id	sid	tid	token	lemma	pos
ejpam-5783	1	1	european	european	PROPN
ejpam-5783	1	2	journal	journal	PROPN
ejpam-5783	1	3	of	of	ADP
ejpam-5783	1	4	pure	pure	ADJ
ejpam-5783	1	5	and	and	CCONJ
ejpam-5783	1	6	applied	applied	ADJ
ejpam-5783	1	7	mathematics	mathematic	NOUN
ejpam-5783	1	8	2025	2025	NUM
ejpam-5783	1	9	,	,	PUNCT
ejpam-5783	1	10	vol	vol	NOUN
ejpam-5783	1	11	.	.	PROPN
ejpam-5783	1	12	18	18	NUM
ejpam-5783	1	13	,	,	PUNCT
ejpam-5783	1	14	issue	issue	NOUN
ejpam-5783	1	15	1	1	NUM
ejpam-5783	1	16	,	,	PUNCT
ejpam-5783	1	17	article	article	NOUN
ejpam-5783	1	18	number	number	NOUN
ejpam-5783	1	19	5783	5783	NUM
ejpam-5783	1	20	issn	issn	PROPN
ejpam-5783	1	21	1307	1307	NUM
ejpam-5783	1	22	-	-	SYM
ejpam-5783	1	23	5543	5543	NUM
ejpam-5783	1	24	–	–	PUNCT
ejpam-5783	1	25	ejpam.com	ejpam.com	X
ejpam-5783	1	26	published	publish	VERB
ejpam-5783	1	27	by	by	ADP
ejpam-5783	1	28	new	new	PROPN
ejpam-5783	1	29	york	york	PROPN
ejpam-5783	1	30	business	business	PROPN
ejpam-5783	1	31	global	global	PROPN
ejpam-5783	1	32	sheffer	sheffer	PROPN
ejpam-5783	1	33	stroke	stroke	PROPN
ejpam-5783	1	34	bn	bn	NOUN
ejpam-5783	1	35	-	-	PUNCT
ejpam-5783	1	36	algebras	algebras	PROPN
ejpam-5783	1	37	and	and	CCONJ
ejpam-5783	1	38	connected	connected	ADJ
ejpam-5783	1	39	topics	topic	NOUN
ejpam-5783	1	40	sri	sri	PROPN
ejpam-5783	1	41	gemawati1,∗	gemawati1,∗	NOUN
ejpam-5783	1	42	,	,	PUNCT
ejpam-5783	1	43	mashadi1	mashadi1	PROPN
ejpam-5783	1	44	,	,	PUNCT
ejpam-5783	1	45	kartini1	kartini1	PROPN
ejpam-5783	1	46	,	,	PUNCT
ejpam-5783	1	47	musraini1	musraini1	PROPN
ejpam-5783	1	48	,	,	PUNCT
ejpam-5783	1	49	elsi	elsi	ADJ
ejpam-5783	1	50	fitria1	fitria1	NOUN
ejpam-5783	1	51	1	1	NUM
ejpam-5783	1	52	department	department	NOUN
ejpam-5783	1	53	of	of	ADP
ejpam-5783	1	54	mathematics	mathematic	NOUN
ejpam-5783	1	55	,	,	PUNCT
ejpam-5783	1	56	faculty	faculty	NOUN
ejpam-5783	1	57	of	of	ADP
ejpam-5783	1	58	mathematics	mathematic	NOUN
ejpam-5783	1	59	and	and	CCONJ
ejpam-5783	1	60	natural	natural	ADJ
ejpam-5783	1	61	science	science	NOUN
ejpam-5783	1	62	,	,	PUNCT
ejpam-5783	1	63	universitas	universita	NOUN
ejpam-5783	1	64	riau	riau	PROPN
ejpam-5783	1	65	,	,	PUNCT
ejpam-5783	1	66	pekanbaru	pekanbaru	PROPN
ejpam-5783	1	67	,	,	PUNCT
ejpam-5783	1	68	indonesia	indonesia	PROPN
ejpam-5783	1	69	abstract	abstract	NOUN
ejpam-5783	1	70	.	.	PUNCT
ejpam-5783	2	1	this	this	DET
ejpam-5783	2	2	article	article	NOUN
ejpam-5783	2	3	introduces	introduce	VERB
ejpam-5783	2	4	the	the	DET
ejpam-5783	2	5	concept	concept	NOUN
ejpam-5783	2	6	of	of	ADP
ejpam-5783	2	7	a	a	DET
ejpam-5783	2	8	sheffer	sheffer	NOUN
ejpam-5783	2	9	stroke	stroke	NOUN
ejpam-5783	2	10	bn	bn	NOUN
ejpam-5783	2	11	-	-	PUNCT
ejpam-5783	2	12	algebra	algebra	NOUN
ejpam-5783	2	13	by	by	ADP
ejpam-5783	2	14	applying	apply	VERB
ejpam-5783	2	15	the	the	DET
ejpam-5783	2	16	sheffer	sheffer	NOUN
ejpam-5783	2	17	stroke	stroke	NOUN
ejpam-5783	2	18	operator	operator	NOUN
ejpam-5783	2	19	|	|	ADV
ejpam-5783	2	20	to	to	ADP
ejpam-5783	2	21	the	the	DET
ejpam-5783	2	22	bn	bn	NOUN
ejpam-5783	2	23	-	-	PUNCT
ejpam-5783	2	24	algebra	algebra	NOUN
ejpam-5783	2	25	axioms	axiom	NOUN
ejpam-5783	2	26	and	and	CCONJ
ejpam-5783	2	27	aligning	align	VERB
ejpam-5783	2	28	it	it	PRON
ejpam-5783	2	29	with	with	ADP
ejpam-5783	2	30	the	the	DET
ejpam-5783	2	31	axioms	axiom	NOUN
ejpam-5783	2	32	of	of	ADP
ejpam-5783	2	33	the	the	DET
ejpam-5783	2	34	sheffer	sheffer	NOUN
ejpam-5783	2	35	stroke	stroke	NOUN
ejpam-5783	2	36	groupoid	groupoid	PROPN
ejpam-5783	2	37	.	.	PUNCT
ejpam-5783	3	1	from	from	ADP
ejpam-5783	3	2	this	this	DET
ejpam-5783	3	3	definition	definition	NOUN
ejpam-5783	3	4	,	,	PUNCT
ejpam-5783	3	5	properties	property	NOUN
ejpam-5783	3	6	of	of	ADP
ejpam-5783	3	7	sheffer	sheffer	PROPN
ejpam-5783	3	8	stroke	stroke	PROPN
ejpam-5783	3	9	bn	bn	NOUN
ejpam-5783	3	10	-	-	PUNCT
ejpam-5783	3	11	algebras	algebra	NOUN
ejpam-5783	3	12	are	be	AUX
ejpam-5783	3	13	derived	derive	VERB
ejpam-5783	3	14	,	,	PUNCT
ejpam-5783	3	15	focusing	focus	VERB
ejpam-5783	3	16	on	on	ADP
ejpam-5783	3	17	the	the	DET
ejpam-5783	3	18	relationship	relationship	NOUN
ejpam-5783	3	19	between	between	ADP
ejpam-5783	3	20	the	the	DET
ejpam-5783	3	21	axioms	axiom	NOUN
ejpam-5783	3	22	and	and	CCONJ
ejpam-5783	3	23	the	the	DET
ejpam-5783	3	24	properties	property	NOUN
ejpam-5783	3	25	of	of	ADP
ejpam-5783	3	26	the	the	DET
ejpam-5783	3	27	special	special	ADJ
ejpam-5783	3	28	element	element	NOUN
ejpam-5783	3	29	0	0	NUM
ejpam-5783	3	30	.	.	PUNCT
ejpam-5783	4	1	furthermore	furthermore	ADV
ejpam-5783	4	2	,	,	PUNCT
ejpam-5783	4	3	the	the	DET
ejpam-5783	4	4	notions	notion	NOUN
ejpam-5783	4	5	of	of	ADP
ejpam-5783	4	6	sheffer	sheffer	PROPN
ejpam-5783	4	7	stroke	stroke	PROPN
ejpam-5783	4	8	bn	bn	PROPN
ejpam-5783	4	9	-	-	PUNCT
ejpam-5783	4	10	subalgebras	subalgebras	PROPN
ejpam-5783	4	11	,	,	PUNCT
ejpam-5783	4	12	bn	bn	NOUN
ejpam-5783	4	13	-	-	PUNCT
ejpam-5783	4	14	ideals	ideal	NOUN
ejpam-5783	4	15	,	,	PUNCT
ejpam-5783	4	16	and	and	CCONJ
ejpam-5783	4	17	bn	bn	NOUN
ejpam-5783	4	18	-	-	PUNCT
ejpam-5783	4	19	homomorphisms	homomorphism	NOUN
ejpam-5783	4	20	are	be	AUX
ejpam-5783	4	21	defined	define	VERB
ejpam-5783	4	22	,	,	PUNCT
ejpam-5783	4	23	along	along	ADP
ejpam-5783	4	24	with	with	ADP
ejpam-5783	4	25	normal	normal	ADJ
ejpam-5783	4	26	subsets	subset	NOUN
ejpam-5783	4	27	of	of	ADP
ejpam-5783	4	28	sheffer	sheffer	PROPN
ejpam-5783	4	29	stroke	stroke	PROPN
ejpam-5783	4	30	bn	bn	NOUN
ejpam-5783	4	31	-	-	PUNCT
ejpam-5783	4	32	algebras	algebras	X
ejpam-5783	4	33	,	,	PUNCT
ejpam-5783	4	34	and	and	CCONJ
ejpam-5783	4	35	the	the	DET
ejpam-5783	4	36	relationships	relationship	NOUN
ejpam-5783	4	37	between	between	ADP
ejpam-5783	4	38	these	these	DET
ejpam-5783	4	39	concepts	concept	NOUN
ejpam-5783	4	40	are	be	AUX
ejpam-5783	4	41	explored	explore	VERB
ejpam-5783	4	42	.	.	PUNCT
ejpam-5783	5	1	it	it	PRON
ejpam-5783	5	2	is	be	AUX
ejpam-5783	5	3	shown	show	VERB
ejpam-5783	5	4	that	that	SCONJ
ejpam-5783	5	5	every	every	DET
ejpam-5783	5	6	normal	normal	ADJ
ejpam-5783	5	7	subset	subset	NOUN
ejpam-5783	5	8	in	in	ADP
ejpam-5783	5	9	a	a	DET
ejpam-5783	5	10	sheffer	sheffer	NOUN
ejpam-5783	5	11	stroke	stroke	NOUN
ejpam-5783	5	12	bn	bn	NOUN
ejpam-5783	5	13	-	-	PUNCT
ejpam-5783	5	14	algebra	algebra	NOUN
ejpam-5783	5	15	is	be	AUX
ejpam-5783	5	16	a	a	DET
ejpam-5783	5	17	sheffer	sheffer	NOUN
ejpam-5783	5	18	stroke	stroke	NOUN
ejpam-5783	5	19	bn	bn	NOUN
ejpam-5783	5	20	-	-	PUNCT
ejpam-5783	5	21	subalgebra	subalgebra	NOUN
ejpam-5783	5	22	,	,	PUNCT
ejpam-5783	5	23	but	but	CCONJ
ejpam-5783	5	24	the	the	DET
ejpam-5783	5	25	converse	converse	NOUN
ejpam-5783	5	26	is	be	AUX
ejpam-5783	5	27	not	not	PART
ejpam-5783	5	28	necessarily	necessarily	ADV
ejpam-5783	5	29	true	true	ADJ
ejpam-5783	5	30	.	.	PUNCT
ejpam-5783	6	1	this	this	PRON
ejpam-5783	6	2	implies	imply	VERB
ejpam-5783	6	3	that	that	SCONJ
ejpam-5783	6	4	every	every	DET
ejpam-5783	6	5	normal	normal	ADJ
ejpam-5783	6	6	bn	bn	NOUN
ejpam-5783	6	7	-	-	PUNCT
ejpam-5783	6	8	ideal	ideal	NOUN
ejpam-5783	6	9	in	in	ADP
ejpam-5783	6	10	a	a	DET
ejpam-5783	6	11	sheffer	sheffer	NOUN
ejpam-5783	6	12	stroke	stroke	NOUN
ejpam-5783	6	13	bn	bn	NOUN
ejpam-5783	6	14	-	-	PUNCT
ejpam-5783	6	15	algebra	algebra	NOUN
ejpam-5783	6	16	is	be	AUX
ejpam-5783	6	17	also	also	ADV
ejpam-5783	6	18	a	a	DET
ejpam-5783	6	19	sheffer	sheffer	NOUN
ejpam-5783	6	20	stroke	stroke	NOUN
ejpam-5783	6	21	bn	bn	NOUN
ejpam-5783	6	22	-	-	PUNCT
ejpam-5783	6	23	subalgebra	subalgebra	NOUN
ejpam-5783	6	24	.	.	PUNCT
ejpam-5783	7	1	finally	finally	ADV
ejpam-5783	7	2	,	,	PUNCT
ejpam-5783	7	3	the	the	DET
ejpam-5783	7	4	properties	property	NOUN
ejpam-5783	7	5	of	of	ADP
ejpam-5783	7	6	the	the	DET
ejpam-5783	7	7	kernel	kernel	NOUN
ejpam-5783	7	8	of	of	ADP
ejpam-5783	7	9	the	the	DET
ejpam-5783	7	10	sheffer	sheffer	NOUN
ejpam-5783	7	11	stroke	stroke	NOUN
ejpam-5783	7	12	bn	bn	NOUN
ejpam-5783	7	13	-	-	PUNCT
ejpam-5783	7	14	homomorphism	homomorphism	NOUN
ejpam-5783	7	15	are	be	AUX
ejpam-5783	7	16	investigated	investigate	VERB
ejpam-5783	7	17	.	.	PUNCT
ejpam-5783	8	1	2020	2020	NUM
ejpam-5783	8	2	mathematics	mathematic	NOUN
ejpam-5783	8	3	subject	subject	NOUN
ejpam-5783	8	4	classifications	classification	NOUN
ejpam-5783	8	5	:	:	PUNCT
ejpam-5783	8	6	03g25	03g25	NUM
ejpam-5783	8	7	,	,	PUNCT
ejpam-5783	8	8	03g10	03g10	NUM
ejpam-5783	8	9	key	key	ADJ
ejpam-5783	8	10	words	word	NOUN
ejpam-5783	8	11	and	and	CCONJ
ejpam-5783	8	12	phrases	phrase	NOUN
ejpam-5783	8	13	:	:	PUNCT
ejpam-5783	8	14	bn	bn	NOUN
ejpam-5783	8	15	-	-	PUNCT
ejpam-5783	8	16	algebra	algebra	NOUN
ejpam-5783	8	17	,	,	PUNCT
ejpam-5783	8	18	sheffer	sheffer	NOUN
ejpam-5783	8	19	stroke	stroke	NOUN
ejpam-5783	8	20	,	,	PUNCT
ejpam-5783	8	21	sheffer	sheffer	VERB
ejpam-5783	8	22	stroke	stroke	NOUN
ejpam-5783	8	23	bn	bn	NOUN
ejpam-5783	8	24	-	-	PUNCT
ejpam-5783	8	25	algebra	algebra	NOUN
ejpam-5783	8	26	,	,	PUNCT
ejpam-5783	8	27	bn	bn	NOUN
ejpam-5783	8	28	-	-	PUNCT
ejpam-5783	8	29	ideal	ideal	ADJ
ejpam-5783	8	30	,	,	PUNCT
ejpam-5783	8	31	bn	bn	NOUN
ejpam-5783	8	32	-	-	PUNCT
ejpam-5783	8	33	subalgebra	subalgebra	NOUN
ejpam-5783	8	34	1	1	NUM
ejpam-5783	8	35	.	.	X
ejpam-5783	8	36	introduction	introduction	NOUN
ejpam-5783	8	37	the	the	DET
ejpam-5783	8	38	sheffer	sheffer	NOUN
ejpam-5783	8	39	stroke	stroke	NOUN
ejpam-5783	8	40	operator	operator	NOUN
ejpam-5783	8	41	is	be	AUX
ejpam-5783	8	42	equivalent	equivalent	ADJ
ejpam-5783	8	43	to	to	ADP
ejpam-5783	8	44	the	the	DET
ejpam-5783	8	45	nand	nand	NOUN
ejpam-5783	8	46	logic	logic	NOUN
ejpam-5783	8	47	gate	gate	NOUN
ejpam-5783	8	48	,	,	PUNCT
ejpam-5783	8	49	a	a	DET
ejpam-5783	8	50	fundamental	fundamental	ADJ
ejpam-5783	8	51	component	component	NOUN
ejpam-5783	8	52	in	in	ADP
ejpam-5783	8	53	digital	digital	ADJ
ejpam-5783	8	54	electronics	electronic	NOUN
ejpam-5783	8	55	.	.	PUNCT
ejpam-5783	9	1	a	a	DET
ejpam-5783	9	2	nand	nand	NOUN
ejpam-5783	9	3	gate	gate	NOUN
ejpam-5783	9	4	is	be	AUX
ejpam-5783	9	5	a	a	DET
ejpam-5783	9	6	type	type	NOUN
ejpam-5783	9	7	of	of	ADP
ejpam-5783	9	8	integrated	integrate	VERB
ejpam-5783	9	9	logic	logic	NOUN
ejpam-5783	9	10	gate	gate	NOUN
ejpam-5783	9	11	with	with	ADP
ejpam-5783	9	12	two	two	NUM
ejpam-5783	9	13	inputs	input	NOUN
ejpam-5783	9	14	and	and	CCONJ
ejpam-5783	9	15	one	one	NUM
ejpam-5783	9	16	output	output	NOUN
ejpam-5783	9	17	,	,	PUNCT
ejpam-5783	9	18	essentially	essentially	ADV
ejpam-5783	9	19	functioning	function	VERB
ejpam-5783	9	20	as	as	ADP
ejpam-5783	9	21	a	a	DET
ejpam-5783	9	22	combination	combination	NOUN
ejpam-5783	9	23	of	of	ADP
ejpam-5783	9	24	a	a	DET
ejpam-5783	9	25	not	not	PART
ejpam-5783	9	26	gate	gate	NOUN
ejpam-5783	9	27	and	and	CCONJ
ejpam-5783	9	28	an	an	PRON
ejpam-5783	9	29	and	and	CCONJ
ejpam-5783	9	30	gate	gate	ADJ
ejpam-5783	9	31	.	.	PUNCT
ejpam-5783	10	1	nand	nand	NOUN
ejpam-5783	10	2	gates	gate	NOUN
ejpam-5783	10	3	work	work	VERB
ejpam-5783	10	4	closely	closely	ADV
ejpam-5783	10	5	with	with	ADP
ejpam-5783	10	6	other	other	ADJ
ejpam-5783	10	7	logic	logic	NOUN
ejpam-5783	10	8	gates	gate	NOUN
ejpam-5783	10	9	to	to	PART
ejpam-5783	10	10	regulate	regulate	VERB
ejpam-5783	10	11	the	the	DET
ejpam-5783	10	12	flow	flow	NOUN
ejpam-5783	10	13	of	of	ADP
ejpam-5783	10	14	information	information	NOUN
ejpam-5783	10	15	and	and	CCONJ
ejpam-5783	10	16	instructions	instruction	NOUN
ejpam-5783	10	17	in	in	ADP
ejpam-5783	10	18	computers	computer	NOUN
ejpam-5783	10	19	,	,	PUNCT
ejpam-5783	10	20	the	the	DET
ejpam-5783	10	21	behavior	behavior	NOUN
ejpam-5783	10	22	of	of	ADP
ejpam-5783	10	23	devices	device	NOUN
ejpam-5783	10	24	such	such	ADJ
ejpam-5783	10	25	as	as	ADP
ejpam-5783	10	26	electric	electric	ADJ
ejpam-5783	10	27	motors	motor	NOUN
ejpam-5783	10	28	and	and	CCONJ
ejpam-5783	10	29	water	water	NOUN
ejpam-5783	10	30	pumps	pump	NOUN
ejpam-5783	10	31	in	in	ADP
ejpam-5783	10	32	industrial	industrial	ADJ
ejpam-5783	10	33	control	control	NOUN
ejpam-5783	10	34	systems	system	NOUN
ejpam-5783	10	35	,	,	PUNCT
ejpam-5783	10	36	and	and	CCONJ
ejpam-5783	10	37	access	access	NOUN
ejpam-5783	10	38	to	to	ADP
ejpam-5783	10	39	buildings	building	NOUN
ejpam-5783	10	40	or	or	CCONJ
ejpam-5783	10	41	spaces	space	NOUN
ejpam-5783	10	42	in	in	ADP
ejpam-5783	10	43	security	security	NOUN
ejpam-5783	10	44	systems	system	NOUN
ejpam-5783	10	45	.	.	PUNCT
ejpam-5783	11	1	in	in	ADP
ejpam-5783	11	2	addition	addition	NOUN
ejpam-5783	11	3	to	to	ADP
ejpam-5783	11	4	having	have	VERB
ejpam-5783	11	5	a	a	DET
ejpam-5783	11	6	wide	wide	ADJ
ejpam-5783	11	7	range	range	NOUN
ejpam-5783	11	8	of	of	ADP
ejpam-5783	11	9	practical	practical	ADJ
ejpam-5783	11	10	applications	application	NOUN
ejpam-5783	11	11	,	,	PUNCT
ejpam-5783	11	12	the	the	DET
ejpam-5783	11	13	sheffer	sheffer	NOUN
ejpam-5783	11	14	stroke	stroke	NOUN
ejpam-5783	11	15	operator	operator	NOUN
ejpam-5783	11	16	has	have	AUX
ejpam-5783	11	17	inspired	inspire	VERB
ejpam-5783	11	18	many	many	ADJ
ejpam-5783	11	19	theoretical	theoretical	ADJ
ejpam-5783	11	20	developments	development	NOUN
ejpam-5783	11	21	in	in	ADP
ejpam-5783	11	22	mathematics	mathematic	NOUN
ejpam-5783	11	23	,	,	PUNCT
ejpam-5783	11	24	including	include	VERB
ejpam-5783	11	25	in	in	ADP
ejpam-5783	11	26	the	the	DET
ejpam-5783	11	27	context	context	NOUN
ejpam-5783	11	28	of	of	ADP
ejpam-5783	11	29	algebra	algebra	NOUN
ejpam-5783	11	30	.	.	PUNCT
ejpam-5783	12	1	∗corresponding	∗corresponde	VERB
ejpam-5783	12	2	author	author	NOUN
ejpam-5783	12	3	.	.	PUNCT
ejpam-5783	13	1	doi	doi	NOUN
ejpam-5783	13	2	:	:	PUNCT
ejpam-5783	13	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5783	https://doi.org/10.29020/nybg.ejpam.v18i1.5783	NOUN
ejpam-5783	13	4	email	email	NOUN
ejpam-5783	13	5	addresses	address	NOUN
ejpam-5783	13	6	:	:	PUNCT
ejpam-5783	13	7	sri.gemawati@lecturer.unri.ac.id	sri.gemawati@lecturer.unri.ac.id	PROPN
ejpam-5783	13	8	(	(	PUNCT
ejpam-5783	13	9	s.	s.	PROPN
ejpam-5783	13	10	gemawati	gemawati	PROPN
ejpam-5783	13	11	)	)	PUNCT
ejpam-5783	13	12	,	,	PUNCT
ejpam-5783	13	13	mashadi@lecturer.unri.ac.id	mashadi@lecturer.unri.ac.id	NOUN
ejpam-5783	13	14	(	(	PUNCT
ejpam-5783	13	15	mashadi	mashadi	NOUN
ejpam-5783	13	16	)	)	PUNCT
ejpam-5783	13	17	,	,	PUNCT
ejpam-5783	13	18	kartini@lecturer.unri.ac.id	kartini@lecturer.unri.ac.id	PROPN
ejpam-5783	13	19	(	(	PUNCT
ejpam-5783	13	20	kartini	kartini	PROPN
ejpam-5783	13	21	)	)	PUNCT
ejpam-5783	13	22	,	,	PUNCT
ejpam-5783	14	1	musraini@lecturer.unri.ac.id	musraini@lecturer.unri.ac.id	PROPN
ejpam-5783	14	2	(	(	PUNCT
ejpam-5783	14	3	musraini	musraini	PROPN
ejpam-5783	14	4	)	)	PUNCT
ejpam-5783	14	5	,	,	PUNCT
ejpam-5783	14	6	elsifitria823@gmail.com	elsifitria823@gmail.com	X
ejpam-5783	14	7	(	(	PUNCT
ejpam-5783	14	8	e.	e.	PROPN
ejpam-5783	14	9	fitria	fitria	PROPN
ejpam-5783	14	10	)	)	PUNCT
ejpam-5783	14	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5783	14	12	1	1	NUM
ejpam-5783	14	13	copyright	copyright	NOUN
ejpam-5783	14	14	:	:	PUNCT
ejpam-5783	14	15	©	©	PROPN
ejpam-5783	14	16	2025	2025	NUM
ejpam-5783	14	17	the	the	DET
ejpam-5783	14	18	author(s	author(s	NOUN
ejpam-5783	14	19	)	)	PUNCT
ejpam-5783	14	20	.	.	PUNCT
ejpam-5783	15	1	(	(	PUNCT
ejpam-5783	15	2	cc	cc	NOUN
ejpam-5783	15	3	by	by	ADP
ejpam-5783	15	4	-	-	PUNCT
ejpam-5783	15	5	nc	nc	PROPN
ejpam-5783	15	6	4.0	4.0	NUM
ejpam-5783	15	7	)	)	PUNCT
ejpam-5783	15	8	s.	s.	PROPN
ejpam-5783	15	9	gemawati	gemawati	PROPN
ejpam-5783	15	10	et	et	PROPN
ejpam-5783	15	11	al	al	PROPN
ejpam-5783	15	12	.	.	PUNCT
ejpam-5783	15	13	/	/	SYM
ejpam-5783	15	14	eur	eur	PROPN
ejpam-5783	15	15	.	.	PUNCT
ejpam-5783	16	1	j.	j.	PROPN
ejpam-5783	16	2	pure	pure	PROPN
ejpam-5783	16	3	appl	appl	PROPN
ejpam-5783	16	4	.	.	PROPN
ejpam-5783	16	5	math	math	PROPN
ejpam-5783	16	6	,	,	PUNCT
ejpam-5783	16	7	18	18	NUM
ejpam-5783	16	8	(	(	PUNCT
ejpam-5783	16	9	1	1	NUM
ejpam-5783	16	10	)	)	PUNCT
ejpam-5783	16	11	(	(	PUNCT
ejpam-5783	16	12	2025	2025	NUM
ejpam-5783	16	13	)	)	PUNCT
ejpam-5783	16	14	,	,	PUNCT
ejpam-5783	16	15	5783	5783	NUM
ejpam-5783	16	16	2	2	NUM
ejpam-5783	16	17	of	of	ADP
ejpam-5783	16	18	12	12	NUM
ejpam-5783	16	19	an	an	DET
ejpam-5783	16	20	operator	operator	NOUN
ejpam-5783	17	1	|	|	ADV
ejpam-5783	17	2	is	be	AUX
ejpam-5783	17	3	called	call	VERB
ejpam-5783	17	4	a	a	DET
ejpam-5783	17	5	sheffer	sheffer	NOUN
ejpam-5783	17	6	stroke	stroke	NOUN
ejpam-5783	17	7	operator	operator	NOUN
ejpam-5783	17	8	in	in	ADP
ejpam-5783	17	9	a	a	DET
ejpam-5783	17	10	groupoid	groupoid	PROPN
ejpam-5783	17	11	t	t	NOUN
ejpam-5783	17	12	if	if	SCONJ
ejpam-5783	17	13	it	it	PRON
ejpam-5783	17	14	satisfies	satisfy	VERB
ejpam-5783	17	15	the	the	DET
ejpam-5783	17	16	following	follow	VERB
ejpam-5783	17	17	four	four	NUM
ejpam-5783	17	18	conditions	condition	NOUN
ejpam-5783	17	19	:	:	PUNCT
ejpam-5783	17	20	(	(	PUNCT
ejpam-5783	17	21	s1	s1	NOUN
ejpam-5783	17	22	)	)	PUNCT
ejpam-5783	17	23	a|b	a|b	NOUN
ejpam-5783	18	1	=	=	PUNCT
ejpam-5783	18	2	b|a	b|a	PROPN
ejpam-5783	18	3	,	,	PUNCT
ejpam-5783	18	4	(	(	PUNCT
ejpam-5783	18	5	s2	s2	PROPN
ejpam-5783	18	6	)	)	PUNCT
ejpam-5783	18	7	(	(	PUNCT
ejpam-5783	18	8	a|a)|(a|b	a|a)|(a|b	PROPN
ejpam-5783	18	9	)	)	PUNCT
ejpam-5783	18	10	=	=	SYM
ejpam-5783	19	1	a	a	PRON
ejpam-5783	19	2	,	,	PUNCT
ejpam-5783	19	3	(	(	PUNCT
ejpam-5783	19	4	s3	s3	NOUN
ejpam-5783	19	5	)	)	PUNCT
ejpam-5783	19	6	a|[(b|c)|(b|c	a|[(b|c)|(b|c	NOUN
ejpam-5783	19	7	)	)	PUNCT
ejpam-5783	19	8	]	]	PUNCT
ejpam-5783	20	1	=	=	PUNCT
ejpam-5783	21	1	[	[	X
ejpam-5783	21	2	(	(	PUNCT
ejpam-5783	21	3	a|b)|(a|b)]|c	a|b)|(a|b)]|c	ADJ
ejpam-5783	21	4	,	,	PUNCT
ejpam-5783	21	5	(	(	PUNCT
ejpam-5783	21	6	s4	s4	PROPN
ejpam-5783	21	7	)	)	PUNCT
ejpam-5783	22	1	[	[	X
ejpam-5783	22	2	a|((a|a)|(b|b))]|[a|((a|a)|(b|b	a|((a|a)|(b|b))]|[a|((a|a)|(b|b	NOUN
ejpam-5783	22	3	)	)	PUNCT
ejpam-5783	22	4	)	)	PUNCT
ejpam-5783	22	5	]	]	PUNCT
ejpam-5783	23	1	=	=	PUNCT
ejpam-5783	23	2	a	a	X
ejpam-5783	23	3	,	,	PUNCT
ejpam-5783	23	4	for	for	ADP
ejpam-5783	23	5	all	all	DET
ejpam-5783	23	6	a	a	DET
ejpam-5783	23	7	,	,	PUNCT
ejpam-5783	23	8	b	b	NOUN
ejpam-5783	23	9	,	,	PUNCT
ejpam-5783	23	10	c	c	PROPN
ejpam-5783	23	11	∈	∈	PROPN
ejpam-5783	23	12	t	t	PROPN
ejpam-5783	24	1	[	[	X
ejpam-5783	24	2	2	2	NUM
ejpam-5783	24	3	]	]	PUNCT
ejpam-5783	24	4	.	.	PUNCT
ejpam-5783	25	1	the	the	DET
ejpam-5783	25	2	functions	function	NOUN
ejpam-5783	25	3	and	and	CCONJ
ejpam-5783	25	4	axioms	axiom	NOUN
ejpam-5783	25	5	of	of	ADP
ejpam-5783	25	6	boolean	boolean	ADJ
ejpam-5783	25	7	algebra	algebra	NOUN
ejpam-5783	25	8	can	can	AUX
ejpam-5783	25	9	be	be	AUX
ejpam-5783	25	10	expressed	express	VERB
ejpam-5783	25	11	using	use	VERB
ejpam-5783	25	12	the	the	DET
ejpam-5783	25	13	sheffer	sheffer	NOUN
ejpam-5783	25	14	stroke	stroke	NOUN
ejpam-5783	25	15	operator	operator	NOUN
ejpam-5783	25	16	,	,	PUNCT
ejpam-5783	25	17	as	as	SCONJ
ejpam-5783	25	18	can	can	AUX
ejpam-5783	25	19	those	those	PRON
ejpam-5783	25	20	of	of	ADP
ejpam-5783	25	21	hilbert	hilbert	PROPN
ejpam-5783	25	22	algebras	algebras	PROPN
ejpam-5783	25	23	[	[	X
ejpam-5783	25	24	15	15	NUM
ejpam-5783	25	25	]	]	PUNCT
ejpam-5783	25	26	.	.	PUNCT
ejpam-5783	26	1	the	the	DET
ejpam-5783	26	2	sheffer	sheffer	NOUN
ejpam-5783	26	3	stroke	stroke	NOUN
ejpam-5783	26	4	operator	operator	NOUN
ejpam-5783	26	5	has	have	AUX
ejpam-5783	26	6	also	also	ADV
ejpam-5783	26	7	been	be	AUX
ejpam-5783	26	8	defined	define	VERB
ejpam-5783	26	9	for	for	ADP
ejpam-5783	26	10	r0	r0	NOUN
ejpam-5783	26	11	-	-	PUNCT
ejpam-5783	26	12	algebras	algebras	PROPN
ejpam-5783	27	1	[	[	X
ejpam-5783	27	2	10	10	NUM
ejpam-5783	27	3	]	]	PUNCT
ejpam-5783	27	4	.	.	PUNCT
ejpam-5783	28	1	an	an	DET
ejpam-5783	28	2	r0	r0	NOUN
ejpam-5783	28	3	-	-	PUNCT
ejpam-5783	28	4	algebra	algebra	NOUN
ejpam-5783	28	5	contains	contain	VERB
ejpam-5783	28	6	a	a	DET
ejpam-5783	28	7	unary	unary	ADJ
ejpam-5783	28	8	operation	operation	NOUN
ejpam-5783	28	9	and	and	CCONJ
ejpam-5783	28	10	three	three	NUM
ejpam-5783	28	11	binary	binary	ADJ
ejpam-5783	28	12	operations	operation	NOUN
ejpam-5783	28	13	.	.	PUNCT
ejpam-5783	29	1	however	however	ADV
ejpam-5783	29	2	,	,	PUNCT
ejpam-5783	29	3	after	after	ADP
ejpam-5783	29	4	defining	define	VERB
ejpam-5783	29	5	the	the	DET
ejpam-5783	29	6	sheffer	sheffer	NOUN
ejpam-5783	29	7	stroke	stroke	NOUN
ejpam-5783	29	8	operator	operator	NOUN
ejpam-5783	29	9	in	in	ADP
ejpam-5783	29	10	the	the	DET
ejpam-5783	29	11	r0	r0	NOUN
ejpam-5783	29	12	-	-	PUNCT
ejpam-5783	29	13	algebra	algebra	PROPN
ejpam-5783	29	14	,	,	PUNCT
ejpam-5783	29	15	the	the	DET
ejpam-5783	29	16	resulting	result	VERB
ejpam-5783	29	17	set	set	NOUN
ejpam-5783	29	18	contains	contain	VERB
ejpam-5783	29	19	only	only	ADV
ejpam-5783	29	20	two	two	NUM
ejpam-5783	29	21	binary	binary	ADJ
ejpam-5783	29	22	operations	operation	NOUN
ejpam-5783	29	23	with	with	ADP
ejpam-5783	29	24	the	the	DET
ejpam-5783	29	25	special	special	ADJ
ejpam-5783	29	26	properties	property	NOUN
ejpam-5783	29	27	of	of	ADP
ejpam-5783	29	28	the	the	DET
ejpam-5783	29	29	sheffer	sheffer	NOUN
ejpam-5783	29	30	stroke	stroke	NOUN
ejpam-5783	29	31	operator	operator	NOUN
ejpam-5783	29	32	.	.	PUNCT
ejpam-5783	30	1	further	further	ADJ
ejpam-5783	30	2	research	research	NOUN
ejpam-5783	30	3	has	have	AUX
ejpam-5783	30	4	explored	explore	VERB
ejpam-5783	30	5	the	the	DET
ejpam-5783	30	6	sheffer	sheffer	NOUN
ejpam-5783	30	7	stroke	stroke	NOUN
ejpam-5783	30	8	and	and	CCONJ
ejpam-5783	30	9	its	its	PRON
ejpam-5783	30	10	properties	property	NOUN
ejpam-5783	30	11	in	in	ADP
ejpam-5783	30	12	additional	additional	ADJ
ejpam-5783	30	13	algebraic	algebraic	ADJ
ejpam-5783	30	14	systems	system	NOUN
ejpam-5783	30	15	[	[	X
ejpam-5783	30	16	1	1	NUM
ejpam-5783	30	17	,	,	PUNCT
ejpam-5783	30	18	12–14	12–14	NUM
ejpam-5783	30	19	,	,	PUNCT
ejpam-5783	30	20	16	16	NUM
ejpam-5783	30	21	,	,	PUNCT
ejpam-5783	30	22	17	17	NUM
ejpam-5783	30	23	]	]	PUNCT
ejpam-5783	30	24	.	.	PUNCT
ejpam-5783	31	1	the	the	DET
ejpam-5783	31	2	extensive	extensive	ADJ
ejpam-5783	31	3	study	study	NOUN
ejpam-5783	31	4	of	of	ADP
ejpam-5783	31	5	bci	bci	NOUN
ejpam-5783	31	6	-	-	NOUN
ejpam-5783	31	7	algebra	algebra	NOUN
ejpam-5783	31	8	and	and	CCONJ
ejpam-5783	31	9	bck	bck	NOUN
ejpam-5783	31	10	-	-	PUNCT
ejpam-5783	31	11	algebra	algebra	NOUN
ejpam-5783	31	12	influenced	influence	VERB
ejpam-5783	31	13	the	the	DET
ejpam-5783	31	14	development	development	NOUN
ejpam-5783	31	15	of	of	ADP
ejpam-5783	31	16	bn	bn	NOUN
ejpam-5783	31	17	-	-	PUNCT
ejpam-5783	31	18	algebras	algebras	PROPN
ejpam-5783	31	19	.	.	PUNCT
ejpam-5783	32	1	a	a	DET
ejpam-5783	32	2	non	non	ADJ
ejpam-5783	32	3	-	-	ADJ
ejpam-5783	32	4	empty	empty	ADJ
ejpam-5783	32	5	set	set	VERB
ejpam-5783	32	6	a	a	DET
ejpam-5783	32	7	equipped	equip	VERB
ejpam-5783	32	8	with	with	ADP
ejpam-5783	32	9	a	a	DET
ejpam-5783	32	10	constant	constant	ADJ
ejpam-5783	32	11	0	0	NUM
ejpam-5783	32	12	and	and	CCONJ
ejpam-5783	32	13	a	a	DET
ejpam-5783	32	14	binary	binary	ADJ
ejpam-5783	32	15	operation	operation	NOUN
ejpam-5783	32	16	∗	∗	NOUN
ejpam-5783	32	17	is	be	AUX
ejpam-5783	32	18	called	call	VERB
ejpam-5783	32	19	a	a	DET
ejpam-5783	32	20	bn	bn	NOUN
ejpam-5783	32	21	-	-	PUNCT
ejpam-5783	32	22	algebra	algebra	NOUN
ejpam-5783	32	23	if	if	SCONJ
ejpam-5783	32	24	it	it	PRON
ejpam-5783	32	25	meets	meet	VERB
ejpam-5783	32	26	the	the	DET
ejpam-5783	32	27	following	following	ADJ
ejpam-5783	32	28	axioms	axiom	NOUN
ejpam-5783	32	29	:	:	PUNCT
ejpam-5783	32	30	(	(	PUNCT
ejpam-5783	32	31	bn1	bn1	PROPN
ejpam-5783	32	32	)	)	PUNCT
ejpam-5783	32	33	a	a	DET
ejpam-5783	32	34	∗	∗	NOUN
ejpam-5783	32	35	a	a	DET
ejpam-5783	32	36	=	=	NOUN
ejpam-5783	32	37	0	0	NUM
ejpam-5783	32	38	,	,	PUNCT
ejpam-5783	32	39	(	(	PUNCT
ejpam-5783	32	40	bn2	bn2	NOUN
ejpam-5783	32	41	)	)	PUNCT
ejpam-5783	32	42	a	a	DET
ejpam-5783	32	43	∗	∗	NOUN
ejpam-5783	32	44	0	0	NUM
ejpam-5783	33	1	=	=	SYM
ejpam-5783	33	2	a	a	PRON
ejpam-5783	33	3	,	,	PUNCT
ejpam-5783	33	4	(	(	PUNCT
ejpam-5783	33	5	bn3	bn3	PROPN
ejpam-5783	33	6	)	)	PUNCT
ejpam-5783	33	7	(	(	PUNCT
ejpam-5783	33	8	a∗	a∗	PROPN
ejpam-5783	33	9	b)∗	b)∗	PROPN
ejpam-5783	33	10	c	c	PROPN
ejpam-5783	34	1	=	=	PUNCT
ejpam-5783	35	1	(	(	PUNCT
ejpam-5783	35	2	0∗	0∗	NOUN
ejpam-5783	35	3	c)∗	c)∗	PROPN
ejpam-5783	35	4	(	(	PUNCT
ejpam-5783	35	5	b∗a	b∗a	X
ejpam-5783	35	6	)	)	PUNCT
ejpam-5783	35	7	for	for	ADP
ejpam-5783	35	8	all	all	DET
ejpam-5783	35	9	a	a	DET
ejpam-5783	35	10	,	,	PUNCT
ejpam-5783	35	11	b	b	NOUN
ejpam-5783	35	12	,	,	PUNCT
ejpam-5783	35	13	c	c	PROPN
ejpam-5783	35	14	∈	∈	PROPN
ejpam-5783	35	15	a	a	PRON
ejpam-5783	36	1	[	[	X
ejpam-5783	36	2	11	11	NUM
ejpam-5783	36	3	]	]	PUNCT
ejpam-5783	36	4	.	.	PUNCT
ejpam-5783	37	1	building	build	VERB
ejpam-5783	37	2	on	on	ADP
ejpam-5783	37	3	a	a	DET
ejpam-5783	37	4	work	work	NOUN
ejpam-5783	37	5	that	that	PRON
ejpam-5783	37	6	researched	research	VERB
ejpam-5783	37	7	ideals	ideal	NOUN
ejpam-5783	37	8	in	in	ADP
ejpam-5783	37	9	bn	bn	NOUN
ejpam-5783	37	10	-	-	PUNCT
ejpam-5783	37	11	algebra	algebra	NOUN
ejpam-5783	37	12	[	[	X
ejpam-5783	37	13	3	3	NUM
ejpam-5783	37	14	]	]	PUNCT
ejpam-5783	37	15	,	,	PUNCT
ejpam-5783	37	16	various	various	ADJ
ejpam-5783	37	17	further	further	ADJ
ejpam-5783	37	18	studies	study	NOUN
ejpam-5783	37	19	have	have	AUX
ejpam-5783	37	20	developed	develop	VERB
ejpam-5783	37	21	the	the	DET
ejpam-5783	37	22	ring	ring	NOUN
ejpam-5783	37	23	-	-	PUNCT
ejpam-5783	37	24	theoretic	theoretic	ADJ
ejpam-5783	37	25	concepts	concept	NOUN
ejpam-5783	37	26	of	of	ADP
ejpam-5783	37	27	ideals	ideal	NOUN
ejpam-5783	37	28	and	and	CCONJ
ejpam-5783	37	29	normality	normality	NOUN
ejpam-5783	37	30	in	in	ADP
ejpam-5783	37	31	bn	bn	NOUN
ejpam-5783	37	32	-	-	PUNCT
ejpam-5783	37	33	algebra	algebra	NOUN
ejpam-5783	37	34	and	and	CCONJ
ejpam-5783	37	35	related	related	ADJ
ejpam-5783	37	36	algebras	algebra	NOUN
ejpam-5783	37	37	,	,	PUNCT
ejpam-5783	37	38	as	as	SCONJ
ejpam-5783	37	39	seen	see	VERB
ejpam-5783	37	40	in	in	ADP
ejpam-5783	37	41	[	[	X
ejpam-5783	37	42	4	4	NUM
ejpam-5783	37	43	,	,	PUNCT
ejpam-5783	37	44	5	5	NUM
ejpam-5783	37	45	,	,	PUNCT
ejpam-5783	37	46	9	9	NUM
