id	sid	tid	token	lemma	pos
ejpam-3219	1	1	european	european	PROPN
ejpam-3219	1	2	journal	journal	PROPN
ejpam-3219	1	3	of	of	ADP
ejpam-3219	1	4	pure	pure	ADJ
ejpam-3219	1	5	and	and	CCONJ
ejpam-3219	1	6	applied	apply	VERB
ejpam-3219	1	7	mathematics	mathematic	NOUN
ejpam-3219	1	8	vol	vol	NOUN
ejpam-3219	1	9	.	.	PUNCT
ejpam-3219	2	1	11	11	NUM
ejpam-3219	2	2	,	,	PUNCT
ejpam-3219	2	3	no	no	INTJ
ejpam-3219	2	4	.	.	NOUN
ejpam-3219	2	5	2	2	NUM
ejpam-3219	2	6	,	,	PUNCT
ejpam-3219	2	7	2018	2018	NUM
ejpam-3219	2	8	,	,	PUNCT
ejpam-3219	2	9	444	444	NUM
ejpam-3219	2	10	-	-	SYM
ejpam-3219	2	11	448	448	NUM
ejpam-3219	2	12	issn	issn	PROPN
ejpam-3219	2	13	1307	1307	NUM
ejpam-3219	2	14	-	-	SYM
ejpam-3219	2	15	5543	5543	NUM
ejpam-3219	2	16	–	–	PUNCT
ejpam-3219	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3219	2	18	published	publish	VERB
ejpam-3219	2	19	by	by	ADP
ejpam-3219	3	1	new	new	PROPN
ejpam-3219	3	2	york	york	PROPN
ejpam-3219	3	3	business	business	PROPN
ejpam-3219	3	4	global	global	ADJ
ejpam-3219	3	5	lie	lie	NOUN
ejpam-3219	3	6	algebras	algebra	VERB
ejpam-3219	3	7	with	with	ADP
ejpam-3219	3	8	bcl	bcl	NOUN
ejpam-3219	3	9	algebras	algebras	PROPN
ejpam-3219	3	10	yonghong	yonghong	PROPN
ejpam-3219	3	11	liu	liu	PROPN
ejpam-3219	3	12	school	school	PROPN
ejpam-3219	3	13	of	of	ADP
ejpam-3219	3	14	automation	automation	NOUN
ejpam-3219	3	15	,	,	PUNCT
ejpam-3219	3	16	wuhan	wuhan	PROPN
ejpam-3219	3	17	university	university	PROPN
ejpam-3219	3	18	of	of	ADP
ejpam-3219	3	19	technology	technology	PROPN
ejpam-3219	3	20	,	,	PUNCT
ejpam-3219	3	21	wuhan	wuhan	PROPN
ejpam-3219	3	22	430070	430070	NUM
ejpam-3219	3	23	,	,	PUNCT
ejpam-3219	3	24	china	china	PROPN
ejpam-3219	3	25	abstract	abstract	PROPN
ejpam-3219	3	26	.	.	PUNCT
ejpam-3219	4	1	the	the	DET
ejpam-3219	4	2	subject	subject	ADJ
ejpam-3219	4	3	matter	matter	NOUN
ejpam-3219	4	4	of	of	ADP
ejpam-3219	4	5	this	this	DET
ejpam-3219	4	6	work	work	NOUN
ejpam-3219	4	7	is	be	AUX
ejpam-3219	4	8	hoping	hope	VERB
ejpam-3219	4	9	for	for	ADP
ejpam-3219	4	10	a	a	DET
ejpam-3219	4	11	new	new	ADJ
ejpam-3219	4	12	relationship	relationship	NOUN
ejpam-3219	4	13	between	between	ADP
ejpam-3219	4	14	the	the	DET
ejpam-3219	4	15	lie	lie	NOUN
ejpam-3219	4	16	algebras	algebra	NOUN
ejpam-3219	4	17	and	and	CCONJ
ejpam-3219	4	18	the	the	DET
ejpam-3219	4	19	algebra	algebra	NOUN
ejpam-3219	4	20	of	of	ADP
ejpam-3219	4	21	logic	logic	NOUN
ejpam-3219	4	22	,	,	PUNCT
ejpam-3219	4	23	which	which	PRON
ejpam-3219	4	24	will	will	AUX
ejpam-3219	4	25	constitute	constitute	VERB
ejpam-3219	4	26	an	an	DET
ejpam-3219	4	27	important	important	ADJ
ejpam-3219	4	28	part	part	NOUN
ejpam-3219	4	29	of	of	ADP
ejpam-3219	4	30	our	our	PRON
ejpam-3219	4	31	study	study	NOUN
ejpam-3219	4	32	of	of	ADP
ejpam-3219	4	33	“	"	PUNCT
ejpam-3219	4	34	pure	pure	ADJ
ejpam-3219	4	35	”	"	PUNCT
ejpam-3219	4	36	algebra	algebra	NOUN
ejpam-3219	4	37	theory	theory	NOUN
ejpam-3219	4	38	.	.	PUNCT
ejpam-3219	5	1	bcl	bcl	NOUN
ejpam-3219	5	2	algebras	algebra	VERB
ejpam-3219	5	3	as	as	ADP
ejpam-3219	5	4	a	a	DET
ejpam-3219	5	5	class	class	NOUN
ejpam-3219	5	6	of	of	ADP
ejpam-3219	5	7	logical	logical	ADJ
ejpam-3219	5	8	algebras	algebra	NOUN
ejpam-3219	5	9	can	can	AUX
ejpam-3219	5	10	be	be	AUX
ejpam-3219	5	11	generated	generate	VERB
ejpam-3219	5	12	by	by	ADP
ejpam-3219	5	13	a	a	DET
ejpam-3219	5	14	lie	lie	NOUN
ejpam-3219	5	15	algebra	algebra	NOUN
ejpam-3219	5	16	.	.	PUNCT
ejpam-3219	6	1	the	the	DET
ejpam-3219	6	2	opposite	opposite	NOUN
ejpam-3219	6	3	is	be	AUX
ejpam-3219	6	4	also	also	ADV
ejpam-3219	6	5	true	true	ADJ
ejpam-3219	6	6	that	that	SCONJ
ejpam-3219	6	7	when	when	SCONJ
ejpam-3219	6	8	special	special	ADJ
ejpam-3219	6	9	conditions	condition	NOUN
ejpam-3219	6	10	occur	occur	VERB
ejpam-3219	6	11	.	.	PUNCT
ejpam-3219	7	1	the	the	DET
ejpam-3219	7	2	aim	aim	NOUN
ejpam-3219	7	3	of	of	ADP
ejpam-3219	7	4	this	this	DET
ejpam-3219	7	5	paper	paper	NOUN
ejpam-3219	7	6	is	be	AUX
ejpam-3219	7	7	to	to	PART
ejpam-3219	7	8	prove	prove	VERB
ejpam-3219	7	9	several	several	ADJ
ejpam-3219	7	10	theorems	theorem	NOUN
ejpam-3219	7	11	on	on	ADP
ejpam-3219	7	12	lie	lie	NOUN
ejpam-3219	7	13	algebras	algebra	NOUN
ejpam-3219	7	14	with	with	SCONJ
ejpam-3219	7	15	bcl	bcl	NOUN
ejpam-3219	7	16	algebras	algebra	VERB
ejpam-3219	7	17	.	.	PUNCT
ejpam-3219	8	1	i	i	PRON
ejpam-3219	8	2	introduce	introduce	VERB
ejpam-3219	8	3	the	the	DET
ejpam-3219	8	4	notion	notion	NOUN
ejpam-3219	8	5	of	of	ADP
ejpam-3219	8	6	a	a	DET
ejpam-3219	8	7	“	"	PUNCT
ejpam-3219	8	8	pseudo	pseudo	NOUN
ejpam-3219	8	9	-	-	NOUN
ejpam-3219	8	10	association	association	NOUN
ejpam-3219	8	11	”	"	PUNCT
ejpam-3219	8	12	which	which	PRON
ejpam-3219	8	13	i	i	PRON
ejpam-3219	8	14	propose	propose	VERB
ejpam-3219	8	15	as	as	ADP
ejpam-3219	8	16	the	the	DET
ejpam-3219	8	17	adjoint	adjoint	NOUN
ejpam-3219	8	18	notion	notion	NOUN
ejpam-3219	8	19	of	of	ADP
ejpam-3219	8	20	bcl	bcl	NOUN
ejpam-3219	8	21	algebra	algebra	NOUN
ejpam-3219	8	22	in	in	ADP
ejpam-3219	8	23	the	the	DET
ejpam-3219	8	24	abelian	abelian	ADJ
ejpam-3219	8	25	group	group	NOUN
ejpam-3219	8	26	.	.	PUNCT
ejpam-3219	9	1	2010	2010	NUM
ejpam-3219	9	2	mathematics	mathematic	NOUN
ejpam-3219	9	3	subject	subject	NOUN
ejpam-3219	9	4	classifications	classification	NOUN
ejpam-3219	9	5	:	:	PUNCT
ejpam-3219	9	6	17b60	17b60	NUM
ejpam-3219	9	7	,	,	PUNCT
ejpam-3219	9	8	03g25	03g25	NOUN
ejpam-3219	9	9	key	key	ADJ
ejpam-3219	9	10	words	word	NOUN
ejpam-3219	9	11	and	and	CCONJ
ejpam-3219	9	12	phrases	phrase	NOUN
ejpam-3219	9	13	:	:	PUNCT
ejpam-3219	9	14	lie	lie	NOUN
ejpam-3219	9	15	algebras	algebra	NOUN
ejpam-3219	9	16	,	,	PUNCT
ejpam-3219	9	17	bcl	bcl	NOUN
ejpam-3219	9	18	algebras	algebra	NOUN
ejpam-3219	9	19	,	,	PUNCT
ejpam-3219	9	20	abelian	abelian	PROPN
ejpam-3219	9	21	lie	lie	NOUN
ejpam-3219	9	22	algebras	algebra	NOUN
ejpam-3219	9	23	,	,	PUNCT
ejpam-3219	9	24	pseudo	pseudo	NOUN
ejpam-3219	9	25	-	-	NOUN
ejpam-3219	9	26	association	association	NOUN
ejpam-3219	9	27	bcl	bcl	NOUN
ejpam-3219	9	28	algrbra	algrbra	VERB
ejpam-3219	9	29	1	1	X
ejpam-3219	9	30	.	.	X
ejpam-3219	10	1	introduction	introduction	NOUN
ejpam-3219	10	2	lie	lie	NOUN
ejpam-3219	10	3	algebras	algebra	NOUN
ejpam-3219	10	4	comprise	comprise	VERB
ejpam-3219	10	5	a	a	DET
ejpam-3219	10	6	significant	significant	ADJ
ejpam-3219	10	7	part	part	NOUN
ejpam-3219	10	8	of	of	ADP
ejpam-3219	10	9	lie	lie	NOUN
ejpam-3219	10	10	group	group	NOUN
ejpam-3219	10	11	theory	theory	NOUN
ejpam-3219	10	12	(	(	PUNCT
ejpam-3219	10	13	see	see	VERB
ejpam-3219	10	14	[	[	X
ejpam-3219	10	15	1	1	NUM
ejpam-3219	10	16	]	]	PUNCT
ejpam-3219	10	17	)	)	PUNCT
ejpam-3219	10	18	and	and	CCONJ
ejpam-3219	10	19	are	be	AUX
ejpam-3219	10	20	being	be	AUX
ejpam-3219	10	21	vibrantly	vibrantly	ADV
ejpam-3219	10	22	studied	study	VERB
ejpam-3219	10	23	.	.	PUNCT
ejpam-3219	11	1	on	on	ADP
ejpam-3219	11	2	the	the	DET
ejpam-3219	11	3	other	other	ADJ
ejpam-3219	11	4	hand	hand	NOUN
ejpam-3219	11	5	,	,	PUNCT
ejpam-3219	11	6	lie	lie	NOUN
ejpam-3219	11	7	algebras	algebra	NOUN
ejpam-3219	11	8	and	and	CCONJ
ejpam-3219	11	9	their	their	PRON
ejpam-3219	11	10	representations	representation	NOUN
ejpam-3219	11	11	are	be	AUX
ejpam-3219	11	12	used	use	VERB
ejpam-3219	11	13	extensively	extensively	ADV
ejpam-3219	11	14	in	in	ADP
ejpam-3219	11	15	physics	physics	NOUN
ejpam-3219	11	16	,	,	PUNCT
ejpam-3219	11	17	notably	notably	ADV
ejpam-3219	11	18	in	in	ADP
ejpam-3219	11	19	quantum	quantum	ADJ
ejpam-3219	11	20	mechanics	mechanic	NOUN
ejpam-3219	11	21	and	and	CCONJ
ejpam-3219	11	22	particle	particle	NOUN
ejpam-3219	11	23	physics	physics	NOUN
ejpam-3219	11	24	.	.	PUNCT
ejpam-3219	12	1	but	but	CCONJ
ejpam-3219	12	2	it	it	PRON
ejpam-3219	12	3	is	be	AUX
ejpam-3219	12	4	significant	significant	ADJ
ejpam-3219	12	5	that	that	SCONJ
ejpam-3219	12	6	our	our	PRON
ejpam-3219	12	7	results	result	NOUN
ejpam-3219	12	8	show	show	VERB
ejpam-3219	12	9	that	that	SCONJ
ejpam-3219	12	10	the	the	DET
ejpam-3219	12	11	lie	lie	NOUN
ejpam-3219	12	12	algebra	algebra	NOUN
ejpam-3219	12	13	and	and	CCONJ
ejpam-3219	12	14	logical	logical	ADJ
ejpam-3219	12	15	algebra	algebra	NOUN
