id	sid	tid	token	lemma	pos
ejpam-6395	1	1	european	european	PROPN
ejpam-6395	1	2	journal	journal	PROPN
ejpam-6395	1	3	of	of	ADP
ejpam-6395	1	4	pure	pure	ADJ
ejpam-6395	1	5	and	and	CCONJ
ejpam-6395	1	6	applied	applied	ADJ
ejpam-6395	1	7	mathematics	mathematic	NOUN
ejpam-6395	1	8	2025	2025	NUM
ejpam-6395	1	9	,	,	PUNCT
ejpam-6395	1	10	vol	vol	NOUN
ejpam-6395	1	11	.	.	PROPN
ejpam-6395	1	12	18	18	NUM
ejpam-6395	1	13	,	,	PUNCT
ejpam-6395	1	14	issue	issue	NOUN
ejpam-6395	1	15	3	3	NUM
ejpam-6395	1	16	,	,	PUNCT
ejpam-6395	1	17	article	article	NOUN
ejpam-6395	1	18	number	number	NOUN
ejpam-6395	1	19	6395	6395	NUM
ejpam-6395	1	20	issn	issn	VERB
ejpam-6395	1	21	1307	1307	NUM
ejpam-6395	1	22	-	-	SYM
ejpam-6395	1	23	5543	5543	NUM
ejpam-6395	1	24	–	–	PUNCT
ejpam-6395	1	25	ejpam.com	ejpam.com	X
ejpam-6395	1	26	published	publish	VERB
ejpam-6395	1	27	by	by	ADP
ejpam-6395	1	28	new	new	PROPN
ejpam-6395	1	29	york	york	PROPN
ejpam-6395	1	30	business	business	PROPN
ejpam-6395	1	31	global	global	ADJ
ejpam-6395	1	32	pure	pure	ADJ
ejpam-6395	1	33	ideals	ideal	NOUN
ejpam-6395	1	34	on	on	ADP
ejpam-6395	1	35	ordered	order	VERB
ejpam-6395	1	36	power	power	NOUN
ejpam-6395	1	37	ternary	ternary	ADJ
ejpam-6395	1	38	semigroups	semigroup	NOUN
ejpam-6395	1	39	on	on	ADP
ejpam-6395	1	40	ternary	ternary	ADJ
ejpam-6395	1	41	semihypergroups	semihypergroup	NOUN
ejpam-6395	1	42	induced	induce	VERB
ejpam-6395	1	43	by	by	ADP
ejpam-6395	1	44	posets	poset	NOUN
ejpam-6395	1	45	anak	anak	PROPN
ejpam-6395	1	46	nongmanee1	nongmanee1	PROPN
ejpam-6395	1	47	,	,	PUNCT
ejpam-6395	1	48	kanruethai	kanruethai	PROPN
ejpam-6395	1	49	jeenkaew2	jeenkaew2	PROPN
ejpam-6395	1	50	,	,	PUNCT
ejpam-6395	1	51	maliwan	maliwan	PRON
ejpam-6395	1	52	phattarachaleekul3,∗	phattarachaleekul3,∗	VERB
ejpam-6395	1	53	1	1	NUM
ejpam-6395	1	54	education	education	NOUN
ejpam-6395	1	55	program	program	NOUN
ejpam-6395	1	56	in	in	ADP
ejpam-6395	1	57	mathematics	mathematic	NOUN
ejpam-6395	1	58	,	,	PUNCT
ejpam-6395	1	59	faculty	faculty	NOUN
ejpam-6395	1	60	of	of	ADP
ejpam-6395	1	61	education	education	NOUN
ejpam-6395	1	62	,	,	PUNCT
ejpam-6395	1	63	suratthani	suratthani	PROPN
ejpam-6395	1	64	rajabhat	rajabhat	PROPN
ejpam-6395	1	65	university	university	NOUN
ejpam-6395	1	66	,	,	PUNCT
ejpam-6395	1	67	suratthani	suratthani	PROPN
ejpam-6395	1	68	84100	84100	NUM
ejpam-6395	1	69	,	,	PUNCT
ejpam-6395	2	1	thailand	thailand	PROPN
ejpam-6395	2	2	2department	2department	NUM
ejpam-6395	2	3	of	of	ADP
ejpam-6395	2	4	mathematics	mathematic	NOUN
ejpam-6395	2	5	,	,	PUNCT
ejpam-6395	2	6	faculty	faculty	NOUN
ejpam-6395	2	7	of	of	ADP
ejpam-6395	2	8	science	science	NOUN
ejpam-6395	2	9	,	,	PUNCT
ejpam-6395	2	10	chiang	chiang	PROPN
ejpam-6395	2	11	mai	mai	PROPN
ejpam-6395	2	12	university	university	PROPN
ejpam-6395	2	13	,	,	PUNCT
ejpam-6395	2	14	chiang	chiang	PROPN
ejpam-6395	2	15	mai	mai	PROPN
ejpam-6395	2	16	50200	50200	NUM
ejpam-6395	2	17	,	,	PUNCT
ejpam-6395	2	18	thailand	thailand	PROPN
ejpam-6395	2	19	3	3	NUM
ejpam-6395	2	20	department	department	NOUN
ejpam-6395	2	21	of	of	ADP
ejpam-6395	2	22	mathematics	mathematic	NOUN
ejpam-6395	2	23	,	,	PUNCT
ejpam-6395	2	24	faculty	faculty	NOUN
ejpam-6395	2	25	of	of	ADP
ejpam-6395	2	26	science	science	NOUN
ejpam-6395	2	27	,	,	PUNCT
ejpam-6395	2	28	mahasarakham	mahasarakham	PROPN
ejpam-6395	2	29	university	university	PROPN
ejpam-6395	2	30	,	,	PUNCT
ejpam-6395	2	31	mahasarakham	mahasarakham	PROPN
ejpam-6395	2	32	44150	44150	NUM
ejpam-6395	2	33	,	,	PUNCT
ejpam-6395	2	34	thailand	thailand	PROPN
ejpam-6395	2	35	abstract	abstract	PROPN
ejpam-6395	2	36	.	.	PUNCT
ejpam-6395	3	1	this	this	DET
ejpam-6395	3	2	article	article	NOUN
ejpam-6395	3	3	is	be	AUX
ejpam-6395	3	4	devoted	devote	VERB
ejpam-6395	3	5	to	to	ADP
ejpam-6395	3	6	the	the	DET
ejpam-6395	3	7	investigation	investigation	NOUN
ejpam-6395	3	8	of	of	ADP
ejpam-6395	3	9	some	some	DET
ejpam-6395	3	10	algebraic	algebraic	ADJ
ejpam-6395	3	11	connections	connection	NOUN
ejpam-6395	3	12	between	between	ADP
ejpam-6395	3	13	algebraic	algebraic	ADJ
ejpam-6395	3	14	structures	structure	NOUN
ejpam-6395	3	15	and	and	CCONJ
ejpam-6395	3	16	algebraic	algebraic	ADJ
ejpam-6395	3	17	hyperstructures	hyperstructure	NOUN
ejpam-6395	3	18	.	.	PUNCT
ejpam-6395	4	1	firstly	firstly	ADV
ejpam-6395	4	2	,	,	PUNCT
ejpam-6395	4	3	we	we	PRON
ejpam-6395	4	4	introduce	introduce	VERB
ejpam-6395	4	5	the	the	DET
ejpam-6395	4	6	concept	concept	NOUN
ejpam-6395	4	7	of	of	ADP
ejpam-6395	4	8	ordered	order	VERB
ejpam-6395	4	9	power	power	NOUN
ejpam-6395	4	10	ternary	ternary	NOUN
ejpam-6395	4	11	semigroups	semigroup	NOUN
ejpam-6395	4	12	on	on	ADP
ejpam-6395	4	13	ternary	ternary	ADJ
ejpam-6395	4	14	semihypergroups	semihypergroup	NOUN
ejpam-6395	4	15	induced	induce	VERB
ejpam-6395	4	16	by	by	ADP
ejpam-6395	4	17	posets	poset	NOUN
ejpam-6395	4	18	which	which	PRON
ejpam-6395	4	19	are	be	AUX
ejpam-6395	4	20	generalizations	generalization	NOUN
ejpam-6395	4	21	of	of	ADP
ejpam-6395	4	22	power	power	NOUN
ejpam-6395	4	23	ternary	ternary	NOUN
ejpam-6395	4	24	semigroups	semigroup	NOUN
ejpam-6395	4	25	on	on	ADP
ejpam-6395	4	26	ternary	ternary	ADJ
ejpam-6395	4	27	semihypergroups	semihypergroup	NOUN
ejpam-6395	4	28	.	.	PUNCT
ejpam-6395	5	1	then	then	ADV
ejpam-6395	5	2	,	,	PUNCT
ejpam-6395	5	3	the	the	DET
ejpam-6395	5	4	ideas	idea	NOUN
ejpam-6395	5	5	of	of	ADP
ejpam-6395	5	6	ideals	ideal	NOUN
ejpam-6395	5	7	and	and	CCONJ
ejpam-6395	5	8	pure	pure	ADJ
ejpam-6395	5	9	ideals	ideal	NOUN
ejpam-6395	5	10	in	in	ADP
ejpam-6395	5	11	ordered	order	VERB
ejpam-6395	5	12	power	power	NOUN
ejpam-6395	5	13	ternary	ternary	ADJ
ejpam-6395	5	14	semigroups	semigroup	NOUN
ejpam-6395	5	15	on	on	ADP
ejpam-6395	5	16	ternary	ternary	ADJ
ejpam-6395	5	17	semihypergroups	semihypergroup	NOUN
ejpam-6395	5	18	induced	induce	VERB
ejpam-6395	5	19	by	by	ADP
ejpam-6395	5	20	posets	poset	NOUN
ejpam-6395	5	21	are	be	AUX
ejpam-6395	5	22	introduced	introduce	VERB
ejpam-6395	5	23	.	.	PUNCT
ejpam-6395	6	1	we	we	PRON
ejpam-6395	6	2	also	also	ADV
ejpam-6395	6	3	study	study	VERB
ejpam-6395	6	4	some	some	DET
ejpam-6395	6	5	algebraic	algebraic	ADJ
ejpam-6395	6	6	properties	property	NOUN
ejpam-6395	6	7	of	of	ADP
ejpam-6395	6	8	pure	pure	ADJ
ejpam-6395	6	9	ideals	ideal	NOUN
ejpam-6395	6	10	and	and	CCONJ
ejpam-6395	6	11	weakly	weakly	ADJ
ejpam-6395	6	12	pure	pure	ADJ
ejpam-6395	6	13	ideals	ideal	NOUN
ejpam-6395	6	14	on	on	ADP
ejpam-6395	6	15	the	the	DET
ejpam-6395	6	16	ordered	order	VERB
ejpam-6395	6	17	ternary	ternary	ADJ
ejpam-6395	6	18	semigroups	semigroup	NOUN
ejpam-6395	6	19	.	.	PUNCT
ejpam-6395	7	1	2020	2020	NUM
ejpam-6395	7	2	mathematics	mathematic	NOUN
ejpam-6395	7	3	subject	subject	NOUN
ejpam-6395	7	4	classifications	classification	NOUN
ejpam-6395	7	5	:	:	PUNCT
ejpam-6395	7	6	06f05	06f05	NUM
ejpam-6395	7	7	,	,	PUNCT
ejpam-6395	7	8	20m75	20m75	NUM
ejpam-6395	7	9	,	,	PUNCT
ejpam-6395	7	10	20m12	20m12	NUM
ejpam-6395	7	11	key	key	ADJ
ejpam-6395	7	12	words	word	NOUN
ejpam-6395	7	13	and	and	CCONJ
ejpam-6395	7	14	phrases	phrase	NOUN
ejpam-6395	7	15	:	:	PUNCT
ejpam-6395	7	16	ternary	ternary	ADJ
ejpam-6395	7	17	semigroups	semigroup	NOUN
ejpam-6395	7	18	,	,	PUNCT
ejpam-6395	7	19	ternary	ternary	ADJ
ejpam-6395	7	20	semihypergroups	semihypergroup	NOUN
ejpam-6395	7	21	,	,	PUNCT
ejpam-6395	7	22	pure	pure	ADJ
ejpam-6395	7	23	ideals	ideal	NOUN
ejpam-6395	7	24	,	,	PUNCT
ejpam-6395	7	25	power	power	NOUN
ejpam-6395	7	26	order	order	NOUN
ejpam-6395	7	27	sets	set	VERB
ejpam-6395	7	28	1	1	NUM
ejpam-6395	7	29	.	.	X
ejpam-6395	8	1	introduction	introduction	NOUN
ejpam-6395	8	2	a	a	DET
ejpam-6395	8	3	ternary	ternary	ADJ
ejpam-6395	8	4	semigroup	semigroup	NOUN
ejpam-6395	8	5	is	be	AUX
ejpam-6395	8	6	a	a	DET
ejpam-6395	8	7	generalization	generalization	NOUN
ejpam-6395	8	8	of	of	ADP
ejpam-6395	8	9	a	a	DET
ejpam-6395	8	10	semigroup	semigroup	NOUN
ejpam-6395	8	11	by	by	ADP
ejpam-6395	8	12	extending	extend	VERB
ejpam-6395	8	13	the	the	DET
ejpam-6395	8	14	binary	binary	ADJ
ejpam-6395	8	15	operation	operation	NOUN
ejpam-6395	8	16	to	to	ADP
ejpam-6395	8	17	a	a	DET
ejpam-6395	8	18	ternary	ternary	ADJ
ejpam-6395	8	19	operation	operation	NOUN
ejpam-6395	8	20	.	.	PUNCT
ejpam-6395	9	1	a	a	DET
ejpam-6395	9	2	ternary	ternary	ADJ
ejpam-6395	9	3	semigroup	semigroup	NOUN
ejpam-6395	9	4	consists	consist	VERB
ejpam-6395	9	5	of	of	ADP
ejpam-6395	9	6	a	a	DET
ejpam-6395	9	7	set	set	NOUN
ejpam-6395	9	8	with	with	ADP
ejpam-6395	9	9	a	a	DET
ejpam-6395	9	10	ternary	ternary	ADJ
ejpam-6395	9	11	operation	operation	NOUN
ejpam-6395	9	12	satisfying	satisfy	VERB
ejpam-6395	9	13	associativity	associativity	NOUN
ejpam-6395	9	14	.	.	PUNCT
ejpam-6395	10	1	the	the	DET
ejpam-6395	10	2	concept	concept	NOUN
ejpam-6395	10	3	of	of	ADP
ejpam-6395	10	4	a	a	DET
ejpam-6395	10	5	ternary	ternary	ADJ
ejpam-6395	10	6	semigroup	semigroup	NOUN
ejpam-6395	10	7	was	be	AUX
ejpam-6395	10	8	introduced	introduce	VERB
ejpam-6395	10	9	by	by	ADP
ejpam-6395	10	10	lehmer	lehmer	PROPN
ejpam-6395	10	11	in	in	ADP
ejpam-6395	10	12	1932	1932	NUM
ejpam-6395	11	1	[	[	X
ejpam-6395	11	2	1	1	NUM
ejpam-6395	11	3	]	]	PUNCT
ejpam-6395	11	4	,	,	PUNCT
ejpam-6395	11	5	who	who	PRON
ejpam-6395	11	6	studied	study	VERB
ejpam-6395	11	7	the	the	DET
ejpam-6395	11	8	so	so	ADV
ejpam-6395	11	9	-	-	PUNCT
ejpam-6395	11	10	called	call	VERB
ejpam-6395	11	11	a	a	DET
ejpam-6395	11	12	triplex	triplex	NOUN
ejpam-6395	11	13	,	,	PUNCT
ejpam-6395	11	14	which	which	PRON
ejpam-6395	11	15	emerges	emerge	VERB
ejpam-6395	11	16	as	as	ADP
ejpam-6395	11	17	a	a	DET
ejpam-6395	11	18	commutative	commutative	ADJ
ejpam-6395	11	19	ternary	ternary	ADJ
ejpam-6395	11	20	group	group	NOUN
ejpam-6395	11	21	.	.	PUNCT
ejpam-6395	12	1	banach	banach	PROPN
ejpam-6395	12	2	gave	give	VERB
ejpam-6395	12	3	an	an	DET
ejpam-6395	12	4	example	example	NOUN
ejpam-6395	12	5	to	to	PART
ejpam-6395	12	6	show	show	VERB
ejpam-6395	12	7	that	that	SCONJ
ejpam-6395	12	8	a	a	DET
ejpam-6395	12	9	ternary	ternary	ADJ
ejpam-6395	12	10	semigroup	semigroup	NOUN
ejpam-6395	12	11	is	be	AUX
ejpam-6395	12	12	not	not	PART
ejpam-6395	12	13	necessarily	necessarily	ADV
ejpam-6395	12	14	reduced	reduce	VERB
ejpam-6395	12	15	to	to	ADP
ejpam-6395	12	16	an	an	DET
ejpam-6395	12	17	ordinary	ordinary	ADJ
ejpam-6395	12	18	semigroup	semigroup	NOUN
ejpam-6395	12	19	.	.	PUNCT
ejpam-6395	13	1	the	the	DET
ejpam-6395	13	2	notion	notion	NOUN
ejpam-6395	13	3	of	of	ADP
ejpam-6395	13	4	ternary	ternary	ADJ
ejpam-6395	13	5	semigroups	semigroup	NOUN
ejpam-6395	13	6	was	be	AUX
ejpam-6395	13	7	introduced	introduce	VERB
ejpam-6395	13	8	by	by	ADP
ejpam-6395	13	9	los	los	PROPN
ejpam-6395	13	10	in	in	ADP
ejpam-6395	13	11	1955	1955	NUM
ejpam-6395	13	12	[	[	X
ejpam-6395	13	13	2	2	NUM
ejpam-6395	13	14	]	]	PUNCT
ejpam-6395	13	15	,	,	PUNCT
ejpam-6395	13	16	who	who	PRON
ejpam-6395	13	17	studied	study	VERB
ejpam-6395	13	18	some	some	DET
ejpam-6395	13	19	properties	property	NOUN
ejpam-6395	13	20	of	of	ADP
ejpam-6395	13	21	ternary	ternary	ADJ
ejpam-6395	13	22	semigroups	semigroup	NOUN
ejpam-6395	13	23	.	.	PUNCT
ejpam-6395	14	1	sioson	sioson	PROPN
ejpam-6395	14	2	introduced	introduce	VERB
ejpam-6395	14	3	the	the	DET
ejpam-6395	14	4	ideal	ideal	ADJ
ejpam-6395	14	5	theory	theory	NOUN
ejpam-6395	14	6	in	in	ADP
ejpam-6395	14	7	ternary	ternary	ADJ
ejpam-6395	14	8	semigroups	semigroup	NOUN
ejpam-6395	14	9	[	[	X
ejpam-6395	14	10	3	3	NUM
ejpam-6395	14	11	]	]	PUNCT
ejpam-6395	14	12	.	.	PUNCT
ejpam-6395	15	1	for	for	ADP
ejpam-6395	15	2	more	more	ADJ
ejpam-6395	15	3	information	information	NOUN
ejpam-6395	15	4	,	,	PUNCT
ejpam-6395	15	5	see	see	VERB
ejpam-6395	15	6	[	[	X
ejpam-6395	15	7	4–7	4–7	NOUN
ejpam-6395	15	8	]	]	X
ejpam-6395	15	9	.	.	PUNCT
ejpam-6395	16	1	∗corresponding	∗corresponde	VERB
ejpam-6395	16	2	author	author	NOUN
ejpam-6395	16	3	.	.	PUNCT
ejpam-6395	17	1	doi	doi	NOUN
ejpam-6395	17	2	:	:	PUNCT
ejpam-6395	17	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6395	https://doi.org/10.29020/nybg.ejpam.v18i3.6395	PROPN
ejpam-6395	17	4	email	email	NOUN
ejpam-6395	17	5	addresses	address	NOUN
ejpam-6395	17	6	:	:	PUNCT
ejpam-6395	17	7	anak.non@sru.ac.th	anak.non@sru.ac.th	PRON
ejpam-6395	17	8	(	(	PUNCT
ejpam-6395	17	9	a.	a.	NOUN
ejpam-6395	17	10	nongmanee	nongmanee	NOUN
ejpam-6395	17	11	)	)	PUNCT
ejpam-6395	17	12	,	,	PUNCT
ejpam-6395	17	13	k.jeenkaew@outlook.com	k.jeenkaew@outlook.com	PROPN
ejpam-6395	17	14	(	(	PUNCT
ejpam-6395	17	15	k.	k.	PROPN
ejpam-6395	17	16	jeenkaew	jeenkaew	PROPN
ejpam-6395	17	17	)	)	PUNCT
ejpam-6395	17	18	,	,	PUNCT
ejpam-6395	17	19	maliwan.t@msu.ac.th	maliwan.t@msu.ac.th	PROPN
ejpam-6395	17	20	(	(	PUNCT
ejpam-6395	17	21	m.	m.	NOUN
ejpam-6395	17	22	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	17	23	)	)	PUNCT
ejpam-6395	17	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6395	18	1	1	1	NUM
ejpam-6395	18	2	copyright	copyright	NOUN
ejpam-6395	18	3	:	:	PUNCT
ejpam-6395	18	4	©	©	PROPN
ejpam-6395	18	5	2025	2025	NUM
ejpam-6395	18	6	the	the	DET
ejpam-6395	18	7	author(s	author(s	NOUN
ejpam-6395	18	8	)	)	PUNCT
ejpam-6395	18	9	.	.	PUNCT
ejpam-6395	19	1	(	(	PUNCT
ejpam-6395	19	2	cc	cc	NOUN
ejpam-6395	19	3	by	by	ADP
ejpam-6395	19	4	-	-	PUNCT
ejpam-6395	19	5	nc	nc	PROPN
ejpam-6395	19	6	4.0	4.0	NUM
ejpam-6395	19	7	)	)	PUNCT
ejpam-6395	19	8	a.	a.	NOUN
ejpam-6395	19	9	nongmanee	nongmanee	NOUN
ejpam-6395	19	10	,	,	PUNCT
ejpam-6395	19	11	k.	k.	PROPN
ejpam-6395	19	12	jeenkaew	jeenkaew	PROPN
ejpam-6395	19	13	,	,	PUNCT
ejpam-6395	19	14	m.	m.	NOUN
ejpam-6395	19	15	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	19	16	/	/	SYM
ejpam-6395	19	17	eur	eur	PROPN
ejpam-6395	19	18	.	.	PUNCT
ejpam-6395	20	1	j.	j.	PROPN
ejpam-6395	20	2	pure	pure	PROPN
ejpam-6395	20	3	appl	appl	PROPN
ejpam-6395	20	4	.	.	PROPN
ejpam-6395	20	5	math	math	PROPN
ejpam-6395	20	6	,	,	PUNCT
ejpam-6395	20	7	18	18	NUM
ejpam-6395	20	8	(	(	PUNCT
ejpam-6395	20	9	3	3	NUM
ejpam-6395	20	10	)	)	PUNCT
ejpam-6395	20	11	(	(	PUNCT
ejpam-6395	20	12	2025	2025	NUM
ejpam-6395	20	13	)	)	PUNCT
ejpam-6395	20	14	,	,	PUNCT
ejpam-6395	20	15	6395	6395	NUM
ejpam-6395	20	16	2	2	NUM
ejpam-6395	20	17	of	of	ADP
ejpam-6395	20	18	12	12	NUM
ejpam-6395	20	19	a	a	DET
ejpam-6395	20	20	ternary	ternary	ADJ
ejpam-6395	20	21	semihypergroup	semihypergroup	NOUN
ejpam-6395	20	22	is	be	AUX
ejpam-6395	20	23	an	an	DET
ejpam-6395	20	24	algebraic	algebraic	ADJ
ejpam-6395	20	25	structure	structure	NOUN
ejpam-6395	20	26	with	with	ADP
ejpam-6395	20	27	an	an	DET
ejpam-6395	20	28	associative	associative	ADJ
ejpam-6395	20	29	ternary	ternary	ADJ
ejpam-6395	20	30	hyperoperation	hyperoperation	NOUN
ejpam-6395	20	31	.	.	PUNCT
ejpam-6395	21	1	davvaz	davvaz	PROPN
ejpam-6395	21	2	,	,	PUNCT
ejpam-6395	21	3	dudek	dudek	PROPN
ejpam-6395	21	4	,	,	PUNCT
ejpam-6395	21	5	and	and	CCONJ
ejpam-6395	21	6	vougiouklis	vougioukli	NOUN
ejpam-6395	21	7	introduced	introduce	VERB
ejpam-6395	21	8	the	the	DET
ejpam-6395	21	9	concept	concept	NOUN
ejpam-6395	21	10	of	of	ADP
ejpam-6395	21	11	an	an	DET
ejpam-6395	21	12	n	n	CCONJ
ejpam-6395	21	13	-	-	PUNCT
ejpam-6395	21	14	ary	ary	NOUN
ejpam-6395	21	15	hypergroup	hypergroup	PROPN
ejpam-6395	21	16	,	,	PUNCT
ejpam-6395	21	17	which	which	PRON
ejpam-6395	21	18	generalizes	generalize	VERB
ejpam-6395	21	19	a	a	DET
ejpam-6395	21	20	hypergroup	hypergroup	NOUN
ejpam-6395	21	21	in	in	ADP
ejpam-6395	21	22	accordance	accordance	NOUN
ejpam-6395	21	23	with	with	ADP
ejpam-6395	21	24	marty	marty	PROPN
ejpam-6395	21	25	’s	’s	PART
ejpam-6395	21	26	definition	definition	NOUN
ejpam-6395	21	27	[	[	X
ejpam-6395	21	28	8	8	NUM
ejpam-6395	21	29	]	]	PUNCT
ejpam-6395	21	30	.	.	PUNCT
ejpam-6395	22	1	a	a	DET
ejpam-6395	22	2	ternary	ternary	ADJ
ejpam-6395	22	3	semihypergroup	semihypergroup	NOUN
ejpam-6395	22	4	is	be	AUX
ejpam-6395	22	5	a	a	DET
ejpam-6395	22	6	specific	specific	ADJ
ejpam-6395	22	7	instance	instance	NOUN
ejpam-6395	22	8	of	of	ADP
ejpam-6395	22	9	an	an	DET
ejpam-6395	22	10	n	n	CCONJ
ejpam-6395	22	11	-	-	PUNCT
ejpam-6395	22	12	ary	ary	NOUN
ejpam-6395	22	13	semihypergroup	semihypergroup	NOUN
ejpam-6395	22	14	with	with	ADP
ejpam-6395	22	15	n	n	NOUN
ejpam-6395	22	16	=	=	SYM
ejpam-6395	22	17	3	3	X
ejpam-6395	22	18	.	.	PUNCT
ejpam-6395	23	1	recently	recently	ADV
ejpam-6395	23	2	,	,	PUNCT
ejpam-6395	23	3	nongmanee	nongmanee	NOUN
ejpam-6395	23	4	and	and	CCONJ
ejpam-6395	23	5	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	23	6	extended	extend	VERB
ejpam-6395	23	7	cayley	cayley	NOUN
ejpam-6395	23	8	’s	’s	PART
ejpam-6395	23	9	theorem	theorem	NOUN
ejpam-6395	23	10	to	to	PART
ejpam-6395	23	11	study	study	VERB
ejpam-6395	23	12	on	on	ADP
ejpam-6395	23	13	ternary	ternary	ADJ
ejpam-6395	23	14	semihypergroups	semihypergroup	NOUN
ejpam-6395	23	15	.	.	PUNCT
ejpam-6395	24	1	moreover	moreover	ADV
ejpam-6395	24	2	,	,	PUNCT
ejpam-6395	24	3	they	they	PRON
ejpam-6395	24	4	discovered	discover	VERB
ejpam-6395	24	5	several	several	ADJ
ejpam-6395	24	6	conditions	condition	NOUN
ejpam-6395	24	7	of	of	ADP
ejpam-6395	24	8	ternary	ternary	ADJ
ejpam-6395	24	9	semihypergroups	semihypergroup	NOUN
ejpam-6395	24	10	which	which	PRON
ejpam-6395	24	11	can	can	AUX
ejpam-6395	24	12	be	be	AUX
ejpam-6395	24	13	reduced	reduce	VERB
ejpam-6395	24	14	to	to	ADP
ejpam-6395	24	15	semihypergroups	semihypergroup	NOUN
ejpam-6395	24	16	[	[	X
ejpam-6395	24	17	9	9	NUM
ejpam-6395	24	18	]	]	PUNCT
ejpam-6395	24	19	.	.	PUNCT
ejpam-6395	25	1	in	in	ADP
ejpam-6395	25	2	2024	2024	NUM
ejpam-6395	25	3	,	,	PUNCT
ejpam-6395	25	4	they	they	PRON
ejpam-6395	25	5	presented	present	VERB
ejpam-6395	25	6	some	some	DET
ejpam-6395	25	7	algebraic	algebraic	ADJ
ejpam-6395	25	8	connections	connection	NOUN
ejpam-6395	25	9	between	between	ADP
ejpam-6395	25	10	ternary	ternary	ADJ
ejpam-6395	25	11	semigroups	semigroup	NOUN
ejpam-6395	25	12	and	and	CCONJ
ejpam-6395	25	13	ternary	ternary	ADJ
ejpam-6395	25	14	semihypergroups	semihypergroup	NOUN
ejpam-6395	25	15	via	via	ADP
ejpam-6395	25	16	regularity	regularity	NOUN
ejpam-6395	25	17	[	[	X
ejpam-6395	25	18	10	10	NUM
ejpam-6395	25	19	]	]	PUNCT
ejpam-6395	25	20	.	.	PUNCT
ejpam-6395	26	1	the	the	DET
ejpam-6395	26	2	concept	concept	NOUN
ejpam-6395	26	3	of	of	ADP
ejpam-6395	26	4	a	a	DET
ejpam-6395	26	5	power	power	NOUN
ejpam-6395	26	6	semigroup	semigroup	NOUN
ejpam-6395	26	7	was	be	AUX
ejpam-6395	26	8	first	first	ADV
ejpam-6395	26	9	explicitly	explicitly	ADV
ejpam-6395	26	10	studied	study	VERB
ejpam-6395	26	11	by	by	ADP
ejpam-6395	26	12	dubreil	dubreil	NOUN
ejpam-6395	26	13	[	[	X
ejpam-6395	26	14	11	11	NUM
ejpam-6395	26	15	]	]	PUNCT
ejpam-6395	26	16	.	.	PUNCT
ejpam-6395	27	1	subsequent	subsequent	ADJ
ejpam-6395	27	2	studies	study	NOUN
ejpam-6395	27	3	on	on	ADP
ejpam-6395	27	4	power	power	NOUN
ejpam-6395	27	5	semigroups	semigroup	NOUN
ejpam-6395	27	6	were	be	AUX
ejpam-6395	27	7	conducted	conduct	VERB
ejpam-6395	27	8	by	by	ADP
ejpam-6395	27	9	many	many	ADJ
ejpam-6395	27	10	authors	author	NOUN
ejpam-6395	27	11	such	such	ADJ
ejpam-6395	27	12	as	as	ADP
ejpam-6395	27	13	tamura	tamura	NOUN
ejpam-6395	27	14	and	and	CCONJ
ejpam-6395	27	15	shafer	shafer	VERB
ejpam-6395	27	16	[	[	X
ejpam-6395	27	17	12	12	NUM
ejpam-6395	27	18	]	]	PUNCT
ejpam-6395	27	19	.	.	PUNCT
ejpam-6395	28	1	they	they	PRON
ejpam-6395	28	2	introduced	introduce	VERB
ejpam-6395	28	3	the	the	DET
ejpam-6395	28	4	notion	notion	NOUN
ejpam-6395	28	5	of	of	ADP
ejpam-6395	28	6	a	a	DET
ejpam-6395	28	7	power	power	NOUN
ejpam-6395	28	8	semigroup	semigroup	NOUN
ejpam-6395	28	9	p	p	X
ejpam-6395	28	10	(	(	PUNCT
ejpam-6395	28	11	s	s	NOUN
ejpam-6395	28	12	)	)	PUNCT
ejpam-6395	28	13	and	and	CCONJ
ejpam-6395	28	14	explored	explore	VERB
ejpam-6395	28	15	isomorphism	isomorphism	NOUN
ejpam-6395	28	16	problems	problem	NOUN
ejpam-6395	28	17	related	relate	VERB
ejpam-6395	28	18	to	to	ADP
ejpam-6395	28	19	a	a	DET
ejpam-6395	28	20	power	power	NOUN
ejpam-6395	28	21	semigroup	semigroup	NOUN
ejpam-6395	29	1	[	[	X
ejpam-6395	29	2	13	13	NUM
ejpam-6395	29	3	]	]	PUNCT
ejpam-6395	29	4	.	.	PUNCT
ejpam-6395	30	1	jeenkeaw	jeenkeaw	PROPN
ejpam-6395	30	2	and	and	CCONJ
ejpam-6395	30	3	leeratanavalee	leeratanavalee	NOUN
ejpam-6395	31	1	[	[	X
ejpam-6395	31	2	14	14	NUM
ejpam-6395	31	3	]	]	PUNCT
ejpam-6395	31	4	introduced	introduce	VERB
ejpam-6395	31	5	the	the	DET
ejpam-6395	31	6	concept	concept	NOUN
ejpam-6395	31	7	of	of	ADP
ejpam-6395	31	8	power	power	NOUN
ejpam-6395	31	9	semigroups	semigroup	NOUN
ejpam-6395	31	10	on	on	ADP
ejpam-6395	31	11	semihypergroups	semihypergroup	NOUN
ejpam-6395	31	12	by	by	ADP
ejpam-6395	31	13	using	use	VERB
ejpam-6395	31	14	the	the	DET
ejpam-6395	31	15	concept	concept	NOUN
ejpam-6395	31	16	of	of	ADP
ejpam-6395	31	17	power	power	NOUN
ejpam-6395	31	18	groups	group	NOUN
ejpam-6395	31	19	on	on	ADP
ejpam-6395	31	20	hypergroups	hypergroup	NOUN
ejpam-6395	31	21	introduced	introduce	VERB
ejpam-6395	31	22	by	by	ADP
ejpam-6395	31	23	ma	ma	PROPN
ejpam-6395	31	24	,	,	PUNCT
ejpam-6395	31	25	mi	mi	PROPN
ejpam-6395	31	26	,	,	PUNCT
ejpam-6395	31	27	and	and	CCONJ
ejpam-6395	31	28	huo	huo	NOUN
ejpam-6395	31	29	[	[	X
ejpam-6395	31	30	15	15	NUM
ejpam-6395	31	31	]	]	PUNCT
ejpam-6395	31	32	.	.	PUNCT
ejpam-6395	32	1	by	by	ADP
ejpam-6395	32	2	extending	extend	VERB
ejpam-6395	32	3	the	the	DET
ejpam-6395	32	4	concept	concept	NOUN
ejpam-6395	32	5	of	of	ADP
ejpam-6395	32	6	power	power	NOUN
ejpam-6395	32	7	semigroup	semigroup	NOUN
ejpam-6395	32	8	on	on	ADP
ejpam-6395	32	9	semihypergroups	semihypergroup	NOUN
ejpam-6395	32	10	,	,	PUNCT
ejpam-6395	32	11	the	the	DET
ejpam-6395	32	12	concept	concept	NOUN
ejpam-6395	32	13	of	of	ADP
ejpam-6395	32	14	ternary	ternary	ADJ
ejpam-6395	32	15	semigroups	semigroup	NOUN
ejpam-6395	32	16	on	on	ADP
ejpam-6395	32	17	ternary	ternary	ADJ
ejpam-6395	32	18	semihypergroups	semihypergroup	NOUN
ejpam-6395	32	19	was	be	AUX
ejpam-6395	32	20	introduced	introduce	VERB
ejpam-6395	32	21	by	by	ADP
ejpam-6395	32	22	nongmanee	nongmanee	NOUN
ejpam-6395	32	23	et	et	PROPN
ejpam-6395	32	24	al	al	PROPN
ejpam-6395	32	25	.	.	PROPN
ejpam-6395	33	1	in	in	ADP
ejpam-6395	33	2	2025	2025	NUM
ejpam-6395	33	3	[	[	X
ejpam-6395	33	4	16	16	NUM
ejpam-6395	33	5	]	]	PUNCT
ejpam-6395	33	6	.	.	PUNCT
ejpam-6395	34	1	the	the	DET
ejpam-6395	34	2	notion	notion	NOUN
ejpam-6395	34	3	of	of	ADP
ejpam-6395	34	4	power	power	NOUN
ejpam-6395	34	5	ordered	order	VERB
ejpam-6395	34	6	sets	set	NOUN
ejpam-6395	34	7	was	be	AUX
ejpam-6395	34	8	presented	present	VERB
ejpam-6395	34	9	by	by	ADP
ejpam-6395	34	10	szymanska	szymanska	NOUN
ejpam-6395	34	11	and	and	CCONJ
ejpam-6395	34	12	schweigert	schweigert	NOUN
ejpam-6395	34	13	[	[	X
ejpam-6395	34	14	17	17	NUM
ejpam-6395	34	15	]	]	PUNCT
ejpam-6395	34	16	.	.	PUNCT
ejpam-6395	35	1	this	this	DET
ejpam-6395	35	2	concept	concept	NOUN
ejpam-6395	35	3	stands	stand	VERB
ejpam-6395	35	4	between	between	ADP
ejpam-6395	35	5	power	power	NOUN
ejpam-6395	35	6	sets	set	NOUN
ejpam-6395	35	7	and	and	CCONJ
ejpam-6395	35	8	power	power	NOUN
ejpam-6395	35	9	relations	relation	NOUN
ejpam-6395	35	10	.	.	PUNCT
ejpam-6395	36	1	they	they	PRON
ejpam-6395	36	2	proved	prove	VERB
ejpam-6395	36	3	that	that	SCONJ
ejpam-6395	36	4	this	this	DET
ejpam-6395	36	5	power	power	NOUN
ejpam-6395	36	6	relation	relation	NOUN
ejpam-6395	36	7	is	be	AUX
ejpam-6395	36	8	antisymmetric	antisymmetric	VERB
ejpam-6395	36	9	by	by	ADP
ejpam-6395	36	10	using	use	VERB
ejpam-6395	36	11	the	the	DET
ejpam-6395	36	12	theorem	theorem	NOUN
ejpam-6395	36	13	of	of	ADP
ejpam-6395	36	14	cantor	cantor	PROPN
ejpam-6395	36	15	-	-	PUNCT
ejpam-6395	36	16	bernstein	bernstein	PROPN
ejpam-6395	36	17	.	.	PUNCT
ejpam-6395	37	1	jeenkeaw	jeenkeaw	PROPN
ejpam-6395	37	2	and	and	CCONJ
ejpam-6395	37	3	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	37	4	combined	combine	VERB
ejpam-6395	37	5	this	this	DET
ejpam-6395	37	6	power	power	NOUN
ejpam-6395	37	7	relation	relation	NOUN
ejpam-6395	37	8	and	and	CCONJ
ejpam-6395	37	9	the	the	DET
ejpam-6395	37	10	concept	concept	NOUN
ejpam-6395	37	11	of	of	ADP
ejpam-6395	37	12	power	power	NOUN
ejpam-6395	37	13	semigroups	semigroup	NOUN
ejpam-6395	37	14	on	on	ADP
ejpam-6395	37	15	semihypergroups	semihypergroup	NOUN
ejpam-6395	37	16	to	to	PART
ejpam-6395	37	17	construct	construct	VERB
ejpam-6395	37	18	the	the	DET
ejpam-6395	37	19	algebraic	algebraic	ADJ
ejpam-6395	37	20	structure	structure	NOUN
ejpam-6395	37	21	called	call	VERB
ejpam-6395	37	22	ordered	order	VERB
ejpam-6395	37	23	power	power	NOUN
ejpam-6395	37	24	semigroups	semigroup	NOUN
ejpam-6395	37	25	on	on	ADP
ejpam-6395	37	26	semihypergroups	semihypergroup	NOUN
ejpam-6395	37	27	induced	induce	VERB
ejpam-6395	37	28	by	by	ADP
ejpam-6395	37	29	posets	poset	NOUN
ejpam-6395	37	30	and	and	CCONJ
ejpam-6395	37	31	study	study	VERB
ejpam-6395	37	32	its	its	PRON
ejpam-6395	37	33	algebraic	algebraic	ADJ
ejpam-6395	37	34	properties	property	NOUN
ejpam-6395	37	35	[	[	X
ejpam-6395	37	36	18	18	NUM
ejpam-6395	37	37	]	]	PUNCT
ejpam-6395	37	38	.	.	PUNCT
ejpam-6395	38	1	ahsan	ahsan	PROPN
ejpam-6395	38	2	and	and	CCONJ
ejpam-6395	38	3	takahashi	takahashi	PROPN
ejpam-6395	38	4	studied	study	VERB
ejpam-6395	38	5	pure	pure	ADJ
ejpam-6395	38	6	ideals	ideal	NOUN
ejpam-6395	38	7	in	in	ADP
ejpam-6395	38	8	semigroups	semigroup	NOUN
ejpam-6395	38	9	[	[	X
ejpam-6395	38	10	19	19	NUM
ejpam-6395	38	11	]	]	PUNCT
ejpam-6395	38	12	.	.	PUNCT
ejpam-6395	39	1	bashir	bashir	PROPN
ejpam-6395	39	2	and	and	CCONJ
ejpam-6395	39	3	shabir	shabir	PROPN
ejpam-6395	39	4	studied	study	VERB
ejpam-6395	39	5	pure	pure	ADJ
ejpam-6395	39	6	ideals	ideal	NOUN
ejpam-6395	39	7	in	in	ADP
ejpam-6395	39	8	ternary	ternary	ADJ
ejpam-6395	39	9	semigroups	semigroup	NOUN
ejpam-6395	39	10	[	[	X
ejpam-6395	39	11	20	20	NUM
ejpam-6395	39	12	]	]	PUNCT
ejpam-6395	39	13	.	.	PUNCT
ejpam-6395	40	1	after	after	ADP
ejpam-6395	40	2	that	that	PRON
ejpam-6395	40	3	,	,	PUNCT
ejpam-6395	40	4	changphas	changphas	ADJ
ejpam-6395	40	5	and	and	CCONJ
ejpam-6395	40	6	sanborisoot	sanborisoot	PROPN
ejpam-6395	40	7	extended	extend	VERB
ejpam-6395	40	8	their	their	PRON
ejpam-6395	40	9	results	result	NOUN
ejpam-6395	40	10	to	to	PART
ejpam-6395	40	11	study	study	VERB
ejpam-6395	40	12	on	on	ADP
ejpam-6395	40	13	ordered	order	VERB
ejpam-6395	40	14	semigroups	semigroup	NOUN
ejpam-6395	40	15	and	and	CCONJ
ejpam-6395	40	16	ordered	order	VERB
ejpam-6395	40	17	ternary	ternary	ADJ
ejpam-6395	40	18	semigroups	semigroup	NOUN
ejpam-6395	40	19	[	[	X
ejpam-6395	40	20	21	21	NUM
ejpam-6395	40	21	,	,	PUNCT
ejpam-6395	40	22	22	22	NUM
ejpam-6395	40	23	]	]	PUNCT
ejpam-6395	40	24	.	.	PUNCT
ejpam-6395	41	1	in	in	ADP
ejpam-6395	41	2	this	this	DET
ejpam-6395	41	3	paper	paper	NOUN
ejpam-6395	41	4	,	,	PUNCT
ejpam-6395	41	5	we	we	PRON
ejpam-6395	41	6	establish	establish	VERB
ejpam-6395	41	7	the	the	DET
ejpam-6395	41	8	notion	notion	NOUN
ejpam-6395	41	9	of	of	ADP
ejpam-6395	41	10	ordered	order	VERB
ejpam-6395	41	11	power	power	NOUN
ejpam-6395	41	12	ternary	ternary	NOUN
ejpam-6395	41	13	semigroups	semigroup	NOUN
ejpam-6395	41	14	on	on	ADP
ejpam-6395	41	15	ternary	ternary	ADJ
ejpam-6395	41	16	semihypergroups	semihypergroup	NOUN
ejpam-6395	41	17	induced	induce	VERB
ejpam-6395	41	18	by	by	ADP
ejpam-6395	41	19	posets	poset	NOUN
ejpam-6395	41	20	.	.	PUNCT
ejpam-6395	42	1	then	then	ADV
ejpam-6395	42	2	,	,	PUNCT
ejpam-6395	42	3	we	we	PRON
ejpam-6395	42	4	study	study	VERB
ejpam-6395	42	5	pure	pure	ADJ
ejpam-6395	42	6	ideals	ideal	NOUN
ejpam-6395	42	7	in	in	ADP
ejpam-6395	42	8	ordered	order	VERB
ejpam-6395	42	9	power	power	NOUN
ejpam-6395	42	10	ternary	ternary	ADJ
ejpam-6395	42	11	semigroups	semigroup	NOUN
ejpam-6395	42	12	on	on	ADP
ejpam-6395	42	13	ternary	ternary	ADJ
ejpam-6395	42	14	semihypergroups	semihypergroup	NOUN
ejpam-6395	42	15	induced	induce	VERB
ejpam-6395	42	16	by	by	ADP
ejpam-6395	42	17	posets	poset	NOUN
ejpam-6395	42	18	and	and	CCONJ
ejpam-6395	42	19	examine	examine	VERB
ejpam-6395	42	20	their	their	PRON
ejpam-6395	42	21	algebraic	algebraic	ADJ
ejpam-6395	42	22	properties	property	NOUN
ejpam-6395	42	23	.	.	PUNCT
ejpam-6395	43	1	finally	finally	ADV
ejpam-6395	43	2	,	,	PUNCT
ejpam-6395	43	3	we	we	PRON
ejpam-6395	43	4	investigate	investigate	VERB
ejpam-6395	43	5	some	some	DET
ejpam-6395	43	6	interesting	interesting	ADJ
ejpam-6395	43	7	results	result	NOUN
ejpam-6395	43	8	of	of	ADP
ejpam-6395	43	9	weakly	weakly	ADJ
ejpam-6395	43	10	pure	pure	ADJ
ejpam-6395	43	11	ideals	ideal	NOUN
ejpam-6395	43	12	in	in	ADP
ejpam-6395	43	13	ordered	order	VERB
ejpam-6395	43	14	power	power	NOUN
ejpam-6395	43	15	ternary	ternary	ADJ
ejpam-6395	43	16	semigroups	semigroup	NOUN
ejpam-6395	43	17	on	on	ADP
ejpam-6395	43	18	ternary	ternary	ADJ
ejpam-6395	43	19	semihypergroups	semihypergroup	NOUN
ejpam-6395	43	20	induced	induce	VERB
ejpam-6395	43	21	by	by	ADP
ejpam-6395	43	22	posets	poset	NOUN
ejpam-6395	43	23	.	.	PUNCT
ejpam-6395	44	1	2	2	X
ejpam-6395	44	2	.	.	X
ejpam-6395	44	3	preliminaries	preliminary	NOUN
ejpam-6395	44	4	first	first	ADV
ejpam-6395	44	5	,	,	PUNCT
ejpam-6395	44	6	we	we	PRON
ejpam-6395	44	7	recall	recall	VERB
ejpam-6395	44	8	the	the	DET
ejpam-6395	44	9	definition	definition	NOUN
ejpam-6395	44	10	of	of	ADP
ejpam-6395	44	11	ternary	ternary	ADJ
ejpam-6395	44	12	semigroups	semigroup	NOUN
ejpam-6395	44	13	by	by	ADP
ejpam-6395	44	14	lehmer	lehmer	NOUN
ejpam-6395	44	15	[	[	X
ejpam-6395	44	16	1	1	NUM
ejpam-6395	44	17	]	]	PUNCT
ejpam-6395	44	18	as	as	SCONJ
ejpam-6395	44	19	follows	follow	VERB
ejpam-6395	44	20	:	:	PUNCT
ejpam-6395	44	21	let	let	VERB
ejpam-6395	44	22	t	t	NOUN
ejpam-6395	44	23	be	be	AUX
ejpam-6395	44	24	a	a	DET
ejpam-6395	44	25	nonempty	nonempty	ADV
ejpam-6395	44	26	set	set	VERB
ejpam-6395	44	27	and	and	CCONJ
ejpam-6395	44	28	∗	∗	NOUN
ejpam-6395	44	29	:	:	PUNCT
ejpam-6395	44	30	t×t×t	t×t×t	NOUN
ejpam-6395	44	31	→	→	SYM
ejpam-6395	44	32	t	t	PROPN
ejpam-6395	44	33	be	be	AUX
ejpam-6395	44	34	a	a	DET
ejpam-6395	44	35	mapping	mapping	NOUN
ejpam-6395	44	36	which	which	PRON
ejpam-6395	44	37	satisfies	satisfy	VERB
ejpam-6395	44	38	the	the	DET
ejpam-6395	44	39	ternary	ternary	ADJ
ejpam-6395	44	40	associative	associative	ADJ
ejpam-6395	44	41	law	law	NOUN
ejpam-6395	44	42	,	,	PUNCT
ejpam-6395	44	43	i.e.	i.e.	X
ejpam-6395	44	44	,	,	PUNCT
ejpam-6395	44	45	∗(∗(a	∗(∗(a	NOUN
ejpam-6395	44	46	,	,	PUNCT
ejpam-6395	44	47	b	b	NOUN
ejpam-6395	44	48	,	,	PUNCT
ejpam-6395	44	49	c	c	NOUN
ejpam-6395	44	50	)	)	PUNCT
ejpam-6395	44	51	,	,	PUNCT
ejpam-6395	45	1	d	d	X
ejpam-6395	45	2	,	,	PUNCT
ejpam-6395	45	3	e	e	NOUN
ejpam-6395	45	4	)	)	PUNCT
ejpam-6395	45	5	=	=	SYM
ejpam-6395	45	6	∗(a	∗(a	NOUN
ejpam-6395	45	7	,	,	PUNCT
ejpam-6395	45	8	∗(b	∗(b	PROPN
ejpam-6395	45	9	,	,	PUNCT
ejpam-6395	45	10	c	c	X
ejpam-6395	45	11	,	,	PUNCT
ejpam-6395	45	12	d	d	NOUN
ejpam-6395	45	13	)	)	PUNCT
ejpam-6395	45	14	,	,	PUNCT
ejpam-6395	45	15	e	e	X
ejpam-6395	45	16	)	)	PUNCT
ejpam-6395	45	17	=	=	SYM
ejpam-6395	46	1	∗(a	∗(a	ADJ
ejpam-6395	46	2	,	,	PUNCT
ejpam-6395	46	3	b	b	NOUN
ejpam-6395	46	4	,	,	PUNCT
ejpam-6395	46	5	∗(c	∗(c	NOUN
ejpam-6395	46	6	,	,	PUNCT
ejpam-6395	46	7	d	d	NOUN
ejpam-6395	46	8	,	,	PUNCT
ejpam-6395	46	9	e	e	NOUN
ejpam-6395	46	10	)	)	PUNCT
ejpam-6395	46	11	)	)	PUNCT
ejpam-6395	46	12	for	for	ADP
ejpam-6395	46	13	all	all	DET
ejpam-6395	46	14	a	a	DET
ejpam-6395	46	15	,	,	PUNCT
ejpam-6395	46	16	b	b	NOUN
ejpam-6395	46	17	,	,	PUNCT
ejpam-6395	46	18	c	c	NOUN
ejpam-6395	46	19	,	,	PUNCT
ejpam-6395	46	20	d	d	NOUN
ejpam-6395	46	21	,	,	PUNCT
ejpam-6395	46	22	e	e	PROPN
ejpam-6395	46	23	∈	∈	PROPN
ejpam-6395	46	24	t	t	PROPN
ejpam-6395	46	25	.	.	PUNCT
ejpam-6395	47	1	then	then	ADV
ejpam-6395	47	2	we	we	PRON
ejpam-6395	47	3	call	call	VERB
ejpam-6395	47	4	(	(	PUNCT
ejpam-6395	47	5	t	t	PROPN
ejpam-6395	47	6	,	,	PUNCT
ejpam-6395	47	7	∗	∗	NOUN
ejpam-6395	47	8	)	)	PUNCT
ejpam-6395	47	9	,	,	PUNCT
ejpam-6395	47	10	a	a	DET
ejpam-6395	47	11	ternary	ternary	ADJ
ejpam-6395	47	12	semigroup	semigroup	NOUN
ejpam-6395	47	13	.	.	PUNCT
ejpam-6395	48	1	let	let	VERB
ejpam-6395	48	2	h	h	PRON
ejpam-6395	48	3	be	be	AUX
ejpam-6395	48	4	a	a	DET
ejpam-6395	48	5	nonempty	nonempty	ADJ
ejpam-6395	48	6	subset	subset	NOUN
ejpam-6395	48	7	of	of	ADP
ejpam-6395	48	8	a	a	DET
ejpam-6395	48	9	ternary	ternary	ADJ
ejpam-6395	48	10	semigroup	semigroup	NOUN
ejpam-6395	48	11	(	(	PUNCT
ejpam-6395	48	12	t	t	PROPN
ejpam-6395	48	13	,	,	PUNCT
ejpam-6395	48	14	∗	∗	NOUN
ejpam-6395	48	15	)	)	PUNCT
ejpam-6395	48	16	.	.	PUNCT
ejpam-6395	49	1	if	if	SCONJ
ejpam-6395	49	2	h	h	NOUN
ejpam-6395	49	3	is	be	AUX
ejpam-6395	49	4	closed	close	VERB
ejpam-6395	49	5	under	under	ADP
ejpam-6395	49	6	∗	∗	NOUN
ejpam-6395	49	7	,	,	PUNCT
ejpam-6395	49	8	i.e.	i.e.	X
ejpam-6395	49	9	,	,	PUNCT
ejpam-6395	49	10	∗(x	∗(x	PROPN
ejpam-6395	49	11	,	,	PUNCT
ejpam-6395	49	12	y	y	PROPN
ejpam-6395	49	13	,	,	PUNCT
ejpam-6395	49	14	z	z	NOUN
ejpam-6395	49	15	)	)	PUNCT
ejpam-6395	49	16	∈	∈	PROPN
ejpam-6395	49	17	h	h	NOUN
ejpam-6395	49	18	for	for	ADP
ejpam-6395	49	19	all	all	DET
ejpam-6395	49	20	x	x	NOUN
ejpam-6395	49	21	,	,	PUNCT
ejpam-6395	49	22	y	y	PROPN
ejpam-6395	49	23	,	,	PUNCT
ejpam-6395	49	24	z	z	PROPN
ejpam-6395	49	25	∈	∈	PROPN
ejpam-6395	49	26	h	h	NOUN
ejpam-6395	49	27	then	then	ADV
ejpam-6395	49	28	(	(	PUNCT
ejpam-6395	49	29	h	h	NOUN
ejpam-6395	49	30	,	,	PUNCT
ejpam-6395	49	31	∗	∗	NOUN
ejpam-6395	49	32	)	)	PUNCT
ejpam-6395	49	33	is	be	AUX
ejpam-6395	49	34	called	call	VERB
ejpam-6395	49	35	a	a	DET
ejpam-6395	49	36	ternary	ternary	ADJ
ejpam-6395	49	37	subsemigroup	subsemigroup	NOUN
ejpam-6395	49	38	.	.	PUNCT
ejpam-6395	50	1	the	the	DET
ejpam-6395	50	2	algebraic	algebraic	ADJ
ejpam-6395	50	3	structures	structure	NOUN
ejpam-6395	50	4	of	of	ADP
ejpam-6395	50	5	ternary	ternary	ADJ
ejpam-6395	50	6	semigroups	semigroup	NOUN
ejpam-6395	50	7	can	can	AUX
ejpam-6395	50	8	be	be	AUX
ejpam-6395	50	9	considered	consider	VERB
ejpam-6395	50	10	as	as	ADP
ejpam-6395	50	11	the	the	DET
ejpam-6395	50	12	special	special	ADJ
ejpam-6395	50	13	case	case	NOUN
ejpam-6395	50	14	of	of	ADP
ejpam-6395	50	15	ternary	ternary	ADJ
ejpam-6395	50	16	semihypergroups	semihypergroup	NOUN
ejpam-6395	50	17	.	.	PUNCT
ejpam-6395	51	1	we	we	PRON
ejpam-6395	51	2	now	now	ADV
ejpam-6395	51	3	recall	recall	VERB
ejpam-6395	51	4	some	some	DET
ejpam-6395	51	5	definitions	definition	NOUN
ejpam-6395	51	6	of	of	ADP
ejpam-6395	51	7	an	an	DET
ejpam-6395	51	8	algebraic	algebraic	ADJ
