id	sid	tid	token	lemma	pos
ejpam-6259	1	1	european	european	PROPN
ejpam-6259	1	2	journal	journal	PROPN
ejpam-6259	1	3	of	of	ADP
ejpam-6259	1	4	pure	pure	ADJ
ejpam-6259	1	5	and	and	CCONJ
ejpam-6259	1	6	applied	applied	ADJ
ejpam-6259	1	7	mathematics	mathematic	NOUN
ejpam-6259	1	8	2025	2025	NUM
ejpam-6259	1	9	,	,	PUNCT
ejpam-6259	1	10	vol	vol	NOUN
ejpam-6259	1	11	.	.	PROPN
ejpam-6259	1	12	18	18	NUM
ejpam-6259	1	13	,	,	PUNCT
ejpam-6259	1	14	issue	issue	NOUN
ejpam-6259	1	15	3	3	NUM
ejpam-6259	1	16	,	,	PUNCT
ejpam-6259	1	17	article	article	NOUN
ejpam-6259	1	18	number	number	NOUN
ejpam-6259	1	19	6259	6259	NUM
ejpam-6259	1	20	issn	issn	VERB
ejpam-6259	1	21	1307	1307	NUM
ejpam-6259	1	22	-	-	SYM
ejpam-6259	1	23	5543	5543	NUM
ejpam-6259	1	24	–	–	PUNCT
ejpam-6259	1	25	ejpam.com	ejpam.com	X
ejpam-6259	1	26	published	publish	VERB
ejpam-6259	1	27	by	by	ADP
ejpam-6259	1	28	new	new	PROPN
ejpam-6259	1	29	york	york	PROPN
ejpam-6259	1	30	business	business	PROPN
ejpam-6259	1	31	global	global	ADJ
ejpam-6259	1	32	almost	almost	ADV
ejpam-6259	1	33	n	n	CCONJ
ejpam-6259	1	34	-	-	PUNCT
ejpam-6259	1	35	ary	ary	NOUN
ejpam-6259	1	36	subsemigroups	subsemigroup	NOUN
ejpam-6259	1	37	and	and	CCONJ
ejpam-6259	1	38	fuzzy	fuzzy	ADJ
ejpam-6259	1	39	almost	almost	ADV
ejpam-6259	1	40	n	n	CCONJ
ejpam-6259	1	41	-	-	PUNCT
ejpam-6259	1	42	ary	ary	PROPN
ejpam-6259	1	43	subsemigroups	subsemigroup	NOUN
ejpam-6259	1	44	of	of	ADP
ejpam-6259	1	45	n	n	CCONJ
ejpam-6259	1	46	-	-	PUNCT
ejpam-6259	1	47	ary	ary	PROPN
ejpam-6259	1	48	semigroups	semigroups	PROPN
ejpam-6259	1	49	ronnason	ronnason	PROPN
ejpam-6259	1	50	chinram1	chinram1	PROPN
ejpam-6259	1	51	,	,	PUNCT
ejpam-6259	1	52	pattarawan	pattarawan	PROPN
ejpam-6259	1	53	singavananda2,∗	singavananda2,∗	VERB
ejpam-6259	1	54	1	1	NUM
ejpam-6259	1	55	division	division	NOUN
ejpam-6259	1	56	of	of	ADP
ejpam-6259	1	57	computational	computational	ADJ
ejpam-6259	1	58	science	science	NOUN
ejpam-6259	1	59	,	,	PUNCT
ejpam-6259	1	60	faculty	faculty	NOUN
ejpam-6259	1	61	of	of	ADP
ejpam-6259	1	62	science	science	NOUN
ejpam-6259	1	63	,	,	PUNCT
ejpam-6259	1	64	prince	prince	NOUN
ejpam-6259	1	65	of	of	ADP
ejpam-6259	1	66	songkla	songkla	PROPN
ejpam-6259	1	67	university	university	PROPN
ejpam-6259	1	68	,	,	PUNCT
ejpam-6259	1	69	hat	hat	PROPN
ejpam-6259	1	70	yai	yai	PROPN
ejpam-6259	1	71	,	,	PUNCT
ejpam-6259	1	72	songkhla	songkhla	VERB
ejpam-6259	1	73	90110	90110	NUM
ejpam-6259	1	74	,	,	PUNCT
ejpam-6259	1	75	thailand	thailand	PROPN
ejpam-6259	1	76	2	2	NUM
ejpam-6259	1	77	mathematics	mathematic	NOUN
ejpam-6259	1	78	program	program	NOUN
ejpam-6259	1	79	,	,	PUNCT
ejpam-6259	1	80	faculty	faculty	NOUN
ejpam-6259	1	81	of	of	ADP
ejpam-6259	1	82	science	science	NOUN
ejpam-6259	1	83	and	and	CCONJ
ejpam-6259	1	84	technology	technology	NOUN
ejpam-6259	1	85	,	,	PUNCT
ejpam-6259	1	86	songkhla	songkhla	VERB
ejpam-6259	1	87	rajabhat	rajabhat	ADJ
ejpam-6259	1	88	university	university	NOUN
ejpam-6259	1	89	,	,	PUNCT
ejpam-6259	1	90	songkhla	songkhla	NOUN
ejpam-6259	1	91	90000	90000	NUM
ejpam-6259	1	92	,	,	PUNCT
ejpam-6259	1	93	thailand	thailand	PROPN
ejpam-6259	1	94	abstract	abstract	PROPN
ejpam-6259	1	95	.	.	PUNCT
ejpam-6259	2	1	an	an	DET
ejpam-6259	2	2	n	n	NUM
ejpam-6259	2	3	-	-	PUNCT
ejpam-6259	2	4	ary	ary	PROPN
ejpam-6259	2	5	semigroup	semigroup	PROPN
ejpam-6259	2	6	is	be	AUX
ejpam-6259	2	7	a	a	DET
ejpam-6259	2	8	non	non	ADJ
ejpam-6259	2	9	-	-	ADJ
ejpam-6259	2	10	empty	empty	ADJ
ejpam-6259	2	11	set	set	NOUN
ejpam-6259	2	12	with	with	ADP
ejpam-6259	2	13	an	an	DET
ejpam-6259	2	14	associative	associative	ADJ
ejpam-6259	2	15	n	n	CCONJ
ejpam-6259	2	16	-	-	PUNCT
ejpam-6259	2	17	ary	ary	PROPN
ejpam-6259	2	18	operation	operation	NOUN
ejpam-6259	2	19	.	.	PUNCT
ejpam-6259	3	1	semigroups	semigroup	NOUN
ejpam-6259	3	2	and	and	CCONJ
ejpam-6259	3	3	ternary	ternary	ADJ
ejpam-6259	3	4	semigroups	semigroup	NOUN
ejpam-6259	3	5	are	be	AUX
ejpam-6259	3	6	special	special	ADJ
ejpam-6259	3	7	cases	case	NOUN
ejpam-6259	3	8	of	of	ADP
ejpam-6259	3	9	n	n	CCONJ
ejpam-6259	3	10	-	-	PUNCT
ejpam-6259	3	11	ary	ary	NOUN
ejpam-6259	3	12	semigroups	semigroup	NOUN
ejpam-6259	3	13	where	where	SCONJ
ejpam-6259	3	14	n	n	NOUN
ejpam-6259	3	15	=	=	SYM
ejpam-6259	3	16	2	2	NUM
ejpam-6259	3	17	and	and	CCONJ
ejpam-6259	3	18	n	n	NOUN
ejpam-6259	3	19	=	=	SYM
ejpam-6259	3	20	3	3	NUM
ejpam-6259	3	21	,	,	PUNCT
ejpam-6259	3	22	respectively	respectively	ADV
ejpam-6259	3	23	.	.	PUNCT
ejpam-6259	4	1	in	in	ADP
ejpam-6259	4	2	this	this	DET
ejpam-6259	4	3	study	study	NOUN
ejpam-6259	4	4	,	,	PUNCT
ejpam-6259	4	5	we	we	PRON
ejpam-6259	4	6	introduce	introduce	VERB
ejpam-6259	4	7	and	and	CCONJ
ejpam-6259	4	8	explore	explore	VERB
ejpam-6259	4	9	the	the	DET
ejpam-6259	4	10	notions	notion	NOUN
ejpam-6259	4	11	of	of	ADP
ejpam-6259	4	12	almost	almost	ADV
ejpam-6259	4	13	n	n	CCONJ
ejpam-6259	4	14	-	-	PUNCT
ejpam-6259	4	15	ary	ary	NOUN
ejpam-6259	4	16	subsemigroups	subsemigroup	NOUN
ejpam-6259	4	17	and	and	CCONJ
ejpam-6259	4	18	their	their	PRON
ejpam-6259	4	19	fuzzy	fuzzy	ADJ
ejpam-6259	4	20	counterparts	counterpart	NOUN
ejpam-6259	4	21	,	,	PUNCT
ejpam-6259	4	22	termed	term	VERB
ejpam-6259	4	23	fuzzy	fuzzy	ADJ
ejpam-6259	4	24	almost	almost	ADV
ejpam-6259	4	25	n	n	CCONJ
ejpam-6259	4	26	-	-	PUNCT
ejpam-6259	4	27	ary	ary	NOUN
ejpam-6259	4	28	subsemigroups	subsemigroup	NOUN
ejpam-6259	4	29	,	,	PUNCT
ejpam-6259	4	30	within	within	ADP
ejpam-6259	4	31	the	the	DET
ejpam-6259	4	32	framework	framework	NOUN
ejpam-6259	4	33	of	of	ADP
ejpam-6259	4	34	n	n	CCONJ
ejpam-6259	4	35	-	-	PUNCT
ejpam-6259	4	36	ary	ary	NOUN
ejpam-6259	4	37	semigroups	semigroup	NOUN
ejpam-6259	4	38	.	.	PUNCT
ejpam-6259	5	1	moreover	moreover	ADV
ejpam-6259	5	2	,	,	PUNCT
ejpam-6259	5	3	we	we	PRON
ejpam-6259	5	4	demonstrate	demonstrate	VERB
ejpam-6259	5	5	certain	certain	ADJ
ejpam-6259	5	6	relationships	relationship	NOUN
ejpam-6259	5	7	between	between	ADP
ejpam-6259	5	8	almost	almost	ADV
ejpam-6259	5	9	n	n	CCONJ
ejpam-6259	5	10	-	-	PUNCT
ejpam-6259	5	11	ary	ary	NOUN
ejpam-6259	5	12	subsemigroups	subsemigroup	NOUN
ejpam-6259	5	13	and	and	CCONJ
ejpam-6259	5	14	fuzzy	fuzzy	ADJ
ejpam-6259	5	15	almost	almost	ADV
ejpam-6259	5	16	n	n	CCONJ
ejpam-6259	5	17	-	-	PUNCT
ejpam-6259	5	18	ary	ary	PROPN
ejpam-6259	5	19	subsemigroups	subsemigroup	NOUN
ejpam-6259	5	20	.	.	PUNCT
ejpam-6259	6	1	2020	2020	NUM
ejpam-6259	6	2	mathematics	mathematic	NOUN
ejpam-6259	6	3	subject	subject	NOUN
ejpam-6259	6	4	classifications	classification	NOUN
ejpam-6259	6	5	:	:	PUNCT
ejpam-6259	6	6	20n15	20n15	NUM
ejpam-6259	6	7	,	,	PUNCT
ejpam-6259	6	8	03e72	03e72	X
ejpam-6259	6	9	key	key	ADJ
ejpam-6259	6	10	words	word	NOUN
ejpam-6259	6	11	and	and	CCONJ
ejpam-6259	6	12	phrases	phrase	NOUN
ejpam-6259	6	13	:	:	PUNCT
ejpam-6259	6	14	n	n	NUM
ejpam-6259	6	15	-	-	PUNCT
ejpam-6259	6	16	ary	ary	NOUN
ejpam-6259	6	17	semigroups	semigroup	NOUN
ejpam-6259	6	18	,	,	PUNCT
ejpam-6259	6	19	almost	almost	ADV
ejpam-6259	6	20	n	n	CCONJ
ejpam-6259	6	21	-	-	PUNCT
ejpam-6259	6	22	ary	ary	NOUN
ejpam-6259	6	23	subsemigroups	subsemigroup	NOUN
ejpam-6259	6	24	,	,	PUNCT
ejpam-6259	6	25	fuzzy	fuzzy	ADJ
ejpam-6259	6	26	almost	almost	ADV
ejpam-6259	6	27	n	n	CCONJ
ejpam-6259	6	28	-	-	PUNCT
ejpam-6259	6	29	ary	ary	PROPN
ejpam-6259	6	30	subsemigroups	subsemigroup	NOUN
ejpam-6259	6	31	,	,	PUNCT
ejpam-6259	6	32	minimal	minimal	ADJ
ejpam-6259	6	33	,	,	PUNCT
ejpam-6259	6	34	prime	prime	ADJ
ejpam-6259	6	35	,	,	PUNCT
ejpam-6259	6	36	semiprime	semiprime	NOUN
ejpam-6259	6	37	.	.	PUNCT
ejpam-6259	7	1	1	1	X
ejpam-6259	7	2	.	.	X
ejpam-6259	7	3	introduction	introduction	NOUN
ejpam-6259	7	4	a	a	DET
ejpam-6259	7	5	fuzzy	fuzzy	ADJ
ejpam-6259	7	6	subset	subset	NOUN
ejpam-6259	7	7	,	,	PUNCT
ejpam-6259	7	8	also	also	ADV
ejpam-6259	7	9	known	know	VERB
ejpam-6259	7	10	as	as	ADP
ejpam-6259	7	11	a	a	DET
ejpam-6259	7	12	fuzzy	fuzzy	ADJ
ejpam-6259	7	13	set	set	NOUN
ejpam-6259	7	14	,	,	PUNCT
ejpam-6259	7	15	is	be	AUX
ejpam-6259	7	16	a	a	DET
ejpam-6259	7	17	generalization	generalization	NOUN
ejpam-6259	7	18	of	of	ADP
ejpam-6259	7	19	the	the	DET
ejpam-6259	7	20	classical	classical	ADJ
ejpam-6259	7	21	set	set	NOUN
ejpam-6259	7	22	.	.	PUNCT
ejpam-6259	8	1	a	a	DET
ejpam-6259	8	2	fuzzy	fuzzy	ADJ
ejpam-6259	8	3	set	set	NOUN
ejpam-6259	8	4	is	be	AUX
ejpam-6259	8	5	represented	represent	VERB
ejpam-6259	8	6	by	by	ADP
ejpam-6259	8	7	a	a	DET
ejpam-6259	8	8	membership	membership	NOUN
ejpam-6259	8	9	function	function	NOUN
ejpam-6259	8	10	of	of	ADP
ejpam-6259	8	11	all	all	DET
ejpam-6259	8	12	elements	element	NOUN
ejpam-6259	8	13	in	in	ADP
ejpam-6259	8	14	a	a	DET
ejpam-6259	8	15	universal	universal	ADJ
ejpam-6259	8	16	set	set	NOUN
ejpam-6259	8	17	assigning	assign	VERB
ejpam-6259	8	18	values	value	NOUN
ejpam-6259	8	19	in	in	ADP
ejpam-6259	8	20	the	the	DET
ejpam-6259	8	21	closed	closed	ADJ
ejpam-6259	8	22	interval	interval	NOUN
ejpam-6259	8	23	[	[	X
ejpam-6259	8	24	0	0	NUM
ejpam-6259	8	25	,	,	PUNCT
ejpam-6259	8	26	1	1	NUM
ejpam-6259	8	27	]	]	PUNCT
ejpam-6259	8	28	.	.	PUNCT
ejpam-6259	9	1	the	the	DET
ejpam-6259	9	2	concept	concept	NOUN
ejpam-6259	9	3	of	of	ADP
ejpam-6259	9	4	fuzzy	fuzzy	ADJ
ejpam-6259	9	5	sets	set	NOUN
ejpam-6259	9	6	was	be	AUX
ejpam-6259	9	7	first	first	ADV
ejpam-6259	9	8	introduced	introduce	VERB
ejpam-6259	9	9	by	by	ADP
ejpam-6259	9	10	zadeh	zadeh	PROPN
ejpam-6259	10	1	[	[	X
ejpam-6259	10	2	1	1	X
ejpam-6259	10	3	]	]	PUNCT
ejpam-6259	10	4	in	in	ADP
ejpam-6259	10	5	1965	1965	NUM
ejpam-6259	10	6	.	.	PUNCT
ejpam-6259	11	1	zadeh	zadeh	PROPN
ejpam-6259	11	2	’s	’s	PART
ejpam-6259	11	3	pioneering	pioneer	VERB
ejpam-6259	11	4	ideas	idea	NOUN
ejpam-6259	11	5	have	have	AUX
ejpam-6259	11	6	found	find	VERB
ejpam-6259	11	7	widespread	widespread	ADJ
ejpam-6259	11	8	applications	application	NOUN
ejpam-6259	11	9	across	across	ADP
ejpam-6259	11	10	various	various	ADJ
ejpam-6259	11	11	fields	field	NOUN
ejpam-6259	11	12	,	,	PUNCT
ejpam-6259	11	13	including	include	VERB
ejpam-6259	11	14	mathematics	mathematic	NOUN
ejpam-6259	11	15	,	,	PUNCT
ejpam-6259	11	16	computer	computer	NOUN
ejpam-6259	11	17	science	science	NOUN
ejpam-6259	11	18	,	,	PUNCT
ejpam-6259	11	19	and	and	CCONJ
ejpam-6259	11	20	engineering	engineering	NOUN
ejpam-6259	11	21	.	.	PUNCT
ejpam-6259	12	1	the	the	DET
ejpam-6259	12	2	concept	concept	NOUN
ejpam-6259	12	3	of	of	ADP
ejpam-6259	12	4	fuzzy	fuzzy	ADJ
ejpam-6259	12	5	sets	set	NOUN
ejpam-6259	12	6	has	have	AUX
ejpam-6259	12	7	been	be	AUX
ejpam-6259	12	8	extensively	extensively	ADV
ejpam-6259	12	9	applied	apply	VERB
ejpam-6259	12	10	in	in	ADP
ejpam-6259	12	11	the	the	DET
ejpam-6259	12	12	study	study	NOUN
ejpam-6259	12	13	of	of	ADP
ejpam-6259	12	14	various	various	ADJ
ejpam-6259	12	15	algebraic	algebraic	ADJ
ejpam-6259	12	16	structures	structure	NOUN
ejpam-6259	12	17	.	.	PUNCT
ejpam-6259	13	1	the	the	DET
ejpam-6259	13	2	generalization	generalization	NOUN
ejpam-6259	13	3	of	of	ADP
ejpam-6259	13	4	binary	binary	PROPN
ejpam-6259	13	5	algebraic	algebraic	PROPN
ejpam-6259	13	6	structures	structure	NOUN
ejpam-6259	13	7	to	to	ADP
ejpam-6259	13	8	n	n	CCONJ
ejpam-6259	13	9	-	-	PUNCT
ejpam-6259	13	10	ary	ary	PROPN
ejpam-6259	13	11	structures	structure	NOUN
ejpam-6259	13	12	was	be	AUX
ejpam-6259	13	13	first	first	ADV
ejpam-6259	13	14	initiated	initiate	VERB
ejpam-6259	13	15	by	by	ADP
ejpam-6259	13	16	kasner	kasner	NOUN
ejpam-6259	13	17	[	[	X
ejpam-6259	13	18	2	2	NUM
ejpam-6259	13	19	]	]	PUNCT
ejpam-6259	13	20	in	in	ADP
ejpam-6259	13	21	1904	1904	NUM
ejpam-6259	13	22	.	.	PUNCT
ejpam-6259	14	1	in	in	ADP
ejpam-6259	14	2	this	this	DET
ejpam-6259	14	3	paper	paper	NOUN
ejpam-6259	14	4	,	,	PUNCT
ejpam-6259	14	5	we	we	PRON
ejpam-6259	14	6	focus	focus	VERB
ejpam-6259	14	7	on	on	ADP
ejpam-6259	14	8	n	n	CCONJ
ejpam-6259	14	9	-	-	PUNCT
ejpam-6259	14	10	ary	ary	NOUN
ejpam-6259	14	11	semigroups	semigroup	NOUN
ejpam-6259	14	12	.	.	PUNCT
ejpam-6259	15	1	notably	notably	ADV
ejpam-6259	15	2	,	,	PUNCT
ejpam-6259	15	3	semigroups	semigroup	NOUN
ejpam-6259	15	4	and	and	CCONJ
ejpam-6259	15	5	ternary	ternary	ADJ
ejpam-6259	15	6	semigroups	semigroup	NOUN
ejpam-6259	15	7	arise	arise	VERB
ejpam-6259	15	8	as	as	ADP
ejpam-6259	15	9	special	special	ADJ
ejpam-6259	15	10	cases	case	NOUN
ejpam-6259	15	11	of	of	ADP
ejpam-6259	15	12	n	n	CCONJ
ejpam-6259	15	13	-	-	PUNCT
ejpam-6259	15	14	ary	ary	NOUN
ejpam-6259	15	15	semigroups	semigroup	NOUN
ejpam-6259	15	16	for	for	ADP
ejpam-6259	15	17	n	n	NOUN
ejpam-6259	15	18	=	=	SYM
ejpam-6259	15	19	2	2	NUM
ejpam-6259	15	20	and	and	CCONJ
ejpam-6259	15	21	n	n	NOUN
ejpam-6259	15	22	=	=	SYM
ejpam-6259	15	23	3	3	NUM
ejpam-6259	15	24	,	,	PUNCT
ejpam-6259	15	25	respectively	respectively	ADV
ejpam-6259	15	26	.	.	PUNCT
ejpam-6259	16	1	the	the	DET
ejpam-6259	16	2	notion	notion	NOUN
ejpam-6259	16	3	of	of	ADP
ejpam-6259	16	4	n	n	CCONJ
ejpam-6259	16	5	-	-	PUNCT
ejpam-6259	16	6	ary	ary	PROPN
ejpam-6259	16	7	semigroups	semigroup	NOUN
ejpam-6259	16	8	has	have	VERB
ejpam-6259	16	9	its	its	PRON
ejpam-6259	16	10	origins	origin	NOUN
ejpam-6259	16	11	in	in	ADP
ejpam-6259	16	12	the	the	DET
ejpam-6259	16	13	investigation	investigation	NOUN
ejpam-6259	16	14	of	of	ADP
ejpam-6259	16	15	algebraic	algebraic	ADJ
ejpam-6259	16	16	structures	structure	NOUN
ejpam-6259	16	17	that	that	PRON
ejpam-6259	16	18	extend	extend	VERB
ejpam-6259	16	19	the	the	DET
ejpam-6259	16	20	classical	classical	ADJ
ejpam-6259	16	21	frameworks	framework	NOUN
ejpam-6259	16	22	of	of	ADP
ejpam-6259	16	23	semigroups	semigroup	NOUN
ejpam-6259	16	24	and	and	CCONJ
ejpam-6259	16	25	ternary	ternary	ADJ
ejpam-6259	16	26	semigroups	semigroup	NOUN
ejpam-6259	16	27	.	.	PUNCT
ejpam-6259	17	1	however	however	ADV
ejpam-6259	17	2	,	,	PUNCT
ejpam-6259	17	3	an	an	DET
ejpam-6259	17	4	n	n	CCONJ
ejpam-6259	17	5	-	-	PUNCT
ejpam-6259	17	6	ary	ary	PROPN
ejpam-6259	17	7	semigroup	semigroup	PROPN
ejpam-6259	17	8	does	do	AUX
ejpam-6259	17	9	not	not	PART
ejpam-6259	17	10	necessarily	necessarily	ADV
ejpam-6259	17	11	reduce	reduce	VERB
ejpam-6259	17	12	to	to	ADP
ejpam-6259	17	13	a	a	DET
ejpam-6259	17	14	semigroup	semigroup	NOUN
ejpam-6259	17	15	or	or	CCONJ
ejpam-6259	17	16	a	a	DET
ejpam-6259	17	17	ternary	ternary	ADJ
ejpam-6259	17	18	∗corresponding	∗corresponding	NOUN
ejpam-6259	17	19	author	author	NOUN
ejpam-6259	17	20	.	.	PUNCT
ejpam-6259	18	1	doi	doi	NOUN
ejpam-6259	18	2	:	:	PUNCT
ejpam-6259	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6259	https://doi.org/10.29020/nybg.ejpam.v18i3.6259	ADJ
ejpam-6259	18	4	email	email	NOUN
ejpam-6259	18	5	addresses	address	NOUN
ejpam-6259	18	6	:	:	PUNCT
ejpam-6259	18	7	ronnason.c@psu.ac.th	ronnason.c@psu.ac.th	PROPN
ejpam-6259	18	8	(	(	PUNCT
ejpam-6259	18	9	r.	r.	PROPN
ejpam-6259	18	10	chinram	chinram	PROPN
ejpam-6259	18	11	)	)	PUNCT
ejpam-6259	18	12	,	,	PUNCT
ejpam-6259	18	13	pattarawan.pe@skru.ac.th	pattarawan.pe@skru.ac.th	INTJ
ejpam-6259	18	14	(	(	PUNCT
ejpam-6259	18	15	p.	p.	NOUN
ejpam-6259	18	16	singavananda	singavananda	NOUN
ejpam-6259	18	17	)	)	PUNCT
ejpam-6259	18	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6259	19	1	1	1	NUM
ejpam-6259	19	2	copyright	copyright	NOUN
ejpam-6259	19	3	:	:	PUNCT
ejpam-6259	19	4	©	©	PROPN
ejpam-6259	19	5	2025	2025	NUM
ejpam-6259	19	6	the	the	DET
ejpam-6259	19	7	author(s	author(s	NOUN
ejpam-6259	19	8	)	)	PUNCT
ejpam-6259	19	9	.	.	PUNCT
ejpam-6259	20	1	(	(	PUNCT
ejpam-6259	20	2	cc	cc	NOUN
ejpam-6259	20	3	by	by	ADP
ejpam-6259	20	4	-	-	PUNCT
ejpam-6259	20	5	nc	nc	PROPN
ejpam-6259	20	6	4.0	4.0	NUM
ejpam-6259	20	7	)	)	PUNCT
ejpam-6259	20	8	r.	r.	PROPN
ejpam-6259	20	9	chinram	chinram	PROPN
ejpam-6259	20	10	,	,	PUNCT
ejpam-6259	20	11	p.	p.	NOUN
ejpam-6259	20	12	singavananda	singavananda	PROPN
ejpam-6259	20	13	/	/	SYM
ejpam-6259	20	14	eur	eur	PROPN
ejpam-6259	20	15	.	.	PUNCT
ejpam-6259	21	1	j.	j.	PROPN
ejpam-6259	21	2	pure	pure	PROPN
ejpam-6259	21	3	appl	appl	PROPN
ejpam-6259	21	4	.	.	PROPN
ejpam-6259	21	5	math	math	PROPN
ejpam-6259	21	6	,	,	PUNCT
ejpam-6259	21	7	18	18	NUM
ejpam-6259	21	8	(	(	PUNCT
ejpam-6259	21	9	3	3	NUM
ejpam-6259	21	10	)	)	PUNCT
ejpam-6259	21	11	(	(	PUNCT
ejpam-6259	21	12	2025	2025	NUM
ejpam-6259	21	13	)	)	PUNCT
ejpam-6259	21	14	,	,	PUNCT
ejpam-6259	21	15	6259	6259	NUM
ejpam-6259	21	16	2	2	NUM
ejpam-6259	21	17	of	of	ADP
ejpam-6259	21	18	10	10	NUM
ejpam-6259	21	19	semigroup	semigroup	NOUN
ejpam-6259	21	20	.	.	PUNCT
ejpam-6259	22	1	for	for	ADP
ejpam-6259	22	2	n	n	PROPN
ejpam-6259	22	3	≥	≥	NUM
ejpam-6259	22	4	3	3	NUM
ejpam-6259	22	5	,	,	PUNCT
ejpam-6259	22	6	dudek	dudek	X
ejpam-6259	23	1	[	[	X
ejpam-6259	23	2	3	3	NUM
ejpam-6259	23	3	]	]	PUNCT
ejpam-6259	23	4	also	also	ADV
ejpam-6259	23	5	investigated	investigate	VERB
ejpam-6259	23	6	the	the	DET
ejpam-6259	23	7	properties	property	NOUN
ejpam-6259	23	8	of	of	ADP
ejpam-6259	23	9	ideals	ideal	NOUN
ejpam-6259	23	10	and	and	CCONJ
ejpam-6259	23	11	some	some	DET
ejpam-6259	23	12	elements	element	NOUN
ejpam-6259	23	13	of	of	ADP
ejpam-6259	23	14	n	n	CCONJ
ejpam-6259	23	15	-	-	PUNCT
ejpam-6259	23	16	ary	ary	NOUN
ejpam-6259	23	17	semigroups	semigroup	NOUN
ejpam-6259	23	18	containing	contain	VERB
ejpam-6259	23	19	an	an	DET
ejpam-6259	23	20	idempotent	idempotent	NOUN
ejpam-6259	23	21	.	.	PUNCT
ejpam-6259	24	1	in	in	ADP
ejpam-6259	24	2	2018	2018	NUM
ejpam-6259	24	3	,	,	PUNCT
ejpam-6259	24	4	ideals	ideal	NOUN
ejpam-6259	24	5	of	of	ADP
ejpam-6259	24	6	fuzzy	fuzzy	ADJ
ejpam-6259	24	7	points	point	NOUN
ejpam-6259	24	8	nary	nary	ADJ
ejpam-6259	24	9	semigroups	semigroup	NOUN
ejpam-6259	24	10	were	be	AUX
ejpam-6259	24	11	studied	study	VERB
ejpam-6259	24	12	by	by	ADP
ejpam-6259	24	13	solano	solano	PROPN
ejpam-6259	24	14	et	et	PROPN
ejpam-6259	24	15	al	al	PROPN
ejpam-6259	24	16	.	.	PUNCT
ejpam-6259	25	1	[	[	X
ejpam-6259	25	2	4	4	NUM
ejpam-6259	25	3	]	]	PUNCT
ejpam-6259	25	4	.	.	PUNCT
ejpam-6259	26	1	in	in	ADP
ejpam-6259	26	2	the	the	DET
ejpam-6259	26	3	next	next	ADJ
ejpam-6259	26	4	year	year	NOUN
ejpam-6259	26	5	,	,	PUNCT
ejpam-6259	26	6	couceiro	couceiro	NOUN
ejpam-6259	26	7	and	and	CCONJ
ejpam-6259	26	8	devillet	devillet	VERB
ejpam-6259	26	9	[	[	X
ejpam-6259	26	10	5	5	NUM
ejpam-6259	26	11	]	]	PUNCT
ejpam-6259	26	12	showed	show	VERB
ejpam-6259	26	13	that	that	SCONJ
ejpam-6259	26	14	every	every	DET
ejpam-6259	26	15	quasitrivial	quasitrivial	ADJ
ejpam-6259	26	16	n	n	CCONJ
ejpam-6259	26	17	-	-	PUNCT
ejpam-6259	26	18	ary	ary	PROPN
ejpam-6259	26	19	semigroup	semigroup	PROPN
ejpam-6259	26	20	is	be	AUX
ejpam-6259	26	21	reducible	reducible	ADJ
ejpam-6259	26	22	to	to	ADP
ejpam-6259	26	23	a	a	DET
ejpam-6259	26	24	binary	binary	PROPN
ejpam-6259	26	25	semigroup	semigroup	NOUN
ejpam-6259	26	26	,	,	PUNCT
ejpam-6259	26	27	and	and	CCONJ
ejpam-6259	26	28	provided	provide	VERB
ejpam-6259	26	29	necessary	necessary	ADJ
ejpam-6259	26	30	and	and	CCONJ
ejpam-6259	26	31	sufficient	sufficient	ADJ
ejpam-6259	26	32	conditions	condition	NOUN
ejpam-6259	26	33	for	for	ADP
ejpam-6259	26	34	such	such	DET
ejpam-6259	26	35	a	a	DET
ejpam-6259	26	36	reduction	reduction	NOUN
ejpam-6259	26	37	to	to	PART
ejpam-6259	26	38	be	be	AUX
ejpam-6259	26	39	unique	unique	ADJ
ejpam-6259	26	40	.	.	PUNCT
ejpam-6259	27	1	in	in	ADP
ejpam-6259	27	2	2020	2020	NUM
ejpam-6259	27	3	,	,	PUNCT
ejpam-6259	27	4	somsup	somsup	NOUN
ejpam-6259	27	5	and	and	CCONJ
ejpam-6259	27	6	leerawat	leerawat	VERB
ejpam-6259	27	7	[	[	X
ejpam-6259	27	8	6	6	NUM
ejpam-6259	27	9	]	]	PUNCT
ejpam-6259	27	10	further	far	ADV
ejpam-6259	27	11	investigated	investigate	VERB
ejpam-6259	27	12	congruences	congruence	NOUN
ejpam-6259	27	13	and	and	CCONJ
ejpam-6259	27	14	homomorphisms	homomorphism	NOUN
ejpam-6259	27	15	on	on	ADP
ejpam-6259	27	16	n	n	CCONJ
ejpam-6259	27	17	-	-	PUNCT
ejpam-6259	27	18	ary	ary	NOUN
ejpam-6259	27	19	semigroups	semigroup	NOUN
ejpam-6259	27	20	.	.	PUNCT
ejpam-6259	28	1	later	later	ADV
ejpam-6259	28	2	,	,	PUNCT
ejpam-6259	28	3	pornsurat	pornsurat	NOUN
ejpam-6259	28	4	and	and	CCONJ
ejpam-6259	28	5	pibaljommee	pibaljommee	NOUN
ejpam-6259	29	1	[	[	X
ejpam-6259	29	2	7	7	NUM
ejpam-6259	29	3	]	]	PUNCT
ejpam-6259	29	4	introduced	introduce	VERB
ejpam-6259	29	5	the	the	DET
ejpam-6259	29	6	notions	notion	NOUN
ejpam-6259	29	7	of	of	ADP
ejpam-6259	29	8	a	a	DET
ejpam-6259	29	9	right	right	ADJ
ejpam-6259	29	10	regularity	regularity	NOUN
ejpam-6259	29	11	,	,	PUNCT
ejpam-6259	29	12	a	a	DET
ejpam-6259	29	13	right	right	ADJ
ejpam-6259	29	14	weak	weak	ADJ
ejpam-6259	29	15	regularity	regularity	NOUN
ejpam-6259	29	16	and	and	CCONJ
ejpam-6259	29	17	a	a	DET
ejpam-6259	29	18	complete	complete	ADJ
ejpam-6259	29	19	regularity	regularity	NOUN
ejpam-6259	29	20	of	of	ADP
ejpam-6259	29	21	n	n	CCONJ
ejpam-6259	29	22	-	-	PUNCT
ejpam-6259	29	23	ary	ary	NOUN
ejpam-6259	29	24	semigroups	semigroup	NOUN
ejpam-6259	29	25	and	and	CCONJ
ejpam-6259	29	26	characterized	characterize	VERB
ejpam-6259	29	27	these	these	DET
ejpam-6259	29	28	regularities	regularity	NOUN
ejpam-6259	29	29	.	.	PUNCT
ejpam-6259	30	1	in	in	ADP
ejpam-6259	30	2	the	the	DET
ejpam-6259	30	3	same	same	ADJ
ejpam-6259	30	4	year	year	NOUN
ejpam-6259	30	5	,	,	PUNCT
ejpam-6259	30	6	some	some	DET
ejpam-6259	30	7	reducibility	reducibility	NOUN
ejpam-6259	30	8	of	of	ADP
ejpam-6259	30	9	n	n	CCONJ
ejpam-6259	30	10	-	-	PUNCT
ejpam-6259	30	11	ary	ary	NOUN
ejpam-6259	30	12	semigroups	semigroup	NOUN
ejpam-6259	30	13	were	be	AUX
ejpam-6259	30	14	investigated	investigate	VERB
ejpam-6259	30	15	in	in	ADP
ejpam-6259	30	16	[	[	X
ejpam-6259	30	17	8	8	NUM
ejpam-6259	30	18	]	]	PUNCT
ejpam-6259	30	19	.	.	PUNCT
ejpam-6259	31	1	in	in	ADP
ejpam-6259	31	2	2023	2023	NUM
ejpam-6259	31	3	,	,	PUNCT
ejpam-6259	31	4	daengsaen	daengsaen	PROPN
ejpam-6259	31	5	and	and	CCONJ
ejpam-6259	31	6	leeratanavalee	leeratanavalee	NOUN
ejpam-6259	31	7	[	[	X
ejpam-6259	31	8	9	9	NUM
ejpam-6259	31	9	]	]	PUNCT
ejpam-6259	31	10	demonstrated	demonstrate	VERB
ejpam-6259	31	11	that	that	SCONJ
ejpam-6259	31	12	every	every	DET
ejpam-6259	31	13	n	n	NUM
ejpam-6259	31	14	-	-	PUNCT
ejpam-6259	31	15	ary	ary	PROPN
ejpam-6259	31	16	semigroup	semigroup	NOUN
ejpam-6259	31	17	that	that	PRON
ejpam-6259	31	18	is	be	AUX
ejpam-6259	31	19	both	both	CCONJ
ejpam-6259	31	20	regular	regular	ADJ
ejpam-6259	31	21	and	and	CCONJ
ejpam-6259	31	22	intra	intra	ADJ
ejpam-6259	31	23	-	-	ADJ
ejpam-6259	31	24	regular	regular	ADJ
ejpam-6259	31	25	can	can	AUX
ejpam-6259	31	26	be	be	AUX
ejpam-6259	31	27	decomposed	decompose	VERB
ejpam-6259	31	28	into	into	ADP
ejpam-6259	31	29	a	a	DET
ejpam-6259	31	30	semilattice	semilattice	NOUN
ejpam-6259	31	31	of	of	ADP
ejpam-6259	31	32	i	i	NOUN
ejpam-6259	31	33	-	-	PUNCT
ejpam-6259	31	34	simple	simple	ADJ
ejpam-6259	31	35	and	and	CCONJ
ejpam-6259	31	36	regular	regular	ADJ
ejpam-6259	31	37	n	n	CCONJ
ejpam-6259	31	38	-	-	PUNCT
ejpam-6259	31	39	ary	ary	NOUN
ejpam-6259	31	40	semigroups	semigroup	NOUN
ejpam-6259	31	41	,	,	PUNCT
ejpam-6259	31	42	and	and	CCONJ
ejpam-6259	31	43	the	the	DET
ejpam-6259	31	44	reverse	reverse	ADJ
ejpam-6259	31	45	assertion	assertion	NOUN
ejpam-6259	31	46	also	also	ADV
ejpam-6259	31	47	holds	hold	VERB
ejpam-6259	31	48	.	.	PUNCT
ejpam-6259	32	1	almost	almost	ADV
ejpam-6259	32	2	ideals	ideal	NOUN
ejpam-6259	32	3	on	on	ADP
ejpam-6259	32	4	semigroups	semigroup	NOUN
ejpam-6259	32	5	were	be	AUX
ejpam-6259	32	6	first	first	ADV
ejpam-6259	32	7	studied	study	VERB
ejpam-6259	32	8	by	by	ADP
ejpam-6259	32	9	grosek	grosek	NOUN
ejpam-6259	32	10	and	and	CCONJ