ejpam-5783	37	47	]	]	PUNCT
ejpam-5783	37	48	.	.	PUNCT
ejpam-5783	38	1	motivated	motivate	VERB
ejpam-5783	38	2	by	by	ADP
ejpam-5783	38	3	the	the	DET
ejpam-5783	38	4	close	close	ADJ
ejpam-5783	38	5	relationship	relationship	NOUN
ejpam-5783	38	6	between	between	ADP
ejpam-5783	38	7	ideals	ideal	NOUN
ejpam-5783	38	8	and	and	CCONJ
ejpam-5783	38	9	normal	normal	ADJ
ejpam-5783	38	10	subsets	subset	NOUN
ejpam-5783	38	11	in	in	ADP
ejpam-5783	38	12	bn	bn	NOUN
ejpam-5783	38	13	-	-	PUNCT
ejpam-5783	38	14	algebra	algebra	NOUN
ejpam-5783	38	15	,	,	PUNCT
ejpam-5783	38	16	as	as	SCONJ
ejpam-5783	38	17	discussed	discuss	VERB
ejpam-5783	38	18	in	in	ADP
ejpam-5783	38	19	previous	previous	ADJ
ejpam-5783	38	20	research	research	NOUN
ejpam-5783	38	21	,	,	PUNCT
ejpam-5783	38	22	and	and	CCONJ
ejpam-5783	38	23	the	the	DET
ejpam-5783	38	24	author	author	NOUN
ejpam-5783	38	25	’s	’s	PART
ejpam-5783	38	26	experience	experience	NOUN
ejpam-5783	38	27	in	in	ADP
ejpam-5783	38	28	abstract	abstract	ADJ
ejpam-5783	38	29	algebra	algebra	NOUN
ejpam-5783	38	30	,	,	PUNCT
ejpam-5783	38	31	especially	especially	ADV
ejpam-5783	38	32	work	work	NOUN
ejpam-5783	38	33	concerning	concern	VERB
ejpam-5783	38	34	the	the	DET
ejpam-5783	38	35	concept	concept	NOUN
ejpam-5783	38	36	of	of	ADP
ejpam-5783	38	37	algebraic	algebraic	ADJ
ejpam-5783	38	38	structures	structure	NOUN
ejpam-5783	38	39	,	,	PUNCT
ejpam-5783	38	40	such	such	ADJ
ejpam-5783	38	41	as	as	ADP
ejpam-5783	38	42	in	in	ADP
ejpam-5783	38	43	[	[	X
ejpam-5783	38	44	6–8	6–8	NOUN
ejpam-5783	38	45	]	]	X
ejpam-5783	38	46	,	,	PUNCT
ejpam-5783	38	47	in	in	ADP
ejpam-5783	38	48	this	this	DET
ejpam-5783	38	49	study	study	NOUN
ejpam-5783	38	50	,	,	PUNCT
ejpam-5783	38	51	the	the	DET
ejpam-5783	38	52	concept	concept	NOUN
ejpam-5783	38	53	of	of	ADP
ejpam-5783	38	54	a	a	DET
ejpam-5783	38	55	sheffer	sheffer	NOUN
ejpam-5783	38	56	stroke	stroke	NOUN
ejpam-5783	38	57	bn	bn	NOUN
ejpam-5783	38	58	-	-	PUNCT
ejpam-5783	38	59	algebra	algebra	NOUN
ejpam-5783	38	60	is	be	AUX
ejpam-5783	38	61	defined	define	VERB
ejpam-5783	38	62	and	and	CCONJ
ejpam-5783	38	63	its	its	PRON
ejpam-5783	38	64	properties	property	NOUN
ejpam-5783	38	65	are	be	AUX
ejpam-5783	38	66	determined	determine	VERB
ejpam-5783	38	67	.	.	PUNCT
ejpam-5783	39	1	then	then	ADV
ejpam-5783	39	2	,	,	PUNCT
ejpam-5783	39	3	the	the	DET
ejpam-5783	39	4	notions	notion	NOUN
ejpam-5783	39	5	of	of	ADP
ejpam-5783	39	6	sheffer	sheffer	PROPN
ejpam-5783	39	7	stroke	stroke	PROPN
ejpam-5783	39	8	bn	bn	PROPN
ejpam-5783	39	9	-	-	PUNCT
ejpam-5783	39	10	subalgebras	subalgebras	PROPN
ejpam-5783	39	11	,	,	PUNCT
ejpam-5783	39	12	bn	bn	NOUN
ejpam-5783	39	13	-	-	PUNCT
ejpam-5783	39	14	ideals	ideal	NOUN
ejpam-5783	39	15	,	,	PUNCT
ejpam-5783	39	16	and	and	CCONJ
ejpam-5783	39	17	bn	bn	NOUN
ejpam-5783	39	18	-	-	PUNCT
ejpam-5783	39	19	homomorphisms	homomorphism	NOUN
ejpam-5783	39	20	and	and	CCONJ
ejpam-5783	39	21	their	their	PRON
ejpam-5783	39	22	kernels	kernel	NOUN
ejpam-5783	39	23	,	,	PUNCT
ejpam-5783	39	24	as	as	ADV
ejpam-5783	39	25	well	well	ADV
ejpam-5783	39	26	as	as	ADP
ejpam-5783	39	27	normal	normal	ADJ
ejpam-5783	39	28	subsets	subset	NOUN
ejpam-5783	39	29	of	of	ADP
ejpam-5783	39	30	sheffer	sheffer	PROPN
ejpam-5783	39	31	stroke	stroke	PROPN
ejpam-5783	39	32	bn	bn	PROPN
ejpam-5783	39	33	-	-	PUNCT
ejpam-5783	39	34	algebras	algebras	X
ejpam-5783	39	35	,	,	PUNCT
ejpam-5783	39	36	are	be	AUX
ejpam-5783	39	37	introduced	introduce	VERB
ejpam-5783	39	38	,	,	PUNCT
ejpam-5783	39	39	and	and	CCONJ
ejpam-5783	39	40	the	the	DET
ejpam-5783	39	41	relationships	relationship	NOUN
ejpam-5783	39	42	between	between	ADP
ejpam-5783	39	43	these	these	DET
ejpam-5783	39	44	concepts	concept	NOUN
ejpam-5783	39	45	are	be	AUX
ejpam-5783	39	46	investigated	investigate	VERB
ejpam-5783	39	47	.	.	PUNCT
ejpam-5783	40	1	2	2	X
ejpam-5783	40	2	.	.	X
ejpam-5783	40	3	preliminaries	preliminary	NOUN
ejpam-5783	40	4	this	this	DET
ejpam-5783	40	5	section	section	NOUN
ejpam-5783	40	6	presents	present	VERB
ejpam-5783	40	7	several	several	ADJ
ejpam-5783	40	8	definitions	definition	NOUN
ejpam-5783	40	9	and	and	CCONJ
ejpam-5783	40	10	properties	property	NOUN
ejpam-5783	40	11	necessary	necessary	ADJ
ejpam-5783	40	12	for	for	ADP
ejpam-5783	40	13	the	the	DET
ejpam-5783	40	14	construction	construction	NOUN
ejpam-5783	40	15	of	of	ADP
ejpam-5783	40	16	sheffer	sheffer	PROPN
ejpam-5783	40	17	stroke	stroke	PROPN
ejpam-5783	40	18	bn	bn	NOUN
ejpam-5783	40	19	-	-	PUNCT
ejpam-5783	40	20	algebras	algebras	PROPN
ejpam-5783	40	21	and	and	CCONJ
ejpam-5783	40	22	the	the	DET
ejpam-5783	40	23	other	other	ADJ
ejpam-5783	40	24	concepts	concept	NOUN
ejpam-5783	40	25	explored	explore	VERB
ejpam-5783	40	26	in	in	ADP
ejpam-5783	40	27	this	this	DET
ejpam-5783	40	28	study	study	NOUN
ejpam-5783	40	29	.	.	PUNCT
ejpam-5783	41	1	definition	definition	NOUN
ejpam-5783	41	2	1	1	NUM
ejpam-5783	41	3	.	.	PUNCT
ejpam-5783	42	1	[	[	X
ejpam-5783	42	2	11	11	NUM
ejpam-5783	42	3	]	]	X
ejpam-5783	42	4	a	a	DET
ejpam-5783	42	5	bn	bn	NOUN
ejpam-5783	42	6	-	-	PUNCT
ejpam-5783	42	7	algebra	algebra	NOUN
ejpam-5783	42	8	is	be	AUX
ejpam-5783	42	9	a	a	DET
ejpam-5783	42	10	non	non	ADJ
ejpam-5783	42	11	-	-	ADJ
ejpam-5783	42	12	empty	empty	ADJ
ejpam-5783	42	13	set	set	VERB
ejpam-5783	42	14	a	a	DET
ejpam-5783	42	15	equipped	equip	VERB
ejpam-5783	42	16	with	with	ADP
ejpam-5783	42	17	a	a	DET
ejpam-5783	42	18	constant	constant	ADJ
ejpam-5783	42	19	0	0	NUM
ejpam-5783	42	20	and	and	CCONJ
ejpam-5783	42	21	a	a	DET
ejpam-5783	42	22	binary	binary	ADJ
ejpam-5783	42	23	operation	operation	NOUN
ejpam-5783	42	24	∗	∗	NOUN
ejpam-5783	42	25	that	that	PRON
ejpam-5783	42	26	meets	meet	VERB
ejpam-5783	42	27	the	the	DET
ejpam-5783	42	28	following	following	ADJ
ejpam-5783	42	29	axioms	axiom	NOUN
ejpam-5783	42	30	:	:	PUNCT
ejpam-5783	42	31	(	(	PUNCT
ejpam-5783	42	32	bn1	bn1	PROPN
ejpam-5783	42	33	)	)	PUNCT
ejpam-5783	42	34	a	a	DET
ejpam-5783	42	35	∗	∗	NOUN
ejpam-5783	42	36	a	a	DET
ejpam-5783	42	37	=	=	NOUN
ejpam-5783	42	38	0	0	NUM
ejpam-5783	42	39	for	for	ADP
ejpam-5783	42	40	all	all	DET
ejpam-5783	42	41	a	a	DET
ejpam-5783	42	42	∈	∈	PROPN
ejpam-5783	42	43	a	a	DET
ejpam-5783	42	44	,	,	PUNCT
ejpam-5783	42	45	(	(	PUNCT
ejpam-5783	42	46	bn2	bn2	NOUN
ejpam-5783	42	47	)	)	PUNCT
ejpam-5783	42	48	a	a	DET
ejpam-5783	42	49	∗	∗	NOUN
ejpam-5783	42	50	0	0	NUM
ejpam-5783	43	1	=	=	SYM
ejpam-5783	43	2	0	0	NUM
ejpam-5783	43	3	for	for	ADP
ejpam-5783	43	4	all	all	DET
ejpam-5783	43	5	a	a	DET
ejpam-5783	43	6	∈	∈	PROPN
ejpam-5783	43	7	a	a	DET
ejpam-5783	43	8	,	,	PUNCT
ejpam-5783	43	9	(	(	PUNCT
ejpam-5783	43	10	bn3	bn3	PROPN
ejpam-5783	43	11	)	)	PUNCT
ejpam-5783	43	12	(	(	PUNCT
ejpam-5783	43	13	a	a	DET
ejpam-5783	43	14	∗	∗	NOUN
ejpam-5783	43	15	b	b	NOUN
ejpam-5783	43	16	)	)	PUNCT
ejpam-5783	43	17	∗	∗	NOUN
ejpam-5783	43	18	c	c	NOUN
ejpam-5783	43	19	=	=	SYM
ejpam-5783	43	20	(	(	PUNCT
ejpam-5783	43	21	0	0	NUM
ejpam-5783	43	22	∗	∗	NOUN
ejpam-5783	43	23	c	c	NOUN
ejpam-5783	43	24	)	)	PUNCT
ejpam-5783	43	25	∗	∗	NOUN
ejpam-5783	43	26	(	(	PUNCT
ejpam-5783	43	27	b	b	NOUN
ejpam-5783	43	28	∗	∗	X
ejpam-5783	43	29	a	a	NOUN
ejpam-5783	43	30	)	)	PUNCT
ejpam-5783	43	31	for	for	ADP
ejpam-5783	43	32	all	all	DET
ejpam-5783	43	33	a	a	DET
ejpam-5783	43	34	,	,	PUNCT
ejpam-5783	43	35	b	b	NOUN
ejpam-5783	43	36	,	,	PUNCT
ejpam-5783	43	37	c	c	PROPN
ejpam-5783	43	38	∈	∈	PROPN
ejpam-5783	43	39	a.	a.	NOUN
ejpam-5783	43	40	theorem	theorem	NOUN
ejpam-5783	43	41	1	1	NUM
ejpam-5783	43	42	.	.	PUNCT
ejpam-5783	44	1	[	[	X
ejpam-5783	44	2	11	11	NUM
ejpam-5783	44	3	]	]	PUNCT
ejpam-5783	44	4	suppose	suppose	VERB
ejpam-5783	44	5	(	(	PUNCT
ejpam-5783	44	6	a	a	X
ejpam-5783	44	7	;	;	PUNCT
ejpam-5783	44	8	∗	∗	NOUN
ejpam-5783	44	9	,	,	PUNCT
ejpam-5783	44	10	0	0	NUM
ejpam-5783	44	11	)	)	PUNCT
ejpam-5783	44	12	be	be	AUX
ejpam-5783	44	13	a	a	DET
ejpam-5783	44	14	bn	bn	NOUN
ejpam-5783	44	15	-	-	PUNCT
ejpam-5783	44	16	algebra	algebra	NOUN
ejpam-5783	44	17	,	,	PUNCT
ejpam-5783	44	18	then	then	ADV
ejpam-5783	44	19	for	for	ADP
ejpam-5783	44	20	all	all	DET
ejpam-5783	44	21	a	a	DET
ejpam-5783	44	22	,	,	PUNCT
ejpam-5783	44	23	b	b	NOUN
ejpam-5783	44	24	,	,	PUNCT
ejpam-5783	44	25	c	c	PROPN
ejpam-5783	44	26	∈	∈	PROPN
ejpam-5783	44	27	a	a	PRON
ejpam-5783	44	28	:	:	PUNCT
ejpam-5783	44	29	(	(	PUNCT
ejpam-5783	44	30	i	i	NOUN
ejpam-5783	44	31	)	)	PUNCT
ejpam-5783	44	32	0	0	NUM
ejpam-5783	45	1	∗	∗	NOUN
ejpam-5783	45	2	(	(	PUNCT
ejpam-5783	45	3	0	0	NUM
ejpam-5783	45	4	∗	∗	NOUN
ejpam-5783	45	5	a	a	NOUN
ejpam-5783	45	6	)	)	PUNCT
ejpam-5783	45	7	=	=	SYM
ejpam-5783	45	8	a	a	PRON
ejpam-5783	45	9	,	,	PUNCT
ejpam-5783	45	10	(	(	PUNCT
ejpam-5783	45	11	ii	ii	NOUN
ejpam-5783	45	12	)	)	PUNCT
ejpam-5783	45	13	b	b	PROPN
ejpam-5783	45	14	∗	∗	NOUN
ejpam-5783	45	15	a	a	DET
ejpam-5783	45	16	=	=	X
ejpam-5783	45	17	(	(	PUNCT
ejpam-5783	45	18	0	0	NUM
ejpam-5783	45	19	∗	∗	NOUN
ejpam-5783	45	20	a	a	NOUN
ejpam-5783	45	21	)	)	PUNCT
ejpam-5783	45	22	∗	∗	NOUN
ejpam-5783	45	23	(	(	PUNCT
ejpam-5783	45	24	0	0	NUM
ejpam-5783	45	25	∗	∗	NUM
ejpam-5783	45	26	b	b	NOUN
ejpam-5783	45	27	)	)	PUNCT
ejpam-5783	45	28	,	,	PUNCT
ejpam-5783	45	29	(	(	PUNCT
ejpam-5783	45	30	iii	iii	X
ejpam-5783	45	31	)	)	PUNCT
ejpam-5783	45	32	(	(	PUNCT
ejpam-5783	45	33	0	0	NUM
ejpam-5783	45	34	∗	∗	NOUN
ejpam-5783	45	35	a	a	NOUN
ejpam-5783	45	36	)	)	PUNCT
ejpam-5783	45	37	∗	∗	NOUN
ejpam-5783	45	38	b	b	NOUN
ejpam-5783	46	1	=	=	SYM
ejpam-5783	47	1	(	(	PUNCT
ejpam-5783	47	2	0	0	NUM
ejpam-5783	47	3	∗	∗	NUM
ejpam-5783	47	4	b	b	NOUN
ejpam-5783	47	5	)	)	PUNCT
ejpam-5783	47	6	∗	∗	NOUN
ejpam-5783	47	7	a	a	PRON
ejpam-5783	47	8	,	,	PUNCT
ejpam-5783	47	9	(	(	PUNCT
ejpam-5783	47	10	iv	iv	X
ejpam-5783	47	11	)	)	PUNCT
ejpam-5783	47	12	if	if	SCONJ
ejpam-5783	47	13	a	a	DET
ejpam-5783	47	14	∗	∗	X
ejpam-5783	47	15	b	b	NOUN
ejpam-5783	47	16	=	=	SYM
ejpam-5783	47	17	0	0	NUM
ejpam-5783	47	18	,	,	PUNCT
ejpam-5783	47	19	then	then	ADV
ejpam-5783	47	20	b	b	NOUN
ejpam-5783	47	21	∗	∗	NOUN
ejpam-5783	47	22	a	a	DET
ejpam-5783	47	23	=	=	SYM
ejpam-5783	47	24	0	0	NUM
ejpam-5783	47	25	,	,	PUNCT
ejpam-5783	47	26	s.	s.	PROPN
ejpam-5783	47	27	gemawati	gemawati	PROPN
ejpam-5783	48	1	et	et	PROPN
ejpam-5783	48	2	al	al	PROPN
ejpam-5783	48	3	.	.	PUNCT
ejpam-5783	48	4	/	/	SYM
ejpam-5783	48	5	eur	eur	PROPN
ejpam-5783	48	6	.	.	PUNCT
ejpam-5783	49	1	j.	j.	PROPN
ejpam-5783	49	2	pure	pure	PROPN
ejpam-5783	49	3	appl	appl	PROPN
ejpam-5783	49	4	.	.	PROPN
ejpam-5783	49	5	math	math	PROPN
ejpam-5783	49	6	,	,	PUNCT
ejpam-5783	49	7	18	18	NUM
ejpam-5783	49	8	(	(	PUNCT
ejpam-5783	49	9	1	1	NUM
ejpam-5783	49	10	)	)	PUNCT
ejpam-5783	49	11	(	(	PUNCT
ejpam-5783	49	12	2025	2025	NUM
ejpam-5783	49	13	)	)	PUNCT
ejpam-5783	49	14	,	,	PUNCT
ejpam-5783	49	15	5783	5783	NUM
ejpam-5783	49	16	3	3	NUM
ejpam-5783	49	17	of	of	ADP
ejpam-5783	49	18	12	12	NUM
ejpam-5783	49	19	(	(	PUNCT
ejpam-5783	49	20	v	v	NOUN
ejpam-5783	49	21	)	)	PUNCT
ejpam-5783	49	22	if	if	SCONJ
ejpam-5783	49	23	0	0	NUM
ejpam-5783	49	24	∗	∗	VERB
ejpam-5783	49	25	a	a	PRON
ejpam-5783	49	26	=	=	SYM
ejpam-5783	49	27	0	0	NUM
ejpam-5783	49	28	∗	∗	NOUN
ejpam-5783	49	29	b	b	PROPN
ejpam-5783	49	30	,	,	PUNCT
ejpam-5783	49	31	then	then	ADV
ejpam-5783	49	32	a	a	DET
ejpam-5783	49	33	=	=	SYM
ejpam-5783	49	34	b	b	PROPN
ejpam-5783	49	35	,	,	PUNCT
ejpam-5783	49	36	(	(	PUNCT
ejpam-5783	49	37	vi	vi	NOUN
ejpam-5783	49	38	)	)	PUNCT
ejpam-5783	49	39	(	(	PUNCT
ejpam-5783	49	40	a	a	DET
ejpam-5783	49	41	∗	∗	NOUN
ejpam-5783	49	42	c	c	NOUN
ejpam-5783	49	43	)	)	PUNCT
ejpam-5783	49	44	∗	∗	NOUN
ejpam-5783	49	45	(	(	PUNCT
ejpam-5783	49	46	b	b	NOUN
ejpam-5783	49	47	∗	∗	NOUN
ejpam-5783	49	48	c	c	NOUN
ejpam-5783	49	49	)	)	PUNCT
ejpam-5783	49	50	=	=	SYM
ejpam-5783	49	51	(	(	PUNCT
ejpam-5783	49	52	c	c	NOUN
ejpam-5783	49	53	∗	∗	X
ejpam-5783	49	54	b	b	NOUN
ejpam-5783	49	55	)	)	PUNCT
ejpam-5783	49	56	∗	∗	NOUN
ejpam-5783	49	57	(	(	PUNCT
ejpam-5783	49	58	c	c	NOUN
ejpam-5783	49	59	∗	∗	X
ejpam-5783	49	60	a	a	NOUN
ejpam-5783	49	61	)	)	PUNCT
ejpam-5783	49	62	.	.	PUNCT
ejpam-5783	50	1	definition	definition	NOUN
ejpam-5783	50	2	2	2	NUM
ejpam-5783	50	3	.	.	PUNCT
ejpam-5783	51	1	[	[	X
ejpam-5783	51	2	11	11	NUM
ejpam-5783	51	3	]	]	X
ejpam-5783	51	4	a	a	DET
ejpam-5783	51	5	bn	bn	NOUN
ejpam-5783	51	6	-	-	PUNCT
ejpam-5783	51	7	algebra	algebra	NOUN
ejpam-5783	51	8	(	(	PUNCT
ejpam-5783	51	9	a	a	NOUN
ejpam-5783	51	10	;	;	PUNCT
ejpam-5783	51	11	∗	∗	NOUN
ejpam-5783	51	12	,	,	PUNCT
ejpam-5783	51	13	0	0	NUM
ejpam-5783	51	14	)	)	PUNCT
ejpam-5783	51	15	that	that	PRON
ejpam-5783	51	16	satisfies	satisfy	VERB
ejpam-5783	51	17	(	(	PUNCT
ejpam-5783	51	18	d	d	X
ejpam-5783	51	19	)	)	PUNCT
ejpam-5783	51	20	(	(	PUNCT
ejpam-5783	51	21	a	a	DET
ejpam-5783	51	22	∗	∗	NOUN
ejpam-5783	51	23	b	b	NOUN
ejpam-5783	51	24	)	)	PUNCT
ejpam-5783	51	25	∗	∗	NOUN
ejpam-5783	51	26	c	c	NOUN
ejpam-5783	51	27	=	=	PUNCT
ejpam-5783	51	28	a	a	DET
ejpam-5783	51	29	∗	∗	NOUN
ejpam-5783	51	30	(	(	PUNCT
ejpam-5783	51	31	c	c	NOUN
ejpam-5783	51	32	∗	∗	X
ejpam-5783	51	33	b	b	NOUN
ejpam-5783	51	34	)	)	PUNCT
ejpam-5783	51	35	for	for	ADP
ejpam-5783	51	36	all	all	DET
ejpam-5783	51	37	a	a	DET
ejpam-5783	51	38	,	,	PUNCT
ejpam-5783	51	39	b	b	NOUN
ejpam-5783	51	40	,	,	PUNCT
ejpam-5783	51	41	c	c	PROPN
ejpam-5783	51	42	∈	∈	PROPN
ejpam-5783	51	43	a	a	PRON
ejpam-5783	51	44	is	be	AUX
ejpam-5783	51	45	called	call	VERB
ejpam-5783	51	46	a	a	DET
ejpam-5783	51	47	bn	bn	NOUN
ejpam-5783	51	48	-	-	PUNCT
ejpam-5783	51	49	algebra	algebra	NOUN
ejpam-5783	51	50	with	with	ADP
ejpam-5783	51	51	condition	condition	NOUN
ejpam-5783	51	52	(	(	PUNCT
ejpam-5783	51	53	d	d	NOUN
ejpam-5783	51	54	)	)	PUNCT
ejpam-5783	51	55	.	.	PUNCT
ejpam-5783	52	1	theorem	theorem	NOUN
ejpam-5783	52	2	2	2	NUM
ejpam-5783	52	3	.	.	PUNCT
ejpam-5783	53	1	[	[	X
ejpam-5783	53	2	11	11	NUM
ejpam-5783	53	3	]	]	PUNCT
ejpam-5783	53	4	suppose	suppose	VERB
ejpam-5783	53	5	(	(	PUNCT
ejpam-5783	53	6	a	a	X
ejpam-5783	53	7	;	;	PUNCT
ejpam-5783	53	8	∗	∗	NOUN
ejpam-5783	53	9	,	,	PUNCT
ejpam-5783	53	10	0	0	NUM
ejpam-5783	53	11	)	)	PUNCT
ejpam-5783	53	12	is	be	AUX
ejpam-5783	53	13	a	a	DET
ejpam-5783	53	14	bn	bn	NOUN
ejpam-5783	53	15	-	-	PUNCT
ejpam-5783	53	16	algebra	algebra	NOUN
ejpam-5783	53	17	with	with	ADP
ejpam-5783	53	18	condition	condition	NOUN
ejpam-5783	53	19	(	(	PUNCT
ejpam-5783	53	20	d	d	NOUN
ejpam-5783	53	21	)	)	PUNCT
ejpam-5783	53	22	.	.	PUNCT
ejpam-5783	54	1	then	then	ADV
ejpam-5783	54	2	,	,	PUNCT
ejpam-5783	54	3	the	the	DET
ejpam-5783	54	4	following	follow	VERB
ejpam-5783	54	5	properties	property	NOUN
ejpam-5783	54	6	are	be	AUX
ejpam-5783	54	7	satisfied	satisfied	ADJ
ejpam-5783	54	8	for	for	ADP
ejpam-5783	54	9	all	all	DET
ejpam-5783	54	10	a	a	DET
ejpam-5783	54	11	,	,	PUNCT
ejpam-5783	54	12	b	b	NOUN
ejpam-5783	54	13	,	,	PUNCT
ejpam-5783	54	14	c	c	PROPN
ejpam-5783	54	15	∈	∈	PROPN
ejpam-5783	54	16	a	a	DET
ejpam-5783	54	17	:	:	PUNCT
ejpam-5783	54	18	(	(	PUNCT
ejpam-5783	54	19	i	i	NOUN
ejpam-5783	54	20	)	)	PUNCT
ejpam-5783	54	21	0	0	NUM
ejpam-5783	54	22	∗	∗	NOUN
ejpam-5783	54	23	a	a	DET
ejpam-5783	54	24	=	=	NOUN
ejpam-5783	54	25	a	a	NOUN
ejpam-5783	54	26	,	,	PUNCT
ejpam-5783	54	27	(	(	PUNCT
ejpam-5783	54	28	ii	ii	NOUN
ejpam-5783	54	29	)	)	PUNCT
ejpam-5783	54	30	a	a	DET
ejpam-5783	54	31	∗	∗	NOUN
ejpam-5783	54	32	b	b	X
ejpam-5783	54	33	=	=	SYM
ejpam-5783	54	34	b	b	PROPN
ejpam-5783	54	35	∗	∗	X
ejpam-5783	54	36	a.	a.	NOUN
ejpam-5783	54	37	definition	definition	NOUN
ejpam-5783	54	38	3	3	NUM
ejpam-5783	54	39	.	.	PUNCT
ejpam-5783	55	1	[	[	X
ejpam-5783	55	2	3	3	X
ejpam-5783	55	3	]	]	PUNCT
ejpam-5783	55	4	suppose	suppose	VERB
ejpam-5783	55	5	(	(	PUNCT
ejpam-5783	55	6	a	a	X
ejpam-5783	55	7	;	;	PUNCT
ejpam-5783	55	8	∗	∗	NOUN
ejpam-5783	55	9	,	,	PUNCT
ejpam-5783	55	10	0	0	NUM
ejpam-5783	55	11	)	)	PUNCT
ejpam-5783	55	12	is	be	AUX
ejpam-5783	55	13	a	a	DET
ejpam-5783	55	14	bn	bn	NOUN
ejpam-5783	55	15	-	-	PUNCT
ejpam-5783	55	16	algebra	algebra	NOUN
ejpam-5783	55	17	.	.	PUNCT
ejpam-5783	56	1	a	a	DET
ejpam-5783	56	2	non	non	ADJ
ejpam-5783	56	3	-	-	ADJ
ejpam-5783	56	4	empty	empty	ADJ
ejpam-5783	56	5	subset	subset	NOUN
ejpam-5783	56	6	i	i	PRON
ejpam-5783	56	7	of	of	ADP
ejpam-5783	56	8	a	a	PRON
ejpam-5783	56	9	is	be	AUX
ejpam-5783	56	10	defined	define	VERB
ejpam-5783	56	11	as	as	ADP
ejpam-5783	56	12	an	an	DET
ejpam-5783	56	13	ideal	ideal	NOUN
ejpam-5783	56	14	in	in	ADP
ejpam-5783	56	15	a	a	PRON
ejpam-5783	56	16	if	if	SCONJ
ejpam-5783	56	17	it	it	PRON
ejpam-5783	56	18	meets	meet	VERB
ejpam-5783	56	19	the	the	DET
ejpam-5783	56	20	following	following	ADJ
ejpam-5783	56	21	conditions	condition	NOUN
ejpam-5783	56	22	:	:	PUNCT
ejpam-5783	56	23	(	(	PUNCT
ejpam-5783	56	24	i	i	NOUN
ejpam-5783	56	25	)	)	PUNCT
ejpam-5783	56	26	0	0	PUNCT
ejpam-5783	57	1	∈	∈	PROPN
ejpam-5783	57	2	i	i	PRON
ejpam-5783	57	3	,	,	PUNCT
ejpam-5783	57	4	and	and	CCONJ
ejpam-5783	57	5	(	(	PUNCT
ejpam-5783	57	6	ii	ii	NOUN
ejpam-5783	57	7	)	)	PUNCT
ejpam-5783	57	8	for	for	ADP
ejpam-5783	57	9	all	all	DET
ejpam-5783	57	10	a	a	PRON
ejpam-5783	57	11	,	,	PUNCT
ejpam-5783	57	12	b	b	X
ejpam-5783	57	13	∈	∈	PROPN
ejpam-5783	57	14	a	a	PRON
ejpam-5783	57	15	,	,	PUNCT
ejpam-5783	57	16	if	if	SCONJ
ejpam-5783	57	17	b	b	X
ejpam-5783	57	18	∈	∈	PROPN
ejpam-5783	57	19	i	i	PRON
ejpam-5783	57	20	and	and	CCONJ
ejpam-5783	57	21	a	a	DET
ejpam-5783	57	22	∗	∗	NOUN
ejpam-5783	57	23	b	b	X
ejpam-5783	57	24	∈	∈	PROPN
ejpam-5783	58	1	i	i	PRON
ejpam-5783	58	2	,	,	PUNCT
ejpam-5783	58	3	implies	imply	VERB
ejpam-5783	58	4	a	a	DET
ejpam-5783	58	5	∈	∈	PROPN
ejpam-5783	58	6	i.	i.	NOUN
ejpam-5783	58	7	suppose	suppose	VERB
ejpam-5783	58	8	(	(	PUNCT
ejpam-5783	58	9	a	a	X
ejpam-5783	58	10	;	;	PUNCT
ejpam-5783	58	11	∗	∗	NOUN
ejpam-5783	58	12	,	,	PUNCT
ejpam-5783	58	13	0	0	NUM
ejpam-5783	58	14	)	)	PUNCT
ejpam-5783	58	15	is	be	AUX
ejpam-5783	58	16	a	a	DET
ejpam-5783	58	17	bn	bn	NOUN
ejpam-5783	58	18	-	-	PUNCT
ejpam-5783	58	19	algebra	algebra	NOUN
ejpam-5783	58	20	.	.	PUNCT
ejpam-5783	59	1	a	a	DET
ejpam-5783	59	2	non	non	ADJ
ejpam-5783	59	3	-	-	ADJ
ejpam-5783	59	4	empty	empty	ADJ
ejpam-5783	59	5	subset	subset	NOUN
ejpam-5783	59	6	s	s	X
ejpam-5783	59	7	is	be	AUX
ejpam-5783	59	8	considered	consider	VERB
ejpam-5783	59	9	a	a	DET
ejpam-5783	59	10	subalgebra	subalgebra	NOUN
ejpam-5783	59	11	of	of	ADP
ejpam-5783	59	12	a	a	PRON
ejpam-5783	59	13	if	if	SCONJ
ejpam-5783	59	14	it	it	PRON
ejpam-5783	59	15	satisfies	satisfy	VERB
ejpam-5783	59	16	a	a	DET
ejpam-5783	59	17	∗	∗	NOUN
ejpam-5783	59	18	b	b	NOUN
ejpam-5783	59	19	∈	∈	NOUN
ejpam-5783	59	20	s	s	X
ejpam-5783	59	21	for	for	ADP
ejpam-5783	59	22	all	all	DET
ejpam-5783	59	23	a	a	PRON
ejpam-5783	59	24	,	,	PUNCT
ejpam-5783	59	25	b	b	X
ejpam-5783	59	26	∈	∈	PROPN
ejpam-5783	59	27	s.	s.	PROPN
ejpam-5783	59	28	a	a	DET
ejpam-5783	59	29	non	non	ADJ
ejpam-5783	59	30	-	-	ADJ
ejpam-5783	59	31	empty	empty	ADJ
ejpam-5783	59	32	subset	subset	NOUN
ejpam-5783	59	33	n	n	PROPN
ejpam-5783	59	34	of	of	ADP
ejpam-5783	59	35	a	a	PRON
ejpam-5783	59	36	is	be	AUX
ejpam-5783	59	37	termed	term	VERB
ejpam-5783	59	38	a	a	DET
ejpam-5783	59	39	normal	normal	ADJ
ejpam-5783	59	40	if	if	SCONJ
ejpam-5783	59	41	it	it	PRON
ejpam-5783	59	42	satisfies	satisfy	VERB
ejpam-5783	59	43	(	(	PUNCT
ejpam-5783	60	1	x	x	X
ejpam-5783	60	2	∗	∗	NOUN
ejpam-5783	60	3	a	a	NOUN
ejpam-5783	60	4	)	)	PUNCT
ejpam-5783	60	5	∗	∗	NOUN
ejpam-5783	60	6	(	(	PUNCT
ejpam-5783	60	7	y	y	PROPN
ejpam-5783	60	8	∗	∗	X
ejpam-5783	60	9	b	b	NOUN
ejpam-5783	60	10	)	)	PUNCT
ejpam-5783	60	11	∈	∈	PROPN
ejpam-5783	60	12	n	n	NOUN
ejpam-5783	60	13	for	for	ADP
ejpam-5783	60	14	all	all	DET
ejpam-5783	60	15	x	x	PROPN
ejpam-5783	60	16	∗	∗	PROPN
ejpam-5783	60	17	y	y	PROPN
ejpam-5783	60	18	,	,	PUNCT
ejpam-5783	60	19	a	a	DET
ejpam-5783	60	20	∗	∗	NOUN
ejpam-5783	60	21	b	b	NOUN
ejpam-5783	60	22	∈	∈	PROPN
ejpam-5783	60	23	n	n	NOUN
ejpam-5783	60	24	,	,	PUNCT
ejpam-5783	60	25	where	where	SCONJ
ejpam-5783	60	26	a	a	DET
ejpam-5783	60	27	,	,	PUNCT
ejpam-5783	60	28	b	b	NOUN
ejpam-5783	60	29	,	,	PUNCT
ejpam-5783	60	30	x	x	X
ejpam-5783	60	31	,	,	PUNCT
ejpam-5783	60	32	y	y	PROPN
ejpam-5783	60	33	∈	∈	PROPN
ejpam-5783	60	34	a.	a.	NOUN
ejpam-5783	60	35	in	in	ADP
ejpam-5783	60	36	a	a	DET
ejpam-5783	60	37	bn	bn	NOUN
ejpam-5783	60	38	-	-	PUNCT
ejpam-5783	60	39	algebra	algebra	NOUN
ejpam-5783	60	40	(	(	PUNCT
ejpam-5783	60	41	a	a	NOUN
ejpam-5783	60	42	;	;	PUNCT
ejpam-5783	60	43	∗	∗	NOUN
ejpam-5783	60	44	,	,	PUNCT
ejpam-5783	60	45	0	0	NUM
ejpam-5783	60	46	)	)	PUNCT
ejpam-5783	60	47	,	,	PUNCT
ejpam-5783	60	48	the	the	DET
ejpam-5783	60	49	operation	operation	NOUN
ejpam-5783	60	50	∧	∧	PROPN
ejpam-5783	60	51	is	be	AUX
ejpam-5783	60	52	defined	define	VERB
ejpam-5783	60	53	as	as	ADP
ejpam-5783	60	54	a	a	DET
ejpam-5783	60	55	∧	∧	PROPN
ejpam-5783	60	56	b	b	PROPN
ejpam-5783	60	57	=	=	SYM
ejpam-5783	60	58	b	b	PROPN
ejpam-5783	60	59	∗	∗	NOUN
ejpam-5783	60	60	(	(	PUNCT
ejpam-5783	60	61	b	b	NOUN
ejpam-5783	60	62	∗	∗	X
ejpam-5783	60	63	a	a	NOUN
ejpam-5783	60	64	)	)	PUNCT
ejpam-5783	60	65	for	for	ADP
ejpam-5783	60	66	all	all	DET
ejpam-5783	60	67	a	a	PRON
ejpam-5783	60	68	,	,	PUNCT
ejpam-5783	60	69	b	b	X
ejpam-5783	60	70	∈	∈	PROPN
ejpam-5783	60	71	a.	a.	NOUN
ejpam-5783	60	72	definition	definition	NOUN
ejpam-5783	60	73	4	4	NUM
ejpam-5783	60	74	.	.	PUNCT
ejpam-5783	61	1	[	[	X
ejpam-5783	61	2	2	2	X
ejpam-5783	61	3	]	]	PUNCT
ejpam-5783	61	4	the	the	DET
ejpam-5783	61	5	operator	operator	NOUN
ejpam-5783	61	6	denoted	denote	VERB
ejpam-5783	61	7	by	by	ADP
ejpam-5783	61	8	|	|	ADV
ejpam-5783	61	9	is	be	AUX
ejpam-5783	61	10	called	call	VERB
ejpam-5783	61	11	a	a	DET
ejpam-5783	61	12	sheffer	sheffer	NOUN
ejpam-5783	61	13	stroke	stroke	NOUN
ejpam-5783	61	14	on	on	ADP
ejpam-5783	61	15	a	a	DET
ejpam-5783	61	16	groupoid	groupoid	PROPN
ejpam-5783	61	17	t	t	PROPN
ejpam-5783	61	18	if	if	SCONJ
ejpam-5783	61	19	the	the	DET
ejpam-5783	61	20	following	follow	VERB
ejpam-5783	61	21	four	four	NUM
ejpam-5783	61	22	conditions	condition	NOUN
ejpam-5783	61	23	are	be	AUX
ejpam-5783	61	24	met	meet	VERB
ejpam-5783	61	25	:	:	PUNCT
ejpam-5783	61	26	for	for	ADP
ejpam-5783	61	27	all	all	DET
ejpam-5783	61	28	a	a	DET
ejpam-5783	61	29	,	,	PUNCT
ejpam-5783	61	30	b	b	NOUN
ejpam-5783	61	31	,	,	PUNCT
ejpam-5783	61	32	c	c	PROPN
ejpam-5783	61	33	∈	∈	PROPN
ejpam-5783	61	34	t	t	PROPN
ejpam-5783	61	35	(	(	PUNCT
ejpam-5783	61	36	s1	s1	PROPN
ejpam-5783	61	37	)	)	PUNCT
ejpam-5783	61	38	a|b	a|b	NOUN
ejpam-5783	62	1	=	=	PUNCT
ejpam-5783	62	2	b|a	b|a	PROPN
ejpam-5783	62	3	,	,	PUNCT
ejpam-5783	62	4	(	(	PUNCT
ejpam-5783	62	5	s2	s2	PROPN
ejpam-5783	62	6	)	)	PUNCT
ejpam-5783	62	7	(	(	PUNCT
ejpam-5783	62	8	a|a)|(a|b	a|a)|(a|b	PROPN
ejpam-5783	62	9	)	)	PUNCT
ejpam-5783	62	10	=	=	SYM
ejpam-5783	63	1	a	a	PRON
ejpam-5783	63	2	,	,	PUNCT
ejpam-5783	63	3	(	(	PUNCT
ejpam-5783	63	4	s3	s3	PROPN
ejpam-5783	63	5	)	)	PUNCT
ejpam-5783	63	6	a|((b|c)|(b|c	a|((b|c)|(b|c	NOUN
ejpam-5783	63	7	)	)	PUNCT
ejpam-5783	63	8	)	)	PUNCT
ejpam-5783	64	1	=	=	SYM
ejpam-5783	64	2	(	(	PUNCT
ejpam-5783	64	3	(	(	PUNCT
ejpam-5783	64	4	a|b)|(a|b))|c	a|b)|(a|b))|c	PROPN
ejpam-5783	64	5	,	,	PUNCT
ejpam-5783	64	6	(	(	PUNCT
ejpam-5783	64	7	s4	s4	PROPN
ejpam-5783	64	8	)	)	PUNCT
ejpam-5783	64	9	(	(	PUNCT
ejpam-5783	64	10	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	NOUN
ejpam-5783	64	11	)	)	PUNCT
ejpam-5783	64	12	)	)	PUNCT
ejpam-5783	64	13	)	)	PUNCT
ejpam-5783	64	14	=	=	PUNCT
ejpam-5783	65	1	a.	a.	NOUN
ejpam-5783	65	2	3	3	NUM
ejpam-5783	65	3	.	.	PUNCT
ejpam-5783	65	4	sheffer	sheffer	PROPN
ejpam-5783	65	5	stroke	stroke	PROPN
ejpam-5783	65	6	bn	bn	NOUN
ejpam-5783	65	7	-	-	PUNCT
ejpam-5783	65	8	algebras	algebras	NOUN
ejpam-5783	65	9	in	in	ADP
ejpam-5783	65	10	this	this	DET
ejpam-5783	65	11	section	section	NOUN
ejpam-5783	65	12	,	,	PUNCT
ejpam-5783	65	13	the	the	DET
ejpam-5783	65	14	sheffer	sheffer	NOUN
ejpam-5783	65	15	stroke	stroke	NOUN
ejpam-5783	65	16	bn	bn	NOUN
ejpam-5783	65	17	-	-	PUNCT
ejpam-5783	65	18	algebra	algebra	NOUN
ejpam-5783	65	19	is	be	AUX
ejpam-5783	65	20	defined	define	VERB
ejpam-5783	65	21	as	as	ADP
ejpam-5783	65	22	an	an	DET
ejpam-5783	65	23	algebra	algebra	NOUN
ejpam-5783	65	24	of	of	ADP
ejpam-5783	65	25	type	type	NOUN
ejpam-5783	65	26	(	(	PUNCT
ejpam-5783	65	27	2,0	2,0	NUM
ejpam-5783	65	28	)	)	PUNCT
ejpam-5783	65	29	with	with	ADP
ejpam-5783	65	30	the	the	DET
ejpam-5783	65	31	sheffer	sheffer	NOUN
ejpam-5783	65	32	stroke	stroke	NOUN
ejpam-5783	65	33	operation	operation	NOUN
ejpam-5783	65	34	|	|	ADV
ejpam-5783	65	35	and	and	CCONJ
ejpam-5783	65	36	the	the	DET
ejpam-5783	65	37	constant	constant	ADJ
ejpam-5783	65	38	element	element	NOUN
ejpam-5783	65	39	0	0	NUM
ejpam-5783	65	40	.	.	PUNCT
ejpam-5783	66	1	in	in	ADP
ejpam-5783	66	2	this	this	DET
ejpam-5783	66	3	algebra	algebra	NOUN
ejpam-5783	66	4	,	,	PUNCT
ejpam-5783	66	5	we	we	PRON
ejpam-5783	66	6	integrate	integrate	VERB
ejpam-5783	66	7	the	the	DET
ejpam-5783	66	8	sheffer	sheffer	NOUN
ejpam-5783	66	9	stroke	stroke	NOUN
ejpam-5783	66	10	operation	operation	NOUN
ejpam-5783	66	11	with	with	ADP
ejpam-5783	66	12	the	the	DET
ejpam-5783	66	13	bn	bn	NOUN
ejpam-5783	66	14	-	-	PUNCT
ejpam-5783	66	15	algebra	algebra	NOUN
ejpam-5783	66	16	axioms	axiom	NOUN
ejpam-5783	66	17	by	by	ADP
ejpam-5783	66	18	examining	examine	VERB
ejpam-5783	66	19	the	the	DET
ejpam-5783	66	20	interrelationships	interrelationship	NOUN
ejpam-5783	66	21	among	among	ADP
ejpam-5783	66	22	these	these	DET
ejpam-5783	66	23	axioms	axiom	NOUN
ejpam-5783	66	24	.	.	PUNCT
ejpam-5783	67	1	two	two	NUM
ejpam-5783	67	2	main	main	ADJ
ejpam-5783	67	3	axioms	axiom	NOUN
ejpam-5783	67	4	are	be	AUX
ejpam-5783	67	5	defined	define	VERB
ejpam-5783	67	6	for	for	ADP
ejpam-5783	67	7	sheffer	sheffer	NOUN
ejpam-5783	67	8	stroke	stroke	PROPN
ejpam-5783	67	9	bn	bn	NOUN
ejpam-5783	67	10	-	-	PUNCT
ejpam-5783	67	11	algebra	algebra	NOUN
ejpam-5783	67	12	,	,	PUNCT
ejpam-5783	67	13	(	(	PUNCT
ejpam-5783	67	14	sbn1	sbn1	ADJ
ejpam-5783	67	15	)	)	PUNCT
ejpam-5783	67	16	and	and	CCONJ
ejpam-5783	67	17	(	(	PUNCT
ejpam-5783	67	18	sbn2	sbn2	NOUN
ejpam-5783	67	19	)	)	PUNCT
ejpam-5783	67	20	.	.	PUNCT