ejpam-6395	51	9	hyperstructure	hyperstructure	NOUN
ejpam-6395	51	10	of	of	ADP
ejpam-6395	51	11	ternary	ternary	ADJ
ejpam-6395	51	12	semihypergroups	semihypergroup	NOUN
ejpam-6395	52	1	[	[	X
ejpam-6395	52	2	9	9	NUM
ejpam-6395	52	3	]	]	PUNCT
ejpam-6395	52	4	as	as	SCONJ
ejpam-6395	52	5	follows	follow	VERB
ejpam-6395	52	6	:	:	PUNCT
ejpam-6395	52	7	let	let	VERB
ejpam-6395	52	8	s	s	PRON
ejpam-6395	52	9	be	be	AUX
ejpam-6395	52	10	a	a	DET
ejpam-6395	52	11	nonempty	nonempty	ADV
ejpam-6395	52	12	set	set	VERB
ejpam-6395	52	13	and	and	CCONJ
ejpam-6395	52	14	⋄	⋄	NOUN
ejpam-6395	52	15	:	:	PUNCT
ejpam-6395	52	16	s	s	AUX
ejpam-6395	52	17	×	×	PROPN
ejpam-6395	52	18	s	s	PART
ejpam-6395	52	19	×	×	NOUN
ejpam-6395	52	20	s	s	X
ejpam-6395	52	21	→	→	SYM
ejpam-6395	52	22	p∗(s	p∗(s	NOUN
ejpam-6395	52	23	)	)	PUNCT
ejpam-6395	52	24	be	be	AUX
ejpam-6395	52	25	a	a	DET
ejpam-6395	52	26	mapping	mapping	NOUN
ejpam-6395	52	27	which	which	PRON
ejpam-6395	52	28	is	be	AUX
ejpam-6395	52	29	called	call	VERB
ejpam-6395	52	30	a	a	DET
ejpam-6395	52	31	ternary	ternary	ADJ
ejpam-6395	52	32	hyperoperation	hyperoperation	NOUN
ejpam-6395	52	33	where	where	SCONJ
ejpam-6395	52	34	p∗(s	p∗(s	NOUN
ejpam-6395	52	35	)	)	PUNCT
ejpam-6395	52	36	a.	a.	NOUN
ejpam-6395	52	37	nongmanee	nongmanee	NOUN
ejpam-6395	52	38	,	,	PUNCT
ejpam-6395	52	39	k.	k.	PROPN
ejpam-6395	52	40	jeenkaew	jeenkaew	PROPN
ejpam-6395	52	41	,	,	PUNCT
ejpam-6395	52	42	m.	m.	NOUN
ejpam-6395	52	43	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	52	44	/	/	SYM
ejpam-6395	52	45	eur	eur	PROPN
ejpam-6395	52	46	.	.	PUNCT
ejpam-6395	53	1	j.	j.	PROPN
ejpam-6395	53	2	pure	pure	PROPN
ejpam-6395	53	3	appl	appl	PROPN
ejpam-6395	53	4	.	.	PROPN
ejpam-6395	53	5	math	math	PROPN
ejpam-6395	53	6	,	,	PUNCT
ejpam-6395	53	7	18	18	NUM
ejpam-6395	53	8	(	(	PUNCT
ejpam-6395	53	9	3	3	NUM
ejpam-6395	53	10	)	)	PUNCT
ejpam-6395	53	11	(	(	PUNCT
ejpam-6395	53	12	2025	2025	NUM
ejpam-6395	53	13	)	)	PUNCT
ejpam-6395	53	14	,	,	PUNCT
ejpam-6395	53	15	6395	6395	NUM
ejpam-6395	53	16	3	3	NUM
ejpam-6395	53	17	of	of	ADP
ejpam-6395	53	18	12	12	NUM
ejpam-6395	53	19	is	be	AUX
ejpam-6395	53	20	the	the	DET
ejpam-6395	53	21	family	family	NOUN
ejpam-6395	53	22	of	of	ADP
ejpam-6395	53	23	nonempty	nonempty	ADJ
ejpam-6395	53	24	subsets	subset	NOUN
ejpam-6395	53	25	of	of	ADP
ejpam-6395	53	26	s.	s.	PROPN
ejpam-6395	53	27	an	an	DET
ejpam-6395	53	28	algebraic	algebraic	ADJ
ejpam-6395	53	29	hyperstructure	hyperstructure	NOUN
ejpam-6395	53	30	(	(	PUNCT
ejpam-6395	53	31	s	s	PROPN
ejpam-6395	53	32	,	,	PUNCT
ejpam-6395	53	33	⋄	⋄	PROPN
ejpam-6395	53	34	)	)	PUNCT
ejpam-6395	53	35	is	be	AUX
ejpam-6395	53	36	called	call	VERB
ejpam-6395	53	37	a	a	DET
ejpam-6395	53	38	ternary	ternary	ADJ
ejpam-6395	53	39	hypergroupoid	hypergroupoid	NOUN
ejpam-6395	53	40	.	.	PUNCT
ejpam-6395	54	1	additionally	additionally	ADV
ejpam-6395	54	2	,	,	PUNCT
ejpam-6395	54	3	for	for	ADP
ejpam-6395	54	4	any	any	DET
ejpam-6395	54	5	a	a	DET
ejpam-6395	54	6	,	,	PUNCT
ejpam-6395	54	7	b	b	NOUN
ejpam-6395	54	8	,	,	PUNCT
ejpam-6395	54	9	c	c	PROPN
ejpam-6395	54	10	∈	∈	PROPN
ejpam-6395	54	11	p∗(s	p∗(s	PROPN
ejpam-6395	54	12	)	)	PUNCT
ejpam-6395	54	13	,	,	PUNCT
ejpam-6395	54	14	we	we	PRON
ejpam-6395	54	15	can	can	AUX
ejpam-6395	54	16	define	define	VERB
ejpam-6395	54	17	⋄(a	⋄(a	PROPN
ejpam-6395	54	18	,	,	PUNCT
ejpam-6395	54	19	b	b	NOUN
ejpam-6395	54	20	,	,	PUNCT
ejpam-6395	54	21	c	c	NOUN
ejpam-6395	54	22	)	)	PUNCT
ejpam-6395	55	1	=	=	NOUN
ejpam-6395	55	2	⋃	⋃	NOUN
ejpam-6395	55	3	a∈a	a∈a	ADJ
ejpam-6395	55	4	,	,	PUNCT
ejpam-6395	55	5	b∈b	b∈b	NOUN
ejpam-6395	55	6	,	,	PUNCT
ejpam-6395	55	7	c∈c	c∈c	NOUN
ejpam-6395	55	8	⋄(a	⋄(a	PROPN
ejpam-6395	55	9	,	,	PUNCT
ejpam-6395	55	10	b	b	NOUN
ejpam-6395	55	11	,	,	PUNCT
ejpam-6395	55	12	c	c	NOUN
ejpam-6395	55	13	)	)	PUNCT
ejpam-6395	55	14	.	.	PUNCT
ejpam-6395	56	1	if	if	SCONJ
ejpam-6395	56	2	a	a	DET
ejpam-6395	56	3	ternary	ternary	ADJ
ejpam-6395	56	4	hyperoperation	hyperoperation	NOUN
ejpam-6395	56	5	⋄	⋄	PROPN
ejpam-6395	56	6	satisfies	satisfy	VERB
ejpam-6395	56	7	the	the	DET
ejpam-6395	56	8	ternary	ternary	ADJ
ejpam-6395	56	9	associative	associative	ADJ
ejpam-6395	56	10	law	law	NOUN
ejpam-6395	56	11	then	then	ADV
ejpam-6395	56	12	(	(	PUNCT
ejpam-6395	56	13	s	s	X
ejpam-6395	56	14	,	,	PUNCT
ejpam-6395	56	15	⋄	⋄	PROPN
ejpam-6395	56	16	)	)	PUNCT
ejpam-6395	56	17	is	be	AUX
ejpam-6395	56	18	called	call	VERB
ejpam-6395	56	19	a	a	DET
ejpam-6395	56	20	ternary	ternary	ADJ
ejpam-6395	56	21	semihypergroup	semihypergroup	NOUN
ejpam-6395	56	22	.	.	PUNCT
ejpam-6395	57	1	definition	definition	NOUN
ejpam-6395	57	2	1	1	NUM
ejpam-6395	57	3	.	.	PUNCT
ejpam-6395	58	1	[	[	X
ejpam-6395	58	2	17	17	NUM
ejpam-6395	58	3	]	]	X
ejpam-6395	58	4	let	let	ADJ
ejpam-6395	58	5	(	(	PUNCT
ejpam-6395	58	6	e,≤	e,≤	VERB
ejpam-6395	58	7	)	)	PUNCT
ejpam-6395	58	8	be	be	AUX
ejpam-6395	58	9	a	a	DET
ejpam-6395	58	10	poset	poset	NOUN
ejpam-6395	58	11	.	.	PUNCT
ejpam-6395	59	1	the	the	DET
ejpam-6395	59	2	relation	relation	NOUN
ejpam-6395	59	3	≤p	≤p	NOUN
ejpam-6395	59	4	is	be	AUX
ejpam-6395	59	5	defined	define	VERB
ejpam-6395	59	6	on	on	ADP
ejpam-6395	59	7	p	p	PROPN
ejpam-6395	59	8	∗(e	∗(e	PROPN
ejpam-6395	59	9	)	)	PUNCT
ejpam-6395	59	10	as	as	SCONJ
ejpam-6395	59	11	follows	follow	VERB
ejpam-6395	59	12	.	.	PUNCT
ejpam-6395	60	1	for	for	ADP
ejpam-6395	60	2	any	any	DET
ejpam-6395	60	3	{	{	PUNCT
ejpam-6395	60	4	ai	ai	VERB
ejpam-6395	60	5	|	|	ADV
ejpam-6395	60	6	i	i	PRON
ejpam-6395	60	7	∈	∈	PROPN
ejpam-6395	60	8	i	i	X
ejpam-6395	60	9	}	}	PUNCT
ejpam-6395	60	10	,	,	PUNCT
ejpam-6395	60	11	{	{	PUNCT
ejpam-6395	60	12	bj	bj	VERB
ejpam-6395	60	13	|	|	ADV
ejpam-6395	60	14	j	j	PROPN
ejpam-6395	60	15	∈	∈	PROPN
ejpam-6395	60	16	j	j	PROPN
ejpam-6395	60	17	}	}	PUNCT
ejpam-6395	60	18	∈	∈	PROPN
ejpam-6395	60	19	p	p	PROPN
ejpam-6395	60	20	∗(e	∗(e	PROPN
ejpam-6395	60	21	)	)	PUNCT
ejpam-6395	60	22	,	,	PUNCT
ejpam-6395	60	23	we	we	PRON
ejpam-6395	60	24	have	have	AUX
ejpam-6395	60	25	{	{	PUNCT
ejpam-6395	60	26	ai	ai	VERB
ejpam-6395	60	27	|	|	ADV
ejpam-6395	61	1	i	i	PRON
ejpam-6395	61	2	∈	∈	PROPN
ejpam-6395	61	3	i	i	PRON
ejpam-6395	61	4	}	}	PUNCT
ejpam-6395	61	5	≤p	≤p	NOUN
ejpam-6395	61	6	{	{	PUNCT
ejpam-6395	61	7	bj	bj	NOUN
ejpam-6395	61	8	|	|	ADV
ejpam-6395	61	9	j	j	PROPN
ejpam-6395	61	10	∈	∈	PROPN
ejpam-6395	61	11	j	j	PROPN
ejpam-6395	61	12	}	}	PUNCT
ejpam-6395	61	13	if	if	SCONJ
ejpam-6395	61	14	and	and	CCONJ
ejpam-6395	61	15	only	only	ADV
ejpam-6395	61	16	if	if	SCONJ
ejpam-6395	61	17	there	there	PRON
ejpam-6395	61	18	exists	exist	VERB
ejpam-6395	61	19	an	an	DET
ejpam-6395	61	20	injective	injective	ADJ
ejpam-6395	61	21	mapping	mapping	NOUN
ejpam-6395	61	22	π	π	NOUN
ejpam-6395	61	23	:	:	PUNCT
ejpam-6395	61	24	{	{	PUNCT
ejpam-6395	61	25	ai	ai	VERB
ejpam-6395	61	26	|	|	ADV
ejpam-6395	62	1	i	i	PRON
ejpam-6395	62	2	∈	∈	PROPN
ejpam-6395	63	1	i	i	PRON
ejpam-6395	63	2	}	}	PUNCT
ejpam-6395	63	3	→	→	PUNCT
ejpam-6395	63	4	{	{	PUNCT
ejpam-6395	63	5	bj	bj	NOUN
ejpam-6395	63	6	|	|	ADV
ejpam-6395	63	7	j	j	PROPN
ejpam-6395	63	8	∈	∈	PROPN
ejpam-6395	63	9	j	j	PROPN
ejpam-6395	63	10	}	}	PUNCT
ejpam-6395	64	1	such	such	ADJ
ejpam-6395	64	2	that	that	PRON
ejpam-6395	64	3	ai	ai	VERB
ejpam-6395	64	4	≤	≤	ADJ
ejpam-6395	64	5	π	π	NOUN
ejpam-6395	64	6	(	(	PUNCT
ejpam-6395	64	7	ai	ai	NOUN
ejpam-6395	64	8	)	)	PUNCT
ejpam-6395	64	9	for	for	ADP
ejpam-6395	64	10	i	i	PRON
ejpam-6395	64	11	∈	∈	PROPN
ejpam-6395	65	1	i	i	PRON
ejpam-6395	65	2	and	and	CCONJ
ejpam-6395	65	3	{	{	PUNCT
ejpam-6395	65	4	π(ai	π(ai	PROPN
ejpam-6395	65	5	)	)	PUNCT
ejpam-6395	66	1	|	|	ADV
ejpam-6395	66	2	i	i	PRON
ejpam-6395	66	3	∈	∈	VERB
ejpam-6395	66	4	i	i	PRON
ejpam-6395	66	5	}	}	PUNCT
ejpam-6395	66	6	⊆	⊆	NUM
ejpam-6395	66	7	{	{	PUNCT
ejpam-6395	66	8	bj	bj	NOUN
ejpam-6395	66	9	|	|	ADV
ejpam-6395	66	10	j	j	PROPN
ejpam-6395	66	11	∈	∈	PROPN
ejpam-6395	66	12	j	j	PROPN
ejpam-6395	66	13	}	}	PUNCT
ejpam-6395	66	14	.	.	PUNCT
ejpam-6395	67	1	theorem	theorem	NOUN
ejpam-6395	67	2	1	1	NUM
ejpam-6395	67	3	.	.	PUNCT
ejpam-6395	68	1	[	[	X
ejpam-6395	68	2	17	17	NUM
ejpam-6395	68	3	]	]	PUNCT
ejpam-6395	68	4	the	the	DET
ejpam-6395	68	5	relation	relation	NOUN
ejpam-6395	68	6	≤p	≤p	NOUN
ejpam-6395	68	7	is	be	AUX
ejpam-6395	68	8	antisymmetric	antisymmetric	ADJ
ejpam-6395	68	9	.	.	PUNCT
ejpam-6395	69	1	we	we	PRON
ejpam-6395	69	2	can	can	AUX
ejpam-6395	69	3	see	see	VERB
ejpam-6395	69	4	that	that	SCONJ
ejpam-6395	69	5	the	the	DET
ejpam-6395	69	6	relation	relation	NOUN
ejpam-6395	69	7	≤p	≤p	NOUN
ejpam-6395	69	8	is	be	AUX
ejpam-6395	69	9	also	also	ADV
ejpam-6395	69	10	reflexive	reflexive	ADJ
ejpam-6395	69	11	and	and	CCONJ
ejpam-6395	69	12	transitive	transitive	ADJ
ejpam-6395	69	13	.	.	PUNCT
ejpam-6395	70	1	that	that	PRON
ejpam-6395	70	2	means	mean	VERB
ejpam-6395	70	3	,	,	PUNCT
ejpam-6395	70	4	it	it	PRON
ejpam-6395	70	5	is	be	AUX
ejpam-6395	70	6	a	a	DET
ejpam-6395	70	7	partial	partial	ADJ
ejpam-6395	70	8	order	order	NOUN
ejpam-6395	70	9	.	.	PUNCT
ejpam-6395	71	1	then	then	ADV
ejpam-6395	71	2	(	(	PUNCT
ejpam-6395	71	3	p	p	NOUN
ejpam-6395	71	4	∗(e),≤p	∗(e),≤p	PROPN
ejpam-6395	71	5	)	)	PUNCT
ejpam-6395	71	6	is	be	AUX
ejpam-6395	71	7	a	a	DET
ejpam-6395	71	8	partially	partially	ADV
ejpam-6395	71	9	ordered	order	VERB
ejpam-6395	71	10	set	set	NOUN
ejpam-6395	71	11	which	which	PRON
ejpam-6395	71	12	is	be	AUX
ejpam-6395	71	13	called	call	VERB
ejpam-6395	71	14	an	an	DET
ejpam-6395	71	15	ordered	order	VERB
ejpam-6395	71	16	power	power	NOUN
ejpam-6395	71	17	set	set	NOUN
ejpam-6395	71	18	[	[	X
ejpam-6395	71	19	17	17	NUM
ejpam-6395	71	20	]	]	PUNCT
ejpam-6395	71	21	.	.	PUNCT
ejpam-6395	72	1	we	we	PRON
ejpam-6395	72	2	now	now	ADV
ejpam-6395	72	3	recall	recall	VERB
ejpam-6395	72	4	the	the	DET
ejpam-6395	72	5	definition	definition	NOUN
ejpam-6395	72	6	of	of	ADP
ejpam-6395	72	7	a	a	DET
ejpam-6395	72	8	power	power	NOUN
ejpam-6395	72	9	ternary	ternary	NOUN
ejpam-6395	72	10	semigroup	semigroup	NOUN
ejpam-6395	72	11	on	on	ADP
ejpam-6395	72	12	a	a	DET
ejpam-6395	72	13	ternary	ternary	ADJ
ejpam-6395	72	14	semihypergroup	semihypergroup	NOUN
ejpam-6395	72	15	.	.	PUNCT
ejpam-6395	73	1	definition	definition	NOUN
ejpam-6395	73	2	2	2	NUM
ejpam-6395	73	3	.	.	PUNCT
ejpam-6395	74	1	[	[	X
ejpam-6395	74	2	16	16	NUM
ejpam-6395	74	3	]	]	X
ejpam-6395	74	4	let	let	VERB
ejpam-6395	74	5	(	(	PUNCT
ejpam-6395	74	6	s	s	X
ejpam-6395	74	7	,	,	PUNCT
ejpam-6395	74	8	⋄	⋄	PROPN
ejpam-6395	74	9	)	)	PUNCT
ejpam-6395	74	10	be	be	VERB
ejpam-6395	74	11	a	a	DET
ejpam-6395	74	12	ternary	ternary	ADJ
ejpam-6395	74	13	semihypergroup	semihypergroup	NOUN
ejpam-6395	74	14	and	and	CCONJ
ejpam-6395	74	15	∅	∅	NOUN
ejpam-6395	74	16	=	=	NOUN
ejpam-6395	74	17	̸	̸	PUNCT
ejpam-6395	74	18	t	t	NOUN
ejpam-6395	74	19	⊆	⊆	NUM
ejpam-6395	74	20	p∗(s	p∗(s	NOUN
ejpam-6395	74	21	)	)	PUNCT
ejpam-6395	74	22	.	.	PUNCT
ejpam-6395	75	1	define	define	VERB
ejpam-6395	75	2	a	a	DET
ejpam-6395	75	3	ternary	ternary	ADJ
ejpam-6395	75	4	operation	operation	NOUN
ejpam-6395	75	5	•	•	NOUN
ejpam-6395	75	6	on	on	ADP
ejpam-6395	75	7	t	t	PROPN
ejpam-6395	75	8	by	by	ADP
ejpam-6395	75	9	•(x	•(x	PROPN
ejpam-6395	75	10	,	,	PUNCT
ejpam-6395	75	11	y	y	PROPN
ejpam-6395	75	12	,	,	PUNCT
ejpam-6395	75	13	z	z	NOUN
ejpam-6395	75	14	)	)	PUNCT
ejpam-6395	75	15	=	=	PUNCT
ejpam-6395	76	1	∪{⋄(x	∪{⋄(x	PROPN
ejpam-6395	76	2	,	,	PUNCT
ejpam-6395	76	3	y	y	PROPN
ejpam-6395	76	4	,	,	PUNCT
ejpam-6395	76	5	z	z	NOUN
ejpam-6395	76	6	)	)	PUNCT
ejpam-6395	77	1	|	|	ADV
ejpam-6395	77	2	x	x	SYM
ejpam-6395	77	3	∈	∈	PROPN
ejpam-6395	77	4	x	x	X
ejpam-6395	77	5	,	,	PUNCT
ejpam-6395	77	6	y	y	PROPN
ejpam-6395	77	7	∈	∈	PROPN
ejpam-6395	77	8	y	y	PROPN
ejpam-6395	77	9	,	,	PUNCT
ejpam-6395	77	10	z	z	PROPN
ejpam-6395	77	11	∈	∈	PROPN
ejpam-6395	78	1	z	z	X
ejpam-6395	78	2	}	}	PUNCT
ejpam-6395	78	3	for	for	ADP
ejpam-6395	78	4	all	all	DET
ejpam-6395	78	5	x	x	NOUN
ejpam-6395	78	6	,	,	PUNCT
ejpam-6395	78	7	y	y	PROPN
ejpam-6395	78	8	,	,	PUNCT
ejpam-6395	78	9	z	z	PROPN
ejpam-6395	78	10	∈	∈	PROPN
ejpam-6395	78	11	t	t	PROPN
ejpam-6395	78	12	.	.	PUNCT
ejpam-6395	79	1	note	note	VERB
ejpam-6395	79	2	here	here	ADV
ejpam-6395	79	3	that	that	SCONJ
ejpam-6395	79	4	the	the	DET
ejpam-6395	79	5	ternary	ternary	ADJ
ejpam-6395	79	6	semigroup	semigroup	NOUN
ejpam-6395	79	7	(	(	PUNCT
ejpam-6395	79	8	t	t	NOUN
ejpam-6395	79	9	,	,	PUNCT
ejpam-6395	79	10	•	•	X
ejpam-6395	79	11	)	)	PUNCT
ejpam-6395	79	12	is	be	AUX
ejpam-6395	79	13	called	call	VERB
ejpam-6395	79	14	a	a	DET
ejpam-6395	79	15	power	power	NOUN
ejpam-6395	79	16	ternary	ternary	NOUN
ejpam-6395	79	17	semigroup	semigroup	NOUN
ejpam-6395	79	18	on	on	ADP
ejpam-6395	79	19	a	a	DET
ejpam-6395	79	20	ternary	ternary	ADJ
ejpam-6395	79	21	semihypergroup	semihypergroup	NOUN
ejpam-6395	79	22	(	(	PUNCT
ejpam-6395	79	23	s	s	X
ejpam-6395	79	24	,	,	PUNCT
ejpam-6395	79	25	⋄	⋄	PROPN
ejpam-6395	79	26	)	)	PUNCT
ejpam-6395	79	27	.	.	PUNCT
ejpam-6395	80	1	from	from	ADP
ejpam-6395	80	2	now	now	ADV
ejpam-6395	80	3	on	on	ADV
ejpam-6395	80	4	,	,	PUNCT
ejpam-6395	80	5	we	we	PRON
ejpam-6395	80	6	will	will	AUX
ejpam-6395	80	7	combine	combine	VERB
ejpam-6395	80	8	the	the	DET
ejpam-6395	80	9	concept	concept	NOUN
ejpam-6395	80	10	of	of	ADP
ejpam-6395	80	11	an	an	DET
ejpam-6395	80	12	ordered	order	VERB
ejpam-6395	80	13	power	power	NOUN
ejpam-6395	80	14	set	set	VERB
ejpam-6395	80	15	together	together	ADV
ejpam-6395	80	16	with	with	ADP
ejpam-6395	80	17	a	a	DET
ejpam-6395	80	18	power	power	NOUN
ejpam-6395	80	19	ternary	ternary	NOUN
ejpam-6395	80	20	semigroup	semigroup	NOUN
ejpam-6395	80	21	on	on	ADP
ejpam-6395	80	22	a	a	DET
ejpam-6395	80	23	ternary	ternary	ADJ
ejpam-6395	80	24	semihypergroup	semihypergroup	NOUN
ejpam-6395	80	25	and	and	CCONJ
ejpam-6395	80	26	construct	construct	VERB
ejpam-6395	80	27	a	a	DET
ejpam-6395	80	28	new	new	ADJ
ejpam-6395	80	29	algebraic	algebraic	ADJ
ejpam-6395	80	30	structure	structure	NOUN
ejpam-6395	80	31	called	call	VERB
ejpam-6395	80	32	an	an	DET
ejpam-6395	80	33	ordered	order	VERB
ejpam-6395	80	34	power	power	NOUN
ejpam-6395	80	35	ternary	ternary	NOUN
ejpam-6395	80	36	semigroup	semigroup	NOUN
ejpam-6395	80	37	on	on	ADP
ejpam-6395	80	38	a	a	DET
ejpam-6395	80	39	ternary	ternary	ADJ
ejpam-6395	80	40	semihypergroup	semihypergroup	NOUN
ejpam-6395	80	41	induced	induce	VERB
ejpam-6395	80	42	by	by	ADP
ejpam-6395	80	43	a	a	DET
ejpam-6395	80	44	poset	poset	NOUN
ejpam-6395	80	45	.	.	PUNCT
ejpam-6395	81	1	3	3	X
ejpam-6395	81	2	.	.	NUM
ejpam-6395	81	3	ordered	order	VERB
ejpam-6395	81	4	power	power	NOUN
ejpam-6395	81	5	ternary	ternary	ADJ
ejpam-6395	81	6	semigroups	semigroup	NOUN
ejpam-6395	81	7	on	on	ADP
ejpam-6395	81	8	ternary	ternary	ADJ
ejpam-6395	81	9	semihypergroups	semihypergroup	NOUN
ejpam-6395	81	10	induced	induce	VERB
ejpam-6395	81	11	by	by	ADP
ejpam-6395	81	12	posets	poset	NOUN
ejpam-6395	81	13	definition	definition	NOUN
ejpam-6395	81	14	3	3	X
ejpam-6395	81	15	.	.	PUNCT
ejpam-6395	82	1	let	let	AUX
ejpam-6395	82	2	(	(	PUNCT
ejpam-6395	82	3	s,≤	s,≤	X
ejpam-6395	82	4	)	)	PUNCT
ejpam-6395	82	5	be	be	AUX
ejpam-6395	82	6	a	a	DET
ejpam-6395	82	7	poset	poset	NOUN
ejpam-6395	82	8	and	and	CCONJ
ejpam-6395	82	9	(	(	PUNCT
ejpam-6395	82	10	t	t	PROPN
ejpam-6395	82	11	,	,	PUNCT
ejpam-6395	82	12	•	•	X
ejpam-6395	82	13	)	)	PUNCT
ejpam-6395	82	14	be	be	AUX
ejpam-6395	82	15	a	a	DET
ejpam-6395	82	16	power	power	NOUN
ejpam-6395	82	17	ternary	ternary	ADJ
ejpam-6395	82	18	semigroup	semigroup	NOUN
ejpam-6395	82	19	on	on	ADP
ejpam-6395	82	20	ternary	ternary	ADJ
ejpam-6395	82	21	semihypergroup	semihypergroup	NOUN
ejpam-6395	82	22	(	(	PUNCT
ejpam-6395	82	23	s	s	X
ejpam-6395	82	24	,	,	PUNCT
ejpam-6395	82	25	⋄	⋄	PROPN
ejpam-6395	82	26	)	)	PUNCT
ejpam-6395	82	27	.	.	PUNCT
ejpam-6395	83	1	if	if	SCONJ
ejpam-6395	83	2	the	the	DET
ejpam-6395	83	3	relation	relation	NOUN
ejpam-6395	83	4	≤p	≤p	PROPN
ejpam-6395	83	5	,	,	PUNCT
ejpam-6395	83	6	which	which	PRON
ejpam-6395	83	7	is	be	AUX
ejpam-6395	83	8	defined	define	VERB
ejpam-6395	83	9	as	as	ADP
ejpam-6395	83	10	in	in	ADP
ejpam-6395	83	11	definition	definition	NOUN
ejpam-6395	83	12	1	1	NUM
ejpam-6395	83	13	,	,	PUNCT
ejpam-6395	83	14	is	be	AUX
ejpam-6395	83	15	compatible	compatible	ADJ
ejpam-6395	83	16	with	with	ADP
ejpam-6395	83	17	the	the	DET
ejpam-6395	83	18	operation	operation	NOUN
ejpam-6395	83	19	•	•	NOUN
ejpam-6395	83	20	restricted	restrict	VERB
ejpam-6395	83	21	to	to	ADP
ejpam-6395	83	22	t	t	PROPN
ejpam-6395	83	23	,	,	PUNCT
ejpam-6395	83	24	i.e.	i.e.	X
ejpam-6395	83	25	for	for	ADP
ejpam-6395	83	26	all	all	DET
ejpam-6395	83	27	x	x	NOUN
ejpam-6395	83	28	,	,	PUNCT
ejpam-6395	83	29	y	y	PROPN
ejpam-6395	83	30	∈	∈	PROPN
ejpam-6395	83	31	t	t	PROPN
ejpam-6395	83	32	,	,	PUNCT
ejpam-6395	83	33	x	x	SYM
ejpam-6395	83	34	≤p	≤p	NOUN
ejpam-6395	83	35	y	y	PROPN
ejpam-6395	83	36	implies	imply	VERB
ejpam-6395	83	37	•(z1	•(z1	ADJ
ejpam-6395	83	38	,	,	PUNCT
ejpam-6395	83	39	z2	z2	PROPN
ejpam-6395	83	40	,	,	PUNCT
ejpam-6395	83	41	x	x	NOUN
ejpam-6395	83	42	)	)	PUNCT
ejpam-6395	83	43	≤p	≤p	ADJ
ejpam-6395	83	44	•(z1	•(z1	NOUN
ejpam-6395	83	45	,	,	PUNCT
ejpam-6395	83	46	z2	z2	PROPN
ejpam-6395	83	47	,	,	PUNCT
ejpam-6395	83	48	y	y	PROPN
ejpam-6395	83	49	)	)	PUNCT
ejpam-6395	83	50	,	,	PUNCT
ejpam-6395	83	51	•(z1	•(z1	PROPN
ejpam-6395	83	52	,	,	PUNCT
ejpam-6395	83	53	x	x	NOUN
ejpam-6395	83	54	,	,	PUNCT
ejpam-6395	83	55	z2	z2	ADJ
ejpam-6395	83	56	)	)	PUNCT
ejpam-6395	83	57	≤p	≤p	ADJ
ejpam-6395	83	58	•(z1	•(z1	NOUN
ejpam-6395	83	59	,	,	PUNCT
ejpam-6395	83	60	y	y	PROPN
ejpam-6395	83	61	,	,	PUNCT
ejpam-6395	83	62	z2	z2	PROPN
ejpam-6395	83	63	)	)	PUNCT
ejpam-6395	83	64	and	and	CCONJ
ejpam-6395	83	65	•(x	•(x	PROPN
ejpam-6395	83	66	,	,	PUNCT
ejpam-6395	83	67	z1	z1	NOUN
ejpam-6395	83	68	,	,	PUNCT
ejpam-6395	83	69	z2	z2	ADJ
ejpam-6395	83	70	)	)	PUNCT
ejpam-6395	83	71	≤p	≤p	ADJ
ejpam-6395	83	72	•(y	•(y	NOUN
ejpam-6395	83	73	,	,	PUNCT
ejpam-6395	83	74	z1	z1	NOUN
ejpam-6395	83	75	,	,	PUNCT
ejpam-6395	83	76	z2	z2	PROPN
ejpam-6395	83	77	)	)	PUNCT
ejpam-6395	83	78	for	for	ADP
ejpam-6395	83	79	all	all	DET
ejpam-6395	83	80	z1	z1	VERB
ejpam-6395	83	81	,	,	PUNCT
ejpam-6395	83	82	z2	z2	PROPN
ejpam-6395	83	83	∈	∈	PROPN
ejpam-6395	83	84	t	t	PROPN
ejpam-6395	83	85	,	,	PUNCT
ejpam-6395	83	86	then	then	ADV
ejpam-6395	83	87	we	we	PRON
ejpam-6395	83	88	call	call	VERB
ejpam-6395	83	89	(	(	PUNCT
ejpam-6395	83	90	t	t	NOUN
ejpam-6395	83	91	,	,	PUNCT
ejpam-6395	83	92	•,≤p	•,≤p	NOUN
ejpam-6395	83	93	)	)	PUNCT
ejpam-6395	83	94	is	be	AUX
ejpam-6395	83	95	an	an	DET
ejpam-6395	83	96	ordered	order	VERB
ejpam-6395	83	97	power	power	NOUN
ejpam-6395	83	98	ternary	ternary	NOUN
ejpam-6395	83	99	semigroup	semigroup	NOUN
ejpam-6395	83	100	on	on	ADP
ejpam-6395	83	101	a	a	DET
ejpam-6395	83	102	ternary	ternary	ADJ
ejpam-6395	83	103	semihypergroup	semihypergroup	NOUN
ejpam-6395	83	104	(	(	PUNCT
ejpam-6395	83	105	s	s	X
ejpam-6395	83	106	,	,	PUNCT
ejpam-6395	83	107	⋄	⋄	PROPN
ejpam-6395	83	108	)	)	PUNCT
ejpam-6395	83	109	induced	induce	VERB
ejpam-6395	83	110	by	by	ADP
ejpam-6395	83	111	a	a	DET
ejpam-6395	83	112	poset	poset	NOUN
ejpam-6395	83	113	(	(	PUNCT
ejpam-6395	83	114	s,≤	s,≤	NOUN
ejpam-6395	83	115	)	)	PUNCT
ejpam-6395	83	116	.	.	PUNCT
ejpam-6395	84	1	let	let	AUX
ejpam-6395	84	2	(	(	PUNCT
ejpam-6395	84	3	t	t	NOUN
ejpam-6395	84	4	,	,	PUNCT
ejpam-6395	84	5	•,≤p	•,≤p	NOUN
ejpam-6395	84	6	)	)	PUNCT
ejpam-6395	84	7	be	be	VERB
ejpam-6395	84	8	an	an	DET
ejpam-6395	84	9	ordered	order	VERB
ejpam-6395	84	10	power	power	NOUN
ejpam-6395	84	11	ternary	ternary	NOUN
ejpam-6395	84	12	semigroup	semigroup	NOUN
ejpam-6395	84	13	on	on	ADP
ejpam-6395	84	14	a	a	DET
ejpam-6395	84	15	ternary	ternary	ADJ
ejpam-6395	84	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	84	17	(	(	PUNCT
ejpam-6395	84	18	s	s	X
ejpam-6395	84	19	,	,	PUNCT
ejpam-6395	84	20	⋄	⋄	PROPN
ejpam-6395	84	21	)	)	PUNCT
ejpam-6395	84	22	induced	induce	VERB
ejpam-6395	84	23	by	by	ADP
ejpam-6395	84	24	a	a	DET
ejpam-6395	84	25	poset	poset	NOUN
ejpam-6395	84	26	(	(	PUNCT
ejpam-6395	84	27	s,≤	s,≤	NOUN
ejpam-6395	84	28	)	)	PUNCT
ejpam-6395	84	29	and	and	CCONJ
ejpam-6395	84	30	∅	∅	NOUN
ejpam-6395	85	1	=	=	NOUN
ejpam-6395	85	2	̸	̸	NUM
ejpam-6395	85	3	a	a	DET
ejpam-6395	85	4	⊆	⊆	NUM
ejpam-6395	85	5	t	t	NOUN
ejpam-6395	85	6	.	.	PUNCT
ejpam-6395	86	1	we	we	PRON
ejpam-6395	86	2	denote	denote	VERB
ejpam-6395	86	3	(	(	PUNCT
ejpam-6395	86	4	a]p	a]p	NOUN
ejpam-6395	86	5	=	=	SYM
ejpam-6395	86	6	{	{	PUNCT
ejpam-6395	86	7	x	x	SYM
ejpam-6395	86	8	∈	∈	PROPN
ejpam-6395	86	9	t	t	NOUN
ejpam-6395	87	1	|	|	ADV
ejpam-6395	87	2	x	x	SYM
ejpam-6395	87	3	≤p	≤p	NOUN
ejpam-6395	87	4	y	y	PROPN
ejpam-6395	87	5	for	for	ADP
ejpam-6395	87	6	some	some	DET
ejpam-6395	87	7	y	y	PROPN
ejpam-6395	87	8	∈	∈	PROPN
ejpam-6395	87	9	a	a	PRON
ejpam-6395	87	10	}	}	PUNCT
ejpam-6395	87	11	.	.	PUNCT
ejpam-6395	88	1	if	if	SCONJ
ejpam-6395	88	2	a	a	PRON
ejpam-6395	88	3	=	=	X
ejpam-6395	88	4	{	{	PUNCT
ejpam-6395	88	5	x	x	NOUN
ejpam-6395	88	6	}	}	PUNCT
ejpam-6395	88	7	then	then	ADV
ejpam-6395	88	8	we	we	PRON
ejpam-6395	88	9	denote	denote	VERB
ejpam-6395	88	10	(	(	PUNCT
ejpam-6395	88	11	a]p	a]p	NOUN
ejpam-6395	88	12	by	by	ADP
ejpam-6395	88	13	(	(	PUNCT
ejpam-6395	88	14	x]p	x]p	PROPN
ejpam-6395	88	15	.	.	PUNCT
ejpam-6395	88	16	example	example	NOUN
ejpam-6395	89	1	1	1	NUM
ejpam-6395	89	2	.	.	PUNCT
ejpam-6395	89	3	let	let	VERB
ejpam-6395	89	4	s	s	VERB
ejpam-6395	89	5	=	=	PUNCT
ejpam-6395	89	6	{	{	PUNCT
ejpam-6395	89	7	x	x	PROPN
ejpam-6395	89	8	,	,	PUNCT
ejpam-6395	89	9	y	y	PROPN
ejpam-6395	89	10	,	,	PUNCT
ejpam-6395	89	11	z	z	NOUN
ejpam-6395	89	12	}	}	PUNCT
ejpam-6395	89	13	and	and	CCONJ
ejpam-6395	89	14	≤=	≤=	PROPN
ejpam-6395	89	15	{	{	PUNCT
ejpam-6395	89	16	(	(	PUNCT
ejpam-6395	89	17	x	x	X
ejpam-6395	89	18	,	,	PUNCT
ejpam-6395	89	19	x	x	NOUN
ejpam-6395	89	20	)	)	PUNCT
ejpam-6395	89	21	,	,	PUNCT
ejpam-6395	89	22	(	(	PUNCT
ejpam-6395	89	23	y	y	PROPN
ejpam-6395	89	24	,	,	PUNCT
ejpam-6395	89	25	y	y	PROPN
ejpam-6395	89	26	)	)	PUNCT
ejpam-6395	89	27	,	,	PUNCT
ejpam-6395	89	28	(	(	PUNCT
ejpam-6395	89	29	z	z	X
ejpam-6395	89	30	,	,	PUNCT
ejpam-6395	89	31	z	z	NOUN
ejpam-6395	89	32	)	)	PUNCT
ejpam-6395	89	33	,	,	PUNCT
ejpam-6395	89	34	(	(	PUNCT
ejpam-6395	89	35	y	y	NOUN
ejpam-6395	89	36	,	,	PUNCT
ejpam-6395	89	37	x	x	NOUN
ejpam-6395	89	38	)	)	PUNCT
ejpam-6395	89	39	}	}	PUNCT
ejpam-6395	89	40	be	be	AUX
ejpam-6395	89	41	a	a	DET
ejpam-6395	89	42	binary	binary	ADJ
ejpam-6395	89	43	relation	relation	NOUN
ejpam-6395	89	44	on	on	ADP
ejpam-6395	89	45	s.	s.	PROPN
ejpam-6395	89	46	it	it	PRON
ejpam-6395	89	47	is	be	AUX
ejpam-6395	89	48	easily	easily	ADV
ejpam-6395	89	49	seen	see	VERB
ejpam-6395	89	50	that	that	SCONJ
ejpam-6395	89	51	(	(	PUNCT
ejpam-6395	89	52	s,≤	s,≤	NOUN
ejpam-6395	89	53	)	)	PUNCT
ejpam-6395	89	54	is	be	AUX
ejpam-6395	89	55	a	a	DET
ejpam-6395	89	56	poset	poset	NOUN
ejpam-6395	89	57	as	as	ADP
ejpam-6395	89	58	hasse	hasse	PROPN
ejpam-6395	89	59	’s	’s	PART
ejpam-6395	89	60	diagram	diagram	NOUN
ejpam-6395	89	61	and	and	CCONJ
ejpam-6395	89	62	we	we	PRON
ejpam-6395	89	63	define	define	VERB
ejpam-6395	89	64	the	the	DET
ejpam-6395	89	65	ternary	ternary	ADJ
ejpam-6395	89	66	hyperoperation	hyperoperation	NOUN
ejpam-6395	89	67	⋄	⋄	PROPN
ejpam-6395	89	68	on	on	ADP
ejpam-6395	89	69	s	s	PRON
ejpam-6395	89	70	as	as	SCONJ
ejpam-6395	89	71	follows	follow	VERB
ejpam-6395	89	72	.	.	PUNCT
ejpam-6395	90	1	a.	a.	NOUN
ejpam-6395	90	2	nongmanee	nongmanee	PROPN
ejpam-6395	90	3	,	,	PUNCT
ejpam-6395	90	4	k.	k.	PROPN
ejpam-6395	90	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	90	6	,	,	PUNCT
ejpam-6395	90	7	m.	m.	NOUN
ejpam-6395	90	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	90	9	/	/	SYM
ejpam-6395	90	10	eur	eur	PROPN
ejpam-6395	90	11	.	.	PUNCT
ejpam-6395	91	1	j.	j.	PROPN
ejpam-6395	91	2	pure	pure	PROPN
ejpam-6395	91	3	appl	appl	PROPN
ejpam-6395	91	4	.	.	PROPN
ejpam-6395	91	5	math	math	PROPN
ejpam-6395	91	6	,	,	PUNCT
ejpam-6395	91	7	18	18	NUM
ejpam-6395	91	8	(	(	PUNCT
ejpam-6395	91	9	3	3	NUM
ejpam-6395	91	10	)	)	PUNCT
ejpam-6395	91	11	(	(	PUNCT
ejpam-6395	91	12	2025	2025	NUM
ejpam-6395	91	13	)	)	PUNCT
ejpam-6395	91	14	,	,	PUNCT
ejpam-6395	91	15	6395	6395	NUM
ejpam-6395	91	16	4	4	NUM
ejpam-6395	91	17	of	of	ADP
ejpam-6395	91	18	12	12	NUM
ejpam-6395	91	19	x	x	SYM
ejpam-6395	91	20	y	y	PROPN
ejpam-6395	91	21	z	z	NOUN
ejpam-6395	91	22	⋄	⋄	PROPN
ejpam-6395	91	23	x	x	PUNCT
ejpam-6395	92	1	y	y	PROPN
ejpam-6395	92	2	z	z	PROPN
ejpam-6395	92	3	x	x	PROPN
ejpam-6395	92	4	,	,	PUNCT
ejpam-6395	92	5	x	x	X
ejpam-6395	92	6	{	{	PUNCT
ejpam-6395	92	7	x	x	NOUN
ejpam-6395	92	8	}	}	PUNCT
ejpam-6395	92	9	{	{	PUNCT
ejpam-6395	92	10	y	y	NOUN
ejpam-6395	92	11	}	}	PUNCT
ejpam-6395	92	12	{	{	PUNCT
ejpam-6395	92	13	z	z	NOUN
ejpam-6395	92	14	}	}	PUNCT
ejpam-6395	92	15	x	x	PROPN
ejpam-6395	92	16	,	,	PUNCT
ejpam-6395	92	17	y	y	PROPN
ejpam-6395	92	18	{	{	PUNCT
ejpam-6395	92	19	y	y	PROPN
ejpam-6395	92	20	}	}	PUNCT
ejpam-6395	92	21	{	{	PUNCT
ejpam-6395	92	22	y	y	NOUN
ejpam-6395	92	23	}	}	PUNCT
ejpam-6395	92	24	{	{	PUNCT
ejpam-6395	92	25	y	y	PROPN
ejpam-6395	92	26	,	,	PUNCT
ejpam-6395	92	27	z	z	NOUN
ejpam-6395	92	28	}	}	PUNCT
ejpam-6395	92	29	x	x	NOUN
ejpam-6395	92	30	,	,	PUNCT
ejpam-6395	92	31	z	z	X
ejpam-6395	92	32	{	{	PUNCT
ejpam-6395	92	33	z	z	NOUN
ejpam-6395	92	34	}	}	PUNCT
ejpam-6395	92	35	{	{	PUNCT
ejpam-6395	92	36	y	y	PROPN
ejpam-6395	92	37	,	,	PUNCT
ejpam-6395	92	38	z	z	NOUN
ejpam-6395	92	39	}	}	PUNCT
ejpam-6395	92	40	{	{	PUNCT
ejpam-6395	92	41	z	z	NOUN
ejpam-6395	92	42	}	}	PUNCT
ejpam-6395	92	43	y	y	PROPN
ejpam-6395	92	44	,	,	PUNCT
ejpam-6395	92	45	x	x	SYM
ejpam-6395	92	46	{	{	PUNCT
ejpam-6395	92	47	y	y	NOUN
ejpam-6395	92	48	}	}	PUNCT
ejpam-6395	92	49	{	{	PUNCT
ejpam-6395	92	50	y	y	NOUN
ejpam-6395	92	51	}	}	PUNCT
ejpam-6395	92	52	{	{	PUNCT
ejpam-6395	92	53	y	y	PROPN
ejpam-6395	92	54	,	,	PUNCT
ejpam-6395	92	55	z	z	NOUN
ejpam-6395	92	56	}	}	PUNCT
ejpam-6395	92	57	y	y	PROPN
ejpam-6395	92	58	,	,	PUNCT
ejpam-6395	92	59	y	y	PROPN
ejpam-6395	92	60	{	{	PUNCT
ejpam-6395	92	61	y	y	PROPN
ejpam-6395	92	62	}	}	PUNCT
ejpam-6395	92	63	{	{	PUNCT
ejpam-6395	92	64	y	y	NOUN
ejpam-6395	92	65	}	}	PUNCT
ejpam-6395	92	66	{	{	PUNCT
ejpam-6395	92	67	y	y	PROPN
ejpam-6395	92	68	,	,	PUNCT
ejpam-6395	92	69	z	z	NOUN
ejpam-6395	92	70	}	}	PUNCT
ejpam-6395	92	71	y	y	PROPN
ejpam-6395	92	72	,	,	PUNCT
ejpam-6395	92	73	z	z	PROPN
ejpam-6395	92	74	{	{	PUNCT
ejpam-6395	92	75	y	y	PROPN
ejpam-6395	92	76	,	,	PUNCT
ejpam-6395	92	77	z	z	NOUN
ejpam-6395	92	78	}	}	PUNCT
ejpam-6395	92	79	{	{	PUNCT
ejpam-6395	92	80	y	y	PROPN
ejpam-6395	92	81	,	,	PUNCT
ejpam-6395	92	82	z	z	NOUN
ejpam-6395	92	83	}	}	PUNCT
ejpam-6395	92	84	{	{	PUNCT
ejpam-6395	92	85	y	y	PROPN
ejpam-6395	92	86	,	,	PUNCT
ejpam-6395	92	87	z	z	NOUN
ejpam-6395	92	88	}	}	PUNCT
ejpam-6395	92	89	z	z	NOUN
ejpam-6395	92	90	,	,	PUNCT
ejpam-6395	92	91	x	x	X
ejpam-6395	92	92	{	{	PUNCT
ejpam-6395	92	93	z	z	NOUN
ejpam-6395	92	94	}	}	PUNCT
ejpam-6395	92	95	{	{	PUNCT
ejpam-6395	92	96	y	y	PROPN
ejpam-6395	92	97	,	,	PUNCT
ejpam-6395	92	98	z	z	NOUN
ejpam-6395	92	99	}	}	PUNCT
ejpam-6395	92	100	{	{	PUNCT
ejpam-6395	92	101	z	z	NOUN
ejpam-6395	92	102	}	}	PUNCT
ejpam-6395	92	103	z	z	PROPN
ejpam-6395	92	104	,	,	PUNCT
ejpam-6395	92	105	y	y	PROPN
ejpam-6395	92	106	{	{	PUNCT
ejpam-6395	92	107	y	y	PROPN
ejpam-6395	92	108	,	,	PUNCT
ejpam-6395	92	109	z	z	NOUN
ejpam-6395	92	110	}	}	PUNCT
ejpam-6395	92	111	{	{	PUNCT
ejpam-6395	92	112	y	y	PROPN
ejpam-6395	92	113	,	,	PUNCT
ejpam-6395	92	114	z	z	NOUN
ejpam-6395	92	115	}	}	PUNCT
ejpam-6395	92	116	{	{	PUNCT
ejpam-6395	92	117	y	y	PROPN
ejpam-6395	92	118	,	,	PUNCT
ejpam-6395	92	119	z	z	NOUN
ejpam-6395	92	120	}	}	PUNCT
ejpam-6395	92	121	z	z	NOUN
ejpam-6395	92	122	,	,	PUNCT
ejpam-6395	92	123	z	z	AUX
ejpam-6395	92	124	{	{	PUNCT
ejpam-6395	92	125	z	z	NOUN
ejpam-6395	92	126	}	}	PUNCT
ejpam-6395	92	127	{	{	PUNCT
ejpam-6395	92	128	y	y	PROPN
ejpam-6395	92	129	,	,	PUNCT
ejpam-6395	92	130	z	z	NOUN
ejpam-6395	92	131	}	}	PUNCT
ejpam-6395	92	132	{	{	PUNCT
ejpam-6395	92	133	z	z	NOUN
ejpam-6395	92	134	}	}	PUNCT
ejpam-6395	92	135	we	we	PRON
ejpam-6395	92	136	can	can	AUX
ejpam-6395	92	137	see	see	VERB
ejpam-6395	92	138	that	that	PRON
ejpam-6395	92	139	(	(	PUNCT
ejpam-6395	92	140	s	s	X
ejpam-6395	92	141	,	,	PUNCT
ejpam-6395	92	142	⋄	⋄	PROPN
ejpam-6395	92	143	)	)	PUNCT
ejpam-6395	92	144	is	be	AUX
ejpam-6395	92	145	a	a	DET
ejpam-6395	92	146	ternary	ternary	ADJ
ejpam-6395	92	147	semihypergroup	semihypergroup	NOUN
ejpam-6395	92	148	.	.	PUNCT
ejpam-6395	93	1	we	we	PRON
ejpam-6395	93	2	defined	define	VERB
ejpam-6395	93	3	≤p	≤p	NOUN
ejpam-6395	93	4	on	on	ADP
ejpam-6395	93	5	p	p	PROPN
ejpam-6395	93	6	∗(s	∗(s	NOUN
ejpam-6395	93	7	)	)	PUNCT
ejpam-6395	93	8	.	.	PUNCT
ejpam-6395	94	1	then	then	ADV
ejpam-6395	94	2	we	we	PRON
ejpam-6395	94	3	have	have	VERB
ejpam-6395	94	4	the	the	DET
ejpam-6395	94	5	following	follow	VERB
ejpam-6395	94	6	hasse	hasse	PROPN
ejpam-6395	94	7	’s	’s	PART
ejpam-6395	94	8	diagram	diagram	NOUN
ejpam-6395	94	9	.	.	PUNCT
ejpam-6395	95	1	let	let	VERB
ejpam-6395	95	2	t	t	NOUN
ejpam-6395	95	3	=	=	PRON
ejpam-6395	95	4	{	{	PUNCT
ejpam-6395	95	5	{	{	PUNCT
ejpam-6395	95	6	x	x	NOUN
ejpam-6395	95	7	}	}	PUNCT
ejpam-6395	95	8	,	,	PUNCT
ejpam-6395	95	9	{	{	PUNCT
ejpam-6395	95	10	x	x	NOUN
ejpam-6395	95	11	,	,	PUNCT
ejpam-6395	95	12	y	y	NOUN
ejpam-6395	95	13	}	}	PUNCT
ejpam-6395	95	14	}	}	PUNCT
ejpam-6395	95	15	be	be	AUX
ejpam-6395	95	16	a	a	DET
ejpam-6395	95	17	subset	subset	NOUN
ejpam-6395	95	18	of	of	ADP
ejpam-6395	95	19	p	p	PROPN
ejpam-6395	95	20	∗(s	∗(s	NOUN
ejpam-6395	95	21	)	)	PUNCT
ejpam-6395	95	22	.	.	PUNCT
ejpam-6395	96	1	we	we	PRON
ejpam-6395	96	2	have	have	VERB
ejpam-6395	96	3	the	the	DET
ejpam-6395	96	4	cayley	cayley	NOUN
ejpam-6395	96	5	’s	’s	NOUN
ejpam-6395	96	6	table	table	NOUN
ejpam-6395	96	7	of	of	ADP
ejpam-6395	96	8	the	the	DET
ejpam-6395	96	9	operation	operation	NOUN
ejpam-6395	96	10	•	•	NOUN
ejpam-6395	96	11	on	on	ADP
ejpam-6395	96	12	t	t	PROPN
ejpam-6395	96	13	as	as	SCONJ
ejpam-6395	96	14	follows	follow	VERB
ejpam-6395	96	15	.	.	PUNCT
ejpam-6395	97	1	{	{	PUNCT
ejpam-6395	97	2	x	x	X
ejpam-6395	97	3	,	,	PUNCT
ejpam-6395	97	4	y	y	PROPN
ejpam-6395	97	5	,	,	PUNCT
ejpam-6395	97	6	z	z	NOUN
ejpam-6395	97	7	}	}	PUNCT
ejpam-6395	97	8	{	{	PUNCT
ejpam-6395	97	9	x	x	NOUN
ejpam-6395	97	10	,	,	PUNCT
ejpam-6395	97	11	y	y	NOUN
ejpam-6395	97	12	}	}	PUNCT
ejpam-6395	97	13	{	{	PUNCT
ejpam-6395	97	14	x	x	NOUN
ejpam-6395	97	15	}	}	PUNCT
ejpam-6395	97	16	{	{	PUNCT
ejpam-6395	97	17	y	y	NOUN
ejpam-6395	97	18	}	}	PUNCT
ejpam-6395	97	19	{	{	PUNCT
ejpam-6395	97	20	x	x	NOUN
ejpam-6395	97	21	,	,	PUNCT
ejpam-6395	97	22	z	z	NOUN
ejpam-6395	97	23	}	}	PUNCT
ejpam-6395	97	24	{	{	PUNCT
ejpam-6395	97	25	y	y	PROPN
ejpam-6395	97	26	,	,	PUNCT
ejpam-6395	97	27	z	z	NOUN
ejpam-6395	97	28	}	}	PUNCT
ejpam-6395	97	29	{	{	PUNCT
ejpam-6395	97	30	z	z	NOUN
ejpam-6395	97	31	}	}	PUNCT
ejpam-6395	97	32	•	•	NOUN
ejpam-6395	97	33	{	{	PUNCT
ejpam-6395	97	34	x	x	NOUN
ejpam-6395	97	35	}	}	PUNCT
ejpam-6395	97	36	{	{	PUNCT
ejpam-6395	97	37	x	x	NOUN
ejpam-6395	97	38	,	,	PUNCT
ejpam-6395	97	39	y	y	NOUN
ejpam-6395	97	40	}	}	PUNCT
ejpam-6395	97	41	{	{	PUNCT
ejpam-6395	97	42	x	x	NOUN
ejpam-6395	97	43	}	}	PUNCT
ejpam-6395	97	44	,	,	PUNCT
ejpam-6395	97	45	{	{	PUNCT
ejpam-6395	97	46	x	x	X
ejpam-6395	97	47	}	}	PUNCT
ejpam-6395	97	48	{	{	PUNCT
ejpam-6395	97	49	x	x	NOUN
ejpam-6395	97	50	}	}	PUNCT
ejpam-6395	97	51	{	{	PUNCT
ejpam-6395	97	52	x	x	NOUN
ejpam-6395	97	53	,	,	PUNCT
ejpam-6395	97	54	y	y	NOUN
ejpam-6395	97	55	}	}	PUNCT
ejpam-6395	97	56	{	{	PUNCT
ejpam-6395	97	57	x	x	NOUN
ejpam-6395	97	58	}	}	PUNCT
ejpam-6395	97	59	,	,	PUNCT
ejpam-6395	97	60	{	{	PUNCT
ejpam-6395	97	61	x	x	NOUN
ejpam-6395	97	62	,	,	PUNCT
ejpam-6395	97	63	y	y	NOUN
ejpam-6395	97	64	}	}	PUNCT
ejpam-6395	97	65	{	{	PUNCT
ejpam-6395	97	66	x	x	NOUN
ejpam-6395	97	67	,	,	PUNCT
ejpam-6395	97	68	y	y	NOUN
ejpam-6395	97	69	}	}	PUNCT
ejpam-6395	97	70	{	{	PUNCT
ejpam-6395	97	71	x	x	NOUN
ejpam-6395	97	72	,	,	PUNCT
ejpam-6395	97	73	y	y	NOUN
ejpam-6395	97	74	}	}	PUNCT
ejpam-6395	97	75	{	{	PUNCT
ejpam-6395	97	76	x	x	NOUN
ejpam-6395	97	77	,	,	PUNCT
ejpam-6395	97	78	y	y	PROPN
ejpam-6395	97	79	}	}	PUNCT
ejpam-6395	97	80	,	,	PUNCT
ejpam-6395	97	81	{	{	PUNCT
ejpam-6395	97	82	x	x	X
ejpam-6395	97	83	}	}	PUNCT
ejpam-6395	97	84	{	{	PUNCT
ejpam-6395	97	85	x	x	NOUN
ejpam-6395	97	86	,	,	PUNCT
ejpam-6395	97	87	y	y	NOUN
ejpam-6395	97	88	}	}	PUNCT
ejpam-6395	97	89	{	{	PUNCT
ejpam-6395	97	90	x	x	NOUN
ejpam-6395	97	91	,	,	PUNCT
ejpam-6395	97	92	y	y	NOUN
ejpam-6395	97	93	}	}	PUNCT
ejpam-6395	97	94	{	{	PUNCT
ejpam-6395	97	95	x	x	NOUN
ejpam-6395	97	96	,	,	PUNCT
ejpam-6395	97	97	y	y	PROPN
ejpam-6395	97	98	}	}	PUNCT
ejpam-6395	97	99	,	,	PUNCT
ejpam-6395	97	100	{	{	PUNCT
ejpam-6395	97	101	x	x	NOUN
ejpam-6395	97	102	,	,	PUNCT
ejpam-6395	97	103	y	y	NOUN
ejpam-6395	97	104	}	}	PUNCT
ejpam-6395	97	105	{	{	PUNCT
ejpam-6395	97	106	x	x	NOUN
ejpam-6395	97	107	,	,	PUNCT
ejpam-6395	97	108	y	y	NOUN
ejpam-6395	97	109	}	}	PUNCT
ejpam-6395	97	110	{	{	PUNCT
ejpam-6395	97	111	x	x	NOUN
ejpam-6395	97	112	,	,	PUNCT
ejpam-6395	97	113	y	y	PROPN
ejpam-6395	97	114	}	}	PUNCT
ejpam-6395	97	115	then	then	ADV
ejpam-6395	97	116	(	(	PUNCT
ejpam-6395	97	117	t	t	NOUN
ejpam-6395	97	118	,	,	PUNCT
ejpam-6395	97	119	•	•	NUM
ejpam-6395	97	120	)	)	PUNCT
ejpam-6395	97	121	is	be	AUX
ejpam-6395	97	122	a	a	DET
ejpam-6395	97	123	power	power	NOUN
ejpam-6395	97	124	ternary	ternary	NOUN
ejpam-6395	97	125	semigroup	semigroup	NOUN
ejpam-6395	97	126	on	on	ADP
ejpam-6395	97	127	a	a	DET
ejpam-6395	97	128	ternary	ternary	ADJ
ejpam-6395	97	129	semihypergroup	semihypergroup	NOUN
ejpam-6395	97	130	(	(	PUNCT
ejpam-6395	97	131	s	s	X
ejpam-6395	97	132	,	,	PUNCT
ejpam-6395	97	133	⋄	⋄	PROPN
ejpam-6395	97	134	)	)	PUNCT
ejpam-6395	97	135	.	.	PUNCT
ejpam-6395	98	1	we	we	PRON
ejpam-6395	98	2	have	have	VERB
ejpam-6395	98	3	{	{	PUNCT
ejpam-6395	98	4	x	x	NOUN
ejpam-6395	98	5	}	}	PUNCT
ejpam-6395	98	6	≤p	≤p	ADJ
ejpam-6395	98	7	{	{	PUNCT
ejpam-6395	98	8	x	x	NOUN
ejpam-6395	98	9	}	}	PUNCT
ejpam-6395	98	10	,	,	PUNCT
ejpam-6395	98	11	{	{	PUNCT
ejpam-6395	98	12	x	x	NOUN
ejpam-6395	98	13	,	,	PUNCT
ejpam-6395	98	14	y	y	PROPN
ejpam-6395	98	15	}	}	PUNCT
ejpam-6395	98	16	≤p	≤p	NOUN
ejpam-6395	98	17	{	{	PUNCT
ejpam-6395	98	18	x	x	NOUN
ejpam-6395	98	19	,	,	PUNCT
