id	sid	tid	token	lemma	pos
ejpam-5646	1	1	european	european	PROPN
ejpam-5646	1	2	journal	journal	PROPN
ejpam-5646	1	3	of	of	ADP
ejpam-5646	1	4	pure	pure	ADJ
ejpam-5646	1	5	and	and	CCONJ
ejpam-5646	1	6	applied	applied	ADJ
ejpam-5646	1	7	mathematics	mathematic	NOUN
ejpam-5646	1	8	2025	2025	NUM
ejpam-5646	1	9	,	,	PUNCT
ejpam-5646	1	10	vol	vol	NOUN
ejpam-5646	1	11	.	.	PROPN
ejpam-5646	1	12	18	18	NUM
ejpam-5646	1	13	,	,	PUNCT
ejpam-5646	1	14	issue	issue	NOUN
ejpam-5646	1	15	1	1	NUM
ejpam-5646	1	16	,	,	PUNCT
ejpam-5646	1	17	article	article	NOUN
ejpam-5646	1	18	number	number	NOUN
ejpam-5646	1	19	5646	5646	NUM
ejpam-5646	1	20	issn	issn	VERB
ejpam-5646	1	21	1307	1307	NUM
ejpam-5646	1	22	-	-	SYM
ejpam-5646	1	23	5543	5543	NUM
ejpam-5646	1	24	–	–	PUNCT
ejpam-5646	1	25	ejpam.com	ejpam.com	X
ejpam-5646	1	26	published	publish	VERB
ejpam-5646	1	27	by	by	ADP
ejpam-5646	1	28	new	new	PROPN
ejpam-5646	1	29	york	york	PROPN
ejpam-5646	1	30	business	business	PROPN
ejpam-5646	1	31	global	global	ADJ
ejpam-5646	1	32	generalization	generalization	NOUN
ejpam-5646	1	33	of	of	ADP
ejpam-5646	1	34	bi	bi	NOUN
ejpam-5646	1	35	-	-	NOUN
ejpam-5646	1	36	antiideals	antiideal	NOUN
ejpam-5646	1	37	in	in	ADP
ejpam-5646	1	38	semigroups	semigroups	X
ejpam-5646	1	39	madeleine	madeleine	PROPN
ejpam-5646	1	40	al	al	PROPN
ejpam-5646	1	41	tahan1	tahan1	PROPN
ejpam-5646	1	42	,	,	PUNCT
ejpam-5646	1	43	sarka	sarka	PROPN
ejpam-5646	1	44	hoskova	hoskova	PROPN
ejpam-5646	1	45	-	-	PUNCT
ejpam-5646	1	46	mayerova2,∗	mayerova2,∗	PROPN
ejpam-5646	1	47	,	,	PUNCT
ejpam-5646	1	48	saba	saba	PROPN
ejpam-5646	1	49	al	al	PROPN
ejpam-5646	1	50	-	-	PUNCT
ejpam-5646	1	51	kaseasbeh3	kaseasbeh3	PROPN
ejpam-5646	1	52	1	1	NUM
ejpam-5646	1	53	department	department	NOUN
ejpam-5646	1	54	of	of	ADP
ejpam-5646	1	55	mathematics	mathematic	NOUN
ejpam-5646	1	56	and	and	CCONJ
ejpam-5646	1	57	statistics	statistic	NOUN
ejpam-5646	1	58	,	,	PUNCT
ejpam-5646	1	59	abu	abu	PROPN
ejpam-5646	1	60	dhabi	dhabi	PROPN
ejpam-5646	1	61	university	university	PROPN
ejpam-5646	1	62	,	,	PUNCT
ejpam-5646	1	63	united	united	PROPN
ejpam-5646	1	64	arab	arab	PROPN
ejpam-5646	1	65	emirates	emirates	PROPN
ejpam-5646	1	66	2	2	NUM
ejpam-5646	1	67	department	department	NOUN
ejpam-5646	1	68	of	of	ADP
ejpam-5646	1	69	mathematics	mathematics	PROPN
ejpam-5646	1	70	and	and	CCONJ
ejpam-5646	1	71	physics	physics	PROPN
ejpam-5646	1	72	,	,	PUNCT
ejpam-5646	1	73	university	university	NOUN
ejpam-5646	1	74	of	of	ADP
ejpam-5646	1	75	defence	defence	NOUN
ejpam-5646	1	76	,	,	PUNCT
ejpam-5646	1	77	czech	czech	PROPN
ejpam-5646	1	78	republic	republic	PROPN
ejpam-5646	1	79	3	3	NUM
ejpam-5646	1	80	department	department	NOUN
ejpam-5646	1	81	of	of	ADP
ejpam-5646	1	82	mathematis	mathematis	PROPN
ejpam-5646	1	83	,	,	PUNCT
ejpam-5646	1	84	tafila	tafila	NOUN
ejpam-5646	1	85	technical	technical	ADJ
ejpam-5646	1	86	university	university	PROPN
ejpam-5646	1	87	,	,	PUNCT
ejpam-5646	1	88	jordan	jordan	PROPN
ejpam-5646	1	89	abstract	abstract	PROPN
ejpam-5646	1	90	.	.	PUNCT
ejpam-5646	2	1	algebraic	algebraic	ADJ
ejpam-5646	2	2	structure	structure	NOUN
ejpam-5646	2	3	consisting	consist	VERB
ejpam-5646	2	4	of	of	ADP
ejpam-5646	2	5	a	a	DET
ejpam-5646	2	6	set	set	NOUN
ejpam-5646	2	7	together	together	ADV
ejpam-5646	2	8	with	with	ADP
ejpam-5646	2	9	an	an	DET
ejpam-5646	2	10	associative	associative	ADJ
ejpam-5646	2	11	internal	internal	ADJ
ejpam-5646	2	12	binary	binary	ADJ
ejpam-5646	2	13	operation	operation	NOUN
ejpam-5646	2	14	on	on	ADP
ejpam-5646	2	15	it	it	PRON
ejpam-5646	2	16	,	,	PUNCT
ejpam-5646	2	17	so	so	ADV
ejpam-5646	2	18	called	call	VERB
ejpam-5646	2	19	semigroup	semigroup	PROPN
ejpam-5646	2	20	has	have	VERB
ejpam-5646	2	21	applications	application	NOUN
ejpam-5646	2	22	in	in	ADP
ejpam-5646	2	23	different	different	ADJ
ejpam-5646	2	24	fields	field	NOUN
ejpam-5646	2	25	of	of	ADP
ejpam-5646	2	26	science	science	NOUN
ejpam-5646	2	27	.	.	PUNCT
ejpam-5646	3	1	for	for	ADP
ejpam-5646	3	2	a	a	DET
ejpam-5646	3	3	better	well	ADJ
ejpam-5646	3	4	understanding	understanding	NOUN
ejpam-5646	3	5	of	of	ADP
ejpam-5646	3	6	these	these	DET
ejpam-5646	3	7	applications	application	NOUN
ejpam-5646	3	8	,	,	PUNCT
ejpam-5646	3	9	semigroups	semigroup	NOUN
ejpam-5646	3	10	are	be	AUX
ejpam-5646	3	11	characterized	characterize	VERB
ejpam-5646	3	12	through	through	ADP
ejpam-5646	3	13	their	their	PRON
ejpam-5646	3	14	subsets	subset	NOUN
ejpam-5646	3	15	.	.	PUNCT
ejpam-5646	4	1	fuzzy	fuzzy	ADJ
ejpam-5646	4	2	sets	set	NOUN
ejpam-5646	4	3	deal	deal	VERB
ejpam-5646	4	4	with	with	ADP
ejpam-5646	4	5	uncertainties	uncertainty	NOUN
ejpam-5646	4	6	,	,	PUNCT
ejpam-5646	4	7	and	and	CCONJ
ejpam-5646	4	8	because	because	SCONJ
ejpam-5646	4	9	many	many	ADJ
ejpam-5646	4	10	real	real	ADJ
ejpam-5646	4	11	-	-	PUNCT
ejpam-5646	4	12	life	life	NOUN
ejpam-5646	4	13	problems	problem	NOUN
ejpam-5646	4	14	have	have	VERB
ejpam-5646	4	15	an	an	DET
ejpam-5646	4	16	associated	associated	ADJ
ejpam-5646	4	17	algebraic	algebraic	ADJ
ejpam-5646	4	18	structure	structure	NOUN
ejpam-5646	4	19	,	,	PUNCT
ejpam-5646	4	20	fuzzification	fuzzification	NOUN
ejpam-5646	4	21	of	of	ADP
ejpam-5646	4	22	these	these	DET
ejpam-5646	4	23	structures	structure	NOUN
ejpam-5646	4	24	makes	make	VERB
ejpam-5646	4	25	sense	sense	NOUN
ejpam-5646	4	26	and	and	CCONJ
ejpam-5646	4	27	is	be	AUX
ejpam-5646	4	28	useful	useful	ADJ
ejpam-5646	4	29	.	.	PUNCT
ejpam-5646	5	1	this	this	DET
ejpam-5646	5	2	paper	paper	NOUN
ejpam-5646	5	3	investigates	investigate	VERB
ejpam-5646	5	4	the	the	DET
ejpam-5646	5	5	generalization	generalization	NOUN
ejpam-5646	5	6	of	of	ADP
ejpam-5646	5	7	bi	bi	NOUN
ejpam-5646	5	8	-	-	NOUN
ejpam-5646	5	9	antiideals	antiideal	NOUN
ejpam-5646	5	10	in	in	ADP
ejpam-5646	5	11	semigroups	semigroup	NOUN
ejpam-5646	5	12	and	and	CCONJ
ejpam-5646	5	13	their	their	PRON
ejpam-5646	5	14	fuzzification	fuzzification	NOUN
ejpam-5646	5	15	to	to	PART
ejpam-5646	5	16	enhance	enhance	VERB
ejpam-5646	5	17	understanding	understanding	NOUN
ejpam-5646	5	18	of	of	ADP
ejpam-5646	5	19	algebraic	algebraic	ADJ
ejpam-5646	5	20	structures	structure	NOUN
ejpam-5646	5	21	with	with	ADP
ejpam-5646	5	22	uncertainties	uncertainty	NOUN
ejpam-5646	5	23	.	.	PUNCT
ejpam-5646	6	1	building	build	VERB
ejpam-5646	6	2	upon	upon	SCONJ
ejpam-5646	6	3	prior	prior	ADJ
ejpam-5646	6	4	research	research	NOUN
ejpam-5646	6	5	,	,	PUNCT
ejpam-5646	6	6	we	we	PRON
ejpam-5646	6	7	define	define	VERB
ejpam-5646	6	8	and	and	CCONJ
ejpam-5646	6	9	explore	explore	VERB
ejpam-5646	6	10	(	(	PUNCT
ejpam-5646	6	11	m	m	NOUN
ejpam-5646	6	12	,	,	PUNCT
ejpam-5646	6	13	n)bi	n)bi	NOUN
ejpam-5646	6	14	-	-	PUNCT
ejpam-5646	6	15	antiideals	antiideal	NOUN
ejpam-5646	6	16	as	as	ADP
ejpam-5646	6	17	an	an	DET
ejpam-5646	6	18	extension	extension	NOUN
ejpam-5646	6	19	of	of	ADP
ejpam-5646	6	20	bi	bi	NOUN
ejpam-5646	6	21	-	-	NOUN
ejpam-5646	6	22	antiideals	antiideal	NOUN
ejpam-5646	6	23	,	,	PUNCT
ejpam-5646	6	24	studying	study	VERB
ejpam-5646	6	25	their	their	PRON
ejpam-5646	6	26	properties	property	NOUN
ejpam-5646	6	27	through	through	ADP
ejpam-5646	6	28	theoretical	theoretical	ADJ
ejpam-5646	6	29	analysis	analysis	NOUN
ejpam-5646	6	30	and	and	CCONJ
ejpam-5646	6	31	illustrative	illustrative	ADJ
ejpam-5646	6	32	examples	example	NOUN
ejpam-5646	6	33	.	.	PUNCT
ejpam-5646	7	1	we	we	PRON
ejpam-5646	7	2	introduce	introduce	VERB
ejpam-5646	7	3	fuzzy	fuzzy	ADJ
ejpam-5646	7	4	(	(	PUNCT
ejpam-5646	7	5	m	m	NOUN
ejpam-5646	7	6	,	,	PUNCT
ejpam-5646	7	7	n)-bi	n)-bi	NOUN
ejpam-5646	7	8	-	-	PUNCT
ejpam-5646	7	9	antiideals	antiideal	NOUN
ejpam-5646	7	10	by	by	ADP
ejpam-5646	7	11	leveraging	leverage	VERB
ejpam-5646	7	12	fuzzy	fuzzy	ADJ
ejpam-5646	7	13	set	set	NOUN
ejpam-5646	7	14	theory	theory	NOUN
ejpam-5646	7	15	to	to	ADP
ejpam-5646	7	16	model	model	NOUN
ejpam-5646	7	17	uncertainties	uncertainty	NOUN
ejpam-5646	7	18	,	,	PUNCT
ejpam-5646	7	19	establishing	establish	VERB
ejpam-5646	7	20	a	a	DET
ejpam-5646	7	21	connection	connection	NOUN
ejpam-5646	7	22	with	with	ADP
ejpam-5646	7	23	(	(	PUNCT
ejpam-5646	7	24	m	m	NOUN
ejpam-5646	7	25	,	,	PUNCT
ejpam-5646	7	26	n)-bi	n)-bi	NOUN
ejpam-5646	7	27	-	-	PUNCT
ejpam-5646	7	28	antiideals	antiideal	NOUN
ejpam-5646	7	29	via	via	ADP
ejpam-5646	7	30	level	level	NOUN
ejpam-5646	7	31	sets	set	NOUN
ejpam-5646	7	32	.	.	PUNCT
ejpam-5646	8	1	2020	2020	NUM
ejpam-5646	8	2	mathematics	mathematic	NOUN
ejpam-5646	8	3	subject	subject	NOUN
ejpam-5646	8	4	classifications	classification	NOUN
ejpam-5646	8	5	:	:	PUNCT
ejpam-5646	8	6	06f05	06f05	NUM
ejpam-5646	8	7	,	,	PUNCT
ejpam-5646	8	8	08a72	08a72	NOUN
ejpam-5646	8	9	key	key	ADJ
ejpam-5646	8	10	words	word	NOUN
ejpam-5646	8	11	and	and	CCONJ
ejpam-5646	8	12	phrases	phrase	NOUN
ejpam-5646	8	13	:	:	PUNCT
ejpam-5646	8	14	antiideal	antiideal	NOUN
ejpam-5646	8	15	,	,	PUNCT
ejpam-5646	8	16	bi	bi	NOUN
ejpam-5646	8	17	-	-	NOUN
ejpam-5646	8	18	antiideal	antiideal	NOUN
ejpam-5646	8	19	,	,	PUNCT
ejpam-5646	8	20	(	(	PUNCT
ejpam-5646	8	21	m	m	NOUN
ejpam-5646	8	22	,	,	PUNCT
ejpam-5646	8	23	n)-bi	n)-bi	NOUN
ejpam-5646	8	24	-	-	PUNCT
ejpam-5646	8	25	antiideal	antiideal	NOUN
ejpam-5646	8	26	,	,	PUNCT
ejpam-5646	8	27	fuzzy	fuzzy	ADJ
ejpam-5646	8	28	(	(	PUNCT
ejpam-5646	8	29	m	m	NOUN
ejpam-5646	8	30	,	,	PUNCT
ejpam-5646	8	31	n)-bi	n)-bi	NOUN
ejpam-5646	8	32	-	-	PUNCT
ejpam-5646	8	33	antiideal	antiideal	NOUN
ejpam-5646	8	34	,	,	PUNCT
ejpam-5646	8	35	level	level	NOUN
ejpam-5646	8	36	set	set	VERB
ejpam-5646	8	37	1	1	NUM
ejpam-5646	8	38	.	.	PUNCT
ejpam-5646	9	1	introduction	introduction	NOUN
ejpam-5646	9	2	the	the	DET
ejpam-5646	9	3	initial	initial	ADJ
ejpam-5646	9	4	paper	paper	NOUN
ejpam-5646	9	5	on	on	ADP
ejpam-5646	9	6	semigroups	semigroup	NOUN
ejpam-5646	9	7	emerged	emerge	VERB
ejpam-5646	9	8	in	in	ADP
ejpam-5646	9	9	1905	1905	NUM
ejpam-5646	9	10	as	as	ADP
ejpam-5646	9	11	a	a	DET
ejpam-5646	9	12	concise	concise	ADJ
ejpam-5646	9	13	work	work	NOUN
ejpam-5646	9	14	by	by	ADP
ejpam-5646	9	15	l.e	l.e	PROPN
ejpam-5646	9	16	.	.	PUNCT
ejpam-5646	9	17	dickson	dickson	PROPN
ejpam-5646	9	18	.	.	PUNCT
ejpam-5646	10	1	however	however	ADV
ejpam-5646	10	2	,	,	PUNCT
ejpam-5646	10	3	the	the	DET
ejpam-5646	10	4	true	true	ADJ
ejpam-5646	10	5	inception	inception	NOUN
ejpam-5646	10	6	of	of	ADP
ejpam-5646	10	7	the	the	DET
ejpam-5646	10	8	theory	theory	NOUN
ejpam-5646	10	9	occurred	occur	VERB
ejpam-5646	10	10	in	in	ADP
ejpam-5646	10	11	1928	1928	NUM
ejpam-5646	10	12	when	when	SCONJ
ejpam-5646	10	13	a.k	a.k	PROPN
ejpam-5646	10	14	.	.	PROPN
ejpam-5646	10	15	suschkewitsch	suschkewitsch	PROPN
ejpam-5646	11	1	[	[	X
ejpam-5646	11	2	20	20	NUM
ejpam-5646	11	3	]	]	PUNCT
ejpam-5646	11	4	published	publish	VERB
ejpam-5646	11	5	a	a	DET
ejpam-5646	11	6	paper	paper	NOUN
ejpam-5646	11	7	of	of	ADP
ejpam-5646	11	8	paramount	paramount	ADJ
ejpam-5646	11	9	significance	significance	NOUN
ejpam-5646	11	10	.	.	PUNCT
ejpam-5646	12	1	in	in	ADP
ejpam-5646	12	2	contemporary	contemporary	ADJ
ejpam-5646	12	3	language	language	NOUN
ejpam-5646	12	4	,	,	PUNCT
ejpam-5646	12	5	he	he	PRON
ejpam-5646	12	6	demonstrated	demonstrate	VERB
ejpam-5646	12	7	that	that	SCONJ
ejpam-5646	12	8	within	within	ADP
ejpam-5646	12	9	any	any	DET
ejpam-5646	12	10	finite	finite	ADJ
ejpam-5646	12	11	semigroup	semigroup	NOUN
ejpam-5646	12	12	,	,	PUNCT
ejpam-5646	12	13	there	there	PRON
ejpam-5646	12	14	exists	exist	VERB
ejpam-5646	12	15	a	a	DET
ejpam-5646	12	16	“	"	PUNCT
ejpam-5646	12	17	kernel	kernel	NOUN
ejpam-5646	12	18	”	"	PUNCT
ejpam-5646	12	19	(	(	PUNCT
ejpam-5646	12	20	referred	refer	VERB
ejpam-5646	12	21	to	to	ADP
ejpam-5646	12	22	as	as	ADP
ejpam-5646	12	23	a	a	DET
ejpam-5646	12	24	simple	simple	ADJ
ejpam-5646	12	25	ideal	ideal	NOUN
ejpam-5646	12	26	)	)	PUNCT
ejpam-5646	12	27	,	,	PUNCT
ejpam-5646	12	28	and	and	CCONJ
ejpam-5646	12	29	he	he	PRON
ejpam-5646	12	30	comprehensively	comprehensively	ADV
ejpam-5646	12	31	characterized	characterize	VERB
ejpam-5646	12	32	the	the	DET
ejpam-5646	12	33	structure	structure	NOUN
ejpam-5646	12	34	of	of	ADP
ejpam-5646	12	35	finite	finite	ADJ
ejpam-5646	12	36	simple	simple	ADJ
ejpam-5646	12	37	semigroups	semigroup	NOUN
ejpam-5646	12	38	.	.	PUNCT
ejpam-5646	13	1	semigroups	semigroup	NOUN
ejpam-5646	13	2	provide	provide	VERB
ejpam-5646	13	3	a	a	DET
ejpam-5646	13	4	foundational	foundational	ADJ
ejpam-5646	13	5	framework	framework	NOUN
ejpam-5646	13	6	for	for	ADP
ejpam-5646	13	7	understanding	understand	VERB
ejpam-5646	13	8	how	how	SCONJ
ejpam-5646	13	9	elements	element	NOUN
ejpam-5646	13	10	combine	combine	VERB
ejpam-5646	13	11	under	under	ADP
ejpam-5646	13	12	certain	certain	ADJ
ejpam-5646	13	13	operations	operation	NOUN
ejpam-5646	13	14	,	,	PUNCT
ejpam-5646	13	15	and	and	CCONJ
ejpam-5646	13	16	their	their	PRON
ejpam-5646	13	17	applications	application	NOUN
ejpam-5646	13	18	span	span	VERB
ejpam-5646	13	19	across	across	ADP
ejpam-5646	13	20	multiple	multiple	ADJ
ejpam-5646	13	21	branches	branch	NOUN
ejpam-5646	13	22	of	of	ADP
ejpam-5646	13	23	mathematics	mathematic	NOUN
ejpam-5646	13	24	and	and	CCONJ
ejpam-5646	13	25	various	various	ADJ
ejpam-5646	13	26	interdisciplinary	interdisciplinary	ADJ
ejpam-5646	13	27	fields	field	NOUN
ejpam-5646	13	28	such	such	ADJ
ejpam-5646	13	29	as	as	ADP
ejpam-5646	13	30	coding	code	VERB
ejpam-5646	13	31	theory	theory	NOUN
ejpam-5646	13	32	,	,	PUNCT
ejpam-5646	13	33	automata	automata	NOUN
ejpam-5646	13	34	,	,	PUNCT
ejpam-5646	13	35	etc	etc	X
ejpam-5646	13	36	.	.	X
ejpam-5646	13	37	for	for	ADP
ejpam-5646	13	38	more	more	ADJ
ejpam-5646	13	39	details	detail	NOUN
ejpam-5646	13	40	about	about	ADP
ejpam-5646	13	41	semigroup	semigroup	ADJ
ejpam-5646	13	42	terminology	terminology	NOUN
ejpam-5646	13	43	and	and	CCONJ
ejpam-5646	13	44	history	history	NOUN
ejpam-5646	13	45	,	,	PUNCT
ejpam-5646	13	46	we	we	PRON
ejpam-5646	13	47	refer	refer	VERB
ejpam-5646	13	48	to	to	ADP
ejpam-5646	13	49	[	[	X
ejpam-5646	13	50	6	6	NUM
ejpam-5646	13	51	]	]	PUNCT
ejpam-5646	13	52	.	.	PUNCT
ejpam-5646	14	1	the	the	DET
ejpam-5646	14	2	history	history	NOUN
ejpam-5646	14	3	of	of	ADP
ejpam-5646	14	4	fuzzy	fuzzy	ADJ
ejpam-5646	14	5	sets	set	NOUN
ejpam-5646	14	6	can	can	AUX
ejpam-5646	14	7	be	be	AUX
ejpam-5646	14	8	traced	trace	VERB
ejpam-5646	14	9	back	back	ADV
ejpam-5646	14	10	to	to	ADP
ejpam-5646	14	11	the	the	DET
ejpam-5646	14	12	mid-20th	mid-20th	NUM
ejpam-5646	14	13	century	century	NOUN
ejpam-5646	14	14	when	when	SCONJ
ejpam-5646	14	15	lotfi	lotfi	PROPN
ejpam-5646	14	16	zadeh	zadeh	PROPN
ejpam-5646	14	17	[	[	X
ejpam-5646	14	18	21	21	NUM
ejpam-5646	14	19	]	]	PUNCT
ejpam-5646	14	20	introduced	introduce	VERB
ejpam-5646	14	21	the	the	DET
ejpam-5646	14	22	concept	concept	NOUN
ejpam-5646	14	23	of	of	ADP
ejpam-5646	14	24	fuzzy	fuzzy	ADJ
ejpam-5646	14	25	logic	logic	NOUN
ejpam-5646	14	26	in	in	ADP
ejpam-5646	14	27	1965	1965	NUM
ejpam-5646	14	28	.	.	PUNCT
ejpam-5646	15	1	zadeh	zadeh	PROPN
ejpam-5646	15	2	’s	’s	PART
ejpam-5646	15	3	groundbreaking	groundbreake	VERB
ejpam-5646	15	4	idea	idea	NOUN
ejpam-5646	15	5	∗corresponding	∗corresponde	VERB
ejpam-5646	15	6	author	author	NOUN
ejpam-5646	15	7	.	.	PUNCT
ejpam-5646	16	1	doi	doi	NOUN
ejpam-5646	16	2	:	:	PUNCT
ejpam-5646	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5646	https://doi.org/10.29020/nybg.ejpam.v18i1.5646	ADJ
ejpam-5646	16	4	email	email	NOUN
ejpam-5646	16	5	addresses	address	VERB
ejpam-5646	16	6	:	:	PUNCT
ejpam-5646	16	7	altahan.madeleine@gmail.com	altahan.madeleine@gmail.com	X
ejpam-5646	16	8	(	(	PUNCT
ejpam-5646	16	9	m.	m.	NOUN
ejpam-5646	16	10	al	al	PROPN
ejpam-5646	16	11	tahan	tahan	PROPN
ejpam-5646	16	12	)	)	PUNCT
ejpam-5646	16	13	,	,	PUNCT
ejpam-5646	16	14	sarka.mayerova@unob.cz	sarka.mayerova@unob.cz	NOUN
ejpam-5646	16	15	(	(	PUNCT
ejpam-5646	16	16	s.	s.	PROPN
ejpam-5646	16	17	hoskova	hoskova	PROPN
ejpam-5646	16	18	-	-	PUNCT
ejpam-5646	16	19	mayerova	mayerova	X
ejpam-5646	16	20	)	)	PUNCT
ejpam-5646	16	21	,	,	PUNCT
ejpam-5646	16	22	saba.alkaseasbeh@gmail.com	saba.alkaseasbeh@gmail.com	PROPN
ejpam-5646	16	23	(	(	PUNCT
ejpam-5646	16	24	s.	s.	PROPN
ejpam-5646	16	25	al	al	PROPN
ejpam-5646	16	26	-	-	PUNCT
ejpam-5646	16	27	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	16	28	)	)	PUNCT
ejpam-5646	16	29	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5646	17	1	1	1	NUM
ejpam-5646	17	2	copyright	copyright	NOUN
ejpam-5646	17	3	:	:	PUNCT
ejpam-5646	17	4	©	©	PROPN
ejpam-5646	17	5	2025	2025	NUM
ejpam-5646	17	6	the	the	DET
ejpam-5646	17	7	author(s	author(s	NOUN
ejpam-5646	17	8	)	)	PUNCT
ejpam-5646	17	9	.	.	PUNCT
ejpam-5646	18	1	(	(	PUNCT
ejpam-5646	18	2	cc	cc	NOUN
ejpam-5646	18	3	by	by	ADP
ejpam-5646	18	4	-	-	PUNCT
ejpam-5646	18	5	nc	nc	PROPN
ejpam-5646	18	6	4.0	4.0	NUM
ejpam-5646	18	7	)	)	PUNCT
ejpam-5646	18	8	m.	m.	NOUN
ejpam-5646	18	9	al	al	PROPN
ejpam-5646	18	10	tahan	tahan	PROPN
ejpam-5646	18	11	,	,	PUNCT
ejpam-5646	18	12	s.	s.	PROPN
ejpam-5646	18	13	hoskova	hoskova	PROPN
ejpam-5646	18	14	-	-	PUNCT
ejpam-5646	18	15	mayerova	mayerova	PROPN
ejpam-5646	18	16	,	,	PUNCT
ejpam-5646	18	17	s.	s.	PROPN
ejpam-5646	18	18	al	al	PROPN
ejpam-5646	18	19	-	-	PUNCT
ejpam-5646	18	20	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	18	21	/	/	SYM
ejpam-5646	18	22	eur	eur	NOUN
ejpam-5646	18	23	.	.	PUNCT
ejpam-5646	19	1	j.	j.	PROPN
ejpam-5646	19	2	pure	pure	PROPN
ejpam-5646	19	3	appl	appl	PROPN
ejpam-5646	19	4	.	.	PROPN
ejpam-5646	19	5	math	math	PROPN
ejpam-5646	19	6	,	,	PUNCT
ejpam-5646	19	7	18	18	NUM
ejpam-5646	19	8	(	(	PUNCT
ejpam-5646	19	9	1	1	NUM
ejpam-5646	19	10	)	)	PUNCT
ejpam-5646	19	11	(	(	PUNCT
ejpam-5646	19	12	2025	2025	NUM
ejpam-5646	19	13	)	)	PUNCT
ejpam-5646	19	14	,	,	PUNCT
ejpam-5646	19	15	5646	5646	NUM
ejpam-5646	19	16	2	2	NUM
ejpam-5646	19	17	of	of	ADP
ejpam-5646	19	18	11	11	NUM
ejpam-5646	19	19	challenged	challenge	VERB
ejpam-5646	19	20	the	the	DET
ejpam-5646	19	21	traditional	traditional	ADJ
ejpam-5646	19	22	binary	binary	ADJ
ejpam-5646	19	23	approach	approach	NOUN
ejpam-5646	19	24	of	of	ADP
ejpam-5646	19	25	classical	classical	ADJ
ejpam-5646	19	26	set	set	NOUN
ejpam-5646	19	27	theory	theory	NOUN
ejpam-5646	19	28	by	by	ADP
ejpam-5646	19	29	allowing	allow	VERB
ejpam-5646	19	30	elements	element	NOUN
ejpam-5646	19	31	to	to	PART
ejpam-5646	19	32	possess	possess	VERB
ejpam-5646	19	33	degrees	degree	NOUN
ejpam-5646	19	34	of	of	ADP
ejpam-5646	19	35	membership	membership	NOUN
ejpam-5646	19	36	in	in	ADP
ejpam-5646	19	37	sets	set	NOUN
ejpam-5646	19	38	,	,	PUNCT
ejpam-5646	19	39	rather	rather	ADV
ejpam-5646	19	40	than	than	ADP
ejpam-5646	19	41	being	be	AUX
ejpam-5646	19	42	strictly	strictly	ADV
ejpam-5646	19	43	classified	classify	VERB
ejpam-5646	19	44	as	as	ADP
ejpam-5646	19	45	either	either	CCONJ
ejpam-5646	19	46	inside	inside	ADP
ejpam-5646	19	47	or	or	CCONJ
ejpam-5646	19	48	outside	outside	ADP
ejpam-5646	19	49	a	a	DET
ejpam-5646	19	50	set	set	NOUN
ejpam-5646	19	51	.	.	PUNCT
ejpam-5646	20	1	this	this	DET
ejpam-5646	20	2	innovative	innovative	ADJ
ejpam-5646	20	3	notion	notion	NOUN
ejpam-5646	20	4	found	find	VERB
ejpam-5646	20	5	its	its	PRON
ejpam-5646	20	6	roots	root	NOUN
ejpam-5646	20	7	in	in	ADP
ejpam-5646	20	8	the	the	DET
ejpam-5646	20	9	observation	observation	NOUN
ejpam-5646	20	10	that	that	SCONJ
ejpam-5646	20	11	many	many	ADJ
ejpam-5646	20	12	real	real	ADJ
ejpam-5646	20	13	-	-	PUNCT
ejpam-5646	20	14	world	world	NOUN
ejpam-5646	20	15	concepts	concept	NOUN
ejpam-5646	20	16	are	be	AUX
ejpam-5646	20	17	not	not	PART
ejpam-5646	20	18	easily	easily	ADV
ejpam-5646	20	19	definable	definable	ADJ
ejpam-5646	20	20	in	in	ADP
ejpam-5646	20	21	precise	precise	ADJ
ejpam-5646	20	22	terms	term	NOUN
ejpam-5646	20	23	.	.	PUNCT
ejpam-5646	21	1	fuzzy	fuzzy	ADJ
ejpam-5646	21	2	sets	set	NOUN
ejpam-5646	21	3	quickly	quickly	ADV
ejpam-5646	21	4	garnered	garner	VERB
ejpam-5646	21	5	attention	attention	NOUN
ejpam-5646	21	6	across	across	ADP
ejpam-5646	21	7	various	various	ADJ
ejpam-5646	21	8	disciplines	discipline	NOUN
ejpam-5646	21	9	,	,	PUNCT
ejpam-5646	21	10	including	include	VERB
ejpam-5646	21	11	algebraic	algebraic	ADJ
ejpam-5646	21	12	structures	structure	NOUN
ejpam-5646	21	13	.	.	PUNCT
ejpam-5646	22	1	the	the	DET
ejpam-5646	22	2	combination	combination	NOUN
ejpam-5646	22	3	of	of	ADP
ejpam-5646	22	4	the	the	DET
ejpam-5646	22	5	two	two	NUM
ejpam-5646	22	6	concepts	concept	NOUN
ejpam-5646	22	7	led	lead	VERB
ejpam-5646	22	8	to	to	ADP
ejpam-5646	22	9	the	the	DET
ejpam-5646	22	10	launch	launch	NOUN
ejpam-5646	22	11	of	of	ADP
ejpam-5646	22	12	fuzzy	fuzzy	ADJ
ejpam-5646	22	13	algebraic	algebraic	ADJ
ejpam-5646	22	14	structures	structure	NOUN
ejpam-5646	22	15	.	.	PUNCT
ejpam-5646	23	1	the	the	DET
ejpam-5646	23	2	latter	latter	ADJ
ejpam-5646	23	3	was	be	AUX
ejpam-5646	23	4	established	establish	VERB
ejpam-5646	23	5	by	by	ADP
ejpam-5646	23	6	rosenfeld	rosenfeld	PROPN
ejpam-5646	23	7	[	[	X
ejpam-5646	23	8	17	17	NUM
ejpam-5646	23	9	]	]	PUNCT
ejpam-5646	23	10	in	in	ADP
ejpam-5646	23	11	1971	1971	NUM
ejpam-5646	23	12	when	when	SCONJ
ejpam-5646	23	13	he	he	PRON
ejpam-5646	23	14	introduced	introduce	VERB
ejpam-5646	23	15	fuzzy	fuzzy	ADJ
ejpam-5646	23	16	groups	group	NOUN
ejpam-5646	23	17	.	.	PUNCT
ejpam-5646	24	1	there	there	PRON
ejpam-5646	24	2	are	be	VERB
ejpam-5646	24	3	many	many	ADJ
ejpam-5646	24	4	research	research	NOUN
ejpam-5646	24	5	items	item	NOUN
ejpam-5646	24	6	in	in	ADP
ejpam-5646	24	7	the	the	DET
ejpam-5646	24	8	literature	literature	NOUN
ejpam-5646	24	9	characterizing	characterize	VERB
ejpam-5646	24	10	semigroups	semigroup	NOUN
ejpam-5646	24	11	through	through	ADP
ejpam-5646	24	12	its	its	PRON
ejpam-5646	24	13	(	(	PUNCT
ejpam-5646	24	14	fuzzy	fuzzy	ADJ
ejpam-5646	24	15	)	)	PUNCT
ejpam-5646	24	16	subsets	subset	NOUN
ejpam-5646	24	17	.	.	PUNCT
ejpam-5646	25	1	for	for	ADP
ejpam-5646	25	2	example	example	NOUN
ejpam-5646	25	3	,	,	PUNCT
ejpam-5646	25	4	(	(	PUNCT
ejpam-5646	25	5	fuzzy	fuzzy	ADJ
ejpam-5646	25	6	)	)	PUNCT
ejpam-5646	25	7	filters	filter	NOUN
ejpam-5646	25	8	of	of	ADP
ejpam-5646	25	9	a	a	DET
ejpam-5646	25	10	semigroup	semigroup	NOUN
ejpam-5646	25	11	were	be	AUX
ejpam-5646	25	12	studied	study	VERB
ejpam-5646	25	13	in	in	ADP
ejpam-5646	25	14	[	[	X
ejpam-5646	25	15	3	3	NUM
ejpam-5646	25	16	,	,	PUNCT
ejpam-5646	25	17	4	4	NUM
ejpam-5646	25	18	,	,	PUNCT
ejpam-5646	25	19	10	10	NUM
ejpam-5646	25	20	]	]	PUNCT
ejpam-5646	25	21	,	,	PUNCT
ejpam-5646	25	22	and	and	CCONJ
ejpam-5646	25	23	(	(	PUNCT
ejpam-5646	25	24	fuzzy	fuzzy	ADJ
ejpam-5646	25	25	)	)	PUNCT
ejpam-5646	25	26	ideals	ideal	NOUN
ejpam-5646	25	27	of	of	ADP
ejpam-5646	25	28	a	a	DET
ejpam-5646	25	29	semigroup	semigroup	NOUN
ejpam-5646	25	30	were	be	AUX
ejpam-5646	25	31	studied	study	VERB
ejpam-5646	25	32	in	in	ADP
ejpam-5646	25	33	[	[	X
ejpam-5646	25	34	12–15	12–15	NUM
ejpam-5646	25	35	]	]	X
ejpam-5646	25	36	.	.	PUNCT
ejpam-5646	26	1	for	for	ADP
ejpam-5646	26	2	further	further	ADJ
ejpam-5646	26	3	details	detail	NOUN
ejpam-5646	26	4	,	,	PUNCT
ejpam-5646	26	5	we	we	PRON
ejpam-5646	26	6	refer	refer	VERB
ejpam-5646	26	7	to	to	ADP
ejpam-5646	26	8	the	the	DET
ejpam-5646	26	9	work	work	NOUN
ejpam-5646	26	10	cited	cite	VERB
ejpam-5646	26	11	in	in	ADP
ejpam-5646	26	12	[	[	X
ejpam-5646	26	13	7	7	NUM
ejpam-5646	26	14	,	,	PUNCT
ejpam-5646	26	15	9	9	NUM
ejpam-5646	26	16	,	,	PUNCT
ejpam-5646	26	17	11	11	NUM
ejpam-5646	26	18	,	,	PUNCT
ejpam-5646	26	19	16	16	NUM
ejpam-5646	26	20	]	]	PUNCT
ejpam-5646	26	21	.	.	PUNCT
ejpam-5646	27	1	inspired	inspire	VERB
ejpam-5646	27	2	by	by	ADP
ejpam-5646	27	3	the	the	DET
ejpam-5646	27	4	literature	literature	NOUN
ejpam-5646	27	5	,	,	PUNCT
ejpam-5646	27	6	our	our	PRON
ejpam-5646	27	7	present	present	ADJ
ejpam-5646	27	8	work	work	NOUN
