id	sid	tid	token	lemma	pos
ejpam-5052	1	1	european	european	PROPN
ejpam-5052	1	2	journal	journal	PROPN
ejpam-5052	1	3	of	of	ADP
ejpam-5052	1	4	pure	pure	ADJ
ejpam-5052	1	5	and	and	CCONJ
ejpam-5052	1	6	applied	apply	VERB
ejpam-5052	1	7	mathematics	mathematic	NOUN
ejpam-5052	1	8	vol	vol	NOUN
ejpam-5052	1	9	.	.	PROPN
ejpam-5052	2	1	17	17	NUM
ejpam-5052	2	2	,	,	PUNCT
ejpam-5052	2	3	no	no	INTJ
ejpam-5052	2	4	.	.	NOUN
ejpam-5052	2	5	2	2	NUM
ejpam-5052	2	6	,	,	PUNCT
ejpam-5052	2	7	2024	2024	NUM
ejpam-5052	2	8	,	,	PUNCT
ejpam-5052	2	9	604	604	NUM
ejpam-5052	2	10	-	-	SYM
ejpam-5052	2	11	615	615	NUM
ejpam-5052	2	12	issn	issn	PROPN
ejpam-5052	2	13	1307	1307	NUM
ejpam-5052	2	14	-	-	SYM
ejpam-5052	2	15	5543	5543	NUM
ejpam-5052	2	16	–	–	PUNCT
ejpam-5052	2	17	ejpam.com	ejpam.com	X
ejpam-5052	2	18	published	publish	VERB
ejpam-5052	2	19	by	by	ADP
ejpam-5052	2	20	new	new	PROPN
ejpam-5052	2	21	york	york	PROPN
ejpam-5052	2	22	business	business	PROPN
ejpam-5052	2	23	global	global	ADJ
ejpam-5052	2	24	relations	relation	NOUN
ejpam-5052	2	25	between	between	ADP
ejpam-5052	2	26	derivations	derivation	NOUN
ejpam-5052	2	27	and	and	CCONJ
ejpam-5052	2	28	homomorphisms	homomorphism	NOUN
ejpam-5052	2	29	of	of	ADP
ejpam-5052	2	30	ordered	order	VERB
ejpam-5052	2	31	hyperrings	hyperring	NOUN
ejpam-5052	2	32	ruiqi	ruiqi	PROPN
ejpam-5052	2	33	cai1	cai1	PROPN
ejpam-5052	2	34	,	,	PUNCT
ejpam-5052	2	35	mashaer	mashaer	PROPN
ejpam-5052	2	36	alsaeedi2	alsaeedi2	ADJ
ejpam-5052	2	37	,	,	PUNCT
ejpam-5052	2	38	maryam	maryam	PROPN
ejpam-5052	2	39	akhoundi3,∗	akhoundi3,∗	PROPN
ejpam-5052	2	40	1	1	NUM
ejpam-5052	2	41	institute	institute	NOUN
ejpam-5052	2	42	of	of	ADP
ejpam-5052	2	43	computing	compute	VERB
ejpam-5052	2	44	science	science	NOUN
ejpam-5052	2	45	and	and	CCONJ
ejpam-5052	2	46	technology	technology	NOUN
ejpam-5052	2	47	,	,	PUNCT
ejpam-5052	2	48	guangzhou	guangzhou	PROPN
ejpam-5052	2	49	university	university	PROPN
ejpam-5052	2	50	,	,	PUNCT
ejpam-5052	2	51	guangzhou	guangzhou	PROPN
ejpam-5052	2	52	510006	510006	NUM
ejpam-5052	2	53	,	,	PUNCT
ejpam-5052	2	54	china	china	PROPN
ejpam-5052	2	55	2	2	NUM
ejpam-5052	2	56	department	department	NOUN
ejpam-5052	2	57	of	of	ADP
ejpam-5052	2	58	mathematics	mathematic	NOUN
ejpam-5052	2	59	,	,	PUNCT
ejpam-5052	2	60	college	college	NOUN
ejpam-5052	2	61	of	of	ADP
ejpam-5052	2	62	sciences	science	NOUN
ejpam-5052	2	63	and	and	CCONJ
ejpam-5052	2	64	humanities	humanity	NOUN
ejpam-5052	2	65	,	,	PUNCT
ejpam-5052	2	66	prince	prince	PROPN
ejpam-5052	2	67	sattam	sattam	PROPN
ejpam-5052	2	68	bin	bin	PROPN
ejpam-5052	2	69	abdulaziz	abdulaziz	PROPN
ejpam-5052	2	70	university	university	PROPN
ejpam-5052	2	71	,	,	PUNCT
ejpam-5052	2	72	al	al	PROPN
ejpam-5052	2	73	-	-	PUNCT
ejpam-5052	2	74	kharj	kharj	PROPN
ejpam-5052	2	75	,	,	PUNCT
ejpam-5052	2	76	saudi	saudi	PROPN
ejpam-5052	2	77	arabia	arabia	PROPN
ejpam-5052	2	78	3	3	NUM
ejpam-5052	2	79	clinical	clinical	ADJ
ejpam-5052	2	80	research	research	NOUN
ejpam-5052	2	81	development	development	NOUN
ejpam-5052	2	82	unit	unit	NOUN
ejpam-5052	2	83	of	of	ADP
ejpam-5052	2	84	rouhani	rouhani	PROPN
ejpam-5052	2	85	hospital	hospital	NOUN
ejpam-5052	2	86	,	,	PUNCT
ejpam-5052	2	87	babol	babol	PROPN
ejpam-5052	2	88	university	university	PROPN
ejpam-5052	2	89	of	of	ADP
ejpam-5052	2	90	medical	medical	ADJ
ejpam-5052	2	91	sciences	sciences	PROPN
ejpam-5052	2	92	,	,	PUNCT
ejpam-5052	2	93	babol	babol	NOUN
ejpam-5052	2	94	,	,	PUNCT
ejpam-5052	2	95	iran	iran	PROPN
ejpam-5052	2	96	abstract	abstract	NOUN
ejpam-5052	2	97	.	.	PUNCT
ejpam-5052	3	1	the	the	DET
ejpam-5052	3	2	present	present	ADJ
ejpam-5052	3	3	study	study	NOUN
ejpam-5052	3	4	investigates	investigate	VERB
ejpam-5052	3	5	the	the	DET
ejpam-5052	3	6	relation	relation	NOUN
ejpam-5052	3	7	between	between	ADP
ejpam-5052	3	8	derivations	derivation	NOUN
ejpam-5052	3	9	and	and	CCONJ
ejpam-5052	3	10	hyperideals	hyperideal	NOUN
ejpam-5052	3	11	on	on	ADP
ejpam-5052	3	12	ordered	order	VERB
ejpam-5052	3	13	hyperrings	hyperring	NOUN