ejpam-6395	98	20	y	y	PROPN
ejpam-6395	98	21	}	}	PUNCT
ejpam-6395	98	22	and	and	CCONJ
ejpam-6395	98	23	{	{	PUNCT
ejpam-6395	98	24	x	x	NOUN
ejpam-6395	98	25	}	}	PUNCT
ejpam-6395	98	26	≤p	≤p	ADJ
ejpam-6395	98	27	{	{	PUNCT
ejpam-6395	98	28	x	x	NOUN
ejpam-6395	98	29	,	,	PUNCT
ejpam-6395	98	30	y	y	PROPN
ejpam-6395	98	31	}	}	PUNCT
ejpam-6395	98	32	.	.	PUNCT
ejpam-6395	99	1	we	we	PRON
ejpam-6395	99	2	can	can	AUX
ejpam-6395	99	3	see	see	VERB
ejpam-6395	99	4	that	that	PRON
ejpam-6395	99	5	≤p	≤p	NOUN
ejpam-6395	99	6	is	be	AUX
ejpam-6395	99	7	compatible	compatible	ADJ
ejpam-6395	99	8	with	with	ADP
ejpam-6395	99	9	the	the	DET
ejpam-6395	99	10	operation	operation	NOUN
ejpam-6395	99	11	•	•	NOUN
ejpam-6395	99	12	restricted	restrict	VERB
ejpam-6395	99	13	to	to	ADP
ejpam-6395	99	14	t	t	PROPN
ejpam-6395	99	15	.	.	PUNCT
ejpam-6395	100	1	therefore	therefore	ADV
ejpam-6395	100	2	(	(	PUNCT
ejpam-6395	100	3	t	t	NOUN
ejpam-6395	100	4	,	,	PUNCT
ejpam-6395	100	5	•,≤p	•,≤p	NOUN
ejpam-6395	100	6	)	)	PUNCT
ejpam-6395	100	7	be	be	VERB
ejpam-6395	100	8	an	an	DET
ejpam-6395	100	9	ordered	order	VERB
ejpam-6395	100	10	power	power	NOUN
ejpam-6395	100	11	ternary	ternary	NOUN
ejpam-6395	100	12	semigroup	semigroup	NOUN
ejpam-6395	100	13	on	on	ADP
ejpam-6395	100	14	a	a	DET
ejpam-6395	100	15	ternary	ternary	ADJ
ejpam-6395	100	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	100	17	(	(	PUNCT
ejpam-6395	100	18	s	s	X
ejpam-6395	100	19	,	,	PUNCT
ejpam-6395	100	20	⋄	⋄	PROPN
ejpam-6395	100	21	)	)	PUNCT
ejpam-6395	100	22	induced	induce	VERB
ejpam-6395	100	23	by	by	ADP
ejpam-6395	100	24	a	a	DET
ejpam-6395	100	25	poset	poset	NOUN
ejpam-6395	100	26	(	(	PUNCT
ejpam-6395	100	27	s,≤	s,≤	NOUN
ejpam-6395	100	28	)	)	PUNCT
ejpam-6395	100	29	.	.	PUNCT
ejpam-6395	101	1	definition	definition	NOUN
ejpam-6395	101	2	4	4	NUM
ejpam-6395	101	3	.	.	PUNCT
ejpam-6395	102	1	let	let	AUX
ejpam-6395	102	2	(	(	PUNCT
ejpam-6395	102	3	t	t	NOUN
ejpam-6395	102	4	,	,	PUNCT
ejpam-6395	102	5	•	•	X
ejpam-6395	102	6	)	)	PUNCT
ejpam-6395	102	7	be	be	AUX
ejpam-6395	102	8	an	an	DET
ejpam-6395	102	9	ordered	order	VERB
ejpam-6395	102	10	power	power	NOUN
ejpam-6395	102	11	ternary	ternary	NOUN
ejpam-6395	102	12	semigroup	semigroup	NOUN
ejpam-6395	102	13	on	on	ADP
ejpam-6395	102	14	a	a	DET
ejpam-6395	102	15	ternary	ternary	ADJ
ejpam-6395	102	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	102	17	(	(	PUNCT
ejpam-6395	102	18	s	s	X
ejpam-6395	102	19	,	,	PUNCT
ejpam-6395	102	20	⋄	⋄	PROPN
ejpam-6395	102	21	)	)	PUNCT
ejpam-6395	102	22	induced	induce	VERB
ejpam-6395	102	23	by	by	ADP
ejpam-6395	102	24	a	a	DET
ejpam-6395	102	25	poset	poset	NOUN
ejpam-6395	102	26	(	(	PUNCT
ejpam-6395	102	27	s,≤	s,≤	NOUN
ejpam-6395	102	28	)	)	PUNCT
ejpam-6395	102	29	.	.	PUNCT
ejpam-6395	103	1	let	let	VERB
ejpam-6395	103	2	w	w	NOUN
ejpam-6395	103	3	be	be	AUX
ejpam-6395	103	4	a	a	DET
ejpam-6395	103	5	nonempty	nonempty	ADJ
ejpam-6395	103	6	subset	subset	NOUN
ejpam-6395	103	7	of	of	ADP
ejpam-6395	103	8	t	t	PROPN
ejpam-6395	103	9	.	.	PUNCT
ejpam-6395	104	1	if	if	SCONJ
ejpam-6395	104	2	•(a	•(a	PROPN
ejpam-6395	104	3	,	,	PUNCT
ejpam-6395	104	4	b	b	NOUN
ejpam-6395	104	5	,	,	PUNCT
ejpam-6395	104	6	c	c	NOUN
ejpam-6395	104	7	)	)	PUNCT
ejpam-6395	104	8	∈	∈	PROPN
ejpam-6395	104	9	w	w	NOUN
ejpam-6395	104	10	for	for	ADP
ejpam-6395	104	11	any	any	DET
ejpam-6395	104	12	a	a	DET
ejpam-6395	104	13	,	,	PUNCT
ejpam-6395	104	14	b	b	NOUN
ejpam-6395	104	15	,	,	PUNCT
ejpam-6395	104	16	c	c	PROPN
ejpam-6395	104	17	∈	∈	PROPN
ejpam-6395	105	1	w	w	NOUN
ejpam-6395	105	2	then	then	ADV
ejpam-6395	105	3	w	w	PROPN
ejpam-6395	105	4	is	be	AUX
ejpam-6395	105	5	a	a	DET
ejpam-6395	105	6	power	power	NOUN
ejpam-6395	105	7	subternary	subternary	NOUN
ejpam-6395	105	8	semigroup	semigroup	NOUN
ejpam-6395	105	9	of	of	ADP
ejpam-6395	105	10	s	s	PRON
ejpam-6395	105	11	and	and	CCONJ
ejpam-6395	105	12	every	every	DET
ejpam-6395	105	13	power	power	NOUN
ejpam-6395	105	14	subternary	subternary	NOUN
ejpam-6395	105	15	semigroup	semigroup	NOUN
ejpam-6395	105	16	of	of	ADP
ejpam-6395	105	17	t	t	PROPN
ejpam-6395	105	18	is	be	AUX
ejpam-6395	105	19	an	an	DET
ejpam-6395	105	20	ordered	order	VERB
ejpam-6395	105	21	power	power	NOUN
ejpam-6395	105	22	ternary	ternary	NOUN
ejpam-6395	105	23	semigroup	semigroup	NOUN
ejpam-6395	105	24	on	on	ADP
ejpam-6395	105	25	a	a	DET
ejpam-6395	105	26	ternary	ternary	ADJ
ejpam-6395	105	27	semihypergroup	semihypergroup	NOUN
ejpam-6395	105	28	(	(	PUNCT
ejpam-6395	105	29	s	s	X
ejpam-6395	105	30	,	,	PUNCT
ejpam-6395	105	31	⋄	⋄	PROPN
ejpam-6395	105	32	)	)	PUNCT
ejpam-6395	105	33	induced	induce	VERB
ejpam-6395	105	34	by	by	ADP
ejpam-6395	105	35	a	a	DET
ejpam-6395	105	36	poset	poset	NOUN
ejpam-6395	105	37	(	(	PUNCT
ejpam-6395	105	38	s,≤	s,≤	NOUN
ejpam-6395	105	39	)	)	PUNCT
ejpam-6395	105	40	.	.	PUNCT
ejpam-6395	106	1	for	for	ADP
ejpam-6395	106	2	nonempty	nonempty	NOUN
ejpam-6395	106	3	subsets	subset	NOUN
ejpam-6395	106	4	a	a	PRON
ejpam-6395	106	5	and	and	CCONJ
ejpam-6395	106	6	b	b	PROPN
ejpam-6395	106	7	of	of	ADP
ejpam-6395	106	8	t	t	PROPN
ejpam-6395	106	9	,	,	PUNCT
ejpam-6395	106	10	let	let	VERB
ejpam-6395	106	11	•(a	•(a	VERB
ejpam-6395	106	12	,	,	PUNCT
ejpam-6395	106	13	b	b	NOUN
ejpam-6395	106	14	,	,	PUNCT
ejpam-6395	106	15	c	c	NOUN
ejpam-6395	106	16	)	)	PUNCT
ejpam-6395	106	17	=	=	PRON
ejpam-6395	106	18	{	{	PUNCT
ejpam-6395	106	19	•(a	•(a	PROPN
ejpam-6395	106	20	,	,	PUNCT
ejpam-6395	106	21	b	b	NOUN
ejpam-6395	106	22	,	,	PUNCT
ejpam-6395	106	23	c	c	NOUN
ejpam-6395	106	24	)	)	PUNCT
ejpam-6395	106	25	|	|	ADV
ejpam-6395	106	26	a	a	DET
ejpam-6395	106	27	∈	∈	PROPN
ejpam-6395	106	28	a	a	DET
ejpam-6395	106	29	,	,	PUNCT
ejpam-6395	106	30	b	b	PROPN
ejpam-6395	106	31	∈	∈	PROPN
ejpam-6395	106	32	b	b	PROPN
ejpam-6395	106	33	and	and	CCONJ
ejpam-6395	106	34	c	c	NOUN
ejpam-6395	106	35	∈	∈	PROPN
ejpam-6395	106	36	c	c	X
ejpam-6395	106	37	}	}	PUNCT
ejpam-6395	106	38	.	.	PUNCT
ejpam-6395	107	1	a	a	DET
ejpam-6395	107	2	nonempty	nonempty	NOUN
ejpam-6395	107	3	subset	subset	VERB
ejpam-6395	107	4	a	a	PRON
ejpam-6395	107	5	of	of	ADP
ejpam-6395	107	6	t	t	PROPN
ejpam-6395	107	7	is	be	AUX
ejpam-6395	107	8	a	a	DET
ejpam-6395	107	9	power	power	NOUN
ejpam-6395	107	10	subternary	subternary	NOUN
ejpam-6395	107	11	semigroup	semigroup	NOUN
ejpam-6395	107	12	of	of	ADP
ejpam-6395	107	13	t	t	PROPN
ejpam-6395	107	14	if	if	SCONJ
ejpam-6395	107	15	and	and	CCONJ
ejpam-6395	107	16	only	only	ADV
ejpam-6395	107	17	if	if	SCONJ
ejpam-6395	107	18	•(a	•(a	PROPN
ejpam-6395	107	19	,	,	PUNCT
ejpam-6395	107	20	a	a	PRON
ejpam-6395	107	21	,	,	PUNCT
ejpam-6395	107	22	a	a	NOUN
ejpam-6395	107	23	)	)	PUNCT
ejpam-6395	107	24	⊆	⊆	NUM
ejpam-6395	107	25	a.	a.	NOUN
ejpam-6395	107	26	we	we	PRON
ejpam-6395	107	27	denote	denote	VERB
ejpam-6395	107	28	•(a	•(a	PROPN
ejpam-6395	107	29	,	,	PUNCT
ejpam-6395	107	30	b	b	NOUN
ejpam-6395	107	31	,	,	PUNCT
ejpam-6395	107	32	{	{	PUNCT
ejpam-6395	107	33	x	x	NOUN
ejpam-6395	107	34	}	}	PUNCT
ejpam-6395	107	35	)	)	PUNCT
ejpam-6395	107	36	=	=	SYM
ejpam-6395	107	37	•(a	•(a	PROPN
ejpam-6395	107	38	,	,	PUNCT
ejpam-6395	107	39	b	b	NOUN
ejpam-6395	107	40	,	,	PUNCT
ejpam-6395	107	41	x	x	NOUN
ejpam-6395	107	42	)	)	PUNCT
ejpam-6395	107	43	,	,	PUNCT
ejpam-6395	107	44	•(a	•(a	PROPN
ejpam-6395	107	45	,	,	PUNCT
ejpam-6395	107	46	{	{	PUNCT
ejpam-6395	107	47	x},b	x},b	ADV
ejpam-6395	107	48	)	)	PUNCT
ejpam-6395	107	49	=	=	SYM
ejpam-6395	107	50	•(a	•(a	PROPN
ejpam-6395	107	51	,	,	PUNCT
ejpam-6395	107	52	x	x	NOUN
ejpam-6395	107	53	,	,	PUNCT
ejpam-6395	107	54	b	b	NOUN
ejpam-6395	107	55	)	)	PUNCT
ejpam-6395	107	56	and	and	CCONJ
ejpam-6395	107	57	•({x},a	•({x},a	PROPN
ejpam-6395	107	58	,	,	PUNCT
ejpam-6395	107	59	b	b	NOUN
ejpam-6395	107	60	)	)	PUNCT
ejpam-6395	107	61	=	=	SYM
ejpam-6395	107	62	•(x	•(x	PROPN
ejpam-6395	107	63	,	,	PUNCT
ejpam-6395	107	64	a	a	DET
ejpam-6395	107	65	,	,	PUNCT
ejpam-6395	107	66	b	b	NOUN
ejpam-6395	107	67	)	)	PUNCT
ejpam-6395	107	68	for	for	ADP
ejpam-6395	107	69	any	any	DET
ejpam-6395	107	70	a	a	PRON
ejpam-6395	107	71	,	,	PUNCT
ejpam-6395	107	72	b	b	PROPN
ejpam-6395	107	73	⊆	⊆	NUM
ejpam-6395	107	74	t	t	NOUN
ejpam-6395	107	75	and	and	CCONJ
ejpam-6395	107	76	x	x	PROPN
ejpam-6395	107	77	∈	∈	PROPN
ejpam-6395	107	78	t	t	NOUN
ejpam-6395	107	79	.	.	PUNCT
ejpam-6395	108	1	corollary	corollary	ADJ
ejpam-6395	108	2	1	1	NUM
ejpam-6395	108	3	.	.	PUNCT
ejpam-6395	109	1	let	let	AUX
ejpam-6395	109	2	(	(	PUNCT
ejpam-6395	109	3	t	t	NOUN
ejpam-6395	109	4	,	,	PUNCT
ejpam-6395	109	5	•	•	X
ejpam-6395	109	6	)	)	PUNCT
ejpam-6395	109	7	be	be	AUX
ejpam-6395	109	8	an	an	DET
ejpam-6395	109	9	ordered	order	VERB
ejpam-6395	109	10	power	power	NOUN
ejpam-6395	109	11	ternary	ternary	NOUN
ejpam-6395	109	12	semigroup	semigroup	NOUN
ejpam-6395	109	13	on	on	ADP
ejpam-6395	109	14	a	a	DET
ejpam-6395	109	15	ternary	ternary	ADJ
ejpam-6395	109	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	109	17	(	(	PUNCT
ejpam-6395	109	18	s	s	X
ejpam-6395	109	19	,	,	PUNCT
ejpam-6395	109	20	⋄	⋄	PROPN
ejpam-6395	109	21	)	)	PUNCT
ejpam-6395	109	22	induced	induce	VERB
ejpam-6395	109	23	by	by	ADP
ejpam-6395	109	24	a	a	DET
ejpam-6395	109	25	poset	poset	NOUN
ejpam-6395	109	26	(	(	PUNCT
ejpam-6395	109	27	s,≤	s,≤	NOUN
ejpam-6395	109	28	)	)	PUNCT
ejpam-6395	109	29	.	.	PUNCT
ejpam-6395	110	1	let	let	VERB
ejpam-6395	110	2	{	{	PUNCT
ejpam-6395	110	3	wi	wi	PROPN
ejpam-6395	111	1	|	|	ADV
ejpam-6395	111	2	i	i	PRON
ejpam-6395	111	3	∈	∈	VERB
ejpam-6395	111	4	i	i	PRON
ejpam-6395	111	5	}	}	PUNCT
ejpam-6395	111	6	be	be	VERB
ejpam-6395	111	7	a	a	DET
ejpam-6395	111	8	nonempty	nonempty	ADJ
ejpam-6395	111	9	family	family	NOUN
ejpam-6395	111	10	of	of	ADP
ejpam-6395	111	11	power	power	NOUN
ejpam-6395	111	12	subternary	subternary	NOUN
ejpam-6395	111	13	semigroups	semigroup	NOUN
ejpam-6395	111	14	of	of	ADP
ejpam-6395	111	15	t	t	PROPN
ejpam-6395	111	16	and	and	CCONJ
ejpam-6395	111	17	⋂	⋂	PROPN
ejpam-6395	111	18	i∈i	i∈i	ADJ
ejpam-6395	111	19	wi	wi	PROPN
ejpam-6395	111	20	is	be	AUX
ejpam-6395	111	21	a	a	DET
ejpam-6395	111	22	nonempty	nonempty	ADV
ejpam-6395	111	23	set	set	VERB
ejpam-6395	111	24	.	.	PUNCT
ejpam-6395	112	1	then	then	ADV
ejpam-6395	112	2	⋂	⋂	PROPN
ejpam-6395	112	3	i∈i	i∈i	ADJ
ejpam-6395	112	4	wi	wi	PROPN
ejpam-6395	112	5	is	be	AUX
ejpam-6395	112	6	a	a	DET
ejpam-6395	112	7	power	power	NOUN
ejpam-6395	112	8	subsemigroup	subsemigroup	NOUN
ejpam-6395	112	9	of	of	ADP
ejpam-6395	112	10	t	t	PROPN
ejpam-6395	112	11	.	.	PUNCT
ejpam-6395	113	1	moreover	moreover	ADV
ejpam-6395	113	2	,	,	PUNCT
ejpam-6395	113	3	⋂	⋂	PROPN
ejpam-6395	113	4	i∈i	i∈i	ADJ
ejpam-6395	113	5	wi	wi	PROPN
ejpam-6395	113	6	is	be	AUX
ejpam-6395	113	7	an	an	DET
ejpam-6395	113	8	ordered	order	VERB
ejpam-6395	113	9	power	power	NOUN
ejpam-6395	113	10	ternary	ternary	NOUN
ejpam-6395	113	11	semigroup	semigroup	NOUN
ejpam-6395	113	12	on	on	ADP
ejpam-6395	113	13	a	a	DET
ejpam-6395	113	14	ternary	ternary	ADJ
ejpam-6395	113	15	semihypergroup	semihypergroup	NOUN
ejpam-6395	113	16	(	(	PUNCT
ejpam-6395	113	17	s	s	X
ejpam-6395	113	18	,	,	PUNCT
ejpam-6395	113	19	⋄	⋄	PROPN
ejpam-6395	113	20	)	)	PUNCT
ejpam-6395	113	21	induced	induce	VERB
ejpam-6395	113	22	by	by	ADP
ejpam-6395	113	23	a	a	DET
ejpam-6395	113	24	poset	poset	NOUN
ejpam-6395	113	25	(	(	PUNCT
ejpam-6395	113	26	s,≤	s,≤	NOUN
ejpam-6395	113	27	)	)	PUNCT
ejpam-6395	113	28	and	and	CCONJ
ejpam-6395	113	29	⋃	⋃	PROPN
ejpam-6395	113	30	i∈i	i∈i	ADJ
ejpam-6395	113	31	wi	wi	PROPN
ejpam-6395	113	32	is	be	AUX
ejpam-6395	113	33	not	not	PART
ejpam-6395	113	34	necessary	necessary	ADJ
ejpam-6395	113	35	be	be	AUX
ejpam-6395	113	36	a	a	DET
ejpam-6395	113	37	power	power	NOUN
ejpam-6395	113	38	subternary	subternary	NOUN
ejpam-6395	113	39	semigroup	semigroup	NOUN
ejpam-6395	113	40	of	of	ADP
ejpam-6395	113	41	s.	s.	PROPN
ejpam-6395	113	42	a.	a.	PROPN
ejpam-6395	113	43	nongmanee	nongmanee	PROPN
ejpam-6395	113	44	,	,	PUNCT
ejpam-6395	113	45	k.	k.	PROPN
ejpam-6395	113	46	jeenkaew	jeenkaew	PROPN
ejpam-6395	113	47	,	,	PUNCT
ejpam-6395	113	48	m.	m.	NOUN
ejpam-6395	113	49	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	113	50	/	/	SYM
ejpam-6395	113	51	eur	eur	PROPN
ejpam-6395	113	52	.	.	PUNCT
ejpam-6395	114	1	j.	j.	PROPN
ejpam-6395	114	2	pure	pure	PROPN
ejpam-6395	114	3	appl	appl	PROPN
ejpam-6395	114	4	.	.	PROPN
ejpam-6395	114	5	math	math	PROPN
ejpam-6395	114	6	,	,	PUNCT
ejpam-6395	114	7	18	18	NUM
ejpam-6395	114	8	(	(	PUNCT
ejpam-6395	114	9	3	3	NUM
ejpam-6395	114	10	)	)	PUNCT
ejpam-6395	114	11	(	(	PUNCT
ejpam-6395	114	12	2025	2025	NUM
ejpam-6395	114	13	)	)	PUNCT
ejpam-6395	114	14	,	,	PUNCT
ejpam-6395	114	15	6395	6395	NUM
ejpam-6395	114	16	5	5	NUM
ejpam-6395	114	17	of	of	ADP
ejpam-6395	114	18	12	12	NUM
ejpam-6395	114	19	let	let	NOUN
ejpam-6395	114	20	(	(	PUNCT
ejpam-6395	114	21	t	t	NOUN
ejpam-6395	114	22	,	,	PUNCT
ejpam-6395	114	23	•	•	X
ejpam-6395	114	24	)	)	PUNCT
ejpam-6395	114	25	be	be	AUX
ejpam-6395	114	26	an	an	DET
ejpam-6395	114	27	ordered	order	VERB
ejpam-6395	114	28	power	power	NOUN
ejpam-6395	114	29	ternary	ternary	NOUN
ejpam-6395	114	30	semigroup	semigroup	NOUN
ejpam-6395	114	31	on	on	ADP
ejpam-6395	114	32	a	a	DET
ejpam-6395	114	33	ternary	ternary	ADJ
ejpam-6395	114	34	semihypergroup	semihypergroup	NOUN
ejpam-6395	114	35	(	(	PUNCT
ejpam-6395	114	36	s	s	X
ejpam-6395	114	37	,	,	PUNCT
ejpam-6395	114	38	⋄	⋄	PROPN
ejpam-6395	114	39	)	)	PUNCT
ejpam-6395	114	40	induced	induce	VERB
ejpam-6395	114	41	by	by	ADP
ejpam-6395	114	42	a	a	DET
ejpam-6395	114	43	poset	poset	NOUN
ejpam-6395	114	44	(	(	PUNCT
ejpam-6395	114	45	s,≤	s,≤	NOUN
ejpam-6395	114	46	)	)	PUNCT
ejpam-6395	114	47	and	and	CCONJ
ejpam-6395	114	48	a	a	DET
ejpam-6395	114	49	⊆	⊆	NUM
ejpam-6395	114	50	t	t	NOUN
ejpam-6395	114	51	.	.	PUNCT
ejpam-6395	115	1	we	we	PRON
ejpam-6395	115	2	denoted	denote	VERB
ejpam-6395	115	3	(	(	PUNCT
ejpam-6395	115	4	a]p	a]p	NOUN
ejpam-6395	115	5	:	:	PUNCT
ejpam-6395	115	6	=	=	SYM
ejpam-6395	115	7	{	{	PUNCT
ejpam-6395	115	8	x	x	SYM
ejpam-6395	115	9	∈	∈	PROPN
ejpam-6395	115	10	t	t	NOUN
ejpam-6395	116	1	|	|	ADV
ejpam-6395	116	2	x	x	SYM
ejpam-6395	116	3	≤p	≤p	NOUN
ejpam-6395	116	4	y	y	PROPN
ejpam-6395	116	5	for	for	ADP
ejpam-6395	116	6	some	some	DET
ejpam-6395	116	7	y	y	PROPN
ejpam-6395	116	8	∈	∈	PROPN
ejpam-6395	116	9	a	a	PRON
ejpam-6395	116	10	}	}	PUNCT
ejpam-6395	116	11	.	.	PUNCT
ejpam-6395	117	1	lemma	lemma	PROPN
ejpam-6395	117	2	1	1	X
ejpam-6395	117	3	.	.	PUNCT
ejpam-6395	118	1	let	let	VERB
ejpam-6395	118	2	(	(	PUNCT
ejpam-6395	118	3	t	t	NOUN
ejpam-6395	118	4	,	,	PUNCT
ejpam-6395	118	5	•	•	X
ejpam-6395	118	6	)	)	PUNCT
ejpam-6395	118	7	be	be	AUX
ejpam-6395	118	8	an	an	DET
ejpam-6395	118	9	ordered	order	VERB
ejpam-6395	118	10	power	power	NOUN
ejpam-6395	118	11	ternary	ternary	NOUN
ejpam-6395	118	12	semigroup	semigroup	NOUN
ejpam-6395	118	13	on	on	ADP
ejpam-6395	118	14	a	a	DET
ejpam-6395	118	15	ternary	ternary	ADJ
ejpam-6395	118	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	118	17	(	(	PUNCT
ejpam-6395	118	18	s	s	X
ejpam-6395	118	19	,	,	PUNCT
ejpam-6395	118	20	⋄	⋄	PROPN
ejpam-6395	118	21	)	)	PUNCT
ejpam-6395	118	22	induced	induce	VERB
ejpam-6395	118	23	by	by	ADP
ejpam-6395	118	24	a	a	DET
ejpam-6395	118	25	poset	poset	NOUN
ejpam-6395	118	26	(	(	PUNCT
ejpam-6395	118	27	s,≤	s,≤	NOUN
ejpam-6395	118	28	)	)	PUNCT
ejpam-6395	118	29	and	and	CCONJ
ejpam-6395	118	30	a	a	DET
ejpam-6395	118	31	,	,	PUNCT
ejpam-6395	118	32	b	b	NOUN
ejpam-6395	118	33	,	,	PUNCT
ejpam-6395	118	34	c	c	PROPN
ejpam-6395	118	35	⊆	⊆	NUM
ejpam-6395	118	36	t	t	NOUN
ejpam-6395	118	37	.	.	PUNCT
ejpam-6395	119	1	then	then	ADV
ejpam-6395	119	2	the	the	DET
ejpam-6395	119	3	following	follow	VERB
ejpam-6395	119	4	statements	statement	NOUN
ejpam-6395	119	5	hold	hold	VERB
ejpam-6395	119	6	.	.	PUNCT
ejpam-6395	120	1	(	(	PUNCT
ejpam-6395	120	2	i	i	NOUN
ejpam-6395	120	3	)	)	PUNCT
ejpam-6395	120	4	a	a	DET
ejpam-6395	120	5	⊆	⊆	NUM
ejpam-6395	120	6	(	(	PUNCT
ejpam-6395	120	7	a]p	a]p	NOUN
ejpam-6395	120	8	.	.	PUNCT
ejpam-6395	121	1	(	(	PUNCT
ejpam-6395	121	2	ii	ii	NOUN
ejpam-6395	121	3	)	)	PUNCT
ejpam-6395	121	4	if	if	SCONJ
ejpam-6395	121	5	a	a	DET
ejpam-6395	121	6	⊆	⊆	NUM
ejpam-6395	121	7	b	b	NOUN
ejpam-6395	121	8	then	then	ADV
ejpam-6395	121	9	(	(	PUNCT
ejpam-6395	121	10	a]p	a]p	VERB
ejpam-6395	121	11	⊆	⊆	NUM
ejpam-6395	121	12	(	(	PUNCT
ejpam-6395	121	13	b]p	b]p	X
ejpam-6395	121	14	.	.	PUNCT
ejpam-6395	122	1	(	(	PUNCT
ejpam-6395	122	2	iii	iii	X
ejpam-6395	122	3	)	)	PUNCT
ejpam-6395	122	4	•((a]p	•((a]p	NOUN
ejpam-6395	122	5	,	,	PUNCT
ejpam-6395	122	6	(	(	PUNCT
ejpam-6395	122	7	b]p	b]p	X
ejpam-6395	122	8	,	,	PUNCT
ejpam-6395	122	9	(	(	PUNCT
ejpam-6395	122	10	c]p	c]p	NOUN
ejpam-6395	122	11	)	)	PUNCT
ejpam-6395	122	12	⊆	⊆	NUM
ejpam-6395	122	13	(	(	PUNCT
ejpam-6395	122	14	•(a	•(a	PROPN
ejpam-6395	122	15	,	,	PUNCT
ejpam-6395	122	16	b	b	PROPN
ejpam-6395	122	17	,	,	PUNCT
ejpam-6395	122	18	c)]p	c)]p	PROPN
ejpam-6395	122	19	.	.	PUNCT
ejpam-6395	123	1	(	(	PUNCT
ejpam-6395	123	2	iv	iv	X
ejpam-6395	123	3	)	)	PUNCT
ejpam-6395	123	4	(	(	PUNCT
ejpam-6395	123	5	(	(	PUNCT
ejpam-6395	123	6	a]p]p	a]p]p	NOUN
ejpam-6395	123	7	=	=	SYM
ejpam-6395	123	8	(	(	PUNCT
ejpam-6395	123	9	a]p	a]p	NOUN
ejpam-6395	123	10	.	.	PUNCT
ejpam-6395	124	1	(	(	PUNCT
ejpam-6395	124	2	v	v	NOUN
ejpam-6395	124	3	)	)	PUNCT
ejpam-6395	124	4	(	(	PUNCT
ejpam-6395	124	5	a	a	DET
ejpam-6395	124	6	∪	∪	X
ejpam-6395	124	7	b]p	b]p	X
ejpam-6395	124	8	=	=	SYM
ejpam-6395	124	9	(	(	PUNCT
ejpam-6395	124	10	a]p	a]p	PROPN
ejpam-6395	124	11	∪	∪	X
ejpam-6395	124	12	(	(	PUNCT
ejpam-6395	124	13	b]p	b]p	X
ejpam-6395	124	14	.	.	PUNCT
ejpam-6395	125	1	(	(	PUNCT
ejpam-6395	125	2	vi	vi	NOUN
ejpam-6395	125	3	)	)	PUNCT
ejpam-6395	125	4	(	(	PUNCT
ejpam-6395	125	5	a	a	DET
ejpam-6395	125	6	∩	∩	X
ejpam-6395	125	7	b]p	b]p	ADJ
ejpam-6395	125	8	⊆	⊆	NUM
ejpam-6395	125	9	(	(	PUNCT
ejpam-6395	125	10	a]p	a]p	NOUN
ejpam-6395	125	11	∩	∩	NOUN
ejpam-6395	125	12	(	(	PUNCT
ejpam-6395	125	13	b]p	b]p	X
ejpam-6395	125	14	.	.	PUNCT
ejpam-6395	125	15	(	(	PUNCT
ejpam-6395	125	16	vii	vii	PROPN
ejpam-6395	125	17	)	)	PUNCT
ejpam-6395	125	18	(	(	PUNCT
ejpam-6395	125	19	•((a]p	•((a]p	INTJ
ejpam-6395	125	20	,	,	PUNCT
ejpam-6395	125	21	(	(	PUNCT
ejpam-6395	125	22	b]p	b]p	X
ejpam-6395	125	23	,	,	PUNCT
ejpam-6395	125	24	(	(	PUNCT
ejpam-6395	125	25	c]p)]p	c]p)]p	X
ejpam-6395	125	26	=	=	PUNCT
ejpam-6395	125	27	(	(	PUNCT
ejpam-6395	125	28	•(a	•(a	PROPN
ejpam-6395	125	29	,	,	PUNCT
ejpam-6395	125	30	b	b	PROPN
ejpam-6395	125	31	,	,	PUNCT
ejpam-6395	125	32	c)]p	c)]p	PROPN
ejpam-6395	125	33	.	.	PUNCT
ejpam-6395	126	1	proof	proof	NOUN
ejpam-6395	126	2	.	.	PUNCT
ejpam-6395	127	1	the	the	DET
ejpam-6395	127	2	proof	proof	NOUN
ejpam-6395	127	3	is	be	AUX
ejpam-6395	127	4	straightforward	straightforward	ADJ
ejpam-6395	127	5	.	.	PUNCT
ejpam-6395	128	1	definition	definition	NOUN
ejpam-6395	128	2	5	5	NUM
ejpam-6395	128	3	.	.	PUNCT
ejpam-6395	129	1	let	let	VERB
ejpam-6395	129	2	(	(	PUNCT
ejpam-6395	129	3	t	t	NOUN
ejpam-6395	129	4	,	,	PUNCT
ejpam-6395	129	5	•	•	X
ejpam-6395	129	6	)	)	PUNCT
ejpam-6395	129	7	be	be	AUX
ejpam-6395	129	8	an	an	DET
ejpam-6395	129	9	ordered	order	VERB
ejpam-6395	129	10	power	power	NOUN
ejpam-6395	129	11	ternary	ternary	NOUN
ejpam-6395	129	12	semigroup	semigroup	NOUN
ejpam-6395	129	13	on	on	ADP
ejpam-6395	129	14	a	a	DET
ejpam-6395	129	15	ternary	ternary	ADJ
ejpam-6395	129	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	129	17	(	(	PUNCT
ejpam-6395	129	18	s	s	X
ejpam-6395	129	19	,	,	PUNCT
ejpam-6395	129	20	⋄	⋄	PROPN
ejpam-6395	129	21	)	)	PUNCT
ejpam-6395	129	22	induced	induce	VERB
ejpam-6395	129	23	by	by	ADP
ejpam-6395	129	24	a	a	DET
ejpam-6395	129	25	poset	poset	NOUN
ejpam-6395	129	26	(	(	PUNCT
ejpam-6395	129	27	s,≤	s,≤	NOUN
ejpam-6395	129	28	)	)	PUNCT
ejpam-6395	129	29	.	.	PUNCT
ejpam-6395	130	1	a	a	DET
ejpam-6395	130	2	nonempty	nonempty	NOUN
ejpam-6395	130	3	subset	subset	VERB
ejpam-6395	130	4	a	a	PRON
ejpam-6395	130	5	of	of	ADP
ejpam-6395	130	6	t	t	PROPN
ejpam-6395	130	7	is	be	AUX
ejpam-6395	130	8	called	call	VERB
ejpam-6395	130	9	a	a	DET
ejpam-6395	130	10	left	left	ADJ
ejpam-6395	130	11	(	(	PUNCT
ejpam-6395	130	12	resp	resp	NOUN
ejpam-6395	130	13	.	.	PUNCT
ejpam-6395	131	1	right	right	ADJ
ejpam-6395	131	2	and	and	CCONJ
ejpam-6395	131	3	lateral	lateral	ADJ
ejpam-6395	131	4	)	)	PUNCT
ejpam-6395	131	5	ideal	ideal	NOUN
ejpam-6395	131	6	of	of	ADP
ejpam-6395	131	7	t	t	PROPN
ejpam-6395	132	1	if	if	SCONJ
ejpam-6395	133	1	and	and	CCONJ
ejpam-6395	133	2	only	only	ADV
ejpam-6395	133	3	if	if	SCONJ
ejpam-6395	133	4	(	(	PUNCT
ejpam-6395	133	5	i	i	NOUN
ejpam-6395	133	6	)	)	PUNCT
ejpam-6395	133	7	•(t	•(t	PROPN
ejpam-6395	133	8	,	,	PUNCT
ejpam-6395	133	9	t	t	PROPN
ejpam-6395	133	10	,	,	PUNCT
ejpam-6395	133	11	a	a	PRON
ejpam-6395	133	12	)	)	PUNCT
ejpam-6395	133	13	⊆	⊆	NUM
ejpam-6395	133	14	a	a	DET
ejpam-6395	133	15	(	(	PUNCT
ejpam-6395	133	16	resp	resp	NOUN
ejpam-6395	133	17	.	.	PUNCT
ejpam-6395	134	1	•(a	•(a	PROPN
ejpam-6395	134	2	,	,	PUNCT
ejpam-6395	134	3	t	t	PROPN
ejpam-6395	134	4	,	,	PUNCT
ejpam-6395	134	5	t	t	PROPN
ejpam-6395	134	6	)	)	PUNCT
ejpam-6395	135	1	⊆	⊆	PROPN
ejpam-6395	135	2	a	a	PRON
ejpam-6395	135	3	and	and	CCONJ
ejpam-6395	135	4	•(t	•(t	NOUN
ejpam-6395	135	5	,	,	PUNCT
ejpam-6395	135	6	a	a	PRON
ejpam-6395	135	7	,	,	PUNCT
ejpam-6395	135	8	t	t	NOUN
ejpam-6395	135	9	)	)	PUNCT
ejpam-6395	135	10	⊆	⊆	PROPN
ejpam-6395	135	11	a	a	NOUN
ejpam-6395	135	12	)	)	PUNCT
ejpam-6395	135	13	;	;	PUNCT
ejpam-6395	135	14	(	(	PUNCT
ejpam-6395	135	15	ii	ii	NOUN
ejpam-6395	135	16	)	)	PUNCT
ejpam-6395	135	17	a	a	PRON
ejpam-6395	135	18	=	=	X
ejpam-6395	135	19	(	(	PUNCT
ejpam-6395	135	20	a]p	a]p	PROPN
ejpam-6395	135	21	.	.	PUNCT
ejpam-6395	136	1	a	a	DET
ejpam-6395	136	2	nonempty	nonempty	NOUN
ejpam-6395	136	3	subset	subset	VERB
ejpam-6395	136	4	a	a	PRON
ejpam-6395	136	5	of	of	ADP
ejpam-6395	136	6	t	t	PROPN
ejpam-6395	136	7	is	be	AUX
ejpam-6395	136	8	called	call	VERB
ejpam-6395	136	9	an	an	DET
ejpam-6395	136	10	ideal	ideal	NOUN
ejpam-6395	136	11	of	of	ADP
ejpam-6395	136	12	t	t	PROPN
ejpam-6395	136	13	if	if	SCONJ
ejpam-6395	136	14	a	a	PRON
ejpam-6395	136	15	is	be	AUX
ejpam-6395	136	16	a	a	DET
ejpam-6395	136	17	left	left	NOUN
ejpam-6395	136	18	,	,	PUNCT
ejpam-6395	136	19	right	right	ADJ
ejpam-6395	136	20	and	and	CCONJ
ejpam-6395	136	21	lateral	lateral	ADJ
ejpam-6395	136	22	ideal	ideal	NOUN
ejpam-6395	136	23	of	of	ADP
ejpam-6395	136	24	t	t	PROPN
ejpam-6395	136	25	.	.	PUNCT
ejpam-6395	137	1	an	an	DET
ejpam-6395	137	2	ideal	ideal	NOUN
ejpam-6395	137	3	a	a	PRON
ejpam-6395	137	4	of	of	ADP
ejpam-6395	137	5	t	t	PROPN
ejpam-6395	137	6	is	be	AUX
ejpam-6395	137	7	called	call	VERB
ejpam-6395	137	8	a	a	DET
ejpam-6395	137	9	proper	proper	ADJ
ejpam-6395	137	10	ideal	ideal	NOUN
ejpam-6395	137	11	if	if	SCONJ
ejpam-6395	137	12	a	a	DET
ejpam-6395	137	13	=	=	NOUN
ejpam-6395	137	14	̸	̸	NOUN
ejpam-6395	137	15	t	t	PROPN
ejpam-6395	137	16	.	.	PUNCT
ejpam-6395	138	1	a	a	DET
ejpam-6395	138	2	proper	proper	ADJ
ejpam-6395	138	3	ideal	ideal	NOUN
ejpam-6395	138	4	a	a	PRON
ejpam-6395	138	5	of	of	ADP
ejpam-6395	138	6	t	t	PROPN
ejpam-6395	138	7	is	be	AUX
ejpam-6395	138	8	called	call	VERB
ejpam-6395	138	9	the	the	DET
ejpam-6395	138	10	greatest	great	ADJ
ejpam-6395	138	11	ideal	ideal	NOUN
ejpam-6395	138	12	if	if	SCONJ
ejpam-6395	138	13	every	every	DET
ejpam-6395	138	14	proper	proper	ADJ
ejpam-6395	138	15	ideal	ideal	NOUN
ejpam-6395	138	16	is	be	AUX
ejpam-6395	138	17	contained	contain	VERB
ejpam-6395	138	18	in	in	ADP
ejpam-6395	138	19	a.	a.	NOUN
ejpam-6395	138	20	a	a	DET
ejpam-6395	138	21	proper	proper	ADJ
ejpam-6395	138	22	ideal	ideal	NOUN
ejpam-6395	138	23	a	a	PRON
ejpam-6395	138	24	of	of	ADP
ejpam-6395	138	25	t	t	PROPN
ejpam-6395	138	26	is	be	AUX
ejpam-6395	138	27	called	call	VERB
ejpam-6395	138	28	a	a	DET
ejpam-6395	138	29	maximal	maximal	ADJ
ejpam-6395	138	30	ideal	ideal	NOUN
ejpam-6395	138	31	if	if	SCONJ
ejpam-6395	138	32	whenever	whenever	SCONJ
ejpam-6395	138	33	there	there	PRON
ejpam-6395	138	34	exists	exist	VERB
ejpam-6395	138	35	an	an	DET
ejpam-6395	138	36	ideal	ideal	ADJ
ejpam-6395	138	37	b	b	PROPN
ejpam-6395	138	38	of	of	ADP
ejpam-6395	138	39	t	t	NOUN
ejpam-6395	138	40	such	such	ADJ
ejpam-6395	138	41	that	that	SCONJ
ejpam-6395	138	42	a	a	DET
ejpam-6395	138	43	⊂	⊂	PROPN
ejpam-6395	138	44	b	b	PROPN
ejpam-6395	138	45	then	then	ADV
ejpam-6395	138	46	b	b	PROPN
ejpam-6395	138	47	=	=	SYM
ejpam-6395	138	48	t	t	PROPN
ejpam-6395	138	49	.	.	PUNCT
ejpam-6395	139	1	if	if	SCONJ
ejpam-6395	139	2	t	t	PROPN
ejpam-6395	139	3	contains	contain	VERB
ejpam-6395	139	4	no	no	DET
ejpam-6395	139	5	proper	proper	ADJ
ejpam-6395	139	6	ideals	ideal	NOUN
ejpam-6395	139	7	then	then	ADV
ejpam-6395	139	8	t	t	PROPN
ejpam-6395	139	9	is	be	AUX
ejpam-6395	139	10	called	call	VERB
ejpam-6395	139	11	simple	simple	ADJ
ejpam-6395	139	12	.	.	PUNCT
ejpam-6395	140	1	proposition	proposition	NOUN
ejpam-6395	140	2	1	1	NUM
ejpam-6395	140	3	.	.	PUNCT
ejpam-6395	141	1	let	let	VERB
ejpam-6395	141	2	(	(	PUNCT
ejpam-6395	141	3	t	t	NOUN
ejpam-6395	141	4	,	,	PUNCT
ejpam-6395	141	5	•	•	X
ejpam-6395	141	6	)	)	PUNCT
ejpam-6395	141	7	be	be	AUX
ejpam-6395	141	8	an	an	DET
ejpam-6395	141	9	ordered	order	VERB
ejpam-6395	141	10	power	power	NOUN
ejpam-6395	141	11	ternary	ternary	NOUN
ejpam-6395	141	12	semigroup	semigroup	NOUN
ejpam-6395	141	13	on	on	ADP
ejpam-6395	141	14	a	a	DET
ejpam-6395	141	15	ternary	ternary	ADJ
ejpam-6395	141	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	141	17	(	(	PUNCT
ejpam-6395	141	18	s	s	X
ejpam-6395	141	19	,	,	PUNCT
ejpam-6395	141	20	⋄	⋄	PROPN
ejpam-6395	141	21	)	)	PUNCT
ejpam-6395	141	22	induced	induce	VERB
ejpam-6395	141	23	by	by	ADP
ejpam-6395	141	24	a	a	DET
ejpam-6395	141	25	poset	poset	NOUN
ejpam-6395	141	26	(	(	PUNCT
ejpam-6395	141	27	s,≤	s,≤	NOUN
ejpam-6395	141	28	)	)	PUNCT
ejpam-6395	141	29	.	.	PUNCT
ejpam-6395	142	1	then	then	ADV
ejpam-6395	142	2	the	the	DET
ejpam-6395	142	3	following	follow	VERB
ejpam-6395	142	4	statements	statement	NOUN
ejpam-6395	142	5	hold	hold	VERB
ejpam-6395	142	6	.	.	PUNCT
ejpam-6395	143	1	(	(	PUNCT
ejpam-6395	143	2	i	i	NOUN
ejpam-6395	143	3	)	)	PUNCT
ejpam-6395	143	4	if	if	SCONJ
ejpam-6395	143	5	a	a	DET
ejpam-6395	143	6	,	,	PUNCT
ejpam-6395	143	7	b	b	NOUN
ejpam-6395	143	8	and	and	CCONJ
ejpam-6395	143	9	c	c	PROPN
ejpam-6395	143	10	are	be	AUX
ejpam-6395	143	11	ideals	ideal	NOUN
ejpam-6395	143	12	of	of	ADP
ejpam-6395	143	13	t	t	NOUN
ejpam-6395	143	14	then	then	ADV
ejpam-6395	143	15	(	(	PUNCT
ejpam-6395	143	16	•(a	•(a	PROPN
ejpam-6395	143	17	,	,	PUNCT
ejpam-6395	143	18	b	b	NOUN
ejpam-6395	143	19	,	,	PUNCT
ejpam-6395	143	20	c)]p	c)]p	PROPN
ejpam-6395	143	21	is	be	AUX
ejpam-6395	143	22	an	an	DET
ejpam-6395	143	23	ideal	ideal	NOUN
ejpam-6395	143	24	of	of	ADP
ejpam-6395	143	25	t	t	PROPN
ejpam-6395	143	26	.	.	PUNCT
ejpam-6395	144	1	(	(	PUNCT
ejpam-6395	144	2	ii	ii	NOUN
ejpam-6395	144	3	)	)	PUNCT
ejpam-6395	144	4	if	if	SCONJ
ejpam-6395	144	5	a1	a1	PROPN
ejpam-6395	144	6	,	,	PUNCT
ejpam-6395	144	7	...	...	PUNCT
ejpam-6395	144	8	,	,	PUNCT
ejpam-6395	144	9	an	an	PRON
ejpam-6395	144	10	are	be	AUX
ejpam-6395	144	11	ideals	ideal	NOUN
ejpam-6395	144	12	of	of	ADP
ejpam-6395	144	13	t	t	PROPN
ejpam-6395	144	14	for	for	ADP
ejpam-6395	144	15	any	any	DET
ejpam-6395	144	16	n	n	NOUN
ejpam-6395	144	17	=	=	SYM
ejpam-6395	144	18	2k	2k	NOUN
ejpam-6395	144	19	+	+	CCONJ
ejpam-6395	144	20	1	1	NUM
ejpam-6395	144	21	and	and	CCONJ
ejpam-6395	144	22	k	k	PROPN
ejpam-6395	144	23	∈	∈	PROPN
ejpam-6395	144	24	n	n	CCONJ
ejpam-6395	144	25	then	then	ADV
ejpam-6395	144	26	•(a1,a2	•(a1,a2	NOUN
ejpam-6395	144	27	,	,	PUNCT
ejpam-6395	144	28	•	•	NUM
ejpam-6395	144	29	...	...	SYM
ejpam-6395	144	30	•	•	PRON
ejpam-6395	144	31	(	(	PUNCT
ejpam-6395	144	32	an−2,an−1,an	an−2,an−1,an	PROPN
ejpam-6395	144	33	)	)	PUNCT
ejpam-6395	144	34	)	)	PUNCT
ejpam-6395	145	1	⊆	⊆	NUM
ejpam-6395	145	2	a1	a1	NOUN
ejpam-6395	145	3	∩	∩	NOUN
ejpam-6395	145	4	...	...	PUNCT
ejpam-6395	145	5	∩	∩	NOUN
ejpam-6395	145	6	an	an	X
ejpam-6395	145	7	.	.	PUNCT
ejpam-6395	145	8	(	(	PUNCT
ejpam-6395	145	9	iii	iii	X
ejpam-6395	145	10	)	)	PUNCT
ejpam-6395	145	11	the	the	DET
ejpam-6395	145	12	union	union	NOUN
ejpam-6395	145	13	of	of	ADP
ejpam-6395	145	14	ideals	ideal	NOUN
ejpam-6395	145	15	of	of	ADP
ejpam-6395	145	16	t	t	PROPN
ejpam-6395	145	17	is	be	AUX
ejpam-6395	145	18	an	an	DET
ejpam-6395	145	19	ideal	ideal	NOUN
ejpam-6395	145	20	of	of	ADP
ejpam-6395	145	21	t	t	PROPN
ejpam-6395	145	22	.	.	PUNCT
ejpam-6395	146	1	(	(	PUNCT
ejpam-6395	146	2	iv	iv	X
ejpam-6395	146	3	)	)	PUNCT
ejpam-6395	146	4	the	the	DET
ejpam-6395	146	5	finite	finite	ADJ
ejpam-6395	146	6	intersection	intersection	NOUN
ejpam-6395	146	7	of	of	ADP
ejpam-6395	146	8	ideals	ideal	NOUN
ejpam-6395	146	9	of	of	ADP
ejpam-6395	146	10	t	t	PROPN
ejpam-6395	146	11	is	be	AUX
ejpam-6395	146	12	an	an	DET
ejpam-6395	146	13	ideal	ideal	NOUN
ejpam-6395	146	14	of	of	ADP
ejpam-6395	146	15	t	t	PROPN
ejpam-6395	146	16	.	.	PUNCT
ejpam-6395	147	1	(	(	PUNCT
ejpam-6395	147	2	v	v	NOUN
ejpam-6395	147	3	)	)	PUNCT
ejpam-6395	147	4	if	if	SCONJ
ejpam-6395	147	5	a	a	DET
ejpam-6395	147	6	⊆	⊆	NUM
ejpam-6395	147	7	t	t	NOUN
ejpam-6395	147	8	then	then	ADV
ejpam-6395	147	9	(	(	PUNCT
ejpam-6395	147	10	•(t	•(t	INTJ
ejpam-6395	147	11	,	,	PUNCT
ejpam-6395	147	12	a	a	PRON
ejpam-6395	147	13	,	,	PUNCT
ejpam-6395	147	14	t	t	NOUN
ejpam-6395	147	15	)	)	PUNCT
ejpam-6395	147	16	]	]	X
ejpam-6395	147	17	p	p	X
ejpam-6395	147	18	is	be	AUX
ejpam-6395	147	19	an	an	DET
ejpam-6395	147	20	ideal	ideal	NOUN
ejpam-6395	147	21	of	of	ADP
ejpam-6395	147	22	t	t	PROPN
ejpam-6395	147	23	.	.	PUNCT
ejpam-6395	148	1	proof	proof	NOUN
ejpam-6395	148	2	.	.	PUNCT
ejpam-6395	149	1	the	the	DET
ejpam-6395	149	2	proof	proof	NOUN
ejpam-6395	149	3	is	be	AUX
ejpam-6395	149	4	straightforward	straightforward	ADJ
ejpam-6395	149	5	.	.	PUNCT
ejpam-6395	150	1	proposition	proposition	NOUN
ejpam-6395	150	2	2	2	NUM
ejpam-6395	150	3	.	.	PUNCT
ejpam-6395	151	1	let	let	AUX
ejpam-6395	151	2	(	(	PUNCT
ejpam-6395	151	3	t	t	NOUN
ejpam-6395	151	4	,	,	PUNCT
ejpam-6395	151	5	•	•	X
ejpam-6395	151	6	)	)	PUNCT
ejpam-6395	151	7	be	be	AUX
ejpam-6395	151	8	an	an	DET
ejpam-6395	151	9	ordered	order	VERB
ejpam-6395	151	10	power	power	NOUN
ejpam-6395	151	11	ternary	ternary	NOUN
ejpam-6395	151	12	semigroup	semigroup	NOUN
ejpam-6395	151	13	on	on	ADP
ejpam-6395	151	14	a	a	DET
ejpam-6395	151	15	ternary	ternary	ADJ
ejpam-6395	151	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	151	17	(	(	PUNCT
ejpam-6395	151	18	s	s	X
ejpam-6395	151	19	,	,	PUNCT
ejpam-6395	151	20	⋄	⋄	PROPN
ejpam-6395	151	21	)	)	PUNCT
ejpam-6395	151	22	induced	induce	VERB
ejpam-6395	151	23	by	by	ADP
ejpam-6395	151	24	a	a	DET
ejpam-6395	151	25	poset	poset	NOUN
ejpam-6395	151	26	(	(	PUNCT
ejpam-6395	151	27	s,≤	s,≤	NOUN
ejpam-6395	151	28	)	)	PUNCT
ejpam-6395	151	29	and	and	CCONJ
ejpam-6395	151	30	∅	∅	NOUN
ejpam-6395	151	31	̸=	̸=	PROPN
ejpam-6395	151	32	a	a	DET
ejpam-6395	151	33	⊆	⊆	NUM
ejpam-6395	151	34	t	t	NOUN
ejpam-6395	151	35	.	.	PUNCT
ejpam-6395	152	1	then	then	ADV
ejpam-6395	152	2	(	(	PUNCT
ejpam-6395	152	3	a	a	DET
ejpam-6395	152	4	∪	∪	ADJ
ejpam-6395	152	5	•(t	•(t	NOUN
ejpam-6395	152	6	,	,	PUNCT
ejpam-6395	152	7	t	t	PROPN
ejpam-6395	152	8	,	,	PUNCT
ejpam-6395	152	9	a)]p	a)]p	PROPN
ejpam-6395	152	10	(	(	PUNCT
ejpam-6395	152	11	resp	resp	NOUN
ejpam-6395	152	12	.	.	PUNCT
ejpam-6395	153	1	(	(	PUNCT
ejpam-6395	153	2	a	a	DET
ejpam-6395	153	3	∪	∪	ADJ
ejpam-6395	153	4	•(a	•(a	PROPN
ejpam-6395	153	5	,	,	PUNCT
ejpam-6395	153	6	t	t	PROPN
ejpam-6395	153	7	,	,	PUNCT
ejpam-6395	153	8	t	t	PROPN
ejpam-6395	153	9	)	)	PUNCT
ejpam-6395	154	1	]	]	X
ejpam-6395	154	2	p	p	X
ejpam-6395	154	3	,	,	PUNCT
ejpam-6395	154	4	(	(	PUNCT
ejpam-6395	154	5	a	a	DET
ejpam-6395	154	6	∪	∪	ADJ
ejpam-6395	154	7	•(t	•(t	NOUN
ejpam-6395	154	8	,	,	PUNCT
ejpam-6395	154	9	a	a	PRON
ejpam-6395	154	10	,	,	PUNCT
ejpam-6395	154	11	t	t	NOUN
ejpam-6395	154	12	)	)	PUNCT
ejpam-6395	155	1	]	]	X
ejpam-6395	155	2	p	p	X
ejpam-6395	155	3	and	and	CCONJ
ejpam-6395	155	4	(	(	PUNCT
ejpam-6395	155	5	a	a	DET
ejpam-6395	155	6	∪	∪	ADJ
ejpam-6395	155	7	•(t	•(t	NOUN
ejpam-6395	155	8	,	,	PUNCT
ejpam-6395	155	9	t	t	PROPN
ejpam-6395	155	10	,	,	PUNCT
ejpam-6395	155	11	a	a	PRON
ejpam-6395	155	12	)	)	PUNCT
ejpam-6395	155	13	∪	∪	ADP
ejpam-6395	155	14	•(a	•(a	PROPN
ejpam-6395	155	15	,	,	PUNCT
ejpam-6395	155	16	t	t	PROPN
ejpam-6395	155	17	,	,	PUNCT
ejpam-6395	155	18	t	t	PROPN
ejpam-6395	155	19	)	)	PUNCT
ejpam-6395	155	20	∪	∪	ADP
ejpam-6395	155	21	•(t	•(t	PROPN
ejpam-6395	155	22	,	,	PUNCT
ejpam-6395	155	23	a	a	PRON
ejpam-6395	155	24	,	,	PUNCT
ejpam-6395	155	25	t	t	NOUN
ejpam-6395	155	26	)	)	PUNCT
ejpam-6395	156	1	]	]	X
ejpam-6395	156	2	p	p	X
ejpam-6395	156	3	)	)	PUNCT
ejpam-6395	156	4	is	be	AUX
ejpam-6395	156	5	the	the	DET
ejpam-6395	156	6	smallest	small	ADJ
ejpam-6395	156	7	left	leave	VERB
ejpam-6395	156	8	ideal	ideal	NOUN
ejpam-6395	156	9	(	(	PUNCT
ejpam-6395	156	10	resp	resp	NOUN
ejpam-6395	156	11	.	.	PUNCT
ejpam-6395	157	1	right	right	ADJ
ejpam-6395	157	2	ideal	ideal	ADJ
ejpam-6395	157	3	,	,	PUNCT
ejpam-6395	157	4	lateral	lateral	ADJ
ejpam-6395	157	5	ideal	ideal	NOUN
ejpam-6395	157	6	and	and	CCONJ
ejpam-6395	157	7	ideal	ideal	ADJ
ejpam-6395	157	8	)	)	PUNCT
ejpam-6395	157	9	of	of	ADP
ejpam-6395	157	10	t	t	NOUN
ejpam-6395	157	11	containing	contain	VERB
ejpam-6395	157	12	a.	a.	NOUN
ejpam-6395	157	13	proof	proof	NOUN
ejpam-6395	157	14	.	.	PUNCT
ejpam-6395	158	1	the	the	DET
ejpam-6395	158	2	proof	proof	NOUN
ejpam-6395	158	3	is	be	AUX
ejpam-6395	158	4	straightforward	straightforward	ADJ
ejpam-6395	158	5	.	.	PUNCT
ejpam-6395	159	1	a.	a.	NOUN
ejpam-6395	159	2	nongmanee	nongmanee	PROPN
ejpam-6395	159	3	,	,	PUNCT
ejpam-6395	159	4	k.	k.	PROPN
ejpam-6395	159	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	159	6	,	,	PUNCT
ejpam-6395	159	7	m.	m.	NOUN
ejpam-6395	159	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	159	9	/	/	SYM
ejpam-6395	159	10	eur	eur	PROPN
ejpam-6395	159	11	.	.	PUNCT
ejpam-6395	160	1	j.	j.	PROPN
ejpam-6395	160	2	pure	pure	PROPN
ejpam-6395	160	3	appl	appl	PROPN
ejpam-6395	160	4	.	.	PROPN
ejpam-6395	160	5	math	math	PROPN
ejpam-6395	160	6	,	,	PUNCT
ejpam-6395	160	7	18	18	NUM
ejpam-6395	160	8	(	(	PUNCT
ejpam-6395	160	9	3	3	NUM
ejpam-6395	160	10	)	)	PUNCT
