUNCT
ejpam-6052	220	11	pbf3	pbf3	PROPN
ejpam-6052	220	12	)	)	PUNCT
ejpam-6052	220	13	,	,	PUNCT
ejpam-6052	220	14	0	0	NUM
ejpam-6052	220	15	-	-	PUNCT
ejpam-6052	220	16	commutativity	commutativity	NOUN
ejpam-6052	220	17	,	,	PUNCT
ejpam-6052	220	18	and	and	CCONJ
ejpam-6052	220	19	(	(	PUNCT
ejpam-6052	220	20	pbn2	pbn2	PROPN
ejpam-6052	220	21	)	)	PUNCT
ejpam-6052	220	22	,	,	PUNCT
ejpam-6052	220	23	we	we	PRON
ejpam-6052	220	24	derive	derive	VERB
ejpam-6052	220	25	:	:	PUNCT
ejpam-6052	220	26	(	(	PUNCT
ejpam-6052	220	27	0	0	NUM
ejpam-6052	220	28	◦	◦	NOUN
ejpam-6052	220	29	z	z	NOUN
ejpam-6052	220	30	)	)	PUNCT
ejpam-6052	220	31	∗	∗	NOUN
ejpam-6052	220	32	(	(	PUNCT
ejpam-6052	220	33	y	y	PROPN
ejpam-6052	220	34	◦	◦	NOUN
ejpam-6052	220	35	x	x	X
ejpam-6052	220	36	)	)	PUNCT
ejpam-6052	220	37	=	=	SYM
ejpam-6052	220	38	(	(	PUNCT
ejpam-6052	220	39	0	0	NUM
ejpam-6052	220	40	◦	◦	NOUN
ejpam-6052	220	41	z	z	NOUN
ejpam-6052	220	42	)	)	PUNCT
ejpam-6052	221	1	∗	∗	NOUN
ejpam-6052	222	1	[	[	X
ejpam-6052	222	2	0	0	NUM
ejpam-6052	222	3	∗	∗	NOUN
ejpam-6052	222	4	(	(	PUNCT
ejpam-6052	222	5	x	x	SYM
ejpam-6052	222	6	◦	◦	VERB
ejpam-6052	222	7	y	y	PROPN
ejpam-6052	222	8	)	)	PUNCT
ejpam-6052	222	9	]	]	PUNCT
ejpam-6052	223	1	=	=	PUNCT
ejpam-6052	223	2	(	(	PUNCT
ejpam-6052	223	3	x	x	SYM
ejpam-6052	223	4	◦	◦	VERB
ejpam-6052	223	5	y	y	NOUN
ejpam-6052	223	6	)	)	PUNCT
ejpam-6052	223	7	∗	∗	NOUN
ejpam-6052	223	8	(	(	PUNCT
ejpam-6052	223	9	z	z	NOUN
ejpam-6052	223	10	◦	◦	NOUN
ejpam-6052	223	11	0	0	NUM
ejpam-6052	223	12	)	)	PUNCT
ejpam-6052	223	13	=	=	PRON
ejpam-6052	224	1	(	(	PUNCT
ejpam-6052	224	2	x	x	SYM
ejpam-6052	224	3	◦	◦	VERB
ejpam-6052	224	4	y	y	NOUN
ejpam-6052	224	5	)	)	PUNCT
ejpam-6052	224	6	∗	∗	NOUN
ejpam-6052	224	7	z.	z.	PROPN
ejpam-6052	224	8	similarly	similarly	ADV
ejpam-6052	224	9	,	,	PUNCT
ejpam-6052	224	10	(	(	PUNCT
ejpam-6052	224	11	0	0	NUM
ejpam-6052	224	12	∗	∗	NOUN
ejpam-6052	224	13	z	z	NOUN
ejpam-6052	224	14	)	)	PUNCT
ejpam-6052	224	15	◦	◦	NOUN
ejpam-6052	224	16	(	(	PUNCT
ejpam-6052	224	17	y	y	PROPN
ejpam-6052	224	18	∗	∗	NOUN
ejpam-6052	224	19	x	x	NOUN
ejpam-6052	224	20	)	)	PUNCT
ejpam-6052	225	1	=	=	SYM
ejpam-6052	225	2	(	(	PUNCT
ejpam-6052	225	3	0	0	NUM
ejpam-6052	225	4	∗	∗	PROPN
ejpam-6052	225	5	z	z	NOUN
ejpam-6052	225	6	)	)	PUNCT
ejpam-6052	225	7	◦	◦	VERB
ejpam-6052	226	1	[	[	X
ejpam-6052	226	2	0	0	NUM
ejpam-6052	226	3	◦	◦	NOUN
ejpam-6052	226	4	(	(	PUNCT
ejpam-6052	226	5	x	x	X
ejpam-6052	226	6	∗	∗	PROPN
ejpam-6052	226	7	y	y	PROPN
ejpam-6052	226	8	)	)	PUNCT
ejpam-6052	226	9	]	]	PUNCT
ejpam-6052	227	1	=	=	PUNCT
ejpam-6052	227	2	(	(	PUNCT
ejpam-6052	227	3	x	x	X
ejpam-6052	227	4	∗	∗	PROPN
ejpam-6052	227	5	y	y	NOUN
ejpam-6052	227	6	)	)	PUNCT
ejpam-6052	227	7	◦	◦	NOUN
ejpam-6052	227	8	(	(	PUNCT
ejpam-6052	227	9	z	z	NOUN
ejpam-6052	227	10	∗	∗	NOUN
ejpam-6052	227	11	0	0	NUM
ejpam-6052	227	12	)	)	PUNCT
ejpam-6052	227	13	=	=	PRON
ejpam-6052	227	14	(	(	PUNCT
ejpam-6052	227	15	x	x	X
ejpam-6052	227	16	∗	∗	PROPN
ejpam-6052	227	17	y	y	NOUN
ejpam-6052	227	18	)	)	PUNCT
ejpam-6052	227	19	◦	◦	NOUN
ejpam-6052	227	20	z.	z.	PROPN
ejpam-6052	227	21	hence	hence	ADV
ejpam-6052	227	22	,	,	PUNCT
ejpam-6052	227	23	(	(	PUNCT
ejpam-6052	227	24	x	x	X
ejpam-6052	227	25	,	,	PUNCT
ejpam-6052	227	26	∗	∗	NOUN
ejpam-6052	227	27	,	,	PUNCT
ejpam-6052	227	28	◦	◦	NOUN
ejpam-6052	227	29	,	,	PUNCT
ejpam-6052	227	30	0	0	NUM
ejpam-6052	227	31	)	)	PUNCT
ejpam-6052	227	32	is	be	AUX
ejpam-6052	227	33	a	a	DET
ejpam-6052	227	34	pseudo	pseudo	NOUN
ejpam-6052	227	35	bn	bn	NOUN
ejpam-6052	227	36	-algebra	-algebra	NOUN
ejpam-6052	227	37	.	.	PUNCT
ejpam-6052	228	1	by	by	ADP
ejpam-6052	228	2	theorem	theorem	NOUN
ejpam-6052	228	3	2	2	NUM
ejpam-6052	228	4	and	and	CCONJ
ejpam-6052	228	5	proposition	proposition	NOUN
ejpam-6052	228	6	4	4	NUM
ejpam-6052	228	7	,	,	PUNCT
ejpam-6052	228	8	we	we	PRON
ejpam-6052	228	9	obtain	obtain	VERB
ejpam-6052	228	10	the	the	DET
ejpam-6052	228	11	following	follow	VERB
ejpam-6052	228	12	result	result	NOUN
ejpam-6052	228	13	.	.	PUNCT
ejpam-6052	229	1	corollary	corollary	ADJ
ejpam-6052	229	2	1	1	NUM
ejpam-6052	229	3	.	.	PUNCT
ejpam-6052	230	1	(	(	PUNCT
ejpam-6052	230	2	x	x	X
ejpam-6052	230	3	,	,	PUNCT
ejpam-6052	230	4	∗	∗	NOUN
ejpam-6052	230	5	,	,	PUNCT
ejpam-6052	230	6	◦	◦	NOUN
ejpam-6052	230	7	,	,	PUNCT
ejpam-6052	230	8	0	0	NUM
ejpam-6052	230	9	)	)	PUNCT
ejpam-6052	230	10	is	be	AUX
ejpam-6052	230	11	a	a	DET
ejpam-6052	230	12	0	0	NUM
ejpam-6052	230	13	-commutative	-commutative	ADJ
ejpam-6052	230	14	pseudo	pseudo	NOUN
ejpam-6052	230	15	bf	bf	NOUN
ejpam-6052	230	16	-algebra	-algebra	NOUN
ejpam-6052	230	17	if	if	SCONJ
ejpam-6052	230	18	and	and	CCONJ
ejpam-6052	230	19	only	only	ADV
ejpam-6052	230	20	if	if	SCONJ
ejpam-6052	230	21	it	it	PRON
ejpam-6052	230	22	is	be	AUX
ejpam-6052	230	23	a	a	DET
ejpam-6052	230	24	pseudo	pseudo	NOUN
ejpam-6052	230	25	bn	bn	NOUN
ejpam-6052	230	26	-algebra	-algebra	NOUN
ejpam-6052	230	27	.	.	PUNCT
ejpam-6052	231	1	3.2	3.2	NUM
ejpam-6052	231	2	.	.	PUNCT
ejpam-6052	232	1	subalgebras	subalgebras	PROPN
ejpam-6052	232	2	and	and	CCONJ
ejpam-6052	232	3	ideals	ideal	NOUN
ejpam-6052	232	4	of	of	ADP
ejpam-6052	232	5	pseudo	pseudo	NOUN
ejpam-6052	232	6	bn	bn	NOUN
ejpam-6052	232	7	-	-	PUNCT
ejpam-6052	232	8	algebras	algebras	NOUN
ejpam-6052	232	9	this	this	DET
ejpam-6052	232	10	subsection	subsection	NOUN
ejpam-6052	232	11	discusses	discuss	VERB
ejpam-6052	232	12	subalgebras	subalgebras	PROPN
ejpam-6052	232	13	and	and	CCONJ
ejpam-6052	232	14	ideals	ideal	NOUN
ejpam-6052	232	15	,	,	PUNCT
ejpam-6052	232	16	exploring	explore	VERB
ejpam-6052	232	17	their	their	PRON
ejpam-6052	232	18	key	key	ADJ
ejpam-6052	232	19	properties	property	NOUN
ejpam-6052	232	20	and	and	CCONJ
ejpam-6052	232	21	the	the	DET
ejpam-6052	232	22	relationships	relationship	NOUN
ejpam-6052	232	23	between	between	ADP
ejpam-6052	232	24	them	they	PRON
ejpam-6052	232	25	.	.	PUNCT
ejpam-6052	233	1	we	we	PRON
ejpam-6052	233	2	examine	examine	VERB
ejpam-6052	233	3	how	how	SCONJ
ejpam-6052	233	4	subalgebras	subalgebra	NOUN
ejpam-6052	233	5	and	and	CCONJ
ejpam-6052	233	6	ideals	ideal	NOUN
ejpam-6052	233	7	interact	interact	VERB
ejpam-6052	233	8	within	within	ADP
ejpam-6052	233	9	algebraic	algebraic	ADJ
ejpam-6052	233	10	structures	structure	NOUN
ejpam-6052	233	11	,	,	PUNCT
ejpam-6052	233	12	highlighting	highlight	VERB
ejpam-6052	233	13	fundamental	fundamental	ADJ
ejpam-6052	233	14	characteristics	characteristic	NOUN
ejpam-6052	233	15	and	and	CCONJ
ejpam-6052	233	16	significant	significant	ADJ
ejpam-6052	233	17	results	result	NOUN
ejpam-6052	233	18	.	.	PUNCT
ejpam-6052	234	1	definition	definition	NOUN
ejpam-6052	234	2	6	6	NUM
ejpam-6052	234	3	.	.	PUNCT
ejpam-6052	235	1	let	let	VERB
ejpam-6052	235	2	(	(	PUNCT
ejpam-6052	235	3	x	x	X
ejpam-6052	235	4	,	,	PUNCT
ejpam-6052	235	5	∗	∗	NOUN
ejpam-6052	235	6	,	,	PUNCT
ejpam-6052	235	7	◦	◦	NOUN
ejpam-6052	235	8	,	,	PUNCT
ejpam-6052	235	9	0	0	NUM
ejpam-6052	235	10	)	)	PUNCT
ejpam-6052	235	11	be	be	AUX
ejpam-6052	235	12	a	a	DET
ejpam-6052	235	13	pseudo	pseudo	NOUN
ejpam-6052	235	14	bn	bn	NOUN
ejpam-6052	235	15	-algebra	-algebra	NOUN
ejpam-6052	235	16	,	,	PUNCT
ejpam-6052	235	17	and	and	CCONJ
ejpam-6052	235	18	let	let	VERB
ejpam-6052	235	19	i	i	PRON
ejpam-6052	235	20	be	be	AUX
ejpam-6052	235	21	a	a	DET
ejpam-6052	235	22	subset	subset	NOUN
ejpam-6052	235	23	of	of	ADP
ejpam-6052	235	24	x	x	PUNCT
ejpam-6052	235	25	containing	contain	VERB
ejpam-6052	235	26	0	0	NUM
ejpam-6052	235	27	.	.	PUNCT
ejpam-6052	236	1	if	if	SCONJ
ejpam-6052	236	2	s	s	NOUN
ejpam-6052	236	3	is	be	AUX
ejpam-6052	236	4	a	a	DET
ejpam-6052	236	5	pseudo	pseudo	NOUN
ejpam-6052	236	6	bn	bn	NOUN
ejpam-6052	236	7	-algebra	-algebra	NOUN
ejpam-6052	236	8	with	with	ADP
ejpam-6052	236	9	respect	respect	NOUN
ejpam-6052	236	10	to	to	ADP
ejpam-6052	236	11	the	the	DET
ejpam-6052	236	12	operations	operation	NOUN
ejpam-6052	236	13	∗	∗	NOUN
ejpam-6052	236	14	and	and	CCONJ
ejpam-6052	236	15	◦	◦	VERB
ejpam-6052	236	16	on	on	ADP
ejpam-6052	236	17	x	x	X
ejpam-6052	236	18	,	,	PUNCT
ejpam-6052	236	19	we	we	PRON
ejpam-6052	236	20	say	say	VERB
ejpam-6052	236	21	that	that	SCONJ
ejpam-6052	236	22	s	s	VERB
ejpam-6052	236	23	is	be	AUX
ejpam-6052	236	24	a	a	DET
ejpam-6052	236	25	subalgebra	subalgebra	NOUN
ejpam-6052	236	26	of	of	ADP
ejpam-6052	236	27	x.	x.	NOUN
ejpam-6052	236	28	theorem	theorem	VERB
ejpam-6052	236	29	4	4	NUM
ejpam-6052	236	30	.	.	PUNCT
ejpam-6052	237	1	let	let	VERB
ejpam-6052	237	2	i	i	PRON
ejpam-6052	237	3	be	be	AUX
ejpam-6052	237	4	a	a	DET
ejpam-6052	237	5	nonempty	nonempty	ADJ
ejpam-6052	237	6	subset	subset	NOUN
ejpam-6052	237	7	of	of	ADP
ejpam-6052	237	8	a	a	DET
ejpam-6052	237	9	pseudo	pseudo	NOUN
ejpam-6052	237	10	bn	bn	NOUN
ejpam-6052	237	11	-algebra	-algebra	NOUN
ejpam-6052	237	12	x.	x.	NOUN
ejpam-6052	238	1	then	then	ADV
ejpam-6052	238	2	i	i	PRON
ejpam-6052	238	3	is	be	AUX
ejpam-6052	238	4	a	a	DET
ejpam-6052	238	5	subalgebra	subalgebra	NOUN
ejpam-6052	238	6	of	of	ADP
ejpam-6052	238	7	x	x	PUNCT
ejpam-6052	238	8	if	if	SCONJ
ejpam-6052	238	9	and	and	CCONJ
ejpam-6052	238	10	only	only	ADV
ejpam-6052	238	11	if	if	SCONJ
ejpam-6052	238	12	x	x	X
ejpam-6052	238	13	∗	∗	VERB
ejpam-6052	238	14	y	y	PROPN
ejpam-6052	238	15	,	,	PUNCT
ejpam-6052	238	16	x	x	VERB
ejpam-6052	238	17	◦	◦	VERB
ejpam-6052	238	18	y	y	PROPN
ejpam-6052	238	19	∈	∈	PROPN
ejpam-6052	239	1	i	i	PRON
ejpam-6052	239	2	,	,	PUNCT
ejpam-6052	239	3	for	for	ADP
ejpam-6052	239	4	all	all	DET
ejpam-6052	239	5	x	x	NOUN
ejpam-6052	239	6	,	,	PUNCT
ejpam-6052	239	7	y	y	PROPN
ejpam-6052	239	8	∈	∈	PROPN
ejpam-6052	239	9	i.	i.	NOUN
ejpam-6052	239	10	proof	proof	PROPN
ejpam-6052	239	11	.	.	PUNCT
ejpam-6052	240	1	suppose	suppose	VERB
ejpam-6052	240	2	i	i	PRON
ejpam-6052	240	3	is	be	AUX
ejpam-6052	240	4	a	a	DET
ejpam-6052	240	5	subalgebra	subalgebra	NOUN
ejpam-6052	240	6	of	of	ADP
ejpam-6052	240	7	x.	x.	NOUN
ejpam-6052	240	8	by	by	ADP
ejpam-6052	240	9	definition	definition	NOUN
ejpam-6052	240	10	,	,	PUNCT
ejpam-6052	240	11	i	i	PRON
ejpam-6052	240	12	must	must	AUX
ejpam-6052	240	13	be	be	AUX
ejpam-6052	240	14	closed	close	VERB
ejpam-6052	240	15	under	under	ADP
ejpam-6052	240	16	the	the	DET
ejpam-6052	240	17	operations	operation	NOUN
ejpam-6052	240	18	of	of	ADP
ejpam-6052	240	19	x	x	PRON
ejpam-6052	240	20	,	,	PUNCT
ejpam-6052	240	21	meaning	mean	VERB
ejpam-6052	240	22	:	:	PUNCT
ejpam-6052	240	23	x	x	SYM
ejpam-6052	240	24	∗	∗	NOUN
ejpam-6052	240	25	y	y	PROPN
ejpam-6052	240	26	∈	∈	PROPN
ejpam-6052	241	1	i	i	PRON
ejpam-6052	241	2	,	,	PUNCT
ejpam-6052	241	3	x	x	VERB
ejpam-6052	241	4	◦	◦	VERB
ejpam-6052	241	5	y	y	PROPN
ejpam-6052	241	6	∈	∈	PROPN
ejpam-6052	242	1	i	i	PRON
ejpam-6052	242	2	,	,	PUNCT
ejpam-6052	242	3	for	for	ADP
ejpam-6052	242	4	all	all	DET
ejpam-6052	242	5	x	x	NOUN
ejpam-6052	242	6	,	,	PUNCT
ejpam-6052	242	7	y	y	PROPN
ejpam-6052	242	8	∈	∈	PROPN
ejpam-6052	242	9	i.	i.	NOUN
ejpam-6052	242	10	conversely	conversely	ADV
ejpam-6052	242	11	,	,	PUNCT
ejpam-6052	242	12	suppose	suppose	VERB
ejpam-6052	242	13	i	i	PRON
ejpam-6052	242	14	is	be	AUX
ejpam-6052	242	15	a	a	DET
ejpam-6052	242	16	nonempty	nonempty	ADJ
ejpam-6052	242	17	subset	subset	NOUN
ejpam-6052	242	18	of	of	ADP
ejpam-6052	242	19	x	x	PUNCT
ejpam-6052	242	20	satisfying	satisfy	VERB
ejpam-6052	242	21	these	these	DET
ejpam-6052	242	22	closure	closure	NOUN
ejpam-6052	242	23	conditions	condition	NOUN
ejpam-6052	242	24	.	.	PUNCT
ejpam-6052	243	1	then	then	ADV
ejpam-6052	243	2	,	,	PUNCT
ejpam-6052	243	3	since	since	SCONJ
ejpam-6052	243	4	i	i	PRON
ejpam-6052	243	5	inherits	inherit	VERB
ejpam-6052	243	6	the	the	DET
ejpam-6052	243	7	algebraic	algebraic	ADJ
ejpam-6052	243	8	structure	structure	NOUN
ejpam-6052	243	9	of	of	ADP
ejpam-6052	243	10	x	x	PUNCT
ejpam-6052	243	11	restricted	restrict	VERB
ejpam-6052	243	12	to	to	ADP
ejpam-6052	243	13	i	i	PRON
ejpam-6052	243	14	,	,	PUNCT
ejpam-6052	243	15	it	it	PRON
ejpam-6052	243	16	follows	follow	VERB
ejpam-6052	243	17	that	that	SCONJ
ejpam-6052	243	18	i	i	PRON
ejpam-6052	243	19	satisfies	satisfy	VERB
ejpam-6052	243	20	the	the	DET
ejpam-6052	243	21	definition	definition	NOUN
ejpam-6052	243	22	of	of	ADP
ejpam-6052	243	23	a	a	DET
ejpam-6052	243	24	subalgebra	subalgebra	NOUN
ejpam-6052	243	25	.	.	PUNCT
ejpam-6052	244	1	example	example	NOUN
ejpam-6052	244	2	13	13	NUM
ejpam-6052	244	3	.	.	PUNCT
ejpam-6052	245	1	given	give	VERB
ejpam-6052	245	2	the	the	DET
ejpam-6052	245	3	pseudo	pseudo	NOUN