ejpam-5783	68	1	then	then	ADV
ejpam-5783	68	2	,	,	PUNCT
ejpam-5783	68	3	its	its	PRON
ejpam-5783	68	4	properties	property	NOUN
ejpam-5783	68	5	are	be	AUX
ejpam-5783	68	6	determined	determine	VERB
ejpam-5783	68	7	.	.	PUNCT
ejpam-5783	69	1	definition	definition	NOUN
ejpam-5783	69	2	5	5	NUM
ejpam-5783	69	3	.	.	PUNCT
ejpam-5783	70	1	a	a	DET
ejpam-5783	70	2	sheffer	sheffer	NOUN
ejpam-5783	70	3	stroke	stroke	NOUN
ejpam-5783	70	4	bn	bn	NOUN
ejpam-5783	70	5	-	-	PUNCT
ejpam-5783	70	6	algebra	algebra	NOUN
ejpam-5783	70	7	is	be	AUX
ejpam-5783	70	8	an	an	DET
ejpam-5783	70	9	algebra	algebra	NOUN
ejpam-5783	70	10	(	(	PUNCT
ejpam-5783	70	11	psbn	psbn	NOUN
ejpam-5783	70	12	;	;	PUNCT
ejpam-5783	70	13	|	|	ADV
ejpam-5783	70	14	,	,	PUNCT
ejpam-5783	70	15	0	0	NUM
ejpam-5783	70	16	)	)	PUNCT
ejpam-5783	70	17	of	of	ADP
ejpam-5783	70	18	type	type	NOUN
ejpam-5783	70	19	(	(	PUNCT
ejpam-5783	70	20	2	2	NUM
ejpam-5783	70	21	,	,	PUNCT
ejpam-5783	70	22	0	0	NUM
ejpam-5783	70	23	)	)	PUNCT
ejpam-5783	70	24	containing	contain	VERB
ejpam-5783	70	25	the	the	DET
ejpam-5783	70	26	constant	constant	ADJ
ejpam-5783	70	27	0	0	NUM
ejpam-5783	70	28	,	,	PUNCT
ejpam-5783	70	29	where	where	SCONJ
ejpam-5783	70	30	|	|	ADV
ejpam-5783	70	31	is	be	AUX
ejpam-5783	70	32	the	the	DET
ejpam-5783	70	33	sheffer	sheffer	NOUN
ejpam-5783	70	34	stroke	stroke	NOUN
ejpam-5783	70	35	operation	operation	NOUN
ejpam-5783	70	36	in	in	ADP
ejpam-5783	70	37	psbn	psbn	NOUN
ejpam-5783	70	38	and	and	CCONJ
ejpam-5783	70	39	the	the	DET
ejpam-5783	70	40	following	following	ADJ
ejpam-5783	70	41	axioms	axiom	NOUN
ejpam-5783	70	42	are	be	AUX
ejpam-5783	70	43	satisfied	satisfied	ADJ
ejpam-5783	70	44	for	for	ADP
ejpam-5783	70	45	all	all	DET
ejpam-5783	70	46	a	a	DET
ejpam-5783	70	47	,	,	PUNCT
ejpam-5783	70	48	b	b	NOUN
ejpam-5783	70	49	,	,	PUNCT
ejpam-5783	70	50	c	c	PROPN
ejpam-5783	70	51	∈	∈	PROPN
ejpam-5783	70	52	psbn	psbn	NOUN
ejpam-5783	70	53	:	:	PUNCT
ejpam-5783	70	54	s.	s.	PROPN
ejpam-5783	70	55	gemawati	gemawati	PROPN
ejpam-5783	70	56	et	et	PROPN
ejpam-5783	70	57	al	al	PROPN
ejpam-5783	70	58	.	.	PUNCT
ejpam-5783	70	59	/	/	SYM
ejpam-5783	70	60	eur	eur	PROPN
ejpam-5783	70	61	.	.	PUNCT
ejpam-5783	71	1	j.	j.	PROPN
ejpam-5783	71	2	pure	pure	PROPN
ejpam-5783	71	3	appl	appl	PROPN
ejpam-5783	71	4	.	.	PROPN
ejpam-5783	71	5	math	math	PROPN
ejpam-5783	71	6	,	,	PUNCT
ejpam-5783	71	7	18	18	NUM
ejpam-5783	71	8	(	(	PUNCT
ejpam-5783	71	9	1	1	NUM
ejpam-5783	71	10	)	)	PUNCT
ejpam-5783	71	11	(	(	PUNCT
ejpam-5783	71	12	2025	2025	NUM
ejpam-5783	71	13	)	)	PUNCT
ejpam-5783	71	14	,	,	PUNCT
ejpam-5783	71	15	5783	5783	NUM
ejpam-5783	71	16	4	4	NUM
ejpam-5783	71	17	of	of	ADP
ejpam-5783	71	18	12	12	NUM
ejpam-5783	71	19	(	(	PUNCT
ejpam-5783	71	20	sbn1	sbn1	PROPN
ejpam-5783	71	21	)	)	PUNCT
ejpam-5783	71	22	(	(	PUNCT
ejpam-5783	71	23	a|(0|0))|(a|(0|0	a|(0|0))|(a|(0|0	PROPN
ejpam-5783	71	24	)	)	PUNCT
ejpam-5783	71	25	)	)	PUNCT
ejpam-5783	72	1	=	=	SYM
ejpam-5783	72	2	a	a	PRON
ejpam-5783	72	3	,	,	PUNCT
ejpam-5783	72	4	(	(	PUNCT
ejpam-5783	72	5	sbn2	sbn2	NOUN
ejpam-5783	72	6	)	)	PUNCT
ejpam-5783	72	7	(	(	PUNCT
ejpam-5783	72	8	a|(b|b))|((0|c)|(0|c	a|(b|b))|((0|c)|(0|c	NOUN
ejpam-5783	72	9	)	)	PUNCT
ejpam-5783	72	10	)	)	PUNCT
ejpam-5783	73	1	=	=	PUNCT
ejpam-5783	74	1	[	[	X
ejpam-5783	74	2	(	(	PUNCT
ejpam-5783	74	3	0|(0|(c|c))|(0|(0|(c|c))]|(b|(a|a	0|(0|(c|c))|(0|(0|(c|c))]|(b|(a|a	NOUN
ejpam-5783	74	4	)	)	PUNCT
ejpam-5783	74	5	)	)	PUNCT
ejpam-5783	74	6	.	.	PUNCT
ejpam-5783	75	1	lemma	lemma	PROPN
ejpam-5783	76	1	1	1	X
ejpam-5783	76	2	.	.	PUNCT
ejpam-5783	77	1	if	if	SCONJ
ejpam-5783	77	2	(	(	PUNCT
ejpam-5783	77	3	psbn	psbn	NOUN
ejpam-5783	77	4	;	;	PUNCT
ejpam-5783	77	5	|	|	ADV
ejpam-5783	77	6	,	,	PUNCT
ejpam-5783	77	7	0	0	NUM
ejpam-5783	77	8	)	)	PUNCT
ejpam-5783	77	9	is	be	AUX
ejpam-5783	77	10	a	a	DET
ejpam-5783	77	11	sheffer	sheffer	NOUN
ejpam-5783	77	12	stroke	stroke	NOUN
ejpam-5783	77	13	bn	bn	NOUN
ejpam-5783	77	14	-	-	PUNCT
ejpam-5783	77	15	algebra	algebra	NOUN
ejpam-5783	77	16	,	,	PUNCT
ejpam-5783	77	17	then	then	ADV
ejpam-5783	77	18	the	the	DET
ejpam-5783	77	19	axioms	axiom	NOUN
ejpam-5783	77	20	(	(	PUNCT
ejpam-5783	77	21	sbn1	sbn1	ADJ
ejpam-5783	77	22	)	)	PUNCT
ejpam-5783	77	23	and	and	CCONJ
ejpam-5783	77	24	(	(	PUNCT
ejpam-5783	77	25	sbn2	sbn2	NOUN
ejpam-5783	77	26	)	)	PUNCT
ejpam-5783	77	27	are	be	AUX
ejpam-5783	77	28	independent	independent	ADJ
ejpam-5783	77	29	.	.	PUNCT
ejpam-5783	78	1	proof	proof	NOUN
ejpam-5783	78	2	.	.	PUNCT
ejpam-5783	79	1	let	let	AUX
ejpam-5783	79	2	(	(	PUNCT
ejpam-5783	79	3	psbn	psbn	NOUN
ejpam-5783	79	4	;	;	PUNCT
ejpam-5783	79	5	|	|	ADV
ejpam-5783	79	6	,	,	PUNCT
ejpam-5783	79	7	0	0	NUM
ejpam-5783	79	8	)	)	PUNCT
ejpam-5783	79	9	be	be	AUX
ejpam-5783	79	10	a	a	DET
ejpam-5783	79	11	sheffer	sheffer	NOUN
ejpam-5783	79	12	stroke	stroke	NOUN
ejpam-5783	79	13	bn	bn	NOUN
ejpam-5783	79	14	-	-	PUNCT
ejpam-5783	79	15	algebra	algebra	NOUN
ejpam-5783	79	16	.	.	PUNCT
ejpam-5783	80	1	we	we	PRON
ejpam-5783	80	2	give	give	VERB
ejpam-5783	80	3	examples	example	NOUN
ejpam-5783	80	4	of	of	ADP
ejpam-5783	80	5	groupoids	groupoid	NOUN
ejpam-5783	80	6	(	(	PUNCT
ejpam-5783	80	7	p	p	X
ejpam-5783	80	8	;	;	PUNCT
ejpam-5783	80	9	|	|	ADV
ejpam-5783	80	10	,	,	PUNCT
ejpam-5783	80	11	0	0	NUM
ejpam-5783	80	12	)	)	PUNCT
ejpam-5783	80	13	and	and	CCONJ
ejpam-5783	80	14	(	(	PUNCT
ejpam-5783	80	15	q	q	NOUN
ejpam-5783	80	16	;	;	PUNCT
ejpam-5783	80	17	|	|	ADV
ejpam-5783	80	18	,	,	PUNCT
ejpam-5783	80	19	0	0	NUM
ejpam-5783	80	20	)	)	PUNCT
ejpam-5783	80	21	to	to	PART
ejpam-5783	80	22	show	show	VERB
ejpam-5783	80	23	that	that	SCONJ
ejpam-5783	80	24	each	each	DET
ejpam-5783	80	25	axiom	axiom	NOUN
ejpam-5783	80	26	can	can	AUX
ejpam-5783	80	27	be	be	AUX
ejpam-5783	80	28	satisfied	satisfied	ADJ
ejpam-5783	80	29	when	when	SCONJ
ejpam-5783	80	30	the	the	DET
ejpam-5783	80	31	other	other	ADJ
ejpam-5783	80	32	is	be	AUX
ejpam-5783	80	33	not	not	PART
ejpam-5783	80	34	.	.	PUNCT
ejpam-5783	81	1	(	(	PUNCT
ejpam-5783	81	2	i	i	NOUN
ejpam-5783	81	3	)	)	PUNCT
ejpam-5783	81	4	independence	independence	NOUN
ejpam-5783	81	5	of	of	ADP
ejpam-5783	81	6	(	(	PUNCT
ejpam-5783	81	7	sbn1	sbn1	PROPN
ejpam-5783	81	8	):	):	PUNCT
ejpam-5783	81	9	we	we	PRON
ejpam-5783	81	10	provide	provide	VERB
ejpam-5783	81	11	an	an	DET
ejpam-5783	81	12	example	example	NOUN
ejpam-5783	81	13	in	in	ADP
ejpam-5783	81	14	which	which	PRON
ejpam-5783	81	15	(	(	PUNCT
ejpam-5783	81	16	sbn1	sbn1	ADJ
ejpam-5783	81	17	)	)	PUNCT
ejpam-5783	81	18	does	do	AUX
ejpam-5783	81	19	not	not	PART
ejpam-5783	81	20	hold	hold	VERB
ejpam-5783	81	21	but	but	CCONJ
ejpam-5783	81	22	(	(	PUNCT
ejpam-5783	81	23	sbn2	sbn2	NOUN
ejpam-5783	81	24	)	)	PUNCT
ejpam-5783	81	25	does	do	VERB
ejpam-5783	81	26	.	.	PUNCT
ejpam-5783	82	1	consider	consider	VERB
ejpam-5783	82	2	the	the	DET
ejpam-5783	82	3	groupoid	groupoid	NOUN
ejpam-5783	82	4	(	(	PUNCT
ejpam-5783	82	5	p	p	NOUN
ejpam-5783	82	6	;	;	PUNCT
ejpam-5783	82	7	|	|	ADV
ejpam-5783	82	8	,	,	PUNCT
ejpam-5783	82	9	0	0	NUM
ejpam-5783	82	10	)	)	PUNCT
ejpam-5783	82	11	,	,	PUNCT
ejpam-5783	82	12	where	where	SCONJ
ejpam-5783	82	13	p	p	NOUN
ejpam-5783	82	14	=	=	X
ejpam-5783	82	15	{	{	PUNCT
ejpam-5783	82	16	0	0	NUM
ejpam-5783	82	17	,	,	PUNCT
ejpam-5783	82	18	1	1	NUM
ejpam-5783	82	19	}	}	PUNCT
ejpam-5783	82	20	,	,	PUNCT
ejpam-5783	82	21	defined	define	VERB
ejpam-5783	82	22	as	as	ADP
ejpam-5783	82	23	in	in	ADP
ejpam-5783	82	24	table	table	NOUN
ejpam-5783	82	25	1	1	NUM
ejpam-5783	82	26	.	.	PUNCT
ejpam-5783	82	27	table	table	NOUN
ejpam-5783	82	28	1	1	NUM
ejpam-5783	82	29	:	:	PUNCT
ejpam-5783	82	30	composition	composition	NOUN
ejpam-5783	82	31	table	table	NOUN
ejpam-5783	82	32	for	for	ADP
ejpam-5783	82	33	(	(	PUNCT
ejpam-5783	82	34	p	p	X
ejpam-5783	82	35	;	;	PUNCT
ejpam-5783	82	36	|	|	ADV
ejpam-5783	82	37	,	,	PUNCT
ejpam-5783	82	38	0	0	NUM
ejpam-5783	82	39	)	)	PUNCT
ejpam-5783	82	40	|	|	ADV
ejpam-5783	82	41	0	0	NUM
ejpam-5783	82	42	1	1	NUM
ejpam-5783	82	43	0	0	NUM
ejpam-5783	82	44	0	0	NUM
ejpam-5783	82	45	1	1	NUM
ejpam-5783	82	46	1	1	NUM
ejpam-5783	82	47	0	0	NUM
ejpam-5783	82	48	0	0	NUM
ejpam-5783	82	49	it	it	PRON
ejpam-5783	82	50	can	can	AUX
ejpam-5783	82	51	be	be	AUX
ejpam-5783	82	52	demonstrated	demonstrate	VERB
ejpam-5783	82	53	that	that	SCONJ
ejpam-5783	82	54	(	(	PUNCT
ejpam-5783	82	55	p	p	X
ejpam-5783	82	56	;	;	PUNCT
ejpam-5783	82	57	|	|	ADV
ejpam-5783	82	58	,	,	PUNCT
ejpam-5783	82	59	0	0	X
ejpam-5783	82	60	)	)	PUNCT
ejpam-5783	82	61	fulfills	fulfill	NOUN
ejpam-5783	82	62	(	(	PUNCT
ejpam-5783	82	63	sbn2	sbn2	NOUN
ejpam-5783	82	64	)	)	PUNCT
ejpam-5783	82	65	,	,	PUNCT
ejpam-5783	82	66	but	but	CCONJ
ejpam-5783	82	67	it	it	PRON
ejpam-5783	82	68	fails	fail	VERB
ejpam-5783	82	69	to	to	PART
ejpam-5783	82	70	satisfy	satisfy	VERB
ejpam-5783	82	71	(	(	PUNCT
ejpam-5783	82	72	sbn1	sbn1	PROPN
ejpam-5783	82	73	)	)	PUNCT
ejpam-5783	82	74	when	when	SCONJ
ejpam-5783	82	75	a	a	DET
ejpam-5783	82	76	=	=	NOUN
ejpam-5783	82	77	1	1	NUM
ejpam-5783	82	78	,	,	PUNCT
ejpam-5783	82	79	since	since	SCONJ
ejpam-5783	82	80	(	(	PUNCT
ejpam-5783	82	81	1|(0|0))|(1|(0|0	1|(0|0))|(1|(0|0	NUM
ejpam-5783	82	82	)	)	PUNCT
ejpam-5783	82	83	)	)	PUNCT
ejpam-5783	83	1	=	=	SYM
ejpam-5783	83	2	(	(	PUNCT
ejpam-5783	83	3	1|0)|(1|0	1|0)|(1|0	NUM
ejpam-5783	83	4	)	)	PUNCT
ejpam-5783	83	5	=	=	SYM
ejpam-5783	84	1	0|0	0|0	PUNCT
ejpam-5783	84	2	=	=	SYM
ejpam-5783	84	3	0	0	NUM
ejpam-5783	85	1	̸=	̸=	PROPN
ejpam-5783	85	2	1	1	NUM
ejpam-5783	85	3	.	.	PUNCT
ejpam-5783	85	4	(	(	PUNCT
ejpam-5783	85	5	ii	ii	NOUN
ejpam-5783	85	6	)	)	PUNCT
ejpam-5783	85	7	independence	independence	NOUN
ejpam-5783	85	8	of	of	ADP
ejpam-5783	85	9	(	(	PUNCT
ejpam-5783	85	10	sbn2	sbn2	NOUN
ejpam-5783	85	11	):	):	PUNCT
ejpam-5783	85	12	we	we	PRON
ejpam-5783	85	13	present	present	VERB
ejpam-5783	85	14	an	an	DET
ejpam-5783	85	15	example	example	NOUN
ejpam-5783	85	16	in	in	ADP
ejpam-5783	85	17	which	which	PRON
ejpam-5783	85	18	(	(	PUNCT
ejpam-5783	85	19	sbn2	sbn2	NOUN
ejpam-5783	85	20	)	)	PUNCT
ejpam-5783	85	21	does	do	AUX
ejpam-5783	85	22	not	not	PART
ejpam-5783	85	23	apply	apply	VERB
ejpam-5783	85	24	while	while	SCONJ
ejpam-5783	85	25	(	(	PUNCT
ejpam-5783	85	26	sbn1	sbn1	ADJ
ejpam-5783	85	27	)	)	PUNCT
ejpam-5783	85	28	remains	remain	VERB
ejpam-5783	85	29	valid	valid	ADJ
ejpam-5783	85	30	.	.	PUNCT
ejpam-5783	86	1	take	take	VERB
ejpam-5783	86	2	the	the	DET
ejpam-5783	86	3	groupoid	groupoid	NOUN
ejpam-5783	86	4	(	(	PUNCT
ejpam-5783	86	5	q	q	NOUN
ejpam-5783	86	6	;	;	PUNCT
ejpam-5783	86	7	|	|	ADV
ejpam-5783	86	8	,	,	PUNCT
ejpam-5783	86	9	0	0	NUM
ejpam-5783	86	10	)	)	PUNCT
ejpam-5783	86	11	,	,	PUNCT
ejpam-5783	86	12	where	where	SCONJ
ejpam-5783	86	13	q	q	NOUN
ejpam-5783	86	14	=	=	PUNCT
ejpam-5783	86	15	{	{	PUNCT
ejpam-5783	86	16	0	0	NUM
ejpam-5783	86	17	,	,	PUNCT
ejpam-5783	86	18	1	1	NUM
ejpam-5783	86	19	}	}	PUNCT
ejpam-5783	86	20	,	,	PUNCT
ejpam-5783	86	21	defined	define	VERB
ejpam-5783	86	22	as	as	ADP
ejpam-5783	86	23	in	in	ADP
ejpam-5783	86	24	table	table	NOUN
ejpam-5783	86	25	2	2	NUM
ejpam-5783	86	26	.	.	PUNCT
ejpam-5783	86	27	table	table	NOUN
ejpam-5783	86	28	2	2	NUM
ejpam-5783	86	29	:	:	PUNCT
ejpam-5783	86	30	composition	composition	NOUN
ejpam-5783	86	31	table	table	NOUN
ejpam-5783	86	32	for	for	ADP
ejpam-5783	86	33	(	(	PUNCT
ejpam-5783	86	34	q	q	NOUN
ejpam-5783	86	35	;	;	PUNCT
ejpam-5783	86	36	|	|	ADV
ejpam-5783	86	37	,	,	PUNCT
ejpam-5783	86	38	0	0	NUM
ejpam-5783	86	39	)	)	PUNCT
ejpam-5783	86	40	|	|	ADV
ejpam-5783	86	41	0	0	NUM
ejpam-5783	86	42	1	1	NUM
ejpam-5783	86	43	0	0	NUM
ejpam-5783	86	44	0	0	NUM
ejpam-5783	86	45	0	0	NUM
ejpam-5783	86	46	1	1	NUM
ejpam-5783	86	47	1	1	NUM
ejpam-5783	86	48	1	1	NUM
ejpam-5783	86	49	it	it	PRON
ejpam-5783	86	50	can	can	AUX
ejpam-5783	86	51	be	be	AUX
ejpam-5783	86	52	shown	show	VERB
ejpam-5783	86	53	that	that	SCONJ
ejpam-5783	86	54	(	(	PUNCT
ejpam-5783	86	55	p	p	X
ejpam-5783	86	56	;	;	PUNCT
ejpam-5783	86	57	|	|	ADV
ejpam-5783	86	58	,	,	PUNCT
ejpam-5783	86	59	0	0	X
ejpam-5783	86	60	)	)	PUNCT
ejpam-5783	86	61	satisfies	satisfie	NOUN
ejpam-5783	86	62	(	(	PUNCT
ejpam-5783	86	63	sbn2	sbn2	NOUN
ejpam-5783	86	64	)	)	PUNCT
ejpam-5783	86	65	,	,	PUNCT
ejpam-5783	86	66	but	but	CCONJ
ejpam-5783	86	67	it	it	PRON
ejpam-5783	86	68	does	do	AUX
ejpam-5783	86	69	not	not	PART
ejpam-5783	86	70	fulfill	fulfill	VERB
ejpam-5783	86	71	(	(	PUNCT
ejpam-5783	86	72	sbn1	sbn1	PROPN
ejpam-5783	86	73	)	)	PUNCT
ejpam-5783	86	74	when	when	SCONJ
ejpam-5783	86	75	a	a	DET
ejpam-5783	86	76	=	=	SYM
ejpam-5783	86	77	1	1	NUM
ejpam-5783	86	78	,	,	PUNCT
ejpam-5783	86	79	b	b	NOUN
ejpam-5783	86	80	=	=	SYM
ejpam-5783	86	81	1	1	NUM
ejpam-5783	86	82	,	,	PUNCT
ejpam-5783	86	83	and	and	CCONJ
ejpam-5783	87	1	c	c	X
ejpam-5783	87	2	=	=	SYM
ejpam-5783	87	3	0	0	PROPN
ejpam-5783	87	4	since	since	SCONJ
ejpam-5783	87	5	the	the	DET
ejpam-5783	87	6	left	left	ADJ
ejpam-5783	87	7	-	-	PUNCT
ejpam-5783	87	8	hand	hand	NOUN
ejpam-5783	87	9	side	side	NOUN
ejpam-5783	87	10	(	(	PUNCT
ejpam-5783	87	11	1|(1|1))|((0|0)|(0|0	1|(1|1))|((0|0)|(0|0	NUM
ejpam-5783	87	12	)	)	PUNCT
ejpam-5783	87	13	)	)	PUNCT
ejpam-5783	88	1	=	=	PUNCT
ejpam-5783	88	2	(	(	PUNCT
ejpam-5783	88	3	1|1)|(0|0	1|1)|(0|0	NUM
ejpam-5783	88	4	)	)	PUNCT
ejpam-5783	88	5	=	=	SYM
ejpam-5783	89	1	1|0	1|0	NUM
ejpam-5783	89	2	=	=	SYM
ejpam-5783	89	3	1	1	NUM
ejpam-5783	89	4	,	,	PUNCT
ejpam-5783	89	5	whereas	whereas	SCONJ
ejpam-5783	89	6	the	the	DET
ejpam-5783	89	7	right	right	ADJ
ejpam-5783	89	8	-	-	PUNCT
ejpam-5783	89	9	hand	hand	NOUN
ejpam-5783	89	10	side	side	NOUN
ejpam-5783	89	11	[	[	X
ejpam-5783	89	12	(	(	PUNCT
ejpam-5783	89	13	0|(0|(0|0))|(0|(0|(0|0))]|(1|(1|1	0|(0|(0|0))|(0|(0|(0|0))]|(1|(1|1	NUM
ejpam-5783	89	14	)	)	PUNCT
ejpam-5783	89	15	)	)	PUNCT
ejpam-5783	90	1	=	=	SYM
ejpam-5783	90	2	(	(	PUNCT
ejpam-5783	90	3	0|(0|0))|(0|(0|0))])|(1|1	0|(0|0))|(0|(0|0))])|(1|1	NUM
ejpam-5783	90	4	)	)	PUNCT
ejpam-5783	90	5	=	=	SYM
ejpam-5783	91	1	0|1	0|1	NUM
ejpam-5783	91	2	=	=	SYM
ejpam-5783	91	3	0	0	X
ejpam-5783	91	4	.	.	PUNCT
ejpam-5783	92	1	next	next	ADV
ejpam-5783	92	2	,	,	PUNCT
ejpam-5783	92	3	an	an	DET
ejpam-5783	92	4	example	example	NOUN
ejpam-5783	92	5	of	of	ADP
ejpam-5783	92	6	an	an	DET
ejpam-5783	92	7	algebra	algebra	NOUN
ejpam-5783	92	8	that	that	PRON
ejpam-5783	92	9	satisfies	satisfy	VERB
ejpam-5783	92	10	the	the	DET
ejpam-5783	92	11	sheffer	sheffer	NOUN
ejpam-5783	92	12	stroke	stroke	NOUN
ejpam-5783	92	13	bn	bn	NOUN
ejpam-5783	92	14	-	-	PUNCT
ejpam-5783	92	15	algebra	algebra	NOUN
ejpam-5783	92	16	property	property	NOUN
ejpam-5783	92	17	is	be	AUX
ejpam-5783	92	18	presented	present	VERB
ejpam-5783	92	19	,	,	PUNCT
ejpam-5783	92	20	showing	show	VERB
ejpam-5783	92	21	the	the	DET
ejpam-5783	92	22	structure	structure	NOUN
ejpam-5783	92	23	of	of	ADP
ejpam-5783	92	24	the	the	DET
ejpam-5783	92	25	algebra	algebra	NOUN
ejpam-5783	92	26	with	with	ADP
ejpam-5783	92	27	elements	element	NOUN
ejpam-5783	92	28	{	{	PUNCT
ejpam-5783	92	29	0	0	NUM
ejpam-5783	92	30	,	,	PUNCT
ejpam-5783	92	31	p	p	X
ejpam-5783	92	32	,	,	PUNCT
ejpam-5783	92	33	q	q	ADJ
ejpam-5783	92	34	,	,	PUNCT
ejpam-5783	92	35	1	1	X
ejpam-5783	92	36	}	}	PUNCT
ejpam-5783	92	37	that	that	PRON
ejpam-5783	92	38	satisfy	satisfy	VERB
ejpam-5783	92	39	the	the	DET
ejpam-5783	92	40	specified	specified	ADJ
ejpam-5783	92	41	axioms	axiom	NOUN
ejpam-5783	92	42	.	.	PUNCT
ejpam-5783	93	1	example	example	NOUN
ejpam-5783	93	2	1	1	NUM
ejpam-5783	93	3	.	.	X
ejpam-5783	94	1	consider	consider	VERB
ejpam-5783	94	2	(	(	PUNCT
ejpam-5783	94	3	psbn	psbn	NOUN
ejpam-5783	94	4	;	;	PUNCT
ejpam-5783	94	5	|	|	ADV
ejpam-5783	94	6	,	,	PUNCT
ejpam-5783	94	7	0	0	NUM
ejpam-5783	94	8	)	)	PUNCT
ejpam-5783	94	9	,	,	PUNCT
ejpam-5783	94	10	an	an	DET
ejpam-5783	94	11	algebra	algebra	NOUN
ejpam-5783	94	12	with	with	ADP
ejpam-5783	94	13	the	the	DET
ejpam-5783	94	14	sheffer	sheffer	NOUN
ejpam-5783	94	15	stroke	stroke	NOUN
ejpam-5783	94	16	operation	operation	NOUN
ejpam-5783	94	17	and	and	CCONJ
ejpam-5783	94	18	the	the	DET
ejpam-5783	94	19	constant	constant	ADJ
ejpam-5783	94	20	0	0	NUM
ejpam-5783	94	21	,	,	PUNCT
ejpam-5783	94	22	defined	define	VERB
ejpam-5783	94	23	as	as	ADP
ejpam-5783	94	24	in	in	ADP
ejpam-5783	94	25	table	table	NOUN
ejpam-5783	94	26	3	3	NUM
ejpam-5783	94	27	.	.	PUNCT
ejpam-5783	95	1	s.	s.	PROPN
ejpam-5783	95	2	gemawati	gemawati	PROPN
ejpam-5783	95	3	et	et	PROPN
ejpam-5783	95	4	al	al	PROPN
ejpam-5783	95	5	.	.	PUNCT
ejpam-5783	95	6	/	/	SYM
ejpam-5783	95	7	eur	eur	PROPN
ejpam-5783	95	8	.	.	PUNCT
ejpam-5783	96	1	j.	j.	PROPN
ejpam-5783	96	2	pure	pure	PROPN
ejpam-5783	96	3	appl	appl	PROPN
ejpam-5783	96	4	.	.	PROPN
ejpam-5783	96	5	math	math	PROPN
ejpam-5783	96	6	,	,	PUNCT
ejpam-5783	96	7	18	18	NUM
ejpam-5783	96	8	(	(	PUNCT
ejpam-5783	96	9	1	1	NUM
ejpam-5783	96	10	)	)	PUNCT
ejpam-5783	96	11	(	(	PUNCT
ejpam-5783	96	12	2025	2025	NUM
ejpam-5783	96	13	)	)	PUNCT
ejpam-5783	96	14	,	,	PUNCT
ejpam-5783	96	15	5783	5783	NUM
ejpam-5783	96	16	5	5	NUM
ejpam-5783	96	17	of	of	ADP
ejpam-5783	96	18	12	12	NUM
ejpam-5783	96	19	table	table	NOUN
ejpam-5783	96	20	3	3	NUM
ejpam-5783	96	21	:	:	PUNCT
ejpam-5783	96	22	composition	composition	NOUN
ejpam-5783	96	23	table	table	NOUN
ejpam-5783	96	24	for	for	ADP
ejpam-5783	96	25	(	(	PUNCT
ejpam-5783	96	26	psbn	psbn	NOUN
ejpam-5783	96	27	;	;	PUNCT
ejpam-5783	96	28	|	|	ADV
ejpam-5783	96	29	,	,	PUNCT
ejpam-5783	96	30	0	0	NUM
ejpam-5783	96	31	)	)	PUNCT
ejpam-5783	97	1	|	|	ADV
ejpam-5783	97	2	0	0	NUM
ejpam-5783	98	1	p	p	NOUN
ejpam-5783	98	2	q	q	NOUN
ejpam-5783	98	3	1	1	NUM
ejpam-5783	98	4	0	0	NUM
ejpam-5783	98	5	1	1	NUM
ejpam-5783	98	6	1	1	NUM
ejpam-5783	98	7	1	1	NUM
ejpam-5783	98	8	1	1	NUM
ejpam-5783	98	9	p	p	NOUN
ejpam-5783	98	10	1	1	NUM
ejpam-5783	98	11	q	q	NOUN
ejpam-5783	98	12	q	q	X
ejpam-5783	98	13	q	q	X
ejpam-5783	98	14	q	q	NOUN
ejpam-5783	98	15	1	1	NUM
ejpam-5783	98	16	q	q	NOUN
ejpam-5783	98	17	p	p	NOUN
ejpam-5783	98	18	p	p	NOUN
ejpam-5783	98	19	1	1	NUM
ejpam-5783	98	20	1	1	NUM
ejpam-5783	98	21	q	q	NOUN
ejpam-5783	98	22	p	p	NOUN
ejpam-5783	98	23	0	0	NUM
ejpam-5783	99	1	it	it	PRON
ejpam-5783	99	2	can	can	AUX
ejpam-5783	99	3	be	be	AUX
ejpam-5783	99	4	shown	show	VERB
ejpam-5783	99	5	that	that	SCONJ
ejpam-5783	99	6	(	(	PUNCT
ejpam-5783	99	7	psbn	psbn	NOUN
ejpam-5783	99	8	;	;	PUNCT
ejpam-5783	99	9	|	|	ADV
ejpam-5783	99	10	,	,	PUNCT
ejpam-5783	99	11	0	0	NUM
ejpam-5783	99	12	)	)	PUNCT
ejpam-5783	99	13	is	be	AUX
ejpam-5783	99	14	a	a	DET
ejpam-5783	99	15	sheffer	sheffer	NOUN
ejpam-5783	99	16	stroke	stroke	NOUN
ejpam-5783	99	17	bn	bn	NOUN
ejpam-5783	99	18	-	-	PUNCT
ejpam-5783	99	19	algebra	algebra	NOUN
ejpam-5783	99	20	.	.	PUNCT
ejpam-5783	100	1	by	by	ADP
ejpam-5783	100	2	applying	apply	VERB
ejpam-5783	100	3	the	the	DET
ejpam-5783	100	4	sheffer	sheffer	NOUN
ejpam-5783	100	5	stroke	stroke	NOUN
ejpam-5783	100	6	operation	operation	NOUN
ejpam-5783	100	7	to	to	ADP
ejpam-5783	100	8	the	the	DET
ejpam-5783	100	9	elements	element	NOUN
ejpam-5783	100	10	in	in	ADP
ejpam-5783	100	11	the	the	DET
ejpam-5783	100	12	algebra	algebra	NOUN
ejpam-5783	100	13	(	(	PUNCT
ejpam-5783	100	14	psbn	psbn	NOUN
ejpam-5783	100	15	;	;	PUNCT
ejpam-5783	100	16	|	|	ADV
ejpam-5783	100	17	,	,	PUNCT
ejpam-5783	100	18	0	0	NUM
ejpam-5783	100	19	)	)	PUNCT
ejpam-5783	100	20	,	,	PUNCT
ejpam-5783	100	21	we	we	PRON
ejpam-5783	100	22	can	can	AUX
ejpam-5783	100	23	discover	discover	VERB
ejpam-5783	100	24	relationships	relationship	NOUN
ejpam-5783	100	25	that	that	PRON
ejpam-5783	100	26	apply	apply	VERB
ejpam-5783	100	27	to	to	ADP
ejpam-5783	100	28	all	all	DET
ejpam-5783	100	29	elements	element	NOUN
ejpam-5783	100	30	in	in	ADP
ejpam-5783	100	31	psbn	psbn	NOUN
ejpam-5783	100	32	.	.	PUNCT
ejpam-5783	101	1	these	these	DET
ejpam-5783	101	2	relationships	relationship	NOUN
ejpam-5783	101	3	show	show	VERB
ejpam-5783	101	4	how	how	SCONJ
ejpam-5783	101	5	the	the	DET
ejpam-5783	101	6	elements	element	NOUN
ejpam-5783	101	7	interact	interact	VERB
ejpam-5783	101	8	through	through	ADP
ejpam-5783	101	9	the	the	DET
ejpam-5783	101	10	operation	operation	NOUN
ejpam-5783	101	11	|	|	ADV
ejpam-5783	101	12	and	and	CCONJ
ejpam-5783	101	13	constant	constant	ADJ
ejpam-5783	101	14	0	0	NUM
ejpam-5783	101	15	,	,	PUNCT
ejpam-5783	101	16	for	for	ADP
ejpam-5783	101	17	example	example	NOUN
ejpam-5783	101	18	,	,	PUNCT
ejpam-5783	101	19	how	how	SCONJ
ejpam-5783	101	20	this	this	DET
ejpam-5783	101	21	operation	operation	NOUN
ejpam-5783	101	22	relates	relate	VERB
ejpam-5783	101	23	to	to	ADP
ejpam-5783	101	24	the	the	DET
ejpam-5783	101	25	identity	identity	NOUN
ejpam-5783	101	26	element	element	NOUN
ejpam-5783	101	27	or	or	CCONJ
ejpam-5783	101	28	changes	change	NOUN
ejpam-5783	101	29	when	when	SCONJ
ejpam-5783	101	30	applied	apply	VERB
ejpam-5783	101	31	to	to	ADP
ejpam-5783	101	32	the	the	DET
ejpam-5783	101	33	same	same	ADJ
ejpam-5783	101	34	or	or	CCONJ
ejpam-5783	101	35	different	different	ADJ
ejpam-5783	101	36	elements	element	NOUN
ejpam-5783	101	37	.	.	PUNCT
ejpam-5783	102	1	in	in	ADP
ejpam-5783	102	2	the	the	DET
ejpam-5783	102	3	following	following	NOUN
ejpam-5783	102	4	theorem	theorem	VERB
ejpam-5783	102	5	,	,	PUNCT
ejpam-5783	102	6	some	some	DET
ejpam-5783	102	7	basic	basic	ADJ
ejpam-5783	102	8	properties	property	NOUN
ejpam-5783	102	9	are	be	AUX
ejpam-5783	102	10	established	establish	VERB
ejpam-5783	102	11	to	to	PART
ejpam-5783	102	12	help	help	VERB
ejpam-5783	102	13	understand	understand	VERB
ejpam-5783	102	14	the	the	DET
ejpam-5783	102	15	structure	structure	NOUN
ejpam-5783	102	16	of	of	ADP
ejpam-5783	102	17	the	the	DET
ejpam-5783	102	18	sheffer	sheffer	NOUN
ejpam-5783	102	19	stroke	stroke	PROPN
ejpam-5783	102	20	bn	bn	NOUN
ejpam-5783	102	21	-	-	PUNCT
ejpam-5783	102	22	algebra	algebra	NOUN
ejpam-5783	102	23	and	and	CCONJ
ejpam-5783	102	24	provide	provide	VERB
ejpam-5783	102	25	a	a	DET
ejpam-5783	102	26	solid	solid	ADJ
ejpam-5783	102	27	basis	basis	NOUN
ejpam-5783	102	28	for	for	ADP
ejpam-5783	102	29	further	further	ADJ
ejpam-5783	102	30	analysis	analysis	NOUN
ejpam-5783	102	31	of	of	ADP
ejpam-5783	102	32	the	the	DET
ejpam-5783	102	33	relationships	relationship	NOUN
ejpam-5783	102	34	between	between	ADP
ejpam-5783	102	35	elements	element	NOUN
ejpam-5783	102	36	in	in	ADP
ejpam-5783	102	37	this	this	DET
ejpam-5783	102	38	algebra	algebra	NOUN
ejpam-5783	102	39	.	.	PUNCT
ejpam-5783	103	1	theorem	theorem	NOUN
ejpam-5783	103	2	3	3	X
ejpam-5783	103	3	.	.	PUNCT
ejpam-5783	104	1	let	let	AUX
ejpam-5783	104	2	(	(	PUNCT
ejpam-5783	104	3	psbn	psbn	NOUN
ejpam-5783	104	4	;	;	PUNCT
ejpam-5783	104	5	|	|	ADV
ejpam-5783	104	6	,	,	PUNCT
ejpam-5783	104	7	0	0	NUM
ejpam-5783	104	8	)	)	PUNCT
ejpam-5783	104	9	be	be	AUX
ejpam-5783	104	10	a	a	DET
ejpam-5783	104	11	sheffer	sheffer	NOUN
ejpam-5783	104	12	stroke	stroke	NOUN
ejpam-5783	104	13	bn	bn	NOUN
ejpam-5783	104	14	-	-	PUNCT
ejpam-5783	104	15	algebra	algebra	NOUN
ejpam-5783	104	16	.	.	PUNCT
ejpam-5783	105	1	then	then	ADV
ejpam-5783	105	2	,	,	PUNCT
ejpam-5783	105	3	the	the	DET
ejpam-5783	105	4	following	follow	VERB
ejpam-5783	105	5	properties	property	NOUN
ejpam-5783	105	6	are	be	AUX
ejpam-5783	105	7	satisfied	satisfied	ADJ
ejpam-5783	105	8	for	for	ADP
ejpam-5783	105	9	all	all	DET
ejpam-5783	105	10	a	a	DET
ejpam-5783	105	11	,	,	PUNCT
ejpam-5783	105	12	b	b	PROPN
ejpam-5783	105	13	∈	∈	PROPN
ejpam-5783	105	14	psbn	psbn	NOUN
ejpam-5783	105	15	:	:	PUNCT
ejpam-5783	105	16	(	(	PUNCT
ejpam-5783	105	17	i	i	NOUN
ejpam-5783	105	18	)	)	PUNCT
ejpam-5783	105	19	a|a	a|a	PUNCT
ejpam-5783	106	1	=	=	PUNCT
ejpam-5783	106	2	a|(0|0	a|(0|0	NOUN
ejpam-5783	106	3	)	)	PUNCT
ejpam-5783	106	4	,	,	PUNCT
ejpam-5783	106	5	(	(	PUNCT
ejpam-5783	106	6	ii	ii	NOUN
ejpam-5783	106	7	)	)	PUNCT
ejpam-5783	107	1	[	[	X
ejpam-5783	107	2	(	(	PUNCT
ejpam-5783	107	3	a|b)|(a|b)]|b	a|b)|(a|b)]|b	NOUN
ejpam-5783	107	4	=	=	SYM
ejpam-5783	107	5	a|b	a|b	NOUN
ejpam-5783	107	6	,	,	PUNCT
ejpam-5783	107	7	(	(	PUNCT
ejpam-5783	107	8	iii	iii	NOUN
ejpam-5783	107	9	)	)	PUNCT
ejpam-5783	107	10	(	(	PUNCT
ejpam-5783	107	11	a|(a|a))|(a|a	a|(a|a))|(a|a	PROPN
ejpam-5783	107	12	)	)	PUNCT
ejpam-5783	107	13	=	=	SYM
ejpam-5783	107	14	a	a	PRON
ejpam-5783	107	15	,	,	PUNCT
ejpam-5783	107	16	(	(	PUNCT
ejpam-5783	107	17	iv	iv	X
ejpam-5783	107	18	)	)	PUNCT
ejpam-5783	107	19	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	107	20	)	)	PUNCT
ejpam-5783	107	21	)	)	PUNCT
ejpam-5783	108	1	=	=	SYM
ejpam-5783	108	2	0|(a|a	0|(a|a	NUM
ejpam-5783	108	3	)	)	PUNCT
ejpam-5783	108	4	,	,	PUNCT
ejpam-5783	108	5	(	(	PUNCT
ejpam-5783	108	6	v	v	NOUN
ejpam-5783	108	7	)	)	PUNCT
ejpam-5783	108	8	0|(a|(b|b	0|(a|(b|b	NOUN
ejpam-5783	108	9	)	)	PUNCT
ejpam-5783	108	10	)	)	PUNCT
ejpam-5783	109	1	=	=	SYM
ejpam-5783	109	2	0|(b|(a|a	0|(b|(a|a	PROPN
ejpam-5783	109	3	)	)	PUNCT
ejpam-5783	109	4	)	)	PUNCT
ejpam-5783	109	5	,	,	PUNCT
ejpam-5783	109	6	(	(	PUNCT
ejpam-5783	109	7	vi	vi	NOUN
ejpam-5783	109	8	)	)	PUNCT
ejpam-5783	109	9	0|(a|a	0|(a|a	NUM
ejpam-5783	109	10	)	)	PUNCT
ejpam-5783	110	1	=	=	PUNCT
ejpam-5783	110	2	0|a	0|a	X
ejpam-5783	110	3	.	.	PUNCT
ejpam-5783	111	1	proof	proof	NOUN
ejpam-5783	111	2	.	.	PUNCT
ejpam-5783	112	1	let	let	AUX
ejpam-5783	112	2	(	(	PUNCT
ejpam-5783	112	3	psbn	psbn	NOUN
ejpam-5783	112	4	;	;	PUNCT
ejpam-5783	112	5	|	|	ADV
ejpam-5783	112	6	,	,	PUNCT
ejpam-5783	112	7	0	0	NUM
ejpam-5783	112	8	)	)	PUNCT
ejpam-5783	112	9	be	be	AUX
ejpam-5783	112	10	a	a	DET
ejpam-5783	112	11	sheffer	sheffer	NOUN
ejpam-5783	112	12	stroke	stroke	NOUN
ejpam-5783	112	13	bn	bn	NOUN
ejpam-5783	112	14	-	-	PUNCT
ejpam-5783	112	15	algebra	algebra	NOUN
ejpam-5783	112	16	.	.	PUNCT
ejpam-5783	113	1	(	(	PUNCT
ejpam-5783	113	2	i	i	NOUN
ejpam-5783	113	3	)	)	PUNCT
ejpam-5783	113	4	by	by	ADP
ejpam-5783	113	5	substituting	substitute	VERB
ejpam-5783	113	6	b	b	NOUN
ejpam-5783	113	7	:	:	PUNCT
ejpam-5783	113	8	=	=	PUNCT
ejpam-5783	113	9	a	a	PROPN
ejpam-5783	113	10	and	and	CCONJ
ejpam-5783	113	11	c	c	NOUN
ejpam-5783	113	12	:	:	PUNCT
ejpam-5783	113	13	=	=	NOUN
ejpam-5783	113	14	0|0	0|0	NUM
ejpam-5783	113	15	into	into	ADP
