id	sid	tid	token	lemma	pos
ejpam-3996	1	1	european	european	PROPN
ejpam-3996	1	2	journal	journal	PROPN
ejpam-3996	1	3	of	of	ADP
ejpam-3996	1	4	pure	pure	ADJ
ejpam-3996	1	5	and	and	CCONJ
ejpam-3996	1	6	applied	apply	VERB
ejpam-3996	1	7	mathematics	mathematic	NOUN
ejpam-3996	1	8	vol	vol	NOUN
ejpam-3996	1	9	.	.	PUNCT
ejpam-3996	2	1	14	14	NUM
ejpam-3996	2	2	,	,	PUNCT
ejpam-3996	2	3	no	no	INTJ
ejpam-3996	2	4	.	.	NOUN
ejpam-3996	2	5	3	3	NUM
ejpam-3996	2	6	,	,	PUNCT
ejpam-3996	2	7	2021	2021	NUM
ejpam-3996	2	8	,	,	PUNCT
ejpam-3996	2	9	895	895	NUM
ejpam-3996	2	10	-	-	SYM
ejpam-3996	2	11	904	904	NUM
ejpam-3996	2	12	issn	issn	PROPN
ejpam-3996	2	13	1307	1307	NUM
ejpam-3996	2	14	-	-	SYM
ejpam-3996	2	15	5543	5543	NUM
ejpam-3996	2	16	–	–	PUNCT
ejpam-3996	3	1	ejpam.com	ejpam.com	X
ejpam-3996	3	2	published	publish	VERB
ejpam-3996	3	3	by	by	ADP
ejpam-3996	3	4	new	new	PROPN
ejpam-3996	3	5	york	york	PROPN
ejpam-3996	3	6	business	business	PROPN
ejpam-3996	3	7	global	global	ADJ
ejpam-3996	3	8	introduction	introduction	NOUN
ejpam-3996	3	9	to	to	ADP
ejpam-3996	3	10	neutrosophic	neutrosophic	PROPN
ejpam-3996	3	11	b	b	X
ejpam-3996	3	12	-	-	PUNCT
ejpam-3996	3	13	algebras	algebras	PROPN
ejpam-3996	3	14	danilo	danilo	PROPN
ejpam-3996	3	15	o.	o.	PROPN
ejpam-3996	3	16	jacobe1,∗	jacobe1,∗	PROPN
ejpam-3996	3	17	,	,	PUNCT
ejpam-3996	3	18	jocelyn	jocelyn	PROPN
ejpam-3996	3	19	p.	p.	PROPN
ejpam-3996	3	20	vilela2	vilela2	PROPN
ejpam-3996	3	21	1	1	NUM
ejpam-3996	3	22	institute	institute	NOUN
ejpam-3996	3	23	of	of	ADP
ejpam-3996	3	24	computing	computing	NOUN
ejpam-3996	3	25	and	and	CCONJ
ejpam-3996	3	26	engineering	engineering	NOUN
ejpam-3996	3	27	,	,	PUNCT
ejpam-3996	3	28	davao	davao	PROPN
ejpam-3996	3	29	oriental	oriental	PROPN
ejpam-3996	3	30	state	state	PROPN
ejpam-3996	3	31	university	university	PROPN
ejpam-3996	3	32	,	,	PUNCT
ejpam-3996	3	33	dahican	dahican	NOUN
ejpam-3996	3	34	,	,	PUNCT
ejpam-3996	3	35	mati	mati	PROPN
ejpam-3996	3	36	city	city	PROPN
ejpam-3996	3	37	,	,	PUNCT
ejpam-3996	3	38	8200	8200	NUM
ejpam-3996	3	39	davao	davao	PROPN
ejpam-3996	3	40	oriental	oriental	NOUN
ejpam-3996	3	41	,	,	PUNCT
ejpam-3996	3	42	philippines	philippines	PROPN
ejpam-3996	3	43	2	2	NUM
ejpam-3996	3	44	department	department	NOUN
ejpam-3996	3	45	of	of	ADP
ejpam-3996	3	46	mathematics	mathematic	NOUN
ejpam-3996	3	47	and	and	CCONJ
ejpam-3996	3	48	statistics	statistic	NOUN
ejpam-3996	3	49	,	,	PUNCT
ejpam-3996	3	50	college	college	NOUN
ejpam-3996	3	51	of	of	ADP
ejpam-3996	3	52	science	science	NOUN
ejpam-3996	3	53	and	and	CCONJ
ejpam-3996	3	54	mathematics	mathematic	NOUN
ejpam-3996	3	55	,	,	PUNCT
ejpam-3996	3	56	center	center	NOUN
ejpam-3996	3	57	of	of	ADP
ejpam-3996	3	58	graph	graph	NOUN
ejpam-3996	3	59	theory	theory	NOUN
ejpam-3996	3	60	,	,	PUNCT
ejpam-3996	3	61	algebra	algebra	NOUN
ejpam-3996	3	62	and	and	CCONJ
ejpam-3996	3	63	analysis	analysis	NOUN
ejpam-3996	3	64	,	,	PUNCT
ejpam-3996	3	65	premier	premier	ADJ
ejpam-3996	3	66	research	research	NOUN
ejpam-3996	3	67	of	of	ADP
ejpam-3996	3	68	institute	institute	PROPN
ejpam-3996	3	69	of	of	ADP
ejpam-3996	3	70	science	science	NOUN
ejpam-3996	3	71	and	and	CCONJ
ejpam-3996	3	72	mathematics	mathematic	NOUN
ejpam-3996	3	73	,	,	PUNCT
ejpam-3996	3	74	mindanao	mindanao	PROPN
ejpam-3996	3	75	state	state	PROPN
ejpam-3996	3	76	university	university	PROPN
ejpam-3996	3	77	-	-	PUNCT
ejpam-3996	3	78	iligan	iligan	PROPN
ejpam-3996	3	79	institute	institute	PROPN
ejpam-3996	3	80	of	of	ADP
ejpam-3996	3	81	technology	technology	PROPN
ejpam-3996	3	82	,	,	PUNCT
ejpam-3996	3	83	tibanga	tibanga	PROPN
ejpam-3996	3	84	,	,	PUNCT
ejpam-3996	3	85	iligan	iligan	ADJ
ejpam-3996	3	86	city	city	NOUN
ejpam-3996	3	87	,	,	PUNCT
ejpam-3996	3	88	9200	9200	NUM
ejpam-3996	3	89	lanao	lanao	PROPN
ejpam-3996	3	90	del	del	PROPN
ejpam-3996	3	91	norte	norte	PROPN
ejpam-3996	3	92	,	,	PUNCT
ejpam-3996	3	93	philippines	philippine	NOUN
ejpam-3996	3	94	abstract	abstract	ADJ
ejpam-3996	3	95	.	.	PUNCT
ejpam-3996	4	1	this	this	DET
ejpam-3996	4	2	paper	paper	NOUN
ejpam-3996	4	3	introduces	introduce	VERB
ejpam-3996	4	4	the	the	DET
ejpam-3996	4	5	notion	notion	NOUN
ejpam-3996	4	6	of	of	ADP
ejpam-3996	4	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	4	8	b	b	X
ejpam-3996	4	9	-	-	PUNCT
ejpam-3996	4	10	algebra	algebra	NOUN
ejpam-3996	4	11	.	.	PUNCT
ejpam-3996	5	1	several	several	ADJ
ejpam-3996	5	2	results	result	NOUN
ejpam-3996	5	3	on	on	ADP
ejpam-3996	5	4	properties	property	NOUN
ejpam-3996	5	5	of	of	ADP
ejpam-3996	5	6	neutrosophic	neutrosophic	ADJ
ejpam-3996	5	7	b	b	X
ejpam-3996	5	8	-	-	PUNCT
ejpam-3996	5	9	algebras	algebras	PROPN
ejpam-3996	5	10	and	and	CCONJ
ejpam-3996	5	11	neutrosophic	neutrosophic	ADJ
ejpam-3996	5	12	subalgebras	subalgebras	PROPN
ejpam-3996	5	13	are	be	AUX
ejpam-3996	5	14	presented	present	VERB
ejpam-3996	5	15	and	and	CCONJ
ejpam-3996	5	16	proved	prove	VERB
ejpam-3996	5	17	.	.	PUNCT
ejpam-3996	6	1	2020	2020	NUM
ejpam-3996	6	2	mathematics	mathematic	NOUN
ejpam-3996	6	3	subject	subject	NOUN
ejpam-3996	6	4	classifications	classification	NOUN
ejpam-3996	6	5	:	:	PUNCT
ejpam-3996	6	6	03g25	03g25	NUM
ejpam-3996	6	7	,	,	PUNCT
ejpam-3996	6	8	06f35	06f35	NUM
ejpam-3996	6	9	key	key	ADJ
ejpam-3996	6	10	words	word	NOUN
ejpam-3996	6	11	and	and	CCONJ
ejpam-3996	6	12	phrases	phrase	NOUN
ejpam-3996	6	13	:	:	PUNCT
ejpam-3996	6	14	neutrosophic	neutrosophic	PROPN
ejpam-3996	6	15	b	b	X
ejpam-3996	6	16	-	-	PUNCT
ejpam-3996	6	17	algebra	algebra	NOUN
ejpam-3996	6	18	,	,	PUNCT
ejpam-3996	6	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	6	20	subalgebra	subalgebra	NOUN
ejpam-3996	6	21	,	,	PUNCT
ejpam-3996	6	22	neutrosophic	neutrosophic	ADJ
ejpam-3996	6	23	algebraic	algebraic	ADJ
ejpam-3996	6	24	structures	structure	NOUN
ejpam-3996	6	25	1	1	NUM
ejpam-3996	6	26	.	.	PUNCT
ejpam-3996	6	27	introduction	introduction	NOUN
ejpam-3996	6	28	in	in	ADP
ejpam-3996	6	29	1995	1995	NUM
ejpam-3996	6	30	,	,	PUNCT
ejpam-3996	6	31	smarandache	smarandache	NOUN
ejpam-3996	7	1	[	[	X
ejpam-3996	7	2	16	16	NUM
ejpam-3996	7	3	]	]	PUNCT
ejpam-3996	7	4	introduced	introduce	VERB
ejpam-3996	7	5	the	the	DET
ejpam-3996	7	6	concept	concept	NOUN
ejpam-3996	7	7	of	of	ADP
ejpam-3996	7	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	7	9	logic	logic	NOUN
ejpam-3996	7	10	as	as	ADP
ejpam-3996	7	11	an	an	DET
ejpam-3996	7	12	extension	extension	NOUN
ejpam-3996	7	13	of	of	ADP
ejpam-3996	7	14	fuzzy	fuzzy	ADJ
ejpam-3996	7	15	logic	logic	NOUN
ejpam-3996	7	16	in	in	ADP
ejpam-3996	7	17	which	which	DET
ejpam-3996	7	18	indeterminacy	indeterminacy	NOUN
ejpam-3996	7	19	is	be	AUX
ejpam-3996	7	20	included	include	VERB
ejpam-3996	7	21	.	.	PUNCT
ejpam-3996	8	1	indeterminacy	indeterminacy	NOUN
ejpam-3996	8	2	means	mean	VERB
ejpam-3996	8	3	degrees	degree	NOUN
ejpam-3996	8	4	of	of	ADP
ejpam-3996	8	5	uncertainty	uncertainty	NOUN
ejpam-3996	8	6	,	,	PUNCT
ejpam-3996	8	7	vagueness	vagueness	NOUN
ejpam-3996	8	8	,	,	PUNCT
ejpam-3996	8	9	imprecision	imprecision	NOUN
ejpam-3996	8	10	,	,	PUNCT
ejpam-3996	8	11	undefined	undefined	ADJ
ejpam-3996	8	12	,	,	PUNCT
ejpam-3996	8	13	unknown	unknown	ADJ
ejpam-3996	8	14	,	,	PUNCT
ejpam-3996	8	15	inconsistency	inconsistency	NOUN
ejpam-3996	8	16	or	or	CCONJ
ejpam-3996	8	17	redundancy	redundancy	NOUN
ejpam-3996	8	18	,	,	PUNCT
ejpam-3996	8	19	for	for	ADP
ejpam-3996	8	20	example	example	NOUN
ejpam-3996	8	21	,	,	PUNCT
ejpam-3996	8	22	in	in	ADP
ejpam-3996	8	23	tossing	toss	VERB
ejpam-3996	8	24	a	a	DET
ejpam-3996	8	25	die	die	NOUN
ejpam-3996	8	26	on	on	ADP
ejpam-3996	8	27	irregular	irregular	ADJ
ejpam-3996	8	28	surface	surface	NOUN
ejpam-3996	8	29	one	one	NOUN
ejpam-3996	8	30	can	can	AUX
ejpam-3996	8	31	get	get	VERB
ejpam-3996	8	32	{	{	PUNCT
ejpam-3996	8	33	1	1	NUM
ejpam-3996	8	34	,	,	PUNCT
ejpam-3996	8	35	2	2	NUM
ejpam-3996	8	36	,	,	PUNCT
ejpam-3996	8	37	3	3	NUM
ejpam-3996	8	38	,	,	PUNCT
ejpam-3996	8	39	4	4	NUM
ejpam-3996	8	40	,	,	PUNCT
ejpam-3996	8	41	5	5	NUM
ejpam-3996	8	42	,	,	PUNCT
ejpam-3996	8	43	6	6	NUM
ejpam-3996	8	44	,	,	PUNCT
ejpam-3996	8	45	indeterminacy	indeterminacy	NOUN
ejpam-3996	8	46	}	}	PUNCT
ejpam-3996	8	47	.	.	PUNCT
ejpam-3996	9	1	in	in	ADP
ejpam-3996	9	2	the	the	DET
ejpam-3996	9	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	9	4	logic	logic	NOUN
ejpam-3996	9	5	,	,	PUNCT
ejpam-3996	9	6	each	each	DET
ejpam-3996	9	7	proposition	proposition	NOUN
ejpam-3996	9	8	is	be	AUX
ejpam-3996	9	9	estimated	estimate	VERB
ejpam-3996	9	10	to	to	PART
ejpam-3996	9	11	have	have	VERB
ejpam-3996	9	12	the	the	DET
ejpam-3996	9	13	percentage	percentage	NOUN
ejpam-3996	9	14	of	of	ADP
ejpam-3996	9	15	truth	truth	NOUN
ejpam-3996	9	16	in	in	ADP
ejpam-3996	9	17	a	a	DET
ejpam-3996	9	18	subset	subset	NOUN
ejpam-3996	9	19	t	t	NOUN
ejpam-3996	9	20	,	,	PUNCT
ejpam-3996	9	21	the	the	DET
ejpam-3996	9	22	percentage	percentage	NOUN
ejpam-3996	9	23	of	of	ADP
ejpam-3996	9	24	indeterminacy	indeterminacy	NOUN
ejpam-3996	9	25	in	in	ADP
ejpam-3996	9	26	a	a	DET
ejpam-3996	9	27	subset	subset	NOUN
ejpam-3996	9	28	i	i	PRON
ejpam-3996	9	29	,	,	PUNCT
ejpam-3996	9	30	and	and	CCONJ
ejpam-3996	9	31	the	the	DET
ejpam-3996	9	32	percentage	percentage	NOUN
ejpam-3996	9	33	of	of	ADP
ejpam-3996	9	34	falsity	falsity	NOUN
ejpam-3996	9	35	in	in	ADP
ejpam-3996	9	36	a	a	DET
ejpam-3996	9	37	subset	subset	NOUN
ejpam-3996	9	38	f.	f.	NOUN
ejpam-3996	9	39	using	use	VERB
ejpam-3996	9	40	neutrosophic	neutrosophic	ADJ
ejpam-3996	9	41	theory	theory	NOUN
ejpam-3996	9	42	,	,	PUNCT
ejpam-3996	9	43	vasantha	vasantha	NOUN
ejpam-3996	9	44	kandasamy	kandasamy	NOUN
ejpam-3996	9	45	and	and	CCONJ
ejpam-3996	9	46	florentin	florentin	PROPN
ejpam-3996	9	47	smarandache	smarandache	NOUN
ejpam-3996	9	48	[	[	X
ejpam-3996	9	49	11	11	NUM
ejpam-3996	9	50	]	]	PUNCT
ejpam-3996	9	51	in	in	ADP
ejpam-3996	9	52	2003	2003	NUM
ejpam-3996	9	53	introduced	introduce	VERB
ejpam-3996	9	54	a	a	DET
ejpam-3996	9	55	neutrosophic	neutrosophic	ADJ
ejpam-3996	9	56	structure	structure	NOUN
ejpam-3996	9	57	based	base	VERB
ejpam-3996	9	58	on	on	ADP
ejpam-3996	9	59	indeterminacy	indeterminacy	NOUN
ejpam-3996	9	60	“	"	PUNCT
ejpam-3996	9	61	i	i	PROPN
ejpam-3996	9	62	”	"	PUNCT
ejpam-3996	9	63	only	only	ADV
ejpam-3996	9	64	,	,	PUNCT
ejpam-3996	9	65	which	which	PRON
ejpam-3996	9	66	they	they	PRON
ejpam-3996	9	67	called	call	VERB
ejpam-3996	9	68	i	i	PRON
ejpam-3996	9	69	-	-	PUNCT
ejpam-3996	9	70	neutrosophic	neutrosophic	ADJ
ejpam-3996	9	71	algebraic	algebraic	ADJ
ejpam-3996	9	72	structures	structure	NOUN
ejpam-3996	9	73	,	,	PUNCT
ejpam-3996	9	74	an	an	DET
ejpam-3996	9	75	algebraic	algebraic	ADJ
ejpam-3996	9	76	structure	structure	NOUN
ejpam-3996	9	77	based	base	VERB
ejpam-3996	9	78	on	on	ADP
ejpam-3996	9	79	sets	set	NOUN
ejpam-3996	9	80	of	of	ADP
ejpam-3996	9	81	neutrosophic	neutrosophic	ADJ
ejpam-3996	9	82	numbers	number	NOUN
ejpam-3996	9	83	of	of	ADP
ejpam-3996	9	84	the	the	DET
ejpam-3996	9	85	form	form	NOUN
ejpam-3996	10	1	n	n	NOUN
ejpam-3996	10	2	=	=	SYM
ejpam-3996	10	3	a	a	DET
ejpam-3996	10	4	+	+	X
ejpam-3996	10	5	bi	bi	NOUN
ejpam-3996	10	6	,	,	PUNCT
ejpam-3996	10	7	where	where	SCONJ
ejpam-3996	10	8	a	a	DET
ejpam-3996	10	9	,	,	PUNCT
ejpam-3996	10	10	b	b	NOUN
ejpam-3996	10	11	are	be	AUX
ejpam-3996	10	12	real	real	ADJ
ejpam-3996	10	13	(	(	PUNCT
ejpam-3996	10	14	or	or	CCONJ
ejpam-3996	10	15	complex	complex	ADJ
ejpam-3996	10	16	)	)	PUNCT
ejpam-3996	10	17	numbers	number	NOUN
ejpam-3996	10	18	,	,	PUNCT
ejpam-3996	10	19	and	and	CCONJ
ejpam-3996	10	20	i	i	PRON
ejpam-3996	10	21	is	be	AUX
ejpam-3996	10	22	called	call	VERB
ejpam-3996	10	23	literal	literal	ADJ
ejpam-3996	10	24	indeterminacy	indeterminacy	NOUN
ejpam-3996	10	25	,	,	PUNCT
ejpam-3996	10	26	which	which	PRON
ejpam-3996	10	27	stands	stand	VERB
ejpam-3996	10	28	for	for	ADP
ejpam-3996	10	29	unknown	unknown	ADJ
ejpam-3996	10	30	or	or	CCONJ
ejpam-3996	10	31	non	non	ADJ
ejpam-3996	10	32	-	-	ADJ
ejpam-3996	10	33	determinate	determinate	ADJ
ejpam-3996	10	34	such	such	ADJ
ejpam-3996	10	35	that	that	DET
ejpam-3996	10	36	i2	i2	PROPN
ejpam-3996	10	37	=	=	PROPN
ejpam-3996	10	38	i.	i.	PROPN
ejpam-3996	10	39	here	here	ADV
ejpam-3996	10	40	,	,	PUNCT
ejpam-3996	10	41	a	a	PRON
ejpam-3996	10	42	is	be	AUX
ejpam-3996	10	43	called	call	VERB
ejpam-3996	10	44	the	the	DET
ejpam-3996	10	45	determinate	determinate	ADJ
ejpam-3996	10	46	part	part	NOUN
ejpam-3996	10	47	of	of	ADP
ejpam-3996	10	48	n	n	PRON
ejpam-3996	10	49	and	and	CCONJ
ejpam-3996	10	50	bi	bi	NOUN
ejpam-3996	10	51	is	be	AUX
ejpam-3996	10	52	called	call	VERB
ejpam-3996	10	53	the	the	DET
ejpam-3996	10	54	indeterminate	indeterminate	ADJ
ejpam-3996	10	55	part	part	NOUN
ejpam-3996	10	56	of	of	ADP
ejpam-3996	10	57	n	n	PROPN
ejpam-3996	10	58	,	,	PUNCT
ejpam-3996	10	59	with	with	ADP
ejpam-3996	10	60	mi	mi	PROPN
ejpam-3996	10	61	+	+	CCONJ
ejpam-3996	10	62	ni	ni	PROPN
ejpam-3996	10	63	=	=	PROPN
ejpam-3996	10	64	(	(	PUNCT
ejpam-3996	10	65	m	m	PROPN
ejpam-3996	10	66	+	+	NOUN
ejpam-3996	10	67	n)i	n)i	NOUN
ejpam-3996	10	68	,	,	PUNCT
ejpam-3996	10	69	0	0	NUM
ejpam-3996	11	1	·	·	PUNCT
ejpam-3996	11	2	i	i	PRON
ejpam-3996	11	3	=	=	NOUN
ejpam-3996	11	4	0	0	X
ejpam-3996	11	5	.	.	PUNCT
ejpam-3996	12	1	the	the	DET
ejpam-3996	12	2	indeterminacy	indeterminacy	NOUN
ejpam-3996	12	3	i	i	PRON
ejpam-3996	12	4	is	be	AUX
ejpam-3996	12	5	different	different	ADJ
ejpam-3996	12	6	from	from	ADP
ejpam-3996	12	7	the	the	DET
ejpam-3996	12	8	imaginary	imaginary	ADJ
ejpam-3996	12	9	i	i	NOUN
ejpam-3996	12	10	=	=	NOUN
ejpam-3996	12	11	√	√	NUM
ejpam-3996	12	12	−1	−1	NOUN
ejpam-3996	12	13	.	.	PUNCT
ejpam-3996	13	1	in	in	ADP
ejpam-3996	13	2	general	general	ADJ
ejpam-3996	13	3	,	,	PUNCT
ejpam-3996	13	4	one	one	NUM
ejpam-3996	13	5	has	have	VERB
ejpam-3996	13	6	in	in	ADP
ejpam-3996	13	7	=	=	PUNCT
ejpam-3996	13	8	i	i	PRON
ejpam-3996	13	9	if	if	SCONJ
ejpam-3996	13	10	n	n	PROPN
ejpam-3996	13	11	>	>	X
ejpam-3996	13	12	0	0	NUM
ejpam-3996	13	13	,	,	PUNCT
ejpam-3996	13	14	and	and	CCONJ
ejpam-3996	13	15	is	be	AUX
ejpam-3996	13	16	undefined	undefined	ADJ
ejpam-3996	13	17	for	for	ADP
ejpam-3996	13	18	n	n	DET
ejpam-3996	13	19	≤	≤	NOUN
ejpam-3996	13	20	0	0	NUM
ejpam-3996	13	21	.	.	PUNCT
ejpam-3996	14	1	∗corresponding	∗corresponde	VERB
ejpam-3996	14	2	author	author	NOUN
ejpam-3996	14	3	.	.	PUNCT
ejpam-3996	15	1	doi	doi	NOUN
ejpam-3996	15	2	:	:	PUNCT
ejpam-3996	15	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3996	https://doi.org/10.29020/nybg.ejpam.v14i3.3996	X
ejpam-3996	15	4	email	email	NOUN
ejpam-3996	15	5	addresses	address	VERB
ejpam-3996	15	6	:	:	PUNCT
ejpam-3996	15	7	danilo.jacobe@g.msuiit.edu.ph	danilo.jacobe@g.msuiit.edu.ph	PROPN
ejpam-3996	15	8	(	(	PUNCT
ejpam-3996	15	9	d.o	d.o	PROPN
ejpam-3996	15	10	.	.	PROPN
ejpam-3996	15	11	jacobe	jacobe	PROPN
ejpam-3996	15	12	)	)	PUNCT
ejpam-3996	15	13	,	,	PUNCT
ejpam-3996	15	14	jocelyn.vilela@g.msuiit.edu.ph	jocelyn.vilela@g.msuiit.edu.ph	PROPN
ejpam-3996	15	15	(	(	PUNCT
ejpam-3996	15	16	j.p	j.p	PROPN
ejpam-3996	15	17	.	.	PROPN
ejpam-3996	15	18	vilela	vilela	PROPN
ejpam-3996	15	19	)	)	PUNCT
ejpam-3996	15	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3996	16	1	895	895	NUM
ejpam-3996	16	2	©	©	PROPN
ejpam-3996	16	3	2021	2021	NUM
ejpam-3996	16	4	ejpam	ejpam	VERB
ejpam-3996	16	5	all	all	DET
ejpam-3996	16	6	rights	right	NOUN
ejpam-3996	16	7	reserved	reserve	VERB
ejpam-3996	16	8	.	.	PUNCT
ejpam-3996	17	1	d.o	d.o	PROPN
ejpam-3996	17	2	.	.	PROPN
ejpam-3996	17	3	jacobe	jacobe	PROPN
ejpam-3996	17	4	,	,	PUNCT
ejpam-3996	17	5	j.p	j.p	PROPN
ejpam-3996	17	6	.	.	PROPN
ejpam-3996	17	7	vilela	vilela	PROPN
ejpam-3996	17	8	/	/	SYM
ejpam-3996	17	9	eur	eur	PROPN
ejpam-3996	17	10	.	.	PUNCT
ejpam-3996	18	1	j.	j.	PROPN
ejpam-3996	18	2	pure	pure	PROPN
ejpam-3996	18	3	appl	appl	PROPN
ejpam-3996	18	4	.	.	PROPN
ejpam-3996	18	5	math	math	PROPN
ejpam-3996	18	6	,	,	PUNCT
ejpam-3996	18	7	14	14	NUM
ejpam-3996	18	8	(	(	PUNCT
ejpam-3996	18	9	3	3	NUM
ejpam-3996	18	10	)	)	PUNCT
ejpam-3996	18	11	(	(	PUNCT
ejpam-3996	18	12	2021	2021	NUM
ejpam-3996	18	13	)	)	PUNCT
ejpam-3996	18	14	,	,	PUNCT
ejpam-3996	18	15	895	895	NUM
ejpam-3996	18	16	-	-	SYM
ejpam-3996	18	17	904	904	NUM
ejpam-3996	18	18	896	896	NUM
ejpam-3996	18	19	in	in	ADP
ejpam-3996	18	20	2006	2006	NUM
ejpam-3996	19	1	,	,	PUNCT
ejpam-3996	19	2	they	they	PRON
ejpam-3996	19	3	introduced	introduce	VERB
ejpam-3996	19	4	some	some	DET
ejpam-3996	19	5	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	6	algebraic	algebraic	ADJ
ejpam-3996	19	7	structures	structure	NOUN
ejpam-3996	19	8	like	like	ADP
ejpam-3996	19	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	10	fields	field	NOUN
ejpam-3996	19	11	,	,	PUNCT
ejpam-3996	19	12	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	13	vector	vector	NOUN
ejpam-3996	19	14	spaces	space	NOUN
ejpam-3996	19	15	,	,	PUNCT
ejpam-3996	19	16	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	17	groups	group	NOUN
ejpam-3996	19	18	,	,	PUNCT
ejpam-3996	19	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	20	bigroups	bigroup	NOUN
ejpam-3996	19	21	,	,	PUNCT
ejpam-3996	19	22	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	23	n	n	PRON
ejpam-3996	19	24	groups	group	NOUN
ejpam-3996	19	25	,	,	PUNCT
ejpam-3996	19	26	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	27	semigroups	semigroup	NOUN
ejpam-3996	19	28	,	,	PUNCT
ejpam-3996	19	29	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	30	bisemigroups	bisemigroup	NOUN
ejpam-3996	19	31	,	,	PUNCT
ejpam-3996	19	32	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	33	n	n	CCONJ
ejpam-3996	19	34	-	-	PUNCT
ejpam-3996	19	35	semigroup	semigroup	PROPN
ejpam-3996	19	36	,	,	PUNCT
ejpam-3996	19	37	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	38	loops	loop	NOUN
ejpam-3996	19	39	,	,	PUNCT
ejpam-3996	19	40	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	41	biloops	biloop	NOUN
ejpam-3996	19	42	,	,	PUNCT
ejpam-3996	19	43	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	44	n	n	CCONJ
ejpam-3996	19	45	-	-	PUNCT
ejpam-3996	19	46	loop	loop	NOUN
ejpam-3996	19	47	,	,	PUNCT
ejpam-3996	19	48	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	49	groupoids	groupoid	NOUN
ejpam-3996	19	50	,	,	PUNCT
ejpam-3996	19	51	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	52	bigroupoids	bigroupoid	NOUN
ejpam-3996	19	53	,	,	PUNCT
ejpam-3996	19	54	and	and	CCONJ
ejpam-3996	19	55	neutrosophic	neutrosophic	ADJ
ejpam-3996	19	56	rings	ring	NOUN
ejpam-3996	19	57	[	[	X
ejpam-3996	19	58	12	12	NUM
ejpam-3996	19	59	,	,	PUNCT
ejpam-3996	19	60	17	17	NUM
ejpam-3996	19	61	]	]	PUNCT
ejpam-3996	19	62	.	.	PUNCT
ejpam-3996	20	1	in	in	ADP
ejpam-3996	20	2	2015	2015	NUM
ejpam-3996	20	3	,	,	PUNCT
ejpam-3996	20	4	a.a.a	a.a.a	PROPN
ejpam-3996	20	5	agboola	agboola	PROPN
ejpam-3996	20	6	and	and	CCONJ
ejpam-3996	20	7	b.	b.	PROPN
ejpam-3996	20	8	davvaz	davvaz	NOUN
ejpam-3996	21	1	[	[	X
ejpam-3996	21	2	1	1	X
ejpam-3996	21	3	]	]	PUNCT
ejpam-3996	21	4	introduced	introduce	VERB
ejpam-3996	21	5	the	the	DET
ejpam-3996	21	6	concept	concept	NOUN
ejpam-3996	21	7	of	of	ADP
ejpam-3996	21	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	21	9	bci	bci	PROPN
ejpam-3996	21	10	/	/	SYM
ejpam-3996	21	11	bck	bck	NOUN
ejpam-3996	21	12	.	.	PUNCT
ejpam-3996	22	1	in	in	ADP
ejpam-3996	22	2	2002	2002	NUM
ejpam-3996	22	3	,	,	PUNCT
ejpam-3996	22	4	j.	j.	PROPN
ejpam-3996	22	5	neggers	neggers	PROPN
ejpam-3996	22	6	and	and	CCONJ
ejpam-3996	22	7	h.s	h.s	PROPN
ejpam-3996	22	8	.	.	PROPN
ejpam-3996	22	9	kim	kim	PROPN
ejpam-3996	23	1	[	[	X
ejpam-3996	23	2	14	14	NUM
ejpam-3996	23	3	,	,	PUNCT
ejpam-3996	23	4	15	15	NUM
ejpam-3996	23	5	]	]	PUNCT
ejpam-3996	23	6	introduced	introduce	VERB
ejpam-3996	23	7	the	the	DET
ejpam-3996	23	8	concept	concept	NOUN
ejpam-3996	23	9	of	of	ADP
ejpam-3996	23	10	b	b	NOUN
ejpam-3996	23	11	-algebra	-algebra	NOUN
ejpam-3996	23	12	and	and	CCONJ
ejpam-3996	23	13	established	establish	VERB
ejpam-3996	23	14	some	some	DET
ejpam-3996	23	15	properties	property	NOUN
ejpam-3996	23	16	of	of	ADP
ejpam-3996	23	17	b	b	NOUN
ejpam-3996	23	18	-homomorphism[14	-homomorphism[14	PROPN
ejpam-3996	23	19	]	]	PUNCT
ejpam-3996	23	20	.	.	PUNCT
ejpam-3996	24	1	from	from	ADP
ejpam-3996	24	2	then	then	ADV
ejpam-3996	24	3	on	on	ADV
ejpam-3996	24	4	,	,	PUNCT
ejpam-3996	24	5	several	several	ADJ
ejpam-3996	24	6	characterizations	characterization	NOUN
ejpam-3996	24	7	as	as	ADP
ejpam-3996	24	8	to	to	ADP
ejpam-3996	24	9	commutativity	commutativity	NOUN
ejpam-3996	24	10	and	and	CCONJ
ejpam-3996	24	11	center	center	NOUN
ejpam-3996	24	12	,	,	PUNCT
ejpam-3996	24	13	cyclicity	cyclicity	NOUN
ejpam-3996	24	14	,	,	PUNCT
ejpam-3996	24	15	isomorphism	isomorphism	NOUN
ejpam-3996	24	16	,	,	PUNCT
ejpam-3996	24	17	direct	direct	ADJ
ejpam-3996	24	18	product	product	NOUN
ejpam-3996	24	19	,	,	PUNCT
ejpam-3996	24	20	lagrange	lagrange	NOUN
ejpam-3996	24	21	and	and	CCONJ
ejpam-3996	24	22	cauchy	cauchy	PROPN
ejpam-3996	24	23	’s	’s	PART
ejpam-3996	24	24	theorems	theorem	NOUN
ejpam-3996	24	25	,	,	PUNCT
ejpam-3996	24	26	b	b	SYM
ejpam-3996	24	27	-action	-action	PROPN
ejpam-3996	24	28	and	and	CCONJ
ejpam-3996	24	29	the	the	DET
ejpam-3996	24	30	sylow	sylow	NOUN
ejpam-3996	24	31	theorems	theorem	VERB
ejpam-3996	24	32	for	for	ADP
ejpam-3996	24	33	b	b	NOUN
ejpam-3996	24	34	-algebras	-algebra	NOUN
ejpam-3996	24	35	as	as	SCONJ
ejpam-3996	24	36	exemplified	exemplify	VERB
ejpam-3996	24	37	by	by	ADP
ejpam-3996	24	38	the	the	DET
ejpam-3996	24	39	following	follow	VERB
ejpam-3996	24	40	literatures	literature	NOUN
ejpam-3996	24	41	[	[	X
ejpam-3996	24	42	2–5	2–5	NOUN
ejpam-3996	24	43	,	,	PUNCT
ejpam-3996	24	44	8–10	8–10	NOUN
ejpam-3996	24	45	,	,	PUNCT
ejpam-3996	24	46	13	13	NUM
ejpam-3996	24	47	]	]	PUNCT
ejpam-3996	24	48	.	.	PUNCT
ejpam-3996	25	1	in	in	ADP
ejpam-3996	25	2	this	this	DET
ejpam-3996	25	3	paper	paper	NOUN
ejpam-3996	25	4	,	,	PUNCT
ejpam-3996	25	5	we	we	PRON
ejpam-3996	25	6	introduce	introduce	VERB
ejpam-3996	25	7	the	the	DET
ejpam-3996	25	8	concepts	concept	NOUN
ejpam-3996	25	9	of	of	ADP
ejpam-3996	25	10	neutrosophic	neutrosophic	ADJ
ejpam-3996	25	11	b	b	PROPN
ejpam-3996	25	12	-algebra	-algebra	PROPN
ejpam-3996	25	13	and	and	CCONJ
ejpam-3996	25	14	neutrosophic	neutrosophic	ADJ
ejpam-3996	25	15	subalgebra	subalgebra	NOUN
ejpam-3996	25	16	.	.	PUNCT
ejpam-3996	26	1	some	some	DET
ejpam-3996	26	2	properties	property	NOUN
ejpam-3996	26	3	of	of	ADP
ejpam-3996	26	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	26	5	b	b	PROPN
ejpam-3996	26	6	-algebras	-algebras	ADJ
ejpam-3996	26	7	and	and	CCONJ
ejpam-3996	26	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	26	9	subalgebras	subalgebras	PROPN
ejpam-3996	26	10	are	be	AUX
ejpam-3996	26	11	presented	present	VERB
ejpam-3996	26	12	and	and	CCONJ
ejpam-3996	26	13	proved	prove	VERB
ejpam-3996	26	14	.	.	PUNCT
ejpam-3996	27	1	2	2	X
ejpam-3996	27	2	.	.	X
ejpam-3996	27	3	preliminaries	preliminary	NOUN
ejpam-3996	27	4	for	for	ADP
ejpam-3996	27	5	convenience	convenience	NOUN
ejpam-3996	27	6	,	,	PUNCT
ejpam-3996	27	7	we	we	PRON
ejpam-3996	27	8	view	view	VERB
ejpam-3996	27	9	the	the	DET
ejpam-3996	27	10	neutrosophic	neutrosophic	ADJ
ejpam-3996	27	11	number	number	NOUN
ejpam-3996	27	12	n	n	NOUN
ejpam-3996	27	13	=	=	SYM
ejpam-3996	27	14	a+	a+	PUNCT
ejpam-3996	27	15	bi	bi	NOUN
ejpam-3996	27	16	as	as	ADP
ejpam-3996	27	17	an	an	DET
ejpam-3996	27	18	ordered	ordered	ADJ
ejpam-3996	27	19	pair	pair	NOUN
ejpam-3996	27	20	(	(	PUNCT
ejpam-3996	27	21	a	a	DET
ejpam-3996	27	22	,	,	PUNCT
ejpam-3996	27	23	bi	bi	NOUN
ejpam-3996	27	24	)	)	PUNCT
ejpam-3996	27	25	.	.	PUNCT
ejpam-3996	28	1	definition	definition	NOUN
ejpam-3996	28	2	2.1	2.1	NUM
ejpam-3996	28	3	.	.	PUNCT
ejpam-3996	29	1	[	[	X
ejpam-3996	29	2	7	7	X
ejpam-3996	29	3	]	]	X
ejpam-3996	29	4	let	let	VERB
ejpam-3996	29	5	x	x	PRON
ejpam-3996	29	6	be	be	AUX
ejpam-3996	29	7	a	a	DET
ejpam-3996	29	8	nonempty	nonempty	ADV
ejpam-3996	29	9	set	set	VERB
ejpam-3996	29	10	and	and	CCONJ
ejpam-3996	29	11	let	let	VERB
ejpam-3996	29	12	i	i	PRON
ejpam-3996	29	13	be	be	AUX
ejpam-3996	29	14	an	an	DET
ejpam-3996	29	15	indeterminate	indeterminate	NOUN
ejpam-3996	29	16	.	.	PUNCT
ejpam-3996	30	1	a	a	DET
ejpam-3996	30	2	set	set	ADJ
ejpam-3996	30	3	x(i	x(i	PROPN
ejpam-3996	30	4	)	)	PUNCT
ejpam-3996	30	5	=	=	PUNCT
ejpam-3996	30	6	〈	〈	PROPN
ejpam-3996	30	7	x	x	PRON
ejpam-3996	30	8	,	,	PUNCT
ejpam-3996	30	9	i	i	PRON
ejpam-3996	30	10	〉	〉	NOUN
ejpam-3996	30	11	=	=	SYM
ejpam-3996	30	12	{	{	PUNCT
ejpam-3996	30	13	(	(	PUNCT
ejpam-3996	30	14	x	x	NOUN
ejpam-3996	30	15	,	,	PUNCT
ejpam-3996	30	16	yi	yi	PROPN
ejpam-3996	30	17	)	)	PUNCT
ejpam-3996	30	18	:	:	PUNCT
ejpam-3996	30	19	x	x	X
ejpam-3996	30	20	,	,	PUNCT
ejpam-3996	30	21	y	y	PROPN
ejpam-3996	30	22	∈	∈	PROPN
ejpam-3996	30	23	x	x	AUX
ejpam-3996	30	24	}	}	PUNCT
ejpam-3996	30	25	is	be	AUX
ejpam-3996	30	26	called	call	VERB
ejpam-3996	30	27	a	a	DET
ejpam-3996	30	28	neutrosophic	neutrosophic	ADJ
ejpam-3996	30	29	set	set	NOUN
ejpam-3996	30	30	generated	generate	VERB
ejpam-3996	30	31	by	by	ADP
ejpam-3996	30	32	x	x	PUNCT
ejpam-3996	30	33	and	and	CCONJ
ejpam-3996	30	34	i.	i.	PROPN
ejpam-3996	30	35	a	a	DET
ejpam-3996	30	36	type	type	NOUN
ejpam-3996	30	37	(	(	PUNCT
ejpam-3996	30	38	2	2	NUM
ejpam-3996	30	39	,	,	PUNCT
ejpam-3996	30	40	0	0	NUM
ejpam-3996	30	41	)	)	PUNCT
ejpam-3996	30	42	algebra	algebra	NOUN
ejpam-3996	30	43	is	be	AUX
ejpam-3996	30	44	an	an	DET
ejpam-3996	30	45	algebra	algebra	NOUN
ejpam-3996	30	46	formed	form	VERB
ejpam-3996	30	47	from	from	ADP
ejpam-3996	30	48	a	a	DET
ejpam-3996	30	49	nonempty	nonempty	ADV
ejpam-3996	30	50	set	set	VERB
ejpam-3996	30	51	x	x	PUNCT
ejpam-3996	30	52	together	together	ADV
ejpam-3996	30	53	with	with	ADP
ejpam-3996	30	54	2	2	NUM
ejpam-3996	30	55	-	-	PUNCT
ejpam-3996	30	56	ary	ary	NOUN
ejpam-3996	30	57	operation	operation	NOUN
ejpam-3996	30	58	∗	∗	NOUN
ejpam-3996	30	59	and	and	CCONJ
ejpam-3996	30	60	a	a	DET
ejpam-3996	30	61	0	0	NUM
ejpam-3996	30	62	-	-	PUNCT
ejpam-3996	30	63	ary	ary	ADJ
ejpam-3996	30	64	operation(with	operation(with	PROPN
ejpam-3996	30	65	constant	constant	ADJ
ejpam-3996	30	66	element	element	NOUN
ejpam-3996	30	67	0	0	NUM
ejpam-3996	30	68	)	)	PUNCT
ejpam-3996	30	69	.	.	PUNCT
ejpam-3996	31	1	definition	definition	NOUN
ejpam-3996	31	2	2.2	2.2	NUM
ejpam-3996	31	3	.	.	PUNCT
ejpam-3996	32	1	[	[	X
ejpam-3996	32	2	15	15	NUM
ejpam-3996	32	3	]	]	PUNCT
ejpam-3996	32	4	let	let	VERB
ejpam-3996	32	5	x	x	PRON
ejpam-3996	32	6	be	be	AUX
ejpam-3996	32	7	a	a	DET
ejpam-3996	32	8	nonempty	nonempty	NOUN
ejpam-3996	32	9	set	set	VERB
ejpam-3996	32	10	with	with	ADP
ejpam-3996	32	11	a	a	DET
ejpam-3996	32	12	binary	binary	ADJ
ejpam-3996	32	13	operation	operation	NOUN
ejpam-3996	32	14	“	"	PUNCT
ejpam-3996	32	15	∗	∗	NOUN
ejpam-3996	32	16	”	"	PUNCT
ejpam-3996	32	17	on	on	ADP
ejpam-3996	32	18	x	x	PUNCT
ejpam-3996	32	19	and	and	CCONJ
ejpam-3996	32	20	a	a	DET
ejpam-3996	32	21	constant	constant	ADJ
ejpam-3996	32	22	0	0	NUM
ejpam-3996	32	23	.	.	PUNCT