ejpam-6052	245	4	bn	bn	NOUN
ejpam-6052	245	5	-algebra	-algebra	NOUN
ejpam-6052	245	6	with	with	ADP
ejpam-6052	245	7	the	the	DET
ejpam-6052	245	8	cayley	cayley	ADJ
ejpam-6052	245	9	table	table	NOUN
ejpam-6052	245	10	found	find	VERB
ejpam-6052	245	11	in	in	ADP
ejpam-6052	245	12	example	example	NOUN
ejpam-6052	245	13	6	6	NUM
ejpam-6052	245	14	.	.	PUNCT
ejpam-6052	246	1	the	the	DET
ejpam-6052	246	2	subalgebras	subalgebra	NOUN
ejpam-6052	246	3	,	,	PUNCT
ejpam-6052	246	4	which	which	PRON
ejpam-6052	246	5	are	be	AUX
ejpam-6052	246	6	closed	close	VERB
ejpam-6052	246	7	under	under	ADP
ejpam-6052	246	8	both	both	DET
ejpam-6052	246	9	operations	operation	NOUN
ejpam-6052	246	10	∗	∗	NOUN
ejpam-6052	246	11	and	and	CCONJ
ejpam-6052	246	12	◦	◦	NOUN
ejpam-6052	246	13	,	,	PUNCT
ejpam-6052	246	14	are	be	AUX
ejpam-6052	246	15	:	:	PUNCT
ejpam-6052	246	16	{	{	PUNCT
ejpam-6052	246	17	0	0	NUM
ejpam-6052	246	18	}	}	PUNCT
ejpam-6052	246	19	,	,	PUNCT
ejpam-6052	246	20	{	{	PUNCT
ejpam-6052	246	21	0	0	NUM
ejpam-6052	246	22	,	,	PUNCT
ejpam-6052	246	23	1	1	NUM
ejpam-6052	246	24	}	}	PUNCT
ejpam-6052	246	25	,	,	PUNCT
ejpam-6052	246	26	{	{	PUNCT
ejpam-6052	246	27	0	0	NUM
ejpam-6052	246	28	,	,	PUNCT
ejpam-6052	246	29	2	2	NUM
ejpam-6052	246	30	}	}	PUNCT
ejpam-6052	246	31	,	,	PUNCT
ejpam-6052	246	32	{	{	PUNCT
ejpam-6052	246	33	0	0	NUM
ejpam-6052	246	34	,	,	PUNCT
ejpam-6052	246	35	3	3	NUM
ejpam-6052	246	36	}	}	PUNCT
ejpam-6052	246	37	,	,	PUNCT
ejpam-6052	246	38	{	{	PUNCT
ejpam-6052	246	39	0	0	NUM
ejpam-6052	246	40	,	,	PUNCT
ejpam-6052	246	41	1	1	NUM
ejpam-6052	246	42	,	,	PUNCT
ejpam-6052	246	43	3	3	NUM
ejpam-6052	246	44	}	}	PUNCT
ejpam-6052	246	45	,	,	PUNCT
ejpam-6052	246	46	{	{	PUNCT
ejpam-6052	246	47	0	0	NUM
ejpam-6052	246	48	,	,	PUNCT
ejpam-6052	246	49	1	1	NUM
ejpam-6052	246	50	,	,	PUNCT
ejpam-6052	246	51	2	2	NUM
ejpam-6052	246	52	,	,	PUNCT
ejpam-6052	246	53	3	3	NUM
ejpam-6052	246	54	}	}	PUNCT
ejpam-6052	246	55	.	.	PUNCT
ejpam-6052	247	1	however	however	ADV
ejpam-6052	247	2	,	,	PUNCT
ejpam-6052	247	3	{	{	PUNCT
ejpam-6052	247	4	0	0	NUM
ejpam-6052	247	5	,	,	PUNCT
ejpam-6052	247	6	1	1	NUM
ejpam-6052	247	7	,	,	PUNCT
ejpam-6052	247	8	2	2	NUM
ejpam-6052	247	9	}	}	PUNCT
ejpam-6052	247	10	is	be	AUX
ejpam-6052	247	11	not	not	PART
ejpam-6052	247	12	a	a	DET
ejpam-6052	247	13	subalgebra	subalgebra	NOUN
ejpam-6052	247	14	since	since	SCONJ
ejpam-6052	247	15	1	1	NUM
ejpam-6052	247	16	◦	◦	NOUN
ejpam-6052	247	17	2	2	NUM
ejpam-6052	247	18	=	=	SYM
ejpam-6052	247	19	3	3	NUM
ejpam-6052	247	20	.	.	PUNCT
ejpam-6052	248	1	also	also	ADV
ejpam-6052	248	2	,	,	PUNCT
ejpam-6052	248	3	{	{	PUNCT
ejpam-6052	248	4	0	0	NUM
ejpam-6052	248	5	,	,	PUNCT
ejpam-6052	248	6	2	2	NUM
ejpam-6052	248	7	,	,	PUNCT
ejpam-6052	248	8	3	3	NUM
ejpam-6052	248	9	}	}	PUNCT
ejpam-6052	248	10	is	be	AUX
ejpam-6052	248	11	not	not	PART
ejpam-6052	248	12	a	a	DET
ejpam-6052	248	13	subalgebra	subalgebra	NOUN
ejpam-6052	248	14	since	since	SCONJ
ejpam-6052	248	15	2	2	NUM
ejpam-6052	248	16	∗	∗	NOUN
ejpam-6052	248	17	3	3	NUM
ejpam-6052	248	18	=	=	SYM
ejpam-6052	248	19	1	1	NUM
ejpam-6052	248	20	.	.	PUNCT
ejpam-6052	248	21	proposition	proposition	NOUN
ejpam-6052	248	22	5	5	NUM
ejpam-6052	248	23	.	.	PUNCT
ejpam-6052	249	1	let	let	VERB
ejpam-6052	249	2	s(x	s(x	PROPN
ejpam-6052	249	3	)	)	PUNCT
ejpam-6052	249	4	denote	denote	VERB
ejpam-6052	249	5	the	the	DET
ejpam-6052	249	6	family	family	NOUN
ejpam-6052	249	7	of	of	ADP
ejpam-6052	249	8	all	all	DET
ejpam-6052	249	9	sub	sub	NOUN
ejpam-6052	249	10	-	-	NOUN
ejpam-6052	249	11	algebras	algebra	NOUN
ejpam-6052	249	12	of	of	ADP
ejpam-6052	249	13	a	a	DET
ejpam-6052	249	14	pseudo	pseudo	NOUN
ejpam-6052	249	15	bn	bn	NOUN
ejpam-6052	249	16	-	-	PUNCT
ejpam-6052	249	17	algebra	algebra	NOUN
ejpam-6052	249	18	x.	x.	NOUN
ejpam-6052	249	19	s(x	s(x	PROPN
ejpam-6052	249	20	)	)	PUNCT
ejpam-6052	249	21	forms	form	VERB
ejpam-6052	249	22	a	a	DET
ejpam-6052	249	23	complete	complete	ADJ
ejpam-6052	249	24	lattice	lattice	NOUN
ejpam-6052	249	25	.	.	PUNCT
ejpam-6052	250	1	i.m	i.m	PROPN
ejpam-6052	250	2	.	.	PROPN
ejpam-6052	250	3	antabo	antabo	PROPN
ejpam-6052	250	4	et	et	PROPN
ejpam-6052	250	5	al	al	PROPN
ejpam-6052	250	6	.	.	PUNCT
ejpam-6052	250	7	/	/	SYM
ejpam-6052	250	8	eur	eur	PROPN
ejpam-6052	250	9	.	.	PUNCT
ejpam-6052	251	1	j.	j.	PROPN
ejpam-6052	251	2	pure	pure	PROPN
ejpam-6052	251	3	appl	appl	PROPN
ejpam-6052	251	4	.	.	PROPN
ejpam-6052	251	5	math	math	PROPN
ejpam-6052	251	6	,	,	PUNCT
ejpam-6052	251	7	18	18	NUM
ejpam-6052	251	8	(	(	PUNCT
ejpam-6052	251	9	2	2	NUM
ejpam-6052	251	10	)	)	PUNCT
ejpam-6052	251	11	(	(	PUNCT
ejpam-6052	251	12	2025	2025	NUM
ejpam-6052	251	13	)	)	PUNCT
ejpam-6052	251	14	,	,	PUNCT
ejpam-6052	251	15	6052	6052	NUM
ejpam-6052	251	16	10	10	NUM
ejpam-6052	251	17	of	of	ADP
ejpam-6052	251	18	14	14	NUM
ejpam-6052	251	19	proof	proof	NOUN
ejpam-6052	251	20	.	.	PUNCT
ejpam-6052	252	1	let	let	VERB
ejpam-6052	252	2	{	{	PUNCT
ejpam-6052	252	3	si}i∈i	si}i∈i	VERB
ejpam-6052	252	4	be	be	AUX
ejpam-6052	252	5	a	a	DET
ejpam-6052	252	6	family	family	NOUN
ejpam-6052	252	7	of	of	ADP
ejpam-6052	252	8	sub	sub	NOUN
ejpam-6052	252	9	-	-	NOUN
ejpam-6052	252	10	algebras	algebra	NOUN
ejpam-6052	252	11	of	of	ADP
ejpam-6052	252	12	pseudo	pseudo	NOUN
ejpam-6052	252	13	bn	bn	NOUN
ejpam-6052	252	14	-	-	NOUN
ejpam-6052	252	15	algebrax	algebrax	NOUN
ejpam-6052	252	16	.	.	PUNCT
ejpam-6052	253	1	then	then	ADV
ejpam-6052	253	2	0	0	NUM
ejpam-6052	253	3	∈	∈	PROPN
ejpam-6052	253	4	⋂	⋂	PROPN
ejpam-6052	253	5	i∈i	i∈i	ADJ
ejpam-6052	253	6	si	si	NOUN
ejpam-6052	253	7	since	since	SCONJ
ejpam-6052	253	8	0	0	NUM
ejpam-6052	253	9	∈	∈	PROPN
ejpam-6052	253	10	si	si	NOUN
ejpam-6052	253	11	for	for	ADP
ejpam-6052	253	12	every	every	DET
ejpam-6052	253	13	i	i	PROPN
ejpam-6052	253	14	∈	∈	PROPN
ejpam-6052	253	15	i.	i.	NOUN
ejpam-6052	253	16	let	let	VERB
ejpam-6052	253	17	us	we	PRON
ejpam-6052	253	18	take	take	VERB
ejpam-6052	253	19	x	x	PRON
ejpam-6052	253	20	,	,	PUNCT
ejpam-6052	253	21	y	y	PROPN
ejpam-6052	253	22	∈	∈	PROPN
ejpam-6052	253	23	x	x	PUNCT
ejpam-6052	253	24	such	such	ADJ
ejpam-6052	253	25	that	that	SCONJ
ejpam-6052	253	26	x	x	SYM
ejpam-6052	253	27	∈	∈	PROPN
ejpam-6052	253	28	⋂	⋂	PROPN
ejpam-6052	253	29	i∈i	i∈i	ADJ
ejpam-6052	253	30	si	si	PROPN
ejpam-6052	253	31	and	and	CCONJ
ejpam-6052	253	32	y	y	PROPN
ejpam-6052	253	33	∈	∈	PROPN
ejpam-6052	253	34	⋂	⋂	PROPN
ejpam-6052	253	35	i∈i	i∈i	ADJ
ejpam-6052	253	36	si	si	PROPN
ejpam-6052	253	37	.	.	PUNCT
ejpam-6052	254	1	this	this	PRON
ejpam-6052	254	2	means	mean	VERB
ejpam-6052	254	3	x	x	X
ejpam-6052	254	4	∈	∈	PROPN
ejpam-6052	254	5	si	si	X
ejpam-6052	254	6	and	and	CCONJ
ejpam-6052	254	7	y	y	PROPN
ejpam-6052	254	8	∈	∈	PROPN
ejpam-6052	254	9	si	si	X
ejpam-6052	254	10	for	for	ADP
ejpam-6052	254	11	each	each	DET
ejpam-6052	254	12	i	i	PROPN
ejpam-6052	254	13	∈	∈	PROPN
ejpam-6052	254	14	i.	i.	NOUN
ejpam-6052	254	15	thus	thus	ADV
ejpam-6052	254	16	x	x	X
ejpam-6052	254	17	∗	∗	VERB
ejpam-6052	254	18	y	y	PROPN
ejpam-6052	254	19	∈	∈	PROPN
ejpam-6052	255	1	si	si	X
ejpam-6052	256	1	for	for	ADP
ejpam-6052	256	2	each	each	DET
ejpam-6052	256	3	i	i	PRON
ejpam-6052	256	4	∈	∈	PROPN
ejpam-6052	256	5	i	i	PRON
ejpam-6052	256	6	because	because	SCONJ
ejpam-6052	256	7	si	si	PROPN
ejpam-6052	256	8	is	be	AUX
ejpam-6052	256	9	a	a	DET
ejpam-6052	256	10	sub	sub	NOUN
ejpam-6052	256	11	-	-	NOUN
ejpam-6052	256	12	algebra	algebra	NOUN
ejpam-6052	256	13	in	in	ADP
ejpam-6052	256	14	x.	x.	NOUN
ejpam-6052	256	15	hence	hence	ADV
ejpam-6052	256	16	x	x	PROPN
ejpam-6052	256	17	∗	∗	NOUN
ejpam-6052	256	18	y	y	PROPN
ejpam-6052	256	19	∈	∈	PROPN
ejpam-6052	256	20	⋂	⋂	PROPN
ejpam-6052	256	21	i∈i	i∈i	ADJ
ejpam-6052	256	22	si	si	AUX
ejpam-6052	256	23	.	.	PROPN
ejpam-6052	256	24	let	let	VERB
ejpam-6052	256	25	y	y	PRON
ejpam-6052	256	26	be	be	AUX
ejpam-6052	256	27	the	the	DET
ejpam-6052	256	28	family	family	NOUN
ejpam-6052	256	29	of	of	ADP
ejpam-6052	256	30	all	all	DET
ejpam-6052	256	31	sub	sub	NOUN
ejpam-6052	256	32	-	-	NOUN
ejpam-6052	256	33	algebras	algebras	ADJ
ejpam-6052	256	34	in	in	ADP
ejpam-6052	256	35	a	a	DET
ejpam-6052	256	36	pseudo	pseudo	NOUN
ejpam-6052	256	37	bn	bn	NOUN
ejpam-6052	256	38	-algebra	-algebra	NOUN
ejpam-6052	256	39	x	x	VERB
ejpam-6052	256	40	that	that	PRON
ejpam-6052	256	41	contain	contain	VERB
ejpam-6052	256	42	⋃	⋃	PUNCT
ejpam-6052	256	43	i∈i	i∈i	ADJ
ejpam-6052	256	44	si	si	NOUN
ejpam-6052	256	45	.	.	PROPN
ejpam-6052	257	1	then	then	ADV
ejpam-6052	257	2	⋂	⋂	PROPN
ejpam-6052	257	3	y	y	PROPN
ejpam-6052	257	4	is	be	AUX
ejpam-6052	257	5	a	a	DET
ejpam-6052	257	6	sub	sub	NOUN
ejpam-6052	257	7	-	-	NOUN
ejpam-6052	257	8	algebra	algebra	NOUN
ejpam-6052	257	9	in	in	ADP
ejpam-6052	257	10	x	x	PUNCT
ejpam-6052	257	11	according	accord	VERB
ejpam-6052	257	12	to	to	ADP
ejpam-6052	257	13	the	the	DET
ejpam-6052	257	14	first	first	ADJ
ejpam-6052	257	15	step	step	NOUN
ejpam-6052	257	16	of	of	ADP
ejpam-6052	257	17	this	this	DET
ejpam-6052	257	18	proof	proof	NOUN
ejpam-6052	257	19	.	.	PUNCT
ejpam-6052	258	1	if	if	SCONJ
ejpam-6052	258	2	we	we	PRON
ejpam-6052	258	3	put∨	put∨	VERB
ejpam-6052	258	4	i∈i	i∈i	ADJ
ejpam-6052	258	5	si	si	X
ejpam-6052	258	6	∧	∧	PROPN
ejpam-6052	258	7	s	s	PART
ejpam-6052	258	8	=	=	SYM
ejpam-6052	258	9	⋂	⋂	PROPN
ejpam-6052	258	10	y	y	PROPN
ejpam-6052	258	11	and	and	CCONJ
ejpam-6052	258	12	∧	∧	PROPN
ejpam-6052	258	13	i∈i	i∈i	ADJ
ejpam-6052	258	14	si	si	PROPN
ejpam-6052	258	15	∨	∨	NUM
ejpam-6052	258	16	s	s	PART
ejpam-6052	258	17	=	=	SYM
ejpam-6052	258	18	⋂	⋂	PROPN
ejpam-6052	258	19	i∈i	i∈i	ADJ
ejpam-6052	258	20	si	si	NOUN
ejpam-6052	258	21	,	,	PUNCT
ejpam-6052	258	22	then	then	ADV
ejpam-6052	258	23	(	(	PUNCT
ejpam-6052	258	24	s(x	s(x	PROPN
ejpam-6052	258	25	)	)	PUNCT
ejpam-6052	258	26	,	,	PUNCT
ejpam-6052	258	27	,	,	PUNCT
ejpam-6052	258	28	∧	∧	PROPN
ejpam-6052	258	29	)	)	PUNCT
ejpam-6052	258	30	is	be	AUX
ejpam-6052	258	31	a	a	DET
ejpam-6052	258	32	complete	complete	ADJ
ejpam-6052	258	33	lattice	lattice	NOUN
ejpam-6052	258	34	.	.	PUNCT
ejpam-6052	259	1	lemma	lemma	PROPN
ejpam-6052	259	2	1	1	X
ejpam-6052	259	3	.	.	PUNCT
ejpam-6052	260	1	let	let	VERB
ejpam-6052	260	2	s	s	PRON
ejpam-6052	260	3	be	be	AUX
ejpam-6052	260	4	a	a	DET
ejpam-6052	260	5	subalgebra	subalgebra	NOUN
ejpam-6052	260	6	of	of	ADP
ejpam-6052	260	7	a	a	DET
ejpam-6052	260	8	pseudo	pseudo	NOUN
ejpam-6052	260	9	bn	bn	NOUN
ejpam-6052	260	10	-algebra	-algebra	NOUN
ejpam-6052	260	11	(	(	PUNCT
ejpam-6052	260	12	x	x	X
ejpam-6052	260	13	,	,	PUNCT
ejpam-6052	260	14	∗	∗	NOUN
ejpam-6052	260	15	,	,	PUNCT
ejpam-6052	260	16	◦	◦	NOUN
ejpam-6052	260	17	,	,	PUNCT
ejpam-6052	260	18	0	0	NUM
ejpam-6052	260	19	)	)	PUNCT
ejpam-6052	260	20	.	.	PUNCT
ejpam-6052	261	1	if	if	SCONJ
ejpam-6052	261	2	x	x	PROPN
ejpam-6052	261	3	∗	∗	VERB
ejpam-6052	261	4	y	y	PROPN
ejpam-6052	261	5	∈	∈	PROPN
ejpam-6052	261	6	s	s	PART
ejpam-6052	261	7	and	and	CCONJ
ejpam-6052	261	8	x	x	PUNCT
ejpam-6052	261	9	◦	◦	NOUN
ejpam-6052	261	10	y	y	PROPN
ejpam-6052	261	11	∈	∈	PROPN
ejpam-6052	261	12	s	s	PROPN
ejpam-6052	261	13	,	,	PUNCT
ejpam-6052	261	14	then	then	ADV
ejpam-6052	261	15	y	y	PROPN
ejpam-6052	261	16	∗	∗	VERB
ejpam-6052	261	17	x	x	PUNCT
ejpam-6052	261	18	∈	∈	NOUN
ejpam-6052	261	19	s	s	X
ejpam-6052	261	20	and	and	CCONJ
ejpam-6052	261	21	y	y	PROPN
ejpam-6052	261	22	◦	◦	NOUN
ejpam-6052	261	23	x	x	SYM
ejpam-6052	261	24	∈	∈	PROPN
ejpam-6052	261	25	s.	s.	PROPN
ejpam-6052	261	26	proof	proof	PROPN
ejpam-6052	261	27	.	.	PUNCT
ejpam-6052	262	1	suppose	suppose	VERB
ejpam-6052	262	2	x	x	X
ejpam-6052	262	3	∗	∗	VERB
ejpam-6052	262	4	y	y	PROPN
ejpam-6052	262	5	∈	∈	PROPN
ejpam-6052	262	6	s	s	PART
ejpam-6052	262	7	and	and	CCONJ
ejpam-6052	262	8	x	x	PUNCT
ejpam-6052	262	9	◦	◦	NOUN
ejpam-6052	262	10	y	y	PROPN
ejpam-6052	262	11	∈	∈	PROPN
ejpam-6052	262	12	s.	s.	PROPN
ejpam-6052	262	13	by	by	ADP
ejpam-6052	262	14	the	the	DET
ejpam-6052	262	15	definition	definition	NOUN
ejpam-6052	262	16	of	of	ADP
ejpam-6052	262	17	a	a	DET
ejpam-6052	262	18	subalgebra	subalgebra	NOUN
ejpam-6052	262	19	,	,	PUNCT
ejpam-6052	262	20	we	we	PRON
ejpam-6052	262	21	have	have	VERB
ejpam-6052	262	22	0	0	NUM
ejpam-6052	262	23	∈	∈	PROPN
ejpam-6052	262	24	s.	s.	PROPN
ejpam-6052	262	25	by	by	ADP
ejpam-6052	262	26	theorem	theorem	ADJ
ejpam-6052	262	27	2	2	NUM
ejpam-6052	262	28	and	and	CCONJ
ejpam-6052	262	29	theorem	theorem	VERB
ejpam-6052	262	30	4	4	NUM
ejpam-6052	262	31	,	,	PUNCT
ejpam-6052	262	32	y	y	PROPN
ejpam-6052	262	33	∗	∗	NOUN