ejpam-5783	113	16	(	(	PUNCT
ejpam-5783	113	17	s3	s3	PROPN
ejpam-5783	113	18	)	)	PUNCT
ejpam-5783	113	19	,	,	PUNCT
ejpam-5783	113	20	for	for	ADP
ejpam-5783	113	21	all	all	DET
ejpam-5783	113	22	a	a	DET
ejpam-5783	113	23	∈	∈	PROPN
ejpam-5783	113	24	psbn	psbn	NOUN
ejpam-5783	113	25	,	,	PUNCT
ejpam-5783	113	26	we	we	PRON
ejpam-5783	113	27	have	have	AUX
ejpam-5783	113	28	a|[(a|(0|0))|(a|(0|0	a|[(a|(0|0))|(a|(0|0	VERB
ejpam-5783	113	29	)	)	PUNCT
ejpam-5783	113	30	)	)	PUNCT
ejpam-5783	113	31	]	]	PUNCT
ejpam-5783	114	1	=	=	PUNCT
ejpam-5783	114	2	(	(	PUNCT
ejpam-5783	114	3	(	(	PUNCT
ejpam-5783	114	4	a|a)|(a|a))|(0|0	a|a)|(a|a))|(0|0	PROPN
ejpam-5783	114	5	)	)	PUNCT
ejpam-5783	114	6	.	.	PUNCT
ejpam-5783	115	1	then	then	ADV
ejpam-5783	115	2	,	,	PUNCT
ejpam-5783	115	3	by	by	ADP
ejpam-5783	115	4	applying	apply	VERB
ejpam-5783	115	5	axioms	axiom	NOUN
ejpam-5783	115	6	(	(	PUNCT
ejpam-5783	115	7	sbn1	sbn1	ADJ
ejpam-5783	115	8	)	)	PUNCT
ejpam-5783	115	9	on	on	ADP
ejpam-5783	115	10	the	the	DET
ejpam-5783	115	11	left	left	ADJ
ejpam-5783	115	12	-	-	PUNCT
ejpam-5783	115	13	hand	hand	NOUN
ejpam-5783	115	14	side	side	NOUN
ejpam-5783	115	15	and	and	CCONJ
ejpam-5783	115	16	(	(	PUNCT
ejpam-5783	115	17	s2	s2	PROPN
ejpam-5783	115	18	)	)	PUNCT
ejpam-5783	115	19	on	on	ADP
ejpam-5783	115	20	the	the	DET
ejpam-5783	115	21	right	right	ADJ
ejpam-5783	115	22	-	-	PUNCT
ejpam-5783	115	23	hand	hand	NOUN
ejpam-5783	115	24	side	side	NOUN
ejpam-5783	115	25	,	,	PUNCT
ejpam-5783	115	26	we	we	PRON
ejpam-5783	115	27	obtain	obtain	VERB
ejpam-5783	115	28	a|a	a|a	PUNCT
ejpam-5783	116	1	=	=	SYM
ejpam-5783	116	2	a|(0|0	a|(0|0	NOUN
ejpam-5783	116	3	)	)	PUNCT
ejpam-5783	116	4	.	.	PUNCT
ejpam-5783	117	1	(	(	PUNCT
ejpam-5783	117	2	ii	ii	NOUN
ejpam-5783	117	3	)	)	PUNCT
ejpam-5783	117	4	by	by	ADP
ejpam-5783	117	5	substituting	substitute	VERB
ejpam-5783	117	6	c	c	NOUN
ejpam-5783	117	7	:	:	PUNCT
ejpam-5783	117	8	=	=	SYM
ejpam-5783	117	9	b	b	X
ejpam-5783	117	10	into	into	ADP
ejpam-5783	117	11	(	(	PUNCT
ejpam-5783	117	12	s3	s3	PROPN
ejpam-5783	117	13	)	)	PUNCT
ejpam-5783	117	14	,	,	PUNCT
ejpam-5783	117	15	we	we	PRON
ejpam-5783	117	16	have	have	VERB
ejpam-5783	117	17	[	[	X
ejpam-5783	117	18	(	(	PUNCT
ejpam-5783	117	19	a|b)|(a|b)]|b	a|b)|(a|b)]|b	NOUN
ejpam-5783	117	20	=	=	SYM
ejpam-5783	117	21	a|[(b|b)|(b|b	a|[(b|b)|(b|b	NOUN
ejpam-5783	117	22	)	)	PUNCT
ejpam-5783	117	23	]	]	PUNCT
ejpam-5783	117	24	.	.	PUNCT
ejpam-5783	118	1	then	then	ADV
ejpam-5783	118	2	,	,	PUNCT
ejpam-5783	118	3	by	by	ADP
ejpam-5783	118	4	using	use	VERB
ejpam-5783	118	5	(	(	PUNCT
ejpam-5783	118	6	s2	s2	PROPN
ejpam-5783	118	7	)	)	PUNCT
ejpam-5783	118	8	we	we	PRON
ejpam-5783	118	9	obtain	obtain	VERB
ejpam-5783	118	10	[	[	X
ejpam-5783	118	11	(	(	PUNCT
ejpam-5783	118	12	a|b)|(a|b)]|b	a|b)|(a|b)]|b	NOUN
ejpam-5783	118	13	=	=	SYM
ejpam-5783	118	14	a|b	a|b	NOUN
ejpam-5783	118	15	for	for	ADP
ejpam-5783	118	16	all	all	DET
ejpam-5783	118	17	a	a	DET
ejpam-5783	118	18	,	,	PUNCT
ejpam-5783	118	19	b	b	PROPN
ejpam-5783	118	20	∈	∈	PROPN
ejpam-5783	118	21	psbn	psbn	NOUN
ejpam-5783	118	22	.	.	PUNCT
ejpam-5783	119	1	(	(	PUNCT
ejpam-5783	119	2	iii	iii	X
ejpam-5783	119	3	)	)	PUNCT
ejpam-5783	119	4	by	by	ADP
ejpam-5783	119	5	using	use	VERB
ejpam-5783	119	6	axioms	axiom	NOUN
ejpam-5783	119	7	(	(	PUNCT
ejpam-5783	119	8	s1	s1	NOUN
ejpam-5783	119	9	)	)	PUNCT
ejpam-5783	119	10	and	and	CCONJ
ejpam-5783	119	11	(	(	PUNCT
ejpam-5783	119	12	s2	s2	PROPN
ejpam-5783	119	13	)	)	PUNCT
ejpam-5783	119	14	,	,	PUNCT
ejpam-5783	119	15	we	we	PRON
ejpam-5783	119	16	find	find	VERB
ejpam-5783	119	17	that	that	SCONJ
ejpam-5783	119	18	(	(	PUNCT
ejpam-5783	119	19	a|(a|a))|(a|a	a|(a|a))|(a|a	ADP
ejpam-5783	119	20	)	)	PUNCT
ejpam-5783	119	21	=	=	SYM
ejpam-5783	119	22	(	(	PUNCT
ejpam-5783	119	23	a|a)|(a|(a|a	a|a)|(a|(a|a	NUM
ejpam-5783	119	24	)	)	PUNCT
ejpam-5783	119	25	)	)	PUNCT
ejpam-5783	120	1	=	=	PUNCT
ejpam-5783	120	2	a	a	X
ejpam-5783	120	3	,	,	PUNCT
ejpam-5783	120	4	for	for	ADP
ejpam-5783	120	5	all	all	DET
ejpam-5783	120	6	a	a	DET
ejpam-5783	120	7	∈	∈	PROPN
ejpam-5783	120	8	psbn	psbn	NOUN
ejpam-5783	120	9	.	.	PUNCT
ejpam-5783	121	1	s.	s.	PROPN
ejpam-5783	121	2	gemawati	gemawati	PROPN
ejpam-5783	121	3	et	et	PROPN
ejpam-5783	121	4	al	al	PROPN
ejpam-5783	121	5	.	.	PUNCT
ejpam-5783	121	6	/	/	SYM
ejpam-5783	121	7	eur	eur	PROPN
ejpam-5783	121	8	.	.	PUNCT
ejpam-5783	122	1	j.	j.	PROPN
ejpam-5783	122	2	pure	pure	PROPN
ejpam-5783	122	3	appl	appl	PROPN
ejpam-5783	122	4	.	.	PROPN
ejpam-5783	122	5	math	math	PROPN
ejpam-5783	122	6	,	,	PUNCT
ejpam-5783	122	7	18	18	NUM
ejpam-5783	122	8	(	(	PUNCT
ejpam-5783	122	9	1	1	NUM
ejpam-5783	122	10	)	)	PUNCT
ejpam-5783	122	11	(	(	PUNCT
ejpam-5783	122	12	2025	2025	NUM
ejpam-5783	122	13	)	)	PUNCT
ejpam-5783	122	14	,	,	PUNCT
ejpam-5783	122	15	5783	5783	NUM
ejpam-5783	122	16	6	6	NUM
ejpam-5783	122	17	of	of	ADP
ejpam-5783	122	18	12	12	NUM
ejpam-5783	122	19	(	(	PUNCT
ejpam-5783	122	20	iv	iv	NUM
ejpam-5783	122	21	)	)	PUNCT
ejpam-5783	122	22	by	by	ADP
ejpam-5783	122	23	substituting	substitute	VERB
ejpam-5783	122	24	c	c	NOUN
ejpam-5783	122	25	:	:	PUNCT
ejpam-5783	122	26	=	=	PUNCT
ejpam-5783	122	27	a	a	DET
ejpam-5783	122	28	and	and	CCONJ
ejpam-5783	122	29	b	b	NOUN
ejpam-5783	122	30	:	:	PUNCT
ejpam-5783	122	31	=	=	SYM
ejpam-5783	122	32	0	0	PROPN
ejpam-5783	122	33	into	into	ADP
ejpam-5783	122	34	(	(	PUNCT
ejpam-5783	122	35	sbn2	sbn2	NOUN
ejpam-5783	122	36	)	)	PUNCT
ejpam-5783	122	37	,	,	PUNCT
ejpam-5783	122	38	and	and	CCONJ
ejpam-5783	122	39	by	by	ADP
ejpam-5783	122	40	using	use	VERB
ejpam-5783	122	41	(	(	PUNCT
ejpam-5783	122	42	i	i	NOUN
ejpam-5783	122	43	)	)	PUNCT
ejpam-5783	122	44	,	,	PUNCT
ejpam-5783	122	45	(	(	PUNCT
ejpam-5783	122	46	ii	ii	NOUN
ejpam-5783	122	47	)	)	PUNCT
ejpam-5783	122	48	,	,	PUNCT
ejpam-5783	122	49	(	(	PUNCT
ejpam-5783	122	50	s1	s1	NOUN
ejpam-5783	122	51	)	)	PUNCT
ejpam-5783	122	52	,	,	PUNCT
ejpam-5783	122	53	and	and	CCONJ
ejpam-5783	122	54	(	(	PUNCT
ejpam-5783	122	55	s2	s2	PROPN
ejpam-5783	122	56	)	)	PUNCT
ejpam-5783	122	57	,	,	PUNCT
ejpam-5783	122	58	for	for	ADP
ejpam-5783	122	59	all	all	DET
ejpam-5783	122	60	a	a	DET
ejpam-5783	122	61	∈	∈	PROPN
ejpam-5783	122	62	psbn	psbn	NOUN
ejpam-5783	122	63	,	,	PUNCT
ejpam-5783	122	64	we	we	PRON
ejpam-5783	122	65	obtain	obtain	VERB
ejpam-5783	122	66	(	(	PUNCT
ejpam-5783	122	67	a|(0|0))|((0|a)|(0|a	a|(0|0))|((0|a)|(0|a	NUM
ejpam-5783	122	68	)	)	PUNCT
ejpam-5783	122	69	)	)	PUNCT
ejpam-5783	123	1	=	=	PUNCT
ejpam-5783	124	1	[	[	X
ejpam-5783	124	2	(	(	PUNCT
ejpam-5783	124	3	0|(0|(a|a))|(0|(0|(a|a))]|(0|(a|a	0|(0|(a|a))|(0|(0|(a|a))]|(0|(a|a	NUM
ejpam-5783	124	4	)	)	PUNCT
ejpam-5783	124	5	)	)	PUNCT
ejpam-5783	124	6	,	,	PUNCT
ejpam-5783	124	7	(	(	PUNCT
ejpam-5783	124	8	a|(0|0))|((0|a)|(0|a	a|(0|0))|((0|a)|(0|a	NUM
ejpam-5783	124	9	)	)	PUNCT
ejpam-5783	124	10	)	)	PUNCT
ejpam-5783	125	1	=	=	SYM
ejpam-5783	125	2	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	125	3	)	)	PUNCT
ejpam-5783	125	4	)	)	PUNCT
ejpam-5783	125	5	,	,	PUNCT
ejpam-5783	125	6	(	(	PUNCT
ejpam-5783	125	7	a|a)|((0|a)|(0|0	a|a)|((0|a)|(0|0	X
ejpam-5783	125	8	)	)	PUNCT
ejpam-5783	125	9	)	)	PUNCT
ejpam-5783	126	1	=	=	SYM
ejpam-5783	126	2	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	126	3	)	)	PUNCT
ejpam-5783	126	4	)	)	PUNCT
ejpam-5783	126	5	,	,	PUNCT
ejpam-5783	126	6	(	(	PUNCT
ejpam-5783	126	7	a|a)|((0|0)|(0|a	a|a)|((0|0)|(0|a	NOUN
ejpam-5783	126	8	)	)	PUNCT
ejpam-5783	126	9	)	)	PUNCT
ejpam-5783	127	1	=	=	SYM
ejpam-5783	127	2	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	127	3	)	)	PUNCT
ejpam-5783	127	4	)	)	PUNCT
ejpam-5783	127	5	,	,	PUNCT
ejpam-5783	127	6	(	(	PUNCT
ejpam-5783	127	7	a|a)|0	a|a)|0	NOUN
ejpam-5783	127	8	=	=	SYM
ejpam-5783	127	9	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	127	10	)	)	PUNCT
ejpam-5783	127	11	)	)	PUNCT
ejpam-5783	127	12	,	,	PUNCT
ejpam-5783	127	13	0|(a|a	0|(a|a	NUM
ejpam-5783	127	14	)	)	PUNCT
ejpam-5783	128	1	=	=	SYM
ejpam-5783	128	2	0|(0|(a|a	0|(0|(a|a	NOUN
ejpam-5783	128	3	)	)	PUNCT
ejpam-5783	128	4	)	)	PUNCT
ejpam-5783	128	5	.	.	PUNCT
ejpam-5783	129	1	(	(	PUNCT
ejpam-5783	129	2	v	v	NOUN
ejpam-5783	129	3	)	)	PUNCT
ejpam-5783	129	4	by	by	ADP
ejpam-5783	129	5	substituting	substitute	VERB
ejpam-5783	129	6	c	c	NOUN
ejpam-5783	129	7	:	:	PUNCT
ejpam-5783	130	1	=	=	SYM
ejpam-5783	130	2	0	0	PUNCT
ejpam-5783	130	3	into	into	ADP
ejpam-5783	130	4	(	(	PUNCT
ejpam-5783	130	5	sbn2	sbn2	NOUN
ejpam-5783	130	6	)	)	PUNCT
ejpam-5783	130	7	,	,	PUNCT
ejpam-5783	130	8	and	and	CCONJ
ejpam-5783	130	9	by	by	ADP
ejpam-5783	130	10	using	use	VERB
ejpam-5783	130	11	(	(	PUNCT
ejpam-5783	130	12	s2	s2	PROPN
ejpam-5783	130	13	)	)	PUNCT
ejpam-5783	130	14	,	,	PUNCT
ejpam-5783	130	15	(	(	PUNCT
ejpam-5783	130	16	iv	iv	X
ejpam-5783	130	17	)	)	PUNCT
ejpam-5783	130	18	,	,	PUNCT
ejpam-5783	130	19	(	(	PUNCT
ejpam-5783	130	20	sbn1	sbn1	ADJ
ejpam-5783	130	21	)	)	PUNCT
ejpam-5783	130	22	,	,	PUNCT
ejpam-5783	130	23	and	and	CCONJ
ejpam-5783	130	24	(	(	PUNCT
ejpam-5783	130	25	s1	s1	NOUN
ejpam-5783	130	26	)	)	PUNCT
ejpam-5783	130	27	,	,	PUNCT
ejpam-5783	130	28	for	for	ADP
ejpam-5783	130	29	all	all	DET
ejpam-5783	130	30	a	a	DET
ejpam-5783	130	31	,	,	PUNCT
ejpam-5783	130	32	b	b	PROPN
ejpam-5783	130	33	∈	∈	PROPN
ejpam-5783	130	34	psbn	psbn	NOUN
ejpam-5783	130	35	,	,	PUNCT
ejpam-5783	130	36	we	we	PRON
ejpam-5783	130	37	have	have	VERB
ejpam-5783	130	38	(	(	PUNCT
ejpam-5783	130	39	a|(b|b))|((0|0)|(0|0	a|(b|b))|((0|0)|(0|0	NOUN
ejpam-5783	130	40	)	)	PUNCT
ejpam-5783	130	41	)	)	PUNCT
ejpam-5783	131	1	=	=	PUNCT
ejpam-5783	132	1	[	[	X
ejpam-5783	132	2	(	(	PUNCT
ejpam-5783	132	3	0|(0|(0|0))|(0|(0|(0|0))]|(b|(a|a	0|(0|(0|0))|(0|(0|(0|0))]|(b|(a|a	NOUN
ejpam-5783	132	4	)	)	PUNCT
ejpam-5783	132	5	)	)	PUNCT
ejpam-5783	132	6	,	,	PUNCT
ejpam-5783	132	7	(	(	PUNCT
ejpam-5783	132	8	a|(b|b))|0	a|(b|b))|0	X
ejpam-5783	132	9	=	=	PUNCT
ejpam-5783	132	10	[	[	X
ejpam-5783	132	11	(	(	PUNCT
ejpam-5783	132	12	0|(0|0))|(0|(0|0))]|(b|(a|a	0|(0|0))|(0|(0|0))]|(b|(a|a	PROPN
ejpam-5783	132	13	)	)	PUNCT
ejpam-5783	132	14	)	)	PUNCT
ejpam-5783	132	15	,	,	PUNCT
ejpam-5783	132	16	(	(	PUNCT
ejpam-5783	132	17	a|(b|b))|0	a|(b|b))|0	PROPN
ejpam-5783	132	18	=	=	SYM
ejpam-5783	132	19	0|(b|(a|a	0|(b|(a|a	PROPN
ejpam-5783	132	20	)	)	PUNCT
ejpam-5783	132	21	)	)	PUNCT
ejpam-5783	132	22	,	,	PUNCT
ejpam-5783	132	23	0|(a|(b|b	0|(a|(b|b	NOUN
ejpam-5783	132	24	)	)	PUNCT
ejpam-5783	132	25	)	)	PUNCT
ejpam-5783	133	1	=	=	SYM
ejpam-5783	133	2	0|(b|(a|a	0|(b|(a|a	PROPN
ejpam-5783	133	3	)	)	PUNCT
ejpam-5783	133	4	)	)	PUNCT
ejpam-5783	133	5	.	.	PUNCT
ejpam-5783	134	1	(	(	PUNCT
ejpam-5783	134	2	vi	vi	X
ejpam-5783	134	3	)	)	PUNCT
ejpam-5783	134	4	by	by	ADP
ejpam-5783	134	5	substituting	substitute	VERB
ejpam-5783	134	6	b	b	NOUN
ejpam-5783	134	7	:	:	PUNCT
ejpam-5783	134	8	=	=	SYM
ejpam-5783	134	9	a|a	a|a	NOUN
ejpam-5783	134	10	into	into	ADP
ejpam-5783	134	11	(	(	PUNCT
ejpam-5783	134	12	v	v	NOUN
ejpam-5783	134	13	)	)	PUNCT
ejpam-5783	134	14	,	,	PUNCT
ejpam-5783	134	15	we	we	PRON
ejpam-5783	134	16	have	have	VERB
ejpam-5783	134	17	0|(a|((a|a)|(a|a	0|(a|((a|a)|(a|a	NOUN
ejpam-5783	134	18	)	)	PUNCT
ejpam-5783	134	19	)	)	PUNCT
ejpam-5783	134	20	)	)	PUNCT
ejpam-5783	135	1	=	=	SYM
ejpam-5783	135	2	0|((a|a)|(a|a	0|((a|a)|(a|a	ADJ
ejpam-5783	135	3	)	)	PUNCT
ejpam-5783	135	4	)	)	PUNCT
ejpam-5783	135	5	,	,	PUNCT
ejpam-5783	135	6	for	for	ADP
ejpam-5783	135	7	all	all	DET
ejpam-5783	135	8	a	a	DET
ejpam-5783	135	9	∈	∈	PROPN
ejpam-5783	135	10	psbn	psbn	NOUN
ejpam-5783	135	11	.	.	PUNCT
ejpam-5783	136	1	then	then	ADV
ejpam-5783	136	2	,	,	PUNCT
ejpam-5783	136	3	by	by	ADP
ejpam-5783	136	4	using	use	VERB
ejpam-5783	136	5	(	(	PUNCT
ejpam-5783	136	6	s2	s2	PROPN
ejpam-5783	136	7	)	)	PUNCT
ejpam-5783	136	8	we	we	PRON
ejpam-5783	136	9	obtain	obtain	VERB
ejpam-5783	136	10	0|(a|a	0|(a|a	NUM
ejpam-5783	136	11	)	)	PUNCT
ejpam-5783	137	1	=	=	SYM
ejpam-5783	138	1	0|a	0|a	ADV
ejpam-5783	138	2	for	for	ADP
ejpam-5783	138	3	all	all	DET
ejpam-5783	138	4	a	a	DET
ejpam-5783	138	5	∈	∈	PROPN
ejpam-5783	138	6	psbn	psbn	NOUN
ejpam-5783	138	7	.	.	PUNCT
ejpam-5783	139	1	in	in	ADP
ejpam-5783	139	2	a	a	DET
ejpam-5783	139	3	sheffer	sheffer	NOUN
ejpam-5783	139	4	stroke	stroke	NOUN
ejpam-5783	139	5	bn	bn	NOUN
ejpam-5783	139	6	-	-	PUNCT
ejpam-5783	139	7	algebra	algebra	NOUN
ejpam-5783	139	8	,	,	PUNCT
ejpam-5783	139	9	we	we	PRON
ejpam-5783	139	10	will	will	AUX
ejpam-5783	139	11	observe	observe	VERB
ejpam-5783	139	12	how	how	SCONJ
ejpam-5783	139	13	certain	certain	ADJ
ejpam-5783	139	14	conditions	condition	NOUN
ejpam-5783	139	15	involving	involve	VERB
ejpam-5783	139	16	the	the	DET
ejpam-5783	139	17	sheffer	sheffer	NOUN
ejpam-5783	139	18	stroke	stroke	NOUN
ejpam-5783	139	19	operation	operation	NOUN
ejpam-5783	139	20	and	and	CCONJ
ejpam-5783	139	21	constant	constant	ADJ
ejpam-5783	139	22	0	0	NUM
ejpam-5783	139	23	can	can	AUX
ejpam-5783	139	24	yield	yield	VERB
ejpam-5783	139	25	important	important	ADJ
ejpam-5783	139	26	conclusions	conclusion	NOUN
ejpam-5783	139	27	about	about	ADP
ejpam-5783	139	28	the	the	DET
ejpam-5783	139	29	relationships	relationship	NOUN
ejpam-5783	139	30	between	between	ADP
ejpam-5783	139	31	elements	element	NOUN
ejpam-5783	139	32	.	.	PUNCT
ejpam-5783	140	1	theorem	theorem	NOUN
ejpam-5783	140	2	4	4	NUM
ejpam-5783	140	3	describes	describe	VERB
ejpam-5783	140	4	a	a	DET
ejpam-5783	140	5	special	special	ADJ
ejpam-5783	140	6	case	case	NOUN
ejpam-5783	140	7	in	in	ADP
ejpam-5783	140	8	which	which	PRON
ejpam-5783	140	9	,	,	PUNCT
ejpam-5783	140	10	if	if	SCONJ
ejpam-5783	140	11	element	element	NOUN
ejpam-5783	140	12	b	b	PROPN
ejpam-5783	140	13	has	have	VERB
ejpam-5783	140	14	a	a	DET
ejpam-5783	140	15	certain	certain	ADJ
ejpam-5783	140	16	association	association	NOUN
ejpam-5783	140	17	with	with	ADP
ejpam-5783	140	18	element	element	NOUN
ejpam-5783	140	19	a	a	PRON
ejpam-5783	140	20	through	through	ADP
ejpam-5783	140	21	this	this	DET
ejpam-5783	140	22	operation	operation	NOUN
ejpam-5783	140	23	,	,	PUNCT
ejpam-5783	140	24	then	then	ADV
ejpam-5783	140	25	the	the	DET
ejpam-5783	140	26	result	result	NOUN
ejpam-5783	140	27	of	of	ADP
ejpam-5783	140	28	the	the	DET
ejpam-5783	140	29	sheffer	sheffer	NOUN
ejpam-5783	140	30	stroke	stroke	NOUN
ejpam-5783	140	31	operation	operation	NOUN
ejpam-5783	140	32	between	between	ADP
ejpam-5783	140	33	0	0	NUM
ejpam-5783	140	34	and	and	CCONJ
ejpam-5783	140	35	b	b	NOUN
ejpam-5783	140	36	will	will	AUX
ejpam-5783	140	37	be	be	AUX
ejpam-5783	140	38	the	the	DET
ejpam-5783	140	39	same	same	ADJ
ejpam-5783	140	40	as	as	ADP
ejpam-5783	140	41	the	the	DET
ejpam-5783	140	42	result	result	NOUN
ejpam-5783	140	43	of	of	ADP
ejpam-5783	140	44	the	the	DET
ejpam-5783	140	45	operation	operation	NOUN
ejpam-5783	140	46	between	between	ADP
ejpam-5783	140	47	0	0	NUM
ejpam-5783	140	48	and	and	CCONJ
ejpam-5783	140	49	a.	a.	NOUN
ejpam-5783	140	50	theorem	theorem	NOUN
ejpam-5783	140	51	4	4	X
ejpam-5783	140	52	.	.	PUNCT
ejpam-5783	141	1	let	let	AUX
ejpam-5783	141	2	(	(	PUNCT
ejpam-5783	141	3	psbn	psbn	NOUN
ejpam-5783	141	4	;	;	PUNCT
ejpam-5783	141	5	|	|	ADV
ejpam-5783	141	6	,	,	PUNCT
ejpam-5783	141	7	0	0	NUM
ejpam-5783	141	8	)	)	PUNCT
ejpam-5783	141	9	be	be	AUX
ejpam-5783	141	10	a	a	DET
ejpam-5783	141	11	sheffer	sheffer	NOUN
ejpam-5783	141	12	stroke	stroke	NOUN
ejpam-5783	141	13	bn	bn	NOUN
ejpam-5783	141	14	-	-	PUNCT
ejpam-5783	141	15	algebra	algebra	NOUN
ejpam-5783	141	16	.	.	PUNCT
ejpam-5783	142	1	if	if	SCONJ
ejpam-5783	142	2	a	a	DET
ejpam-5783	142	3	=	=	SYM
ejpam-5783	142	4	b|(a|a	b|(a|a	PROPN
ejpam-5783	142	5	)	)	PUNCT
ejpam-5783	142	6	for	for	ADP
ejpam-5783	142	7	all	all	DET
ejpam-5783	142	8	a	a	DET
ejpam-5783	142	9	,	,	PUNCT
ejpam-5783	142	10	b	b	PROPN
ejpam-5783	142	11	∈	∈	PROPN
ejpam-5783	142	12	psbn	psbn	NOUN
ejpam-5783	142	13	,	,	PUNCT
ejpam-5783	142	14	then	then	ADV
ejpam-5783	142	15	0|b	0|b	PUNCT
ejpam-5783	142	16	=	=	PUNCT
ejpam-5783	143	1	0|a	0|a	X
ejpam-5783	143	2	.	.	PUNCT
ejpam-5783	144	1	proof	proof	NOUN
ejpam-5783	144	2	.	.	PUNCT
ejpam-5783	145	1	let	let	AUX
ejpam-5783	145	2	(	(	PUNCT
ejpam-5783	145	3	psbn	psbn	NOUN
ejpam-5783	145	4	;	;	PUNCT
ejpam-5783	145	5	|	|	ADV
ejpam-5783	145	6	,	,	PUNCT
ejpam-5783	145	7	0	0	NUM
ejpam-5783	145	8	)	)	PUNCT
ejpam-5783	145	9	be	be	AUX
ejpam-5783	145	10	a	a	DET
ejpam-5783	145	11	sheffer	sheffer	NOUN
ejpam-5783	145	12	stroke	stroke	NOUN
ejpam-5783	145	13	bn	bn	NOUN
ejpam-5783	145	14	-	-	PUNCT
ejpam-5783	145	15	algebra	algebra	NOUN
ejpam-5783	145	16	.	.	PUNCT
ejpam-5783	146	1	since	since	SCONJ
ejpam-5783	146	2	a	a	DET
ejpam-5783	146	3	:	:	PUNCT
ejpam-5783	146	4	=	=	SYM
ejpam-5783	146	5	b|(a|a	b|(a|a	PROPN
ejpam-5783	146	6	)	)	PUNCT
ejpam-5783	146	7	for	for	ADP
ejpam-5783	146	8	all	all	DET
ejpam-5783	146	9	a	a	DET
ejpam-5783	146	10	,	,	PUNCT
ejpam-5783	146	11	b	b	PROPN
ejpam-5783	146	12	∈	∈	PROPN
ejpam-5783	146	13	psbn	psbn	NOUN
ejpam-5783	146	14	,	,	PUNCT
ejpam-5783	146	15	by	by	ADP
ejpam-5783	146	16	using	use	VERB
ejpam-5783	146	17	(	(	PUNCT
ejpam-5783	146	18	v	v	NOUN
ejpam-5783	146	19	)	)	PUNCT
ejpam-5783	146	20	,	,	PUNCT
ejpam-5783	146	21	(	(	PUNCT
ejpam-5783	146	22	s1	s1	NOUN
ejpam-5783	146	23	)	)	PUNCT
ejpam-5783	146	24	,	,	PUNCT
ejpam-5783	146	25	and	and	CCONJ
ejpam-5783	146	26	(	(	PUNCT
ejpam-5783	146	27	s2	s2	PROPN
ejpam-5783	146	28	)	)	PUNCT
ejpam-5783	146	29	,	,	PUNCT
ejpam-5783	146	30	we	we	PRON
ejpam-5783	146	31	have	have	VERB
ejpam-5783	146	32	0|(b|(a|a	0|(b|(a|a	NOUN
ejpam-5783	146	33	)	)	PUNCT
ejpam-5783	146	34	)	)	PUNCT
ejpam-5783	147	1	=	=	PUNCT
ejpam-5783	147	2	0|(a|(b|b	0|(a|(b|b	NOUN
ejpam-5783	147	3	)	)	PUNCT
ejpam-5783	147	4	)	)	PUNCT
ejpam-5783	147	5	,	,	PUNCT
ejpam-5783	147	6	0|a	0|a	PUNCT
ejpam-5783	147	7	=	=	SYM
ejpam-5783	147	8	0|((b|(a|a))|(b|b	0|((b|(a|a))|(b|b	NOUN
ejpam-5783	147	9	)	)	PUNCT
ejpam-5783	147	10	)	)	PUNCT
ejpam-5783	147	11	,	,	PUNCT
ejpam-5783	147	12	0|a	0|a	PUNCT
ejpam-5783	148	1	=	=	SYM
ejpam-5783	148	2	0|((b|b)|(b|(a|a	0|((b|b)|(b|(a|a	PROPN
ejpam-5783	148	3	)	)	PUNCT
ejpam-5783	148	4	)	)	PUNCT
ejpam-5783	148	5	)	)	PUNCT
ejpam-5783	148	6	,	,	PUNCT
ejpam-5783	148	7	0|a	0|a	PUNCT
ejpam-5783	149	1	=	=	SYM
ejpam-5783	149	2	0|b	0|b	PROPN
ejpam-5783	149	3	.	.	PUNCT
ejpam-5783	150	1	s.	s.	PROPN
ejpam-5783	150	2	gemawati	gemawati	PROPN
ejpam-5783	150	3	et	et	PROPN
ejpam-5783	150	4	al	al	PROPN
ejpam-5783	150	5	.	.	PUNCT
ejpam-5783	150	6	/	/	SYM
ejpam-5783	150	7	eur	eur	PROPN
ejpam-5783	150	8	.	.	PUNCT
ejpam-5783	151	1	j.	j.	PROPN
ejpam-5783	151	2	pure	pure	PROPN
ejpam-5783	151	3	appl	appl	PROPN
ejpam-5783	151	4	.	.	PROPN
ejpam-5783	151	5	math	math	PROPN
ejpam-5783	151	6	,	,	PUNCT
ejpam-5783	151	7	18	18	NUM
ejpam-5783	151	8	(	(	PUNCT
ejpam-5783	151	9	1	1	NUM
ejpam-5783	151	10	)	)	PUNCT
ejpam-5783	151	11	(	(	PUNCT
ejpam-5783	151	12	2025	2025	NUM
ejpam-5783	151	13	)	)	PUNCT
ejpam-5783	151	14	,	,	PUNCT
ejpam-5783	151	15	5783	5783	NUM
ejpam-5783	151	16	7	7	NUM
ejpam-5783	151	17	of	of	ADP
ejpam-5783	151	18	12	12	NUM
ejpam-5783	151	19	we	we	PRON
ejpam-5783	151	20	next	next	ADV
ejpam-5783	151	21	define	define	VERB
ejpam-5783	151	22	some	some	DET
ejpam-5783	151	23	additional	additional	ADJ
ejpam-5783	151	24	concepts	concept	NOUN
ejpam-5783	151	25	,	,	PUNCT
ejpam-5783	151	26	but	but	CCONJ
ejpam-5783	151	27	first	first	ADV
ejpam-5783	151	28	let	let	VERB
ejpam-5783	151	29	us	we	PRON
ejpam-5783	151	30	look	look	VERB
ejpam-5783	151	31	at	at	ADP
ejpam-5783	151	32	the	the	DET
ejpam-5783	151	33	role	role	NOUN
ejpam-5783	151	34	of	of	ADP
ejpam-5783	151	35	subsets	subset	NOUN
ejpam-5783	151	36	in	in	ADP
ejpam-5783	151	37	the	the	DET
ejpam-5783	151	38	study	study	NOUN
ejpam-5783	151	39	of	of	ADP
ejpam-5783	151	40	sheffer	sheffer	PROPN
ejpam-5783	151	41	stroke	stroke	PROPN
ejpam-5783	151	42	bn	bn	NOUN
ejpam-5783	151	43	-	-	PUNCT
ejpam-5783	151	44	algebra	algebra	NOUN
ejpam-5783	151	45	,	,	PUNCT
ejpam-5783	151	46	namely	namely	ADV
ejpam-5783	151	47	,	,	PUNCT
ejpam-5783	151	48	sheffer	sheffer	NOUN
ejpam-5783	151	49	stroke	stroke	NOUN
ejpam-5783	151	50	bn	bn	PROPN
ejpam-5783	151	51	-	-	PUNCT
ejpam-5783	151	52	subalgebras	subalgebras	PROPN
ejpam-5783	151	53	,	,	PUNCT
ejpam-5783	151	54	normal	normal	ADJ
ejpam-5783	151	55	subsets	subset	NOUN
ejpam-5783	151	56	,	,	PUNCT
ejpam-5783	151	57	and	and	CCONJ
ejpam-5783	151	58	sheffer	sheffer	VERB
ejpam-5783	151	59	stroke	stroke	PROPN
ejpam-5783	151	60	bn	bn	NOUN
ejpam-5783	151	61	-	-	PUNCT
ejpam-5783	151	62	ideals	ideal	NOUN
ejpam-5783	151	63	,	,	PUNCT
ejpam-5783	151	64	have	have	VERB
ejpam-5783	151	65	an	an	DET
ejpam-5783	151	66	important	important	ADJ
ejpam-5783	151	67	function	function	NOUN
ejpam-5783	151	68	in	in	ADP
ejpam-5783	151	69	maintaining	maintain	VERB
ejpam-5783	151	70	the	the	DET
ejpam-5783	151	71	regularity	regularity	NOUN
ejpam-5783	151	72	of	of	ADP
ejpam-5783	151	73	this	this	DET
ejpam-5783	151	74	algebra	algebra	NOUN
ejpam-5783	151	75	.	.	PUNCT
ejpam-5783	152	1	a	a	DET
ejpam-5783	152	2	sheffer	sheffer	NOUN
ejpam-5783	152	3	stroke	stroke	NOUN
ejpam-5783	152	4	bn	bn	NOUN
ejpam-5783	152	5	-	-	PUNCT
ejpam-5783	152	6	subalgebra	subalgebra	NOUN
ejpam-5783	152	7	is	be	AUX
ejpam-5783	152	8	a	a	DET
ejpam-5783	152	9	part	part	NOUN
ejpam-5783	152	10	of	of	ADP
ejpam-5783	152	11	the	the	DET
ejpam-5783	152	12	algebra	algebra	NOUN
ejpam-5783	152	13	that	that	PRON
ejpam-5783	152	14	is	be	AUX
ejpam-5783	152	15	closed	close	VERB
ejpam-5783	152	16	under	under	ADP
ejpam-5783	152	17	the	the	DET
ejpam-5783	152	18	sheffer	sheffer	NOUN
ejpam-5783	152	19	stroke	stroke	NOUN
ejpam-5783	152	20	operation	operation	NOUN
ejpam-5783	152	21	,	,	PUNCT
ejpam-5783	152	22	meaning	mean	VERB
ejpam-5783	152	23	that	that	SCONJ
ejpam-5783	152	24	the	the	DET
ejpam-5783	152	25	result	result	NOUN
ejpam-5783	152	26	of	of	ADP
ejpam-5783	152	27	each	each	DET
ejpam-5783	152	28	such	such	ADJ
ejpam-5783	152	29	operation	operation	NOUN
ejpam-5783	152	30	will	will	AUX
ejpam-5783	152	31	be	be	AUX
ejpam-5783	152	32	in	in	ADP
ejpam-5783	152	33	the	the	DET
ejpam-5783	152	34	subset	subset	NOUN
ejpam-5783	152	35	itself	itself	PRON
ejpam-5783	152	36	.	.	PUNCT
ejpam-5783	153	1	a	a	DET
ejpam-5783	153	2	normal	normal	ADJ
ejpam-5783	153	3	subset	subset	NOUN
ejpam-5783	153	4	is	be	AUX
ejpam-5783	153	5	a	a	DET
ejpam-5783	153	6	special	special	ADJ
ejpam-5783	153	7	subset	subset	NOUN
ejpam-5783	153	8	that	that	PRON
ejpam-5783	153	9	makes	make	VERB
ejpam-5783	153	10	an	an	DET
ejpam-5783	153	11	algebraic	algebraic	ADJ
ejpam-5783	153	12	structure	structure	NOUN
ejpam-5783	153	13	more	more	ADV
ejpam-5783	153	14	symmetrical	symmetrical	ADJ
ejpam-5783	153	15	,	,	PUNCT
ejpam-5783	153	16	preserving	preserve	VERB
ejpam-5783	153	17	order	order	NOUN
ejpam-5783	153	18	among	among	ADP
ejpam-5783	153	19	certain	certain	ADJ
ejpam-5783	153	20	elements	element	NOUN
ejpam-5783	153	21	.	.	PUNCT
ejpam-5783	154	1	a	a	DET
ejpam-5783	154	2	sheffer	sheffer	NOUN
ejpam-5783	154	3	stroke	stroke	NOUN
ejpam-5783	154	4	bn	bn	NOUN
ejpam-5783	154	5	-	-	PUNCT
ejpam-5783	154	6	ideal	ideal	NOUN
ejpam-5783	154	7	is	be	AUX
ejpam-5783	154	8	a	a	DET
ejpam-5783	154	9	subset	subset	NOUN
ejpam-5783	154	10	that	that	PRON
ejpam-5783	154	11	contains	contain	VERB
ejpam-5783	154	12	the	the	DET
ejpam-5783	154	13	constant	constant	ADJ
ejpam-5783	154	14	0	0	NUM
ejpam-5783	154	15	and	and	CCONJ
ejpam-5783	154	16	meets	meet	VERB
ejpam-5783	154	17	certain	certain	ADJ
ejpam-5783	154	18	rules	rule	NOUN
ejpam-5783	154	19	so	so	SCONJ
ejpam-5783	154	20	that	that	SCONJ
ejpam-5783	154	21	it	it	PRON
ejpam-5783	154	22	remains	remain	VERB
ejpam-5783	154	23	consistent	consistent	ADJ
ejpam-5783	154	24	under	under	ADP
ejpam-5783	154	25	sheffer	sheffer	NOUN
ejpam-5783	154	26	stroke	stroke	NOUN
ejpam-5783	154	27	operations	operation	NOUN
ejpam-5783	154	28	.	.	PUNCT
ejpam-5783	155	1	these	these	DET
ejpam-5783	155	2	three	three	NUM
ejpam-5783	155	3	types	type	NOUN
ejpam-5783	155	4	of	of	ADP
ejpam-5783	155	5	subsets	subset	NOUN
ejpam-5783	155	6	help	help	AUX
ejpam-5783	155	7	understand	understand	VERB
ejpam-5783	155	8	patterns	pattern	NOUN
ejpam-5783	155	9	and	and	CCONJ
ejpam-5783	155	10	stability	stability	NOUN
ejpam-5783	155	11	in	in	ADP
ejpam-5783	155	12	sheffer	sheffer	PROPN
ejpam-5783	155	13	stroke	stroke	PROPN
ejpam-5783	155	14	bn	bn	NOUN
ejpam-5783	155	15	-	-	PUNCT
ejpam-5783	155	16	algebra	algebra	NOUN
ejpam-5783	155	17	.	.	PUNCT
ejpam-5783	156	1	definition	definition	NOUN
ejpam-5783	156	2	6	6	NUM
ejpam-5783	156	3	.	.	PUNCT
ejpam-5783	157	1	let	let	AUX
ejpam-5783	157	2	(	(	PUNCT
ejpam-5783	157	3	psbn	psbn	NOUN
ejpam-5783	157	4	;	;	PUNCT
ejpam-5783	157	5	|	|	ADV
ejpam-5783	157	6	,	,	PUNCT
ejpam-5783	157	7	0	0	NUM
ejpam-5783	157	8	)	)	PUNCT
ejpam-5783	157	9	be	be	AUX
ejpam-5783	157	10	a	a	DET
ejpam-5783	157	11	sheffer	sheffer	NOUN
ejpam-5783	157	12	stroke	stroke	NOUN
ejpam-5783	157	13	bn	bn	NOUN
ejpam-5783	157	14	-	-	PUNCT
ejpam-5783	157	15	algebra	algebra	PROPN
ejpam-5783	157	16	and	and	CCONJ
ejpam-5783	157	17	s	s	VERB
ejpam-5783	157	18	a	a	DET
ejpam-5783	157	19	non	non	ADJ
ejpam-5783	157	20	-	-	ADJ
ejpam-5783	157	21	empty	empty	ADJ
ejpam-5783	157	22	subset	subset	NOUN
ejpam-5783	157	23	of	of	ADP
ejpam-5783	157	24	psbn	psbn	NOUN
ejpam-5783	157	25	.	.	PUNCT
ejpam-5783	158	1	the	the	DET
ejpam-5783	158	2	set	set	NOUN
ejpam-5783	158	3	s	s	PART
ejpam-5783	158	4	is	be	AUX
ejpam-5783	158	5	called	call	VERB
ejpam-5783	158	6	a	a	DET
ejpam-5783	158	7	sheffer	sheffer	NOUN
ejpam-5783	158	8	stroke	stroke	NOUN
ejpam-5783	158	9	bn	bn	NOUN
ejpam-5783	158	10	-	-	PUNCT
ejpam-5783	158	11	subalgebra	subalgebra	NOUN
ejpam-5783	158	12	of	of	ADP
ejpam-5783	158	13	psbn	psbn	NOUN
ejpam-5783	158	14	if	if	SCONJ
ejpam-5783	158	15	it	it	PRON
ejpam-5783	158	16	satisfies	satisfy	VERB
ejpam-5783	158	17	(	(	PUNCT
ejpam-5783	158	18	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	158	19	)	)	PUNCT
ejpam-5783	158	20	)	)	PUNCT
ejpam-5783	159	1	∈	∈	PROPN
ejpam-5783	159	2	s	s	VERB
ejpam-5783	159	3	for	for	ADP