ejpam-3996	33	1	then	then	ADV
ejpam-3996	33	2	the	the	DET
ejpam-3996	33	3	algebra	algebra	NOUN
ejpam-3996	33	4	(	(	PUNCT
ejpam-3996	33	5	x	x	NOUN
ejpam-3996	33	6	;	;	PUNCT
ejpam-3996	33	7	∗	∗	NOUN
ejpam-3996	33	8	,	,	PUNCT
ejpam-3996	33	9	0	0	NUM
ejpam-3996	33	10	)	)	PUNCT
ejpam-3996	33	11	of	of	ADP
ejpam-3996	33	12	type	type	NOUN
ejpam-3996	33	13	(	(	PUNCT
ejpam-3996	33	14	2	2	NUM
ejpam-3996	33	15	,	,	PUNCT
ejpam-3996	33	16	0	0	NUM
ejpam-3996	33	17	)	)	PUNCT
ejpam-3996	33	18	is	be	AUX
ejpam-3996	33	19	called	call	VERB
ejpam-3996	33	20	a	a	DET
ejpam-3996	33	21	b	b	NOUN
ejpam-3996	33	22	-	-	PUNCT
ejpam-3996	33	23	algebra	algebra	NOUN
ejpam-3996	33	24	if	if	SCONJ
ejpam-3996	33	25	it	it	PRON
ejpam-3996	33	26	satisfies	satisfy	VERB
ejpam-3996	33	27	the	the	DET
ejpam-3996	33	28	following	follow	VERB
ejpam-3996	33	29	axioms	axiom	NOUN
ejpam-3996	33	30	:	:	PUNCT
ejpam-3996	33	31	for	for	ADP
ejpam-3996	33	32	all	all	DET
ejpam-3996	33	33	x	x	NOUN
ejpam-3996	33	34	,	,	PUNCT
ejpam-3996	33	35	y	y	PROPN
ejpam-3996	33	36	,	,	PUNCT
ejpam-3996	33	37	z	z	PROPN
ejpam-3996	33	38	∈	∈	PROPN
ejpam-3996	33	39	x	x	X
ejpam-3996	33	40	,	,	PUNCT
ejpam-3996	33	41	(	(	PUNCT
ejpam-3996	33	42	b1	b1	NOUN
ejpam-3996	33	43	)	)	PUNCT
ejpam-3996	33	44	x	x	SYM
ejpam-3996	33	45	∗	∗	NOUN
ejpam-3996	33	46	x	x	X
ejpam-3996	33	47	=	=	SYM
ejpam-3996	33	48	0	0	NUM
ejpam-3996	33	49	;	;	PUNCT
ejpam-3996	33	50	(	(	PUNCT
ejpam-3996	33	51	b2	b2	NOUN
ejpam-3996	33	52	)	)	PUNCT
ejpam-3996	33	53	x	x	SYM
ejpam-3996	33	54	∗	∗	NOUN
ejpam-3996	33	55	0	0	NUM
ejpam-3996	34	1	=	=	SYM
ejpam-3996	34	2	x	x	X
ejpam-3996	34	3	;	;	PUNCT
ejpam-3996	34	4	(	(	PUNCT
ejpam-3996	34	5	b3	b3	PROPN
ejpam-3996	34	6	)	)	PUNCT
ejpam-3996	34	7	(	(	PUNCT
ejpam-3996	34	8	x	x	SYM
ejpam-3996	34	9	∗	∗	PROPN
ejpam-3996	34	10	y	y	NOUN
ejpam-3996	34	11	)	)	PUNCT
ejpam-3996	34	12	∗	∗	NOUN
ejpam-3996	34	13	z	z	NOUN
ejpam-3996	35	1	=	=	SYM
ejpam-3996	35	2	x	x	X
ejpam-3996	35	3	∗	∗	NOUN
ejpam-3996	35	4	(	(	PUNCT
ejpam-3996	35	5	z	z	NOUN
ejpam-3996	35	6	∗	∗	NOUN
ejpam-3996	35	7	(	(	PUNCT
ejpam-3996	35	8	0	0	NUM
ejpam-3996	35	9	∗	∗	PROPN
ejpam-3996	35	10	y	y	PROPN
ejpam-3996	35	11	)	)	PUNCT
ejpam-3996	35	12	)	)	PUNCT
ejpam-3996	35	13	.	.	PUNCT
ejpam-3996	36	1	example	example	NOUN
ejpam-3996	36	2	2.3	2.3	NUM
ejpam-3996	36	3	.	.	PUNCT
ejpam-3996	37	1	the	the	DET
ejpam-3996	37	2	following	follow	VERB
ejpam-3996	37	3	are	be	AUX
ejpam-3996	37	4	examples	example	NOUN
ejpam-3996	37	5	of	of	ADP
ejpam-3996	37	6	b	b	NOUN
ejpam-3996	37	7	-algebra	-algebra	NOUN
ejpam-3996	37	8	.	.	PUNCT
ejpam-3996	38	1	(	(	PUNCT
ejpam-3996	38	2	i	i	NOUN
ejpam-3996	38	3	)	)	PUNCT
ejpam-3996	39	1	[	[	X
ejpam-3996	39	2	15	15	NUM
ejpam-3996	39	3	]	]	X
ejpam-3996	39	4	let	let	VERB
ejpam-3996	39	5	x	x	PUNCT
ejpam-3996	39	6	=	=	PUNCT
ejpam-3996	39	7	{	{	PUNCT
ejpam-3996	39	8	0	0	NUM
ejpam-3996	39	9	,	,	PUNCT
ejpam-3996	39	10	1	1	NUM
ejpam-3996	39	11	,	,	PUNCT
ejpam-3996	39	12	2	2	NUM
ejpam-3996	39	13	}	}	PUNCT
ejpam-3996	39	14	.	.	PUNCT
ejpam-3996	40	1	define	define	VERB
ejpam-3996	40	2	the	the	DET
ejpam-3996	40	3	operation	operation	NOUN
ejpam-3996	40	4	“	"	PUNCT
ejpam-3996	40	5	∗	∗	NOUN
ejpam-3996	40	6	”	"	PUNCT
ejpam-3996	40	7	by	by	ADP
ejpam-3996	40	8	the	the	DET
ejpam-3996	40	9	cayley	cayley	ADJ
ejpam-3996	40	10	table	table	NOUN
ejpam-3996	40	11	shown	show	VERB
ejpam-3996	40	12	below	below	ADV
ejpam-3996	40	13	.	.	PUNCT
ejpam-3996	41	1	∗	∗	NOUN
ejpam-3996	41	2	0	0	NUM
ejpam-3996	41	3	1	1	NUM
ejpam-3996	41	4	2	2	NUM
ejpam-3996	41	5	0	0	NUM
ejpam-3996	41	6	0	0	NUM
ejpam-3996	41	7	2	2	NUM
ejpam-3996	41	8	1	1	NUM
ejpam-3996	41	9	1	1	NUM
ejpam-3996	41	10	1	1	NUM
ejpam-3996	41	11	0	0	NUM
ejpam-3996	41	12	2	2	NUM
ejpam-3996	41	13	2	2	NUM
ejpam-3996	41	14	2	2	NUM
ejpam-3996	41	15	1	1	NUM
ejpam-3996	41	16	0	0	NUM
ejpam-3996	41	17	(	(	PUNCT
ejpam-3996	41	18	ii	ii	NOUN
ejpam-3996	41	19	)	)	PUNCT
ejpam-3996	42	1	[	[	X
ejpam-3996	42	2	15	15	NUM
ejpam-3996	42	3	]	]	X
ejpam-3996	42	4	let	let	VERB
ejpam-3996	42	5	x	x	PUNCT
ejpam-3996	42	6	=	=	PUNCT
ejpam-3996	42	7	{	{	PUNCT
ejpam-3996	42	8	0	0	NUM
ejpam-3996	42	9	,	,	PUNCT
ejpam-3996	42	10	1	1	NUM
ejpam-3996	42	11	,	,	PUNCT
ejpam-3996	42	12	2	2	NUM
ejpam-3996	42	13	,	,	PUNCT
ejpam-3996	42	14	3	3	NUM
ejpam-3996	42	15	,	,	PUNCT
ejpam-3996	42	16	4	4	NUM
ejpam-3996	42	17	,	,	PUNCT
ejpam-3996	42	18	5	5	NUM
ejpam-3996	42	19	}	}	PUNCT
ejpam-3996	42	20	.	.	PUNCT
ejpam-3996	43	1	define	define	VERB
ejpam-3996	43	2	the	the	DET
ejpam-3996	43	3	operation	operation	NOUN
ejpam-3996	43	4	“	"	PUNCT
ejpam-3996	43	5	∗	∗	NOUN
ejpam-3996	43	6	”	"	PUNCT
ejpam-3996	43	7	by	by	ADP
ejpam-3996	43	8	the	the	DET
ejpam-3996	43	9	cayley	cayley	ADJ
ejpam-3996	43	10	table	table	NOUN
ejpam-3996	43	11	shown	show	VERB
ejpam-3996	43	12	below	below	ADV
ejpam-3996	43	13	.	.	PUNCT
ejpam-3996	44	1	∗	∗	NOUN
ejpam-3996	44	2	0	0	NUM
ejpam-3996	44	3	1	1	NUM
ejpam-3996	44	4	2	2	NUM
ejpam-3996	44	5	3	3	NUM
ejpam-3996	44	6	4	4	NUM
ejpam-3996	44	7	5	5	NUM
ejpam-3996	44	8	0	0	NUM
ejpam-3996	44	9	0	0	NUM
ejpam-3996	44	10	2	2	NUM
ejpam-3996	44	11	1	1	NUM
ejpam-3996	44	12	3	3	NUM
ejpam-3996	44	13	4	4	NUM
ejpam-3996	44	14	5	5	NUM
ejpam-3996	44	15	1	1	NUM
ejpam-3996	44	16	1	1	NUM
ejpam-3996	44	17	0	0	NUM
ejpam-3996	44	18	2	2	NUM
ejpam-3996	44	19	4	4	NUM
ejpam-3996	44	20	5	5	NUM
ejpam-3996	44	21	3	3	NUM
ejpam-3996	44	22	2	2	NUM
ejpam-3996	44	23	2	2	NUM
ejpam-3996	44	24	1	1	NUM
ejpam-3996	44	25	0	0	NUM
ejpam-3996	44	26	5	5	NUM
ejpam-3996	44	27	3	3	NUM
ejpam-3996	44	28	4	4	NUM
ejpam-3996	44	29	3	3	NUM
ejpam-3996	44	30	3	3	NUM
ejpam-3996	44	31	4	4	NUM
ejpam-3996	44	32	5	5	NUM
ejpam-3996	44	33	0	0	NUM
ejpam-3996	44	34	2	2	NUM
ejpam-3996	44	35	1	1	NUM
ejpam-3996	44	36	4	4	NUM
ejpam-3996	44	37	4	4	NUM
ejpam-3996	44	38	5	5	NUM
ejpam-3996	44	39	3	3	NUM
ejpam-3996	44	40	1	1	NUM
ejpam-3996	44	41	0	0	NUM
ejpam-3996	44	42	2	2	NUM
ejpam-3996	44	43	5	5	NUM
ejpam-3996	44	44	5	5	NUM
ejpam-3996	44	45	3	3	NUM
ejpam-3996	44	46	4	4	NUM
ejpam-3996	44	47	2	2	NUM
ejpam-3996	44	48	1	1	NUM
ejpam-3996	44	49	0	0	NUM
ejpam-3996	44	50	d.o	d.o	PROPN
ejpam-3996	44	51	.	.	PROPN
ejpam-3996	44	52	jacobe	jacobe	PROPN
ejpam-3996	44	53	,	,	PUNCT
ejpam-3996	44	54	j.p	j.p	PROPN
ejpam-3996	44	55	.	.	PROPN
ejpam-3996	44	56	vilela	vilela	PROPN
ejpam-3996	44	57	/	/	SYM
ejpam-3996	44	58	eur	eur	PROPN
ejpam-3996	44	59	.	.	PUNCT
ejpam-3996	45	1	j.	j.	PROPN
ejpam-3996	45	2	pure	pure	PROPN
ejpam-3996	45	3	appl	appl	PROPN
ejpam-3996	45	4	.	.	PROPN
ejpam-3996	45	5	math	math	PROPN
ejpam-3996	45	6	,	,	PUNCT
ejpam-3996	45	7	14	14	NUM
ejpam-3996	45	8	(	(	PUNCT
ejpam-3996	45	9	3	3	NUM
ejpam-3996	45	10	)	)	PUNCT
ejpam-3996	45	11	(	(	PUNCT
ejpam-3996	45	12	2021	2021	NUM
ejpam-3996	45	13	)	)	PUNCT
ejpam-3996	45	14	,	,	PUNCT
ejpam-3996	45	15	895	895	NUM
ejpam-3996	45	16	-	-	SYM
ejpam-3996	45	17	904	904	NUM
ejpam-3996	45	18	897	897	NUM
ejpam-3996	45	19	the	the	DET
ejpam-3996	45	20	following	follow	VERB
ejpam-3996	45	21	properties	property	NOUN
ejpam-3996	45	22	of	of	ADP
ejpam-3996	45	23	b	b	NOUN
ejpam-3996	45	24	-	-	PUNCT
ejpam-3996	45	25	algebra	algebra	NOUN
ejpam-3996	45	26	can	can	AUX
ejpam-3996	45	27	be	be	AUX
ejpam-3996	45	28	found	find	VERB
ejpam-3996	45	29	in	in	ADP
ejpam-3996	45	30	[	[	X
ejpam-3996	45	31	15	15	NUM
ejpam-3996	45	32	]	]	PUNCT
ejpam-3996	45	33	and	and	CCONJ
ejpam-3996	45	34	[	[	X
ejpam-3996	45	35	18	18	NUM
ejpam-3996	45	36	]	]	PUNCT
ejpam-3996	45	37	.	.	PUNCT
ejpam-3996	46	1	let	let	VERB
ejpam-3996	46	2	(	(	PUNCT
ejpam-3996	46	3	x	x	X
ejpam-3996	46	4	;	;	PUNCT
ejpam-3996	46	5	∗	∗	NOUN
ejpam-3996	46	6	,	,	PUNCT
ejpam-3996	46	7	0	0	NUM
ejpam-3996	46	8	)	)	PUNCT
ejpam-3996	46	9	be	be	AUX
ejpam-3996	46	10	a	a	DET
ejpam-3996	46	11	b	b	NOUN
ejpam-3996	46	12	-algebra	-algebra	NOUN
ejpam-3996	46	13	.	.	PUNCT
ejpam-3996	47	1	then	then	ADV
ejpam-3996	47	2	for	for	ADP
ejpam-3996	47	3	any	any	DET
ejpam-3996	47	4	x	x	NOUN
ejpam-3996	47	5	,	,	PUNCT
ejpam-3996	47	6	y	y	PROPN
ejpam-3996	47	7	,	,	PUNCT
ejpam-3996	47	8	z	z	PROPN
ejpam-3996	47	9	∈	∈	PROPN
ejpam-3996	47	10	x	x	X
ejpam-3996	47	11	,	,	PUNCT
ejpam-3996	47	12	(	(	PUNCT
ejpam-3996	47	13	p1	p1	NOUN
ejpam-3996	47	14	):	):	PUNCT
ejpam-3996	47	15	0	0	NUM
ejpam-3996	47	16	∗	∗	NOUN
ejpam-3996	47	17	(	(	PUNCT
ejpam-3996	47	18	0	0	NUM
ejpam-3996	47	19	∗	∗	NOUN
ejpam-3996	47	20	x	x	NOUN
ejpam-3996	47	21	)	)	PUNCT
ejpam-3996	47	22	=	=	SYM
ejpam-3996	48	1	x	x	NOUN
ejpam-3996	48	2	,	,	PUNCT
ejpam-3996	48	3	(	(	PUNCT
ejpam-3996	48	4	p2	p2	X
ejpam-3996	48	5	):	):	PUNCT
ejpam-3996	48	6	0	0	NUM
ejpam-3996	48	7	∗	∗	NOUN
ejpam-3996	48	8	(	(	PUNCT
ejpam-3996	48	9	x	x	X
ejpam-3996	48	10	∗	∗	NOUN
ejpam-3996	48	11	y	y	NOUN
ejpam-3996	48	12	)	)	PUNCT
ejpam-3996	49	1	=	=	SYM
ejpam-3996	49	2	y	y	PROPN
ejpam-3996	49	3	∗	∗	NOUN
ejpam-3996	49	4	x	x	PROPN
ejpam-3996	49	5	,	,	PUNCT
ejpam-3996	49	6	(	(	PUNCT
ejpam-3996	49	7	p3	p3	PROPN
ejpam-3996	49	8	):	):	PUNCT
ejpam-3996	49	9	(	(	PUNCT
ejpam-3996	49	10	x	x	X
ejpam-3996	49	11	∗	∗	PROPN
ejpam-3996	49	12	z	z	NOUN
ejpam-3996	49	13	)	)	PUNCT
ejpam-3996	49	14	∗	∗	NOUN
ejpam-3996	49	15	(	(	PUNCT
ejpam-3996	49	16	y	y	PROPN
ejpam-3996	49	17	∗	∗	PROPN
ejpam-3996	49	18	z	z	NOUN
ejpam-3996	49	19	)	)	PUNCT
ejpam-3996	49	20	=	=	PUNCT
ejpam-3996	50	1	x	x	PROPN
ejpam-3996	50	2	∗	∗	NOUN
ejpam-3996	50	3	y	y	PROPN
ejpam-3996	50	4	,	,	PUNCT
ejpam-3996	50	5	and	and	CCONJ
ejpam-3996	50	6	(	(	PUNCT
ejpam-3996	50	7	p4	p4	ADJ
ejpam-3996	50	8	):	):	PUNCT
ejpam-3996	50	9	x	x	PROPN
ejpam-3996	51	1	∗	∗	NOUN
ejpam-3996	51	2	y	y	NOUN
ejpam-3996	51	3	=	=	SYM
ejpam-3996	51	4	0	0	PUNCT
ejpam-3996	52	1	=	=	NOUN
ejpam-3996	52	2	⇒	⇒	NOUN
ejpam-3996	52	3	x	x	PUNCT
ejpam-3996	53	1	=	=	PUNCT
ejpam-3996	53	2	y.	y.	PROPN
ejpam-3996	53	3	lemma	lemma	PROPN
ejpam-3996	53	4	2.4	2.4	NUM
ejpam-3996	53	5	.	.	PUNCT
ejpam-3996	54	1	let	let	VERB
ejpam-3996	54	2	x	x	PRON
ejpam-3996	54	3	be	be	AUX
ejpam-3996	54	4	a	a	DET
ejpam-3996	54	5	b	b	NOUN
ejpam-3996	54	6	-	-	PUNCT
ejpam-3996	54	7	algebra	algebra	NOUN
ejpam-3996	54	8	.	.	PUNCT
ejpam-3996	55	1	then	then	ADV
ejpam-3996	55	2	for	for	ADP
ejpam-3996	55	3	any	any	DET
ejpam-3996	55	4	x	x	NOUN
ejpam-3996	55	5	,	,	PUNCT
ejpam-3996	55	6	y	y	PROPN
ejpam-3996	55	7	,	,	PUNCT
ejpam-3996	55	8	z	z	PROPN
ejpam-3996	55	9	∈	∈	PROPN
ejpam-3996	55	10	x	x	X
ejpam-3996	55	11	,	,	PUNCT
ejpam-3996	55	12	(	(	PUNCT
ejpam-3996	55	13	i	i	NOUN
ejpam-3996	55	14	)	)	PUNCT
ejpam-3996	56	1	[	[	X
ejpam-3996	56	2	6	6	NUM
ejpam-3996	56	3	]	]	PUNCT
ejpam-3996	56	4	(	(	PUNCT
ejpam-3996	56	5	left	leave	VERB
ejpam-3996	56	6	cancellation	cancellation	NOUN
ejpam-3996	56	7	law	law	NOUN
ejpam-3996	56	8	)	)	PUNCT
ejpam-3996	57	1	x	x	SYM
ejpam-3996	57	2	∗	∗	NOUN
ejpam-3996	57	3	y	y	NOUN
ejpam-3996	57	4	=	=	PUNCT
ejpam-3996	58	1	x	x	SYM
ejpam-3996	58	2	∗	∗	NOUN
ejpam-3996	58	3	z	z	PROPN
ejpam-3996	58	4	implies	imply	VERB
ejpam-3996	58	5	y	y	PROPN
ejpam-3996	58	6	=	=	SYM
ejpam-3996	58	7	z.	z.	PROPN
ejpam-3996	58	8	(	(	PUNCT
ejpam-3996	58	9	ii	ii	PROPN
ejpam-3996	58	10	)	)	PUNCT
ejpam-3996	59	1	[	[	X
ejpam-3996	59	2	15	15	NUM
ejpam-3996	59	3	]	]	X
ejpam-3996	59	4	x	x	X
ejpam-3996	59	5	∗	∗	NOUN
ejpam-3996	59	6	(	(	PUNCT
ejpam-3996	59	7	y	y	PROPN
ejpam-3996	59	8	∗	∗	PROPN
ejpam-3996	59	9	z	z	NOUN
ejpam-3996	59	10	)	)	PUNCT
ejpam-3996	59	11	=	=	SYM
ejpam-3996	60	1	(	(	PUNCT
ejpam-3996	60	2	x	x	SYM
ejpam-3996	60	3	∗	∗	NOUN
ejpam-3996	60	4	(	(	PUNCT
ejpam-3996	60	5	0	0	NUM
ejpam-3996	60	6	∗	∗	NOUN
ejpam-3996	60	7	z	z	NOUN
ejpam-3996	60	8	)	)	PUNCT
ejpam-3996	60	9	)	)	PUNCT
ejpam-3996	60	10	∗	∗	NOUN
ejpam-3996	60	11	y.	y.	PROPN
ejpam-3996	60	12	definition	definition	NOUN
ejpam-3996	60	13	2.5	2.5	NUM
ejpam-3996	60	14	.	.	PUNCT
ejpam-3996	61	1	[	[	X
ejpam-3996	61	2	15	15	NUM
ejpam-3996	61	3	]	]	X
ejpam-3996	61	4	a	a	DET
ejpam-3996	61	5	b	b	X
ejpam-3996	61	6	-	-	PUNCT
ejpam-3996	61	7	algebra	algebra	NOUN
ejpam-3996	61	8	(	(	PUNCT
ejpam-3996	61	9	x	x	NOUN
ejpam-3996	61	10	;	;	PUNCT
ejpam-3996	61	11	∗	∗	NOUN
ejpam-3996	61	12	,	,	PUNCT
ejpam-3996	61	13	0	0	NUM
ejpam-3996	61	14	)	)	PUNCT
ejpam-3996	61	15	is	be	AUX
ejpam-3996	61	16	said	say	VERB
ejpam-3996	61	17	to	to	PART
ejpam-3996	61	18	be	be	AUX
ejpam-3996	61	19	commutative	commutative	ADJ
ejpam-3996	61	20	if	if	SCONJ
ejpam-3996	61	21	a	a	DET
ejpam-3996	61	22	∗	∗	NOUN
ejpam-3996	61	23	(	(	PUNCT
ejpam-3996	61	24	0	0	NUM
ejpam-3996	61	25	∗	∗	NUM
ejpam-3996	61	26	b	b	NOUN
ejpam-3996	61	27	)	)	PUNCT
ejpam-3996	61	28	=	=	SYM
ejpam-3996	61	29	b	b	NOUN
ejpam-3996	61	30	∗	∗	NOUN
ejpam-3996	61	31	(	(	PUNCT
ejpam-3996	61	32	0	0	NUM
ejpam-3996	61	33	∗	∗	NOUN
ejpam-3996	61	34	a	a	NOUN
ejpam-3996	61	35	)	)	PUNCT
ejpam-3996	61	36	for	for	ADP
ejpam-3996	61	37	any	any	PRON
ejpam-3996	61	38	a	a	PRON
ejpam-3996	61	39	,	,	PUNCT
ejpam-3996	61	40	b	b	X
ejpam-3996	61	41	∈	∈	PROPN
ejpam-3996	61	42	x.	x.	NOUN
ejpam-3996	61	43	lemma	lemma	PROPN
ejpam-3996	61	44	2.6	2.6	NUM
ejpam-3996	61	45	.	.	PUNCT
ejpam-3996	62	1	[	[	X
ejpam-3996	62	2	15	15	NUM
ejpam-3996	62	3	]	]	PUNCT
ejpam-3996	62	4	let	let	VERB
ejpam-3996	62	5	x	x	PRON
ejpam-3996	62	6	be	be	AUX
ejpam-3996	62	7	a	a	DET
ejpam-3996	62	8	commutative	commutative	ADJ
ejpam-3996	62	9	b	b	NOUN
ejpam-3996	62	10	-	-	PUNCT
ejpam-3996	62	11	algebra	algebra	NOUN
ejpam-3996	62	12	.	.	PUNCT
ejpam-3996	63	1	then	then	ADV
ejpam-3996	63	2	for	for	ADP
ejpam-3996	63	3	any	any	DET
ejpam-3996	63	4	x	x	NOUN
ejpam-3996	63	5	,	,	PUNCT
ejpam-3996	63	6	y	y	PROPN
ejpam-3996	63	7	,	,	PUNCT
ejpam-3996	63	8	z	z	PROPN
ejpam-3996	63	9	∈	∈	PROPN
ejpam-3996	63	10	x	x	X
ejpam-3996	63	11	,	,	PUNCT
ejpam-3996	63	12	x∗(x∗y	x∗(x∗y	X
ejpam-3996	63	13	)	)	PUNCT
ejpam-3996	63	14	=	=	PUNCT
ejpam-3996	64	1	y.	y.	NOUN
ejpam-3996	64	2	definition	definition	NOUN
ejpam-3996	64	3	2.7	2.7	NUM
ejpam-3996	64	4	.	.	PUNCT
ejpam-3996	65	1	[	[	X
ejpam-3996	65	2	14	14	NUM
ejpam-3996	65	3	]	]	X
ejpam-3996	65	4	let	let	VERB
ejpam-3996	65	5	(	(	PUNCT
ejpam-3996	65	6	x	x	NOUN
ejpam-3996	65	7	;	;	PUNCT
ejpam-3996	65	8	∗	∗	NOUN
ejpam-3996	65	9	,	,	PUNCT
ejpam-3996	65	10	0	0	NUM
ejpam-3996	65	11	)	)	PUNCT
ejpam-3996	65	12	be	be	AUX
ejpam-3996	65	13	a	a	DET
ejpam-3996	65	14	b	b	NOUN
ejpam-3996	65	15	-algebra	-algebra	NOUN
ejpam-3996	65	16	.	.	PUNCT
ejpam-3996	66	1	a	a	DET
ejpam-3996	66	2	nonempty	nonempty	NOUN
ejpam-3996	66	3	subset	subset	VERB
ejpam-3996	66	4	n	n	PROPN
ejpam-3996	66	5	of	of	ADP
ejpam-3996	66	6	x	x	VERB
ejpam-3996	66	7	is	be	AUX
ejpam-3996	66	8	said	say	VERB
ejpam-3996	66	9	to	to	PART
ejpam-3996	66	10	be	be	AUX
ejpam-3996	66	11	a	a	DET
ejpam-3996	66	12	subalgebra	subalgebra	NOUN
ejpam-3996	66	13	of	of	ADP
ejpam-3996	66	14	x	x	PRON
ejpam-3996	66	15	if	if	SCONJ
ejpam-3996	66	16	a	a	DET
ejpam-3996	66	17	∗	∗	NOUN
ejpam-3996	66	18	b	b	NOUN
ejpam-3996	66	19	∈	∈	PROPN
ejpam-3996	66	20	n	n	X
ejpam-3996	66	21	for	for	ADP
ejpam-3996	66	22	all	all	DET
ejpam-3996	66	23	a	a	DET
ejpam-3996	66	24	,	,	PUNCT
ejpam-3996	66	25	b	b	X
ejpam-3996	66	26	∈	∈	PROPN
ejpam-3996	66	27	n	n	X
ejpam-3996	66	28	.	.	PUNCT
ejpam-3996	67	1	n	n	PRON
ejpam-3996	67	2	is	be	AUX
ejpam-3996	67	3	said	say	VERB
ejpam-3996	67	4	to	to	PART
ejpam-3996	67	5	be	be	AUX
ejpam-3996	67	6	normal	normal	ADJ
ejpam-3996	67	7	if	if	SCONJ
ejpam-3996	67	8	for	for	ADP
ejpam-3996	67	9	any	any	DET
ejpam-3996	67	10	x	x	PROPN
ejpam-3996	67	11	∗	∗	PROPN
ejpam-3996	67	12	y	y	PROPN
ejpam-3996	67	13	,	,	PUNCT
ejpam-3996	68	1	a	a	DET
ejpam-3996	68	2	∗	∗	NOUN
ejpam-3996	68	3	b	b	NOUN
ejpam-3996	68	4	∈	∈	PROPN
ejpam-3996	68	5	n	n	PRON
ejpam-3996	68	6	implies	imply	VERB
ejpam-3996	68	7	(	(	PUNCT
ejpam-3996	68	8	x	x	SYM
ejpam-3996	68	9	∗	∗	X
ejpam-3996	68	10	a	a	NOUN
ejpam-3996	68	11	)	)	PUNCT
ejpam-3996	68	12	∗	∗	NOUN
ejpam-3996	68	13	(	(	PUNCT
ejpam-3996	68	14	y	y	PROPN
ejpam-3996	68	15	∗	∗	X
ejpam-3996	68	16	b	b	NOUN
ejpam-3996	68	17	)	)	PUNCT
ejpam-3996	68	18	∈	∈	PROPN
ejpam-3996	68	19	n	n	X
ejpam-3996	68	20	.	.	PUNCT
ejpam-3996	69	1	lemma	lemma	PROPN
ejpam-3996	69	2	2.8	2.8	NUM
ejpam-3996	69	3	.	.	PUNCT
ejpam-3996	70	1	[	[	X
ejpam-3996	70	2	9	9	NUM
ejpam-3996	70	3	]	]	PUNCT
ejpam-3996	70	4	let	let	VERB
ejpam-3996	70	5	x	x	PRON
ejpam-3996	70	6	be	be	AUX
ejpam-3996	70	7	a	a	DET
ejpam-3996	70	8	b	b	NOUN
ejpam-3996	70	9	-	-	PUNCT
ejpam-3996	70	10	algebra	algebra	NOUN
ejpam-3996	70	11	.	.	PUNCT
ejpam-3996	71	1	if	if	SCONJ
ejpam-3996	71	2	{	{	PUNCT
ejpam-3996	71	3	nα	nα	NOUN
ejpam-3996	71	4	:	:	PUNCT
ejpam-3996	71	5	α	α	PROPN
ejpam-3996	71	6	∈	∈	PROPN
ejpam-3996	71	7	a	a	PRON
ejpam-3996	71	8	}	}	PUNCT
ejpam-3996	71	9	is	be	AUX
ejpam-3996	71	10	any	any	DET
ejpam-3996	71	11	nonempty	nonempty	ADJ
ejpam-3996	71	12	collection	collection	NOUN
ejpam-3996	71	13	of	of	ADP
ejpam-3996	71	14	subalgebras	subalgebras	PROPN
ejpam-3996	71	15	(	(	PUNCT
ejpam-3996	71	16	resp	resp	NOUN
ejpam-3996	71	17	.	.	PUNCT
ejpam-3996	72	1	,	,	PUNCT
ejpam-3996	72	2	normal	normal	ADJ
ejpam-3996	72	3	subalgebras	subalgebra	NOUN
ejpam-3996	72	4	)	)	PUNCT
ejpam-3996	72	5	of	of	ADP
ejpam-3996	72	6	x	x	PRON
ejpam-3996	72	7	,	,	PUNCT
ejpam-3996	72	8	then	then	ADV
ejpam-3996	72	9	⋂	⋂	PROPN
ejpam-3996	72	10	α∈a	α∈a	VERB
ejpam-3996	72	11	nα	nα	VERB
ejpam-3996	72	12	is	be	AUX
ejpam-3996	72	13	a	a	DET
ejpam-3996	72	14	subalgebra	subalgebra	NOUN
ejpam-3996	72	15	(	(	PUNCT
ejpam-3996	72	16	resp	resp	NOUN
ejpam-3996	72	17	.	.	PUNCT
ejpam-3996	73	1	,	,	PUNCT
ejpam-3996	73	2	normal	normal	ADJ
ejpam-3996	73	3	subalgebra	subalgebra	NOUN
ejpam-3996	73	4	)	)	PUNCT
ejpam-3996	73	5	of	of	ADP
ejpam-3996	73	6	x.	x.	NOUN
ejpam-3996	73	7	3	3	X
ejpam-3996	73	8	.	.	PUNCT
ejpam-3996	74	1	some	some	DET
ejpam-3996	74	2	properties	property	NOUN
ejpam-3996	74	3	of	of	ADP
ejpam-3996	74	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	74	5	b	b	X
ejpam-3996	74	6	-	-	PUNCT
ejpam-3996	74	7	algebras	algebras	PROPN
ejpam-3996	74	8	and	and	CCONJ
ejpam-3996	74	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	74	10	subalgebras	subalgebras	PROPN
ejpam-3996	74	11	definition	definition	NOUN
ejpam-3996	74	12	3.1	3.1	NUM
ejpam-3996	74	13	.	.	PUNCT
ejpam-3996	75	1	let	let	VERB
ejpam-3996	75	2	(	(	PUNCT
ejpam-3996	75	3	x	x	X
ejpam-3996	75	4	;	;	PUNCT
ejpam-3996	75	5	∗	∗	NOUN
ejpam-3996	75	6	,	,	PUNCT
ejpam-3996	75	7	0	0	NUM
ejpam-3996	75	8	)	)	PUNCT
ejpam-3996	75	9	be	be	AUX
ejpam-3996	75	10	any	any	DET
ejpam-3996	75	11	b	b	NOUN
ejpam-3996	75	12	-algebra	-algebra	NOUN
ejpam-3996	75	13	.	.	PUNCT
ejpam-3996	76	1	the	the	DET
ejpam-3996	76	2	set	set	NOUN
ejpam-3996	76	3	x(i	x(i	PROPN
ejpam-3996	76	4	)	)	PUNCT
ejpam-3996	76	5	=	=	PRON
ejpam-3996	76	6	{	{	PUNCT
ejpam-3996	76	7	(	(	PUNCT
ejpam-3996	76	8	x	x	NOUN
ejpam-3996	76	9	,	,	PUNCT
ejpam-3996	76	10	yi	yi	PROPN
ejpam-3996	76	11	)	)	PUNCT
ejpam-3996	76	12	:	:	PUNCT
ejpam-3996	76	13	x	x	X
ejpam-3996	76	14	,	,	PUNCT
ejpam-3996	76	15	y	y	PROPN
ejpam-3996	76	16	∈	∈	PROPN
ejpam-3996	76	17	x	x	VERB
ejpam-3996	76	18	}	}	PUNCT
ejpam-3996	76	19	is	be	AUX
ejpam-3996	76	20	the	the	DET
ejpam-3996	76	21	neutrosophic	neutrosophic	ADJ
ejpam-3996	76	22	set	set	NOUN
ejpam-3996	76	23	determined	determine	VERB
ejpam-3996	76	24	by	by	ADP
ejpam-3996	76	25	x	x	PUNCT
ejpam-3996	76	26	and	and	CCONJ
ejpam-3996	76	27	i.	i.	PROPN
ejpam-3996	76	28	moreover	moreover	ADV
ejpam-3996	76	29	,	,	PUNCT
ejpam-3996	76	30	(	(	PUNCT
ejpam-3996	76	31	a	a	DET
ejpam-3996	76	32	,	,	PUNCT
ejpam-3996	76	33	bi	bi	NOUN
ejpam-3996	76	34	)	)	PUNCT
ejpam-3996	76	35	=	=	SYM
ejpam-3996	76	36	(	(	PUNCT
ejpam-3996	76	37	c	c	X
ejpam-3996	76	38	,	,	PUNCT
ejpam-3996	76	39	di	di	NOUN
ejpam-3996	76	40	)	)	PUNCT
ejpam-3996	76	41	in	in	ADP
ejpam-3996	76	42	x(i	x(i	PROPN
ejpam-3996	76	43	)	)	PUNCT
ejpam-3996	77	1	if	if	SCONJ
ejpam-3996	77	2	and	and	CCONJ
ejpam-3996	77	3	only	only	ADV
ejpam-3996	77	4	if	if	SCONJ
ejpam-3996	77	5	a	a	DET
ejpam-3996	77	6	=	=	SYM
ejpam-3996	77	7	c	c	NOUN
ejpam-3996	77	8	and	and	CCONJ
ejpam-3996	77	9	b	b	X
ejpam-3996	77	10	=	=	SYM
ejpam-3996	77	11	d.	d.	PROPN
ejpam-3996	77	12	definition	definition	NOUN
ejpam-3996	77	13	3.2	3.2	NUM
ejpam-3996	77	14	.	.	PUNCT
ejpam-3996	78	1	let	let	VERB
ejpam-3996	78	2	(	(	PUNCT
ejpam-3996	78	3	x	x	X
ejpam-3996	78	4	;	;	PUNCT
ejpam-3996	78	5	∗	∗	NOUN
ejpam-3996	78	6	,	,	PUNCT
ejpam-3996	78	7	0	0	NUM
ejpam-3996	78	8	)	)	PUNCT
ejpam-3996	78	9	be	be	AUX
ejpam-3996	78	10	any	any	DET
ejpam-3996	78	11	b	b	NOUN
ejpam-3996	78	12	-algebra	-algebra	NOUN
ejpam-3996	78	13	.	.	PUNCT
ejpam-3996	79	1	for	for	ADP
ejpam-3996	79	2	any	any	DET
ejpam-3996	79	3	x	x	NOUN
ejpam-3996	79	4	,	,	PUNCT
ejpam-3996	79	5	y	y	PROPN
ejpam-3996	79	6	∈	∈	PROPN
ejpam-3996	79	7	x	x	X
ejpam-3996	79	8	,	,	PUNCT
ejpam-3996	79	9	we	we	PRON
ejpam-3996	79	10	denote	denote	VERB
ejpam-3996	79	11	x	x	PUNCT
ejpam-3996	79	12	∧	∧	NOUN
ejpam-3996	79	13	y	y	NOUN
ejpam-3996	79	14	=	=	PUNCT
ejpam-3996	79	15	x	x	SYM
ejpam-3996	79	16	∗	∗	NOUN
ejpam-3996	79	17	(	(	PUNCT
ejpam-3996	79	18	x	x	X
ejpam-3996	79	19	∗	∗	PROPN
ejpam-3996	79	20	y	y	PROPN
ejpam-3996	79	21	)	)	PUNCT
ejpam-3996	79	22	.	.	PUNCT
ejpam-3996	80	1	lemma	lemma	PROPN
ejpam-3996	80	2	3.3	3.3	NUM
ejpam-3996	80	3	.	.	PUNCT
ejpam-3996	81	1	the	the	DET
ejpam-3996	81	2	mapping	mapping	NOUN
ejpam-3996	81	3	λ	λ	PROPN
ejpam-3996	81	4	:	:	PUNCT
ejpam-3996	81	5	x(i	x(i	PROPN
ejpam-3996	81	6	)	)	PUNCT
ejpam-3996	81	7	×	×	PROPN
ejpam-3996	81	8	x(i	x(i	PROPN
ejpam-3996	81	9	)	)	PUNCT
ejpam-3996	81	10	→	→	SYM
ejpam-3996	81	11	x(i	x(i	PROPN
ejpam-3996	81	12	)	)	PUNCT
ejpam-3996	81	13	defined	define	VERB
ejpam-3996	81	14	by	by	ADP
ejpam-3996	81	15	λ((a	λ((a	PROPN
ejpam-3996	81	16	,	,	PUNCT
ejpam-3996	81	17	bi	bi	NOUN
ejpam-3996	81	18	)	)	PUNCT
ejpam-3996	81	19	,	,	PUNCT
ejpam-3996	81	20	(	(	PUNCT
ejpam-3996	81	21	c	c	X
ejpam-3996	81	22	,	,	PUNCT
ejpam-3996	81	23	di	di	NOUN
ejpam-3996	81	24	)	)	PUNCT
ejpam-3996	81	25	)	)	PUNCT
ejpam-3996	82	1	=	=	PRON
ejpam-3996	82	2	(	(	PUNCT
ejpam-3996	82	3	a	a	PRON
ejpam-3996	82	4	,	,	PUNCT
ejpam-3996	82	5	bi	bi	NOUN
ejpam-3996	82	6	)	)	PUNCT
ejpam-3996	82	7	·	·	PUNCT
ejpam-3996	83	1	(	(	PUNCT
ejpam-3996	83	2	c	c	X
ejpam-3996	83	3	,	,	PUNCT
ejpam-3996	83	4	di	di	NOUN
ejpam-3996	83	5	)	)	PUNCT
ejpam-3996	83	6	=	=	SYM
ejpam-3996	83	7	(	(	PUNCT
ejpam-3996	83	8	a∗c	a∗c	PUNCT
ejpam-3996	83	9	,	,	PUNCT
ejpam-3996	83	10	(	(	PUNCT
ejpam-3996	83	11	(	(	PUNCT
ejpam-3996	83	12	a∗d∧b∗c)∧b∗d)i	a∗d∧b∗c)∧b∗d)i	PROPN
ejpam-3996	83	13	)	)	PUNCT
ejpam-3996	83	14	for	for	ADP
ejpam-3996	83	15	any	any	DET
ejpam-3996	83	16	(	(	PUNCT
ejpam-3996	83	17	a	a	PRON
ejpam-3996	83	18	,	,	PUNCT
ejpam-3996	83	19	bi	bi	NOUN
ejpam-3996	83	20	)	)	PUNCT
ejpam-3996	83	21	,	,	PUNCT
ejpam-3996	83	22	(	(	PUNCT
ejpam-3996	83	23	c	c	X
ejpam-3996	83	24	,	,	PUNCT
ejpam-3996	83	25	di	di	NOUN
ejpam-3996	83	26	)	)	PUNCT
ejpam-3996	83	27	∈	∈	PROPN
ejpam-3996	83	28	x(i	x(i	PROPN
ejpam-3996	83	29	)	)	PUNCT
ejpam-3996	83	30	is	be	AUX
ejpam-3996	83	31	well	well	ADV
ejpam-3996	83	32	-	-	PUNCT
ejpam-3996	83	33	defined	define	VERB
ejpam-3996	83	34	.	.	PUNCT
ejpam-3996	84	1	proof	proof	NOUN
ejpam-3996	84	2	:	:	PUNCT
ejpam-3996	84	3	let	let	VERB
ejpam-3996	84	4	(	(	PUNCT
ejpam-3996	84	5	a	a	DET
ejpam-3996	84	6	,	,	PUNCT
ejpam-3996	84	7	bi	bi	NOUN
ejpam-3996	84	8	)	)	PUNCT
ejpam-3996	84	9	,	,	PUNCT
ejpam-3996	84	10	(	(	PUNCT
ejpam-3996	84	11	c	c	X
ejpam-3996	84	12	,	,	PUNCT
ejpam-3996	84	13	di	di	NOUN
ejpam-3996	84	14	)	)	PUNCT
ejpam-3996	84	15	,	,	PUNCT
ejpam-3996	84	16	(	(	PUNCT
ejpam-3996	84	17	x	x	NOUN
ejpam-3996	84	18	,	,	PUNCT
ejpam-3996	84	19	yi	yi	PROPN
ejpam-3996	84	20	)	)	PUNCT
ejpam-3996	84	21	,	,	PUNCT
ejpam-3996	84	22	(	(	PUNCT
ejpam-3996	84	23	u	u	NOUN
ejpam-3996	84	24	,	,	PUNCT
ejpam-3996	84	25	vi	vi	NOUN
ejpam-3996	84	26	)	)	PUNCT
ejpam-3996	84	27	∈	∈	PROPN
ejpam-3996	84	28	x(i	x(i	PROPN
ejpam-3996	84	29	)	)	PUNCT
ejpam-3996	84	30	such	such	ADJ
ejpam-3996	84	31	that	that	SCONJ
ejpam-3996	84	32	(	(	PUNCT
ejpam-3996	84	33	a	a	DET
ejpam-3996	84	34	,	,	PUNCT
ejpam-3996	84	35	bi	bi	NOUN
ejpam-3996	84	36	)	)	PUNCT
ejpam-3996	84	37	=	=	SYM
ejpam-3996	84	38	(	(	PUNCT
ejpam-3996	84	39	x	x	NOUN
ejpam-3996	84	40	,	,	PUNCT
ejpam-3996	84	41	yi	yi	PROPN
ejpam-3996	84	42	)	)	PUNCT
ejpam-3996	84	43	and	and	CCONJ
ejpam-3996	84	44	(	(	PUNCT
ejpam-3996	84	45	c	c	NOUN
ejpam-3996	84	46	,	,	PUNCT
ejpam-3996	84	47	di	di	NOUN
ejpam-3996	84	48	)	)	PUNCT
ejpam-3996	84	49	=	=	SYM
ejpam-3996	84	50	(	(	PUNCT
ejpam-3996	84	51	u	u	NOUN
ejpam-3996	84	52	,	,	PUNCT
ejpam-3996	84	53	vi	vi	PROPN
ejpam-3996	84	54	)	)	PUNCT
ejpam-3996	84	55	.	.	PUNCT
ejpam-3996	85	1	then	then	ADV
ejpam-3996	85	2	λ	λ	X
ejpam-3996	85	3	(	(	PUNCT
ejpam-3996	85	4	(	(	PUNCT
ejpam-3996	85	5	a	a	DET
ejpam-3996	85	6	,	,	PUNCT
ejpam-3996	85	7	bi	bi	NOUN
ejpam-3996	85	8	)	)	PUNCT
ejpam-3996	85	9	,	,	PUNCT
ejpam-3996	85	10	(	(	PUNCT
ejpam-3996	85	11	c	c	X
ejpam-3996	85	12	,	,	PUNCT
ejpam-3996	85	13	di	di	NOUN
ejpam-3996	85	14	)	)	PUNCT
ejpam-3996	85	15	)	)	PUNCT
ejpam-3996	86	1	=	=	PUNCT
ejpam-3996	86	2	(	(	PUNCT
ejpam-3996	86	3	a	a	PRON
ejpam-3996	86	4	,	,	PUNCT
ejpam-3996	86	5	bi	bi	NOUN
ejpam-3996	86	6	)	)	PUNCT
ejpam-3996	86	7	·	·	PUNCT
ejpam-3996	87	1	(	(	PUNCT
ejpam-3996	87	2	c	c	X
ejpam-3996	87	3	,	,	PUNCT
ejpam-3996	87	4	di	di	NOUN
ejpam-3996	87	5	)	)	PUNCT
ejpam-3996	87	6	=	=	SYM
ejpam-3996	87	7	(	(	PUNCT
ejpam-3996	87	8	a	a	DET
ejpam-3996	87	9	∗	∗	NOUN
ejpam-3996	87	10	c	c	NOUN
ejpam-3996	87	11	,	,	PUNCT
ejpam-3996	87	12	(	(	PUNCT
ejpam-3996	87	13	(	(	PUNCT
ejpam-3996	87	14	a	a	DET
ejpam-3996	87	15	∗	∗	X
ejpam-3996	87	16	d	d	X
ejpam-3996	87	17	∧	∧	PROPN
ejpam-3996	87	18	b	b	PROPN
ejpam-3996	87	19	∗	∗	X
ejpam-3996	87	20	c	c	NOUN
ejpam-3996	87	21	)	)	PUNCT
ejpam-3996	87	22	∧	∧	PROPN
ejpam-3996	87	23	b	b	PROPN
ejpam-3996	87	24	∗	∗	X
ejpam-3996	87	25	d)i	d)i	NOUN
ejpam-3996	87	26	)	)	PUNCT
ejpam-3996	87	27	=(	=(	NOUN
ejpam-3996	88	1	x	x	X
ejpam-3996	88	2	∗	∗	NOUN
ejpam-3996	88	3	u	u	NOUN
ejpam-3996	88	4	,	,	PUNCT
ejpam-3996	88	5	(	(	PUNCT
ejpam-3996	88	6	(	(	PUNCT
ejpam-3996	88	7	x	x	SYM
ejpam-3996	88	8	∗	∗	X
ejpam-3996	88	9	v	v	NUM
ejpam-3996	88	10	∧	∧	PROPN
ejpam-3996	88	11	y	y	PROPN
ejpam-3996	88	12	∗	∗	X
ejpam-3996	88	13	u	u	NOUN
ejpam-3996	88	14	)	)	PUNCT
ejpam-3996	88	15	∧	∧	PROPN
ejpam-3996	88	16	y	y	PROPN
ejpam-3996	88	17	∗	∗	NOUN
ejpam-3996	88	18	v)i	v)i	PUNCT
ejpam-3996	88	19	)	)	PUNCT
ejpam-3996	88	20	=	=	SYM
ejpam-3996	88	21	(	(	PUNCT
ejpam-3996	88	22	x	x	NOUN
ejpam-3996	88	23	,	,	PUNCT
ejpam-3996	88	24	yi	yi	PROPN
ejpam-3996	88	25	)	)	PUNCT
ejpam-3996	88	26	·	·	PUNCT
ejpam-3996	89	1	(	(	PUNCT
ejpam-3996	89	2	u	u	NOUN
ejpam-3996	89	3	,	,	PUNCT
ejpam-3996	89	4	vi	vi	NOUN
ejpam-3996	89	5	)	)	PUNCT
ejpam-3996	89	6	=	=	SYM
ejpam-3996	89	7	λ	λ	INTJ
ejpam-3996	89	8	(	(	PUNCT
ejpam-3996	89	9	(	(	PUNCT
ejpam-3996	89	10	x	x	NOUN
ejpam-3996	89	11	,	,	PUNCT
ejpam-3996	89	12	yi	yi	PROPN
ejpam-3996	89	13	)	)	PUNCT
ejpam-3996	89	14	,	,	PUNCT
ejpam-3996	89	15	(	(	PUNCT
ejpam-3996	89	16	u	u	NOUN
ejpam-3996	89	17	,	,	PUNCT
ejpam-3996	89	18	vi	vi	PROPN
ejpam-3996	89	19	)	)	PUNCT