ejpam-6052	262	34	x	x	PUNCT
ejpam-6052	263	1	=	=	SYM
ejpam-6052	263	2	0	0	NUM
ejpam-6052	263	3	◦	◦	NOUN
ejpam-6052	263	4	(	(	PUNCT
ejpam-6052	263	5	x	x	X
ejpam-6052	263	6	∗	∗	PROPN
ejpam-6052	263	7	y	y	NOUN
ejpam-6052	263	8	)	)	PUNCT
ejpam-6052	263	9	∈	∈	PROPN
ejpam-6052	263	10	s	s	PART
ejpam-6052	263	11	and	and	CCONJ
ejpam-6052	263	12	y	y	PROPN
ejpam-6052	263	13	◦	◦	NOUN
ejpam-6052	263	14	x	x	X
ejpam-6052	263	15	=	=	SYM
ejpam-6052	263	16	0	0	NUM
ejpam-6052	263	17	∗	∗	NOUN
ejpam-6052	263	18	(	(	PUNCT
ejpam-6052	263	19	x	x	SYM
ejpam-6052	263	20	◦	◦	NOUN
ejpam-6052	263	21	y	y	NOUN
ejpam-6052	263	22	)	)	PUNCT
ejpam-6052	263	23	∈	∈	PROPN
ejpam-6052	263	24	s.	s.	PROPN
ejpam-6052	264	1	thus	thus	ADV
ejpam-6052	264	2	,	,	PUNCT
ejpam-6052	264	3	y	y	PROPN
ejpam-6052	264	4	∗	∗	NOUN
ejpam-6052	264	5	x	x	PUNCT
ejpam-6052	264	6	∈	∈	NOUN
ejpam-6052	264	7	s	s	X
ejpam-6052	264	8	and	and	CCONJ
ejpam-6052	264	9	y	y	PROPN
ejpam-6052	264	10	◦	◦	NOUN
ejpam-6052	264	11	x	x	SYM
ejpam-6052	264	12	∈	∈	PROPN
ejpam-6052	264	13	s.	s.	PROPN
ejpam-6052	265	1	we	we	PRON
ejpam-6052	265	2	will	will	AUX
ejpam-6052	265	3	now	now	ADV
ejpam-6052	265	4	explore	explore	VERB
ejpam-6052	265	5	ideals	ideal	NOUN
ejpam-6052	265	6	of	of	ADP
ejpam-6052	265	7	pseudo	pseudo	NOUN
ejpam-6052	265	8	bn	bn	NOUN
ejpam-6052	265	9	-algebras	-algebra	NOUN
ejpam-6052	265	10	.	.	PUNCT
ejpam-6052	266	1	in	in	ADP
ejpam-6052	266	2	what	what	PRON
ejpam-6052	266	3	follows	follow	VERB
ejpam-6052	266	4	,	,	PUNCT
ejpam-6052	266	5	we	we	PRON
ejpam-6052	266	6	consider	consider	VERB
ejpam-6052	266	7	x	x	PRON
ejpam-6052	266	8	as	as	ADP
ejpam-6052	266	9	the	the	DET
ejpam-6052	266	10	pseudo	pseudo	NOUN
ejpam-6052	266	11	bn	bn	NOUN
ejpam-6052	266	12	-algebra	-algebra	NOUN
ejpam-6052	266	13	(	(	PUNCT
ejpam-6052	266	14	x	x	X
ejpam-6052	266	15	,	,	PUNCT
ejpam-6052	266	16	∗	∗	NOUN
ejpam-6052	266	17	,	,	PUNCT
ejpam-6052	266	18	◦	◦	NOUN
ejpam-6052	266	19	,	,	PUNCT
ejpam-6052	266	20	0	0	NUM
ejpam-6052	266	21	)	)	PUNCT
ejpam-6052	266	22	.	.	PUNCT
ejpam-6052	267	1	definition	definition	NOUN
ejpam-6052	267	2	7	7	NUM
ejpam-6052	267	3	.	.	PUNCT
ejpam-6052	268	1	the	the	DET
ejpam-6052	268	2	set	set	NOUN
ejpam-6052	268	3	i	i	PRON
ejpam-6052	268	4	is	be	AUX
ejpam-6052	268	5	called	call	VERB
ejpam-6052	268	6	an	an	DET
ejpam-6052	268	7	ideal	ideal	NOUN
ejpam-6052	268	8	of	of	ADP
ejpam-6052	268	9	x	x	PRON
ejpam-6052	268	10	if	if	SCONJ
ejpam-6052	268	11	it	it	PRON
ejpam-6052	268	12	satisfies	satisfy	VERB
ejpam-6052	268	13	the	the	DET
ejpam-6052	268	14	following	following	NOUN
ejpam-6052	268	15	:	:	PUNCT
ejpam-6052	268	16	(	(	PUNCT
ejpam-6052	268	17	pi1	pi1	NOUN
ejpam-6052	268	18	):	):	PUNCT
ejpam-6052	268	19	0	0	NUM
ejpam-6052	268	20	∈	∈	PROPN
ejpam-6052	268	21	i	i	PRON
ejpam-6052	268	22	;	;	PUNCT
ejpam-6052	268	23	(	(	PUNCT
ejpam-6052	268	24	pi2	pi2	NOUN
ejpam-6052	268	25	):	):	PUNCT
ejpam-6052	268	26	x	x	SYM
ejpam-6052	268	27	∗	∗	NOUN
ejpam-6052	268	28	y	y	PROPN
ejpam-6052	268	29	∈	∈	PROPN
ejpam-6052	269	1	i	i	PRON
ejpam-6052	269	2	,	,	PUNCT
ejpam-6052	269	3	x	x	VERB
ejpam-6052	269	4	◦	◦	VERB
ejpam-6052	269	5	y	y	NOUN
ejpam-6052	269	6	∈	∈	PROPN
ejpam-6052	270	1	i	i	PRON
ejpam-6052	270	2	and	and	CCONJ
ejpam-6052	270	3	y	y	PROPN
ejpam-6052	270	4	∈	∈	PROPN
ejpam-6052	271	1	i	i	PRON
ejpam-6052	271	2	imply	imply	VERB
ejpam-6052	271	3	x	x	X
ejpam-6052	271	4	∈	∈	PROPN
ejpam-6052	271	5	i	i	PRON
ejpam-6052	271	6	for	for	ADP
ejpam-6052	271	7	any	any	DET
ejpam-6052	271	8	x	x	NOUN
ejpam-6052	271	9	,	,	PUNCT
ejpam-6052	271	10	y	y	PROPN
ejpam-6052	271	11	∈	∈	PROPN
ejpam-6052	271	12	x.	x.	NOUN
ejpam-6052	272	1	in	in	ADP
ejpam-6052	272	2	example	example	NOUN
ejpam-6052	272	3	6	6	NUM
ejpam-6052	272	4	,	,	PUNCT
ejpam-6052	272	5	the	the	DET
ejpam-6052	272	6	only	only	ADJ
ejpam-6052	272	7	ideals	ideal	NOUN
ejpam-6052	272	8	are	be	AUX
ejpam-6052	272	9	{	{	PUNCT
ejpam-6052	272	10	0	0	NUM
ejpam-6052	272	11	}	}	PUNCT
ejpam-6052	272	12	and	and	CCONJ
ejpam-6052	272	13	{	{	PUNCT
ejpam-6052	272	14	0	0	NUM
ejpam-6052	272	15	,	,	PUNCT
ejpam-6052	272	16	1	1	NUM
ejpam-6052	272	17	,	,	PUNCT
ejpam-6052	272	18	2	2	NUM
ejpam-6052	272	19	,	,	PUNCT
ejpam-6052	272	20	3	3	NUM
ejpam-6052	272	21	}	}	PUNCT
ejpam-6052	272	22	.	.	PUNCT
ejpam-6052	273	1	so	so	ADV
ejpam-6052	273	2	,	,	PUNCT
ejpam-6052	273	3	let	let	VERB
ejpam-6052	273	4	us	we	PRON
ejpam-6052	273	5	consider	consider	VERB
ejpam-6052	273	6	another	another	DET
ejpam-6052	273	7	example	example	NOUN
ejpam-6052	273	8	.	.	PUNCT
ejpam-6052	274	1	example	example	NOUN
ejpam-6052	274	2	14	14	NUM
ejpam-6052	274	3	.	.	PUNCT
ejpam-6052	275	1	define	define	VERB
ejpam-6052	275	2	the	the	DET
ejpam-6052	275	3	operations	operation	NOUN
ejpam-6052	275	4	“	"	PUNCT
ejpam-6052	275	5	∗	∗	NOUN
ejpam-6052	275	6	”	"	PUNCT
ejpam-6052	275	7	and	and	CCONJ
ejpam-6052	275	8	“	"	PUNCT
ejpam-6052	275	9	◦	◦	NOUN
ejpam-6052	275	10	”	"	PUNCT
ejpam-6052	275	11	on	on	ADP
ejpam-6052	275	12	x	x	X
ejpam-6052	275	13	=	=	SYM
ejpam-6052	275	14	{	{	PUNCT
ejpam-6052	275	15	0	0	NUM
ejpam-6052	275	16	,	,	PUNCT
ejpam-6052	275	17	1	1	NUM
ejpam-6052	275	18	,	,	PUNCT
ejpam-6052	275	19	2	2	NUM
ejpam-6052	275	20	,	,	PUNCT
ejpam-6052	275	21	3	3	NUM
ejpam-6052	275	22	,	,	PUNCT
ejpam-6052	275	23	4	4	NUM
ejpam-6052	275	24	}	}	PUNCT
ejpam-6052	275	25	,	,	PUNCT
ejpam-6052	275	26	by	by	ADP
ejpam-6052	275	27	the	the	DET
ejpam-6052	275	28	following	following	ADJ
ejpam-6052	275	29	cayley	cayley	ADJ
ejpam-6052	275	30	tables	table	NOUN
ejpam-6052	275	31	:	:	PUNCT
ejpam-6052	275	32	∗	∗	NOUN
ejpam-6052	275	33	0	0	NUM
ejpam-6052	275	34	1	1	NUM
ejpam-6052	275	35	2	2	NUM
ejpam-6052	275	36	3	3	NUM
ejpam-6052	275	37	4	4	NUM
ejpam-6052	275	38	0	0	NUM
ejpam-6052	275	39	0	0	NUM
ejpam-6052	275	40	1	1	NUM
ejpam-6052	275	41	2	2	NUM
ejpam-6052	275	42	3	3	NUM
ejpam-6052	275	43	4	4	NUM
ejpam-6052	275	44	1	1	NUM
ejpam-6052	275	45	1	1	NUM
ejpam-6052	275	46	0	0	NUM
ejpam-6052	275	47	4	4	NUM
ejpam-6052	275	48	2	2	NUM
ejpam-6052	275	49	3	3	NUM
ejpam-6052	275	50	2	2	NUM
ejpam-6052	275	51	2	2	NUM
ejpam-6052	275	52	4	4	NUM
ejpam-6052	275	53	0	0	NUM
ejpam-6052	275	54	3	3	NUM
ejpam-6052	275	55	0	0	NUM
ejpam-6052	275	56	3	3	NUM
ejpam-6052	275	57	3	3	NUM
ejpam-6052	275	58	2	2	NUM
ejpam-6052	275	59	3	3	NUM
ejpam-6052	275	60	0	0	NUM
ejpam-6052	275	61	2	2	NUM
ejpam-6052	275	62	4	4	NUM
ejpam-6052	275	63	4	4	NUM
ejpam-6052	275	64	3	3	NUM
ejpam-6052	275	65	0	0	NUM
ejpam-6052	275	66	2	2	NUM
ejpam-6052	275	67	0	0	NUM
ejpam-6052	275	68	◦	◦	NOUN
ejpam-6052	275	69	0	0	NUM
ejpam-6052	275	70	1	1	NUM
ejpam-6052	275	71	2	2	NUM
ejpam-6052	275	72	3	3	NUM
ejpam-6052	275	73	4	4	NUM
ejpam-6052	275	74	0	0	NUM
ejpam-6052	275	75	0	0	NUM
ejpam-6052	275	76	1	1	NUM
ejpam-6052	275	77	2	2	NUM
ejpam-6052	275	78	3	3	NUM
ejpam-6052	275	79	4	4	NUM
ejpam-6052	275	80	1	1	NUM
ejpam-6052	275	81	1	1	NUM
ejpam-6052	275	82	0	0	NUM
ejpam-6052	275	83	3	3	NUM
ejpam-6052	275	84	4	4	NUM
ejpam-6052	275	85	2	2	NUM
ejpam-6052	275	86	2	2	NUM
ejpam-6052	275	87	2	2	NUM
ejpam-6052	275	88	3	3	NUM
ejpam-6052	275	89	0	0	NUM
ejpam-6052	275	90	4	4	NUM
ejpam-6052	275	91	1	1	NUM
ejpam-6052	275	92	3	3	NUM
ejpam-6052	275	93	3	3	NUM
ejpam-6052	275	94	4	4	NUM
ejpam-6052	275	95	4	4	NUM
ejpam-6052	275	96	0	0	NUM
ejpam-6052	275	97	2	2	NUM
ejpam-6052	275	98	4	4	NUM
ejpam-6052	275	99	4	4	NUM
ejpam-6052	275	100	2	2	NUM
ejpam-6052	275	101	1	1	NUM
ejpam-6052	275	102	2	2	NUM
ejpam-6052	275	103	0	0	NUM
ejpam-6052	275	104	subset	subset	NOUN
ejpam-6052	275	105	j2	j2	NOUN
ejpam-6052	275	106	=	=	SYM
ejpam-6052	275	107	{	{	PUNCT
ejpam-6052	275	108	0	0	NUM
ejpam-6052	275	109	,	,	PUNCT
ejpam-6052	275	110	2	2	NUM
ejpam-6052	275	111	}	}	PUNCT
ejpam-6052	275	112	is	be	AUX
ejpam-6052	275	113	not	not	PART
ejpam-6052	275	114	an	an	DET
ejpam-6052	275	115	ideal	ideal	NOUN
ejpam-6052	275	116	in	in	ADP
ejpam-6052	275	117	x	x	PUNCT
ejpam-6052	275	118	because	because	SCONJ
ejpam-6052	275	119	,	,	PUNCT
ejpam-6052	275	120	for	for	ADP
ejpam-6052	275	121	example	example	NOUN
ejpam-6052	275	122	,	,	PUNCT
ejpam-6052	275	123	we	we	PRON
ejpam-6052	275	124	have	have	VERB
ejpam-6052	275	125	4	4	NUM
ejpam-6052	275	126	∗	∗	NOUN
ejpam-6052	275	127	2	2	NUM
ejpam-6052	275	128	=	=	SYM
ejpam-6052	275	129	0	0	NUM
ejpam-6052	275	130	∈	∈	PROPN
ejpam-6052	275	131	j2	j2	NOUN
ejpam-6052	275	132	and	and	CCONJ
ejpam-6052	275	133	2	2	NUM
ejpam-6052	275	134	∈	∈	PROPN
ejpam-6052	275	135	j2	j2	NOUN
ejpam-6052	275	136	but	but	CCONJ
ejpam-6052	275	137	4	4	NUM
ejpam-6052	275	138	/∈	/∈	NOUN
ejpam-6052	275	139	j2	j2	PROPN
ejpam-6052	275	140	.	.	PROPN
ejpam-6052	276	1	subset	subset	PROPN
ejpam-6052	276	2	j3	j3	PROPN
ejpam-6052	276	3	=	=	SYM
ejpam-6052	276	4	{	{	PUNCT
ejpam-6052	276	5	0	0	NUM
ejpam-6052	276	6	,	,	PUNCT
ejpam-6052	276	7	3	3	NUM
ejpam-6052	276	8	}	}	PUNCT
ejpam-6052	276	9	is	be	AUX
ejpam-6052	276	10	not	not	PART
ejpam-6052	276	11	an	an	DET
ejpam-6052	276	12	ideal	ideal	NOUN
ejpam-6052	276	13	in	in	ADP
ejpam-6052	276	14	x	x	PUNCT
ejpam-6052	276	15	because	because	SCONJ
ejpam-6052	276	16	,	,	PUNCT
ejpam-6052	276	17	for	for	ADP
ejpam-6052	276	18	example	example	NOUN
ejpam-6052	276	19	,	,	PUNCT
ejpam-6052	276	20	we	we	PRON
ejpam-6052	276	21	have	have	VERB
ejpam-6052	276	22	2	2	NUM
ejpam-6052	276	23	∗	∗	NOUN
ejpam-6052	276	24	3	3	NUM
ejpam-6052	276	25	=	=	SYM
ejpam-6052	276	26	3	3	NUM
ejpam-6052	276	27	∈	∈	PROPN
ejpam-6052	276	28	j3	j3	NOUN
ejpam-6052	276	29	and	and	CCONJ
ejpam-6052	276	30	3	3	NUM
ejpam-6052	276	31	∈	∈	PROPN
ejpam-6052	276	32	j3	j3	NOUN
ejpam-6052	276	33	but	but	CCONJ
ejpam-6052	276	34	2	2	NUM
ejpam-6052	276	35	/∈	/∈	PUNCT
ejpam-6052	276	36	j3	j3	PROPN
ejpam-6052	276	37	.	.	PUNCT
ejpam-6052	277	1	i.m	i.m	PROPN
ejpam-6052	277	2	.	.	PROPN
ejpam-6052	277	3	antabo	antabo	PROPN
ejpam-6052	277	4	et	et	PROPN
ejpam-6052	277	5	al	al	PROPN
ejpam-6052	277	6	.	.	PUNCT
ejpam-6052	277	7	/	/	SYM
ejpam-6052	277	8	eur	eur	PROPN
ejpam-6052	277	9	.	.	PUNCT
ejpam-6052	278	1	j.	j.	PROPN
ejpam-6052	278	2	pure	pure	PROPN
ejpam-6052	278	3	appl	appl	PROPN
ejpam-6052	278	4	.	.	PROPN
ejpam-6052	278	5	math	math	PROPN
ejpam-6052	278	6	,	,	PUNCT
ejpam-6052	278	7	18	18	NUM
ejpam-6052	278	8	(	(	PUNCT
ejpam-6052	278	9	2	2	NUM
ejpam-6052	278	10	)	)	PUNCT
ejpam-6052	278	11	(	(	PUNCT
ejpam-6052	278	12	2025	2025	NUM
ejpam-6052	278	13	)	)	PUNCT
ejpam-6052	278	14	,	,	PUNCT
ejpam-6052	278	15	6052	6052	NUM
ejpam-6052	278	16	11	11	NUM
ejpam-6052	278	17	of	of	ADP
ejpam-6052	278	18	14	14	NUM
ejpam-6052	278	19	subset	subset	NOUN
ejpam-6052	278	20	j4	j4	PROPN
ejpam-6052	278	21	=	=	SYM
ejpam-6052	278	22	{	{	PUNCT
ejpam-6052	278	23	0	0	NUM
ejpam-6052	278	24	,	,	PUNCT
ejpam-6052	278	25	4	4	NUM
ejpam-6052	278	26	}	}	PUNCT
ejpam-6052	278	27	is	be	AUX
ejpam-6052	278	28	not	not	PART
ejpam-6052	278	29	an	an	DET
ejpam-6052	278	30	ideal	ideal	NOUN
ejpam-6052	278	31	in	in	ADP
ejpam-6052	278	32	x	x	PUNCT
ejpam-6052	278	33	because	because	SCONJ
ejpam-6052	278	34	,	,	PUNCT
ejpam-6052	278	35	for	for	ADP
ejpam-6052	278	36	example	example	NOUN
ejpam-6052	278	37	,	,	PUNCT
ejpam-6052	278	38	we	we	PRON
ejpam-6052	278	39	have	have	VERB
ejpam-6052	278	40	2	2	NUM
ejpam-6052	278	41	∗	∗	NOUN
ejpam-6052	278	42	4	4	NUM
ejpam-6052	278	43	=	=	SYM
ejpam-6052	278	44	0	0	NUM
ejpam-6052	278	45	∈	∈	PROPN
ejpam-6052	278	46	j4	j4	NOUN
ejpam-6052	278	47	and	and	CCONJ
ejpam-6052	278	48	4	4	NUM
ejpam-6052	278	49	∈	∈	PROPN
ejpam-6052	278	50	j4	j4	NOUN
ejpam-6052	278	51	but	but	CCONJ
ejpam-6052	278	52	2	2	NUM
ejpam-6052	278	53	/∈	/∈	NOUN
ejpam-6052	278	54	j4	j4	PROPN
ejpam-6052	278	55	.	.	PUNCT
ejpam-6052	278	56	subset	subset	PROPN
ejpam-6052	278	57	j5	j5	PROPN
ejpam-6052	278	58	=	=	PUNCT
ejpam-6052	278	59	{	{	PUNCT
ejpam-6052	278	60	0	0	NUM
ejpam-6052	278	61	,	,	PUNCT
ejpam-6052	278	62	1	1	NUM
ejpam-6052	278	63	,	,	PUNCT
ejpam-6052	278	64	2	2	NUM
ejpam-6052	278	65	}	}	PUNCT
ejpam-6052	278	66	is	be	AUX
ejpam-6052	278	67	not	not	PART
ejpam-6052	278	68	an	an	DET
ejpam-6052	278	69	ideal	ideal	NOUN
ejpam-6052	278	70	in	in	ADP
ejpam-6052	278	71	x	x	PUNCT
ejpam-6052	278	72	because	because	SCONJ
ejpam-6052	278	73	,	,	PUNCT
ejpam-6052	278	74	for	for	ADP
ejpam-6052	278	75	example	example	NOUN
ejpam-6052	278	76	,	,	PUNCT
ejpam-6052	278	77	we	we	PRON
ejpam-6052	278	78	have	have	VERB
ejpam-6052	278	79	3	3	NUM
ejpam-6052	278	80	∗	∗	NOUN
ejpam-6052	278	81	2	2	NUM
ejpam-6052	278	82	=	=	SYM
ejpam-6052	278	83	1	1	NUM
ejpam-6052	278	84	∈	∈	PROPN
