id	sid	tid	token	lemma	pos
ejpam-3591	1	1	european	european	PROPN
ejpam-3591	1	2	journal	journal	PROPN
ejpam-3591	1	3	of	of	ADP
ejpam-3591	1	4	pure	pure	ADJ
ejpam-3591	1	5	and	and	CCONJ
ejpam-3591	1	6	applied	apply	VERB
ejpam-3591	1	7	mathematics	mathematic	NOUN
ejpam-3591	1	8	vol	vol	NOUN
ejpam-3591	1	9	.	.	PROPN
ejpam-3591	2	1	12	12	NUM
ejpam-3591	2	2	,	,	PUNCT
ejpam-3591	2	3	no	no	INTJ
ejpam-3591	2	4	.	.	NOUN
ejpam-3591	2	5	4	4	NUM
ejpam-3591	2	6	,	,	PUNCT
ejpam-3591	2	7	2019	2019	NUM
ejpam-3591	2	8	,	,	PUNCT
ejpam-3591	2	9	1771	1771	NUM
ejpam-3591	2	10	-	-	SYM
ejpam-3591	2	11	1778	1778	NUM
ejpam-3591	2	12	issn	issn	PROPN
ejpam-3591	2	13	1307	1307	NUM
ejpam-3591	2	14	-	-	SYM
ejpam-3591	2	15	5543	5543	NUM
ejpam-3591	2	16	–	–	PUNCT
ejpam-3591	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3591	2	18	published	publish	VERB
ejpam-3591	2	19	by	by	ADP
ejpam-3591	2	20	new	new	PROPN
ejpam-3591	2	21	york	york	PROPN
ejpam-3591	2	22	business	business	PROPN
ejpam-3591	2	23	global	global	PROPN
ejpam-3591	2	24	on	on	ADP
ejpam-3591	2	25	the	the	DET
ejpam-3591	2	26	paper	paper	NOUN
ejpam-3591	2	27	“	"	PUNCT
ejpam-3591	2	28	on	on	ADP
ejpam-3591	2	29	hyperideals	hyperideal	NOUN
ejpam-3591	2	30	of	of	ADP
ejpam-3591	2	31	ordered	order	VERB
ejpam-3591	2	32	semihypergroups	semihypergroup	NOUN
ejpam-3591	2	33	”	"	PUNCT
ejpam-3591	2	34	by	by	ADP
ejpam-3591	2	35	ze	ze	PROPN
ejpam-3591	2	36	gu	gu	NOUN
ejpam-3591	2	37	in	in	ADP
ejpam-3591	2	38	ital	ital	PROPN
ejpam-3591	2	39	.	.	PUNCT
ejpam-3591	3	1	j.	j.	PROPN
ejpam-3591	3	2	pure	pure	PROPN
ejpam-3591	3	3	appl	appl	PROPN
ejpam-3591	3	4	.	.	PUNCT
ejpam-3591	3	5	math	math	PROPN
ejpam-3591	3	6	.	.	PUNCT
ejpam-3591	4	1	niovi	niovi	PROPN
ejpam-3591	4	2	kehayopulu	kehayopulu	ADJ
ejpam-3591	4	3	abstract	abstract	NOUN
ejpam-3591	4	4	.	.	PUNCT
ejpam-3591	5	1	giving	give	VERB
ejpam-3591	5	2	the	the	DET
ejpam-3591	5	3	proper	proper	ADJ
ejpam-3591	5	4	citations	citation	NOUN
ejpam-3591	5	5	,	,	PUNCT
ejpam-3591	5	6	it	it	PRON
ejpam-3591	5	7	is	be	AUX
ejpam-3591	5	8	shown	show	VERB
ejpam-3591	5	9	that	that	SCONJ
ejpam-3591	5	10	,	,	PUNCT
ejpam-3591	5	11	except	except	SCONJ
ejpam-3591	5	12	of	of	ADP
ejpam-3591	5	13	lemma	lemma	PROPN
ejpam-3591	5	14	2.4	2.4	NUM
ejpam-3591	5	15	and	and	CCONJ
ejpam-3591	5	16	theorem	theorem	VERB
ejpam-3591	5	17	2.6	2.6	NUM
ejpam-3591	5	18	,	,	PUNCT
ejpam-3591	5	19	almost	almost	ADV
ejpam-3591	5	20	all	all	DET
ejpam-3591	5	21	the	the	DET
ejpam-3591	5	22	results	result	NOUN
ejpam-3591	5	23	of	of	ADP
ejpam-3591	5	24	the	the	DET
ejpam-3591	5	25	paper	paper	NOUN
ejpam-3591	5	26	in	in	ADP
ejpam-3591	5	27	the	the	DET
ejpam-3591	5	28	title	title	NOUN
ejpam-3591	5	29	have	have	AUX
ejpam-3591	5	30	been	be	AUX
ejpam-3591	5	31	previously	previously	ADV
ejpam-3591	5	32	published	publish	VERB
ejpam-3591	5	33	for	for	ADP
ejpam-3591	5	34	ordered	order	VERB
ejpam-3591	5	35	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	5	36	in	in	ADP
ejpam-3591	5	37	eur	eur	PROPN
ejpam-3591	5	38	.	.	PUNCT
ejpam-3591	6	1	j.	j.	PROPN
ejpam-3591	6	2	pure	pure	PROPN
ejpam-3591	6	3	appl	appl	PROPN
ejpam-3591	6	4	.	.	PUNCT
ejpam-3591	6	5	math	math	PROPN
ejpam-3591	6	6	.	.	PUNCT
ejpam-3591	7	1	and	and	CCONJ
ejpam-3591	7	2	they	they	PRON
ejpam-3591	7	3	are	be	AUX
ejpam-3591	7	4	not	not	PART
ejpam-3591	7	5	new	new	ADJ
ejpam-3591	7	6	.	.	PUNCT
ejpam-3591	8	1	there	there	PRON
ejpam-3591	8	2	are	be	VERB
ejpam-3591	8	3	also	also	ADV
ejpam-3591	8	4	two	two	NUM
ejpam-3591	8	5	results	result	NOUN
ejpam-3591	8	6	obtained	obtain	VERB
ejpam-3591	8	7	from	from	ADP
ejpam-3591	8	8	ordered	order	VERB
ejpam-3591	8	9	semigroups	semigroup	NOUN
ejpam-3591	8	10	just	just	ADV
ejpam-3591	8	11	putting	put	VERB
ejpam-3591	8	12	a	a	DET
ejpam-3591	8	13	“	"	PUNCT
ejpam-3591	8	14	◦	◦	NOUN
ejpam-3591	8	15	”	"	PUNCT
ejpam-3591	8	16	instead	instead	ADV
ejpam-3591	8	17	of	of	ADP
ejpam-3591	8	18	“	"	PUNCT
ejpam-3591	8	19	·	·	PUNCT
ejpam-3591	8	20	”	"	PUNCT
ejpam-3591	8	21	(	(	PUNCT
ejpam-3591	8	22	that	that	PRON
ejpam-3591	8	23	is	be	AUX
ejpam-3591	8	24	n’t	not	PART
ejpam-3591	8	25	a	a	DET
ejpam-3591	8	26	correct	correct	ADJ
ejpam-3591	8	27	way	way	NOUN
ejpam-3591	8	28	to	to	ADP
ejpam-3591	8	29	work	work	VERB
ejpam-3591	8	30	)	)	PUNCT
ejpam-3591	8	31	,	,	PUNCT
ejpam-3591	8	32	without	without	ADP
ejpam-3591	8	33	reference	reference	NOUN
ejpam-3591	8	34	to	to	PART
ejpam-3591	8	35	ordered	order	VERB
ejpam-3591	8	36	semigroups	semigroup	NOUN
ejpam-3591	8	37	on	on	ADP
ejpam-3591	8	38	which	which	PRON
ejpam-3591	8	39	the	the	DET
ejpam-3591	8	40	results	result	NOUN
ejpam-3591	8	41	on	on	ADP
ejpam-3591	8	42	ordered	order	VERB
ejpam-3591	8	43	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	8	44	are	be	AUX
ejpam-3591	8	45	based	base	VERB
ejpam-3591	8	46	.	.	PUNCT
ejpam-3591	9	1	one	one	NUM
ejpam-3591	9	2	of	of	ADP
ejpam-3591	9	3	them	they	PRON
ejpam-3591	9	4	can	can	AUX
ejpam-3591	9	5	be	be	AUX
ejpam-3591	9	6	obtained	obtain	VERB
ejpam-3591	9	7	as	as	ADP
ejpam-3591	9	8	corollary	corollary	ADJ
ejpam-3591	9	9	to	to	ADP
ejpam-3591	9	10	a	a	DET
ejpam-3591	9	11	theorem	theorem	NOUN
ejpam-3591	9	12	in	in	ADP
ejpam-3591	9	13	eur	eur	PROPN
ejpam-3591	9	14	.	.	PUNCT
ejpam-3591	10	1	j.	j.	PROPN
ejpam-3591	10	2	pure	pure	PROPN
ejpam-3591	10	3	appl	appl	PROPN
ejpam-3591	10	4	.	.	PUNCT
ejpam-3591	10	5	math	math	NOUN
ejpam-3591	10	6	.	.	PUNCT
ejpam-3591	11	1	as	as	ADV
ejpam-3591	11	2	well	well	ADV
ejpam-3591	11	3	,	,	PUNCT
ejpam-3591	11	4	and	and	CCONJ
ejpam-3591	11	5	it	it	PRON
ejpam-3591	11	6	is	be	AUX
ejpam-3591	11	7	not	not	PART
ejpam-3591	11	8	new	new	ADJ
ejpam-3591	11	9	.	.	PUNCT
ejpam-3591	12	1	2010	2010	NUM
ejpam-3591	12	2	mathematics	mathematic	NOUN
ejpam-3591	12	3	subject	subject	NOUN
ejpam-3591	12	4	classifications	classification	NOUN
ejpam-3591	12	5	:	:	PUNCT
ejpam-3591	12	6	06f99	06f99	X
ejpam-3591	12	7	key	key	ADJ
ejpam-3591	12	8	words	word	NOUN
ejpam-3591	12	9	and	and	CCONJ
ejpam-3591	12	10	phrases	phrase	NOUN
ejpam-3591	12	11	:	:	PUNCT
ejpam-3591	12	12	ordered	order	VERB
ejpam-3591	12	13	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	12	14	,	,	PUNCT
ejpam-3591	12	15	ideal	ideal	ADJ
ejpam-3591	12	16	,	,	PUNCT
ejpam-3591	12	17	prime	prime	ADJ
ejpam-3591	12	18	,	,	PUNCT
ejpam-3591	12	19	weakly	weakly	ADJ
ejpam-3591	12	20	prime	prime	ADJ
ejpam-3591	12	21	,	,	PUNCT
ejpam-3591	12	22	semiprime	semiprime	NOUN
ejpam-3591	12	23	,	,	PUNCT
ejpam-3591	12	24	weakly	weakly	ADJ
ejpam-3591	12	25	semiprime	semiprime	NOUN
ejpam-3591	12	26	,	,	PUNCT
ejpam-3591	12	27	irreducible	irreducible	ADJ
ejpam-3591	12	28	1	1	NUM
ejpam-3591	12	29	.	.	PUNCT
ejpam-3591	13	1	introduction	introduction	NOUN
ejpam-3591	13	2	the	the	DET
ejpam-3591	13	3	paper	paper	NOUN
ejpam-3591	13	4	consists	consist	VERB
ejpam-3591	13	5	of	of	ADP
ejpam-3591	13	6	lemma	lemma	PROPN
ejpam-3591	13	7	2.3	2.3	NUM
ejpam-3591	13	8	,	,	PUNCT
ejpam-3591	13	9	lemma	lemma	PROPN
ejpam-3591	13	10	2.4	2.4	NUM
ejpam-3591	13	11	,	,	PUNCT
ejpam-3591	13	12	theorem	theorem	VERB
ejpam-3591	13	13	2.5	2.5	NUM
ejpam-3591	13	14	,	,	PUNCT
ejpam-3591	13	15	theorem	theorem	VERB
ejpam-3591	13	16	2.6	2.6	NUM
ejpam-3591	13	17	,	,	PUNCT
ejpam-3591	13	18	theorem	theorem	VERB
ejpam-3591	13	19	3.1	3.1	NUM
ejpam-3591	13	20	,	,	PUNCT
ejpam-3591	13	21	theorem	theorem	VERB
ejpam-3591	13	22	3.2	3.2	NUM
ejpam-3591	13	23	,	,	PUNCT
ejpam-3591	13	24	theorem	theorem	VERB
ejpam-3591	13	25	3.3	3.3	NUM
ejpam-3591	13	26	,	,	PUNCT
ejpam-3591	13	27	theorem	theorem	VERB
ejpam-3591	13	28	3.4	3.4	NUM
ejpam-3591	13	29	and	and	CCONJ
ejpam-3591	13	30	the	the	DET
ejpam-3591	13	31	example	example	NOUN
ejpam-3591	13	32	3.5	3.5	NUM
ejpam-3591	13	33	.	.	PUNCT
ejpam-3591	14	1	lemma	lemma	PROPN
ejpam-3591	14	2	2.3	2.3	NUM
ejpam-3591	14	3	is	be	AUX
ejpam-3591	14	4	known	know	VERB
ejpam-3591	14	5	,	,	PUNCT
ejpam-3591	14	6	a	a	DET
ejpam-3591	14	7	reference	reference	NOUN
ejpam-3591	14	8	was	be	AUX
ejpam-3591	14	9	needed	need	VERB
ejpam-3591	14	10	in	in	ADP
ejpam-3591	14	11	it	it	PRON
ejpam-3591	14	12	.	.	PUNCT
ejpam-3591	15	1	concerning	concern	VERB
ejpam-3591	15	2	theorem	theorem	VERB
ejpam-3591	15	3	2.5	2.5	NUM
ejpam-3591	15	4	(	(	PUNCT
ejpam-3591	15	5	one	one	NUM
ejpam-3591	15	6	of	of	ADP
ejpam-3591	15	7	the	the	DET
ejpam-3591	15	8	main	main	ADJ
ejpam-3591	15	9	theorems	theorem	NOUN
ejpam-3591	15	10	of	of	ADP
ejpam-3591	15	11	the	the	DET
ejpam-3591	15	12	paper	paper	NOUN
ejpam-3591	15	13	):	):	PUNCT
ejpam-3591	15	14	the	the	DET
ejpam-3591	15	15	proposition	proposition	NOUN
ejpam-3591	15	16	in	in	ADP
ejpam-3591	15	17	[	[	X
ejpam-3591	15	18	7	7	NUM
ejpam-3591	15	19	]	]	PUNCT
ejpam-3591	15	20	published	publish	VERB
ejpam-3591	15	21	for	for	ADP
ejpam-3591	15	22	ordered	order	VERB
ejpam-3591	15	23	semigroups	semigroup	NOUN
ejpam-3591	15	24	in	in	ADP
ejpam-3591	15	25	1992	1992	NUM
ejpam-3591	15	26	,	,	PUNCT
ejpam-3591	15	27	has	have	AUX
ejpam-3591	15	28	been	be	AUX
ejpam-3591	15	29	transferred	transfer	VERB
ejpam-3591	15	30	to	to	PART
ejpam-3591	15	31	ordered	order	VERB
ejpam-3591	15	32	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	15	33	just	just	ADV
ejpam-3591	15	34	putting	put	VERB
ejpam-3591	15	35	“	"	PUNCT
ejpam-3591	15	36	◦	◦	NOUN
ejpam-3591	15	37	”	"	PUNCT
ejpam-3591	15	38	instead	instead	ADV
ejpam-3591	15	39	of	of	ADP
ejpam-3591	15	40	“	"	PUNCT
ejpam-3591	15	41	·	·	PUNCT
ejpam-3591	15	42	”	"	PUNCT
ejpam-3591	15	43	.	.	PUNCT
ejpam-3591	16	1	except	except	SCONJ
ejpam-3591	16	2	of	of	ADP
ejpam-3591	16	3	the	the	DET
ejpam-3591	16	4	fact	fact	NOUN
ejpam-3591	16	5	that	that	SCONJ
ejpam-3591	16	6	this	this	PRON
ejpam-3591	16	7	is	be	AUX
ejpam-3591	16	8	not	not	PART
ejpam-3591	16	9	enough	enough	ADJ
ejpam-3591	16	10	to	to	PART
ejpam-3591	16	11	pass	pass	VERB
ejpam-3591	16	12	from	from	ADP
ejpam-3591	16	13	ordered	order	VERB
ejpam-3591	16	14	semigroup	semigroup	PROPN
ejpam-3591	16	15	to	to	PART
ejpam-3591	16	16	ordered	order	VERB
ejpam-3591	16	17	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	16	18	(	(	PUNCT
ejpam-3591	16	19	symbols	symbol	NOUN
ejpam-3591	16	20	like	like	ADP
ejpam-3591	16	21	s	s	NOUN
ejpam-3591	16	22	◦	◦	NOUN
ejpam-3591	16	23	b	b	PRON
ejpam-3591	16	24	◦	◦	NOUN
ejpam-3591	16	25	s	s	NOUN
ejpam-3591	16	26	◦	◦	NOUN
ejpam-3591	16	27	s	s	NOUN
ejpam-3591	16	28	◦	◦	NOUN
ejpam-3591	16	29	a	a	DET
ejpam-3591	16	30	◦	◦	NOUN
ejpam-3591	16	31	s	s	PART
ejpam-3591	16	32	have	have	AUX
ejpam-3591	16	33	no	no	DET
ejpam-3591	16	34	sense	sense	NOUN
ejpam-3591	16	35	)	)	PUNCT
ejpam-3591	16	36	and	and	CCONJ
ejpam-3591	16	37	that	that	SCONJ
ejpam-3591	16	38	there	there	PRON
ejpam-3591	16	39	is	be	VERB
ejpam-3591	16	40	no	no	DET
ejpam-3591	16	41	reference	reference	NOUN
ejpam-3591	16	42	to	to	PART
ejpam-3591	16	43	ordered	order	VERB
ejpam-3591	16	44	semigroup	semigroup	NOUN
ejpam-3591	16	45	on	on	ADP
ejpam-3591	16	46	which	which	PRON
ejpam-3591	16	47	it	it	PRON
ejpam-3591	16	48	is	be	AUX
ejpam-3591	16	49	based	base	VERB
ejpam-3591	16	50	,	,	PUNCT
ejpam-3591	16	51	this	this	DET
ejpam-3591	16	52	theorem	theorem	NOUN
ejpam-3591	16	53	is	be	AUX
ejpam-3591	16	54	an	an	DET
ejpam-3591	16	55	immediate	immediate	ADJ
ejpam-3591	16	56	consequence	consequence	NOUN
ejpam-3591	16	57	of	of	ADP
ejpam-3591	16	58	theorem	theorem	NOUN
ejpam-3591	16	59	23	23	NUM
ejpam-3591	16	60	in	in	ADP
ejpam-3591	16	61	[	[	X
ejpam-3591	16	62	10	10	NUM
ejpam-3591	16	63	]	]	PUNCT
ejpam-3591	16	64	and	and	CCONJ
ejpam-3591	16	65	it	it	PRON
ejpam-3591	16	66	is	be	AUX
ejpam-3591	16	67	not	not	PART
ejpam-3591	16	68	new	new	ADJ
ejpam-3591	16	69	(	(	PUNCT
ejpam-3591	16	70	see	see	VERB
ejpam-3591	16	71	also	also	ADV
ejpam-3591	16	72	the	the	DET
ejpam-3591	16	73	equivalence	equivalence	NOUN
ejpam-3591	16	74	(	(	PUNCT
ejpam-3591	16	75	1)⇔	1)⇔	NUM
ejpam-3591	16	76	(	(	PUNCT
ejpam-3591	16	77	2	2	NUM
ejpam-3591	16	78	)	)	PUNCT
ejpam-3591	16	79	in	in	ADP
ejpam-3591	16	80	corollary	corollary	ADJ
ejpam-3591	16	81	24	24	NUM
ejpam-3591	16	82	in	in	ADP
ejpam-3591	16	83	[	[	X
ejpam-3591	16	84	10	10	NUM
ejpam-3591	16	85	]	]	PUNCT
ejpam-3591	16	86	and	and	CCONJ
ejpam-3591	16	87	the	the	DET
ejpam-3591	16	88	remark	remark	NOUN
ejpam-3591	16	89	after	after	ADP
ejpam-3591	16	90	that	that	PRON
ejpam-3591	16	91	)	)	PUNCT
ejpam-3591	16	92	.	.	PUNCT
ejpam-3591	17	1	theorem	theorem	VERB
ejpam-3591	17	2	3.1	3.1	NUM
ejpam-3591	17	3	(	(	PUNCT
ejpam-3591	17	4	one	one	NUM
ejpam-3591	17	5	of	of	ADP
ejpam-3591	17	6	the	the	DET
ejpam-3591	17	7	main	main	ADJ
ejpam-3591	17	8	theorems	theorem	NOUN
ejpam-3591	17	9	)	)	PUNCT
ejpam-3591	17	10	is	be	AUX
ejpam-3591	17	11	not	not	PART
ejpam-3591	17	12	new	new	ADJ
ejpam-3591	17	13	.	.	PUNCT
ejpam-3591	18	1	it	it	PRON
ejpam-3591	18	2	has	have	AUX
ejpam-3591	18	3	been	be	AUX
ejpam-3591	18	4	published	publish	VERB
ejpam-3591	18	5	in	in	ADP
ejpam-3591	18	6	theorems	theorem	NOUN
ejpam-3591	18	7	9	9	NUM
ejpam-3591	18	8	and	and	CCONJ
ejpam-3591	18	9	18	18	NUM
ejpam-3591	18	10	in	in	ADP
ejpam-3591	18	11	[	[	X
ejpam-3591	18	12	10	10	NUM
ejpam-3591	18	13	]	]	PUNCT
ejpam-3591	18	14	.	.	PUNCT
ejpam-3591	19	1	regarding	regard	VERB
ejpam-3591	19	2	the	the	DET
ejpam-3591	19	3	proof	proof	NOUN
ejpam-3591	19	4	of	of	ADP
ejpam-3591	19	5	the	the	DET
ejpam-3591	19	6	implication	implication	NOUN
ejpam-3591	19	7	(	(	PUNCT
ejpam-3591	19	8	4)⇒	4)⇒	X
ejpam-3591	19	9	(	(	PUNCT
ejpam-3591	19	10	1	1	NUM
ejpam-3591	19	11	)	)	PUNCT
ejpam-3591	19	12	of	of	ADP
ejpam-3591	19	13	this	this	DET
ejpam-3591	19	14	theorem	theorem	NOUN
ejpam-3591	19	15	,	,	PUNCT
ejpam-3591	19	16	this	this	PRON
ejpam-3591	19	17	is	be	AUX
ejpam-3591	19	18	actually	actually	ADV
ejpam-3591	19	19	the	the	DET
ejpam-3591	19	20	proof	proof	NOUN
ejpam-3591	19	21	of	of	ADP
ejpam-3591	19	22	(	(	PUNCT
ejpam-3591	19	23	3)⇒	3)⇒	NUM
ejpam-3591	19	24	(	(	PUNCT
ejpam-3591	19	25	1	1	NUM
ejpam-3591	19	26	)	)	PUNCT
ejpam-3591	19	27	of	of	ADP
ejpam-3591	19	28	the	the	DET
ejpam-3591	19	29	same	same	ADJ
ejpam-3591	19	30	theorem	theorem	NOUN
ejpam-3591	19	31	.	.	PUNCT
ejpam-3591	20	1	it	it	PRON
ejpam-3591	20	2	is	be	AUX
ejpam-3591	20	3	well	well	ADV
ejpam-3591	20	4	known	know	VERB
ejpam-3591	20	5	that	that	SCONJ
ejpam-3591	20	6	an	an	DET
ejpam-3591	20	7	ordered	order	VERB
ejpam-3591	20	8	semigroup	semigroup	NOUN
ejpam-3591	20	9	s	s	VERB
ejpam-3591	20	10	is	be	AUX
ejpam-3591	20	11	intra	intra	ADJ
ejpam-3591	20	12	-	-	ADJ
ejpam-3591	20	13	regular	regular	ADJ
ejpam-3591	20	14	if	if	SCONJ
ejpam-3591	20	15	and	and	CCONJ
ejpam-3591	20	16	only	only	ADV
ejpam-3591	20	17	if	if	SCONJ
ejpam-3591	20	18	every	every	DET
ejpam-3591	20	19	ideal	ideal	NOUN
ejpam-3591	20	20	of	of	ADP
ejpam-3591	20	21	s	s	PROPN
ejpam-3591	20	22	is	be	AUX
ejpam-3591	20	23	semiprime	semiprime	NOUN
ejpam-3591	20	24	.	.	PUNCT
ejpam-3591	21	1	see	see	VERB
ejpam-3591	21	2	,	,	PUNCT
ejpam-3591	21	3	for	for	ADP
ejpam-3591	21	4	example	example	NOUN
ejpam-3591	21	5	,	,	PUNCT
ejpam-3591	21	6	remark	remark	VERB
ejpam-3591	21	7	3	3	NUM
ejpam-3591	21	8	in	in	ADP
ejpam-3591	21	9	[	[	X
ejpam-3591	21	10	8	8	NUM
ejpam-3591	21	11	]	]	PUNCT
ejpam-3591	21	12	or	or	CCONJ
ejpam-3591	21	13	the	the	DET
ejpam-3591	21	14	proof	proof	NOUN
ejpam-3591	21	15	of	of	ADP
ejpam-3591	21	16	theorem	theorem	NOUN
ejpam-3591	21	17	2	2	NUM
ejpam-3591	21	18	in	in	ADP
ejpam-3591	21	19	[	[	X
ejpam-3591	21	20	7	7	NUM
ejpam-3591	21	21	]	]	PUNCT
ejpam-3591	21	22	.	.	PUNCT
ejpam-3591	22	1	if	if	SCONJ
ejpam-3591	22	2	doi	doi	X
ejpam-3591	22	3	:	:	PUNCT
ejpam-3591	22	4	https://doi.org/10.29020/nybg.ejpam.v12i4.3592	https://doi.org/10.29020/nybg.ejpam.v12i4.3592	DET
ejpam-3591	22	5	email	email	NOUN
ejpam-3591	22	6	address	address	NOUN
ejpam-3591	22	7	:	:	PUNCT
ejpam-3591	22	8	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3591	22	9	(	(	PUNCT
ejpam-3591	22	10	n.	n.	PROPN
ejpam-3591	22	11	kehayopulu	kehayopulu	PROPN
ejpam-3591	22	12	)	)	PUNCT
ejpam-3591	22	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3591	22	14	1771	1771	NUM
ejpam-3591	23	1	c	c	X
ejpam-3591	23	2	©	©	PROPN
ejpam-3591	23	3	2019	2019	NUM
ejpam-3591	23	4	ejpam	ejpam	NOUN
ejpam-3591	23	5	all	all	DET
ejpam-3591	23	6	rights	right	NOUN
ejpam-3591	23	7	reserved	reserve	VERB
ejpam-3591	23	8	.	.	PUNCT
ejpam-3591	24	1	n.	n.	PROPN
ejpam-3591	24	2	kehayopulu	kehayopulu	PROPN
ejpam-3591	24	3	/	/	SYM
ejpam-3591	24	4	eur	eur	PROPN
ejpam-3591	24	5	.	.	PUNCT
ejpam-3591	25	1	j.	j.	PROPN
ejpam-3591	25	2	pure	pure	PROPN
ejpam-3591	25	3	appl	appl	PROPN
ejpam-3591	25	4	.	.	PROPN
ejpam-3591	25	5	math	math	PROPN
ejpam-3591	25	6	,	,	PUNCT
ejpam-3591	25	7	12	12	NUM
ejpam-3591	25	8	(	(	PUNCT
ejpam-3591	25	9	4	4	NUM
ejpam-3591	25	10	)	)	PUNCT
ejpam-3591	25	11	(	(	PUNCT
ejpam-3591	25	12	2019	2019	NUM
ejpam-3591	25	13	)	)	PUNCT
ejpam-3591	25	14	,	,	PUNCT
ejpam-3591	25	15	1771	1771	NUM
ejpam-3591	25	16	-	-	SYM
ejpam-3591	25	17	1778	1778	NUM
ejpam-3591	25	18	1772	1772	NUM
ejpam-3591	25	19	we	we	PRON
ejpam-3591	25	20	get	get	VERB
ejpam-3591	25	21	the	the	DET
ejpam-3591	25	22	proof	proof	NOUN
ejpam-3591	25	23	from	from	ADP
ejpam-3591	25	24	[	[	X
ejpam-3591	25	25	7	7	NUM
ejpam-3591	25	26	]	]	PUNCT
ejpam-3591	25	27	,	,	PUNCT
ejpam-3591	25	28	delete	delete	VERB
ejpam-3591	25	29	the	the	DET
ejpam-3591	25	30	“	"	PUNCT
ejpam-3591	25	31	·	·	PUNCT
ejpam-3591	25	32	”	"	PUNCT
ejpam-3591	25	33	and	and	CCONJ
ejpam-3591	25	34	put	put	VERB