ejpam-3996	89	20	)	)	PUNCT
ejpam-3996	89	21	.	.	PUNCT
ejpam-3996	90	1	hence	hence	ADV
ejpam-3996	90	2	,	,	PUNCT
ejpam-3996	90	3	the	the	DET
ejpam-3996	90	4	λ	λ	PROPN
ejpam-3996	90	5	is	be	AUX
ejpam-3996	90	6	well	well	ADV
ejpam-3996	90	7	-	-	PUNCT
ejpam-3996	90	8	defined	define	VERB
ejpam-3996	90	9	.	.	PUNCT
ejpam-3996	91	1	�	�	PROPN
ejpam-3996	91	2	definition	definition	NOUN
ejpam-3996	91	3	3.4	3.4	NUM
ejpam-3996	91	4	.	.	PUNCT
ejpam-3996	92	1	the	the	DET
ejpam-3996	92	2	triple	triple	ADJ
ejpam-3996	92	3	(	(	PUNCT
ejpam-3996	92	4	x(i	x(i	PROPN
ejpam-3996	92	5	)	)	PUNCT
ejpam-3996	92	6	;	;	PUNCT
ejpam-3996	92	7	·	·	PUNCT
ejpam-3996	92	8	,	,	PUNCT
ejpam-3996	92	9	(	(	PUNCT
ejpam-3996	92	10	0	0	NUM
ejpam-3996	92	11	,	,	PUNCT
ejpam-3996	92	12	0i	0i	NOUN
ejpam-3996	92	13	)	)	PUNCT
ejpam-3996	92	14	)	)	PUNCT
ejpam-3996	92	15	is	be	AUX
ejpam-3996	92	16	called	call	VERB
ejpam-3996	92	17	a	a	DET
ejpam-3996	92	18	neutrosophic	neutrosophic	ADJ
ejpam-3996	92	19	b	b	X
ejpam-3996	92	20	-	-	PUNCT
ejpam-3996	92	21	algebra	algebra	NOUN
ejpam-3996	92	22	determined	determine	VERB
ejpam-3996	92	23	by	by	ADP
ejpam-3996	92	24	x	x	PUNCT
ejpam-3996	92	25	and	and	CCONJ
ejpam-3996	92	26	i	i	PRON
ejpam-3996	92	27	with	with	ADP
ejpam-3996	92	28	the	the	DET
ejpam-3996	92	29	binary	binary	PROPN
ejpam-3996	92	30	operation	operation	NOUN
ejpam-3996	92	31	·	·	PUNCT
ejpam-3996	92	32	defined	define	VERB
ejpam-3996	92	33	in	in	ADP
ejpam-3996	92	34	lemma	lemma	PROPN
ejpam-3996	92	35	3.3	3.3	NUM
ejpam-3996	92	36	and	and	CCONJ
ejpam-3996	92	37	(	(	PUNCT
ejpam-3996	92	38	0	0	NUM
ejpam-3996	92	39	,	,	PUNCT
ejpam-3996	92	40	0i	0i	NOUN
ejpam-3996	92	41	)	)	PUNCT
ejpam-3996	92	42	as	as	ADP
ejpam-3996	92	43	its	its	PRON
ejpam-3996	92	44	constant	constant	ADJ
ejpam-3996	92	45	element	element	NOUN
ejpam-3996	92	46	.	.	PUNCT
ejpam-3996	93	1	remark	remark	NOUN
ejpam-3996	93	2	3.5	3.5	NUM
ejpam-3996	93	3	.	.	PUNCT
ejpam-3996	94	1	every	every	DET
ejpam-3996	94	2	nonzero	nonzero	PROPN
ejpam-3996	94	3	neutrosophic	neutrosophic	PROPN
ejpam-3996	94	4	b	b	X
ejpam-3996	94	5	-	-	PUNCT
ejpam-3996	94	6	algebra	algebra	NOUN
ejpam-3996	94	7	x(i	x(i	PROPN
ejpam-3996	94	8	)	)	PUNCT
ejpam-3996	94	9	always	always	ADV
ejpam-3996	94	10	contains	contain	VERB
ejpam-3996	94	11	the	the	DET
ejpam-3996	94	12	b	b	NOUN
ejpam-3996	94	13	-	-	PUNCT
ejpam-3996	94	14	algebra	algebra	NOUN
ejpam-3996	94	15	x	x	NOUN
ejpam-3996	94	16	′	′	NUM
ejpam-3996	94	17	=	=	SYM
ejpam-3996	94	18	{	{	PUNCT
ejpam-3996	94	19	(	(	PUNCT
ejpam-3996	94	20	x	x	X
ejpam-3996	94	21	,	,	PUNCT
ejpam-3996	94	22	0i	0i	NUM
ejpam-3996	94	23	)	)	PUNCT
ejpam-3996	94	24	:	:	PUNCT
ejpam-3996	95	1	x	x	X
ejpam-3996	95	2	∈	∈	NOUN
ejpam-3996	95	3	x	x	X
ejpam-3996	95	4	}	}	PUNCT
ejpam-3996	95	5	as	as	ADP
ejpam-3996	95	6	a	a	DET
ejpam-3996	95	7	proper	proper	ADJ
ejpam-3996	95	8	subset	subset	NOUN
ejpam-3996	95	9	.	.	PUNCT
ejpam-3996	96	1	d.o	d.o	PROPN
ejpam-3996	96	2	.	.	PROPN
ejpam-3996	96	3	jacobe	jacobe	PROPN
ejpam-3996	96	4	,	,	PUNCT
ejpam-3996	96	5	j.p	j.p	PROPN
ejpam-3996	96	6	.	.	PROPN
ejpam-3996	96	7	vilela	vilela	PROPN
ejpam-3996	96	8	/	/	SYM
ejpam-3996	96	9	eur	eur	PROPN
ejpam-3996	96	10	.	.	PUNCT
ejpam-3996	97	1	j.	j.	PROPN
ejpam-3996	97	2	pure	pure	PROPN
ejpam-3996	97	3	appl	appl	PROPN
ejpam-3996	97	4	.	.	PROPN
ejpam-3996	97	5	math	math	PROPN
ejpam-3996	97	6	,	,	PUNCT
ejpam-3996	97	7	14	14	NUM
ejpam-3996	97	8	(	(	PUNCT
ejpam-3996	97	9	3	3	NUM
ejpam-3996	97	10	)	)	PUNCT
ejpam-3996	97	11	(	(	PUNCT
ejpam-3996	97	12	2021	2021	NUM
ejpam-3996	97	13	)	)	PUNCT
ejpam-3996	97	14	,	,	PUNCT
ejpam-3996	97	15	895	895	NUM
ejpam-3996	97	16	-	-	SYM
ejpam-3996	97	17	904	904	NUM
ejpam-3996	97	18	898	898	NUM
ejpam-3996	97	19	let	let	VERB
ejpam-3996	97	20	x(i	x(i	PROPN
ejpam-3996	97	21	)	)	PUNCT
ejpam-3996	97	22	stand	stand	VERB
ejpam-3996	97	23	for	for	ADP
ejpam-3996	97	24	a	a	DET
ejpam-3996	97	25	neutrosophic	neutrosophic	ADJ
ejpam-3996	97	26	b	b	X
ejpam-3996	97	27	-	-	PUNCT
ejpam-3996	97	28	algebra	algebra	NOUN
ejpam-3996	97	29	(	(	PUNCT
ejpam-3996	97	30	x(i	x(i	PROPN
ejpam-3996	97	31	)	)	PUNCT
ejpam-3996	97	32	;	;	PUNCT
ejpam-3996	97	33	·	·	PUNCT
ejpam-3996	97	34	,	,	PUNCT
ejpam-3996	97	35	(	(	PUNCT
ejpam-3996	97	36	0	0	NUM
ejpam-3996	97	37	,	,	PUNCT
ejpam-3996	97	38	0i	0i	NOUN
ejpam-3996	97	39	)	)	PUNCT
ejpam-3996	97	40	)	)	PUNCT
ejpam-3996	97	41	,	,	PUNCT
ejpam-3996	97	42	unless	unless	SCONJ
ejpam-3996	97	43	otherwise	otherwise	ADV
ejpam-3996	97	44	stated	state	VERB
ejpam-3996	97	45	.	.	PUNCT
ejpam-3996	98	1	example	example	NOUN
ejpam-3996	98	2	3.6	3.6	NUM
ejpam-3996	98	3	.	.	PUNCT
ejpam-3996	99	1	consider	consider	VERB
ejpam-3996	99	2	the	the	DET
ejpam-3996	99	3	commutative	commutative	ADJ
ejpam-3996	99	4	b	b	NOUN
ejpam-3996	99	5	-	-	PUNCT
ejpam-3996	99	6	algebra	algebra	NOUN
ejpam-3996	99	7	x	x	X
ejpam-3996	99	8	=	=	SYM
ejpam-3996	99	9	{	{	PUNCT
ejpam-3996	99	10	0	0	NUM
ejpam-3996	99	11	,	,	PUNCT
ejpam-3996	99	12	1	1	NUM
ejpam-3996	99	13	,	,	PUNCT
ejpam-3996	99	14	2	2	NUM
ejpam-3996	99	15	}	}	PUNCT
ejpam-3996	99	16	in	in	ADP
ejpam-3996	99	17	example	example	NOUN
ejpam-3996	99	18	2.3(i	2.3(i	NUM
ejpam-3996	99	19	)	)	PUNCT
ejpam-3996	99	20	.	.	PUNCT
ejpam-3996	100	1	then	then	ADV
ejpam-3996	100	2	the	the	DET
ejpam-3996	100	3	neutrosophicb	neutrosophicb	NOUN
ejpam-3996	100	4	-	-	PUNCT
ejpam-3996	100	5	algebra	algebra	NOUN
ejpam-3996	100	6	determined	determine	VERB
ejpam-3996	100	7	byx	byx	NOUN
ejpam-3996	100	8	and	and	CCONJ
ejpam-3996	100	9	i	i	PRON
ejpam-3996	100	10	is	be	AUX
ejpam-3996	100	11	given	give	VERB
ejpam-3996	100	12	byx(i	byx(i	PROPN
ejpam-3996	100	13	)	)	PUNCT
ejpam-3996	100	14	=	=	SYM
ejpam-3996	100	15	{	{	PUNCT
ejpam-3996	100	16	(	(	PUNCT
ejpam-3996	100	17	0	0	NUM
ejpam-3996	100	18	,	,	PUNCT
ejpam-3996	100	19	0i	0i	NOUN
ejpam-3996	100	20	)	)	PUNCT
ejpam-3996	100	21	,	,	PUNCT
ejpam-3996	100	22	(	(	PUNCT
ejpam-3996	100	23	0	0	NUM
ejpam-3996	100	24	,	,	PUNCT
ejpam-3996	100	25	i	i	NOUN
ejpam-3996	100	26	)	)	PUNCT
ejpam-3996	100	27	,	,	PUNCT
ejpam-3996	100	28	(	(	PUNCT
ejpam-3996	100	29	0	0	NUM
ejpam-3996	100	30	,	,	PUNCT
ejpam-3996	100	31	2i	2i	NUM
ejpam-3996	100	32	)	)	PUNCT
ejpam-3996	100	33	,	,	PUNCT
ejpam-3996	100	34	(	(	PUNCT
ejpam-3996	100	35	1	1	NUM
ejpam-3996	100	36	,	,	PUNCT
ejpam-3996	100	37	0i	0i	NOUN
ejpam-3996	100	38	)	)	PUNCT
ejpam-3996	100	39	,	,	PUNCT
ejpam-3996	100	40	(	(	PUNCT
ejpam-3996	100	41	1	1	X
ejpam-3996	100	42	,	,	PUNCT
ejpam-3996	100	43	i	i	NOUN
ejpam-3996	100	44	)	)	PUNCT
ejpam-3996	100	45	,	,	PUNCT
ejpam-3996	100	46	(	(	PUNCT
ejpam-3996	100	47	1	1	NUM
ejpam-3996	100	48	,	,	PUNCT
ejpam-3996	100	49	2i	2i	NUM
ejpam-3996	100	50	)	)	PUNCT
ejpam-3996	100	51	,	,	PUNCT
ejpam-3996	100	52	(	(	PUNCT
ejpam-3996	100	53	2	2	NUM
ejpam-3996	100	54	,	,	PUNCT
ejpam-3996	100	55	0i	0i	NOUN
ejpam-3996	100	56	)	)	PUNCT
ejpam-3996	100	57	,	,	PUNCT
ejpam-3996	100	58	(	(	PUNCT
ejpam-3996	100	59	2	2	NUM
ejpam-3996	100	60	,	,	PUNCT
ejpam-3996	100	61	i	i	NOUN
ejpam-3996	100	62	)	)	PUNCT
ejpam-3996	100	63	,	,	PUNCT
ejpam-3996	100	64	(	(	PUNCT
ejpam-3996	100	65	2	2	NUM
ejpam-3996	100	66	,	,	PUNCT
ejpam-3996	100	67	2i	2i	NUM
ejpam-3996	100	68	)	)	PUNCT
ejpam-3996	100	69	}	}	PUNCT
ejpam-3996	100	70	.	.	PUNCT
ejpam-3996	101	1	lemma	lemma	PROPN
ejpam-3996	101	2	3.7	3.7	NUM
ejpam-3996	101	3	.	.	PUNCT
ejpam-3996	102	1	let	let	VERB
ejpam-3996	102	2	x	x	PRON
ejpam-3996	102	3	be	be	AUX
ejpam-3996	102	4	a	a	DET
ejpam-3996	102	5	b	b	NOUN
ejpam-3996	102	6	-	-	PUNCT
ejpam-3996	102	7	algebra	algebra	NOUN
ejpam-3996	102	8	.	.	PUNCT
ejpam-3996	103	1	then	then	ADV
ejpam-3996	103	2	for	for	ADP
ejpam-3996	103	3	any	any	DET
ejpam-3996	103	4	x	x	NOUN
ejpam-3996	103	5	,	,	PUNCT
ejpam-3996	103	6	y	y	PROPN
ejpam-3996	103	7	∈	∈	PROPN
ejpam-3996	103	8	x	x	X
ejpam-3996	103	9	,	,	PUNCT
ejpam-3996	103	10	(	(	PUNCT
ejpam-3996	103	11	i	i	NOUN
ejpam-3996	103	12	)	)	PUNCT
ejpam-3996	103	13	x	x	PUNCT
ejpam-3996	104	1	∧	∧	NOUN
ejpam-3996	104	2	x	x	X
ejpam-3996	104	3	=	=	SYM
ejpam-3996	104	4	x	x	X
ejpam-3996	104	5	,	,	PUNCT
ejpam-3996	104	6	(	(	PUNCT
ejpam-3996	104	7	iv	iv	X
ejpam-3996	104	8	)	)	PUNCT
ejpam-3996	104	9	x	x	PROPN
ejpam-3996	104	10	∗	∗	NOUN
ejpam-3996	104	11	y	y	PROPN
ejpam-3996	104	12	∧	∧	PROPN
ejpam-3996	104	13	y	y	PROPN
ejpam-3996	104	14	∗	∗	NOUN
ejpam-3996	104	15	x	x	PUNCT
ejpam-3996	105	1	=	=	SYM
ejpam-3996	105	2	y	y	PROPN
ejpam-3996	105	3	∗	∗	NOUN
ejpam-3996	105	4	x	x	PROPN
ejpam-3996	105	5	,	,	PUNCT
ejpam-3996	105	6	(	(	PUNCT
ejpam-3996	105	7	ii	ii	NOUN
ejpam-3996	105	8	)	)	PUNCT
ejpam-3996	105	9	x	x	SYM
ejpam-3996	105	10	∧	∧	NOUN
ejpam-3996	105	11	0	0	NUM
ejpam-3996	105	12	=	=	SYM
ejpam-3996	105	13	0	0	NUM
ejpam-3996	105	14	,	,	PUNCT
ejpam-3996	105	15	(	(	PUNCT
ejpam-3996	105	16	v	v	NOUN
ejpam-3996	105	17	)	)	PUNCT
ejpam-3996	105	18	x	x	X
ejpam-3996	106	1	∧	∧	NOUN
ejpam-3996	106	2	y	y	NOUN
ejpam-3996	106	3	=	=	NOUN
ejpam-3996	106	4	0	0	PUNCT
ejpam-3996	107	1	if	if	SCONJ
ejpam-3996	107	2	and	and	CCONJ
ejpam-3996	107	3	only	only	ADV
ejpam-3996	107	4	if	if	SCONJ
ejpam-3996	107	5	y	y	PROPN
ejpam-3996	107	6	=	=	NOUN
ejpam-3996	107	7	0	0	PROPN
ejpam-3996	107	8	.	.	PUNCT
ejpam-3996	107	9	(	(	PUNCT
ejpam-3996	107	10	iii	iii	NOUN
ejpam-3996	107	11	)	)	PUNCT
ejpam-3996	107	12	0	0	NUM
ejpam-3996	108	1	∧	∧	NOUN
ejpam-3996	108	2	x	x	X
ejpam-3996	108	3	=	=	SYM
ejpam-3996	108	4	x	x	NOUN
ejpam-3996	108	5	,	,	PUNCT
ejpam-3996	108	6	proof	proof	NOUN
ejpam-3996	108	7	:	:	PUNCT
ejpam-3996	108	8	(	(	PUNCT
ejpam-3996	108	9	i	i	NOUN
ejpam-3996	108	10	)	)	PUNCT
ejpam-3996	108	11	by	by	ADP
ejpam-3996	108	12	(	(	PUNCT
ejpam-3996	108	13	b1	b1	NOUN
ejpam-3996	108	14	)	)	PUNCT
ejpam-3996	108	15	and	and	CCONJ
ejpam-3996	108	16	(	(	PUNCT
ejpam-3996	108	17	b2	b2	NOUN
ejpam-3996	108	18	)	)	PUNCT
ejpam-3996	108	19	,	,	PUNCT
ejpam-3996	108	20	x	x	X
ejpam-3996	108	21	∧	∧	NOUN
ejpam-3996	108	22	x	x	X
ejpam-3996	108	23	=	=	PUNCT
ejpam-3996	108	24	x	x	SYM
ejpam-3996	108	25	∗	∗	NOUN
ejpam-3996	108	26	(	(	PUNCT
ejpam-3996	108	27	x	x	X
ejpam-3996	108	28	∗	∗	NOUN
ejpam-3996	108	29	x	x	NOUN
ejpam-3996	108	30	)	)	PUNCT
ejpam-3996	108	31	=	=	PUNCT
ejpam-3996	109	1	x	x	X
ejpam-3996	109	2	∗	∗	NOUN
ejpam-3996	109	3	0	0	NUM
ejpam-3996	110	1	=	=	SYM
ejpam-3996	110	2	x	x	X
ejpam-3996	110	3	;	;	PUNCT
ejpam-3996	110	4	(	(	PUNCT
ejpam-3996	110	5	ii	ii	NOUN
ejpam-3996	110	6	)	)	PUNCT
ejpam-3996	110	7	by	by	ADP
ejpam-3996	110	8	(	(	PUNCT
ejpam-3996	110	9	b2	b2	NOUN
ejpam-3996	110	10	)	)	PUNCT
ejpam-3996	110	11	and	and	CCONJ
ejpam-3996	110	12	(	(	PUNCT
ejpam-3996	110	13	b1	b1	NOUN
ejpam-3996	110	14	)	)	PUNCT
ejpam-3996	110	15	,	,	PUNCT
ejpam-3996	110	16	x∧	x∧	PROPN
ejpam-3996	110	17	0	0	NUM
ejpam-3996	111	1	=	=	SYM
ejpam-3996	111	2	x	x	X
ejpam-3996	111	3	∗	∗	NOUN
ejpam-3996	111	4	(	(	PUNCT
ejpam-3996	111	5	x	x	X
ejpam-3996	111	6	∗	∗	NOUN
ejpam-3996	111	7	0	0	NUM
ejpam-3996	111	8	)	)	PUNCT
ejpam-3996	111	9	=	=	PUNCT
ejpam-3996	112	1	x	x	X
ejpam-3996	112	2	∗x	∗x	PUNCT
ejpam-3996	112	3	=	=	SYM
ejpam-3996	112	4	0	0	NUM
ejpam-3996	112	5	;	;	PUNCT
ejpam-3996	112	6	(	(	PUNCT
ejpam-3996	112	7	iii	iii	NOUN
ejpam-3996	112	8	)	)	PUNCT
ejpam-3996	112	9	by	by	ADP
ejpam-3996	112	10	(	(	PUNCT
ejpam-3996	112	11	p1	p1	PROPN
ejpam-3996	112	12	)	)	PUNCT
ejpam-3996	112	13	,	,	PUNCT
ejpam-3996	112	14	0∧x	0∧x	PROPN
ejpam-3996	112	15	=	=	SYM
ejpam-3996	112	16	0	0	NUM
ejpam-3996	112	17	∗	∗	NOUN
ejpam-3996	112	18	(	(	PUNCT
ejpam-3996	112	19	0	0	NUM
ejpam-3996	112	20	∗x	∗x	NOUN
ejpam-3996	112	21	)	)	PUNCT
ejpam-3996	112	22	=	=	SYM
ejpam-3996	112	23	x	x	X
ejpam-3996	112	24	;	;	PUNCT
ejpam-3996	112	25	(	(	PUNCT
ejpam-3996	112	26	iv	iv	X
ejpam-3996	112	27	)	)	PUNCT
ejpam-3996	112	28	by	by	ADP
ejpam-3996	112	29	lemma	lemma	PROPN
ejpam-3996	112	30	2.4(ii	2.4(ii	NUM
ejpam-3996	112	31	)	)	PUNCT
ejpam-3996	112	32	,	,	PUNCT
ejpam-3996	112	33	(	(	PUNCT
ejpam-3996	112	34	b1	b1	NOUN
ejpam-3996	112	35	)	)	PUNCT
ejpam-3996	112	36	and	and	CCONJ
ejpam-3996	112	37	(	(	PUNCT
ejpam-3996	112	38	p3	p3	PROPN
ejpam-3996	112	39	)	)	PUNCT
ejpam-3996	112	40	,	,	PUNCT
ejpam-3996	112	41	x	x	PUNCT
ejpam-3996	112	42	∗	∗	VERB
ejpam-3996	112	43	y	y	PROPN
ejpam-3996	112	44	∧	∧	PROPN
ejpam-3996	112	45	y	y	PROPN
ejpam-3996	112	46	∗	∗	NOUN
ejpam-3996	112	47	x	x	PUNCT
ejpam-3996	112	48	=	=	PUNCT
ejpam-3996	112	49	(	(	PUNCT
ejpam-3996	112	50	x	x	X
ejpam-3996	112	51	∗	∗	PROPN
ejpam-3996	112	52	y	y	NOUN
ejpam-3996	112	53	)	)	PUNCT
ejpam-3996	112	54	∗	∗	NOUN
ejpam-3996	113	1	[	[	X
ejpam-3996	113	2	(	(	PUNCT
ejpam-3996	113	3	x	x	X
ejpam-3996	113	4	∗	∗	PROPN
ejpam-3996	113	5	y	y	NOUN
ejpam-3996	113	6	)	)	PUNCT
ejpam-3996	113	7	∗	∗	NOUN
ejpam-3996	113	8	(	(	PUNCT
ejpam-3996	113	9	y	y	PROPN
ejpam-3996	113	10	∗	∗	NOUN
ejpam-3996	113	11	x	x	NOUN
ejpam-3996	113	12	)	)	PUNCT
ejpam-3996	113	13	]	]	PUNCT
ejpam-3996	114	1	=	=	PUNCT
ejpam-3996	115	1	[	[	X
ejpam-3996	115	2	(	(	PUNCT
ejpam-3996	115	3	x	x	X
ejpam-3996	115	4	∗	∗	PROPN
ejpam-3996	115	5	y	y	NOUN
ejpam-3996	115	6	)	)	PUNCT
ejpam-3996	115	7	∗	∗	NOUN
ejpam-3996	115	8	[	[	X
ejpam-3996	115	9	0	0	NUM
ejpam-3996	115	10	∗	∗	NOUN
ejpam-3996	115	11	(	(	PUNCT
ejpam-3996	115	12	y	y	PROPN
ejpam-3996	115	13	∗	∗	NOUN
ejpam-3996	115	14	x	x	NOUN
ejpam-3996	115	15	)	)	PUNCT
ejpam-3996	115	16	]	]	PUNCT
ejpam-3996	115	17	]	]	X
ejpam-3996	116	1	∗	∗	NOUN
ejpam-3996	116	2	(	(	PUNCT
ejpam-3996	116	3	x	x	X
ejpam-3996	116	4	∗	∗	NOUN
ejpam-3996	116	5	y	y	NOUN
ejpam-3996	116	6	)	)	PUNCT
ejpam-3996	116	7	=	=	PUNCT
ejpam-3996	117	1	[	[	X
ejpam-3996	117	2	(	(	PUNCT
ejpam-3996	117	3	x	x	X
ejpam-3996	117	4	∗	∗	PROPN
ejpam-3996	117	5	y	y	NOUN
ejpam-3996	117	6	)	)	PUNCT
ejpam-3996	117	7	∗	∗	NOUN
ejpam-3996	117	8	(	(	PUNCT
ejpam-3996	117	9	x	x	X
ejpam-3996	117	10	∗	∗	PROPN
ejpam-3996	117	11	y	y	PROPN
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ejpam-3996	117	13	]	]	PUNCT
ejpam-3996	118	1	∗	∗	NOUN
ejpam-3996	118	2	(	(	PUNCT
ejpam-3996	118	3	x	x	X
ejpam-3996	118	4	∗	∗	NOUN
ejpam-3996	118	5	y	y	NOUN
ejpam-3996	118	6	)	)	PUNCT
ejpam-3996	118	7	=	=	SYM
ejpam-3996	118	8	0	0	NUM
ejpam-3996	118	9	∗	∗	NOUN
ejpam-3996	118	10	(	(	PUNCT
ejpam-3996	118	11	x	x	X
ejpam-3996	118	12	∗	∗	NOUN
ejpam-3996	118	13	y	y	NOUN
ejpam-3996	118	14	)	)	PUNCT
ejpam-3996	119	1	=	=	SYM
ejpam-3996	119	2	y	y	PROPN
ejpam-3996	119	3	∗	∗	NOUN
ejpam-3996	119	4	x	x	PROPN
ejpam-3996	119	5	;	;	PUNCT
ejpam-3996	119	6	(	(	PUNCT
ejpam-3996	119	7	v	v	NOUN
ejpam-3996	119	8	)	)	PUNCT
ejpam-3996	119	9	x	x	X
ejpam-3996	119	10	∧	∧	NOUN
ejpam-3996	119	11	y	y	NOUN
ejpam-3996	119	12	=	=	SYM
ejpam-3996	119	13	0	0	NUM
ejpam-3996	119	14	implies	imply	VERB
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ejpam-3996	119	16	x	x	SYM
ejpam-3996	119	17	∗	∗	NOUN
ejpam-3996	119	18	(	(	PUNCT
ejpam-3996	119	19	x	x	X
ejpam-3996	119	20	∗	∗	NOUN
ejpam-3996	119	21	y	y	NOUN
ejpam-3996	119	22	)	)	PUNCT
ejpam-3996	119	23	=	=	SYM
ejpam-3996	120	1	0	0	X
ejpam-3996	120	2	.	.	PUNCT
ejpam-3996	121	1	by	by	ADP
ejpam-3996	121	2	(	(	PUNCT
ejpam-3996	121	3	p4	p4	ADJ
ejpam-3996	121	4	)	)	PUNCT
ejpam-3996	121	5	,	,	PUNCT
ejpam-3996	121	6	x	x	X
ejpam-3996	121	7	=	=	PUNCT
ejpam-3996	121	8	x	x	SYM
ejpam-3996	121	9	∗	∗	X
ejpam-3996	121	10	y	y	NOUN
ejpam-3996	121	11	which	which	PRON
ejpam-3996	121	12	can	can	AUX
ejpam-3996	121	13	be	be	AUX
ejpam-3996	121	14	written	write	VERB
ejpam-3996	121	15	as	as	ADP
ejpam-3996	121	16	x	x	X
ejpam-3996	121	17	∗	∗	NOUN
ejpam-3996	121	18	0	0	NUM
ejpam-3996	122	1	=	=	SYM
ejpam-3996	122	2	x	x	SYM
ejpam-3996	122	3	∗	∗	NOUN
ejpam-3996	122	4	y.	y.	PROPN
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ejpam-3996	122	6	,	,	PUNCT
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ejpam-3996	122	8	lemma	lemma	PROPN
ejpam-3996	122	9	2.4(i	2.4(i	NUM
ejpam-3996	122	10	)	)	PUNCT
ejpam-3996	122	11	,	,	PUNCT
ejpam-3996	122	12	y	y	PROPN
ejpam-3996	122	13	=	=	PUNCT
ejpam-3996	122	14	0	0	PROPN
ejpam-3996	122	15	.	.	PUNCT
ejpam-3996	123	1	the	the	DET
ejpam-3996	123	2	converse	converse	NOUN
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ejpam-3996	123	4	directly	directly	ADV
ejpam-3996	123	5	from	from	ADP
ejpam-3996	123	6	(	(	PUNCT
ejpam-3996	123	7	ii	ii	NOUN
ejpam-3996	123	8	)	)	PUNCT
ejpam-3996	123	9	.	.	PUNCT
ejpam-3996	124	1	�	�	PROPN
ejpam-3996	124	2	lemma	lemma	PROPN
ejpam-3996	124	3	3.8	3.8	NUM
ejpam-3996	124	4	.	.	PUNCT
ejpam-3996	125	1	if	if	SCONJ
ejpam-3996	125	2	x(i	x(i	PROPN
ejpam-3996	125	3	)	)	PUNCT
ejpam-3996	125	4	is	be	AUX
ejpam-3996	125	5	a	a	DET
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ejpam-3996	125	7	b	b	X
ejpam-3996	125	8	-	-	PUNCT
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ejpam-3996	125	10	,	,	PUNCT
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ejpam-3996	125	13	any	any	DET
ejpam-3996	125	14	(	(	PUNCT
ejpam-3996	125	15	a	a	PRON
ejpam-3996	125	16	,	,	PUNCT
ejpam-3996	125	17	bi	bi	NOUN
ejpam-3996	125	18	)	)	PUNCT
ejpam-3996	125	19	,	,	PUNCT
ejpam-3996	125	20	(	(	PUNCT
ejpam-3996	125	21	c	c	X
ejpam-3996	125	22	,	,	PUNCT
ejpam-3996	125	23	di	di	NOUN
ejpam-3996	125	24	)	)	PUNCT
ejpam-3996	125	25	∈	∈	PROPN
ejpam-3996	125	26	x(i	x(i	PROPN
ejpam-3996	125	27	)	)	PUNCT
ejpam-3996	125	28	,	,	PUNCT
ejpam-3996	125	29	(	(	PUNCT
ejpam-3996	125	30	i	i	NOUN
ejpam-3996	125	31	)	)	PUNCT
ejpam-3996	125	32	(	(	PUNCT
ejpam-3996	125	33	a	a	DET
ejpam-3996	125	34	,	,	PUNCT
ejpam-3996	125	35	bi	bi	NOUN
ejpam-3996	125	36	)	)	PUNCT
ejpam-3996	125	37	·	·	PUNCT
ejpam-3996	125	38	(	(	PUNCT
ejpam-3996	125	39	0	0	NUM
ejpam-3996	125	40	,	,	PUNCT
ejpam-3996	125	41	0i	0i	NOUN
ejpam-3996	125	42	)	)	PUNCT
ejpam-3996	126	1	=	=	PRON
ejpam-3996	126	2	(	(	PUNCT
ejpam-3996	126	3	a	a	PRON
ejpam-3996	126	4	,	,	PUNCT
ejpam-3996	126	5	(	(	PUNCT
ejpam-3996	126	6	(	(	PUNCT
ejpam-3996	126	7	a	a	DET
ejpam-3996	126	8	∧	∧	PROPN
ejpam-3996	126	9	b	b	NOUN
ejpam-3996	126	10	)	)	PUNCT
ejpam-3996	126	11	∧	∧	NOUN
ejpam-3996	126	12	b)i	b)i	NOUN
ejpam-3996	126	13	)	)	PUNCT
ejpam-3996	126	14	,	,	PUNCT
ejpam-3996	126	15	(	(	PUNCT
ejpam-3996	126	16	ii	ii	NOUN
ejpam-3996	126	17	)	)	PUNCT
ejpam-3996	126	18	(	(	PUNCT
ejpam-3996	126	19	a	a	DET
ejpam-3996	126	20	,	,	PUNCT
ejpam-3996	126	21	ci	ci	NOUN
ejpam-3996	126	22	)	)	PUNCT
ejpam-3996	126	23	·	·	PUNCT
ejpam-3996	126	24	(	(	PUNCT
ejpam-3996	126	25	b	b	X
ejpam-3996	126	26	,	,	PUNCT
ejpam-3996	126	27	ci	ci	NOUN
ejpam-3996	126	28	)	)	PUNCT
ejpam-3996	126	29	=	=	PUNCT
ejpam-3996	126	30	(	(	PUNCT
ejpam-3996	126	31	a	a	DET
ejpam-3996	126	32	∗	∗	NOUN
ejpam-3996	126	33	b	b	NOUN
ejpam-3996	126	34	,	,	PUNCT
ejpam-3996	126	35	0i	0i	PROPN
ejpam-3996	126	36	)	)	PUNCT
ejpam-3996	126	37	,	,	PUNCT
ejpam-3996	126	38	(	(	PUNCT
ejpam-3996	126	39	iii	iii	X
ejpam-3996	126	40	)	)	PUNCT
ejpam-3996	126	41	(	(	PUNCT
ejpam-3996	126	42	a	a	DET
ejpam-3996	126	43	,	,	PUNCT
ejpam-3996	126	44	ai	ai	NOUN
ejpam-3996	126	45	)	)	PUNCT
ejpam-3996	126	46	·	·	PUNCT
ejpam-3996	126	47	(	(	PUNCT
ejpam-3996	126	48	b	b	X
ejpam-3996	126	49	,	,	PUNCT
ejpam-3996	126	50	bi	bi	NOUN
ejpam-3996	126	51	)	)	PUNCT
ejpam-3996	126	52	=	=	SYM
ejpam-3996	126	53	(	(	PUNCT
ejpam-3996	126	54	a	a	DET
ejpam-3996	126	55	∗	∗	NOUN
ejpam-3996	126	56	b	b	NOUN
ejpam-3996	126	57	,	,	PUNCT
ejpam-3996	126	58	(	(	PUNCT
ejpam-3996	126	59	a	a	DET
ejpam-3996	126	60	∗	∗	NOUN
ejpam-3996	126	61	b)i	b)i	NOUN
ejpam-3996	126	62	)	)	PUNCT
ejpam-3996	126	63	,	,	PUNCT
ejpam-3996	126	64	(	(	PUNCT
ejpam-3996	126	65	iv	iv	X
ejpam-3996	126	66	)	)	PUNCT
ejpam-3996	126	67	(	(	PUNCT
ejpam-3996	126	68	a	a	DET
ejpam-3996	126	69	,	,	PUNCT
ejpam-3996	126	70	bi	bi	NOUN
ejpam-3996	126	71	)	)	PUNCT
ejpam-3996	126	72	·	·	PUNCT
ejpam-3996	126	73	(	(	PUNCT
ejpam-3996	126	74	c	c	X
ejpam-3996	126	75	,	,	PUNCT
ejpam-3996	126	76	di	di	NOUN
ejpam-3996	126	77	)	)	PUNCT
ejpam-3996	126	78	=	=	SYM
ejpam-3996	126	79	(	(	PUNCT
ejpam-3996	126	80	0	0	NUM
ejpam-3996	126	81	,	,	PUNCT
ejpam-3996	126	82	0i	0i	NOUN
ejpam-3996	126	83	)	)	PUNCT
ejpam-3996	127	1	if	if	SCONJ
ejpam-3996	127	2	and	and	CCONJ
ejpam-3996	127	3	only	only	ADV
ejpam-3996	127	4	if	if	SCONJ
ejpam-3996	127	5	(	(	PUNCT
ejpam-3996	127	6	a	a	DET
ejpam-3996	127	7	,	,	PUNCT
ejpam-3996	127	8	bi	bi	NOUN
ejpam-3996	127	9	)	)	PUNCT
ejpam-3996	127	10	=	=	SYM
ejpam-3996	127	11	(	(	PUNCT
ejpam-3996	127	12	c	c	X
ejpam-3996	127	13	,	,	PUNCT
ejpam-3996	127	14	di	di	NOUN
ejpam-3996	127	15	)	)	PUNCT
ejpam-3996	127	16	.	.	PUNCT
ejpam-3996	128	1	proof	proof	NOUN
ejpam-3996	128	2	:	:	PUNCT
ejpam-3996	128	3	(	(	PUNCT
ejpam-3996	128	4	i	i	NOUN
ejpam-3996	128	5	)	)	PUNCT
ejpam-3996	128	6	by	by	ADP
ejpam-3996	128	7	definition	definition	NOUN
ejpam-3996	128	8	3.4	3.4	NUM
ejpam-3996	128	9	and	and	CCONJ
ejpam-3996	128	10	(	(	PUNCT
ejpam-3996	128	11	b2	b2	NOUN
ejpam-3996	128	12	)	)	PUNCT
ejpam-3996	128	13	,	,	PUNCT
ejpam-3996	128	14	(	(	PUNCT
ejpam-3996	128	15	a	a	PRON
ejpam-3996	128	16	,	,	PUNCT
ejpam-3996	128	17	bi	bi	NOUN
ejpam-3996	128	18	)	)	PUNCT
ejpam-3996	128	19	·	·	PUNCT
ejpam-3996	128	20	(	(	PUNCT
ejpam-3996	128	21	0	0	NUM
ejpam-3996	128	22	,	,	PUNCT
ejpam-3996	128	23	0i	0i	NOUN
ejpam-3996	128	24	)	)	PUNCT
ejpam-3996	129	1	=	=	PRON
ejpam-3996	129	2	(	(	PUNCT
ejpam-3996	129	3	a	a	DET
ejpam-3996	129	4	∗	∗	NOUN
ejpam-3996	129	5	0	0	NUM
ejpam-3996	129	6	,	,	PUNCT
ejpam-3996	129	7	(	(	PUNCT
ejpam-3996	129	8	(	(	PUNCT
ejpam-3996	129	9	a	a	DET
ejpam-3996	129	10	∗	∗	NOUN
ejpam-3996	129	11	0	0	NUM
ejpam-3996	129	12	∧	∧	PROPN
ejpam-3996	129	13	b	b	PROPN
ejpam-3996	129	14	∗	∗	NOUN
ejpam-3996	129	15	0	0	NUM
ejpam-3996	129	16	)	)	PUNCT
ejpam-3996	130	1	∧	∧	PROPN
ejpam-3996	130	2	b	b	PROPN
ejpam-3996	130	3	∗	∗	X
ejpam-3996	130	4	0)i	0)i	NUM
ejpam-3996	130	5	)	)	PUNCT
ejpam-3996	131	1	=	=	PUNCT
ejpam-3996	131	2	(	(	PUNCT
ejpam-3996	131	3	a	a	PRON
ejpam-3996	131	4	,	,	PUNCT
ejpam-3996	131	5	(	(	PUNCT
ejpam-3996	131	6	(	(	PUNCT
ejpam-3996	131	7	a	a	DET
ejpam-3996	131	8	∧	∧	PROPN
ejpam-3996	131	9	b	b	NOUN
ejpam-3996	131	10	)	)	PUNCT
ejpam-3996	131	11	∧	∧	NOUN
ejpam-3996	131	12	b)i	b)i	NOUN
ejpam-3996	131	13	)	)	PUNCT
ejpam-3996	131	14	;	;	PUNCT
ejpam-3996	131	15	(	(	PUNCT
ejpam-3996	131	16	ii	ii	NOUN
ejpam-3996	131	17	)	)	PUNCT
ejpam-3996	131	18	by	by	ADP
ejpam-3996	131	19	definition	definition	NOUN
ejpam-3996	131	20	3.4	3.4	NUM
ejpam-3996	131	21	,	,	PUNCT
ejpam-3996	131	22	(	(	PUNCT
ejpam-3996	131	23	b1	b1	NOUN
ejpam-3996	131	24	)	)	PUNCT
ejpam-3996	131	25	,	,	PUNCT
ejpam-3996	131	26	(	(	PUNCT
ejpam-3996	131	27	b2	b2	NOUN
ejpam-3996	131	28	)	)	PUNCT
ejpam-3996	131	29	and	and	CCONJ
ejpam-3996	131	30	lemma	lemma	PROPN
ejpam-3996	131	31	3.7(ii	3.7(ii	NUM
ejpam-3996	131	32	)	)	PUNCT
ejpam-3996	131	33	,	,	PUNCT
ejpam-3996	131	34	(	(	PUNCT
ejpam-3996	131	35	a	a	DET
ejpam-3996	131	36	,	,	PUNCT
ejpam-3996	131	37	ci	ci	NOUN
ejpam-3996	131	38	)	)	PUNCT
ejpam-3996	131	39	·	·	PUNCT
ejpam-3996	132	1	(	(	PUNCT
ejpam-3996	132	2	b	b	X
ejpam-3996	132	3	,	,	PUNCT
ejpam-3996	132	4	ci	ci	NOUN
ejpam-3996	132	5	)	)	PUNCT
ejpam-3996	132	6	=	=	PUNCT
ejpam-3996	132	7	(	(	PUNCT
ejpam-3996	132	8	a∗b	a∗b	PROPN
ejpam-3996	132	9	,	,	PUNCT
ejpam-3996	132	10	(	(	PUNCT
ejpam-3996	132	11	(	(	PUNCT
ejpam-3996	132	12	a∗c∧c∗b)∧c∗c)i	a∗c∧c∗b)∧c∗c)i	NOUN
ejpam-3996	132	13	)	)	PUNCT
ejpam-3996	133	1	=	=	SYM
ejpam-3996	133	2	(	(	PUNCT
ejpam-3996	133	3	a∗b	a∗b	PROPN
ejpam-3996	133	4	,	,	PUNCT
ejpam-3996	133	5	(	(	PUNCT
ejpam-3996	133	6	(	(	PUNCT
ejpam-3996	133	7	a∗c∧c∗b)∧0)i	a∗c∧c∗b)∧0)i	ADJ
ejpam-3996	133	8	)	)	PUNCT
ejpam-3996	133	9	=	=	SYM
ejpam-3996	133	10	(	(	PUNCT
ejpam-3996	133	11	a∗b	a∗b	PROPN
ejpam-3996	133	12	,	,	PUNCT
ejpam-3996	133	13	0i	0i	NOUN
ejpam-3996	133	14	)	)	PUNCT
ejpam-3996	133	15	;	;	PUNCT
ejpam-3996	133	16	(	(	PUNCT
ejpam-3996	133	17	iii	iii	X
ejpam-3996	133	18	)	)	PUNCT
ejpam-3996	133	19	follows	follow	VERB
ejpam-3996	133	20	directly	directly	ADV
ejpam-3996	133	21	from	from	ADP
ejpam-3996	133	22	definition	definition	NOUN
ejpam-3996	133	23	3.4	3.4	NUM
ejpam-3996	133	24	and	and	CCONJ
ejpam-3996	133	25	lemma	lemma	PROPN
ejpam-3996	133	26	3.7(i	3.7(i	NUM
ejpam-3996	133	27	)	)	PUNCT
ejpam-3996	133	28	;	;	PUNCT
ejpam-3996	133	29	(	(	PUNCT
ejpam-3996	133	30	iv	iv	X
ejpam-3996	133	31	)	)	PUNCT
ejpam-3996	133	32	by	by	ADP
ejpam-3996	133	33	definition	definition	NOUN
ejpam-3996	133	34	3.4	3.4	NUM
ejpam-3996	133	35	,	,	PUNCT
ejpam-3996	133	36	(	(	PUNCT
ejpam-3996	133	37	a	a	DET
ejpam-3996	133	38	,	,	PUNCT
ejpam-3996	133	39	bi	bi	NOUN
ejpam-3996	133	40	)	)	PUNCT
ejpam-3996	133	41	·	·	PUNCT
ejpam-3996	134	1	(	(	PUNCT
ejpam-3996	134	2	c	c	X
ejpam-3996	134	3	,	,	PUNCT
ejpam-3996	134	4	di	di	NOUN
ejpam-3996	134	5	)	)	PUNCT
ejpam-3996	134	6	=	=	SYM
ejpam-3996	134	7	(	(	PUNCT
ejpam-3996	134	8	0	0	NUM
ejpam-3996	134	9	,	,	PUNCT
ejpam-3996	134	10	0i	0i	NOUN
ejpam-3996	134	11	)	)	PUNCT
ejpam-3996	134	12	implies	imply	VERB
ejpam-3996	134	13	that	that	SCONJ
ejpam-3996	134	14	(	(	PUNCT
ejpam-3996	134	15	a∗c	a∗c	PUNCT
ejpam-3996	134	16	,	,	PUNCT
ejpam-3996	134	17	(	(	PUNCT
ejpam-3996	134	18	(	(	PUNCT
ejpam-3996	134	19	a∗d∧b∗c)∧b∗d)i	a∗d∧b∗c)∧b∗d)i	PROPN
ejpam-3996	134	20	)	)	PUNCT
ejpam-3996	134	21	=	=	SYM
ejpam-3996	134	22	(	(	PUNCT
ejpam-3996	134	23	0	0	NUM
ejpam-3996	134	24	,	,	PUNCT
ejpam-3996	134	25	0i	0i	NOUN
ejpam-3996	134	26	)	)	PUNCT
ejpam-3996	134	27	.	.	PUNCT
ejpam-3996	135	1	that	that	PRON
ejpam-3996	135	2	is	be	AUX
ejpam-3996	135	3	,	,	PUNCT
ejpam-3996	135	4	a∗c	a∗c	PROPN
ejpam-3996	135	5	=	=	SYM
ejpam-3996	135	6	0	0	PUNCT
ejpam-3996	135	7	and	and	CCONJ
ejpam-3996	135	8	(	(	PUNCT
ejpam-3996	135	9	a∗d∧b∗c)∧b∗d	a∗d∧b∗c)∧b∗d	VERB
ejpam-3996	135	10	=	=	NOUN
ejpam-3996	135	11	0	0	NUM
ejpam-3996	135	12	.	.	PUNCT
ejpam-3996	136	1	by	by	ADP
ejpam-3996	136	2	(	(	PUNCT
ejpam-3996	136	3	p4	p4	ADJ
ejpam-3996	136	4	)	)	PUNCT
ejpam-3996	136	5	,	,	PUNCT
ejpam-3996	136	6	a	a	DET
ejpam-3996	136	7	=	=	SYM
ejpam-3996	136	8	c	c	NOUN
ejpam-3996	136	9	and	and	CCONJ
ejpam-3996	136	10	by	by	ADP
ejpam-3996	136	11	lemma	lemma	PROPN
ejpam-3996	136	12	3.7(v	3.7(v	NUM
ejpam-3996	136	13	)	)	PUNCT
ejpam-3996	136	14	,	,	PUNCT
ejpam-3996	136	15	b∗d	b∗d	PROPN
ejpam-3996	136	16	=	=	SYM
ejpam-3996	136	17	0	0	NUM
ejpam-3996	136	18	.	.	PUNCT
ejpam-3996	137	1	thus	thus	ADV
ejpam-3996	137	2	,	,	PUNCT
ejpam-3996	137	3	by	by	ADP
ejpam-3996	137	4	(	(	PUNCT
ejpam-3996	137	5	p4	p4	ADJ
ejpam-3996	137	6	)	)	PUNCT
ejpam-3996	137	7	,	,	PUNCT
ejpam-3996	137	8	b	b	X
ejpam-3996	137	9	=	=	SYM
ejpam-3996	137	10	d.	d.	PROPN
ejpam-3996	137	11	hence	hence	ADV
ejpam-3996	137	12	,	,	PUNCT
ejpam-3996	137	13	(	(	PUNCT
ejpam-3996	137	14	a	a	DET
ejpam-3996	137	15	,	,	PUNCT
ejpam-3996	137	16	bi	bi	NOUN
ejpam-3996	137	17	)	)	PUNCT
ejpam-3996	137	18	=	=	SYM
ejpam-3996	137	19	(	(	PUNCT
ejpam-3996	137	20	c	c	X
ejpam-3996	137	21	,	,	PUNCT
ejpam-3996	137	22	di	di	NOUN
ejpam-3996	137	23	)	)	PUNCT
ejpam-3996	137	24	.	.	PUNCT
ejpam-3996	138	1	conversely	conversely	ADV
ejpam-3996	138	2	,	,	PUNCT
ejpam-3996	138	3	let	let	VERB
ejpam-3996	138	4	(	(	PUNCT
ejpam-3996	138	5	a	a	DET
ejpam-3996	138	6	,	,	PUNCT