ejpam-5052	3	14	with	with	ADP
ejpam-5052	3	15	no	no	DET
ejpam-5052	3	16	zero	zero	NUM
ejpam-5052	3	17	divisors	divisor	NOUN
ejpam-5052	3	18	.	.	PUNCT
ejpam-5052	4	1	also	also	ADV
ejpam-5052	4	2	,	,	PUNCT
ejpam-5052	4	3	we	we	PRON
ejpam-5052	4	4	identify	identify	VERB
ejpam-5052	4	5	some	some	DET
ejpam-5052	4	6	results	result	NOUN
ejpam-5052	4	7	for	for	ADP
ejpam-5052	4	8	the	the	DET
ejpam-5052	4	9	ordered	order	VERB
ejpam-5052	4	10	hyperrings	hyperring	NOUN
ejpam-5052	4	11	induced	induce	VERB
ejpam-5052	4	12	by	by	ADP
ejpam-5052	4	13	the	the	DET
ejpam-5052	4	14	homomorphism	homomorphism	NOUN
ejpam-5052	4	15	of	of	ADP
ejpam-5052	4	16	the	the	DET
ejpam-5052	4	17	ordered	order	VERB
ejpam-5052	4	18	hyperrings	hyperring	NOUN
ejpam-5052	4	19	by	by	ADP
ejpam-5052	4	20	derivations	derivation	NOUN
ejpam-5052	4	21	.	.	PUNCT
ejpam-5052	5	1	the	the	DET
ejpam-5052	5	2	present	present	ADJ
ejpam-5052	5	3	work	work	NOUN
ejpam-5052	5	4	explores	explore	VERB
ejpam-5052	5	5	some	some	DET
ejpam-5052	5	6	aspects	aspect	NOUN
ejpam-5052	5	7	of	of	ADP
ejpam-5052	5	8	derivations	derivation	NOUN
ejpam-5052	5	9	in	in	ADP
ejpam-5052	5	10	ordered	order	VERB
ejpam-5052	5	11	hyperrings	hyperring	NOUN
ejpam-5052	5	12	.	.	PUNCT
ejpam-5052	6	1	also	also	ADV
ejpam-5052	6	2	,	,	PUNCT
ejpam-5052	6	3	we	we	PRON
ejpam-5052	6	4	establish	establish	VERB
ejpam-5052	6	5	some	some	DET
ejpam-5052	6	6	results	result	NOUN
ejpam-5052	6	7	in	in	ADP
ejpam-5052	6	8	connection	connection	NOUN
ejpam-5052	6	9	with	with	ADP
ejpam-5052	6	10	homomorphisms	homomorphism	NOUN
ejpam-5052	6	11	and	and	CCONJ
ejpam-5052	6	12	hyperideals	hyperideal	NOUN
ejpam-5052	6	13	.	.	PUNCT
ejpam-5052	7	1	furthermore	furthermore	ADV
ejpam-5052	7	2	,	,	PUNCT
ejpam-5052	7	3	we	we	PRON
ejpam-5052	7	4	describe	describe	VERB
ejpam-5052	7	5	prime	prime	ADJ
ejpam-5052	7	6	hyperideals	hyperideal	NOUN
ejpam-5052	7	7	associated	associate	VERB
ejpam-5052	7	8	to	to	ADP
ejpam-5052	7	9	a	a	DET
ejpam-5052	7	10	derivation	derivation	NOUN
ejpam-5052	7	11	d	d	NOUN
ejpam-5052	7	12	on	on	ADP
ejpam-5052	7	13	an	an	DET
ejpam-5052	7	14	ordered	ordered	ADJ
ejpam-5052	7	15	hyperring	hyperring	NOUN
ejpam-5052	7	16	t	t	NOUN
ejpam-5052	7	17	and	and	CCONJ
ejpam-5052	7	18	derive	derive	VERB
ejpam-5052	7	19	several	several	ADJ
ejpam-5052	7	20	results	result	NOUN
ejpam-5052	7	21	about	about	ADP
ejpam-5052	7	22	homomorphisms	homomorphism	NOUN
ejpam-5052	7	23	and	and	CCONJ
ejpam-5052	7	24	derivations	derivation	NOUN
ejpam-5052	7	25	on	on	ADP
ejpam-5052	7	26	ordered	order	VERB
ejpam-5052	7	27	hyperrings	hyperring	NOUN
ejpam-5052	7	28	.	.	PUNCT
ejpam-5052	8	1	2020	2020	NUM
ejpam-5052	8	2	mathematics	mathematic	NOUN
ejpam-5052	8	3	subject	subject	NOUN
ejpam-5052	8	4	classifications	classification	NOUN
ejpam-5052	8	5	:	:	PUNCT
ejpam-5052	8	6	13n15	13n15	NUM
ejpam-5052	8	7	,	,	PUNCT
ejpam-5052	8	8	16y99	16y99	NUM
ejpam-5052	8	9	key	key	ADJ
ejpam-5052	8	10	words	word	NOUN
ejpam-5052	8	11	and	and	CCONJ
ejpam-5052	8	12	phrases	phrase	NOUN
ejpam-5052	8	13	:	:	PUNCT
ejpam-5052	8	14	krasner	krasner	PROPN
ejpam-5052	8	15	hyperring	hyperring	NOUN
ejpam-5052	8	16	,	,	PUNCT
ejpam-5052	8	17	ordered	order	VERB
ejpam-5052	8	18	hyperring	hyperring	NOUN
ejpam-5052	8	19	,	,	PUNCT
ejpam-5052	8	20	derivation	derivation	NOUN
ejpam-5052	8	21	,	,	PUNCT
ejpam-5052	8	22	homomorphism	homomorphism	NOUN
ejpam-5052	8	23	,	,	PUNCT
ejpam-5052	8	24	hyperideal	hyperideal	ADJ
ejpam-5052	8	25	1	1	NUM
ejpam-5052	8	26	.	.	PUNCT
ejpam-5052	9	1	introduction	introduction	NOUN
ejpam-5052	9	2	marty	marty	PROPN
ejpam-5052	9	3	presented	present	VERB
ejpam-5052	9	4	the	the	DET
ejpam-5052	9	5	hypergroup	hypergroup	NOUN
ejpam-5052	9	6	ideas	idea	NOUN
ejpam-5052	9	7	in	in	ADP
ejpam-5052	9	8	1934	1934	NUM
ejpam-5052	9	9	[	[	X
ejpam-5052	9	10	1	1	NUM
ejpam-5052	9	11	]	]	PUNCT
ejpam-5052	9	12	.	.	PUNCT
ejpam-5052	10	1	krasner	krasner	PROPN
ejpam-5052	10	2	originally	originally	ADV
ejpam-5052	10	3	considered	consider	VERB