ejpam-3591	25	35	“	"	PUNCT
ejpam-3591	25	36	◦	◦	NOUN
ejpam-3591	25	37	”	"	PUNCT
ejpam-3591	25	38	instead	instead	ADV
ejpam-3591	25	39	,	,	PUNCT
ejpam-3591	25	40	then	then	ADV
ejpam-3591	25	41	this	this	PRON
ejpam-3591	25	42	is	be	AUX
ejpam-3591	25	43	the	the	DET
ejpam-3591	25	44	theorem	theorem	ADJ
ejpam-3591	25	45	3.2	3.2	NUM
ejpam-3591	25	46	in	in	ADP
ejpam-3591	25	47	[	[	X
ejpam-3591	25	48	4	4	NUM
ejpam-3591	25	49	]	]	PUNCT
ejpam-3591	25	50	;	;	PUNCT
ejpam-3591	25	51	without	without	ADP
ejpam-3591	25	52	reference	reference	NOUN
ejpam-3591	25	53	to	to	PART
ejpam-3591	25	54	ordered	order	VERB
ejpam-3591	25	55	semigroups	semigroup	NOUN
ejpam-3591	25	56	and	and	CCONJ
ejpam-3591	25	57	with	with	ADP
ejpam-3591	25	58	the	the	DET
ejpam-3591	25	59	problem	problem	NOUN
ejpam-3591	25	60	of	of	ADP
ejpam-3591	25	61	using	use	VERB
ejpam-3591	25	62	symbols	symbol	NOUN
ejpam-3591	25	63	like	like	ADP
ejpam-3591	25	64	s	s	PRON
ejpam-3591	25	65	◦	◦	NOUN
ejpam-3591	25	66	a	a	DET
ejpam-3591	25	67	◦	◦	NOUN
ejpam-3591	25	68	a	a	DET
ejpam-3591	25	69	◦	◦	NOUN
ejpam-3591	25	70	s	s	NUM
ejpam-3591	25	71	in	in	ADP
ejpam-3591	25	72	its	its	PRON
ejpam-3591	25	73	proof	proof	NOUN
ejpam-3591	25	74	.	.	PUNCT
ejpam-3591	26	1	theorem	theorem	VERB
ejpam-3591	26	2	3.3	3.3	NUM
ejpam-3591	26	3	is	be	AUX
ejpam-3591	26	4	the	the	DET
ejpam-3591	26	5	theorem	theorem	NOUN
ejpam-3591	26	6	19	19	NUM
ejpam-3591	26	7	in	in	ADP
ejpam-3591	26	8	[	[	X
ejpam-3591	26	9	10	10	NUM
ejpam-3591	26	10	]	]	PUNCT
ejpam-3591	26	11	.	.	PUNCT
ejpam-3591	27	1	this	this	PRON
ejpam-3591	27	2	is	be	AUX
ejpam-3591	27	3	because	because	SCONJ
ejpam-3591	27	4	an	an	DET
ejpam-3591	27	5	ordered	order	VERB
ejpam-3591	27	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	27	7	s	s	PART
ejpam-3591	27	8	is	be	AUX
ejpam-3591	27	9	semisimple	semisimple	ADJ
ejpam-3591	27	10	if	if	SCONJ
ejpam-3591	27	11	and	and	CCONJ
ejpam-3591	27	12	only	only	ADV
ejpam-3591	27	13	it	it	PRON
ejpam-3591	27	14	the	the	DET
ejpam-3591	27	15	ideals	ideal	NOUN
ejpam-3591	27	16	of	of	ADP
ejpam-3591	27	17	s	s	NOUN
ejpam-3591	27	18	are	be	AUX
ejpam-3591	27	19	idempotent	idempotent	ADJ
ejpam-3591	27	20	(	(	PUNCT
ejpam-3591	27	21	see	see	VERB
ejpam-3591	27	22	the	the	DET
ejpam-3591	27	23	theorem	theorem	NOUN
ejpam-3591	27	24	18	18	NUM
ejpam-3591	27	25	in	in	ADP
ejpam-3591	27	26	[	[	X
ejpam-3591	27	27	10	10	NUM
ejpam-3591	27	28	]	]	NUM
ejpam-3591	27	29	)	)	PUNCT
ejpam-3591	27	30	.	.	PUNCT
ejpam-3591	28	1	theorem	theorem	VERB
ejpam-3591	28	2	3.4	3.4	NUM
ejpam-3591	28	3	is	be	AUX
ejpam-3591	28	4	the	the	DET
ejpam-3591	28	5	theorem	theorem	NOUN
ejpam-3591	28	6	23	23	NUM
ejpam-3591	28	7	in	in	ADP
ejpam-3591	28	8	[	[	X
ejpam-3591	28	9	10	10	NUM
ejpam-3591	28	10	]	]	PUNCT
ejpam-3591	28	11	.	.	PUNCT
ejpam-3591	29	1	this	this	DET
ejpam-3591	29	2	theorem	theorem	NOUN
ejpam-3591	29	3	is	be	AUX
ejpam-3591	29	4	correct	correct	ADJ
ejpam-3591	29	5	,	,	PUNCT
ejpam-3591	29	6	but	but	CCONJ
ejpam-3591	29	7	its	its	PRON
ejpam-3591	29	8	proof	proof	NOUN
ejpam-3591	29	9	is	be	AUX
ejpam-3591	29	10	wrong	wrong	ADJ
ejpam-3591	29	11	in	in	ADP
ejpam-3591	29	12	[	[	X
ejpam-3591	29	13	4	4	NUM
ejpam-3591	29	14	]	]	PUNCT
ejpam-3591	29	15	.	.	PUNCT
ejpam-3591	30	1	see	see	VERB
ejpam-3591	30	2	the	the	DET
ejpam-3591	30	3	proof	proof	NOUN
ejpam-3591	30	4	of	of	ADP
ejpam-3591	30	5	theorem	theorem	NOUN
ejpam-3591	30	6	23	23	NUM
ejpam-3591	30	7	in	in	ADP
ejpam-3591	30	8	[	[	X
ejpam-3591	30	9	10	10	NUM
ejpam-3591	30	10	]	]	PUNCT
ejpam-3591	30	11	.	.	PUNCT
ejpam-3591	31	1	the	the	DET
ejpam-3591	31	2	example	example	NOUN
ejpam-3591	31	3	3.5	3.5	NUM
ejpam-3591	31	4	is	be	AUX
ejpam-3591	31	5	the	the	DET
ejpam-3591	31	6	example	example	NOUN
ejpam-3591	31	7	b	b	NOUN
ejpam-3591	31	8	in	in	ADP
ejpam-3591	31	9	[	[	X
ejpam-3591	31	10	10	10	NUM
ejpam-3591	31	11	]	]	PUNCT
ejpam-3591	31	12	,	,	PUNCT
ejpam-3591	31	13	there	there	PRON
ejpam-3591	31	14	is	be	VERB
ejpam-3591	31	15	reference	reference	NOUN
ejpam-3591	31	16	to	to	ADP
ejpam-3591	31	17	this	this	DET
ejpam-3591	31	18	example	example	NOUN
ejpam-3591	31	19	.	.	PUNCT
ejpam-3591	32	1	according	accord	VERB
ejpam-3591	32	2	to	to	ADP
ejpam-3591	32	3	the	the	DET
ejpam-3591	32	4	author	author	NOUN
ejpam-3591	32	5	,	,	PUNCT
ejpam-3591	32	6	one	one	PRON
ejpam-3591	32	7	can	can	AUX
ejpam-3591	32	8	check	check	VERB
ejpam-3591	32	9	that	that	SCONJ
ejpam-3591	32	10	this	this	PRON
ejpam-3591	32	11	is	be	AUX
ejpam-3591	32	12	really	really	ADV
ejpam-3591	32	13	an	an	DET
ejpam-3591	32	14	ordered	order	VERB
ejpam-3591	32	15	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	32	16	.	.	PUNCT
ejpam-3591	33	1	we	we	PRON
ejpam-3591	33	2	never	never	ADV
ejpam-3591	33	3	check	check	VERB
ejpam-3591	33	4	the	the	DET
ejpam-3591	33	5	ordered	order	VERB
ejpam-3591	33	6	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	33	7	given	give	VERB
ejpam-3591	33	8	by	by	ADP
ejpam-3591	33	9	a	a	DET
ejpam-3591	33	10	table	table	NOUN
ejpam-3591	33	11	and	and	CCONJ
ejpam-3591	33	12	an	an	DET
ejpam-3591	33	13	order	order	NOUN
ejpam-3591	33	14	by	by	ADP
ejpam-3591	33	15	hand	hand	NOUN
ejpam-3591	33	16	.	.	PUNCT
ejpam-3591	34	1	everything	everything	PRON
ejpam-3591	34	2	is	be	AUX
ejpam-3591	34	3	explained	explain	VERB
ejpam-3591	34	4	in	in	ADP
ejpam-3591	34	5	detail	detail	NOUN
ejpam-3591	34	6	in	in	ADP
ejpam-3591	34	7	the	the	DET
ejpam-3591	34	8	next	next	ADJ
ejpam-3591	34	9	section	section	NOUN
ejpam-3591	34	10	.	.	PUNCT
ejpam-3591	35	1	2	2	X
ejpam-3591	35	2	.	.	X
ejpam-3591	35	3	remarks	remark	NOUN
ejpam-3591	35	4	this	this	PRON
ejpam-3591	35	5	is	be	AUX
ejpam-3591	35	6	from	from	ADP
ejpam-3591	35	7	the	the	DET
ejpam-3591	35	8	introduction	introduction	NOUN
ejpam-3591	35	9	of	of	ADP
ejpam-3591	35	10	the	the	DET
ejpam-3591	35	11	paper	paper	NOUN
ejpam-3591	35	12	in	in	ADP
ejpam-3591	35	13	the	the	DET
ejpam-3591	35	14	title	title	NOUN
ejpam-3591	35	15	:	:	PUNCT
ejpam-3591	35	16	“	"	PUNCT
ejpam-3591	35	17	motivated	motivate	VERB
ejpam-3591	35	18	by	by	ADP
ejpam-3591	35	19	the	the	DET
ejpam-3591	35	20	previous	previous	ADJ
ejpam-3591	35	21	work	work	NOUN
ejpam-3591	35	22	on	on	ADP
ejpam-3591	35	23	hyperideals	hyperideal	NOUN
ejpam-3591	35	24	of	of	ADP
ejpam-3591	35	25	(	(	PUNCT
ejpam-3591	35	26	ordered	order	VERB
ejpam-3591	35	27	)	)	PUNCT
ejpam-3591	35	28	semihypergroups	semihypergroup	NOUN
ejpam-3591	35	29	,	,	PUNCT
ejpam-3591	35	30	we	we	PRON
ejpam-3591	35	31	attempt	attempt	VERB
ejpam-3591	35	32	in	in	ADP
ejpam-3591	35	33	the	the	DET
ejpam-3591	35	34	present	present	ADJ
ejpam-3591	35	35	paper	paper	NOUN
ejpam-3591	35	36	to	to	PART
ejpam-3591	35	37	study	study	VERB
ejpam-3591	35	38	hyperideals	hyperideal	NOUN
ejpam-3591	35	39	of	of	ADP
ejpam-3591	35	40	ordered	order	VERB
ejpam-3591	35	41	semihypergroups	semihypergroup	NOUN
ejpam-3591	35	42	in	in	ADP
ejpam-3591	35	43	detail	detail	NOUN
ejpam-3591	35	44	.	.	PUNCT
ejpam-3591	36	1	in	in	ADP
ejpam-3591	36	2	this	this	DET
ejpam-3591	36	3	article	article	NOUN
ejpam-3591	36	4	,	,	PUNCT
ejpam-3591	36	5	we	we	PRON
ejpam-3591	36	6	introduce	introduce	VERB
ejpam-3591	36	7	the	the	DET
ejpam-3591	36	8	notion	notion	NOUN
ejpam-3591	36	9	of	of	ADP
ejpam-3591	36	10	weakly	weakly	ADJ
ejpam-3591	36	11	semiprime	semiprime	NOUN
ejpam-3591	36	12	and	and	CCONJ
ejpam-3591	36	13	irreducible	irreducible	ADJ
ejpam-3591	36	14	hyperideals	hyperideal	NOUN
ejpam-3591	36	15	in	in	ADP
ejpam-3591	36	16	ordered	order	VERB
ejpam-3591	36	17	semihypergroups	semihypergroup	NOUN
ejpam-3591	36	18	,	,	PUNCT
ejpam-3591	36	19	and	and	CCONJ
ejpam-3591	36	20	moreover	moreover	ADV
ejpam-3591	36	21	establish	establish	VERB
ejpam-3591	36	22	the	the	DET
ejpam-3591	36	23	relationship	relationship	NOUN
ejpam-3591	36	24	between	between	ADP
ejpam-3591	36	25	the	the	DET
ejpam-3591	36	26	five	five	NUM
ejpam-3591	36	27	classes	class	NOUN
ejpam-3591	36	28	of	of	ADP
ejpam-3591	36	29	hyperideals	hyperideal	NOUN
ejpam-3591	36	30	.	.	PUNCT
ejpam-3591	37	1	finally	finally	ADV
ejpam-3591	37	2	semisimple	semisimple	PROPN
ejpam-3591	37	3	ordered	order	VERB
ejpam-3591	37	4	semihypergroups	semihypergroup	NOUN
ejpam-3591	37	5	and	and	CCONJ
ejpam-3591	37	6	intra	intra	ADJ
ejpam-3591	37	7	-	-	ADJ
ejpam-3591	37	8	regular	regular	ADJ
ejpam-3591	37	9	ordered	order	VERB
ejpam-3591	37	10	semihypergroups	semihypergroup	NOUN
ejpam-3591	37	11	are	be	AUX
ejpam-3591	37	12	characterized	characterize	VERB
ejpam-3591	37	13	in	in	ADP
ejpam-3591	37	14	terms	term	NOUN
ejpam-3591	37	15	of	of	ADP
ejpam-3591	37	16	these	these	DET
ejpam-3591	37	17	hyperideals	hyperideal	NOUN
ejpam-3591	37	18	.	.	PUNCT
ejpam-3591	38	1	partial	partial	ADJ
ejpam-3591	38	2	results	result	NOUN
ejpam-3591	38	3	which	which	PRON
ejpam-3591	38	4	are	be	AUX
ejpam-3591	38	5	consistent	consistent	ADJ
ejpam-3591	38	6	with	with	ADP
ejpam-3591	38	7	the	the	DET
ejpam-3591	38	8	conclusions	conclusion	NOUN
ejpam-3591	38	9	in	in	ADP
ejpam-3591	38	10	[	[	X
ejpam-3591	38	11	n.	n.	NOUN
ejpam-3591	38	12	kehayopulu	kehayopulu	PROPN
ejpam-3591	38	13	,	,	PUNCT
ejpam-3591	38	14	on	on	ADP
ejpam-3591	38	15	ordered	order	VERB
ejpam-3591	38	16	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	38	17	with	with	ADP
ejpam-3591	38	18	idempotent	idempotent	ADJ
ejpam-3591	38	19	ideals	ideal	NOUN
ejpam-3591	38	20	,	,	PUNCT
ejpam-3591	38	21	prime	prime	ADJ
ejpam-3591	38	22	or	or	CCONJ
ejpam-3591	38	23	weakly	weakly	ADJ
ejpam-3591	38	24	prime	prime	ADJ
ejpam-3591	38	25	ideals	ideal	NOUN
ejpam-3591	38	26	,	,	PUNCT
ejpam-3591	38	27	european	european	PROPN
ejpam-3591	38	28	journal	journal	PROPN
ejpam-3591	38	29	of	of	ADP
ejpam-3591	38	30	pure	pure	ADJ
ejpam-3591	38	31	and	and	CCONJ
ejpam-3591	38	32	applied	applied	ADJ
ejpam-3591	38	33	mathematics	mathematic	NOUN
ejpam-3591	38	34	,	,	PUNCT
ejpam-3591	38	35	11	11	NUM
ejpam-3591	38	36	(	(	PUNCT
ejpam-3591	38	37	2018	2018	NUM
ejpam-3591	38	38	)	)	PUNCT
ejpam-3591	38	39	,	,	PUNCT
ejpam-3591	38	40	10–22	10–22	NUM
ejpam-3591	38	41	]	]	PUNCT
ejpam-3591	38	42	are	be	AUX
ejpam-3591	38	43	reorganized	reorganize	VERB
ejpam-3591	38	44	and	and	CCONJ
ejpam-3591	38	45	proved	prove	VERB
ejpam-3591	38	46	.	.	PUNCT
ejpam-3591	38	47	”	"	PUNCT
ejpam-3591	39	1	we	we	PRON
ejpam-3591	39	2	have	have	VERB
ejpam-3591	39	3	to	to	PART
ejpam-3591	39	4	do	do	VERB
ejpam-3591	39	5	some	some	DET
ejpam-3591	39	6	comments	comment	NOUN
ejpam-3591	39	7	on	on	ADP
ejpam-3591	39	8	this	this	DET
ejpam-3591	39	9	paper	paper	NOUN
ejpam-3591	39	10	.	.	PUNCT
ejpam-3591	40	1	we	we	PRON
ejpam-3591	40	2	call	call	VERB
ejpam-3591	40	3	“	"	PUNCT
ejpam-3591	40	4	ideal	ideal	ADJ
ejpam-3591	40	5	”	"	PUNCT
ejpam-3591	40	6	what	what	PRON
ejpam-3591	40	7	the	the	DET
ejpam-3591	40	8	author	author	NOUN
ejpam-3591	40	9	in	in	ADP
ejpam-3591	40	10	[	[	X
ejpam-3591	40	11	4	4	X
ejpam-3591	40	12	]	]	PUNCT
ejpam-3591	40	13	calls	call	VERB
ejpam-3591	40	14	“	"	PUNCT
ejpam-3591	40	15	hyperideal	hyperideal	NOUN
ejpam-3591	40	16	”	"	PUNCT
ejpam-3591	40	17	and	and	CCONJ
ejpam-3591	40	18	“	"	PUNCT
ejpam-3591	40	19	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	40	20	”	"	PUNCT
ejpam-3591	40	21	what	what	PRON
ejpam-3591	40	22	the	the	DET
ejpam-3591	40	23	author	author	NOUN
ejpam-3591	40	24	calls	call	VERB
ejpam-3591	40	25	“	"	PUNCT
ejpam-3591	40	26	semihypergroup	semihypergroup	PROPN
ejpam-3591	40	27	”	"	PUNCT
ejpam-3591	40	28	.	.	PUNCT
ejpam-3591	41	1	we	we	PRON
ejpam-3591	41	2	use	use	VERB
ejpam-3591	41	3	the	the	DET
ejpam-3591	41	4	symbol	symbol	NOUN
ejpam-3591	41	5	“	"	PUNCT
ejpam-3591	41	6	∗	∗	NOUN
ejpam-3591	41	7	”	"	PUNCT
ejpam-3591	41	8	when	when	SCONJ
ejpam-3591	41	9	the	the	DET
ejpam-3591	41	10	operation	operation	NOUN
ejpam-3591	41	11	is	be	AUX
ejpam-3591	41	12	between	between	ADP
ejpam-3591	41	13	sets	set	NOUN
ejpam-3591	41	14	(	(	PUNCT
ejpam-3591	41	15	however	however	ADV
ejpam-3591	41	16	,	,	PUNCT
ejpam-3591	41	17	we	we	PRON
ejpam-3591	41	18	keep	keep	VERB
ejpam-3591	41	19	the	the	DET
ejpam-3591	41	20	“	"	PUNCT
ejpam-3591	41	21	◦	◦	NOUN
ejpam-3591	41	22	”	"	PUNCT
ejpam-3591	41	23	for	for	SCONJ
ejpam-3591	41	24	the	the	DET
ejpam-3591	41	25	results	result	NOUN
ejpam-3591	41	26	given	give	VERB
ejpam-3591	41	27	by	by	ADP
ejpam-3591	41	28	gu	gu	NOUN
ejpam-3591	41	29	to	to	PART
ejpam-3591	41	30	avoid	avoid	VERB
ejpam-3591	41	31	any	any	DET
ejpam-3591	41	32	misunderstanding	misunderstanding	NOUN
ejpam-3591	41	33	)	)	PUNCT
ejpam-3591	41	34	;	;	PUNCT
ejpam-3591	41	35	for	for	ADP
ejpam-3591	41	36	further	further	ADJ
ejpam-3591	41	37	information	information	NOUN
ejpam-3591	41	38	we	we	PRON
ejpam-3591	41	39	refer	refer	VERB
ejpam-3591	41	40	to	to	ADP
ejpam-3591	41	41	[	[	X
ejpam-3591	41	42	10	10	NUM
ejpam-3591	41	43	]	]	PUNCT
ejpam-3591	41	44	.	.	PUNCT
ejpam-3591	42	1	the	the	DET
ejpam-3591	42	2	results	result	NOUN
ejpam-3591	42	3	of	of	ADP
ejpam-3591	42	4	this	this	DET
ejpam-3591	42	5	paper	paper	NOUN
ejpam-3591	42	6	,	,	PUNCT
ejpam-3591	42	7	except	except	SCONJ
ejpam-3591	42	8	of	of	ADP
ejpam-3591	42	9	lemma	lemma	PROPN
ejpam-3591	42	10	2.4	2.4	NUM
ejpam-3591	42	11	and	and	CCONJ
ejpam-3591	42	12	theorem	theorem	VERB
ejpam-3591	42	13	2.6	2.6	NUM
ejpam-3591	42	14	,	,	PUNCT
ejpam-3591	42	15	have	have	AUX
ejpam-3591	42	16	been	be	AUX
ejpam-3591	42	17	published	publish	VERB
ejpam-3591	42	18	by	by	ADP
ejpam-3591	42	19	the	the	DET
ejpam-3591	42	20	author	author	NOUN
ejpam-3591	42	21	of	of	ADP
ejpam-3591	42	22	the	the	DET
ejpam-3591	42	23	present	present	ADJ
ejpam-3591	42	24	paper	paper	NOUN
ejpam-3591	42	25	,	,	PUNCT
ejpam-3591	42	26	most	most	ADJ
ejpam-3591	42	27	of	of	ADP
ejpam-3591	42	28	them	they	PRON
ejpam-3591	42	29	in	in	ADP
ejpam-3591	42	30	[	[	X
ejpam-3591	42	31	10	10	NUM
ejpam-3591	42	32	]	]	PUNCT
ejpam-3591	42	33	,	,	PUNCT
ejpam-3591	42	34	in	in	ADP
ejpam-3591	42	35	an	an	DET
ejpam-3591	42	36	attempt	attempt	NOUN
ejpam-3591	42	37	to	to	PART
ejpam-3591	42	38	show	show	VERB
ejpam-3591	42	39	how	how	SCONJ
ejpam-3591	42	40	a	a	DET
ejpam-3591	42	41	right	right	ADJ
ejpam-3591	42	42	paper	paper	NOUN
ejpam-3591	42	43	on	on	ADP
ejpam-3591	42	44	an	an	DET
ejpam-3591	42	45	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	42	46	or	or	CCONJ
ejpam-3591	42	47	on	on	ADP
ejpam-3591	42	48	ordered	order	VERB
ejpam-3591	42	49	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	42	50	should	should	AUX
ejpam-3591	42	51	be	be	AUX
ejpam-3591	42	52	written	write	VERB
ejpam-3591	42	53	.	.	PUNCT
ejpam-3591	43	1	the	the	DET
ejpam-3591	43	2	purpose	purpose	NOUN
ejpam-3591	43	3	was	be	AUX
ejpam-3591	43	4	to	to	PART
ejpam-3591	43	5	show	show	VERB
ejpam-3591	43	6	that	that	SCONJ
ejpam-3591	43	7	we	we	PRON
ejpam-3591	43	8	can	can	AUX
ejpam-3591	43	9	never	never	ADV
ejpam-3591	43	10	indicate	indicate	VERB
ejpam-3591	43	11	the	the	DET
ejpam-3591	43	12	operations	operation	NOUN
ejpam-3591	43	13	between	between	ADP
ejpam-3591	43	14	elements	element	NOUN
ejpam-3591	43	15	and	and	CCONJ
ejpam-3591	43	16	subsets	subset	NOUN
ejpam-3591	43	17	of	of	ADP
ejpam-3591	43	18	an	an	DET
ejpam-3591	43	19	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	43	20	by	by	ADP
ejpam-3591	43	21	the	the	DET
ejpam-3591	43	22	same	same	ADJ
ejpam-3591	43	23	symbol	symbol	NOUN
ejpam-3591	43	24	,	,	PUNCT
ejpam-3591	43	25	in	in	ADP
ejpam-3591	43	26	which	which	DET
ejpam-3591	43	27	case	case	NOUN
ejpam-3591	43	28	we	we	PRON
ejpam-3591	43	29	get	get	VERB
ejpam-3591	43	30	a	a	DET
ejpam-3591	43	31	result	result	NOUN
ejpam-3591	43	32	on	on	ADP
ejpam-3591	43	33	an	an	DET
ejpam-3591	43	34	ordered	order	VERB
ejpam-3591	43	35	semigroup	semigroup	NOUN
ejpam-3591	43	36	,	,	PUNCT
ejpam-3591	43	37	delete	delete	VERB
ejpam-3591	43	38	the	the	DET
ejpam-3591	43	39	multiplication	multiplication	NOUN
ejpam-3591	43	40	“	"	PUNCT
ejpam-3591	43	41	·	·	PUNCT
ejpam-3591	43	42	”	"	PUNCT
ejpam-3591	43	43	of	of	ADP
ejpam-3591	43	44	the	the	DET
ejpam-3591	43	45	semigroup	semigroup	NOUN
ejpam-3591	43	46	and	and	CCONJ
ejpam-3591	43	47	put	put	VERB
ejpam-3591	43	48	“	"	PUNCT
ejpam-3591	43	49	◦	◦	NOUN
ejpam-3591	43	50	”	"	PUNCT
ejpam-3591	43	51	in	in	ADP
ejpam-3591	43	52	its	its	PRON
ejpam-3591	43	53	place	place	NOUN
ejpam-3591	43	54	to	to	PART
ejpam-3591	43	55	pass	pass	VERB
ejpam-3591	43	56	from	from	ADP
ejpam-3591	43	57	an	an	DET
ejpam-3591	43	58	ordered	order	VERB
ejpam-3591	43	59	semigroup	semigroup	NOUN
ejpam-3591	43	60	to	to	ADP
ejpam-3591	43	61	an	an	DET
ejpam-3591	43	62	ordered	order	VERB
ejpam-3591	43	63	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	43	64	.	.	PUNCT
ejpam-3591	44	1	the	the	DET
ejpam-3591	44	2	notions	notion	NOUN
ejpam-3591	44	3	of	of	ADP
ejpam-3591	44	4	prime	prime	ADJ
ejpam-3591	44	5	and	and	CCONJ
ejpam-3591	44	6	weakly	weakly	ADJ
ejpam-3591	44	7	prime	prime	ADJ
ejpam-3591	44	8	subsets	subset	NOUN
ejpam-3591	44	9	of	of	ADP
ejpam-3591	44	10	an	an	DET
ejpam-3591	44	11	hypergroupoid	hypergroupoid	NOUN
ejpam-3591	44	12	or	or	CCONJ
ejpam-3591	44	13	ordered	order	VERB
ejpam-3591	44	14	hypergroupoid	hypergroupoid	PROPN
ejpam-3591	44	15	(	(	PUNCT
ejpam-3591	44	16	natural	natural	ADJ
ejpam-3591	44	17	extension	extension	NOUN
ejpam-3591	44	18	of	of	ADP
ejpam-3591	44	19	the	the	DET
ejpam-3591	44	20	concept	concept	NOUN
ejpam-3591	44	21	of	of	ADP
ejpam-3591	44	22	weakly	weakly	ADJ
ejpam-3591	44	23	prime	prime	ADJ
ejpam-3591	44	24	subset	subset	NOUN