ejpam-3996	138	7	bi	bi	NOUN
ejpam-3996	138	8	)	)	PUNCT
ejpam-3996	138	9	=	=	SYM
ejpam-3996	138	10	(	(	PUNCT
ejpam-3996	138	11	c	c	X
ejpam-3996	138	12	,	,	PUNCT
ejpam-3996	138	13	di	di	NOUN
ejpam-3996	138	14	)	)	PUNCT
ejpam-3996	138	15	.	.	PUNCT
ejpam-3996	139	1	then	then	ADV
ejpam-3996	139	2	a	a	DET
ejpam-3996	139	3	=	=	SYM
ejpam-3996	139	4	c	c	PROPN
ejpam-3996	139	5	and	and	CCONJ
ejpam-3996	139	6	b	b	X
ejpam-3996	139	7	=	=	PROPN
ejpam-3996	139	8	d.	d.	PROPN
ejpam-3996	139	9	thus	thus	ADV
ejpam-3996	139	10	,	,	PUNCT
ejpam-3996	139	11	by	by	ADP
ejpam-3996	139	12	definition	definition	NOUN
ejpam-3996	139	13	3.4	3.4	NUM
ejpam-3996	139	14	,	,	PUNCT
ejpam-3996	139	15	(	(	PUNCT
ejpam-3996	139	16	b1	b1	NOUN
ejpam-3996	139	17	)	)	PUNCT
ejpam-3996	139	18	and	and	CCONJ
ejpam-3996	139	19	lemma	lemma	PROPN
ejpam-3996	139	20	3.7(ii	3.7(ii	NUM
ejpam-3996	139	21	and	and	CCONJ
ejpam-3996	139	22	iv	iv	NUM
ejpam-3996	139	23	)	)	PUNCT
ejpam-3996	139	24	,	,	PUNCT
ejpam-3996	139	25	(	(	PUNCT
ejpam-3996	139	26	a	a	DET
ejpam-3996	139	27	,	,	PUNCT
ejpam-3996	139	28	bi	bi	NOUN
ejpam-3996	139	29	)	)	PUNCT
ejpam-3996	139	30	·	·	PUNCT
ejpam-3996	140	1	(	(	PUNCT
ejpam-3996	140	2	c	c	X
ejpam-3996	140	3	,	,	PUNCT
ejpam-3996	140	4	di	di	NOUN
ejpam-3996	140	5	)	)	PUNCT
ejpam-3996	140	6	=	=	SYM
ejpam-3996	140	7	(	(	PUNCT
ejpam-3996	140	8	a	a	DET
ejpam-3996	140	9	∗	∗	NOUN
ejpam-3996	140	10	c	c	NOUN
ejpam-3996	140	11	,	,	PUNCT
ejpam-3996	140	12	(	(	PUNCT
ejpam-3996	140	13	(	(	PUNCT
ejpam-3996	140	14	a	a	DET
ejpam-3996	140	15	∗	∗	NOUN
ejpam-3996	140	16	d∧	d∧	NOUN
ejpam-3996	140	17	b	b	PROPN
ejpam-3996	140	18	∗	∗	X
ejpam-3996	140	19	c)∧	c)∧	PROPN
ejpam-3996	140	20	b	b	PROPN
ejpam-3996	140	21	∗	∗	NOUN
ejpam-3996	140	22	d)i	d)i	NOUN
ejpam-3996	140	23	)	)	PUNCT
ejpam-3996	140	24	=	=	SYM
ejpam-3996	140	25	(	(	PUNCT
ejpam-3996	140	26	a	a	DET
ejpam-3996	140	27	∗	∗	X
ejpam-3996	140	28	a	a	PRON
ejpam-3996	140	29	,	,	PUNCT
ejpam-3996	140	30	(	(	PUNCT
ejpam-3996	140	31	(	(	PUNCT
ejpam-3996	140	32	a	a	DET
ejpam-3996	140	33	∗	∗	NOUN
ejpam-3996	141	1	b∧	b∧	PROPN
ejpam-3996	141	2	b	b	PROPN
ejpam-3996	141	3	∗	∗	X
ejpam-3996	141	4	a	a	NOUN
ejpam-3996	141	5	)	)	PUNCT
ejpam-3996	141	6	∧	∧	PROPN
ejpam-3996	141	7	b	b	PROPN
ejpam-3996	141	8	∗	∗	X
ejpam-3996	141	9	b)i	b)i	NOUN
ejpam-3996	141	10	)	)	PUNCT
ejpam-3996	142	1	=	=	SYM
ejpam-3996	142	2	(	(	PUNCT
ejpam-3996	142	3	0	0	NUM
ejpam-3996	142	4	,	,	PUNCT
ejpam-3996	142	5	(	(	PUNCT
ejpam-3996	142	6	(	(	PUNCT
ejpam-3996	142	7	b	b	NOUN
ejpam-3996	142	8	∗	∗	ADP
ejpam-3996	142	9	a	a	NOUN
ejpam-3996	142	10	)	)	PUNCT
ejpam-3996	142	11	∧	∧	NOUN
ejpam-3996	142	12	0)i	0)i	NOUN
ejpam-3996	142	13	)	)	PUNCT
ejpam-3996	142	14	=	=	SYM
ejpam-3996	142	15	(	(	PUNCT
ejpam-3996	142	16	0	0	NUM
ejpam-3996	142	17	,	,	PUNCT
ejpam-3996	142	18	0i	0i	NOUN
ejpam-3996	142	19	)	)	PUNCT
ejpam-3996	142	20	.	.	PUNCT
ejpam-3996	143	1	�	�	PROPN
ejpam-3996	143	2	lemma	lemma	PROPN
ejpam-3996	143	3	3.9	3.9	NUM
ejpam-3996	143	4	.	.	PUNCT
ejpam-3996	144	1	if	if	SCONJ
ejpam-3996	144	2	x	x	PRON
ejpam-3996	144	3	is	be	AUX
ejpam-3996	144	4	a	a	DET
ejpam-3996	144	5	commutative	commutative	ADJ
ejpam-3996	144	6	b	b	NOUN
ejpam-3996	144	7	-	-	PUNCT
ejpam-3996	144	8	algebra	algebra	NOUN
ejpam-3996	144	9	,	,	PUNCT
ejpam-3996	144	10	then	then	ADV
ejpam-3996	144	11	for	for	ADP
ejpam-3996	144	12	any	any	DET
ejpam-3996	144	13	x	x	NOUN
ejpam-3996	144	14	,	,	PUNCT
ejpam-3996	144	15	y	y	PROPN
ejpam-3996	144	16	,	,	PUNCT
ejpam-3996	144	17	z	z	PROPN
ejpam-3996	144	18	∈	∈	PROPN
ejpam-3996	144	19	x	x	X
ejpam-3996	144	20	,	,	PUNCT
ejpam-3996	144	21	(	(	PUNCT
ejpam-3996	144	22	i	i	NOUN
ejpam-3996	144	23	)	)	PUNCT
ejpam-3996	144	24	x	x	PUNCT
ejpam-3996	144	25	∧	∧	NOUN
ejpam-3996	144	26	y	y	PROPN
ejpam-3996	144	27	=	=	SYM
ejpam-3996	144	28	y	y	PROPN
ejpam-3996	144	29	,	,	PUNCT
ejpam-3996	144	30	(	(	PUNCT
ejpam-3996	144	31	ii	ii	NOUN
ejpam-3996	144	32	)	)	PUNCT
ejpam-3996	144	33	(	(	PUNCT
ejpam-3996	144	34	x	x	PUNCT
ejpam-3996	144	35	∧	∧	PROPN
ejpam-3996	144	36	y	y	NOUN
ejpam-3996	144	37	)	)	PUNCT
ejpam-3996	144	38	∧	∧	NOUN
ejpam-3996	144	39	z	z	NOUN
ejpam-3996	144	40	=	=	PUNCT
ejpam-3996	144	41	x	x	SYM
ejpam-3996	144	42	∧	∧	PROPN
ejpam-3996	144	43	(	(	PUNCT
ejpam-3996	144	44	y	y	PROPN
ejpam-3996	144	45	∧	∧	PROPN
ejpam-3996	144	46	z	z	PROPN
ejpam-3996	144	47	)	)	PUNCT
ejpam-3996	144	48	=	=	PUNCT
ejpam-3996	145	1	z.	z.	PROPN
ejpam-3996	145	2	proof	proof	NOUN
ejpam-3996	145	3	:	:	PUNCT
ejpam-3996	145	4	let	let	VERB
ejpam-3996	145	5	x	x	PRON
ejpam-3996	145	6	,	,	PUNCT
ejpam-3996	145	7	y	y	PROPN
ejpam-3996	145	8	,	,	PUNCT
ejpam-3996	145	9	z	z	PROPN
ejpam-3996	145	10	∈	∈	PROPN
ejpam-3996	145	11	x.	x.	NOUN
ejpam-3996	145	12	(	(	PUNCT
ejpam-3996	145	13	i	i	NOUN
ejpam-3996	145	14	)	)	PUNCT
ejpam-3996	145	15	by	by	ADP
ejpam-3996	145	16	definition	definition	NOUN
ejpam-3996	145	17	3.4	3.4	NUM
ejpam-3996	145	18	and	and	CCONJ
ejpam-3996	145	19	lemma	lemma	PROPN
ejpam-3996	145	20	2.6	2.6	NUM
ejpam-3996	145	21	,	,	PUNCT
ejpam-3996	145	22	x	x	PUNCT
ejpam-3996	145	23	∧	∧	NOUN
ejpam-3996	145	24	y	y	NOUN
ejpam-3996	145	25	=	=	PUNCT
ejpam-3996	145	26	x	x	SYM
ejpam-3996	145	27	∗	∗	NOUN
ejpam-3996	145	28	(	(	PUNCT
ejpam-3996	145	29	x	x	X
ejpam-3996	145	30	∗	∗	NOUN
ejpam-3996	145	31	y	y	NOUN
ejpam-3996	145	32	)	)	PUNCT
ejpam-3996	145	33	=	=	SYM
ejpam-3996	145	34	y	y	PROPN
ejpam-3996	145	35	;	;	PUNCT
ejpam-3996	145	36	(	(	PUNCT
ejpam-3996	145	37	ii	ii	NOUN
ejpam-3996	145	38	)	)	PUNCT
ejpam-3996	145	39	by	by	ADP
ejpam-3996	145	40	(	(	PUNCT
ejpam-3996	145	41	i	i	NOUN
ejpam-3996	145	42	)	)	PUNCT
ejpam-3996	145	43	,	,	PUNCT
ejpam-3996	145	44	(	(	PUNCT
ejpam-3996	145	45	x	x	PUNCT
ejpam-3996	145	46	∧	∧	PROPN
ejpam-3996	145	47	y	y	NOUN
ejpam-3996	145	48	)	)	PUNCT
ejpam-3996	145	49	∧	∧	NOUN
ejpam-3996	145	50	z	z	NOUN
ejpam-3996	145	51	=	=	SYM
ejpam-3996	145	52	y	y	PROPN
ejpam-3996	145	53	∧	∧	PROPN
ejpam-3996	145	54	z	z	NOUN
ejpam-3996	145	55	=	=	PUNCT
ejpam-3996	145	56	z	z	NOUN
ejpam-3996	145	57	=	=	PUNCT
ejpam-3996	145	58	x	x	SYM
ejpam-3996	145	59	∧	∧	PROPN
ejpam-3996	145	60	z	z	NOUN
ejpam-3996	145	61	=	=	PUNCT
ejpam-3996	145	62	x	x	SYM
ejpam-3996	145	63	∧	∧	PROPN
ejpam-3996	145	64	(	(	PUNCT
ejpam-3996	145	65	y	y	PROPN
ejpam-3996	145	66	∧	∧	PROPN
ejpam-3996	145	67	z	z	PROPN
ejpam-3996	145	68	)	)	PUNCT
ejpam-3996	145	69	.	.	PUNCT
ejpam-3996	146	1	�	�	PROPN
ejpam-3996	146	2	theorem	theorem	VERB
ejpam-3996	146	3	3.10	3.10	NUM
ejpam-3996	146	4	.	.	PUNCT
ejpam-3996	147	1	if	if	SCONJ
ejpam-3996	147	2	x	x	PRON
ejpam-3996	147	3	is	be	AUX
ejpam-3996	147	4	commutative	commutative	ADJ
ejpam-3996	147	5	,	,	PUNCT
ejpam-3996	147	6	then	then	ADV
ejpam-3996	147	7	x(i	x(i	PROPN
ejpam-3996	147	8	)	)	PUNCT
ejpam-3996	147	9	is	be	AUX
ejpam-3996	147	10	a	a	DET
ejpam-3996	147	11	b	b	NOUN
ejpam-3996	147	12	-	-	PUNCT
ejpam-3996	147	13	algebra	algebra	NOUN
ejpam-3996	147	14	.	.	PUNCT
ejpam-3996	148	1	proof	proof	NOUN
ejpam-3996	148	2	:	:	PUNCT
ejpam-3996	148	3	let	let	VERB
ejpam-3996	148	4	(	(	PUNCT
ejpam-3996	148	5	a	a	DET
ejpam-3996	148	6	,	,	PUNCT
ejpam-3996	148	7	bi	bi	NOUN
ejpam-3996	148	8	)	)	PUNCT
ejpam-3996	148	9	,	,	PUNCT
ejpam-3996	148	10	(	(	PUNCT
ejpam-3996	148	11	c	c	X
ejpam-3996	148	12	,	,	PUNCT
ejpam-3996	148	13	di	di	NOUN
ejpam-3996	148	14	)	)	PUNCT
ejpam-3996	148	15	∈	∈	PROPN
ejpam-3996	148	16	x(i	x(i	PROPN
ejpam-3996	148	17	)	)	PUNCT
ejpam-3996	148	18	.	.	PUNCT
ejpam-3996	149	1	by	by	ADP
ejpam-3996	149	2	lemma	lemma	PROPN
ejpam-3996	149	3	3.9(ii	3.9(ii	NUM
ejpam-3996	149	4	)	)	PUNCT
ejpam-3996	149	5	,	,	PUNCT
ejpam-3996	149	6	the	the	DET
ejpam-3996	149	7	binary	binary	PROPN
ejpam-3996	149	8	operation	operation	NOUN
ejpam-3996	149	9	in	in	ADP
ejpam-3996	149	10	x(i	x(i	PROPN
ejpam-3996	149	11	)	)	PUNCT
ejpam-3996	149	12	is	be	AUX
ejpam-3996	149	13	(	(	PUNCT
ejpam-3996	149	14	a	a	DET
ejpam-3996	149	15	,	,	PUNCT
ejpam-3996	149	16	bi	bi	NOUN
ejpam-3996	149	17	)	)	PUNCT
ejpam-3996	149	18	·	·	PUNCT
ejpam-3996	150	1	(	(	PUNCT
ejpam-3996	150	2	c	c	X
ejpam-3996	150	3	,	,	PUNCT
ejpam-3996	150	4	di	di	NOUN
ejpam-3996	150	5	)	)	PUNCT
ejpam-3996	150	6	=	=	SYM
ejpam-3996	150	7	(	(	PUNCT
ejpam-3996	150	8	a	a	DET
ejpam-3996	150	9	∗	∗	NOUN
ejpam-3996	150	10	c	c	NOUN
ejpam-3996	150	11	,	,	PUNCT
ejpam-3996	150	12	(	(	PUNCT
ejpam-3996	150	13	(	(	PUNCT
ejpam-3996	150	14	a	a	DET
ejpam-3996	150	15	∗	∗	NOUN
ejpam-3996	150	16	d∧	d∧	NOUN
ejpam-3996	150	17	b	b	PROPN
ejpam-3996	150	18	∗	∗	X
ejpam-3996	150	19	c)∧	c)∧	PROPN
ejpam-3996	150	20	b	b	PROPN
ejpam-3996	150	21	∗	∗	NOUN
ejpam-3996	150	22	d)i	d)i	NOUN
ejpam-3996	150	23	)	)	PUNCT
ejpam-3996	150	24	=	=	SYM
ejpam-3996	150	25	(	(	PUNCT
ejpam-3996	150	26	a	a	DET
ejpam-3996	150	27	∗	∗	NOUN
ejpam-3996	150	28	c	c	NOUN
ejpam-3996	150	29	,	,	PUNCT
ejpam-3996	150	30	(	(	PUNCT
ejpam-3996	150	31	b	b	NOUN
ejpam-3996	150	32	∗	∗	NOUN
ejpam-3996	150	33	d)i	d)i	NOUN
ejpam-3996	150	34	)	)	PUNCT
ejpam-3996	150	35	.	.	PUNCT
ejpam-3996	151	1	this	this	PRON
ejpam-3996	151	2	coincides	coincide	VERB
ejpam-3996	151	3	with	with	ADP
ejpam-3996	151	4	the	the	DET
ejpam-3996	151	5	binary	binary	ADJ
ejpam-3996	151	6	operation	operation	NOUN
ejpam-3996	151	7	of	of	ADP
ejpam-3996	151	8	x	x	PRON
ejpam-3996	151	9	×x	×x	VERB
ejpam-3996	151	10	as	as	ADP
ejpam-3996	151	11	a	a	DET
ejpam-3996	151	12	b	b	NOUN
ejpam-3996	151	13	-	-	PUNCT
ejpam-3996	151	14	algebra	algebra	NOUN
ejpam-3996	151	15	.	.	PUNCT
ejpam-3996	152	1	therefore	therefore	ADV
ejpam-3996	152	2	,	,	PUNCT
ejpam-3996	152	3	x(i	x(i	PROPN
ejpam-3996	152	4	)	)	PUNCT
ejpam-3996	152	5	is	be	AUX
ejpam-3996	152	6	a	a	DET
ejpam-3996	152	7	b	b	NOUN
ejpam-3996	152	8	-	-	PUNCT
ejpam-3996	152	9	algebra	algebra	NOUN
ejpam-3996	152	10	.	.	PUNCT
ejpam-3996	153	1	�	�	PROPN
ejpam-3996	153	2	d.o	d.o	PROPN
ejpam-3996	153	3	.	.	PROPN
ejpam-3996	153	4	jacobe	jacobe	PROPN
ejpam-3996	153	5	,	,	PUNCT
ejpam-3996	153	6	j.p	j.p	PROPN
ejpam-3996	153	7	.	.	PROPN
ejpam-3996	153	8	vilela	vilela	PROPN
ejpam-3996	153	9	/	/	SYM
ejpam-3996	153	10	eur	eur	PROPN
ejpam-3996	153	11	.	.	PUNCT
ejpam-3996	154	1	j.	j.	PROPN
ejpam-3996	154	2	pure	pure	PROPN
ejpam-3996	154	3	appl	appl	PROPN
ejpam-3996	154	4	.	.	PROPN
ejpam-3996	154	5	math	math	PROPN
ejpam-3996	154	6	,	,	PUNCT
ejpam-3996	154	7	14	14	NUM
ejpam-3996	154	8	(	(	PUNCT
ejpam-3996	154	9	3	3	NUM
ejpam-3996	154	10	)	)	PUNCT
ejpam-3996	154	11	(	(	PUNCT
ejpam-3996	154	12	2021	2021	NUM
ejpam-3996	154	13	)	)	PUNCT
ejpam-3996	154	14	,	,	PUNCT
ejpam-3996	154	15	895	895	NUM
ejpam-3996	154	16	-	-	SYM
ejpam-3996	154	17	904	904	NUM
ejpam-3996	154	18	899	899	NUM
ejpam-3996	154	19	remark	remark	NOUN
ejpam-3996	154	20	3.11	3.11	NUM
ejpam-3996	154	21	.	.	PUNCT
ejpam-3996	155	1	by	by	ADP
ejpam-3996	155	2	theorem	theorem	NOUN
ejpam-3996	155	3	3.10	3.10	NUM
ejpam-3996	155	4	,	,	PUNCT
ejpam-3996	155	5	the	the	DET
ejpam-3996	155	6	neutrosophic	neutrosophic	ADJ
ejpam-3996	155	7	b	b	X
ejpam-3996	155	8	-	-	PUNCT
ejpam-3996	155	9	algebra	algebra	NOUN
ejpam-3996	155	10	x(i	x(i	PROPN
ejpam-3996	155	11	)	)	PUNCT
ejpam-3996	155	12	in	in	ADP
ejpam-3996	155	13	example	example	NOUN
ejpam-3996	155	14	3.6	3.6	NUM
ejpam-3996	155	15	is	be	AUX
ejpam-3996	155	16	a	a	DET
ejpam-3996	155	17	b	b	NOUN
ejpam-3996	155	18	-	-	PUNCT
ejpam-3996	155	19	algebra	algebra	NOUN
ejpam-3996	155	20	.	.	PUNCT
ejpam-3996	156	1	however	however	ADV
ejpam-3996	156	2	,	,	PUNCT
ejpam-3996	156	3	a	a	DET
ejpam-3996	156	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	156	5	b	b	X
ejpam-3996	156	6	-	-	PUNCT
ejpam-3996	156	7	algebra	algebra	NOUN
ejpam-3996	156	8	is	be	AUX
ejpam-3996	156	9	not	not	PART
ejpam-3996	156	10	a	a	DET
ejpam-3996	156	11	b	b	NOUN
ejpam-3996	156	12	-	-	PUNCT
ejpam-3996	156	13	algebra	algebra	NOUN
ejpam-3996	156	14	in	in	ADP
ejpam-3996	156	15	general	general	ADJ
ejpam-3996	156	16	as	as	SCONJ
ejpam-3996	156	17	shown	show	VERB
ejpam-3996	156	18	in	in	ADP
ejpam-3996	156	19	the	the	DET
ejpam-3996	156	20	following	follow	VERB
ejpam-3996	156	21	example	example	NOUN
ejpam-3996	156	22	.	.	PUNCT
ejpam-3996	157	1	example	example	NOUN
ejpam-3996	158	1	3.12	3.12	NUM
ejpam-3996	158	2	.	.	PUNCT
ejpam-3996	158	3	consider	consider	VERB
ejpam-3996	158	4	the	the	DET
ejpam-3996	158	5	non	non	ADJ
ejpam-3996	158	6	-	-	ADJ
ejpam-3996	158	7	commutative	commutative	ADJ
ejpam-3996	158	8	b	b	NOUN
ejpam-3996	158	9	-	-	NOUN
ejpam-3996	158	10	algebrax	algebrax	NOUN
ejpam-3996	158	11	=	=	SYM
ejpam-3996	158	12	{	{	PUNCT
ejpam-3996	158	13	0	0	NUM
ejpam-3996	158	14	,	,	PUNCT
ejpam-3996	158	15	1	1	NUM
ejpam-3996	158	16	,	,	PUNCT
ejpam-3996	158	17	2	2	NUM
ejpam-3996	158	18	,	,	PUNCT
ejpam-3996	158	19	3	3	NUM
ejpam-3996	158	20	,	,	PUNCT
ejpam-3996	158	21	4	4	NUM
ejpam-3996	158	22	,	,	PUNCT
ejpam-3996	158	23	5	5	NUM
ejpam-3996	158	24	}	}	PUNCT
ejpam-3996	158	25	in	in	ADP
ejpam-3996	158	26	example	example	NOUN
ejpam-3996	158	27	2.3(ii	2.3(ii	NUM
ejpam-3996	158	28	)	)	PUNCT
ejpam-3996	158	29	.	.	PUNCT
ejpam-3996	159	1	then	then	ADV
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ejpam-3996	159	3	setx(i	setx(i	NOUN
ejpam-3996	159	4	)	)	PUNCT
ejpam-3996	159	5	=	=	PRON
ejpam-3996	159	6	{	{	PUNCT
ejpam-3996	159	7	(	(	PUNCT
ejpam-3996	159	8	0	0	NUM
ejpam-3996	159	9	,	,	PUNCT
ejpam-3996	159	10	0i	0i	NOUN
ejpam-3996	159	11	)	)	PUNCT
ejpam-3996	159	12	,	,	PUNCT
ejpam-3996	159	13	(	(	PUNCT
ejpam-3996	159	14	1	1	NUM
ejpam-3996	159	15	,	,	PUNCT
ejpam-3996	159	16	0i	0i	NOUN
ejpam-3996	159	17	)	)	PUNCT
ejpam-3996	159	18	,	,	PUNCT
ejpam-3996	159	19	...	...	PUNCT
ejpam-3996	159	20	,	,	PUNCT
ejpam-3996	159	21	(	(	PUNCT
ejpam-3996	159	22	5	5	NUM
ejpam-3996	159	23	,	,	PUNCT
ejpam-3996	159	24	0i	0i	NOUN
ejpam-3996	159	25	)	)	PUNCT
ejpam-3996	159	26	,	,	PUNCT
ejpam-3996	159	27	(	(	PUNCT
ejpam-3996	159	28	0	0	NUM
ejpam-3996	159	29	,	,	PUNCT
ejpam-3996	159	30	i	i	NOUN
ejpam-3996	159	31	)	)	PUNCT
ejpam-3996	159	32	,	,	PUNCT
ejpam-3996	159	33	(	(	PUNCT
ejpam-3996	159	34	1	1	X
ejpam-3996	159	35	,	,	PUNCT
ejpam-3996	159	36	i	i	NOUN
ejpam-3996	159	37	)	)	PUNCT
ejpam-3996	159	38	,	,	PUNCT
ejpam-3996	159	39	...	...	PUNCT
ejpam-3996	159	40	,	,	PUNCT
ejpam-3996	159	41	(	(	PUNCT
ejpam-3996	159	42	5	5	NUM
ejpam-3996	159	43	,	,	PUNCT
ejpam-3996	159	44	i	i	PROPN
ejpam-3996	159	45	)	)	PUNCT
ejpam-3996	159	46	,	,	PUNCT
ejpam-3996	159	47	(	(	PUNCT
ejpam-3996	159	48	0	0	NUM
ejpam-3996	159	49	,	,	PUNCT
ejpam-3996	159	50	2i	2i	NUM
ejpam-3996	159	51	)	)	PUNCT
ejpam-3996	159	52	,	,	PUNCT
ejpam-3996	159	53	(	(	PUNCT
ejpam-3996	159	54	1	1	NUM
ejpam-3996	159	55	,	,	PUNCT
ejpam-3996	159	56	2i	2i	NUM
ejpam-3996	159	57	)	)	PUNCT
ejpam-3996	159	58	,	,	PUNCT
ejpam-3996	159	59	...	...	PUNCT
ejpam-3996	159	60	,	,	PUNCT
ejpam-3996	159	61	(	(	PUNCT
ejpam-3996	159	62	5	5	NUM
ejpam-3996	159	63	,	,	PUNCT
ejpam-3996	159	64	2i	2i	NUM
ejpam-3996	159	65	)	)	PUNCT
ejpam-3996	159	66	,	,	PUNCT
ejpam-3996	159	67	(	(	PUNCT
ejpam-3996	159	68	0	0	NUM
ejpam-3996	159	69	,	,	PUNCT
ejpam-3996	159	70	3i	3i	NOUN
ejpam-3996	159	71	)	)	PUNCT
ejpam-3996	159	72	,	,	PUNCT
ejpam-3996	159	73	(	(	PUNCT
ejpam-3996	159	74	1	1	NUM
ejpam-3996	159	75	,	,	PUNCT
ejpam-3996	159	76	3i	3i	NUM
ejpam-3996	159	77	)	)	PUNCT
ejpam-3996	159	78	,	,	PUNCT
ejpam-3996	159	79	...	...	PUNCT
ejpam-3996	159	80	,	,	PUNCT
ejpam-3996	159	81	(	(	PUNCT
ejpam-3996	159	82	5	5	NUM
ejpam-3996	159	83	,	,	PUNCT
ejpam-3996	159	84	3i	3i	NUM
ejpam-3996	159	85	)	)	PUNCT
ejpam-3996	159	86	,	,	PUNCT
ejpam-3996	159	87	(	(	PUNCT
ejpam-3996	159	88	0	0	NUM
ejpam-3996	159	89	,	,	PUNCT
ejpam-3996	159	90	4i	4i	NUM
ejpam-3996	159	91	)	)	PUNCT
ejpam-3996	159	92	,	,	PUNCT
ejpam-3996	159	93	(	(	PUNCT
ejpam-3996	159	94	1	1	NUM
ejpam-3996	159	95	,	,	PUNCT
ejpam-3996	159	96	4i	4i	NUM
ejpam-3996	159	97	)	)	PUNCT
ejpam-3996	159	98	,	,	PUNCT
ejpam-3996	159	99	...	...	PUNCT
ejpam-3996	159	100	,	,	PUNCT
ejpam-3996	159	101	(	(	PUNCT
ejpam-3996	159	102	5	5	NUM
ejpam-3996	159	103	,	,	PUNCT
ejpam-3996	159	104	4i	4i	NUM
ejpam-3996	159	105	)	)	PUNCT
ejpam-3996	159	106	,	,	PUNCT
ejpam-3996	159	107	(	(	PUNCT
ejpam-3996	159	108	0	0	NUM
ejpam-3996	159	109	,	,	PUNCT
ejpam-3996	159	110	5i	5i	NUM
ejpam-3996	159	111	)	)	PUNCT
ejpam-3996	159	112	,	,	PUNCT
ejpam-3996	159	113	(	(	PUNCT
ejpam-3996	159	114	1	1	NUM
ejpam-3996	159	115	,	,	PUNCT
ejpam-3996	159	116	5i	5i	NUM
ejpam-3996	159	117	)	)	PUNCT
ejpam-3996	159	118	,	,	PUNCT
ejpam-3996	159	119	...	...	PUNCT
ejpam-3996	159	120	,	,	PUNCT
ejpam-3996	159	121	(	(	PUNCT
ejpam-3996	159	122	5	5	NUM
ejpam-3996	159	123	,	,	PUNCT
ejpam-3996	159	124	5i	5i	NUM
ejpam-3996	159	125	)	)	PUNCT
ejpam-3996	159	126	}	}	PUNCT
ejpam-3996	159	127	is	be	AUX
ejpam-3996	159	128	the	the	DET
ejpam-3996	159	129	neutrosophic	neutrosophic	ADJ
ejpam-3996	159	130	b	b	SYM
ejpam-3996	159	131	-algebra	-algebra	NOUN
ejpam-3996	159	132	determined	determine	VERB
ejpam-3996	159	133	by	by	ADP
ejpam-3996	159	134	x	x	PUNCT
ejpam-3996	159	135	and	and	CCONJ
ejpam-3996	159	136	i.	i.	PROPN
ejpam-3996	159	137	x(i	x(i	PROPN
ejpam-3996	159	138	)	)	PUNCT
ejpam-3996	159	139	is	be	AUX
ejpam-3996	159	140	not	not	PART
ejpam-3996	159	141	a	a	DET
ejpam-3996	159	142	b	b	NOUN
ejpam-3996	159	143	-	-	PUNCT
ejpam-3996	159	144	algebra	algebra	NOUN
ejpam-3996	159	145	since	since	SCONJ
ejpam-3996	159	146	by	by	ADP
ejpam-3996	159	147	lemma	lemma	PROPN
ejpam-3996	159	148	3.8(i	3.8(i	PROPN
ejpam-3996	159	149	)	)	PUNCT
ejpam-3996	159	150	,	,	PUNCT
ejpam-3996	159	151	(	(	PUNCT
ejpam-3996	159	152	3	3	NUM
ejpam-3996	159	153	,	,	PUNCT
ejpam-3996	159	154	4i	4i	NUM
ejpam-3996	159	155	)	)	PUNCT
ejpam-3996	159	156	·	·	PUNCT
ejpam-3996	160	1	(	(	PUNCT
ejpam-3996	160	2	0	0	NUM
ejpam-3996	160	3	,	,	PUNCT
ejpam-3996	160	4	0i	0i	NOUN
ejpam-3996	160	5	)	)	PUNCT
ejpam-3996	161	1	=	=	PUNCT
ejpam-3996	161	2	(	(	PUNCT
ejpam-3996	161	3	3	3	NUM
ejpam-3996	161	4	,	,	PUNCT
ejpam-3996	161	5	(	(	PUNCT
ejpam-3996	161	6	(	(	PUNCT
ejpam-3996	161	7	3	3	NUM
ejpam-3996	161	8	∧	∧	NOUN
ejpam-3996	161	9	4	4	NUM
ejpam-3996	161	10	)	)	PUNCT
ejpam-3996	161	11	∧	∧	NOUN
ejpam-3996	161	12	4)i	4)i	NUM
ejpam-3996	161	13	)	)	PUNCT
ejpam-3996	161	14	=	=	PUNCT
ejpam-3996	161	15	(	(	PUNCT
ejpam-3996	161	16	3	3	NUM
ejpam-3996	161	17	,	,	PUNCT
ejpam-3996	161	18	(	(	PUNCT
ejpam-3996	161	19	5	5	NUM
ejpam-3996	161	20	∧	∧	PROPN
ejpam-3996	161	21	4)i	4)i	NUM
ejpam-3996	161	22	)	)	PUNCT
ejpam-3996	161	23	=	=	SYM
ejpam-3996	161	24	(	(	PUNCT
ejpam-3996	161	25	3	3	NUM
ejpam-3996	161	26	,	,	PUNCT
ejpam-3996	161	27	3i	3i	NUM
ejpam-3996	161	28	)	)	PUNCT
ejpam-3996	161	29	6=	6=	ADP
ejpam-3996	161	30	(	(	PUNCT
ejpam-3996	161	31	3	3	NUM
ejpam-3996	161	32	,	,	PUNCT
ejpam-3996	161	33	4i	4i	NUM
ejpam-3996	161	34	)	)	PUNCT
ejpam-3996	161	35	.	.	PUNCT
ejpam-3996	162	1	definition	definition	NOUN
ejpam-3996	162	2	3.13	3.13	NUM
ejpam-3996	162	3	.	.	PUNCT
ejpam-3996	163	1	a	a	DET
ejpam-3996	163	2	neutrosophic	neutrosophic	ADJ
ejpam-3996	163	3	b	b	X
ejpam-3996	163	4	-	-	PUNCT
ejpam-3996	163	5	algebra	algebra	NOUN
ejpam-3996	163	6	x(i	x(i	PROPN
ejpam-3996	163	7	)	)	PUNCT
ejpam-3996	163	8	is	be	AUX
ejpam-3996	163	9	said	say	VERB
ejpam-3996	163	10	to	to	PART
ejpam-3996	163	11	be	be	AUX
ejpam-3996	163	12	commutative	commutative	ADJ
ejpam-3996	163	13	if	if	SCONJ
ejpam-3996	163	14	(	(	PUNCT
ejpam-3996	163	15	a	a	DET
ejpam-3996	163	16	,	,	PUNCT
ejpam-3996	163	17	bi	bi	NOUN
ejpam-3996	163	18	)	)	PUNCT
ejpam-3996	163	19	·	·	PUNCT
ejpam-3996	164	1	[	[	X
ejpam-3996	164	2	(	(	PUNCT
ejpam-3996	164	3	0	0	NUM
ejpam-3996	164	4	,	,	PUNCT
ejpam-3996	164	5	0i	0i	NOUN
ejpam-3996	164	6	)	)	PUNCT
ejpam-3996	164	7	·	·	PUNCT
ejpam-3996	165	1	(	(	PUNCT
ejpam-3996	165	2	c	c	X
ejpam-3996	165	3	,	,	PUNCT
ejpam-3996	165	4	di	di	NOUN
ejpam-3996	165	5	)	)	PUNCT
ejpam-3996	165	6	]	]	PUNCT
ejpam-3996	166	1	=	=	PUNCT
ejpam-3996	166	2	(	(	PUNCT
ejpam-3996	166	3	c	c	X
ejpam-3996	166	4	,	,	PUNCT
ejpam-3996	166	5	di	di	NOUN
ejpam-3996	166	6	)	)	PUNCT
ejpam-3996	166	7	·	·	PUNCT
ejpam-3996	167	1	[	[	X
ejpam-3996	167	2	(	(	PUNCT
ejpam-3996	167	3	0	0	NUM
ejpam-3996	167	4	,	,	PUNCT
ejpam-3996	167	5	0i	0i	NOUN
ejpam-3996	167	6	)	)	PUNCT
ejpam-3996	167	7	·	·	PUNCT
ejpam-3996	168	1	(	(	PUNCT
ejpam-3996	168	2	a	a	DET
ejpam-3996	168	3	,	,	PUNCT
ejpam-3996	168	4	bi	bi	NOUN
ejpam-3996	168	5	)	)	PUNCT
ejpam-3996	168	6	]	]	PUNCT
ejpam-3996	168	7	for	for	ADP
ejpam-3996	168	8	any	any	DET
ejpam-3996	168	9	(	(	PUNCT
ejpam-3996	168	10	a	a	PRON
ejpam-3996	168	11	,	,	PUNCT
ejpam-3996	168	12	bi	bi	NOUN
ejpam-3996	168	13	)	)	PUNCT
ejpam-3996	168	14	,	,	PUNCT
ejpam-3996	168	15	(	(	PUNCT
ejpam-3996	168	16	c	c	X
ejpam-3996	168	17	,	,	PUNCT
ejpam-3996	168	18	di	di	NOUN
ejpam-3996	168	19	)	)	PUNCT
ejpam-3996	168	20	∈	∈	PROPN
ejpam-3996	168	21	x(i	x(i	PROPN
ejpam-3996	168	22	)	)	PUNCT
ejpam-3996	168	23	.	.	PUNCT
ejpam-3996	169	1	remark	remark	PROPN
ejpam-3996	169	2	3.14	3.14	NUM
ejpam-3996	169	3	.	.	PUNCT
ejpam-3996	170	1	if	if	SCONJ
ejpam-3996	170	2	x(i	x(i	PROPN
ejpam-3996	170	3	)	)	PUNCT
ejpam-3996	170	4	is	be	AUX
ejpam-3996	170	5	a	a	DET
ejpam-3996	170	6	commutative	commutative	ADJ
ejpam-3996	170	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	170	8	b	b	X
ejpam-3996	170	9	-	-	PUNCT
ejpam-3996	170	10	algebra	algebra	NOUN
ejpam-3996	170	11	,	,	PUNCT
ejpam-3996	170	12	then	then	ADV
ejpam-3996	170	13	x	x	ADP
ejpam-3996	170	14	′	′	NOUN
ejpam-3996	170	15	=	=	SYM
ejpam-3996	170	16	{	{	PUNCT
ejpam-3996	170	17	(	(	PUNCT
ejpam-3996	170	18	x	x	X
ejpam-3996	170	19	,	,	PUNCT
ejpam-3996	170	20	0i	0i	NUM
ejpam-3996	170	21	)	)	PUNCT
ejpam-3996	170	22	:	:	PUNCT
ejpam-3996	171	1	x	x	X
ejpam-3996	171	2	∈	∈	NOUN
ejpam-3996	171	3	x	x	PRON
ejpam-3996	171	4	}	}	PUNCT
ejpam-3996	171	5	is	be	AUX
ejpam-3996	171	6	a	a	DET
ejpam-3996	171	7	commutative	commutative	ADJ
ejpam-3996	171	8	b	b	NOUN
ejpam-3996	171	9	-	-	PUNCT
ejpam-3996	171	10	algebra	algebra	NOUN
ejpam-3996	171	11	.	.	PUNCT
ejpam-3996	172	1	in	in	ADP
ejpam-3996	172	2	example	example	NOUN
ejpam-3996	172	3	3.12	3.12	NUM
ejpam-3996	172	4	,	,	PUNCT
ejpam-3996	172	5	x(i	x(i	PROPN
ejpam-3996	172	6	)	)	PUNCT
ejpam-3996	172	7	is	be	AUX
ejpam-3996	172	8	not	not	PART
ejpam-3996	172	9	commutative	commutative	ADJ
ejpam-3996	172	10	since	since	SCONJ
ejpam-3996	172	11	(	(	PUNCT
ejpam-3996	172	12	2	2	NUM
ejpam-3996	172	13	,	,	PUNCT
ejpam-3996	172	14	2i	2i	NUM
ejpam-3996	172	15	)	)	PUNCT
ejpam-3996	172	16	,	,	PUNCT
ejpam-3996	172	17	(	(	PUNCT
ejpam-3996	172	18	5	5	NUM
ejpam-3996	172	19	,	,	PUNCT
ejpam-3996	172	20	5i	5i	NUM
ejpam-3996	172	21	)	)	PUNCT
ejpam-3996	172	22	∈	∈	PROPN
ejpam-3996	172	23	x(i	x(i	PROPN
ejpam-3996	172	24	)	)	PUNCT
ejpam-3996	172	25	but	but	CCONJ
ejpam-3996	172	26	by	by	ADP
ejpam-3996	172	27	lemma	lemma	PROPN
ejpam-3996	172	28	3.8(iii	3.8(iii	NUM
ejpam-3996	172	29	)	)	PUNCT
ejpam-3996	172	30	,	,	PUNCT
ejpam-3996	172	31	(	(	PUNCT
ejpam-3996	172	32	2	2	NUM
ejpam-3996	172	33	,	,	PUNCT
ejpam-3996	172	34	2i	2i	NUM
ejpam-3996	172	35	)	)	PUNCT
ejpam-3996	172	36	·	·	PUNCT
ejpam-3996	173	1	[	[	X
ejpam-3996	173	2	(	(	PUNCT
ejpam-3996	173	3	0	0	NUM
ejpam-3996	173	4	,	,	PUNCT
ejpam-3996	173	5	0i	0i	NOUN
ejpam-3996	173	6	)	)	PUNCT
ejpam-3996	173	7	·	·	PUNCT
ejpam-3996	174	1	(	(	PUNCT
ejpam-3996	174	2	5	5	NUM
ejpam-3996	174	3	,	,	PUNCT
ejpam-3996	174	4	5i	5i	NUM
ejpam-3996	174	5	)	)	PUNCT
ejpam-3996	174	6	]	]	PUNCT
ejpam-3996	175	1	=	=	PUNCT
ejpam-3996	175	2	(	(	PUNCT
ejpam-3996	175	3	4	4	NUM
ejpam-3996	175	4	,	,	PUNCT
ejpam-3996	175	5	4i	4i	NUM
ejpam-3996	175	6	)	)	PUNCT
ejpam-3996	175	7	6=	6=	ADP
ejpam-3996	175	8	(	(	PUNCT
ejpam-3996	175	9	3	3	NUM
ejpam-3996	175	10	,	,	PUNCT
ejpam-3996	175	11	3i	3i	NUM
ejpam-3996	175	12	)	)	PUNCT
ejpam-3996	175	13	=	=	SYM
ejpam-3996	175	14	(	(	PUNCT
ejpam-3996	175	15	5	5	NUM
ejpam-3996	175	16	,	,	PUNCT
ejpam-3996	175	17	5i	5i	NUM
ejpam-3996	175	18	)	)	PUNCT
ejpam-3996	175	19	·	·	PUNCT
ejpam-3996	176	1	[	[	X
ejpam-3996	176	2	(	(	PUNCT
ejpam-3996	176	3	0	0	NUM
ejpam-3996	176	4	,	,	PUNCT
ejpam-3996	176	5	0i	0i	NOUN
ejpam-3996	176	6	)	)	PUNCT
ejpam-3996	176	7	·	·	PUNCT
ejpam-3996	177	1	(	(	PUNCT
ejpam-3996	177	2	2	2	NUM
ejpam-3996	177	3	,	,	PUNCT
ejpam-3996	177	4	2i	2i	NUM
ejpam-3996	177	5	)	)	PUNCT
ejpam-3996	177	6	]	]	PUNCT
ejpam-3996	177	7	.	.	PUNCT
ejpam-3996	178	1	in	in	ADP
ejpam-3996	178	2	example	example	NOUN
ejpam-3996	178	3	3.6	3.6	NUM
ejpam-3996	178	4	,	,	PUNCT
ejpam-3996	178	5	x	x	X
ejpam-3996	178	6	is	be	AUX
ejpam-3996	178	7	a	a	DET
ejpam-3996	178	8	commutative	commutative	ADJ
ejpam-3996	178	9	b	b	NOUN
ejpam-3996	178	10	-	-	PUNCT
ejpam-3996	178	11	algebra	algebra	NOUN
ejpam-3996	178	12	and	and	CCONJ
ejpam-3996	178	13	it	it	PRON
ejpam-3996	178	14	can	can	AUX
ejpam-3996	178	15	be	be	AUX
ejpam-3996	178	16	verified	verify	VERB
ejpam-3996	178	17	that	that	SCONJ
ejpam-3996	178	18	x(i	x(i	PROPN
ejpam-3996	178	19	)	)	PUNCT
ejpam-3996	178	20	is	be	AUX
ejpam-3996	178	21	also	also	ADV
ejpam-3996	178	22	commutative	commutative	ADJ
ejpam-3996	178	23	.	.	PUNCT
ejpam-3996	179	1	this	this	DET
ejpam-3996	179	2	observation	observation	NOUN
ejpam-3996	179	3	is	be	AUX
ejpam-3996	179	4	generalized	generalize	VERB
ejpam-3996	179	5	in	in	ADP
ejpam-3996	179	6	the	the	DET
ejpam-3996	179	7	following	follow	VERB
ejpam-3996	179	8	result	result	NOUN
ejpam-3996	179	9	.	.	PUNCT
ejpam-3996	180	1	theorem	theorem	VERB
ejpam-3996	180	2	3.15	3.15	NUM
ejpam-3996	180	3	.	.	PUNCT
ejpam-3996	181	1	x	x	PRON
ejpam-3996	181	2	is	be	AUX
ejpam-3996	181	3	commutative	commutative	ADJ
ejpam-3996	181	4	if	if	SCONJ
ejpam-3996	181	5	and	and	CCONJ
ejpam-3996	181	6	only	only	ADV
ejpam-3996	181	7	if	if	SCONJ
ejpam-3996	181	8	x(i	x(i	PROPN
ejpam-3996	181	9	)	)	PUNCT
ejpam-3996	181	10	is	be	AUX
ejpam-3996	181	11	commutative	commutative	ADJ
ejpam-3996	181	12	.	.	PUNCT
ejpam-3996	182	1	proof	proof	NOUN
ejpam-3996	182	2	:	:	PUNCT
ejpam-3996	182	3	let	let	VERB
ejpam-3996	182	4	(	(	PUNCT
ejpam-3996	182	5	a	a	DET
ejpam-3996	182	6	,	,	PUNCT
ejpam-3996	182	7	bi	bi	NOUN
ejpam-3996	182	8	)	)	PUNCT
ejpam-3996	182	9	,	,	PUNCT
ejpam-3996	182	10	(	(	PUNCT
ejpam-3996	182	11	c	c	X
ejpam-3996	182	12	,	,	PUNCT
ejpam-3996	182	13	di	di	NOUN
ejpam-3996	182	14	)	)	PUNCT
ejpam-3996	182	15	∈	∈	PROPN
ejpam-3996	182	16	x(i	x(i	PROPN
ejpam-3996	182	17	)	)	PUNCT
ejpam-3996	182	18	.	.	PUNCT
ejpam-3996	183	1	suppose	suppose	VERB
ejpam-3996	183	2	that	that	SCONJ
ejpam-3996	183	3	x	x	PRON
ejpam-3996	183	4	is	be	AUX
ejpam-3996	183	5	commutative	commutative	ADJ
ejpam-3996	183	6	.	.	PUNCT
ejpam-3996	184	1	then	then	ADV
ejpam-3996	184	2	by	by	ADP
ejpam-3996	184	3	definition	definition	NOUN
ejpam-3996	184	4	3.4	3.4	NUM
ejpam-3996	184	5	and	and	CCONJ
ejpam-3996	184	6	lemma	lemma	PROPN
ejpam-3996	184	7	3.9	3.9	NUM
ejpam-3996	184	8	(	(	PUNCT
ejpam-3996	184	9	ii	ii	NOUN
ejpam-3996	184	10	)	)	PUNCT
ejpam-3996	184	11	,	,	PUNCT
ejpam-3996	184	12	(	(	PUNCT
ejpam-3996	184	13	a	a	DET
ejpam-3996	184	14	,	,	PUNCT
ejpam-3996	184	15	bi	bi	NOUN
ejpam-3996	184	16	)	)	PUNCT
ejpam-3996	184	17	·	·	PUNCT
ejpam-3996	185	1	[	[	X