ejpam-5052	10	4	hyperring	hyperring	NOUN
ejpam-5052	10	5	,	,	PUNCT
ejpam-5052	10	6	which	which	PRON
ejpam-5052	10	7	is	be	AUX
ejpam-5052	10	8	a	a	DET
ejpam-5052	10	9	development	development	NOUN
ejpam-5052	10	10	of	of	ADP
ejpam-5052	10	11	ring	ring	NOUN
ejpam-5052	10	12	,	,	PUNCT
ejpam-5052	10	13	in	in	ADP
ejpam-5052	10	14	[	[	PUNCT
ejpam-5052	10	15	2	2	NUM
ejpam-5052	10	16	]	]	PUNCT
ejpam-5052	10	17	.	.	PUNCT
ejpam-5052	11	1	the	the	DET
ejpam-5052	11	2	study	study	NOUN
ejpam-5052	11	3	of	of	ADP
ejpam-5052	11	4	hyperideals	hyperideal	NOUN
ejpam-5052	11	5	have	have	AUX
ejpam-5052	11	6	been	be	AUX
ejpam-5052	11	7	made	make	VERB
ejpam-5052	11	8	by	by	ADP
ejpam-5052	11	9	heidari	heidari	ADJ
ejpam-5052	11	10	and	and	CCONJ
ejpam-5052	11	11	davvaz	davvaz	NOUN
ejpam-5052	11	12	in	in	ADP
ejpam-5052	11	13	the	the	DET
ejpam-5052	11	14	context	context	NOUN
ejpam-5052	11	15	of	of	ADP
ejpam-5052	11	16	ordered	order	VERB
ejpam-5052	11	17	semihypergroups	semihypergroup	NOUN
ejpam-5052	11	18	in	in	ADP
ejpam-5052	11	19	[	[	X
ejpam-5052	11	20	3	3	NUM
ejpam-5052	11	21	]	]	PUNCT
ejpam-5052	11	22	.	.	PUNCT
ejpam-5052	12	1	the	the	DET
ejpam-5052	12	2	study	study	NOUN
ejpam-5052	12	3	also	also	ADV
ejpam-5052	12	4	demonstrated	demonstrate	VERB
ejpam-5052	12	5	that	that	SCONJ
ejpam-5052	12	6	the	the	DET
ejpam-5052	12	7	direct	direct	ADJ
ejpam-5052	12	8	product	product	NOUN
ejpam-5052	12	9	of	of	ADP
ejpam-5052	12	10	ordered	order	VERB
ejpam-5052	12	11	hyperstructures	hyperstructure	NOUN
ejpam-5052	12	12	are	be	AUX
ejpam-5052	12	13	ordered	order	VERB
ejpam-5052	12	14	hyperstructures	hyperstructure	NOUN
ejpam-5052	12	15	.	.	PUNCT
ejpam-5052	13	1	later	later	ADV
ejpam-5052	13	2	on	on	ADV
ejpam-5052	13	3	,	,	PUNCT
ejpam-5052	13	4	davvaz	davvaz	NOUN
ejpam-5052	13	5	et	et	PROPN
ejpam-5052	13	6	al	al	PROPN
ejpam-5052	13	7	.	.	PUNCT
ejpam-5052	14	1	[	[	X
ejpam-5052	14	2	4	4	NUM
ejpam-5052	14	3	]	]	X
ejpam-5052	14	4	utilized	utilize	VERB
ejpam-5052	14	5	pseudoorders	pseudoorder	NOUN
ejpam-5052	14	6	to	to	PART
ejpam-5052	14	7	construct	construct	VERB
ejpam-5052	14	8	strongly	strongly	ADV
ejpam-5052	14	9	regular	regular	ADJ
ejpam-5052	14	10	relations	relation	NOUN
ejpam-5052	14	11	in	in	ADP
ejpam-5052	14	12	ordered	order	VERB
ejpam-5052	14	13	semihypergroups	semihypergroup	NOUN
ejpam-5052	14	14	and	and	CCONJ
ejpam-5052	14	15	examined	examine	VERB
ejpam-5052	14	16	the	the	DET
ejpam-5052	14	17	relationships	relationship	NOUN
ejpam-5052	14	18	between	between	ADP
ejpam-5052	14	19	ordered	order	VERB
ejpam-5052	14	20	hyperstructures	hyperstructure	NOUN
ejpam-5052	14	21	and	and	CCONJ
ejpam-5052	14	22	ordered	order	VERB
ejpam-5052	14	23	structures	structure	NOUN
ejpam-5052	14	24	.	.	PUNCT
ejpam-5052	15	1	also	also	ADV
ejpam-5052	15	2	,	,	PUNCT
ejpam-5052	15	3	see	see	VERB
ejpam-5052	15	4	[	[	X
ejpam-5052	15	5	5	5	NUM
ejpam-5052	15	6	,	,	PUNCT
ejpam-5052	15	7	6	6	NUM
ejpam-5052	15	8	]	]	PUNCT
ejpam-5052	15	9	.	.	PUNCT
ejpam-5052	16	1	al	al	PROPN
ejpam-5052	16	2	-	-	PUNCT
ejpam-5052	16	3	tahan	tahan	PROPN
ejpam-5052	16	4	and	and	CCONJ
ejpam-5052	16	5	davvaz	davvaz	NOUN
ejpam-5052	17	1	[	[	X
ejpam-5052	17	2	7	7	X
ejpam-5052	17	3	]	]	PUNCT
ejpam-5052	17	4	use	use	NOUN
ejpam-5052	17	5	the	the	DET
ejpam-5052	17	6	ordered	order	VERB
ejpam-5052	17	7	hyperstructure	hyperstructure	NOUN
ejpam-5052	17	8	to	to	PART
ejpam-5052	17	9	communicate	communicate	VERB
ejpam-5052	17	10	with	with	ADP
ejpam-5052	17	11	biological	biological	ADJ
ejpam-5052	17	12	inheritance	inheritance	NOUN
ejpam-5052	17	13	and	and	CCONJ
ejpam-5052	17	14	genetics	genetic	NOUN
ejpam-5052	17	15	to	to	PART
ejpam-5052	17	16	do	do	VERB
ejpam-5052	17	17	research	research	NOUN
ejpam-5052	17	18	,	,	PUNCT
ejpam-5052	17	19	and	and	CCONJ
ejpam-5052	17	20	to	to	ADP
ejpam-5052	17	21	access	access	NOUN
ejpam-5052	17	22	applications	application	NOUN
ejpam-5052	17	23	.	.	PUNCT
ejpam-5052	18	1	∗corresponding	∗corresponde	VERB
ejpam-5052	18	2	author	author	NOUN
ejpam-5052	18	3	.	.	PUNCT