ejpam-3219	12	16	are	be	AUX
ejpam-3219	12	17	closely	closely	ADV
ejpam-3219	12	18	linked	link	VERB
ejpam-3219	12	19	.	.	PUNCT
ejpam-3219	13	1	sure	sure	ADJ
ejpam-3219	13	2	,	,	PUNCT
ejpam-3219	13	3	bcl	bcl	NOUN
ejpam-3219	13	4	algebras	algebra	VERB
ejpam-3219	13	5	as	as	SCONJ
ejpam-3219	13	6	a	a	DET
ejpam-3219	13	7	class	class	NOUN
ejpam-3219	13	8	of	of	ADP
ejpam-3219	13	9	logical	logical	ADJ
ejpam-3219	13	10	algebras	algebra	NOUN
ejpam-3219	13	11	were	be	AUX
ejpam-3219	13	12	introduced	introduce	VERB
ejpam-3219	13	13	by	by	ADP
ejpam-3219	13	14	liu	liu	PROPN
ejpam-3219	13	15	in	in	ADP
ejpam-3219	13	16	2011	2011	NUM
ejpam-3219	14	1	[	[	X
ejpam-3219	14	2	2	2	NUM
ejpam-3219	14	3	]	]	PUNCT
ejpam-3219	14	4	.	.	PUNCT
ejpam-3219	15	1	the	the	DET
ejpam-3219	15	2	last	last	ADJ
ejpam-3219	15	3	results	result	NOUN
ejpam-3219	15	4	was	be	AUX
ejpam-3219	15	5	discovered	discover	VERB
ejpam-3219	15	6	and	and	CCONJ
ejpam-3219	15	7	developed	develop	VERB
ejpam-3219	15	8	in	in	ADP
ejpam-3219	15	9	[	[	PUNCT
ejpam-3219	15	10	3	3	NUM
ejpam-3219	15	11	-	-	SYM
ejpam-3219	15	12	15	15	NUM
ejpam-3219	15	13	]	]	PUNCT
ejpam-3219	15	14	.	.	PUNCT
ejpam-3219	16	1	from	from	ADP
ejpam-3219	16	2	set	set	ADJ
ejpam-3219	16	3	theory	theory	NOUN
ejpam-3219	16	4	perspective	perspective	NOUN
ejpam-3219	16	5	,	,	PUNCT
ejpam-3219	16	6	bcl	bcl	NOUN
ejpam-3219	16	7	algebras	algebra	NOUN
ejpam-3219	16	8	are	be	AUX
ejpam-3219	16	9	the	the	DET
ejpam-3219	16	10	algebraic	algebraic	ADJ
ejpam-3219	16	11	formulations	formulation	NOUN
ejpam-3219	16	12	of	of	ADP
ejpam-3219	16	13	the	the	DET
ejpam-3219	16	14	set	set	ADJ
ejpam-3219	16	15	difference	difference	NOUN
ejpam-3219	16	16	together	together	ADV
ejpam-3219	16	17	with	with	ADP
ejpam-3219	16	18	its	its	PRON
ejpam-3219	16	19	properties	property	NOUN
ejpam-3219	16	20	.	.	PUNCT
ejpam-3219	17	1	in	in	ADP
ejpam-3219	17	2	the	the	DET
ejpam-3219	17	3	paper	paper	NOUN
ejpam-3219	17	4	,	,	PUNCT
ejpam-3219	17	5	i	i	PRON
ejpam-3219	17	6	just	just	ADV
ejpam-3219	17	7	want	want	VERB
ejpam-3219	17	8	to	to	PART
ejpam-3219	17	9	prove	prove	VERB
ejpam-3219	17	10	that	that	SCONJ
ejpam-3219	17	11	the	the	DET
ejpam-3219	17	12	connectivity	connectivity	NOUN
ejpam-3219	17	13	theorems	theorem	NOUN
ejpam-3219	17	14	but	but	CCONJ
ejpam-3219	17	15	that	that	SCONJ
ejpam-3219	17	16	i	i	PRON
ejpam-3219	17	17	have	have	AUX
ejpam-3219	17	18	suspected	suspect	VERB
ejpam-3219	17	19	for	for	ADP
ejpam-3219	17	20	a	a	DET
ejpam-3219	17	21	long	long	ADJ
ejpam-3219	17	22	time	time	NOUN
ejpam-3219	17	23	,	,	PUNCT
ejpam-3219	17	24	which	which	PRON
ejpam-3219	17	25	is	be	AUX
ejpam-3219	17	26	the	the	DET
ejpam-3219	17	27	relationship	relationship	NOUN
ejpam-3219	17	28	between	between	ADP
ejpam-3219	17	29	the	the	DET
ejpam-3219	17	30	lie	lie	NOUN
ejpam-3219	17	31	algebras	algebra	NOUN
ejpam-3219	17	32	and	and	CCONJ
ejpam-3219	17	33	the	the	DET
ejpam-3219	17	34	bcl	bcl	NOUN
ejpam-3219	17	35	algebras	algebra	VERB
ejpam-3219	17	36	.	.	PUNCT
ejpam-3219	18	1	more	more	ADV
ejpam-3219	18	2	importantly	importantly	ADV
ejpam-3219	18	3	,	,	PUNCT
ejpam-3219	18	4	we	we	PRON
ejpam-3219	18	5	developed	develop	VERB
ejpam-3219	18	6	the	the	DET
ejpam-3219	18	7	theory	theory	NOUN
ejpam-3219	18	8	that	that	PRON
ejpam-3219	18	9	lie	lie	NOUN
ejpam-3219	18	10	algebras	algebra	NOUN
ejpam-3219	18	11	do	do	AUX
ejpam-3219	18	12	have	have	AUX
ejpam-3219	18	13	a	a	DET
ejpam-3219	18	14	preferred	preferred	ADJ
ejpam-3219	18	15	direction	direction	NOUN
ejpam-3219	18	16	that	that	PRON
ejpam-3219	18	17	causes	cause	VERB
ejpam-3219	18	18	us	we	PRON
ejpam-3219	18	19	to	to	ADP
ejpam-3219	18	20	the	the	DET
ejpam-3219	18	21	study	study	NOUN
ejpam-3219	18	22	of	of	ADP
ejpam-3219	18	23	logic	logic	NOUN
ejpam-3219	18	24	issues	issue	NOUN
ejpam-3219	18	25	so	so	SCONJ
ejpam-3219	18	26	we	we	PRON
ejpam-3219	18	27	can	can	AUX
ejpam-3219	18	28	capture	capture	VERB
ejpam-3219	18	29	new	new	ADJ
ejpam-3219	18	30	method	method	NOUN
ejpam-3219	18	31	.	.	PUNCT
ejpam-3219	19	1	meanwhile	meanwhile	ADV
ejpam-3219	19	2	,	,	PUNCT
ejpam-3219	19	3	let	let	VERB
ejpam-3219	19	4	the	the	DET
ejpam-3219	19	5	theory	theory	NOUN
ejpam-3219	19	6	of	of	ADP
ejpam-3219	19	7	bcl	bcl	NOUN
ejpam-3219	19	8	algebras	algebra	NOUN
ejpam-3219	19	9	becomes	become	VERB
ejpam-3219	19	10	strong	strong	ADJ
ejpam-3219	19	11	enough	enough	ADV
ejpam-3219	19	12	.	.	PUNCT
ejpam-3219	20	1	email	email	NOUN
ejpam-3219	20	2	address	address	NOUN
ejpam-3219	20	3	:	:	PUNCT
ejpam-3219	20	4	hylinin@163.com	hylinin@163.com	PROPN
ejpam-3219	20	5	(	(	PUNCT
ejpam-3219	20	6	y.	y.	PROPN
ejpam-3219	20	7	liu	liu	PROPN
ejpam-3219	20	8	)	)	PUNCT
ejpam-3219	20	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3219	21	1	444	444	NUM
ejpam-3219	21	2	c	c	NOUN
ejpam-3219	21	3	©	©	PROPN
ejpam-3219	21	4	2018	2018	NUM
ejpam-3219	21	5	ejpam	ejpam	VERB
ejpam-3219	21	6	all	all	DET
ejpam-3219	21	7	rights	right	NOUN
ejpam-3219	21	8	reserved	reserve	VERB
ejpam-3219	21	9	.	.	PUNCT
ejpam-3219	22	1	yonghong	yonghong	PROPN
ejpam-3219	22	2	l.	l.	PROPN
ejpam-3219	22	3	/	/	SYM
ejpam-3219	22	4	eur	eur	PROPN
ejpam-3219	22	5	.	.	PUNCT
ejpam-3219	23	1	j.	j.	PROPN
ejpam-3219	23	2	pure	pure	PROPN
ejpam-3219	23	3	appl	appl	PROPN
ejpam-3219	23	4	.	.	PROPN
ejpam-3219	23	5	math	math	PROPN
ejpam-3219	23	6	,	,	PUNCT
ejpam-3219	23	7	11	11	NUM
ejpam-3219	23	8	(	(	PUNCT
ejpam-3219	23	9	2	2	NUM
ejpam-3219	23	10	)	)	PUNCT
ejpam-3219	23	11	(	(	PUNCT
ejpam-3219	23	12	2018	2018	NUM
ejpam-3219	23	13	)	)	PUNCT
ejpam-3219	23	14	,	,	PUNCT
ejpam-3219	23	15	444	444	NUM
ejpam-3219	23	16	-	-	SYM
ejpam-3219	23	17	448	448	NUM
ejpam-3219	23	18	445	445	NUM
ejpam-3219	23	19	2	2	NUM
ejpam-3219	23	20	.	.	PUNCT
ejpam-3219	23	21	basic	basic	ADJ
ejpam-3219	23	22	definitions	definition	NOUN
ejpam-3219	23	23	in	in	ADP
ejpam-3219	23	24	this	this	DET
ejpam-3219	23	25	section	section	NOUN
ejpam-3219	23	26	,	,	PUNCT
ejpam-3219	23	27	we	we	PRON
ejpam-3219	23	28	list	list	VERB
ejpam-3219	23	29	two	two	NUM
ejpam-3219	23	30	definitions	definition	NOUN
ejpam-3219	23	31	from	from	ADP
ejpam-3219	23	32	the	the	DET
ejpam-3219	23	33	literature	literature	NOUN
ejpam-3219	23	34	that	that	PRON
ejpam-3219	23	35	will	will	AUX
ejpam-3219	23	36	be	be	AUX
ejpam-3219	23	37	used	use	VERB
ejpam-3219	23	38	in	in	ADP
ejpam-3219	23	39	the	the	DET
ejpam-3219	23	40	sequel	sequel	NOUN
ejpam-3219	23	41	.	.	PUNCT
ejpam-3219	24	1	definition	definition	NOUN
ejpam-3219	24	2	2.1	2.1	NUM
ejpam-3219	24	3	a	a	DET
ejpam-3219	24	4	lie	lie	NOUN
ejpam-3219	24	5	algebra	algebra	NOUN
ejpam-3219	24	6	over	over	ADP
ejpam-3219	24	7	a	a	DET
ejpam-3219	24	8	field	field	NOUN
ejpam-3219	25	1	k	k	X
ejpam-3219	25	2	is	be	AUX
ejpam-3219	25	3	a	a	DET
ejpam-3219	25	4	vector	vector	NOUN
ejpam-3219	25	5	space	space	NOUN
ejpam-3219	25	6	g	g	NOUN
ejpam-3219	25	7	over	over	ADP
ejpam-3219	25	8	k	k	PROPN
ejpam-3219	25	9	together	together	ADV
ejpam-3219	25	10	with	with	ADP
ejpam-3219	25	11	a	a	DET
ejpam-3219	25	12	k	k	ADJ
ejpam-3219	25	13	-	-	PUNCT
ejpam-3219	25	14	bilinear	bilinear	ADJ
ejpam-3219	25	15	map	map	NOUN
ejpam-3219	25	16	[	[	PUNCT
ejpam-3219	25	17	,	,	PUNCT
ejpam-3219	25	18	]	]	X
ejpam-3219	25	19	:	:	PUNCT
ejpam-3219	25	20	g	g	ADP
ejpam-3219	25	21	×	×	PROPN
ejpam-3219	25	22	g	g	PROPN
ejpam-3219	25	23	→	→	SYM
ejpam-3219	25	24	g	g	PROPN
ejpam-3219	25	25	(	(	PUNCT
ejpam-3219	25	26	called	call	VERB
ejpam-3219	25	27	the	the	DET
ejpam-3219	25	28	bracket	bracket	NOUN
ejpam-3219	25	29	)	)	PUNCT
ejpam-3219	25	30	such	such	ADJ
ejpam-3219	25	31	that	that	PRON
ejpam-3219	25	32	(	(	PUNCT
ejpam-3219	25	33	lie	lie	NOUN
ejpam-3219	25	34	1	1	NUM
ejpam-3219	25	35	)	)	PUNCT
ejpam-3219	26	1	[	[	X
ejpam-3219	26	2	x	x	X
ejpam-3219	26	3	,	,	PUNCT
ejpam-3219	26	4	x	x	X
ejpam-3219	26	5	]	]	X
ejpam-3219	26	6	=	=	SYM
ejpam-3219	26	7	0	0	NUM
ejpam-3219	26	8	for	for	ADP
ejpam-3219	26	9	all	all	DET
ejpam-3219	26	10	x	x	SYM
ejpam-3219	26	11	∈	∈	PROPN
ejpam-3219	26	12	g	g	NOUN
ejpam-3219	26	13	(	(	PUNCT
ejpam-3219	26	14	lie	lie	NOUN
ejpam-3219	26	15	2	2	NUM
ejpam-3219	26	16	)	)	PUNCT
ejpam-3219	27	1	[	[	X
ejpam-3219	27	2	x	x	X
ejpam-3219	27	3	,	,	PUNCT
