id	sid	tid	token	lemma	pos
ejpam-5837	1	1	european	european	PROPN
ejpam-5837	1	2	journal	journal	PROPN
ejpam-5837	1	3	of	of	ADP
ejpam-5837	1	4	pure	pure	ADJ
ejpam-5837	1	5	and	and	CCONJ
ejpam-5837	1	6	applied	applied	ADJ
ejpam-5837	1	7	mathematics	mathematic	NOUN
ejpam-5837	1	8	2025	2025	NUM
ejpam-5837	1	9	,	,	PUNCT
ejpam-5837	1	10	vol	vol	NOUN
ejpam-5837	1	11	.	.	PROPN
ejpam-5837	1	12	18	18	NUM
ejpam-5837	1	13	,	,	PUNCT
ejpam-5837	1	14	issue	issue	NOUN
ejpam-5837	1	15	2	2	NUM
ejpam-5837	1	16	,	,	PUNCT
ejpam-5837	1	17	article	article	NOUN
ejpam-5837	1	18	number	number	NOUN
ejpam-5837	1	19	5837	5837	NUM
ejpam-5837	1	20	issn	issn	VERB
ejpam-5837	1	21	1307	1307	NUM
ejpam-5837	1	22	-	-	SYM
ejpam-5837	1	23	5543	5543	NUM
ejpam-5837	1	24	–	–	PUNCT
ejpam-5837	1	25	ejpam.com	ejpam.com	X
ejpam-5837	1	26	published	publish	VERB
ejpam-5837	1	27	by	by	ADP
ejpam-5837	1	28	new	new	PROPN
ejpam-5837	1	29	york	york	PROPN
ejpam-5837	1	30	business	business	PROPN
ejpam-5837	1	31	global	global	PROPN
ejpam-5837	1	32	almost	almost	ADV
ejpam-5837	1	33	(	(	PUNCT
ejpam-5837	1	34	m	m	PROPN
ejpam-5837	1	35	,	,	PUNCT
ejpam-5837	1	36	n)-quasi	n)-quasi	NOUN
ejpam-5837	1	37	-	-	NOUN
ejpam-5837	1	38	ideals	ideal	NOUN
ejpam-5837	1	39	and	and	CCONJ
ejpam-5837	1	40	fuzzy	fuzzy	ADJ
ejpam-5837	1	41	almost	almost	ADV
ejpam-5837	1	42	(	(	PUNCT
ejpam-5837	1	43	m	m	PROPN
ejpam-5837	1	44	,	,	PUNCT
ejpam-5837	1	45	n)-quasi	n)-quasi	NOUN
ejpam-5837	1	46	-	-	NOUN
ejpam-5837	1	47	ideals	ideal	NOUN
ejpam-5837	1	48	in	in	ADP
ejpam-5837	1	49	ordered	order	VERB
ejpam-5837	1	50	semigroups	semigroup	NOUN
ejpam-5837	1	51	p.	p.	PROPN
ejpam-5837	1	52	khamrot1	khamrot1	PROPN
ejpam-5837	1	53	,	,	PUNCT
ejpam-5837	1	54	p.	p.	PROPN
ejpam-5837	1	55	chaisuwan	chaisuwan	PROPN
ejpam-5837	1	56	,	,	PUNCT
ejpam-5837	1	57	p.	p.	PROPN
ejpam-5837	1	58	keawton	keawton	PROPN
ejpam-5837	1	59	,	,	PUNCT
ejpam-5837	1	60	c.	c.	PROPN
ejpam-5837	1	61	wangsamphao2	wangsamphao2	PROPN
ejpam-5837	1	62	,	,	PUNCT
ejpam-5837	1	63	t.	t.	PROPN
ejpam-5837	1	64	gaketem3,∗	gaketem3,∗	PROPN
ejpam-5837	1	65	1	1	NUM
ejpam-5837	1	66	department	department	NOUN
ejpam-5837	1	67	of	of	ADP
ejpam-5837	1	68	mathematics	mathematic	NOUN
ejpam-5837	1	69	,	,	PUNCT
ejpam-5837	1	70	faculty	faculty	NOUN
ejpam-5837	1	71	of	of	ADP
ejpam-5837	1	72	science	science	NOUN
ejpam-5837	1	73	and	and	CCONJ
ejpam-5837	1	74	agricultural	agricultural	ADJ
ejpam-5837	1	75	technology	technology	NOUN
ejpam-5837	1	76	,	,	PUNCT
ejpam-5837	1	77	rajamangala	rajamangala	PROPN
ejpam-5837	1	78	university	university	PROPN
ejpam-5837	1	79	of	of	ADP
ejpam-5837	1	80	technology	technology	PROPN
ejpam-5837	1	81	lanna	lanna	PROPN
ejpam-5837	1	82	of	of	ADP
ejpam-5837	1	83	phitsanulok	phitsanulok	PROPN
ejpam-5837	1	84	,	,	PUNCT
ejpam-5837	1	85	phitsanulok	phitsanulok	PROPN
ejpam-5837	1	86	,	,	PUNCT
ejpam-5837	1	87	thailand	thailand	PROPN
ejpam-5837	1	88	2	2	NUM
ejpam-5837	1	89	department	department	NOUN
ejpam-5837	1	90	of	of	ADP
ejpam-5837	1	91	mathematics	mathematic	NOUN
ejpam-5837	1	92	,	,	PUNCT
ejpam-5837	1	93	school	school	NOUN
ejpam-5837	1	94	of	of	ADP
ejpam-5837	1	95	education	education	NOUN
ejpam-5837	1	96	,	,	PUNCT
ejpam-5837	1	97	university	university	NOUN
ejpam-5837	1	98	of	of	ADP
ejpam-5837	1	99	phayao	phayao	NOUN
ejpam-5837	1	100	,	,	PUNCT
ejpam-5837	1	101	phayao	phayao	NOUN
ejpam-5837	1	102	,	,	PUNCT
ejpam-5837	1	103	thailand	thailand	PROPN
ejpam-5837	1	104	3	3	NUM
ejpam-5837	1	105	department	department	NOUN
ejpam-5837	1	106	of	of	ADP
ejpam-5837	1	107	mathematics	mathematic	NOUN
ejpam-5837	1	108	,	,	PUNCT
ejpam-5837	1	109	school	school	NOUN
ejpam-5837	1	110	of	of	ADP
ejpam-5837	1	111	science	science	NOUN
ejpam-5837	1	112	,	,	PUNCT
ejpam-5837	1	113	university	university	NOUN
ejpam-5837	1	114	of	of	ADP
ejpam-5837	1	115	phayao	phayao	NOUN
ejpam-5837	1	116	,	,	PUNCT
ejpam-5837	1	117	phayao	phayao	NOUN
ejpam-5837	1	118	56000	56000	NUM
ejpam-5837	1	119	,	,	PUNCT
ejpam-5837	1	120	thailand	thailand	PROPN
ejpam-5837	1	121	abstract	abstract	NOUN
ejpam-5837	1	122	.	.	PUNCT
ejpam-5837	2	1	the	the	DET
ejpam-5837	2	2	ordered	order	VERB
ejpam-5837	2	3	semigroups	semigroup	NOUN
ejpam-5837	2	4	are	be	AUX
ejpam-5837	2	5	algebraic	algebraic	ADJ
ejpam-5837	2	6	systems	system	NOUN
ejpam-5837	2	7	consisting	consist	VERB
ejpam-5837	2	8	of	of	ADP
ejpam-5837	2	9	a	a	DET
ejpam-5837	2	10	non	non	ADJ
ejpam-5837	2	11	-	-	ADJ
ejpam-5837	2	12	empty	empty	ADJ
ejpam-5837	2	13	set	set	NOUN
ejpam-5837	2	14	,	,	PUNCT
ejpam-5837	2	15	an	an	DET
ejpam-5837	2	16	associative	associative	ADJ
ejpam-5837	2	17	binary	binary	ADJ
ejpam-5837	2	18	operation	operation	NOUN
ejpam-5837	2	19	,	,	PUNCT
ejpam-5837	2	20	and	and	CCONJ
ejpam-5837	2	21	a	a	DET
ejpam-5837	2	22	partial	partial	ADJ
ejpam-5837	2	23	order	order	NOUN
ejpam-5837	2	24	compatible	compatible	ADJ
ejpam-5837	2	25	with	with	ADP
ejpam-5837	2	26	this	this	DET
ejpam-5837	2	27	binary	binary	ADJ
ejpam-5837	2	28	operation	operation	NOUN
ejpam-5837	2	29	.	.	PUNCT
ejpam-5837	3	1	this	this	DET
ejpam-5837	3	2	paper	paper	NOUN
ejpam-5837	3	3	aims	aim	VERB
ejpam-5837	3	4	to	to	PART
ejpam-5837	3	5	define	define	VERB
ejpam-5837	3	6	almost	almost	ADV
ejpam-5837	3	7	(	(	PUNCT
ejpam-5837	3	8	m	m	PROPN
ejpam-5837	3	9	,	,	PUNCT
ejpam-5837	3	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	3	11	-	-	NOUN
ejpam-5837	3	12	ideals	ideal	NOUN
ejpam-5837	3	13	and	and	CCONJ
ejpam-5837	3	14	fuzzy	fuzzy	ADJ
ejpam-5837	3	15	almost	almost	ADV
ejpam-5837	3	16	(	(	PUNCT
ejpam-5837	3	17	m	m	NOUN
ejpam-5837	3	18	,	,	PUNCT
ejpam-5837	3	19	n)-qausi	n)-qausi	NOUN
ejpam-5837	3	20	-	-	NOUN
ejpam-5837	3	21	ideals	ideal	NOUN
ejpam-5837	3	22	in	in	ADP
ejpam-5837	3	23	ordered	order	VERB
ejpam-5837	3	24	semigroups	semigroup	NOUN
ejpam-5837	3	25	.	.	PUNCT
ejpam-5837	4	1	we	we	PRON
ejpam-5837	4	2	prove	prove	VERB
ejpam-5837	4	3	the	the	DET
ejpam-5837	4	4	union	union	NOUN
ejpam-5837	4	5	of	of	ADP
ejpam-5837	4	6	almost	almost	ADV
ejpam-5837	4	7	(	(	PUNCT
ejpam-5837	4	8	m	m	PROPN
ejpam-5837	4	9	,	,	PUNCT
ejpam-5837	4	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	4	11	-	-	NOUN
ejpam-5837	4	12	ideals	ideal	NOUN
ejpam-5837	4	13	,	,	PUNCT
ejpam-5837	4	14	including	include	VERB
ejpam-5837	4	15	almost	almost	ADV
ejpam-5837	4	16	(	(	PUNCT
ejpam-5837	4	17	m	m	NOUN
ejpam-5837	4	18	,	,	PUNCT
ejpam-5837	4	19	n)-qausi	n)-qausi	NOUN
ejpam-5837	4	20	-	-	NOUN
ejpam-5837	4	21	ideals	ideal	NOUN
ejpam-5837	4	22	in	in	ADP
ejpam-5837	4	23	ordered	order	VERB
ejpam-5837	4	24	semigroups	semigroup	NOUN
ejpam-5837	4	25	.	.	PUNCT
ejpam-5837	5	1	in	in	ADP
ejpam-5837	5	2	class	class	NOUN
ejpam-5837	5	3	,	,	PUNCT
ejpam-5837	5	4	fuzzifications	fuzzification	NOUN
ejpam-5837	5	5	are	be	AUX
ejpam-5837	5	6	the	the	DET
ejpam-5837	5	7	same	same	ADJ
ejpam-5837	5	8	.	.	PUNCT
ejpam-5837	6	1	finally	finally	ADV
ejpam-5837	6	2	,	,	PUNCT
ejpam-5837	6	3	we	we	PRON
ejpam-5837	6	4	connect	connect	VERB
ejpam-5837	6	5	relation	relation	NOUN
ejpam-5837	6	6	almost	almost	ADV
ejpam-5837	6	7	(	(	PUNCT
ejpam-5837	6	8	m	m	PROPN
ejpam-5837	6	9	,	,	PUNCT
ejpam-5837	6	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	6	11	-	-	NOUN
ejpam-5837	6	12	ideals	ideal	NOUN
ejpam-5837	6	13	and	and	CCONJ
ejpam-5837	6	14	fuzzy	fuzzy	ADJ
ejpam-5837	6	15	almost	almost	ADV
ejpam-5837	6	16	(	(	PUNCT
ejpam-5837	6	17	m	m	PROPN
ejpam-5837	6	18	,	,	PUNCT
ejpam-5837	6	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	6	20	-	-	NOUN
ejpam-5837	6	21	ideals	ideal	NOUN
ejpam-5837	6	22	in	in	ADP
ejpam-5837	6	23	ordered	order	VERB
ejpam-5837	6	24	semigroups	semigroup	NOUN
ejpam-5837	6	25	.	.	PUNCT
ejpam-5837	7	1	2020	2020	NUM
ejpam-5837	7	2	mathematics	mathematic	NOUN
ejpam-5837	7	3	subject	subject	NOUN
ejpam-5837	7	4	classifications	classification	NOUN
ejpam-5837	7	5	:	:	PUNCT
ejpam-5837	7	6	20m12	20m12	NUM
ejpam-5837	7	7	,	,	PUNCT
ejpam-5837	7	8	06f05	06f05	PRON
ejpam-5837	7	9	key	key	ADJ
ejpam-5837	7	10	words	word	NOUN
ejpam-5837	7	11	and	and	CCONJ
ejpam-5837	7	12	phrases	phrase	NOUN
ejpam-5837	7	13	:	:	PUNCT
ejpam-5837	7	14	ordered	order	VERB
ejpam-5837	7	15	almost	almost	ADV
ejpam-5837	7	16	(	(	PUNCT
ejpam-5837	7	17	m	m	PROPN
ejpam-5837	7	18	,	,	PUNCT
ejpam-5837	7	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	7	20	-	-	PUNCT
ejpam-5837	7	21	ideal	ideal	ADJ
ejpam-5837	7	22	,	,	PUNCT
ejpam-5837	7	23	fuzzy	fuzzy	ADJ
ejpam-5837	7	24	ordered	order	VERB
ejpam-5837	7	25	almost	almost	ADV
ejpam-5837	7	26	(	(	PUNCT
ejpam-5837	7	27	m	m	NOUN
ejpam-5837	7	28	,	,	PUNCT
ejpam-5837	7	29	n)-quasiideal	n)-quasiideal	ADJ
ejpam-5837	7	30	,	,	PUNCT
ejpam-5837	7	31	ordered	order	VERB
ejpam-5837	7	32	semigroups	semigroup	NOUN
ejpam-5837	7	33	1	1	X
ejpam-5837	7	34	.	.	X
ejpam-5837	7	35	introduction	introduction	NOUN
ejpam-5837	7	36	ordered	order	VERB
ejpam-5837	7	37	semigroup	semigroup	PROPN
ejpam-5837	7	38	is	be	AUX
ejpam-5837	7	39	an	an	DET
ejpam-5837	7	40	algebraic	algebraic	ADJ
ejpam-5837	7	41	structure	structure	NOUN
ejpam-5837	7	42	in	in	ADP
ejpam-5837	7	43	a	a	DET
ejpam-5837	7	44	binary	binary	ADJ
ejpam-5837	7	45	operation	operation	NOUN
ejpam-5837	7	46	satisfying	satisfy	VERB
ejpam-5837	7	47	associative	associative	ADJ
ejpam-5837	7	48	property	property	NOUN
ejpam-5837	7	49	and	and	CCONJ
ejpam-5837	7	50	a	a	DET
ejpam-5837	7	51	partial	partial	ADJ
ejpam-5837	7	52	order	order	NOUN
ejpam-5837	7	53	with	with	ADP
ejpam-5837	7	54	the	the	DET
ejpam-5837	7	55	compatibility	compatibility	NOUN
ejpam-5837	7	56	.	.	PUNCT
ejpam-5837	8	1	the	the	DET
ejpam-5837	8	2	concepts	concept	NOUN
ejpam-5837	8	3	of	of	ADP
ejpam-5837	8	4	quasi	quasi	NOUN
ejpam-5837	8	5	-	-	NOUN
ejpam-5837	8	6	ideals	ideal	NOUN
ejpam-5837	8	7	of	of	ADP
ejpam-5837	8	8	semigroups	semigroup	NOUN
ejpam-5837	8	9	presented	present	VERB
ejpam-5837	8	10	by	by	ADP
ejpam-5837	8	11	steinfied	steinfie	VERB
ejpam-5837	8	12	[	[	X
ejpam-5837	8	13	1	1	X
ejpam-5837	8	14	]	]	PUNCT
ejpam-5837	8	15	in	in	ADP
ejpam-5837	8	16	1956	1956	NUM
ejpam-5837	8	17	.	.	PUNCT
ejpam-5837	9	1	the	the	DET
ejpam-5837	9	2	dealing	deal	VERB
ejpam-5837	9	3	with	with	ADP
ejpam-5837	9	4	various	various	ADJ
ejpam-5837	9	5	problems	problem	NOUN
ejpam-5837	9	6	related	relate	VERB
ejpam-5837	9	7	to	to	ADP
ejpam-5837	9	8	uncertain	uncertain	ADJ
ejpam-5837	9	9	conditions	condition	NOUN
ejpam-5837	9	10	by	by	ADP
ejpam-5837	9	11	fuzzy	fuzzy	ADJ
ejpam-5837	9	12	sets	set	NOUN
ejpam-5837	9	13	by	by	ADP
ejpam-5837	9	14	zadeh	zadeh	PROPN
ejpam-5837	9	15	in	in	ADP
ejpam-5837	9	16	1965	1965	NUM
ejpam-5837	9	17	,	,	PUNCT
ejpam-5837	9	18	[	[	X
ejpam-5837	9	19	2	2	NUM
ejpam-5837	9	20	]	]	PUNCT
ejpam-5837	9	21	.	.	PUNCT
ejpam-5837	10	1	these	these	DET
ejpam-5837	10	2	concepts	concept	NOUN
ejpam-5837	10	3	were	be	AUX
ejpam-5837	10	4	applied	apply	VERB
ejpam-5837	10	5	in	in	ADP
ejpam-5837	10	6	many	many	ADJ
ejpam-5837	10	7	areas	area	NOUN
ejpam-5837	10	8	,	,	PUNCT
ejpam-5837	10	9	such	such	ADJ
ejpam-5837	10	10	as	as	ADP
ejpam-5837	10	11	medical	medical	ADJ
ejpam-5837	10	12	science	science	NOUN
ejpam-5837	10	13	,	,	PUNCT
ejpam-5837	10	14	theoretical	theoretical	ADJ
ejpam-5837	10	15	physics	physics	NOUN
ejpam-5837	10	16	,	,	PUNCT
ejpam-5837	10	17	robotics	robotic	NOUN
ejpam-5837	10	18	,	,	PUNCT
ejpam-5837	10	19	computer	computer	NOUN
ejpam-5837	10	20	science	science	NOUN
ejpam-5837	10	21	,	,	PUNCT
ejpam-5837	10	22	control	control	NOUN
ejpam-5837	10	23	engineering	engineering	NOUN
ejpam-5837	10	24	,	,	PUNCT
ejpam-5837	10	25	information	information	NOUN
ejpam-5837	10	26	science	science	NOUN
ejpam-5837	10	27	,	,	PUNCT
ejpam-5837	10	28	measure	measure	NOUN
ejpam-5837	10	29	theory	theory	NOUN
ejpam-5837	10	30	,	,	PUNCT
ejpam-5837	10	31	logic	logic	NOUN
ejpam-5837	10	32	,	,	PUNCT
ejpam-5837	10	33	set	set	ADJ
ejpam-5837	10	34	theory	theory	NOUN
ejpam-5837	10	35	,	,	PUNCT
ejpam-5837	10	36	and	and	CCONJ
ejpam-5837	10	37	topology	topology	NOUN
ejpam-5837	10	38	.	.	PUNCT
ejpam-5837	11	1	rosenfeld	rosenfeld	PROPN
ejpam-5837	11	2	studied	study	VERB
ejpam-5837	11	3	concent	concent	NOUN
ejpam-5837	11	4	of	of	ADP
ejpam-5837	11	5	fuzzy	fuzzy	ADJ
ejpam-5837	11	6	subgroups	subgroup	NOUN
ejpam-5837	11	7	and	and	CCONJ
ejpam-5837	11	8	fuzzy	fuzzy	ADJ
ejpam-5837	11	9	ideals	ideal	NOUN
ejpam-5837	11	10	.	.	PUNCT
ejpam-5837	12	1	in	in	ADP
ejpam-5837	12	2	1981	1981	NUM
ejpam-5837	12	3	kuroki	kuroki	NOUN
ejpam-5837	12	4	studied	study	VERB
ejpam-5837	12	5	the	the	DET
ejpam-5837	12	6	typers	typer	NOUN
ejpam-5837	12	7	of	of	ADP
ejpam-5837	12	8	fuzzy	fuzzy	ADJ
ejpam-5837	12	9	subsemigroups	subsemigroup	NOUN
ejpam-5837	12	10	.	.	PUNCT
ejpam-5837	13	1	in	in	ADP
ejpam-5837	13	2	the	the	DET
ejpam-5837	13	3	same	same	ADJ
ejpam-5837	13	4	year	year	NOUN
ejpam-5837	13	5	satko	satko	NOUN
ejpam-5837	13	6	and	and	CCONJ
ejpam-5837	13	7	grosek	grosek	NOUN
ejpam-5837	13	8	[	[	X
ejpam-5837	13	9	3	3	X
ejpam-5837	13	10	]	]	PUNCT
ejpam-5837	13	11	discussed	discuss	VERB
ejpam-5837	13	12	concept	concept	NOUN
ejpam-5837	13	13	of	of	ADP
ejpam-5837	13	14	an	an	DET
ejpam-5837	13	15	almost	almost	ADV
ejpam-5837	13	16	-	-	PUNCT
ejpam-5837	13	17	ideal	ideal	NOUN
ejpam-5837	13	18	(	(	PUNCT
ejpam-5837	13	19	a	a	DET
ejpam-5837	13	20	-	-	PUNCT
ejpam-5837	13	21	ideal	ideal	NOUN
ejpam-5837	13	22	)	)	PUNCT
ejpam-5837	13	23	in	in	ADP
ejpam-5837	13	24	a	a	DET
ejpam-5837	13	25	semilattice	semilattice	NOUN
ejpam-5837	13	26	.	.	PUNCT
ejpam-5837	14	1	and	and	CCONJ
ejpam-5837	14	2	s.	s.	PROPN
ejpam-5837	14	3	bogdanovic	bogdanovic	PROPN
ejpam-5837	15	1	[	[	X
ejpam-5837	15	2	4	4	X
ejpam-5837	15	3	]	]	PUNCT
ejpam-5837	15	4	gave	give	VERB
ejpam-5837	15	5	the	the	DET
ejpam-5837	15	6	concept	concept	NOUN
ejpam-5837	15	7	of	of	ADP
ejpam-5837	15	8	almost	almost	ADV
ejpam-5837	15	9	bi	bi	NOUN
ejpam-5837	15	10	-	-	NOUN
ejpam-5837	15	11	ideals	ideal	NOUN
ejpam-5837	15	12	in	in	ADP
ejpam-5837	15	13	semigroups	semigroup	NOUN
ejpam-5837	15	14	.	.	PUNCT
ejpam-5837	16	1	in	in	ADP
ejpam-5837	16	2	2019	2019	NUM
ejpam-5837	16	3	,	,	PUNCT
ejpam-5837	16	4	s.	s.	PROPN
ejpam-5837	16	5	suebsung	suebsung	PROPN
ejpam-5837	16	6	et	et	PROPN
ejpam-5837	16	7	al	al	PROPN
ejpam-5837	16	8	.	.	PUNCT
ejpam-5837	17	1	[	[	X
ejpam-5837	17	2	5	5	NUM
ejpam-5837	17	3	]	]	PUNCT
ejpam-5837	17	4	investigated	investigate	VERB
ejpam-5837	17	5	almost	almost	ADV
ejpam-5837	17	6	ideals	ideal	NOUN
ejpam-5837	17	7	and	and	CCONJ
ejpam-5837	17	8	fuzzy	fuzzy	ADJ
ejpam-5837	17	9	almost	almost	ADV
ejpam-5837	17	10	ideals	ideal	NOUN
ejpam-5837	17	11	in	in	ADP
ejpam-5837	17	12	ternary	ternary	ADJ
ejpam-5837	17	13	semigroups	semigroup	NOUN
ejpam-5837	17	14	.	.	PUNCT
ejpam-5837	18	1	in	in	ADP
ejpam-5837	18	2	2020	2020	NUM
ejpam-5837	18	3	,	,	PUNCT
ejpam-5837	18	4	chinram	chinram	PROPN
ejpam-5837	18	5	et	et	PROPN
ejpam-5837	18	6	al	al	PROPN
ejpam-5837	18	7	.	.	PUNCT
ejpam-5837	19	1	[	[	X
ejpam-5837	19	2	6	6	NUM
ejpam-5837	19	3	]	]	PUNCT
ejpam-5837	19	4	discussed	discuss	VERB
ejpam-5837	19	5	almost	almost	ADV
ejpam-5837	19	6	∗corresponding	∗corresponde	VERB
ejpam-5837	19	7	author	author	NOUN
ejpam-5837	19	8	.	.	PUNCT
ejpam-5837	20	1	doi	doi	NOUN
ejpam-5837	20	2	:	:	PUNCT
ejpam-5837	20	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5837	https://doi.org/10.29020/nybg.ejpam.v18i2.5837	NOUN
ejpam-5837	20	4	email	email	NOUN
ejpam-5837	20	5	addresses	address	VERB
ejpam-5837	20	6	:	:	PUNCT
ejpam-5837	21	1	thiti.ga@up.ac.th	thiti.ga@up.ac.th	PROPN
ejpam-5837	21	2	(	(	PUNCT
ejpam-5837	21	3	t.	t.	NOUN
ejpam-5837	21	4	gaketem	gaketem	PROPN
ejpam-5837	21	5	)	)	PUNCT
ejpam-5837	21	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5837	22	1	1	1	NUM
ejpam-5837	22	2	copyright	copyright	NOUN
ejpam-5837	22	3	:	:	PUNCT
ejpam-5837	22	4	©	©	PROPN
ejpam-5837	22	5	2025	2025	NUM
ejpam-5837	22	6	the	the	DET
ejpam-5837	22	7	author(s	author(s	NOUN
ejpam-5837	22	8	)	)	PUNCT
ejpam-5837	22	9	.	.	PUNCT
ejpam-5837	23	1	(	(	PUNCT
ejpam-5837	23	2	cc	cc	NOUN
ejpam-5837	23	3	by	by	ADP
ejpam-5837	23	4	-	-	PUNCT
ejpam-5837	23	5	nc	nc	PROPN
ejpam-5837	23	6	4.0	4.0	NUM
ejpam-5837	23	7	)	)	PUNCT
ejpam-5837	23	8	p.	p.	NOUN
ejpam-5837	23	9	khamrot	khamrot	PROPN
ejpam-5837	24	1	et	et	PROPN
ejpam-5837	24	2	al	al	PROPN
ejpam-5837	24	3	.	.	PUNCT
ejpam-5837	24	4	/	/	SYM
ejpam-5837	24	5	eur	eur	PROPN
ejpam-5837	24	6	.	.	PUNCT
ejpam-5837	25	1	j.	j.	PROPN
ejpam-5837	25	2	pure	pure	PROPN
ejpam-5837	25	3	appl	appl	PROPN
ejpam-5837	25	4	.	.	PROPN
ejpam-5837	25	5	math	math	PROPN
ejpam-5837	25	6	,	,	PUNCT
ejpam-5837	25	7	18	18	NUM
ejpam-5837	25	8	(	(	PUNCT
ejpam-5837	25	9	2	2	NUM
ejpam-5837	25	10	)	)	PUNCT
ejpam-5837	25	11	(	(	PUNCT
ejpam-5837	25	12	2025	2025	NUM
ejpam-5837	25	13	)	)	PUNCT
ejpam-5837	25	14	,	,	PUNCT
ejpam-5837	25	15	5837	5837	NUM
ejpam-5837	25	16	2	2	NUM
ejpam-5837	25	17	of	of	ADP
ejpam-5837	25	18	13	13	NUM
ejpam-5837	25	19	interior	interior	ADJ
ejpam-5837	25	20	ideals	ideal	NOUN
ejpam-5837	25	21	and	and	CCONJ
ejpam-5837	25	22	weakly	weakly	ADJ
ejpam-5837	25	23	almost	almost	ADV
ejpam-5837	25	24	interior	interior	ADJ
ejpam-5837	25	25	ideals	ideal	NOUN
ejpam-5837	25	26	in	in	ADP
ejpam-5837	25	27	semigroups	semigroup	NOUN
ejpam-5837	25	28	and	and	CCONJ
ejpam-5837	25	29	studied	study	VERB
ejpam-5837	25	30	the	the	DET
ejpam-5837	25	31	relationship	relationship	NOUN
ejpam-5837	25	32	between	between	ADP
ejpam-5837	25	33	almost	almost	ADV
ejpam-5837	25	34	interior	interior	ADJ
ejpam-5837	25	35	ideals	ideal	NOUN
ejpam-5837	25	36	and	and	CCONJ
ejpam-5837	25	37	weakly	weakly	ADJ
ejpam-5837	25	38	almost	almost	ADV
ejpam-5837	25	39	interior	interior	ADJ
ejpam-5837	25	40	ideals	ideal	NOUN
ejpam-5837	25	41	in	in	ADP
ejpam-5837	25	42	semigroups	semigroup	NOUN
ejpam-5837	25	43	.	.	PUNCT
ejpam-5837	26	1	the	the	DET
ejpam-5837	26	2	research	research	NOUN
ejpam-5837	26	3	of	of	ADP
ejpam-5837	26	4	almost	almost	ADV
ejpam-5837	26	5	ideals	ideal	NOUN
ejpam-5837	26	6	studied	study	VERB
ejpam-5837	26	7	in	in	ADP
ejpam-5837	26	8	semihypergroups	semihypergroup	NOUN
ejpam-5837	26	9	such	such	ADJ
ejpam-5837	26	10	that	that	PRON
ejpam-5837	26	11	in	in	ADP
ejpam-5837	26	12	2021	2021	NUM
ejpam-5837	26	13	,	,	PUNCT
ejpam-5837	26	14	p.	p.	NOUN
ejpam-5837	26	15	muangdoo	muangdoo	VERB
ejpam-5837	26	16	et	et	PROPN
ejpam-5837	26	17	al	al	PROPN
ejpam-5837	26	18	.	.	PUNCT
ejpam-5837	27	1	[	[	X
ejpam-5837	27	2	7	7	X
ejpam-5837	27	3	]	]	PUNCT
ejpam-5837	27	4	studied	study	VERB
ejpam-5837	27	5	almost	almost	ADV
ejpam-5837	27	6	bi	bi	NOUN
ejpam-5837	27	7	-	-	NOUN
ejpam-5837	27	8	hyperideals	hyperideal	NOUN
ejpam-5837	27	9	and	and	CCONJ
ejpam-5837	27	10	their	their	PRON
ejpam-5837	27	11	fuzzification	fuzzification	NOUN
ejpam-5837	27	12	of	of	ADP
ejpam-5837	27	13	semihypergroups	semihypergroup	NOUN
ejpam-5837	27	14	.	.	PUNCT
ejpam-5837	28	1	w.	w.	PROPN
ejpam-5837	28	2	nakkhasen	nakkhasen	PROPN
ejpam-5837	28	3	et	et	PROPN
ejpam-5837	28	4	al	al	PROPN
ejpam-5837	28	5	.	.	PUNCT
ejpam-5837	29	1	[	[	X
ejpam-5837	29	2	8	8	NUM
ejpam-5837	29	3	]	]	PUNCT
ejpam-5837	29	4	discussed	discuss	VERB
ejpam-5837	29	5	fuzzy	fuzzy	ADJ
ejpam-5837	29	6	,	,	PUNCT
ejpam-5837	29	7	almost	almost	ADV
ejpam-5837	29	8	interior	interior	ADJ
ejpam-5837	29	9	hyperideals	hyperideal	NOUN
ejpam-5837	29	10	of	of	ADP
ejpam-5837	29	11	semihypergroups	semihypergroup	NOUN
ejpam-5837	29	12	.	.	PUNCT
ejpam-5837	30	1	in	in	ADP
ejpam-5837	30	2	2022	2022	NUM
ejpam-5837	30	3	,	,	PUNCT
ejpam-5837	30	4	s.	s.	PROPN
ejpam-5837	30	5	suebsung	suebsung	PROPN
ejpam-5837	30	6	et	et	PROPN
ejpam-5837	30	7	al	al	PROPN
ejpam-5837	30	8	.	.	PUNCT
ejpam-5837	31	1	[	[	X
ejpam-5837	31	2	9	9	NUM
ejpam-5837	31	3	]	]	PUNCT
ejpam-5837	31	4	introduced	introduce	VERB
ejpam-5837	31	5	almost	almost	ADV
ejpam-5837	31	6	ideals	ideal	NOUN
ejpam-5837	31	7	in	in	ADP
ejpam-5837	31	8	ordered	order	VERB
ejpam-5837	31	9	semigroups	semigroup	NOUN
ejpam-5837	31	10	.	.	PUNCT
ejpam-5837	32	1	in	in	ADP
ejpam-5837	32	2	the	the	DET
ejpam-5837	32	3	same	same	ADJ
ejpam-5837	32	4	year	year	NOUN
ejpam-5837	32	5	t.	t.	NOUN
ejpam-5837	32	6	gaketem	gaketem	PROPN
ejpam-5837	32	7	and	and	CCONJ
ejpam-5837	32	8	p.	p.	NOUN
ejpam-5837	32	9	khamrot	khamrot	NOUN
ejpam-5837	33	1	[	[	X
ejpam-5837	33	2	10	10	NUM
ejpam-5837	33	3	]	]	PUNCT
ejpam-5837	33	4	explored	explore	VERB
ejpam-5837	33	5	the	the	DET
ejpam-5837	33	6	concept	concept	NOUN
ejpam-5837	33	7	of	of	ADP
ejpam-5837	33	8	almost	almost	ADV
ejpam-5837	33	9	ideals	ideal	NOUN
ejpam-5837	33	10	within	within	ADP
ejpam-5837	33	11	the	the	DET
ejpam-5837	33	12	framework	framework	NOUN
ejpam-5837	33	13	of	of	ADP
ejpam-5837	33	14	bipolar	bipolar	ADJ
ejpam-5837	33	15	fuzzy	fuzzy	ADJ
ejpam-5837	33	16	sets	set	NOUN
ejpam-5837	33	17	,	,	PUNCT
ejpam-5837	33	18	specifically	specifically	ADV
ejpam-5837	33	19	focusing	focus	VERB
ejpam-5837	33	20	on	on	ADP
ejpam-5837	33	21	bipolar	bipolar	ADJ
ejpam-5837	33	22	fuzzy	fuzzy	ADJ
ejpam-5837	33	23	almost	almost	ADV
ejpam-5837	33	24	bi	bi	NOUN
ejpam-5837	33	25	-	-	NOUN
ejpam-5837	33	26	ideals	ideal	NOUN
ejpam-5837	33	27	in	in	ADP
ejpam-5837	33	28	semigroups	semigroup	NOUN
ejpam-5837	33	29	.	.	PUNCT
ejpam-5837	34	1	in	in	ADP
ejpam-5837	34	2	2023	2023	NUM
ejpam-5837	34	3	,	,	PUNCT
ejpam-5837	34	4	r.	r.	PROPN
ejpam-5837	34	5	chinram	chinram	PROPN
ejpam-5837	34	6	et	et	PROPN
ejpam-5837	34	7	.	.	PUNCT
ejpam-5837	35	1	al	al	PROPN
ejpam-5837	36	1	[	[	X
ejpam-5837	36	2	11	11	NUM
ejpam-5837	36	3	]	]	PUNCT
ejpam-5837	36	4	studied	study	VERB
ejpam-5837	36	5	concept	concept	NOUN
ejpam-5837	36	6	almost	almost	ADV
ejpam-5837	36	7	(	(	PUNCT
ejpam-5837	36	8	m	m	PROPN
ejpam-5837	36	9	,	,	PUNCT
ejpam-5837	36	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	36	11	-	-	NOUN
ejpam-5837	36	12	ideals	ideal	NOUN
ejpam-5837	36	13	in	in	ADP
ejpam-5837	36	14	semigroups	semigroup	NOUN
ejpam-5837	36	15	and	and	CCONJ
ejpam-5837	36	16	their	their	PRON
ejpam-5837	36	17	fuzzifications	fuzzification	NOUN
ejpam-5837	36	18	.	.	PUNCT
ejpam-5837	37	1	in	in	ADP
ejpam-5837	37	2	the	the	DET
ejpam-5837	37	3	same	same	ADJ
ejpam-5837	37	4	year	year	NOUN
ejpam-5837	37	5	,	,	PUNCT
ejpam-5837	37	6	t.	t.	PROPN
ejpam-5837	37	7	gaketem	gaketem	PROPN
ejpam-5837	37	8	and	and	CCONJ
ejpam-5837	37	9	p.	p.	NOUN
ejpam-5837	37	10	khamrot	khamrot	NOUN
ejpam-5837	38	1	[	[	X
ejpam-5837	38	2	12	12	NUM
ejpam-5837	38	3	]	]	PUNCT
ejpam-5837	38	4	studied	study	VERB
ejpam-5837	38	5	bipolar	bipolar	ADJ
ejpam-5837	38	6	fuzzy	fuzzy	ADJ
ejpam-5837	38	7	almost	almost	ADV
ejpam-5837	38	8	interior	interior	ADJ
ejpam-5837	38	9	ideals	ideal	NOUN
ejpam-5837	38	10	in	in	ADP
ejpam-5837	38	11	semigroups	semigroup	NOUN
ejpam-5837	38	12	.	.	PUNCT
ejpam-5837	39	1	in	in	ADP
ejpam-5837	39	2	2024	2024	NUM
ejpam-5837	39	3	,	,	PUNCT
ejpam-5837	39	4	t.	t.	PROPN
ejpam-5837	39	5	gaketem	gaketem	PROPN
ejpam-5837	39	6	and	and	CCONJ
ejpam-5837	39	7	p.	p.	NOUN
ejpam-5837	39	8	khamrot	khamrot	NOUN
ejpam-5837	40	1	[	[	X
ejpam-5837	40	2	13	13	NUM
ejpam-5837	40	3	]	]	PUNCT
ejpam-5837	40	4	discussed	discuss	VERB
ejpam-5837	40	5	bipolar	bipolar	ADJ
ejpam-5837	40	6	fuzzy	fuzzy	ADJ
ejpam-5837	40	7	almost	almost	ADV
ejpam-5837	40	8	ideals	ideal	NOUN
ejpam-5837	40	9	in	in	ADP
ejpam-5837	40	10	semigroups	semigroup	NOUN
ejpam-5837	40	11	.	.	PUNCT
ejpam-5837	41	1	in	in	ADP
ejpam-5837	41	2	addition	addition	NOUN
ejpam-5837	41	3	,	,	PUNCT
ejpam-5837	41	4	almost	almost	ADV
ejpam-5837	41	5	ideal	ideal	ADJ
ejpam-5837	41	6	’s	’s	PART
ejpam-5837	41	7	work	work	NOUN
ejpam-5837	41	8	also	also	ADV
ejpam-5837	41	9	has	have	VERB
ejpam-5837	41	10	many	many	ADJ
ejpam-5837	41	11	studies	study	NOUN
ejpam-5837	41	12	,	,	PUNCT
ejpam-5837	41	13	such	such	ADJ
ejpam-5837	41	14	as	as	ADP
ejpam-5837	41	15	almost	almost	ADV
ejpam-5837	41	16	ideals	ideal	NOUN
ejpam-5837	41	17	in	in	ADP
ejpam-5837	41	18	ordered	order	VERB
ejpam-5837	41	19	semigroup	semigroup	NOUN
ejpam-5837	42	1	[	[	X
ejpam-5837	42	2	14	14	NUM
ejpam-5837	42	3	]	]	X
ejpam-5837	42	4	,	,	PUNCT
ejpam-5837	42	5	almost	almost	ADV
ejpam-5837	42	6	ideals	ideal	NOUN
ejpam-5837	42	7	in	in	ADP
ejpam-5837	42	8	semirings	semiring	NOUN
ejpam-5837	42	9	[	[	X
ejpam-5837	42	10	15	15	NUM
ejpam-5837	42	11	]	]	PUNCT
ejpam-5837	42	12	,	,	PUNCT
ejpam-5837	42	13	almost	almost	ADV
ejpam-5837	42	14	ideals	ideal	NOUN
ejpam-5837	42	15	in	in	ADP
ejpam-5837	42	16	ternary	ternary	ADJ
ejpam-5837	42	17	semiring	semiring	NOUN
ejpam-5837	43	1	[	[	X
ejpam-5837	43	2	16	16	NUM
ejpam-5837	43	3	]	]	PUNCT
ejpam-5837	43	4	,	,	PUNCT
ejpam-5837	43	5	etc	etc	X
ejpam-5837	43	6	.	.	X
ejpam-5837	43	7	not	not	PART
ejpam-5837	43	8	long	long	ADV
ejpam-5837	43	9	ago	ago	ADV
ejpam-5837	43	10	in	in	ADP
ejpam-5837	43	11	2025	2025	NUM
ejpam-5837	43	12	p.	p.	NOUN
ejpam-5837	43	13	khamrot	khamrot	PROPN
ejpam-5837	43	14	et	et	PROPN
ejpam-5837	43	15	al	al	PROPN
ejpam-5837	43	16	.	.	PUNCT
ejpam-5837	44	1	[	[	X
ejpam-5837	44	2	17	17	NUM
ejpam-5837	44	3	]	]	PUNCT
ejpam-5837	44	4	studied	study	VERB
ejpam-5837	44	5	fuzzy	fuzzy	ADJ
ejpam-5837	44	6	(	(	PUNCT
ejpam-5837	44	7	m	m	NOUN
ejpam-5837	44	8	,	,	PUNCT
ejpam-5837	44	9	n)-ideals	n)-ideal	NOUN
ejpam-5837	44	10	and	and	CCONJ
ejpam-5837	44	11	n	n	CCONJ
ejpam-5837	44	12	-	-	PUNCT
ejpam-5837	44	13	interior	interior	ADJ
ejpam-5837	44	14	ideals	ideal	NOUN
ejpam-5837	44	15	in	in	ADP
ejpam-5837	44	16	ordered	order	VERB
ejpam-5837	44	17	semigroups	semigroup	NOUN
ejpam-5837	44	18	.	.	PUNCT
ejpam-5837	45	1	in	in	ADP
ejpam-5837	45	2	the	the	DET
ejpam-5837	45	3	same	same	ADJ
ejpam-5837	45	4	year	year	NOUN
ejpam-5837	45	5	,	,	PUNCT
ejpam-5837	45	6	p.	p.	NOUN
ejpam-5837	45	7	khamrot	khamrot	NOUN
ejpam-5837	45	8	et	et	PROPN
ejpam-5837	45	9	al	al	PROPN
ejpam-5837	45	10	.	.	PUNCT
ejpam-5837	46	1	[	[	X
ejpam-5837	46	2	18	18	NUM
ejpam-5837	46	3	]	]	PUNCT
ejpam-5837	46	4	extend	extend	NOUN
ejpam-5837	46	5	concepts	concept	NOUN
ejpam-5837	46	6	fuzzy	fuzzy	ADJ
ejpam-5837	46	7	(	(	PUNCT
ejpam-5837	46	8	m	m	NOUN
ejpam-5837	46	9	,	,	PUNCT
ejpam-5837	46	10	n)-ideals	n)-ideal	NOUN
ejpam-5837	46	11	and	and	CCONJ
ejpam-5837	46	12	n	n	CCONJ
ejpam-5837	46	13	-	-	PUNCT
ejpam-5837	46	14	interior	interior	ADJ
ejpam-5837	46	15	ideals	ideal	NOUN
ejpam-5837	46	16	to	to	PART
ejpam-5837	46	17	biploar	biploar	VERB
ejpam-5837	46	18	fuzzy	fuzzy	ADJ
ejpam-5837	46	19	sets	set	NOUN
ejpam-5837	46	20	.	.	PUNCT
ejpam-5837	47	1	in	in	ADP
ejpam-5837	47	2	this	this	DET
ejpam-5837	47	3	paper	paper	NOUN
ejpam-5837	47	4	we	we	PRON
ejpam-5837	47	5	extend	extend	VERB
ejpam-5837	47	6	the	the	DET
ejpam-5837	47	7	definition	definition	NOUN
ejpam-5837	47	8	of	of	ADP
ejpam-5837	47	9	almost	almost	ADV
ejpam-5837	47	10	(	(	PUNCT
ejpam-5837	47	11	m	m	PROPN
ejpam-5837	47	12	,	,	PUNCT
ejpam-5837	47	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	47	14	-	-	NOUN
ejpam-5837	47	15	ideals	ideal	NOUN
ejpam-5837	47	16	in	in	ADP
ejpam-5837	47	17	semigroups	semigroup	NOUN
ejpam-5837	47	18	go	go	VERB
ejpam-5837	47	19	to	to	ADP
ejpam-5837	47	20	ordered	order	VERB
ejpam-5837	47	21	semigroups	semigroup	NOUN
ejpam-5837	47	22	.	.	PUNCT
ejpam-5837	48	1	we	we	PRON
ejpam-5837	48	2	discussed	discuss	VERB
ejpam-5837	48	3	the	the	DET
ejpam-5837	48	4	union	union	NOUN
ejpam-5837	48	5	of	of	ADP
ejpam-5837	48	6	almost	almost	ADV
ejpam-5837	48	7	(	(	PUNCT
ejpam-5837	48	8	m	m	PROPN
ejpam-5837	48	9	,	,	PUNCT
ejpam-5837	48	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	48	11	-	-	NOUN
ejpam-5837	48	12	ideals	ideal	NOUN
ejpam-5837	48	13	,	,	PUNCT
ejpam-5837	48	14	including	include	VERB
ejpam-5837	48	15	almost	almost	ADV
ejpam-5837	48	16	(	(	PUNCT
ejpam-5837	48	17	m	m	PROPN
ejpam-5837	48	18	,	,	PUNCT
ejpam-5837	48	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	48	20	-	-	NOUN
ejpam-5837	48	21	ideals	ideal	NOUN
ejpam-5837	48	22	in	in	ADP
ejpam-5837	48	23	ordered	order	VERB
ejpam-5837	48	24	semigroups	semigroup	NOUN
ejpam-5837	48	25	.	.	PUNCT
ejpam-5837	49	1	in	in	ADP
ejpam-5837	49	2	class	class	NOUN
ejpam-5837	49	3	,	,	PUNCT
ejpam-5837	49	4	fuzzifications	fuzzification	NOUN
ejpam-5837	49	5	are	be	AUX
ejpam-5837	49	6	the	the	DET
ejpam-5837	49	7	same	same	ADJ
ejpam-5837	49	8	.	.	PUNCT
ejpam-5837	50	1	finally	finally	ADV
ejpam-5837	50	2	,	,	PUNCT
ejpam-5837	50	3	we	we	PRON
ejpam-5837	50	4	connect	connect	VERB
ejpam-5837	50	5	relation	relation	NOUN
ejpam-5837	50	6	almost	almost	ADV
ejpam-5837	50	7	(	(	PUNCT
ejpam-5837	50	8	m	m	PROPN
ejpam-5837	50	9	,	,	PUNCT
ejpam-5837	50	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	50	11	-	-	NOUN
ejpam-5837	50	12	ideals	ideal	NOUN
ejpam-5837	50	13	and	and	CCONJ
ejpam-5837	50	14	fuzzy	fuzzy	ADJ
ejpam-5837	50	15	almost	almost	ADV
ejpam-5837	50	16	(	(	PUNCT
ejpam-5837	50	17	m	m	PROPN
ejpam-5837	50	18	,	,	PUNCT
ejpam-5837	50	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	50	20	-	-	NOUN
ejpam-5837	50	21	ideals	ideal	NOUN
ejpam-5837	50	22	in	in	ADP
ejpam-5837	50	23	ordered	order	VERB
ejpam-5837	50	24	semigroups	semigroup	NOUN
ejpam-5837	50	25	.	.	PUNCT
ejpam-5837	51	1	2	2	X
ejpam-5837	51	2	.	.	X
ejpam-5837	51	3	preliminaries	preliminary	NOUN
ejpam-5837	51	4	now	now	ADV
ejpam-5837	51	5	,	,	PUNCT
ejpam-5837	51	6	we	we	PRON
ejpam-5837	51	7	recall	recall	VERB
ejpam-5837	51	8	the	the	DET
ejpam-5837	51	9	concept	concept	NOUN
ejpam-5837	51	10	of	of	ADP
ejpam-5837	51	11	ordered	order	VERB
ejpam-5837	51	12	semigroups	semigroup	NOUN
ejpam-5837	51	13	and	and	CCONJ
ejpam-5837	51	14	fuzzy	fuzzy	ADJ
ejpam-5837	51	15	sets	set	NOUN
ejpam-5837	51	16	.	.	PUNCT
ejpam-5837	52	1	additionally	additionally	ADV
ejpam-5837	52	2	,	,	PUNCT
ejpam-5837	52	3	their	their	PRON
ejpam-5837	52	4	preliminary	preliminary	ADJ
ejpam-5837	52	5	results	result	NOUN
ejpam-5837	52	6	are	be	AUX
ejpam-5837	52	7	provided	provide	VERB
ejpam-5837	52	8	.	.	PUNCT
ejpam-5837	53	1	definition	definition	NOUN
ejpam-5837	53	2	1	1	NUM
ejpam-5837	53	3	.	.	PUNCT
ejpam-5837	54	1	[	[	X
ejpam-5837	54	2	19	19	NUM
ejpam-5837	54	3	]	]	PUNCT
ejpam-5837	54	4	.	.	PUNCT
ejpam-5837	55	1	let	let	VERB
ejpam-5837	55	2	t	t	NOUN
ejpam-5837	55	3	be	be	AUX
ejpam-5837	55	4	a	a	DET
ejpam-5837	55	5	set	set	NOUN
ejpam-5837	55	6	with	with	ADP
ejpam-5837	55	7	a	a	DET
ejpam-5837	55	8	binary	binary	ADJ
ejpam-5837	55	9	opeation	opeation	NOUN
ejpam-5837	55	10	·	·	PUNCT
ejpam-5837	55	11	and	and	CCONJ
ejpam-5837	55	12	a	a	DET
ejpam-5837	55	13	binary	binary	ADJ
ejpam-5837	55	14	opeation	opeation	NOUN
ejpam-5837	55	15	relation	relation	NOUN
ejpam-5837	55	16	≤.	≤.	PROPN
ejpam-5837	55	17	then	then	ADV
ejpam-5837	55	18	(	(	PUNCT
ejpam-5837	55	19	t	t	PROPN
ejpam-5837	55	20	,	,	PUNCT
ejpam-5837	55	21	·	·	PUNCT
ejpam-5837	55	22	,	,	PUNCT
ejpam-5837	55	23	≤	≤	NUM
ejpam-5837	55	24	)	)	PUNCT
ejpam-5837	55	25	is	be	AUX
ejpam-5837	55	26	called	call	VERB
ejpam-5837	55	27	an	an	DET
ejpam-5837	55	28	ordred	ordre	VERB
ejpam-5837	55	29	semigroup	semigroup	NOUN
ejpam-5837	56	1	if	if	SCONJ
ejpam-5837	56	2	(	(	PUNCT
ejpam-5837	56	3	1	1	NUM
ejpam-5837	56	4	)	)	PUNCT
ejpam-5837	56	5	(	(	PUNCT
ejpam-5837	56	6	t	t	PROPN
ejpam-5837	56	7	,	,	PUNCT
ejpam-5837	56	8	·	·	PUNCT
ejpam-5837	56	9	)	)	PUNCT
ejpam-5837	56	10	is	be	AUX
ejpam-5837	56	11	a	a	DET
ejpam-5837	56	12	semigroup	semigroup	NOUN
ejpam-5837	56	13	,	,	PUNCT
ejpam-5837	56	14	(	(	PUNCT
ejpam-5837	56	15	2	2	NUM
ejpam-5837	56	16	)	)	PUNCT
ejpam-5837	56	17	(	(	PUNCT
ejpam-5837	56	18	t,≤	t,≤	NOUN
ejpam-5837	56	19	)	)	PUNCT
ejpam-5837	56	20	is	be	AUX
ejpam-5837	56	21	a	a	DET
ejpam-5837	56	22	partially	partially	ADV
ejpam-5837	56	23	ordered	order	VERB
ejpam-5837	56	24	set	set	NOUN
ejpam-5837	56	25	,	,	PUNCT
ejpam-5837	56	26	(	(	PUNCT
ejpam-5837	56	27	3	3	X
ejpam-5837	56	28	)	)	PUNCT
ejpam-5837	56	29	for	for	ADP
ejpam-5837	56	30	all	all	DET
ejpam-5837	56	31	a	a	DET
ejpam-5837	56	32	,	,	PUNCT
ejpam-5837	56	33	b	b	NOUN
ejpam-5837	56	34	,	,	PUNCT
ejpam-5837	56	35	c	c	PROPN
ejpam-5837	56	36	∈	∈	PROPN
ejpam-5837	56	37	t	t	PROPN
ejpam-5837	56	38	,	,	PUNCT
ejpam-5837	56	39	we	we	PRON
ejpam-5837	56	40	have	have	VERB
ejpam-5837	56	41	a	a	DET
ejpam-5837	56	42	≤	≤	NUM
ejpam-5837	56	43	b	b	NOUN
ejpam-5837	56	44	then	then	ADV
ejpam-5837	56	45	ac	ac	PROPN
ejpam-5837	56	46	≤	≤	PUNCT
ejpam-5837	56	47	bc	bc	PROPN
ejpam-5837	56	48	and	and	CCONJ
ejpam-5837	56	49	ca	can	AUX
ejpam-5837	56	50	≤	≤	NUM
ejpam-5837	56	51	cb	cb	PROPN
ejpam-5837	56	52	.	.	PROPN