ejpam-5646	27	9	sets	set	VERB
ejpam-5646	27	10	out	out	ADP
ejpam-5646	27	11	on	on	ADP
ejpam-5646	27	12	an	an	DET
ejpam-5646	27	13	exploration	exploration	NOUN
ejpam-5646	27	14	of	of	ADP
ejpam-5646	27	15	specific	specific	ADJ
ejpam-5646	27	16	subsets	subset	NOUN
ejpam-5646	27	17	within	within	ADP
ejpam-5646	27	18	semigroups	semigroup	NOUN
ejpam-5646	27	19	and	and	CCONJ
ejpam-5646	27	20	fuzzifies	fuzzifie	NOUN
ejpam-5646	27	21	them	they	PRON
ejpam-5646	27	22	.	.	PUNCT
ejpam-5646	28	1	the	the	DET
ejpam-5646	28	2	remaining	remain	VERB
ejpam-5646	28	3	part	part	NOUN
ejpam-5646	28	4	is	be	AUX
ejpam-5646	28	5	constructed	construct	VERB
ejpam-5646	28	6	as	as	SCONJ
ejpam-5646	28	7	follows	follow	VERB
ejpam-5646	28	8	.	.	PUNCT
ejpam-5646	29	1	after	after	ADP
ejpam-5646	29	2	an	an	DET
ejpam-5646	29	3	introduction	introduction	NOUN
ejpam-5646	29	4	,	,	PUNCT
ejpam-5646	29	5	in	in	ADP
ejpam-5646	29	6	section	section	NOUN
ejpam-5646	29	7	2	2	NUM
ejpam-5646	29	8	we	we	PRON
ejpam-5646	29	9	present	present	VERB
ejpam-5646	29	10	some	some	DET
ejpam-5646	29	11	results	result	NOUN
ejpam-5646	29	12	about	about	ADP
ejpam-5646	29	13	(	(	PUNCT
ejpam-5646	29	14	fuzzy	fuzzy	ADJ
ejpam-5646	29	15	)	)	PUNCT
ejpam-5646	29	16	antiideals	antiideal	NOUN
ejpam-5646	29	17	and	and	CCONJ
ejpam-5646	29	18	(	(	PUNCT
ejpam-5646	29	19	fuzzy	fuzzy	ADJ
ejpam-5646	29	20	)	)	PUNCT
ejpam-5646	29	21	bi	bi	NOUN
ejpam-5646	29	22	-	-	NOUN
ejpam-5646	29	23	antiideals	antiideal	NOUN
ejpam-5646	29	24	of	of	ADP
ejpam-5646	29	25	semigroups	semigroup	NOUN
ejpam-5646	29	26	that	that	PRON
ejpam-5646	29	27	are	be	AUX
ejpam-5646	29	28	used	use	VERB
ejpam-5646	29	29	in	in	ADP
ejpam-5646	29	30	the	the	DET
ejpam-5646	29	31	subsequent	subsequent	ADJ
ejpam-5646	29	32	sections	section	NOUN
ejpam-5646	29	33	.	.	PUNCT
ejpam-5646	30	1	in	in	ADP
ejpam-5646	30	2	section	section	NOUN
ejpam-5646	30	3	3	3	NUM
ejpam-5646	30	4	we	we	PRON
ejpam-5646	30	5	generalizes	generalize	VERB
ejpam-5646	30	6	bi	bi	NOUN
ejpam-5646	30	7	-	-	NOUN
ejpam-5646	30	8	antiideals	antiideal	NOUN
ejpam-5646	30	9	to	to	ADP
ejpam-5646	30	10	(	(	PUNCT
ejpam-5646	30	11	m	m	NOUN
ejpam-5646	30	12	,	,	PUNCT
ejpam-5646	30	13	n)-bi	n)-bi	NOUN
ejpam-5646	30	14	-	-	PUNCT
ejpam-5646	30	15	antiideals	antiideal	NOUN
ejpam-5646	30	16	,	,	PUNCT
ejpam-5646	30	17	discuss	discuss	VERB
ejpam-5646	30	18	some	some	PRON
ejpam-5646	30	19	of	of	ADP
ejpam-5646	30	20	their	their	PRON
ejpam-5646	30	21	properties	property	NOUN
ejpam-5646	30	22	,	,	PUNCT
ejpam-5646	30	23	and	and	CCONJ
ejpam-5646	30	24	give	give	VERB
ejpam-5646	30	25	some	some	DET
ejpam-5646	30	26	non	non	ADJ
ejpam-5646	30	27	-	-	ADJ
ejpam-5646	30	28	trivial	trivial	ADJ
ejpam-5646	30	29	examples	example	NOUN
ejpam-5646	30	30	.	.	PUNCT
ejpam-5646	31	1	in	in	ADP
ejpam-5646	31	2	section	section	NOUN
ejpam-5646	31	3	4	4	NUM
ejpam-5646	31	4	we	we	PRON
ejpam-5646	31	5	fuzzify	fuzzify	VERB
ejpam-5646	31	6	(	(	PUNCT
ejpam-5646	31	7	m	m	PROPN
ejpam-5646	31	8	,	,	PUNCT
ejpam-5646	31	9	n)-biantiideals	n)-biantiideal	VERB
ejpam-5646	31	10	by	by	ADP
ejpam-5646	31	11	introducing	introduce	VERB
ejpam-5646	31	12	fuzzy	fuzzy	ADJ
ejpam-5646	31	13	(	(	PUNCT
ejpam-5646	31	14	m	m	NOUN
ejpam-5646	31	15	,	,	PUNCT
ejpam-5646	31	16	n)-bi	n)-bi	NOUN
ejpam-5646	31	17	-	-	PUNCT
ejpam-5646	31	18	antiideals	antiideal	NOUN
ejpam-5646	31	19	of	of	ADP
ejpam-5646	31	20	a	a	DET
ejpam-5646	31	21	semigroup	semigroup	NOUN
ejpam-5646	31	22	.	.	PUNCT
ejpam-5646	32	1	moreover	moreover	ADV
ejpam-5646	32	2	,	,	PUNCT
ejpam-5646	32	3	we	we	PRON
ejpam-5646	32	4	link	link	VERB
ejpam-5646	32	5	the	the	DET
ejpam-5646	32	6	two	two	NUM
ejpam-5646	32	7	new	new	ADJ
ejpam-5646	32	8	notions	notion	NOUN
ejpam-5646	32	9	by	by	ADP
ejpam-5646	32	10	means	mean	NOUN
ejpam-5646	32	11	of	of	ADP
ejpam-5646	32	12	level	level	NOUN
ejpam-5646	32	13	sets	set	NOUN
ejpam-5646	32	14	.	.	PUNCT
ejpam-5646	33	1	2	2	X
ejpam-5646	33	2	.	.	X
ejpam-5646	33	3	(	(	PUNCT
ejpam-5646	33	4	fuzzy	fuzzy	ADJ
ejpam-5646	33	5	)	)	PUNCT
ejpam-5646	33	6	left(right	left(right	PROPN
ejpam-5646	33	7	)	)	PUNCT
ejpam-5646	33	8	antiideals	antiideal	NOUN
ejpam-5646	33	9	and	and	CCONJ
ejpam-5646	33	10	bi	bi	NOUN
ejpam-5646	33	11	-	-	NOUN
ejpam-5646	33	12	antiideals	antiideal	NOUN
ejpam-5646	33	13	of	of	ADP
ejpam-5646	33	14	a	a	DET
ejpam-5646	33	15	semigroup	semigroup	NOUN
ejpam-5646	33	16	in	in	ADP
ejpam-5646	33	17	this	this	DET
ejpam-5646	33	18	section	section	NOUN
ejpam-5646	33	19	,	,	PUNCT
ejpam-5646	33	20	we	we	PRON
ejpam-5646	33	21	present	present	VERB
ejpam-5646	33	22	some	some	DET
ejpam-5646	33	23	definitions	definition	NOUN
ejpam-5646	33	24	and	and	CCONJ
ejpam-5646	33	25	results	result	NOUN
ejpam-5646	33	26	that	that	PRON
ejpam-5646	33	27	are	be	AUX
ejpam-5646	33	28	used	use	VERB
ejpam-5646	33	29	throughout	throughout	ADP
ejpam-5646	33	30	the	the	DET
ejpam-5646	33	31	paper	paper	NOUN
ejpam-5646	33	32	.	.	PUNCT
ejpam-5646	34	1	antiideals	antiideal	NOUN
ejpam-5646	34	2	were	be	AUX
ejpam-5646	34	3	introduced	introduce	VERB
ejpam-5646	34	4	by	by	ADP
ejpam-5646	34	5	schwarz	schwarz	PROPN
ejpam-5646	34	6	[	[	X
ejpam-5646	34	7	19	19	NUM
ejpam-5646	34	8	]	]	PUNCT
ejpam-5646	34	9	and	and	CCONJ
ejpam-5646	34	10	were	be	AUX
ejpam-5646	34	11	studied	study	VERB
ejpam-5646	34	12	and	and	CCONJ
ejpam-5646	34	13	generalized	generalize	VERB
ejpam-5646	34	14	by	by	ADP
ejpam-5646	34	15	iseksi	iseksi	NOUN
ejpam-5646	35	1	[	[	X
ejpam-5646	35	2	8	8	NUM
ejpam-5646	35	3	,	,	PUNCT
ejpam-5646	35	4	9	9	NUM
ejpam-5646	35	5	]	]	PUNCT
ejpam-5646	35	6	.	.	PUNCT
ejpam-5646	36	1	other	other	ADJ
ejpam-5646	36	2	antiideals	antiideal	NOUN
ejpam-5646	36	3	of	of	ADP
ejpam-5646	36	4	semigroups	semigroup	NOUN
ejpam-5646	36	5	were	be	AUX
ejpam-5646	36	6	introduced	introduce	VERB
ejpam-5646	36	7	.	.	PUNCT
ejpam-5646	37	1	for	for	ADP
ejpam-5646	37	2	example	example	NOUN
ejpam-5646	37	3	,	,	PUNCT
ejpam-5646	37	4	al	al	PROPN
ejpam-5646	37	5	-	-	PUNCT
ejpam-5646	37	6	tahan	tahan	PROPN
ejpam-5646	37	7	and	and	CCONJ
ejpam-5646	37	8	sarka	sarka	NOUN
ejpam-5646	38	1	[	[	X
ejpam-5646	38	2	5	5	NUM
ejpam-5646	38	3	]	]	PUNCT
ejpam-5646	38	4	introduced	introduce	VERB
ejpam-5646	38	5	interior	interior	ADJ
ejpam-5646	38	6	antiideals	antiideal	NOUN
ejpam-5646	38	7	of	of	ADP
ejpam-5646	38	8	a	a	DET
ejpam-5646	38	9	semigroup	semigroup	NOUN
ejpam-5646	38	10	and	and	CCONJ
ejpam-5646	38	11	investigated	investigate	VERB
ejpam-5646	38	12	their	their	PRON
ejpam-5646	38	13	properties	property	NOUN
ejpam-5646	38	14	and	and	CCONJ
ejpam-5646	38	15	al	al	PROPN
ejpam-5646	38	16	-	-	PUNCT
ejpam-5646	38	17	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	38	18	et	et	PROPN
ejpam-5646	38	19	al	al	PROPN
ejpam-5646	38	20	.	.	PUNCT
ejpam-5646	39	1	[	[	X
ejpam-5646	39	2	18	18	NUM
ejpam-5646	39	3	]	]	PUNCT
ejpam-5646	39	4	studied	study	VERB
ejpam-5646	39	5	antiideals	antiideal	NOUN
ejpam-5646	39	6	of	of	ADP
ejpam-5646	39	7	a	a	DET
ejpam-5646	39	8	semiring	semiring	NOUN
ejpam-5646	39	9	.	.	PUNCT
ejpam-5646	40	1	a	a	DET
ejpam-5646	40	2	non	non	ADJ
ejpam-5646	40	3	-	-	ADJ
ejpam-5646	40	4	empty	empty	ADJ
ejpam-5646	40	5	set	set	NOUN
ejpam-5646	40	6	x	x	PUNCT
ejpam-5646	40	7	with	with	ADP
ejpam-5646	40	8	an	an	DET
ejpam-5646	40	9	associative	associative	ADJ
ejpam-5646	40	10	binary	binary	ADJ
ejpam-5646	40	11	operation	operation	NOUN
ejpam-5646	40	12	is	be	AUX
ejpam-5646	40	13	called	call	VERB
ejpam-5646	40	14	a	a	DET
ejpam-5646	40	15	semigroup	semigroup	NOUN
ejpam-5646	40	16	and	and	CCONJ
ejpam-5646	40	17	a	a	DET
ejpam-5646	40	18	non	non	ADJ
ejpam-5646	40	19	-	-	ADJ
ejpam-5646	40	20	empty	empty	ADJ
ejpam-5646	40	21	subset	subset	NOUN
ejpam-5646	40	22	a	a	PRON
ejpam-5646	40	23	of	of	ADP
ejpam-5646	40	24	x	x	PUNCT
ejpam-5646	40	25	is	be	AUX
ejpam-5646	40	26	a	a	DET
ejpam-5646	40	27	subsemigroup	subsemigroup	NOUN
ejpam-5646	40	28	of	of	ADP
ejpam-5646	40	29	x	x	PRON
ejpam-5646	40	30	if	if	SCONJ
ejpam-5646	40	31	it	it	PRON
ejpam-5646	40	32	is	be	AUX
ejpam-5646	40	33	a	a	DET
ejpam-5646	40	34	semigroup	semigroup	NOUN
ejpam-5646	40	35	.	.	PUNCT
ejpam-5646	41	1	if	if	SCONJ
ejpam-5646	41	2	x	x	PRON
ejpam-5646	41	3	has	have	VERB
ejpam-5646	41	4	an	an	DET
ejpam-5646	41	5	identity	identity	NOUN
ejpam-5646	41	6	,	,	PUNCT
ejpam-5646	41	7	then	then	ADV
ejpam-5646	41	8	it	it	PRON
ejpam-5646	41	9	is	be	AUX
ejpam-5646	41	10	called	call	VERB
ejpam-5646	41	11	a	a	DET
ejpam-5646	41	12	monoid	monoid	NOUN
ejpam-5646	41	13	.	.	PUNCT
ejpam-5646	42	1	as	as	ADP
ejpam-5646	42	2	simple	simple	ADJ
ejpam-5646	42	3	examples	example	NOUN
ejpam-5646	42	4	,	,	PUNCT
ejpam-5646	42	5	the	the	DET
ejpam-5646	42	6	set	set	NOUN
ejpam-5646	42	7	of	of	ADP
ejpam-5646	42	8	non	non	ADJ
ejpam-5646	42	9	-	-	ADJ
ejpam-5646	42	10	negative	negative	ADJ
ejpam-5646	42	11	even	even	ADV
ejpam-5646	42	12	integers	integer	NOUN
ejpam-5646	42	13	under	under	ADP
ejpam-5646	42	14	standard	standard	ADJ
ejpam-5646	42	15	addition	addition	NOUN
ejpam-5646	42	16	is	be	AUX
ejpam-5646	42	17	a	a	DET
ejpam-5646	42	18	semigroup	semigroup	NOUN
ejpam-5646	42	19	and	and	CCONJ
ejpam-5646	42	20	the	the	DET
ejpam-5646	42	21	set	set	NOUN
ejpam-5646	42	22	of	of	ADP
ejpam-5646	42	23	positive	positive	ADJ
ejpam-5646	42	24	real	real	ADJ
ejpam-5646	42	25	numbers	number	NOUN
ejpam-5646	42	26	under	under	ADP
ejpam-5646	42	27	standard	standard	ADJ
ejpam-5646	42	28	multiplication	multiplication	NOUN
ejpam-5646	42	29	is	be	AUX
ejpam-5646	42	30	a	a	DET
ejpam-5646	42	31	semigroup	semigroup	NOUN
ejpam-5646	42	32	.	.	PUNCT
ejpam-5646	43	1	definition	definition	NOUN
ejpam-5646	43	2	1	1	NUM
ejpam-5646	43	3	.	.	PUNCT
ejpam-5646	44	1	[	[	X
ejpam-5646	44	2	8	8	NUM
ejpam-5646	44	3	]	]	X
ejpam-5646	44	4	let	let	VERB
ejpam-5646	44	5	(	(	PUNCT
ejpam-5646	44	6	x	x	NOUN
ejpam-5646	44	7	,	,	PUNCT
ejpam-5646	44	8	·	·	PUNCT
ejpam-5646	44	9	)	)	PUNCT
ejpam-5646	44	10	be	be	AUX
ejpam-5646	44	11	a	a	DET
ejpam-5646	44	12	semigroup	semigroup	NOUN
ejpam-5646	44	13	and	and	CCONJ
ejpam-5646	44	14	a	a	DET
ejpam-5646	44	15	̸=	̸=	PROPN
ejpam-5646	44	16	∅	∅	NOUN
ejpam-5646	44	17	⊆	⊆	NUM
ejpam-5646	44	18	x.	x.	NOUN
ejpam-5646	45	1	then	then	ADV
ejpam-5646	45	2	(	(	PUNCT
ejpam-5646	45	3	i	i	NOUN
ejpam-5646	45	4	)	)	PUNCT
ejpam-5646	45	5	a	a	PRON
ejpam-5646	45	6	is	be	AUX
ejpam-5646	45	7	a	a	DET
ejpam-5646	45	8	left	left	ADJ
ejpam-5646	45	9	antiideal	antiideal	NOUN
ejpam-5646	45	10	of	of	ADP
ejpam-5646	45	11	x	x	PRON
ejpam-5646	45	12	if	if	SCONJ
ejpam-5646	45	13	xa	xa	PROPN
ejpam-5646	45	14	∩a	∩a	NOUN
ejpam-5646	45	15	=	=	PUNCT
ejpam-5646	45	16	∅	∅	NOUN
ejpam-5646	45	17	;	;	PUNCT
ejpam-5646	45	18	(	(	PUNCT
ejpam-5646	45	19	ii	ii	NOUN
ejpam-5646	45	20	)	)	PUNCT
ejpam-5646	45	21	a	a	PRON
ejpam-5646	45	22	is	be	AUX
ejpam-5646	45	23	a	a	DET
ejpam-5646	45	24	right	right	ADJ
ejpam-5646	45	25	antiideal	antiideal	NOUN
ejpam-5646	45	26	of	of	ADP
ejpam-5646	45	27	x	x	PRON
ejpam-5646	45	28	if	if	SCONJ
ejpam-5646	45	29	ax	ax	NOUN
ejpam-5646	46	1	∩a	∩a	NOUN
ejpam-5646	46	2	=	=	NOUN
ejpam-5646	46	3	∅	∅	NOUN
ejpam-5646	46	4	;	;	PUNCT
ejpam-5646	46	5	(	(	PUNCT
ejpam-5646	46	6	iii	iii	X
ejpam-5646	46	7	)	)	PUNCT
ejpam-5646	46	8	a	a	PRON
ejpam-5646	46	9	is	be	AUX
ejpam-5646	46	10	an	an	DET
ejpam-5646	46	11	antiideal	antiideal	NOUN
ejpam-5646	46	12	of	of	ADP
ejpam-5646	46	13	x	x	PRON
ejpam-5646	46	14	if	if	SCONJ
ejpam-5646	46	15	it	it	PRON
ejpam-5646	46	16	is	be	AUX
ejpam-5646	46	17	both	both	CCONJ
ejpam-5646	46	18	a	a	DET
ejpam-5646	46	19	left	left	ADJ
ejpam-5646	46	20	and	and	CCONJ
ejpam-5646	46	21	right	right	ADJ
ejpam-5646	46	22	antiideal	antiideal	NOUN
ejpam-5646	46	23	of	of	ADP
ejpam-5646	46	24	x.	x.	PROPN
ejpam-5646	46	25	example	example	NOUN
ejpam-5646	47	1	1	1	X
ejpam-5646	47	2	.	.	PUNCT
ejpam-5646	48	1	let	let	VERB
ejpam-5646	48	2	(	(	PUNCT
ejpam-5646	48	3	k	k	NOUN
ejpam-5646	48	4	,	,	PUNCT
ejpam-5646	48	5	·	·	PUNCT
ejpam-5646	48	6	)	)	PUNCT
ejpam-5646	48	7	be	be	AUX
ejpam-5646	48	8	the	the	DET
ejpam-5646	48	9	semigroup	semigroup	NOUN
ejpam-5646	48	10	of	of	ADP
ejpam-5646	48	11	integers	integer	NOUN
ejpam-5646	48	12	greater	great	ADJ
ejpam-5646	48	13	than	than	ADP
ejpam-5646	48	14	1	1	NUM
ejpam-5646	48	15	under	under	ADP
ejpam-5646	48	16	standard	standard	ADJ
ejpam-5646	48	17	multiplication	multiplication	NOUN
ejpam-5646	48	18	of	of	ADP
ejpam-5646	48	19	integers	integer	NOUN
ejpam-5646	48	20	and	and	CCONJ
ejpam-5646	48	21	a	a	PRON
ejpam-5646	48	22	=	=	X
ejpam-5646	48	23	{	{	PUNCT
ejpam-5646	48	24	2	2	NUM
ejpam-5646	48	25	,	,	PUNCT
ejpam-5646	48	26	3	3	NUM
ejpam-5646	48	27	}	}	PUNCT
ejpam-5646	48	28	.	.	PUNCT
ejpam-5646	49	1	then	then	ADV
ejpam-5646	49	2	a	a	PRON
ejpam-5646	49	3	is	be	AUX
ejpam-5646	49	4	an	an	DET
ejpam-5646	49	5	antiideal	antiideal	NOUN
ejpam-5646	49	6	of	of	ADP
ejpam-5646	49	7	k.	k.	PROPN
ejpam-5646	49	8	this	this	PRON
ejpam-5646	49	9	is	be	AUX
ejpam-5646	49	10	clear	clear	ADJ
ejpam-5646	49	11	as	as	ADP
ejpam-5646	50	1	ka	ka	PROPN
ejpam-5646	50	2	∩a	∩a	PROPN
ejpam-5646	50	3	=	=	PROPN
ejpam-5646	50	4	ak	ak	PROPN
ejpam-5646	50	5	∩a	∩a	PROPN
ejpam-5646	50	6	=	=	PUNCT
ejpam-5646	50	7	{	{	PUNCT
ejpam-5646	50	8	4	4	NUM
ejpam-5646	50	9	,	,	PUNCT
ejpam-5646	50	10	6	6	NUM
ejpam-5646	50	11	,	,	PUNCT
ejpam-5646	50	12	8	8	NUM
ejpam-5646	50	13	,	,	PUNCT
ejpam-5646	50	14	9	9	NUM
ejpam-5646	50	15	,	,	PUNCT
ejpam-5646	50	16	.	.	PUNCT
ejpam-5646	50	17	.	.	PUNCT
ejpam-5646	50	18	.	.	PUNCT
ejpam-5646	50	19	}	}	PUNCT
ejpam-5646	51	1	∩	∩	NOUN
ejpam-5646	51	2	{	{	PUNCT
ejpam-5646	51	3	2	2	NUM
ejpam-5646	51	4	,	,	PUNCT
ejpam-5646	51	5	3	3	NUM
ejpam-5646	51	6	}	}	PUNCT
ejpam-5646	51	7	=	=	X
ejpam-5646	51	8	∅.	∅.	PRON
ejpam-5646	51	9	m.	m.	NOUN
ejpam-5646	51	10	al	al	PROPN
ejpam-5646	51	11	tahan	tahan	PROPN
ejpam-5646	51	12	,	,	PUNCT
ejpam-5646	51	13	s.	s.	PROPN
ejpam-5646	51	14	hoskova	hoskova	PROPN
ejpam-5646	51	15	-	-	PUNCT
ejpam-5646	51	16	mayerova	mayerova	PROPN
ejpam-5646	51	17	,	,	PUNCT
ejpam-5646	51	18	s.	s.	PROPN
ejpam-5646	51	19	al	al	PROPN
ejpam-5646	51	20	-	-	PUNCT
ejpam-5646	51	21	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	51	22	/	/	SYM
ejpam-5646	51	23	eur	eur	NOUN
ejpam-5646	51	24	.	.	PUNCT
ejpam-5646	52	1	j.	j.	PROPN
ejpam-5646	52	2	pure	pure	PROPN
ejpam-5646	52	3	appl	appl	PROPN
ejpam-5646	52	4	.	.	PROPN
ejpam-5646	52	5	math	math	PROPN
ejpam-5646	52	6	,	,	PUNCT
ejpam-5646	52	7	18	18	NUM
ejpam-5646	52	8	(	(	PUNCT
ejpam-5646	52	9	1	1	NUM
ejpam-5646	52	10	)	)	PUNCT
ejpam-5646	52	11	(	(	PUNCT
ejpam-5646	52	12	2025	2025	NUM
ejpam-5646	52	13	)	)	PUNCT
ejpam-5646	52	14	,	,	PUNCT
ejpam-5646	52	15	5646	5646	NUM
ejpam-5646	52	16	3	3	NUM
ejpam-5646	52	17	of	of	ADP
ejpam-5646	52	18	11	11	NUM
ejpam-5646	52	19	we	we	PRON
ejpam-5646	52	20	present	present	VERB
ejpam-5646	52	21	an	an	DET
ejpam-5646	52	22	example	example	NOUN
ejpam-5646	52	23	of	of	ADP
ejpam-5646	52	24	an	an	DET
ejpam-5646	52	25	infinite	infinite	ADJ
ejpam-5646	52	26	antiideal	antiideal	NOUN
ejpam-5646	52	27	.	.	PUNCT
ejpam-5646	53	1	example	example	NOUN
ejpam-5646	54	1	2	2	NUM
ejpam-5646	54	2	.	.	PUNCT
ejpam-5646	54	3	let	let	VERB
ejpam-5646	54	4	m	m	VERB
ejpam-5646	54	5	=	=	PUNCT
ejpam-5646	54	6	{	{	PUNCT
ejpam-5646	54	7	1	1	NUM
ejpam-5646	54	8	,	,	PUNCT
ejpam-5646	54	9	2	2	NUM
ejpam-5646	54	10	,	,	PUNCT
ejpam-5646	54	11	3	3	NUM
ejpam-5646	54	12	,	,	PUNCT
ejpam-5646	54	13	4	4	NUM
ejpam-5646	54	14	,	,	PUNCT
ejpam-5646	54	15	.	.	PUNCT
ejpam-5646	54	16	.	.	PUNCT
ejpam-5646	54	17	.	.	PUNCT
ejpam-5646	54	18	}	}	PUNCT
ejpam-5646	54	19	and	and	CCONJ
ejpam-5646	54	20	define	define	VERB
ejpam-5646	54	21	the	the	DET
ejpam-5646	54	22	semigroup	semigroup	NOUN
ejpam-5646	54	23	(	(	PUNCT
ejpam-5646	54	24	m,⋆	m,⋆	PROPN
ejpam-5646	54	25	)	)	PUNCT
ejpam-5646	54	26	as	as	SCONJ
ejpam-5646	54	27	follows	follow	VERB
ejpam-5646	54	28	.	.	PUNCT
ejpam-5646	55	1	x	x	PUNCT
ejpam-5646	55	2	⋆	⋆	VERB
ejpam-5646	55	3	y	y	PROPN
ejpam-5646	55	4	=	=	PUNCT
ejpam-5646	55	5	{	{	PUNCT
ejpam-5646	55	6	1	1	NUM
ejpam-5646	55	7	if	if	SCONJ
ejpam-5646	55	8	x	x	PRON
ejpam-5646	55	9	is	be	AUX
ejpam-5646	55	10	an	an	DET
ejpam-5646	55	11	odd	odd	ADJ
ejpam-5646	55	12	number	number	NOUN
ejpam-5646	55	13	;	;	PUNCT
ejpam-5646	55	14	y	y	PROPN
ejpam-5646	55	15	otherwise	otherwise	ADV
ejpam-5646	55	16	.	.	PUNCT
ejpam-5646	56	1	then	then	ADV
ejpam-5646	56	2	a	a	X
ejpam-5646	56	3	=	=	X
ejpam-5646	56	4	{	{	PUNCT
ejpam-5646	56	5	3	3	NUM
ejpam-5646	56	6	,	,	PUNCT
ejpam-5646	56	7	5	5	NUM
ejpam-5646	56	8	,	,	PUNCT
ejpam-5646	56	9	7	7	NUM
ejpam-5646	56	10	,	,	PUNCT
ejpam-5646	56	11	9	9	NUM
ejpam-5646	56	12	,	,	PUNCT
ejpam-5646	56	13	.	.	PUNCT
ejpam-5646	56	14	.	.	PUNCT
ejpam-5646	56	15	.	.	PUNCT
ejpam-5646	56	16	}	}	PUNCT
ejpam-5646	56	17	is	be	AUX
ejpam-5646	56	18	an	an	DET
ejpam-5646	56	19	antiideal	antiideal	NOUN
ejpam-5646	56	20	of	of	ADP
ejpam-5646	56	21	m	m	PROPN
ejpam-5646	56	22	.	.	PUNCT
ejpam-5646	57	1	this	this	PRON
ejpam-5646	57	2	is	be	AUX
ejpam-5646	57	3	clear	clear	ADJ
ejpam-5646	57	4	as	as	SCONJ
ejpam-5646	57	5	am	be	AUX
ejpam-5646	57	6	∩a	∩a	NOUN
ejpam-5646	57	7	=	=	PUNCT
ejpam-5646	57	8	{	{	PUNCT
ejpam-5646	57	9	1	1	NUM
ejpam-5646	57	10	}	}	PUNCT
ejpam-5646	57	11	∩a	∩a	NOUN
ejpam-5646	57	12	=	=	PUNCT
ejpam-5646	57	13	∅.	∅.	PROPN
ejpam-5646	57	14	al	al	PROPN
ejpam-5646	57	15	-	-	PUNCT
ejpam-5646	57	16	tahan	tahan	PROPN
ejpam-5646	57	17	et	et	PROPN
ejpam-5646	57	18	al	al	PROPN
ejpam-5646	57	19	.	.	PUNCT
ejpam-5646	58	1	[	[	X
ejpam-5646	58	2	2	2	X
ejpam-5646	58	3	]	]	PUNCT
ejpam-5646	58	4	introduced	introduce	VERB
ejpam-5646	58	5	bi	bi	NOUN
ejpam-5646	58	6	-	-	NOUN
ejpam-5646	58	7	antiideals	antiideal	NOUN
ejpam-5646	58	8	of	of	ADP
ejpam-5646	58	9	a	a	DET
ejpam-5646	58	10	semigroup	semigroup	NOUN
ejpam-5646	58	11	.	.	PUNCT
ejpam-5646	59	1	we	we	PRON
ejpam-5646	59	2	present	present	VERB
ejpam-5646	59	3	some	some	PRON
ejpam-5646	59	4	of	of	ADP
ejpam-5646	59	5	their	their	PRON
ejpam-5646	59	6	results	result	NOUN
ejpam-5646	59	7	.	.	PUNCT
ejpam-5646	60	1	definition	definition	NOUN
ejpam-5646	60	2	2	2	NUM
ejpam-5646	60	3	.	.	PUNCT
ejpam-5646	61	1	[	[	X
ejpam-5646	61	2	2	2	NUM
ejpam-5646	61	3	]	]	X
ejpam-5646	61	4	let	let	VERB
ejpam-5646	61	5	(	(	PUNCT
ejpam-5646	61	6	x	x	NOUN
ejpam-5646	61	7	,	,	PUNCT
ejpam-5646	61	8	·	·	PUNCT
ejpam-5646	61	9	)	)	PUNCT
ejpam-5646	61	10	be	be	AUX
ejpam-5646	61	11	a	a	DET
ejpam-5646	61	12	semigroup	semigroup	NOUN
ejpam-5646	61	13	and	and	CCONJ
ejpam-5646	61	14	a	a	DET
ejpam-5646	61	15	̸=	̸=	PROPN
ejpam-5646	61	16	∅	∅	NOUN
ejpam-5646	61	17	⊆	⊆	NUM
ejpam-5646	61	18	x.	x.	NOUN
ejpam-5646	61	19	then	then	ADV
ejpam-5646	61	20	a	a	PRON
ejpam-5646	61	21	is	be	AUX
ejpam-5646	61	22	a	a	DET
ejpam-5646	61	23	bi	bi	NOUN
ejpam-5646	61	24	-	-	NOUN
ejpam-5646	61	25	antiideal	antiideal	NOUN
ejpam-5646	61	26	of	of	ADP
ejpam-5646	61	27	x	x	PART
ejpam-5646	61	28	if	if	SCONJ
ejpam-5646	61	29	axa	axa	NOUN
ejpam-5646	61	30	∩a	∩a	PROPN
ejpam-5646	62	1	=	=	PUNCT
ejpam-5646	62	2	∅.	∅.	PRON
ejpam-5646	62	3	example	example	NOUN
ejpam-5646	62	4	3	3	X
ejpam-5646	62	5	.	.	PUNCT
ejpam-5646	63	1	let	let	VERB
ejpam-5646	63	2	(	(	PUNCT
ejpam-5646	63	3	k	k	NOUN
ejpam-5646	63	4	,	,	PUNCT
ejpam-5646	63	5	·	·	PUNCT
ejpam-5646	63	6	)	)	PUNCT
ejpam-5646	63	7	be	be	VERB
ejpam-5646	63	8	the	the	DET
ejpam-5646	63	9	semigroup	semigroup	NOUN
ejpam-5646	63	10	defined	define	VERB
ejpam-5646	63	11	in	in	ADP
ejpam-5646	63	12	example	example	NOUN
ejpam-5646	63	13	1	1	NUM
ejpam-5646	63	14	and	and	CCONJ
ejpam-5646	63	15	b	b	X
ejpam-5646	63	16	=	=	PUNCT
ejpam-5646	63	17	{	{	PUNCT
ejpam-5646	63	18	2	2	NUM
ejpam-5646	63	19	,	,	PUNCT
ejpam-5646	63	20	3	3	NUM
ejpam-5646	63	21	,	,	PUNCT
ejpam-5646	63	22	4	4	NUM
ejpam-5646	63	23	}	}	PUNCT
ejpam-5646	63	24	.	.	PUNCT
ejpam-5646	64	1	then	then	ADV
ejpam-5646	64	2	b	b	X
ejpam-5646	64	3	is	be	AUX
ejpam-5646	64	4	a	a	DET
ejpam-5646	64	5	bi	bi	NOUN
ejpam-5646	64	6	-	-	NOUN
ejpam-5646	64	7	antiideal	antiideal	NOUN
ejpam-5646	64	8	of	of	ADP
ejpam-5646	64	9	k.	k.	PROPN
ejpam-5646	64	10	moreover	moreover	ADV
ejpam-5646	64	11	,	,	PUNCT
ejpam-5646	64	12	it	it	PRON
ejpam-5646	64	13	is	be	AUX
ejpam-5646	64	14	not	not	PART
ejpam-5646	64	15	a	a	DET
ejpam-5646	64	16	left(right	left(right	PROPN
ejpam-5646	64	17	)	)	PUNCT
ejpam-5646	64	18	antiideal	antiideal	NOUN
ejpam-5646	64	19	of	of	ADP
ejpam-5646	64	20	k.	k.	PROPN
ejpam-5646	65	1	this	this	PRON
ejpam-5646	65	2	is	be	AUX
ejpam-5646	65	3	clear	clear	ADJ
ejpam-5646	65	4	as	as	SCONJ
ejpam-5646	65	5	bk	bk	NOUN
ejpam-5646	65	6	∩b	∩b	NOUN
ejpam-5646	65	7	=	=	SYM
ejpam-5646	65	8	{	{	PUNCT
ejpam-5646	65	9	4	4	NUM
ejpam-5646	65	10	}	}	PUNCT
ejpam-5646	65	11	=	=	NOUN
ejpam-5646	65	12	̸	̸	ADV
ejpam-5646	65	13	∅.	∅.	VERB
ejpam-5646	65	14	proposition	proposition	NOUN
ejpam-5646	65	15	1	1	NUM
ejpam-5646	65	16	.	.	PUNCT
ejpam-5646	66	1	[	[	X
ejpam-5646	66	2	4	4	X
ejpam-5646	66	3	]	]	SYM
ejpam-5646	66	4	evey	evey	NOUN
ejpam-5646	66	5	left(right	left(right	PROPN
ejpam-5646	66	6	)	)	PUNCT
ejpam-5646	66	7	antiideal	antiideal	NOUN
ejpam-5646	66	8	of	of	ADP
ejpam-5646	66	9	a	a	DET
ejpam-5646	66	10	semigroup	semigroup	NOUN
ejpam-5646	66	11	x	x	X
ejpam-5646	66	12	is	be	AUX
ejpam-5646	66	13	a	a	DET
ejpam-5646	66	14	bi	bi	NOUN
ejpam-5646	66	15	-	-	NOUN
ejpam-5646	66	16	antiideal	antiideal	NOUN
ejpam-5646	66	17	of	of	ADP
ejpam-5646	66	18	x.	x.	PROPN
ejpam-5646	66	19	fuzzy	fuzzy	ADJ
ejpam-5646	66	20	sets	set	NOUN
ejpam-5646	66	21	were	be	AUX
ejpam-5646	66	22	introduced	introduce	VERB
ejpam-5646	66	23	by	by	ADP
ejpam-5646	66	24	zadeh	zadeh	PROPN
ejpam-5646	67	1	[	[	X
ejpam-5646	67	2	21	21	NUM
ejpam-5646	67	3	]	]	PUNCT
ejpam-5646	67	4	in	in	ADP
ejpam-5646	67	5	1965	1965	NUM
ejpam-5646	67	6	to	to	PART
ejpam-5646	67	7	accommodate	accommodate	VERB
ejpam-5646	67	8	uncertainties	uncertainty	NOUN
ejpam-5646	67	9	that	that	SCONJ
ejpam-5646	67	10	classical	classical	ADJ
ejpam-5646	67	11	sets	set	NOUN
ejpam-5646	67	12	fail	fail	VERB
ejpam-5646	67	13	to	to	PART
ejpam-5646	67	14	deal	deal	VERB
ejpam-5646	67	15	with	with	ADP
ejpam-5646	67	16	.	.	PUNCT
ejpam-5646	68	1	in	in	ADP
ejpam-5646	68	2	a	a	DET
ejpam-5646	68	3	fuzzy	fuzzy	ADJ
ejpam-5646	68	4	set	set	NOUN
ejpam-5646	68	5	,	,	PUNCT
ejpam-5646	68	6	the	the	DET
ejpam-5646	68	7	element	element	NOUN
ejpam-5646	68	8	’s	’s	PART
ejpam-5646	68	9	membership	membership	NOUN
ejpam-5646	68	10	is	be	AUX
ejpam-5646	68	11	a	a	DET
ejpam-5646	68	12	real	real	ADJ
ejpam-5646	68	13	number	number	NOUN
ejpam-5646	68	14	in	in	ADP
ejpam-5646	68	15	the	the	DET
ejpam-5646	68	16	unit	unit	NOUN
ejpam-5646	68	17	interval	interval	NOUN
ejpam-5646	68	18	.	.	PUNCT
ejpam-5646	69	1	definition	definition	NOUN
ejpam-5646	69	2	3	3	NUM
ejpam-5646	69	3	.	.	PUNCT
ejpam-5646	70	1	[	[	X
ejpam-5646	70	2	21	21	NUM
ejpam-5646	70	3	]	]	X
ejpam-5646	70	4	let	let	VERB
ejpam-5646	70	5	x	x	PRON
ejpam-5646	70	6	be	be	AUX
ejpam-5646	70	7	a	a	DET
ejpam-5646	70	8	universal	universal	ADJ
ejpam-5646	70	9	set	set	NOUN
ejpam-5646	70	10	,	,	PUNCT
ejpam-5646	70	11	i	i	PRON
ejpam-5646	70	12	=	=	PUNCT
ejpam-5646	71	1	[	[	X
ejpam-5646	71	2	0	0	NUM
ejpam-5646	71	3	,	,	PUNCT
ejpam-5646	71	4	1	1	NUM
ejpam-5646	71	5	]	]	PUNCT
ejpam-5646	71	6	,	,	PUNCT
ejpam-5646	71	7	and	and	CCONJ
ejpam-5646	71	8	µ	µ	X
ejpam-5646	71	9	:	:	PUNCT
ejpam-5646	71	10	x	x	X
ejpam-5646	71	11	→	→	SYM
ejpam-5646	71	12	i.	i.	NOUN
ejpam-5646	71	13	then	then	ADV
ejpam-5646	71	14	a	a	DET
ejpam-5646	71	15	fuzzy	fuzzy	ADJ
ejpam-5646	71	16	set	set	NOUN
ejpam-5646	71	17	of	of	ADP
ejpam-5646	71	18	x	x	PROPN
ejpam-5646	71	19	is	be	AUX
ejpam-5646	71	20	given	give	VERB
ejpam-5646	71	21	as	as	ADP
ejpam-5646	71	22	:	:	PUNCT
ejpam-5646	71	23	a	a	PRON
ejpam-5646	71	24	=	=	X
ejpam-5646	71	25	{	{	PUNCT