ejpam-5783	159	4	all	all	DET
ejpam-5783	159	5	a	a	PRON
ejpam-5783	159	6	,	,	PUNCT
ejpam-5783	159	7	b	b	X
ejpam-5783	159	8	∈	∈	PROPN
ejpam-5783	159	9	s.	s.	PROPN
ejpam-5783	159	10	definition	definition	NOUN
ejpam-5783	159	11	7	7	NUM
ejpam-5783	159	12	.	.	PUNCT
ejpam-5783	160	1	let	let	AUX
ejpam-5783	160	2	(	(	PUNCT
ejpam-5783	160	3	psbn	psbn	NOUN
ejpam-5783	160	4	;	;	PUNCT
ejpam-5783	160	5	|	|	ADV
ejpam-5783	160	6	,	,	PUNCT
ejpam-5783	160	7	0	0	NUM
ejpam-5783	160	8	)	)	PUNCT
ejpam-5783	160	9	be	be	AUX
ejpam-5783	160	10	a	a	DET
ejpam-5783	160	11	sheffer	sheffer	NOUN
ejpam-5783	160	12	stroke	stroke	NOUN
ejpam-5783	160	13	bn	bn	NOUN
ejpam-5783	160	14	-	-	PUNCT
ejpam-5783	160	15	algebra	algebra	PROPN
ejpam-5783	160	16	and	and	CCONJ
ejpam-5783	160	17	n	n	DET
ejpam-5783	160	18	a	a	DET
ejpam-5783	160	19	non	non	ADJ
ejpam-5783	160	20	-	-	ADJ
ejpam-5783	160	21	empty	empty	ADJ
ejpam-5783	160	22	subset	subset	NOUN
ejpam-5783	160	23	of	of	ADP
ejpam-5783	160	24	psbn	psbn	NOUN
ejpam-5783	160	25	.	.	PUNCT
ejpam-5783	161	1	the	the	DET
ejpam-5783	161	2	set	set	NOUN
ejpam-5783	161	3	n	n	PRON
ejpam-5783	161	4	is	be	AUX
ejpam-5783	161	5	called	call	VERB
ejpam-5783	161	6	a	a	DET
ejpam-5783	161	7	normal	normal	ADJ
ejpam-5783	161	8	subset	subset	NOUN
ejpam-5783	161	9	of	of	ADP
ejpam-5783	161	10	the	the	DET
ejpam-5783	161	11	sheffer	sheffer	NOUN
ejpam-5783	161	12	stroke	stroke	PROPN
ejpam-5783	161	13	bn	bn	NOUN
ejpam-5783	161	14	-	-	PUNCT
ejpam-5783	161	15	algebra	algebra	NOUN
ejpam-5783	161	16	psbn	psbn	NOUN
ejpam-5783	161	17	if	if	SCONJ
ejpam-5783	161	18	it	it	PRON
ejpam-5783	161	19	satisfies	satisfy	VERB
ejpam-5783	161	20	(	(	PUNCT
ejpam-5783	161	21	(	(	PUNCT
ejpam-5783	161	22	(	(	PUNCT
ejpam-5783	161	23	a|(p|p))|(a|(p|p)))|(b|(q|q)))|(((a|(p|p))|(a|(p|p)))|(b|(q|q	a|(p|p))|(a|(p|p)))|(b|(q|q)))|(((a|(p|p))|(a|(p|p)))|(b|(q|q	NOUN
ejpam-5783	161	24	)	)	PUNCT
ejpam-5783	161	25	)	)	PUNCT
ejpam-5783	161	26	)	)	PUNCT
ejpam-5783	162	1	∈	∈	PROPN
ejpam-5783	162	2	n	n	CCONJ
ejpam-5783	162	3	,	,	PUNCT
ejpam-5783	162	4	for	for	ADP
ejpam-5783	162	5	any	any	DET
ejpam-5783	162	6	(	(	PUNCT
ejpam-5783	162	7	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	162	8	)	)	PUNCT
ejpam-5783	162	9	)	)	PUNCT
ejpam-5783	162	10	,	,	PUNCT
ejpam-5783	162	11	(	(	PUNCT
ejpam-5783	162	12	p|(q|q))|(p|(q|q	p|(q|q))|(p|(q|q	NOUN
ejpam-5783	162	13	)	)	PUNCT
ejpam-5783	162	14	)	)	PUNCT
ejpam-5783	163	1	∈	∈	PROPN
ejpam-5783	163	2	n	n	X
ejpam-5783	163	3	.	.	PUNCT
ejpam-5783	164	1	definition	definition	NOUN
ejpam-5783	164	2	8	8	NUM
ejpam-5783	164	3	.	.	PUNCT
ejpam-5783	165	1	let	let	AUX
ejpam-5783	165	2	(	(	PUNCT
ejpam-5783	165	3	psbn	psbn	NOUN
ejpam-5783	165	4	;	;	PUNCT
ejpam-5783	165	5	|	|	ADV
ejpam-5783	165	6	,	,	PUNCT
ejpam-5783	165	7	0	0	NUM
ejpam-5783	165	8	)	)	PUNCT
ejpam-5783	165	9	be	be	AUX
ejpam-5783	165	10	a	a	DET
ejpam-5783	165	11	sheffer	sheffer	NOUN
ejpam-5783	165	12	stroke	stroke	NOUN
ejpam-5783	165	13	bn	bn	NOUN
ejpam-5783	165	14	-	-	PUNCT
ejpam-5783	165	15	algebra	algebra	NOUN
ejpam-5783	165	16	and	and	CCONJ
ejpam-5783	165	17	i	i	PRON
ejpam-5783	165	18	a	a	DET
ejpam-5783	165	19	non	non	ADJ
ejpam-5783	165	20	-	-	ADJ
ejpam-5783	165	21	empty	empty	ADJ
ejpam-5783	165	22	subset	subset	NOUN
ejpam-5783	165	23	of	of	ADP
ejpam-5783	165	24	psbn	psbn	NOUN
ejpam-5783	165	25	.	.	PUNCT
ejpam-5783	166	1	the	the	DET
ejpam-5783	166	2	set	set	NOUN
ejpam-5783	166	3	i	i	PRON
ejpam-5783	166	4	is	be	AUX
ejpam-5783	166	5	called	call	VERB
ejpam-5783	166	6	a	a	DET
ejpam-5783	166	7	sheffer	sheffer	NOUN
ejpam-5783	166	8	stroke	stroke	NOUN
ejpam-5783	166	9	bn	bn	NOUN
ejpam-5783	166	10	-	-	PUNCT
ejpam-5783	166	11	ideal	ideal	NOUN
ejpam-5783	166	12	of	of	ADP
ejpam-5783	166	13	psbn	psbn	NOUN
ejpam-5783	166	14	if	if	SCONJ
ejpam-5783	166	15	it	it	PRON
ejpam-5783	166	16	satisfies	satisfy	VERB
ejpam-5783	166	17	the	the	DET
ejpam-5783	166	18	following	follow	VERB
ejpam-5783	166	19	conditions	condition	NOUN
ejpam-5783	166	20	:	:	PUNCT
ejpam-5783	166	21	(	(	PUNCT
ejpam-5783	166	22	i	i	NOUN
ejpam-5783	166	23	)	)	PUNCT
ejpam-5783	166	24	0	0	PUNCT
ejpam-5783	167	1	∈	∈	PROPN
ejpam-5783	168	1	i	i	PRON
ejpam-5783	168	2	,	,	PUNCT
ejpam-5783	168	3	(	(	PUNCT
ejpam-5783	168	4	ii	ii	NOUN
ejpam-5783	168	5	)	)	PUNCT
ejpam-5783	168	6	b	b	NOUN
ejpam-5783	168	7	∈	∈	PROPN
ejpam-5783	169	1	i	i	PRON
ejpam-5783	169	2	and	and	CCONJ
ejpam-5783	169	3	(	(	PUNCT
ejpam-5783	169	4	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	169	5	)	)	PUNCT
ejpam-5783	169	6	)	)	PUNCT
ejpam-5783	170	1	∈	∈	NOUN
ejpam-5783	170	2	i	i	PRON
ejpam-5783	170	3	imply	imply	VERB
ejpam-5783	170	4	a	a	DET
ejpam-5783	170	5	∈	∈	NOUN
ejpam-5783	170	6	i	i	PRON
ejpam-5783	170	7	for	for	ADP
ejpam-5783	170	8	all	all	DET
ejpam-5783	170	9	a	a	DET
ejpam-5783	170	10	,	,	PUNCT
ejpam-5783	170	11	b	b	PROPN
ejpam-5783	170	12	∈	∈	PROPN
ejpam-5783	170	13	psbn	psbn	NOUN
ejpam-5783	170	14	.	.	PUNCT
ejpam-5783	171	1	before	before	ADP
ejpam-5783	171	2	deriving	derive	VERB
ejpam-5783	171	3	results	result	NOUN
ejpam-5783	171	4	about	about	ADP
ejpam-5783	171	5	sheffer	sheffer	PROPN
ejpam-5783	171	6	stroke	stroke	PROPN
ejpam-5783	171	7	bn	bn	NOUN
ejpam-5783	171	8	-	-	PUNCT
ejpam-5783	171	9	ideals	ideal	NOUN
ejpam-5783	171	10	,	,	PUNCT
ejpam-5783	171	11	sheffer	sheffer	NOUN
ejpam-5783	171	12	stroke	stroke	NOUN
ejpam-5783	171	13	bn	bn	PROPN
ejpam-5783	171	14	-	-	PUNCT
ejpam-5783	171	15	subalgebras	subalgebras	X
ejpam-5783	171	16	,	,	PUNCT
ejpam-5783	171	17	and	and	CCONJ
ejpam-5783	171	18	normal	normal	ADJ
ejpam-5783	171	19	subsets	subset	NOUN
ejpam-5783	171	20	in	in	ADP
ejpam-5783	171	21	sheffer	sheffer	PROPN
ejpam-5783	171	22	stroke	stroke	PROPN
ejpam-5783	171	23	bn	bn	PROPN
ejpam-5783	171	24	-	-	PUNCT
ejpam-5783	171	25	algebras	algebras	X
ejpam-5783	171	26	,	,	PUNCT
ejpam-5783	171	27	we	we	PRON
ejpam-5783	171	28	will	will	AUX
ejpam-5783	171	29	look	look	VERB
ejpam-5783	171	30	at	at	ADP
ejpam-5783	171	31	a	a	DET
ejpam-5783	171	32	concrete	concrete	ADJ
ejpam-5783	171	33	example	example	NOUN
ejpam-5783	171	34	.	.	PUNCT
ejpam-5783	172	1	this	this	DET
ejpam-5783	172	2	example	example	NOUN
ejpam-5783	172	3	aims	aim	VERB
ejpam-5783	172	4	to	to	PART
ejpam-5783	172	5	show	show	VERB
ejpam-5783	172	6	how	how	SCONJ
ejpam-5783	172	7	the	the	DET
ejpam-5783	172	8	elements	element	NOUN
ejpam-5783	172	9	in	in	ADP
ejpam-5783	172	10	the	the	DET
ejpam-5783	172	11	algebra	algebra	NOUN
ejpam-5783	172	12	fit	fit	ADJ
ejpam-5783	172	13	into	into	ADP
ejpam-5783	172	14	these	these	DET
ejpam-5783	172	15	categories	category	NOUN
ejpam-5783	172	16	of	of	ADP
ejpam-5783	172	17	subset	subset	ADJ
ejpam-5783	172	18	categories	category	NOUN
ejpam-5783	172	19	according	accord	VERB
ejpam-5783	172	20	to	to	ADP
ejpam-5783	172	21	the	the	DET
ejpam-5783	172	22	properties	property	NOUN
ejpam-5783	172	23	of	of	ADP
ejpam-5783	172	24	the	the	DET
ejpam-5783	172	25	sheffer	sheffer	NOUN
ejpam-5783	172	26	stroke	stroke	NOUN
ejpam-5783	172	27	operation	operation	NOUN
ejpam-5783	172	28	.	.	PUNCT
ejpam-5783	173	1	example	example	NOUN
ejpam-5783	174	1	2	2	NUM
ejpam-5783	174	2	.	.	X
ejpam-5783	174	3	consider	consider	VERB
ejpam-5783	174	4	the	the	DET
ejpam-5783	174	5	same	same	ADJ
ejpam-5783	174	6	sheffer	sheffer	NOUN
ejpam-5783	174	7	stroke	stroke	NOUN
ejpam-5783	174	8	bn	bn	NOUN
ejpam-5783	174	9	-	-	PUNCT
ejpam-5783	174	10	algebra	algebra	NOUN
ejpam-5783	174	11	(	(	PUNCT
ejpam-5783	174	12	psbn	psbn	NOUN
ejpam-5783	174	13	;	;	PUNCT
ejpam-5783	174	14	|	|	ADV
ejpam-5783	174	15	,	,	PUNCT
ejpam-5783	174	16	0	0	NUM
ejpam-5783	174	17	)	)	PUNCT
ejpam-5783	174	18	defined	define	VERB
ejpam-5783	174	19	in	in	ADP
ejpam-5783	174	20	example	example	NOUN
ejpam-5783	174	21	1	1	X
ejpam-5783	174	22	.	.	PUNCT
ejpam-5783	175	1	the	the	DET
ejpam-5783	175	2	set	set	NOUN
ejpam-5783	175	3	of	of	ADP
ejpam-5783	175	4	sheffer	sheffer	PROPN
ejpam-5783	175	5	stroke	stroke	PROPN
ejpam-5783	175	6	bn	bn	NOUN
ejpam-5783	175	7	-	-	PUNCT
ejpam-5783	175	8	ideals	ideal	NOUN
ejpam-5783	175	9	of	of	ADP
ejpam-5783	175	10	psbn	psbn	NOUN
ejpam-5783	175	11	consists	consist	VERB
ejpam-5783	175	12	of	of	ADP
ejpam-5783	175	13	{	{	PUNCT
ejpam-5783	175	14	0	0	NUM
ejpam-5783	175	15	}	}	PUNCT
ejpam-5783	175	16	,	,	PUNCT
ejpam-5783	175	17	{	{	PUNCT
ejpam-5783	175	18	0	0	NUM
ejpam-5783	175	19	,	,	PUNCT
ejpam-5783	175	20	p	p	NOUN
ejpam-5783	175	21	}	}	PUNCT
ejpam-5783	175	22	,	,	PUNCT
ejpam-5783	175	23	{	{	PUNCT
ejpam-5783	175	24	0	0	NUM
ejpam-5783	175	25	,	,	PUNCT
ejpam-5783	175	26	q	q	NOUN
ejpam-5783	175	27	}	}	PUNCT
ejpam-5783	175	28	,	,	PUNCT
ejpam-5783	175	29	and	and	CCONJ
ejpam-5783	175	30	psbn	psbn	NOUN
ejpam-5783	175	31	.	.	PUNCT
ejpam-5783	176	1	the	the	DET
ejpam-5783	176	2	subsets	subset	NOUN
ejpam-5783	176	3	{	{	PUNCT
ejpam-5783	176	4	0	0	NUM
ejpam-5783	176	5	}	}	PUNCT
ejpam-5783	176	6	,	,	PUNCT
ejpam-5783	176	7	{	{	PUNCT
ejpam-5783	176	8	0	0	NUM
ejpam-5783	176	9	,	,	PUNCT
ejpam-5783	176	10	p	p	NOUN
ejpam-5783	176	11	}	}	PUNCT
ejpam-5783	176	12	,	,	PUNCT
ejpam-5783	176	13	{	{	PUNCT
ejpam-5783	176	14	0	0	NUM
ejpam-5783	176	15	,	,	PUNCT
ejpam-5783	176	16	1	1	NUM
ejpam-5783	176	17	}	}	PUNCT
ejpam-5783	176	18	,	,	PUNCT
ejpam-5783	176	19	{	{	PUNCT
ejpam-5783	176	20	0	0	NUM
ejpam-5783	176	21	,	,	PUNCT
ejpam-5783	176	22	p	p	X
ejpam-5783	176	23	,	,	PUNCT
ejpam-5783	176	24	q	q	NOUN
ejpam-5783	176	25	}	}	PUNCT
ejpam-5783	176	26	,	,	PUNCT
ejpam-5783	176	27	and	and	CCONJ
ejpam-5783	176	28	psbn	psbn	NOUN
ejpam-5783	176	29	are	be	AUX
ejpam-5783	176	30	sheffer	sheffer	NOUN
ejpam-5783	176	31	stroke	stroke	NOUN
ejpam-5783	176	32	bn	bn	NOUN
ejpam-5783	176	33	-	-	PUNCT
ejpam-5783	176	34	subalgebras	subalgebras	PROPN
ejpam-5783	176	35	of	of	ADP
ejpam-5783	176	36	psbn	psbn	NOUN
ejpam-5783	176	37	.	.	PUNCT
ejpam-5783	177	1	the	the	DET
ejpam-5783	177	2	normal	normal	ADJ
ejpam-5783	177	3	subsets	subset	NOUN
ejpam-5783	177	4	in	in	ADP
ejpam-5783	177	5	psbn	psbn	NOUN
ejpam-5783	177	6	are	be	AUX
ejpam-5783	177	7	{	{	PUNCT
ejpam-5783	177	8	0	0	NUM
ejpam-5783	177	9	}	}	PUNCT
ejpam-5783	177	10	,	,	PUNCT
ejpam-5783	177	11	{	{	PUNCT
ejpam-5783	177	12	0	0	NUM
ejpam-5783	177	13	,	,	PUNCT
ejpam-5783	177	14	p	p	NOUN
ejpam-5783	177	15	}	}	PUNCT
ejpam-5783	177	16	,	,	PUNCT
ejpam-5783	177	17	and	and	CCONJ
ejpam-5783	177	18	psbn	psbn	NOUN
ejpam-5783	177	19	.	.	PUNCT
ejpam-5783	178	1	in	in	ADP
ejpam-5783	178	2	the	the	DET
ejpam-5783	178	3	following	following	NOUN
ejpam-5783	178	4	theorem	theorem	NOUN
ejpam-5783	178	5	,	,	PUNCT
ejpam-5783	178	6	we	we	PRON
ejpam-5783	178	7	will	will	AUX
ejpam-5783	178	8	see	see	VERB
ejpam-5783	178	9	how	how	SCONJ
ejpam-5783	178	10	the	the	DET
ejpam-5783	178	11	existence	existence	NOUN
ejpam-5783	178	12	of	of	ADP
ejpam-5783	178	13	a	a	DET
ejpam-5783	178	14	sheffer	sheffer	NOUN
ejpam-5783	178	15	stroke	stroke	NOUN
ejpam-5783	178	16	bn	bn	NOUN
ejpam-5783	178	17	-	-	PUNCT
ejpam-5783	178	18	ideal	ideal	NOUN
ejpam-5783	178	19	can	can	AUX
ejpam-5783	178	20	affect	affect	VERB
ejpam-5783	178	21	the	the	DET
ejpam-5783	178	22	membership	membership	NOUN
ejpam-5783	178	23	of	of	ADP
ejpam-5783	178	24	other	other	ADJ
ejpam-5783	178	25	elements	element	NOUN
ejpam-5783	178	26	.	.	PUNCT
ejpam-5783	179	1	the	the	DET
ejpam-5783	179	2	theorem	theorem	NOUN
ejpam-5783	179	3	shows	show	VERB
ejpam-5783	179	4	that	that	SCONJ
ejpam-5783	179	5	if	if	SCONJ
ejpam-5783	179	6	an	an	DET
ejpam-5783	179	7	element	element	NOUN
ejpam-5783	179	8	is	be	AUX
ejpam-5783	179	9	in	in	ADP
ejpam-5783	179	10	the	the	DET
ejpam-5783	179	11	sheffer	sheffer	NOUN
ejpam-5783	179	12	stroke	stroke	NOUN
ejpam-5783	179	13	bn	bn	NOUN
ejpam-5783	179	14	-	-	PUNCT
ejpam-5783	179	15	ideal	ideal	NOUN
ejpam-5783	179	16	and	and	CCONJ
ejpam-5783	179	17	fulfills	fulfill	VERB
ejpam-5783	179	18	certain	certain	ADJ
ejpam-5783	179	19	relationships	relationship	NOUN
ejpam-5783	179	20	,	,	PUNCT
ejpam-5783	179	21	then	then	ADV
ejpam-5783	179	22	there	there	PRON
ejpam-5783	179	23	are	be	VERB
ejpam-5783	179	24	other	other	ADJ
ejpam-5783	179	25	elements	element	NOUN
ejpam-5783	179	26	that	that	PRON
ejpam-5783	179	27	are	be	AUX
ejpam-5783	179	28	also	also	ADV
ejpam-5783	179	29	included	include	VERB
ejpam-5783	179	30	in	in	ADP
ejpam-5783	179	31	the	the	DET
ejpam-5783	179	32	sheffer	sheffer	NOUN
ejpam-5783	179	33	stroke	stroke	NOUN
ejpam-5783	179	34	bn	bn	NOUN
ejpam-5783	179	35	-	-	PUNCT
ejpam-5783	179	36	ideal	ideal	NOUN
ejpam-5783	179	37	.	.	PUNCT
ejpam-5783	180	1	theorem	theorem	NOUN
ejpam-5783	180	2	5	5	NUM
ejpam-5783	180	3	.	.	PUNCT
ejpam-5783	181	1	let	let	AUX
ejpam-5783	181	2	(	(	PUNCT
ejpam-5783	181	3	psbn	psbn	NOUN
ejpam-5783	181	4	;	;	PUNCT
ejpam-5783	181	5	|	|	ADV
ejpam-5783	181	6	,	,	PUNCT
ejpam-5783	181	7	0	0	NUM
ejpam-5783	181	8	)	)	PUNCT
ejpam-5783	181	9	be	be	AUX
ejpam-5783	181	10	a	a	DET
ejpam-5783	181	11	sheffer	sheffer	NOUN
ejpam-5783	181	12	stroke	stroke	NOUN
ejpam-5783	181	13	bn	bn	NOUN
ejpam-5783	181	14	-	-	PUNCT
ejpam-5783	181	15	algebra	algebra	NOUN
ejpam-5783	181	16	and	and	CCONJ
ejpam-5783	181	17	let	let	VERB
ejpam-5783	181	18	i	i	PRON
ejpam-5783	181	19	be	be	AUX
ejpam-5783	181	20	a	a	DET
ejpam-5783	181	21	sheffer	sheffer	NOUN
ejpam-5783	181	22	stroke	stroke	NOUN
ejpam-5783	181	23	bn	bn	NOUN
ejpam-5783	181	24	-	-	PUNCT
ejpam-5783	181	25	ideal	ideal	NOUN
ejpam-5783	181	26	of	of	ADP
ejpam-5783	181	27	psbn	psbn	NOUN
ejpam-5783	181	28	.	.	PUNCT
ejpam-5783	182	1	if	if	SCONJ
ejpam-5783	182	2	b	b	X
ejpam-5783	182	3	∈	∈	PROPN
ejpam-5783	182	4	i	i	PRON
ejpam-5783	182	5	and	and	CCONJ
ejpam-5783	182	6	(	(	PUNCT
ejpam-5783	182	7	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	182	8	)	)	PUNCT
ejpam-5783	182	9	)	)	PUNCT
ejpam-5783	183	1	=	=	SYM
ejpam-5783	183	2	0	0	NUM
ejpam-5783	183	3	,	,	PUNCT
ejpam-5783	183	4	then	then	ADV
ejpam-5783	183	5	a	a	DET
ejpam-5783	183	6	∈	∈	NOUN
ejpam-5783	183	7	i	i	PRON
ejpam-5783	183	8	for	for	ADP
ejpam-5783	183	9	all	all	DET
ejpam-5783	183	10	a	a	DET
ejpam-5783	183	11	,	,	PUNCT
ejpam-5783	183	12	b	b	PROPN
ejpam-5783	183	13	∈	∈	PROPN
ejpam-5783	183	14	psbn	psbn	NOUN
ejpam-5783	183	15	.	.	PUNCT
ejpam-5783	184	1	s.	s.	PROPN
ejpam-5783	184	2	gemawati	gemawati	PROPN
ejpam-5783	184	3	et	et	PROPN
ejpam-5783	184	4	al	al	PROPN
ejpam-5783	184	5	.	.	PUNCT
ejpam-5783	184	6	/	/	SYM
ejpam-5783	184	7	eur	eur	PROPN
ejpam-5783	184	8	.	.	PUNCT
ejpam-5783	185	1	j.	j.	PROPN
ejpam-5783	185	2	pure	pure	PROPN
ejpam-5783	185	3	appl	appl	PROPN
ejpam-5783	185	4	.	.	PROPN
ejpam-5783	185	5	math	math	PROPN
ejpam-5783	185	6	,	,	PUNCT
ejpam-5783	185	7	18	18	NUM
ejpam-5783	185	8	(	(	PUNCT
ejpam-5783	185	9	1	1	NUM
ejpam-5783	185	10	)	)	PUNCT
ejpam-5783	185	11	(	(	PUNCT
ejpam-5783	185	12	2025	2025	NUM
ejpam-5783	185	13	)	)	PUNCT
ejpam-5783	185	14	,	,	PUNCT
ejpam-5783	185	15	5783	5783	NUM
ejpam-5783	185	16	8	8	NUM
ejpam-5783	185	17	of	of	ADP
ejpam-5783	185	18	12	12	NUM
ejpam-5783	185	19	proof	proof	NOUN
ejpam-5783	185	20	.	.	PUNCT
ejpam-5783	186	1	let	let	AUX
ejpam-5783	186	2	(	(	PUNCT
ejpam-5783	186	3	psbn	psbn	NOUN
ejpam-5783	186	4	;	;	PUNCT
ejpam-5783	186	5	|	|	ADV
ejpam-5783	186	6	,	,	PUNCT
ejpam-5783	186	7	0	0	NUM
ejpam-5783	186	8	)	)	PUNCT
ejpam-5783	186	9	be	be	AUX
ejpam-5783	186	10	a	a	DET
ejpam-5783	186	11	sheffer	sheffer	NOUN
ejpam-5783	186	12	stroke	stroke	NOUN
ejpam-5783	186	13	bn	bn	NOUN
ejpam-5783	186	14	-	-	PUNCT
ejpam-5783	186	15	algebra	algebra	NOUN
ejpam-5783	186	16	.	.	PUNCT
ejpam-5783	187	1	since	since	SCONJ
ejpam-5783	187	2	i	i	PRON
ejpam-5783	187	3	is	be	AUX
ejpam-5783	187	4	a	a	DET
ejpam-5783	187	5	sheffer	sheffer	NOUN
ejpam-5783	187	6	stroke	stroke	NOUN
ejpam-5783	187	7	bn	bn	NOUN
ejpam-5783	187	8	-	-	PUNCT
ejpam-5783	187	9	ideal	ideal	NOUN
ejpam-5783	187	10	of	of	ADP
ejpam-5783	187	11	psbn	psbn	NOUN
ejpam-5783	187	12	,	,	PUNCT
ejpam-5783	187	13	we	we	PRON
ejpam-5783	187	14	have	have	VERB
ejpam-5783	187	15	0	0	NUM
ejpam-5783	187	16	∈	∈	PROPN
ejpam-5783	187	17	i.	i.	NOUN
ejpam-5783	187	18	given	give	VERB
ejpam-5783	187	19	that	that	DET
ejpam-5783	187	20	b	b	X
ejpam-5783	187	21	∈	∈	PROPN
ejpam-5783	187	22	i	i	PRON
ejpam-5783	187	23	,	,	PUNCT
ejpam-5783	187	24	(	(	PUNCT
ejpam-5783	187	25	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	187	26	)	)	PUNCT
ejpam-5783	187	27	)	)	PUNCT
ejpam-5783	188	1	∈	∈	PROPN
ejpam-5783	189	1	i	i	PRON
ejpam-5783	189	2	,	,	PUNCT
ejpam-5783	189	3	it	it	PRON
ejpam-5783	189	4	follows	follow	VERB
ejpam-5783	189	5	that	that	SCONJ
ejpam-5783	189	6	a	a	DET
ejpam-5783	189	7	∈	∈	PROPN
ejpam-5783	189	8	i.	i.	NOUN
ejpam-5783	189	9	moreover	moreover	ADV
ejpam-5783	189	10	,	,	PUNCT
ejpam-5783	189	11	since	since	SCONJ
ejpam-5783	189	12	(	(	PUNCT
ejpam-5783	189	13	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	189	14	)	)	PUNCT
ejpam-5783	189	15	)	)	PUNCT
ejpam-5783	190	1	=	=	SYM
ejpam-5783	190	2	0	0	PUNCT
ejpam-5783	191	1	∈	∈	PROPN
ejpam-5783	191	2	i	i	PRON
ejpam-5783	191	3	,	,	PUNCT
ejpam-5783	191	4	we	we	PRON
ejpam-5783	191	5	conclude	conclude	VERB
ejpam-5783	191	6	that	that	SCONJ
ejpam-5783	191	7	a	a	DET
ejpam-5783	191	8	∈	∈	NOUN
ejpam-5783	191	9	i	i	PRON
ejpam-5783	191	10	for	for	ADP
ejpam-5783	191	11	all	all	DET
ejpam-5783	191	12	a	a	DET
ejpam-5783	191	13	,	,	PUNCT
ejpam-5783	191	14	b	b	PROPN
ejpam-5783	191	15	∈	∈	PROPN
ejpam-5783	191	16	psbn	psbn	NOUN
ejpam-5783	191	17	.	.	PUNCT
ejpam-5783	192	1	the	the	DET
ejpam-5783	192	2	following	follow	VERB
ejpam-5783	192	3	theorem	theorem	ADJ
ejpam-5783	192	4	addresses	address	NOUN
ejpam-5783	192	5	the	the	DET
ejpam-5783	192	6	relationship	relationship	NOUN
ejpam-5783	192	7	between	between	ADP
ejpam-5783	192	8	sheffer	sheffer	PROPN
ejpam-5783	192	9	stroke	stroke	PROPN
ejpam-5783	192	10	bn	bn	PROPN
ejpam-5783	192	11	-	-	PUNCT
ejpam-5783	192	12	subalgebras	subalgebras	PROPN
ejpam-5783	192	13	,	,	PUNCT
ejpam-5783	192	14	normal	normal	ADJ
ejpam-5783	192	15	subsets	subset	NOUN
ejpam-5783	192	16	,	,	PUNCT
ejpam-5783	192	17	and	and	CCONJ
ejpam-5783	192	18	sheffer	sheffer	VERB
ejpam-5783	192	19	stroke	stroke	PROPN
ejpam-5783	192	20	bn	bn	NOUN
ejpam-5783	192	21	-	-	PUNCT
ejpam-5783	192	22	ideals	ideal	NOUN
ejpam-5783	192	23	.	.	PUNCT
ejpam-5783	193	1	theorem	theorem	NOUN
ejpam-5783	193	2	6	6	NUM
ejpam-5783	193	3	.	.	PUNCT
ejpam-5783	194	1	let	let	AUX
ejpam-5783	194	2	(	(	PUNCT
ejpam-5783	194	3	psbn	psbn	NOUN
ejpam-5783	194	4	;	;	PUNCT
ejpam-5783	194	5	|	|	ADV
ejpam-5783	194	6	,	,	PUNCT
ejpam-5783	194	7	0	0	NUM
ejpam-5783	194	8	)	)	PUNCT
ejpam-5783	194	9	be	be	AUX
ejpam-5783	194	10	a	a	DET
ejpam-5783	194	11	sheffer	sheffer	NOUN
ejpam-5783	194	12	stroke	stroke	NOUN
ejpam-5783	194	13	bn	bn	NOUN
ejpam-5783	194	14	-	-	PUNCT
ejpam-5783	194	15	algebra	algebra	NOUN
ejpam-5783	194	16	.	.	PUNCT
ejpam-5783	195	1	if	if	SCONJ
ejpam-5783	195	2	n	n	PRON
ejpam-5783	195	3	is	be	AUX
ejpam-5783	195	4	a	a	DET
ejpam-5783	195	5	normal	normal	ADJ
ejpam-5783	195	6	subset	subset	NOUN
ejpam-5783	195	7	of	of	ADP
ejpam-5783	195	8	psbn	psbn	NOUN
ejpam-5783	195	9	,	,	PUNCT
ejpam-5783	195	10	then	then	ADV
ejpam-5783	195	11	n	n	PRON
ejpam-5783	195	12	is	be	AUX
ejpam-5783	195	13	a	a	DET
ejpam-5783	195	14	sheffer	sheffer	NOUN
ejpam-5783	195	15	stroke	stroke	NOUN
ejpam-5783	195	16	bn	bn	NOUN
ejpam-5783	195	17	-	-	PUNCT
ejpam-5783	195	18	subalgebra	subalgebra	NOUN
ejpam-5783	195	19	of	of	ADP
ejpam-5783	195	20	psbn	psbn	NOUN
ejpam-5783	195	21	.	.	PUNCT
ejpam-5783	196	1	proof	proof	NOUN
ejpam-5783	196	2	.	.	PUNCT
ejpam-5783	197	1	let	let	AUX
ejpam-5783	197	2	(	(	PUNCT
ejpam-5783	197	3	psbn	psbn	NOUN
ejpam-5783	197	4	;	;	PUNCT
ejpam-5783	197	5	|	|	ADV
ejpam-5783	197	6	,	,	PUNCT
ejpam-5783	197	7	0	0	NUM
ejpam-5783	197	8	)	)	PUNCT
ejpam-5783	197	9	be	be	AUX
ejpam-5783	197	10	a	a	DET
ejpam-5783	197	11	sheffer	sheffer	NOUN
ejpam-5783	197	12	stroke	stroke	NOUN
ejpam-5783	197	13	bn	bn	NOUN
ejpam-5783	197	14	-	-	PUNCT
ejpam-5783	197	15	algebra	algebra	NOUN
ejpam-5783	197	16	and	and	CCONJ
ejpam-5783	197	17	a	a	DET
ejpam-5783	197	18	,	,	PUNCT
ejpam-5783	197	19	b	b	PROPN
ejpam-5783	197	20	∈	∈	PROPN
ejpam-5783	197	21	n	n	ADV
ejpam-5783	197	22	.	.	PUNCT
ejpam-5783	198	1	by	by	ADP
ejpam-5783	198	2	using	use	VERB
ejpam-5783	198	3	axiom	axiom	NOUN
ejpam-5783	198	4	(	(	PUNCT
ejpam-5783	198	5	sbn1	sbn1	PROPN
ejpam-5783	198	6	)	)	PUNCT
ejpam-5783	198	7	,	,	PUNCT
ejpam-5783	198	8	we	we	PRON
ejpam-5783	198	9	obtain	obtain	VERB
ejpam-5783	198	10	(	(	PUNCT
ejpam-5783	198	11	a|(0|0))|(a|(0|0	a|(0|0))|(a|(0|0	PROPN
ejpam-5783	198	12	)	)	PUNCT
ejpam-5783	198	13	)	)	PUNCT
ejpam-5783	199	1	∈	∈	PROPN
ejpam-5783	199	2	n	n	NOUN
ejpam-5783	199	3	and	and	CCONJ
ejpam-5783	199	4	(	(	PUNCT
ejpam-5783	199	5	b|(0|0))|(b|(0|0	b|(0|0))|(b|(0|0	PROPN
ejpam-5783	199	6	)	)	PUNCT
ejpam-5783	199	7	)	)	PUNCT
ejpam-5783	200	1	∈	∈	PROPN
ejpam-5783	200	2	n	n	ADV
ejpam-5783	200	3	.	.	PUNCT
ejpam-5783	201	1	then	then	ADV
ejpam-5783	201	2	,	,	PUNCT
ejpam-5783	201	3	by	by	ADP
ejpam-5783	201	4	using	use	VERB
ejpam-5783	201	5	axiom	axiom	NOUN
ejpam-5783	201	6	(	(	PUNCT
ejpam-5783	201	7	sbn1	sbn1	PROPN
ejpam-5783	201	8	)	)	PUNCT
ejpam-5783	201	9	,	,	PUNCT
ejpam-5783	201	10	theorem	theorem	VERB
ejpam-5783	201	11	3	3	NUM
ejpam-5783	201	12	(	(	PUNCT
ejpam-5783	201	13	iv	iv	NUM
ejpam-5783	201	14	)	)	PUNCT
ejpam-5783	201	15	,	,	PUNCT
ejpam-5783	201	16	and	and	CCONJ
ejpam-5783	201	17	the	the	DET
ejpam-5783	201	18	fact	fact	NOUN
ejpam-5783	201	19	that	that	SCONJ
ejpam-5783	201	20	n	n	PRON
ejpam-5783	201	21	is	be	AUX
ejpam-5783	201	22	a	a	DET
ejpam-5783	201	23	normal	normal	ADJ
ejpam-5783	201	24	subset	subset	NOUN
ejpam-5783	201	25	of	of	ADP
ejpam-5783	201	26	psbn	psbn	NOUN
ejpam-5783	201	27	,	,	PUNCT
ejpam-5783	201	28	we	we	PRON
ejpam-5783	201	29	obtain	obtain	VERB
ejpam-5783	201	30	(	(	PUNCT
ejpam-5783	201	31	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	201	32	)	)	PUNCT
ejpam-5783	201	33	)	)	PUNCT
ejpam-5783	202	1	=	=	PUNCT
ejpam-5783	202	2	(	(	PUNCT
ejpam-5783	202	3	(	(	PUNCT
ejpam-5783	202	4	(	(	PUNCT
ejpam-5783	202	5	a|(b|b))|(a|(b|b)))|(0|0))|(((a|(b|b))|(a|(b|b)))|(0|0	a|(b|b))|(a|(b|b)))|(0|0))|(((a|(b|b))|(a|(b|b)))|(0|0	NUM
ejpam-5783	202	6	)	)	PUNCT
ejpam-5783	202	7	)	)	PUNCT
ejpam-5783	202	8	,	,	PUNCT
ejpam-5783	202	9	such	such	ADJ
ejpam-5783	202	10	that	that	SCONJ
ejpam-5783	202	11	,	,	PUNCT
ejpam-5783	202	12	(	(	PUNCT
ejpam-5783	202	13	(	(	PUNCT
ejpam-5783	202	14	(	(	PUNCT
ejpam-5783	202	15	a|(b|b))|(a|(b|b)))|(0|(0|0)))|(((a|(b|b))|(a|(b|b)))|(0|(0|0	a|(b|b))|(a|(b|b)))|(0|(0|0)))|(((a|(b|b))|(a|(b|b)))|(0|(0|0	NOUN
ejpam-5783	202	16	)	)	PUNCT
ejpam-5783	202	17	)	)	PUNCT
ejpam-5783	202	18	)	)	PUNCT
ejpam-5783	203	1	∈	∈	PROPN
ejpam-5783	203	2	n	n	NOUN
ejpam-5783	203	3	.	.	PUNCT
ejpam-5783	204	1	thus	thus	ADV
ejpam-5783	204	2	,	,	PUNCT
ejpam-5783	204	3	it	it	PRON
ejpam-5783	204	4	has	have	AUX
ejpam-5783	204	5	been	be	AUX
ejpam-5783	204	6	proven	prove	VERB
ejpam-5783	204	7	that	that	SCONJ
ejpam-5783	204	8	n	n	PRON
ejpam-5783	204	9	is	be	AUX
ejpam-5783	204	10	a	a	DET
ejpam-5783	204	11	bn	bn	NOUN
ejpam-5783	204	12	-	-	PUNCT
ejpam-5783	204	13	subalgebra	subalgebra	NOUN
ejpam-5783	204	14	of	of	ADP
ejpam-5783	204	15	psbn	psbn	NOUN
ejpam-5783	204	16	.	.	PUNCT
ejpam-5783	205	1	the	the	DET
ejpam-5783	205	2	converse	converse	NOUN
ejpam-5783	205	3	of	of	ADP
ejpam-5783	205	4	theorem	theorem	NOUN
ejpam-5783	205	5	6	6	NUM
ejpam-5783	205	6	does	do	AUX
ejpam-5783	205	7	not	not	PART
ejpam-5783	205	8	hold	hold	VERB
ejpam-5783	205	9	in	in	ADP
ejpam-5783	205	10	general	general	ADJ
ejpam-5783	205	11	.	.	PUNCT
ejpam-5783	206	1	in	in	ADP
ejpam-5783	206	2	sheffer	sheffer	PROPN
ejpam-5783	206	3	stroke	stroke	PROPN
ejpam-5783	206	4	bn	bn	PROPN
ejpam-5783	206	5	-	-	PUNCT
ejpam-5783	206	6	algebras	algebras	X
ejpam-5783	206	7	,	,	PUNCT
ejpam-5783	206	8	it	it	PRON
ejpam-5783	206	9	is	be	AUX
ejpam-5783	206	10	important	important	ADJ
ejpam-5783	206	11	to	to	PART
ejpam-5783	206	12	understand	understand	VERB
ejpam-5783	206	13	that	that	SCONJ
ejpam-5783	206	14	normal	normal	ADJ
ejpam-5783	206	15	sets	set	NOUN
ejpam-5783	206	16	always	always	ADV
ejpam-5783	206	17	form	form	VERB
ejpam-5783	206	18	bn	bn	NOUN
ejpam-5783	206	19	-	-	PUNCT
ejpam-5783	206	20	subalgebras	subalgebras	PROPN
ejpam-5783	206	21	.	.	PUNCT
ejpam-5783	207	1	theorem	theorem	ADJ
ejpam-5783	207	2	6	6	NUM
ejpam-5783	207	3	shows	show	VERB
ejpam-5783	207	4	that	that	SCONJ
ejpam-5783	207	5	if	if	SCONJ
ejpam-5783	207	6	a	a	DET
ejpam-5783	207	7	subset	subset	NOUN
ejpam-5783	207	8	is	be	AUX
ejpam-5783	207	9	normal	normal	ADJ
ejpam-5783	207	10	,	,	PUNCT
ejpam-5783	207	11	then	then	ADV
ejpam-5783	207	12	its	its	PRON
ejpam-5783	207	13	elements	element	NOUN
ejpam-5783	207	14	will	will	AUX
ejpam-5783	207	15	remain	remain	VERB
ejpam-5783	207	16	connected	connected	ADJ
ejpam-5783	207	17	via	via	ADP
ejpam-5783	207	18	the	the	DET
ejpam-5783	207	19	sheffer	sheffer	NOUN
ejpam-5783	207	20	stroke	stroke	NOUN
ejpam-5783	207	21	operation	operation	NOUN
ejpam-5783	207	22	,	,	PUNCT
ejpam-5783	207	23	satisfying	satisfy	VERB
ejpam-5783	207	24	the	the	DET
ejpam-5783	207	25	condition	condition	NOUN
ejpam-5783	207	26	for	for	SCONJ
ejpam-5783	207	27	it	it	PRON
ejpam-5783	207	28	to	to	PART
ejpam-5783	207	29	be	be	AUX
ejpam-5783	207	30	a	a	DET
ejpam-5783	207	31	bn	bn	NOUN
ejpam-5783	207	32	-	-	PUNCT
ejpam-5783	207	33	subalgebra	subalgebra	NOUN
ejpam-5783	207	34	.	.	PUNCT
ejpam-5783	208	1	however	however	ADV
ejpam-5783	208	2	,	,	PUNCT
ejpam-5783	208	3	not	not	PART
ejpam-5783	208	4	all	all	DET
ejpam-5783	208	5	bn	bn	NOUN
ejpam-5783	208	6	-	-	PUNCT
ejpam-5783	208	7	subalgebras	subalgebra	NOUN
ejpam-5783	208	8	are	be	AUX
ejpam-5783	208	9	normal	normal	ADJ
ejpam-5783	208	10	,	,	PUNCT
ejpam-5783	208	11	as	as	SCONJ
ejpam-5783	208	12	shown	show	VERB
ejpam-5783	208	13	in	in	ADP
ejpam-5783	208	14	example	example	NOUN
ejpam-5783	208	15	2	2	NUM
ejpam-5783	208	16	.	.	PUNCT
ejpam-5783	209	1	the	the	DET
ejpam-5783	209	2	subset	subset	NOUN
ejpam-5783	209	3	n	n	NOUN