ejpam-5837	57	1	for	for	ADP
ejpam-5837	57	2	a	a	DET
ejpam-5837	57	3	nonempty	nonempty	NOUN
ejpam-5837	57	4	subset	subset	NOUN
ejpam-5837	57	5	x	x	PUNCT
ejpam-5837	57	6	and	and	CCONJ
ejpam-5837	57	7	y	y	PROPN
ejpam-5837	57	8	of	of	ADP
ejpam-5837	57	9	ordered	order	VERB
ejpam-5837	57	10	semigroup	semigroup	PROPN
ejpam-5837	57	11	t	t	PROPN
ejpam-5837	57	12	,	,	PUNCT
ejpam-5837	57	13	we	we	PRON
ejpam-5837	57	14	write	write	VERB
ejpam-5837	57	15	(	(	PUNCT
ejpam-5837	57	16	x	x	X
ejpam-5837	57	17	]	]	X
ejpam-5837	57	18	:	:	PUNCT
ejpam-5837	57	19	=	=	SYM
ejpam-5837	57	20	{	{	PUNCT
ejpam-5837	57	21	a	a	DET
ejpam-5837	57	22	∈	∈	PROPN
ejpam-5837	57	23	t	t	NOUN
ejpam-5837	57	24	|	|	ADV
ejpam-5837	57	25	a	a	DET
ejpam-5837	57	26	≤	≤	NUM
ejpam-5837	57	27	b	b	NOUN
ejpam-5837	57	28	for	for	ADP
ejpam-5837	57	29	some	some	DET
ejpam-5837	57	30	b	b	NOUN
ejpam-5837	57	31	∈	∈	PROPN
ejpam-5837	57	32	x	x	NOUN
ejpam-5837	57	33	}	}	PUNCT
ejpam-5837	57	34	and	and	CCONJ
ejpam-5837	57	35	xy	xy	INTJ
ejpam-5837	57	36	:	:	PUNCT
ejpam-5837	57	37	=	=	X
ejpam-5837	57	38	{	{	PUNCT
ejpam-5837	58	1	xy	xy	INTJ
ejpam-5837	59	1	|	|	ADV
ejpam-5837	59	2	x	x	SYM
ejpam-5837	59	3	∈	∈	PROPN
ejpam-5837	59	4	x	x	X
ejpam-5837	59	5	and	and	CCONJ
ejpam-5837	59	6	y	y	PROPN
ejpam-5837	59	7	∈	∈	PROPN
ejpam-5837	59	8	y	y	PROPN
ejpam-5837	59	9	}	}	PUNCT
ejpam-5837	59	10	.	.	PUNCT
ejpam-5837	60	1	it	it	PRON
ejpam-5837	60	2	is	be	AUX
ejpam-5837	60	3	observed	observe	VERB
ejpam-5837	60	4	that	that	SCONJ
ejpam-5837	60	5	(	(	PUNCT
ejpam-5837	60	6	1	1	X
ejpam-5837	60	7	)	)	PUNCT
ejpam-5837	60	8	x	x	X
ejpam-5837	61	1	⊆	⊆	X
ejpam-5837	61	2	(	(	PUNCT
ejpam-5837	61	3	x	x	X
ejpam-5837	61	4	]	]	X
ejpam-5837	61	5	,	,	PUNCT
ejpam-5837	61	6	(	(	PUNCT
ejpam-5837	61	7	2	2	X
ejpam-5837	61	8	)	)	PUNCT
ejpam-5837	61	9	if	if	SCONJ
ejpam-5837	61	10	x	x	PROPN
ejpam-5837	61	11	⊆	⊆	NUM
ejpam-5837	61	12	y	y	NOUN
ejpam-5837	61	13	,	,	PUNCT
ejpam-5837	61	14	then	then	ADV
ejpam-5837	61	15	(	(	PUNCT
ejpam-5837	61	16	x	x	X
ejpam-5837	61	17	]	]	X
ejpam-5837	61	18	⊆	⊆	NUM
ejpam-5837	61	19	(	(	PUNCT
ejpam-5837	61	20	y	y	NOUN
ejpam-5837	61	21	]	]	X
ejpam-5837	61	22	,	,	PUNCT
ejpam-5837	61	23	(	(	PUNCT
ejpam-5837	61	24	3	3	X
ejpam-5837	61	25	)	)	PUNCT
ejpam-5837	61	26	(	(	PUNCT
ejpam-5837	61	27	(	(	PUNCT
ejpam-5837	61	28	x	x	X
ejpam-5837	61	29	]	]	X
ejpam-5837	61	30	]	]	X
ejpam-5837	61	31	=	=	SYM
ejpam-5837	61	32	(	(	PUNCT
ejpam-5837	61	33	x	x	X
ejpam-5837	61	34	]	]	X
ejpam-5837	61	35	,	,	PUNCT
ejpam-5837	61	36	p.	p.	NOUN
ejpam-5837	61	37	khamrot	khamrot	PROPN
ejpam-5837	61	38	et	et	PROPN
ejpam-5837	61	39	al	al	PROPN
ejpam-5837	61	40	.	.	PUNCT
ejpam-5837	61	41	/	/	SYM
ejpam-5837	61	42	eur	eur	PROPN
ejpam-5837	61	43	.	.	PUNCT
ejpam-5837	62	1	j.	j.	PROPN
ejpam-5837	62	2	pure	pure	PROPN
ejpam-5837	62	3	appl	appl	PROPN
ejpam-5837	62	4	.	.	PROPN
ejpam-5837	62	5	math	math	PROPN
ejpam-5837	62	6	,	,	PUNCT
ejpam-5837	62	7	18	18	NUM
ejpam-5837	62	8	(	(	PUNCT
ejpam-5837	62	9	2	2	NUM
ejpam-5837	62	10	)	)	PUNCT
ejpam-5837	62	11	(	(	PUNCT
ejpam-5837	62	12	2025	2025	NUM
ejpam-5837	62	13	)	)	PUNCT
ejpam-5837	62	14	,	,	PUNCT
ejpam-5837	62	15	5837	5837	NUM
ejpam-5837	62	16	3	3	NUM
ejpam-5837	62	17	of	of	ADP
ejpam-5837	62	18	13	13	NUM
ejpam-5837	62	19	(	(	PUNCT
ejpam-5837	62	20	4	4	NUM
ejpam-5837	62	21	)	)	PUNCT
ejpam-5837	62	22	(	(	PUNCT
ejpam-5837	62	23	x](y	x](y	X
ejpam-5837	62	24	]	]	X
ejpam-5837	63	1	⊆	⊆	NUM
ejpam-5837	63	2	(	(	PUNCT
ejpam-5837	63	3	xy	xy	PROPN
ejpam-5837	63	4	]	]	X
ejpam-5837	63	5	,	,	PUNCT
ejpam-5837	63	6	(	(	PUNCT
ejpam-5837	63	7	5	5	NUM
ejpam-5837	63	8	)	)	PUNCT
ejpam-5837	63	9	(	(	PUNCT
ejpam-5837	63	10	(	(	PUNCT
ejpam-5837	63	11	x](y	x](y	X
ejpam-5837	63	12	]	]	X
ejpam-5837	63	13	]	]	X
ejpam-5837	63	14	=	=	X
ejpam-5837	63	15	(	(	PUNCT
ejpam-5837	63	16	xy	xy	PROPN
ejpam-5837	63	17	]	]	X
ejpam-5837	63	18	,	,	PUNCT
ejpam-5837	63	19	(	(	PUNCT
ejpam-5837	63	20	6	6	NUM
ejpam-5837	63	21	)	)	PUNCT
ejpam-5837	63	22	(	(	PUNCT
ejpam-5837	63	23	x	x	X
ejpam-5837	63	24	∪y	∪y	NUM
ejpam-5837	63	25	]	]	X
ejpam-5837	63	26	=	=	SYM
ejpam-5837	63	27	(	(	PUNCT
ejpam-5837	63	28	x	x	X
ejpam-5837	63	29	]	]	X
ejpam-5837	63	30	∪	∪	X
ejpam-5837	63	31	(	(	PUNCT
ejpam-5837	63	32	y	y	NOUN
ejpam-5837	63	33	]	]	X
ejpam-5837	63	34	,	,	PUNCT
ejpam-5837	63	35	(	(	PUNCT
ejpam-5837	63	36	7	7	NUM
ejpam-5837	63	37	)	)	PUNCT
ejpam-5837	63	38	(	(	PUNCT
ejpam-5837	63	39	x	x	SYM
ejpam-5837	63	40	∩y	∩y	NOUN
ejpam-5837	63	41	]	]	X
ejpam-5837	63	42	=	=	SYM
ejpam-5837	63	43	(	(	PUNCT
ejpam-5837	63	44	x	x	SYM
ejpam-5837	63	45	]	]	X
ejpam-5837	63	46	∩	∩	NOUN
ejpam-5837	63	47	(	(	PUNCT
ejpam-5837	63	48	y	y	NOUN
ejpam-5837	63	49	]	]	PUNCT
ejpam-5837	63	50	.	.	PUNCT
ejpam-5837	64	1	let	let	AUX
ejpam-5837	64	2	(	(	PUNCT
ejpam-5837	64	3	t	t	PROPN
ejpam-5837	64	4	,	,	PUNCT
ejpam-5837	64	5	·	·	PUNCT
ejpam-5837	64	6	,	,	PUNCT
ejpam-5837	64	7	≤	≤	NUM
ejpam-5837	64	8	)	)	PUNCT
ejpam-5837	64	9	be	be	VERB
ejpam-5837	64	10	an	an	DET
ejpam-5837	64	11	ordered	order	VERB
ejpam-5837	64	12	semigroup	semigroup	NOUN
ejpam-5837	64	13	,	,	PUNCT
ejpam-5837	64	14	(	(	PUNCT
ejpam-5837	64	15	∅	∅	NOUN
ejpam-5837	64	16	̸=)k	̸=)k	NOUN
ejpam-5837	64	17	⊆	⊆	NUM
ejpam-5837	64	18	t	t	PROPN
ejpam-5837	64	19	is	be	AUX
ejpam-5837	64	20	called	call	VERB
ejpam-5837	64	21	a	a	DET
ejpam-5837	64	22	subsemigroup	subsemigroup	NOUN
ejpam-5837	64	23	such	such	ADJ
ejpam-5837	64	24	that	that	SCONJ
ejpam-5837	64	25	k2	k2	PROPN
ejpam-5837	64	26	⊆	⊆	NUM
ejpam-5837	64	27	k.	k.	PROPN
ejpam-5837	64	28	a	a	DET
ejpam-5837	64	29	left	left	ADJ
ejpam-5837	64	30	(	(	PUNCT
ejpam-5837	64	31	right	right	ADJ
ejpam-5837	64	32	)	)	PUNCT
ejpam-5837	64	33	ideal	ideal	NOUN
ejpam-5837	64	34	of	of	ADP
ejpam-5837	64	35	a	a	DET
ejpam-5837	64	36	ordered	order	VERB
ejpam-5837	64	37	semigroup	semigroup	NOUN
ejpam-5837	64	38	(	(	PUNCT
ejpam-5837	64	39	t	t	PROPN
ejpam-5837	64	40	,	,	PUNCT
ejpam-5837	64	41	·	·	PUNCT
ejpam-5837	64	42	,	,	PUNCT
ejpam-5837	64	43	≤	≤	NUM
ejpam-5837	64	44	)	)	PUNCT
ejpam-5837	64	45	is	be	AUX
ejpam-5837	64	46	a	a	DET
ejpam-5837	64	47	non	non	ADJ
ejpam-5837	64	48	-	-	ADJ
ejpam-5837	64	49	empty	empty	ADJ
ejpam-5837	64	50	set	set	NOUN
ejpam-5837	64	51	k	k	PROPN
ejpam-5837	64	52	of	of	ADP
ejpam-5837	64	53	t	t	PROPN
ejpam-5837	65	1	such	such	ADJ
ejpam-5837	65	2	that	that	PRON
ejpam-5837	65	3	sk	sk	VERB
ejpam-5837	65	4	⊆	⊆	NUM
ejpam-5837	65	5	k	k	X
ejpam-5837	65	6	(	(	PUNCT
ejpam-5837	65	7	ks	ks	PROPN
ejpam-5837	65	8	⊆	⊆	NUM
ejpam-5837	65	9	k	k	NOUN
ejpam-5837	65	10	)	)	PUNCT
ejpam-5837	65	11	and	and	CCONJ
ejpam-5837	65	12	(	(	PUNCT
ejpam-5837	65	13	k	k	X
ejpam-5837	65	14	]	]	X
ejpam-5837	65	15	.	.	PUNCT
ejpam-5837	66	1	by	by	ADP
ejpam-5837	66	2	an	an	DET
ejpam-5837	66	3	ideal	ideal	NOUN
ejpam-5837	66	4	of	of	ADP
ejpam-5837	66	5	an	an	DET
ejpam-5837	66	6	ordered	order	VERB
ejpam-5837	66	7	semigroup	semigroup	NOUN
ejpam-5837	66	8	(	(	PUNCT
ejpam-5837	66	9	t	t	PROPN
ejpam-5837	66	10	,	,	PUNCT
ejpam-5837	66	11	·	·	PUNCT
ejpam-5837	66	12	,	,	PUNCT
ejpam-5837	66	13	≤	≤	NUM
ejpam-5837	66	14	)	)	PUNCT
ejpam-5837	66	15	,	,	PUNCT
ejpam-5837	66	16	we	we	PRON
ejpam-5837	66	17	mean	mean	VERB
ejpam-5837	66	18	a	a	DET
ejpam-5837	66	19	non	non	ADJ
ejpam-5837	66	20	-	-	ADJ
ejpam-5837	66	21	empty	empty	ADJ
ejpam-5837	66	22	set	set	NOUN
ejpam-5837	66	23	of	of	ADP
ejpam-5837	66	24	t	t	PROPN
ejpam-5837	66	25	which	which	PRON
ejpam-5837	66	26	is	be	AUX
ejpam-5837	66	27	both	both	CCONJ
ejpam-5837	66	28	a	a	DET
ejpam-5837	66	29	left	left	NOUN
ejpam-5837	66	30	and	and	CCONJ
ejpam-5837	66	31	a	a	DET
ejpam-5837	66	32	right	right	ADJ
ejpam-5837	66	33	ideal	ideal	NOUN
ejpam-5837	66	34	of	of	ADP
ejpam-5837	66	35	t.	t.	ADJ
ejpam-5837	66	36	definition	definition	NOUN
ejpam-5837	66	37	2	2	NUM
ejpam-5837	66	38	.	.	PUNCT
ejpam-5837	67	1	[	[	X
ejpam-5837	67	2	20	20	NUM
ejpam-5837	67	3	]	]	PUNCT
ejpam-5837	67	4	a	a	DET
ejpam-5837	67	5	subsemigroup	subsemigroup	NOUN
ejpam-5837	67	6	k	k	PROPN
ejpam-5837	67	7	of	of	ADP
ejpam-5837	67	8	an	an	DET
ejpam-5837	67	9	ordered	order	VERB
ejpam-5837	67	10	semigroup	semigroup	NOUN
ejpam-5837	67	11	(	(	PUNCT
ejpam-5837	67	12	t	t	PROPN
ejpam-5837	67	13	,	,	PUNCT
ejpam-5837	67	14	·	·	PUNCT
ejpam-5837	67	15	,	,	PUNCT
ejpam-5837	67	16	≤	≤	NUM
ejpam-5837	67	17	)	)	PUNCT
ejpam-5837	67	18	is	be	AUX
ejpam-5837	67	19	called	call	VERB
ejpam-5837	67	20	an	an	DET
ejpam-5837	67	21	(	(	PUNCT
ejpam-5837	67	22	m	m	PROPN
ejpam-5837	67	23	,	,	PUNCT
ejpam-5837	67	24	n)ideal	n)ideal	PROPN
ejpam-5837	67	25	of	of	ADP
ejpam-5837	67	26	t	t	PROPN
ejpam-5837	67	27	if	if	SCONJ
ejpam-5837	67	28	k	k	PROPN
ejpam-5837	67	29	satisfies	satisfy	VERB
ejpam-5837	67	30	the	the	DET
ejpam-5837	67	31	following	follow	VERB
ejpam-5837	67	32	conditions	condition	NOUN
ejpam-5837	67	33	:	:	PUNCT
ejpam-5837	67	34	(	(	PUNCT
ejpam-5837	67	35	1	1	X
ejpam-5837	67	36	)	)	PUNCT
ejpam-5837	67	37	kmtkn	kmtkn	PROPN
ejpam-5837	67	38	⊆	⊆	NUM
ejpam-5837	67	39	k.	k.	PROPN
ejpam-5837	67	40	(	(	PUNCT
ejpam-5837	67	41	2	2	NUM
ejpam-5837	67	42	)	)	PUNCT
ejpam-5837	67	43	k	k	NOUN
ejpam-5837	68	1	=	=	SYM
ejpam-5837	68	2	(	(	PUNCT
ejpam-5837	68	3	k	k	X
ejpam-5837	68	4	]	]	X
ejpam-5837	68	5	,	,	PUNCT
ejpam-5837	68	6	that	that	PRON
ejpam-5837	68	7	is	be	AUX
ejpam-5837	68	8	for	for	ADP
ejpam-5837	68	9	x	x	PROPN
ejpam-5837	68	10	∈	∈	PROPN
ejpam-5837	68	11	k	k	PROPN
ejpam-5837	68	12	and	and	CCONJ
ejpam-5837	68	13	y	y	PROPN
ejpam-5837	68	14	∈	∈	PROPN
ejpam-5837	68	15	t	t	PROPN
ejpam-5837	68	16	,	,	PUNCT
ejpam-5837	68	17	y	y	PROPN
ejpam-5837	68	18	≤	≤	NUM
ejpam-5837	68	19	x	x	PUNCT
ejpam-5837	68	20	implies	imply	VERB
ejpam-5837	68	21	y	y	PROPN
ejpam-5837	68	22	∈	∈	PROPN
ejpam-5837	68	23	k.	k.	PROPN
ejpam-5837	68	24	where	where	SCONJ
ejpam-5837	68	25	m	m	PROPN
ejpam-5837	68	26	,	,	PUNCT
ejpam-5837	68	27	n	n	PRON
ejpam-5837	68	28	are	be	AUX
ejpam-5837	68	29	non	non	ADJ
ejpam-5837	68	30	-	-	ADJ
ejpam-5837	68	31	negative	negative	ADJ
ejpam-5837	68	32	integers	integer	NOUN
ejpam-5837	68	33	.	.	PUNCT
ejpam-5837	69	1	definition	definition	NOUN
ejpam-5837	69	2	3	3	NUM
ejpam-5837	69	3	.	.	PUNCT
ejpam-5837	70	1	[	[	X
ejpam-5837	70	2	20	20	NUM
ejpam-5837	70	3	]	]	PUNCT
ejpam-5837	70	4	an	an	DET
ejpam-5837	70	5	non	non	ADJ
ejpam-5837	70	6	-	-	ADJ
ejpam-5837	70	7	empty	empty	ADJ
ejpam-5837	70	8	subset	subset	NOUN
ejpam-5837	70	9	k	k	PROPN
ejpam-5837	70	10	of	of	ADP
ejpam-5837	70	11	an	an	DET
ejpam-5837	70	12	ordered	order	VERB
ejpam-5837	70	13	semigroup	semigroup	NOUN
ejpam-5837	70	14	(	(	PUNCT
ejpam-5837	70	15	t	t	PROPN
ejpam-5837	70	16	,	,	PUNCT
ejpam-5837	70	17	·	·	PUNCT
ejpam-5837	70	18	,	,	PUNCT
ejpam-5837	70	19	≤	≤	NUM
ejpam-5837	70	20	)	)	PUNCT
ejpam-5837	70	21	is	be	AUX
ejpam-5837	70	22	called	call	VERB
ejpam-5837	70	23	an	an	DET
ejpam-5837	70	24	(	(	PUNCT
ejpam-5837	70	25	m	m	PROPN
ejpam-5837	70	26	,	,	PUNCT
ejpam-5837	70	27	n)-quasi	n)-quasi	NOUN
ejpam-5837	70	28	-	-	NOUN
ejpam-5837	70	29	ideal	ideal	NOUN
ejpam-5837	70	30	of	of	ADP
ejpam-5837	70	31	t	t	PROPN
ejpam-5837	70	32	if	if	SCONJ
ejpam-5837	70	33	k	k	PROPN
ejpam-5837	70	34	satisfies	satisfy	VERB
ejpam-5837	70	35	the	the	DET
ejpam-5837	70	36	following	follow	VERB
ejpam-5837	70	37	conditions	condition	NOUN
ejpam-5837	70	38	:	:	PUNCT
ejpam-5837	70	39	(	(	PUNCT
ejpam-5837	70	40	1	1	X
ejpam-5837	70	41	)	)	PUNCT
ejpam-5837	70	42	(	(	PUNCT
ejpam-5837	70	43	kmt	kmt	PROPN
ejpam-5837	70	44	]	]	X
ejpam-5837	70	45	∩	∩	NOUN
ejpam-5837	70	46	(	(	PUNCT
ejpam-5837	70	47	tkn	tkn	X
ejpam-5837	70	48	]	]	PUNCT
ejpam-5837	70	49	⊆	⊆	NUM
ejpam-5837	70	50	k.	k.	NOUN
ejpam-5837	70	51	(	(	PUNCT
ejpam-5837	70	52	2	2	NUM
ejpam-5837	70	53	)	)	PUNCT
ejpam-5837	70	54	k	k	NOUN
ejpam-5837	71	1	=	=	SYM
ejpam-5837	71	2	(	(	PUNCT
ejpam-5837	71	3	k	k	X
ejpam-5837	71	4	]	]	X
ejpam-5837	71	5	,	,	PUNCT
ejpam-5837	71	6	that	that	PRON
ejpam-5837	71	7	is	be	AUX
ejpam-5837	71	8	for	for	ADP
ejpam-5837	71	9	x	x	PROPN
ejpam-5837	71	10	∈	∈	PROPN
ejpam-5837	71	11	k	k	PROPN
ejpam-5837	71	12	and	and	CCONJ
ejpam-5837	71	13	y	y	PROPN
ejpam-5837	71	14	∈	∈	PROPN
ejpam-5837	71	15	t	t	PROPN
ejpam-5837	71	16	,	,	PUNCT
ejpam-5837	71	17	y	y	PROPN
ejpam-5837	71	18	≤	≤	NUM
ejpam-5837	71	19	x	x	PUNCT
ejpam-5837	71	20	implies	imply	VERB
ejpam-5837	71	21	y	y	PROPN
ejpam-5837	71	22	∈	∈	PROPN
ejpam-5837	71	23	k.	k.	PROPN
ejpam-5837	71	24	where	where	SCONJ
ejpam-5837	71	25	m	m	PROPN
ejpam-5837	71	26	,	,	PUNCT
ejpam-5837	71	27	n	n	PRON
ejpam-5837	71	28	are	be	AUX
ejpam-5837	71	29	non	non	ADJ
ejpam-5837	71	30	-	-	ADJ
ejpam-5837	71	31	negative	negative	ADJ
ejpam-5837	71	32	integers	integer	NOUN
ejpam-5837	71	33	.	.	PUNCT
ejpam-5837	72	1	definition	definition	NOUN
ejpam-5837	72	2	4	4	NUM
ejpam-5837	72	3	.	.	PUNCT
ejpam-5837	73	1	[	[	X
ejpam-5837	73	2	9	9	NUM
ejpam-5837	73	3	]	]	PUNCT
ejpam-5837	73	4	a	a	DET
ejpam-5837	73	5	nonempty	nonempty	NOUN
ejpam-5837	73	6	subset	subset	NOUN
ejpam-5837	73	7	of	of	ADP
ejpam-5837	73	8	k	k	PROPN
ejpam-5837	73	9	an	an	DET
ejpam-5837	73	10	ordered	order	VERB
ejpam-5837	73	11	semigroup	semigroup	PROPN
ejpam-5837	73	12	t	t	PROPN
ejpam-5837	73	13	is	be	AUX
ejpam-5837	73	14	called	call	VERB
ejpam-5837	73	15	a	a	DET
ejpam-5837	73	16	left	left	NOUN
ejpam-5837	73	17	ordered	order	VERB
ejpam-5837	73	18	almost	almost	ADV
ejpam-5837	73	19	ideal	ideal	ADJ
ejpam-5837	73	20	of	of	ADP
ejpam-5837	73	21	t	t	PROPN
ejpam-5837	73	22	if	if	SCONJ
ejpam-5837	73	23	(	(	PUNCT
ejpam-5837	73	24	tk	tk	PROPN
ejpam-5837	73	25	]	]	X
ejpam-5837	73	26	∩	∩	NOUN
ejpam-5837	73	27	k	k	PROPN
ejpam-5837	73	28	̸=	̸=	PROPN
ejpam-5837	73	29	∅	∅	NOUN
ejpam-5837	73	30	for	for	ADP
ejpam-5837	73	31	all	all	DET
ejpam-5837	73	32	t	t	PROPN
ejpam-5837	73	33	∈	∈	PROPN
ejpam-5837	73	34	s.	s.	PROPN
ejpam-5837	73	35	definition	definition	NOUN
ejpam-5837	73	36	5	5	NUM
ejpam-5837	73	37	.	.	PUNCT
ejpam-5837	74	1	[	[	X
ejpam-5837	74	2	9	9	NUM
ejpam-5837	74	3	]	]	PUNCT
ejpam-5837	74	4	a	a	DET
ejpam-5837	74	5	nonempty	nonempty	NOUN
ejpam-5837	74	6	subset	subset	NOUN
ejpam-5837	74	7	of	of	ADP
ejpam-5837	74	8	k	k	PROPN
ejpam-5837	74	9	an	an	DET
ejpam-5837	74	10	ordered	order	VERB
ejpam-5837	74	11	semigroup	semigroup	PROPN
ejpam-5837	74	12	t	t	PROPN
ejpam-5837	74	13	is	be	AUX
ejpam-5837	74	14	called	call	VERB
ejpam-5837	74	15	a	a	DET
ejpam-5837	74	16	right	right	NOUN
ejpam-5837	74	17	ordered	order	VERB
ejpam-5837	74	18	almost	almost	ADV
ejpam-5837	74	19	ideal	ideal	ADJ
ejpam-5837	74	20	of	of	ADP
ejpam-5837	74	21	t	t	PROPN
ejpam-5837	74	22	if	if	SCONJ
ejpam-5837	74	23	(	(	PUNCT
ejpam-5837	74	24	kt	kt	X
ejpam-5837	74	25	]	]	X
ejpam-5837	74	26	∩	∩	NOUN
ejpam-5837	74	27	k	k	PROPN
ejpam-5837	74	28	̸=	̸=	PROPN
ejpam-5837	74	29	∅	∅	NOUN
ejpam-5837	74	30	for	for	ADP
ejpam-5837	74	31	all	all	DET
ejpam-5837	74	32	t	t	NOUN
ejpam-5837	74	33	∈	∈	PROPN
ejpam-5837	74	34	t	t	PROPN
ejpam-5837	74	35	.	.	PUNCT
ejpam-5837	75	1	for	for	ADP
ejpam-5837	75	2	any	any	DET
ejpam-5837	75	3	hi	hi	NOUN
ejpam-5837	75	4	∈	∈	PROPN
ejpam-5837	76	1	[	[	X
ejpam-5837	76	2	0	0	NUM
ejpam-5837	76	3	,	,	PUNCT
ejpam-5837	76	4	1	1	NUM
ejpam-5837	76	5	]	]	PUNCT
ejpam-5837	76	6	,	,	PUNCT
ejpam-5837	76	7	i	i	PROPN
ejpam-5837	76	8	∈	∈	PROPN
ejpam-5837	76	9	f	f	PROPN
ejpam-5837	76	10	,	,	PUNCT
ejpam-5837	76	11	define	define	VERB
ejpam-5837	76	12	∨	∨	NUM
ejpam-5837	76	13	i∈f	i∈f	VERB
ejpam-5837	76	14	hi	hi	INTJ
ejpam-5837	76	15	:	:	PUNCT
ejpam-5837	76	16	=	=	NOUN
ejpam-5837	76	17	sup	sup	NOUN
ejpam-5837	76	18	i∈f	i∈f	VERB
ejpam-5837	76	19	{	{	PUNCT
ejpam-5837	76	20	hi	hi	INTJ
ejpam-5837	76	21	}	}	PUNCT
ejpam-5837	76	22	and	and	CCONJ
ejpam-5837	76	23	∧	∧	PROPN
ejpam-5837	76	24	i∈f	i∈f	VERB
ejpam-5837	76	25	hi	hi	INTJ
ejpam-5837	76	26	:	:	PUNCT
ejpam-5837	76	27	=	=	SYM
ejpam-5837	76	28	inf	inf	PROPN
ejpam-5837	76	29	i∈f	i∈f	VERB
ejpam-5837	76	30	{	{	PUNCT
ejpam-5837	76	31	hi	hi	INTJ
ejpam-5837	76	32	}	}	PUNCT
ejpam-5837	76	33	.	.	PUNCT
ejpam-5837	77	1	we	we	PRON
ejpam-5837	77	2	see	see	VERB
ejpam-5837	77	3	that	that	PRON
ejpam-5837	77	4	for	for	ADP
ejpam-5837	77	5	any	any	DET
ejpam-5837	77	6	h	h	NOUN
ejpam-5837	77	7	,	,	PUNCT
ejpam-5837	77	8	r	r	NOUN
ejpam-5837	77	9	∈	∈	PROPN
ejpam-5837	78	1	[	[	X
ejpam-5837	78	2	0	0	NUM
ejpam-5837	78	3	,	,	PUNCT
ejpam-5837	78	4	1	1	NUM
ejpam-5837	78	5	]	]	PUNCT
ejpam-5837	78	6	,	,	PUNCT
ejpam-5837	78	7	we	we	PRON
ejpam-5837	78	8	have	have	VERB
ejpam-5837	78	9	h	h	NOUN
ejpam-5837	78	10	∨	∨	NUM
ejpam-5837	78	11	r	r	NOUN
ejpam-5837	78	12	=	=	SYM
ejpam-5837	78	13	max{h	max{h	PROPN
ejpam-5837	78	14	,	,	PUNCT
ejpam-5837	78	15	r	r	NOUN
ejpam-5837	78	16	}	}	PUNCT
ejpam-5837	78	17	and	and	CCONJ
ejpam-5837	78	18	h	h	NOUN
ejpam-5837	78	19	∧	∧	NOUN
ejpam-5837	78	20	r	r	NOUN
ejpam-5837	78	21	=	=	SYM
ejpam-5837	78	22	min{h	min{h	ADJ
ejpam-5837	78	23	,	,	PUNCT
ejpam-5837	78	24	r	r	NOUN
ejpam-5837	78	25	}	}	PUNCT
ejpam-5837	78	26	.	.	PUNCT
ejpam-5837	79	1	a	a	DET
ejpam-5837	79	2	fuzzy	fuzzy	ADJ
ejpam-5837	79	3	set	set	VERB
ejpam-5837	79	4	ϑ	ϑ	NOUN
ejpam-5837	79	5	in	in	ADP
ejpam-5837	79	6	a	a	DET
ejpam-5837	79	7	nonempty	nonempty	ADJ
ejpam-5837	79	8	set	set	VERB
ejpam-5837	79	9	t	t	PROPN
ejpam-5837	79	10	is	be	AUX
ejpam-5837	79	11	a	a	DET
ejpam-5837	79	12	function	function	NOUN
ejpam-5837	79	13	from	from	ADP
ejpam-5837	79	14	t	t	PROPN
ejpam-5837	79	15	into	into	ADP
ejpam-5837	79	16	the	the	DET
ejpam-5837	79	17	unit	unit	NOUN
ejpam-5837	79	18	closed	close	VERB
ejpam-5837	79	19	interval	interval	NOUN
ejpam-5837	79	20	[	[	X
ejpam-5837	79	21	0	0	NUM
ejpam-5837	79	22	,	,	PUNCT
ejpam-5837	79	23	1	1	NUM
ejpam-5837	79	24	]	]	PUNCT
ejpam-5837	79	25	of	of	ADP
ejpam-5837	79	26	real	real	ADJ
ejpam-5837	79	27	numbers	number	NOUN
ejpam-5837	79	28	,	,	PUNCT
ejpam-5837	79	29	i.e.	i.e.	X
ejpam-5837	79	30	,	,	PUNCT
ejpam-5837	79	31	ϑ	ϑ	X
ejpam-5837	79	32	:	:	PUNCT
ejpam-5837	79	33	t	t	X
ejpam-5837	79	34	→	→	SYM
ejpam-5837	80	1	[	[	X
ejpam-5837	80	2	0	0	NUM
ejpam-5837	80	3	,	,	PUNCT
ejpam-5837	80	4	1	1	NUM
ejpam-5837	80	5	]	]	PUNCT
ejpam-5837	80	6	.	.	PUNCT
ejpam-5837	81	1	for	for	ADP
ejpam-5837	81	2	any	any	DET
ejpam-5837	81	3	two	two	NUM
ejpam-5837	81	4	fuzzy	fuzzy	ADJ
ejpam-5837	81	5	sets	set	NOUN
ejpam-5837	81	6	ϑ	ϑ	X
ejpam-5837	81	7	and	and	CCONJ
ejpam-5837	81	8	ξ	ξ	PROPN
ejpam-5837	81	9	of	of	ADP
ejpam-5837	81	10	a	a	DET
ejpam-5837	81	11	non	non	ADJ
ejpam-5837	81	12	-	-	ADJ
ejpam-5837	81	13	empty	empty	ADJ
ejpam-5837	81	14	set	set	ADJ
ejpam-5837	81	15	t	t	PROPN
ejpam-5837	81	16	,	,	PUNCT
ejpam-5837	81	17	define	define	VERB
ejpam-5837	81	18	the	the	DET
ejpam-5837	81	19	symbol	symbol	NOUN
ejpam-5837	81	20	as	as	SCONJ
ejpam-5837	81	21	follows	follow	VERB
ejpam-5837	81	22	:	:	PUNCT
ejpam-5837	81	23	(	(	PUNCT
ejpam-5837	81	24	1	1	X
ejpam-5837	81	25	)	)	PUNCT
ejpam-5837	81	26	ϑ	ϑ	X
ejpam-5837	81	27	≤	≤	PROPN
ejpam-5837	81	28	ξ	ξ	PUNCT
ejpam-5837	81	29	⇔	⇔	X
ejpam-5837	81	30	ϑ(h	ϑ(h	PROPN
ejpam-5837	81	31	)	)	PUNCT
ejpam-5837	81	32	≤	≤	NUM
ejpam-5837	81	33	ξ(h	ξ(h	NOUN
ejpam-5837	81	34	)	)	PUNCT
ejpam-5837	81	35	for	for	ADP
ejpam-5837	81	36	all	all	DET
ejpam-5837	81	37	h	h	NOUN
ejpam-5837	81	38	∈	∈	PROPN
ejpam-5837	81	39	t	t	PROPN
ejpam-5837	81	40	,	,	PUNCT
ejpam-5837	81	41	p.	p.	NOUN
ejpam-5837	81	42	khamrot	khamrot	PROPN
ejpam-5837	82	1	et	et	PROPN
ejpam-5837	82	2	al	al	PROPN
ejpam-5837	82	3	.	.	PUNCT
ejpam-5837	82	4	/	/	SYM
ejpam-5837	82	5	eur	eur	PROPN
ejpam-5837	82	6	.	.	PUNCT
ejpam-5837	83	1	j.	j.	PROPN
ejpam-5837	83	2	pure	pure	PROPN
ejpam-5837	83	3	appl	appl	PROPN
ejpam-5837	83	4	.	.	PROPN
ejpam-5837	83	5	math	math	PROPN
ejpam-5837	83	6	,	,	PUNCT
ejpam-5837	83	7	18	18	NUM
ejpam-5837	83	8	(	(	PUNCT
ejpam-5837	83	9	2	2	NUM
ejpam-5837	83	10	)	)	PUNCT
ejpam-5837	83	11	(	(	PUNCT
ejpam-5837	83	12	2025	2025	NUM
ejpam-5837	83	13	)	)	PUNCT
ejpam-5837	83	14	,	,	PUNCT
ejpam-5837	83	15	5837	5837	NUM
ejpam-5837	83	16	4	4	NUM
ejpam-5837	83	17	of	of	ADP
ejpam-5837	83	18	13	13	NUM
ejpam-5837	83	19	(	(	PUNCT
ejpam-5837	83	20	2	2	NUM
ejpam-5837	83	21	)	)	PUNCT
ejpam-5837	83	22	ϑ	ϑ	X
ejpam-5837	83	23	=	=	SYM
ejpam-5837	83	24	ξ	ξ	PROPN
ejpam-5837	83	25	⇔	⇔	X
ejpam-5837	83	26	ϑ	ϑ	X
ejpam-5837	83	27	≤	≤	PROPN
ejpam-5837	83	28	ξ	ξ	PROPN
ejpam-5837	83	29	and	and	CCONJ
ejpam-5837	83	30	ξ	ξ	X
ejpam-5837	83	31	≤	≤	NUM
ejpam-5837	83	32	ϑ	ϑ	X
ejpam-5837	83	33	,	,	PUNCT
ejpam-5837	83	34	(	(	PUNCT
ejpam-5837	83	35	3	3	NUM
ejpam-5837	83	36	)	)	PUNCT
ejpam-5837	83	37	(	(	PUNCT
ejpam-5837	83	38	ϑ	ϑ	X
ejpam-5837	83	39	∧	∧	NOUN
ejpam-5837	83	40	ξ)(h	ξ)(h	NUM
ejpam-5837	83	41	)	)	PUNCT
ejpam-5837	83	42	=	=	SYM
ejpam-5837	84	1	min{ϑ(h	min{ϑ(h	PROPN
ejpam-5837	84	2	)	)	PUNCT
ejpam-5837	84	3	,	,	PUNCT
ejpam-5837	84	4	ξ(h	ξ(h	NOUN
ejpam-5837	84	5	)	)	PUNCT
ejpam-5837	84	6	}	}	PUNCT
ejpam-5837	84	7	=	=	SYM
ejpam-5837	84	8	ϑ(h	ϑ(h	ADJ
ejpam-5837	84	9	)	)	PUNCT
ejpam-5837	84	10	∧	∧	NOUN
ejpam-5837	84	11	ξ(h	ξ(h	PROPN
ejpam-5837	84	12	)	)	PUNCT
ejpam-5837	84	13	for	for	ADP
ejpam-5837	84	14	all	all	DET
ejpam-5837	84	15	h	h	NOUN
ejpam-5837	84	16	∈	∈	PROPN
ejpam-5837	84	17	t	t	PROPN
ejpam-5837	84	18	,	,	PUNCT
ejpam-5837	84	19	(	(	PUNCT
ejpam-5837	84	20	4	4	NUM
ejpam-5837	84	21	)	)	PUNCT
ejpam-5837	84	22	(	(	PUNCT
ejpam-5837	84	23	ϑ	ϑ	X
ejpam-5837	84	24	∨	∨	NUM
ejpam-5837	84	25	ξ)(h	ξ)(h	NUM
ejpam-5837	84	26	)	)	PUNCT
ejpam-5837	84	27	=	=	SYM
ejpam-5837	85	1	max{ϑ(h	max{ϑ(h	ADJ
ejpam-5837	85	2	)	)	PUNCT
ejpam-5837	85	3	,	,	PUNCT
ejpam-5837	85	4	ξ(h	ξ(h	NOUN
ejpam-5837	85	5	)	)	PUNCT
ejpam-5837	85	6	}	}	PUNCT
ejpam-5837	85	7	=	=	SYM
ejpam-5837	85	8	ϑ(h	ϑ(h	ADJ
ejpam-5837	85	9	)	)	PUNCT
ejpam-5837	85	10	∨	∨	NUM
ejpam-5837	85	11	ξ(h	ξ(h	PROPN
ejpam-5837	85	12	)	)	PUNCT
ejpam-5837	85	13	for	for	ADP
ejpam-5837	85	14	all	all	DET
ejpam-5837	85	15	h	h	NOUN
ejpam-5837	85	16	∈	∈	PROPN
ejpam-5837	85	17	t	t	PROPN
ejpam-5837	85	18	,	,	PUNCT
ejpam-5837	85	19	(	(	PUNCT
ejpam-5837	85	20	5	5	X
ejpam-5837	85	21	)	)	PUNCT
ejpam-5837	85	22	the	the	DET
ejpam-5837	85	23	support	support	NOUN
ejpam-5837	85	24	of	of	ADP
ejpam-5837	85	25	ϑ	ϑ	PRON
ejpam-5837	85	26	instead	instead	ADV
ejpam-5837	85	27	by	by	ADP
ejpam-5837	85	28	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	85	29	)	)	PUNCT
ejpam-5837	85	30	=	=	PRON
ejpam-5837	85	31	{	{	PUNCT
ejpam-5837	85	32	h	h	NOUN
ejpam-5837	85	33	∈	∈	PROPN
ejpam-5837	85	34	t	t	PROPN
ejpam-5837	85	35	|	|	ADV
ejpam-5837	85	36	ϑ(h	ϑ(h	PROPN
ejpam-5837	85	37	)	)	PUNCT
ejpam-5837	85	38	̸=	̸=	PROPN
ejpam-5837	85	39	0	0	NUM
ejpam-5837	85	40	}	}	PUNCT
ejpam-5837	85	41	.	.	PUNCT
ejpam-5837	86	1	for	for	ADP
ejpam-5837	86	2	the	the	DET
ejpam-5837	86	3	symbol	symbol	NOUN
ejpam-5837	86	4	ϑ	ϑ	X
ejpam-5837	86	5	≥	≥	X
ejpam-5837	86	6	ξ	ξ	NOUN
ejpam-5837	86	7	,	,	PUNCT
ejpam-5837	86	8	we	we	PRON
ejpam-5837	86	9	mean	mean	VERB
ejpam-5837	86	10	ξ	ξ	PRON
ejpam-5837	86	11	≤	≤	ADJ
ejpam-5837	86	12	ϑ.	ϑ.	NOUN
ejpam-5837	86	13	if	if	SCONJ
ejpam-5837	86	14	k	k	PROPN
ejpam-5837	86	15	⊆	⊆	NUM
ejpam-5837	86	16	t	t	NOUN
ejpam-5837	86	17	̸=	̸=	PROPN
ejpam-5837	86	18	∅	∅	NOUN
ejpam-5837	86	19	,	,	PUNCT
ejpam-5837	86	20	then	then	ADV
ejpam-5837	86	21	the	the	DET
ejpam-5837	86	22	characteristic	characteristic	ADJ
ejpam-5837	86	23	function	function	NOUN
ejpam-5837	86	24	χk	χk	PROPN
ejpam-5837	86	25	of	of	ADP
ejpam-5837	86	26	t	t	PROPN
ejpam-5837	86	27	is	be	AUX
ejpam-5837	86	28	a	a	DET
ejpam-5837	86	29	function	function	NOUN
ejpam-5837	86	30	from	from	ADP
ejpam-5837	86	31	t	t	PROPN
ejpam-5837	86	32	into	into	ADP
ejpam-5837	86	33	{	{	PUNCT
ejpam-5837	86	34	0	0	NUM
ejpam-5837	86	35	,	,	PUNCT
ejpam-5837	86	36	1	1	NUM
ejpam-5837	86	37	}	}	PUNCT
ejpam-5837	86	38	defined	define	VERB
ejpam-5837	86	39	as	as	ADP
ejpam-5837	86	40	follows	follow	VERB
ejpam-5837	86	41	:	:	PUNCT
ejpam-5837	86	42	χk(x	χk(x	X
ejpam-5837	86	43	)	)	PUNCT
ejpam-5837	87	1	=	=	PRON
ejpam-5837	87	2	{	{	PUNCT
ejpam-5837	87	3	1	1	NUM
ejpam-5837	87	4	if	if	SCONJ
ejpam-5837	87	5	x	x	PROPN
ejpam-5837	87	6	∈	∈	PROPN
ejpam-5837	87	7	k	k	NOUN
ejpam-5837	87	8	0	0	PUNCT
ejpam-5837	87	9	otherwise	otherwise	ADV
ejpam-5837	87	10	.	.	PUNCT
ejpam-5837	88	1	for	for	ADP
ejpam-5837	88	2	all	all	DET
ejpam-5837	88	3	x	x	SYM
ejpam-5837	88	4	∈	∈	PROPN
ejpam-5837	88	5	t	t	X
ejpam-5837	88	6	lemma	lemma	PROPN
ejpam-5837	88	7	1	1	X
ejpam-5837	88	8	.	.	PUNCT
ejpam-5837	89	1	if	if	SCONJ
ejpam-5837	89	2	i	i	PRON
ejpam-5837	89	3	and	and	CCONJ
ejpam-5837	89	4	l	l	NOUN
ejpam-5837	89	5	are	be	AUX
ejpam-5837	89	6	nonempty	nonempty	ADJ
ejpam-5837	89	7	subsets	subset	NOUN
ejpam-5837	89	8	of	of	ADP
ejpam-5837	89	9	an	an	DET
ejpam-5837	89	10	oredred	oredre	VERB
ejpam-5837	89	11	semigroup	semigroup	PROPN
ejpam-5837	89	12	t	t	PROPN
ejpam-5837	89	13	,	,	PUNCT
ejpam-5837	89	14	then	then	ADV
ejpam-5837	89	15	the	the	DET
ejpam-5837	89	16	following	follow	VERB
ejpam-5837	89	17	are	be	AUX
ejpam-5837	89	18	true	true	ADJ
ejpam-5837	89	19	:	:	PUNCT
ejpam-5837	89	20	(	(	PUNCT
ejpam-5837	89	21	1	1	X
ejpam-5837	89	22	)	)	PUNCT
ejpam-5837	89	23	χi	χi	NOUN
ejpam-5837	89	24	∧	∧	PROPN
ejpam-5837	89	25	χl	χl	PART
ejpam-5837	89	26	=	=	NOUN
ejpam-5837	89	27	χi∩l	χi∩l	PROPN
ejpam-5837	89	28	.	.	PUNCT
ejpam-5837	90	1	(	(	PUNCT
ejpam-5837	90	2	2	2	X
ejpam-5837	90	3	)	)	PUNCT
ejpam-5837	90	4	if	if	SCONJ
ejpam-5837	90	5	i	i	PRON
ejpam-5837	90	6	⊆	⊆	NUM
ejpam-5837	90	7	l	l	NOUN
ejpam-5837	90	8	,	,	PUNCT
ejpam-5837	90	9	then	then	ADV
ejpam-5837	90	10	χi	χi	PROPN
ejpam-5837	90	11	⪯	⪯	PROPN
ejpam-5837	90	12	χl	χl	PROPN
ejpam-5837	90	13	.	.	PROPN
ejpam-5837	91	1	(	(	PUNCT
ejpam-5837	91	2	3	3	NUM
ejpam-5837	91	3	)	)	PUNCT
ejpam-5837	91	4	χi	χi	NOUN
ejpam-5837	91	5	◦	◦	NOUN
ejpam-5837	91	6	χl	χl	PART
ejpam-5837	91	7	=	=	PROPN
ejpam-5837	91	8	χil	χil	PROPN
ejpam-5837	91	9	.	.	PUNCT
ejpam-5837	92	1	definition	definition	NOUN
ejpam-5837	92	2	6	6	NUM
ejpam-5837	92	3	.	.	PUNCT
ejpam-5837	93	1	let	let	VERB
ejpam-5837	93	2	t	t	PROPN
ejpam-5837	93	3	be	be	AUX
ejpam-5837	93	4	an	an	DET
ejpam-5837	93	5	ordered	order	VERB
ejpam-5837	93	6	semigroup	semigroup	NOUN
ejpam-5837	93	7	and	and	CCONJ
ejpam-5837	93	8	fu	fu	NOUN
ejpam-5837	93	9	be	be	AUX
ejpam-5837	93	10	a	a	DET
ejpam-5837	93	11	non	non	ADJ
ejpam-5837	93	12	-	-	ADJ
ejpam-5837	93	13	empty	empty	ADJ
ejpam-5837	93	14	subset	subset	NOUN
ejpam-5837	93	15	of	of	ADP
ejpam-5837	93	16	t	t	PROPN
ejpam-5837	93	17	,	,	PUNCT
ejpam-5837	93	18	we	we	PRON
ejpam-5837	93	19	define	define	VERB
ejpam-5837	93	20	the	the	DET
ejpam-5837	93	21	set	set	NOUN
ejpam-5837	93	22	fu	fu	NOUN
ejpam-5837	93	23	by	by	ADP
ejpam-5837	93	24	fu	fu	NOUN
ejpam-5837	93	25	:	:	PUNCT
ejpam-5837	93	26	=	=	SYM
ejpam-5837	93	27	{	{	PUNCT
ejpam-5837	93	28	(	(	PUNCT
ejpam-5837	93	29	x	x	NOUN
ejpam-5837	93	30	,	,	PUNCT
ejpam-5837	93	31	y	y	NOUN
ejpam-5837	93	32	)	)	PUNCT
ejpam-5837	93	33	∈	∈	PROPN
ejpam-5837	93	34	t×	t×	NOUN
ejpam-5837	93	35	t	t	NOUN
ejpam-5837	93	36	|	|	ADV
ejpam-5837	93	37	u	u	X
ejpam-5837	93	38	≤	≤	X
ejpam-5837	93	39	xy	xy	ADP
ejpam-5837	93	40	}	}	PUNCT
ejpam-5837	93	41	.	.	PUNCT
ejpam-5837	94	1	definition	definition	NOUN
ejpam-5837	94	2	7	7	NUM
ejpam-5837	94	3	.	.	PUNCT
ejpam-5837	95	1	[	[	X
ejpam-5837	95	2	21	21	NUM
ejpam-5837	95	3	]	]	PUNCT
ejpam-5837	95	4	let	let	VERB
ejpam-5837	95	5	ϑ	ϑ	X
ejpam-5837	95	6	and	and	CCONJ
ejpam-5837	95	7	η	η	PROPN
ejpam-5837	95	8	be	be	AUX
ejpam-5837	95	9	fuzzy	fuzzy	ADJ
ejpam-5837	95	10	sets	set	NOUN
ejpam-5837	95	11	of	of	ADP
ejpam-5837	95	12	an	an	DET
ejpam-5837	95	13	ordered	order	VERB
ejpam-5837	95	14	semigroup	semigroup	NOUN
ejpam-5837	95	15	t.	t.	PROPN
ejpam-5837	95	16	the	the	DET
ejpam-5837	95	17	product	product	NOUN
ejpam-5837	95	18	of	of	ADP
ejpam-5837	95	19	fuzzy	fuzzy	ADJ
ejpam-5837	95	20	subsets	subset	NOUN
ejpam-5837	95	21	ϑ	ϑ	X
ejpam-5837	95	22	and	and	CCONJ
ejpam-5837	95	23	η	η	PROPN
ejpam-5837	95	24	of	of	ADP
ejpam-5837	95	25	t	t	PROPN
ejpam-5837	95	26	is	be	AUX
ejpam-5837	95	27	defined	define	VERB
ejpam-5837	95	28	as	as	ADP
ejpam-5837	95	29	follow	follow	NOUN
ejpam-5837	95	30	,	,	PUNCT
ejpam-5837	95	31	for	for	ADP
ejpam-5837	95	32	all	all	DET
ejpam-5837	95	33	u	u	PROPN
ejpam-5837	95	34	∈	∈	PROPN
ejpam-5837	95	35	t	t	NOUN
ejpam-5837	95	36	(	(	PUNCT
ejpam-5837	95	37	ϑ	ϑ	X
ejpam-5837	95	38	◦	◦	NOUN
ejpam-5837	95	39	η)(u	η)(u	ADJ
ejpam-5837	95	40	)	)	PUNCT
ejpam-5837	95	41	=	=	SYM
ejpam-5837	96	1			PROPN
ejpam-5837	96	2	∨	∨	NOUN
ejpam-5837	96	3	(	(	PUNCT
ejpam-5837	96	4	x	x	X
ejpam-5837	96	5	,	,	PUNCT
ejpam-5837	96	6	y)∈fu	y)∈fu	PROPN
ejpam-5837	96	7	{	{	PUNCT
ejpam-5837	96	8	ϑ(x	ϑ(x	PROPN
ejpam-5837	96	9	)	)	PUNCT
ejpam-5837	96	10	∧	∧	PROPN
ejpam-5837	96	11	η(y	η(y	NOUN
ejpam-5837	96	12	)	)	PUNCT
ejpam-5837	96	13	}	}	PUNCT
ejpam-5837	96	14	if	if	SCONJ
ejpam-5837	96	15	fu	fu	ADJ
ejpam-5837	96	16	̸=	̸=	PROPN
ejpam-5837	96	17	∅	∅	NOUN
ejpam-5837	96	18	,	,	PUNCT
ejpam-5837	96	19	0	0	PUNCT
ejpam-5837	96	20	if	if	SCONJ
ejpam-5837	96	21	fu	fu	NOUN
ejpam-5837	96	22	=	=	PUNCT
ejpam-5837	96	23	∅.	∅.	NOUN
ejpam-5837	96	24	for	for	ADP
ejpam-5837	96	25	u	u	PROPN
ejpam-5837	96	26	∈	∈	PROPN
ejpam-5837	96	27	t	t	PROPN
ejpam-5837	96	28	and	and	CCONJ
ejpam-5837	96	29	t	t	PROPN
ejpam-5837	96	30	∈	∈	PROPN
ejpam-5837	96	31	(	(	PUNCT
ejpam-5837	96	32	0	0	NUM
ejpam-5837	96	33	,	,	PUNCT
ejpam-5837	96	34	1	1	NUM
ejpam-5837	96	35	]	]	PUNCT
ejpam-5837	96	36	,	,	PUNCT
ejpam-5837	96	37	a	a	DET
ejpam-5837	96	38	fuzzy	fuzzy	ADJ
ejpam-5837	96	39	point	point	NOUN
ejpam-5837	96	40	xt	xt	ADP
ejpam-5837	96	41	of	of	ADP
ejpam-5837	96	42	a	a	DET
ejpam-5837	96	43	set	set	NOUN
ejpam-5837	96	44	t	t	NOUN
ejpam-5837	96	45	is	be	AUX
ejpam-5837	96	46	a	a	DET
ejpam-5837	96	47	fuzzy	fuzzy	ADJ
ejpam-5837	96	48	subset	subset	NOUN
ejpam-5837	96	49	of	of	ADP
ejpam-5837	96	50	t	t	PROPN
ejpam-5837	96	51	defined	define	VERB
ejpam-5837	96	52	by	by	ADP
ejpam-5837	96	53	xt(e	xt(e	NOUN
ejpam-5837	96	54	)	)	PUNCT
ejpam-5837	97	1	=	=	PRON
ejpam-5837	97	2	{	{	PUNCT
ejpam-5837	97	3	t	t	X
ejpam-5837	97	4	if	if	SCONJ
ejpam-5837	97	5	e	e	PROPN
ejpam-5837	97	6	=	=	SYM
ejpam-5837	97	7	u	u	PROPN
ejpam-5837	97	8	,	,	PUNCT
ejpam-5837	97	9	0	0	NUM
ejpam-5837	97	10	otherwise	otherwise	ADV
ejpam-5837	97	11	.	.	PUNCT
ejpam-5837	98	1	for	for	ADP
ejpam-5837	98	2	k	k	PROPN
ejpam-5837	98	3	∈	∈	PROPN
ejpam-5837	98	4	n	n	CCONJ
ejpam-5837	98	5	,	,	PUNCT
ejpam-5837	98	6	let	let	VERB
ejpam-5837	98	7	ϑn	ϑn	NOUN
ejpam-5837	98	8	:	:	PUNCT
ejpam-5837	98	9	=	=	SYM
ejpam-5837	98	10	ϑ	ϑ	X
ejpam-5837	98	11	◦	◦	NOUN
ejpam-5837	98	12	ϑ	ϑ	X
ejpam-5837	98	13	◦	◦	NOUN
ejpam-5837	98	14	·	·	PUNCT
ejpam-5837	98	15	·	·	PUNCT
ejpam-5837	98	16	·	·	PUNCT
ejpam-5837	99	1	◦	◦	VERB
ejpam-5837	99	2	ϑ︸	ϑ︸	ADJ
ejpam-5837	99	3	︷︷	︷︷	PROPN
ejpam-5837	99	4	︸	︸	SYM
ejpam-5837	99	5	n	n	CCONJ
ejpam-5837	99	6	-	-	PUNCT
ejpam-5837	99	7	times	time	NOUN
ejpam-5837	99	8	.	.	PUNCT
ejpam-5837	100	1	lemma	lemma	PROPN
ejpam-5837	100	2	2	2	NUM
ejpam-5837	100	3	.	.	PUNCT
ejpam-5837	101	1	[	[	X
ejpam-5837	101	2	14	14	NUM
ejpam-5837	101	3	]	]	X
ejpam-5837	101	4	if	if	SCONJ
ejpam-5837	101	5	φ	φ	PROPN
ejpam-5837	101	6	,	,	PUNCT
ejpam-5837	101	7	ν	ν	NOUN
ejpam-5837	101	8	and	and	CCONJ
ejpam-5837	101	9	ξ	ξ	PROPN
ejpam-5837	101	10	are	be	AUX
ejpam-5837	101	11	fuzzy	fuzzy	ADJ
ejpam-5837	101	12	sets	set	NOUN
ejpam-5837	101	13	of	of	ADP
ejpam-5837	101	14	an	an	DET
ejpam-5837	101	15	ordered	order	VERB
ejpam-5837	101	16	semigroup	semigroup	PROPN
ejpam-5837	101	17	s	s	PROPN
ejpam-5837	101	18	,	,	PUNCT
ejpam-5837	101	19	then	then	ADV
ejpam-5837	101	20	the	the	DET
ejpam-5837	101	21	following	follow	VERB
ejpam-5837	101	22	are	be	AUX
ejpam-5837	101	23	true	true	ADJ
ejpam-5837	101	24	:	:	PUNCT
ejpam-5837	101	25	(	(	PUNCT
ejpam-5837	101	26	1	1	X
ejpam-5837	101	27	)	)	PUNCT
ejpam-5837	101	28	if	if	SCONJ
ejpam-5837	101	29	φ	φ	PROPN
ejpam-5837	101	30	⪯	⪯	VERB
ejpam-5837	101	31	ν	ν	NOUN
ejpam-5837	101	32	,	,	PUNCT
ejpam-5837	101	33	then	then	ADV
ejpam-5837	101	34	φn	φn	ADP
ejpam-5837	101	35	⪯	⪯	NOUN
ejpam-5837	101	36	νn	νn	VERB
ejpam-5837	101	37	p.	p.	NOUN
ejpam-5837	101	38	khamrot	khamrot	PROPN
ejpam-5837	101	39	et	et	PROPN
ejpam-5837	101	40	al	al	PROPN
ejpam-5837	101	41	.	.	PUNCT
ejpam-5837	101	42	/	/	SYM
ejpam-5837	101	43	eur	eur	PROPN
ejpam-5837	101	44	.	.	PUNCT
ejpam-5837	102	1	j.	j.	PROPN
ejpam-5837	102	2	pure	pure	PROPN
ejpam-5837	102	3	appl	appl	PROPN
ejpam-5837	102	4	.	.	PROPN
ejpam-5837	102	5	math	math	PROPN
ejpam-5837	102	6	,	,	PUNCT
ejpam-5837	102	7	18	18	NUM
ejpam-5837	102	8	(	(	PUNCT