ejpam-3591	44	25	of	of	ADP
ejpam-3591	44	26	a	a	DET
ejpam-3591	44	27	groupoid	groupoid	NOUN
ejpam-3591	44	28	or	or	CCONJ
ejpam-3591	44	29	ordered	order	VERB
ejpam-3591	44	30	groupoid	groupoid	PROPN
ejpam-3591	45	1	[	[	X
ejpam-3591	45	2	6	6	NUM
ejpam-3591	45	3	,	,	PUNCT
ejpam-3591	45	4	7	7	NUM
ejpam-3591	45	5	]	]	PUNCT
ejpam-3591	45	6	)	)	PUNCT
ejpam-3591	45	7	have	have	AUX
ejpam-3591	45	8	been	be	AUX
ejpam-3591	45	9	given	give	VERB
ejpam-3591	45	10	in	in	ADP
ejpam-3591	45	11	definition	definition	NOUN
ejpam-3591	45	12	3	3	NUM
ejpam-3591	45	13	in	in	ADP
ejpam-3591	45	14	[	[	X
ejpam-3591	45	15	10	10	NUM
ejpam-3591	45	16	]	]	PUNCT
ejpam-3591	45	17	,	,	PUNCT
ejpam-3591	45	18	and	and	CCONJ
ejpam-3591	45	19	it	it	PRON
ejpam-3591	45	20	is	be	AUX
ejpam-3591	45	21	obvious	obvious	ADJ
ejpam-3591	45	22	now	now	ADV
ejpam-3591	45	23	what	what	PRON
ejpam-3591	45	24	the	the	DET
ejpam-3591	45	25	notion	notion	NOUN
ejpam-3591	45	26	of	of	ADP
ejpam-3591	45	27	a	a	DET
ejpam-3591	45	28	weakly	weakly	ADJ
ejpam-3591	45	29	semiprime	semiprime	NOUN
ejpam-3591	45	30	subset	subset	NOUN
ejpam-3591	45	31	is	be	AUX
ejpam-3591	45	32	.	.	PUNCT
ejpam-3591	46	1	an	an	DET
ejpam-3591	46	2	weakly	weakly	ADJ
ejpam-3591	46	3	semiprime	semiprime	NOUN
ejpam-3591	46	4	ideal	ideal	NOUN
ejpam-3591	46	5	of	of	ADP
ejpam-3591	46	6	an	an	DET
ejpam-3591	46	7	ordered	order	VERB
ejpam-3591	46	8	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	46	9	s	s	X
ejpam-3591	46	10	is	be	AUX
ejpam-3591	46	11	clearly	clearly	ADV
ejpam-3591	46	12	an	an	DET
ejpam-3591	46	13	ideal	ideal	NOUN
ejpam-3591	46	14	that	that	PRON
ejpam-3591	46	15	is	be	AUX
ejpam-3591	46	16	at	at	ADP
ejpam-3591	46	17	the	the	DET
ejpam-3591	46	18	same	same	ADJ
ejpam-3591	46	19	time	time	NOUN
ejpam-3591	46	20	an	an	DET
ejpam-3591	46	21	weakly	weakly	ADJ
ejpam-3591	46	22	semiprime	semiprime	NOUN
ejpam-3591	46	23	subset	subset	NOUN
ejpam-3591	46	24	of	of	ADP
ejpam-3591	46	25	s.	s.	PROPN
ejpam-3591	46	26	n.	n.	PROPN
ejpam-3591	46	27	kehayopulu	kehayopulu	PROPN
ejpam-3591	46	28	/	/	SYM
ejpam-3591	46	29	eur	eur	PROPN
ejpam-3591	46	30	.	.	PUNCT
ejpam-3591	47	1	j.	j.	PROPN
ejpam-3591	47	2	pure	pure	PROPN
ejpam-3591	47	3	appl	appl	PROPN
ejpam-3591	47	4	.	.	PROPN
ejpam-3591	47	5	math	math	PROPN
ejpam-3591	47	6	,	,	PUNCT
ejpam-3591	47	7	12	12	NUM
ejpam-3591	47	8	(	(	PUNCT
ejpam-3591	47	9	4	4	NUM
ejpam-3591	47	10	)	)	PUNCT
ejpam-3591	47	11	(	(	PUNCT
ejpam-3591	47	12	2019	2019	NUM
ejpam-3591	47	13	)	)	PUNCT
ejpam-3591	47	14	,	,	PUNCT
ejpam-3591	47	15	1771	1771	NUM
ejpam-3591	47	16	-	-	SYM
ejpam-3591	47	17	1778	1778	NUM
ejpam-3591	47	18	1773	1773	NUM
ejpam-3591	47	19	the	the	DET
ejpam-3591	47	20	concept	concept	NOUN
ejpam-3591	47	21	of	of	ADP
ejpam-3591	47	22	irreducible	irreducible	ADJ
ejpam-3591	47	23	ideal	ideal	NOUN
ejpam-3591	47	24	of	of	ADP
ejpam-3591	47	25	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	48	1	[	[	X
ejpam-3591	48	2	1	1	X
ejpam-3591	48	3	]	]	PUNCT
ejpam-3591	48	4	and	and	CCONJ
ejpam-3591	48	5	the	the	DET
ejpam-3591	48	6	concept	concept	NOUN
ejpam-3591	48	7	of	of	ADP
ejpam-3591	48	8	irreducible	irreducible	ADJ
ejpam-3591	48	9	ideal	ideal	NOUN
ejpam-3591	48	10	of	of	ADP
ejpam-3591	48	11	ordered	order	VERB
ejpam-3591	48	12	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	49	1	[	[	X
ejpam-3591	49	2	4	4	NUM
ejpam-3591	49	3	]	]	PUNCT
ejpam-3591	49	4	are	be	AUX
ejpam-3591	49	5	the	the	DET
ejpam-3591	49	6	same	same	ADJ
ejpam-3591	49	7	.	.	PUNCT
ejpam-3591	50	1	in	in	ADP
ejpam-3591	50	2	addition	addition	NOUN
ejpam-3591	50	3	,	,	PUNCT
ejpam-3591	50	4	all	all	DET
ejpam-3591	50	5	these	these	DET
ejpam-3591	50	6	concepts	concept	NOUN
ejpam-3591	50	7	have	have	AUX
ejpam-3591	50	8	been	be	AUX
ejpam-3591	50	9	introduced	introduce	VERB
ejpam-3591	50	10	many	many	ADJ
ejpam-3591	50	11	years	year	NOUN
ejpam-3591	50	12	ago	ago	ADV
ejpam-3591	50	13	for	for	ADP
ejpam-3591	50	14	more	more	ADJ
ejpam-3591	50	15	general	general	ADJ
ejpam-3591	50	16	structures	structure	NOUN
ejpam-3591	50	17	.	.	PUNCT
ejpam-3591	51	1	for	for	ADP
ejpam-3591	51	2	the	the	DET
ejpam-3591	51	3	concepts	concept	NOUN
ejpam-3591	51	4	of	of	ADP
ejpam-3591	51	5	weakly	weakly	ADJ
ejpam-3591	51	6	prime	prime	ADJ
ejpam-3591	51	7	,	,	PUNCT
ejpam-3591	51	8	weakly	weakly	ADJ
ejpam-3591	51	9	semiprime	semiprime	NOUN
ejpam-3591	51	10	and	and	CCONJ
ejpam-3591	51	11	prime	prime	ADJ
ejpam-3591	51	12	ideal	ideal	ADJ
ejpam-3591	51	13	elements	element	NOUN
ejpam-3591	51	14	in	in	ADP
ejpam-3591	51	15	poe	poe	PROPN
ejpam-3591	51	16	-	-	PUNCT
ejpam-3591	51	17	semigroups	semigroup	NOUN
ejpam-3591	51	18	see	see	VERB
ejpam-3591	51	19	[	[	X
ejpam-3591	51	20	5	5	NUM
ejpam-3591	51	21	]	]	PUNCT
ejpam-3591	51	22	;	;	PUNCT
ejpam-3591	51	23	for	for	ADP
ejpam-3591	51	24	the	the	DET
ejpam-3591	51	25	concepts	concept	NOUN
ejpam-3591	51	26	of	of	ADP
ejpam-3591	51	27	meet	meet	VERB
ejpam-3591	51	28	-	-	PUNCT
ejpam-3591	51	29	irreducible	irreducible	ADJ
ejpam-3591	51	30	and	and	CCONJ
ejpam-3591	51	31	join	join	NOUN
ejpam-3591	51	32	-	-	PUNCT
ejpam-3591	51	33	irreducible	irreducible	ADJ
ejpam-3591	51	34	elements	element	NOUN
ejpam-3591	51	35	of	of	ADP
ejpam-3591	51	36	ordered	order	VERB
ejpam-3591	51	37	sets	set	NOUN
ejpam-3591	51	38	see	see	VERB
ejpam-3591	51	39	[	[	X
ejpam-3591	51	40	3	3	NUM
ejpam-3591	51	41	]	]	PUNCT
ejpam-3591	51	42	.	.	PUNCT
ejpam-3591	52	1	the	the	DET
ejpam-3591	52	2	irreducible	irreducible	ADJ
ejpam-3591	52	3	ideal	ideal	NOUN
ejpam-3591	52	4	in	in	ADP
ejpam-3591	52	5	the	the	DET
ejpam-3591	52	6	paper	paper	NOUN
ejpam-3591	52	7	by	by	ADP
ejpam-3591	52	8	gu	gu	NOUN
ejpam-3591	53	1	[	[	X
ejpam-3591	53	2	4	4	X
ejpam-3591	53	3	]	]	PUNCT
ejpam-3591	53	4	is	be	AUX
ejpam-3591	53	5	the	the	DET
ejpam-3591	53	6	meet	meet	ADJ
ejpam-3591	53	7	-	-	PUNCT
ejpam-3591	53	8	irreducible	irreducible	ADJ
ejpam-3591	53	9	ideal	ideal	ADJ
ejpam-3591	53	10	element	element	NOUN
ejpam-3591	53	11	in	in	ADP
ejpam-3591	53	12	the	the	DET
ejpam-3591	53	13	sense	sense	NOUN
ejpam-3591	53	14	of	of	ADP
ejpam-3591	53	15	grätzer	grätzer	NOUN
ejpam-3591	53	16	[	[	X
ejpam-3591	53	17	3	3	NUM
ejpam-3591	53	18	]	]	PUNCT
ejpam-3591	53	19	.	.	PUNCT
ejpam-3591	54	1	it	it	PRON
ejpam-3591	54	2	might	might	AUX
ejpam-3591	54	3	be	be	AUX
ejpam-3591	54	4	mentioned	mention	VERB
ejpam-3591	54	5	here	here	ADV
ejpam-3591	54	6	that	that	SCONJ
ejpam-3591	54	7	the	the	DET
ejpam-3591	54	8	∨-irreducible	∨-irreducible	ADJ
ejpam-3591	54	9	element	element	NOUN
ejpam-3591	54	10	in	in	ADP
ejpam-3591	54	11	a	a	DET
ejpam-3591	54	12	∨-semilattice	∨-semilattice	NOUN
ejpam-3591	54	13	has	have	AUX
ejpam-3591	54	14	been	be	AUX
ejpam-3591	54	15	defined	define	VERB
ejpam-3591	54	16	much	much	ADV
ejpam-3591	54	17	earlier	early	ADV
ejpam-3591	54	18	,	,	PUNCT
ejpam-3591	54	19	in	in	ADP
ejpam-3591	54	20	1953	1953	NUM
ejpam-3591	54	21	,	,	PUNCT
ejpam-3591	54	22	by	by	ADP
ejpam-3591	54	23	dubreil	dubreil	NOUN
ejpam-3591	54	24	et	et	PROPN
ejpam-3591	54	25	al	al	PROPN
ejpam-3591	54	26	.	.	PUNCT
ejpam-3591	55	1	[	[	X
ejpam-3591	55	2	2	2	NUM
ejpam-3591	55	3	,	,	PUNCT
ejpam-3591	55	4	p.	p.	NOUN
ejpam-3591	55	5	117	117	NUM
ejpam-3591	55	6	]	]	PUNCT
ejpam-3591	55	7	(	(	PUNCT
ejpam-3591	55	8	and	and	CCONJ
ejpam-3591	55	9	can	can	AUX
ejpam-3591	55	10	be	be	AUX
ejpam-3591	55	11	defined	define	VERB
ejpam-3591	55	12	in	in	ADP
ejpam-3591	55	13	any	any	DET
ejpam-3591	55	14	ordered	order	VERB
ejpam-3591	55	15	set	set	NOUN
ejpam-3591	55	16	,	,	PUNCT
ejpam-3591	55	17	as	as	ADV
ejpam-3591	55	18	well	well	ADV
ejpam-3591	55	19	)	)	PUNCT
ejpam-3591	55	20	.	.	PUNCT
ejpam-3591	56	1	so	so	ADV
ejpam-3591	56	2	the	the	DET
ejpam-3591	56	3	concepts	concept	NOUN
ejpam-3591	56	4	of	of	ADP
ejpam-3591	56	5	weakly	weakly	ADJ
ejpam-3591	56	6	semiprime	semiprime	NOUN
ejpam-3591	56	7	and	and	CCONJ
ejpam-3591	56	8	irreducible	irreducible	ADJ
ejpam-3591	56	9	ideals	ideal	NOUN
ejpam-3591	56	10	can	can	AUX
ejpam-3591	56	11	not	not	PART
ejpam-3591	56	12	due	due	ADP
ejpam-3591	56	13	to	to	ADP
ejpam-3591	56	14	the	the	DET
ejpam-3591	56	15	author	author	NOUN
ejpam-3591	56	16	and	and	CCONJ
ejpam-3591	56	17	a	a	DET
ejpam-3591	56	18	proper	proper	ADJ
ejpam-3591	56	19	reference	reference	NOUN
ejpam-3591	56	20	list	list	NOUN
ejpam-3591	56	21	for	for	ADP
ejpam-3591	56	22	these	these	DET
ejpam-3591	56	23	concepts	concept	NOUN
ejpam-3591	56	24	was	be	AUX
ejpam-3591	56	25	needed	need	VERB
ejpam-3591	56	26	.	.	PUNCT
ejpam-3591	57	1	to	to	PART
ejpam-3591	57	2	be	be	AUX
ejpam-3591	57	3	easier	easy	ADJ
ejpam-3591	57	4	for	for	SCONJ
ejpam-3591	57	5	the	the	DET
ejpam-3591	57	6	readers	reader	NOUN
ejpam-3591	57	7	to	to	PART
ejpam-3591	57	8	follow	follow	VERB
ejpam-3591	57	9	this	this	DET
ejpam-3591	57	10	note	note	NOUN
ejpam-3591	57	11	,	,	PUNCT
ejpam-3591	57	12	we	we	PRON
ejpam-3591	57	13	will	will	AUX
ejpam-3591	57	14	write	write	VERB
ejpam-3591	57	15	below	below	ADP
ejpam-3591	57	16	zg	zg	PROPN
ejpam-3591	57	17	,	,	PUNCT
ejpam-3591	57	18	nk	nk	PROPN
ejpam-3591	57	19	,	,	PUNCT
ejpam-3591	57	20	for	for	ADP
ejpam-3591	57	21	the	the	DET
ejpam-3591	57	22	papers	paper	NOUN
ejpam-3591	57	23	due	due	ADP
ejpam-3591	57	24	to	to	ADP
ejpam-3591	57	25	gu	gu	NOUN
ejpam-3591	57	26	and	and	CCONJ
ejpam-3591	57	27	kehayopulu	kehayopulu	VERB
ejpam-3591	57	28	,	,	PUNCT
ejpam-3591	57	29	respectively	respectively	ADV
ejpam-3591	57	30	.	.	PUNCT
ejpam-3591	58	1	lemma	lemma	PROPN
ejpam-3591	58	2	2.3	2.3	NUM
ejpam-3591	58	3	in	in	ADP
ejpam-3591	58	4	[	[	X
ejpam-3591	58	5	4](zg	4](zg	NUM
ejpam-3591	58	6	)	)	PUNCT
ejpam-3591	58	7	let	let	VERB
ejpam-3591	58	8	s	s	PRON
ejpam-3591	58	9	be	be	AUX
ejpam-3591	58	10	an	an	DET
ejpam-3591	58	11	ordered	order	VERB
ejpam-3591	58	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	58	13	.	.	PUNCT
ejpam-3591	59	1	then	then	ADV
ejpam-3591	59	2	(	(	PUNCT
ejpam-3591	59	3	1	1	X
ejpam-3591	59	4	)	)	PUNCT
ejpam-3591	59	5	a	a	DET
ejpam-3591	59	6	⊆	⊆	NUM
ejpam-3591	59	7	(	(	PUNCT
ejpam-3591	59	8	a	a	PRON
ejpam-3591	59	9	]	]	X
ejpam-3591	59	10	,	,	PUNCT
ejpam-3591	59	11	(	(	PUNCT
ejpam-3591	59	12	(	(	PUNCT
ejpam-3591	59	13	a	a	X
ejpam-3591	59	14	]	]	X
ejpam-3591	59	15	]	]	X
ejpam-3591	59	16	=	=	X
ejpam-3591	59	17	(	(	PUNCT
ejpam-3591	59	18	a	a	X
ejpam-3591	59	19	]	]	X
ejpam-3591	59	20	for	for	ADP
ejpam-3591	59	21	all	all	DET
ejpam-3591	59	22	a	a	DET
ejpam-3591	59	23	⊆	⊆	NUM
ejpam-3591	59	24	s.	s.	PROPN
ejpam-3591	59	25	(	(	PUNCT
ejpam-3591	59	26	2	2	NUM
ejpam-3591	59	27	)	)	PUNCT
ejpam-3591	59	28	if	if	SCONJ
ejpam-3591	59	29	a	a	DET
ejpam-3591	59	30	⊆	⊆	NUM
ejpam-3591	59	31	b	b	NOUN
ejpam-3591	59	32	⊆	⊆	NUM
ejpam-3591	59	33	s	s	NOUN
ejpam-3591	59	34	,	,	PUNCT
ejpam-3591	59	35	then	then	ADV
ejpam-3591	59	36	(	(	PUNCT
ejpam-3591	59	37	a	a	X
ejpam-3591	59	38	]	]	X
ejpam-3591	59	39	⊆	⊆	NUM
ejpam-3591	59	40	(	(	PUNCT
ejpam-3591	59	41	b	b	NOUN
ejpam-3591	59	42	]	]	X
ejpam-3591	59	43	.	.	PUNCT
ejpam-3591	60	1	(	(	PUNCT
ejpam-3591	60	2	3	3	X
ejpam-3591	60	3	)	)	PUNCT
ejpam-3591	60	4	(	(	PUNCT
ejpam-3591	60	5	a	a	PRON
ejpam-3591	60	6	]	]	X
ejpam-3591	60	7	◦	◦	NOUN
ejpam-3591	60	8	(	(	PUNCT
ejpam-3591	60	9	b	b	X
ejpam-3591	60	10	]	]	X
ejpam-3591	60	11	⊆	⊆	NUM
ejpam-3591	60	12	(	(	PUNCT
ejpam-3591	60	13	a	a	DET
ejpam-3591	60	14	◦	◦	NOUN
ejpam-3591	60	15	b	b	NOUN
ejpam-3591	60	16	]	]	X
ejpam-3591	60	17	,	,	PUNCT
ejpam-3591	60	18	(	(	PUNCT
ejpam-3591	60	19	(	(	PUNCT
ejpam-3591	60	20	a	a	PRON
ejpam-3591	60	21	]	]	X
ejpam-3591	60	22	◦	◦	NOUN
ejpam-3591	60	23	(	(	PUNCT
ejpam-3591	60	24	b	b	X
ejpam-3591	60	25	]	]	X
ejpam-3591	60	26	]	]	X
ejpam-3591	61	1	=	=	X
ejpam-3591	61	2	(	(	PUNCT
ejpam-3591	61	3	a	a	DET
ejpam-3591	61	4	◦	◦	NOUN
ejpam-3591	61	5	b	b	NOUN
ejpam-3591	61	6	]	]	X
ejpam-3591	61	7	.	.	PUNCT
ejpam-3591	62	1	(	(	PUNCT
ejpam-3591	62	2	4	4	NUM
ejpam-3591	62	3	)	)	PUNCT
ejpam-3591	62	4	(	(	PUNCT
ejpam-3591	62	5	t	t	X
ejpam-3591	62	6	]	]	PUNCT
ejpam-3591	62	7	=	=	PUNCT
ejpam-3591	62	8	t	t	PROPN
ejpam-3591	62	9	for	for	ADP
ejpam-3591	62	10	every	every	DET
ejpam-3591	62	11	ideal	ideal	ADJ
ejpam-3591	62	12	t	t	PROPN
ejpam-3591	62	13	of	of	ADP
ejpam-3591	62	14	s.	s.	PROPN
ejpam-3591	62	15	(	(	PUNCT
ejpam-3591	62	16	5	5	NUM
ejpam-3591	62	17	)	)	PUNCT
ejpam-3591	62	18	if	if	SCONJ
ejpam-3591	62	19	a	a	DET
ejpam-3591	62	20	,	,	PUNCT
ejpam-3591	62	21	b	b	NOUN
ejpam-3591	62	22	are	be	AUX
ejpam-3591	62	23	ideals	ideal	NOUN
ejpam-3591	62	24	of	of	ADP
ejpam-3591	62	25	s	s	NOUN
ejpam-3591	62	26	,	,	PUNCT
ejpam-3591	62	27	then	then	ADV
ejpam-3591	62	28	(	(	PUNCT
ejpam-3591	62	29	a	a	DET
ejpam-3591	62	30	◦	◦	NOUN
ejpam-3591	62	31	b	b	NOUN
ejpam-3591	62	32	]	]	X
ejpam-3591	62	33	,	,	PUNCT
ejpam-3591	62	34	a	a	DET
ejpam-3591	62	35	∩b	∩b	NOUN
ejpam-3591	62	36	and	and	CCONJ
ejpam-3591	62	37	a	a	DET
ejpam-3591	62	38	∪b	∪b	NOUN
ejpam-3591	62	39	are	be	AUX
ejpam-3591	62	40	ideals	ideal	NOUN
ejpam-3591	62	41	of	of	ADP
ejpam-3591	62	42	s.	s.	PROPN
ejpam-3591	62	43	(	(	PUNCT
ejpam-3591	62	44	6	6	NUM
ejpam-3591	62	45	)	)	PUNCT
ejpam-3591	62	46	(	(	PUNCT
ejpam-3591	62	47	s	s	AUX
ejpam-3591	62	48	◦	◦	NOUN
ejpam-3591	62	49	a	a	DET
ejpam-3591	62	50	◦	◦	NOUN
ejpam-3591	62	51	s	s	PART
ejpam-3591	62	52	]	]	X
ejpam-3591	62	53	is	be	AUX
ejpam-3591	62	54	an	an	DET
ejpam-3591	62	55	ideal	ideal	NOUN
ejpam-3591	62	56	of	of	ADP
ejpam-3591	62	57	s	s	PRON
ejpam-3591	62	58	for	for	ADP
ejpam-3591	62	59	all	all	DET
ejpam-3591	62	60	a	a	DET
ejpam-3591	62	61	⊆	⊆	NUM
ejpam-3591	62	62	s.	s.	PROPN
ejpam-3591	62	63	according	accord	VERB
ejpam-3591	62	64	to	to	ADP
ejpam-3591	62	65	[	[	X
ejpam-3591	62	66	4	4	NUM
ejpam-3591	62	67	]	]	PUNCT
ejpam-3591	62	68	,	,	PUNCT
ejpam-3591	62	69	this	this	DET
ejpam-3591	62	70	lemma	lemma	PROPN
ejpam-3591	62	71	can	can	AUX
ejpam-3591	62	72	be	be	AUX
ejpam-3591	62	73	easily	easily	ADV
ejpam-3591	62	74	obtained	obtain	VERB
ejpam-3591	62	75	,	,	PUNCT
ejpam-3591	62	76	giving	give	VERB
ejpam-3591	62	77	the	the	DET
ejpam-3591	62	78	expression	expression	NOUN
ejpam-3591	62	79	that	that	PRON
ejpam-3591	62	80	it	it	PRON
ejpam-3591	62	81	is	be	AUX
ejpam-3591	62	82	new	new	ADJ
ejpam-3591	62	83	;	;	PUNCT
ejpam-3591	62	84	since	since	SCONJ
ejpam-3591	62	85	it	it	PRON
ejpam-3591	62	86	is	be	AUX
ejpam-3591	62	87	not	not	PART
ejpam-3591	62	88	new	new	ADJ
ejpam-3591	62	89	,	,	PUNCT
ejpam-3591	62	90	a	a	DET
ejpam-3591	62	91	proper	proper	ADJ
ejpam-3591	62	92	reference	reference	NOUN
ejpam-3591	62	93	for	for	ADP
ejpam-3591	62	94	this	this	DET
ejpam-3591	62	95	lemma	lemma	PROPN
ejpam-3591	62	96	was	be	AUX
ejpam-3591	62	97	needed	need	VERB
ejpam-3591	62	98	.	.	PUNCT
ejpam-3591	63	1	for	for	ADP
ejpam-3591	63	2	the	the	DET
ejpam-3591	63	3	obvious	obvious	ADJ
ejpam-3591	63	4	properties	property	NOUN
ejpam-3591	63	5	(	(	PUNCT
ejpam-3591	63	6	1	1	NUM
ejpam-3591	63	7	)	)	PUNCT
ejpam-3591	63	8	,	,	PUNCT
ejpam-3591	63	9	(	(	PUNCT
ejpam-3591	63	10	2	2	X
ejpam-3591	63	11	)	)	PUNCT
ejpam-3591	63	12	and	and	CCONJ
ejpam-3591	63	13	(	(	PUNCT
ejpam-3591	63	14	4	4	NUM
ejpam-3591	63	15	)	)	PUNCT
ejpam-3591	63	16	of	of	ADP
ejpam-3591	63	17	this	this	DET
ejpam-3591	63	18	lemma	lemma	PROPN
ejpam-3591	63	19	see	see	NOUN
ejpam-3591	63	20	,	,	PUNCT
ejpam-3591	63	21	for	for	ADP
ejpam-3591	63	22	example	example	NOUN
ejpam-3591	63	23	,	,	PUNCT
ejpam-3591	63	24	the	the	DET
ejpam-3591	63	25	lemma	lemma	PROPN
ejpam-3591	63	26	1	1	NUM
ejpam-3591	63	27	in	in	ADP
ejpam-3591	63	28	[	[	X
ejpam-3591	63	29	7	7	NUM
ejpam-3591	63	30	]	]	PUNCT
ejpam-3591	63	31	,	,	PUNCT
ejpam-3591	63	32	as	as	SCONJ
ejpam-3591	63	33	these	these	DET
ejpam-3591	63	34	properties	property	NOUN
ejpam-3591	63	35	hold	hold	VERB
ejpam-3591	63	36	in	in	ADP
ejpam-3591	63	37	ordered	order	VERB
ejpam-3591	63	38	groupoids	groupoid	NOUN
ejpam-3591	63	39	in	in	ADP
ejpam-3591	63	40	general	general	ADJ
ejpam-3591	63	41	(	(	PUNCT
ejpam-3591	63	42	the	the	DET
ejpam-3591	63	43	hyperoperation	hyperoperation	NOUN
ejpam-3591	63	44	does	do	AUX
ejpam-3591	63	45	not	not	PART
ejpam-3591	63	46	play	play	VERB
ejpam-3591	63	47	any	any	DET
ejpam-3591	63	48	role	role	NOUN
ejpam-3591	63	49	in	in	ADP
ejpam-3591	63	50	them	they	PRON
ejpam-3591	63	51	)	)	PUNCT
ejpam-3591	63	52	.	.	PUNCT
ejpam-3591	64	1	for	for	ADP
ejpam-3591	64	2	a	a	DET
ejpam-3591	64	3	detailed	detailed	ADJ
ejpam-3591	64	4	proof	proof	NOUN
ejpam-3591	64	5	of	of	ADP
ejpam-3591	64	6	the	the	DET
ejpam-3591	64	7	rest	rest	NOUN
ejpam-3591	64	8	(	(	PUNCT
ejpam-3591	64	9	that	that	PRON
ejpam-3591	64	10	can	can	AUX
ejpam-3591	64	11	be	be	AUX
ejpam-3591	64	12	naturally	naturally	ADV
ejpam-3591	64	13	transferred	transfer	VERB
ejpam-3591	64	14	from	from	ADP
ejpam-3591	64	15	ordered	order	VERB
ejpam-3591	64	16	semigroups	semigroup	NOUN
ejpam-3591	64	17	)	)	PUNCT
ejpam-3591	64	18	using	use	VERB
ejpam-3591	64	19	the	the	DET
ejpam-3591	64	20	symbols	symbol	NOUN
ejpam-3591	64	21	“	"	PUNCT
ejpam-3591	64	22	◦	◦	NOUN
ejpam-3591	64	23	”	"	PUNCT
ejpam-3591	64	24	as	as	ADP
ejpam-3591	64	25	the	the	DET
ejpam-3591	64	26	“	"	PUNCT
ejpam-3591	64	27	operation	operation	NOUN
ejpam-3591	64	28	”	"	PUNCT
ejpam-3591	64	29	between	between	ADP
ejpam-3591	64	30	elements	element	NOUN
ejpam-3591	64	31	and	and	CCONJ
ejpam-3591	64	32	“	"	PUNCT
ejpam-3591	64	33	∗	∗	NOUN
ejpam-3591	64	34	”	"	PUNCT
ejpam-3591	64	35	as	as	ADP
ejpam-3591	64	36	the	the	DET
ejpam-3591	64	37	operation	operation	NOUN