ejpam-3996	185	2	(	(	PUNCT
ejpam-3996	185	3	0	0	NUM
ejpam-3996	185	4	,	,	PUNCT
ejpam-3996	185	5	0i	0i	NOUN
ejpam-3996	185	6	)	)	PUNCT
ejpam-3996	185	7	·	·	PUNCT
ejpam-3996	186	1	(	(	PUNCT
ejpam-3996	186	2	c	c	X
ejpam-3996	186	3	,	,	PUNCT
ejpam-3996	186	4	di	di	NOUN
ejpam-3996	186	5	)	)	PUNCT
ejpam-3996	186	6	]	]	PUNCT
ejpam-3996	187	1	=	=	PUNCT
ejpam-3996	187	2	(	(	PUNCT
ejpam-3996	187	3	a	a	PRON
ejpam-3996	187	4	,	,	PUNCT
ejpam-3996	187	5	bi	bi	NOUN
ejpam-3996	187	6	)	)	PUNCT
ejpam-3996	187	7	·	·	PUNCT
ejpam-3996	188	1	(	(	PUNCT
ejpam-3996	188	2	0	0	NUM
ejpam-3996	188	3	∗	∗	NOUN
ejpam-3996	188	4	c	c	NOUN
ejpam-3996	188	5	,	,	PUNCT
ejpam-3996	188	6	(	(	PUNCT
ejpam-3996	188	7	(	(	PUNCT
ejpam-3996	188	8	0	0	NUM
ejpam-3996	188	9	∗	∗	NOUN
ejpam-3996	188	10	d	d	X
ejpam-3996	188	11	∧	∧	PROPN
ejpam-3996	188	12	0	0	NUM
ejpam-3996	188	13	∗	∗	NOUN
ejpam-3996	188	14	c	c	NOUN
ejpam-3996	188	15	)	)	PUNCT
ejpam-3996	188	16	∧	∧	NOUN
ejpam-3996	188	17	0	0	NUM
ejpam-3996	188	18	∗	∗	NOUN
ejpam-3996	188	19	d)i	d)i	NOUN
ejpam-3996	188	20	)	)	PUNCT
ejpam-3996	188	21	=	=	SYM
ejpam-3996	188	22	(	(	PUNCT
ejpam-3996	188	23	a	a	PRON
ejpam-3996	188	24	,	,	PUNCT
ejpam-3996	188	25	bi	bi	NOUN
ejpam-3996	188	26	)	)	PUNCT
ejpam-3996	188	27	·	·	PUNCT
ejpam-3996	188	28	(	(	PUNCT
ejpam-3996	188	29	0	0	NUM
ejpam-3996	188	30	∗	∗	NOUN
ejpam-3996	188	31	c	c	NOUN
ejpam-3996	188	32	,	,	PUNCT
ejpam-3996	188	33	(	(	PUNCT
ejpam-3996	188	34	0	0	NUM
ejpam-3996	188	35	∗	∗	NOUN
ejpam-3996	188	36	d)i	d)i	NOUN
ejpam-3996	188	37	)	)	PUNCT
ejpam-3996	188	38	=	=	SYM
ejpam-3996	188	39	(	(	PUNCT
ejpam-3996	188	40	a	a	DET
ejpam-3996	188	41	∗	∗	NOUN
ejpam-3996	188	42	(	(	PUNCT
ejpam-3996	188	43	0	0	NUM
ejpam-3996	188	44	∗	∗	NOUN
ejpam-3996	188	45	c	c	NOUN
ejpam-3996	188	46	)	)	PUNCT
ejpam-3996	188	47	,	,	PUNCT
ejpam-3996	188	48	[	[	X
ejpam-3996	188	49	(	(	PUNCT
ejpam-3996	188	50	a	a	DET
ejpam-3996	188	51	∗	∗	NOUN
ejpam-3996	188	52	(	(	PUNCT
ejpam-3996	188	53	0	0	NUM
ejpam-3996	188	54	∗	∗	NOUN
ejpam-3996	188	55	d	d	NOUN
ejpam-3996	188	56	)	)	PUNCT
ejpam-3996	188	57	∧	∧	PROPN
ejpam-3996	188	58	b	b	PROPN
ejpam-3996	188	59	∗	∗	X
ejpam-3996	188	60	(	(	PUNCT
ejpam-3996	188	61	0	0	NUM
ejpam-3996	188	62	∗	∗	NOUN
ejpam-3996	188	63	c	c	NOUN
ejpam-3996	188	64	)	)	PUNCT
ejpam-3996	188	65	)	)	PUNCT
ejpam-3996	189	1	∧	∧	PROPN
ejpam-3996	189	2	b	b	PROPN
ejpam-3996	189	3	∗	∗	X
ejpam-3996	189	4	(	(	PUNCT
ejpam-3996	189	5	0	0	NUM
ejpam-3996	189	6	∗	∗	NOUN
ejpam-3996	189	7	d	d	NOUN
ejpam-3996	189	8	)	)	PUNCT
ejpam-3996	189	9	]	]	PUNCT
ejpam-3996	190	1	i	i	NOUN
ejpam-3996	190	2	)	)	PUNCT
ejpam-3996	190	3	=	=	PRON
ejpam-3996	190	4	(	(	PUNCT
ejpam-3996	190	5	a	a	DET
ejpam-3996	190	6	∗	∗	NOUN
ejpam-3996	190	7	(	(	PUNCT
ejpam-3996	190	8	0	0	NUM
ejpam-3996	190	9	∗	∗	NOUN
ejpam-3996	190	10	c	c	NOUN
ejpam-3996	190	11	)	)	PUNCT
ejpam-3996	190	12	,	,	PUNCT
ejpam-3996	191	1	[	[	X
ejpam-3996	191	2	b	b	X
ejpam-3996	191	3	∗	∗	NOUN
ejpam-3996	191	4	(	(	PUNCT
ejpam-3996	191	5	0	0	NUM
ejpam-3996	191	6	∗	∗	NOUN
ejpam-3996	191	7	d)]i	d)]i	NOUN
ejpam-3996	191	8	)	)	PUNCT
ejpam-3996	191	9	=	=	PUNCT
ejpam-3996	191	10	(	(	PUNCT
ejpam-3996	191	11	c	c	NOUN
ejpam-3996	191	12	∗	∗	NOUN
ejpam-3996	191	13	(	(	PUNCT
ejpam-3996	191	14	0	0	NUM
ejpam-3996	191	15	∗	∗	NOUN
ejpam-3996	191	16	a	a	NOUN
ejpam-3996	191	17	)	)	PUNCT
ejpam-3996	191	18	,	,	PUNCT
ejpam-3996	192	1	[	[	X
ejpam-3996	192	2	d	d	X
ejpam-3996	192	3	∗	∗	X
ejpam-3996	192	4	(	(	PUNCT
ejpam-3996	192	5	0	0	NUM
ejpam-3996	192	6	∗	∗	NOUN
ejpam-3996	192	7	b)]i	b)]i	ADP
ejpam-3996	192	8	)	)	PUNCT
ejpam-3996	192	9	=	=	PUNCT
ejpam-3996	192	10	(	(	PUNCT
ejpam-3996	192	11	c	c	NOUN
ejpam-3996	192	12	∗	∗	NOUN
ejpam-3996	192	13	(	(	PUNCT
ejpam-3996	192	14	0	0	NUM
ejpam-3996	192	15	∗	∗	NOUN
ejpam-3996	192	16	a	a	NOUN
ejpam-3996	192	17	)	)	PUNCT
ejpam-3996	192	18	,	,	PUNCT
ejpam-3996	192	19	[	[	X
ejpam-3996	192	20	(	(	PUNCT
ejpam-3996	192	21	c	c	NOUN
ejpam-3996	192	22	∗	∗	X
ejpam-3996	192	23	(	(	PUNCT
ejpam-3996	192	24	0	0	NUM
ejpam-3996	192	25	∗	∗	NOUN
ejpam-3996	192	26	b	b	NOUN
ejpam-3996	192	27	)	)	PUNCT
ejpam-3996	192	28	∧	∧	PROPN
ejpam-3996	192	29	d	d	PROPN
ejpam-3996	192	30	∗	∗	NOUN
ejpam-3996	192	31	(	(	PUNCT
ejpam-3996	192	32	0	0	NUM
ejpam-3996	192	33	∗	∗	NOUN
ejpam-3996	192	34	a	a	NOUN
ejpam-3996	192	35	)	)	PUNCT
ejpam-3996	192	36	)	)	PUNCT
ejpam-3996	193	1	∧	∧	PROPN
ejpam-3996	193	2	d	d	PROPN
ejpam-3996	193	3	∗	∗	X
ejpam-3996	193	4	(	(	PUNCT
ejpam-3996	193	5	0	0	NUM
ejpam-3996	193	6	∗	∗	NUM
ejpam-3996	193	7	b	b	NOUN
ejpam-3996	193	8	)	)	PUNCT
ejpam-3996	193	9	]	]	PUNCT
ejpam-3996	194	1	i	i	NOUN
ejpam-3996	194	2	)	)	PUNCT
ejpam-3996	194	3	=	=	PUNCT
ejpam-3996	195	1	(	(	PUNCT
ejpam-3996	195	2	c	c	X
ejpam-3996	195	3	,	,	PUNCT
ejpam-3996	195	4	di	di	NOUN
ejpam-3996	195	5	)	)	PUNCT
ejpam-3996	195	6	·	·	PUNCT
ejpam-3996	196	1	(	(	PUNCT
ejpam-3996	196	2	0	0	NUM
ejpam-3996	196	3	∗	∗	NOUN
ejpam-3996	196	4	a	a	NOUN
ejpam-3996	196	5	,	,	PUNCT
ejpam-3996	196	6	(	(	PUNCT
ejpam-3996	196	7	0	0	NUM
ejpam-3996	196	8	∗	∗	NOUN
ejpam-3996	196	9	b)i	b)i	NOUN
ejpam-3996	196	10	)	)	PUNCT
ejpam-3996	197	1	=	=	SYM
ejpam-3996	197	2	(	(	PUNCT
ejpam-3996	197	3	c	c	X
ejpam-3996	197	4	,	,	PUNCT
ejpam-3996	197	5	di	di	NOUN
ejpam-3996	197	6	)	)	PUNCT
ejpam-3996	197	7	·	·	PUNCT
ejpam-3996	198	1	(	(	PUNCT
ejpam-3996	198	2	0	0	NUM
ejpam-3996	198	3	∗	∗	NOUN
ejpam-3996	198	4	a	a	NOUN
ejpam-3996	198	5	,	,	PUNCT
ejpam-3996	198	6	(	(	PUNCT
ejpam-3996	198	7	(	(	PUNCT
ejpam-3996	198	8	0	0	NUM
ejpam-3996	198	9	∗	∗	NOUN
ejpam-3996	198	10	b	b	X
ejpam-3996	198	11	∧	∧	PROPN
ejpam-3996	198	12	0	0	NUM
ejpam-3996	198	13	∗	∗	NOUN
ejpam-3996	198	14	a	a	NOUN
ejpam-3996	198	15	)	)	PUNCT
ejpam-3996	198	16	∧	∧	NOUN
ejpam-3996	198	17	0	0	NUM
ejpam-3996	198	18	∗	∗	NOUN
ejpam-3996	198	19	b)i	b)i	NOUN
ejpam-3996	198	20	)	)	PUNCT
ejpam-3996	199	1	=	=	SYM
ejpam-3996	199	2	(	(	PUNCT
ejpam-3996	199	3	c	c	X
ejpam-3996	199	4	,	,	PUNCT
ejpam-3996	199	5	di	di	NOUN
ejpam-3996	199	6	)	)	PUNCT
ejpam-3996	199	7	·	·	PUNCT
ejpam-3996	200	1	[	[	X
ejpam-3996	200	2	(	(	PUNCT
ejpam-3996	200	3	0	0	NUM
ejpam-3996	200	4	,	,	PUNCT
ejpam-3996	200	5	0i	0i	NOUN
ejpam-3996	200	6	)	)	PUNCT
ejpam-3996	200	7	·	·	PUNCT
ejpam-3996	201	1	(	(	PUNCT
ejpam-3996	201	2	a	a	DET
ejpam-3996	201	3	,	,	PUNCT
ejpam-3996	201	4	bi	bi	NOUN
ejpam-3996	201	5	)	)	PUNCT
ejpam-3996	201	6	]	]	PUNCT
ejpam-3996	201	7	.	.	PUNCT
ejpam-3996	202	1	therefore	therefore	ADV
ejpam-3996	202	2	,	,	PUNCT
ejpam-3996	202	3	x(i	x(i	PROPN
ejpam-3996	202	4	)	)	PUNCT
ejpam-3996	202	5	is	be	AUX
ejpam-3996	202	6	commutative	commutative	ADJ
ejpam-3996	202	7	.	.	PUNCT
ejpam-3996	203	1	conversely	conversely	ADV
ejpam-3996	203	2	,	,	PUNCT
ejpam-3996	203	3	suppose	suppose	VERB
ejpam-3996	203	4	that	that	SCONJ
ejpam-3996	203	5	x(i	x(i	PROPN
ejpam-3996	203	6	)	)	PUNCT
ejpam-3996	203	7	is	be	AUX
ejpam-3996	203	8	commutative	commutative	ADJ
ejpam-3996	203	9	.	.	PUNCT
ejpam-3996	204	1	then	then	ADV
ejpam-3996	204	2	by	by	ADP
ejpam-3996	204	3	remark	remark	NOUN
ejpam-3996	204	4	3.14	3.14	NUM
ejpam-3996	204	5	,	,	PUNCT
ejpam-3996	204	6	x	x	PUNCT
ejpam-3996	204	7	′	′	NOUN
ejpam-3996	204	8	is	be	AUX
ejpam-3996	204	9	commutative	commutative	ADJ
ejpam-3996	204	10	so	so	SCONJ
ejpam-3996	204	11	that	that	SCONJ
ejpam-3996	204	12	for	for	ADP
ejpam-3996	204	13	any	any	DET
ejpam-3996	204	14	(	(	PUNCT
ejpam-3996	204	15	x	x	NOUN
ejpam-3996	204	16	,	,	PUNCT
ejpam-3996	204	17	0i	0i	NOUN
ejpam-3996	204	18	)	)	PUNCT
ejpam-3996	204	19	,	,	PUNCT
ejpam-3996	204	20	(	(	PUNCT
ejpam-3996	204	21	y	y	PROPN
ejpam-3996	204	22	,	,	PUNCT
ejpam-3996	204	23	0i	0i	NOUN
ejpam-3996	204	24	)	)	PUNCT
ejpam-3996	204	25	∈	∈	PROPN
ejpam-3996	204	26	x	x	SYM
ejpam-3996	204	27	′	′	NOUN
ejpam-3996	204	28	,	,	PUNCT
ejpam-3996	204	29	x∗	x∗	X
ejpam-3996	204	30	(	(	PUNCT
ejpam-3996	204	31	0∗y	0∗y	NOUN
ejpam-3996	204	32	)	)	PUNCT
ejpam-3996	204	33	=	=	SYM
ejpam-3996	204	34	y	y	PROPN
ejpam-3996	204	35	∗	∗	NOUN
ejpam-3996	204	36	(	(	PUNCT
ejpam-3996	204	37	0∗x	0∗x	NOUN
ejpam-3996	204	38	)	)	PUNCT
ejpam-3996	204	39	for	for	ADP
ejpam-3996	204	40	any	any	DET
ejpam-3996	204	41	x	x	NOUN
ejpam-3996	204	42	,	,	PUNCT
ejpam-3996	204	43	y	y	PROPN
ejpam-3996	204	44	∈	∈	PROPN
ejpam-3996	204	45	x.	x.	NOUN
ejpam-3996	204	46	hence	hence	ADV
ejpam-3996	204	47	,	,	PUNCT
ejpam-3996	204	48	by	by	ADP
ejpam-3996	204	49	definition	definition	NOUN
ejpam-3996	204	50	2.5	2.5	NUM
ejpam-3996	204	51	,	,	PUNCT
ejpam-3996	204	52	x	x	X
ejpam-3996	204	53	is	be	AUX
ejpam-3996	204	54	commutative	commutative	ADJ
ejpam-3996	204	55	.	.	PUNCT
ejpam-3996	205	1	�	�	PROPN
ejpam-3996	205	2	corollary	corollary	PROPN
ejpam-3996	205	3	3.16	3.16	NUM
ejpam-3996	205	4	.	.	PUNCT
ejpam-3996	206	1	if	if	SCONJ
ejpam-3996	206	2	x(i	x(i	PROPN
ejpam-3996	206	3	)	)	PUNCT
ejpam-3996	206	4	is	be	AUX
ejpam-3996	206	5	commutative	commutative	ADJ
ejpam-3996	206	6	,	,	PUNCT
ejpam-3996	206	7	then	then	ADV
ejpam-3996	206	8	x(i	x(i	PROPN
ejpam-3996	206	9	)	)	PUNCT
ejpam-3996	206	10	is	be	AUX
ejpam-3996	206	11	a	a	DET
ejpam-3996	206	12	b	b	NOUN
ejpam-3996	206	13	-	-	PUNCT
ejpam-3996	206	14	algebra	algebra	NOUN
ejpam-3996	206	15	.	.	PUNCT
ejpam-3996	207	1	the	the	DET
ejpam-3996	207	2	notion	notion	NOUN
ejpam-3996	207	3	of	of	ADP
ejpam-3996	207	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	207	5	subalgebra	subalgebra	NOUN
ejpam-3996	207	6	of	of	ADP
ejpam-3996	207	7	a	a	DET
ejpam-3996	207	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	207	9	b	b	X
ejpam-3996	207	10	-	-	PUNCT
ejpam-3996	207	11	algebra	algebra	NOUN
ejpam-3996	207	12	will	will	AUX
ejpam-3996	207	13	now	now	ADV
ejpam-3996	207	14	be	be	AUX
ejpam-3996	207	15	introduced	introduce	VERB
ejpam-3996	207	16	.	.	PUNCT
ejpam-3996	208	1	d.o	d.o	PROPN
ejpam-3996	208	2	.	.	PROPN
ejpam-3996	208	3	jacobe	jacobe	PROPN
ejpam-3996	208	4	,	,	PUNCT
ejpam-3996	208	5	j.p	j.p	PROPN
ejpam-3996	208	6	.	.	PROPN
ejpam-3996	208	7	vilela	vilela	PROPN
ejpam-3996	208	8	/	/	SYM
ejpam-3996	208	9	eur	eur	PROPN
ejpam-3996	208	10	.	.	PUNCT
ejpam-3996	209	1	j.	j.	PROPN
ejpam-3996	209	2	pure	pure	PROPN
ejpam-3996	209	3	appl	appl	PROPN
ejpam-3996	209	4	.	.	PROPN
ejpam-3996	209	5	math	math	PROPN
ejpam-3996	209	6	,	,	PUNCT
ejpam-3996	209	7	14	14	NUM
ejpam-3996	209	8	(	(	PUNCT
ejpam-3996	209	9	3	3	NUM
ejpam-3996	209	10	)	)	PUNCT
ejpam-3996	209	11	(	(	PUNCT
ejpam-3996	209	12	2021	2021	NUM
ejpam-3996	209	13	)	)	PUNCT
ejpam-3996	209	14	,	,	PUNCT
ejpam-3996	209	15	895	895	NUM
ejpam-3996	209	16	-	-	SYM
ejpam-3996	209	17	904	904	NUM
ejpam-3996	209	18	900	900	NUM
ejpam-3996	209	19	definition	definition	NOUN
ejpam-3996	209	20	3.17	3.17	NUM
ejpam-3996	209	21	.	.	PUNCT
ejpam-3996	210	1	let	let	VERB
ejpam-3996	210	2	x(i	x(i	PROPN
ejpam-3996	210	3	)	)	PUNCT
ejpam-3996	210	4	be	be	AUX
ejpam-3996	210	5	a	a	DET
ejpam-3996	210	6	neutrosophic	neutrosophic	ADJ
ejpam-3996	210	7	b	b	X
ejpam-3996	210	8	-	-	PUNCT
ejpam-3996	210	9	algebra	algebra	NOUN
ejpam-3996	210	10	.	.	PUNCT
ejpam-3996	211	1	a	a	DET
ejpam-3996	211	2	subset	subset	NOUN
ejpam-3996	211	3	p	p	X
ejpam-3996	211	4	(	(	PUNCT
ejpam-3996	211	5	i	i	NOUN
ejpam-3996	211	6	)	)	PUNCT
ejpam-3996	211	7	of	of	ADP
ejpam-3996	211	8	x(i	x(i	PROPN
ejpam-3996	211	9	)	)	PUNCT
ejpam-3996	211	10	is	be	AUX
ejpam-3996	211	11	said	say	VERB
ejpam-3996	211	12	to	to	PART
ejpam-3996	211	13	be	be	AUX
ejpam-3996	211	14	a	a	DET
ejpam-3996	211	15	proper	proper	ADJ
ejpam-3996	211	16	subset	subset	NOUN
ejpam-3996	211	17	of	of	ADP
ejpam-3996	211	18	x(i	x(i	PROPN
ejpam-3996	211	19	)	)	PUNCT
ejpam-3996	211	20	if	if	SCONJ
ejpam-3996	211	21	p	p	PROPN
ejpam-3996	211	22	(	(	PUNCT
ejpam-3996	211	23	i	i	NOUN
ejpam-3996	211	24	)	)	PUNCT
ejpam-3996	211	25	6=	6=	PROPN
ejpam-3996	211	26	x(i	x(i	PROPN
ejpam-3996	211	27	)	)	PUNCT
ejpam-3996	211	28	.	.	PUNCT
ejpam-3996	212	1	definition	definition	NOUN
ejpam-3996	212	2	3.18	3.18	NUM
ejpam-3996	212	3	.	.	PUNCT
ejpam-3996	213	1	a	a	DET
ejpam-3996	213	2	nonempty	nonempty	NOUN
ejpam-3996	213	3	subset	subset	VERB
ejpam-3996	213	4	s(i	s(i	PROPN
ejpam-3996	213	5	)	)	PUNCT
ejpam-3996	213	6	of	of	ADP
ejpam-3996	213	7	a	a	DET
ejpam-3996	213	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	213	9	b	b	X
ejpam-3996	213	10	-	-	PUNCT
ejpam-3996	213	11	algebra	algebra	NOUN
ejpam-3996	213	12	x(i	x(i	PROPN
ejpam-3996	213	13	)	)	PUNCT
ejpam-3996	213	14	is	be	AUX
ejpam-3996	213	15	said	say	VERB
ejpam-3996	213	16	to	to	PART
ejpam-3996	213	17	be	be	AUX
ejpam-3996	213	18	a	a	DET
ejpam-3996	213	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	213	20	subalgebra	subalgebra	NOUN
ejpam-3996	213	21	of	of	ADP
ejpam-3996	213	22	x(i	x(i	PROPN
ejpam-3996	213	23	)	)	PUNCT
ejpam-3996	213	24	if	if	SCONJ
ejpam-3996	213	25	the	the	DET
ejpam-3996	213	26	following	follow	VERB
ejpam-3996	213	27	conditions	condition	NOUN
ejpam-3996	213	28	hold	hold	VERB
ejpam-3996	213	29	:	:	PUNCT
ejpam-3996	213	30	(	(	PUNCT
ejpam-3996	213	31	i	i	NOUN
ejpam-3996	213	32	)	)	PUNCT
ejpam-3996	213	33	(	(	PUNCT
ejpam-3996	213	34	a	a	DET
ejpam-3996	213	35	,	,	PUNCT
ejpam-3996	213	36	bi	bi	NOUN
ejpam-3996	213	37	)	)	PUNCT
ejpam-3996	213	38	·	·	PUNCT
ejpam-3996	214	1	(	(	PUNCT
ejpam-3996	214	2	c	c	X
ejpam-3996	214	3	,	,	PUNCT
ejpam-3996	214	4	di	di	NOUN
ejpam-3996	214	5	)	)	PUNCT
ejpam-3996	214	6	∈	∈	PROPN
ejpam-3996	214	7	s(i	s(i	PROPN
ejpam-3996	214	8	)	)	PUNCT
ejpam-3996	214	9	for	for	ADP
ejpam-3996	214	10	all	all	PRON
ejpam-3996	214	11	(	(	PUNCT
ejpam-3996	214	12	a	a	PRON
ejpam-3996	214	13	,	,	PUNCT
ejpam-3996	214	14	bi	bi	NOUN
ejpam-3996	214	15	)	)	PUNCT
ejpam-3996	214	16	,	,	PUNCT
ejpam-3996	214	17	(	(	PUNCT
ejpam-3996	214	18	c	c	X
ejpam-3996	214	19	,	,	PUNCT
ejpam-3996	214	20	di	di	NOUN
ejpam-3996	214	21	)	)	PUNCT
ejpam-3996	214	22	∈	∈	PROPN
ejpam-3996	214	23	s(i	s(i	PROPN
ejpam-3996	214	24	)	)	PUNCT
ejpam-3996	214	25	,	,	PUNCT
ejpam-3996	214	26	and	and	CCONJ
ejpam-3996	214	27	(	(	PUNCT
ejpam-3996	214	28	ii	ii	NOUN
ejpam-3996	214	29	)	)	PUNCT
ejpam-3996	214	30	s(i	s(i	PROPN
ejpam-3996	214	31	)	)	PUNCT
ejpam-3996	214	32	contains	contain	VERB
ejpam-3996	214	33	a	a	DET
ejpam-3996	214	34	proper	proper	ADJ
ejpam-3996	214	35	subset	subset	NOUN
ejpam-3996	214	36	which	which	PRON
ejpam-3996	214	37	is	be	AUX
ejpam-3996	214	38	a	a	DET
ejpam-3996	214	39	b	b	NOUN
ejpam-3996	214	40	-	-	PUNCT
ejpam-3996	214	41	algebra	algebra	NOUN
ejpam-3996	214	42	.	.	PUNCT
ejpam-3996	215	1	in	in	ADP
ejpam-3996	215	2	view	view	NOUN
ejpam-3996	215	3	of	of	ADP
ejpam-3996	215	4	lemma	lemma	PROPN
ejpam-3996	215	5	3.8(iv	3.8(iv	NUM
ejpam-3996	215	6	)	)	PUNCT
ejpam-3996	215	7	,	,	PUNCT
ejpam-3996	215	8	(	(	PUNCT
ejpam-3996	215	9	0	0	NUM
ejpam-3996	215	10	,	,	PUNCT
ejpam-3996	215	11	0i	0i	NUM
ejpam-3996	215	12	)	)	PUNCT
ejpam-3996	215	13	is	be	AUX
ejpam-3996	215	14	an	an	DET
ejpam-3996	215	15	element	element	NOUN
ejpam-3996	215	16	of	of	ADP
ejpam-3996	215	17	any	any	DET
ejpam-3996	215	18	neutrosophic	neutrosophic	ADJ
ejpam-3996	215	19	subalgebra	subalgebra	NOUN
ejpam-3996	215	20	s(i	s(i	PROPN
ejpam-3996	215	21	)	)	PUNCT
ejpam-3996	215	22	of	of	ADP
ejpam-3996	215	23	x(i	x(i	PROPN
ejpam-3996	215	24	)	)	PUNCT
ejpam-3996	215	25	.	.	PUNCT
ejpam-3996	216	1	remark	remark	PROPN
ejpam-3996	216	2	3.19	3.19	NUM
ejpam-3996	216	3	.	.	PUNCT
ejpam-3996	217	1	let	let	VERB
ejpam-3996	217	2	x(i	x(i	PROPN
ejpam-3996	217	3	)	)	PUNCT
ejpam-3996	217	4	be	be	AUX
ejpam-3996	217	5	a	a	DET
ejpam-3996	217	6	nonzero	nonzero	ADJ
ejpam-3996	217	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	217	8	b	b	X
ejpam-3996	217	9	-	-	PUNCT
ejpam-3996	217	10	algebra	algebra	NOUN
ejpam-3996	217	11	.	.	PUNCT
ejpam-3996	218	1	(	(	PUNCT
ejpam-3996	218	2	i	i	NOUN
ejpam-3996	218	3	)	)	PUNCT
ejpam-3996	218	4	then	then	ADV
ejpam-3996	218	5	x(i	x(i	PROPN
ejpam-3996	218	6	)	)	PUNCT
ejpam-3996	218	7	is	be	AUX
ejpam-3996	218	8	a	a	DET
ejpam-3996	218	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	218	10	subalgebra	subalgebra	NOUN
ejpam-3996	218	11	of	of	ADP
ejpam-3996	218	12	itself	itself	PRON
ejpam-3996	218	13	.	.	PUNCT
ejpam-3996	219	1	however	however	ADV
ejpam-3996	219	2	,	,	PUNCT
ejpam-3996	219	3	{	{	PUNCT
ejpam-3996	219	4	(	(	PUNCT
ejpam-3996	219	5	0	0	NUM
ejpam-3996	219	6	,	,	PUNCT
ejpam-3996	219	7	0i	0i	NOUN
ejpam-3996	219	8	)	)	PUNCT
ejpam-3996	219	9	}	}	PUNCT
ejpam-3996	219	10	is	be	AUX
ejpam-3996	219	11	not	not	PART
ejpam-3996	219	12	a	a	DET
ejpam-3996	219	13	neutrosophic	neutrosophic	ADJ
ejpam-3996	219	14	subalgebra	subalgebra	NOUN
ejpam-3996	219	15	of	of	ADP
ejpam-3996	219	16	x(i	x(i	PROPN
ejpam-3996	219	17	)	)	PUNCT
ejpam-3996	219	18	since	since	SCONJ
ejpam-3996	219	19	it	it	PRON
ejpam-3996	219	20	does	do	AUX
ejpam-3996	219	21	contain	contain	VERB
ejpam-3996	219	22	a	a	DET
ejpam-3996	219	23	proper	proper	ADJ
ejpam-3996	219	24	subset	subset	NOUN
ejpam-3996	219	25	which	which	PRON
ejpam-3996	219	26	is	be	AUX
ejpam-3996	219	27	a	a	DET
ejpam-3996	219	28	b	b	NOUN
ejpam-3996	219	29	-	-	PUNCT
ejpam-3996	219	30	algebra	algebra	NOUN
ejpam-3996	219	31	but	but	CCONJ
ejpam-3996	219	32	{	{	PUNCT
ejpam-3996	219	33	(	(	PUNCT
ejpam-3996	219	34	0	0	NUM
ejpam-3996	219	35	,	,	PUNCT
ejpam-3996	219	36	0i	0i	NOUN
ejpam-3996	219	37	)	)	PUNCT
ejpam-3996	219	38	}	}	PUNCT
ejpam-3996	219	39	is	be	AUX
ejpam-3996	219	40	a	a	DET
ejpam-3996	219	41	b	b	NOUN
ejpam-3996	219	42	-	-	PUNCT
ejpam-3996	219	43	algebra	algebra	NOUN
ejpam-3996	219	44	.	.	PUNCT
ejpam-3996	220	1	(	(	PUNCT
ejpam-3996	220	2	ii	ii	NOUN
ejpam-3996	220	3	)	)	PUNCT
ejpam-3996	220	4	if	if	SCONJ
ejpam-3996	220	5	s(i	s(i	PROPN
ejpam-3996	220	6	)	)	PUNCT
ejpam-3996	220	7	is	be	AUX
ejpam-3996	220	8	a	a	DET
ejpam-3996	220	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	220	10	subalgebra	subalgebra	NOUN
ejpam-3996	220	11	of	of	ADP
ejpam-3996	220	12	x(i	x(i	PROPN
ejpam-3996	220	13	)	)	PUNCT
ejpam-3996	220	14	,	,	PUNCT
ejpam-3996	220	15	then	then	ADV
ejpam-3996	220	16	s(i	s(i	PROPN
ejpam-3996	220	17	)	)	PUNCT
ejpam-3996	221	1	is	be	AUX
ejpam-3996	221	2	a	a	DET
ejpam-3996	221	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	221	4	b	b	X
ejpam-3996	221	5	-	-	PUNCT
ejpam-3996	221	6	algebra	algebra	NOUN
ejpam-3996	221	7	in	in	ADP
ejpam-3996	221	8	its	its	PRON
ejpam-3996	221	9	own	own	ADJ
ejpam-3996	221	10	right	right	NOUN
ejpam-3996	221	11	.	.	PUNCT
ejpam-3996	222	1	theorem	theorem	VERB
ejpam-3996	222	2	3.20	3.20	NUM
ejpam-3996	222	3	.	.	PUNCT
ejpam-3996	223	1	let	let	VERB
ejpam-3996	223	2	x(i	x(i	PROPN
ejpam-3996	223	3	)	)	PUNCT
ejpam-3996	223	4	be	be	AUX
ejpam-3996	223	5	a	a	DET
ejpam-3996	223	6	nonzero	nonzero	ADJ
ejpam-3996	223	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	223	8	b	b	X
ejpam-3996	223	9	-	-	PUNCT
ejpam-3996	223	10	algebra	algebra	NOUN
ejpam-3996	223	11	.	.	PUNCT
ejpam-3996	224	1	then	then	ADV
ejpam-3996	224	2	(	(	PUNCT
ejpam-3996	224	3	i	i	NOUN
ejpam-3996	224	4	)	)	PUNCT
ejpam-3996	224	5	x	x	PUNCT
ejpam-3996	225	1	′	′	NUM
ejpam-3996	225	2	=	=	SYM
ejpam-3996	225	3	{	{	PUNCT
ejpam-3996	225	4	(	(	PUNCT
ejpam-3996	225	5	x	x	X
ejpam-3996	225	6	,	,	PUNCT
ejpam-3996	225	7	0i	0i	NUM
ejpam-3996	225	8	)	)	PUNCT
ejpam-3996	225	9	:	:	PUNCT
ejpam-3996	226	1	x	x	X
ejpam-3996	226	2	∈	∈	NOUN
ejpam-3996	226	3	x	x	PRON
ejpam-3996	226	4	}	}	PUNCT
ejpam-3996	226	5	is	be	AUX
ejpam-3996	226	6	a	a	DET
ejpam-3996	226	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	226	8	subalgebra	subalgebra	NOUN
ejpam-3996	226	9	of	of	ADP
ejpam-3996	226	10	x(i	x(i	PROPN
ejpam-3996	226	11	)	)	PUNCT
ejpam-3996	226	12	.	.	PUNCT
ejpam-3996	227	1	(	(	PUNCT
ejpam-3996	227	2	ii	ii	NOUN
ejpam-3996	227	3	)	)	PUNCT
ejpam-3996	227	4	x	x	X
ejpam-3996	228	1	′′	′′	NOUN
ejpam-3996	228	2	=	=	PRON
ejpam-3996	228	3	{	{	PUNCT
ejpam-3996	228	4	(	(	PUNCT
ejpam-3996	228	5	0	0	NUM
ejpam-3996	228	6	,	,	PUNCT
ejpam-3996	228	7	xi	xi	PROPN
ejpam-3996	228	8	)	)	PUNCT
ejpam-3996	228	9	:	:	PUNCT
ejpam-3996	228	10	x	x	X
ejpam-3996	228	11	∈	∈	NOUN
ejpam-3996	228	12	x	x	PRON
ejpam-3996	228	13	}	}	PUNCT
ejpam-3996	228	14	is	be	AUX
ejpam-3996	228	15	a	a	DET
ejpam-3996	228	16	neutrosophic	neutrosophic	ADJ
ejpam-3996	228	17	subalgebra	subalgebra	NOUN
ejpam-3996	228	18	of	of	ADP
ejpam-3996	228	19	x(i	x(i	PROPN
ejpam-3996	228	20	)	)	PUNCT
ejpam-3996	228	21	.	.	PUNCT
ejpam-3996	229	1	(	(	PUNCT
ejpam-3996	229	2	iii	iii	NOUN
ejpam-3996	229	3	)	)	PUNCT
ejpam-3996	229	4	xω(i	xω(i	PUNCT
ejpam-3996	229	5	)	)	PUNCT
ejpam-3996	230	1	=	=	PRON
ejpam-3996	230	2	{	{	PUNCT
ejpam-3996	230	3	(	(	PUNCT
ejpam-3996	230	4	a	a	PRON
ejpam-3996	230	5	,	,	PUNCT
ejpam-3996	230	6	ai	ai	NOUN
ejpam-3996	230	7	)	)	PUNCT
ejpam-3996	230	8	:	:	PUNCT
ejpam-3996	230	9	a	a	DET
ejpam-3996	230	10	∈	∈	PROPN
ejpam-3996	230	11	x	x	PRON
ejpam-3996	230	12	}	}	PUNCT
ejpam-3996	230	13	is	be	AUX
ejpam-3996	230	14	a	a	DET
ejpam-3996	230	15	neutrosophic	neutrosophic	ADJ
ejpam-3996	230	16	subalgebra	subalgebra	NOUN
ejpam-3996	230	17	of	of	ADP
ejpam-3996	230	18	x(i	x(i	PROPN
ejpam-3996	230	19	)	)	PUNCT
ejpam-3996	230	20	.	.	PUNCT
ejpam-3996	231	1	proof	proof	NOUN
ejpam-3996	231	2	:	:	PUNCT
ejpam-3996	231	3	(	(	PUNCT
ejpam-3996	231	4	i	i	NOUN
ejpam-3996	231	5	)	)	PUNCT
ejpam-3996	231	6	clearly	clearly	ADV
ejpam-3996	231	7	,	,	PUNCT
ejpam-3996	231	8	(	(	PUNCT
ejpam-3996	231	9	0	0	NUM
ejpam-3996	231	10	,	,	PUNCT
ejpam-3996	231	11	0i	0i	NOUN
ejpam-3996	231	12	)	)	PUNCT
ejpam-3996	232	1	∈	∈	PROPN
ejpam-3996	232	2	x	x	NOUN
ejpam-3996	232	3	′.	′.	NOUN
ejpam-3996	232	4	suppose	suppose	VERB
ejpam-3996	232	5	that(a	that(a	PROPN
ejpam-3996	232	6	,	,	PUNCT
ejpam-3996	232	7	0i	0i	NOUN
ejpam-3996	232	8	)	)	PUNCT
ejpam-3996	232	9	,	,	PUNCT
ejpam-3996	232	10	(	(	PUNCT
ejpam-3996	232	11	b	b	X
ejpam-3996	232	12	,	,	PUNCT
ejpam-3996	232	13	0i	0i	NOUN
ejpam-3996	232	14	)	)	PUNCT
ejpam-3996	233	1	∈	∈	PROPN
ejpam-3996	233	2	x	x	NOUN
ejpam-3996	233	3	′.	′.	NOUN
ejpam-3996	233	4	then	then	ADV
ejpam-3996	233	5	by	by	ADP
ejpam-3996	233	6	remark	remark	NOUN
ejpam-3996	233	7	3.5	3.5	NUM
ejpam-3996	233	8	,	,	PUNCT
ejpam-3996	233	9	(	(	PUNCT
ejpam-3996	233	10	a	a	PRON
ejpam-3996	233	11	,	,	PUNCT
ejpam-3996	233	12	0i	0i	NOUN
ejpam-3996	233	13	)	)	PUNCT
ejpam-3996	233	14	·	·	PUNCT
ejpam-3996	234	1	(	(	PUNCT
ejpam-3996	234	2	b	b	X
ejpam-3996	234	3	,	,	PUNCT
ejpam-3996	234	4	0i	0i	NOUN
ejpam-3996	234	5	)	)	PUNCT
ejpam-3996	235	1	∈	∈	PROPN
ejpam-3996	235	2	x	x	NOUN
ejpam-3996	235	3	′.	′.	NOUN
ejpam-3996	235	4	moreover	moreover	ADV
ejpam-3996	235	5	,	,	PUNCT
ejpam-3996	235	6	{	{	PUNCT
ejpam-3996	235	7	(	(	PUNCT
ejpam-3996	235	8	0	0	NUM
ejpam-3996	235	9	,	,	PUNCT
ejpam-3996	235	10	0i	0i	NOUN
ejpam-3996	235	11	)	)	PUNCT
ejpam-3996	235	12	}	}	PUNCT
ejpam-3996	235	13	(	(	PUNCT
ejpam-3996	235	14	x	x	X
ejpam-3996	235	15	′	′	NOUN
ejpam-3996	235	16	is	be	AUX
ejpam-3996	235	17	a	a	DET
ejpam-3996	235	18	b	b	NOUN
ejpam-3996	235	19	-	-	PUNCT
ejpam-3996	235	20	algebra	algebra	NOUN
ejpam-3996	235	21	.	.	PUNCT
ejpam-3996	236	1	hence	hence	ADV
ejpam-3996	236	2	,	,	PUNCT
ejpam-3996	236	3	x	x	PUNCT
ejpam-3996	236	4	′	′	NOUN
ejpam-3996	236	5	is	be	AUX
ejpam-3996	236	6	a	a	DET
ejpam-3996	236	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	236	8	subalgebra	subalgebra	NOUN
ejpam-3996	236	9	of	of	ADP
ejpam-3996	236	10	x(i	x(i	PROPN
ejpam-3996	236	11	)	)	PUNCT
ejpam-3996	236	12	.	.	PUNCT
ejpam-3996	237	1	(	(	PUNCT
ejpam-3996	237	2	ii	ii	NOUN
ejpam-3996	237	3	)	)	PUNCT
ejpam-3996	237	4	clearly	clearly	ADV
ejpam-3996	237	5	,	,	PUNCT
ejpam-3996	237	6	(	(	PUNCT
ejpam-3996	237	7	0	0	NUM
ejpam-3996	237	8	,	,	PUNCT
ejpam-3996	237	9	0i	0i	NOUN
ejpam-3996	237	10	)	)	PUNCT
ejpam-3996	238	1	∈	∈	PROPN
ejpam-3996	238	2	x	x	PUNCT
ejpam-3996	238	3	′′.	′′.	PROPN
ejpam-3996	238	4	suppose	suppose	VERB
ejpam-3996	238	5	that(0	that(0	PROPN
ejpam-3996	238	6	,	,	PUNCT
ejpam-3996	238	7	ai	ai	VERB
ejpam-3996	238	8	)	)	PUNCT
ejpam-3996	238	9	,	,	PUNCT
ejpam-3996	238	10	(	(	PUNCT
ejpam-3996	238	11	0	0	NUM
ejpam-3996	238	12	,	,	PUNCT
ejpam-3996	238	13	bi	bi	ADJ
ejpam-3996	238	14	)	)	PUNCT
ejpam-3996	238	15	∈	∈	NOUN
ejpam-3996	238	16	x	x	PUNCT
ejpam-3996	238	17	′′.	′′.	NOUN
ejpam-3996	238	18	then	then	ADV
ejpam-3996	238	19	a	a	PRON
ejpam-3996	238	20	,	,	PUNCT
ejpam-3996	238	21	b	b	X
ejpam-3996	238	22	∈	∈	PROPN
ejpam-3996	238	23	x	x	X
ejpam-3996	238	24	and	and	CCONJ
ejpam-3996	238	25	(	(	PUNCT
ejpam-3996	238	26	0	0	NUM
ejpam-3996	238	27	,	,	PUNCT
ejpam-3996	238	28	ai	ai	VERB
ejpam-3996	238	29	)	)	PUNCT
ejpam-3996	238	30	·	·	PUNCT
ejpam-3996	238	31	(	(	PUNCT
ejpam-3996	238	32	0	0	NUM
ejpam-3996	238	33	,	,	PUNCT
ejpam-3996	238	34	bi	bi	NOUN
ejpam-3996	238	35	)	)	PUNCT
ejpam-3996	238	36	=	=	SYM
ejpam-3996	238	37	(	(	PUNCT
ejpam-3996	238	38	0	0	NUM
ejpam-3996	238	39	,	,	PUNCT
ejpam-3996	238	40	(	(	PUNCT
ejpam-3996	238	41	(	(	PUNCT
ejpam-3996	238	42	0	0	NUM
ejpam-3996	238	43	∗	∗	NOUN
ejpam-3996	238	44	b	b	NOUN
ejpam-3996	238	45	∧	∧	PROPN
ejpam-3996	238	46	a	a	DET
ejpam-3996	238	47	∗	∗	NOUN
ejpam-3996	238	48	0	0	NUM
ejpam-3996	238	49	)	)	PUNCT
ejpam-3996	238	50	∧	∧	NOUN
ejpam-3996	238	51	a	a	DET
ejpam-3996	238	52	∗	∗	NOUN
ejpam-3996	238	53	b)i	b)i	NOUN
ejpam-3996	238	54	)	)	PUNCT
ejpam-3996	238	55	.	.	PUNCT
ejpam-3996	239	1	since	since	SCONJ
ejpam-3996	239	2	x	x	PRON
ejpam-3996	239	3	is	be	AUX
ejpam-3996	239	4	a	a	DET
ejpam-3996	239	5	b	b	NOUN
ejpam-3996	239	6	-	-	PUNCT
ejpam-3996	239	7	algebra	algebra	NOUN
ejpam-3996	239	8	,	,	PUNCT
ejpam-3996	239	9	(	(	PUNCT
ejpam-3996	239	10	0	0	NUM
ejpam-3996	239	11	∗	∗	NOUN
ejpam-3996	239	12	b	b	NOUN
ejpam-3996	239	13	∧	∧	PROPN
ejpam-3996	239	14	a	a	DET
ejpam-3996	239	15	∗	∗	NOUN
ejpam-3996	239	16	0	0	NUM
ejpam-3996	239	17	)	)	PUNCT
ejpam-3996	239	18	∧	∧	NOUN
ejpam-3996	239	19	a	a	DET
ejpam-3996	239	20	∗	∗	NOUN
ejpam-3996	239	21	b	b	NOUN
ejpam-3996	239	22	∈	∈	PROPN
ejpam-3996	239	23	x	x	X
ejpam-3996	239	24	and	and	CCONJ
ejpam-3996	239	25	so	so	ADV
ejpam-3996	239	26	(	(	PUNCT
ejpam-3996	239	27	0	0	NUM
ejpam-3996	239	28	,	,	PUNCT
ejpam-3996	239	29	ai	ai	VERB
ejpam-3996	239	30	)	)	PUNCT
ejpam-3996	239	31	·	·	PUNCT
ejpam-3996	240	1	(	(	PUNCT
ejpam-3996	240	2	0	0	NUM
ejpam-3996	240	3	,	,	PUNCT
ejpam-3996	240	4	bi	bi	NOUN
ejpam-3996	240	5	)	)	PUNCT
ejpam-3996	240	6	=	=	SYM
ejpam-3996	241	1	(	(	PUNCT
ejpam-3996	241	2	0	0	NUM
ejpam-3996	241	3	,	,	PUNCT
ejpam-3996	241	4	(	(	PUNCT
ejpam-3996	241	5	(	(	PUNCT
ejpam-3996	241	6	0	0	NUM
ejpam-3996	241	7	∗	∗	NOUN
ejpam-3996	241	8	b	b	NOUN
ejpam-3996	241	9	∧	∧	PROPN
ejpam-3996	242	1	a	a	DET
ejpam-3996	242	2	∗	∗	NOUN
ejpam-3996	242	3	0	0	NUM
ejpam-3996	242	4	)	)	PUNCT
ejpam-3996	242	5	∧	∧	NOUN
ejpam-3996	242	6	a	a	DET
ejpam-3996	242	7	∗	∗	NOUN
ejpam-3996	242	8	b)i	b)i	NOUN
ejpam-3996	242	9	)	)	PUNCT
ejpam-3996	242	10	∈	∈	NOUN
ejpam-3996	243	1	x	x	PUNCT
ejpam-3996	243	2	′′.	′′.	PROPN
ejpam-3996	243	3	moreover	moreover	ADV
ejpam-3996	243	4	,	,	PUNCT
ejpam-3996	243	5	{	{	PUNCT
ejpam-3996	243	6	(	(	PUNCT
ejpam-3996	243	7	0	0	NUM
ejpam-3996	243	8	,	,	PUNCT
ejpam-3996	243	9	0i	0i	NOUN