ejpam-6395	160	11	(	(	PUNCT
ejpam-6395	160	12	2025	2025	NUM
ejpam-6395	160	13	)	)	PUNCT
ejpam-6395	160	14	,	,	PUNCT
ejpam-6395	160	15	6395	6395	NUM
ejpam-6395	160	16	6	6	NUM
ejpam-6395	160	17	of	of	ADP
ejpam-6395	160	18	12	12	NUM
ejpam-6395	160	19	4	4	NUM
ejpam-6395	160	20	.	.	PUNCT
ejpam-6395	161	1	pure	pure	ADJ
ejpam-6395	161	2	ideals	ideal	NOUN
ejpam-6395	161	3	and	and	CCONJ
ejpam-6395	161	4	weakly	weakly	ADJ
ejpam-6395	161	5	pure	pure	ADJ
ejpam-6395	161	6	ideals	ideal	NOUN
ejpam-6395	161	7	in	in	ADP
ejpam-6395	161	8	ordered	order	VERB
ejpam-6395	161	9	power	power	NOUN
ejpam-6395	161	10	ternary	ternary	ADJ
ejpam-6395	161	11	semigroups	semigroup	NOUN
ejpam-6395	161	12	on	on	ADP
ejpam-6395	161	13	ternary	ternary	ADJ
ejpam-6395	161	14	semihypergroups	semihypergroup	NOUN
ejpam-6395	161	15	induced	induce	VERB
ejpam-6395	161	16	by	by	ADP
ejpam-6395	161	17	posets	poset	NOUN
ejpam-6395	161	18	definition	definition	NOUN
ejpam-6395	161	19	6	6	NUM
ejpam-6395	161	20	.	.	PUNCT
ejpam-6395	162	1	let	let	AUX
ejpam-6395	162	2	(	(	PUNCT
ejpam-6395	162	3	t	t	NOUN
ejpam-6395	162	4	,	,	PUNCT
ejpam-6395	162	5	•,≤p	•,≤p	NOUN
ejpam-6395	162	6	)	)	PUNCT
ejpam-6395	162	7	be	be	VERB
ejpam-6395	162	8	an	an	DET
ejpam-6395	162	9	ordered	order	VERB
ejpam-6395	162	10	power	power	NOUN
ejpam-6395	162	11	ternary	ternary	NOUN
ejpam-6395	162	12	semigroup	semigroup	NOUN
ejpam-6395	162	13	on	on	ADP
ejpam-6395	162	14	a	a	DET
ejpam-6395	162	15	ternary	ternary	ADJ
ejpam-6395	162	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	162	17	(	(	PUNCT
ejpam-6395	162	18	s	s	X
ejpam-6395	162	19	,	,	PUNCT
ejpam-6395	162	20	⋄	⋄	PROPN
ejpam-6395	162	21	)	)	PUNCT
ejpam-6395	162	22	induced	induce	VERB
ejpam-6395	162	23	by	by	ADP
ejpam-6395	162	24	a	a	DET
ejpam-6395	162	25	poset	poset	NOUN
ejpam-6395	162	26	(	(	PUNCT
ejpam-6395	162	27	s,≤	s,≤	NOUN
ejpam-6395	162	28	)	)	PUNCT
ejpam-6395	162	29	.	.	PUNCT
ejpam-6395	163	1	a	a	DET
ejpam-6395	163	2	left	left	ADJ
ejpam-6395	163	3	(	(	PUNCT
ejpam-6395	163	4	resp	resp	NOUN
ejpam-6395	163	5	.	.	PUNCT
ejpam-6395	164	1	right	right	ADJ
ejpam-6395	164	2	,	,	PUNCT
ejpam-6395	164	3	lateral	lateral	ADJ
ejpam-6395	164	4	)	)	PUNCT
ejpam-6395	164	5	ideal	ideal	NOUN
ejpam-6395	164	6	a	a	PRON
ejpam-6395	164	7	of	of	ADP
ejpam-6395	164	8	t	t	PROPN
ejpam-6395	164	9	is	be	AUX
ejpam-6395	164	10	called	call	VERB
ejpam-6395	164	11	a	a	DET
ejpam-6395	164	12	one	one	NUM
ejpam-6395	164	13	-	-	PUNCT
ejpam-6395	164	14	sided	sided	ADJ
ejpam-6395	164	15	left	left	NOUN
ejpam-6395	164	16	(	(	PUNCT
ejpam-6395	164	17	resp	resp	NOUN
ejpam-6395	164	18	.	.	PUNCT
ejpam-6395	165	1	right	right	ADJ
ejpam-6395	165	2	,	,	PUNCT
ejpam-6395	165	3	lateral	lateral	ADJ
ejpam-6395	165	4	)	)	PUNCT
ejpam-6395	165	5	pure	pure	ADJ
ejpam-6395	165	6	ideal	ideal	NOUN
ejpam-6395	165	7	if	if	SCONJ
ejpam-6395	165	8	for	for	ADP
ejpam-6395	165	9	x	x	PROPN
ejpam-6395	165	10	∈	∈	PROPN
ejpam-6395	165	11	a	a	PRON
ejpam-6395	165	12	,	,	PUNCT
ejpam-6395	165	13	there	there	PRON
ejpam-6395	165	14	exists	exist	VERB
ejpam-6395	165	15	y	y	PROPN
ejpam-6395	165	16	,	,	PUNCT
ejpam-6395	165	17	z	z	PROPN
ejpam-6395	165	18	∈	∈	PROPN
ejpam-6395	165	19	a	a	DET
ejpam-6395	165	20	such	such	ADJ
ejpam-6395	165	21	that	that	SCONJ
ejpam-6395	165	22	x	x	SYM
ejpam-6395	165	23	≤p	≤p	NOUN
ejpam-6395	165	24	•(y	•(y	NOUN
ejpam-6395	165	25	,	,	PUNCT
ejpam-6395	165	26	z	z	NOUN
ejpam-6395	165	27	,	,	PUNCT
ejpam-6395	165	28	x	x	X
ejpam-6395	165	29	)	)	PUNCT
ejpam-6395	165	30	(	(	PUNCT
ejpam-6395	165	31	resp	resp	NOUN
ejpam-6395	165	32	.	.	PUNCT
ejpam-6395	166	1	x	x	SYM
ejpam-6395	166	2	≤p	≤p	PROPN
ejpam-6395	166	3	•(x	•(x	PROPN
ejpam-6395	166	4	,	,	PUNCT
ejpam-6395	166	5	y	y	PROPN
ejpam-6395	166	6	,	,	PUNCT
ejpam-6395	166	7	z	z	NOUN
ejpam-6395	166	8	)	)	PUNCT
ejpam-6395	166	9	,	,	PUNCT
ejpam-6395	166	10	x	x	SYM
ejpam-6395	166	11	≤p	≤p	ADJ
ejpam-6395	166	12	•(y	•(y	NOUN
ejpam-6395	166	13	,	,	PUNCT
ejpam-6395	166	14	x	x	NOUN
ejpam-6395	166	15	,	,	PUNCT
ejpam-6395	166	16	z	z	NOUN
ejpam-6395	166	17	)	)	PUNCT
ejpam-6395	166	18	)	)	PUNCT
ejpam-6395	166	19	.	.	PUNCT
ejpam-6395	167	1	definition	definition	NOUN
ejpam-6395	167	2	7	7	NUM
ejpam-6395	167	3	.	.	PUNCT
ejpam-6395	168	1	let	let	AUX
ejpam-6395	168	2	(	(	PUNCT
ejpam-6395	168	3	t	t	NOUN
ejpam-6395	168	4	,	,	PUNCT
ejpam-6395	168	5	•,≤p	•,≤p	NOUN
ejpam-6395	168	6	)	)	PUNCT
ejpam-6395	168	7	be	be	VERB
ejpam-6395	168	8	an	an	DET
ejpam-6395	168	9	ordered	order	VERB
ejpam-6395	168	10	power	power	NOUN
ejpam-6395	168	11	ternary	ternary	NOUN
ejpam-6395	168	12	semigroup	semigroup	NOUN
ejpam-6395	168	13	on	on	ADP
ejpam-6395	168	14	a	a	DET
ejpam-6395	168	15	ternary	ternary	ADJ
ejpam-6395	168	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	168	17	(	(	PUNCT
ejpam-6395	168	18	s	s	X
ejpam-6395	168	19	,	,	PUNCT
ejpam-6395	168	20	⋄	⋄	PROPN
ejpam-6395	168	21	)	)	PUNCT
ejpam-6395	168	22	induced	induce	VERB
ejpam-6395	168	23	by	by	ADP
ejpam-6395	168	24	a	a	DET
ejpam-6395	168	25	poset	poset	NOUN
ejpam-6395	168	26	(	(	PUNCT
ejpam-6395	168	27	s,≤	s,≤	NOUN
ejpam-6395	168	28	)	)	PUNCT
ejpam-6395	168	29	.	.	PUNCT
ejpam-6395	169	1	an	an	DET
ejpam-6395	169	2	ideal	ideal	NOUN
ejpam-6395	169	3	a	a	PRON
ejpam-6395	169	4	of	of	ADP
ejpam-6395	169	5	t	t	PROPN
ejpam-6395	169	6	is	be	AUX
ejpam-6395	169	7	called	call	VERB
ejpam-6395	169	8	a	a	DET
ejpam-6395	169	9	left	left	ADJ
ejpam-6395	169	10	(	(	PUNCT
ejpam-6395	169	11	resp	resp	NOUN
ejpam-6395	169	12	.	.	PUNCT
ejpam-6395	170	1	right	right	ADJ
ejpam-6395	170	2	,	,	PUNCT
ejpam-6395	170	3	lateral	lateral	ADJ
ejpam-6395	170	4	)	)	PUNCT
ejpam-6395	170	5	pure	pure	ADJ
ejpam-6395	170	6	ideal	ideal	NOUN
ejpam-6395	170	7	if	if	SCONJ
ejpam-6395	170	8	for	for	ADP
ejpam-6395	170	9	x	x	PROPN
ejpam-6395	170	10	∈	∈	PROPN
ejpam-6395	170	11	a	a	DET
ejpam-6395	170	12	there	there	PRON
ejpam-6395	170	13	exists	exist	VERB
ejpam-6395	170	14	y	y	PROPN
ejpam-6395	170	15	,	,	PUNCT
ejpam-6395	170	16	z	z	PROPN
ejpam-6395	170	17	∈	∈	PROPN
ejpam-6395	170	18	a	a	DET
ejpam-6395	170	19	such	such	ADJ
ejpam-6395	170	20	that	that	SCONJ
ejpam-6395	170	21	x	x	SYM
ejpam-6395	170	22	≤p	≤p	NOUN
ejpam-6395	170	23	•(y	•(y	NOUN
ejpam-6395	170	24	,	,	PUNCT
ejpam-6395	170	25	z	z	NOUN
ejpam-6395	170	26	,	,	PUNCT
ejpam-6395	170	27	x	x	X
ejpam-6395	170	28	)	)	PUNCT
ejpam-6395	170	29	(	(	PUNCT
ejpam-6395	170	30	resp	resp	NOUN
ejpam-6395	170	31	.	.	PUNCT
ejpam-6395	171	1	x	x	SYM
ejpam-6395	171	2	≤p	≤p	PROPN
ejpam-6395	171	3	•(x	•(x	PROPN
ejpam-6395	171	4	,	,	PUNCT
ejpam-6395	171	5	y	y	PROPN
ejpam-6395	171	6	,	,	PUNCT
ejpam-6395	171	7	z	z	NOUN
ejpam-6395	171	8	)	)	PUNCT
ejpam-6395	171	9	,	,	PUNCT
ejpam-6395	171	10	x	x	SYM
ejpam-6395	171	11	≤p	≤p	ADJ
ejpam-6395	171	12	•(y	•(y	NOUN
ejpam-6395	171	13	,	,	PUNCT
ejpam-6395	171	14	x	x	NOUN
ejpam-6395	171	15	,	,	PUNCT
ejpam-6395	171	16	z	z	NOUN
ejpam-6395	171	17	)	)	PUNCT
ejpam-6395	171	18	)	)	PUNCT
ejpam-6395	171	19	.	.	PUNCT
ejpam-6395	172	1	we	we	PRON
ejpam-6395	172	2	can	can	AUX
ejpam-6395	172	3	say	say	VERB
ejpam-6395	172	4	that	that	SCONJ
ejpam-6395	172	5	an	an	DET
ejpam-6395	172	6	ideal	ideal	NOUN
ejpam-6395	172	7	a	a	PRON
ejpam-6395	172	8	of	of	ADP
ejpam-6395	172	9	t	t	PROPN
ejpam-6395	172	10	is	be	AUX
ejpam-6395	172	11	called	call	VERB
ejpam-6395	172	12	a	a	DET
ejpam-6395	172	13	left	left	ADJ
ejpam-6395	172	14	(	(	PUNCT
ejpam-6395	172	15	resp	resp	NOUN
ejpam-6395	172	16	.	.	PUNCT
ejpam-6395	173	1	right	right	ADJ
ejpam-6395	173	2	,	,	PUNCT
ejpam-6395	173	3	lateral	lateral	ADJ
ejpam-6395	173	4	)	)	PUNCT
ejpam-6395	173	5	pure	pure	ADJ
ejpam-6395	173	6	ideal	ideal	NOUN
ejpam-6395	173	7	if	if	SCONJ
ejpam-6395	173	8	x	x	SYM
ejpam-6395	173	9	∈	∈	PROPN
ejpam-6395	173	10	(	(	PUNCT
ejpam-6395	173	11	•(a	•(a	PROPN
ejpam-6395	173	12	,	,	PUNCT
ejpam-6395	173	13	a	a	PRON
ejpam-6395	173	14	,	,	PUNCT
ejpam-6395	173	15	x)]p	x)]p	PROPN
ejpam-6395	173	16	(	(	PUNCT
ejpam-6395	173	17	resp	resp	NOUN
ejpam-6395	173	18	.	.	PUNCT
ejpam-6395	174	1	x	x	X
ejpam-6395	174	2	∈	∈	PROPN
ejpam-6395	174	3	(	(	PUNCT
ejpam-6395	174	4	•(x	•(x	PROPN
ejpam-6395	174	5	,	,	PUNCT
ejpam-6395	174	6	a	a	DET
ejpam-6395	174	7	,	,	PUNCT
ejpam-6395	174	8	a)]p	a)]p	PROPN
ejpam-6395	174	9	,	,	PUNCT
ejpam-6395	174	10	x	x	SYM
ejpam-6395	174	11	∈	∈	PROPN
ejpam-6395	174	12	(	(	PUNCT
ejpam-6395	174	13	•(a	•(a	PROPN
ejpam-6395	174	14	,	,	PUNCT
ejpam-6395	174	15	x	x	NOUN
ejpam-6395	174	16	,	,	PUNCT
ejpam-6395	174	17	a)]p	a)]p	PROPN
ejpam-6395	174	18	)	)	PUNCT
ejpam-6395	174	19	.	.	PUNCT
ejpam-6395	175	1	example	example	NOUN
ejpam-6395	176	1	2	2	NUM
ejpam-6395	176	2	.	.	X
ejpam-6395	176	3	from	from	ADP
ejpam-6395	176	4	example	example	NOUN
ejpam-6395	176	5	1	1	NUM
ejpam-6395	176	6	,	,	PUNCT
ejpam-6395	176	7	let	let	VERB
ejpam-6395	176	8	h	h	NOUN
ejpam-6395	176	9	=	=	PRON
ejpam-6395	176	10	{	{	PUNCT
ejpam-6395	176	11	{	{	PUNCT
ejpam-6395	176	12	x	x	NOUN
ejpam-6395	176	13	}	}	PUNCT
ejpam-6395	176	14	,	,	PUNCT
ejpam-6395	176	15	{	{	PUNCT
ejpam-6395	176	16	y	y	NOUN
ejpam-6395	176	17	}	}	PUNCT
ejpam-6395	176	18	,	,	PUNCT
ejpam-6395	176	19	{	{	PUNCT
ejpam-6395	176	20	x	x	NOUN
ejpam-6395	176	21	,	,	PUNCT
ejpam-6395	176	22	y	y	NOUN
ejpam-6395	176	23	}	}	PUNCT
ejpam-6395	176	24	}	}	PUNCT
ejpam-6395	176	25	.	.	PUNCT
ejpam-6395	177	1	we	we	PRON
ejpam-6395	177	2	have	have	VERB
ejpam-6395	177	3	the	the	DET
ejpam-6395	177	4	cayley	cayley	NOUN
ejpam-6395	177	5	’s	’s	NOUN
ejpam-6395	177	6	table	table	NOUN
ejpam-6395	177	7	of	of	ADP
ejpam-6395	177	8	the	the	DET
ejpam-6395	177	9	operation	operation	NOUN
ejpam-6395	177	10	•	•	NOUN
ejpam-6395	177	11	on	on	ADP
ejpam-6395	177	12	h	h	NOUN
ejpam-6395	177	13	as	as	SCONJ
ejpam-6395	177	14	follows	follow	VERB
ejpam-6395	177	15	.	.	PUNCT
ejpam-6395	178	1	we	we	PRON
ejpam-6395	178	2	can	can	AUX
ejpam-6395	178	3	see	see	VERB
ejpam-6395	178	4	that	that	PRON
ejpam-6395	178	5	(	(	PUNCT
ejpam-6395	178	6	h	h	NOUN
ejpam-6395	178	7	,	,	PUNCT
ejpam-6395	178	8	•,≤p	•,≤p	NOUN
ejpam-6395	178	9	)	)	PUNCT
ejpam-6395	178	10	is	be	AUX
ejpam-6395	178	11	an	an	DET
ejpam-6395	178	12	ordered	order	VERB
ejpam-6395	178	13	power	power	NOUN
ejpam-6395	178	14	ternary	ternary	NOUN
ejpam-6395	178	15	semigroup	semigroup	NOUN
ejpam-6395	178	16	on	on	ADP
ejpam-6395	178	17	a	a	DET
ejpam-6395	178	18	ternary	ternary	ADJ
ejpam-6395	178	19	semihypergroup	semihypergroup	NOUN
ejpam-6395	178	20	(	(	PUNCT
ejpam-6395	178	21	s	s	X
ejpam-6395	178	22	,	,	PUNCT
ejpam-6395	178	23	⋄	⋄	PROPN
ejpam-6395	178	24	)	)	PUNCT
ejpam-6395	178	25	induced	induce	VERB
ejpam-6395	178	26	by	by	ADP
ejpam-6395	178	27	a	a	DET
ejpam-6395	178	28	poset	poset	NOUN
ejpam-6395	178	29	(	(	PUNCT
ejpam-6395	178	30	s,≤	s,≤	NOUN
ejpam-6395	178	31	)	)	PUNCT
ejpam-6395	178	32	.	.	PUNCT
ejpam-6395	179	1	•	•	NUM
ejpam-6395	179	2	{	{	PUNCT
ejpam-6395	179	3	x	x	NOUN
ejpam-6395	179	4	}	}	PUNCT
ejpam-6395	179	5	{	{	PUNCT
ejpam-6395	179	6	y	y	NOUN
ejpam-6395	179	7	}	}	PUNCT
ejpam-6395	179	8	{	{	PUNCT
ejpam-6395	179	9	x	x	NOUN
ejpam-6395	179	10	,	,	PUNCT
ejpam-6395	179	11	y	y	NOUN
ejpam-6395	179	12	}	}	PUNCT
ejpam-6395	179	13	{	{	PUNCT
ejpam-6395	179	14	x	x	NOUN
ejpam-6395	179	15	}	}	PUNCT
ejpam-6395	179	16	,	,	PUNCT
ejpam-6395	179	17	{	{	PUNCT
ejpam-6395	179	18	x	x	X
ejpam-6395	179	19	}	}	PUNCT
ejpam-6395	179	20	{	{	PUNCT
ejpam-6395	179	21	x	x	NOUN
ejpam-6395	179	22	}	}	PUNCT
ejpam-6395	179	23	{	{	PUNCT
ejpam-6395	179	24	y	y	NOUN
ejpam-6395	179	25	}	}	PUNCT
ejpam-6395	179	26	{	{	PUNCT
ejpam-6395	179	27	x	x	NOUN
ejpam-6395	179	28	,	,	PUNCT
ejpam-6395	179	29	y	y	NOUN
ejpam-6395	179	30	}	}	PUNCT
ejpam-6395	179	31	{	{	PUNCT
ejpam-6395	179	32	x	x	NOUN
ejpam-6395	179	33	}	}	PUNCT
ejpam-6395	179	34	,	,	PUNCT
ejpam-6395	179	35	{	{	PUNCT
ejpam-6395	179	36	y	y	NOUN
ejpam-6395	179	37	}	}	PUNCT
ejpam-6395	179	38	{	{	PUNCT
ejpam-6395	179	39	y	y	NOUN
ejpam-6395	179	40	}	}	PUNCT
ejpam-6395	179	41	{	{	PUNCT
ejpam-6395	179	42	y	y	NOUN
ejpam-6395	179	43	}	}	PUNCT
ejpam-6395	179	44	{	{	PUNCT
ejpam-6395	179	45	x	x	NOUN
ejpam-6395	179	46	,	,	PUNCT
ejpam-6395	179	47	y	y	NOUN
ejpam-6395	179	48	}	}	PUNCT
ejpam-6395	179	49	{	{	PUNCT
ejpam-6395	179	50	x	x	NOUN
ejpam-6395	179	51	}	}	PUNCT
ejpam-6395	179	52	,	,	PUNCT
ejpam-6395	179	53	{	{	PUNCT
ejpam-6395	179	54	x	x	NOUN
ejpam-6395	179	55	,	,	PUNCT
ejpam-6395	179	56	y	y	NOUN
ejpam-6395	179	57	}	}	PUNCT
ejpam-6395	179	58	{	{	PUNCT
ejpam-6395	179	59	x	x	NOUN
ejpam-6395	179	60	,	,	PUNCT
ejpam-6395	179	61	y	y	NOUN
ejpam-6395	179	62	}	}	PUNCT
ejpam-6395	179	63	{	{	PUNCT
ejpam-6395	179	64	y	y	NOUN
ejpam-6395	179	65	}	}	PUNCT
ejpam-6395	179	66	{	{	PUNCT
ejpam-6395	179	67	x	x	NOUN
ejpam-6395	179	68	,	,	PUNCT
ejpam-6395	179	69	y	y	NOUN
ejpam-6395	179	70	}	}	PUNCT
ejpam-6395	179	71	{	{	PUNCT
ejpam-6395	179	72	y	y	NOUN
ejpam-6395	179	73	}	}	PUNCT
ejpam-6395	179	74	,	,	PUNCT
ejpam-6395	179	75	{	{	PUNCT
ejpam-6395	179	76	x	x	X
ejpam-6395	179	77	}	}	PUNCT
ejpam-6395	179	78	{	{	PUNCT
ejpam-6395	179	79	y	y	NOUN
ejpam-6395	179	80	}	}	PUNCT
ejpam-6395	179	81	{	{	PUNCT
ejpam-6395	179	82	y	y	NOUN
ejpam-6395	179	83	}	}	PUNCT
ejpam-6395	179	84	{	{	PUNCT
ejpam-6395	179	85	y	y	NOUN
ejpam-6395	179	86	}	}	PUNCT
ejpam-6395	179	87	{	{	PUNCT
ejpam-6395	179	88	y	y	NOUN
ejpam-6395	179	89	}	}	PUNCT
ejpam-6395	179	90	,	,	PUNCT
ejpam-6395	179	91	{	{	PUNCT
ejpam-6395	179	92	y	y	NOUN
ejpam-6395	179	93	}	}	PUNCT
ejpam-6395	179	94	{	{	PUNCT
ejpam-6395	179	95	y	y	NOUN
ejpam-6395	179	96	}	}	PUNCT
ejpam-6395	179	97	{	{	PUNCT
ejpam-6395	179	98	y	y	NOUN
ejpam-6395	179	99	}	}	PUNCT
ejpam-6395	179	100	{	{	PUNCT
ejpam-6395	179	101	y	y	NOUN
ejpam-6395	179	102	}	}	PUNCT
ejpam-6395	179	103	{	{	PUNCT
ejpam-6395	179	104	y	y	NOUN
ejpam-6395	179	105	}	}	PUNCT
ejpam-6395	179	106	,	,	PUNCT
ejpam-6395	179	107	{	{	PUNCT
ejpam-6395	179	108	x	x	NOUN
ejpam-6395	179	109	,	,	PUNCT
ejpam-6395	179	110	y	y	NOUN
ejpam-6395	179	111	}	}	PUNCT
ejpam-6395	179	112	{	{	PUNCT
ejpam-6395	179	113	y	y	NOUN
ejpam-6395	179	114	}	}	PUNCT
ejpam-6395	179	115	{	{	PUNCT
ejpam-6395	179	116	y	y	NOUN
ejpam-6395	179	117	}	}	PUNCT
ejpam-6395	179	118	{	{	PUNCT
ejpam-6395	179	119	y	y	NOUN
ejpam-6395	179	120	}	}	PUNCT
ejpam-6395	179	121	{	{	PUNCT
ejpam-6395	179	122	x	x	NOUN
ejpam-6395	179	123	,	,	PUNCT
ejpam-6395	179	124	y	y	PROPN
ejpam-6395	179	125	}	}	PUNCT
ejpam-6395	179	126	,	,	PUNCT
ejpam-6395	179	127	{	{	PUNCT
ejpam-6395	179	128	x	x	X
ejpam-6395	179	129	}	}	PUNCT
ejpam-6395	179	130	{	{	PUNCT
ejpam-6395	179	131	x	x	NOUN
ejpam-6395	179	132	,	,	PUNCT
ejpam-6395	179	133	y	y	NOUN
ejpam-6395	179	134	}	}	PUNCT
ejpam-6395	179	135	{	{	PUNCT
ejpam-6395	179	136	y	y	NOUN
ejpam-6395	179	137	}	}	PUNCT
ejpam-6395	179	138	{	{	PUNCT
ejpam-6395	179	139	x	x	NOUN
ejpam-6395	179	140	,	,	PUNCT
ejpam-6395	179	141	y	y	NOUN
ejpam-6395	179	142	}	}	PUNCT
ejpam-6395	179	143	{	{	PUNCT
ejpam-6395	179	144	x	x	NOUN
ejpam-6395	179	145	,	,	PUNCT
ejpam-6395	179	146	y	y	PROPN
ejpam-6395	179	147	}	}	PUNCT
ejpam-6395	179	148	,	,	PUNCT
ejpam-6395	179	149	{	{	PUNCT
ejpam-6395	179	150	y	y	NOUN
ejpam-6395	179	151	}	}	PUNCT
ejpam-6395	179	152	{	{	PUNCT
ejpam-6395	179	153	y	y	NOUN
ejpam-6395	179	154	}	}	PUNCT
ejpam-6395	179	155	{	{	PUNCT
ejpam-6395	179	156	y	y	NOUN
ejpam-6395	179	157	}	}	PUNCT
ejpam-6395	179	158	{	{	PUNCT
ejpam-6395	179	159	y	y	NOUN
ejpam-6395	179	160	}	}	PUNCT
ejpam-6395	179	161	{	{	PUNCT
ejpam-6395	179	162	x	x	NOUN
ejpam-6395	179	163	,	,	PUNCT
ejpam-6395	179	164	y	y	PROPN
ejpam-6395	179	165	}	}	PUNCT
ejpam-6395	179	166	,	,	PUNCT
ejpam-6395	179	167	{	{	PUNCT
ejpam-6395	179	168	x	x	NOUN
ejpam-6395	179	169	,	,	PUNCT
ejpam-6395	179	170	y	y	NOUN
ejpam-6395	179	171	}	}	PUNCT
ejpam-6395	179	172	{	{	PUNCT
ejpam-6395	179	173	x	x	NOUN
ejpam-6395	179	174	,	,	PUNCT
ejpam-6395	179	175	y	y	NOUN
ejpam-6395	179	176	}	}	PUNCT
ejpam-6395	179	177	{	{	PUNCT
ejpam-6395	179	178	y	y	NOUN
ejpam-6395	179	179	}	}	PUNCT
ejpam-6395	179	180	{	{	PUNCT
ejpam-6395	179	181	x	x	NOUN
ejpam-6395	179	182	,	,	PUNCT
ejpam-6395	179	183	y	y	PROPN
ejpam-6395	179	184	}	}	PUNCT
ejpam-6395	179	185	let	let	VERB
ejpam-6395	179	186	a	a	PRON
ejpam-6395	179	187	=	=	X
ejpam-6395	179	188	{	{	PUNCT
ejpam-6395	179	189	{	{	PUNCT
ejpam-6395	179	190	y	y	NOUN
ejpam-6395	179	191	}	}	PUNCT
ejpam-6395	179	192	}	}	PUNCT
ejpam-6395	179	193	be	be	AUX
ejpam-6395	179	194	a	a	DET
ejpam-6395	179	195	subset	subset	NOUN
ejpam-6395	179	196	of	of	ADP
ejpam-6395	179	197	h.	h.	NOUN
ejpam-6395	179	198	we	we	PRON
ejpam-6395	179	199	can	can	AUX
ejpam-6395	179	200	see	see	VERB
ejpam-6395	179	201	that	that	DET
ejpam-6395	179	202	•(h	•(h	PROPN
ejpam-6395	179	203	,	,	PUNCT
ejpam-6395	179	204	h	h	NOUN
ejpam-6395	179	205	,	,	PUNCT
ejpam-6395	179	206	a	a	PRON
ejpam-6395	179	207	)	)	PUNCT
ejpam-6395	179	208	⊆	⊆	PROPN
ejpam-6395	179	209	a	a	PRON
ejpam-6395	179	210	and	and	CCONJ
ejpam-6395	179	211	a	a	DET
ejpam-6395	179	212	=	=	X
ejpam-6395	179	213	(	(	PUNCT
ejpam-6395	179	214	a]p	a]p	PROPN
ejpam-6395	179	215	.	.	PUNCT
ejpam-6395	180	1	then	then	ADV
ejpam-6395	180	2	a	a	PRON
ejpam-6395	180	3	is	be	AUX
ejpam-6395	180	4	a	a	DET
ejpam-6395	180	5	left	left	ADJ
ejpam-6395	180	6	ideal	ideal	NOUN
ejpam-6395	180	7	of	of	ADP
ejpam-6395	180	8	h.	h.	PROPN
ejpam-6395	180	9	there	there	PRON
ejpam-6395	180	10	exists	exist	VERB
ejpam-6395	180	11	{	{	PUNCT
ejpam-6395	180	12	y	y	NOUN
ejpam-6395	180	13	}	}	PUNCT
ejpam-6395	180	14	∈	∈	PROPN
ejpam-6395	180	15	a	a	DET
ejpam-6395	180	16	such	such	ADJ
ejpam-6395	180	17	that	that	SCONJ
ejpam-6395	180	18	{	{	PUNCT
ejpam-6395	180	19	y	y	NOUN
ejpam-6395	180	20	}	}	PUNCT
ejpam-6395	180	21	≤p	≤p	NOUN
ejpam-6395	180	22	•({y	•({y	PROPN
ejpam-6395	180	23	}	}	PUNCT
ejpam-6395	180	24	,	,	PUNCT
ejpam-6395	180	25	{	{	PUNCT
ejpam-6395	180	26	y	y	NOUN
ejpam-6395	180	27	}	}	PUNCT
ejpam-6395	180	28	,	,	PUNCT
ejpam-6395	180	29	{	{	PUNCT
ejpam-6395	180	30	y	y	NOUN
ejpam-6395	180	31	}	}	PUNCT
ejpam-6395	180	32	)	)	PUNCT
ejpam-6395	181	1	=	=	PRON
ejpam-6395	181	2	{	{	PUNCT
ejpam-6395	181	3	y	y	NOUN
ejpam-6395	181	4	}	}	PUNCT
ejpam-6395	181	5	.	.	PUNCT
ejpam-6395	182	1	then	then	ADV
ejpam-6395	182	2	a	a	PRON
ejpam-6395	182	3	is	be	AUX
ejpam-6395	182	4	a	a	DET
ejpam-6395	182	5	one	one	NUM
ejpam-6395	182	6	-	-	PUNCT
ejpam-6395	182	7	sided	sided	ADJ
ejpam-6395	182	8	left	leave	VERB
ejpam-6395	182	9	pure	pure	ADJ
ejpam-6395	182	10	ideal	ideal	NOUN
ejpam-6395	182	11	of	of	ADP
ejpam-6395	182	12	h.	h.	PROPN
ejpam-6395	183	1	moreover	moreover	ADV
ejpam-6395	183	2	,	,	PUNCT
ejpam-6395	183	3	we	we	PRON
ejpam-6395	183	4	have	have	AUX
ejpam-6395	183	5	•(h	•(h	PROPN
ejpam-6395	183	6	,	,	PUNCT
ejpam-6395	183	7	a	a	DET
ejpam-6395	183	8	,	,	PUNCT
ejpam-6395	183	9	h	h	NOUN
ejpam-6395	183	10	)	)	PUNCT
ejpam-6395	183	11	⊆	⊆	NUM
ejpam-6395	183	12	a	a	PRON
ejpam-6395	183	13	and	and	CCONJ
ejpam-6395	183	14	•(a	•(a	PROPN
ejpam-6395	183	15	,	,	PUNCT
ejpam-6395	183	16	h	h	NOUN
ejpam-6395	183	17	,	,	PUNCT
ejpam-6395	183	18	h	h	NOUN
ejpam-6395	183	19	)	)	PUNCT
ejpam-6395	183	20	⊆	⊆	NUM
ejpam-6395	183	21	a.	a.	NOUN
ejpam-6395	183	22	so	so	ADV
ejpam-6395	183	23	,	,	PUNCT
ejpam-6395	183	24	a	a	PRON
ejpam-6395	183	25	is	be	AUX
ejpam-6395	183	26	an	an	DET
ejpam-6395	183	27	ideal	ideal	NOUN
ejpam-6395	183	28	of	of	ADP
ejpam-6395	183	29	h.	h.	PROPN
ejpam-6395	183	30	therefore	therefore	ADV
ejpam-6395	183	31	,	,	PUNCT
ejpam-6395	183	32	a	a	PRON
ejpam-6395	183	33	is	be	AUX
ejpam-6395	183	34	a	a	DET
ejpam-6395	183	35	left	left	ADJ
ejpam-6395	183	36	pure	pure	ADJ
ejpam-6395	183	37	ideal	ideal	NOUN
ejpam-6395	183	38	of	of	ADP
ejpam-6395	183	39	h.	h.	PROPN
ejpam-6395	183	40	theorem	theorem	PROPN
ejpam-6395	183	41	2	2	X
ejpam-6395	183	42	.	.	PUNCT
ejpam-6395	184	1	let	let	VERB
ejpam-6395	184	2	(	(	PUNCT
ejpam-6395	184	3	t	t	NOUN
ejpam-6395	184	4	,	,	PUNCT
ejpam-6395	184	5	•,≤p	•,≤p	NOUN
ejpam-6395	184	6	)	)	PUNCT
ejpam-6395	184	7	be	be	AUX
ejpam-6395	184	8	an	an	DET
ejpam-6395	184	9	ordered	order	VERB
ejpam-6395	184	10	power	power	NOUN
ejpam-6395	184	11	ternary	ternary	NOUN
ejpam-6395	184	12	semigroup	semigroup	NOUN
ejpam-6395	184	13	on	on	ADP
ejpam-6395	184	14	a	a	DET
ejpam-6395	184	15	ternary	ternary	ADJ
ejpam-6395	184	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	184	17	(	(	PUNCT
ejpam-6395	184	18	s	s	X
ejpam-6395	184	19	,	,	PUNCT
ejpam-6395	184	20	⋄	⋄	PROPN
ejpam-6395	184	21	)	)	PUNCT
ejpam-6395	184	22	induced	induce	VERB
ejpam-6395	184	23	by	by	ADP
ejpam-6395	184	24	a	a	DET
ejpam-6395	184	25	poset	poset	NOUN
ejpam-6395	184	26	(	(	PUNCT
ejpam-6395	184	27	s,≤	s,≤	NOUN
ejpam-6395	184	28	)	)	PUNCT
ejpam-6395	184	29	and	and	CCONJ
ejpam-6395	184	30	a	a	PRON
ejpam-6395	184	31	be	be	AUX
ejpam-6395	184	32	an	an	DET
ejpam-6395	184	33	ideal	ideal	NOUN
ejpam-6395	184	34	of	of	ADP
ejpam-6395	184	35	t	t	PROPN
ejpam-6395	184	36	.	.	PUNCT
ejpam-6395	185	1	then	then	ADV
ejpam-6395	185	2	a	a	PRON
ejpam-6395	185	3	is	be	AUX
ejpam-6395	185	4	a	a	DET
ejpam-6395	185	5	left	left	ADJ
ejpam-6395	185	6	(	(	PUNCT
ejpam-6395	185	7	resp	resp	NOUN
ejpam-6395	185	8	.	.	PUNCT
ejpam-6395	186	1	right	right	ADJ
ejpam-6395	186	2	)	)	PUNCT
ejpam-6395	186	3	pure	pure	ADJ
ejpam-6395	186	4	ideal	ideal	NOUN
ejpam-6395	187	1	if	if	SCONJ
ejpam-6395	187	2	and	and	CCONJ
ejpam-6395	187	3	only	only	ADV
ejpam-6395	187	4	if	if	SCONJ
ejpam-6395	187	5	a∩b∩c	a∩b∩c	PROPN
ejpam-6395	187	6	=	=	PRON
ejpam-6395	187	7	(	(	PUNCT
ejpam-6395	187	8	•(a	•(a	PROPN
ejpam-6395	187	9	,	,	PUNCT
ejpam-6395	187	10	b	b	NOUN
ejpam-6395	187	11	,	,	PUNCT
ejpam-6395	187	12	c)]p	c)]p	PROPN
ejpam-6395	187	13	for	for	ADP
ejpam-6395	187	14	all	all	DET
ejpam-6395	187	15	left	leave	VERB
ejpam-6395	187	16	ideals	ideal	NOUN
ejpam-6395	187	17	c	c	NOUN
ejpam-6395	187	18	,	,	PUNCT
ejpam-6395	187	19	all	all	DET
ejpam-6395	187	20	lateral	lateral	ADJ
ejpam-6395	187	21	ideal	ideal	ADJ
ejpam-6395	187	22	b	b	PROPN
ejpam-6395	187	23	of	of	ADP
ejpam-6395	187	24	t	t	PROPN
ejpam-6395	187	25	(	(	PUNCT
ejpam-6395	187	26	resp	resp	PROPN
ejpam-6395	187	27	.	.	PUNCT
ejpam-6395	188	1	a	a	DET
ejpam-6395	188	2	∩	∩	ADJ
ejpam-6395	188	3	b	b	NOUN
ejpam-6395	188	4	∩	∩	NOUN
ejpam-6395	188	5	c	c	NOUN
ejpam-6395	188	6	=	=	SYM
ejpam-6395	188	7	(	(	PUNCT
ejpam-6395	188	8	•(b	•(b	PROPN
ejpam-6395	188	9	,	,	PUNCT
ejpam-6395	188	10	c	c	NOUN
ejpam-6395	188	11	,	,	PUNCT
ejpam-6395	188	12	a)]p	a)]p	NOUN
ejpam-6395	188	13	for	for	ADP
ejpam-6395	188	14	all	all	DET
ejpam-6395	188	15	right	right	ADJ
ejpam-6395	188	16	ideals	ideal	NOUN
ejpam-6395	188	17	b	b	NUM
ejpam-6395	188	18	,	,	PUNCT
ejpam-6395	188	19	all	all	DET
ejpam-6395	188	20	lateral	lateral	ADJ
ejpam-6395	188	21	ideal	ideal	ADJ
ejpam-6395	188	22	c	c	PROPN
ejpam-6395	188	23	of	of	ADP
ejpam-6395	188	24	t	t	PROPN
ejpam-6395	188	25	and	and	CCONJ
ejpam-6395	188	26	a	a	DET
ejpam-6395	188	27	∩	∩	ADJ
ejpam-6395	188	28	b	b	NOUN
ejpam-6395	188	29	∩	∩	NOUN
ejpam-6395	188	30	c	c	NOUN
ejpam-6395	188	31	=	=	SYM
ejpam-6395	188	32	(	(	PUNCT
ejpam-6395	188	33	•(b	•(b	PROPN
ejpam-6395	188	34	,	,	PUNCT
ejpam-6395	188	35	a	a	PRON
ejpam-6395	188	36	,	,	PUNCT
ejpam-6395	188	37	c)]p	c)]p	PROPN
ejpam-6395	188	38	for	for	ADP
ejpam-6395	188	39	all	all	DET
ejpam-6395	188	40	left	leave	VERB
ejpam-6395	188	41	ideals	ideal	NOUN
ejpam-6395	188	42	b	b	NOUN
ejpam-6395	188	43	,	,	PUNCT
ejpam-6395	188	44	all	all	DET
ejpam-6395	188	45	right	right	ADJ
ejpam-6395	188	46	ideal	ideal	NOUN
ejpam-6395	188	47	c	c	PROPN
ejpam-6395	188	48	of	of	ADP
ejpam-6395	188	49	t	t	PROPN
ejpam-6395	188	50	)	)	PUNCT
ejpam-6395	188	51	.	.	PUNCT
ejpam-6395	189	1	proof	proof	NOUN
ejpam-6395	189	2	.	.	PUNCT
ejpam-6395	190	1	(	(	PUNCT
ejpam-6395	190	2	⇒	⇒	PROPN
ejpam-6395	190	3	)	)	PUNCT
ejpam-6395	190	4	let	let	VERB
ejpam-6395	190	5	a	a	PRON
ejpam-6395	190	6	be	be	AUX
ejpam-6395	190	7	a	a	DET
ejpam-6395	190	8	left	left	ADJ
ejpam-6395	190	9	pure	pure	ADJ
ejpam-6395	190	10	ideal	ideal	NOUN
ejpam-6395	190	11	and	and	CCONJ
ejpam-6395	190	12	b	b	NOUN
ejpam-6395	190	13	,	,	PUNCT
ejpam-6395	190	14	c	c	AUX
ejpam-6395	190	15	be	be	AUX
ejpam-6395	190	16	a	a	DET
ejpam-6395	190	17	left	left	ADJ
ejpam-6395	190	18	ideal	ideal	NOUN
ejpam-6395	190	19	of	of	ADP
ejpam-6395	190	20	t	t	PROPN
ejpam-6395	190	21	.	.	PUNCT
ejpam-6395	191	1	then	then	ADV
ejpam-6395	191	2	•(a	•(a	VERB
ejpam-6395	191	3	,	,	PUNCT
ejpam-6395	191	4	b	b	NOUN
ejpam-6395	191	5	,	,	PUNCT
ejpam-6395	191	6	c	c	NOUN
ejpam-6395	191	7	)	)	PUNCT
ejpam-6395	191	8	⊆	⊆	NUM
ejpam-6395	191	9	•(a	•(a	NOUN
ejpam-6395	191	10	,	,	PUNCT
ejpam-6395	191	11	t	t	PROPN
ejpam-6395	191	12	,	,	PUNCT
ejpam-6395	191	13	t	t	PROPN
ejpam-6395	191	14	)	)	PUNCT
ejpam-6395	192	1	⊆	⊆	NUM
ejpam-6395	192	2	a.	a.	NOUN
ejpam-6395	192	3	let	let	VERB
ejpam-6395	192	4	x	x	X
ejpam-6395	192	5	∈	∈	PROPN
ejpam-6395	192	6	(	(	PUNCT
ejpam-6395	192	7	•(a	•(a	PROPN
ejpam-6395	192	8	,	,	PUNCT
ejpam-6395	192	9	b	b	PROPN
ejpam-6395	192	10	,	,	PUNCT
ejpam-6395	192	11	c)]p	c)]p	PROPN
ejpam-6395	192	12	.	.	PUNCT
ejpam-6395	193	1	then	then	ADV
ejpam-6395	193	2	there	there	PRON
ejpam-6395	193	3	exists	exist	VERB
ejpam-6395	193	4	y	y	PROPN
ejpam-6395	193	5	∈	∈	PROPN
ejpam-6395	193	6	•(a	•(a	PROPN
ejpam-6395	193	7	,	,	PUNCT
ejpam-6395	193	8	b	b	NOUN
ejpam-6395	193	9	,	,	PUNCT
ejpam-6395	193	10	c	c	NOUN
ejpam-6395	193	11	)	)	PUNCT
ejpam-6395	193	12	such	such	ADJ
ejpam-6395	193	13	that	that	SCONJ
ejpam-6395	193	14	x	x	SYM
ejpam-6395	193	15	≤p	≤p	NOUN
ejpam-6395	193	16	y	y	PROPN
ejpam-6395	193	17	.	.	PUNCT
ejpam-6395	194	1	that	that	PRON
ejpam-6395	194	2	is	be	AUX
ejpam-6395	194	3	,	,	PUNCT
ejpam-6395	194	4	y	y	PROPN
ejpam-6395	194	5	∈	∈	PROPN
ejpam-6395	194	6	•(a	•(a	PROPN
ejpam-6395	194	7	,	,	PUNCT
ejpam-6395	194	8	b	b	NOUN
ejpam-6395	194	9	,	,	PUNCT
ejpam-6395	194	10	c	c	NOUN
ejpam-6395	194	11	)	)	PUNCT
ejpam-6395	194	12	⊆	⊆	NUM
ejpam-6395	194	13	a.	a.	NOUN
ejpam-6395	194	14	since	since	SCONJ
ejpam-6395	194	15	a	a	PRON
ejpam-6395	194	16	is	be	AUX
ejpam-6395	194	17	an	an	DET
ejpam-6395	194	18	ideal	ideal	NOUN
ejpam-6395	194	19	of	of	ADP
ejpam-6395	194	20	t	t	PROPN
ejpam-6395	194	21	,	,	PUNCT
ejpam-6395	194	22	x	x	SYM
ejpam-6395	194	23	≤p	≤p	NOUN
ejpam-6395	194	24	y	y	PROPN
ejpam-6395	194	25	and	and	CCONJ
ejpam-6395	194	26	y	y	PROPN
ejpam-6395	194	27	∈	∈	PROPN
ejpam-6395	194	28	a	a	X
ejpam-6395	194	29	,	,	PUNCT
ejpam-6395	194	30	we	we	PRON
ejpam-6395	194	31	have	have	VERB
ejpam-6395	194	32	x	x	PART
ejpam-6395	194	33	∈	∈	VERB
ejpam-6395	194	34	a.	a.	NOUN
ejpam-6395	194	35	also	also	ADV
ejpam-6395	194	36	,	,	PUNCT
ejpam-6395	194	37	y	y	PROPN
ejpam-6395	194	38	∈	∈	PROPN
ejpam-6395	194	39	•(a	•(a	PROPN
ejpam-6395	194	40	,	,	PUNCT
ejpam-6395	194	41	b	b	NOUN
ejpam-6395	194	42	,	,	PUNCT
ejpam-6395	194	43	c	c	NOUN
ejpam-6395	194	44	)	)	PUNCT
ejpam-6395	194	45	⊆	⊆	NUM
ejpam-6395	194	46	•(t	•(t	NOUN
ejpam-6395	194	47	,	,	PUNCT
ejpam-6395	194	48	t	t	PROPN
ejpam-6395	194	49	,	,	PUNCT
ejpam-6395	194	50	c	c	X
ejpam-6395	194	51	)	)	PUNCT
ejpam-6395	194	52	⊆	⊆	NUM
ejpam-6395	194	53	c.	c.	NOUN
ejpam-6395	194	54	since	since	SCONJ
ejpam-6395	194	55	c	c	PROPN
ejpam-6395	194	56	is	be	AUX
ejpam-6395	194	57	a	a	DET
ejpam-6395	194	58	left	left	ADJ
ejpam-6395	194	59	ideal	ideal	NOUN
ejpam-6395	194	60	of	of	ADP
ejpam-6395	194	61	t	t	PROPN
ejpam-6395	194	62	,	,	PUNCT
ejpam-6395	194	63	x	x	SYM
ejpam-6395	194	64	≤p	≤p	NOUN
ejpam-6395	194	65	y	y	PROPN
ejpam-6395	194	66	and	and	CCONJ
ejpam-6395	194	67	y	y	PROPN
ejpam-6395	194	68	∈	∈	PROPN
ejpam-6395	195	1	c	c	X
ejpam-6395	195	2	,	,	PUNCT
ejpam-6395	195	3	we	we	PRON
ejpam-6395	195	4	have	have	VERB
ejpam-6395	195	5	x	x	PROPN
ejpam-6395	195	6	∈	∈	PROPN
ejpam-6395	195	7	c.	c.	NOUN
ejpam-6395	195	8	also	also	ADV
ejpam-6395	195	9	,	,	PUNCT
ejpam-6395	195	10	y	y	PROPN
ejpam-6395	195	11	∈	∈	PROPN
ejpam-6395	195	12	•(a	•(a	PROPN
ejpam-6395	195	13	,	,	PUNCT
ejpam-6395	195	14	b	b	NOUN
ejpam-6395	195	15	,	,	PUNCT
ejpam-6395	195	16	c	c	NOUN
ejpam-6395	195	17	)	)	PUNCT
ejpam-6395	195	18	⊆	⊆	NUM
ejpam-6395	195	19	•(t	•(t	NOUN
ejpam-6395	195	20	,	,	PUNCT
ejpam-6395	195	21	b	b	NOUN
ejpam-6395	195	22	,	,	PUNCT
ejpam-6395	195	23	t	t	PROPN
ejpam-6395	195	24	)	)	PUNCT
ejpam-6395	195	25	⊆	⊆	NUM
ejpam-6395	195	26	b.	b.	NOUN
ejpam-6395	195	27	since	since	SCONJ
ejpam-6395	195	28	b	b	PROPN
ejpam-6395	195	29	a.	a.	NOUN
ejpam-6395	195	30	nongmanee	nongmanee	NOUN
ejpam-6395	195	31	,	,	PUNCT
ejpam-6395	195	32	k.	k.	PROPN
ejpam-6395	196	1	jeenkaew	jeenkaew	PROPN
ejpam-6395	196	2	,	,	PUNCT
ejpam-6395	196	3	m.	m.	NOUN
ejpam-6395	196	4	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	196	5	/	/	SYM
ejpam-6395	196	6	eur	eur	PROPN
ejpam-6395	196	7	.	.	PUNCT
ejpam-6395	197	1	j.	j.	PROPN
ejpam-6395	197	2	pure	pure	PROPN
ejpam-6395	197	3	appl	appl	PROPN
ejpam-6395	197	4	.	.	PROPN
ejpam-6395	197	5	math	math	PROPN
ejpam-6395	197	6	,	,	PUNCT
ejpam-6395	197	7	18	18	NUM
ejpam-6395	197	8	(	(	PUNCT
ejpam-6395	197	9	3	3	NUM
ejpam-6395	197	10	)	)	PUNCT
ejpam-6395	197	11	(	(	PUNCT
ejpam-6395	197	12	2025	2025	NUM
ejpam-6395	197	13	)	)	PUNCT
ejpam-6395	197	14	,	,	PUNCT
ejpam-6395	197	15	6395	6395	NUM
ejpam-6395	197	16	7	7	NUM
ejpam-6395	197	17	of	of	ADP
ejpam-6395	197	18	12	12	NUM
ejpam-6395	197	19	is	be	AUX
ejpam-6395	197	20	a	a	DET
ejpam-6395	197	21	lateral	lateral	ADJ
ejpam-6395	197	22	ideal	ideal	NOUN
ejpam-6395	197	23	of	of	ADP
ejpam-6395	197	24	t	t	PROPN
ejpam-6395	197	25	,	,	PUNCT
ejpam-6395	197	26	x	x	SYM
ejpam-6395	197	27	≤p	≤p	NOUN
ejpam-6395	197	28	y	y	PROPN
ejpam-6395	197	29	and	and	CCONJ
ejpam-6395	197	30	y	y	PROPN
ejpam-6395	197	31	∈	∈	PROPN
ejpam-6395	197	32	b	b	PROPN
ejpam-6395	197	33	,	,	PUNCT
ejpam-6395	197	34	we	we	PRON
ejpam-6395	197	35	have	have	VERB
ejpam-6395	197	36	x	x	PROPN
ejpam-6395	197	37	∈	∈	PROPN
ejpam-6395	197	38	b.	b.	NOUN
ejpam-6395	198	1	hence	hence	ADV
ejpam-6395	198	2	x	x	X
ejpam-6395	198	3	∈	∈	PROPN
ejpam-6395	198	4	a	a	DET
ejpam-6395	198	5	∩	∩	ADJ
ejpam-6395	198	6	b	b	NOUN
ejpam-6395	198	7	∩	∩	ADJ
ejpam-6395	198	8	c.	c.	NOUN
ejpam-6395	198	9	then	then	ADV
ejpam-6395	198	10	(	(	PUNCT
ejpam-6395	198	11	•(a	•(a	PROPN
ejpam-6395	198	12	,	,	PUNCT
ejpam-6395	198	13	b	b	NOUN
ejpam-6395	198	14	,	,	PUNCT
ejpam-6395	198	15	c)]p	c)]p	PROPN
ejpam-6395	198	16	⊆	⊆	NUM
ejpam-6395	198	17	a	a	DET
ejpam-6395	198	18	∩	∩	ADJ
ejpam-6395	198	19	b	b	NOUN
ejpam-6395	198	20	∩	∩	PROPN
ejpam-6395	198	21	c.	c.	NOUN
ejpam-6395	198	22	now	now	ADV
ejpam-6395	198	23	,	,	PUNCT
ejpam-6395	198	24	let	let	VERB
ejpam-6395	198	25	x	x	PART
ejpam-6395	198	26	∈	∈	PROPN
ejpam-6395	198	27	a	a	DET
ejpam-6395	198	28	∩	∩	ADJ
ejpam-6395	198	29	b	b	NOUN
ejpam-6395	198	30	∩	∩	ADJ
ejpam-6395	198	31	c.	c.	NOUN
ejpam-6395	198	32	since	since	SCONJ
ejpam-6395	198	33	a	a	PRON
ejpam-6395	198	34	is	be	AUX
ejpam-6395	198	35	left	leave	VERB
ejpam-6395	198	36	pure	pure	ADJ
ejpam-6395	198	37	ideal	ideal	NOUN
ejpam-6395	198	38	,	,	PUNCT
ejpam-6395	198	39	there	there	PRON
ejpam-6395	198	40	exists	exist	VERB
ejpam-6395	198	41	y	y	PROPN
ejpam-6395	198	42	,	,	PUNCT
ejpam-6395	198	43	z	z	PROPN
ejpam-6395	198	44	∈	∈	PROPN
ejpam-6395	198	45	a	a	DET
ejpam-6395	198	46	such	such	ADJ
ejpam-6395	198	47	that	that	SCONJ
ejpam-6395	198	48	x	x	SYM
ejpam-6395	198	49	≤p	≤p	NOUN
ejpam-6395	198	50	•(y	•(y	NOUN
ejpam-6395	198	51	,	,	PUNCT
ejpam-6395	198	52	z	z	NOUN
ejpam-6395	198	53	,	,	PUNCT
ejpam-6395	198	54	x	x	NOUN
ejpam-6395	198	55	)	)	PUNCT
ejpam-6395	198	56	.	.	PUNCT
ejpam-6395	199	1	since	since	SCONJ
ejpam-6395	199	2	•(y	•(y	NOUN
ejpam-6395	199	3	,	,	PUNCT
ejpam-6395	199	4	z	z	NOUN
ejpam-6395	199	5	,	,	PUNCT
ejpam-6395	199	6	x	x	X
ejpam-6395	199	7	)	)	PUNCT
ejpam-6395	199	8	∈	∈	PROPN
ejpam-6395	199	9	•(a	•(a	PROPN
ejpam-6395	199	10	,	,	PUNCT
ejpam-6395	199	11	b	b	NOUN
ejpam-6395	199	12	,	,	PUNCT
ejpam-6395	199	13	c	c	NOUN
ejpam-6395	199	14	)	)	PUNCT
ejpam-6395	199	15	and	and	CCONJ
ejpam-6395	199	16	x	x	SYM
ejpam-6395	199	17	≤p	≤p	ADJ
ejpam-6395	199	18	•(y	•(y	NOUN
ejpam-6395	199	19	,	,	PUNCT
ejpam-6395	199	20	z	z	NOUN
ejpam-6395	199	21	,	,	PUNCT
ejpam-6395	199	22	x	x	NOUN
ejpam-6395	199	23	)	)	PUNCT
ejpam-6395	199	24	,	,	PUNCT
ejpam-6395	199	25	we	we	PRON
ejpam-6395	199	26	have	have	VERB
ejpam-6395	199	27	x	x	SYM
ejpam-6395	199	28	∈	∈	PROPN
ejpam-6395	199	29	(	(	PUNCT
ejpam-6395	199	30	•(a	•(a	PROPN
ejpam-6395	199	31	,	,	PUNCT
ejpam-6395	199	32	b	b	PROPN
ejpam-6395	199	33	,	,	PUNCT
ejpam-6395	199	34	c)]p	c)]p	PROPN
ejpam-6395	199	35	.	.	PUNCT
ejpam-6395	200	1	hence	hence	ADV
ejpam-6395	200	2	a	a	DET
ejpam-6395	200	3	∩	∩	ADJ
ejpam-6395	200	4	b	b	NOUN
ejpam-6395	200	5	∩	∩	NOUN
ejpam-6395	200	6	b	b	X
ejpam-6395	200	7	⊆	⊆	NUM
ejpam-6395	200	8	(	(	PUNCT
ejpam-6395	200	9	•(a	•(a	PROPN
ejpam-6395	200	10	,	,	PUNCT
ejpam-6395	200	11	b	b	PROPN
ejpam-6395	200	12	,	,	PUNCT
ejpam-6395	200	13	c)]p	c)]p	PROPN
ejpam-6395	200	14	.	.	PUNCT
ejpam-6395	201	1	therefore	therefore	ADV
ejpam-6395	201	2	a	a	DET
ejpam-6395	201	3	∩	∩	ADJ
ejpam-6395	201	4	b	b	NOUN
ejpam-6395	201	5	∩	∩	NOUN
ejpam-6395	201	6	c	c	NOUN
ejpam-6395	201	7	=	=	SYM
ejpam-6395	201	8	(	(	PUNCT
ejpam-6395	201	9	•(a	•(a	PROPN
ejpam-6395	201	10	,	,	PUNCT
ejpam-6395	201	11	b	b	NOUN
ejpam-6395	201	12	,	,	PUNCT
ejpam-6395	201	13	c)]p	c)]p	PROPN
ejpam-6395	201	14	for	for	ADP
ejpam-6395	201	15	all	all	DET
ejpam-6395	201	16	left	leave	VERB
ejpam-6395	201	17	ideals	ideal	NOUN
ejpam-6395	201	18	c	c	NOUN
ejpam-6395	201	19	,	,	PUNCT
ejpam-6395	201	20	all	all	DET
ejpam-6395	201	21	lateral	lateral	ADJ
ejpam-6395	201	22	ideals	ideal	NOUN
ejpam-6395	201	23	b	b	PROPN
ejpam-6395	201	24	of	of	ADP
ejpam-6395	201	25	t	t	PROPN
ejpam-6395	201	26	.	.	PUNCT
ejpam-6395	202	1	(	(	PUNCT
ejpam-6395	202	2	⇐	⇐	ADJ
ejpam-6395	202	3	)	)	PUNCT
ejpam-6395	202	4	let	let	VERB
ejpam-6395	202	5	a∩b∩c	a∩b∩c	ADV
ejpam-6395	203	1	=	=	PRON
ejpam-6395	203	2	(	(	PUNCT
ejpam-6395	203	3	•(a	•(a	PROPN
ejpam-6395	203	4	,	,	PUNCT
ejpam-6395	203	5	b	b	NOUN
ejpam-6395	203	6	,	,	PUNCT
ejpam-6395	203	7	c)]p	c)]p	PROPN
ejpam-6395	203	8	for	for	ADP
ejpam-6395	203	9	all	all	DET
ejpam-6395	203	10	left	leave	VERB
ejpam-6395	203	11	ideals	ideal	NOUN
ejpam-6395	203	12	c	c	NOUN
ejpam-6395	203	13	,	,	PUNCT
ejpam-6395	203	14	all	all	DET
ejpam-6395	203	15	lateral	lateral	ADJ
ejpam-6395	203	16	ideals	ideal	NOUN
ejpam-6395	203	17	b	b	PROPN
ejpam-6395	203	18	of	of	ADP
ejpam-6395	203	19	t	t	PROPN
ejpam-6395	203	20	and	and	CCONJ
ejpam-6395	203	21	x	x	PUNCT
ejpam-6395	203	22	∈	∈	NOUN