ejpam-5646	71	26	(	(	PUNCT
ejpam-5646	71	27	x	x	NOUN
ejpam-5646	71	28	,	,	PUNCT
ejpam-5646	71	29	µ(x	µ(x	NOUN
ejpam-5646	71	30	)	)	PUNCT
ejpam-5646	71	31	)	)	PUNCT
ejpam-5646	71	32	:	:	PUNCT
ejpam-5646	72	1	x	x	X
ejpam-5646	72	2	∈	∈	NOUN
ejpam-5646	72	3	x	x	X
ejpam-5646	72	4	}	}	PUNCT
ejpam-5646	72	5	.	.	PUNCT
ejpam-5646	73	1	here	here	ADV
ejpam-5646	73	2	µ(x	µ(x	NOUN
ejpam-5646	73	3	)	)	PUNCT
ejpam-5646	73	4	denotes	denote	VERB
ejpam-5646	73	5	the	the	DET
ejpam-5646	73	6	membership	membership	NOUN
ejpam-5646	73	7	’s	’s	PART
ejpam-5646	73	8	grade	grade	NOUN
ejpam-5646	73	9	of	of	ADP
ejpam-5646	73	10	the	the	DET
ejpam-5646	73	11	element	element	NOUN
ejpam-5646	73	12	x	x	PUNCT
ejpam-5646	73	13	in	in	ADP
ejpam-5646	73	14	x.	x.	NOUN
ejpam-5646	73	15	definition	definition	NOUN
ejpam-5646	73	16	4	4	NUM
ejpam-5646	73	17	.	.	PUNCT
ejpam-5646	74	1	[	[	X
ejpam-5646	74	2	7	7	X
ejpam-5646	74	3	]	]	PUNCT
ejpam-5646	74	4	for	for	SCONJ
ejpam-5646	74	5	the	the	DET
ejpam-5646	74	6	fuzzy	fuzzy	ADJ
ejpam-5646	74	7	sets	set	NOUN
ejpam-5646	74	8	µ1	µ1	PROPN
ejpam-5646	74	9	,	,	PUNCT
ejpam-5646	74	10	µ2	µ2	PROPN
ejpam-5646	74	11	of	of	ADP
ejpam-5646	74	12	x	x	PRON
ejpam-5646	74	13	,	,	PUNCT
ejpam-5646	74	14	the	the	DET
ejpam-5646	74	15	fuzzy	fuzzy	ADJ
ejpam-5646	74	16	sets	set	VERB
ejpam-5646	74	17	µ1	µ1	PROPN
ejpam-5646	74	18	∧	∧	PROPN
ejpam-5646	74	19	µ2	µ2	PROPN
ejpam-5646	74	20	,	,	PUNCT
ejpam-5646	74	21	µ1	µ1	PROPN
ejpam-5646	74	22	∨	∨	NOUN
ejpam-5646	74	23	µ2	µ2	PROPN
ejpam-5646	74	24	of	of	ADP
ejpam-5646	74	25	x	x	PRON
ejpam-5646	74	26	are	be	AUX
ejpam-5646	74	27	defined	define	VERB
ejpam-5646	74	28	as	as	ADP
ejpam-5646	74	29	follows	follow	VERB
ejpam-5646	74	30	.	.	PUNCT
ejpam-5646	75	1	(	(	PUNCT
ejpam-5646	75	2	µ1	µ1	PROPN
ejpam-5646	75	3	∧	∧	PROPN
ejpam-5646	75	4	µ2)(x	µ2)(x	PROPN
ejpam-5646	75	5	)	)	PUNCT
ejpam-5646	75	6	=	=	SYM
ejpam-5646	75	7	min{µ1(x	min{µ1(x	NOUN
ejpam-5646	75	8	)	)	PUNCT
ejpam-5646	75	9	,	,	PUNCT
ejpam-5646	75	10	µ2(x	µ2(x	PROPN
ejpam-5646	75	11	)	)	PUNCT
ejpam-5646	75	12	}	}	PUNCT
ejpam-5646	75	13	for	for	ADP
ejpam-5646	75	14	all	all	PRON
ejpam-5646	75	15	x	x	SYM
ejpam-5646	75	16	∈	∈	ADJ
ejpam-5646	75	17	x.	x.	NOUN
ejpam-5646	76	1	(	(	PUNCT
ejpam-5646	76	2	µ1	µ1	PROPN
ejpam-5646	76	3	∨	∨	PROPN
ejpam-5646	76	4	µ2)(x	µ2)(x	PROPN
ejpam-5646	76	5	)	)	PUNCT
ejpam-5646	76	6	=	=	SYM
ejpam-5646	76	7	max{µ1(x	max{µ1(x	NOUN
ejpam-5646	76	8	)	)	PUNCT
ejpam-5646	76	9	,	,	PUNCT
ejpam-5646	76	10	µ2(x	µ2(x	PROPN
ejpam-5646	76	11	)	)	PUNCT
ejpam-5646	76	12	}	}	PUNCT
ejpam-5646	76	13	for	for	ADP
ejpam-5646	76	14	all	all	DET
ejpam-5646	76	15	x	x	SYM
ejpam-5646	76	16	∈	∈	NOUN
ejpam-5646	76	17	x.	x.	NOUN
ejpam-5646	76	18	definition	definition	NOUN
ejpam-5646	76	19	5	5	NUM
ejpam-5646	76	20	.	.	PUNCT
ejpam-5646	77	1	[	[	X
ejpam-5646	77	2	7	7	X
ejpam-5646	77	3	]	]	X
ejpam-5646	77	4	let	let	VERB
ejpam-5646	77	5	x1	x1	NUM
ejpam-5646	77	6	,	,	PUNCT
ejpam-5646	77	7	x2	x2	PROPN
ejpam-5646	77	8	be	be	VERB
ejpam-5646	77	9	non	non	ADJ
ejpam-5646	77	10	-	-	ADJ
ejpam-5646	77	11	empty	empty	ADJ
ejpam-5646	77	12	sets	set	NOUN
ejpam-5646	77	13	and	and	CCONJ
ejpam-5646	77	14	µ1	µ1	PROPN
ejpam-5646	77	15	,	,	PUNCT
ejpam-5646	77	16	µ2	µ2	PROPN
ejpam-5646	77	17	be	be	VERB
ejpam-5646	77	18	fuzzy	fuzzy	ADJ
ejpam-5646	77	19	sets	set	NOUN
ejpam-5646	77	20	of	of	ADP
ejpam-5646	77	21	x1	x1	PROPN
ejpam-5646	77	22	,	,	PUNCT
ejpam-5646	77	23	x2	x2	PROPN
ejpam-5646	77	24	respectively	respectively	ADV
ejpam-5646	77	25	.	.	PUNCT
ejpam-5646	78	1	then	then	ADV
ejpam-5646	78	2	the	the	DET
ejpam-5646	78	3	fuzzy	fuzzy	ADJ
ejpam-5646	78	4	set	set	VERB
ejpam-5646	78	5	µ	µ	NOUN
ejpam-5646	78	6	=	=	SYM
ejpam-5646	78	7	µ1	µ1	NOUN
ejpam-5646	78	8	×	×	NOUN
ejpam-5646	78	9	µ2	µ2	NOUN
ejpam-5646	78	10	of	of	ADP
ejpam-5646	78	11	x1	x1	PROPN
ejpam-5646	78	12	×x2	×x2	PROPN
ejpam-5646	78	13	is	be	AUX
ejpam-5646	78	14	defined	define	VERB
ejpam-5646	78	15	as	as	ADP
ejpam-5646	78	16	follows	follow	VERB
ejpam-5646	78	17	.	.	PUNCT
ejpam-5646	79	1	µ((x1	µ((x1	NOUN
ejpam-5646	79	2	,	,	PUNCT
ejpam-5646	79	3	x2	x2	PROPN
ejpam-5646	79	4	)	)	PUNCT
ejpam-5646	79	5	)	)	PUNCT
ejpam-5646	80	1	=	=	PUNCT
ejpam-5646	81	1	min{µ1(x1	min{µ1(x1	PROPN
ejpam-5646	81	2	)	)	PUNCT
ejpam-5646	81	3	,	,	PUNCT
ejpam-5646	81	4	µ2(x2	µ2(x2	NOUN
ejpam-5646	81	5	)	)	PUNCT
ejpam-5646	81	6	}	}	PUNCT
ejpam-5646	81	7	for	for	ADP
ejpam-5646	81	8	all	all	DET
ejpam-5646	81	9	x1	x1	PROPN
ejpam-5646	81	10	∈	∈	PROPN
ejpam-5646	81	11	x1	x1	PROPN
ejpam-5646	81	12	,	,	PUNCT
ejpam-5646	81	13	x2	x2	PROPN
ejpam-5646	81	14	∈	∈	PROPN
ejpam-5646	81	15	x2	x2	PROPN
ejpam-5646	81	16	.	.	PUNCT
ejpam-5646	82	1	definition	definition	NOUN
ejpam-5646	82	2	6	6	NUM
ejpam-5646	82	3	.	.	PUNCT
ejpam-5646	83	1	[	[	X
ejpam-5646	83	2	2	2	NUM
ejpam-5646	83	3	]	]	X
ejpam-5646	83	4	let	let	VERB
ejpam-5646	83	5	(	(	PUNCT
ejpam-5646	83	6	x	x	NOUN
ejpam-5646	83	7	,	,	PUNCT
ejpam-5646	83	8	·	·	PUNCT
ejpam-5646	83	9	)	)	PUNCT
ejpam-5646	83	10	be	be	AUX
ejpam-5646	83	11	a	a	DET
ejpam-5646	83	12	semigroup	semigroup	NOUN
ejpam-5646	83	13	and	and	CCONJ
ejpam-5646	83	14	µ	µ	NOUN
ejpam-5646	83	15	:	:	PUNCT
ejpam-5646	83	16	x	x	SYM
ejpam-5646	83	17	→	→	SYM
ejpam-5646	83	18	[	[	X
ejpam-5646	83	19	0	0	NUM
ejpam-5646	83	20	,	,	PUNCT
ejpam-5646	83	21	1	1	NUM
ejpam-5646	83	22	]	]	PUNCT
ejpam-5646	83	23	be	be	AUX
ejpam-5646	83	24	a	a	DET
ejpam-5646	83	25	non	non	ADJ
ejpam-5646	83	26	-	-	ADJ
ejpam-5646	83	27	zero	zero	ADJ
ejpam-5646	83	28	fuzzy	fuzzy	ADJ
ejpam-5646	83	29	set	set	NOUN
ejpam-5646	83	30	of	of	ADP
ejpam-5646	83	31	x.	x.	NOUN
ejpam-5646	83	32	then	then	ADV
ejpam-5646	83	33	(	(	PUNCT
ejpam-5646	83	34	i	i	NOUN
ejpam-5646	83	35	)	)	PUNCT
ejpam-5646	83	36	µ	µ	PROPN
ejpam-5646	83	37	is	be	AUX
ejpam-5646	83	38	a	a	DET
ejpam-5646	83	39	fuzzy	fuzzy	ADJ
ejpam-5646	83	40	left	leave	VERB
ejpam-5646	83	41	antiideal	antiideal	NOUN
ejpam-5646	83	42	of	of	ADP
ejpam-5646	83	43	x	x	PRON
ejpam-5646	83	44	if	if	SCONJ
ejpam-5646	83	45	µ(ra	µ(ra	PROPN
ejpam-5646	83	46	)	)	PUNCT
ejpam-5646	83	47	∧	∧	NOUN
ejpam-5646	83	48	µ(a	µ(a	PROPN
ejpam-5646	83	49	)	)	PUNCT
ejpam-5646	83	50	=	=	SYM
ejpam-5646	83	51	0	0	NUM
ejpam-5646	83	52	for	for	ADP
ejpam-5646	83	53	all	all	DET
ejpam-5646	83	54	r	r	NOUN
ejpam-5646	83	55	,	,	PUNCT
ejpam-5646	83	56	a	a	DET
ejpam-5646	83	57	∈	∈	NOUN
ejpam-5646	83	58	x	x	X
ejpam-5646	83	59	;	;	PUNCT
ejpam-5646	83	60	(	(	PUNCT
ejpam-5646	83	61	ii	ii	NOUN
ejpam-5646	83	62	)	)	PUNCT
ejpam-5646	83	63	µ	µ	PROPN
ejpam-5646	83	64	is	be	AUX
ejpam-5646	83	65	a	a	DET
ejpam-5646	83	66	fuzzy	fuzzy	ADJ
ejpam-5646	83	67	right	right	ADJ
ejpam-5646	83	68	antiideal	antiideal	NOUN
ejpam-5646	83	69	of	of	ADP
ejpam-5646	83	70	x	x	PRON
ejpam-5646	83	71	if	if	SCONJ
ejpam-5646	83	72	µ(ar	µ(ar	NOUN
ejpam-5646	83	73	)	)	PUNCT
ejpam-5646	83	74	∧	∧	NOUN
ejpam-5646	83	75	µ(a	µ(a	PROPN
ejpam-5646	83	76	)	)	PUNCT
ejpam-5646	83	77	=	=	SYM
ejpam-5646	83	78	0	0	NUM
ejpam-5646	83	79	for	for	ADP
ejpam-5646	83	80	all	all	DET
ejpam-5646	83	81	r	r	NOUN
ejpam-5646	83	82	,	,	PUNCT
ejpam-5646	83	83	a	a	DET
ejpam-5646	83	84	∈	∈	PROPN
ejpam-5646	83	85	x	x	NOUN
ejpam-5646	83	86	;	;	PUNCT
ejpam-5646	83	87	m.	m.	NOUN
ejpam-5646	83	88	al	al	PROPN
ejpam-5646	83	89	tahan	tahan	PROPN
ejpam-5646	83	90	,	,	PUNCT
ejpam-5646	83	91	s.	s.	PROPN
ejpam-5646	83	92	hoskova	hoskova	PROPN
ejpam-5646	83	93	-	-	PUNCT
ejpam-5646	83	94	mayerova	mayerova	PROPN
ejpam-5646	83	95	,	,	PUNCT
ejpam-5646	83	96	s.	s.	PROPN
ejpam-5646	83	97	al	al	PROPN
ejpam-5646	83	98	-	-	PUNCT
ejpam-5646	83	99	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	83	100	/	/	SYM
ejpam-5646	83	101	eur	eur	NOUN
ejpam-5646	83	102	.	.	PUNCT
ejpam-5646	84	1	j.	j.	PROPN
ejpam-5646	84	2	pure	pure	PROPN
ejpam-5646	84	3	appl	appl	PROPN
ejpam-5646	84	4	.	.	PROPN
ejpam-5646	84	5	math	math	PROPN
ejpam-5646	84	6	,	,	PUNCT
ejpam-5646	84	7	18	18	NUM
ejpam-5646	84	8	(	(	PUNCT
ejpam-5646	84	9	1	1	NUM
ejpam-5646	84	10	)	)	PUNCT
ejpam-5646	84	11	(	(	PUNCT
ejpam-5646	84	12	2025	2025	NUM
ejpam-5646	84	13	)	)	PUNCT
ejpam-5646	84	14	,	,	PUNCT
ejpam-5646	84	15	5646	5646	NUM
ejpam-5646	84	16	4	4	NUM
ejpam-5646	84	17	of	of	ADP
ejpam-5646	84	18	11	11	NUM
ejpam-5646	84	19	(	(	PUNCT
ejpam-5646	84	20	iii	iii	NOUN
ejpam-5646	84	21	)	)	PUNCT
ejpam-5646	84	22	µ	µ	NOUN
ejpam-5646	84	23	is	be	AUX
ejpam-5646	84	24	a	a	DET
ejpam-5646	84	25	fuzzy	fuzzy	ADJ
ejpam-5646	84	26	antiideal	antiideal	NOUN
ejpam-5646	84	27	of	of	ADP
ejpam-5646	84	28	x	x	PRON
ejpam-5646	84	29	if	if	SCONJ
ejpam-5646	84	30	µ	µ	PRON
ejpam-5646	84	31	is	be	AUX
ejpam-5646	84	32	a	a	DET
ejpam-5646	84	33	fuzzy	fuzzy	ADJ
ejpam-5646	84	34	left	leave	VERB
ejpam-5646	84	35	antiideal	antiideal	NOUN
ejpam-5646	84	36	of	of	ADP
ejpam-5646	84	37	x	x	X
ejpam-5646	84	38	and	and	CCONJ
ejpam-5646	84	39	a	a	DET
ejpam-5646	84	40	fuzzy	fuzzy	ADJ
ejpam-5646	84	41	right	right	ADJ
ejpam-5646	84	42	antiideal	antiideal	NOUN
ejpam-5646	84	43	of	of	ADP
ejpam-5646	84	44	x	x	PRON
ejpam-5646	84	45	;	;	PUNCT
ejpam-5646	84	46	(	(	PUNCT
ejpam-5646	84	47	iv	iv	X
ejpam-5646	84	48	)	)	PUNCT
ejpam-5646	84	49	µ	µ	X
ejpam-5646	84	50	is	be	AUX
ejpam-5646	84	51	a	a	DET
ejpam-5646	84	52	fuzzy	fuzzy	ADJ
ejpam-5646	84	53	bi	bi	NOUN
ejpam-5646	84	54	-	-	NOUN
ejpam-5646	84	55	antiideal	antiideal	NOUN
ejpam-5646	84	56	of	of	ADP
ejpam-5646	84	57	x	x	SYM
ejpam-5646	84	58	if	if	SCONJ
ejpam-5646	84	59	µ(xry	µ(xry	PROPN
ejpam-5646	84	60	)	)	PUNCT
ejpam-5646	84	61	∧	∧	NOUN
ejpam-5646	84	62	µ(x	µ(x	VERB
ejpam-5646	84	63	)	)	PUNCT
ejpam-5646	84	64	∧	∧	PROPN
ejpam-5646	84	65	µ(y	µ(y	PROPN
ejpam-5646	84	66	)	)	PUNCT
ejpam-5646	84	67	=	=	SYM
ejpam-5646	84	68	0	0	NUM
ejpam-5646	84	69	for	for	ADP
ejpam-5646	84	70	all	all	DET
ejpam-5646	84	71	r	r	NOUN
ejpam-5646	84	72	,	,	PUNCT
ejpam-5646	84	73	x	x	PRON
ejpam-5646	84	74	,	,	PUNCT
ejpam-5646	84	75	y	y	PROPN
ejpam-5646	84	76	∈	∈	PROPN
ejpam-5646	84	77	x.	x.	NOUN
ejpam-5646	84	78	definition	definition	NOUN
ejpam-5646	84	79	7	7	NUM
ejpam-5646	84	80	.	.	PUNCT
ejpam-5646	85	1	[	[	X
ejpam-5646	85	2	7	7	X
ejpam-5646	85	3	]	]	X
ejpam-5646	85	4	let	let	VERB
ejpam-5646	85	5	(	(	PUNCT
ejpam-5646	85	6	x	x	NOUN
ejpam-5646	85	7	,	,	PUNCT
ejpam-5646	85	8	·	·	PUNCT
ejpam-5646	85	9	)	)	PUNCT
ejpam-5646	85	10	be	be	AUX
ejpam-5646	85	11	a	a	DET
ejpam-5646	85	12	semigroup	semigroup	NOUN
ejpam-5646	85	13	,	,	PUNCT
ejpam-5646	85	14	µ	µ	X
ejpam-5646	85	15	be	be	VERB
ejpam-5646	85	16	a	a	DET
ejpam-5646	85	17	non	non	ADJ
ejpam-5646	85	18	-	-	ADJ
ejpam-5646	85	19	zero	zero	ADJ
ejpam-5646	85	20	fuzzy	fuzzy	ADJ
ejpam-5646	85	21	set	set	NOUN
ejpam-5646	85	22	of	of	ADP
ejpam-5646	85	23	x	x	NOUN
ejpam-5646	85	24	,	,	PUNCT
ejpam-5646	85	25	and	and	CCONJ
ejpam-5646	85	26	t	t	PROPN
ejpam-5646	85	27	∈	∈	PROPN
ejpam-5646	86	1	[	[	X
ejpam-5646	86	2	0	0	NUM
ejpam-5646	86	3	,	,	PUNCT
ejpam-5646	86	4	1	1	NUM
ejpam-5646	86	5	]	]	PUNCT
ejpam-5646	86	6	.	.	PUNCT
ejpam-5646	87	1	then	then	ADV
ejpam-5646	87	2	the	the	DET
ejpam-5646	87	3	level	level	NOUN
ejpam-5646	87	4	set	set	NOUN
ejpam-5646	87	5	µt	µt	PRON
ejpam-5646	87	6	is	be	AUX
ejpam-5646	87	7	defined	define	VERB
ejpam-5646	87	8	as	as	SCONJ
ejpam-5646	87	9	follows	follow	VERB
ejpam-5646	87	10	.	.	PUNCT
ejpam-5646	88	1	µt	µt	X
ejpam-5646	88	2	=	=	PUNCT
ejpam-5646	88	3	{	{	PUNCT
ejpam-5646	88	4	x	x	SYM
ejpam-5646	88	5	∈	∈	PROPN
ejpam-5646	88	6	x	x	X
ejpam-5646	88	7	:	:	PUNCT
ejpam-5646	88	8	µ(x	µ(x	NUM
ejpam-5646	88	9	)	)	PUNCT
ejpam-5646	88	10	≥	≥	NOUN
ejpam-5646	88	11	t	t	PROPN
ejpam-5646	88	12	}	}	PUNCT
ejpam-5646	88	13	.	.	PUNCT
ejpam-5646	89	1	example	example	NOUN
ejpam-5646	90	1	4	4	X
ejpam-5646	90	2	.	.	PUNCT
ejpam-5646	91	1	let	let	VERB
ejpam-5646	91	2	(	(	PUNCT
ejpam-5646	91	3	k	k	NOUN
ejpam-5646	91	4	,	,	PUNCT
ejpam-5646	91	5	·	·	PUNCT
ejpam-5646	91	6	)	)	PUNCT
ejpam-5646	91	7	be	be	VERB
ejpam-5646	91	8	the	the	DET
ejpam-5646	91	9	semigroup	semigroup	NOUN
ejpam-5646	91	10	defined	define	VERB
ejpam-5646	91	11	in	in	ADP
ejpam-5646	91	12	example	example	NOUN
ejpam-5646	91	13	1	1	NUM
ejpam-5646	91	14	and	and	CCONJ
ejpam-5646	91	15	define	define	VERB
ejpam-5646	91	16	the	the	DET
ejpam-5646	91	17	fuzzy	fuzzy	ADJ
ejpam-5646	91	18	sets	set	NOUN
ejpam-5646	91	19	µ1	µ1	PROPN
ejpam-5646	91	20	,	,	PUNCT
ejpam-5646	91	21	µ2	µ2	PROPN
ejpam-5646	91	22	on	on	ADP
ejpam-5646	91	23	k	k	PROPN
ejpam-5646	91	24	as	as	SCONJ
ejpam-5646	91	25	follows	follow	VERB
ejpam-5646	91	26	.	.	PUNCT
ejpam-5646	92	1	µ1(k	µ1(k	X
ejpam-5646	92	2	)	)	PUNCT
ejpam-5646	92	3	=	=	NOUN
ejpam-5646	92	4	{	{	PUNCT
ejpam-5646	92	5	0.54	0.54	NUM
ejpam-5646	92	6	if	if	SCONJ
ejpam-5646	92	7	k	k	PROPN
ejpam-5646	92	8	=	=	SYM
ejpam-5646	92	9	2	2	NUM
ejpam-5646	92	10	;	;	PUNCT
ejpam-5646	92	11	0	0	NUM
ejpam-5646	92	12	otherwise	otherwise	ADV
ejpam-5646	92	13	.	.	PUNCT
ejpam-5646	93	1	and	and	CCONJ
ejpam-5646	93	2	µ2(k	µ2(k	VERB
ejpam-5646	93	3	)	)	PUNCT
ejpam-5646	93	4	=	=	PUNCT
ejpam-5646	94	1			NOUN
ejpam-5646	94	2	0.65	0.65	NUM
ejpam-5646	95	1	if	if	SCONJ
ejpam-5646	95	2	k	k	PROPN
ejpam-5646	95	3	=	=	NOUN
ejpam-5646	95	4	4	4	NUM
ejpam-5646	95	5	;	;	PUNCT
ejpam-5646	95	6	0.6	0.6	NUM
ejpam-5646	95	7	if	if	SCONJ
ejpam-5646	95	8	k	k	PROPN
ejpam-5646	95	9	=	=	SYM
ejpam-5646	95	10	3	3	NUM
ejpam-5646	95	11	;	;	PUNCT
ejpam-5646	95	12	0.55	0.55	NUM
ejpam-5646	96	1	if	if	SCONJ
ejpam-5646	96	2	k	k	PROPN
ejpam-5646	96	3	=	=	SYM
ejpam-5646	96	4	2	2	NUM
ejpam-5646	96	5	;	;	PUNCT
ejpam-5646	96	6	0	0	NUM
ejpam-5646	96	7	otherwise	otherwise	ADV
ejpam-5646	96	8	.	.	PUNCT
ejpam-5646	97	1	then	then	ADV
ejpam-5646	97	2	µ1	µ1	PROPN
ejpam-5646	97	3	is	be	AUX
ejpam-5646	97	4	a	a	DET
ejpam-5646	97	5	fuzzy	fuzzy	ADJ
ejpam-5646	97	6	antiideal	antiideal	NOUN
ejpam-5646	97	7	of	of	ADP
ejpam-5646	97	8	k	k	PROPN
ejpam-5646	97	9	and	and	CCONJ
ejpam-5646	97	10	µ2	µ2	PROPN
ejpam-5646	97	11	is	be	AUX
ejpam-5646	97	12	a	a	DET
ejpam-5646	97	13	fuzzy	fuzzy	ADJ
ejpam-5646	97	14	bi	bi	NOUN
ejpam-5646	97	15	-	-	NOUN
ejpam-5646	97	16	antiideal	antiideal	NOUN
ejpam-5646	97	17	of	of	ADP
ejpam-5646	97	18	k.	k.	PROPN
ejpam-5646	97	19	theorem	theorem	PROPN
ejpam-5646	97	20	1	1	NUM
ejpam-5646	97	21	.	.	PUNCT
ejpam-5646	98	1	[	[	X
ejpam-5646	98	2	2	2	X
ejpam-5646	98	3	]	]	PUNCT
ejpam-5646	98	4	let	let	VERB
ejpam-5646	98	5	x	x	PRON
ejpam-5646	98	6	be	be	AUX
ejpam-5646	98	7	a	a	DET
ejpam-5646	98	8	semigroup	semigroup	NOUN
ejpam-5646	98	9	,	,	PUNCT
ejpam-5646	98	10	t	t	PROPN
ejpam-5646	98	11	∈]0	∈]0	ADJ
ejpam-5646	98	12	,	,	PUNCT
ejpam-5646	98	13	1	1	NUM
ejpam-5646	98	14	]	]	PUNCT
ejpam-5646	98	15	,	,	PUNCT
ejpam-5646	98	16	and	and	CCONJ
ejpam-5646	98	17	µ	µ	DET
ejpam-5646	98	18	a	a	DET
ejpam-5646	98	19	non	non	ADJ
ejpam-5646	98	20	-	-	ADJ
ejpam-5646	98	21	zero	zero	ADJ
ejpam-5646	98	22	fuzzy	fuzzy	ADJ
ejpam-5646	98	23	set	set	NOUN
ejpam-5646	98	24	of	of	ADP
ejpam-5646	98	25	x.	x.	NOUN
ejpam-5646	98	26	then	then	ADV
ejpam-5646	98	27	the	the	DET
ejpam-5646	98	28	following	follow	VERB
ejpam-5646	98	29	statements	statement	NOUN
ejpam-5646	98	30	hold	hold	VERB
ejpam-5646	98	31	.	.	PUNCT
ejpam-5646	99	1	(	(	PUNCT
ejpam-5646	99	2	i	i	NOUN
ejpam-5646	99	3	)	)	PUNCT
ejpam-5646	99	4	µ	µ	PROPN
ejpam-5646	99	5	is	be	AUX
ejpam-5646	99	6	a	a	DET
ejpam-5646	99	7	fuzzy	fuzzy	ADJ
ejpam-5646	99	8	left(right	left(right	PROPN
ejpam-5646	99	9	)	)	PUNCT
ejpam-5646	99	10	antiideal	antiideal	NOUN
ejpam-5646	99	11	of	of	ADP
ejpam-5646	99	12	x	x	SYM
ejpam-5646	99	13	if	if	SCONJ
ejpam-5646	99	14	and	and	CCONJ
ejpam-5646	99	15	only	only	ADV
ejpam-5646	99	16	of	of	ADP
ejpam-5646	99	17	µt	µt	DET
ejpam-5646	99	18	̸=	̸=	PROPN
ejpam-5646	99	19	∅	∅	NOUN
ejpam-5646	99	20	is	be	AUX
ejpam-5646	99	21	a	a	DET
ejpam-5646	99	22	left(right	left(right	PROPN
ejpam-5646	99	23	)	)	PUNCT
ejpam-5646	99	24	antiideal	antiideal	NOUN
ejpam-5646	99	25	of	of	ADP
ejpam-5646	99	26	x.	x.	PROPN
ejpam-5646	99	27	(	(	PUNCT
ejpam-5646	99	28	ii	ii	PROPN
ejpam-5646	99	29	)	)	PUNCT
ejpam-5646	99	30	µ	µ	PROPN
ejpam-5646	99	31	is	be	AUX
ejpam-5646	99	32	a	a	DET
ejpam-5646	99	33	fuzzy	fuzzy	ADJ
ejpam-5646	99	34	bi	bi	NOUN
ejpam-5646	99	35	-	-	NOUN
ejpam-5646	99	36	antiideal	antiideal	NOUN
ejpam-5646	99	37	of	of	ADP
ejpam-5646	99	38	x	x	SYM
ejpam-5646	99	39	if	if	SCONJ
ejpam-5646	99	40	and	and	CCONJ
ejpam-5646	99	41	only	only	ADV
ejpam-5646	99	42	of	of	ADP
ejpam-5646	99	43	µt	µt	PRON
ejpam-5646	99	44	̸=	̸=	PROPN
ejpam-5646	99	45	∅	∅	NOUN
ejpam-5646	99	46	is	be	AUX
ejpam-5646	99	47	a	a	DET
ejpam-5646	99	48	bi	bi	NOUN
ejpam-5646	99	49	-	-	NOUN
ejpam-5646	99	50	antiideal	antiideal	NOUN
ejpam-5646	99	51	of	of	ADP
ejpam-5646	99	52	x.	x.	NOUN
ejpam-5646	99	53	3	3	NUM
ejpam-5646	99	54	.	.	PUNCT
ejpam-5646	100	1	(	(	PUNCT
ejpam-5646	100	2	m	m	NOUN
ejpam-5646	100	3	,	,	PUNCT
ejpam-5646	100	4	n)-bi	n)-bi	NOUN
ejpam-5646	100	5	-	-	PUNCT
ejpam-5646	100	6	antiideals	antiideal	NOUN
ejpam-5646	100	7	of	of	ADP
ejpam-5646	100	8	a	a	DET
ejpam-5646	100	9	semigroup	semigroup	NOUN
ejpam-5646	100	10	in	in	ADP
ejpam-5646	100	11	this	this	DET
ejpam-5646	100	12	section	section	NOUN
ejpam-5646	100	13	and	and	CCONJ
ejpam-5646	100	14	inspired	inspire	VERB
ejpam-5646	100	15	by	by	ADP
ejpam-5646	100	16	(	(	PUNCT
ejpam-5646	100	17	m	m	PROPN
ejpam-5646	100	18	,	,	PUNCT
ejpam-5646	100	19	n)-antiideals	n)-antiideal	NOUN
ejpam-5646	100	20	[	[	X
ejpam-5646	100	21	1	1	NUM
ejpam-5646	100	22	,	,	PUNCT
ejpam-5646	100	23	8	8	NUM
ejpam-5646	100	24	]	]	PUNCT
ejpam-5646	100	25	and	and	CCONJ
ejpam-5646	100	26	by	by	ADP
ejpam-5646	100	27	bi	bi	NOUN
ejpam-5646	100	28	-	-	NOUN
ejpam-5646	100	29	antiideals	antiideal	NOUN
ejpam-5646	100	30	[	[	X
ejpam-5646	100	31	2	2	NUM
ejpam-5646	100	32	]	]	PUNCT
ejpam-5646	100	33	,	,	PUNCT
ejpam-5646	100	34	we	we	PRON
ejpam-5646	100	35	introduce	introduce	VERB
ejpam-5646	100	36	(	(	PUNCT
ejpam-5646	100	37	m	m	NOUN
ejpam-5646	100	38	,	,	PUNCT
ejpam-5646	100	39	n)-bi	n)-bi	NOUN
ejpam-5646	100	40	-	-	PUNCT
ejpam-5646	100	41	antiideals	antiideal	NOUN
ejpam-5646	100	42	of	of	ADP
ejpam-5646	100	43	a	a	DET
ejpam-5646	100	44	semigroup	semigroup	NOUN
ejpam-5646	100	45	as	as	ADP
ejpam-5646	100	46	a	a	DET
ejpam-5646	100	47	generalization	generalization	NOUN
ejpam-5646	100	48	of	of	ADP
ejpam-5646	100	49	bi	bi	ADJ
ejpam-5646	100	50	-	-	NOUN
ejpam-5646	100	51	antiideals	antiideal	NOUN
ejpam-5646	100	52	and	and	CCONJ
ejpam-5646	100	53	study	study	VERB
ejpam-5646	100	54	their	their	PRON
ejpam-5646	100	55	properties	property	NOUN
ejpam-5646	100	56	.	.	PUNCT
ejpam-5646	101	1	the	the	DET
ejpam-5646	101	2	results	result	NOUN
ejpam-5646	101	3	of	of	ADP
ejpam-5646	101	4	this	this	DET
ejpam-5646	101	5	section	section	NOUN
ejpam-5646	101	6	are	be	AUX
ejpam-5646	101	7	considered	consider	VERB
ejpam-5646	101	8	as	as	ADP
ejpam-5646	101	9	a	a	DET
ejpam-5646	101	10	generalization	generalization	NOUN
ejpam-5646	101	11	of	of	ADP
ejpam-5646	101	12	some	some	DET
ejpam-5646	101	13	results	result	NOUN
ejpam-5646	101	14	in	in	ADP
ejpam-5646	101	15	[	[	X
ejpam-5646	101	16	2	2	NUM
ejpam-5646	101	17	]	]	PUNCT
ejpam-5646	101	18	.	.	PUNCT
ejpam-5646	102	1	definition	definition	NOUN
ejpam-5646	102	2	8	8	NUM
ejpam-5646	102	3	.	.	PUNCT
ejpam-5646	103	1	let	let	VERB
ejpam-5646	103	2	(	(	PUNCT
ejpam-5646	103	3	x	x	NOUN
ejpam-5646	103	4	,	,	PUNCT
ejpam-5646	103	5	·	·	PUNCT
ejpam-5646	103	6	)	)	PUNCT
ejpam-5646	103	7	be	be	AUX
ejpam-5646	103	8	a	a	DET
ejpam-5646	103	9	semigroup	semigroup	NOUN
ejpam-5646	103	10	,	,	PUNCT
ejpam-5646	103	11	m	m	PROPN
ejpam-5646	103	12	,	,	PUNCT
ejpam-5646	103	13	n	n	PRON
ejpam-5646	103	14	be	be	VERB
ejpam-5646	103	15	positive	positive	ADJ
ejpam-5646	103	16	integers	integer	NOUN
ejpam-5646	103	17	,	,	PUNCT
ejpam-5646	103	18	and	and	CCONJ
ejpam-5646	103	19	a	a	DET
ejpam-5646	103	20	̸=	̸=	PROPN
ejpam-5646	103	21	∅	∅	NOUN
ejpam-5646	103	22	⊆	⊆	NUM
ejpam-5646	103	23	x.	x.	NOUN
ejpam-5646	103	24	then	then	ADV
ejpam-5646	103	25	a	a	PRON
ejpam-5646	103	26	is	be	AUX
ejpam-5646	103	27	an	an	DET
ejpam-5646	103	28	(	(	PUNCT
ejpam-5646	103	29	m	m	NOUN
ejpam-5646	103	30	,	,	PUNCT
ejpam-5646	103	31	n)-bi	n)-bi	NOUN
ejpam-5646	103	32	-	-	PUNCT
ejpam-5646	103	33	antiideal	antiideal	NOUN
ejpam-5646	103	34	of	of	ADP
ejpam-5646	103	35	x	x	PRON
ejpam-5646	103	36	if	if	SCONJ
ejpam-5646	103	37	amxan	amxan	VERB
ejpam-5646	103	38	∩a	∩a	PROPN
ejpam-5646	103	39	=	=	PUNCT
ejpam-5646	103	40	∅.	∅.	PRON
ejpam-5646	103	41	remark	remark	NOUN
ejpam-5646	103	42	1	1	NUM
ejpam-5646	103	43	.	.	PUNCT
ejpam-5646	104	1	a	a	DET
ejpam-5646	104	2	monoid	monoid	NOUN
ejpam-5646	104	3	can	can	AUX
ejpam-5646	104	4	have	have	VERB
ejpam-5646	104	5	(	(	PUNCT
ejpam-5646	104	6	m	m	NOUN
ejpam-5646	104	7	,	,	PUNCT
ejpam-5646	104	8	n)-bi	n)-bi	NOUN
ejpam-5646	104	9	-	-	PUNCT
ejpam-5646	104	10	antiideals	antiideal	NOUN
ejpam-5646	104	11	.	.	PUNCT
ejpam-5646	105	1	(	(	PUNCT
ejpam-5646	105	2	see	see	VERB
ejpam-5646	105	3	example	example	NOUN
ejpam-5646	105	4	5	5	NUM
ejpam-5646	105	5	.	.	PUNCT
ejpam-5646	105	6	)	)	PUNCT
ejpam-5646	105	7	example	example	NOUN
ejpam-5646	106	1	5	5	NUM
ejpam-5646	106	2	.	.	PUNCT
ejpam-5646	107	1	let	let	AUX
ejpam-5646	107	2	(	(	PUNCT
ejpam-5646	107	3	p0,+	p0,+	ADV
ejpam-5646	107	4	)	)	PUNCT
ejpam-5646	107	5	be	be	VERB
ejpam-5646	107	6	the	the	DET
ejpam-5646	107	7	monoid	monoid	NOUN
ejpam-5646	107	8	of	of	ADP
ejpam-5646	107	9	non	non	ADJ
ejpam-5646	107	10	-	-	ADJ
ejpam-5646	107	11	negative	negative	ADJ
ejpam-5646	107	12	integers	integer	NOUN
ejpam-5646	107	13	under	under	ADP
ejpam-5646	107	14	standard	standard	ADJ
ejpam-5646	107	15	addition	addition	NOUN
ejpam-5646	107	16	of	of	ADP
ejpam-5646	107	17	integers	integer	NOUN
ejpam-5646	107	18	.	.	PUNCT
ejpam-5646	108	1	then	then	ADV
ejpam-5646	108	2	{	{	PUNCT
ejpam-5646	108	3	1	1	NUM
ejpam-5646	108	4	,	,	PUNCT
ejpam-5646	108	5	2	2	NUM
ejpam-5646	108	6	}	}	PUNCT
ejpam-5646	108	7	is	be	AUX
ejpam-5646	108	8	a	a	DET
ejpam-5646	108	9	(	(	PUNCT
ejpam-5646	108	10	2	2	NUM
ejpam-5646	108	11	,	,	PUNCT
ejpam-5646	108	12	1)-bi	1)-bi	NUM
ejpam-5646	108	13	-	-	PUNCT
ejpam-5646	108	14	antiideal	antiideal	NOUN
ejpam-5646	108	15	of	of	ADP
ejpam-5646	108	16	p0	p0	NOUN
ejpam-5646	108	17	.	.	PUNCT
ejpam-5646	109	1	this	this	PRON
ejpam-5646	109	2	is	be	AUX
ejpam-5646	109	3	clear	clear	ADJ
ejpam-5646	109	4	as	as	ADP
ejpam-5646	109	5	(	(	PUNCT
ejpam-5646	109	6	{	{	PUNCT
ejpam-5646	109	7	1	1	NUM
ejpam-5646	109	8	,	,	PUNCT
ejpam-5646	109	9	2}+	2}+	NUM
ejpam-5646	109	10	{	{	PUNCT
ejpam-5646	109	11	1	1	NUM
ejpam-5646	109	12	,	,	PUNCT
ejpam-5646	109	13	2}+	2}+	NUM
ejpam-5646	109	14	p0	p0	NOUN
ejpam-5646	109	15	+	+	CCONJ
ejpam-5646	109	16	{	{	PUNCT
ejpam-5646	109	17	1	1	NUM
ejpam-5646	109	18	,	,	PUNCT
ejpam-5646	109	19	2	2	NUM
ejpam-5646	109	20	}	}	PUNCT
ejpam-5646	109	21	)	)	PUNCT
ejpam-5646	109	22	∩	∩	NOUN
ejpam-5646	109	23	{	{	PUNCT
ejpam-5646	109	24	1	1	NUM
ejpam-5646	109	25	,	,	PUNCT
ejpam-5646	109	26	2	2	NUM
ejpam-5646	109	27	}	}	PUNCT
ejpam-5646	109	28	=	=	PRON
ejpam-5646	109	29	{	{	PUNCT
ejpam-5646	109	30	x	x	PUNCT
ejpam-5646	109	31	∈	∈	NOUN
ejpam-5646	109	32	p0	p0	NOUN
ejpam-5646	109	33	:	:	PUNCT
ejpam-5646	110	1	x	x	X
ejpam-5646	110	2	≥	≥	NUM
ejpam-5646	110	3	3	3	NUM
ejpam-5646	110	4	}	}	PUNCT
ejpam-5646	110	5	∩	∩	NOUN
ejpam-5646	110	6	{	{	PUNCT
ejpam-5646	110	7	1	1	NUM
ejpam-5646	110	8	,	,	PUNCT
ejpam-5646	110	9	2	2	NUM
ejpam-5646	110	10	}	}	PUNCT
ejpam-5646	110	11	=	=	X
ejpam-5646	110	12	∅.	∅.	NOUN
ejpam-5646	110	13	proposition	proposition	NOUN
ejpam-5646	110	14	2	2	NUM
ejpam-5646	110	15	.	.	PUNCT
ejpam-5646	111	1	let	let	VERB
ejpam-5646	111	2	(	(	PUNCT
ejpam-5646	111	3	x	x	NOUN
ejpam-5646	111	4	,	,	PUNCT
ejpam-5646	111	5	·	·	PUNCT
ejpam-5646	111	6	)	)	PUNCT
ejpam-5646	111	7	be	be	AUX
ejpam-5646	111	8	a	a	DET