ejpam-3996	243	10	)	)	PUNCT
ejpam-3996	243	11	}	}	PUNCT
ejpam-3996	244	1	(	(	PUNCT
ejpam-3996	244	2	x	x	X
ejpam-3996	244	3	′′	′′	PROPN
ejpam-3996	244	4	is	be	AUX
ejpam-3996	244	5	a	a	DET
ejpam-3996	244	6	b	b	NOUN
ejpam-3996	244	7	-	-	PUNCT
ejpam-3996	244	8	algebra	algebra	NOUN
ejpam-3996	244	9	.	.	PUNCT
ejpam-3996	245	1	therefore	therefore	ADV
ejpam-3996	245	2	,	,	PUNCT
ejpam-3996	245	3	x	x	X
ejpam-3996	245	4	′′	′′	PROPN
ejpam-3996	245	5	is	be	AUX
ejpam-3996	245	6	a	a	DET
ejpam-3996	245	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	245	8	subalgebra	subalgebra	NOUN
ejpam-3996	245	9	of	of	ADP
ejpam-3996	245	10	x(i	x(i	PROPN
ejpam-3996	245	11	)	)	PUNCT
ejpam-3996	245	12	.	.	PUNCT
ejpam-3996	246	1	(	(	PUNCT
ejpam-3996	246	2	iii	iii	X
ejpam-3996	246	3	)	)	PUNCT
ejpam-3996	246	4	clearly	clearly	ADV
ejpam-3996	246	5	,	,	PUNCT
ejpam-3996	246	6	(	(	PUNCT
ejpam-3996	246	7	0	0	NUM
ejpam-3996	246	8	,	,	PUNCT
ejpam-3996	246	9	0i	0i	NOUN
ejpam-3996	246	10	)	)	PUNCT
ejpam-3996	246	11	∈	∈	PROPN
ejpam-3996	246	12	xω(i	xω(i	NUM
ejpam-3996	246	13	)	)	PUNCT
ejpam-3996	246	14	and	and	CCONJ
ejpam-3996	246	15	{	{	PUNCT
ejpam-3996	246	16	(	(	PUNCT
ejpam-3996	246	17	0	0	NUM
ejpam-3996	246	18	,	,	PUNCT
ejpam-3996	246	19	0i	0i	NOUN
ejpam-3996	246	20	)	)	PUNCT
ejpam-3996	246	21	}	}	PUNCT
ejpam-3996	246	22	(	(	PUNCT
ejpam-3996	246	23	xω(i	xω(i	NUM
ejpam-3996	246	24	)	)	PUNCT
ejpam-3996	246	25	.	.	PUNCT
ejpam-3996	247	1	let	let	VERB
ejpam-3996	247	2	(	(	PUNCT
ejpam-3996	247	3	a	a	DET
ejpam-3996	247	4	,	,	PUNCT
ejpam-3996	247	5	ai	ai	NOUN
ejpam-3996	247	6	)	)	PUNCT
ejpam-3996	247	7	,	,	PUNCT
ejpam-3996	247	8	(	(	PUNCT
ejpam-3996	247	9	b	b	X
ejpam-3996	247	10	,	,	PUNCT
ejpam-3996	247	11	bi	bi	ADJ
ejpam-3996	247	12	)	)	PUNCT
ejpam-3996	247	13	∈	∈	PROPN
ejpam-3996	247	14	xω(i	xω(i	NUM
ejpam-3996	247	15	)	)	PUNCT
ejpam-3996	247	16	.	.	PUNCT
ejpam-3996	248	1	then	then	ADV
ejpam-3996	248	2	by	by	ADP
ejpam-3996	248	3	lemma	lemma	PROPN
ejpam-3996	248	4	3.8(iii	3.8(iii	NUM
ejpam-3996	248	5	)	)	PUNCT
ejpam-3996	248	6	,	,	PUNCT
ejpam-3996	248	7	(	(	PUNCT
ejpam-3996	248	8	a	a	DET
ejpam-3996	248	9	,	,	PUNCT
ejpam-3996	248	10	ai	ai	NOUN
ejpam-3996	248	11	)	)	PUNCT
ejpam-3996	248	12	·	·	PUNCT
ejpam-3996	249	1	(	(	PUNCT
ejpam-3996	249	2	b	b	X
ejpam-3996	249	3	,	,	PUNCT
ejpam-3996	249	4	bi	bi	NOUN
ejpam-3996	249	5	)	)	PUNCT
ejpam-3996	249	6	=	=	SYM
ejpam-3996	249	7	(	(	PUNCT
ejpam-3996	249	8	a	a	DET
ejpam-3996	249	9	∗	∗	NOUN
ejpam-3996	249	10	b	b	NOUN
ejpam-3996	249	11	,	,	PUNCT
ejpam-3996	249	12	(	(	PUNCT
ejpam-3996	249	13	a	a	DET
ejpam-3996	249	14	∗	∗	X
ejpam-3996	249	15	b)i	b)i	NOUN
ejpam-3996	249	16	)	)	PUNCT
ejpam-3996	249	17	∈	∈	PROPN
ejpam-3996	249	18	xω(i	xω(i	NUM
ejpam-3996	249	19	)	)	PUNCT
ejpam-3996	249	20	.	.	PUNCT
ejpam-3996	250	1	therefore	therefore	ADV
ejpam-3996	250	2	,	,	PUNCT
ejpam-3996	250	3	xω(i	xω(i	PUNCT
ejpam-3996	250	4	)	)	PUNCT
ejpam-3996	250	5	is	be	AUX
ejpam-3996	250	6	a	a	DET
ejpam-3996	250	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	250	8	subalgebra	subalgebra	NOUN
ejpam-3996	250	9	of	of	ADP
ejpam-3996	250	10	x(i	x(i	PROPN
ejpam-3996	250	11	)	)	PUNCT
ejpam-3996	250	12	.	.	PUNCT
ejpam-3996	251	1	�	�	PROPN
ejpam-3996	251	2	definition	definition	NOUN
ejpam-3996	251	3	3.21	3.21	NUM
ejpam-3996	251	4	.	.	PUNCT
ejpam-3996	252	1	a	a	DET
ejpam-3996	252	2	neutrosophic	neutrosophic	ADJ
ejpam-3996	252	3	subalgebra	subalgebra	NOUN
ejpam-3996	252	4	n(i	n(i	PROPN
ejpam-3996	252	5	)	)	PUNCT
ejpam-3996	252	6	of	of	ADP
ejpam-3996	252	7	x(i	x(i	PROPN
ejpam-3996	252	8	)	)	PUNCT
ejpam-3996	252	9	is	be	AUX
ejpam-3996	252	10	normal	normal	ADJ
ejpam-3996	252	11	if	if	SCONJ
ejpam-3996	252	12	for	for	ADP
ejpam-3996	252	13	any	any	DET
ejpam-3996	252	14	(	(	PUNCT
ejpam-3996	252	15	a	a	PRON
ejpam-3996	252	16	,	,	PUNCT
ejpam-3996	252	17	bi	bi	NOUN
ejpam-3996	252	18	)	)	PUNCT
ejpam-3996	252	19	·	·	PUNCT
ejpam-3996	253	1	(	(	PUNCT
ejpam-3996	253	2	c	c	X
ejpam-3996	253	3	,	,	PUNCT
ejpam-3996	253	4	di	di	NOUN
ejpam-3996	253	5	)	)	PUNCT
ejpam-3996	253	6	,	,	PUNCT
ejpam-3996	253	7	(	(	PUNCT
ejpam-3996	253	8	x	x	NOUN
ejpam-3996	253	9	,	,	PUNCT
ejpam-3996	253	10	yi	yi	PROPN
ejpam-3996	253	11	)	)	PUNCT
ejpam-3996	253	12	·	·	PUNCT
ejpam-3996	253	13	(	(	PUNCT
ejpam-3996	253	14	u	u	NOUN
ejpam-3996	253	15	,	,	PUNCT
ejpam-3996	253	16	vi	vi	NOUN
ejpam-3996	253	17	)	)	PUNCT
ejpam-3996	253	18	∈	∈	PROPN
ejpam-3996	253	19	n(i	n(i	PROPN
ejpam-3996	253	20	)	)	PUNCT
ejpam-3996	253	21	,	,	PUNCT
ejpam-3996	254	1	[	[	X
ejpam-3996	254	2	(	(	PUNCT
ejpam-3996	254	3	a	a	PRON
ejpam-3996	254	4	,	,	PUNCT
ejpam-3996	254	5	bi	bi	NOUN
ejpam-3996	254	6	)	)	PUNCT
ejpam-3996	254	7	·	·	PUNCT
ejpam-3996	254	8	(	(	PUNCT
ejpam-3996	254	9	x	x	NOUN
ejpam-3996	254	10	,	,	PUNCT
ejpam-3996	254	11	yi	yi	PROPN
ejpam-3996	254	12	)	)	PUNCT
ejpam-3996	254	13	]	]	PUNCT
ejpam-3996	254	14	·	·	PUNCT
ejpam-3996	255	1	[	[	X
ejpam-3996	255	2	(	(	PUNCT
ejpam-3996	255	3	c	c	NOUN
ejpam-3996	255	4	,	,	PUNCT
ejpam-3996	255	5	di	di	NOUN
ejpam-3996	255	6	)	)	PUNCT
ejpam-3996	255	7	·	·	PUNCT
ejpam-3996	255	8	(	(	PUNCT
ejpam-3996	255	9	u	u	NOUN
ejpam-3996	255	10	,	,	PUNCT
ejpam-3996	255	11	vi	vi	PROPN
ejpam-3996	255	12	)	)	PUNCT
ejpam-3996	255	13	]	]	PUNCT
ejpam-3996	255	14	∈	∈	PROPN
ejpam-3996	255	15	n(i	n(i	PROPN
ejpam-3996	255	16	)	)	PUNCT
ejpam-3996	255	17	.	.	PUNCT
ejpam-3996	256	1	example	example	NOUN
ejpam-3996	257	1	3.22	3.22	NUM
ejpam-3996	257	2	.	.	PUNCT
ejpam-3996	257	3	consider	consider	VERB
ejpam-3996	257	4	the	the	DET
ejpam-3996	257	5	neutrosophic	neutrosophic	ADJ
ejpam-3996	257	6	b	b	X
ejpam-3996	257	7	-	-	PUNCT
ejpam-3996	257	8	algebra	algebra	NOUN
ejpam-3996	257	9	x(i	x(i	PROPN
ejpam-3996	257	10	)	)	PUNCT
ejpam-3996	257	11	in	in	ADP
ejpam-3996	257	12	example	example	NOUN
ejpam-3996	257	13	3.12	3.12	NUM
ejpam-3996	257	14	and	and	CCONJ
ejpam-3996	257	15	its	its	PRON
ejpam-3996	257	16	subset	subset	NOUN
ejpam-3996	257	17	n(i	n(i	NOUN
ejpam-3996	257	18	)	)	PUNCT
ejpam-3996	257	19	=	=	PRON
ejpam-3996	257	20	{	{	PUNCT
ejpam-3996	257	21	(	(	PUNCT
ejpam-3996	257	22	0	0	NUM
ejpam-3996	257	23	,	,	PUNCT
ejpam-3996	257	24	0i	0i	NOUN
ejpam-3996	257	25	)	)	PUNCT
ejpam-3996	257	26	,	,	PUNCT
ejpam-3996	257	27	(	(	PUNCT
ejpam-3996	257	28	0	0	NUM
ejpam-3996	257	29	,	,	PUNCT
ejpam-3996	257	30	i	i	NOUN
ejpam-3996	257	31	)	)	PUNCT
ejpam-3996	257	32	,	,	PUNCT
ejpam-3996	257	33	(	(	PUNCT
ejpam-3996	257	34	0	0	NUM
ejpam-3996	257	35	,	,	PUNCT
ejpam-3996	257	36	2i	2i	NUM
ejpam-3996	257	37	)	)	PUNCT
ejpam-3996	257	38	,	,	PUNCT
ejpam-3996	257	39	(	(	PUNCT
ejpam-3996	257	40	1	1	NUM
ejpam-3996	257	41	,	,	PUNCT
ejpam-3996	257	42	0i	0i	NOUN
ejpam-3996	257	43	)	)	PUNCT
ejpam-3996	257	44	,	,	PUNCT
ejpam-3996	257	45	(	(	PUNCT
ejpam-3996	257	46	1	1	X
ejpam-3996	257	47	,	,	PUNCT
ejpam-3996	257	48	i	i	NOUN
ejpam-3996	257	49	)	)	PUNCT
ejpam-3996	257	50	,	,	PUNCT
ejpam-3996	257	51	(	(	PUNCT
ejpam-3996	257	52	1	1	NUM
ejpam-3996	257	53	,	,	PUNCT
ejpam-3996	257	54	2i	2i	NUM
ejpam-3996	257	55	)	)	PUNCT
ejpam-3996	257	56	,	,	PUNCT
ejpam-3996	257	57	(	(	PUNCT
ejpam-3996	257	58	2	2	NUM
ejpam-3996	257	59	,	,	PUNCT
ejpam-3996	257	60	0i	0i	NOUN
ejpam-3996	257	61	)	)	PUNCT
ejpam-3996	257	62	,	,	PUNCT
ejpam-3996	257	63	(	(	PUNCT
ejpam-3996	257	64	2	2	NUM
ejpam-3996	257	65	,	,	PUNCT
ejpam-3996	257	66	i	i	NOUN
ejpam-3996	257	67	)	)	PUNCT
ejpam-3996	257	68	,	,	PUNCT
ejpam-3996	257	69	(	(	PUNCT
ejpam-3996	257	70	2	2	NUM
ejpam-3996	257	71	,	,	PUNCT
ejpam-3996	257	72	2i	2i	NUM
ejpam-3996	257	73	)	)	PUNCT
ejpam-3996	257	74	}	}	PUNCT
ejpam-3996	257	75	determined	determine	VERB
ejpam-3996	257	76	by	by	ADP
ejpam-3996	257	77	n	n	NOUN
ejpam-3996	257	78	=	=	PUNCT
ejpam-3996	257	79	{	{	PUNCT
ejpam-3996	257	80	0	0	NUM
ejpam-3996	257	81	,	,	PUNCT
ejpam-3996	257	82	1	1	NUM
ejpam-3996	257	83	,	,	PUNCT
ejpam-3996	257	84	2	2	NUM
ejpam-3996	257	85	}	}	PUNCT
ejpam-3996	257	86	and	and	CCONJ
ejpam-3996	257	87	i.	i.	NOUN
ejpam-3996	257	88	it	it	PRON
ejpam-3996	257	89	can	can	AUX
ejpam-3996	257	90	be	be	AUX
ejpam-3996	257	91	verified	verify	VERB
ejpam-3996	257	92	that	that	SCONJ
ejpam-3996	257	93	n(i	n(i	PROPN
ejpam-3996	257	94	)	)	PUNCT
ejpam-3996	257	95	is	be	AUX
ejpam-3996	257	96	a	a	DET
ejpam-3996	257	97	normal	normal	ADJ
ejpam-3996	257	98	neutrosophic	neutrosophic	ADJ
ejpam-3996	257	99	subalgebra	subalgebra	NOUN
ejpam-3996	257	100	of	of	ADP
ejpam-3996	257	101	x(i	x(i	PROPN
ejpam-3996	257	102	)	)	PUNCT
ejpam-3996	257	103	with	with	ADP
ejpam-3996	257	104	{	{	PUNCT
ejpam-3996	257	105	(	(	PUNCT
ejpam-3996	257	106	0	0	NUM
ejpam-3996	257	107	,	,	PUNCT
ejpam-3996	257	108	0i	0i	NOUN
ejpam-3996	257	109	)	)	PUNCT
ejpam-3996	257	110	,	,	PUNCT
ejpam-3996	257	111	(	(	PUNCT
ejpam-3996	257	112	1	1	NUM
ejpam-3996	257	113	,	,	PUNCT
ejpam-3996	257	114	0i	0i	NOUN
ejpam-3996	257	115	)	)	PUNCT
ejpam-3996	257	116	,	,	PUNCT
ejpam-3996	257	117	(	(	PUNCT
ejpam-3996	257	118	2	2	NUM
ejpam-3996	257	119	,	,	PUNCT
ejpam-3996	257	120	0i	0i	NOUN
ejpam-3996	257	121	)	)	PUNCT
ejpam-3996	257	122	}	}	PUNCT
ejpam-3996	257	123	as	as	ADP
ejpam-3996	257	124	its	its	PRON
ejpam-3996	257	125	proper	proper	ADJ
ejpam-3996	257	126	subset	subset	NOUN
ejpam-3996	257	127	which	which	PRON
ejpam-3996	257	128	is	be	AUX
ejpam-3996	257	129	a	a	DET
ejpam-3996	257	130	b	b	NOUN
ejpam-3996	257	131	-	-	PUNCT
ejpam-3996	257	132	algebra	algebra	NOUN
ejpam-3996	257	133	..	..	PUNCT
ejpam-3996	257	134	it	it	PRON
ejpam-3996	257	135	can	can	AUX
ejpam-3996	257	136	also	also	ADV
ejpam-3996	257	137	be	be	AUX
ejpam-3996	257	138	verified	verify	VERB
ejpam-3996	257	139	that	that	SCONJ
ejpam-3996	257	140	n	n	PRON
ejpam-3996	257	141	is	be	AUX
ejpam-3996	257	142	a	a	DET
ejpam-3996	257	143	normal	normal	ADJ
ejpam-3996	257	144	subalgebra	subalgebra	NOUN
ejpam-3996	257	145	of	of	ADP
ejpam-3996	257	146	x.	x.	PROPN
ejpam-3996	257	147	d.o	d.o	PROPN
ejpam-3996	257	148	.	.	PROPN
ejpam-3996	257	149	jacobe	jacobe	PROPN
ejpam-3996	257	150	,	,	PUNCT
ejpam-3996	257	151	j.p	j.p	PROPN
ejpam-3996	257	152	.	.	PROPN
ejpam-3996	257	153	vilela	vilela	PROPN
ejpam-3996	257	154	/	/	SYM
ejpam-3996	257	155	eur	eur	PROPN
ejpam-3996	257	156	.	.	PUNCT
ejpam-3996	258	1	j.	j.	PROPN
ejpam-3996	258	2	pure	pure	PROPN
ejpam-3996	258	3	appl	appl	PROPN
ejpam-3996	258	4	.	.	PROPN
ejpam-3996	258	5	math	math	PROPN
ejpam-3996	258	6	,	,	PUNCT
ejpam-3996	258	7	14	14	NUM
ejpam-3996	258	8	(	(	PUNCT
ejpam-3996	258	9	3	3	NUM
ejpam-3996	258	10	)	)	PUNCT
ejpam-3996	258	11	(	(	PUNCT
ejpam-3996	258	12	2021	2021	NUM
ejpam-3996	258	13	)	)	PUNCT
ejpam-3996	258	14	,	,	PUNCT
ejpam-3996	258	15	895	895	NUM
ejpam-3996	258	16	-	-	SYM
ejpam-3996	258	17	904	904	NUM
ejpam-3996	258	18	901	901	NUM
ejpam-3996	258	19	the	the	DET
ejpam-3996	258	20	observation	observation	NOUN
ejpam-3996	258	21	in	in	ADP
ejpam-3996	258	22	the	the	DET
ejpam-3996	258	23	preceding	precede	VERB
ejpam-3996	258	24	example	example	NOUN
ejpam-3996	258	25	are	be	AUX
ejpam-3996	258	26	generalized	generalize	VERB
ejpam-3996	258	27	in	in	ADP
ejpam-3996	258	28	the	the	DET
ejpam-3996	258	29	next	next	ADJ
ejpam-3996	258	30	theorem	theorem	PROPN
ejpam-3996	258	31	.	.	PUNCT
ejpam-3996	258	32	theorem	theorem	VERB
ejpam-3996	258	33	3.23	3.23	NUM
ejpam-3996	258	34	.	.	PUNCT
ejpam-3996	259	1	let	let	VERB
ejpam-3996	259	2	s(i	s(i	PROPN
ejpam-3996	259	3	)	)	PUNCT
ejpam-3996	260	1	=	=	PRON
ejpam-3996	260	2	{	{	PUNCT
ejpam-3996	260	3	(	(	PUNCT
ejpam-3996	260	4	a	a	PRON
ejpam-3996	260	5	,	,	PUNCT
ejpam-3996	260	6	bi	bi	ADJ
ejpam-3996	260	7	)	)	PUNCT
ejpam-3996	260	8	∈	∈	PROPN
ejpam-3996	260	9	x(i	x(i	PROPN
ejpam-3996	260	10	)	)	PUNCT
ejpam-3996	260	11	:	:	PUNCT
ejpam-3996	260	12	a	a	X
ejpam-3996	260	13	,	,	PUNCT
ejpam-3996	260	14	b	b	PROPN
ejpam-3996	260	15	∈	∈	PROPN
ejpam-3996	260	16	s	s	PROPN
ejpam-3996	260	17	,	,	PUNCT
ejpam-3996	260	18	s	s	VERB
ejpam-3996	260	19	⊆	⊆	NUM
ejpam-3996	260	20	x	x	SYM
ejpam-3996	260	21	}	}	PUNCT
ejpam-3996	260	22	.	.	PUNCT
ejpam-3996	261	1	then	then	ADV
ejpam-3996	261	2	s(i	s(i	PROPN
ejpam-3996	261	3	)	)	PUNCT
ejpam-3996	261	4	is	be	AUX
ejpam-3996	261	5	a	a	DET
ejpam-3996	261	6	neutrosophic	neutrosophic	ADJ
ejpam-3996	261	7	subalgebra	subalgebra	NOUN
ejpam-3996	261	8	of	of	ADP
ejpam-3996	261	9	x(i	x(i	PROPN
ejpam-3996	261	10	)	)	PUNCT
ejpam-3996	262	1	if	if	SCONJ
ejpam-3996	262	2	and	and	CCONJ
ejpam-3996	262	3	only	only	ADV
ejpam-3996	262	4	if	if	SCONJ
ejpam-3996	262	5	s	s	NOUN
ejpam-3996	262	6	is	be	AUX
ejpam-3996	262	7	a	a	DET
ejpam-3996	262	8	nonzero	nonzero	ADJ
ejpam-3996	262	9	subalgebra	subalgebra	NOUN
ejpam-3996	262	10	of	of	ADP
ejpam-3996	262	11	x.	x.	NOUN
ejpam-3996	262	12	moreover	moreover	ADV
ejpam-3996	262	13	,	,	PUNCT
ejpam-3996	262	14	if	if	SCONJ
ejpam-3996	262	15	s(i	s(i	PROPN
ejpam-3996	262	16	)	)	PUNCT
ejpam-3996	262	17	is	be	AUX
ejpam-3996	262	18	normal	normal	ADJ
ejpam-3996	262	19	in	in	ADP
ejpam-3996	262	20	x(i	x(i	PROPN
ejpam-3996	262	21	)	)	PUNCT
ejpam-3996	262	22	,	,	PUNCT
ejpam-3996	262	23	then	then	ADV
ejpam-3996	262	24	s	s	VERB
ejpam-3996	262	25	is	be	AUX
ejpam-3996	262	26	normal	normal	ADJ
ejpam-3996	262	27	in	in	ADP
ejpam-3996	262	28	x.	x.	NOUN
ejpam-3996	262	29	proof	proof	NOUN
ejpam-3996	262	30	:	:	PUNCT
ejpam-3996	262	31	let	let	VERB
ejpam-3996	262	32	s	s	PRON
ejpam-3996	262	33	be	be	AUX
ejpam-3996	262	34	a	a	DET
ejpam-3996	262	35	nonzero	nonzero	NOUN
ejpam-3996	262	36	subalgebra	subalgebra	NOUN
ejpam-3996	262	37	of	of	ADP
ejpam-3996	262	38	x.	x.	NOUN
ejpam-3996	262	39	let	let	VERB
ejpam-3996	262	40	(	(	PUNCT
ejpam-3996	262	41	a	a	DET
ejpam-3996	262	42	,	,	PUNCT
ejpam-3996	262	43	bi	bi	NOUN
ejpam-3996	262	44	)	)	PUNCT
ejpam-3996	262	45	,	,	PUNCT
ejpam-3996	262	46	(	(	PUNCT
ejpam-3996	262	47	c	c	X
ejpam-3996	262	48	,	,	PUNCT
ejpam-3996	262	49	di	di	NOUN
ejpam-3996	262	50	)	)	PUNCT
ejpam-3996	262	51	∈	∈	PROPN
ejpam-3996	262	52	s(i	s(i	PROPN
ejpam-3996	262	53	)	)	PUNCT
ejpam-3996	262	54	.	.	PUNCT
ejpam-3996	263	1	then	then	ADV
ejpam-3996	263	2	a	a	DET
ejpam-3996	263	3	,	,	PUNCT
ejpam-3996	263	4	b	b	NOUN
ejpam-3996	263	5	,	,	PUNCT
ejpam-3996	263	6	c	c	NOUN
ejpam-3996	263	7	,	,	PUNCT
ejpam-3996	263	8	d	d	PROPN
ejpam-3996	263	9	∈	∈	PROPN
ejpam-3996	263	10	s	s	X
ejpam-3996	263	11	and	and	CCONJ
ejpam-3996	263	12	(	(	PUNCT
ejpam-3996	263	13	a	a	PRON
ejpam-3996	263	14	,	,	PUNCT
ejpam-3996	263	15	bi	bi	NOUN
ejpam-3996	263	16	)	)	PUNCT
ejpam-3996	263	17	·	·	PUNCT
ejpam-3996	263	18	(	(	PUNCT
ejpam-3996	263	19	c	c	X
ejpam-3996	263	20	,	,	PUNCT
ejpam-3996	263	21	di	di	NOUN
ejpam-3996	263	22	)	)	PUNCT
ejpam-3996	263	23	=	=	SYM
ejpam-3996	263	24	(	(	PUNCT
ejpam-3996	263	25	a∗c	a∗c	PUNCT
ejpam-3996	263	26	,	,	PUNCT
ejpam-3996	263	27	(	(	PUNCT
ejpam-3996	263	28	(	(	PUNCT
ejpam-3996	263	29	a∗d∧b∗c)∧b∗d)i	a∗d∧b∗c)∧b∗d)i	PROPN
ejpam-3996	263	30	)	)	PUNCT
ejpam-3996	263	31	.	.	PUNCT
ejpam-3996	264	1	since	since	SCONJ
ejpam-3996	264	2	s	s	PROPN
ejpam-3996	264	3	is	be	AUX
ejpam-3996	264	4	a	a	DET
ejpam-3996	264	5	subalgebra	subalgebra	NOUN
ejpam-3996	264	6	of	of	ADP
ejpam-3996	264	7	x	x	PRON
ejpam-3996	264	8	,	,	PUNCT
ejpam-3996	264	9	a∗c	a∗c	ADJ
ejpam-3996	264	10	,	,	PUNCT
ejpam-3996	264	11	a∗d	a∗d	NUM
ejpam-3996	264	12	,	,	PUNCT
ejpam-3996	264	13	b	b	NOUN
ejpam-3996	264	14	∗	∗	NOUN
ejpam-3996	264	15	c	c	NOUN
ejpam-3996	264	16	,	,	PUNCT
ejpam-3996	264	17	b	b	NOUN
ejpam-3996	264	18	∗	∗	X
ejpam-3996	264	19	d	d	X
ejpam-3996	264	20	∈	∈	NOUN
ejpam-3996	264	21	s	s	VERB
ejpam-3996	265	1	so	so	SCONJ
ejpam-3996	265	2	that	that	SCONJ
ejpam-3996	265	3	(	(	PUNCT
ejpam-3996	265	4	a	a	DET
ejpam-3996	265	5	∗	∗	NOUN
ejpam-3996	265	6	d∧	d∧	NOUN
ejpam-3996	265	7	b	b	PROPN
ejpam-3996	265	8	∗	∗	X
ejpam-3996	265	9	c)∧	c)∧	PROPN
ejpam-3996	265	10	b	b	PROPN
ejpam-3996	265	11	∗	∗	X
ejpam-3996	265	12	d	d	PROPN
ejpam-3996	265	13	∈	∈	PROPN
ejpam-3996	265	14	s.	s.	PROPN
ejpam-3996	265	15	thus	thus	ADV
ejpam-3996	265	16	,	,	PUNCT
ejpam-3996	265	17	(	(	PUNCT
ejpam-3996	265	18	a	a	DET
ejpam-3996	265	19	,	,	PUNCT
ejpam-3996	265	20	bi	bi	NOUN
ejpam-3996	265	21	)	)	PUNCT
ejpam-3996	265	22	·	·	PUNCT
ejpam-3996	265	23	(	(	PUNCT
ejpam-3996	265	24	c	c	X
ejpam-3996	265	25	,	,	PUNCT
ejpam-3996	265	26	di	di	NOUN
ejpam-3996	265	27	)	)	PUNCT
ejpam-3996	265	28	∈	∈	PROPN
ejpam-3996	265	29	s(i	s(i	PROPN
ejpam-3996	265	30	)	)	PUNCT
ejpam-3996	265	31	.	.	PUNCT
ejpam-3996	266	1	by	by	ADP
ejpam-3996	266	2	definition	definition	NOUN
ejpam-3996	266	3	3.4	3.4	NUM
ejpam-3996	266	4	,	,	PUNCT
ejpam-3996	266	5	s(i	s(i	PROPN
ejpam-3996	266	6	)	)	PUNCT
ejpam-3996	266	7	is	be	AUX
ejpam-3996	266	8	a	a	DET
ejpam-3996	266	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	266	10	b	b	X
ejpam-3996	266	11	-	-	PUNCT
ejpam-3996	266	12	algebra	algebra	NOUN
ejpam-3996	266	13	determined	determine	VERB
ejpam-3996	266	14	by	by	ADP
ejpam-3996	266	15	s	s	NOUN
ejpam-3996	266	16	and	and	CCONJ
ejpam-3996	266	17	i.	i.	PROPN
ejpam-3996	266	18	hence	hence	ADV
ejpam-3996	266	19	,	,	PUNCT
ejpam-3996	266	20	by	by	ADP
ejpam-3996	266	21	remark	remark	NOUN
ejpam-3996	266	22	3.5	3.5	NUM
ejpam-3996	266	23	,	,	PUNCT
ejpam-3996	266	24	s(i	s(i	PROPN
ejpam-3996	266	25	)	)	PUNCT
ejpam-3996	266	26	contains	contain	VERB
ejpam-3996	266	27	the	the	DET
ejpam-3996	266	28	b	b	NOUN
ejpam-3996	266	29	-	-	PUNCT
ejpam-3996	266	30	algebra	algebra	NOUN
ejpam-3996	266	31	s′	s′	VERB
ejpam-3996	266	32	=	=	PUNCT
ejpam-3996	266	33	{	{	PUNCT
ejpam-3996	266	34	(	(	PUNCT
ejpam-3996	266	35	x	x	X
ejpam-3996	266	36	,	,	PUNCT
ejpam-3996	266	37	0i	0i	NUM
ejpam-3996	266	38	)	)	PUNCT
ejpam-3996	266	39	:	:	PUNCT
ejpam-3996	267	1	x	x	X
ejpam-3996	267	2	∈	∈	PROPN
ejpam-3996	267	3	s	s	VERB
ejpam-3996	267	4	}	}	PUNCT
ejpam-3996	267	5	as	as	ADP
ejpam-3996	267	6	a	a	DET
ejpam-3996	267	7	proper	proper	ADJ
ejpam-3996	267	8	subset	subset	NOUN
ejpam-3996	267	9	.	.	PUNCT
ejpam-3996	268	1	therefore	therefore	ADV
ejpam-3996	268	2	,	,	PUNCT
ejpam-3996	268	3	s(i	s(i	PROPN
ejpam-3996	268	4	)	)	PUNCT
ejpam-3996	268	5	is	be	AUX
ejpam-3996	268	6	a	a	DET
ejpam-3996	268	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	268	8	subalgebra	subalgebra	NOUN
ejpam-3996	268	9	of	of	ADP
ejpam-3996	268	10	x(i	x(i	PROPN
ejpam-3996	268	11	)	)	PUNCT
ejpam-3996	268	12	.	.	PUNCT
ejpam-3996	269	1	conversely	conversely	ADV
ejpam-3996	269	2	,	,	PUNCT
ejpam-3996	269	3	let	let	VERB
ejpam-3996	269	4	s(i	s(i	PROPN
ejpam-3996	269	5	)	)	PUNCT
ejpam-3996	269	6	be	be	AUX
ejpam-3996	269	7	a	a	DET
ejpam-3996	269	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	269	9	subalgebra	subalgebra	NOUN
ejpam-3996	269	10	of	of	ADP
ejpam-3996	269	11	x(i	x(i	PROPN
ejpam-3996	269	12	)	)	PUNCT
ejpam-3996	269	13	.	.	PUNCT
ejpam-3996	270	1	then	then	ADV
ejpam-3996	270	2	s	s	VERB
ejpam-3996	270	3	6=	6=	NOUN
ejpam-3996	270	4	∅	∅	NOUN
ejpam-3996	270	5	and	and	CCONJ
ejpam-3996	270	6	s	s	PROPN
ejpam-3996	270	7	6=	6=	X
ejpam-3996	270	8	{	{	PUNCT
ejpam-3996	270	9	0	0	NUM
ejpam-3996	270	10	}	}	PUNCT
ejpam-3996	270	11	.	.	PUNCT
ejpam-3996	271	1	by	by	ADP
ejpam-3996	271	2	remark	remark	NOUN
ejpam-3996	271	3	3.19(ii	3.19(ii	NUM
ejpam-3996	271	4	)	)	PUNCT
ejpam-3996	271	5	,	,	PUNCT
ejpam-3996	271	6	s(i	s(i	PROPN
ejpam-3996	271	7	)	)	PUNCT
ejpam-3996	271	8	is	be	AUX
ejpam-3996	271	9	a	a	DET
ejpam-3996	271	10	neutrosophic	neutrosophic	ADJ
ejpam-3996	271	11	b	b	X
ejpam-3996	271	12	-	-	PUNCT
ejpam-3996	271	13	algebra	algebra	NOUN
ejpam-3996	271	14	.	.	PUNCT
ejpam-3996	272	1	thus	thus	ADV
ejpam-3996	272	2	,	,	PUNCT
ejpam-3996	272	3	s	s	VERB
ejpam-3996	272	4	is	be	AUX
ejpam-3996	272	5	a	a	DET
ejpam-3996	272	6	b	b	NOUN
ejpam-3996	272	7	-	-	PUNCT
ejpam-3996	272	8	algebra	algebra	NOUN
ejpam-3996	272	9	by	by	ADP
ejpam-3996	272	10	definition	definition	NOUN
ejpam-3996	272	11	3.4	3.4	NUM
ejpam-3996	272	12	.	.	PUNCT
ejpam-3996	273	1	hence	hence	ADV
ejpam-3996	273	2	,	,	PUNCT
ejpam-3996	273	3	s	s	VERB
ejpam-3996	273	4	is	be	AUX
ejpam-3996	273	5	a	a	DET
ejpam-3996	273	6	nonzero	nonzero	NOUN
ejpam-3996	273	7	subalgebra	subalgebra	NOUN
ejpam-3996	273	8	of	of	ADP
ejpam-3996	273	9	x.	x.	NOUN
ejpam-3996	273	10	moreover	moreover	ADV
ejpam-3996	273	11	,	,	PUNCT
ejpam-3996	273	12	let	let	VERB
ejpam-3996	273	13	a	a	DET
ejpam-3996	273	14	∗	∗	NOUN
ejpam-3996	273	15	b	b	NOUN
ejpam-3996	273	16	,	,	PUNCT
ejpam-3996	273	17	c	c	NOUN
ejpam-3996	273	18	∗	∗	NOUN
ejpam-3996	273	19	d	d	X
ejpam-3996	273	20	∈	∈	PROPN
ejpam-3996	273	21	s.	s.	PROPN
ejpam-3996	273	22	by	by	ADP
ejpam-3996	273	23	definition	definition	NOUN
ejpam-3996	273	24	of	of	ADP
ejpam-3996	273	25	s(i	s(i	PROPN
ejpam-3996	273	26	)	)	PUNCT
ejpam-3996	273	27	and	and	CCONJ
ejpam-3996	273	28	lemma	lemma	PROPN
ejpam-3996	273	29	3.8(ii	3.8(ii	NUM
ejpam-3996	273	30	)	)	PUNCT
ejpam-3996	273	31	,	,	PUNCT
ejpam-3996	273	32	(	(	PUNCT
ejpam-3996	273	33	a	a	DET
ejpam-3996	273	34	∗	∗	NOUN
ejpam-3996	273	35	b	b	NOUN
ejpam-3996	273	36	,	,	PUNCT
ejpam-3996	273	37	0i	0i	NOUN
ejpam-3996	273	38	)	)	PUNCT
ejpam-3996	274	1	=	=	PRON
ejpam-3996	274	2	(	(	PUNCT
ejpam-3996	274	3	a	a	DET
ejpam-3996	274	4	,	,	PUNCT
ejpam-3996	274	5	0i)·(b	0i)·(b	PROPN
ejpam-3996	274	6	,	,	PUNCT
ejpam-3996	274	7	0i	0i	NOUN
ejpam-3996	274	8	)	)	PUNCT
ejpam-3996	274	9	,	,	PUNCT
ejpam-3996	274	10	(	(	PUNCT
ejpam-3996	274	11	c∗d	c∗d	NOUN
ejpam-3996	274	12	,	,	PUNCT
ejpam-3996	274	13	0i	0i	NOUN
ejpam-3996	274	14	)	)	PUNCT
ejpam-3996	275	1	=	=	PRON
ejpam-3996	275	2	(	(	PUNCT
ejpam-3996	275	3	c	c	X
ejpam-3996	275	4	,	,	PUNCT
ejpam-3996	275	5	0i)·(d	0i)·(d	PROPN
ejpam-3996	275	6	,	,	PUNCT
ejpam-3996	275	7	0i	0i	NOUN
ejpam-3996	275	8	)	)	PUNCT
ejpam-3996	275	9	∈	∈	PROPN
ejpam-3996	275	10	s(i	s(i	PROPN
ejpam-3996	275	11	)	)	PUNCT
ejpam-3996	275	12	.	.	PUNCT
ejpam-3996	276	1	by	by	ADP
ejpam-3996	276	2	normality	normality	NOUN
ejpam-3996	276	3	of	of	ADP
ejpam-3996	276	4	s(i	s(i	PROPN
ejpam-3996	276	5	)	)	PUNCT
ejpam-3996	276	6	and	and	CCONJ
ejpam-3996	276	7	lemma	lemma	PROPN
ejpam-3996	276	8	3.8(ii	3.8(ii	NUM
ejpam-3996	276	9	)	)	PUNCT
ejpam-3996	276	10	,	,	PUNCT
ejpam-3996	276	11	[	[	X
ejpam-3996	276	12	(	(	PUNCT
ejpam-3996	276	13	a	a	DET
ejpam-3996	276	14	,	,	PUNCT
ejpam-3996	276	15	0i	0i	NOUN
ejpam-3996	276	16	)	)	PUNCT
ejpam-3996	276	17	·	·	PUNCT
ejpam-3996	276	18	(	(	PUNCT
ejpam-3996	276	19	c	c	X
ejpam-3996	276	20	,	,	PUNCT
ejpam-3996	276	21	0i	0i	NOUN
ejpam-3996	276	22	)	)	PUNCT
ejpam-3996	276	23	]	]	PUNCT
ejpam-3996	276	24	·	·	PUNCT
ejpam-3996	277	1	[	[	X
ejpam-3996	277	2	(	(	PUNCT
ejpam-3996	277	3	b	b	NOUN
ejpam-3996	277	4	,	,	PUNCT
ejpam-3996	277	5	0i	0i	NOUN
ejpam-3996	277	6	)	)	PUNCT
ejpam-3996	277	7	·	·	PUNCT
ejpam-3996	277	8	(	(	PUNCT
ejpam-3996	277	9	d	d	X
ejpam-3996	277	10	,	,	PUNCT
ejpam-3996	277	11	0i	0i	NOUN
ejpam-3996	277	12	)	)	PUNCT
ejpam-3996	277	13	]	]	PUNCT
ejpam-3996	278	1	=	=	PUNCT
ejpam-3996	278	2	[	[	PUNCT
ejpam-3996	278	3	(	(	PUNCT
ejpam-3996	278	4	a	a	DET
ejpam-3996	278	5	∗	∗	NOUN
ejpam-3996	278	6	c	c	NOUN
ejpam-3996	278	7	,	,	PUNCT
ejpam-3996	278	8	0i	0i	NOUN
ejpam-3996	278	9	)	)	PUNCT
ejpam-3996	278	10	·	·	PUNCT
ejpam-3996	279	1	(	(	PUNCT
ejpam-3996	279	2	b	b	X
ejpam-3996	279	3	∗	∗	X
ejpam-3996	279	4	d	d	PROPN
ejpam-3996	279	5	,	,	PUNCT
ejpam-3996	279	6	0i	0i	NOUN
ejpam-3996	279	7	)	)	PUNCT
ejpam-3996	279	8	]	]	PUNCT
ejpam-3996	280	1	=	=	PUNCT
ejpam-3996	280	2	(	(	PUNCT
ejpam-3996	280	3	[	[	X
ejpam-3996	280	4	(	(	PUNCT
ejpam-3996	280	5	a	a	DET
ejpam-3996	280	6	∗	∗	NOUN
ejpam-3996	280	7	c	c	NOUN
ejpam-3996	280	8	)	)	PUNCT
ejpam-3996	280	9	∗	∗	NOUN
ejpam-3996	280	10	(	(	PUNCT
ejpam-3996	280	11	b	b	NOUN
ejpam-3996	280	12	∗	∗	X
ejpam-3996	280	13	d	d	NOUN
ejpam-3996	280	14	)	)	PUNCT
ejpam-3996	280	15	]	]	PUNCT
ejpam-3996	280	16	,	,	PUNCT
ejpam-3996	280	17	0i	0i	X
ejpam-3996	280	18	)	)	PUNCT
ejpam-3996	281	1	∈	∈	PROPN
ejpam-3996	281	2	s(i	s(i	PROPN
ejpam-3996	281	3	)	)	PUNCT
ejpam-3996	281	4	.	.	PUNCT
ejpam-3996	282	1	by	by	ADP
ejpam-3996	282	2	definition	definition	NOUN
ejpam-3996	282	3	of	of	ADP
ejpam-3996	282	4	s(i	s(i	PROPN
ejpam-3996	282	5	)	)	PUNCT
ejpam-3996	282	6	,	,	PUNCT
ejpam-3996	282	7	[	[	X
ejpam-3996	282	8	(	(	PUNCT
ejpam-3996	282	9	a	a	DET
ejpam-3996	282	10	∗	∗	NOUN
ejpam-3996	282	11	c	c	NOUN
ejpam-3996	282	12	)	)	PUNCT
ejpam-3996	282	13	∗	∗	NOUN
ejpam-3996	282	14	(	(	PUNCT
ejpam-3996	282	15	b	b	NOUN
ejpam-3996	282	16	∗	∗	X
ejpam-3996	282	17	d	d	NOUN
ejpam-3996	282	18	)	)	PUNCT
ejpam-3996	282	19	]	]	PUNCT
ejpam-3996	283	1	∈	∈	PROPN
ejpam-3996	283	2	s	s	X
ejpam-3996	283	3	and	and	CCONJ
ejpam-3996	283	4	hence	hence	ADV
ejpam-3996	283	5	s	s	VERB
ejpam-3996	283	6	is	be	AUX
ejpam-3996	283	7	normal	normal	ADJ
ejpam-3996	283	8	in	in	ADP
ejpam-3996	283	9	x.	x.	PROPN
ejpam-3996	283	10	�	�	PROPN
ejpam-3996	283	11	since	since	SCONJ
ejpam-3996	283	12	a	a	DET
ejpam-3996	283	13	neutrosophic	neutrosophic	ADJ
ejpam-3996	283	14	subalgebra	subalgebra	NOUN
ejpam-3996	283	15	is	be	AUX
ejpam-3996	283	16	also	also	ADV
ejpam-3996	283	17	a	a	DET
ejpam-3996	283	18	neutrosophic	neutrosophic	ADJ
ejpam-3996	283	19	b	b	X
ejpam-3996	283	20	-	-	PUNCT
ejpam-3996	283	21	algebra	algebra	NOUN
ejpam-3996	283	22	contained	contain	VERB
ejpam-3996	283	23	in	in	ADP
ejpam-3996	283	24	a	a	DET
ejpam-3996	283	25	given	give	VERB
ejpam-3996	283	26	neutrosophic	neutrosophic	ADJ
ejpam-3996	283	27	b	b	X
ejpam-3996	283	28	-	-	PUNCT
ejpam-3996	283	29	algebra	algebra	NOUN
ejpam-3996	283	30	,	,	PUNCT
ejpam-3996	283	31	the	the	DET
ejpam-3996	283	32	following	follow	VERB
ejpam-3996	283	33	remark	remark	NOUN
ejpam-3996	283	34	follows	follow	VERB
ejpam-3996	283	35	.	.	PUNCT
ejpam-3996	284	1	remark	remark	VERB
ejpam-3996	284	2	3.24	3.24	NUM
ejpam-3996	284	3	.	.	PUNCT
ejpam-3996	285	1	if	if	SCONJ
ejpam-3996	285	2	n(i	n(i	PROPN
ejpam-3996	285	3	)	)	PUNCT
ejpam-3996	285	4	is	be	AUX
ejpam-3996	285	5	a	a	DET
ejpam-3996	285	6	normal	normal	ADJ
ejpam-3996	285	7	neutrosophic	neutrosophic	ADJ
ejpam-3996	285	8	subalgebra	subalgebra	NOUN
ejpam-3996	285	9	of	of	ADP
ejpam-3996	285	10	x(i	x(i	PROPN
ejpam-3996	285	11	)	)	PUNCT
ejpam-3996	285	12	,	,	PUNCT
ejpam-3996	285	13	then	then	ADV
ejpam-3996	285	14	n(i	n(i	PROPN
ejpam-3996	285	15	)	)	PUNCT
ejpam-3996	286	1	is	be	AUX
ejpam-3996	286	2	normal	normal	ADJ
ejpam-3996	286	3	in	in	ADP
ejpam-3996	286	4	every	every	DET
ejpam-3996	286	5	neutrosophic	neutrosophic	ADJ
ejpam-3996	286	6	subalgebra	subalgebra	NOUN
ejpam-3996	286	7	of	of	ADP
ejpam-3996	286	8	x(i	x(i	PROPN
ejpam-3996	286	9	)	)	PUNCT
ejpam-3996	286	10	containing	contain	VERB
ejpam-3996	286	11	n(i	n(i	PROPN
ejpam-3996	286	12	)	)	PUNCT
ejpam-3996	286	13	.	.	PUNCT
ejpam-3996	287	1	example	example	NOUN
ejpam-3996	288	1	3.25	3.25	NUM
ejpam-3996	288	2	.	.	PUNCT
ejpam-3996	289	1	in	in	ADP
ejpam-3996	289	2	the	the	DET
ejpam-3996	289	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	289	4	b	b	X
ejpam-3996	289	5	-	-	PUNCT
ejpam-3996	289	6	algebra	algebra	NOUN
ejpam-3996	289	7	x(i	x(i	PROPN
ejpam-3996	289	8	)	)	PUNCT
ejpam-3996	289	9	in	in	ADP
ejpam-3996	289	10	example	example	NOUN
ejpam-3996	289	11	3.6	3.6	NUM