ejpam-6395	203	23	a.	a.	NOUN
ejpam-6395	203	24	we	we	PRON
ejpam-6395	203	25	will	will	AUX
ejpam-6395	203	26	show	show	VERB
ejpam-6395	203	27	that	that	SCONJ
ejpam-6395	203	28	x	x	SYM
ejpam-6395	203	29	∈	∈	PROPN
ejpam-6395	203	30	(	(	PUNCT
ejpam-6395	203	31	•(a	•(a	PROPN
ejpam-6395	203	32	,	,	PUNCT
ejpam-6395	203	33	a	a	DET
ejpam-6395	203	34	,	,	PUNCT
ejpam-6395	203	35	x)]p	x)]p	PROPN
ejpam-6395	203	36	.	.	PUNCT
ejpam-6395	203	37	consider	consider	VERB
ejpam-6395	203	38	x	x	X
ejpam-6395	203	39	∈	∈	PROPN
ejpam-6395	203	40	a	a	DET
ejpam-6395	203	41	∩	∩	ADJ
ejpam-6395	203	42	a	a	DET
ejpam-6395	203	43	∩	∩	NOUN
ejpam-6395	203	44	{	{	PUNCT
ejpam-6395	203	45	x	x	NOUN
ejpam-6395	203	46	}	}	PUNCT
ejpam-6395	203	47	=	=	SYM
ejpam-6395	203	48	(	(	PUNCT
ejpam-6395	203	49	•(a	•(a	PROPN
ejpam-6395	203	50	,	,	PUNCT
ejpam-6395	203	51	a	a	PRON
ejpam-6395	203	52	,	,	PUNCT
ejpam-6395	203	53	x)]p	x)]p	PROPN
ejpam-6395	203	54	.	.	PUNCT
ejpam-6395	204	1	therefore	therefore	ADV
ejpam-6395	204	2	a	a	PRON
ejpam-6395	204	3	is	be	AUX
ejpam-6395	204	4	a	a	DET
ejpam-6395	204	5	left	left	ADJ
ejpam-6395	204	6	pure	pure	ADJ
ejpam-6395	204	7	ideal	ideal	NOUN
ejpam-6395	204	8	.	.	PUNCT
ejpam-6395	205	1	similarly	similarly	ADV
ejpam-6395	205	2	,	,	PUNCT
ejpam-6395	205	3	we	we	PRON
ejpam-6395	205	4	can	can	AUX
ejpam-6395	205	5	proof	proof	VERB
ejpam-6395	205	6	that	that	SCONJ
ejpam-6395	205	7	a	a	PRON
ejpam-6395	205	8	is	be	AUX
ejpam-6395	205	9	a	a	DET
ejpam-6395	205	10	right	right	ADJ
ejpam-6395	205	11	(	(	PUNCT
ejpam-6395	205	12	resp	resp	NOUN
ejpam-6395	205	13	.	.	PUNCT
ejpam-6395	206	1	lateral	lateral	ADJ
ejpam-6395	206	2	)	)	PUNCT
ejpam-6395	206	3	pure	pure	ADJ
ejpam-6395	206	4	ideal	ideal	NOUN
ejpam-6395	207	1	if	if	SCONJ
ejpam-6395	207	2	and	and	CCONJ
ejpam-6395	207	3	only	only	ADV
ejpam-6395	207	4	if	if	SCONJ
ejpam-6395	207	5	a	a	DET
ejpam-6395	207	6	∩	∩	ADJ
ejpam-6395	207	7	b	b	NOUN
ejpam-6395	207	8	∩	∩	NOUN
ejpam-6395	207	9	c	c	NOUN
ejpam-6395	207	10	=	=	SYM
ejpam-6395	207	11	(	(	PUNCT
ejpam-6395	207	12	•(b	•(b	PROPN
ejpam-6395	207	13	,	,	PUNCT
ejpam-6395	207	14	c	c	NOUN
ejpam-6395	207	15	,	,	PUNCT
ejpam-6395	207	16	a)]p	a)]p	NOUN
ejpam-6395	207	17	for	for	ADP
ejpam-6395	207	18	all	all	DET
ejpam-6395	207	19	right	right	ADJ
ejpam-6395	207	20	ideals	ideal	NOUN
ejpam-6395	207	21	b	b	NUM
ejpam-6395	207	22	,	,	PUNCT
ejpam-6395	207	23	all	all	DET
ejpam-6395	207	24	lateral	lateral	ADJ
ejpam-6395	207	25	ideal	ideal	ADJ
ejpam-6395	207	26	c	c	PROPN
ejpam-6395	207	27	of	of	ADP
ejpam-6395	207	28	t	t	PROPN
ejpam-6395	207	29	and	and	CCONJ
ejpam-6395	207	30	a	a	DET
ejpam-6395	207	31	∩	∩	ADJ
ejpam-6395	207	32	b	b	NOUN
ejpam-6395	207	33	∩	∩	NOUN
ejpam-6395	207	34	c	c	NOUN
ejpam-6395	207	35	=	=	SYM
ejpam-6395	207	36	(	(	PUNCT
ejpam-6395	207	37	•(b	•(b	PROPN
ejpam-6395	207	38	,	,	PUNCT
ejpam-6395	207	39	a	a	PRON
ejpam-6395	207	40	,	,	PUNCT
ejpam-6395	207	41	c)]p	c)]p	PROPN
ejpam-6395	207	42	for	for	ADP
ejpam-6395	207	43	all	all	DET
ejpam-6395	207	44	left	leave	VERB
ejpam-6395	207	45	ideals	ideal	NOUN
ejpam-6395	207	46	b	b	NOUN
ejpam-6395	207	47	,	,	PUNCT
ejpam-6395	207	48	all	all	DET
ejpam-6395	207	49	right	right	ADJ
ejpam-6395	207	50	ideal	ideal	NOUN
ejpam-6395	207	51	c	c	PROPN
ejpam-6395	207	52	of	of	ADP
ejpam-6395	207	53	t	t	PROPN
ejpam-6395	207	54	)	)	PUNCT
ejpam-6395	207	55	.	.	PUNCT
ejpam-6395	208	1	definition	definition	NOUN
ejpam-6395	208	2	8	8	NUM
ejpam-6395	208	3	.	.	PUNCT
ejpam-6395	209	1	let	let	AUX
ejpam-6395	209	2	(	(	PUNCT
ejpam-6395	209	3	t	t	NOUN
ejpam-6395	209	4	,	,	PUNCT
ejpam-6395	209	5	•,≤p	•,≤p	NOUN
ejpam-6395	209	6	)	)	PUNCT
ejpam-6395	209	7	be	be	VERB
ejpam-6395	209	8	an	an	DET
ejpam-6395	209	9	ordered	order	VERB
ejpam-6395	209	10	power	power	NOUN
ejpam-6395	209	11	ternary	ternary	NOUN
ejpam-6395	209	12	semigroup	semigroup	NOUN
ejpam-6395	209	13	on	on	ADP
ejpam-6395	209	14	a	a	DET
ejpam-6395	209	15	ternary	ternary	ADJ
ejpam-6395	209	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	209	17	(	(	PUNCT
ejpam-6395	209	18	s	s	X
ejpam-6395	209	19	,	,	PUNCT
ejpam-6395	209	20	⋄	⋄	PROPN
ejpam-6395	209	21	)	)	PUNCT
ejpam-6395	209	22	induced	induce	VERB
ejpam-6395	209	23	by	by	ADP
ejpam-6395	209	24	a	a	DET
ejpam-6395	209	25	poset	poset	NOUN
ejpam-6395	209	26	(	(	PUNCT
ejpam-6395	209	27	s,≤	s,≤	NOUN
ejpam-6395	209	28	)	)	PUNCT
ejpam-6395	209	29	and	and	CCONJ
ejpam-6395	209	30	x	x	PUNCT
ejpam-6395	209	31	∈	∈	PROPN
ejpam-6395	209	32	t	t	NOUN
ejpam-6395	209	33	.	.	PUNCT
ejpam-6395	210	1	if	if	SCONJ
ejpam-6395	210	2	•(x	•(x	PROPN
ejpam-6395	210	3	,	,	PUNCT
ejpam-6395	210	4	y	y	PROPN
ejpam-6395	210	5	,	,	PUNCT
ejpam-6395	210	6	z	z	NOUN
ejpam-6395	210	7	)	)	PUNCT
ejpam-6395	210	8	=	=	SYM
ejpam-6395	210	9	•(y	•(y	NOUN
ejpam-6395	210	10	,	,	PUNCT
ejpam-6395	210	11	x	x	NOUN
ejpam-6395	210	12	,	,	PUNCT
ejpam-6395	210	13	z	z	NOUN
ejpam-6395	210	14	)	)	PUNCT
ejpam-6395	210	15	=	=	SYM
ejpam-6395	210	16	•(z	•(z	PROPN
ejpam-6395	210	17	,	,	PUNCT
ejpam-6395	210	18	y	y	PROPN
ejpam-6395	210	19	,	,	PUNCT
ejpam-6395	210	20	x	x	NOUN
ejpam-6395	210	21	)	)	PUNCT
ejpam-6395	210	22	=	=	SYM
ejpam-6395	210	23	x	x	PUNCT
ejpam-6395	210	24	for	for	ADP
ejpam-6395	210	25	all	all	DET
ejpam-6395	210	26	y	y	PROPN
ejpam-6395	210	27	,	,	PUNCT
ejpam-6395	210	28	z	z	PROPN
ejpam-6395	210	29	∈	∈	PROPN
ejpam-6395	210	30	t	t	NOUN
ejpam-6395	210	31	then	then	ADV
ejpam-6395	210	32	{	{	PUNCT
ejpam-6395	210	33	x	x	X
ejpam-6395	210	34	}	}	PUNCT
ejpam-6395	210	35	is	be	AUX
ejpam-6395	210	36	called	call	VERB
ejpam-6395	210	37	a	a	DET
ejpam-6395	210	38	zero	zero	NUM
ejpam-6395	210	39	element	element	NOUN
ejpam-6395	210	40	of	of	ADP
ejpam-6395	210	41	t	t	PROPN
ejpam-6395	210	42	,	,	PUNCT
ejpam-6395	210	43	denoted	denote	VERB
ejpam-6395	210	44	by	by	ADP
ejpam-6395	210	45	0	0	NUM
ejpam-6395	210	46	.	.	PUNCT
ejpam-6395	210	47	theorem	theorem	NOUN
ejpam-6395	210	48	3	3	X
ejpam-6395	210	49	.	.	PUNCT
ejpam-6395	211	1	let	let	AUX
ejpam-6395	211	2	(	(	PUNCT
ejpam-6395	211	3	t	t	NOUN
ejpam-6395	211	4	,	,	PUNCT
ejpam-6395	211	5	•,≤p	•,≤p	NOUN
ejpam-6395	211	6	)	)	PUNCT
ejpam-6395	211	7	be	be	VERB
ejpam-6395	211	8	an	an	DET
ejpam-6395	211	9	ordered	order	VERB
ejpam-6395	211	10	power	power	NOUN
ejpam-6395	211	11	ternary	ternary	NOUN
ejpam-6395	211	12	semigroup	semigroup	NOUN
ejpam-6395	211	13	on	on	ADP
ejpam-6395	211	14	a	a	DET
ejpam-6395	211	15	ternary	ternary	ADJ
ejpam-6395	211	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	211	17	(	(	PUNCT
ejpam-6395	211	18	s	s	X
ejpam-6395	211	19	,	,	PUNCT
ejpam-6395	211	20	⋄	⋄	PROPN
ejpam-6395	211	21	)	)	PUNCT
ejpam-6395	211	22	induced	induce	VERB
ejpam-6395	211	23	by	by	ADP
ejpam-6395	211	24	a	a	DET
ejpam-6395	211	25	poset	poset	NOUN
ejpam-6395	211	26	(	(	PUNCT
ejpam-6395	211	27	s,≤	s,≤	NOUN
ejpam-6395	211	28	)	)	PUNCT
ejpam-6395	211	29	with	with	ADP
ejpam-6395	211	30	a	a	DET
ejpam-6395	211	31	zero	zero	NUM
ejpam-6395	211	32	element	element	NOUN
ejpam-6395	211	33	0	0	NUM
ejpam-6395	211	34	.	.	PUNCT
ejpam-6395	212	1	then	then	ADV
ejpam-6395	212	2	(	(	PUNCT
ejpam-6395	212	3	i	i	NOUN
ejpam-6395	212	4	)	)	PUNCT
ejpam-6395	212	5	{	{	PUNCT
ejpam-6395	212	6	0	0	NUM
ejpam-6395	212	7	}	}	PUNCT
ejpam-6395	212	8	is	be	AUX
ejpam-6395	212	9	both	both	PRON
ejpam-6395	212	10	a	a	DET
ejpam-6395	212	11	left	left	ADJ
ejpam-6395	212	12	and	and	CCONJ
ejpam-6395	212	13	right	right	ADJ
ejpam-6395	212	14	pure	pure	ADJ
ejpam-6395	212	15	ideal	ideal	NOUN
ejpam-6395	212	16	of	of	ADP
ejpam-6395	212	17	t	t	PROPN
ejpam-6395	212	18	.	.	PUNCT
ejpam-6395	213	1	(	(	PUNCT
ejpam-6395	213	2	ii	ii	NOUN
ejpam-6395	213	3	)	)	PUNCT
ejpam-6395	213	4	the	the	DET
ejpam-6395	213	5	union	union	NOUN
ejpam-6395	213	6	of	of	ADP
ejpam-6395	213	7	left	left	PROPN
ejpam-6395	213	8	(	(	PUNCT
ejpam-6395	213	9	resp	resp	NOUN
ejpam-6395	213	10	.	.	PUNCT
ejpam-6395	214	1	right	right	ADJ
ejpam-6395	214	2	)	)	PUNCT
ejpam-6395	214	3	pure	pure	ADJ
ejpam-6395	214	4	ideals	ideal	NOUN
ejpam-6395	214	5	of	of	ADP
ejpam-6395	214	6	t	t	PROPN
ejpam-6395	214	7	is	be	AUX
ejpam-6395	214	8	a	a	DET
ejpam-6395	214	9	left	left	ADJ
ejpam-6395	214	10	(	(	PUNCT
ejpam-6395	214	11	resp	resp	NOUN
ejpam-6395	214	12	.	.	PUNCT
ejpam-6395	215	1	right	right	ADJ
ejpam-6395	215	2	)	)	PUNCT
ejpam-6395	215	3	pure	pure	ADJ
ejpam-6395	215	4	ideal	ideal	NOUN
ejpam-6395	215	5	of	of	ADP
ejpam-6395	215	6	t	t	PROPN
ejpam-6395	215	7	.	.	PUNCT
ejpam-6395	216	1	(	(	PUNCT
ejpam-6395	216	2	iii	iii	X
ejpam-6395	216	3	)	)	PUNCT
ejpam-6395	216	4	the	the	DET
ejpam-6395	216	5	finite	finite	ADJ
ejpam-6395	216	6	intersection	intersection	NOUN
ejpam-6395	216	7	of	of	ADP
ejpam-6395	216	8	left	left	ADJ
ejpam-6395	216	9	(	(	PUNCT
ejpam-6395	216	10	resp	resp	NOUN
ejpam-6395	216	11	.	.	PUNCT
ejpam-6395	217	1	right	right	ADJ
ejpam-6395	217	2	)	)	PUNCT
ejpam-6395	217	3	pure	pure	ADJ
ejpam-6395	217	4	ideals	ideal	NOUN
ejpam-6395	217	5	of	of	ADP
ejpam-6395	217	6	t	t	PROPN
ejpam-6395	217	7	is	be	AUX
ejpam-6395	217	8	a	a	DET
ejpam-6395	217	9	left	left	ADJ
ejpam-6395	217	10	(	(	PUNCT
ejpam-6395	217	11	resp	resp	NOUN
ejpam-6395	217	12	.	.	PUNCT
ejpam-6395	218	1	right	right	ADJ
ejpam-6395	218	2	)	)	PUNCT
ejpam-6395	218	3	pure	pure	ADJ
ejpam-6395	218	4	ideal	ideal	NOUN
ejpam-6395	218	5	of	of	ADP
ejpam-6395	218	6	t	t	PROPN
ejpam-6395	218	7	.	.	PUNCT
ejpam-6395	219	1	proof	proof	NOUN
ejpam-6395	219	2	.	.	PUNCT
ejpam-6395	220	1	(	(	PUNCT
ejpam-6395	220	2	i	i	NOUN
ejpam-6395	220	3	)	)	PUNCT
ejpam-6395	220	4	since	since	SCONJ
ejpam-6395	220	5	{	{	PUNCT
ejpam-6395	220	6	0	0	NUM
ejpam-6395	220	7	}	}	PUNCT
ejpam-6395	220	8	is	be	AUX
ejpam-6395	220	9	an	an	DET
ejpam-6395	220	10	ideal	ideal	NOUN
ejpam-6395	220	11	of	of	ADP
ejpam-6395	220	12	t	t	PROPN
ejpam-6395	220	13	and	and	CCONJ
ejpam-6395	220	14	0	0	NUM
ejpam-6395	220	15	≤p	≤p	NOUN
ejpam-6395	220	16	0	0	NUM
ejpam-6395	220	17	=	=	SYM
ejpam-6395	220	18	•(0	•(0	PROPN
ejpam-6395	220	19	,	,	PUNCT
ejpam-6395	220	20	0	0	NUM
ejpam-6395	220	21	,	,	PUNCT
ejpam-6395	220	22	0	0	NUM
ejpam-6395	220	23	)	)	PUNCT
ejpam-6395	220	24	,	,	PUNCT
ejpam-6395	220	25	we	we	PRON
ejpam-6395	220	26	have	have	VERB
ejpam-6395	220	27	{	{	PUNCT
ejpam-6395	220	28	0	0	NUM
ejpam-6395	220	29	}	}	PUNCT
ejpam-6395	220	30	is	be	AUX
ejpam-6395	220	31	both	both	PRON
ejpam-6395	220	32	a	a	DET
ejpam-6395	220	33	left	left	ADJ
ejpam-6395	220	34	and	and	CCONJ
ejpam-6395	220	35	right	right	ADJ
ejpam-6395	220	36	pure	pure	ADJ
ejpam-6395	220	37	ideal	ideal	NOUN
ejpam-6395	220	38	of	of	ADP
ejpam-6395	220	39	t	t	PROPN
ejpam-6395	220	40	.	.	PUNCT
ejpam-6395	221	1	(	(	PUNCT
ejpam-6395	221	2	ii	ii	NOUN
ejpam-6395	221	3	)	)	PUNCT
ejpam-6395	221	4	let	let	VERB
ejpam-6395	221	5	{	{	PUNCT
ejpam-6395	221	6	ai	ai	VERB
ejpam-6395	221	7	|	|	ADV
ejpam-6395	222	1	i	i	PRON
ejpam-6395	222	2	∈	∈	PROPN
ejpam-6395	223	1	i	i	PRON
ejpam-6395	223	2	}	}	PUNCT
ejpam-6395	223	3	be	be	VERB
ejpam-6395	223	4	a	a	DET
ejpam-6395	223	5	family	family	NOUN
ejpam-6395	223	6	of	of	ADP
ejpam-6395	223	7	left	left	ADJ
ejpam-6395	223	8	(	(	PUNCT
ejpam-6395	223	9	resp	resp	NOUN
ejpam-6395	223	10	.	.	PUNCT
ejpam-6395	224	1	right	right	ADJ
ejpam-6395	224	2	)	)	PUNCT
ejpam-6395	224	3	pure	pure	ADJ
ejpam-6395	224	4	ideals	ideal	NOUN
ejpam-6395	224	5	of	of	ADP
ejpam-6395	224	6	t	t	PROPN
ejpam-6395	224	7	.	.	PUNCT
ejpam-6395	225	1	then	then	ADV
ejpam-6395	225	2	⋃	⋃	PUNCT
ejpam-6395	225	3	i∈i	i∈i	ADJ
ejpam-6395	225	4	ai	ai	VERB
ejpam-6395	225	5	is	be	AUX
ejpam-6395	225	6	an	an	DET
ejpam-6395	225	7	ideal	ideal	NOUN
ejpam-6395	225	8	of	of	ADP
ejpam-6395	225	9	t	t	PROPN
ejpam-6395	225	10	.	.	PUNCT
ejpam-6395	226	1	let	let	VERB
ejpam-6395	226	2	x	x	PUNCT
ejpam-6395	226	3	∈	∈	PROPN
ejpam-6395	226	4	⋃	⋃	NOUN
ejpam-6395	226	5	i∈i	i∈i	ADJ
ejpam-6395	226	6	ai	ai	VERB
ejpam-6395	226	7	.	.	PUNCT
ejpam-6395	227	1	then	then	ADV
ejpam-6395	227	2	x	x	SYM
ejpam-6395	227	3	∈	∈	PROPN
ejpam-6395	227	4	aj	aj	PROPN
ejpam-6395	227	5	for	for	ADP
ejpam-6395	227	6	some	some	DET
ejpam-6395	227	7	j	j	PROPN
ejpam-6395	227	8	∈	∈	PROPN
ejpam-6395	227	9	i.	i.	NOUN
ejpam-6395	227	10	since	since	SCONJ
ejpam-6395	227	11	aj	aj	PROPN
ejpam-6395	227	12	is	be	AUX
ejpam-6395	227	13	a	a	DET
ejpam-6395	227	14	left	left	ADJ
ejpam-6395	227	15	(	(	PUNCT
ejpam-6395	227	16	resp	resp	NOUN
ejpam-6395	227	17	.	.	PUNCT
ejpam-6395	228	1	right	right	ADJ
ejpam-6395	228	2	)	)	PUNCT
ejpam-6395	228	3	pure	pure	ADJ
ejpam-6395	228	4	ideal	ideal	NOUN
ejpam-6395	228	5	,	,	PUNCT
ejpam-6395	228	6	there	there	PRON
ejpam-6395	228	7	exists	exist	VERB
ejpam-6395	228	8	y	y	PROPN
ejpam-6395	228	9	,	,	PUNCT
ejpam-6395	228	10	z	z	PROPN
ejpam-6395	228	11	∈	∈	PROPN
ejpam-6395	228	12	aj	aj	PROPN
ejpam-6395	228	13	such	such	ADJ
ejpam-6395	228	14	that	that	SCONJ
ejpam-6395	228	15	x	x	SYM
ejpam-6395	228	16	≤p	≤p	NOUN
ejpam-6395	228	17	•(y	•(y	NOUN
ejpam-6395	228	18	,	,	PUNCT
ejpam-6395	228	19	z	z	NOUN
ejpam-6395	228	20	,	,	PUNCT
ejpam-6395	228	21	x	x	X
ejpam-6395	228	22	)	)	PUNCT
ejpam-6395	228	23	(	(	PUNCT
ejpam-6395	228	24	resp	resp	NOUN
ejpam-6395	228	25	.	.	PUNCT
ejpam-6395	229	1	x	x	SYM
ejpam-6395	229	2	≤p	≤p	PROPN
ejpam-6395	229	3	•(x	•(x	PROPN
ejpam-6395	229	4	,	,	PUNCT
ejpam-6395	229	5	y	y	PROPN
ejpam-6395	229	6	,	,	PUNCT
ejpam-6395	229	7	z	z	NOUN
ejpam-6395	229	8	)	)	PUNCT
ejpam-6395	229	9	)	)	PUNCT
ejpam-6395	229	10	.	.	PUNCT
ejpam-6395	230	1	we	we	PRON
ejpam-6395	230	2	have	have	VERB
ejpam-6395	230	3	y	y	PROPN
ejpam-6395	230	4	,	,	PUNCT
ejpam-6395	230	5	z	z	PROPN
ejpam-6395	230	6	∈	∈	PROPN
ejpam-6395	230	7	aj	aj	PROPN
ejpam-6395	230	8	⊆	⊆	NUM
ejpam-6395	230	9	⋃	⋃	PROPN
ejpam-6395	230	10	i∈i	i∈i	ADJ
ejpam-6395	230	11	ai	ai	NOUN
ejpam-6395	230	12	.	.	PUNCT
ejpam-6395	231	1	then	then	ADV
ejpam-6395	231	2	⋃	⋃	PUNCT
ejpam-6395	231	3	i∈i	i∈i	ADJ
ejpam-6395	231	4	ai	ai	VERB
ejpam-6395	231	5	is	be	AUX
ejpam-6395	231	6	a	a	DET
ejpam-6395	231	7	left	left	ADJ
ejpam-6395	231	8	(	(	PUNCT
ejpam-6395	231	9	resp	resp	NOUN
ejpam-6395	231	10	.	.	PUNCT
ejpam-6395	232	1	right	right	ADJ
ejpam-6395	232	2	)	)	PUNCT
ejpam-6395	232	3	pure	pure	ADJ
ejpam-6395	232	4	ideal	ideal	NOUN
ejpam-6395	232	5	of	of	ADP
ejpam-6395	232	6	t	t	PROPN
ejpam-6395	232	7	.	.	PUNCT
ejpam-6395	233	1	(	(	PUNCT
ejpam-6395	233	2	iii	iii	X
ejpam-6395	233	3	)	)	PUNCT
ejpam-6395	233	4	let	let	VERB
ejpam-6395	233	5	{	{	PUNCT
ejpam-6395	233	6	a1,a2	a1,a2	PROPN
ejpam-6395	233	7	,	,	PUNCT
ejpam-6395	233	8	...	...	PUNCT
ejpam-6395	233	9	,	,	PUNCT
ejpam-6395	233	10	an	an	PRON
ejpam-6395	233	11	}	}	PUNCT
ejpam-6395	233	12	be	be	AUX
ejpam-6395	233	13	a	a	DET
ejpam-6395	233	14	finite	finite	ADJ
ejpam-6395	233	15	family	family	NOUN
ejpam-6395	233	16	of	of	ADP
ejpam-6395	233	17	left	left	PROPN
ejpam-6395	233	18	(	(	PUNCT
ejpam-6395	233	19	resp	resp	NOUN
ejpam-6395	233	20	.	.	PUNCT
ejpam-6395	234	1	right	right	ADJ
ejpam-6395	234	2	)	)	PUNCT
ejpam-6395	234	3	pure	pure	ADJ
ejpam-6395	234	4	ideals	ideal	NOUN
ejpam-6395	234	5	of	of	ADP
ejpam-6395	234	6	t	t	PROPN
ejpam-6395	234	7	.	.	PUNCT
ejpam-6395	235	1	then⋂n	then⋂n	NOUN
ejpam-6395	235	2	i=1ai	i=1ai	NUM
ejpam-6395	235	3	is	be	AUX
ejpam-6395	235	4	an	an	DET
ejpam-6395	235	5	ideal	ideal	NOUN
ejpam-6395	235	6	of	of	ADP
ejpam-6395	235	7	t	t	PROPN
ejpam-6395	235	8	.	.	PUNCT
ejpam-6395	236	1	let	let	VERB
ejpam-6395	236	2	x	x	PUNCT
ejpam-6395	236	3	=	=	PRON
ejpam-6395	236	4	⋂n	⋂n	PROPN
ejpam-6395	236	5	i=1ai	i=1ai	ADV
ejpam-6395	236	6	.	.	PUNCT
ejpam-6395	237	1	then	then	ADV
ejpam-6395	237	2	x	x	X
ejpam-6395	237	3	∈	∈	PROPN
ejpam-6395	237	4	(	(	PUNCT
ejpam-6395	237	5	•(aj	•(aj	X
ejpam-6395	237	6	,	,	PUNCT
ejpam-6395	237	7	ak	ak	PROPN
ejpam-6395	237	8	,	,	PUNCT
ejpam-6395	237	9	x)]p	x)]p	PROPN
ejpam-6395	237	10	(	(	PUNCT
ejpam-6395	237	11	resp	resp	NOUN
ejpam-6395	237	12	.	.	PUNCT
ejpam-6395	238	1	x	x	X
ejpam-6395	238	2	∈	∈	PROPN
ejpam-6395	238	3	(	(	PUNCT
ejpam-6395	238	4	•(x	•(x	PROPN
ejpam-6395	238	5	,	,	PUNCT
ejpam-6395	238	6	aj	aj	PROPN
ejpam-6395	238	7	,	,	PUNCT
ejpam-6395	238	8	ak)]p	ak)]p	PROPN
ejpam-6395	238	9	)	)	PUNCT
ejpam-6395	238	10	,	,	PUNCT
ejpam-6395	238	11	for	for	ADP
ejpam-6395	238	12	some	some	DET
ejpam-6395	238	13	j	j	PROPN
ejpam-6395	238	14	,	,	PUNCT
ejpam-6395	238	15	k	k	PROPN
ejpam-6395	238	16	∈	∈	PROPN
ejpam-6395	238	17	{	{	PUNCT
ejpam-6395	238	18	1	1	NUM
ejpam-6395	238	19	,	,	PUNCT
ejpam-6395	238	20	...	...	PUNCT
ejpam-6395	238	21	,	,	PUNCT
ejpam-6395	238	22	n	n	CCONJ
ejpam-6395	238	23	}	}	PUNCT
ejpam-6395	238	24	.	.	PUNCT
ejpam-6395	239	1	that	that	PRON
ejpam-6395	239	2	is	be	AUX
ejpam-6395	239	3	,	,	PUNCT
ejpam-6395	239	4	⋂n	⋂n	PROPN
ejpam-6395	239	5	i=1ai	i=1ai	ADV
ejpam-6395	239	6	is	be	AUX
ejpam-6395	239	7	a	a	DET
ejpam-6395	239	8	left	left	ADJ
ejpam-6395	239	9	(	(	PUNCT
ejpam-6395	239	10	resp	resp	NOUN
ejpam-6395	239	11	.	.	PUNCT
ejpam-6395	240	1	right	right	ADJ
ejpam-6395	240	2	)	)	PUNCT
ejpam-6395	240	3	pure	pure	ADJ
ejpam-6395	240	4	ideal	ideal	NOUN
ejpam-6395	240	5	of	of	ADP
ejpam-6395	240	6	t	t	PROPN
ejpam-6395	240	7	.	.	PUNCT
ejpam-6395	241	1	theorem	theorem	ADJ
ejpam-6395	241	2	4	4	NUM
ejpam-6395	241	3	.	.	PUNCT
ejpam-6395	242	1	let	let	AUX
ejpam-6395	242	2	(	(	PUNCT
ejpam-6395	242	3	t	t	NOUN
ejpam-6395	242	4	,	,	PUNCT
ejpam-6395	242	5	•,≤p	•,≤p	NOUN
ejpam-6395	242	6	)	)	PUNCT
ejpam-6395	242	7	be	be	VERB
ejpam-6395	242	8	an	an	DET
ejpam-6395	242	9	ordered	order	VERB
ejpam-6395	242	10	power	power	NOUN
ejpam-6395	242	11	ternary	ternary	NOUN
ejpam-6395	242	12	semigroup	semigroup	NOUN
ejpam-6395	242	13	on	on	ADP
ejpam-6395	242	14	a	a	DET
ejpam-6395	242	15	ternary	ternary	ADJ
ejpam-6395	242	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	242	17	(	(	PUNCT
ejpam-6395	242	18	s	s	X
ejpam-6395	242	19	,	,	PUNCT
ejpam-6395	242	20	⋄	⋄	PROPN
ejpam-6395	242	21	)	)	PUNCT
ejpam-6395	242	22	induced	induce	VERB
ejpam-6395	242	23	by	by	ADP
ejpam-6395	242	24	a	a	DET
ejpam-6395	242	25	poset	poset	NOUN
ejpam-6395	242	26	(	(	PUNCT
ejpam-6395	242	27	s,≤	s,≤	NOUN
ejpam-6395	242	28	)	)	PUNCT
ejpam-6395	242	29	with	with	ADP
ejpam-6395	242	30	a	a	DET
ejpam-6395	242	31	zero	zero	NUM
ejpam-6395	242	32	element	element	NOUN
ejpam-6395	242	33	0	0	NUM
ejpam-6395	242	34	and	and	CCONJ
ejpam-6395	242	35	a	a	DET
ejpam-6395	242	36	be	be	AUX
ejpam-6395	242	37	an	an	DET
ejpam-6395	242	38	ideal	ideal	NOUN
ejpam-6395	242	39	of	of	ADP
ejpam-6395	242	40	t	t	PROPN
ejpam-6395	242	41	.	.	PUNCT
ejpam-6395	243	1	then	then	ADV
ejpam-6395	243	2	a	a	PRON
ejpam-6395	243	3	contains	contain	VERB
ejpam-6395	243	4	the	the	DET
ejpam-6395	243	5	largest	large	ADJ
ejpam-6395	243	6	left	left	ADJ
ejpam-6395	243	7	and	and	CCONJ
ejpam-6395	243	8	right	right	ADJ
ejpam-6395	243	9	pure	pure	ADJ
ejpam-6395	243	10	ideals	ideal	NOUN
ejpam-6395	243	11	of	of	ADP
ejpam-6395	243	12	t	t	PROPN
ejpam-6395	243	13	,	,	PUNCT
ejpam-6395	243	14	denoted	denote	VERB
ejpam-6395	243	15	by	by	ADP
ejpam-6395	243	16	t	t	PROPN
ejpam-6395	243	17	(	(	PUNCT
ejpam-6395	243	18	a	a	NOUN
ejpam-6395	243	19	)	)	PUNCT
ejpam-6395	243	20	.	.	PUNCT
ejpam-6395	244	1	a.	a.	NOUN
ejpam-6395	244	2	nongmanee	nongmanee	PROPN
ejpam-6395	244	3	,	,	PUNCT
ejpam-6395	244	4	k.	k.	PROPN
ejpam-6395	244	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	244	6	,	,	PUNCT
ejpam-6395	244	7	m.	m.	NOUN
ejpam-6395	244	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	244	9	/	/	SYM
ejpam-6395	244	10	eur	eur	PROPN
ejpam-6395	244	11	.	.	PUNCT
ejpam-6395	245	1	j.	j.	PROPN
ejpam-6395	245	2	pure	pure	PROPN
ejpam-6395	245	3	appl	appl	PROPN
ejpam-6395	245	4	.	.	PROPN
ejpam-6395	245	5	math	math	PROPN
ejpam-6395	245	6	,	,	PUNCT
ejpam-6395	245	7	18	18	NUM
ejpam-6395	245	8	(	(	PUNCT
ejpam-6395	245	9	3	3	NUM
ejpam-6395	245	10	)	)	PUNCT
ejpam-6395	245	11	(	(	PUNCT
ejpam-6395	245	12	2025	2025	NUM
ejpam-6395	245	13	)	)	PUNCT
ejpam-6395	245	14	,	,	PUNCT
ejpam-6395	245	15	6395	6395	NUM
ejpam-6395	245	16	8	8	NUM
ejpam-6395	245	17	of	of	ADP
ejpam-6395	245	18	12	12	NUM
ejpam-6395	245	19	proof	proof	NOUN
ejpam-6395	245	20	.	.	PUNCT
ejpam-6395	246	1	by	by	ADP
ejpam-6395	246	2	theorem	theorem	NOUN
ejpam-6395	246	3	3(i	3(i	NUM
ejpam-6395	246	4	)	)	PUNCT
ejpam-6395	246	5	,	,	PUNCT
ejpam-6395	246	6	we	we	PRON
ejpam-6395	246	7	have	have	VERB
ejpam-6395	246	8	{	{	PUNCT
ejpam-6395	246	9	0	0	NUM
ejpam-6395	246	10	}	}	PUNCT
ejpam-6395	246	11	is	be	AUX
ejpam-6395	246	12	both	both	PRON
ejpam-6395	246	13	a	a	DET
ejpam-6395	246	14	left	left	ADJ
ejpam-6395	246	15	and	and	CCONJ
ejpam-6395	246	16	right	right	ADJ
ejpam-6395	246	17	pure	pure	ADJ
ejpam-6395	246	18	ideal	ideal	NOUN
ejpam-6395	246	19	contained	contain	VERB
ejpam-6395	246	20	in	in	ADP
ejpam-6395	246	21	a.	a.	NOUN
ejpam-6395	246	22	then	then	ADV
ejpam-6395	246	23	there	there	PRON
ejpam-6395	246	24	exists	exist	VERB
ejpam-6395	246	25	the	the	DET
ejpam-6395	246	26	union	union	NOUN
ejpam-6395	246	27	of	of	ADP
ejpam-6395	246	28	all	all	PRON
ejpam-6395	246	29	left	left	ADJ
ejpam-6395	246	30	and	and	CCONJ
ejpam-6395	246	31	right	right	ADJ
ejpam-6395	246	32	pure	pure	ADJ
ejpam-6395	246	33	ideals	ideal	NOUN
ejpam-6395	246	34	of	of	ADP
ejpam-6395	246	35	t	t	PROPN
ejpam-6395	246	36	contained	contain	VERB
ejpam-6395	246	37	in	in	ADP
ejpam-6395	246	38	a.	a.	NOUN
ejpam-6395	246	39	that	that	PRON
ejpam-6395	246	40	is	be	AUX
ejpam-6395	246	41	,	,	PUNCT
ejpam-6395	246	42	the	the	DET
ejpam-6395	246	43	largest	large	ADJ
ejpam-6395	246	44	left	leave	VERB
ejpam-6395	246	45	and	and	CCONJ
ejpam-6395	246	46	right	right	ADJ
ejpam-6395	246	47	pure	pure	ADJ
ejpam-6395	246	48	ideals	ideal	NOUN
ejpam-6395	246	49	of	of	ADP
ejpam-6395	246	50	t	t	PROPN
ejpam-6395	246	51	contained	contain	VERB
ejpam-6395	246	52	in	in	ADP
ejpam-6395	246	53	a.	a.	NOUN
ejpam-6395	246	54	theorem	theorem	NOUN
ejpam-6395	246	55	5	5	X
ejpam-6395	246	56	.	.	PUNCT
ejpam-6395	247	1	let	let	AUX
ejpam-6395	247	2	(	(	PUNCT
ejpam-6395	247	3	t	t	NOUN
ejpam-6395	247	4	,	,	PUNCT
ejpam-6395	247	5	•,≤p	•,≤p	NOUN
ejpam-6395	247	6	)	)	PUNCT
ejpam-6395	247	7	be	be	VERB
ejpam-6395	247	8	an	an	DET
ejpam-6395	247	9	ordered	order	VERB
ejpam-6395	247	10	power	power	NOUN
ejpam-6395	247	11	ternary	ternary	NOUN
ejpam-6395	247	12	semigroup	semigroup	NOUN
ejpam-6395	247	13	on	on	ADP
ejpam-6395	247	14	a	a	DET
ejpam-6395	247	15	ternary	ternary	ADJ
ejpam-6395	247	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	247	17	(	(	PUNCT
ejpam-6395	247	18	s	s	X
ejpam-6395	247	19	,	,	PUNCT
ejpam-6395	247	20	⋄	⋄	PROPN
ejpam-6395	247	21	)	)	PUNCT
ejpam-6395	247	22	induced	induce	VERB
ejpam-6395	247	23	by	by	ADP
ejpam-6395	247	24	a	a	DET
ejpam-6395	247	25	poset	poset	NOUN
ejpam-6395	247	26	(	(	PUNCT
ejpam-6395	247	27	s,≤	s,≤	NOUN
ejpam-6395	247	28	)	)	PUNCT
ejpam-6395	247	29	with	with	ADP
ejpam-6395	247	30	a	a	DET
ejpam-6395	247	31	zero	zero	NUM
ejpam-6395	247	32	element	element	NOUN
ejpam-6395	247	33	0	0	NUM
ejpam-6395	247	34	and	and	CCONJ
ejpam-6395	247	35	a	a	DET
ejpam-6395	247	36	,	,	PUNCT
ejpam-6395	247	37	b	b	NOUN
ejpam-6395	247	38	,	,	PUNCT
ejpam-6395	247	39	ai	ai	VERB
ejpam-6395	247	40	be	be	AUX
ejpam-6395	247	41	ideals	ideal	NOUN
ejpam-6395	247	42	of	of	ADP
ejpam-6395	247	43	t	t	PROPN
ejpam-6395	247	44	for	for	ADP
ejpam-6395	247	45	all	all	PRON
ejpam-6395	247	46	i	i	PRON
ejpam-6395	247	47	∈	∈	PROPN
ejpam-6395	247	48	i.	i.	NOUN
ejpam-6395	247	49	then	then	ADV
ejpam-6395	247	50	the	the	DET
ejpam-6395	247	51	following	follow	VERB
ejpam-6395	247	52	statements	statement	NOUN
ejpam-6395	247	53	hold	hold	VERB
ejpam-6395	247	54	.	.	PUNCT
ejpam-6395	248	1	(	(	PUNCT
ejpam-6395	248	2	i	i	NOUN
ejpam-6395	248	3	)	)	PUNCT
ejpam-6395	248	4	t	t	PROPN
ejpam-6395	248	5	(	(	PUNCT
ejpam-6395	248	6	a	a	DET
ejpam-6395	248	7	∩	∩	ADJ
ejpam-6395	248	8	b	b	NOUN
ejpam-6395	248	9	)	)	PUNCT
ejpam-6395	248	10	=	=	SYM
ejpam-6395	248	11	t	t	PROPN
ejpam-6395	248	12	(	(	PUNCT
ejpam-6395	248	13	a	a	NOUN
ejpam-6395	248	14	)	)	PUNCT
ejpam-6395	248	15	∩	∩	ADJ
ejpam-6395	248	16	s(b	s(b	NOUN
ejpam-6395	248	17	)	)	PUNCT
ejpam-6395	248	18	.	.	PUNCT
ejpam-6395	249	1	(	(	PUNCT
ejpam-6395	249	2	ii	ii	NOUN
ejpam-6395	249	3	)	)	PUNCT
ejpam-6395	249	4	⋃	⋃	VERB
ejpam-6395	249	5	i∈i	i∈i	ADJ
ejpam-6395	249	6	t	t	PROPN
ejpam-6395	249	7	(	(	PUNCT
ejpam-6395	249	8	ai	ai	NOUN
ejpam-6395	249	9	)	)	PUNCT
ejpam-6395	249	10	⊆	⊆	NUM
ejpam-6395	249	11	t	t	NOUN
ejpam-6395	249	12	(	(	PUNCT
ejpam-6395	249	13	⋃	⋃	PROPN
ejpam-6395	249	14	i∈i	i∈i	ADJ
ejpam-6395	249	15	ai	ai	NOUN
ejpam-6395	249	16	)	)	PUNCT
ejpam-6395	249	17	.	.	PUNCT
ejpam-6395	250	1	proof	proof	NOUN
ejpam-6395	250	2	.	.	PUNCT
ejpam-6395	251	1	(	(	PUNCT
ejpam-6395	251	2	i	i	NOUN
ejpam-6395	251	3	)	)	PUNCT
ejpam-6395	251	4	since	since	SCONJ
ejpam-6395	251	5	t	t	PROPN
ejpam-6395	251	6	(	(	PUNCT
ejpam-6395	251	7	a	a	NOUN
ejpam-6395	251	8	)	)	PUNCT
ejpam-6395	251	9	is	be	AUX
ejpam-6395	251	10	the	the	DET
ejpam-6395	251	11	largest	large	ADJ
ejpam-6395	251	12	left	left	ADJ
ejpam-6395	251	13	and	and	CCONJ
ejpam-6395	251	14	right	right	ADJ
ejpam-6395	251	15	pure	pure	ADJ
ejpam-6395	251	16	ideals	ideal	NOUN
ejpam-6395	251	17	of	of	ADP
ejpam-6395	251	18	t	t	PROPN
ejpam-6395	251	19	contained	contain	VERB
ejpam-6395	251	20	in	in	ADP
ejpam-6395	251	21	a	a	PRON
ejpam-6395	251	22	,	,	PUNCT
ejpam-6395	251	23	t	t	PROPN
ejpam-6395	251	24	(	(	PUNCT
ejpam-6395	251	25	a	a	NOUN
ejpam-6395	251	26	)	)	PUNCT
ejpam-6395	251	27	⊆	⊆	NUM
ejpam-6395	251	28	a.	a.	NOUN
ejpam-6395	251	29	likewise	likewise	ADV
ejpam-6395	251	30	,	,	PUNCT
ejpam-6395	251	31	t	t	PROPN
ejpam-6395	251	32	(	(	PUNCT
ejpam-6395	251	33	b	b	NOUN
ejpam-6395	251	34	)	)	PUNCT
ejpam-6395	251	35	⊆	⊆	NUM
ejpam-6395	251	36	b.	b.	PROPN
ejpam-6395	251	37	then	then	ADV
ejpam-6395	251	38	t	t	PROPN
ejpam-6395	251	39	(	(	PUNCT
ejpam-6395	251	40	a	a	NOUN
ejpam-6395	251	41	)	)	PUNCT
ejpam-6395	251	42	∩	∩	ADJ
ejpam-6395	251	43	t	t	PROPN
ejpam-6395	251	44	(	(	PUNCT
ejpam-6395	251	45	b	b	NOUN
ejpam-6395	251	46	)	)	PUNCT
ejpam-6395	251	47	⊆	⊆	NUM
ejpam-6395	251	48	a	a	DET
ejpam-6395	251	49	∩	∩	ADJ
ejpam-6395	251	50	b.	b.	NOUN
ejpam-6395	251	51	by	by	ADP
ejpam-6395	251	52	theorem	theorem	ADJ
ejpam-6395	251	53	3.11.(iii	3.11.(iii	NUM
ejpam-6395	251	54	)	)	PUNCT
ejpam-6395	251	55	,	,	PUNCT
ejpam-6395	251	56	we	we	PRON
ejpam-6395	251	57	have	have	VERB
ejpam-6395	251	58	t	t	NOUN
ejpam-6395	251	59	(	(	PUNCT
ejpam-6395	251	60	a	a	NOUN
ejpam-6395	251	61	)	)	PUNCT
ejpam-6395	251	62	∩	∩	ADJ
ejpam-6395	251	63	t	t	PROPN
ejpam-6395	251	64	(	(	PUNCT
ejpam-6395	251	65	b	b	NOUN
ejpam-6395	251	66	)	)	PUNCT
ejpam-6395	251	67	is	be	AUX
ejpam-6395	251	68	a	a	DET
ejpam-6395	251	69	pure	pure	ADJ
ejpam-6395	251	70	ideal	ideal	NOUN
ejpam-6395	251	71	of	of	ADP
ejpam-6395	251	72	t	t	PROPN
ejpam-6395	251	73	contained	contain	VERB
ejpam-6395	251	74	in	in	ADP
ejpam-6395	251	75	a∩	a∩	PROPN
ejpam-6395	251	76	b.	b.	PROPN
ejpam-6395	251	77	since	since	SCONJ
ejpam-6395	251	78	t	t	PROPN
ejpam-6395	251	79	(	(	PUNCT
ejpam-6395	251	80	a∩	a∩	PROPN
ejpam-6395	251	81	b	b	X
ejpam-6395	251	82	)	)	PUNCT
ejpam-6395	251	83	is	be	AUX
ejpam-6395	251	84	the	the	DET
ejpam-6395	251	85	largest	large	ADJ
ejpam-6395	251	86	left	left	ADJ
ejpam-6395	251	87	and	and	CCONJ
ejpam-6395	251	88	right	right	ADJ
ejpam-6395	251	89	pure	pure	ADJ
ejpam-6395	251	90	ideals	ideal	NOUN
ejpam-6395	251	91	of	of	ADP
ejpam-6395	251	92	t	t	PROPN
ejpam-6395	251	93	contained	contain	VERB
ejpam-6395	251	94	in	in	ADP
ejpam-6395	251	95	a	a	DET
ejpam-6395	251	96	∩	∩	ADJ
ejpam-6395	251	97	b	b	NOUN
ejpam-6395	251	98	,	,	PUNCT
ejpam-6395	252	1	so	so	SCONJ
ejpam-6395	252	2	t	t	PROPN
ejpam-6395	252	3	(	(	PUNCT
ejpam-6395	252	4	a	a	NOUN
ejpam-6395	252	5	)	)	PUNCT
ejpam-6395	252	6	∩	∩	ADJ
ejpam-6395	252	7	t	t	PROPN
ejpam-6395	252	8	(	(	PUNCT
ejpam-6395	252	9	b	b	NOUN
ejpam-6395	252	10	)	)	PUNCT
ejpam-6395	252	11	⊆	⊆	NUM
ejpam-6395	252	12	t	t	NOUN
ejpam-6395	252	13	(	(	PUNCT
ejpam-6395	252	14	a	a	DET
ejpam-6395	252	15	∩	∩	ADJ
ejpam-6395	252	16	b	b	NOUN
ejpam-6395	252	17	)	)	PUNCT
ejpam-6395	252	18	.	.	PUNCT
ejpam-6395	253	1	since	since	SCONJ
ejpam-6395	253	2	t	t	PROPN
ejpam-6395	253	3	(	(	PUNCT
ejpam-6395	253	4	a∩b	a∩b	PROPN
ejpam-6395	253	5	)	)	PUNCT
ejpam-6395	253	6	⊆	⊆	NUM
ejpam-6395	253	7	a∩b	a∩b	NOUN
ejpam-6395	253	8	⊆	⊆	NUM
ejpam-6395	253	9	a	a	PRON
ejpam-6395	253	10	,	,	PUNCT
ejpam-6395	253	11	t	t	PROPN
ejpam-6395	253	12	(	(	PUNCT
ejpam-6395	253	13	a∩b	a∩b	PROPN
ejpam-6395	253	14	)	)	PUNCT
ejpam-6395	253	15	⊆	⊆	NUM
ejpam-6395	253	16	t	t	NOUN
ejpam-6395	253	17	(	(	PUNCT
ejpam-6395	253	18	a	a	NOUN
ejpam-6395	253	19	)	)	PUNCT
ejpam-6395	253	20	.	.	PUNCT
ejpam-6395	254	1	similarly	similarly	ADV
ejpam-6395	254	2	,	,	PUNCT
ejpam-6395	254	3	t	t	PROPN
ejpam-6395	254	4	(	(	PUNCT
ejpam-6395	254	5	a∩b	a∩b	PROPN
ejpam-6395	254	6	)	)	PUNCT
ejpam-6395	254	7	⊆	⊆	NUM
ejpam-6395	254	8	t	t	NOUN
ejpam-6395	254	9	(	(	PUNCT
ejpam-6395	254	10	b	b	NOUN
ejpam-6395	254	11	)	)	PUNCT
ejpam-6395	254	12	.	.	PUNCT
ejpam-6395	255	1	then	then	ADV
ejpam-6395	255	2	t	t	PROPN
ejpam-6395	255	3	(	(	PUNCT
ejpam-6395	255	4	a	a	DET
ejpam-6395	255	5	∩	∩	ADJ
ejpam-6395	255	6	b	b	X
ejpam-6395	255	7	)	)	PUNCT
ejpam-6395	255	8	⊆	⊆	NUM
ejpam-6395	255	9	t	t	NOUN
ejpam-6395	255	10	(	(	PUNCT
ejpam-6395	255	11	a	a	NOUN
ejpam-6395	255	12	)	)	PUNCT
ejpam-6395	255	13	∩	∩	ADJ
ejpam-6395	255	14	t	t	PROPN
ejpam-6395	255	15	(	(	PUNCT
ejpam-6395	255	16	b	b	NOUN
ejpam-6395	255	17	)	)	PUNCT
ejpam-6395	255	18	.	.	PUNCT
ejpam-6395	256	1	therefore	therefore	ADV
ejpam-6395	256	2	t	t	PROPN
ejpam-6395	256	3	(	(	PUNCT
ejpam-6395	256	4	a	a	DET
ejpam-6395	256	5	∩	∩	ADJ
ejpam-6395	256	6	b	b	NOUN
ejpam-6395	256	7	)	)	PUNCT
ejpam-6395	256	8	=	=	SYM
ejpam-6395	256	9	t	t	PROPN
ejpam-6395	256	10	(	(	PUNCT
ejpam-6395	256	11	a	a	NOUN
ejpam-6395	256	12	)	)	PUNCT
ejpam-6395	256	13	∩	∩	ADJ
ejpam-6395	256	14	s(b	s(b	NOUN
ejpam-6395	256	15	)	)	PUNCT
ejpam-6395	256	16	.	.	PUNCT
ejpam-6395	257	1	(	(	PUNCT
ejpam-6395	257	2	ii	ii	NOUN
ejpam-6395	257	3	)	)	PUNCT
ejpam-6395	257	4	since	since	SCONJ
ejpam-6395	257	5	t	t	PROPN
ejpam-6395	257	6	(	(	PUNCT
ejpam-6395	257	7	ai	ai	PROPN
ejpam-6395	257	8	)	)	PUNCT
ejpam-6395	257	9	is	be	AUX
ejpam-6395	257	10	the	the	DET
ejpam-6395	257	11	largest	large	ADJ
ejpam-6395	257	12	left	left	ADJ
ejpam-6395	257	13	and	and	CCONJ
ejpam-6395	257	14	right	right	ADJ
ejpam-6395	257	15	pure	pure	ADJ
ejpam-6395	257	16	ideals	ideal	NOUN
ejpam-6395	257	17	of	of	ADP
ejpam-6395	257	18	t	t	PROPN
ejpam-6395	257	19	contained	contain	VERB
ejpam-6395	257	20	in	in	ADP
ejpam-6395	257	21	ai	ai	PROPN
ejpam-6395	257	22	,	,	PUNCT
ejpam-6395	257	23	t	t	PROPN
ejpam-6395	257	24	(	(	PUNCT
ejpam-6395	257	25	ai	ai	PROPN
ejpam-6395	257	26	)	)	PUNCT
ejpam-6395	257	27	⊆	⊆	NUM
ejpam-6395	257	28	ai	ai	VERB
ejpam-6395	257	29	for	for	ADP
ejpam-6395	257	30	all	all	DET
ejpam-6395	257	31	i	i	PRON
ejpam-6395	257	32	∈	∈	PROPN
ejpam-6395	257	33	i.	i.	NOUN
ejpam-6395	257	34	then	then	ADV
ejpam-6395	257	35	⋃	⋃	PUNCT
ejpam-6395	257	36	i∈i	i∈i	ADJ
ejpam-6395	257	37	t	t	PROPN
ejpam-6395	257	38	(	(	PUNCT
ejpam-6395	257	39	ai	ai	NOUN
ejpam-6395	257	40	)	)	PUNCT
ejpam-6395	257	41	⊆	⊆	NUM
ejpam-6395	257	42	⋃	⋃	NOUN
ejpam-6395	257	43	i∈i	i∈i	ADJ
ejpam-6395	257	44	ai	ai	NOUN
ejpam-6395	257	45	.	.	PUNCT
ejpam-6395	258	1	by	by	ADP
ejpam-6395	258	2	theorem	theorem	ADJ
ejpam-6395	258	3	3(ii	3(ii	NUM
ejpam-6395	258	4	)	)	PUNCT
ejpam-6395	258	5	,	,	PUNCT
ejpam-6395	258	6	we	we	PRON
ejpam-6395	258	7	have	have	VERB
ejpam-6395	258	8	⋃	⋃	PROPN
ejpam-6395	258	9	i∈i	i∈i	ADJ
ejpam-6395	258	10	t	t	NOUN
ejpam-6395	258	11	(	(	PUNCT
ejpam-6395	258	12	ai	ai	PROPN
ejpam-6395	258	13	)	)	PUNCT
ejpam-6395	258	14	is	be	AUX
ejpam-6395	258	15	both	both	CCONJ
ejpam-6395	258	16	a	a	DET
ejpam-6395	258	17	left	left	ADJ
ejpam-6395	258	18	and	and	CCONJ
ejpam-6395	258	19	right	right	ADJ
ejpam-6395	258	20	pure	pure	ADJ
ejpam-6395	258	21	ideals	ideal	NOUN
ejpam-6395	258	22	of	of	ADP
ejpam-6395	258	23	s	s	PRON
ejpam-6395	258	24	contained	contain	VERB
ejpam-6395	258	25	in	in	ADP
ejpam-6395	258	26	⋃	⋃	PROPN
ejpam-6395	258	27	i∈i	i∈i	NOUN
ejpam-6395	258	28	ai	ai	VERB
ejpam-6395	258	29	for	for	ADP
ejpam-6395	258	30	all	all	DET
ejpam-6395	258	31	i	i	PRON
ejpam-6395	258	32	∈	∈	PROPN
ejpam-6395	258	33	i.	i.	NOUN
ejpam-6395	258	34	therefore⋃	therefore⋃	PROPN
ejpam-6395	258	35	i∈i	i∈i	PROPN
ejpam-6395	258	36	t	t	PROPN
ejpam-6395	258	37	(	(	PUNCT
ejpam-6395	258	38	ai	ai	NOUN
ejpam-6395	258	39	)	)	PUNCT
ejpam-6395	258	40	⊆	⊆	NUM
ejpam-6395	258	41	t	t	NOUN
ejpam-6395	258	42	(	(	PUNCT
ejpam-6395	258	43	⋃	⋃	PROPN
ejpam-6395	258	44	i∈i	i∈i	ADJ
ejpam-6395	258	45	ai	ai	NOUN
ejpam-6395	258	46	)	)	PUNCT
ejpam-6395	258	47	.	.	PUNCT
ejpam-6395	259	1	definition	definition	NOUN
ejpam-6395	259	2	9	9	NUM
ejpam-6395	259	3	.	.	PUNCT
ejpam-6395	260	1	let	let	AUX
ejpam-6395	260	2	(	(	PUNCT
ejpam-6395	260	3	t	t	NOUN
ejpam-6395	260	4	,	,	PUNCT
ejpam-6395	260	5	•,≤p	•,≤p	NOUN
ejpam-6395	260	6	)	)	PUNCT
ejpam-6395	260	7	be	be	VERB
ejpam-6395	260	8	an	an	DET
ejpam-6395	260	9	ordered	order	VERB
ejpam-6395	260	10	power	power	NOUN
ejpam-6395	260	11	ternary	ternary	NOUN
ejpam-6395	260	12	semigroup	semigroup	NOUN
ejpam-6395	260	13	on	on	ADP
ejpam-6395	260	14	a	a	DET
ejpam-6395	260	15	ternary	ternary	ADJ
ejpam-6395	260	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	260	17	(	(	PUNCT
ejpam-6395	260	18	s	s	X
ejpam-6395	260	19	,	,	PUNCT
ejpam-6395	260	20	⋄	⋄	PROPN
ejpam-6395	260	21	)	)	PUNCT
ejpam-6395	260	22	induced	induce	VERB
ejpam-6395	260	23	by	by	ADP
ejpam-6395	260	24	a	a	DET
ejpam-6395	260	25	poset	poset	NOUN
ejpam-6395	260	26	(	(	PUNCT
ejpam-6395	260	27	s,≤	s,≤	NOUN
ejpam-6395	260	28	)	)	PUNCT
ejpam-6395	260	29	.	.	PUNCT
ejpam-6395	261	1	a	a	DET
ejpam-6395	261	2	left	left	ADJ
ejpam-6395	261	3	(	(	PUNCT
ejpam-6395	261	4	resp	resp	NOUN
ejpam-6395	261	5	.	.	PUNCT
ejpam-6395	262	1	right	right	ADJ
ejpam-6395	262	2	)	)	PUNCT
ejpam-6395	262	3	pure	pure	ADJ
ejpam-6395	262	4	ideal	ideal	NOUN
ejpam-6395	262	5	a	a	PRON
ejpam-6395	262	6	of	of	ADP
ejpam-6395	262	7	t	t	PROPN
ejpam-6395	262	8	is	be	AUX
ejpam-6395	262	9	said	say	VERB
ejpam-6395	262	10	to	to	PART
ejpam-6395	262	11	be	be	AUX
ejpam-6395	262	12	left	leave	VERB
ejpam-6395	262	13	(	(	PUNCT
ejpam-6395	262	14	resp	resp	NOUN
ejpam-6395	262	15	.	.	PUNCT
ejpam-6395	263	1	right	right	ADJ
ejpam-6395	263	2	)	)	PUNCT
ejpam-6395	264	1	purely	purely	ADV
ejpam-6395	264	2	maximal	maximal	ADJ