ejpam-5646	111	9	semigroup	semigroup	NOUN
ejpam-5646	111	10	and	and	CCONJ
ejpam-5646	111	11	a	a	DET
ejpam-5646	111	12	̸=	̸=	PROPN
ejpam-5646	111	13	∅	∅	NOUN
ejpam-5646	111	14	⊆	⊆	NUM
ejpam-5646	111	15	x	x	PUNCT
ejpam-5646	111	16	be	be	AUX
ejpam-5646	111	17	a	a	DET
ejpam-5646	111	18	bi	bi	NOUN
ejpam-5646	111	19	-	-	NOUN
ejpam-5646	111	20	antiideal	antiideal	NOUN
ejpam-5646	111	21	of	of	ADP
ejpam-5646	111	22	x.	x.	NOUN
ejpam-5646	111	23	then	then	ADV
ejpam-5646	111	24	a	a	PRON
ejpam-5646	111	25	is	be	AUX
ejpam-5646	111	26	an	an	DET
ejpam-5646	111	27	(	(	PUNCT
ejpam-5646	111	28	m	m	NOUN
ejpam-5646	111	29	,	,	PUNCT
ejpam-5646	111	30	n)-bi	n)-bi	NOUN
ejpam-5646	111	31	-	-	PUNCT
ejpam-5646	111	32	antiideal	antiideal	NOUN
ejpam-5646	111	33	of	of	ADP
ejpam-5646	111	34	x.	x.	PROPN
ejpam-5646	111	35	m.	m.	PROPN
ejpam-5646	111	36	al	al	PROPN
ejpam-5646	111	37	tahan	tahan	PROPN
ejpam-5646	111	38	,	,	PUNCT
ejpam-5646	111	39	s.	s.	PROPN
ejpam-5646	111	40	hoskova	hoskova	PROPN
ejpam-5646	111	41	-	-	PUNCT
ejpam-5646	111	42	mayerova	mayerova	PROPN
ejpam-5646	111	43	,	,	PUNCT
ejpam-5646	111	44	s.	s.	PROPN
ejpam-5646	111	45	al	al	PROPN
ejpam-5646	111	46	-	-	PUNCT
ejpam-5646	111	47	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	111	48	/	/	SYM
ejpam-5646	111	49	eur	eur	NOUN
ejpam-5646	111	50	.	.	PUNCT
ejpam-5646	112	1	j.	j.	PROPN
ejpam-5646	112	2	pure	pure	PROPN
ejpam-5646	112	3	appl	appl	PROPN
ejpam-5646	112	4	.	.	PROPN
ejpam-5646	112	5	math	math	PROPN
ejpam-5646	112	6	,	,	PUNCT
ejpam-5646	112	7	18	18	NUM
ejpam-5646	112	8	(	(	PUNCT
ejpam-5646	112	9	1	1	NUM
ejpam-5646	112	10	)	)	PUNCT
ejpam-5646	112	11	(	(	PUNCT
ejpam-5646	112	12	2025	2025	NUM
ejpam-5646	112	13	)	)	PUNCT
ejpam-5646	112	14	,	,	PUNCT
ejpam-5646	112	15	5646	5646	NUM
ejpam-5646	112	16	5	5	NUM
ejpam-5646	112	17	of	of	ADP
ejpam-5646	112	18	11	11	NUM
ejpam-5646	112	19	proof	proof	NOUN
ejpam-5646	112	20	.	.	PUNCT
ejpam-5646	113	1	the	the	DET
ejpam-5646	113	2	proof	proof	NOUN
ejpam-5646	113	3	results	result	VERB
ejpam-5646	113	4	form	form	VERB
ejpam-5646	113	5	having	having	AUX
ejpam-5646	113	6	amxan	amxan	VERB
ejpam-5646	113	7	∩a	∩a	PROPN
ejpam-5646	114	1	=	=	PUNCT
ejpam-5646	115	1	a(am−1xan−1)a	a(am−1xan−1)a	PROPN
ejpam-5646	115	2	∩a	∩a	PROPN
ejpam-5646	115	3	⊆	⊆	NUM
ejpam-5646	115	4	axa	axa	NOUN
ejpam-5646	115	5	∩a	∩a	NOUN
ejpam-5646	115	6	=	=	PUNCT
ejpam-5646	115	7	∅.	∅.	PRON
ejpam-5646	115	8	remark	remark	NOUN
ejpam-5646	115	9	2	2	NUM
ejpam-5646	115	10	.	.	PUNCT
ejpam-5646	116	1	the	the	DET
ejpam-5646	116	2	converse	converse	NOUN
ejpam-5646	116	3	of	of	ADP
ejpam-5646	116	4	proposition	proposition	NOUN
ejpam-5646	116	5	2	2	NUM
ejpam-5646	116	6	may	may	AUX
ejpam-5646	116	7	not	not	PART
ejpam-5646	116	8	hold	hold	VERB
ejpam-5646	116	9	.	.	PUNCT
ejpam-5646	117	1	(	(	PUNCT
ejpam-5646	117	2	see	see	VERB
ejpam-5646	117	3	example	example	NOUN
ejpam-5646	117	4	6	6	NUM
ejpam-5646	117	5	.	.	PUNCT
ejpam-5646	117	6	)	)	PUNCT
ejpam-5646	117	7	example	example	NOUN
ejpam-5646	118	1	6	6	NUM
ejpam-5646	118	2	.	.	PUNCT
ejpam-5646	118	3	let	let	VERB
ejpam-5646	118	4	m2(p0	m2(p0	NOUN
ejpam-5646	118	5	)	)	PUNCT
ejpam-5646	118	6	be	be	AUX
ejpam-5646	118	7	the	the	DET
ejpam-5646	118	8	semigroup	semigroup	NOUN
ejpam-5646	118	9	of	of	ADP
ejpam-5646	118	10	all	all	DET
ejpam-5646	118	11	two	two	NUM
ejpam-5646	118	12	by	by	ADP
ejpam-5646	118	13	two	two	NUM
ejpam-5646	118	14	matrices	matrix	NOUN
ejpam-5646	118	15	with	with	ADP
ejpam-5646	118	16	non	non	ADJ
ejpam-5646	118	17	-	-	ADJ
ejpam-5646	118	18	negative	negative	ADJ
ejpam-5646	118	19	integral	integral	ADJ
ejpam-5646	118	20	entries	entry	NOUN
ejpam-5646	118	21	under	under	ADP
ejpam-5646	118	22	multiplication	multiplication	NOUN
ejpam-5646	118	23	of	of	ADP
ejpam-5646	118	24	matrices	matrix	NOUN
ejpam-5646	118	25	and	and	CCONJ
ejpam-5646	118	26	a	a	DET
ejpam-5646	118	27	=	=	X
ejpam-5646	118	28	{	{	PUNCT
ejpam-5646	118	29	(	(	PUNCT
ejpam-5646	118	30	2	2	NUM
ejpam-5646	118	31	0	0	NUM
ejpam-5646	118	32	0	0	NUM
ejpam-5646	118	33	0	0	NUM
ejpam-5646	118	34	)	)	PUNCT
ejpam-5646	118	35	,	,	PUNCT
ejpam-5646	118	36	(	(	PUNCT
ejpam-5646	118	37	4	4	NUM
ejpam-5646	118	38	0	0	NUM
ejpam-5646	118	39	0	0	NUM
ejpam-5646	118	40	0	0	NUM
ejpam-5646	118	41	)	)	PUNCT
ejpam-5646	118	42	}	}	PUNCT
ejpam-5646	118	43	.	.	PUNCT
ejpam-5646	119	1	then	then	ADV
ejpam-5646	119	2	a	a	PRON
ejpam-5646	119	3	is	be	AUX
ejpam-5646	119	4	a	a	DET
ejpam-5646	119	5	(	(	PUNCT
ejpam-5646	119	6	2	2	NUM
ejpam-5646	119	7	,	,	PUNCT
ejpam-5646	119	8	1)-bi	1)-bi	NUM
ejpam-5646	119	9	-	-	PUNCT
ejpam-5646	119	10	antiideal	antiideal	NOUN
ejpam-5646	119	11	of	of	ADP
ejpam-5646	119	12	m2(p0	m2(p0	NOUN
ejpam-5646	119	13	)	)	PUNCT
ejpam-5646	119	14	.	.	PUNCT
ejpam-5646	120	1	furthermore	furthermore	ADV
ejpam-5646	120	2	,	,	PUNCT
ejpam-5646	120	3	it	it	PRON
ejpam-5646	120	4	is	be	AUX
ejpam-5646	120	5	not	not	PART
ejpam-5646	120	6	a	a	DET
ejpam-5646	120	7	bi	bi	NOUN
ejpam-5646	120	8	-	-	NOUN
ejpam-5646	120	9	antiideal	antiideal	NOUN
ejpam-5646	120	10	of	of	ADP
ejpam-5646	120	11	m2(p0	m2(p0	NOUN
ejpam-5646	120	12	)	)	PUNCT
ejpam-5646	120	13	.	.	PUNCT
ejpam-5646	121	1	proposition	proposition	NOUN
ejpam-5646	121	2	3	3	X
ejpam-5646	121	3	.	.	PUNCT
ejpam-5646	122	1	let	let	AUX
ejpam-5646	122	2	(	(	PUNCT
ejpam-5646	122	3	x	x	NOUN
ejpam-5646	122	4	,	,	PUNCT
ejpam-5646	122	5	·	·	PUNCT
ejpam-5646	122	6	)	)	PUNCT
ejpam-5646	122	7	be	be	AUX
ejpam-5646	122	8	a	a	DET
ejpam-5646	122	9	semigroup	semigroup	NOUN
ejpam-5646	122	10	and	and	CCONJ
ejpam-5646	122	11	a	a	DET
ejpam-5646	122	12	̸=	̸=	PROPN
ejpam-5646	122	13	∅	∅	NOUN
ejpam-5646	122	14	⊆	⊆	NUM
ejpam-5646	122	15	x	x	PUNCT
ejpam-5646	122	16	be	be	AUX
ejpam-5646	122	17	an	an	DET
ejpam-5646	122	18	(	(	PUNCT
ejpam-5646	122	19	m	m	NOUN
ejpam-5646	122	20	,	,	PUNCT
ejpam-5646	122	21	n)-bi	n)-bi	NOUN
ejpam-5646	122	22	-	-	PUNCT
ejpam-5646	122	23	antiideal	antiideal	NOUN
ejpam-5646	122	24	of	of	ADP
ejpam-5646	122	25	x.	x.	NOUN
ejpam-5646	122	26	if	if	SCONJ
ejpam-5646	122	27	k	k	PROPN
ejpam-5646	122	28	≥	≥	PROPN
ejpam-5646	122	29	m	m	PROPN
ejpam-5646	122	30	,	,	PUNCT
ejpam-5646	122	31	andl	andl	NOUN
ejpam-5646	122	32	≥	≥	NOUN
ejpam-5646	122	33	n	n	CCONJ
ejpam-5646	122	34	,	,	PUNCT
ejpam-5646	122	35	then	then	ADV
ejpam-5646	122	36	a	a	PRON
ejpam-5646	122	37	is	be	AUX
ejpam-5646	122	38	a	a	DET
ejpam-5646	122	39	(	(	PUNCT
ejpam-5646	122	40	k	k	NOUN
ejpam-5646	122	41	,	,	PUNCT
ejpam-5646	122	42	l)-bi	l)-bi	NOUN
ejpam-5646	122	43	-	-	NOUN
ejpam-5646	122	44	antiideal	antiideal	NOUN
ejpam-5646	122	45	of	of	ADP
ejpam-5646	122	46	x.	x.	NOUN
ejpam-5646	122	47	proof	proof	NOUN
ejpam-5646	122	48	.	.	PUNCT
ejpam-5646	123	1	the	the	DET
ejpam-5646	123	2	proof	proof	NOUN
ejpam-5646	123	3	results	result	VERB
ejpam-5646	123	4	form	form	VERB
ejpam-5646	123	5	having	have	VERB
ejpam-5646	123	6	akxal	akxal	ADJ
ejpam-5646	123	7	∩a	∩a	PROPN
ejpam-5646	123	8	=	=	PUNCT
ejpam-5646	123	9	am(ak−mxal−n)an	am(ak−mxal−n)an	PROPN
ejpam-5646	124	1	∩a	∩a	NOUN
ejpam-5646	124	2	⊆	⊆	NUM
ejpam-5646	124	3	amxan	amxan	NOUN
ejpam-5646	124	4	∩a	∩a	PROPN
ejpam-5646	125	1	=	=	PUNCT
ejpam-5646	126	1	∅.	∅.	PRON
ejpam-5646	126	2	example	example	NOUN
ejpam-5646	126	3	7	7	NUM
ejpam-5646	126	4	.	.	PUNCT
ejpam-5646	127	1	let	let	VERB
ejpam-5646	127	2	n	n	PRON
ejpam-5646	127	3	be	be	AUX
ejpam-5646	127	4	the	the	DET
ejpam-5646	127	5	senigroup	senigroup	NOUN
ejpam-5646	127	6	of	of	ADP
ejpam-5646	127	7	natural	natural	ADJ
ejpam-5646	127	8	numbers	number	NOUN
ejpam-5646	127	9	under	under	ADP
ejpam-5646	127	10	standard	standard	ADJ
ejpam-5646	127	11	multiplication	multiplication	NOUN
ejpam-5646	127	12	and	and	CCONJ
ejpam-5646	127	13	a	a	PRON
ejpam-5646	127	14	=	=	X
ejpam-5646	127	15	{	{	PUNCT
ejpam-5646	127	16	2	2	NUM
ejpam-5646	127	17	,	,	PUNCT
ejpam-5646	127	18	3	3	NUM
ejpam-5646	127	19	,	,	PUNCT
ejpam-5646	127	20	6	6	NUM
ejpam-5646	127	21	,	,	PUNCT
ejpam-5646	127	22	12	12	NUM
ejpam-5646	127	23	}	}	PUNCT
ejpam-5646	127	24	.	.	PUNCT
ejpam-5646	128	1	then	then	ADV
ejpam-5646	128	2	a	a	PRON
ejpam-5646	128	3	is	be	AUX
ejpam-5646	128	4	a	a	DET
ejpam-5646	128	5	(	(	PUNCT
ejpam-5646	128	6	3	3	NUM
ejpam-5646	128	7	,	,	PUNCT
ejpam-5646	128	8	1)-bi	1)-bi	NUM
ejpam-5646	128	9	-	-	PUNCT
ejpam-5646	128	10	antiideal	antiideal	NOUN
ejpam-5646	128	11	of	of	ADP
ejpam-5646	128	12	n	n	PROPN
ejpam-5646	128	13	that	that	PRON
ejpam-5646	128	14	is	be	AUX
ejpam-5646	128	15	not	not	PART
ejpam-5646	128	16	a	a	DET
ejpam-5646	128	17	(	(	PUNCT
ejpam-5646	128	18	2	2	NUM
ejpam-5646	128	19	,	,	PUNCT
ejpam-5646	128	20	1)-bi	1)-bi	NUM
ejpam-5646	128	21	-	-	PUNCT
ejpam-5646	128	22	antiideal	antiideal	NOUN
ejpam-5646	128	23	of	of	ADP
ejpam-5646	128	24	n.	n.	PROPN
ejpam-5646	128	25	this	this	PRON
ejpam-5646	128	26	is	be	AUX
ejpam-5646	128	27	clear	clear	ADJ
ejpam-5646	128	28	as	as	ADP
ejpam-5646	128	29	2(3)(1)(2	2(3)(1)(2	NOUN
ejpam-5646	128	30	)	)	PUNCT
ejpam-5646	128	31	∈	∈	NOUN
ejpam-5646	128	32	a2na	a2na	PUNCT
ejpam-5646	129	1	∩a	∩a	PROPN
ejpam-5646	129	2	.	.	PUNCT
ejpam-5646	130	1	proposition	proposition	NOUN
ejpam-5646	130	2	4	4	NUM
ejpam-5646	130	3	.	.	PUNCT
ejpam-5646	131	1	let	let	AUX
ejpam-5646	131	2	(	(	PUNCT
ejpam-5646	131	3	x	x	NOUN
ejpam-5646	131	4	,	,	PUNCT
ejpam-5646	131	5	·	·	PUNCT
ejpam-5646	131	6	)	)	PUNCT
ejpam-5646	131	7	be	be	AUX
ejpam-5646	131	8	a	a	DET
ejpam-5646	131	9	semigroup	semigroup	NOUN
ejpam-5646	131	10	and	and	CCONJ
ejpam-5646	131	11	a	a	DET
ejpam-5646	131	12	̸=	̸=	PROPN
ejpam-5646	131	13	∅	∅	NOUN
ejpam-5646	131	14	⊆	⊆	NUM
ejpam-5646	131	15	x	x	PUNCT
ejpam-5646	131	16	be	be	AUX
ejpam-5646	131	17	an	an	DET
ejpam-5646	131	18	(	(	PUNCT
ejpam-5646	131	19	m	m	NOUN
ejpam-5646	131	20	,	,	PUNCT
ejpam-5646	131	21	n)-bi	n)-bi	NOUN
ejpam-5646	131	22	-	-	PUNCT
ejpam-5646	131	23	antiideal	antiideal	NOUN
ejpam-5646	131	24	of	of	ADP
ejpam-5646	131	25	x.	x.	NOUN
ejpam-5646	131	26	then	then	ADV
ejpam-5646	131	27	a	a	PRON
ejpam-5646	131	28	is	be	AUX
ejpam-5646	131	29	not	not	PART
ejpam-5646	131	30	a	a	DET
ejpam-5646	131	31	subsemigroup	subsemigroup	NOUN
ejpam-5646	131	32	of	of	ADP
ejpam-5646	131	33	x.	x.	NOUN
ejpam-5646	131	34	proof	proof	PROPN
ejpam-5646	131	35	.	.	PUNCT
ejpam-5646	132	1	let	let	VERB
ejpam-5646	132	2	a	a	DET
ejpam-5646	132	3	be	be	AUX
ejpam-5646	132	4	an	an	DET
ejpam-5646	132	5	(	(	PUNCT
ejpam-5646	132	6	m	m	NOUN
ejpam-5646	132	7	,	,	PUNCT
ejpam-5646	132	8	n)-bi	n)-bi	NOUN
ejpam-5646	132	9	-	-	PUNCT
ejpam-5646	132	10	antiideal	antiideal	NOUN
ejpam-5646	132	11	ofx	ofx	NOUN
ejpam-5646	132	12	that	that	PRON
ejpam-5646	132	13	is	be	AUX
ejpam-5646	132	14	subsemigroup	subsemigroup	NOUN
ejpam-5646	132	15	of	of	ADP
ejpam-5646	132	16	a.	a.	NOUN
ejpam-5646	132	17	then	then	ADV
ejpam-5646	132	18	am+n+1	am+n+1	ADV
ejpam-5646	132	19	=	=	SYM
ejpam-5646	132	20	amaan	amaan	PROPN
ejpam-5646	132	21	̸=	̸=	PROPN
ejpam-5646	132	22	∅	∅	NOUN
ejpam-5646	132	23	⊆	⊆	NUM
ejpam-5646	132	24	amxan	amxan	NOUN
ejpam-5646	132	25	∩a	∩a	PROPN
ejpam-5646	132	26	=	=	PUNCT
ejpam-5646	133	1	∅.	∅.	PROPN
ejpam-5646	133	2	al	al	PROPN
ejpam-5646	133	3	-	-	PUNCT
ejpam-5646	133	4	tahan	tahan	PROPN
ejpam-5646	133	5	et	et	PROPN
ejpam-5646	133	6	al	al	PROPN
ejpam-5646	133	7	.	.	PUNCT
ejpam-5646	134	1	[	[	X
ejpam-5646	134	2	2	2	X
ejpam-5646	134	3	]	]	PUNCT
ejpam-5646	134	4	proved	prove	VERB
ejpam-5646	134	5	that	that	SCONJ
ejpam-5646	134	6	every	every	DET
ejpam-5646	134	7	left(right	left(right	PROPN
ejpam-5646	134	8	)	)	PUNCT
ejpam-5646	134	9	antiideal	antiideal	NOUN
ejpam-5646	134	10	of	of	ADP
ejpam-5646	134	11	a	a	DET
ejpam-5646	134	12	semigroup	semigroup	NOUN
ejpam-5646	134	13	x	x	X
ejpam-5646	134	14	is	be	AUX
ejpam-5646	134	15	a	a	DET
ejpam-5646	134	16	biantiideal	biantiideal	NOUN
ejpam-5646	134	17	of	of	ADP
ejpam-5646	134	18	x.	x.	PROPN
ejpam-5646	134	19	example	example	NOUN
ejpam-5646	134	20	8	8	NUM
ejpam-5646	134	21	shows	show	VERB
ejpam-5646	134	22	that	that	SCONJ
ejpam-5646	134	23	the	the	DET
ejpam-5646	134	24	converse	converse	NOUN
ejpam-5646	134	25	may	may	AUX
ejpam-5646	134	26	not	not	PART
ejpam-5646	134	27	hold	hold	VERB
ejpam-5646	134	28	.	.	PUNCT
ejpam-5646	135	1	example	example	NOUN
ejpam-5646	135	2	8	8	NUM
ejpam-5646	135	3	.	.	PUNCT
ejpam-5646	136	1	let	let	VERB
ejpam-5646	136	2	m2(p0	m2(p0	NOUN
ejpam-5646	136	3	)	)	PUNCT
ejpam-5646	136	4	be	be	AUX
ejpam-5646	136	5	the	the	DET
ejpam-5646	136	6	semigroup	semigroup	NOUN
ejpam-5646	136	7	of	of	ADP
ejpam-5646	136	8	all	all	DET
ejpam-5646	136	9	two	two	NUM
ejpam-5646	136	10	by	by	ADP
ejpam-5646	136	11	two	two	NUM
ejpam-5646	136	12	matrices	matrix	NOUN
ejpam-5646	136	13	with	with	ADP
ejpam-5646	136	14	non	non	ADJ
ejpam-5646	136	15	-	-	ADJ
ejpam-5646	136	16	negative	negative	ADJ
ejpam-5646	136	17	integer	integer	NOUN
ejpam-5646	136	18	entries	entry	NOUN
ejpam-5646	136	19	and	and	CCONJ
ejpam-5646	136	20	a	a	DET
ejpam-5646	136	21	=	=	X
ejpam-5646	136	22	{	{	PUNCT
ejpam-5646	136	23	(	(	PUNCT
ejpam-5646	136	24	2	2	NUM
ejpam-5646	136	25	0	0	NUM
ejpam-5646	136	26	0	0	NUM
ejpam-5646	136	27	0	0	NUM
ejpam-5646	136	28	)	)	PUNCT
ejpam-5646	136	29	}	}	PUNCT
ejpam-5646	136	30	.	.	PUNCT
ejpam-5646	137	1	then	then	ADV
ejpam-5646	137	2	a	a	PRON
ejpam-5646	137	3	is	be	AUX
ejpam-5646	137	4	a	a	DET
ejpam-5646	137	5	bi	bi	NOUN
ejpam-5646	137	6	-	-	NOUN
ejpam-5646	137	7	antiideal	antiideal	NOUN
ejpam-5646	137	8	of	of	ADP
ejpam-5646	137	9	m2(p0	m2(p0	NOUN
ejpam-5646	137	10	)	)	PUNCT
ejpam-5646	137	11	.	.	PUNCT
ejpam-5646	138	1	furthermore	furthermore	ADV
ejpam-5646	138	2	,	,	PUNCT
ejpam-5646	138	3	it	it	PRON
ejpam-5646	138	4	is	be	AUX
ejpam-5646	138	5	not	not	PART
ejpam-5646	138	6	a	a	DET
ejpam-5646	138	7	left(right	left(right	PROPN
ejpam-5646	138	8	)	)	PUNCT
ejpam-5646	138	9	antiideal	antiideal	NOUN
ejpam-5646	138	10	of	of	ADP
ejpam-5646	138	11	p0	p0	NOUN
ejpam-5646	138	12	.	.	PUNCT
ejpam-5646	139	1	proposition	proposition	NOUN
ejpam-5646	139	2	5	5	NUM
ejpam-5646	139	3	.	.	PUNCT
ejpam-5646	140	1	let	let	VERB
ejpam-5646	140	2	(	(	PUNCT
ejpam-5646	140	3	x	x	NOUN
ejpam-5646	140	4	,	,	PUNCT
ejpam-5646	140	5	·	·	PUNCT
ejpam-5646	140	6	)	)	PUNCT
ejpam-5646	140	7	be	be	AUX
ejpam-5646	140	8	a	a	DET
ejpam-5646	140	9	semigroup	semigroup	NOUN
ejpam-5646	140	10	and	and	CCONJ
ejpam-5646	140	11	a	a	DET
ejpam-5646	140	12	̸=	̸=	PROPN
ejpam-5646	140	13	∅	∅	NOUN
ejpam-5646	140	14	⊆	⊆	NUM
ejpam-5646	140	15	x	x	PUNCT
ejpam-5646	140	16	be	be	AUX
ejpam-5646	140	17	an	an	DET
ejpam-5646	140	18	(	(	PUNCT
ejpam-5646	140	19	m	m	NOUN
ejpam-5646	140	20	,	,	PUNCT
ejpam-5646	140	21	n)-bi	n)-bi	NOUN
ejpam-5646	140	22	-	-	PUNCT
ejpam-5646	140	23	antiideal	antiideal	NOUN
ejpam-5646	140	24	of	of	ADP
ejpam-5646	140	25	x.	x.	NOUN
ejpam-5646	140	26	then	then	ADV
ejpam-5646	140	27	every	every	DET
ejpam-5646	140	28	non	non	ADJ
ejpam-5646	140	29	-	-	ADJ
ejpam-5646	140	30	empty	empty	ADJ
ejpam-5646	140	31	subset	subset	NOUN
ejpam-5646	140	32	of	of	ADP
ejpam-5646	140	33	a	a	PRON
ejpam-5646	140	34	is	be	AUX
ejpam-5646	140	35	an	an	DET
ejpam-5646	140	36	(	(	PUNCT
ejpam-5646	140	37	m	m	NOUN
ejpam-5646	140	38	,	,	PUNCT
ejpam-5646	140	39	n)-bi	n)-bi	NOUN
ejpam-5646	140	40	-	-	PUNCT
ejpam-5646	140	41	antiideal	antiideal	NOUN
ejpam-5646	140	42	of	of	ADP
ejpam-5646	140	43	x.	x.	NOUN
ejpam-5646	140	44	proof	proof	NOUN
ejpam-5646	140	45	.	.	PUNCT
ejpam-5646	141	1	the	the	DET
ejpam-5646	141	2	proof	proof	NOUN
ejpam-5646	141	3	is	be	AUX
ejpam-5646	141	4	straightforward	straightforward	ADJ
ejpam-5646	141	5	.	.	PUNCT
ejpam-5646	142	1	corollary	corollary	ADJ
ejpam-5646	142	2	1	1	NUM
ejpam-5646	142	3	.	.	PUNCT
ejpam-5646	143	1	let	let	VERB
ejpam-5646	143	2	(	(	PUNCT
ejpam-5646	143	3	x	x	NOUN
ejpam-5646	143	4	,	,	PUNCT
ejpam-5646	143	5	·	·	PUNCT
ejpam-5646	143	6	)	)	PUNCT
ejpam-5646	143	7	be	be	AUX
ejpam-5646	143	8	a	a	DET
ejpam-5646	143	9	semigroup	semigroup	NOUN
ejpam-5646	143	10	and	and	CCONJ
ejpam-5646	143	11	ai	ai	VERB
ejpam-5646	143	12	̸=	̸=	PROPN
ejpam-5646	143	13	∅	∅	NOUN
ejpam-5646	143	14	⊆	⊆	NUM
ejpam-5646	143	15	x	x	PUNCT
ejpam-5646	143	16	for	for	ADP
ejpam-5646	143	17	i	i	PRON
ejpam-5646	143	18	∈	∈	PROPN
ejpam-5646	143	19	n.	n.	NOUN
ejpam-5646	143	20	if	if	SCONJ
ejpam-5646	143	21	ai	ai	VERB
ejpam-5646	143	22	is	be	AUX
ejpam-5646	143	23	an	an	DET
ejpam-5646	143	24	(	(	PUNCT
ejpam-5646	143	25	m	m	PROPN
ejpam-5646	143	26	,	,	PUNCT
ejpam-5646	143	27	n)bi	n)bi	PROPN
ejpam-5646	143	28	-	-	PUNCT
ejpam-5646	143	29	antiideal	antiideal	NOUN
ejpam-5646	143	30	of	of	ADP
ejpam-5646	143	31	x	x	PUNCT
ejpam-5646	143	32	for	for	ADP
ejpam-5646	143	33	some	some	DET
ejpam-5646	143	34	i	i	PRON
ejpam-5646	143	35	∈	∈	PROPN
ejpam-5646	143	36	n	n	CCONJ
ejpam-5646	143	37	,	,	PUNCT
ejpam-5646	143	38	then	then	ADV
ejpam-5646	143	39	every	every	DET
ejpam-5646	143	40	non	non	ADJ
ejpam-5646	143	41	-	-	ADJ
ejpam-5646	143	42	empty	empty	ADJ
ejpam-5646	143	43	intersection	intersection	NOUN
ejpam-5646	143	44	of	of	ADP
ejpam-5646	143	45	ai	ai	NOUN
ejpam-5646	143	46	is	be	AUX
ejpam-5646	143	47	an	an	DET
ejpam-5646	143	48	(	(	PUNCT
ejpam-5646	143	49	m	m	PROPN
ejpam-5646	143	50	,	,	PUNCT
ejpam-5646	143	51	n)-biantiideal	n)-biantiideal	NOUN
ejpam-5646	143	52	of	of	ADP
ejpam-5646	143	53	x.	x.	PROPN
ejpam-5646	143	54	m.	m.	PROPN
ejpam-5646	143	55	al	al	PROPN
ejpam-5646	143	56	tahan	tahan	PROPN
ejpam-5646	143	57	,	,	PUNCT
ejpam-5646	143	58	s.	s.	PROPN
ejpam-5646	143	59	hoskova	hoskova	PROPN
ejpam-5646	143	60	-	-	PUNCT
ejpam-5646	143	61	mayerova	mayerova	PROPN
ejpam-5646	143	62	,	,	PUNCT
ejpam-5646	143	63	s.	s.	PROPN
ejpam-5646	143	64	al	al	PROPN
ejpam-5646	143	65	-	-	PUNCT
ejpam-5646	143	66	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	143	67	/	/	SYM
ejpam-5646	143	68	eur	eur	NOUN
ejpam-5646	143	69	.	.	PUNCT
ejpam-5646	144	1	j.	j.	PROPN
ejpam-5646	144	2	pure	pure	PROPN
ejpam-5646	144	3	appl	appl	PROPN
ejpam-5646	144	4	.	.	PROPN
ejpam-5646	144	5	math	math	PROPN
ejpam-5646	144	6	,	,	PUNCT
ejpam-5646	144	7	18	18	NUM
ejpam-5646	144	8	(	(	PUNCT
ejpam-5646	144	9	1	1	NUM
ejpam-5646	144	10	)	)	PUNCT
ejpam-5646	144	11	(	(	PUNCT
ejpam-5646	144	12	2025	2025	NUM
ejpam-5646	144	13	)	)	PUNCT
ejpam-5646	144	14	,	,	PUNCT
ejpam-5646	144	15	5646	5646	NUM
ejpam-5646	144	16	6	6	NUM
ejpam-5646	144	17	of	of	ADP
ejpam-5646	144	18	11	11	NUM
ejpam-5646	144	19	theorem	theorem	NOUN
ejpam-5646	144	20	2	2	NUM
ejpam-5646	144	21	.	.	PUNCT
ejpam-5646	145	1	let	let	VERB
ejpam-5646	145	2	x1	x1	NUM
ejpam-5646	145	3	,	,	PUNCT
ejpam-5646	145	4	x2	x2	PROPN
ejpam-5646	145	5	be	be	VERB
ejpam-5646	145	6	semigroups	semigroup	NOUN
ejpam-5646	145	7	,	,	PUNCT
ejpam-5646	145	8	f	f	X
ejpam-5646	145	9	:	:	PUNCT
ejpam-5646	146	1	x1	x1	PROPN
ejpam-5646	146	2	→	→	PUNCT
ejpam-5646	146	3	x2	x2	PROPN
ejpam-5646	146	4	be	be	AUX
ejpam-5646	146	5	an	an	PRON
ejpam-5646	146	6	onto	onto	ADP
ejpam-5646	146	7	semigroup	semigroup	ADJ
ejpam-5646	146	8	homomorphism	homomorphism	NOUN
ejpam-5646	146	9	,	,	PUNCT
ejpam-5646	146	10	and	and	CCONJ
ejpam-5646	146	11	a1	a1	PROPN
ejpam-5646	146	12	̸=	̸=	PROPN
ejpam-5646	146	13	∅	∅	VERB
ejpam-5646	146	14	⊆	⊆	NUM
ejpam-5646	146	15	x1	x1	PROPN
ejpam-5646	146	16	an	an	DET
ejpam-5646	146	17	(	(	PUNCT
ejpam-5646	146	18	m	m	NOUN
ejpam-5646	146	19	,	,	PUNCT
ejpam-5646	146	20	n)-bi	n)-bi	NOUN
ejpam-5646	146	21	-	-	PUNCT
ejpam-5646	146	22	antiideal	antiideal	NOUN
ejpam-5646	146	23	of	of	ADP
ejpam-5646	146	24	x1	x1	PROPN
ejpam-5646	146	25	.	.	PUNCT
ejpam-5646	147	1	then	then	ADV
ejpam-5646	147	2	f(a1	f(a1	VERB
ejpam-5646	147	3	)	)	PUNCT
ejpam-5646	147	4	is	be	AUX
ejpam-5646	147	5	an	an	DET
ejpam-5646	147	6	(	(	PUNCT
ejpam-5646	147	7	m	m	NOUN
ejpam-5646	147	8	,	,	PUNCT
ejpam-5646	147	9	n)-bi	n)-bi	NOUN
ejpam-5646	147	10	-	-	PUNCT
ejpam-5646	147	11	antiideal	antiideal	NOUN
ejpam-5646	147	12	of	of	ADP
ejpam-5646	147	13	x2	x2	PROPN
ejpam-5646	147	14	.	.	PUNCT
ejpam-5646	148	1	proof	proof	NOUN
ejpam-5646	148	2	.	.	PUNCT
ejpam-5646	149	1	let	let	VERB
ejpam-5646	149	2	y	y	PROPN
ejpam-5646	149	3	∈	∈	PROPN
ejpam-5646	149	4	f(a1	f(a1	NOUN
ejpam-5646	149	5	)	)	PUNCT
ejpam-5646	149	6	mx2f(a1	mx2f(a1	PROPN
ejpam-5646	149	7	)	)	PUNCT
ejpam-5646	149	8	n	n	PART
ejpam-5646	149	9	∩	∩	NOUN
ejpam-5646	149	10	f(a1	f(a1	NOUN
ejpam-5646	149	11	)	)	PUNCT
ejpam-5646	149	12	.	.	PUNCT
ejpam-5646	150	1	then	then	ADV
ejpam-5646	150	2	there	there	PRON
ejpam-5646	150	3	exist	exist	VERB
ejpam-5646	150	4	x1	x1	PROPN
ejpam-5646	150	5	,	,	PUNCT
ejpam-5646	150	6	.	.	PUNCT
ejpam-5646	150	7	.	.	PUNCT
ejpam-5646	151	1	.	.	PUNCT
ejpam-5646	152	1	,	,	PUNCT
ejpam-5646	152	2	xm	xm	PROPN
ejpam-5646	152	3	,	,	PUNCT
ejpam-5646	152	4	z1	z1	PROPN
ejpam-5646	152	5	,	,	PUNCT
ejpam-5646	152	6	.	.	PUNCT
ejpam-5646	152	7	.	.	PUNCT
ejpam-5646	152	8	.	.	PUNCT
ejpam-5646	153	1	,	,	PUNCT
ejpam-5646	153	2	zm	zm	PROPN
ejpam-5646	153	3	∈	∈	PROPN
ejpam-5646	153	4	a1	a1	NOUN
ejpam-5646	153	5	,	,	PUNCT
ejpam-5646	153	6	x	x	SYM
ejpam-5646	153	7	∈	∈	PROPN
ejpam-5646	153	8	x1	x1	PROPN
ejpam-5646	153	9	,	,	PUNCT
ejpam-5646	153	10	r	r	NOUN
ejpam-5646	153	11	=	=	SYM
ejpam-5646	153	12	f(x	f(x	PROPN
ejpam-5646	153	13	)	)	PUNCT
ejpam-5646	153	14	∈	∈	PROPN
ejpam-5646	154	1	x2	x2	NOUN
ejpam-5646	154	2	with	with	ADP
ejpam-5646	154	3	y	y	PROPN
ejpam-5646	154	4	=	=	PUNCT
ejpam-5646	154	5	f(x1	f(x1	NOUN
ejpam-5646	154	6	)	)	PUNCT
ejpam-5646	154	7	.	.	PUNCT
ejpam-5646	154	8	.	.	PUNCT
ejpam-5646	154	9	.	.	PUNCT
ejpam-5646	155	1	f(xm)f(r)f(y1	f(xm)f(r)f(y1	NOUN
ejpam-5646	155	2	)	)	PUNCT
ejpam-5646	155	3	.	.	PUNCT
ejpam-5646	156	1	.	.	PUNCT
ejpam-5646	156	2	.	.	PUNCT
ejpam-5646	157	1	f(yn	f(yn	X
ejpam-5646	157	2	)	)	PUNCT
ejpam-5646	157	3	∈	∈	NOUN
ejpam-5646	157	4	f(a1	f(a1	NOUN
ejpam-5646	157	5	)	)	PUNCT
ejpam-5646	157	6	.	.	PUNCT
ejpam-5646	158	1	having	have	VERB
ejpam-5646	158	2	f	f	PRON
ejpam-5646	158	3	a	a	DET
ejpam-5646	158	4	semigroup	semigroup	PROPN
ejpam-5646	158	5	homomorphism	homomorphism	NOUN
ejpam-5646	158	6	implies	imply	VERB
ejpam-5646	158	7	that	that	SCONJ
ejpam-5646	158	8	y	y	PROPN
ejpam-5646	158	9	=	=	PUNCT
ejpam-5646	158	10	f(x1	f(x1	ADJ
ejpam-5646	158	11	.	.	PUNCT
ejpam-5646	158	12	.	.	PUNCT
ejpam-5646	158	13	.	.	PUNCT
ejpam-5646	159	1	xmry1	xmry1	PROPN
ejpam-5646	159	2	.	.	PUNCT
ejpam-5646	159	3	.	.	PUNCT
ejpam-5646	159	4	.	.	PUNCT
ejpam-5646	160	1	yn	yn	X
ejpam-5646	160	2	)	)	PUNCT
ejpam-5646	160	3	∈	∈	PROPN
ejpam-5646	160	4	f(a1	f(a1	NOUN
ejpam-5646	160	5	)	)	PUNCT
ejpam-5646	160	6	and	and	CCONJ
ejpam-5646	160	7	hence	hence	ADV
ejpam-5646	160	8	,	,	PUNCT
ejpam-5646	160	9	x1	x1	PROPN
ejpam-5646	160	10	.	.	PUNCT
ejpam-5646	160	11	.	.	PUNCT
ejpam-5646	160	12	.	.	PUNCT
ejpam-5646	161	1	xmry1	xmry1	PROPN
ejpam-5646	161	2	.	.	PUNCT
ejpam-5646	161	3	.	.	PUNCT
ejpam-5646	161	4	.	.	PUNCT
ejpam-5646	162	1	yn	yn	PROPN
ejpam-5646	162	2	∈	∈	PROPN
ejpam-5646	162	3	am	be	AUX
ejpam-5646	162	4	1	1	NUM
ejpam-5646	162	5	x1a	x1a	PROPN
ejpam-5646	162	6	n	n	PRON
ejpam-5646	162	7	1	1	NUM
ejpam-5646	162	8	∩a1	∩a1	X
ejpam-5646	162	9	=	=	PRON
ejpam-5646	162	10	∅.	∅.	NOUN
ejpam-5646	162	11	theorem	theorem	ADJ
ejpam-5646	162	12	3	3	X
ejpam-5646	162	13	.	.	PUNCT
ejpam-5646	163	1	let	let	VERB
ejpam-5646	163	2	x1	x1	NUM
ejpam-5646	163	3	,	,	PUNCT
ejpam-5646	163	4	x2	x2	PROPN
ejpam-5646	163	5	be	be	VERB
ejpam-5646	163	6	semigroups	semigroup	NOUN
ejpam-5646	163	7	,	,	PUNCT
ejpam-5646	163	8	f	f	X
ejpam-5646	163	9	:	:	PUNCT
ejpam-5646	164	1	x1	x1	PROPN
ejpam-5646	164	2	→	→	PUNCT
ejpam-5646	164	3	x2	x2	PROPN
ejpam-5646	164	4	be	be	AUX
ejpam-5646	164	5	a	a	DET
ejpam-5646	164	6	semigroup	semigroup	ADJ
ejpam-5646	164	7	homomorphism	homomorphism	NOUN
ejpam-5646	164	8	,	,	PUNCT
ejpam-5646	164	9	and	and	CCONJ
ejpam-5646	164	10	a2	a2	PROPN
ejpam-5646	164	11	̸=	̸=	PROPN