ejpam-6052	278	85	j5	j5	NOUN
ejpam-6052	278	86	and	and	CCONJ
ejpam-6052	278	87	2	2	NUM
ejpam-6052	278	88	∈	∈	PROPN
ejpam-6052	278	89	j5	j5	NOUN
ejpam-6052	278	90	but	but	CCONJ
ejpam-6052	278	91	3	3	NUM
ejpam-6052	278	92	/∈	/∈	SYM
ejpam-6052	278	93	j5	j5	PROPN
ejpam-6052	278	94	.	.	PROPN
ejpam-6052	279	1	subset	subset	PROPN
ejpam-6052	279	2	j6	j6	PROPN
ejpam-6052	279	3	=	=	PUNCT
ejpam-6052	279	4	{	{	PUNCT
ejpam-6052	279	5	0	0	NUM
ejpam-6052	279	6	,	,	PUNCT
ejpam-6052	279	7	1	1	NUM
ejpam-6052	279	8	,	,	PUNCT
ejpam-6052	279	9	3	3	NUM
ejpam-6052	279	10	}	}	PUNCT
ejpam-6052	279	11	is	be	AUX
ejpam-6052	279	12	not	not	PART
ejpam-6052	279	13	an	an	DET
ejpam-6052	279	14	ideal	ideal	NOUN
ejpam-6052	279	15	in	in	ADP
ejpam-6052	279	16	x	x	PUNCT
ejpam-6052	279	17	because	because	SCONJ
ejpam-6052	279	18	,	,	PUNCT
ejpam-6052	279	19	for	for	ADP
ejpam-6052	279	20	example	example	NOUN
ejpam-6052	279	21	,	,	PUNCT
ejpam-6052	279	22	we	we	PRON
ejpam-6052	279	23	have	have	VERB
ejpam-6052	279	24	4	4	NUM
ejpam-6052	279	25	∗	∗	NOUN
ejpam-6052	279	26	1	1	NUM
ejpam-6052	279	27	=	=	SYM
ejpam-6052	279	28	3	3	NUM
ejpam-6052	279	29	∈	∈	PROPN
ejpam-6052	279	30	j6	j6	PROPN
ejpam-6052	279	31	and	and	CCONJ
ejpam-6052	279	32	1	1	NUM
ejpam-6052	279	33	∈	∈	PROPN
ejpam-6052	279	34	j6	j6	PROPN
ejpam-6052	279	35	but	but	CCONJ
ejpam-6052	279	36	4	4	NUM
ejpam-6052	279	37	/∈	/∈	PUNCT
ejpam-6052	279	38	j6	j6	PROPN
ejpam-6052	279	39	.	.	PUNCT
ejpam-6052	280	1	the	the	DET
ejpam-6052	280	2	subsets	subset	NOUN
ejpam-6052	280	3	{	{	PUNCT
ejpam-6052	280	4	0	0	NUM
ejpam-6052	280	5	,	,	PUNCT
ejpam-6052	280	6	1	1	NUM
ejpam-6052	280	7	,	,	PUNCT
ejpam-6052	280	8	4	4	NUM
ejpam-6052	280	9	}	}	PUNCT
ejpam-6052	280	10	,	,	PUNCT
ejpam-6052	280	11	{	{	PUNCT
ejpam-6052	280	12	0	0	NUM
ejpam-6052	280	13	,	,	PUNCT
ejpam-6052	280	14	2	2	NUM
ejpam-6052	280	15	,	,	PUNCT
ejpam-6052	280	16	3	3	NUM
ejpam-6052	280	17	}	}	PUNCT
ejpam-6052	280	18	,	,	PUNCT
ejpam-6052	280	19	{	{	PUNCT
ejpam-6052	280	20	0	0	NUM
ejpam-6052	280	21	,	,	PUNCT
ejpam-6052	280	22	2	2	NUM
ejpam-6052	280	23	,	,	PUNCT
ejpam-6052	280	24	4	4	NUM
ejpam-6052	280	25	}	}	PUNCT
ejpam-6052	280	26	,	,	PUNCT
ejpam-6052	280	27	and	and	CCONJ
ejpam-6052	280	28	{	{	PUNCT
ejpam-6052	280	29	0	0	NUM
ejpam-6052	280	30	,	,	PUNCT
ejpam-6052	280	31	3	3	NUM
ejpam-6052	280	32	,	,	PUNCT
ejpam-6052	280	33	4	4	NUM
ejpam-6052	280	34	}	}	PUNCT
ejpam-6052	280	35	are	be	AUX
ejpam-6052	280	36	not	not	PART
ejpam-6052	280	37	ideals	ideal	NOUN
ejpam-6052	280	38	in	in	ADP
ejpam-6052	280	39	x	x	PUNCT
ejpam-6052	280	40	either	either	ADV
ejpam-6052	280	41	.	.	PUNCT
ejpam-6052	281	1	then	then	ADV
ejpam-6052	281	2	(	(	PUNCT
ejpam-6052	281	3	x	x	X
ejpam-6052	281	4	,	,	PUNCT
ejpam-6052	281	5	∗	∗	NOUN
ejpam-6052	281	6	,	,	PUNCT
ejpam-6052	281	7	◦	◦	NOUN
ejpam-6052	281	8	,	,	PUNCT
ejpam-6052	281	9	0	0	NUM
ejpam-6052	281	10	)	)	PUNCT
ejpam-6052	281	11	is	be	AUX
ejpam-6052	281	12	a	a	DET
ejpam-6052	281	13	pseudo	pseudo	NOUN
ejpam-6052	281	14	bn	bn	NOUN
ejpam-6052	281	15	-algebra	-algebra	NOUN
ejpam-6052	281	16	.	.	PUNCT
ejpam-6052	282	1	now	now	ADV
ejpam-6052	282	2	,	,	PUNCT
ejpam-6052	282	3	the	the	DET
ejpam-6052	282	4	ideals	ideal	NOUN
ejpam-6052	282	5	are	be	AUX
ejpam-6052	282	6	{	{	PUNCT
ejpam-6052	282	7	0	0	NUM
ejpam-6052	282	8	}	}	PUNCT
ejpam-6052	282	9	,	,	PUNCT
ejpam-6052	282	10	{	{	PUNCT
ejpam-6052	282	11	0	0	NUM
ejpam-6052	282	12	,	,	PUNCT
ejpam-6052	282	13	1	1	NUM
ejpam-6052	282	14	}	}	PUNCT
ejpam-6052	282	15	,	,	PUNCT
ejpam-6052	282	16	{	{	PUNCT
ejpam-6052	282	17	0	0	NUM
ejpam-6052	282	18	,	,	PUNCT
ejpam-6052	282	19	2	2	NUM
ejpam-6052	282	20	}	}	PUNCT
ejpam-6052	282	21	,	,	PUNCT
ejpam-6052	282	22	{	{	PUNCT
ejpam-6052	282	23	0	0	NUM
ejpam-6052	282	24	,	,	PUNCT
ejpam-6052	282	25	3	3	NUM
ejpam-6052	282	26	}	}	PUNCT
ejpam-6052	282	27	,	,	PUNCT
ejpam-6052	282	28	{	{	PUNCT
ejpam-6052	282	29	0	0	NUM
ejpam-6052	282	30	,	,	PUNCT
ejpam-6052	282	31	4	4	NUM
ejpam-6052	282	32	}	}	PUNCT
ejpam-6052	282	33	,	,	PUNCT
ejpam-6052	282	34	{	{	PUNCT
ejpam-6052	282	35	0	0	NUM
ejpam-6052	282	36	,	,	PUNCT
ejpam-6052	282	37	1	1	NUM
ejpam-6052	282	38	,	,	PUNCT
ejpam-6052	282	39	3	3	NUM
ejpam-6052	282	40	}	}	PUNCT
ejpam-6052	282	41	,	,	PUNCT
ejpam-6052	282	42	and	and	CCONJ
ejpam-6052	282	43	x.	x.	NOUN
ejpam-6052	282	44	remark	remark	NOUN
ejpam-6052	282	45	5	5	NUM
ejpam-6052	282	46	.	.	PUNCT
ejpam-6052	282	47	{	{	PUNCT
ejpam-6052	282	48	0	0	NUM
ejpam-6052	282	49	}	}	PUNCT
ejpam-6052	282	50	and	and	CCONJ
ejpam-6052	282	51	x	x	PRON
ejpam-6052	282	52	are	be	AUX
ejpam-6052	282	53	always	always	ADV
ejpam-6052	282	54	ideals	ideal	NOUN
ejpam-6052	282	55	of	of	ADP
ejpam-6052	282	56	x.	x.	NOUN
ejpam-6052	282	57	proposition	proposition	NOUN
ejpam-6052	282	58	6	6	NUM
ejpam-6052	282	59	.	.	PUNCT
ejpam-6052	283	1	let	let	AUX
ejpam-6052	283	2	j(x	j(x	NOUN
ejpam-6052	283	3	)	)	PUNCT
ejpam-6052	283	4	denote	denote	VERB
ejpam-6052	283	5	the	the	DET
ejpam-6052	283	6	family	family	NOUN
ejpam-6052	283	7	of	of	ADP
ejpam-6052	283	8	all	all	DET
ejpam-6052	283	9	ideals	ideal	NOUN
ejpam-6052	283	10	of	of	ADP
ejpam-6052	283	11	a	a	DET
ejpam-6052	283	12	pseudo	pseudo	NOUN
ejpam-6052	283	13	bn	bn	NOUN
ejpam-6052	283	14	-	-	PUNCT
ejpam-6052	283	15	algebra	algebra	NOUN
ejpam-6052	283	16	x.	x.	NOUN
ejpam-6052	283	17	j(x	j(x	PROPN
ejpam-6052	283	18	)	)	PUNCT
ejpam-6052	283	19	forms	form	VERB
ejpam-6052	283	20	a	a	DET
ejpam-6052	283	21	complete	complete	ADJ
ejpam-6052	283	22	lattice	lattice	NOUN
ejpam-6052	283	23	.	.	PUNCT
ejpam-6052	284	1	proof	proof	NOUN
ejpam-6052	284	2	.	.	PUNCT
ejpam-6052	285	1	analogous	analogous	ADJ
ejpam-6052	285	2	to	to	ADP
ejpam-6052	285	3	the	the	DET
ejpam-6052	285	4	proof	proof	NOUN
ejpam-6052	285	5	of	of	ADP
ejpam-6052	285	6	proposition	proposition	NOUN
ejpam-6052	285	7	5	5	NUM
ejpam-6052	285	8	.	.	X
ejpam-6052	285	9	letx	letx	PROPN
ejpam-6052	285	10	be	be	AUX
ejpam-6052	285	11	a	a	DET
ejpam-6052	285	12	pseudo	pseudo	NOUN
ejpam-6052	285	13	bn	bn	NOUN
ejpam-6052	285	14	-	-	PUNCT
ejpam-6052	285	15	algebra	algebra	NOUN
ejpam-6052	285	16	as	as	ADP
ejpam-6052	285	17	in	in	ADP
ejpam-6052	285	18	example	example	NOUN
ejpam-6052	285	19	14	14	NUM
ejpam-6052	285	20	.	.	PUNCT
ejpam-6052	286	1	the	the	DET
ejpam-6052	286	2	subsets	subset	NOUN
ejpam-6052	286	3	{	{	PUNCT
ejpam-6052	286	4	0	0	NUM
ejpam-6052	286	5	}	}	PUNCT
ejpam-6052	286	6	,	,	PUNCT
ejpam-6052	286	7	{	{	PUNCT
ejpam-6052	286	8	0	0	NUM
ejpam-6052	286	9	,	,	PUNCT
ejpam-6052	286	10	1	1	NUM
ejpam-6052	286	11	}	}	PUNCT
ejpam-6052	286	12	,	,	PUNCT
ejpam-6052	286	13	{	{	PUNCT
ejpam-6052	286	14	0	0	NUM
ejpam-6052	286	15	,	,	PUNCT
ejpam-6052	286	16	2	2	NUM
ejpam-6052	286	17	}	}	PUNCT
ejpam-6052	286	18	,	,	PUNCT
ejpam-6052	286	19	{	{	PUNCT
ejpam-6052	286	20	0	0	NUM
ejpam-6052	286	21	,	,	PUNCT
ejpam-6052	286	22	3	3	NUM
ejpam-6052	286	23	}	}	PUNCT
ejpam-6052	286	24	,	,	PUNCT
ejpam-6052	286	25	and	and	CCONJ
ejpam-6052	286	26	{	{	PUNCT
ejpam-6052	286	27	0	0	NUM
ejpam-6052	286	28	,	,	PUNCT
ejpam-6052	286	29	4	4	NUM
ejpam-6052	286	30	}	}	PUNCT
ejpam-6052	286	31	are	be	AUX
ejpam-6052	286	32	sub	sub	NOUN
ejpam-6052	286	33	-	-	ADJ
ejpam-6052	286	34	algebras	algebras	ADJ
ejpam-6052	286	35	in	in	ADP
ejpam-6052	286	36	x	x	PRON
ejpam-6052	286	37	,	,	PUNCT
ejpam-6052	286	38	while	while	SCONJ
ejpam-6052	286	39	the	the	DET
ejpam-6052	286	40	subsets	subset	NOUN
ejpam-6052	286	41	{	{	PUNCT
ejpam-6052	286	42	0	0	NUM
ejpam-6052	286	43	,	,	PUNCT
ejpam-6052	286	44	1	1	NUM
ejpam-6052	286	45	,	,	PUNCT
ejpam-6052	286	46	2	2	NUM
ejpam-6052	286	47	}	}	PUNCT
ejpam-6052	286	48	,	,	PUNCT
ejpam-6052	286	49	{	{	PUNCT
ejpam-6052	286	50	0	0	NUM
ejpam-6052	286	51	,	,	PUNCT
ejpam-6052	286	52	1	1	NUM
ejpam-6052	286	53	,	,	PUNCT
ejpam-6052	286	54	3	3	NUM
ejpam-6052	286	55	}	}	PUNCT
ejpam-6052	286	56	,	,	PUNCT
ejpam-6052	286	57	{	{	PUNCT
ejpam-6052	286	58	0	0	NUM
ejpam-6052	286	59	,	,	PUNCT
ejpam-6052	286	60	1	1	NUM
ejpam-6052	286	61	,	,	PUNCT
ejpam-6052	286	62	4	4	NUM
ejpam-6052	286	63	}	}	PUNCT
ejpam-6052	286	64	,	,	PUNCT
ejpam-6052	286	65	{	{	PUNCT
ejpam-6052	286	66	0	0	NUM
ejpam-6052	286	67	,	,	PUNCT
ejpam-6052	286	68	2	2	NUM
ejpam-6052	286	69	,	,	PUNCT
ejpam-6052	286	70	3	3	NUM
ejpam-6052	286	71	}	}	PUNCT
ejpam-6052	286	72	,	,	PUNCT
ejpam-6052	286	73	{	{	PUNCT
ejpam-6052	286	74	0	0	NUM
ejpam-6052	286	75	,	,	PUNCT
ejpam-6052	286	76	2	2	NUM
ejpam-6052	286	77	,	,	PUNCT
ejpam-6052	286	78	4	4	NUM
ejpam-6052	286	79	}	}	PUNCT
ejpam-6052	286	80	,	,	PUNCT
ejpam-6052	286	81	and	and	CCONJ
ejpam-6052	286	82	{	{	PUNCT
ejpam-6052	286	83	0	0	NUM
ejpam-6052	286	84	,	,	PUNCT
ejpam-6052	286	85	3	3	NUM
ejpam-6052	286	86	,	,	PUNCT
ejpam-6052	286	87	4	4	NUM
ejpam-6052	286	88	}	}	PUNCT
ejpam-6052	286	89	are	be	AUX
ejpam-6052	286	90	not	not	PART
ejpam-6052	286	91	.	.	PUNCT
ejpam-6052	287	1	remark	remark	VERB
ejpam-6052	287	2	6	6	NUM
ejpam-6052	287	3	.	.	PUNCT
ejpam-6052	288	1	sub	sub	NOUN
ejpam-6052	288	2	-	-	NOUN
ejpam-6052	288	3	algebra	algebra	NOUN
ejpam-6052	288	4	of	of	ADP
ejpam-6052	288	5	x	x	PUNCT
ejpam-6052	288	6	need	need	AUX
ejpam-6052	288	7	not	not	PART
ejpam-6052	288	8	be	be	AUX
ejpam-6052	288	9	an	an	DET
ejpam-6052	288	10	ideal	ideal	NOUN
ejpam-6052	288	11	in	in	ADP
ejpam-6052	288	12	x	x	PRON
ejpam-6052	288	13	,	,	PUNCT
ejpam-6052	288	14	as	as	SCONJ
ejpam-6052	288	15	shown	show	VERB
ejpam-6052	288	16	in	in	ADP
ejpam-6052	288	17	example	example	NOUN
ejpam-6052	288	18	14	14	NUM
ejpam-6052	288	19	.	.	PUNCT
ejpam-6052	289	1	for	for	ADP
ejpam-6052	289	2	example	example	NOUN
ejpam-6052	289	3	,	,	PUNCT
ejpam-6052	289	4	the	the	DET
ejpam-6052	289	5	sub	sub	NOUN
ejpam-6052	289	6	-	-	NOUN
ejpam-6052	289	7	algebra	algebra	ADJ
ejpam-6052	289	8	{	{	PUNCT
ejpam-6052	289	9	0	0	NUM
ejpam-6052	289	10	,	,	PUNCT
ejpam-6052	289	11	2	2	NUM
ejpam-6052	289	12	}	}	PUNCT
ejpam-6052	289	13	in	in	ADP
ejpam-6052	289	14	x	x	PRON
ejpam-6052	289	15	is	be	AUX
ejpam-6052	289	16	not	not	PART
ejpam-6052	289	17	an	an	DET
ejpam-6052	289	18	ideal	ideal	NOUN
ejpam-6052	289	19	in	in	ADP
ejpam-6052	289	20	x	x	NOUN
ejpam-6052	289	21	,	,	PUNCT
ejpam-6052	289	22	and	and	CCONJ
ejpam-6052	289	23	vice	vice	ADV
ejpam-6052	289	24	versa	versa	ADV
ejpam-6052	289	25	.	.	PUNCT
ejpam-6052	290	1	definition	definition	NOUN
ejpam-6052	290	2	8	8	NUM
ejpam-6052	290	3	.	.	PUNCT
ejpam-6052	291	1	a	a	DET
ejpam-6052	291	2	nonempty	nonempty	NOUN
ejpam-6052	291	3	subset	subset	VERB
ejpam-6052	291	4	n	n	PROPN
ejpam-6052	291	5	of	of	ADP
ejpam-6052	291	6	x	x	VERB
ejpam-6052	291	7	is	be	AUX
ejpam-6052	291	8	said	say	VERB
ejpam-6052	291	9	to	to	PART
ejpam-6052	291	10	be	be	AUX
ejpam-6052	291	11	pseudo	pseudo	NOUN
ejpam-6052	291	12	-	-	ADJ
ejpam-6052	291	13	normal	normal	ADJ
ejpam-6052	291	14	if	if	SCONJ
ejpam-6052	291	15	it	it	PRON
ejpam-6052	291	16	satisfies	satisfy	VERB
ejpam-6052	291	17	the	the	DET
ejpam-6052	291	18	following	follow	VERB
ejpam-6052	291	19	conditions	condition	NOUN
ejpam-6052	291	20	:	:	PUNCT
ejpam-6052	291	21	(	(	PUNCT
ejpam-6052	291	22	i	i	NOUN
ejpam-6052	291	23	)	)	PUNCT
ejpam-6052	291	24	if	if	SCONJ
ejpam-6052	291	25	x	x	PROPN
ejpam-6052	291	26	∗	∗	PROPN
ejpam-6052	291	27	y	y	PROPN
ejpam-6052	291	28	,	,	PUNCT
ejpam-6052	291	29	a	a	DET
ejpam-6052	291	30	∗	∗	NOUN
ejpam-6052	291	31	b	b	NOUN
ejpam-6052	291	32	∈	∈	PROPN
ejpam-6052	291	33	n	n	NOUN
ejpam-6052	291	34	,	,	PUNCT
ejpam-6052	291	35	then	then	ADV
ejpam-6052	291	36	(	(	PUNCT
ejpam-6052	291	37	x	x	SYM
ejpam-6052	291	38	∗	∗	NOUN
ejpam-6052	291	39	a	a	PRON
ejpam-6052	291	40	)	)	PUNCT
ejpam-6052	291	41	◦	◦	NOUN
ejpam-6052	291	42	(	(	PUNCT
ejpam-6052	291	43	y	y	PROPN
ejpam-6052	291	44	∗	∗	NOUN
ejpam-6052	291	45	b	b	NOUN
ejpam-6052	291	46	)	)	PUNCT
ejpam-6052	291	47	∈	∈	PROPN
ejpam-6052	291	48	n.	n.	NOUN
ejpam-6052	291	49	(	(	PUNCT
ejpam-6052	291	50	ii	ii	NOUN
ejpam-6052	291	51	)	)	PUNCT
ejpam-6052	291	52	if	if	SCONJ
ejpam-6052	291	53	x	x	PART
ejpam-6052	291	54	◦	◦	NOUN
ejpam-6052	291	55	y	y	PROPN
ejpam-6052	291	56	,	,	PUNCT
ejpam-6052	291	57	a	a	DET
ejpam-6052	291	58	◦	◦	NOUN
ejpam-6052	291	59	b	b	NOUN
ejpam-6052	291	60	∈	∈	NOUN
ejpam-6052	291	61	n	n	NOUN
ejpam-6052	291	62	,	,	PUNCT
ejpam-6052	291	63	then	then	ADV
ejpam-6052	291	64	(	(	PUNCT
ejpam-6052	291	65	x	x	X
ejpam-6052	291	66	◦	◦	VERB
ejpam-6052	291	67	a	a	X
ejpam-6052	291	68	)	)	PUNCT
ejpam-6052	291	69	∗	∗	NOUN
ejpam-6052	291	70	(	(	PUNCT
ejpam-6052	291	71	y	y	PROPN
ejpam-6052	291	72	◦	◦	NOUN
ejpam-6052	291	73	b	b	NUM