ejpam-6395	264	3	if	if	SCONJ
ejpam-6395	264	4	for	for	ADP
ejpam-6395	264	5	any	any	DET
ejpam-6395	264	6	proper	proper	ADJ
ejpam-6395	264	7	left	left	NOUN
ejpam-6395	264	8	(	(	PUNCT
ejpam-6395	264	9	resp	resp	NOUN
ejpam-6395	264	10	.	.	PUNCT
ejpam-6395	265	1	right	right	ADJ
ejpam-6395	265	2	)	)	PUNCT
ejpam-6395	265	3	pure	pure	ADJ
ejpam-6395	265	4	ideal	ideal	PROPN
ejpam-6395	265	5	b	b	PROPN
ejpam-6395	265	6	of	of	ADP
ejpam-6395	265	7	t	t	PROPN
ejpam-6395	265	8	then	then	ADV
ejpam-6395	265	9	a	a	DET
ejpam-6395	265	10	⊆	⊆	NUM
ejpam-6395	265	11	b	b	NOUN
ejpam-6395	265	12	implies	imply	VERB
ejpam-6395	265	13	a	a	DET
ejpam-6395	265	14	=	=	SYM
ejpam-6395	265	15	b.	b.	NOUN
ejpam-6395	265	16	definition	definition	NOUN
ejpam-6395	265	17	10	10	NUM
ejpam-6395	265	18	.	.	PUNCT
ejpam-6395	266	1	let	let	AUX
ejpam-6395	266	2	(	(	PUNCT
ejpam-6395	266	3	t	t	NOUN
ejpam-6395	266	4	,	,	PUNCT
ejpam-6395	266	5	•,≤p	•,≤p	NOUN
ejpam-6395	266	6	)	)	PUNCT
ejpam-6395	266	7	be	be	VERB
ejpam-6395	266	8	an	an	DET
ejpam-6395	266	9	ordered	order	VERB
ejpam-6395	266	10	power	power	NOUN
ejpam-6395	266	11	ternary	ternary	NOUN
ejpam-6395	266	12	semigroup	semigroup	NOUN
ejpam-6395	266	13	on	on	ADP
ejpam-6395	266	14	a	a	DET
ejpam-6395	266	15	ternary	ternary	ADJ
ejpam-6395	266	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	266	17	(	(	PUNCT
ejpam-6395	266	18	s	s	X
ejpam-6395	266	19	,	,	PUNCT
ejpam-6395	266	20	⋄	⋄	PROPN
ejpam-6395	266	21	)	)	PUNCT
ejpam-6395	266	22	induced	induce	VERB
ejpam-6395	266	23	by	by	ADP
ejpam-6395	266	24	a	a	DET
ejpam-6395	266	25	poset	poset	NOUN
ejpam-6395	266	26	(	(	PUNCT
ejpam-6395	266	27	s,≤	s,≤	NOUN
ejpam-6395	266	28	)	)	PUNCT
ejpam-6395	266	29	.	.	PUNCT
ejpam-6395	267	1	let	let	VERB
ejpam-6395	267	2	a	a	PRON
ejpam-6395	267	3	be	be	AUX
ejpam-6395	267	4	a	a	DET
ejpam-6395	267	5	proper	proper	ADJ
ejpam-6395	267	6	left	left	NOUN
ejpam-6395	267	7	(	(	PUNCT
ejpam-6395	267	8	resp	resp	NOUN
ejpam-6395	267	9	.	.	PUNCT
ejpam-6395	268	1	right	right	ADJ
ejpam-6395	268	2	)	)	PUNCT
ejpam-6395	268	3	pure	pure	ADJ
ejpam-6395	268	4	ideal	ideal	NOUN
ejpam-6395	268	5	of	of	ADP
ejpam-6395	268	6	t	t	PROPN
ejpam-6395	268	7	.	.	PUNCT
ejpam-6395	269	1	then	then	ADV
ejpam-6395	269	2	a	a	PRON
ejpam-6395	269	3	is	be	AUX
ejpam-6395	269	4	called	call	VERB
ejpam-6395	269	5	left	left	ADJ
ejpam-6395	269	6	(	(	PUNCT
ejpam-6395	269	7	resp	resp	NOUN
ejpam-6395	269	8	.	.	PUNCT
ejpam-6395	270	1	right	right	ADJ
ejpam-6395	270	2	)	)	PUNCT
ejpam-6395	270	3	purely	purely	ADV
ejpam-6395	270	4	prime	prime	ADJ
ejpam-6395	270	5	if	if	SCONJ
ejpam-6395	270	6	b1	b1	VERB
ejpam-6395	270	7	∩b2	∩b2	PROPN
ejpam-6395	270	8	⊆	⊆	NUM
ejpam-6395	270	9	a	a	DET
ejpam-6395	270	10	implies	implie	NOUN
ejpam-6395	270	11	b1	b1	VERB
ejpam-6395	270	12	⊆	⊆	NUM
ejpam-6395	270	13	a	a	PRON
ejpam-6395	270	14	or	or	CCONJ
ejpam-6395	270	15	b2	b2	VERB
ejpam-6395	270	16	⊆	⊆	NUM
ejpam-6395	270	17	a	a	PRON
ejpam-6395	270	18	for	for	ADP
ejpam-6395	270	19	any	any	DET
ejpam-6395	270	20	left	left	ADJ
ejpam-6395	270	21	(	(	PUNCT
ejpam-6395	270	22	resp	resp	NOUN
ejpam-6395	270	23	.	.	PUNCT
ejpam-6395	271	1	right	right	ADJ
ejpam-6395	271	2	)	)	PUNCT
ejpam-6395	271	3	pure	pure	ADJ
ejpam-6395	271	4	ideals	ideal	NOUN
ejpam-6395	271	5	b1,b2	b1,b2	PROPN
ejpam-6395	271	6	of	of	ADP
ejpam-6395	271	7	t	t	PROPN
ejpam-6395	271	8	.	.	PUNCT
ejpam-6395	272	1	theorem	theorem	ADJ
ejpam-6395	272	2	6	6	NUM
ejpam-6395	272	3	.	.	PUNCT
ejpam-6395	273	1	let	let	AUX
ejpam-6395	273	2	(	(	PUNCT
ejpam-6395	273	3	t	t	NOUN
ejpam-6395	273	4	,	,	PUNCT
ejpam-6395	273	5	•,≤p	•,≤p	NOUN
ejpam-6395	273	6	)	)	PUNCT
ejpam-6395	273	7	be	be	VERB
ejpam-6395	273	8	an	an	DET
ejpam-6395	273	9	ordered	order	VERB
ejpam-6395	273	10	power	power	NOUN
ejpam-6395	273	11	ternary	ternary	NOUN
ejpam-6395	273	12	semigroup	semigroup	NOUN
ejpam-6395	273	13	on	on	ADP
ejpam-6395	273	14	a	a	DET
ejpam-6395	273	15	ternary	ternary	ADJ
ejpam-6395	273	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	273	17	(	(	PUNCT
ejpam-6395	273	18	s	s	X
ejpam-6395	273	19	,	,	PUNCT
ejpam-6395	273	20	⋄	⋄	PROPN
ejpam-6395	273	21	)	)	PUNCT
ejpam-6395	273	22	induced	induce	VERB
ejpam-6395	273	23	by	by	ADP
ejpam-6395	273	24	a	a	DET
ejpam-6395	273	25	poset	poset	NOUN
ejpam-6395	273	26	(	(	PUNCT
ejpam-6395	273	27	s,≤	s,≤	NOUN
ejpam-6395	273	28	)	)	PUNCT
ejpam-6395	273	29	.	.	PUNCT
ejpam-6395	274	1	then	then	ADV
ejpam-6395	274	2	every	every	DET
ejpam-6395	274	3	left	left	NOUN
ejpam-6395	274	4	(	(	PUNCT
ejpam-6395	274	5	resp	resp	NOUN
ejpam-6395	274	6	.	.	PUNCT
ejpam-6395	275	1	right	right	ADJ
ejpam-6395	275	2	)	)	PUNCT
ejpam-6395	275	3	purely	purely	ADV
ejpam-6395	275	4	maximal	maximal	ADJ
ejpam-6395	275	5	ideal	ideal	NOUN
ejpam-6395	275	6	of	of	ADP
ejpam-6395	275	7	t	t	PROPN
ejpam-6395	275	8	is	be	AUX
ejpam-6395	275	9	purely	purely	ADV
ejpam-6395	275	10	prime	prime	ADJ
ejpam-6395	275	11	.	.	PUNCT
ejpam-6395	276	1	proof	proof	NOUN
ejpam-6395	276	2	.	.	PUNCT
ejpam-6395	277	1	let	let	VERB
ejpam-6395	277	2	a	a	DET
ejpam-6395	277	3	be	be	AUX
ejpam-6395	277	4	a	a	DET
ejpam-6395	277	5	left	left	ADJ
ejpam-6395	277	6	(	(	PUNCT
ejpam-6395	277	7	resp	resp	NOUN
ejpam-6395	277	8	.	.	PUNCT
ejpam-6395	278	1	right	right	ADJ
ejpam-6395	278	2	)	)	PUNCT
ejpam-6395	278	3	purely	purely	ADV
ejpam-6395	278	4	maximal	maximal	ADJ
ejpam-6395	278	5	ideal	ideal	NOUN
ejpam-6395	278	6	of	of	ADP
ejpam-6395	278	7	t	t	PROPN
ejpam-6395	278	8	and	and	CCONJ
ejpam-6395	278	9	b	b	X
ejpam-6395	278	10	,	,	PUNCT
ejpam-6395	278	11	c	c	PROPN
ejpam-6395	278	12	be	be	AUX
ejpam-6395	278	13	left	leave	VERB
ejpam-6395	278	14	(	(	PUNCT
ejpam-6395	278	15	resp	resp	NOUN
ejpam-6395	278	16	.	.	PUNCT
ejpam-6395	279	1	right	right	ADJ
ejpam-6395	279	2	)	)	PUNCT
ejpam-6395	279	3	pure	pure	ADJ
ejpam-6395	279	4	ideals	ideal	NOUN
ejpam-6395	279	5	of	of	ADP
ejpam-6395	279	6	t	t	NOUN
ejpam-6395	279	7	such	such	ADJ
ejpam-6395	279	8	that	that	DET
ejpam-6395	279	9	b	b	NOUN
ejpam-6395	279	10	∩	∩	NOUN
ejpam-6395	279	11	c	c	NOUN
ejpam-6395	279	12	⊆	⊆	NUM
ejpam-6395	279	13	a	a	PRON
ejpam-6395	279	14	and	and	CCONJ
ejpam-6395	279	15	b	b	NOUN
ejpam-6395	279	16	⊈	⊈	PROPN
ejpam-6395	279	17	a.	a.	NOUN
ejpam-6395	279	18	since	since	SCONJ
ejpam-6395	279	19	a	a	DET
ejpam-6395	279	20	,	,	PUNCT
ejpam-6395	279	21	b	b	NOUN
ejpam-6395	279	22	are	be	AUX
ejpam-6395	279	23	left	leave	VERB
ejpam-6395	279	24	(	(	PUNCT
ejpam-6395	279	25	resp	resp	NOUN
ejpam-6395	279	26	.	.	PUNCT
ejpam-6395	280	1	right	right	ADJ
ejpam-6395	280	2	)	)	PUNCT
ejpam-6395	280	3	pure	pure	ADJ
ejpam-6395	280	4	ideals	ideal	NOUN
ejpam-6395	280	5	of	of	ADP
ejpam-6395	280	6	t	t	PROPN
ejpam-6395	280	7	and	and	CCONJ
ejpam-6395	280	8	b	b	X
ejpam-6395	280	9	⊈	⊈	PROPN
ejpam-6395	280	10	a	a	PRON
ejpam-6395	280	11	,	,	PUNCT
ejpam-6395	280	12	a	a	DET
ejpam-6395	280	13	∪	∪	ADJ
ejpam-6395	280	14	b	b	NOUN
ejpam-6395	280	15	is	be	AUX
ejpam-6395	280	16	a	a	DET
ejpam-6395	280	17	left	left	ADJ
ejpam-6395	280	18	(	(	PUNCT
ejpam-6395	280	19	resp	resp	NOUN
ejpam-6395	280	20	.	.	PUNCT
ejpam-6395	281	1	right	right	ADJ
ejpam-6395	281	2	)	)	PUNCT
ejpam-6395	281	3	pure	pure	ADJ
ejpam-6395	281	4	ideal	ideal	NOUN
ejpam-6395	281	5	of	of	ADP
ejpam-6395	281	6	s	s	PRON
ejpam-6395	281	7	such	such	ADJ
ejpam-6395	281	8	that	that	SCONJ
ejpam-6395	281	9	a	a	DET
ejpam-6395	281	10	⊂	⊂	PROPN
ejpam-6395	281	11	a	a	DET
ejpam-6395	281	12	∪	∪	X
ejpam-6395	281	13	b.	b.	NOUN
ejpam-6395	281	14	since	since	SCONJ
ejpam-6395	281	15	a	a	PRON
ejpam-6395	281	16	is	be	AUX
ejpam-6395	281	17	a	a	DET
ejpam-6395	281	18	left	left	ADJ
ejpam-6395	281	19	(	(	PUNCT
ejpam-6395	281	20	resp	resp	NOUN
ejpam-6395	281	21	.	.	PUNCT
ejpam-6395	282	1	right	right	ADJ
ejpam-6395	282	2	)	)	PUNCT
ejpam-6395	282	3	purely	purely	ADV
ejpam-6395	282	4	maximal	maximal	ADJ
ejpam-6395	282	5	ideal	ideal	NOUN
ejpam-6395	282	6	of	of	ADP
ejpam-6395	282	7	t	t	PROPN
ejpam-6395	282	8	,	,	PUNCT
ejpam-6395	282	9	t	t	PROPN
ejpam-6395	282	10	=	=	PUNCT
ejpam-6395	282	11	a	a	DET
ejpam-6395	282	12	∪	∪	X
ejpam-6395	282	13	b.	b.	NOUN
ejpam-6395	283	1	then	then	ADV
ejpam-6395	283	2	c	c	X
ejpam-6395	283	3	=	=	SYM
ejpam-6395	283	4	s	s	PART
ejpam-6395	283	5	∩	∩	NOUN
ejpam-6395	283	6	c	c	NOUN
ejpam-6395	283	7	=	=	SYM
ejpam-6395	283	8	(	(	PUNCT
ejpam-6395	283	9	a∪b	a∪b	ADJ
ejpam-6395	283	10	)	)	PUNCT
ejpam-6395	283	11	∩	∩	NOUN
ejpam-6395	283	12	c	c	NOUN
ejpam-6395	283	13	=	=	SYM
ejpam-6395	283	14	(	(	PUNCT
ejpam-6395	283	15	a∩	a∩	PROPN
ejpam-6395	283	16	c	c	X
ejpam-6395	283	17	)	)	PUNCT
ejpam-6395	283	18	∪	∪	NOUN
ejpam-6395	283	19	(	(	PUNCT
ejpam-6395	283	20	b	b	NOUN
ejpam-6395	283	21	∩	∩	ADJ
ejpam-6395	283	22	c	c	X
ejpam-6395	283	23	)	)	PUNCT
ejpam-6395	283	24	⊆	⊆	NUM
ejpam-6395	283	25	a.	a.	NOUN
ejpam-6395	283	26	so	so	ADV
ejpam-6395	283	27	a	a	PRON
ejpam-6395	283	28	is	be	AUX
ejpam-6395	283	29	left	leave	VERB
ejpam-6395	283	30	(	(	PUNCT
ejpam-6395	283	31	resp	resp	NOUN
ejpam-6395	283	32	.	.	PUNCT
ejpam-6395	284	1	right	right	ADJ
ejpam-6395	284	2	)	)	PUNCT
ejpam-6395	284	3	purely	purely	ADV
ejpam-6395	284	4	prime	prime	ADJ
ejpam-6395	284	5	.	.	PUNCT
ejpam-6395	285	1	a.	a.	NOUN
ejpam-6395	285	2	nongmanee	nongmanee	PROPN
ejpam-6395	285	3	,	,	PUNCT
ejpam-6395	285	4	k.	k.	PROPN
ejpam-6395	285	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	285	6	,	,	PUNCT
ejpam-6395	285	7	m.	m.	NOUN
ejpam-6395	285	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	285	9	/	/	SYM
ejpam-6395	285	10	eur	eur	PROPN
ejpam-6395	285	11	.	.	PUNCT
ejpam-6395	286	1	j.	j.	PROPN
ejpam-6395	286	2	pure	pure	PROPN
ejpam-6395	286	3	appl	appl	PROPN
ejpam-6395	286	4	.	.	PROPN
ejpam-6395	286	5	math	math	PROPN
ejpam-6395	286	6	,	,	PUNCT
ejpam-6395	286	7	18	18	NUM
ejpam-6395	286	8	(	(	PUNCT
ejpam-6395	286	9	3	3	NUM
ejpam-6395	286	10	)	)	PUNCT
ejpam-6395	286	11	(	(	PUNCT
ejpam-6395	286	12	2025	2025	NUM
ejpam-6395	286	13	)	)	PUNCT
ejpam-6395	286	14	,	,	PUNCT
ejpam-6395	286	15	6395	6395	NUM
ejpam-6395	286	16	9	9	NUM
ejpam-6395	286	17	of	of	ADP
ejpam-6395	286	18	12	12	NUM
ejpam-6395	286	19	theorem	theorem	NOUN
ejpam-6395	286	20	7	7	NUM
ejpam-6395	286	21	.	.	PUNCT
ejpam-6395	287	1	let	let	AUX
ejpam-6395	287	2	(	(	PUNCT
ejpam-6395	287	3	t	t	NOUN
ejpam-6395	287	4	,	,	PUNCT
ejpam-6395	287	5	•,≤p	•,≤p	NOUN
ejpam-6395	287	6	)	)	PUNCT
ejpam-6395	287	7	be	be	VERB
ejpam-6395	287	8	an	an	DET
ejpam-6395	287	9	ordered	order	VERB
ejpam-6395	287	10	power	power	NOUN
ejpam-6395	287	11	ternary	ternary	NOUN
ejpam-6395	287	12	semigroup	semigroup	NOUN
ejpam-6395	287	13	on	on	ADP
ejpam-6395	287	14	a	a	DET
ejpam-6395	287	15	ternary	ternary	ADJ
ejpam-6395	287	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	287	17	(	(	PUNCT
ejpam-6395	287	18	s	s	X
ejpam-6395	287	19	,	,	PUNCT
ejpam-6395	287	20	⋄	⋄	PROPN
ejpam-6395	287	21	)	)	PUNCT
ejpam-6395	287	22	induced	induce	VERB
ejpam-6395	287	23	by	by	ADP
ejpam-6395	287	24	a	a	DET
ejpam-6395	287	25	poset	poset	NOUN
ejpam-6395	287	26	(	(	PUNCT
ejpam-6395	287	27	s,≤	s,≤	NOUN
ejpam-6395	287	28	)	)	PUNCT
ejpam-6395	287	29	with	with	ADP
ejpam-6395	287	30	a	a	DET
ejpam-6395	287	31	zero	zero	NUM
ejpam-6395	287	32	element	element	NOUN
ejpam-6395	287	33	0	0	NUM
ejpam-6395	287	34	.	.	PUNCT
ejpam-6395	288	1	then	then	ADV
ejpam-6395	288	2	t	t	PROPN
ejpam-6395	288	3	(	(	PUNCT
ejpam-6395	288	4	a	a	PRON
ejpam-6395	288	5	)	)	PUNCT
ejpam-6395	288	6	is	be	AUX
ejpam-6395	288	7	a	a	DET
ejpam-6395	288	8	left	left	ADJ
ejpam-6395	288	9	(	(	PUNCT
ejpam-6395	288	10	resp	resp	NOUN
ejpam-6395	288	11	.	.	PUNCT
ejpam-6395	289	1	right	right	ADJ
ejpam-6395	289	2	)	)	PUNCT
ejpam-6395	289	3	purely	purely	ADV
ejpam-6395	289	4	prime	prime	ADJ
ejpam-6395	289	5	for	for	ADP
ejpam-6395	289	6	any	any	DET
ejpam-6395	289	7	left	left	ADJ
ejpam-6395	289	8	(	(	PUNCT
ejpam-6395	289	9	resp	resp	NOUN
ejpam-6395	289	10	.	.	PUNCT
ejpam-6395	290	1	right	right	ADJ
ejpam-6395	290	2	)	)	PUNCT
ejpam-6395	290	3	maximal	maximal	ADJ
ejpam-6395	290	4	ideal	ideal	NOUN
ejpam-6395	290	5	a	a	PRON
ejpam-6395	290	6	of	of	ADP
ejpam-6395	290	7	t	t	NOUN
ejpam-6395	290	8	.	.	PUNCT
ejpam-6395	291	1	proof	proof	NOUN
ejpam-6395	291	2	.	.	PUNCT
ejpam-6395	292	1	let	let	VERB
ejpam-6395	292	2	a	a	DET
ejpam-6395	292	3	be	be	AUX
ejpam-6395	292	4	a	a	DET
ejpam-6395	292	5	left	left	ADJ
ejpam-6395	292	6	(	(	PUNCT
ejpam-6395	292	7	resp	resp	NOUN
ejpam-6395	292	8	.	.	PUNCT
ejpam-6395	293	1	right	right	ADJ
ejpam-6395	293	2	)	)	PUNCT
ejpam-6395	293	3	maximal	maximal	ADJ
ejpam-6395	293	4	ideal	ideal	NOUN
ejpam-6395	293	5	of	of	ADP
ejpam-6395	293	6	t	t	PROPN
ejpam-6395	293	7	.	.	PUNCT
ejpam-6395	294	1	we	we	PRON
ejpam-6395	294	2	will	will	AUX
ejpam-6395	294	3	show	show	VERB
ejpam-6395	294	4	that	that	SCONJ
ejpam-6395	294	5	t	t	PROPN
ejpam-6395	294	6	(	(	PUNCT
ejpam-6395	294	7	a	a	PRON
ejpam-6395	294	8	)	)	PUNCT
ejpam-6395	294	9	is	be	AUX
ejpam-6395	294	10	a	a	DET
ejpam-6395	294	11	left	left	ADJ
ejpam-6395	294	12	(	(	PUNCT
ejpam-6395	294	13	resp	resp	NOUN
ejpam-6395	294	14	.	.	PUNCT
ejpam-6395	295	1	right)purely	right)purely	ADV
ejpam-6395	295	2	prime	prime	ADJ
ejpam-6395	295	3	.	.	PUNCT
ejpam-6395	296	1	let	let	VERB
ejpam-6395	296	2	b	b	X
ejpam-6395	296	3	,	,	PUNCT
ejpam-6395	296	4	c	c	PROPN
ejpam-6395	296	5	be	be	AUX
ejpam-6395	296	6	left	leave	VERB
ejpam-6395	296	7	(	(	PUNCT
ejpam-6395	296	8	resp	resp	NOUN
ejpam-6395	296	9	.	.	PUNCT
ejpam-6395	297	1	right	right	ADJ
ejpam-6395	297	2	)	)	PUNCT
ejpam-6395	297	3	pure	pure	ADJ
ejpam-6395	297	4	ideals	ideal	NOUN
ejpam-6395	297	5	of	of	ADP
ejpam-6395	297	6	t	t	NOUN
ejpam-6395	297	7	such	such	ADJ
ejpam-6395	297	8	that	that	DET
ejpam-6395	297	9	b	b	NOUN
ejpam-6395	297	10	∩	∩	NOUN
ejpam-6395	297	11	c	c	NOUN
ejpam-6395	297	12	⊆	⊆	NUM
ejpam-6395	297	13	s(a	s(a	NOUN
ejpam-6395	297	14	)	)	PUNCT
ejpam-6395	297	15	.	.	PUNCT
ejpam-6395	298	1	if	if	SCONJ
ejpam-6395	298	2	b	b	PROPN
ejpam-6395	298	3	⊆	⊆	SYM
ejpam-6395	298	4	a	a	DET
ejpam-6395	298	5	then	then	ADV
ejpam-6395	298	6	b	b	PROPN
ejpam-6395	298	7	⊆	⊆	NUM
ejpam-6395	298	8	t	t	NOUN
ejpam-6395	298	9	(	(	PUNCT
ejpam-6395	298	10	a	a	NOUN
ejpam-6395	298	11	)	)	PUNCT
ejpam-6395	298	12	.	.	PUNCT
ejpam-6395	298	13	suppose	suppose	VERB
ejpam-6395	298	14	b	b	X
ejpam-6395	298	15	⊈	⊈	PROPN
ejpam-6395	298	16	a.	a.	NOUN
ejpam-6395	298	17	since	since	SCONJ
ejpam-6395	298	18	a	a	PRON
ejpam-6395	298	19	,	,	PUNCT
ejpam-6395	298	20	b	b	PROPN
ejpam-6395	298	21	is	be	AUX
ejpam-6395	298	22	left	leave	VERB
ejpam-6395	298	23	(	(	PUNCT
ejpam-6395	298	24	resp	resp	NOUN
ejpam-6395	298	25	.	.	PUNCT
ejpam-6395	299	1	right	right	ADJ
ejpam-6395	299	2	)	)	PUNCT
ejpam-6395	299	3	pure	pure	ADJ
ejpam-6395	299	4	ideals	ideal	NOUN
ejpam-6395	299	5	of	of	ADP
ejpam-6395	299	6	t	t	PROPN
ejpam-6395	299	7	and	and	CCONJ
ejpam-6395	299	8	b	b	X
ejpam-6395	299	9	⊈	⊈	PROPN
ejpam-6395	299	10	a	a	PRON
ejpam-6395	299	11	,	,	PUNCT
ejpam-6395	299	12	a	a	DET
ejpam-6395	299	13	∪	∪	ADJ
ejpam-6395	299	14	b	b	NOUN
ejpam-6395	299	15	is	be	AUX
ejpam-6395	299	16	a	a	DET
ejpam-6395	299	17	left	left	ADJ
ejpam-6395	299	18	(	(	PUNCT
ejpam-6395	299	19	resp	resp	NOUN
ejpam-6395	299	20	.	.	PUNCT
ejpam-6395	300	1	right	right	ADJ
ejpam-6395	300	2	)	)	PUNCT
ejpam-6395	300	3	pure	pure	ADJ
ejpam-6395	300	4	ideal	ideal	NOUN
ejpam-6395	300	5	of	of	ADP
ejpam-6395	300	6	t	t	PROPN
ejpam-6395	300	7	such	such	ADJ
ejpam-6395	300	8	that	that	SCONJ
ejpam-6395	300	9	a	a	DET
ejpam-6395	300	10	⊂	⊂	PROPN
ejpam-6395	300	11	a	a	DET
ejpam-6395	300	12	∪	∪	X
ejpam-6395	300	13	b.	b.	NOUN
ejpam-6395	300	14	since	since	SCONJ
ejpam-6395	300	15	a	a	PRON
ejpam-6395	300	16	is	be	AUX
ejpam-6395	300	17	a	a	DET
ejpam-6395	300	18	left	left	ADJ
ejpam-6395	300	19	(	(	PUNCT
ejpam-6395	300	20	resp	resp	NOUN
ejpam-6395	300	21	.	.	PUNCT
ejpam-6395	301	1	right	right	ADJ
ejpam-6395	301	2	)	)	PUNCT
ejpam-6395	301	3	maximal	maximal	ADJ
ejpam-6395	301	4	ideal	ideal	NOUN
ejpam-6395	301	5	of	of	ADP
ejpam-6395	301	6	t	t	PROPN
ejpam-6395	301	7	,	,	PUNCT
ejpam-6395	301	8	t	t	PROPN
ejpam-6395	301	9	=	=	PUNCT
ejpam-6395	301	10	a	a	DET
ejpam-6395	301	11	∪	∪	X
ejpam-6395	301	12	b.	b.	NOUN
ejpam-6395	302	1	then	then	ADV
ejpam-6395	302	2	c	c	X
ejpam-6395	302	3	=	=	SYM
ejpam-6395	302	4	t	t	PROPN
ejpam-6395	302	5	∩	∩	NOUN
ejpam-6395	302	6	c	c	X
ejpam-6395	302	7	=	=	SYM
ejpam-6395	302	8	(	(	PUNCT
ejpam-6395	302	9	a∪b	a∪b	ADJ
ejpam-6395	302	10	)	)	PUNCT
ejpam-6395	302	11	∩	∩	NOUN
ejpam-6395	302	12	c	c	NOUN
ejpam-6395	302	13	=	=	SYM
ejpam-6395	302	14	(	(	PUNCT
ejpam-6395	302	15	a∩	a∩	PROPN
ejpam-6395	302	16	c	c	X
ejpam-6395	302	17	)	)	PUNCT
ejpam-6395	302	18	∪	∪	NOUN
ejpam-6395	302	19	(	(	PUNCT
ejpam-6395	302	20	b	b	NOUN
ejpam-6395	302	21	∩	∩	ADJ
ejpam-6395	302	22	c	c	X
ejpam-6395	302	23	)	)	PUNCT
ejpam-6395	302	24	⊆	⊆	NUM
ejpam-6395	302	25	a.	a.	NOUN
ejpam-6395	302	26	that	that	PRON
ejpam-6395	302	27	is	be	AUX
ejpam-6395	302	28	,	,	PUNCT
ejpam-6395	302	29	c	c	PROPN
ejpam-6395	302	30	⊆	⊆	NUM
ejpam-6395	302	31	t	t	NOUN
ejpam-6395	302	32	(	(	PUNCT
ejpam-6395	302	33	a	a	NOUN
ejpam-6395	302	34	)	)	PUNCT
ejpam-6395	302	35	.	.	PUNCT
ejpam-6395	303	1	therefore	therefore	ADV
ejpam-6395	303	2	t	t	PROPN
ejpam-6395	303	3	(	(	PUNCT
ejpam-6395	303	4	a	a	PRON
ejpam-6395	303	5	)	)	PUNCT
ejpam-6395	303	6	is	be	AUX
ejpam-6395	303	7	a	a	DET
ejpam-6395	303	8	left	left	ADJ
ejpam-6395	303	9	(	(	PUNCT
ejpam-6395	303	10	resp	resp	NOUN
ejpam-6395	303	11	.	.	PUNCT
ejpam-6395	304	1	right	right	ADJ
ejpam-6395	304	2	)	)	PUNCT
ejpam-6395	304	3	purely	purely	ADV
ejpam-6395	304	4	prime	prime	ADJ
ejpam-6395	304	5	.	.	PUNCT
ejpam-6395	305	1	theorem	theorem	ADJ
ejpam-6395	305	2	8	8	NUM
ejpam-6395	305	3	.	.	PUNCT
ejpam-6395	306	1	let	let	AUX
ejpam-6395	306	2	(	(	PUNCT
ejpam-6395	306	3	t	t	NOUN
ejpam-6395	306	4	,	,	PUNCT
ejpam-6395	306	5	•,≤p	•,≤p	NOUN
ejpam-6395	306	6	)	)	PUNCT
ejpam-6395	306	7	be	be	VERB
ejpam-6395	306	8	an	an	DET
ejpam-6395	306	9	ordered	order	VERB
ejpam-6395	306	10	power	power	NOUN
ejpam-6395	306	11	ternary	ternary	NOUN
ejpam-6395	306	12	semigroup	semigroup	NOUN
ejpam-6395	306	13	on	on	ADP
ejpam-6395	306	14	a	a	DET
ejpam-6395	306	15	ternary	ternary	ADJ
ejpam-6395	306	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	306	17	(	(	PUNCT
ejpam-6395	306	18	s	s	X
ejpam-6395	306	19	,	,	PUNCT
ejpam-6395	306	20	⋄	⋄	PROPN
ejpam-6395	306	21	)	)	PUNCT
ejpam-6395	306	22	induced	induce	VERB
ejpam-6395	306	23	by	by	ADP
ejpam-6395	306	24	a	a	DET
ejpam-6395	306	25	poset	poset	NOUN
ejpam-6395	306	26	(	(	PUNCT
ejpam-6395	306	27	s,≤	s,≤	NOUN
ejpam-6395	306	28	)	)	PUNCT
ejpam-6395	306	29	and	and	CCONJ
ejpam-6395	306	30	a	a	DET
ejpam-6395	306	31	be	be	AUX
ejpam-6395	306	32	a	a	DET
ejpam-6395	306	33	left	left	ADJ
ejpam-6395	306	34	(	(	PUNCT
ejpam-6395	306	35	resp	resp	NOUN
ejpam-6395	306	36	.	.	PUNCT
ejpam-6395	307	1	right	right	ADJ
ejpam-6395	307	2	)	)	PUNCT
ejpam-6395	307	3	pure	pure	ADJ
ejpam-6395	307	4	ideal	ideal	NOUN
ejpam-6395	307	5	of	of	ADP
ejpam-6395	307	6	t	t	PROPN
ejpam-6395	307	7	.	.	PUNCT
ejpam-6395	308	1	if	if	SCONJ
ejpam-6395	308	2	x	x	PROPN
ejpam-6395	308	3	∈	∈	PROPN
ejpam-6395	308	4	t	t	NOUN
ejpam-6395	308	5	\a	\a	VERB
ejpam-6395	308	6	then	then	ADV
ejpam-6395	308	7	there	there	PRON
ejpam-6395	308	8	exists	exist	VERB
ejpam-6395	308	9	a	a	DET
ejpam-6395	308	10	left	left	ADJ
ejpam-6395	308	11	(	(	PUNCT
ejpam-6395	308	12	resp	resp	NOUN
ejpam-6395	308	13	.	.	PUNCT
ejpam-6395	309	1	right	right	ADJ
ejpam-6395	309	2	)	)	PUNCT
ejpam-6395	309	3	purely	purely	ADV
ejpam-6395	309	4	prime	prime	ADJ
ejpam-6395	309	5	ideal	ideal	PROPN
ejpam-6395	309	6	b	b	PROPN
ejpam-6395	309	7	of	of	ADP
ejpam-6395	309	8	t	t	NOUN
ejpam-6395	310	1	such	such	ADJ
ejpam-6395	310	2	that	that	SCONJ
ejpam-6395	310	3	a	a	DET
ejpam-6395	310	4	⊆	⊆	NUM
ejpam-6395	310	5	b	b	NOUN
ejpam-6395	310	6	and	and	CCONJ
ejpam-6395	310	7	x	x	PROPN
ejpam-6395	310	8	/∈	/∈	PROPN
ejpam-6395	310	9	b.	b.	PROPN
ejpam-6395	310	10	proof	proof	NOUN
ejpam-6395	310	11	.	.	PUNCT
ejpam-6395	311	1	let	let	VERB
ejpam-6395	311	2	x	x	SYM
ejpam-6395	311	3	∈	∈	PROPN
ejpam-6395	311	4	t	t	PROPN
ejpam-6395	311	5	\a	\a	VERB
ejpam-6395	311	6	.	.	PUNCT
ejpam-6395	312	1	we	we	PRON
ejpam-6395	312	2	set	set	VERB
ejpam-6395	312	3	p	p	NOUN
ejpam-6395	312	4	=	=	PUNCT
ejpam-6395	312	5	{	{	PUNCT
ejpam-6395	312	6	b	b	PROPN
ejpam-6395	312	7	|	|	NOUN
ejpam-6395	312	8	b	b	PROPN
ejpam-6395	312	9	is	be	AUX
ejpam-6395	312	10	a	a	DET
ejpam-6395	312	11	left	left	ADJ
ejpam-6395	312	12	(	(	PUNCT
ejpam-6395	312	13	resp	resp	NOUN
ejpam-6395	312	14	.	.	PUNCT
ejpam-6395	313	1	right	right	ADJ
ejpam-6395	313	2	)	)	PUNCT
ejpam-6395	313	3	pure	pure	ADJ
ejpam-6395	313	4	ideal	ideal	NOUN
ejpam-6395	313	5	of	of	ADP
ejpam-6395	313	6	t	t	PROPN
ejpam-6395	313	7	,	,	PUNCT
ejpam-6395	313	8	a	a	DET
ejpam-6395	313	9	⊆	⊆	NUM
ejpam-6395	313	10	b	b	NOUN
ejpam-6395	313	11	and	and	CCONJ
ejpam-6395	313	12	x	x	NOUN
ejpam-6395	313	13	/∈	/∈	PUNCT
ejpam-6395	314	1	b	b	X
ejpam-6395	314	2	}	}	PUNCT
ejpam-6395	314	3	.	.	PUNCT
ejpam-6395	315	1	since	since	SCONJ
ejpam-6395	315	2	a	a	DET
ejpam-6395	315	3	∈	∈	PROPN
ejpam-6395	315	4	p	p	NOUN
ejpam-6395	315	5	,	,	PUNCT
ejpam-6395	315	6	p	p	PROPN
ejpam-6395	315	7	̸=	̸=	PROPN
ejpam-6395	315	8	∅.	∅.	ADV
ejpam-6395	315	9	we	we	PRON
ejpam-6395	315	10	have	have	VERB
ejpam-6395	315	11	p	p	NOUN
ejpam-6395	315	12	is	be	AUX
ejpam-6395	315	13	a	a	DET
ejpam-6395	315	14	partially	partially	ADV
ejpam-6395	315	15	ordered	order	VERB
ejpam-6395	315	16	set	set	VERB
ejpam-6395	315	17	under	under	ADP
ejpam-6395	315	18	the	the	DET
ejpam-6395	315	19	usual	usual	ADJ
ejpam-6395	315	20	inclusion	inclusion	NOUN
ejpam-6395	315	21	.	.	PUNCT
ejpam-6395	316	1	let	let	VERB
ejpam-6395	316	2	{	{	PUNCT
ejpam-6395	316	3	bi	bi	NOUN
ejpam-6395	317	1	|	|	ADV
ejpam-6395	317	2	i	i	PRON
ejpam-6395	317	3	∈	∈	VERB
ejpam-6395	317	4	i	i	PRON
ejpam-6395	317	5	}	}	PUNCT
ejpam-6395	317	6	be	be	VERB
ejpam-6395	317	7	any	any	DET
ejpam-6395	317	8	totally	totally	ADV
ejpam-6395	317	9	ordered	order	VERB
ejpam-6395	317	10	subset	subset	NOUN
ejpam-6395	317	11	of	of	ADP
ejpam-6395	317	12	p	p	PROPN
ejpam-6395	317	13	.	.	PUNCT
ejpam-6395	318	1	by	by	ADP
ejpam-6395	318	2	theorem	theorem	NOUN
ejpam-6395	318	3	3.11	3.11	NUM
ejpam-6395	318	4	.	.	PUNCT
ejpam-6395	318	5	,	,	PUNCT
ejpam-6395	318	6	⋃	⋃	ADP
ejpam-6395	318	7	i∈i	i∈i	ADJ
ejpam-6395	318	8	bi	bi	NOUN
ejpam-6395	318	9	is	be	AUX
ejpam-6395	318	10	a	a	DET
ejpam-6395	318	11	left	left	ADJ
ejpam-6395	318	12	(	(	PUNCT
ejpam-6395	318	13	resp	resp	NOUN
ejpam-6395	318	14	.	.	PUNCT
ejpam-6395	319	1	right	right	ADJ
ejpam-6395	319	2	)	)	PUNCT
ejpam-6395	319	3	pure	pure	ADJ
ejpam-6395	319	4	ideal	ideal	NOUN
ejpam-6395	319	5	.	.	PUNCT
ejpam-6395	320	1	since	since	SCONJ
ejpam-6395	320	2	a	a	DET
ejpam-6395	320	3	⊆	⊆	NUM
ejpam-6395	320	4	⋃	⋃	NOUN
ejpam-6395	320	5	i∈i	i∈i	ADJ
ejpam-6395	320	6	bi	bi	NOUN
ejpam-6395	320	7	and	and	CCONJ
ejpam-6395	320	8	x	x	NOUN
ejpam-6395	320	9	/∈	/∈	PUNCT
ejpam-6395	320	10	⋃	⋃	VERB
ejpam-6395	320	11	i∈i	i∈i	ADJ
ejpam-6395	320	12	bi	bi	NOUN
ejpam-6395	320	13	,	,	PUNCT
ejpam-6395	320	14	⋃	⋃	ADP
ejpam-6395	320	15	i∈i	i∈i	ADJ
ejpam-6395	320	16	bi	bi	NOUN
ejpam-6395	320	17	∈	∈	PROPN
ejpam-6395	320	18	p	p	PROPN
ejpam-6395	320	19	.	.	PUNCT
ejpam-6395	321	1	by	by	ADP
ejpam-6395	321	2	zorn	zorn	PROPN
ejpam-6395	321	3	’s	’s	PART
ejpam-6395	321	4	lemma	lemma	PROPN
ejpam-6395	321	5	,	,	PUNCT
ejpam-6395	321	6	p	p	PROPN
ejpam-6395	321	7	has	have	VERB
ejpam-6395	321	8	a	a	DET
ejpam-6395	321	9	maximal	maximal	ADJ
ejpam-6395	321	10	element	element	NOUN
ejpam-6395	321	11	.	.	PUNCT
ejpam-6395	322	1	let	let	VERB
ejpam-6395	322	2	m	m	PRON
ejpam-6395	322	3	be	be	AUX
ejpam-6395	322	4	a	a	DET
ejpam-6395	322	5	maximal	maximal	ADJ
ejpam-6395	322	6	element	element	NOUN
ejpam-6395	322	7	of	of	ADP
ejpam-6395	322	8	p	p	NOUN
ejpam-6395	322	9	.	.	PUNCT
ejpam-6395	323	1	we	we	PRON
ejpam-6395	323	2	will	will	AUX
ejpam-6395	323	3	show	show	VERB
ejpam-6395	323	4	that	that	SCONJ
ejpam-6395	323	5	m	m	PROPN
ejpam-6395	323	6	is	be	AUX
ejpam-6395	323	7	left	leave	VERB
ejpam-6395	323	8	(	(	PUNCT
ejpam-6395	323	9	resp	resp	NOUN
ejpam-6395	323	10	.	.	PUNCT
ejpam-6395	324	1	right	right	ADJ
ejpam-6395	324	2	)	)	PUNCT
ejpam-6395	324	3	purely	purely	ADV
ejpam-6395	324	4	prime	prime	ADJ
ejpam-6395	324	5	ideal	ideal	NOUN
ejpam-6395	324	6	.	.	PUNCT
ejpam-6395	325	1	suppose	suppose	VERB
ejpam-6395	325	2	that	that	SCONJ
ejpam-6395	325	3	b1,b2	b1,b2	PROPN
ejpam-6395	325	4	are	be	AUX
ejpam-6395	325	5	left	leave	VERB
ejpam-6395	325	6	(	(	PUNCT
ejpam-6395	325	7	resp	resp	NOUN
ejpam-6395	325	8	.	.	PUNCT
ejpam-6395	326	1	right	right	ADJ
ejpam-6395	326	2	)	)	PUNCT
ejpam-6395	326	3	pure	pure	ADJ
ejpam-6395	326	4	ideals	ideal	NOUN
ejpam-6395	326	5	of	of	ADP
ejpam-6395	326	6	t	t	NOUN
ejpam-6395	326	7	such	such	ADJ
ejpam-6395	326	8	that	that	DET
ejpam-6395	326	9	b1	b1	VERB
ejpam-6395	326	10	⊈	⊈	PROPN
ejpam-6395	326	11	m	m	NOUN
ejpam-6395	326	12	and	and	CCONJ
ejpam-6395	326	13	b2	b2	VERB
ejpam-6395	326	14	⊈	⊈	PROPN
ejpam-6395	326	15	m.	m.	NOUN
ejpam-6395	326	16	since	since	SCONJ
ejpam-6395	326	17	b1,b2,m	b1,b2,m	PROPN
ejpam-6395	326	18	are	be	AUX
ejpam-6395	326	19	left	leave	VERB
ejpam-6395	326	20	(	(	PUNCT
ejpam-6395	326	21	resp	resp	NOUN
ejpam-6395	326	22	.	.	PUNCT
ejpam-6395	327	1	right	right	ADJ
ejpam-6395	327	2	)	)	PUNCT
ejpam-6395	327	3	pure	pure	ADJ
ejpam-6395	327	4	ideals	ideal	NOUN
ejpam-6395	327	5	of	of	ADP
ejpam-6395	327	6	s	s	PROPN
ejpam-6395	327	7	,	,	PUNCT
ejpam-6395	327	8	b1	b1	PROPN
ejpam-6395	327	9	∪	∪	NOUN
ejpam-6395	327	10	m	m	PROPN
ejpam-6395	327	11	,	,	PUNCT
ejpam-6395	327	12	b2	b2	NOUN
ejpam-6395	327	13	∪	∪	NOUN
ejpam-6395	327	14	m	m	VERB
ejpam-6395	327	15	are	be	AUX
ejpam-6395	327	16	left	leave	VERB
ejpam-6395	327	17	(	(	PUNCT
ejpam-6395	327	18	resp	resp	NOUN
ejpam-6395	327	19	.	.	PUNCT
ejpam-6395	328	1	right	right	ADJ
ejpam-6395	328	2	)	)	PUNCT
ejpam-6395	328	3	pure	pure	ADJ
ejpam-6395	328	4	ideals	ideal	NOUN
ejpam-6395	328	5	of	of	ADP
ejpam-6395	328	6	t	t	PROPN
ejpam-6395	328	7	.	.	PUNCT
ejpam-6395	329	1	since	since	SCONJ
ejpam-6395	329	2	b1∪m	b1∪m	PROPN
ejpam-6395	329	3	,	,	PUNCT
ejpam-6395	329	4	b2∪m	b2∪m	VERB
ejpam-6395	329	5	are	be	AUX
ejpam-6395	329	6	left	leave	VERB
ejpam-6395	329	7	(	(	PUNCT
ejpam-6395	329	8	resp	resp	NOUN
ejpam-6395	329	9	.	.	PUNCT
ejpam-6395	330	1	right	right	ADJ
ejpam-6395	330	2	)	)	PUNCT
ejpam-6395	331	1	pure	pure	ADJ
ejpam-6395	331	2	,	,	PUNCT
ejpam-6395	331	3	a	a	DET
ejpam-6395	331	4	⊆	⊆	NUM
ejpam-6395	331	5	b1∪m	b1∪m	PROPN
ejpam-6395	331	6	,	,	PUNCT
ejpam-6395	331	7	a	a	DET
ejpam-6395	331	8	⊆	⊆	NUM
ejpam-6395	331	9	b2∪m	b2∪m	PUNCT
ejpam-6395	331	10	and	and	CCONJ
ejpam-6395	331	11	m	m	PROPN
ejpam-6395	331	12	is	be	AUX
ejpam-6395	331	13	a	a	DET
ejpam-6395	331	14	maximal	maximal	ADJ
ejpam-6395	331	15	element	element	NOUN
ejpam-6395	331	16	of	of	ADP
ejpam-6395	331	17	p	p	NOUN
ejpam-6395	331	18	,	,	PUNCT
ejpam-6395	331	19	then	then	ADV
ejpam-6395	331	20	x	x	PART
ejpam-6395	331	21	∈	∈	PROPN
ejpam-6395	331	22	b1	b1	NOUN
ejpam-6395	331	23	∪	∪	PROPN
ejpam-6395	331	24	m	m	PROPN
ejpam-6395	331	25	,	,	PUNCT
ejpam-6395	331	26	b2	b2	NOUN
ejpam-6395	331	27	∪	∪	NOUN
ejpam-6395	331	28	m.	m.	NOUN
ejpam-6395	331	29	since	since	SCONJ
ejpam-6395	331	30	x	x	PROPN
ejpam-6395	331	31	∈	∈	PROPN
ejpam-6395	331	32	b1	b1	NOUN
ejpam-6395	331	33	∪	∪	VERB
ejpam-6395	331	34	m	m	PROPN
ejpam-6395	331	35	and	and	CCONJ
ejpam-6395	331	36	x	x	PROPN
ejpam-6395	331	37	/∈	/∈	PROPN
ejpam-6395	331	38	m	m	VERB
ejpam-6395	331	39	,	,	PUNCT
ejpam-6395	331	40	x	x	SYM
ejpam-6395	331	41	∈	∈	PROPN
ejpam-6395	331	42	b1	b1	NOUN
ejpam-6395	331	43	.	.	PUNCT
ejpam-6395	332	1	similarly	similarly	ADV
ejpam-6395	332	2	,	,	PUNCT
ejpam-6395	332	3	x	x	PROPN
ejpam-6395	332	4	∈	∈	NOUN
ejpam-6395	332	5	b2	b2	NOUN
ejpam-6395	332	6	.	.	PUNCT
ejpam-6395	333	1	then	then	ADV
ejpam-6395	333	2	x	x	SYM
ejpam-6395	333	3	∈	∈	PROPN
ejpam-6395	333	4	b1∩b2	b1∩b2	PROPN
ejpam-6395	333	5	.	.	PUNCT
ejpam-6395	334	1	that	that	PRON
ejpam-6395	334	2	is	be	AUX
ejpam-6395	334	3	,	,	PUNCT
ejpam-6395	334	4	b1∩b2	b1∩b2	PROPN
ejpam-6395	334	5	⊈	⊈	PROPN
ejpam-6395	334	6	m.	m.	NOUN
ejpam-6395	334	7	therefore	therefore	ADV
ejpam-6395	334	8	m	m	VERB
ejpam-6395	334	9	is	be	AUX
ejpam-6395	334	10	a	a	DET
ejpam-6395	334	11	left	left	ADJ
ejpam-6395	334	12	(	(	PUNCT
ejpam-6395	334	13	resp	resp	NOUN
ejpam-6395	334	14	.	.	PUNCT
ejpam-6395	335	1	right	right	ADJ
ejpam-6395	335	2	)	)	PUNCT
ejpam-6395	335	3	purely	purely	ADV
ejpam-6395	335	4	prime	prime	ADJ
ejpam-6395	335	5	ideal	ideal	NOUN
ejpam-6395	335	6	.	.	PUNCT
ejpam-6395	336	1	theorem	theorem	NOUN
ejpam-6395	336	2	9	9	NUM
ejpam-6395	336	3	.	.	PUNCT
ejpam-6395	337	1	let	let	AUX
ejpam-6395	337	2	(	(	PUNCT
ejpam-6395	337	3	t	t	NOUN
ejpam-6395	337	4	,	,	PUNCT
ejpam-6395	337	5	•,≤p	•,≤p	NOUN
ejpam-6395	337	6	)	)	PUNCT
ejpam-6395	337	7	be	be	VERB
ejpam-6395	337	8	an	an	DET
ejpam-6395	337	9	ordered	order	VERB
ejpam-6395	337	10	power	power	NOUN
ejpam-6395	337	11	ternary	ternary	NOUN
ejpam-6395	337	12	semigroup	semigroup	NOUN
ejpam-6395	337	13	on	on	ADP
ejpam-6395	337	14	a	a	DET
ejpam-6395	337	15	ternary	ternary	ADJ
ejpam-6395	337	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	337	17	(	(	PUNCT
ejpam-6395	337	18	s	s	X
ejpam-6395	337	19	,	,	PUNCT
ejpam-6395	337	20	⋄	⋄	PROPN
ejpam-6395	337	21	)	)	PUNCT
ejpam-6395	337	22	induced	induce	VERB
ejpam-6395	337	23	by	by	ADP
ejpam-6395	337	24	a	a	DET
ejpam-6395	337	25	poset	poset	NOUN
ejpam-6395	337	26	(	(	PUNCT
ejpam-6395	337	27	s,≤	s,≤	NOUN
ejpam-6395	337	28	)	)	PUNCT
ejpam-6395	337	29	and	and	CCONJ
ejpam-6395	337	30	a	a	DET
ejpam-6395	337	31	be	be	AUX
ejpam-6395	337	32	a	a	DET
ejpam-6395	337	33	proper	proper	ADJ
ejpam-6395	337	34	left	left	NOUN
ejpam-6395	337	35	(	(	PUNCT
ejpam-6395	337	36	resp	resp	NOUN
ejpam-6395	337	37	.	.	PUNCT
ejpam-6395	338	1	right	right	ADJ
ejpam-6395	338	2	)	)	PUNCT
ejpam-6395	338	3	pure	pure	ADJ
ejpam-6395	338	4	ideal	ideal	NOUN
ejpam-6395	338	5	of	of	ADP
ejpam-6395	338	6	t	t	PROPN
ejpam-6395	338	7	.	.	PUNCT
ejpam-6395	339	1	then	then	ADV
ejpam-6395	339	2	a	a	PRON
ejpam-6395	339	3	is	be	AUX
ejpam-6395	339	4	an	an	DET
ejpam-6395	339	5	intersection	intersection	NOUN
ejpam-6395	339	6	of	of	ADP
ejpam-6395	339	7	all	all	DET
ejpam-6395	339	8	the	the	DET
ejpam-6395	339	9	left	left	NOUN
ejpam-6395	339	10	(	(	PUNCT
ejpam-6395	339	11	resp	resp	NOUN
ejpam-6395	339	12	.	.	PUNCT
ejpam-6395	340	1	right	right	ADJ
ejpam-6395	340	2	)	)	PUNCT
ejpam-6395	340	3	purely	purely	ADV
ejpam-6395	340	4	prime	prime	ADJ
ejpam-6395	340	5	ideals	ideal	NOUN
ejpam-6395	340	6	of	of	ADP
ejpam-6395	340	7	t	t	NOUN
ejpam-6395	340	8	containing	contain	VERB
ejpam-6395	340	9	a.	a.	NOUN
ejpam-6395	340	10	proof	proof	NOUN
ejpam-6395	340	11	.	.	PUNCT
ejpam-6395	341	1	let	let	VERB
ejpam-6395	341	2	a	a	PRON
ejpam-6395	341	3	be	be	AUX
ejpam-6395	341	4	a	a	DET
ejpam-6395	341	5	proper	proper	ADJ
ejpam-6395	341	6	left	left	NOUN
ejpam-6395	341	7	(	(	PUNCT
ejpam-6395	341	8	resp	resp	NOUN
ejpam-6395	341	9	.	.	PUNCT
ejpam-6395	342	1	right	right	ADJ
ejpam-6395	342	2	)	)	PUNCT
ejpam-6395	342	3	pure	pure	ADJ
ejpam-6395	342	4	ideal	ideal	NOUN
ejpam-6395	342	5	of	of	ADP
ejpam-6395	342	6	t	t	PROPN
ejpam-6395	342	7	.	.	PUNCT
ejpam-6395	343	1	by	by	ADP
ejpam-6395	343	2	theorem	theorem	NOUN
ejpam-6395	343	3	8	8	NUM
ejpam-6395	343	4	,	,	PUNCT
ejpam-6395	343	5	there	there	PRON
ejpam-6395	343	6	exists	exist	VERB
ejpam-6395	343	7	a	a	DET
ejpam-6395	343	8	left	left	ADJ
ejpam-6395	343	9	(	(	PUNCT
ejpam-6395	343	10	resp	resp	NOUN
ejpam-6395	343	11	.	.	PUNCT
ejpam-6395	344	1	right	right	ADJ
ejpam-6395	344	2	)	)	PUNCT
ejpam-6395	344	3	purely	purely	ADV
ejpam-6395	344	4	prime	prime	ADJ
ejpam-6395	344	5	ideal	ideal	NOUN
ejpam-6395	344	6	of	of	ADP
ejpam-6395	344	7	t	t	PROPN
ejpam-6395	344	8	containing	contain	VERB
ejpam-6395	344	9	a.	a.	NOUN
ejpam-6395	344	10	let	let	VERB
ejpam-6395	344	11	{	{	PUNCT
ejpam-6395	344	12	bi	bi	NOUN
ejpam-6395	344	13	|	|	ADV
ejpam-6395	344	14	i	i	PRON
ejpam-6395	344	15	∈	∈	VERB
ejpam-6395	345	1	i	i	PRON
ejpam-6395	345	2	}	}	PUNCT
ejpam-6395	345	3	be	be	VERB
ejpam-6395	345	4	a	a	DET
ejpam-6395	345	5	family	family	NOUN
ejpam-6395	345	6	of	of	ADP
ejpam-6395	345	7	all	all	DET
ejpam-6395	345	8	purely	purely	ADV
ejpam-6395	345	9	prime	prime	ADJ
ejpam-6395	345	10	ideals	ideal	NOUN
ejpam-6395	345	11	of	of	ADP
ejpam-6395	345	12	t	t	NOUN
ejpam-6395	345	13	containing	contain	VERB
ejpam-6395	345	14	a.	a.	NOUN
ejpam-6395	345	15	then	then	ADV
ejpam-6395	345	16	a	a	DET
ejpam-6395	345	17	⊆	⊆	NUM
ejpam-6395	345	18	⋂	⋂	PROPN
ejpam-6395	345	19	i∈i	i∈i	ADJ
ejpam-6395	345	20	bi	bi	NOUN
ejpam-6395	345	21	.	.	PUNCT
ejpam-6395	346	1	let	let	VERB
ejpam-6395	346	2	x	x	SYM
ejpam-6395	346	3	∈	∈	PROPN
ejpam-6395	346	4	⋂	⋂	PROPN
ejpam-6395	346	5	i∈i	i∈i	ADJ
ejpam-6395	346	6	bi	bi	NOUN
ejpam-6395	346	7	.	.	PUNCT
ejpam-6395	347	1	then	then	ADV
ejpam-6395	347	2	x	x	SYM
ejpam-6395	347	3	∈	∈	PROPN
ejpam-6395	347	4	bi	bi	NOUN
ejpam-6395	347	5	for	for	ADP
ejpam-6395	347	6	all	all	PRON
ejpam-6395	347	7	i	i	PRON
ejpam-6395	347	8	∈	∈	PROPN
ejpam-6395	347	9	i.	i.	NOUN
ejpam-6395	347	10	suppose	suppose	VERB
ejpam-6395	347	11	x	x	X
ejpam-6395	347	12	/∈	/∈	PUNCT
ejpam-6395	347	13	a.	a.	NOUN
ejpam-6395	348	1	we	we	PRON
ejpam-6395	348	2	have	have	VERB
ejpam-6395	348	3	x	x	PROPN
ejpam-6395	348	4	∈	∈	PROPN
ejpam-6395	348	5	t	t	NOUN
ejpam-6395	348	6	\a	\a	ADJ
ejpam-6395	348	7	and	and	CCONJ
ejpam-6395	348	8	a	a	PRON
ejpam-6395	348	9	is	be	AUX
ejpam-6395	348	10	a	a	DET
ejpam-6395	348	11	left	left	ADJ
ejpam-6395	348	12	(	(	PUNCT
ejpam-6395	348	13	resp	resp	NOUN
ejpam-6395	348	14	.	.	PUNCT
ejpam-6395	349	1	right	right	ADJ
ejpam-6395	349	2	)	)	PUNCT
ejpam-6395	349	3	pure	pure	ADJ
ejpam-6395	349	4	ideal	ideal	NOUN
ejpam-6395	349	5	of	of	ADP
ejpam-6395	349	6	t	t	PROPN
ejpam-6395	349	7	.	.	PUNCT
ejpam-6395	350	1	by	by	ADP
ejpam-6395	350	2	theorem	theorem	NOUN
ejpam-6395	350	3	8	8	NUM
ejpam-6395	350	4	,	,	PUNCT
ejpam-6395	350	5	there	there	PRON
ejpam-6395	350	6	exists	exist	VERB
ejpam-6395	350	7	a	a	DET
ejpam-6395	350	8	left	left	ADJ
ejpam-6395	350	9	(	(	PUNCT
ejpam-6395	350	10	resp	resp	NOUN
ejpam-6395	350	11	.	.	PUNCT
ejpam-6395	351	1	right	right	ADJ
ejpam-6395	351	2	)	)	PUNCT
ejpam-6395	351	3	purely	purely	ADV
ejpam-6395	351	4	prime	prime	ADJ