ejpam-3591	64	38	between	between	ADP
ejpam-3591	64	39	sets	set	NOUN
ejpam-3591	64	40	,	,	PUNCT
ejpam-3591	64	41	see	see	VERB
ejpam-3591	64	42	the	the	DET
ejpam-3591	64	43	lemma	lemma	PROPN
ejpam-3591	64	44	2.8	2.8	NUM
ejpam-3591	64	45	in	in	ADP
ejpam-3591	64	46	[	[	PUNCT
ejpam-3591	64	47	9	9	NUM
ejpam-3591	64	48	]	]	PUNCT
ejpam-3591	64	49	,	,	PUNCT
ejpam-3591	64	50	the	the	DET
ejpam-3591	64	51	proposition	proposition	NOUN
ejpam-3591	64	52	11	11	NUM
ejpam-3591	64	53	in	in	ADP
ejpam-3591	64	54	[	[	X
ejpam-3591	64	55	10	10	NUM
ejpam-3591	64	56	]	]	PUNCT
ejpam-3591	64	57	,	,	PUNCT
ejpam-3591	64	58	the	the	DET
ejpam-3591	64	59	corollary	corollary	ADJ
ejpam-3591	64	60	15	15	NUM
ejpam-3591	64	61	in	in	ADP
ejpam-3591	64	62	[	[	X
ejpam-3591	64	63	10	10	NUM
ejpam-3591	64	64	]	]	PUNCT
ejpam-3591	64	65	,	,	PUNCT
ejpam-3591	64	66	the	the	DET
ejpam-3591	64	67	proposition	proposition	NOUN
ejpam-3591	64	68	7	7	NUM
ejpam-3591	64	69	in	in	ADP
ejpam-3591	64	70	[	[	X
ejpam-3591	64	71	10	10	NUM
ejpam-3591	64	72	]	]	PUNCT
ejpam-3591	64	73	.	.	PUNCT
ejpam-3591	65	1	as	as	ADP
ejpam-3591	65	2	an	an	DET
ejpam-3591	65	3	example	example	NOUN
ejpam-3591	65	4	,	,	PUNCT
ejpam-3591	65	5	let	let	VERB
ejpam-3591	65	6	us	we	PRON
ejpam-3591	65	7	look	look	VERB
ejpam-3591	65	8	at	at	ADP
ejpam-3591	65	9	property	property	NOUN
ejpam-3591	65	10	(	(	PUNCT
ejpam-3591	65	11	3	3	NUM
ejpam-3591	65	12	)	)	PUNCT
ejpam-3591	65	13	(	(	PUNCT
ejpam-3591	65	14	that	that	PRON
ejpam-3591	65	15	is	be	AUX
ejpam-3591	65	16	part	part	NOUN
ejpam-3591	65	17	of	of	ADP
ejpam-3591	65	18	proposition	proposition	NOUN
ejpam-3591	65	19	11	11	NUM
ejpam-3591	65	20	in	in	ADP
ejpam-3591	65	21	[	[	X
ejpam-3591	65	22	10	10	NUM
ejpam-3591	65	23	]	]	PUNCT
ejpam-3591	65	24	)	)	PUNCT
ejpam-3591	65	25	and	and	CCONJ
ejpam-3591	65	26	at	at	ADP
ejpam-3591	65	27	the	the	DET
ejpam-3591	65	28	proof	proof	NOUN
ejpam-3591	65	29	of	of	ADP
ejpam-3591	65	30	proposition	proposition	NOUN
ejpam-3591	65	31	11	11	NUM
ejpam-3591	65	32	in	in	ADP
ejpam-3591	65	33	[	[	X
ejpam-3591	65	34	10	10	NUM
ejpam-3591	65	35	]	]	PUNCT
ejpam-3591	65	36	in	in	ADP
ejpam-3591	65	37	which	which	PRON
ejpam-3591	65	38	the	the	DET
ejpam-3591	65	39	role	role	NOUN
ejpam-3591	65	40	of	of	ADP
ejpam-3591	65	41	the	the	DET
ejpam-3591	65	42	two	two	NUM
ejpam-3591	65	43	operations	operation	NOUN
ejpam-3591	65	44	◦	◦	NOUN
ejpam-3591	65	45	and	and	CCONJ
ejpam-3591	65	46	∗	∗	NOUN
ejpam-3591	65	47	is	be	AUX
ejpam-3591	65	48	indicated	indicate	VERB
ejpam-3591	65	49	in	in	ADP
ejpam-3591	65	50	a	a	DET
ejpam-3591	65	51	clear	clear	ADJ
ejpam-3591	65	52	way	way	NOUN
ejpam-3591	65	53	.	.	PUNCT
ejpam-3591	66	1	proposition	proposition	NOUN
ejpam-3591	66	2	11	11	NUM
ejpam-3591	66	3	in	in	ADP
ejpam-3591	66	4	[	[	X
ejpam-3591	66	5	10](nk	10](nk	NUM
ejpam-3591	66	6	):	):	PUNCT
ejpam-3591	66	7	let	let	VERB
ejpam-3591	66	8	(	(	PUNCT
ejpam-3591	66	9	h	h	NOUN
ejpam-3591	66	10	,	,	PUNCT
ejpam-3591	66	11	◦	◦	NOUN
ejpam-3591	66	12	,	,	PUNCT
ejpam-3591	66	13	≤	≤	NUM
ejpam-3591	66	14	)	)	PUNCT
ejpam-3591	66	15	be	be	VERB
ejpam-3591	66	16	an	an	DET
ejpam-3591	66	17	ordered	ordered	ADJ
ejpam-3591	66	18	hypergroupoid	hypergroupoid	NOUN
ejpam-3591	66	19	and	and	CCONJ
ejpam-3591	66	20	a	a	DET
ejpam-3591	66	21	,	,	PUNCT
ejpam-3591	66	22	b	b	NOUN
ejpam-3591	66	23	nonempty	nonempty	ADJ
ejpam-3591	66	24	subsets	subset	NOUN
ejpam-3591	66	25	of	of	ADP
ejpam-3591	66	26	h.	h.	PROPN
ejpam-3591	67	1	then	then	ADV
ejpam-3591	67	2	we	we	PRON
ejpam-3591	67	3	have	have	VERB
ejpam-3591	67	4	(	(	PUNCT
ejpam-3591	67	5	a	a	DET
ejpam-3591	67	6	∗b	∗b	NOUN
ejpam-3591	67	7	]	]	X
ejpam-3591	67	8	=	=	SYM
ejpam-3591	67	9	(	(	PUNCT
ejpam-3591	67	10	(	(	PUNCT
ejpam-3591	67	11	a	a	PRON
ejpam-3591	67	12	]	]	X
ejpam-3591	67	13	∗	∗	NOUN
ejpam-3591	67	14	(	(	PUNCT
ejpam-3591	67	15	b	b	NOUN
ejpam-3591	67	16	]	]	X
ejpam-3591	67	17	]	]	PUNCT
ejpam-3591	68	1	=	=	PUNCT
ejpam-3591	68	2	(	(	PUNCT
ejpam-3591	68	3	(	(	PUNCT
ejpam-3591	68	4	a	a	PRON
ejpam-3591	68	5	]	]	X
ejpam-3591	68	6	∗b	∗b	X
ejpam-3591	68	7	]	]	X
ejpam-3591	68	8	=	=	PUNCT
ejpam-3591	68	9	(	(	PUNCT
ejpam-3591	68	10	a	a	DET
ejpam-3591	68	11	∗	∗	NOUN
ejpam-3591	68	12	(	(	PUNCT
ejpam-3591	68	13	b	b	NOUN
ejpam-3591	68	14	]	]	X
ejpam-3591	68	15	]	]	PUNCT
ejpam-3591	68	16	.	.	PUNCT
ejpam-3591	69	1	n.	n.	PROPN
ejpam-3591	69	2	kehayopulu	kehayopulu	PROPN
ejpam-3591	69	3	/	/	SYM
ejpam-3591	69	4	eur	eur	PROPN
ejpam-3591	69	5	.	.	PUNCT
ejpam-3591	70	1	j.	j.	PROPN
ejpam-3591	70	2	pure	pure	PROPN
ejpam-3591	70	3	appl	appl	PROPN
ejpam-3591	70	4	.	.	PROPN
ejpam-3591	70	5	math	math	PROPN
ejpam-3591	70	6	,	,	PUNCT
ejpam-3591	70	7	12	12	NUM
ejpam-3591	70	8	(	(	PUNCT
ejpam-3591	70	9	4	4	NUM
ejpam-3591	70	10	)	)	PUNCT
ejpam-3591	70	11	(	(	PUNCT
ejpam-3591	70	12	2019	2019	NUM
ejpam-3591	70	13	)	)	PUNCT
ejpam-3591	70	14	,	,	PUNCT
ejpam-3591	70	15	1771	1771	NUM
ejpam-3591	70	16	-	-	SYM
ejpam-3591	70	17	1778	1778	NUM
ejpam-3591	70	18	1774	1774	NUM
ejpam-3591	70	19	lemma	lemma	PROPN
ejpam-3591	70	20	2.4	2.4	NUM
ejpam-3591	70	21	in	in	ADP
ejpam-3591	70	22	[	[	X
ejpam-3591	70	23	4](zg	4](zg	NUM
ejpam-3591	70	24	)	)	PUNCT
ejpam-3591	70	25	let	let	VERB
ejpam-3591	70	26	s	s	PRON
ejpam-3591	70	27	be	be	AUX
ejpam-3591	70	28	an	an	DET
ejpam-3591	70	29	ordered	order	VERB
ejpam-3591	70	30	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	70	31	and	and	CCONJ
ejpam-3591	70	32	i	i	PRON
ejpam-3591	70	33	an	an	DET
ejpam-3591	70	34	hyperideal	hyperideal	NOUN
ejpam-3591	70	35	of	of	ADP
ejpam-3591	70	36	s.	s.	PROPN
ejpam-3591	70	37	then	then	ADV
ejpam-3591	70	38	i	i	PRON
ejpam-3591	70	39	is	be	AUX
ejpam-3591	70	40	the	the	DET
ejpam-3591	70	41	intersection	intersection	NOUN
ejpam-3591	70	42	of	of	ADP
ejpam-3591	70	43	all	all	DET
ejpam-3591	70	44	irreducible	irreducible	ADJ
ejpam-3591	70	45	hyperideals	hyperideal	NOUN
ejpam-3591	70	46	of	of	ADP
ejpam-3591	70	47	s	s	NOUN
ejpam-3591	70	48	containing	contain	VERB
ejpam-3591	70	49	i.	i.	NOUN
ejpam-3591	70	50	we	we	PRON
ejpam-3591	70	51	sketch	sketch	VERB
ejpam-3591	70	52	the	the	DET
ejpam-3591	70	53	proof	proof	NOUN
ejpam-3591	70	54	of	of	ADP
ejpam-3591	70	55	this	this	DET
ejpam-3591	70	56	lemma	lemma	PROPN
ejpam-3591	70	57	,	,	PUNCT
ejpam-3591	70	58	to	to	PART
ejpam-3591	70	59	make	make	VERB
ejpam-3591	70	60	it	it	PRON
ejpam-3591	70	61	clear	clear	ADJ
ejpam-3591	70	62	.	.	PUNCT
ejpam-3591	71	1	let	let	VERB
ejpam-3591	71	2	us	we	PRON
ejpam-3591	71	3	assume	assume	VERB
ejpam-3591	71	4	{	{	PUNCT
ejpam-3591	71	5	iα	iα	INTJ
ejpam-3591	72	1	|	|	ADV
ejpam-3591	72	2	α	α	PROPN
ejpam-3591	72	3	∈	∈	PROPN
ejpam-3591	72	4	γ	γ	X
ejpam-3591	72	5	}	}	PUNCT
ejpam-3591	72	6	is	be	AUX
ejpam-3591	72	7	the	the	DET
ejpam-3591	72	8	set	set	NOUN
ejpam-3591	72	9	of	of	ADP
ejpam-3591	72	10	all	all	DET
ejpam-3591	72	11	irreducible	irreducible	ADJ
ejpam-3591	72	12	ideals	ideal	NOUN
ejpam-3591	72	13	of	of	ADP
ejpam-3591	72	14	s	s	NOUN
ejpam-3591	72	15	containing	contain	VERB
ejpam-3591	72	16	i	i	PRON
ejpam-3591	72	17	,	,	PUNCT
ejpam-3591	72	18	and	and	CCONJ
ejpam-3591	72	19	let	let	VERB
ejpam-3591	72	20	a	a	DET
ejpam-3591	72	21	∈	∈	PROPN
ejpam-3591	72	22	⋂	⋂	PROPN
ejpam-3591	72	23	α∈γ	α∈γ	NUM
ejpam-3591	72	24	iα	iα	NOUN
ejpam-3591	72	25	such	such	ADJ
ejpam-3591	72	26	that	that	SCONJ
ejpam-3591	72	27	a	a	DET
ejpam-3591	72	28	6∈	6∈	PROPN
ejpam-3591	72	29	i.	i.	NOUN
ejpam-3591	72	30	the	the	DET
ejpam-3591	72	31	set	set	PROPN
ejpam-3591	72	32	ω	ω	NOUN
ejpam-3591	72	33	:	:	PUNCT
ejpam-3591	73	1	=	=	SYM
ejpam-3591	73	2	{	{	PUNCT
ejpam-3591	73	3	h	h	NOUN
ejpam-3591	73	4	|	|	ADV
ejpam-3591	74	1	h	h	NOUN
ejpam-3591	75	1	ideal	ideal	NOUN
ejpam-3591	75	2	of	of	ADP
ejpam-3591	75	3	s	s	PROPN
ejpam-3591	75	4	,	,	PUNCT
ejpam-3591	76	1	h	h	PROPN
ejpam-3591	76	2	⊇	⊇	PROPN
ejpam-3591	76	3	i	i	PROPN
ejpam-3591	76	4	,	,	PUNCT
ejpam-3591	76	5	a	a	DET
ejpam-3591	76	6	6∈	6∈	NOUN
ejpam-3591	76	7	h	h	NOUN
ejpam-3591	76	8	}	}	PUNCT
ejpam-3591	76	9	has	have	VERB
ejpam-3591	76	10	a	a	DET
ejpam-3591	76	11	maximal	maximal	ADJ
ejpam-3591	76	12	element	element	NOUN
ejpam-3591	76	13	,	,	PUNCT
ejpam-3591	76	14	say	say	VERB
ejpam-3591	76	15	m	m	PRON
ejpam-3591	76	16	.	.	PUNCT
ejpam-3591	77	1	the	the	DET
ejpam-3591	77	2	set	set	NOUN
ejpam-3591	77	3	m	m	VERB
ejpam-3591	77	4	is	be	AUX
ejpam-3591	77	5	irreducible	irreducible	ADJ
ejpam-3591	77	6	.	.	PUNCT
ejpam-3591	78	1	indeed	indeed	ADV
ejpam-3591	78	2	:	:	PUNCT
ejpam-3591	78	3	let	let	VERB
ejpam-3591	78	4	a	a	DET
ejpam-3591	78	5	,	,	PUNCT
ejpam-3591	78	6	b	b	NOUN
ejpam-3591	78	7	be	be	AUX
ejpam-3591	78	8	ideals	ideal	NOUN
ejpam-3591	78	9	of	of	ADP
ejpam-3591	78	10	m	m	NOUN
ejpam-3591	78	11	such	such	ADJ
ejpam-3591	78	12	that	that	SCONJ
ejpam-3591	78	13	a	a	DET
ejpam-3591	78	14	∩	∩	ADJ
ejpam-3591	78	15	b	b	NOUN
ejpam-3591	78	16	=	=	NOUN
ejpam-3591	78	17	m	m	PROPN
ejpam-3591	78	18	.	.	PUNCT
ejpam-3591	79	1	since	since	SCONJ
ejpam-3591	79	2	a	a	DET
ejpam-3591	79	3	6∈	6∈	NOUN
ejpam-3591	79	4	m	m	VERB
ejpam-3591	79	5	,	,	PUNCT
ejpam-3591	79	6	we	we	PRON
ejpam-3591	79	7	have	have	VERB
ejpam-3591	79	8	a	a	DET
ejpam-3591	79	9	/∈	/∈	NOUN
ejpam-3591	79	10	a	a	DET
ejpam-3591	79	11	∩	∩	ADJ
ejpam-3591	79	12	b.	b.	NOUN
ejpam-3591	79	13	if	if	SCONJ
ejpam-3591	79	14	a	a	PRON
ejpam-3591	79	15	/∈	/∈	NOUN
ejpam-3591	80	1	a	a	PRON
ejpam-3591	80	2	then	then	ADV
ejpam-3591	80	3	,	,	PUNCT
ejpam-3591	80	4	since	since	SCONJ
ejpam-3591	80	5	a	a	PRON
ejpam-3591	80	6	is	be	AUX
ejpam-3591	80	7	an	an	DET
ejpam-3591	80	8	ideal	ideal	NOUN
ejpam-3591	80	9	of	of	ADP
ejpam-3591	80	10	s	s	PRON
ejpam-3591	80	11	and	and	CCONJ
ejpam-3591	80	12	a	a	DET
ejpam-3591	80	13	⊇	⊇	NOUN
ejpam-3591	80	14	m	m	PROPN
ejpam-3591	80	15	⊇	⊇	NOUN
ejpam-3591	80	16	i	i	PRON
ejpam-3591	80	17	,	,	PUNCT
ejpam-3591	80	18	we	we	PRON
ejpam-3591	80	19	have	have	VERB
ejpam-3591	80	20	a	a	DET
ejpam-3591	80	21	∈	∈	PROPN
ejpam-3591	80	22	ω	ω	NOUN
ejpam-3591	80	23	.	.	PUNCT
ejpam-3591	81	1	since	since	SCONJ
ejpam-3591	81	2	a	a	DET
ejpam-3591	81	3	⊇m	⊇m	ADJ
ejpam-3591	81	4	and	and	CCONJ
ejpam-3591	81	5	m	m	NOUN
ejpam-3591	81	6	is	be	AUX
ejpam-3591	81	7	maximal	maximal	ADJ
ejpam-3591	81	8	in	in	ADP
ejpam-3591	81	9	ω	ω	NUM
ejpam-3591	81	10	,	,	PUNCT
ejpam-3591	81	11	we	we	PRON
ejpam-3591	81	12	have	have	VERB
ejpam-3591	81	13	a	a	DET
ejpam-3591	81	14	=	=	NOUN
ejpam-3591	81	15	m	m	NOUN
ejpam-3591	81	16	.	.	PUNCT
ejpam-3591	82	1	similarly	similarly	ADV
ejpam-3591	82	2	b	b	X
ejpam-3591	82	3	=	=	NOUN
ejpam-3591	82	4	m	m	VERB
ejpam-3591	82	5	.	.	PUNCT
ejpam-3591	83	1	since	since	SCONJ
ejpam-3591	83	2	m	m	PROPN
ejpam-3591	83	3	is	be	AUX
ejpam-3591	83	4	an	an	DET
ejpam-3591	83	5	irreducible	irreducible	ADJ
ejpam-3591	83	6	ideal	ideal	NOUN
ejpam-3591	83	7	of	of	ADP
ejpam-3591	83	8	s	s	PROPN
ejpam-3591	83	9	,	,	PUNCT
ejpam-3591	83	10	we	we	PRON
ejpam-3591	83	11	have	have	VERB
ejpam-3591	83	12	a	a	DET
ejpam-3591	83	13	∈	∈	NOUN
ejpam-3591	83	14	iβ	iβ	ADP
ejpam-3591	83	15	for	for	ADP
ejpam-3591	83	16	some	some	DET
ejpam-3591	83	17	β	β	NOUN
ejpam-3591	83	18	∈	∈	PROPN
ejpam-3591	83	19	γ	γ	X
ejpam-3591	83	20	.	.	PROPN
ejpam-3591	84	1	since	since	SCONJ
ejpam-3591	84	2	a	a	DET
ejpam-3591	84	3	∈	∈	PROPN
ejpam-3591	84	4	⋂	⋂	PROPN
ejpam-3591	84	5	α∈γ	α∈γ	NUM
ejpam-3591	84	6	iα	iα	NOUN
ejpam-3591	84	7	,	,	PUNCT
ejpam-3591	84	8	we	we	PRON
ejpam-3591	84	9	have	have	VERB
ejpam-3591	84	10	a	a	DET
ejpam-3591	84	11	∈	∈	PROPN
ejpam-3591	84	12	iβ	iβ	NOUN
ejpam-3591	84	13	.	.	PROPN
ejpam-3591	85	1	then	then	ADV
ejpam-3591	85	2	a	a	DET
ejpam-3591	85	3	∈m	∈m	NOUN
ejpam-3591	85	4	that	that	PRON
ejpam-3591	85	5	is	be	AUX
ejpam-3591	85	6	impossible	impossible	ADJ
ejpam-3591	85	7	.	.	PUNCT
ejpam-3591	86	1	regarding	regard	VERB
ejpam-3591	86	2	the	the	DET
ejpam-3591	86	3	proof	proof	NOUN
ejpam-3591	86	4	that	that	SCONJ
ejpam-3591	86	5	the	the	DET
ejpam-3591	86	6	maximal	maximal	ADJ
ejpam-3591	86	7	subset	subset	NOUN
ejpam-3591	86	8	m	m	PROPN
ejpam-3591	86	9	of	of	ADP
ejpam-3591	86	10	ω	ω	PROPN
ejpam-3591	86	11	is	be	AUX
ejpam-3591	86	12	irreducible	irreducible	ADJ
ejpam-3591	86	13	,	,	PUNCT
ejpam-3591	86	14	the	the	DET
ejpam-3591	86	15	proof	proof	NOUN
ejpam-3591	86	16	is	be	AUX
ejpam-3591	86	17	the	the	DET
ejpam-3591	86	18	same	same	ADJ
ejpam-3591	86	19	with	with	ADP
ejpam-3591	86	20	the	the	DET
ejpam-3591	86	21	proof	proof	NOUN
ejpam-3591	86	22	of	of	ADP
ejpam-3591	86	23	proposition	proposition	NOUN
ejpam-3591	86	24	3.5	3.5	NUM
ejpam-3591	86	25	in	in	ADP
ejpam-3591	86	26	[	[	X
ejpam-3591	86	27	1	1	NUM
ejpam-3591	86	28	]	]	PUNCT
ejpam-3591	86	29	.	.	PUNCT
ejpam-3591	87	1	to	to	PART
ejpam-3591	87	2	apply	apply	VERB
ejpam-3591	87	3	zorn	zorn	PROPN
ejpam-3591	87	4	’s	’s	PART
ejpam-3591	87	5	lemma	lemma	PROPN
ejpam-3591	87	6	it	it	PRON
ejpam-3591	87	7	should	should	AUX
ejpam-3591	87	8	be	be	AUX
ejpam-3591	87	9	mentioned	mention	VERB
ejpam-3591	87	10	that	that	SCONJ
ejpam-3591	87	11	every	every	DET
ejpam-3591	87	12	totally	totally	ADV
ejpam-3591	87	13	ordered	order	VERB
ejpam-3591	87	14	subset	subset	NOUN
ejpam-3591	87	15	of	of	ADP
ejpam-3591	87	16	ω	ω	PROPN
ejpam-3591	87	17	has	have	VERB
ejpam-3591	87	18	an	an	DET
ejpam-3591	87	19	upper	upper	ADJ
ejpam-3591	87	20	bound	bind	VERB
ejpam-3591	87	21	in	in	ADP
ejpam-3591	87	22	ω	ω	NOUN
ejpam-3591	87	23	as	as	ADP
ejpam-3591	87	24	in	in	ADP
ejpam-3591	87	25	the	the	DET
ejpam-3591	87	26	proof	proof	NOUN
ejpam-3591	87	27	of	of	ADP
ejpam-3591	87	28	proposition	proposition	NOUN
ejpam-3591	87	29	3.5	3.5	NUM
ejpam-3591	87	30	in	in	ADP
ejpam-3591	87	31	[	[	X
ejpam-3591	87	32	1	1	NUM
ejpam-3591	87	33	]	]	PUNCT
ejpam-3591	87	34	.	.	PUNCT
ejpam-3591	88	1	this	this	DET
ejpam-3591	88	2	lemma	lemma	PROPN
ejpam-3591	88	3	holds	hold	VERB
ejpam-3591	88	4	for	for	ADP
ejpam-3591	88	5	ordered	order	VERB
ejpam-3591	88	6	hypergroupoids	hypergroupoid	NOUN
ejpam-3591	88	7	and	and	CCONJ
ejpam-3591	88	8	hypergroupoids	hypergroupoid	NOUN
ejpam-3591	88	9	(	(	PUNCT
ejpam-3591	88	10	without	without	ADP
ejpam-3591	88	11	order	order	NOUN
ejpam-3591	88	12	)	)	PUNCT
ejpam-3591	88	13	and	and	CCONJ
ejpam-3591	88	14	it	it	PRON
ejpam-3591	88	15	is	be	AUX
ejpam-3591	88	16	not	not	PART
ejpam-3591	88	17	needed	need	VERB
ejpam-3591	88	18	for	for	ADP
ejpam-3591	88	19	the	the	DET
ejpam-3591	88	20	rest	rest	NOUN
ejpam-3591	88	21	of	of	ADP
ejpam-3591	88	22	the	the	DET
ejpam-3591	88	23	paper	paper	NOUN
ejpam-3591	88	24	.	.	PUNCT
ejpam-3591	89	1	the	the	DET
ejpam-3591	89	2	proposition	proposition	NOUN
ejpam-3591	89	3	in	in	ADP
ejpam-3591	89	4	[	[	X
ejpam-3591	89	5	7](nk	7](nk	NUM
ejpam-3591	89	6	):	):	PUNCT
ejpam-3591	89	7	an	an	DET
ejpam-3591	89	8	ideal	ideal	NOUN
ejpam-3591	89	9	of	of	ADP
ejpam-3591	89	10	a	a	DET
ejpam-3591	89	11	po	po	NOUN
ejpam-3591	89	12	-	-	PUNCT
ejpam-3591	89	13	semigroup	semigroup	PROPN
ejpam-3591	89	14	is	be	AUX
ejpam-3591	89	15	prime	prime	ADJ
ejpam-3591	89	16	if	if	SCONJ
ejpam-3591	90	1	and	and	CCONJ
ejpam-3591	90	2	only	only	ADV
ejpam-3591	90	3	if	if	SCONJ
ejpam-3591	90	4	it	it	PRON
ejpam-3591	90	5	is	be	AUX
ejpam-3591	90	6	both	both	PRON
ejpam-3591	90	7	semiprime	semiprime	NOUN
ejpam-3591	90	8	and	and	CCONJ
ejpam-3591	90	9	weakly	weakly	ADJ
ejpam-3591	90	10	prime	prime	NOUN
ejpam-3591	90	11	.	.	PUNCT
ejpam-3591	91	1	in	in	ADP
ejpam-3591	91	2	commutative	commutative	PROPN
ejpam-3591	91	3	po	po	NOUN
ejpam-3591	91	4	-	-	PUNCT
ejpam-3591	91	5	semigroups	semigroups	X
ejpam-3591	91	6	the	the	DET
ejpam-3591	91	7	prime	prime	ADJ
ejpam-3591	91	8	and	and	CCONJ
ejpam-3591	91	9	weakly	weakly	ADJ
ejpam-3591	91	10	prime	prime	ADJ
ejpam-3591	91	11	ideals	ideal	NOUN
ejpam-3591	91	12	coincide	coincide	NOUN
ejpam-3591	91	13	.	.	PUNCT
ejpam-3591	92	1	theorem	theorem	VERB
ejpam-3591	92	2	2.5	2.5	NUM
ejpam-3591	92	3	in	in	ADP
ejpam-3591	92	4	[	[	X
ejpam-3591	92	5	4](zg	4](zg	NUM
ejpam-3591	92	6	):	):	PUNCT
ejpam-3591	92	7	let	let	VERB
ejpam-3591	92	8	s	s	PRON
ejpam-3591	92	9	be	be	AUX
ejpam-3591	92	10	an	an	DET
ejpam-3591	92	11	ordered	ordered	ADJ
ejpam-3591	92	12	semihypergroup	semihypergroup	NOUN
ejpam-3591	93	1	and	and	CCONJ
ejpam-3591	93	2	i	i	PRON
ejpam-3591	93	3	a	a	DET
ejpam-3591	93	4	hyperideal	hyperideal	NOUN
ejpam-3591	93	5	of	of	ADP
ejpam-3591	93	6	s.	s.	PROPN
ejpam-3591	93	7	then	then	ADV
ejpam-3591	93	8	i	i	PRON
ejpam-3591	93	9	is	be	AUX
ejpam-3591	93	10	prime	prime	ADJ
ejpam-3591	93	11	if	if	SCONJ
ejpam-3591	94	1	and	and	CCONJ
ejpam-3591	94	2	only	only	ADV
ejpam-3591	94	3	if	if	SCONJ
ejpam-3591	94	4	it	it	PRON
ejpam-3591	94	5	is	be	AUX
ejpam-3591	94	6	semiprime	semiprime	NOUN
ejpam-3591	94	7	and	and	CCONJ
ejpam-3591	94	8	weakly	weakly	ADJ
ejpam-3591	94	9	prime	prime	NOUN
ejpam-3591	94	10	.	.	PUNCT
ejpam-3591	95	1	in	in	ADP
ejpam-3591	95	2	particular	particular	ADJ
ejpam-3591	95	3	,	,	PUNCT
ejpam-3591	95	4	if	if	SCONJ
ejpam-3591	95	5	s	s	NOUN
ejpam-3591	95	6	is	be	AUX
ejpam-3591	95	7	commutative	commutative	ADJ
ejpam-3591	95	8	,	,	PUNCT
ejpam-3591	95	9	then	then	ADV
ejpam-3591	95	10	the	the	DET
ejpam-3591	95	11	prime	prime	ADJ
ejpam-3591	95	12	and	and	CCONJ
ejpam-3591	95	13	weakly	weakly	ADJ
ejpam-3591	95	14	hyperideals	hyperideal	NOUN
ejpam-3591	95	15	coincide	coincide	NOUN
ejpam-3591	95	16	.	.	PUNCT
ejpam-3591	96	1	if	if	SCONJ
ejpam-3591	96	2	we	we	PRON
ejpam-3591	96	3	get	get	VERB
ejpam-3591	96	4	the	the	DET
ejpam-3591	96	5	proof	proof	NOUN
ejpam-3591	96	6	of	of	ADP