ejpam-6052	291	74	)	)	PUNCT
ejpam-6052	291	75	∈	∈	PROPN
ejpam-6052	291	76	n.	n.	NOUN
ejpam-6052	291	77	since	since	SCONJ
ejpam-6052	291	78	n	n	ADV
ejpam-6052	291	79	is	be	AUX
ejpam-6052	291	80	pseudo	pseudo	NOUN
ejpam-6052	291	81	-	-	ADJ
ejpam-6052	291	82	normal	normal	ADJ
ejpam-6052	291	83	,	,	PUNCT
ejpam-6052	291	84	any	any	DET
ejpam-6052	291	85	element	element	NOUN
ejpam-6052	291	86	x	x	SYM
ejpam-6052	291	87	∈	∈	NOUN
ejpam-6052	291	88	n	n	PRON
ejpam-6052	291	89	satisfies	satisfy	VERB
ejpam-6052	291	90	x	x	X
ejpam-6052	291	91	∗	∗	NOUN
ejpam-6052	291	92	0	0	NUM
ejpam-6052	292	1	=	=	SYM
ejpam-6052	292	2	x	x	SYM
ejpam-6052	292	3	∈	∈	PROPN
ejpam-6052	292	4	n	n	X
ejpam-6052	292	5	by	by	ADP
ejpam-6052	292	6	pbn2	pbn2	NOUN
ejpam-6052	292	7	.	.	PUNCT
ejpam-6052	293	1	furthermore	furthermore	ADV
ejpam-6052	293	2	,	,	PUNCT
ejpam-6052	293	3	using	use	VERB
ejpam-6052	293	4	pbn1	pbn1	NOUN
ejpam-6052	293	5	,	,	PUNCT
ejpam-6052	293	6	we	we	PRON
ejpam-6052	293	7	obtain	obtain	VERB
ejpam-6052	293	8	0	0	NUM
ejpam-6052	294	1	=	=	SYM
ejpam-6052	294	2	0	0	NUM
ejpam-6052	294	3	◦	◦	NOUN
ejpam-6052	294	4	0	0	NUM
ejpam-6052	295	1	=	=	SYM
ejpam-6052	295	2	(	(	PUNCT
ejpam-6052	295	3	x	x	X
ejpam-6052	295	4	∗	∗	NOUN
ejpam-6052	295	5	x	x	NOUN
ejpam-6052	295	6	)	)	PUNCT
ejpam-6052	295	7	◦	◦	NOUN
ejpam-6052	295	8	(	(	PUNCT
ejpam-6052	295	9	0	0	NUM
ejpam-6052	295	10	∗	∗	NOUN
ejpam-6052	295	11	0	0	NUM
ejpam-6052	295	12	)	)	PUNCT
ejpam-6052	295	13	.	.	PUNCT
ejpam-6052	296	1	but	but	CCONJ
ejpam-6052	296	2	(	(	PUNCT
ejpam-6052	296	3	x	x	X
ejpam-6052	296	4	∗	∗	NOUN
ejpam-6052	296	5	x	x	NOUN
ejpam-6052	296	6	)	)	PUNCT
ejpam-6052	296	7	◦	◦	NOUN
ejpam-6052	296	8	(	(	PUNCT
ejpam-6052	296	9	0	0	NUM
ejpam-6052	296	10	∗	∗	NOUN
ejpam-6052	296	11	0	0	NUM
ejpam-6052	296	12	)	)	PUNCT
ejpam-6052	296	13	∈	∈	PROPN
ejpam-6052	296	14	b	b	PROPN
ejpam-6052	296	15	by	by	ADP
ejpam-6052	296	16	pseudo	pseudo	NOUN
ejpam-6052	296	17	-	-	NOUN
ejpam-6052	296	18	normality	normality	NOUN
ejpam-6052	296	19	of	of	ADP
ejpam-6052	296	20	n	n	PRON
ejpam-6052	296	21	which	which	PRON
ejpam-6052	296	22	implies	imply	VERB
ejpam-6052	296	23	that	that	SCONJ
ejpam-6052	296	24	0	0	NUM
ejpam-6052	296	25	∈	∈	PROPN
ejpam-6052	296	26	n	n	NOUN
ejpam-6052	296	27	.	.	PUNCT
ejpam-6052	297	1	this	this	PRON
ejpam-6052	297	2	leads	lead	VERB
ejpam-6052	297	3	us	we	PRON
ejpam-6052	297	4	to	to	ADP
ejpam-6052	297	5	the	the	DET
ejpam-6052	297	6	following	follow	VERB
ejpam-6052	297	7	observation	observation	NOUN
ejpam-6052	297	8	.	.	PUNCT
ejpam-6052	298	1	remark	remark	PROPN
ejpam-6052	298	2	7	7	NUM
ejpam-6052	298	3	.	.	PUNCT
ejpam-6052	299	1	if	if	SCONJ
ejpam-6052	299	2	n	n	PRON
ejpam-6052	299	3	is	be	AUX
ejpam-6052	299	4	pseudo	pseudo	NOUN
ejpam-6052	299	5	-	-	ADJ
ejpam-6052	299	6	normal	normal	ADJ
ejpam-6052	299	7	,	,	PUNCT
ejpam-6052	299	8	then	then	ADV
ejpam-6052	299	9	0	0	NUM
ejpam-6052	299	10	∈	∈	PROPN
ejpam-6052	299	11	n	n	NOUN
ejpam-6052	299	12	.	.	PUNCT
ejpam-6052	299	13	example	example	NOUN
ejpam-6052	299	14	15	15	NUM
ejpam-6052	299	15	.	.	PUNCT
ejpam-6052	300	1	given	give	VERB
ejpam-6052	300	2	the	the	DET
ejpam-6052	300	3	pseudo	pseudo	NOUN
ejpam-6052	300	4	bn	bn	NOUN
ejpam-6052	300	5	-algebra	-algebra	NOUN
ejpam-6052	300	6	with	with	ADP
ejpam-6052	300	7	the	the	DET
ejpam-6052	300	8	following	following	ADJ
ejpam-6052	300	9	cayley	cayley	ADJ
ejpam-6052	300	10	tables	table	NOUN
ejpam-6052	300	11	:	:	PUNCT
ejpam-6052	300	12	∗	∗	NOUN
ejpam-6052	300	13	0	0	NUM
ejpam-6052	300	14	1	1	NUM
ejpam-6052	300	15	2	2	NUM
ejpam-6052	300	16	3	3	NUM
ejpam-6052	300	17	0	0	NUM
ejpam-6052	300	18	0	0	NUM
ejpam-6052	300	19	1	1	NUM
ejpam-6052	300	20	2	2	NUM
ejpam-6052	300	21	3	3	NUM
ejpam-6052	300	22	1	1	NUM
ejpam-6052	300	23	1	1	NUM
ejpam-6052	300	24	0	0	NUM
ejpam-6052	300	25	3	3	NUM
ejpam-6052	300	26	1	1	NUM
ejpam-6052	300	27	2	2	NUM
ejpam-6052	300	28	2	2	NUM
ejpam-6052	300	29	3	3	NUM
ejpam-6052	300	30	0	0	NUM
ejpam-6052	300	31	2	2	NUM
ejpam-6052	300	32	3	3	NUM
ejpam-6052	300	33	3	3	NUM
ejpam-6052	300	34	1	1	NUM
ejpam-6052	300	35	2	2	NUM
ejpam-6052	300	36	0	0	NUM
ejpam-6052	300	37	◦	◦	NOUN
ejpam-6052	300	38	0	0	NUM
ejpam-6052	300	39	1	1	NUM
ejpam-6052	300	40	2	2	NUM
ejpam-6052	300	41	3	3	NUM
ejpam-6052	300	42	0	0	NUM
ejpam-6052	300	43	0	0	NUM
ejpam-6052	300	44	1	1	NUM
ejpam-6052	300	45	2	2	NUM
ejpam-6052	300	46	3	3	NUM
ejpam-6052	300	47	1	1	NUM
ejpam-6052	300	48	1	1	NUM
ejpam-6052	300	49	0	0	NUM
ejpam-6052	300	50	3	3	NUM
ejpam-6052	300	51	2	2	NUM
ejpam-6052	300	52	2	2	NUM
ejpam-6052	300	53	2	2	NUM
ejpam-6052	300	54	3	3	NUM
ejpam-6052	300	55	0	0	NUM
ejpam-6052	300	56	1	1	NUM
ejpam-6052	300	57	3	3	NUM
ejpam-6052	300	58	3	3	NUM
ejpam-6052	300	59	2	2	NUM
ejpam-6052	300	60	1	1	NUM
ejpam-6052	300	61	0	0	NUM
ejpam-6052	300	62	the	the	DET
ejpam-6052	300	63	following	following	NOUN
ejpam-6052	300	64	are	be	AUX
ejpam-6052	300	65	the	the	DET
ejpam-6052	300	66	pseudo	pseudo	NOUN
ejpam-6052	300	67	-	-	ADJ
ejpam-6052	300	68	normal	normal	ADJ
ejpam-6052	300	69	subsets	subset	NOUN
ejpam-6052	300	70	of	of	ADP
ejpam-6052	300	71	x	x	NOUN
ejpam-6052	300	72	:	:	PUNCT
ejpam-6052	300	73	{	{	PUNCT
ejpam-6052	300	74	0	0	NUM
ejpam-6052	300	75	}	}	PUNCT
ejpam-6052	300	76	,	,	PUNCT
ejpam-6052	300	77	{	{	PUNCT
ejpam-6052	300	78	0	0	NUM
ejpam-6052	300	79	,	,	PUNCT
ejpam-6052	300	80	3	3	NUM
ejpam-6052	300	81	}	}	PUNCT
ejpam-6052	300	82	,	,	PUNCT
ejpam-6052	300	83	and	and	CCONJ
ejpam-6052	300	84	x.	x.	PROPN
ejpam-6052	300	85	i.m	i.m	PROPN
ejpam-6052	300	86	.	.	PROPN
ejpam-6052	300	87	antabo	antabo	PROPN
ejpam-6052	300	88	et	et	PROPN
ejpam-6052	300	89	al	al	PROPN
ejpam-6052	300	90	.	.	PUNCT
ejpam-6052	300	91	/	/	SYM
ejpam-6052	300	92	eur	eur	PROPN
ejpam-6052	300	93	.	.	PUNCT
ejpam-6052	301	1	j.	j.	PROPN
ejpam-6052	301	2	pure	pure	PROPN
ejpam-6052	301	3	appl	appl	PROPN
ejpam-6052	301	4	.	.	PROPN
ejpam-6052	301	5	math	math	PROPN
ejpam-6052	301	6	,	,	PUNCT
ejpam-6052	301	7	18	18	NUM
ejpam-6052	301	8	(	(	PUNCT
ejpam-6052	301	9	2	2	NUM
ejpam-6052	301	10	)	)	PUNCT
ejpam-6052	301	11	(	(	PUNCT
ejpam-6052	301	12	2025	2025	NUM
ejpam-6052	301	13	)	)	PUNCT
ejpam-6052	301	14	,	,	PUNCT
ejpam-6052	301	15	6052	6052	NUM
ejpam-6052	301	16	12	12	NUM
ejpam-6052	301	17	of	of	ADP
ejpam-6052	301	18	14	14	NUM
ejpam-6052	301	19	example	example	NOUN
ejpam-6052	301	20	16	16	NUM
ejpam-6052	301	21	.	.	PUNCT
ejpam-6052	302	1	in	in	ADP
ejpam-6052	302	2	example	example	NOUN
ejpam-6052	302	3	14	14	NUM
ejpam-6052	302	4	,	,	PUNCT
ejpam-6052	302	5	the	the	DET
ejpam-6052	302	6	set	set	NOUN
ejpam-6052	302	7	i	i	NOUN
ejpam-6052	302	8	=	=	PUNCT
ejpam-6052	302	9	{	{	PUNCT
ejpam-6052	302	10	0	0	NUM
ejpam-6052	302	11	}	}	PUNCT
ejpam-6052	302	12	is	be	AUX
ejpam-6052	302	13	not	not	PART
ejpam-6052	302	14	pseudo	pseudo	NOUN
ejpam-6052	302	15	-	-	ADJ
ejpam-6052	302	16	normal	normal	ADJ
ejpam-6052	302	17	because	because	SCONJ
ejpam-6052	302	18	(	(	PUNCT
ejpam-6052	302	19	1∗1	1∗1	NUM
ejpam-6052	302	20	)	)	PUNCT
ejpam-6052	302	21	=	=	SYM
ejpam-6052	303	1	0	0	NUM
ejpam-6052	303	2	∈	∈	PROPN
ejpam-6052	304	1	i	i	PRON
ejpam-6052	304	2	and	and	CCONJ
ejpam-6052	304	3	(	(	PUNCT
ejpam-6052	304	4	2	2	NUM
ejpam-6052	304	5	∗	∗	NOUN
ejpam-6052	304	6	4	4	NUM
ejpam-6052	304	7	)	)	PUNCT
ejpam-6052	304	8	=	=	SYM
ejpam-6052	304	9	0	0	PUNCT
ejpam-6052	305	1	∈	∈	NOUN
ejpam-6052	306	1	i	i	PRON
ejpam-6052	306	2	but	but	CCONJ
ejpam-6052	306	3	(	(	PUNCT
ejpam-6052	306	4	1	1	NUM
ejpam-6052	306	5	∗	∗	NOUN
ejpam-6052	306	6	2	2	NUM
ejpam-6052	306	7	)	)	PUNCT
ejpam-6052	306	8	◦	◦	NOUN
ejpam-6052	306	9	(	(	PUNCT
ejpam-6052	306	10	1	1	NUM
ejpam-6052	306	11	∗	∗	NOUN
ejpam-6052	306	12	4	4	NUM
ejpam-6052	306	13	)	)	PUNCT
ejpam-6052	306	14	=	=	SYM
ejpam-6052	306	15	4	4	NUM
ejpam-6052	306	16	◦	◦	NOUN
ejpam-6052	306	17	3	3	NUM
ejpam-6052	306	18	=	=	SYM
ejpam-6052	306	19	2	2	NUM
ejpam-6052	306	20	/∈	/∈	NOUN
ejpam-6052	306	21	i.	i.	NOUN
ejpam-6052	306	22	remark	remark	PROPN
ejpam-6052	306	23	8	8	NUM
ejpam-6052	306	24	.	.	PUNCT
ejpam-6052	307	1	in	in	ADP
ejpam-6052	307	2	general	general	ADJ
ejpam-6052	307	3	,	,	PUNCT
ejpam-6052	307	4	the	the	DET
ejpam-6052	307	5	set	set	NOUN
ejpam-6052	307	6	{	{	PUNCT
ejpam-6052	307	7	0	0	NUM
ejpam-6052	307	8	}	}	PUNCT
ejpam-6052	307	9	is	be	AUX
ejpam-6052	307	10	not	not	PART
ejpam-6052	307	11	pseudo	pseudo	NOUN
ejpam-6052	307	12	-	-	ADJ
ejpam-6052	307	13	normal	normal	ADJ
ejpam-6052	307	14	.	.	PUNCT
ejpam-6052	308	1	proposition	proposition	NOUN
ejpam-6052	308	2	7	7	NUM
ejpam-6052	308	3	.	.	PUNCT
ejpam-6052	309	1	let	let	AUX
ejpam-6052	309	2	n(x	n(x	PRON
ejpam-6052	309	3	)	)	PUNCT
ejpam-6052	309	4	denote	denote	VERB
ejpam-6052	309	5	the	the	DET
ejpam-6052	309	6	family	family	NOUN
ejpam-6052	309	7	of	of	ADP
ejpam-6052	309	8	all	all	DET
ejpam-6052	309	9	pseudo	pseudo	NOUN
ejpam-6052	309	10	-	-	ADJ
ejpam-6052	309	11	normal	normal	ADJ
ejpam-6052	309	12	subsets	subset	NOUN
ejpam-6052	309	13	of	of	ADP
ejpam-6052	309	14	a	a	DET
ejpam-6052	309	15	pseudo	pseudo	NOUN
ejpam-6052	309	16	bn	bn	NOUN
ejpam-6052	309	17	-	-	PUNCT
ejpam-6052	309	18	algebra	algebra	NOUN
ejpam-6052	309	19	x.	x.	NOUN
ejpam-6052	309	20	n(x	n(x	PROPN
ejpam-6052	309	21	)	)	PUNCT
ejpam-6052	309	22	forms	form	VERB
ejpam-6052	309	23	a	a	DET
ejpam-6052	309	24	complete	complete	ADJ
ejpam-6052	309	25	lattice	lattice	NOUN
ejpam-6052	309	26	.	.	PUNCT
ejpam-6052	310	1	proof	proof	NOUN
ejpam-6052	310	2	.	.	PUNCT
ejpam-6052	311	1	analogous	analogous	ADJ
ejpam-6052	311	2	to	to	ADP
ejpam-6052	311	3	the	the	DET
ejpam-6052	311	4	proof	proof	NOUN
ejpam-6052	311	5	of	of	ADP
ejpam-6052	311	6	proposition	proposition	NOUN
ejpam-6052	311	7	5	5	NUM
ejpam-6052	311	8	.	.	PUNCT
ejpam-6052	312	1	proposition	proposition	NOUN
ejpam-6052	312	2	8	8	NUM
ejpam-6052	312	3	.	.	PUNCT
ejpam-6052	313	1	every	every	DET
ejpam-6052	313	2	pseudo	pseudo	NOUN
ejpam-6052	313	3	-	-	ADJ
ejpam-6052	313	4	normal	normal	ADJ
ejpam-6052	313	5	subset	subset	NOUN
ejpam-6052	313	6	n	n	PROPN
ejpam-6052	313	7	of	of	ADP
ejpam-6052	313	8	a	a	DET
ejpam-6052	313	9	pseudo	pseudo	NOUN
ejpam-6052	313	10	bn	bn	NOUN
ejpam-6052	313	11	-algebra	-algebra	NOUN
ejpam-6052	313	12	(	(	PUNCT
ejpam-6052	313	13	x	x	X
ejpam-6052	313	14	,	,	PUNCT
ejpam-6052	313	15	∗	∗	NOUN
ejpam-6052	313	16	,	,	PUNCT
ejpam-6052	313	17	◦	◦	NOUN
ejpam-6052	313	18	,	,	PUNCT
ejpam-6052	313	19	0	0	NUM
ejpam-6052	313	20	)	)	PUNCT
ejpam-6052	313	21	is	be	AUX
ejpam-6052	313	22	a	a	DET
ejpam-6052	313	23	subalgebra	subalgebra	NOUN
ejpam-6052	313	24	of	of	ADP
ejpam-6052	313	25	x.	x.	NOUN
ejpam-6052	313	26	proof	proof	NOUN
ejpam-6052	313	27	.	.	PUNCT
ejpam-6052	314	1	suppose	suppose	VERB
ejpam-6052	314	2	n	n	PRON
ejpam-6052	314	3	is	be	AUX
ejpam-6052	314	4	a	a	DET
ejpam-6052	314	5	subset	subset	NOUN
ejpam-6052	314	6	of	of	ADP
ejpam-6052	314	7	x	x	PUNCT
ejpam-6052	314	8	and	and	CCONJ
ejpam-6052	314	9	x	x	NOUN
ejpam-6052	314	10	,	,	PUNCT
ejpam-6052	314	11	y	y	PROPN
ejpam-6052	314	12	∈	∈	PROPN
ejpam-6052	314	13	n	n	ADV
ejpam-6052	314	14	.	.	PUNCT
ejpam-6052	315	1	then	then	ADV
ejpam-6052	315	2	by	by	ADP
ejpam-6052	315	3	(	(	PUNCT
ejpam-6052	315	4	pbn2	pbn2	PROPN
ejpam-6052	315	5	)	)	PUNCT
ejpam-6052	315	6	,	,	PUNCT
ejpam-6052	315	7	x	x	X
ejpam-6052	315	8	∗	∗	NOUN
ejpam-6052	315	9	0	0	NUM
ejpam-6052	315	10	,	,	PUNCT
ejpam-6052	315	11	y	y	PROPN
ejpam-6052	315	12	∗	∗	NOUN
ejpam-6052	315	13	0	0	NUM
ejpam-6052	315	14	,	,	PUNCT
ejpam-6052	315	15	x	x	PUNCT
ejpam-6052	315	16	◦	◦	NOUN
ejpam-6052	315	17	0	0	NUM
ejpam-6052	315	18	,	,	PUNCT
ejpam-6052	315	19	y	y	PROPN
ejpam-6052	315	20	◦	◦	NOUN
ejpam-6052	315	21	0	0	NUM
ejpam-6052	316	1	∈	∈	PROPN
ejpam-6052	316	2	n	n	NOUN
ejpam-6052	316	3	.	.	PUNCT
ejpam-6052	317	1	by	by	ADP
ejpam-6052	317	2	pbn2	pbn2	NOUN
ejpam-6052	317	3	and	and	CCONJ
ejpam-6052	317	4	pseudo	pseudo	NOUN
ejpam-6052	317	5	-	-	NOUN
ejpam-6052	317	6	normalily	normalily	ADV
ejpam-6052	317	7	of	of	ADP
ejpam-6052	317	8	n	n	NOUN
ejpam-6052	317	9	,	,	PUNCT
ejpam-6052	317	10	we	we	PRON
ejpam-6052	317	11	obtain	obtain	VERB
ejpam-6052	317	12	x	x	PUNCT
ejpam-6052	317	13	∗	∗	NOUN
ejpam-6052	317	14	y	y	NOUN
ejpam-6052	317	15	=	=	SYM
ejpam-6052	317	16	(	(	PUNCT
ejpam-6052	317	17	x	x	X
ejpam-6052	317	18	∗	∗	PROPN
ejpam-6052	317	19	y	y	NOUN
ejpam-6052	317	20	)	)	PUNCT
ejpam-6052	317	21	◦	◦	NOUN
ejpam-6052	317	22	0	0	NUM
ejpam-6052	318	1	=	=	SYM
ejpam-6052	318	2	(	(	PUNCT
ejpam-6052	318	3	x	x	X
ejpam-6052	318	4	∗	∗	PROPN
ejpam-6052	318	5	y	y	NOUN
ejpam-6052	318	6	)	)	PUNCT