ejpam-5837	102	9	2	2	NUM
ejpam-5837	102	10	)	)	PUNCT
ejpam-5837	102	11	(	(	PUNCT
ejpam-5837	102	12	2025	2025	NUM
ejpam-5837	102	13	)	)	PUNCT
ejpam-5837	102	14	,	,	PUNCT
ejpam-5837	102	15	5837	5837	NUM
ejpam-5837	102	16	5	5	NUM
ejpam-5837	102	17	of	of	ADP
ejpam-5837	102	18	13	13	NUM
ejpam-5837	102	19	(	(	PUNCT
ejpam-5837	102	20	2	2	NUM
ejpam-5837	102	21	)	)	PUNCT
ejpam-5837	102	22	if	if	SCONJ
ejpam-5837	102	23	φ	φ	PROPN
ejpam-5837	102	24	⪯	⪯	VERB
ejpam-5837	102	25	ν	ν	NOUN
ejpam-5837	102	26	,	,	PUNCT
ejpam-5837	102	27	then	then	ADV
ejpam-5837	102	28	φ	φ	PROPN
ejpam-5837	102	29	◦	◦	PROPN
ejpam-5837	102	30	ξ	ξ	X
ejpam-5837	102	31	⪯	⪯	NOUN
ejpam-5837	102	32	ν	ν	X
ejpam-5837	102	33	◦	◦	NOUN
ejpam-5837	102	34	ξ	ξ	PROPN
ejpam-5837	102	35	.	.	PUNCT
ejpam-5837	103	1	(	(	PUNCT
ejpam-5837	103	2	3	3	X
ejpam-5837	103	3	)	)	PUNCT
ejpam-5837	103	4	if	if	SCONJ
ejpam-5837	103	5	φ	φ	PROPN
ejpam-5837	103	6	⪯	⪯	VERB
ejpam-5837	103	7	ν	ν	NOUN
ejpam-5837	103	8	,	,	PUNCT
ejpam-5837	103	9	then	then	ADV
ejpam-5837	103	10	φ	φ	PROPN
ejpam-5837	103	11	∨	∨	PROPN
ejpam-5837	103	12	ξ	ξ	X
ejpam-5837	103	13	⪯	⪯	NOUN
ejpam-5837	103	14	ν	ν	X
ejpam-5837	103	15	∨	∨	NUM
ejpam-5837	103	16	ξ	ξ	PROPN
ejpam-5837	103	17	.	.	PUNCT
ejpam-5837	104	1	(	(	PUNCT
ejpam-5837	104	2	4	4	X
ejpam-5837	104	3	)	)	PUNCT
ejpam-5837	104	4	if	if	SCONJ
ejpam-5837	104	5	φ	φ	PROPN
ejpam-5837	104	6	⪯	⪯	VERB
ejpam-5837	104	7	ν	ν	NOUN
ejpam-5837	104	8	,	,	PUNCT
ejpam-5837	104	9	then	then	ADV
ejpam-5837	104	10	φ	φ	PROPN
ejpam-5837	104	11	∧	∧	PROPN
ejpam-5837	104	12	ξ	ξ	PROPN
ejpam-5837	104	13	⪯	⪯	NOUN
ejpam-5837	104	14	ν	ν	ADP
ejpam-5837	104	15	∧	∧	PROPN
ejpam-5837	104	16	ξ	ξ	PROPN
ejpam-5837	104	17	.	.	PUNCT
ejpam-5837	105	1	(	(	PUNCT
ejpam-5837	105	2	5	5	NUM
ejpam-5837	105	3	)	)	PUNCT
ejpam-5837	105	4	if	if	SCONJ
ejpam-5837	105	5	φ	φ	PROPN
ejpam-5837	105	6	⪯	⪯	VERB
ejpam-5837	105	7	ν	ν	NOUN
ejpam-5837	105	8	,	,	PUNCT
ejpam-5837	105	9	then	then	ADV
ejpam-5837	105	10	supp(φ	supp(φ	VERB
ejpam-5837	105	11	)	)	PUNCT
ejpam-5837	105	12	⪯	⪯	PROPN
ejpam-5837	105	13	supp(ν	supp(ν	PROPN
ejpam-5837	105	14	)	)	PUNCT
ejpam-5837	105	15	.	.	PUNCT
ejpam-5837	106	1	for	for	ADP
ejpam-5837	106	2	a	a	DET
ejpam-5837	106	3	fuzzy	fuzzy	ADJ
ejpam-5837	106	4	set	set	VERB
ejpam-5837	106	5	φ	φ	PROPN
ejpam-5837	106	6	of	of	ADP
ejpam-5837	106	7	an	an	DET
ejpam-5837	106	8	ordered	order	VERB
ejpam-5837	106	9	semigroup	semigroup	NOUN
ejpam-5837	106	10	s	s	PROPN
ejpam-5837	106	11	,	,	PUNCT
ejpam-5837	106	12	we	we	PRON
ejpam-5837	106	13	define	define	VERB
ejpam-5837	106	14	(	(	PUNCT
ejpam-5837	106	15	φ	φ	PROPN
ejpam-5837	106	16	]	]	X
ejpam-5837	106	17	:	:	PUNCT
ejpam-5837	106	18	s	s	X
ejpam-5837	106	19	→	→	SYM
ejpam-5837	106	20	[	[	X
ejpam-5837	106	21	0	0	NUM
ejpam-5837	106	22	,	,	PUNCT
ejpam-5837	106	23	1	1	NUM
ejpam-5837	106	24	]	]	PUNCT
ejpam-5837	106	25	by	by	ADP
ejpam-5837	106	26	(	(	PUNCT
ejpam-5837	106	27	φ	φ	PROPN
ejpam-5837	106	28	]	]	X
ejpam-5837	106	29	:	:	PUNCT
ejpam-5837	106	30	=	=	SYM
ejpam-5837	106	31	sup	sup	NOUN
ejpam-5837	106	32	a≤b	a≤b	PROPN
ejpam-5837	106	33	φ(b	φ(b	ADV
ejpam-5837	106	34	)	)	PUNCT
ejpam-5837	106	35	for	for	ADP
ejpam-5837	106	36	all	all	DET
ejpam-5837	106	37	a	a	DET
ejpam-5837	106	38	∈	∈	PROPN
ejpam-5837	106	39	s.	s.	PROPN
ejpam-5837	106	40	lemma	lemma	PROPN
ejpam-5837	107	1	3	3	X
ejpam-5837	107	2	.	.	PUNCT
ejpam-5837	108	1	[	[	X
ejpam-5837	108	2	14	14	NUM
ejpam-5837	108	3	]	]	X
ejpam-5837	108	4	if	if	SCONJ
ejpam-5837	108	5	φ	φ	PROPN
ejpam-5837	108	6	,	,	PUNCT
ejpam-5837	108	7	ν	ν	NOUN
ejpam-5837	108	8	and	and	CCONJ
ejpam-5837	108	9	ξ	ξ	PROPN
ejpam-5837	108	10	are	be	AUX
ejpam-5837	108	11	fuzzy	fuzzy	ADJ
ejpam-5837	108	12	sets	set	NOUN
ejpam-5837	108	13	of	of	ADP
ejpam-5837	108	14	an	an	DET
ejpam-5837	108	15	ordered	order	VERB
ejpam-5837	108	16	semigroup	semigroup	PROPN
ejpam-5837	108	17	s	s	PROPN
ejpam-5837	108	18	,	,	PUNCT
ejpam-5837	108	19	then	then	ADV
ejpam-5837	108	20	the	the	DET
ejpam-5837	108	21	following	follow	VERB
ejpam-5837	108	22	are	be	AUX
ejpam-5837	108	23	true	true	ADJ
ejpam-5837	108	24	:	:	PUNCT
ejpam-5837	108	25	(	(	PUNCT
ejpam-5837	108	26	1	1	X
ejpam-5837	108	27	)	)	PUNCT
ejpam-5837	108	28	φ	φ	PROPN
ejpam-5837	108	29	⪯	⪯	PROPN
ejpam-5837	108	30	(	(	PUNCT
ejpam-5837	108	31	φ	φ	NOUN
ejpam-5837	108	32	]	]	X
ejpam-5837	108	33	.	.	PUNCT
ejpam-5837	109	1	(	(	PUNCT
ejpam-5837	109	2	2	2	X
ejpam-5837	109	3	)	)	PUNCT
ejpam-5837	109	4	if	if	SCONJ
ejpam-5837	109	5	φ	φ	PROPN
ejpam-5837	109	6	⪯	⪯	VERB
ejpam-5837	109	7	ν	ν	NOUN
ejpam-5837	109	8	,	,	PUNCT
ejpam-5837	109	9	then	then	ADV
ejpam-5837	109	10	(	(	PUNCT
ejpam-5837	109	11	φ	φ	NOUN
ejpam-5837	109	12	]	]	X
ejpam-5837	109	13	⪯	⪯	X
ejpam-5837	109	14	(	(	PUNCT
ejpam-5837	109	15	ξ	ξ	NOUN
ejpam-5837	109	16	]	]	X
ejpam-5837	109	17	.	.	PUNCT
ejpam-5837	110	1	(	(	PUNCT
ejpam-5837	110	2	3	3	X
ejpam-5837	110	3	)	)	PUNCT
ejpam-5837	110	4	if	if	SCONJ
ejpam-5837	110	5	φ	φ	PROPN
ejpam-5837	110	6	⪯	⪯	VERB
ejpam-5837	110	7	ν	ν	NOUN
ejpam-5837	110	8	,	,	PUNCT
ejpam-5837	110	9	then	then	ADV
ejpam-5837	110	10	(	(	PUNCT
ejpam-5837	110	11	φ	φ	X
ejpam-5837	110	12	◦	◦	PROPN
ejpam-5837	110	13	ξ	ξ	X
ejpam-5837	110	14	]	]	X
ejpam-5837	110	15	⪯	⪯	NOUN
ejpam-5837	110	16	(	(	PUNCT
ejpam-5837	110	17	ν	ν	X
ejpam-5837	110	18	◦	◦	NOUN
ejpam-5837	110	19	ξ	ξ	X
ejpam-5837	110	20	]	]	PUNCT
ejpam-5837	110	21	and	and	CCONJ
ejpam-5837	110	22	(	(	PUNCT
ejpam-5837	110	23	ξ	ξ	X
ejpam-5837	110	24	◦	◦	NOUN
ejpam-5837	110	25	φ	φ	X
ejpam-5837	110	26	]	]	X
ejpam-5837	110	27	⪯	⪯	X
ejpam-5837	110	28	(	(	PUNCT
ejpam-5837	110	29	ξ	ξ	X
ejpam-5837	110	30	◦	◦	NOUN
ejpam-5837	110	31	ν	ν	X
ejpam-5837	110	32	]	]	PUNCT
ejpam-5837	110	33	.	.	PUNCT
ejpam-5837	111	1	lemma	lemma	PROPN
ejpam-5837	111	2	4	4	NUM
ejpam-5837	111	3	.	.	PUNCT
ejpam-5837	112	1	[	[	X
ejpam-5837	112	2	14	14	NUM
ejpam-5837	112	3	]	]	X
ejpam-5837	112	4	if	if	SCONJ
ejpam-5837	112	5	φ	φ	PROPN
ejpam-5837	112	6	is	be	AUX
ejpam-5837	112	7	a	a	DET
ejpam-5837	112	8	fuzzy	fuzzy	ADJ
ejpam-5837	112	9	set	set	NOUN
ejpam-5837	112	10	of	of	ADP
ejpam-5837	112	11	an	an	DET
ejpam-5837	112	12	ordered	order	VERB
ejpam-5837	112	13	semigroup	semigroup	PROPN
ejpam-5837	112	14	s	s	PROPN
ejpam-5837	112	15	,	,	PUNCT
ejpam-5837	112	16	then	then	ADV
ejpam-5837	112	17	the	the	DET
ejpam-5837	112	18	following	following	NOUN
ejpam-5837	112	19	are	be	AUX
ejpam-5837	112	20	equivalent	equivalent	ADJ
ejpam-5837	112	21	.	.	PUNCT
ejpam-5837	113	1	(	(	PUNCT
ejpam-5837	113	2	1	1	X
ejpam-5837	113	3	)	)	PUNCT
ejpam-5837	113	4	if	if	SCONJ
ejpam-5837	113	5	a	a	DET
ejpam-5837	113	6	≤	≤	NUM
ejpam-5837	113	7	b	b	NOUN
ejpam-5837	113	8	,	,	PUNCT
ejpam-5837	113	9	then	then	ADV
ejpam-5837	113	10	φ(a	φ(a	ADJ
ejpam-5837	113	11	)	)	PUNCT
ejpam-5837	113	12	⪯	⪯	NOUN
ejpam-5837	113	13	φ(b	φ(b	NOUN
ejpam-5837	113	14	)	)	PUNCT
ejpam-5837	113	15	.	.	PUNCT
ejpam-5837	114	1	(	(	PUNCT
ejpam-5837	114	2	2	2	X
ejpam-5837	114	3	)	)	PUNCT
ejpam-5837	114	4	(	(	PUNCT
ejpam-5837	114	5	φ	φ	X
ejpam-5837	114	6	]	]	X
ejpam-5837	114	7	=	=	SYM
ejpam-5837	114	8	φ	φ	PROPN
ejpam-5837	114	9	.	.	PUNCT
ejpam-5837	114	10	definition	definition	NOUN
ejpam-5837	114	11	8	8	NUM
ejpam-5837	114	12	.	.	PUNCT
ejpam-5837	115	1	[	[	X
ejpam-5837	115	2	14	14	NUM
ejpam-5837	115	3	]	]	X
ejpam-5837	115	4	a	a	DET
ejpam-5837	115	5	fuzzy	fuzzy	ADJ
ejpam-5837	115	6	set	set	VERB
ejpam-5837	115	7	δ	δ	PROPN
ejpam-5837	115	8	of	of	ADP
ejpam-5837	115	9	a	a	DET
ejpam-5837	115	10	semigroup	semigroup	PROPN
ejpam-5837	115	11	t	t	PROPN
ejpam-5837	115	12	is	be	AUX
ejpam-5837	115	13	said	say	VERB
ejpam-5837	115	14	to	to	PART
ejpam-5837	115	15	be	be	AUX
ejpam-5837	115	16	a	a	DET
ejpam-5837	115	17	fuzzy	fuzzy	ADJ
ejpam-5837	115	18	ideal	ideal	NOUN
ejpam-5837	115	19	of	of	ADP
ejpam-5837	115	20	t	t	PROPN
ejpam-5837	115	21	if	if	SCONJ
ejpam-5837	115	22	δ(uv	δ(uv	NOUN
ejpam-5837	115	23	)	)	PUNCT
ejpam-5837	115	24	≥	≥	NOUN
ejpam-5837	115	25	δ(u	δ(u	NOUN
ejpam-5837	115	26	)	)	PUNCT
ejpam-5837	115	27	∨	∨	NOUN
ejpam-5837	115	28	δ(v	δ(v	PROPN
ejpam-5837	115	29	)	)	PUNCT
ejpam-5837	115	30	for	for	ADP
ejpam-5837	115	31	all	all	DET
ejpam-5837	115	32	u	u	NOUN
ejpam-5837	115	33	,	,	PUNCT
ejpam-5837	115	34	v	v	NOUN
ejpam-5837	115	35	∈	∈	NOUN
ejpam-5837	115	36	t.	t.	NOUN
ejpam-5837	115	37	definition	definition	NOUN
ejpam-5837	115	38	9	9	NUM
ejpam-5837	115	39	.	.	PUNCT
ejpam-5837	116	1	[	[	X
ejpam-5837	116	2	19	19	NUM
ejpam-5837	116	3	]	]	X
ejpam-5837	116	4	a	a	DET
ejpam-5837	116	5	fuzzy	fuzzy	ADJ
ejpam-5837	116	6	subsemigroup	subsemigroup	PROPN
ejpam-5837	116	7	δ	δ	PROPN
ejpam-5837	116	8	of	of	ADP
ejpam-5837	116	9	a	a	DET
ejpam-5837	116	10	ordered	order	VERB
ejpam-5837	116	11	semigroup	semigroup	PROPN
ejpam-5837	116	12	t	t	PROPN
ejpam-5837	116	13	is	be	AUX
ejpam-5837	116	14	said	say	VERB
ejpam-5837	116	15	to	to	PART
ejpam-5837	116	16	be	be	AUX
ejpam-5837	116	17	a	a	DET
ejpam-5837	116	18	fuzzy	fuzzy	ADJ
ejpam-5837	116	19	(	(	PUNCT
ejpam-5837	116	20	m	m	PROPN
ejpam-5837	116	21	,	,	PUNCT
ejpam-5837	116	22	n)-ideal	n)-ideal	NOUN
ejpam-5837	116	23	of	of	ADP
ejpam-5837	116	24	t	t	PROPN
ejpam-5837	116	25	if	if	SCONJ
ejpam-5837	116	26	(	(	PUNCT
ejpam-5837	116	27	1	1	X
ejpam-5837	116	28	)	)	PUNCT
ejpam-5837	116	29	δ(u1u2	δ(u1u2	X
ejpam-5837	116	30	·	·	PUNCT
ejpam-5837	116	31	·	·	PUNCT
ejpam-5837	116	32	·	·	PUNCT
ejpam-5837	116	33	umzv1v2	umzv1v2	X
ejpam-5837	116	34	·	·	PUNCT
ejpam-5837	116	35	·	·	PUNCT
ejpam-5837	116	36	·	·	PUNCT
ejpam-5837	116	37	vn	vn	X
ejpam-5837	116	38	)	)	PUNCT
ejpam-5837	116	39	≥	≥	NOUN
ejpam-5837	116	40	δ(u1	δ(u1	NOUN
ejpam-5837	116	41	)	)	PUNCT
ejpam-5837	116	42	∧	∧	PROPN
ejpam-5837	116	43	δ(u2	δ(u2	NOUN
ejpam-5837	116	44	)	)	PUNCT
ejpam-5837	116	45	∧	∧	NOUN
ejpam-5837	116	46	...	...	PUNCT
ejpam-5837	117	1	∧	∧	NOUN
ejpam-5837	117	2	δ(um	δ(um	PROPN
ejpam-5837	117	3	)	)	PUNCT
ejpam-5837	117	4	∧	∧	PROPN
ejpam-5837	117	5	δ(v1	δ(v1	NOUN
ejpam-5837	117	6	)	)	PUNCT
ejpam-5837	117	7	∧	∧	NOUN
ejpam-5837	117	8	δ(v2	δ(v2	NOUN
ejpam-5837	117	9	)	)	PUNCT
ejpam-5837	117	10	∧	∧	NOUN
ejpam-5837	117	11	...	...	PUNCT
ejpam-5837	118	1	∧	∧	NOUN
ejpam-5837	118	2	δ(vn	δ(vn	PROPN
ejpam-5837	118	3	)	)	PUNCT
ejpam-5837	118	4	for	for	ADP
ejpam-5837	118	5	all	all	DET
ejpam-5837	118	6	u1	u1	NOUN
ejpam-5837	118	7	,	,	PUNCT
ejpam-5837	118	8	u2	u2	NOUN
ejpam-5837	118	9	,	,	PUNCT
ejpam-5837	118	10	...	...	PUNCT
ejpam-5837	118	11	,	,	PUNCT
ejpam-5837	118	12	um	um	INTJ
ejpam-5837	118	13	,	,	PUNCT
ejpam-5837	118	14	v1	v1	PROPN
ejpam-5837	118	15	,	,	PUNCT
ejpam-5837	118	16	v2	v2	PROPN
ejpam-5837	118	17	,	,	PUNCT
ejpam-5837	118	18	...	...	PUNCT
ejpam-5837	118	19	,	,	PUNCT
ejpam-5837	118	20	vn	vn	INTJ
ejpam-5837	118	21	,	,	PUNCT
ejpam-5837	118	22	z	z	PROPN
ejpam-5837	118	23	∈	∈	PROPN
ejpam-5837	118	24	t	t	PROPN
ejpam-5837	118	25	and	and	CCONJ
ejpam-5837	118	26	m	m	PROPN
ejpam-5837	118	27	,	,	PUNCT
ejpam-5837	118	28	n	n	PROPN
ejpam-5837	118	29	∈	∈	PROPN
ejpam-5837	118	30	n.	n.	NOUN
ejpam-5837	118	31	(	(	PUNCT
ejpam-5837	118	32	2	2	NUM
ejpam-5837	118	33	)	)	PUNCT
ejpam-5837	118	34	if	if	SCONJ
ejpam-5837	118	35	u1	u1	VERB
ejpam-5837	118	36	≤	≤	NOUN
ejpam-5837	118	37	u2	u2	NOUN
ejpam-5837	118	38	,	,	PUNCT
ejpam-5837	118	39	then	then	ADV
ejpam-5837	118	40	δ(u1	δ(u1	NOUN
ejpam-5837	118	41	)	)	PUNCT
ejpam-5837	118	42	≥	≥	NUM
ejpam-5837	118	43	δ(u2	δ(u2	NOUN
ejpam-5837	118	44	)	)	PUNCT
ejpam-5837	118	45	,	,	PUNCT
ejpam-5837	118	46	for	for	ADP
ejpam-5837	118	47	all	all	DET
ejpam-5837	118	48	u1	u1	NOUN
ejpam-5837	118	49	,	,	PUNCT
ejpam-5837	118	50	u2	u2	PROPN
ejpam-5837	118	51	∈	∈	PROPN
ejpam-5837	118	52	t.	t.	NOUN
ejpam-5837	118	53	definition	definition	NOUN
ejpam-5837	118	54	10	10	NUM
ejpam-5837	118	55	.	.	PUNCT
ejpam-5837	119	1	[	[	X
ejpam-5837	119	2	9	9	NUM
ejpam-5837	119	3	]	]	PUNCT
ejpam-5837	119	4	a	a	DET
ejpam-5837	119	5	nonempty	nonempty	NOUN
ejpam-5837	119	6	subset	subset	NOUN
ejpam-5837	119	7	of	of	ADP
ejpam-5837	119	8	k	k	PROPN
ejpam-5837	119	9	an	an	DET
ejpam-5837	119	10	ordered	order	VERB
ejpam-5837	119	11	semigroup	semigroup	PROPN
ejpam-5837	119	12	t	t	PROPN
ejpam-5837	119	13	is	be	AUX
ejpam-5837	119	14	called	call	VERB
ejpam-5837	119	15	a	a	DET
ejpam-5837	119	16	left	left	NOUN
ejpam-5837	119	17	ordered	order	VERB
ejpam-5837	119	18	almost	almost	ADV
ejpam-5837	119	19	ideal	ideal	ADJ
ejpam-5837	119	20	(	(	PUNCT
ejpam-5837	119	21	right	right	ADV
ejpam-5837	119	22	ordered	order	VERB
ejpam-5837	119	23	almost	almost	ADV
ejpam-5837	119	24	ideal	ideal	ADJ
ejpam-5837	119	25	)	)	PUNCT
ejpam-5837	119	26	of	of	ADP
ejpam-5837	119	27	t	t	PROPN
ejpam-5837	119	28	if	if	SCONJ
ejpam-5837	119	29	(	(	PUNCT
ejpam-5837	119	30	tk]∩k	tk]∩k	NOUN
ejpam-5837	119	31	̸=	̸=	PROPN
ejpam-5837	119	32	∅	∅	NOUN
ejpam-5837	119	33	(	(	PUNCT
ejpam-5837	119	34	(	(	PUNCT
ejpam-5837	119	35	k]t]∩k	k]t]∩k	NOUN
ejpam-5837	119	36	̸=	̸=	PROPN
ejpam-5837	119	37	∅	∅	NOUN
ejpam-5837	119	38	)	)	PUNCT
ejpam-5837	119	39	for	for	ADP
ejpam-5837	119	40	all	all	DET
ejpam-5837	119	41	t	t	NOUN
ejpam-5837	119	42	∈	∈	PROPN
ejpam-5837	119	43	t.	t.	NOUN
ejpam-5837	119	44	3	3	NUM
ejpam-5837	119	45	.	.	PUNCT
ejpam-5837	119	46	main	main	ADJ
ejpam-5837	119	47	results	result	NOUN
ejpam-5837	119	48	in	in	ADP
ejpam-5837	119	49	this	this	DET
ejpam-5837	119	50	section	section	NOUN
ejpam-5837	119	51	,	,	PUNCT
ejpam-5837	119	52	we	we	PRON
ejpam-5837	119	53	define	define	VERB
ejpam-5837	119	54	the	the	DET
ejpam-5837	119	55	almost	almost	ADV
ejpam-5837	119	56	(	(	PUNCT
ejpam-5837	119	57	m	m	PROPN
ejpam-5837	119	58	,	,	PUNCT
ejpam-5837	119	59	n)-quasi	n)-quasi	NOUN
ejpam-5837	119	60	-	-	PUNCT
ejpam-5837	119	61	ideal	ideal	ADJ
ejpam-5837	119	62	and	and	CCONJ
ejpam-5837	119	63	fuzzy	fuzzy	ADJ
ejpam-5837	119	64	almost	almost	ADV
ejpam-5837	119	65	(	(	PUNCT
ejpam-5837	119	66	m	m	NOUN
ejpam-5837	119	67	,	,	PUNCT
ejpam-5837	119	68	n)-quasiideal	n)-quasiideal	ADJ
ejpam-5837	119	69	in	in	ADP
ejpam-5837	119	70	ordered	order	VERB
ejpam-5837	119	71	semigroup	semigroup	NOUN
ejpam-5837	119	72	.	.	PUNCT
ejpam-5837	120	1	we	we	PRON
ejpam-5837	120	2	prove	prove	VERB
ejpam-5837	120	3	some	some	DET
ejpam-5837	120	4	basic	basic	ADJ
ejpam-5837	120	5	interesting	interesting	ADJ
ejpam-5837	120	6	properties	property	NOUN
ejpam-5837	120	7	of	of	ADP
ejpam-5837	120	8	almost	almost	ADV
ejpam-5837	120	9	(	(	PUNCT
ejpam-5837	120	10	m	m	PROPN
ejpam-5837	120	11	,	,	PUNCT
ejpam-5837	120	12	n)quasi	n)quasi	ADJ
ejpam-5837	120	13	-	-	PUNCT
ejpam-5837	120	14	ideal	ideal	ADJ
ejpam-5837	120	15	and	and	CCONJ
ejpam-5837	120	16	fuzzy	fuzzy	ADJ
ejpam-5837	120	17	almost	almost	ADV
ejpam-5837	120	18	(	(	PUNCT
ejpam-5837	120	19	m	m	PROPN
ejpam-5837	120	20	,	,	PUNCT
ejpam-5837	120	21	n)-quasi	n)-quasi	NOUN
ejpam-5837	120	22	-	-	NOUN
ejpam-5837	120	23	ideal	ideal	NOUN
ejpam-5837	120	24	in	in	ADP
ejpam-5837	120	25	ordered	order	VERB
ejpam-5837	120	26	semigroup	semigroup	PROPN
ejpam-5837	120	27	.	.	PUNCT
ejpam-5837	121	1	definition	definition	NOUN
ejpam-5837	121	2	11	11	NUM
ejpam-5837	121	3	.	.	PUNCT
ejpam-5837	122	1	a	a	DET
ejpam-5837	122	2	non	non	ADJ
ejpam-5837	122	3	-	-	ADJ
ejpam-5837	122	4	empty	empty	ADJ
ejpam-5837	122	5	subset	subset	NOUN
ejpam-5837	122	6	b	b	NOUN
ejpam-5837	122	7	on	on	ADP
ejpam-5837	122	8	an	an	DET
ejpam-5837	122	9	ordered	order	VERB
ejpam-5837	122	10	semigroup	semigroup	PROPN
ejpam-5837	122	11	t	t	PROPN
ejpam-5837	122	12	is	be	AUX
ejpam-5837	122	13	called	call	VERB
ejpam-5837	122	14	an	an	DET
ejpam-5837	122	15	almost	almost	ADV
ejpam-5837	122	16	(	(	PUNCT
ejpam-5837	122	17	m	m	PROPN
ejpam-5837	122	18	,	,	PUNCT
ejpam-5837	122	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	122	20	-	-	NOUN
ejpam-5837	122	21	ideal	ideal	NOUN
ejpam-5837	122	22	of	of	ADP
ejpam-5837	122	23	t	t	PROPN
ejpam-5837	122	24	if	if	SCONJ
ejpam-5837	122	25	(	(	PUNCT
ejpam-5837	122	26	bmt	bmt	NOUN
ejpam-5837	122	27	]	]	PUNCT
ejpam-5837	122	28	∩	∩	NOUN
ejpam-5837	122	29	(	(	PUNCT
ejpam-5837	122	30	tbn	tbn	NOUN
ejpam-5837	122	31	]	]	X
ejpam-5837	122	32	∩b	∩b	X
ejpam-5837	122	33	̸=	̸=	PROPN
ejpam-5837	122	34	∅	∅	NOUN
ejpam-5837	122	35	for	for	ADP
ejpam-5837	122	36	all	all	DET
ejpam-5837	122	37	t	t	NOUN
ejpam-5837	122	38	∈	∈	PROPN
ejpam-5837	122	39	t	t	PROPN
ejpam-5837	122	40	where	where	SCONJ
ejpam-5837	122	41	m	m	VERB
ejpam-5837	122	42	,	,	PUNCT
ejpam-5837	122	43	n	n	PRON
ejpam-5837	122	44	∈	∈	PROPN
ejpam-5837	122	45	{	{	PUNCT
ejpam-5837	122	46	1	1	NUM
ejpam-5837	122	47	,	,	PUNCT
ejpam-5837	122	48	2	2	NUM
ejpam-5837	122	49	,	,	PUNCT
ejpam-5837	122	50	...	...	PUNCT
ejpam-5837	122	51	,	,	PUNCT
ejpam-5837	122	52	n	n	CCONJ
ejpam-5837	122	53	}	}	PUNCT
ejpam-5837	122	54	.	.	PUNCT
ejpam-5837	123	1	p.	p.	NOUN
ejpam-5837	123	2	khamrot	khamrot	PROPN
ejpam-5837	124	1	et	et	PROPN
ejpam-5837	124	2	al	al	PROPN
ejpam-5837	124	3	.	.	PUNCT
ejpam-5837	124	4	/	/	SYM
ejpam-5837	124	5	eur	eur	PROPN
ejpam-5837	124	6	.	.	PUNCT
ejpam-5837	125	1	j.	j.	PROPN
ejpam-5837	125	2	pure	pure	PROPN
ejpam-5837	125	3	appl	appl	PROPN
ejpam-5837	125	4	.	.	PROPN
ejpam-5837	125	5	math	math	PROPN
ejpam-5837	125	6	,	,	PUNCT
ejpam-5837	125	7	18	18	NUM
ejpam-5837	125	8	(	(	PUNCT
ejpam-5837	125	9	2	2	NUM
ejpam-5837	125	10	)	)	PUNCT
ejpam-5837	125	11	(	(	PUNCT
ejpam-5837	125	12	2025	2025	NUM
ejpam-5837	125	13	)	)	PUNCT
ejpam-5837	125	14	,	,	PUNCT
ejpam-5837	125	15	5837	5837	NUM
ejpam-5837	125	16	6	6	NUM
ejpam-5837	125	17	of	of	ADP
ejpam-5837	125	18	13	13	NUM
ejpam-5837	125	19	example	example	NOUN
ejpam-5837	125	20	1	1	NUM
ejpam-5837	125	21	.	.	PUNCT
ejpam-5837	126	1	(	(	PUNCT
ejpam-5837	126	2	1	1	X
ejpam-5837	126	3	)	)	PUNCT
ejpam-5837	126	4	an	an	DET
ejpam-5837	126	5	almost	almost	ADV
ejpam-5837	126	6	(	(	PUNCT
ejpam-5837	126	7	1	1	NUM
ejpam-5837	126	8	,	,	PUNCT
ejpam-5837	126	9	1)-ideal	1)-ideal	NUM
ejpam-5837	126	10	of	of	ADP
ejpam-5837	126	11	an	an	DET
ejpam-5837	126	12	ordered	order	VERB
ejpam-5837	126	13	semigroup	semigroup	PROPN
ejpam-5837	126	14	t	t	PROPN
ejpam-5837	126	15	is	be	AUX
ejpam-5837	126	16	a	a	DET
ejpam-5837	126	17	right	right	NOUN
ejpam-5837	126	18	almost	almost	ADV
ejpam-5837	126	19	quasiideal	quasiideal	ADJ
ejpam-5837	126	20	of	of	ADP
ejpam-5837	126	21	t.	t.	PROPN
ejpam-5837	126	22	(	(	PUNCT
ejpam-5837	126	23	2	2	X
ejpam-5837	126	24	)	)	PUNCT
ejpam-5837	126	25	consider	consider	VERB
ejpam-5837	126	26	the	the	DET
ejpam-5837	126	27	ordered	order	VERB
ejpam-5837	126	28	semigroup	semigroup	PROPN
ejpam-5837	126	29	z6	z6	PROPN
ejpam-5837	126	30	under	under	ADP
ejpam-5837	126	31	the	the	DET
ejpam-5837	126	32	usual	usual	ADJ
ejpam-5837	126	33	addition	addition	NOUN
ejpam-5837	126	34	and	and	CCONJ
ejpam-5837	126	35	the	the	DET
ejpam-5837	126	36	partial	partial	ADJ
ejpam-5837	126	37	ordered	order	VERB
ejpam-5837	126	38	≤:=	≤:=	PROPN
ejpam-5837	126	39	{	{	PUNCT
ejpam-5837	126	40	(	(	PUNCT
ejpam-5837	126	41	a	a	DET
ejpam-5837	126	42	,	,	PUNCT
ejpam-5837	126	43	a	a	NOUN
ejpam-5837	126	44	)	)	PUNCT
ejpam-5837	126	45	|	|	ADV
ejpam-5837	126	46	a	a	DET
ejpam-5837	126	47	∈	∈	PROPN
ejpam-5837	126	48	z6	z6	NUM
ejpam-5837	126	49	}	}	PUNCT
ejpam-5837	126	50	.	.	PUNCT
ejpam-5837	127	1	we	we	PRON
ejpam-5837	127	2	have	have	VERB
ejpam-5837	127	3	a	a	DET
ejpam-5837	127	4	=	=	SYM
ejpam-5837	127	5	{	{	PUNCT
ejpam-5837	127	6	1	1	NUM
ejpam-5837	127	7	,	,	PUNCT
ejpam-5837	127	8	4	4	NUM
ejpam-5837	127	9	,	,	PUNCT
ejpam-5837	127	10	5	5	NUM
ejpam-5837	127	11	}	}	PUNCT
ejpam-5837	127	12	is	be	AUX
ejpam-5837	127	13	an	an	DET
ejpam-5837	127	14	almsot	almsot	ADJ
ejpam-5837	127	15	(	(	PUNCT
ejpam-5837	127	16	1	1	NUM
ejpam-5837	127	17	,	,	PUNCT
ejpam-5837	127	18	1)-quasi	1)-quasi	NOUN
ejpam-5837	127	19	-	-	NOUN
ejpam-5837	127	20	ideal	ideal	NOUN
ejpam-5837	127	21	of	of	ADP
ejpam-5837	127	22	z6	z6	PROPN
ejpam-5837	127	23	.	.	PUNCT
ejpam-5837	128	1	(	(	PUNCT
ejpam-5837	128	2	3	3	X
ejpam-5837	128	3	)	)	PUNCT
ejpam-5837	128	4	the	the	DET
ejpam-5837	128	5	almost	almost	ADV
ejpam-5837	128	6	(	(	PUNCT
ejpam-5837	128	7	m	m	PROPN
ejpam-5837	128	8	,	,	PUNCT
ejpam-5837	128	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	128	10	-	-	NOUN
ejpam-5837	128	11	ideal	ideal	NOUN
ejpam-5837	128	12	of	of	ADP
ejpam-5837	128	13	an	an	DET
ejpam-5837	128	14	ordered	order	VERB
ejpam-5837	128	15	semigroup	semigroup	PROPN
ejpam-5837	128	16	t	t	PROPN
ejpam-5837	128	17	is	be	AUX
ejpam-5837	128	18	not	not	PART
ejpam-5837	128	19	(	(	PUNCT
ejpam-5837	128	20	m	m	PROPN
ejpam-5837	128	21	,	,	PUNCT
ejpam-5837	128	22	n)-quasi	n)-quasi	NOUN
ejpam-5837	128	23	-	-	NOUN
ejpam-5837	128	24	ideal	ideal	NOUN
ejpam-5837	128	25	of	of	ADP
ejpam-5837	128	26	t.	t.	PROPN
ejpam-5837	128	27	theorem	theorem	PROPN
ejpam-5837	128	28	1	1	NUM
ejpam-5837	128	29	.	.	PUNCT
ejpam-5837	129	1	every	every	DET
ejpam-5837	129	2	(	(	PUNCT
ejpam-5837	129	3	m	m	PROPN
ejpam-5837	129	4	,	,	PUNCT
ejpam-5837	129	5	n)-quasi	n)-quasi	NOUN
ejpam-5837	129	6	-	-	NOUN
ejpam-5837	129	7	ideal	ideal	NOUN
ejpam-5837	129	8	of	of	ADP
ejpam-5837	129	9	an	an	DET
ejpam-5837	129	10	ordered	order	VERB
ejpam-5837	129	11	semigroup	semigroup	PROPN
ejpam-5837	129	12	t	t	PROPN
ejpam-5837	129	13	is	be	AUX
ejpam-5837	129	14	an	an	DET
ejpam-5837	129	15	almost	almost	ADV
ejpam-5837	129	16	(	(	PUNCT
ejpam-5837	129	17	m	m	PROPN
ejpam-5837	129	18	,	,	PUNCT
ejpam-5837	129	19	n)quasi	n)quasi	NOUN
ejpam-5837	129	20	-	-	PUNCT
ejpam-5837	129	21	ideal	ideal	NOUN
ejpam-5837	129	22	of	of	ADP
ejpam-5837	129	23	t.	t.	NOUN
ejpam-5837	129	24	proof	proof	NOUN
ejpam-5837	129	25	.	.	PUNCT
ejpam-5837	130	1	assume	assume	VERB
ejpam-5837	130	2	that	that	SCONJ
ejpam-5837	130	3	b	b	PROPN
ejpam-5837	130	4	is	be	AUX
ejpam-5837	130	5	an	an	DET
ejpam-5837	130	6	(	(	PUNCT
ejpam-5837	130	7	m	m	PROPN
ejpam-5837	130	8	,	,	PUNCT
ejpam-5837	130	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	130	10	-	-	NOUN
ejpam-5837	130	11	ideal	ideal	NOUN
ejpam-5837	130	12	of	of	ADP
ejpam-5837	130	13	t	t	PROPN
ejpam-5837	130	14	and	and	CCONJ
ejpam-5837	130	15	let	let	VERB
ejpam-5837	130	16	t	t	PROPN
ejpam-5837	130	17	∈	∈	PROPN
ejpam-5837	130	18	t.	t.	NOUN
ejpam-5837	130	19	then	then	ADV
ejpam-5837	130	20	(	(	PUNCT
ejpam-5837	130	21	bmt]∩(tbn	bmt]∩(tbn	NOUN
ejpam-5837	130	22	]	]	PUNCT
ejpam-5837	130	23	⊆	⊆	NUM
ejpam-5837	130	24	(	(	PUNCT
ejpam-5837	130	25	bmt	bmt	NOUN
ejpam-5837	130	26	]	]	PUNCT
ejpam-5837	130	27	∩	∩	NOUN
ejpam-5837	130	28	(	(	PUNCT
ejpam-5837	130	29	tbn	tbn	NOUN
ejpam-5837	130	30	]	]	X
ejpam-5837	130	31	.	.	PUNCT
ejpam-5837	131	1	thus	thus	ADV
ejpam-5837	131	2	(	(	PUNCT
ejpam-5837	131	3	bmtbn	bmtbn	NOUN
ejpam-5837	131	4	]	]	PUNCT
ejpam-5837	131	5	∩b	∩b	NOUN
ejpam-5837	131	6	̸=	̸=	PROPN
ejpam-5837	131	7	∅.	∅.	NOUN
ejpam-5837	132	1	we	we	PRON
ejpam-5837	132	2	conclude	conclude	VERB
ejpam-5837	132	3	that	that	SCONJ
ejpam-5837	132	4	b	b	NOUN
ejpam-5837	132	5	is	be	AUX
ejpam-5837	132	6	an	an	DET
ejpam-5837	132	7	almost	almost	ADV
ejpam-5837	132	8	(	(	PUNCT
ejpam-5837	132	9	m	m	NOUN
ejpam-5837	132	10	,	,	PUNCT
ejpam-5837	132	11	n)-quasiideal	n)-quasiideal	NOUN
ejpam-5837	132	12	of	of	ADP
ejpam-5837	132	13	t.	t.	PROPN
ejpam-5837	132	14	theorem	theorem	PROPN
ejpam-5837	132	15	2	2	X
ejpam-5837	132	16	.	.	PUNCT
ejpam-5837	133	1	let	let	VERB
ejpam-5837	133	2	b1	b1	NOUN
ejpam-5837	133	3	and	and	CCONJ
ejpam-5837	133	4	b2	b2	NOUN
ejpam-5837	133	5	be	be	AUX
ejpam-5837	133	6	two	two	NUM
ejpam-5837	133	7	non	non	ADJ
ejpam-5837	133	8	-	-	ADJ
ejpam-5837	133	9	empty	empty	ADJ
ejpam-5837	133	10	subsets	subset	NOUN
ejpam-5837	133	11	of	of	ADP
ejpam-5837	133	12	an	an	DET
ejpam-5837	133	13	ordered	order	VERB
ejpam-5837	133	14	semigroup	semigroup	PROPN
ejpam-5837	133	15	t	t	PROPN
ejpam-5837	133	16	such	such	ADJ
ejpam-5837	133	17	that	that	PRON
ejpam-5837	133	18	b1	b1	NOUN
ejpam-5837	133	19	⊆	⊆	NUM
ejpam-5837	133	20	b2	b2	NOUN
ejpam-5837	133	21	.	.	PUNCT
ejpam-5837	134	1	if	if	SCONJ
ejpam-5837	134	2	b1	b1	NOUN
ejpam-5837	134	3	is	be	AUX
ejpam-5837	134	4	an	an	DET
ejpam-5837	134	5	almost	almost	ADV
ejpam-5837	134	6	(	(	PUNCT
ejpam-5837	134	7	m	m	PROPN
ejpam-5837	134	8	,	,	PUNCT
ejpam-5837	134	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	134	10	-	-	NOUN
ejpam-5837	134	11	ideal	ideal	NOUN
ejpam-5837	134	12	of	of	ADP
ejpam-5837	134	13	t	t	PROPN
ejpam-5837	134	14	,	,	PUNCT
ejpam-5837	134	15	then	then	ADV
ejpam-5837	134	16	b2	b2	NOUN
ejpam-5837	134	17	is	be	AUX
ejpam-5837	134	18	also	also	ADV
ejpam-5837	134	19	an	an	DET
ejpam-5837	134	20	almost	almost	ADV
ejpam-5837	134	21	(	(	PUNCT
ejpam-5837	134	22	m	m	PROPN
ejpam-5837	134	23	,	,	PUNCT
ejpam-5837	134	24	n)-quasi	n)-quasi	NOUN
ejpam-5837	134	25	-	-	NOUN
ejpam-5837	134	26	ideal	ideal	NOUN
ejpam-5837	134	27	of	of	ADP
ejpam-5837	134	28	t.	t.	NOUN
ejpam-5837	134	29	proof	proof	NOUN
ejpam-5837	134	30	.	.	PUNCT
ejpam-5837	135	1	let	let	VERB
ejpam-5837	135	2	b1	b1	NOUN
ejpam-5837	135	3	be	be	AUX
ejpam-5837	135	4	an	an	DET
ejpam-5837	135	5	almost	almost	ADV
ejpam-5837	135	6	(	(	PUNCT
ejpam-5837	135	7	m	m	PROPN
ejpam-5837	135	8	,	,	PUNCT
ejpam-5837	135	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	135	10	-	-	NOUN
ejpam-5837	135	11	ideal	ideal	NOUN
ejpam-5837	135	12	of	of	ADP
ejpam-5837	135	13	t	t	PROPN
ejpam-5837	135	14	with	with	ADP
ejpam-5837	135	15	b1	b1	NOUN
ejpam-5837	135	16	⊆	⊆	NUM
ejpam-5837	135	17	b2	b2	NOUN
ejpam-5837	135	18	and	and	CCONJ
ejpam-5837	135	19	let	let	VERB
ejpam-5837	135	20	t	t	PROPN
ejpam-5837	135	21	∈	∈	PROPN
ejpam-5837	135	22	t	t	PROPN
ejpam-5837	135	23	then	then	ADV
ejpam-5837	135	24	(	(	PUNCT
ejpam-5837	135	25	bm	bm	PROPN
ejpam-5837	135	26	1	1	NUM
ejpam-5837	135	27	t	t	PROPN
ejpam-5837	135	28	]	]	PUNCT
ejpam-5837	135	29	∩	∩	NOUN
ejpam-5837	135	30	(	(	PUNCT
ejpam-5837	135	31	tbn	tbn	NOUN
ejpam-5837	135	32	1	1	NUM
ejpam-5837	135	33	]	]	PUNCT
ejpam-5837	135	34	⊆	⊆	NUM
ejpam-5837	135	35	(	(	PUNCT
ejpam-5837	135	36	bm	bm	PROPN
ejpam-5837	135	37	2	2	NUM
ejpam-5837	135	38	t	t	PROPN
ejpam-5837	135	39	]	]	PUNCT
ejpam-5837	135	40	∩	∩	NOUN
ejpam-5837	135	41	(	(	PUNCT
ejpam-5837	135	42	tbn	tbn	PROPN
ejpam-5837	135	43	2	2	NUM
ejpam-5837	135	44	]	]	PUNCT
ejpam-5837	135	45	thus	thus	ADV
ejpam-5837	135	46	,	,	PUNCT
ejpam-5837	135	47	(	(	PUNCT
ejpam-5837	135	48	b	b	X
ejpam-5837	135	49	m	m	VERB
ejpam-5837	135	50	2	2	NUM
ejpam-5837	135	51	tbn	tbn	NOUN
ejpam-5837	135	52	2	2	NUM
ejpam-5837	135	53	]	]	PUNCT
ejpam-5837	135	54	∩b2	∩b2	PROPN
ejpam-5837	135	55	̸=	̸=	PROPN
ejpam-5837	135	56	∅.	∅.	PRON
ejpam-5837	135	57	hence	hence	ADV
ejpam-5837	135	58	,	,	PUNCT
ejpam-5837	135	59	b2	b2	PROPN
ejpam-5837	135	60	is	be	AUX
ejpam-5837	135	61	an	an	DET
ejpam-5837	135	62	almost	almost	ADV
ejpam-5837	135	63	(	(	PUNCT
ejpam-5837	135	64	m	m	PROPN
ejpam-5837	135	65	,	,	PUNCT
ejpam-5837	135	66	n)-quasi	n)-quasi	NOUN
ejpam-5837	135	67	-	-	NOUN
ejpam-5837	135	68	ideal	ideal	NOUN
ejpam-5837	135	69	of	of	ADP
ejpam-5837	135	70	t.	t.	PROPN
ejpam-5837	135	71	corollary	corollary	ADJ
ejpam-5837	135	72	1	1	NUM
ejpam-5837	135	73	.	.	PUNCT
ejpam-5837	136	1	let	let	VERB
ejpam-5837	136	2	b1	b1	NOUN
ejpam-5837	136	3	and	and	CCONJ
ejpam-5837	136	4	b2	b2	NOUN
ejpam-5837	136	5	be	be	VERB
ejpam-5837	136	6	almost	almost	ADV
ejpam-5837	136	7	(	(	PUNCT
ejpam-5837	136	8	m	m	PROPN
ejpam-5837	136	9	,	,	PUNCT
ejpam-5837	136	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	136	11	-	-	NOUN
ejpam-5837	136	12	ideals	ideal	NOUN
ejpam-5837	136	13	of	of	ADP
ejpam-5837	136	14	an	an	DET
ejpam-5837	136	15	ordered	order	VERB
ejpam-5837	136	16	semigroup	semigroup	NOUN
ejpam-5837	136	17	t.	t.	PROPN
ejpam-5837	136	18	thus	thus	ADV
ejpam-5837	136	19	b1	b1	NOUN
ejpam-5837	136	20	∪b2	∪b2	ADJ
ejpam-5837	136	21	is	be	AUX
ejpam-5837	136	22	also	also	ADV
ejpam-5837	136	23	an	an	DET
ejpam-5837	136	24	almost	almost	ADV
ejpam-5837	136	25	(	(	PUNCT
ejpam-5837	136	26	m	m	PROPN
ejpam-5837	136	27	,	,	PUNCT
ejpam-5837	136	28	n)-quasi	n)-quasi	NOUN
ejpam-5837	136	29	-	-	NOUN
ejpam-5837	136	30	ideal	ideal	NOUN
ejpam-5837	136	31	of	of	ADP
ejpam-5837	136	32	t.	t.	NOUN
ejpam-5837	136	33	proof	proof	NOUN
ejpam-5837	136	34	.	.	PUNCT
ejpam-5837	137	1	since	since	SCONJ
ejpam-5837	137	2	b1	b1	NOUN
ejpam-5837	137	3	and	and	CCONJ
ejpam-5837	137	4	b1	b1	NOUN
ejpam-5837	137	5	are	be	AUX
ejpam-5837	137	6	subsets	subset	NOUN
ejpam-5837	137	7	of	of	ADP
ejpam-5837	137	8	b1	b1	NOUN
ejpam-5837	137	9	∪b2	∪b2	ADJ
ejpam-5837	137	10	,	,	PUNCT
ejpam-5837	137	11	by	by	ADP
ejpam-5837	137	12	theorem	theorem	NOUN
ejpam-5837	137	13	2	2	NUM
ejpam-5837	137	14	,	,	PUNCT
ejpam-5837	137	15	b1	b1	NOUN
ejpam-5837	137	16	∪b2	∪b2	ADJ
ejpam-5837	137	17	is	be	AUX
ejpam-5837	137	18	an	an	DET
ejpam-5837	137	19	almost	almost	ADV
ejpam-5837	137	20	(	(	PUNCT
ejpam-5837	137	21	m	m	PROPN
ejpam-5837	137	22	,	,	PUNCT
ejpam-5837	137	23	n)-quasi	n)-quasi	NOUN
ejpam-5837	137	24	-	-	NOUN
ejpam-5837	137	25	ideal	ideal	NOUN
ejpam-5837	137	26	of	of	ADP
ejpam-5837	137	27	t.	t.	PROPN
ejpam-5837	137	28	corollary	corollary	ADJ
ejpam-5837	137	29	2	2	NUM
ejpam-5837	137	30	.	.	PUNCT
ejpam-5837	138	1	let	let	VERB
ejpam-5837	138	2	b1	b1	NOUN
ejpam-5837	138	3	and	and	CCONJ
ejpam-5837	138	4	b2	b2	NOUN
ejpam-5837	138	5	be	be	VERB
ejpam-5837	138	6	nonempty	nonempty	ADJ
ejpam-5837	138	7	subsets	subset	NOUN
ejpam-5837	138	8	of	of	ADP
ejpam-5837	138	9	an	an	DET
ejpam-5837	138	10	ordered	order	VERB
ejpam-5837	138	11	semigroup	semigroup	NOUN
ejpam-5837	138	12	t.	t.	PROPN
ejpam-5837	138	13	if	if	SCONJ
ejpam-5837	138	14	b1	b1	PROPN
ejpam-5837	138	15	is	be	AUX
ejpam-5837	138	16	an	an	DET
ejpam-5837	138	17	almost	almost	ADV
ejpam-5837	138	18	(	(	PUNCT
ejpam-5837	138	19	m	m	PROPN
ejpam-5837	138	20	,	,	PUNCT
ejpam-5837	138	21	n)-quasi	n)-quasi	NOUN
ejpam-5837	138	22	-	-	NOUN
ejpam-5837	138	23	ideal	ideal	NOUN
ejpam-5837	138	24	of	of	ADP
ejpam-5837	138	25	t	t	PROPN
ejpam-5837	138	26	,	,	PUNCT
ejpam-5837	138	27	then	then	ADV
ejpam-5837	138	28	b1	b1	VERB
ejpam-5837	138	29	∪b2	∪b2	ADJ
ejpam-5837	138	30	is	be	AUX
ejpam-5837	138	31	an	an	DET
ejpam-5837	138	32	almost	almost	ADV
ejpam-5837	138	33	(	(	PUNCT
ejpam-5837	138	34	m	m	PROPN
ejpam-5837	138	35	,	,	PUNCT
ejpam-5837	138	36	n)-quasi	n)-quasi	NOUN
ejpam-5837	138	37	-	-	NOUN
ejpam-5837	138	38	ideal	ideal	NOUN
ejpam-5837	138	39	of	of	ADP
ejpam-5837	138	40	t.	t.	NOUN
ejpam-5837	138	41	proof	proof	NOUN
ejpam-5837	138	42	.	.	PUNCT
ejpam-5837	139	1	by	by	ADP
ejpam-5837	139	2	corollary	corollary	ADJ
ejpam-5837	139	3	1	1	NUM
ejpam-5837	139	4	,	,	PUNCT
ejpam-5837	139	5	and	and	CCONJ
ejpam-5837	139	6	b1	b1	VERB
ejpam-5837	139	7	⊆	⊆	NUM
ejpam-5837	139	8	b1	b1	NOUN
ejpam-5837	139	9	∪b2	∪b2	ADJ
ejpam-5837	139	10	.	.	PUNCT
ejpam-5837	140	1	thus	thus	ADV
ejpam-5837	140	2	,	,	PUNCT
ejpam-5837	140	3	b1	b1	NOUN
ejpam-5837	140	4	∪b2	∪b2	ADJ
ejpam-5837	140	5	is	be	AUX
ejpam-5837	140	6	an	an	DET
ejpam-5837	140	7	almost	almost	ADV
ejpam-5837	140	8	(	(	PUNCT
ejpam-5837	140	9	m	m	NOUN
ejpam-5837	140	10	,	,	PUNCT
ejpam-5837	140	11	n)-quasiideal	n)-quasiideal	NOUN
ejpam-5837	140	12	of	of	ADP
ejpam-5837	140	13	t.	t.	PROPN
ejpam-5837	140	14	corollary	corollary	ADJ
ejpam-5837	140	15	3	3	NUM
ejpam-5837	140	16	.	.	PUNCT
ejpam-5837	141	1	the	the	DET
ejpam-5837	141	2	finite	finite	PROPN
ejpam-5837	141	3	union	union	NOUN
ejpam-5837	141	4	of	of	ADP
ejpam-5837	141	5	almost	almost	ADV
ejpam-5837	141	6	(	(	PUNCT
ejpam-5837	141	7	m	m	PROPN
ejpam-5837	141	8	,	,	PUNCT
ejpam-5837	141	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	141	10	-	-	NOUN
ejpam-5837	141	11	ideals	ideal	NOUN
ejpam-5837	141	12	of	of	ADP
ejpam-5837	141	13	an	an	DET
ejpam-5837	141	14	ordered	order	VERB
ejpam-5837	141	15	semigroup	semigroup	PROPN
ejpam-5837	141	16	t	t	PROPN
ejpam-5837	141	17	is	be	AUX
ejpam-5837	141	18	an	an	DET
ejpam-5837	141	19	almost	almost	ADV
ejpam-5837	141	20	(	(	PUNCT
ejpam-5837	141	21	m	m	PROPN
ejpam-5837	141	22	,	,	PUNCT
ejpam-5837	141	23	n)-quasi	n)-quasi	NOUN
ejpam-5837	141	24	-	-	NOUN
ejpam-5837	141	25	ideal	ideal	NOUN
ejpam-5837	141	26	of	of	ADP
ejpam-5837	141	27	t.	t.	PROPN
ejpam-5837	141	28	example	example	NOUN
ejpam-5837	141	29	2	2	X
ejpam-5837	141	30	.	.	X
ejpam-5837	141	31	consider	consider	VERB
ejpam-5837	141	32	the	the	DET
ejpam-5837	141	33	ordered	order	VERB
ejpam-5837	141	34	semigroup	semigroup	PROPN
ejpam-5837	141	35	z6	z6	PROPN
ejpam-5837	141	36	under	under	ADP
ejpam-5837	141	37	the	the	DET
ejpam-5837	141	38	usual	usual	ADJ