ejpam-3219	27	4	[	[	X
ejpam-3219	27	5	y	y	X
ejpam-3219	27	6	,	,	PUNCT
ejpam-3219	27	7	z	z	X
ejpam-3219	27	8	]	]	X
ejpam-3219	27	9	]	]	PUNCT
ejpam-3219	28	1	+	+	CCONJ
ejpam-3219	28	2	[	[	X
ejpam-3219	28	3	y	y	X
ejpam-3219	28	4	,	,	PUNCT
ejpam-3219	28	5	[	[	X
ejpam-3219	28	6	z	z	X
ejpam-3219	28	7	,	,	PUNCT
ejpam-3219	28	8	x	x	X
ejpam-3219	28	9	]	]	X
ejpam-3219	28	10	]	]	PUNCT
ejpam-3219	29	1	+	+	CCONJ
ejpam-3219	30	1	[	[	X
ejpam-3219	30	2	z	z	X
ejpam-3219	30	3	,	,	PUNCT
ejpam-3219	30	4	[	[	X
ejpam-3219	30	5	x	x	X
ejpam-3219	30	6	,	,	PUNCT
ejpam-3219	30	7	y	y	PROPN
ejpam-3219	30	8	]	]	X
ejpam-3219	30	9	]	]	X
ejpam-3219	30	10	=	=	SYM
ejpam-3219	30	11	0	0	NUM
ejpam-3219	30	12	for	for	ADP
ejpam-3219	30	13	all	all	DET
ejpam-3219	30	14	x	x	NOUN
ejpam-3219	30	15	,	,	PUNCT
ejpam-3219	30	16	y	y	PROPN
ejpam-3219	30	17	,	,	PUNCT
ejpam-3219	30	18	z	z	PROPN
ejpam-3219	30	19	∈	∈	PROPN
ejpam-3219	30	20	g.	g.	NOUN
ejpam-3219	30	21	a	a	DET
ejpam-3219	30	22	homomorphism	homomorphism	NOUN
ejpam-3219	30	23	of	of	ADP
ejpam-3219	30	24	lie	lie	NOUN
ejpam-3219	30	25	algebras	algebras	PROPN
ejpam-3219	30	26	is	be	AUX
ejpam-3219	30	27	a	a	DET
ejpam-3219	30	28	k	k	ADJ
ejpam-3219	30	29	-	-	PUNCT
ejpam-3219	30	30	linear	linear	ADJ
ejpam-3219	30	31	map	map	NOUN
ejpam-3219	30	32	α	α	NOUN
ejpam-3219	30	33	:	:	PUNCT
ejpam-3219	30	34	g	g	PROPN
ejpam-3219	30	35	→	→	SYM
ejpam-3219	30	36	g′	g′	NOUN
ejpam-3219	30	37	such	such	ADJ
ejpam-3219	30	38	that	that	DET
ejpam-3219	30	39	α([x	α([x	PROPN
ejpam-3219	30	40	,	,	PUNCT
ejpam-3219	30	41	y	y	NOUN
ejpam-3219	30	42	]	]	X
ejpam-3219	30	43	)	)	PUNCT
ejpam-3219	30	44	=	=	PUNCT
ejpam-3219	31	1	[	[	X
ejpam-3219	31	2	α(x	α(x	NOUN
ejpam-3219	31	3	)	)	PUNCT
ejpam-3219	31	4	,	,	PUNCT
ejpam-3219	31	5	α(y	α(y	NOUN
ejpam-3219	31	6	)	)	PUNCT
ejpam-3219	31	7	]	]	PUNCT
ejpam-3219	31	8	for	for	ADP
ejpam-3219	31	9	all	all	DET
ejpam-3219	31	10	x	x	PROPN
ejpam-3219	31	11	,	,	PUNCT
ejpam-3219	31	12	y	y	PROPN
ejpam-3219	31	13	,	,	PUNCT
ejpam-3219	31	14	z	z	PROPN
ejpam-3219	31	15	∈	∈	PROPN
ejpam-3219	31	16	g.	g.	NOUN
ejpam-3219	31	17	condition	condition	NOUN
ejpam-3219	31	18	(	(	PUNCT
ejpam-3219	31	19	lie	lie	NOUN
ejpam-3219	31	20	2	2	NUM
ejpam-3219	31	21	)	)	PUNCT
ejpam-3219	31	22	is	be	AUX
ejpam-3219	31	23	called	call	VERB
ejpam-3219	31	24	the	the	DET
ejpam-3219	31	25	jacobi	jacobi	PROPN
ejpam-3219	31	26	identity	identity	NOUN
ejpam-3219	31	27	.	.	PUNCT
ejpam-3219	32	1	note	note	VERB
ejpam-3219	32	2	that	that	SCONJ
ejpam-3219	32	3	(	(	PUNCT
ejpam-3219	32	4	lie	lie	NOUN
ejpam-3219	32	5	1	1	NUM
ejpam-3219	32	6	)	)	PUNCT
ejpam-3219	32	7	applied	apply	VERB
ejpam-3219	32	8	to	to	ADP
ejpam-3219	32	9	[	[	X
ejpam-3219	32	10	x	x	X
ejpam-3219	32	11	+	+	NUM
ejpam-3219	32	12	y	y	NOUN
ejpam-3219	32	13	,	,	PUNCT
ejpam-3219	32	14	x	x	PUNCT
ejpam-3219	33	1	+	+	NUM
ejpam-3219	33	2	y	y	X
ejpam-3219	33	3	]	]	PUNCT
ejpam-3219	33	4	shows	show	VERB
ejpam-3219	33	5	that	that	SCONJ
ejpam-3219	33	6	the	the	DET
ejpam-3219	33	7	lie	lie	NOUN
ejpam-3219	33	8	bracket	bracket	NOUN
ejpam-3219	33	9	is	be	AUX
ejpam-3219	33	10	skew	skew	ADJ
ejpam-3219	33	11	-	-	PUNCT
ejpam-3219	33	12	symmetric	symmetric	ADJ
ejpam-3219	33	13	.	.	PUNCT
ejpam-3219	34	1	[	[	X
ejpam-3219	34	2	x	x	X
ejpam-3219	34	3	,	,	PUNCT
ejpam-3219	34	4	y	y	PROPN
ejpam-3219	34	5	]	]	X
ejpam-3219	34	6	=	=	PUNCT
ejpam-3219	35	1	−	−	PROPN
ejpam-3219	36	1	[	[	X
ejpam-3219	36	2	y	y	PROPN
ejpam-3219	36	3	,	,	PUNCT
ejpam-3219	36	4	x	x	X
ejpam-3219	36	5	]	]	X
ejpam-3219	36	6	for	for	ADP
ejpam-3219	36	7	all	all	DET
ejpam-3219	36	8	x	x	PROPN
ejpam-3219	36	9	,	,	PUNCT
ejpam-3219	36	10	y	y	PROPN
ejpam-3219	36	11	,	,	PUNCT
ejpam-3219	36	12	z	z	PROPN
ejpam-3219	36	13	∈	∈	PROPN
ejpam-3219	36	14	g.	g.	NOUN
ejpam-3219	36	15	definition	definition	NOUN
ejpam-3219	36	16	2.2	2.2	NUM
ejpam-3219	36	17	(	(	PUNCT
ejpam-3219	36	18	[	[	X
ejpam-3219	36	19	2	2	NUM
ejpam-3219	36	20	]	]	PUNCT
ejpam-3219	36	21	,	,	PUNCT
ejpam-3219	36	22	definition	definition	NOUN
ejpam-3219	36	23	2.1	2.1	NUM
ejpam-3219	36	24	.	.	PUNCT
ejpam-3219	36	25	)	)	PUNCT
ejpam-3219	37	1	a	a	DET
ejpam-3219	37	2	bcl	bcl	NOUN
ejpam-3219	37	3	algebra	algebra	NOUN
ejpam-3219	37	4	is	be	AUX
ejpam-3219	37	5	a	a	DET
ejpam-3219	37	6	triple	triple	ADJ
ejpam-3219	37	7	(	(	PUNCT
ejpam-3219	37	8	a	a	PRON
ejpam-3219	37	9	;	;	PUNCT
ejpam-3219	37	10	→	→	NOUN
ejpam-3219	37	11	,	,	PUNCT
ejpam-3219	37	12	0	0	NUM
ejpam-3219	37	13	)	)	PUNCT
ejpam-3219	37	14	,	,	PUNCT
ejpam-3219	37	15	where	where	SCONJ
ejpam-3219	37	16	a	a	PRON
ejpam-3219	37	17	is	be	AUX
ejpam-3219	37	18	a	a	DET
ejpam-3219	37	19	nonempty	nonempty	ADJ
ejpam-3219	37	20	set	set	VERB
ejpam-3219	37	21	,	,	PUNCT
ejpam-3219	37	22	→	→	X
ejpam-3219	37	23	is	be	AUX
ejpam-3219	37	24	a	a	DET
ejpam-3219	37	25	binary	binary	ADJ
ejpam-3219	37	26	operation	operation	NOUN
ejpam-3219	37	27	on	on	ADP
ejpam-3219	37	28	a	a	PRON
ejpam-3219	37	29	,	,	PUNCT
ejpam-3219	37	30	the	the	DET
ejpam-3219	37	31	following	follow	VERB
ejpam-3219	37	32	three	three	NUM
ejpam-3219	37	33	axioms	axiom	NOUN
ejpam-3219	37	34	hold	hold	VERB
ejpam-3219	37	35	for	for	ADP
ejpam-3219	37	36	any	any	DET
ejpam-3219	37	37	x	x	NOUN
ejpam-3219	37	38	,	,	PUNCT
ejpam-3219	37	39	y	y	PROPN
ejpam-3219	37	40	,	,	PUNCT
ejpam-3219	37	41	z	z	PROPN
ejpam-3219	37	42	∈	∈	PROPN
ejpam-3219	37	43	a.	a.	NOUN
ejpam-3219	37	44	(	(	PUNCT
ejpam-3219	37	45	bcl	bcl	NOUN
ejpam-3219	37	46	1	1	NUM
ejpam-3219	37	47	)	)	PUNCT
ejpam-3219	37	48	x	x	PUNCT
ejpam-3219	38	1	→	→	PUNCT
ejpam-3219	38	2	x	x	SYM
ejpam-3219	38	3	=	=	SYM
ejpam-3219	38	4	0	0	NUM
ejpam-3219	38	5	.	.	PUNCT
ejpam-3219	39	1	(	(	PUNCT
ejpam-3219	39	2	bcl	bcl	NOUN
ejpam-3219	39	3	2	2	NUM
ejpam-3219	39	4	)	)	PUNCT
ejpam-3219	39	5	x	x	PUNCT
ejpam-3219	40	1	→	→	PUNCT
ejpam-3219	40	2	y	y	PROPN
ejpam-3219	40	3	=	=	SYM
ejpam-3219	40	4	0	0	PROPN
ejpam-3219	40	5	and	and	CCONJ
ejpam-3219	40	6	y	y	PROPN
ejpam-3219	40	7	→	→	SYM
ejpam-3219	40	8	x	x	SYM
ejpam-3219	40	9	=	=	SYM
ejpam-3219	40	10	0	0	NUM
ejpam-3219	40	11	imply	imply	VERB
ejpam-3219	40	12	x	x	X
ejpam-3219	41	1	=	=	SYM
ejpam-3219	41	2	y.	y.	NOUN
ejpam-3219	41	3	(	(	PUNCT
ejpam-3219	41	4	bcl	bcl	NOUN
ejpam-3219	41	5	3	3	NUM
ejpam-3219	41	6	)	)	PUNCT
ejpam-3219	41	7	(	(	PUNCT
ejpam-3219	41	8	(	(	PUNCT
ejpam-3219	41	9	(	(	PUNCT
ejpam-3219	41	10	x	x	SYM
ejpam-3219	41	11	→	→	SYM
ejpam-3219	41	12	y	y	NOUN
ejpam-3219	41	13	)	)	PUNCT
ejpam-3219	41	14	→	→	SYM
ejpam-3219	41	15	z	z	X
ejpam-3219	41	16	)	)	PUNCT
ejpam-3219	41	17	→	→	X
ejpam-3219	41	18	(	(	PUNCT
ejpam-3219	41	19	(	(	PUNCT
ejpam-3219	41	20	x	x	SYM
ejpam-3219	41	21	→	→	SYM
ejpam-3219	41	22	z	z	NOUN
ejpam-3219	41	23	)	)	PUNCT
ejpam-3219	41	24	→	→	SYM
ejpam-3219	41	25	y	y	PROPN
ejpam-3219	41	26	)	)	PUNCT
ejpam-3219	41	27	)	)	PUNCT
ejpam-3219	41	28	→	→	PUNCT
ejpam-3219	41	29	(	(	PUNCT
ejpam-3219	41	30	(	(	PUNCT
ejpam-3219	41	31	z	z	NOUN
ejpam-3219	41	32	→	→	SYM
ejpam-3219	41	33	y	y	NOUN
ejpam-3219	41	34	)	)	PUNCT
ejpam-3219	41	35	→	→	SYM
ejpam-3219	41	36	x	x	X
ejpam-3219	41	37	)	)	PUNCT
ejpam-3219	41	38	=	=	SYM
ejpam-3219	41	39	0	0	NUM
ejpam-3219	41	40	.	.	NOUN
ejpam-3219	41	41	3	3	X
ejpam-3219	41	42	.	.	X
ejpam-3219	41	43	results	result	NOUN
ejpam-3219	41	44	theorem	theorem	VERB
ejpam-3219	41	45	3.1	3.1	NUM
ejpam-3219	41	46	let	let	VERB
ejpam-3219	41	47	l	l	NOUN
ejpam-3219	41	48	be	be	AUX
ejpam-3219	41	49	lie	lie	NOUN
ejpam-3219	41	50	algebras	algebra	NOUN
ejpam-3219	41	51	.	.	PUNCT
ejpam-3219	42	1	define	define	VERB
ejpam-3219	42	2	x	x	X
ejpam-3219	42	3	→	→	SYM
ejpam-3219	42	4	y	y	NOUN
ejpam-3219	42	5	=	=	PUNCT
ejpam-3219	43	1	[	[	X
ejpam-3219	43	2	x	x	X
ejpam-3219	43	3	,	,	PUNCT
ejpam-3219	43	4	y]−	y]−	PROPN
ejpam-3219	44	1	[	[	X
ejpam-3219	44	2	y	y	PROPN
ejpam-3219	44	3	,	,	PUNCT
ejpam-3219	44	4	x	x	X
ejpam-3219	44	5	]	]	X
ejpam-3219	44	6	,	,	PUNCT
ejpam-3219	44	7	(	(	PUNCT
ejpam-3219	44	8	x	x	X
ejpam-3219	44	9	→	→	SYM
ejpam-3219	44	10	y	y	NOUN
ejpam-3219	44	11	)	)	PUNCT
ejpam-3219	44	12	→	→	PUNCT
ejpam-3219	44	13	z	z	NOUN
ejpam-3219	44	14	=	=	PUNCT
ejpam-3219	45	1	[	[	X
ejpam-3219	45	2	[	[	X
ejpam-3219	45	3	x	x	X
ejpam-3219	45	4	,	,	PUNCT