ejpam-6259	32	11	satko	satko	NOUN
ejpam-6259	33	1	[	[	X
ejpam-6259	33	2	10	10	NUM
ejpam-6259	33	3	]	]	PUNCT
ejpam-6259	33	4	in	in	ADP
ejpam-6259	33	5	1980	1980	NUM
ejpam-6259	33	6	.	.	PUNCT
ejpam-6259	34	1	later	later	ADV
ejpam-6259	34	2	,	,	PUNCT
ejpam-6259	34	3	wattanatripop	wattanatripop	PROPN
ejpam-6259	34	4	et	et	PROPN
ejpam-6259	34	5	al	al	PROPN
ejpam-6259	34	6	.	.	PUNCT
ejpam-6259	35	1	[	[	X
ejpam-6259	35	2	11	11	NUM
ejpam-6259	35	3	]	]	PUNCT
ejpam-6259	35	4	introduced	introduce	VERB
ejpam-6259	35	5	almost	almost	ADV
ejpam-6259	35	6	fuzzy	fuzzy	ADJ
ejpam-6259	35	7	ideals	ideal	NOUN
ejpam-6259	35	8	of	of	ADP
ejpam-6259	35	9	semigroups	semigroup	NOUN
ejpam-6259	35	10	and	and	CCONJ
ejpam-6259	35	11	investigated	investigate	VERB
ejpam-6259	35	12	relationships	relationship	NOUN
ejpam-6259	35	13	between	between	ADP
ejpam-6259	35	14	almost	almost	ADV
ejpam-6259	35	15	ideals	ideal	NOUN
ejpam-6259	35	16	and	and	CCONJ
ejpam-6259	35	17	almost	almost	ADV
ejpam-6259	35	18	fuzzy	fuzzy	ADJ
ejpam-6259	35	19	ideals	ideal	NOUN
ejpam-6259	35	20	.	.	PUNCT
ejpam-6259	36	1	additionally	additionally	ADV
ejpam-6259	36	2	,	,	PUNCT
ejpam-6259	36	3	khamrot	khamrot	ADJ
ejpam-6259	36	4	and	and	CCONJ
ejpam-6259	36	5	gaketem	gaketem	NOUN
ejpam-6259	37	1	[	[	X
ejpam-6259	37	2	12	12	NUM
ejpam-6259	37	3	]	]	PUNCT
ejpam-6259	37	4	and	and	CCONJ
ejpam-6259	37	5	[	[	X
ejpam-6259	37	6	13	13	NUM
ejpam-6259	37	7	]	]	PUNCT
ejpam-6259	37	8	introduced	introduce	VERB
ejpam-6259	37	9	the	the	DET
ejpam-6259	37	10	concepts	concept	NOUN
ejpam-6259	37	11	of	of	ADP
ejpam-6259	37	12	bipolar	bipolar	ADJ
ejpam-6259	37	13	fuzzy	fuzzy	ADJ
ejpam-6259	37	14	almost	almost	ADV
ejpam-6259	37	15	ideals	ideal	NOUN
ejpam-6259	37	16	and	and	CCONJ
ejpam-6259	37	17	picture	picture	NOUN
ejpam-6259	37	18	fuzzy	fuzzy	ADJ
ejpam-6259	37	19	almost	almost	ADV
ejpam-6259	37	20	ideals	ideal	NOUN
ejpam-6259	37	21	in	in	ADP
ejpam-6259	37	22	semigroups	semigroup	NOUN
ejpam-6259	37	23	,	,	PUNCT
ejpam-6259	37	24	respectively	respectively	ADV
ejpam-6259	37	25	.	.	PUNCT
ejpam-6259	38	1	subsequently	subsequently	ADV
ejpam-6259	38	2	,	,	PUNCT
ejpam-6259	38	3	the	the	DET
ejpam-6259	38	4	concepts	concept	NOUN
ejpam-6259	38	5	of	of	ADP
ejpam-6259	38	6	almost	almost	ADV
ejpam-6259	38	7	and	and	CCONJ
ejpam-6259	38	8	fuzzy	fuzzy	ADJ
ejpam-6259	38	9	almost	almost	ADV
ejpam-6259	38	10	ideals	ideal	NOUN
ejpam-6259	38	11	were	be	AUX
ejpam-6259	38	12	applied	apply	VERB
ejpam-6259	38	13	to	to	ADP
ejpam-6259	38	14	several	several	ADJ
ejpam-6259	38	15	subalgebras	subalgebra	NOUN
ejpam-6259	38	16	within	within	ADP
ejpam-6259	38	17	various	various	ADJ
ejpam-6259	38	18	algebraic	algebraic	ADJ
ejpam-6259	38	19	structures	structure	NOUN
ejpam-6259	38	20	.	.	PUNCT
ejpam-6259	39	1	for	for	ADP
ejpam-6259	39	2	instance	instance	NOUN
ejpam-6259	39	3	,	,	PUNCT
ejpam-6259	39	4	almost	almost	ADV
ejpam-6259	39	5	subsemigroups	subsemigroup	NOUN
ejpam-6259	39	6	and	and	CCONJ
ejpam-6259	39	7	fuzzy	fuzzy	ADJ
ejpam-6259	39	8	almost	almost	ADV
ejpam-6259	39	9	subsemigroups	subsemigroup	NOUN
ejpam-6259	39	10	in	in	ADP
ejpam-6259	39	11	semigroups	semigroup	NOUN
ejpam-6259	39	12	[	[	X
ejpam-6259	39	13	14	14	NUM
ejpam-6259	39	14	]	]	X
ejpam-6259	39	15	;	;	PUNCT
ejpam-6259	39	16	almost	almost	ADV
ejpam-6259	39	17	subsemigroups	subsemigroup	NOUN
ejpam-6259	39	18	and	and	CCONJ
ejpam-6259	39	19	fuzzy	fuzzy	ADJ
ejpam-6259	39	20	almost	almost	ADV
ejpam-6259	39	21	ternary	ternary	ADJ
ejpam-6259	39	22	subsemigroups	subsemigroup	NOUN
ejpam-6259	39	23	in	in	ADP
ejpam-6259	39	24	ternary	ternary	ADJ
ejpam-6259	39	25	semigroups	semigroup	NOUN
ejpam-6259	40	1	[	[	X
ejpam-6259	40	2	15	15	NUM
ejpam-6259	40	3	]	]	X
ejpam-6259	40	4	;	;	PUNCT
ejpam-6259	40	5	almost	almost	ADV
ejpam-6259	40	6	subsemirings	subsemiring	NOUN
ejpam-6259	40	7	and	and	CCONJ
ejpam-6259	40	8	fuzzy	fuzzy	ADJ
ejpam-6259	40	9	almost	almost	ADV
ejpam-6259	40	10	subsemirings	subsemiring	NOUN
ejpam-6259	40	11	in	in	ADP
ejpam-6259	40	12	semirings	semiring	NOUN
ejpam-6259	40	13	[	[	X
ejpam-6259	40	14	16	16	NUM
ejpam-6259	40	15	]	]	X
ejpam-6259	40	16	;	;	PUNCT
ejpam-6259	40	17	and	and	CCONJ
ejpam-6259	40	18	almost	almost	ADV
ejpam-6259	40	19	ternary	ternary	ADJ
ejpam-6259	40	20	subsemirings	subsemiring	NOUN
ejpam-6259	40	21	and	and	CCONJ
ejpam-6259	40	22	fuzzy	fuzzy	ADJ
ejpam-6259	40	23	almost	almost	ADV
ejpam-6259	40	24	ternary	ternary	ADJ
ejpam-6259	40	25	subsemirings	subsemiring	NOUN
ejpam-6259	40	26	in	in	ADP
ejpam-6259	40	27	ternary	ternary	ADJ
ejpam-6259	40	28	semirings	semiring	NOUN
ejpam-6259	40	29	[	[	X
ejpam-6259	40	30	17	17	NUM
ejpam-6259	40	31	]	]	PUNCT
ejpam-6259	40	32	etc	etc	X
ejpam-6259	40	33	.	.	X
ejpam-6259	41	1	this	this	DET
ejpam-6259	41	2	paper	paper	NOUN
ejpam-6259	41	3	aims	aim	VERB
ejpam-6259	41	4	to	to	PART
ejpam-6259	41	5	generalize	generalize	VERB
ejpam-6259	41	6	the	the	DET
ejpam-6259	41	7	findings	finding	NOUN
ejpam-6259	41	8	presented	present	VERB
ejpam-6259	41	9	in	in	ADP
ejpam-6259	41	10	[	[	X
ejpam-6259	41	11	14	14	NUM
ejpam-6259	41	12	]	]	PUNCT
ejpam-6259	41	13	and	and	CCONJ
ejpam-6259	41	14	[	[	X
ejpam-6259	41	15	15	15	NUM
ejpam-6259	41	16	]	]	PUNCT
ejpam-6259	41	17	.	.	PUNCT
ejpam-6259	42	1	basic	basic	ADJ
ejpam-6259	42	2	notations	notation	NOUN
ejpam-6259	42	3	and	and	CCONJ
ejpam-6259	42	4	definitions	definition	NOUN
ejpam-6259	42	5	are	be	AUX
ejpam-6259	42	6	provided	provide	VERB
ejpam-6259	42	7	in	in	ADP
ejpam-6259	42	8	section	section	NOUN
ejpam-6259	42	9	2	2	NUM
ejpam-6259	42	10	.	.	PUNCT
ejpam-6259	43	1	in	in	ADP
ejpam-6259	43	2	section	section	NOUN
ejpam-6259	43	3	3	3	NUM
ejpam-6259	43	4	,	,	PUNCT
ejpam-6259	43	5	we	we	PRON
ejpam-6259	43	6	extend	extend	VERB
ejpam-6259	43	7	the	the	DET
ejpam-6259	43	8	main	main	ADJ
ejpam-6259	43	9	results	result	NOUN
ejpam-6259	43	10	.	.	PUNCT
ejpam-6259	44	1	we	we	PRON
ejpam-6259	44	2	introduce	introduce	VERB
ejpam-6259	44	3	the	the	DET
ejpam-6259	44	4	concepts	concept	NOUN
ejpam-6259	44	5	of	of	ADP
ejpam-6259	44	6	almost	almost	ADV
ejpam-6259	44	7	n	n	CCONJ
ejpam-6259	44	8	-	-	PUNCT
ejpam-6259	44	9	ary	ary	NOUN
ejpam-6259	44	10	subsemigroups	subsemigroup	NOUN
ejpam-6259	44	11	and	and	CCONJ
ejpam-6259	44	12	fuzzy	fuzzy	ADJ
ejpam-6259	44	13	almost	almost	ADV
ejpam-6259	44	14	n	n	CCONJ
ejpam-6259	44	15	-	-	PUNCT
ejpam-6259	44	16	ary	ary	PROPN
ejpam-6259	44	17	subsemigroups	subsemigroup	NOUN
ejpam-6259	44	18	of	of	ADP
ejpam-6259	44	19	n	n	CCONJ
ejpam-6259	44	20	-	-	PUNCT
ejpam-6259	44	21	ary	ary	NOUN
ejpam-6259	44	22	semigroups	semigroup	NOUN
ejpam-6259	44	23	,	,	PUNCT
ejpam-6259	44	24	and	and	CCONJ
ejpam-6259	44	25	present	present	VERB
ejpam-6259	44	26	their	their	PRON
ejpam-6259	44	27	properties	property	NOUN
ejpam-6259	44	28	.	.	PUNCT
ejpam-6259	45	1	moreover	moreover	ADV
ejpam-6259	45	2	,	,	PUNCT
ejpam-6259	45	3	we	we	PRON
ejpam-6259	45	4	establish	establish	VERB
ejpam-6259	45	5	some	some	DET
ejpam-6259	45	6	relationships	relationship	NOUN
ejpam-6259	45	7	between	between	ADP
ejpam-6259	45	8	almost	almost	ADV
ejpam-6259	45	9	n	n	CCONJ
ejpam-6259	45	10	-	-	PUNCT
ejpam-6259	45	11	ary	ary	NOUN
ejpam-6259	45	12	subsemigroups	subsemigroup	NOUN
ejpam-6259	45	13	and	and	CCONJ
ejpam-6259	45	14	fuzzy	fuzzy	ADJ
ejpam-6259	45	15	almost	almost	ADV
ejpam-6259	45	16	n	n	CCONJ
ejpam-6259	45	17	-	-	PUNCT
ejpam-6259	45	18	ary	ary	NOUN
ejpam-6259	45	19	subsemigroups	subsemigroup	NOUN
ejpam-6259	45	20	.	.	PUNCT
ejpam-6259	46	1	2	2	X
ejpam-6259	46	2	.	.	X
ejpam-6259	46	3	preliminaries	preliminary	NOUN
ejpam-6259	46	4	the	the	DET
ejpam-6259	46	5	aim	aim	NOUN
ejpam-6259	46	6	of	of	ADP
ejpam-6259	46	7	this	this	DET
ejpam-6259	46	8	section	section	NOUN
ejpam-6259	46	9	is	be	AUX
ejpam-6259	46	10	to	to	PART
ejpam-6259	46	11	review	review	VERB
ejpam-6259	46	12	some	some	DET
ejpam-6259	46	13	notations	notation	NOUN
ejpam-6259	46	14	and	and	CCONJ
ejpam-6259	46	15	definitions	definition	NOUN
ejpam-6259	46	16	of	of	ADP
ejpam-6259	46	17	n	n	CCONJ
ejpam-6259	46	18	-	-	PUNCT
ejpam-6259	46	19	ary	ary	NOUN
ejpam-6259	46	20	semigroups	semigroup	NOUN
ejpam-6259	46	21	and	and	CCONJ
ejpam-6259	46	22	fuzzy	fuzzy	ADJ
ejpam-6259	46	23	sets	set	NOUN
ejpam-6259	46	24	.	.	PUNCT
ejpam-6259	47	1	2.1	2.1	NUM
ejpam-6259	47	2	.	.	PUNCT
ejpam-6259	47	3	n	n	CCONJ
ejpam-6259	47	4	-	-	PUNCT
ejpam-6259	47	5	ary	ary	PROPN
ejpam-6259	47	6	semigroups	semigroup	NOUN
ejpam-6259	47	7	to	to	PART
ejpam-6259	47	8	ensure	ensure	VERB
ejpam-6259	47	9	completeness	completeness	NOUN
ejpam-6259	47	10	,	,	PUNCT
ejpam-6259	47	11	we	we	PRON
ejpam-6259	47	12	state	state	VERB
ejpam-6259	47	13	some	some	DET
ejpam-6259	47	14	definitions	definition	NOUN
ejpam-6259	47	15	in	in	ADP
ejpam-6259	47	16	the	the	DET
ejpam-6259	47	17	same	same	ADJ
ejpam-6259	47	18	fashion	fashion	NOUN
ejpam-6259	47	19	as	as	SCONJ
ejpam-6259	47	20	found	find	VERB
ejpam-6259	47	21	in	in	ADP
ejpam-6259	47	22	[	[	X
ejpam-6259	47	23	3	3	NUM
ejpam-6259	47	24	]	]	PUNCT
ejpam-6259	47	25	and	and	CCONJ
ejpam-6259	47	26	[	[	X
ejpam-6259	47	27	18	18	NUM
ejpam-6259	47	28	]	]	PUNCT
ejpam-6259	47	29	which	which	PRON
ejpam-6259	47	30	are	be	AUX
ejpam-6259	47	31	used	use	VERB
ejpam-6259	47	32	throughout	throughout	ADP
ejpam-6259	47	33	this	this	DET
ejpam-6259	47	34	paper	paper	NOUN
ejpam-6259	47	35	.	.	PUNCT
ejpam-6259	48	1	first	first	ADV
ejpam-6259	48	2	,	,	PUNCT
ejpam-6259	48	3	we	we	PRON
ejpam-6259	48	4	recall	recall	VERB
ejpam-6259	48	5	the	the	DET
ejpam-6259	48	6	definition	definition	NOUN
ejpam-6259	48	7	of	of	ADP
ejpam-6259	48	8	an	an	DET
ejpam-6259	48	9	n	n	CCONJ
ejpam-6259	48	10	-	-	PUNCT
ejpam-6259	48	11	ary	ary	NOUN
ejpam-6259	48	12	semigroup	semigroup	NOUN
ejpam-6259	48	13	,	,	PUNCT
ejpam-6259	48	14	where	where	SCONJ
ejpam-6259	48	15	n	n	PRON
ejpam-6259	48	16	is	be	AUX
ejpam-6259	48	17	a	a	DET
ejpam-6259	48	18	positive	positive	ADJ
ejpam-6259	48	19	integer	integer	NOUN
ejpam-6259	48	20	such	such	ADJ
ejpam-6259	48	21	that	that	SCONJ
ejpam-6259	48	22	n	n	CCONJ
ejpam-6259	48	23	≥	≥	NOUN
ejpam-6259	48	24	2	2	NUM
ejpam-6259	48	25	.	.	PUNCT
ejpam-6259	49	1	a	a	DET
ejpam-6259	49	2	nonempty	nonempty	NOUN
ejpam-6259	49	3	set	set	VERB
ejpam-6259	49	4	a	a	DET
ejpam-6259	49	5	together	together	NOUN
ejpam-6259	49	6	with	with	ADP
ejpam-6259	49	7	an	an	DET
ejpam-6259	49	8	n	n	CCONJ
ejpam-6259	49	9	-	-	PUNCT
ejpam-6259	49	10	ary	ary	NOUN
ejpam-6259	49	11	operation	operation	NOUN
ejpam-6259	49	12	given	give	VERB
ejpam-6259	49	13	by	by	ADP
ejpam-6259	49	14	f	f	PROPN
ejpam-6259	49	15	:	:	PUNCT
ejpam-6259	49	16	an	an	DET
ejpam-6259	49	17	→	→	SYM
ejpam-6259	49	18	a	a	NOUN
ejpam-6259	49	19	,	,	PUNCT
ejpam-6259	49	20	where	where	SCONJ
ejpam-6259	49	21	n	n	PRON
ejpam-6259	49	22	≥	≥	NOUN
ejpam-6259	49	23	2	2	NUM
ejpam-6259	49	24	,	,	PUNCT
ejpam-6259	49	25	is	be	AUX
ejpam-6259	49	26	called	call	VERB
ejpam-6259	49	27	an	an	DET
ejpam-6259	49	28	n	n	CCONJ
ejpam-6259	49	29	-	-	PUNCT
ejpam-6259	49	30	ary	ary	NOUN
ejpam-6259	49	31	groupoid	groupoid	PROPN
ejpam-6259	49	32	and	and	CCONJ
ejpam-6259	49	33	is	be	AUX
ejpam-6259	49	34	denoted	denote	VERB
ejpam-6259	49	35	by	by	ADP
ejpam-6259	49	36	the	the	DET
ejpam-6259	49	37	notation	notation	NOUN
ejpam-6259	49	38	(	(	PUNCT
ejpam-6259	49	39	a	a	PRON
ejpam-6259	49	40	,	,	PUNCT
ejpam-6259	49	41	f	f	NOUN
ejpam-6259	49	42	)	)	PUNCT
ejpam-6259	49	43	.	.	PUNCT
ejpam-6259	50	1	according	accord	VERB
ejpam-6259	50	2	to	to	ADP
ejpam-6259	50	3	the	the	DET
ejpam-6259	50	4	general	general	ADJ
ejpam-6259	50	5	convention	convention	NOUN
ejpam-6259	50	6	used	use	VERB
ejpam-6259	50	7	in	in	ADP
ejpam-6259	50	8	the	the	DET
ejpam-6259	50	9	symbols	symbol	NOUN
ejpam-6259	50	10	of	of	ADP
ejpam-6259	50	11	n	n	CCONJ
ejpam-6259	50	12	-	-	PUNCT
ejpam-6259	50	13	ary	ary	PROPN
ejpam-6259	50	14	groupoids	groupoid	NOUN
ejpam-6259	50	15	,	,	PUNCT
ejpam-6259	50	16	the	the	DET
ejpam-6259	50	17	sequence	sequence	NOUN
ejpam-6259	50	18	of	of	ADP
ejpam-6259	50	19	elements	element	NOUN
ejpam-6259	50	20	ai	ai	VERB
ejpam-6259	50	21	,	,	PUNCT
ejpam-6259	50	22	ai+1	ai+1	PROPN
ejpam-6259	50	23	,	,	PUNCT
ejpam-6259	50	24	.	.	PUNCT
ejpam-6259	50	25	.	.	PUNCT
ejpam-6259	51	1	.	.	PUNCT
ejpam-6259	52	1	,	,	PUNCT
ejpam-6259	52	2	aj	aj	PROPN
ejpam-6259	52	3	is	be	AUX
ejpam-6259	52	4	denoted	denote	VERB
ejpam-6259	52	5	by	by	ADP
ejpam-6259	52	6	aji	aji	PROPN
ejpam-6259	52	7	.	.	PUNCT
ejpam-6259	53	1	in	in	ADP
ejpam-6259	53	2	the	the	DET
ejpam-6259	53	3	case	case	NOUN
ejpam-6259	53	4	j	j	X
ejpam-6259	53	5	<	<	X
ejpam-6259	53	6	i	i	X
ejpam-6259	53	7	,	,	PUNCT
ejpam-6259	53	8	it	it	PRON
ejpam-6259	53	9	is	be	AUX
ejpam-6259	53	10	the	the	DET
ejpam-6259	53	11	empty	empty	ADJ
ejpam-6259	53	12	symbol	symbol	NOUN
ejpam-6259	53	13	.	.	PUNCT
ejpam-6259	54	1	if	if	SCONJ
ejpam-6259	54	2	ai+1	ai+1	NUM
ejpam-6259	54	3	=	=	SYM
ejpam-6259	54	4	ai+2	ai+2	NUM
ejpam-6259	54	5	=	=	SYM
ejpam-6259	54	6	·	·	PUNCT
ejpam-6259	54	7	·	·	PUNCT
ejpam-6259	54	8	·	·	PUNCT
ejpam-6259	55	1	=	=	PUNCT
ejpam-6259	55	2	ai+t	ai+t	PUNCT
ejpam-6259	55	3	=	=	SYM
ejpam-6259	55	4	a	a	PROPN
ejpam-6259	55	5	,	,	PUNCT
ejpam-6259	55	6	then	then	ADV
ejpam-6259	55	7	we	we	PRON
ejpam-6259	55	8	will	will	AUX
ejpam-6259	55	9	write	write	VERB
ejpam-6259	55	10	at	at	ADP
ejpam-6259	55	11	instead	instead	ADV
ejpam-6259	55	12	of	of	ADP
ejpam-6259	55	13	ai+t	ai+t	PROPN
ejpam-6259	55	14	i+1	i+1	NOUN
ejpam-6259	55	15	.	.	PUNCT
ejpam-6259	56	1	in	in	ADP
ejpam-6259	56	2	this	this	DET
ejpam-6259	56	3	convention	convention	NOUN
ejpam-6259	56	4	,	,	PUNCT
ejpam-6259	56	5	we	we	PRON
ejpam-6259	56	6	have	have	VERB
ejpam-6259	56	7	r.	r.	PROPN
ejpam-6259	56	8	chinram	chinram	PROPN
ejpam-6259	56	9	,	,	PUNCT
ejpam-6259	56	10	p.	p.	NOUN
ejpam-6259	56	11	singavananda	singavananda	PROPN
ejpam-6259	56	12	/	/	SYM
ejpam-6259	56	13	eur	eur	PROPN
ejpam-6259	56	14	.	.	PUNCT
ejpam-6259	57	1	j.	j.	PROPN
ejpam-6259	57	2	pure	pure	PROPN
ejpam-6259	57	3	appl	appl	PROPN
ejpam-6259	57	4	.	.	PROPN
ejpam-6259	57	5	math	math	PROPN
ejpam-6259	57	6	,	,	PUNCT
ejpam-6259	57	7	18	18	NUM
ejpam-6259	57	8	(	(	PUNCT
ejpam-6259	57	9	3	3	NUM
ejpam-6259	57	10	)	)	PUNCT
ejpam-6259	57	11	(	(	PUNCT
ejpam-6259	57	12	2025	2025	NUM
ejpam-6259	57	13	)	)	PUNCT
ejpam-6259	57	14	,	,	PUNCT
ejpam-6259	57	15	6259	6259	NUM
ejpam-6259	57	16	3	3	NUM
ejpam-6259	57	17	of	of	ADP
ejpam-6259	57	18	10	10	NUM
ejpam-6259	57	19	f(a1	f(a1	NOUN
ejpam-6259	57	20	,	,	PUNCT
ejpam-6259	57	21	a2	a2	PROPN
ejpam-6259	57	22	,	,	PUNCT
ejpam-6259	57	23	.	.	PUNCT
ejpam-6259	57	24	.	.	PUNCT
ejpam-6259	58	1	.	.	PUNCT
ejpam-6259	59	1	,	,	PUNCT
ejpam-6259	59	2	an	an	X
ejpam-6259	59	3	)	)	PUNCT
ejpam-6259	59	4	=	=	SYM
ejpam-6259	59	5	f(an1	f(an1	X
ejpam-6259	59	6	)	)	PUNCT
ejpam-6259	59	7	and	and	CCONJ
ejpam-6259	59	8	f(a1	f(a1	NOUN
ejpam-6259	59	9	,	,	PUNCT
ejpam-6259	59	10	.	.	PUNCT
ejpam-6259	59	11	.	.	PUNCT
ejpam-6259	60	1	.	.	PUNCT
ejpam-6259	61	1	,	,	PUNCT
ejpam-6259	61	2	ai	ai	VERB
ejpam-6259	61	3	,	,	PUNCT
ejpam-6259	61	4	a	a	PRON
ejpam-6259	61	5	.	.	PUNCT
ejpam-6259	61	6	.	.	PUNCT
ejpam-6259	62	1	.	.	PUNCT
ejpam-6259	63	1	,	,	PUNCT
ejpam-6259	63	2	a︸	a︸	ADV
ejpam-6259	63	3	︷︷	︷︷	PROPN
ejpam-6259	63	4	︸	︸	ADP
ejpam-6259	63	5	t	t	PROPN
ejpam-6259	63	6	,	,	PUNCT
ejpam-6259	63	7	ai+t+1	ai+t+1	PROPN
ejpam-6259	63	8	,	,	PUNCT
ejpam-6259	63	9	.	.	PUNCT
ejpam-6259	63	10	.	.	PUNCT
ejpam-6259	64	1	.	.	PUNCT
ejpam-6259	65	1	,	,	PUNCT
ejpam-6259	65	2	an	an	X
ejpam-6259	65	3	)	)	PUNCT
ejpam-6259	65	4	=	=	PUNCT
ejpam-6259	65	5	f(ai1	f(ai1	PROPN
ejpam-6259	65	6	,	,	PUNCT
ejpam-6259	65	7	a	a	DET
ejpam-6259	65	8	t	t	PROPN
ejpam-6259	65	9	,	,	PUNCT
ejpam-6259	65	10	ani+t+1	ani+t+1	PROPN
ejpam-6259	65	11	)	)	PUNCT
ejpam-6259	65	12	.	.	PUNCT
ejpam-6259	66	1	an	an	DET
ejpam-6259	66	2	n	n	NUM
ejpam-6259	66	3	-	-	PUNCT
ejpam-6259	66	4	ary	ary	NOUN
ejpam-6259	66	5	groupoid	groupoid	PROPN
ejpam-6259	66	6	(	(	PUNCT
ejpam-6259	66	7	a	a	DET
ejpam-6259	66	8	,	,	PUNCT
ejpam-6259	66	9	f	f	X
ejpam-6259	66	10	)	)	PUNCT
ejpam-6259	66	11	is	be	AUX
ejpam-6259	66	12	called	call	VERB
ejpam-6259	66	13	(	(	PUNCT
ejpam-6259	66	14	i	i	PROPN
ejpam-6259	66	15	,	,	PUNCT
ejpam-6259	66	16	j)-associative	j)-associative	ADJ
ejpam-6259	66	17	if	if	SCONJ
ejpam-6259	66	18	f(ai−1	f(ai−1	PROPN
ejpam-6259	66	19	1	1	NUM
ejpam-6259	66	20	,	,	PUNCT
ejpam-6259	66	21	f(an+i−1	f(an+i−1	PROPN
ejpam-6259	66	22	i	i	PROPN
ejpam-6259	66	23	)	)	PUNCT
ejpam-6259	66	24	,	,	PUNCT
ejpam-6259	66	25	a2n−1	a2n−1	PROPN
ejpam-6259	66	26	n+i	n+i	NUM
ejpam-6259	66	27	)	)	PUNCT
ejpam-6259	67	1	=	=	PRON
ejpam-6259	67	2	f(aj−1	f(aj−1	NOUN
ejpam-6259	67	3	1	1	NUM
ejpam-6259	67	4	,	,	PUNCT
ejpam-6259	67	5	f(an+j−1	f(an+j−1	PROPN
ejpam-6259	67	6	j	j	PROPN
ejpam-6259	67	7	)	)	PUNCT
ejpam-6259	67	8	,	,	PUNCT
ejpam-6259	67	9	a2n−1	a2n−1	PROPN
ejpam-6259	67	10	n+j	n+j	PROPN
ejpam-6259	67	11	)	)	PUNCT
ejpam-6259	67	12	holds	hold	VERB
ejpam-6259	67	13	for	for	ADP
ejpam-6259	67	14	all	all	DET
ejpam-6259	67	15	a1	a1	NOUN
ejpam-6259	67	16	,	,	PUNCT
ejpam-6259	67	17	a2	a2	PROPN
ejpam-6259	67	18	,	,	PUNCT
ejpam-6259	67	19	.	.	PUNCT
ejpam-6259	67	20	.	.	PUNCT
ejpam-6259	68	1	.	.	PUNCT
ejpam-6259	69	1	,	,	PUNCT
ejpam-6259	69	2	a2n−1	a2n−1	PROPN
ejpam-6259	69	3	∈	∈	PROPN
ejpam-6259	69	4	a.	a.	NOUN
ejpam-6259	69	5	the	the	DET
ejpam-6259	69	6	n	n	NUM
ejpam-6259	69	7	-	-	PUNCT
ejpam-6259	69	8	ary	ary	PROPN
ejpam-6259	69	9	operation	operation	NOUN
ejpam-6259	69	10	f	f	PROPN
ejpam-6259	69	11	is	be	AUX
ejpam-6259	69	12	called	call	VERB
ejpam-6259	69	13	associative	associative	ADJ
ejpam-6259	69	14	if	if	SCONJ
ejpam-6259	69	15	the	the	DET
ejpam-6259	69	16	above	above	ADJ
ejpam-6259	69	17	identity	identity	NOUN
ejpam-6259	69	18	holds	hold	VERB
ejpam-6259	69	19	for	for	ADP
ejpam-6259	69	20	every	every	DET
ejpam-6259	69	21	1	1	NUM
ejpam-6259	69	22	≤	≤	NUM
ejpam-6259	70	1	i	i	PRON
ejpam-6259	70	2	≤	≤	NUM
ejpam-6259	70	3	j	j	PROPN
ejpam-6259	70	4	≤	≤	PROPN
ejpam-6259	70	5	n.	n.	NOUN
ejpam-6259	70	6	in	in	ADP
ejpam-6259	70	7	the	the	DET
ejpam-6259	70	8	case	case	NOUN
ejpam-6259	70	9	of	of	ADP
ejpam-6259	70	10	the	the	DET
ejpam-6259	70	11	n	n	CCONJ
ejpam-6259	70	12	-	-	PUNCT
ejpam-6259	70	13	ary	ary	PROPN
ejpam-6259	70	14	operation	operation	NOUN
ejpam-6259	70	15	f	f	PROPN
ejpam-6259	70	16	is	be	AUX
ejpam-6259	70	17	associate	associate	ADJ
ejpam-6259	70	18	,	,	PUNCT
ejpam-6259	70	19	(	(	PUNCT
ejpam-6259	70	20	a	a	DET
ejpam-6259	70	21	,	,	PUNCT
ejpam-6259	70	22	f	f	X
ejpam-6259	70	23	)	)	PUNCT
ejpam-6259	70	24	is	be	AUX
ejpam-6259	70	25	called	call	VERB
ejpam-6259	70	26	an	an	DET
ejpam-6259	70	27	n	n	CCONJ
ejpam-6259	70	28	-	-	PUNCT
ejpam-6259	70	29	ary	ary	NOUN
ejpam-6259	70	30	semigroup	semigroup	PROPN
ejpam-6259	70	31	.	.	PUNCT
ejpam-6259	71	1	a	a	DET
ejpam-6259	71	2	nonempty	nonempty	ADV
ejpam-6259	71	3	subset	subset	VERB
ejpam-6259	71	4	s	s	NOUN
ejpam-6259	71	5	of	of	ADP
ejpam-6259	71	6	an	an	DET
ejpam-6259	71	7	n	n	CCONJ
ejpam-6259	71	8	-	-	PUNCT
ejpam-6259	71	9	ary	ary	NOUN
ejpam-6259	71	10	semigroup	semigroup	NOUN
ejpam-6259	71	11	(	(	PUNCT
ejpam-6259	71	12	a	a	PRON
ejpam-6259	71	13	,	,	PUNCT
ejpam-6259	71	14	f	f	X
ejpam-6259	71	15	)	)	PUNCT
ejpam-6259	71	16	is	be	AUX
ejpam-6259	71	17	called	call	VERB
ejpam-6259	71	18	an	an	DET
ejpam-6259	71	19	n	n	CCONJ
ejpam-6259	71	20	-	-	PUNCT
ejpam-6259	71	21	ary	ary	NOUN
ejpam-6259	71	22	subsemigroup	subsemigroup	NOUN
ejpam-6259	71	23	of	of	ADP
ejpam-6259	71	24	a	a	DET
ejpam-6259	71	25	if	if	NOUN
ejpam-6259	71	26	f(an1	f(an1	PROPN
ejpam-6259	72	1	)	)	PUNCT
ejpam-6259	72	2	∈	∈	PROPN
ejpam-6259	72	3	s	s	X
ejpam-6259	72	4	for	for	ADP
ejpam-6259	72	5	all	all	DET
ejpam-6259	72	6	a1	a1	NOUN
ejpam-6259	72	7	,	,	PUNCT
ejpam-6259	72	8	a2	a2	PROPN
ejpam-6259	72	9	,	,	PUNCT
ejpam-6259	72	10	.	.	PUNCT
ejpam-6259	72	11	.	.	PUNCT
ejpam-6259	73	1	.	.	PUNCT
ejpam-6259	74	1	,	,	PUNCT
ejpam-6259	74	2	an	an	DET
ejpam-6259	74	3	∈	∈	PROPN
ejpam-6259	74	4	s.	s.	PROPN
ejpam-6259	74	5	for	for	ADP
ejpam-6259	74	6	nonempty	nonempty	ADJ
ejpam-6259	74	7	subsets	subset	NOUN
ejpam-6259	74	8	s1	s1	NOUN
ejpam-6259	74	9	,	,	PUNCT
ejpam-6259	74	10	s2	s2	PROPN
ejpam-6259	74	11	,	,	PUNCT
ejpam-6259	74	12	.	.	PUNCT
ejpam-6259	74	13	.	.	PUNCT
ejpam-6259	75	1	.	.	PUNCT
ejpam-6259	76	1	,	,	PUNCT
ejpam-6259	76	2	sn	sn	PROPN
ejpam-6259	76	3	of	of	ADP
ejpam-6259	76	4	a	a	PRON
ejpam-6259	76	5	,	,	PUNCT
ejpam-6259	76	6	let	let	VERB
ejpam-6259	76	7	f(sn	f(sn	PROPN
ejpam-6259	76	8	1	1	NUM
ejpam-6259	76	9	)	)	PUNCT
ejpam-6259	76	10	:	:	PUNCT
ejpam-6259	77	1	=	=	SYM
ejpam-6259	77	2	{	{	PUNCT
ejpam-6259	77	3	f(an1	f(an1	PROPN
ejpam-6259	77	4	)	)	PUNCT
ejpam-6259	78	1	|	|	ADV
ejpam-6259	78	2	ai	ai	VERB
ejpam-6259	78	3	∈	∈	PROPN
ejpam-6259	78	4	si	si	X
ejpam-6259	78	5	for	for	ADP
ejpam-6259	78	6	all	all	PRON
ejpam-6259	78	7	i	i	PRON
ejpam-6259	78	8	∈	∈	PROPN
ejpam-6259	78	9	{	{	PUNCT
ejpam-6259	78	10	1	1	NUM
ejpam-6259	78	11	,	,	PUNCT
ejpam-6259	78	12	2	2	NUM
ejpam-6259	78	13	,	,	PUNCT
ejpam-6259	78	14	.	.	PUNCT
ejpam-6259	78	15	.	.	PUNCT
ejpam-6259	79	1	.	.	PUNCT
ejpam-6259	79	2	,	,	PUNCT
ejpam-6259	80	1	n	n	CCONJ
ejpam-6259	80	2	}	}	PUNCT
ejpam-6259	80	3	}	}	PUNCT
ejpam-6259	80	4	.	.	PUNCT
ejpam-6259	81	1	if	if	SCONJ
ejpam-6259	81	2	s1	s1	PROPN
ejpam-6259	81	3	=	=	PUNCT
ejpam-6259	81	4	{	{	PUNCT
ejpam-6259	81	5	a1	a1	NOUN
ejpam-6259	81	6	}	}	PUNCT
ejpam-6259	81	7	,	,	PUNCT
ejpam-6259	81	8	then	then	ADV
ejpam-6259	81	9	we	we	PRON
ejpam-6259	81	10	write	write	VERB
ejpam-6259	81	11	f({a1	f({a1	NOUN
ejpam-6259	81	12	}	}	PUNCT
ejpam-6259	81	13	,	,	PUNCT
ejpam-6259	81	14	sn	sn	PROPN
ejpam-6259	81	15	2	2	NUM
ejpam-6259	81	16	)	)	PUNCT
ejpam-6259	81	17	as	as	ADP
ejpam-6259	81	18	f(a1	f(a1	NOUN
ejpam-6259	81	19	,	,	PUNCT
ejpam-6259	81	20	s	s	VERB
ejpam-6259	81	21	n	n	PRON
ejpam-6259	81	22	2	2	NUM
ejpam-6259	81	23	)	)	PUNCT
ejpam-6259	81	24	,	,	PUNCT
ejpam-6259	81	25	and	and	CCONJ
ejpam-6259	81	26	similarly	similarly	ADV
ejpam-6259	81	27	in	in	ADP
ejpam-6259	81	28	another	another	DET
ejpam-6259	81	29	case	case	NOUN
ejpam-6259	81	30	such	such	ADJ
ejpam-6259	81	31	as	as	SCONJ
ejpam-6259	81	32	we	we	PRON
ejpam-6259	81	33	write	write	VERB
ejpam-6259	81	34	f({a1	f({a1	PROPN
ejpam-6259	81	35	}	}	PUNCT
ejpam-6259	81	36	,	,	PUNCT
ejpam-6259	81	37	sn−1	sn−1	PROPN
ejpam-6259	81	38	2	2	NUM
ejpam-6259	81	39	,	,	PUNCT
ejpam-6259	81	40	{	{	PUNCT
ejpam-6259	81	41	an	an	NOUN
ejpam-6259	81	42	}	}	PUNCT
ejpam-6259	81	43	)	)	PUNCT
ejpam-6259	81	44	as	as	ADP
ejpam-6259	81	45	f(a1	f(a1	NOUN
ejpam-6259	81	46	,	,	PUNCT
ejpam-6259	81	47	sn−1	sn−1	PROPN
ejpam-6259	81	48	2	2	NUM
ejpam-6259	81	49	,	,	PUNCT
ejpam-6259	81	50	an	an	PRON
ejpam-6259	81	51	)	)	PUNCT
ejpam-6259	81	52	and	and	CCONJ
ejpam-6259	81	53	so	so	ADV
ejpam-6259	81	54	on	on	ADV
ejpam-6259	81	55	.	.	PUNCT
ejpam-6259	82	1	for	for	ADP
ejpam-6259	82	2	any	any	DET
ejpam-6259	82	3	subset	subset	NOUN
ejpam-6259	82	4	s	s	NOUN
ejpam-6259	82	5	of	of	ADP
ejpam-6259	82	6	a	a	PRON
ejpam-6259	82	7	,	,	PUNCT
ejpam-6259	82	8	we	we	PRON
ejpam-6259	82	9	let	let	VERB
ejpam-6259	82	10	f(sn	f(sn	PRON
ejpam-6259	82	11	)	)	PUNCT
ejpam-6259	82	12	=	=	PRON
ejpam-6259	82	13	{	{	PUNCT
ejpam-6259	82	14	f(an1	f(an1	PROPN
ejpam-6259	82	15	)	)	PUNCT
ejpam-6259	82	16	|	|	ADV
ejpam-6259	82	17	a1	a1	NOUN
ejpam-6259	82	18	,	,	PUNCT
ejpam-6259	82	19	a2	a2	PROPN
ejpam-6259	82	20	,	,	PUNCT
ejpam-6259	82	21	.	.	PUNCT