ejpam-5837	141	39	addtion	addtion	NOUN
ejpam-5837	141	40	and	and	CCONJ
ejpam-5837	141	41	the	the	DET
ejpam-5837	141	42	partial	partial	ADJ
ejpam-5837	141	43	ordered	order	VERB
ejpam-5837	141	44	≤:=	≤:=	PROPN
ejpam-5837	141	45	{	{	PUNCT
ejpam-5837	141	46	(	(	PUNCT
ejpam-5837	141	47	a	a	DET
ejpam-5837	141	48	,	,	PUNCT
ejpam-5837	141	49	a	a	NOUN
ejpam-5837	141	50	)	)	PUNCT
ejpam-5837	141	51	|	|	ADV
ejpam-5837	141	52	a	a	DET
ejpam-5837	141	53	∈	∈	PROPN
ejpam-5837	141	54	z6	z6	NUM
ejpam-5837	141	55	}	}	PUNCT
ejpam-5837	141	56	.	.	PUNCT
ejpam-5837	142	1	we	we	PRON
ejpam-5837	142	2	have	have	VERB
ejpam-5837	142	3	a	a	DET
ejpam-5837	142	4	=	=	SYM
ejpam-5837	142	5	{	{	PUNCT
ejpam-5837	142	6	1	1	NUM
ejpam-5837	142	7	,	,	PUNCT
ejpam-5837	142	8	4	4	NUM
ejpam-5837	142	9	,	,	PUNCT
ejpam-5837	142	10	5	5	NUM
ejpam-5837	142	11	}	}	PUNCT
ejpam-5837	142	12	and	and	CCONJ
ejpam-5837	142	13	b	b	X
ejpam-5837	142	14	=	=	SYM
ejpam-5837	142	15	{	{	PUNCT
ejpam-5837	142	16	1	1	NUM
ejpam-5837	142	17	,	,	PUNCT
ejpam-5837	142	18	2	2	NUM
ejpam-5837	142	19	,	,	PUNCT
ejpam-5837	142	20	5	5	NUM
ejpam-5837	142	21	}	}	PUNCT
ejpam-5837	142	22	are	be	AUX
ejpam-5837	142	23	almost	almost	ADV
ejpam-5837	142	24	(	(	PUNCT
ejpam-5837	142	25	1	1	NUM
ejpam-5837	142	26	,	,	PUNCT
ejpam-5837	142	27	1)quasi	1)quasi	NUM
ejpam-5837	142	28	-	-	PUNCT
ejpam-5837	142	29	ideals	ideal	NOUN
ejpam-5837	142	30	of	of	ADP
ejpam-5837	142	31	z6	z6	PROPN
ejpam-5837	142	32	.	.	PUNCT
ejpam-5837	143	1	consider	consider	VERB
ejpam-5837	143	2	a	a	DET
ejpam-5837	143	3	∩b	∩b	NOUN
ejpam-5837	143	4	=	=	SYM
ejpam-5837	143	5	{	{	PUNCT
ejpam-5837	143	6	1	1	NUM
ejpam-5837	143	7	,	,	PUNCT
ejpam-5837	143	8	5	5	NUM
ejpam-5837	143	9	}	}	PUNCT
ejpam-5837	143	10	then	then	ADV
ejpam-5837	143	11	a	a	DET
ejpam-5837	143	12	∩b2	∩b2	PROPN
ejpam-5837	143	13	∩	∩	ADJ
ejpam-5837	143	14	2a	2a	NUM
ejpam-5837	143	15	∩b	∩b	NOUN
ejpam-5837	143	16	∩	∩	NOUN
ejpam-5837	143	17	a	a	DET
ejpam-5837	143	18	∩b	∩b	NOUN
ejpam-5837	143	19	=	=	X
ejpam-5837	143	20	∅.	∅.	NOUN
ejpam-5837	143	21	thus	thus	ADV
ejpam-5837	143	22	,	,	PUNCT
ejpam-5837	143	23	a	a	DET
ejpam-5837	143	24	∩b	∩b	NOUN
ejpam-5837	143	25	=	=	SYM
ejpam-5837	143	26	{	{	PUNCT
ejpam-5837	143	27	1	1	NUM
ejpam-5837	143	28	,	,	PUNCT
ejpam-5837	143	29	5	5	NUM
ejpam-5837	143	30	}	}	PUNCT
ejpam-5837	143	31	is	be	AUX
ejpam-5837	143	32	not	not	PART
ejpam-5837	143	33	an	an	DET
ejpam-5837	143	34	almost	almost	ADV
ejpam-5837	143	35	(	(	PUNCT
ejpam-5837	143	36	1	1	NUM
ejpam-5837	143	37	,	,	PUNCT
ejpam-5837	143	38	1)-quasi	1)-quasi	NOUN
ejpam-5837	143	39	-	-	NOUN
ejpam-5837	143	40	ideal	ideal	NOUN
ejpam-5837	143	41	of	of	ADP
ejpam-5837	143	42	z6	z6	PROPN
ejpam-5837	143	43	.	.	PUNCT
ejpam-5837	144	1	definition	definition	NOUN
ejpam-5837	144	2	12	12	NUM
ejpam-5837	144	3	.	.	PUNCT
ejpam-5837	145	1	a	a	DET
ejpam-5837	145	2	fuzzy	fuzzy	ADJ
ejpam-5837	145	3	set	set	VERB
ejpam-5837	145	4	ϑ	ϑ	NOUN
ejpam-5837	145	5	on	on	ADP
ejpam-5837	145	6	an	an	DET
ejpam-5837	145	7	ordered	order	VERB
ejpam-5837	145	8	semigroup	semigroup	PROPN
ejpam-5837	145	9	t	t	PROPN
ejpam-5837	145	10	is	be	AUX
ejpam-5837	145	11	called	call	VERB
ejpam-5837	145	12	a	a	DET
ejpam-5837	145	13	fuzzy	fuzzy	ADJ
ejpam-5837	145	14	almost	almost	ADV
ejpam-5837	145	15	(	(	PUNCT
ejpam-5837	145	16	m	m	NOUN
ejpam-5837	145	17	,	,	PUNCT
ejpam-5837	145	18	n)quasi	n)quasi	NOUN
ejpam-5837	145	19	-	-	PUNCT
ejpam-5837	145	20	ideal	ideal	NOUN
ejpam-5837	145	21	of	of	ADP
ejpam-5837	145	22	t	t	PROPN
ejpam-5837	145	23	if	if	SCONJ
ejpam-5837	145	24	(	(	PUNCT
ejpam-5837	145	25	ϑm	ϑm	ADP
ejpam-5837	145	26	◦	◦	NOUN
ejpam-5837	145	27	xt	xt	ADP
ejpam-5837	145	28	]	]	X
ejpam-5837	145	29	∧	∧	PROPN
ejpam-5837	145	30	(	(	PUNCT
ejpam-5837	145	31	xt	xt	ADP
ejpam-5837	145	32	◦	◦	NOUN
ejpam-5837	145	33	ϑn	ϑn	NOUN
ejpam-5837	145	34	]	]	X
ejpam-5837	145	35	∧	∧	PROPN
ejpam-5837	145	36	ϑ	ϑ	X
ejpam-5837	145	37	̸=	̸=	PROPN
ejpam-5837	145	38	0	0	NUM
ejpam-5837	145	39	.	.	PUNCT
ejpam-5837	146	1	for	for	ADP
ejpam-5837	146	2	any	any	DET
ejpam-5837	146	3	fuzzy	fuzzy	ADJ
ejpam-5837	146	4	point	point	NOUN
ejpam-5837	146	5	xt	xt	PUNCT
ejpam-5837	146	6	∈	∈	PROPN
ejpam-5837	146	7	t	t	PROPN
ejpam-5837	146	8	where	where	SCONJ
ejpam-5837	146	9	m	m	VERB
ejpam-5837	146	10	,	,	PUNCT
ejpam-5837	146	11	n	n	PRON
ejpam-5837	146	12	∈	∈	PROPN
ejpam-5837	146	13	{	{	PUNCT
ejpam-5837	146	14	1	1	NUM
ejpam-5837	146	15	,	,	PUNCT
ejpam-5837	146	16	2	2	NUM
ejpam-5837	146	17	,	,	PUNCT
ejpam-5837	146	18	...	...	PUNCT
ejpam-5837	146	19	,	,	PUNCT
ejpam-5837	146	20	n	n	CCONJ
ejpam-5837	146	21	}	}	PUNCT
ejpam-5837	146	22	.	.	PUNCT
ejpam-5837	147	1	p.	p.	NOUN
ejpam-5837	147	2	khamrot	khamrot	PROPN
ejpam-5837	148	1	et	et	PROPN
ejpam-5837	148	2	al	al	PROPN
ejpam-5837	148	3	.	.	PUNCT
ejpam-5837	148	4	/	/	SYM
ejpam-5837	148	5	eur	eur	PROPN
ejpam-5837	148	6	.	.	PUNCT
ejpam-5837	149	1	j.	j.	PROPN
ejpam-5837	149	2	pure	pure	PROPN
ejpam-5837	149	3	appl	appl	PROPN
ejpam-5837	149	4	.	.	PROPN
ejpam-5837	149	5	math	math	PROPN
ejpam-5837	149	6	,	,	PUNCT
ejpam-5837	149	7	18	18	NUM
ejpam-5837	149	8	(	(	PUNCT
ejpam-5837	149	9	2	2	NUM
ejpam-5837	149	10	)	)	PUNCT
ejpam-5837	149	11	(	(	PUNCT
ejpam-5837	149	12	2025	2025	NUM
ejpam-5837	149	13	)	)	PUNCT
ejpam-5837	149	14	,	,	PUNCT
ejpam-5837	149	15	5837	5837	NUM
ejpam-5837	149	16	7	7	NUM
ejpam-5837	149	17	of	of	ADP
ejpam-5837	149	18	13	13	NUM
ejpam-5837	149	19	theorem	theorem	NOUN
ejpam-5837	149	20	3	3	NUM
ejpam-5837	149	21	.	.	PUNCT
ejpam-5837	150	1	if	if	SCONJ
ejpam-5837	150	2	ϑ	ϑ	X
ejpam-5837	150	3	is	be	AUX
ejpam-5837	150	4	a	a	DET
ejpam-5837	150	5	fuzzy	fuzzy	ADJ
ejpam-5837	150	6	almost	almost	ADV
ejpam-5837	150	7	(	(	PUNCT
ejpam-5837	150	8	m	m	PROPN
ejpam-5837	150	9	,	,	PUNCT
ejpam-5837	150	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	150	11	-	-	NOUN
ejpam-5837	150	12	ideal	ideal	NOUN
ejpam-5837	150	13	of	of	ADP
ejpam-5837	150	14	an	an	DET
ejpam-5837	150	15	ordered	order	VERB
ejpam-5837	150	16	semigroup	semigroup	PROPN
ejpam-5837	150	17	t	t	PROPN
ejpam-5837	150	18	and	and	CCONJ
ejpam-5837	150	19	ξ	ξ	PROPN
ejpam-5837	150	20	is	be	AUX
ejpam-5837	150	21	a	a	DET
ejpam-5837	150	22	fuzzy	fuzzy	ADJ
ejpam-5837	150	23	subset	subset	NOUN
ejpam-5837	150	24	of	of	ADP
ejpam-5837	150	25	t	t	NOUN
ejpam-5837	150	26	such	such	ADJ
ejpam-5837	150	27	that	that	SCONJ
ejpam-5837	150	28	ϑ	ϑ	PROPN
ejpam-5837	150	29	≤	≤	PROPN
ejpam-5837	150	30	ξ	ξ	PROPN
ejpam-5837	150	31	,	,	PUNCT
ejpam-5837	150	32	then	then	ADV
ejpam-5837	150	33	ξ	ξ	PROPN
ejpam-5837	150	34	is	be	AUX
ejpam-5837	150	35	a	a	DET
ejpam-5837	150	36	fuzzy	fuzzy	ADJ
ejpam-5837	150	37	almost	almost	ADV
ejpam-5837	150	38	(	(	PUNCT
ejpam-5837	150	39	m	m	PROPN
ejpam-5837	150	40	,	,	PUNCT
ejpam-5837	150	41	n)-quasi	n)-quasi	NOUN
ejpam-5837	150	42	-	-	NOUN
ejpam-5837	150	43	ideal	ideal	NOUN
ejpam-5837	150	44	of	of	ADP
ejpam-5837	150	45	t.	t.	NOUN
ejpam-5837	150	46	proof	proof	NOUN
ejpam-5837	150	47	.	.	PUNCT
ejpam-5837	151	1	suppose	suppose	VERB
ejpam-5837	151	2	that	that	SCONJ
ejpam-5837	151	3	ϑ	ϑ	PROPN
ejpam-5837	151	4	is	be	AUX
ejpam-5837	151	5	a	a	DET
ejpam-5837	151	6	fuzzy	fuzzy	ADJ
ejpam-5837	151	7	almost	almost	ADV
ejpam-5837	151	8	(	(	PUNCT
ejpam-5837	151	9	m	m	PROPN
ejpam-5837	151	10	,	,	PUNCT
ejpam-5837	151	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	151	12	-	-	NOUN
ejpam-5837	151	13	ideal	ideal	NOUN
ejpam-5837	151	14	of	of	ADP
ejpam-5837	151	15	t	t	PROPN
ejpam-5837	151	16	and	and	CCONJ
ejpam-5837	151	17	ξ	ξ	PROPN
ejpam-5837	151	18	is	be	AUX
ejpam-5837	151	19	a	a	DET
ejpam-5837	151	20	fuzzy	fuzzy	ADJ
ejpam-5837	151	21	subset	subset	NOUN
ejpam-5837	151	22	of	of	ADP
ejpam-5837	151	23	t	t	NOUN
ejpam-5837	151	24	such	such	ADJ
ejpam-5837	151	25	that	that	SCONJ
ejpam-5837	151	26	ϑ	ϑ	PROPN
ejpam-5837	151	27	≤	≤	PROPN
ejpam-5837	151	28	ξ	ξ	PROPN
ejpam-5837	151	29	.	.	PUNCT
ejpam-5837	152	1	then	then	ADV
ejpam-5837	152	2	for	for	ADP
ejpam-5837	152	3	any	any	DET
ejpam-5837	152	4	fuzzy	fuzzy	ADJ
ejpam-5837	152	5	points	point	NOUN
ejpam-5837	152	6	xt	xt	ADP
ejpam-5837	152	7	∈	∈	PROPN
ejpam-5837	152	8	t	t	PROPN
ejpam-5837	152	9	,	,	PUNCT
ejpam-5837	152	10	we	we	PRON
ejpam-5837	152	11	obtain	obtain	VERB
ejpam-5837	152	12	that	that	DET
ejpam-5837	152	13	(	(	PUNCT
ejpam-5837	152	14	ϑm	ϑm	ADP
ejpam-5837	152	15	◦	◦	NOUN
ejpam-5837	152	16	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	152	17	◦	◦	NOUN
ejpam-5837	152	18	ϑn]∧ϑ	ϑn]∧ϑ	NOUN
ejpam-5837	152	19	̸=	̸=	PROPN
ejpam-5837	152	20	0	0	NUM
ejpam-5837	152	21	.	.	PUNCT
ejpam-5837	153	1	thus	thus	ADV
ejpam-5837	153	2	,	,	PUNCT
ejpam-5837	153	3	(	(	PUNCT
ejpam-5837	153	4	ϑm	ϑm	ADP
ejpam-5837	153	5	◦	◦	NOUN
ejpam-5837	153	6	xt	xt	ADP
ejpam-5837	153	7	]	]	X
ejpam-5837	153	8	∧	∧	PROPN
ejpam-5837	153	9	(	(	PUNCT
ejpam-5837	153	10	xt	xt	ADP
ejpam-5837	153	11	◦	◦	NOUN
ejpam-5837	153	12	ϑn	ϑn	NOUN
ejpam-5837	153	13	]	]	X
ejpam-5837	153	14	∧	∧	PROPN
ejpam-5837	153	15	ϑ	ϑ	X
ejpam-5837	153	16	≤	≤	X
ejpam-5837	153	17	(	(	PUNCT
ejpam-5837	153	18	ξm	ξm	NUM
ejpam-5837	153	19	◦	◦	NOUN
ejpam-5837	153	20	xt	xt	ADP
ejpam-5837	153	21	]	]	X
ejpam-5837	153	22	∧	∧	PROPN
ejpam-5837	153	23	(	(	PUNCT
ejpam-5837	153	24	xt	xt	ADP
ejpam-5837	153	25	◦	◦	PROPN
ejpam-5837	153	26	ξn	ξn	X
ejpam-5837	153	27	]	]	X
ejpam-5837	153	28	∧	∧	PROPN
ejpam-5837	153	29	ξ	ξ	PROPN
ejpam-5837	153	30	̸=	̸=	PROPN
ejpam-5837	153	31	0	0	NUM
ejpam-5837	153	32	.	.	PUNCT
ejpam-5837	154	1	hence	hence	ADV
ejpam-5837	154	2	,	,	PUNCT
ejpam-5837	154	3	(	(	PUNCT
ejpam-5837	154	4	ξm	ξm	NUM
ejpam-5837	154	5	◦	◦	NOUN
ejpam-5837	154	6	xt	xt	ADP
ejpam-5837	154	7	]	]	X
ejpam-5837	154	8	∧	∧	PROPN
ejpam-5837	154	9	(	(	PUNCT
ejpam-5837	154	10	xt	xt	ADP
ejpam-5837	154	11	◦	◦	PROPN
ejpam-5837	154	12	ξn	ξn	X
ejpam-5837	154	13	]	]	X
ejpam-5837	154	14	∧	∧	PROPN
ejpam-5837	154	15	ξ	ξ	PROPN
ejpam-5837	154	16	̸=	̸=	PROPN
ejpam-5837	154	17	0	0	NUM
ejpam-5837	154	18	.	.	PUNCT
ejpam-5837	155	1	therefore	therefore	ADV
ejpam-5837	155	2	,	,	PUNCT
ejpam-5837	155	3	ξ	ξ	PROPN
ejpam-5837	155	4	is	be	AUX
ejpam-5837	155	5	a	a	DET
ejpam-5837	155	6	fuzzy	fuzzy	ADJ
ejpam-5837	155	7	almost	almost	ADV
ejpam-5837	155	8	(	(	PUNCT
ejpam-5837	155	9	m	m	PROPN
ejpam-5837	155	10	,	,	PUNCT
ejpam-5837	155	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	155	12	-	-	NOUN
ejpam-5837	155	13	ideal	ideal	NOUN
ejpam-5837	155	14	of	of	ADP
ejpam-5837	155	15	t.	t.	NOUN
ejpam-5837	155	16	the	the	DET
ejpam-5837	155	17	following	following	ADJ
ejpam-5837	155	18	result	result	NOUN
ejpam-5837	155	19	is	be	AUX
ejpam-5837	155	20	an	an	DET
ejpam-5837	155	21	obvious	obvious	ADJ
ejpam-5837	155	22	of	of	ADP
ejpam-5837	155	23	theorem	theorem	ADJ
ejpam-5837	155	24	3	3	NUM
ejpam-5837	155	25	.	.	PUNCT
ejpam-5837	155	26	theorem	theorem	NOUN
ejpam-5837	155	27	4	4	NUM
ejpam-5837	155	28	.	.	PUNCT
ejpam-5837	156	1	let	let	VERB
ejpam-5837	156	2	ϑ	ϑ	X
ejpam-5837	156	3	and	and	CCONJ
ejpam-5837	156	4	ξ	ξ	PROPN
ejpam-5837	156	5	be	be	AUX
ejpam-5837	156	6	fuzzy	fuzzy	ADJ
ejpam-5837	156	7	almost	almost	ADV
ejpam-5837	156	8	(	(	PUNCT
ejpam-5837	156	9	m	m	PROPN
ejpam-5837	156	10	,	,	PUNCT
ejpam-5837	156	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	156	12	-	-	NOUN
ejpam-5837	156	13	ideal	ideal	NOUN
ejpam-5837	156	14	of	of	ADP
ejpam-5837	156	15	an	an	DET
ejpam-5837	156	16	ordered	order	VERB
ejpam-5837	156	17	semigroup	semigroup	NOUN
ejpam-5837	156	18	t.	t.	PROPN
ejpam-5837	156	19	then	then	ADV
ejpam-5837	156	20	ϑ	ϑ	PROPN
ejpam-5837	156	21	∨	∨	PROPN
ejpam-5837	156	22	ξ	ξ	PROPN
ejpam-5837	156	23	is	be	AUX
ejpam-5837	156	24	also	also	ADV
ejpam-5837	156	25	a	a	DET
ejpam-5837	156	26	fuzzy	fuzzy	ADJ
ejpam-5837	156	27	almost	almost	ADV
ejpam-5837	156	28	(	(	PUNCT
ejpam-5837	156	29	m	m	PROPN
ejpam-5837	156	30	,	,	PUNCT
ejpam-5837	156	31	n)-quasi	n)-quasi	NOUN
ejpam-5837	156	32	-	-	NOUN
ejpam-5837	156	33	ideal	ideal	NOUN
ejpam-5837	156	34	of	of	ADP
ejpam-5837	156	35	t.	t.	NOUN
ejpam-5837	156	36	proof	proof	NOUN
ejpam-5837	156	37	.	.	PUNCT
ejpam-5837	157	1	since	since	SCONJ
ejpam-5837	157	2	ϑ	ϑ	PRON
ejpam-5837	157	3	≤	≤	NUM
ejpam-5837	157	4	ϑ	ϑ	PROPN
ejpam-5837	157	5	∨	∨	NUM
ejpam-5837	157	6	ξ	ξ	PROPN
ejpam-5837	157	7	,	,	PUNCT
ejpam-5837	157	8	by	by	ADP
ejpam-5837	157	9	theorem	theorem	NOUN
ejpam-5837	157	10	3	3	NUM
ejpam-5837	157	11	,	,	PUNCT
ejpam-5837	157	12	ϑ	ϑ	X
ejpam-5837	157	13	∨	∨	PROPN
ejpam-5837	157	14	ξ	ξ	PROPN
ejpam-5837	157	15	is	be	AUX
ejpam-5837	157	16	also	also	ADV
ejpam-5837	157	17	a	a	DET
ejpam-5837	157	18	fuzzy	fuzzy	ADJ
ejpam-5837	157	19	almost	almost	ADV
ejpam-5837	157	20	(	(	PUNCT
ejpam-5837	157	21	m	m	PROPN
ejpam-5837	157	22	,	,	PUNCT
ejpam-5837	157	23	n)-quasi	n)-quasi	NOUN
ejpam-5837	157	24	-	-	NOUN
ejpam-5837	157	25	ideal	ideal	NOUN
ejpam-5837	157	26	of	of	ADP
ejpam-5837	157	27	t.	t.	PROPN
ejpam-5837	157	28	theorem	theorem	PROPN
ejpam-5837	157	29	5	5	NUM
ejpam-5837	157	30	.	.	PUNCT
ejpam-5837	158	1	if	if	SCONJ
ejpam-5837	158	2	ϑ	ϑ	X
ejpam-5837	158	3	fuzzy	fuzzy	ADJ
ejpam-5837	158	4	almost	almost	ADV
ejpam-5837	158	5	(	(	PUNCT
ejpam-5837	158	6	m	m	PROPN
ejpam-5837	158	7	,	,	PUNCT
ejpam-5837	158	8	n)-quasi	n)-quasi	NOUN
ejpam-5837	158	9	-	-	NOUN
ejpam-5837	158	10	ideal	ideal	NOUN
ejpam-5837	158	11	of	of	ADP
ejpam-5837	158	12	an	an	DET
ejpam-5837	158	13	ordered	order	VERB
ejpam-5837	158	14	semigroup	semigroup	PROPN
ejpam-5837	158	15	t	t	PROPN
ejpam-5837	158	16	and	and	CCONJ
ejpam-5837	158	17	ξ	ξ	PROPN
ejpam-5837	158	18	is	be	AUX
ejpam-5837	158	19	a	a	DET
ejpam-5837	158	20	fuzzy	fuzzy	ADJ
ejpam-5837	158	21	set	set	NOUN
ejpam-5837	158	22	,	,	PUNCT
ejpam-5837	158	23	then	then	ADV
ejpam-5837	158	24	ϑ	ϑ	PROPN
ejpam-5837	158	25	∨	∨	PROPN
ejpam-5837	158	26	ξ	ξ	PROPN
ejpam-5837	158	27	is	be	AUX
ejpam-5837	158	28	a	a	DET
ejpam-5837	158	29	fuzzy	fuzzy	ADJ
ejpam-5837	158	30	almost	almost	ADV
ejpam-5837	158	31	(	(	PUNCT
ejpam-5837	158	32	m	m	PROPN
ejpam-5837	158	33	,	,	PUNCT
ejpam-5837	158	34	n)-quasi	n)-quasi	NOUN
ejpam-5837	158	35	-	-	NOUN
ejpam-5837	158	36	ideal	ideal	NOUN
ejpam-5837	158	37	of	of	ADP
ejpam-5837	158	38	t.	t.	NOUN
ejpam-5837	158	39	proof	proof	NOUN
ejpam-5837	158	40	.	.	PUNCT
ejpam-5837	159	1	by	by	ADP
ejpam-5837	159	2	theorem	theorem	NOUN
ejpam-5837	159	3	3	3	NUM
ejpam-5837	159	4	,	,	PUNCT
ejpam-5837	159	5	and	and	CCONJ
ejpam-5837	159	6	ϑ	ϑ	X
ejpam-5837	159	7	≤	≤	NUM
ejpam-5837	159	8	ϑ	ϑ	PROPN
ejpam-5837	159	9	∨	∨	NUM
ejpam-5837	159	10	ξ	ξ	NUM
ejpam-5837	159	11	.	.	PUNCT
ejpam-5837	160	1	thus	thus	ADV
ejpam-5837	160	2	,	,	PUNCT
ejpam-5837	160	3	ϑ	ϑ	X
ejpam-5837	160	4	∨	∨	PROPN
ejpam-5837	160	5	ξ	ξ	PROPN
ejpam-5837	160	6	is	be	AUX
ejpam-5837	160	7	a	a	DET
ejpam-5837	160	8	fuzzy	fuzzy	ADJ
ejpam-5837	160	9	almost	almost	ADV
ejpam-5837	160	10	(	(	PUNCT
ejpam-5837	160	11	m	m	PROPN
ejpam-5837	160	12	,	,	PUNCT
ejpam-5837	160	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	160	14	-	-	NOUN
ejpam-5837	160	15	ideal	ideal	NOUN
ejpam-5837	160	16	of	of	ADP
ejpam-5837	160	17	t.	t.	PROPN
ejpam-5837	160	18	corollary	corollary	ADJ
ejpam-5837	160	19	4	4	NUM
ejpam-5837	160	20	.	.	PUNCT
ejpam-5837	161	1	let	let	VERB
ejpam-5837	161	2	t	t	PROPN
ejpam-5837	161	3	be	be	AUX
ejpam-5837	161	4	an	an	DET
ejpam-5837	161	5	ordered	order	VERB
ejpam-5837	161	6	semigroup	semigroup	NOUN
ejpam-5837	161	7	.	.	PUNCT
ejpam-5837	162	1	then	then	ADV
ejpam-5837	162	2	the	the	DET
ejpam-5837	162	3	finite	finite	ADJ
ejpam-5837	162	4	maximum	maximum	NOUN
ejpam-5837	162	5	of	of	ADP
ejpam-5837	162	6	fuzzy	fuzzy	ADJ
ejpam-5837	162	7	almost	almost	ADV
ejpam-5837	162	8	(	(	PUNCT
ejpam-5837	162	9	m	m	PROPN
ejpam-5837	162	10	,	,	PUNCT
ejpam-5837	162	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	162	12	-	-	NOUN
ejpam-5837	162	13	ideals	ideal	NOUN
ejpam-5837	162	14	of	of	ADP
ejpam-5837	162	15	t	t	PROPN
ejpam-5837	162	16	is	be	AUX
ejpam-5837	162	17	a	a	DET
ejpam-5837	162	18	fuzzy	fuzzy	ADJ
ejpam-5837	162	19	almost	almost	ADV
ejpam-5837	162	20	(	(	PUNCT
ejpam-5837	162	21	m	m	PROPN
ejpam-5837	162	22	,	,	PUNCT
ejpam-5837	162	23	n)-quasi	n)-quasi	NOUN
ejpam-5837	162	24	-	-	NOUN
ejpam-5837	162	25	ideal	ideal	NOUN
ejpam-5837	162	26	of	of	ADP
ejpam-5837	162	27	t.	t.	PROPN
ejpam-5837	162	28	example	example	NOUN
ejpam-5837	162	29	3	3	X
ejpam-5837	162	30	.	.	X
ejpam-5837	162	31	consider	consider	VERB
ejpam-5837	162	32	the	the	DET
ejpam-5837	162	33	ordered	order	VERB
ejpam-5837	162	34	semigroup	semigroup	PROPN
ejpam-5837	162	35	z6	z6	PROPN
ejpam-5837	162	36	under	under	ADP
ejpam-5837	162	37	the	the	DET
ejpam-5837	162	38	usual	usual	ADJ
ejpam-5837	162	39	addition	addition	NOUN
ejpam-5837	162	40	and	and	CCONJ
ejpam-5837	162	41	the	the	DET
ejpam-5837	162	42	partial	partial	ADJ
ejpam-5837	162	43	ordered	order	VERB
ejpam-5837	162	44	≤:=	≤:=	PROPN
ejpam-5837	162	45	{	{	PUNCT
ejpam-5837	162	46	(	(	PUNCT
ejpam-5837	162	47	a	a	DET
ejpam-5837	162	48	,	,	PUNCT
ejpam-5837	162	49	a	a	NOUN
ejpam-5837	162	50	)	)	PUNCT
ejpam-5837	162	51	|	|	ADV
ejpam-5837	162	52	a	a	DET
ejpam-5837	162	53	∈	∈	PROPN
ejpam-5837	162	54	z6	z6	PROPN
ejpam-5837	162	55	}	}	PUNCT
ejpam-5837	162	56	.	.	PUNCT
ejpam-5837	163	1	ϑ	ϑ	X
ejpam-5837	163	2	:	:	PUNCT
ejpam-5837	163	3	z6	z6	PROPN
ejpam-5837	163	4	→	→	PUNCT
ejpam-5837	163	5	[	[	X
ejpam-5837	163	6	0	0	NUM
ejpam-5837	163	7	,	,	PUNCT
ejpam-5837	163	8	1	1	NUM
ejpam-5837	163	9	]	]	PUNCT
ejpam-5837	163	10	is	be	AUX
ejpam-5837	163	11	defined	define	VERB
ejpam-5837	163	12	by	by	ADP
ejpam-5837	163	13	ϑ(0	ϑ(0	PROPN
ejpam-5837	163	14	)	)	PUNCT
ejpam-5837	163	15	=	=	SYM
ejpam-5837	163	16	0	0	NUM
ejpam-5837	163	17	,	,	PUNCT
ejpam-5837	163	18	ϑ(1	ϑ(1	NOUN
ejpam-5837	163	19	)	)	PUNCT
ejpam-5837	163	20	=	=	SYM
ejpam-5837	163	21	0.2	0.2	NUM
ejpam-5837	163	22	,	,	PUNCT
ejpam-5837	163	23	ϑ(2	ϑ(2	PROPN
ejpam-5837	163	24	)	)	PUNCT
ejpam-5837	163	25	=	=	SYM
ejpam-5837	163	26	0	0	NUM
ejpam-5837	163	27	,	,	PUNCT
ejpam-5837	163	28	ϑ(3	ϑ(3	PROPN
ejpam-5837	163	29	)	)	PUNCT
ejpam-5837	163	30	=	=	SYM
ejpam-5837	163	31	0	0	NUM
ejpam-5837	163	32	,	,	PUNCT
ejpam-5837	163	33	ϑ(4	ϑ(4	PROPN
ejpam-5837	163	34	)	)	PUNCT
ejpam-5837	163	35	=	=	NOUN
ejpam-5837	163	36	0.5	0.5	NUM
ejpam-5837	163	37	,	,	PUNCT
ejpam-5837	163	38	ϑ(5	ϑ(5	PROPN
ejpam-5837	163	39	)	)	PUNCT
ejpam-5837	163	40	=	=	NOUN
ejpam-5837	163	41	0.4	0.4	NUM
ejpam-5837	163	42	and	and	CCONJ
ejpam-5837	163	43	ν	ν	NOUN
ejpam-5837	163	44	:	:	PUNCT
ejpam-5837	163	45	z6	z6	PROPN
ejpam-5837	163	46	→	→	PUNCT
ejpam-5837	163	47	[	[	X
ejpam-5837	163	48	0	0	NUM
ejpam-5837	163	49	,	,	PUNCT
ejpam-5837	163	50	1	1	NUM
ejpam-5837	163	51	]	]	PUNCT
ejpam-5837	163	52	is	be	AUX
ejpam-5837	163	53	defined	define	VERB
ejpam-5837	163	54	by	by	ADP
ejpam-5837	163	55	ν(0	ν(0	PROPN
ejpam-5837	163	56	)	)	PUNCT
ejpam-5837	163	57	=	=	SYM
ejpam-5837	163	58	0	0	NUM
ejpam-5837	163	59	,	,	PUNCT
ejpam-5837	163	60	ν(1	ν(1	PROPN
ejpam-5837	163	61	)	)	PUNCT
ejpam-5837	163	62	=	=	PUNCT
ejpam-5837	163	63	0.8	0.8	NUM
ejpam-5837	163	64	,	,	PUNCT
ejpam-5837	163	65	ν(2	ν(2	PROPN
ejpam-5837	163	66	)	)	PUNCT
ejpam-5837	163	67	=	=	SYM
ejpam-5837	163	68	0.4	0.4	NUM
ejpam-5837	163	69	,	,	PUNCT
ejpam-5837	163	70	ν(3	ν(3	PROPN
ejpam-5837	163	71	)	)	PUNCT
ejpam-5837	163	72	=	=	PUNCT
ejpam-5837	163	73	0.3	0.3	NUM
ejpam-5837	163	74	,	,	PUNCT
ejpam-5837	163	75	ν(4	ν(4	PROPN
ejpam-5837	163	76	)	)	PUNCT
ejpam-5837	163	77	=	=	SYM
ejpam-5837	163	78	0	0	NUM
ejpam-5837	163	79	,	,	PUNCT
ejpam-5837	163	80	ν(5	ν(5	PROPN
ejpam-5837	163	81	)	)	PUNCT
ejpam-5837	163	82	=	=	PUNCT
ejpam-5837	163	83	0.3	0.3	NUM
ejpam-5837	163	84	.	.	PUNCT
ejpam-5837	164	1	we	we	PRON
ejpam-5837	164	2	have	have	VERB
ejpam-5837	164	3	ϑ	ϑ	NOUN
ejpam-5837	164	4	and	and	CCONJ
ejpam-5837	164	5	ν	ν	NOUN
ejpam-5837	164	6	are	be	AUX
ejpam-5837	164	7	fuzzy	fuzzy	ADJ
ejpam-5837	164	8	almost	almost	ADV
ejpam-5837	164	9	(	(	PUNCT
ejpam-5837	164	10	1	1	NUM
ejpam-5837	164	11	,	,	PUNCT
ejpam-5837	164	12	1)-quasi	1)-quasi	NUM
ejpam-5837	164	13	-	-	NOUN
ejpam-5837	164	14	ideals	ideal	NOUN
ejpam-5837	164	15	of	of	ADP
ejpam-5837	164	16	z6	z6	PROPN
ejpam-5837	164	17	but	but	CCONJ
ejpam-5837	164	18	(	(	PUNCT
ejpam-5837	164	19	ϑ	ϑ	X
ejpam-5837	164	20	∧	∧	PROPN
ejpam-5837	164	21	ν)(0	ν)(0	NUM
ejpam-5837	164	22	)	)	PUNCT
ejpam-5837	164	23	is	be	AUX
ejpam-5837	164	24	not	not	PART
ejpam-5837	164	25	a	a	DET
ejpam-5837	164	26	fuzzy	fuzzy	ADJ
ejpam-5837	164	27	almost	almost	ADV
ejpam-5837	164	28	(	(	PUNCT
ejpam-5837	164	29	1	1	NUM
ejpam-5837	164	30	,	,	PUNCT
ejpam-5837	164	31	1)-quasi	1)-quasi	NOUN
ejpam-5837	164	32	-	-	NOUN
ejpam-5837	164	33	ideal	ideal	NOUN
ejpam-5837	164	34	of	of	ADP
ejpam-5837	164	35	z6	z6	PROPN
ejpam-5837	164	36	.	.	PUNCT
ejpam-5837	165	1	remark	remark	VERB
ejpam-5837	165	2	the	the	DET
ejpam-5837	165	3	minimum	minimum	NOUN
ejpam-5837	165	4	is	be	AUX
ejpam-5837	165	5	not	not	PART
ejpam-5837	165	6	fuzzy	fuzzy	ADJ
ejpam-5837	165	7	almost	almost	ADV
ejpam-5837	165	8	(	(	PUNCT
ejpam-5837	165	9	1	1	NUM
ejpam-5837	165	10	,	,	PUNCT
ejpam-5837	165	11	1)-quasi	1)-quasi	NOUN
ejpam-5837	165	12	-	-	NOUN
ejpam-5837	165	13	ideal	ideal	NOUN
ejpam-5837	165	14	of	of	ADP
ejpam-5837	165	15	an	an	DET
ejpam-5837	165	16	ordered	order	VERB
ejpam-5837	165	17	semigroup	semigroup	NOUN
ejpam-5837	165	18	by	by	ADP
ejpam-5837	165	19	example	example	NOUN
ejpam-5837	165	20	3	3	NUM
ejpam-5837	165	21	lemma	lemma	PROPN
ejpam-5837	165	22	5	5	NUM
ejpam-5837	165	23	.	.	PUNCT
ejpam-5837	166	1	let	let	VERB
ejpam-5837	166	2	a	a	DET
ejpam-5837	166	3	be	be	AUX
ejpam-5837	166	4	a	a	DET
ejpam-5837	166	5	subset	subset	NOUN
ejpam-5837	166	6	of	of	ADP
ejpam-5837	166	7	t	t	PROPN
ejpam-5837	166	8	and	and	CCONJ
ejpam-5837	166	9	n	n	CCONJ
ejpam-5837	166	10	∈	∈	PROPN
ejpam-5837	166	11	n	n	NOUN
ejpam-5837	166	12	∪	∪	X
ejpam-5837	166	13	{	{	PUNCT
ejpam-5837	166	14	0	0	NUM
ejpam-5837	166	15	}	}	PUNCT
ejpam-5837	166	16	.	.	PUNCT
ejpam-5837	167	1	then	then	ADV
ejpam-5837	167	2	(	(	PUNCT
ejpam-5837	167	3	χa	χa	NOUN
ejpam-5837	167	4	)	)	PUNCT
ejpam-5837	167	5	n	n	NOUN
ejpam-5837	167	6	=	=	NOUN
ejpam-5837	167	7	χan	χan	NOUN
ejpam-5837	167	8	theorem	theorem	VERB
ejpam-5837	167	9	6	6	NUM
ejpam-5837	167	10	.	.	PUNCT
ejpam-5837	168	1	let	let	VERB
ejpam-5837	168	2	b	b	X
ejpam-5837	168	3	be	be	AUX
ejpam-5837	168	4	a	a	DET
ejpam-5837	168	5	nonempty	nonempty	ADJ
ejpam-5837	168	6	subset	subset	NOUN
ejpam-5837	168	7	of	of	ADP
ejpam-5837	168	8	an	an	DET
ejpam-5837	168	9	ordered	order	VERB
ejpam-5837	168	10	semigroup	semigroup	NOUN
ejpam-5837	168	11	t.	t.	PROPN
ejpam-5837	168	12	then	then	ADV
ejpam-5837	168	13	b	b	PROPN
ejpam-5837	168	14	is	be	AUX
ejpam-5837	168	15	an	an	DET
ejpam-5837	168	16	almost	almost	ADV
ejpam-5837	168	17	(	(	PUNCT
ejpam-5837	168	18	m	m	PROPN
ejpam-5837	168	19	,	,	PUNCT
ejpam-5837	168	20	n)-quasi	n)-quasi	NOUN
ejpam-5837	168	21	-	-	NOUN
ejpam-5837	168	22	ideal	ideal	NOUN
ejpam-5837	168	23	of	of	ADP
ejpam-5837	168	24	t	t	PROPN
ejpam-5837	169	1	if	if	SCONJ
ejpam-5837	169	2	and	and	CCONJ
ejpam-5837	169	3	only	only	ADV
ejpam-5837	169	4	if	if	SCONJ
ejpam-5837	169	5	χb	χb	PROPN
ejpam-5837	169	6	is	be	AUX
ejpam-5837	169	7	a	a	DET
ejpam-5837	169	8	fuzzy	fuzzy	ADJ
ejpam-5837	169	9	almost	almost	ADV
ejpam-5837	169	10	(	(	PUNCT
ejpam-5837	169	11	m	m	PROPN
ejpam-5837	169	12	,	,	PUNCT
ejpam-5837	169	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	169	14	-	-	NOUN
ejpam-5837	169	15	ideal	ideal	NOUN
ejpam-5837	169	16	of	of	ADP
ejpam-5837	169	17	t.	t.	NOUN
ejpam-5837	169	18	proof	proof	NOUN
ejpam-5837	169	19	.	.	PUNCT
ejpam-5837	170	1	suppose	suppose	VERB
ejpam-5837	170	2	thatb	thatb	NOUN
ejpam-5837	170	3	is	be	AUX
ejpam-5837	170	4	an	an	DET
ejpam-5837	170	5	almost	almost	ADV
ejpam-5837	170	6	(	(	PUNCT
ejpam-5837	170	7	m	m	PROPN
ejpam-5837	170	8	,	,	PUNCT
ejpam-5837	170	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	170	10	-	-	NOUN
ejpam-5837	170	11	ideal	ideal	NOUN
ejpam-5837	170	12	of	of	ADP
ejpam-5837	170	13	t.	t.	PROPN
ejpam-5837	170	14	then	then	ADV
ejpam-5837	170	15	(	(	PUNCT
ejpam-5837	170	16	bmt]∩(tbn]∩b	bmt]∩(tbn]∩b	ADP
ejpam-5837	170	17	̸=	̸=	PROPN
ejpam-5837	170	18	∅	∅	NOUN
ejpam-5837	170	19	for	for	ADP
ejpam-5837	170	20	all	all	DET
ejpam-5837	170	21	t	t	NOUN
ejpam-5837	170	22	∈	∈	PROPN
ejpam-5837	170	23	t	t	PROPN
ejpam-5837	170	24	and	and	CCONJ
ejpam-5837	170	25	m	m	PROPN
ejpam-5837	170	26	,	,	PUNCT
ejpam-5837	170	27	n	n	PRON
ejpam-5837	170	28	∈	∈	PROPN
ejpam-5837	170	29	{	{	PUNCT
ejpam-5837	170	30	1	1	NUM
ejpam-5837	170	31	,	,	PUNCT
ejpam-5837	170	32	2	2	NUM
ejpam-5837	170	33	,	,	PUNCT
ejpam-5837	170	34	...	...	PUNCT
ejpam-5837	170	35	,	,	PUNCT
ejpam-5837	170	36	n	n	CCONJ
ejpam-5837	170	37	}	}	PUNCT
ejpam-5837	170	38	.	.	PUNCT
ejpam-5837	171	1	thus	thus	ADV
ejpam-5837	171	2	there	there	PRON
ejpam-5837	171	3	exists	exist	VERB
ejpam-5837	171	4	c	c	PROPN
ejpam-5837	171	5	∈	∈	PROPN
ejpam-5837	171	6	t	t	NOUN
ejpam-5837	171	7	such	such	ADJ
ejpam-5837	171	8	that	that	SCONJ
ejpam-5837	171	9	c	c	PROPN
ejpam-5837	171	10	∈	∈	PROPN
ejpam-5837	171	11	(	(	PUNCT
ejpam-5837	171	12	bmt	bmt	NOUN
ejpam-5837	171	13	]	]	PUNCT
ejpam-5837	171	14	∩	∩	NOUN
ejpam-5837	171	15	(	(	PUNCT
ejpam-5837	171	16	tbn	tbn	NOUN
ejpam-5837	171	17	]	]	X
ejpam-5837	171	18	and	and	CCONJ
ejpam-5837	171	19	c	c	PROPN
ejpam-5837	171	20	∈	∈	PROPN
ejpam-5837	171	21	b.	b.	PROPN
ejpam-5837	171	22	let	let	VERB
ejpam-5837	171	23	xt	xt	PROPN
ejpam-5837	171	24	∈	∈	PROPN
ejpam-5837	171	25	t	t	PROPN
ejpam-5837	171	26	and	and	CCONJ
ejpam-5837	171	27	t	t	PROPN
ejpam-5837	171	28	∈	∈	PROPN
ejpam-5837	171	29	(	(	PUNCT
ejpam-5837	171	30	0	0	NUM
ejpam-5837	171	31	,	,	PUNCT
ejpam-5837	171	32	1	1	NUM
ejpam-5837	171	33	]	]	PUNCT
ejpam-5837	171	34	.	.	PUNCT
ejpam-5837	172	1	then	then	ADV
ejpam-5837	172	2	(	(	PUNCT
ejpam-5837	172	3	(	(	PUNCT
ejpam-5837	172	4	χbm	χbm	NOUN
ejpam-5837	172	5	◦	◦	NOUN
ejpam-5837	172	6	xt	xt	NOUN
ejpam-5837	172	7	]	]	X
ejpam-5837	172	8	◦	◦	NOUN
ejpam-5837	172	9	∧(xt	∧(xt	NOUN
ejpam-5837	172	10	◦	◦	NOUN
ejpam-5837	172	11	χbn	χbn	NOUN
ejpam-5837	172	12	]	]	X
ejpam-5837	172	13	)	)	PUNCT
ejpam-5837	172	14	(	(	PUNCT
ejpam-5837	172	15	c	c	X
ejpam-5837	172	16	)	)	PUNCT
ejpam-5837	172	17	̸=	̸=	NOUN
ejpam-5837	172	18	0	0	NUM
ejpam-5837	172	19	and	and	CCONJ
ejpam-5837	172	20	χb(c	χb(c	NOUN
ejpam-5837	172	21	)	)	PUNCT
ejpam-5837	172	22	̸=	̸=	PROPN
ejpam-5837	172	23	0	0	NUM
ejpam-5837	172	24	and	and	CCONJ
ejpam-5837	172	25	m	m	PROPN
ejpam-5837	172	26	,	,	PUNCT
ejpam-5837	172	27	n	n	PRON
ejpam-5837	172	28	∈	∈	PROPN
ejpam-5837	172	29	{	{	PUNCT
ejpam-5837	172	30	1	1	NUM
ejpam-5837	172	31	,	,	PUNCT
ejpam-5837	172	32	2	2	NUM
ejpam-5837	172	33	,	,	PUNCT
ejpam-5837	172	34	...	...	PUNCT
ejpam-5837	172	35	,	,	PUNCT
ejpam-5837	172	36	n	n	CCONJ
ejpam-5837	172	37	}	}	PUNCT
ejpam-5837	172	38	.	.	PUNCT
ejpam-5837	173	1	thus	thus	ADV
ejpam-5837	173	2	,	,	PUNCT
ejpam-5837	173	3	(	(	PUNCT
ejpam-5837	173	4	(	(	PUNCT
ejpam-5837	173	5	χbm	χbm	NOUN
ejpam-5837	173	6	◦	◦	NOUN
ejpam-5837	173	7	xt	xt	ADP
ejpam-5837	173	8	]	]	X
ejpam-5837	173	9	◦	◦	NOUN
ejpam-5837	173	10	∧(xt	∧(xt	NOUN
ejpam-5837	173	11	◦	◦	NOUN
ejpam-5837	173	12	χbn	χbn	ADV
ejpam-5837	173	13	]	]	PUNCT
ejpam-5837	173	14	∧	∧	PROPN
ejpam-5837	173	15	χb)(c	χb)(c	PROPN
ejpam-5837	173	16	)	)	PUNCT
ejpam-5837	174	1	=	=	PRON
ejpam-5837	174	2	(	(	PUNCT
ejpam-5837	174	3	(	(	PUNCT
ejpam-5837	174	4	(	(	PUNCT
ejpam-5837	174	5	χb	χb	NOUN
ejpam-5837	174	6	)	)	PUNCT
ejpam-5837	174	7	m	m	VERB
ejpam-5837	174	8	◦	◦	NOUN
ejpam-5837	174	9	xt	xt	ADP
ejpam-5837	174	10	]	]	X
ejpam-5837	174	11	◦	◦	NOUN
ejpam-5837	174	12	∧(xt	∧(xt	NOUN
ejpam-5837	174	13	◦	◦	NOUN
ejpam-5837	174	14	(	(	PUNCT
ejpam-5837	174	15	χb	χb	NOUN
ejpam-5837	174	16	)	)	PUNCT
ejpam-5837	174	17	n])(c	n])(c	PROPN
ejpam-5837	174	18	)	)	PUNCT
ejpam-5837	175	1	̸=	̸=	NOUN
ejpam-5837	175	2	0	0	NUM
ejpam-5837	175	3	and	and	CCONJ
ejpam-5837	175	4	m	m	PROPN
ejpam-5837	175	5	,	,	PUNCT
ejpam-5837	175	6	n	n	PRON
ejpam-5837	175	7	∈	∈	PROPN
ejpam-5837	175	8	{	{	PUNCT
ejpam-5837	175	9	1	1	NUM
ejpam-5837	175	10	,	,	PUNCT
ejpam-5837	175	11	2	2	NUM
ejpam-5837	175	12	,	,	PUNCT
ejpam-5837	175	13	...	...	PUNCT
ejpam-5837	175	14	,	,	PUNCT
ejpam-5837	175	15	n	n	CCONJ
ejpam-5837	175	16	}	}	PUNCT
ejpam-5837	175	17	.	.	PUNCT
ejpam-5837	176	1	so	so	ADV
ejpam-5837	176	2	,	,	PUNCT
ejpam-5837	176	3	(	(	PUNCT
ejpam-5837	176	4	χbm	χbm	NOUN
ejpam-5837	176	5	◦	◦	NOUN
ejpam-5837	176	6	xt	xt	ADP
ejpam-5837	176	7	]	]	X
ejpam-5837	176	8	◦	◦	NOUN
ejpam-5837	176	9	∧(xt	∧(xt	NOUN
ejpam-5837	176	10	◦	◦	NOUN
ejpam-5837	176	11	χbn	χbn	ADV
ejpam-5837	176	12	]	]	PUNCT
ejpam-5837	176	13	∧	∧	PROPN
ejpam-5837	176	14	χb	χb	PROPN
ejpam-5837	176	15	)	)	PUNCT
ejpam-5837	176	16	̸=	̸=	PROPN
ejpam-5837	176	17	0	0	NUM
ejpam-5837	176	18	.	.	PUNCT
ejpam-5837	177	1	hence	hence	ADV
ejpam-5837	177	2	,	,	PUNCT
ejpam-5837	177	3	χb	χb	PROPN
ejpam-5837	177	4	is	be	AUX
ejpam-5837	177	5	a	a	DET
ejpam-5837	177	6	fuzzy	fuzzy	ADJ
ejpam-5837	177	7	almost	almost	ADV
ejpam-5837	177	8	(	(	PUNCT
ejpam-5837	177	9	m	m	PROPN
ejpam-5837	177	10	,	,	PUNCT
ejpam-5837	177	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	177	12	-	-	NOUN
ejpam-5837	177	13	ideal	ideal	NOUN
ejpam-5837	177	14	of	of	ADP
ejpam-5837	177	15	t.	t.	PROPN
ejpam-5837	177	16	p.	p.	PROPN
ejpam-5837	177	17	khamrot	khamrot	PROPN
ejpam-5837	177	18	et	et	PROPN
ejpam-5837	177	19	al	al	PROPN
ejpam-5837	177	20	.	.	PUNCT
ejpam-5837	177	21	/	/	SYM
ejpam-5837	177	22	eur	eur	PROPN
ejpam-5837	177	23	.	.	PUNCT
ejpam-5837	178	1	j.	j.	PROPN
ejpam-5837	178	2	pure	pure	PROPN
ejpam-5837	178	3	appl	appl	PROPN
ejpam-5837	178	4	.	.	PROPN
ejpam-5837	178	5	math	math	PROPN
ejpam-5837	178	6	,	,	PUNCT
ejpam-5837	178	7	18	18	NUM
ejpam-5837	178	8	(	(	PUNCT
ejpam-5837	178	9	2	2	NUM
ejpam-5837	178	10	)	)	PUNCT
ejpam-5837	178	11	(	(	PUNCT
ejpam-5837	178	12	2025	2025	NUM
ejpam-5837	178	13	)	)	PUNCT
ejpam-5837	178	14	,	,	PUNCT
ejpam-5837	178	15	5837	5837	NUM
ejpam-5837	178	16	8	8	NUM
ejpam-5837	178	17	of	of	ADP
ejpam-5837	178	18	13	13	NUM
ejpam-5837	178	19	conversely	conversely	ADV
ejpam-5837	178	20	,	,	PUNCT
ejpam-5837	178	21	suppose	suppose	VERB
ejpam-5837	178	22	that	that	SCONJ
ejpam-5837	178	23	χb	χb	PROPN
ejpam-5837	178	24	is	be	AUX
ejpam-5837	178	25	a	a	DET
ejpam-5837	178	26	fuzzy	fuzzy	ADJ
ejpam-5837	178	27	almost	almost	ADV
ejpam-5837	178	28	(	(	PUNCT
ejpam-5837	178	29	m	m	PROPN
ejpam-5837	178	30	,	,	PUNCT
ejpam-5837	178	31	n)-quasi	n)-quasi	NOUN
ejpam-5837	178	32	-	-	NOUN
ejpam-5837	178	33	ideal	ideal	NOUN
ejpam-5837	178	34	of	of	ADP
ejpam-5837	178	35	t	t	PROPN
ejpam-5837	178	36	and	and	CCONJ
ejpam-5837	178	37	let	let	VERB
ejpam-5837	178	38	xt	xt	PROPN
ejpam-5837	178	39	∈	∈	PROPN
ejpam-5837	178	40	t	t	PROPN
ejpam-5837	178	41	and	and	CCONJ
ejpam-5837	178	42	t	t	PROPN
ejpam-5837	178	43	∈	∈	PROPN
ejpam-5837	178	44	(	(	PUNCT
ejpam-5837	178	45	0	0	NUM
ejpam-5837	178	46	,	,	PUNCT
ejpam-5837	178	47	1	1	NUM
ejpam-5837	178	48	]	]	PUNCT
ejpam-5837	178	49	where	where	SCONJ
ejpam-5837	178	50	m	m	VERB
ejpam-5837	178	51	,	,	PUNCT
ejpam-5837	178	52	n	n	PRON
ejpam-5837	178	53	∈	∈	PROPN
ejpam-5837	178	54	{	{	PUNCT
ejpam-5837	178	55	1	1	NUM
ejpam-5837	178	56	,	,	PUNCT
ejpam-5837	178	57	2	2	NUM
ejpam-5837	178	58	,	,	PUNCT
ejpam-5837	178	59	...	...	PUNCT
ejpam-5837	178	60	,	,	PUNCT
ejpam-5837	178	61	n	n	CCONJ
ejpam-5837	178	62	}	}	PUNCT
ejpam-5837	178	63	.	.	PUNCT
ejpam-5837	179	1	then	then	ADV
ejpam-5837	179	2	(	(	PUNCT
ejpam-5837	179	3	(	(	PUNCT
ejpam-5837	179	4	χbm	χbm	NOUN
ejpam-5837	179	5	◦	◦	NOUN
ejpam-5837	179	6	xt	xt	ADP
ejpam-5837	179	7	]	]	X
ejpam-5837	179	8	◦	◦	NOUN
ejpam-5837	179	9	∧(xt	∧(xt	NOUN
ejpam-5837	179	10	◦	◦	NOUN
ejpam-5837	179	11	χbn	χbn	ADV
ejpam-5837	179	12	]	]	PUNCT
ejpam-5837	179	13	∧	∧	PROPN
ejpam-5837	179	14	χb	χb	PROPN
ejpam-5837	179	15	)	)	PUNCT
ejpam-5837	179	16	̸=	̸=	PROPN
ejpam-5837	179	17	0	0	NUM
ejpam-5837	179	18	.	.	PUNCT
ejpam-5837	180	1	thus	thus	ADV
ejpam-5837	180	2	,	,	PUNCT
ejpam-5837	180	3	there	there	PRON
ejpam-5837	180	4	exists	exist	VERB
ejpam-5837	180	5	c	c	PROPN
ejpam-5837	180	6	∈	∈	PROPN
ejpam-5837	180	7	b	b	PROPN
ejpam-5837	180	8	such	such	ADJ
ejpam-5837	180	9	that	that	PRON
ejpam-5837	180	10	(	(	PUNCT
ejpam-5837	180	11	(	(	PUNCT
ejpam-5837	180	12	χbm	χbm	NOUN
ejpam-5837	180	13	◦	◦	NOUN
ejpam-5837	180	14	xt	xt	ADP
ejpam-5837	180	15	]	]	X
ejpam-5837	180	16	◦	◦	NOUN