ejpam-3996	289	12	,	,	PUNCT
ejpam-3996	289	13	x(i	x(i	PROPN
ejpam-3996	289	14	)	)	PUNCT
ejpam-3996	289	15	has	have	VERB
ejpam-3996	289	16	three	three	NUM
ejpam-3996	289	17	neutrosophic	neutrosophic	ADJ
ejpam-3996	289	18	subalgebras	subalgebra	NOUN
ejpam-3996	289	19	:	:	PUNCT
ejpam-3996	289	20	{	{	PUNCT
ejpam-3996	289	21	(	(	PUNCT
ejpam-3996	289	22	0	0	NUM
ejpam-3996	289	23	,	,	PUNCT
ejpam-3996	289	24	0i	0i	NOUN
ejpam-3996	289	25	)	)	PUNCT
ejpam-3996	289	26	,	,	PUNCT
ejpam-3996	289	27	(	(	PUNCT
ejpam-3996	289	28	0	0	NUM
ejpam-3996	289	29	,	,	PUNCT
ejpam-3996	289	30	i	i	NOUN
ejpam-3996	289	31	)	)	PUNCT
ejpam-3996	289	32	,	,	PUNCT
ejpam-3996	289	33	(	(	PUNCT
ejpam-3996	289	34	0	0	NUM
ejpam-3996	289	35	,	,	PUNCT
ejpam-3996	289	36	2i	2i	NUM
ejpam-3996	289	37	)	)	PUNCT
ejpam-3996	289	38	}	}	PUNCT
ejpam-3996	289	39	,	,	PUNCT
ejpam-3996	289	40	{	{	PUNCT
ejpam-3996	289	41	(	(	PUNCT
ejpam-3996	289	42	0	0	NUM
ejpam-3996	289	43	,	,	PUNCT
ejpam-3996	289	44	0i	0i	NOUN
ejpam-3996	289	45	)	)	PUNCT
ejpam-3996	289	46	,	,	PUNCT
ejpam-3996	289	47	(	(	PUNCT
ejpam-3996	289	48	1	1	NUM
ejpam-3996	289	49	,	,	PUNCT
ejpam-3996	289	50	0i	0i	NOUN
ejpam-3996	289	51	)	)	PUNCT
ejpam-3996	289	52	,	,	PUNCT
ejpam-3996	289	53	(	(	PUNCT
ejpam-3996	289	54	2	2	NUM
ejpam-3996	289	55	,	,	PUNCT
ejpam-3996	289	56	0i	0i	NOUN
ejpam-3996	289	57	)	)	PUNCT
ejpam-3996	289	58	}	}	PUNCT
ejpam-3996	289	59	and	and	CCONJ
ejpam-3996	289	60	itself	itself	PRON
ejpam-3996	289	61	.	.	PUNCT
ejpam-3996	290	1	the	the	DET
ejpam-3996	290	2	first	first	ADJ
ejpam-3996	290	3	two	two	NUM
ejpam-3996	290	4	have	have	VERB
ejpam-3996	290	5	{	{	PUNCT
ejpam-3996	290	6	(	(	PUNCT
ejpam-3996	290	7	0	0	NUM
ejpam-3996	290	8	,	,	PUNCT
ejpam-3996	290	9	0i	0i	NOUN
ejpam-3996	290	10	)	)	PUNCT
ejpam-3996	290	11	}	}	PUNCT
ejpam-3996	290	12	as	as	ADP
ejpam-3996	290	13	their	their	PRON
ejpam-3996	290	14	proper	proper	ADJ
ejpam-3996	290	15	subset	subset	NOUN
ejpam-3996	290	16	which	which	PRON
ejpam-3996	290	17	is	be	AUX
ejpam-3996	290	18	a	a	DET
ejpam-3996	290	19	b	b	NOUN
ejpam-3996	290	20	-	-	PUNCT
ejpam-3996	290	21	algebra	algebra	NOUN
ejpam-3996	290	22	and	and	CCONJ
ejpam-3996	290	23	the	the	DET
ejpam-3996	290	24	latter	latter	ADJ
ejpam-3996	290	25	has	have	AUX
ejpam-3996	290	26	{	{	PUNCT
ejpam-3996	290	27	(	(	PUNCT
ejpam-3996	290	28	0	0	NUM
ejpam-3996	290	29	,	,	PUNCT
ejpam-3996	290	30	0i	0i	NOUN
ejpam-3996	290	31	)	)	PUNCT
ejpam-3996	290	32	,	,	PUNCT
ejpam-3996	290	33	(	(	PUNCT
ejpam-3996	290	34	1	1	NUM
ejpam-3996	290	35	,	,	PUNCT
ejpam-3996	290	36	0i	0i	NOUN
ejpam-3996	290	37	)	)	PUNCT
ejpam-3996	290	38	,	,	PUNCT
ejpam-3996	290	39	(	(	PUNCT
ejpam-3996	290	40	2	2	NUM
ejpam-3996	290	41	,	,	PUNCT
ejpam-3996	290	42	0i	0i	NOUN
ejpam-3996	290	43	)	)	PUNCT
ejpam-3996	290	44	}	}	PUNCT
ejpam-3996	290	45	.	.	PUNCT
ejpam-3996	291	1	in	in	ADP
ejpam-3996	291	2	the	the	DET
ejpam-3996	291	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	291	4	b	b	X
ejpam-3996	291	5	-	-	PUNCT
ejpam-3996	291	6	algebra	algebra	NOUN
ejpam-3996	291	7	x(i	x(i	PROPN
ejpam-3996	291	8	)	)	PUNCT
ejpam-3996	291	9	in	in	ADP
ejpam-3996	291	10	example	example	NOUN
ejpam-3996	291	11	3.12	3.12	NUM
ejpam-3996	291	12	,	,	PUNCT
ejpam-3996	291	13	the	the	DET
ejpam-3996	291	14	following	follow	VERB
ejpam-3996	291	15	are	be	AUX
ejpam-3996	291	16	some	some	PRON
ejpam-3996	291	17	of	of	ADP
ejpam-3996	291	18	its	its	PRON
ejpam-3996	291	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	291	20	subalgebras	subalgebra	NOUN
ejpam-3996	291	21	:	:	PUNCT
ejpam-3996	291	22	s(i)1	s(i)1	PROPN
ejpam-3996	291	23	=	=	SYM
ejpam-3996	291	24	x(i	x(i	PROPN
ejpam-3996	291	25	)	)	PUNCT
ejpam-3996	291	26	=	=	PRON
ejpam-3996	291	27	{	{	PUNCT
ejpam-3996	291	28	(	(	PUNCT
ejpam-3996	291	29	0	0	NUM
ejpam-3996	291	30	,	,	PUNCT
ejpam-3996	291	31	0i	0i	NOUN
ejpam-3996	291	32	)	)	PUNCT
ejpam-3996	291	33	,	,	PUNCT
ejpam-3996	291	34	(	(	PUNCT
ejpam-3996	291	35	1	1	NUM
ejpam-3996	291	36	,	,	PUNCT
ejpam-3996	291	37	0i	0i	NOUN
ejpam-3996	291	38	)	)	PUNCT
ejpam-3996	291	39	,	,	PUNCT
ejpam-3996	291	40	(	(	PUNCT
ejpam-3996	291	41	2	2	NUM
ejpam-3996	291	42	,	,	PUNCT
ejpam-3996	291	43	0i	0i	NOUN
ejpam-3996	291	44	)	)	PUNCT
ejpam-3996	291	45	,	,	PUNCT
ejpam-3996	291	46	(	(	PUNCT
ejpam-3996	291	47	3	3	NUM
ejpam-3996	291	48	,	,	PUNCT
ejpam-3996	291	49	0i	0i	NOUN
ejpam-3996	291	50	)	)	PUNCT
ejpam-3996	291	51	,	,	PUNCT
ejpam-3996	291	52	(	(	PUNCT
ejpam-3996	291	53	4	4	NUM
ejpam-3996	291	54	,	,	PUNCT
ejpam-3996	291	55	0i	0i	NOUN
ejpam-3996	291	56	)	)	PUNCT
ejpam-3996	291	57	,	,	PUNCT
ejpam-3996	291	58	(	(	PUNCT
ejpam-3996	291	59	5	5	NUM
ejpam-3996	291	60	,	,	PUNCT
ejpam-3996	291	61	0i	0i	NOUN
ejpam-3996	291	62	)	)	PUNCT
ejpam-3996	291	63	,	,	PUNCT
ejpam-3996	291	64	(	(	PUNCT
ejpam-3996	291	65	0	0	NUM
ejpam-3996	291	66	,	,	PUNCT
ejpam-3996	291	67	i	i	NOUN
ejpam-3996	291	68	)	)	PUNCT
ejpam-3996	291	69	,	,	PUNCT
ejpam-3996	291	70	(	(	PUNCT
ejpam-3996	291	71	1	1	X
ejpam-3996	291	72	,	,	PUNCT
ejpam-3996	291	73	i	i	NOUN
ejpam-3996	291	74	)	)	PUNCT
ejpam-3996	291	75	,	,	PUNCT
ejpam-3996	291	76	(	(	PUNCT
ejpam-3996	291	77	2	2	NUM
ejpam-3996	291	78	,	,	PUNCT
ejpam-3996	291	79	i	i	NOUN
ejpam-3996	291	80	)	)	PUNCT
ejpam-3996	291	81	,	,	PUNCT
ejpam-3996	291	82	(	(	PUNCT
ejpam-3996	291	83	3	3	X
ejpam-3996	291	84	,	,	PUNCT
ejpam-3996	291	85	i	i	PROPN
ejpam-3996	291	86	)	)	PUNCT
ejpam-3996	291	87	,	,	PUNCT
ejpam-3996	291	88	(	(	PUNCT
ejpam-3996	291	89	4	4	NUM
ejpam-3996	291	90	,	,	PUNCT
ejpam-3996	291	91	i	i	PROPN
ejpam-3996	291	92	)	)	PUNCT
ejpam-3996	291	93	,	,	PUNCT
ejpam-3996	291	94	(	(	PUNCT
ejpam-3996	291	95	5	5	NUM
ejpam-3996	291	96	,	,	PUNCT
ejpam-3996	291	97	i	i	PROPN
ejpam-3996	291	98	)	)	PUNCT
ejpam-3996	291	99	,	,	PUNCT
ejpam-3996	291	100	(	(	PUNCT
ejpam-3996	291	101	0	0	NUM
ejpam-3996	291	102	,	,	PUNCT
ejpam-3996	291	103	2i	2i	NUM
ejpam-3996	291	104	)	)	PUNCT
ejpam-3996	291	105	,	,	PUNCT
ejpam-3996	291	106	(	(	PUNCT
ejpam-3996	291	107	1	1	NUM
ejpam-3996	291	108	,	,	PUNCT
ejpam-3996	291	109	2i	2i	NUM
ejpam-3996	291	110	)	)	PUNCT
ejpam-3996	291	111	,	,	PUNCT
ejpam-3996	291	112	(	(	PUNCT
ejpam-3996	291	113	2	2	NUM
ejpam-3996	291	114	,	,	PUNCT
ejpam-3996	291	115	2i	2i	NUM
ejpam-3996	291	116	)	)	PUNCT
ejpam-3996	291	117	,	,	PUNCT
ejpam-3996	291	118	(	(	PUNCT
ejpam-3996	291	119	3	3	NUM
ejpam-3996	291	120	,	,	PUNCT
ejpam-3996	291	121	2i	2i	NUM
ejpam-3996	291	122	)	)	PUNCT
ejpam-3996	291	123	,	,	PUNCT
ejpam-3996	291	124	(	(	PUNCT
ejpam-3996	291	125	4	4	NUM
ejpam-3996	291	126	,	,	PUNCT
ejpam-3996	291	127	2i	2i	NUM
ejpam-3996	291	128	)	)	PUNCT
ejpam-3996	291	129	,	,	PUNCT
ejpam-3996	291	130	(	(	PUNCT
ejpam-3996	291	131	5	5	NUM
ejpam-3996	291	132	,	,	PUNCT
ejpam-3996	291	133	2i	2i	NUM
ejpam-3996	291	134	)	)	PUNCT
ejpam-3996	291	135	,	,	PUNCT
ejpam-3996	291	136	(	(	PUNCT
ejpam-3996	291	137	0	0	NUM
ejpam-3996	291	138	,	,	PUNCT
ejpam-3996	291	139	3i	3i	NOUN
ejpam-3996	291	140	)	)	PUNCT
ejpam-3996	291	141	,	,	PUNCT
ejpam-3996	291	142	(	(	PUNCT
ejpam-3996	291	143	1	1	NUM
ejpam-3996	291	144	,	,	PUNCT
ejpam-3996	291	145	3i	3i	NUM
ejpam-3996	291	146	)	)	PUNCT
ejpam-3996	291	147	,	,	PUNCT
ejpam-3996	291	148	(	(	PUNCT
ejpam-3996	291	149	2	2	NUM
ejpam-3996	291	150	,	,	PUNCT
ejpam-3996	291	151	3i	3i	NUM
ejpam-3996	291	152	)	)	PUNCT
ejpam-3996	291	153	,	,	PUNCT
ejpam-3996	291	154	(	(	PUNCT
ejpam-3996	291	155	3	3	NUM
ejpam-3996	291	156	,	,	PUNCT
ejpam-3996	291	157	3i	3i	NUM
ejpam-3996	291	158	)	)	PUNCT
ejpam-3996	291	159	,	,	PUNCT
ejpam-3996	291	160	(	(	PUNCT
ejpam-3996	291	161	4	4	NUM
ejpam-3996	291	162	,	,	PUNCT
ejpam-3996	291	163	3i	3i	NUM
ejpam-3996	291	164	)	)	PUNCT
ejpam-3996	291	165	,	,	PUNCT
ejpam-3996	291	166	(	(	PUNCT
ejpam-3996	291	167	5	5	NUM
ejpam-3996	291	168	,	,	PUNCT
ejpam-3996	291	169	3i	3i	NUM
ejpam-3996	291	170	)	)	PUNCT
ejpam-3996	291	171	,	,	PUNCT
ejpam-3996	291	172	(	(	PUNCT
ejpam-3996	291	173	0	0	NUM
ejpam-3996	291	174	,	,	PUNCT
ejpam-3996	291	175	4i	4i	NUM
ejpam-3996	291	176	)	)	PUNCT
ejpam-3996	291	177	,	,	PUNCT
ejpam-3996	291	178	(	(	PUNCT
ejpam-3996	291	179	1	1	NUM
ejpam-3996	291	180	,	,	PUNCT
ejpam-3996	291	181	4i	4i	NUM
ejpam-3996	291	182	)	)	PUNCT
ejpam-3996	291	183	,	,	PUNCT
ejpam-3996	291	184	(	(	PUNCT
ejpam-3996	291	185	2	2	NUM
ejpam-3996	291	186	,	,	PUNCT
ejpam-3996	291	187	4i	4i	NUM
ejpam-3996	291	188	)	)	PUNCT
ejpam-3996	291	189	,	,	PUNCT
ejpam-3996	291	190	(	(	PUNCT
ejpam-3996	291	191	3	3	NUM
ejpam-3996	291	192	,	,	PUNCT
ejpam-3996	291	193	4i	4i	NUM
ejpam-3996	291	194	)	)	PUNCT
ejpam-3996	291	195	,	,	PUNCT
ejpam-3996	291	196	(	(	PUNCT
ejpam-3996	291	197	4	4	NUM
ejpam-3996	291	198	,	,	PUNCT
ejpam-3996	291	199	4i	4i	NUM
ejpam-3996	291	200	)	)	PUNCT
ejpam-3996	291	201	,	,	PUNCT
ejpam-3996	291	202	(	(	PUNCT
ejpam-3996	291	203	5	5	NUM
ejpam-3996	291	204	,	,	PUNCT
ejpam-3996	291	205	4i	4i	NUM
ejpam-3996	291	206	)	)	PUNCT
ejpam-3996	291	207	,	,	PUNCT
ejpam-3996	291	208	(	(	PUNCT
ejpam-3996	291	209	0	0	NUM
ejpam-3996	291	210	,	,	PUNCT
ejpam-3996	291	211	5i	5i	NUM
ejpam-3996	291	212	)	)	PUNCT
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ejpam-3996	294	12	i	i	NOUN
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ejpam-3996	294	14	,	,	PUNCT
ejpam-3996	294	15	(	(	PUNCT
ejpam-3996	294	16	2	2	NUM
ejpam-3996	294	17	,	,	PUNCT
ejpam-3996	294	18	2i	2i	NUM
ejpam-3996	294	19	)	)	PUNCT
ejpam-3996	294	20	,	,	PUNCT
ejpam-3996	294	21	(	(	PUNCT
ejpam-3996	294	22	3	3	NUM
ejpam-3996	294	23	,	,	PUNCT
ejpam-3996	294	24	3i	3i	NUM
ejpam-3996	294	25	)	)	PUNCT
ejpam-3996	294	26	,	,	PUNCT
ejpam-3996	294	27	(	(	PUNCT
ejpam-3996	294	28	4	4	NUM
ejpam-3996	294	29	,	,	PUNCT
ejpam-3996	294	30	4i	4i	NUM
ejpam-3996	294	31	)	)	PUNCT
ejpam-3996	294	32	,	,	PUNCT
ejpam-3996	294	33	(	(	PUNCT
ejpam-3996	294	34	5	5	NUM
ejpam-3996	294	35	,	,	PUNCT
ejpam-3996	294	36	5i	5i	NUM
ejpam-3996	294	37	)	)	PUNCT
ejpam-3996	294	38	}	}	PUNCT
ejpam-3996	294	39	aside	aside	ADV
ejpam-3996	294	40	from	from	ADP
ejpam-3996	294	41	{	{	PUNCT
ejpam-3996	294	42	(	(	PUNCT
ejpam-3996	294	43	0	0	NUM
ejpam-3996	294	44	,	,	PUNCT
ejpam-3996	294	45	0i	0i	NOUN
ejpam-3996	294	46	)	)	PUNCT
ejpam-3996	294	47	}	}	PUNCT
ejpam-3996	294	48	,	,	PUNCT
ejpam-3996	294	49	setsx	setsx	NOUN
ejpam-3996	294	50	′	′	NOUN
ejpam-3996	294	51	,	,	PUNCT
ejpam-3996	294	52	{	{	PUNCT
ejpam-3996	294	53	(	(	PUNCT
ejpam-3996	294	54	0	0	NUM
ejpam-3996	294	55	,	,	PUNCT
ejpam-3996	294	56	0i	0i	NOUN
ejpam-3996	294	57	)	)	PUNCT
ejpam-3996	294	58	,	,	PUNCT
ejpam-3996	294	59	(	(	PUNCT
ejpam-3996	294	60	1	1	NUM
ejpam-3996	294	61	,	,	PUNCT
ejpam-3996	294	62	0i	0i	NOUN
ejpam-3996	294	63	)	)	PUNCT
ejpam-3996	294	64	,	,	PUNCT
ejpam-3996	294	65	(	(	PUNCT
ejpam-3996	294	66	2	2	NUM
ejpam-3996	294	67	,	,	PUNCT
ejpam-3996	294	68	0i	0i	NOUN
ejpam-3996	294	69	)	)	PUNCT
ejpam-3996	294	70	}	}	PUNCT
ejpam-3996	294	71	,	,	PUNCT
ejpam-3996	294	72	{	{	PUNCT
ejpam-3996	294	73	(	(	PUNCT
ejpam-3996	294	74	0	0	NUM
ejpam-3996	294	75	,	,	PUNCT
ejpam-3996	294	76	0i	0i	NOUN
ejpam-3996	294	77	)	)	PUNCT
ejpam-3996	294	78	,	,	PUNCT
ejpam-3996	294	79	(	(	PUNCT
ejpam-3996	294	80	3	3	NUM
ejpam-3996	294	81	,	,	PUNCT
ejpam-3996	294	82	3i	3i	NUM
ejpam-3996	294	83	)	)	PUNCT
ejpam-3996	294	84	}	}	PUNCT
ejpam-3996	294	85	,	,	PUNCT
ejpam-3996	294	86	{	{	PUNCT
ejpam-3996	294	87	(	(	PUNCT
ejpam-3996	294	88	0	0	NUM
ejpam-3996	294	89	,	,	PUNCT
ejpam-3996	294	90	0i	0i	NOUN
ejpam-3996	294	91	)	)	PUNCT
ejpam-3996	294	92	,	,	PUNCT
ejpam-3996	294	93	(	(	PUNCT
ejpam-3996	294	94	4	4	NUM
ejpam-3996	294	95	,	,	PUNCT
ejpam-3996	294	96	4i	4i	NUM
ejpam-3996	294	97	)	)	PUNCT
ejpam-3996	294	98	}	}	PUNCT
ejpam-3996	294	99	,	,	PUNCT
ejpam-3996	294	100	{	{	PUNCT
ejpam-3996	294	101	(	(	PUNCT
ejpam-3996	294	102	0	0	NUM
ejpam-3996	294	103	,	,	PUNCT
ejpam-3996	294	104	0i	0i	NOUN
ejpam-3996	294	105	)	)	PUNCT
ejpam-3996	294	106	,	,	PUNCT
ejpam-3996	294	107	(	(	PUNCT
ejpam-3996	294	108	5	5	NUM
ejpam-3996	294	109	,	,	PUNCT
ejpam-3996	294	110	5i	5i	NUM
ejpam-3996	294	111	)	)	PUNCT
ejpam-3996	294	112	}	}	PUNCT
ejpam-3996	294	113	and	and	CCONJ
ejpam-3996	294	114	{	{	PUNCT
ejpam-3996	294	115	(	(	PUNCT
ejpam-3996	294	116	0	0	NUM
ejpam-3996	294	117	,	,	PUNCT
ejpam-3996	294	118	0i	0i	NOUN
ejpam-3996	294	119	)	)	PUNCT
ejpam-3996	294	120	,	,	PUNCT
ejpam-3996	294	121	(	(	PUNCT
ejpam-3996	294	122	1	1	X
ejpam-3996	294	123	,	,	PUNCT
ejpam-3996	294	124	i	i	NOUN
ejpam-3996	294	125	)	)	PUNCT
ejpam-3996	294	126	,	,	PUNCT
ejpam-3996	294	127	(	(	PUNCT
ejpam-3996	294	128	2	2	NUM
ejpam-3996	294	129	,	,	PUNCT
ejpam-3996	294	130	2i	2i	NUM
ejpam-3996	294	131	)	)	PUNCT
ejpam-3996	294	132	}	}	PUNCT
ejpam-3996	294	133	are	be	AUX
ejpam-3996	294	134	proper	proper	ADJ
ejpam-3996	294	135	subsets	subset	NOUN
ejpam-3996	294	136	of	of	ADP
ejpam-3996	294	137	s(i)i	s(i)i	NOUN
ejpam-3996	294	138	,	,	PUNCT
ejpam-3996	294	139	i	i	PRON
ejpam-3996	294	140	=	=	NOUN
ejpam-3996	294	141	1	1	NUM
ejpam-3996	294	142	,	,	PUNCT
ejpam-3996	294	143	2	2	NUM
ejpam-3996	294	144	,	,	PUNCT
ejpam-3996	294	145	3	3	NUM
ejpam-3996	294	146	,	,	PUNCT
ejpam-3996	294	147	4	4	NUM
ejpam-3996	294	148	,	,	PUNCT
ejpam-3996	294	149	5	5	NUM
ejpam-3996	294	150	,	,	PUNCT
ejpam-3996	294	151	6	6	NUM
ejpam-3996	294	152	,	,	PUNCT
ejpam-3996	294	153	respectively	respectively	ADV
ejpam-3996	294	154	,	,	PUNCT
ejpam-3996	294	155	which	which	PRON
ejpam-3996	294	156	are	be	AUX
ejpam-3996	294	157	b	b	NOUN
ejpam-3996	294	158	-	-	PUNCT
ejpam-3996	294	159	algbras	algbra	NOUN
ejpam-3996	294	160	.	.	PUNCT
ejpam-3996	295	1	notice	notice	VERB
ejpam-3996	295	2	that	that	SCONJ
ejpam-3996	295	3	the	the	DET
ejpam-3996	295	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	295	5	b	b	X
ejpam-3996	295	6	-	-	PUNCT
ejpam-3996	295	7	algebra	algebra	NOUN
ejpam-3996	295	8	in	in	ADP
ejpam-3996	295	9	example	example	NOUN
ejpam-3996	295	10	3.6	3.6	NUM
ejpam-3996	295	11	is	be	AUX
ejpam-3996	295	12	a	a	DET
ejpam-3996	295	13	neutrosophic	neutrosophic	ADJ
ejpam-3996	295	14	subalgebra	subalgebra	NOUN
ejpam-3996	295	15	of	of	ADP
ejpam-3996	295	16	the	the	DET
ejpam-3996	295	17	neutrosophic	neutrosophic	ADJ
ejpam-3996	295	18	b	b	X
ejpam-3996	295	19	-	-	PUNCT
ejpam-3996	295	20	algebra	algebra	NOUN
ejpam-3996	295	21	in	in	ADP
ejpam-3996	295	22	example	example	NOUN
ejpam-3996	295	23	3.12	3.12	NUM
ejpam-3996	295	24	.	.	PUNCT
ejpam-3996	296	1	in	in	ADP
ejpam-3996	296	2	a	a	DET
ejpam-3996	296	3	b	b	NOUN
ejpam-3996	296	4	-	-	PUNCT
ejpam-3996	296	5	algebra	algebra	NOUN
ejpam-3996	296	6	,	,	PUNCT
ejpam-3996	296	7	the	the	DET
ejpam-3996	296	8	intersection	intersection	NOUN
ejpam-3996	296	9	of	of	ADP
ejpam-3996	296	10	any	any	DET
ejpam-3996	296	11	collection	collection	NOUN
ejpam-3996	296	12	of	of	ADP
ejpam-3996	296	13	subalgebras	subalgebras	PROPN
ejpam-3996	296	14	is	be	AUX
ejpam-3996	296	15	also	also	ADV
ejpam-3996	296	16	a	a	DET
ejpam-3996	296	17	subalgebra	subalgebra	NOUN
ejpam-3996	296	18	by	by	ADP
ejpam-3996	296	19	lemma	lemma	PROPN
ejpam-3996	296	20	2.8	2.8	NUM
ejpam-3996	296	21	.	.	PUNCT
ejpam-3996	297	1	however	however	ADV
ejpam-3996	297	2	,	,	PUNCT
ejpam-3996	297	3	this	this	PRON
ejpam-3996	297	4	is	be	AUX
ejpam-3996	297	5	not	not	PART
ejpam-3996	297	6	always	always	ADV
ejpam-3996	297	7	the	the	DET
ejpam-3996	297	8	case	case	NOUN
ejpam-3996	297	9	for	for	ADP
ejpam-3996	297	10	neutrosophic	neutrosophic	ADJ
ejpam-3996	297	11	b	b	X
ejpam-3996	297	12	-	-	PUNCT
ejpam-3996	297	13	algebra	algebra	NOUN
ejpam-3996	297	14	.	.	PUNCT
ejpam-3996	298	1	consider	consider	VERB
ejpam-3996	298	2	the	the	DET
ejpam-3996	298	3	following	follow	VERB
ejpam-3996	298	4	example	example	NOUN
ejpam-3996	298	5	.	.	PUNCT
ejpam-3996	299	1	example	example	NOUN
ejpam-3996	299	2	3.26	3.26	NUM
ejpam-3996	299	3	.	.	PUNCT
ejpam-3996	300	1	consider	consider	VERB
ejpam-3996	300	2	the	the	DET
ejpam-3996	300	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	300	4	b	b	X
ejpam-3996	300	5	-	-	PUNCT
ejpam-3996	300	6	algebra	algebra	NOUN
ejpam-3996	300	7	in	in	ADP
ejpam-3996	300	8	example	example	NOUN
ejpam-3996	300	9	3.12	3.12	NUM
ejpam-3996	300	10	and	and	CCONJ
ejpam-3996	300	11	a	a	DET
ejpam-3996	300	12	collection	collection	NOUN
ejpam-3996	300	13	of	of	ADP
ejpam-3996	300	14	its	its	PRON
ejpam-3996	300	15	neutrosophic	neutrosophic	ADJ
ejpam-3996	300	16	subalgebras	subalgebras	NOUN
ejpam-3996	300	17	in	in	ADP
ejpam-3996	300	18	example	example	NOUN
ejpam-3996	300	19	3.25	3.25	NUM
ejpam-3996	300	20	.	.	PUNCT
ejpam-3996	301	1	clearly	clearly	ADV
ejpam-3996	301	2	,	,	PUNCT
ejpam-3996	301	3	6⋂	6⋂	NOUN
ejpam-3996	301	4	i=1	i=1	VERB
ejpam-3996	301	5	s(i)i	s(i)i	PROPN
ejpam-3996	301	6	=	=	PUNCT
ejpam-3996	301	7	{	{	PUNCT
ejpam-3996	301	8	(	(	PUNCT
ejpam-3996	301	9	0	0	NUM
ejpam-3996	301	10	,	,	PUNCT
ejpam-3996	301	11	0i	0i	NOUN
ejpam-3996	301	12	)	)	PUNCT
ejpam-3996	301	13	}	}	PUNCT
ejpam-3996	301	14	is	be	AUX
ejpam-3996	301	15	not	not	PART
ejpam-3996	301	16	a	a	DET
ejpam-3996	301	17	neutrosophic	neutrosophic	ADJ
ejpam-3996	301	18	subalgebra	subalgebra	NOUN
ejpam-3996	301	19	of	of	ADP
ejpam-3996	301	20	x(i	x(i	PROPN
ejpam-3996	301	21	)	)	PUNCT
ejpam-3996	301	22	by	by	ADP
ejpam-3996	301	23	remark	remark	NOUN
ejpam-3996	301	24	3.19	3.19	NUM
ejpam-3996	301	25	.	.	PUNCT
ejpam-3996	302	1	however	however	ADV
ejpam-3996	302	2	,	,	PUNCT
ejpam-3996	302	3	5⋂	5⋂	NUM
ejpam-3996	302	4	i=1	i=1	X
ejpam-3996	302	5	s(i)i	s(i)i	PROPN
ejpam-3996	302	6	=	=	PUNCT
ejpam-3996	302	7	{	{	PUNCT
ejpam-3996	302	8	(	(	PUNCT
ejpam-3996	302	9	0	0	NUM
ejpam-3996	302	10	,	,	PUNCT
ejpam-3996	302	11	0i	0i	NOUN
ejpam-3996	302	12	)	)	PUNCT
ejpam-3996	302	13	,	,	PUNCT
ejpam-3996	302	14	(	(	PUNCT
ejpam-3996	302	15	0	0	NUM
ejpam-3996	302	16	,	,	PUNCT
ejpam-3996	302	17	i	i	NOUN
ejpam-3996	302	18	)	)	PUNCT
ejpam-3996	302	19	,	,	PUNCT
ejpam-3996	302	20	(	(	PUNCT
ejpam-3996	302	21	0	0	NUM
ejpam-3996	302	22	,	,	PUNCT
ejpam-3996	302	23	2i	2i	NUM
ejpam-3996	302	24	)	)	PUNCT
ejpam-3996	302	25	}	}	PUNCT
ejpam-3996	302	26	is	be	AUX
ejpam-3996	302	27	a	a	DET
ejpam-3996	302	28	neutrosophic	neutrosophic	ADJ
ejpam-3996	302	29	subalgebra	subalgebra	NOUN
ejpam-3996	302	30	of	of	ADP
ejpam-3996	302	31	x(i	x(i	PROPN
ejpam-3996	302	32	)	)	PUNCT
ejpam-3996	302	33	with	with	ADP
ejpam-3996	302	34	{	{	PUNCT
ejpam-3996	302	35	(	(	PUNCT
ejpam-3996	302	36	0	0	NUM
ejpam-3996	302	37	,	,	PUNCT
ejpam-3996	302	38	0i	0i	NOUN
ejpam-3996	302	39	)	)	PUNCT
ejpam-3996	302	40	}	}	PUNCT
ejpam-3996	302	41	as	as	ADP
ejpam-3996	302	42	its	its	PRON
ejpam-3996	302	43	proper	proper	ADJ
ejpam-3996	302	44	subset	subset	NOUN
ejpam-3996	302	45	which	which	PRON
ejpam-3996	302	46	is	be	AUX
ejpam-3996	302	47	a	a	DET
ejpam-3996	302	48	b	b	NOUN
ejpam-3996	302	49	-	-	PUNCT
ejpam-3996	302	50	algebra	algebra	NOUN
ejpam-3996	302	51	.	.	PUNCT
ejpam-3996	303	1	the	the	DET
ejpam-3996	303	2	following	follow	VERB
ejpam-3996	303	3	theorem	theorem	NOUN
ejpam-3996	303	4	provides	provide	VERB
ejpam-3996	303	5	a	a	DET
ejpam-3996	303	6	necessary	necessary	ADJ
ejpam-3996	303	7	and	and	CCONJ
ejpam-3996	303	8	sufficient	sufficient	ADJ
ejpam-3996	303	9	condition	condition	NOUN
ejpam-3996	303	10	for	for	ADP
ejpam-3996	303	11	the	the	DET
ejpam-3996	303	12	intersection	intersection	NOUN
ejpam-3996	303	13	of	of	ADP
ejpam-3996	303	14	neutrosophic	neutrosophic	ADJ
ejpam-3996	303	15	subalgebras	subalgebras	PROPN
ejpam-3996	303	16	to	to	PART
ejpam-3996	303	17	be	be	AUX
ejpam-3996	303	18	a	a	DET
ejpam-3996	303	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	303	20	subalgebra	subalgebra	NOUN
ejpam-3996	303	21	.	.	PUNCT
ejpam-3996	304	1	theorem	theorem	VERB
ejpam-3996	304	2	3.27	3.27	NUM
ejpam-3996	304	3	.	.	PUNCT
ejpam-3996	305	1	let	let	VERB
ejpam-3996	305	2	{	{	PUNCT
ejpam-3996	305	3	s(i)α	s(i)α	X
ejpam-3996	305	4	:	:	PUNCT
ejpam-3996	305	5	α	α	X
ejpam-3996	305	6	∈	∈	PROPN
ejpam-3996	305	7	a	a	DET
ejpam-3996	305	8	}	}	PUNCT
ejpam-3996	305	9	be	be	AUX
ejpam-3996	305	10	any	any	DET
ejpam-3996	305	11	nonempty	nonempty	ADJ
ejpam-3996	305	12	collection	collection	NOUN
ejpam-3996	305	13	of	of	ADP
ejpam-3996	305	14	neutrosophic	neutrosophic	ADJ
ejpam-3996	305	15	subalgebras	subalgebras	PROPN
ejpam-3996	305	16	(	(	PUNCT
ejpam-3996	305	17	resp	resp	NOUN
ejpam-3996	305	18	.	.	PUNCT
ejpam-3996	305	19	,	,	PUNCT
ejpam-3996	305	20	normal	normal	ADJ
ejpam-3996	305	21	neutrosophic	neutrosophic	ADJ
ejpam-3996	305	22	subalgebras	subalgebra	NOUN
ejpam-3996	305	23	)	)	PUNCT
ejpam-3996	305	24	of	of	ADP
ejpam-3996	305	25	a	a	DET
ejpam-3996	305	26	neutrosophic	neutrosophic	ADJ
ejpam-3996	305	27	b	b	X
ejpam-3996	305	28	-	-	PUNCT
ejpam-3996	305	29	algebra	algebra	NOUN
ejpam-3996	305	30	x(i	x(i	PROPN
ejpam-3996	305	31	)	)	PUNCT
ejpam-3996	305	32	.	.	PUNCT
ejpam-3996	306	1	if⋂	if⋂	ADJ
ejpam-3996	306	2	α∈a	α∈a	NOUN
ejpam-3996	306	3	s(i)α	s(i)α	VERB
ejpam-3996	306	4	6=	6=	X
ejpam-3996	306	5	{	{	PUNCT
ejpam-3996	306	6	(	(	PUNCT
ejpam-3996	306	7	0	0	NUM
ejpam-3996	306	8	,	,	PUNCT
ejpam-3996	306	9	0i	0i	NOUN
ejpam-3996	306	10	)	)	PUNCT
ejpam-3996	306	11	}	}	PUNCT
ejpam-3996	306	12	,	,	PUNCT
ejpam-3996	306	13	then	then	ADV
ejpam-3996	306	14	⋂	⋂	PROPN
ejpam-3996	306	15	α∈a	α∈a	NOUN
ejpam-3996	306	16	s(i)α	s(i)α	PROPN
ejpam-3996	306	17	is	be	AUX
ejpam-3996	306	18	a	a	DET
ejpam-3996	306	19	neutrosophic	neutrosophic	ADJ
ejpam-3996	306	20	subalgebra	subalgebra	NOUN
ejpam-3996	306	21	(	(	PUNCT
ejpam-3996	306	22	resp	resp	NOUN
ejpam-3996	306	23	.	.	PUNCT
ejpam-3996	307	1	,	,	PUNCT
ejpam-3996	307	2	normal	normal	ADJ
ejpam-3996	307	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	307	4	subalgebra	subalgebra	NOUN
ejpam-3996	307	5	)	)	PUNCT
ejpam-3996	307	6	of	of	ADP
ejpam-3996	307	7	x(i	x(i	PROPN
ejpam-3996	307	8	)	)	PUNCT
ejpam-3996	307	9	.	.	PUNCT
ejpam-3996	308	1	proof	proof	NOUN
ejpam-3996	308	2	:	:	PUNCT
ejpam-3996	308	3	since	since	SCONJ
ejpam-3996	308	4	(	(	PUNCT
ejpam-3996	308	5	0	0	NUM
ejpam-3996	308	6	,	,	PUNCT
ejpam-3996	308	7	0i	0i	NOUN
ejpam-3996	308	8	)	)	PUNCT
ejpam-3996	308	9	∈	∈	PROPN
ejpam-3996	308	10	s(i)α	s(i)α	VERB
ejpam-3996	308	11	for	for	ADP
ejpam-3996	308	12	every	every	DET
ejpam-3996	308	13	α	α	NOUN
ejpam-3996	308	14	∈	∈	PROPN
ejpam-3996	308	15	a	a	PRON
ejpam-3996	308	16	,	,	PUNCT
ejpam-3996	308	17	(	(	PUNCT
ejpam-3996	308	18	0	0	NUM
ejpam-3996	308	19	,	,	PUNCT
ejpam-3996	308	20	0i	0i	NOUN
ejpam-3996	308	21	)	)	PUNCT
ejpam-3996	309	1	∈	∈	PROPN
ejpam-3996	309	2	⋂	⋂	PROPN
ejpam-3996	309	3	α∈a	α∈a	NOUN
ejpam-3996	309	4	s(i)α	s(i)α	PROPN
ejpam-3996	309	5	so	so	SCONJ
ejpam-3996	309	6	that	that	SCONJ
ejpam-3996	309	7	⋂	⋂	PROPN
ejpam-3996	309	8	α∈a	α∈a	ADV
ejpam-3996	309	9	s(i)α	s(i)α	PROPN
ejpam-3996	309	10	6=	6=	ADP
ejpam-3996	309	11	∅.	∅.	VERB
ejpam-3996	309	12	since	since	SCONJ
ejpam-3996	309	13	⋂	⋂	PROPN
ejpam-3996	309	14	α∈a	α∈a	ADV
ejpam-3996	309	15	s(i)α	s(i)α	X
ejpam-3996	309	16	6=	6=	X
ejpam-3996	309	17	{	{	PUNCT
ejpam-3996	309	18	(	(	PUNCT
ejpam-3996	309	19	0	0	NUM
ejpam-3996	309	20	,	,	PUNCT
ejpam-3996	309	21	0i	0i	NOUN
ejpam-3996	309	22	)	)	PUNCT
ejpam-3996	309	23	}	}	PUNCT
ejpam-3996	309	24	,	,	PUNCT
ejpam-3996	309	25	there	there	PRON
ejpam-3996	309	26	exists	exist	VERB
ejpam-3996	309	27	(	(	PUNCT
ejpam-3996	309	28	a	a	PRON
ejpam-3996	309	29	,	,	PUNCT
ejpam-3996	309	30	bi	bi	ADJ
ejpam-3996	309	31	)	)	PUNCT
ejpam-3996	309	32	∈	∈	PROPN
ejpam-3996	309	33	⋂	⋂	PROPN
ejpam-3996	309	34	α∈a	α∈a	NOUN
ejpam-3996	309	35	s(i)α	s(i)α	VERB
ejpam-3996	309	36	such	such	ADJ
ejpam-3996	309	37	that	that	SCONJ
ejpam-3996	309	38	(	(	PUNCT
ejpam-3996	309	39	a	a	PRON
ejpam-3996	309	40	,	,	PUNCT
ejpam-3996	309	41	bi	bi	NOUN
ejpam-3996	309	42	)	)	PUNCT
ejpam-3996	309	43	6=	6=	ADP
ejpam-3996	309	44	(	(	PUNCT
ejpam-3996	309	45	0	0	NUM
ejpam-3996	309	46	,	,	PUNCT
ejpam-3996	309	47	0i	0i	NOUN
ejpam-3996	309	48	)	)	PUNCT
ejpam-3996	309	49	.	.	PUNCT
ejpam-3996	310	1	thus	thus	ADV
ejpam-3996	310	2	,	,	PUNCT
ejpam-3996	310	3	{	{	PUNCT
ejpam-3996	310	4	(	(	PUNCT
ejpam-3996	310	5	0	0	NUM
ejpam-3996	310	6	,	,	PUNCT
ejpam-3996	310	7	0i	0i	NOUN
ejpam-3996	310	8	)	)	PUNCT
ejpam-3996	310	9	}	}	PUNCT
ejpam-3996	310	10	(	(	PUNCT
ejpam-3996	310	11	⋂	⋂	PROPN
ejpam-3996	310	12	α∈a	α∈a	NOUN
ejpam-3996	310	13	s(i)α	s(i)α	PROPN
ejpam-3996	310	14	which	which	PRON
ejpam-3996	310	15	is	be	AUX
ejpam-3996	310	16	a	a	DET
ejpam-3996	310	17	b	b	NOUN
ejpam-3996	310	18	-	-	PUNCT
ejpam-3996	310	19	algebra	algebra	NOUN
ejpam-3996	310	20	.	.	PUNCT
ejpam-3996	311	1	let	let	VERB
ejpam-3996	311	2	(	(	PUNCT
ejpam-3996	311	3	a	a	DET
ejpam-3996	311	4	,	,	PUNCT
ejpam-3996	311	5	bi	bi	NOUN
ejpam-3996	311	6	)	)	PUNCT
ejpam-3996	311	7	,	,	PUNCT
ejpam-3996	311	8	(	(	PUNCT
ejpam-3996	311	9	c	c	X
ejpam-3996	311	10	,	,	PUNCT
ejpam-3996	311	11	di	di	NOUN
ejpam-3996	311	12	)	)	PUNCT
ejpam-3996	311	13	∈	∈	PROPN
ejpam-3996	311	14	⋂	⋂	PROPN
ejpam-3996	311	15	α∈a	α∈a	PROPN
ejpam-3996	311	16	s(i)α	s(i)α	PROPN
ejpam-3996	311	17	.	.	PUNCT
ejpam-3996	312	1	then	then	ADV
ejpam-3996	312	2	(	(	PUNCT
ejpam-3996	312	3	a	a	PRON
ejpam-3996	312	4	,	,	PUNCT
ejpam-3996	312	5	bi	bi	NOUN
ejpam-3996	312	6	)	)	PUNCT
ejpam-3996	312	7	,	,	PUNCT
ejpam-3996	312	8	(	(	PUNCT
ejpam-3996	312	9	c	c	X
ejpam-3996	312	10	,	,	PUNCT
ejpam-3996	312	11	di	di	NOUN
ejpam-3996	312	12	)	)	PUNCT
ejpam-3996	312	13	∈	∈	NOUN
ejpam-3996	312	14	s(i)α	s(i)α	VERB
ejpam-3996	312	15	for	for	ADP
ejpam-3996	312	16	every	every	DET
ejpam-3996	312	17	α	α	NOUN
ejpam-3996	312	18	∈	∈	PROPN
ejpam-3996	312	19	a	a	PRON
ejpam-3996	312	20	.	.	PUNCT
ejpam-3996	313	1	since	since	SCONJ
ejpam-3996	313	2	for	for	ADP
ejpam-3996	313	3	every	every	DET
ejpam-3996	313	4	α	α	NOUN
ejpam-3996	313	5	∈	∈	PROPN
ejpam-3996	313	6	a	a	PRON
ejpam-3996	313	7	,	,	PUNCT
ejpam-3996	313	8	s(i)α	s(i)α	PROPN
ejpam-3996	313	9	is	be	AUX
ejpam-3996	313	10	a	a	DET
ejpam-3996	313	11	neutrosophic	neutrosophic	ADJ
ejpam-3996	313	12	subalgebra	subalgebra	NOUN
ejpam-3996	313	13	of	of	ADP
ejpam-3996	313	14	x(i	x(i	PROPN
ejpam-3996	313	15	)	)	PUNCT
ejpam-3996	313	16	,	,	PUNCT
ejpam-3996	313	17	(	(	PUNCT
ejpam-3996	313	18	a	a	DET
ejpam-3996	313	19	,	,	PUNCT
ejpam-3996	313	20	bi	bi	NOUN
ejpam-3996	313	21	)	)	PUNCT
ejpam-3996	313	22	·	·	PUNCT
ejpam-3996	314	1	(	(	PUNCT
ejpam-3996	314	2	c	c	X
ejpam-3996	314	3	,	,	PUNCT
ejpam-3996	314	4	di	di	NOUN
ejpam-3996	314	5	)	)	PUNCT
ejpam-3996	314	6	∈	∈	NOUN
ejpam-3996	314	7	s(i)α	s(i)α	VERB
ejpam-3996	314	8	for	for	ADP
ejpam-3996	314	9	every	every	DET
ejpam-3996	314	10	α	α	NOUN
ejpam-3996	314	11	∈	∈	PROPN
ejpam-3996	314	12	a	a	PRON
ejpam-3996	314	13	.	.	PUNCT
ejpam-3996	315	1	thus	thus	ADV
ejpam-3996	315	2	,	,	PUNCT
ejpam-3996	315	3	(	(	PUNCT
ejpam-3996	315	4	a	a	DET
ejpam-3996	315	5	,	,	PUNCT
ejpam-3996	315	6	bi	bi	NOUN
ejpam-3996	315	7	)	)	PUNCT
ejpam-3996	315	8	·	·	PUNCT
ejpam-3996	316	1	(	(	PUNCT
ejpam-3996	316	2	c	c	X
ejpam-3996	316	3	,	,	PUNCT
ejpam-3996	316	4	di	di	NOUN
ejpam-3996	316	5	)	)	PUNCT
ejpam-3996	316	6	∈⋂	∈⋂	PROPN
ejpam-3996	316	7	α∈a	α∈a	PROPN
ejpam-3996	316	8	s(i)α	s(i)α	PROPN
ejpam-3996	316	9	.	.	PUNCT