ejpam-3219	45	5	y	y	PROPN
ejpam-3219	45	6	]	]	X
ejpam-3219	45	7	,	,	PUNCT
ejpam-3219	45	8	z	z	X
ejpam-3219	45	9	]	]	X
ejpam-3219	45	10	,	,	PUNCT
ejpam-3219	45	11	and	and	CCONJ
ejpam-3219	45	12	0	0	NUM
ejpam-3219	45	13	→	→	SYM
ejpam-3219	45	14	x	x	SYM
ejpam-3219	45	15	=	=	SYM
ejpam-3219	45	16	0	0	PUNCT
ejpam-3219	45	17	=	=	PUNCT
ejpam-3219	46	1	[	[	X
ejpam-3219	46	2	x	x	X
ejpam-3219	46	3	,	,	PUNCT
ejpam-3219	46	4	x	x	X
ejpam-3219	46	5	]	]	X
ejpam-3219	46	6	.	.	PUNCT
ejpam-3219	47	1	then	then	ADV
ejpam-3219	47	2	l	l	NOUN
ejpam-3219	47	3	be	be	AUX
ejpam-3219	47	4	bcl	bcl	NOUN
ejpam-3219	47	5	algebras	algebra	NOUN
ejpam-3219	47	6	.	.	PUNCT
ejpam-3219	48	1	proof	proof	NOUN
ejpam-3219	48	2	.	.	PUNCT
ejpam-3219	49	1	let	let	VERB
ejpam-3219	49	2	x	x	PRON
ejpam-3219	49	3	,	,	PUNCT
ejpam-3219	49	4	y	y	PROPN
ejpam-3219	49	5	,	,	PUNCT
ejpam-3219	49	6	z	z	PROPN
ejpam-3219	49	7	∈	∈	PROPN
ejpam-3219	49	8	l.	l.	NOUN
ejpam-3219	49	9	then	then	ADV
ejpam-3219	49	10	yonghong	yonghong	PROPN
ejpam-3219	49	11	l.	l.	PROPN
ejpam-3219	49	12	/	/	SYM
ejpam-3219	49	13	eur	eur	PROPN
ejpam-3219	49	14	.	.	PUNCT
ejpam-3219	50	1	j.	j.	PROPN
ejpam-3219	50	2	pure	pure	PROPN
ejpam-3219	50	3	appl	appl	PROPN
ejpam-3219	50	4	.	.	PROPN
ejpam-3219	50	5	math	math	PROPN
ejpam-3219	50	6	,	,	PUNCT
ejpam-3219	50	7	11	11	NUM
ejpam-3219	50	8	(	(	PUNCT
ejpam-3219	50	9	2	2	NUM
ejpam-3219	50	10	)	)	PUNCT
ejpam-3219	50	11	(	(	PUNCT
ejpam-3219	50	12	2018	2018	NUM
ejpam-3219	50	13	)	)	PUNCT
ejpam-3219	50	14	,	,	PUNCT
ejpam-3219	50	15	444	444	NUM
ejpam-3219	50	16	-	-	SYM
ejpam-3219	50	17	448	448	NUM
ejpam-3219	50	18	446	446	NUM
ejpam-3219	50	19	(	(	PUNCT
ejpam-3219	50	20	1	1	NUM
ejpam-3219	50	21	)	)	PUNCT
ejpam-3219	50	22	x	x	PUNCT
ejpam-3219	51	1	→	→	PUNCT
ejpam-3219	51	2	x	x	X
ejpam-3219	51	3	=	=	PUNCT
ejpam-3219	52	1	[	[	X
ejpam-3219	52	2	x	x	X
ejpam-3219	52	3	,	,	PUNCT
ejpam-3219	52	4	x]−	x]−	PUNCT
ejpam-3219	53	1	[	[	X
ejpam-3219	53	2	x	x	X
ejpam-3219	53	3	,	,	PUNCT
ejpam-3219	53	4	x	x	X
ejpam-3219	53	5	]	]	X
ejpam-3219	53	6	=	=	SYM
ejpam-3219	53	7	0	0	X
ejpam-3219	53	8	.	.	PUNCT
ejpam-3219	54	1	(	(	PUNCT
ejpam-3219	54	2	2	2	X
ejpam-3219	54	3	)	)	PUNCT
ejpam-3219	55	1	[	[	X
ejpam-3219	55	2	x	x	X
ejpam-3219	55	3	,	,	PUNCT
ejpam-3219	55	4	x	x	X
ejpam-3219	55	5	]	]	X
ejpam-3219	55	6	=	=	SYM
ejpam-3219	55	7	0	0	PUNCT
ejpam-3219	55	8	=	=	SYM
ejpam-3219	55	9	x	x	PUNCT
ejpam-3219	55	10	→	→	SYM
ejpam-3219	55	11	y	y	PROPN
ejpam-3219	55	12	and	and	CCONJ
ejpam-3219	55	13	[	[	X
ejpam-3219	55	14	y	y	PROPN
ejpam-3219	55	15	,	,	PUNCT
ejpam-3219	55	16	y	y	PROPN
ejpam-3219	55	17	]	]	X
ejpam-3219	55	18	=	=	SYM
ejpam-3219	55	19	0	0	PUNCT
ejpam-3219	55	20	=	=	SYM
ejpam-3219	55	21	y	y	PROPN
ejpam-3219	55	22	→	→	PUNCT
ejpam-3219	55	23	x	x	X
ejpam-3219	55	24	imply	imply	ADV
ejpam-3219	55	25	x	x	X
ejpam-3219	55	26	=	=	SYM
ejpam-3219	55	27	y.	y.	NOUN
ejpam-3219	55	28	(	(	PUNCT
ejpam-3219	55	29	3	3	NUM
ejpam-3219	55	30	)	)	PUNCT
ejpam-3219	56	1	[	[	X
ejpam-3219	56	2	[	[	X
ejpam-3219	56	3	[	[	X
ejpam-3219	56	4	[	[	X
ejpam-3219	56	5	x	x	X
ejpam-3219	56	6	,	,	PUNCT
ejpam-3219	56	7	y	y	PROPN
ejpam-3219	56	8	]	]	X
ejpam-3219	56	9	,	,	PUNCT
ejpam-3219	56	10	z	z	X
ejpam-3219	56	11	]	]	X
ejpam-3219	56	12	,	,	PUNCT
ejpam-3219	57	1	[	[	X
ejpam-3219	57	2	[	[	X
ejpam-3219	57	3	x	x	X
ejpam-3219	57	4	,	,	PUNCT
ejpam-3219	57	5	z	z	NOUN
ejpam-3219	57	6	]	]	X
ejpam-3219	57	7	,	,	PUNCT
ejpam-3219	57	8	y	y	PROPN
ejpam-3219	57	9	]	]	X
ejpam-3219	57	10	]	]	X
ejpam-3219	57	11	,	,	PUNCT
ejpam-3219	57	12	[	[	X
ejpam-3219	57	13	[	[	X
ejpam-3219	57	14	z	z	X
ejpam-3219	57	15	,	,	PUNCT
ejpam-3219	57	16	y	y	PROPN
ejpam-3219	57	17	]	]	X
ejpam-3219	57	18	,	,	PUNCT
ejpam-3219	57	19	x	x	X
ejpam-3219	57	20	]	]	X
ejpam-3219	57	21	]	]	X
ejpam-3219	57	22	=	=	SYM
ejpam-3219	57	23	0	0	X
ejpam-3219	57	24	.	.	PUNCT
ejpam-3219	57	25	clearly	clearly	ADV
ejpam-3219	57	26	,	,	PUNCT
ejpam-3219	57	27	proving	prove	VERB
ejpam-3219	57	28	(	(	PUNCT
ejpam-3219	57	29	1	1	NUM
ejpam-3219	57	30	)	)	PUNCT
ejpam-3219	57	31	and	and	CCONJ
ejpam-3219	57	32	(	(	PUNCT
ejpam-3219	57	33	2	2	NUM
ejpam-3219	57	34	)	)	PUNCT
ejpam-3219	57	35	.	.	PUNCT
ejpam-3219	58	1	now	now	ADV
ejpam-3219	58	2	we	we	PRON
ejpam-3219	58	3	need	need	VERB
ejpam-3219	58	4	to	to	PART
ejpam-3219	58	5	prove	prove	VERB
ejpam-3219	58	6	(	(	PUNCT
ejpam-3219	58	7	3	3	NUM
ejpam-3219	58	8	)	)	PUNCT
ejpam-3219	58	9	,	,	PUNCT
ejpam-3219	58	10	we	we	PRON
ejpam-3219	58	11	define	define	VERB
ejpam-3219	58	12	[	[	X
ejpam-3219	58	13	x	x	NOUN
ejpam-3219	58	14	,	,	PUNCT
ejpam-3219	58	15	y	y	PROPN
ejpam-3219	58	16	]	]	X
ejpam-3219	58	17	=	=	PUNCT
ejpam-3219	59	1	x	x	PUNCT
ejpam-3219	59	2	+	+	CCONJ
ejpam-3219	59	3	y.	y.	NOUN
ejpam-3219	60	1	then	then	ADV
ejpam-3219	61	1	[	[	X
ejpam-3219	61	2	[	[	X
ejpam-3219	61	3	z	z	PROPN
ejpam-3219	61	4	,	,	PUNCT
ejpam-3219	61	5	y	y	PROPN
ejpam-3219	61	6	]	]	X
ejpam-3219	61	7	,	,	PUNCT
ejpam-3219	61	8	x	x	X
ejpam-3219	61	9	]	]	X
ejpam-3219	61	10	=	=	PUNCT
ejpam-3219	62	1	[	[	X
ejpam-3219	62	2	x	x	X
ejpam-3219	62	3	,	,	PUNCT
ejpam-3219	62	4	[	[	X
ejpam-3219	62	5	z	z	X
ejpam-3219	62	6	,	,	PUNCT
ejpam-3219	62	7	y	y	PROPN
ejpam-3219	62	8	]	]	X
ejpam-3219	62	9	]	]	PUNCT
ejpam-3219	62	10	⊆	⊆	NUM
ejpam-3219	62	11	[	[	X
ejpam-3219	62	12	z	z	X
ejpam-3219	62	13	,	,	PUNCT
ejpam-3219	62	14	[	[	X
ejpam-3219	62	15	y	y	X
ejpam-3219	62	16	,	,	PUNCT
ejpam-3219	62	17	x	x	X
ejpam-3219	62	18	]	]	X
ejpam-3219	62	19	]	]	PUNCT
ejpam-3219	63	1	+	+	CCONJ
ejpam-3219	63	2	[	[	X
ejpam-3219	63	3	y	y	X
ejpam-3219	63	4	,	,	PUNCT
ejpam-3219	63	5	[	[	X
ejpam-3219	63	6	x	x	X
ejpam-3219	63	7	,	,	PUNCT
ejpam-3219	63	8	z	z	X
ejpam-3219	63	9	]	]	X
ejpam-3219	63	10	]	]	X
ejpam-3219	63	11	=	=	PUNCT
ejpam-3219	64	1	[	[	X
ejpam-3219	64	2	[	[	X
ejpam-3219	64	3	x	x	X
ejpam-3219	64	4	,	,	PUNCT
ejpam-3219	64	5	y	y	PROPN
ejpam-3219	64	6	]	]	X
ejpam-3219	64	7	,	,	PUNCT
ejpam-3219	64	8	z	z	X
ejpam-3219	64	9	]	]	X
ejpam-3219	65	1	+	+	CCONJ
ejpam-3219	66	1	[	[	X
ejpam-3219	66	2	[	[	X
ejpam-3219	66	3	x	x	X
ejpam-3219	66	4	,	,	PUNCT
ejpam-3219	66	5	z	z	NOUN
ejpam-3219	66	6	]	]	X
ejpam-3219	66	7	,	,	PUNCT
ejpam-3219	66	8	y	y	PROPN
ejpam-3219	66	9	]	]	X
ejpam-3219	66	10	⊆	⊆	NUM
ejpam-3219	66	11	[	[	X
ejpam-3219	66	12	[	[	X
ejpam-3219	66	13	x	x	X
ejpam-3219	66	14	,	,	PUNCT
ejpam-3219	66	15	y	y	PROPN
ejpam-3219	66	16	]	]	X
ejpam-3219	66	17	,	,	PUNCT
ejpam-3219	66	18	z	z	X
ejpam-3219	66	19	]	]	X
ejpam-3219	66	20	,	,	PUNCT
ejpam-3219	66	21	[	[	X
ejpam-3219	66	22	[	[	X
ejpam-3219	66	23	x	x	X
ejpam-3219	66	24	,	,	PUNCT
ejpam-3219	66	25	z	z	NOUN
ejpam-3219	66	26	]	]	X
ejpam-3219	66	27	,	,	PUNCT
ejpam-3219	66	28	y	y	PROPN
ejpam-3219	66	29	]	]	X
ejpam-3219	66	30	]	]	X
ejpam-3219	66	31	,	,	PUNCT
ejpam-3219	66	32	and	and	CCONJ
ejpam-3219	66	33	(	(	PUNCT
ejpam-3219	66	34	3	3	X
ejpam-3219	66	35	)	)	PUNCT
ejpam-3219	66	36	is	be	AUX
ejpam-3219	66	37	proved	prove	VERB
ejpam-3219	66	38	.	.	PUNCT
ejpam-3219	67	1	we	we	PRON
ejpam-3219	67	2	see	see	VERB
ejpam-3219	67	3	that	that	SCONJ
ejpam-3219	67	4	l	l	NOUN
ejpam-3219	67	5	be	be	VERB
ejpam-3219	67	6	bcl	bcl	NOUN
ejpam-3219	67	7	algebras	algebra	NOUN
ejpam-3219	67	8	.	.	PUNCT
ejpam-3219	68	1	theorem	theorem	VERB
ejpam-3219	68	2	3.2	3.2	NUM
ejpam-3219	68	3	let	let	VERB
ejpam-3219	68	4	x	x	PRON
ejpam-3219	68	5	,	,	PUNCT
ejpam-3219	68	6	y	y	PROPN
ejpam-3219	68	7	,	,	PUNCT
ejpam-3219	68	8	z	z	PROPN
ejpam-3219	68	9	∈	∈	PROPN
ejpam-3219	68	10	p	p	NOUN
ejpam-3219	68	11	be	be	AUX
ejpam-3219	68	12	bcl	bcl	NOUN
ejpam-3219	68	13	algrbras	algrbras	PROPN
ejpam-3219	68	14	.	.	PUNCT
ejpam-3219	69	1	then	then	ADV
ejpam-3219	69	2	p	p	NOUN
ejpam-3219	69	3	is	be	AUX
ejpam-3219	69	4	abelian	abelian	ADJ
ejpam-3219	69	5	lie	lie	NOUN
ejpam-3219	69	6	algebra	algebra	NOUN
ejpam-3219	69	7	iff	iff	PROPN
ejpam-3219	69	8	x	x	PROPN
ejpam-3219	70	1	=	=	PUNCT
ejpam-3219	70	2	y	y	PROPN
ejpam-3219	70	3	=	=	PUNCT
ejpam-3219	70	4	z.	z.	PROPN
ejpam-3219	70	5	proof	proof	NOUN
ejpam-3219	70	6	.	.	PUNCT
ejpam-3219	71	1	assume	assume	VERB
ejpam-3219	71	2	that	that	SCONJ
ejpam-3219	71	3	p	p	NOUN
ejpam-3219	71	4	is	be	AUX
ejpam-3219	71	5	abelian	abelian	ADJ