ejpam-6259	82	22	.	.	PUNCT
ejpam-6259	83	1	.	.	PUNCT
ejpam-6259	84	1	,	,	PUNCT
ejpam-6259	84	2	an	an	DET
ejpam-6259	84	3	∈	∈	NOUN
ejpam-6259	84	4	s	s	PART
ejpam-6259	84	5	}	}	PUNCT
ejpam-6259	84	6	and	and	CCONJ
ejpam-6259	84	7	we	we	PRON
ejpam-6259	84	8	let	let	VERB
ejpam-6259	84	9	f(an	f(an	NOUN
ejpam-6259	84	10	)	)	PUNCT
ejpam-6259	84	11	=	=	PRON
ejpam-6259	84	12	{	{	PUNCT
ejpam-6259	84	13	f(an1	f(an1	PROPN
ejpam-6259	84	14	)	)	PUNCT
ejpam-6259	84	15	|	|	ADV
ejpam-6259	84	16	a1	a1	NOUN
ejpam-6259	84	17	,	,	PUNCT
ejpam-6259	84	18	a2	a2	PROPN
ejpam-6259	84	19	,	,	PUNCT
ejpam-6259	84	20	.	.	PUNCT
ejpam-6259	84	21	.	.	PUNCT
ejpam-6259	85	1	.	.	PUNCT
ejpam-6259	86	1	,	,	PUNCT
ejpam-6259	86	2	an	an	DET
ejpam-6259	86	3	∈	∈	PROPN
ejpam-6259	86	4	a	a	PRON
ejpam-6259	86	5	}	}	PUNCT
ejpam-6259	86	6	.	.	PUNCT
ejpam-6259	87	1	2.2	2.2	NUM
ejpam-6259	87	2	.	.	PUNCT
ejpam-6259	88	1	fuzzy	fuzzy	ADJ
ejpam-6259	88	2	subsets	subset	NOUN
ejpam-6259	88	3	a	a	DET
ejpam-6259	88	4	fuzzy	fuzzy	ADJ
ejpam-6259	88	5	subset	subset	NOUN
ejpam-6259	88	6	of	of	ADP
ejpam-6259	88	7	a	a	DET
ejpam-6259	88	8	set	set	NOUN
ejpam-6259	88	9	a	a	PRON
ejpam-6259	88	10	is	be	AUX
ejpam-6259	88	11	defined	define	VERB
ejpam-6259	88	12	as	as	ADP
ejpam-6259	88	13	a	a	DET
ejpam-6259	88	14	membership	membership	NOUN
ejpam-6259	88	15	function	function	NOUN
ejpam-6259	88	16	from	from	ADP
ejpam-6259	88	17	a	a	PRON
ejpam-6259	88	18	into	into	ADP
ejpam-6259	88	19	the	the	DET
ejpam-6259	88	20	closed	closed	ADJ
ejpam-6259	88	21	unit	unit	NOUN
ejpam-6259	88	22	interval	interval	NOUN
ejpam-6259	88	23	[	[	X
ejpam-6259	88	24	0	0	NUM
ejpam-6259	88	25	,	,	PUNCT
ejpam-6259	88	26	1	1	NUM
ejpam-6259	88	27	]	]	PUNCT
ejpam-6259	88	28	.	.	PUNCT
ejpam-6259	89	1	we	we	PRON
ejpam-6259	89	2	now	now	ADV
ejpam-6259	89	3	recall	recall	VERB
ejpam-6259	89	4	some	some	DET
ejpam-6259	89	5	notations	notation	NOUN
ejpam-6259	89	6	in	in	ADP
ejpam-6259	89	7	fuzzy	fuzzy	ADJ
ejpam-6259	89	8	sets	set	NOUN
ejpam-6259	89	9	,	,	PUNCT
ejpam-6259	89	10	as	as	SCONJ
ejpam-6259	89	11	presented	present	VERB
ejpam-6259	89	12	in	in	ADP
ejpam-6259	89	13	[	[	X
ejpam-6259	89	14	19	19	NUM
ejpam-6259	89	15	]	]	PUNCT
ejpam-6259	89	16	.	.	PUNCT
ejpam-6259	90	1	let	let	VERB
ejpam-6259	90	2	g	g	NOUN
ejpam-6259	90	3	and	and	CCONJ
ejpam-6259	90	4	h	h	NOUN
ejpam-6259	90	5	be	be	VERB
ejpam-6259	90	6	two	two	NUM
ejpam-6259	90	7	fuzzy	fuzzy	ADJ
ejpam-6259	90	8	subsets	subset	NOUN
ejpam-6259	90	9	of	of	ADP
ejpam-6259	90	10	a	a	DET
ejpam-6259	90	11	nonempty	nonempty	ADV
ejpam-6259	90	12	set	set	VERB
ejpam-6259	90	13	a.	a.	NOUN
ejpam-6259	90	14	1	1	NUM
ejpam-6259	90	15	.	.	PUNCT
ejpam-6259	91	1	the	the	DET
ejpam-6259	91	2	intersection	intersection	NOUN
ejpam-6259	91	3	of	of	ADP
ejpam-6259	91	4	g	g	PROPN
ejpam-6259	91	5	and	and	CCONJ
ejpam-6259	91	6	h	h	NOUN
ejpam-6259	91	7	,	,	PUNCT
ejpam-6259	91	8	denoted	denote	VERB
ejpam-6259	91	9	by	by	ADP
ejpam-6259	91	10	g	g	PROPN
ejpam-6259	91	11	∩	∩	ADJ
ejpam-6259	91	12	h	h	NOUN
ejpam-6259	91	13	,	,	PUNCT
ejpam-6259	91	14	is	be	AUX
ejpam-6259	91	15	a	a	DET
ejpam-6259	91	16	fuzzy	fuzzy	ADJ
ejpam-6259	91	17	subset	subset	NOUN
ejpam-6259	91	18	of	of	ADP
ejpam-6259	91	19	a	a	PRON
ejpam-6259	91	20	defined	define	VERB
ejpam-6259	91	21	by	by	ADP
ejpam-6259	91	22	(	(	PUNCT
ejpam-6259	91	23	g	g	PROPN
ejpam-6259	91	24	∩	∩	ADJ
ejpam-6259	91	25	h)(a	h)(a	NOUN
ejpam-6259	91	26	)	)	PUNCT
ejpam-6259	91	27	=	=	SYM
ejpam-6259	91	28	min{g(a	min{g(a	PROPN
ejpam-6259	91	29	)	)	PUNCT
ejpam-6259	91	30	,	,	PUNCT
ejpam-6259	91	31	h(a	h(a	PROPN
ejpam-6259	91	32	)	)	PUNCT
ejpam-6259	91	33	}	}	PUNCT
ejpam-6259	91	34	for	for	ADP
ejpam-6259	91	35	all	all	DET
ejpam-6259	91	36	a	a	DET
ejpam-6259	91	37	∈	∈	PROPN
ejpam-6259	91	38	a.	a.	NOUN
ejpam-6259	91	39	2	2	NUM
ejpam-6259	91	40	.	.	PUNCT
ejpam-6259	92	1	the	the	DET
ejpam-6259	92	2	union	union	NOUN
ejpam-6259	92	3	of	of	ADP
ejpam-6259	92	4	g	g	PROPN
ejpam-6259	92	5	and	and	CCONJ
ejpam-6259	92	6	h	h	NOUN
ejpam-6259	92	7	,	,	PUNCT
ejpam-6259	92	8	denoted	denote	VERB
ejpam-6259	92	9	by	by	ADP
ejpam-6259	92	10	g∪h	g∪h	NOUN
ejpam-6259	92	11	,	,	PUNCT
ejpam-6259	92	12	is	be	AUX
ejpam-6259	92	13	a	a	DET
ejpam-6259	92	14	fuzzy	fuzzy	ADJ
ejpam-6259	92	15	subset	subset	NOUN
ejpam-6259	92	16	of	of	ADP
ejpam-6259	92	17	a	a	PRON
ejpam-6259	92	18	defined	define	VERB
ejpam-6259	92	19	by	by	ADP
ejpam-6259	92	20	(	(	PUNCT
ejpam-6259	92	21	g∪h)(a	g∪h)(a	NOUN
ejpam-6259	92	22	)	)	PUNCT
ejpam-6259	92	23	=	=	PUNCT
ejpam-6259	92	24	max{g(a	max{g(a	PROPN
ejpam-6259	92	25	)	)	PUNCT
ejpam-6259	92	26	,	,	PUNCT
ejpam-6259	92	27	h(a	h(a	PROPN
ejpam-6259	92	28	)	)	PUNCT
ejpam-6259	92	29	}	}	PUNCT
ejpam-6259	92	30	for	for	ADP
ejpam-6259	92	31	all	all	DET
ejpam-6259	92	32	a	a	DET
ejpam-6259	92	33	∈	∈	PROPN
ejpam-6259	92	34	a.	a.	NOUN
ejpam-6259	92	35	3	3	NUM
ejpam-6259	92	36	.	.	PUNCT
ejpam-6259	93	1	g	g	PROPN
ejpam-6259	93	2	⊆	⊆	NUM
ejpam-6259	93	3	h	h	NOUN
ejpam-6259	93	4	if	if	SCONJ
ejpam-6259	93	5	g(a	g(a	PROPN
ejpam-6259	93	6	)	)	PUNCT
ejpam-6259	93	7	≤	≤	PROPN
ejpam-6259	93	8	h(a	h(a	PROPN
ejpam-6259	93	9	)	)	PUNCT
ejpam-6259	93	10	for	for	ADP
ejpam-6259	93	11	all	all	DET
ejpam-6259	93	12	a	a	DET
ejpam-6259	93	13	∈	∈	NOUN
ejpam-6259	93	14	a.	a.	NOUN
ejpam-6259	93	15	for	for	ADP
ejpam-6259	93	16	a	a	DET
ejpam-6259	93	17	fuzzy	fuzzy	ADJ
ejpam-6259	93	18	subset	subset	NOUN
ejpam-6259	93	19	g	g	NOUN
ejpam-6259	93	20	of	of	ADP
ejpam-6259	93	21	a	a	PRON
ejpam-6259	93	22	,	,	PUNCT
ejpam-6259	93	23	the	the	DET
ejpam-6259	93	24	support	support	NOUN
ejpam-6259	93	25	of	of	ADP
ejpam-6259	93	26	g	g	PROPN
ejpam-6259	93	27	is	be	AUX
ejpam-6259	93	28	defined	define	VERB
ejpam-6259	93	29	by	by	ADP
ejpam-6259	93	30	supp(g	supp(g	NUM
ejpam-6259	93	31	)	)	PUNCT
ejpam-6259	93	32	=	=	PRON
ejpam-6259	93	33	{	{	PUNCT
ejpam-6259	93	34	a	a	DET
ejpam-6259	93	35	∈	∈	PROPN
ejpam-6259	93	36	a	a	DET
ejpam-6259	93	37	|	|	NOUN
ejpam-6259	93	38	g(a	g(a	PROPN
ejpam-6259	93	39	)	)	PUNCT
ejpam-6259	93	40	̸=	̸=	PROPN
ejpam-6259	93	41	0	0	NUM
ejpam-6259	93	42	}	}	PUNCT
ejpam-6259	93	43	.	.	PUNCT
ejpam-6259	94	1	the	the	DET
ejpam-6259	94	2	characteristic	characteristic	ADJ
ejpam-6259	94	3	mapping	mapping	NOUN
ejpam-6259	94	4	of	of	ADP
ejpam-6259	94	5	a	a	DET
ejpam-6259	94	6	subset	subset	NOUN
ejpam-6259	94	7	s	s	NOUN
ejpam-6259	94	8	of	of	ADP
ejpam-6259	94	9	a	a	PRON
ejpam-6259	94	10	is	be	AUX
ejpam-6259	94	11	a	a	DET
ejpam-6259	94	12	fuzzy	fuzzy	ADJ
ejpam-6259	94	13	subset	subset	NOUN
ejpam-6259	94	14	of	of	ADP
ejpam-6259	94	15	a	a	PRON
ejpam-6259	94	16	defined	define	VERB
ejpam-6259	94	17	by	by	ADP
ejpam-6259	94	18	χs(a	χs(a	NOUN
ejpam-6259	94	19	)	)	PUNCT
ejpam-6259	95	1	=	=	PRON
ejpam-6259	95	2	{	{	PUNCT
ejpam-6259	95	3	1	1	NUM
ejpam-6259	95	4	a	a	DET
ejpam-6259	95	5	∈	∈	PROPN
ejpam-6259	95	6	s	s	NOUN
ejpam-6259	95	7	,	,	PUNCT
ejpam-6259	95	8	0	0	NUM
ejpam-6259	95	9	a	a	PRON
ejpam-6259	95	10	/∈	/∈	PUNCT
ejpam-6259	95	11	s.	s.	PROPN
ejpam-6259	95	12	r.	r.	PROPN
ejpam-6259	95	13	chinram	chinram	PROPN
ejpam-6259	95	14	,	,	PUNCT
ejpam-6259	95	15	p.	p.	NOUN
ejpam-6259	95	16	singavananda	singavananda	PROPN
ejpam-6259	95	17	/	/	SYM
ejpam-6259	95	18	eur	eur	PROPN
ejpam-6259	95	19	.	.	PUNCT
ejpam-6259	96	1	j.	j.	PROPN
ejpam-6259	96	2	pure	pure	PROPN
ejpam-6259	96	3	appl	appl	PROPN
ejpam-6259	96	4	.	.	PROPN
ejpam-6259	96	5	math	math	PROPN
ejpam-6259	96	6	,	,	PUNCT
ejpam-6259	96	7	18	18	NUM
ejpam-6259	96	8	(	(	PUNCT
ejpam-6259	96	9	3	3	NUM
ejpam-6259	96	10	)	)	PUNCT
ejpam-6259	96	11	(	(	PUNCT
ejpam-6259	96	12	2025	2025	NUM
ejpam-6259	96	13	)	)	PUNCT
ejpam-6259	96	14	,	,	PUNCT
ejpam-6259	96	15	6259	6259	NUM
ejpam-6259	96	16	4	4	NUM
ejpam-6259	96	17	of	of	ADP
ejpam-6259	96	18	10	10	NUM
ejpam-6259	96	19	a	a	DET
ejpam-6259	96	20	fuzzy	fuzzy	ADJ
ejpam-6259	96	21	subset	subset	NOUN
ejpam-6259	96	22	g	g	NOUN
ejpam-6259	96	23	of	of	ADP
ejpam-6259	96	24	an	an	DET
ejpam-6259	96	25	n	n	CCONJ
ejpam-6259	96	26	-	-	PUNCT
ejpam-6259	96	27	ary	ary	NOUN
ejpam-6259	96	28	semigroup	semigroup	NOUN
ejpam-6259	96	29	a	a	PRON
ejpam-6259	96	30	is	be	AUX
ejpam-6259	96	31	called	call	VERB
ejpam-6259	96	32	a	a	DET
ejpam-6259	96	33	fuzzy	fuzzy	ADJ
ejpam-6259	96	34	n	n	CCONJ
ejpam-6259	96	35	-	-	PUNCT
ejpam-6259	96	36	ary	ary	NOUN
ejpam-6259	96	37	subsemigroup	subsemigroup	NOUN
ejpam-6259	96	38	of	of	ADP
ejpam-6259	96	39	a	a	DET
ejpam-6259	96	40	if	if	SCONJ
ejpam-6259	96	41	g(an1	g(an1	PROPN
ejpam-6259	96	42	)	)	PUNCT
ejpam-6259	96	43	≥	≥	PRON
ejpam-6259	96	44	min{g(a1	min{g(a1	NOUN
ejpam-6259	96	45	)	)	PUNCT
ejpam-6259	96	46	,	,	PUNCT
ejpam-6259	96	47	g(a2	g(a2	PROPN
ejpam-6259	96	48	)	)	PUNCT
ejpam-6259	96	49	,	,	PUNCT
ejpam-6259	96	50	.	.	PUNCT
ejpam-6259	96	51	.	.	PUNCT
ejpam-6259	97	1	.	.	PUNCT
ejpam-6259	98	1	,	,	PUNCT
ejpam-6259	98	2	g(an	g(an	PROPN
ejpam-6259	98	3	)	)	PUNCT
ejpam-6259	98	4	}	}	PUNCT
ejpam-6259	98	5	for	for	ADP
ejpam-6259	98	6	all	all	DET
ejpam-6259	98	7	a1	a1	NOUN
ejpam-6259	98	8	,	,	PUNCT
ejpam-6259	98	9	a2	a2	PROPN
ejpam-6259	98	10	,	,	PUNCT
ejpam-6259	98	11	.	.	PUNCT
ejpam-6259	98	12	.	.	PUNCT
ejpam-6259	99	1	.	.	PUNCT
ejpam-6259	100	1	,	,	PUNCT
ejpam-6259	100	2	an	an	DET
ejpam-6259	100	3	∈	∈	PROPN
ejpam-6259	100	4	a.	a.	NOUN
ejpam-6259	100	5	let	let	AUX
ejpam-6259	100	6	f(a	f(a	PROPN
ejpam-6259	100	7	)	)	PUNCT
ejpam-6259	100	8	be	be	VERB
ejpam-6259	100	9	the	the	DET
ejpam-6259	100	10	set	set	NOUN
ejpam-6259	100	11	of	of	ADP
ejpam-6259	100	12	all	all	DET
ejpam-6259	100	13	fuzzy	fuzzy	ADJ
ejpam-6259	100	14	subsets	subset	NOUN
ejpam-6259	100	15	in	in	ADP
ejpam-6259	100	16	an	an	DET
ejpam-6259	100	17	n	n	CCONJ
ejpam-6259	100	18	-	-	PUNCT
ejpam-6259	100	19	ary	ary	PROPN
ejpam-6259	100	20	semigroup	semigroup	PROPN
ejpam-6259	100	21	a.	a.	NOUN
ejpam-6259	100	22	define	define	NOUN
ejpam-6259	100	23	n	n	CCONJ
ejpam-6259	100	24	-	-	PUNCT
ejpam-6259	100	25	ary	ary	NOUN
ejpam-6259	100	26	operator	operator	NOUN
ejpam-6259	100	27	f	f	PROPN
ejpam-6259	100	28	on	on	ADP
ejpam-6259	100	29	f(a	f(a	PROPN
ejpam-6259	100	30	)	)	PUNCT
ejpam-6259	100	31	by	by	ADP
ejpam-6259	100	32	f(gn1	f(gn1	NOUN
ejpam-6259	100	33	)	)	PUNCT
ejpam-6259	100	34	(	(	PUNCT
ejpam-6259	100	35	a	a	X
ejpam-6259	100	36	)	)	PUNCT
ejpam-6259	100	37	:	:	PUNCT
ejpam-6259	100	38	=	=	SYM
ejpam-6259	100	39	f(g1	f(g1	NOUN
ejpam-6259	100	40	,	,	PUNCT
ejpam-6259	100	41	g2	g2	PROPN
ejpam-6259	100	42	,	,	PUNCT
ejpam-6259	100	43	.	.	PUNCT
ejpam-6259	100	44	.	.	PUNCT
ejpam-6259	100	45	.	.	PUNCT
ejpam-6259	101	1	,	,	PUNCT
ejpam-6259	101	2	gn)(a	gn)(a	NOUN
ejpam-6259	101	3	)	)	PUNCT
ejpam-6259	102	1	=	=	PUNCT
ejpam-6259	102	2			PUNCT
ejpam-6259	102	3	sup	sup	NOUN
ejpam-6259	102	4	a	a	DET
ejpam-6259	102	5	=	=	NOUN
ejpam-6259	102	6	f(an1	f(an1	NOUN
ejpam-6259	102	7	)	)	PUNCT
ejpam-6259	102	8	min{g1(a1	min{g1(a1	NOUN
ejpam-6259	102	9	)	)	PUNCT
ejpam-6259	102	10	,	,	PUNCT
ejpam-6259	102	11	g2(a2	g2(a2	PROPN
ejpam-6259	102	12	)	)	PUNCT
ejpam-6259	102	13	,	,	PUNCT
ejpam-6259	102	14	.	.	PUNCT
ejpam-6259	102	15	.	.	PUNCT
ejpam-6259	103	1	.	.	PUNCT
ejpam-6259	104	1	,	,	PUNCT
ejpam-6259	104	2	gn(an	gn(an	NOUN
ejpam-6259	104	3	)	)	PUNCT
ejpam-6259	104	4	}	}	PUNCT
ejpam-6259	104	5	if	if	SCONJ
ejpam-6259	104	6	a	a	DET
ejpam-6259	104	7	∈	∈	PROPN
ejpam-6259	104	8	f(an	f(an	NOUN
ejpam-6259	104	9	)	)	PUNCT
ejpam-6259	104	10	,	,	PUNCT
ejpam-6259	104	11	0	0	NUM
ejpam-6259	104	12	otherwise	otherwise	ADV
ejpam-6259	104	13	,	,	PUNCT
ejpam-6259	104	14	for	for	ADP
ejpam-6259	104	15	all	all	DET
ejpam-6259	104	16	g1	g1	NOUN
ejpam-6259	104	17	,	,	PUNCT
ejpam-6259	104	18	g2	g2	PROPN
ejpam-6259	104	19	,	,	PUNCT
ejpam-6259	104	20	.	.	PUNCT
ejpam-6259	104	21	.	.	PUNCT
ejpam-6259	104	22	.	.	PUNCT
ejpam-6259	105	1	,	,	PUNCT
ejpam-6259	105	2	gn	gn	PROPN
ejpam-6259	105	3	∈	∈	PROPN
ejpam-6259	105	4	f(a	f(a	PROPN
ejpam-6259	105	5	)	)	PUNCT
ejpam-6259	105	6	and	and	CCONJ
ejpam-6259	105	7	a	a	DET
ejpam-6259	105	8	∈	∈	NOUN
ejpam-6259	105	9	a.	a.	NOUN
ejpam-6259	105	10	proposition	proposition	NOUN
ejpam-6259	105	11	1	1	NUM
ejpam-6259	105	12	.	.	PUNCT
ejpam-6259	106	1	a	a	DET
ejpam-6259	106	2	fuzzy	fuzzy	ADJ
ejpam-6259	106	3	subset	subset	VERB
ejpam-6259	106	4	g	g	NOUN
ejpam-6259	106	5	of	of	ADP
ejpam-6259	106	6	an	an	DET
ejpam-6259	106	7	n	n	CCONJ
ejpam-6259	106	8	-	-	PUNCT
ejpam-6259	106	9	ary	ary	NOUN
ejpam-6259	106	10	semigroup	semigroup	NOUN
ejpam-6259	106	11	a	a	PRON
ejpam-6259	106	12	is	be	AUX
ejpam-6259	106	13	a	a	DET
ejpam-6259	106	14	fuzzy	fuzzy	ADJ
ejpam-6259	106	15	n	n	CCONJ
ejpam-6259	106	16	-	-	PUNCT
ejpam-6259	106	17	ary	ary	NOUN
ejpam-6259	106	18	subsemigroup	subsemigroup	NOUN
ejpam-6259	106	19	of	of	ADP
ejpam-6259	106	20	a	a	DET
ejpam-6259	106	21	if	if	NOUN
ejpam-6259	106	22	and	and	CCONJ
ejpam-6259	106	23	only	only	ADV
ejpam-6259	106	24	if	if	SCONJ
ejpam-6259	106	25	f(gn	f(gn	NOUN
ejpam-6259	106	26	)	)	PUNCT
ejpam-6259	106	27	⊆	⊆	NUM
ejpam-6259	106	28	g.	g.	NOUN
ejpam-6259	106	29	3	3	NUM
ejpam-6259	106	30	.	.	PUNCT
ejpam-6259	106	31	main	main	ADJ
ejpam-6259	106	32	results	result	NOUN
ejpam-6259	106	33	3.1	3.1	NUM
ejpam-6259	106	34	.	.	PUNCT
ejpam-6259	107	1	almost	almost	ADV
ejpam-6259	107	2	n	n	CCONJ
ejpam-6259	107	3	-	-	PUNCT
ejpam-6259	107	4	ary	ary	PROPN
ejpam-6259	107	5	subsemigroups	subsemigroup	NOUN
ejpam-6259	107	6	we	we	PRON
ejpam-6259	107	7	begin	begin	VERB
ejpam-6259	107	8	by	by	ADP
ejpam-6259	107	9	introducing	introduce	VERB
ejpam-6259	107	10	the	the	DET
ejpam-6259	107	11	definition	definition	NOUN
ejpam-6259	107	12	of	of	ADP
ejpam-6259	107	13	almost	almost	ADV
ejpam-6259	107	14	n	n	CCONJ
ejpam-6259	107	15	-	-	PUNCT
ejpam-6259	107	16	ary	ary	PROPN
ejpam-6259	107	17	subsemigroups	subsemigroup	NOUN
ejpam-6259	107	18	of	of	ADP
ejpam-6259	107	19	n	n	CCONJ
ejpam-6259	107	20	-	-	PUNCT
ejpam-6259	107	21	ary	ary	NOUN
ejpam-6259	107	22	semigroups	semigroup	NOUN
ejpam-6259	107	23	.	.	PUNCT
ejpam-6259	108	1	definition	definition	NOUN
ejpam-6259	108	2	1	1	NUM
ejpam-6259	108	3	.	.	PUNCT
ejpam-6259	109	1	a	a	DET
ejpam-6259	109	2	nonempty	nonempty	ADJ
ejpam-6259	109	3	subset	subset	VERB
ejpam-6259	109	4	s	s	NOUN
ejpam-6259	109	5	of	of	ADP
ejpam-6259	109	6	an	an	DET
ejpam-6259	109	7	n	n	CCONJ
ejpam-6259	109	8	-	-	PUNCT
ejpam-6259	109	9	ary	ary	NOUN
ejpam-6259	109	10	semigroup	semigroup	NOUN
ejpam-6259	109	11	a	a	PRON
ejpam-6259	109	12	is	be	AUX
ejpam-6259	109	13	called	call	VERB
ejpam-6259	109	14	an	an	DET
ejpam-6259	109	15	almost	almost	ADV
ejpam-6259	109	16	n	n	CCONJ
ejpam-6259	109	17	-	-	PUNCT
ejpam-6259	109	18	ary	ary	NOUN
ejpam-6259	109	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	109	20	of	of	ADP
ejpam-6259	109	21	a	a	DET
ejpam-6259	109	22	if	if	SCONJ
ejpam-6259	109	23	f(sn	f(sn	NOUN
ejpam-6259	109	24	)	)	PUNCT
ejpam-6259	109	25	∩	∩	NOUN
ejpam-6259	109	26	s	s	PART
ejpam-6259	109	27	̸=	̸=	PROPN
ejpam-6259	109	28	∅.	∅.	ADP
ejpam-6259	109	29	every	every	DET
ejpam-6259	109	30	n	n	CCONJ
ejpam-6259	109	31	-	-	PUNCT
ejpam-6259	109	32	ary	ary	NOUN
ejpam-6259	109	33	subsemigroup	subsemigroup	NOUN
ejpam-6259	109	34	of	of	ADP
ejpam-6259	109	35	an	an	DET
ejpam-6259	109	36	n	n	CCONJ
ejpam-6259	109	37	-	-	PUNCT
ejpam-6259	109	38	ary	ary	NOUN
ejpam-6259	109	39	semigroup	semigroup	NOUN
ejpam-6259	109	40	a	a	PRON
ejpam-6259	109	41	is	be	AUX
ejpam-6259	109	42	clearly	clearly	ADV
ejpam-6259	109	43	an	an	DET
ejpam-6259	109	44	almost	almost	ADV
ejpam-6259	109	45	n	n	CCONJ
ejpam-6259	109	46	-	-	PUNCT
ejpam-6259	109	47	ary	ary	NOUN
ejpam-6259	109	48	subsemigroup	subsemigroup	NOUN
ejpam-6259	109	49	of	of	ADP
ejpam-6259	109	50	a.	a.	NOUN
ejpam-6259	109	51	example	example	NOUN
ejpam-6259	110	1	1	1	X
ejpam-6259	110	2	.	.	X
ejpam-6259	110	3	we	we	PRON
ejpam-6259	110	4	consider	consider	VERB
ejpam-6259	110	5	an	an	DET
ejpam-6259	110	6	n	n	CCONJ
ejpam-6259	110	7	-	-	PUNCT
ejpam-6259	110	8	ary	ary	NOUN
ejpam-6259	110	9	semigroup	semigroup	PROPN
ejpam-6259	110	10	n	n	PROPN
ejpam-6259	110	11	under	under	ADP
ejpam-6259	110	12	the	the	DET
ejpam-6259	110	13	usual	usual	ADJ
ejpam-6259	110	14	n	n	CCONJ
ejpam-6259	110	15	-	-	PUNCT
ejpam-6259	110	16	ary	ary	NOUN
ejpam-6259	110	17	multiplication	multiplication	NOUN
ejpam-6259	110	18	of	of	ADP
ejpam-6259	110	19	integers	integer	NOUN
ejpam-6259	110	20	.	.	PUNCT
ejpam-6259	111	1	let	let	VERB
ejpam-6259	111	2	s	s	PRON
ejpam-6259	111	3	=	=	X
ejpam-6259	111	4	{	{	PUNCT
ejpam-6259	111	5	2	2	NUM
ejpam-6259	111	6	,	,	PUNCT
ejpam-6259	111	7	2n	2n	NUM
ejpam-6259	111	8	}	}	PUNCT
ejpam-6259	111	9	and	and	CCONJ
ejpam-6259	111	10	t	t	NOUN
ejpam-6259	111	11	=	=	SYM
ejpam-6259	111	12	{	{	PUNCT
ejpam-6259	111	13	2n	2n	NUM
ejpam-6259	111	14	,	,	PUNCT
ejpam-6259	111	15	2n2	2n2	NUM
ejpam-6259	111	16	}	}	PUNCT
ejpam-6259	111	17	.	.	PUNCT
ejpam-6259	112	1	clearly	clearly	ADV
ejpam-6259	112	2	,	,	PUNCT
ejpam-6259	112	3	s	s	PRON
ejpam-6259	112	4	and	and	CCONJ
ejpam-6259	112	5	t	t	PROPN
ejpam-6259	112	6	are	be	AUX
ejpam-6259	112	7	almost	almost	ADV
ejpam-6259	112	8	n	n	CCONJ
ejpam-6259	112	9	-	-	PUNCT
ejpam-6259	112	10	ary	ary	NOUN
ejpam-6259	112	11	subsemigroups	subsemigroup	NOUN
ejpam-6259	112	12	but	but	CCONJ
ejpam-6259	112	13	are	be	AUX
ejpam-6259	112	14	not	not	PART
ejpam-6259	112	15	n	n	CCONJ
ejpam-6259	112	16	-	-	PUNCT
ejpam-6259	112	17	ary	ary	PROPN
ejpam-6259	112	18	subsemigroups	subsemigroup	NOUN
ejpam-6259	112	19	of	of	ADP
ejpam-6259	112	20	n.	n.	PROPN
ejpam-6259	112	21	however	however	ADV
ejpam-6259	112	22	,	,	PUNCT
ejpam-6259	112	23	s	s	VERB
ejpam-6259	112	24	∩	∩	ADJ
ejpam-6259	112	25	t	t	NOUN
ejpam-6259	112	26	=	=	SYM
ejpam-6259	112	27	{	{	PUNCT
ejpam-6259	112	28	2n	2n	NUM
ejpam-6259	112	29	}	}	PUNCT
ejpam-6259	112	30	is	be	AUX
ejpam-6259	112	31	not	not	PART
ejpam-6259	112	32	an	an	DET
ejpam-6259	112	33	almost	almost	ADV
ejpam-6259	112	34	n	n	CCONJ
ejpam-6259	112	35	-	-	PUNCT
ejpam-6259	112	36	ary	ary	NOUN
ejpam-6259	112	37	subsemigroup	subsemigroup	NOUN
ejpam-6259	112	38	of	of	ADP
ejpam-6259	112	39	n.	n.	NOUN
ejpam-6259	112	40	from	from	ADP
ejpam-6259	112	41	example	example	NOUN
ejpam-6259	112	42	1	1	NUM
ejpam-6259	112	43	,	,	PUNCT
ejpam-6259	112	44	we	we	PRON
ejpam-6259	112	45	can	can	AUX
ejpam-6259	112	46	draw	draw	VERB
ejpam-6259	112	47	the	the	DET
ejpam-6259	112	48	following	following	ADJ
ejpam-6259	112	49	conclusions	conclusion	NOUN
ejpam-6259	112	50	.	.	PUNCT
ejpam-6259	113	1	(	(	PUNCT
ejpam-6259	113	2	1	1	X
ejpam-6259	113	3	)	)	PUNCT
ejpam-6259	113	4	in	in	ADP
ejpam-6259	113	5	general	general	ADJ
ejpam-6259	113	6	,	,	PUNCT
ejpam-6259	113	7	an	an	DET
ejpam-6259	113	8	almost	almost	ADV
ejpam-6259	113	9	n	n	CCONJ
ejpam-6259	113	10	-	-	PUNCT
ejpam-6259	113	11	ary	ary	NOUN
ejpam-6259	113	12	subsemigroup	subsemigroup	NOUN
ejpam-6259	113	13	of	of	ADP
ejpam-6259	113	14	an	an	DET
ejpam-6259	113	15	n	n	CCONJ
ejpam-6259	113	16	-	-	PUNCT
ejpam-6259	113	17	ary	ary	NOUN
ejpam-6259	113	18	semigroup	semigroup	NOUN
ejpam-6259	113	19	a	a	DET
ejpam-6259	113	20	need	need	NOUN
ejpam-6259	113	21	not	not	PART
ejpam-6259	113	22	be	be	AUX
ejpam-6259	113	23	a	a	DET
ejpam-6259	113	24	n	n	CCONJ
ejpam-6259	113	25	-	-	PUNCT
ejpam-6259	113	26	ary	ary	NOUN
ejpam-6259	113	27	subsemigroup	subsemigroup	NOUN
ejpam-6259	113	28	of	of	ADP
ejpam-6259	113	29	a.	a.	NOUN
ejpam-6259	113	30	(	(	PUNCT
ejpam-6259	113	31	2	2	NUM
ejpam-6259	113	32	)	)	PUNCT
ejpam-6259	113	33	the	the	DET
ejpam-6259	113	34	intersection	intersection	NOUN
ejpam-6259	113	35	of	of	ADP
ejpam-6259	113	36	almost	almost	ADV
ejpam-6259	113	37	n	n	CCONJ
ejpam-6259	113	38	-	-	PUNCT
ejpam-6259	113	39	ary	ary	PROPN
ejpam-6259	113	40	subsemigroups	subsemigroup	NOUN
ejpam-6259	113	41	of	of	ADP
ejpam-6259	113	42	an	an	DET
ejpam-6259	113	43	n	n	CCONJ
ejpam-6259	113	44	-	-	PUNCT
ejpam-6259	113	45	ary	ary	NOUN
ejpam-6259	113	46	semigroup	semigroup	NOUN
ejpam-6259	113	47	a	a	DET
ejpam-6259	113	48	need	need	NOUN
ejpam-6259	113	49	not	not	PART
ejpam-6259	113	50	be	be	AUX
ejpam-6259	113	51	an	an	DET
ejpam-6259	113	52	almost	almost	ADV
ejpam-6259	113	53	n	n	CCONJ
ejpam-6259	113	54	-	-	PUNCT
ejpam-6259	113	55	ary	ary	NOUN
ejpam-6259	113	56	subsemigroup	subsemigroup	NOUN
ejpam-6259	113	57	of	of	ADP
ejpam-6259	113	58	a.	a.	NOUN
ejpam-6259	113	59	theorem	theorem	NOUN
ejpam-6259	113	60	1	1	X
ejpam-6259	113	61	.	.	PUNCT
ejpam-6259	114	1	let	let	VERB
ejpam-6259	114	2	s	s	PRON
ejpam-6259	114	3	be	be	AUX
ejpam-6259	114	4	an	an	DET
ejpam-6259	114	5	almost	almost	ADV
ejpam-6259	114	6	n	n	CCONJ
ejpam-6259	114	7	-	-	PUNCT
ejpam-6259	114	8	ary	ary	NOUN
ejpam-6259	114	9	subsemigroup	subsemigroup	NOUN
ejpam-6259	114	10	of	of	ADP
ejpam-6259	114	11	an	an	DET
ejpam-6259	114	12	n	n	CCONJ
ejpam-6259	114	13	-	-	PUNCT
ejpam-6259	114	14	ary	ary	PROPN
ejpam-6259	114	15	semigroup	semigroup	PROPN
ejpam-6259	114	16	a.	a.	NOUN
ejpam-6259	114	17	if	if	SCONJ
ejpam-6259	114	18	t	t	PROPN
ejpam-6259	114	19	be	be	AUX
ejpam-6259	114	20	a	a	DET
ejpam-6259	114	21	nonempty	nonempty	ADJ
ejpam-6259	114	22	subset	subset	NOUN
ejpam-6259	114	23	of	of	ADP
ejpam-6259	114	24	a	a	DET
ejpam-6259	114	25	such	such	ADJ
ejpam-6259	114	26	that	that	DET
ejpam-6259	114	27	s	s	VERB
ejpam-6259	114	28	⊆	⊆	NUM
ejpam-6259	114	29	t	t	NOUN
ejpam-6259	114	30	,	,	PUNCT
ejpam-6259	114	31	then	then	ADV
ejpam-6259	114	32	t	t	PROPN
ejpam-6259	114	33	is	be	AUX
ejpam-6259	114	34	also	also	ADV
ejpam-6259	114	35	an	an	DET
ejpam-6259	114	36	almost	almost	ADV
ejpam-6259	114	37	n	n	CCONJ
ejpam-6259	114	38	-	-	PUNCT
ejpam-6259	114	39	ary	ary	NOUN
ejpam-6259	114	40	subsemigroup	subsemigroup	NOUN
ejpam-6259	114	41	of	of	ADP
ejpam-6259	114	42	a.	a.	NOUN
ejpam-6259	114	43	proof	proof	NOUN
ejpam-6259	114	44	.	.	PUNCT
ejpam-6259	115	1	let	let	VERB
ejpam-6259	115	2	s	s	PRON
ejpam-6259	115	3	be	be	AUX
ejpam-6259	115	4	an	an	DET
ejpam-6259	115	5	almost	almost	ADV
ejpam-6259	115	6	n	n	CCONJ
ejpam-6259	115	7	-	-	PUNCT
ejpam-6259	115	8	ary	ary	NOUN
ejpam-6259	115	9	subsemigroup	subsemigroup	NOUN
ejpam-6259	115	10	of	of	ADP
ejpam-6259	115	11	a	a	PRON
ejpam-6259	115	12	and	and	CCONJ
ejpam-6259	115	13	t	t	PROPN
ejpam-6259	115	14	be	be	AUX
ejpam-6259	115	15	a	a	DET
ejpam-6259	115	16	nonempty	nonempty	ADJ
ejpam-6259	115	17	subset	subset	NOUN
ejpam-6259	115	18	of	of	ADP
ejpam-6259	115	19	a	a	DET
ejpam-6259	115	20	such	such	ADJ
ejpam-6259	115	21	that	that	DET
ejpam-6259	115	22	s	s	VERB
ejpam-6259	115	23	⊆	⊆	NUM
ejpam-6259	115	24	t	t	NOUN
ejpam-6259	115	25	.	.	PUNCT
ejpam-6259	116	1	thus	thus	ADV
ejpam-6259	116	2	f(sn)∩s	f(sn)∩s	PROPN
ejpam-6259	116	3	̸=	̸=	PROPN
ejpam-6259	116	4	∅.	∅.	ADV
ejpam-6259	116	5	since	since	SCONJ
ejpam-6259	116	6	s	s	PROPN
ejpam-6259	116	7	⊆	⊆	NUM
ejpam-6259	116	8	t	t	NOUN
ejpam-6259	116	9	,	,	PUNCT
ejpam-6259	116	10	f(sn)∩s	f(sn)∩s	PROPN
ejpam-6259	116	11	⊆	⊆	NUM
ejpam-6259	116	12	f(tn)∩t	f(tn)∩t	X
ejpam-6259	116	13	.	.	PUNCT
ejpam-6259	117	1	this	this	PRON
ejpam-6259	117	2	implies	imply	VERB
ejpam-6259	117	3	that	that	SCONJ
ejpam-6259	117	4	f(tn	f(tn	NOUN
ejpam-6259	117	5	)	)	PUNCT
ejpam-6259	117	6	∩	∩	NOUN
ejpam-6259	117	7	t	t	PROPN
ejpam-6259	117	8	̸=	̸=	PROPN
ejpam-6259	117	9	∅.	∅.	PROPN
ejpam-6259	117	10	it	it	PRON
ejpam-6259	117	11	conclude	conclude	VERB
ejpam-6259	117	12	that	that	SCONJ
ejpam-6259	117	13	t	t	PROPN
ejpam-6259	117	14	is	be	AUX
ejpam-6259	117	15	an	an	DET
ejpam-6259	117	16	almost	almost	ADV
ejpam-6259	117	17	n	n	CCONJ
ejpam-6259	117	18	-	-	PUNCT