ejpam-5646	164	12	∅	∅	VERB
ejpam-5646	164	13	⊆	⊆	NUM
ejpam-5646	164	14	x2	x2	PROPN
ejpam-5646	164	15	an	an	DET
ejpam-5646	164	16	(	(	PUNCT
ejpam-5646	164	17	m	m	NOUN
ejpam-5646	164	18	,	,	PUNCT
ejpam-5646	164	19	n)-bi	n)-bi	NOUN
ejpam-5646	164	20	-	-	PUNCT
ejpam-5646	164	21	antiideal	antiideal	NOUN
ejpam-5646	164	22	of	of	ADP
ejpam-5646	164	23	x2	x2	PROPN
ejpam-5646	164	24	.	.	PUNCT
ejpam-5646	165	1	then	then	ADV
ejpam-5646	165	2	f−1(a2	f−1(a2	NOUN
ejpam-5646	165	3	)	)	PUNCT
ejpam-5646	165	4	̸=	̸=	NOUN
ejpam-5646	165	5	∅	∅	NOUN
ejpam-5646	165	6	is	be	AUX
ejpam-5646	165	7	an	an	DET
ejpam-5646	165	8	(	(	PUNCT
ejpam-5646	165	9	m	m	NOUN
ejpam-5646	165	10	,	,	PUNCT
ejpam-5646	165	11	n)-bi	n)-bi	NOUN
ejpam-5646	165	12	-	-	PUNCT
ejpam-5646	165	13	antiideal	antiideal	NOUN
ejpam-5646	165	14	of	of	ADP
ejpam-5646	165	15	x1	x1	PROPN
ejpam-5646	165	16	.	.	PUNCT
ejpam-5646	166	1	proof	proof	NOUN
ejpam-5646	166	2	.	.	PUNCT
ejpam-5646	167	1	let	let	VERB
ejpam-5646	167	2	x	x	PUNCT
ejpam-5646	167	3	∈	∈	PROPN
ejpam-5646	167	4	f−1(a2	f−1(a2	NOUN
ejpam-5646	167	5	)	)	PUNCT
ejpam-5646	167	6	mx1f	mx1f	PROPN
ejpam-5646	167	7	−1(a2	−1(a2	NOUN
ejpam-5646	167	8	)	)	PUNCT
ejpam-5646	167	9	n	n	NOUN
ejpam-5646	167	10	∩	∩	NOUN
ejpam-5646	167	11	f−1(a2	f−1(a2	NOUN
ejpam-5646	167	12	)	)	PUNCT
ejpam-5646	167	13	.	.	PUNCT
ejpam-5646	168	1	then	then	ADV
ejpam-5646	168	2	there	there	PRON
ejpam-5646	168	3	exist	exist	VERB
ejpam-5646	168	4	xi	xi	PROPN
ejpam-5646	168	5	,	,	PUNCT
ejpam-5646	168	6	zj	zj	PROPN
ejpam-5646	168	7	∈	∈	PROPN
ejpam-5646	168	8	f−1(a2	f−1(a2	NOUN
ejpam-5646	168	9	)	)	PUNCT
ejpam-5646	168	10	with	with	ADP
ejpam-5646	168	11	i	i	PRON
ejpam-5646	168	12	∈	∈	PROPN
ejpam-5646	168	13	{	{	PUNCT
ejpam-5646	168	14	1	1	NUM
ejpam-5646	168	15	,	,	PUNCT
ejpam-5646	168	16	.	.	PUNCT
ejpam-5646	168	17	.	.	PUNCT
ejpam-5646	168	18	.	.	PUNCT
ejpam-5646	169	1	,	,	PUNCT
ejpam-5646	169	2	m	m	VERB
ejpam-5646	169	3	}	}	PUNCT
ejpam-5646	169	4	,	,	PUNCT
ejpam-5646	169	5	j	j	PROPN
ejpam-5646	169	6	∈	∈	PROPN
ejpam-5646	169	7	{	{	PUNCT
ejpam-5646	169	8	1	1	NUM
ejpam-5646	169	9	,	,	PUNCT
ejpam-5646	169	10	.	.	PUNCT
ejpam-5646	169	11	.	.	PUNCT
ejpam-5646	169	12	.	.	PUNCT
ejpam-5646	169	13	,	,	PUNCT
ejpam-5646	169	14	n	n	CCONJ
ejpam-5646	169	15	}	}	PUNCT
ejpam-5646	169	16	,	,	PUNCT
ejpam-5646	169	17	r	r	NOUN
ejpam-5646	169	18	∈	∈	NOUN
ejpam-5646	170	1	x1	x1	NUM
ejpam-5646	170	2	satisfying	satisfy	VERB
ejpam-5646	170	3	x	x	X
ejpam-5646	170	4	=	=	SYM
ejpam-5646	170	5	x1	x1	PROPN
ejpam-5646	170	6	.	.	PUNCT
ejpam-5646	170	7	.	.	PUNCT
ejpam-5646	170	8	.	.	PUNCT
ejpam-5646	171	1	xmry1	xmry1	PROPN
ejpam-5646	171	2	.	.	PUNCT
ejpam-5646	171	3	.	.	PUNCT
ejpam-5646	171	4	.	.	PUNCT
ejpam-5646	172	1	yn	yn	PRON
ejpam-5646	172	2	∈	∈	PROPN
ejpam-5646	172	3	f−1(a2	f−1(a2	NOUN
ejpam-5646	172	4	)	)	PUNCT
ejpam-5646	172	5	and	and	CCONJ
ejpam-5646	172	6	hence	hence	ADV
ejpam-5646	172	7	f(x	f(x	PROPN
ejpam-5646	172	8	)	)	PUNCT
ejpam-5646	172	9	=	=	PUNCT
ejpam-5646	173	1	f(x1	f(x1	ADJ
ejpam-5646	173	2	.	.	PUNCT
ejpam-5646	173	3	.	.	PUNCT
ejpam-5646	173	4	.	.	PUNCT
ejpam-5646	174	1	xmry1	xmry1	PROPN
ejpam-5646	174	2	.	.	PUNCT
ejpam-5646	174	3	.	.	PUNCT
ejpam-5646	174	4	.	.	PUNCT
ejpam-5646	175	1	yn	yn	X
ejpam-5646	175	2	)	)	PUNCT
ejpam-5646	175	3	∈	∈	PROPN
ejpam-5646	175	4	a2	a2	PROPN
ejpam-5646	175	5	.	.	PUNCT
ejpam-5646	176	1	having	have	VERB
ejpam-5646	176	2	f	f	PRON
ejpam-5646	176	3	a	a	DET
ejpam-5646	176	4	semigroup	semigroup	PROPN
ejpam-5646	176	5	homomorphism	homomorphism	NOUN
ejpam-5646	176	6	implies	imply	VERB
ejpam-5646	176	7	that	that	SCONJ
ejpam-5646	176	8	y	y	PROPN
ejpam-5646	176	9	=	=	PUNCT
ejpam-5646	176	10	f(x1	f(x1	NOUN
ejpam-5646	176	11	)	)	PUNCT
ejpam-5646	176	12	.	.	PUNCT
ejpam-5646	176	13	.	.	PUNCT
ejpam-5646	176	14	.	.	PUNCT
ejpam-5646	177	1	f(xm)f(r)f(y1	f(xm)f(r)f(y1	NOUN
ejpam-5646	177	2	)	)	PUNCT
ejpam-5646	177	3	.	.	PUNCT
ejpam-5646	178	1	.	.	PUNCT
ejpam-5646	178	2	.	.	PUNCT
ejpam-5646	179	1	f(yn	f(yn	NOUN
ejpam-5646	179	2	)	)	PUNCT
ejpam-5646	179	3	∈	∈	PROPN
ejpam-5646	179	4	a2	a2	PROPN
ejpam-5646	179	5	and	and	CCONJ
ejpam-5646	179	6	hence	hence	ADV
ejpam-5646	179	7	,	,	PUNCT
ejpam-5646	179	8	y	y	PROPN
ejpam-5646	179	9	∈	∈	PROPN
ejpam-5646	179	10	am	be	AUX
ejpam-5646	179	11	2	2	NUM
ejpam-5646	179	12	x2a	x2a	PROPN
ejpam-5646	179	13	n	n	CCONJ
ejpam-5646	179	14	2	2	NUM
ejpam-5646	179	15	∩a2	∩a2	NOUN
ejpam-5646	179	16	=	=	PRON
ejpam-5646	179	17	∅.	∅.	PRON
ejpam-5646	179	18	example	example	NOUN
ejpam-5646	179	19	9	9	NUM
ejpam-5646	179	20	.	.	PUNCT
ejpam-5646	179	21	let	let	VERB
ejpam-5646	179	22	m2(p0	m2(p0	NOUN
ejpam-5646	179	23	)	)	PUNCT
ejpam-5646	179	24	,	,	PUNCT
ejpam-5646	179	25	m2(2p0	m2(2p0	NUM
ejpam-5646	179	26	)	)	PUNCT
ejpam-5646	179	27	be	be	VERB
ejpam-5646	179	28	the	the	DET
ejpam-5646	179	29	semigroups	semigroup	NOUN
ejpam-5646	179	30	of	of	ADP
ejpam-5646	179	31	all	all	DET
ejpam-5646	179	32	two	two	NUM
ejpam-5646	179	33	by	by	ADP
ejpam-5646	179	34	two	two	NUM
ejpam-5646	179	35	matrices	matrix	NOUN
ejpam-5646	179	36	with	with	ADP
ejpam-5646	179	37	nonnegative	nonnegative	ADJ
ejpam-5646	179	38	integer	integer	NOUN
ejpam-5646	179	39	entries	entry	NOUN
ejpam-5646	179	40	and	and	CCONJ
ejpam-5646	179	41	with	with	ADP
ejpam-5646	179	42	non	non	ADJ
ejpam-5646	179	43	-	-	ADJ
ejpam-5646	179	44	negative	negative	ADJ
ejpam-5646	179	45	even	even	ADV
ejpam-5646	179	46	integral	integral	ADJ
ejpam-5646	179	47	entries	entry	NOUN
ejpam-5646	179	48	under	under	ADP
ejpam-5646	179	49	multiplication	multiplication	NOUN
ejpam-5646	179	50	of	of	ADP
ejpam-5646	179	51	matrices	matrix	NOUN
ejpam-5646	179	52	respectively	respectively	ADV
ejpam-5646	179	53	defined	define	VERB
ejpam-5646	179	54	in	in	ADP
ejpam-5646	179	55	example	example	NOUN
ejpam-5646	179	56	6	6	NUM
ejpam-5646	179	57	and	and	CCONJ
ejpam-5646	179	58	f	f	NOUN
ejpam-5646	179	59	:	:	PUNCT
ejpam-5646	179	60	m2(p0	m2(p0	NOUN
ejpam-5646	179	61	)	)	PUNCT
ejpam-5646	179	62	→	→	SYM
ejpam-5646	179	63	m2(2p0	m2(2p0	NUM
ejpam-5646	179	64	)	)	PUNCT
ejpam-5646	179	65	be	be	AUX
ejpam-5646	179	66	defined	define	VERB
ejpam-5646	179	67	as	as	SCONJ
ejpam-5646	179	68	follows	follow	VERB
ejpam-5646	179	69	.	.	PUNCT
ejpam-5646	180	1	for	for	ADP
ejpam-5646	180	2	every	every	DET
ejpam-5646	180	3	matrix	matrix	NOUN
ejpam-5646	180	4	m	m	NOUN
ejpam-5646	180	5	∈	∈	PROPN
ejpam-5646	180	6	m2(p0	m2(p0	NOUN
ejpam-5646	180	7	)	)	PUNCT
ejpam-5646	180	8	,	,	PUNCT
ejpam-5646	180	9	f(m	f(m	PROPN
ejpam-5646	180	10	)	)	PUNCT
ejpam-5646	180	11	=	=	PUNCT
ejpam-5646	181	1	2	2	NUM
ejpam-5646	181	2	m	m	NOUN
ejpam-5646	181	3	.	.	PUNCT
ejpam-5646	182	1	from	from	ADP
ejpam-5646	182	2	example	example	NOUN
ejpam-5646	182	3	8	8	NUM
ejpam-5646	182	4	,	,	PUNCT
ejpam-5646	182	5	we	we	PRON
ejpam-5646	182	6	have	have	VERB
ejpam-5646	182	7	a	a	DET
ejpam-5646	182	8	=	=	X
ejpam-5646	182	9	{	{	PUNCT
ejpam-5646	182	10	(	(	PUNCT
ejpam-5646	182	11	2	2	NUM
ejpam-5646	182	12	0	0	NUM
ejpam-5646	182	13	0	0	NUM
ejpam-5646	182	14	0	0	NUM
ejpam-5646	182	15	)	)	PUNCT
ejpam-5646	182	16	,	,	PUNCT
ejpam-5646	182	17	(	(	PUNCT
ejpam-5646	182	18	4	4	NUM
ejpam-5646	182	19	0	0	NUM
ejpam-5646	182	20	0	0	NUM
ejpam-5646	182	21	0	0	NUM
ejpam-5646	182	22	)	)	PUNCT
ejpam-5646	182	23	}	}	PUNCT
ejpam-5646	182	24	is	be	AUX
ejpam-5646	182	25	a	a	DET
ejpam-5646	182	26	(	(	PUNCT
ejpam-5646	182	27	2	2	NUM
ejpam-5646	182	28	,	,	PUNCT
ejpam-5646	182	29	1)-bi	1)-bi	NUM
ejpam-5646	182	30	-	-	PUNCT
ejpam-5646	182	31	antiideal	antiideal	NOUN
ejpam-5646	182	32	of	of	ADP
ejpam-5646	182	33	m2(p0	m2(p0	NOUN
ejpam-5646	182	34	)	)	PUNCT
ejpam-5646	182	35	.	.	PUNCT
ejpam-5646	183	1	having	have	VERB
ejpam-5646	183	2	f	f	PRON
ejpam-5646	183	3	an	an	PRON
ejpam-5646	183	4	onto	onto	ADP
ejpam-5646	183	5	semigroup	semigroup	ADJ
ejpam-5646	183	6	homorphism	homorphism	NOUN
ejpam-5646	183	7	implies	imply	VERB
ejpam-5646	183	8	that	that	SCONJ
ejpam-5646	183	9	f(a	f(a	NOUN
ejpam-5646	183	10	)	)	PUNCT
ejpam-5646	184	1	=	=	PRON
ejpam-5646	184	2	{	{	PUNCT
ejpam-5646	184	3	(	(	PUNCT
ejpam-5646	184	4	4	4	NUM
ejpam-5646	184	5	0	0	NUM
ejpam-5646	184	6	0	0	NUM
ejpam-5646	184	7	0	0	NUM
ejpam-5646	184	8	)	)	PUNCT
ejpam-5646	184	9	,	,	PUNCT
ejpam-5646	184	10	(	(	PUNCT
ejpam-5646	184	11	8	8	NUM
ejpam-5646	184	12	0	0	NUM
ejpam-5646	184	13	0	0	NUM
ejpam-5646	184	14	0	0	NUM
ejpam-5646	184	15	)	)	PUNCT
ejpam-5646	184	16	}	}	PUNCT
ejpam-5646	184	17	is	be	AUX
ejpam-5646	184	18	a	a	DET
ejpam-5646	184	19	(	(	PUNCT
ejpam-5646	184	20	2	2	NUM
ejpam-5646	184	21	,	,	PUNCT
ejpam-5646	184	22	1)-bi	1)-bi	NUM
ejpam-5646	184	23	-	-	PUNCT
ejpam-5646	184	24	antiideal	antiideal	NOUN
ejpam-5646	184	25	of	of	ADP
ejpam-5646	184	26	m2(2p0	m2(2p0	NUM
ejpam-5646	184	27	)	)	PUNCT
ejpam-5646	184	28	.	.	PUNCT
ejpam-5646	185	1	4	4	X
ejpam-5646	185	2	.	.	X
ejpam-5646	185	3	fuzzy	fuzzy	ADJ
ejpam-5646	185	4	(	(	PUNCT
ejpam-5646	185	5	m	m	NOUN
ejpam-5646	185	6	,	,	PUNCT
ejpam-5646	185	7	n)-bi	n)-bi	NOUN
ejpam-5646	185	8	-	-	PUNCT
ejpam-5646	185	9	antiideals	antiideal	NOUN
ejpam-5646	185	10	of	of	ADP
ejpam-5646	185	11	a	a	DET
ejpam-5646	185	12	semigroup	semigroup	NOUN
ejpam-5646	185	13	in	in	ADP
ejpam-5646	185	14	this	this	DET
ejpam-5646	185	15	section	section	NOUN
ejpam-5646	185	16	,	,	PUNCT
ejpam-5646	185	17	we	we	PRON
ejpam-5646	185	18	introduce	introduce	VERB
ejpam-5646	185	19	new	new	ADJ
ejpam-5646	185	20	fuzzy	fuzzy	ADJ
ejpam-5646	185	21	algebraic	algebraic	ADJ
ejpam-5646	185	22	structures	structure	NOUN
ejpam-5646	185	23	and	and	CCONJ
ejpam-5646	185	24	study	study	VERB
ejpam-5646	185	25	their	their	PRON
ejpam-5646	185	26	properties	property	NOUN
ejpam-5646	185	27	.	.	PUNCT
ejpam-5646	186	1	more	more	ADV
ejpam-5646	186	2	precisely	precisely	ADV
ejpam-5646	186	3	and	and	CCONJ
ejpam-5646	186	4	inspired	inspire	VERB
ejpam-5646	186	5	by	by	ADP
ejpam-5646	186	6	fuzzy	fuzzy	ADJ
ejpam-5646	186	7	interior	interior	ADJ
ejpam-5646	186	8	antiideals	antiideal	NOUN
ejpam-5646	186	9	introduced	introduce	VERB
ejpam-5646	186	10	in	in	ADP
ejpam-5646	186	11	[	[	X
ejpam-5646	186	12	2	2	NUM
ejpam-5646	186	13	]	]	PUNCT
ejpam-5646	186	14	and	and	CCONJ
ejpam-5646	186	15	fuzzy	fuzzy	ADJ
ejpam-5646	186	16	antiideals	antiideal	NOUN
ejpam-5646	186	17	of	of	ADP
ejpam-5646	186	18	a	a	DET
ejpam-5646	186	19	semiring	semiring	NOUN
ejpam-5646	186	20	[	[	X
ejpam-5646	186	21	18	18	NUM
ejpam-5646	186	22	]	]	PUNCT
ejpam-5646	186	23	,	,	PUNCT
ejpam-5646	186	24	we	we	PRON
ejpam-5646	186	25	define	define	VERB
ejpam-5646	186	26	fuzzy	fuzzy	ADJ
ejpam-5646	186	27	(	(	PUNCT
ejpam-5646	186	28	m	m	NOUN
ejpam-5646	186	29	,	,	PUNCT
ejpam-5646	186	30	n)-bi	n)-bi	NOUN
ejpam-5646	186	31	-	-	PUNCT
ejpam-5646	186	32	antiideals	antiideal	NOUN
ejpam-5646	186	33	of	of	ADP
ejpam-5646	186	34	a	a	DET
ejpam-5646	186	35	semigroup	semigroup	NOUN
ejpam-5646	186	36	.	.	PUNCT
ejpam-5646	187	1	definition	definition	NOUN
ejpam-5646	187	2	9	9	NUM
ejpam-5646	187	3	.	.	PUNCT
ejpam-5646	188	1	let	let	VERB
ejpam-5646	188	2	(	(	PUNCT
ejpam-5646	188	3	x	x	NOUN
ejpam-5646	188	4	,	,	PUNCT
ejpam-5646	188	5	·	·	PUNCT
ejpam-5646	188	6	)	)	PUNCT
ejpam-5646	188	7	be	be	AUX
ejpam-5646	188	8	a	a	DET
ejpam-5646	188	9	semigroup	semigroup	NOUN
ejpam-5646	188	10	,	,	PUNCT
ejpam-5646	188	11	m	m	PROPN
ejpam-5646	188	12	,	,	PUNCT
ejpam-5646	188	13	n	n	PRON
ejpam-5646	188	14	be	be	VERB
ejpam-5646	188	15	positive	positive	ADJ
ejpam-5646	188	16	integers	integer	NOUN
ejpam-5646	188	17	,	,	PUNCT
ejpam-5646	188	18	and	and	CCONJ
ejpam-5646	188	19	µ	µ	X
ejpam-5646	188	20	:	:	PUNCT
ejpam-5646	188	21	x	x	SYM
ejpam-5646	188	22	→	→	SYM
ejpam-5646	188	23	[	[	X
ejpam-5646	188	24	0	0	NUM
ejpam-5646	188	25	,	,	PUNCT
ejpam-5646	188	26	1	1	NUM
ejpam-5646	188	27	]	]	PUNCT
ejpam-5646	188	28	be	be	AUX
ejpam-5646	188	29	a	a	DET
ejpam-5646	188	30	non	non	ADJ
ejpam-5646	188	31	-	-	ADJ
ejpam-5646	188	32	zero	zero	ADJ
ejpam-5646	188	33	fuzzy	fuzzy	ADJ
ejpam-5646	188	34	set	set	NOUN
ejpam-5646	188	35	of	of	ADP
ejpam-5646	188	36	x.	x.	NOUN
ejpam-5646	188	37	then	then	ADV
ejpam-5646	188	38	µ	µ	PROPN
ejpam-5646	188	39	is	be	AUX
ejpam-5646	188	40	a	a	DET
ejpam-5646	188	41	fuzzy	fuzzy	ADJ
ejpam-5646	188	42	(	(	PUNCT
ejpam-5646	188	43	m	m	NOUN
ejpam-5646	188	44	,	,	PUNCT
ejpam-5646	188	45	n)-bi	n)-bi	NOUN
ejpam-5646	188	46	-	-	PUNCT
ejpam-5646	188	47	antiideal	antiideal	NOUN
ejpam-5646	188	48	of	of	ADP
ejpam-5646	188	49	x	x	PRON
ejpam-5646	188	50	if	if	SCONJ
ejpam-5646	188	51	for	for	ADP
ejpam-5646	188	52	all	all	DET
ejpam-5646	188	53	xi	xi	PROPN
ejpam-5646	188	54	,	,	PUNCT
ejpam-5646	188	55	yj	yj	PROPN
ejpam-5646	188	56	,	,	PUNCT
ejpam-5646	188	57	r	r	NOUN
ejpam-5646	188	58	∈	∈	PROPN
ejpam-5646	188	59	x	x	NOUN
ejpam-5646	188	60	,	,	PUNCT
ejpam-5646	188	61	µ(x1	µ(x1	ADJ
ejpam-5646	188	62	.	.	PUNCT
ejpam-5646	188	63	.	.	PUNCT
ejpam-5646	188	64	.	.	PUNCT
ejpam-5646	189	1	xmry1	xmry1	PROPN
ejpam-5646	189	2	.	.	PUNCT
ejpam-5646	189	3	.	.	PUNCT
ejpam-5646	189	4	.	.	PUNCT
ejpam-5646	190	1	yn	yn	X
ejpam-5646	190	2	)	)	PUNCT
ejpam-5646	190	3	∧	∧	PROPN
ejpam-5646	190	4	µ(x1	µ(x1	ADJ
ejpam-5646	190	5	)	)	PUNCT
ejpam-5646	190	6	∧	∧	NOUN
ejpam-5646	190	7	.	.	PUNCT
ejpam-5646	190	8	.	.	PUNCT
ejpam-5646	190	9	.	.	PUNCT
ejpam-5646	191	1	∧	∧	PROPN
ejpam-5646	191	2	µ(xm	µ(xm	PROPN
ejpam-5646	191	3	)	)	PUNCT
ejpam-5646	191	4	∧	∧	NOUN
ejpam-5646	191	5	µ(y1	µ(y1	NOUN
ejpam-5646	191	6	)	)	PUNCT
ejpam-5646	191	7	∧	∧	NOUN
ejpam-5646	191	8	.	.	PUNCT
ejpam-5646	191	9	.	.	PUNCT
ejpam-5646	191	10	.	.	PUNCT
ejpam-5646	192	1	∧	∧	NOUN
ejpam-5646	192	2	µ(yn	µ(yn	NOUN
ejpam-5646	192	3	)	)	PUNCT
ejpam-5646	192	4	=	=	SYM
ejpam-5646	192	5	0	0	X
ejpam-5646	192	6	.	.	PUNCT
ejpam-5646	192	7	m.	m.	NOUN
ejpam-5646	192	8	al	al	PROPN
ejpam-5646	192	9	tahan	tahan	PROPN
ejpam-5646	192	10	,	,	PUNCT
ejpam-5646	192	11	s.	s.	PROPN
ejpam-5646	192	12	hoskova	hoskova	PROPN
ejpam-5646	192	13	-	-	PUNCT
ejpam-5646	192	14	mayerova	mayerova	PROPN
ejpam-5646	192	15	,	,	PUNCT
ejpam-5646	192	16	s.	s.	PROPN
ejpam-5646	192	17	al	al	PROPN
ejpam-5646	192	18	-	-	PUNCT
ejpam-5646	192	19	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	192	20	/	/	SYM
ejpam-5646	192	21	eur	eur	NOUN
ejpam-5646	192	22	.	.	PUNCT
ejpam-5646	193	1	j.	j.	PROPN
ejpam-5646	193	2	pure	pure	PROPN
ejpam-5646	193	3	appl	appl	PROPN
ejpam-5646	193	4	.	.	PROPN
ejpam-5646	193	5	math	math	PROPN
ejpam-5646	193	6	,	,	PUNCT
ejpam-5646	193	7	18	18	NUM
ejpam-5646	193	8	(	(	PUNCT
ejpam-5646	193	9	1	1	NUM
ejpam-5646	193	10	)	)	PUNCT
ejpam-5646	193	11	(	(	PUNCT
ejpam-5646	193	12	2025	2025	NUM
ejpam-5646	193	13	)	)	PUNCT
ejpam-5646	193	14	,	,	PUNCT
ejpam-5646	193	15	5646	5646	NUM
ejpam-5646	193	16	7	7	NUM
ejpam-5646	193	17	of	of	ADP
ejpam-5646	193	18	11	11	NUM
ejpam-5646	193	19	example	example	NOUN
ejpam-5646	193	20	10	10	NUM
ejpam-5646	193	21	.	.	PUNCT
ejpam-5646	194	1	let	let	VERB
ejpam-5646	194	2	p0	p0	NOUN
ejpam-5646	194	3	be	be	AUX
ejpam-5646	194	4	the	the	DET
ejpam-5646	194	5	semigroup	semigroup	NOUN
ejpam-5646	194	6	of	of	ADP
ejpam-5646	194	7	non	non	ADJ
ejpam-5646	194	8	-	-	ADJ
ejpam-5646	194	9	negative	negative	ADJ
ejpam-5646	194	10	integers	integer	NOUN
ejpam-5646	194	11	under	under	ADP
ejpam-5646	194	12	standard	standard	ADJ
ejpam-5646	194	13	addition	addition	NOUN
ejpam-5646	194	14	and	and	CCONJ
ejpam-5646	194	15	µ	µ	PRON
ejpam-5646	194	16	be	be	AUX
ejpam-5646	194	17	the	the	DET
ejpam-5646	194	18	fuzzy	fuzzy	ADJ
ejpam-5646	194	19	set	set	NOUN
ejpam-5646	194	20	on	on	ADP
ejpam-5646	194	21	p0	p0	NOUN
ejpam-5646	194	22	defined	define	VERB
ejpam-5646	194	23	as	as	ADP
ejpam-5646	194	24	follows	follow	VERB
ejpam-5646	194	25	.	.	PUNCT
ejpam-5646	195	1	µ(k	µ(k	NOUN
ejpam-5646	195	2	)	)	PUNCT
ejpam-5646	196	1	=	=	SYM
ejpam-5646	197	1			NOUN
ejpam-5646	197	2	0.65	0.65	NUM
ejpam-5646	197	3	if	if	SCONJ
ejpam-5646	197	4	k=1	k=1	X
ejpam-5646	197	5	;	;	PUNCT
ejpam-5646	197	6	0.54	0.54	NUM
ejpam-5646	197	7	if	if	SCONJ
ejpam-5646	197	8	k=2	k=2	PROPN
ejpam-5646	197	9	;	;	PUNCT
ejpam-5646	197	10	0	0	NUM
ejpam-5646	197	11	otherwise	otherwise	ADV
ejpam-5646	197	12	.	.	PUNCT
ejpam-5646	198	1	then	then	ADV
ejpam-5646	198	2	µ	µ	X
ejpam-5646	198	3	is	be	AUX
ejpam-5646	198	4	a	a	DET
ejpam-5646	198	5	fuzzy	fuzzy	ADJ
ejpam-5646	198	6	(	(	PUNCT
ejpam-5646	198	7	2	2	NUM
ejpam-5646	198	8	,	,	PUNCT
ejpam-5646	198	9	1)-bi	1)-bi	NUM
ejpam-5646	198	10	-	-	PUNCT
ejpam-5646	198	11	antiideal	antiideal	NOUN
ejpam-5646	198	12	of	of	ADP
ejpam-5646	198	13	p0	p0	NOUN
ejpam-5646	198	14	.	.	PUNCT
ejpam-5646	199	1	moreover	moreover	ADV
ejpam-5646	199	2	,	,	PUNCT
ejpam-5646	199	3	it	it	PRON
ejpam-5646	199	4	is	be	AUX
ejpam-5646	199	5	not	not	PART
ejpam-5646	199	6	a	a	DET
ejpam-5646	199	7	fuzzy	fuzzy	ADJ
ejpam-5646	199	8	bi	bi	NOUN
ejpam-5646	199	9	-	-	NOUN
ejpam-5646	199	10	antiideal	antiideal	NOUN
ejpam-5646	199	11	of	of	ADP
ejpam-5646	199	12	p0	p0	NOUN
ejpam-5646	199	13	.	.	PUNCT
ejpam-5646	200	1	this	this	PRON
ejpam-5646	200	2	is	be	AUX
ejpam-5646	200	3	clear	clear	ADJ
ejpam-5646	200	4	as	as	ADP
ejpam-5646	200	5	0.54	0.54	NUM
ejpam-5646	200	6	=	=	SYM
ejpam-5646	200	7	µ(2	µ(2	PROPN
ejpam-5646	200	8	)	)	PUNCT
ejpam-5646	200	9	∧	∧	PROPN
ejpam-5646	200	10	µ(1	µ(1	PROPN
ejpam-5646	200	11	)	)	PUNCT
ejpam-5646	200	12	=	=	PUNCT
ejpam-5646	201	1	µ(1	µ(1	PROPN
ejpam-5646	202	1	+	+	NUM
ejpam-5646	202	2	0	0	NUM
ejpam-5646	203	1	+	+	CCONJ
ejpam-5646	203	2	1	1	X
ejpam-5646	203	3	)	)	PUNCT
ejpam-5646	203	4	∧	∧	PROPN
ejpam-5646	203	5	µ(1	µ(1	PROPN
ejpam-5646	203	6	)	)	PUNCT
ejpam-5646	203	7	.	.	PUNCT
ejpam-5646	204	1	next	next	ADV
ejpam-5646	204	2	,	,	PUNCT
ejpam-5646	204	3	we	we	PRON
ejpam-5646	204	4	study	study	VERB
ejpam-5646	204	5	fuzzy	fuzzy	ADJ
ejpam-5646	204	6	(	(	PUNCT
ejpam-5646	204	7	m	m	NOUN
ejpam-5646	204	8	,	,	PUNCT
ejpam-5646	204	9	n)-bi	n)-bi	NOUN
ejpam-5646	204	10	-	-	PUNCT
ejpam-5646	204	11	antiideals	antiideal	NOUN
ejpam-5646	204	12	of	of	ADP
ejpam-5646	204	13	a	a	DET
ejpam-5646	204	14	semigroup	semigroup	NOUN
ejpam-5646	204	15	under	under	ADP
ejpam-5646	204	16	some	some	DET
ejpam-5646	204	17	operations	operation	NOUN
ejpam-5646	204	18	of	of	ADP
ejpam-5646	204	19	fuzzy	fuzzy	ADJ
ejpam-5646	204	20	sets	set	NOUN
ejpam-5646	204	21	such	such	ADJ
ejpam-5646	204	22	as	as	ADP
ejpam-5646	204	23	the	the	DET
ejpam-5646	204	24	intersection	intersection	NOUN
ejpam-5646	204	25	,	,	PUNCT
ejpam-5646	204	26	union	union	NOUN
ejpam-5646	204	27	,	,	PUNCT
ejpam-5646	204	28	and	and	CCONJ
ejpam-5646	204	29	product	product	NOUN
ejpam-5646	204	30	of	of	ADP
ejpam-5646	204	31	fuzzy	fuzzy	ADJ
ejpam-5646	204	32	sets	set	NOUN
ejpam-5646	204	33	.	.	PUNCT
ejpam-5646	205	1	theorem	theorem	ADJ
ejpam-5646	205	2	4	4	NUM
ejpam-5646	205	3	.	.	PUNCT
ejpam-5646	206	1	let	let	AUX
ejpam-5646	206	2	(	(	PUNCT
ejpam-5646	206	3	x	x	NOUN
ejpam-5646	206	4	,	,	PUNCT
ejpam-5646	206	5	·	·	PUNCT
ejpam-5646	206	6	)	)	PUNCT
ejpam-5646	206	7	be	be	AUX
ejpam-5646	206	8	a	a	DET
ejpam-5646	206	9	semigroup	semigroup	NOUN
ejpam-5646	206	10	and	and	CCONJ
ejpam-5646	206	11	µi	µi	PROPN
ejpam-5646	206	12	be	be	AUX
ejpam-5646	206	13	a	a	DET
ejpam-5646	206	14	non	non	ADJ
ejpam-5646	206	15	-	-	ADJ
ejpam-5646	206	16	zero	zero	ADJ
ejpam-5646	206	17	fuzzy	fuzzy	ADJ
ejpam-5646	206	18	set	set	NOUN
ejpam-5646	206	19	of	of	ADP
ejpam-5646	206	20	x	x	PUNCT
ejpam-5646	206	21	for	for	ADP
ejpam-5646	206	22	i	i	PRON
ejpam-5646	206	23	=	=	NOUN
ejpam-5646	206	24	1	1	NUM
ejpam-5646	206	25	,	,	PUNCT
ejpam-5646	206	26	.	.	PUNCT
ejpam-5646	206	27	.	.	PUNCT
ejpam-5646	207	1	.	.	PUNCT
ejpam-5646	208	1	,	,	PUNCT
ejpam-5646	208	2	k.	k.	PROPN
ejpam-5646	208	3	if	if	SCONJ
ejpam-5646	208	4	µi	µi	PROPN
ejpam-5646	208	5	is	be	AUX
ejpam-5646	208	6	a	a	DET
ejpam-5646	208	7	fuzzy	fuzzy	ADJ
ejpam-5646	208	8	(	(	PUNCT
ejpam-5646	208	9	m	m	NOUN
ejpam-5646	208	10	,	,	PUNCT
ejpam-5646	208	11	n)-bi	n)-bi	NOUN
ejpam-5646	208	12	-	-	PUNCT
ejpam-5646	208	13	antiideal	antiideal	NOUN
ejpam-5646	208	14	of	of	ADP
ejpam-5646	208	15	x	x	PUNCT
ejpam-5646	208	16	for	for	ADP
ejpam-5646	208	17	some	some	DET
ejpam-5646	208	18	i	i	PRON
ejpam-5646	208	19	∈	∈	PROPN
ejpam-5646	208	20	{	{	PUNCT
ejpam-5646	208	21	1	1	NUM
ejpam-5646	208	22	,	,	PUNCT
ejpam-5646	208	23	.	.	PUNCT
ejpam-5646	208	24	.	.	PUNCT
ejpam-5646	209	1	.	.	PUNCT
ejpam-5646	210	1	,	,	PUNCT
ejpam-5646	210	2	k	k	X
ejpam-5646	210	3	}	}	PUNCT
ejpam-5646	210	4	,	,	PUNCT
ejpam-5646	210	5	then	then	ADV
ejpam-5646	210	6	so	so	ADV
ejpam-5646	210	7	is	be	AUX
ejpam-5646	210	8	µ	µ	NOUN
ejpam-5646	210	9	=	=	SYM
ejpam-5646	210	10	µ1	µ1	NOUN
ejpam-5646	210	11	∧	∧	PROPN
ejpam-5646	210	12	µ2	µ2	PROPN
ejpam-5646	210	13	∧	∧	PROPN
ejpam-5646	210	14	.	.	PUNCT
ejpam-5646	210	15	.	.	PUNCT
ejpam-5646	210	16	.	.	PUNCT
ejpam-5646	211	1	∧	∧	NOUN
ejpam-5646	211	2	µk	µk	NOUN
ejpam-5646	211	3	.	.	PUNCT
ejpam-5646	211	4	proof	proof	NOUN
ejpam-5646	211	5	.	.	PUNCT
ejpam-5646	212	1	let	let	VERB
ejpam-5646	212	2	x1	x1	NUM
ejpam-5646	212	3	,	,	PUNCT
ejpam-5646	212	4	.	.	PUNCT
ejpam-5646	212	5	.	.	PUNCT
ejpam-5646	213	1	.	.	PUNCT
ejpam-5646	214	1	,	,	PUNCT
ejpam-5646	214	2	xm	xm	PROPN
ejpam-5646	214	3	,	,	PUNCT
ejpam-5646	214	4	r	r	NOUN
ejpam-5646	214	5	,	,	PUNCT
ejpam-5646	214	6	y1	y1	NOUN
ejpam-5646	214	7	,	,	PUNCT
ejpam-5646	214	8	.	.	PUNCT
ejpam-5646	214	9	.	.	PUNCT
ejpam-5646	214	10	.	.	PUNCT
ejpam-5646	215	1	,	,	PUNCT
ejpam-5646	215	2	yn	yn	PROPN
ejpam-5646	215	3	∈	∈	PROPN
ejpam-5646	215	4	x.	x.	NOUN
ejpam-5646	215	5	without	without	ADP
ejpam-5646	215	6	loss	loss	NOUN
ejpam-5646	215	7	of	of	ADP
ejpam-5646	215	8	generality	generality	NOUN
ejpam-5646	215	9	,	,	PUNCT
ejpam-5646	215	10	let	let	VERB
ejpam-5646	215	11	µ1	µ1	PROPN
ejpam-5646	215	12	be	be	AUX
ejpam-5646	215	13	a	a	DET
ejpam-5646	215	14	fuzzy	fuzzy	ADJ
ejpam-5646	215	15	(	(	PUNCT
ejpam-5646	215	16	m	m	NOUN
ejpam-5646	215	17	,	,	PUNCT
ejpam-5646	215	18	n)-bi	n)-bi	NOUN
ejpam-5646	215	19	-	-	PUNCT
ejpam-5646	215	20	antiideal	antiideal	NOUN
ejpam-5646	215	21	of	of	ADP
ejpam-5646	215	22	x.	x.	NOUN
ejpam-5646	215	23	then	then	ADV
ejpam-5646	215	24	µ(x1	µ(x1	PROPN
ejpam-5646	215	25	.	.	PUNCT
ejpam-5646	215	26	.	.	PUNCT
ejpam-5646	215	27	.	.	PUNCT
ejpam-5646	216	1	xmry1	xmry1	PROPN
ejpam-5646	216	2	.	.	PUNCT
ejpam-5646	216	3	.	.	PUNCT
ejpam-5646	216	4	.	.	PUNCT
ejpam-5646	217	1	yn	yn	X
ejpam-5646	217	2	)	)	PUNCT
ejpam-5646	217	3	∧	∧	PROPN
ejpam-5646	217	4	µ(x1	µ(x1	ADJ
ejpam-5646	217	5	)	)	PUNCT
ejpam-5646	217	6	∧	∧	NOUN
ejpam-5646	217	7	.	.	PUNCT
ejpam-5646	217	8	.	.	PUNCT
ejpam-5646	217	9	.	.	PUNCT
ejpam-5646	218	1	µ(xm	µ(xm	ADJ
ejpam-5646	218	2	)	)	PUNCT
ejpam-5646	218	3	∧	∧	NOUN
ejpam-5646	218	4	µ(y1	µ(y1	NOUN
ejpam-5646	218	5	)	)	PUNCT
ejpam-5646	218	6	∧	∧	NOUN
ejpam-5646	218	7	.	.	PUNCT
ejpam-5646	218	8	.	.	PUNCT
ejpam-5646	218	9	.	.	PUNCT
ejpam-5646	219	1	∧	∧	NOUN
ejpam-5646	219	2	µ(yn	µ(yn	PROPN
ejpam-5646	219	3	)	)	PUNCT
ejpam-5646	219	4	≤	≤	NOUN
ejpam-5646	219	5	µ1(x1	µ1(x1	PROPN
ejpam-5646	219	6	.	.	PUNCT
ejpam-5646	219	7	.	.	PUNCT
ejpam-5646	219	8	.	.	PUNCT
ejpam-5646	220	1	xmry1	xmry1	PROPN
ejpam-5646	220	2	.	.	PUNCT
ejpam-5646	220	3	.	.	PUNCT
ejpam-5646	220	4	.	.	PUNCT
ejpam-5646	221	1	yn	yn	X
ejpam-5646	221	2	)	)	PUNCT
ejpam-5646	221	3	∧	∧	PROPN
ejpam-5646	221	4	µ1(x1	µ1(x1	PROPN
ejpam-5646	221	5	)	)	PUNCT
ejpam-5646	221	6	∧	∧	PROPN
ejpam-5646	221	7	.	.	PUNCT
ejpam-5646	221	8	.	.	PUNCT
ejpam-5646	221	9	.	.	PUNCT
ejpam-5646	222	1	µ1(xm	µ1(xm	X
ejpam-5646	222	2	)	)	PUNCT
ejpam-5646	222	3	∧	∧	PROPN
ejpam-5646	222	4	µ1(y1	µ1(y1	PROPN
ejpam-5646	222	5	)	)	PUNCT
ejpam-5646	222	6	∧	∧	PROPN
ejpam-5646	222	7	.	.	PUNCT
ejpam-5646	222	8	.	.	PUNCT
ejpam-5646	222	9	.	.	PUNCT
ejpam-5646	223	1	∧	∧	PROPN
ejpam-5646	223	2	µ1(yn	µ1(yn	PROPN
ejpam-5646	223	3	)	)	PUNCT