ejpam-3219	71	6	lie	lie	NOUN
ejpam-3219	71	7	algebra	algebra	NOUN
ejpam-3219	71	8	,	,	PUNCT
ejpam-3219	72	1	sine	sine	NOUN
ejpam-3219	72	2	x	x	NOUN
ejpam-3219	72	3	,	,	PUNCT
ejpam-3219	72	4	y	y	PROPN
ejpam-3219	72	5	,	,	PUNCT
ejpam-3219	72	6	z	z	PROPN
ejpam-3219	72	7	∈	∈	PROPN
ejpam-3219	72	8	p	p	NOUN
ejpam-3219	72	9	,	,	PUNCT
ejpam-3219	72	10	we	we	PRON
ejpam-3219	72	11	have	have	VERB
ejpam-3219	72	12	[	[	X
ejpam-3219	72	13	x	x	X
ejpam-3219	72	14	,	,	PUNCT
ejpam-3219	72	15	y	y	PROPN
ejpam-3219	72	16	]	]	X
ejpam-3219	72	17	=	=	SYM
ejpam-3219	72	18	0	0	PUNCT
ejpam-3219	73	1	=	=	PUNCT
ejpam-3219	74	1	[	[	X
ejpam-3219	74	2	y	y	PROPN
ejpam-3219	74	3	,	,	PUNCT
ejpam-3219	74	4	z	z	NOUN
ejpam-3219	74	5	]	]	X
ejpam-3219	74	6	.	.	PUNCT
ejpam-3219	75	1	therefore	therefore	ADV
ejpam-3219	75	2	,	,	PUNCT
ejpam-3219	75	3	x	x	PUNCT
ejpam-3219	75	4	=	=	PUNCT
ejpam-3219	75	5	y	y	PROPN
ejpam-3219	75	6	=	=	PUNCT
ejpam-3219	75	7	z.	z.	PROPN
ejpam-3219	75	8	conversely	conversely	ADV
ejpam-3219	75	9	,	,	PUNCT
ejpam-3219	75	10	assume	assume	VERB
ejpam-3219	75	11	x	x	X
ejpam-3219	75	12	=	=	SYM
ejpam-3219	75	13	y	y	PROPN
ejpam-3219	75	14	=	=	PUNCT
ejpam-3219	75	15	z.	z.	PROPN
ejpam-3219	75	16	to	to	PART
ejpam-3219	75	17	prove	prove	VERB
ejpam-3219	75	18	that	that	SCONJ
ejpam-3219	75	19	this	this	DET
ejpam-3219	75	20	algebra	algebra	NOUN
ejpam-3219	75	21	is	be	AUX
ejpam-3219	75	22	a	a	DET
ejpam-3219	75	23	bcl	bcl	NOUN
ejpam-3219	75	24	algebra	algebra	NOUN
ejpam-3219	75	25	.	.	PUNCT
ejpam-3219	76	1	let	let	VERB
ejpam-3219	76	2	x	x	PRON
ejpam-3219	76	3	,	,	PUNCT
ejpam-3219	76	4	y	y	PROPN
ejpam-3219	76	5	,	,	PUNCT
ejpam-3219	76	6	z	z	PROPN
ejpam-3219	76	7	∈	∈	PROPN
ejpam-3219	76	8	p	p	X
ejpam-3219	76	9	.	.	PUNCT
ejpam-3219	77	1	by	by	ADP
ejpam-3219	77	2	theorem	theorem	NOUN
ejpam-3219	77	3	2.1	2.1	NUM
ejpam-3219	77	4	.	.	PUNCT
ejpam-3219	78	1	then	then	ADV
ejpam-3219	78	2	(	(	PUNCT
ejpam-3219	78	3	4	4	X
ejpam-3219	78	4	)	)	PUNCT
ejpam-3219	79	1	[	[	X
ejpam-3219	79	2	x	x	X
ejpam-3219	79	3	,	,	PUNCT
ejpam-3219	79	4	x	x	X
ejpam-3219	79	5	]	]	X
ejpam-3219	79	6	=	=	SYM
ejpam-3219	79	7	0	0	PUNCT
ejpam-3219	79	8	=	=	SYM
ejpam-3219	79	9	x	x	X
ejpam-3219	79	10	→	→	SYM
ejpam-3219	79	11	x.	x.	NOUN
ejpam-3219	79	12	(	(	PUNCT
ejpam-3219	79	13	5	5	NUM
ejpam-3219	79	14	)	)	PUNCT
ejpam-3219	80	1	[	[	X
ejpam-3219	80	2	x	x	X
ejpam-3219	80	3	,	,	PUNCT
ejpam-3219	80	4	x	x	X
ejpam-3219	80	5	]	]	X
ejpam-3219	80	6	=	=	SYM
ejpam-3219	80	7	0	0	PUNCT
ejpam-3219	80	8	=	=	SYM
ejpam-3219	80	9	x	x	PUNCT
ejpam-3219	80	10	→	→	SYM
ejpam-3219	80	11	y	y	PROPN
ejpam-3219	80	12	and	and	CCONJ
ejpam-3219	80	13	[	[	X
ejpam-3219	80	14	y	y	PROPN
ejpam-3219	80	15	,	,	PUNCT
ejpam-3219	80	16	y	y	PROPN
ejpam-3219	80	17	]	]	X
ejpam-3219	80	18	=	=	SYM
ejpam-3219	80	19	0	0	PUNCT
ejpam-3219	80	20	=	=	SYM
ejpam-3219	80	21	y	y	PROPN
ejpam-3219	80	22	→	→	PUNCT
ejpam-3219	80	23	x	x	X
ejpam-3219	80	24	imply	imply	ADV
ejpam-3219	80	25	x	x	X
ejpam-3219	80	26	=	=	SYM
ejpam-3219	80	27	y.	y.	NOUN
ejpam-3219	80	28	(	(	PUNCT
ejpam-3219	80	29	6	6	NUM
ejpam-3219	80	30	)	)	PUNCT
ejpam-3219	81	1	[	[	X
ejpam-3219	81	2	0	0	NUM
ejpam-3219	81	3	,	,	PUNCT
ejpam-3219	81	4	[	[	X
ejpam-3219	81	5	0	0	NUM
ejpam-3219	81	6	,	,	PUNCT
ejpam-3219	81	7	x	x	X
ejpam-3219	81	8	]	]	X
ejpam-3219	81	9	]	]	X
ejpam-3219	81	10	=	=	PUNCT
ejpam-3219	82	1	[	[	X
ejpam-3219	82	2	[	[	X
ejpam-3219	82	3	0	0	NUM
ejpam-3219	82	4	,	,	PUNCT
ejpam-3219	82	5	x	x	NOUN
ejpam-3219	82	6	]	]	X
ejpam-3219	82	7	,	,	PUNCT
ejpam-3219	82	8	0	0	NUM
ejpam-3219	82	9	]	]	X
ejpam-3219	82	10	=	=	SYM
ejpam-3219	82	11	(	(	PUNCT
ejpam-3219	82	12	0	0	NUM
ejpam-3219	82	13	→	→	SYM
ejpam-3219	82	14	x)→	x)→	PROPN
ejpam-3219	82	15	0	0	X
ejpam-3219	82	16	=	=	SYM
ejpam-3219	82	17	0→	0→	PROPN
ejpam-3219	82	18	0	0	NUM
ejpam-3219	82	19	=	=	SYM
ejpam-3219	82	20	0	0	PROPN
ejpam-3219	82	21	.	.	PUNCT
ejpam-3219	83	1	this	this	PRON
ejpam-3219	83	2	completes	complete	VERB
ejpam-3219	83	3	the	the	DET
ejpam-3219	83	4	proof	proof	NOUN
ejpam-3219	83	5	.	.	PUNCT
ejpam-3219	84	1	definition	definition	NOUN
ejpam-3219	84	2	3.1	3.1	NUM
ejpam-3219	84	3	let	let	VERB
ejpam-3219	84	4	(	(	PUNCT
ejpam-3219	84	5	g	g	NOUN
ejpam-3219	84	6	,	,	PUNCT
ejpam-3219	84	7	+	+	ADJ
ejpam-3219	84	8	)	)	PUNCT
ejpam-3219	84	9	be	be	AUX
ejpam-3219	84	10	an	an	DET
ejpam-3219	84	11	abelian	abelian	NOUN
ejpam-3219	84	12	,	,	PUNCT
ejpam-3219	84	13	(	(	PUNCT
ejpam-3219	84	14	g	g	NOUN
ejpam-3219	84	15	;	;	PUNCT
ejpam-3219	84	16	−	−	PROPN
ejpam-3219	84	17	,	,	PUNCT
ejpam-3219	84	18	0	0	NUM
ejpam-3219	84	19	)	)	PUNCT
ejpam-3219	84	20	be	be	VERB
ejpam-3219	84	21	an	an	DET
ejpam-3219	84	22	adjoint	adjoint	NOUN
ejpam-3219	84	23	bcl	bcl	NOUN
ejpam-3219	84	24	algrbras	algrbras	PROPN
ejpam-3219	84	25	and	and	CCONJ
ejpam-3219	84	26	yonghong	yonghong	PROPN
ejpam-3219	84	27	l.	l.	PROPN
ejpam-3219	84	28	/	/	SYM
ejpam-3219	84	29	eur	eur	PROPN
ejpam-3219	84	30	.	.	PUNCT
ejpam-3219	85	1	j.	j.	PROPN
ejpam-3219	85	2	pure	pure	PROPN
ejpam-3219	85	3	appl	appl	PROPN
ejpam-3219	85	4	.	.	PROPN
ejpam-3219	85	5	math	math	PROPN
ejpam-3219	85	6	,	,	PUNCT
ejpam-3219	85	7	11	11	NUM
ejpam-3219	85	8	(	(	PUNCT
ejpam-3219	85	9	2	2	NUM
ejpam-3219	85	10	)	)	PUNCT
ejpam-3219	85	11	(	(	PUNCT
ejpam-3219	85	12	2018	2018	NUM
ejpam-3219	85	13	)	)	PUNCT
ejpam-3219	85	14	,	,	PUNCT
ejpam-3219	85	15	444	444	NUM
ejpam-3219	85	16	-	-	SYM
ejpam-3219	85	17	448	448	NUM
ejpam-3219	85	18	447	447	NUM
ejpam-3219	85	19	(	(	PUNCT
ejpam-3219	85	20	g	g	NOUN
ejpam-3219	85	21	;	;	PUNCT
ejpam-3219	85	22	→	→	NOUN
ejpam-3219	85	23	,	,	PUNCT
ejpam-3219	85	24	0	0	NUM
ejpam-3219	85	25	)	)	PUNCT
ejpam-3219	85	26	be	be	AUX
ejpam-3219	85	27	a	a	DET
ejpam-3219	85	28	pseudo	pseudo	NOUN
ejpam-3219	85	29	-	-	NOUN
ejpam-3219	85	30	association	association	NOUN
ejpam-3219	85	31	bcl	bcl	NOUN
ejpam-3219	85	32	algrbras	algrbras	PROPN
ejpam-3219	85	33	.	.	PUNCT
ejpam-3219	86	1	suppose	suppose	VERB
ejpam-3219	86	2	the	the	DET
ejpam-3219	86	3	following	follow	VERB
ejpam-3219	86	4	conditions	condition	NOUN
ejpam-3219	86	5	hold	hold	VERB
ejpam-3219	86	6	:	:	PUNCT
ejpam-3219	86	7	(	(	PUNCT
ejpam-3219	86	8	gpa	gpa	PROPN
ejpam-3219	86	9	1	1	NUM
ejpam-3219	86	10	)	)	PUNCT
ejpam-3219	87	1	x	x	NOUN
ejpam-3219	87	2	−	−	PROPN
ejpam-3219	87	3	(	(	PUNCT
ejpam-3219	87	4	0	0	NUM
ejpam-3219	87	5	−	−	PROPN
ejpam-3219	87	6	y	y	NOUN
ejpam-3219	87	7	)	)	PUNCT
ejpam-3219	87	8	=	=	PUNCT
ejpam-3219	88	1	x	x	PUNCT
ejpam-3219	89	1	+	+	CCONJ
ejpam-3219	89	2	y.	y.	PROPN
ejpam-3219	89	3	(	(	PUNCT
ejpam-3219	89	4	gpa	gpa	PROPN
ejpam-3219	89	5	2	2	NUM
ejpam-3219	89	6	)	)	PUNCT
ejpam-3219	89	7	x	x	X
ejpam-3219	89	8	−	−	PROPN
ejpam-3219	89	9	y	y	PROPN
ejpam-3219	89	10	=	=	PUNCT
ejpam-3219	89	11	x→	x→	PROPN
ejpam-3219	89	12	y.	y.	PROPN
ejpam-3219	89	13	then	then	ADV
ejpam-3219	89	14	adjoint	adjoint	PROPN
ejpam-3219	89	15	group	group	NOUN
ejpam-3219	89	16	of	of	ADP
ejpam-3219	89	17	(	(	PUNCT
ejpam-3219	89	18	g	g	NOUN
ejpam-3219	89	19	;	;	PUNCT
ejpam-3219	89	20	−	−	PROPN
ejpam-3219	89	21	,	,	PUNCT
ejpam-3219	89	22	0	0	NUM
ejpam-3219	89	23	)	)	PUNCT
ejpam-3219	89	24	is	be	AUX
ejpam-3219	89	25	abelian	abelian	ADJ
ejpam-3219	89	26	(	(	PUNCT
ejpam-3219	89	27	g	g	NOUN
ejpam-3219	89	28	,	,	PUNCT
ejpam-3219	89	29	+	+	NOUN
ejpam-3219	89	30	)	)	PUNCT
ejpam-3219	89	31	,	,	PUNCT
ejpam-3219	89	32	and	and	CCONJ
ejpam-3219	89	33	adjoint	adjoint	PROPN
ejpam-3219	89	34	bcl	bcl	NOUN
ejpam-3219	89	35	algrbras	algrbras	PROPN
ejpam-3219	89	36	of	of	ADP
ejpam-3219	89	37	abelian	abelian	PROPN
ejpam-3219	89	38	(	(	PUNCT
ejpam-3219	89	39	g	g	PROPN
ejpam-3219	89	40	,	,	PUNCT
ejpam-3219	89	41	+	+	NOUN
ejpam-3219	89	42	)	)	PUNCT
ejpam-3219	89	43	is	be	AUX
ejpam-3219	89	44	(	(	PUNCT
ejpam-3219	89	45	g	g	NOUN
ejpam-3219	89	46	;	;	PUNCT
ejpam-3219	89	47	→	→	NOUN
ejpam-3219	89	48	,	,	PUNCT
ejpam-3219	89	49	0	0	NUM
ejpam-3219	89	50	)	)	PUNCT
ejpam-3219	89	51	.	.	PUNCT
ejpam-3219	90	1	theorem	theorem	VERB
ejpam-3219	90	2	3.3	3.3	NUM
ejpam-3219	90	3	let	let	VERB
ejpam-3219	90	4	p	p	PRON
ejpam-3219	90	5	be	be	AUX
ejpam-3219	90	6	a	a	DET
ejpam-3219	90	7	pseudo	pseudo	NOUN
ejpam-3219	90	8	-	-	NOUN