ejpam-3591	96	7	proposition	proposition	NOUN
ejpam-3591	96	8	in	in	ADP
ejpam-3591	96	9	[	[	X
ejpam-3591	96	10	7	7	NUM
ejpam-3591	96	11	]	]	PUNCT
ejpam-3591	96	12	,	,	PUNCT
ejpam-3591	96	13	delete	delete	VERB
ejpam-3591	96	14	the	the	DET
ejpam-3591	96	15	“	"	PUNCT
ejpam-3591	96	16	·	·	PUNCT
ejpam-3591	96	17	”	"	PUNCT
ejpam-3591	96	18	and	and	CCONJ
ejpam-3591	96	19	write	write	VERB
ejpam-3591	96	20	“	"	PUNCT
ejpam-3591	96	21	◦	◦	NOUN
ejpam-3591	96	22	”	"	PUNCT
ejpam-3591	96	23	instead	instead	ADV
ejpam-3591	96	24	,	,	PUNCT
ejpam-3591	96	25	then	then	ADV
ejpam-3591	96	26	this	this	PRON
ejpam-3591	96	27	the	the	DET
ejpam-3591	96	28	proof	proof	NOUN
ejpam-3591	96	29	of	of	ADP
ejpam-3591	96	30	theorem	theorem	ADJ
ejpam-3591	96	31	2.5	2.5	NUM
ejpam-3591	96	32	in	in	ADP
ejpam-3591	96	33	[	[	X
ejpam-3591	96	34	4	4	NUM
ejpam-3591	96	35	]	]	PUNCT
ejpam-3591	96	36	(	(	PUNCT
ejpam-3591	96	37	is	be	AUX
ejpam-3591	96	38	this	this	PRON
ejpam-3591	96	39	a	a	DET
ejpam-3591	96	40	right	right	ADJ
ejpam-3591	96	41	way	way	NOUN
ejpam-3591	96	42	to	to	PART
ejpam-3591	96	43	work	work	VERB
ejpam-3591	96	44	without	without	ADP
ejpam-3591	96	45	any	any	DET
ejpam-3591	96	46	explanation	explanation	NOUN
ejpam-3591	96	47	if	if	SCONJ
ejpam-3591	96	48	we	we	PRON
ejpam-3591	96	49	have	have	VERB
ejpam-3591	96	50	the	the	DET
ejpam-3591	96	51	right	right	NOUN
ejpam-3591	96	52	to	to	PART
ejpam-3591	96	53	combine	combine	VERB
ejpam-3591	96	54	elements	element	NOUN
ejpam-3591	96	55	with	with	ADP
ejpam-3591	96	56	sets	set	NOUN
ejpam-3591	96	57	?	?	PUNCT
ejpam-3591	96	58	)	)	PUNCT
ejpam-3591	96	59	.	.	PUNCT
ejpam-3591	97	1	the	the	DET
ejpam-3591	97	2	paper	paper	NOUN
ejpam-3591	97	3	in	in	ADP
ejpam-3591	97	4	[	[	X
ejpam-3591	97	5	7	7	NUM
ejpam-3591	97	6	]	]	PUNCT
ejpam-3591	97	7	is	be	AUX
ejpam-3591	97	8	not	not	PART
ejpam-3591	97	9	cited	cite	VERB
ejpam-3591	97	10	in	in	ADP
ejpam-3591	97	11	[	[	X
ejpam-3591	97	12	4	4	NUM
ejpam-3591	97	13	]	]	PUNCT
ejpam-3591	97	14	.	.	PUNCT
ejpam-3591	98	1	later	later	ADV
ejpam-3591	98	2	,	,	PUNCT
ejpam-3591	98	3	at	at	ADP
ejpam-3591	98	4	the	the	DET
ejpam-3591	98	5	end	end	NOUN
ejpam-3591	98	6	of	of	ADP
ejpam-3591	98	7	this	this	DET
ejpam-3591	98	8	note	note	NOUN
ejpam-3591	98	9	,	,	PUNCT
ejpam-3591	98	10	we	we	PRON
ejpam-3591	98	11	will	will	AUX
ejpam-3591	98	12	see	see	VERB
ejpam-3591	98	13	that	that	SCONJ
ejpam-3591	98	14	the	the	DET
ejpam-3591	98	15	first	first	ADJ
ejpam-3591	98	16	part	part	NOUN
ejpam-3591	98	17	of	of	ADP
ejpam-3591	98	18	theorem	theorem	ADJ
ejpam-3591	98	19	2.5	2.5	NUM
ejpam-3591	98	20	in	in	ADP
ejpam-3591	98	21	[	[	X
ejpam-3591	98	22	4	4	NUM
ejpam-3591	98	23	]	]	PUNCT
ejpam-3591	98	24	is	be	AUX
ejpam-3591	98	25	not	not	PART
ejpam-3591	98	26	new	new	ADJ
ejpam-3591	98	27	,	,	PUNCT
ejpam-3591	98	28	and	and	CCONJ
ejpam-3591	98	29	there	there	PRON
ejpam-3591	98	30	is	be	VERB
ejpam-3591	98	31	a	a	DET
ejpam-3591	98	32	remark	remark	NOUN
ejpam-3591	98	33	for	for	ADP
ejpam-3591	98	34	the	the	DET
ejpam-3591	98	35	second	second	ADJ
ejpam-3591	98	36	part	part	NOUN
ejpam-3591	98	37	.	.	PUNCT
ejpam-3591	99	1	theorem	theorem	VERB
ejpam-3591	99	2	3.1	3.1	NUM
ejpam-3591	99	3	in	in	ADP
ejpam-3591	99	4	[	[	NOUN
ejpam-3591	99	5	4](zg	4](zg	NUM
ejpam-3591	99	6	):	):	PUNCT
ejpam-3591	99	7	let	let	VERB
ejpam-3591	99	8	s	s	PRON
ejpam-3591	99	9	be	be	AUX
ejpam-3591	99	10	an	an	DET
ejpam-3591	99	11	ordered	order	VERB
ejpam-3591	99	12	semihypergroup	semihypergroup	NOUN
ejpam-3591	99	13	.	.	PUNCT
ejpam-3591	100	1	then	then	ADV
ejpam-3591	100	2	the	the	DET
ejpam-3591	100	3	following	follow	VERB
ejpam-3591	100	4	statements	statement	NOUN
ejpam-3591	100	5	are	be	AUX
ejpam-3591	100	6	equivalent	equivalent	ADJ
ejpam-3591	100	7	:	:	PUNCT
ejpam-3591	100	8	(	(	PUNCT
ejpam-3591	100	9	1	1	X
ejpam-3591	100	10	)	)	PUNCT
ejpam-3591	100	11	s	s	VERB
ejpam-3591	100	12	is	be	AUX
ejpam-3591	100	13	semisimple	semisimple	ADJ
ejpam-3591	100	14	.	.	PUNCT
ejpam-3591	101	1	(	(	PUNCT
ejpam-3591	101	2	2	2	X
ejpam-3591	101	3	)	)	PUNCT
ejpam-3591	101	4	a	a	DET
ejpam-3591	101	5	∩b	∩b	NOUN
ejpam-3591	101	6	=	=	SYM
ejpam-3591	101	7	(	(	PUNCT
ejpam-3591	101	8	a	a	DET
ejpam-3591	101	9	◦	◦	NOUN
ejpam-3591	101	10	b	b	NOUN
ejpam-3591	101	11	]	]	X
ejpam-3591	101	12	for	for	ADP
ejpam-3591	101	13	all	all	DET
ejpam-3591	101	14	hyperideals	hyperideal	NOUN
ejpam-3591	101	15	a	a	DET
ejpam-3591	101	16	,	,	PUNCT
ejpam-3591	101	17	b	b	PROPN
ejpam-3591	101	18	of	of	ADP
ejpam-3591	101	19	s.	s.	PROPN
ejpam-3591	101	20	(	(	PUNCT
ejpam-3591	101	21	3	3	NUM
ejpam-3591	101	22	)	)	PUNCT
ejpam-3591	101	23	(	(	PUNCT
ejpam-3591	101	24	a2	a2	PROPN
ejpam-3591	101	25	]	]	PUNCT
ejpam-3591	101	26	=	=	PUNCT
ejpam-3591	101	27	a	a	PRON
ejpam-3591	101	28	for	for	ADP
ejpam-3591	101	29	every	every	DET
ejpam-3591	101	30	hyperideal	hyperideal	NOUN
ejpam-3591	101	31	a	a	PRON
ejpam-3591	101	32	of	of	ADP
ejpam-3591	101	33	s.	s.	PROPN
ejpam-3591	101	34	(	(	PUNCT
ejpam-3591	101	35	4	4	X
ejpam-3591	101	36	)	)	PUNCT
ejpam-3591	101	37	every	every	DET
ejpam-3591	101	38	hyperideal	hyperideal	NOUN
ejpam-3591	101	39	of	of	ADP
ejpam-3591	101	40	s	s	NOUN
ejpam-3591	101	41	is	be	AUX
ejpam-3591	101	42	weakly	weakly	ADJ
ejpam-3591	101	43	semiprime	semiprime	NOUN
ejpam-3591	101	44	.	.	PUNCT
ejpam-3591	102	1	theorem	theorem	VERB
ejpam-3591	102	2	18	18	NUM
ejpam-3591	102	3	in	in	ADP
ejpam-3591	102	4	[	[	X
ejpam-3591	102	5	10](nk	10](nk	NUM
ejpam-3591	102	6	):	):	PUNCT
ejpam-3591	102	7	an	an	DET
ejpam-3591	102	8	ordered	order	VERB
ejpam-3591	102	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	102	10	(	(	PUNCT
ejpam-3591	102	11	h	h	NOUN
ejpam-3591	102	12	,	,	PUNCT
ejpam-3591	102	13	◦	◦	NOUN
ejpam-3591	102	14	,	,	PUNCT
ejpam-3591	102	15	≤	≤	NUM
ejpam-3591	102	16	)	)	PUNCT
ejpam-3591	102	17	is	be	AUX
ejpam-3591	102	18	semisimple	semisimple	ADJ
ejpam-3591	102	19	if	if	SCONJ
ejpam-3591	102	20	and	and	CCONJ
ejpam-3591	102	21	only	only	ADV
ejpam-3591	102	22	if	if	SCONJ
ejpam-3591	102	23	the	the	DET
ejpam-3591	102	24	ideals	ideal	NOUN
ejpam-3591	102	25	of	of	ADP
ejpam-3591	102	26	h	h	NOUN
ejpam-3591	102	27	are	be	AUX
ejpam-3591	102	28	idempotent	idempotent	ADJ
ejpam-3591	102	29	.	.	PUNCT
ejpam-3591	103	1	theorem	theorem	ADJ
ejpam-3591	103	2	9	9	NUM
ejpam-3591	103	3	in	in	ADP
ejpam-3591	103	4	[	[	NOUN
ejpam-3591	103	5	10](nk	10](nk	NUM
ejpam-3591	103	6	):	):	PUNCT
ejpam-3591	103	7	let	let	VERB
ejpam-3591	103	8	(	(	PUNCT
ejpam-3591	103	9	h	h	NOUN
ejpam-3591	103	10	,	,	PUNCT
ejpam-3591	103	11	◦	◦	NOUN
ejpam-3591	103	12	,	,	PUNCT
ejpam-3591	103	13	≤	≤	NUM
ejpam-3591	103	14	)	)	PUNCT
ejpam-3591	103	15	be	be	VERB
ejpam-3591	103	16	an	an	DET
ejpam-3591	103	17	ordered	order	VERB
ejpam-3591	103	18	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	103	19	.	.	PUNCT
ejpam-3591	104	1	the	the	DET
ejpam-3591	104	2	ideals	ideal	NOUN
ejpam-3591	104	3	of	of	ADP
ejpam-3591	104	4	h	h	NOUN
ejpam-3591	104	5	are	be	AUX
ejpam-3591	104	6	idempotent	idempotent	ADJ
ejpam-3591	104	7	if	if	SCONJ
ejpam-3591	104	8	and	and	CCONJ
ejpam-3591	104	9	only	only	ADV
ejpam-3591	104	10	if	if	SCONJ
ejpam-3591	104	11	for	for	ADP
ejpam-3591	104	12	any	any	DET
ejpam-3591	104	13	two	two	NUM
ejpam-3591	104	14	ideals	ideal	NOUN
ejpam-3591	104	15	a	a	PRON
ejpam-3591	104	16	and	and	CCONJ
ejpam-3591	104	17	b	b	NOUN
ejpam-3591	104	18	of	of	ADP
ejpam-3591	104	19	h	h	NOUN
ejpam-3591	104	20	,	,	PUNCT
ejpam-3591	104	21	we	we	PRON
ejpam-3591	104	22	have	have	VERB
ejpam-3591	104	23	a	a	DET
ejpam-3591	104	24	∩b	∩b	NOUN
ejpam-3591	104	25	=	=	PUNCT
ejpam-3591	104	26	(	(	PUNCT
ejpam-3591	104	27	a	a	DET
ejpam-3591	104	28	∗b	∗b	NOUN
ejpam-3591	104	29	]	]	PUNCT
ejpam-3591	104	30	.	.	PUNCT
ejpam-3591	105	1	n.	n.	PROPN
ejpam-3591	105	2	kehayopulu	kehayopulu	PROPN
ejpam-3591	105	3	/	/	SYM
ejpam-3591	105	4	eur	eur	PROPN
ejpam-3591	105	5	.	.	PUNCT
ejpam-3591	106	1	j.	j.	PROPN
ejpam-3591	106	2	pure	pure	PROPN
ejpam-3591	106	3	appl	appl	PROPN
ejpam-3591	106	4	.	.	PROPN
ejpam-3591	106	5	math	math	PROPN
ejpam-3591	106	6	,	,	PUNCT
ejpam-3591	106	7	12	12	NUM
ejpam-3591	106	8	(	(	PUNCT
ejpam-3591	106	9	4	4	NUM
ejpam-3591	106	10	)	)	PUNCT
ejpam-3591	106	11	(	(	PUNCT
ejpam-3591	106	12	2019	2019	NUM
ejpam-3591	106	13	)	)	PUNCT
ejpam-3591	106	14	,	,	PUNCT
ejpam-3591	106	15	1771	1771	NUM
ejpam-3591	106	16	-	-	SYM
ejpam-3591	106	17	1778	1778	NUM
ejpam-3591	106	18	1775	1775	NUM
ejpam-3591	106	19	so	so	ADV
ejpam-3591	106	20	,	,	PUNCT
ejpam-3591	106	21	the	the	DET
ejpam-3591	106	22	equivalence	equivalence	NOUN
ejpam-3591	106	23	(	(	PUNCT
ejpam-3591	106	24	1)⇔	1)⇔	NUM
ejpam-3591	106	25	(	(	PUNCT
ejpam-3591	106	26	3	3	NUM
ejpam-3591	106	27	)	)	PUNCT
ejpam-3591	106	28	in	in	ADP
ejpam-3591	106	29	[	[	X
ejpam-3591	106	30	4	4	NUM
ejpam-3591	106	31	,	,	PUNCT
ejpam-3591	106	32	theorem	theorem	VERB
ejpam-3591	106	33	3.1	3.1	NUM
ejpam-3591	106	34	]	]	PUNCT
ejpam-3591	106	35	,	,	PUNCT
ejpam-3591	106	36	is	be	AUX
ejpam-3591	106	37	the	the	DET
ejpam-3591	106	38	theorem	theorem	ADJ
ejpam-3591	106	39	18	18	NUM
ejpam-3591	106	40	in	in	ADP
ejpam-3591	106	41	[	[	X
ejpam-3591	106	42	10	10	NUM
ejpam-3591	106	43	]	]	PUNCT
ejpam-3591	106	44	.	.	PUNCT
ejpam-3591	107	1	the	the	DET
ejpam-3591	107	2	equivalence	equivalence	NOUN
ejpam-3591	107	3	(	(	PUNCT
ejpam-3591	107	4	2)⇔	2)⇔	NUM
ejpam-3591	107	5	(	(	PUNCT
ejpam-3591	107	6	3	3	NUM
ejpam-3591	107	7	)	)	PUNCT
ejpam-3591	107	8	in	in	ADP
ejpam-3591	107	9	[	[	X
ejpam-3591	107	10	4	4	NUM
ejpam-3591	107	11	,	,	PUNCT
ejpam-3591	107	12	theorem	theorem	VERB
ejpam-3591	107	13	3.1	3.1	NUM
ejpam-3591	107	14	]	]	PUNCT
ejpam-3591	107	15	,	,	PUNCT
ejpam-3591	107	16	is	be	AUX
ejpam-3591	107	17	the	the	DET
ejpam-3591	107	18	theorem	theorem	NOUN
ejpam-3591	107	19	9	9	NUM
ejpam-3591	107	20	in	in	ADP
ejpam-3591	107	21	[	[	X
ejpam-3591	107	22	10	10	NUM
ejpam-3591	107	23	]	]	PUNCT
ejpam-3591	107	24	.	.	PUNCT
ejpam-3591	108	1	the	the	DET
ejpam-3591	108	2	implication	implication	NOUN
ejpam-3591	108	3	(	(	PUNCT
ejpam-3591	108	4	4)⇒	4)⇒	X
ejpam-3591	108	5	(	(	PUNCT
ejpam-3591	108	6	3	3	NUM
ejpam-3591	108	7	)	)	PUNCT
ejpam-3591	108	8	in	in	ADP
ejpam-3591	108	9	[	[	X
ejpam-3591	108	10	4	4	NUM
ejpam-3591	108	11	,	,	PUNCT
ejpam-3591	108	12	theorem	theorem	VERB
ejpam-3591	108	13	3.1	3.1	NUM
ejpam-3591	108	14	]	]	PUNCT
ejpam-3591	108	15	,	,	PUNCT
ejpam-3591	108	16	is	be	AUX
ejpam-3591	108	17	obvious	obvious	ADJ
ejpam-3591	108	18	as	as	ADP
ejpam-3591	108	19	for	for	ADP
ejpam-3591	108	20	any	any	DET
ejpam-3591	108	21	ideal	ideal	NOUN
ejpam-3591	108	22	a	a	PRON
ejpam-3591	108	23	of	of	ADP
ejpam-3591	108	24	s	s	PROPN
ejpam-3591	108	25	,	,	PUNCT
ejpam-3591	108	26	the	the	DET
ejpam-3591	108	27	set	set	NOUN
ejpam-3591	108	28	(	(	PUNCT
ejpam-3591	108	29	a	a	DET
ejpam-3591	108	30	∗a	∗a	PROPN
ejpam-3591	108	31	]	]	PUNCT
ejpam-3591	108	32	is	be	AUX
ejpam-3591	108	33	an	an	DET
ejpam-3591	108	34	ideal	ideal	NOUN
ejpam-3591	108	35	of	of	ADP
ejpam-3591	108	36	s	s	PRON
ejpam-3591	108	37	that	that	PRON
ejpam-3591	108	38	contains	contain	VERB
ejpam-3591	108	39	a	a	DET
ejpam-3591	108	40	∗a	∗a	PROPN
ejpam-3591	108	41	.	.	PUNCT
ejpam-3591	109	1	so	so	ADV
ejpam-3591	109	2	the	the	DET
ejpam-3591	109	3	proof	proof	NOUN
ejpam-3591	109	4	of	of	ADP
ejpam-3591	109	5	(	(	PUNCT
ejpam-3591	109	6	4)⇒	4)⇒	X
ejpam-3591	109	7	(	(	PUNCT
ejpam-3591	109	8	1	1	NUM
ejpam-3591	109	9	)	)	PUNCT
ejpam-3591	109	10	in	in	ADP
ejpam-3591	109	11	theorem	theorem	NOUN
ejpam-3591	109	12	3.1	3.1	NUM
ejpam-3591	109	13	in	in	ADP
ejpam-3591	109	14	[	[	X
ejpam-3591	109	15	4	4	NUM
ejpam-3591	109	16	]	]	PUNCT
ejpam-3591	109	17	is	be	AUX
ejpam-3591	109	18	actually	actually	ADV
ejpam-3591	109	19	the	the	DET
ejpam-3591	109	20	proof	proof	NOUN
ejpam-3591	109	21	of	of	ADP
ejpam-3591	109	22	(	(	PUNCT
ejpam-3591	109	23	3)⇒	3)⇒	NUM
ejpam-3591	109	24	(	(	PUNCT
ejpam-3591	109	25	1	1	NUM
ejpam-3591	109	26	)	)	PUNCT
ejpam-3591	109	27	in	in	ADP
ejpam-3591	109	28	theorem	theorem	NOUN
ejpam-3591	109	29	18	18	NUM
ejpam-3591	109	30	in	in	ADP
ejpam-3591	109	31	[	[	X
ejpam-3591	109	32	10	10	NUM
ejpam-3591	109	33	]	]	PUNCT
ejpam-3591	109	34	.	.	PUNCT
ejpam-3591	110	1	the	the	DET
ejpam-3591	110	2	proofs	proof	NOUN
ejpam-3591	110	3	of	of	ADP
ejpam-3591	110	4	theorem	theorem	ADJ
ejpam-3591	110	5	2.5	2.5	NUM
ejpam-3591	110	6	and	and	CCONJ
ejpam-3591	110	7	theorem	theorem	VERB
ejpam-3591	110	8	3.1	3.1	NUM
ejpam-3591	110	9	in	in	ADP
ejpam-3591	110	10	[	[	PUNCT
ejpam-3591	110	11	4	4	NUM
ejpam-3591	110	12	]	]	PUNCT
ejpam-3591	110	13	should	should	AUX
ejpam-3591	110	14	be	be	AUX
ejpam-3591	110	15	corrected	correct	VERB
ejpam-3591	110	16	as	as	ADP
ejpam-3591	110	17	notations	notation	NOUN
ejpam-3591	110	18	of	of	ADP
ejpam-3591	110	19	the	the	DET
ejpam-3591	110	20	form	form	NOUN
ejpam-3591	110	21	s	s	PART
ejpam-3591	110	22	◦	◦	NOUN
ejpam-3591	110	23	b	b	DET
ejpam-3591	110	24	◦	◦	NOUN
ejpam-3591	110	25	s	s	NOUN
ejpam-3591	110	26	◦	◦	NOUN
ejpam-3591	110	27	s	s	NOUN
ejpam-3591	110	28	◦	◦	NOUN
ejpam-3591	110	29	a	a	DET
ejpam-3591	110	30	◦	◦	NOUN
ejpam-3591	110	31	s	s	PART
ejpam-3591	110	32	,	,	PUNCT
ejpam-3591	110	33	a	a	DET
ejpam-3591	110	34	being	be	AUX
ejpam-3591	110	35	an	an	DET
ejpam-3591	110	36	element	element	NOUN
ejpam-3591	110	37	,	,	PUNCT
ejpam-3591	110	38	s	s	VERB
ejpam-3591	110	39	being	be	AUX
ejpam-3591	110	40	a	a	DET
ejpam-3591	110	41	set	set	NOUN
ejpam-3591	110	42	and	and	CCONJ
ejpam-3591	110	43	◦	◦	NOUN
ejpam-3591	110	44	being	be	AUX
ejpam-3591	110	45	an	an	DET
ejpam-3591	110	46	“	"	PUNCT
ejpam-3591	110	47	operation	operation	NOUN
ejpam-3591	110	48	”	"	PUNCT
ejpam-3591	110	49	between	between	ADP
ejpam-3591	110	50	elements	element	NOUN
ejpam-3591	110	51	have	have	VERB
ejpam-3591	110	52	no	no	DET
ejpam-3591	110	53	sense	sense	NOUN
ejpam-3591	110	54	;	;	PUNCT
ejpam-3591	110	55	or	or	CCONJ
ejpam-3591	110	56	a	a	DET
ejpam-3591	110	57	satisfactory	satisfactory	ADJ
ejpam-3591	110	58	explanation	explanation	NOUN
ejpam-3591	110	59	should	should	AUX
ejpam-3591	110	60	be	be	AUX
ejpam-3591	110	61	given	give	VERB
ejpam-3591	110	62	in	in	ADP
ejpam-3591	110	63	the	the	DET
ejpam-3591	110	64	paper	paper	NOUN
ejpam-3591	110	65	.	.	PUNCT
ejpam-3591	111	1	in	in	ADP
ejpam-3591	111	2	addition	addition	NOUN
ejpam-3591	111	3	,	,	PUNCT
ejpam-3591	111	4	the	the	DET
ejpam-3591	111	5	proof	proof	NOUN
ejpam-3591	111	6	of	of	ADP
ejpam-3591	111	7	theorem	theorem	ADJ
ejpam-3591	111	8	3.1	3.1	NUM
ejpam-3591	111	9	in	in	ADP
ejpam-3591	111	10	[	[	X
ejpam-3591	111	11	4	4	NUM
ejpam-3591	111	12	]	]	PUNCT
ejpam-3591	111	13	is	be	AUX
ejpam-3591	111	14	a	a	DET
ejpam-3591	111	15	modification	modification	NOUN
ejpam-3591	111	16	of	of	ADP
ejpam-3591	111	17	the	the	DET
ejpam-3591	111	18	proof	proof	NOUN
ejpam-3591	111	19	of	of	ADP
ejpam-3591	111	20	lemma	lemma	PROPN
ejpam-3591	111	21	2	2	NUM
ejpam-3591	111	22	in	in	ADP
ejpam-3591	111	23	[	[	X
ejpam-3591	111	24	7	7	NUM
ejpam-3591	111	25	]	]	PUNCT
ejpam-3591	111	26	,	,	PUNCT
ejpam-3591	111	27	which	which	PRON
ejpam-3591	111	28	is	be	AUX
ejpam-3591	111	29	the	the	DET
ejpam-3591	111	30	following	following	NOUN
ejpam-3591	111	31	;	;	PUNCT
ejpam-3591	111	32	not	not	PART
ejpam-3591	111	33	cited	cite	VERB
ejpam-3591	111	34	in	in	ADP
ejpam-3591	111	35	[	[	X
ejpam-3591	111	36	4	4	NUM
ejpam-3591	111	37	]	]	PUNCT
ejpam-3591	111	38	.	.	PUNCT
ejpam-3591	112	1	lemma	lemma	PROPN
ejpam-3591	112	2	2	2	NUM
ejpam-3591	112	3	in	in	ADP
ejpam-3591	112	4	[	[	NOUN
ejpam-3591	112	5	7](nk	7](nk	NUM
ejpam-3591	112	6	):	):	PUNCT
ejpam-3591	112	7	let	let	VERB
ejpam-3591	112	8	s	s	PRON
ejpam-3591	112	9	be	be	AUX
ejpam-3591	112	10	a	a	DET
ejpam-3591	112	11	po	po	NOUN
ejpam-3591	112	12	-	-	PUNCT
ejpam-3591	112	13	semigroup	semigroup	NOUN
ejpam-3591	112	14	.	.	PUNCT
ejpam-3591	113	1	the	the	DET
ejpam-3591	113	2	following	follow	VERB
ejpam-3591	113	3	are	be	AUX
ejpam-3591	113	4	equivalent	equivalent	ADJ
ejpam-3591	113	5	:	:	PUNCT
ejpam-3591	113	6	(	(	PUNCT
ejpam-3591	113	7	1	1	X
ejpam-3591	113	8	)	)	PUNCT
ejpam-3591	113	9	(	(	PUNCT
ejpam-3591	113	10	a2	a2	PROPN
ejpam-3591	113	11	]	]	PUNCT
ejpam-3591	113	12	=	=	PUNCT
ejpam-3591	113	13	a	a	PRON
ejpam-3591	113	14	for	for	ADP
ejpam-3591	113	15	every	every	DET
ejpam-3591	113	16	ideal	ideal	NOUN
ejpam-3591	113	17	a	a	PRON
ejpam-3591	113	18	of	of	ADP
ejpam-3591	113	19	s.	s.	PROPN
ejpam-3591	113	20	(	(	PUNCT
ejpam-3591	113	21	2	2	X
ejpam-3591	113	22	)	)	PUNCT
ejpam-3591	113	23	a	a	DET
ejpam-3591	113	24	∩b	∩b	NOUN
ejpam-3591	113	25	=	=	SYM
ejpam-3591	113	26	(	(	PUNCT
ejpam-3591	113	27	ab	ab	X
ejpam-3591	113	28	]	]	X
ejpam-3591	113	29	for	for	ADP
ejpam-3591	113	30	all	all	DET
ejpam-3591	113	31	ideals	ideal	NOUN
ejpam-3591	113	32	a	a	DET
ejpam-3591	113	33	,	,	PUNCT
ejpam-3591	113	34	b	b	PROPN
ejpam-3591	113	35	of	of	ADP
ejpam-3591	113	36	s.	s.	PROPN
ejpam-3591	113	37	(	(	PUNCT
ejpam-3591	113	38	3	3	X
ejpam-3591	113	39	)	)	PUNCT
ejpam-3591	113	40	i(a	i(a	PROPN
ejpam-3591	113	41	)	)	PUNCT
ejpam-3591	113	42	∩	∩	NOUN
ejpam-3591	113	43	i(b	i(b	NOUN
ejpam-3591	113	44	)	)	PUNCT
ejpam-3591	114	1	=	=	PUNCT
ejpam-3591	114	2	(	(	PUNCT
ejpam-3591	114	3	i(a)i(b	i(a)i(b	NOUN
ejpam-3591	114	4	)	)	PUNCT
ejpam-3591	114	5	]	]	PUNCT
ejpam-3591	114	6	for	for	ADP
ejpam-3591	114	7	all	all	DET
ejpam-3591	114	8	a	a	PRON
ejpam-3591	114	9	,	,	PUNCT
ejpam-3591	114	10	b	b	PROPN
ejpam-3591	114	11	∈	∈	PROPN