ejpam-3996	317	1	hence	hence	ADV
ejpam-3996	317	2	,	,	PUNCT
ejpam-3996	317	3	⋂	⋂	PROPN
ejpam-3996	317	4	α∈a	α∈a	NOUN
ejpam-3996	317	5	s(i)α	s(i)α	PROPN
ejpam-3996	317	6	is	be	AUX
ejpam-3996	317	7	a	a	DET
ejpam-3996	317	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	317	9	subalgebra	subalgebra	NOUN
ejpam-3996	317	10	of	of	ADP
ejpam-3996	317	11	x(i	x(i	PROPN
ejpam-3996	317	12	)	)	PUNCT
ejpam-3996	317	13	.	.	PUNCT
ejpam-3996	318	1	moreover	moreover	ADV
ejpam-3996	318	2	,	,	PUNCT
ejpam-3996	318	3	let	let	VERB
ejpam-3996	318	4	{	{	PUNCT
ejpam-3996	318	5	s(i)α	s(i)α	X
ejpam-3996	318	6	:	:	PUNCT
ejpam-3996	318	7	α	α	X
ejpam-3996	318	8	∈	∈	PROPN
ejpam-3996	318	9	a	a	DET
ejpam-3996	318	10	}	}	PUNCT
ejpam-3996	318	11	be	be	AUX
ejpam-3996	318	12	any	any	DET
ejpam-3996	318	13	nonempty	nonempty	ADJ
ejpam-3996	318	14	collection	collection	NOUN
ejpam-3996	318	15	of	of	ADP
ejpam-3996	318	16	normal	normal	ADJ
ejpam-3996	318	17	neutrosophic	neutrosophic	ADJ
ejpam-3996	318	18	subalgebras	subalgebra	NOUN
ejpam-3996	318	19	of	of	ADP
ejpam-3996	318	20	a	a	DET
ejpam-3996	318	21	x(i	x(i	PROPN
ejpam-3996	318	22	)	)	PUNCT
ejpam-3996	318	23	and	and	CCONJ
ejpam-3996	318	24	(	(	PUNCT
ejpam-3996	318	25	a	a	DET
ejpam-3996	318	26	,	,	PUNCT
ejpam-3996	318	27	bi)·(c	bi)·(c	NOUN
ejpam-3996	318	28	,	,	PUNCT
ejpam-3996	318	29	di	di	NOUN
ejpam-3996	318	30	)	)	PUNCT
ejpam-3996	318	31	,	,	PUNCT
ejpam-3996	318	32	(	(	PUNCT
ejpam-3996	318	33	x	x	X
ejpam-3996	318	34	,	,	PUNCT
ejpam-3996	318	35	yi)·(u	yi)·(u	NOUN
ejpam-3996	318	36	,	,	PUNCT
ejpam-3996	318	37	vi	vi	NOUN
ejpam-3996	318	38	)	)	PUNCT
ejpam-3996	318	39	∈	∈	PROPN
ejpam-3996	318	40	⋂	⋂	PROPN
ejpam-3996	318	41	α∈a	α∈a	PROPN
ejpam-3996	318	42	s(i)α	s(i)α	PROPN
ejpam-3996	318	43	.	.	PUNCT
ejpam-3996	319	1	then	then	ADV
ejpam-3996	319	2	(	(	PUNCT
ejpam-3996	319	3	a	a	DET
ejpam-3996	319	4	,	,	PUNCT
ejpam-3996	319	5	bi)·(c	bi)·(c	NOUN
ejpam-3996	319	6	,	,	PUNCT
ejpam-3996	319	7	di	di	NOUN
ejpam-3996	319	8	)	)	PUNCT
ejpam-3996	319	9	,	,	PUNCT
ejpam-3996	319	10	(	(	PUNCT
ejpam-3996	319	11	x	x	X
ejpam-3996	319	12	,	,	PUNCT
ejpam-3996	319	13	yi)·(u	yi)·(u	NOUN
ejpam-3996	319	14	,	,	PUNCT
ejpam-3996	319	15	vi	vi	NOUN
ejpam-3996	319	16	)	)	PUNCT
ejpam-3996	319	17	∈	∈	NOUN
ejpam-3996	319	18	s(i)α	s(i)α	VERB
ejpam-3996	319	19	for	for	ADP
ejpam-3996	319	20	every	every	DET
ejpam-3996	319	21	α	α	NOUN
ejpam-3996	319	22	∈	∈	PROPN
ejpam-3996	319	23	a	a	PRON
ejpam-3996	319	24	.	.	PUNCT
ejpam-3996	320	1	since	since	SCONJ
ejpam-3996	320	2	s(i)α	s(i)α	PROPN
ejpam-3996	320	3	is	be	AUX
ejpam-3996	320	4	normal	normal	ADJ
ejpam-3996	320	5	for	for	ADP
ejpam-3996	320	6	every	every	DET
ejpam-3996	320	7	α	α	NOUN
ejpam-3996	320	8	∈	∈	PROPN
ejpam-3996	320	9	a	a	DET
ejpam-3996	320	10	,	,	PUNCT
ejpam-3996	320	11	[	[	X
ejpam-3996	320	12	(	(	PUNCT
ejpam-3996	320	13	a	a	DET
ejpam-3996	320	14	,	,	PUNCT
ejpam-3996	320	15	bi	bi	NOUN
ejpam-3996	320	16	)	)	PUNCT
ejpam-3996	320	17	·	·	PUNCT
ejpam-3996	321	1	(	(	PUNCT
ejpam-3996	321	2	x	x	NOUN
ejpam-3996	321	3	,	,	PUNCT
ejpam-3996	321	4	yi	yi	PROPN
ejpam-3996	321	5	)	)	PUNCT
ejpam-3996	321	6	]	]	PUNCT
ejpam-3996	321	7	·	·	PUNCT
ejpam-3996	322	1	[	[	X
ejpam-3996	322	2	(	(	PUNCT
ejpam-3996	322	3	c	c	NOUN
ejpam-3996	322	4	,	,	PUNCT
ejpam-3996	322	5	di	di	NOUN
ejpam-3996	322	6	)	)	PUNCT
ejpam-3996	322	7	·	·	PUNCT
ejpam-3996	322	8	(	(	PUNCT
ejpam-3996	322	9	u	u	NOUN
ejpam-3996	322	10	,	,	PUNCT
ejpam-3996	322	11	vi	vi	PROPN
ejpam-3996	322	12	)	)	PUNCT
ejpam-3996	322	13	]	]	PUNCT
ejpam-3996	322	14	∈	∈	PROPN
ejpam-3996	322	15	references	reference	NOUN
ejpam-3996	322	16	903	903	NUM
ejpam-3996	322	17	s(i)α	s(i)α	VERB
ejpam-3996	322	18	for	for	ADP
ejpam-3996	322	19	every	every	DET
ejpam-3996	322	20	α	α	NOUN
ejpam-3996	322	21	∈	∈	PROPN
ejpam-3996	322	22	a	a	PRON
ejpam-3996	322	23	.	.	PUNCT
ejpam-3996	323	1	hence	hence	ADV
ejpam-3996	323	2	,	,	PUNCT
ejpam-3996	323	3	[	[	X
ejpam-3996	323	4	(	(	PUNCT
ejpam-3996	323	5	a	a	DET
ejpam-3996	323	6	,	,	PUNCT
ejpam-3996	323	7	bi	bi	NOUN
ejpam-3996	323	8	)	)	PUNCT
ejpam-3996	323	9	·	·	PUNCT
ejpam-3996	323	10	(	(	PUNCT
ejpam-3996	323	11	x	x	NOUN
ejpam-3996	323	12	,	,	PUNCT
ejpam-3996	323	13	yi	yi	PROPN
ejpam-3996	323	14	)	)	PUNCT
ejpam-3996	323	15	]	]	PUNCT
ejpam-3996	323	16	·	·	PUNCT
ejpam-3996	324	1	[	[	X
ejpam-3996	324	2	(	(	PUNCT
ejpam-3996	324	3	c	c	NOUN
ejpam-3996	324	4	,	,	PUNCT
ejpam-3996	324	5	di	di	NOUN
ejpam-3996	324	6	)	)	PUNCT
ejpam-3996	324	7	·	·	PUNCT
ejpam-3996	324	8	(	(	PUNCT
ejpam-3996	324	9	u	u	NOUN
ejpam-3996	324	10	,	,	PUNCT
ejpam-3996	324	11	vi	vi	PROPN
ejpam-3996	324	12	)	)	PUNCT
ejpam-3996	324	13	]	]	PUNCT
ejpam-3996	324	14	∈	∈	PROPN
ejpam-3996	324	15	⋂	⋂	PROPN
ejpam-3996	324	16	α∈a	α∈a	PROPN
ejpam-3996	324	17	s(i)α	s(i)α	PROPN
ejpam-3996	324	18	.	.	PROPN
ejpam-3996	324	19	therefore,⋂	therefore,⋂	NOUN
ejpam-3996	324	20	α∈a	α∈a	NOUN
ejpam-3996	325	1	s(i)α	s(i)α	PROPN
ejpam-3996	325	2	is	be	AUX
ejpam-3996	325	3	a	a	DET
ejpam-3996	325	4	normal	normal	ADJ
ejpam-3996	325	5	neutrosophic	neutrosophic	ADJ
ejpam-3996	325	6	subalgebra	subalgebra	NOUN
ejpam-3996	325	7	of	of	ADP
ejpam-3996	325	8	x(i	x(i	PROPN
ejpam-3996	325	9	)	)	PUNCT
ejpam-3996	325	10	.	.	PUNCT
ejpam-3996	326	1	�	�	PROPN
ejpam-3996	326	2	example	example	NOUN
ejpam-3996	326	3	3.28	3.28	NUM
ejpam-3996	326	4	.	.	PUNCT
ejpam-3996	327	1	consider	consider	VERB
ejpam-3996	327	2	the	the	DET
ejpam-3996	327	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	327	4	b	b	X
ejpam-3996	327	5	-	-	PUNCT
ejpam-3996	327	6	algebra	algebra	NOUN
ejpam-3996	327	7	in	in	ADP
ejpam-3996	327	8	example	example	NOUN
ejpam-3996	327	9	3.12	3.12	NUM
ejpam-3996	327	10	and	and	CCONJ
ejpam-3996	327	11	a	a	DET
ejpam-3996	327	12	collection	collection	NOUN
ejpam-3996	327	13	of	of	ADP
ejpam-3996	327	14	its	its	PRON
ejpam-3996	327	15	neutrosophic	neutrosophic	ADJ
ejpam-3996	327	16	subalgebras	subalgebras	NOUN
ejpam-3996	327	17	in	in	ADP
ejpam-3996	327	18	example	example	NOUN
ejpam-3996	327	19	3.25	3.25	NUM
ejpam-3996	327	20	.	.	PUNCT
ejpam-3996	328	1	the	the	DET
ejpam-3996	328	2	union	union	NOUN
ejpam-3996	328	3	6⋃	6⋃	NUM
ejpam-3996	328	4	i=4	i=4	ADJ
ejpam-3996	328	5	s(i)i	s(i)i	NOUN
ejpam-3996	328	6	is	be	AUX
ejpam-3996	328	7	not	not	PART
ejpam-3996	328	8	a	a	DET
ejpam-3996	328	9	neutrosophic	neutrosophic	ADJ
ejpam-3996	328	10	subalgebra	subalgebra	NOUN
ejpam-3996	328	11	of	of	ADP
ejpam-3996	328	12	x(i	x(i	PROPN
ejpam-3996	328	13	)	)	PUNCT
ejpam-3996	328	14	since	since	SCONJ
ejpam-3996	328	15	(	(	PUNCT
ejpam-3996	328	16	1	1	NUM
ejpam-3996	328	17	,	,	PUNCT
ejpam-3996	328	18	i	i	NOUN
ejpam-3996	328	19	)	)	PUNCT
ejpam-3996	328	20	,	,	PUNCT
ejpam-3996	328	21	(	(	PUNCT
ejpam-3996	328	22	0	0	NUM
ejpam-3996	328	23	,	,	PUNCT
ejpam-3996	328	24	5i	5i	NUM
ejpam-3996	328	25	)	)	PUNCT
ejpam-3996	328	26	∈	∈	PROPN
ejpam-3996	328	27	6⋃	6⋃	NUM
ejpam-3996	328	28	i=4	i=4	ADJ
ejpam-3996	328	29	s(i)i	s(i)i	NOUN
ejpam-3996	328	30	but	but	CCONJ
ejpam-3996	328	31	(	(	PUNCT
ejpam-3996	328	32	1	1	NUM
ejpam-3996	328	33	,	,	PUNCT
ejpam-3996	328	34	i	i	NOUN
ejpam-3996	328	35	)	)	PUNCT
ejpam-3996	328	36	·	·	PUNCT
ejpam-3996	329	1	(	(	PUNCT
ejpam-3996	329	2	0	0	NUM
ejpam-3996	329	3	,	,	PUNCT
ejpam-3996	329	4	5i	5i	NUM
ejpam-3996	329	5	)	)	PUNCT
ejpam-3996	329	6	=	=	SYM
ejpam-3996	329	7	(	(	PUNCT
ejpam-3996	329	8	1	1	NUM
ejpam-3996	329	9	,	,	PUNCT
ejpam-3996	329	10	4i	4i	NUM
ejpam-3996	329	11	)	)	PUNCT
ejpam-3996	329	12	/∈	/∈	PUNCT
ejpam-3996	330	1	6⋃	6⋃	NUM
ejpam-3996	330	2	i=4	i=4	ADJ
ejpam-3996	330	3	s(i)i	s(i)i	NOUN
ejpam-3996	330	4	.	.	PUNCT
ejpam-3996	331	1	theorem	theorem	VERB
ejpam-3996	331	2	3.29	3.29	NUM
ejpam-3996	331	3	.	.	PUNCT
ejpam-3996	332	1	let	let	VERB
ejpam-3996	332	2	{	{	PUNCT
ejpam-3996	332	3	s(i)i	s(i)i	VERB
ejpam-3996	332	4	:	:	PUNCT
ejpam-3996	333	1	i	i	PRON
ejpam-3996	333	2	∈	∈	VERB
ejpam-3996	333	3	i	i	PRON
ejpam-3996	333	4	}	}	PUNCT
ejpam-3996	333	5	be	be	VERB
ejpam-3996	333	6	any	any	DET
ejpam-3996	333	7	nonempty	nonempty	ADJ
ejpam-3996	333	8	collection	collection	NOUN
ejpam-3996	333	9	of	of	ADP
ejpam-3996	333	10	neutrosophic	neutrosophic	ADJ
ejpam-3996	333	11	subalgebras	subalgebra	NOUN
ejpam-3996	333	12	of	of	ADP
ejpam-3996	333	13	a	a	DET
ejpam-3996	333	14	neutrosophic	neutrosophic	ADJ
ejpam-3996	333	15	b	b	X
ejpam-3996	333	16	-	-	PUNCT
ejpam-3996	333	17	algebra	algebra	NOUN
ejpam-3996	333	18	x(i	x(i	PROPN
ejpam-3996	333	19	)	)	PUNCT
ejpam-3996	333	20	such	such	ADJ
ejpam-3996	333	21	that	that	SCONJ
ejpam-3996	333	22	s(i)1	s(i)1	NOUN
ejpam-3996	333	23	⊆	⊆	SYM
ejpam-3996	333	24	s(i)2	s(i)2	NOUN
ejpam-3996	333	25	⊆	⊆	NUM
ejpam-3996	333	26	s(i)3	s(i)3	PROPN
ejpam-3996	333	27	⊆	⊆	NUM
ejpam-3996	333	28	·	·	PUNCT
ejpam-3996	333	29	·	·	PUNCT
ejpam-3996	333	30	·	·	PUNCT
ejpam-3996	333	31	.	.	PUNCT
ejpam-3996	334	1	then⋃	then⋃	PROPN
ejpam-3996	334	2	i∈i	i∈i	PROPN
ejpam-3996	334	3	s(i)i	s(i)i	PROPN
ejpam-3996	334	4	is	be	AUX
ejpam-3996	334	5	a	a	DET
ejpam-3996	334	6	neutrosophic	neutrosophic	ADJ
ejpam-3996	334	7	subalgebra	subalgebra	NOUN
ejpam-3996	334	8	of	of	ADP
ejpam-3996	334	9	x(i	x(i	PROPN
ejpam-3996	334	10	)	)	PUNCT
ejpam-3996	334	11	.	.	PUNCT
ejpam-3996	335	1	proof	proof	NOUN
ejpam-3996	335	2	:	:	PUNCT
ejpam-3996	335	3	clearly	clearly	ADV
ejpam-3996	335	4	,	,	PUNCT
ejpam-3996	335	5	⋃	⋃	ADP
ejpam-3996	335	6	i∈i	i∈i	ADJ
ejpam-3996	335	7	s(i)i	s(i)i	NOUN
ejpam-3996	335	8	6=	6=	ADP
ejpam-3996	335	9	∅.	∅.	AUX
ejpam-3996	335	10	let	let	VERB
ejpam-3996	335	11	(	(	PUNCT
ejpam-3996	335	12	a	a	DET
ejpam-3996	335	13	,	,	PUNCT
ejpam-3996	335	14	bi	bi	NOUN
ejpam-3996	335	15	)	)	PUNCT
ejpam-3996	335	16	,	,	PUNCT
ejpam-3996	335	17	(	(	PUNCT
ejpam-3996	335	18	c	c	X
ejpam-3996	335	19	,	,	PUNCT
ejpam-3996	335	20	di	di	NOUN
ejpam-3996	335	21	)	)	PUNCT
ejpam-3996	335	22	∈	∈	PROPN
ejpam-3996	335	23	⋃	⋃	NOUN
ejpam-3996	335	24	i∈i	i∈i	ADJ
ejpam-3996	335	25	s(i)i	s(i)i	NOUN
ejpam-3996	335	26	.	.	PUNCT
ejpam-3996	336	1	then	then	ADV
ejpam-3996	336	2	for	for	ADP
ejpam-3996	336	3	some	some	DET
ejpam-3996	336	4	i	i	PRON
ejpam-3996	336	5	∈	∈	PROPN
ejpam-3996	337	1	i	i	PRON
ejpam-3996	337	2	,	,	PUNCT
ejpam-3996	337	3	(	(	PUNCT
ejpam-3996	337	4	a	a	PRON
ejpam-3996	337	5	,	,	PUNCT
ejpam-3996	337	6	bi	bi	NOUN
ejpam-3996	337	7	)	)	PUNCT
ejpam-3996	337	8	,	,	PUNCT
ejpam-3996	337	9	(	(	PUNCT
ejpam-3996	337	10	c	c	X
ejpam-3996	337	11	,	,	PUNCT
ejpam-3996	337	12	di	di	NOUN
ejpam-3996	337	13	)	)	PUNCT
ejpam-3996	337	14	∈	∈	PROPN
ejpam-3996	337	15	s(i)i	s(i)i	NOUN
ejpam-3996	337	16	and	and	CCONJ
ejpam-3996	337	17	(	(	PUNCT
ejpam-3996	337	18	a	a	DET
ejpam-3996	337	19	,	,	PUNCT
ejpam-3996	337	20	bi	bi	NOUN
ejpam-3996	337	21	)	)	PUNCT
ejpam-3996	337	22	·	·	PUNCT
ejpam-3996	337	23	(	(	PUNCT
ejpam-3996	337	24	c	c	X
ejpam-3996	337	25	,	,	PUNCT
ejpam-3996	337	26	di	di	NOUN
ejpam-3996	337	27	)	)	PUNCT
ejpam-3996	337	28	∈	∈	PROPN
ejpam-3996	337	29	s(i)i	s(i)i	NOUN
ejpam-3996	337	30	.	.	PUNCT
ejpam-3996	338	1	thus	thus	ADV
ejpam-3996	338	2	,	,	PUNCT
ejpam-3996	338	3	(	(	PUNCT
ejpam-3996	338	4	a	a	DET
ejpam-3996	338	5	,	,	PUNCT
ejpam-3996	338	6	bi	bi	NOUN
ejpam-3996	338	7	)	)	PUNCT
ejpam-3996	338	8	·	·	PUNCT
ejpam-3996	338	9	(	(	PUNCT
ejpam-3996	338	10	c	c	X
ejpam-3996	338	11	,	,	PUNCT
ejpam-3996	338	12	di	di	NOUN
ejpam-3996	338	13	)	)	PUNCT
ejpam-3996	338	14	∈	∈	PROPN
ejpam-3996	338	15	⋃	⋃	PROPN
ejpam-3996	338	16	i∈i	i∈i	ADJ
ejpam-3996	338	17	s(i)i	s(i)i	NOUN
ejpam-3996	338	18	.	.	PUNCT
ejpam-3996	339	1	let	let	VERB
ejpam-3996	339	2	p	p	NOUN
ejpam-3996	339	3	(	(	PUNCT
ejpam-3996	339	4	i)i	i)i	NOUN
ejpam-3996	339	5	be	be	AUX
ejpam-3996	339	6	a	a	DET
ejpam-3996	339	7	proper	proper	ADJ
ejpam-3996	339	8	subset	subset	NOUN
ejpam-3996	339	9	of	of	ADP
ejpam-3996	339	10	s(i)i	s(i)i	PROPN
ejpam-3996	339	11	,	,	PUNCT
ejpam-3996	339	12	for	for	ADP
ejpam-3996	339	13	every	every	DET
ejpam-3996	339	14	i	i	NOUN
ejpam-3996	339	15	∈	∈	PROPN
ejpam-3996	339	16	i	i	PRON
ejpam-3996	339	17	which	which	PRON
ejpam-3996	339	18	is	be	AUX
ejpam-3996	339	19	a	a	DET
ejpam-3996	339	20	b	b	NOUN
ejpam-3996	339	21	-	-	PUNCT
ejpam-3996	339	22	algebra	algebra	NOUN
ejpam-3996	339	23	.	.	PUNCT
ejpam-3996	340	1	then	then	ADV
ejpam-3996	340	2	for	for	ADP
ejpam-3996	340	3	any	any	DET
ejpam-3996	340	4	i	i	PRON
ejpam-3996	340	5	∈	∈	PROPN
ejpam-3996	340	6	i	i	PRON
ejpam-3996	340	7	,	,	PUNCT
ejpam-3996	340	8	p	p	X
ejpam-3996	340	9	(	(	PUNCT
ejpam-3996	340	10	i)i	i)i	NOUN
ejpam-3996	340	11	(	(	PUNCT
ejpam-3996	340	12	⋃	⋃	ADP
ejpam-3996	340	13	i∈i	i∈i	ADJ
ejpam-3996	340	14	s(i)i	s(i)i	NOUN
ejpam-3996	340	15	.	.	PUNCT
ejpam-3996	341	1	therefore	therefore	ADV
ejpam-3996	341	2	,	,	PUNCT
ejpam-3996	341	3	⋃	⋃	ADP
ejpam-3996	341	4	i∈i	i∈i	ADJ
ejpam-3996	341	5	s(i)i	s(i)i	NOUN
ejpam-3996	341	6	is	be	AUX
ejpam-3996	341	7	a	a	DET
ejpam-3996	341	8	neutrosophic	neutrosophic	ADJ
ejpam-3996	341	9	subalgebra	subalgebra	NOUN
ejpam-3996	341	10	of	of	ADP
ejpam-3996	341	11	x(i	x(i	PROPN
ejpam-3996	341	12	)	)	PUNCT
ejpam-3996	341	13	.	.	PUNCT
ejpam-3996	342	1	�	�	PROPN
ejpam-3996	342	2	references	reference	NOUN
ejpam-3996	342	3	[	[	X
ejpam-3996	342	4	1	1	NUM
ejpam-3996	342	5	]	]	PUNCT
ejpam-3996	342	6	adesina	adesina	PROPN
ejpam-3996	342	7	abdul	abdul	PROPN
ejpam-3996	342	8	akeem	akeem	PROPN
ejpam-3996	342	9	agboola	agboola	PROPN
ejpam-3996	342	10	and	and	CCONJ
ejpam-3996	342	11	bijan	bijan	PROPN
ejpam-3996	342	12	davvaz	davvaz	PROPN
ejpam-3996	342	13	.	.	PUNCT
ejpam-3996	343	1	introduction	introduction	NOUN
ejpam-3996	343	2	to	to	ADP
ejpam-3996	343	3	neutrosophic	neutrosophic	ADJ
ejpam-3996	343	4	bci	bci	PROPN
ejpam-3996	343	5	/	/	SYM
ejpam-3996	343	6	bck	bck	NOUN
ejpam-3996	343	7	-	-	PUNCT
ejpam-3996	343	8	algebras	algebras	PROPN
ejpam-3996	343	9	.	.	PUNCT
ejpam-3996	344	1	international	international	ADJ
ejpam-3996	344	2	journal	journal	PROPN
ejpam-3996	344	3	of	of	ADP
ejpam-3996	344	4	mathematics	mathematics	PROPN
ejpam-3996	344	5	and	and	CCONJ
ejpam-3996	344	6	mathematical	mathematical	ADJ
ejpam-3996	344	7	sciences	science	NOUN
ejpam-3996	344	8	,	,	PUNCT
ejpam-3996	344	9	2015	2015	NUM
ejpam-3996	344	10	,	,	PUNCT
ejpam-3996	344	11	2015	2015	NUM
ejpam-3996	344	12	.	.	PUNCT
ejpam-3996	345	1	[	[	X
ejpam-3996	345	2	2	2	X
ejpam-3996	345	3	]	]	X
ejpam-3996	345	4	pj	pj	PROPN
ejpam-3996	345	5	allen	allen	PROPN
ejpam-3996	345	6	,	,	PUNCT
ejpam-3996	345	7	j	j	PROPN
ejpam-3996	345	8	neggers	negger	NOUN
ejpam-3996	345	9	,	,	PUNCT
ejpam-3996	345	10	and	and	CCONJ
ejpam-3996	345	11	hee	hee	PROPN
ejpam-3996	345	12	sik	sik	PROPN
ejpam-3996	345	13	kim	kim	PROPN
ejpam-3996	345	14	.	.	PUNCT
ejpam-3996	346	1	b	b	X
ejpam-3996	346	2	-	-	PUNCT
ejpam-3996	346	3	algebras	algebra	NOUN
ejpam-3996	346	4	and	and	CCONJ
ejpam-3996	346	5	groups	group	NOUN
ejpam-3996	346	6	.	.	PUNCT
ejpam-3996	347	1	scientiae	scientiae	PROPN
ejpam-3996	347	2	mathematicae	mathematicae	PROPN
ejpam-3996	347	3	japonicae	japonicae	PROPN
ejpam-3996	347	4	,	,	PUNCT
ejpam-3996	347	5	59(1):23–30	59(1):23–30	NUM
ejpam-3996	347	6	,	,	PUNCT
ejpam-3996	347	7	2004	2004	NUM
ejpam-3996	347	8	.	.	PUNCT
ejpam-3996	348	1	[	[	X
ejpam-3996	348	2	3	3	X
ejpam-3996	348	3	]	]	PUNCT
ejpam-3996	348	4	ec	ec	PROPN
ejpam-3996	348	5	banagua	banagua	PROPN
ejpam-3996	348	6	.	.	PUNCT
ejpam-3996	349	1	b	b	X
ejpam-3996	349	2	-	-	PUNCT
ejpam-3996	349	3	algebras	algebras	ADV
ejpam-3996	349	4	acting	act	VERB
ejpam-3996	349	5	on	on	ADP
ejpam-3996	349	6	sets	set	NOUN
ejpam-3996	349	7	and	and	CCONJ
ejpam-3996	349	8	sylow	sylow	VERB
ejpam-3996	349	9	theorems	theorem	NOUN
ejpam-3996	349	10	for	for	ADP
ejpam-3996	349	11	b	b	NOUN
ejpam-3996	349	12	-	-	PUNCT
ejpam-3996	349	13	algebras	algebra	NOUN
ejpam-3996	349	14	,	,	PUNCT
ejpam-3996	349	15	2018	2018	NUM
ejpam-3996	349	16	.	.	PUNCT
ejpam-3996	350	1	[	[	X
ejpam-3996	350	2	4	4	NUM
ejpam-3996	350	3	]	]	X
ejpam-3996	350	4	j	j	PROPN
ejpam-3996	350	5	bantug	bantug	PROPN
ejpam-3996	350	6	.	.	PUNCT
ejpam-3996	351	1	lagrange	lagrange	PROPN
ejpam-3996	351	2	’s	’s	PART
ejpam-3996	351	3	theorem	theorem	PROPN
ejpam-3996	351	4	and	and	CCONJ
ejpam-3996	351	5	cauchy	cauchy	PROPN
ejpam-3996	351	6	’s	’s	PART
ejpam-3996	351	7	theorem	theorem	NOUN
ejpam-3996	351	8	for	for	ADP
ejpam-3996	351	9	b	b	NOUN
ejpam-3996	351	10	-	-	PUNCT
ejpam-3996	351	11	algebras	algebra	NOUN
ejpam-3996	351	12	,	,	PUNCT
ejpam-3996	351	13	2017	2017	NUM
ejpam-3996	351	14	.	.	PUNCT
ejpam-3996	352	1	[	[	X
ejpam-3996	352	2	5	5	NUM
ejpam-3996	352	3	]	]	X
ejpam-3996	352	4	jenette	jenette	PROPN
ejpam-3996	352	5	s	s	PROPN
ejpam-3996	352	6	bantug	bantug	PROPN
ejpam-3996	352	7	and	and	CCONJ
ejpam-3996	352	8	joemar	joemar	PROPN
ejpam-3996	352	9	c	c	PROPN
ejpam-3996	352	10	endam	endam	PROPN
ejpam-3996	352	11	.	.	PUNCT
ejpam-3996	353	1	lagrange	lagrange	PROPN
ejpam-3996	353	2	’s	’s	PART
ejpam-3996	353	3	theorem	theorem	NOUN
ejpam-3996	353	4	for	for	ADP
ejpam-3996	353	5	b	b	NOUN
ejpam-3996	353	6	-	-	PUNCT
ejpam-3996	353	7	algebras	algebras	PROPN
ejpam-3996	353	8	.	.	PUNCT
ejpam-3996	354	1	international	international	ADJ
ejpam-3996	354	2	journal	journal	PROPN
ejpam-3996	354	3	of	of	ADP
ejpam-3996	354	4	algebra	algebra	PROPN
ejpam-3996	354	5	,	,	PUNCT
ejpam-3996	354	6	11(1):15–23	11(1):15–23	NUM
ejpam-3996	354	7	,	,	PUNCT
ejpam-3996	354	8	2017	2017	NUM
ejpam-3996	354	9	.	.	PUNCT
ejpam-3996	355	1	[	[	X
ejpam-3996	355	2	6	6	NUM
ejpam-3996	355	3	]	]	X
ejpam-3996	355	4	jung	jung	PROPN
ejpam-3996	355	5	r	r	PROPN
ejpam-3996	355	6	cho	cho	PROPN
ejpam-3996	355	7	and	and	CCONJ
ejpam-3996	355	8	hee	hee	PROPN
ejpam-3996	355	9	-	-	PROPN
ejpam-3996	355	10	sik	sik	NOUN
ejpam-3996	355	11	kim	kim	PROPN
ejpam-3996	355	12	.	.	PUNCT
ejpam-3996	356	1	on	on	ADP
ejpam-3996	356	2	b	b	NOUN
ejpam-3996	356	3	-	-	PUNCT
ejpam-3996	356	4	algebras	algebra	NOUN
ejpam-3996	356	5	and	and	CCONJ
ejpam-3996	356	6	quasigroups	quasigroup	NOUN
ejpam-3996	356	7	.	.	PUNCT
ejpam-3996	357	1	quasigroups	quasigroup	NOUN
ejpam-3996	357	2	and	and	CCONJ
ejpam-3996	357	3	related	related	ADJ
ejpam-3996	357	4	systems	system	NOUN
ejpam-3996	357	5	,	,	PUNCT
ejpam-3996	357	6	8(1):1–6	8(1):1–6	NUM
ejpam-3996	357	7	,	,	PUNCT
ejpam-3996	357	8	2001	2001	NUM
ejpam-3996	357	9	.	.	PUNCT
ejpam-3996	358	1	[	[	X
ejpam-3996	358	2	7	7	NUM
ejpam-3996	358	3	]	]	SYM
ejpam-3996	358	4	bijan	bijan	PROPN
ejpam-3996	358	5	davvaz	davvaz	PROPN
ejpam-3996	358	6	.	.	PUNCT
ejpam-3996	359	1	neutrosophic	neutrosophic	ADJ
ejpam-3996	359	2	ideals	ideal	NOUN
ejpam-3996	359	3	of	of	ADP
ejpam-3996	359	4	neutrosophic	neutrosophic	ADJ
ejpam-3996	359	5	ku	ku	PROPN
ejpam-3996	359	6	-	-	PUNCT
ejpam-3996	359	7	algebras	algebras	PROPN
ejpam-3996	359	8	.	.	PUNCT
ejpam-3996	360	1	gazi	gazi	PROPN
ejpam-3996	360	2	university	university	PROPN
ejpam-3996	360	3	journal	journal	PROPN
ejpam-3996	360	4	of	of	ADP
ejpam-3996	360	5	science	science	NOUN
ejpam-3996	360	6	,	,	PUNCT
ejpam-3996	360	7	30(4):463–472	30(4):463–472	NUM
ejpam-3996	360	8	,	,	PUNCT
ejpam-3996	360	9	2017	2017	NUM
ejpam-3996	360	10	.	.	PUNCT
ejpam-3996	361	1	references	reference	NOUN
ejpam-3996	361	2	904	904	NUM
ejpam-3996	362	1	[	[	X
ejpam-3996	362	2	8	8	NUM
ejpam-3996	362	3	]	]	PUNCT
ejpam-3996	362	4	joemar	joemar	PROPN
ejpam-3996	362	5	c	c	PROPN
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ejpam-3996	362	7	and	and	CCONJ
ejpam-3996	362	8	randy	randy	PROPN
ejpam-3996	362	9	c	c	PROPN
ejpam-3996	362	10	teves	teve	NOUN
ejpam-3996	362	11	.	.	PUNCT
ejpam-3996	363	1	some	some	DET
ejpam-3996	363	2	properties	property	NOUN
ejpam-3996	363	3	of	of	ADP
ejpam-3996	363	4	cyclic	cyclic	ADJ
ejpam-3996	363	5	b	b	NOUN
ejpam-3996	363	6	-	-	PUNCT
ejpam-3996	363	7	algebras	algebras	PROPN
ejpam-3996	363	8	.	.	PUNCT
ejpam-3996	364	1	in	in	ADP
ejpam-3996	364	2	international	international	PROPN
ejpam-3996	364	3	mathematical	mathematical	ADJ
ejpam-3996	364	4	forum	forum	PROPN
ejpam-3996	364	5	,	,	PUNCT
ejpam-3996	364	6	volume	volume	NOUN
ejpam-3996	364	7	11	11	NUM
ejpam-3996	364	8	,	,	PUNCT
ejpam-3996	364	9	pages	page	NOUN
ejpam-3996	364	10	387–394	387–394	NUM
ejpam-3996	364	11	,	,	PUNCT
ejpam-3996	364	12	2016	2016	NUM
ejpam-3996	364	13	.	.	PUNCT
ejpam-3996	365	1	[	[	X
ejpam-3996	365	2	9	9	X
ejpam-3996	365	3	]	]	PUNCT
ejpam-3996	365	4	joemar	joemar	PROPN
ejpam-3996	365	5	c	c	PROPN
ejpam-3996	365	6	endam	endam	PROPN
ejpam-3996	365	7	and	and	CCONJ
ejpam-3996	365	8	jocelyn	jocelyn	PROPN
ejpam-3996	365	9	p	p	PROPN
ejpam-3996	365	10	vilela	vilela	PROPN
ejpam-3996	365	11	.	.	PUNCT
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ejpam-3996	366	4	theorem	theorem	NOUN
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ejpam-3996	366	6	balgebras	balgebras	PROPN
ejpam-3996	366	7	.	.	PROPN
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ejpam-3996	366	11	,	,	PUNCT
ejpam-3996	366	12	8(38):1865–1872	8(38):1865–1872	NUM
ejpam-3996	366	13	,	,	PUNCT
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ejpam-3996	366	15	.	.	PUNCT
ejpam-3996	367	1	[	[	X
ejpam-3996	367	2	10	10	NUM
ejpam-3996	367	3	]	]	X
ejpam-3996	367	4	nc	nc	PROPN
ejpam-3996	367	5	gonzaga	gonzaga	PROPN
ejpam-3996	367	6	and	and	CCONJ
ejpam-3996	367	7	jocelyn	jocelyn	PROPN
ejpam-3996	367	8	p	p	PROPN
ejpam-3996	367	9	vilela	vilela	PROPN
ejpam-3996	367	10	.	.	PUNCT
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ejpam-3996	368	4	-	-	PUNCT
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ejpam-3996	368	6	.	.	PUNCT
ejpam-3996	369	1	applied	apply	VERB
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ejpam-3996	369	3	sciences	sciences	PROPN
ejpam-3996	369	4	,	,	PUNCT
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ejpam-3996	369	6	,	,	PUNCT
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ejpam-3996	369	8	.	.	PUNCT
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ejpam-3996	370	3	]	]	PUNCT
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ejpam-3996	370	5	vasantha	vasantha	PROPN
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ejpam-3996	370	7	and	and	CCONJ
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ejpam-3996	370	9	smarandache	smarandache	PROPN
ejpam-3996	370	10	.	.	PUNCT
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ejpam-3996	371	9	fuzzy	fuzzy	ADJ
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ejpam-3996	371	19	,	,	PUNCT
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ejpam-3996	371	21	.	.	PUNCT
ejpam-3996	372	1	[	[	X
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ejpam-3996	372	4	wb	wb	PROPN
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ejpam-3996	372	7	and	and	CCONJ
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ejpam-3996	372	10	.	.	PUNCT
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ejpam-3996	373	5	and	and	CCONJ
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ejpam-3996	373	8	-	-	PUNCT
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ejpam-3996	373	11	.	.	PUNCT
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ejpam-3996	374	3	,	,	PUNCT
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ejpam-3996	374	5	.	.	PUNCT
ejpam-3996	375	1	[	[	X
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ejpam-3996	375	3	]	]	PUNCT
ejpam-3996	375	4	ja	ja	PROPN
ejpam-3996	375	5	lingcong	lingcong	PROPN
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ejpam-3996	375	10	.	.	PUNCT
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ejpam-3996	376	5	-	-	PUNCT
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ejpam-3996	376	7	.	.	PUNCT
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ejpam-3996	377	5	,	,	PUNCT
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ejpam-3996	377	7	,	,	PUNCT
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ejpam-3996	377	9	.	.	PUNCT
ejpam-3996	378	1	[	[	X
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ejpam-3996	379	6	-	-	PUNCT
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ejpam-3996	379	10	-	-	PUNCT
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ejpam-3996	379	12	.	.	PUNCT
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ejpam-3996	379	16	.	.	PUNCT
ejpam-3996	380	1	j.	j.	PROPN
ejpam-3996	380	2	,	,	PUNCT
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ejpam-3996	380	4	,	,	PUNCT
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ejpam-3996	380	6	.	.	PUNCT
ejpam-3996	381	1	[	[	X
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ejpam-3996	381	3	]	]	X
ejpam-3996	381	4	j	j	PROPN
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ejpam-3996	381	7	kim	kim	PROPN
ejpam-3996	381	8	sik	sik	PROPN
ejpam-3996	381	9	.	.	PUNCT
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ejpam-3996	382	3	-	-	PUNCT
ejpam-3996	382	4	algebras	algebras	X
ejpam-3996	382	5	.	.	PUNCT
ejpam-3996	383	1	matematički	matematički	PROPN
ejpam-3996	383	2	vesnik	vesnik	PROPN
ejpam-3996	383	3	,	,	PUNCT
ejpam-3996	383	4	54(1	54(1	PROPN
ejpam-3996	383	5	-	-	SYM
ejpam-3996	383	6	2):21–29	2):21–29	NUM
ejpam-3996	383	7	,	,	PUNCT
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ejpam-3996	383	9	.	.	PUNCT
ejpam-3996	384	1	[	[	X
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ejpam-3996	384	3	]	]	PUNCT
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ejpam-3996	384	6	.	.	PUNCT
ejpam-3996	385	1	a	a	DET
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ejpam-3996	385	6	:	:	PUNCT
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ejpam-3996	385	8	logic	logic	NOUN
ejpam-3996	385	9	.	.	PUNCT
ejpam-3996	386	1	neutrosophy	neutrosophy	NOUN
ejpam-3996	386	2	,	,	PUNCT
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ejpam-3996	386	4	set	set	NOUN
ejpam-3996	386	5	,	,	PUNCT
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ejpam-3996	387	2	.	.	PUNCT
ejpam-3996	388	1	[	[	X
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ejpam-3996	388	4	wb	wb	PROPN
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ejpam-3996	388	10	.	.	PUNCT
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ejpam-3996	389	3	.	.	PUNCT
ejpam-3996	390	1	arxiv	arxiv	PROPN
ejpam-3996	390	2	mathematics	mathematics	PROPN
ejpam-3996	390	3	e	e	PROPN
ejpam-3996	391	1	-	-	NOUN
ejpam-3996	391	2	prints	print	NOUN
ejpam-3996	391	3	,	,	PUNCT
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ejpam-3996	391	6	,	,	PUNCT
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ejpam-3996	391	8	.	.	PUNCT
ejpam-3996	392	1	[	[	X
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ejpam-3996	392	6	.	.	PUNCT
ejpam-3996	393	1	a	a	DET
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ejpam-3996	393	8	-	-	PUNCT
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ejpam-3996	393	10	.	.	PUNCT
ejpam-3996	394	1	scientiae	scientiae	PROPN
ejpam-3996	394	2	mathematicae	mathematicae	PROPN
ejpam-3996	394	3	japonicae	japonicae	PROPN
ejpam-3996	394	4	,	,	PUNCT
ejpam-3996	394	5	62(1):1	62(1):1	PROPN
ejpam-3996	394	6	,	,	PUNCT
ejpam-3996	394	7	2005	2005	NUM
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