ejpam-3219	90	9	association	association	NOUN
ejpam-3219	90	10	bcl	bcl	NOUN
ejpam-3219	90	11	algrbra	algrbra	PROPN
ejpam-3219	90	12	.	.	PUNCT
ejpam-3219	91	1	the	the	DET
ejpam-3219	91	2	bracket	bracket	NOUN
ejpam-3219	91	3	[	[	X
ejpam-3219	91	4	x	x	X
ejpam-3219	91	5	,	,	PUNCT
ejpam-3219	91	6	y	y	PROPN
ejpam-3219	91	7	]	]	X
ejpam-3219	91	8	=	=	PUNCT
ejpam-3219	91	9	x	x	PUNCT
ejpam-3219	91	10	→	→	SYM
ejpam-3219	91	11	y	y	PROPN
ejpam-3219	91	12	−	−	PROPN
ejpam-3219	91	13	(	(	PUNCT
ejpam-3219	91	14	y	y	PROPN
ejpam-3219	91	15	→	→	SYM
ejpam-3219	91	16	x	x	X
ejpam-3219	91	17	)	)	PUNCT
ejpam-3219	91	18	,	,	PUNCT
ejpam-3219	91	19	for	for	ADP
ejpam-3219	91	20	all	all	DET
ejpam-3219	91	21	x	x	NOUN
ejpam-3219	91	22	,	,	PUNCT
ejpam-3219	91	23	y	y	PROPN
ejpam-3219	91	24	∈	∈	PROPN
ejpam-3219	91	25	p	p	PROPN
ejpam-3219	91	26	.	.	PUNCT
ejpam-3219	92	1	then	then	ADV
ejpam-3219	92	2	p	p	NOUN
ejpam-3219	92	3	be	be	AUX
ejpam-3219	92	4	a	a	DET
ejpam-3219	92	5	lie	lie	NOUN
ejpam-3219	92	6	algebras	algebra	NOUN
ejpam-3219	92	7	about	about	ADP
ejpam-3219	92	8	the	the	DET
ejpam-3219	92	9	bracket	bracket	NOUN
ejpam-3219	92	10	[	[	PUNCT
ejpam-3219	92	11	,	,	PUNCT
ejpam-3219	92	12	]	]	PUNCT
ejpam-3219	92	13	and	and	CCONJ
ejpam-3219	92	14	we	we	PRON
ejpam-3219	92	15	use	use	VERB
ejpam-3219	92	16	notation	notation	NOUN
ejpam-3219	92	17	pl	pl	PROPN
ejpam-3219	92	18	,	,	PUNCT
ejpam-3219	92	19	for	for	SCONJ
ejpam-3219	92	20	the	the	DET
ejpam-3219	92	21	lie	lie	NOUN
ejpam-3219	92	22	algebra	algebra	NOUN
ejpam-3219	92	23	is	be	AUX
ejpam-3219	92	24	generated	generate	VERB
ejpam-3219	92	25	by	by	ADP
ejpam-3219	92	26	the	the	DET
ejpam-3219	92	27	pseudo	pseudo	NOUN
ejpam-3219	92	28	-	-	NOUN
ejpam-3219	92	29	association	association	NOUN
ejpam-3219	92	30	bcl	bcl	NOUN
ejpam-3219	92	31	algrbra	algrbra	NOUN
ejpam-3219	92	32	.	.	PUNCT
ejpam-3219	93	1	proof	proof	NOUN
ejpam-3219	93	2	.	.	PUNCT
ejpam-3219	94	1	by	by	ADP
ejpam-3219	94	2	definition	definition	NOUN
ejpam-3219	94	3	of	of	ADP
ejpam-3219	94	4	the	the	DET
ejpam-3219	94	5	bracket	bracket	NOUN
ejpam-3219	94	6	,	,	PUNCT
ejpam-3219	94	7	[	[	X
ejpam-3219	94	8	x	x	X
ejpam-3219	94	9	,	,	PUNCT
ejpam-3219	94	10	x	x	X
ejpam-3219	94	11	]	]	X
ejpam-3219	94	12	=	=	SYM
ejpam-3219	94	13	0	0	NUM
ejpam-3219	94	14	trivially	trivially	ADV
ejpam-3219	94	15	hoid	hoid	ADJ
ejpam-3219	94	16	.	.	PUNCT
ejpam-3219	95	1	to	to	PART
ejpam-3219	95	2	prove	prove	VERB
ejpam-3219	95	3	bilinear	bilinear	NOUN
ejpam-3219	95	4	,	,	PUNCT
ejpam-3219	95	5	sine	sine	VERB
ejpam-3219	95	6	x1	x1	PROPN
ejpam-3219	95	7	,	,	PUNCT
ejpam-3219	95	8	x2	x2	PROPN
ejpam-3219	95	9	,	,	PUNCT
ejpam-3219	95	10	y	y	PROPN
ejpam-3219	95	11	∈	∈	PROPN
ejpam-3219	95	12	pl	pl	PROPN
ejpam-3219	95	13	,	,	PUNCT
ejpam-3219	95	14	and	and	CCONJ
ejpam-3219	95	15	λ1	λ1	ADJ
ejpam-3219	95	16	,	,	PUNCT
ejpam-3219	95	17	λ2	λ2	PROPN
ejpam-3219	95	18	∈	∈	PROPN
ejpam-3219	95	19	pl	pl	NOUN
ejpam-3219	95	20	,	,	PUNCT
ejpam-3219	95	21	we	we	PRON
ejpam-3219	95	22	have	have	VERB
ejpam-3219	96	1	[	[	X
ejpam-3219	96	2	λ1	λ1	ADJ
ejpam-3219	96	3	x1	x1	PROPN
ejpam-3219	96	4	+	+	NUM
ejpam-3219	96	5	λ2	λ2	NOUN
ejpam-3219	96	6	x2	x2	PROPN
ejpam-3219	96	7	,	,	PUNCT
ejpam-3219	96	8	y	y	NOUN
ejpam-3219	96	9	]	]	X
ejpam-3219	96	10	=	=	SYM
ejpam-3219	96	11	(	(	PUNCT
ejpam-3219	96	12	(	(	PUNCT
ejpam-3219	96	13	λ1	λ1	PROPN
ejpam-3219	96	14	x1	x1	PROPN
ejpam-3219	97	1	+	+	NUM
ejpam-3219	97	2	λ2	λ2	NOUN
ejpam-3219	97	3	x2)→	x2)→	VERB
ejpam-3219	98	1	y)−	y)−	PROPN
ejpam-3219	98	2	(	(	PUNCT
ejpam-3219	98	3	y	y	PROPN
ejpam-3219	98	4	→	→	PUNCT
ejpam-3219	98	5	(	(	PUNCT
ejpam-3219	98	6	λ1	λ1	PROPN
ejpam-3219	98	7	x1	x1	PROPN
ejpam-3219	98	8	+	+	NUM
ejpam-3219	98	9	λ2	λ2	NOUN
ejpam-3219	98	10	x2	x2	PROPN
ejpam-3219	98	11	)	)	PUNCT
ejpam-3219	98	12	)	)	PUNCT
ejpam-3219	99	1	=	=	PRON
ejpam-3219	99	2	(	(	PUNCT
ejpam-3219	99	3	λ1(x1	λ1(x1	PROPN
ejpam-3219	99	4	→	→	SYM
ejpam-3219	99	5	y	y	PROPN
ejpam-3219	99	6	)	)	PUNCT
ejpam-3219	99	7	+	+	NUM
ejpam-3219	99	8	λ2(x2	λ2(x2	NOUN
ejpam-3219	99	9	→	→	PUNCT
ejpam-3219	99	10	y))−	y))−	NOUN
ejpam-3219	99	11	(	(	PUNCT
ejpam-3219	99	12	λ1(y	λ1(y	PROPN
ejpam-3219	99	13	→	→	SYM
ejpam-3219	99	14	x1	x1	PROPN
ejpam-3219	99	15	)	)	PUNCT
ejpam-3219	100	1	+	+	CCONJ
ejpam-3219	100	2	λ2(y	λ2(y	ADP
ejpam-3219	100	3	→	→	SYM
ejpam-3219	100	4	λ2	λ2	NOUN
ejpam-3219	100	5	x2	x2	PROPN
ejpam-3219	100	6	)	)	PUNCT
ejpam-3219	100	7	)	)	PUNCT
ejpam-3219	101	1	=	=	SYM
ejpam-3219	102	1	λ1[x1	λ1[x1	PROPN
ejpam-3219	102	2	,	,	PUNCT
ejpam-3219	102	3	y	y	NOUN
ejpam-3219	102	4	]	]	X
ejpam-3219	102	5	+	+	CCONJ
ejpam-3219	102	6	λ2[x2	λ2[x2	PROPN
ejpam-3219	102	7	,	,	PUNCT
ejpam-3219	102	8	y	y	PROPN
ejpam-3219	102	9	]	]	PUNCT
ejpam-3219	102	10	to	to	PART
ejpam-3219	102	11	prove	prove	VERB
ejpam-3219	102	12	jacobi	jacobi	PROPN
ejpam-3219	102	13	identity	identity	NOUN
ejpam-3219	102	14	,	,	PUNCT
ejpam-3219	102	15	sine	sine	NOUN
ejpam-3219	102	16	x	x	NOUN
ejpam-3219	102	17	,	,	PUNCT
ejpam-3219	102	18	y	y	PROPN
ejpam-3219	102	19	,	,	PUNCT
ejpam-3219	102	20	z	z	PROPN
ejpam-3219	102	21	∈	∈	PROPN
ejpam-3219	102	22	pl	pl	X
ejpam-3219	102	23	,	,	PUNCT
ejpam-3219	102	24	we	we	PRON
ejpam-3219	102	25	have	have	VERB
ejpam-3219	102	26	(	(	PUNCT
ejpam-3219	102	27	7	7	NUM
ejpam-3219	102	28	)	)	PUNCT
ejpam-3219	103	1	[	[	X
ejpam-3219	103	2	x	x	X
ejpam-3219	103	3	,	,	PUNCT
ejpam-3219	103	4	[	[	X
ejpam-3219	103	5	y	y	X
ejpam-3219	103	6	,	,	PUNCT
ejpam-3219	103	7	z	z	X
ejpam-3219	103	8	]	]	X
ejpam-3219	103	9	]	]	X
ejpam-3219	103	10	=	=	PUNCT
ejpam-3219	104	1	[	[	X
ejpam-3219	104	2	x	x	X
ejpam-3219	104	3	,	,	PUNCT
ejpam-3219	104	4	y	y	PROPN
ejpam-3219	104	5	→	→	SYM
ejpam-3219	104	6	z	z	NOUN
ejpam-3219	104	7	−	−	PROPN
ejpam-3219	104	8	(	(	PUNCT
ejpam-3219	104	9	z	z	PROPN
ejpam-3219	104	10	→	→	SYM
ejpam-3219	104	11	y	y	PROPN
ejpam-3219	104	12	)	)	PUNCT
ejpam-3219	104	13	]	]	PUNCT
ejpam-3219	105	1	=	=	PUNCT
ejpam-3219	105	2	x→	x→	PUNCT
ejpam-3219	106	1	(	(	PUNCT
ejpam-3219	106	2	y	y	PROPN
ejpam-3219	106	3	→	→	SYM
ejpam-3219	106	4	z	z	NOUN
ejpam-3219	106	5	−	−	PROPN
ejpam-3219	107	1	(	(	PUNCT
ejpam-3219	107	2	z	z	NOUN
ejpam-3219	107	3	→	→	PUNCT
ejpam-3219	107	4	y))−	y))−	NOUN
ejpam-3219	107	5	(	(	PUNCT
ejpam-3219	107	6	(	(	PUNCT
ejpam-3219	107	7	y	y	PROPN
ejpam-3219	107	8	→	→	SYM
ejpam-3219	107	9	z	z	NOUN
ejpam-3219	107	10	−	−	PROPN
ejpam-3219	108	1	(	(	PUNCT
ejpam-3219	108	2	z	z	NOUN
ejpam-3219	108	3	→	→	SYM
ejpam-3219	108	4	y))→	y))→	PROPN
ejpam-3219	108	5	x	x	X
ejpam-3219	108	6	)	)	PUNCT
ejpam-3219	108	7	=	=	PUNCT
ejpam-3219	108	8	x→	x→	PUNCT
ejpam-3219	109	1	y	y	PROPN
ejpam-3219	109	2	→	→	SYM
ejpam-3219	109	3	z	z	NOUN
ejpam-3219	110	1	−	−	NOUN
ejpam-3219	110	2	x→	x→	PUNCT
ejpam-3219	111	1	z	z	X
ejpam-3219	111	2	→	→	SYM
ejpam-3219	111	3	y	y	PROPN
ejpam-3219	111	4	−	−	PROPN
ejpam-3219	111	5	y	y	PROPN
ejpam-3219	111	6	→	→	SYM
ejpam-3219	111	7	z	z	PROPN
ejpam-3219	111	8	→	→	SYM
ejpam-3219	111	9	x+	x+	ADJ
ejpam-3219	111	10	z	z	X
ejpam-3219	111	11	→	→	SYM
ejpam-3219	111	12	y	y	PROPN
ejpam-3219	111	13	→	→	PUNCT
ejpam-3219	111	14	x.	x.	PROPN
ejpam-3219	111	15	(	(	PUNCT
ejpam-3219	111	16	8)	8)	NUM
ejpam-3219	111	17	[	[	X
ejpam-3219	111	18	y	y	PROPN
ejpam-3219	111	19	,	,	PUNCT
ejpam-3219	111	20	[	[	X
ejpam-3219	111	21	z	z	X
ejpam-3219	111	22	,	,	PUNCT
ejpam-3219	111	23	x	x	X
ejpam-3219	111	24	]	]	X
ejpam-3219	111	25	]	]	X
ejpam-3219	111	26	=	=	PUNCT
ejpam-3219	111	27	y	y	PROPN
ejpam-3219	111	28	→	→	SYM
ejpam-3219	111	29	z	z	PROPN
ejpam-3219	111	30	→	→	SYM
ejpam-3219	111	31	x−	x−	PROPN
ejpam-3219	111	32	y	y	PROPN
ejpam-3219	111	33	→	→	PUNCT
ejpam-3219	111	34	x→	x→	PROPN
ejpam-3219	112	1	z	z	NOUN
ejpam-3219	112	2	−	−	PROPN
ejpam-3219	112	3	z	z	PROPN
ejpam-3219	112	4	→	→	SYM
ejpam-3219	112	5	x→	x→	PUNCT
ejpam-3219	113	1	y	y	PROPN
ejpam-3219	113	2	+	+	NUM
ejpam-3219	113	3	x→	x→	SYM
ejpam-3219	113	4	z	z	X
ejpam-3219	113	5	→	→	PUNCT
ejpam-3219	113	6	y.	y.	NOUN
ejpam-3219	113	7	(	(	PUNCT
ejpam-3219	113	8	9	9	NUM
ejpam-3219	113	9	)	)	PUNCT
ejpam-3219	114	1	[	[	X
ejpam-3219	114	2	z	z	X
ejpam-3219	114	3	,	,	PUNCT
ejpam-3219	114	4	[	[	X
ejpam-3219	114	5	x	x	X
ejpam-3219	114	6	,	,	PUNCT
ejpam-3219	114	7	y	y	PROPN