ejpam-3591	114	12	s.	s.	PROPN
ejpam-3591	114	13	(	(	PUNCT
ejpam-3591	114	14	4	4	NUM
ejpam-3591	114	15	)	)	PUNCT
ejpam-3591	114	16	i(a	i(a	PROPN
ejpam-3591	114	17	)	)	PUNCT
ejpam-3591	114	18	=	=	PRON
ejpam-3591	115	1	(	(	PUNCT
ejpam-3591	115	2	(	(	PUNCT
ejpam-3591	115	3	i(a))2	i(a))2	PROPN
ejpam-3591	115	4	]	]	PUNCT
ejpam-3591	115	5	for	for	ADP
ejpam-3591	115	6	every	every	DET
ejpam-3591	115	7	a	a	DET
ejpam-3591	115	8	∈	∈	PROPN
ejpam-3591	115	9	s.	s.	PROPN
ejpam-3591	115	10	(	(	PUNCT
ejpam-3591	115	11	5	5	X
ejpam-3591	115	12	)	)	PUNCT
ejpam-3591	115	13	a	a	DET
ejpam-3591	115	14	∈	∈	PROPN
ejpam-3591	115	15	(	(	PUNCT
ejpam-3591	115	16	sasas	sasa	NOUN
ejpam-3591	115	17	]	]	PUNCT
ejpam-3591	115	18	for	for	ADP
ejpam-3591	115	19	every	every	DET
ejpam-3591	115	20	a	a	DET
ejpam-3591	115	21	∈	∈	NOUN
ejpam-3591	115	22	s	s	X
ejpam-3591	115	23	(	(	PUNCT
ejpam-3591	115	24	that	that	PRON
ejpam-3591	115	25	means	mean	VERB
ejpam-3591	115	26	that	that	SCONJ
ejpam-3591	115	27	s	s	VERB
ejpam-3591	115	28	is	be	AUX
ejpam-3591	115	29	semisimple	semisimple	ADJ
ejpam-3591	115	30	)	)	PUNCT
ejpam-3591	115	31	.	.	PUNCT
ejpam-3591	116	1	theorem	theorem	VERB
ejpam-3591	116	2	3.2	3.2	NUM
ejpam-3591	116	3	in	in	ADP
ejpam-3591	116	4	[	[	X
ejpam-3591	116	5	4](zg	4](zg	NUM
ejpam-3591	116	6	):	):	PUNCT
ejpam-3591	116	7	let	let	VERB
ejpam-3591	116	8	s	s	PRON
ejpam-3591	116	9	be	be	AUX
ejpam-3591	116	10	an	an	DET
ejpam-3591	116	11	ordered	order	VERB
ejpam-3591	116	12	semihypergroup	semihypergroup	NOUN
ejpam-3591	116	13	.	.	PUNCT
ejpam-3591	117	1	then	then	ADV
ejpam-3591	117	2	s	s	VERB
ejpam-3591	117	3	is	be	AUX
ejpam-3591	117	4	intra	intra	ADJ
ejpam-3591	117	5	-	-	ADJ
ejpam-3591	117	6	regular	regular	ADJ
ejpam-3591	117	7	if	if	SCONJ
ejpam-3591	117	8	and	and	CCONJ
ejpam-3591	117	9	only	only	ADV
ejpam-3591	117	10	if	if	SCONJ
ejpam-3591	117	11	every	every	DET
ejpam-3591	117	12	hyperideal	hyperideal	NOUN
ejpam-3591	117	13	of	of	ADP
ejpam-3591	117	14	s	s	NOUN
ejpam-3591	117	15	is	be	AUX
ejpam-3591	117	16	semiprime	semiprime	NOUN
ejpam-3591	117	17	.	.	PUNCT
ejpam-3591	118	1	it	it	PRON
ejpam-3591	118	2	is	be	AUX
ejpam-3591	118	3	well	well	ADV
ejpam-3591	118	4	known	know	VERB
ejpam-3591	118	5	that	that	SCONJ
ejpam-3591	118	6	an	an	DET
ejpam-3591	118	7	ordered	order	VERB
ejpam-3591	118	8	semigroup	semigroup	NOUN
ejpam-3591	118	9	s	s	VERB
ejpam-3591	118	10	is	be	AUX
ejpam-3591	118	11	intra	intra	ADJ
ejpam-3591	118	12	-	-	ADJ
ejpam-3591	118	13	regular	regular	ADJ
ejpam-3591	118	14	if	if	SCONJ
ejpam-3591	118	15	and	and	CCONJ
ejpam-3591	118	16	only	only	ADV
ejpam-3591	118	17	if	if	SCONJ
ejpam-3591	118	18	the	the	DET
ejpam-3591	118	19	ideals	ideal	NOUN
ejpam-3591	118	20	of	of	ADP
ejpam-3591	118	21	s	s	NOUN
ejpam-3591	118	22	are	be	AUX
ejpam-3591	118	23	semiprime	semiprime	NOUN
ejpam-3591	118	24	.	.	PUNCT
ejpam-3591	119	1	let	let	VERB
ejpam-3591	119	2	us	we	PRON
ejpam-3591	119	3	give	give	VERB
ejpam-3591	119	4	a	a	DET
ejpam-3591	119	5	proof	proof	NOUN
ejpam-3591	119	6	of	of	ADP
ejpam-3591	119	7	it	it	PRON
ejpam-3591	119	8	:	:	PUNCT
ejpam-3591	119	9	⇒.	⇒.	PRON
ejpam-3591	119	10	let	let	VERB
ejpam-3591	119	11	i	i	PRON
ejpam-3591	119	12	be	be	AUX
ejpam-3591	119	13	an	an	DET
ejpam-3591	119	14	ideal	ideal	NOUN
ejpam-3591	119	15	of	of	ADP
ejpam-3591	119	16	s	s	PRON
ejpam-3591	119	17	and	and	CCONJ
ejpam-3591	119	18	a	a	DET
ejpam-3591	119	19	∈	∈	NOUN
ejpam-3591	119	20	s	s	VERB
ejpam-3591	119	21	such	such	ADJ
ejpam-3591	119	22	that	that	SCONJ
ejpam-3591	119	23	a2	a2	PROPN
ejpam-3591	119	24	∈	∈	PROPN
ejpam-3591	119	25	i.	i.	NOUN
ejpam-3591	119	26	since	since	SCONJ
ejpam-3591	119	27	s	s	PROPN
ejpam-3591	119	28	is	be	AUX
ejpam-3591	119	29	intra	intra	ADJ
ejpam-3591	119	30	-	-	ADJ
ejpam-3591	119	31	regular	regular	ADJ
ejpam-3591	119	32	,	,	PUNCT
ejpam-3591	119	33	we	we	PRON
ejpam-3591	119	34	have	have	VERB
ejpam-3591	119	35	a	a	DET
ejpam-3591	119	36	∈	∈	PROPN
ejpam-3591	119	37	(	(	PUNCT
ejpam-3591	119	38	sa2s	sa2s	NOUN
ejpam-3591	119	39	]	]	PUNCT
ejpam-3591	119	40	⊆	⊆	NUM
ejpam-3591	119	41	(	(	PUNCT
ejpam-3591	119	42	sis	sis	NOUN
ejpam-3591	119	43	]	]	X
ejpam-3591	119	44	⊆	⊆	NUM
ejpam-3591	119	45	(	(	PUNCT
ejpam-3591	119	46	i	i	NOUN
ejpam-3591	119	47	]	]	X
ejpam-3591	119	48	=	=	PUNCT
ejpam-3591	119	49	i.	i.	PROPN
ejpam-3591	119	50	⇐	⇐	PROPN
ejpam-3591	119	51	.	.	PUNCT
ejpam-3591	120	1	let	let	VERB
ejpam-3591	120	2	a	a	DET
ejpam-3591	120	3	∈	∈	NOUN
ejpam-3591	120	4	s.	s.	PROPN
ejpam-3591	120	5	the	the	DET
ejpam-3591	120	6	set	set	PROPN
ejpam-3591	120	7	(	(	PUNCT
ejpam-3591	120	8	sa2s	sa2s	NOUN
ejpam-3591	120	9	]	]	PUNCT
ejpam-3591	120	10	is	be	AUX
ejpam-3591	120	11	an	an	DET
ejpam-3591	120	12	ideal	ideal	NOUN
ejpam-3591	120	13	of	of	ADP
ejpam-3591	120	14	s	s	NOUN
ejpam-3591	120	15	and	and	CCONJ
ejpam-3591	120	16	a4	a4	NOUN
ejpam-3591	120	17	∈	∈	PROPN
ejpam-3591	120	18	(	(	PUNCT
ejpam-3591	120	19	sa2s	sa2s	NOUN
ejpam-3591	120	20	]	]	PUNCT
ejpam-3591	120	21	.	.	PUNCT
ejpam-3591	121	1	since	since	SCONJ
ejpam-3591	121	2	(	(	PUNCT
ejpam-3591	121	3	sa2s	sa2s	NOUN
ejpam-3591	121	4	]	]	PUNCT
ejpam-3591	121	5	is	be	AUX
ejpam-3591	121	6	semiprime	semiprime	NOUN
ejpam-3591	121	7	,	,	PUNCT
ejpam-3591	121	8	we	we	PRON
ejpam-3591	121	9	have	have	VERB
ejpam-3591	121	10	a2	a2	PROPN
ejpam-3591	121	11	∈	∈	PROPN
ejpam-3591	121	12	(	(	PUNCT
ejpam-3591	121	13	sa2s	sa2s	NOUN
ejpam-3591	121	14	]	]	PUNCT
ejpam-3591	121	15	and	and	CCONJ
ejpam-3591	121	16	a	a	DET
ejpam-3591	121	17	∈	∈	PROPN
ejpam-3591	121	18	(	(	PUNCT
ejpam-3591	121	19	sa2s	sa2s	NOUN
ejpam-3591	121	20	]	]	PUNCT
ejpam-3591	121	21	,	,	PUNCT
ejpam-3591	121	22	so	so	CCONJ
ejpam-3591	121	23	s	s	NOUN
ejpam-3591	121	24	is	be	AUX
ejpam-3591	121	25	intra	intra	ADJ
ejpam-3591	121	26	-	-	ADJ
ejpam-3591	121	27	regular	regular	ADJ
ejpam-3591	121	28	.	.	PUNCT
ejpam-3591	122	1	if	if	SCONJ
ejpam-3591	122	2	we	we	PRON
ejpam-3591	122	3	get	get	VERB
ejpam-3591	122	4	this	this	DET
ejpam-3591	122	5	proof	proof	NOUN
ejpam-3591	122	6	,	,	PUNCT
ejpam-3591	122	7	delete	delete	VERB
ejpam-3591	122	8	the	the	PRON
ejpam-3591	122	9	“	"	PUNCT
ejpam-3591	122	10	·	·	PUNCT
ejpam-3591	122	11	”	"	PUNCT
ejpam-3591	122	12	and	and	CCONJ
ejpam-3591	122	13	put	put	VERB
ejpam-3591	122	14	“	"	PUNCT
ejpam-3591	122	15	◦	◦	NOUN
ejpam-3591	122	16	”	"	PUNCT
ejpam-3591	122	17	instead	instead	ADV
ejpam-3591	122	18	,	,	PUNCT
ejpam-3591	122	19	then	then	ADV
ejpam-3591	122	20	this	this	PRON
ejpam-3591	122	21	is	be	AUX
ejpam-3591	122	22	the	the	DET
ejpam-3591	122	23	theorem	theorem	ADJ
ejpam-3591	122	24	3.2	3.2	NUM
ejpam-3591	122	25	in	in	ADP
ejpam-3591	122	26	[	[	X
ejpam-3591	122	27	4	4	NUM
ejpam-3591	122	28	]	]	PUNCT
ejpam-3591	122	29	.	.	PUNCT
ejpam-3591	123	1	no	no	DET
ejpam-3591	123	2	mention	mention	NOUN
ejpam-3591	123	3	about	about	ADP
ejpam-3591	123	4	the	the	DET
ejpam-3591	123	5	theorem	theorem	NOUN
ejpam-3591	123	6	on	on	ADP
ejpam-3591	123	7	ordered	order	VERB
ejpam-3591	123	8	semigroups	semigroup	NOUN
ejpam-3591	123	9	is	be	AUX
ejpam-3591	123	10	given	give	VERB
ejpam-3591	123	11	in	in	ADP
ejpam-3591	123	12	[	[	X
ejpam-3591	123	13	4	4	NUM
ejpam-3591	123	14	]	]	PUNCT
ejpam-3591	123	15	.	.	PUNCT
ejpam-3591	124	1	but	but	CCONJ
ejpam-3591	124	2	anyway	anyway	ADV
ejpam-3591	124	3	,	,	PUNCT
ejpam-3591	124	4	it	it	PRON
ejpam-3591	124	5	’s	’	VERB
ejpam-3591	124	6	not	not	PART
ejpam-3591	124	7	enough	enough	ADJ
ejpam-3591	124	8	to	to	PART
ejpam-3591	124	9	put	put	VERB
ejpam-3591	124	10	“	"	PUNCT
ejpam-3591	124	11	◦	◦	NOUN
ejpam-3591	124	12	”	"	PUNCT
ejpam-3591	124	13	instead	instead	ADV
ejpam-3591	124	14	of	of	ADP
ejpam-3591	124	15	“	"	PUNCT
ejpam-3591	124	16	·	·	PUNCT
ejpam-3591	124	17	”	"	PUNCT
ejpam-3591	124	18	to	to	PART
ejpam-3591	124	19	pass	pass	VERB
ejpam-3591	124	20	from	from	ADP
ejpam-3591	124	21	an	an	DET
ejpam-3591	124	22	ordered	order	VERB
ejpam-3591	124	23	semigroup	semigroup	NOUN
ejpam-3591	124	24	to	to	ADP
ejpam-3591	124	25	an	an	DET
ejpam-3591	124	26	ordered	order	VERB
ejpam-3591	124	27	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	124	28	.	.	PUNCT
ejpam-3591	125	1	theorem	theorem	VERB
ejpam-3591	125	2	19	19	NUM
ejpam-3591	125	3	in	in	ADP
ejpam-3591	125	4	[	[	NOUN
ejpam-3591	125	5	10](nk	10](nk	NUM
ejpam-3591	125	6	):	):	PUNCT
ejpam-3591	125	7	let	let	VERB
ejpam-3591	125	8	(	(	PUNCT
ejpam-3591	125	9	h	h	NOUN
ejpam-3591	125	10	,	,	PUNCT
ejpam-3591	125	11	◦	◦	NOUN
ejpam-3591	125	12	,	,	PUNCT
ejpam-3591	125	13	≤	≤	NUM
ejpam-3591	125	14	)	)	PUNCT
ejpam-3591	125	15	be	be	VERB
ejpam-3591	125	16	an	an	DET
ejpam-3591	125	17	ordered	order	VERB
ejpam-3591	125	18	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	125	19	.	.	PUNCT
ejpam-3591	126	1	the	the	DET
ejpam-3591	126	2	ideals	ideal	NOUN
ejpam-3591	126	3	of	of	ADP
ejpam-3591	126	4	h	h	NOUN
ejpam-3591	126	5	are	be	AUX
ejpam-3591	126	6	weakly	weakly	ADV
ejpam-3591	126	7	prime	prime	ADJ
ejpam-3591	126	8	if	if	SCONJ
ejpam-3591	127	1	and	and	CCONJ
ejpam-3591	127	2	only	only	ADV
ejpam-3591	127	3	if	if	SCONJ
ejpam-3591	127	4	they	they	PRON
ejpam-3591	127	5	are	be	AUX
ejpam-3591	127	6	idempotent	idempotent	ADJ
ejpam-3591	127	7	and	and	CCONJ
ejpam-3591	127	8	they	they	PRON
ejpam-3591	127	9	form	form	VERB
ejpam-3591	127	10	a	a	DET
ejpam-3591	127	11	chain	chain	NOUN
ejpam-3591	127	12	.	.	PUNCT
ejpam-3591	128	1	theorem	theorem	VERB
ejpam-3591	128	2	3.3	3.3	NUM
ejpam-3591	128	3	in	in	ADP
ejpam-3591	128	4	[	[	X
ejpam-3591	128	5	4](zg	4](zg	NUM
ejpam-3591	128	6	):	):	PUNCT
ejpam-3591	128	7	let	let	VERB
ejpam-3591	128	8	s	s	PRON
ejpam-3591	128	9	be	be	AUX
ejpam-3591	128	10	an	an	DET
ejpam-3591	128	11	ordered	order	VERB
ejpam-3591	128	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	128	13	and	and	CCONJ
ejpam-3591	128	14	θ	θ	PROPN
ejpam-3591	128	15	be	be	VERB
ejpam-3591	128	16	the	the	DET
ejpam-3591	128	17	set	set	NOUN
ejpam-3591	128	18	of	of	ADP
ejpam-3591	128	19	all	all	DET
ejpam-3591	128	20	hyperideals	hyperideal	NOUN
ejpam-3591	128	21	of	of	ADP
ejpam-3591	128	22	s.	s.	PROPN
ejpam-3591	129	1	then	then	ADV
ejpam-3591	129	2	i	i	PRON
ejpam-3591	129	3	is	be	AUX
ejpam-3591	129	4	weakly	weakly	ADJ
ejpam-3591	129	5	prime	prime	ADJ
ejpam-3591	129	6	for	for	ADP
ejpam-3591	129	7	every	every	DET
ejpam-3591	129	8	i	i	NOUN
ejpam-3591	129	9	∈	∈	NOUN
ejpam-3591	129	10	θ	θ	NOUN
ejpam-3591	129	11	if	if	SCONJ
ejpam-3591	129	12	and	and	CCONJ
ejpam-3591	129	13	only	only	ADV
ejpam-3591	129	14	if	if	SCONJ
ejpam-3591	129	15	s	s	NOUN
ejpam-3591	129	16	is	be	AUX
ejpam-3591	129	17	semisimple	semisimple	ADJ
ejpam-3591	129	18	and	and	CCONJ
ejpam-3591	129	19	θ	θ	PROPN
ejpam-3591	129	20	is	be	AUX
ejpam-3591	129	21	a	a	DET
ejpam-3591	129	22	chain	chain	NOUN
ejpam-3591	129	23	.	.	PUNCT
ejpam-3591	130	1	as	as	SCONJ
ejpam-3591	130	2	an	an	DET
ejpam-3591	130	3	ordered	ordered	ADJ
ejpam-3591	130	4	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	130	5	s	s	PART
ejpam-3591	130	6	is	be	AUX
ejpam-3591	130	7	semisimple	semisimple	ADJ
ejpam-3591	130	8	if	if	SCONJ
ejpam-3591	130	9	and	and	CCONJ
ejpam-3591	130	10	only	only	ADV
ejpam-3591	130	11	if	if	SCONJ
ejpam-3591	130	12	the	the	DET
ejpam-3591	130	13	ideals	ideal	NOUN
ejpam-3591	130	14	of	of	ADP
ejpam-3591	130	15	s	s	PRON
ejpam-3591	130	16	are	be	AUX
ejpam-3591	130	17	idempotent	idempotent	ADJ
ejpam-3591	130	18	(	(	PUNCT
ejpam-3591	130	19	[	[	X
ejpam-3591	130	20	4	4	NUM
ejpam-3591	130	21	,	,	PUNCT
ejpam-3591	130	22	theorem	theorem	VERB
ejpam-3591	130	23	3.1	3.1	NUM
ejpam-3591	130	24	]	]	PUNCT
ejpam-3591	130	25	or	or	CCONJ
ejpam-3591	130	26	[	[	X
ejpam-3591	130	27	10	10	NUM
ejpam-3591	130	28	,	,	PUNCT
ejpam-3591	130	29	theorem	theorem	VERB
ejpam-3591	130	30	18	18	NUM
ejpam-3591	130	31	]	]	PUNCT
ejpam-3591	130	32	)	)	PUNCT
ejpam-3591	130	33	,	,	PUNCT
ejpam-3591	130	34	the	the	DET
ejpam-3591	130	35	theorem	theorem	ADJ
ejpam-3591	130	36	3.3	3.3	NUM
ejpam-3591	130	37	in	in	ADP
ejpam-3591	130	38	[	[	X
ejpam-3591	130	39	4	4	NUM
ejpam-3591	130	40	]	]	PUNCT
ejpam-3591	130	41	is	be	AUX
ejpam-3591	130	42	the	the	DET
ejpam-3591	130	43	theorem	theorem	NOUN
ejpam-3591	130	44	19	19	NUM
ejpam-3591	130	45	in	in	ADP
ejpam-3591	130	46	[	[	X
ejpam-3591	130	47	10	10	NUM
ejpam-3591	130	48	]	]	PUNCT
ejpam-3591	130	49	;	;	PUNCT
ejpam-3591	130	50	and	and	CCONJ
ejpam-3591	130	51	it	it	PRON
ejpam-3591	130	52	is	be	AUX
ejpam-3591	130	53	not	not	PART
ejpam-3591	130	54	new	new	ADJ
ejpam-3591	130	55	.	.	PUNCT
ejpam-3591	131	1	according	accord	VERB
ejpam-3591	131	2	to	to	ADP
ejpam-3591	131	3	[	[	X
ejpam-3591	131	4	4	4	NUM
ejpam-3591	131	5	]	]	PUNCT
ejpam-3591	131	6	,	,	PUNCT
ejpam-3591	131	7	from	from	ADP
ejpam-3591	131	8	theorems	theorems	PROPN
ejpam-3591	131	9	3.1	3.1	NUM
ejpam-3591	131	10	,	,	PUNCT
ejpam-3591	131	11	3.2	3.2	NUM
ejpam-3591	131	12	and	and	CCONJ
ejpam-3591	131	13	3.3	3.3	NUM
ejpam-3591	131	14	in	in	ADP
ejpam-3591	131	15	[	[	X
ejpam-3591	131	16	4	4	NUM
ejpam-3591	131	17	]	]	PUNCT
ejpam-3591	131	18	,	,	PUNCT
ejpam-3591	131	19	the	the	DET
ejpam-3591	131	20	theorem	theorem	NOUN
ejpam-3591	131	21	3.4	3.4	NUM
ejpam-3591	131	22	in	in	ADP
ejpam-3591	131	23	[	[	X
ejpam-3591	131	24	4	4	NUM
ejpam-3591	131	25	]	]	PUNCT
ejpam-3591	131	26	can	can	AUX
ejpam-3591	131	27	be	be	AUX
ejpam-3591	131	28	easily	easily	ADV
ejpam-3591	131	29	obtained	obtain	VERB
ejpam-3591	131	30	.	.	PUNCT
ejpam-3591	132	1	n.	n.	PROPN
ejpam-3591	132	2	kehayopulu	kehayopulu	PROPN
ejpam-3591	132	3	/	/	SYM
ejpam-3591	132	4	eur	eur	PROPN
ejpam-3591	132	5	.	.	PUNCT
ejpam-3591	133	1	j.	j.	PROPN
ejpam-3591	133	2	pure	pure	PROPN
ejpam-3591	133	3	appl	appl	PROPN
ejpam-3591	133	4	.	.	PROPN
ejpam-3591	133	5	math	math	PROPN
ejpam-3591	133	6	,	,	PUNCT
ejpam-3591	133	7	12	12	NUM
ejpam-3591	133	8	(	(	PUNCT
ejpam-3591	133	9	4	4	NUM
ejpam-3591	133	10	)	)	PUNCT
ejpam-3591	133	11	(	(	PUNCT
ejpam-3591	133	12	2019	2019	NUM
ejpam-3591	133	13	)	)	PUNCT
ejpam-3591	133	14	,	,	PUNCT
ejpam-3591	133	15	1771	1771	NUM
ejpam-3591	133	16	-	-	SYM
ejpam-3591	133	17	1778	1778	NUM
ejpam-3591	133	18	1776	1776	NUM
ejpam-3591	133	19	theorem	theorem	VERB
ejpam-3591	133	20	3.4	3.4	NUM
ejpam-3591	133	21	in	in	ADP
ejpam-3591	133	22	[	[	NOUN
ejpam-3591	133	23	4](zg	4](zg	NUM
ejpam-3591	133	24	):	):	PUNCT
ejpam-3591	133	25	let	let	VERB
ejpam-3591	133	26	s	s	PRON
ejpam-3591	133	27	be	be	AUX
ejpam-3591	133	28	an	an	DET
ejpam-3591	133	29	ordered	order	VERB
ejpam-3591	133	30	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	133	31	and	and	CCONJ
ejpam-3591	133	32	θ	θ	PROPN
ejpam-3591	133	33	be	be	VERB
ejpam-3591	133	34	the	the	DET
ejpam-3591	133	35	set	set	NOUN
ejpam-3591	133	36	of	of	ADP
ejpam-3591	133	37	all	all	DET
ejpam-3591	133	38	hyperideals	hyperideal	NOUN
ejpam-3591	133	39	of	of	ADP
ejpam-3591	133	40	s.	s.	PROPN
ejpam-3591	134	1	then	then	ADV
ejpam-3591	134	2	i	i	PRON
ejpam-3591	134	3	is	be	AUX
ejpam-3591	134	4	prime	prime	ADJ
ejpam-3591	134	5	for	for	ADP
ejpam-3591	134	6	every	every	DET
ejpam-3591	134	7	i	i	NOUN
ejpam-3591	134	8	∈	∈	NOUN
ejpam-3591	134	9	θ	θ	NOUN
ejpam-3591	135	1	if	if	SCONJ
ejpam-3591	136	1	and	and	CCONJ
ejpam-3591	136	2	only	only	ADV
ejpam-3591	136	3	if	if	SCONJ
ejpam-3591	136	4	s	s	NOUN
ejpam-3591	136	5	is	be	AUX
ejpam-3591	136	6	intra	intra	ADJ
ejpam-3591	136	7	-	-	ADJ
ejpam-3591	136	8	regular	regular	ADJ
ejpam-3591	136	9	and	and	CCONJ
ejpam-3591	136	10	θ	θ	PROPN
ejpam-3591	136	11	is	be	AUX
ejpam-3591	136	12	a	a	DET
ejpam-3591	136	13	chain	chain	NOUN
ejpam-3591	136	14	.	.	PUNCT
ejpam-3591	137	1	theorem	theorem	VERB
ejpam-3591	137	2	23	23	NUM
ejpam-3591	137	3	in	in	ADP
ejpam-3591	137	4	[	[	X
ejpam-3591	137	5	10](nk	10](nk	NUM
ejpam-3591	137	6	):	):	PUNCT
ejpam-3591	137	7	let	let	VERB
ejpam-3591	137	8	s	s	PRON
ejpam-3591	137	9	be	be	AUX
ejpam-3591	137	10	an	an	DET
ejpam-3591	137	11	ordered	order	VERB
ejpam-3591	137	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	137	13	.	.	PUNCT
ejpam-3591	138	1	if	if	SCONJ
ejpam-3591	138	2	the	the	DET
ejpam-3591	138	3	ideals	ideal	NOUN
ejpam-3591	138	4	of	of	ADP
ejpam-3591	138	5	s	s	NOUN
ejpam-3591	138	6	are	be	AUX
ejpam-3591	138	7	weakly	weakly	ADV
ejpam-3591	138	8	prime	prime	ADJ
ejpam-3591	138	9	and	and	CCONJ
ejpam-3591	138	10	semiprime	semiprime	NOUN
ejpam-3591	138	11	,	,	PUNCT
ejpam-3591	138	12	then	then	ADV
ejpam-3591	138	13	they	they	PRON
ejpam-3591	138	14	form	form	VERB
ejpam-3591	138	15	a	a	DET
ejpam-3591	138	16	chain	chain	NOUN
ejpam-3591	138	17	and	and	CCONJ
ejpam-3591	138	18	s	s	NOUN
ejpam-3591	138	19	is	be	AUX
ejpam-3591	138	20	intra	intra	ADJ
ejpam-3591	138	21	-	-	ADJ
ejpam-3591	138	22	regular	regular	ADJ
ejpam-3591	138	23	.	.	PUNCT
ejpam-3591	139	1	“	"	PUNCT
ejpam-3591	139	2	conversely	conversely	ADV
ejpam-3591	139	3	”	"	PUNCT
ejpam-3591	139	4	,	,	PUNCT
ejpam-3591	139	5	if	if	SCONJ
ejpam-3591	139	6	the	the	DET
ejpam-3591	139	7	ideals	ideal	NOUN
ejpam-3591	139	8	of	of	ADP
ejpam-3591	139	9	s	s	NOUN
ejpam-3591	139	10	form	form	NOUN
ejpam-3591	139	11	a	a	DET
ejpam-3591	139	12	chain	chain	NOUN
ejpam-3591	139	13	and	and	CCONJ
ejpam-3591	139	14	s	s	NOUN
ejpam-3591	139	15	is	be	AUX
ejpam-3591	139	16	intra	intra	ADJ
ejpam-3591	139	17	-	-	ADJ
ejpam-3591	139	18	regular	regular	ADJ
ejpam-3591	139	19	,	,	PUNCT
ejpam-3591	139	20	then	then	ADV
ejpam-3591	139	21	the	the	DET
ejpam-3591	139	22	ideals	ideal	NOUN
ejpam-3591	139	23	of	of	ADP
ejpam-3591	139	24	s	s	NOUN