ejpam-5052	19	1	doi	doi	NOUN
ejpam-5052	19	2	:	:	PUNCT
ejpam-5052	19	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5052	https://doi.org/10.29020/nybg.ejpam.v17i2.5052	NOUN
ejpam-5052	19	4	email	email	NOUN
ejpam-5052	19	5	addresses	address	VERB
ejpam-5052	19	6	:	:	PUNCT
ejpam-5052	19	7	cairic@e.gzhu.edu.cn	cairic@e.gzhu.edu.cn	NOUN
ejpam-5052	19	8	(	(	PUNCT
ejpam-5052	19	9	r.	r.	PROPN
ejpam-5052	19	10	cai	cai	PROPN
ejpam-5052	19	11	)	)	PUNCT
ejpam-5052	19	12	,	,	PUNCT
ejpam-5052	19	13	m.alsaedi@psau.edu.sa	m.alsaedi@psau.edu.sa	PROPN
ejpam-5052	19	14	(	(	PUNCT
ejpam-5052	19	15	m.	m.	NOUN
ejpam-5052	19	16	alsaeedi	alsaeedi	PROPN
ejpam-5052	19	17	)	)	PUNCT
ejpam-5052	19	18	,	,	PUNCT
ejpam-5052	19	19	maryam.akhoundi@mubabol.ac.ir	maryam.akhoundi@mubabol.ac.ir	NUM
ejpam-5052	19	20	(	(	PUNCT
ejpam-5052	19	21	m.	m.	NOUN
ejpam-5052	19	22	akhoundi	akhoundi	ADJ
ejpam-5052	19	23	)	)	PUNCT
ejpam-5052	19	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5052	20	1	604	604	NUM
ejpam-5052	20	2	©	©	ADP
ejpam-5052	20	3	2024	2024	NUM
ejpam-5052	20	4	ejpam	ejpam	NOUN
ejpam-5052	20	5	all	all	DET
ejpam-5052	20	6	rights	right	NOUN
ejpam-5052	20	7	reserved	reserve	VERB
ejpam-5052	20	8	.	.	PUNCT
ejpam-5052	21	1	r.	r.	PROPN
ejpam-5052	21	2	cai	cai	PROPN
ejpam-5052	21	3	,	,	PUNCT
ejpam-5052	21	4	m.	m.	NOUN
ejpam-5052	21	5	alsaeedi	alsaeedi	PROPN
ejpam-5052	21	6	,	,	PUNCT
ejpam-5052	21	7	m.	m.	NOUN
ejpam-5052	21	8	akhoundi	akhoundi	PROPN
ejpam-5052	21	9	/	/	SYM
ejpam-5052	21	10	eur	eur	PROPN
ejpam-5052	21	11	.	.	PUNCT
ejpam-5052	22	1	j.	j.	PROPN
ejpam-5052	22	2	pure	pure	PROPN
ejpam-5052	22	3	appl	appl	PROPN
ejpam-5052	22	4	.	.	PROPN
ejpam-5052	22	5	math	math	PROPN
ejpam-5052	22	6	,	,	PUNCT
ejpam-5052	22	7	17	17	NUM
ejpam-5052	22	8	(	(	PUNCT
ejpam-5052	22	9	2	2	NUM
ejpam-5052	22	10	)	)	PUNCT
ejpam-5052	22	11	(	(	PUNCT
ejpam-5052	22	12	2024	2024	NUM
ejpam-5052	22	13	)	)	PUNCT
ejpam-5052	22	14	,	,	PUNCT
ejpam-5052	22	15	604	604	NUM
ejpam-5052	22	16	-	-	SYM
ejpam-5052	22	17	615	615	NUM
ejpam-5052	22	18	605	605	NUM
ejpam-5052	22	19	derivation	derivation	NOUN
ejpam-5052	22	20	in	in	ADP
ejpam-5052	22	21	rings	ring	NOUN
ejpam-5052	22	22	was	be	AUX
ejpam-5052	22	23	first	first	ADV
ejpam-5052	22	24	explored	explore	VERB
ejpam-5052	22	25	by	by	ADP
ejpam-5052	22	26	posner	posner	NOUN
ejpam-5052	22	27	[	[	X
ejpam-5052	22	28	8	8	NUM
ejpam-5052	22	29	]	]	PUNCT
ejpam-5052	22	30	and	and	CCONJ
ejpam-5052	22	31	later	later	ADV
ejpam-5052	22	32	on	on	ADP
ejpam-5052	22	33	hyperrings	hyperring	NOUN
ejpam-5052	22	34	by	by	ADP
ejpam-5052	22	35	asokkumar	asokkumar	PROPN
ejpam-5052	22	36	[	[	X
ejpam-5052	22	37	9	9	NUM
ejpam-5052	22	38	]	]	PUNCT
ejpam-5052	22	39	and	and	CCONJ
ejpam-5052	22	40	kamali	kamali	NOUN
ejpam-5052	22	41	and	and	CCONJ
ejpam-5052	22	42	davvaz	davvaz	NOUN
ejpam-5052	23	1	[	[	X
ejpam-5052	23	2	10	10	NUM
ejpam-5052	23	3	]	]	PUNCT
ejpam-5052	23	4	.	.	PUNCT
ejpam-5052	24	1	derivation	derivation	NOUN
ejpam-5052	24	2	on	on	ADP
ejpam-5052	24	3	ordered	order	VERB
ejpam-5052	24	4	semihyperring	semihyperring	NOUN
ejpam-5052	24	5	was	be	AUX
ejpam-5052	24	6	presented	present	VERB
ejpam-5052	24	7	by	by	ADP
ejpam-5052	24	8	rao	rao	PROPN
ejpam-5052	24	9	et	et	PROPN
ejpam-5052	24	10	al	al	PROPN
ejpam-5052	24	11	.	.	PUNCT
ejpam-5052	25	1	in	in	ADP
ejpam-5052	25	2	[	[	X
ejpam-5052	25	3	11	11	NUM
ejpam-5052	25	4	]	]	PUNCT
ejpam-5052	25	5	.	.	PUNCT
ejpam-5052	26	1	omidi	omidi	NOUN
ejpam-5052	26	2	and	and	CCONJ
ejpam-5052	26	3	davvaz	davvaz	NOUN
ejpam-5052	26	4	considered	consider	VERB
ejpam-5052	26	5	ordered	order	VERB
ejpam-5052	26	6	hyperring	hyperring	NOUN
ejpam-5052	26	7	,	,	PUNCT
ejpam-5052	26	8	which	which	PRON
ejpam-5052	26	9	is	be	AUX
ejpam-5052	26	10	a	a	DET
ejpam-5052	26	11	development	development	NOUN
ejpam-5052	26	12	of	of	ADP
ejpam-5052	26	13	ordered	order	VERB
ejpam-5052	26	14	ring	ring	NOUN
ejpam-5052	26	15	,	,	PUNCT
ejpam-5052	26	16	in	in	ADP
ejpam-5052	26	17	[	[	X
ejpam-5052	26	18	12	12	NUM
ejpam-5052	26	19	]	]	PUNCT