ejpam-6259	117	19	ary	ary	NOUN
ejpam-6259	117	20	subsemigroup	subsemigroup	NOUN
ejpam-6259	117	21	of	of	ADP
ejpam-6259	117	22	a.	a.	NOUN
ejpam-6259	117	23	the	the	DET
ejpam-6259	117	24	following	follow	VERB
ejpam-6259	117	25	corollary	corollary	NOUN
ejpam-6259	117	26	directly	directly	ADV
ejpam-6259	117	27	follows	follow	VERB
ejpam-6259	117	28	from	from	ADP
ejpam-6259	117	29	theorem	theorem	ADJ
ejpam-6259	117	30	1	1	NUM
ejpam-6259	117	31	.	.	PUNCT
ejpam-6259	117	32	r.	r.	PROPN
ejpam-6259	117	33	chinram	chinram	PROPN
ejpam-6259	117	34	,	,	PUNCT
ejpam-6259	117	35	p.	p.	NOUN
ejpam-6259	117	36	singavananda	singavananda	PROPN
ejpam-6259	117	37	/	/	SYM
ejpam-6259	117	38	eur	eur	PROPN
ejpam-6259	117	39	.	.	PUNCT
ejpam-6259	118	1	j.	j.	PROPN
ejpam-6259	118	2	pure	pure	PROPN
ejpam-6259	118	3	appl	appl	PROPN
ejpam-6259	118	4	.	.	PROPN
ejpam-6259	118	5	math	math	PROPN
ejpam-6259	118	6	,	,	PUNCT
ejpam-6259	118	7	18	18	NUM
ejpam-6259	118	8	(	(	PUNCT
ejpam-6259	118	9	3	3	NUM
ejpam-6259	118	10	)	)	PUNCT
ejpam-6259	118	11	(	(	PUNCT
ejpam-6259	118	12	2025	2025	NUM
ejpam-6259	118	13	)	)	PUNCT
ejpam-6259	118	14	,	,	PUNCT
ejpam-6259	118	15	6259	6259	NUM
ejpam-6259	118	16	5	5	NUM
ejpam-6259	118	17	of	of	ADP
ejpam-6259	118	18	10	10	NUM
ejpam-6259	118	19	corollary	corollary	ADJ
ejpam-6259	118	20	1	1	NUM
ejpam-6259	118	21	.	.	PUNCT
ejpam-6259	119	1	the	the	DET
ejpam-6259	119	2	union	union	NOUN
ejpam-6259	119	3	of	of	ADP
ejpam-6259	119	4	almost	almost	ADV
ejpam-6259	119	5	n	n	CCONJ
ejpam-6259	119	6	-	-	PUNCT
ejpam-6259	119	7	ary	ary	PROPN
ejpam-6259	119	8	subsemigroups	subsemigroup	NOUN
ejpam-6259	119	9	of	of	ADP
ejpam-6259	119	10	an	an	DET
ejpam-6259	119	11	n	n	CCONJ
ejpam-6259	119	12	-	-	PUNCT
ejpam-6259	119	13	ary	ary	NOUN
ejpam-6259	119	14	semigroup	semigroup	NOUN
ejpam-6259	119	15	a	a	PRON
ejpam-6259	119	16	is	be	AUX
ejpam-6259	119	17	also	also	ADV
ejpam-6259	119	18	an	an	DET
ejpam-6259	119	19	almost	almost	ADV
ejpam-6259	119	20	n	n	CCONJ
ejpam-6259	119	21	-	-	PUNCT
ejpam-6259	119	22	ary	ary	NOUN
ejpam-6259	119	23	subsemigroup	subsemigroup	NOUN
ejpam-6259	119	24	of	of	ADP
ejpam-6259	119	25	a.	a.	NOUN
ejpam-6259	119	26	an	an	DET
ejpam-6259	119	27	element	element	NOUN
ejpam-6259	119	28	a	a	PRON
ejpam-6259	119	29	of	of	ADP
ejpam-6259	119	30	an	an	DET
ejpam-6259	119	31	n	n	CCONJ
ejpam-6259	119	32	-	-	PUNCT
ejpam-6259	119	33	ary	ary	NOUN
ejpam-6259	119	34	semigroup	semigroup	NOUN
ejpam-6259	119	35	a	a	PRON
ejpam-6259	119	36	is	be	AUX
ejpam-6259	119	37	called	call	VERB
ejpam-6259	119	38	a	a	DET
ejpam-6259	119	39	selfpotent	selfpotent	NOUN
ejpam-6259	119	40	if	if	SCONJ
ejpam-6259	119	41	a	a	DET
ejpam-6259	119	42	=	=	SYM
ejpam-6259	119	43	f(an	f(an	NOUN
ejpam-6259	119	44	)	)	PUNCT
ejpam-6259	119	45	.	.	PUNCT
ejpam-6259	120	1	proposition	proposition	NOUN
ejpam-6259	120	2	2	2	NUM
ejpam-6259	120	3	.	.	PUNCT
ejpam-6259	120	4	let	let	VERB
ejpam-6259	120	5	a	a	DET
ejpam-6259	120	6	be	be	AUX
ejpam-6259	120	7	any	any	DET
ejpam-6259	120	8	element	element	NOUN
ejpam-6259	120	9	of	of	ADP
ejpam-6259	120	10	a	a	DET
ejpam-6259	120	11	n	n	CCONJ
ejpam-6259	120	12	-	-	PUNCT
ejpam-6259	120	13	ary	ary	PROPN
ejpam-6259	120	14	semigroup	semigroup	PROPN
ejpam-6259	120	15	a.	a.	NOUN
ejpam-6259	120	16	(	(	PUNCT
ejpam-6259	120	17	1	1	X
ejpam-6259	120	18	)	)	PUNCT
ejpam-6259	120	19	if	if	SCONJ
ejpam-6259	120	20	a	a	PRON
ejpam-6259	120	21	is	be	AUX
ejpam-6259	120	22	a	a	DET
ejpam-6259	120	23	selfpotent	selfpotent	NOUN
ejpam-6259	120	24	,	,	PUNCT
ejpam-6259	120	25	then	then	ADV
ejpam-6259	120	26	{	{	PUNCT
ejpam-6259	120	27	a	a	PRON
ejpam-6259	120	28	}	}	PUNCT
ejpam-6259	120	29	is	be	AUX
ejpam-6259	120	30	an	an	DET
ejpam-6259	120	31	almost	almost	ADV
ejpam-6259	120	32	n	n	CCONJ
ejpam-6259	120	33	-	-	PUNCT
ejpam-6259	120	34	ary	ary	NOUN
ejpam-6259	120	35	subsemigroup	subsemigroup	NOUN
ejpam-6259	120	36	of	of	ADP
ejpam-6259	120	37	a.	a.	NOUN
ejpam-6259	120	38	(	(	PUNCT
ejpam-6259	120	39	2	2	NUM
ejpam-6259	120	40	)	)	PUNCT
ejpam-6259	120	41	if	if	SCONJ
ejpam-6259	120	42	a	a	PRON
ejpam-6259	120	43	is	be	AUX
ejpam-6259	120	44	not	not	PART
ejpam-6259	120	45	a	a	DET
ejpam-6259	120	46	selfpotent	selfpotent	NOUN
ejpam-6259	120	47	,	,	PUNCT
ejpam-6259	120	48	then	then	ADV
ejpam-6259	120	49	{	{	PUNCT
ejpam-6259	120	50	a	a	PRON
ejpam-6259	120	51	,	,	PUNCT
ejpam-6259	120	52	f(an	f(an	NOUN
ejpam-6259	120	53	)	)	PUNCT
ejpam-6259	120	54	}	}	PUNCT
ejpam-6259	120	55	is	be	AUX
ejpam-6259	120	56	an	an	DET
ejpam-6259	120	57	almost	almost	ADV
ejpam-6259	120	58	n	n	CCONJ
ejpam-6259	120	59	-	-	PUNCT
ejpam-6259	120	60	ary	ary	NOUN
ejpam-6259	120	61	subsemigroup	subsemigroup	NOUN
ejpam-6259	120	62	of	of	ADP
ejpam-6259	120	63	a.	a.	PROPN
ejpam-6259	120	64	3.2	3.2	NUM
ejpam-6259	120	65	.	.	PUNCT
ejpam-6259	121	1	fuzzy	fuzzy	ADJ
ejpam-6259	121	2	almost	almost	ADV
ejpam-6259	121	3	n	n	CCONJ
ejpam-6259	121	4	-	-	PUNCT
ejpam-6259	121	5	ary	ary	PROPN
ejpam-6259	121	6	subsemigroups	subsemigroup	NOUN
ejpam-6259	121	7	in	in	ADP
ejpam-6259	121	8	this	this	DET
ejpam-6259	121	9	subsection	subsection	NOUN
ejpam-6259	121	10	,	,	PUNCT
ejpam-6259	121	11	we	we	PRON
ejpam-6259	121	12	define	define	VERB
ejpam-6259	121	13	fuzzy	fuzzy	ADJ
ejpam-6259	121	14	almost	almost	ADV
ejpam-6259	121	15	n	n	CCONJ
ejpam-6259	121	16	-	-	PUNCT
ejpam-6259	121	17	ary	ary	PROPN
ejpam-6259	121	18	subsemigroups	subsemigroup	NOUN
ejpam-6259	121	19	of	of	ADP
ejpam-6259	121	20	n	n	CCONJ
ejpam-6259	121	21	-	-	PUNCT
ejpam-6259	121	22	ary	ary	NOUN
ejpam-6259	121	23	semigroups	semigroup	NOUN
ejpam-6259	121	24	and	and	CCONJ
ejpam-6259	121	25	present	present	VERB
ejpam-6259	121	26	their	their	PRON
ejpam-6259	121	27	notable	notable	ADJ
ejpam-6259	121	28	properties	property	NOUN
ejpam-6259	121	29	.	.	PUNCT
ejpam-6259	122	1	a	a	DET
ejpam-6259	122	2	fuzzy	fuzzy	ADJ
ejpam-6259	122	3	subset	subset	VERB
ejpam-6259	122	4	g	g	NOUN
ejpam-6259	122	5	of	of	ADP
ejpam-6259	122	6	an	an	DET
ejpam-6259	122	7	n	n	CCONJ
ejpam-6259	122	8	-	-	PUNCT
ejpam-6259	122	9	ary	ary	NOUN
ejpam-6259	122	10	semigroup	semigroup	NOUN
ejpam-6259	122	11	a	a	PRON
ejpam-6259	122	12	is	be	AUX
ejpam-6259	122	13	called	call	VERB
ejpam-6259	122	14	a	a	DET
ejpam-6259	122	15	zero	zero	NUM
ejpam-6259	122	16	fuzzy	fuzzy	NOUN
ejpam-6259	122	17	subset	subset	VERB
ejpam-6259	122	18	if	if	SCONJ
ejpam-6259	122	19	g(a	g(a	PROPN
ejpam-6259	122	20	)	)	PUNCT
ejpam-6259	122	21	=	=	SYM
ejpam-6259	122	22	0	0	NUM
ejpam-6259	123	1	for	for	ADP
ejpam-6259	123	2	all	all	DET
ejpam-6259	123	3	a	a	DET
ejpam-6259	123	4	∈	∈	NOUN
ejpam-6259	123	5	a.	a.	NOUN
ejpam-6259	123	6	if	if	SCONJ
ejpam-6259	123	7	there	there	PRON
ejpam-6259	123	8	exists	exist	VERB
ejpam-6259	123	9	a	a	DET
ejpam-6259	123	10	∈	∈	NOUN
ejpam-6259	123	11	a	a	DET
ejpam-6259	123	12	such	such	ADJ
ejpam-6259	123	13	that	that	PRON
ejpam-6259	123	14	g(a	g(a	PROPN
ejpam-6259	123	15	)	)	PUNCT
ejpam-6259	123	16	̸=	̸=	PROPN
ejpam-6259	123	17	0	0	NUM
ejpam-6259	123	18	,	,	PUNCT
ejpam-6259	123	19	then	then	ADV
ejpam-6259	123	20	g	g	PROPN
ejpam-6259	123	21	is	be	AUX
ejpam-6259	123	22	called	call	VERB
ejpam-6259	123	23	a	a	DET
ejpam-6259	123	24	nonzero	nonzero	ADJ
ejpam-6259	123	25	fuzzy	fuzzy	ADJ
ejpam-6259	123	26	subset	subset	NOUN
ejpam-6259	123	27	of	of	ADP
ejpam-6259	123	28	a	a	PRON
ejpam-6259	123	29	and	and	CCONJ
ejpam-6259	123	30	we	we	PRON
ejpam-6259	123	31	use	use	VERB
ejpam-6259	123	32	the	the	DET
ejpam-6259	123	33	notation	notation	NOUN
ejpam-6259	123	34	g	g	PROPN
ejpam-6259	123	35	̸=	̸=	PROPN
ejpam-6259	123	36	0	0	NUM
ejpam-6259	123	37	.	.	PUNCT
ejpam-6259	124	1	definition	definition	NOUN
ejpam-6259	124	2	2	2	NUM
ejpam-6259	124	3	.	.	PUNCT
ejpam-6259	125	1	a	a	DET
ejpam-6259	125	2	fuzzy	fuzzy	ADJ
ejpam-6259	125	3	subset	subset	VERB
ejpam-6259	125	4	g	g	NOUN
ejpam-6259	125	5	of	of	ADP
ejpam-6259	125	6	an	an	DET
ejpam-6259	125	7	n	n	CCONJ
ejpam-6259	125	8	-	-	PUNCT
ejpam-6259	125	9	ary	ary	NOUN
ejpam-6259	125	10	semigroup	semigroup	NOUN
ejpam-6259	125	11	a	a	PRON
ejpam-6259	125	12	is	be	AUX
ejpam-6259	125	13	called	call	VERB
ejpam-6259	125	14	a	a	DET
ejpam-6259	125	15	fuzzy	fuzzy	ADJ
ejpam-6259	125	16	almost	almost	ADV
ejpam-6259	125	17	n	n	CCONJ
ejpam-6259	125	18	-	-	PUNCT
ejpam-6259	125	19	ary	ary	NOUN
ejpam-6259	125	20	subsemigroup	subsemigroup	NOUN
ejpam-6259	125	21	of	of	ADP
ejpam-6259	125	22	a	a	PRON
ejpam-6259	126	1	if	if	SCONJ
ejpam-6259	126	2	f(gn	f(gn	NOUN
ejpam-6259	126	3	)	)	PUNCT
ejpam-6259	126	4	∩	∩	NOUN
ejpam-6259	126	5	g	g	PROPN
ejpam-6259	126	6	is	be	AUX
ejpam-6259	126	7	not	not	PART
ejpam-6259	126	8	a	a	DET
ejpam-6259	126	9	zero	zero	NUM
ejpam-6259	126	10	fuzzy	fuzzy	ADJ
ejpam-6259	126	11	subset	subset	NOUN
ejpam-6259	126	12	of	of	ADP
ejpam-6259	126	13	a.	a.	NOUN
ejpam-6259	126	14	it	it	PRON
ejpam-6259	126	15	is	be	AUX
ejpam-6259	126	16	evident	evident	ADJ
ejpam-6259	126	17	that	that	SCONJ
ejpam-6259	126	18	a	a	DET
ejpam-6259	126	19	zero	zero	NUM
ejpam-6259	126	20	fuzzy	fuzzy	ADJ
ejpam-6259	126	21	subset	subset	NOUN
ejpam-6259	126	22	of	of	ADP
ejpam-6259	126	23	an	an	DET
ejpam-6259	126	24	n	n	CCONJ
ejpam-6259	126	25	-	-	PUNCT
ejpam-6259	126	26	ary	ary	NOUN
ejpam-6259	126	27	semigroup	semigroup	NOUN
ejpam-6259	126	28	a	a	PRON
ejpam-6259	126	29	is	be	AUX
ejpam-6259	126	30	a	a	DET
ejpam-6259	126	31	fuzzy	fuzzy	ADJ
ejpam-6259	126	32	n	n	CCONJ
ejpam-6259	126	33	-	-	PUNCT
ejpam-6259	126	34	ary	ary	NOUN
ejpam-6259	126	35	subsemigroup	subsemigroup	NOUN
ejpam-6259	126	36	but	but	CCONJ
ejpam-6259	126	37	not	not	PART
ejpam-6259	126	38	an	an	DET
ejpam-6259	126	39	almost	almost	ADV
ejpam-6259	126	40	fuzzy	fuzzy	ADJ
ejpam-6259	126	41	n	n	CCONJ
ejpam-6259	126	42	-	-	PUNCT
ejpam-6259	126	43	ary	ary	NOUN
ejpam-6259	126	44	subsemigroup	subsemigroup	NOUN
ejpam-6259	126	45	of	of	ADP
ejpam-6259	126	46	a.	a.	NOUN
ejpam-6259	126	47	next	next	ADV
ejpam-6259	126	48	,	,	PUNCT
ejpam-6259	126	49	let	let	VERB
ejpam-6259	126	50	g	g	PRON
ejpam-6259	126	51	be	be	AUX
ejpam-6259	126	52	a	a	DET
ejpam-6259	126	53	nonzero	nonzero	ADJ
ejpam-6259	126	54	fuzzy	fuzzy	ADJ
ejpam-6259	126	55	n	n	CCONJ
ejpam-6259	126	56	-	-	PUNCT
ejpam-6259	126	57	ary	ary	NOUN
ejpam-6259	126	58	subsemigroup	subsemigroup	NOUN
ejpam-6259	126	59	of	of	ADP
ejpam-6259	126	60	an	an	DET
ejpam-6259	126	61	n	n	CCONJ
ejpam-6259	126	62	-	-	PUNCT
ejpam-6259	126	63	ary	ary	PROPN
ejpam-6259	126	64	semigroup	semigroup	PROPN
ejpam-6259	126	65	a.	a.	NOUN
ejpam-6259	126	66	by	by	ADP
ejpam-6259	126	67	proposition	proposition	NOUN
ejpam-6259	126	68	1	1	NUM
ejpam-6259	126	69	,	,	PUNCT
ejpam-6259	126	70	we	we	PRON
ejpam-6259	126	71	have	have	VERB
ejpam-6259	126	72	f(gn	f(gn	NOUN
ejpam-6259	126	73	)	)	PUNCT
ejpam-6259	126	74	⊆	⊆	NUM
ejpam-6259	126	75	g.	g.	NOUN
ejpam-6259	126	76	this	this	PRON
ejpam-6259	126	77	implies	imply	VERB
ejpam-6259	126	78	that	that	SCONJ
ejpam-6259	126	79	f(gn	f(gn	NOUN
ejpam-6259	126	80	)	)	PUNCT
ejpam-6259	126	81	∩	∩	NOUN
ejpam-6259	126	82	g	g	PROPN
ejpam-6259	126	83	=	=	SYM
ejpam-6259	126	84	f(gn	f(gn	PROPN
ejpam-6259	126	85	)	)	PUNCT
ejpam-6259	126	86	.	.	PUNCT
ejpam-6259	127	1	since	since	SCONJ
ejpam-6259	127	2	g	g	PROPN
ejpam-6259	127	3	̸=	̸=	PROPN
ejpam-6259	127	4	0	0	NUM
ejpam-6259	127	5	,	,	PUNCT
ejpam-6259	127	6	there	there	PRON
ejpam-6259	127	7	exists	exist	VERB
ejpam-6259	127	8	a	a	DET
ejpam-6259	127	9	∈	∈	NOUN
ejpam-6259	127	10	a	a	DET
ejpam-6259	127	11	such	such	ADJ
ejpam-6259	127	12	that	that	DET
ejpam-6259	127	13	g(a	g(a	PROPN
ejpam-6259	127	14	)	)	PUNCT
ejpam-6259	127	15	̸=	̸=	PROPN
ejpam-6259	127	16	0	0	NUM
ejpam-6259	127	17	.	.	PUNCT
ejpam-6259	128	1	then	then	ADV
ejpam-6259	128	2	f(gn)(f(an	f(gn)(f(an	NOUN
ejpam-6259	128	3	)	)	PUNCT
ejpam-6259	128	4	)	)	PUNCT
ejpam-6259	129	1	̸=	̸=	PROPN
ejpam-6259	129	2	0	0	NUM
ejpam-6259	129	3	.	.	PUNCT
ejpam-6259	130	1	hence	hence	ADV
ejpam-6259	130	2	f(gn	f(gn	NOUN
ejpam-6259	130	3	)	)	PUNCT
ejpam-6259	130	4	∩	∩	NOUN
ejpam-6259	130	5	g	g	PROPN
ejpam-6259	130	6	=	=	SYM
ejpam-6259	130	7	f(gn	f(gn	PROPN
ejpam-6259	130	8	)	)	PUNCT
ejpam-6259	130	9	̸=	̸=	PROPN
ejpam-6259	130	10	0	0	NUM
ejpam-6259	130	11	.	.	PUNCT
ejpam-6259	131	1	therefore	therefore	ADV
ejpam-6259	131	2	,	,	PUNCT
ejpam-6259	131	3	g	g	PROPN
ejpam-6259	131	4	is	be	AUX
ejpam-6259	131	5	a	a	DET
ejpam-6259	131	6	fuzzy	fuzzy	ADJ
ejpam-6259	131	7	almost	almost	ADV
ejpam-6259	131	8	n	n	CCONJ
ejpam-6259	131	9	-	-	PUNCT
ejpam-6259	131	10	ary	ary	NOUN
ejpam-6259	131	11	subsemigroup	subsemigroup	NOUN
ejpam-6259	131	12	of	of	ADP
ejpam-6259	131	13	a.	a.	NOUN
ejpam-6259	131	14	we	we	PRON
ejpam-6259	131	15	can	can	AUX
ejpam-6259	131	16	conclude	conclude	VERB
ejpam-6259	131	17	that	that	SCONJ
ejpam-6259	131	18	every	every	DET
ejpam-6259	131	19	nonzero	nonzero	NOUN
ejpam-6259	131	20	fuzzy	fuzzy	ADJ
ejpam-6259	131	21	n	n	CCONJ
ejpam-6259	131	22	-	-	PUNCT
ejpam-6259	131	23	ary	ary	NOUN
ejpam-6259	131	24	subsemigroup	subsemigroup	NOUN
ejpam-6259	131	25	of	of	ADP
ejpam-6259	131	26	an	an	DET
ejpam-6259	131	27	n	n	CCONJ
ejpam-6259	131	28	-	-	PUNCT
ejpam-6259	131	29	ary	ary	NOUN
ejpam-6259	131	30	semigroup	semigroup	NOUN
ejpam-6259	131	31	a	a	PRON
ejpam-6259	131	32	is	be	AUX
ejpam-6259	131	33	a	a	DET
ejpam-6259	131	34	fuzzy	fuzzy	ADJ
ejpam-6259	131	35	almost	almost	ADV
ejpam-6259	131	36	n	n	CCONJ
ejpam-6259	131	37	-	-	PUNCT
ejpam-6259	131	38	ary	ary	NOUN
ejpam-6259	131	39	subsemigroup	subsemigroup	NOUN
ejpam-6259	131	40	of	of	ADP
ejpam-6259	131	41	a.	a.	NOUN
ejpam-6259	131	42	example	example	NOUN
ejpam-6259	131	43	2	2	X
ejpam-6259	131	44	.	.	X
ejpam-6259	131	45	we	we	PRON
ejpam-6259	131	46	consider	consider	VERB
ejpam-6259	131	47	an	an	DET
ejpam-6259	131	48	n	n	CCONJ
ejpam-6259	131	49	-	-	PUNCT
ejpam-6259	131	50	ary	ary	NOUN
ejpam-6259	131	51	semigroup	semigroup	PROPN
ejpam-6259	131	52	n	n	PROPN
ejpam-6259	131	53	under	under	ADP
ejpam-6259	131	54	the	the	DET
ejpam-6259	131	55	usual	usual	ADJ
ejpam-6259	131	56	n	n	CCONJ
ejpam-6259	131	57	-	-	PUNCT
ejpam-6259	131	58	ary	ary	NOUN
ejpam-6259	131	59	multiplication	multiplication	NOUN
ejpam-6259	131	60	of	of	ADP
ejpam-6259	131	61	integers	integer	NOUN
ejpam-6259	131	62	.	.	PUNCT
ejpam-6259	132	1	let	let	VERB
ejpam-6259	132	2	g	g	NOUN
ejpam-6259	132	3	and	and	CCONJ
ejpam-6259	132	4	h	h	NOUN
ejpam-6259	132	5	be	be	VERB
ejpam-6259	132	6	fuzzy	fuzzy	ADJ
ejpam-6259	132	7	subsets	subset	NOUN
ejpam-6259	132	8	of	of	ADP
ejpam-6259	132	9	n	n	PRON
ejpam-6259	132	10	as	as	SCONJ
ejpam-6259	132	11	follows	follow	VERB
ejpam-6259	132	12	:	:	PUNCT
ejpam-6259	132	13	g(a	g(a	PROPN
ejpam-6259	132	14	)	)	PUNCT
ejpam-6259	133	1	=	=	PRON
ejpam-6259	133	2	{	{	PUNCT
ejpam-6259	133	3	0.5	0.5	NUM
ejpam-6259	133	4	if	if	SCONJ
ejpam-6259	133	5	a	a	DET
ejpam-6259	133	6	=	=	SYM
ejpam-6259	133	7	2	2	NUM
ejpam-6259	133	8	or	or	CCONJ
ejpam-6259	133	9	2n	2n	NUM
ejpam-6259	133	10	,	,	PUNCT
ejpam-6259	133	11	0	0	NUM
ejpam-6259	133	12	otherwise	otherwise	ADV
ejpam-6259	133	13	,	,	PUNCT
ejpam-6259	133	14	and	and	CCONJ
ejpam-6259	133	15	h(a	h(a	PROPN
ejpam-6259	133	16	)	)	PUNCT
ejpam-6259	134	1	=	=	PRON
ejpam-6259	134	2	{	{	PUNCT
ejpam-6259	134	3	0.4	0.4	NUM
ejpam-6259	134	4	if	if	SCONJ
ejpam-6259	134	5	a	a	DET
ejpam-6259	134	6	=	=	SYM
ejpam-6259	134	7	2n	2n	NUM
ejpam-6259	134	8	or	or	CCONJ
ejpam-6259	134	9	2n	2n	NUM
ejpam-6259	134	10	2	2	NUM
ejpam-6259	134	11	,	,	PUNCT
ejpam-6259	134	12	0	0	NUM
ejpam-6259	134	13	otherwise	otherwise	ADV
ejpam-6259	134	14	.	.	PUNCT
ejpam-6259	135	1	clearly	clearly	ADV
ejpam-6259	135	2	,	,	PUNCT
ejpam-6259	135	3	g	g	PROPN
ejpam-6259	135	4	and	and	CCONJ
ejpam-6259	135	5	h	h	NOUN
ejpam-6259	135	6	are	be	AUX
ejpam-6259	135	7	fuzzy	fuzzy	ADJ
ejpam-6259	135	8	almost	almost	ADV
ejpam-6259	135	9	n	n	CCONJ
ejpam-6259	135	10	-	-	PUNCT
ejpam-6259	135	11	ary	ary	NOUN
ejpam-6259	135	12	subsemigroups	subsemigroup	NOUN
ejpam-6259	135	13	but	but	CCONJ
ejpam-6259	135	14	are	be	AUX
ejpam-6259	135	15	not	not	PART
ejpam-6259	135	16	fuzzy	fuzzy	ADJ
ejpam-6259	135	17	n	n	CCONJ
ejpam-6259	135	18	-	-	PUNCT
ejpam-6259	135	19	ary	ary	PROPN
ejpam-6259	135	20	subsemigroups	subsemigroup	NOUN
ejpam-6259	135	21	of	of	ADP
ejpam-6259	135	22	n.	n.	PROPN
ejpam-6259	135	23	however	however	ADV
ejpam-6259	135	24	,	,	PUNCT
ejpam-6259	135	25	g	g	PROPN
ejpam-6259	135	26	∩	∩	ADJ
ejpam-6259	135	27	h	h	NOUN
ejpam-6259	135	28	is	be	AUX
ejpam-6259	135	29	not	not	PART
ejpam-6259	135	30	a	a	DET
ejpam-6259	135	31	fuzzy	fuzzy	ADJ
ejpam-6259	135	32	almost	almost	ADV
ejpam-6259	135	33	n	n	CCONJ
ejpam-6259	135	34	-	-	PUNCT
ejpam-6259	135	35	ary	ary	NOUN
ejpam-6259	135	36	subsemigroup	subsemigroup	NOUN
ejpam-6259	135	37	of	of	ADP
ejpam-6259	135	38	n.	n.	NOUN
ejpam-6259	135	39	from	from	ADP
ejpam-6259	135	40	example	example	NOUN
ejpam-6259	135	41	2	2	NUM
ejpam-6259	135	42	,	,	PUNCT
ejpam-6259	135	43	we	we	PRON
ejpam-6259	135	44	obtain	obtain	VERB
ejpam-6259	135	45	the	the	DET
ejpam-6259	135	46	following	follow	VERB
ejpam-6259	135	47	conclusions	conclusion	NOUN
ejpam-6259	135	48	.	.	PUNCT
ejpam-6259	136	1	(	(	PUNCT
ejpam-6259	136	2	1	1	X
ejpam-6259	136	3	)	)	PUNCT
ejpam-6259	136	4	a	a	DET
ejpam-6259	136	5	fuzzy	fuzzy	ADJ
ejpam-6259	136	6	almost	almost	ADV
ejpam-6259	136	7	n	n	CCONJ
ejpam-6259	136	8	-	-	PUNCT
ejpam-6259	136	9	ary	ary	NOUN
ejpam-6259	136	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	136	11	of	of	ADP
ejpam-6259	136	12	an	an	DET
ejpam-6259	136	13	n	n	CCONJ
ejpam-6259	136	14	-	-	PUNCT
ejpam-6259	136	15	ary	ary	NOUN
ejpam-6259	136	16	semigroup	semigroup	NOUN
ejpam-6259	136	17	a	a	DET
ejpam-6259	136	18	need	need	NOUN
ejpam-6259	136	19	not	not	PART
ejpam-6259	136	20	be	be	AUX
ejpam-6259	136	21	a	a	DET
ejpam-6259	136	22	fuzzy	fuzzy	ADJ
ejpam-6259	136	23	n	n	CCONJ
ejpam-6259	136	24	-	-	PUNCT
ejpam-6259	136	25	ary	ary	NOUN
ejpam-6259	136	26	subsemigroup	subsemigroup	NOUN
ejpam-6259	136	27	of	of	ADP
ejpam-6259	136	28	a.	a.	PROPN
ejpam-6259	136	29	r.	r.	PROPN
ejpam-6259	136	30	chinram	chinram	PROPN
ejpam-6259	136	31	,	,	PUNCT
ejpam-6259	136	32	p.	p.	NOUN
ejpam-6259	136	33	singavananda	singavananda	PROPN
ejpam-6259	136	34	/	/	SYM
ejpam-6259	136	35	eur	eur	PROPN
ejpam-6259	136	36	.	.	PUNCT
ejpam-6259	137	1	j.	j.	PROPN
ejpam-6259	137	2	pure	pure	PROPN
ejpam-6259	137	3	appl	appl	PROPN
ejpam-6259	137	4	.	.	PROPN
ejpam-6259	137	5	math	math	PROPN
ejpam-6259	137	6	,	,	PUNCT
ejpam-6259	137	7	18	18	NUM
ejpam-6259	137	8	(	(	PUNCT
ejpam-6259	137	9	3	3	NUM
ejpam-6259	137	10	)	)	PUNCT
ejpam-6259	137	11	(	(	PUNCT
ejpam-6259	137	12	2025	2025	NUM
ejpam-6259	137	13	)	)	PUNCT
ejpam-6259	137	14	,	,	PUNCT
ejpam-6259	137	15	6259	6259	NUM
ejpam-6259	137	16	6	6	NUM
ejpam-6259	137	17	of	of	ADP
ejpam-6259	137	18	10	10	NUM
ejpam-6259	137	19	(	(	PUNCT
ejpam-6259	137	20	2	2	NUM
ejpam-6259	137	21	)	)	PUNCT
ejpam-6259	137	22	the	the	DET
ejpam-6259	137	23	intersection	intersection	NOUN
ejpam-6259	137	24	of	of	ADP
ejpam-6259	137	25	fuzzy	fuzzy	ADJ
ejpam-6259	137	26	almost	almost	ADV
ejpam-6259	137	27	n	n	CCONJ
ejpam-6259	137	28	-	-	PUNCT
ejpam-6259	137	29	ary	ary	PROPN
ejpam-6259	137	30	subsemigroups	subsemigroup	NOUN
ejpam-6259	137	31	of	of	ADP
ejpam-6259	137	32	an	an	DET
ejpam-6259	137	33	n	n	CCONJ
ejpam-6259	137	34	-	-	PUNCT
ejpam-6259	137	35	ary	ary	NOUN
ejpam-6259	137	36	semigroup	semigroup	NOUN
ejpam-6259	137	37	a	a	DET
ejpam-6259	137	38	need	need	NOUN
ejpam-6259	137	39	not	not	PART
ejpam-6259	137	40	be	be	AUX
ejpam-6259	137	41	a	a	DET
ejpam-6259	137	42	fuzzy	fuzzy	ADJ
ejpam-6259	137	43	almost	almost	ADV
ejpam-6259	137	44	n	n	CCONJ
ejpam-6259	137	45	-	-	PUNCT
ejpam-6259	137	46	ary	ary	NOUN
ejpam-6259	137	47	subsemigroup	subsemigroup	NOUN
ejpam-6259	137	48	of	of	ADP
ejpam-6259	137	49	a.	a.	NOUN
ejpam-6259	137	50	theorem	theorem	NOUN
ejpam-6259	137	51	2	2	X
ejpam-6259	137	52	.	.	PUNCT
ejpam-6259	138	1	let	let	VERB
ejpam-6259	138	2	g	g	PRON
ejpam-6259	138	3	be	be	AUX
ejpam-6259	138	4	a	a	DET
ejpam-6259	138	5	fuzzy	fuzzy	ADJ
ejpam-6259	138	6	almost	almost	ADV
ejpam-6259	138	7	n	n	CCONJ
ejpam-6259	138	8	-	-	PUNCT
ejpam-6259	138	9	ary	ary	NOUN
ejpam-6259	138	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	138	11	of	of	ADP
ejpam-6259	138	12	an	an	DET
ejpam-6259	138	13	n	n	CCONJ
ejpam-6259	138	14	-	-	PUNCT
ejpam-6259	138	15	ary	ary	PROPN
ejpam-6259	138	16	semigroup	semigroup	PROPN
ejpam-6259	138	17	a.	a.	NOUN
ejpam-6259	138	18	if	if	SCONJ
ejpam-6259	138	19	h	h	NOUN
ejpam-6259	138	20	is	be	AUX
ejpam-6259	138	21	a	a	DET
ejpam-6259	138	22	fuzzy	fuzzy	ADJ
ejpam-6259	138	23	subset	subset	NOUN
ejpam-6259	138	24	of	of	ADP
ejpam-6259	138	25	a	a	DET
ejpam-6259	138	26	such	such	ADJ
ejpam-6259	138	27	that	that	SCONJ
ejpam-6259	138	28	g	g	PROPN
ejpam-6259	138	29	⊆	⊆	NUM
ejpam-6259	138	30	h	h	NOUN
ejpam-6259	138	31	,	,	PUNCT
ejpam-6259	138	32	then	then	ADV
ejpam-6259	138	33	h	h	NOUN
ejpam-6259	138	34	is	be	AUX
ejpam-6259	138	35	also	also	ADV
ejpam-6259	138	36	a	a	DET
ejpam-6259	138	37	fuzzy	fuzzy	ADJ
ejpam-6259	138	38	almost	almost	ADV
ejpam-6259	138	39	n	n	CCONJ
ejpam-6259	138	40	-	-	PUNCT
ejpam-6259	138	41	ary	ary	NOUN
ejpam-6259	138	42	subsemigroup	subsemigroup	NOUN
ejpam-6259	138	43	of	of	ADP
ejpam-6259	138	44	a.	a.	NOUN
ejpam-6259	138	45	proof	proof	NOUN
ejpam-6259	138	46	.	.	PUNCT
ejpam-6259	139	1	since	since	SCONJ
ejpam-6259	139	2	g	g	PROPN
ejpam-6259	139	3	is	be	AUX
ejpam-6259	139	4	a	a	DET
ejpam-6259	139	5	fuzzy	fuzzy	ADJ
ejpam-6259	139	6	almost	almost	ADV
ejpam-6259	139	7	n	n	CCONJ
ejpam-6259	139	8	-	-	PUNCT
ejpam-6259	139	9	ary	ary	NOUN
ejpam-6259	139	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	139	11	of	of	ADP
ejpam-6259	139	12	a	a	DET
ejpam-6259	139	13	,	,	PUNCT
ejpam-6259	139	14	f(gn	f(gn	NOUN
ejpam-6259	139	15	)	)	PUNCT
ejpam-6259	139	16	∩	∩	NOUN
ejpam-6259	139	17	g	g	PROPN
ejpam-6259	139	18	̸=	̸=	PROPN
ejpam-6259	139	19	0	0	NUM
ejpam-6259	139	20	.	.	PUNCT
ejpam-6259	140	1	since	since	SCONJ
ejpam-6259	140	2	g	g	PROPN
ejpam-6259	140	3	⊆	⊆	NUM
ejpam-6259	140	4	h	h	NOUN
ejpam-6259	140	5	,	,	PUNCT
ejpam-6259	140	6	f(gn	f(gn	NOUN
ejpam-6259	140	7	)	)	PUNCT
ejpam-6259	140	8	∩	∩	NOUN
ejpam-6259	140	9	g	g	ADP
ejpam-6259	140	10	⊆	⊆	NUM
ejpam-6259	140	11	f(hn	f(hn	NUM
ejpam-6259	140	12	)	)	PUNCT
ejpam-6259	140	13	∩	∩	NOUN
ejpam-6259	140	14	h.	h.	NOUN
ejpam-6259	140	15	this	this	PRON
ejpam-6259	140	16	implies	imply	VERB
ejpam-6259	140	17	that	that	SCONJ
ejpam-6259	140	18	f(hn	f(hn	NOUN
ejpam-6259	140	19	)	)	PUNCT
ejpam-6259	140	20	∩	∩	NOUN
ejpam-6259	140	21	h	h	NOUN
ejpam-6259	140	22	̸=	̸=	PROPN
ejpam-6259	140	23	0	0	NUM
ejpam-6259	140	24	.	.	PUNCT
ejpam-6259	141	1	so	so	ADV
ejpam-6259	141	2	the	the	DET
ejpam-6259	141	3	proof	proof	NOUN
ejpam-6259	141	4	is	be	AUX
ejpam-6259	141	5	completed	complete	VERB
ejpam-6259	141	6	.	.	PUNCT
ejpam-6259	142	1	as	as	ADP
ejpam-6259	142	2	a	a	DET
ejpam-6259	142	3	direct	direct	ADJ
ejpam-6259	142	4	consequence	consequence	NOUN
ejpam-6259	142	5	of	of	ADP
ejpam-6259	142	6	theorem	theorem	NOUN
ejpam-6259	142	7	2	2	NUM
ejpam-6259	142	8	,	,	PUNCT
ejpam-6259	142	9	we	we	PRON
ejpam-6259	142	10	obtain	obtain	VERB
ejpam-6259	142	11	the	the	DET
ejpam-6259	142	12	following	follow	VERB
ejpam-6259	142	13	corollary	corollary	NOUN
ejpam-6259	142	14	.	.	PUNCT
ejpam-6259	143	1	corollary	corollary	ADJ
ejpam-6259	143	2	2	2	NUM
ejpam-6259	143	3	.	.	PUNCT
ejpam-6259	144	1	the	the	DET
ejpam-6259	144	2	union	union	NOUN
ejpam-6259	144	3	of	of	ADP