ejpam-5646	223	4	=	=	SYM
ejpam-5646	223	5	0	0	X
ejpam-5646	223	6	.	.	PUNCT
ejpam-5646	223	7	remark	remark	PROPN
ejpam-5646	223	8	3	3	NUM
ejpam-5646	223	9	.	.	PUNCT
ejpam-5646	224	1	the	the	DET
ejpam-5646	224	2	union	union	NOUN
ejpam-5646	224	3	of	of	ADP
ejpam-5646	224	4	fuzzy	fuzzy	ADJ
ejpam-5646	224	5	(	(	PUNCT
ejpam-5646	224	6	m	m	NOUN
ejpam-5646	224	7	,	,	PUNCT
ejpam-5646	224	8	n)-bi	n)-bi	NOUN
ejpam-5646	224	9	-	-	PUNCT
ejpam-5646	224	10	antiideals	antiideal	NOUN
ejpam-5646	224	11	is	be	AUX
ejpam-5646	224	12	not	not	PART
ejpam-5646	224	13	necessarily	necessarily	ADV
ejpam-5646	224	14	a	a	DET
ejpam-5646	224	15	fuzzy	fuzzy	ADJ
ejpam-5646	224	16	(	(	PUNCT
ejpam-5646	224	17	m	m	NOUN
ejpam-5646	224	18	,	,	PUNCT
ejpam-5646	224	19	n)-biantiideal	n)-biantiideal	NOUN
ejpam-5646	224	20	.	.	PUNCT
ejpam-5646	225	1	(	(	PUNCT
ejpam-5646	225	2	see	see	VERB
ejpam-5646	225	3	example	example	NOUN
ejpam-5646	225	4	11	11	NUM
ejpam-5646	225	5	.	.	PUNCT
ejpam-5646	225	6	)	)	PUNCT
ejpam-5646	225	7	example	example	NOUN
ejpam-5646	226	1	11	11	NUM
ejpam-5646	226	2	.	.	PUNCT
ejpam-5646	227	1	let	let	VERB
ejpam-5646	227	2	m2(p0	m2(p0	NOUN
ejpam-5646	227	3	)	)	PUNCT
ejpam-5646	227	4	be	be	AUX
ejpam-5646	227	5	the	the	DET
ejpam-5646	227	6	semigroup	semigroup	NOUN
ejpam-5646	227	7	defined	define	VERB
ejpam-5646	227	8	in	in	ADP
ejpam-5646	227	9	example	example	NOUN
ejpam-5646	227	10	6	6	NUM
ejpam-5646	227	11	and	and	CCONJ
ejpam-5646	227	12	µ1	µ1	PROPN
ejpam-5646	227	13	,	,	PUNCT
ejpam-5646	227	14	µ2	µ2	PROPN
ejpam-5646	227	15	be	be	AUX
ejpam-5646	227	16	defined	define	VERB
ejpam-5646	227	17	as	as	ADP
ejpam-5646	227	18	follows	follow	VERB
ejpam-5646	227	19	.	.	PUNCT
ejpam-5646	228	1	µ1(b	µ1(b	VERB
ejpam-5646	228	2	)	)	PUNCT
ejpam-5646	229	1	=	=	SYM
ejpam-5646	229	2	0.6	0.6	PROPN
ejpam-5646	229	3	if	if	SCONJ
ejpam-5646	229	4	b	b	PROPN
ejpam-5646	229	5	=	=	SYM
ejpam-5646	229	6	(	(	PUNCT
ejpam-5646	229	7	2	2	NUM
ejpam-5646	229	8	0	0	NUM
ejpam-5646	229	9	0	0	NUM
ejpam-5646	229	10	0	0	NUM
ejpam-5646	229	11	)	)	PUNCT
ejpam-5646	229	12	;	;	PUNCT
ejpam-5646	229	13	0	0	NUM
ejpam-5646	229	14	otherwise	otherwise	ADV
ejpam-5646	229	15	.	.	PUNCT
ejpam-5646	230	1	and	and	CCONJ
ejpam-5646	230	2	µ2(b	µ2(b	PROPN
ejpam-5646	230	3	)	)	PUNCT
ejpam-5646	230	4	=	=	PUNCT
ejpam-5646	230	5			NUM
ejpam-5646	230	6	0.8	0.8	NUM
ejpam-5646	231	1	if	if	SCONJ
ejpam-5646	231	2	b	b	X
ejpam-5646	231	3	=	=	SYM
ejpam-5646	231	4	(	(	PUNCT
ejpam-5646	231	5	4	4	NUM
ejpam-5646	231	6	0	0	NUM
ejpam-5646	231	7	0	0	NUM
ejpam-5646	231	8	0	0	NUM
ejpam-5646	231	9	)	)	PUNCT
ejpam-5646	231	10	;	;	PUNCT
ejpam-5646	231	11	0.7	0.7	NUM
ejpam-5646	231	12	if	if	SCONJ
ejpam-5646	231	13	b	b	X
ejpam-5646	231	14	=	=	SYM
ejpam-5646	231	15	(	(	PUNCT
ejpam-5646	231	16	16	16	NUM
ejpam-5646	231	17	0	0	NUM
ejpam-5646	231	18	0	0	NUM
ejpam-5646	231	19	0	0	NUM
ejpam-5646	231	20	)	)	PUNCT
ejpam-5646	231	21	;	;	PUNCT
ejpam-5646	231	22	0	0	NUM
ejpam-5646	231	23	otherwise	otherwise	ADV
ejpam-5646	231	24	.	.	PUNCT
ejpam-5646	232	1	then	then	ADV
ejpam-5646	232	2	µ1	µ1	PROPN
ejpam-5646	232	3	,	,	PUNCT
ejpam-5646	232	4	µ2	µ2	PROPN
ejpam-5646	232	5	are	be	AUX
ejpam-5646	232	6	fuzzy	fuzzy	ADJ
ejpam-5646	232	7	(	(	PUNCT
ejpam-5646	232	8	2	2	NUM
ejpam-5646	232	9	,	,	PUNCT
ejpam-5646	232	10	1)-bi	1)-bi	NUM
ejpam-5646	232	11	-	-	PUNCT
ejpam-5646	232	12	antiideals	antiideal	NOUN
ejpam-5646	232	13	of	of	ADP
ejpam-5646	232	14	m2(p0	m2(p0	NOUN
ejpam-5646	232	15	)	)	PUNCT
ejpam-5646	232	16	.	.	PUNCT
ejpam-5646	233	1	the	the	DET
ejpam-5646	233	2	fuzzy	fuzzy	ADJ
ejpam-5646	233	3	set	set	VERB
ejpam-5646	233	4	µ	µ	NOUN
ejpam-5646	233	5	=	=	SYM
ejpam-5646	233	6	µ1	µ1	PROPN
ejpam-5646	233	7	∨	∨	NOUN
ejpam-5646	233	8	µ2	µ2	PROPN
ejpam-5646	233	9	of	of	ADP
ejpam-5646	233	10	m2(p0	m2(p0	NOUN
ejpam-5646	233	11	)	)	PUNCT
ejpam-5646	233	12	is	be	AUX
ejpam-5646	233	13	given	give	VERB
ejpam-5646	233	14	by	by	ADP
ejpam-5646	233	15	:	:	PUNCT
ejpam-5646	233	16	µ(b	µ(b	PROPN
ejpam-5646	233	17	)	)	PUNCT
ejpam-5646	233	18	=	=	SYM
ejpam-5646	234	1			NUM
ejpam-5646	234	2	0.6	0.6	NUM
ejpam-5646	235	1	if	if	SCONJ
ejpam-5646	235	2	b	b	NOUN
ejpam-5646	235	3	=	=	SYM
ejpam-5646	235	4	m1	m1	PROPN
ejpam-5646	235	5	=	=	SYM
ejpam-5646	235	6	(	(	PUNCT
ejpam-5646	235	7	2	2	NUM
ejpam-5646	235	8	0	0	NUM
ejpam-5646	235	9	0	0	NUM
ejpam-5646	235	10	0	0	NUM
ejpam-5646	235	11	)	)	PUNCT
ejpam-5646	235	12	;	;	PUNCT
ejpam-5646	235	13	0.8	0.8	NUM
ejpam-5646	235	14	if	if	SCONJ
ejpam-5646	235	15	b	b	PROPN
ejpam-5646	235	16	=	=	SYM
ejpam-5646	235	17	m2	m2	PROPN
ejpam-5646	235	18	=	=	PUNCT
ejpam-5646	235	19	(	(	PUNCT
ejpam-5646	235	20	4	4	NUM
ejpam-5646	235	21	0	0	NUM
ejpam-5646	235	22	0	0	NUM
ejpam-5646	235	23	0	0	NUM
ejpam-5646	235	24	)	)	PUNCT
ejpam-5646	235	25	;	;	PUNCT
ejpam-5646	235	26	0.7	0.7	NUM
ejpam-5646	235	27	if	if	SCONJ
ejpam-5646	235	28	b	b	PROPN
ejpam-5646	235	29	=	=	SYM
ejpam-5646	235	30	m3	m3	PROPN
ejpam-5646	235	31	=	=	PUNCT
ejpam-5646	235	32	(	(	PUNCT
ejpam-5646	235	33	16	16	NUM
ejpam-5646	235	34	0	0	NUM
ejpam-5646	235	35	0	0	NUM
ejpam-5646	235	36	0	0	NUM
ejpam-5646	235	37	)	)	PUNCT
ejpam-5646	235	38	;	;	PUNCT
ejpam-5646	235	39	0	0	NUM
ejpam-5646	235	40	otherwise	otherwise	ADV
ejpam-5646	235	41	.	.	PUNCT
ejpam-5646	236	1	m.	m.	NOUN
ejpam-5646	236	2	al	al	PROPN
ejpam-5646	236	3	tahan	tahan	PROPN
ejpam-5646	236	4	,	,	PUNCT
ejpam-5646	236	5	s.	s.	PROPN
ejpam-5646	236	6	hoskova	hoskova	PROPN
ejpam-5646	236	7	-	-	PUNCT
ejpam-5646	236	8	mayerova	mayerova	PROPN
ejpam-5646	236	9	,	,	PUNCT
ejpam-5646	236	10	s.	s.	PROPN
ejpam-5646	236	11	al	al	PROPN
ejpam-5646	236	12	-	-	PUNCT
ejpam-5646	236	13	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	236	14	/	/	SYM
ejpam-5646	236	15	eur	eur	NOUN
ejpam-5646	236	16	.	.	PUNCT
ejpam-5646	237	1	j.	j.	PROPN
ejpam-5646	237	2	pure	pure	PROPN
ejpam-5646	237	3	appl	appl	PROPN
ejpam-5646	237	4	.	.	PROPN
ejpam-5646	237	5	math	math	PROPN
ejpam-5646	237	6	,	,	PUNCT
ejpam-5646	237	7	18	18	NUM
ejpam-5646	237	8	(	(	PUNCT
ejpam-5646	237	9	1	1	NUM
ejpam-5646	237	10	)	)	PUNCT
ejpam-5646	237	11	(	(	PUNCT
ejpam-5646	237	12	2025	2025	NUM
ejpam-5646	237	13	)	)	PUNCT
ejpam-5646	237	14	,	,	PUNCT
ejpam-5646	237	15	5646	5646	NUM
ejpam-5646	237	16	8	8	NUM
ejpam-5646	237	17	of	of	ADP
ejpam-5646	237	18	11	11	NUM
ejpam-5646	237	19	having	have	VERB
ejpam-5646	237	20	m3	m3	PROPN
ejpam-5646	237	21	=	=	PUNCT
ejpam-5646	238	1	m1m1	m1m1	X
ejpam-5646	238	2	(	(	PUNCT
ejpam-5646	238	3	1	1	NUM
ejpam-5646	238	4	0	0	NUM
ejpam-5646	238	5	0	0	NUM
ejpam-5646	238	6	0	0	NUM
ejpam-5646	238	7	)	)	PUNCT
ejpam-5646	238	8	m2	m2	PROPN
ejpam-5646	238	9	and	and	CCONJ
ejpam-5646	238	10	0.7	0.7	NUM
ejpam-5646	238	11	=	=	SYM
ejpam-5646	238	12	µ(m3	µ(m3	ADJ
ejpam-5646	238	13	)	)	PUNCT
ejpam-5646	238	14	implies	imply	VERB
ejpam-5646	238	15	that	that	SCONJ
ejpam-5646	238	16	µ(m1m1	µ(m1m1	ADP
ejpam-5646	238	17	(	(	PUNCT
ejpam-5646	238	18	1	1	NUM
ejpam-5646	238	19	0	0	NUM
ejpam-5646	238	20	0	0	NUM
ejpam-5646	238	21	0	0	NUM
ejpam-5646	238	22	)	)	PUNCT
ejpam-5646	238	23	m2	m2	PROPN
ejpam-5646	238	24	)	)	PUNCT
ejpam-5646	238	25	∧	∧	NOUN
ejpam-5646	238	26	µ(m1	µ(m1	VERB
ejpam-5646	238	27	)	)	PUNCT
ejpam-5646	238	28	∧	∧	PROPN
ejpam-5646	238	29	µ(m2	µ(m2	NOUN
ejpam-5646	238	30	)	)	PUNCT
ejpam-5646	238	31	̸=	̸=	PROPN
ejpam-5646	238	32	0	0	NUM
ejpam-5646	238	33	.	.	PUNCT
ejpam-5646	239	1	theorem	theorem	NOUN
ejpam-5646	239	2	5	5	NUM
ejpam-5646	239	3	.	.	PUNCT
ejpam-5646	240	1	let	let	VERB
ejpam-5646	240	2	x1	x1	NUM
ejpam-5646	240	3	,	,	PUNCT
ejpam-5646	240	4	x2	x2	PROPN
ejpam-5646	240	5	be	be	VERB
ejpam-5646	240	6	semigroups	semigroup	NOUN
ejpam-5646	240	7	and	and	CCONJ
ejpam-5646	240	8	µ1	µ1	PROPN
ejpam-5646	240	9	,	,	PUNCT
ejpam-5646	240	10	µ2	µ2	PROPN
ejpam-5646	240	11	be	be	VERB
ejpam-5646	240	12	non	non	ADJ
ejpam-5646	240	13	-	-	ADJ
ejpam-5646	240	14	zero	zero	ADJ
ejpam-5646	240	15	fuzzy	fuzzy	ADJ
ejpam-5646	240	16	sets	set	NOUN
ejpam-5646	240	17	of	of	ADP
ejpam-5646	240	18	x1	x1	PROPN
ejpam-5646	240	19	,	,	PUNCT
ejpam-5646	240	20	x2	x2	PROPN
ejpam-5646	240	21	respectively	respectively	ADV
ejpam-5646	240	22	.	.	PUNCT
ejpam-5646	241	1	if	if	SCONJ
ejpam-5646	241	2	µ1	µ1	PROPN
ejpam-5646	241	3	or	or	CCONJ
ejpam-5646	241	4	µ2	µ2	PROPN
ejpam-5646	241	5	is	be	AUX
ejpam-5646	241	6	a	a	DET
ejpam-5646	241	7	fuzzy	fuzzy	ADJ
ejpam-5646	241	8	(	(	PUNCT
ejpam-5646	241	9	m	m	NOUN
ejpam-5646	241	10	,	,	PUNCT
ejpam-5646	241	11	n)-bi	n)-bi	NOUN
ejpam-5646	241	12	-	-	PUNCT
ejpam-5646	241	13	antiideal	antiideal	NOUN
ejpam-5646	241	14	of	of	ADP
ejpam-5646	241	15	x1	x1	PROPN
ejpam-5646	241	16	,	,	PUNCT
ejpam-5646	241	17	x2	x2	PROPN
ejpam-5646	241	18	,	,	PUNCT
ejpam-5646	241	19	then	then	ADV
ejpam-5646	241	20	µ	µ	X
ejpam-5646	241	21	=	=	SYM
ejpam-5646	241	22	µ1	µ1	PROPN
ejpam-5646	241	23	×µ2	×µ2	NOUN
ejpam-5646	241	24	is	be	AUX
ejpam-5646	241	25	a	a	DET
ejpam-5646	241	26	fuzzy	fuzzy	ADJ
ejpam-5646	241	27	(	(	PUNCT
ejpam-5646	241	28	m	m	NOUN
ejpam-5646	241	29	,	,	PUNCT
ejpam-5646	241	30	n)-bi	n)-bi	NOUN
ejpam-5646	241	31	-	-	PUNCT
ejpam-5646	241	32	antiideal	antiideal	NOUN
ejpam-5646	241	33	of	of	ADP
ejpam-5646	241	34	x1	x1	PROPN
ejpam-5646	241	35	×x2	×x2	PROPN
ejpam-5646	241	36	.	.	PUNCT
ejpam-5646	242	1	proof	proof	NOUN
ejpam-5646	242	2	.	.	PUNCT
ejpam-5646	243	1	let	let	VERB
ejpam-5646	243	2	x1	x1	NUM
ejpam-5646	243	3	,	,	PUNCT
ejpam-5646	243	4	.	.	PUNCT
ejpam-5646	243	5	.	.	PUNCT
ejpam-5646	244	1	.	.	PUNCT
ejpam-5646	245	1	,	,	PUNCT
ejpam-5646	245	2	xm	xm	PROPN
ejpam-5646	245	3	,	,	PUNCT
ejpam-5646	245	4	r	r	NOUN
ejpam-5646	245	5	,	,	PUNCT
ejpam-5646	245	6	y1	y1	NOUN
ejpam-5646	245	7	,	,	PUNCT
ejpam-5646	245	8	.	.	PUNCT
ejpam-5646	245	9	.	.	PUNCT
ejpam-5646	245	10	.	.	PUNCT
ejpam-5646	246	1	,	,	PUNCT
ejpam-5646	246	2	yn	yn	PROPN
ejpam-5646	246	3	∈	∈	PROPN
ejpam-5646	246	4	x1	x1	PROPN
ejpam-5646	246	5	,	,	PUNCT
ejpam-5646	246	6	z1	z1	PROPN
ejpam-5646	246	7	,	,	PUNCT
ejpam-5646	246	8	.	.	PUNCT
ejpam-5646	246	9	.	.	PUNCT
ejpam-5646	246	10	.	.	PUNCT
ejpam-5646	247	1	,	,	PUNCT
ejpam-5646	247	2	zm	zm	PROPN
ejpam-5646	247	3	,	,	PUNCT
ejpam-5646	247	4	r′	r′	PROPN
ejpam-5646	247	5	,	,	PUNCT
ejpam-5646	247	6	w1	w1	NOUN
ejpam-5646	247	7	,	,	PUNCT
ejpam-5646	247	8	.	.	PUNCT
ejpam-5646	247	9	.	.	PUNCT
ejpam-5646	248	1	.	.	PUNCT
ejpam-5646	249	1	,	,	PUNCT
ejpam-5646	249	2	wn	wn	PROPN
ejpam-5646	249	3	∈	∈	PROPN
ejpam-5646	249	4	x2	x2	PROPN
ejpam-5646	249	5	.	.	PUNCT
ejpam-5646	250	1	without	without	ADP
ejpam-5646	250	2	loss	loss	NOUN
ejpam-5646	250	3	of	of	ADP
ejpam-5646	250	4	generality	generality	NOUN
ejpam-5646	250	5	,	,	PUNCT
ejpam-5646	250	6	let	let	VERB
ejpam-5646	250	7	µ1	µ1	PROPN
ejpam-5646	250	8	be	be	AUX
ejpam-5646	250	9	a	a	DET
ejpam-5646	250	10	fuzzy	fuzzy	ADJ
ejpam-5646	250	11	(	(	PUNCT
ejpam-5646	250	12	m	m	NOUN
ejpam-5646	250	13	,	,	PUNCT
ejpam-5646	250	14	n)-bi	n)-bi	NOUN
ejpam-5646	250	15	-	-	PUNCT
ejpam-5646	250	16	antiideal	antiideal	NOUN
ejpam-5646	250	17	of	of	ADP
ejpam-5646	250	18	x1	x1	PROPN
ejpam-5646	250	19	.	.	PUNCT
ejpam-5646	251	1	then	then	ADV
ejpam-5646	251	2	µ((x1	µ((x1	NOUN
ejpam-5646	251	3	,	,	PUNCT
ejpam-5646	251	4	z1	z1	NOUN
ejpam-5646	251	5	)	)	PUNCT
ejpam-5646	251	6	.	.	PUNCT
ejpam-5646	251	7	.	.	PUNCT
ejpam-5646	251	8	.	.	PUNCT
ejpam-5646	252	1	(	(	PUNCT
ejpam-5646	252	2	xm	xm	INTJ
ejpam-5646	252	3	,	,	PUNCT
ejpam-5646	252	4	zm)(r	zm)(r	PROPN
ejpam-5646	252	5	,	,	PUNCT
ejpam-5646	252	6	r′)(y1	r′)(y1	PROPN
ejpam-5646	252	7	,	,	PUNCT
ejpam-5646	252	8	w1	w1	NOUN
ejpam-5646	252	9	)	)	PUNCT
ejpam-5646	252	10	.	.	PUNCT
ejpam-5646	252	11	.	.	PUNCT
ejpam-5646	252	12	.	.	PUNCT
ejpam-5646	253	1	(	(	PUNCT
ejpam-5646	253	2	yn	yn	INTJ
ejpam-5646	253	3	,	,	PUNCT
ejpam-5646	253	4	wn)∧µ((x1	wn)∧µ((x1	ADJ
ejpam-5646	253	5	,	,	PUNCT
ejpam-5646	253	6	z1))∧	z1))∧	PROPN
ejpam-5646	253	7	.	.	PUNCT
ejpam-5646	253	8	.	.	PUNCT
ejpam-5646	253	9	.	.	PUNCT
ejpam-5646	254	1	µ((xm	µ((xm	PROPN
ejpam-5646	254	2	,	,	PUNCT
ejpam-5646	254	3	zm))∧µ((y1	zm))∧µ((y1	PROPN
ejpam-5646	254	4	,	,	PUNCT
ejpam-5646	254	5	w1))∧	w1))∧	NOUN
ejpam-5646	254	6	.	.	PUNCT
ejpam-5646	254	7	.	.	PUNCT
ejpam-5646	255	1	.∧µ((yn	.∧µ((yn	PROPN
ejpam-5646	255	2	,	,	PUNCT
ejpam-5646	255	3	wn	wn	PROPN
ejpam-5646	255	4	)	)	PUNCT
ejpam-5646	255	5	)	)	PUNCT
ejpam-5646	255	6	≤	≤	PROPN
ejpam-5646	255	7	µ1(x1	µ1(x1	PROPN
ejpam-5646	255	8	.	.	PUNCT
ejpam-5646	255	9	.	.	PUNCT
ejpam-5646	255	10	.	.	PUNCT
ejpam-5646	256	1	xmry1	xmry1	PROPN
ejpam-5646	256	2	.	.	PUNCT
ejpam-5646	256	3	.	.	PUNCT
ejpam-5646	256	4	.	.	PUNCT
ejpam-5646	257	1	yn)∧µ1(x1)∧	yn)∧µ1(x1)∧	PROPN
ejpam-5646	257	2	.	.	PUNCT
ejpam-5646	257	3	.	.	PUNCT
ejpam-5646	257	4	.	.	PUNCT
ejpam-5646	258	1	µ1(xm)∧µ1(y1)∧	µ1(xm)∧µ1(y1)∧	NUM
ejpam-5646	258	2	.	.	PUNCT
ejpam-5646	258	3	.	.	PUNCT
ejpam-5646	259	1	.∧µ1(yn	.∧µ1(yn	PUNCT
ejpam-5646	259	2	)	)	PUNCT
ejpam-5646	260	1	=	=	SYM
ejpam-5646	260	2	0	0	X
ejpam-5646	260	3	.	.	PUNCT
ejpam-5646	260	4	theorem	theorem	NOUN
ejpam-5646	260	5	6	6	NUM
ejpam-5646	260	6	.	.	PUNCT
ejpam-5646	261	1	let	let	AUX
ejpam-5646	261	2	(	(	PUNCT
ejpam-5646	261	3	xi	xi	ADJ
ejpam-5646	261	4	,	,	PUNCT
ejpam-5646	261	5	·	·	PUNCT
ejpam-5646	261	6	)	)	PUNCT
ejpam-5646	261	7	be	be	AUX
ejpam-5646	261	8	a	a	DET
ejpam-5646	261	9	semigroup	semigroup	NOUN
ejpam-5646	261	10	for	for	ADP
ejpam-5646	261	11	i	i	PROPN
ejpam-5646	261	12	=	=	NOUN
ejpam-5646	261	13	1	1	NUM
ejpam-5646	261	14	,	,	PUNCT
ejpam-5646	261	15	2	2	NUM
ejpam-5646	261	16	,	,	PUNCT
ejpam-5646	261	17	.	.	PUNCT
ejpam-5646	261	18	.	.	PUNCT
ejpam-5646	262	1	.	.	PUNCT
ejpam-5646	263	1	,	,	PUNCT
ejpam-5646	263	2	k	k	PROPN
ejpam-5646	263	3	and	and	CCONJ
ejpam-5646	263	4	µi	µi	PROPN
ejpam-5646	263	5	be	be	AUX
ejpam-5646	263	6	a	a	DET
ejpam-5646	263	7	non	non	ADJ
ejpam-5646	263	8	-	-	ADJ
ejpam-5646	263	9	zero	zero	ADJ
ejpam-5646	263	10	fuzzy	fuzzy	ADJ
ejpam-5646	263	11	set	set	NOUN
ejpam-5646	263	12	of	of	ADP
ejpam-5646	263	13	xi	xi	PROPN
ejpam-5646	263	14	for	for	ADP
ejpam-5646	263	15	i	i	PRON
ejpam-5646	263	16	=	=	NOUN
ejpam-5646	263	17	1	1	NUM
ejpam-5646	263	18	,	,	PUNCT
ejpam-5646	263	19	.	.	PUNCT
ejpam-5646	263	20	.	.	PUNCT
ejpam-5646	264	1	.	.	PUNCT
ejpam-5646	265	1	,	,	PUNCT
ejpam-5646	265	2	k.	k.	PROPN
ejpam-5646	265	3	if	if	SCONJ
ejpam-5646	265	4	µi	µi	PROPN
ejpam-5646	265	5	is	be	AUX
ejpam-5646	265	6	a	a	DET
ejpam-5646	265	7	fuzzy	fuzzy	ADJ
ejpam-5646	265	8	(	(	PUNCT
ejpam-5646	265	9	m	m	NOUN
ejpam-5646	265	10	,	,	PUNCT
ejpam-5646	265	11	n)-bi	n)-bi	NOUN
ejpam-5646	265	12	-	-	PUNCT
ejpam-5646	265	13	antiideal	antiideal	NOUN
ejpam-5646	265	14	of	of	ADP
ejpam-5646	265	15	xi	xi	NUM
ejpam-5646	265	16	for	for	ADP
ejpam-5646	265	17	some	some	DET
ejpam-5646	265	18	i	i	PRON
ejpam-5646	265	19	∈	∈	PROPN
ejpam-5646	265	20	{	{	PUNCT
ejpam-5646	265	21	1	1	NUM
ejpam-5646	265	22	,	,	PUNCT
ejpam-5646	265	23	.	.	PUNCT
ejpam-5646	265	24	.	.	PUNCT
ejpam-5646	266	1	.	.	PUNCT
ejpam-5646	267	1	,	,	PUNCT
ejpam-5646	267	2	k	k	X
ejpam-5646	267	3	}	}	PUNCT
ejpam-5646	267	4	,	,	PUNCT
ejpam-5646	267	5	then	then	ADV
ejpam-5646	267	6	µ	µ	X
ejpam-5646	267	7	=	=	SYM
ejpam-5646	267	8	µ1	µ1	NOUN
ejpam-5646	267	9	×	×	NOUN
ejpam-5646	267	10	µ2	µ2	PROPN
ejpam-5646	267	11	×	×	NOUN
ejpam-5646	267	12	.	.	PUNCT
ejpam-5646	267	13	.	.	PUNCT
ejpam-5646	268	1	.×	.×	NOUN
ejpam-5646	268	2	µk	µk	PROPN
ejpam-5646	268	3	is	be	AUX
ejpam-5646	268	4	a	a	DET
ejpam-5646	268	5	fuzzy	fuzzy	ADJ
ejpam-5646	268	6	(	(	PUNCT
ejpam-5646	268	7	m	m	NOUN
ejpam-5646	268	8	,	,	PUNCT
ejpam-5646	268	9	n)-bi	n)-bi	NOUN
ejpam-5646	268	10	-	-	PUNCT
ejpam-5646	268	11	antiideal	antiideal	NOUN
ejpam-5646	268	12	of	of	ADP
ejpam-5646	268	13	x1	x1	PROPN
ejpam-5646	268	14	×	×	NOUN
ejpam-5646	268	15	.	.	PUNCT
ejpam-5646	268	16	.	.	PUNCT
ejpam-5646	269	1	.×xk	.×xk	NOUN
ejpam-5646	269	2	.	.	PUNCT
ejpam-5646	270	1	proof	proof	NOUN
ejpam-5646	270	2	.	.	PUNCT
ejpam-5646	271	1	the	the	DET
ejpam-5646	271	2	proof	proof	NOUN
ejpam-5646	271	3	is	be	AUX
ejpam-5646	271	4	similar	similar	ADJ
ejpam-5646	271	5	to	to	ADP
ejpam-5646	271	6	that	that	PRON
ejpam-5646	271	7	of	of	ADP
ejpam-5646	271	8	theorem	theorem	NOUN
ejpam-5646	271	9	5	5	NUM
ejpam-5646	271	10	.	.	PUNCT
ejpam-5646	272	1	next	next	ADV
ejpam-5646	272	2	,	,	PUNCT
ejpam-5646	272	3	we	we	PRON
ejpam-5646	272	4	link	link	VERB
ejpam-5646	272	5	fuzzy	fuzzy	ADJ
ejpam-5646	272	6	(	(	PUNCT
ejpam-5646	272	7	m	m	NOUN
ejpam-5646	272	8	,	,	PUNCT
ejpam-5646	272	9	n)-bi	n)-bi	NOUN
ejpam-5646	272	10	-	-	PUNCT
ejpam-5646	272	11	antiideals	antiideal	NOUN
ejpam-5646	272	12	of	of	ADP
ejpam-5646	272	13	a	a	DET
ejpam-5646	272	14	semigroup	semigroup	NOUN
ejpam-5646	272	15	x	x	X
ejpam-5646	272	16	to	to	ADP
ejpam-5646	272	17	(	(	PUNCT
ejpam-5646	272	18	m	m	NOUN
ejpam-5646	272	19	,	,	PUNCT
ejpam-5646	272	20	n)-bi	n)-bi	NOUN
ejpam-5646	272	21	-	-	PUNCT
ejpam-5646	272	22	antiideals	antiideal	NOUN
ejpam-5646	272	23	of	of	ADP
ejpam-5646	272	24	x.	x.	NOUN
ejpam-5646	272	25	theorem	theorem	VERB
ejpam-5646	272	26	7	7	NUM
ejpam-5646	272	27	.	.	PUNCT
ejpam-5646	273	1	let	let	AUX
ejpam-5646	273	2	(	(	PUNCT
ejpam-5646	273	3	x	x	NOUN
ejpam-5646	273	4	,	,	PUNCT
ejpam-5646	273	5	·	·	PUNCT
ejpam-5646	273	6	)	)	PUNCT
ejpam-5646	273	7	be	be	AUX
ejpam-5646	273	8	a	a	DET
ejpam-5646	273	9	semigroup	semigroup	NOUN
ejpam-5646	273	10	,	,	PUNCT
ejpam-5646	273	11	µ	µ	X
ejpam-5646	273	12	be	be	VERB
ejpam-5646	273	13	a	a	DET
ejpam-5646	273	14	non	non	ADJ
ejpam-5646	273	15	-	-	ADJ
ejpam-5646	273	16	zero	zero	ADJ
ejpam-5646	273	17	fuzzy	fuzzy	ADJ
ejpam-5646	273	18	set	set	NOUN
ejpam-5646	273	19	of	of	ADP
ejpam-5646	273	20	x	x	NOUN
ejpam-5646	273	21	,	,	PUNCT
ejpam-5646	273	22	and	and	CCONJ
ejpam-5646	273	23	t	t	PROPN
ejpam-5646	273	24	∈	∈	PROPN
ejpam-5646	274	1	[	[	X
ejpam-5646	274	2	0	0	NUM
ejpam-5646	274	3	,	,	PUNCT
ejpam-5646	274	4	1	1	NUM
ejpam-5646	274	5	]	]	PUNCT
ejpam-5646	274	6	.	.	PUNCT
ejpam-5646	275	1	then	then	ADV
ejpam-5646	275	2	µ	µ	X
ejpam-5646	275	3	is	be	AUX
ejpam-5646	275	4	a	a	DET
ejpam-5646	275	5	fuzzy	fuzzy	ADJ
ejpam-5646	275	6	(	(	PUNCT
ejpam-5646	275	7	m	m	NOUN
ejpam-5646	275	8	,	,	PUNCT
ejpam-5646	275	9	n)-bi	n)-bi	NOUN
ejpam-5646	275	10	-	-	PUNCT
ejpam-5646	275	11	antiideal	antiideal	NOUN
ejpam-5646	275	12	of	of	ADP
ejpam-5646	275	13	x	x	SYM
ejpam-5646	275	14	if	if	SCONJ
ejpam-5646	275	15	and	and	CCONJ
ejpam-5646	275	16	only	only	ADV
ejpam-5646	275	17	if	if	SCONJ
ejpam-5646	275	18	µt	µt	PRON
ejpam-5646	275	19	is	be	AUX
ejpam-5646	275	20	either	either	CCONJ
ejpam-5646	275	21	the	the	DET
ejpam-5646	275	22	empty	empty	ADJ
ejpam-5646	275	23	set	set	NOUN
ejpam-5646	275	24	or	or	CCONJ
ejpam-5646	275	25	an	an	DET
ejpam-5646	275	26	(	(	PUNCT
ejpam-5646	275	27	m	m	NOUN
ejpam-5646	275	28	,	,	PUNCT
ejpam-5646	275	29	n)-bi	n)-bi	NOUN
ejpam-5646	275	30	-	-	PUNCT
ejpam-5646	275	31	antiideal	antiideal	NOUN
ejpam-5646	275	32	of	of	ADP
ejpam-5646	275	33	x.	x.	NOUN
ejpam-5646	275	34	proof	proof	NOUN
ejpam-5646	275	35	.	.	PUNCT
ejpam-5646	276	1	let	let	VERB
ejpam-5646	276	2	µ	µ	X
ejpam-5646	276	3	be	be	AUX
ejpam-5646	276	4	a	a	DET
ejpam-5646	276	5	fuzzy	fuzzy	ADJ
ejpam-5646	276	6	(	(	PUNCT
ejpam-5646	276	7	m	m	NOUN
ejpam-5646	276	8	,	,	PUNCT
ejpam-5646	276	9	n)-bi	n)-bi	NOUN
ejpam-5646	276	10	-	-	PUNCT
ejpam-5646	276	11	antiideal	antiideal	NOUN
ejpam-5646	276	12	of	of	ADP
ejpam-5646	276	13	x	x	NOUN
ejpam-5646	276	14	,	,	PUNCT
ejpam-5646	276	15	and	and	CCONJ
ejpam-5646	276	16	α	α	PRON
ejpam-5646	276	17	∈	∈	PROPN
ejpam-5646	276	18	µm	µm	ADP
ejpam-5646	276	19	t	t	PROPN
ejpam-5646	276	20	xµn	xµn	PROPN
ejpam-5646	276	21	t	t	PROPN
ejpam-5646	276	22	∩	∩	NOUN
ejpam-5646	276	23	µt	µt	ADP
ejpam-5646	276	24	̸=	̸=	PROPN
ejpam-5646	276	25	∅.	∅.	VERB
ejpam-5646	276	26	then	then	ADV
ejpam-5646	276	27	there	there	PRON
ejpam-5646	276	28	exist	exist	VERB
ejpam-5646	276	29	x1	x1	PROPN
ejpam-5646	276	30	,	,	PUNCT
ejpam-5646	276	31	.	.	PUNCT
ejpam-5646	276	32	.	.	PUNCT
ejpam-5646	277	1	.	.	PUNCT
ejpam-5646	278	1	,	,	PUNCT
ejpam-5646	278	2	xm	xm	PROPN
ejpam-5646	278	3	,	,	PUNCT
ejpam-5646	278	4	y1	y1	PROPN
ejpam-5646	278	5	,	,	PUNCT
ejpam-5646	278	6	.	.	PUNCT
ejpam-5646	278	7	.	.	PUNCT
ejpam-5646	279	1	.	.	PUNCT
ejpam-5646	280	1	,	,	PUNCT
ejpam-5646	280	2	yn	yn	PROPN
ejpam-5646	280	3	∈	∈	PROPN
ejpam-5646	280	4	µt	µt	ADP
ejpam-5646	280	5	,	,	PUNCT
ejpam-5646	280	6	r	r	NOUN
ejpam-5646	280	7	∈	∈	PROPN
ejpam-5646	280	8	x	x	PUNCT
ejpam-5646	280	9	with	with	ADP
ejpam-5646	280	10	α	α	NOUN
ejpam-5646	280	11	=	=	SYM
ejpam-5646	280	12	x1	x1	PROPN
ejpam-5646	280	13	.	.	PUNCT
ejpam-5646	280	14	.	.	PUNCT
ejpam-5646	280	15	.	.	PUNCT
ejpam-5646	281	1	xmry1	xmry1	PROPN
ejpam-5646	281	2	.	.	PUNCT
ejpam-5646	281	3	.	.	PUNCT
ejpam-5646	281	4	.	.	PUNCT
ejpam-5646	282	1	yn	yn	INTJ
ejpam-5646	282	2	.	.	PUNCT
ejpam-5646	283	1	having	have	VERB
ejpam-5646	283	2	α	α	PRON
ejpam-5646	283	3	,	,	PUNCT
ejpam-5646	283	4	x1	x1	PROPN
ejpam-5646	283	5	,	,	PUNCT
ejpam-5646	283	6	.	.	PUNCT
ejpam-5646	283	7	.	.	PUNCT
ejpam-5646	284	1	.	.	PUNCT
ejpam-5646	285	1	,	,	PUNCT
ejpam-5646	285	2	xm	xm	PROPN
ejpam-5646	285	3	,	,	PUNCT
ejpam-5646	285	4	y1	y1	PROPN
ejpam-5646	285	5	,	,	PUNCT
ejpam-5646	285	6	.	.	PUNCT
ejpam-5646	285	7	.	.	PUNCT
ejpam-5646	286	1	.	.	PUNCT
ejpam-5646	287	1	,	,	PUNCT
ejpam-5646	287	2	yn	yn	PROPN
ejpam-5646	287	3	∈	∈	PROPN
ejpam-5646	287	4	µt	µt	PRON
ejpam-5646	287	5	implies	imply	VERB
ejpam-5646	287	6	that	that	SCONJ
ejpam-5646	287	7	0	0	NUM
ejpam-5646	287	8	=	=	NOUN
ejpam-5646	287	9	µ(x1	µ(x1	ADJ
ejpam-5646	287	10	.	.	PUNCT
ejpam-5646	287	11	.	.	PUNCT
ejpam-5646	287	12	.	.	PUNCT
ejpam-5646	288	1	xmry1	xmry1	PROPN
ejpam-5646	288	2	.	.	PUNCT
ejpam-5646	288	3	.	.	PUNCT
ejpam-5646	288	4	.	.	PUNCT
ejpam-5646	289	1	yn	yn	X
ejpam-5646	289	2	)	)	PUNCT
ejpam-5646	289	3	∧	∧	PROPN
ejpam-5646	289	4	µ(x1	µ(x1	ADJ
ejpam-5646	289	5	)	)	PUNCT
ejpam-5646	289	6	∧	∧	NOUN
ejpam-5646	289	7	.	.	PUNCT
ejpam-5646	289	8	.	.	PUNCT
ejpam-5646	289	9	.	.	PUNCT
ejpam-5646	290	1	∧	∧	PROPN
ejpam-5646	290	2	µ(xm	µ(xm	PROPN
ejpam-5646	290	3	)	)	PUNCT
ejpam-5646	290	4	∧	∧	NOUN
ejpam-5646	290	5	µ(y1	µ(y1	NOUN
ejpam-5646	290	6	)	)	PUNCT
ejpam-5646	290	7	∧	∧	NOUN
ejpam-5646	290	8	.	.	PUNCT
ejpam-5646	290	9	.	.	PUNCT
ejpam-5646	290	10	.	.	PUNCT
ejpam-5646	291	1	∧	∧	NOUN
ejpam-5646	291	2	µ(yn	µ(yn	PROPN
ejpam-5646	291	3	)	)	PUNCT
ejpam-5646	291	4	≥	≥	NOUN
ejpam-5646	291	5	t.	t.	NOUN
ejpam-5646	291	6	conversely	conversely	ADV
ejpam-5646	291	7	,	,	PUNCT
ejpam-5646	291	8	let	let	VERB
ejpam-5646	291	9	µ(x1	µ(x1	ADJ
ejpam-5646	291	10	.	.	PUNCT
ejpam-5646	291	11	.	.	PUNCT
ejpam-5646	291	12	.	.	PUNCT
ejpam-5646	292	1	xmry1	xmry1	PROPN
ejpam-5646	292	2	.	.	PUNCT
ejpam-5646	292	3	.	.	PUNCT
ejpam-5646	292	4	.	.	PUNCT
ejpam-5646	293	1	yn)∧µ(x1)∧	yn)∧µ(x1)∧	PROPN
ejpam-5646	293	2	.	.	PUNCT
ejpam-5646	293	3	.	.	PUNCT
ejpam-5646	294	1	.∧µ(xm)∧µ(y1)∧	.∧µ(xm)∧µ(y1)∧	PUNCT
ejpam-5646	294	2	.	.	PUNCT
ejpam-5646	294	3	.	.	PUNCT
ejpam-5646	295	1	.∧µ(yn	.∧µ(yn	PROPN
ejpam-5646	295	2	)	)	PUNCT
ejpam-5646	296	1	=	=	SYM
ejpam-5646	296	2	t	t	X
ejpam-5646	296	3	>	>	X
ejpam-5646	296	4	0	0	PROPN
ejpam-5646	296	5	.	.	PUNCT
ejpam-5646	297	1	then	then	ADV
ejpam-5646	297	2	x1	x1	INTJ
ejpam-5646	297	3	.	.	PUNCT
ejpam-5646	297	4	.	.	PUNCT
ejpam-5646	297	5	.	.	PUNCT
ejpam-5646	298	1	xmry1	xmry1	PROPN
ejpam-5646	298	2	.	.	PUNCT
ejpam-5646	298	3	.	.	PUNCT
ejpam-5646	298	4	.	.	PUNCT
ejpam-5646	299	1	yn	yn	INTJ
ejpam-5646	299	2	,	,	PUNCT
ejpam-5646	299	3	x1	x1	PROPN
ejpam-5646	299	4	,	,	PUNCT
ejpam-5646	299	5	.	.	PUNCT
ejpam-5646	299	6	.	.	PUNCT
ejpam-5646	299	7	.	.	PUNCT
ejpam-5646	300	1	,	,	PUNCT
ejpam-5646	300	2	xm	xm	PROPN
ejpam-5646	300	3	,	,	PUNCT
ejpam-5646	300	4	y1	y1	PROPN
ejpam-5646	300	5	,	,	PUNCT