ejpam-5052	26	20	.	.	PUNCT
ejpam-5052	27	1	also	also	ADV
ejpam-5052	27	2	,	,	PUNCT
ejpam-5052	27	3	see	see	VERB
ejpam-5052	27	4	[	[	X
ejpam-5052	27	5	13–16	13–16	NOUN
ejpam-5052	27	6	]	]	X
ejpam-5052	27	7	.	.	PUNCT
ejpam-5052	28	1	the	the	DET
ejpam-5052	28	2	present	present	ADJ
ejpam-5052	28	3	work	work	NOUN
ejpam-5052	28	4	explores	explore	VERB
ejpam-5052	28	5	some	some	DET
ejpam-5052	28	6	aspects	aspect	NOUN
ejpam-5052	28	7	of	of	ADP
ejpam-5052	28	8	derivations	derivation	NOUN
ejpam-5052	28	9	in	in	ADP
ejpam-5052	28	10	ordered	order	VERB
ejpam-5052	28	11	hyperrings	hyperring	NOUN
ejpam-5052	28	12	.	.	PUNCT
ejpam-5052	29	1	also	also	ADV
ejpam-5052	29	2	,	,	PUNCT
ejpam-5052	29	3	we	we	PRON
ejpam-5052	29	4	establish	establish	VERB
ejpam-5052	29	5	some	some	DET
ejpam-5052	29	6	results	result	NOUN
ejpam-5052	29	7	in	in	ADP
ejpam-5052	29	8	connection	connection	NOUN
ejpam-5052	29	9	with	with	ADP
ejpam-5052	29	10	homomorphisms	homomorphism	NOUN
ejpam-5052	29	11	and	and	CCONJ
ejpam-5052	29	12	hyperideals	hyperideal	NOUN
ejpam-5052	29	13	.	.	PUNCT
ejpam-5052	30	1	2	2	X
ejpam-5052	30	2	.	.	X
ejpam-5052	30	3	preliminaries	preliminary	NOUN
ejpam-5052	30	4	we	we	PRON
ejpam-5052	30	5	set	set	VERB
ejpam-5052	30	6	that	that	DET
ejpam-5052	30	7	okh	okh	NOUN
ejpam-5052	30	8	:	:	PUNCT
ejpam-5052	30	9	the	the	DET
ejpam-5052	30	10	set	set	NOUN
ejpam-5052	30	11	of	of	ADP
ejpam-5052	30	12	all	all	DET
ejpam-5052	30	13	ordered	order	VERB
ejpam-5052	30	14	krasner	krasner	NOUN
ejpam-5052	30	15	hyperrings	hyperring	NOUN
ejpam-5052	30	16	(	(	PUNCT
ejpam-5052	30	17	e,⊕,⊙,≤	e,⊕,⊙,≤	NOUN
ejpam-5052	30	18	)	)	PUNCT
ejpam-5052	30	19	,	,	PUNCT
ejpam-5052	30	20	der(e	der(e	PROPN
ejpam-5052	30	21	):	):	PUNCT
ejpam-5052	30	22	the	the	DET
ejpam-5052	30	23	set	set	NOUN
ejpam-5052	30	24	of	of	ADP
ejpam-5052	30	25	all	all	DET
ejpam-5052	30	26	derivations	derivation	NOUN
ejpam-5052	30	27	of	of	ADP
ejpam-5052	30	28	e.	e.	PROPN
ejpam-5052	30	29	definition	definition	NOUN
ejpam-5052	30	30	1	1	NUM
ejpam-5052	30	31	.	.	PUNCT
ejpam-5052	31	1	[	[	X
ejpam-5052	31	2	2	2	NUM
ejpam-5052	31	3	]	]	PUNCT
ejpam-5052	31	4	(	(	PUNCT
ejpam-5052	31	5	e,⊕,⊙	e,⊕,⊙	PROPN
ejpam-5052	31	6	)	)	PUNCT
ejpam-5052	31	7	is	be	AUX
ejpam-5052	31	8	a	a	DET
ejpam-5052	31	9	krasner	krasner	NOUN
ejpam-5052	31	10	hyperring	hyperre	VERB
ejpam-5052	31	11	if	if	SCONJ
ejpam-5052	31	12	:	:	PUNCT
ejpam-5052	31	13	(	(	PUNCT
ejpam-5052	31	14	1	1	X
ejpam-5052	31	15	)	)	PUNCT
ejpam-5052	31	16	(	(	PUNCT
ejpam-5052	31	17	e,⊕	e,⊕	PROPN
ejpam-5052	31	18	)	)	PUNCT
ejpam-5052	31	19	is	be	AUX
ejpam-5052	31	20	a	a	DET
ejpam-5052	31	21	canonical	canonical	ADJ
ejpam-5052	31	22	hypergroup	hypergroup	NOUN
ejpam-5052	31	23	;	;	PUNCT
ejpam-5052	31	24	(	(	PUNCT
ejpam-5052	31	25	2	2	X
ejpam-5052	31	26	)	)	PUNCT
ejpam-5052	31	27	(	(	PUNCT
ejpam-5052	31	28	e,⊙	e,⊙	NOUN
ejpam-5052	31	29	)	)	PUNCT
ejpam-5052	31	30	is	be	AUX
ejpam-5052	31	31	a	a	DET
ejpam-5052	31	32	semigroup	semigroup	NOUN
ejpam-5052	31	33	and	and	CCONJ
ejpam-5052	31	34	z	z	NOUN
ejpam-5052	31	35	⊙	⊙	NOUN
ejpam-5052	31	36	0	0	PUNCT
ejpam-5052	32	1	=	=	SYM
ejpam-5052	32	2	0⊙	0⊙	NOUN
ejpam-5052	32	3	z	z	NOUN
ejpam-5052	32	4	=	=	SYM
ejpam-5052	32	5	{	{	PUNCT
ejpam-5052	32	6	0	0	NUM
ejpam-5052	32	7	}	}	PUNCT
ejpam-5052	32	8	,	,	PUNCT
ejpam-5052	32	9	∀z	∀z	X
ejpam-5052	32	10	∈	∈	PROPN
ejpam-5052	32	11	e	e	NOUN
ejpam-5052	32	12	;	;	PUNCT
ejpam-5052	32	13	(	(	PUNCT
ejpam-5052	32	14	3	3	X
ejpam-5052	32	15	)	)	PUNCT
ejpam-5052	32	16	⊙	⊙	NOUN
ejpam-5052	32	17	is	be	AUX
ejpam-5052	32	18	distributive	distributive	ADJ
ejpam-5052	32	19	with	with	ADP
ejpam-5052	32	20	respect	respect	NOUN
ejpam-5052	32	21	to	to	ADP
ejpam-5052	32	22	the	the	DET
ejpam-5052	32	23	hyperaddition	hyperaddition	NOUN
ejpam-5052	32	24	⊕.	⊕.	NOUN
ejpam-5052	32	25	definition	definition	NOUN
ejpam-5052	32	26	2	2	NUM
ejpam-5052	32	27	.	.	PUNCT
ejpam-5052	33	1	[	[	X
ejpam-5052	33	2	12	12	NUM
ejpam-5052	33	3	]	]	X
ejpam-5052	33	4	let	let	ADJ