ejpam-6259	144	4	fuzzy	fuzzy	ADJ
ejpam-6259	144	5	almost	almost	ADV
ejpam-6259	144	6	n	n	CCONJ
ejpam-6259	144	7	-	-	PUNCT
ejpam-6259	144	8	ary	ary	PROPN
ejpam-6259	144	9	subsemigroups	subsemigroup	NOUN
ejpam-6259	144	10	of	of	ADP
ejpam-6259	144	11	an	an	DET
ejpam-6259	144	12	n	n	CCONJ
ejpam-6259	144	13	-	-	PUNCT
ejpam-6259	144	14	ary	ary	NOUN
ejpam-6259	144	15	semigroup	semigroup	NOUN
ejpam-6259	144	16	a	a	PRON
ejpam-6259	144	17	is	be	AUX
ejpam-6259	144	18	also	also	ADV
ejpam-6259	144	19	a	a	DET
ejpam-6259	144	20	fuzzy	fuzzy	ADJ
ejpam-6259	144	21	almost	almost	ADV
ejpam-6259	144	22	n	n	CCONJ
ejpam-6259	144	23	-	-	PUNCT
ejpam-6259	144	24	ary	ary	NOUN
ejpam-6259	144	25	subsemigroup	subsemigroup	NOUN
ejpam-6259	144	26	of	of	ADP
ejpam-6259	144	27	a.	a.	NOUN
ejpam-6259	144	28	3.3	3.3	NUM
ejpam-6259	144	29	.	.	PUNCT
ejpam-6259	145	1	the	the	DET
ejpam-6259	145	2	relationships	relationship	NOUN
ejpam-6259	145	3	between	between	ADP
ejpam-6259	145	4	almost	almost	ADV
ejpam-6259	145	5	n	n	CCONJ
ejpam-6259	145	6	-	-	PUNCT
ejpam-6259	145	7	ary	ary	NOUN
ejpam-6259	145	8	subsemigroups	subsemigroup	NOUN
ejpam-6259	145	9	and	and	CCONJ
ejpam-6259	145	10	their	their	PRON
ejpam-6259	145	11	fuzzifications	fuzzification	NOUN
ejpam-6259	145	12	this	this	DET
ejpam-6259	145	13	subsection	subsection	NOUN
ejpam-6259	145	14	is	be	AUX
ejpam-6259	145	15	devoted	devote	VERB
ejpam-6259	145	16	to	to	ADP
ejpam-6259	145	17	examining	examine	VERB
ejpam-6259	145	18	the	the	DET
ejpam-6259	145	19	relationships	relationship	NOUN
ejpam-6259	145	20	between	between	ADP
ejpam-6259	145	21	almost	almost	ADV
ejpam-6259	145	22	n	n	CCONJ
ejpam-6259	145	23	-	-	PUNCT
ejpam-6259	145	24	ary	ary	NOUN
ejpam-6259	145	25	subsemigroups	subsemigroup	NOUN
ejpam-6259	145	26	and	and	CCONJ
ejpam-6259	145	27	fuzzy	fuzzy	ADJ
ejpam-6259	145	28	almost	almost	ADV
ejpam-6259	145	29	n	n	CCONJ
ejpam-6259	145	30	-	-	PUNCT
ejpam-6259	145	31	ary	ary	PROPN
ejpam-6259	145	32	subsemigroups	subsemigroup	NOUN
ejpam-6259	145	33	of	of	ADP
ejpam-6259	145	34	n	n	CCONJ
ejpam-6259	145	35	-	-	PUNCT
ejpam-6259	145	36	ary	ary	PROPN
ejpam-6259	145	37	semigroups	semigroup	NOUN
ejpam-6259	145	38	.	.	PUNCT
ejpam-6259	146	1	theorem	theorem	NOUN
ejpam-6259	146	2	3	3	X
ejpam-6259	146	3	.	.	PUNCT
ejpam-6259	147	1	let	let	VERB
ejpam-6259	147	2	s	s	PRON
ejpam-6259	147	3	be	be	AUX
ejpam-6259	147	4	a	a	DET
ejpam-6259	147	5	subset	subset	NOUN
ejpam-6259	147	6	of	of	ADP
ejpam-6259	147	7	an	an	DET
ejpam-6259	147	8	n	n	CCONJ
ejpam-6259	147	9	-	-	PUNCT
ejpam-6259	147	10	ary	ary	PROPN
ejpam-6259	147	11	semigroup	semigroup	PROPN
ejpam-6259	147	12	a.	a.	NOUN
ejpam-6259	148	1	then	then	ADV
ejpam-6259	148	2	s	s	AUX
ejpam-6259	148	3	is	be	AUX
ejpam-6259	148	4	an	an	DET
ejpam-6259	148	5	almost	almost	ADV
ejpam-6259	148	6	n	n	CCONJ
ejpam-6259	148	7	-	-	PUNCT
ejpam-6259	148	8	ary	ary	NOUN
ejpam-6259	148	9	subsemigroup	subsemigroup	NOUN
ejpam-6259	148	10	of	of	ADP
ejpam-6259	148	11	a	a	DET
ejpam-6259	148	12	if	if	NOUN
ejpam-6259	148	13	and	and	CCONJ
ejpam-6259	148	14	only	only	ADV
ejpam-6259	148	15	if	if	SCONJ
ejpam-6259	148	16	χs	χs	NOUN
ejpam-6259	148	17	is	be	AUX
ejpam-6259	148	18	a	a	DET
ejpam-6259	148	19	fuzzy	fuzzy	ADJ
ejpam-6259	148	20	almost	almost	ADV
ejpam-6259	148	21	n	n	CCONJ
ejpam-6259	148	22	-	-	PUNCT
ejpam-6259	148	23	ary	ary	NOUN
ejpam-6259	148	24	subsemigroup	subsemigroup	NOUN
ejpam-6259	148	25	of	of	ADP
ejpam-6259	148	26	a.	a.	NOUN
ejpam-6259	148	27	proof	proof	NOUN
ejpam-6259	148	28	.	.	PUNCT
ejpam-6259	149	1	assume	assume	VERB
ejpam-6259	149	2	that	that	SCONJ
ejpam-6259	149	3	s	s	VERB
ejpam-6259	149	4	is	be	AUX
ejpam-6259	149	5	an	an	DET
ejpam-6259	149	6	almost	almost	ADV
ejpam-6259	149	7	n	n	CCONJ
ejpam-6259	149	8	-	-	PUNCT
ejpam-6259	149	9	ary	ary	NOUN
ejpam-6259	149	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	149	11	of	of	ADP
ejpam-6259	149	12	a.	a.	NOUN
ejpam-6259	149	13	then	then	ADV
ejpam-6259	149	14	s	s	VERB
ejpam-6259	149	15	̸=	̸=	PROPN
ejpam-6259	149	16	∅	∅	NOUN
ejpam-6259	149	17	and	and	CCONJ
ejpam-6259	149	18	f(sn)∩s	f(sn)∩s	PROPN
ejpam-6259	149	19	̸=	̸=	PROPN
ejpam-6259	149	20	∅.	∅.	PRON
ejpam-6259	149	21	hence	hence	ADV
ejpam-6259	149	22	,	,	PUNCT
ejpam-6259	149	23	there	there	PRON
ejpam-6259	149	24	exists	exist	VERB
ejpam-6259	149	25	an	an	DET
ejpam-6259	149	26	element	element	NOUN
ejpam-6259	149	27	a	a	PRON
ejpam-6259	149	28	in	in	ADP
ejpam-6259	149	29	s	s	PRON
ejpam-6259	149	30	such	such	ADJ
ejpam-6259	149	31	that	that	SCONJ
ejpam-6259	149	32	a	a	DET
ejpam-6259	149	33	∈	∈	PROPN
ejpam-6259	149	34	f(sn)∩s	f(sn)∩s	PROPN
ejpam-6259	149	35	,	,	PUNCT
ejpam-6259	149	36	therefore	therefore	ADV
ejpam-6259	149	37	,	,	PUNCT
ejpam-6259	149	38	a	a	DET
ejpam-6259	149	39	=	=	X
ejpam-6259	149	40	f(an1	f(an1	X
ejpam-6259	149	41	)	)	PUNCT
ejpam-6259	149	42	for	for	ADP
ejpam-6259	149	43	some	some	DET
ejpam-6259	149	44	a1	a1	NOUN
ejpam-6259	149	45	,	,	PUNCT
ejpam-6259	149	46	a2	a2	PROPN
ejpam-6259	149	47	,	,	PUNCT
ejpam-6259	149	48	.	.	PUNCT
ejpam-6259	149	49	.	.	PUNCT
ejpam-6259	150	1	.	.	PUNCT
ejpam-6259	151	1	,	,	PUNCT
ejpam-6259	151	2	an	an	DET
ejpam-6259	151	3	∈	∈	NOUN
ejpam-6259	151	4	s	s	X
ejpam-6259	151	5	and	and	CCONJ
ejpam-6259	151	6	a	a	DET
ejpam-6259	151	7	∈	∈	NOUN
ejpam-6259	151	8	s.	s.	PROPN
ejpam-6259	152	1	it	it	PRON
ejpam-6259	152	2	follows	follow	VERB
ejpam-6259	152	3	that	that	SCONJ
ejpam-6259	152	4	f((χs	f((χs	NOUN
ejpam-6259	152	5	)	)	PUNCT
ejpam-6259	152	6	n)(a	n)(a	NUM
ejpam-6259	152	7	)	)	PUNCT
ejpam-6259	153	1	=	=	SYM
ejpam-6259	153	2	1	1	NUM
ejpam-6259	153	3	and	and	CCONJ
ejpam-6259	153	4	χs(a	χs(a	NUM
ejpam-6259	153	5	)	)	PUNCT
ejpam-6259	154	1	=	=	SYM
ejpam-6259	154	2	1	1	NUM
ejpam-6259	154	3	,	,	PUNCT
ejpam-6259	154	4	which	which	PRON
ejpam-6259	154	5	implies	imply	VERB
ejpam-6259	154	6	that	that	SCONJ
ejpam-6259	154	7	(	(	PUNCT
ejpam-6259	154	8	f((χs	f((χs	NOUN
ejpam-6259	154	9	)	)	PUNCT
ejpam-6259	154	10	n	n	CCONJ
ejpam-6259	154	11	)	)	PUNCT
ejpam-6259	154	12	∩	∩	NOUN
ejpam-6259	154	13	χs)(a	χs)(a	NUM
ejpam-6259	154	14	)	)	PUNCT
ejpam-6259	154	15	=	=	SYM
ejpam-6259	154	16	1	1	NUM
ejpam-6259	154	17	̸=	̸=	PROPN
ejpam-6259	154	18	0	0	NUM
ejpam-6259	154	19	.	.	PUNCT
ejpam-6259	155	1	we	we	PRON
ejpam-6259	155	2	can	can	AUX
ejpam-6259	155	3	conclude	conclude	VERB
ejpam-6259	155	4	that	that	PRON
ejpam-6259	155	5	f((χs	f((χs	NOUN
ejpam-6259	155	6	)	)	PUNCT
ejpam-6259	155	7	n	n	CCONJ
ejpam-6259	155	8	)	)	PUNCT
ejpam-6259	155	9	∩	∩	NOUN
ejpam-6259	155	10	χs	χs	ADP
ejpam-6259	155	11	̸=	̸=	PROPN
ejpam-6259	155	12	0	0	NUM
ejpam-6259	155	13	.	.	PUNCT
ejpam-6259	156	1	hence	hence	ADV
ejpam-6259	156	2	,	,	PUNCT
ejpam-6259	156	3	χs	χs	PROPN
ejpam-6259	156	4	is	be	AUX
ejpam-6259	156	5	a	a	DET
ejpam-6259	156	6	fuzzy	fuzzy	ADJ
ejpam-6259	156	7	almost	almost	ADV
ejpam-6259	156	8	n	n	CCONJ
ejpam-6259	156	9	-	-	PUNCT
ejpam-6259	156	10	ary	ary	NOUN
ejpam-6259	156	11	subsemigroup	subsemigroup	NOUN
ejpam-6259	156	12	of	of	ADP
ejpam-6259	156	13	a.	a.	NOUN
ejpam-6259	156	14	conversely	conversely	ADV
ejpam-6259	156	15	,	,	PUNCT
ejpam-6259	156	16	assume	assume	VERB
ejpam-6259	156	17	that	that	SCONJ
ejpam-6259	156	18	χs	χs	PROPN
ejpam-6259	156	19	is	be	AUX
ejpam-6259	156	20	a	a	DET
ejpam-6259	156	21	fuzzy	fuzzy	ADJ
ejpam-6259	156	22	almost	almost	ADV
ejpam-6259	156	23	n	n	CCONJ
ejpam-6259	156	24	-	-	PUNCT
ejpam-6259	156	25	ary	ary	NOUN
ejpam-6259	156	26	subsemigroup	subsemigroup	NOUN
ejpam-6259	156	27	of	of	ADP
ejpam-6259	156	28	a.	a.	NOUN
ejpam-6259	156	29	we	we	PRON
ejpam-6259	156	30	have	have	VERB
ejpam-6259	156	31	χs	χs	NOUN
ejpam-6259	156	32	is	be	AUX
ejpam-6259	156	33	a	a	DET
ejpam-6259	156	34	nonzero	nonzero	ADJ
ejpam-6259	156	35	fuzzy	fuzzy	ADJ
ejpam-6259	156	36	subset	subset	NOUN
ejpam-6259	156	37	of	of	ADP
ejpam-6259	156	38	a	a	PRON
ejpam-6259	156	39	and	and	CCONJ
ejpam-6259	156	40	f((χs	f((χs	NUM
ejpam-6259	156	41	)	)	PUNCT
ejpam-6259	156	42	n	n	CCONJ
ejpam-6259	156	43	)	)	PUNCT
ejpam-6259	156	44	∩	∩	NOUN
ejpam-6259	156	45	χs	χs	ADP
ejpam-6259	156	46	̸=	̸=	PROPN
ejpam-6259	156	47	0	0	NUM
ejpam-6259	156	48	.	.	PUNCT
ejpam-6259	157	1	then	then	ADV
ejpam-6259	157	2	there	there	PRON
ejpam-6259	157	3	exists	exist	VERB
ejpam-6259	157	4	an	an	DET
ejpam-6259	157	5	element	element	NOUN
ejpam-6259	157	6	a	a	PRON
ejpam-6259	157	7	of	of	ADP
ejpam-6259	157	8	a	a	DET
ejpam-6259	157	9	such	such	ADJ
ejpam-6259	157	10	that	that	SCONJ
ejpam-6259	157	11	(	(	PUNCT
ejpam-6259	157	12	f((χs	f((χs	NOUN
ejpam-6259	157	13	)	)	PUNCT
ejpam-6259	157	14	n	n	CCONJ
ejpam-6259	157	15	)	)	PUNCT
ejpam-6259	157	16	∩	∩	NOUN
ejpam-6259	157	17	χs)(a	χs)(a	NOUN
ejpam-6259	157	18	)	)	PUNCT
ejpam-6259	157	19	̸=	̸=	PROPN
ejpam-6259	157	20	0	0	NUM
ejpam-6259	157	21	.	.	PUNCT
ejpam-6259	158	1	so	so	ADV
ejpam-6259	158	2	f((χs	f((χ	NOUN
ejpam-6259	158	3	)	)	PUNCT
ejpam-6259	158	4	n)(a	n)(a	NUM
ejpam-6259	158	5	)	)	PUNCT
ejpam-6259	159	1	̸=	̸=	NOUN
ejpam-6259	159	2	0	0	NUM
ejpam-6259	159	3	and	and	CCONJ
ejpam-6259	159	4	χs(a	χs(a	NUM
ejpam-6259	159	5	)	)	PUNCT
ejpam-6259	159	6	̸=	̸=	NOUN
ejpam-6259	159	7	0	0	NUM
ejpam-6259	159	8	.	.	PUNCT
ejpam-6259	160	1	this	this	PRON
ejpam-6259	160	2	implies	imply	VERB
ejpam-6259	160	3	that	that	SCONJ
ejpam-6259	160	4	f((χs	f((χs	NOUN
ejpam-6259	160	5	)	)	PUNCT
ejpam-6259	160	6	n)(a	n)(a	NUM
ejpam-6259	160	7	)	)	PUNCT
ejpam-6259	161	1	=	=	SYM
ejpam-6259	161	2	1	1	NUM
ejpam-6259	161	3	and	and	CCONJ
ejpam-6259	161	4	χs(a	χs(a	NUM
ejpam-6259	161	5	)	)	PUNCT
ejpam-6259	162	1	=	=	SYM
ejpam-6259	162	2	1	1	X
ejpam-6259	162	3	.	.	X
ejpam-6259	163	1	hence	hence	ADV
ejpam-6259	163	2	,	,	PUNCT
ejpam-6259	163	3	a	a	DET
ejpam-6259	163	4	∈	∈	NOUN
ejpam-6259	163	5	f(sn	f(sn	NOUN
ejpam-6259	163	6	)	)	PUNCT
ejpam-6259	163	7	and	and	CCONJ
ejpam-6259	163	8	a	a	DET
ejpam-6259	163	9	∈	∈	PROPN
ejpam-6259	163	10	s.	s.	PROPN
ejpam-6259	163	11	eventually	eventually	ADV
ejpam-6259	163	12	,	,	PUNCT
ejpam-6259	163	13	f(sn	f(sn	NOUN
ejpam-6259	163	14	)	)	PUNCT
ejpam-6259	163	15	∩	∩	NOUN
ejpam-6259	163	16	s	s	PART
ejpam-6259	163	17	̸=	̸=	PROPN
ejpam-6259	163	18	∅.	∅.	ADP
ejpam-6259	163	19	this	this	PRON
ejpam-6259	163	20	concludes	conclude	VERB
ejpam-6259	163	21	that	that	SCONJ
ejpam-6259	163	22	s	s	VERB
ejpam-6259	163	23	is	be	AUX
ejpam-6259	163	24	an	an	DET
ejpam-6259	163	25	almost	almost	ADV
ejpam-6259	163	26	n	n	CCONJ
ejpam-6259	163	27	-	-	PUNCT
ejpam-6259	163	28	ary	ary	NOUN
ejpam-6259	163	29	subsemigroup	subsemigroup	NOUN
ejpam-6259	163	30	of	of	ADP
ejpam-6259	163	31	a.	a.	NOUN
ejpam-6259	163	32	theorem	theorem	NOUN
ejpam-6259	163	33	4	4	X
ejpam-6259	163	34	.	.	PUNCT
ejpam-6259	164	1	let	let	VERB
ejpam-6259	164	2	g	g	PRON
ejpam-6259	164	3	be	be	AUX
ejpam-6259	164	4	a	a	DET
ejpam-6259	164	5	fuzzy	fuzzy	ADJ
ejpam-6259	164	6	subset	subset	NOUN
ejpam-6259	164	7	of	of	ADP
ejpam-6259	164	8	an	an	DET
ejpam-6259	164	9	n	n	CCONJ
ejpam-6259	164	10	-	-	PUNCT
ejpam-6259	164	11	ary	ary	PROPN
ejpam-6259	164	12	semigroup	semigroup	PROPN
ejpam-6259	164	13	a.	a.	NOUN
ejpam-6259	165	1	then	then	ADV
ejpam-6259	165	2	g	g	PROPN
ejpam-6259	165	3	is	be	AUX
ejpam-6259	165	4	a	a	DET
ejpam-6259	165	5	fuzzy	fuzzy	ADJ
ejpam-6259	165	6	almost	almost	ADV
ejpam-6259	165	7	n	n	CCONJ
ejpam-6259	165	8	-	-	PUNCT
ejpam-6259	165	9	ary	ary	NOUN
ejpam-6259	165	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	165	11	of	of	ADP
ejpam-6259	165	12	a	a	DET
ejpam-6259	165	13	if	if	NOUN
ejpam-6259	165	14	and	and	CCONJ
ejpam-6259	165	15	only	only	ADV
ejpam-6259	165	16	if	if	SCONJ
ejpam-6259	165	17	supp(g	supp(g	NUM
ejpam-6259	165	18	)	)	PUNCT
ejpam-6259	165	19	is	be	AUX
ejpam-6259	165	20	an	an	DET
ejpam-6259	165	21	almost	almost	ADV
ejpam-6259	165	22	n	n	CCONJ
ejpam-6259	165	23	-	-	PUNCT
ejpam-6259	165	24	ary	ary	NOUN
ejpam-6259	165	25	subsemigroup	subsemigroup	NOUN
ejpam-6259	165	26	of	of	ADP
ejpam-6259	165	27	a.	a.	NOUN
ejpam-6259	165	28	proof	proof	NOUN
ejpam-6259	165	29	.	.	PUNCT
ejpam-6259	166	1	let	let	VERB
ejpam-6259	166	2	g	g	PRON
ejpam-6259	166	3	be	be	AUX
ejpam-6259	166	4	a	a	DET
ejpam-6259	166	5	fuzzy	fuzzy	ADJ
ejpam-6259	166	6	almost	almost	ADV
ejpam-6259	166	7	n	n	CCONJ
ejpam-6259	166	8	-	-	PUNCT
ejpam-6259	166	9	ary	ary	NOUN
ejpam-6259	166	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	166	11	of	of	ADP
ejpam-6259	166	12	a.	a.	NOUN
ejpam-6259	166	13	we	we	PRON
ejpam-6259	166	14	have	have	VERB
ejpam-6259	166	15	that	that	DET
ejpam-6259	166	16	f(gn	f(gn	NOUN
ejpam-6259	166	17	)	)	PUNCT
ejpam-6259	166	18	∩	∩	NOUN
ejpam-6259	166	19	g	g	PROPN
ejpam-6259	166	20	is	be	AUX
ejpam-6259	166	21	not	not	PART
ejpam-6259	166	22	a	a	DET
ejpam-6259	166	23	zero	zero	NUM
ejpam-6259	166	24	fuzzy	fuzzy	ADJ
ejpam-6259	166	25	subset	subset	NOUN
ejpam-6259	166	26	of	of	ADP
ejpam-6259	166	27	a.	a.	NOUN
ejpam-6259	166	28	thus	thus	ADV
ejpam-6259	166	29	,	,	PUNCT
ejpam-6259	166	30	there	there	PRON
ejpam-6259	166	31	exists	exist	VERB
ejpam-6259	166	32	a	a	DET
ejpam-6259	166	33	∈	∈	NOUN
ejpam-6259	166	34	a	a	DET
ejpam-6259	166	35	such	such	ADJ
ejpam-6259	166	36	that	that	SCONJ
ejpam-6259	166	37	(	(	PUNCT
ejpam-6259	166	38	f(gn	f(gn	NOUN
ejpam-6259	166	39	)	)	PUNCT
ejpam-6259	166	40	∩	∩	NOUN
ejpam-6259	166	41	g)(a	g)(a	VERB
ejpam-6259	166	42	)	)	PUNCT
ejpam-6259	166	43	̸=	̸=	PROPN
ejpam-6259	166	44	0	0	NUM
ejpam-6259	166	45	.	.	PUNCT
ejpam-6259	167	1	then	then	ADV
ejpam-6259	167	2	g(a	g(a	PROPN
ejpam-6259	167	3	)	)	PUNCT
ejpam-6259	167	4	̸=	̸=	PROPN
ejpam-6259	167	5	0	0	NUM
ejpam-6259	167	6	and	and	CCONJ
ejpam-6259	167	7	f(gn)(a	f(gn)(a	PROPN
ejpam-6259	167	8	)	)	PUNCT
ejpam-6259	167	9	̸=	̸=	PROPN
ejpam-6259	167	10	0	0	NUM
ejpam-6259	167	11	.	.	PUNCT
ejpam-6259	168	1	so	so	ADV
ejpam-6259	168	2	a	a	DET
ejpam-6259	168	3	=	=	X
ejpam-6259	168	4	f(an1	f(an1	X
ejpam-6259	168	5	)	)	PUNCT
ejpam-6259	168	6	for	for	ADP
ejpam-6259	168	7	some	some	DET
ejpam-6259	168	8	a1	a1	NOUN
ejpam-6259	168	9	,	,	PUNCT
ejpam-6259	168	10	a2	a2	PROPN
ejpam-6259	168	11	,	,	PUNCT
ejpam-6259	168	12	.	.	PUNCT
ejpam-6259	168	13	.	.	PUNCT
ejpam-6259	169	1	.	.	PUNCT
ejpam-6259	170	1	,	,	PUNCT
ejpam-6259	170	2	an	an	DET
ejpam-6259	170	3	∈	∈	PROPN
ejpam-6259	170	4	a	a	DET
ejpam-6259	170	5	such	such	ADJ
ejpam-6259	170	6	that	that	DET
ejpam-6259	170	7	g(ai	g(ai	ADJ
ejpam-6259	170	8	)	)	PUNCT
ejpam-6259	170	9	̸=	̸=	PROPN
ejpam-6259	170	10	0	0	NUM
ejpam-6259	170	11	for	for	ADP
ejpam-6259	170	12	all	all	PRON
ejpam-6259	170	13	i	i	PRON
ejpam-6259	170	14	∈	∈	PROPN
ejpam-6259	170	15	{	{	PUNCT
ejpam-6259	170	16	1	1	NUM
ejpam-6259	170	17	,	,	PUNCT
ejpam-6259	170	18	2	2	NUM
ejpam-6259	170	19	,	,	PUNCT
ejpam-6259	170	20	.	.	PUNCT
ejpam-6259	170	21	.	.	PUNCT
ejpam-6259	171	1	.	.	PUNCT
ejpam-6259	171	2	,	,	PUNCT
ejpam-6259	171	3	n	n	CCONJ
ejpam-6259	171	4	}	}	PUNCT
ejpam-6259	171	5	.	.	PUNCT
ejpam-6259	172	1	this	this	PRON
ejpam-6259	172	2	implies	imply	VERB
ejpam-6259	172	3	that	that	SCONJ
ejpam-6259	172	4	a1	a1	NOUN
ejpam-6259	172	5	,	,	PUNCT
ejpam-6259	172	6	a2	a2	PROPN
ejpam-6259	172	7	,	,	PUNCT
ejpam-6259	172	8	.	.	PUNCT
ejpam-6259	172	9	.	.	PUNCT
ejpam-6259	173	1	.	.	PUNCT
ejpam-6259	174	1	,	,	PUNCT
ejpam-6259	174	2	an	an	DET
ejpam-6259	174	3	∈	∈	PROPN
ejpam-6259	174	4	supp(g	supp(g	NOUN
ejpam-6259	174	5	)	)	PUNCT
ejpam-6259	174	6	.	.	PUNCT
ejpam-6259	175	1	therefore	therefore	ADV
ejpam-6259	175	2	f((χsupp(g	f((χsupp(g	ADJ
ejpam-6259	175	3	)	)	PUNCT
ejpam-6259	175	4	)	)	PUNCT
ejpam-6259	176	1	n)(a	n)(a	NUM
ejpam-6259	176	2	)	)	PUNCT
ejpam-6259	177	1	̸=	̸=	NOUN
ejpam-6259	177	2	0	0	NUM
ejpam-6259	177	3	and	and	CCONJ
ejpam-6259	177	4	χsupp(g)(a	χsupp(g)(a	NOUN
ejpam-6259	177	5	)	)	PUNCT
ejpam-6259	177	6	̸=	̸=	PROPN
ejpam-6259	177	7	0	0	NUM
ejpam-6259	177	8	.	.	PUNCT
ejpam-6259	178	1	hence	hence	ADV
ejpam-6259	178	2	,	,	PUNCT
ejpam-6259	178	3	(	(	PUNCT
ejpam-6259	178	4	f((χsupp(g	f((χsupp(g	X
ejpam-6259	178	5	)	)	PUNCT
ejpam-6259	178	6	)	)	PUNCT
ejpam-6259	178	7	n	n	CCONJ
ejpam-6259	178	8	)	)	PUNCT
ejpam-6259	178	9	∩	∩	PROPN
ejpam-6259	178	10	χsupp(g))(a	χsupp(g))(a	PROPN
ejpam-6259	178	11	)	)	PUNCT
ejpam-6259	178	12	̸=	̸=	PROPN
ejpam-6259	178	13	0	0	NUM
ejpam-6259	178	14	.	.	PUNCT
ejpam-6259	179	1	so	so	ADV
ejpam-6259	179	2	,	,	PUNCT
ejpam-6259	179	3	χsupp(g	χsupp(g	PROPN
ejpam-6259	179	4	)	)	PUNCT
ejpam-6259	179	5	is	be	AUX
ejpam-6259	179	6	a	a	DET
ejpam-6259	179	7	fuzzy	fuzzy	ADJ
ejpam-6259	179	8	almost	almost	ADV
ejpam-6259	179	9	n	n	CCONJ
ejpam-6259	179	10	-	-	PUNCT
ejpam-6259	179	11	ary	ary	NOUN
ejpam-6259	179	12	subsemigroup	subsemigroup	NOUN
ejpam-6259	179	13	of	of	ADP
ejpam-6259	179	14	a.	a.	NOUN
ejpam-6259	179	15	by	by	ADP
ejpam-6259	179	16	theorem	theorem	ADJ
ejpam-6259	179	17	3	3	NUM
ejpam-6259	179	18	,	,	PUNCT
ejpam-6259	179	19	supp(g	supp(g	NOUN
ejpam-6259	179	20	)	)	PUNCT
ejpam-6259	179	21	is	be	AUX
ejpam-6259	179	22	an	an	DET
ejpam-6259	179	23	almost	almost	ADV
ejpam-6259	179	24	nary	nary	ADJ
ejpam-6259	179	25	subsemigroup	subsemigroup	NOUN
ejpam-6259	179	26	of	of	ADP
ejpam-6259	179	27	a.	a.	NOUN
ejpam-6259	179	28	conversely	conversely	ADV
ejpam-6259	179	29	,	,	PUNCT
ejpam-6259	179	30	assume	assume	VERB
ejpam-6259	179	31	that	that	SCONJ
ejpam-6259	179	32	supp(g	supp(g	NOUN
ejpam-6259	179	33	)	)	PUNCT
ejpam-6259	179	34	is	be	AUX
ejpam-6259	179	35	an	an	DET
ejpam-6259	179	36	almost	almost	ADV
ejpam-6259	179	37	n	n	CCONJ
ejpam-6259	179	38	-	-	PUNCT
ejpam-6259	179	39	ary	ary	NOUN
ejpam-6259	179	40	subsemigroup	subsemigroup	NOUN
ejpam-6259	179	41	of	of	ADP
ejpam-6259	179	42	a.	a.	NOUN
ejpam-6259	179	43	by	by	ADP
ejpam-6259	179	44	theorem	theorem	NOUN
ejpam-6259	179	45	3	3	NUM
ejpam-6259	179	46	,	,	PUNCT
ejpam-6259	179	47	we	we	PRON
ejpam-6259	179	48	have	have	VERB
ejpam-6259	179	49	χsupp(g	χsupp(g	NOUN
ejpam-6259	179	50	)	)	PUNCT
ejpam-6259	179	51	is	be	AUX
ejpam-6259	179	52	a	a	DET
ejpam-6259	179	53	fuzzy	fuzzy	ADJ
ejpam-6259	179	54	almost	almost	ADV
ejpam-6259	179	55	n	n	CCONJ
ejpam-6259	179	56	-	-	PUNCT
ejpam-6259	179	57	ary	ary	NOUN
ejpam-6259	179	58	subsemigroup	subsemigroup	NOUN
ejpam-6259	179	59	of	of	ADP
ejpam-6259	179	60	a.	a.	NOUN
ejpam-6259	179	61	thus	thus	ADV
ejpam-6259	179	62	r.	r.	PROPN
ejpam-6259	179	63	chinram	chinram	PROPN
ejpam-6259	179	64	,	,	PUNCT
ejpam-6259	180	1	p.	p.	NOUN
ejpam-6259	180	2	singavananda	singavananda	PROPN
ejpam-6259	180	3	/	/	SYM
ejpam-6259	180	4	eur	eur	PROPN
ejpam-6259	180	5	.	.	PUNCT
ejpam-6259	181	1	j.	j.	PROPN
ejpam-6259	181	2	pure	pure	PROPN
ejpam-6259	181	3	appl	appl	PROPN
ejpam-6259	181	4	.	.	PROPN
ejpam-6259	181	5	math	math	PROPN
ejpam-6259	181	6	,	,	PUNCT
ejpam-6259	181	7	18	18	NUM
ejpam-6259	181	8	(	(	PUNCT
ejpam-6259	181	9	3	3	NUM
ejpam-6259	181	10	)	)	PUNCT
ejpam-6259	181	11	(	(	PUNCT
ejpam-6259	181	12	2025	2025	NUM
ejpam-6259	181	13	)	)	PUNCT
ejpam-6259	181	14	,	,	PUNCT
ejpam-6259	181	15	6259	6259	NUM
ejpam-6259	181	16	7	7	NUM
ejpam-6259	181	17	of	of	ADP
ejpam-6259	181	18	10	10	NUM
ejpam-6259	181	19	f((χsupp(g	f((χsupp(g	ADJ
ejpam-6259	181	20	)	)	PUNCT
ejpam-6259	181	21	)	)	PUNCT
ejpam-6259	181	22	n)∩χsupp(g	n)∩χsupp(g	NOUN
ejpam-6259	181	23	)	)	PUNCT
ejpam-6259	181	24	̸=	̸=	PROPN
ejpam-6259	181	25	0	0	NUM
ejpam-6259	181	26	.	.	PUNCT
ejpam-6259	182	1	then	then	ADV
ejpam-6259	182	2	there	there	PRON
ejpam-6259	182	3	is	be	VERB
ejpam-6259	182	4	a	a	DET
ejpam-6259	182	5	∈	∈	PROPN
ejpam-6259	182	6	a	a	DET
ejpam-6259	182	7	such	such	ADJ
ejpam-6259	182	8	that	that	SCONJ
ejpam-6259	182	9	(	(	PUNCT
ejpam-6259	182	10	f((χsupp(g	f((χsupp(g	NOUN
ejpam-6259	182	11	)	)	PUNCT
ejpam-6259	182	12	)	)	PUNCT
ejpam-6259	183	1	n)∩χsupp(g))(a	n)∩χsupp(g))(a	NUM
ejpam-6259	183	2	)	)	PUNCT
ejpam-6259	184	1	̸=	̸=	PROPN
ejpam-6259	184	2	0	0	NUM
ejpam-6259	184	3	.	.	PUNCT
ejpam-6259	185	1	hence	hence	ADV
ejpam-6259	185	2	,	,	PUNCT
ejpam-6259	185	3	f((χsupp(g	f((χsupp(g	ADJ
ejpam-6259	185	4	)	)	PUNCT
ejpam-6259	185	5	)	)	PUNCT
ejpam-6259	185	6	n)(a	n)(a	NUM
ejpam-6259	185	7	)	)	PUNCT
ejpam-6259	186	1	̸=	̸=	NOUN
ejpam-6259	186	2	0	0	NUM
ejpam-6259	186	3	and	and	CCONJ
ejpam-6259	186	4	χsupp(g)(a	χsupp(g)(a	NOUN
ejpam-6259	186	5	)	)	PUNCT
ejpam-6259	186	6	̸=	̸=	PROPN
ejpam-6259	186	7	0	0	NUM
ejpam-6259	186	8	.	.	PUNCT
ejpam-6259	187	1	then	then	ADV
ejpam-6259	187	2	there	there	PRON
ejpam-6259	187	3	exist	exist	VERB
ejpam-6259	187	4	a1	a1	NOUN
ejpam-6259	187	5	,	,	PUNCT
ejpam-6259	187	6	a2	a2	PROPN
ejpam-6259	187	7	,	,	PUNCT
ejpam-6259	187	8	.	.	PUNCT
ejpam-6259	187	9	.	.	PUNCT
ejpam-6259	188	1	.	.	PUNCT
ejpam-6259	189	1	,	,	PUNCT
ejpam-6259	189	2	an	an	DET
ejpam-6259	189	3	∈	∈	PROPN
ejpam-6259	189	4	supp(g	supp(g	NOUN
ejpam-6259	189	5	)	)	PUNCT
ejpam-6259	189	6	and	and	CCONJ
ejpam-6259	189	7	a	a	DET
ejpam-6259	189	8	=	=	X
ejpam-6259	189	9	f(an1	f(an1	PROPN
ejpam-6259	189	10	)	)	PUNCT
ejpam-6259	189	11	.	.	PUNCT
ejpam-6259	190	1	therefore	therefore	ADV
ejpam-6259	190	2	g(ai	g(ai	PROPN
ejpam-6259	190	3	)	)	PUNCT
ejpam-6259	190	4	̸=	̸=	PROPN
ejpam-6259	190	5	0	0	NUM
ejpam-6259	190	6	for	for	ADP
ejpam-6259	190	7	all	all	PRON
ejpam-6259	190	8	i	i	PRON
ejpam-6259	190	9	∈	∈	PROPN
ejpam-6259	190	10	{	{	PUNCT
ejpam-6259	190	11	1	1	NUM
ejpam-6259	190	12	,	,	PUNCT
ejpam-6259	190	13	2	2	NUM
ejpam-6259	190	14	,	,	PUNCT
ejpam-6259	190	15	.	.	PUNCT
ejpam-6259	190	16	.	.	PUNCT
ejpam-6259	190	17	.	.	PUNCT
ejpam-6259	190	18	,	,	PUNCT
ejpam-6259	190	19	n	n	CCONJ
ejpam-6259	190	20	}	}	PUNCT
ejpam-6259	190	21	.	.	PUNCT
ejpam-6259	191	1	hence	hence	ADV
ejpam-6259	191	2	,	,	PUNCT
ejpam-6259	191	3	f(gn)(a	f(gn)(a	PROPN
ejpam-6259	191	4	)	)	PUNCT
ejpam-6259	191	5	̸=	̸=	PROPN
ejpam-6259	191	6	0	0	NUM
ejpam-6259	191	7	.	.	PUNCT
ejpam-6259	192	1	this	this	PRON
ejpam-6259	192	2	implies	imply	VERB
ejpam-6259	192	3	that	that	SCONJ
ejpam-6259	192	4	(	(	PUNCT
ejpam-6259	192	5	f(gn	f(gn	NOUN
ejpam-6259	192	6	)	)	PUNCT
ejpam-6259	192	7	∩	∩	NOUN
ejpam-6259	192	8	g)(a	g)(a	VERB
ejpam-6259	192	9	)	)	PUNCT
ejpam-6259	192	10	̸=	̸=	PROPN
ejpam-6259	192	11	0	0	NUM
ejpam-6259	192	12	.	.	PUNCT
ejpam-6259	193	1	consequently	consequently	ADV
ejpam-6259	193	2	,	,	PUNCT
ejpam-6259	193	3	g	g	PROPN
ejpam-6259	193	4	is	be	AUX
ejpam-6259	193	5	a	a	DET
ejpam-6259	193	6	fuzzy	fuzzy	ADJ
ejpam-6259	193	7	almost	almost	ADV
ejpam-6259	193	8	n	n	CCONJ
ejpam-6259	193	9	-	-	PUNCT
ejpam-6259	193	10	ary	ary	NOUN
ejpam-6259	193	11	subsemigroup	subsemigroup	NOUN
ejpam-6259	193	12	of	of	ADP
ejpam-6259	193	13	a.	a.	NOUN
ejpam-6259	193	14	an	an	DET
ejpam-6259	193	15	almost	almost	ADV
ejpam-6259	193	16	n	n	CCONJ
ejpam-6259	193	17	-	-	PUNCT
ejpam-6259	193	18	ary	ary	NOUN
ejpam-6259	193	19	subsemigroup	subsemigroup	PROPN
ejpam-6259	193	20	s	s	PROPN
ejpam-6259	193	21	of	of	ADP
ejpam-6259	193	22	an	an	DET
ejpam-6259	193	23	n	n	CCONJ
ejpam-6259	193	24	-	-	PUNCT
ejpam-6259	193	25	ary	ary	NOUN
ejpam-6259	193	26	semigroup	semigroup	NOUN
ejpam-6259	193	27	a	a	PRON
ejpam-6259	193	28	is	be	AUX
ejpam-6259	193	29	called	call	VERB
ejpam-6259	193	30	minimal	minimal	ADJ
ejpam-6259	193	31	if	if	SCONJ
ejpam-6259	193	32	for	for	ADP
ejpam-6259	193	33	any	any	DET
ejpam-6259	193	34	almost	almost	ADV
ejpam-6259	193	35	n	n	CCONJ
ejpam-6259	193	36	-	-	PUNCT
ejpam-6259	193	37	ary	ary	NOUN
ejpam-6259	193	38	subsemigroup	subsemigroup	PROPN
ejpam-6259	193	39	t	t	PROPN
ejpam-6259	193	40	of	of	ADP
ejpam-6259	193	41	a	a	DET
ejpam-6259	193	42	such	such	ADJ
ejpam-6259	193	43	that	that	SCONJ
ejpam-6259	193	44	t	t	PROPN