ejpam-6395	351	5	ideal	ideal	PROPN
ejpam-6395	351	6	b	b	PROPN
ejpam-6395	351	7	of	of	ADP
ejpam-6395	351	8	t	t	NOUN
ejpam-6395	351	9	containing	contain	VERB
ejpam-6395	351	10	a	a	DET
ejpam-6395	351	11	and	and	CCONJ
ejpam-6395	351	12	x	x	PROPN
ejpam-6395	351	13	/∈	/∈	PROPN
ejpam-6395	351	14	b.	b.	PROPN
ejpam-6395	351	15	contradiction	contradiction	NOUN
ejpam-6395	351	16	with	with	ADP
ejpam-6395	351	17	x	x	PROPN
ejpam-6395	351	18	∈	∈	PROPN
ejpam-6395	351	19	bi	bi	NOUN
ejpam-6395	351	20	for	for	ADP
ejpam-6395	351	21	all	all	PRON
ejpam-6395	351	22	i	i	PRON
ejpam-6395	351	23	∈	∈	PROPN
ejpam-6395	351	24	i.	i.	NOUN
ejpam-6395	351	25	then	then	ADV
ejpam-6395	351	26	x	x	SYM
ejpam-6395	351	27	∈	∈	NOUN
ejpam-6395	351	28	a.	a.	NOUN
ejpam-6395	352	1	hence⋂	hence⋂	X
ejpam-6395	352	2	i∈i	i∈i	ADJ
ejpam-6395	352	3	bi	bi	NOUN
ejpam-6395	352	4	⊆	⊆	NUM
ejpam-6395	352	5	a.	a.	NOUN
ejpam-6395	352	6	therefore	therefore	ADV
ejpam-6395	352	7	a	a	DET
ejpam-6395	352	8	=	=	SYM
ejpam-6395	352	9	⋂	⋂	PROPN
ejpam-6395	352	10	i∈i	i∈i	ADJ
ejpam-6395	352	11	bi	bi	NOUN
ejpam-6395	352	12	.	.	PUNCT
ejpam-6395	353	1	next	next	ADV
ejpam-6395	353	2	,	,	PUNCT
ejpam-6395	353	3	we	we	PRON
ejpam-6395	353	4	introduce	introduce	VERB
ejpam-6395	353	5	the	the	DET
ejpam-6395	353	6	concept	concept	NOUN
ejpam-6395	353	7	of	of	ADP
ejpam-6395	353	8	weakly	weakly	ADJ
ejpam-6395	353	9	pure	pure	ADJ
ejpam-6395	353	10	ideal	ideal	NOUN
ejpam-6395	353	11	in	in	ADP
ejpam-6395	353	12	ordered	order	VERB
ejpam-6395	353	13	power	power	NOUN
ejpam-6395	353	14	ternary	ternary	ADJ
ejpam-6395	353	15	semigroups	semigroup	NOUN
ejpam-6395	353	16	on	on	ADP
ejpam-6395	353	17	ternary	ternary	ADJ
ejpam-6395	353	18	semihypergroups	semihypergroup	NOUN
ejpam-6395	353	19	induced	induce	VERB
ejpam-6395	353	20	by	by	ADP
ejpam-6395	353	21	posets	poset	NOUN
ejpam-6395	353	22	.	.	PUNCT
ejpam-6395	354	1	a.	a.	NOUN
ejpam-6395	354	2	nongmanee	nongmanee	PROPN
ejpam-6395	354	3	,	,	PUNCT
ejpam-6395	354	4	k.	k.	PROPN
ejpam-6395	354	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	354	6	,	,	PUNCT
ejpam-6395	354	7	m.	m.	NOUN
ejpam-6395	354	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	354	9	/	/	SYM
ejpam-6395	354	10	eur	eur	PROPN
ejpam-6395	354	11	.	.	PUNCT
ejpam-6395	355	1	j.	j.	PROPN
ejpam-6395	355	2	pure	pure	PROPN
ejpam-6395	355	3	appl	appl	PROPN
ejpam-6395	355	4	.	.	PROPN
ejpam-6395	355	5	math	math	PROPN
ejpam-6395	355	6	,	,	PUNCT
ejpam-6395	355	7	18	18	NUM
ejpam-6395	355	8	(	(	PUNCT
ejpam-6395	355	9	3	3	NUM
ejpam-6395	355	10	)	)	PUNCT
ejpam-6395	355	11	(	(	PUNCT
ejpam-6395	355	12	2025	2025	NUM
ejpam-6395	355	13	)	)	PUNCT
ejpam-6395	355	14	,	,	PUNCT
ejpam-6395	355	15	6395	6395	NUM
ejpam-6395	355	16	10	10	NUM
ejpam-6395	355	17	of	of	ADP
ejpam-6395	355	18	12	12	NUM
ejpam-6395	355	19	definition	definition	NOUN
ejpam-6395	355	20	11	11	NUM
ejpam-6395	355	21	.	.	PUNCT
ejpam-6395	356	1	let	let	AUX
ejpam-6395	356	2	(	(	PUNCT
ejpam-6395	356	3	t	t	NOUN
ejpam-6395	356	4	,	,	PUNCT
ejpam-6395	356	5	•,≤p	•,≤p	NOUN
ejpam-6395	356	6	)	)	PUNCT
ejpam-6395	356	7	be	be	VERB
ejpam-6395	356	8	an	an	DET
ejpam-6395	356	9	ordered	order	VERB
ejpam-6395	356	10	power	power	NOUN
ejpam-6395	356	11	ternary	ternary	NOUN
ejpam-6395	356	12	semigroup	semigroup	NOUN
ejpam-6395	356	13	on	on	ADP
ejpam-6395	356	14	a	a	DET
ejpam-6395	356	15	ternary	ternary	ADJ
ejpam-6395	356	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	356	17	(	(	PUNCT
ejpam-6395	356	18	s	s	X
ejpam-6395	356	19	,	,	PUNCT
ejpam-6395	356	20	⋄	⋄	PROPN
ejpam-6395	356	21	)	)	PUNCT
ejpam-6395	356	22	induced	induce	VERB
ejpam-6395	356	23	by	by	ADP
ejpam-6395	356	24	a	a	DET
ejpam-6395	356	25	poset	poset	NOUN
ejpam-6395	356	26	(	(	PUNCT
ejpam-6395	356	27	s,≤	s,≤	NOUN
ejpam-6395	356	28	)	)	PUNCT
ejpam-6395	356	29	.	.	PUNCT
ejpam-6395	357	1	an	an	DET
ejpam-6395	357	2	ideal	ideal	NOUN
ejpam-6395	357	3	a	a	PRON
ejpam-6395	357	4	of	of	ADP
ejpam-6395	357	5	t	t	PROPN
ejpam-6395	357	6	is	be	AUX
ejpam-6395	357	7	said	say	VERB
ejpam-6395	357	8	to	to	PART
ejpam-6395	357	9	be	be	AUX
ejpam-6395	357	10	left	leave	VERB
ejpam-6395	357	11	(	(	PUNCT
ejpam-6395	357	12	resp	resp	NOUN
ejpam-6395	357	13	.	.	PUNCT
ejpam-6395	358	1	right	right	ADJ
ejpam-6395	358	2	)	)	PUNCT
ejpam-6395	358	3	weakly	weakly	ADV
ejpam-6395	358	4	pure	pure	ADJ
ejpam-6395	358	5	if	if	SCONJ
ejpam-6395	358	6	a∩b	a∩b	PROPN
ejpam-6395	358	7	=	=	PRON
ejpam-6395	358	8	(	(	PUNCT
ejpam-6395	358	9	•(a	•(a	PROPN
ejpam-6395	358	10	,	,	PUNCT
ejpam-6395	358	11	a	a	PRON
ejpam-6395	358	12	,	,	PUNCT
ejpam-6395	358	13	b)]p	b)]p	PROPN
ejpam-6395	358	14	(	(	PUNCT
ejpam-6395	358	15	resp	resp	NOUN
ejpam-6395	358	16	.	.	PUNCT
ejpam-6395	359	1	a∩b	a∩b	PROPN
ejpam-6395	360	1	=	=	PUNCT
ejpam-6395	360	2	(	(	PUNCT
ejpam-6395	360	3	•(b	•(b	PROPN
ejpam-6395	360	4	,	,	PUNCT
ejpam-6395	360	5	a	a	DET
ejpam-6395	360	6	,	,	PUNCT
ejpam-6395	360	7	a)]p	a)]p	PROPN
ejpam-6395	360	8	)	)	PUNCT
ejpam-6395	360	9	for	for	ADP
ejpam-6395	360	10	all	all	DET
ejpam-6395	360	11	two	two	NUM
ejpam-6395	360	12	-	-	PUNCT
ejpam-6395	360	13	sided	sided	ADJ
ejpam-6395	360	14	ideals	ideal	NOUN
ejpam-6395	360	15	b	b	PROPN
ejpam-6395	360	16	of	of	ADP
ejpam-6395	360	17	s.	s.	PROPN
ejpam-6395	360	18	lemma	lemma	PROPN
ejpam-6395	360	19	2	2	X
ejpam-6395	360	20	.	.	PUNCT
ejpam-6395	361	1	let	let	VERB
ejpam-6395	361	2	(	(	PUNCT
ejpam-6395	361	3	t	t	NOUN
ejpam-6395	361	4	,	,	PUNCT
ejpam-6395	361	5	•,≤p	•,≤p	NOUN
ejpam-6395	361	6	)	)	PUNCT
ejpam-6395	361	7	be	be	AUX
ejpam-6395	361	8	an	an	DET
ejpam-6395	361	9	ordered	order	VERB
ejpam-6395	361	10	power	power	NOUN
ejpam-6395	361	11	ternary	ternary	NOUN
ejpam-6395	361	12	semigroup	semigroup	NOUN
ejpam-6395	361	13	on	on	ADP
ejpam-6395	361	14	a	a	DET
ejpam-6395	361	15	ternary	ternary	ADJ
ejpam-6395	361	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	361	17	(	(	PUNCT
ejpam-6395	361	18	s	s	X
ejpam-6395	361	19	,	,	PUNCT
ejpam-6395	361	20	⋄	⋄	PROPN
ejpam-6395	361	21	)	)	PUNCT
ejpam-6395	361	22	induced	induce	VERB
ejpam-6395	361	23	by	by	ADP
ejpam-6395	361	24	a	a	DET
ejpam-6395	361	25	poset	poset	NOUN
ejpam-6395	361	26	(	(	PUNCT
ejpam-6395	361	27	s,≤	s,≤	NOUN
ejpam-6395	361	28	)	)	PUNCT
ejpam-6395	361	29	.	.	PUNCT
ejpam-6395	362	1	every	every	DET
ejpam-6395	362	2	left	left	ADJ
ejpam-6395	362	3	(	(	PUNCT
ejpam-6395	362	4	resp	resp	NOUN
ejpam-6395	362	5	.	.	PUNCT
ejpam-6395	363	1	right	right	ADJ
ejpam-6395	363	2	)	)	PUNCT
ejpam-6395	363	3	pure	pure	ADJ
ejpam-6395	363	4	ideal	ideal	NOUN
ejpam-6395	363	5	of	of	ADP
ejpam-6395	363	6	t	t	PROPN
ejpam-6395	363	7	is	be	AUX
ejpam-6395	363	8	left	leave	VERB
ejpam-6395	363	9	(	(	PUNCT
ejpam-6395	363	10	resp	resp	NOUN
ejpam-6395	363	11	.	.	PUNCT
ejpam-6395	364	1	right	right	ADJ
ejpam-6395	364	2	)	)	PUNCT
ejpam-6395	364	3	weakly	weakly	ADV
ejpam-6395	364	4	pure	pure	ADJ
ejpam-6395	364	5	.	.	PUNCT
ejpam-6395	365	1	proof	proof	NOUN
ejpam-6395	365	2	.	.	PUNCT
ejpam-6395	366	1	let	let	VERB
ejpam-6395	366	2	a	a	DET
ejpam-6395	366	3	be	be	AUX
ejpam-6395	366	4	a	a	DET
ejpam-6395	366	5	left	left	ADJ
ejpam-6395	366	6	pure	pure	ADJ
ejpam-6395	366	7	ideal	ideal	NOUN
ejpam-6395	366	8	of	of	ADP
ejpam-6395	366	9	t	t	PROPN
ejpam-6395	366	10	and	and	CCONJ
ejpam-6395	366	11	x	x	PUNCT
ejpam-6395	366	12	∈	∈	NOUN
ejpam-6395	366	13	a.	a.	NOUN
ejpam-6395	366	14	let	let	VERB
ejpam-6395	366	15	x	x	PART
ejpam-6395	366	16	∈	∈	PROPN
ejpam-6395	366	17	a	a	DET
ejpam-6395	366	18	∩	∩	ADJ
ejpam-6395	366	19	b	b	NOUN
ejpam-6395	366	20	for	for	ADP
ejpam-6395	366	21	all	all	DET
ejpam-6395	366	22	two	two	NUM
ejpam-6395	366	23	-	-	PUNCT
ejpam-6395	366	24	sided	sided	ADJ
ejpam-6395	366	25	ideals	ideal	NOUN
ejpam-6395	366	26	b	b	PROPN
ejpam-6395	366	27	of	of	ADP
ejpam-6395	366	28	t	t	PROPN
ejpam-6395	366	29	.	.	PUNCT
ejpam-6395	367	1	then	then	ADV
ejpam-6395	367	2	x	x	X
ejpam-6395	367	3	∈	∈	PROPN
ejpam-6395	367	4	a	a	PRON
ejpam-6395	367	5	and	and	CCONJ
ejpam-6395	367	6	x	x	PROPN
ejpam-6395	367	7	∈	∈	PROPN
ejpam-6395	367	8	b.	b.	PROPN
ejpam-6395	367	9	since	since	SCONJ
ejpam-6395	367	10	a	a	DET
ejpam-6395	367	11	be	be	AUX
ejpam-6395	367	12	a	a	DET
ejpam-6395	367	13	left	left	ADJ
ejpam-6395	367	14	pure	pure	ADJ
ejpam-6395	367	15	ideal	ideal	NOUN
ejpam-6395	367	16	of	of	ADP
ejpam-6395	367	17	t	t	PROPN
ejpam-6395	367	18	,	,	PUNCT
ejpam-6395	367	19	there	there	PRON
ejpam-6395	367	20	exists	exist	VERB
ejpam-6395	367	21	y	y	PROPN
ejpam-6395	367	22	,	,	PUNCT
ejpam-6395	367	23	z	z	PROPN
ejpam-6395	367	24	∈	∈	PROPN
ejpam-6395	367	25	a	a	DET
ejpam-6395	367	26	such	such	ADJ
ejpam-6395	367	27	that	that	SCONJ
ejpam-6395	367	28	x	x	SYM
ejpam-6395	367	29	≤p	≤p	NOUN
ejpam-6395	367	30	•(y	•(y	NOUN
ejpam-6395	367	31	,	,	PUNCT
ejpam-6395	367	32	z	z	NOUN
ejpam-6395	367	33	,	,	PUNCT
ejpam-6395	367	34	x	x	NOUN
ejpam-6395	367	35	)	)	PUNCT
ejpam-6395	367	36	.	.	PUNCT
ejpam-6395	368	1	since	since	SCONJ
ejpam-6395	368	2	y	y	PROPN
ejpam-6395	368	3	,	,	PUNCT
ejpam-6395	368	4	z	z	PROPN
ejpam-6395	368	5	∈	∈	PROPN
ejpam-6395	368	6	a	a	PRON
ejpam-6395	368	7	and	and	CCONJ
ejpam-6395	368	8	x	x	SYM
ejpam-6395	368	9	∈	∈	PROPN
ejpam-6395	368	10	b	b	PROPN
ejpam-6395	368	11	,	,	PUNCT
ejpam-6395	368	12	•(y	•(y	NOUN
ejpam-6395	368	13	,	,	PUNCT
ejpam-6395	368	14	z	z	NOUN
ejpam-6395	368	15	,	,	PUNCT
ejpam-6395	368	16	x	x	X
ejpam-6395	368	17	)	)	PUNCT
ejpam-6395	368	18	∈	∈	PROPN
ejpam-6395	368	19	•(a	•(a	PROPN
ejpam-6395	368	20	,	,	PUNCT
ejpam-6395	368	21	a	a	DET
ejpam-6395	368	22	,	,	PUNCT
ejpam-6395	368	23	b	b	NOUN
ejpam-6395	368	24	)	)	PUNCT
ejpam-6395	368	25	.	.	PUNCT
ejpam-6395	369	1	then	then	ADV
ejpam-6395	369	2	x	x	X
ejpam-6395	369	3	∈	∈	PROPN
ejpam-6395	369	4	(	(	PUNCT
ejpam-6395	369	5	•(a	•(a	PROPN
ejpam-6395	369	6	,	,	PUNCT
ejpam-6395	369	7	a	a	DET
ejpam-6395	369	8	,	,	PUNCT
ejpam-6395	369	9	b)]p	b)]p	PROPN
ejpam-6395	369	10	.	.	PUNCT
ejpam-6395	370	1	hence	hence	ADV
ejpam-6395	370	2	a	a	DET
ejpam-6395	370	3	∩	∩	ADJ
ejpam-6395	370	4	b	b	NOUN
ejpam-6395	370	5	⊆	⊆	NUM
ejpam-6395	370	6	(	(	PUNCT
ejpam-6395	370	7	•(a	•(a	PROPN
ejpam-6395	370	8	,	,	PUNCT
ejpam-6395	370	9	a	a	DET
ejpam-6395	370	10	,	,	PUNCT
ejpam-6395	370	11	b)]p	b)]p	PROPN
ejpam-6395	370	12	.	.	PUNCT
ejpam-6395	371	1	let	let	VERB
ejpam-6395	371	2	x	x	X
ejpam-6395	371	3	∈	∈	PROPN
ejpam-6395	371	4	(	(	PUNCT
ejpam-6395	371	5	•(a	•(a	PROPN
ejpam-6395	371	6	,	,	PUNCT
ejpam-6395	371	7	a	a	DET
ejpam-6395	371	8	,	,	PUNCT
ejpam-6395	371	9	b)]p	b)]p	PROPN
ejpam-6395	371	10	.	.	PUNCT
ejpam-6395	372	1	there	there	PRON
ejpam-6395	372	2	exists	exist	VERB
ejpam-6395	372	3	y	y	PROPN
ejpam-6395	372	4	=	=	SYM
ejpam-6395	372	5	•(y1	•(y1	PROPN
ejpam-6395	372	6	,	,	PUNCT
ejpam-6395	372	7	y2	y2	PROPN
ejpam-6395	372	8	,	,	PUNCT
ejpam-6395	372	9	y3	y3	PROPN
ejpam-6395	372	10	)	)	PUNCT
ejpam-6395	372	11	∈	∈	PROPN
ejpam-6395	372	12	•(a	•(a	PROPN
ejpam-6395	372	13	,	,	PUNCT
ejpam-6395	372	14	a	a	DET
ejpam-6395	372	15	,	,	PUNCT
ejpam-6395	372	16	b	b	NOUN
ejpam-6395	372	17	)	)	PUNCT
ejpam-6395	372	18	such	such	ADJ
ejpam-6395	372	19	that	that	SCONJ
ejpam-6395	372	20	x	x	SYM
ejpam-6395	372	21	≤p	≤p	NOUN
ejpam-6395	372	22	y	y	PROPN
ejpam-6395	372	23	.	.	PUNCT
ejpam-6395	373	1	since	since	SCONJ
ejpam-6395	373	2	y1	y1	PROPN
ejpam-6395	373	3	,	,	PUNCT
ejpam-6395	373	4	y2	y2	PROPN
ejpam-6395	373	5	∈	∈	PROPN
ejpam-6395	373	6	a	a	DET
ejpam-6395	373	7	,	,	PUNCT
ejpam-6395	373	8	y3	y3	PROPN
ejpam-6395	373	9	∈	∈	PROPN
ejpam-6395	373	10	b	b	PROPN
ejpam-6395	373	11	and	and	CCONJ
ejpam-6395	373	12	b	b	PROPN
ejpam-6395	373	13	is	be	AUX
ejpam-6395	373	14	a	a	DET
ejpam-6395	373	15	two	two	NUM
ejpam-6395	373	16	-	-	PUNCT
ejpam-6395	373	17	sided	sided	ADJ
ejpam-6395	373	18	ideal	ideal	NOUN
ejpam-6395	373	19	of	of	ADP
ejpam-6395	373	20	t	t	PROPN
ejpam-6395	373	21	,	,	PUNCT
ejpam-6395	373	22	we	we	PRON
ejpam-6395	373	23	have	have	VERB
ejpam-6395	373	24	y	y	PROPN
ejpam-6395	373	25	=	=	PUNCT
ejpam-6395	373	26	•(y1	•(y1	PROPN
ejpam-6395	373	27	,	,	PUNCT
ejpam-6395	373	28	y2	y2	PROPN
ejpam-6395	373	29	,	,	PUNCT
ejpam-6395	373	30	y3	y3	PROPN
ejpam-6395	373	31	)	)	PUNCT
ejpam-6395	373	32	∈	∈	PROPN
ejpam-6395	373	33	b.	b.	PROPN
ejpam-6395	373	34	since	since	SCONJ
ejpam-6395	373	35	b	b	PROPN
ejpam-6395	373	36	is	be	AUX
ejpam-6395	373	37	a	a	DET
ejpam-6395	373	38	two	two	NUM
ejpam-6395	373	39	-	-	PUNCT
ejpam-6395	373	40	sided	sided	ADJ
ejpam-6395	373	41	ideal	ideal	NOUN
ejpam-6395	373	42	of	of	ADP
ejpam-6395	373	43	t	t	PROPN
ejpam-6395	373	44	,	,	PUNCT
ejpam-6395	373	45	x	x	PROPN
ejpam-6395	373	46	∈	∈	PROPN
ejpam-6395	373	47	a	a	X
ejpam-6395	373	48	,	,	PUNCT
ejpam-6395	373	49	y	y	PROPN
ejpam-6395	373	50	∈	∈	PROPN
ejpam-6395	373	51	b	b	PROPN
ejpam-6395	373	52	and	and	CCONJ
ejpam-6395	373	53	x	x	SYM
ejpam-6395	373	54	≤p	≤p	PROPN
ejpam-6395	373	55	y	y	PROPN
ejpam-6395	373	56	,	,	PUNCT
ejpam-6395	373	57	we	we	PRON
ejpam-6395	373	58	have	have	VERB
ejpam-6395	373	59	x	x	PROPN
ejpam-6395	373	60	∈	∈	PROPN
ejpam-6395	373	61	b.	b.	NOUN
ejpam-6395	374	1	hence	hence	ADV
ejpam-6395	374	2	x	x	X
ejpam-6395	374	3	∈	∈	PROPN
ejpam-6395	374	4	a	a	DET
ejpam-6395	374	5	∩	∩	X
ejpam-6395	374	6	b.	b.	NOUN
ejpam-6395	375	1	therefore	therefore	ADV
ejpam-6395	375	2	a	a	DET
ejpam-6395	375	3	∩	∩	ADJ
ejpam-6395	375	4	b	b	NOUN
ejpam-6395	375	5	=	=	SYM
ejpam-6395	375	6	(	(	PUNCT
ejpam-6395	375	7	•(a	•(a	PROPN
ejpam-6395	375	8	,	,	PUNCT
ejpam-6395	375	9	a	a	DET
ejpam-6395	375	10	,	,	PUNCT
ejpam-6395	375	11	b)]p	b)]p	PROPN
ejpam-6395	375	12	.	.	PUNCT
ejpam-6395	376	1	similarly	similarly	ADV
ejpam-6395	376	2	,	,	PUNCT
ejpam-6395	376	3	we	we	PRON
ejpam-6395	376	4	can	can	AUX
ejpam-6395	376	5	proof	proof	VERB
ejpam-6395	376	6	that	that	SCONJ
ejpam-6395	376	7	if	if	SCONJ
ejpam-6395	376	8	a	a	PRON
ejpam-6395	376	9	is	be	AUX
ejpam-6395	376	10	a	a	DET
ejpam-6395	376	11	right	right	ADJ
ejpam-6395	376	12	pure	pure	ADJ
ejpam-6395	376	13	ideal	ideal	NOUN
ejpam-6395	376	14	of	of	ADP
ejpam-6395	376	15	t	t	PROPN
ejpam-6395	376	16	then	then	ADV
ejpam-6395	376	17	a	a	DET
ejpam-6395	376	18	∩	∩	ADJ
ejpam-6395	376	19	b	b	NOUN
ejpam-6395	376	20	=	=	SYM
ejpam-6395	376	21	(	(	PUNCT
ejpam-6395	376	22	•(b	•(b	PROPN
ejpam-6395	376	23	,	,	PUNCT
ejpam-6395	376	24	a	a	PRON
ejpam-6395	376	25	,	,	PUNCT
ejpam-6395	376	26	a)]p	a)]p	NOUN
ejpam-6395	376	27	for	for	ADP
ejpam-6395	376	28	all	all	DET
ejpam-6395	376	29	two	two	NUM
ejpam-6395	376	30	-	-	PUNCT
ejpam-6395	376	31	sided	sided	ADJ
ejpam-6395	376	32	ideals	ideal	NOUN
ejpam-6395	376	33	b	b	PROPN
ejpam-6395	376	34	of	of	ADP
ejpam-6395	376	35	t	t	PROPN
ejpam-6395	376	36	.	.	PUNCT
ejpam-6395	377	1	theorem	theorem	ADJ
ejpam-6395	377	2	10	10	NUM
ejpam-6395	377	3	.	.	PUNCT
ejpam-6395	378	1	let	let	AUX
ejpam-6395	378	2	(	(	PUNCT
ejpam-6395	378	3	t	t	NOUN
ejpam-6395	378	4	,	,	PUNCT
ejpam-6395	378	5	•,≤p	•,≤p	NOUN
ejpam-6395	378	6	)	)	PUNCT
ejpam-6395	378	7	be	be	VERB
ejpam-6395	378	8	an	an	DET
ejpam-6395	378	9	ordered	order	VERB
ejpam-6395	378	10	power	power	NOUN
ejpam-6395	378	11	ternary	ternary	NOUN
ejpam-6395	378	12	semigroup	semigroup	NOUN
ejpam-6395	378	13	on	on	ADP
ejpam-6395	378	14	a	a	DET
ejpam-6395	378	15	ternary	ternary	ADJ
ejpam-6395	378	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	378	17	(	(	PUNCT
ejpam-6395	378	18	s	s	X
ejpam-6395	378	19	,	,	PUNCT
ejpam-6395	378	20	⋄	⋄	PROPN
ejpam-6395	378	21	)	)	PUNCT
ejpam-6395	378	22	induced	induce	VERB
ejpam-6395	378	23	by	by	ADP
ejpam-6395	378	24	a	a	DET
ejpam-6395	378	25	poset	poset	NOUN
ejpam-6395	378	26	(	(	PUNCT
ejpam-6395	378	27	s,≤	s,≤	NOUN
ejpam-6395	378	28	)	)	PUNCT
ejpam-6395	378	29	with	with	ADP
ejpam-6395	378	30	a	a	DET
ejpam-6395	378	31	zero	zero	NUM
ejpam-6395	378	32	element	element	NOUN
ejpam-6395	378	33	0	0	NUM
ejpam-6395	378	34	and	and	CCONJ
ejpam-6395	378	35	a	a	PRON
ejpam-6395	378	36	,	,	PUNCT
ejpam-6395	378	37	b	b	PROPN
ejpam-6395	378	38	be	be	AUX
ejpam-6395	378	39	two	two	NUM
ejpam-6395	378	40	-	-	PUNCT
ejpam-6395	378	41	sided	sided	ADJ
ejpam-6395	378	42	ideals	ideal	NOUN
ejpam-6395	378	43	of	of	ADP
ejpam-6395	378	44	t	t	PROPN
ejpam-6395	378	45	.	.	PUNCT
ejpam-6395	379	1	then	then	ADV
ejpam-6395	379	2	ba−1	ba−1	VERB
ejpam-6395	379	3	=	=	PUNCT
ejpam-6395	379	4	{	{	PUNCT
ejpam-6395	379	5	t	t	PROPN
ejpam-6395	379	6	∈	∈	PROPN
ejpam-6395	379	7	t	t	X
ejpam-6395	379	8	|	|	ADV
ejpam-6395	379	9	for	for	ADP
ejpam-6395	379	10	all	all	DET
ejpam-6395	379	11	x	x	NOUN
ejpam-6395	379	12	,	,	PUNCT
ejpam-6395	379	13	y	y	PROPN
ejpam-6395	379	14	∈	∈	PROPN
ejpam-6395	379	15	a	a	PRON
ejpam-6395	379	16	,	,	PUNCT
ejpam-6395	379	17	•(x	•(x	PROPN
ejpam-6395	379	18	,	,	PUNCT
ejpam-6395	379	19	y	y	PROPN
ejpam-6395	379	20	,	,	PUNCT
ejpam-6395	379	21	t	t	NOUN
ejpam-6395	379	22	)	)	PUNCT
ejpam-6395	379	23	∈	∈	PROPN
ejpam-6395	380	1	b	b	X
ejpam-6395	380	2	}	}	PUNCT
ejpam-6395	380	3	and	and	CCONJ
ejpam-6395	380	4	a−1b	a−1b	NOUN
ejpam-6395	380	5	=	=	PUNCT
ejpam-6395	380	6	{	{	PUNCT
ejpam-6395	380	7	t	t	PROPN
ejpam-6395	380	8	∈	∈	PROPN
ejpam-6395	380	9	t	t	X
ejpam-6395	380	10	|	|	ADV
ejpam-6395	380	11	for	for	ADP
ejpam-6395	380	12	all	all	DET
ejpam-6395	380	13	x	x	NOUN
ejpam-6395	380	14	,	,	PUNCT
ejpam-6395	380	15	y	y	PROPN
ejpam-6395	380	16	∈	∈	PROPN
ejpam-6395	380	17	a	a	PRON
ejpam-6395	380	18	,	,	PUNCT
ejpam-6395	380	19	•(t	•(t	PROPN
ejpam-6395	380	20	,	,	PUNCT
ejpam-6395	380	21	x	x	NOUN
ejpam-6395	380	22	,	,	PUNCT
ejpam-6395	380	23	y	y	PROPN
ejpam-6395	380	24	)	)	PUNCT
ejpam-6395	380	25	∈	∈	PROPN
ejpam-6395	381	1	b	b	X
ejpam-6395	381	2	}	}	PUNCT
ejpam-6395	381	3	are	be	AUX
ejpam-6395	381	4	two	two	NUM
ejpam-6395	381	5	-	-	PUNCT
ejpam-6395	381	6	sided	sided	ADJ
ejpam-6395	381	7	ideals	ideal	NOUN
ejpam-6395	381	8	of	of	ADP
ejpam-6395	381	9	t	t	PROPN
ejpam-6395	381	10	.	.	PUNCT
ejpam-6395	382	1	proof	proof	NOUN
ejpam-6395	382	2	.	.	PUNCT
ejpam-6395	383	1	since	since	SCONJ
ejpam-6395	383	2	0	0	NUM
ejpam-6395	383	3	∈	∈	PROPN
ejpam-6395	383	4	t	t	PROPN
ejpam-6395	383	5	and	and	CCONJ
ejpam-6395	383	6	b	b	PROPN
ejpam-6395	383	7	is	be	AUX
ejpam-6395	383	8	a	a	DET
ejpam-6395	383	9	two	two	NUM
ejpam-6395	383	10	-	-	PUNCT
ejpam-6395	383	11	sided	sided	ADJ
ejpam-6395	383	12	ideal	ideal	NOUN
ejpam-6395	383	13	,	,	PUNCT
ejpam-6395	383	14	then	then	ADV
ejpam-6395	383	15	•(x	•(x	PROPN
ejpam-6395	383	16	,	,	PUNCT
ejpam-6395	383	17	y	y	PROPN
ejpam-6395	383	18	,	,	PUNCT
ejpam-6395	383	19	0	0	NUM
ejpam-6395	383	20	)	)	PUNCT
ejpam-6395	383	21	=	=	SYM
ejpam-6395	383	22	0	0	NUM
ejpam-6395	383	23	∈	∈	PROPN
ejpam-6395	383	24	b	b	PROPN
ejpam-6395	383	25	for	for	ADP
ejpam-6395	383	26	all	all	DET
ejpam-6395	383	27	x	x	NOUN
ejpam-6395	383	28	,	,	PUNCT
ejpam-6395	383	29	y	y	PROPN
ejpam-6395	383	30	∈	∈	PROPN
ejpam-6395	383	31	a.	a.	NOUN
ejpam-6395	383	32	we	we	PRON
ejpam-6395	383	33	have	have	VERB
ejpam-6395	383	34	0	0	NUM
ejpam-6395	383	35	∈	∈	PROPN
ejpam-6395	383	36	ba−1	ba−1	NOUN
ejpam-6395	383	37	.	.	PUNCT
ejpam-6395	384	1	that	that	PRON
ejpam-6395	384	2	is	is	ADV
ejpam-6395	384	3	,	,	PUNCT
ejpam-6395	384	4	ba−1	ba−1	VERB
ejpam-6395	384	5	̸=	̸=	PROPN
ejpam-6395	384	6	∅.	∅.	ADV
ejpam-6395	384	7	let	let	VERB
ejpam-6395	384	8	u	u	NOUN
ejpam-6395	384	9	,	,	PUNCT
ejpam-6395	384	10	v	v	PROPN
ejpam-6395	384	11	∈	∈	PROPN
ejpam-6395	384	12	t	t	NOUN
ejpam-6395	384	13	and	and	CCONJ
ejpam-6395	384	14	t	t	PROPN
ejpam-6395	384	15	∈	∈	PROPN
ejpam-6395	384	16	ba−1	ba−1	NOUN
ejpam-6395	384	17	.	.	PUNCT
ejpam-6395	385	1	we	we	PRON
ejpam-6395	385	2	will	will	AUX
ejpam-6395	385	3	show	show	VERB
ejpam-6395	385	4	that	that	DET
ejpam-6395	385	5	•(u	•(u	NOUN
ejpam-6395	385	6	,	,	PUNCT
ejpam-6395	385	7	v	v	NOUN
ejpam-6395	385	8	,	,	PUNCT
ejpam-6395	385	9	t	t	NOUN
ejpam-6395	385	10	)	)	PUNCT
ejpam-6395	385	11	∈	∈	PROPN
ejpam-6395	385	12	ba−1	ba−1	NOUN
ejpam-6395	385	13	.	.	PUNCT
ejpam-6395	386	1	let	let	VERB
ejpam-6395	386	2	x	x	PRON
ejpam-6395	386	3	,	,	PUNCT
ejpam-6395	386	4	y	y	PROPN
ejpam-6395	386	5	∈	∈	PROPN
ejpam-6395	386	6	a.	a.	NOUN
ejpam-6395	386	7	since	since	SCONJ
ejpam-6395	386	8	•(y	•(y	NOUN
ejpam-6395	386	9	,	,	PUNCT
ejpam-6395	386	10	u	u	NOUN
ejpam-6395	386	11	,	,	PUNCT
ejpam-6395	386	12	v	v	NOUN
ejpam-6395	386	13	)	)	PUNCT
ejpam-6395	386	14	∈	∈	PROPN
ejpam-6395	386	15	a	a	PRON
ejpam-6395	386	16	,	,	PUNCT
ejpam-6395	386	17	we	we	PRON
ejpam-6395	386	18	have	have	VERB
ejpam-6395	386	19	•(x	•(x	PROPN
ejpam-6395	386	20	,	,	PUNCT
ejpam-6395	386	21	y	y	PROPN
ejpam-6395	386	22	,	,	PUNCT
ejpam-6395	386	23	•(u	•(u	NOUN
ejpam-6395	386	24	,	,	PUNCT
ejpam-6395	386	25	v	v	NOUN
ejpam-6395	386	26	,	,	PUNCT
ejpam-6395	386	27	t	t	NOUN
ejpam-6395	386	28	)	)	PUNCT
ejpam-6395	386	29	)	)	PUNCT
ejpam-6395	387	1	=	=	PUNCT
ejpam-6395	387	2	•(x	•(x	PROPN
ejpam-6395	387	3	,	,	PUNCT
ejpam-6395	387	4	•(y	•(y	NOUN
ejpam-6395	387	5	,	,	PUNCT
ejpam-6395	387	6	u	u	NOUN
ejpam-6395	387	7	,	,	PUNCT
ejpam-6395	387	8	v	v	NOUN
ejpam-6395	387	9	)	)	PUNCT
ejpam-6395	387	10	,	,	PUNCT
ejpam-6395	387	11	t	t	X
ejpam-6395	387	12	)	)	PUNCT
ejpam-6395	387	13	∈	∈	PROPN
ejpam-6395	387	14	b.	b.	PROPN
ejpam-6395	388	1	then	then	ADV
ejpam-6395	388	2	•(u	•(u	PROPN
ejpam-6395	388	3	,	,	PUNCT
ejpam-6395	388	4	v	v	NOUN
ejpam-6395	388	5	,	,	PUNCT
ejpam-6395	388	6	t	t	NOUN
ejpam-6395	388	7	)	)	PUNCT
ejpam-6395	388	8	∈	∈	PROPN
ejpam-6395	388	9	ba−1	ba−1	NOUN
ejpam-6395	388	10	.	.	PUNCT
ejpam-6395	389	1	let	let	VERB
ejpam-6395	389	2	x	x	SYM
ejpam-6395	389	3	∈	∈	PROPN
ejpam-6395	389	4	ba−1andy	ba−1andy	PROPN
ejpam-6395	389	5	∈	∈	PROPN
ejpam-6395	389	6	t	t	NOUN
ejpam-6395	389	7	such	such	ADJ
ejpam-6395	389	8	that	that	SCONJ
ejpam-6395	389	9	y	y	PROPN
ejpam-6395	389	10	≤p	≤p	PROPN
ejpam-6395	389	11	x.	x.	PROPN
ejpam-6395	389	12	let	let	VERB
ejpam-6395	389	13	w	w	NOUN
ejpam-6395	389	14	,	,	PUNCT
ejpam-6395	389	15	z	z	PROPN
ejpam-6395	389	16	∈	∈	PROPN
ejpam-6395	389	17	a.	a.	NOUN
ejpam-6395	389	18	since	since	SCONJ
ejpam-6395	389	19	•(w	•(w	NOUN
ejpam-6395	389	20	,	,	PUNCT
ejpam-6395	389	21	z	z	NOUN
ejpam-6395	389	22	,	,	PUNCT
ejpam-6395	389	23	y	y	PROPN
ejpam-6395	389	24	)	)	PUNCT
ejpam-6395	389	25	≤p	≤p	ADJ
ejpam-6395	389	26	•(w	•(w	NOUN
ejpam-6395	389	27	,	,	PUNCT
ejpam-6395	389	28	z	z	NOUN
ejpam-6395	389	29	,	,	PUNCT
ejpam-6395	389	30	x	x	NOUN
ejpam-6395	389	31	)	)	PUNCT
ejpam-6395	389	32	and	and	CCONJ
ejpam-6395	389	33	•(w	•(w	NOUN
ejpam-6395	389	34	,	,	PUNCT
ejpam-6395	389	35	z	z	NOUN
ejpam-6395	389	36	,	,	PUNCT
ejpam-6395	389	37	x	x	NOUN
ejpam-6395	389	38	)	)	PUNCT
ejpam-6395	389	39	∈	∈	PROPN
ejpam-6395	389	40	b	b	NOUN
ejpam-6395	389	41	,	,	PUNCT
ejpam-6395	389	42	we	we	PRON
ejpam-6395	389	43	have	have	VERB
ejpam-6395	389	44	•(w	•(w	NOUN
ejpam-6395	389	45	,	,	PUNCT
ejpam-6395	389	46	z	z	NOUN
ejpam-6395	389	47	,	,	PUNCT
ejpam-6395	389	48	y	y	PROPN
ejpam-6395	389	49	)	)	PUNCT
ejpam-6395	389	50	∈	∈	PROPN
ejpam-6395	390	1	b.	b.	PROPN
ejpam-6395	390	2	hence	hence	ADV
ejpam-6395	390	3	y	y	PROPN
ejpam-6395	390	4	∈	∈	PROPN
ejpam-6395	390	5	ba−1.therefore	ba−1.therefore	NOUN
ejpam-6395	390	6	ba−1	ba−1	NOUN
ejpam-6395	390	7	is	be	AUX
ejpam-6395	390	8	a	a	DET
ejpam-6395	390	9	two	two	NUM
ejpam-6395	390	10	-	-	PUNCT
ejpam-6395	390	11	sided	sided	ADJ
ejpam-6395	390	12	ideal	ideal	NOUN
ejpam-6395	390	13	of	of	ADP
ejpam-6395	390	14	t	t	PROPN
ejpam-6395	390	15	.	.	PUNCT
ejpam-6395	391	1	similarly	similarly	ADV
ejpam-6395	391	2	,	,	PUNCT
ejpam-6395	391	3	we	we	PRON
ejpam-6395	391	4	can	can	AUX
ejpam-6395	391	5	proof	proof	VERB
ejpam-6395	391	6	that	that	SCONJ
ejpam-6395	391	7	a−1b	a−1b	PROPN
ejpam-6395	391	8	is	be	AUX
ejpam-6395	391	9	a	a	DET
ejpam-6395	391	10	two	two	NUM
ejpam-6395	391	11	-	-	PUNCT
ejpam-6395	391	12	sided	sided	ADJ
ejpam-6395	391	13	ideal	ideal	NOUN
ejpam-6395	391	14	of	of	ADP
ejpam-6395	391	15	t	t	PROPN
ejpam-6395	391	16	.	.	PUNCT
ejpam-6395	392	1	theorem	theorem	ADJ
ejpam-6395	392	2	11	11	NUM
ejpam-6395	392	3	.	.	PUNCT
ejpam-6395	393	1	let	let	AUX
ejpam-6395	393	2	(	(	PUNCT
ejpam-6395	393	3	t	t	NOUN
ejpam-6395	393	4	,	,	PUNCT
ejpam-6395	393	5	•,≤p	•,≤p	NOUN
ejpam-6395	393	6	)	)	PUNCT
ejpam-6395	393	7	be	be	VERB
ejpam-6395	393	8	an	an	DET
ejpam-6395	393	9	ordered	order	VERB
ejpam-6395	393	10	power	power	NOUN
ejpam-6395	393	11	ternary	ternary	NOUN
ejpam-6395	393	12	semigroup	semigroup	NOUN
ejpam-6395	393	13	on	on	ADP
ejpam-6395	393	14	a	a	DET
ejpam-6395	393	15	ternary	ternary	ADJ
ejpam-6395	393	16	semihypergroup	semihypergroup	NOUN
ejpam-6395	393	17	(	(	PUNCT
ejpam-6395	393	18	s	s	X
ejpam-6395	393	19	,	,	PUNCT
ejpam-6395	393	20	⋄	⋄	PROPN
ejpam-6395	393	21	)	)	PUNCT
ejpam-6395	393	22	induced	induce	VERB
ejpam-6395	393	23	by	by	ADP
ejpam-6395	393	24	a	a	DET
ejpam-6395	393	25	poset	poset	NOUN
ejpam-6395	393	26	(	(	PUNCT
ejpam-6395	393	27	s,≤	s,≤	NOUN
ejpam-6395	393	28	)	)	PUNCT
ejpam-6395	393	29	and	and	CCONJ
ejpam-6395	393	30	a	a	DET
ejpam-6395	393	31	be	be	AUX
ejpam-6395	393	32	a	a	DET
ejpam-6395	393	33	two	two	NUM
ejpam-6395	393	34	-	-	PUNCT
ejpam-6395	393	35	sided	sided	ADJ
ejpam-6395	393	36	ideal	ideal	NOUN
ejpam-6395	393	37	of	of	ADP
ejpam-6395	393	38	t	t	PROPN
ejpam-6395	393	39	.	.	PUNCT
ejpam-6395	394	1	then	then	ADV
ejpam-6395	394	2	a	a	PRON
ejpam-6395	394	3	is	be	AUX
ejpam-6395	394	4	a	a	DET
ejpam-6395	394	5	left	left	ADJ
ejpam-6395	394	6	(	(	PUNCT
ejpam-6395	394	7	resp	resp	NOUN
ejpam-6395	394	8	.	.	PUNCT
ejpam-6395	395	1	right	right	ADJ
ejpam-6395	395	2	)	)	PUNCT
ejpam-6395	395	3	weakly	weakly	ADV
ejpam-6395	395	4	pure	pure	ADJ
ejpam-6395	395	5	if	if	SCONJ
ejpam-6395	396	1	and	and	CCONJ
ejpam-6395	396	2	only	only	ADV
ejpam-6395	396	3	if	if	SCONJ
ejpam-6395	396	4	a∩	a∩	PROPN
ejpam-6395	396	5	b	b	PROPN
ejpam-6395	396	6	=	=	SYM
ejpam-6395	396	7	a∩	a∩	PROPN
ejpam-6395	396	8	(	(	PUNCT
ejpam-6395	396	9	ba−1	ba−1	NOUN
ejpam-6395	396	10	)	)	PUNCT
ejpam-6395	396	11	(	(	PUNCT
ejpam-6395	396	12	resp	resp	NOUN
ejpam-6395	396	13	.	.	PUNCT
ejpam-6395	397	1	a∩	a∩	PROPN
ejpam-6395	397	2	b	b	X
ejpam-6395	397	3	=	=	X
ejpam-6395	397	4	a∩	a∩	PROPN
ejpam-6395	397	5	(	(	PUNCT
ejpam-6395	397	6	a−1b	a−1b	NOUN
ejpam-6395	397	7	)	)	PUNCT
ejpam-6395	397	8	)	)	PUNCT
ejpam-6395	397	9	for	for	ADP
ejpam-6395	397	10	all	all	DET
ejpam-6395	397	11	ideals	ideal	NOUN
ejpam-6395	397	12	b	b	PROPN
ejpam-6395	397	13	of	of	ADP
ejpam-6395	397	14	t	t	PROPN
ejpam-6395	397	15	.	.	PUNCT
ejpam-6395	398	1	proof	proof	NOUN
ejpam-6395	398	2	.	.	PUNCT
ejpam-6395	399	1	(	(	PUNCT
ejpam-6395	399	2	⇒	⇒	PROPN
ejpam-6395	399	3	)	)	PUNCT
ejpam-6395	399	4	let	let	VERB
ejpam-6395	399	5	a	a	PRON
ejpam-6395	399	6	be	be	AUX
ejpam-6395	399	7	a	a	DET
ejpam-6395	399	8	left	left	ADJ
ejpam-6395	399	9	weakly	weakly	ADJ
ejpam-6395	399	10	pure	pure	ADJ
ejpam-6395	399	11	and	and	CCONJ
ejpam-6395	399	12	b	b	NOUN
ejpam-6395	399	13	be	be	AUX
ejpam-6395	399	14	an	an	DET
ejpam-6395	399	15	ideal	ideal	NOUN
ejpam-6395	399	16	of	of	ADP
ejpam-6395	399	17	t	t	PROPN
ejpam-6395	399	18	.	.	PUNCT
ejpam-6395	400	1	by	by	ADP
ejpam-6395	400	2	theorem	theorem	NOUN
ejpam-6395	400	3	10	10	NUM
ejpam-6395	400	4	,	,	PUNCT
ejpam-6395	400	5	ba−1	ba−1	NOUN
ejpam-6395	400	6	is	be	AUX
ejpam-6395	400	7	an	an	DET
ejpam-6395	400	8	ideal	ideal	NOUN
ejpam-6395	400	9	of	of	ADP
ejpam-6395	400	10	t	t	PROPN
ejpam-6395	400	11	.	.	PUNCT
ejpam-6395	401	1	since	since	SCONJ
ejpam-6395	401	2	a	a	PRON
ejpam-6395	401	3	is	be	AUX
ejpam-6395	401	4	a	a	DET
ejpam-6395	401	5	left	left	ADJ
ejpam-6395	401	6	weakly	weakly	ADV
ejpam-6395	401	7	pure	pure	ADJ
ejpam-6395	401	8	and	and	CCONJ
ejpam-6395	401	9	ba−1	ba−1	NOUN
ejpam-6395	401	10	is	be	AUX
ejpam-6395	401	11	an	an	DET
ejpam-6395	401	12	ideal	ideal	NOUN
ejpam-6395	401	13	of	of	ADP
ejpam-6395	401	14	t	t	PROPN
ejpam-6395	401	15	,	,	PUNCT
ejpam-6395	401	16	we	we	PRON
ejpam-6395	401	17	have	have	VERB
ejpam-6395	401	18	a	a	DET
ejpam-6395	401	19	∩	∩	NOUN
ejpam-6395	401	20	(	(	PUNCT
ejpam-6395	401	21	ba−1	ba−1	NOUN
ejpam-6395	401	22	)	)	PUNCT
ejpam-6395	401	23	=	=	PRON
ejpam-6395	401	24	(	(	PUNCT
ejpam-6395	401	25	•(a	•(a	PROPN
ejpam-6395	401	26	,	,	PUNCT
ejpam-6395	401	27	a	a	PRON
ejpam-6395	401	28	,	,	PUNCT
ejpam-6395	401	29	ba−1)]p	ba−1)]p	PROPN
ejpam-6395	401	30	.	.	PROPN
ejpam-6395	402	1	since	since	SCONJ
ejpam-6395	402	2	•(a	•(a	PROPN
ejpam-6395	402	3	,	,	PUNCT
ejpam-6395	402	4	a	a	DET
ejpam-6395	402	5	,	,	PUNCT
ejpam-6395	402	6	ba−1	ba−1	NOUN
ejpam-6395	402	7	)	)	PUNCT
ejpam-6395	402	8	⊆	⊆	NUM
ejpam-6395	402	9	•(a	•(a	PROPN
ejpam-6395	402	10	,	,	PUNCT
ejpam-6395	402	11	a	a	PRON
ejpam-6395	402	12	,	,	PUNCT
ejpam-6395	402	13	t	t	NOUN
ejpam-6395	402	14	)	)	PUNCT
ejpam-6395	402	15	⊆	⊆	PROPN
ejpam-6395	402	16	a	a	PRON
ejpam-6395	402	17	,	,	PUNCT
ejpam-6395	402	18	we	we	PRON
ejpam-6395	402	19	have	have	AUX
ejpam-6395	402	20	(	(	PUNCT
ejpam-6395	402	21	•(a	•(a	PROPN
ejpam-6395	402	22	,	,	PUNCT
ejpam-6395	402	23	a	a	PRON
ejpam-6395	402	24	,	,	PUNCT
ejpam-6395	402	25	ba−1)]p	ba−1)]p	PROPN
ejpam-6395	402	26	⊆	⊆	NUM
ejpam-6395	402	27	(	(	PUNCT
ejpam-6395	402	28	a]p	a]p	NOUN
ejpam-6395	402	29	=	=	NOUN
ejpam-6395	402	30	a.	a.	NOUN
ejpam-6395	402	31	let	let	VERB
ejpam-6395	402	32	z	z	PROPN
ejpam-6395	402	33	∈	∈	PROPN
ejpam-6395	402	34	(	(	PUNCT
ejpam-6395	402	35	•(a	•(a	PROPN
ejpam-6395	402	36	,	,	PUNCT
ejpam-6395	402	37	a	a	PRON
ejpam-6395	402	38	,	,	PUNCT
ejpam-6395	402	39	ba−1)]p	ba−1)]p	PROPN
ejpam-6395	402	40	.	.	PUNCT
ejpam-6395	403	1	there	there	PRON
ejpam-6395	403	2	exists	exist	VERB
ejpam-6395	403	3	•(x	•(x	PROPN
ejpam-6395	403	4	,	,	PUNCT
ejpam-6395	403	5	y	y	PROPN
ejpam-6395	403	6	,	,	PUNCT
ejpam-6395	403	7	z	z	NOUN
ejpam-6395	403	8	)	)	PUNCT
ejpam-6395	403	9	∈	∈	PROPN
ejpam-6395	403	10	•(a	•(a	PROPN
ejpam-6395	403	11	,	,	PUNCT
ejpam-6395	403	12	a	a	DET
ejpam-6395	403	13	,	,	PUNCT
ejpam-6395	403	14	ba−1	ba−1	NOUN
ejpam-6395	403	15	)	)	PUNCT
ejpam-6395	403	16	such	such	ADJ
ejpam-6395	403	17	that	that	SCONJ
ejpam-6395	403	18	z	z	PROPN
ejpam-6395	403	19	≤p	≤p	PROPN
ejpam-6395	403	20	•(x	•(x	PROPN
ejpam-6395	403	21	,	,	PUNCT
ejpam-6395	403	22	y	y	PROPN
ejpam-6395	403	23	,	,	PUNCT
ejpam-6395	403	24	z	z	NOUN
ejpam-6395	403	25	)	)	PUNCT
ejpam-6395	403	26	.	.	PUNCT
ejpam-6395	404	1	by	by	ADP
ejpam-6395	404	2	the	the	DET
ejpam-6395	404	3	definition	definition	NOUN
ejpam-6395	404	4	of	of	ADP
ejpam-6395	404	5	ba−1	ba−1	NOUN
ejpam-6395	404	6	,	,	PUNCT
ejpam-6395	404	7	we	we	PRON
ejpam-6395	404	8	have	have	VERB
ejpam-6395	404	9	z	z	PROPN
ejpam-6395	404	10	∈	∈	PROPN
ejpam-6395	404	11	b.	b.	PROPN
ejpam-6395	404	12	hence	hence	ADV
ejpam-6395	404	13	a	a	DET
ejpam-6395	404	14	∩	∩	NOUN
ejpam-6395	404	15	(	(	PUNCT
ejpam-6395	404	16	ba−1	ba−1	NOUN
ejpam-6395	404	17	)	)	PUNCT
ejpam-6395	404	18	⊆	⊆	NUM
ejpam-6395	404	19	a	a	DET
ejpam-6395	404	20	∩	∩	ADJ
ejpam-6395	404	21	b.	b.	NOUN
ejpam-6395	404	22	let	let	VERB
ejpam-6395	404	23	x	x	SYM
ejpam-6395	404	24	∈	∈	PROPN
ejpam-6395	404	25	a	a	DET
ejpam-6395	404	26	∩	∩	X
ejpam-6395	404	27	b.	b.	PROPN
ejpam-6395	404	28	since	since	SCONJ
ejpam-6395	404	29	•(u	•(u	PROPN
ejpam-6395	404	30	,	,	PUNCT
ejpam-6395	404	31	v	v	NOUN
ejpam-6395	404	32	,	,	PUNCT
ejpam-6395	404	33	x	x	NOUN
ejpam-6395	404	34	)	)	PUNCT
ejpam-6395	404	35	∈	∈	PROPN
ejpam-6395	404	36	b	b	PROPN
ejpam-6395	404	37	for	for	ADP
ejpam-6395	404	38	any	any	DET
ejpam-6395	404	39	u	u	NOUN
ejpam-6395	404	40	,	,	PUNCT
ejpam-6395	404	41	v	v	ADP
ejpam-6395	404	42	∈	∈	PROPN
ejpam-6395	404	43	a	a	PRON
ejpam-6395	404	44	,	,	PUNCT
ejpam-6395	404	45	we	we	PRON
ejpam-6395	404	46	have	have	VERB
ejpam-6395	404	47	x	x	PART
ejpam-6395	404	48	∈	∈	PROPN
ejpam-6395	404	49	ba−1	ba−1	NOUN
ejpam-6395	404	50	.	.	PUNCT
ejpam-6395	405	1	that	that	PRON
ejpam-6395	405	2	is	be	AUX
ejpam-6395	405	3	,	,	PUNCT
ejpam-6395	405	4	x	x	SYM
ejpam-6395	405	5	∈	∈	PROPN
ejpam-6395	405	6	a	a	DET
ejpam-6395	405	7	∩	∩	NOUN
ejpam-6395	405	8	(	(	PUNCT
ejpam-6395	405	9	ba−1	ba−1	NOUN
ejpam-6395	405	10	)	)	PUNCT
ejpam-6395	405	11	.	.	PUNCT
ejpam-6395	406	1	then	then	ADV
ejpam-6395	406	2	a	a	DET
ejpam-6395	406	3	∩	∩	ADJ
ejpam-6395	406	4	b	b	NOUN
ejpam-6395	406	5	⊆	⊆	NUM
ejpam-6395	406	6	a	a	DET
ejpam-6395	406	7	∩	∩	NOUN
ejpam-6395	406	8	(	(	PUNCT
ejpam-6395	406	9	ba−1	ba−1	NOUN
ejpam-6395	406	10	)	)	PUNCT
ejpam-6395	406	11	.	.	PUNCT
ejpam-6395	407	1	therefore	therefore	ADV
ejpam-6395	407	2	a	a	DET
ejpam-6395	407	3	∩	∩	ADJ
ejpam-6395	407	4	b	b	NOUN
ejpam-6395	407	5	=	=	SYM
ejpam-6395	407	6	a	a	DET
ejpam-6395	407	7	∩	∩	NOUN
ejpam-6395	407	8	(	(	PUNCT
ejpam-6395	407	9	ba−1	ba−1	NOUN
ejpam-6395	407	10	)	)	PUNCT
ejpam-6395	407	11	for	for	ADP
ejpam-6395	407	12	all	all	DET
ejpam-6395	407	13	ideals	ideal	NOUN
ejpam-6395	407	14	b	b	PROPN
ejpam-6395	407	15	of	of	ADP
ejpam-6395	407	16	t	t	PROPN
ejpam-6395	407	17	.	.	PUNCT
ejpam-6395	408	1	(	(	PUNCT
ejpam-6395	408	2	⇐	⇐	ADJ
ejpam-6395	408	3	)	)	PUNCT
ejpam-6395	408	4	let	let	VERB
ejpam-6395	408	5	a	a	DET
ejpam-6395	408	6	∩	∩	ADJ
ejpam-6395	408	7	b	b	NOUN
ejpam-6395	408	8	=	=	SYM
ejpam-6395	408	9	a	a	DET
ejpam-6395	408	10	∩	∩	NOUN
ejpam-6395	408	11	(	(	PUNCT
ejpam-6395	408	12	ba−1	ba−1	NOUN
ejpam-6395	408	13	)	)	PUNCT
ejpam-6395	408	14	for	for	ADP
ejpam-6395	408	15	all	all	DET
ejpam-6395	408	16	ideals	ideal	NOUN
ejpam-6395	408	17	b	b	NOUN
ejpam-6395	408	18	a.	a.	NOUN
ejpam-6395	408	19	nongmanee	nongmanee	NOUN
ejpam-6395	408	20	,	,	PUNCT
ejpam-6395	408	21	k.	k.	PROPN
ejpam-6395	408	22	jeenkaew	jeenkaew	PROPN
ejpam-6395	408	23	,	,	PUNCT
ejpam-6395	408	24	m.	m.	NOUN
ejpam-6395	408	25	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	408	26	/	/	SYM
ejpam-6395	408	27	eur	eur	PROPN
ejpam-6395	408	28	.	.	PUNCT
ejpam-6395	409	1	j.	j.	PROPN
ejpam-6395	409	2	pure	pure	PROPN
ejpam-6395	409	3	appl	appl	PROPN
ejpam-6395	409	4	.	.	PROPN
ejpam-6395	409	5	math	math	PROPN
ejpam-6395	409	6	,	,	PUNCT
ejpam-6395	409	7	18	18	NUM
ejpam-6395	409	8	(	(	PUNCT
ejpam-6395	409	9	3	3	NUM
ejpam-6395	409	10	)	)	PUNCT
ejpam-6395	409	11	(	(	PUNCT
ejpam-6395	409	12	2025	2025	NUM
ejpam-6395	409	13	)	)	PUNCT
ejpam-6395	409	14	,	,	PUNCT
ejpam-6395	409	15	6395	6395	NUM
ejpam-6395	409	16	11	11	NUM
ejpam-6395	409	17	of	of	ADP
ejpam-6395	409	18	12	12	NUM
ejpam-6395	409	19	of	of	ADP
ejpam-6395	409	20	t	t	PROPN
ejpam-6395	409	21	.	.	PUNCT
ejpam-6395	410	1	we	we	PRON
ejpam-6395	410	2	will	will	AUX
ejpam-6395	410	3	show	show	VERB
ejpam-6395	410	4	that	that	SCONJ
ejpam-6395	410	5	a	a	DET
ejpam-6395	410	6	∩	∩	ADJ
ejpam-6395	410	7	c	c	NOUN
ejpam-6395	410	8	=	=	SYM
ejpam-6395	410	9	(	(	PUNCT