ejpam-3219	114	8	]	]	X
ejpam-3219	114	9	]	]	X
ejpam-3219	114	10	=	=	PUNCT
ejpam-3219	114	11	z	z	X
ejpam-3219	114	12	→	→	SYM
ejpam-3219	114	13	x→	x→	PROPN
ejpam-3219	115	1	y	y	PROPN
ejpam-3219	115	2	−	−	PROPN
ejpam-3219	115	3	z	z	PROPN
ejpam-3219	115	4	→	→	SYM
ejpam-3219	115	5	y	y	PROPN
ejpam-3219	115	6	→	→	SYM
ejpam-3219	115	7	x−	x−	PROPN
ejpam-3219	115	8	x→	x→	PUNCT
ejpam-3219	116	1	y	y	PROPN
ejpam-3219	116	2	→	→	SYM
ejpam-3219	116	3	z	z	PROPN
ejpam-3219	117	1	+	+	NUM
ejpam-3219	117	2	y	y	PROPN
ejpam-3219	117	3	→	→	PUNCT
ejpam-3219	117	4	x→	x→	PROPN
ejpam-3219	117	5	z.	z.	PROPN
ejpam-3219	117	6	therefore	therefore	ADV
ejpam-3219	117	7	,	,	PUNCT
ejpam-3219	117	8	the	the	DET
ejpam-3219	117	9	sum	sum	NOUN
ejpam-3219	117	10	of	of	ADP
ejpam-3219	117	11	three	three	NUM
ejpam-3219	117	12	brackets	bracket	NOUN
ejpam-3219	117	13	,	,	PUNCT
ejpam-3219	117	14	i.e.	i.e.	X
ejpam-3219	117	15	,	,	PUNCT
ejpam-3219	117	16	(	(	PUNCT
ejpam-3219	117	17	7	7	NUM
ejpam-3219	117	18	)	)	PUNCT
ejpam-3219	117	19	,	,	PUNCT
ejpam-3219	117	20	(	(	PUNCT
ejpam-3219	117	21	8)	8)	NUM
ejpam-3219	117	22	and	and	CCONJ
ejpam-3219	117	23	(	(	PUNCT
ejpam-3219	117	24	9	9	X
ejpam-3219	117	25	)	)	PUNCT
ejpam-3219	117	26	satisfying	satisfy	VERB
ejpam-3219	117	27	the	the	DET
ejpam-3219	117	28	jacobi	jacobi	PROPN
ejpam-3219	117	29	identity	identity	NOUN
ejpam-3219	117	30	(	(	PUNCT
ejpam-3219	117	31	10	10	NUM
ejpam-3219	117	32	)	)	PUNCT
ejpam-3219	118	1	[	[	X
ejpam-3219	118	2	x	x	X
ejpam-3219	118	3	,	,	PUNCT
ejpam-3219	118	4	[	[	X
ejpam-3219	118	5	y	y	X
ejpam-3219	118	6	,	,	PUNCT
ejpam-3219	118	7	z	z	X
ejpam-3219	118	8	]	]	X
ejpam-3219	118	9	]	]	PUNCT
ejpam-3219	119	1	+	+	CCONJ
ejpam-3219	119	2	[	[	X
ejpam-3219	119	3	y	y	X
ejpam-3219	119	4	,	,	PUNCT
ejpam-3219	119	5	[	[	X
ejpam-3219	119	6	z	z	X
ejpam-3219	119	7	,	,	PUNCT
ejpam-3219	119	8	x	x	X
ejpam-3219	119	9	]	]	X
ejpam-3219	119	10	]	]	PUNCT
ejpam-3219	120	1	+	+	CCONJ
ejpam-3219	121	1	[	[	X
ejpam-3219	121	2	z	z	X
ejpam-3219	121	3	,	,	PUNCT
ejpam-3219	121	4	[	[	X
ejpam-3219	121	5	x	x	X
ejpam-3219	121	6	,	,	PUNCT
ejpam-3219	121	7	y	y	PROPN
ejpam-3219	121	8	]	]	X
ejpam-3219	121	9	]	]	X
ejpam-3219	121	10	=	=	SYM
ejpam-3219	121	11	0	0	X
ejpam-3219	121	12	.	.	PUNCT
ejpam-3219	121	13	references	reference	NOUN
ejpam-3219	121	14	448	448	NUM
ejpam-3219	121	15	references	reference	NOUN
ejpam-3219	121	16	[	[	X
ejpam-3219	121	17	1	1	NUM
ejpam-3219	121	18	]	]	PUNCT
ejpam-3219	121	19	serre	serre	PROPN
ejpam-3219	121	20	j	j	PROPN
ejpam-3219	121	21	-	-	PROPN
ejpam-3219	121	22	p.	p.	PROPN
ejpam-3219	121	23	lie	lie	NOUN
ejpam-3219	121	24	algebras	algebra	NOUN
ejpam-3219	121	25	and	and	CCONJ
ejpam-3219	121	26	lie	lie	NOUN
ejpam-3219	121	27	groups	group	NOUN
ejpam-3219	121	28	(	(	PUNCT
ejpam-3219	121	29	2nd	2nd	ADJ
ejpam-3219	121	30	ed	ed	NOUN
ejpam-3219	121	31	.	.	PUNCT
ejpam-3219	121	32	)	)	PUNCT
ejpam-3219	121	33	,	,	PUNCT
ejpam-3219	121	34	springer	springer	NOUN
ejpam-3219	121	35	(	(	PUNCT
ejpam-3219	121	36	2006	2006	NUM
ejpam-3219	121	37	)	)	PUNCT
ejpam-3219	122	1	[	[	X
ejpam-3219	122	2	2	2	NUM
ejpam-3219	122	3	]	]	PUNCT
ejpam-3219	122	4	yonghong	yonghong	PROPN
ejpam-3219	122	5	l.	l.	PROPN
ejpam-3219	122	6	a	a	DET
ejpam-3219	122	7	new	new	ADJ
ejpam-3219	122	8	branch	branch	NOUN
ejpam-3219	122	9	of	of	ADP
ejpam-3219	122	10	the	the	DET
ejpam-3219	122	11	pure	pure	ADJ
ejpam-3219	122	12	algebra	algebra	NOUN
ejpam-3219	122	13	:	:	PUNCT
ejpam-3219	122	14	bcl	bcl	NOUN
ejpam-3219	122	15	-	-	PUNCT
ejpam-3219	122	16	algebras	algebra	NOUN
ejpam-3219	122	17	,	,	PUNCT
ejpam-3219	122	18	advances	advance	NOUN
ejpam-3219	122	19	in	in	ADP
ejpam-3219	122	20	pure	pure	ADJ
ejpam-3219	122	21	mathematics	mathematic	NOUN
ejpam-3219	122	22	,	,	PUNCT
ejpam-3219	122	23	1	1	NUM
ejpam-3219	122	24	,	,	PUNCT
ejpam-3219	122	25	297	297	NUM
ejpam-3219	122	26	-	-	SYM
ejpam-3219	122	27	299	299	NUM
ejpam-3219	122	28	(	(	PUNCT
ejpam-3219	122	29	2011	2011	NUM
ejpam-3219	122	30	)	)	PUNCT
ejpam-3219	122	31	,	,	PUNCT
ejpam-3219	123	1	https://dx.doi.org/10.4236/apm.2011.15054	https://dx.doi.org/10.4236/apm.2011.15054	CCONJ
ejpam-3219	124	1	[	[	X
ejpam-3219	124	2	3	3	X
ejpam-3219	124	3	]	]	X
ejpam-3219	124	4	yonghong	yonghong	PROPN
ejpam-3219	124	5	l.	l.	PROPN
ejpam-3219	124	6	on	on	ADP
ejpam-3219	124	7	bcl+-algebras	bcl+-algebra	NOUN
ejpam-3219	124	8	,	,	PUNCT
ejpam-3219	124	9	advances	advance	NOUN
ejpam-3219	124	10	in	in	ADP
ejpam-3219	124	11	pure	pure	ADJ
ejpam-3219	124	12	mathematics	mathematic	NOUN
ejpam-3219	124	13	,	,	PUNCT
ejpam-3219	124	14	2	2	NUM
ejpam-3219	124	15	,	,	PUNCT
ejpam-3219	124	16	59	59	NUM
ejpam-3219	124	17	-	-	SYM
ejpam-3219	124	18	61	61	NUM
ejpam-3219	124	19	(	(	PUNCT
ejpam-3219	124	20	2012	2012	NUM
ejpam-3219	124	21	)	)	PUNCT
ejpam-3219	124	22	,	,	PUNCT
ejpam-3219	124	23	https://dx.doi.org/10.4236/apm.2012.21012	https://dx.doi.org/10.4236/apm.2012.21012	NOUN
ejpam-3219	125	1	[	[	X
ejpam-3219	125	2	4	4	NUM
ejpam-3219	125	3	]	]	X
ejpam-3219	125	4	al	al	PROPN
ejpam-3219	125	5	-	-	PUNCT
ejpam-3219	125	6	kadi	kadi	PROPN
ejpam-3219	125	7	d.	d.	PROPN
ejpam-3219	125	8	and	and	CCONJ
ejpam-3219	125	9	hosny	hosny	PROPN
ejpam-3219	125	10	r.	r.	PROPN
ejpam-3219	125	11	on	on	ADP
ejpam-3219	125	12	bcl	bcl	PROPN
ejpam-3219	125	13	-	-	PUNCT
ejpam-3219	125	14	algebra	algebra	PROPN
ejpam-3219	125	15	,	,	PUNCT
ejpam-3219	125	16	journal	journal	NOUN
ejpam-3219	125	17	of	of	ADP
ejpam-3219	125	18	advances	advance	NOUN
ejpam-3219	125	19	in	in	ADP
ejpam-3219	125	20	mathematics	mathematic	NOUN
ejpam-3219	125	21	,	,	PUNCT
ejpam-3219	125	22	3	3	NUM
ejpam-3219	125	23	,	,	PUNCT
ejpam-3219	125	24	184	184	NUM
ejpam-3219	125	25	-	-	SYM
ejpam-3219	125	26	190	190	NUM
ejpam-3219	125	27	(	(	PUNCT
ejpam-3219	125	28	2013	2013	NUM
ejpam-3219	125	29	)	)	PUNCT
ejpam-3219	125	30	.	.	PUNCT
ejpam-3219	126	1	[	[	X
ejpam-3219	126	2	5	5	NUM
ejpam-3219	126	3	]	]	X
ejpam-3219	126	4	al	al	PROPN
ejpam-3219	126	5	-	-	PUNCT
ejpam-3219	126	6	kadi	kadi	PROPN
ejpam-3219	126	7	d.	d.	PROPN
ejpam-3219	126	8	soft	soft	PROPN
ejpam-3219	126	9	bcl	bcl	PROPN
ejpam-3219	126	10	-	-	NOUN
ejpam-3219	126	11	algebra	algebra	PROPN
ejpam-3219	126	12	,	,	PUNCT
ejpam-3219	126	13	international	international	ADJ
ejpam-3219	126	14	journal	journal	NOUN
ejpam-3219	126	15	of	of	ADP
ejpam-3219	126	16	algebra	algebra	PROPN
ejpam-3219	126	17	,	,	PUNCT
ejpam-3219	126	18	8	8	NUM
ejpam-3219	126	19	,	,	PUNCT
ejpam-3219	126	20	57	57	NUM
ejpam-3219	126	21	-	-	SYM
ejpam-3219	126	22	65	65	NUM
ejpam-3219	126	23	(	(	PUNCT
ejpam-3219	126	24	2014	2014	NUM
ejpam-3219	126	25	)	)	PUNCT
ejpam-3219	126	26	,	,	PUNCT
ejpam-3219	126	27	https://dx.doi.org/10.12988/ija.2014.311122	https://dx.doi.org/10.12988/ija.2014.311122	X
ejpam-3219	127	1	[	[	X
ejpam-3219	127	2	6	6	NUM
ejpam-3219	127	3	]	]	PUNCT
ejpam-3219	127	4	yonghong	yonghong	PROPN
ejpam-3219	127	5	l.	l.	PROPN
ejpam-3219	127	6	partial	partial	ADJ
ejpam-3219	127	7	orders	order	NOUN
ejpam-3219	127	8	in	in	ADP
ejpam-3219	127	9	bcl+-algebra	bcl+-algebra	PROPN
ejpam-3219	127	10	,	,	PUNCT
ejpam-3219	127	11	journal	journal	NOUN
ejpam-3219	127	12	of	of	ADP
ejpam-3219	127	13	advances	advance	NOUN
ejpam-3219	127	14	in	in	ADP
ejpam-3219	127	15	mathematics	mathematic	NOUN
ejpam-3219	127	16	,	,	PUNCT
ejpam-3219	127	17	5	5	NUM
ejpam-3219	127	18	,	,	PUNCT
ejpam-3219	127	19	630	630	NUM
ejpam-3219	127	20	-	-	SYM
ejpam-3219	127	21	634	634	NUM
ejpam-3219	127	22	(	(	PUNCT
ejpam-3219	127	23	2013	2013	NUM
ejpam-3219	127	24	)	)	PUNCT
ejpam-3219	127	25	.	.	PUNCT
ejpam-3219	128	1	[	[	X
ejpam-3219	128	2	7	7	X
ejpam-3219	128	3	]	]	SYM
ejpam-3219	128	4	yonghong	yonghong	PROPN
ejpam-3219	128	5	l.	l.	PROPN
ejpam-3219	128	6	topological	topological	PROPN
ejpam-3219	128	7	bcl+-algebras	bcl+-algebras	PROPN
ejpam-3219	128	8	,	,	PUNCT
ejpam-3219	128	9	pure	pure	ADJ
ejpam-3219	128	10	and	and	CCONJ
ejpam-3219	128	11	applied	applied	ADJ
ejpam-3219	128	12	mathematics	mathematic	NOUN
ejpam-3219	128	13	journal	journal	NOUN
ejpam-3219	128	14	,	,	PUNCT
ejpam-3219	128	15	3	3	NUM
ejpam-3219	128	16	,	,	PUNCT
ejpam-3219	128	17	11	11	NUM
ejpam-3219	128	18	-	-	SYM