ejpam-6259	193	45	⊆	⊆	NUM
ejpam-6259	193	46	s	s	NOUN
ejpam-6259	193	47	,	,	PUNCT
ejpam-6259	193	48	it	it	PRON
ejpam-6259	193	49	follows	follow	VERB
ejpam-6259	193	50	that	that	SCONJ
ejpam-6259	193	51	t	t	PROPN
ejpam-6259	193	52	=	=	PUNCT
ejpam-6259	193	53	s.	s.	PROPN
ejpam-6259	193	54	next	next	ADV
ejpam-6259	193	55	,	,	PUNCT
ejpam-6259	193	56	we	we	PRON
ejpam-6259	193	57	examine	examine	VERB
ejpam-6259	193	58	the	the	DET
ejpam-6259	193	59	minimality	minimality	NOUN
ejpam-6259	193	60	of	of	ADP
ejpam-6259	193	61	fuzzy	fuzzy	ADJ
ejpam-6259	193	62	almost	almost	ADV
ejpam-6259	193	63	n	n	CCONJ
ejpam-6259	193	64	-	-	PUNCT
ejpam-6259	193	65	ary	ary	PROPN
ejpam-6259	193	66	subsemigroups	subsemigroup	NOUN
ejpam-6259	193	67	.	.	PUNCT
ejpam-6259	194	1	a	a	DET
ejpam-6259	194	2	fuzzy	fuzzy	ADJ
ejpam-6259	194	3	almost	almost	ADV
ejpam-6259	194	4	n	n	CCONJ
ejpam-6259	194	5	-	-	PUNCT
ejpam-6259	194	6	ary	ary	NOUN
ejpam-6259	194	7	subsemigroup	subsemigroup	PROPN
ejpam-6259	194	8	g	g	PROPN
ejpam-6259	194	9	of	of	ADP
ejpam-6259	194	10	an	an	DET
ejpam-6259	194	11	n	n	CCONJ
ejpam-6259	194	12	-	-	PUNCT
ejpam-6259	194	13	ary	ary	NOUN
ejpam-6259	194	14	semigroup	semigroup	NOUN
ejpam-6259	194	15	a	a	PRON
ejpam-6259	194	16	is	be	AUX
ejpam-6259	194	17	called	call	VERB
ejpam-6259	194	18	minimal	minimal	ADJ
ejpam-6259	194	19	if	if	SCONJ
ejpam-6259	194	20	for	for	ADP
ejpam-6259	194	21	any	any	DET
ejpam-6259	194	22	fuzzy	fuzzy	ADJ
ejpam-6259	194	23	almost	almost	ADV
ejpam-6259	194	24	n	n	CCONJ
ejpam-6259	194	25	-	-	PUNCT
ejpam-6259	194	26	ary	ary	NOUN
ejpam-6259	194	27	subsemigroup	subsemigroup	PROPN
ejpam-6259	194	28	h	h	PROPN
ejpam-6259	194	29	of	of	ADP
ejpam-6259	194	30	a	a	DET
ejpam-6259	194	31	contained	contain	VERB
ejpam-6259	194	32	in	in	ADP
ejpam-6259	194	33	g	g	NOUN
ejpam-6259	194	34	,	,	PUNCT
ejpam-6259	194	35	it	it	PRON
ejpam-6259	194	36	follows	follow	VERB
ejpam-6259	194	37	that	that	PRON
ejpam-6259	194	38	supp(g	supp(g	NOUN
ejpam-6259	194	39	)	)	PUNCT
ejpam-6259	194	40	=	=	SYM
ejpam-6259	194	41	supp(h	supp(h	NOUN
ejpam-6259	194	42	)	)	PUNCT
ejpam-6259	194	43	.	.	PUNCT
ejpam-6259	195	1	now	now	ADV
ejpam-6259	195	2	,	,	PUNCT
ejpam-6259	195	3	we	we	PRON
ejpam-6259	195	4	provide	provide	VERB
ejpam-6259	195	5	the	the	DET
ejpam-6259	195	6	relationship	relationship	NOUN
ejpam-6259	195	7	between	between	ADP
ejpam-6259	195	8	minimal	minimal	ADJ
ejpam-6259	195	9	almost	almost	ADV
ejpam-6259	195	10	n	n	CCONJ
ejpam-6259	195	11	-	-	PUNCT
ejpam-6259	195	12	ary	ary	NOUN
ejpam-6259	195	13	subsemigroup	subsemigroup	NOUN
ejpam-6259	195	14	and	and	CCONJ
ejpam-6259	195	15	their	their	PRON
ejpam-6259	195	16	fuzzifications	fuzzification	NOUN
ejpam-6259	195	17	.	.	PUNCT
ejpam-6259	196	1	theorem	theorem	NOUN
ejpam-6259	196	2	5	5	NUM
ejpam-6259	196	3	.	.	PUNCT
ejpam-6259	197	1	a	a	DET
ejpam-6259	197	2	nonempty	nonempty	ADJ
ejpam-6259	197	3	subset	subset	VERB
ejpam-6259	197	4	s	s	NOUN
ejpam-6259	197	5	of	of	ADP
ejpam-6259	197	6	an	an	DET
ejpam-6259	197	7	n	n	CCONJ
ejpam-6259	197	8	-	-	PUNCT
ejpam-6259	197	9	ary	ary	NOUN
ejpam-6259	197	10	semigroup	semigroup	NOUN
ejpam-6259	197	11	a	a	PRON
ejpam-6259	197	12	is	be	AUX
ejpam-6259	197	13	a	a	DET
ejpam-6259	197	14	minimal	minimal	ADJ
ejpam-6259	197	15	almost	almost	ADV
ejpam-6259	197	16	n	n	CCONJ
ejpam-6259	197	17	-	-	PUNCT
ejpam-6259	197	18	ary	ary	NOUN
ejpam-6259	197	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	197	20	of	of	ADP
ejpam-6259	197	21	a	a	DET
ejpam-6259	197	22	if	if	NOUN
ejpam-6259	197	23	and	and	CCONJ
ejpam-6259	197	24	only	only	ADV
ejpam-6259	197	25	if	if	SCONJ
ejpam-6259	197	26	χs	χs	NOUN
ejpam-6259	197	27	is	be	AUX
ejpam-6259	197	28	a	a	DET
ejpam-6259	197	29	minimal	minimal	ADJ
ejpam-6259	197	30	fuzzy	fuzzy	ADJ
ejpam-6259	197	31	almost	almost	ADV
ejpam-6259	197	32	n	n	CCONJ
ejpam-6259	197	33	-	-	PUNCT
ejpam-6259	197	34	ary	ary	NOUN
ejpam-6259	197	35	subsemigroup	subsemigroup	NOUN
ejpam-6259	197	36	of	of	ADP
ejpam-6259	197	37	a.	a.	NOUN
ejpam-6259	197	38	proof	proof	NOUN
ejpam-6259	197	39	.	.	PUNCT
ejpam-6259	198	1	let	let	VERB
ejpam-6259	198	2	s	s	PRON
ejpam-6259	198	3	be	be	AUX
ejpam-6259	198	4	a	a	DET
ejpam-6259	198	5	minimal	minimal	ADJ
ejpam-6259	198	6	almost	almost	ADV
ejpam-6259	198	7	n	n	CCONJ
ejpam-6259	198	8	-	-	PUNCT
ejpam-6259	198	9	ary	ary	NOUN
ejpam-6259	199	1	subsemigroup	subsemigroup	NOUN
ejpam-6259	199	2	of	of	ADP
ejpam-6259	199	3	an	an	DET
ejpam-6259	199	4	n	n	CCONJ
ejpam-6259	199	5	-	-	PUNCT
ejpam-6259	199	6	ary	ary	PROPN
ejpam-6259	199	7	semigroup	semigroup	PROPN
ejpam-6259	199	8	a.	a.	NOUN
ejpam-6259	199	9	by	by	ADP
ejpam-6259	199	10	theorem	theorem	NOUN
ejpam-6259	199	11	3	3	NUM
ejpam-6259	199	12	,	,	PUNCT
ejpam-6259	199	13	we	we	PRON
ejpam-6259	199	14	have	have	AUX
ejpam-6259	199	15	that	that	PRON
ejpam-6259	199	16	χs	χs	PROPN
ejpam-6259	199	17	is	be	AUX
ejpam-6259	199	18	a	a	DET
ejpam-6259	199	19	fuzzy	fuzzy	ADJ
ejpam-6259	199	20	almost	almost	ADV
ejpam-6259	199	21	n	n	CCONJ
ejpam-6259	199	22	-	-	PUNCT
ejpam-6259	199	23	ary	ary	NOUN
ejpam-6259	199	24	subsemigroup	subsemigroup	NOUN
ejpam-6259	199	25	of	of	ADP
ejpam-6259	199	26	a.	a.	NOUN
ejpam-6259	199	27	suppose	suppose	VERB
ejpam-6259	199	28	that	that	SCONJ
ejpam-6259	199	29	g	g	PROPN
ejpam-6259	199	30	is	be	AUX
ejpam-6259	199	31	a	a	DET
ejpam-6259	199	32	fuzzy	fuzzy	ADJ
ejpam-6259	199	33	almost	almost	ADV
ejpam-6259	199	34	n	n	CCONJ
ejpam-6259	199	35	-	-	PUNCT
ejpam-6259	199	36	ary	ary	NOUN
ejpam-6259	199	37	subsemigroup	subsemigroup	NOUN
ejpam-6259	199	38	of	of	ADP
ejpam-6259	199	39	a	a	DET
ejpam-6259	199	40	contained	contain	VERB
ejpam-6259	199	41	in	in	ADP
ejpam-6259	199	42	χs	χs	NOUN
ejpam-6259	199	43	.	.	PUNCT
ejpam-6259	200	1	by	by	ADP
ejpam-6259	200	2	theorem	theorem	ADJ
ejpam-6259	200	3	4	4	NUM
ejpam-6259	200	4	,	,	PUNCT
ejpam-6259	200	5	supp(g	supp(g	NUM
ejpam-6259	200	6	)	)	PUNCT
ejpam-6259	200	7	is	be	AUX
ejpam-6259	200	8	an	an	DET
ejpam-6259	200	9	almost	almost	ADV
ejpam-6259	200	10	n	n	CCONJ
ejpam-6259	200	11	-	-	PUNCT
ejpam-6259	200	12	ary	ary	NOUN
ejpam-6259	200	13	subsemigroup	subsemigroup	NOUN
ejpam-6259	200	14	of	of	ADP
ejpam-6259	200	15	a.	a.	NOUN
ejpam-6259	200	16	since	since	SCONJ
ejpam-6259	200	17	g	g	PROPN
ejpam-6259	200	18	⊆	⊆	NUM
ejpam-6259	200	19	χs	χs	NOUN
ejpam-6259	200	20	,	,	PUNCT
ejpam-6259	200	21	supp(g	supp(g	PROPN
ejpam-6259	200	22	)	)	PUNCT
ejpam-6259	200	23	⊆	⊆	NUM
ejpam-6259	200	24	supp(χs	supp(χs	ADV
ejpam-6259	200	25	)	)	PUNCT
ejpam-6259	200	26	=	=	VERB
ejpam-6259	200	27	s.	s.	PROPN
ejpam-6259	200	28	because	because	SCONJ
ejpam-6259	200	29	s	s	PROPN
ejpam-6259	200	30	is	be	AUX
ejpam-6259	200	31	minimal	minimal	ADJ
ejpam-6259	200	32	,	,	PUNCT
ejpam-6259	200	33	we	we	PRON
ejpam-6259	200	34	conclude	conclude	VERB
ejpam-6259	200	35	that	that	DET
ejpam-6259	200	36	supp(g	supp(g	NOUN
ejpam-6259	200	37	)	)	PUNCT
ejpam-6259	201	1	=	=	SYM
ejpam-6259	201	2	s	s	NOUN
ejpam-6259	201	3	=	=	PUNCT
ejpam-6259	201	4	supp(χs	supp(χs	PROPN
ejpam-6259	201	5	)	)	PUNCT
ejpam-6259	201	6	.	.	PUNCT
ejpam-6259	202	1	therefore	therefore	ADV
ejpam-6259	202	2	,	,	PUNCT
ejpam-6259	202	3	χs	χs	PROPN
ejpam-6259	202	4	is	be	AUX
ejpam-6259	202	5	minimal	minimal	ADJ
ejpam-6259	202	6	.	.	PUNCT
ejpam-6259	203	1	conversely	conversely	ADV
ejpam-6259	203	2	,	,	PUNCT
ejpam-6259	203	3	suppose	suppose	VERB
ejpam-6259	203	4	that	that	SCONJ
ejpam-6259	203	5	χs	χs	PROPN
ejpam-6259	203	6	is	be	AUX
ejpam-6259	203	7	a	a	DET
ejpam-6259	203	8	minimal	minimal	ADJ
ejpam-6259	203	9	fuzzy	fuzzy	ADJ
ejpam-6259	203	10	almost	almost	ADV
ejpam-6259	203	11	n	n	CCONJ
ejpam-6259	203	12	-	-	PUNCT
ejpam-6259	203	13	ary	ary	NOUN
ejpam-6259	203	14	subsemigroup	subsemigroup	NOUN
ejpam-6259	203	15	of	of	ADP
ejpam-6259	203	16	a	a	PRON
ejpam-6259	203	17	,	,	PUNCT
ejpam-6259	203	18	and	and	CCONJ
ejpam-6259	203	19	let	let	VERB
ejpam-6259	203	20	t	t	PROPN
ejpam-6259	203	21	be	be	AUX
ejpam-6259	203	22	an	an	DET
ejpam-6259	203	23	almost	almost	ADV
ejpam-6259	203	24	n	n	CCONJ
ejpam-6259	203	25	-	-	PUNCT
ejpam-6259	203	26	ary	ary	NOUN
ejpam-6259	203	27	subsemigroup	subsemigroup	NOUN
ejpam-6259	203	28	of	of	ADP
ejpam-6259	203	29	a	a	DET
ejpam-6259	203	30	contained	contain	VERB
ejpam-6259	203	31	in	in	ADP
ejpam-6259	203	32	s.	s.	PROPN
ejpam-6259	203	33	by	by	ADP
ejpam-6259	203	34	theorem	theorem	NOUN
ejpam-6259	203	35	3	3	NUM
ejpam-6259	203	36	,	,	PUNCT
ejpam-6259	203	37	we	we	PRON
ejpam-6259	203	38	have	have	VERB
ejpam-6259	203	39	that	that	PRON
ejpam-6259	203	40	χt	χt	NOUN
ejpam-6259	203	41	is	be	AUX
ejpam-6259	203	42	a	a	DET
ejpam-6259	203	43	fuzzy	fuzzy	ADJ
ejpam-6259	203	44	almost	almost	ADV
ejpam-6259	203	45	n	n	CCONJ
ejpam-6259	203	46	-	-	PUNCT
ejpam-6259	203	47	ary	ary	NOUN
ejpam-6259	203	48	subsemigroup	subsemigroup	NOUN
ejpam-6259	203	49	of	of	ADP
ejpam-6259	203	50	a	a	PRON
ejpam-6259	203	51	and	and	CCONJ
ejpam-6259	203	52	χt	χt	ADP
ejpam-6259	203	53	⊆	⊆	NUM
ejpam-6259	203	54	χs	χs	NOUN
ejpam-6259	203	55	.	.	PUNCT
ejpam-6259	204	1	thus	thus	ADV
ejpam-6259	204	2	,	,	PUNCT
ejpam-6259	204	3	t	t	NOUN
ejpam-6259	204	4	=	=	SYM
ejpam-6259	204	5	supp(χt	supp(χt	ADJ
ejpam-6259	204	6	)	)	PUNCT
ejpam-6259	204	7	=	=	SYM
ejpam-6259	204	8	supp(χs	supp(χs	ADV
ejpam-6259	204	9	)	)	PUNCT
ejpam-6259	204	10	=	=	VERB
ejpam-6259	205	1	s.	s.	PROPN
ejpam-6259	205	2	we	we	PRON
ejpam-6259	205	3	conclude	conclude	VERB
ejpam-6259	205	4	that	that	PRON
ejpam-6259	205	5	s	s	VERB
ejpam-6259	205	6	is	be	AUX
ejpam-6259	205	7	minimal	minimal	ADJ
ejpam-6259	205	8	.	.	PUNCT
ejpam-6259	206	1	corollary	corollary	ADJ
ejpam-6259	206	2	3	3	NUM
ejpam-6259	206	3	.	.	PUNCT
ejpam-6259	207	1	an	an	DET
ejpam-6259	207	2	n	n	NUM
ejpam-6259	207	3	-	-	PUNCT
ejpam-6259	207	4	ary	ary	NOUN
ejpam-6259	207	5	semigroup	semigroup	NOUN
ejpam-6259	207	6	a	a	PRON
ejpam-6259	207	7	has	have	VERB
ejpam-6259	207	8	no	no	DET
ejpam-6259	207	9	proper	proper	ADJ
ejpam-6259	207	10	almost	almost	ADV
ejpam-6259	207	11	n	n	CCONJ
ejpam-6259	207	12	-	-	PUNCT
ejpam-6259	207	13	ary	ary	NOUN
ejpam-6259	207	14	subsemigroups	subsemigroup	NOUN
ejpam-6259	207	15	if	if	SCONJ
ejpam-6259	207	16	and	and	CCONJ
ejpam-6259	207	17	only	only	ADV
ejpam-6259	207	18	if	if	SCONJ
ejpam-6259	207	19	for	for	ADP
ejpam-6259	207	20	all	all	PRON
ejpam-6259	207	21	fuzzy	fuzzy	ADJ
ejpam-6259	207	22	almost	almost	ADV
ejpam-6259	207	23	n	n	CCONJ
ejpam-6259	207	24	-	-	PUNCT
ejpam-6259	207	25	ary	ary	NOUN
ejpam-6259	207	26	subsemigroup	subsemigroup	PROPN
ejpam-6259	207	27	g	g	PROPN
ejpam-6259	207	28	of	of	ADP
ejpam-6259	207	29	a	a	DET
ejpam-6259	207	30	,	,	PUNCT
ejpam-6259	207	31	supp(g	supp(g	NOUN
ejpam-6259	207	32	)	)	PUNCT
ejpam-6259	207	33	=	=	NOUN
ejpam-6259	207	34	a.	a.	NOUN
ejpam-6259	207	35	proof	proof	NOUN
ejpam-6259	207	36	.	.	PUNCT
ejpam-6259	208	1	assume	assume	VERB
ejpam-6259	208	2	that	that	SCONJ
ejpam-6259	208	3	a	a	PRON
ejpam-6259	208	4	has	have	VERB
ejpam-6259	208	5	no	no	DET
ejpam-6259	208	6	proper	proper	ADJ
ejpam-6259	208	7	almost	almost	ADV
ejpam-6259	208	8	n	n	CCONJ
ejpam-6259	208	9	-	-	PUNCT
ejpam-6259	208	10	ary	ary	NOUN
ejpam-6259	208	11	subsemigroups	subsemigroup	NOUN
ejpam-6259	208	12	,	,	PUNCT
ejpam-6259	208	13	and	and	CCONJ
ejpam-6259	208	14	let	let	VERB
ejpam-6259	208	15	g	g	PRON
ejpam-6259	208	16	be	be	AUX
ejpam-6259	208	17	a	a	DET
ejpam-6259	208	18	fuzzy	fuzzy	ADJ
ejpam-6259	208	19	almost	almost	ADV
ejpam-6259	208	20	n	n	CCONJ
ejpam-6259	208	21	-	-	PUNCT
ejpam-6259	208	22	ary	ary	NOUN
ejpam-6259	208	23	subsemigroup	subsemigroup	NOUN
ejpam-6259	208	24	of	of	ADP
ejpam-6259	208	25	a.	a.	NOUN
ejpam-6259	208	26	by	by	ADP
ejpam-6259	208	27	theorem	theorem	NOUN
ejpam-6259	208	28	4	4	NUM
ejpam-6259	208	29	,	,	PUNCT
ejpam-6259	208	30	we	we	PRON
ejpam-6259	208	31	have	have	VERB
ejpam-6259	208	32	supp(g	supp(g	NUM
ejpam-6259	208	33	)	)	PUNCT
ejpam-6259	208	34	is	be	AUX
ejpam-6259	208	35	an	an	DET
ejpam-6259	208	36	almost	almost	ADV
ejpam-6259	208	37	n	n	CCONJ
ejpam-6259	208	38	-	-	PUNCT
ejpam-6259	208	39	ary	ary	NOUN
ejpam-6259	208	40	subsemigroup	subsemigroup	NOUN
ejpam-6259	208	41	of	of	ADP
ejpam-6259	208	42	a.	a.	NOUN
ejpam-6259	208	43	by	by	ADP
ejpam-6259	208	44	assumption	assumption	NOUN
ejpam-6259	208	45	,	,	PUNCT
ejpam-6259	208	46	we	we	PRON
ejpam-6259	208	47	have	have	VERB
ejpam-6259	208	48	supp(g	supp(g	NUM
ejpam-6259	208	49	)	)	PUNCT
ejpam-6259	208	50	=	=	SYM
ejpam-6259	208	51	a.	a.	NOUN
ejpam-6259	208	52	to	to	PART
ejpam-6259	208	53	prove	prove	VERB
ejpam-6259	208	54	the	the	DET
ejpam-6259	208	55	converse	converse	NOUN
ejpam-6259	208	56	,	,	PUNCT
ejpam-6259	208	57	we	we	PRON
ejpam-6259	208	58	let	let	VERB
ejpam-6259	208	59	s	s	PRON
ejpam-6259	208	60	be	be	AUX
ejpam-6259	208	61	any	any	DET
ejpam-6259	208	62	almost	almost	ADV
ejpam-6259	208	63	n	n	CCONJ
ejpam-6259	208	64	-	-	PUNCT
ejpam-6259	208	65	ary	ary	NOUN
ejpam-6259	208	66	subsemigroup	subsemigroup	NOUN
ejpam-6259	208	67	of	of	ADP
ejpam-6259	208	68	a.	a.	NOUN
ejpam-6259	208	69	by	by	ADP
ejpam-6259	208	70	theorem	theorem	NOUN
ejpam-6259	208	71	3	3	NUM
ejpam-6259	208	72	,	,	PUNCT
ejpam-6259	208	73	we	we	PRON
ejpam-6259	208	74	have	have	VERB
ejpam-6259	208	75	that	that	DET
ejpam-6259	208	76	χs	χs	PROPN
ejpam-6259	208	77	is	be	AUX
ejpam-6259	208	78	a	a	DET
ejpam-6259	208	79	fuzzy	fuzzy	ADJ
ejpam-6259	208	80	almost	almost	ADV
ejpam-6259	208	81	n	n	CCONJ
ejpam-6259	208	82	-	-	PUNCT
ejpam-6259	208	83	ary	ary	NOUN
ejpam-6259	208	84	subsemigroup	subsemigroup	NOUN
ejpam-6259	208	85	of	of	ADP
ejpam-6259	208	86	a.	a.	NOUN
ejpam-6259	208	87	by	by	ADP
ejpam-6259	208	88	assumption	assumption	NOUN
ejpam-6259	208	89	,	,	PUNCT
ejpam-6259	208	90	we	we	PRON
ejpam-6259	208	91	get	get	VERB
ejpam-6259	208	92	s	s	NOUN
ejpam-6259	208	93	=	=	X
ejpam-6259	208	94	supp(χs	supp(χs	ADV
ejpam-6259	208	95	)	)	PUNCT
ejpam-6259	208	96	=	=	VERB
ejpam-6259	209	1	a.	a.	NOUN
ejpam-6259	209	2	we	we	PRON
ejpam-6259	209	3	can	can	AUX
ejpam-6259	209	4	conclude	conclude	VERB
ejpam-6259	209	5	that	that	SCONJ
ejpam-6259	209	6	a	a	PRON
ejpam-6259	209	7	has	have	VERB
ejpam-6259	209	8	no	no	DET
ejpam-6259	209	9	proper	proper	ADJ
ejpam-6259	209	10	almost	almost	ADV
ejpam-6259	209	11	n	n	CCONJ
ejpam-6259	209	12	-	-	PUNCT
ejpam-6259	209	13	ary	ary	PROPN
ejpam-6259	209	14	subsemigroups	subsemigroup	NOUN
ejpam-6259	209	15	.	.	PUNCT
ejpam-6259	210	1	let	let	VERB
ejpam-6259	210	2	a	a	DET
ejpam-6259	210	3	be	be	AUX
ejpam-6259	210	4	an	an	DET
ejpam-6259	210	5	n	n	CCONJ
ejpam-6259	210	6	-	-	PUNCT
ejpam-6259	210	7	ary	ary	NOUN
ejpam-6259	210	8	semigroup	semigroup	PROPN
ejpam-6259	210	9	.	.	PUNCT
ejpam-6259	211	1	an	an	DET
ejpam-6259	211	2	almost	almost	ADV
ejpam-6259	211	3	n	n	CCONJ
ejpam-6259	211	4	-	-	PUNCT
ejpam-6259	211	5	ary	ary	NOUN
ejpam-6259	211	6	subsemigroup	subsemigroup	PROPN
ejpam-6259	211	7	s	s	PROPN
ejpam-6259	211	8	of	of	ADP
ejpam-6259	211	9	a	a	PRON
ejpam-6259	211	10	is	be	AUX
ejpam-6259	211	11	called	call	VERB
ejpam-6259	211	12	prime	prime	ADJ
ejpam-6259	211	13	if	if	SCONJ
ejpam-6259	211	14	for	for	ADP
ejpam-6259	211	15	all	all	DET
ejpam-6259	211	16	a1	a1	NOUN
ejpam-6259	211	17	,	,	PUNCT
ejpam-6259	211	18	a2	a2	PROPN
ejpam-6259	211	19	,	,	PUNCT
ejpam-6259	211	20	.	.	PUNCT
ejpam-6259	211	21	.	.	PUNCT
ejpam-6259	212	1	.	.	PUNCT
ejpam-6259	213	1	,	,	PUNCT
ejpam-6259	213	2	an	an	DET
ejpam-6259	213	3	∈	∈	PROPN
ejpam-6259	213	4	a	a	PRON
ejpam-6259	213	5	,	,	PUNCT
ejpam-6259	213	6	f(an1	f(an1	PROPN
ejpam-6259	213	7	)	)	PUNCT
ejpam-6259	213	8	∈	∈	PROPN
ejpam-6259	213	9	s	s	PART
ejpam-6259	213	10	implies	imply	VERB
ejpam-6259	213	11	ai	ai	VERB
ejpam-6259	213	12	∈	∈	PROPN
ejpam-6259	213	13	s	s	NOUN
ejpam-6259	213	14	for	for	ADP
ejpam-6259	213	15	some	some	DET
ejpam-6259	213	16	i	i	PRON
ejpam-6259	213	17	∈	∈	PROPN
ejpam-6259	213	18	{	{	PUNCT
ejpam-6259	213	19	1	1	NUM
ejpam-6259	213	20	,	,	PUNCT
ejpam-6259	213	21	2	2	NUM
ejpam-6259	213	22	,	,	PUNCT
ejpam-6259	213	23	.	.	PUNCT
ejpam-6259	213	24	.	.	PUNCT
ejpam-6259	214	1	.	.	PUNCT
ejpam-6259	214	2	,	,	PUNCT
ejpam-6259	214	3	n	n	CCONJ
ejpam-6259	214	4	}	}	PUNCT
ejpam-6259	214	5	.	.	PUNCT
ejpam-6259	215	1	a	a	DET
ejpam-6259	215	2	fuzzy	fuzzy	ADJ
ejpam-6259	215	3	almost	almost	ADV
ejpam-6259	215	4	n	n	CCONJ
ejpam-6259	215	5	-	-	PUNCT
ejpam-6259	215	6	ary	ary	NOUN
ejpam-6259	215	7	subsemigroup	subsemigroup	PROPN
ejpam-6259	215	8	g	g	PROPN
ejpam-6259	215	9	of	of	ADP
ejpam-6259	215	10	a	a	PRON
ejpam-6259	215	11	is	be	AUX
ejpam-6259	215	12	called	call	VERB
ejpam-6259	215	13	prime	prime	NOUN
ejpam-6259	215	14	if	if	SCONJ
ejpam-6259	215	15	g(f(an1	g(f(an1	PROPN
ejpam-6259	215	16	)	)	PUNCT
ejpam-6259	215	17	)	)	PUNCT
ejpam-6259	215	18	≤	≤	NUM
ejpam-6259	215	19	max{g(a1	max{g(a1	NOUN
ejpam-6259	215	20	)	)	PUNCT
ejpam-6259	215	21	,	,	PUNCT
ejpam-6259	215	22	g(a2	g(a2	PROPN
ejpam-6259	215	23	)	)	PUNCT
ejpam-6259	215	24	,	,	PUNCT
ejpam-6259	215	25	.	.	PUNCT
ejpam-6259	215	26	.	.	PUNCT
ejpam-6259	216	1	.	.	PUNCT
ejpam-6259	217	1	,	,	PUNCT
ejpam-6259	217	2	g(an	g(an	PROPN
ejpam-6259	217	3	)	)	PUNCT
ejpam-6259	217	4	}	}	PUNCT
ejpam-6259	217	5	for	for	ADP
ejpam-6259	217	6	all	all	DET
ejpam-6259	217	7	a1	a1	NOUN
ejpam-6259	217	8	,	,	PUNCT
ejpam-6259	217	9	g2	g2	PROPN
ejpam-6259	217	10	,	,	PUNCT
ejpam-6259	217	11	.	.	PUNCT
ejpam-6259	217	12	.	.	PUNCT
ejpam-6259	218	1	.	.	PUNCT
ejpam-6259	219	1	,	,	PUNCT
ejpam-6259	219	2	an	an	DET
ejpam-6259	219	3	∈	∈	PROPN
ejpam-6259	219	4	a.	a.	NOUN
ejpam-6259	219	5	next	next	ADV
ejpam-6259	219	6	,	,	PUNCT
ejpam-6259	219	7	we	we	PRON
ejpam-6259	219	8	investigate	investigate	VERB
ejpam-6259	219	9	a	a	DET
ejpam-6259	219	10	relationship	relationship	NOUN
ejpam-6259	219	11	between	between	ADP
ejpam-6259	219	12	prime	prime	NOUN
ejpam-6259	219	13	almost	almost	ADV
ejpam-6259	219	14	n	n	CCONJ
ejpam-6259	219	15	-	-	PUNCT
ejpam-6259	219	16	ary	ary	NOUN
ejpam-6259	219	17	subsemigroups	subsemigroup	NOUN
ejpam-6259	219	18	and	and	CCONJ
ejpam-6259	219	19	their	their	PRON
ejpam-6259	219	20	fuzzifications	fuzzification	NOUN
ejpam-6259	219	21	.	.	PUNCT
ejpam-6259	220	1	theorem	theorem	VERB
ejpam-6259	220	2	6	6	NUM
ejpam-6259	220	3	.	.	PUNCT
ejpam-6259	221	1	a	a	DET
ejpam-6259	221	2	nonempty	nonempty	ADJ
ejpam-6259	221	3	subset	subset	VERB
ejpam-6259	221	4	s	s	NOUN
ejpam-6259	221	5	of	of	ADP
ejpam-6259	221	6	an	an	DET
ejpam-6259	221	7	n	n	CCONJ
ejpam-6259	221	8	-	-	PUNCT
ejpam-6259	221	9	ary	ary	NOUN
ejpam-6259	221	10	semigroup	semigroup	NOUN
ejpam-6259	221	11	a	a	PRON
ejpam-6259	221	12	is	be	AUX
ejpam-6259	221	13	a	a	DET
ejpam-6259	221	14	prime	prime	NOUN
ejpam-6259	221	15	almost	almost	ADV
ejpam-6259	221	16	n	n	CCONJ
ejpam-6259	221	17	-	-	PUNCT
ejpam-6259	221	18	ary	ary	NOUN
ejpam-6259	221	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	221	20	of	of	ADP
ejpam-6259	221	21	a	a	DET
ejpam-6259	221	22	if	if	NOUN
ejpam-6259	221	23	and	and	CCONJ
ejpam-6259	221	24	only	only	ADV
ejpam-6259	221	25	if	if	SCONJ
ejpam-6259	221	26	χs	χs	NOUN
ejpam-6259	221	27	is	be	AUX
ejpam-6259	221	28	a	a	DET
ejpam-6259	221	29	prime	prime	ADJ
ejpam-6259	221	30	fuzzy	fuzzy	ADJ
ejpam-6259	221	31	almost	almost	ADV
ejpam-6259	221	32	n	n	CCONJ
ejpam-6259	221	33	-	-	PUNCT
ejpam-6259	221	34	ary	ary	NOUN
ejpam-6259	221	35	subsemigroup	subsemigroup	NOUN
ejpam-6259	221	36	of	of	ADP
ejpam-6259	221	37	a.	a.	PROPN
ejpam-6259	221	38	r.	r.	PROPN
ejpam-6259	221	39	chinram	chinram	PROPN
ejpam-6259	221	40	,	,	PUNCT
ejpam-6259	221	41	p.	p.	NOUN
ejpam-6259	221	42	singavananda	singavananda	PROPN
ejpam-6259	221	43	/	/	SYM
ejpam-6259	221	44	eur	eur	PROPN
ejpam-6259	221	45	.	.	PUNCT
ejpam-6259	222	1	j.	j.	PROPN
ejpam-6259	222	2	pure	pure	PROPN
ejpam-6259	222	3	appl	appl	PROPN
ejpam-6259	222	4	.	.	PROPN
ejpam-6259	222	5	math	math	PROPN
ejpam-6259	222	6	,	,	PUNCT
ejpam-6259	222	7	18	18	NUM
ejpam-6259	222	8	(	(	PUNCT
ejpam-6259	222	9	3	3	NUM
ejpam-6259	222	10	)	)	PUNCT
ejpam-6259	222	11	(	(	PUNCT
ejpam-6259	222	12	2025	2025	NUM
ejpam-6259	222	13	)	)	PUNCT
ejpam-6259	222	14	,	,	PUNCT
ejpam-6259	222	15	6259	6259	NUM
ejpam-6259	222	16	8	8	NUM
ejpam-6259	222	17	of	of	ADP
ejpam-6259	222	18	10	10	NUM
ejpam-6259	222	19	proof	proof	NOUN
ejpam-6259	222	20	.	.	PUNCT
ejpam-6259	223	1	let	let	VERB
ejpam-6259	223	2	s	s	PRON
ejpam-6259	223	3	be	be	AUX
ejpam-6259	223	4	any	any	DET
ejpam-6259	223	5	prime	prime	NOUN
ejpam-6259	223	6	almost	almost	ADV
ejpam-6259	223	7	n	n	CCONJ
ejpam-6259	223	8	-	-	PUNCT
ejpam-6259	223	9	ary	ary	NOUN
ejpam-6259	223	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	223	11	of	of	ADP
ejpam-6259	223	12	a.	a.	NOUN
ejpam-6259	223	13	by	by	ADP
ejpam-6259	223	14	theorem	theorem	NOUN
ejpam-6259	223	15	3	3	NUM
ejpam-6259	223	16	,	,	PUNCT
ejpam-6259	223	17	we	we	PRON
ejpam-6259	223	18	have	have	VERB
ejpam-6259	223	19	that	that	PRON
ejpam-6259	223	20	χs	χs	PROPN
ejpam-6259	223	21	is	be	AUX
ejpam-6259	223	22	a	a	DET
ejpam-6259	223	23	fuzzy	fuzzy	ADJ
ejpam-6259	223	24	almost	almost	ADV
ejpam-6259	223	25	n	n	CCONJ
ejpam-6259	223	26	-	-	PUNCT
ejpam-6259	223	27	ary	ary	NOUN
ejpam-6259	223	28	subsemigroup	subsemigroup	NOUN
ejpam-6259	223	29	of	of	ADP
ejpam-6259	223	30	a.	a.	NOUN
ejpam-6259	223	31	let	let	VERB
ejpam-6259	223	32	a1	a1	PROPN
ejpam-6259	223	33	,	,	PUNCT
ejpam-6259	223	34	a2	a2	PROPN
ejpam-6259	223	35	,	,	PUNCT
ejpam-6259	223	36	.	.	PUNCT
ejpam-6259	223	37	.	.	PUNCT
ejpam-6259	224	1	.	.	PUNCT
ejpam-6259	225	1	,	,	PUNCT
ejpam-6259	225	2	an	an	DET
ejpam-6259	225	3	be	be	AUX
ejpam-6259	225	4	any	any	PRON
ejpam-6259	225	5	n	n	ADP
ejpam-6259	225	6	elements	element	NOUN
ejpam-6259	225	7	in	in	ADP
ejpam-6259	225	8	a.	a.	NOUN
ejpam-6259	225	9	if	if	SCONJ
ejpam-6259	225	10	f(an1	f(an1	PROPN
ejpam-6259	225	11	)	)	PUNCT
ejpam-6259	226	1	∈	∈	PROPN
ejpam-6259	226	2	s	s	NOUN
ejpam-6259	226	3	,	,	PUNCT
ejpam-6259	226	4	then	then	ADV
ejpam-6259	226	5	ai	ai	VERB
ejpam-6259	226	6	∈	∈	PROPN
ejpam-6259	226	7	s	s	NOUN
ejpam-6259	226	8	for	for	ADP
ejpam-6259	226	9	some	some	DET
ejpam-6259	226	10	i	i	PRON
ejpam-6259	226	11	∈	∈	PROPN
ejpam-6259	226	12	{	{	PUNCT
ejpam-6259	226	13	1	1	NUM
ejpam-6259	226	14	,	,	PUNCT
ejpam-6259	226	15	2	2	NUM
ejpam-6259	226	16	,	,	PUNCT
ejpam-6259	226	17	.	.	PUNCT
ejpam-6259	226	18	.	.	PUNCT
ejpam-6259	227	1	.	.	PUNCT
ejpam-6259	228	1	,	,	PUNCT
ejpam-6259	228	2	n	n	CCONJ
ejpam-6259	228	3	}	}	PUNCT
ejpam-6259	228	4	because	because	SCONJ
ejpam-6259	228	5	s	s	NOUN
ejpam-6259	228	6	is	be	AUX
ejpam-6259	228	7	prime	prime	ADJ
ejpam-6259	228	8	.	.	PUNCT
ejpam-6259	229	1	then	then	ADV
ejpam-6259	229	2	χs(ai	χs(ai	PROPN
ejpam-6259	229	3	)	)	PUNCT
ejpam-6259	229	4	=	=	SYM
ejpam-6259	229	5	1	1	NUM
ejpam-6259	229	6	for	for	ADP
ejpam-6259	229	7	some	some	DET
ejpam-6259	229	8	i	i	PRON
ejpam-6259	229	9	∈	∈	PROPN
ejpam-6259	229	10	{	{	PUNCT
ejpam-6259	229	11	1	1	NUM
ejpam-6259	229	12	,	,	PUNCT
ejpam-6259	229	13	2	2	NUM
ejpam-6259	229	14	,	,	PUNCT
ejpam-6259	229	15	.	.	PUNCT
ejpam-6259	229	16	.	.	PUNCT
ejpam-6259	230	1	.	.	PUNCT
ejpam-6259	230	2	,	,	PUNCT
ejpam-6259	230	3	n	n	CCONJ
ejpam-6259	230	4	}	}	PUNCT
ejpam-6259	230	5	.	.	PUNCT
ejpam-6259	231	1	so	so	ADV
ejpam-6259	231	2	χs(f(a	χs(f(a	VERB
ejpam-6259	231	3	n	n	PRON
ejpam-6259	231	4	1	1	NUM
ejpam-6259	231	5	)	)	PUNCT
ejpam-6259	231	6	)	)	PUNCT
ejpam-6259	231	7	≤	≤	ADV
ejpam-6259	231	8	1	1	NUM
ejpam-6259	231	9	=	=	SYM
ejpam-6259	231	10	max{χs(a1	max{χs(a1	X
ejpam-6259	231	11	)	)	PUNCT