ejpam-5783	209	4	=	=	SYM
ejpam-5783	209	5	{	{	PUNCT
ejpam-5783	209	6	0	0	NUM
ejpam-5783	209	7	,	,	PUNCT
ejpam-5783	209	8	1	1	NUM
ejpam-5783	209	9	}	}	PUNCT
ejpam-5783	209	10	is	be	AUX
ejpam-5783	209	11	a	a	DET
ejpam-5783	209	12	sheffer	sheffer	NOUN
ejpam-5783	209	13	stroke	stroke	NOUN
ejpam-5783	209	14	bn	bn	NOUN
ejpam-5783	209	15	-	-	PUNCT
ejpam-5783	209	16	subalgebra	subalgebra	NOUN
ejpam-5783	209	17	of	of	ADP
ejpam-5783	209	18	psbn	psbn	NOUN
ejpam-5783	209	19	,	,	PUNCT
ejpam-5783	209	20	but	but	CCONJ
ejpam-5783	209	21	it	it	PRON
ejpam-5783	209	22	is	be	AUX
ejpam-5783	209	23	not	not	PART
ejpam-5783	209	24	a	a	DET
ejpam-5783	209	25	normal	normal	ADJ
ejpam-5783	209	26	subset	subset	NOUN
ejpam-5783	209	27	of	of	ADP
ejpam-5783	209	28	psbn	psbn	NOUN
ejpam-5783	209	29	,	,	PUNCT
ejpam-5783	209	30	since	since	SCONJ
ejpam-5783	209	31	(	(	PUNCT
ejpam-5783	209	32	1|(1|1))|1|(1|1	1|(1|1))|1|(1|1	NUM
ejpam-5783	209	33	)	)	PUNCT
ejpam-5783	209	34	)	)	PUNCT
ejpam-5783	210	1	=	=	SYM
ejpam-5783	210	2	(	(	PUNCT
ejpam-5783	210	3	1|0)|(1|0	1|0)|(1|0	NUM
ejpam-5783	210	4	)	)	PUNCT
ejpam-5783	210	5	=	=	SYM
ejpam-5783	211	1	1|1	1|1	NUM
ejpam-5783	211	2	=	=	SYM
ejpam-5783	211	3	0	0	PUNCT
ejpam-5783	211	4	∈	∈	PROPN
ejpam-5783	211	5	i	i	PRON
ejpam-5783	211	6	,	,	PUNCT
ejpam-5783	211	7	and	and	CCONJ
ejpam-5783	211	8	(	(	PUNCT
ejpam-5783	211	9	0|(p|p))|(0|(p|p	0|(p|p))|(0|(p|p	PROPN
ejpam-5783	211	10	)	)	PUNCT
ejpam-5783	211	11	)	)	PUNCT
ejpam-5783	212	1	=	=	PRON
ejpam-5783	212	2	(	(	PUNCT
ejpam-5783	212	3	0|q)|(0|q	0|q)|(0|q	PROPN
ejpam-5783	212	4	)	)	PUNCT
ejpam-5783	212	5	=	=	PUNCT
ejpam-5783	213	1	1|1	1|1	NUM
ejpam-5783	213	2	=	=	SYM
ejpam-5783	213	3	0	0	NUM
ejpam-5783	213	4	∈	∈	PROPN
ejpam-5783	213	5	i.	i.	NOUN
ejpam-5783	213	6	however	however	ADV
ejpam-5783	213	7	,	,	PUNCT
ejpam-5783	213	8	(	(	PUNCT
ejpam-5783	213	9	(	(	PUNCT
ejpam-5783	213	10	1|(0|0))|(1|(0|0)))|(1|(p|p	1|(0|0))|(1|(0|0)))|(1|(p|p	NUM
ejpam-5783	213	11	)	)	PUNCT
ejpam-5783	213	12	)	)	PUNCT
ejpam-5783	214	1	=	=	SYM
ejpam-5783	214	2	(	(	PUNCT
ejpam-5783	214	3	(	(	PUNCT
ejpam-5783	214	4	1|1)|(1|1))|(1|q	1|1)|(1|1))|(1|q	NUM
ejpam-5783	214	5	)	)	PUNCT
ejpam-5783	214	6	=	=	PUNCT
ejpam-5783	215	1	(	(	PUNCT
ejpam-5783	215	2	0|0)|p	0|0)|p	NOUN
ejpam-5783	215	3	=	=	SYM
ejpam-5783	216	1	1|p	1|p	NUM
ejpam-5783	216	2	=	=	SYM
ejpam-5783	217	1	q	q	ADJ
ejpam-5783	217	2	,	,	PUNCT
ejpam-5783	217	3	and	and	CCONJ
ejpam-5783	217	4	hence	hence	ADV
ejpam-5783	217	5	(	(	PUNCT
ejpam-5783	217	6	(	(	PUNCT
ejpam-5783	217	7	1|(0|0))|(1|(0|0)))|(1|(p|p))|((1|(0|0))|(1|(0|0)))|(1|(p|p	1|(0|0))|(1|(0|0)))|(1|(p|p))|((1|(0|0))|(1|(0|0)))|(1|(p|p	NUM
ejpam-5783	217	8	)	)	PUNCT
ejpam-5783	217	9	)	)	PUNCT
ejpam-5783	218	1	=	=	PUNCT
ejpam-5783	218	2	q|q	q|q	X
ejpam-5783	219	1	=	=	PUNCT
ejpam-5783	219	2	p	p	X
ejpam-5783	219	3	∈	∈	PROPN
ejpam-5783	219	4	n	n	X
ejpam-5783	219	5	.	.	PUNCT
ejpam-5783	220	1	s.	s.	PROPN
ejpam-5783	220	2	gemawati	gemawati	PROPN
ejpam-5783	220	3	et	et	PROPN
ejpam-5783	220	4	al	al	PROPN
ejpam-5783	220	5	.	.	PUNCT
ejpam-5783	220	6	/	/	SYM
ejpam-5783	220	7	eur	eur	PROPN
ejpam-5783	220	8	.	.	PUNCT
ejpam-5783	221	1	j.	j.	PROPN
ejpam-5783	221	2	pure	pure	PROPN
ejpam-5783	221	3	appl	appl	PROPN
ejpam-5783	221	4	.	.	PROPN
ejpam-5783	221	5	math	math	PROPN
ejpam-5783	221	6	,	,	PUNCT
ejpam-5783	221	7	18	18	NUM
ejpam-5783	221	8	(	(	PUNCT
ejpam-5783	221	9	1	1	NUM
ejpam-5783	221	10	)	)	PUNCT
ejpam-5783	221	11	(	(	PUNCT
ejpam-5783	221	12	2025	2025	NUM
ejpam-5783	221	13	)	)	PUNCT
ejpam-5783	221	14	,	,	PUNCT
ejpam-5783	221	15	5783	5783	NUM
ejpam-5783	221	16	9	9	NUM
ejpam-5783	221	17	of	of	ADP
ejpam-5783	221	18	12	12	NUM
ejpam-5783	221	19	corollary	corollary	ADJ
ejpam-5783	221	20	1	1	NUM
ejpam-5783	221	21	.	.	PUNCT
ejpam-5783	222	1	let	let	AUX
ejpam-5783	222	2	(	(	PUNCT
ejpam-5783	222	3	psbn	psbn	NOUN
ejpam-5783	222	4	;	;	PUNCT
ejpam-5783	222	5	|	|	ADV
ejpam-5783	222	6	,	,	PUNCT
ejpam-5783	222	7	0	0	NUM
ejpam-5783	222	8	)	)	PUNCT
ejpam-5783	222	9	be	be	AUX
ejpam-5783	222	10	a	a	DET
ejpam-5783	222	11	sheffer	sheffer	NOUN
ejpam-5783	222	12	stroke	stroke	NOUN
ejpam-5783	222	13	bn	bn	NOUN
ejpam-5783	222	14	-	-	PUNCT
ejpam-5783	222	15	algebra	algebra	NOUN
ejpam-5783	222	16	.	.	PUNCT
ejpam-5783	223	1	if	if	SCONJ
ejpam-5783	223	2	i	i	PRON
ejpam-5783	223	3	is	be	AUX
ejpam-5783	223	4	a	a	DET
ejpam-5783	223	5	sheffer	sheffer	NOUN
ejpam-5783	223	6	stroke	stroke	NOUN
ejpam-5783	223	7	normal	normal	ADJ
ejpam-5783	223	8	bn	bn	NOUN
ejpam-5783	223	9	-	-	PUNCT
ejpam-5783	223	10	ideal	ideal	NOUN
ejpam-5783	223	11	of	of	ADP
ejpam-5783	223	12	psbn	psbn	NOUN
ejpam-5783	223	13	,	,	PUNCT
ejpam-5783	223	14	then	then	ADV
ejpam-5783	223	15	i	i	PRON
ejpam-5783	223	16	is	be	AUX
ejpam-5783	223	17	a	a	DET
ejpam-5783	223	18	sheffer	sheffer	NOUN
ejpam-5783	223	19	stroke	stroke	NOUN
ejpam-5783	223	20	bn	bn	NOUN
ejpam-5783	223	21	-	-	PUNCT
ejpam-5783	223	22	subalgebra	subalgebra	NOUN
ejpam-5783	223	23	of	of	ADP
ejpam-5783	223	24	psbn	psbn	NOUN
ejpam-5783	223	25	.	.	PUNCT
ejpam-5783	224	1	proof	proof	NOUN
ejpam-5783	224	2	.	.	PUNCT
ejpam-5783	225	1	let	let	AUX
ejpam-5783	225	2	(	(	PUNCT
ejpam-5783	225	3	psbn	psbn	NOUN
ejpam-5783	225	4	;	;	PUNCT
ejpam-5783	225	5	|	|	ADV
ejpam-5783	225	6	,	,	PUNCT
ejpam-5783	225	7	0	0	NUM
ejpam-5783	225	8	)	)	PUNCT
ejpam-5783	225	9	be	be	AUX
ejpam-5783	225	10	a	a	DET
ejpam-5783	225	11	sheffer	sheffer	NOUN
ejpam-5783	225	12	stroke	stroke	NOUN
ejpam-5783	225	13	bn	bn	NOUN
ejpam-5783	225	14	-	-	PUNCT
ejpam-5783	225	15	algebra	algebra	NOUN
ejpam-5783	225	16	.	.	PUNCT
ejpam-5783	226	1	since	since	SCONJ
ejpam-5783	226	2	i	i	PRON
ejpam-5783	226	3	is	be	AUX
ejpam-5783	226	4	both	both	CCONJ
ejpam-5783	226	5	a	a	DET
ejpam-5783	226	6	bn	bn	ADJ
ejpam-5783	226	7	-	-	PUNCT
ejpam-5783	226	8	ideal	ideal	NOUN
ejpam-5783	226	9	and	and	CCONJ
ejpam-5783	226	10	normal	normal	ADJ
ejpam-5783	226	11	in	in	ADP
ejpam-5783	226	12	psbn	psbn	NOUN
ejpam-5783	226	13	,	,	PUNCT
ejpam-5783	226	14	it	it	PRON
ejpam-5783	226	15	follows	follow	VERB
ejpam-5783	226	16	from	from	ADP
ejpam-5783	226	17	theorem	theorem	NOUN
ejpam-5783	226	18	6	6	NUM
ejpam-5783	226	19	that	that	SCONJ
ejpam-5783	226	20	i	i	PRON
ejpam-5783	226	21	is	be	AUX
ejpam-5783	226	22	a	a	DET
ejpam-5783	226	23	sheffer	sheffer	NOUN
ejpam-5783	226	24	stroke	stroke	NOUN
ejpam-5783	226	25	bn	bn	NOUN
ejpam-5783	226	26	-	-	PUNCT
ejpam-5783	226	27	subalgebra	subalgebra	NOUN
ejpam-5783	226	28	of	of	ADP
ejpam-5783	226	29	psbn	psbn	NOUN
ejpam-5783	226	30	.	.	PUNCT
ejpam-5783	227	1	the	the	DET
ejpam-5783	227	2	converse	converse	NOUN
ejpam-5783	227	3	of	of	ADP
ejpam-5783	227	4	corollary	corollary	ADJ
ejpam-5783	227	5	1	1	NUM
ejpam-5783	227	6	does	do	AUX
ejpam-5783	227	7	not	not	PART
ejpam-5783	227	8	hold	hold	VERB
ejpam-5783	227	9	in	in	ADP
ejpam-5783	227	10	general	general	ADJ
ejpam-5783	227	11	.	.	PUNCT
ejpam-5783	228	1	corollary	corollary	ADJ
ejpam-5783	228	2	1	1	NUM
ejpam-5783	228	3	reinforces	reinforce	VERB
ejpam-5783	228	4	the	the	DET
ejpam-5783	228	5	idea	idea	NOUN
ejpam-5783	228	6	that	that	SCONJ
ejpam-5783	228	7	in	in	ADP
ejpam-5783	228	8	a	a	DET
ejpam-5783	228	9	sheffer	sheffer	NOUN
ejpam-5783	228	10	stroke	stroke	NOUN
ejpam-5783	228	11	bn	bn	NOUN
ejpam-5783	228	12	-	-	PUNCT
ejpam-5783	228	13	algebra	algebra	NOUN
ejpam-5783	228	14	,	,	PUNCT
ejpam-5783	228	15	sets	set	NOUN
ejpam-5783	228	16	that	that	PRON
ejpam-5783	228	17	are	be	AUX
ejpam-5783	228	18	both	both	PRON
ejpam-5783	228	19	bn	bn	ADJ
ejpam-5783	228	20	-	-	PUNCT
ejpam-5783	228	21	ideal	ideal	ADJ
ejpam-5783	228	22	and	and	CCONJ
ejpam-5783	228	23	normal	normal	ADJ
ejpam-5783	228	24	necessarily	necessarily	ADV
ejpam-5783	228	25	form	form	VERB
ejpam-5783	228	26	bn	bn	NOUN
ejpam-5783	228	27	-	-	PUNCT
ejpam-5783	228	28	subalgebras	subalgebras	PROPN
ejpam-5783	228	29	.	.	PUNCT
ejpam-5783	229	1	this	this	PRON
ejpam-5783	229	2	underlines	underline	VERB
ejpam-5783	229	3	that	that	SCONJ
ejpam-5783	229	4	the	the	DET
ejpam-5783	229	5	normality	normality	NOUN
ejpam-5783	229	6	and	and	CCONJ
ejpam-5783	229	7	ideality	ideality	NOUN
ejpam-5783	229	8	properties	property	NOUN
ejpam-5783	229	9	in	in	ADP
ejpam-5783	229	10	this	this	DET
ejpam-5783	229	11	algebra	algebra	NOUN
ejpam-5783	229	12	have	have	VERB
ejpam-5783	229	13	a	a	DET
ejpam-5783	229	14	direct	direct	ADJ
ejpam-5783	229	15	effect	effect	NOUN
ejpam-5783	229	16	on	on	ADP
ejpam-5783	229	17	the	the	DET
ejpam-5783	229	18	structure	structure	NOUN
ejpam-5783	229	19	of	of	ADP
ejpam-5783	229	20	its	its	PRON
ejpam-5783	229	21	bnsubalgebra	bnsubalgebra	NOUN
ejpam-5783	229	22	.	.	PUNCT
ejpam-5783	230	1	however	however	ADV
ejpam-5783	230	2	,	,	PUNCT
ejpam-5783	230	3	not	not	PART
ejpam-5783	230	4	all	all	DET
ejpam-5783	230	5	bn	bn	NOUN
ejpam-5783	230	6	-	-	PUNCT
ejpam-5783	230	7	subalgebras	subalgebra	NOUN
ejpam-5783	230	8	are	be	AUX
ejpam-5783	230	9	both	both	PRON
ejpam-5783	230	10	bn	bn	ADJ
ejpam-5783	230	11	-	-	PUNCT
ejpam-5783	230	12	ideal	ideal	ADJ
ejpam-5783	230	13	and	and	CCONJ
ejpam-5783	230	14	normal	normal	ADJ
ejpam-5783	230	15	.	.	PUNCT
ejpam-5783	231	1	example	example	NOUN
ejpam-5783	231	2	2	2	NUM
ejpam-5783	231	3	shows	show	VERB
ejpam-5783	231	4	that	that	SCONJ
ejpam-5783	231	5	although	although	SCONJ
ejpam-5783	231	6	the	the	DET
ejpam-5783	231	7	sets	set	NOUN
ejpam-5783	231	8	{	{	PUNCT
ejpam-5783	231	9	0	0	NUM
ejpam-5783	231	10	,	,	PUNCT
ejpam-5783	231	11	1	1	NUM
ejpam-5783	231	12	}	}	PUNCT
ejpam-5783	231	13	and	and	CCONJ
ejpam-5783	231	14	{	{	PUNCT
ejpam-5783	231	15	0	0	NUM
ejpam-5783	231	16	,	,	PUNCT
ejpam-5783	231	17	p	p	X
ejpam-5783	231	18	,	,	PUNCT
ejpam-5783	231	19	q	q	ADJ
ejpam-5783	231	20	}	}	PUNCT
ejpam-5783	231	21	are	be	AUX
ejpam-5783	231	22	bn	bn	NOUN
ejpam-5783	231	23	-	-	PUNCT
ejpam-5783	231	24	subalgebras	subalgebras	PROPN
ejpam-5783	231	25	,	,	PUNCT
ejpam-5783	231	26	they	they	PRON
ejpam-5783	231	27	do	do	AUX
ejpam-5783	231	28	not	not	PART
ejpam-5783	231	29	qualify	qualify	VERB
ejpam-5783	231	30	as	as	ADP
ejpam-5783	231	31	bn	bn	NOUN
ejpam-5783	231	32	-	-	PUNCT
ejpam-5783	231	33	ideals	ideal	NOUN
ejpam-5783	231	34	or	or	CCONJ
ejpam-5783	231	35	normal	normal	ADJ
ejpam-5783	231	36	subsets	subset	NOUN
ejpam-5783	231	37	in	in	ADP
ejpam-5783	231	38	the	the	DET
ejpam-5783	231	39	sheffer	sheffer	NOUN
ejpam-5783	231	40	stroke	stroke	NOUN
ejpam-5783	231	41	bn	bn	NOUN
ejpam-5783	231	42	-	-	PUNCT
ejpam-5783	231	43	algebra	algebra	NOUN
ejpam-5783	231	44	.	.	PUNCT
ejpam-5783	232	1	this	this	PRON
ejpam-5783	232	2	emphasizes	emphasize	VERB
ejpam-5783	232	3	that	that	SCONJ
ejpam-5783	232	4	normal	normal	ADJ
ejpam-5783	232	5	subsets	subset	NOUN
ejpam-5783	232	6	and	and	CCONJ
ejpam-5783	232	7	bn	bn	NOUN
ejpam-5783	232	8	-	-	PUNCT
ejpam-5783	232	9	ideals	ideal	NOUN
ejpam-5783	232	10	have	have	VERB
ejpam-5783	232	11	additional	additional	ADJ
ejpam-5783	232	12	structure	structure	NOUN
ejpam-5783	232	13	compared	compare	VERB
ejpam-5783	232	14	with	with	ADP
ejpam-5783	232	15	ordinary	ordinary	ADJ
ejpam-5783	232	16	bn	bn	NOUN
ejpam-5783	232	17	-	-	PUNCT
ejpam-5783	232	18	subalgebras	subalgebras	PROPN
ejpam-5783	232	19	.	.	PUNCT
ejpam-5783	233	1	for	for	ADP
ejpam-5783	233	2	a	a	DET
ejpam-5783	233	3	sheffer	sheffer	NOUN
ejpam-5783	233	4	stroke	stroke	NOUN
ejpam-5783	233	5	bn	bn	NOUN
ejpam-5783	233	6	-	-	PUNCT
ejpam-5783	233	7	algebra	algebra	NOUN
ejpam-5783	233	8	,	,	PUNCT
ejpam-5783	233	9	we	we	PRON
ejpam-5783	233	10	will	will	AUX
ejpam-5783	233	11	define	define	VERB
ejpam-5783	233	12	a	a	DET
ejpam-5783	233	13	mapping	mapping	NOUN
ejpam-5783	233	14	called	call	VERB
ejpam-5783	233	15	a	a	DET
ejpam-5783	233	16	sheffer	sheffer	NOUN
ejpam-5783	233	17	stroke	stroke	NOUN
ejpam-5783	233	18	bnhomomorphism	bnhomomorphism	NOUN
ejpam-5783	233	19	.	.	PUNCT
ejpam-5783	234	1	this	this	DET
ejpam-5783	234	2	mapping	mapping	NOUN
ejpam-5783	234	3	connects	connect	VERB
ejpam-5783	234	4	two	two	NUM
ejpam-5783	234	5	sheffer	sheffer	NOUN
ejpam-5783	234	6	stroke	stroke	NOUN
ejpam-5783	234	7	bn	bn	NOUN
ejpam-5783	234	8	-	-	PUNCT
ejpam-5783	234	9	algebras	algebras	PROPN
ejpam-5783	234	10	by	by	ADP
ejpam-5783	234	11	ensuring	ensure	VERB
ejpam-5783	234	12	that	that	SCONJ
ejpam-5783	234	13	the	the	DET
ejpam-5783	234	14	sheffer	sheffer	NOUN
ejpam-5783	234	15	stroke	stroke	NOUN
ejpam-5783	234	16	operations	operation	NOUN
ejpam-5783	234	17	in	in	ADP
ejpam-5783	234	18	one	one	NUM
ejpam-5783	234	19	set	set	NOUN
ejpam-5783	234	20	are	be	AUX
ejpam-5783	234	21	applied	apply	VERB
ejpam-5783	234	22	consistently	consistently	ADV
ejpam-5783	234	23	in	in	ADP
ejpam-5783	234	24	the	the	DET
ejpam-5783	234	25	other	other	ADJ
ejpam-5783	234	26	set	set	NOUN
ejpam-5783	234	27	.	.	PUNCT
ejpam-5783	235	1	the	the	DET
ejpam-5783	235	2	following	follow	VERB
ejpam-5783	235	3	definition	definition	NOUN
ejpam-5783	235	4	explains	explain	VERB
ejpam-5783	235	5	the	the	DET
ejpam-5783	235	6	conditions	condition	NOUN
ejpam-5783	235	7	that	that	PRON
ejpam-5783	235	8	must	must	AUX
ejpam-5783	235	9	be	be	AUX
ejpam-5783	235	10	met	meet	VERB
ejpam-5783	235	11	by	by	ADP
ejpam-5783	235	12	this	this	DET
ejpam-5783	235	13	mapping	mapping	NOUN
ejpam-5783	235	14	.	.	PUNCT
ejpam-5783	236	1	definition	definition	NOUN
ejpam-5783	236	2	9	9	NUM
ejpam-5783	236	3	.	.	PUNCT
ejpam-5783	237	1	let	let	VERB
ejpam-5783	237	2	(	(	PUNCT
ejpam-5783	237	3	psbn	psbn	NOUN
ejpam-5783	237	4	;	;	PUNCT
ejpam-5783	237	5	|p	|p	NOUN
ejpam-5783	237	6	,	,	PUNCT
ejpam-5783	237	7	0	0	NUM
ejpam-5783	237	8	)	)	PUNCT
ejpam-5783	237	9	and	and	CCONJ
ejpam-5783	237	10	(	(	PUNCT
ejpam-5783	237	11	qsbn	qsbn	NOUN
ejpam-5783	237	12	;	;	PUNCT
ejpam-5783	237	13	|q	|q	NOUN
ejpam-5783	237	14	,	,	PUNCT
ejpam-5783	237	15	0	0	NUM
ejpam-5783	237	16	)	)	PUNCT
ejpam-5783	237	17	be	be	VERB
ejpam-5783	237	18	two	two	NUM
ejpam-5783	237	19	sheffer	sheffer	NOUN
ejpam-5783	237	20	stroke	stroke	NOUN
ejpam-5783	237	21	bn	bn	NOUN
ejpam-5783	237	22	-	-	PUNCT
ejpam-5783	237	23	algebras	algebras	PROPN
ejpam-5783	237	24	.	.	PUNCT
ejpam-5783	238	1	a	a	DET
ejpam-5783	238	2	map	map	NOUN
ejpam-5783	238	3	φ	φ	NOUN
ejpam-5783	238	4	:	:	PUNCT
ejpam-5783	238	5	psbn	psbn	PROPN
ejpam-5783	238	6	→	→	SYM
ejpam-5783	238	7	qsbn	qsbn	PROPN
ejpam-5783	238	8	is	be	AUX
ejpam-5783	238	9	called	call	VERB
ejpam-5783	238	10	a	a	DET
ejpam-5783	238	11	sheffer	sheffer	NOUN
ejpam-5783	238	12	stroke	stroke	NOUN
ejpam-5783	238	13	bn	bn	NOUN
ejpam-5783	238	14	-	-	PUNCT
ejpam-5783	238	15	homomorphism	homomorphism	NOUN
ejpam-5783	238	16	if	if	SCONJ
ejpam-5783	238	17	it	it	PRON
ejpam-5783	238	18	satisfies	satisfy	VERB
ejpam-5783	238	19	φ(a|p	φ(a|p	PROPN
ejpam-5783	238	20	b	b	NOUN
ejpam-5783	238	21	)	)	PUNCT
ejpam-5783	238	22	=	=	PUNCT
ejpam-5783	238	23	φ(a)|qφ(b	φ(a)|qφ(b	ADJ
ejpam-5783	238	24	)	)	PUNCT
ejpam-5783	238	25	for	for	ADP
ejpam-5783	238	26	all	all	DET
ejpam-5783	238	27	a	a	DET
ejpam-5783	238	28	,	,	PUNCT
ejpam-5783	238	29	b	b	PROPN
ejpam-5783	238	30	∈	∈	PROPN
ejpam-5783	238	31	psbn	psbn	NOUN
ejpam-5783	238	32	.	.	PUNCT
ejpam-5783	239	1	we	we	PRON
ejpam-5783	239	2	assume	assume	VERB
ejpam-5783	239	3	φ(0	φ(0	ADJ
ejpam-5783	239	4	)	)	PUNCT
ejpam-5783	239	5	=	=	SYM
ejpam-5783	240	1	0	0	X
ejpam-5783	240	2	.	.	PUNCT
ejpam-5783	241	1	in	in	ADP
ejpam-5783	241	2	sheffer	sheffer	PROPN
ejpam-5783	241	3	stroke	stroke	PROPN
ejpam-5783	241	4	bn	bn	PROPN
ejpam-5783	241	5	algebras	algebras	PROPN
ejpam-5783	241	6	,	,	PUNCT
ejpam-5783	241	7	homomorphisms	homomorphism	NOUN
ejpam-5783	241	8	are	be	AUX
ejpam-5783	241	9	mappings	mapping	NOUN
ejpam-5783	241	10	that	that	PRON
ejpam-5783	241	11	keep	keep	VERB
ejpam-5783	241	12	algebraic	algebraic	ADJ
ejpam-5783	241	13	operations	operation	NOUN
ejpam-5783	241	14	consistent	consistent	ADJ
ejpam-5783	241	15	.	.	PUNCT
ejpam-5783	242	1	for	for	ADP
ejpam-5783	242	2	example	example	NOUN
ejpam-5783	242	3	,	,	PUNCT
ejpam-5783	242	4	if	if	SCONJ
ejpam-5783	242	5	we	we	PRON
ejpam-5783	242	6	have	have	VERB
ejpam-5783	242	7	two	two	NUM
ejpam-5783	242	8	sheffer	sheffer	NOUN
ejpam-5783	242	9	stroke	stroke	NOUN
ejpam-5783	242	10	bn	bn	NOUN
ejpam-5783	242	11	-	-	PUNCT
ejpam-5783	242	12	algebras	algebras	X
ejpam-5783	242	13	,	,	PUNCT
ejpam-5783	242	14	(	(	PUNCT
ejpam-5783	242	15	psbn	psbn	NOUN
ejpam-5783	242	16	;	;	PUNCT
ejpam-5783	242	17	|p	|p	NOUN
ejpam-5783	242	18	,	,	PUNCT
ejpam-5783	242	19	0	0	NUM
ejpam-5783	242	20	)	)	PUNCT
ejpam-5783	242	21	and	and	CCONJ
ejpam-5783	242	22	(	(	PUNCT
ejpam-5783	242	23	qsbn	qsbn	NOUN
ejpam-5783	242	24	;	;	PUNCT
ejpam-5783	242	25	|q	|q	NOUN
ejpam-5783	242	26	,	,	PUNCT
ejpam-5783	242	27	0	0	NUM
ejpam-5783	242	28	)	)	PUNCT
ejpam-5783	242	29	,	,	PUNCT
ejpam-5783	242	30	and	and	CCONJ
ejpam-5783	242	31	a	a	DET
ejpam-5783	242	32	mapping	mapping	NOUN
ejpam-5783	242	33	φ	φ	NOUN
ejpam-5783	242	34	:	:	PUNCT
ejpam-5783	242	35	psbn	psbn	PROPN
ejpam-5783	242	36	→	→	SYM
ejpam-5783	242	37	qsbn	qsbn	NOUN
ejpam-5783	242	38	that	that	PRON
ejpam-5783	242	39	satisfies	satisfy	VERB
ejpam-5783	242	40	the	the	DET
ejpam-5783	242	41	properties	property	NOUN
ejpam-5783	242	42	of	of	ADP
ejpam-5783	242	43	a	a	DET
ejpam-5783	242	44	sheffer	sheffer	NOUN
ejpam-5783	242	45	stroke	stroke	NOUN
ejpam-5783	242	46	bn	bn	NOUN
ejpam-5783	242	47	-	-	PUNCT
ejpam-5783	242	48	homomorphism	homomorphism	NOUN
ejpam-5783	242	49	,	,	PUNCT
ejpam-5783	242	50	we	we	PRON
ejpam-5783	242	51	can	can	AUX
ejpam-5783	242	52	examine	examine	VERB
ejpam-5783	242	53	the	the	DET
ejpam-5783	242	54	kernel	kernel	NOUN
ejpam-5783	242	55	of	of	ADP
ejpam-5783	242	56	this	this	DET
ejpam-5783	242	57	mapping	mapping	NOUN
ejpam-5783	242	58	.	.	PUNCT
ejpam-5783	243	1	the	the	DET
ejpam-5783	243	2	kernel	kernel	NOUN
ejpam-5783	243	3	is	be	AUX
ejpam-5783	243	4	the	the	DET
ejpam-5783	243	5	set	set	NOUN
ejpam-5783	243	6	of	of	ADP
ejpam-5783	243	7	elements	element	NOUN
ejpam-5783	243	8	that	that	PRON
ejpam-5783	243	9	map	map	VERB
ejpam-5783	243	10	to	to	ADP
ejpam-5783	243	11	the	the	DET
ejpam-5783	243	12	zero	zero	NUM
ejpam-5783	243	13	elements	element	NOUN
ejpam-5783	243	14	in	in	ADP
ejpam-5783	243	15	the	the	DET
ejpam-5783	243	16	goal	goal	NOUN
ejpam-5783	243	17	algebra	algebra	NOUN
ejpam-5783	243	18	.	.	PUNCT
ejpam-5783	244	1	we	we	PRON
ejpam-5783	244	2	define	define	VERB
ejpam-5783	244	3	kerφ	kerφ	PROPN
ejpam-5783	244	4	=	=	PUNCT
ejpam-5783	244	5	{	{	PUNCT
ejpam-5783	244	6	a	a	DET
ejpam-5783	244	7	∈	∈	PROPN
ejpam-5783	244	8	psbn	psbn	NOUN
ejpam-5783	244	9	:	:	PUNCT
ejpam-5783	244	10	φ(a	φ(a	ADJ
ejpam-5783	244	11	)	)	PUNCT
ejpam-5783	244	12	=	=	SYM
ejpam-5783	244	13	0	0	NUM
ejpam-5783	244	14	}	}	PUNCT
ejpam-5783	244	15	.	.	PUNCT
ejpam-5783	245	1	the	the	DET
ejpam-5783	245	2	following	follow	VERB
ejpam-5783	245	3	theorem	theorem	NOUN
ejpam-5783	245	4	will	will	AUX
ejpam-5783	245	5	show	show	VERB
ejpam-5783	245	6	that	that	SCONJ
ejpam-5783	245	7	the	the	DET
ejpam-5783	245	8	kernel	kernel	NOUN
ejpam-5783	245	9	of	of	ADP
ejpam-5783	245	10	a	a	DET
ejpam-5783	245	11	sheffer	sheffer	NOUN
ejpam-5783	245	12	stroke	stroke	NOUN
ejpam-5783	245	13	bn	bn	NOUN
ejpam-5783	245	14	-	-	PUNCT
ejpam-5783	245	15	homomorphism	homomorphism	NOUN
ejpam-5783	245	16	always	always	ADV
ejpam-5783	245	17	forms	form	VERB
ejpam-5783	245	18	a	a	DET
ejpam-5783	245	19	bn	bn	NOUN
ejpam-5783	245	20	-	-	PUNCT
ejpam-5783	245	21	subalgebra	subalgebra	NOUN
ejpam-5783	245	22	in	in	ADP
ejpam-5783	245	23	the	the	DET
ejpam-5783	245	24	source	source	NOUN
ejpam-5783	245	25	algebra	algebra	NOUN
ejpam-5783	245	26	.	.	PUNCT
ejpam-5783	246	1	in	in	ADP
ejpam-5783	246	2	other	other	ADJ
ejpam-5783	246	3	words	word	NOUN
ejpam-5783	246	4	,	,	PUNCT
ejpam-5783	246	5	the	the	DET
ejpam-5783	246	6	elements	element	NOUN
ejpam-5783	246	7	that	that	PRON
ejpam-5783	246	8	map	map	VERB
ejpam-5783	246	9	to	to	ADP
ejpam-5783	246	10	zero	zero	NUM
ejpam-5783	246	11	form	form	VERB
ejpam-5783	246	12	the	the	DET
ejpam-5783	246	13	corresponding	corresponding	ADJ
ejpam-5783	246	14	algebraic	algebraic	ADJ
ejpam-5783	246	15	structure	structure	NOUN
ejpam-5783	246	16	in	in	ADP
ejpam-5783	246	17	the	the	DET
ejpam-5783	246	18	source	source	NOUN
ejpam-5783	246	19	algebra	algebra	NOUN
ejpam-5783	246	20	.	.	PUNCT
ejpam-5783	247	1	theorem	theorem	VERB
ejpam-5783	247	2	7	7	NUM
ejpam-5783	247	3	.	.	PUNCT
ejpam-5783	248	1	let	let	VERB
ejpam-5783	248	2	(	(	PUNCT
ejpam-5783	248	3	psbn	psbn	NOUN
ejpam-5783	248	4	;	;	PUNCT
ejpam-5783	248	5	|p	|p	NOUN
ejpam-5783	248	6	,	,	PUNCT
ejpam-5783	248	7	0	0	NUM
ejpam-5783	248	8	)	)	PUNCT
ejpam-5783	248	9	and	and	CCONJ
ejpam-5783	248	10	(	(	PUNCT
ejpam-5783	248	11	qsbn	qsbn	NOUN
ejpam-5783	248	12	;	;	PUNCT
ejpam-5783	248	13	|q	|q	NOUN
ejpam-5783	248	14	,	,	PUNCT
ejpam-5783	248	15	0	0	NUM
ejpam-5783	248	16	)	)	PUNCT
ejpam-5783	248	17	be	be	VERB
ejpam-5783	248	18	two	two	NUM
ejpam-5783	248	19	sheffer	sheffer	NOUN
ejpam-5783	248	20	stroke	stroke	NOUN
ejpam-5783	248	21	bn	bn	NOUN
ejpam-5783	248	22	-	-	PUNCT
ejpam-5783	248	23	algebras	algebras	PROPN
ejpam-5783	248	24	.	.	PUNCT
ejpam-5783	249	1	if	if	SCONJ
ejpam-5783	249	2	φ	φ	PROPN
ejpam-5783	249	3	:	:	PUNCT
ejpam-5783	249	4	psbn	psbn	PROPN
ejpam-5783	249	5	→	→	SYM
ejpam-5783	249	6	qsbn	qsbn	PROPN
ejpam-5783	249	7	is	be	AUX
ejpam-5783	249	8	a	a	DET
ejpam-5783	249	9	sheffer	sheffer	NOUN
ejpam-5783	249	10	stroke	stroke	NOUN
ejpam-5783	249	11	bn	bn	NOUN
ejpam-5783	249	12	-	-	PUNCT
ejpam-5783	249	13	homomorphism	homomorphism	NOUN
ejpam-5783	249	14	,	,	PUNCT
ejpam-5783	249	15	then	then	ADV
ejpam-5783	249	16	kerφ	kerφ	PROPN
ejpam-5783	249	17	is	be	AUX
ejpam-5783	249	18	a	a	DET
ejpam-5783	249	19	sheffer	sheffer	NOUN
ejpam-5783	249	20	stroke	stroke	NOUN
ejpam-5783	249	21	bn	bn	NOUN
ejpam-5783	249	22	-	-	PUNCT
ejpam-5783	249	23	subalgebra	subalgebra	NOUN
ejpam-5783	249	24	of	of	ADP
ejpam-5783	249	25	psbn	psbn	NOUN
ejpam-5783	249	26	.	.	PUNCT
ejpam-5783	250	1	proof	proof	NOUN
ejpam-5783	250	2	.	.	PUNCT
ejpam-5783	251	1	let	let	VERB
ejpam-5783	251	2	(	(	PUNCT
ejpam-5783	251	3	psbn	psbn	NOUN
ejpam-5783	251	4	;	;	PUNCT
ejpam-5783	251	5	|p	|p	NOUN
ejpam-5783	251	6	,	,	PUNCT
ejpam-5783	251	7	0	0	NUM
ejpam-5783	251	8	)	)	PUNCT
ejpam-5783	251	9	and	and	CCONJ
ejpam-5783	251	10	(	(	PUNCT
ejpam-5783	251	11	qsbn	qsbn	NOUN
ejpam-5783	251	12	;	;	PUNCT
ejpam-5783	251	13	|q	|q	NOUN
ejpam-5783	251	14	,	,	PUNCT
ejpam-5783	251	15	0	0	NUM
ejpam-5783	251	16	)	)	PUNCT
ejpam-5783	251	17	be	be	VERB
ejpam-5783	251	18	two	two	NUM
ejpam-5783	251	19	sheffer	sheffer	NOUN
ejpam-5783	251	20	stroke	stroke	NOUN
ejpam-5783	251	21	bn	bn	NOUN
ejpam-5783	251	22	-	-	PUNCT
ejpam-5783	251	23	algebras	algebras	PROPN
ejpam-5783	251	24	and	and	CCONJ
ejpam-5783	251	25	φ	φ	PROPN
ejpam-5783	251	26	:	:	PUNCT
ejpam-5783	251	27	psbn	psbn	PROPN
ejpam-5783	251	28	→	→	SYM
ejpam-5783	251	29	qsbn	qsbn	PROPN
ejpam-5783	251	30	a	a	DET
ejpam-5783	251	31	sheffer	sheffer	NOUN
ejpam-5783	251	32	stroke	stroke	NOUN
ejpam-5783	251	33	bn	bn	NOUN
ejpam-5783	251	34	-	-	PUNCT
ejpam-5783	251	35	homomorphism	homomorphism	NOUN
ejpam-5783	251	36	.	.	PUNCT
ejpam-5783	252	1	let	let	VERB
ejpam-5783	252	2	a	a	DET
ejpam-5783	252	3	,	,	PUNCT
ejpam-5783	252	4	b	b	PROPN
ejpam-5783	252	5	∈	∈	PROPN
ejpam-5783	252	6	kerφ	kerφ	PROPN
ejpam-5783	252	7	,	,	PUNCT
ejpam-5783	252	8	we	we	PRON
ejpam-5783	252	9	have	have	AUX
ejpam-5783	252	10	φ(a	φ(a	ADJ
ejpam-5783	252	11	)	)	PUNCT
ejpam-5783	252	12	=	=	SYM
ejpam-5783	252	13	0	0	NUM
ejpam-5783	252	14	and	and	CCONJ
ejpam-5783	252	15	φ(b	φ(b	PROPN
ejpam-5783	252	16	)	)	PUNCT
ejpam-5783	252	17	=	=	SYM
ejpam-5783	253	1	0	0	X
ejpam-5783	253	2	.	.	PUNCT
ejpam-5783	253	3	by	by	ADP
ejpam-5783	253	4	using	use	VERB
ejpam-5783	253	5	(	(	PUNCT
ejpam-5783	253	6	sbn1	sbn1	ADJ
ejpam-5783	253	7	)	)	PUNCT
ejpam-5783	253	8	,	,	PUNCT
ejpam-5783	253	9	we	we	PRON
ejpam-5783	253	10	obtain	obtain	VERB
ejpam-5783	253	11	φ((a|p	φ((a|p	PUNCT
ejpam-5783	253	12	(	(	PUNCT
ejpam-5783	253	13	b|p	b|p	PROPN
ejpam-5783	253	14	b))|p	b))|p	PROPN
ejpam-5783	253	15	(	(	PUNCT
ejpam-5783	253	16	a|p	a|p	PROPN
ejpam-5783	253	17	(	(	PUNCT
ejpam-5783	253	18	b|p	b|p	PROPN
ejpam-5783	253	19	b	b	X
ejpam-5783	253	20	)	)	PUNCT
ejpam-5783	253	21	)	)	PUNCT
ejpam-5783	253	22	)	)	PUNCT
ejpam-5783	254	1	=	=	SYM
ejpam-5783	254	2	φ(a|p	φ(a|p	PROPN
ejpam-5783	254	3	(	(	PUNCT
ejpam-5783	254	4	b|p	b|p	PROPN
ejpam-5783	254	5	b))|qφ(a|p	b))|qφ(a|p	PROPN
ejpam-5783	254	6	(	(	PUNCT
ejpam-5783	254	7	b|p	b|p	PROPN
ejpam-5783	254	8	b	b	X
ejpam-5783	254	9	)	)	PUNCT
ejpam-5783	254	10	)	)	PUNCT
ejpam-5783	254	11	,	,	PUNCT
ejpam-5783	254	12	=	=	PRON
ejpam-5783	254	13	(	(	PUNCT
ejpam-5783	254	14	φ(a)|q(φ(b)|q(b)))|q(φ(a)|q(φ(b)|qφ(b	φ(a)|q(φ(b)|q(b)))|q(φ(a)|q(φ(b)|qφ(b	PROPN
ejpam-5783	254	15	)	)	PUNCT
ejpam-5783	254	16	)	)	PUNCT
ejpam-5783	254	17	)	)	PUNCT
ejpam-5783	254	18	,	,	PUNCT
ejpam-5783	254	19	=	=	PRON
ejpam-5783	254	20	(	(	PUNCT
ejpam-5783	254	21	0|q(0|q0))|q(0|q(0|q0	0|q(0|q0))|q(0|q(0|q0	PROPN
ejpam-5783	254	22	)	)	PUNCT
ejpam-5783	254	23	)	)	PUNCT
ejpam-5783	254	24	,	,	PUNCT
ejpam-5783	254	25	s.	s.	PROPN
ejpam-5783	254	26	gemawati	gemawati	PROPN
ejpam-5783	254	27	et	et	PROPN
ejpam-5783	254	28	al	al	PROPN
ejpam-5783	254	29	.	.	PUNCT
ejpam-5783	254	30	/	/	SYM
ejpam-5783	254	31	eur	eur	PROPN
ejpam-5783	254	32	.	.	PUNCT
ejpam-5783	255	1	j.	j.	PROPN
ejpam-5783	255	2	pure	pure	PROPN
ejpam-5783	255	3	appl	appl	PROPN
ejpam-5783	255	4	.	.	PROPN
ejpam-5783	255	5	math	math	PROPN
ejpam-5783	255	6	,	,	PUNCT
ejpam-5783	255	7	18	18	NUM
ejpam-5783	255	8	(	(	PUNCT
ejpam-5783	255	9	1	1	NUM
ejpam-5783	255	10	)	)	PUNCT
ejpam-5783	255	11	(	(	PUNCT
ejpam-5783	255	12	2025	2025	NUM
ejpam-5783	255	13	)	)	PUNCT
ejpam-5783	255	14	,	,	PUNCT
ejpam-5783	255	15	5783	5783	NUM
ejpam-5783	255	16	10	10	NUM
ejpam-5783	255	17	of	of	ADP
ejpam-5783	255	18	12	12	NUM
ejpam-5783	255	19	φ((a|p	φ((a|p	PUNCT
ejpam-5783	255	20	(	(	PUNCT
ejpam-5783	255	21	b|p	b|p	PROPN
ejpam-5783	255	22	b))|p	b))|p	PROPN
ejpam-5783	255	23	(	(	PUNCT
ejpam-5783	255	24	a|p	a|p	PROPN