ejpam-6395	410	10	•(a	•(a	PROPN
ejpam-6395	410	11	,	,	PUNCT
ejpam-6395	410	12	a	a	PRON
ejpam-6395	410	13	,	,	PUNCT
ejpam-6395	410	14	c)]p	c)]p	PROPN
ejpam-6395	410	15	for	for	ADP
ejpam-6395	410	16	all	all	DET
ejpam-6395	410	17	ideals	ideal	NOUN
ejpam-6395	410	18	c	c	PROPN
ejpam-6395	410	19	of	of	ADP
ejpam-6395	410	20	s.	s.	PROPN
ejpam-6395	410	21	let	let	VERB
ejpam-6395	410	22	c	c	NOUN
ejpam-6395	410	23	be	be	AUX
ejpam-6395	410	24	an	an	DET
ejpam-6395	410	25	ideal	ideal	NOUN
ejpam-6395	410	26	of	of	ADP
ejpam-6395	410	27	t	t	PROPN
ejpam-6395	410	28	.	.	PUNCT
ejpam-6395	411	1	by	by	ADP
ejpam-6395	411	2	assumption	assumption	NOUN
ejpam-6395	411	3	,	,	PUNCT
ejpam-6395	411	4	a	a	DET
ejpam-6395	411	5	∩	∩	ADJ
ejpam-6395	411	6	c	c	NOUN
ejpam-6395	411	7	=	=	PUNCT
ejpam-6395	411	8	a	a	DET
ejpam-6395	411	9	∩	∩	NOUN
ejpam-6395	411	10	(	(	PUNCT
ejpam-6395	411	11	ca−1	ca−1	NOUN
ejpam-6395	411	12	)	)	PUNCT
ejpam-6395	411	13	.	.	PUNCT
ejpam-6395	412	1	since	since	SCONJ
ejpam-6395	412	2	c	c	PROPN
ejpam-6395	412	3	⊆	⊆	NUM
ejpam-6395	412	4	s	s	NOUN
ejpam-6395	412	5	and	and	CCONJ
ejpam-6395	412	6	a	a	PRON
ejpam-6395	412	7	is	be	AUX
ejpam-6395	412	8	an	an	DET
ejpam-6395	412	9	ideal	ideal	NOUN
ejpam-6395	412	10	of	of	ADP
ejpam-6395	412	11	s	s	PROPN
ejpam-6395	412	12	,	,	PUNCT
ejpam-6395	412	13	we	we	PRON
ejpam-6395	412	14	have	have	AUX
ejpam-6395	412	15	•(a	•(a	PROPN
ejpam-6395	412	16	,	,	PUNCT
ejpam-6395	412	17	a	a	PRON
ejpam-6395	412	18	,	,	PUNCT
ejpam-6395	412	19	c	c	NOUN
ejpam-6395	412	20	)	)	PUNCT
ejpam-6395	412	21	⊆	⊆	NUM
ejpam-6395	412	22	•(a	•(a	PROPN
ejpam-6395	412	23	,	,	PUNCT
ejpam-6395	412	24	a	a	PRON
ejpam-6395	412	25	,	,	PUNCT
ejpam-6395	412	26	t	t	NOUN
ejpam-6395	412	27	)	)	PUNCT
ejpam-6395	413	1	⊆	⊆	NUM
ejpam-6395	413	2	a.	a.	NOUN
ejpam-6395	413	3	then	then	ADV
ejpam-6395	413	4	(	(	PUNCT
ejpam-6395	413	5	•(a	•(a	PROPN
ejpam-6395	413	6	,	,	PUNCT
ejpam-6395	413	7	a	a	PRON
ejpam-6395	413	8	,	,	PUNCT
ejpam-6395	413	9	c)]p	c)]p	PROPN
ejpam-6395	413	10	⊆	⊆	NUM
ejpam-6395	413	11	(	(	PUNCT
ejpam-6395	413	12	a]p	a]p	NOUN
ejpam-6395	413	13	.	.	PUNCT
ejpam-6395	414	1	since	since	SCONJ
ejpam-6395	414	2	a	a	PRON
ejpam-6395	414	3	is	be	AUX
ejpam-6395	414	4	an	an	DET
ejpam-6395	414	5	ideal	ideal	NOUN
ejpam-6395	414	6	of	of	ADP
ejpam-6395	414	7	t	t	PROPN
ejpam-6395	414	8	,	,	PUNCT
ejpam-6395	414	9	we	we	PRON
ejpam-6395	414	10	have	have	AUX
ejpam-6395	414	11	(	(	PUNCT
ejpam-6395	414	12	•(a	•(a	PROPN
ejpam-6395	414	13	,	,	PUNCT
ejpam-6395	414	14	a	a	PRON
ejpam-6395	414	15	,	,	PUNCT
ejpam-6395	414	16	c)]p	c)]p	PROPN
ejpam-6395	414	17	⊆	⊆	NUM
ejpam-6395	414	18	a.	a.	NOUN
ejpam-6395	414	19	let	let	VERB
ejpam-6395	414	20	x	x	X
ejpam-6395	414	21	∈	∈	PROPN
ejpam-6395	414	22	(	(	PUNCT
ejpam-6395	414	23	•(a	•(a	PROPN
ejpam-6395	414	24	,	,	PUNCT
ejpam-6395	414	25	a	a	PRON
ejpam-6395	414	26	,	,	PUNCT
ejpam-6395	414	27	c)]p	c)]p	PROPN
ejpam-6395	414	28	.	.	PUNCT
ejpam-6395	415	1	there	there	PRON
ejpam-6395	415	2	exists	exist	VERB
ejpam-6395	415	3	y	y	PROPN
ejpam-6395	415	4	∈	∈	PROPN
ejpam-6395	415	5	•(a	•(a	PROPN
ejpam-6395	415	6	,	,	PUNCT
ejpam-6395	415	7	a	a	DET
ejpam-6395	415	8	,	,	PUNCT
ejpam-6395	415	9	c	c	NOUN
ejpam-6395	415	10	)	)	PUNCT
ejpam-6395	415	11	such	such	ADJ
ejpam-6395	415	12	that	that	SCONJ
ejpam-6395	415	13	x	x	SYM
ejpam-6395	415	14	≤p	≤p	NOUN
ejpam-6395	415	15	y	y	PROPN
ejpam-6395	415	16	.	.	PUNCT
ejpam-6395	416	1	then	then	ADV
ejpam-6395	416	2	y	y	PROPN
ejpam-6395	416	3	=	=	PUNCT
ejpam-6395	416	4	•(y1	•(y1	PROPN
ejpam-6395	416	5	,	,	PUNCT
ejpam-6395	416	6	y2	y2	PROPN
ejpam-6395	416	7	,	,	PUNCT
ejpam-6395	416	8	y3	y3	PROPN
ejpam-6395	416	9	)	)	PUNCT
ejpam-6395	416	10	for	for	ADP
ejpam-6395	416	11	some	some	DET
ejpam-6395	416	12	y1	y1	NOUN
ejpam-6395	416	13	,	,	PUNCT
ejpam-6395	416	14	y2	y2	PROPN
ejpam-6395	416	15	∈	∈	PROPN
ejpam-6395	416	16	a	a	PRON
ejpam-6395	416	17	,	,	PUNCT
ejpam-6395	416	18	y3	y3	PROPN
ejpam-6395	416	19	∈	∈	PROPN
ejpam-6395	416	20	c.	c.	NOUN
ejpam-6395	417	1	then	then	ADV
ejpam-6395	417	2	x	x	SYM
ejpam-6395	417	3	≤p	≤p	PROPN
ejpam-6395	417	4	•(y1	•(y1	PROPN
ejpam-6395	417	5	,	,	PUNCT
ejpam-6395	417	6	y2	y2	PROPN
ejpam-6395	417	7	,	,	PUNCT
ejpam-6395	417	8	y3	y3	PROPN
ejpam-6395	417	9	)	)	PUNCT
ejpam-6395	417	10	.	.	PUNCT
ejpam-6395	418	1	let	let	VERB
ejpam-6395	418	2	u	u	NOUN
ejpam-6395	418	3	,	,	PUNCT
ejpam-6395	418	4	v	v	PROPN
ejpam-6395	418	5	∈	∈	PROPN
ejpam-6395	418	6	a.	a.	NOUN
ejpam-6395	418	7	since	since	SCONJ
ejpam-6395	418	8	•(u	•(u	NOUN
ejpam-6395	418	9	,	,	PUNCT
ejpam-6395	418	10	•(v	•(v	NOUN
ejpam-6395	418	11	,	,	PUNCT
ejpam-6395	418	12	y1	y1	NOUN
ejpam-6395	418	13	,	,	PUNCT
ejpam-6395	418	14	y2	y2	PROPN
ejpam-6395	418	15	)	)	PUNCT
ejpam-6395	418	16	,	,	PUNCT
ejpam-6395	418	17	y3	y3	PROPN
ejpam-6395	418	18	)	)	PUNCT
ejpam-6395	418	19	=	=	PUNCT
ejpam-6395	418	20	•(u	•(u	NOUN
ejpam-6395	418	21	,	,	PUNCT
ejpam-6395	418	22	v	v	NOUN
ejpam-6395	418	23	,	,	PUNCT
ejpam-6395	418	24	•(y1	•(y1	ADJ
ejpam-6395	418	25	,	,	PUNCT
ejpam-6395	418	26	y2	y2	NOUN
ejpam-6395	418	27	,	,	PUNCT
ejpam-6395	418	28	y3	y3	NOUN
ejpam-6395	418	29	)	)	PUNCT
ejpam-6395	418	30	)	)	PUNCT
ejpam-6395	419	1	∈	∈	PROPN
ejpam-6395	419	2	c	c	X
ejpam-6395	419	3	,	,	PUNCT
ejpam-6395	419	4	we	we	PRON
ejpam-6395	419	5	have	have	VERB
ejpam-6395	419	6	•(y1	•(y1	PROPN
ejpam-6395	419	7	,	,	PUNCT
ejpam-6395	419	8	y2	y2	PROPN
ejpam-6395	419	9	,	,	PUNCT
ejpam-6395	419	10	y3	y3	PROPN
ejpam-6395	419	11	)	)	PUNCT
ejpam-6395	419	12	∈	∈	PROPN
ejpam-6395	419	13	ca−1	ca−1	NOUN
ejpam-6395	419	14	.	.	PUNCT
ejpam-6395	420	1	that	that	PRON
ejpam-6395	420	2	is	be	AUX
ejpam-6395	420	3	,	,	PUNCT
ejpam-6395	420	4	x	x	PROPN
ejpam-6395	420	5	∈	∈	PROPN
ejpam-6395	420	6	ca−1	ca−1	NOUN
ejpam-6395	420	7	.	.	PUNCT
ejpam-6395	421	1	then	then	ADV
ejpam-6395	421	2	(	(	PUNCT
ejpam-6395	421	3	•(a	•(a	PROPN
ejpam-6395	421	4	,	,	PUNCT
ejpam-6395	421	5	a	a	PRON
ejpam-6395	421	6	,	,	PUNCT
ejpam-6395	421	7	c)]p	c)]p	PROPN
ejpam-6395	421	8	⊆	⊆	NUM
ejpam-6395	421	9	ca−1	ca−1	NOUN
ejpam-6395	421	10	.	.	PUNCT
ejpam-6395	422	1	therefore	therefore	ADV
ejpam-6395	422	2	(	(	PUNCT
ejpam-6395	422	3	•(a	•(a	PROPN
ejpam-6395	422	4	,	,	PUNCT
ejpam-6395	422	5	a	a	PRON
ejpam-6395	422	6	,	,	PUNCT
ejpam-6395	422	7	c)]p	c)]p	PROPN
ejpam-6395	422	8	⊆	⊆	NUM
ejpam-6395	422	9	a∩c	a∩c	PROPN
ejpam-6395	422	10	.	.	PUNCT
ejpam-6395	423	1	for	for	ADP
ejpam-6395	423	2	the	the	DET
ejpam-6395	423	3	reverse	reverse	ADJ
ejpam-6395	423	4	inclusion	inclusion	NOUN
ejpam-6395	423	5	,	,	PUNCT
ejpam-6395	423	6	let	let	VERB
ejpam-6395	423	7	c	c	NOUN
ejpam-6395	423	8	∈	∈	PROPN
ejpam-6395	423	9	c	c	PROPN
ejpam-6395	423	10	,	,	PUNCT
ejpam-6395	423	11	a	a	PRON
ejpam-6395	423	12	,	,	PUNCT
ejpam-6395	423	13	b	b	PROPN
ejpam-6395	423	14	∈	∈	PROPN
ejpam-6395	423	15	a	a	X
ejpam-6395	423	16	,	,	PUNCT
ejpam-6395	423	17	we	we	PRON
ejpam-6395	423	18	have	have	AUX
ejpam-6395	423	19	•(a	•(a	PROPN
ejpam-6395	423	20	,	,	PUNCT
ejpam-6395	423	21	b	b	NOUN
ejpam-6395	423	22	,	,	PUNCT
ejpam-6395	423	23	c	c	NOUN
ejpam-6395	423	24	)	)	PUNCT
ejpam-6395	423	25	∈	∈	PROPN
ejpam-6395	423	26	•(a	•(a	PROPN
ejpam-6395	423	27	,	,	PUNCT
ejpam-6395	423	28	a	a	PRON
ejpam-6395	423	29	,	,	PUNCT
ejpam-6395	423	30	c	c	NOUN
ejpam-6395	423	31	)	)	PUNCT
ejpam-6395	423	32	⊆	⊆	NUM
ejpam-6395	423	33	(	(	PUNCT
ejpam-6395	423	34	•(a	•(a	PROPN
ejpam-6395	423	35	,	,	PUNCT
ejpam-6395	423	36	a	a	PRON
ejpam-6395	423	37	,	,	PUNCT
ejpam-6395	423	38	c)]p	c)]p	PROPN
ejpam-6395	423	39	.	.	PUNCT
ejpam-6395	424	1	then	then	ADV
ejpam-6395	424	2	c	c	PROPN
ejpam-6395	424	3	⊆	⊆	NUM
ejpam-6395	424	4	(	(	PUNCT
ejpam-6395	424	5	•(a	•(a	PROPN
ejpam-6395	424	6	,	,	PUNCT
ejpam-6395	424	7	a	a	PRON
ejpam-6395	424	8	,	,	PUNCT
ejpam-6395	424	9	c)]pa−1	c)]pa−1	NOUN
ejpam-6395	424	10	.	.	PUNCT
ejpam-6395	425	1	hence	hence	ADV
ejpam-6395	425	2	a	a	DET
ejpam-6395	425	3	∩	∩	ADJ
ejpam-6395	425	4	c	c	NOUN
ejpam-6395	425	5	⊆	⊆	NUM
ejpam-6395	425	6	a	a	DET
ejpam-6395	425	7	∩	∩	NOUN
ejpam-6395	425	8	(	(	PUNCT
ejpam-6395	425	9	•(a	•(a	PROPN
ejpam-6395	425	10	,	,	PUNCT
ejpam-6395	425	11	a	a	PRON
ejpam-6395	425	12	,	,	PUNCT
ejpam-6395	425	13	c)]pa−1	c)]pa−1	NOUN
ejpam-6395	425	14	=	=	PUNCT
ejpam-6395	425	15	a	a	DET
ejpam-6395	425	16	∩	∩	NOUN
ejpam-6395	425	17	(	(	PUNCT
ejpam-6395	425	18	•(a	•(a	PROPN
ejpam-6395	425	19	,	,	PUNCT
ejpam-6395	425	20	a	a	PRON
ejpam-6395	425	21	,	,	PUNCT
ejpam-6395	425	22	c)]p	c)]p	PROPN
ejpam-6395	425	23	⊆	⊆	NUM
ejpam-6395	425	24	(	(	PUNCT
ejpam-6395	425	25	•(a	•(a	PROPN
ejpam-6395	425	26	,	,	PUNCT
ejpam-6395	425	27	a	a	PRON
ejpam-6395	425	28	,	,	PUNCT
ejpam-6395	425	29	c)]p	c)]p	PROPN
ejpam-6395	425	30	.	.	PUNCT
ejpam-6395	426	1	therefore	therefore	ADV
ejpam-6395	426	2	a	a	PRON
ejpam-6395	426	3	is	be	AUX
ejpam-6395	426	4	a	a	DET
ejpam-6395	426	5	left	left	ADJ
ejpam-6395	426	6	weakly	weakly	ADV
ejpam-6395	426	7	pure	pure	ADJ
ejpam-6395	426	8	if	if	SCONJ
ejpam-6395	426	9	and	and	CCONJ
ejpam-6395	426	10	only	only	ADV
ejpam-6395	426	11	if	if	SCONJ
ejpam-6395	426	12	a	a	DET
ejpam-6395	426	13	∩	∩	ADJ
ejpam-6395	426	14	b	b	NOUN
ejpam-6395	426	15	=	=	SYM
ejpam-6395	426	16	a	a	DET
ejpam-6395	426	17	∩	∩	NOUN
ejpam-6395	426	18	(	(	PUNCT
ejpam-6395	426	19	ba−1	ba−1	NOUN
ejpam-6395	426	20	)	)	PUNCT
ejpam-6395	426	21	for	for	ADP
ejpam-6395	426	22	all	all	DET
ejpam-6395	426	23	ideals	ideal	NOUN
ejpam-6395	426	24	b	b	PROPN
ejpam-6395	426	25	of	of	ADP
ejpam-6395	426	26	s.	s.	PROPN
ejpam-6395	426	27	similarly	similarly	ADV
ejpam-6395	426	28	,	,	PUNCT
ejpam-6395	426	29	we	we	PRON
ejpam-6395	426	30	can	can	AUX
ejpam-6395	426	31	proof	proof	VERB
ejpam-6395	426	32	that	that	SCONJ
ejpam-6395	426	33	a	a	PRON
ejpam-6395	426	34	is	be	AUX
ejpam-6395	426	35	a	a	DET
ejpam-6395	426	36	right	right	ADJ
ejpam-6395	426	37	weakly	weakly	ADJ
ejpam-6395	426	38	pure	pure	ADJ
ejpam-6395	426	39	if	if	SCONJ
ejpam-6395	426	40	and	and	CCONJ
ejpam-6395	426	41	only	only	ADV
ejpam-6395	426	42	if	if	SCONJ
ejpam-6395	426	43	a	a	DET
ejpam-6395	426	44	∩	∩	ADJ
ejpam-6395	426	45	b	b	NOUN
ejpam-6395	426	46	=	=	SYM
ejpam-6395	426	47	a	a	DET
ejpam-6395	426	48	∩	∩	NOUN
ejpam-6395	426	49	(	(	PUNCT
ejpam-6395	426	50	a−1b	a−1b	NOUN
ejpam-6395	426	51	)	)	PUNCT
ejpam-6395	426	52	for	for	ADP
ejpam-6395	426	53	all	all	DET
ejpam-6395	426	54	ideals	ideal	NOUN
ejpam-6395	426	55	b	b	PROPN
ejpam-6395	426	56	of	of	ADP
ejpam-6395	426	57	s.	s.	PROPN
ejpam-6395	426	58	5	5	NUM
ejpam-6395	426	59	.	.	PUNCT
ejpam-6395	426	60	conclusion	conclusion	NOUN
ejpam-6395	426	61	in	in	ADP
ejpam-6395	426	62	this	this	DET
ejpam-6395	426	63	article	article	NOUN
ejpam-6395	426	64	,	,	PUNCT
ejpam-6395	426	65	we	we	PRON
ejpam-6395	426	66	introduced	introduce	VERB
ejpam-6395	426	67	the	the	DET
ejpam-6395	426	68	notion	notion	NOUN
ejpam-6395	426	69	of	of	ADP
ejpam-6395	426	70	ordered	order	VERB
ejpam-6395	426	71	power	power	NOUN
ejpam-6395	426	72	ternary	ternary	NOUN
ejpam-6395	426	73	semigroups	semigroup	NOUN
ejpam-6395	426	74	on	on	ADP
ejpam-6395	426	75	ternary	ternary	ADJ
ejpam-6395	426	76	semihypergroups	semihypergroup	NOUN
ejpam-6395	426	77	induced	induce	VERB
ejpam-6395	426	78	by	by	ADP
ejpam-6395	426	79	posets	poset	NOUN
ejpam-6395	426	80	which	which	PRON
ejpam-6395	426	81	is	be	AUX
ejpam-6395	426	82	an	an	DET
ejpam-6395	426	83	extension	extension	NOUN
ejpam-6395	426	84	of	of	ADP
ejpam-6395	426	85	power	power	NOUN
ejpam-6395	426	86	ternary	ternary	NOUN
ejpam-6395	426	87	semigroup	semigroup	NOUN
ejpam-6395	426	88	on	on	ADP
ejpam-6395	426	89	ternary	ternary	ADJ
ejpam-6395	426	90	semihypergroups	semihypergroup	NOUN
ejpam-6395	426	91	.	.	PUNCT
ejpam-6395	427	1	particularly	particularly	ADV
ejpam-6395	427	2	,	,	PUNCT
ejpam-6395	427	3	we	we	PRON
ejpam-6395	427	4	investigated	investigate	VERB
ejpam-6395	427	5	their	their	PRON
ejpam-6395	427	6	algebraic	algebraic	ADJ
ejpam-6395	427	7	properties	property	NOUN
ejpam-6395	427	8	including	include	VERB
ejpam-6395	427	9	pure	pure	ADJ
ejpam-6395	427	10	ideals	ideal	NOUN
ejpam-6395	427	11	and	and	CCONJ
ejpam-6395	427	12	weakly	weakly	ADJ
ejpam-6395	427	13	pure	pure	ADJ
ejpam-6395	427	14	ideals	ideal	NOUN
ejpam-6395	427	15	.	.	PUNCT
ejpam-6395	428	1	acknowledgements	acknowledgement	NOUN
ejpam-6395	428	2	this	this	DET
ejpam-6395	428	3	research	research	NOUN
ejpam-6395	428	4	project	project	NOUN
ejpam-6395	428	5	was	be	AUX
ejpam-6395	428	6	financially	financially	ADV
ejpam-6395	428	7	supported	support	VERB
ejpam-6395	428	8	by	by	ADP
ejpam-6395	428	9	mahasarakham	mahasarakham	PROPN
ejpam-6395	428	10	university	university	PROPN
ejpam-6395	428	11	,	,	PUNCT
ejpam-6395	428	12	thailand	thailand	PROPN
ejpam-6395	428	13	.	.	PUNCT
ejpam-6395	429	1	the	the	DET
ejpam-6395	429	2	authors	author	NOUN
ejpam-6395	429	3	would	would	AUX
ejpam-6395	429	4	like	like	VERB
ejpam-6395	429	5	to	to	PART
ejpam-6395	429	6	thank	thank	VERB
ejpam-6395	429	7	the	the	DET
ejpam-6395	429	8	reviewers	reviewer	NOUN
ejpam-6395	429	9	for	for	ADP
ejpam-6395	429	10	their	their	PRON
ejpam-6395	429	11	valuable	valuable	ADJ
ejpam-6395	429	12	comments	comment	NOUN
ejpam-6395	429	13	.	.	PUNCT
ejpam-6395	430	1	references	reference	NOUN
ejpam-6395	430	2	[	[	X
ejpam-6395	430	3	1	1	NUM
ejpam-6395	430	4	]	]	PUNCT
ejpam-6395	430	5	d	d	NOUN
ejpam-6395	430	6	h	h	NUM
ejpam-6395	430	7	lehmer	lehmer	NOUN
ejpam-6395	430	8	.	.	PUNCT
ejpam-6395	431	1	a	a	DET
ejpam-6395	431	2	ternary	ternary	ADJ
ejpam-6395	431	3	analogue	analogue	NOUN
ejpam-6395	431	4	of	of	ADP
ejpam-6395	431	5	abelian	abelian	ADJ
ejpam-6395	431	6	groups	group	NOUN
ejpam-6395	431	7	.	.	PUNCT
ejpam-6395	432	1	american	american	ADJ
ejpam-6395	432	2	journal	journal	PROPN
ejpam-6395	432	3	of	of	ADP
ejpam-6395	432	4	mathematics	mathematics	PROPN
ejpam-6395	432	5	,	,	PUNCT
ejpam-6395	432	6	54(2):329–338	54(2):329–338	PROPN
ejpam-6395	432	7	,	,	PUNCT
ejpam-6395	432	8	1932	1932	NUM
ejpam-6395	432	9	.	.	PUNCT
ejpam-6395	433	1	[	[	X
ejpam-6395	433	2	2	2	NUM
ejpam-6395	433	3	]	]	PUNCT
ejpam-6395	433	4	j	j	NOUN
ejpam-6395	433	5	loś.	loś.	ADJ
ejpam-6395	433	6	on	on	ADP
ejpam-6395	433	7	the	the	DET
ejpam-6395	433	8	extending	extending	NOUN
ejpam-6395	433	9	of	of	ADP
ejpam-6395	433	10	models	model	NOUN
ejpam-6395	433	11	(	(	PUNCT
ejpam-6395	433	12	i	i	NOUN
ejpam-6395	433	13	)	)	PUNCT
ejpam-6395	433	14	.	.	PUNCT
ejpam-6395	434	1	fundamenta	fundamenta	PROPN
ejpam-6395	434	2	mathematicae	mathematicae	PROPN
ejpam-6395	434	3	,	,	PUNCT
ejpam-6395	434	4	42(1):38–54	42(1):38–54	NUM
ejpam-6395	434	5	,	,	PUNCT
ejpam-6395	434	6	1955	1955	NUM
ejpam-6395	434	7	.	.	PUNCT
ejpam-6395	435	1	[	[	X
ejpam-6395	435	2	3	3	X
ejpam-6395	435	3	]	]	X
ejpam-6395	435	4	f	f	PROPN
ejpam-6395	435	5	m	m	PROPN
ejpam-6395	435	6	sioson	sioson	PROPN
ejpam-6395	435	7	.	.	PUNCT
ejpam-6395	435	8	ideal	ideal	ADJ
ejpam-6395	435	9	theory	theory	NOUN
ejpam-6395	435	10	in	in	ADP
ejpam-6395	435	11	ternary	ternary	ADJ
ejpam-6395	435	12	semigroups	semigroup	NOUN
ejpam-6395	435	13	.	.	PUNCT
ejpam-6395	436	1	mathematica	mathematica	PROPN
ejpam-6395	436	2	japonica	japonica	PROPN
ejpam-6395	436	3	,	,	PUNCT
ejpam-6395	436	4	10:63–84	10:63–84	NOUN
ejpam-6395	436	5	,	,	PUNCT
ejpam-6395	436	6	1965	1965	NUM
ejpam-6395	436	7	.	.	PUNCT
ejpam-6395	437	1	[	[	X
ejpam-6395	437	2	4	4	NUM
ejpam-6395	437	3	]	]	SYM
ejpam-6395	437	4	b	b	X
ejpam-6395	437	5	davvaz	davvaz	NOUN
ejpam-6395	437	6	,	,	PUNCT
ejpam-6395	437	7	w	w	ADP
ejpam-6395	437	8	a	a	DET
ejpam-6395	437	9	dudek	dudek	PROPN
ejpam-6395	437	10	,	,	PUNCT
ejpam-6395	437	11	and	and	CCONJ
ejpam-6395	437	12	s	s	VERB
ejpam-6395	437	13	mirvakili	mirvakili	NOUN
ejpam-6395	437	14	.	.	PUNCT
ejpam-6395	438	1	neutral	neutral	ADJ
ejpam-6395	438	2	elements	element	NOUN
ejpam-6395	438	3	,	,	PUNCT
ejpam-6395	438	4	fundamental	fundamental	ADJ
ejpam-6395	438	5	relations	relation	NOUN
ejpam-6395	438	6	and	and	CCONJ
ejpam-6395	438	7	n	n	CCONJ
ejpam-6395	438	8	-	-	PUNCT
ejpam-6395	438	9	ary	ary	PROPN
ejpam-6395	438	10	hypersemigroups	hypersemigroup	NOUN
ejpam-6395	438	11	.	.	PUNCT
ejpam-6395	439	1	international	international	ADJ
ejpam-6395	439	2	journal	journal	PROPN
ejpam-6395	439	3	of	of	ADP
ejpam-6395	439	4	algebra	algebra	NOUN
ejpam-6395	439	5	and	and	CCONJ
ejpam-6395	439	6	computation	computation	NOUN
ejpam-6395	439	7	,	,	PUNCT
ejpam-6395	439	8	19(4):567–583	19(4):567–583	PROPN
ejpam-6395	439	9	,	,	PUNCT
ejpam-6395	439	10	2009	2009	NUM
ejpam-6395	439	11	.	.	PUNCT
ejpam-6395	440	1	[	[	X
ejpam-6395	440	2	5	5	NUM
ejpam-6395	440	3	]	]	PUNCT
ejpam-6395	440	4	a	a	DET
ejpam-6395	440	5	nongmanee	nongmanee	NOUN
ejpam-6395	440	6	and	and	CCONJ
ejpam-6395	440	7	s	s	NOUN
ejpam-6395	440	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	440	9	.	.	PUNCT
ejpam-6395	441	1	ternary	ternary	ADJ
ejpam-6395	441	2	menger	menger	PROPN
ejpam-6395	441	3	algebras	algebra	VERB
ejpam-6395	441	4	:	:	PUNCT
ejpam-6395	441	5	a	a	DET
ejpam-6395	441	6	generalization	generalization	NOUN
ejpam-6395	441	7	of	of	ADP
ejpam-6395	441	8	ternary	ternary	ADJ
ejpam-6395	441	9	semigroups	semigroup	NOUN
ejpam-6395	441	10	.	.	PUNCT
ejpam-6395	442	1	mathematics	mathematic	NOUN
ejpam-6395	442	2	,	,	PUNCT
ejpam-6395	442	3	9(5):553	9(5):553	NUM
ejpam-6395	442	4	,	,	PUNCT
ejpam-6395	442	5	2021	2021	NUM
ejpam-6395	442	6	.	.	PUNCT
ejpam-6395	443	1	[	[	X
ejpam-6395	443	2	6	6	NUM
ejpam-6395	443	3	]	]	PUNCT
ejpam-6395	443	4	a	a	DET
ejpam-6395	443	5	nongmanee	nongmanee	NOUN
ejpam-6395	443	6	and	and	CCONJ
ejpam-6395	443	7	s	s	NOUN
ejpam-6395	443	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	443	9	.	.	PUNCT
ejpam-6395	444	1	v	v	X
ejpam-6395	444	2	-	-	PUNCT
ejpam-6395	444	3	regular	regular	ADJ
ejpam-6395	444	4	ternary	ternary	ADJ
ejpam-6395	444	5	menger	menger	NOUN
ejpam-6395	444	6	algebras	algebra	NOUN
ejpam-6395	444	7	and	and	CCONJ
ejpam-6395	444	8	left	leave	VERB
ejpam-6395	444	9	translations	translation	NOUN
ejpam-6395	444	10	of	of	ADP
ejpam-6395	444	11	ternary	ternary	ADJ
ejpam-6395	444	12	menger	menger	PROPN
ejpam-6395	444	13	algebras	algebra	NOUN
ejpam-6395	444	14	.	.	PUNCT
ejpam-6395	445	1	mathematics	mathematic	NOUN
ejpam-6395	445	2	,	,	PUNCT
ejpam-6395	445	3	9(21):2691	9(21):2691	NUM
ejpam-6395	445	4	,	,	PUNCT
ejpam-6395	445	5	2021	2021	NUM
ejpam-6395	445	6	.	.	PUNCT
ejpam-6395	446	1	[	[	X
ejpam-6395	446	2	7	7	X
ejpam-6395	446	3	]	]	X
ejpam-6395	446	4	a	a	DET
ejpam-6395	446	5	nongmanee	nongmanee	NOUN
ejpam-6395	446	6	and	and	CCONJ
ejpam-6395	446	7	s	s	NOUN
ejpam-6395	446	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	446	9	.	.	PUNCT
ejpam-6395	447	1	quaternary	quaternary	ADJ
ejpam-6395	447	2	rectangular	rectangular	ADJ
ejpam-6395	447	3	bands	band	NOUN
ejpam-6395	447	4	and	and	CCONJ
ejpam-6395	447	5	representations	representation	NOUN
ejpam-6395	447	6	of	of	ADP
ejpam-6395	447	7	ternary	ternary	ADJ
ejpam-6395	447	8	semigroups	semigroup	NOUN
ejpam-6395	447	9	.	.	PUNCT
ejpam-6395	448	1	thai	thai	PROPN
ejpam-6395	448	2	journal	journal	PROPN
ejpam-6395	448	3	of	of	ADP
ejpam-6395	448	4	mathematics	mathematic	NOUN
ejpam-6395	448	5	,	,	PUNCT
ejpam-6395	448	6	20(2):729–745	20(2):729–745	NUM
ejpam-6395	448	7	,	,	PUNCT
ejpam-6395	448	8	2022	2022	NUM
ejpam-6395	448	9	.	.	PUNCT
ejpam-6395	449	1	[	[	X
ejpam-6395	449	2	8	8	NUM
ejpam-6395	449	3	]	]	SYM
ejpam-6395	449	4	b	b	X
ejpam-6395	449	5	davvaz	davvaz	NOUN
ejpam-6395	449	6	,	,	PUNCT
ejpam-6395	449	7	w	w	ADP
ejpam-6395	449	8	a	a	DET
ejpam-6395	449	9	dudek	dudek	PROPN
ejpam-6395	449	10	,	,	PUNCT
ejpam-6395	449	11	and	and	CCONJ
ejpam-6395	449	12	t	t	PROPN
ejpam-6395	449	13	vougiouklis	vougioukli	VERB
ejpam-6395	449	14	.	.	PUNCT
ejpam-6395	450	1	a	a	DET
ejpam-6395	450	2	generalization	generalization	NOUN
ejpam-6395	450	3	of	of	ADP
ejpam-6395	450	4	n	n	CCONJ
ejpam-6395	450	5	-	-	PUNCT
ejpam-6395	450	6	ary	ary	ADJ
ejpam-6395	450	7	algebraic	algebraic	PROPN
ejpam-6395	450	8	systems	system	NOUN
ejpam-6395	450	9	.	.	PUNCT
ejpam-6395	451	1	communications	communication	NOUN
ejpam-6395	451	2	in	in	ADP
ejpam-6395	451	3	algebra	algebra	NOUN
ejpam-6395	451	4	,	,	PUNCT
ejpam-6395	451	5	37(4):1248–1263	37(4):1248–1263	NUM
ejpam-6395	451	6	,	,	PUNCT
ejpam-6395	451	7	2009	2009	NUM
ejpam-6395	451	8	.	.	PUNCT
ejpam-6395	452	1	a.	a.	NOUN
ejpam-6395	452	2	nongmanee	nongmanee	PROPN
ejpam-6395	452	3	,	,	PUNCT
ejpam-6395	452	4	k.	k.	PROPN
ejpam-6395	452	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	452	6	,	,	PUNCT
ejpam-6395	452	7	m.	m.	NOUN
ejpam-6395	452	8	phattarachaleekul	phattarachaleekul	PROPN
ejpam-6395	452	9	/	/	SYM
ejpam-6395	452	10	eur	eur	PROPN
ejpam-6395	452	11	.	.	PUNCT
ejpam-6395	453	1	j.	j.	PROPN
ejpam-6395	453	2	pure	pure	PROPN
ejpam-6395	453	3	appl	appl	PROPN
ejpam-6395	453	4	.	.	PROPN
ejpam-6395	453	5	math	math	PROPN
ejpam-6395	453	6	,	,	PUNCT
ejpam-6395	453	7	18	18	NUM
ejpam-6395	453	8	(	(	PUNCT
ejpam-6395	453	9	3	3	NUM
ejpam-6395	453	10	)	)	PUNCT
ejpam-6395	453	11	(	(	PUNCT
ejpam-6395	453	12	2025	2025	NUM
ejpam-6395	453	13	)	)	PUNCT
ejpam-6395	453	14	,	,	PUNCT
ejpam-6395	453	15	6395	6395	NUM
ejpam-6395	453	16	12	12	NUM
ejpam-6395	453	17	of	of	ADP
ejpam-6395	453	18	12	12	NUM
ejpam-6395	453	19	[	[	X
ejpam-6395	453	20	9	9	NUM
ejpam-6395	453	21	]	]	PUNCT
ejpam-6395	453	22	a	a	DET
ejpam-6395	453	23	nongmanee	nongmanee	NOUN
ejpam-6395	453	24	and	and	CCONJ
ejpam-6395	453	25	s	s	NOUN
ejpam-6395	453	26	leeratanavalee	leeratanavalee	X
ejpam-6395	453	27	.	.	PUNCT
ejpam-6395	454	1	representations	representation	NOUN
ejpam-6395	454	2	,	,	PUNCT
ejpam-6395	454	3	translations	translation	NOUN
ejpam-6395	454	4	and	and	CCONJ
ejpam-6395	454	5	reductions	reduction	NOUN
ejpam-6395	454	6	for	for	ADP
ejpam-6395	454	7	ternary	ternary	ADJ
ejpam-6395	454	8	semihypergroups	semihypergroup	NOUN
ejpam-6395	454	9	.	.	PUNCT
ejpam-6395	455	1	axioms	axiom	NOUN
ejpam-6395	455	2	,	,	PUNCT
ejpam-6395	455	3	11:626	11:626	NUM
ejpam-6395	455	4	,	,	PUNCT
ejpam-6395	455	5	2022	2022	NUM
ejpam-6395	455	6	.	.	PUNCT
ejpam-6395	456	1	[	[	X
ejpam-6395	456	2	10	10	NUM
ejpam-6395	456	3	]	]	X
ejpam-6395	456	4	a	a	DET
ejpam-6395	456	5	nongmanee	nongmanee	NOUN
ejpam-6395	456	6	and	and	CCONJ
ejpam-6395	456	7	s	s	NOUN
ejpam-6395	456	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	456	9	.	.	PUNCT
ejpam-6395	457	1	regularity	regularity	NOUN
ejpam-6395	457	2	in	in	ADP
ejpam-6395	457	3	ternary	ternary	ADJ
ejpam-6395	457	4	semihypergroups	semihypergroup	NOUN
ejpam-6395	457	5	induced	induce	VERB
ejpam-6395	457	6	by	by	ADP
ejpam-6395	457	7	subsets	subset	NOUN
ejpam-6395	457	8	of	of	ADP
ejpam-6395	457	9	ternary	ternary	ADJ
ejpam-6395	457	10	semigroups	semigroup	NOUN
ejpam-6395	457	11	.	.	PUNCT
ejpam-6395	458	1	thai	thai	PROPN
ejpam-6395	458	2	journal	journal	PROPN
ejpam-6395	458	3	of	of	ADP
ejpam-6395	458	4	mathematics	mathematic	NOUN
ejpam-6395	458	5	,	,	PUNCT
ejpam-6395	458	6	22(1):73–84	22(1):73–84	NOUN
ejpam-6395	458	7	,	,	PUNCT
ejpam-6395	458	8	2024	2024	NUM
ejpam-6395	458	9	.	.	PUNCT
ejpam-6395	459	1	[	[	X
ejpam-6395	459	2	11	11	NUM
ejpam-6395	459	3	]	]	X
ejpam-6395	459	4	p	p	X
ejpam-6395	459	5	dubreil	dubreil	NOUN
ejpam-6395	459	6	.	.	PUNCT
ejpam-6395	460	1	contribution	contribution	NOUN
ejpam-6395	460	2	à	à	PROPN
ejpam-6395	460	3	la	la	PROPN
ejpam-6395	460	4	théorie	théorie	PROPN
ejpam-6395	460	5	des	des	PROPN
ejpam-6395	460	6	demi	demi	PROPN
ejpam-6395	460	7	-	-	PUNCT
ejpam-6395	460	8	groupes	groupe	NOUN
ejpam-6395	460	9	.	.	PUNCT
ejpam-6395	460	10	iii	iii	X
ejpam-6395	460	11	.	.	PUNCT
ejpam-6395	460	12	bulletin	bulletin	PROPN
ejpam-6395	460	13	de	de	PROPN
ejpam-6395	460	14	la	la	PROPN
ejpam-6395	460	15	société	société	PROPN
ejpam-6395	460	16	mathématique	mathématique	PROPN
ejpam-6395	460	17	de	de	X
ejpam-6395	460	18	france	france	PROPN
ejpam-6395	460	19	,	,	PUNCT
ejpam-6395	460	20	81:289–306	81:289–306	PROPN
ejpam-6395	460	21	,	,	PUNCT
ejpam-6395	460	22	1953	1953	NUM
ejpam-6395	460	23	.	.	PUNCT
ejpam-6395	461	1	[	[	X
ejpam-6395	461	2	12	12	NUM
ejpam-6395	461	3	]	]	PUNCT
ejpam-6395	461	4	t	t	PROPN
ejpam-6395	461	5	tamura	tamura	PROPN
ejpam-6395	461	6	and	and	CCONJ
ejpam-6395	461	7	j	j	PROPN
ejpam-6395	461	8	shafer	shafer	PROPN
ejpam-6395	461	9	.	.	PUNCT
ejpam-6395	462	1	power	power	NOUN
ejpam-6395	462	2	semigroups	semigroups	PROPN
ejpam-6395	462	3	.	.	PUNCT
ejpam-6395	463	1	mathematica	mathematica	PROPN
ejpam-6395	463	2	japonica	japonica	PROPN
ejpam-6395	463	3	,	,	PUNCT
ejpam-6395	463	4	12:25–32	12:25–32	PROPN
ejpam-6395	463	5	,	,	PUNCT
ejpam-6395	463	6	1967	1967	NUM
ejpam-6395	463	7	.	.	PUNCT
ejpam-6395	464	1	[	[	X
ejpam-6395	464	2	13	13	NUM
ejpam-6395	464	3	]	]	PUNCT
ejpam-6395	464	4	t	t	PROPN
ejpam-6395	464	5	tamura	tamura	PROPN
ejpam-6395	464	6	.	.	PUNCT
ejpam-6395	465	1	isomorphism	isomorphism	NOUN
ejpam-6395	465	2	problem	problem	NOUN
ejpam-6395	465	3	of	of	ADP
ejpam-6395	465	4	power	power	NOUN
ejpam-6395	465	5	semigroups	semigroup	NOUN
ejpam-6395	465	6	of	of	ADP
ejpam-6395	465	7	completely	completely	ADV
ejpam-6395	465	8	0	0	NUM
ejpam-6395	465	9	-	-	PUNCT
ejpam-6395	465	10	simple	simple	ADJ
ejpam-6395	465	11	semigroups	semigroup	NOUN
ejpam-6395	465	12	.	.	PUNCT
ejpam-6395	466	1	journal	journal	NOUN
ejpam-6395	466	2	of	of	ADP
ejpam-6395	466	3	algebra	algebra	PROPN
ejpam-6395	466	4	,	,	PUNCT
ejpam-6395	466	5	98(2):319–361	98(2):319–361	NOUN
ejpam-6395	466	6	,	,	PUNCT
ejpam-6395	466	7	1986	1986	NUM
ejpam-6395	466	8	.	.	PUNCT
ejpam-6395	467	1	[	[	X
ejpam-6395	467	2	14	14	NUM
ejpam-6395	467	3	]	]	X
ejpam-6395	467	4	k	k	PROPN
ejpam-6395	467	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	467	6	and	and	CCONJ
ejpam-6395	467	7	s	s	VERB
ejpam-6395	467	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	467	9	.	.	PUNCT
ejpam-6395	468	1	power	power	NOUN
ejpam-6395	468	2	semigroups	semigroup	NOUN
ejpam-6395	468	3	on	on	ADP
ejpam-6395	468	4	semihypergroups	semihypergroup	NOUN
ejpam-6395	468	5	.	.	PUNCT
ejpam-6395	469	1	international	international	ADJ
ejpam-6395	469	2	journal	journal	NOUN
ejpam-6395	469	3	of	of	ADP
ejpam-6395	469	4	open	open	ADJ
ejpam-6395	469	5	problems	problem	NOUN
ejpam-6395	469	6	in	in	ADP
ejpam-6395	469	7	computer	computer	NOUN
ejpam-6395	469	8	science	science	NOUN
ejpam-6395	469	9	and	and	CCONJ
ejpam-6395	469	10	mathematics	mathematic	NOUN
ejpam-6395	469	11	,	,	PUNCT
ejpam-6395	469	12	15(1):70	15(1):70	NUM
ejpam-6395	469	13	,	,	PUNCT
ejpam-6395	469	14	2022	2022	NUM
ejpam-6395	469	15	.	.	PUNCT
ejpam-6395	470	1	[	[	X
ejpam-6395	470	2	15	15	NUM
ejpam-6395	470	3	]	]	X
ejpam-6395	470	4	s	s	X
ejpam-6395	470	5	ma	ma	PROPN
ejpam-6395	470	6	,	,	PUNCT
ejpam-6395	470	7	h	h	PROPN
ejpam-6395	470	8	mi	mi	PROPN
ejpam-6395	470	9	,	,	PUNCT
ejpam-6395	470	10	and	and	CCONJ
ejpam-6395	470	11	l	l	NOUN
ejpam-6395	470	12	huo	huo	NOUN
ejpam-6395	470	13	.	.	PUNCT
ejpam-6395	471	1	power	power	NOUN
ejpam-6395	471	2	group	group	NOUN
ejpam-6395	471	3	on	on	ADP
ejpam-6395	471	4	hypergroup	hypergroup	NOUN
ejpam-6395	471	5	.	.	PUNCT
ejpam-6395	472	1	in	in	ADP
ejpam-6395	472	2	2010	2010	NUM
ejpam-6395	472	3	seventh	seventh	ADJ
ejpam-6395	472	4	international	international	ADJ
ejpam-6395	472	5	conference	conference	NOUN
ejpam-6395	472	6	on	on	ADP
ejpam-6395	472	7	fuzzy	fuzzy	ADJ
ejpam-6395	472	8	systems	system	NOUN
ejpam-6395	472	9	and	and	CCONJ
ejpam-6395	472	10	knowledge	knowledge	NOUN
ejpam-6395	472	11	discovery	discovery	NOUN
ejpam-6395	472	12	,	,	PUNCT
ejpam-6395	472	13	volume	volume	NOUN
ejpam-6395	472	14	1	1	NUM
ejpam-6395	472	15	,	,	PUNCT
ejpam-6395	472	16	pages	page	NOUN
ejpam-6395	472	17	269–274	269–274	NUM
ejpam-6395	472	18	,	,	PUNCT
ejpam-6395	472	19	2010	2010	NUM
ejpam-6395	472	20	.	.	PUNCT
ejpam-6395	473	1	[	[	X
ejpam-6395	473	2	16	16	NUM
ejpam-6395	473	3	]	]	PUNCT
ejpam-6395	473	4	a	a	DET
ejpam-6395	473	5	nongmanee	nongmanee	NOUN
ejpam-6395	473	6	,	,	PUNCT
ejpam-6395	473	7	k	k	PROPN
ejpam-6395	473	8	jeenkaew	jeenkaew	PROPN
ejpam-6395	473	9	,	,	PUNCT
ejpam-6395	473	10	and	and	CCONJ
ejpam-6395	473	11	s	s	VERB
ejpam-6395	473	12	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	473	13	.	.	PUNCT
ejpam-6395	474	1	power	power	NOUN
ejpam-6395	474	2	ternary	ternary	NOUN
ejpam-6395	474	3	semigroups	semigroup	NOUN
ejpam-6395	474	4	on	on	ADP
ejpam-6395	474	5	ternary	ternary	ADJ
ejpam-6395	474	6	semihypergroups	semihypergroup	NOUN
ejpam-6395	474	7	.	.	PUNCT
ejpam-6395	475	1	thai	thai	PROPN
ejpam-6395	475	2	journal	journal	PROPN
ejpam-6395	475	3	of	of	ADP
ejpam-6395	475	4	mathematics	mathematic	NOUN
ejpam-6395	475	5	,	,	PUNCT
ejpam-6395	475	6	2025	2025	NUM
ejpam-6395	475	7	(	(	PUNCT
ejpam-6395	475	8	submitted	submit	VERB
ejpam-6395	475	9	)	)	PUNCT
ejpam-6395	475	10	.	.	PUNCT
ejpam-6395	476	1	[	[	X
ejpam-6395	476	2	17	17	NUM
ejpam-6395	476	3	]	]	X
ejpam-6395	476	4	m	m	NOUN
ejpam-6395	476	5	szymanska	szymanska	NOUN
ejpam-6395	476	6	and	and	CCONJ
ejpam-6395	476	7	d	d	NOUN
ejpam-6395	476	8	schweigert	schweigert	NOUN
ejpam-6395	476	9	.	.	PUNCT
ejpam-6395	477	1	structures	structure	NOUN
ejpam-6395	477	2	on	on	ADP
ejpam-6395	477	3	the	the	DET
ejpam-6395	477	4	power	power	NOUN
ejpam-6395	477	5	set	set	NOUN
ejpam-6395	477	6	.	.	PUNCT
ejpam-6395	478	1	in	in	ADP
ejpam-6395	478	2	proceedings	proceeding	NOUN
ejpam-6395	478	3	of	of	ADP
ejpam-6395	478	4	the	the	DET
ejpam-6395	478	5	sixth	sixth	ADJ
ejpam-6395	478	6	international	international	ADJ
ejpam-6395	478	7	conference	conference	NOUN
ejpam-6395	478	8	on	on	ADP
ejpam-6395	478	9	discrete	discrete	ADJ
ejpam-6395	478	10	mathematics	mathematic	NOUN
ejpam-6395	478	11	and	and	CCONJ
ejpam-6395	478	12	applications	application	NOUN
ejpam-6395	478	13	,	,	PUNCT
ejpam-6395	478	14	31.08.200102.09.2001	31.08.200102.09.2001	NUM
ejpam-6395	478	15	,	,	PUNCT
ejpam-6395	478	16	bansko	bansko	PROPN
ejpam-6395	478	17	,	,	PUNCT
ejpam-6395	478	18	bulgaria	bulgaria	PROPN
ejpam-6395	478	19	,	,	PUNCT
ejpam-6395	478	20	pages	page	NOUN
ejpam-6395	478	21	71–76	71–76	NUM
ejpam-6395	478	22	,	,	PUNCT
ejpam-6395	478	23	2001	2001	NUM
ejpam-6395	478	24	.	.	PUNCT
ejpam-6395	479	1	[	[	X
ejpam-6395	479	2	18	18	NUM
ejpam-6395	479	3	]	]	X
ejpam-6395	479	4	k	k	PROPN
ejpam-6395	479	5	jeenkaew	jeenkaew	PROPN
ejpam-6395	479	6	and	and	CCONJ
ejpam-6395	479	7	s	s	VERB
ejpam-6395	479	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6395	479	9	.	.	PUNCT
ejpam-6395	480	1	pure	pure	ADJ
ejpam-6395	480	2	ideals	ideal	NOUN
ejpam-6395	480	3	in	in	ADP
ejpam-6395	480	4	ordered	order	VERB
ejpam-6395	480	5	power	power	NOUN
ejpam-6395	480	6	semigroups	semigroup	NOUN
ejpam-6395	480	7	on	on	ADP
ejpam-6395	480	8	semihypergroups	semihypergroup	NOUN
ejpam-6395	480	9	induced	induce	VERB
ejpam-6395	480	10	by	by	ADP
ejpam-6395	480	11	posets	poset	NOUN
ejpam-6395	480	12	.	.	PUNCT
ejpam-6395	481	1	journal	journal	NOUN
ejpam-6395	481	2	of	of	ADP
ejpam-6395	481	3	algebra	algebra	PROPN
ejpam-6395	481	4	and	and	CCONJ
ejpam-6395	481	5	applied	apply	VERB
ejpam-6395	481	6	mathematics	mathematic	NOUN
ejpam-6395	481	7	,	,	PUNCT
ejpam-6395	481	8	22(1):1–15	22(1):1–15	NUM
ejpam-6395	481	9	,	,	PUNCT
ejpam-6395	481	10	2024	2024	NUM
ejpam-6395	481	11	.	.	PUNCT
ejpam-6395	482	1	[	[	X
ejpam-6395	482	2	19	19	NUM
ejpam-6395	482	3	]	]	X
ejpam-6395	482	4	j	j	PROPN
ejpam-6395	482	5	ahsan	ahsan	PROPN
ejpam-6395	482	6	and	and	CCONJ
ejpam-6395	482	7	m	m	PROPN
ejpam-6395	482	8	takahashi	takahashi	PROPN
ejpam-6395	482	9	.	.	PUNCT
ejpam-6395	483	1	pure	pure	ADJ
ejpam-6395	483	2	spectrum	spectrum	NOUN
ejpam-6395	483	3	of	of	ADP
ejpam-6395	483	4	a	a	DET
ejpam-6395	483	5	monoid	monoid	NOUN
ejpam-6395	483	6	with	with	ADP
ejpam-6395	483	7	zero	zero	NUM
ejpam-6395	483	8	.	.	PUNCT
ejpam-6395	484	1	kobe	kobe	PROPN
ejpam-6395	484	2	journal	journal	PROPN
ejpam-6395	484	3	of	of	ADP
ejpam-6395	484	4	mathematics	mathematic	NOUN
ejpam-6395	484	5	,	,	PUNCT
ejpam-6395	484	6	6(2):163–181	6(2):163–181	NOUN
ejpam-6395	484	7	,	,	PUNCT
ejpam-6395	484	8	1989	1989	NUM
ejpam-6395	484	9	.	.	PUNCT
ejpam-6395	485	1	[	[	X
ejpam-6395	485	2	20	20	NUM
ejpam-6395	485	3	]	]	PUNCT
ejpam-6395	485	4	s	s	VERB
ejpam-6395	485	5	bashir	bashir	NOUN
ejpam-6395	485	6	and	and	CCONJ
ejpam-6395	485	7	m	m	PROPN
ejpam-6395	485	8	shabir	shabir	PROPN
ejpam-6395	485	9	.	.	PUNCT
ejpam-6395	486	1	pure	pure	ADJ
ejpam-6395	486	2	ideals	ideal	NOUN
ejpam-6395	486	3	in	in	ADP
ejpam-6395	486	4	ternary	ternary	ADJ
ejpam-6395	486	5	semigroups	semigroup	NOUN
ejpam-6395	486	6	.	.	PUNCT
ejpam-6395	487	1	quasigroups	quasigroup	NOUN
ejpam-6395	487	2	and	and	CCONJ
ejpam-6395	487	3	related	related	ADJ
ejpam-6395	487	4	systems	system	NOUN
ejpam-6395	487	5	,	,	PUNCT
ejpam-6395	487	6	17:149–160	17:149–160	PROPN
ejpam-6395	487	7	,	,	PUNCT
ejpam-6395	487	8	2009	2009	NUM
ejpam-6395	487	9	.	.	PUNCT
ejpam-6395	488	1	[	[	X
ejpam-6395	488	2	21	21	NUM
ejpam-6395	488	3	]	]	X
ejpam-6395	488	4	t	t	PROPN
ejpam-6395	488	5	changphas	changphas	PROPN
ejpam-6395	488	6	and	and	CCONJ
ejpam-6395	488	7	j	j	PROPN
ejpam-6395	488	8	sanborisoot	sanborisoot	NOUN
ejpam-6395	488	9	.	.	PUNCT
ejpam-6395	489	1	on	on	ADP
ejpam-6395	489	2	pure	pure	ADJ
ejpam-6395	489	3	ideals	ideal	NOUN
ejpam-6395	489	4	in	in	ADP
ejpam-6395	489	5	ordered	order	VERB
ejpam-6395	489	6	ternary	ternary	ADJ
ejpam-6395	489	7	semigroups	semigroup	NOUN
ejpam-6395	489	8	.	.	PUNCT
ejpam-6395	490	1	thai	thai	PROPN
ejpam-6395	490	2	journal	journal	PROPN
ejpam-6395	490	3	of	of	ADP
ejpam-6395	490	4	mathematics	mathematic	NOUN
ejpam-6395	490	5	,	,	PUNCT
ejpam-6395	490	6	12(2):455–464	12(2):455–464	PROPN
ejpam-6395	490	7	,	,	PUNCT
ejpam-6395	490	8	2014	2014	NUM
ejpam-6395	490	9	.	.	PUNCT
ejpam-6395	491	1	[	[	X
ejpam-6395	491	2	22	22	NUM
ejpam-6395	491	3	]	]	X
ejpam-6395	491	4	t	t	PROPN
ejpam-6395	491	5	changphas	changphas	PROPN
ejpam-6395	491	6	and	and	CCONJ
ejpam-6395	491	7	j	j	PROPN
ejpam-6395	491	8	sanborisoot	sanborisoot	PROPN
ejpam-6395	491	9	.	.	PUNCT
ejpam-6395	492	1	pure	pure	ADJ
ejpam-6395	492	2	ideals	ideal	NOUN
ejpam-6395	492	3	in	in	ADP
ejpam-6395	492	4	ordered	order	VERB
ejpam-6395	492	5	semigroups	semigroup	NOUN
ejpam-6395	492	6	.	.	PUNCT
ejpam-6395	493	1	kyungpook	kyungpook	PROPN
ejpam-6395	493	2	mathematical	mathematical	PROPN
ejpam-6395	493	3	journal	journal	PROPN
ejpam-6395	493	4	,	,	PUNCT
ejpam-6395	493	5	54(1):123–129	54(1):123–129	PROPN
ejpam-6395	493	6	,	,	PUNCT
ejpam-6395	493	7	2014	2014	NUM
ejpam-6395	493	8	.	.	PUNCT