ejpam-3591	139	25	are	be	AUX
ejpam-3591	139	26	prime	prime	ADJ
ejpam-3591	139	27	.	.	PUNCT
ejpam-3591	140	1	the	the	DET
ejpam-3591	140	2	“	"	PUNCT
ejpam-3591	140	3	⇒”-part	⇒”-part	PROPN
ejpam-3591	140	4	in	in	ADP
ejpam-3591	140	5	[	[	X
ejpam-3591	140	6	4	4	NUM
ejpam-3591	140	7	,	,	PUNCT
ejpam-3591	140	8	theorem	theorem	VERB
ejpam-3591	140	9	3.4	3.4	NUM
ejpam-3591	140	10	]	]	PUNCT
ejpam-3591	140	11	holds	hold	NOUN
ejpam-3591	140	12	,	,	PUNCT
ejpam-3591	140	13	more	more	ADV
ejpam-3591	140	14	generally	generally	ADV
ejpam-3591	140	15	for	for	ADP
ejpam-3591	140	16	ordered	order	VERB
ejpam-3591	140	17	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	140	18	in	in	ADP
ejpam-3591	140	19	which	which	PRON
ejpam-3591	140	20	the	the	DET
ejpam-3591	140	21	ideals	ideal	NOUN
ejpam-3591	140	22	are	be	AUX
ejpam-3591	140	23	weakly	weakly	ADV
ejpam-3591	140	24	prime	prime	ADJ
ejpam-3591	140	25	and	and	CCONJ
ejpam-3591	140	26	semiprime	semiprime	NOUN
ejpam-3591	140	27	(	(	PUNCT
ejpam-3591	140	28	see	see	VERB
ejpam-3591	140	29	[	[	X
ejpam-3591	140	30	10	10	NUM
ejpam-3591	140	31	,	,	PUNCT
ejpam-3591	140	32	theorem	theorem	VERB
ejpam-3591	140	33	23	23	NUM
ejpam-3591	140	34	]	]	PUNCT
ejpam-3591	140	35	)	)	PUNCT
ejpam-3591	140	36	.	.	PUNCT
ejpam-3591	141	1	regarding	regard	VERB
ejpam-3591	141	2	the	the	DET
ejpam-3591	141	3	“	"	PUNCT
ejpam-3591	141	4	converse	converse	NOUN
ejpam-3591	141	5	”	"	PUNCT
ejpam-3591	141	6	statement	statement	NOUN
ejpam-3591	141	7	,	,	PUNCT
ejpam-3591	141	8	let	let	VERB
ejpam-3591	141	9	s	s	PRON
ejpam-3591	141	10	be	be	AUX
ejpam-3591	141	11	intra	intra	ADJ
ejpam-3591	141	12	-	-	ADJ
ejpam-3591	141	13	regular	regular	ADJ
ejpam-3591	141	14	and	and	CCONJ
ejpam-3591	141	15	θ	θ	PROPN
ejpam-3591	141	16	be	be	AUX
ejpam-3591	141	17	a	a	DET
ejpam-3591	141	18	chain	chain	NOUN
ejpam-3591	141	19	.	.	PUNCT
ejpam-3591	142	1	since	since	SCONJ
ejpam-3591	142	2	s	s	PROPN
ejpam-3591	142	3	is	be	AUX
ejpam-3591	142	4	intra	intra	ADJ
ejpam-3591	142	5	-	-	ADJ
ejpam-3591	142	6	regular	regular	ADJ
ejpam-3591	142	7	,	,	PUNCT
ejpam-3591	142	8	by	by	ADP
ejpam-3591	142	9	theorem	theorem	NOUN
ejpam-3591	142	10	3.2	3.2	NUM
ejpam-3591	142	11	in	in	ADP
ejpam-3591	142	12	[	[	X
ejpam-3591	142	13	4	4	NUM
ejpam-3591	142	14	]	]	PUNCT
ejpam-3591	142	15	,	,	PUNCT
ejpam-3591	142	16	every	every	DET
ejpam-3591	142	17	ideal	ideal	NOUN
ejpam-3591	142	18	of	of	ADP
ejpam-3591	142	19	s	s	PROPN
ejpam-3591	142	20	is	be	AUX
ejpam-3591	142	21	semiprime	semiprime	NOUN
ejpam-3591	142	22	,	,	PUNCT
ejpam-3591	142	23	and	and	CCONJ
ejpam-3591	142	24	so	so	ADV
ejpam-3591	142	25	weakly	weakly	ADJ
ejpam-3591	142	26	semiprime	semiprime	NOUN
ejpam-3591	142	27	as	as	ADV
ejpam-3591	142	28	well	well	ADV
ejpam-3591	142	29	.	.	PUNCT
ejpam-3591	143	1	since	since	SCONJ
ejpam-3591	143	2	every	every	DET
ejpam-3591	143	3	ideal	ideal	NOUN
ejpam-3591	143	4	of	of	ADP
ejpam-3591	143	5	s	s	NOUN
ejpam-3591	143	6	is	be	AUX
ejpam-3591	143	7	weakly	weakly	ADJ
ejpam-3591	143	8	semiprime	semiprime	NOUN
ejpam-3591	143	9	,	,	PUNCT
ejpam-3591	143	10	by	by	ADP
ejpam-3591	143	11	theorem	theorem	NOUN
ejpam-3591	143	12	3.1	3.1	NUM
ejpam-3591	143	13	in	in	ADP
ejpam-3591	143	14	[	[	PUNCT
ejpam-3591	143	15	4	4	NUM
ejpam-3591	143	16	]	]	PUNCT
ejpam-3591	143	17	,	,	PUNCT
ejpam-3591	143	18	s	s	X
ejpam-3591	143	19	is	be	AUX
ejpam-3591	143	20	semisimple	semisimple	ADJ
ejpam-3591	143	21	.	.	PUNCT
ejpam-3591	144	1	since	since	SCONJ
ejpam-3591	144	2	s	s	NOUN
ejpam-3591	144	3	is	be	AUX
ejpam-3591	144	4	semisimple	semisimple	ADJ
ejpam-3591	144	5	and	and	CCONJ
ejpam-3591	144	6	the	the	DET
ejpam-3591	144	7	ideals	ideal	NOUN
ejpam-3591	144	8	of	of	ADP
ejpam-3591	144	9	s	s	NOUN
ejpam-3591	144	10	form	form	NOUN
ejpam-3591	144	11	a	a	DET
ejpam-3591	144	12	chain	chain	NOUN
ejpam-3591	144	13	,	,	PUNCT
ejpam-3591	144	14	by	by	ADP
ejpam-3591	144	15	theorem	theorem	NOUN
ejpam-3591	144	16	3.3	3.3	NUM
ejpam-3591	144	17	in	in	ADP
ejpam-3591	144	18	[	[	X
ejpam-3591	144	19	4	4	NUM
ejpam-3591	144	20	]	]	PUNCT
ejpam-3591	144	21	,	,	PUNCT
ejpam-3591	144	22	every	every	DET
ejpam-3591	144	23	ideal	ideal	NOUN
ejpam-3591	144	24	of	of	ADP
ejpam-3591	144	25	s	s	NOUN
ejpam-3591	144	26	is	be	AUX
ejpam-3591	144	27	weakly	weakly	ADJ
ejpam-3591	144	28	prime	prime	ADJ
ejpam-3591	144	29	.	.	PUNCT
ejpam-3591	145	1	so	so	ADV
ejpam-3591	145	2	the	the	DET
ejpam-3591	145	3	“	"	PUNCT
ejpam-3591	145	4	⇐	⇐	ADJ
ejpam-3591	145	5	”	"	PUNCT
ejpam-3591	145	6	-part	-part	NOUN
ejpam-3591	145	7	of	of	ADP
ejpam-3591	145	8	theorem	theorem	ADJ
ejpam-3591	145	9	3.4	3.4	NUM
ejpam-3591	145	10	in	in	ADP
ejpam-3591	145	11	[	[	X
ejpam-3591	145	12	4	4	NUM
ejpam-3591	145	13	]	]	PUNCT
ejpam-3591	145	14	can	can	AUX
ejpam-3591	145	15	not	not	PART
ejpam-3591	145	16	be	be	AUX
ejpam-3591	145	17	easily	easily	ADV
ejpam-3591	145	18	obtained	obtain	VERB
ejpam-3591	145	19	by	by	ADP
ejpam-3591	145	20	theorems	theorem	NOUN
ejpam-3591	145	21	3.1	3.1	NUM
ejpam-3591	145	22	,	,	PUNCT
ejpam-3591	145	23	3.2	3.2	NUM
ejpam-3591	145	24	and	and	CCONJ
ejpam-3591	145	25	3.3	3.3	NUM
ejpam-3591	145	26	in	in	ADP
ejpam-3591	145	27	[	[	X
ejpam-3591	145	28	4	4	NUM
ejpam-3591	145	29	]	]	PUNCT
ejpam-3591	145	30	as	as	SCONJ
ejpam-3591	145	31	the	the	DET
ejpam-3591	145	32	author	author	NOUN
ejpam-3591	145	33	says	say	VERB
ejpam-3591	145	34	.	.	PUNCT
ejpam-3591	146	1	the	the	DET
ejpam-3591	146	2	proof	proof	NOUN
ejpam-3591	146	3	of	of	ADP
ejpam-3591	146	4	the	the	DET
ejpam-3591	146	5	“	"	PUNCT
ejpam-3591	146	6	⇐	⇐	ADJ
ejpam-3591	146	7	”	"	PUNCT
ejpam-3591	146	8	-part	-part	NOUN
ejpam-3591	146	9	of	of	ADP
ejpam-3591	146	10	this	this	PRON
ejpam-3591	146	11	theorem	theorem	NOUN
ejpam-3591	146	12	in	in	ADP
ejpam-3591	146	13	[	[	X
ejpam-3591	146	14	4	4	NUM
ejpam-3591	146	15	]	]	PUNCT
ejpam-3591	146	16	is	be	AUX
ejpam-3591	146	17	wrong	wrong	ADJ
ejpam-3591	146	18	;	;	PUNCT
ejpam-3591	146	19	the	the	DET
ejpam-3591	146	20	right	right	ADJ
ejpam-3591	146	21	way	way	NOUN
ejpam-3591	146	22	to	to	PART
ejpam-3591	146	23	say	say	VERB
ejpam-3591	146	24	it	it	PRON
ejpam-3591	146	25	is	be	AUX
ejpam-3591	146	26	to	to	PART
ejpam-3591	146	27	give	give	VERB
ejpam-3591	146	28	an	an	DET
ejpam-3591	146	29	example	example	NOUN
ejpam-3591	146	30	,	,	PUNCT
ejpam-3591	146	31	but	but	CCONJ
ejpam-3591	146	32	this	this	PRON
ejpam-3591	146	33	is	be	AUX
ejpam-3591	146	34	out	out	ADP
ejpam-3591	146	35	of	of	ADP
ejpam-3591	146	36	the	the	DET
ejpam-3591	146	37	aim	aim	NOUN
ejpam-3591	146	38	of	of	ADP
ejpam-3591	146	39	the	the	DET
ejpam-3591	146	40	present	present	ADJ
ejpam-3591	146	41	note	note	NOUN
ejpam-3591	146	42	.	.	PUNCT
ejpam-3591	147	1	however	however	ADV
ejpam-3591	147	2	,	,	PUNCT
ejpam-3591	147	3	the	the	DET
ejpam-3591	147	4	theorem	theorem	NOUN
ejpam-3591	147	5	3.4	3.4	NUM
ejpam-3591	147	6	in	in	ADP
ejpam-3591	147	7	[	[	X
ejpam-3591	147	8	4	4	NUM
ejpam-3591	147	9	]	]	PUNCT
ejpam-3591	147	10	is	be	AUX
ejpam-3591	147	11	correct	correct	ADJ
ejpam-3591	147	12	,	,	PUNCT
ejpam-3591	147	13	and	and	CCONJ
ejpam-3591	147	14	its	its	PRON
ejpam-3591	147	15	proof	proof	NOUN
ejpam-3591	147	16	has	have	AUX
ejpam-3591	147	17	been	be	AUX
ejpam-3591	147	18	given	give	VERB
ejpam-3591	147	19	in	in	ADP
ejpam-3591	147	20	theorem	theorem	NOUN
ejpam-3591	147	21	23	23	NUM
ejpam-3591	147	22	in	in	ADP
ejpam-3591	147	23	[	[	X
ejpam-3591	147	24	10	10	NUM
ejpam-3591	147	25	]	]	PUNCT
ejpam-3591	147	26	.	.	PUNCT
ejpam-3591	148	1	the	the	DET
ejpam-3591	148	2	proof	proof	NOUN
ejpam-3591	148	3	of	of	ADP
ejpam-3591	148	4	the	the	DET
ejpam-3591	148	5	“	"	PUNCT
ejpam-3591	148	6	⇐	⇐	ADJ
ejpam-3591	148	7	”	"	PUNCT
ejpam-3591	148	8	-part	-part	NOUN
ejpam-3591	148	9	,	,	PUNCT
ejpam-3591	148	10	that	that	PRON
ejpam-3591	148	11	needs	need	VERB
ejpam-3591	148	12	many	many	ADJ
ejpam-3591	148	13	technical	technical	ADJ
ejpam-3591	148	14	details	detail	NOUN
ejpam-3591	148	15	to	to	PART
ejpam-3591	148	16	transfer	transfer	VERB
ejpam-3591	148	17	the	the	DET
ejpam-3591	148	18	proof	proof	NOUN
ejpam-3591	148	19	from	from	ADP
ejpam-3591	148	20	ordered	order	VERB
ejpam-3591	148	21	semigroups	semigroup	NOUN
ejpam-3591	148	22	to	to	PART
ejpam-3591	148	23	ordered	order	VERB
ejpam-3591	148	24	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	148	25	,	,	PUNCT
ejpam-3591	148	26	is	be	AUX
ejpam-3591	148	27	the	the	DET
ejpam-3591	148	28	main	main	ADJ
ejpam-3591	148	29	part	part	NOUN
ejpam-3591	148	30	of	of	ADP
ejpam-3591	148	31	the	the	DET
ejpam-3591	148	32	theorem	theorem	NOUN
ejpam-3591	148	33	in	in	ADP
ejpam-3591	148	34	[	[	X
ejpam-3591	148	35	10	10	NUM
ejpam-3591	148	36	]	]	PUNCT
ejpam-3591	148	37	.	.	PUNCT
ejpam-3591	149	1	from	from	ADP
ejpam-3591	149	2	theorem	theorem	NOUN
ejpam-3591	149	3	23	23	NUM
ejpam-3591	149	4	in	in	ADP
ejpam-3591	149	5	[	[	X
ejpam-3591	149	6	10	10	NUM
ejpam-3591	149	7	]	]	PUNCT
ejpam-3591	149	8	,	,	PUNCT
ejpam-3591	149	9	we	we	PRON
ejpam-3591	149	10	have	have	VERB
ejpam-3591	149	11	the	the	DET
ejpam-3591	149	12	following	follow	VERB
ejpam-3591	149	13	corollary	corollary	NOUN
ejpam-3591	149	14	.	.	PUNCT
ejpam-3591	150	1	we	we	PRON
ejpam-3591	150	2	add	add	VERB
ejpam-3591	150	3	the	the	DET
ejpam-3591	150	4	word	word	NOUN
ejpam-3591	150	5	“	"	PUNCT
ejpam-3591	150	6	ordered	order	VERB
ejpam-3591	150	7	”	"	PUNCT
ejpam-3591	150	8	that	that	SCONJ
ejpam-3591	150	9	,	,	PUNCT
ejpam-3591	150	10	by	by	ADP
ejpam-3591	150	11	mistake	mistake	NOUN
ejpam-3591	150	12	,	,	PUNCT
ejpam-3591	150	13	was	be	AUX
ejpam-3591	150	14	missing	miss	VERB
ejpam-3591	150	15	in	in	ADP
ejpam-3591	150	16	[	[	X
ejpam-3591	150	17	10	10	NUM
ejpam-3591	150	18	]	]	PUNCT
ejpam-3591	150	19	.	.	PUNCT
ejpam-3591	151	1	corollary	corollary	ADJ
ejpam-3591	151	2	24	24	NUM
ejpam-3591	151	3	in	in	ADP
ejpam-3591	151	4	[	[	NOUN
ejpam-3591	151	5	10](nk	10](nk	NUM
ejpam-3591	151	6	):	):	PUNCT
ejpam-3591	151	7	let	let	VERB
ejpam-3591	151	8	s	s	PRON
ejpam-3591	151	9	be	be	AUX
ejpam-3591	151	10	an	an	DET
ejpam-3591	151	11	ordered	order	VERB
ejpam-3591	151	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	151	13	.	.	PUNCT
ejpam-3591	152	1	the	the	DET
ejpam-3591	152	2	following	follow	VERB
ejpam-3591	152	3	are	be	AUX
ejpam-3591	152	4	equivalent	equivalent	ADJ
ejpam-3591	152	5	:	:	PUNCT
ejpam-3591	152	6	(	(	PUNCT
ejpam-3591	152	7	1	1	X
ejpam-3591	152	8	)	)	PUNCT
ejpam-3591	152	9	the	the	DET
ejpam-3591	152	10	ideals	ideal	NOUN
ejpam-3591	152	11	of	of	ADP
ejpam-3591	152	12	s	s	NOUN
ejpam-3591	152	13	are	be	AUX
ejpam-3591	152	14	prime	prime	ADJ
ejpam-3591	152	15	.	.	PUNCT
ejpam-3591	153	1	(	(	PUNCT
ejpam-3591	153	2	2	2	X
ejpam-3591	153	3	)	)	PUNCT
ejpam-3591	153	4	the	the	DET
ejpam-3591	153	5	ideals	ideal	NOUN
ejpam-3591	153	6	of	of	ADP
ejpam-3591	153	7	s	s	NOUN
ejpam-3591	153	8	are	be	AUX
ejpam-3591	153	9	weakly	weakly	ADV
ejpam-3591	153	10	prime	prime	ADJ
ejpam-3591	153	11	and	and	CCONJ
ejpam-3591	153	12	semiprime	semiprime	NOUN
ejpam-3591	153	13	.	.	PUNCT
ejpam-3591	154	1	(	(	PUNCT
ejpam-3591	154	2	3	3	X
ejpam-3591	154	3	)	)	PUNCT
ejpam-3591	154	4	the	the	DET
ejpam-3591	154	5	ideals	ideal	NOUN
ejpam-3591	154	6	of	of	ADP
ejpam-3591	154	7	s	s	NOUN
ejpam-3591	154	8	form	form	NOUN
ejpam-3591	154	9	a	a	DET
ejpam-3591	154	10	chain	chain	NOUN
ejpam-3591	154	11	and	and	CCONJ
ejpam-3591	154	12	s	s	NOUN
ejpam-3591	154	13	is	be	AUX
ejpam-3591	154	14	intra	intra	ADJ
ejpam-3591	154	15	-	-	ADJ
ejpam-3591	154	16	regular	regular	ADJ
ejpam-3591	154	17	.	.	PUNCT
ejpam-3591	155	1	(	(	PUNCT
ejpam-3591	155	2	the	the	DET
ejpam-3591	155	3	above	above	ADJ
ejpam-3591	155	4	corollary	corollary	NOUN
ejpam-3591	155	5	,	,	PUNCT
ejpam-3591	155	6	for	for	ADP
ejpam-3591	155	7	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	155	8	-without	-without	PROPN
ejpam-3591	155	9	order	order	NOUN
ejpam-3591	155	10	also	also	ADV
ejpam-3591	155	11	holds	hold	VERB
ejpam-3591	155	12	)	)	PUNCT
ejpam-3591	155	13	.	.	PUNCT
ejpam-3591	156	1	let	let	VERB
ejpam-3591	156	2	us	we	PRON
ejpam-3591	156	3	give	give	VERB
ejpam-3591	156	4	once	once	ADV
ejpam-3591	156	5	more	more	ADV
ejpam-3591	156	6	the	the	DET
ejpam-3591	156	7	theorem	theorem	ADJ
ejpam-3591	156	8	2.5	2.5	NUM
ejpam-3591	156	9	in	in	ADP
ejpam-3591	156	10	[	[	X
ejpam-3591	156	11	4	4	NUM
ejpam-3591	156	12	]	]	PUNCT
ejpam-3591	156	13	to	to	PART
ejpam-3591	156	14	compare	compare	VERB
ejpam-3591	156	15	it	it	PRON
ejpam-3591	156	16	with	with	ADP
ejpam-3591	156	17	the	the	DET
ejpam-3591	156	18	corollary	corollary	ADJ
ejpam-3591	156	19	24	24	NUM
ejpam-3591	156	20	in	in	ADP
ejpam-3591	156	21	[	[	X
ejpam-3591	156	22	10	10	NUM
ejpam-3591	156	23	]	]	PUNCT
ejpam-3591	156	24	.	.	PUNCT
ejpam-3591	157	1	theorem	theorem	VERB
ejpam-3591	157	2	2.5	2.5	NUM
ejpam-3591	157	3	in	in	ADP
ejpam-3591	157	4	[	[	X
ejpam-3591	157	5	4](zg	4](zg	NUM
ejpam-3591	157	6	):	):	PUNCT
ejpam-3591	157	7	let	let	VERB
ejpam-3591	157	8	s	s	PRON
ejpam-3591	157	9	be	be	AUX
ejpam-3591	157	10	an	an	DET
ejpam-3591	157	11	ordered	ordered	ADJ
ejpam-3591	157	12	semihypergroup	semihypergroup	NOUN
ejpam-3591	158	1	and	and	CCONJ
ejpam-3591	158	2	i	i	PRON
ejpam-3591	158	3	a	a	DET
ejpam-3591	158	4	hyperideal	hyperideal	NOUN
ejpam-3591	158	5	of	of	ADP
ejpam-3591	158	6	s.	s.	PROPN
ejpam-3591	158	7	then	then	ADV
ejpam-3591	158	8	i	i	PRON
ejpam-3591	158	9	is	be	AUX
ejpam-3591	158	10	prime	prime	ADJ
ejpam-3591	158	11	if	if	SCONJ
ejpam-3591	159	1	and	and	CCONJ
ejpam-3591	159	2	only	only	ADV
ejpam-3591	159	3	if	if	SCONJ
ejpam-3591	159	4	it	it	PRON
ejpam-3591	159	5	is	be	AUX
ejpam-3591	159	6	semiprime	semiprime	NOUN
ejpam-3591	159	7	and	and	CCONJ
ejpam-3591	159	8	weakly	weakly	ADJ
ejpam-3591	159	9	prime	prime	NOUN
ejpam-3591	159	10	.	.	PUNCT
ejpam-3591	160	1	in	in	ADP
ejpam-3591	160	2	particular	particular	ADJ
ejpam-3591	160	3	,	,	PUNCT
ejpam-3591	160	4	if	if	SCONJ
ejpam-3591	160	5	s	s	NOUN
ejpam-3591	160	6	is	be	AUX
ejpam-3591	160	7	commutative	commutative	ADJ
ejpam-3591	160	8	,	,	PUNCT
ejpam-3591	160	9	then	then	ADV
ejpam-3591	160	10	the	the	DET
ejpam-3591	160	11	prime	prime	ADJ
ejpam-3591	160	12	and	and	CCONJ
ejpam-3591	160	13	weakly	weakly	ADJ
ejpam-3591	160	14	hyperideals	hyperideal	NOUN
ejpam-3591	160	15	coincide	coincide	NOUN
ejpam-3591	160	16	.	.	PUNCT
ejpam-3591	161	1	as	as	SCONJ
ejpam-3591	161	2	we	we	PRON
ejpam-3591	161	3	see	see	VERB
ejpam-3591	161	4	now	now	ADV
ejpam-3591	161	5	,	,	PUNCT
ejpam-3591	161	6	the	the	DET
ejpam-3591	161	7	first	first	ADJ
ejpam-3591	161	8	part	part	NOUN
ejpam-3591	161	9	of	of	ADP
ejpam-3591	161	10	the	the	DET
ejpam-3591	161	11	theorem	theorem	ADJ
ejpam-3591	161	12	2.5	2.5	NUM
ejpam-3591	161	13	in	in	ADP
ejpam-3591	161	14	[	[	X
ejpam-3591	161	15	4	4	NUM
ejpam-3591	161	16	]	]	PUNCT
ejpam-3591	161	17	is	be	AUX
ejpam-3591	161	18	the	the	DET
ejpam-3591	161	19	equivalence	equivalence	NOUN
ejpam-3591	161	20	(	(	PUNCT
ejpam-3591	161	21	1)⇔	1)⇔	NUM
ejpam-3591	161	22	(	(	PUNCT
ejpam-3591	161	23	2	2	NUM
ejpam-3591	161	24	)	)	PUNCT
ejpam-3591	161	25	in	in	ADP
ejpam-3591	161	26	corollary	corollary	ADJ
ejpam-3591	161	27	24	24	NUM
ejpam-3591	161	28	in	in	ADP
ejpam-3591	161	29	[	[	PUNCT
ejpam-3591	161	30	10	10	NUM
ejpam-3591	161	31	]	]	PUNCT
ejpam-3591	161	32	proved	prove	VERB
ejpam-3591	161	33	independently	independently	ADV
ejpam-3591	161	34	of	of	ADP
ejpam-3591	161	35	the	the	DET
ejpam-3591	161	36	proposition	proposition	NOUN
ejpam-3591	161	37	in	in	ADP
ejpam-3591	161	38	[	[	X
ejpam-3591	161	39	7	7	NUM
ejpam-3591	161	40	]	]	PUNCT
ejpam-3591	161	41	.	.	PUNCT
ejpam-3591	162	1	regarding	regard	VERB
ejpam-3591	162	2	the	the	DET
ejpam-3591	162	3	second	second	ADJ
ejpam-3591	162	4	part	part	NOUN
ejpam-3591	162	5	of	of	ADP
ejpam-3591	162	6	the	the	DET
ejpam-3591	162	7	theorem	theorem	ADJ
ejpam-3591	162	8	2.5	2.5	NUM
ejpam-3591	162	9	in	in	ADP
ejpam-3591	162	10	[	[	X
ejpam-3591	162	11	4	4	NUM
ejpam-3591	162	12	]	]	X
ejpam-3591	162	13	(	(	PUNCT
ejpam-3591	162	14	if	if	SCONJ
ejpam-3591	162	15	s	s	NOUN
ejpam-3591	162	16	is	be	AUX
ejpam-3591	162	17	commutative	commutative	ADJ
ejpam-3591	162	18	...	...	PUNCT
ejpam-3591	162	19	)	)	PUNCT
ejpam-3591	162	20	,	,	PUNCT
ejpam-3591	162	21	the	the	DET
ejpam-3591	162	22	following	follow	VERB
ejpam-3591	162	23	is	be	AUX
ejpam-3591	162	24	from	from	ADP
ejpam-3591	162	25	the	the	DET
ejpam-3591	162	26	last	last	ADJ
ejpam-3591	162	27	four	four	NUM
ejpam-3591	162	28	lines	line	NOUN
ejpam-3591	162	29	of	of	ADP
ejpam-3591	162	30	remark	remark	NOUN
ejpam-3591	162	31	2.5	2.5	NUM
ejpam-3591	162	32	in	in	ADP
ejpam-3591	162	33	[	[	X
ejpam-3591	162	34	10	10	NUM
ejpam-3591	162	35	]	]	SYM
ejpam-3591	162	36	:	:	PUNCT
ejpam-3591	162	37	references	reference	NOUN
ejpam-3591	162	38	1777	1777	NUM
ejpam-3591	162	39	“	"	PUNCT
ejpam-3591	162	40	it	it	PRON
ejpam-3591	162	41	might	might	AUX
ejpam-3591	162	42	be	be	AUX
ejpam-3591	162	43	finally	finally	ADV
ejpam-3591	162	44	mentioned	mention	VERB
ejpam-3591	162	45	that	that	SCONJ
ejpam-3591	162	46	in	in	ADP
ejpam-3591	162	47	commutative	commutative	ADJ
ejpam-3591	162	48	ordered	order	VERB
ejpam-3591	162	49	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	162	50	the	the	DET
ejpam-3591	162	51	prime	prime	ADJ
ejpam-3591	162	52	and	and	CCONJ
ejpam-3591	162	53	weakly	weakly	ADJ
ejpam-3591	162	54	prime	prime	ADJ
ejpam-3591	162	55	ideals	ideal	NOUN
ejpam-3591	162	56	coincide	coincide	VERB
ejpam-3591	162	57	–	–	PUNCT