ejpam-5783	255	25	(	(	PUNCT
ejpam-5783	255	26	b|p	b|p	PROPN
ejpam-5783	255	27	b	b	X
ejpam-5783	255	28	)	)	PUNCT
ejpam-5783	255	29	)	)	PUNCT
ejpam-5783	255	30	)	)	PUNCT
ejpam-5783	256	1	=	=	PUNCT
ejpam-5783	256	2	0	0	X
ejpam-5783	256	3	.	.	PUNCT
ejpam-5783	257	1	hence	hence	ADV
ejpam-5783	257	2	,	,	PUNCT
ejpam-5783	257	3	we	we	PRON
ejpam-5783	257	4	have	have	VERB
ejpam-5783	257	5	(	(	PUNCT
ejpam-5783	257	6	(	(	PUNCT
ejpam-5783	257	7	a|p	a|p	X
ejpam-5783	257	8	(	(	PUNCT
ejpam-5783	257	9	b|p	b|p	PROPN
ejpam-5783	257	10	b))|p	b))|p	PROPN
ejpam-5783	257	11	(	(	PUNCT
ejpam-5783	257	12	a|p	a|p	PROPN
ejpam-5783	257	13	(	(	PUNCT
ejpam-5783	257	14	b|p	b|p	PROPN
ejpam-5783	257	15	b	b	X
ejpam-5783	257	16	)	)	PUNCT
ejpam-5783	257	17	)	)	PUNCT
ejpam-5783	257	18	)	)	PUNCT
ejpam-5783	258	1	∈	∈	PROPN
ejpam-5783	258	2	kerφ	kerφ	PROPN
ejpam-5783	258	3	.	.	PUNCT
ejpam-5783	259	1	this	this	PRON
ejpam-5783	259	2	shows	show	VERB
ejpam-5783	259	3	that	that	SCONJ
ejpam-5783	259	4	kerφ	kerφ	PROPN
ejpam-5783	259	5	is	be	AUX
ejpam-5783	259	6	a	a	DET
ejpam-5783	259	7	sheffer	sheffer	NOUN
ejpam-5783	259	8	stroke	stroke	NOUN
ejpam-5783	259	9	bn	bn	NOUN
ejpam-5783	259	10	-	-	PUNCT
ejpam-5783	259	11	subalgebra	subalgebra	NOUN
ejpam-5783	259	12	of	of	ADP
ejpam-5783	259	13	psbn	psbn	NOUN
ejpam-5783	259	14	.	.	PUNCT
ejpam-5783	260	1	in	in	ADP
ejpam-5783	260	2	theorem	theorem	NOUN
ejpam-5783	260	3	8	8	NUM
ejpam-5783	260	4	,	,	PUNCT
ejpam-5783	260	5	the	the	DET
ejpam-5783	260	6	kernel	kernel	NOUN
ejpam-5783	260	7	of	of	ADP
ejpam-5783	260	8	the	the	DET
ejpam-5783	260	9	sheffer	sheffer	NOUN
ejpam-5783	260	10	stroke	stroke	NOUN
ejpam-5783	260	11	bn	bn	NOUN
ejpam-5783	260	12	-	-	PUNCT
ejpam-5783	260	13	homomorphism	homomorphism	NOUN
ejpam-5783	260	14	φ	φ	PROPN
ejpam-5783	260	15	is	be	AUX
ejpam-5783	260	16	the	the	DET
ejpam-5783	260	17	set	set	NOUN
ejpam-5783	260	18	of	of	ADP
ejpam-5783	260	19	elements	element	NOUN
ejpam-5783	260	20	in	in	ADP
ejpam-5783	260	21	psbn	psbn	NOUN
ejpam-5783	260	22	that	that	DET
ejpam-5783	260	23	map	map	NOUN
ejpam-5783	260	24	to	to	ADP
ejpam-5783	260	25	zero	zero	NUM
ejpam-5783	260	26	elements	element	NOUN
ejpam-5783	260	27	in	in	ADP
ejpam-5783	260	28	qsbn	qsbn	NOUN
ejpam-5783	260	29	.	.	PUNCT
ejpam-5783	261	1	the	the	DET
ejpam-5783	261	2	property	property	NOUN
ejpam-5783	261	3	proven	prove	VERB
ejpam-5783	261	4	by	by	ADP
ejpam-5783	261	5	theorem	theorem	NOUN
ejpam-5783	261	6	8	8	NUM
ejpam-5783	261	7	is	be	AUX
ejpam-5783	261	8	that	that	SCONJ
ejpam-5783	261	9	the	the	DET
ejpam-5783	261	10	kernel	kernel	NOUN
ejpam-5783	261	11	of	of	ADP
ejpam-5783	261	12	a	a	DET
ejpam-5783	261	13	sheffer	sheffer	NOUN
ejpam-5783	261	14	stroke	stroke	NOUN
ejpam-5783	261	15	bn	bn	NOUN
ejpam-5783	261	16	-	-	PUNCT
ejpam-5783	261	17	homomorphism	homomorphism	NOUN
ejpam-5783	261	18	not	not	PART
ejpam-5783	261	19	only	only	ADV
ejpam-5783	261	20	forms	form	VERB
ejpam-5783	261	21	a	a	DET
ejpam-5783	261	22	sheffer	sheffer	NOUN
ejpam-5783	261	23	stroke	stroke	NOUN
ejpam-5783	261	24	bn	bn	NOUN
ejpam-5783	261	25	-	-	PUNCT
ejpam-5783	261	26	subalgebra	subalgebra	NOUN
ejpam-5783	261	27	of	of	ADP
ejpam-5783	261	28	psbn	psbn	NOUN
ejpam-5783	261	29	but	but	CCONJ
ejpam-5783	261	30	also	also	ADV
ejpam-5783	261	31	forms	form	VERB
ejpam-5783	261	32	a	a	DET
ejpam-5783	261	33	bn	bn	NOUN
ejpam-5783	261	34	-	-	PUNCT
ejpam-5783	261	35	ideal	ideal	NOUN
ejpam-5783	261	36	.	.	PUNCT
ejpam-5783	262	1	it	it	PRON
ejpam-5783	262	2	provides	provide	VERB
ejpam-5783	262	3	an	an	DET
ejpam-5783	262	4	understanding	understanding	NOUN
ejpam-5783	262	5	of	of	ADP
ejpam-5783	262	6	the	the	DET
ejpam-5783	262	7	algebraic	algebraic	ADJ
ejpam-5783	262	8	structures	structure	NOUN
ejpam-5783	262	9	preserved	preserve	VERB
ejpam-5783	262	10	and	and	CCONJ
ejpam-5783	262	11	changed	change	VERB
ejpam-5783	262	12	by	by	ADP
ejpam-5783	262	13	homomorphisms	homomorphism	NOUN
ejpam-5783	262	14	,	,	PUNCT
ejpam-5783	262	15	as	as	ADV
ejpam-5783	262	16	well	well	ADV
ejpam-5783	262	17	as	as	ADP
ejpam-5783	262	18	the	the	DET
ejpam-5783	262	19	importance	importance	NOUN
ejpam-5783	262	20	of	of	ADP
ejpam-5783	262	21	kernels	kernel	NOUN
ejpam-5783	262	22	in	in	ADP
ejpam-5783	262	23	preserving	preserve	VERB
ejpam-5783	262	24	ideal	ideal	ADJ
ejpam-5783	262	25	properties	property	NOUN
ejpam-5783	262	26	and	and	CCONJ
ejpam-5783	262	27	algebraic	algebraic	ADJ
ejpam-5783	262	28	structures	structure	NOUN
ejpam-5783	262	29	in	in	ADP
ejpam-5783	262	30	the	the	DET
ejpam-5783	262	31	context	context	NOUN
ejpam-5783	262	32	of	of	ADP
ejpam-5783	262	33	homomorphisms	homomorphism	NOUN
ejpam-5783	262	34	.	.	PUNCT
ejpam-5783	263	1	theorem	theorem	ADJ
ejpam-5783	263	2	8	8	NUM
ejpam-5783	263	3	.	.	PUNCT
ejpam-5783	264	1	let	let	VERB
ejpam-5783	264	2	(	(	PUNCT
ejpam-5783	264	3	psbn	psbn	NOUN
ejpam-5783	264	4	;	;	PUNCT
ejpam-5783	264	5	|p	|p	NOUN
ejpam-5783	264	6	,	,	PUNCT
ejpam-5783	264	7	0	0	NUM
ejpam-5783	264	8	)	)	PUNCT
ejpam-5783	264	9	and	and	CCONJ
ejpam-5783	264	10	(	(	PUNCT
ejpam-5783	264	11	qsbn	qsbn	NOUN
ejpam-5783	264	12	;	;	PUNCT
ejpam-5783	264	13	|q	|q	NOUN
ejpam-5783	264	14	,	,	PUNCT
ejpam-5783	264	15	0	0	NUM
ejpam-5783	264	16	)	)	PUNCT
ejpam-5783	264	17	be	be	VERB
ejpam-5783	264	18	two	two	NUM
ejpam-5783	264	19	sheffer	sheffer	NOUN
ejpam-5783	264	20	stroke	stroke	NOUN
ejpam-5783	264	21	bn	bn	NOUN
ejpam-5783	264	22	-	-	PUNCT
ejpam-5783	264	23	algebras	algebras	PROPN
ejpam-5783	264	24	.	.	PUNCT
ejpam-5783	265	1	if	if	SCONJ
ejpam-5783	265	2	φ	φ	PROPN
ejpam-5783	265	3	:	:	PUNCT
ejpam-5783	265	4	psbn	psbn	PROPN
ejpam-5783	265	5	→	→	SYM
ejpam-5783	265	6	qsbn	qsbn	PROPN
ejpam-5783	265	7	is	be	AUX
ejpam-5783	265	8	a	a	DET
ejpam-5783	265	9	sheffer	sheffer	NOUN
ejpam-5783	265	10	stroke	stroke	NOUN
ejpam-5783	265	11	bn	bn	NOUN
ejpam-5783	265	12	-	-	PUNCT
ejpam-5783	265	13	homomorphism	homomorphism	NOUN
ejpam-5783	265	14	,	,	PUNCT
ejpam-5783	265	15	then	then	ADV
ejpam-5783	265	16	kerφ	kerφ	PROPN
ejpam-5783	265	17	is	be	AUX
ejpam-5783	265	18	a	a	DET
ejpam-5783	265	19	sheffer	sheffer	NOUN
ejpam-5783	265	20	stroke	stroke	NOUN
ejpam-5783	265	21	bn	bn	NOUN
ejpam-5783	265	22	-	-	PUNCT
ejpam-5783	265	23	ideal	ideal	NOUN
ejpam-5783	265	24	of	of	ADP
ejpam-5783	265	25	psbn	psbn	NOUN
ejpam-5783	265	26	.	.	PUNCT
ejpam-5783	266	1	proof	proof	NOUN
ejpam-5783	266	2	.	.	PUNCT
ejpam-5783	267	1	let	let	VERB
ejpam-5783	267	2	(	(	PUNCT
ejpam-5783	267	3	psbn	psbn	NOUN
ejpam-5783	267	4	;	;	PUNCT
ejpam-5783	267	5	|p	|p	NOUN
ejpam-5783	267	6	,	,	PUNCT
ejpam-5783	267	7	0	0	NUM
ejpam-5783	267	8	)	)	PUNCT
ejpam-5783	267	9	and	and	CCONJ
ejpam-5783	267	10	(	(	PUNCT
ejpam-5783	267	11	qsbn	qsbn	NOUN
ejpam-5783	267	12	;	;	PUNCT
ejpam-5783	267	13	|q	|q	NOUN
ejpam-5783	267	14	,	,	PUNCT
ejpam-5783	267	15	0	0	NUM
ejpam-5783	267	16	)	)	PUNCT
ejpam-5783	267	17	be	be	VERB
ejpam-5783	267	18	two	two	NUM
ejpam-5783	267	19	sheffer	sheffer	NOUN
ejpam-5783	267	20	stroke	stroke	NOUN
ejpam-5783	267	21	bn	bn	NOUN
ejpam-5783	267	22	-	-	PUNCT
ejpam-5783	267	23	algebras	algebras	PROPN
ejpam-5783	267	24	and	and	CCONJ
ejpam-5783	267	25	φ	φ	PROPN
ejpam-5783	267	26	:	:	PUNCT
ejpam-5783	267	27	psbn	psbn	PROPN
ejpam-5783	267	28	→	→	SYM
ejpam-5783	267	29	qsbn	qsbn	PROPN
ejpam-5783	267	30	a	a	DET
ejpam-5783	267	31	sheffer	sheffer	NOUN
ejpam-5783	267	32	stroke	stroke	NOUN
ejpam-5783	267	33	bn	bn	NOUN
ejpam-5783	267	34	-	-	PUNCT
ejpam-5783	267	35	homomorphism	homomorphism	NOUN
ejpam-5783	267	36	.	.	PUNCT
ejpam-5783	268	1	since	since	SCONJ
ejpam-5783	268	2	φ(0	φ(0	ADJ
ejpam-5783	268	3	)	)	PUNCT
ejpam-5783	268	4	=	=	SYM
ejpam-5783	268	5	0	0	NUM
ejpam-5783	268	6	,	,	PUNCT
ejpam-5783	268	7	we	we	PRON
ejpam-5783	268	8	have	have	VERB
ejpam-5783	268	9	0	0	NUM
ejpam-5783	268	10	∈	∈	PROPN
ejpam-5783	268	11	kerφ	kerφ	PROPN
ejpam-5783	268	12	.	.	PUNCT
ejpam-5783	269	1	let	let	VERB
ejpam-5783	269	2	b	b	X
ejpam-5783	269	3	∈	∈	PROPN
ejpam-5783	269	4	kerφ	kerφ	PROPN
ejpam-5783	269	5	,	,	PUNCT
ejpam-5783	269	6	we	we	PRON
ejpam-5783	269	7	have	have	VERB
ejpam-5783	269	8	φ(b	φ(b	NOUN
ejpam-5783	269	9	)	)	PUNCT
ejpam-5783	269	10	=	=	SYM
ejpam-5783	270	1	0	0	X
ejpam-5783	270	2	.	.	PUNCT
ejpam-5783	271	1	let	let	VERB
ejpam-5783	271	2	(	(	PUNCT
ejpam-5783	271	3	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5783	271	4	)	)	PUNCT
ejpam-5783	271	5	)	)	PUNCT
ejpam-5783	272	1	∈	∈	PROPN
ejpam-5783	272	2	kerφ	kerφ	PROPN
ejpam-5783	272	3	,	,	PUNCT
ejpam-5783	272	4	then	then	ADV
ejpam-5783	272	5	by	by	ADP
ejpam-5783	272	6	using	use	VERB
ejpam-5783	272	7	(	(	PUNCT
ejpam-5783	272	8	sbn1	sbn1	ADJ
ejpam-5783	272	9	)	)	PUNCT
ejpam-5783	272	10	,	,	PUNCT
ejpam-5783	272	11	we	we	PRON
ejpam-5783	272	12	obtain	obtain	VERB
ejpam-5783	272	13	φ((a|p	φ((a|p	PUNCT
ejpam-5783	272	14	(	(	PUNCT
ejpam-5783	272	15	b|p	b|p	PROPN
ejpam-5783	272	16	b))|p	b))|p	PROPN
ejpam-5783	272	17	(	(	PUNCT
ejpam-5783	272	18	a|p	a|p	PROPN
ejpam-5783	272	19	(	(	PUNCT
ejpam-5783	272	20	b|p	b|p	PROPN
ejpam-5783	272	21	b	b	X
ejpam-5783	272	22	)	)	PUNCT
ejpam-5783	272	23	)	)	PUNCT
ejpam-5783	272	24	)	)	PUNCT
ejpam-5783	273	1	=	=	PUNCT
ejpam-5783	273	2	0	0	NUM
ejpam-5783	273	3	,	,	PUNCT
ejpam-5783	273	4	=	=	PUNCT
ejpam-5783	273	5	(	(	PUNCT
ejpam-5783	273	6	φ(a)|q(φ(b)|qφ(b)))|q(φ(a)|q(φ(b)|qφ(b	φ(a)|q(φ(b)|qφ(b)))|q(φ(a)|q(φ(b)|qφ(b	NUM
ejpam-5783	273	7	)	)	PUNCT
ejpam-5783	273	8	)	)	PUNCT
ejpam-5783	273	9	)	)	PUNCT
ejpam-5783	273	10	,	,	PUNCT
ejpam-5783	273	11	=	=	SYM
ejpam-5783	273	12	(	(	PUNCT
ejpam-5783	273	13	φ(a)|q(0|q0))|q(φ(a)|q(0|q0	φ(a)|q(0|q0))|q(φ(a)|q(0|q0	NOUN
ejpam-5783	273	14	)	)	PUNCT
ejpam-5783	273	15	)	)	PUNCT
ejpam-5783	273	16	,	,	PUNCT
ejpam-5783	273	17	φ(a	φ(a	ADJ
ejpam-5783	273	18	)	)	PUNCT
ejpam-5783	273	19	=	=	SYM
ejpam-5783	273	20	0	0	X
ejpam-5783	273	21	.	.	PUNCT
ejpam-5783	274	1	we	we	PRON
ejpam-5783	274	2	have	have	VERB
ejpam-5783	274	3	a	a	DET
ejpam-5783	274	4	∈	∈	PROPN
ejpam-5783	274	5	kerφ	kerφ	PROPN
ejpam-5783	274	6	.	.	PUNCT
ejpam-5783	275	1	hence	hence	ADV
ejpam-5783	275	2	,	,	PUNCT
ejpam-5783	275	3	kerφ	kerφ	PROPN
ejpam-5783	275	4	is	be	AUX
ejpam-5783	275	5	a	a	DET
ejpam-5783	275	6	sheffer	sheffer	NOUN
ejpam-5783	275	7	stroke	stroke	NOUN
ejpam-5783	275	8	bn	bn	NOUN
ejpam-5783	275	9	-	-	PUNCT
ejpam-5783	275	10	ideal	ideal	NOUN
ejpam-5783	275	11	of	of	ADP
ejpam-5783	275	12	psbn	psbn	NOUN
ejpam-5783	275	13	.	.	PUNCT
ejpam-5783	276	1	the	the	DET
ejpam-5783	276	2	following	follow	VERB
ejpam-5783	276	3	two	two	NUM
ejpam-5783	276	4	theorems	theorem	NOUN
ejpam-5783	276	5	further	far	ADV
ejpam-5783	276	6	characterize	characterize	VERB
ejpam-5783	276	7	the	the	DET
ejpam-5783	276	8	properties	property	NOUN
ejpam-5783	276	9	of	of	ADP
ejpam-5783	276	10	the	the	DET
ejpam-5783	276	11	kernel	kernel	NOUN
ejpam-5783	276	12	of	of	ADP
ejpam-5783	276	13	a	a	DET
ejpam-5783	276	14	sheffer	sheffer	NOUN
ejpam-5783	276	15	stroke	stroke	NOUN
ejpam-5783	276	16	bn	bn	NOUN
ejpam-5783	276	17	-	-	PUNCT
ejpam-5783	276	18	homomorphism	homomorphism	NOUN
ejpam-5783	276	19	kerφ	kerφ	PROPN
ejpam-5783	276	20	.	.	PUNCT
ejpam-5783	276	21	theorem	theorem	VERB
ejpam-5783	276	22	9	9	NUM
ejpam-5783	276	23	shows	show	VERB
ejpam-5783	276	24	that	that	SCONJ
ejpam-5783	276	25	if	if	SCONJ
ejpam-5783	276	26	an	an	DET
ejpam-5783	276	27	element	element	NOUN
ejpam-5783	276	28	a	a	PRON
ejpam-5783	276	29	is	be	AUX
ejpam-5783	276	30	in	in	ADP
ejpam-5783	276	31	kerφ	kerφ	PROPN
ejpam-5783	276	32	,	,	PUNCT
ejpam-5783	276	33	then	then	ADV
ejpam-5783	276	34	the	the	DET
ejpam-5783	276	35	result	result	NOUN
ejpam-5783	276	36	of	of	ADP
ejpam-5783	276	37	a	a	DET
ejpam-5783	276	38	particular	particular	ADJ
ejpam-5783	276	39	operation	operation	NOUN
ejpam-5783	276	40	involving	involve	VERB
ejpam-5783	276	41	a	a	DET
ejpam-5783	276	42	and	and	CCONJ
ejpam-5783	276	43	other	other	ADJ
ejpam-5783	276	44	elements	element	NOUN
ejpam-5783	276	45	in	in	ADP
ejpam-5783	276	46	psbn	psbn	NOUN
ejpam-5783	276	47	remains	remain	VERB
ejpam-5783	276	48	within	within	ADP
ejpam-5783	276	49	kerφ	kerφ	PROPN
ejpam-5783	276	50	.	.	PUNCT
ejpam-5783	277	1	the	the	DET
ejpam-5783	277	2	same	same	ADJ
ejpam-5783	277	3	applies	apply	VERB
ejpam-5783	277	4	to	to	ADP
ejpam-5783	277	5	pairs	pair	NOUN
ejpam-5783	277	6	of	of	ADP
ejpam-5783	277	7	elements	element	NOUN
ejpam-5783	277	8	a	a	PRON
ejpam-5783	277	9	and	and	CCONJ
ejpam-5783	277	10	b	b	NOUN
ejpam-5783	277	11	that	that	PRON
ejpam-5783	277	12	are	be	AUX
ejpam-5783	277	13	both	both	PRON
ejpam-5783	277	14	in	in	ADP
ejpam-5783	277	15	kerφ	kerφ	PROPN
ejpam-5783	277	16	,	,	PUNCT
ejpam-5783	277	17	as	as	SCONJ
ejpam-5783	277	18	shown	show	VERB
ejpam-5783	277	19	by	by	ADP
ejpam-5783	277	20	theorem	theorem	NOUN
ejpam-5783	277	21	10	10	NUM
ejpam-5783	277	22	.	.	PUNCT
ejpam-5783	278	1	these	these	DET
ejpam-5783	278	2	two	two	NUM
ejpam-5783	278	3	theorems	theorem	NOUN
ejpam-5783	278	4	provide	provide	VERB
ejpam-5783	278	5	further	further	ADJ
ejpam-5783	278	6	insight	insight	NOUN
ejpam-5783	278	7	into	into	ADP
ejpam-5783	278	8	the	the	DET
ejpam-5783	278	9	relationship	relationship	NOUN
ejpam-5783	278	10	between	between	ADP
ejpam-5783	278	11	kernels	kernel	NOUN
ejpam-5783	278	12	and	and	CCONJ
ejpam-5783	278	13	operations	operation	NOUN
ejpam-5783	278	14	in	in	ADP
ejpam-5783	278	15	a	a	DET
ejpam-5783	278	16	sheffer	sheffer	NOUN
ejpam-5783	278	17	stroke	stroke	NOUN
ejpam-5783	278	18	bn	bn	NOUN
ejpam-5783	278	19	-	-	PUNCT
ejpam-5783	278	20	algebra	algebra	NOUN
ejpam-5783	278	21	,	,	PUNCT
ejpam-5783	278	22	as	as	ADV
ejpam-5783	278	23	well	well	ADV
ejpam-5783	278	24	as	as	ADP
ejpam-5783	278	25	how	how	SCONJ
ejpam-5783	278	26	elements	element	NOUN
ejpam-5783	278	27	in	in	ADP
ejpam-5783	278	28	the	the	DET
ejpam-5783	278	29	kernel	kernel	NOUN
ejpam-5783	278	30	behave	behave	VERB
ejpam-5783	278	31	under	under	ADP
ejpam-5783	278	32	certain	certain	ADJ
ejpam-5783	278	33	operations	operation	NOUN
ejpam-5783	278	34	in	in	ADP
ejpam-5783	278	35	the	the	DET
ejpam-5783	278	36	algebraic	algebraic	ADJ
ejpam-5783	278	37	structure	structure	NOUN
ejpam-5783	278	38	.	.	PUNCT
ejpam-5783	279	1	theorem	theorem	VERB
ejpam-5783	279	2	9	9	NUM
ejpam-5783	279	3	.	.	PUNCT
ejpam-5783	280	1	let	let	VERB
ejpam-5783	280	2	(	(	PUNCT
ejpam-5783	280	3	psbn	psbn	NOUN
ejpam-5783	280	4	;	;	PUNCT
ejpam-5783	280	5	|p	|p	NOUN
ejpam-5783	280	6	,	,	PUNCT
ejpam-5783	280	7	0	0	NUM
ejpam-5783	280	8	)	)	PUNCT
ejpam-5783	280	9	and	and	CCONJ
ejpam-5783	280	10	(	(	PUNCT
ejpam-5783	280	11	qsbn	qsbn	NOUN
ejpam-5783	280	12	;	;	PUNCT
ejpam-5783	280	13	|q	|q	NOUN
ejpam-5783	280	14	,	,	PUNCT
ejpam-5783	280	15	0	0	NUM
ejpam-5783	280	16	)	)	PUNCT
ejpam-5783	280	17	be	be	VERB
ejpam-5783	280	18	two	two	NUM
ejpam-5783	280	19	sheffer	sheffer	NOUN
ejpam-5783	280	20	stroke	stroke	NOUN
ejpam-5783	280	21	bn	bn	NOUN
ejpam-5783	280	22	-	-	PUNCT
ejpam-5783	280	23	algebras	algebras	PROPN
ejpam-5783	280	24	and	and	CCONJ
ejpam-5783	280	25	φ	φ	PROPN
ejpam-5783	280	26	:	:	PUNCT
ejpam-5783	280	27	psbn	psbn	PROPN
ejpam-5783	280	28	→	→	SYM
ejpam-5783	280	29	qsbn	qsbn	PROPN
ejpam-5783	280	30	a	a	DET
ejpam-5783	280	31	sheffer	sheffer	NOUN
ejpam-5783	280	32	stroke	stroke	NOUN
ejpam-5783	280	33	bn	bn	NOUN
ejpam-5783	280	34	-	-	PUNCT
ejpam-5783	280	35	homomorphism	homomorphism	NOUN
ejpam-5783	280	36	.	.	PUNCT
ejpam-5783	281	1	if	if	SCONJ
ejpam-5783	281	2	a	a	DET
ejpam-5783	281	3	∈	∈	PROPN
ejpam-5783	281	4	kerφ	kerφ	PROPN
ejpam-5783	281	5	,	,	PUNCT
ejpam-5783	281	6	then	then	ADV
ejpam-5783	281	7	(	(	PUNCT
ejpam-5783	281	8	0|p	0|p	PRON
ejpam-5783	281	9	(	(	PUNCT
ejpam-5783	281	10	a|pa))|p	a|pa))|p	PROPN
ejpam-5783	281	11	(	(	PUNCT
ejpam-5783	281	12	a|p	a|p	NOUN
ejpam-5783	281	13	b	b	X
ejpam-5783	281	14	)	)	PUNCT
ejpam-5783	281	15	∈	∈	PROPN
ejpam-5783	281	16	kerφ	kerφ	PROPN
ejpam-5783	281	17	.	.	PUNCT
ejpam-5783	282	1	proof	proof	NOUN
ejpam-5783	282	2	.	.	PUNCT
ejpam-5783	283	1	let	let	VERB
ejpam-5783	283	2	(	(	PUNCT
ejpam-5783	283	3	psbn	psbn	NOUN
ejpam-5783	283	4	;	;	PUNCT
ejpam-5783	283	5	|p	|p	NOUN
ejpam-5783	283	6	,	,	PUNCT
ejpam-5783	283	7	0	0	NUM
ejpam-5783	283	8	)	)	PUNCT
ejpam-5783	283	9	and	and	CCONJ
ejpam-5783	283	10	(	(	PUNCT
ejpam-5783	283	11	qsbn	qsbn	NOUN
ejpam-5783	283	12	;	;	PUNCT
ejpam-5783	283	13	|q	|q	NOUN
ejpam-5783	283	14	,	,	PUNCT
ejpam-5783	283	15	0	0	NUM
ejpam-5783	283	16	)	)	PUNCT
ejpam-5783	283	17	be	be	VERB
ejpam-5783	283	18	two	two	NUM
ejpam-5783	283	19	sheffer	sheffer	NOUN
ejpam-5783	283	20	stroke	stroke	NOUN
ejpam-5783	283	21	bn	bn	NOUN
ejpam-5783	283	22	-	-	PUNCT
ejpam-5783	283	23	algebras	algebras	PROPN
ejpam-5783	283	24	and	and	CCONJ
ejpam-5783	283	25	φ	φ	PROPN
ejpam-5783	283	26	:	:	PUNCT
ejpam-5783	283	27	psbn	psbn	PROPN
ejpam-5783	283	28	→	→	SYM
ejpam-5783	283	29	qsbn	qsbn	PROPN
ejpam-5783	283	30	a	a	DET
ejpam-5783	283	31	sheffer	sheffer	NOUN
ejpam-5783	283	32	stroke	stroke	NOUN
ejpam-5783	283	33	bn	bn	NOUN
ejpam-5783	283	34	-	-	PUNCT
ejpam-5783	283	35	homomorphism	homomorphism	NOUN
ejpam-5783	283	36	.	.	PUNCT
ejpam-5783	284	1	let	let	VERB
ejpam-5783	284	2	a	a	DET
ejpam-5783	284	3	∈	∈	PROPN
ejpam-5783	284	4	kerφ	kerφ	PROPN
ejpam-5783	284	5	,	,	PUNCT
ejpam-5783	284	6	we	we	PRON
ejpam-5783	284	7	have	have	VERB
ejpam-5783	284	8	φ(a	φ(a	ADJ
ejpam-5783	284	9	)	)	PUNCT
ejpam-5783	284	10	=	=	SYM
ejpam-5783	285	1	0	0	X
ejpam-5783	285	2	.	.	PUNCT
ejpam-5783	285	3	by	by	ADP
ejpam-5783	285	4	using	use	VERB
ejpam-5783	285	5	theorem	theorem	ADJ
ejpam-5783	285	6	3	3	NUM
ejpam-5783	285	7	(	(	PUNCT
ejpam-5783	285	8	vi	vi	NOUN
ejpam-5783	285	9	)	)	PUNCT
ejpam-5783	285	10	and	and	CCONJ
ejpam-5783	285	11	(	(	PUNCT
ejpam-5783	285	12	s2	s2	PROPN
ejpam-5783	285	13	)	)	PUNCT
ejpam-5783	285	14	,	,	PUNCT
ejpam-5783	285	15	we	we	PRON
ejpam-5783	285	16	obtain	obtain	VERB
ejpam-5783	285	17	φ((0|p	φ((0|p	ADJ
ejpam-5783	285	18	(	(	PUNCT
ejpam-5783	285	19	a|pa))|p	a|pa))|p	PROPN
ejpam-5783	285	20	(	(	PUNCT
ejpam-5783	285	21	a|p	a|p	PROPN
ejpam-5783	285	22	b	b	X
ejpam-5783	285	23	)	)	PUNCT
ejpam-5783	285	24	)	)	PUNCT
ejpam-5783	286	1	=	=	SYM
ejpam-5783	286	2	φ(0|p	φ(0|p	PROPN
ejpam-5783	286	3	(	(	PUNCT
ejpam-5783	286	4	a|pa))|q(φ(a|p	a|pa))|q(φ(a|p	NOUN
ejpam-5783	286	5	b	b	X
ejpam-5783	286	6	)	)	PUNCT
ejpam-5783	286	7	,	,	PUNCT
ejpam-5783	286	8	s.	s.	PROPN
ejpam-5783	286	9	gemawati	gemawati	PROPN
ejpam-5783	286	10	et	et	PROPN
ejpam-5783	286	11	al	al	PROPN
ejpam-5783	286	12	.	.	PUNCT
ejpam-5783	286	13	/	/	SYM
ejpam-5783	286	14	eur	eur	PROPN
ejpam-5783	286	15	.	.	PUNCT
ejpam-5783	287	1	j.	j.	PROPN
ejpam-5783	287	2	pure	pure	PROPN
ejpam-5783	287	3	appl	appl	PROPN
ejpam-5783	287	4	.	.	PROPN
ejpam-5783	287	5	math	math	PROPN
ejpam-5783	287	6	,	,	PUNCT
ejpam-5783	287	7	18	18	NUM
ejpam-5783	287	8	(	(	PUNCT
ejpam-5783	287	9	1	1	NUM
ejpam-5783	287	10	)	)	PUNCT
ejpam-5783	287	11	(	(	PUNCT
ejpam-5783	287	12	2025	2025	NUM
ejpam-5783	287	13	)	)	PUNCT
ejpam-5783	287	14	,	,	PUNCT
ejpam-5783	287	15	5783	5783	NUM
ejpam-5783	287	16	11	11	NUM
ejpam-5783	287	17	of	of	ADP
ejpam-5783	287	18	12	12	NUM
ejpam-5783	287	19	=	=	SYM
ejpam-5783	287	20	(	(	PUNCT
ejpam-5783	287	21	φ(0)|q(φ(a)|qφ(a)))|q((φ(a)|q(φ(b	φ(0)|q(φ(a)|qφ(a)))|q((φ(a)|q(φ(b	PROPN
ejpam-5783	287	22	)	)	PUNCT
ejpam-5783	287	23	)	)	PUNCT
ejpam-5783	287	24	,	,	PUNCT
ejpam-5783	287	25	=	=	PUNCT
ejpam-5783	287	26	(	(	PUNCT
ejpam-5783	287	27	0|q(0|q0))|q((0|q(φ(b	0|q(0|q0))|q((0|q(φ(b	NUM
ejpam-5783	287	28	)	)	PUNCT
ejpam-5783	287	29	)	)	PUNCT
ejpam-5783	287	30	,	,	PUNCT
ejpam-5783	287	31	=	=	PUNCT
ejpam-5783	287	32	(	(	PUNCT
ejpam-5783	287	33	0|q0)|q((0|q(φ(b	0|q0)|q((0|q(φ(b	NUM
ejpam-5783	287	34	)	)	PUNCT
ejpam-5783	287	35	)	)	PUNCT
ejpam-5783	287	36	,	,	PUNCT
ejpam-5783	287	37	φ((0|p	φ((0|p	X
ejpam-5783	287	38	(	(	PUNCT
ejpam-5783	287	39	a|pa))|p	a|pa))|p	PROPN
ejpam-5783	287	40	(	(	PUNCT
ejpam-5783	287	41	a|p	a|p	PROPN
ejpam-5783	287	42	b	b	X
ejpam-5783	287	43	)	)	PUNCT
ejpam-5783	287	44	)	)	PUNCT
ejpam-5783	288	1	=	=	SYM
ejpam-5783	288	2	0	0	X
ejpam-5783	288	3	.	.	PUNCT
ejpam-5783	289	1	therefore	therefore	ADV
ejpam-5783	289	2	,	,	PUNCT
ejpam-5783	289	3	we	we	PRON
ejpam-5783	289	4	have	have	VERB
ejpam-5783	289	5	(	(	PUNCT
ejpam-5783	289	6	(	(	PUNCT
ejpam-5783	289	7	0|p	0|p	X
ejpam-5783	289	8	(	(	PUNCT
ejpam-5783	289	9	a|pa))|p	a|pa))|p	PROPN
ejpam-5783	289	10	(	(	PUNCT
ejpam-5783	289	11	a|p	a|p	PROPN
ejpam-5783	289	12	b	b	X
ejpam-5783	289	13	)	)	PUNCT
ejpam-5783	289	14	)	)	PUNCT
ejpam-5783	290	1	∈	∈	PROPN
ejpam-5783	290	2	kerφ	kerφ	PROPN
ejpam-5783	290	3	.	.	PUNCT
ejpam-5783	291	1	theorem	theorem	VERB
ejpam-5783	291	2	10	10	NUM
ejpam-5783	291	3	.	.	PUNCT
ejpam-5783	292	1	let	let	VERB
ejpam-5783	292	2	(	(	PUNCT
ejpam-5783	292	3	psbn	psbn	NOUN
ejpam-5783	292	4	;	;	PUNCT
ejpam-5783	292	5	|p	|p	NOUN
ejpam-5783	292	6	,	,	PUNCT
ejpam-5783	292	7	0	0	NUM
ejpam-5783	292	8	)	)	PUNCT
ejpam-5783	292	9	and	and	CCONJ
ejpam-5783	292	10	(	(	PUNCT
ejpam-5783	292	11	qsbn	qsbn	NOUN
ejpam-5783	292	12	;	;	PUNCT
ejpam-5783	292	13	|q	|q	NOUN
ejpam-5783	292	14	,	,	PUNCT
ejpam-5783	292	15	0	0	NUM
ejpam-5783	292	16	)	)	PUNCT
ejpam-5783	292	17	be	be	VERB
ejpam-5783	292	18	two	two	NUM
ejpam-5783	292	19	sheffer	sheffer	NOUN
ejpam-5783	292	20	stroke	stroke	NOUN
ejpam-5783	292	21	bn	bn	NOUN
ejpam-5783	292	22	-	-	PUNCT
ejpam-5783	292	23	algebras	algebras	PROPN
ejpam-5783	292	24	and	and	CCONJ
ejpam-5783	292	25	φ	φ	PROPN
ejpam-5783	292	26	:	:	PUNCT
ejpam-5783	292	27	psbn	psbn	PROPN
ejpam-5783	292	28	→	→	SYM
ejpam-5783	292	29	qsbn	qsbn	PROPN
ejpam-5783	292	30	a	a	DET
ejpam-5783	292	31	sheffer	sheffer	NOUN
ejpam-5783	292	32	stroke	stroke	NOUN
ejpam-5783	292	33	bn	bn	NOUN
ejpam-5783	292	34	-	-	PUNCT
ejpam-5783	292	35	homomorphism	homomorphism	NOUN
ejpam-5783	292	36	.	.	PUNCT
ejpam-5783	293	1	if	if	SCONJ
ejpam-5783	293	2	a	a	PRON
ejpam-5783	293	3	,	,	PUNCT
ejpam-5783	293	4	b	b	PROPN
ejpam-5783	293	5	∈	∈	PROPN
ejpam-5783	293	6	kerφ	kerφ	PROPN
ejpam-5783	293	7	,	,	PUNCT
ejpam-5783	293	8	then	then	ADV
ejpam-5783	293	9	(	(	PUNCT
ejpam-5783	293	10	b|p	b|p	X
ejpam-5783	293	11	(	(	PUNCT
ejpam-5783	293	12	b|p	b|p	PROPN
ejpam-5783	293	13	b))|p	b))|p	PROPN
ejpam-5783	293	14	(	(	PUNCT
ejpam-5783	293	15	a|pa	a|pa	NOUN
ejpam-5783	293	16	)	)	PUNCT
ejpam-5783	293	17	∈	∈	PROPN
ejpam-5783	293	18	kerφ	kerφ	PROPN
ejpam-5783	293	19	.	.	PUNCT
ejpam-5783	293	20	proof	proof	NOUN
ejpam-5783	293	21	.	.	PUNCT
ejpam-5783	294	1	let	let	VERB
ejpam-5783	294	2	(	(	PUNCT
ejpam-5783	294	3	psbn	psbn	NOUN
ejpam-5783	294	4	;	;	PUNCT
ejpam-5783	294	5	|p	|p	NOUN
ejpam-5783	294	6	,	,	PUNCT
ejpam-5783	294	7	0	0	NUM
ejpam-5783	294	8	)	)	PUNCT
ejpam-5783	294	9	and	and	CCONJ
ejpam-5783	294	10	(	(	PUNCT
ejpam-5783	294	11	qsbn	qsbn	NOUN
ejpam-5783	294	12	;	;	PUNCT
ejpam-5783	294	13	|q	|q	NOUN
ejpam-5783	294	14	,	,	PUNCT
ejpam-5783	294	15	0	0	NUM
ejpam-5783	294	16	)	)	PUNCT
ejpam-5783	294	17	be	be	VERB
ejpam-5783	294	18	two	two	NUM
ejpam-5783	294	19	sheffer	sheffer	NOUN
ejpam-5783	294	20	stroke	stroke	NOUN
ejpam-5783	294	21	bn	bn	NOUN
ejpam-5783	294	22	-	-	PUNCT
ejpam-5783	294	23	algebras	algebras	PROPN
ejpam-5783	294	24	and	and	CCONJ
ejpam-5783	294	25	φ	φ	PROPN
ejpam-5783	294	26	:	:	PUNCT
ejpam-5783	294	27	psbn	psbn	PROPN
ejpam-5783	294	28	→	→	SYM
ejpam-5783	294	29	qsbn	qsbn	PROPN
ejpam-5783	294	30	a	a	DET
ejpam-5783	294	31	sheffer	sheffer	NOUN
ejpam-5783	294	32	stroke	stroke	NOUN
ejpam-5783	294	33	bn	bn	NOUN
ejpam-5783	294	34	-	-	PUNCT
ejpam-5783	294	35	homomorphism	homomorphism	NOUN
ejpam-5783	294	36	.	.	PUNCT
ejpam-5783	295	1	let	let	VERB
ejpam-5783	295	2	a	a	DET
ejpam-5783	295	3	,	,	PUNCT
ejpam-5783	295	4	b	b	PROPN
ejpam-5783	295	5	∈	∈	PROPN
ejpam-5783	295	6	kerφ	kerφ	PROPN
ejpam-5783	295	7	,	,	PUNCT
ejpam-5783	295	8	we	we	PRON
ejpam-5783	295	9	have	have	AUX
ejpam-5783	295	10	φ(a	φ(a	ADJ
ejpam-5783	295	11	)	)	PUNCT
ejpam-5783	295	12	=	=	SYM
ejpam-5783	295	13	0	0	NUM
ejpam-5783	295	14	and	and	CCONJ
ejpam-5783	295	15	φ(b	φ(b	PROPN
ejpam-5783	295	16	)	)	PUNCT
ejpam-5783	295	17	=	=	SYM
ejpam-5783	296	1	0	0	X
ejpam-5783	296	2	.	.	PUNCT
ejpam-5783	296	3	by	by	ADP
ejpam-5783	296	4	using	use	VERB
ejpam-5783	296	5	theorem	theorem	ADJ
ejpam-5783	296	6	3	3	NUM
ejpam-5783	296	7	(	(	PUNCT
ejpam-5783	296	8	vi	vi	NOUN
ejpam-5783	296	9	)	)	PUNCT
ejpam-5783	296	10	and	and	CCONJ
ejpam-5783	296	11	(	(	PUNCT
ejpam-5783	296	12	s2	s2	PROPN
ejpam-5783	296	13	)	)	PUNCT
ejpam-5783	296	14	,	,	PUNCT
ejpam-5783	296	15	we	we	PRON
ejpam-5783	296	16	obtain	obtain	VERB
ejpam-5783	296	17	φ((b|p	φ((b|p	PUNCT
ejpam-5783	296	18	(	(	PUNCT
ejpam-5783	296	19	b|p	b|p	PROPN
ejpam-5783	296	20	b))|p	b))|p	PROPN
ejpam-5783	296	21	(	(	PUNCT
ejpam-5783	296	22	a|pa	a|pa	NOUN
ejpam-5783	296	23	)	)	PUNCT
ejpam-5783	296	24	)	)	PUNCT
ejpam-5783	297	1	=	=	SYM
ejpam-5783	297	2	φ(b|p	φ(b|p	NUM
ejpam-5783	297	3	(	(	PUNCT
ejpam-5783	297	4	b|p	b|p	PROPN
ejpam-5783	297	5	b))|qφ(a|pa	b))|qφ(a|pa	PROPN
ejpam-5783	297	6	)	)	PUNCT
ejpam-5783	297	7	,	,	PUNCT
ejpam-5783	297	8	=	=	PUNCT
ejpam-5783	297	9	(	(	PUNCT
ejpam-5783	297	10	φ(b)|q(φ(b)|qφ(b)))|q((φ(a)|q(φ(a	φ(b)|q(φ(b)|qφ(b)))|q((φ(a)|q(φ(a	NOUN
ejpam-5783	297	11	)	)	PUNCT
ejpam-5783	297	12	)	)	PUNCT
ejpam-5783	297	13	,	,	PUNCT
ejpam-5783	297	14	=	=	SYM
ejpam-5783	297	15	(	(	PUNCT
ejpam-5783	297	16	0|q(0|q0))|q((0|q(0	0|q(0|q0))|q((0|q(0	NOUN
ejpam-5783	297	17	)	)	PUNCT
ejpam-5783	297	18	,	,	PUNCT
ejpam-5783	297	19	φ((b|p	φ((b|p	PUNCT
ejpam-5783	297	20	(	(	PUNCT
ejpam-5783	297	21	b|p	b|p	PROPN
ejpam-5783	297	22	b))|p	b))|p	PROPN
ejpam-5783	297	23	(	(	PUNCT
ejpam-5783	297	24	a|pa	a|pa	NOUN
ejpam-5783	297	25	)	)	PUNCT
ejpam-5783	297	26	)	)	PUNCT
ejpam-5783	298	1	=	=	PUNCT
ejpam-5783	298	2	0	0	X
ejpam-5783	298	3	.	.	PUNCT
ejpam-5783	299	1	hence	hence	ADV
ejpam-5783	299	2	,	,	PUNCT
ejpam-5783	299	3	it	it	PRON
ejpam-5783	299	4	is	be	AUX
ejpam-5783	299	5	proven	prove	VERB
ejpam-5783	299	6	that	that	SCONJ
ejpam-5783	299	7	(	(	PUNCT
ejpam-5783	299	8	(	(	PUNCT
ejpam-5783	299	9	b|p	b|p	X
ejpam-5783	299	10	(	(	PUNCT
ejpam-5783	299	11	b|p	b|p	PROPN