ejpam-6052	318	7	◦	◦	NOUN
ejpam-6052	318	8	(	(	PUNCT
ejpam-6052	318	9	0	0	NUM
ejpam-6052	318	10	∗	∗	NOUN
ejpam-6052	318	11	0	0	NUM
ejpam-6052	318	12	)	)	PUNCT
ejpam-6052	318	13	∈	∈	PROPN
ejpam-6052	318	14	n	n	CCONJ
ejpam-6052	318	15	,	,	PUNCT
ejpam-6052	318	16	x	x	VERB
ejpam-6052	318	17	◦	◦	NOUN
ejpam-6052	318	18	y	y	NOUN
ejpam-6052	318	19	=	=	SYM
ejpam-6052	318	20	(	(	PUNCT
ejpam-6052	318	21	x	x	SYM
ejpam-6052	318	22	◦	◦	VERB
ejpam-6052	318	23	y	y	NOUN
ejpam-6052	318	24	)	)	PUNCT
ejpam-6052	318	25	∗	∗	NOUN
ejpam-6052	318	26	0	0	NUM
ejpam-6052	319	1	=	=	SYM
ejpam-6052	319	2	(	(	PUNCT
ejpam-6052	319	3	x	x	SYM
ejpam-6052	319	4	◦	◦	VERB
ejpam-6052	319	5	y	y	NOUN
ejpam-6052	319	6	)	)	PUNCT
ejpam-6052	319	7	∗	∗	NOUN
ejpam-6052	319	8	(	(	PUNCT
ejpam-6052	319	9	0	0	NUM
ejpam-6052	319	10	◦	◦	NOUN
ejpam-6052	319	11	0	0	NUM
ejpam-6052	319	12	)	)	PUNCT
ejpam-6052	319	13	∈	∈	PROPN
ejpam-6052	319	14	n.	n.	NOUN
ejpam-6052	319	15	by	by	ADP
ejpam-6052	319	16	theorem	theorem	NOUN
ejpam-6052	319	17	4	4	NUM
ejpam-6052	319	18	,	,	PUNCT
ejpam-6052	319	19	n	n	PRON
ejpam-6052	319	20	is	be	AUX
ejpam-6052	319	21	a	a	DET
ejpam-6052	319	22	subalgebra	subalgebra	NOUN
ejpam-6052	319	23	of	of	ADP
ejpam-6052	319	24	x.	x.	NOUN
ejpam-6052	319	25	the	the	DET
ejpam-6052	319	26	converse	converse	NOUN
ejpam-6052	319	27	of	of	ADP
ejpam-6052	319	28	proposition	proposition	NOUN
ejpam-6052	319	29	8	8	NUM
ejpam-6052	319	30	is	be	AUX
ejpam-6052	319	31	not	not	PART
ejpam-6052	319	32	true	true	ADJ
ejpam-6052	319	33	in	in	ADP
ejpam-6052	319	34	general	general	ADJ
ejpam-6052	319	35	.	.	PUNCT
ejpam-6052	320	1	the	the	DET
ejpam-6052	320	2	set	set	NOUN
ejpam-6052	320	3	i	i	PRON
ejpam-6052	320	4	=	=	PUNCT
ejpam-6052	320	5	{	{	PUNCT
ejpam-6052	320	6	0	0	NUM
ejpam-6052	320	7	}	}	PUNCT
ejpam-6052	320	8	in	in	ADP
ejpam-6052	320	9	example	example	NOUN
ejpam-6052	320	10	14	14	NUM
ejpam-6052	320	11	is	be	AUX
ejpam-6052	320	12	a	a	DET
ejpam-6052	320	13	subalgebra	subalgebra	NOUN
ejpam-6052	320	14	but	but	CCONJ
ejpam-6052	320	15	not	not	PART
ejpam-6052	320	16	pseudo	pseudo	NOUN
ejpam-6052	320	17	-	-	NOUN
ejpam-6052	320	18	normal	normal	ADJ
ejpam-6052	320	19	as	as	SCONJ
ejpam-6052	320	20	shown	show	VERB
ejpam-6052	320	21	in	in	ADP
ejpam-6052	320	22	example	example	NOUN
ejpam-6052	320	23	16	16	NUM
ejpam-6052	320	24	.	.	PUNCT
ejpam-6052	321	1	a	a	DET
ejpam-6052	321	2	pseudo	pseudo	NOUN
ejpam-6052	321	3	-	-	ADJ
ejpam-6052	321	4	normal	normal	ADJ
ejpam-6052	321	5	subalgebra	subalgebra	NOUN
ejpam-6052	321	6	is	be	AUX
ejpam-6052	321	7	a	a	DET
ejpam-6052	321	8	special	special	ADJ
ejpam-6052	321	9	type	type	NOUN
ejpam-6052	321	10	of	of	ADP
ejpam-6052	321	11	subalgebra	subalgebra	NOUN
ejpam-6052	321	12	in	in	ADP
ejpam-6052	321	13	a	a	DET
ejpam-6052	321	14	pseudo	pseudo	NOUN
ejpam-6052	321	15	bn	bn	NOUN
ejpam-6052	321	16	-algebra	-algebra	NOUN
ejpam-6052	321	17	.	.	PUNCT
ejpam-6052	322	1	it	it	PRON
ejpam-6052	322	2	is	be	AUX
ejpam-6052	322	3	formed	form	VERB
ejpam-6052	322	4	by	by	ADP
ejpam-6052	322	5	a	a	DET
ejpam-6052	322	6	subset	subset	NOUN
ejpam-6052	322	7	that	that	PRON
ejpam-6052	322	8	follows	follow	VERB
ejpam-6052	322	9	the	the	DET
ejpam-6052	322	10	pseudo	pseudo	NOUN
ejpam-6052	322	11	-	-	ADJ
ejpam-6052	322	12	normality	normality	ADJ
ejpam-6052	322	13	conditions	condition	NOUN
ejpam-6052	322	14	.	.	PUNCT
ejpam-6052	323	1	this	this	DET
ejpam-6052	323	2	naming	naming	NOUN
ejpam-6052	323	3	helps	help	VERB
ejpam-6052	323	4	distinguish	distinguish	VERB
ejpam-6052	323	5	it	it	PRON
ejpam-6052	323	6	from	from	ADP
ejpam-6052	323	7	other	other	ADJ
ejpam-6052	323	8	subalgebras	subalgebra	NOUN
ejpam-6052	323	9	that	that	PRON
ejpam-6052	323	10	do	do	AUX
ejpam-6052	323	11	not	not	PART
ejpam-6052	323	12	necessarily	necessarily	ADV
ejpam-6052	323	13	follow	follow	VERB
ejpam-6052	323	14	the	the	DET
ejpam-6052	323	15	pseudo	pseudo	NOUN
ejpam-6052	323	16	-	-	ADJ
ejpam-6052	323	17	normality	normality	ADJ
ejpam-6052	323	18	conditions	condition	NOUN
ejpam-6052	323	19	,	,	PUNCT
ejpam-6052	323	20	making	make	VERB
ejpam-6052	323	21	its	its	PRON
ejpam-6052	323	22	role	role	NOUN
ejpam-6052	323	23	in	in	ADP
ejpam-6052	323	24	the	the	DET
ejpam-6052	323	25	structure	structure	NOUN
ejpam-6052	323	26	clear	clear	ADJ
ejpam-6052	323	27	.	.	PUNCT
ejpam-6052	324	1	definition	definition	NOUN
ejpam-6052	324	2	9	9	NUM
ejpam-6052	324	3	.	.	PUNCT
ejpam-6052	325	1	a	a	DET
ejpam-6052	325	2	pseudo	pseudo	NOUN
ejpam-6052	325	3	-	-	ADJ
ejpam-6052	325	4	normal	normal	ADJ
ejpam-6052	325	5	ideal	ideal	NOUN
ejpam-6052	325	6	is	be	AUX
ejpam-6052	325	7	an	an	DET
ejpam-6052	325	8	ideal	ideal	NOUN
ejpam-6052	325	9	which	which	PRON
ejpam-6052	325	10	satisfies	satisfy	VERB
ejpam-6052	325	11	the	the	DET
ejpam-6052	325	12	pseudo	pseudo	NOUN
ejpam-6052	325	13	-	-	ADJ
ejpam-6052	325	14	normality	normality	ADJ
ejpam-6052	325	15	conditions	condition	NOUN
ejpam-6052	325	16	.	.	PUNCT
ejpam-6052	326	1	example	example	NOUN
ejpam-6052	326	2	17	17	NUM
ejpam-6052	326	3	.	.	PUNCT
ejpam-6052	327	1	in	in	ADP
ejpam-6052	327	2	example	example	NOUN
ejpam-6052	327	3	15	15	NUM
ejpam-6052	327	4	,	,	PUNCT
ejpam-6052	327	5	it	it	PRON
ejpam-6052	327	6	can	can	AUX
ejpam-6052	327	7	be	be	AUX
ejpam-6052	327	8	shown	show	VERB
ejpam-6052	327	9	that	that	SCONJ
ejpam-6052	327	10	the	the	DET
ejpam-6052	327	11	set	set	NOUN
ejpam-6052	327	12	i	i	NOUN
ejpam-6052	327	13	=	=	PUNCT
ejpam-6052	327	14	{	{	PUNCT
ejpam-6052	327	15	0	0	NUM
ejpam-6052	327	16	,	,	PUNCT
ejpam-6052	327	17	3	3	NUM
ejpam-6052	327	18	}	}	PUNCT
ejpam-6052	327	19	is	be	AUX
ejpam-6052	327	20	a	a	DET
ejpam-6052	327	21	pseudonormal	pseudonormal	ADJ
ejpam-6052	327	22	ideal	ideal	NOUN
ejpam-6052	327	23	.	.	PUNCT
ejpam-6052	328	1	however	however	ADV
ejpam-6052	328	2	,	,	PUNCT
ejpam-6052	328	3	in	in	ADP
ejpam-6052	328	4	example	example	NOUN
ejpam-6052	328	5	14	14	NUM
ejpam-6052	328	6	,	,	PUNCT
ejpam-6052	328	7	the	the	DET
ejpam-6052	328	8	ideal	ideal	NOUN
ejpam-6052	328	9	j	j	PROPN
ejpam-6052	328	10	=	=	PUNCT
ejpam-6052	328	11	{	{	PUNCT
ejpam-6052	328	12	0	0	NUM
ejpam-6052	328	13	,	,	PUNCT
ejpam-6052	328	14	3	3	NUM
ejpam-6052	328	15	}	}	PUNCT
ejpam-6052	328	16	is	be	AUX
ejpam-6052	328	17	not	not	PART
ejpam-6052	328	18	pseudo	pseudo	NOUN
ejpam-6052	328	19	-	-	ADJ
ejpam-6052	328	20	normal	normal	ADJ
ejpam-6052	328	21	since	since	SCONJ
ejpam-6052	328	22	(	(	PUNCT
ejpam-6052	328	23	4	4	NUM
ejpam-6052	328	24	∗	∗	NOUN
ejpam-6052	328	25	1	1	NUM
ejpam-6052	328	26	)	)	PUNCT
ejpam-6052	328	27	=	=	SYM
ejpam-6052	328	28	3	3	NUM
ejpam-6052	328	29	∈	∈	PROPN
ejpam-6052	328	30	j	j	PROPN
ejpam-6052	328	31	and	and	CCONJ
ejpam-6052	328	32	(	(	PUNCT
ejpam-6052	328	33	2	2	NUM
ejpam-6052	328	34	∗	∗	NOUN
ejpam-6052	328	35	3	3	NUM
ejpam-6052	328	36	)	)	PUNCT
ejpam-6052	328	37	=	=	SYM
ejpam-6052	328	38	3	3	NUM
ejpam-6052	328	39	∈	∈	PROPN
ejpam-6052	328	40	j	j	NOUN
ejpam-6052	328	41	but	but	CCONJ
ejpam-6052	328	42	(	(	PUNCT
ejpam-6052	328	43	4	4	NUM
ejpam-6052	328	44	∗	∗	NOUN
ejpam-6052	328	45	2	2	NUM
ejpam-6052	328	46	)	)	PUNCT
ejpam-6052	328	47	◦	◦	NOUN
ejpam-6052	328	48	(	(	PUNCT
ejpam-6052	328	49	1	1	NUM
ejpam-6052	328	50	∗	∗	NOUN
ejpam-6052	328	51	3	3	NUM
ejpam-6052	328	52	)	)	PUNCT
ejpam-6052	328	53	=	=	SYM
ejpam-6052	328	54	0	0	PUNCT
ejpam-6052	329	1	◦	◦	NOUN
ejpam-6052	329	2	2	2	NUM
ejpam-6052	329	3	=	=	SYM
ejpam-6052	329	4	2	2	NUM
ejpam-6052	329	5	/∈	/∈	SYM
ejpam-6052	329	6	j	j	PROPN
ejpam-6052	329	7	.	.	PUNCT
ejpam-6052	330	1	hence	hence	ADV
ejpam-6052	330	2	,	,	PUNCT
ejpam-6052	330	3	j	j	PROPN
ejpam-6052	330	4	is	be	AUX
ejpam-6052	330	5	not	not	PART
ejpam-6052	330	6	a	a	DET
ejpam-6052	330	7	pseudo	pseudo	NOUN
ejpam-6052	330	8	-	-	ADJ
ejpam-6052	330	9	normal	normal	ADJ
ejpam-6052	330	10	ideal	ideal	NOUN
ejpam-6052	330	11	.	.	PUNCT
ejpam-6052	331	1	the	the	DET
ejpam-6052	331	2	next	next	ADJ
ejpam-6052	331	3	result	result	NOUN
ejpam-6052	331	4	follows	follow	VERB
ejpam-6052	331	5	from	from	ADP
ejpam-6052	331	6	propositions	proposition	NOUN
ejpam-6052	331	7	6	6	NUM
ejpam-6052	331	8	and	and	CCONJ
ejpam-6052	331	9	7	7	NUM
ejpam-6052	331	10	.	.	PUNCT
ejpam-6052	331	11	corollary	corollary	ADJ
ejpam-6052	331	12	2	2	NUM
ejpam-6052	331	13	.	.	PUNCT
ejpam-6052	332	1	let	let	VERB
ejpam-6052	332	2	x	x	PRON
ejpam-6052	332	3	be	be	AUX
ejpam-6052	332	4	a	a	DET
ejpam-6052	332	5	pseudo	pseudo	NOUN
ejpam-6052	332	6	bn	bn	NOUN
ejpam-6052	332	7	-algebra	-algebra	NOUN
ejpam-6052	332	8	and	and	CCONJ
ejpam-6052	332	9	{	{	PUNCT
ejpam-6052	332	10	ni	ni	NOUN
ejpam-6052	333	1	|	|	ADV
ejpam-6052	333	2	i	i	PRON
ejpam-6052	333	3	∈	∈	PROPN
ejpam-6052	333	4	i	i	PRON
ejpam-6052	333	5	}	}	PUNCT
ejpam-6052	333	6	be	be	VERB
ejpam-6052	333	7	a	a	DET
ejpam-6052	333	8	nonempty	nonempty	ADJ
ejpam-6052	333	9	family	family	NOUN
ejpam-6052	333	10	of	of	ADP
ejpam-6052	333	11	pseudo	pseudo	NOUN
ejpam-6052	333	12	-	-	ADJ
ejpam-6052	333	13	normal	normal	ADJ
ejpam-6052	333	14	ideals	ideal	NOUN
ejpam-6052	333	15	,	,	PUNCT
ejpam-6052	333	16	then	then	ADV
ejpam-6052	333	17	⋂	⋂	PROPN
ejpam-6052	333	18	i∈i	i∈i	ADJ
ejpam-6052	333	19	ni	ni	PROPN
ejpam-6052	333	20	is	be	AUX
ejpam-6052	333	21	also	also	ADV
ejpam-6052	333	22	a	a	DET
ejpam-6052	333	23	pseudo	pseudo	NOUN
ejpam-6052	333	24	-	-	ADJ
ejpam-6052	333	25	normal	normal	ADJ
ejpam-6052	333	26	ideal	ideal	NOUN
ejpam-6052	333	27	in	in	ADP
ejpam-6052	333	28	x.	x.	NOUN
ejpam-6052	333	29	the	the	DET
ejpam-6052	333	30	next	next	ADJ
ejpam-6052	333	31	result	result	NOUN
ejpam-6052	333	32	established	establish	VERB
ejpam-6052	333	33	the	the	DET
ejpam-6052	333	34	equivalency	equivalency	NOUN
ejpam-6052	333	35	of	of	ADP
ejpam-6052	333	36	pseudo	pseudo	NOUN
ejpam-6052	333	37	-	-	ADJ
ejpam-6052	333	38	normal	normal	ADJ
ejpam-6052	333	39	subalgebra	subalgebra	NOUN
ejpam-6052	333	40	and	and	CCONJ
ejpam-6052	333	41	pseudonormal	pseudonormal	ADJ
ejpam-6052	333	42	ideal	ideal	NOUN
ejpam-6052	333	43	of	of	ADP
ejpam-6052	333	44	a	a	DET
ejpam-6052	333	45	pseudo	pseudo	NOUN
ejpam-6052	333	46	bn	bn	NOUN
ejpam-6052	333	47	-algebra	-algebra	NOUN
ejpam-6052	333	48	.	.	PUNCT
ejpam-6052	334	1	theorem	theorem	NOUN
ejpam-6052	334	2	5	5	NUM
ejpam-6052	334	3	.	.	PUNCT
ejpam-6052	335	1	let	let	VERB
ejpam-6052	335	2	x	x	PRON
ejpam-6052	335	3	be	be	AUX
ejpam-6052	335	4	a	a	DET
ejpam-6052	335	5	pseudo	pseudo	NOUN
ejpam-6052	335	6	bn	bn	NOUN
ejpam-6052	335	7	-algebra	-algebra	NOUN
ejpam-6052	335	8	and	and	CCONJ
ejpam-6052	335	9	let	let	VERB
ejpam-6052	335	10	n	n	PRON
ejpam-6052	335	11	⊆	⊆	NUM
ejpam-6052	335	12	x.	x.	NOUN
ejpam-6052	335	13	then	then	ADV
ejpam-6052	335	14	n	n	PRON
ejpam-6052	335	15	is	be	AUX
ejpam-6052	335	16	a	a	DET
ejpam-6052	335	17	pseudo	pseudo	NOUN
ejpam-6052	335	18	-	-	ADJ
ejpam-6052	335	19	normal	normal	ADJ
ejpam-6052	335	20	subalgebra	subalgebra	NOUN
ejpam-6052	335	21	of	of	ADP
ejpam-6052	335	22	x	x	PRON
ejpam-6052	335	23	if	if	SCONJ
ejpam-6052	335	24	and	and	CCONJ
ejpam-6052	335	25	only	only	ADV
ejpam-6052	335	26	if	if	SCONJ
ejpam-6052	335	27	n	n	PRON
ejpam-6052	335	28	is	be	AUX
ejpam-6052	335	29	a	a	DET
ejpam-6052	335	30	pseudo	pseudo	NOUN
ejpam-6052	335	31	-	-	ADJ
ejpam-6052	335	32	normal	normal	ADJ
ejpam-6052	335	33	ideal	ideal	NOUN
ejpam-6052	335	34	of	of	ADP
ejpam-6052	335	35	x.	x.	PROPN
ejpam-6052	335	36	i.m	i.m	PROPN
ejpam-6052	335	37	.	.	PROPN
ejpam-6052	335	38	antabo	antabo	PROPN
ejpam-6052	335	39	et	et	PROPN
ejpam-6052	335	40	al	al	PROPN
ejpam-6052	335	41	.	.	PUNCT
ejpam-6052	335	42	/	/	SYM
ejpam-6052	335	43	eur	eur	PROPN
ejpam-6052	335	44	.	.	PUNCT
ejpam-6052	336	1	j.	j.	PROPN
ejpam-6052	336	2	pure	pure	PROPN
ejpam-6052	336	3	appl	appl	PROPN
ejpam-6052	336	4	.	.	PROPN
ejpam-6052	336	5	math	math	PROPN
ejpam-6052	336	6	,	,	PUNCT
ejpam-6052	336	7	18	18	NUM
ejpam-6052	336	8	(	(	PUNCT
ejpam-6052	336	9	2	2	NUM
ejpam-6052	336	10	)	)	PUNCT
ejpam-6052	336	11	(	(	PUNCT
ejpam-6052	336	12	2025	2025	NUM
ejpam-6052	336	13	)	)	PUNCT
ejpam-6052	336	14	,	,	PUNCT
ejpam-6052	336	15	6052	6052	NUM
ejpam-6052	336	16	13	13	NUM
ejpam-6052	336	17	of	of	ADP
ejpam-6052	336	18	14	14	NUM
ejpam-6052	336	19	proof	proof	NOUN
ejpam-6052	336	20	.	.	PUNCT
ejpam-6052	337	1	suppose	suppose	VERB
ejpam-6052	337	2	x	x	PRON
ejpam-6052	337	3	is	be	AUX
ejpam-6052	337	4	a	a	DET
ejpam-6052	337	5	pseudo	pseudo	NOUN
ejpam-6052	337	6	bn	bn	NOUN
ejpam-6052	337	7	-algebra	-algebra	NOUN
ejpam-6052	337	8	and	and	CCONJ
ejpam-6052	337	9	n	n	PRON
ejpam-6052	337	10	⊆	⊆	NUM