ejpam-6259	231	12	,	,	PUNCT
ejpam-6259	231	13	χs(a2	χs(a2	NOUN
ejpam-6259	231	14	)	)	PUNCT
ejpam-6259	231	15	,	,	PUNCT
ejpam-6259	231	16	.	.	PUNCT
ejpam-6259	231	17	.	.	PUNCT
ejpam-6259	231	18	.	.	PUNCT
ejpam-6259	232	1	,	,	PUNCT
ejpam-6259	232	2	χs(an	χs(an	NOUN
ejpam-6259	232	3	)	)	PUNCT
ejpam-6259	232	4	}	}	PUNCT
ejpam-6259	232	5	.	.	PUNCT
ejpam-6259	233	1	if	if	SCONJ
ejpam-6259	233	2	f(an1	f(an1	PROPN
ejpam-6259	233	3	)	)	PUNCT
ejpam-6259	233	4	̸∈	̸∈	PROPN
ejpam-6259	233	5	a	a	PROPN
ejpam-6259	233	6	,	,	PUNCT
ejpam-6259	233	7	then	then	ADV
ejpam-6259	233	8	χs(f(a	χs(f(a	X
ejpam-6259	233	9	n	n	PRON
ejpam-6259	233	10	1	1	NUM
ejpam-6259	233	11	)	)	PUNCT
ejpam-6259	233	12	=	=	SYM
ejpam-6259	233	13	0	0	X
ejpam-6259	233	14	≤	≤	NUM
ejpam-6259	233	15	max{χs(a1	max{χs(a1	X
ejpam-6259	233	16	)	)	PUNCT
ejpam-6259	233	17	,	,	PUNCT
ejpam-6259	233	18	χs(a2	χs(a2	NOUN
ejpam-6259	233	19	)	)	PUNCT
ejpam-6259	233	20	,	,	PUNCT
ejpam-6259	233	21	.	.	PUNCT
ejpam-6259	233	22	.	.	PUNCT
ejpam-6259	233	23	.	.	PUNCT
ejpam-6259	234	1	,	,	PUNCT
ejpam-6259	234	2	χs(an	χs(an	NOUN
ejpam-6259	234	3	)	)	PUNCT
ejpam-6259	234	4	}	}	PUNCT
ejpam-6259	234	5	.	.	PUNCT
ejpam-6259	235	1	by	by	ADP
ejpam-6259	235	2	both	both	DET
ejpam-6259	235	3	cases	case	NOUN
ejpam-6259	235	4	,	,	PUNCT
ejpam-6259	235	5	we	we	PRON
ejpam-6259	235	6	can	can	AUX
ejpam-6259	235	7	conclude	conclude	VERB
ejpam-6259	235	8	that	that	PRON
ejpam-6259	235	9	χs(f(a	χs(f(a	NOUN
ejpam-6259	235	10	n	n	CCONJ
ejpam-6259	235	11	1	1	NUM
ejpam-6259	235	12	)	)	PUNCT
ejpam-6259	235	13	≤	≤	NOUN
ejpam-6259	235	14	max{χs(a1	max{χs(a1	X
ejpam-6259	235	15	)	)	PUNCT
ejpam-6259	235	16	,	,	PUNCT
ejpam-6259	235	17	χs(a2	χs(a2	NOUN
ejpam-6259	235	18	)	)	PUNCT
ejpam-6259	235	19	,	,	PUNCT
ejpam-6259	235	20	.	.	PUNCT
ejpam-6259	235	21	.	.	PUNCT
ejpam-6259	235	22	.	.	PUNCT
ejpam-6259	236	1	,	,	PUNCT
ejpam-6259	236	2	χs(an	χs(an	NOUN
ejpam-6259	236	3	)	)	PUNCT
ejpam-6259	236	4	}	}	PUNCT
ejpam-6259	236	5	.	.	PUNCT
ejpam-6259	237	1	therefore	therefore	ADV
ejpam-6259	237	2	,	,	PUNCT
ejpam-6259	237	3	χs	χs	PROPN
ejpam-6259	237	4	is	be	AUX
ejpam-6259	237	5	a	a	DET
ejpam-6259	237	6	prime	prime	ADJ
ejpam-6259	237	7	fuzzy	fuzzy	ADJ
ejpam-6259	237	8	almost	almost	ADV
ejpam-6259	237	9	n	n	CCONJ
ejpam-6259	237	10	-	-	PUNCT
ejpam-6259	237	11	ary	ary	NOUN
ejpam-6259	237	12	subsemigroup	subsemigroup	NOUN
ejpam-6259	237	13	of	of	ADP
ejpam-6259	237	14	a.	a.	NOUN
ejpam-6259	237	15	to	to	PART
ejpam-6259	237	16	prove	prove	VERB
ejpam-6259	237	17	the	the	DET
ejpam-6259	237	18	converse	converse	NOUN
ejpam-6259	237	19	,	,	PUNCT
ejpam-6259	237	20	suppose	suppose	VERB
ejpam-6259	237	21	that	that	SCONJ
ejpam-6259	237	22	χs	χs	PROPN
ejpam-6259	237	23	is	be	AUX
ejpam-6259	237	24	a	a	DET
ejpam-6259	237	25	prime	prime	ADJ
ejpam-6259	237	26	fuzzy	fuzzy	ADJ
ejpam-6259	237	27	almost	almost	ADV
ejpam-6259	237	28	n	n	CCONJ
ejpam-6259	237	29	-	-	PUNCT
ejpam-6259	237	30	ary	ary	NOUN
ejpam-6259	237	31	subsemigroup	subsemigroup	NOUN
ejpam-6259	237	32	of	of	ADP
ejpam-6259	237	33	a.	a.	NOUN
ejpam-6259	237	34	by	by	ADP
ejpam-6259	237	35	theorem	theorem	NOUN
ejpam-6259	237	36	3	3	NUM
ejpam-6259	237	37	,	,	PUNCT
ejpam-6259	237	38	we	we	PRON
ejpam-6259	237	39	have	have	VERB
ejpam-6259	237	40	that	that	DET
ejpam-6259	237	41	s	s	NOUN
ejpam-6259	237	42	is	be	AUX
ejpam-6259	237	43	an	an	DET
ejpam-6259	237	44	almost	almost	ADV
ejpam-6259	237	45	n	n	CCONJ
ejpam-6259	237	46	-	-	PUNCT
ejpam-6259	237	47	ary	ary	NOUN
ejpam-6259	237	48	semigroup	semigroup	NOUN
ejpam-6259	237	49	of	of	ADP
ejpam-6259	237	50	a.	a.	NOUN
ejpam-6259	237	51	let	let	VERB
ejpam-6259	237	52	a1	a1	PROPN
ejpam-6259	237	53	,	,	PUNCT
ejpam-6259	237	54	a2	a2	PROPN
ejpam-6259	237	55	,	,	PUNCT
ejpam-6259	237	56	.	.	PUNCT
ejpam-6259	237	57	.	.	PUNCT
ejpam-6259	238	1	.	.	PUNCT
ejpam-6259	239	1	,	,	PUNCT
ejpam-6259	239	2	an	an	DET
ejpam-6259	239	3	be	be	AUX
ejpam-6259	239	4	any	any	PRON
ejpam-6259	239	5	n	n	DET
ejpam-6259	239	6	elements	element	NOUN
ejpam-6259	239	7	in	in	ADP
ejpam-6259	239	8	a	a	DET
ejpam-6259	239	9	such	such	ADJ
ejpam-6259	239	10	that	that	PRON
ejpam-6259	239	11	f(an1	f(an1	PROPN
ejpam-6259	239	12	)	)	PUNCT
ejpam-6259	239	13	∈	∈	PROPN
ejpam-6259	239	14	s.	s.	PROPN
ejpam-6259	240	1	thus	thus	ADV
ejpam-6259	240	2	,	,	PUNCT
ejpam-6259	240	3	χs(f(a	χs(f(a	INTJ
ejpam-6259	240	4	n	n	PRON
ejpam-6259	240	5	1	1	NUM
ejpam-6259	240	6	)	)	PUNCT
ejpam-6259	240	7	)	)	PUNCT
ejpam-6259	241	1	=	=	PUNCT
ejpam-6259	241	2	1	1	X
ejpam-6259	241	3	.	.	PUNCT
ejpam-6259	241	4	by	by	ADP
ejpam-6259	241	5	assumption	assumption	NOUN
ejpam-6259	241	6	,	,	PUNCT
ejpam-6259	241	7	we	we	PRON
ejpam-6259	241	8	have	have	VERB
ejpam-6259	241	9	that	that	PRON
ejpam-6259	241	10	1	1	NUM
ejpam-6259	241	11	=	=	SYM
ejpam-6259	241	12	χs(f(a	χs(f(a	NOUN
ejpam-6259	241	13	n	n	CCONJ
ejpam-6259	241	14	1	1	NUM
ejpam-6259	241	15	)	)	PUNCT
ejpam-6259	241	16	)	)	PUNCT
ejpam-6259	241	17	≤	≤	X
ejpam-6259	241	18	max{χs(a1	max{χs(a1	X
ejpam-6259	241	19	)	)	PUNCT
ejpam-6259	241	20	,	,	PUNCT
ejpam-6259	241	21	χs(a2	χs(a2	NOUN
ejpam-6259	241	22	)	)	PUNCT
ejpam-6259	241	23	,	,	PUNCT
ejpam-6259	241	24	.	.	PUNCT
ejpam-6259	241	25	.	.	PUNCT
ejpam-6259	241	26	.	.	PUNCT
ejpam-6259	242	1	,	,	PUNCT
ejpam-6259	242	2	χs(an	χs(an	NOUN
ejpam-6259	242	3	)	)	PUNCT
ejpam-6259	242	4	}	}	PUNCT
ejpam-6259	242	5	.	.	PUNCT
ejpam-6259	243	1	hence	hence	ADV
ejpam-6259	243	2	,	,	PUNCT
ejpam-6259	243	3	max{χs(a1	max{χs(a1	PROPN
ejpam-6259	243	4	)	)	PUNCT
ejpam-6259	243	5	,	,	PUNCT
ejpam-6259	243	6	χs(a2	χs(a2	NOUN
ejpam-6259	243	7	)	)	PUNCT
ejpam-6259	243	8	,	,	PUNCT
ejpam-6259	243	9	.	.	PUNCT
ejpam-6259	243	10	.	.	PUNCT
ejpam-6259	243	11	.	.	PUNCT
ejpam-6259	244	1	,	,	PUNCT
ejpam-6259	244	2	χs(an	χs(an	NOUN
ejpam-6259	244	3	)	)	PUNCT
ejpam-6259	244	4	}	}	PUNCT
ejpam-6259	245	1	=	=	SYM
ejpam-6259	245	2	1	1	X
ejpam-6259	245	3	.	.	X
ejpam-6259	246	1	we	we	PRON
ejpam-6259	246	2	can	can	AUX
ejpam-6259	246	3	conclude	conclude	VERB
ejpam-6259	246	4	that	that	PRON
ejpam-6259	246	5	χs(ai	χs(ai	PROPN
ejpam-6259	246	6	)	)	PUNCT
ejpam-6259	246	7	=	=	SYM
ejpam-6259	246	8	1	1	NUM
ejpam-6259	246	9	for	for	ADP
ejpam-6259	246	10	some	some	DET
ejpam-6259	246	11	i	i	PRON
ejpam-6259	246	12	∈	∈	PROPN
ejpam-6259	246	13	{	{	PUNCT
ejpam-6259	246	14	1	1	NUM
ejpam-6259	246	15	,	,	PUNCT
ejpam-6259	246	16	2	2	NUM
ejpam-6259	246	17	,	,	PUNCT
ejpam-6259	246	18	.	.	PUNCT
ejpam-6259	246	19	.	.	PUNCT
ejpam-6259	247	1	.	.	PUNCT
ejpam-6259	247	2	,	,	PUNCT
ejpam-6259	247	3	n	n	CCONJ
ejpam-6259	247	4	}	}	PUNCT
ejpam-6259	247	5	.	.	PUNCT
ejpam-6259	248	1	thus	thus	ADV
ejpam-6259	248	2	ai	ai	VERB
ejpam-6259	248	3	∈	∈	PROPN
ejpam-6259	248	4	s	s	NOUN
ejpam-6259	248	5	for	for	ADP
ejpam-6259	248	6	some	some	DET
ejpam-6259	248	7	i	i	PRON
ejpam-6259	248	8	∈	∈	PROPN
ejpam-6259	248	9	{	{	PUNCT
ejpam-6259	248	10	1	1	NUM
ejpam-6259	248	11	,	,	PUNCT
ejpam-6259	248	12	2	2	NUM
ejpam-6259	248	13	,	,	PUNCT
ejpam-6259	248	14	.	.	PUNCT
ejpam-6259	248	15	.	.	PUNCT
ejpam-6259	249	1	.	.	PUNCT
ejpam-6259	249	2	,	,	PUNCT
ejpam-6259	249	3	n	n	CCONJ
ejpam-6259	249	4	}	}	PUNCT
ejpam-6259	249	5	.	.	PUNCT
ejpam-6259	250	1	therefore	therefore	ADV
ejpam-6259	250	2	,	,	PUNCT
ejpam-6259	250	3	s	s	VERB
ejpam-6259	250	4	is	be	AUX
ejpam-6259	250	5	a	a	DET
ejpam-6259	250	6	prime	prime	NOUN
ejpam-6259	250	7	almost	almost	ADV
ejpam-6259	250	8	n	n	CCONJ
ejpam-6259	250	9	-	-	PUNCT
ejpam-6259	250	10	ary	ary	NOUN
ejpam-6259	250	11	subsemigroup	subsemigroup	NOUN
ejpam-6259	250	12	of	of	ADP
ejpam-6259	250	13	a.	a.	NOUN
ejpam-6259	250	14	let	let	VERB
ejpam-6259	250	15	a	a	DET
ejpam-6259	250	16	be	be	AUX
ejpam-6259	250	17	an	an	DET
ejpam-6259	250	18	n	n	CCONJ
ejpam-6259	250	19	-	-	PUNCT
ejpam-6259	250	20	ary	ary	NOUN
ejpam-6259	250	21	semigroup	semigroup	PROPN
ejpam-6259	250	22	.	.	PUNCT
ejpam-6259	251	1	an	an	DET
ejpam-6259	251	2	almost	almost	ADV
ejpam-6259	251	3	n	n	CCONJ
ejpam-6259	251	4	-	-	PUNCT
ejpam-6259	251	5	ary	ary	NOUN
ejpam-6259	251	6	subsemigroup	subsemigroup	PROPN
ejpam-6259	251	7	s	s	PROPN
ejpam-6259	251	8	of	of	ADP
ejpam-6259	251	9	a	a	PRON
ejpam-6259	251	10	is	be	AUX
ejpam-6259	251	11	said	say	VERB
ejpam-6259	251	12	to	to	PART
ejpam-6259	251	13	be	be	AUX
ejpam-6259	251	14	semiprime	semiprime	NOUN
ejpam-6259	251	15	if	if	SCONJ
ejpam-6259	251	16	for	for	ADP
ejpam-6259	251	17	all	all	DET
ejpam-6259	251	18	a	a	DET
ejpam-6259	251	19	∈	∈	PROPN
ejpam-6259	251	20	a	a	PRON
ejpam-6259	251	21	,	,	PUNCT
ejpam-6259	251	22	f(an	f(an	PROPN
ejpam-6259	251	23	)	)	PUNCT
ejpam-6259	251	24	∈	∈	PROPN
ejpam-6259	251	25	s	s	PART
ejpam-6259	251	26	implies	imply	VERB
ejpam-6259	251	27	a	a	DET
ejpam-6259	251	28	∈	∈	PROPN
ejpam-6259	251	29	s.	s.	PROPN
ejpam-6259	251	30	a	a	DET
ejpam-6259	251	31	fuzzy	fuzzy	ADJ
ejpam-6259	251	32	almost	almost	ADV
ejpam-6259	251	33	n	n	CCONJ
ejpam-6259	251	34	-	-	PUNCT
ejpam-6259	251	35	ary	ary	NOUN
ejpam-6259	251	36	subsemigroup	subsemigroup	PROPN
ejpam-6259	251	37	g	g	PROPN
ejpam-6259	251	38	of	of	ADP
ejpam-6259	251	39	a	a	PRON
ejpam-6259	251	40	is	be	AUX
ejpam-6259	251	41	said	say	VERB
ejpam-6259	251	42	to	to	PART
ejpam-6259	251	43	be	be	AUX
ejpam-6259	251	44	semiprime	semiprime	NOUN
ejpam-6259	251	45	if	if	SCONJ
ejpam-6259	251	46	g(f(an	g(f(an	NOUN
ejpam-6259	251	47	)	)	PUNCT
ejpam-6259	251	48	)	)	PUNCT
ejpam-6259	252	1	≤	≤	PROPN
ejpam-6259	252	2	g(a	g(a	PROPN
ejpam-6259	252	3	)	)	PUNCT
ejpam-6259	252	4	for	for	ADP
ejpam-6259	252	5	all	all	DET
ejpam-6259	252	6	a	a	DET
ejpam-6259	252	7	∈	∈	NOUN
ejpam-6259	252	8	a.	a.	NOUN
ejpam-6259	252	9	it	it	PRON
ejpam-6259	252	10	is	be	AUX
ejpam-6259	252	11	clear	clear	ADJ
ejpam-6259	252	12	that	that	SCONJ
ejpam-6259	252	13	every	every	DET
ejpam-6259	252	14	prime	prime	NOUN
ejpam-6259	252	15	almost	almost	ADV
ejpam-6259	252	16	n	n	CCONJ
ejpam-6259	252	17	-	-	PUNCT
ejpam-6259	252	18	ary	ary	NOUN
ejpam-6259	252	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	252	20	of	of	ADP
ejpam-6259	252	21	a	a	PRON
ejpam-6259	252	22	is	be	AUX
ejpam-6259	252	23	semiprime	semiprime	NOUN
ejpam-6259	252	24	.	.	PUNCT
ejpam-6259	253	1	similarly	similarly	ADV
ejpam-6259	253	2	,	,	PUNCT
ejpam-6259	253	3	every	every	DET
ejpam-6259	253	4	prime	prime	ADJ
ejpam-6259	253	5	fuzzy	fuzzy	ADJ
ejpam-6259	253	6	almost	almost	ADV
ejpam-6259	253	7	n	n	CCONJ
ejpam-6259	253	8	-	-	PUNCT
ejpam-6259	253	9	ary	ary	NOUN
ejpam-6259	253	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	253	11	of	of	ADP
ejpam-6259	253	12	a	a	PRON
ejpam-6259	253	13	is	be	AUX
ejpam-6259	253	14	also	also	ADV
ejpam-6259	253	15	semiprime	semiprime	NOUN
ejpam-6259	253	16	.	.	PUNCT
ejpam-6259	254	1	finally	finally	ADV
ejpam-6259	254	2	,	,	PUNCT
ejpam-6259	254	3	we	we	PRON
ejpam-6259	254	4	present	present	VERB
ejpam-6259	254	5	the	the	DET
ejpam-6259	254	6	relationship	relationship	NOUN
ejpam-6259	254	7	between	between	ADP
ejpam-6259	254	8	semiprime	semiprime	NOUN
ejpam-6259	254	9	almost	almost	ADV
ejpam-6259	254	10	n	n	CCONJ
ejpam-6259	254	11	-	-	PUNCT
ejpam-6259	254	12	ary	ary	PROPN
ejpam-6259	254	13	subsemigroups	subsemigroup	NOUN
ejpam-6259	254	14	and	and	CCONJ
ejpam-6259	254	15	their	their	PRON
ejpam-6259	254	16	fuzzifications	fuzzification	NOUN
ejpam-6259	254	17	.	.	PUNCT
ejpam-6259	255	1	theorem	theorem	VERB
ejpam-6259	255	2	7	7	NUM
ejpam-6259	255	3	.	.	PUNCT
ejpam-6259	256	1	a	a	DET
ejpam-6259	256	2	nonempty	nonempty	ADJ
ejpam-6259	256	3	subset	subset	VERB
ejpam-6259	256	4	s	s	NOUN
ejpam-6259	256	5	of	of	ADP
ejpam-6259	256	6	an	an	DET
ejpam-6259	256	7	n	n	CCONJ
ejpam-6259	256	8	-	-	PUNCT
ejpam-6259	256	9	ary	ary	NOUN
ejpam-6259	256	10	semigroup	semigroup	NOUN
ejpam-6259	256	11	a	a	PRON
ejpam-6259	256	12	is	be	AUX
ejpam-6259	256	13	a	a	DET
ejpam-6259	256	14	semiprime	semiprime	NOUN
ejpam-6259	256	15	almost	almost	ADV
ejpam-6259	256	16	n	n	CCONJ
ejpam-6259	256	17	-	-	PUNCT
ejpam-6259	256	18	ary	ary	NOUN
ejpam-6259	256	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	256	20	of	of	ADP
ejpam-6259	256	21	a	a	DET
ejpam-6259	256	22	if	if	NOUN
ejpam-6259	256	23	and	and	CCONJ
ejpam-6259	256	24	only	only	ADV
ejpam-6259	256	25	if	if	SCONJ
ejpam-6259	256	26	χs	χs	NOUN
ejpam-6259	256	27	is	be	AUX
ejpam-6259	256	28	a	a	DET
ejpam-6259	256	29	semiprime	semiprime	NOUN
ejpam-6259	256	30	fuzzy	fuzzy	ADJ
ejpam-6259	256	31	almost	almost	ADV
ejpam-6259	256	32	n	n	CCONJ
ejpam-6259	256	33	-	-	PUNCT
ejpam-6259	256	34	ary	ary	NOUN
ejpam-6259	256	35	subsemigroup	subsemigroup	NOUN
ejpam-6259	256	36	of	of	ADP
ejpam-6259	256	37	a.	a.	NOUN
ejpam-6259	256	38	proof	proof	NOUN
ejpam-6259	256	39	.	.	PUNCT
ejpam-6259	257	1	let	let	VERB
ejpam-6259	257	2	s	s	PRON
ejpam-6259	257	3	be	be	AUX
ejpam-6259	257	4	a	a	DET
ejpam-6259	257	5	semiprime	semiprime	NOUN
ejpam-6259	257	6	almost	almost	ADV
ejpam-6259	257	7	n	n	CCONJ
ejpam-6259	257	8	-	-	PUNCT
ejpam-6259	257	9	ary	ary	NOUN
ejpam-6259	257	10	subsemigroup	subsemigroup	NOUN
ejpam-6259	257	11	of	of	ADP
ejpam-6259	257	12	a.	a.	NOUN
ejpam-6259	257	13	by	by	ADP
ejpam-6259	257	14	theorem	theorem	NOUN
ejpam-6259	257	15	3	3	NUM
ejpam-6259	257	16	,	,	PUNCT
ejpam-6259	257	17	χs	χs	X
ejpam-6259	257	18	is	be	AUX
ejpam-6259	257	19	a	a	DET
ejpam-6259	257	20	fuzzy	fuzzy	ADJ
ejpam-6259	257	21	almost	almost	ADV
ejpam-6259	257	22	n	n	CCONJ
ejpam-6259	257	23	-	-	PUNCT
ejpam-6259	257	24	ary	ary	NOUN
ejpam-6259	257	25	subsemigroup	subsemigroup	NOUN
ejpam-6259	257	26	of	of	ADP
ejpam-6259	257	27	a.	a.	NOUN
ejpam-6259	257	28	let	let	VERB
ejpam-6259	257	29	a	a	DET
ejpam-6259	257	30	∈	∈	NOUN
ejpam-6259	257	31	a.	a.	NOUN
ejpam-6259	257	32	if	if	SCONJ
ejpam-6259	257	33	f(an	f(an	PROPN
ejpam-6259	257	34	)	)	PUNCT
ejpam-6259	257	35	∈	∈	PROPN
ejpam-6259	257	36	s	s	PROPN
ejpam-6259	257	37	,	,	PUNCT
ejpam-6259	257	38	then	then	ADV
ejpam-6259	257	39	a	a	DET
ejpam-6259	257	40	∈	∈	NOUN
ejpam-6259	257	41	s	s	X
ejpam-6259	257	42	because	because	SCONJ
ejpam-6259	257	43	s	s	PROPN
ejpam-6259	257	44	is	be	AUX
ejpam-6259	257	45	semiprime	semiprime	NOUN
ejpam-6259	257	46	.	.	PUNCT
ejpam-6259	258	1	thus	thus	ADV
ejpam-6259	258	2	χs(a	χs(a	PUNCT
ejpam-6259	258	3	)	)	PUNCT
ejpam-6259	259	1	=	=	SYM
ejpam-6259	260	1	1	1	X
ejpam-6259	260	2	.	.	PUNCT
ejpam-6259	261	1	hence	hence	ADV
ejpam-6259	261	2	,	,	PUNCT
ejpam-6259	261	3	χs(f(a	χs(f(a	NOUN
ejpam-6259	261	4	n	n	CCONJ
ejpam-6259	261	5	)	)	PUNCT
ejpam-6259	261	6	)	)	PUNCT
ejpam-6259	261	7	≤	≤	NOUN
ejpam-6259	261	8	χs(a	χs(a	PUNCT
ejpam-6259	261	9	)	)	PUNCT
ejpam-6259	261	10	.	.	PUNCT
ejpam-6259	262	1	if	if	SCONJ
ejpam-6259	262	2	f(an	f(an	PROPN
ejpam-6259	262	3	)	)	PUNCT
ejpam-6259	262	4	̸∈	̸∈	PROPN
ejpam-6259	262	5	s	s	PROPN
ejpam-6259	262	6	,	,	PUNCT
ejpam-6259	262	7	then	then	ADV
ejpam-6259	262	8	χs(f(a	χs(f(a	ADJ
ejpam-6259	262	9	n	n	CCONJ
ejpam-6259	262	10	)	)	PUNCT
ejpam-6259	262	11	)	)	PUNCT
ejpam-6259	263	1	=	=	SYM
ejpam-6259	263	2	0	0	NUM
ejpam-6259	263	3	≤	≤	NOUN
ejpam-6259	263	4	χs(a	χs(a	PUNCT
ejpam-6259	263	5	)	)	PUNCT
ejpam-6259	263	6	.	.	PUNCT
ejpam-6259	264	1	in	in	ADP
ejpam-6259	264	2	both	both	DET
ejpam-6259	264	3	cases	case	NOUN
ejpam-6259	264	4	,	,	PUNCT
ejpam-6259	264	5	we	we	PRON
ejpam-6259	264	6	conclude	conclude	VERB
ejpam-6259	264	7	that	that	SCONJ
ejpam-6259	264	8	χs(f(a	χs(f(a	NOUN
ejpam-6259	264	9	n	n	CCONJ
ejpam-6259	264	10	)	)	PUNCT
ejpam-6259	264	11	)	)	PUNCT
ejpam-6259	264	12	≤	≤	NOUN
ejpam-6259	264	13	χs(a	χs(a	CCONJ
ejpam-6259	264	14	)	)	PUNCT
ejpam-6259	264	15	for	for	ADP
ejpam-6259	264	16	all	all	DET
ejpam-6259	264	17	a	a	DET
ejpam-6259	264	18	∈	∈	PROPN
ejpam-6259	264	19	a.	a.	NOUN
ejpam-6259	264	20	therefore	therefore	ADV
ejpam-6259	264	21	,	,	PUNCT
ejpam-6259	264	22	χs	χs	PROPN
ejpam-6259	264	23	is	be	AUX
ejpam-6259	264	24	a	a	DET
ejpam-6259	264	25	semiprime	semiprime	NOUN
ejpam-6259	264	26	fuzzy	fuzzy	ADJ
ejpam-6259	264	27	almost	almost	ADV
ejpam-6259	264	28	n	n	CCONJ
ejpam-6259	264	29	-	-	PUNCT
ejpam-6259	264	30	ary	ary	NOUN
ejpam-6259	264	31	subsemigroup	subsemigroup	NOUN
ejpam-6259	264	32	of	of	ADP
ejpam-6259	264	33	a.	a.	NOUN
ejpam-6259	264	34	conversely	conversely	ADV
ejpam-6259	264	35	,	,	PUNCT
ejpam-6259	264	36	suppose	suppose	VERB
ejpam-6259	264	37	that	that	SCONJ
ejpam-6259	264	38	χs	χs	PROPN
ejpam-6259	264	39	is	be	AUX
ejpam-6259	264	40	a	a	DET
ejpam-6259	264	41	semiprime	semiprime	NOUN
ejpam-6259	264	42	fuzzy	fuzzy	ADJ
ejpam-6259	264	43	n	n	CCONJ
ejpam-6259	264	44	-	-	PUNCT
ejpam-6259	264	45	ary	ary	NOUN
ejpam-6259	264	46	subsemigroup	subsemigroup	NOUN
ejpam-6259	264	47	of	of	ADP
ejpam-6259	264	48	a.	a.	NOUN
ejpam-6259	264	49	by	by	ADP
ejpam-6259	264	50	theorem	theorem	NOUN
ejpam-6259	264	51	3	3	NUM
ejpam-6259	264	52	,	,	PUNCT
ejpam-6259	264	53	we	we	PRON
ejpam-6259	264	54	have	have	VERB
ejpam-6259	264	55	that	that	DET
ejpam-6259	264	56	s	s	NOUN
ejpam-6259	264	57	is	be	AUX
ejpam-6259	264	58	an	an	DET
ejpam-6259	264	59	almost	almost	ADV
ejpam-6259	264	60	n	n	CCONJ
ejpam-6259	264	61	-	-	PUNCT
ejpam-6259	264	62	ary	ary	NOUN
ejpam-6259	264	63	subsemigroup	subsemigroup	NOUN
ejpam-6259	264	64	of	of	ADP
ejpam-6259	264	65	a.	a.	NOUN
ejpam-6259	264	66	let	let	VERB
ejpam-6259	264	67	a	a	PRON
ejpam-6259	264	68	be	be	AUX
ejpam-6259	264	69	an	an	DET
ejpam-6259	264	70	element	element	NOUN
ejpam-6259	264	71	in	in	ADP
ejpam-6259	264	72	a	a	DET
ejpam-6259	264	73	such	such	ADJ
ejpam-6259	264	74	that	that	DET
ejpam-6259	264	75	f(an	f(an	PROPN
ejpam-6259	264	76	)	)	PUNCT
ejpam-6259	264	77	∈	∈	PROPN
ejpam-6259	264	78	s.	s.	PROPN
ejpam-6259	264	79	then	then	ADV
ejpam-6259	264	80	χs(f(a	χs(f(a	ADJ
ejpam-6259	264	81	n	n	CCONJ
ejpam-6259	264	82	)	)	PUNCT
ejpam-6259	264	83	)	)	PUNCT
ejpam-6259	265	1	=	=	PUNCT
ejpam-6259	265	2	1	1	X
ejpam-6259	265	3	.	.	PUNCT
ejpam-6259	265	4	since	since	SCONJ
ejpam-6259	265	5	χs	χs	PROPN
ejpam-6259	265	6	is	be	AUX
ejpam-6259	265	7	semiprime	semiprime	NOUN
ejpam-6259	265	8	,	,	PUNCT
ejpam-6259	265	9	we	we	PRON
ejpam-6259	265	10	have	have	VERB
ejpam-6259	265	11	χs(f(a	χs(f(a	NOUN
ejpam-6259	265	12	n	n	CCONJ
ejpam-6259	265	13	)	)	PUNCT
ejpam-6259	265	14	)	)	PUNCT
ejpam-6259	265	15	≤	≤	NOUN
ejpam-6259	265	16	χs(a	χs(a	PUNCT
ejpam-6259	265	17	)	)	PUNCT
ejpam-6259	265	18	.	.	PUNCT
ejpam-6259	266	1	it	it	PRON
ejpam-6259	266	2	follows	follow	VERB
ejpam-6259	266	3	that	that	PRON
ejpam-6259	266	4	χs(a	χs(a	PUNCT
ejpam-6259	266	5	)	)	PUNCT
ejpam-6259	266	6	=	=	SYM
ejpam-6259	266	7	1	1	NUM
ejpam-6259	266	8	,	,	PUNCT
ejpam-6259	266	9	and	and	CCONJ
ejpam-6259	266	10	hence	hence	ADV
ejpam-6259	266	11	a	a	DET
ejpam-6259	266	12	∈	∈	NOUN
ejpam-6259	266	13	s.	s.	PROPN
ejpam-6259	266	14	consequently	consequently	ADV
ejpam-6259	266	15	,	,	PUNCT
ejpam-6259	266	16	s	s	PROPN
ejpam-6259	266	17	is	be	AUX
ejpam-6259	266	18	a	a	DET
ejpam-6259	266	19	semiprime	semiprime	NOUN
ejpam-6259	266	20	almost	almost	ADV
ejpam-6259	266	21	n	n	CCONJ
ejpam-6259	266	22	-	-	PUNCT
ejpam-6259	266	23	ary	ary	NOUN
ejpam-6259	266	24	subsemigroup	subsemigroup	NOUN
ejpam-6259	266	25	of	of	ADP
ejpam-6259	266	26	a.	a.	PROPN
ejpam-6259	266	27	4	4	NUM
ejpam-6259	266	28	.	.	PUNCT
ejpam-6259	266	29	conclusion	conclusion	NOUN
ejpam-6259	266	30	in	in	ADP
ejpam-6259	266	31	this	this	DET
ejpam-6259	266	32	paper	paper	NOUN
ejpam-6259	266	33	,	,	PUNCT
ejpam-6259	266	34	we	we	PRON
ejpam-6259	266	35	introduce	introduce	VERB
ejpam-6259	266	36	the	the	DET
ejpam-6259	266	37	notions	notion	NOUN
ejpam-6259	266	38	of	of	ADP
ejpam-6259	266	39	almost	almost	ADV
ejpam-6259	266	40	n	n	CCONJ
ejpam-6259	266	41	-	-	PUNCT
ejpam-6259	266	42	ary	ary	NOUN
ejpam-6259	266	43	subsemigroups	subsemigroup	NOUN
ejpam-6259	266	44	and	and	CCONJ
ejpam-6259	266	45	fuzzy	fuzzy	ADJ
ejpam-6259	266	46	almost	almost	ADV
ejpam-6259	266	47	n	n	CCONJ
ejpam-6259	266	48	-	-	PUNCT
ejpam-6259	266	49	ary	ary	PROPN
ejpam-6259	266	50	subsemigroups	subsemigroup	NOUN
ejpam-6259	266	51	of	of	ADP
ejpam-6259	266	52	n	n	CCONJ
ejpam-6259	266	53	-	-	PUNCT
ejpam-6259	266	54	ary	ary	NOUN
ejpam-6259	266	55	semigroups	semigroup	NOUN
ejpam-6259	266	56	.	.	PUNCT
ejpam-6259	267	1	we	we	PRON
ejpam-6259	267	2	prove	prove	VERB
ejpam-6259	267	3	that	that	SCONJ
ejpam-6259	267	4	every	every	DET
ejpam-6259	267	5	n	n	NUM
ejpam-6259	267	6	-	-	PUNCT
ejpam-6259	267	7	ary	ary	PROPN
ejpam-6259	267	8	semigroup	semigroup	PROPN
ejpam-6259	267	9	is	be	AUX
ejpam-6259	267	10	also	also	ADV
ejpam-6259	267	11	an	an	DET
ejpam-6259	267	12	almost	almost	ADV
ejpam-6259	267	13	n	n	CCONJ
ejpam-6259	267	14	-	-	PUNCT
ejpam-6259	267	15	ary	ary	NOUN
ejpam-6259	267	16	semigroup	semigroup	PROPN
ejpam-6259	267	17	;	;	PUNCT
ejpam-6259	267	18	however	however	ADV
ejpam-6259	267	19	,	,	PUNCT
ejpam-6259	267	20	the	the	DET
ejpam-6259	267	21	converse	converse	NOUN
ejpam-6259	267	22	does	do	AUX
ejpam-6259	267	23	not	not	PART
ejpam-6259	267	24	hold	hold	VERB
ejpam-6259	267	25	in	in	ADP
ejpam-6259	267	26	general	general	ADJ
ejpam-6259	267	27	.	.	PUNCT
ejpam-6259	268	1	moreover	moreover	ADV
ejpam-6259	268	2	,	,	PUNCT
ejpam-6259	268	3	we	we	PRON
ejpam-6259	268	4	show	show	VERB
ejpam-6259	268	5	that	that	SCONJ
ejpam-6259	268	6	the	the	DET
ejpam-6259	268	7	union	union	NOUN
ejpam-6259	268	8	of	of	ADP
ejpam-6259	268	9	two	two	NUM
ejpam-6259	268	10	almost	almost	ADV
ejpam-6259	268	11	n	n	CCONJ
ejpam-6259	268	12	-	-	PUNCT
ejpam-6259	268	13	ary	ary	PROPN
ejpam-6259	268	14	subsemigroups	subsemigroup	NOUN
ejpam-6259	268	15	is	be	AUX
ejpam-6259	268	16	also	also	ADV
ejpam-6259	268	17	an	an	DET
ejpam-6259	268	18	almost	almost	ADV
ejpam-6259	268	19	n	n	CCONJ
ejpam-6259	268	20	-	-	PUNCT
ejpam-6259	268	21	ary	ary	NOUN
ejpam-6259	268	22	subsemigroup	subsemigroup	NOUN
ejpam-6259	268	23	.	.	PUNCT
ejpam-6259	269	1	however	however	ADV
ejpam-6259	269	2	,	,	PUNCT
ejpam-6259	269	3	the	the	DET
ejpam-6259	269	4	same	same	ADJ
ejpam-6259	269	5	does	do	AUX
ejpam-6259	269	6	not	not	PART
ejpam-6259	269	7	generally	generally	ADV
ejpam-6259	269	8	hold	hold	VERB
ejpam-6259	269	9	for	for	ADP
ejpam-6259	269	10	their	their	PRON
ejpam-6259	269	11	intersection	intersection	NOUN
ejpam-6259	269	12	.	.	PUNCT
ejpam-6259	270	1	similarly	similarly	ADV
ejpam-6259	270	2	,	,	PUNCT
ejpam-6259	270	3	we	we	PRON
ejpam-6259	270	4	have	have	VERB
ejpam-6259	270	5	that	that	SCONJ
ejpam-6259	270	6	the	the	DET
ejpam-6259	270	7	union	union	NOUN
ejpam-6259	270	8	of	of	ADP
ejpam-6259	270	9	two	two	NUM
ejpam-6259	270	10	fuzzy	fuzzy	ADJ
ejpam-6259	270	11	almost	almost	ADV
ejpam-6259	270	12	n	n	CCONJ
ejpam-6259	270	13	-	-	PUNCT
ejpam-6259	270	14	ary	ary	PROPN
ejpam-6259	270	15	subsemigroups	subsemigroup	NOUN
ejpam-6259	270	16	is	be	AUX
ejpam-6259	270	17	also	also	ADV
ejpam-6259	270	18	a	a	DET
ejpam-6259	270	19	fuzzy	fuzzy	ADJ
ejpam-6259	270	20	almost	almost	ADV
ejpam-6259	270	21	n	n	CCONJ
ejpam-6259	270	22	-	-	PUNCT
ejpam-6259	270	23	ary	ary	PROPN
ejpam-6259	270	24	r.	r.	PROPN
ejpam-6259	270	25	chinram	chinram	PROPN
ejpam-6259	270	26	,	,	PUNCT
ejpam-6259	271	1	p.	p.	NOUN
ejpam-6259	271	2	singavananda	singavananda	PROPN
ejpam-6259	271	3	/	/	SYM
ejpam-6259	271	4	eur	eur	PROPN
ejpam-6259	271	5	.	.	PUNCT
ejpam-6259	272	1	j.	j.	PROPN
ejpam-6259	272	2	pure	pure	PROPN
ejpam-6259	272	3	appl	appl	PROPN
ejpam-6259	272	4	.	.	PROPN
ejpam-6259	272	5	math	math	PROPN
ejpam-6259	272	6	,	,	PUNCT
ejpam-6259	272	7	18	18	NUM
ejpam-6259	272	8	(	(	PUNCT
ejpam-6259	272	9	3	3	NUM
ejpam-6259	272	10	)	)	PUNCT