ejpam-5837	180	17	∧(xt	∧(xt	NOUN
ejpam-5837	180	18	◦	◦	NOUN
ejpam-5837	180	19	χbn	χbn	ADV
ejpam-5837	180	20	]	]	PUNCT
ejpam-5837	180	21	∧	∧	PROPN
ejpam-5837	180	22	χb)(c	χb)(c	PROPN
ejpam-5837	180	23	)	)	PUNCT
ejpam-5837	180	24	̸=	̸=	PROPN
ejpam-5837	180	25	0	0	NUM
ejpam-5837	180	26	.	.	PUNCT
ejpam-5837	181	1	it	it	PRON
ejpam-5837	181	2	implies	imply	VERB
ejpam-5837	181	3	that	that	SCONJ
ejpam-5837	181	4	(	(	PUNCT
ejpam-5837	181	5	(	(	PUNCT
ejpam-5837	181	6	χbm	χbm	NOUN
ejpam-5837	181	7	◦	◦	NOUN
ejpam-5837	181	8	xt	xt	ADP
ejpam-5837	181	9	]	]	X
ejpam-5837	181	10	◦	◦	NOUN
ejpam-5837	181	11	∧(xt	∧(xt	NOUN
ejpam-5837	181	12	◦	◦	NOUN
ejpam-5837	181	13	χbn	χbn	ADV
ejpam-5837	181	14	]	]	PUNCT
ejpam-5837	181	15	)	)	PUNCT
ejpam-5837	181	16	(	(	PUNCT
ejpam-5837	181	17	c	c	X
ejpam-5837	181	18	)	)	PUNCT
ejpam-5837	181	19	̸=	̸=	NOUN
ejpam-5837	181	20	0	0	NUM
ejpam-5837	181	21	and	and	CCONJ
ejpam-5837	181	22	χb(c	χb(c	NOUN
ejpam-5837	181	23	)	)	PUNCT
ejpam-5837	181	24	̸=	̸=	PROPN
ejpam-5837	181	25	0	0	NUM
ejpam-5837	181	26	and	and	CCONJ
ejpam-5837	181	27	m	m	PROPN
ejpam-5837	181	28	,	,	PUNCT
ejpam-5837	181	29	n	n	PRON
ejpam-5837	181	30	∈	∈	PROPN
ejpam-5837	181	31	{	{	PUNCT
ejpam-5837	181	32	1	1	NUM
ejpam-5837	181	33	,	,	PUNCT
ejpam-5837	181	34	2	2	NUM
ejpam-5837	181	35	,	,	PUNCT
ejpam-5837	181	36	...	...	PUNCT
ejpam-5837	181	37	,	,	PUNCT
ejpam-5837	181	38	n	n	CCONJ
ejpam-5837	181	39	}	}	PUNCT
ejpam-5837	181	40	.	.	PUNCT
ejpam-5837	182	1	hence	hence	ADV
ejpam-5837	182	2	c	c	NOUN
ejpam-5837	182	3	∈	∈	PROPN
ejpam-5837	182	4	t	t	NOUN
ejpam-5837	182	5	such	such	ADJ
ejpam-5837	182	6	that	that	SCONJ
ejpam-5837	182	7	c	c	PROPN
ejpam-5837	182	8	∈	∈	PROPN
ejpam-5837	182	9	(	(	PUNCT
ejpam-5837	182	10	bmt	bmt	NOUN
ejpam-5837	182	11	]	]	PUNCT
ejpam-5837	182	12	∩	∩	NOUN
ejpam-5837	182	13	(	(	PUNCT
ejpam-5837	182	14	tbn	tbn	NOUN
ejpam-5837	182	15	]	]	X
ejpam-5837	182	16	and	and	CCONJ
ejpam-5837	182	17	c	c	PROPN
ejpam-5837	182	18	∈	∈	PROPN
ejpam-5837	182	19	b.	b.	PROPN
ejpam-5837	183	1	so	so	ADV
ejpam-5837	183	2	(	(	PUNCT
ejpam-5837	183	3	bmt	bmt	PROPN
ejpam-5837	183	4	]	]	PUNCT
ejpam-5837	183	5	∩	∩	NOUN
ejpam-5837	183	6	(	(	PUNCT
ejpam-5837	183	7	tbn	tbn	NOUN
ejpam-5837	183	8	]	]	X
ejpam-5837	183	9	∩	∩	PROPN
ejpam-5837	183	10	b	b	PROPN
ejpam-5837	183	11	̸=	̸=	PROPN
ejpam-5837	183	12	∅	∅	NOUN
ejpam-5837	183	13	for	for	ADP
ejpam-5837	183	14	all	all	DET
ejpam-5837	183	15	t	t	NOUN
ejpam-5837	183	16	∈	∈	PROPN
ejpam-5837	183	17	t	t	PROPN
ejpam-5837	183	18	and	and	CCONJ
ejpam-5837	183	19	m	m	PROPN
ejpam-5837	183	20	,	,	PUNCT
ejpam-5837	183	21	n	n	PRON
ejpam-5837	183	22	∈	∈	PROPN
ejpam-5837	183	23	{	{	PUNCT
ejpam-5837	183	24	1	1	NUM
ejpam-5837	183	25	,	,	PUNCT
ejpam-5837	183	26	2	2	NUM
ejpam-5837	183	27	,	,	PUNCT
ejpam-5837	183	28	...	...	PUNCT
ejpam-5837	183	29	,	,	PUNCT
ejpam-5837	183	30	n	n	CCONJ
ejpam-5837	183	31	}	}	PUNCT
ejpam-5837	183	32	.	.	PUNCT
ejpam-5837	184	1	we	we	PRON
ejpam-5837	184	2	conclude	conclude	VERB
ejpam-5837	184	3	that	that	SCONJ
ejpam-5837	184	4	b	b	NOUN
ejpam-5837	184	5	is	be	AUX
ejpam-5837	184	6	an	an	DET
ejpam-5837	184	7	almost	almost	ADV
ejpam-5837	184	8	(	(	PUNCT
ejpam-5837	184	9	m	m	PROPN
ejpam-5837	184	10	,	,	PUNCT
ejpam-5837	184	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	184	12	-	-	NOUN
ejpam-5837	184	13	ideal	ideal	NOUN
ejpam-5837	184	14	of	of	ADP
ejpam-5837	184	15	t.	t.	PROPN
ejpam-5837	184	16	theorem	theorem	PROPN
ejpam-5837	184	17	7	7	X
ejpam-5837	184	18	.	.	PUNCT
ejpam-5837	185	1	let	let	VERB
ejpam-5837	185	2	ϑ	ϑ	X
ejpam-5837	185	3	be	be	AUX
ejpam-5837	185	4	a	a	DET
ejpam-5837	185	5	fuzzy	fuzzy	ADJ
ejpam-5837	185	6	subset	subset	NOUN
ejpam-5837	185	7	of	of	ADP
ejpam-5837	185	8	an	an	DET
ejpam-5837	185	9	ordered	order	VERB
ejpam-5837	185	10	semigroup	semigroup	NOUN
ejpam-5837	185	11	t.	t.	PROPN
ejpam-5837	185	12	then	then	ADV
ejpam-5837	185	13	ϑ	ϑ	PROPN
ejpam-5837	185	14	is	be	AUX
ejpam-5837	185	15	a	a	DET
ejpam-5837	185	16	fuzzy	fuzzy	ADJ
ejpam-5837	185	17	almost	almost	ADV
ejpam-5837	185	18	(	(	PUNCT
ejpam-5837	185	19	m	m	PROPN
ejpam-5837	185	20	,	,	PUNCT
ejpam-5837	185	21	n)-quasi	n)-quasi	NOUN
ejpam-5837	185	22	-	-	NOUN
ejpam-5837	185	23	ideal	ideal	NOUN
ejpam-5837	185	24	of	of	ADP
ejpam-5837	185	25	t	t	PROPN
ejpam-5837	185	26	if	if	SCONJ
ejpam-5837	185	27	and	and	CCONJ
ejpam-5837	185	28	only	only	ADV
ejpam-5837	185	29	if	if	SCONJ
ejpam-5837	185	30	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	185	31	)	)	PUNCT
ejpam-5837	185	32	is	be	AUX
ejpam-5837	185	33	an	an	DET
ejpam-5837	185	34	almost	almost	ADV
ejpam-5837	185	35	(	(	PUNCT
ejpam-5837	185	36	m	m	PROPN
ejpam-5837	185	37	,	,	PUNCT
ejpam-5837	185	38	n)-quasi	n)-quasi	NOUN
ejpam-5837	185	39	-	-	NOUN
ejpam-5837	185	40	ideal	ideal	NOUN
ejpam-5837	185	41	of	of	ADP
ejpam-5837	185	42	t.	t.	NOUN
ejpam-5837	185	43	proof	proof	NOUN
ejpam-5837	185	44	.	.	PUNCT
ejpam-5837	186	1	assume	assume	VERB
ejpam-5837	186	2	that	that	SCONJ
ejpam-5837	186	3	ϑ	ϑ	NOUN
ejpam-5837	186	4	is	be	AUX
ejpam-5837	186	5	a	a	DET
ejpam-5837	186	6	fuzzy	fuzzy	ADJ
ejpam-5837	186	7	almost	almost	ADV
ejpam-5837	186	8	(	(	PUNCT
ejpam-5837	186	9	m	m	PROPN
ejpam-5837	186	10	,	,	PUNCT
ejpam-5837	186	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	186	12	-	-	NOUN
ejpam-5837	186	13	ideal	ideal	NOUN
ejpam-5837	186	14	of	of	ADP
ejpam-5837	186	15	t	t	PROPN
ejpam-5837	186	16	and	and	CCONJ
ejpam-5837	186	17	let	let	VERB
ejpam-5837	186	18	xt	xt	PROPN
ejpam-5837	186	19	∈	∈	PROPN
ejpam-5837	186	20	t	t	PROPN
ejpam-5837	186	21	and	and	CCONJ
ejpam-5837	186	22	t	t	PROPN
ejpam-5837	186	23	∈	∈	PROPN
ejpam-5837	186	24	(	(	PUNCT
ejpam-5837	186	25	0	0	NUM
ejpam-5837	186	26	,	,	PUNCT
ejpam-5837	186	27	1	1	NUM
ejpam-5837	186	28	]	]	PUNCT
ejpam-5837	186	29	.	.	PUNCT
ejpam-5837	187	1	then	then	ADV
ejpam-5837	187	2	(	(	PUNCT
ejpam-5837	187	3	ϑm	ϑm	ADP
ejpam-5837	187	4	◦	◦	NOUN
ejpam-5837	187	5	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	187	6	◦	◦	NOUN
ejpam-5837	187	7	ϑn]∧ϑ	ϑn]∧ϑ	NOUN
ejpam-5837	187	8	̸=	̸=	PROPN
ejpam-5837	187	9	0	0	NUM
ejpam-5837	187	10	for	for	ADP
ejpam-5837	187	11	allm	allm	NOUN
ejpam-5837	187	12	,	,	PUNCT
ejpam-5837	187	13	n	n	PRON
ejpam-5837	187	14	∈	∈	PROPN
ejpam-5837	187	15	{	{	PUNCT
ejpam-5837	187	16	1	1	NUM
ejpam-5837	187	17	,	,	PUNCT
ejpam-5837	187	18	2	2	NUM
ejpam-5837	187	19	,	,	PUNCT
ejpam-5837	187	20	...	...	PUNCT
ejpam-5837	187	21	,	,	PUNCT
ejpam-5837	187	22	n	n	CCONJ
ejpam-5837	187	23	}	}	PUNCT
ejpam-5837	187	24	.	.	PUNCT
ejpam-5837	188	1	thus	thus	ADV
ejpam-5837	188	2	,	,	PUNCT
ejpam-5837	188	3	there	there	PRON
ejpam-5837	188	4	exists	exist	VERB
ejpam-5837	188	5	z	z	PROPN
ejpam-5837	188	6	∈	∈	PROPN
ejpam-5837	188	7	t	t	NOUN
ejpam-5837	188	8	such	such	ADJ
ejpam-5837	188	9	that	that	PRON
ejpam-5837	188	10	(	(	PUNCT
ejpam-5837	188	11	(	(	PUNCT
ejpam-5837	188	12	ϑm	ϑm	ADP
ejpam-5837	188	13	◦	◦	NOUN
ejpam-5837	188	14	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	188	15	◦	◦	NOUN
ejpam-5837	188	16	ϑn]∧ϑ)(z	ϑn]∧ϑ)(z	NOUN
ejpam-5837	188	17	)	)	PUNCT
ejpam-5837	188	18	̸=	̸=	PROPN
ejpam-5837	188	19	0	0	NUM
ejpam-5837	188	20	.	.	PUNCT
ejpam-5837	189	1	so	so	ADV
ejpam-5837	189	2	ϑ(z	ϑ(z	NOUN
ejpam-5837	189	3	)	)	PUNCT
ejpam-5837	189	4	̸=	̸=	PROPN
ejpam-5837	189	5	0	0	NUM
ejpam-5837	189	6	and	and	CCONJ
ejpam-5837	189	7	z	z	NOUN
ejpam-5837	189	8	=	=	PUNCT
ejpam-5837	189	9	a1a2	a1a2	PROPN
ejpam-5837	189	10	·	·	PUNCT
ejpam-5837	189	11	·	·	PUNCT
ejpam-5837	189	12	·	·	PUNCT
ejpam-5837	189	13	amx	amx	NOUN
ejpam-5837	189	14	=	=	SYM
ejpam-5837	189	15	xb1b2	xb1b2	PROPN
ejpam-5837	189	16	·	·	PUNCT
ejpam-5837	189	17	·	·	PUNCT
ejpam-5837	189	18	·	·	PUNCT
ejpam-5837	190	1	bn	bn	CCONJ
ejpam-5837	190	2	for	for	ADP
ejpam-5837	190	3	some	some	PRON
ejpam-5837	190	4	a1a2	a1a2	X
ejpam-5837	190	5	·	·	PUNCT
ejpam-5837	190	6	·	·	PUNCT
ejpam-5837	190	7	·	·	PUNCT
ejpam-5837	190	8	am	be	AUX
ejpam-5837	190	9	,	,	PUNCT
ejpam-5837	190	10	b1b2	b1b2	X
ejpam-5837	190	11	·	·	PUNCT
ejpam-5837	190	12	·	·	PUNCT
ejpam-5837	190	13	·	·	PUNCT
ejpam-5837	190	14	bn	bn	X
ejpam-5837	190	15	∈	∈	PROPN
ejpam-5837	190	16	t	t	NOUN
ejpam-5837	190	17	such	such	ADJ
ejpam-5837	190	18	that	that	DET
ejpam-5837	190	19	ϑ(a1	ϑ(a1	NOUN
ejpam-5837	190	20	)	)	PUNCT
ejpam-5837	190	21	̸=	̸=	PROPN
ejpam-5837	190	22	0	0	NUM
ejpam-5837	190	23	,	,	PUNCT
ejpam-5837	190	24	ϑ(a2	ϑ(a2	NOUN
ejpam-5837	190	25	)	)	PUNCT
ejpam-5837	190	26	̸=	̸=	PROPN
ejpam-5837	190	27	0	0	NUM
ejpam-5837	190	28	,	,	PUNCT
ejpam-5837	190	29	·	·	PUNCT
ejpam-5837	190	30	·	·	PUNCT
ejpam-5837	190	31	·	·	PUNCT
ejpam-5837	190	32	,	,	PUNCT
ejpam-5837	190	33	ϑ(am	ϑ(am	NUM
ejpam-5837	190	34	)	)	PUNCT
ejpam-5837	190	35	̸=	̸=	PROPN
ejpam-5837	190	36	0	0	NUM
ejpam-5837	190	37	ϑ(b1	ϑ(b1	NOUN
ejpam-5837	190	38	)	)	PUNCT
ejpam-5837	190	39	̸=	̸=	PROPN
ejpam-5837	190	40	0	0	NUM
ejpam-5837	190	41	,	,	PUNCT
ejpam-5837	190	42	ϑ(b2	ϑ(b2	NOUN
ejpam-5837	190	43	)	)	PUNCT
ejpam-5837	190	44	̸=	̸=	PROPN
ejpam-5837	190	45	0	0	NUM
ejpam-5837	190	46	,	,	PUNCT
ejpam-5837	190	47	·	·	PUNCT
ejpam-5837	190	48	·	·	PUNCT
ejpam-5837	190	49	·	·	PUNCT
ejpam-5837	190	50	ϑ(bn	ϑ(bn	X
ejpam-5837	190	51	)	)	PUNCT
ejpam-5837	190	52	̸=	̸=	PROPN
ejpam-5837	190	53	0	0	NUM
ejpam-5837	190	54	.	.	PUNCT
ejpam-5837	191	1	thus	thus	ADV
ejpam-5837	191	2	,	,	PUNCT
ejpam-5837	191	3	a1a2	a1a2	X
ejpam-5837	191	4	·	·	PUNCT
ejpam-5837	191	5	am	be	AUX
ejpam-5837	191	6	,	,	PUNCT
ejpam-5837	191	7	b1b2	b1b2	X
ejpam-5837	191	8	·	·	PUNCT
ejpam-5837	191	9	·	·	PUNCT
ejpam-5837	191	10	·	·	PUNCT
ejpam-5837	192	1	bn	bn	NUM
ejpam-5837	192	2	∈	∈	PROPN
ejpam-5837	192	3	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	192	4	)	)	PUNCT
ejpam-5837	192	5	.	.	PUNCT
ejpam-5837	193	1	it	it	PRON
ejpam-5837	193	2	implies	imply	VERB
ejpam-5837	193	3	that	that	SCONJ
ejpam-5837	193	4	(	(	PUNCT
ejpam-5837	193	5	(	(	PUNCT
ejpam-5837	193	6	χsupp(ϑ)m	χsupp(ϑ)m	PUNCT
ejpam-5837	193	7	◦	◦	NOUN
ejpam-5837	193	8	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	193	9	◦	◦	NOUN
ejpam-5837	193	10	χsupp(ϑ)n	χsupp(ϑ)n	NOUN
ejpam-5837	193	11	]	]	X
ejpam-5837	193	12	∧χsupp(ϑ))(z	∧χsupp(ϑ))(z	X
ejpam-5837	193	13	)	)	PUNCT
ejpam-5837	193	14	̸=	̸=	PROPN
ejpam-5837	193	15	0	0	NUM
ejpam-5837	193	16	.	.	PUNCT
ejpam-5837	194	1	hence	hence	ADV
ejpam-5837	194	2	,	,	PUNCT
ejpam-5837	194	3	(	(	PUNCT
ejpam-5837	194	4	χsupp(ϑ)m	χsupp(ϑ)m	NUM
ejpam-5837	194	5	◦	◦	NOUN
ejpam-5837	194	6	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	194	7	◦	◦	NOUN
ejpam-5837	194	8	χsupp(ϑ)n	χsupp(ϑ)n	NOUN
ejpam-5837	194	9	]	]	SYM
ejpam-5837	194	10	∧χsupp(ϑ	∧χsupp(ϑ	X
ejpam-5837	194	11	)	)	PUNCT
ejpam-5837	194	12	̸=	̸=	PROPN
ejpam-5837	194	13	0	0	NUM
ejpam-5837	194	14	.	.	PUNCT
ejpam-5837	195	1	for	for	ADP
ejpam-5837	195	2	all	all	DET
ejpam-5837	195	3	m	m	PROPN
ejpam-5837	195	4	,	,	PUNCT
ejpam-5837	195	5	n	n	PRON
ejpam-5837	195	6	∈	∈	PROPN
ejpam-5837	195	7	{	{	PUNCT
ejpam-5837	195	8	1	1	NUM
ejpam-5837	195	9	,	,	PUNCT
ejpam-5837	195	10	2	2	NUM
ejpam-5837	195	11	,	,	PUNCT
ejpam-5837	195	12	...	...	PUNCT
ejpam-5837	195	13	,	,	PUNCT
ejpam-5837	195	14	n	n	CCONJ
ejpam-5837	195	15	}	}	PUNCT
ejpam-5837	195	16	.	.	PUNCT
ejpam-5837	196	1	therefore	therefore	ADV
ejpam-5837	196	2	,	,	PUNCT
ejpam-5837	196	3	χsupp(ϑ	χsupp(ϑ	ADV
ejpam-5837	196	4	)	)	PUNCT
ejpam-5837	196	5	is	be	AUX
ejpam-5837	196	6	a	a	DET
ejpam-5837	196	7	fuzzy	fuzzy	ADJ
ejpam-5837	196	8	almost	almost	ADV
ejpam-5837	196	9	(	(	PUNCT
ejpam-5837	196	10	m	m	PROPN
ejpam-5837	196	11	,	,	PUNCT
ejpam-5837	196	12	n)-quasi	n)-quasi	NOUN
ejpam-5837	196	13	-	-	NOUN
ejpam-5837	196	14	ideal	ideal	NOUN
ejpam-5837	196	15	of	of	ADP
ejpam-5837	196	16	t.	t.	PROPN
ejpam-5837	196	17	by	by	ADP
ejpam-5837	196	18	theorem	theorem	ADJ
ejpam-5837	196	19	6	6	NUM
ejpam-5837	196	20	,	,	PUNCT
ejpam-5837	196	21	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	196	22	)	)	PUNCT
ejpam-5837	196	23	is	be	AUX
ejpam-5837	196	24	an	an	DET
ejpam-5837	196	25	almost	almost	ADV
ejpam-5837	196	26	(	(	PUNCT
ejpam-5837	196	27	m	m	PROPN
ejpam-5837	196	28	,	,	PUNCT
ejpam-5837	196	29	n)-quasi	n)-quasi	NOUN
ejpam-5837	196	30	-	-	NOUN
ejpam-5837	196	31	ideal	ideal	NOUN
ejpam-5837	196	32	of	of	ADP
ejpam-5837	196	33	t.	t.	NOUN
ejpam-5837	196	34	conversely	conversely	ADV
ejpam-5837	196	35	,	,	PUNCT
ejpam-5837	196	36	suppose	suppose	VERB
ejpam-5837	196	37	that	that	SCONJ
ejpam-5837	196	38	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	196	39	)	)	PUNCT
ejpam-5837	196	40	is	be	AUX
ejpam-5837	196	41	an	an	DET
ejpam-5837	196	42	almost	almost	ADV
ejpam-5837	196	43	almost	almost	ADV
ejpam-5837	196	44	(	(	PUNCT
ejpam-5837	196	45	m	m	PROPN
ejpam-5837	196	46	,	,	PUNCT
ejpam-5837	196	47	n)-quasi	n)-quasi	NOUN
ejpam-5837	196	48	-	-	NOUN
ejpam-5837	196	49	ideal	ideal	NOUN
ejpam-5837	196	50	of	of	ADP
ejpam-5837	196	51	t.	t.	PROPN
ejpam-5837	196	52	by	by	ADP
ejpam-5837	196	53	theorem	theorem	ADJ
ejpam-5837	196	54	6	6	NUM
ejpam-5837	196	55	,	,	PUNCT
ejpam-5837	196	56	χsupp(ϑ	χsupp(ϑ	NOUN
ejpam-5837	196	57	)	)	PUNCT
ejpam-5837	196	58	is	be	AUX
ejpam-5837	196	59	a	a	DET
ejpam-5837	196	60	fuzzy	fuzzy	ADJ
ejpam-5837	196	61	almost	almost	ADV
ejpam-5837	196	62	(	(	PUNCT
ejpam-5837	196	63	m	m	PROPN
ejpam-5837	196	64	,	,	PUNCT
ejpam-5837	196	65	n)-quasi	n)-quasi	NOUN
ejpam-5837	196	66	-	-	NOUN
ejpam-5837	196	67	ideal	ideal	NOUN
ejpam-5837	196	68	of	of	ADP
ejpam-5837	196	69	t.	t.	PROPN
ejpam-5837	196	70	then	then	ADV
ejpam-5837	196	71	for	for	ADP
ejpam-5837	196	72	any	any	DET
ejpam-5837	196	73	fuzzy	fuzzy	ADJ
ejpam-5837	196	74	point	point	NOUN
ejpam-5837	196	75	xt	xt	ADP
ejpam-5837	196	76	∈	∈	PROPN
ejpam-5837	196	77	t	t	PROPN
ejpam-5837	196	78	and	and	CCONJ
ejpam-5837	196	79	m	m	PROPN
ejpam-5837	196	80	,	,	PUNCT
ejpam-5837	196	81	n	n	PRON
ejpam-5837	196	82	∈	∈	PROPN
ejpam-5837	196	83	{	{	PUNCT
ejpam-5837	196	84	1	1	NUM
ejpam-5837	196	85	,	,	PUNCT
ejpam-5837	196	86	2	2	NUM
ejpam-5837	196	87	,	,	PUNCT
ejpam-5837	196	88	...	...	PUNCT
ejpam-5837	196	89	,	,	PUNCT
ejpam-5837	196	90	n	n	CCONJ
ejpam-5837	196	91	}	}	PUNCT
ejpam-5837	196	92	,	,	PUNCT
ejpam-5837	196	93	we	we	PRON
ejpam-5837	196	94	have	have	VERB
ejpam-5837	196	95	(	(	PUNCT
ejpam-5837	196	96	χsupp(ϑ)m	χsupp(ϑ)m	NUM
ejpam-5837	196	97	◦	◦	NOUN
ejpam-5837	196	98	xt	xt	ADP
ejpam-5837	196	99	]	]	X
ejpam-5837	196	100	∧	∧	PROPN
ejpam-5837	196	101	(	(	PUNCT
ejpam-5837	196	102	xt	xt	ADP
ejpam-5837	196	103	◦	◦	VERB
ejpam-5837	196	104	χsupp(ϑ)n	χsupp(ϑ)n	X
ejpam-5837	196	105	]	]	PUNCT
ejpam-5837	197	1	∧	∧	NOUN
ejpam-5837	197	2	χsupp(ϑ	χsupp(ϑ	NOUN
ejpam-5837	197	3	)	)	PUNCT
ejpam-5837	197	4	̸=	̸=	PROPN
ejpam-5837	197	5	0	0	NUM
ejpam-5837	197	6	.	.	PUNCT
ejpam-5837	198	1	thus	thus	ADV
ejpam-5837	198	2	,	,	PUNCT
ejpam-5837	198	3	there	there	PRON
ejpam-5837	198	4	exists	exist	VERB
ejpam-5837	198	5	z	z	PROPN
ejpam-5837	198	6	∈	∈	PROPN
ejpam-5837	198	7	t	t	NOUN
ejpam-5837	198	8	such	such	ADJ
ejpam-5837	198	9	that	that	SCONJ
ejpam-5837	198	10	(	(	PUNCT
ejpam-5837	198	11	(	(	PUNCT
ejpam-5837	198	12	χsupp(ϑ)m	χsupp(ϑ)m	NUM
ejpam-5837	198	13	◦	◦	NOUN
ejpam-5837	198	14	xt	xt	ADP
ejpam-5837	198	15	]	]	X
ejpam-5837	198	16	∧	∧	PROPN
ejpam-5837	198	17	(	(	PUNCT
ejpam-5837	198	18	xt	xt	ADP
ejpam-5837	198	19	◦	◦	VERB
ejpam-5837	198	20	χsupp(ϑ)n	χsupp(ϑ)n	X
ejpam-5837	198	21	]	]	PUNCT
ejpam-5837	199	1	∧	∧	PROPN
ejpam-5837	199	2	χsupp(ϑ))(z	χsupp(ϑ))(z	PROPN
ejpam-5837	199	3	)	)	PUNCT
ejpam-5837	199	4	̸=	̸=	PROPN
ejpam-5837	199	5	0	0	NUM
ejpam-5837	199	6	.	.	PUNCT
ejpam-5837	200	1	so	so	ADV
ejpam-5837	200	2	ϑ(z	ϑ(z	NOUN
ejpam-5837	200	3	)	)	PUNCT
ejpam-5837	200	4	̸=	̸=	PROPN
ejpam-5837	200	5	0	0	NUM
ejpam-5837	200	6	and	and	CCONJ
ejpam-5837	200	7	z	z	NOUN
ejpam-5837	200	8	=	=	PUNCT
ejpam-5837	200	9	a1a2	a1a2	PROPN
ejpam-5837	200	10	·	·	PUNCT
ejpam-5837	200	11	·	·	PUNCT
ejpam-5837	200	12	·	·	PUNCT
ejpam-5837	200	13	amx	amx	NOUN
ejpam-5837	200	14	=	=	SYM
ejpam-5837	200	15	xb1b2	xb1b2	PROPN
ejpam-5837	200	16	·	·	PUNCT
ejpam-5837	200	17	·	·	PUNCT
ejpam-5837	200	18	·	·	PUNCT
ejpam-5837	201	1	bn	bn	CCONJ
ejpam-5837	201	2	for	for	ADP
ejpam-5837	201	3	some	some	PRON
ejpam-5837	201	4	a1a2	a1a2	X
ejpam-5837	201	5	·	·	PUNCT
ejpam-5837	201	6	·	·	PUNCT
ejpam-5837	201	7	·	·	PUNCT
ejpam-5837	201	8	am	be	AUX
ejpam-5837	201	9	,	,	PUNCT
ejpam-5837	201	10	b1b2	b1b2	X
ejpam-5837	201	11	·	·	PUNCT
ejpam-5837	201	12	·	·	PUNCT
ejpam-5837	201	13	·	·	PUNCT
ejpam-5837	201	14	bn	bn	X
ejpam-5837	201	15	∈	∈	PROPN
ejpam-5837	201	16	t	t	NOUN
ejpam-5837	201	17	such	such	ADJ
ejpam-5837	201	18	that	that	DET
ejpam-5837	201	19	ϑ(a1	ϑ(a1	NOUN
ejpam-5837	201	20	)	)	PUNCT
ejpam-5837	201	21	̸=	̸=	PROPN
ejpam-5837	201	22	0	0	NUM
ejpam-5837	201	23	,	,	PUNCT
ejpam-5837	201	24	ϑ(a2	ϑ(a2	NOUN
ejpam-5837	201	25	)	)	PUNCT
ejpam-5837	201	26	̸=	̸=	PROPN
ejpam-5837	201	27	0	0	NUM
ejpam-5837	201	28	,	,	PUNCT
ejpam-5837	201	29	·	·	PUNCT
ejpam-5837	201	30	·	·	PUNCT
ejpam-5837	201	31	·	·	PUNCT
ejpam-5837	201	32	,	,	PUNCT
ejpam-5837	201	33	ϑ(am	ϑ(am	NUM
ejpam-5837	201	34	)	)	PUNCT
ejpam-5837	201	35	̸=	̸=	PROPN
ejpam-5837	201	36	0	0	NUM
ejpam-5837	201	37	ϑ(b1	ϑ(b1	NOUN
ejpam-5837	201	38	)	)	PUNCT
ejpam-5837	201	39	̸=	̸=	PROPN
ejpam-5837	201	40	0	0	NUM
ejpam-5837	201	41	,	,	PUNCT
ejpam-5837	201	42	ϑ(b2	ϑ(b2	NOUN
ejpam-5837	201	43	)	)	PUNCT
ejpam-5837	201	44	̸=	̸=	PROPN
ejpam-5837	201	45	0	0	NUM
ejpam-5837	201	46	,	,	PUNCT
ejpam-5837	201	47	·	·	PUNCT
ejpam-5837	201	48	·	·	PUNCT
ejpam-5837	201	49	·	·	PUNCT
ejpam-5837	201	50	ϑ(bn	ϑ(bn	X
ejpam-5837	201	51	)	)	PUNCT
ejpam-5837	201	52	̸=	̸=	PROPN
ejpam-5837	201	53	0	0	NUM
ejpam-5837	201	54	.	.	PUNCT
ejpam-5837	202	1	thus	thus	ADV
ejpam-5837	202	2	,	,	PUNCT
ejpam-5837	202	3	a1a2	a1a2	X
ejpam-5837	202	4	·	·	PUNCT
ejpam-5837	202	5	am	be	AUX
ejpam-5837	202	6	,	,	PUNCT
ejpam-5837	202	7	b1b2	b1b2	X
ejpam-5837	202	8	·	·	PUNCT
ejpam-5837	202	9	·	·	PUNCT
ejpam-5837	202	10	·	·	PUNCT
ejpam-5837	203	1	bn	bn	NUM
ejpam-5837	203	2	∈	∈	PROPN
ejpam-5837	203	3	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	203	4	)	)	PUNCT
ejpam-5837	203	5	.	.	PUNCT
ejpam-5837	204	1	so	so	ADV
ejpam-5837	204	2	,	,	PUNCT
ejpam-5837	204	3	there	there	PRON
ejpam-5837	204	4	exists	exist	VERB
ejpam-5837	204	5	z	z	PROPN
ejpam-5837	204	6	∈	∈	PROPN
ejpam-5837	204	7	t	t	NOUN
ejpam-5837	204	8	such	such	ADJ
ejpam-5837	204	9	that	that	PRON
ejpam-5837	204	10	(	(	PUNCT
ejpam-5837	204	11	(	(	PUNCT
ejpam-5837	204	12	ϑm	ϑm	ADP
ejpam-5837	204	13	◦	◦	NOUN
ejpam-5837	204	14	xt]∧(xt	xt]∧(xt	NOUN
ejpam-5837	204	15	◦	◦	NOUN
ejpam-5837	204	16	ϑn]∧ϑ)(z	ϑn]∧ϑ)(z	NOUN
ejpam-5837	204	17	)	)	PUNCT
ejpam-5837	204	18	̸=	̸=	PROPN
ejpam-5837	204	19	0	0	NUM
ejpam-5837	204	20	.	.	PUNCT
ejpam-5837	205	1	hence	hence	ADV
ejpam-5837	205	2	,	,	PUNCT
ejpam-5837	205	3	(	(	PUNCT
ejpam-5837	205	4	ϑm	ϑm	ADP
ejpam-5837	205	5	◦	◦	NOUN
ejpam-5837	205	6	xt	xt	ADP
ejpam-5837	205	7	]	]	X
ejpam-5837	205	8	∧	∧	PROPN
ejpam-5837	205	9	(	(	PUNCT
ejpam-5837	205	10	xt	xt	ADP
ejpam-5837	205	11	◦	◦	NOUN
ejpam-5837	205	12	ϑn	ϑn	NOUN
ejpam-5837	205	13	]	]	X
ejpam-5837	205	14	∧	∧	PROPN
ejpam-5837	205	15	ϑ	ϑ	X
ejpam-5837	205	16	̸=	̸=	PROPN
ejpam-5837	205	17	0	0	NUM
ejpam-5837	205	18	for	for	ADP
ejpam-5837	205	19	all	all	DET
ejpam-5837	205	20	m	m	PROPN
ejpam-5837	205	21	,	,	PUNCT
ejpam-5837	205	22	n	n	PRON
ejpam-5837	205	23	∈	∈	PROPN
ejpam-5837	205	24	{	{	PUNCT
ejpam-5837	205	25	1	1	NUM
ejpam-5837	205	26	,	,	PUNCT
ejpam-5837	205	27	2	2	NUM
ejpam-5837	205	28	,	,	PUNCT
ejpam-5837	205	29	...	...	PUNCT
ejpam-5837	205	30	,	,	PUNCT
ejpam-5837	205	31	n	n	CCONJ
ejpam-5837	205	32	}	}	PUNCT
ejpam-5837	205	33	.	.	PUNCT
ejpam-5837	206	1	therefore	therefore	ADV
ejpam-5837	206	2	,	,	PUNCT
ejpam-5837	206	3	ϑ	ϑ	X
ejpam-5837	206	4	is	be	AUX
ejpam-5837	206	5	a	a	DET
ejpam-5837	206	6	fuzzy	fuzzy	ADJ
ejpam-5837	206	7	almost	almost	ADV
ejpam-5837	206	8	(	(	PUNCT
ejpam-5837	206	9	m	m	PROPN
ejpam-5837	206	10	,	,	PUNCT
ejpam-5837	206	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	206	12	-	-	NOUN
ejpam-5837	206	13	ideal	ideal	NOUN
ejpam-5837	206	14	of	of	ADP
ejpam-5837	206	15	t.	t.	PROPN
ejpam-5837	206	16	next	next	ADV
ejpam-5837	206	17	,	,	PUNCT
ejpam-5837	206	18	we	we	PRON
ejpam-5837	206	19	investigate	investigate	VERB
ejpam-5837	206	20	connection	connection	NOUN
ejpam-5837	206	21	between	between	ADP
ejpam-5837	206	22	minimal	minimal	ADJ
ejpam-5837	206	23	and	and	CCONJ
ejpam-5837	206	24	maximal	maximal	ADJ
ejpam-5837	206	25	almost	almost	ADV
ejpam-5837	206	26	(	(	PUNCT
ejpam-5837	206	27	m	m	NOUN
ejpam-5837	206	28	,	,	PUNCT
ejpam-5837	206	29	n)-quasiideals	n)-quasiideal	NOUN
ejpam-5837	206	30	and	and	CCONJ
ejpam-5837	206	31	minimal	minimal	ADJ
ejpam-5837	206	32	and	and	CCONJ
ejpam-5837	206	33	maximal	maximal	ADJ
ejpam-5837	206	34	fuzzy	fuzzy	ADJ
ejpam-5837	206	35	almost	almost	ADV
ejpam-5837	206	36	(	(	PUNCT
ejpam-5837	206	37	m	m	PROPN
ejpam-5837	206	38	,	,	PUNCT
ejpam-5837	206	39	n)-quasi	n)-quasi	NOUN
ejpam-5837	206	40	-	-	NOUN
ejpam-5837	206	41	ideals	ideal	NOUN
ejpam-5837	206	42	of	of	ADP
ejpam-5837	206	43	ordered	order	VERB
ejpam-5837	206	44	semigroups	semigroup	NOUN
ejpam-5837	206	45	.	.	PUNCT
ejpam-5837	207	1	definition	definition	NOUN
ejpam-5837	207	2	13	13	NUM
ejpam-5837	207	3	.	.	PUNCT
ejpam-5837	208	1	an	an	DET
ejpam-5837	208	2	almost	almost	ADV
ejpam-5837	208	3	(	(	PUNCT
ejpam-5837	208	4	m	m	PROPN
ejpam-5837	208	5	,	,	PUNCT
ejpam-5837	208	6	n)-quasi	n)-quasi	NOUN
ejpam-5837	208	7	-	-	PUNCT
ejpam-5837	208	8	ideal	ideal	ADJ
ejpam-5837	208	9	b	b	PROPN
ejpam-5837	208	10	of	of	ADP
ejpam-5837	208	11	an	an	DET
ejpam-5837	208	12	ordered	order	VERB
ejpam-5837	208	13	semigroup	semigroup	PROPN
ejpam-5837	208	14	t	t	PROPN
ejpam-5837	208	15	is	be	AUX
ejpam-5837	208	16	called	call	VERB
ejpam-5837	208	17	(	(	PUNCT
ejpam-5837	208	18	1	1	NUM
ejpam-5837	208	19	)	)	PUNCT
ejpam-5837	208	20	a	a	DET
ejpam-5837	208	21	minimal	minimal	ADJ
ejpam-5837	208	22	if	if	SCONJ
ejpam-5837	208	23	for	for	ADP
ejpam-5837	208	24	any	any	DET
ejpam-5837	208	25	almost	almost	ADV
ejpam-5837	208	26	(	(	PUNCT
ejpam-5837	208	27	m	m	PROPN
ejpam-5837	208	28	,	,	PUNCT
ejpam-5837	208	29	n)-quasi	n)-quasi	NOUN
ejpam-5837	208	30	-	-	PUNCT
ejpam-5837	208	31	ideal	ideal	ADJ
ejpam-5837	208	32	r	r	NOUN
ejpam-5837	208	33	of	of	ADP
ejpam-5837	208	34	t	t	NOUN
ejpam-5837	208	35	if	if	SCONJ
ejpam-5837	208	36	whenever	whenever	SCONJ
ejpam-5837	208	37	r	r	PROPN
ejpam-5837	208	38	⊆	⊆	NUM
ejpam-5837	208	39	b	b	NOUN
ejpam-5837	208	40	,	,	PUNCT
ejpam-5837	208	41	then	then	ADV
ejpam-5837	208	42	r	r	NOUN
ejpam-5837	208	43	=	=	SYM
ejpam-5837	208	44	b	b	PROPN
ejpam-5837	208	45	,	,	PUNCT
ejpam-5837	208	46	(	(	PUNCT
ejpam-5837	208	47	2	2	X
ejpam-5837	208	48	)	)	PUNCT
ejpam-5837	208	49	a	a	DET
ejpam-5837	208	50	maximal	maximal	ADJ
ejpam-5837	208	51	if	if	SCONJ
ejpam-5837	208	52	for	for	ADP
ejpam-5837	208	53	any	any	DET
ejpam-5837	208	54	almost	almost	ADV
ejpam-5837	208	55	(	(	PUNCT
ejpam-5837	208	56	m	m	PROPN
ejpam-5837	208	57	,	,	PUNCT
ejpam-5837	208	58	n)-quasi	n)-quasi	NOUN
ejpam-5837	208	59	-	-	PUNCT
ejpam-5837	208	60	ideal	ideal	ADJ
ejpam-5837	208	61	r	r	NOUN
ejpam-5837	208	62	of	of	ADP
ejpam-5837	208	63	t	t	NOUN
ejpam-5837	208	64	if	if	SCONJ
ejpam-5837	208	65	whenever	whenever	SCONJ
ejpam-5837	208	66	b	b	PROPN
ejpam-5837	208	67	⊆	⊆	NUM
ejpam-5837	208	68	r	r	NOUN
ejpam-5837	208	69	,	,	PUNCT
ejpam-5837	208	70	then	then	ADV
ejpam-5837	208	71	r	r	PROPN
ejpam-5837	208	72	=	=	SYM
ejpam-5837	208	73	b.	b.	PROPN
ejpam-5837	208	74	definition	definition	NOUN
ejpam-5837	208	75	14	14	NUM
ejpam-5837	208	76	.	.	PUNCT
ejpam-5837	209	1	a	a	DET
ejpam-5837	209	2	fuzzy	fuzzy	ADJ
ejpam-5837	209	3	almost	almost	ADV
ejpam-5837	209	4	(	(	PUNCT
ejpam-5837	209	5	m	m	PROPN
ejpam-5837	209	6	,	,	PUNCT
ejpam-5837	209	7	n)-quasi	n)-quasi	NOUN
ejpam-5837	209	8	-	-	PUNCT
ejpam-5837	209	9	ideal	ideal	ADJ
ejpam-5837	209	10	ϑ	ϑ	X
ejpam-5837	209	11	of	of	ADP
ejpam-5837	209	12	an	an	DET
ejpam-5837	209	13	ordered	order	VERB
ejpam-5837	209	14	semigroup	semigroup	PROPN
ejpam-5837	209	15	t	t	PROPN
ejpam-5837	209	16	is	be	AUX
ejpam-5837	209	17	called	call	VERB
ejpam-5837	209	18	(	(	PUNCT
ejpam-5837	209	19	1	1	NUM
ejpam-5837	209	20	)	)	PUNCT
ejpam-5837	209	21	a	a	DET
ejpam-5837	209	22	minimal	minimal	ADJ
ejpam-5837	209	23	if	if	SCONJ
ejpam-5837	209	24	for	for	ADP
ejpam-5837	209	25	any	any	DET
ejpam-5837	209	26	fuzzy	fuzzy	NOUN
ejpam-5837	209	27	almost	almost	ADV
ejpam-5837	209	28	(	(	PUNCT
ejpam-5837	209	29	m	m	PROPN
ejpam-5837	209	30	,	,	PUNCT
ejpam-5837	209	31	n)-quasi	n)-quasi	NOUN
ejpam-5837	209	32	-	-	PUNCT
ejpam-5837	209	33	ideal	ideal	ADJ
ejpam-5837	209	34	ξ	ξ	PROPN
ejpam-5837	209	35	of	of	ADP
ejpam-5837	209	36	t	t	PROPN
ejpam-5837	209	37	if	if	SCONJ
ejpam-5837	209	38	whenever	whenever	SCONJ
ejpam-5837	209	39	ξ	ξ	X
ejpam-5837	209	40	≤	≤	X
ejpam-5837	209	41	ϑ	ϑ	X
ejpam-5837	209	42	,	,	PUNCT
ejpam-5837	209	43	then	then	ADV
ejpam-5837	209	44	supp(ξ	supp(ξ	PROPN
ejpam-5837	209	45	)	)	PUNCT
ejpam-5837	209	46	=	=	SYM
ejpam-5837	209	47	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	209	48	)	)	PUNCT
ejpam-5837	209	49	,	,	PUNCT
ejpam-5837	209	50	(	(	PUNCT
ejpam-5837	209	51	2	2	X
ejpam-5837	209	52	)	)	PUNCT
ejpam-5837	209	53	a	a	DET
ejpam-5837	209	54	maximal	maximal	ADJ
ejpam-5837	209	55	if	if	SCONJ
ejpam-5837	209	56	for	for	ADP
ejpam-5837	209	57	any	any	DET
ejpam-5837	209	58	fuzzy	fuzzy	NOUN
ejpam-5837	209	59	almost	almost	ADV
ejpam-5837	209	60	(	(	PUNCT
ejpam-5837	209	61	m	m	PROPN
ejpam-5837	209	62	,	,	PUNCT
ejpam-5837	209	63	n)-quasi	n)-quasi	NOUN
ejpam-5837	209	64	-	-	PUNCT
ejpam-5837	209	65	ideal	ideal	ADJ
ejpam-5837	209	66	ξ	ξ	PROPN
ejpam-5837	209	67	of	of	ADP
ejpam-5837	209	68	t	t	PROPN
ejpam-5837	209	69	if	if	SCONJ
ejpam-5837	209	70	whenever	whenever	SCONJ
ejpam-5837	209	71	ϑ	ϑ	X
ejpam-5837	209	72	≤	≤	PROPN
ejpam-5837	209	73	ξ	ξ	PROPN
ejpam-5837	209	74	,	,	PUNCT
ejpam-5837	209	75	then	then	ADV
ejpam-5837	209	76	supp(ξ	supp(ξ	PROPN
ejpam-5837	209	77	)	)	PUNCT
ejpam-5837	209	78	=	=	SYM
ejpam-5837	209	79	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	209	80	)	)	PUNCT
ejpam-5837	209	81	.	.	PUNCT
ejpam-5837	210	1	p.	p.	NOUN
ejpam-5837	210	2	khamrot	khamrot	PROPN
ejpam-5837	211	1	et	et	PROPN
ejpam-5837	211	2	al	al	PROPN
ejpam-5837	211	3	.	.	PUNCT
ejpam-5837	211	4	/	/	SYM
ejpam-5837	211	5	eur	eur	PROPN
ejpam-5837	211	6	.	.	PUNCT
ejpam-5837	212	1	j.	j.	PROPN
ejpam-5837	212	2	pure	pure	PROPN
ejpam-5837	212	3	appl	appl	PROPN
ejpam-5837	212	4	.	.	PROPN
ejpam-5837	212	5	math	math	PROPN
ejpam-5837	212	6	,	,	PUNCT
ejpam-5837	212	7	18	18	NUM
ejpam-5837	212	8	(	(	PUNCT
ejpam-5837	212	9	2	2	NUM
ejpam-5837	212	10	)	)	PUNCT
ejpam-5837	212	11	(	(	PUNCT
ejpam-5837	212	12	2025	2025	NUM
ejpam-5837	212	13	)	)	PUNCT
ejpam-5837	212	14	,	,	PUNCT
ejpam-5837	212	15	5837	5837	NUM
ejpam-5837	212	16	9	9	NUM
ejpam-5837	212	17	of	of	ADP
ejpam-5837	212	18	13	13	NUM
ejpam-5837	212	19	theorem	theorem	NOUN
ejpam-5837	212	20	8	8	NUM
ejpam-5837	212	21	.	.	PUNCT
ejpam-5837	213	1	let	let	VERB
ejpam-5837	213	2	b	b	X
ejpam-5837	213	3	be	be	AUX
ejpam-5837	213	4	a	a	DET
ejpam-5837	213	5	nonempty	nonempty	ADJ
ejpam-5837	213	6	subset	subset	NOUN
ejpam-5837	213	7	of	of	ADP
ejpam-5837	213	8	an	an	DET
ejpam-5837	213	9	ordered	order	VERB
ejpam-5837	213	10	semigroup	semigroup	NOUN
ejpam-5837	213	11	t.	t.	PROPN
ejpam-5837	213	12	then	then	ADV
ejpam-5837	213	13	(	(	PUNCT
ejpam-5837	213	14	1	1	X
ejpam-5837	213	15	)	)	PUNCT
ejpam-5837	213	16	b	b	NOUN
ejpam-5837	213	17	is	be	AUX
ejpam-5837	213	18	a	a	DET
ejpam-5837	213	19	minimal	minimal	ADJ
ejpam-5837	213	20	almost	almost	ADV
ejpam-5837	213	21	(	(	PUNCT
ejpam-5837	213	22	m	m	PROPN
ejpam-5837	213	23	,	,	PUNCT
ejpam-5837	213	24	n)-quasi	n)-quasi	NOUN
ejpam-5837	213	25	-	-	NOUN
ejpam-5837	213	26	ideal	ideal	NOUN
ejpam-5837	213	27	of	of	ADP
ejpam-5837	213	28	t	t	PROPN
ejpam-5837	213	29	if	if	SCONJ
ejpam-5837	214	1	and	and	CCONJ
ejpam-5837	214	2	only	only	ADV
ejpam-5837	214	3	if	if	SCONJ
ejpam-5837	214	4	χb	χb	PROPN
ejpam-5837	214	5	is	be	AUX
ejpam-5837	214	6	a	a	DET
ejpam-5837	214	7	minimal	minimal	ADJ
ejpam-5837	214	8	fuzzy	fuzzy	NOUN
ejpam-5837	214	9	almost	almost	ADV
ejpam-5837	214	10	(	(	PUNCT
ejpam-5837	214	11	m	m	PROPN
ejpam-5837	214	12	,	,	PUNCT
ejpam-5837	214	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	214	14	-	-	NOUN
ejpam-5837	214	15	ideal	ideal	NOUN
ejpam-5837	214	16	of	of	ADP
ejpam-5837	214	17	t.	t.	PROPN
ejpam-5837	214	18	(	(	PUNCT
ejpam-5837	214	19	2	2	NUM
ejpam-5837	214	20	)	)	PUNCT
ejpam-5837	214	21	b	b	NOUN
ejpam-5837	214	22	is	be	AUX
ejpam-5837	214	23	a	a	DET
ejpam-5837	214	24	maximal	maximal	ADJ
ejpam-5837	214	25	almost	almost	ADV
ejpam-5837	214	26	(	(	PUNCT
ejpam-5837	214	27	m	m	PROPN
ejpam-5837	214	28	,	,	PUNCT
ejpam-5837	214	29	n)-quasi	n)-quasi	NOUN
ejpam-5837	214	30	-	-	NOUN
ejpam-5837	214	31	ideal	ideal	NOUN
ejpam-5837	214	32	of	of	ADP
ejpam-5837	214	33	t	t	PROPN
ejpam-5837	214	34	if	if	SCONJ
ejpam-5837	214	35	and	and	CCONJ
ejpam-5837	214	36	only	only	ADV
ejpam-5837	214	37	if	if	SCONJ
ejpam-5837	214	38	χb	χb	PROPN
ejpam-5837	214	39	is	be	AUX
ejpam-5837	214	40	a	a	DET
ejpam-5837	214	41	maximal	maximal	ADJ
ejpam-5837	214	42	fuzzy	fuzzy	NOUN
ejpam-5837	214	43	almost	almost	ADV
ejpam-5837	214	44	(	(	PUNCT
ejpam-5837	214	45	m	m	PROPN
ejpam-5837	214	46	,	,	PUNCT
ejpam-5837	214	47	n)-quasi	n)-quasi	NOUN
ejpam-5837	214	48	-	-	NOUN
ejpam-5837	214	49	ideal	ideal	NOUN
ejpam-5837	214	50	of	of	ADP
ejpam-5837	214	51	t.	t.	NOUN
ejpam-5837	214	52	proof	proof	NOUN
ejpam-5837	214	53	.	.	PUNCT
ejpam-5837	215	1	(	(	PUNCT
ejpam-5837	215	2	1	1	X
ejpam-5837	215	3	)	)	PUNCT
ejpam-5837	215	4	assume	assume	VERB
ejpam-5837	215	5	that	that	SCONJ
ejpam-5837	215	6	b	b	PROPN
ejpam-5837	215	7	is	be	AUX
ejpam-5837	215	8	a	a	DET
ejpam-5837	215	9	minimal	minimal	ADJ
ejpam-5837	215	10	almost	almost	ADV
ejpam-5837	215	11	(	(	PUNCT
ejpam-5837	215	12	m	m	PROPN
ejpam-5837	215	13	,	,	PUNCT
ejpam-5837	215	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	215	15	-	-	NOUN
ejpam-5837	215	16	ideal	ideal	NOUN
ejpam-5837	215	17	of	of	ADP
ejpam-5837	215	18	t.	t.	PROPN
ejpam-5837	215	19	then	then	ADV
ejpam-5837	215	20	b	b	PROPN
ejpam-5837	215	21	is	be	AUX
ejpam-5837	215	22	an	an	DET
ejpam-5837	215	23	almost	almost	ADV
ejpam-5837	215	24	(	(	PUNCT
ejpam-5837	215	25	m	m	PROPN
ejpam-5837	215	26	,	,	PUNCT
ejpam-5837	215	27	n)-quasi	n)-quasi	NOUN
ejpam-5837	215	28	-	-	NOUN
ejpam-5837	215	29	ideal	ideal	NOUN
ejpam-5837	215	30	of	of	ADP
ejpam-5837	215	31	t.	t.	PROPN
ejpam-5837	215	32	thus	thus	ADV
ejpam-5837	215	33	by	by	ADP
ejpam-5837	215	34	theorem	theorem	NOUN
ejpam-5837	215	35	6	6	NUM
ejpam-5837	215	36	,	,	PUNCT
ejpam-5837	215	37	χb	χb	PROPN
ejpam-5837	215	38	is	be	AUX
ejpam-5837	215	39	a	a	DET
ejpam-5837	215	40	fuzzy	fuzzy	ADJ
ejpam-5837	215	41	almost	almost	ADV
ejpam-5837	215	42	(	(	PUNCT
ejpam-5837	215	43	m	m	PROPN
ejpam-5837	215	44	,	,	PUNCT
ejpam-5837	215	45	n)-quasi	n)-quasi	NOUN
ejpam-5837	215	46	-	-	NOUN
ejpam-5837	215	47	ideal	ideal	NOUN
ejpam-5837	215	48	of	of	ADP
ejpam-5837	215	49	t.	t.	PROPN
ejpam-5837	215	50	let	let	VERB
ejpam-5837	215	51	ξ	ξ	X
ejpam-5837	215	52	be	be	AUX
ejpam-5837	215	53	a	a	DET
ejpam-5837	215	54	fuzzy	fuzzy	ADJ
ejpam-5837	215	55	almost	almost	ADV
ejpam-5837	215	56	(	(	PUNCT
ejpam-5837	215	57	m	m	PROPN
ejpam-5837	215	58	,	,	PUNCT
ejpam-5837	215	59	n)-quasi	n)-quasi	NOUN
ejpam-5837	215	60	-	-	NOUN
ejpam-5837	215	61	ideal	ideal	NOUN
ejpam-5837	215	62	of	of	ADP
ejpam-5837	215	63	t	t	PROPN
ejpam-5837	216	1	such	such	ADJ
ejpam-5837	216	2	that	that	SCONJ
ejpam-5837	216	3	ξ	ξ	PROPN
ejpam-5837	216	4	≤	≤	NOUN
ejpam-5837	216	5	χb	χb	PROPN
ejpam-5837	216	6	.	.	PUNCT
ejpam-5837	217	1	then	then	ADV
ejpam-5837	217	2	by	by	ADP
ejpam-5837	217	3	theorem	theorem	ADJ
ejpam-5837	217	4	7	7	NUM
ejpam-5837	217	5	,	,	PUNCT
ejpam-5837	217	6	supp(ξ	supp(ξ	PROPN
ejpam-5837	217	7	)	)	PUNCT
ejpam-5837	217	8	is	be	AUX
ejpam-5837	217	9	an	an	DET
ejpam-5837	217	10	almost	almost	ADV
ejpam-5837	217	11	(	(	PUNCT
ejpam-5837	217	12	m	m	PROPN
ejpam-5837	217	13	,	,	PUNCT
ejpam-5837	217	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	217	15	-	-	NOUN
ejpam-5837	217	16	ideal	ideal	NOUN
ejpam-5837	217	17	of	of	ADP
ejpam-5837	217	18	t	t	PROPN
ejpam-5837	217	19	such	such	ADJ