ejpam-6052	337	11	x.	x.	NOUN
ejpam-6052	337	12	assume	assume	VERB
ejpam-6052	337	13	that	that	SCONJ
ejpam-6052	337	14	n	n	PRON
ejpam-6052	337	15	is	be	AUX
ejpam-6052	337	16	a	a	DET
ejpam-6052	337	17	pseudonormal	pseudonormal	ADJ
ejpam-6052	337	18	subalgebra	subalgebra	NOUN
ejpam-6052	337	19	of	of	ADP
ejpam-6052	337	20	x.	x.	NOUN
ejpam-6052	337	21	by	by	ADP
ejpam-6052	337	22	remark	remark	NOUN
ejpam-6052	337	23	7	7	NUM
ejpam-6052	337	24	,	,	PUNCT
ejpam-6052	337	25	we	we	PRON
ejpam-6052	337	26	have	have	VERB
ejpam-6052	337	27	0	0	NUM
ejpam-6052	337	28	∈	∈	PROPN
ejpam-6052	337	29	n	n	NOUN
ejpam-6052	337	30	,	,	PUNCT
ejpam-6052	337	31	satisfying	satisfy	VERB
ejpam-6052	337	32	(	(	PUNCT
ejpam-6052	337	33	pi1	pi1	NOUN
ejpam-6052	337	34	)	)	PUNCT
ejpam-6052	337	35	of	of	ADP
ejpam-6052	337	36	definition	definition	NOUN
ejpam-6052	337	37	7	7	NUM
ejpam-6052	337	38	.	.	PUNCT
ejpam-6052	337	39	to	to	PART
ejpam-6052	337	40	verify	verify	VERB
ejpam-6052	337	41	(	(	PUNCT
ejpam-6052	337	42	pi2	pi2	PROPN
ejpam-6052	337	43	)	)	PUNCT
ejpam-6052	337	44	,	,	PUNCT
ejpam-6052	337	45	suppose	suppose	VERB
ejpam-6052	337	46	x	x	PUNCT
ejpam-6052	337	47	∗	∗	VERB
ejpam-6052	337	48	y	y	PROPN
ejpam-6052	337	49	∈	∈	PROPN
ejpam-6052	337	50	n	n	NOUN
ejpam-6052	337	51	,	,	PUNCT
ejpam-6052	337	52	x	x	PUNCT
ejpam-6052	337	53	◦	◦	VERB
ejpam-6052	337	54	y	y	PROPN
ejpam-6052	337	55	∈	∈	PROPN
ejpam-6052	337	56	n	n	CCONJ
ejpam-6052	337	57	,	,	PUNCT
ejpam-6052	337	58	and	and	CCONJ
ejpam-6052	337	59	y	y	PROPN
ejpam-6052	337	60	∈	∈	PROPN
ejpam-6052	337	61	n	n	ADV
ejpam-6052	337	62	.	.	PUNCT
ejpam-6052	338	1	since	since	SCONJ
ejpam-6052	338	2	0	0	NUM
ejpam-6052	338	3	∈	∈	PROPN
ejpam-6052	338	4	n	n	NOUN
ejpam-6052	338	5	,	,	PUNCT
ejpam-6052	338	6	by	by	ADP
ejpam-6052	338	7	theorem	theorem	NOUN
ejpam-6052	338	8	4	4	NUM
ejpam-6052	338	9	,	,	PUNCT
ejpam-6052	338	10	0	0	NUM
ejpam-6052	338	11	∗	∗	NOUN
ejpam-6052	338	12	y	y	PROPN
ejpam-6052	338	13	,	,	PUNCT
ejpam-6052	338	14	0	0	PUNCT
ejpam-6052	339	1	◦	◦	VERB
ejpam-6052	339	2	y	y	PROPN
ejpam-6052	339	3	∈	∈	PROPN
ejpam-6052	339	4	n	n	ADV
ejpam-6052	339	5	.	.	PUNCT
ejpam-6052	340	1	by	by	ADP
ejpam-6052	340	2	pbn2	pbn2	NOUN
ejpam-6052	340	3	[	[	AUX
ejpam-6052	340	4	applied	apply	VERB
ejpam-6052	340	5	twice	twice	ADV
ejpam-6052	340	6	]	]	PUNCT
ejpam-6052	340	7	and	and	CCONJ
ejpam-6052	340	8	pseudo	pseudo	NOUN
ejpam-6052	340	9	-	-	NOUN
ejpam-6052	340	10	normality	normality	NOUN
ejpam-6052	340	11	in	in	ADP
ejpam-6052	340	12	n	n	PROPN
ejpam-6052	340	13	,	,	PUNCT
ejpam-6052	340	14	x	x	PUNCT
ejpam-6052	341	1	=	=	PUNCT
ejpam-6052	341	2	x	x	SYM
ejpam-6052	341	3	∗	∗	NOUN
ejpam-6052	341	4	0	0	NUM
ejpam-6052	342	1	=	=	SYM
ejpam-6052	342	2	(	(	PUNCT
ejpam-6052	342	3	x	x	X
ejpam-6052	342	4	∗	∗	NOUN
ejpam-6052	342	5	0	0	NUM
ejpam-6052	342	6	)	)	PUNCT
ejpam-6052	342	7	◦	◦	NOUN
ejpam-6052	342	8	0	0	NUM
ejpam-6052	343	1	=	=	SYM
ejpam-6052	343	2	(	(	PUNCT
ejpam-6052	343	3	x	x	X
ejpam-6052	343	4	∗	∗	NOUN
ejpam-6052	343	5	0	0	NUM
ejpam-6052	343	6	)	)	PUNCT
ejpam-6052	343	7	◦	◦	NOUN
ejpam-6052	343	8	(	(	PUNCT
ejpam-6052	343	9	y	y	PROPN
ejpam-6052	343	10	∗	∗	PROPN
ejpam-6052	343	11	y	y	PROPN
ejpam-6052	343	12	)	)	PUNCT
ejpam-6052	343	13	∈	∈	PROPN
ejpam-6052	343	14	n.	n.	NOUN
ejpam-6052	343	15	hence	hence	ADV
ejpam-6052	343	16	,	,	PUNCT
ejpam-6052	343	17	n	n	PRON
ejpam-6052	343	18	is	be	AUX
ejpam-6052	343	19	a	a	DET
ejpam-6052	343	20	pseudo	pseudo	NOUN
ejpam-6052	343	21	-	-	ADJ
ejpam-6052	343	22	normal	normal	ADJ
ejpam-6052	343	23	ideal	ideal	NOUN
ejpam-6052	343	24	of	of	ADP
ejpam-6052	343	25	x.	x.	NOUN
ejpam-6052	343	26	the	the	DET
ejpam-6052	343	27	converse	converse	NOUN
ejpam-6052	343	28	follows	follow	VERB
ejpam-6052	343	29	directly	directly	ADV
ejpam-6052	343	30	from	from	ADP
ejpam-6052	343	31	proposition	proposition	NOUN
ejpam-6052	343	32	8	8	NUM
ejpam-6052	343	33	.	.	PUNCT
ejpam-6052	343	34	notice	notice	NOUN
ejpam-6052	343	35	in	in	ADP
ejpam-6052	343	36	the	the	DET
ejpam-6052	343	37	proof	proof	NOUN
ejpam-6052	343	38	of	of	ADP
ejpam-6052	343	39	theorem	theorem	NOUN
ejpam-6052	343	40	5	5	NUM
ejpam-6052	343	41	,	,	PUNCT
ejpam-6052	343	42	we	we	PRON
ejpam-6052	343	43	did	do	AUX
ejpam-6052	343	44	not	not	PART
ejpam-6052	343	45	use	use	VERB
ejpam-6052	343	46	x	x	PUNCT
ejpam-6052	343	47	◦	◦	VERB
ejpam-6052	343	48	y	y	PROPN
ejpam-6052	343	49	∈	∈	PROPN
ejpam-6052	343	50	n	n	NOUN
ejpam-6052	343	51	and	and	CCONJ
ejpam-6052	343	52	0	0	NUM
ejpam-6052	343	53	◦	◦	NOUN
ejpam-6052	343	54	y	y	PROPN
ejpam-6052	343	55	∈	∈	PROPN
ejpam-6052	343	56	n	n	ADV
ejpam-6052	343	57	.	.	PUNCT
ejpam-6052	344	1	but	but	CCONJ
ejpam-6052	344	2	we	we	PRON
ejpam-6052	344	3	can	can	AUX
ejpam-6052	344	4	also	also	ADV
ejpam-6052	344	5	show	show	VERB
ejpam-6052	344	6	that	that	SCONJ
ejpam-6052	344	7	x	x	SYM
ejpam-6052	344	8	∈	∈	NOUN
ejpam-6052	344	9	n	n	ADP
ejpam-6052	344	10	using	use	VERB
ejpam-6052	344	11	these	these	PRON
ejpam-6052	344	12	:	:	PUNCT
ejpam-6052	344	13	x	x	SYM
ejpam-6052	344	14	=	=	PUNCT
ejpam-6052	344	15	x	x	PUNCT
ejpam-6052	344	16	◦	◦	NOUN
ejpam-6052	344	17	0	0	NUM
ejpam-6052	344	18	=	=	SYM
ejpam-6052	344	19	(	(	PUNCT
ejpam-6052	344	20	x	x	PART
ejpam-6052	344	21	◦	◦	NOUN
ejpam-6052	344	22	0	0	NUM
ejpam-6052	344	23	)	)	PUNCT
ejpam-6052	344	24	∗	∗	NOUN
ejpam-6052	344	25	0	0	NUM
ejpam-6052	345	1	=	=	SYM
ejpam-6052	345	2	(	(	PUNCT
ejpam-6052	345	3	x	x	PART
ejpam-6052	345	4	◦	◦	NOUN
ejpam-6052	345	5	0	0	NUM
ejpam-6052	345	6	)	)	PUNCT
ejpam-6052	345	7	∗	∗	NOUN
ejpam-6052	345	8	(	(	PUNCT
ejpam-6052	345	9	y	y	PROPN
ejpam-6052	345	10	◦	◦	PROPN
ejpam-6052	345	11	y	y	PROPN
ejpam-6052	345	12	)	)	PUNCT
ejpam-6052	345	13	∈	∈	PROPN
ejpam-6052	345	14	n.	n.	NOUN
ejpam-6052	345	15	4	4	NUM
ejpam-6052	345	16	.	.	PUNCT
ejpam-6052	345	17	conclusion	conclusion	NOUN
ejpam-6052	345	18	in	in	ADP
ejpam-6052	345	19	this	this	DET
ejpam-6052	345	20	paper	paper	NOUN
ejpam-6052	345	21	,	,	PUNCT
ejpam-6052	345	22	we	we	PRON
ejpam-6052	345	23	introduced	introduce	VERB
ejpam-6052	345	24	the	the	DET
ejpam-6052	345	25	concept	concept	NOUN
ejpam-6052	345	26	of	of	ADP
ejpam-6052	345	27	pseudo	pseudo	NOUN
ejpam-6052	345	28	bn	bn	NOUN
ejpam-6052	345	29	-algebras	-algebra	NOUN
ejpam-6052	345	30	as	as	ADP
ejpam-6052	345	31	a	a	DET
ejpam-6052	345	32	natural	natural	ADJ
ejpam-6052	345	33	extension	extension	NOUN
ejpam-6052	345	34	of	of	ADP
ejpam-6052	345	35	bn	bn	NOUN
ejpam-6052	345	36	-algebras	-algebra	NOUN
ejpam-6052	345	37	,	,	PUNCT
ejpam-6052	345	38	relaxing	relax	VERB
ejpam-6052	345	39	commutativity	commutativity	NOUN
ejpam-6052	345	40	constraints	constraint	NOUN
ejpam-6052	345	41	to	to	PART
ejpam-6052	345	42	explore	explore	VERB
ejpam-6052	345	43	broader	broad	ADJ
ejpam-6052	345	44	algebraic	algebraic	ADJ
ejpam-6052	345	45	structures	structure	NOUN
ejpam-6052	345	46	.	.	PUNCT
ejpam-6052	346	1	we	we	PRON
ejpam-6052	346	2	established	establish	VERB
ejpam-6052	346	3	fundamental	fundamental	ADJ
ejpam-6052	346	4	properties	property	NOUN
ejpam-6052	346	5	of	of	ADP
ejpam-6052	346	6	pseudo	pseudo	NOUN
ejpam-6052	346	7	bn	bn	X
ejpam-6052	346	8	-algebras	-algebra	NOUN
ejpam-6052	346	9	,	,	PUNCT
ejpam-6052	346	10	analyzed	analyze	VERB
ejpam-6052	346	11	their	their	PRON
ejpam-6052	346	12	relationships	relationship	NOUN
ejpam-6052	346	13	with	with	ADP
ejpam-6052	346	14	pseudo	pseudo	NOUN
ejpam-6052	346	15	bf	bf	NOUN
ejpam-6052	346	16	-algebras	-algebra	NOUN
ejpam-6052	346	17	,	,	PUNCT
ejpam-6052	346	18	and	and	CCONJ
ejpam-6052	346	19	examined	examine	VERB
ejpam-6052	346	20	their	their	PRON
ejpam-6052	346	21	structural	structural	ADJ
ejpam-6052	346	22	components	component	NOUN
ejpam-6052	346	23	,	,	PUNCT
ejpam-6052	346	24	including	include	VERB
ejpam-6052	346	25	subalgebras	subalgebra	NOUN
ejpam-6052	346	26	and	and	CCONJ
ejpam-6052	346	27	ideals	ideal	NOUN
ejpam-6052	346	28	.	.	PUNCT
ejpam-6052	347	1	finally	finally	ADV
ejpam-6052	347	2	,	,	PUNCT
ejpam-6052	347	3	we	we	PRON
ejpam-6052	347	4	established	establish	VERB
ejpam-6052	347	5	the	the	DET
ejpam-6052	347	6	equivalency	equivalency	NOUN
ejpam-6052	347	7	of	of	ADP
ejpam-6052	347	8	subalgebras	subalgebra	NOUN
ejpam-6052	347	9	and	and	CCONJ
ejpam-6052	347	10	ideals	ideal	NOUN
ejpam-6052	347	11	in	in	ADP
ejpam-6052	347	12	terms	term	NOUN
ejpam-6052	347	13	of	of	ADP
ejpam-6052	347	14	pseudo	pseudo	NOUN
ejpam-6052	347	15	-	-	NOUN
ejpam-6052	347	16	normality	normality	NOUN
ejpam-6052	347	17	.	.	PUNCT
ejpam-6052	348	1	these	these	DET
ejpam-6052	348	2	investigations	investigation	NOUN
ejpam-6052	348	3	provide	provide	VERB
ejpam-6052	348	4	a	a	DET
ejpam-6052	348	5	deeper	deep	ADJ
ejpam-6052	348	6	understanding	understanding	NOUN
ejpam-6052	348	7	of	of	ADP
ejpam-6052	348	8	their	their	PRON
ejpam-6052	348	9	internal	internal	ADJ
ejpam-6052	348	10	organization	organization	NOUN
ejpam-6052	348	11	and	and	CCONJ
ejpam-6052	348	12	potential	potential	ADJ
ejpam-6052	348	13	applications	application	NOUN
ejpam-6052	348	14	in	in	ADP
ejpam-6052	348	15	non	non	ADJ
ejpam-6052	348	16	-	-	ADJ
ejpam-6052	348	17	classical	classical	ADJ
ejpam-6052	348	18	logic	logic	NOUN
ejpam-6052	348	19	and	and	CCONJ
ejpam-6052	348	20	abstract	abstract	ADJ
ejpam-6052	348	21	algebra	algebra	NOUN
ejpam-6052	348	22	.	.	PUNCT
ejpam-6052	349	1	acknowledgements	acknowledgement	NOUN
ejpam-6052	349	2	the	the	DET
ejpam-6052	349	3	authors	author	NOUN
ejpam-6052	349	4	thank	thank	VERB
ejpam-6052	349	5	the	the	DET
ejpam-6052	349	6	department	department	PROPN
ejpam-6052	349	7	of	of	ADP
ejpam-6052	349	8	science	science	NOUN
ejpam-6052	349	9	and	and	CCONJ
ejpam-6052	349	10	technology	technology	NOUN
ejpam-6052	349	11	(	(	PUNCT
ejpam-6052	349	12	dost	dost	NOUN
ejpam-6052	349	13	)	)	PUNCT
ejpam-6052	349	14	of	of	ADP
ejpam-6052	349	15	the	the	DET
ejpam-6052	349	16	philippines	philippine	NOUN
ejpam-6052	349	17	through	through	ADP
ejpam-6052	349	18	the	the	DET
ejpam-6052	349	19	accelerated	accelerated	ADJ
ejpam-6052	349	20	science	science	NOUN
ejpam-6052	349	21	and	and	CCONJ
ejpam-6052	349	22	technology	technology	NOUN
ejpam-6052	349	23	human	human	ADJ
ejpam-6052	349	24	resource	resource	NOUN
ejpam-6052	349	25	development	development	NOUN
ejpam-6052	349	26	program	program	NOUN
ejpam-6052	349	27	(	(	PUNCT
ejpam-6052	349	28	asthrdp	asthrdp	PROPN
ejpam-6052	349	29	)	)	PUNCT
ejpam-6052	349	30	and	and	CCONJ
ejpam-6052	349	31	the	the	DET
ejpam-6052	349	32	office	office	NOUN
ejpam-6052	349	33	of	of	ADP
ejpam-6052	349	34	the	the	DET
ejpam-6052	349	35	vice	vice	NOUN
ejpam-6052	349	36	chancellor	chancellor	NOUN
ejpam-6052	349	37	for	for	ADP
ejpam-6052	349	38	research	research	NOUN
ejpam-6052	349	39	and	and	CCONJ
ejpam-6052	349	40	enterprise	enterprise	NOUN
ejpam-6052	349	41	through	through	ADP
ejpam-6052	349	42	the	the	DET
ejpam-6052	349	43	research	research	NOUN
ejpam-6052	349	44	management	management	NOUN
ejpam-6052	349	45	office	office	NOUN
ejpam-6052	349	46	of	of	ADP
ejpam-6052	349	47	msu	msu	PROPN
ejpam-6052	349	48	iligan	iligan	PROPN
ejpam-6052	349	49	institute	institute	PROPN
ejpam-6052	349	50	of	of	ADP
ejpam-6052	349	51	technology	technology	NOUN
ejpam-6052	349	52	for	for	ADP
ejpam-6052	349	53	the	the	DET
ejpam-6052	349	54	financial	financial	ADJ
ejpam-6052	349	55	support	support	NOUN
ejpam-6052	349	56	.	.	PUNCT
ejpam-6052	350	1	references	reference	NOUN
ejpam-6052	350	2	[	[	X
ejpam-6052	350	3	1	1	NUM
ejpam-6052	350	4	]	]	X
ejpam-6052	350	5	y.	y.	PROPN
ejpam-6052	350	6	imai	imai	PROPN
ejpam-6052	350	7	and	and	CCONJ
ejpam-6052	350	8	k.	k.	PROPN
ejpam-6052	350	9	iséki	iséki	PROPN
ejpam-6052	350	10	.	.	PROPN
ejpam-6052	351	1	on	on	ADP
ejpam-6052	351	2	axiom	axiom	NOUN
ejpam-6052	351	3	systems	system	NOUN
ejpam-6052	351	4	of	of	ADP
ejpam-6052	351	5	propositional	propositional	ADJ
ejpam-6052	351	6	calculi	calculi	PROPN
ejpam-6052	351	7	xiv	xiv	PROPN
ejpam-6052	351	8	.	.	PUNCT
ejpam-6052	352	1	proceedings	proceeding	NOUN
ejpam-6052	352	2	of	of	ADP
ejpam-6052	352	3	the	the	DET
ejpam-6052	352	4	japan	japan	PROPN
ejpam-6052	352	5	academy	academy	PROPN
ejpam-6052	352	6	,	,	PUNCT
ejpam-6052	352	7	42(1):19–22	42(1):19–22	NUM
ejpam-6052	352	8	,	,	PUNCT
ejpam-6052	352	9	1966	1966	NUM
ejpam-6052	352	10	.	.	PUNCT
ejpam-6052	353	1	[	[	X
ejpam-6052	353	2	2	2	NUM
ejpam-6052	353	3	]	]	PUNCT
ejpam-6052	353	4	k.	k.	PROPN
ejpam-6052	353	5	iséki	iséki	PROPN
ejpam-6052	353	6	.	.	PUNCT
ejpam-6052	354	1	an	an	DET