ejpam-6259	272	11	(	(	PUNCT
ejpam-6259	272	12	2025	2025	NUM
ejpam-6259	272	13	)	)	PUNCT
ejpam-6259	272	14	,	,	PUNCT
ejpam-6259	272	15	6259	6259	NUM
ejpam-6259	272	16	9	9	NUM
ejpam-6259	272	17	of	of	ADP
ejpam-6259	272	18	10	10	NUM
ejpam-6259	272	19	subsemigroup	subsemigroup	NOUN
ejpam-6259	272	20	.	.	PUNCT
ejpam-6259	273	1	nevertheless	nevertheless	ADV
ejpam-6259	273	2	,	,	PUNCT
ejpam-6259	273	3	this	this	PRON
ejpam-6259	273	4	is	be	AUX
ejpam-6259	273	5	not	not	PART
ejpam-6259	273	6	generally	generally	ADV
ejpam-6259	273	7	true	true	ADJ
ejpam-6259	273	8	for	for	ADP
ejpam-6259	273	9	their	their	PRON
ejpam-6259	273	10	intersection	intersection	NOUN
ejpam-6259	273	11	.	.	PUNCT
ejpam-6259	274	1	furthermore	furthermore	ADV
ejpam-6259	274	2	,	,	PUNCT
ejpam-6259	274	3	we	we	PRON
ejpam-6259	274	4	present	present	VERB
ejpam-6259	274	5	the	the	DET
ejpam-6259	274	6	relationships	relationship	NOUN
ejpam-6259	274	7	between	between	ADP
ejpam-6259	274	8	almost	almost	ADV
ejpam-6259	274	9	n	n	CCONJ
ejpam-6259	274	10	-	-	PUNCT
ejpam-6259	274	11	ary	ary	NOUN
ejpam-6259	274	12	subsemigroups	subsemigroup	NOUN
ejpam-6259	274	13	and	and	CCONJ
ejpam-6259	274	14	their	their	PRON
ejpam-6259	274	15	corresponding	correspond	VERB
ejpam-6259	274	16	fuzzifications	fuzzification	NOUN
ejpam-6259	274	17	(	(	PUNCT
ejpam-6259	274	18	theorem	theorem	VERB
ejpam-6259	274	19	3	3	NUM
ejpam-6259	274	20	-	-	SYM
ejpam-6259	274	21	7	7	NUM
ejpam-6259	274	22	)	)	PUNCT
ejpam-6259	274	23	.	.	PUNCT
ejpam-6259	275	1	in	in	ADP
ejpam-6259	275	2	future	future	ADJ
ejpam-6259	275	3	work	work	NOUN
ejpam-6259	275	4	,	,	PUNCT
ejpam-6259	275	5	we	we	PRON
ejpam-6259	275	6	aim	aim	VERB
ejpam-6259	275	7	to	to	PART
ejpam-6259	275	8	study	study	VERB
ejpam-6259	275	9	other	other	ADJ
ejpam-6259	275	10	various	various	ADJ
ejpam-6259	275	11	types	type	NOUN
ejpam-6259	275	12	of	of	ADP
ejpam-6259	275	13	ideals	ideal	NOUN
ejpam-6259	275	14	of	of	ADP
ejpam-6259	275	15	n	n	CCONJ
ejpam-6259	275	16	-	-	PUNCT
ejpam-6259	275	17	ary	ary	NOUN
ejpam-6259	275	18	semigroups	semigroup	NOUN
ejpam-6259	275	19	and	and	CCONJ
ejpam-6259	275	20	their	their	PRON
ejpam-6259	275	21	corresponding	correspond	VERB
ejpam-6259	275	22	fuzzifications	fuzzification	NOUN
ejpam-6259	275	23	.	.	PUNCT
ejpam-6259	276	1	acknowledgements	acknowledgement	NOUN
ejpam-6259	276	2	the	the	DET
ejpam-6259	276	3	authors	author	NOUN
ejpam-6259	276	4	gratefully	gratefully	ADV
ejpam-6259	276	5	acknowledge	acknowledge	VERB
ejpam-6259	276	6	the	the	DET
ejpam-6259	276	7	reviewers	reviewer	NOUN
ejpam-6259	276	8	for	for	ADP
ejpam-6259	276	9	their	their	PRON
ejpam-6259	276	10	time	time	NOUN
ejpam-6259	276	11	,	,	PUNCT
ejpam-6259	276	12	effort	effort	NOUN
ejpam-6259	276	13	,	,	PUNCT
ejpam-6259	276	14	and	and	CCONJ
ejpam-6259	276	15	invaluable	invaluable	ADJ
ejpam-6259	276	16	feedback	feedback	NOUN
ejpam-6259	276	17	.	.	PUNCT
ejpam-6259	277	1	their	their	PRON
ejpam-6259	277	2	constructive	constructive	ADJ
ejpam-6259	277	3	critiques	critique	NOUN
ejpam-6259	277	4	and	and	CCONJ
ejpam-6259	277	5	thoughtful	thoughtful	ADJ
ejpam-6259	277	6	recommendations	recommendation	NOUN
ejpam-6259	277	7	have	have	AUX
ejpam-6259	277	8	played	play	VERB
ejpam-6259	277	9	a	a	DET
ejpam-6259	277	10	vital	vital	ADJ
ejpam-6259	277	11	role	role	NOUN
ejpam-6259	277	12	in	in	ADP
ejpam-6259	277	13	refining	refine	VERB
ejpam-6259	277	14	the	the	DET
ejpam-6259	277	15	quality	quality	NOUN
ejpam-6259	277	16	of	of	ADP
ejpam-6259	277	17	this	this	DET
ejpam-6259	277	18	research	research	NOUN
ejpam-6259	277	19	.	.	PUNCT
ejpam-6259	278	1	references	reference	NOUN
ejpam-6259	278	2	[	[	X
ejpam-6259	278	3	1	1	NUM
ejpam-6259	278	4	]	]	PUNCT
ejpam-6259	278	5	l.	l.	PROPN
ejpam-6259	278	6	a.	a.	PROPN
ejpam-6259	278	7	zadeh	zadeh	PROPN
ejpam-6259	278	8	.	.	PUNCT
ejpam-6259	279	1	fuzzy	fuzzy	ADJ
ejpam-6259	279	2	sets	set	NOUN
ejpam-6259	279	3	.	.	PUNCT
ejpam-6259	280	1	information	information	NOUN
ejpam-6259	280	2	and	and	CCONJ
ejpam-6259	280	3	control	control	NOUN
ejpam-6259	280	4	,	,	PUNCT
ejpam-6259	280	5	8(3):338–353	8(3):338–353	NUM
ejpam-6259	280	6	,	,	PUNCT
ejpam-6259	280	7	1965	1965	NUM
ejpam-6259	280	8	.	.	PUNCT
ejpam-6259	281	1	[	[	X
ejpam-6259	281	2	2	2	NUM
ejpam-6259	281	3	]	]	X
ejpam-6259	281	4	r.	r.	PROPN
ejpam-6259	281	5	kasner	kasner	PROPN
ejpam-6259	281	6	.	.	PUNCT
ejpam-6259	282	1	an	an	DET
ejpam-6259	282	2	extension	extension	NOUN
ejpam-6259	282	3	of	of	ADP
ejpam-6259	282	4	the	the	DET
ejpam-6259	282	5	group	group	NOUN
ejpam-6259	282	6	concepts	concept	NOUN
ejpam-6259	282	7	.	.	PUNCT
ejpam-6259	283	1	bulletin	bulletin	NOUN
ejpam-6259	283	2	of	of	ADP
ejpam-6259	283	3	the	the	DET
ejpam-6259	283	4	american	american	PROPN
ejpam-6259	283	5	mathematical	mathematical	PROPN
ejpam-6259	283	6	society	society	NOUN
ejpam-6259	283	7	,	,	PUNCT
ejpam-6259	283	8	10:290–291	10:290–291	NUM
ejpam-6259	283	9	,	,	PUNCT
ejpam-6259	283	10	1904	1904	NUM
ejpam-6259	283	11	.	.	PUNCT
ejpam-6259	284	1	[	[	X
ejpam-6259	284	2	3	3	X
ejpam-6259	284	3	]	]	PUNCT
ejpam-6259	284	4	w.	w.	PROPN
ejpam-6259	284	5	a.	a.	PROPN
ejpam-6259	284	6	dudek	dudek	PROPN
ejpam-6259	284	7	.	.	PUNCT
ejpam-6259	285	1	idempotents	idempotent	NOUN
ejpam-6259	285	2	in	in	ADP
ejpam-6259	285	3	n	n	CCONJ
ejpam-6259	285	4	-	-	PUNCT
ejpam-6259	285	5	ary	ary	NOUN
ejpam-6259	285	6	semigroups	semigroup	NOUN
ejpam-6259	285	7	.	.	PUNCT
ejpam-6259	286	1	southeast	southeast	ADJ
ejpam-6259	286	2	asian	asian	ADJ
ejpam-6259	286	3	bulletin	bulletin	NOUN
ejpam-6259	286	4	of	of	ADP
ejpam-6259	286	5	mathematics	mathematic	NOUN
ejpam-6259	286	6	,	,	PUNCT
ejpam-6259	286	7	25:97–104	25:97–104	NUM
ejpam-6259	286	8	,	,	PUNCT
ejpam-6259	286	9	2011	2011	NUM
ejpam-6259	286	10	.	.	PUNCT
ejpam-6259	287	1	[	[	X
ejpam-6259	287	2	4	4	X
ejpam-6259	287	3	]	]	PUNCT
ejpam-6259	287	4	j.	j.	PROPN
ejpam-6259	287	5	p.	p.	PROPN
ejpam-6259	287	6	solano	solano	PROPN
ejpam-6259	287	7	;	;	PUNCT
ejpam-6259	287	8	s.	s.	PROPN
ejpam-6259	287	9	suebsung	suebsung	PROPN
ejpam-6259	287	10	and	and	CCONJ
ejpam-6259	287	11	r.	r.	PROPN
ejpam-6259	287	12	chinram	chinram	PROPN
ejpam-6259	287	13	.	.	PUNCT
ejpam-6259	288	1	on	on	ADP
ejpam-6259	288	2	ideals	ideal	NOUN
ejpam-6259	288	3	of	of	ADP
ejpam-6259	288	4	fuzzy	fuzzy	ADJ
ejpam-6259	288	5	points	point	NOUN
ejpam-6259	288	6	n	n	CCONJ
ejpam-6259	288	7	-	-	PUNCT
ejpam-6259	288	8	ary	ary	NOUN
ejpam-6259	288	9	semigroups	semigroup	NOUN
ejpam-6259	288	10	.	.	PUNCT
ejpam-6259	289	1	international	international	ADJ
ejpam-6259	289	2	journal	journal	NOUN
ejpam-6259	289	3	of	of	ADP
ejpam-6259	289	4	mathematics	mathematic	NOUN
ejpam-6259	289	5	and	and	CCONJ
ejpam-6259	289	6	computer	computer	NOUN
ejpam-6259	289	7	science	science	NOUN
ejpam-6259	289	8	,	,	PUNCT
ejpam-6259	289	9	13(2):179–186	13(2):179–186	PROPN
ejpam-6259	289	10	,	,	PUNCT
ejpam-6259	289	11	2018	2018	NUM
ejpam-6259	289	12	.	.	PUNCT
ejpam-6259	290	1	[	[	X
ejpam-6259	290	2	5	5	X
ejpam-6259	290	3	]	]	PUNCT
ejpam-6259	290	4	m.	m.	NOUN
ejpam-6259	290	5	couceiro	couceiro	NOUN
ejpam-6259	290	6	and	and	CCONJ
ejpam-6259	290	7	j.	j.	PROPN
ejpam-6259	290	8	devillet	devillet	PROPN
ejpam-6259	290	9	.	.	PUNCT
ejpam-6259	291	1	every	every	DET
ejpam-6259	291	2	quasitrivial	quasitrivial	ADJ
ejpam-6259	291	3	n	n	CCONJ
ejpam-6259	291	4	-	-	PUNCT
ejpam-6259	291	5	ary	ary	PROPN
ejpam-6259	291	6	semigroup	semigroup	PROPN
ejpam-6259	291	7	is	be	AUX
ejpam-6259	291	8	reducible	reducible	ADJ
ejpam-6259	291	9	to	to	ADP
ejpam-6259	291	10	a	a	DET
ejpam-6259	291	11	semigroup	semigroup	NOUN
ejpam-6259	291	12	.	.	PUNCT
ejpam-6259	292	1	algebra	algebra	PROPN
ejpam-6259	292	2	universalis	universali	VERB
ejpam-6259	292	3	,	,	PUNCT
ejpam-6259	292	4	80(4):51	80(4):51	NUM
ejpam-6259	292	5	,	,	PUNCT
ejpam-6259	292	6	2019	2019	NUM
ejpam-6259	292	7	.	.	PUNCT
ejpam-6259	293	1	[	[	X
ejpam-6259	293	2	6	6	NUM
ejpam-6259	293	3	]	]	X
ejpam-6259	293	4	c.	c.	NOUN
ejpam-6259	293	5	somsup	somsup	NOUN
ejpam-6259	293	6	and	and	CCONJ
ejpam-6259	293	7	u.	u.	PROPN
ejpam-6259	293	8	leerawat	leerawat	PROPN
ejpam-6259	293	9	.	.	PUNCT
ejpam-6259	294	1	congruences	congruence	NOUN
ejpam-6259	294	2	and	and	CCONJ
ejpam-6259	294	3	homomorphisms	homomorphism	NOUN
ejpam-6259	294	4	on	on	ADP
ejpam-6259	294	5	n	n	CCONJ
ejpam-6259	294	6	-	-	PUNCT
ejpam-6259	294	7	ary	ary	NOUN
ejpam-6259	294	8	semigroups	semigroup	NOUN
ejpam-6259	294	9	.	.	PUNCT
ejpam-6259	295	1	international	international	ADJ
ejpam-6259	295	2	journal	journal	NOUN
ejpam-6259	295	3	of	of	ADP
ejpam-6259	295	4	mathematics	mathematic	NOUN
ejpam-6259	295	5	and	and	CCONJ
ejpam-6259	295	6	computer	computer	NOUN
ejpam-6259	295	7	science	science	NOUN
ejpam-6259	295	8	,	,	PUNCT
ejpam-6259	295	9	15(2):671–682	15(2):671–682	ADV
ejpam-6259	295	10	,	,	PUNCT
ejpam-6259	295	11	2020	2020	NUM
ejpam-6259	295	12	.	.	PUNCT
ejpam-6259	296	1	[	[	X
ejpam-6259	296	2	7	7	X
ejpam-6259	296	3	]	]	X
ejpam-6259	296	4	p.	p.	NOUN
ejpam-6259	296	5	pornsurat	pornsurat	NOUN
ejpam-6259	296	6	and	and	CCONJ
ejpam-6259	296	7	b.	b.	PROPN
ejpam-6259	296	8	pibaljommee	pibaljommee	PROPN
ejpam-6259	296	9	.	.	PUNCT
ejpam-6259	296	10	left	leave	VERB
ejpam-6259	296	11	regular	regular	ADV
ejpam-6259	296	12	and	and	CCONJ
ejpam-6259	296	13	left	leave	VERB
ejpam-6259	296	14	weakly	weakly	ADV
ejpam-6259	296	15	regular	regular	ADJ
ejpam-6259	296	16	n	n	CCONJ
ejpam-6259	296	17	-	-	PUNCT
ejpam-6259	296	18	ary	ary	NOUN
ejpam-6259	296	19	semigroups	semigroup	NOUN
ejpam-6259	296	20	.	.	PUNCT
ejpam-6259	297	1	kyungpook	kyungpook	PROPN
ejpam-6259	297	2	mathematical	mathematical	PROPN
ejpam-6259	297	3	journal	journal	PROPN
ejpam-6259	297	4	,	,	PUNCT
ejpam-6259	297	5	62(1):29–41	62(1):29–41	NUM
ejpam-6259	297	6	,	,	PUNCT
ejpam-6259	297	7	2022	2022	NUM
ejpam-6259	297	8	.	.	PUNCT
ejpam-6259	298	1	[	[	X
ejpam-6259	298	2	8	8	NUM
ejpam-6259	298	3	]	]	X
ejpam-6259	298	4	m.	m.	NOUN
ejpam-6259	298	5	couceiro	couceiro	NOUN
ejpam-6259	298	6	;	;	PUNCT
ejpam-6259	298	7	j.	j.	PROPN
ejpam-6259	298	8	devillet	devillet	PROPN
ejpam-6259	298	9	;	;	PUNCT
ejpam-6259	298	10	j.	j.	PROPN
ejpam-6259	298	11	l.	l.	PROPN
ejpam-6259	298	12	marichal	marichal	PROPN
ejpam-6259	298	13	and	and	CCONJ
ejpam-6259	298	14	p.	p.	PROPN
ejpam-6259	298	15	mathonet	mathonet	PROPN
ejpam-6259	298	16	.	.	PUNCT
ejpam-6259	299	1	reducibility	reducibility	PROPN
ejpam-6259	299	2	of	of	ADP
ejpam-6259	299	3	n	n	CCONJ
ejpam-6259	299	4	-	-	PUNCT
ejpam-6259	299	5	ary	ary	NOUN
ejpam-6259	299	6	semigroups	semigroup	NOUN
ejpam-6259	299	7	:	:	PUNCT
ejpam-6259	299	8	from	from	ADP
ejpam-6259	299	9	quasitriviality	quasitriviality	NOUN
ejpam-6259	299	10	towards	towards	ADP
ejpam-6259	299	11	idempotency	idempotency	NOUN
ejpam-6259	299	12	.	.	PUNCT
ejpam-6259	300	1	beitrage	beitrage	NOUN
ejpam-6259	300	2	zur	zur	NOUN
ejpam-6259	300	3	algebra	algebra	PROPN
ejpam-6259	300	4	und	und	NOUN
ejpam-6259	300	5	geometrie	geometrie	NOUN
ejpam-6259	300	6	,	,	PUNCT
ejpam-6259	300	7	63(1):149–166	63(1):149–166	PROPN
ejpam-6259	300	8	,	,	PUNCT
ejpam-6259	300	9	2022	2022	NUM
ejpam-6259	300	10	.	.	PUNCT
ejpam-6259	301	1	[	[	X
ejpam-6259	301	2	9	9	X
ejpam-6259	301	3	]	]	PUNCT
ejpam-6259	301	4	j.	j.	PROPN
ejpam-6259	301	5	daengsaen	daengsaen	PROPN
ejpam-6259	301	6	and	and	CCONJ
ejpam-6259	301	7	s.	s.	PROPN
ejpam-6259	301	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6259	301	9	.	.	PUNCT
ejpam-6259	302	1	semilattices	semilattice	NOUN
ejpam-6259	302	2	of	of	ADP
ejpam-6259	302	3	simple	simple	ADJ
ejpam-6259	302	4	and	and	CCONJ
ejpam-6259	302	5	regular	regular	ADJ
ejpam-6259	302	6	n	n	CCONJ
ejpam-6259	302	7	-	-	PUNCT
ejpam-6259	302	8	ary	ary	NOUN
ejpam-6259	302	9	semigroups	semigroup	NOUN
ejpam-6259	302	10	.	.	PUNCT
ejpam-6259	303	1	semigroup	semigroup	PROPN
ejpam-6259	303	2	forum	forum	PROPN
ejpam-6259	303	3	,	,	PUNCT
ejpam-6259	303	4	107(2):294–314	107(2):294–314	NUM
ejpam-6259	303	5	,	,	PUNCT
ejpam-6259	303	6	2023	2023	NUM
ejpam-6259	303	7	.	.	PUNCT
ejpam-6259	304	1	[	[	X
ejpam-6259	304	2	10	10	NUM
ejpam-6259	304	3	]	]	X
ejpam-6259	304	4	o.	o.	NOUN
ejpam-6259	304	5	grosek	grosek	PROPN
ejpam-6259	304	6	and	and	CCONJ
ejpam-6259	304	7	l.	l.	PROPN
ejpam-6259	304	8	k.	k.	PROPN
ejpam-6259	304	9	satko	satko	PROPN
ejpam-6259	304	10	.	.	PUNCT
ejpam-6259	305	1	a	a	DET
ejpam-6259	305	2	new	new	ADJ
ejpam-6259	305	3	notion	notion	NOUN
ejpam-6259	305	4	in	in	ADP
ejpam-6259	305	5	the	the	DET
ejpam-6259	305	6	theory	theory	NOUN
ejpam-6259	305	7	of	of	ADP
ejpam-6259	305	8	semigroup	semigroup	PROPN
ejpam-6259	305	9	.	.	PUNCT
ejpam-6259	306	1	semigroup	semigroup	PROPN
ejpam-6259	306	2	forum	forum	PROPN
ejpam-6259	306	3	,	,	PUNCT
ejpam-6259	306	4	21(5):233–240	21(5):233–240	NUM
ejpam-6259	306	5	,	,	PUNCT
ejpam-6259	306	6	1980	1980	NUM
ejpam-6259	306	7	.	.	PUNCT
ejpam-6259	307	1	[	[	X
ejpam-6259	307	2	11	11	NUM
ejpam-6259	307	3	]	]	PUNCT
ejpam-6259	307	4	k.	k.	PROPN
ejpam-6259	307	5	wattanatripop	wattanatripop	PROPN
ejpam-6259	307	6	;	;	PUNCT
ejpam-6259	307	7	r.	r.	PROPN
ejpam-6259	307	8	chinram	chinram	PROPN
ejpam-6259	307	9	and	and	CCONJ
ejpam-6259	307	10	t.	t.	PROPN
ejpam-6259	307	11	changphas	changphas	PROPN
ejpam-6259	307	12	.	.	PUNCT
ejpam-6259	308	1	quasi	quasi	VERB
ejpam-6259	308	2	-	-	DET
ejpam-6259	308	3	a	a	DET
ejpam-6259	308	4	-	-	PUNCT
ejpam-6259	308	5	ideals	ideal	NOUN
ejpam-6259	308	6	and	and	CCONJ
ejpam-6259	308	7	fuzzy	fuzzy	ADJ
ejpam-6259	308	8	aideals	aideal	NOUN
ejpam-6259	308	9	in	in	ADP
ejpam-6259	308	10	semigroups	semigroup	NOUN
ejpam-6259	308	11	.	.	PUNCT
ejpam-6259	309	1	journal	journal	NOUN
ejpam-6259	309	2	of	of	ADP
ejpam-6259	309	3	discrete	discrete	ADJ
ejpam-6259	309	4	mathematical	mathematical	ADJ
ejpam-6259	309	5	sciences	science	NOUN
ejpam-6259	309	6	and	and	CCONJ
ejpam-6259	309	7	cryptography	cryptography	NOUN
ejpam-6259	309	8	,	,	PUNCT
ejpam-6259	309	9	21(5):1131–1138	21(5):1131–1138	NUM
ejpam-6259	309	10	,	,	PUNCT
ejpam-6259	309	11	2018	2018	NUM
ejpam-6259	309	12	.	.	PUNCT
ejpam-6259	310	1	[	[	X
ejpam-6259	310	2	12	12	NUM
ejpam-6259	310	3	]	]	PUNCT
ejpam-6259	310	4	p.	p.	NOUN
ejpam-6259	310	5	khamrot	khamrot	PROPN
ejpam-6259	310	6	and	and	CCONJ
ejpam-6259	310	7	t.	t.	PROPN
ejpam-6259	310	8	gaketem	gaketem	PROPN
ejpam-6259	310	9	.	.	PUNCT
ejpam-6259	311	1	applications	application	NOUN
ejpam-6259	311	2	of	of	ADP
ejpam-6259	311	3	bipolar	bipolar	ADJ
ejpam-6259	311	4	fuzzy	fuzzy	ADJ
ejpam-6259	311	5	almost	almost	ADV
ejpam-6259	311	6	ideals	ideal	NOUN
ejpam-6259	311	7	in	in	ADP
ejpam-6259	311	8	semigroups	semigroup	NOUN
ejpam-6259	311	9	.	.	PUNCT
ejpam-6259	312	1	international	international	ADJ
ejpam-6259	312	2	journal	journal	NOUN
ejpam-6259	312	3	of	of	ADP
ejpam-6259	312	4	analysis	analysis	NOUN
ejpam-6259	312	5	and	and	CCONJ
ejpam-6259	312	6	applications	application	NOUN
ejpam-6259	312	7	,	,	PUNCT
ejpam-6259	312	8	22	22	NUM
ejpam-6259	312	9	:	:	PUNCT
ejpam-6259	312	10	art	art	NOUN
ejpam-6259	312	11	.	.	PUNCT
ejpam-6259	313	1	no	no	INTJ
ejpam-6259	313	2	.	.	NOUN
ejpam-6259	313	3	8	8	NUM
ejpam-6259	313	4	,	,	PUNCT
ejpam-6259	313	5	2024	2024	NUM
ejpam-6259	313	6	.	.	PUNCT
ejpam-6259	314	1	[	[	X
ejpam-6259	314	2	13	13	NUM
ejpam-6259	314	3	]	]	PUNCT
ejpam-6259	314	4	p.	p.	NOUN
ejpam-6259	314	5	khamrot	khamrot	PROPN
ejpam-6259	314	6	and	and	CCONJ
ejpam-6259	314	7	t.	t.	PROPN
ejpam-6259	314	8	gaketem	gaketem	PROPN
ejpam-6259	314	9	.	.	PUNCT
ejpam-6259	315	1	on	on	ADP
ejpam-6259	315	2	picture	picture	NOUN
ejpam-6259	315	3	fuzzy	fuzzy	ADJ
ejpam-6259	315	4	almost	almost	ADV
ejpam-6259	315	5	ideals	ideal	NOUN
ejpam-6259	315	6	of	of	ADP
ejpam-6259	315	7	semigroups	semigroup	NOUN
ejpam-6259	315	8	.	.	PUNCT
ejpam-6259	316	1	journal	journal	NOUN
ejpam-6259	316	2	of	of	ADP
ejpam-6259	316	3	discrete	discrete	ADJ
ejpam-6259	316	4	mathematical	mathematical	ADJ
ejpam-6259	316	5	sciences	science	NOUN
ejpam-6259	316	6	and	and	CCONJ
ejpam-6259	316	7	cryptography	cryptography	NOUN
ejpam-6259	316	8	,	,	PUNCT
ejpam-6259	316	9	27(6):1817–1830	27(6):1817–1830	NUM
ejpam-6259	316	10	,	,	PUNCT
ejpam-6259	316	11	2024	2024	NUM
ejpam-6259	316	12	.	.	PUNCT
ejpam-6259	317	1	[	[	X
ejpam-6259	317	2	14	14	NUM
ejpam-6259	317	3	]	]	PUNCT
ejpam-6259	317	4	a.	a.	NOUN
ejpam-6259	317	5	iampan	iampan	PROPN
ejpam-6259	317	6	;	;	PUNCT
ejpam-6259	317	7	r.	r.	PROPN
ejpam-6259	317	8	chinram	chinram	PROPN
ejpam-6259	317	9	and	and	CCONJ
ejpam-6259	317	10	p.	p.	NOUN
ejpam-6259	317	11	petchkaew	petchkaew	NOUN
ejpam-6259	317	12	.	.	PUNCT
ejpam-6259	318	1	a	a	DET
ejpam-6259	318	2	note	note	NOUN
ejpam-6259	318	3	on	on	ADP
ejpam-6259	318	4	almost	almost	ADV
ejpam-6259	318	5	subsemigroups	subsemigroup	NOUN
ejpam-6259	318	6	of	of	ADP
ejpam-6259	318	7	semir	semir	PROPN
ejpam-6259	318	8	.	.	PUNCT
ejpam-6259	319	1	chinram	chinram	PROPN
ejpam-6259	319	2	,	,	PUNCT
ejpam-6259	319	3	p.	p.	NOUN
ejpam-6259	319	4	singavananda	singavananda	PROPN
ejpam-6259	319	5	/	/	SYM
ejpam-6259	319	6	eur	eur	PROPN
ejpam-6259	319	7	.	.	PUNCT
ejpam-6259	320	1	j.	j.	PROPN
ejpam-6259	320	2	pure	pure	PROPN
ejpam-6259	320	3	appl	appl	PROPN
ejpam-6259	320	4	.	.	PROPN
ejpam-6259	320	5	math	math	PROPN
ejpam-6259	320	6	,	,	PUNCT
ejpam-6259	320	7	18	18	NUM
ejpam-6259	320	8	(	(	PUNCT
ejpam-6259	320	9	3	3	NUM
ejpam-6259	320	10	)	)	PUNCT
ejpam-6259	320	11	(	(	PUNCT
ejpam-6259	320	12	2025	2025	NUM
ejpam-6259	320	13	)	)	PUNCT
ejpam-6259	320	14	,	,	PUNCT
ejpam-6259	320	15	6259	6259	NUM
ejpam-6259	320	16	10	10	NUM
ejpam-6259	320	17	of	of	ADP
ejpam-6259	320	18	10	10	NUM
ejpam-6259	320	19	groups	group	NOUN
ejpam-6259	320	20	.	.	PUNCT
ejpam-6259	321	1	international	international	ADJ
ejpam-6259	321	2	journal	journal	PROPN
ejpam-6259	321	3	of	of	ADP
ejpam-6259	321	4	mathematics	mathematic	NOUN
ejpam-6259	321	5	and	and	CCONJ
ejpam-6259	321	6	computer	computer	NOUN
ejpam-6259	321	7	science	science	NOUN
ejpam-6259	321	8	,	,	PUNCT
ejpam-6259	321	9	16(4):1623	16(4):1623	NUM
ejpam-6259	321	10	–	–	PUNCT
ejpam-6259	321	11	1629	1629	NUM
ejpam-6259	321	12	,	,	PUNCT
ejpam-6259	321	13	2021	2021	NUM
ejpam-6259	321	14	.	.	PUNCT
ejpam-6259	322	1	[	[	X
ejpam-6259	322	2	15	15	NUM
ejpam-6259	322	3	]	]	X
ejpam-6259	322	4	r.	r.	PROPN
ejpam-6259	322	5	chinram	chinram	PROPN
ejpam-6259	322	6	;	;	PUNCT
ejpam-6259	322	7	s.	s.	PROPN
ejpam-6259	322	8	kaewchay	kaewchay	PROPN
ejpam-6259	322	9	;	;	PUNCT
ejpam-6259	322	10	a.	a.	NOUN
ejpam-6259	322	11	iampan	iampan	NOUN
ejpam-6259	322	12	and	and	CCONJ
ejpam-6259	322	13	p.	p.	PROPN
ejpam-6259	322	14	singavananda	singavananda	PROPN
ejpam-6259	322	15	.	.	PUNCT
ejpam-6259	323	1	characterization	characterization	NOUN
ejpam-6259	323	2	of	of	ADP
ejpam-6259	323	3	almost	almost	ADV
ejpam-6259	323	4	ternary	ternary	ADJ
ejpam-6259	323	5	subsemigroups	subsemigroup	NOUN
ejpam-6259	323	6	and	and	CCONJ
ejpam-6259	323	7	their	their	PRON
ejpam-6259	323	8	fuzzifications	fuzzification	NOUN
ejpam-6259	323	9	.	.	PUNCT
ejpam-6259	324	1	journal	journal	NOUN
ejpam-6259	324	2	of	of	ADP
ejpam-6259	324	3	mathematics	mathematic	NOUN
ejpam-6259	324	4	and	and	CCONJ
ejpam-6259	324	5	computer	computer	NOUN
ejpam-6259	324	6	science	science	NOUN
ejpam-6259	324	7	,	,	PUNCT
ejpam-6259	324	8	27(2):97–104	27(2):97–104	PROPN
ejpam-6259	324	9	,	,	PUNCT
ejpam-6259	324	10	2022	2022	NUM
ejpam-6259	324	11	.	.	PUNCT
ejpam-6259	325	1	[	[	X
ejpam-6259	325	2	16	16	NUM
ejpam-6259	325	3	]	]	X
ejpam-6259	325	4	r.	r.	PROPN
ejpam-6259	325	5	rittichuai	rittichuai	PROPN
ejpam-6259	325	6	;	;	PUNCT
ejpam-6259	325	7	a.	a.	NOUN
ejpam-6259	325	8	iampan	iampan	PROPN
ejpam-6259	325	9	;	;	PUNCT
ejpam-6259	325	10	r.	r.	PROPN
ejpam-6259	325	11	chinram	chinram	PROPN
ejpam-6259	325	12	and	and	CCONJ
ejpam-6259	325	13	p.	p.	PROPN
ejpam-6259	325	14	singavananda	singavananda	PROPN
ejpam-6259	325	15	.	.	PUNCT
ejpam-6259	326	1	almost	almost	ADV
ejpam-6259	326	2	subsemirings	subsemiring	NOUN
ejpam-6259	326	3	and	and	CCONJ
ejpam-6259	326	4	fuzzifications	fuzzification	NOUN
ejpam-6259	326	5	.	.	PUNCT
ejpam-6259	327	1	international	international	ADJ
ejpam-6259	327	2	journal	journal	NOUN
ejpam-6259	327	3	of	of	ADP
ejpam-6259	327	4	mathematics	mathematic	NOUN
ejpam-6259	327	5	and	and	CCONJ
ejpam-6259	327	6	computer	computer	NOUN
ejpam-6259	327	7	science	science	NOUN
ejpam-6259	327	8	,	,	PUNCT
ejpam-6259	327	9	17(4):1491–1497	17(4):1491–1497	NUM
ejpam-6259	327	10	,	,	PUNCT
ejpam-6259	327	11	2022	2022	NUM
ejpam-6259	327	12	.	.	PUNCT
ejpam-6259	328	1	[	[	X
ejpam-6259	328	2	17	17	NUM
ejpam-6259	328	3	]	]	X
ejpam-6259	328	4	n.	n.	NOUN
ejpam-6259	328	5	sarasit	sarasit	PROPN
ejpam-6259	328	6	;	;	PUNCT
ejpam-6259	328	7	r.	r.	PROPN
ejpam-6259	328	8	chinram	chinram	PROPN
ejpam-6259	328	9	and	and	CCONJ
ejpam-6259	328	10	a.	a.	NOUN
ejpam-6259	328	11	rattana	rattana	PROPN
ejpam-6259	328	12	.	.	PUNCT
ejpam-6259	329	1	applications	application	NOUN
ejpam-6259	329	2	of	of	ADP
ejpam-6259	329	3	fuzzy	fuzzy	ADJ
ejpam-6259	329	4	set	set	NOUN
ejpam-6259	329	5	for	for	ADP
ejpam-6259	329	6	almostity	almostity	NOUN
ejpam-6259	329	7	of	of	ADP
ejpam-6259	329	8	ternary	ternary	ADJ
ejpam-6259	329	9	subsemirings	subsemiring	NOUN
ejpam-6259	329	10	.	.	PUNCT
ejpam-6259	330	1	international	international	ADJ
ejpam-6259	330	2	journal	journal	NOUN
ejpam-6259	330	3	of	of	ADP
ejpam-6259	330	4	applied	apply	VERB
ejpam-6259	330	5	mathematics	mathematic	NOUN
ejpam-6259	330	6	,	,	PUNCT
ejpam-6259	330	7	36(4):497–508	36(4):497–508	PROPN
ejpam-6259	330	8	,	,	PUNCT
ejpam-6259	330	9	2023	2023	NUM
ejpam-6259	330	10	.	.	PUNCT
ejpam-6259	331	1	[	[	X
ejpam-6259	331	2	18	18	NUM
ejpam-6259	331	3	]	]	PUNCT
ejpam-6259	331	4	p.	p.	NOUN
ejpam-6259	331	5	petchkaew	petchkaew	NOUN
ejpam-6259	331	6	and	and	CCONJ
ejpam-6259	331	7	r.	r.	PROPN
ejpam-6259	331	8	chinram	chinram	PROPN
ejpam-6259	331	9	.	.	PUNCT
ejpam-6259	332	1	the	the	DET
ejpam-6259	332	2	minimality	minimality	NOUN
ejpam-6259	332	3	and	and	CCONJ
ejpam-6259	332	4	maximality	maximality	PROPN
ejpam-6259	332	5	of	of	ADP
ejpam-6259	332	6	n	n	CCONJ
ejpam-6259	332	7	-	-	PUNCT
ejpam-6259	332	8	ideals	ideal	NOUN
ejpam-6259	332	9	in	in	ADP
ejpam-6259	332	10	nary	nary	ADJ
ejpam-6259	332	11	semigroups	semigroup	NOUN
ejpam-6259	332	12	.	.	PUNCT
ejpam-6259	333	1	european	european	ADJ
ejpam-6259	333	2	journal	journal	PROPN
ejpam-6259	333	3	of	of	ADP
ejpam-6259	333	4	pure	pure	ADJ
ejpam-6259	333	5	and	and	CCONJ
ejpam-6259	333	6	applied	applied	ADJ
ejpam-6259	333	7	mathematics	mathematic	NOUN
ejpam-6259	333	8	,	,	PUNCT
ejpam-6259	333	9	11(3):762–773	11(3):762–773	PROPN
ejpam-6259	333	10	,	,	PUNCT
ejpam-6259	333	11	2018	2018	NUM
ejpam-6259	333	12	.	.	PUNCT
ejpam-6259	334	1	[	[	X
ejpam-6259	334	2	19	19	NUM
ejpam-6259	334	3	]	]	X
ejpam-6259	334	4	j.	j.	PROPN
ejpam-6259	334	5	n.	n.	PROPN
ejpam-6259	334	6	mordeson	mordeson	PROPN
ejpam-6259	334	7	;	;	PUNCT
ejpam-6259	334	8	d.	d.	PROPN
ejpam-6259	334	9	s.	s.	PROPN
ejpam-6259	334	10	malik	malik	PROPN
ejpam-6259	334	11	and	and	CCONJ
ejpam-6259	334	12	n.	n.	PROPN
ejpam-6259	334	13	kuroki	kuroki	PROPN
ejpam-6259	334	14	.	.	PUNCT
ejpam-6259	335	1	fuzzy	fuzzy	ADJ
ejpam-6259	335	2	semigroups	semigroup	NOUN
ejpam-6259	335	3	.	.	PUNCT
ejpam-6259	335	4	springer	springer	NOUN
ejpam-6259	335	5	-	-	PUNCT
ejpam-6259	335	6	verlag	verlag	PROPN
ejpam-6259	335	7	,	,	PUNCT
ejpam-6259	335	8	berlin	berlin	PROPN
ejpam-6259	335	9	,	,	PUNCT
ejpam-6259	335	10	2012	2012	NUM
ejpam-6259	335	11	.	.	PUNCT