ejpam-5646	300	6	.	.	PUNCT
ejpam-5646	300	7	.	.	PUNCT
ejpam-5646	301	1	.	.	PUNCT
ejpam-5646	302	1	,	,	PUNCT
ejpam-5646	302	2	yn	yn	PROPN
ejpam-5646	302	3	∈	∈	PROPN
ejpam-5646	302	4	µt	µt	ADP
ejpam-5646	302	5	̸=	̸=	PROPN
ejpam-5646	302	6	∅	∅	NOUN
ejpam-5646	302	7	and	and	CCONJ
ejpam-5646	302	8	hence	hence	ADV
ejpam-5646	302	9	,	,	PUNCT
ejpam-5646	302	10	x1	x1	PROPN
ejpam-5646	302	11	.	.	PUNCT
ejpam-5646	302	12	.	.	PUNCT
ejpam-5646	302	13	.	.	PUNCT
ejpam-5646	303	1	xmry1	xmry1	PROPN
ejpam-5646	303	2	.	.	PUNCT
ejpam-5646	303	3	.	.	PUNCT
ejpam-5646	303	4	.	.	PUNCT
ejpam-5646	304	1	yn	yn	PRON
ejpam-5646	304	2	∈	∈	PROPN
ejpam-5646	304	3	µm	µm	ADP
ejpam-5646	304	4	t	t	PROPN
ejpam-5646	304	5	xµn	xµn	PROPN
ejpam-5646	304	6	t	t	PROPN
ejpam-5646	304	7	∩	∩	NOUN
ejpam-5646	304	8	µt	µt	ADP
ejpam-5646	304	9	=	=	SYM
ejpam-5646	304	10	∅.	∅.	NOUN
ejpam-5646	304	11	theorem	theorem	ADJ
ejpam-5646	304	12	8	8	NUM
ejpam-5646	304	13	.	.	PUNCT
ejpam-5646	305	1	let	let	AUX
ejpam-5646	305	2	(	(	PUNCT
ejpam-5646	305	3	x	x	NOUN
ejpam-5646	305	4	,	,	PUNCT
ejpam-5646	305	5	·	·	PUNCT
ejpam-5646	305	6	)	)	PUNCT
ejpam-5646	305	7	be	be	AUX
ejpam-5646	305	8	a	a	DET
ejpam-5646	305	9	semigroup	semigroup	NOUN
ejpam-5646	305	10	.	.	PUNCT
ejpam-5646	306	1	then	then	ADV
ejpam-5646	306	2	every	every	DET
ejpam-5646	306	3	(	(	PUNCT
ejpam-5646	306	4	m	m	NOUN
ejpam-5646	306	5	,	,	PUNCT
ejpam-5646	306	6	n)-bi	n)-bi	NOUN
ejpam-5646	306	7	-	-	PUNCT
ejpam-5646	306	8	antiideal	antiideal	NOUN
ejpam-5646	306	9	of	of	ADP
ejpam-5646	306	10	x	x	PUNCT
ejpam-5646	306	11	can	can	AUX
ejpam-5646	306	12	be	be	AUX
ejpam-5646	306	13	represented	represent	VERB
ejpam-5646	306	14	as	as	ADP
ejpam-5646	306	15	a	a	DET
ejpam-5646	306	16	level	level	NOUN
ejpam-5646	306	17	set	set	NOUN
ejpam-5646	306	18	of	of	ADP
ejpam-5646	306	19	a	a	DET
ejpam-5646	306	20	fuzzy	fuzzy	ADJ
ejpam-5646	306	21	(	(	PUNCT
ejpam-5646	306	22	m	m	NOUN
ejpam-5646	306	23	,	,	PUNCT
ejpam-5646	306	24	n)-bi	n)-bi	NOUN
ejpam-5646	306	25	-	-	PUNCT
ejpam-5646	306	26	antiideal	antiideal	NOUN
ejpam-5646	306	27	of	of	ADP
ejpam-5646	306	28	x.	x.	NOUN
ejpam-5646	306	29	proof	proof	NOUN
ejpam-5646	306	30	.	.	PUNCT
ejpam-5646	307	1	let	let	VERB
ejpam-5646	307	2	a	a	DET
ejpam-5646	307	3	be	be	AUX
ejpam-5646	307	4	an	an	DET
ejpam-5646	307	5	(	(	PUNCT
ejpam-5646	307	6	m	m	NOUN
ejpam-5646	307	7	,	,	PUNCT
ejpam-5646	307	8	n)-bi	n)-bi	NOUN
ejpam-5646	307	9	-	-	PUNCT
ejpam-5646	307	10	antiideal	antiideal	NOUN
ejpam-5646	307	11	of	of	ADP
ejpam-5646	307	12	x	x	PUNCT
ejpam-5646	307	13	and	and	CCONJ
ejpam-5646	307	14	define	define	VERB
ejpam-5646	307	15	the	the	DET
ejpam-5646	307	16	fuzzy	fuzzy	ADJ
ejpam-5646	307	17	set	set	VERB
ejpam-5646	307	18	µ	µ	NOUN
ejpam-5646	307	19	of	of	ADP
ejpam-5646	307	20	x	x	PUNCT
ejpam-5646	307	21	as	as	SCONJ
ejpam-5646	307	22	follows	follow	VERB
ejpam-5646	307	23	.	.	PUNCT
ejpam-5646	308	1	µ(x	µ(x	VERB
ejpam-5646	308	2	)	)	PUNCT
ejpam-5646	308	3	=	=	SYM
ejpam-5646	308	4	{	{	PUNCT
ejpam-5646	308	5	0.94	0.94	NUM
ejpam-5646	308	6	if	if	SCONJ
ejpam-5646	308	7	x	x	PROPN
ejpam-5646	308	8	∈	∈	PROPN
ejpam-5646	308	9	a	a	X
ejpam-5646	308	10	;	;	PUNCT
ejpam-5646	308	11	0	0	NUM
ejpam-5646	308	12	otherwise	otherwise	ADV
ejpam-5646	308	13	.	.	PUNCT
ejpam-5646	309	1	one	one	PRON
ejpam-5646	309	2	can	can	AUX
ejpam-5646	309	3	easily	easily	ADV
ejpam-5646	309	4	see	see	VERB
ejpam-5646	309	5	that	that	PRON
ejpam-5646	309	6	µ0.94	µ0.94	PROPN
ejpam-5646	309	7	=	=	PROPN
ejpam-5646	309	8	a	a	PROPN
ejpam-5646	309	9	and	and	CCONJ
ejpam-5646	309	10	that	that	SCONJ
ejpam-5646	309	11	µ	µ	NOUN
ejpam-5646	309	12	is	be	AUX
ejpam-5646	309	13	a	a	DET
ejpam-5646	309	14	fuzzy	fuzzy	ADJ
ejpam-5646	309	15	(	(	PUNCT
ejpam-5646	309	16	m	m	NOUN
ejpam-5646	309	17	,	,	PUNCT
ejpam-5646	309	18	n)-bi	n)-bi	NOUN
ejpam-5646	309	19	-	-	PUNCT
ejpam-5646	309	20	antiideal	antiideal	NOUN
ejpam-5646	309	21	of	of	ADP
ejpam-5646	309	22	x.	x.	PROPN
ejpam-5646	309	23	m.	m.	PROPN
ejpam-5646	309	24	al	al	PROPN
ejpam-5646	309	25	tahan	tahan	PROPN
ejpam-5646	309	26	,	,	PUNCT
ejpam-5646	309	27	s.	s.	PROPN
ejpam-5646	309	28	hoskova	hoskova	PROPN
ejpam-5646	309	29	-	-	PUNCT
ejpam-5646	309	30	mayerova	mayerova	PROPN
ejpam-5646	309	31	,	,	PUNCT
ejpam-5646	309	32	s.	s.	PROPN
ejpam-5646	309	33	al	al	PROPN
ejpam-5646	309	34	-	-	PUNCT
ejpam-5646	309	35	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	309	36	/	/	SYM
ejpam-5646	309	37	eur	eur	NOUN
ejpam-5646	309	38	.	.	PUNCT
ejpam-5646	310	1	j.	j.	PROPN
ejpam-5646	310	2	pure	pure	PROPN
ejpam-5646	310	3	appl	appl	PROPN
ejpam-5646	310	4	.	.	PROPN
ejpam-5646	310	5	math	math	PROPN
ejpam-5646	310	6	,	,	PUNCT
ejpam-5646	310	7	18	18	NUM
ejpam-5646	310	8	(	(	PUNCT
ejpam-5646	310	9	1	1	NUM
ejpam-5646	310	10	)	)	PUNCT
ejpam-5646	310	11	(	(	PUNCT
ejpam-5646	310	12	2025	2025	NUM
ejpam-5646	310	13	)	)	PUNCT
ejpam-5646	310	14	,	,	PUNCT
ejpam-5646	310	15	5646	5646	NUM
ejpam-5646	310	16	9	9	NUM
ejpam-5646	310	17	of	of	ADP
ejpam-5646	310	18	11	11	NUM
ejpam-5646	310	19	corollary	corollary	ADJ
ejpam-5646	310	20	2	2	NUM
ejpam-5646	310	21	.	.	PUNCT
ejpam-5646	311	1	every	every	DET
ejpam-5646	311	2	fuzzy	fuzzy	ADJ
ejpam-5646	311	3	bi	bi	NOUN
ejpam-5646	311	4	-	-	NOUN
ejpam-5646	311	5	antiideal	antiideal	NOUN
ejpam-5646	311	6	of	of	ADP
ejpam-5646	311	7	a	a	DET
ejpam-5646	311	8	semigroup	semigroup	NOUN
ejpam-5646	311	9	x	x	X
ejpam-5646	311	10	is	be	AUX
ejpam-5646	311	11	a	a	DET
ejpam-5646	311	12	fuzzy	fuzzy	ADJ
ejpam-5646	311	13	(	(	PUNCT
ejpam-5646	311	14	m	m	NOUN
ejpam-5646	311	15	,	,	PUNCT
ejpam-5646	311	16	n)-bi	n)-bi	NOUN
ejpam-5646	311	17	-	-	PUNCT
ejpam-5646	311	18	antiideal	antiideal	NOUN
ejpam-5646	311	19	of	of	ADP
ejpam-5646	311	20	x.	x.	NOUN
ejpam-5646	311	21	proof	proof	NOUN
ejpam-5646	311	22	.	.	PUNCT
ejpam-5646	312	1	the	the	DET
ejpam-5646	312	2	proof	proof	NOUN
ejpam-5646	312	3	follows	follow	VERB
ejpam-5646	312	4	from	from	ADP
ejpam-5646	312	5	theorem	theorem	ADJ
ejpam-5646	312	6	1	1	NUM
ejpam-5646	312	7	,	,	PUNCT
ejpam-5646	312	8	proposition	proposition	NOUN
ejpam-5646	312	9	2	2	NUM
ejpam-5646	312	10	and	and	CCONJ
ejpam-5646	312	11	theorem	theorem	VERB
ejpam-5646	312	12	8	8	NUM
ejpam-5646	312	13	.	.	PUNCT
ejpam-5646	312	14	corollary	corollary	ADJ
ejpam-5646	312	15	3	3	NUM
ejpam-5646	312	16	.	.	PUNCT
ejpam-5646	313	1	every	every	DET
ejpam-5646	313	2	fuzzy	fuzzy	ADJ
ejpam-5646	313	3	left(right	left(right	PROPN
ejpam-5646	313	4	)	)	PUNCT
ejpam-5646	313	5	antiideal	antiideal	NOUN
ejpam-5646	313	6	is	be	AUX
ejpam-5646	313	7	a	a	DET
ejpam-5646	313	8	fuzzy	fuzzy	ADJ
ejpam-5646	313	9	(	(	PUNCT
ejpam-5646	313	10	m	m	NOUN
ejpam-5646	313	11	,	,	PUNCT
ejpam-5646	313	12	n)-bi	n)-bi	NOUN
ejpam-5646	313	13	-	-	PUNCT
ejpam-5646	313	14	antiideal	antiideal	NOUN
ejpam-5646	313	15	.	.	PUNCT
ejpam-5646	314	1	proof	proof	NOUN
ejpam-5646	314	2	.	.	PUNCT
ejpam-5646	315	1	the	the	DET
ejpam-5646	315	2	proof	proof	NOUN
ejpam-5646	315	3	follows	follow	VERB
ejpam-5646	315	4	from	from	ADP
ejpam-5646	315	5	proposition	proposition	NOUN
ejpam-5646	315	6	1	1	NUM
ejpam-5646	315	7	,	,	PUNCT
ejpam-5646	315	8	proposition	proposition	NOUN
ejpam-5646	315	9	2	2	NUM
ejpam-5646	315	10	,	,	PUNCT
ejpam-5646	315	11	and	and	CCONJ
ejpam-5646	315	12	theorem	theorem	VERB
ejpam-5646	315	13	8	8	NUM
ejpam-5646	315	14	.	.	PUNCT
ejpam-5646	316	1	theorem	theorem	NOUN
ejpam-5646	316	2	9	9	NUM
ejpam-5646	316	3	.	.	PUNCT
ejpam-5646	317	1	let	let	AUX
ejpam-5646	317	2	(	(	PUNCT
ejpam-5646	317	3	x	x	NOUN
ejpam-5646	317	4	,	,	PUNCT
ejpam-5646	317	5	·	·	PUNCT
ejpam-5646	317	6	)	)	PUNCT
ejpam-5646	317	7	be	be	AUX
ejpam-5646	317	8	a	a	DET
ejpam-5646	317	9	semigroup	semigroup	NOUN
ejpam-5646	317	10	and	and	CCONJ
ejpam-5646	317	11	a	a	DET
ejpam-5646	317	12	̸=	̸=	PROPN
ejpam-5646	317	13	∅	∅	NOUN
ejpam-5646	317	14	⊆	⊆	NUM
ejpam-5646	317	15	x.	x.	NOUN
ejpam-5646	317	16	then	then	ADV
ejpam-5646	317	17	a	a	PRON
ejpam-5646	317	18	is	be	AUX
ejpam-5646	317	19	an	an	DET
ejpam-5646	317	20	(	(	PUNCT
ejpam-5646	317	21	m	m	NOUN
ejpam-5646	317	22	,	,	PUNCT
ejpam-5646	317	23	n)-bi	n)-bi	NOUN
ejpam-5646	317	24	-	-	PUNCT
ejpam-5646	317	25	antiideal	antiideal	NOUN
ejpam-5646	317	26	of	of	ADP
ejpam-5646	317	27	x	x	SYM
ejpam-5646	317	28	if	if	SCONJ
ejpam-5646	317	29	and	and	CCONJ
ejpam-5646	317	30	only	only	ADV
ejpam-5646	317	31	if	if	SCONJ
ejpam-5646	317	32	µa	µa	NOUN
ejpam-5646	317	33	is	be	AUX
ejpam-5646	317	34	a	a	DET
ejpam-5646	317	35	fuzzy	fuzzy	ADJ
ejpam-5646	317	36	(	(	PUNCT
ejpam-5646	317	37	m	m	NOUN
ejpam-5646	317	38	,	,	PUNCT
ejpam-5646	317	39	n)-bi	n)-bi	NOUN
ejpam-5646	317	40	-	-	PUNCT
ejpam-5646	317	41	antiideal	antiideal	NOUN
ejpam-5646	317	42	of	of	ADP
ejpam-5646	317	43	x.	x.	NOUN
ejpam-5646	317	44	here	here	ADV
ejpam-5646	317	45	,	,	PUNCT
ejpam-5646	317	46	for	for	ADP
ejpam-5646	317	47	all	all	DET
ejpam-5646	317	48	x	x	SYM
ejpam-5646	317	49	∈	∈	PROPN
ejpam-5646	317	50	x	x	NOUN
ejpam-5646	317	51	,	,	PUNCT
ejpam-5646	317	52	µa(x	µa(x	ADV
ejpam-5646	317	53	)	)	PUNCT
ejpam-5646	317	54	=	=	PRON
ejpam-5646	317	55	{	{	PUNCT
ejpam-5646	317	56	1	1	NUM
ejpam-5646	317	57	if	if	SCONJ
ejpam-5646	317	58	x	x	PROPN
ejpam-5646	317	59	∈	∈	PROPN
ejpam-5646	317	60	a	a	X
ejpam-5646	317	61	;	;	PUNCT
ejpam-5646	317	62	0	0	NUM
ejpam-5646	317	63	otherwise	otherwise	ADV
ejpam-5646	317	64	.	.	PUNCT
ejpam-5646	318	1	proof	proof	NOUN
ejpam-5646	318	2	.	.	PUNCT
ejpam-5646	319	1	let	let	VERB
ejpam-5646	319	2	a	a	DET
ejpam-5646	319	3	be	be	AUX
ejpam-5646	319	4	an	an	DET
ejpam-5646	319	5	(	(	PUNCT
ejpam-5646	319	6	m	m	NOUN
ejpam-5646	319	7	,	,	PUNCT
ejpam-5646	319	8	n)-bi	n)-bi	NOUN
ejpam-5646	319	9	-	-	PUNCT
ejpam-5646	319	10	antiideal	antiideal	NOUN
ejpam-5646	319	11	of	of	ADP
ejpam-5646	319	12	x	x	PROPN
ejpam-5646	319	13	and	and	CCONJ
ejpam-5646	319	14	x1	x1	NUM
ejpam-5646	319	15	,	,	PUNCT
ejpam-5646	319	16	.	.	PUNCT
ejpam-5646	319	17	.	.	PUNCT
ejpam-5646	320	1	.	.	PUNCT
ejpam-5646	321	1	,	,	PUNCT
ejpam-5646	321	2	xm	xm	PROPN
ejpam-5646	321	3	,	,	PUNCT
ejpam-5646	321	4	r	r	NOUN
ejpam-5646	321	5	,	,	PUNCT
ejpam-5646	321	6	y1	y1	NOUN
ejpam-5646	321	7	,	,	PUNCT
ejpam-5646	321	8	.	.	PUNCT
ejpam-5646	321	9	.	.	PUNCT
ejpam-5646	321	10	.	.	PUNCT
ejpam-5646	322	1	,	,	PUNCT
ejpam-5646	322	2	yn	yn	PROPN
ejpam-5646	322	3	∈	∈	PROPN
ejpam-5646	322	4	x.	x.	NOUN
ejpam-5646	323	1	if	if	SCONJ
ejpam-5646	323	2	there	there	PRON
ejpam-5646	323	3	exist	exist	VERB
ejpam-5646	323	4	i	i	PRON
ejpam-5646	323	5	∈	∈	PROPN
ejpam-5646	323	6	{	{	PUNCT
ejpam-5646	323	7	1	1	NUM
ejpam-5646	323	8	,	,	PUNCT
ejpam-5646	323	9	.	.	PUNCT
ejpam-5646	324	1	.	.	PUNCT
ejpam-5646	324	2	.	.	PUNCT
ejpam-5646	325	1	,	,	PUNCT
ejpam-5646	325	2	m	m	VERB
ejpam-5646	325	3	}	}	PUNCT
ejpam-5646	325	4	or	or	CCONJ
ejpam-5646	325	5	j	j	PROPN
ejpam-5646	325	6	∈	∈	PROPN
ejpam-5646	325	7	{	{	PUNCT
ejpam-5646	325	8	1	1	NUM
ejpam-5646	325	9	,	,	PUNCT
ejpam-5646	325	10	.	.	PUNCT
ejpam-5646	325	11	.	.	PUNCT
ejpam-5646	325	12	.	.	PUNCT
ejpam-5646	326	1	,	,	PUNCT
ejpam-5646	326	2	n	n	CCONJ
ejpam-5646	326	3	}	}	PUNCT
ejpam-5646	326	4	with	with	ADP
ejpam-5646	326	5	xi	xi	PROPN
ejpam-5646	326	6	/∈	/∈	PROPN
ejpam-5646	327	1	a	a	PRON
ejpam-5646	327	2	or	or	CCONJ
ejpam-5646	327	3	yj	yj	PROPN
ejpam-5646	327	4	/∈	/∈	PROPN
ejpam-5646	328	1	a	a	PRON
ejpam-5646	328	2	,	,	PUNCT
ejpam-5646	328	3	then	then	ADV
ejpam-5646	328	4	µa(x1	µa(x1	VERB
ejpam-5646	328	5	.	.	PUNCT
ejpam-5646	328	6	.	.	PUNCT
ejpam-5646	328	7	.	.	PUNCT
ejpam-5646	329	1	xmry1	xmry1	PROPN
ejpam-5646	329	2	.	.	PUNCT
ejpam-5646	329	3	.	.	PUNCT
ejpam-5646	329	4	.	.	PUNCT
ejpam-5646	330	1	yn)∧	yn)∧	ADJ
ejpam-5646	330	2	µa(x1)∧	µa(x1)∧	PROPN
ejpam-5646	330	3	.	.	PUNCT
ejpam-5646	330	4	.	.	PUNCT
ejpam-5646	331	1	.∧µa(xm)∧µa(y1)∧	.∧µa(xm)∧µa(y1)∧	INTJ
ejpam-5646	331	2	.	.	PUNCT
ejpam-5646	331	3	.	.	PUNCT
ejpam-5646	332	1	.∧µa(yn	.∧µa(yn	X
ejpam-5646	332	2	)	)	PUNCT
ejpam-5646	333	1	=	=	SYM
ejpam-5646	333	2	0	0	X
ejpam-5646	333	3	.	.	PUNCT
ejpam-5646	334	1	otherwise	otherwise	ADV
ejpam-5646	334	2	and	and	CCONJ
ejpam-5646	334	3	having	have	VERB
ejpam-5646	334	4	amxan∩a	amxan∩a	PROPN
ejpam-5646	334	5	=	=	NOUN
ejpam-5646	334	6	∅	∅	NOUN
ejpam-5646	334	7	implies	imply	VERB
ejpam-5646	334	8	that	that	SCONJ
ejpam-5646	334	9	x1	x1	PROPN
ejpam-5646	334	10	.	.	PUNCT
ejpam-5646	334	11	.	.	PUNCT
ejpam-5646	334	12	.	.	PUNCT
ejpam-5646	335	1	xmry1	xmry1	PROPN
ejpam-5646	335	2	.	.	PUNCT
ejpam-5646	335	3	.	.	PUNCT
ejpam-5646	335	4	.	.	PUNCT
ejpam-5646	336	1	yn	yn	INTJ
ejpam-5646	336	2	/∈	/∈	PUNCT
ejpam-5646	337	1	a	a	PRON
ejpam-5646	337	2	and	and	CCONJ
ejpam-5646	337	3	hence	hence	ADV
ejpam-5646	337	4	,	,	PUNCT
ejpam-5646	337	5	µa(x1	µa(x1	INTJ
ejpam-5646	337	6	.	.	PUNCT
ejpam-5646	337	7	.	.	PUNCT
ejpam-5646	337	8	.	.	PUNCT
ejpam-5646	338	1	xmry1	xmry1	PROPN
ejpam-5646	338	2	.	.	PUNCT
ejpam-5646	338	3	.	.	PUNCT
ejpam-5646	338	4	.	.	PUNCT
ejpam-5646	339	1	yn)∧µa(x1)∧µa(xm)∧	yn)∧µa(x1)∧µa(xm)∧	PROPN
ejpam-5646	339	2	µa(y1	µa(y1	NOUN
ejpam-5646	339	3	)	)	PUNCT
ejpam-5646	339	4	∧	∧	PROPN
ejpam-5646	339	5	µa(yn	µa(yn	NOUN
ejpam-5646	339	6	)	)	PUNCT
ejpam-5646	340	1	=	=	SYM
ejpam-5646	340	2	0	0	X
ejpam-5646	340	3	.	.	PUNCT
ejpam-5646	341	1	conversely	conversely	ADV
ejpam-5646	341	2	,	,	PUNCT
ejpam-5646	341	3	let	let	VERB
ejpam-5646	341	4	µa	µa	PART
ejpam-5646	341	5	be	be	AUX
ejpam-5646	341	6	a	a	DET
ejpam-5646	341	7	fuzzy	fuzzy	ADJ
ejpam-5646	341	8	(	(	PUNCT
ejpam-5646	341	9	m	m	NOUN
ejpam-5646	341	10	,	,	PUNCT
ejpam-5646	341	11	n)-bi	n)-bi	NOUN
ejpam-5646	341	12	-	-	PUNCT
ejpam-5646	341	13	antiideal	antiideal	NOUN
ejpam-5646	341	14	of	of	ADP
ejpam-5646	341	15	x	x	PUNCT
ejpam-5646	341	16	and	and	CCONJ
ejpam-5646	341	17	α	α	PROPN
ejpam-5646	341	18	∈	∈	PROPN
ejpam-5646	341	19	amxan	amxan	NOUN
ejpam-5646	341	20	∩	∩	NOUN
ejpam-5646	341	21	a.	a.	NOUN
ejpam-5646	341	22	then	then	ADV
ejpam-5646	341	23	there	there	PRON
ejpam-5646	341	24	exist	exist	VERB
ejpam-5646	341	25	x1	x1	PROPN
ejpam-5646	341	26	,	,	PUNCT
ejpam-5646	341	27	.	.	PUNCT
ejpam-5646	341	28	.	.	PUNCT
ejpam-5646	342	1	.	.	PUNCT
ejpam-5646	343	1	,	,	PUNCT
ejpam-5646	343	2	xm	xm	PROPN
ejpam-5646	343	3	,	,	PUNCT
ejpam-5646	343	4	y1	y1	PROPN
ejpam-5646	343	5	,	,	PUNCT
ejpam-5646	343	6	.	.	PUNCT
ejpam-5646	343	7	.	.	PUNCT
ejpam-5646	344	1	.	.	PUNCT
ejpam-5646	345	1	,	,	PUNCT
ejpam-5646	345	2	yn	yn	PROPN
ejpam-5646	345	3	∈	∈	PROPN
ejpam-5646	345	4	a	a	PRON
ejpam-5646	345	5	,	,	PUNCT
ejpam-5646	345	6	r	r	NOUN
ejpam-5646	345	7	∈	∈	PROPN
ejpam-5646	345	8	x	x	PUNCT
ejpam-5646	345	9	with	with	ADP
ejpam-5646	345	10	α	α	NOUN
ejpam-5646	345	11	=	=	SYM
ejpam-5646	345	12	x1	x1	PROPN
ejpam-5646	345	13	.	.	PUNCT
ejpam-5646	345	14	.	.	PUNCT
ejpam-5646	345	15	.	.	PUNCT
ejpam-5646	346	1	xmry1	xmry1	PROPN
ejpam-5646	346	2	.	.	PUNCT
ejpam-5646	346	3	.	.	PUNCT
ejpam-5646	346	4	.	.	PUNCT
ejpam-5646	347	1	yn	yn	PRON
ejpam-5646	347	2	∈	∈	PROPN
ejpam-5646	347	3	a.	a.	NOUN
ejpam-5646	347	4	the	the	DET
ejpam-5646	347	5	latter	latter	ADJ
ejpam-5646	347	6	implies	imply	VERB
ejpam-5646	347	7	that	that	SCONJ
ejpam-5646	347	8	µa(x1	µa(x1	VERB
ejpam-5646	347	9	.	.	PUNCT
ejpam-5646	347	10	.	.	PUNCT
ejpam-5646	347	11	.	.	PUNCT
ejpam-5646	348	1	xmry1	xmry1	PROPN
ejpam-5646	348	2	.	.	PUNCT
ejpam-5646	348	3	.	.	PUNCT
ejpam-5646	348	4	.	.	PUNCT
ejpam-5646	349	1	yn	yn	X
ejpam-5646	349	2	)	)	PUNCT
ejpam-5646	349	3	∧	∧	PROPN
ejpam-5646	349	4	µa(x1	µa(x1	NOUN
ejpam-5646	349	5	)	)	PUNCT
ejpam-5646	349	6	∧	∧	PROPN
ejpam-5646	349	7	µa(xm	µa(xm	NOUN
ejpam-5646	349	8	)	)	PUNCT
ejpam-5646	349	9	∧	∧	NOUN
ejpam-5646	349	10	µa(y1	µa(y1	NOUN
ejpam-5646	349	11	)	)	PUNCT
ejpam-5646	349	12	∧	∧	NOUN
ejpam-5646	349	13	µa(yn	µa(yn	NOUN
ejpam-5646	349	14	)	)	PUNCT
ejpam-5646	349	15	=	=	SYM
ejpam-5646	349	16	1	1	NUM
ejpam-5646	349	17	̸=	̸=	PROPN
ejpam-5646	349	18	0	0	NUM
ejpam-5646	349	19	.	.	PROPN
ejpam-5646	350	1	5	5	NUM
ejpam-5646	350	2	.	.	X
ejpam-5646	350	3	conclusion	conclusion	NOUN
ejpam-5646	350	4	in	in	ADP
ejpam-5646	350	5	this	this	DET
ejpam-5646	350	6	paper	paper	NOUN
ejpam-5646	350	7	,	,	PUNCT
ejpam-5646	350	8	we	we	PRON
ejpam-5646	350	9	have	have	AUX
ejpam-5646	350	10	extended	extend	VERB
ejpam-5646	350	11	the	the	DET
ejpam-5646	350	12	theory	theory	NOUN
ejpam-5646	350	13	of	of	ADP
ejpam-5646	350	14	semigroups	semigroup	NOUN
ejpam-5646	350	15	by	by	ADP
ejpam-5646	350	16	introducing	introduce	VERB
ejpam-5646	350	17	and	and	CCONJ
ejpam-5646	350	18	characterizing	characterizing	NOUN
ejpam-5646	350	19	(	(	PUNCT
ejpam-5646	350	20	m	m	NOUN
ejpam-5646	350	21	,	,	PUNCT
ejpam-5646	350	22	n)-bi	n)-bi	NOUN
ejpam-5646	350	23	-	-	PUNCT
ejpam-5646	350	24	antiideals	antiideal	NOUN
ejpam-5646	350	25	and	and	CCONJ
ejpam-5646	350	26	their	their	PRON
ejpam-5646	350	27	fuzzy	fuzzy	ADJ
ejpam-5646	350	28	counterparts	counterpart	NOUN
ejpam-5646	350	29	.	.	PUNCT
ejpam-5646	351	1	our	our	PRON
ejpam-5646	351	2	exploration	exploration	NOUN
ejpam-5646	351	3	began	begin	VERB
ejpam-5646	351	4	with	with	ADP
ejpam-5646	351	5	a	a	DET
ejpam-5646	351	6	review	review	NOUN
ejpam-5646	351	7	of	of	ADP
ejpam-5646	351	8	the	the	DET
ejpam-5646	351	9	foundational	foundational	ADJ
ejpam-5646	351	10	concepts	concept	NOUN
ejpam-5646	351	11	of	of	ADP
ejpam-5646	351	12	antiideals	antiideal	NOUN
ejpam-5646	351	13	and	and	CCONJ
ejpam-5646	351	14	bi	bi	NOUN
ejpam-5646	351	15	-	-	NOUN
ejpam-5646	351	16	antiideals	antiideal	NOUN
ejpam-5646	351	17	,	,	PUNCT
ejpam-5646	351	18	followed	follow	VERB
ejpam-5646	351	19	by	by	ADP
ejpam-5646	351	20	the	the	DET
ejpam-5646	351	21	generalization	generalization	NOUN
ejpam-5646	351	22	to	to	ADP
ejpam-5646	351	23	(	(	PUNCT
ejpam-5646	351	24	m	m	NOUN
ejpam-5646	351	25	,	,	PUNCT
ejpam-5646	351	26	n)-bi	n)-bi	NOUN
ejpam-5646	351	27	-	-	PUNCT
ejpam-5646	351	28	antiideals	antiideal	NOUN
ejpam-5646	351	29	.	.	PUNCT
ejpam-5646	352	1	we	we	PRON
ejpam-5646	352	2	demonstrated	demonstrate	VERB
ejpam-5646	352	3	the	the	DET
ejpam-5646	352	4	properties	property	NOUN
ejpam-5646	352	5	of	of	ADP
ejpam-5646	352	6	these	these	DET
ejpam-5646	352	7	new	new	ADJ
ejpam-5646	352	8	structures	structure	NOUN
ejpam-5646	352	9	through	through	ADP
ejpam-5646	352	10	various	various	ADJ
ejpam-5646	352	11	propositions	proposition	NOUN
ejpam-5646	352	12	and	and	CCONJ
ejpam-5646	352	13	examples	example	NOUN
ejpam-5646	352	14	.	.	PUNCT
ejpam-5646	353	1	furthermore	furthermore	ADV
ejpam-5646	353	2	,	,	PUNCT
ejpam-5646	353	3	we	we	PRON
ejpam-5646	353	4	incorporated	incorporate	VERB
ejpam-5646	353	5	fuzzy	fuzzy	ADJ
ejpam-5646	353	6	set	set	NOUN
ejpam-5646	353	7	theory	theory	NOUN
ejpam-5646	353	8	to	to	PART
ejpam-5646	353	9	handle	handle	VERB
ejpam-5646	353	10	uncertainties	uncertainty	NOUN
ejpam-5646	353	11	in	in	ADP
ejpam-5646	353	12	semigroups	semigroup	NOUN
ejpam-5646	353	13	,	,	PUNCT
ejpam-5646	353	14	defining	define	VERB
ejpam-5646	353	15	and	and	CCONJ
ejpam-5646	353	16	analyzing	analyze	VERB
ejpam-5646	353	17	fuzzy	fuzzy	ADJ
ejpam-5646	353	18	(	(	PUNCT
ejpam-5646	353	19	m	m	NOUN
ejpam-5646	353	20	,	,	PUNCT
ejpam-5646	353	21	n)-bi	n)-bi	NOUN
ejpam-5646	353	22	-	-	PUNCT
ejpam-5646	353	23	antiideals	antiideal	NOUN
ejpam-5646	353	24	.	.	PUNCT
ejpam-5646	354	1	we	we	PRON
ejpam-5646	354	2	established	establish	VERB
ejpam-5646	354	3	connections	connection	NOUN
ejpam-5646	354	4	between	between	ADP
ejpam-5646	354	5	fuzzy	fuzzy	ADJ
ejpam-5646	354	6	(	(	PUNCT
ejpam-5646	354	7	m	m	NOUN
ejpam-5646	354	8	,	,	PUNCT
ejpam-5646	354	9	n)-bi	n)-bi	NOUN
ejpam-5646	354	10	-	-	PUNCT
ejpam-5646	354	11	antiideals	antiideal	NOUN
ejpam-5646	354	12	and	and	CCONJ
ejpam-5646	354	13	their	their	PRON
ejpam-5646	354	14	classical	classical	ADJ
ejpam-5646	354	15	counterparts	counterpart	NOUN
ejpam-5646	354	16	using	use	VERB
ejpam-5646	354	17	level	level	NOUN
ejpam-5646	354	18	sets	set	NOUN
ejpam-5646	354	19	,	,	PUNCT
ejpam-5646	354	20	providing	provide	VERB
ejpam-5646	354	21	a	a	DET
ejpam-5646	354	22	comprehensive	comprehensive	ADJ
ejpam-5646	354	23	framework	framework	NOUN
ejpam-5646	354	24	for	for	ADP
ejpam-5646	354	25	understanding	understand	VERB
ejpam-5646	354	26	these	these	DET
ejpam-5646	354	27	concepts	concept	NOUN
ejpam-5646	354	28	.	.	PUNCT
ejpam-5646	355	1	our	our	PRON
ejpam-5646	355	2	findings	finding	NOUN
ejpam-5646	355	3	contribute	contribute	VERB
ejpam-5646	355	4	to	to	ADP
ejpam-5646	355	5	the	the	DET
ejpam-5646	355	6	broader	broad	ADJ
ejpam-5646	355	7	understanding	understanding	NOUN
ejpam-5646	355	8	of	of	ADP
ejpam-5646	355	9	semigroups	semigroup	NOUN
ejpam-5646	355	10	and	and	CCONJ
ejpam-5646	355	11	their	their	PRON
ejpam-5646	355	12	applications	application	NOUN
ejpam-5646	355	13	in	in	ADP
ejpam-5646	355	14	different	different	ADJ
ejpam-5646	355	15	fields	field	NOUN
ejpam-5646	355	16	of	of	ADP
ejpam-5646	355	17	mathematics	mathematic	NOUN
ejpam-5646	355	18	and	and	CCONJ
ejpam-5646	355	19	science	science	NOUN
ejpam-5646	355	20	.	.	PUNCT
ejpam-5646	356	1	future	future	ADJ
ejpam-5646	356	2	research	research	NOUN
ejpam-5646	356	3	could	could	AUX
ejpam-5646	356	4	focus	focus	VERB
ejpam-5646	356	5	on	on	ADP
ejpam-5646	356	6	exploring	explore	VERB
ejpam-5646	356	7	additional	additional	ADJ
ejpam-5646	356	8	properties	property	NOUN
ejpam-5646	356	9	of	of	ADP
ejpam-5646	356	10	(	(	PUNCT
ejpam-5646	356	11	m	m	PROPN
ejpam-5646	356	12	,	,	PUNCT
ejpam-5646	356	13	n)-bi	n)-bi	NOUN
ejpam-5646	356	14	-	-	PUNCT
ejpam-5646	356	15	antiideals	antiideal	NOUN
ejpam-5646	356	16	,	,	PUNCT
ejpam-5646	356	17	identifying	identify	VERB
ejpam-5646	356	18	all	all	DET
ejpam-5646	356	19	antiideals	antiideal	NOUN
ejpam-5646	356	20	in	in	ADP
ejpam-5646	356	21	specific	specific	ADJ
ejpam-5646	356	22	semigroups	semigroup	NOUN
ejpam-5646	356	23	,	,	PUNCT
ejpam-5646	356	24	extending	extend	VERB
ejpam-5646	356	25	the	the	DET
ejpam-5646	356	26	theory	theory	NOUN
ejpam-5646	356	27	to	to	ADP
ejpam-5646	356	28	other	other	ADJ
ejpam-5646	356	29	algebraic	algebraic	ADJ
ejpam-5646	356	30	structures	structure	NOUN
ejpam-5646	356	31	,	,	PUNCT
ejpam-5646	356	32	and	and	CCONJ
ejpam-5646	356	33	finding	find	VERB
ejpam-5646	356	34	practical	practical	ADJ
ejpam-5646	356	35	applications	application	NOUN
ejpam-5646	356	36	for	for	ADP
ejpam-5646	356	37	these	these	DET
ejpam-5646	356	38	theoretical	theoretical	ADJ
ejpam-5646	356	39	concepts	concept	NOUN
ejpam-5646	356	40	.	.	PUNCT
ejpam-5646	357	1	by	by	ADP
ejpam-5646	357	2	advancing	advance	VERB
ejpam-5646	357	3	the	the	DET
ejpam-5646	357	4	study	study	NOUN
ejpam-5646	357	5	of	of	ADP
ejpam-5646	357	6	semigroups	semigroup	NOUN
ejpam-5646	357	7	and	and	CCONJ
ejpam-5646	357	8	their	their	PRON
ejpam-5646	357	9	fuzzy	fuzzy	ADJ
ejpam-5646	357	10	generalizations	generalization	NOUN
ejpam-5646	357	11	,	,	PUNCT
ejpam-5646	357	12	we	we	PRON
ejpam-5646	357	13	hope	hope	VERB
ejpam-5646	357	14	to	to	PART
ejpam-5646	357	15	inspire	inspire	VERB
ejpam-5646	357	16	further	further	ADJ
ejpam-5646	357	17	investigations	investigation	NOUN
ejpam-5646	357	18	and	and	CCONJ
ejpam-5646	357	19	applications	application	NOUN
ejpam-5646	357	20	in	in	ADP
ejpam-5646	357	21	both	both	CCONJ
ejpam-5646	357	22	theoretical	theoretical	ADJ
ejpam-5646	357	23	and	and	CCONJ
ejpam-5646	357	24	applied	applied	ADJ
ejpam-5646	357	25	mathematics	mathematic	NOUN
ejpam-5646	357	26	.	.	PUNCT
ejpam-5646	358	1	m.	m.	NOUN
ejpam-5646	358	2	al	al	PROPN
ejpam-5646	358	3	tahan	tahan	PROPN
ejpam-5646	358	4	,	,	PUNCT
ejpam-5646	358	5	s.	s.	PROPN
ejpam-5646	358	6	hoskova	hoskova	PROPN
ejpam-5646	358	7	-	-	PUNCT
ejpam-5646	358	8	mayerova	mayerova	PROPN
ejpam-5646	358	9	,	,	PUNCT
ejpam-5646	358	10	s.	s.	PROPN
ejpam-5646	358	11	al	al	PROPN
ejpam-5646	358	12	-	-	PUNCT