ejpam-3219	128	19	13	13	NUM
ejpam-3219	128	20	(	(	PUNCT
ejpam-3219	128	21	2014	2014	NUM
ejpam-3219	128	22	)	)	PUNCT
ejpam-3219	128	23	.	.	PUNCT
ejpam-3219	129	1	[	[	X
ejpam-3219	129	2	8	8	NUM
ejpam-3219	129	3	]	]	X
ejpam-3219	129	4	yonghong	yonghong	PROPN
ejpam-3219	129	5	l.	l.	PROPN
ejpam-3219	129	6	some	some	DET
ejpam-3219	129	7	distributions	distribution	NOUN
ejpam-3219	129	8	of	of	ADP
ejpam-3219	129	9	bcl+-algebras	bcl+-algebra	NOUN
ejpam-3219	129	10	,	,	PUNCT
ejpam-3219	129	11	international	international	ADJ
ejpam-3219	129	12	journal	journal	NOUN
ejpam-3219	129	13	of	of	ADP
ejpam-3219	129	14	algebra	algebra	PROPN
ejpam-3219	129	15	,	,	PUNCT
ejpam-3219	129	16	8	8	NUM
ejpam-3219	129	17	,	,	PUNCT
ejpam-3219	129	18	495	495	NUM
ejpam-3219	129	19	-	-	SYM
ejpam-3219	129	20	503	503	NUM
ejpam-3219	129	21	(	(	PUNCT
ejpam-3219	129	22	2014	2014	NUM
ejpam-3219	129	23	)	)	PUNCT
ejpam-3219	129	24	.	.	PUNCT
ejpam-3219	130	1	https://dx.doi.org/10.12988/ija.2014.4556	https://dx.doi.org/10.12988/ija.2014.4556	PUNCT
ejpam-3219	131	1	[	[	X
ejpam-3219	131	2	9	9	NUM
ejpam-3219	131	3	]	]	SYM
ejpam-3219	131	4	yonghong	yonghong	PROPN
ejpam-3219	131	5	l.	l.	PROPN
ejpam-3219	131	6	filtrations	filtration	NOUN
ejpam-3219	131	7	and	and	CCONJ
ejpam-3219	131	8	deductive	deductive	ADJ
ejpam-3219	131	9	systems	system	NOUN
ejpam-3219	131	10	in	in	ADP
ejpam-3219	131	11	bcl+	bcl+	PROPN
ejpam-3219	131	12	algebras	algebra	NOUN
ejpam-3219	131	13	,	,	PUNCT
ejpam-3219	131	14	british	british	ADJ
ejpam-3219	131	15	journal	journal	PROPN
ejpam-3219	131	16	of	of	ADP
ejpam-3219	131	17	mathematics	mathematics	PROPN
ejpam-3219	131	18	&	&	CCONJ
ejpam-3219	131	19	computer	computer	NOUN
ejpam-3219	131	20	science	science	NOUN
ejpam-3219	131	21	,	,	PUNCT
ejpam-3219	131	22	8	8	NUM
ejpam-3219	131	23	,	,	PUNCT
ejpam-3219	131	24	274	274	NUM
ejpam-3219	131	25	-	-	SYM
ejpam-3219	131	26	285	285	NUM
ejpam-3219	131	27	(	(	PUNCT
ejpam-3219	131	28	2015	2015	NUM
ejpam-3219	131	29	)	)	PUNCT
ejpam-3219	131	30	.	.	PUNCT
ejpam-3219	132	1	[	[	X
ejpam-3219	132	2	10	10	NUM
ejpam-3219	132	3	]	]	X
ejpam-3219	132	4	yonghong	yonghong	PROPN
ejpam-3219	132	5	l.	l.	PROPN
ejpam-3219	132	6	funnels	funnel	NOUN
ejpam-3219	132	7	in	in	ADP
ejpam-3219	132	8	bcl+	bcl+	PROPN
ejpam-3219	132	9	algebras	algebra	NOUN
ejpam-3219	132	10	,	,	PUNCT
ejpam-3219	132	11	international	international	ADJ
ejpam-3219	132	12	journal	journal	NOUN
ejpam-3219	132	13	of	of	ADP
ejpam-3219	132	14	mathematical	mathematical	ADJ
ejpam-3219	132	15	sciences	sciences	PROPN
ejpam-3219	132	16	&	&	CCONJ
ejpam-3219	132	17	engineering	engineering	NOUN
ejpam-3219	132	18	applications	application	NOUN
ejpam-3219	132	19	,	,	PUNCT
ejpam-3219	132	20	9	9	NUM
ejpam-3219	132	21	,	,	PUNCT
ejpam-3219	132	22	179	179	NUM
ejpam-3219	132	23	-	-	SYM
ejpam-3219	132	24	185	185	NUM
ejpam-3219	132	25	(	(	PUNCT
ejpam-3219	132	26	2015	2015	NUM
ejpam-3219	132	27	)	)	PUNCT
ejpam-3219	132	28	.	.	PUNCT
ejpam-3219	133	1	[	[	X
ejpam-3219	133	2	11	11	NUM
ejpam-3219	133	3	]	]	SYM
ejpam-3219	133	4	yonghong	yonghong	PROPN
ejpam-3219	133	5	l.	l.	PROPN
ejpam-3219	133	6	liu	liu	PROPN
ejpam-3219	133	7	’s	’s	PART
ejpam-3219	133	8	laws	law	NOUN
ejpam-3219	133	9	and	and	CCONJ
ejpam-3219	133	10	p	p	PROPN
ejpam-3219	133	11	-	-	PUNCT
ejpam-3219	133	12	bcl+	bcl+	PROPN
ejpam-3219	133	13	algebras	algebra	NOUN
ejpam-3219	133	14	,	,	PUNCT
ejpam-3219	133	15	international	international	ADJ
ejpam-3219	133	16	journal	journal	NOUN
ejpam-3219	133	17	of	of	ADP
ejpam-3219	133	18	pure	pure	PROPN
ejpam-3219	133	19	&	&	CCONJ
ejpam-3219	133	20	engineering	engineering	NOUN
ejpam-3219	133	21	mathematics	mathematic	NOUN
ejpam-3219	133	22	,	,	PUNCT
ejpam-3219	133	23	3	3	NUM
ejpam-3219	133	24	,	,	PUNCT
ejpam-3219	133	25	51	51	NUM
ejpam-3219	133	26	-	-	SYM
ejpam-3219	133	27	58	58	NUM
ejpam-3219	133	28	(	(	PUNCT
ejpam-3219	133	29	2015	2015	NUM
ejpam-3219	133	30	)	)	PUNCT
ejpam-3219	133	31	.	.	PUNCT
ejpam-3219	134	1	[	[	X
ejpam-3219	134	2	12	12	NUM
ejpam-3219	134	3	]	]	X
ejpam-3219	134	4	yonghong	yonghong	PROPN
ejpam-3219	134	5	l.	l.	PROPN
ejpam-3219	134	6	standard	standard	PROPN
ejpam-3219	134	7	ideals	ideal	NOUN
ejpam-3219	134	8	in	in	ADP
ejpam-3219	134	9	bcl+	bcl+	PROPN
ejpam-3219	134	10	algebras	algebra	NOUN
ejpam-3219	134	11	,	,	PUNCT
ejpam-3219	134	12	journal	journal	NOUN
ejpam-3219	134	13	of	of	ADP
ejpam-3219	134	14	mathematics	mathematics	PROPN
ejpam-3219	134	15	research	research	NOUN
ejpam-3219	134	16	,	,	PUNCT
ejpam-3219	134	17	8	8	NUM
ejpam-3219	134	18	,	,	PUNCT
ejpam-3219	134	19	37	37	NUM
ejpam-3219	134	20	-	-	SYM
ejpam-3219	134	21	44	44	NUM
ejpam-3219	134	22	(	(	PUNCT
ejpam-3219	134	23	2016	2016	NUM
ejpam-3219	134	24	)	)	PUNCT
ejpam-3219	134	25	.	.	PUNCT
ejpam-3219	135	1	[	[	X
ejpam-3219	135	2	13	13	NUM
ejpam-3219	135	3	]	]	SYM
ejpam-3219	135	4	yonghong	yonghong	PROPN
ejpam-3219	135	5	l.	l.	PROPN
ejpam-3219	135	6	on	on	ADP
ejpam-3219	135	7	liu	liu	PROPN
ejpam-3219	135	8	algebras	algebras	PROPN
ejpam-3219	135	9	:	:	PUNCT
ejpam-3219	135	10	a	a	DET
ejpam-3219	135	11	new	new	ADJ
ejpam-3219	135	12	composite	composite	ADJ
ejpam-3219	135	13	structure	structure	NOUN
ejpam-3219	135	14	of	of	ADP
ejpam-3219	135	15	the	the	DET
ejpam-3219	135	16	bcl+	bcl+	PROPN
ejpam-3219	135	17	algebras	algebra	NOUN
ejpam-3219	135	18	and	and	CCONJ
ejpam-3219	135	19	the	the	DET
ejpam-3219	135	20	semigroups	semigroup	NOUN
ejpam-3219	135	21	,	,	PUNCT
ejpam-3219	135	22	journal	journal	NOUN
ejpam-3219	135	23	of	of	ADP
ejpam-3219	135	24	semigroup	semigroup	PROPN
ejpam-3219	135	25	theory	theory	NOUN
ejpam-3219	135	26	and	and	CCONJ
ejpam-3219	135	27	applications	application	NOUN
ejpam-3219	135	28	,	,	PUNCT
ejpam-3219	135	29	2	2	NUM
ejpam-3219	135	30	,	,	PUNCT
ejpam-3219	135	31	1	1	NUM
ejpam-3219	135	32	-	-	SYM
ejpam-3219	135	33	16	16	NUM
ejpam-3219	135	34	(	(	PUNCT
ejpam-3219	135	35	2017	2017	NUM
ejpam-3219	135	36	)	)	PUNCT
ejpam-3219	135	37	.	.	PUNCT
ejpam-3219	136	1	[	[	X
ejpam-3219	136	2	14	14	NUM
ejpam-3219	136	3	]	]	X
ejpam-3219	136	4	khalil	khalil	PROPN
ejpam-3219	136	5	s.	s.	PROPN
ejpam-3219	136	6	m.	m.	PROPN
ejpam-3219	136	7	and	and	CCONJ
ejpam-3219	136	8	musawi	musawi	PROPN
ejpam-3219	136	9	a.	a.	PROPN
ejpam-3219	136	10	f.	f.	PROPN
ejpam-3219	136	11	m.	m.	PROPN
ejpam-3219	137	1	j.	j.	PROPN
ejpam-3219	137	2	soft	soft	PROPN
ejpam-3219	137	3	bcl	bcl	PROPN
ejpam-3219	137	4	-	-	PUNCT
ejpam-3219	137	5	algebras	algebra	NOUN
ejpam-3219	137	6	of	of	ADP
ejpam-3219	137	7	the	the	DET
ejpam-3219	137	8	power	power	NOUN
ejpam-3219	137	9	sets	set	NOUN
ejpam-3219	137	10	,	,	PUNCT
ejpam-3219	137	11	international	international	ADJ
ejpam-3219	137	12	journal	journal	NOUN
ejpam-3219	137	13	of	of	ADP
ejpam-3219	137	14	algebra	algebra	PROPN
ejpam-3219	137	15	,	,	PUNCT
ejpam-3219	137	16	11	11	NUM
ejpam-3219	137	17	,	,	PUNCT
ejpam-3219	137	18	329	329	NUM
ejpam-3219	137	19	-	-	SYM
ejpam-3219	137	20	341	341	NUM
ejpam-3219	137	21	(	(	PUNCT
ejpam-3219	137	22	2017	2017	NUM
ejpam-3219	137	23	)	)	PUNCT
ejpam-3219	137	24	,	,	PUNCT
ejpam-3219	137	25	https://doi.org/10.12988/ija.2017.7735	https://doi.org/10.12988/ija.2017.7735	PROPN
ejpam-3219	137	26	[	[	X
ejpam-3219	137	27	15	15	NUM
ejpam-3219	137	28	]	]	X
ejpam-3219	137	29	yonghong	yonghong	PROPN
ejpam-3219	137	30	l.	l.	PROPN
ejpam-3219	137	31	pa	pa	PROPN
ejpam-3219	137	32	-	-	PROPN
ejpam-3219	137	33	bcl+	bcl+	PROPN
ejpam-3219	137	34	algebras	algebra	NOUN
ejpam-3219	137	35	and	and	CCONJ
ejpam-3219	137	36	groups	group	NOUN
ejpam-3219	137	37	,	,	PUNCT
ejpam-3219	137	38	applied	apply	VERB
ejpam-3219	137	39	mathematics	mathematics	PROPN
ejpam-3219	137	40	&	&	CCONJ
ejpam-3219	137	41	information	information	NOUN
ejpam-3219	137	42	sciences	sciences	PROPN
ejpam-3219	137	43	,	,	PUNCT
ejpam-3219	137	44	11	11	NUM
ejpam-3219	137	45	,	,	PUNCT
ejpam-3219	137	46	891	891	NUM
ejpam-3219	137	47	-	-	SYM
ejpam-3219	137	48	897	897	NUM
ejpam-3219	137	49	(	(	PUNCT
ejpam-3219	137	50	2017	2017	NUM
ejpam-3219	137	51	)	)	PUNCT
ejpam-3219	137	52	,	,	PUNCT
ejpam-3219	137	53	http://dx.doi.org/10.18576/amis/110329	http://dx.doi.org/10.18576/amis/110329	PROPN