ejpam-5052	33	5	(	(	PUNCT
ejpam-5052	33	6	e,⊕,⊙	e,⊕,⊙	PROPN
ejpam-5052	33	7	)	)	PUNCT
ejpam-5052	33	8	be	be	VERB
ejpam-5052	33	9	a	a	DET
ejpam-5052	33	10	krasner	krasner	NOUN
ejpam-5052	33	11	hyperring	hyperring	NOUN
ejpam-5052	33	12	.	.	PUNCT
ejpam-5052	34	1	(	(	PUNCT
ejpam-5052	34	2	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	34	3	)	)	PUNCT
ejpam-5052	34	4	∈	∈	NOUN
ejpam-5052	34	5	okh	okh	VERB
ejpam-5052	34	6	if	if	SCONJ
ejpam-5052	34	7	(	(	PUNCT
ejpam-5052	34	8	1	1	NUM
ejpam-5052	34	9	)	)	PUNCT
ejpam-5052	34	10	(	(	PUNCT
ejpam-5052	34	11	e,≤	e,≤	NOUN
ejpam-5052	34	12	)	)	PUNCT
ejpam-5052	34	13	is	be	AUX
ejpam-5052	34	14	a	a	DET
ejpam-5052	34	15	partially	partially	ADV
ejpam-5052	34	16	ordered	order	VERB
ejpam-5052	34	17	set	set	NOUN
ejpam-5052	34	18	;	;	PUNCT
ejpam-5052	34	19	(	(	PUNCT
ejpam-5052	34	20	2	2	X
ejpam-5052	34	21	)	)	PUNCT
ejpam-5052	34	22	(	(	PUNCT
ejpam-5052	34	23	l	l	NOUN
ejpam-5052	34	24	,	,	PUNCT
ejpam-5052	34	25	l′	l′	NUM
ejpam-5052	34	26	)	)	PUNCT
ejpam-5052	34	27	∈≤⇒	∈≤⇒	ADP
ejpam-5052	34	28	l	l	PROPN
ejpam-5052	34	29	⊕	⊕	PROPN
ejpam-5052	34	30	t	t	PROPN
ejpam-5052	34	31	⪯	⪯	PROPN
ejpam-5052	34	32	l′	l′	PROPN
ejpam-5052	35	1	⊕	⊕	PROPN
ejpam-5052	35	2	t,∀l	t,∀l	PROPN
ejpam-5052	35	3	,	,	PUNCT
ejpam-5052	35	4	l′	l′	PROPN
ejpam-5052	35	5	,	,	PUNCT
ejpam-5052	35	6	t	t	PROPN
ejpam-5052	35	7	∈	∈	PROPN
ejpam-5052	35	8	e	e	X
ejpam-5052	35	9	;	;	PUNCT
ejpam-5052	35	10	(	(	PUNCT
ejpam-5052	35	11	3	3	X
ejpam-5052	35	12	)	)	PUNCT
ejpam-5052	35	13	(	(	PUNCT
ejpam-5052	35	14	l	l	NOUN
ejpam-5052	35	15	,	,	PUNCT
ejpam-5052	35	16	l′	l′	NUM
ejpam-5052	35	17	)	)	PUNCT
ejpam-5052	35	18	∈≤	∈≤	PROPN
ejpam-5052	35	19	and	and	CCONJ
ejpam-5052	35	20	(	(	PUNCT
ejpam-5052	35	21	0	0	NUM
ejpam-5052	35	22	,	,	PUNCT
ejpam-5052	35	23	t	t	PROPN
ejpam-5052	35	24	)	)	PUNCT
ejpam-5052	35	25	∈≤⇒	∈≤⇒	PROPN
ejpam-5052	35	26	(	(	PUNCT
ejpam-5052	35	27	l	l	PROPN
ejpam-5052	35	28	⊙	⊙	PROPN
ejpam-5052	35	29	t	t	PROPN
ejpam-5052	35	30	,	,	PUNCT
ejpam-5052	35	31	l′	l′	PROPN
ejpam-5052	35	32	⊙	⊙	PROPN
ejpam-5052	35	33	t	t	PROPN
ejpam-5052	35	34	)	)	PUNCT
ejpam-5052	35	35	∈≤	∈≤	PROPN
ejpam-5052	35	36	and	and	CCONJ
ejpam-5052	35	37	(	(	PUNCT
ejpam-5052	35	38	t⊙	t⊙	PROPN
ejpam-5052	35	39	l	l	NOUN
ejpam-5052	35	40	,	,	PUNCT
ejpam-5052	35	41	t⊙	t⊙	NOUN
ejpam-5052	35	42	l′	l′	NOUN
ejpam-5052	35	43	)	)	PUNCT
ejpam-5052	36	1	∈≤.	∈≤.	X
ejpam-5052	36	2	note	note	VERB
ejpam-5052	36	3	that	that	SCONJ
ejpam-5052	36	4	for	for	ADP
ejpam-5052	36	5	every	every	DET
ejpam-5052	36	6	∅	∅	NOUN
ejpam-5052	36	7	=	=	NOUN
ejpam-5052	36	8	̸	̸	PUNCT
ejpam-5052	36	9	l	l	NOUN
ejpam-5052	36	10	,	,	PUNCT
ejpam-5052	36	11	l′	l′	VERB
ejpam-5052	36	12	⊆	⊆	NUM
ejpam-5052	36	13	e	e	NOUN
ejpam-5052	36	14	,	,	PUNCT
ejpam-5052	36	15	l	l	PROPN
ejpam-5052	36	16	⪯	⪯	PROPN
ejpam-5052	36	17	l′	l′	VERB
ejpam-5052	36	18	⇔	⇔	PROPN
ejpam-5052	36	19	∀l	∀l	NOUN
ejpam-5052	36	20	∈	∈	PROPN
ejpam-5052	36	21	l,∃l′	l,∃l′	PROPN
ejpam-5052	36	22	∈	∈	PROPN
ejpam-5052	36	23	l′	l′	VERB
ejpam-5052	36	24	such	such	ADJ
ejpam-5052	36	25	that	that	SCONJ
ejpam-5052	36	26	(	(	PUNCT
ejpam-5052	36	27	l	l	NOUN
ejpam-5052	36	28	,	,	PUNCT
ejpam-5052	36	29	l′	l′	NUM
ejpam-5052	36	30	)	)	PUNCT
ejpam-5052	37	1	∈≤.	∈≤.	X
ejpam-5052	37	2	definition	definition	NOUN
ejpam-5052	37	3	3	3	NUM
ejpam-5052	37	4	.	.	PUNCT
ejpam-5052	38	1	[	[	X
ejpam-5052	38	2	12	12	NUM
ejpam-5052	38	3	]	]	X
ejpam-5052	38	4	let	let	ADJ
ejpam-5052	38	5	(	(	PUNCT
ejpam-5052	38	6	e,⊕,⊙,≤	e,⊕,⊙,≤	NUM
ejpam-5052	38	7	)	)	PUNCT
ejpam-5052	38	8	and	and	CCONJ
ejpam-5052	38	9	(	(	PUNCT
ejpam-5052	38	10	e′,⊕′,⊙′,≤′	e′,⊕′,⊙′,≤′	ADJ
ejpam-5052	38	11	)	)	PUNCT
ejpam-5052	38	12	∈	∈	NOUN
ejpam-5052	38	13	okh	okh	NOUN
ejpam-5052	38	14	.	.	PUNCT
ejpam-5052	39	1	a	a	DET
ejpam-5052	39	2	function	function	NOUN
ejpam-5052	39	3	λ	λ	NOUN
ejpam-5052	39	4	:	:	PUNCT
ejpam-5052	39	5	e	e	X
ejpam-5052	39	6	→	→	SYM
ejpam-5052	39	7	e′	e′	X
ejpam-5052	39	8	is	be	AUX
ejpam-5052	39	9	a	a	DET
ejpam-5052	39	10	homomorphism	homomorphism	NOUN