ejpam-5837	217	20	that	that	DET
ejpam-5837	217	21	supp(ξ	supp(ξ	PROPN
ejpam-5837	217	22	)	)	PUNCT
ejpam-5837	217	23	⊆	⊆	NUM
ejpam-5837	217	24	supp(χb	supp(χb	NOUN
ejpam-5837	217	25	)	)	PUNCT
ejpam-5837	217	26	=	=	SYM
ejpam-5837	217	27	b.	b.	PROPN
ejpam-5837	217	28	since	since	SCONJ
ejpam-5837	217	29	b	b	PROPN
ejpam-5837	217	30	is	be	AUX
ejpam-5837	217	31	minimal	minimal	ADJ
ejpam-5837	217	32	we	we	PRON
ejpam-5837	217	33	have	have	AUX
ejpam-5837	217	34	supp(ξ	supp(ξ	NOUN
ejpam-5837	217	35	)	)	PUNCT
ejpam-5837	218	1	=	=	SYM
ejpam-5837	218	2	b	b	X
ejpam-5837	218	3	=	=	PUNCT
ejpam-5837	218	4	supp(χb	supp(χb	PROPN
ejpam-5837	218	5	)	)	PUNCT
ejpam-5837	218	6	.	.	PUNCT
ejpam-5837	219	1	therefore	therefore	ADV
ejpam-5837	219	2	,	,	PUNCT
ejpam-5837	219	3	χb	χb	PROPN
ejpam-5837	219	4	is	be	AUX
ejpam-5837	219	5	minimal	minimal	ADJ
ejpam-5837	219	6	.	.	PUNCT
ejpam-5837	220	1	conversely	conversely	ADV
ejpam-5837	220	2	,	,	PUNCT
ejpam-5837	220	3	suppose	suppose	VERB
ejpam-5837	220	4	that	that	SCONJ
ejpam-5837	220	5	χb	χb	PROPN
ejpam-5837	220	6	is	be	AUX
ejpam-5837	220	7	a	a	DET
ejpam-5837	220	8	minimal	minimal	ADJ
ejpam-5837	220	9	fuzzy	fuzzy	NOUN
ejpam-5837	220	10	almost	almost	ADV
ejpam-5837	220	11	(	(	PUNCT
ejpam-5837	220	12	m	m	PROPN
ejpam-5837	220	13	,	,	PUNCT
ejpam-5837	220	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	220	15	-	-	NOUN
ejpam-5837	220	16	ideal	ideal	NOUN
ejpam-5837	220	17	of	of	ADP
ejpam-5837	220	18	t.	t.	PROPN
ejpam-5837	220	19	then	then	ADV
ejpam-5837	220	20	χb	χb	PROPN
ejpam-5837	220	21	is	be	AUX
ejpam-5837	220	22	a	a	DET
ejpam-5837	220	23	fuzzy	fuzzy	ADJ
ejpam-5837	220	24	almost	almost	ADV
ejpam-5837	220	25	(	(	PUNCT
ejpam-5837	220	26	m	m	PROPN
ejpam-5837	220	27	,	,	PUNCT
ejpam-5837	220	28	n)-quasi	n)-quasi	NOUN
ejpam-5837	220	29	-	-	NOUN
ejpam-5837	220	30	ideal	ideal	NOUN
ejpam-5837	220	31	of	of	ADP
ejpam-5837	220	32	t.	t.	PROPN
ejpam-5837	220	33	thus	thus	ADV
ejpam-5837	220	34	by	by	ADP
ejpam-5837	220	35	theorem	theorem	NOUN
ejpam-5837	220	36	6	6	NUM
ejpam-5837	220	37	,	,	PUNCT
ejpam-5837	220	38	b	b	NOUN
ejpam-5837	220	39	is	be	AUX
ejpam-5837	220	40	an	an	DET
ejpam-5837	220	41	almost	almost	ADV
ejpam-5837	220	42	(	(	PUNCT
ejpam-5837	220	43	m	m	PROPN
ejpam-5837	220	44	,	,	PUNCT
ejpam-5837	220	45	n)-quasi	n)-quasi	NOUN
ejpam-5837	220	46	-	-	NOUN
ejpam-5837	220	47	ideal	ideal	NOUN
ejpam-5837	220	48	of	of	ADP
ejpam-5837	220	49	t.	t.	PROPN
ejpam-5837	220	50	let	let	VERB
ejpam-5837	220	51	r	r	NOUN
ejpam-5837	220	52	be	be	AUX
ejpam-5837	220	53	an	an	DET
ejpam-5837	220	54	almost	almost	ADV
ejpam-5837	220	55	(	(	PUNCT
ejpam-5837	220	56	m	m	PROPN
ejpam-5837	220	57	,	,	PUNCT
ejpam-5837	220	58	n)-quasi	n)-quasi	NOUN
ejpam-5837	220	59	-	-	NOUN
ejpam-5837	220	60	ideal	ideal	NOUN
ejpam-5837	220	61	of	of	ADP
ejpam-5837	220	62	t	t	PROPN
ejpam-5837	220	63	such	such	ADJ
ejpam-5837	220	64	that	that	SCONJ
ejpam-5837	220	65	r	r	PROPN
ejpam-5837	220	66	⊆	⊆	NUM
ejpam-5837	220	67	b.	b.	NOUN
ejpam-5837	220	68	then	then	ADV
ejpam-5837	220	69	χr	χr	PROPN
ejpam-5837	220	70	is	be	AUX
ejpam-5837	220	71	a	a	DET
ejpam-5837	220	72	fuzzy	fuzzy	ADJ
ejpam-5837	220	73	almost	almost	ADV
ejpam-5837	220	74	(	(	PUNCT
ejpam-5837	220	75	m	m	PROPN
ejpam-5837	220	76	,	,	PUNCT
ejpam-5837	220	77	n)-quasi	n)-quasi	NOUN
ejpam-5837	220	78	-	-	NOUN
ejpam-5837	220	79	ideal	ideal	NOUN
ejpam-5837	220	80	of	of	ADP
ejpam-5837	220	81	t	t	PROPN
ejpam-5837	220	82	such	such	ADJ
ejpam-5837	220	83	that	that	PRON
ejpam-5837	220	84	χr	χr	VERB
ejpam-5837	220	85	≤	≤	X
ejpam-5837	220	86	χb	χb	PRON
ejpam-5837	220	87	.	.	PUNCT
ejpam-5837	221	1	hence	hence	ADV
ejpam-5837	221	2	,	,	PUNCT
ejpam-5837	221	3	r	r	NOUN
ejpam-5837	221	4	=	=	SYM
ejpam-5837	221	5	supp(χr	supp(χr	ADJ
ejpam-5837	221	6	)	)	PUNCT
ejpam-5837	221	7	=	=	SYM
ejpam-5837	221	8	supp(χb	supp(χb	PROPN
ejpam-5837	221	9	)	)	PUNCT
ejpam-5837	221	10	=	=	SYM
ejpam-5837	221	11	b.	b.	PROPN
ejpam-5837	221	12	therefore	therefore	ADV
ejpam-5837	221	13	,	,	PUNCT
ejpam-5837	221	14	b	b	PROPN
ejpam-5837	221	15	is	be	AUX
ejpam-5837	221	16	minimal	minimal	ADJ
ejpam-5837	221	17	.	.	PUNCT
ejpam-5837	222	1	(	(	PUNCT
ejpam-5837	222	2	2	2	X
ejpam-5837	222	3	)	)	PUNCT
ejpam-5837	222	4	assume	assume	VERB
ejpam-5837	222	5	that	that	SCONJ
ejpam-5837	222	6	b	b	PROPN
ejpam-5837	222	7	is	be	AUX
ejpam-5837	222	8	a	a	DET
ejpam-5837	222	9	maximal	maximal	ADJ
ejpam-5837	222	10	almost	almost	ADV
ejpam-5837	222	11	(	(	PUNCT
ejpam-5837	222	12	m	m	PROPN
ejpam-5837	222	13	,	,	PUNCT
ejpam-5837	222	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	222	15	-	-	NOUN
ejpam-5837	222	16	ideal	ideal	NOUN
ejpam-5837	222	17	of	of	ADP
ejpam-5837	222	18	t.	t.	PROPN
ejpam-5837	222	19	then	then	ADV
ejpam-5837	222	20	b	b	PROPN
ejpam-5837	222	21	is	be	AUX
ejpam-5837	222	22	an	an	DET
ejpam-5837	222	23	almost	almost	ADV
ejpam-5837	222	24	(	(	PUNCT
ejpam-5837	222	25	m	m	PROPN
ejpam-5837	222	26	,	,	PUNCT
ejpam-5837	222	27	n)-quasi	n)-quasi	NOUN
ejpam-5837	222	28	-	-	NOUN
ejpam-5837	222	29	ideal	ideal	NOUN
ejpam-5837	222	30	of	of	ADP
ejpam-5837	222	31	t.	t.	PROPN
ejpam-5837	222	32	thus	thus	ADV
ejpam-5837	222	33	by	by	ADP
ejpam-5837	222	34	theorem	theorem	NOUN
ejpam-5837	222	35	6	6	NUM
ejpam-5837	222	36	,	,	PUNCT
ejpam-5837	222	37	χb	χb	PROPN
ejpam-5837	222	38	is	be	AUX
ejpam-5837	222	39	a	a	DET
ejpam-5837	222	40	fuzzy	fuzzy	ADJ
ejpam-5837	222	41	almost	almost	ADV
ejpam-5837	222	42	(	(	PUNCT
ejpam-5837	222	43	m	m	PROPN
ejpam-5837	222	44	,	,	PUNCT
ejpam-5837	222	45	n)-quasi	n)-quasi	NOUN
ejpam-5837	222	46	-	-	NOUN
ejpam-5837	222	47	ideal	ideal	NOUN
ejpam-5837	222	48	of	of	ADP
ejpam-5837	222	49	t.	t.	PROPN
ejpam-5837	222	50	let	let	VERB
ejpam-5837	222	51	ξ	ξ	X
ejpam-5837	222	52	be	be	AUX
ejpam-5837	222	53	a	a	DET
ejpam-5837	222	54	fuzzy	fuzzy	ADJ
ejpam-5837	222	55	almost	almost	ADV
ejpam-5837	222	56	(	(	PUNCT
ejpam-5837	222	57	m	m	PROPN
ejpam-5837	222	58	,	,	PUNCT
ejpam-5837	222	59	n)-quasi	n)-quasi	NOUN
ejpam-5837	222	60	-	-	NOUN
ejpam-5837	222	61	ideal	ideal	NOUN
ejpam-5837	222	62	of	of	ADP
ejpam-5837	222	63	t	t	PROPN
ejpam-5837	222	64	such	such	ADJ
ejpam-5837	222	65	that	that	SCONJ
ejpam-5837	222	66	χb	χb	PROPN
ejpam-5837	222	67	≤	≤	NOUN
ejpam-5837	222	68	ξ	ξ	X
ejpam-5837	222	69	.	.	PUNCT
ejpam-5837	223	1	then	then	ADV
ejpam-5837	223	2	by	by	ADP
ejpam-5837	223	3	theorem	theorem	ADJ
ejpam-5837	223	4	7	7	NUM
ejpam-5837	223	5	,	,	PUNCT
ejpam-5837	223	6	supp(ξ	supp(ξ	PROPN
ejpam-5837	223	7	)	)	PUNCT
ejpam-5837	223	8	is	be	AUX
ejpam-5837	223	9	an	an	DET
ejpam-5837	223	10	almost	almost	ADV
ejpam-5837	223	11	(	(	PUNCT
ejpam-5837	223	12	m	m	PROPN
ejpam-5837	223	13	,	,	PUNCT
ejpam-5837	223	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	223	15	-	-	NOUN
ejpam-5837	223	16	ideal	ideal	NOUN
ejpam-5837	223	17	of	of	ADP
ejpam-5837	223	18	t	t	NOUN
ejpam-5837	223	19	such	such	ADJ
ejpam-5837	223	20	that	that	PRON
ejpam-5837	223	21	b	b	X
ejpam-5837	223	22	=	=	SYM
ejpam-5837	223	23	supp(χb	supp(χb	PROPN
ejpam-5837	223	24	)	)	PUNCT
ejpam-5837	223	25	⊆	⊆	NUM
ejpam-5837	223	26	supp(ξ	supp(ξ	PROPN
ejpam-5837	223	27	)	)	PUNCT
ejpam-5837	223	28	.	.	PUNCT
ejpam-5837	224	1	since	since	SCONJ
ejpam-5837	224	2	b	b	NOUN
ejpam-5837	224	3	is	be	AUX
ejpam-5837	224	4	maximal	maximal	ADJ
ejpam-5837	224	5	we	we	PRON
ejpam-5837	224	6	have	have	VERB
ejpam-5837	224	7	supp(ξ	supp(ξ	NOUN
ejpam-5837	224	8	)	)	PUNCT
ejpam-5837	224	9	=	=	SYM
ejpam-5837	224	10	b	b	X
ejpam-5837	224	11	=	=	PUNCT
ejpam-5837	224	12	supp(χb	supp(χb	PROPN
ejpam-5837	224	13	)	)	PUNCT
ejpam-5837	224	14	.	.	PUNCT
ejpam-5837	225	1	therefore	therefore	ADV
ejpam-5837	225	2	,	,	PUNCT
ejpam-5837	225	3	χb	χb	PROPN
ejpam-5837	225	4	is	be	AUX
ejpam-5837	225	5	maximal	maximal	ADJ
ejpam-5837	225	6	.	.	PUNCT
ejpam-5837	226	1	conversely	conversely	ADV
ejpam-5837	226	2	,	,	PUNCT
ejpam-5837	226	3	suppose	suppose	VERB
ejpam-5837	226	4	that	that	SCONJ
ejpam-5837	226	5	χb	χb	PROPN
ejpam-5837	226	6	is	be	AUX
ejpam-5837	226	7	a	a	DET
ejpam-5837	226	8	maximal	maximal	ADJ
ejpam-5837	226	9	fuzzy	fuzzy	NOUN
ejpam-5837	226	10	almost	almost	ADV
ejpam-5837	226	11	(	(	PUNCT
ejpam-5837	226	12	m	m	PROPN
ejpam-5837	226	13	,	,	PUNCT
ejpam-5837	226	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	226	15	-	-	NOUN
ejpam-5837	226	16	ideal	ideal	NOUN
ejpam-5837	226	17	of	of	ADP
ejpam-5837	226	18	t.	t.	PROPN
ejpam-5837	226	19	then	then	ADV
ejpam-5837	226	20	χb	χb	PROPN
ejpam-5837	226	21	is	be	AUX
ejpam-5837	226	22	a	a	DET
ejpam-5837	226	23	fuzzy	fuzzy	ADJ
ejpam-5837	226	24	almost	almost	ADV
ejpam-5837	226	25	(	(	PUNCT
ejpam-5837	226	26	m	m	PROPN
ejpam-5837	226	27	,	,	PUNCT
ejpam-5837	226	28	n)-quasi	n)-quasi	NOUN
ejpam-5837	226	29	-	-	NOUN
ejpam-5837	226	30	ideal	ideal	NOUN
ejpam-5837	226	31	of	of	ADP
ejpam-5837	226	32	t.	t.	PROPN
ejpam-5837	226	33	by	by	ADP
ejpam-5837	226	34	theorem	theorem	NOUN
ejpam-5837	226	35	6	6	NUM
ejpam-5837	226	36	,	,	PUNCT
ejpam-5837	226	37	b	b	NOUN
ejpam-5837	226	38	is	be	AUX
ejpam-5837	226	39	an	an	DET
ejpam-5837	226	40	almost	almost	ADV
ejpam-5837	226	41	(	(	PUNCT
ejpam-5837	226	42	m	m	PROPN
ejpam-5837	226	43	,	,	PUNCT
ejpam-5837	226	44	n)quasi	n)quasi	NOUN
ejpam-5837	226	45	-	-	PUNCT
ejpam-5837	226	46	ideal	ideal	NOUN
ejpam-5837	226	47	of	of	ADP
ejpam-5837	226	48	t.	t.	PROPN
ejpam-5837	226	49	let	let	VERB
ejpam-5837	226	50	r	r	NOUN
ejpam-5837	226	51	be	be	AUX
ejpam-5837	226	52	an	an	DET
ejpam-5837	226	53	almost	almost	ADV
ejpam-5837	226	54	(	(	PUNCT
ejpam-5837	226	55	m	m	PROPN
ejpam-5837	226	56	,	,	PUNCT
ejpam-5837	226	57	n)-quasi	n)-quasi	NOUN
ejpam-5837	226	58	-	-	NOUN
ejpam-5837	226	59	ideal	ideal	NOUN
ejpam-5837	226	60	of	of	ADP
ejpam-5837	226	61	t	t	NOUN
ejpam-5837	226	62	such	such	ADJ
ejpam-5837	226	63	that	that	PRON
ejpam-5837	226	64	b	b	NOUN
ejpam-5837	227	1	⊆	⊆	NUM
ejpam-5837	227	2	r.	r.	PROPN
ejpam-5837	227	3	then	then	ADV
ejpam-5837	227	4	χr	χr	PROPN
ejpam-5837	227	5	is	be	AUX
ejpam-5837	227	6	a	a	DET
ejpam-5837	227	7	fuzzy	fuzzy	ADJ
ejpam-5837	227	8	almost	almost	ADV
ejpam-5837	227	9	(	(	PUNCT
ejpam-5837	227	10	m	m	PROPN
ejpam-5837	227	11	,	,	PUNCT
ejpam-5837	227	12	n)-quasi	n)-quasi	NOUN
ejpam-5837	227	13	-	-	NOUN
ejpam-5837	227	14	ideal	ideal	NOUN
ejpam-5837	227	15	of	of	ADP
ejpam-5837	227	16	t	t	PROPN
ejpam-5837	227	17	such	such	ADJ
ejpam-5837	227	18	that	that	SCONJ
ejpam-5837	227	19	χb	χb	PRON
ejpam-5837	227	20	≤	≤	PROPN
ejpam-5837	227	21	χr	χr	VERB
ejpam-5837	227	22	.	.	PUNCT
ejpam-5837	228	1	since	since	SCONJ
ejpam-5837	228	2	χb	χb	PROPN
ejpam-5837	228	3	is	be	AUX
ejpam-5837	228	4	a	a	DET
ejpam-5837	228	5	maximal	maximal	ADJ
ejpam-5837	228	6	we	we	PRON
ejpam-5837	228	7	have	have	VERB
ejpam-5837	228	8	r	r	NOUN
ejpam-5837	228	9	=	=	SYM
ejpam-5837	228	10	supp(χr	supp(χr	ADJ
ejpam-5837	228	11	)	)	PUNCT
ejpam-5837	228	12	=	=	SYM
ejpam-5837	228	13	supp(χb	supp(χb	PROPN
ejpam-5837	228	14	)	)	PUNCT
ejpam-5837	228	15	=	=	SYM
ejpam-5837	228	16	b.	b.	PROPN
ejpam-5837	228	17	therefore	therefore	ADV
ejpam-5837	228	18	,	,	PUNCT
ejpam-5837	228	19	b	b	PROPN
ejpam-5837	228	20	is	be	AUX
ejpam-5837	228	21	maximal	maximal	ADJ
ejpam-5837	228	22	.	.	PUNCT
ejpam-5837	229	1	corollary	corollary	ADJ
ejpam-5837	229	2	5	5	NUM
ejpam-5837	229	3	.	.	PUNCT
ejpam-5837	230	1	let	let	VERB
ejpam-5837	230	2	t	t	PROPN
ejpam-5837	230	3	be	be	AUX
ejpam-5837	230	4	an	an	DET
ejpam-5837	230	5	ordered	order	VERB
ejpam-5837	230	6	semigroup	semigroup	NOUN
ejpam-5837	230	7	.	.	PUNCT
ejpam-5837	231	1	then	then	ADV
ejpam-5837	231	2	t	t	PROPN
ejpam-5837	231	3	has	have	VERB
ejpam-5837	231	4	no	no	DET
ejpam-5837	231	5	proper	proper	ADJ
ejpam-5837	231	6	almost	almost	ADV
ejpam-5837	231	7	(	(	PUNCT
ejpam-5837	231	8	m	m	NOUN
ejpam-5837	231	9	,	,	PUNCT
ejpam-5837	231	10	n)-quasiideal	n)-quasiideal	ADJ
ejpam-5837	231	11	if	if	SCONJ
ejpam-5837	231	12	and	and	CCONJ
ejpam-5837	231	13	only	only	ADV
ejpam-5837	231	14	if	if	SCONJ
ejpam-5837	231	15	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	231	16	)	)	PUNCT
ejpam-5837	232	1	=	=	SYM
ejpam-5837	232	2	t	t	NOUN
ejpam-5837	232	3	for	for	ADP
ejpam-5837	232	4	every	every	DET
ejpam-5837	232	5	fuzzy	fuzzy	NOUN
ejpam-5837	232	6	almost	almost	ADV
ejpam-5837	232	7	(	(	PUNCT
ejpam-5837	232	8	m	m	PROPN
ejpam-5837	232	9	,	,	PUNCT
ejpam-5837	232	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	232	11	-	-	PUNCT
ejpam-5837	232	12	ideal	ideal	ADJ
ejpam-5837	232	13	ϑ	ϑ	X
ejpam-5837	232	14	of	of	ADP
ejpam-5837	232	15	t.	t.	PROPN
ejpam-5837	232	16	next	next	ADV
ejpam-5837	232	17	,	,	PUNCT
ejpam-5837	232	18	we	we	PRON
ejpam-5837	232	19	give	give	VERB
ejpam-5837	232	20	definition	definition	NOUN
ejpam-5837	232	21	of	of	ADP
ejpam-5837	232	22	prime	prime	ADJ
ejpam-5837	232	23	(	(	PUNCT
ejpam-5837	232	24	resp	resp	NOUN
ejpam-5837	232	25	.	.	PUNCT
ejpam-5837	232	26	,	,	PUNCT
ejpam-5837	232	27	semiprime	semiprime	NOUN
ejpam-5837	232	28	,	,	PUNCT
ejpam-5837	232	29	strongly	strongly	ADV
ejpam-5837	232	30	prime	prime	ADJ
ejpam-5837	232	31	)	)	PUNCT
ejpam-5837	232	32	almost	almost	ADV
ejpam-5837	232	33	(	(	PUNCT
ejpam-5837	232	34	m	m	PROPN
ejpam-5837	232	35	,	,	PUNCT
ejpam-5837	232	36	n)quasi	n)quasi	NOUN
ejpam-5837	232	37	-	-	PUNCT
ejpam-5837	232	38	ideals	ideal	NOUN
ejpam-5837	232	39	and	and	CCONJ
ejpam-5837	232	40	prime	prime	ADJ
ejpam-5837	232	41	(	(	PUNCT
ejpam-5837	232	42	resp	resp	NOUN
ejpam-5837	232	43	.	.	PUNCT
ejpam-5837	232	44	,	,	PUNCT
ejpam-5837	232	45	semiprime	semiprime	NOUN
ejpam-5837	232	46	strongly	strongly	ADV
ejpam-5837	232	47	prime	prime	ADJ
ejpam-5837	232	48	)	)	PUNCT
ejpam-5837	232	49	fuzzy	fuzzy	ADJ
ejpam-5837	232	50	almost	almost	ADV
ejpam-5837	232	51	(	(	PUNCT
ejpam-5837	232	52	m	m	PROPN
ejpam-5837	232	53	,	,	PUNCT
ejpam-5837	232	54	n)-quasi	n)-quasi	NOUN
ejpam-5837	232	55	-	-	NOUN
ejpam-5837	232	56	ideals	ideal	NOUN
ejpam-5837	232	57	.	.	PUNCT
ejpam-5837	233	1	we	we	PRON
ejpam-5837	233	2	study	study	VERB
ejpam-5837	233	3	the	the	DET
ejpam-5837	233	4	relationships	relationship	NOUN
ejpam-5837	233	5	between	between	ADP
ejpam-5837	233	6	prime	prime	NOUN
ejpam-5837	233	7	(	(	PUNCT
ejpam-5837	233	8	resp	resp	NOUN
ejpam-5837	233	9	.	.	PUNCT
ejpam-5837	233	10	,	,	PUNCT
ejpam-5837	233	11	semiprime	semiprime	NOUN
ejpam-5837	233	12	strongly	strongly	ADV
ejpam-5837	233	13	prime	prime	ADJ
ejpam-5837	233	14	)	)	PUNCT
ejpam-5837	233	15	almost	almost	ADV
ejpam-5837	233	16	(	(	PUNCT
ejpam-5837	233	17	m	m	PROPN
ejpam-5837	233	18	,	,	PUNCT
ejpam-5837	233	19	n)quasi	n)quasi	NOUN
ejpam-5837	233	20	-	-	NOUN
ejpam-5837	233	21	ideals	ideal	NOUN
ejpam-5837	233	22	and	and	CCONJ
ejpam-5837	233	23	their	their	PRON
ejpam-5837	233	24	fuzzification	fuzzification	NOUN
ejpam-5837	233	25	of	of	ADP
ejpam-5837	233	26	ordered	order	VERB
ejpam-5837	233	27	semigroups	semigroup	NOUN
ejpam-5837	233	28	.	.	PUNCT
ejpam-5837	234	1	definition	definition	NOUN
ejpam-5837	234	2	15	15	NUM
ejpam-5837	234	3	.	.	PUNCT
ejpam-5837	235	1	let	let	VERB
ejpam-5837	235	2	b	b	X
ejpam-5837	235	3	be	be	AUX
ejpam-5837	235	4	an	an	DET
ejpam-5837	235	5	almost	almost	ADV
ejpam-5837	235	6	(	(	PUNCT
ejpam-5837	235	7	m	m	PROPN
ejpam-5837	235	8	,	,	PUNCT
ejpam-5837	235	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	235	10	-	-	NOUN
ejpam-5837	235	11	ideal	ideal	NOUN
ejpam-5837	235	12	of	of	ADP
ejpam-5837	235	13	an	an	DET
ejpam-5837	235	14	ordered	order	VERB
ejpam-5837	235	15	semigroup	semigroup	NOUN
ejpam-5837	236	1	t.	t.	NOUN
ejpam-5837	237	1	then	then	ADV
ejpam-5837	237	2	we	we	PRON
ejpam-5837	237	3	called	call	VERB
ejpam-5837	237	4	(	(	PUNCT
ejpam-5837	237	5	1	1	NUM
ejpam-5837	237	6	)	)	PUNCT
ejpam-5837	237	7	b	b	NOUN
ejpam-5837	237	8	is	be	AUX
ejpam-5837	237	9	a	a	DET
ejpam-5837	237	10	prime	prime	NOUN
ejpam-5837	237	11	if	if	SCONJ
ejpam-5837	237	12	for	for	ADP
ejpam-5837	237	13	any	any	DET
ejpam-5837	237	14	two	two	NUM
ejpam-5837	237	15	almost	almost	ADV
ejpam-5837	237	16	(	(	PUNCT
ejpam-5837	237	17	m	m	PROPN
ejpam-5837	237	18	,	,	PUNCT
ejpam-5837	237	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	237	20	-	-	PUNCT
ejpam-5837	237	21	ideals	ideal	NOUN
ejpam-5837	237	22	n	n	NOUN
ejpam-5837	237	23	and	and	CCONJ
ejpam-5837	237	24	h	h	PROPN
ejpam-5837	237	25	of	of	ADP
ejpam-5837	237	26	t	t	PROPN
ejpam-5837	237	27	such	such	ADJ
ejpam-5837	237	28	that	that	SCONJ
ejpam-5837	237	29	nh	nh	PROPN
ejpam-5837	237	30	⊆	⊆	NUM
ejpam-5837	237	31	b	b	PROPN
ejpam-5837	237	32	implies	imply	VERB
ejpam-5837	237	33	that	that	SCONJ
ejpam-5837	237	34	n	n	PROPN
ejpam-5837	237	35	⊆	⊆	NUM
ejpam-5837	237	36	b	b	NOUN
ejpam-5837	237	37	or	or	CCONJ
ejpam-5837	237	38	h	h	NOUN
ejpam-5837	237	39	⊆	⊆	NUM
ejpam-5837	237	40	b.	b.	PROPN
ejpam-5837	237	41	p.	p.	NOUN
ejpam-5837	237	42	khamrot	khamrot	PROPN
ejpam-5837	238	1	et	et	PROPN
ejpam-5837	238	2	al	al	PROPN
ejpam-5837	238	3	.	.	PUNCT
ejpam-5837	238	4	/	/	SYM
ejpam-5837	238	5	eur	eur	PROPN
ejpam-5837	238	6	.	.	PUNCT
ejpam-5837	239	1	j.	j.	PROPN
ejpam-5837	239	2	pure	pure	PROPN
ejpam-5837	239	3	appl	appl	PROPN
ejpam-5837	239	4	.	.	PROPN
ejpam-5837	239	5	math	math	PROPN
ejpam-5837	239	6	,	,	PUNCT
ejpam-5837	239	7	18	18	NUM
ejpam-5837	239	8	(	(	PUNCT
ejpam-5837	239	9	2	2	NUM
ejpam-5837	239	10	)	)	PUNCT
ejpam-5837	239	11	(	(	PUNCT
ejpam-5837	239	12	2025	2025	NUM
ejpam-5837	239	13	)	)	PUNCT
ejpam-5837	239	14	,	,	PUNCT
ejpam-5837	239	15	5837	5837	NUM
ejpam-5837	239	16	10	10	NUM
ejpam-5837	239	17	of	of	ADP
ejpam-5837	239	18	13	13	NUM
ejpam-5837	239	19	(	(	PUNCT
ejpam-5837	239	20	2	2	NUM
ejpam-5837	239	21	)	)	PUNCT
ejpam-5837	239	22	b	b	NOUN
ejpam-5837	239	23	is	be	AUX
ejpam-5837	239	24	a	a	DET
ejpam-5837	239	25	semiprime	semiprime	NOUN
ejpam-5837	239	26	if	if	SCONJ
ejpam-5837	239	27	for	for	ADP
ejpam-5837	239	28	any	any	DET
ejpam-5837	239	29	almost	almost	ADV
ejpam-5837	239	30	(	(	PUNCT
ejpam-5837	239	31	m	m	PROPN
ejpam-5837	239	32	,	,	PUNCT
ejpam-5837	239	33	n)-quasi	n)-quasi	NOUN
ejpam-5837	239	34	-	-	PUNCT
ejpam-5837	239	35	ideal	ideal	ADJ
ejpam-5837	239	36	n	n	PROPN
ejpam-5837	239	37	of	of	ADP
ejpam-5837	239	38	t	t	NOUN
ejpam-5837	239	39	such	such	ADJ
ejpam-5837	239	40	that	that	DET
ejpam-5837	239	41	n2	n2	ADJ
ejpam-5837	239	42	⊆	⊆	NUM
ejpam-5837	239	43	n	n	PRON
ejpam-5837	239	44	implies	imply	VERB
ejpam-5837	239	45	that	that	SCONJ
ejpam-5837	239	46	n	n	PROPN
ejpam-5837	239	47	⊆	⊆	NUM
ejpam-5837	239	48	b.	b.	PROPN
ejpam-5837	239	49	(	(	PUNCT
ejpam-5837	239	50	3	3	NUM
ejpam-5837	239	51	)	)	PUNCT
ejpam-5837	239	52	b	b	NOUN
ejpam-5837	239	53	is	be	AUX
ejpam-5837	239	54	a	a	DET
ejpam-5837	239	55	strongly	strongly	ADV
ejpam-5837	239	56	prime	prime	ADJ
ejpam-5837	239	57	if	if	SCONJ
ejpam-5837	239	58	for	for	ADP
ejpam-5837	239	59	any	any	DET
ejpam-5837	239	60	almost	almost	ADV
ejpam-5837	239	61	(	(	PUNCT
ejpam-5837	239	62	m	m	PROPN
ejpam-5837	239	63	,	,	PUNCT
ejpam-5837	239	64	n)-quasi	n)-quasi	NOUN
ejpam-5837	239	65	-	-	PUNCT
ejpam-5837	239	66	ideals	ideal	NOUN
ejpam-5837	239	67	n	n	NOUN
ejpam-5837	239	68	and	and	CCONJ
ejpam-5837	239	69	h	h	PROPN
ejpam-5837	239	70	of	of	ADP
ejpam-5837	239	71	t	t	PROPN
ejpam-5837	239	72	such	such	ADJ
ejpam-5837	239	73	that	that	DET
ejpam-5837	239	74	nh	nh	PROPN
ejpam-5837	239	75	∩	∩	NOUN
ejpam-5837	239	76	hn	hn	PROPN
ejpam-5837	239	77	⊆	⊆	PROPN
ejpam-5837	239	78	b	b	PROPN
ejpam-5837	239	79	implies	imply	VERB
ejpam-5837	239	80	that	that	SCONJ
ejpam-5837	239	81	n	n	PROPN
ejpam-5837	239	82	⊆	⊆	NUM
ejpam-5837	239	83	b	b	NOUN
ejpam-5837	239	84	or	or	CCONJ
ejpam-5837	239	85	h	h	NOUN
ejpam-5837	239	86	⊆	⊆	NUM
ejpam-5837	239	87	b.	b.	NOUN
ejpam-5837	239	88	definition	definition	NOUN
ejpam-5837	239	89	16	16	NUM
ejpam-5837	239	90	.	.	PUNCT
ejpam-5837	240	1	a	a	DET
ejpam-5837	240	2	fuzzy	fuzzy	ADJ
ejpam-5837	240	3	almost	almost	ADV
ejpam-5837	240	4	(	(	PUNCT
ejpam-5837	240	5	m	m	PROPN
ejpam-5837	240	6	,	,	PUNCT
ejpam-5837	240	7	n)-quasi	n)-quasi	NOUN
ejpam-5837	240	8	-	-	PUNCT
ejpam-5837	240	9	ideal	ideal	ADJ
ejpam-5837	240	10	ϑ	ϑ	X
ejpam-5837	240	11	on	on	ADP
ejpam-5837	240	12	an	an	DET
ejpam-5837	240	13	ordered	order	VERB
ejpam-5837	240	14	semigroup	semigroup	NOUN
ejpam-5837	240	15	t.	t.	NOUN
ejpam-5837	241	1	then	then	ADV
ejpam-5837	241	2	we	we	PRON
ejpam-5837	241	3	called	call	VERB
ejpam-5837	241	4	(	(	PUNCT
ejpam-5837	241	5	1	1	NUM
ejpam-5837	241	6	)	)	PUNCT
ejpam-5837	241	7	ϑ	ϑ	NOUN
ejpam-5837	241	8	is	be	AUX
ejpam-5837	241	9	a	a	DET
ejpam-5837	241	10	prime	prime	NOUN
ejpam-5837	241	11	if	if	SCONJ
ejpam-5837	241	12	for	for	ADP
ejpam-5837	241	13	any	any	DET
ejpam-5837	241	14	two	two	NUM
ejpam-5837	241	15	fuzzy	fuzzy	ADJ
ejpam-5837	241	16	almost	almost	ADV
ejpam-5837	241	17	(	(	PUNCT
ejpam-5837	241	18	m	m	PROPN
ejpam-5837	241	19	,	,	PUNCT
ejpam-5837	241	20	n)-quasi	n)-quasi	NOUN
ejpam-5837	241	21	-	-	NOUN
ejpam-5837	241	22	ideals	ideal	NOUN
ejpam-5837	241	23	ξ	ξ	NOUN
ejpam-5837	241	24	and	and	CCONJ
ejpam-5837	241	25	ν	ν	NOUN
ejpam-5837	241	26	of	of	ADP
ejpam-5837	241	27	t	t	NOUN
ejpam-5837	241	28	such	such	ADJ
ejpam-5837	241	29	that	that	SCONJ
ejpam-5837	241	30	ξ	ξ	PROPN
ejpam-5837	241	31	◦	◦	NOUN
ejpam-5837	241	32	ν	ν	X
ejpam-5837	241	33	≤	≤	NOUN
ejpam-5837	241	34	ϑ	ϑ	PROPN
ejpam-5837	241	35	implies	imply	VERB
ejpam-5837	241	36	that	that	SCONJ
ejpam-5837	241	37	ξ	ξ	PROPN
ejpam-5837	241	38	≤	≤	NOUN
ejpam-5837	241	39	ϑ	ϑ	X
ejpam-5837	241	40	or	or	CCONJ
ejpam-5837	241	41	ν	ν	X
ejpam-5837	241	42	≤	≤	ADJ
ejpam-5837	241	43	ϑ.	ϑ.	NOUN
ejpam-5837	241	44	(	(	PUNCT
ejpam-5837	241	45	2	2	X
ejpam-5837	241	46	)	)	PUNCT
ejpam-5837	242	1	ϑ	ϑ	NOUN
ejpam-5837	242	2	is	be	AUX
ejpam-5837	242	3	a	a	DET
ejpam-5837	242	4	semiprime	semiprime	NOUN
ejpam-5837	242	5	if	if	SCONJ
ejpam-5837	242	6	for	for	ADP
ejpam-5837	242	7	any	any	DET
ejpam-5837	242	8	fuzzy	fuzzy	NOUN
ejpam-5837	242	9	almost	almost	ADV
ejpam-5837	242	10	(	(	PUNCT
ejpam-5837	242	11	m	m	PROPN
ejpam-5837	242	12	,	,	PUNCT
ejpam-5837	242	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	14	-	-	PUNCT
ejpam-5837	242	15	ideal	ideal	ADJ
ejpam-5837	242	16	ξ	ξ	PROPN
ejpam-5837	242	17	of	of	ADP
ejpam-5837	242	18	t	t	PROPN
ejpam-5837	242	19	such	such	ADJ
ejpam-5837	242	20	that	that	SCONJ
ejpam-5837	242	21	ξ	ξ	X
ejpam-5837	242	22	◦	◦	NOUN
ejpam-5837	242	23	ξ	ξ	X
ejpam-5837	242	24	≤	≤	PRON
ejpam-5837	242	25	ξ	ξ	PROPN
ejpam-5837	242	26	implies	imply	VERB
ejpam-5837	242	27	that	that	SCONJ
ejpam-5837	242	28	ξ	ξ	PROPN
ejpam-5837	242	29	≤	≤	ADJ
ejpam-5837	242	30	ϑ.	ϑ.	NOUN
ejpam-5837	242	31	(	(	PUNCT
ejpam-5837	242	32	3	3	X
ejpam-5837	242	33	)	)	PUNCT
ejpam-5837	242	34	ϑ	ϑ	NOUN
ejpam-5837	242	35	is	be	AUX
ejpam-5837	242	36	a	a	DET
ejpam-5837	242	37	strongly	strongly	ADV
ejpam-5837	242	38	prime	prime	ADJ
ejpam-5837	242	39	if	if	SCONJ
ejpam-5837	242	40	for	for	ADP
ejpam-5837	242	41	any	any	DET
ejpam-5837	242	42	two	two	NUM
ejpam-5837	242	43	fuzzy	fuzzy	ADJ
ejpam-5837	242	44	almost	almost	ADV
ejpam-5837	242	45	(	(	PUNCT
ejpam-5837	242	46	m	m	PROPN
ejpam-5837	242	47	,	,	PUNCT
ejpam-5837	242	48	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	49	-	-	NOUN
ejpam-5837	242	50	ideals	ideal	NOUN
ejpam-5837	242	51	ξ	ξ	NOUN
ejpam-5837	242	52	and	and	CCONJ
ejpam-5837	242	53	ν	ν	NOUN
ejpam-5837	242	54	of	of	ADP
ejpam-5837	242	55	t	t	NOUN
ejpam-5837	242	56	such	such	ADJ
ejpam-5837	242	57	that	that	SCONJ
ejpam-5837	242	58	(	(	PUNCT
ejpam-5837	242	59	ξ	ξ	X
ejpam-5837	242	60	◦	◦	NOUN
ejpam-5837	242	61	ν	ν	NOUN
ejpam-5837	242	62	)	)	PUNCT
ejpam-5837	242	63	∧	∧	PROPN
ejpam-5837	242	64	(	(	PUNCT
ejpam-5837	242	65	ν	ν	X
ejpam-5837	242	66	◦	◦	NOUN
ejpam-5837	242	67	ξ	ξ	NUM
ejpam-5837	242	68	)	)	PUNCT
ejpam-5837	242	69	≤	≤	NOUN
ejpam-5837	242	70	ϑ	ϑ	X
ejpam-5837	242	71	implies	imply	VERB
ejpam-5837	242	72	that	that	SCONJ
ejpam-5837	242	73	ξ	ξ	PROPN
ejpam-5837	242	74	≤	≤	NOUN
ejpam-5837	242	75	ϑ	ϑ	X
ejpam-5837	242	76	or	or	CCONJ
ejpam-5837	242	77	ν	ν	X
ejpam-5837	242	78	≤	≤	NUM
ejpam-5837	242	79	ϑ.	ϑ.	NOUN
ejpam-5837	242	80	it	it	PRON
ejpam-5837	242	81	is	be	AUX
ejpam-5837	242	82	clearly	clearly	ADV
ejpam-5837	242	83	,	,	PUNCT
ejpam-5837	242	84	every	every	DET
ejpam-5837	242	85	fuzzy	fuzzy	ADJ
ejpam-5837	242	86	strongly	strongly	ADV
ejpam-5837	242	87	prime	prime	ADJ
ejpam-5837	242	88	almost	almost	ADV
ejpam-5837	242	89	(	(	PUNCT
ejpam-5837	242	90	m	m	PROPN
ejpam-5837	242	91	,	,	PUNCT
ejpam-5837	242	92	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	93	-	-	NOUN
ejpam-5837	242	94	ideal	ideal	NOUN
ejpam-5837	242	95	of	of	ADP
ejpam-5837	242	96	a	a	DET
ejpam-5837	242	97	ternary	ternary	ADJ
ejpam-5837	242	98	semigroup	semigroup	NOUN
ejpam-5837	242	99	is	be	AUX
ejpam-5837	242	100	a	a	DET
ejpam-5837	242	101	fuzzy	fuzzy	ADJ
ejpam-5837	242	102	prime	prime	NOUN
ejpam-5837	242	103	almost	almost	ADV
ejpam-5837	242	104	(	(	PUNCT
ejpam-5837	242	105	m	m	PROPN
ejpam-5837	242	106	,	,	PUNCT
ejpam-5837	242	107	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	108	-	-	NOUN
ejpam-5837	242	109	ideal	ideal	ADJ
ejpam-5837	242	110	,	,	PUNCT
ejpam-5837	242	111	and	and	CCONJ
ejpam-5837	242	112	every	every	DET
ejpam-5837	242	113	fuzzy	fuzzy	ADJ
ejpam-5837	242	114	prime	prime	NOUN
ejpam-5837	242	115	almost	almost	ADV
ejpam-5837	242	116	(	(	PUNCT
ejpam-5837	242	117	m	m	PROPN
ejpam-5837	242	118	,	,	PUNCT
ejpam-5837	242	119	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	120	-	-	NOUN
ejpam-5837	242	121	ideal	ideal	NOUN
ejpam-5837	242	122	of	of	ADP
ejpam-5837	242	123	a	a	DET
ejpam-5837	242	124	ternary	ternary	ADJ
ejpam-5837	242	125	semigroup	semigroup	NOUN
ejpam-5837	242	126	is	be	AUX
ejpam-5837	242	127	a	a	DET
ejpam-5837	242	128	fuzzy	fuzzy	ADJ
ejpam-5837	242	129	semiprime	semiprime	NOUN
ejpam-5837	242	130	almost	almost	ADV
ejpam-5837	242	131	(	(	PUNCT
ejpam-5837	242	132	m	m	PROPN
ejpam-5837	242	133	,	,	PUNCT
ejpam-5837	242	134	n)-quasi	n)-quasi	NOUN
ejpam-5837	242	135	-	-	PUNCT
ejpam-5837	242	136	ideal	ideal	ADJ
ejpam-5837	242	137	.	.	PUNCT
ejpam-5837	243	1	theorem	theorem	NOUN
ejpam-5837	243	2	9	9	NUM
ejpam-5837	243	3	.	.	PUNCT
ejpam-5837	244	1	let	let	VERB
ejpam-5837	244	2	b	b	X
ejpam-5837	244	3	be	be	AUX
ejpam-5837	244	4	a	a	DET
ejpam-5837	244	5	nonempty	nonempty	ADJ
ejpam-5837	244	6	subset	subset	NOUN
ejpam-5837	244	7	of	of	ADP
ejpam-5837	244	8	an	an	DET
ejpam-5837	244	9	ordered	order	VERB
ejpam-5837	244	10	semigroup	semigroup	NOUN
ejpam-5837	244	11	t.	t.	PROPN
ejpam-5837	244	12	then	then	ADV
ejpam-5837	244	13	b	b	PROPN
ejpam-5837	244	14	is	be	AUX
ejpam-5837	244	15	a	a	DET
ejpam-5837	244	16	prime	prime	NOUN
ejpam-5837	244	17	almost	almost	ADV
ejpam-5837	244	18	(	(	PUNCT
ejpam-5837	244	19	m	m	PROPN
ejpam-5837	244	20	,	,	PUNCT
ejpam-5837	244	21	n)-quasi	n)-quasi	NOUN
ejpam-5837	244	22	-	-	NOUN
ejpam-5837	244	23	ideal	ideal	NOUN
ejpam-5837	244	24	of	of	ADP
ejpam-5837	244	25	t	t	PROPN
ejpam-5837	245	1	if	if	SCONJ
ejpam-5837	245	2	and	and	CCONJ
ejpam-5837	245	3	only	only	ADV
ejpam-5837	245	4	if	if	SCONJ
ejpam-5837	245	5	χb	χb	PROPN
ejpam-5837	245	6	is	be	AUX
ejpam-5837	245	7	a	a	DET
ejpam-5837	245	8	prime	prime	ADJ
ejpam-5837	245	9	fuzzy	fuzzy	NOUN
ejpam-5837	245	10	almost	almost	ADV
ejpam-5837	245	11	(	(	PUNCT
ejpam-5837	245	12	m	m	PROPN
ejpam-5837	245	13	,	,	PUNCT
ejpam-5837	245	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	245	15	-	-	NOUN
ejpam-5837	245	16	ideal	ideal	NOUN
ejpam-5837	245	17	of	of	ADP
ejpam-5837	245	18	t.	t.	NOUN
ejpam-5837	245	19	proof	proof	NOUN
ejpam-5837	245	20	.	.	PUNCT
ejpam-5837	246	1	suppose	suppose	VERB
ejpam-5837	246	2	that	that	SCONJ
ejpam-5837	246	3	b	b	PROPN
ejpam-5837	246	4	is	be	AUX
ejpam-5837	246	5	a	a	DET
ejpam-5837	246	6	prime	prime	NOUN
ejpam-5837	246	7	almost	almost	ADV
ejpam-5837	246	8	(	(	PUNCT
ejpam-5837	246	9	m	m	PROPN
ejpam-5837	246	10	,	,	PUNCT
ejpam-5837	246	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	246	12	-	-	NOUN
ejpam-5837	246	13	ideal	ideal	NOUN
ejpam-5837	246	14	of	of	ADP
ejpam-5837	246	15	t.	t.	PROPN
ejpam-5837	246	16	then	then	ADV
ejpam-5837	246	17	b	b	PROPN
ejpam-5837	246	18	is	be	AUX
ejpam-5837	246	19	an	an	DET
ejpam-5837	246	20	almost	almost	ADV
ejpam-5837	246	21	(	(	PUNCT
ejpam-5837	246	22	m	m	PROPN
ejpam-5837	246	23	,	,	PUNCT
ejpam-5837	246	24	n)-quasi	n)-quasi	NOUN
ejpam-5837	246	25	-	-	NOUN
ejpam-5837	246	26	ideal	ideal	NOUN
ejpam-5837	246	27	of	of	ADP
ejpam-5837	246	28	t.	t.	PROPN
ejpam-5837	246	29	thus	thus	ADV
ejpam-5837	246	30	by	by	ADP
ejpam-5837	246	31	theorem	theorem	NOUN
ejpam-5837	246	32	6	6	NUM
ejpam-5837	246	33	,	,	PUNCT
ejpam-5837	246	34	χb	χb	PROPN
ejpam-5837	246	35	is	be	AUX
ejpam-5837	246	36	a	a	DET
ejpam-5837	246	37	fuzzy	fuzzy	ADJ
ejpam-5837	246	38	almost	almost	ADV
ejpam-5837	246	39	(	(	PUNCT
ejpam-5837	246	40	m	m	PROPN
ejpam-5837	246	41	,	,	PUNCT
ejpam-5837	246	42	n)-quasi	n)-quasi	NOUN
ejpam-5837	246	43	-	-	NOUN
ejpam-5837	246	44	ideal	ideal	NOUN
ejpam-5837	246	45	of	of	ADP
ejpam-5837	246	46	t.	t.	PROPN
ejpam-5837	246	47	let	let	VERB
ejpam-5837	246	48	ϑ	ϑ	X
ejpam-5837	246	49	and	and	CCONJ
ejpam-5837	246	50	ξ	ξ	PROPN
ejpam-5837	246	51	be	be	AUX
ejpam-5837	246	52	fuzzy	fuzzy	ADJ
ejpam-5837	246	53	almost	almost	ADV
ejpam-5837	246	54	(	(	PUNCT
ejpam-5837	246	55	m	m	PROPN
ejpam-5837	246	56	,	,	PUNCT
ejpam-5837	246	57	n)-quasi	n)-quasi	NOUN
ejpam-5837	246	58	-	-	NOUN
ejpam-5837	246	59	ideals	ideal	NOUN
ejpam-5837	246	60	such	such	ADJ
ejpam-5837	246	61	that	that	SCONJ
ejpam-5837	246	62	ϑ	ϑ	VERB
ejpam-5837	246	63	◦	◦	NOUN
ejpam-5837	246	64	ξ	ξ	X
ejpam-5837	246	65	≤	≤	NOUN
ejpam-5837	247	1	χb	χb	PROPN
ejpam-5837	247	2	.	.	PUNCT
ejpam-5837	248	1	assume	assume	VERB
ejpam-5837	248	2	that	that	SCONJ
ejpam-5837	248	3	ϑ	ϑ	X
ejpam-5837	248	4	≰	≰	PROPN
ejpam-5837	248	5	χb	χb	PROPN
ejpam-5837	248	6	and	and	CCONJ
ejpam-5837	248	7	ξ	ξ	PRON
ejpam-5837	248	8	≰	≰	PROPN
ejpam-5837	248	9	χb	χb	PROPN
ejpam-5837	248	10	.	.	PUNCT
ejpam-5837	249	1	then	then	ADV
ejpam-5837	249	2	there	there	PRON
ejpam-5837	249	3	exist	exist	VERB
ejpam-5837	249	4	h	h	NOUN
ejpam-5837	249	5	,	,	PUNCT
ejpam-5837	249	6	r	r	NOUN
ejpam-5837	249	7	∈	∈	PROPN
ejpam-5837	249	8	t	t	NOUN
ejpam-5837	249	9	such	such	ADJ
ejpam-5837	249	10	that	that	PRON
ejpam-5837	249	11	ϑ(h	ϑ(h	NOUN
ejpam-5837	249	12	)	)	PUNCT
ejpam-5837	249	13	̸=	̸=	PROPN
ejpam-5837	249	14	0	0	NUM
ejpam-5837	249	15	and	and	CCONJ
ejpam-5837	249	16	ξ(r	ξ(r	PROPN
ejpam-5837	249	17	)	)	PUNCT
ejpam-5837	249	18	̸=	̸=	PROPN
ejpam-5837	249	19	0	0	NUM
ejpam-5837	249	20	.	.	PUNCT
ejpam-5837	250	1	while	while	SCONJ
ejpam-5837	250	2	χb(h	χb(h	NOUN
ejpam-5837	250	3	)	)	PUNCT
ejpam-5837	250	4	=	=	SYM
ejpam-5837	250	5	0	0	NUM
ejpam-5837	250	6	and	and	CCONJ
ejpam-5837	250	7	χb(r	χb(r	NOUN
ejpam-5837	250	8	)	)	PUNCT
ejpam-5837	251	1	=	=	SYM
ejpam-5837	251	2	0	0	X
ejpam-5837	251	3	.	.	PUNCT
ejpam-5837	252	1	thus	thus	ADV
ejpam-5837	252	2	,	,	PUNCT
ejpam-5837	252	3	h	h	PROPN
ejpam-5837	252	4	∈	∈	PROPN
ejpam-5837	252	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	252	6	)	)	PUNCT
ejpam-5837	252	7	and	and	CCONJ
ejpam-5837	252	8	r	r	NOUN
ejpam-5837	252	9	∈	∈	PROPN
ejpam-5837	252	10	supp(ξ	supp(ξ	PROPN
ejpam-5837	252	11	)	)	PUNCT
ejpam-5837	252	12	,	,	PUNCT
ejpam-5837	252	13	but	but	CCONJ
ejpam-5837	252	14	h	h	NOUN
ejpam-5837	252	15	,	,	PUNCT
ejpam-5837	252	16	r	r	NOUN
ejpam-5837	252	17	/∈	/∈	PROPN
ejpam-5837	252	18	b.	b.	NOUN
ejpam-5837	253	1	so	so	ADV
ejpam-5837	253	2	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	253	3	)	)	PUNCT
ejpam-5837	253	4	⊈	⊈	PROPN
ejpam-5837	254	1	b	b	PROPN
ejpam-5837	254	2	and	and	CCONJ
ejpam-5837	254	3	supp(ξ	supp(ξ	PROPN
ejpam-5837	254	4	)	)	PUNCT
ejpam-5837	254	5	⊈	⊈	PROPN
ejpam-5837	255	1	b.	b.	PROPN
ejpam-5837	255	2	since	since	SCONJ
ejpam-5837	255	3	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	255	4	)	)	PUNCT
ejpam-5837	255	5	and	and	CCONJ
ejpam-5837	255	6	supp(ξ	supp(ξ	PROPN
ejpam-5837	255	7	)	)	PUNCT
ejpam-5837	255	8	are	be	AUX
ejpam-5837	255	9	almost	almost	ADV
ejpam-5837	255	10	(	(	PUNCT
ejpam-5837	255	11	m	m	PROPN
ejpam-5837	255	12	,	,	PUNCT
ejpam-5837	255	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	255	14	-	-	NOUN
ejpam-5837	255	15	ideals	ideal	NOUN
ejpam-5837	255	16	of	of	ADP
ejpam-5837	255	17	t	t	NOUN
ejpam-5837	255	18	we	we	PRON
ejpam-5837	255	19	have	have	VERB
ejpam-5837	255	20	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	255	21	)	)	PUNCT