ejpam-5646	358	13	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	358	14	/	/	SYM
ejpam-5646	358	15	eur	eur	NOUN
ejpam-5646	358	16	.	.	PUNCT
ejpam-5646	359	1	j.	j.	PROPN
ejpam-5646	359	2	pure	pure	PROPN
ejpam-5646	359	3	appl	appl	PROPN
ejpam-5646	359	4	.	.	PROPN
ejpam-5646	359	5	math	math	PROPN
ejpam-5646	359	6	,	,	PUNCT
ejpam-5646	359	7	18	18	NUM
ejpam-5646	359	8	(	(	PUNCT
ejpam-5646	359	9	1	1	NUM
ejpam-5646	359	10	)	)	PUNCT
ejpam-5646	359	11	(	(	PUNCT
ejpam-5646	359	12	2025	2025	NUM
ejpam-5646	359	13	)	)	PUNCT
ejpam-5646	359	14	,	,	PUNCT
ejpam-5646	359	15	5646	5646	NUM
ejpam-5646	359	16	10	10	NUM
ejpam-5646	359	17	of	of	ADP
ejpam-5646	359	18	11	11	NUM
ejpam-5646	359	19	acknowledgements	acknowledgement	NOUN
ejpam-5646	359	20	this	this	DET
ejpam-5646	359	21	research	research	NOUN
ejpam-5646	359	22	was	be	AUX
ejpam-5646	359	23	supported	support	VERB
ejpam-5646	359	24	by	by	ADP
ejpam-5646	359	25	abu	abu	PROPN
ejpam-5646	359	26	dhabi	dhabi	PROPN
ejpam-5646	359	27	university	university	PROPN
ejpam-5646	359	28	with	with	ADP
ejpam-5646	359	29	grant	grant	NOUN
ejpam-5646	359	30	number	number	NOUN
ejpam-5646	359	31	:	:	PUNCT
ejpam-5646	359	32	19300884	19300884	NUM
ejpam-5646	359	33	.	.	PUNCT
ejpam-5646	360	1	this	this	DET
ejpam-5646	360	2	research	research	NOUN
ejpam-5646	360	3	(	(	PUNCT
ejpam-5646	360	4	apc	apc	PROPN
ejpam-5646	360	5	)	)	PUNCT
ejpam-5646	360	6	was	be	AUX
ejpam-5646	360	7	also	also	ADV
ejpam-5646	360	8	supported	support	VERB
ejpam-5646	360	9	by	by	ADP
ejpam-5646	360	10	the	the	DET
ejpam-5646	360	11	grant	grant	NOUN
ejpam-5646	360	12	varops	varop	NOUN
ejpam-5646	360	13	granted	grant	VERB
ejpam-5646	360	14	by	by	ADP
ejpam-5646	360	15	the	the	DET
ejpam-5646	360	16	ministry	ministry	PROPN
ejpam-5646	360	17	of	of	ADP
ejpam-5646	360	18	defence	defence	PROPN
ejpam-5646	360	19	of	of	ADP
ejpam-5646	360	20	the	the	DET
ejpam-5646	360	21	czech	czech	PROPN
ejpam-5646	360	22	republic	republic	NOUN
ejpam-5646	360	23	.	.	PUNCT
ejpam-5646	361	1	the	the	DET
ejpam-5646	361	2	authors	author	NOUN
ejpam-5646	361	3	declare	declare	VERB
ejpam-5646	361	4	no	no	DET
ejpam-5646	361	5	conflict	conflict	NOUN
ejpam-5646	361	6	of	of	ADP
ejpam-5646	361	7	interest	interest	NOUN
ejpam-5646	361	8	.	.	PUNCT
ejpam-5646	362	1	references	reference	NOUN
ejpam-5646	362	2	[	[	X
ejpam-5646	362	3	1	1	NUM
ejpam-5646	362	4	]	]	PUNCT
ejpam-5646	362	5	m.	m.	NOUN
ejpam-5646	362	6	al	al	PROPN
ejpam-5646	362	7	-	-	PUNCT
ejpam-5646	362	8	tahan	tahan	PROPN
ejpam-5646	362	9	and	and	CCONJ
ejpam-5646	362	10	i.	i.	PROPN
ejpam-5646	362	11	cristea	cristea	PROPN
ejpam-5646	362	12	.	.	PUNCT
ejpam-5646	363	1	a	a	DET
ejpam-5646	363	2	classical	classical	ADJ
ejpam-5646	363	3	and	and	CCONJ
ejpam-5646	363	4	a	a	DET
ejpam-5646	363	5	fuzzy	fuzzy	ADJ
ejpam-5646	363	6	approach	approach	NOUN
ejpam-5646	363	7	to	to	PART
ejpam-5646	363	8	study	study	VERB
ejpam-5646	363	9	the	the	DET
ejpam-5646	363	10	(	(	PUNCT
ejpam-5646	363	11	m	m	PROPN
ejpam-5646	363	12	,	,	PUNCT
ejpam-5646	363	13	n)-antiideals	n)-antiideal	NOUN
ejpam-5646	363	14	of	of	ADP
ejpam-5646	363	15	a	a	DET
ejpam-5646	363	16	semigroup	semigroup	NOUN
ejpam-5646	363	17	.	.	PUNCT
ejpam-5646	363	18	journal	journal	PROPN
ejpam-5646	363	19	of	of	ADP
ejpam-5646	363	20	multiple	multiple	ADV
ejpam-5646	363	21	-	-	PUNCT
ejpam-5646	363	22	valued	value	VERB
ejpam-5646	363	23	logic	logic	NOUN
ejpam-5646	363	24	&	&	CCONJ
ejpam-5646	363	25	soft	soft	ADJ
ejpam-5646	363	26	computing	computing	NOUN
ejpam-5646	363	27	,	,	PUNCT
ejpam-5646	363	28	44:291–302	44:291–302	PROPN
ejpam-5646	363	29	,	,	PUNCT
ejpam-5646	363	30	2025	2025	NUM
ejpam-5646	363	31	.	.	PUNCT
ejpam-5646	364	1	[	[	X
ejpam-5646	364	2	2	2	NUM
ejpam-5646	364	3	]	]	PUNCT
ejpam-5646	364	4	m.	m.	NOUN
ejpam-5646	364	5	al	al	PROPN
ejpam-5646	364	6	-	-	PUNCT
ejpam-5646	364	7	tahan	tahan	PROPN
ejpam-5646	364	8	,	,	PUNCT
ejpam-5646	364	9	b.	b.	PROPN
ejpam-5646	364	10	davvaz	davvaz	PROPN
ejpam-5646	364	11	,	,	PUNCT
ejpam-5646	364	12	p.	p.	PROPN
ejpam-5646	364	13	k.	k.	PROPN
ejpam-5646	365	1	harikrishnan	harikrishnan	PROPN
ejpam-5646	365	2	,	,	PUNCT
ejpam-5646	365	3	and	and	CCONJ
ejpam-5646	365	4	s.	s.	PROPN
ejpam-5646	365	5	hoskova	hoskova	PROPN
ejpam-5646	365	6	-	-	PUNCT
ejpam-5646	365	7	mayerova	mayerova	PROPN
ejpam-5646	365	8	.	.	PUNCT
ejpam-5646	366	1	antiideal	antiideal	NOUN
ejpam-5646	366	2	theory	theory	NOUN
ejpam-5646	366	3	in	in	ADP
ejpam-5646	366	4	semigroups	semigroup	NOUN
ejpam-5646	366	5	and	and	CCONJ
ejpam-5646	366	6	its	its	PRON
ejpam-5646	366	7	fuzzification	fuzzification	NOUN
ejpam-5646	366	8	.	.	PUNCT
ejpam-5646	367	1	2023	2023	NUM
ejpam-5646	367	2	.	.	PUNCT
ejpam-5646	367	3	submitted	submit	VERB
ejpam-5646	367	4	.	.	PUNCT
ejpam-5646	368	1	[	[	X
ejpam-5646	368	2	3	3	X
ejpam-5646	368	3	]	]	PUNCT
ejpam-5646	368	4	m.	m.	NOUN
ejpam-5646	368	5	al	al	PROPN
ejpam-5646	368	6	-	-	PUNCT
ejpam-5646	368	7	tahan	tahan	PROPN
ejpam-5646	368	8	,	,	PUNCT
ejpam-5646	368	9	b.	b.	PROPN
ejpam-5646	368	10	davvaz	davvaz	PROPN
ejpam-5646	368	11	,	,	PUNCT
ejpam-5646	368	12	a.	a.	PROPN
ejpam-5646	368	13	mahboob	mahboob	PROPN
ejpam-5646	368	14	,	,	PUNCT
ejpam-5646	368	15	s.	s.	PROPN
ejpam-5646	368	16	hoskova	hoskova	PROPN
ejpam-5646	368	17	-	-	PUNCT
ejpam-5646	368	18	mayerova	mayerova	NOUN
ejpam-5646	368	19	,	,	PUNCT
ejpam-5646	368	20	and	and	CCONJ
ejpam-5646	368	21	a.	a.	PROPN
ejpam-5646	368	22	vagaská.	vagaská.	PROPN
ejpam-5646	368	23	on	on	ADP
ejpam-5646	368	24	new	new	ADJ
ejpam-5646	368	25	filters	filter	NOUN
ejpam-5646	368	26	in	in	ADP
ejpam-5646	368	27	ordered	order	VERB
ejpam-5646	368	28	semigroups	semigroup	NOUN
ejpam-5646	368	29	.	.	PUNCT
ejpam-5646	368	30	symmetry	symmetry	NOUN
ejpam-5646	368	31	,	,	PUNCT
ejpam-5646	368	32	14(8):1564	14(8):1564	NUM
ejpam-5646	368	33	,	,	PUNCT
ejpam-5646	368	34	2022	2022	NUM
ejpam-5646	368	35	.	.	PUNCT
ejpam-5646	369	1	[	[	X
ejpam-5646	369	2	4	4	X
ejpam-5646	369	3	]	]	PUNCT
ejpam-5646	369	4	m.	m.	NOUN
ejpam-5646	369	5	al	al	PROPN
ejpam-5646	369	6	-	-	PUNCT
ejpam-5646	369	7	tahan	tahan	PROPN
ejpam-5646	369	8	,	,	PUNCT
ejpam-5646	369	9	b.	b.	PROPN
ejpam-5646	369	10	davvaz	davvaz	PROPN
ejpam-5646	369	11	,	,	PUNCT
ejpam-5646	369	12	a.	a.	NOUN
ejpam-5646	369	13	mahboob	mahboob	PROPN
ejpam-5646	369	14	,	,	PUNCT
ejpam-5646	369	15	and	and	CCONJ
ejpam-5646	369	16	n.	n.	PROPN
ejpam-5646	369	17	m.	m.	PROPN
ejpam-5646	369	18	khan	khan	PROPN
ejpam-5646	369	19	.	.	PUNCT
ejpam-5646	370	1	on	on	ADP
ejpam-5646	370	2	a	a	DET
ejpam-5646	370	3	generalization	generalization	NOUN
ejpam-5646	370	4	of	of	ADP
ejpam-5646	370	5	fuzzy	fuzzy	ADJ
ejpam-5646	370	6	filters	filter	NOUN
ejpam-5646	370	7	of	of	ADP
ejpam-5646	370	8	ordered	order	VERB
ejpam-5646	370	9	semigroups	semigroup	NOUN
ejpam-5646	370	10	.	.	PUNCT
ejpam-5646	371	1	new	new	ADJ
ejpam-5646	371	2	math	math	PROPN
ejpam-5646	371	3	nat	nat	PROPN
ejpam-5646	371	4	comput	comput	NOUN
ejpam-5646	371	5	.	.	PUNCT
ejpam-5646	371	6	,	,	PUNCT
ejpam-5646	371	7	19(2):489–502	19(2):489–502	PROPN
ejpam-5646	371	8	,	,	PUNCT
ejpam-5646	371	9	2023	2023	NUM
ejpam-5646	371	10	.	.	PUNCT
ejpam-5646	372	1	[	[	X
ejpam-5646	372	2	5	5	X
ejpam-5646	372	3	]	]	PUNCT
ejpam-5646	372	4	m.	m.	NOUN
ejpam-5646	372	5	al	al	PROPN
ejpam-5646	372	6	-	-	PUNCT
ejpam-5646	372	7	tahan	tahan	PROPN
ejpam-5646	372	8	and	and	CCONJ
ejpam-5646	372	9	s.	s.	PROPN
ejpam-5646	372	10	hoskova	hoskova	PROPN
ejpam-5646	372	11	-	-	PUNCT
ejpam-5646	372	12	mayerova	mayerova	NOUN
ejpam-5646	372	13	.	.	PUNCT
ejpam-5646	373	1	characterizing	characterize	VERB
ejpam-5646	373	2	a	a	DET
ejpam-5646	373	3	semigroup	semigroup	NOUN
ejpam-5646	373	4	by	by	ADP
ejpam-5646	373	5	its	its	PRON
ejpam-5646	373	6	fuzzy	fuzzy	ADJ
ejpam-5646	373	7	interior	interior	ADJ
ejpam-5646	373	8	antiideals	antiideal	NOUN
ejpam-5646	373	9	.	.	PUNCT
ejpam-5646	374	1	in	in	ADP
ejpam-5646	374	2	the	the	DET
ejpam-5646	374	3	seventeenth	seventeenth	ADJ
ejpam-5646	374	4	international	international	ADJ
ejpam-5646	374	5	conference	conference	NOUN
ejpam-5646	374	6	on	on	ADP
ejpam-5646	374	7	fuzzy	fuzzy	ADJ
ejpam-5646	374	8	set	set	NOUN
ejpam-5646	374	9	theory	theory	NOUN
ejpam-5646	374	10	and	and	CCONJ
ejpam-5646	374	11	applications	application	NOUN
ejpam-5646	374	12	,	,	PUNCT
ejpam-5646	374	13	liptovsky	liptovsky	PROPN
ejpam-5646	374	14	jan	jan	PROPN
ejpam-5646	374	15	,	,	PUNCT
ejpam-5646	374	16	slovakia	slovakia	PROPN
ejpam-5646	374	17	,	,	PUNCT
ejpam-5646	374	18	january	january	PROPN
ejpam-5646	374	19	28	28	NUM
ejpam-5646	374	20	february	february	PROPN
ejpam-5646	374	21	2	2	NUM
ejpam-5646	374	22	2024	2024	NUM
ejpam-5646	374	23	.	.	PUNCT
ejpam-5646	375	1	[	[	X
ejpam-5646	375	2	6	6	NUM
ejpam-5646	375	3	]	]	PUNCT
ejpam-5646	375	4	a.	a.	NOUN
ejpam-5646	375	5	h.	h.	PROPN
ejpam-5646	375	6	clifford	clifford	PROPN
ejpam-5646	375	7	and	and	CCONJ
ejpam-5646	375	8	g.	g.	PROPN
ejpam-5646	375	9	b.	b.	PROPN
ejpam-5646	375	10	preston	preston	PROPN
ejpam-5646	375	11	.	.	PUNCT
ejpam-5646	376	1	introduction	introduction	NOUN
ejpam-5646	376	2	to	to	ADP
ejpam-5646	376	3	the	the	DET
ejpam-5646	376	4	theory	theory	NOUN
ejpam-5646	376	5	of	of	ADP
ejpam-5646	376	6	semigroups	semigroup	NOUN
ejpam-5646	376	7	.	.	PUNCT
ejpam-5646	377	1	american	american	PROPN
ejpam-5646	377	2	mathematical	mathematical	PROPN
ejpam-5646	377	3	society	society	NOUN
ejpam-5646	377	4	,	,	PUNCT
ejpam-5646	377	5	1961	1961	NUM
ejpam-5646	377	6	.	.	PUNCT
ejpam-5646	378	1	[	[	X
ejpam-5646	378	2	7	7	X
ejpam-5646	378	3	]	]	X
ejpam-5646	378	4	b.	b.	PROPN
ejpam-5646	378	5	davvaz	davvaz	PROPN
ejpam-5646	378	6	and	and	CCONJ
ejpam-5646	378	7	i.	i.	PROPN
ejpam-5646	378	8	cristea	cristea	PROPN
ejpam-5646	378	9	.	.	PUNCT
ejpam-5646	379	1	fuzzy	fuzzy	ADJ
ejpam-5646	379	2	algebraic	algebraic	PROPN
ejpam-5646	379	3	hyperstructuresan	hyperstructuresan	ADJ
ejpam-5646	379	4	introduction	introduction	NOUN
ejpam-5646	379	5	.	.	PUNCT
ejpam-5646	380	1	studies	study	NOUN
ejpam-5646	380	2	in	in	ADP
ejpam-5646	380	3	fuzziness	fuzziness	NOUN
ejpam-5646	380	4	and	and	CCONJ
ejpam-5646	380	5	soft	soft	ADJ
ejpam-5646	380	6	computing	computing	NOUN
ejpam-5646	380	7	321	321	NUM
ejpam-5646	380	8	.	.	PUNCT
ejpam-5646	381	1	cham	cham	PROPN
ejpam-5646	381	2	:	:	PUNCT
ejpam-5646	381	3	springer	springer	NOUN
ejpam-5646	381	4	,	,	PUNCT
ejpam-5646	381	5	2015	2015	NUM
ejpam-5646	381	6	.	.	PUNCT
ejpam-5646	382	1	[	[	X
ejpam-5646	382	2	8	8	NUM
ejpam-5646	382	3	]	]	PUNCT
ejpam-5646	382	4	k.	k.	PROPN
ejpam-5646	382	5	iseki	iseki	PROPN
ejpam-5646	382	6	.	.	PUNCT
ejpam-5646	383	1	on	on	ADP
ejpam-5646	383	2	(	(	PUNCT
ejpam-5646	383	3	m	m	PROPN
ejpam-5646	383	4	,	,	PUNCT
ejpam-5646	383	5	n)-antiideals	n)-antiideal	NOUN
ejpam-5646	383	6	in	in	ADP
ejpam-5646	383	7	semigroup	semigroup	PROPN
ejpam-5646	383	8	.	.	PUNCT
ejpam-5646	383	9	proc	proc	PROPN
ejpam-5646	383	10	.	.	PUNCT
ejpam-5646	384	1	japan	japan	PROPN
ejpam-5646	384	2	acad	acad	PROPN
ejpam-5646	384	3	.	.	PUNCT
ejpam-5646	384	4	,	,	PUNCT
ejpam-5646	385	1	38(7):316–317	38(7):316–317	NUM
ejpam-5646	385	2	,	,	PUNCT
ejpam-5646	385	3	1962	1962	NUM
ejpam-5646	385	4	.	.	PUNCT
ejpam-5646	386	1	[	[	X
ejpam-5646	386	2	9	9	NUM
ejpam-5646	386	3	]	]	PUNCT
ejpam-5646	386	4	k.	k.	PROPN
ejpam-5646	386	5	iseki	iseki	PROPN
ejpam-5646	386	6	.	.	PUNCT
ejpam-5646	387	1	on	on	ADP
ejpam-5646	387	2	(	(	PUNCT
ejpam-5646	387	3	m	m	PROPN
ejpam-5646	387	4	,	,	PUNCT
ejpam-5646	387	5	n)-mutant	n)-mutant	NOUN
ejpam-5646	387	6	in	in	ADP
ejpam-5646	387	7	semigroup	semigroup	PROPN
ejpam-5646	387	8	.	.	PUNCT
ejpam-5646	387	9	proc	proc	PROPN
ejpam-5646	387	10	.	.	PUNCT
ejpam-5646	388	1	japan	japan	PROPN
ejpam-5646	388	2	acad	acad	PROPN
ejpam-5646	388	3	.	.	PROPN
ejpam-5646	388	4	,	,	PUNCT
ejpam-5646	388	5	38:269–270	38:269–270	PROPN
ejpam-5646	388	6	,	,	PUNCT
ejpam-5646	388	7	1962	1962	NUM
ejpam-5646	388	8	.	.	PUNCT
ejpam-5646	389	1	[	[	X
ejpam-5646	389	2	10	10	NUM
ejpam-5646	389	3	]	]	X
ejpam-5646	389	4	n.	n.	NOUN
ejpam-5646	389	5	kehayopulu	kehayopulu	PROPN
ejpam-5646	389	6	,	,	PUNCT
ejpam-5646	389	7	x.	x.	PROPN
ejpam-5646	389	8	y.	y.	PROPN
ejpam-5646	389	9	xiang	xiang	PROPN
ejpam-5646	389	10	-	-	PUNCT
ejpam-5646	389	11	yun	yun	PROPN
ejpam-5646	389	12	,	,	PUNCT
ejpam-5646	389	13	and	and	CCONJ
ejpam-5646	389	14	m.	m.	NOUN
ejpam-5646	389	15	tsingelis	tsingelis	PROPN
ejpam-5646	389	16	.	.	PUNCT
ejpam-5646	390	1	a	a	DET
ejpam-5646	390	2	characterization	characterization	NOUN
ejpam-5646	390	3	of	of	ADP
ejpam-5646	390	4	prime	prime	ADJ
ejpam-5646	390	5	and	and	CCONJ
ejpam-5646	390	6	semiprime	semiprime	NOUN
ejpam-5646	390	7	ideals	ideal	NOUN
ejpam-5646	390	8	of	of	ADP
ejpam-5646	390	9	semigroups	semigroup	NOUN
ejpam-5646	390	10	in	in	ADP
ejpam-5646	390	11	terms	term	NOUN
ejpam-5646	390	12	of	of	ADP
ejpam-5646	390	13	fuzzy	fuzzy	ADJ
ejpam-5646	390	14	subsets	subset	NOUN
ejpam-5646	390	15	.	.	PUNCT
ejpam-5646	391	1	soochow	soochow	PROPN
ejpam-5646	391	2	journal	journal	PROPN
ejpam-5646	391	3	of	of	ADP
ejpam-5646	391	4	mathematics	mathematic	NOUN
ejpam-5646	391	5	,	,	PUNCT
ejpam-5646	391	6	27:139–144	27:139–144	NUM
ejpam-5646	391	7	,	,	PUNCT
ejpam-5646	391	8	2001	2001	NUM
ejpam-5646	391	9	.	.	PUNCT
ejpam-5646	392	1	[	[	X
ejpam-5646	392	2	11	11	NUM
ejpam-5646	392	3	]	]	PUNCT
ejpam-5646	392	4	a.	a.	NOUN
ejpam-5646	392	5	khan	khan	PROPN
ejpam-5646	392	6	,	,	PUNCT
ejpam-5646	392	7	a.	a.	PROPN
ejpam-5646	392	8	h.	h.	PROPN
ejpam-5646	392	9	sarmin	sarmin	PROPN
ejpam-5646	392	10	,	,	PUNCT
ejpam-5646	392	11	b.	b.	PROPN
ejpam-5646	392	12	davvaz	davvaz	PROPN
ejpam-5646	392	13	,	,	PUNCT
ejpam-5646	392	14	and	and	CCONJ
ejpam-5646	392	15	f.	f.	PROPN
ejpam-5646	392	16	m.	m.	PROPN
ejpam-5646	392	17	khan	khan	PROPN
ejpam-5646	392	18	.	.	PUNCT
ejpam-5646	393	1	new	new	ADJ
ejpam-5646	393	2	types	type	NOUN
ejpam-5646	393	3	of	of	ADP
ejpam-5646	393	4	fuzzy	fuzzy	ADJ
ejpam-5646	393	5	bi	bi	NOUN
ejpam-5646	393	6	-	-	NOUN
ejpam-5646	393	7	ideals	ideal	NOUN
ejpam-5646	393	8	in	in	ADP
ejpam-5646	393	9	ordered	order	VERB
ejpam-5646	393	10	semigroups	semigroup	NOUN
ejpam-5646	393	11	.	.	PUNCT
ejpam-5646	394	1	neural	neural	ADJ
ejpam-5646	394	2	computing	computing	NOUN
ejpam-5646	394	3	and	and	CCONJ
ejpam-5646	394	4	applications	application	NOUN
ejpam-5646	394	5	,	,	PUNCT
ejpam-5646	394	6	21:295–305	21:295–305	NUM
ejpam-5646	394	7	,	,	PUNCT
ejpam-5646	394	8	2012	2012	NUM
ejpam-5646	394	9	.	.	PUNCT
ejpam-5646	395	1	[	[	X
ejpam-5646	395	2	12	12	NUM
ejpam-5646	395	3	]	]	X
ejpam-5646	395	4	s.	s.	PROPN
ejpam-5646	395	5	lajos	lajos	PROPN
ejpam-5646	395	6	.	.	PUNCT
ejpam-5646	396	1	on	on	ADP
ejpam-5646	396	2	generalized	generalized	ADJ
ejpam-5646	396	3	ideals	ideal	NOUN
ejpam-5646	396	4	in	in	ADP
ejpam-5646	396	5	semigroups	semigroup	NOUN
ejpam-5646	396	6	.	.	PUNCT
ejpam-5646	397	1	matematikai	matematikai	NOUN
ejpam-5646	397	2	lapok	lapok	PROPN
ejpam-5646	397	3	,	,	PUNCT
ejpam-5646	397	4	10:351	10:351	NUM
ejpam-5646	397	5	,	,	PUNCT
ejpam-5646	397	6	1959	1959	NUM
ejpam-5646	397	7	.	.	PUNCT
ejpam-5646	398	1	[	[	X
ejpam-5646	398	2	13	13	NUM
ejpam-5646	398	3	]	]	X
ejpam-5646	398	4	s.	s.	PROPN
ejpam-5646	398	5	lajos	lajos	PROPN
ejpam-5646	398	6	.	.	PUNCT
ejpam-5646	399	1	notes	note	NOUN
ejpam-5646	399	2	on	on	ADP
ejpam-5646	399	3	(	(	PUNCT
ejpam-5646	399	4	m	m	PROPN
ejpam-5646	399	5	,	,	PUNCT
ejpam-5646	399	6	n)-ideals	n)-ideal	VERB
ejpam-5646	399	7	i.	i.	PROPN
ejpam-5646	399	8	proc	proc	PROPN
ejpam-5646	399	9	jpn	jpn	PROPN
ejpam-5646	399	10	acad	acad	PROPN
ejpam-5646	399	11	,	,	PUNCT
ejpam-5646	399	12	39:419–421	39:419–421	PROPN
ejpam-5646	399	13	,	,	PUNCT
ejpam-5646	399	14	1963	1963	NUM
ejpam-5646	399	15	.	.	PUNCT
ejpam-5646	400	1	[	[	X
ejpam-5646	400	2	14	14	NUM
ejpam-5646	400	3	]	]	X
ejpam-5646	400	4	s.	s.	PROPN
ejpam-5646	400	5	lajos	lajos	PROPN
ejpam-5646	400	6	.	.	PUNCT
ejpam-5646	401	1	notes	note	NOUN
ejpam-5646	401	2	on	on	ADP
ejpam-5646	401	3	(	(	PUNCT
ejpam-5646	401	4	m	m	PROPN
ejpam-5646	401	5	,	,	PUNCT
ejpam-5646	401	6	n)-ideals	n)-ideal	VERB
ejpam-5646	401	7	ii	ii	NOUN
ejpam-5646	401	8	.	.	PUNCT
ejpam-5646	402	1	proc	proc	PROPN
ejpam-5646	402	2	japan	japan	PROPN
ejpam-5646	402	3	acad	acad	PROPN
ejpam-5646	402	4	.	.	PROPN
ejpam-5646	402	5	,	,	PUNCT
ejpam-5646	402	6	40:631–632	40:631–632	PROPN
ejpam-5646	402	7	,	,	PUNCT
ejpam-5646	402	8	1964	1964	NUM
ejpam-5646	402	9	.	.	PUNCT
ejpam-5646	403	1	[	[	X
ejpam-5646	403	2	15	15	NUM
ejpam-5646	403	3	]	]	X
ejpam-5646	403	4	s.	s.	PROPN
ejpam-5646	403	5	k.	k.	PROPN
ejpam-5646	403	6	lee	lee	PROPN
ejpam-5646	403	7	and	and	CCONJ
ejpam-5646	403	8	s.	s.	PROPN
ejpam-5646	403	9	s.	s.	PROPN
ejpam-5646	403	10	lee	lee	PROPN
ejpam-5646	403	11	.	.	PUNCT
ejpam-5646	404	1	left(right)-filters	left(right)-filter	NOUN
ejpam-5646	404	2	on	on	ADP
ejpam-5646	404	3	po	po	NOUN
ejpam-5646	404	4	-	-	PUNCT
ejpam-5646	404	5	semigroups	semigroup	NOUN
ejpam-5646	404	6	.	.	PUNCT
ejpam-5646	405	1	kangweon	kangweon	NOUN
ejpam-5646	405	2	-	-	PUNCT
ejpam-5646	405	3	kyungki	kyungki	NOUN
ejpam-5646	405	4	math	math	PROPN
ejpam-5646	405	5	j.	j.	PROPN
ejpam-5646	405	6	,	,	PUNCT
ejpam-5646	405	7	8(1):43–45	8(1):43–45	NUM
ejpam-5646	405	8	,	,	PUNCT
ejpam-5646	405	9	2000	2000	NUM
ejpam-5646	405	10	.	.	PUNCT
ejpam-5646	406	1	[	[	X
ejpam-5646	406	2	16	16	NUM
ejpam-5646	406	3	]	]	X
ejpam-5646	406	4	p.	p.	PROPN
ejpam-5646	406	5	pal	pal	NOUN
ejpam-5646	406	6	,	,	PUNCT
ejpam-5646	406	7	s.	s.	PROPN
ejpam-5646	406	8	k.	k.	PROPN
ejpam-5646	406	9	majumder	majumder	PROPN
ejpam-5646	406	10	,	,	PUNCT
ejpam-5646	406	11	b.	b.	PROPN
ejpam-5646	406	12	davvaz	davvaz	PROPN
ejpam-5646	406	13	,	,	PUNCT
ejpam-5646	406	14	and	and	CCONJ
ejpam-5646	406	15	s.	s.	PROPN
ejpam-5646	406	16	k.	k.	PROPN
ejpam-5646	406	17	sardar	sardar	PROPN
ejpam-5646	406	18	.	.	PUNCT
ejpam-5646	407	1	regularity	regularity	NOUN
ejpam-5646	407	2	of	of	ADP
ejpam-5646	407	3	po	po	NOUN
ejpam-5646	407	4	-	-	PUNCT
ejpam-5646	407	5	γ	γ	NOUN
ejpam-5646	407	6	-	-	PUNCT
ejpam-5646	407	7	semigroups	semigroup	NOUN
ejpam-5646	407	8	in	in	ADP
ejpam-5646	407	9	terms	term	NOUN
ejpam-5646	407	10	of	of	ADP
ejpam-5646	407	11	fuzzy	fuzzy	ADJ
ejpam-5646	407	12	subsemigroups	subsemigroup	NOUN
ejpam-5646	407	13	and	and	CCONJ
ejpam-5646	407	14	fuzzy	fuzzy	ADJ
ejpam-5646	407	15	bi	bi	NOUN
ejpam-5646	407	16	-	-	NOUN
ejpam-5646	407	17	ideals	ideal	NOUN
ejpam-5646	407	18	.	.	PUNCT
ejpam-5646	408	1	fuzzy	fuzzy	ADJ
ejpam-5646	408	2	information	information	NOUN
ejpam-5646	408	3	and	and	CCONJ
ejpam-5646	408	4	engineering	engineering	NOUN
ejpam-5646	408	5	,	,	PUNCT
ejpam-5646	408	6	7(2):165–182	7(2):165–182	PROPN
ejpam-5646	408	7	,	,	PUNCT
ejpam-5646	408	8	2015	2015	NUM
ejpam-5646	408	9	.	.	PUNCT
ejpam-5646	409	1	[	[	X
ejpam-5646	409	2	17	17	NUM
ejpam-5646	409	3	]	]	PUNCT
ejpam-5646	409	4	a.	a.	NOUN
ejpam-5646	409	5	rosenfeld	rosenfeld	PROPN
ejpam-5646	409	6	.	.	PUNCT
ejpam-5646	410	1	fuzzy	fuzzy	ADJ
ejpam-5646	410	2	groups	group	NOUN
ejpam-5646	410	3	.	.	PUNCT
ejpam-5646	411	1	journal	journal	PROPN
ejpam-5646	411	2	of	of	ADP
ejpam-5646	411	3	mathematical	mathematical	ADJ
ejpam-5646	411	4	analysis	analysis	NOUN
ejpam-5646	411	5	and	and	CCONJ
ejpam-5646	411	6	applications	application	NOUN
ejpam-5646	411	7	,	,	PUNCT
ejpam-5646	411	8	35(3):512–517	35(3):512–517	PROPN
ejpam-5646	411	9	,	,	PUNCT
ejpam-5646	411	10	1971	1971	NUM
ejpam-5646	411	11	.	.	PUNCT
ejpam-5646	412	1	[	[	X
ejpam-5646	412	2	18	18	NUM
ejpam-5646	412	3	]	]	X
ejpam-5646	412	4	r.	r.	PROPN
ejpam-5646	412	5	saadeh	saadeh	PROPN
ejpam-5646	412	6	,	,	PUNCT
ejpam-5646	412	7	a.	a.	NOUN
ejpam-5646	412	8	qazza	qazza	PROPN
ejpam-5646	412	9	,	,	PUNCT
ejpam-5646	412	10	and	and	CCONJ
ejpam-5646	412	11	a.	a.	NOUN
ejpam-5646	412	12	burqan	burqan	PROPN
ejpam-5646	412	13	.	.	PUNCT
ejpam-5646	413	1	a	a	DET
ejpam-5646	413	2	new	new	ADJ
ejpam-5646	413	3	integral	integral	ADJ
ejpam-5646	413	4	transform	transform	NOUN
ejpam-5646	413	5	:	:	PUNCT
ejpam-5646	413	6	ara	ara	NOUN
ejpam-5646	413	7	transform	transform	NOUN
ejpam-5646	413	8	and	and	CCONJ
ejpam-5646	413	9	its	its	PRON
ejpam-5646	413	10	properties	property	NOUN
ejpam-5646	413	11	and	and	CCONJ
ejpam-5646	413	12	applications	application	NOUN
ejpam-5646	413	13	.	.	PUNCT
ejpam-5646	414	1	symmetry	symmetry	NOUN
ejpam-5646	414	2	,	,	PUNCT
ejpam-5646	414	3	12:925	12:925	NUM
ejpam-5646	414	4	,	,	PUNCT
ejpam-5646	414	5	2020	2020	NUM
ejpam-5646	414	6	.	.	PUNCT
ejpam-5646	415	1	m.	m.	NOUN
ejpam-5646	415	2	al	al	PROPN
ejpam-5646	415	3	tahan	tahan	PROPN
ejpam-5646	415	4	,	,	PUNCT
ejpam-5646	415	5	s.	s.	PROPN
ejpam-5646	415	6	hoskova	hoskova	PROPN
ejpam-5646	415	7	-	-	PUNCT
ejpam-5646	415	8	mayerova	mayerova	PROPN
ejpam-5646	415	9	,	,	PUNCT
ejpam-5646	415	10	s.	s.	PROPN
ejpam-5646	415	11	al	al	PROPN
ejpam-5646	415	12	-	-	PUNCT
ejpam-5646	415	13	kaseasbeh	kaseasbeh	PROPN
ejpam-5646	415	14	/	/	SYM
ejpam-5646	415	15	eur	eur	NOUN
ejpam-5646	415	16	.	.	PUNCT
ejpam-5646	416	1	j.	j.	PROPN
ejpam-5646	416	2	pure	pure	PROPN
ejpam-5646	416	3	appl	appl	PROPN
ejpam-5646	416	4	.	.	PROPN
ejpam-5646	416	5	math	math	PROPN
ejpam-5646	416	6	,	,	PUNCT
ejpam-5646	416	7	18	18	NUM
ejpam-5646	416	8	(	(	PUNCT
ejpam-5646	416	9	1	1	NUM
ejpam-5646	416	10	)	)	PUNCT
ejpam-5646	416	11	(	(	PUNCT
ejpam-5646	416	12	2025	2025	NUM
ejpam-5646	416	13	)	)	PUNCT
ejpam-5646	416	14	,	,	PUNCT
ejpam-5646	416	15	5646	5646	NUM
ejpam-5646	416	16	11	11	NUM
ejpam-5646	416	17	of	of	ADP
ejpam-5646	416	18	11	11	NUM
ejpam-5646	416	19	[	[	SYM
ejpam-5646	416	20	19	19	NUM
ejpam-5646	416	21	]	]	X
ejpam-5646	416	22	f.	f.	PROPN
ejpam-5646	416	23	schwarz	schwarz	PROPN
ejpam-5646	416	24	.	.	PUNCT
ejpam-5646	417	1	on	on	ADP
ejpam-5646	417	2	maximal	maximal	ADJ
ejpam-5646	417	3	ideals	ideal	NOUN
ejpam-5646	417	4	in	in	ADP
ejpam-5646	417	5	the	the	DET
ejpam-5646	417	6	theory	theory	NOUN
ejpam-5646	417	7	of	of	ADP
ejpam-5646	417	8	semigroups	semigroup	NOUN
ejpam-5646	417	9	.	.	PUNCT
ejpam-5646	418	1	czechoslovak	czechoslovak	ADJ
ejpam-5646	418	2	math	math	NOUN
ejpam-5646	418	3	.	.	PUNCT
ejpam-5646	419	1	jour	jour	PROPN
ejpam-5646	419	2	.	.	PROPN
ejpam-5646	419	3	,	,	PUNCT
ejpam-5646	419	4	3(78):139–153	3(78):139–153	NUM
ejpam-5646	419	5	,	,	PUNCT
ejpam-5646	419	6	365–383	365–383	NUM
ejpam-5646	419	7	,	,	PUNCT
ejpam-5646	419	8	1953	1953	NUM
ejpam-5646	419	9	.	.	PUNCT
ejpam-5646	420	1	[	[	X
ejpam-5646	420	2	20	20	NUM
ejpam-5646	420	3	]	]	PUNCT
ejpam-5646	420	4	a.	a.	NOUN
ejpam-5646	420	5	suschkewitsch	suschkewitsch	PROPN
ejpam-5646	420	6	.	.	PUNCT
ejpam-5646	421	1	fiber	fiber	NOUN
ejpam-5646	421	2	die	die	VERB
ejpam-5646	421	3	endlichen	endlichen	PROPN
ejpam-5646	421	4	gruppen	gruppen	PROPN
ejpam-5646	421	5	ohne	ohne	NOUN
ejpam-5646	421	6	das	das	PROPN
ejpam-5646	421	7	gesetz	gesetz	VERB
ejpam-5646	421	8	der	der	ADJ
ejpam-5646	421	9	eindeutigen	eindeutigen	NOUN
ejpam-5646	421	10	umkehrbarkeit	umkehrbarkeit	NOUN
ejpam-5646	421	11	.	.	PUNCT
ejpam-5646	422	1	math	math	PROPN
ejpam-5646	422	2	.	.	PUNCT
ejpam-5646	423	1	ann	ann	PROPN
ejpam-5646	423	2	.	.	PROPN
ejpam-5646	423	3	,	,	PUNCT
ejpam-5646	423	4	99:30–50	99:30–50	NUM
ejpam-5646	423	5	,	,	PUNCT
ejpam-5646	423	6	1928	1928	NUM
ejpam-5646	423	7	.	.	PUNCT
ejpam-5646	424	1	[	[	X
ejpam-5646	424	2	21	21	NUM
ejpam-5646	424	3	]	]	X
ejpam-5646	424	4	l.	l.	PROPN
ejpam-5646	424	5	a.	a.	PROPN
ejpam-5646	424	6	zadeh	zadeh	PROPN
ejpam-5646	424	7	.	.	PUNCT
ejpam-5646	424	8	fuzzy	fuzzy	ADJ
ejpam-5646	424	9	sets	set	NOUN
ejpam-5646	424	10	.	.	PUNCT
ejpam-5646	425	1	inform	inform	NOUN
ejpam-5646	425	2	and	and	CCONJ
ejpam-5646	425	3	control	control	NOUN
ejpam-5646	425	4	,	,	PUNCT
ejpam-5646	425	5	8:338–353	8:338–353	NUM
ejpam-5646	425	6	,	,	PUNCT
ejpam-5646	425	7	1965	1965	NUM
ejpam-5646	425	8	.	.	PUNCT