ejpam-5052	39	11	if	if	SCONJ
ejpam-5052	39	12	∀l	∀l	NOUN
ejpam-5052	39	13	,	,	PUNCT
ejpam-5052	39	14	l′	l′	NOUN
ejpam-5052	39	15	∈	∈	PROPN
ejpam-5052	39	16	e	e	NOUN
ejpam-5052	39	17	,	,	PUNCT
ejpam-5052	39	18	(	(	PUNCT
ejpam-5052	39	19	1	1	X
ejpam-5052	39	20	)	)	PUNCT
ejpam-5052	39	21	λ(l	λ(l	PROPN
ejpam-5052	39	22	⊕	⊕	PROPN
ejpam-5052	39	23	l′	l′	NOUN
ejpam-5052	39	24	)	)	PUNCT
ejpam-5052	39	25	⊆	⊆	NUM
ejpam-5052	39	26	λ(l)⊕′	λ(l)⊕′	NOUN
ejpam-5052	39	27	λ(l′	λ(l′	NUM
ejpam-5052	39	28	)	)	PUNCT
ejpam-5052	39	29	;	;	PUNCT
ejpam-5052	39	30	(	(	PUNCT
ejpam-5052	39	31	2	2	X
ejpam-5052	39	32	)	)	PUNCT
ejpam-5052	39	33	λ(l	λ(l	PROPN
ejpam-5052	39	34	⊙	⊙	PROPN
ejpam-5052	39	35	l′	l′	PROPN
ejpam-5052	39	36	)	)	PUNCT
ejpam-5052	40	1	=	=	SYM
ejpam-5052	41	1	λ(l)⊙′	λ(l)⊙′	PROPN
ejpam-5052	41	2	λ(l′	λ(l′	PROPN
ejpam-5052	41	3	)	)	PUNCT
ejpam-5052	41	4	;	;	PUNCT
ejpam-5052	41	5	(	(	PUNCT
ejpam-5052	41	6	3	3	X
ejpam-5052	41	7	)	)	PUNCT
ejpam-5052	41	8	(	(	PUNCT
ejpam-5052	41	9	l	l	NOUN
ejpam-5052	41	10	,	,	PUNCT
ejpam-5052	41	11	l′	l′	NUM
ejpam-5052	41	12	)	)	PUNCT
ejpam-5052	41	13	∈≤⇒	∈≤⇒	ADP
ejpam-5052	41	14	(	(	PUNCT
ejpam-5052	41	15	λ(l),λ(l′	λ(l),λ(l′	PROPN
ejpam-5052	41	16	)	)	PUNCT
ejpam-5052	41	17	)	)	PUNCT
ejpam-5052	42	1	∈≤′.	∈≤′.	NOUN
ejpam-5052	42	2	definition	definition	NOUN
ejpam-5052	42	3	4	4	NUM
ejpam-5052	42	4	.	.	PUNCT
ejpam-5052	43	1	[	[	X
ejpam-5052	43	2	3	3	X
ejpam-5052	43	3	]	]	X
ejpam-5052	43	4	let	let	VERB
ejpam-5052	43	5	(	(	PUNCT
ejpam-5052	43	6	e,⊕,⊙,≤	e,⊕,⊙,≤	NUM
ejpam-5052	43	7	)	)	PUNCT
ejpam-5052	43	8	∈	∈	NOUN
ejpam-5052	43	9	okh	okh	VERB
ejpam-5052	43	10	.	.	PUNCT
ejpam-5052	43	11	∅	∅	NOUN
ejpam-5052	43	12	=	=	NOUN
ejpam-5052	43	13	̸	̸	NUM
ejpam-5052	43	14	x	x	PUNCT
ejpam-5052	44	1	⊆	⊆	NUM
ejpam-5052	44	2	e	e	NOUN
ejpam-5052	44	3	is	be	AUX
ejpam-5052	44	4	a	a	DET
ejpam-5052	44	5	hyperideal	hyperideal	NOUN
ejpam-5052	44	6	of	of	ADP
ejpam-5052	44	7	e	e	NOUN
ejpam-5052	44	8	if	if	SCONJ
ejpam-5052	44	9	(	(	PUNCT
ejpam-5052	44	10	1	1	NUM
ejpam-5052	44	11	)	)	PUNCT
ejpam-5052	44	12	(	(	PUNCT
ejpam-5052	44	13	x,⊕	x,⊕	PROPN
ejpam-5052	44	14	)	)	PUNCT
ejpam-5052	44	15	is	be	AUX
ejpam-5052	44	16	a	a	DET
ejpam-5052	44	17	canonical	canonical	ADJ
ejpam-5052	44	18	subhypergroup	subhypergroup	NOUN
ejpam-5052	44	19	of	of	ADP
ejpam-5052	44	20	(	(	PUNCT
ejpam-5052	44	21	e,⊕	e,⊕	PROPN
ejpam-5052	44	22	)	)	PUNCT
ejpam-5052	44	23	;	;	PUNCT
ejpam-5052	44	24	(	(	PUNCT
ejpam-5052	44	25	2	2	X
ejpam-5052	44	26	)	)	PUNCT
ejpam-5052	44	27	l	l	NOUN
ejpam-5052	44	28	⊙	⊙	PROPN
ejpam-5052	44	29	x	x	SYM
ejpam-5052	44	30	,	,	PUNCT
ejpam-5052	44	31	x⊙	x⊙	PROPN
ejpam-5052	44	32	l	l	PROPN
ejpam-5052	44	33	∈	∈	PROPN
ejpam-5052	45	1	x,∀l	x,∀l	PUNCT
ejpam-5052	45	2	∈	∈	PROPN
ejpam-5052	45	3	e,∀x	e,∀x	NOUN
ejpam-5052	45	4	∈	∈	PROPN
ejpam-5052	45	5	x	x	NOUN
ejpam-5052	45	6	;	;	PUNCT
ejpam-5052	45	7	r.	r.	PROPN
ejpam-5052	45	8	cai	cai	PROPN
ejpam-5052	45	9	,	,	PUNCT
ejpam-5052	45	10	m.	m.	NOUN
ejpam-5052	45	11	alsaeedi	alsaeedi	PROPN
ejpam-5052	45	12	,	,	PUNCT
ejpam-5052	45	13	m.	m.	NOUN
ejpam-5052	45	14	akhoundi	akhoundi	PROPN
ejpam-5052	45	15	/	/	SYM
ejpam-5052	45	16	eur	eur	PROPN
ejpam-5052	45	17	.	.	PUNCT
ejpam-5052	46	1	j.	j.	PROPN
ejpam-5052	46	2	pure	pure	PROPN
ejpam-5052	46	3	appl	appl	PROPN
ejpam-5052	46	4	.	.	PROPN
ejpam-5052	46	5	math	math	PROPN
ejpam-5052	46	6	,	,	PUNCT
ejpam-5052	46	7	17	17	NUM
ejpam-5052	46	8	(	(	PUNCT
ejpam-5052	46	9	2	2	NUM
ejpam-5052	46	10	)	)	PUNCT
ejpam-5052	46	11	(	(	PUNCT
ejpam-5052	46	12	2024	2024	NUM
ejpam-5052	46	13	)	)	PUNCT
ejpam-5052	46	14	,	,	PUNCT
ejpam-5052	46	15	604	604	NUM
ejpam-5052	46	16	-	-	SYM
ejpam-5052	46	17	615	615	NUM
ejpam-5052	46	18	606	606	NUM
ejpam-5052	46	19	(	(	PUNCT
ejpam-5052	46	20	3	3	NUM
ejpam-5052	46	21	)	)	PUNCT
ejpam-5052	46	22	(	(	PUNCT
ejpam-5052	46	23	x	x	X
ejpam-5052	46	24	]	]	X
ejpam-5052	46	25	:	:	PUNCT
ejpam-5052	46	26	=	=	SYM
ejpam-5052	46	27	{	{	PUNCT
ejpam-5052	46	28	l	l	NOUN
ejpam-5052	46	29	∈	∈	PROPN
ejpam-5052	46	30	e	e	NOUN