ejpam-5837	255	22	supp(ξ	supp(ξ	PROPN
ejpam-5837	255	23	)	)	PUNCT
ejpam-5837	255	24	⊈	⊈	PROPN
ejpam-5837	256	1	b.	b.	PROPN
ejpam-5837	257	1	thus	thus	ADV
ejpam-5837	257	2	,	,	PUNCT
ejpam-5837	257	3	there	there	PRON
ejpam-5837	257	4	exists	exist	VERB
ejpam-5837	257	5	m	m	VERB
ejpam-5837	257	6	=	=	SYM
ejpam-5837	257	7	pq	pq	NOUN
ejpam-5837	257	8	for	for	ADP
ejpam-5837	257	9	some	some	DET
ejpam-5837	257	10	p	p	PROPN
ejpam-5837	257	11	∈	∈	PROPN
ejpam-5837	257	12	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	257	13	)	)	PUNCT
ejpam-5837	257	14	and	and	CCONJ
ejpam-5837	257	15	q	q	PROPN
ejpam-5837	257	16	∈	∈	PROPN
ejpam-5837	257	17	supp(ξ	supp(ξ	PROPN
ejpam-5837	257	18	)	)	PUNCT
ejpam-5837	257	19	such	such	ADJ
ejpam-5837	257	20	that	that	SCONJ
ejpam-5837	257	21	m	m	PROPN
ejpam-5837	257	22	∈	∈	PROPN
ejpam-5837	257	23	b.	b.	NOUN
ejpam-5837	257	24	hence	hence	ADV
ejpam-5837	257	25	χb(m	χb(m	ADV
ejpam-5837	257	26	)	)	PUNCT
ejpam-5837	258	1	=	=	SYM
ejpam-5837	258	2	0	0	NUM
ejpam-5837	258	3	implies	imply	VERB
ejpam-5837	258	4	that	that	SCONJ
ejpam-5837	258	5	(	(	PUNCT
ejpam-5837	258	6	ϑ	ϑ	X
ejpam-5837	258	7	◦	◦	NOUN
ejpam-5837	258	8	ξ)(m	ξ)(m	NUM
ejpam-5837	258	9	)	)	PUNCT
ejpam-5837	258	10	=	=	SYM
ejpam-5837	259	1	0	0	X
ejpam-5837	259	2	.	.	PUNCT
ejpam-5837	260	1	since	since	SCONJ
ejpam-5837	260	2	ϑ	ϑ	X
ejpam-5837	260	3	◦	◦	NOUN
ejpam-5837	260	4	ξ	ξ	X
ejpam-5837	260	5	≤	≤	NOUN
ejpam-5837	260	6	χb	χb	PROPN
ejpam-5837	260	7	.	.	PUNCT
ejpam-5837	261	1	we	we	PRON
ejpam-5837	261	2	have	have	VERB
ejpam-5837	261	3	p	p	PROPN
ejpam-5837	261	4	∈	∈	PROPN
ejpam-5837	261	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	261	6	)	)	PUNCT
ejpam-5837	261	7	and	and	CCONJ
ejpam-5837	261	8	q	q	PROPN
ejpam-5837	261	9	∈	∈	PROPN
ejpam-5837	261	10	supp(ξ	supp(ξ	PROPN
ejpam-5837	261	11	)	)	PUNCT
ejpam-5837	261	12	.	.	PUNCT
ejpam-5837	262	1	thus	thus	ADV
ejpam-5837	262	2	ϑ(p	ϑ(p	X
ejpam-5837	262	3	)	)	PUNCT
ejpam-5837	262	4	̸=	̸=	PROPN
ejpam-5837	262	5	0	0	NUM
ejpam-5837	262	6	,	,	PUNCT
ejpam-5837	262	7	and	and	CCONJ
ejpam-5837	262	8	ξ(q	ξ(q	NOUN
ejpam-5837	262	9	)	)	PUNCT
ejpam-5837	262	10	̸=	̸=	PROPN
ejpam-5837	262	11	0	0	NUM
ejpam-5837	262	12	.	.	PUNCT
ejpam-5837	263	1	it	it	PRON
ejpam-5837	263	2	implies	imply	VERB
ejpam-5837	263	3	that	that	SCONJ
ejpam-5837	263	4	(	(	PUNCT
ejpam-5837	263	5	ϑ	ϑ	X
ejpam-5837	263	6	◦	◦	NOUN
ejpam-5837	263	7	ξ)(m	ξ)(m	NUM
ejpam-5837	263	8	)	)	PUNCT
ejpam-5837	263	9	=	=	SYM
ejpam-5837	264	1	∨	∨	X
ejpam-5837	264	2	(	(	PUNCT
ejpam-5837	264	3	p	p	X
ejpam-5837	264	4	,	,	PUNCT
ejpam-5837	264	5	q)∈fm	q)∈fm	PROPN
ejpam-5837	264	6	{	{	PUNCT
ejpam-5837	264	7	ϑ(p	ϑ(p	PROPN
ejpam-5837	264	8	)	)	PUNCT
ejpam-5837	264	9	∧	∧	PROPN
ejpam-5837	264	10	ξ(q	ξ(q	PROPN
ejpam-5837	264	11	)	)	PUNCT
ejpam-5837	264	12	}	}	PUNCT
ejpam-5837	265	1	=	=	SYM
ejpam-5837	265	2	̸	̸	NUM
ejpam-5837	265	3	0	0	NUM
ejpam-5837	266	1	it	it	PRON
ejpam-5837	266	2	is	be	AUX
ejpam-5837	266	3	a	a	DET
ejpam-5837	266	4	contradiction	contradiction	NOUN
ejpam-5837	266	5	so	so	SCONJ
ejpam-5837	266	6	ϑ	ϑ	ADJ
ejpam-5837	266	7	≤	≤	X
ejpam-5837	266	8	χb	χb	ADP
ejpam-5837	266	9	or	or	CCONJ
ejpam-5837	266	10	ξ	ξ	PRON
ejpam-5837	266	11	≤	≤	NOUN
ejpam-5837	267	1	χb	χb	PROPN
ejpam-5837	267	2	.	.	PUNCT
ejpam-5837	268	1	therefore	therefore	ADV
ejpam-5837	268	2	χb	χb	PROPN
ejpam-5837	268	3	is	be	AUX
ejpam-5837	268	4	a	a	DET
ejpam-5837	268	5	prime	prime	ADJ
ejpam-5837	268	6	fuzzy	fuzzy	NOUN
ejpam-5837	268	7	almost	almost	ADV
ejpam-5837	268	8	(	(	PUNCT
ejpam-5837	268	9	m	m	NOUN
ejpam-5837	268	10	,	,	PUNCT
ejpam-5837	268	11	n)quasi	n)quasi	NOUN
ejpam-5837	268	12	-	-	PUNCT
ejpam-5837	268	13	ideal	ideal	NOUN
ejpam-5837	268	14	of	of	ADP
ejpam-5837	268	15	t.	t.	NOUN
ejpam-5837	268	16	conversely	conversely	ADV
ejpam-5837	268	17	,	,	PUNCT
ejpam-5837	268	18	suppose	suppose	VERB
ejpam-5837	268	19	that	that	SCONJ
ejpam-5837	268	20	χb	χb	PROPN
ejpam-5837	268	21	is	be	AUX
ejpam-5837	268	22	a	a	DET
ejpam-5837	268	23	prime	prime	ADJ
ejpam-5837	268	24	fuzzy	fuzzy	NOUN
ejpam-5837	268	25	almost	almost	ADV
ejpam-5837	268	26	(	(	PUNCT
ejpam-5837	268	27	m	m	PROPN
ejpam-5837	268	28	,	,	PUNCT
ejpam-5837	268	29	n)-quasi	n)-quasi	NOUN
ejpam-5837	268	30	-	-	NOUN
ejpam-5837	268	31	ideal	ideal	NOUN
ejpam-5837	268	32	of	of	ADP
ejpam-5837	268	33	t.	t.	PROPN
ejpam-5837	268	34	then	then	ADV
ejpam-5837	268	35	χb	χb	PROPN
ejpam-5837	268	36	is	be	AUX
ejpam-5837	268	37	a	a	DET
ejpam-5837	268	38	fuzzy	fuzzy	ADJ
ejpam-5837	268	39	almost	almost	ADV
ejpam-5837	268	40	(	(	PUNCT
ejpam-5837	268	41	m	m	PROPN
ejpam-5837	268	42	,	,	PUNCT
ejpam-5837	268	43	n)-quasi	n)-quasi	NOUN
ejpam-5837	268	44	-	-	NOUN
ejpam-5837	268	45	ideal	ideal	NOUN
ejpam-5837	268	46	of	of	ADP
ejpam-5837	268	47	t.	t.	PROPN
ejpam-5837	268	48	thus	thus	ADV
ejpam-5837	268	49	by	by	ADP
ejpam-5837	268	50	theorem	theorem	NOUN
ejpam-5837	268	51	6	6	NUM
ejpam-5837	268	52	,	,	PUNCT
ejpam-5837	268	53	b	b	NOUN
ejpam-5837	268	54	is	be	AUX
ejpam-5837	268	55	an	an	DET
ejpam-5837	268	56	almost	almost	ADV
ejpam-5837	268	57	(	(	PUNCT
ejpam-5837	268	58	m	m	PROPN
ejpam-5837	268	59	,	,	PUNCT
ejpam-5837	268	60	n)quasi	n)quasi	NOUN
ejpam-5837	268	61	-	-	PUNCT
ejpam-5837	268	62	ideal	ideal	NOUN
ejpam-5837	268	63	of	of	ADP
ejpam-5837	268	64	t.	t.	PROPN
ejpam-5837	268	65	let	let	VERB
ejpam-5837	268	66	n	n	PRON
ejpam-5837	268	67	and	and	CCONJ
ejpam-5837	268	68	h	h	NOUN
ejpam-5837	268	69	be	be	AUX
ejpam-5837	268	70	almost	almost	ADV
ejpam-5837	268	71	(	(	PUNCT
ejpam-5837	268	72	m	m	PROPN
ejpam-5837	268	73	,	,	PUNCT
ejpam-5837	268	74	n)-quasi	n)-quasi	NOUN
ejpam-5837	268	75	-	-	NOUN
ejpam-5837	268	76	ideal	ideal	NOUN
ejpam-5837	268	77	of	of	ADP
ejpam-5837	268	78	t	t	PROPN
ejpam-5837	268	79	such	such	ADJ
ejpam-5837	268	80	that	that	SCONJ
ejpam-5837	268	81	nh	nh	PROPN
ejpam-5837	268	82	⊆	⊆	NUM
ejpam-5837	268	83	b.	b.	NOUN
ejpam-5837	268	84	then	then	ADV
ejpam-5837	268	85	χb	χb	PROPN
ejpam-5837	268	86	and	and	CCONJ
ejpam-5837	268	87	χh	χh	PROPN
ejpam-5837	268	88	are	be	AUX
ejpam-5837	268	89	fuzzy	fuzzy	ADJ
ejpam-5837	268	90	almost	almost	ADV
ejpam-5837	268	91	(	(	PUNCT
ejpam-5837	268	92	m	m	PROPN
ejpam-5837	268	93	,	,	PUNCT
ejpam-5837	268	94	n)-quasi	n)-quasi	NOUN
ejpam-5837	268	95	-	-	NOUN
ejpam-5837	268	96	ideals	ideal	NOUN
ejpam-5837	268	97	of	of	ADP
ejpam-5837	268	98	t.	t.	PROPN
ejpam-5837	268	99	by	by	ADP
ejpam-5837	268	100	lemma	lemma	PROPN
ejpam-5837	268	101	1	1	NUM
ejpam-5837	268	102	χn	χn	INTJ
ejpam-5837	268	103	◦	◦	VERB
ejpam-5837	268	104	χh	χh	X
ejpam-5837	268	105	=	=	PUNCT
ejpam-5837	268	106	χnh	χnh	PROPN
ejpam-5837	268	107	≤	≤	PUNCT
ejpam-5837	269	1	χb	χb	PROPN
ejpam-5837	269	2	.	.	PUNCT
ejpam-5837	270	1	by	by	ADP
ejpam-5837	270	2	assumption	assumption	NOUN
ejpam-5837	270	3	,	,	PUNCT
ejpam-5837	270	4	χn	χn	ADP
ejpam-5837	270	5	≤	≤	X
ejpam-5837	270	6	χb	χb	ADV
ejpam-5837	270	7	or	or	CCONJ
ejpam-5837	270	8	χb	χb	PRON
ejpam-5837	270	9	≤	≤	PROPN
ejpam-5837	270	10	χh	χh	NOUN
ejpam-5837	270	11	.	.	PUNCT
ejpam-5837	271	1	thus	thus	ADV
ejpam-5837	271	2	n	n	CCONJ
ejpam-5837	271	3	⊆	⊆	NUM
ejpam-5837	271	4	b	b	NOUN
ejpam-5837	271	5	or	or	CCONJ
ejpam-5837	271	6	h	h	PROPN
ejpam-5837	271	7	⊆	⊆	NUM
ejpam-5837	271	8	b.	b.	NOUN
ejpam-5837	272	1	we	we	PRON
ejpam-5837	272	2	conclude	conclude	VERB
ejpam-5837	272	3	that	that	SCONJ
ejpam-5837	272	4	b	b	PROPN
ejpam-5837	272	5	is	be	AUX
ejpam-5837	272	6	a	a	DET
ejpam-5837	272	7	prime	prime	NOUN
ejpam-5837	272	8	almost	almost	ADV
ejpam-5837	272	9	(	(	PUNCT
ejpam-5837	272	10	m	m	PROPN
ejpam-5837	272	11	,	,	PUNCT
ejpam-5837	272	12	n)-quasi	n)-quasi	NOUN
ejpam-5837	272	13	-	-	NOUN
ejpam-5837	272	14	ideal	ideal	NOUN
ejpam-5837	272	15	of	of	ADP
ejpam-5837	272	16	t.	t.	PROPN
ejpam-5837	272	17	p.	p.	PROPN
ejpam-5837	272	18	khamrot	khamrot	PROPN
ejpam-5837	272	19	et	et	PROPN
ejpam-5837	272	20	al	al	PROPN
ejpam-5837	272	21	.	.	PUNCT
ejpam-5837	272	22	/	/	SYM
ejpam-5837	272	23	eur	eur	PROPN
ejpam-5837	272	24	.	.	PUNCT
ejpam-5837	273	1	j.	j.	PROPN
ejpam-5837	273	2	pure	pure	PROPN
ejpam-5837	273	3	appl	appl	PROPN
ejpam-5837	273	4	.	.	PROPN
ejpam-5837	273	5	math	math	PROPN
ejpam-5837	273	6	,	,	PUNCT
ejpam-5837	273	7	18	18	NUM
ejpam-5837	273	8	(	(	PUNCT
ejpam-5837	273	9	2	2	NUM
ejpam-5837	273	10	)	)	PUNCT
ejpam-5837	273	11	(	(	PUNCT
ejpam-5837	273	12	2025	2025	NUM
ejpam-5837	273	13	)	)	PUNCT
ejpam-5837	273	14	,	,	PUNCT
ejpam-5837	273	15	5837	5837	NUM
ejpam-5837	273	16	11	11	NUM
ejpam-5837	273	17	of	of	ADP
ejpam-5837	273	18	13	13	NUM
ejpam-5837	273	19	theorem	theorem	VERB
ejpam-5837	273	20	10	10	NUM
ejpam-5837	273	21	.	.	PUNCT
ejpam-5837	274	1	let	let	VERB
ejpam-5837	274	2	b	b	X
ejpam-5837	274	3	be	be	AUX
ejpam-5837	274	4	a	a	DET
ejpam-5837	274	5	nonempty	nonempty	ADJ
ejpam-5837	274	6	subset	subset	NOUN
ejpam-5837	274	7	of	of	ADP
ejpam-5837	274	8	an	an	DET
ejpam-5837	274	9	ordered	order	VERB
ejpam-5837	274	10	semigroup	semigroup	NOUN
ejpam-5837	274	11	t.	t.	PROPN
ejpam-5837	274	12	then	then	ADV
ejpam-5837	274	13	b	b	PROPN
ejpam-5837	274	14	is	be	AUX
ejpam-5837	274	15	a	a	DET
ejpam-5837	274	16	semiprime	semiprime	NOUN
ejpam-5837	274	17	almost	almost	ADV
ejpam-5837	274	18	(	(	PUNCT
ejpam-5837	274	19	m	m	PROPN
ejpam-5837	274	20	,	,	PUNCT
ejpam-5837	274	21	n)-quasi	n)-quasi	NOUN
ejpam-5837	274	22	-	-	NOUN
ejpam-5837	274	23	ideal	ideal	NOUN
ejpam-5837	274	24	of	of	ADP
ejpam-5837	274	25	t	t	PROPN
ejpam-5837	275	1	if	if	SCONJ
ejpam-5837	275	2	and	and	CCONJ
ejpam-5837	275	3	only	only	ADV
ejpam-5837	275	4	if	if	SCONJ
ejpam-5837	275	5	χb	χb	PROPN
ejpam-5837	275	6	is	be	AUX
ejpam-5837	275	7	a	a	DET
ejpam-5837	275	8	semiprime	semiprime	NOUN
ejpam-5837	275	9	fuzzy	fuzzy	ADJ
ejpam-5837	275	10	almost	almost	ADV
ejpam-5837	275	11	(	(	PUNCT
ejpam-5837	275	12	m	m	PROPN
ejpam-5837	275	13	,	,	PUNCT
ejpam-5837	275	14	n)-quasi	n)-quasi	NOUN
ejpam-5837	275	15	-	-	NOUN
ejpam-5837	275	16	ideal	ideal	NOUN
ejpam-5837	275	17	of	of	ADP
ejpam-5837	275	18	t.	t.	NOUN
ejpam-5837	275	19	proof	proof	NOUN
ejpam-5837	275	20	.	.	PUNCT
ejpam-5837	276	1	suppose	suppose	VERB
ejpam-5837	276	2	that	that	SCONJ
ejpam-5837	276	3	b	b	PROPN
ejpam-5837	276	4	is	be	AUX
ejpam-5837	276	5	a	a	DET
ejpam-5837	276	6	semiprime	semiprime	NOUN
ejpam-5837	276	7	almost	almost	ADV
ejpam-5837	276	8	(	(	PUNCT
ejpam-5837	276	9	m	m	PROPN
ejpam-5837	276	10	,	,	PUNCT
ejpam-5837	276	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	276	12	-	-	NOUN
ejpam-5837	276	13	ideal	ideal	NOUN
ejpam-5837	276	14	of	of	ADP
ejpam-5837	276	15	t.	t.	PROPN
ejpam-5837	276	16	then	then	ADV
ejpam-5837	276	17	b	b	PROPN
ejpam-5837	276	18	is	be	AUX
ejpam-5837	276	19	an	an	DET
ejpam-5837	276	20	almost	almost	ADV
ejpam-5837	276	21	(	(	PUNCT
ejpam-5837	276	22	m	m	PROPN
ejpam-5837	276	23	,	,	PUNCT
ejpam-5837	276	24	n)-quasi	n)-quasi	NOUN
ejpam-5837	276	25	-	-	NOUN
ejpam-5837	276	26	ideal	ideal	NOUN
ejpam-5837	276	27	of	of	ADP
ejpam-5837	276	28	t.	t.	PROPN
ejpam-5837	276	29	thus	thus	ADV
ejpam-5837	276	30	by	by	ADP
ejpam-5837	276	31	theorem	theorem	NOUN
ejpam-5837	276	32	6	6	NUM
ejpam-5837	276	33	,	,	PUNCT
ejpam-5837	276	34	χb	χb	PROPN
ejpam-5837	276	35	is	be	AUX
ejpam-5837	276	36	a	a	DET
ejpam-5837	276	37	fuzzy	fuzzy	ADJ
ejpam-5837	276	38	almost	almost	ADV
ejpam-5837	276	39	(	(	PUNCT
ejpam-5837	276	40	m	m	NOUN
ejpam-5837	276	41	,	,	PUNCT
ejpam-5837	276	42	n)-quasiideal	n)-quasiideal	NOUN
ejpam-5837	276	43	of	of	ADP
ejpam-5837	276	44	t.	t.	PROPN
ejpam-5837	276	45	let	let	VERB
ejpam-5837	276	46	ϑ	ϑ	X
ejpam-5837	276	47	be	be	AUX
ejpam-5837	276	48	fuzzy	fuzzy	ADJ
ejpam-5837	276	49	almost	almost	ADV
ejpam-5837	276	50	(	(	PUNCT
ejpam-5837	276	51	m	m	PROPN
ejpam-5837	276	52	,	,	PUNCT
ejpam-5837	276	53	n)-quasi	n)-quasi	NOUN
ejpam-5837	276	54	-	-	PUNCT
ejpam-5837	276	55	ideal	ideal	NOUN
ejpam-5837	276	56	such	such	ADJ
ejpam-5837	276	57	that	that	SCONJ
ejpam-5837	276	58	ϑ	ϑ	X
ejpam-5837	276	59	◦	◦	NOUN
ejpam-5837	276	60	ϑ	ϑ	PRON
ejpam-5837	276	61	≤	≤	X
ejpam-5837	276	62	χb	χb	PROPN
ejpam-5837	276	63	.	.	PUNCT
ejpam-5837	277	1	assume	assume	VERB
ejpam-5837	277	2	that	that	SCONJ
ejpam-5837	277	3	ϑ	ϑ	PRON
ejpam-5837	277	4	≰	≰	PROPN
ejpam-5837	277	5	χb	χb	PROPN
ejpam-5837	277	6	.	.	PUNCT
ejpam-5837	278	1	then	then	ADV
ejpam-5837	278	2	there	there	PRON
ejpam-5837	278	3	exist	exist	VERB
ejpam-5837	278	4	h	h	NOUN
ejpam-5837	278	5	∈	∈	PROPN
ejpam-5837	278	6	t	t	NOUN
ejpam-5837	279	1	such	such	ADJ
ejpam-5837	279	2	that	that	PRON
ejpam-5837	279	3	ϑ(h	ϑ(h	NOUN
ejpam-5837	279	4	)	)	PUNCT
ejpam-5837	279	5	̸=	̸=	PROPN
ejpam-5837	279	6	0	0	NUM
ejpam-5837	279	7	.	.	PUNCT
ejpam-5837	280	1	while	while	SCONJ
ejpam-5837	280	2	χb(h	χb(h	NOUN
ejpam-5837	280	3	)	)	PUNCT
ejpam-5837	281	1	=	=	SYM
ejpam-5837	281	2	0	0	X
ejpam-5837	281	3	.	.	PUNCT
ejpam-5837	282	1	thus	thus	ADV
ejpam-5837	282	2	,	,	PUNCT
ejpam-5837	282	3	h	h	PROPN
ejpam-5837	282	4	∈	∈	PROPN
ejpam-5837	282	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	282	6	)	)	PUNCT
ejpam-5837	282	7	,	,	PUNCT
ejpam-5837	282	8	but	but	CCONJ
ejpam-5837	282	9	h	h	PROPN
ejpam-5837	282	10	/∈	/∈	PROPN
ejpam-5837	282	11	b.	b.	PROPN
ejpam-5837	283	1	so	so	ADV
ejpam-5837	283	2	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	283	3	)	)	PUNCT
ejpam-5837	283	4	⊈	⊈	PROPN
ejpam-5837	284	1	b.	b.	PROPN
ejpam-5837	284	2	since	since	SCONJ
ejpam-5837	284	3	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	284	4	)	)	PUNCT
ejpam-5837	284	5	are	be	AUX
ejpam-5837	284	6	almost	almost	ADV
ejpam-5837	284	7	(	(	PUNCT
ejpam-5837	284	8	m	m	PROPN
ejpam-5837	284	9	,	,	PUNCT
ejpam-5837	284	10	n)-quasi	n)-quasi	NOUN
ejpam-5837	284	11	-	-	NOUN
ejpam-5837	284	12	ideals	ideal	NOUN
ejpam-5837	284	13	of	of	ADP
ejpam-5837	284	14	t	t	NOUN
ejpam-5837	284	15	we	we	PRON
ejpam-5837	284	16	have	have	VERB
ejpam-5837	284	17	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	284	18	)	)	PUNCT
ejpam-5837	284	19	⊈	⊈	PROPN
ejpam-5837	285	1	b.	b.	PROPN
ejpam-5837	285	2	thus	thus	ADV
ejpam-5837	285	3	h	h	PROPN
ejpam-5837	285	4	∈	∈	PROPN
ejpam-5837	285	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	285	6	)	)	PUNCT
ejpam-5837	285	7	such	such	ADJ
ejpam-5837	285	8	that	that	SCONJ
ejpam-5837	285	9	m	m	PROPN
ejpam-5837	285	10	∈	∈	PROPN
ejpam-5837	285	11	b.	b.	NOUN
ejpam-5837	285	12	hence	hence	ADV
ejpam-5837	285	13	χb(m	χb(m	ADV
ejpam-5837	285	14	)	)	PUNCT
ejpam-5837	285	15	=	=	SYM
ejpam-5837	285	16	0	0	NUM
ejpam-5837	285	17	implies	imply	VERB
ejpam-5837	285	18	that	that	SCONJ
ejpam-5837	285	19	(	(	PUNCT
ejpam-5837	285	20	ϑ	ϑ	X
ejpam-5837	285	21	◦	◦	NOUN
ejpam-5837	285	22	ϑ)(m	ϑ)(m	ADJ
ejpam-5837	285	23	)	)	PUNCT
ejpam-5837	285	24	=	=	SYM
ejpam-5837	286	1	0	0	X
ejpam-5837	286	2	.	.	PUNCT
ejpam-5837	287	1	since	since	SCONJ
ejpam-5837	287	2	ϑ	ϑ	PRON
ejpam-5837	287	3	◦	◦	NOUN
ejpam-5837	287	4	ϑ	ϑ	PRON
ejpam-5837	287	5	≤	≤	ADJ
ejpam-5837	287	6	χb	χb	PROPN
ejpam-5837	287	7	.	.	PUNCT
ejpam-5837	288	1	we	we	PRON
ejpam-5837	288	2	have	have	VERB
ejpam-5837	288	3	p	p	PROPN
ejpam-5837	288	4	∈	∈	PROPN
ejpam-5837	288	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	288	6	)	)	PUNCT
ejpam-5837	288	7	.	.	PUNCT
ejpam-5837	289	1	thus	thus	ADV
ejpam-5837	289	2	ϑ(p	ϑ(p	X
ejpam-5837	289	3	)	)	PUNCT
ejpam-5837	289	4	̸=	̸=	PROPN
ejpam-5837	289	5	0	0	NUM
ejpam-5837	289	6	.	.	PUNCT
ejpam-5837	290	1	it	it	PRON
ejpam-5837	290	2	implies	imply	VERB
ejpam-5837	290	3	that	that	SCONJ
ejpam-5837	290	4	(	(	PUNCT
ejpam-5837	290	5	ϑ	ϑ	X
ejpam-5837	290	6	◦	◦	NOUN
ejpam-5837	290	7	ϑ)(m	ϑ)(m	NUM
ejpam-5837	290	8	)	)	PUNCT
ejpam-5837	290	9	=	=	SYM
ejpam-5837	291	1	∨	∨	X
ejpam-5837	291	2	(	(	PUNCT
ejpam-5837	291	3	p	p	X
ejpam-5837	291	4	,	,	PUNCT
ejpam-5837	291	5	b)∈fm	b)∈fm	PROPN
ejpam-5837	291	6	{	{	PUNCT
ejpam-5837	291	7	ϑ(p	ϑ(p	PROPN
ejpam-5837	291	8	)	)	PUNCT
ejpam-5837	291	9	∧	∧	NOUN
ejpam-5837	291	10	ϑ(b	ϑ(b	VERB
ejpam-5837	291	11	)	)	PUNCT
ejpam-5837	291	12	}	}	PUNCT
ejpam-5837	292	1	=	=	SYM
ejpam-5837	292	2	̸	̸	NUM
ejpam-5837	292	3	0	0	NUM
ejpam-5837	293	1	it	it	PRON
ejpam-5837	293	2	is	be	AUX
ejpam-5837	293	3	a	a	DET
ejpam-5837	293	4	contradiction	contradiction	NOUN
ejpam-5837	293	5	so	so	SCONJ
ejpam-5837	293	6	ϑ	ϑ	ADJ
ejpam-5837	293	7	≤	≤	ADV
ejpam-5837	294	1	χb	χb	PROPN
ejpam-5837	294	2	.	.	PUNCT
ejpam-5837	295	1	therefore	therefore	ADV
ejpam-5837	295	2	χb	χb	PROPN
ejpam-5837	295	3	is	be	AUX
ejpam-5837	295	4	a	a	DET
ejpam-5837	295	5	semiprime	semiprime	NOUN
ejpam-5837	295	6	fuzzy	fuzzy	ADJ
ejpam-5837	295	7	almost	almost	ADV
ejpam-5837	295	8	(	(	PUNCT
ejpam-5837	295	9	m	m	NOUN
ejpam-5837	295	10	,	,	PUNCT
ejpam-5837	295	11	n)-quasiideal	n)-quasiideal	NOUN
ejpam-5837	295	12	of	of	ADP
ejpam-5837	295	13	t.	t.	NOUN
ejpam-5837	295	14	conversely	conversely	ADV
ejpam-5837	295	15	,	,	PUNCT
ejpam-5837	295	16	suppose	suppose	VERB
ejpam-5837	295	17	that	that	SCONJ
ejpam-5837	295	18	χb	χb	PROPN
ejpam-5837	295	19	is	be	AUX
ejpam-5837	295	20	a	a	DET
ejpam-5837	295	21	semiprime	semiprime	NOUN
ejpam-5837	295	22	fuzzy	fuzzy	ADJ
ejpam-5837	295	23	almost	almost	ADV
ejpam-5837	295	24	(	(	PUNCT
ejpam-5837	295	25	m	m	PROPN
ejpam-5837	295	26	,	,	PUNCT
ejpam-5837	295	27	n)-quasi	n)-quasi	NOUN
ejpam-5837	295	28	-	-	NOUN
ejpam-5837	295	29	ideal	ideal	NOUN
ejpam-5837	295	30	of	of	ADP
ejpam-5837	295	31	t.	t.	PROPN
ejpam-5837	295	32	then	then	ADV
ejpam-5837	295	33	χb	χb	PROPN
ejpam-5837	295	34	is	be	AUX
ejpam-5837	295	35	a	a	DET
ejpam-5837	295	36	fuzzy	fuzzy	ADJ
ejpam-5837	295	37	almost	almost	ADV
ejpam-5837	295	38	(	(	PUNCT
ejpam-5837	295	39	m	m	PROPN
ejpam-5837	295	40	,	,	PUNCT
ejpam-5837	295	41	n)-quasi	n)-quasi	NOUN
ejpam-5837	295	42	-	-	NOUN
ejpam-5837	295	43	ideal	ideal	NOUN
ejpam-5837	295	44	of	of	ADP
ejpam-5837	295	45	t.	t.	PROPN
ejpam-5837	295	46	thus	thus	ADV
ejpam-5837	295	47	by	by	ADP
ejpam-5837	295	48	theorem	theorem	NOUN
ejpam-5837	295	49	6	6	NUM
ejpam-5837	295	50	,	,	PUNCT
ejpam-5837	295	51	b	b	NOUN
ejpam-5837	295	52	is	be	AUX
ejpam-5837	295	53	an	an	DET
ejpam-5837	295	54	almost	almost	ADV
ejpam-5837	295	55	(	(	PUNCT
ejpam-5837	295	56	m	m	PROPN
ejpam-5837	295	57	,	,	PUNCT
ejpam-5837	295	58	n)quasi	n)quasi	NOUN
ejpam-5837	295	59	-	-	PUNCT
ejpam-5837	295	60	ideal	ideal	NOUN
ejpam-5837	295	61	of	of	ADP
ejpam-5837	295	62	t.	t.	PROPN
ejpam-5837	295	63	let	let	VERB
ejpam-5837	295	64	n	n	PRON
ejpam-5837	295	65	be	be	AUX
ejpam-5837	295	66	almost	almost	ADV
ejpam-5837	295	67	(	(	PUNCT
ejpam-5837	295	68	m	m	PROPN
ejpam-5837	295	69	,	,	PUNCT
ejpam-5837	295	70	n)-quasi	n)-quasi	NOUN
ejpam-5837	295	71	-	-	NOUN
ejpam-5837	295	72	ideal	ideal	NOUN
ejpam-5837	295	73	of	of	ADP
ejpam-5837	295	74	t	t	PROPN
ejpam-5837	295	75	such	such	ADJ
ejpam-5837	295	76	that	that	DET
ejpam-5837	295	77	n2	n2	PROPN
ejpam-5837	295	78	⊆	⊆	NUM
ejpam-5837	295	79	b.	b.	NOUN
ejpam-5837	295	80	then	then	ADV
ejpam-5837	295	81	χn	χn	X
ejpam-5837	295	82	is	be	AUX
ejpam-5837	295	83	a	a	DET
ejpam-5837	295	84	fuzzy	fuzzy	ADJ
ejpam-5837	295	85	almost	almost	ADV
ejpam-5837	295	86	(	(	PUNCT
ejpam-5837	295	87	m	m	PROPN
ejpam-5837	295	88	,	,	PUNCT
ejpam-5837	295	89	n)-quasi	n)-quasi	NOUN
ejpam-5837	295	90	-	-	NOUN
ejpam-5837	295	91	ideal	ideal	NOUN
ejpam-5837	295	92	of	of	ADP
ejpam-5837	295	93	t.	t.	PROPN
ejpam-5837	295	94	by	by	ADP
ejpam-5837	295	95	lemma	lemma	PROPN
ejpam-5837	295	96	1	1	NUM
ejpam-5837	295	97	χn	χn	INTJ
ejpam-5837	295	98	◦	◦	NOUN
ejpam-5837	295	99	χn	χn	ADV
ejpam-5837	295	100	=	=	PUNCT
ejpam-5837	295	101	χn2	χn2	VERB
ejpam-5837	295	102	≤	≤	X
ejpam-5837	296	1	χb	χb	PRON
ejpam-5837	296	2	.	.	PUNCT
ejpam-5837	297	1	by	by	ADP
ejpam-5837	297	2	assumption	assumption	NOUN
ejpam-5837	297	3	,	,	PUNCT
ejpam-5837	297	4	χn	χn	ADP
ejpam-5837	297	5	≤	≤	ADV
ejpam-5837	297	6	χb	χb	PROPN
ejpam-5837	297	7	.	.	PUNCT
ejpam-5837	298	1	thus	thus	ADV
ejpam-5837	298	2	n	n	PROPN
ejpam-5837	298	3	⊆	⊆	NUM
ejpam-5837	298	4	b.	b.	NOUN
ejpam-5837	298	5	we	we	PRON
ejpam-5837	298	6	conclude	conclude	VERB
ejpam-5837	298	7	that	that	SCONJ
ejpam-5837	298	8	b	b	PROPN
ejpam-5837	298	9	is	be	AUX
ejpam-5837	298	10	a	a	DET
ejpam-5837	298	11	semiprime	semiprime	NOUN
ejpam-5837	298	12	almost	almost	ADV
ejpam-5837	298	13	(	(	PUNCT
ejpam-5837	298	14	m	m	PROPN
ejpam-5837	298	15	,	,	PUNCT
ejpam-5837	298	16	n)-quasi	n)-quasi	NOUN
ejpam-5837	298	17	-	-	NOUN
ejpam-5837	298	18	ideal	ideal	NOUN
ejpam-5837	298	19	of	of	ADP
ejpam-5837	298	20	t.	t.	PROPN
ejpam-5837	298	21	theorem	theorem	PROPN
ejpam-5837	298	22	11	11	NUM
ejpam-5837	298	23	.	.	PUNCT
ejpam-5837	299	1	let	let	VERB
ejpam-5837	299	2	b	b	X
ejpam-5837	299	3	be	be	AUX
ejpam-5837	299	4	a	a	DET
ejpam-5837	299	5	nonempty	nonempty	ADJ
ejpam-5837	299	6	subset	subset	NOUN
ejpam-5837	299	7	of	of	ADP
ejpam-5837	299	8	an	an	DET
ejpam-5837	299	9	ordered	order	VERB
ejpam-5837	299	10	semigroup	semigroup	NOUN
ejpam-5837	299	11	t.	t.	PROPN
ejpam-5837	299	12	then	then	ADV
ejpam-5837	299	13	b	b	PROPN
ejpam-5837	299	14	is	be	AUX
ejpam-5837	299	15	a	a	DET
ejpam-5837	299	16	strongly	strongly	ADV
ejpam-5837	299	17	prime	prime	NOUN
ejpam-5837	299	18	almost	almost	ADV
ejpam-5837	299	19	(	(	PUNCT
ejpam-5837	299	20	m	m	PROPN
ejpam-5837	299	21	,	,	PUNCT
ejpam-5837	299	22	n)-quasi	n)-quasi	NOUN
ejpam-5837	299	23	-	-	NOUN
ejpam-5837	299	24	ideal	ideal	NOUN
ejpam-5837	299	25	of	of	ADP
ejpam-5837	299	26	t	t	PROPN
ejpam-5837	300	1	if	if	SCONJ
ejpam-5837	300	2	and	and	CCONJ
ejpam-5837	300	3	only	only	ADV
ejpam-5837	300	4	if	if	SCONJ
ejpam-5837	300	5	χb	χb	PROPN
ejpam-5837	300	6	is	be	AUX
ejpam-5837	300	7	a	a	DET
ejpam-5837	300	8	fuzzy	fuzzy	ADJ
ejpam-5837	300	9	strongly	strongly	ADV
ejpam-5837	300	10	prime	prime	ADJ
ejpam-5837	300	11	almost	almost	ADV
ejpam-5837	300	12	(	(	PUNCT
ejpam-5837	300	13	m	m	PROPN
ejpam-5837	300	14	,	,	PUNCT
ejpam-5837	300	15	n)-quasi	n)-quasi	NOUN
ejpam-5837	300	16	-	-	NOUN
ejpam-5837	300	17	ideal	ideal	NOUN
ejpam-5837	300	18	of	of	ADP
ejpam-5837	300	19	t.	t.	NOUN
ejpam-5837	300	20	proof	proof	NOUN
ejpam-5837	300	21	.	.	PUNCT
ejpam-5837	301	1	suppose	suppose	VERB
ejpam-5837	301	2	thatb	thatb	NOUN
ejpam-5837	301	3	is	be	AUX
ejpam-5837	301	4	a	a	DET
ejpam-5837	301	5	strongly	strongly	ADV
ejpam-5837	301	6	prime	prime	NOUN
ejpam-5837	301	7	almost	almost	ADV
ejpam-5837	301	8	(	(	PUNCT
ejpam-5837	301	9	m	m	PROPN
ejpam-5837	301	10	,	,	PUNCT
ejpam-5837	301	11	n)-quasi	n)-quasi	NOUN
ejpam-5837	301	12	-	-	NOUN
ejpam-5837	301	13	ideal	ideal	NOUN
ejpam-5837	301	14	of	of	ADP
ejpam-5837	301	15	t.	t.	NOUN
ejpam-5837	301	16	thenb	thenb	NOUN
ejpam-5837	301	17	is	be	AUX
ejpam-5837	301	18	an	an	DET
ejpam-5837	301	19	almost	almost	ADV
ejpam-5837	301	20	(	(	PUNCT
ejpam-5837	301	21	m	m	PROPN
ejpam-5837	301	22	,	,	PUNCT
ejpam-5837	301	23	n)-quasi	n)-quasi	NOUN
ejpam-5837	301	24	-	-	NOUN
ejpam-5837	301	25	ideal	ideal	NOUN
ejpam-5837	301	26	of	of	ADP
ejpam-5837	301	27	t.	t.	PROPN
ejpam-5837	301	28	thus	thus	ADV
ejpam-5837	301	29	by	by	ADP
ejpam-5837	301	30	theorem	theorem	NOUN
ejpam-5837	301	31	6	6	NUM
ejpam-5837	301	32	,	,	PUNCT
ejpam-5837	301	33	χb	χb	PROPN
ejpam-5837	301	34	is	be	AUX
ejpam-5837	301	35	a	a	DET
ejpam-5837	301	36	fuzzy	fuzzy	ADJ
ejpam-5837	301	37	almost	almost	ADV
ejpam-5837	301	38	(	(	PUNCT
ejpam-5837	301	39	m	m	PROPN
ejpam-5837	301	40	,	,	PUNCT
ejpam-5837	301	41	n)-quasi	n)-quasi	NOUN
ejpam-5837	301	42	-	-	NOUN
ejpam-5837	301	43	ideal	ideal	NOUN
ejpam-5837	301	44	of	of	ADP
ejpam-5837	301	45	t.	t.	PROPN
ejpam-5837	301	46	let	let	VERB
ejpam-5837	301	47	ϑ	ϑ	X
ejpam-5837	301	48	and	and	CCONJ
ejpam-5837	301	49	ξ	ξ	PROPN
ejpam-5837	301	50	be	be	AUX
ejpam-5837	301	51	fuzzy	fuzzy	ADJ
ejpam-5837	301	52	almost	almost	ADV
ejpam-5837	301	53	(	(	PUNCT
ejpam-5837	301	54	m	m	PROPN
ejpam-5837	301	55	,	,	PUNCT
ejpam-5837	301	56	n)-quasi	n)-quasi	NOUN
ejpam-5837	301	57	-	-	NOUN
ejpam-5837	301	58	ideals	ideal	NOUN
ejpam-5837	301	59	of	of	ADP
ejpam-5837	301	60	t	t	NOUN
ejpam-5837	301	61	such	such	ADJ
ejpam-5837	301	62	that	that	PRON
ejpam-5837	301	63	(	(	PUNCT
ejpam-5837	301	64	ϑ	ϑ	X
ejpam-5837	301	65	◦	◦	NOUN
ejpam-5837	301	66	ξ)∧	ξ)∧	PROPN
ejpam-5837	301	67	(	(	PUNCT
ejpam-5837	301	68	ξ	ξ	X
ejpam-5837	301	69	◦	◦	NOUN
ejpam-5837	301	70	ϑ	ϑ	NOUN
ejpam-5837	301	71	)	)	PUNCT
ejpam-5837	301	72	≤	≤	NOUN
ejpam-5837	301	73	χb	χb	PROPN
ejpam-5837	301	74	.	.	PUNCT
ejpam-5837	301	75	assume	assume	VERB
ejpam-5837	301	76	that	that	SCONJ
ejpam-5837	301	77	ϑ	ϑ	X
ejpam-5837	301	78	≰	≰	PROPN
ejpam-5837	301	79	χb	χb	PROPN
ejpam-5837	301	80	and	and	CCONJ
ejpam-5837	301	81	ξ	ξ	PRON
ejpam-5837	301	82	≰	≰	PROPN
ejpam-5837	301	83	χb	χb	PROPN
ejpam-5837	301	84	.	.	PUNCT
ejpam-5837	302	1	then	then	ADV
ejpam-5837	302	2	there	there	PRON
ejpam-5837	302	3	exist	exist	VERB
ejpam-5837	302	4	h	h	NOUN
ejpam-5837	302	5	,	,	PUNCT
ejpam-5837	302	6	b	b	PROPN
ejpam-5837	302	7	∈	∈	PROPN
ejpam-5837	302	8	t	t	NOUN
ejpam-5837	302	9	such	such	ADJ
ejpam-5837	302	10	that	that	PRON
ejpam-5837	302	11	ϑ(h	ϑ(h	NOUN
ejpam-5837	302	12	)	)	PUNCT
ejpam-5837	302	13	̸=	̸=	PROPN
ejpam-5837	302	14	0	0	NUM
ejpam-5837	302	15	and	and	CCONJ
ejpam-5837	302	16	ξ(b	ξ(b	PROPN
ejpam-5837	302	17	)	)	PUNCT
ejpam-5837	302	18	̸=	̸=	PROPN
ejpam-5837	302	19	0	0	NUM
ejpam-5837	302	20	.	.	PUNCT
ejpam-5837	303	1	while	while	SCONJ
ejpam-5837	303	2	χb(h	χb(h	NOUN
ejpam-5837	303	3	)	)	PUNCT
ejpam-5837	303	4	=	=	SYM
ejpam-5837	303	5	0	0	NUM
ejpam-5837	303	6	and	and	CCONJ
ejpam-5837	303	7	χb(b	χb(b	NOUN
ejpam-5837	303	8	)	)	PUNCT
ejpam-5837	303	9	=	=	SYM
ejpam-5837	303	10	0	0	X
ejpam-5837	303	11	.	.	PUNCT
ejpam-5837	304	1	thus	thus	ADV
ejpam-5837	304	2	,	,	PUNCT
ejpam-5837	304	3	h	h	PROPN
ejpam-5837	304	4	∈	∈	PROPN
ejpam-5837	304	5	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	304	6	)	)	PUNCT
ejpam-5837	304	7	and	and	CCONJ
ejpam-5837	304	8	b	b	X
ejpam-5837	304	9	∈	∈	PROPN
ejpam-5837	304	10	supp(ξ	supp(ξ	PROPN
ejpam-5837	304	11	)	)	PUNCT
ejpam-5837	304	12	,	,	PUNCT
ejpam-5837	304	13	but	but	CCONJ
ejpam-5837	304	14	h	h	NOUN
ejpam-5837	304	15	,	,	PUNCT
ejpam-5837	304	16	b	b	PROPN
ejpam-5837	304	17	/∈	/∈	PROPN
ejpam-5837	304	18	b.	b.	PROPN
ejpam-5837	305	1	so	so	ADV
ejpam-5837	305	2	,	,	PUNCT
ejpam-5837	305	3	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	305	4	)	)	PUNCT
ejpam-5837	305	5	⊈	⊈	PROPN
ejpam-5837	306	1	b	b	PROPN
ejpam-5837	306	2	and	and	CCONJ
ejpam-5837	306	3	supp(ξ	supp(ξ	PROPN
ejpam-5837	306	4	)	)	PUNCT
ejpam-5837	306	5	⊈	⊈	PROPN
ejpam-5837	307	1	b.	b.	PROPN
ejpam-5837	307	2	hence	hence	ADV
ejpam-5837	307	3	,	,	PUNCT
ejpam-5837	307	4	there	there	PRON
ejpam-5837	307	5	exists	exist	VERB
ejpam-5837	307	6	m	m	VERB
ejpam-5837	307	7	∈	∈	PROPN
ejpam-5837	308	1	[	[	X
ejpam-5837	308	2	supp(ϑ	supp(ϑ	ADJ
ejpam-5837	308	3	)	)	PUNCT
ejpam-5837	308	4	supp(ξ)]∩	supp(ξ)]∩	PROPN
ejpam-5837	308	5	(	(	PUNCT
ejpam-5837	308	6	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	308	7	)	)	PUNCT
ejpam-5837	308	8	supp(ξ	supp(ξ	PROPN
ejpam-5837	308	9	)	)	PUNCT
ejpam-5837	308	10	)	)	PUNCT
ejpam-5837	308	11	such	such	ADJ
ejpam-5837	308	12	that	that	SCONJ
ejpam-5837	308	13	m	m	PROPN
ejpam-5837	308	14	/∈	/∈	PROPN
ejpam-5837	308	15	b.	b.	PROPN
ejpam-5837	309	1	thus	thus	ADV
ejpam-5837	309	2	,	,	PUNCT
ejpam-5837	309	3	χb(m	χb(m	ADV
ejpam-5837	309	4	)	)	PUNCT
ejpam-5837	310	1	=	=	SYM
ejpam-5837	311	1	0	0	X
ejpam-5837	311	2	.	.	PUNCT
ejpam-5837	312	1	since	since	SCONJ
ejpam-5837	312	2	m	m	PROPN
ejpam-5837	312	3	∈	∈	PROPN
ejpam-5837	312	4	supp(ϑ	supp(ϑ	PROPN
ejpam-5837	312	5	)	)	PUNCT
ejpam-5837	312	6	supp(ξ	supp(ξ	PROPN
ejpam-5837	312	7	)	)	PUNCT
ejpam-5837	312	8	and	and	CCONJ
ejpam-5837	312	9	m	m	PROPN
ejpam-5837	312	10	∈	∈	PROPN
ejpam-5837	312	11	supp(ξ	supp(ξ	PROPN
ejpam-5837	312	12	)	)	PUNCT
ejpam-5837	312	13	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	312	14	)	)	PUNCT
ejpam-5837	312	15	we	we	PRON
ejpam-5837	312	16	have	have	VERB
ejpam-5837	312	17	m	m	NOUN
ejpam-5837	312	18	=	=	ADJ
ejpam-5837	312	19	dk	dk	PROPN
ejpam-5837	312	20	and	and	CCONJ
ejpam-5837	312	21	m	m	PROPN
ejpam-5837	312	22	=	=	NOUN
ejpam-5837	312	23	gq	gq	VERB
ejpam-5837	312	24	for	for	ADP
ejpam-5837	312	25	some	some	DET
ejpam-5837	312	26	d	d	NOUN
ejpam-5837	312	27	,	,	PUNCT
ejpam-5837	312	28	q	q	PROPN
ejpam-5837	312	29	∈	∈	PROPN
ejpam-5837	312	30	supp(ϑ	supp(ϑ	NOUN
ejpam-5837	312	31	)	)	PUNCT
ejpam-5837	312	32	,	,	PUNCT
ejpam-5837	312	33	and	and	CCONJ
ejpam-5837	312	34	for	for	ADP
ejpam-5837	312	35	some	some	DET
ejpam-5837	312	36	k	k	NOUN
ejpam-5837	312	37	,	,	PUNCT
ejpam-5837	312	38	g	g	PROPN
ejpam-5837	312	39	∈	∈	PROPN
ejpam-5837	312	40	supp(ξ	supp(ξ	PROPN
ejpam-5837	312	41	)	)	PUNCT
ejpam-5837	312	42	.	.	PUNCT
ejpam-5837	313	1	we	we	PRON
ejpam-5837	313	2	have	have	VERB
ejpam-5837	313	3	(	(	PUNCT
ejpam-5837	313	4	ϑ	ϑ	X
ejpam-5837	313	5	◦	◦	NOUN
ejpam-5837	313	6	ξ)(m	ξ)(m	NUM
ejpam-5837	313	7	)	)	PUNCT
ejpam-5837	313	8	=	=	SYM
ejpam-5837	314	1	∨	∨	X
ejpam-5837	314	2	(	(	PUNCT
ejpam-5837	314	3	d	d	X
ejpam-5837	314	4	,	,	PUNCT
ejpam-5837	314	5	e)∈fm	e)∈fm	PROPN
ejpam-5837	314	6	{	{	PUNCT
ejpam-5837	314	7	ϑ(d	ϑ(d	NOUN
ejpam-5837	314	8	)	)	PUNCT
ejpam-5837	314	9	∧	∧	NOUN
ejpam-5837	314	10	ξp(k	ξp(k	NOUN
ejpam-5837	314	11	)	)	PUNCT
ejpam-5837	314	12	}	}	PUNCT
ejpam-5837	315	1	=	=	SYM
ejpam-5837	315	2	̸	̸	NUM
ejpam-5837	315	3	0	0	NOUN
ejpam-5837	315	4	.	.	PUNCT
ejpam-5837	316	1	similarly	similarly	ADV
ejpam-5837	316	2	(	(	PUNCT
ejpam-5837	316	3	ξ	ξ	X
ejpam-5837	316	4	◦	◦	NOUN
ejpam-5837	316	5	ϑ)(m	ϑ)(m	NUM
ejpam-5837	316	6	)	)	PUNCT
ejpam-5837	317	1	=	=	SYM
ejpam-5837	317	2	∨	∨	X
ejpam-5837	317	3	(	(	PUNCT
ejpam-5837	317	4	g	g	NOUN
ejpam-5837	317	5	,	,	PUNCT
ejpam-5837	317	6	q)∈fm	q)∈fm	PROPN
ejpam-5837	317	7	{	{	PUNCT
ejpam-5837	317	8	ξ(g	ξ(g	PROPN
ejpam-5837	317	9	)	)	PUNCT
ejpam-5837	317	10	∧	∧	PROPN
ejpam-5837	317	11	ϑ(q	ϑ(q	PROPN
ejpam-5837	317	12	)	)	PUNCT
ejpam-5837	317	13	}	}	PUNCT
ejpam-5837	317	14	.	.	PUNCT
ejpam-5837	318	1	p.	p.	NOUN
ejpam-5837	318	2	khamrot	khamrot	PROPN
ejpam-5837	319	1	et	et	PROPN
ejpam-5837	319	2	al	al	PROPN
ejpam-5837	319	3	.	.	PUNCT
ejpam-5837	319	4	/	/	SYM
ejpam-5837	319	5	eur	eur	PROPN
ejpam-5837	319	6	.	.	PUNCT
ejpam-5837	320	1	j.	j.	PROPN
ejpam-5837	320	2	pure	pure	PROPN
ejpam-5837	320	3	appl	appl	PROPN
ejpam-5837	320	4	.	.	PROPN
ejpam-5837	320	5	math	math	PROPN
ejpam-5837	320	6	,	,	PUNCT
ejpam-5837	320	7	18	18	NUM
ejpam-5837	320	8	(	(	PUNCT
ejpam-5837	320	9	2	2	NUM
ejpam-5837	320	10	)	)	PUNCT
ejpam-5837	320	11	(	(	PUNCT
ejpam-5837	320	12	2025	2025	NUM
ejpam-5837	320	13	)	)	PUNCT
ejpam-5837	320	14	,	,	PUNCT
ejpam-5837	320	15	5837	5837	NUM
ejpam-5837	320	16	12	12	NUM
ejpam-5837	320	17	of	of	ADP
ejpam-5837	320	18	13	13	NUM
ejpam-5837	321	1	so	so	ADV
ejpam-5837	321	2	(	(	PUNCT
ejpam-5837	321	3	ϑ	ϑ	X
ejpam-5837	321	4	◦	◦	NOUN
ejpam-5837	321	5	ξ)(m	ξ)(m	NUM
ejpam-5837	321	6	)	)	PUNCT
ejpam-5837	322	1	∧	∧	NOUN
ejpam-5837	322	2	(	(	PUNCT
ejpam-5837	322	3	ξ	ξ	X
ejpam-5837	322	4	◦	◦	NOUN
ejpam-5837	322	5	ϑ)(m	ϑ)(m	NUM
ejpam-5837	322	6	)	)	PUNCT
ejpam-5837	322	7	̸=	̸=	PROPN
ejpam-5837	322	8	0	0	NUM
ejpam-5837	322	9	.	.	PUNCT
ejpam-5837	323	1	it	it	PRON
ejpam-5837	323	2	is	be	AUX
ejpam-5837	323	3	a	a	DET
ejpam-5837	323	4	contradiction	contradiction	NOUN
ejpam-5837	323	5	so	so	ADV
ejpam-5837	323	6	,	,	PUNCT
ejpam-5837	323	7	ϑ	ϑ	X
ejpam-5837	323	8	≤	≤	X
ejpam-5837	323	9	χb	χb	ADP
ejpam-5837	323	10	or	or	CCONJ
ejpam-5837	323	11	ξ	ξ	PRON
ejpam-5837	323	12	≤	≤	NOUN
ejpam-5837	324	1	χb	χb	PROPN
ejpam-5837	324	2	.	.	PUNCT
ejpam-5837	325	1	therefore	therefore	ADV
ejpam-5837	325	2	,	,	PUNCT
ejpam-5837	325	3	χb	χb	PROPN
ejpam-5837	325	4	is	be	AUX
ejpam-5837	325	5	a	a	DET
ejpam-5837	325	6	fuzzy	fuzzy	ADJ
ejpam-5837	325	7	strongly	strongly	ADV
ejpam-5837	325	8	prime	prime	ADJ
ejpam-5837	325	9	almost	almost	ADV
ejpam-5837	325	10	(	(	PUNCT
ejpam-5837	325	11	m	m	PROPN
ejpam-5837	325	12	,	,	PUNCT
ejpam-5837	325	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	14	-	-	NOUN
ejpam-5837	325	15	ideal	ideal	NOUN
ejpam-5837	325	16	of	of	ADP
ejpam-5837	325	17	t.	t.	NOUN
ejpam-5837	325	18	conversely	conversely	ADV
ejpam-5837	325	19	,	,	PUNCT
ejpam-5837	325	20	suppose	suppose	VERB
ejpam-5837	325	21	that	that	SCONJ
ejpam-5837	325	22	χb	χb	PROPN
ejpam-5837	325	23	is	be	AUX
ejpam-5837	325	24	a	a	DET
ejpam-5837	325	25	fuzzy	fuzzy	ADJ
ejpam-5837	325	26	strongly	strongly	ADV
ejpam-5837	325	27	prime	prime	ADJ
ejpam-5837	325	28	almost	almost	ADV