ejpam-6052	354	2	algebra	algebra	NOUN
ejpam-6052	354	3	related	relate	VERB
ejpam-6052	354	4	with	with	ADP
ejpam-6052	354	5	a	a	DET
ejpam-6052	354	6	propositional	propositional	ADJ
ejpam-6052	354	7	calculus	calculus	NOUN
ejpam-6052	354	8	.	.	PUNCT
ejpam-6052	355	1	proceedings	proceeding	NOUN
ejpam-6052	355	2	of	of	ADP
ejpam-6052	355	3	the	the	DET
ejpam-6052	355	4	japan	japan	PROPN
ejpam-6052	355	5	academy	academy	PROPN
ejpam-6052	355	6	,	,	PUNCT
ejpam-6052	355	7	42(1):26–29	42(1):26–29	NUM
ejpam-6052	355	8	,	,	PUNCT
ejpam-6052	355	9	1966	1966	NUM
ejpam-6052	355	10	.	.	PUNCT
ejpam-6052	356	1	[	[	X
ejpam-6052	356	2	3	3	X
ejpam-6052	356	3	]	]	X
ejpam-6052	356	4	c.	c.	PROPN
ejpam-6052	356	5	c.	c.	PROPN
ejpam-6052	356	6	chang	chang	PROPN
ejpam-6052	356	7	.	.	PUNCT
ejpam-6052	357	1	algebraic	algebraic	ADJ
ejpam-6052	357	2	analysis	analysis	NOUN
ejpam-6052	357	3	of	of	ADP
ejpam-6052	357	4	many	many	ADJ
ejpam-6052	357	5	valued	value	VERB
ejpam-6052	357	6	logics	logic	NOUN
ejpam-6052	357	7	.	.	PUNCT
ejpam-6052	358	1	transactions	transaction	NOUN
ejpam-6052	358	2	of	of	ADP
ejpam-6052	358	3	the	the	DET
ejpam-6052	358	4	american	american	PROPN
ejpam-6052	358	5	mathematical	mathematical	PROPN
ejpam-6052	358	6	society	society	NOUN
ejpam-6052	358	7	,	,	PUNCT
ejpam-6052	358	8	88(2):467–490	88(2):467–490	NUM
ejpam-6052	358	9	,	,	PUNCT
ejpam-6052	358	10	1958	1958	NUM
ejpam-6052	358	11	.	.	PUNCT
ejpam-6052	359	1	[	[	X
ejpam-6052	359	2	4	4	X
ejpam-6052	359	3	]	]	X
ejpam-6052	359	4	p.	p.	NOUN
ejpam-6052	359	5	hájek	hájek	NOUN
ejpam-6052	359	6	.	.	PUNCT
ejpam-6052	360	1	metamathematics	metamathematic	NOUN
ejpam-6052	360	2	of	of	ADP
ejpam-6052	360	3	fuzzy	fuzzy	ADJ
ejpam-6052	360	4	logic	logic	NOUN
ejpam-6052	360	5	.	.	PUNCT
ejpam-6052	361	1	kluwer	kluwer	NOUN
ejpam-6052	361	2	academic	academic	ADJ
ejpam-6052	361	3	publishers	publisher	NOUN
ejpam-6052	361	4	,	,	PUNCT
ejpam-6052	361	5	dordrecht	dordrecht	PROPN
ejpam-6052	361	6	,	,	PUNCT
ejpam-6052	361	7	1998	1998	NUM
ejpam-6052	361	8	.	.	PUNCT
ejpam-6052	362	1	i.m	i.m	PROPN
ejpam-6052	362	2	.	.	PROPN
ejpam-6052	362	3	antabo	antabo	PROPN
ejpam-6052	362	4	et	et	PROPN
ejpam-6052	362	5	al	al	PROPN
ejpam-6052	362	6	.	.	PUNCT
ejpam-6052	362	7	/	/	SYM
ejpam-6052	362	8	eur	eur	PROPN
ejpam-6052	362	9	.	.	PUNCT
ejpam-6052	363	1	j.	j.	PROPN
ejpam-6052	363	2	pure	pure	PROPN
ejpam-6052	363	3	appl	appl	PROPN
ejpam-6052	363	4	.	.	PROPN
ejpam-6052	363	5	math	math	PROPN
ejpam-6052	363	6	,	,	PUNCT
ejpam-6052	363	7	18	18	NUM
ejpam-6052	363	8	(	(	PUNCT
ejpam-6052	363	9	2	2	NUM
ejpam-6052	363	10	)	)	PUNCT
ejpam-6052	363	11	(	(	PUNCT
ejpam-6052	363	12	2025	2025	NUM
ejpam-6052	363	13	)	)	PUNCT
ejpam-6052	363	14	,	,	PUNCT
ejpam-6052	363	15	6052	6052	NUM
ejpam-6052	363	16	14	14	NUM
ejpam-6052	363	17	of	of	ADP
ejpam-6052	363	18	14	14	NUM
ejpam-6052	363	19	[	[	SYM
ejpam-6052	363	20	5	5	NUM
ejpam-6052	363	21	]	]	PUNCT
ejpam-6052	363	22	c.	c.	PROPN
ejpam-6052	363	23	kim	kim	PROPN
ejpam-6052	363	24	and	and	CCONJ
ejpam-6052	363	25	h.	h.	PROPN
ejpam-6052	363	26	kim	kim	PROPN
ejpam-6052	363	27	.	.	PUNCT
ejpam-6052	364	1	on	on	ADP
ejpam-6052	364	2	bn	bn	X
ejpam-6052	364	3	-algebras	-algebras	PROPN
ejpam-6052	364	4	.	.	PUNCT
ejpam-6052	364	5	kyungpook	kyungpook	PROPN
ejpam-6052	364	6	mathematical	mathematical	PROPN
ejpam-6052	364	7	journal	journal	PROPN
ejpam-6052	364	8	,	,	PUNCT
ejpam-6052	364	9	53(2):175	53(2):175	NUM
ejpam-6052	364	10	–	–	PUNCT
ejpam-6052	364	11	184	184	NUM
ejpam-6052	364	12	,	,	PUNCT
ejpam-6052	364	13	2013	2013	NUM
ejpam-6052	364	14	.	.	PUNCT
ejpam-6052	365	1	[	[	X
ejpam-6052	365	2	6	6	NUM
ejpam-6052	365	3	]	]	PUNCT
ejpam-6052	365	4	a.	a.	NOUN
ejpam-6052	365	5	walendziak	walendziak	PROPN
ejpam-6052	365	6	.	.	PUNCT
ejpam-6052	366	1	on	on	ADP
ejpam-6052	366	2	bf	bf	NOUN
ejpam-6052	366	3	-algebras	-algebras	PROPN
ejpam-6052	366	4	.	.	PUNCT
ejpam-6052	367	1	mathematica	mathematica	PROPN
ejpam-6052	367	2	slovaca	slovaca	PROPN
ejpam-6052	367	3	,	,	PUNCT
ejpam-6052	367	4	57(2):119–128	57(2):119–128	PROPN
ejpam-6052	367	5	,	,	PUNCT
ejpam-6052	367	6	2007	2007	NUM
ejpam-6052	367	7	.	.	PUNCT
ejpam-6052	368	1	[	[	X
ejpam-6052	368	2	7	7	X
ejpam-6052	368	3	]	]	X
ejpam-6052	368	4	g.	g.	PROPN
ejpam-6052	368	5	georgescu	georgescu	PROPN
ejpam-6052	368	6	and	and	CCONJ
ejpam-6052	368	7	a.	a.	NOUN
ejpam-6052	368	8	iorgulescu	iorgulescu	NOUN
ejpam-6052	368	9	.	.	PUNCT
ejpam-6052	369	1	pseudo	pseudo	NOUN
ejpam-6052	369	2	bck	bck	NOUN
ejpam-6052	369	3	-	-	PUNCT
ejpam-6052	369	4	algebras	algebra	NOUN
ejpam-6052	369	5	:	:	PUNCT
ejpam-6052	369	6	an	an	DET
ejpam-6052	369	7	extension	extension	NOUN
ejpam-6052	369	8	of	of	ADP
ejpam-6052	369	9	bckalgebras	bckalgebras	PROPN
ejpam-6052	369	10	.	.	PUNCT
ejpam-6052	370	1	pages	page	NOUN
ejpam-6052	370	2	97–114	97–114	NUM
ejpam-6052	370	3	,	,	PUNCT
ejpam-6052	370	4	2001	2001	NUM
ejpam-6052	370	5	.	.	PUNCT
ejpam-6052	371	1	[	[	X
ejpam-6052	371	2	8	8	NUM
ejpam-6052	371	3	]	]	X
ejpam-6052	371	4	w.	w.	PROPN
ejpam-6052	371	5	a.	a.	PROPN
ejpam-6052	371	6	dudek	dudek	PROPN
ejpam-6052	371	7	and	and	CCONJ
ejpam-6052	371	8	y.	y.	PROPN
ejpam-6052	371	9	b.	b.	PROPN
ejpam-6052	371	10	jun	jun	PROPN
ejpam-6052	371	11	.	.	PROPN
ejpam-6052	371	12	pseudobci	pseudobci	PROPN
ejpam-6052	371	13	-	-	PUNCT
ejpam-6052	371	14	algebras	algebras	PROPN
ejpam-6052	371	15	.	.	PUNCT
ejpam-6052	372	1	east	east	PROPN
ejpam-6052	372	2	asian	asian	PROPN
ejpam-6052	372	3	mathematical	mathematical	ADJ
ejpam-6052	372	4	journal	journal	NOUN
ejpam-6052	372	5	,	,	PUNCT
ejpam-6052	372	6	24(2):187–190	24(2):187–190	PROPN
ejpam-6052	372	7	,	,	PUNCT
ejpam-6052	372	8	2008	2008	NUM
ejpam-6052	372	9	.	.	PUNCT
ejpam-6052	373	1	[	[	X
ejpam-6052	373	2	9	9	NUM
ejpam-6052	373	3	]	]	X
ejpam-6052	373	4	g.	g.	PROPN
ejpam-6052	373	5	georgescu	georgescu	PROPN
ejpam-6052	373	6	and	and	CCONJ
ejpam-6052	373	7	a.	a.	NOUN
ejpam-6052	373	8	iorgulescu	iorgulescu	NOUN
ejpam-6052	373	9	.	.	PUNCT
ejpam-6052	374	1	pseudo	pseudo	NOUN
ejpam-6052	374	2	mv	mv	PROPN
ejpam-6052	374	3	-algebras	-algebras	PROPN
ejpam-6052	374	4	.	.	PUNCT
ejpam-6052	375	1	multiple	multiple	ADV
ejpam-6052	375	2	-	-	PUNCT
ejpam-6052	375	3	valued	value	VERB
ejpam-6052	375	4	logic	logic	NOUN
ejpam-6052	375	5	,	,	PUNCT
ejpam-6052	375	6	6(12):95–135	6(12):95–135	PROPN
ejpam-6052	375	7	,	,	PUNCT
ejpam-6052	375	8	2001	2001	NUM
ejpam-6052	375	9	.	.	PUNCT
ejpam-6052	376	1	[	[	X
ejpam-6052	376	2	10	10	NUM
ejpam-6052	376	3	]	]	X
ejpam-6052	376	4	a.	a.	NOUN
ejpam-6052	376	5	di	di	PROPN
ejpam-6052	376	6	nola	nola	PROPN
ejpam-6052	376	7	,	,	PUNCT
ejpam-6052	376	8	g.	g.	PROPN
ejpam-6052	376	9	georgescu	georgescu	PROPN
ejpam-6052	376	10	,	,	PUNCT
ejpam-6052	376	11	and	and	CCONJ
ejpam-6052	376	12	a.	a.	NOUN
ejpam-6052	376	13	iorgulescu	iorgulescu	NOUN
ejpam-6052	376	14	.	.	PUNCT
ejpam-6052	377	1	pseudo	pseudo	NOUN
ejpam-6052	377	2	bl	bl	PROPN
ejpam-6052	377	3	-	-	PUNCT
ejpam-6052	377	4	algebras	algebras	PROPN
ejpam-6052	377	5	:	:	PUNCT
ejpam-6052	377	6	part	part	NOUN
ejpam-6052	377	7	i.	i.	PROPN
ejpam-6052	377	8	multiplevalued	multiplevalue	VERB
ejpam-6052	377	9	logic	logic	NOUN
ejpam-6052	377	10	,	,	PUNCT
ejpam-6052	377	11	8(5	8(5	PROPN
ejpam-6052	377	12	-	-	SYM
ejpam-6052	377	13	6):673–714	6):673–714	NUM
ejpam-6052	377	14	,	,	PUNCT
ejpam-6052	377	15	2002	2002	NUM
ejpam-6052	377	16	.	.	PUNCT
ejpam-6052	378	1	[	[	X
ejpam-6052	378	2	11	11	NUM
ejpam-6052	378	3	]	]	PUNCT
ejpam-6052	378	4	a.	a.	NOUN
ejpam-6052	378	5	di	di	PROPN
ejpam-6052	378	6	nola	nola	PROPN
ejpam-6052	378	7	,	,	PUNCT
ejpam-6052	378	8	g.	g.	PROPN
ejpam-6052	378	9	georgescu	georgescu	PROPN
ejpam-6052	378	10	,	,	PUNCT
ejpam-6052	378	11	and	and	CCONJ
ejpam-6052	378	12	a.	a.	NOUN
ejpam-6052	378	13	iorgulescu	iorgulescu	NOUN
ejpam-6052	378	14	.	.	PUNCT
ejpam-6052	379	1	pseudo	pseudo	NOUN
ejpam-6052	379	2	bl	bl	PROPN
ejpam-6052	379	3	-	-	PUNCT
ejpam-6052	379	4	algebras	algebras	PROPN
ejpam-6052	379	5	:	:	PUNCT
ejpam-6052	379	6	part	part	PROPN
ejpam-6052	379	7	ii	ii	PROPN
ejpam-6052	379	8	.	.	PROPN
ejpam-6052	379	9	multiplevalued	multiplevalue	VERB
ejpam-6052	379	10	logic	logic	NOUN
ejpam-6052	379	11	,	,	PUNCT
ejpam-6052	379	12	8(5	8(5	PROPN
ejpam-6052	379	13	-	-	PUNCT
ejpam-6052	379	14	6):717–750	6):717–750	NUM
ejpam-6052	379	15	,	,	PUNCT
ejpam-6052	379	16	2002	2002	NUM
ejpam-6052	379	17	.	.	PUNCT
ejpam-6052	380	1	[	[	X
ejpam-6052	380	2	12	12	NUM
ejpam-6052	380	3	]	]	PUNCT
ejpam-6052	380	4	x.	x.	PROPN
ejpam-6052	380	5	zhang	zhang	PROPN
ejpam-6052	380	6	and	and	CCONJ
ejpam-6052	380	7	x.	x.	PROPN
ejpam-6052	380	8	fan	fan	PROPN
ejpam-6052	380	9	.	.	PUNCT
ejpam-6052	381	1	pseudo	pseudo	NOUN
ejpam-6052	381	2	bl	bl	NOUN
ejpam-6052	381	3	-	-	PUNCT
ejpam-6052	381	4	algebras	algebras	PROPN
ejpam-6052	381	5	and	and	CCONJ
ejpam-6052	381	6	pseudo	pseudo	NOUN
ejpam-6052	381	7	effect	effect	NOUN
ejpam-6052	381	8	algebras	algebra	NOUN
ejpam-6052	381	9	.	.	PUNCT
ejpam-6052	382	1	fuzzy	fuzzy	ADJ
ejpam-6052	382	2	sets	set	NOUN
ejpam-6052	382	3	and	and	CCONJ
ejpam-6052	382	4	systems	system	NOUN
ejpam-6052	382	5	,	,	PUNCT
ejpam-6052	382	6	159(1):95–106	159(1):95–106	NUM
ejpam-6052	382	7	,	,	PUNCT
ejpam-6052	382	8	2008	2008	NUM
ejpam-6052	382	9	.	.	PUNCT
ejpam-6052	383	1	[	[	X
ejpam-6052	383	2	13	13	NUM
ejpam-6052	383	3	]	]	X
ejpam-6052	383	4	j.	j.	PROPN
ejpam-6052	383	5	zhan	zhan	PROPN
ejpam-6052	383	6	,	,	PUNCT
ejpam-6052	383	7	y.	y.	PROPN
ejpam-6052	383	8	b.	b.	PROPN
ejpam-6052	383	9	jun	jun	PROPN
ejpam-6052	383	10	,	,	PUNCT
ejpam-6052	383	11	and	and	CCONJ
ejpam-6052	383	12	h.	h.	PROPN
ejpam-6052	383	13	s.	s.	PROPN
ejpam-6052	383	14	kim	kim	PROPN
ejpam-6052	383	15	.	.	PUNCT
ejpam-6052	384	1	some	some	DET
ejpam-6052	384	2	types	type	NOUN
ejpam-6052	384	3	of	of	ADP
ejpam-6052	384	4	falling	fall	VERB
ejpam-6052	384	5	fuzzy	fuzzy	ADJ
ejpam-6052	384	6	filters	filter	NOUN
ejpam-6052	384	7	of	of	ADP
ejpam-6052	384	8	bl	bl	NOUN
ejpam-6052	384	9	-	-	PUNCT
ejpam-6052	384	10	algebras	algebras	PROPN
ejpam-6052	384	11	and	and	CCONJ
ejpam-6052	384	12	its	its	PRON
ejpam-6052	384	13	applications	application	NOUN
ejpam-6052	384	14	.	.	PUNCT
ejpam-6052	385	1	journal	journal	NOUN
ejpam-6052	385	2	of	of	ADP
ejpam-6052	385	3	intelligent	intelligent	ADJ
ejpam-6052	385	4	&	&	CCONJ
ejpam-6052	385	5	fuzzy	fuzzy	ADJ
ejpam-6052	385	6	systems	system	NOUN
ejpam-6052	385	7	,	,	PUNCT
ejpam-6052	385	8	26(4):1675–1685	26(4):1675–1685	NUM
ejpam-6052	385	9	,	,	PUNCT
ejpam-6052	385	10	2014	2014	NUM
ejpam-6052	385	11	.	.	PUNCT
ejpam-6052	386	1	[	[	X
ejpam-6052	386	2	14	14	NUM
ejpam-6052	386	3	]	]	X
ejpam-6052	386	4	g.	g.	PROPN
ejpam-6052	386	5	dymek	dymek	PROPN
ejpam-6052	386	6	and	and	CCONJ
ejpam-6052	386	7	a.	a.	PROPN
ejpam-6052	386	8	walendziak	walendziak	PROPN
ejpam-6052	386	9	.	.	PUNCT
ejpam-6052	387	1	(	(	PUNCT
ejpam-6052	387	2	fuzzy	fuzzy	ADJ
ejpam-6052	387	3	)	)	PUNCT
ejpam-6052	387	4	ideals	ideal	NOUN
ejpam-6052	387	5	of	of	ADP
ejpam-6052	387	6	bn	bn	NOUN
ejpam-6052	387	7	-algebras	-algebra	NOUN
ejpam-6052	387	8	.	.	PUNCT
ejpam-6052	388	1	the	the	DET
ejpam-6052	388	2	scientific	scientific	ADJ
ejpam-6052	388	3	world	world	NOUN
ejpam-6052	388	4	journal	journal	NOUN
ejpam-6052	388	5	,	,	PUNCT
ejpam-6052	388	6	2015:925040	2015:925040	NUM
ejpam-6052	388	7	,	,	PUNCT
ejpam-6052	388	8	2015	2015	NUM
ejpam-6052	388	9	.	.	PUNCT
ejpam-6052	389	1	[	[	X
ejpam-6052	389	2	15	15	NUM
ejpam-6052	389	3	]	]	X
ejpam-6052	389	4	h.	h.	PROPN
ejpam-6052	389	5	al	al	PROPN
ejpam-6052	389	6	-	-	PUNCT
ejpam-6052	389	7	malki	malki	PROPN
ejpam-6052	389	8	and	and	CCONJ
ejpam-6052	389	9	d.	d.	PROPN
ejpam-6052	389	10	al	al	PROPN
ejpam-6052	389	11	-	-	PUNCT
ejpam-6052	389	12	kadi	kadi	PROPN
ejpam-6052	389	13	.	.	PUNCT
ejpam-6052	390	1	the	the	DET
ejpam-6052	390	2	structure	structure	NOUN
ejpam-6052	390	3	of	of	ADP
ejpam-6052	390	4	pseudo	pseudo	NOUN
ejpam-6052	390	5	-	-	PUNCT
ejpam-6052	390	6	bf	bf	NOUN
ejpam-6052	390	7	/	/	SYM
ejpam-6052	390	8	bf	bf	NOUN
ejpam-6052	390	9	∗-algebra	∗-algebra	NOUN
ejpam-6052	390	10	.	.	PUNCT
ejpam-6052	391	1	european	european	PROPN
ejpam-6052	391	2	journal	journal	PROPN
ejpam-6052	391	3	of	of	ADP
ejpam-6052	391	4	pure	pure	ADJ
ejpam-6052	391	5	and	and	CCONJ
ejpam-6052	391	6	applied	applied	ADJ
ejpam-6052	391	7	mathematics	mathematic	NOUN
ejpam-6052	391	8	,	,	PUNCT
ejpam-6052	391	9	13(3):498–512	13(3):498–512	NUM
ejpam-6052	391	10	,	,	PUNCT
ejpam-6052	391	11	2020	2020	NUM
ejpam-6052	391	12	.	.	PUNCT