ejpam-3591	162	58	the	the	DET
ejpam-3591	162	59	proof	proof	NOUN
ejpam-3591	162	60	is	be	AUX
ejpam-3591	162	61	the	the	DET
ejpam-3591	162	62	same	same	ADJ
ejpam-3591	162	63	with	with	ADP
ejpam-3591	162	64	the	the	DET
ejpam-3591	162	65	proposition	proposition	NOUN
ejpam-3591	162	66	in	in	ADP
ejpam-3591	162	67	[	[	X
ejpam-3591	162	68	n.	n.	NOUN
ejpam-3591	162	69	kehayopulu	kehayopulu	PROPN
ejpam-3591	162	70	,	,	PUNCT
ejpam-3591	162	71	on	on	ADP
ejpam-3591	162	72	prime	prime	ADJ
ejpam-3591	162	73	,	,	PUNCT
ejpam-3591	162	74	weakly	weakly	ADJ
ejpam-3591	162	75	prime	prime	ADJ
ejpam-3591	162	76	ideals	ideal	NOUN
ejpam-3591	162	77	in	in	ADP
ejpam-3591	162	78	ordered	order	VERB
ejpam-3591	162	79	semigroups	semigroup	NOUN
ejpam-3591	162	80	,	,	PUNCT
ejpam-3591	162	81	semigroup	semigroup	PROPN
ejpam-3591	162	82	forum	forum	PROPN
ejpam-3591	162	83	44	44	NUM
ejpam-3591	162	84	,	,	PUNCT
ejpam-3591	162	85	no	no	INTJ
ejpam-3591	162	86	.	.	NOUN
ejpam-3591	162	87	3	3	NUM
ejpam-3591	162	88	(	(	PUNCT
ejpam-3591	162	89	1992	1992	NUM
ejpam-3591	162	90	)	)	PUNCT
ejpam-3591	162	91	,	,	PUNCT
ejpam-3591	162	92	341–346	341–346	NUM
ejpam-3591	162	93	]	]	PUNCT
ejpam-3591	162	94	,	,	PUNCT
ejpam-3591	162	95	we	we	PRON
ejpam-3591	162	96	just	just	ADV
ejpam-3591	162	97	have	have	VERB
ejpam-3591	162	98	to	to	PART
ejpam-3591	162	99	replace	replace	VERB
ejpam-3591	162	100	the	the	DET
ejpam-3591	162	101	operation	operation	NOUN
ejpam-3591	162	102	“	"	PUNCT
ejpam-3591	162	103	·	·	PUNCT
ejpam-3591	162	104	”	"	PUNCT
ejpam-3591	162	105	of	of	ADP
ejpam-3591	162	106	the	the	DET
ejpam-3591	162	107	semigroup	semigroup	NOUN
ejpam-3591	162	108	by	by	ADP
ejpam-3591	162	109	the	the	DET
ejpam-3591	162	110	hyperoperation	hyperoperation	NOUN
ejpam-3591	162	111	“	"	PUNCT
ejpam-3591	162	112	◦	◦	NOUN
ejpam-3591	162	113	”	"	PUNCT
ejpam-3591	162	114	of	of	ADP
ejpam-3591	162	115	the	the	DET
ejpam-3591	162	116	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	162	117	.	.	PUNCT
ejpam-3591	162	118	”	"	PUNCT
ejpam-3591	163	1	the	the	DET
ejpam-3591	163	2	example	example	NOUN
ejpam-3591	163	3	3.5	3.5	NUM
ejpam-3591	163	4	is	be	AUX
ejpam-3591	163	5	the	the	DET
ejpam-3591	163	6	example	example	NOUN
ejpam-3591	163	7	b	b	NOUN
ejpam-3591	163	8	in	in	ADP
ejpam-3591	163	9	[	[	X
ejpam-3591	163	10	10	10	NUM
ejpam-3591	163	11	]	]	PUNCT
ejpam-3591	163	12	(	(	PUNCT
ejpam-3591	163	13	cited	cite	VERB
ejpam-3591	163	14	[	[	X
ejpam-3591	163	15	19	19	NUM
ejpam-3591	163	16	]	]	PUNCT
ejpam-3591	163	17	in	in	ADP
ejpam-3591	163	18	the	the	DET
ejpam-3591	163	19	references	reference	NOUN
ejpam-3591	163	20	in	in	ADP
ejpam-3591	163	21	[	[	X
ejpam-3591	163	22	4	4	NUM
ejpam-3591	163	23	]	]	PUNCT
ejpam-3591	163	24	)	)	PUNCT
ejpam-3591	163	25	and	and	CCONJ
ejpam-3591	163	26	,	,	PUNCT
ejpam-3591	163	27	according	accord	VERB
ejpam-3591	163	28	to	to	ADP
ejpam-3591	163	29	[	[	X
ejpam-3591	163	30	4	4	X
ejpam-3591	163	31	]	]	PUNCT
ejpam-3591	163	32	one	one	PRON
ejpam-3591	163	33	can	can	AUX
ejpam-3591	163	34	check	check	VERB
ejpam-3591	163	35	that	that	SCONJ
ejpam-3591	163	36	this	this	PRON
ejpam-3591	163	37	is	be	AUX
ejpam-3591	163	38	an	an	DET
ejpam-3591	163	39	ordered	order	VERB
ejpam-3591	163	40	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	163	41	.	.	PUNCT
ejpam-3591	164	1	we	we	PRON
ejpam-3591	164	2	never	never	ADV
ejpam-3591	164	3	check	check	VERB
ejpam-3591	164	4	examples	example	NOUN
ejpam-3591	164	5	on	on	ADP
ejpam-3591	164	6	ordered	order	VERB
ejpam-3591	164	7	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	164	8	given	give	VERB
ejpam-3591	164	9	by	by	ADP
ejpam-3591	164	10	a	a	DET
ejpam-3591	164	11	table	table	NOUN
ejpam-3591	164	12	by	by	ADP
ejpam-3591	164	13	hand	hand	NOUN
ejpam-3591	164	14	.	.	PUNCT
ejpam-3591	165	1	we	we	PRON
ejpam-3591	165	2	have	have	AUX
ejpam-3591	165	3	ordered	order	VERB
ejpam-3591	165	4	semigroups	semigroup	NOUN
ejpam-3591	165	5	using	use	VERB
ejpam-3591	165	6	computer	computer	NOUN
ejpam-3591	165	7	programs	program	NOUN
ejpam-3591	165	8	.	.	PUNCT
ejpam-3591	166	1	the	the	DET
ejpam-3591	166	2	example	example	NOUN
ejpam-3591	166	3	3.5	3.5	NUM
ejpam-3591	166	4	has	have	AUX
ejpam-3591	166	5	been	be	AUX
ejpam-3591	166	6	constructed	construct	VERB
ejpam-3591	166	7	in	in	ADP
ejpam-3591	166	8	[	[	X
ejpam-3591	166	9	10	10	NUM
ejpam-3591	166	10	]	]	PUNCT
ejpam-3591	166	11	from	from	ADP
ejpam-3591	166	12	one	one	NUM
ejpam-3591	166	13	of	of	ADP
ejpam-3591	166	14	them	they	PRON
ejpam-3591	166	15	using	use	VERB
ejpam-3591	166	16	the	the	DET
ejpam-3591	166	17	methodology	methodology	NOUN
ejpam-3591	166	18	described	describe	VERB
ejpam-3591	166	19	in	in	ADP
ejpam-3591	166	20	[	[	X
ejpam-3591	166	21	11	11	NUM
ejpam-3591	166	22	]	]	PUNCT
ejpam-3591	166	23	.	.	PUNCT
ejpam-3591	167	1	there	there	PRON
ejpam-3591	167	2	are	be	VERB
ejpam-3591	167	3	many	many	ADJ
ejpam-3591	167	4	papers	paper	NOUN
ejpam-3591	167	5	on	on	ADP
ejpam-3591	167	6	hyper	hyper	NOUN
ejpam-3591	167	7	...	...	PUNCT
ejpam-3591	167	8	in	in	ADP
ejpam-3591	167	9	the	the	DET
ejpam-3591	167	10	references	reference	NOUN
ejpam-3591	167	11	of	of	ADP
ejpam-3591	167	12	[	[	X
ejpam-3591	167	13	4	4	X
ejpam-3591	167	14	]	]	PUNCT
ejpam-3591	167	15	not	not	PART
ejpam-3591	167	16	related	relate	VERB
ejpam-3591	167	17	with	with	ADP
ejpam-3591	167	18	the	the	DET
ejpam-3591	167	19	contain	contain	NOUN
ejpam-3591	167	20	of	of	ADP
ejpam-3591	167	21	[	[	X
ejpam-3591	167	22	4	4	NUM
ejpam-3591	167	23	]	]	PUNCT
ejpam-3591	167	24	,	,	PUNCT
ejpam-3591	167	25	while	while	SCONJ
ejpam-3591	167	26	the	the	DET
ejpam-3591	167	27	paper	paper	NOUN
ejpam-3591	167	28	is	be	AUX
ejpam-3591	167	29	based	base	VERB
ejpam-3591	167	30	only	only	ADV
ejpam-3591	167	31	on	on	ADP
ejpam-3591	167	32	the	the	DET
ejpam-3591	167	33	3–4	3–4	NUM
ejpam-3591	167	34	papers	paper	NOUN
ejpam-3591	167	35	on	on	ADP
ejpam-3591	167	36	ordered	order	VERB
ejpam-3591	167	37	semigroups	semigroup	NOUN
ejpam-3591	167	38	indicated	indicate	VERB
ejpam-3591	167	39	in	in	ADP
ejpam-3591	167	40	the	the	DET
ejpam-3591	167	41	present	present	ADJ
ejpam-3591	167	42	note	note	NOUN
ejpam-3591	167	43	.	.	PUNCT
ejpam-3591	168	1	i	i	PRON
ejpam-3591	168	2	would	would	AUX
ejpam-3591	168	3	like	like	VERB
ejpam-3591	168	4	to	to	PART
ejpam-3591	168	5	thank	thank	VERB
ejpam-3591	168	6	the	the	DET
ejpam-3591	168	7	editor	editor	NOUN
ejpam-3591	168	8	and	and	CCONJ
ejpam-3591	168	9	the	the	DET
ejpam-3591	168	10	referee	referee	NOUN
ejpam-3591	168	11	for	for	ADP
ejpam-3591	168	12	the	the	DET
ejpam-3591	168	13	helpful	helpful	ADJ
ejpam-3591	168	14	discussions	discussion	NOUN
ejpam-3591	168	15	we	we	PRON
ejpam-3591	168	16	had	have	AUX
ejpam-3591	168	17	concerning	concern	VERB
ejpam-3591	168	18	this	this	DET
ejpam-3591	168	19	paper	paper	NOUN
ejpam-3591	168	20	and	and	CCONJ
ejpam-3591	168	21	their	their	PRON
ejpam-3591	168	22	interest	interest	NOUN
ejpam-3591	168	23	in	in	ADP
ejpam-3591	168	24	my	my	PRON
ejpam-3591	168	25	work	work	NOUN
ejpam-3591	168	26	.	.	PUNCT
ejpam-3591	169	1	references	reference	NOUN
ejpam-3591	169	2	[	[	X
ejpam-3591	169	3	1	1	NUM
ejpam-3591	169	4	]	]	PUNCT
ejpam-3591	169	5	p.	p.	NOUN
ejpam-3591	169	6	corsini	corsini	PROPN
ejpam-3591	169	7	,	,	PUNCT
ejpam-3591	169	8	m.	m.	NOUN
ejpam-3591	169	9	shabir	shabir	PROPN
ejpam-3591	169	10	,	,	PUNCT
ejpam-3591	169	11	t.	t.	PROPN
ejpam-3591	169	12	mahmood	mahmood	PROPN
ejpam-3591	169	13	.	.	PUNCT
ejpam-3591	170	1	semisimple	semisimple	NOUN
ejpam-3591	170	2	semihypergroups	semihypergroup	NOUN
ejpam-3591	170	3	in	in	ADP
ejpam-3591	170	4	terms	term	NOUN
ejpam-3591	170	5	of	of	ADP
ejpam-3591	170	6	hyperideals	hyperideal	NOUN
ejpam-3591	170	7	and	and	CCONJ
ejpam-3591	170	8	fuzzy	fuzzy	ADJ
ejpam-3591	170	9	hyperideals	hyperideal	NOUN
ejpam-3591	170	10	.	.	PUNCT
ejpam-3591	171	1	iran	iran	PROPN
ejpam-3591	171	2	.	.	PUNCT
ejpam-3591	172	1	j.	j.	PROPN
ejpam-3591	172	2	fuzzy	fuzzy	PROPN
ejpam-3591	172	3	syst	syst	PROPN
ejpam-3591	172	4	.	.	PUNCT
ejpam-3591	173	1	8(1):95–111	8(1):95–111	NUM
ejpam-3591	173	2	,	,	PUNCT
ejpam-3591	173	3	2011	2011	NUM
ejpam-3591	173	4	.	.	PUNCT
ejpam-3591	174	1	[	[	X
ejpam-3591	174	2	2	2	X
ejpam-3591	174	3	]	]	X
ejpam-3591	174	4	m.l	m.l	PROPN
ejpam-3591	174	5	.	.	PROPN
ejpam-3591	174	6	dubreil	dubreil	PROPN
ejpam-3591	174	7	–	–	PUNCT
ejpam-3591	174	8	jacotin	jacotin	PROPN
ejpam-3591	174	9	,	,	PUNCT
ejpam-3591	174	10	l.	l.	PROPN
ejpam-3591	174	11	lesieur	lesieur	PROPN
ejpam-3591	174	12	,	,	PUNCT
ejpam-3591	174	13	r.	r.	PROPN
ejpam-3591	174	14	croisot	croisot	PROPN
ejpam-3591	174	15	.	.	PUNCT
ejpam-3591	175	1	leçons	leçon	NOUN
ejpam-3591	175	2	sur	sur	PROPN
ejpam-3591	175	3	la	la	X
ejpam-3591	175	4	théorie	théorie	PROPN
ejpam-3591	175	5	des	des	PROPN
ejpam-3591	175	6	trellis	trellis	PROPN
ejpam-3591	175	7	,	,	PUNCT
ejpam-3591	175	8	des	des	X
ejpam-3591	175	9	structures	structure	NOUN
ejpam-3591	175	10	algébriques	algébriques	PROPN
ejpam-3591	175	11	ordonnées	ordonnée	NOUN
ejpam-3591	175	12	et	et	PROPN
ejpam-3591	175	13	des	des	X
ejpam-3591	175	14	treills	treill	NOUN
ejpam-3591	175	15	géométriques	géométrique	NOUN
ejpam-3591	175	16	.	.	PUNCT
ejpam-3591	176	1	paris	paris	PROPN
ejpam-3591	176	2	,	,	PUNCT
ejpam-3591	176	3	france	france	PROPN
ejpam-3591	176	4	:	:	PUNCT
ejpam-3591	176	5	gauthier	gauthier	NOUN
ejpam-3591	176	6	-	-	PUNCT
ejpam-3591	176	7	villars	villar	NOUN
ejpam-3591	176	8	viii+385pp	viii+385pp	NOUN
ejpam-3591	176	9	,	,	PUNCT
ejpam-3591	176	10	1953	1953	NUM
ejpam-3591	176	11	.	.	PUNCT
ejpam-3591	177	1	[	[	X
ejpam-3591	177	2	3	3	X
ejpam-3591	177	3	]	]	X
ejpam-3591	177	4	g.	g.	PROPN
ejpam-3591	177	5	grätzer	grätzer	PROPN
ejpam-3591	177	6	.	.	PUNCT
ejpam-3591	177	7	general	general	PROPN
ejpam-3591	177	8	lattice	lattice	PROPN
ejpam-3591	177	9	theory	theory	NOUN
ejpam-3591	177	10	.	.	PUNCT
ejpam-3591	178	1	academic	academic	ADJ
ejpam-3591	178	2	press	press	NOUN
ejpam-3591	178	3	,	,	PUNCT
ejpam-3591	178	4	new	new	PROPN
ejpam-3591	178	5	york	york	PROPN
ejpam-3591	178	6	,	,	PUNCT
ejpam-3591	178	7	san	san	PROPN
ejpam-3591	178	8	fransisco	fransisco	PROPN
ejpam-3591	178	9	xiii+381pp	xiii+381pp	PROPN
ejpam-3591	178	10	,	,	PUNCT
ejpam-3591	178	11	1978	1978	NUM
ejpam-3591	178	12	.	.	PUNCT
ejpam-3591	179	1	[	[	X
ejpam-3591	179	2	4	4	X
ejpam-3591	179	3	]	]	PUNCT
ejpam-3591	179	4	ze	ze	PROPN
ejpam-3591	179	5	gu	gu	PROPN
ejpam-3591	179	6	.	.	PUNCT
ejpam-3591	180	1	on	on	ADP
ejpam-3591	180	2	hyperideals	hyperideal	NOUN
ejpam-3591	180	3	of	of	ADP
ejpam-3591	180	4	ordered	order	VERB
ejpam-3591	180	5	semihypergroups	semihypergroup	NOUN
ejpam-3591	180	6	.	.	PUNCT
ejpam-3591	181	1	ital	ital	PROPN
ejpam-3591	181	2	.	.	PUNCT
ejpam-3591	182	1	j.	j.	PROPN
ejpam-3591	182	2	pure	pure	PROPN
ejpam-3591	182	3	appl	appl	PROPN
ejpam-3591	182	4	.	.	PUNCT
ejpam-3591	182	5	math	math	NOUN
ejpam-3591	182	6	.	.	PUNCT
ejpam-3591	183	1	no	no	INTJ
ejpam-3591	183	2	.	.	NOUN
ejpam-3591	183	3	40	40	NUM
ejpam-3591	183	4	:	:	PUNCT
ejpam-3591	184	1	692–698	692–698	NUM
ejpam-3591	184	2	,	,	PUNCT
ejpam-3591	184	3	2018	2018	NUM
ejpam-3591	184	4	.	.	PUNCT
ejpam-3591	185	1	[	[	X
ejpam-3591	185	2	5	5	NUM
ejpam-3591	185	3	]	]	PUNCT
ejpam-3591	185	4	n.	n.	NOUN
ejpam-3591	185	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	185	6	.	.	PUNCT
ejpam-3591	186	1	on	on	ADP
ejpam-3591	186	2	weakly	weakly	ADJ
ejpam-3591	186	3	prime	prime	ADJ
ejpam-3591	186	4	,	,	PUNCT
ejpam-3591	186	5	weakly	weakly	ADJ
ejpam-3591	186	6	semiprime	semiprime	NOUN
ejpam-3591	186	7	,	,	PUNCT
ejpam-3591	186	8	prime	prime	ADJ
ejpam-3591	186	9	ideal	ideal	ADJ
ejpam-3591	186	10	elements	element	NOUN
ejpam-3591	186	11	in	in	ADP
ejpam-3591	186	12	poesemigroups	poesemigroup	NOUN
ejpam-3591	186	13	.	.	PUNCT
ejpam-3591	187	1	math	math	NOUN
ejpam-3591	187	2	.	.	PUNCT
ejpam-3591	188	1	japon	japon	PROPN
ejpam-3591	188	2	.	.	PUNCT
ejpam-3591	189	1	34(3	34(3	NUM
ejpam-3591	189	2	):	):	PUNCT
ejpam-3591	189	3	381–389	381–389	NUM
ejpam-3591	189	4	,	,	PUNCT
ejpam-3591	189	5	1989	1989	NUM
ejpam-3591	189	6	.	.	PUNCT
ejpam-3591	190	1	[	[	X
ejpam-3591	190	2	6	6	NUM
ejpam-3591	190	3	]	]	X
ejpam-3591	190	4	n.	n.	NOUN
ejpam-3591	190	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	190	6	.	.	PUNCT
ejpam-3591	191	1	on	on	ADP
ejpam-3591	191	2	weakly	weakly	ADJ
ejpam-3591	191	3	prime	prime	ADJ
ejpam-3591	191	4	ideals	ideal	NOUN
ejpam-3591	191	5	of	of	ADP
ejpam-3591	191	6	ordered	order	VERB
ejpam-3591	191	7	semigroups	semigroup	NOUN
ejpam-3591	191	8	.	.	PUNCT
ejpam-3591	191	9	math	math	NOUN
ejpam-3591	191	10	.	.	PUNCT
ejpam-3591	192	1	japon	japon	PROPN
ejpam-3591	192	2	.	.	PUNCT
ejpam-3591	193	1	35(6):1051–1056	35(6):1051–1056	NUM
ejpam-3591	193	2	,	,	PUNCT
ejpam-3591	193	3	1990	1990	NUM
ejpam-3591	193	4	.	.	PUNCT
ejpam-3591	194	1	[	[	X
ejpam-3591	194	2	7	7	X
ejpam-3591	194	3	]	]	X
ejpam-3591	194	4	n.	n.	NOUN
ejpam-3591	194	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	194	6	.	.	PUNCT
ejpam-3591	195	1	on	on	ADP
ejpam-3591	195	2	prime	prime	ADJ
ejpam-3591	195	3	,	,	PUNCT
ejpam-3591	195	4	weakly	weakly	ADJ
ejpam-3591	195	5	prime	prime	ADJ
ejpam-3591	195	6	ideals	ideal	NOUN
ejpam-3591	195	7	in	in	ADP
ejpam-3591	195	8	ordered	order	VERB
ejpam-3591	195	9	semigroups	semigroup	NOUN
ejpam-3591	195	10	.	.	PUNCT
ejpam-3591	196	1	semigroup	semigroup	PROPN
ejpam-3591	196	2	forum	forum	PROPN
ejpam-3591	196	3	44(3):341–346	44(3):341–346	PROPN
ejpam-3591	196	4	,	,	PUNCT
ejpam-3591	196	5	1992	1992	NUM
ejpam-3591	196	6	.	.	PUNCT
ejpam-3591	197	1	[	[	X
ejpam-3591	197	2	8	8	NUM
ejpam-3591	197	3	]	]	X
ejpam-3591	197	4	n.	n.	NOUN
ejpam-3591	197	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	197	6	.	.	PUNCT
ejpam-3591	198	1	on	on	ADP
ejpam-3591	198	2	intra	intra	ADJ
ejpam-3591	198	3	-	-	ADJ
ejpam-3591	198	4	regular	regular	ADJ
ejpam-3591	198	5	ordered	order	VERB
ejpam-3591	198	6	semigroups	semigroup	NOUN
ejpam-3591	198	7	.	.	PUNCT
ejpam-3591	199	1	semigroup	semigroup	PROPN
ejpam-3591	199	2	forum	forum	PROPN
ejpam-3591	199	3	46(3	46(3	PROPN
ejpam-3591	199	4	):	):	PUNCT
ejpam-3591	199	5	271	271	NUM
ejpam-3591	199	6	–	–	PUNCT
ejpam-3591	199	7	278	278	NUM
ejpam-3591	199	8	,	,	PUNCT
ejpam-3591	199	9	1993	1993	NUM
ejpam-3591	199	10	.	.	PUNCT
ejpam-3591	200	1	[	[	X
ejpam-3591	200	2	9	9	NUM
ejpam-3591	200	3	]	]	X
ejpam-3591	200	4	n.	n.	NOUN
ejpam-3591	200	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	200	6	.	.	PUNCT
ejpam-3591	201	1	left	leave	VERB
ejpam-3591	201	2	regular	regular	ADJ
ejpam-3591	201	3	and	and	CCONJ
ejpam-3591	201	4	intra	intra	ADJ
ejpam-3591	201	5	-	-	ADJ
ejpam-3591	201	6	regular	regular	ADJ
ejpam-3591	201	7	ordered	order	VERB
ejpam-3591	201	8	hypersemigroup	hypersemigroup	NOUN
ejpam-3591	201	9	in	in	ADP
ejpam-3591	201	10	terms	term	NOUN
ejpam-3591	201	11	of	of	ADP
ejpam-3591	201	12	semiprime	semiprime	NOUN
ejpam-3591	201	13	and	and	CCONJ
ejpam-3591	201	14	fuzzy	fuzzy	ADJ
ejpam-3591	201	15	semiprime	semiprime	NOUN
ejpam-3591	201	16	subsets	subset	NOUN
ejpam-3591	201	17	.	.	PUNCT
ejpam-3591	202	1	sci	sci	PROPN
ejpam-3591	202	2	.	.	PROPN
ejpam-3591	202	3	math	math	PROPN
ejpam-3591	202	4	.	.	PUNCT
ejpam-3591	203	1	jpn	jpn	PROPN
ejpam-3591	203	2	.	.	PUNCT
ejpam-3591	204	1	80(3):295–305	80(3):295–305	PROPN
ejpam-3591	204	2	,	,	PUNCT
ejpam-3591	204	3	2017	2017	NUM
ejpam-3591	204	4	.	.	PUNCT
ejpam-3591	205	1	references	reference	NOUN
ejpam-3591	205	2	1778	1778	NUM
ejpam-3591	205	3	[	[	X
ejpam-3591	205	4	10	10	NUM
ejpam-3591	205	5	]	]	X
ejpam-3591	205	6	n.	n.	NOUN
ejpam-3591	205	7	kehayopulu	kehayopulu	PROPN
ejpam-3591	205	8	.	.	PUNCT
ejpam-3591	206	1	on	on	ADP
ejpam-3591	206	2	ordered	order	VERB
ejpam-3591	206	3	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	206	4	with	with	ADP
ejpam-3591	206	5	idempotent	idempotent	ADJ
ejpam-3591	206	6	ideals	ideal	NOUN
ejpam-3591	206	7	,	,	PUNCT
ejpam-3591	206	8	prime	prime	ADJ
ejpam-3591	206	9	or	or	CCONJ
ejpam-3591	206	10	weakly	weakly	ADJ
ejpam-3591	206	11	prime	prime	ADJ
ejpam-3591	206	12	ideals	ideal	NOUN
ejpam-3591	206	13	.	.	PUNCT
ejpam-3591	207	1	eur	eur	PROPN
ejpam-3591	207	2	.	.	PUNCT
ejpam-3591	208	1	j.	j.	PROPN
ejpam-3591	208	2	pure	pure	PROPN
ejpam-3591	208	3	appl	appl	PROPN
ejpam-3591	208	4	.	.	PUNCT
ejpam-3591	208	5	math	math	NOUN
ejpam-3591	208	6	.	.	PUNCT
ejpam-3591	209	1	11(1):10–22	11(1):10–22	NUM
ejpam-3591	209	2	,	,	PUNCT
ejpam-3591	209	3	2018	2018	NUM
ejpam-3591	209	4	.	.	PUNCT
ejpam-3591	210	1	[	[	X
ejpam-3591	210	2	11	11	NUM
ejpam-3591	210	3	]	]	X
ejpam-3591	210	4	n.	n.	NOUN
ejpam-3591	210	5	kehayopulu	kehayopulu	PROPN
ejpam-3591	210	6	.	.	PUNCT
ejpam-3591	211	1	on	on	ADP
ejpam-3591	211	2	ordered	order	VERB
ejpam-3591	211	3	hypersemigroups	hypersemigroup	NOUN
ejpam-3591	211	4	given	give	VERB
ejpam-3591	211	5	by	by	ADP
ejpam-3591	211	6	a	a	DET
ejpam-3591	211	7	table	table	NOUN
ejpam-3591	211	8	of	of	ADP
ejpam-3591	211	9	multiplication	multiplication	NOUN
ejpam-3591	211	10	and	and	CCONJ
ejpam-3591	211	11	a	a	DET
ejpam-3591	211	12	figure	figure	NOUN
ejpam-3591	211	13	.	.	PUNCT
ejpam-3591	212	1	turkish	turkish	ADJ
ejpam-3591	212	2	j.	j.	PROPN
ejpam-3591	212	3	math	math	PROPN
ejpam-3591	212	4	.	.	PUNCT
ejpam-3591	213	1	42(4	42(4	PROPN
ejpam-3591	213	2	):	):	PUNCT
ejpam-3591	213	3	2045–2060	2045–2060	NUM
ejpam-3591	213	4	,	,	PUNCT
ejpam-3591	213	5	2018	2018	NUM
ejpam-3591	213	6	.	.	PUNCT