ejpam-5837	325	29	(	(	PUNCT
ejpam-5837	325	30	m	m	PROPN
ejpam-5837	325	31	,	,	PUNCT
ejpam-5837	325	32	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	33	-	-	NOUN
ejpam-5837	325	34	ideal	ideal	NOUN
ejpam-5837	325	35	of	of	ADP
ejpam-5837	325	36	t.	t.	PROPN
ejpam-5837	325	37	then	then	ADV
ejpam-5837	325	38	χb	χb	PROPN
ejpam-5837	325	39	is	be	AUX
ejpam-5837	325	40	a	a	DET
ejpam-5837	325	41	fuzzy	fuzzy	ADJ
ejpam-5837	325	42	almost	almost	ADV
ejpam-5837	325	43	(	(	PUNCT
ejpam-5837	325	44	m	m	PROPN
ejpam-5837	325	45	,	,	PUNCT
ejpam-5837	325	46	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	47	-	-	NOUN
ejpam-5837	325	48	ideal	ideal	NOUN
ejpam-5837	325	49	of	of	ADP
ejpam-5837	325	50	t.	t.	PROPN
ejpam-5837	325	51	thus	thus	ADV
ejpam-5837	325	52	,	,	PUNCT
ejpam-5837	325	53	by	by	ADP
ejpam-5837	325	54	theorem	theorem	NOUN
ejpam-5837	325	55	6	6	NUM
ejpam-5837	325	56	,	,	PUNCT
ejpam-5837	325	57	b	b	NOUN
ejpam-5837	325	58	is	be	AUX
ejpam-5837	325	59	an	an	DET
ejpam-5837	325	60	almost	almost	ADV
ejpam-5837	325	61	(	(	PUNCT
ejpam-5837	325	62	m	m	PROPN
ejpam-5837	325	63	,	,	PUNCT
ejpam-5837	325	64	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	65	-	-	NOUN
ejpam-5837	325	66	ideal	ideal	NOUN
ejpam-5837	325	67	of	of	ADP
ejpam-5837	325	68	t.	t.	PROPN
ejpam-5837	325	69	let	let	VERB
ejpam-5837	325	70	n	n	PRON
ejpam-5837	325	71	and	and	CCONJ
ejpam-5837	325	72	h	h	NOUN
ejpam-5837	325	73	be	be	AUX
ejpam-5837	325	74	almost	almost	ADV
ejpam-5837	325	75	(	(	PUNCT
ejpam-5837	325	76	m	m	PROPN
ejpam-5837	325	77	,	,	PUNCT
ejpam-5837	325	78	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	79	-	-	NOUN
ejpam-5837	325	80	ideals	ideal	NOUN
ejpam-5837	325	81	of	of	ADP
ejpam-5837	325	82	t	t	NOUN
ejpam-5837	325	83	such	such	ADJ
ejpam-5837	325	84	that	that	DET
ejpam-5837	325	85	nh	nh	PROPN
ejpam-5837	325	86	∩	∩	NOUN
ejpam-5837	325	87	hn	hn	PROPN
ejpam-5837	325	88	≤	≤	PROPN
ejpam-5837	325	89	b.	b.	PROPN
ejpam-5837	325	90	then	then	ADV
ejpam-5837	325	91	χn	χn	X
ejpam-5837	325	92	and	and	CCONJ
ejpam-5837	325	93	χh	χh	PROPN
ejpam-5837	325	94	are	be	AUX
ejpam-5837	325	95	fuzzy	fuzzy	ADJ
ejpam-5837	325	96	almost	almost	ADV
ejpam-5837	325	97	(	(	PUNCT
ejpam-5837	325	98	m	m	PROPN
ejpam-5837	325	99	,	,	PUNCT
ejpam-5837	325	100	n)-quasi	n)-quasi	NOUN
ejpam-5837	325	101	-	-	NOUN
ejpam-5837	325	102	ideals	ideal	NOUN
ejpam-5837	325	103	of	of	ADP
ejpam-5837	325	104	t.	t.	PROPN
ejpam-5837	325	105	by	by	ADP
ejpam-5837	325	106	lemma	lemma	PROPN
ejpam-5837	326	1	1	1	NUM
ejpam-5837	326	2	χnh	χnh	PROPN
ejpam-5837	326	3	=	=	SYM
ejpam-5837	326	4	χn	χn	X
ejpam-5837	326	5	◦	◦	NOUN
ejpam-5837	326	6	χh	χh	NOUN
ejpam-5837	326	7	and	and	CCONJ
ejpam-5837	326	8	χhn	χhn	NOUN
ejpam-5837	326	9	=	=	SYM
ejpam-5837	326	10	χh	χh	PROPN
ejpam-5837	326	11	◦	◦	NOUN
ejpam-5837	326	12	χn	χn	NOUN
ejpam-5837	326	13	.	.	PUNCT
ejpam-5837	327	1	thus	thus	ADV
ejpam-5837	327	2	(	(	PUNCT
ejpam-5837	327	3	χn	χn	X
ejpam-5837	327	4	◦	◦	NOUN
ejpam-5837	327	5	χh)∧(χh	χh)∧(χh	NOUN
ejpam-5837	327	6	◦	◦	NOUN
ejpam-5837	327	7	χn	χn	NOUN
ejpam-5837	327	8	)	)	PUNCT
ejpam-5837	327	9	=	=	SYM
ejpam-5837	327	10	χnh∧χhn	χnh∧χhn	NOUN
ejpam-5837	327	11	=	=	NOUN
ejpam-5837	327	12	χnh∩hn	χnh∩hn	NOUN
ejpam-5837	327	13	≤	≤	PUNCT
ejpam-5837	327	14	χb	χb	PROPN
ejpam-5837	327	15	.	.	PUNCT
ejpam-5837	328	1	by	by	ADP
ejpam-5837	328	2	assumption	assumption	NOUN
ejpam-5837	328	3	,	,	PUNCT
ejpam-5837	328	4	χn	χn	ADP
ejpam-5837	328	5	≤	≤	X
ejpam-5837	328	6	χb	χb	PROPN
ejpam-5837	328	7	and	and	CCONJ
ejpam-5837	328	8	χn	χn	X
ejpam-5837	328	9	≤	≤	ADJ
ejpam-5837	328	10	χb	χb	PROPN
ejpam-5837	328	11	.	.	PUNCT
ejpam-5837	329	1	thus	thus	ADV
ejpam-5837	329	2	n	n	CCONJ
ejpam-5837	329	3	⊆	⊆	NUM
ejpam-5837	329	4	b	b	NOUN
ejpam-5837	329	5	or	or	CCONJ
ejpam-5837	329	6	h	h	PROPN
ejpam-5837	329	7	⊆	⊆	NUM
ejpam-5837	329	8	b.	b.	NOUN
ejpam-5837	330	1	we	we	PRON
ejpam-5837	330	2	conclude	conclude	VERB
ejpam-5837	330	3	that	that	SCONJ
ejpam-5837	330	4	b	b	PROPN
ejpam-5837	330	5	is	be	AUX
ejpam-5837	330	6	a	a	DET
ejpam-5837	330	7	strongly	strongly	ADV
ejpam-5837	330	8	prime	prime	NOUN
ejpam-5837	330	9	almost	almost	ADV
ejpam-5837	330	10	(	(	PUNCT
ejpam-5837	330	11	m	m	PROPN
ejpam-5837	330	12	,	,	PUNCT
ejpam-5837	330	13	n)-quasi	n)-quasi	NOUN
ejpam-5837	330	14	-	-	NOUN
ejpam-5837	330	15	ideal	ideal	NOUN
ejpam-5837	330	16	of	of	ADP
ejpam-5837	330	17	t.	t.	PROPN
ejpam-5837	330	18	4	4	NUM
ejpam-5837	330	19	.	.	PUNCT
ejpam-5837	330	20	conclusion	conclusion	NOUN
ejpam-5837	330	21	the	the	DET
ejpam-5837	330	22	aim	aim	NOUN
ejpam-5837	330	23	paper	paper	NOUN
ejpam-5837	330	24	gives	give	VERB
ejpam-5837	330	25	the	the	DET
ejpam-5837	330	26	concept	concept	NOUN
ejpam-5837	330	27	of	of	ADP
ejpam-5837	330	28	almost	almost	ADV
ejpam-5837	330	29	(	(	PUNCT
ejpam-5837	330	30	m	m	PROPN
ejpam-5837	330	31	,	,	PUNCT
ejpam-5837	330	32	n)-quasi	n)-quasi	NOUN
ejpam-5837	330	33	-	-	NOUN
ejpam-5837	330	34	ideals	ideal	NOUN
ejpam-5837	330	35	in	in	ADP
ejpam-5837	330	36	ordered	order	VERB
ejpam-5837	330	37	semigroups	semigroup	NOUN
ejpam-5837	330	38	.	.	PUNCT
ejpam-5837	331	1	the	the	DET
ejpam-5837	331	2	union	union	NOUN
ejpam-5837	331	3	of	of	ADP
ejpam-5837	331	4	two	two	NUM
ejpam-5837	331	5	almost	almost	ADV
ejpam-5837	331	6	(	(	PUNCT
ejpam-5837	331	7	m	m	PROPN
ejpam-5837	331	8	,	,	PUNCT
ejpam-5837	331	9	n)-quasi	n)-quasi	NOUN
ejpam-5837	331	10	-	-	PUNCT
ejpam-5837	331	11	ideals	ideal	NOUN
ejpam-5837	331	12	is	be	AUX
ejpam-5837	331	13	also	also	ADV
ejpam-5837	331	14	an	an	DET
ejpam-5837	331	15	almost	almost	ADV
ejpam-5837	331	16	(	(	PUNCT
ejpam-5837	331	17	m	m	PROPN
ejpam-5837	331	18	,	,	PUNCT
ejpam-5837	331	19	n)-quasi	n)-quasi	NOUN
ejpam-5837	331	20	-	-	NOUN
ejpam-5837	331	21	ideal	ideal	NOUN
ejpam-5837	331	22	in	in	ADP
ejpam-5837	331	23	ordered	order	VERB
ejpam-5837	331	24	semigroups	semigroup	NOUN
ejpam-5837	331	25	,	,	PUNCT
ejpam-5837	331	26	and	and	CCONJ
ejpam-5837	331	27	the	the	DET
ejpam-5837	331	28	results	result	NOUN
ejpam-5837	331	29	in	in	ADP
ejpam-5837	331	30	class	class	NOUN
ejpam-5837	331	31	fuzzifications	fuzzification	NOUN
ejpam-5837	331	32	are	be	AUX
ejpam-5837	331	33	the	the	DET
ejpam-5837	331	34	same	same	ADJ
ejpam-5837	331	35	.	.	PUNCT
ejpam-5837	332	1	in	in	ADP
ejpam-5837	332	2	theorems	theorem	NOUN
ejpam-5837	332	3	6	6	NUM
ejpam-5837	332	4	,	,	PUNCT
ejpam-5837	332	5	7	7	NUM
ejpam-5837	332	6	,	,	PUNCT
ejpam-5837	332	7	8	8	NUM
ejpam-5837	332	8	,	,	PUNCT
ejpam-5837	332	9	10	10	NUM
ejpam-5837	332	10	,	,	PUNCT
ejpam-5837	332	11	and	and	CCONJ
ejpam-5837	332	12	11	11	NUM
ejpam-5837	332	13	.	.	PUNCT
ejpam-5837	333	1	finally	finally	ADV
ejpam-5837	333	2	we	we	PRON
ejpam-5837	333	3	prove	prove	VERB
ejpam-5837	333	4	that	that	SCONJ
ejpam-5837	333	5	if	if	SCONJ
ejpam-5837	333	6	k	k	PROPN
ejpam-5837	333	7	is	be	AUX
ejpam-5837	333	8	a	a	DET
ejpam-5837	333	9	(	(	PUNCT
ejpam-5837	333	10	minimal/	minimal/	NUM
ejpam-5837	333	11	maximal	maximal	ADJ
ejpam-5837	333	12	/	/	SYM
ejpam-5837	333	13	prime	prime	ADJ
ejpam-5837	333	14	/	/	SYM
ejpam-5837	333	15	semiprime	semiprime	NOUN
ejpam-5837	333	16	/	/	SYM
ejpam-5837	333	17	strongly	strongly	ADV
ejpam-5837	333	18	prime	prime	NOUN
ejpam-5837	333	19	)	)	PUNCT
ejpam-5837	333	20	almost	almost	ADV
ejpam-5837	333	21	(	(	PUNCT
ejpam-5837	333	22	m	m	PROPN
ejpam-5837	333	23	,	,	PUNCT
ejpam-5837	333	24	n)-quasi	n)-quasi	NOUN
ejpam-5837	333	25	-	-	NOUN
ejpam-5837	333	26	ideals	ideal	NOUN
ejpam-5837	333	27	of	of	ADP
ejpam-5837	333	28	t	t	PROPN
ejpam-5837	333	29	if	if	SCONJ
ejpam-5837	333	30	and	and	CCONJ
ejpam-5837	333	31	only	only	ADV
ejpam-5837	333	32	if	if	SCONJ
ejpam-5837	333	33	χa	χa	PROPN
ejpam-5837	333	34	is	be	AUX
ejpam-5837	333	35	(	(	PUNCT
ejpam-5837	333	36	minimal/	minimal/	NUM
ejpam-5837	333	37	maximal	maximal	ADJ
ejpam-5837	333	38	/	/	SYM
ejpam-5837	333	39	prime	prime	ADJ
ejpam-5837	333	40	/	/	SYM
ejpam-5837	333	41	semiprime	semiprime	NOUN
ejpam-5837	333	42	strongly	strongly	ADV
ejpam-5837	333	43	prime	prime	ADJ
ejpam-5837	333	44	)	)	PUNCT
ejpam-5837	333	45	fuzzy	fuzzy	ADJ
ejpam-5837	333	46	almost	almost	ADV
ejpam-5837	333	47	(	(	PUNCT
ejpam-5837	333	48	m	m	PROPN
ejpam-5837	333	49	,	,	PUNCT
ejpam-5837	333	50	n)-quasi	n)-quasi	NOUN
ejpam-5837	333	51	-	-	NOUN
ejpam-5837	333	52	ideals	ideal	NOUN
ejpam-5837	333	53	of	of	ADP
ejpam-5837	333	54	t.	t.	PROPN
ejpam-5837	333	55	in	in	ADP
ejpam-5837	333	56	future	future	ADJ
ejpam-5837	333	57	work	work	NOUN
ejpam-5837	333	58	,	,	PUNCT
ejpam-5837	333	59	we	we	PRON
ejpam-5837	333	60	can	can	AUX
ejpam-5837	333	61	study	study	VERB
ejpam-5837	333	62	other	other	ADJ
ejpam-5837	333	63	kinds	kind	NOUN
ejpam-5837	333	64	of	of	ADP
ejpam-5837	333	65	almost	almost	ADV
ejpam-5837	333	66	ideals	ideal	NOUN
ejpam-5837	333	67	and	and	CCONJ
ejpam-5837	333	68	their	their	PRON
ejpam-5837	333	69	fuzzifications	fuzzification	NOUN
ejpam-5837	333	70	in	in	ADP
ejpam-5837	333	71	ordered	order	VERB
ejpam-5837	333	72	ternary	ternary	ADJ
ejpam-5837	333	73	semigroup	semigroup	NOUN
ejpam-5837	333	74	.	.	PUNCT
ejpam-5837	334	1	acknowledgements	acknowledgement	NOUN
ejpam-5837	334	2	this	this	DET
ejpam-5837	334	3	research	research	NOUN
ejpam-5837	334	4	was	be	AUX
ejpam-5837	334	5	supported	support	VERB
ejpam-5837	334	6	by	by	ADP
ejpam-5837	334	7	the	the	DET
ejpam-5837	334	8	school	school	NOUN
ejpam-5837	334	9	of	of	ADP
ejpam-5837	334	10	science	science	PROPN
ejpam-5837	334	11	university	university	PROPN
ejpam-5837	334	12	of	of	ADP
ejpam-5837	334	13	phayao	phayao	NOUN
ejpam-5837	334	14	.	.	PUNCT
ejpam-5837	335	1	references	reference	NOUN
ejpam-5837	335	2	[	[	X
ejpam-5837	335	3	1	1	NUM
ejpam-5837	335	4	]	]	X
ejpam-5837	335	5	o.	o.	NOUN
ejpam-5837	335	6	steinfeid	steinfeid	PROPN
ejpam-5837	335	7	.	.	PUNCT
ejpam-5837	336	1	uber	uber	PROPN
ejpam-5837	336	2	die	die	VERB
ejpam-5837	336	3	quasiidale	quasiidale	PROPN
ejpam-5837	336	4	von	von	PROPN
ejpam-5837	336	5	albgtuppen	albgtuppen	PROPN
ejpam-5837	336	6	.	.	PUNCT
ejpam-5837	337	1	publ	publ	PROPN
ejpam-5837	337	2	.	.	PUNCT
ejpam-5837	338	1	math	math	NOUN
ejpam-5837	338	2	.	.	PUNCT
ejpam-5837	339	1	debreecen	debreecen	PROPN
ejpam-5837	339	2	,	,	PUNCT
ejpam-5837	339	3	4:262–275	4:262–275	PROPN
ejpam-5837	339	4	,	,	PUNCT
ejpam-5837	339	5	1956	1956	NUM
ejpam-5837	339	6	.	.	PUNCT
ejpam-5837	340	1	[	[	X
ejpam-5837	340	2	2	2	NUM
ejpam-5837	340	3	]	]	X
ejpam-5837	340	4	l.a	l.a	PROPN
ejpam-5837	340	5	.	.	PROPN
ejpam-5837	340	6	zadeh	zadeh	PROPN
ejpam-5837	340	7	.	.	PUNCT
ejpam-5837	340	8	fuzzy	fuzzy	ADJ
ejpam-5837	340	9	sets	set	NOUN
ejpam-5837	340	10	.	.	PUNCT
ejpam-5837	341	1	information	information	NOUN
ejpam-5837	341	2	and	and	CCONJ
ejpam-5837	341	3	control	control	NOUN
ejpam-5837	341	4	,	,	PUNCT
ejpam-5837	341	5	8:338–353	8:338–353	NUM
ejpam-5837	341	6	,	,	PUNCT
ejpam-5837	341	7	1965	1965	NUM
ejpam-5837	341	8	.	.	PUNCT
ejpam-5837	342	1	[	[	X
ejpam-5837	342	2	3	3	X
ejpam-5837	342	3	]	]	X
ejpam-5837	342	4	l.	l.	NOUN
ejpam-5837	342	5	satko	satko	PROPN
ejpam-5837	342	6	and	and	CCONJ
ejpam-5837	342	7	o.	o.	NOUN
ejpam-5837	342	8	grosek	grosek	NOUN
ejpam-5837	342	9	.	.	PUNCT
ejpam-5837	343	1	on	on	ADP
ejpam-5837	343	2	minimal	minimal	ADJ
ejpam-5837	343	3	a	a	DET
ejpam-5837	343	4	-	-	PUNCT
ejpam-5837	343	5	ideals	ideal	NOUN
ejpam-5837	343	6	of	of	ADP
ejpam-5837	343	7	semigroups	semigroup	NOUN
ejpam-5837	343	8	.	.	PUNCT
ejpam-5837	344	1	semigroup	semigroup	PROPN
ejpam-5837	344	2	forum	forum	PROPN
ejpam-5837	344	3	,	,	PUNCT
ejpam-5837	344	4	23:283–295	23:283–295	PROPN
ejpam-5837	344	5	,	,	PUNCT
ejpam-5837	344	6	1981	1981	NUM
ejpam-5837	344	7	.	.	PUNCT
ejpam-5837	345	1	[	[	X
ejpam-5837	345	2	4	4	X
ejpam-5837	345	3	]	]	PUNCT
ejpam-5837	345	4	s.	s.	PROPN
ejpam-5837	345	5	bogdanovic	bogdanovic	PROPN
ejpam-5837	345	6	.	.	PUNCT
ejpam-5837	346	1	semigroups	semigroup	NOUN
ejpam-5837	346	2	in	in	ADP
ejpam-5837	346	3	which	which	PRON
ejpam-5837	346	4	some	some	DET
ejpam-5837	346	5	bi	bi	NOUN
ejpam-5837	346	6	-	-	NOUN
ejpam-5837	346	7	ideals	ideal	NOUN
ejpam-5837	346	8	is	be	AUX
ejpam-5837	346	9	a	a	DET
ejpam-5837	346	10	group	group	NOUN
ejpam-5837	346	11	.	.	PUNCT
ejpam-5837	347	1	review	review	NOUN
ejpam-5837	347	2	of	of	ADP
ejpam-5837	347	3	research	research	NOUN
ejpam-5837	347	4	faculty	faculty	NOUN
ejpam-5837	347	5	of	of	ADP
ejpam-5837	347	6	science	science	NOUN
ejpam-5837	347	7	-	-	PUNCT
ejpam-5837	347	8	university	university	NOUN
ejpam-5837	347	9	of	of	ADP
ejpam-5837	347	10	novi	novi	PROPN
ejpam-5837	347	11	sad	sad	PROPN
ejpam-5837	347	12	,	,	PUNCT
ejpam-5837	347	13	11:261–266	11:261–266	PROPN
ejpam-5837	347	14	,	,	PUNCT
ejpam-5837	347	15	1981	1981	NUM
ejpam-5837	347	16	.	.	PUNCT
ejpam-5837	348	1	[	[	X
ejpam-5837	348	2	5	5	X
ejpam-5837	348	3	]	]	PUNCT
ejpam-5837	348	4	k.	k.	PROPN
ejpam-5837	348	5	wattanatripop	wattanatripop	PROPN
ejpam-5837	348	6	s.	s.	PROPN
ejpam-5837	348	7	suebsung	suebsung	PROPN
ejpam-5837	348	8	and	and	CCONJ
ejpam-5837	348	9	r.	r.	PROPN
ejpam-5837	348	10	chinram	chinram	PROPN
ejpam-5837	348	11	.	.	PUNCT
ejpam-5837	349	1	on	on	ADP
ejpam-5837	349	2	almost	almost	ADV
ejpam-5837	349	3	(	(	PUNCT
ejpam-5837	349	4	m	m	NOUN
ejpam-5837	349	5	,	,	PUNCT
ejpam-5837	349	6	n)-ideals	n)-ideal	NOUN
ejpam-5837	349	7	and	and	CCONJ
ejpam-5837	349	8	fuzzy	fuzzy	ADJ
ejpam-5837	349	9	almost	almost	ADV
ejpam-5837	349	10	(	(	PUNCT
ejpam-5837	349	11	m	m	PROPN
ejpam-5837	349	12	,	,	PUNCT
ejpam-5837	349	13	n)-ideals	n)-ideal	NOUN
ejpam-5837	349	14	in	in	ADP
ejpam-5837	349	15	semigroups	semigroup	NOUN
ejpam-5837	349	16	.	.	PUNCT
ejpam-5837	350	1	journal	journal	PROPN
ejpam-5837	350	2	of	of	ADP
ejpam-5837	350	3	taibah	taibah	PROPN
ejpam-5837	350	4	universtiy	universtiy	PROPN
ejpam-5837	350	5	for	for	ADP
ejpam-5837	350	6	science	science	NOUN
ejpam-5837	350	7	,	,	PUNCT
ejpam-5837	350	8	13:897	13:897	NUM
ejpam-5837	350	9	–	–	PUNCT
ejpam-5837	350	10	902	902	NUM
ejpam-5837	350	11	,	,	PUNCT
ejpam-5837	350	12	2019	2019	NUM
ejpam-5837	350	13	.	.	PUNCT
ejpam-5837	351	1	[	[	X
ejpam-5837	351	2	6	6	NUM
ejpam-5837	351	3	]	]	PUNCT
ejpam-5837	351	4	t.	t.	PROPN
ejpam-5837	351	5	kaewnoi	kaewnoi	PROPN
ejpam-5837	351	6	n.	n.	PROPN
ejpam-5837	351	7	kaopusek	kaopusek	PROPN
ejpam-5837	351	8	and	and	CCONJ
ejpam-5837	351	9	r.	r.	PROPN
ejpam-5837	351	10	chinram	chinram	PROPN
ejpam-5837	351	11	.	.	PUNCT
ejpam-5837	352	1	on	on	ADP
ejpam-5837	352	2	almost	almost	ADV
ejpam-5837	352	3	interior	interior	ADJ
ejpam-5837	352	4	ideals	ideal	NOUN
ejpam-5837	352	5	and	and	CCONJ
ejpam-5837	352	6	weakly	weakly	ADJ
ejpam-5837	352	7	almost	almost	ADV
ejpam-5837	352	8	interior	interior	ADJ
ejpam-5837	352	9	ideals	ideal	NOUN
ejpam-5837	352	10	of	of	ADP
ejpam-5837	352	11	semigroups	semigroup	NOUN
ejpam-5837	352	12	.	.	PUNCT
ejpam-5837	353	1	journal	journal	NOUN
ejpam-5837	353	2	of	of	ADP
ejpam-5837	353	3	discrete	discrete	ADJ
ejpam-5837	353	4	mathematical	mathematical	ADJ
ejpam-5837	353	5	sciences	science	NOUN
ejpam-5837	353	6	and	and	CCONJ
ejpam-5837	353	7	cryptography	cryptography	NOUN
ejpam-5837	353	8	,	,	PUNCT
ejpam-5837	353	9	23(3):773–778	23(3):773–778	PROPN
ejpam-5837	353	10	,	,	PUNCT
ejpam-5837	353	11	2020	2020	NUM
ejpam-5837	353	12	.	.	PUNCT
ejpam-5837	354	1	[	[	X
ejpam-5837	354	2	7	7	X
ejpam-5837	354	3	]	]	PUNCT
ejpam-5837	354	4	t.	t.	NOUN
ejpam-5837	354	5	chuta	chuta	PROPN
ejpam-5837	354	6	p.	p.	PROPN
ejpam-5837	354	7	muangdoo	muangdoo	PROPN
ejpam-5837	354	8	and	and	CCONJ
ejpam-5837	354	9	w.nakkhasen	w.nakkhasen	VERB
ejpam-5837	354	10	.	.	PUNCT
ejpam-5837	355	1	almost	almost	ADV
ejpam-5837	355	2	bi	bi	NOUN
ejpam-5837	355	3	-	-	NOUN
ejpam-5837	355	4	hyperideals	hyperideal	NOUN
ejpam-5837	355	5	and	and	CCONJ
ejpam-5837	355	6	their	their	PRON
ejpam-5837	355	7	fuzzification	fuzzification	NOUN
ejpam-5837	355	8	of	of	ADP
ejpam-5837	355	9	semihypergroups	semihypergroup	NOUN
ejpam-5837	355	10	.	.	PUNCT
ejpam-5837	356	1	journal	journal	PROPN
ejpam-5837	356	2	of	of	ADP
ejpam-5837	356	3	mathematics	mathematics	PROPN
ejpam-5837	356	4	computre	computre	PROPN
ejpam-5837	356	5	science	science	NOUN
ejpam-5837	356	6	,	,	PUNCT
ejpam-5837	356	7	11(3):2755–2767	11(3):2755–2767	NUM
ejpam-5837	356	8	,	,	PUNCT
ejpam-5837	356	9	2021	2021	NUM
ejpam-5837	356	10	.	.	PUNCT
ejpam-5837	357	1	p.	p.	NOUN
ejpam-5837	357	2	khamrot	khamrot	PROPN
ejpam-5837	357	3	et	et	PROPN
ejpam-5837	357	4	al	al	PROPN
ejpam-5837	357	5	.	.	PUNCT
ejpam-5837	357	6	/	/	SYM
ejpam-5837	357	7	eur	eur	PROPN
ejpam-5837	357	8	.	.	PUNCT
ejpam-5837	358	1	j.	j.	PROPN
ejpam-5837	358	2	pure	pure	PROPN
ejpam-5837	358	3	appl	appl	PROPN
ejpam-5837	358	4	.	.	PROPN
ejpam-5837	358	5	math	math	PROPN
ejpam-5837	358	6	,	,	PUNCT
ejpam-5837	358	7	18	18	NUM
ejpam-5837	358	8	(	(	PUNCT
ejpam-5837	358	9	2	2	NUM
ejpam-5837	358	10	)	)	PUNCT
ejpam-5837	358	11	(	(	PUNCT
ejpam-5837	358	12	2025	2025	NUM
ejpam-5837	358	13	)	)	PUNCT
ejpam-5837	358	14	,	,	PUNCT
ejpam-5837	358	15	5837	5837	NUM
ejpam-5837	358	16	13	13	NUM
ejpam-5837	358	17	of	of	ADP
ejpam-5837	358	18	13	13	NUM
ejpam-5837	359	1	[	[	SYM
ejpam-5837	359	2	8	8	NUM
ejpam-5837	359	3	]	]	PUNCT
ejpam-5837	359	4	p.	p.	NOUN
ejpam-5837	359	5	khathipphathi	khathipphathi	PROPN
ejpam-5837	359	6	w.	w.	PROPN
ejpam-5837	359	7	nakkhasen	nakkhasen	PROPN
ejpam-5837	359	8	and	and	CCONJ
ejpam-5837	359	9	s.	s.	PROPN
ejpam-5837	359	10	panmuang	panmuang	PROPN
ejpam-5837	359	11	.	.	PUNCT
ejpam-5837	360	1	a	a	DET
ejpam-5837	360	2	note	note	NOUN
ejpam-5837	360	3	on	on	ADP
ejpam-5837	360	4	fuzzy	fuzzy	ADJ
ejpam-5837	360	5	almost	almost	ADV
ejpam-5837	360	6	interior	interior	ADJ
ejpam-5837	360	7	hyperideals	hyperideal	NOUN
ejpam-5837	360	8	of	of	ADP
ejpam-5837	360	9	semihypergroups	semihypergroup	NOUN
ejpam-5837	360	10	.	.	PUNCT
ejpam-5837	361	1	international	international	ADJ
ejpam-5837	361	2	journal	journal	PROPN
ejpam-5837	361	3	of	of	ADP
ejpam-5837	361	4	mathematics	mathematic	NOUN
ejpam-5837	361	5	and	and	CCONJ
ejpam-5837	361	6	computer	computer	NOUN
ejpam-5837	361	7	science	science	NOUN
ejpam-5837	361	8	,	,	PUNCT
ejpam-5837	361	9	17(3):1419–1426	17(3):1419–1426	NUM
ejpam-5837	361	10	,	,	PUNCT
ejpam-5837	361	11	2022	2022	NUM
ejpam-5837	361	12	.	.	PUNCT
ejpam-5837	362	1	[	[	X
ejpam-5837	362	2	9	9	NUM
ejpam-5837	362	3	]	]	PUNCT
ejpam-5837	362	4	w.	w.	PROPN
ejpam-5837	362	5	yonthanthum	yonthanthum	PROPN
ejpam-5837	362	6	s.	s.	PROPN
ejpam-5837	362	7	suebsung	suebsung	PROPN
ejpam-5837	362	8	and	and	CCONJ
ejpam-5837	362	9	r.	r.	PROPN
ejpam-5837	362	10	chinram	chinram	PROPN
ejpam-5837	362	11	.	.	PUNCT
ejpam-5837	363	1	ordered	order	VERB
ejpam-5837	363	2	almost	almost	ADV
ejpam-5837	363	3	ideals	ideal	NOUN
ejpam-5837	363	4	and	and	CCONJ
ejpam-5837	363	5	fuzzy	fuzzy	ADJ
ejpam-5837	363	6	ordered	order	VERB
ejpam-5837	363	7	almost	almost	ADV
ejpam-5837	363	8	ideals	ideal	NOUN
ejpam-5837	363	9	in	in	ADP
ejpam-5837	363	10	ordered	order	VERB
ejpam-5837	363	11	semigroups	semigroup	NOUN
ejpam-5837	363	12	.	.	PUNCT
ejpam-5837	364	1	italian	italian	ADJ
ejpam-5837	364	2	journal	journal	NOUN
ejpam-5837	364	3	of	of	ADP
ejpam-5837	364	4	pure	pure	ADJ
ejpam-5837	364	5	and	and	CCONJ
ejpam-5837	364	6	applied	applied	ADJ
ejpam-5837	364	7	mathematics	mathematic	NOUN
ejpam-5837	364	8	,	,	PUNCT
ejpam-5837	364	9	48:1206–1217	48:1206–1217	NUM
ejpam-5837	364	10	,	,	PUNCT
ejpam-5837	364	11	2022	2022	NUM
ejpam-5837	364	12	.	.	PUNCT
ejpam-5837	365	1	[	[	X
ejpam-5837	365	2	10	10	NUM
ejpam-5837	365	3	]	]	PUNCT
ejpam-5837	365	4	t.	t.	PROPN
ejpam-5837	365	5	gaketem	gaketem	PROPN
ejpam-5837	365	6	and	and	CCONJ
ejpam-5837	365	7	p.	p.	PROPN
ejpam-5837	365	8	khamrot	khamrot	PROPN
ejpam-5837	365	9	.	.	PUNCT
ejpam-5837	366	1	bipolar	bipolar	ADJ
ejpam-5837	366	2	fuzzy	fuzzy	ADJ
ejpam-5837	366	3	almost	almost	ADV
ejpam-5837	366	4	bi	bi	NOUN
ejpam-5837	366	5	-	-	NOUN
ejpam-5837	366	6	ideals	ideal	NOUN
ejpam-5837	366	7	in	in	ADP
ejpam-5837	366	8	semigroups	semigroup	NOUN
ejpam-5837	366	9	.	.	PUNCT
ejpam-5837	367	1	international	international	ADJ
ejpam-5837	367	2	journal	journal	NOUN
ejpam-5837	367	3	of	of	ADP
ejpam-5837	367	4	mathematics	mathematic	NOUN
ejpam-5837	367	5	and	and	CCONJ
ejpam-5837	367	6	computer	computer	NOUN
ejpam-5837	367	7	science	science	NOUN
ejpam-5837	367	8	,	,	PUNCT
ejpam-5837	367	9	17(1):345–352	17(1):345–352	NUM
ejpam-5837	367	10	,	,	PUNCT
ejpam-5837	367	11	2022	2022	NUM
ejpam-5837	367	12	.	.	PUNCT
ejpam-5837	368	1	[	[	X
ejpam-5837	368	2	11	11	NUM
ejpam-5837	368	3	]	]	PUNCT
ejpam-5837	368	4	a.	a.	NOUN
ejpam-5837	368	5	iampan	iampan	PROPN
ejpam-5837	368	6	r.	r.	PROPN
ejpam-5837	368	7	chinram	chinram	PROPN
ejpam-5837	368	8	,	,	PUNCT
ejpam-5837	368	9	a.	a.	NOUN
ejpam-5837	368	10	simuen	simuen	PROPN
ejpam-5837	368	11	and	and	CCONJ
ejpam-5837	368	12	p.	p.	NOUN
ejpam-5837	368	13	singavanda	singavanda	NOUN
ejpam-5837	368	14	.	.	PUNCT
ejpam-5837	369	1	on	on	ADP
ejpam-5837	369	2	almost	almost	ADV
ejpam-5837	369	3	(	(	PUNCT
ejpam-5837	369	4	m	m	NOUN
ejpam-5837	369	5	,	,	PUNCT
ejpam-5837	369	6	n)-quasiideals	n)-quasiideal	NOUN
ejpam-5837	369	7	of	of	ADP
ejpam-5837	369	8	semigroups	semigroup	NOUN
ejpam-5837	369	9	and	and	CCONJ
ejpam-5837	369	10	their	their	PRON
ejpam-5837	369	11	fuzzifications	fuzzification	NOUN
ejpam-5837	369	12	.	.	PUNCT
ejpam-5837	370	1	asia	asia	PROPN
ejpam-5837	370	2	pacific	pacific	PROPN
ejpam-5837	370	3	journal	journal	PROPN
ejpam-5837	370	4	of	of	ADP
ejpam-5837	370	5	mathematics	mathematic	NOUN
ejpam-5837	370	6	,	,	PUNCT
ejpam-5837	370	7	10(52):1–10	10(52):1–10	NUM
ejpam-5837	370	8	,	,	PUNCT
ejpam-5837	370	9	2023	2023	NUM
ejpam-5837	370	10	.	.	PUNCT
ejpam-5837	371	1	[	[	X
ejpam-5837	371	2	12	12	NUM
ejpam-5837	371	3	]	]	PUNCT
ejpam-5837	371	4	t.	t.	NOUN
ejpam-5837	371	5	gaketem	gaketem	PROPN
ejpam-5837	371	6	.	.	PUNCT
ejpam-5837	372	1	bipoalr	bipoalr	PROPN
ejpam-5837	372	2	almost	almost	ADV
ejpam-5837	372	3	interior	interior	ADJ
ejpam-5837	372	4	ideals	ideal	NOUN
ejpam-5837	372	5	in	in	ADP
ejpam-5837	372	6	semigroups	semigroup	NOUN
ejpam-5837	372	7	.	.	PUNCT
ejpam-5837	373	1	icic	icic	PROPN
ejpam-5837	373	2	express	express	PROPN
ejpam-5837	373	3	lettes	lette	NOUN
ejpam-5837	373	4	,	,	PUNCT
ejpam-5837	373	5	17(4):381–387	17(4):381–387	NOUN
ejpam-5837	373	6	,	,	PUNCT
ejpam-5837	373	7	2023	2023	NUM
ejpam-5837	373	8	.	.	PUNCT
ejpam-5837	374	1	[	[	X
ejpam-5837	374	2	13	13	NUM
ejpam-5837	374	3	]	]	PUNCT
ejpam-5837	374	4	p.	p.	NOUN
ejpam-5837	374	5	khamrot	khamrot	PROPN
ejpam-5837	374	6	and	and	CCONJ
ejpam-5837	374	7	t.	t.	PROPN
ejpam-5837	374	8	gaketem	gaketem	PROPN
ejpam-5837	374	9	.	.	PUNCT
ejpam-5837	375	1	applications	application	NOUN
ejpam-5837	375	2	of	of	ADP
ejpam-5837	375	3	bipolar	bipolar	ADJ
ejpam-5837	375	4	fuzzy	fuzzy	ADJ
ejpam-5837	375	5	almost	almost	ADV
ejpam-5837	375	6	ideals	ideal	NOUN
ejpam-5837	375	7	in	in	ADP
ejpam-5837	375	8	semigroups	semigroup	NOUN
ejpam-5837	375	9	.	.	PUNCT
ejpam-5837	376	1	international	international	ADJ
ejpam-5837	376	2	journal	journal	NOUN
ejpam-5837	376	3	of	of	ADP
ejpam-5837	376	4	analysis	analysis	NOUN
ejpam-5837	376	5	and	and	CCONJ
ejpam-5837	376	6	applications	application	NOUN
ejpam-5837	376	7	,	,	PUNCT
ejpam-5837	376	8	22(8):1–10	22(8):1–10	NUM
ejpam-5837	376	9	,	,	PUNCT
ejpam-5837	376	10	2024	2024	NUM
ejpam-5837	376	11	.	.	PUNCT
ejpam-5837	377	1	[	[	X
ejpam-5837	377	2	14	14	NUM
ejpam-5837	377	3	]	]	PUNCT
ejpam-5837	377	4	a.	a.	NOUN
ejpam-5837	377	5	iampan	iampan	PROPN
ejpam-5837	377	6	r.	r.	PROPN
ejpam-5837	377	7	chinram	chinram	PROPN
ejpam-5837	377	8	,	,	PUNCT
ejpam-5837	377	9	s.	s.	PROPN
ejpam-5837	377	10	baupradist	baupradist	PROPN
ejpam-5837	377	11	and	and	CCONJ
ejpam-5837	377	12	p.	p.	PROPN
ejpam-5837	377	13	singvananda	singvananda	PROPN
ejpam-5837	377	14	.	.	PUNCT
ejpam-5837	378	1	chracterizations	chracterization	NOUN
ejpam-5837	378	2	of	of	ADP
ejpam-5837	378	3	ordered	order	VERB
ejpam-5837	378	4	almost	almost	ADV
ejpam-5837	378	5	ideals	ideal	NOUN
ejpam-5837	378	6	and	and	CCONJ
ejpam-5837	378	7	fuzzifications	fuzzification	NOUN
ejpam-5837	378	8	in	in	ADP
ejpam-5837	378	9	partially	partially	ADV
ejpam-5837	378	10	ordered	order	VERB
ejpam-5837	378	11	ternary	ternary	ADJ
ejpam-5837	378	12	semigroups	semigroup	NOUN
ejpam-5837	378	13	.	.	PUNCT
ejpam-5837	379	1	icic	icic	PROPN
ejpam-5837	379	2	express	express	PROPN
ejpam-5837	379	3	lettes	lette	NOUN
ejpam-5837	379	4	,	,	PUNCT
ejpam-5837	379	5	17(6):631–639	17(6):631–639	PROPN
ejpam-5837	379	6	,	,	PUNCT
ejpam-5837	379	7	2023	2023	NUM
ejpam-5837	379	8	.	.	PUNCT
ejpam-5837	380	1	[	[	X
ejpam-5837	380	2	15	15	NUM
ejpam-5837	380	3	]	]	X
ejpam-5837	380	4	r.	r.	PROPN
ejpam-5837	380	5	chinram	chinram	PROPN
ejpam-5837	380	6	r.	r.	PROPN
ejpam-5837	380	7	rittichuai	rittichuai	PROPN
ejpam-5837	380	8	,	,	PUNCT
ejpam-5837	380	9	a.	a.	NOUN
ejpam-5837	380	10	iampan	iampan	NOUN
ejpam-5837	380	11	and	and	CCONJ
ejpam-5837	380	12	p.	p.	NOUN
ejpam-5837	380	13	singavanda	singavanda	NOUN
ejpam-5837	380	14	.	.	PUNCT
ejpam-5837	381	1	almost	almost	ADV
ejpam-5837	381	2	subsemirings	subsemiring	NOUN
ejpam-5837	381	3	and	and	CCONJ
ejpam-5837	381	4	fuzzificaion	fuzzificaion	NOUN
ejpam-5837	381	5	.	.	PUNCT
ejpam-5837	382	1	international	international	ADJ
ejpam-5837	382	2	journal	journal	PROPN
ejpam-5837	382	3	of	of	ADP
ejpam-5837	382	4	mathematics	mathematic	NOUN
ejpam-5837	382	5	and	and	CCONJ
ejpam-5837	382	6	computer	computer	NOUN
ejpam-5837	382	7	science	science	NOUN
ejpam-5837	382	8	,	,	PUNCT
ejpam-5837	382	9	17(4):1491–1497	17(4):1491–1497	NUM
ejpam-5837	382	10	,	,	PUNCT
ejpam-5837	382	11	2022	2022	NUM
ejpam-5837	382	12	.	.	PUNCT
ejpam-5837	383	1	[	[	X
ejpam-5837	383	2	16	16	NUM
ejpam-5837	383	3	]	]	X
ejpam-5837	383	4	r.	r.	PROPN
ejpam-5837	383	5	chinram	chinram	PROPN
ejpam-5837	383	6	n.	n.	PROPN
ejpam-5837	383	7	sarasit	sarasit	PROPN
ejpam-5837	383	8	and	and	CCONJ
ejpam-5837	383	9	a.	a.	NOUN
ejpam-5837	383	10	rattana	rattana	PROPN
ejpam-5837	383	11	.	.	PUNCT
ejpam-5837	384	1	applications	application	NOUN
ejpam-5837	384	2	of	of	ADP
ejpam-5837	384	3	fuzzy	fuzzy	ADJ
ejpam-5837	384	4	setes	sete	NOUN
ejpam-5837	384	5	for	for	ADP
ejpam-5837	384	6	almostity	almostity	NOUN
ejpam-5837	384	7	of	of	ADP
ejpam-5837	384	8	ternary	ternary	ADJ
ejpam-5837	384	9	subsemirings	subsemiring	NOUN
ejpam-5837	384	10	.	.	PUNCT
ejpam-5837	385	1	international	international	ADJ
ejpam-5837	385	2	journal	journal	NOUN
ejpam-5837	385	3	of	of	ADP
ejpam-5837	385	4	applied	apply	VERB
ejpam-5837	385	5	mathematics	mathematic	NOUN
ejpam-5837	385	6	,	,	PUNCT
ejpam-5837	385	7	17(4):497–507	17(4):497–507	NOUN
ejpam-5837	385	8	,	,	PUNCT
ejpam-5837	385	9	2023	2023	NUM
ejpam-5837	385	10	.	.	PUNCT
ejpam-5837	386	1	[	[	X
ejpam-5837	386	2	17	17	NUM
ejpam-5837	386	3	]	]	PUNCT
ejpam-5837	386	4	a.	a.	NOUN
ejpam-5837	386	5	iampan	iampan	PROPN
ejpam-5837	386	6	p.	p.	PROPN
ejpam-5837	386	7	khamrot	khamrot	PROPN
ejpam-5837	386	8	and	and	CCONJ
ejpam-5837	386	9	t.	t.	PROPN
ejpam-5837	386	10	gaketem	gaketem	PROPN
ejpam-5837	386	11	.	.	PUNCT
ejpam-5837	387	1	fuzzy	fuzzy	ADJ
ejpam-5837	387	2	(	(	PUNCT
ejpam-5837	387	3	m	m	NOUN
ejpam-5837	387	4	,	,	PUNCT
ejpam-5837	387	5	n)-ideals	n)-ideal	NOUN
ejpam-5837	387	6	and	and	CCONJ
ejpam-5837	387	7	n	n	CCONJ
ejpam-5837	387	8	-	-	PUNCT
ejpam-5837	387	9	interior	interior	ADJ
ejpam-5837	387	10	ideals	ideal	NOUN
ejpam-5837	387	11	in	in	ADP
ejpam-5837	387	12	ordered	order	VERB
ejpam-5837	387	13	semigroups	semigroup	NOUN
ejpam-5837	387	14	.	.	PUNCT
ejpam-5837	388	1	european	european	ADJ
ejpam-5837	388	2	journal	journal	PROPN
ejpam-5837	388	3	of	of	ADP
ejpam-5837	388	4	pure	pure	ADJ
ejpam-5837	388	5	and	and	CCONJ
ejpam-5837	388	6	appleid	appleid	ADJ
ejpam-5837	388	7	mathematics	mathematic	NOUN
ejpam-5837	388	8	,	,	PUNCT
ejpam-5837	388	9	18(1):1–12	18(1):1–12	NUM
ejpam-5837	388	10	,	,	PUNCT
ejpam-5837	388	11	2025	2025	NUM
ejpam-5837	388	12	.	.	PUNCT
ejpam-5837	389	1	[	[	X
ejpam-5837	389	2	18	18	NUM
ejpam-5837	389	3	]	]	PUNCT
ejpam-5837	389	4	a.	a.	NOUN
ejpam-5837	389	5	iampan	iampan	PROPN
ejpam-5837	389	6	p.	p.	PROPN
ejpam-5837	389	7	khamrot	khamrot	PROPN
ejpam-5837	389	8	and	and	CCONJ
ejpam-5837	389	9	t.	t.	PROPN
ejpam-5837	389	10	gaketem	gaketem	PROPN
ejpam-5837	389	11	.	.	PUNCT
ejpam-5837	390	1	bipolar	bipolar	ADJ
ejpam-5837	390	2	fuzzy	fuzzy	ADJ
ejpam-5837	390	3	(	(	PUNCT
ejpam-5837	390	4	m	m	NOUN
ejpam-5837	390	5	,	,	PUNCT
ejpam-5837	390	6	n)-ideals	n)-ideal	NOUN
ejpam-5837	390	7	and	and	CCONJ
ejpam-5837	390	8	n	n	CCONJ
ejpam-5837	390	9	-	-	ADJ
ejpam-5837	390	10	interior	interior	ADJ
ejpam-5837	390	11	ideals	ideal	NOUN
ejpam-5837	390	12	of	of	ADP
ejpam-5837	390	13	semigroups	semigroup	NOUN
ejpam-5837	390	14	.	.	PUNCT
ejpam-5837	391	1	iaeng	iaeng	PROPN
ejpam-5837	391	2	international	international	PROPN
ejpam-5837	391	3	journal	journal	PROPN
ejpam-5837	391	4	of	of	ADP
ejpam-5837	391	5	computer	computer	NOUN
ejpam-5837	391	6	science	science	NOUN
ejpam-5837	391	7	,	,	PUNCT
ejpam-5837	391	8	52(3):598	52(3):598	NUM
ejpam-5837	391	9	–	–	PUNCT
ejpam-5837	391	10	605	605	NUM
ejpam-5837	391	11	,	,	PUNCT
ejpam-5837	391	12	2025	2025	NUM
ejpam-5837	391	13	.	.	PUNCT
ejpam-5837	392	1	[	[	X
ejpam-5837	392	2	19	19	NUM
ejpam-5837	392	3	]	]	PUNCT
ejpam-5837	392	4	m.	m.	NOUN
ejpam-5837	392	5	al	al	PROPN
ejpam-5837	392	6	-	-	PUNCT
ejpam-5837	392	7	tahan	tahan	PROPN
ejpam-5837	392	8	a.	a.	NOUN
ejpam-5837	392	9	mahboob	mahboob	PROPN
ejpam-5837	392	10	and	and	CCONJ
ejpam-5837	392	11	g.	g.	PROPN
ejpam-5837	392	12	muhiuddin	muhiuddin	PROPN
ejpam-5837	392	13	.	.	PUNCT
ejpam-5837	393	1	characterizations	characterization	NOUN
ejpam-5837	393	2	of	of	ADP
ejpam-5837	393	3	ordered	order	VERB
ejpam-5837	393	4	semigroups	semigroup	NOUN
ejpam-5837	393	5	in	in	ADP
ejpam-5837	393	6	terms	term	NOUN
ejpam-5837	393	7	of	of	ADP
ejpam-5837	393	8	fuzzy	fuzzy	ADJ
ejpam-5837	393	9	(	(	PUNCT
ejpam-5837	393	10	m	m	PROPN
ejpam-5837	393	11	,	,	PUNCT
ejpam-5837	393	12	n)-substructures	n)-substructure	NOUN
ejpam-5837	393	13	.	.	NOUN
ejpam-5837	393	14	soft	soft	ADJ
ejpam-5837	393	15	computing	computing	NOUN
ejpam-5837	393	16	,	,	PUNCT
ejpam-5837	393	17	pages	page	NOUN
ejpam-5837	393	18	1–8	1–8	NUM
ejpam-5837	393	19	,	,	PUNCT
ejpam-5837	393	20	2024	2024	NUM
ejpam-5837	393	21	.	.	PUNCT
ejpam-5837	394	1	[	[	X
ejpam-5837	394	2	20	20	NUM
ejpam-5837	394	3	]	]	PUNCT
ejpam-5837	394	4	t.	t.	NOUN
ejpam-5837	394	5	changphas	changphas	PROPN
ejpam-5837	394	6	.	.	PUNCT
ejpam-5837	395	1	on	on	ADP
ejpam-5837	395	2	(	(	PUNCT
ejpam-5837	395	3	m	m	PROPN
ejpam-5837	395	4	,	,	PUNCT
ejpam-5837	395	5	n)-ideals	n)-ideal	NOUN
ejpam-5837	395	6	of	of	ADP
ejpam-5837	395	7	an	an	DET
ejpam-5837	395	8	ordered	order	VERB
ejpam-5837	395	9	semigroups	semigroup	NOUN
ejpam-5837	395	10	.	.	PUNCT
ejpam-5837	396	1	international	international	ADJ
ejpam-5837	396	2	journal	journal	NOUN
ejpam-5837	396	3	of	of	ADP
ejpam-5837	396	4	pure	pure	ADJ
ejpam-5837	396	5	and	and	CCONJ
ejpam-5837	396	6	applied	applied	ADJ
ejpam-5837	396	7	mathematics	mathematic	NOUN
ejpam-5837	396	8	,	,	PUNCT
ejpam-5837	396	9	100(1):1–5	100(1):1–5	NUM
ejpam-5837	396	10	,	,	PUNCT
ejpam-5837	396	11	2015	2015	NUM
ejpam-5837	396	12	.	.	PUNCT
ejpam-5837	397	1	[	[	X
ejpam-5837	397	2	21	21	NUM
ejpam-5837	397	3	]	]	X
ejpam-5837	397	4	r.	r.	PROPN
ejpam-5837	397	5	chinram	chinram	PROPN
ejpam-5837	397	6	s.	s.	PROPN
ejpam-5837	397	7	suebsung	suebsung	PROPN
ejpam-5837	397	8	,	,	PUNCT
ejpam-5837	397	9	k.	k.	PROPN
ejpam-5837	397	10	wattanatripop	wattanatripop	PROPN
ejpam-5837	397	11	.	.	PUNCT
ejpam-5837	398	1	a	a	DET
ejpam-5837	398	2	-	-	PUNCT
ejpam-5837	398	3	ideals	ideal	NOUN
ejpam-5837	398	4	and	and	CCONJ
ejpam-5837	398	5	fuzzy	fuzzy	ADJ
ejpam-5837	398	6	a	a	DET
ejpam-5837	398	7	-	-	PUNCT
ejpam-5837	398	8	ideals	ideal	NOUN
ejpam-5837	398	9	of	of	ADP
ejpam-5837	398	10	ternary	ternary	ADJ
ejpam-5837	398	11	semigroups	semigroup	NOUN
ejpam-5837	398	12	.	.	PUNCT
ejpam-5837	399	1	songklanakarin	songklanakarin	PROPN
ejpam-5837	399	2	journal	journal	PROPN
ejpam-5837	399	3	of	of	ADP
ejpam-5837	399	4	science	science	NOUN
ejpam-5837	399	5	and	and	CCONJ
ejpam-5837	399	6	technology	technology	NOUN
ejpam-5837	399	7	,	,	PUNCT
ejpam-5837	399	8	41(2):299–304	41(2):299–304	PROPN
ejpam-5837	399	9	,	,	PUNCT
ejpam-5837	399	10	2019	2019	NUM
ejpam-5837	399	11	.	.	PUNCT