ejpam-5783	299	12	b))|p	b))|p	PROPN
ejpam-5783	299	13	(	(	PUNCT
ejpam-5783	299	14	a|pa	a|pa	NOUN
ejpam-5783	299	15	)	)	PUNCT
ejpam-5783	299	16	)	)	PUNCT
ejpam-5783	299	17	∈	∈	PROPN
ejpam-5783	299	18	kerφ	kerφ	PROPN
ejpam-5783	299	19	.	.	PUNCT
ejpam-5783	300	1	4	4	NUM
ejpam-5783	300	2	.	.	X
ejpam-5783	300	3	conclusions	conclusion	NOUN
ejpam-5783	300	4	in	in	ADP
ejpam-5783	300	5	this	this	DET
ejpam-5783	300	6	paper	paper	NOUN
ejpam-5783	300	7	,	,	PUNCT
ejpam-5783	300	8	the	the	DET
ejpam-5783	300	9	concept	concept	NOUN
ejpam-5783	300	10	of	of	ADP
ejpam-5783	300	11	a	a	DET
ejpam-5783	300	12	sheffer	sheffer	NOUN
ejpam-5783	300	13	stroke	stroke	NOUN
ejpam-5783	300	14	bn	bn	NOUN
ejpam-5783	300	15	-	-	PUNCT
ejpam-5783	300	16	algebra	algebra	NOUN
ejpam-5783	300	17	is	be	AUX
ejpam-5783	300	18	introduced	introduce	VERB
ejpam-5783	300	19	,	,	PUNCT
ejpam-5783	300	20	and	and	CCONJ
ejpam-5783	300	21	its	its	PRON
ejpam-5783	300	22	key	key	ADJ
ejpam-5783	300	23	properties	property	NOUN
ejpam-5783	300	24	are	be	AUX
ejpam-5783	300	25	thoroughly	thoroughly	ADV
ejpam-5783	300	26	examined	examine	VERB
ejpam-5783	300	27	.	.	PUNCT
ejpam-5783	301	1	these	these	PRON
ejpam-5783	301	2	include	include	VERB
ejpam-5783	301	3	the	the	DET
ejpam-5783	301	4	independence	independence	NOUN
ejpam-5783	301	5	of	of	ADP
ejpam-5783	301	6	the	the	DET
ejpam-5783	301	7	axioms	axiom	NOUN
ejpam-5783	301	8	and	and	CCONJ
ejpam-5783	301	9	the	the	DET
ejpam-5783	301	10	special	special	ADJ
ejpam-5783	301	11	properties	property	NOUN
ejpam-5783	301	12	related	relate	VERB
ejpam-5783	301	13	to	to	ADP
ejpam-5783	301	14	the	the	DET
ejpam-5783	301	15	element	element	NOUN
ejpam-5783	301	16	0	0	NUM
ejpam-5783	301	17	.	.	PUNCT
ejpam-5783	302	1	furthermore	furthermore	ADV
ejpam-5783	302	2	,	,	PUNCT
ejpam-5783	302	3	the	the	DET
ejpam-5783	302	4	paper	paper	NOUN
ejpam-5783	302	5	defines	define	VERB
ejpam-5783	302	6	the	the	DET
ejpam-5783	302	7	notions	notion	NOUN
ejpam-5783	302	8	of	of	ADP
ejpam-5783	302	9	sheffer	sheffer	PROPN
ejpam-5783	302	10	stroke	stroke	PROPN
ejpam-5783	302	11	bn	bn	PROPN
ejpam-5783	302	12	-	-	PUNCT
ejpam-5783	302	13	subalgebras	subalgebras	PROPN
ejpam-5783	302	14	,	,	PUNCT
ejpam-5783	302	15	bn	bn	NOUN
ejpam-5783	302	16	-	-	PUNCT
ejpam-5783	302	17	ideals	ideal	NOUN
ejpam-5783	302	18	,	,	PUNCT
ejpam-5783	302	19	and	and	CCONJ
ejpam-5783	302	20	bn	bn	NOUN
ejpam-5783	302	21	-	-	PUNCT
ejpam-5783	302	22	homomorphisms	homomorphism	NOUN
ejpam-5783	302	23	,	,	PUNCT
ejpam-5783	302	24	along	along	ADP
ejpam-5783	302	25	with	with	ADP
ejpam-5783	302	26	normal	normal	ADJ
ejpam-5783	302	27	subsets	subset	NOUN
ejpam-5783	302	28	of	of	ADP
ejpam-5783	302	29	sheffer	sheffer	PROPN
ejpam-5783	302	30	stroke	stroke	PROPN
ejpam-5783	302	31	bn	bn	NOUN
ejpam-5783	302	32	-	-	PUNCT
ejpam-5783	302	33	algebras	algebras	PROPN
ejpam-5783	302	34	.	.	PUNCT
ejpam-5783	303	1	the	the	DET
ejpam-5783	303	2	interrelationships	interrelationship	NOUN
ejpam-5783	303	3	between	between	ADP
ejpam-5783	303	4	these	these	DET
ejpam-5783	303	5	concepts	concept	NOUN
ejpam-5783	303	6	are	be	AUX
ejpam-5783	303	7	explored	explore	VERB
ejpam-5783	303	8	,	,	PUNCT
ejpam-5783	303	9	providing	provide	VERB
ejpam-5783	303	10	a	a	DET
ejpam-5783	303	11	clear	clear	ADJ
ejpam-5783	303	12	framework	framework	NOUN
ejpam-5783	303	13	for	for	ADP
ejpam-5783	303	14	understanding	understand	VERB
ejpam-5783	303	15	their	their	PRON
ejpam-5783	303	16	connections	connection	NOUN
ejpam-5783	303	17	.	.	PUNCT
ejpam-5783	304	1	finally	finally	ADV
ejpam-5783	304	2	,	,	PUNCT
ejpam-5783	304	3	the	the	DET
ejpam-5783	304	4	paper	paper	NOUN
ejpam-5783	304	5	outlines	outline	VERB
ejpam-5783	304	6	potential	potential	ADJ
ejpam-5783	304	7	avenues	avenue	NOUN
ejpam-5783	304	8	for	for	ADP
ejpam-5783	304	9	future	future	ADJ
ejpam-5783	304	10	research	research	NOUN
ejpam-5783	304	11	,	,	PUNCT
ejpam-5783	304	12	particularly	particularly	ADV
ejpam-5783	304	13	focusing	focus	VERB
ejpam-5783	304	14	on	on	ADP
ejpam-5783	304	15	the	the	DET
ejpam-5783	304	16	exploration	exploration	NOUN
ejpam-5783	304	17	of	of	ADP
ejpam-5783	304	18	the	the	DET
ejpam-5783	304	19	filter	filter	NOUN
ejpam-5783	304	20	and	and	CCONJ
ejpam-5783	304	21	derivation	derivation	NOUN
ejpam-5783	304	22	concepts	concept	NOUN
ejpam-5783	304	23	within	within	ADP
ejpam-5783	304	24	the	the	DET
ejpam-5783	304	25	context	context	NOUN
ejpam-5783	304	26	of	of	ADP
ejpam-5783	304	27	sheffer	sheffer	PROPN
ejpam-5783	304	28	stroke	stroke	PROPN
ejpam-5783	304	29	bn	bn	NOUN
ejpam-5783	304	30	-	-	PUNCT
ejpam-5783	304	31	algebras	algebra	NOUN
ejpam-5783	304	32	.	.	PUNCT
ejpam-5783	305	1	acknowledgements	acknowledgement	NOUN
ejpam-5783	305	2	we	we	PRON
ejpam-5783	305	3	would	would	AUX
ejpam-5783	305	4	like	like	VERB
ejpam-5783	305	5	to	to	PART
ejpam-5783	305	6	thank	thank	VERB
ejpam-5783	305	7	you	you	PRON
ejpam-5783	305	8	to	to	ADP
ejpam-5783	305	9	the	the	DET
ejpam-5783	305	10	directorate	directorate	ADJ
ejpam-5783	305	11	general	general	NOUN
ejpam-5783	305	12	of	of	ADP
ejpam-5783	305	13	higher	high	ADJ
ejpam-5783	305	14	education	education	NOUN
ejpam-5783	305	15	,	,	PUNCT
ejpam-5783	305	16	research	research	NOUN
ejpam-5783	305	17	,	,	PUNCT
ejpam-5783	305	18	and	and	CCONJ
ejpam-5783	305	19	technology	technology	NOUN
ejpam-5783	305	20	(	(	PUNCT
ejpam-5783	305	21	dghert	dghert	ADJ
ejpam-5783	305	22	)	)	PUNCT
ejpam-5783	305	23	of	of	ADP
ejpam-5783	305	24	the	the	DET
ejpam-5783	305	25	ministry	ministry	PROPN
ejpam-5783	305	26	of	of	ADP
ejpam-5783	305	27	education	education	PROPN
ejpam-5783	305	28	,	,	PUNCT
ejpam-5783	305	29	culture	culture	NOUN
ejpam-5783	305	30	,	,	PUNCT
ejpam-5783	305	31	research	research	NOUN
ejpam-5783	305	32	,	,	PUNCT
ejpam-5783	305	33	and	and	CCONJ
ejpam-5783	305	34	technology	technology	NOUN
ejpam-5783	305	35	(	(	PUNCT
ejpam-5783	305	36	moecrt	moecrt	NOUN
ejpam-5783	305	37	)	)	PUNCT
ejpam-5783	305	38	of	of	ADP
ejpam-5783	305	39	the	the	DET
ejpam-5783	305	40	republic	republic	NOUN
ejpam-5783	305	41	of	of	ADP
ejpam-5783	305	42	indonesia	indonesia	PROPN
ejpam-5783	305	43	for	for	ADP
ejpam-5783	305	44	the	the	DET
ejpam-5783	305	45	funding	funding	NOUN
ejpam-5783	305	46	support	support	NOUN
ejpam-5783	305	47	provided	provide	VERB
ejpam-5783	305	48	through	through	ADP
ejpam-5783	305	49	the	the	DET
ejpam-5783	305	50	2024	2024	NUM
ejpam-5783	305	51	research	research	NOUN
ejpam-5783	305	52	scheme	scheme	NOUN
ejpam-5783	305	53	with	with	ADP
ejpam-5783	305	54	contract	contract	NOUN
ejpam-5783	305	55	number	number	NOUN
ejpam-5783	305	56	083	083	NUM
ejpam-5783	305	57	/	/	SYM
ejpam-5783	305	58	e5	e5	PROPN
ejpam-5783	305	59	/	/	SYM
ejpam-5783	305	60	pg.02.00.pl/2024	pg.02.00.pl/2024	PROPN
ejpam-5783	305	61	,	,	PUNCT
ejpam-5783	305	62	so	so	SCONJ
ejpam-5783	305	63	that	that	SCONJ
ejpam-5783	305	64	this	this	DET
ejpam-5783	305	65	research	research	NOUN
ejpam-5783	305	66	can	can	AUX
ejpam-5783	305	67	be	be	AUX
ejpam-5783	305	68	carried	carry	VERB
ejpam-5783	305	69	out	out	ADP
ejpam-5783	305	70	well	well	ADV
ejpam-5783	305	71	.	.	PUNCT
ejpam-5783	306	1	s.	s.	PROPN
ejpam-5783	306	2	gemawati	gemawati	PROPN
ejpam-5783	306	3	et	et	PROPN
ejpam-5783	306	4	al	al	PROPN
ejpam-5783	306	5	.	.	PUNCT
ejpam-5783	306	6	/	/	SYM
ejpam-5783	306	7	eur	eur	PROPN
ejpam-5783	306	8	.	.	PUNCT
ejpam-5783	307	1	j.	j.	PROPN
ejpam-5783	307	2	pure	pure	PROPN
ejpam-5783	307	3	appl	appl	PROPN
ejpam-5783	307	4	.	.	PROPN
ejpam-5783	307	5	math	math	PROPN
ejpam-5783	307	6	,	,	PUNCT
ejpam-5783	307	7	18	18	NUM
ejpam-5783	307	8	(	(	PUNCT
ejpam-5783	307	9	1	1	NUM
ejpam-5783	307	10	)	)	PUNCT
ejpam-5783	307	11	(	(	PUNCT
ejpam-5783	307	12	2025	2025	NUM
ejpam-5783	307	13	)	)	PUNCT
ejpam-5783	307	14	,	,	PUNCT
ejpam-5783	307	15	5783	5783	NUM
ejpam-5783	307	16	12	12	NUM
ejpam-5783	307	17	of	of	ADP
ejpam-5783	307	18	12	12	NUM
ejpam-5783	307	19	references	reference	NOUN
ejpam-5783	307	20	[	[	X
ejpam-5783	307	21	1	1	X
ejpam-5783	307	22	]	]	PUNCT
ejpam-5783	307	23	s.	s.	PROPN
ejpam-5783	307	24	s.	s.	PROPN
ejpam-5783	307	25	ahn	ahn	PROPN
ejpam-5783	307	26	,	,	PUNCT
ejpam-5783	307	27	h.	h.	PROPN
ejpam-5783	307	28	s.	s.	PROPN
ejpam-5783	307	29	kim	kim	PROPN
ejpam-5783	307	30	,	,	PUNCT
ejpam-5783	307	31	s.	s.	PROPN
ejpam-5783	307	32	song	song	PROPN
ejpam-5783	307	33	,	,	PUNCT
ejpam-5783	307	34	and	and	CCONJ
ejpam-5783	308	1	y.	y.	PROPN
ejpam-5783	308	2	b.	b.	PROPN
ejpam-5783	308	3	jun	jun	PROPN
ejpam-5783	308	4	.	.	PUNCT
ejpam-5783	309	1	dokdo	dokdo	PROPN
ejpam-5783	309	2	filters	filter	NOUN
ejpam-5783	309	3	and	and	CCONJ
ejpam-5783	309	4	deductive	deductive	ADJ
ejpam-5783	309	5	systems	system	NOUN
ejpam-5783	309	6	of	of	ADP
ejpam-5783	309	7	sheffer	sheffer	PROPN
ejpam-5783	309	8	stroke	stroke	PROPN
ejpam-5783	309	9	hilbert	hilbert	PROPN
ejpam-5783	309	10	algebras	algebras	PROPN
ejpam-5783	309	11	.	.	PUNCT
ejpam-5783	310	1	european	european	PROPN
ejpam-5783	310	2	journal	journal	PROPN
ejpam-5783	310	3	of	of	ADP
ejpam-5783	310	4	pure	pure	ADJ
ejpam-5783	310	5	and	and	CCONJ
ejpam-5783	310	6	applied	applied	ADJ
ejpam-5783	310	7	mathematics	mathematic	NOUN
ejpam-5783	310	8	,	,	PUNCT
ejpam-5783	310	9	16:1862–1877	16:1862–1877	NUM
ejpam-5783	310	10	,	,	PUNCT
ejpam-5783	310	11	2023	2023	NUM
ejpam-5783	310	12	.	.	PUNCT
ejpam-5783	311	1	[	[	X
ejpam-5783	311	2	2	2	NUM
ejpam-5783	311	3	]	]	PUNCT
ejpam-5783	311	4	i.	i.	NOUN
ejpam-5783	311	5	chajda	chajda	PROPN
ejpam-5783	311	6	.	.	PUNCT
ejpam-5783	312	1	sheffer	sheffer	PROPN
ejpam-5783	312	2	operation	operation	NOUN
ejpam-5783	312	3	in	in	ADP
ejpam-5783	312	4	ortholattices	ortholattice	NOUN
ejpam-5783	312	5	.	.	PUNCT
ejpam-5783	313	1	acta	acta	PROPN
ejpam-5783	313	2	univ	univ	PROPN
ejpam-5783	313	3	.	.	PUNCT
ejpam-5783	314	1	palacki	palacki	PROPN
ejpam-5783	314	2	.	.	PUNCT
ejpam-5783	315	1	olomuc	olomuc	PROPN
ejpam-5783	315	2	.	.	PUNCT
ejpam-5783	315	3	,	,	PUNCT
ejpam-5783	315	4	fac	fac	PROPN
ejpam-5783	315	5	.	.	PROPN
ejpam-5783	315	6	rer	rer	PROPN
ejpam-5783	315	7	.	.	PUNCT
ejpam-5783	316	1	nat	nat	PROPN
ejpam-5783	316	2	.	.	PROPN
ejpam-5783	316	3	,	,	PUNCT
ejpam-5783	316	4	mathematica	mathematica	PROPN
ejpam-5783	316	5	,	,	PUNCT
ejpam-5783	316	6	44:19–23	44:19–23	PROPN
ejpam-5783	316	7	,	,	PUNCT
ejpam-5783	316	8	2005	2005	NUM
ejpam-5783	316	9	.	.	PUNCT
ejpam-5783	317	1	[	[	X
ejpam-5783	317	2	3	3	X
ejpam-5783	317	3	]	]	X
ejpam-5783	317	4	g.	g.	PROPN
ejpam-5783	317	5	dymek	dymek	PROPN
ejpam-5783	317	6	and	and	CCONJ
ejpam-5783	317	7	a.	a.	PROPN
ejpam-5783	317	8	walendziak	walendziak	PROPN
ejpam-5783	317	9	.	.	PUNCT
ejpam-5783	318	1	(	(	PUNCT
ejpam-5783	318	2	fuzzy	fuzzy	ADJ
ejpam-5783	318	3	)	)	PUNCT
ejpam-5783	318	4	ideals	ideal	NOUN
ejpam-5783	318	5	of	of	ADP
ejpam-5783	318	6	bn	bn	NOUN
ejpam-5783	318	7	-	-	PUNCT
ejpam-5783	318	8	algebras	algebras	PROPN
ejpam-5783	318	9	.	.	PUNCT
ejpam-5783	319	1	scientific	scientific	ADJ
ejpam-5783	319	2	world	world	PROPN
ejpam-5783	319	3	journal	journal	NOUN
ejpam-5783	319	4	,	,	PUNCT
ejpam-5783	319	5	pages	page	NOUN
ejpam-5783	319	6	1–9	1–9	NUM
ejpam-5783	319	7	,	,	PUNCT
ejpam-5783	319	8	2015	2015	NUM
ejpam-5783	319	9	.	.	PUNCT
ejpam-5783	320	1	[	[	X
ejpam-5783	320	2	4	4	X
ejpam-5783	320	3	]	]	X
ejpam-5783	320	4	e.	e.	PROPN
ejpam-5783	320	5	fitria	fitria	PROPN
ejpam-5783	320	6	,	,	PUNCT
ejpam-5783	320	7	s.	s.	PROPN
ejpam-5783	320	8	gemawati	gemawati	PROPN
ejpam-5783	320	9	,	,	PUNCT
ejpam-5783	320	10	and	and	CCONJ
ejpam-5783	320	11	kartini	kartini	NOUN
ejpam-5783	320	12	.	.	PUNCT
ejpam-5783	321	1	prime	prime	ADJ
ejpam-5783	321	2	ideals	ideal	NOUN
ejpam-5783	321	3	in	in	ADP
ejpam-5783	321	4	b	b	NOUN
ejpam-5783	321	5	-	-	PUNCT
ejpam-5783	321	6	algebras	algebras	PROPN
ejpam-5783	321	7	.	.	PUNCT
ejpam-5783	322	1	international	international	ADJ
ejpam-5783	322	2	journal	journal	PROPN
ejpam-5783	322	3	of	of	ADP
ejpam-5783	322	4	algebra	algebra	PROPN
ejpam-5783	322	5	,	,	PUNCT
ejpam-5783	322	6	11:301–309	11:301–309	PROPN
ejpam-5783	322	7	,	,	PUNCT
ejpam-5783	322	8	2017	2017	NUM
ejpam-5783	322	9	.	.	PUNCT
ejpam-5783	323	1	[	[	X
ejpam-5783	323	2	5	5	X
ejpam-5783	323	3	]	]	PUNCT
ejpam-5783	323	4	s.	s.	PROPN
ejpam-5783	323	5	gemawati	gemawati	PROPN
ejpam-5783	323	6	,	,	PUNCT
ejpam-5783	323	7	e.	e.	PROPN
ejpam-5783	323	8	fitria	fitria	PROPN
ejpam-5783	323	9	,	,	PUNCT
ejpam-5783	323	10	a.	a.	NOUN
ejpam-5783	323	11	hadi	hadi	PROPN
ejpam-5783	323	12	,	,	PUNCT
ejpam-5783	323	13	and	and	CCONJ
ejpam-5783	323	14	m.	m.	PROPN
ejpam-5783	323	15	musraini	musraini	PROPN
ejpam-5783	323	16	.	.	PUNCT
ejpam-5783	324	1	complete	complete	ADJ
ejpam-5783	324	2	ideal	ideal	NOUN
ejpam-5783	324	3	and	and	CCONJ
ejpam-5783	324	4	n	n	CCONJ
ejpam-5783	324	5	-	-	PUNCT
ejpam-5783	324	6	ideal	ideal	NOUN
ejpam-5783	324	7	of	of	ADP
ejpam-5783	324	8	bn	bn	NOUN
ejpam-5783	324	9	-	-	PUNCT
ejpam-5783	324	10	algebras	algebras	PROPN
ejpam-5783	324	11	.	.	PUNCT
ejpam-5783	325	1	international	international	ADJ
ejpam-5783	325	2	journal	journal	PROPN
ejpam-5783	325	3	of	of	ADP
ejpam-5783	325	4	mathematics	mathematics	NOUN
ejpam-5783	325	5	trends	trend	NOUN
ejpam-5783	325	6	and	and	CCONJ
ejpam-5783	325	7	technology	technology	NOUN
ejpam-5783	325	8	,	,	PUNCT
ejpam-5783	325	9	66:52–59	66:52–59	PROPN
ejpam-5783	325	10	,	,	PUNCT
ejpam-5783	325	11	2020	2020	NUM
ejpam-5783	325	12	.	.	PUNCT
ejpam-5783	326	1	[	[	X
ejpam-5783	326	2	6	6	NUM
ejpam-5783	326	3	]	]	PUNCT
ejpam-5783	326	4	s.	s.	PROPN
ejpam-5783	326	5	gemawati	gemawati	PROPN
ejpam-5783	326	6	,	,	PUNCT
ejpam-5783	326	7	mashadi	mashadi	NOUN
ejpam-5783	326	8	,	,	PUNCT
ejpam-5783	326	9	m.	m.	NOUN
ejpam-5783	326	10	m	m	PROPN
ejpam-5783	326	11	,	,	PUNCT
ejpam-5783	326	12	and	and	CCONJ
ejpam-5783	326	13	e.	e.	PROPN
ejpam-5783	326	14	fitria	fitria	PROPN
ejpam-5783	326	15	.	.	PUNCT
ejpam-5783	327	1	fq	fq	NOUN
ejpam-5783	327	2	-	-	NOUN
ejpam-5783	327	3	derivation	derivation	NOUN
ejpam-5783	327	4	of	of	ADP
ejpam-5783	327	5	bp	bp	PROPN
ejpam-5783	327	6	-	-	PUNCT
ejpam-5783	327	7	algebras	algebras	PROPN
ejpam-5783	327	8	.	.	PUNCT
ejpam-5783	328	1	journal	journal	PROPN
ejpam-5783	328	2	of	of	ADP
ejpam-5783	328	3	the	the	DET
ejpam-5783	328	4	indonesian	indonesian	PROPN
ejpam-5783	328	5	mathematical	mathematical	ADJ
ejpam-5783	328	6	society	society	NOUN
ejpam-5783	328	7	,	,	PUNCT
ejpam-5783	328	8	pages	page	NOUN
ejpam-5783	328	9	235–244	235–244	NUM
ejpam-5783	328	10	,	,	PUNCT
ejpam-5783	328	11	2023	2023	NUM
ejpam-5783	328	12	.	.	PUNCT
ejpam-5783	329	1	[	[	X
ejpam-5783	329	2	7	7	X
ejpam-5783	329	3	]	]	X
ejpam-5783	329	4	s.	s.	PROPN
ejpam-5783	329	5	gemawati	gemawati	PROPN
ejpam-5783	329	6	,	,	PUNCT
ejpam-5783	329	7	m.	m.	NOUN
ejpam-5783	329	8	musraini	musraini	PROPN
ejpam-5783	329	9	,	,	PUNCT
ejpam-5783	329	10	a.	a.	NOUN
ejpam-5783	329	11	hadi	hadi	PROPN
ejpam-5783	329	12	,	,	PUNCT
ejpam-5783	329	13	l.	l.	PROPN
ejpam-5783	329	14	zakaria	zakaria	PROPN
ejpam-5783	329	15	,	,	PUNCT
ejpam-5783	329	16	and	and	CCONJ
ejpam-5783	329	17	e.	e.	PROPN
ejpam-5783	329	18	fitria	fitria	PROPN
ejpam-5783	329	19	.	.	PUNCT
ejpam-5783	330	1	on	on	ADP
ejpam-5783	330	2	r	r	NOUN
ejpam-5783	330	3	-	-	PUNCT
ejpam-5783	330	4	ideals	ideal	NOUN
ejpam-5783	330	5	and	and	CCONJ
ejpam-5783	330	6	m	m	PROPN
ejpam-5783	330	7	-	-	ADJ
ejpam-5783	330	8	k	k	NOUN
ejpam-5783	330	9	-	-	NOUN
ejpam-5783	330	10	ideals	ideal	NOUN
ejpam-5783	330	11	in	in	ADP
ejpam-5783	330	12	bn	bn	NOUN
ejpam-5783	330	13	-	-	PUNCT
ejpam-5783	330	14	algebras	algebra	NOUN
ejpam-5783	330	15	.	.	PUNCT
ejpam-5783	331	1	axioms	axiom	NOUN
ejpam-5783	331	2	,	,	PUNCT
ejpam-5783	331	3	11	11	NUM
ejpam-5783	331	4	,	,	PUNCT
ejpam-5783	331	5	2022	2022	NUM
ejpam-5783	331	6	.	.	PUNCT
ejpam-5783	332	1	[	[	X
ejpam-5783	332	2	8	8	NUM
ejpam-5783	332	3	]	]	PUNCT
ejpam-5783	332	4	s.	s.	PROPN
ejpam-5783	332	5	gemawati	gemawati	PROPN
ejpam-5783	332	6	,	,	PUNCT
ejpam-5783	332	7	a.	a.	NOUN
ejpam-5783	332	8	sirait	sirait	PROPN
ejpam-5783	332	9	,	,	PUNCT
ejpam-5783	332	10	m.	m.	NOUN
ejpam-5783	332	11	m	m	PROPN
ejpam-5783	332	12	,	,	PUNCT
ejpam-5783	332	13	and	and	CCONJ
ejpam-5783	332	14	e.	e.	PROPN
ejpam-5783	332	15	fitria	fitria	PROPN
ejpam-5783	332	16	.	.	PUNCT
ejpam-5783	333	1	fq	fq	PROPN
ejpam-5783	333	2	-	-	NOUN
ejpam-5783	333	3	derivations	derivation	NOUN
ejpam-5783	333	4	of	of	ADP
ejpam-5783	333	5	bn1	bn1	PROPN
ejpam-5783	333	6	-	-	PUNCT
ejpam-5783	333	7	algebras	algebras	PROPN
ejpam-5783	333	8	.	.	PUNCT
ejpam-5783	334	1	international	international	ADJ
ejpam-5783	334	2	journal	journal	PROPN
ejpam-5783	334	3	of	of	ADP
ejpam-5783	334	4	mathematics	mathematics	NOUN
ejpam-5783	334	5	trends	trend	NOUN
ejpam-5783	334	6	and	and	CCONJ
ejpam-5783	334	7	technology	technology	NOUN
ejpam-5783	334	8	,	,	PUNCT
ejpam-5783	334	9	67:1–13	67:1–13	NOUN
ejpam-5783	334	10	,	,	PUNCT
ejpam-5783	334	11	2021	2021	NUM
ejpam-5783	334	12	.	.	PUNCT
ejpam-5783	335	1	[	[	X
ejpam-5783	335	2	9	9	NUM
ejpam-5783	335	3	]	]	PUNCT
ejpam-5783	335	4	t.	t.	NOUN
ejpam-5783	335	5	gerima	gerima	NOUN
ejpam-5783	335	6	,	,	PUNCT
ejpam-5783	335	7	y.	y.	PROPN
ejpam-5783	335	8	endris	endris	PROPN
ejpam-5783	335	9	,	,	PUNCT
ejpam-5783	335	10	and	and	CCONJ
ejpam-5783	335	11	g.	g.	PROPN
ejpam-5783	335	12	fasil	fasil	PROPN
ejpam-5783	335	13	.	.	PUNCT
ejpam-5783	336	1	ideals	ideal	NOUN
ejpam-5783	336	2	and	and	CCONJ
ejpam-5783	336	3	filters	filter	NOUN
ejpam-5783	336	4	on	on	ADP
ejpam-5783	336	5	implication	implication	NOUN
ejpam-5783	336	6	algebras	algebra	NOUN
ejpam-5783	336	7	.	.	PUNCT
ejpam-5783	337	1	advances	advance	NOUN
ejpam-5783	337	2	in	in	ADP
ejpam-5783	337	3	mathematics	mathematic	NOUN
ejpam-5783	337	4	:	:	PUNCT
ejpam-5783	337	5	scientific	scientific	ADJ
ejpam-5783	337	6	journal	journal	NOUN
ejpam-5783	337	7	,	,	PUNCT
ejpam-5783	337	8	10:1167–1174	10:1167–1174	NUM
ejpam-5783	337	9	,	,	PUNCT
ejpam-5783	337	10	2020	2020	NUM
ejpam-5783	337	11	.	.	PUNCT
ejpam-5783	338	1	[	[	X
ejpam-5783	338	2	10	10	NUM
ejpam-5783	338	3	]	]	X
ejpam-5783	338	4	t.	t.	PROPN
ejpam-5783	338	5	katican	katican	PROPN
ejpam-5783	338	6	,	,	PUNCT
ejpam-5783	338	7	t.	t.	PROPN
ejpam-5783	338	8	oner	oner	NOUN
ejpam-5783	338	9	,	,	PUNCT
ejpam-5783	338	10	and	and	CCONJ
ejpam-5783	338	11	a.	a.	PROPN
ejpam-5783	338	12	b.	b.	PROPN
ejpam-5783	338	13	saeid	saeid	PROPN
ejpam-5783	338	14	.	.	PUNCT
ejpam-5783	339	1	sheffer	sheffer	PROPN
ejpam-5783	339	2	stroke	stroke	PROPN
ejpam-5783	339	3	r0	r0	NOUN
ejpam-5783	339	4	-	-	PUNCT
ejpam-5783	339	5	algebras	algebras	PROPN
ejpam-5783	339	6	.	.	PUNCT
ejpam-5783	340	1	algebraic	algebraic	ADJ
ejpam-5783	340	2	structures	structure	NOUN
ejpam-5783	340	3	and	and	CCONJ
ejpam-5783	340	4	their	their	PRON
ejpam-5783	340	5	applications	application	NOUN
ejpam-5783	340	6	,	,	PUNCT
ejpam-5783	340	7	10:65–85	10:65–85	NUM
ejpam-5783	340	8	,	,	PUNCT
ejpam-5783	340	9	2023	2023	NUM
ejpam-5783	340	10	.	.	PUNCT
ejpam-5783	341	1	[	[	X
ejpam-5783	341	2	11	11	NUM
ejpam-5783	341	3	]	]	X
ejpam-5783	341	4	c.	c.	PROPN
ejpam-5783	341	5	b.	b.	PROPN
ejpam-5783	341	6	kim	kim	PROPN
ejpam-5783	341	7	and	and	CCONJ
ejpam-5783	341	8	h.	h.	PROPN
ejpam-5783	341	9	s.	s.	PROPN
ejpam-5783	341	10	kim	kim	PROPN
ejpam-5783	341	11	.	.	PUNCT
ejpam-5783	342	1	on	on	ADP
ejpam-5783	342	2	bn	bn	NOUN
ejpam-5783	342	3	-	-	PUNCT
ejpam-5783	342	4	algebras	algebras	PROPN
ejpam-5783	342	5	.	.	PUNCT
ejpam-5783	343	1	kyungpook	kyungpook	PROPN
ejpam-5783	343	2	mathematical	mathematical	PROPN
ejpam-5783	343	3	journal	journal	PROPN
ejpam-5783	343	4	,	,	PUNCT
ejpam-5783	343	5	53:175	53:175	NUM
ejpam-5783	343	6	–	–	PUNCT
ejpam-5783	343	7	184	184	NUM
ejpam-5783	343	8	,	,	PUNCT
ejpam-5783	343	9	2013	2013	NUM
ejpam-5783	343	10	.	.	PUNCT
ejpam-5783	344	1	[	[	X
ejpam-5783	344	2	12	12	NUM
ejpam-5783	344	3	]	]	PUNCT
ejpam-5783	344	4	a.	a.	NOUN
ejpam-5783	344	5	molkhasi	molkhasi	NOUN
ejpam-5783	344	6	.	.	PUNCT
ejpam-5783	345	1	representations	representation	NOUN
ejpam-5783	345	2	of	of	ADP
ejpam-5783	345	3	sheffer	sheffer	NOUN
ejpam-5783	345	4	stroke	stroke	NOUN
ejpam-5783	345	5	algebras	algebra	NOUN
ejpam-5783	345	6	and	and	CCONJ
ejpam-5783	345	7	visser	visser	PROPN
ejpam-5783	345	8	algebras	algebras	PROPN
ejpam-5783	345	9	.	.	PUNCT
ejpam-5783	345	10	soft	soft	ADJ
ejpam-5783	345	11	computing	computing	NOUN
ejpam-5783	345	12	,	,	PUNCT
ejpam-5783	345	13	25:8533–8538	25:8533–8538	NUM
ejpam-5783	345	14	,	,	PUNCT
ejpam-5783	345	15	2021	2021	NUM
ejpam-5783	345	16	.	.	PUNCT
ejpam-5783	346	1	[	[	X
ejpam-5783	346	2	13	13	NUM
ejpam-5783	346	3	]	]	PUNCT
ejpam-5783	346	4	t.	t.	NOUN
ejpam-5783	346	5	oner	oner	NOUN
ejpam-5783	346	6	,	,	PUNCT
ejpam-5783	346	7	t.	t.	PROPN
ejpam-5783	346	8	kalkan	kalkan	PROPN
ejpam-5783	346	9	,	,	PUNCT
ejpam-5783	346	10	and	and	CCONJ
ejpam-5783	346	11	a.	a.	PROPN
ejpam-5783	346	12	borumand	borumand	PROPN
ejpam-5783	346	13	saeid	saeid	PROPN
ejpam-5783	346	14	.	.	PUNCT
ejpam-5783	347	1	class	class	NOUN
ejpam-5783	347	2	of	of	ADP
ejpam-5783	347	3	sheffer	sheffer	PROPN
ejpam-5783	347	4	stroke	stroke	NOUN
ejpam-5783	347	5	bck	bck	PROPN
ejpam-5783	347	6	-	-	PUNCT
ejpam-5783	347	7	algebras	algebras	PROPN
ejpam-5783	347	8	.	.	PUNCT
ejpam-5783	348	1	analele	analele	PROPN
ejpam-5783	348	2	stiintifice	stiintifice	PROPN
ejpam-5783	348	3	ale	ale	PROPN
ejpam-5783	348	4	universitatii	universitatii	PROPN
ejpam-5783	348	5	ovidius	ovidius	PROPN
ejpam-5783	348	6	constanta	constanta	PROPN
ejpam-5783	348	7	,	,	PUNCT
ejpam-5783	348	8	seria	seria	PROPN
ejpam-5783	348	9	matematica	matematica	PROPN
ejpam-5783	348	10	,	,	PUNCT
ejpam-5783	348	11	30:247–269	30:247–269	PROPN
ejpam-5783	348	12	,	,	PUNCT
ejpam-5783	348	13	2022	2022	NUM
ejpam-5783	348	14	.	.	PUNCT
ejpam-5783	349	1	[	[	X
ejpam-5783	349	2	14	14	NUM
ejpam-5783	349	3	]	]	X
ejpam-5783	349	4	t.	t.	NOUN
ejpam-5783	349	5	oner	oner	NOUN
ejpam-5783	349	6	,	,	PUNCT
ejpam-5783	349	7	t.	t.	PROPN
ejpam-5783	349	8	katican	katican	PROPN
ejpam-5783	349	9	,	,	PUNCT
ejpam-5783	349	10	a.	a.	PROPN
ejpam-5783	349	11	b.	b.	PROPN
ejpam-5783	349	12	saeid	saeid	PROPN
ejpam-5783	349	13	,	,	PUNCT
ejpam-5783	349	14	and	and	CCONJ
ejpam-5783	349	15	m.	m.	NOUN
ejpam-5783	349	16	terziler	terziler	PROPN
ejpam-5783	349	17	.	.	PUNCT
ejpam-5783	350	1	filters	filter	NOUN
ejpam-5783	350	2	of	of	ADP
ejpam-5783	350	3	strong	strong	ADJ
ejpam-5783	350	4	sheffer	sheffer	NOUN
ejpam-5783	350	5	stroke	stroke	NOUN
ejpam-5783	350	6	nonassociative	nonassociative	ADJ
ejpam-5783	350	7	mv	mv	PROPN
ejpam-5783	350	8	-	-	PUNCT
ejpam-5783	350	9	algebras	algebras	X
ejpam-5783	350	10	.	.	PUNCT
ejpam-5783	351	1	analele	analele	PROPN
ejpam-5783	351	2	universitatii	universitatii	PROPN
ejpam-5783	351	3	ovidius	ovidius	PROPN
ejpam-5783	351	4	constanta	constanta	PROPN
ejpam-5783	351	5	-	-	PUNCT
ejpam-5783	351	6	seria	seria	PROPN
ejpam-5783	351	7	matematica	matematica	PROPN
ejpam-5783	351	8	,	,	PUNCT
ejpam-5783	351	9	29:143–164	29:143–164	PROPN
ejpam-5783	351	10	,	,	PUNCT
ejpam-5783	351	11	2021	2021	NUM
ejpam-5783	351	12	.	.	PUNCT
ejpam-5783	352	1	[	[	X
ejpam-5783	352	2	15	15	NUM
ejpam-5783	352	3	]	]	X
ejpam-5783	352	4	t.	t.	NOUN
ejpam-5783	352	5	oner	oner	NOUN
ejpam-5783	352	6	,	,	PUNCT
ejpam-5783	352	7	t.	t.	PROPN
ejpam-5783	352	8	katican	katican	PROPN
ejpam-5783	352	9	,	,	PUNCT
ejpam-5783	352	10	and	and	CCONJ
ejpam-5783	352	11	a.	a.	PROPN
ejpam-5783	352	12	borumand	borumand	PROPN
ejpam-5783	352	13	saeid	saeid	PROPN
ejpam-5783	352	14	.	.	PUNCT
ejpam-5783	353	1	relation	relation	NOUN
ejpam-5783	353	2	between	between	ADP
ejpam-5783	353	3	sheffer	sheffer	PROPN
ejpam-5783	353	4	stroke	stroke	PROPN
ejpam-5783	353	5	and	and	CCONJ
ejpam-5783	353	6	hilbert	hilbert	PROPN
ejpam-5783	353	7	algebras	algebras	PROPN
ejpam-5783	353	8	.	.	PUNCT
ejpam-5783	353	9	categories	category	NOUN
ejpam-5783	353	10	and	and	CCONJ
ejpam-5783	353	11	general	general	ADJ
ejpam-5783	353	12	algebraic	algebraic	ADJ
ejpam-5783	353	13	structures	structure	NOUN
ejpam-5783	353	14	with	with	ADP
ejpam-5783	353	15	application	application	NOUN
ejpam-5783	353	16	,	,	PUNCT
ejpam-5783	353	17	14:245–268	14:245–268	NUM
ejpam-5783	353	18	,	,	PUNCT
ejpam-5783	353	19	2021	2021	NUM
ejpam-5783	353	20	.	.	PUNCT
ejpam-5783	354	1	[	[	X
ejpam-5783	354	2	16	16	NUM
ejpam-5783	354	3	]	]	PUNCT
ejpam-5783	354	4	a.	a.	PROPN
ejpam-5783	354	5	borumand	borumand	PROPN
ejpam-5783	354	6	saeid	saeid	PROPN
ejpam-5783	354	7	,	,	PUNCT
ejpam-5783	354	8	t.	t.	PROPN
ejpam-5783	354	9	katican	katican	PROPN
ejpam-5783	354	10	,	,	PUNCT
ejpam-5783	354	11	and	and	CCONJ
ejpam-5783	354	12	t.	t.	PROPN
ejpam-5783	354	13	oner	oner	NOUN
ejpam-5783	354	14	.	.	PUNCT
ejpam-5783	355	1	on	on	ADP
ejpam-5783	355	2	sheffer	sheffer	PROPN
ejpam-5783	355	3	stroke	stroke	PROPN
ejpam-5783	355	4	up	up	ADP
ejpam-5783	355	5	-	-	PUNCT
ejpam-5783	355	6	algebras	algebras	X
ejpam-5783	355	7	.	.	PUNCT
ejpam-5783	356	1	discussiones	discussione	NOUN
ejpam-5783	356	2	mathematicae	mathematicae	VERB
ejpam-5783	356	3	general	general	ADJ
ejpam-5783	356	4	algebra	algebra	PROPN
ejpam-5783	356	5	and	and	CCONJ
ejpam-5783	356	6	applications	application	NOUN
ejpam-5783	356	7	,	,	PUNCT
ejpam-5783	356	8	41:381–394	41:381–394	NUM
ejpam-5783	356	9	,	,	PUNCT
ejpam-5783	356	10	2021	2021	NUM
ejpam-5783	356	11	.	.	PUNCT
ejpam-5783	357	1	[	[	X
ejpam-5783	357	2	17	17	NUM
ejpam-5783	357	3	]	]	X
ejpam-5783	357	4	i.	i.	NOUN
ejpam-5783	357	5	senturk	senturk	PROPN
ejpam-5783	357	6	.	.	PUNCT
ejpam-5783	358	1	a	a	DET
ejpam-5783	358	2	view	view	NOUN
ejpam-5783	358	3	on	on	ADP
ejpam-5783	358	4	state	state	NOUN
ejpam-5783	358	5	operators	operator	NOUN
ejpam-5783	358	6	in	in	ADP
ejpam-5783	358	7	sheffer	sheffer	PROPN
ejpam-5783	358	8	stroke	stroke	NOUN
ejpam-5783	358	9	basic	basic	ADJ
ejpam-5783	358	10	algebras	algebra	NOUN
ejpam-5783	358	11	.	.	PUNCT
ejpam-5783	358	12	soft	soft	ADJ
ejpam-5783	358	13	computing	computing	NOUN
ejpam-5783	358	14	,	,	PUNCT
ejpam-5783	358	15	25:11471–11484	25:11471–11484	NUM
ejpam-5783	358	16	,	,	PUNCT
ejpam-5783	358	17	2021	2021	NUM
ejpam-5783	358	18	.	.	PUNCT