ejpam-5052	46	31	|	|	NOUN
ejpam-5052	46	32	l	l	PROPN
ejpam-5052	46	33	≤	≤	NUM
ejpam-5052	46	34	x	x	X
ejpam-5052	46	35	,	,	PUNCT
ejpam-5052	46	36	for	for	ADP
ejpam-5052	46	37	some	some	DET
ejpam-5052	46	38	x	x	SYM
ejpam-5052	46	39	∈	∈	PROPN
ejpam-5052	46	40	x	x	PROPN
ejpam-5052	46	41	}	}	PUNCT
ejpam-5052	46	42	⊆	⊆	NUM
ejpam-5052	46	43	x.	x.	NOUN
ejpam-5052	46	44	definition	definition	NOUN
ejpam-5052	46	45	5	5	NUM
ejpam-5052	46	46	.	.	PUNCT
ejpam-5052	47	1	[	[	X
ejpam-5052	47	2	11	11	NUM
ejpam-5052	47	3	]	]	X
ejpam-5052	47	4	let	let	VERB
ejpam-5052	47	5	(	(	PUNCT
ejpam-5052	47	6	e,⊕,⊙,≤	e,⊕,⊙,≤	NUM
ejpam-5052	47	7	)	)	PUNCT
ejpam-5052	47	8	∈	∈	NOUN
ejpam-5052	47	9	okh	okh	NOUN
ejpam-5052	47	10	.	.	PUNCT
ejpam-5052	48	1	d	d	X
ejpam-5052	48	2	∈	∈	PROPN
ejpam-5052	48	3	der(e	der(e	PROPN
ejpam-5052	48	4	)	)	PUNCT
ejpam-5052	48	5	if	if	SCONJ
ejpam-5052	48	6	for	for	ADP
ejpam-5052	48	7	all	all	DET
ejpam-5052	48	8	l	l	NOUN
ejpam-5052	48	9	,	,	PUNCT
ejpam-5052	48	10	l′	l′	PROPN
ejpam-5052	48	11	∈	∈	PROPN
ejpam-5052	48	12	e	e	NOUN
ejpam-5052	48	13	,	,	PUNCT
ejpam-5052	48	14	(	(	PUNCT
ejpam-5052	48	15	1	1	X
ejpam-5052	48	16	)	)	PUNCT
ejpam-5052	48	17	d(l	d(l	SCONJ
ejpam-5052	48	18	⊕	⊕	PROPN
ejpam-5052	48	19	l′	l′	VERB
ejpam-5052	48	20	)	)	PUNCT
ejpam-5052	49	1	⊆	⊆	NUM
ejpam-5052	49	2	d(l)⊕	d(l)⊕	PROPN
ejpam-5052	49	3	d(l′	d(l′	PROPN
ejpam-5052	49	4	)	)	PUNCT
ejpam-5052	49	5	;	;	PUNCT
ejpam-5052	49	6	(	(	PUNCT
ejpam-5052	49	7	2	2	X
ejpam-5052	49	8	)	)	PUNCT
ejpam-5052	49	9	d(l	d(l	SCONJ
ejpam-5052	49	10	⊙	⊙	PROPN
ejpam-5052	49	11	l′	l′	PROPN
ejpam-5052	49	12	)	)	PUNCT
ejpam-5052	49	13	∈	∈	PROPN
ejpam-5052	49	14	d(l)⊙	d(l)⊙	NUM
ejpam-5052	49	15	l′	l′	NUM
ejpam-5052	49	16	⊕	⊕	PROPN
ejpam-5052	49	17	l	l	PROPN
ejpam-5052	49	18	⊙	⊙	PROPN
ejpam-5052	49	19	d(l′	d(l′	PROPN
ejpam-5052	49	20	)	)	PUNCT
ejpam-5052	49	21	;	;	PUNCT
ejpam-5052	49	22	(	(	PUNCT
ejpam-5052	49	23	3	3	X
ejpam-5052	49	24	)	)	PUNCT
ejpam-5052	49	25	(	(	PUNCT
ejpam-5052	49	26	l	l	NOUN
ejpam-5052	49	27	,	,	PUNCT
ejpam-5052	49	28	l′	l′	NUM
ejpam-5052	49	29	)	)	PUNCT
ejpam-5052	49	30	∈≤⇒	∈≤⇒	ADP
ejpam-5052	49	31	(	(	PUNCT
ejpam-5052	49	32	d(l	d(l	ADJ
ejpam-5052	49	33	)	)	PUNCT
ejpam-5052	49	34	,	,	PUNCT
ejpam-5052	49	35	d(l′	d(l′	PROPN
ejpam-5052	49	36	)	)	PUNCT
ejpam-5052	49	37	)	)	PUNCT
ejpam-5052	50	1	∈≤.	∈≤.	ADP
ejpam-5052	51	1	3	3	X
ejpam-5052	51	2	.	.	X
ejpam-5052	51	3	main	main	ADJ
ejpam-5052	51	4	results	result	NOUN
ejpam-5052	51	5	let	let	VERB
ejpam-5052	51	6	(	(	PUNCT
ejpam-5052	51	7	e,⊕,⊙,≤	e,⊕,⊙,≤	NUM
ejpam-5052	51	8	)	)	PUNCT
ejpam-5052	51	9	∈	∈	NOUN
ejpam-5052	51	10	okh	okh	NOUN
ejpam-5052	51	11	.	.	PUNCT
ejpam-5052	52	1	then	then	ADV
ejpam-5052	52	2	,	,	PUNCT
ejpam-5052	52	3	0	0	NUM
ejpam-5052	52	4	̸=	̸=	PROPN
ejpam-5052	52	5	z	z	NOUN
ejpam-5052	52	6	∈	∈	PROPN
ejpam-5052	52	7	e	e	NOUN
ejpam-5052	52	8	is	be	AUX
ejpam-5052	52	9	a	a	DET
ejpam-5052	52	10	zero	zero	NUM
ejpam-5052	52	11	divisor	divisor	NOUN
ejpam-5052	52	12	if	if	SCONJ
ejpam-5052	52	13	∃	∃	PROPN
ejpam-5052	52	14	0	0	NUM
ejpam-5052	52	15	̸=	̸=	PROPN
ejpam-5052	52	16	v	v	ADP
ejpam-5052	52	17	∈	∈	NOUN
ejpam-5052	52	18	e	e	NOUN
ejpam-5052	52	19	such	such	ADJ
ejpam-5052	52	20	that	that	SCONJ
ejpam-5052	52	21	z	z	PROPN
ejpam-5052	52	22	⊙	⊙	PROPN
ejpam-5052	52	23	v	v	ADP
ejpam-5052	52	24	=	=	SYM
ejpam-5052	52	25	0	0	PUNCT
ejpam-5052	52	26	=	=	SYM
ejpam-5052	52	27	v	v	PROPN
ejpam-5052	52	28	⊙	⊙	PROPN
ejpam-5052	52	29	z.	z.	PROPN
ejpam-5052	52	30	theorem	theorem	VERB
ejpam-5052	52	31	1	1	X
ejpam-5052	52	32	.	.	PUNCT
ejpam-5052	53	1	let	let	VERB
ejpam-5052	53	2	(	(	PUNCT
ejpam-5052	53	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	53	4	)	)	PUNCT
ejpam-5052	53	5	∈	∈	NOUN
ejpam-5052	53	6	okh	okh	VERB
ejpam-5052	53	7	with	with	ADP
ejpam-5052	53	8	no	no	DET
ejpam-5052	53	9	zero	zero	NUM
ejpam-5052	53	10	divisors	divisor	NOUN
ejpam-5052	53	11	and	and	CCONJ
ejpam-5052	53	12	0	0	NUM
ejpam-5052	53	13	̸=	̸=	PROPN
ejpam-5052	53	14	d	d	PROPN
ejpam-5052	53	15	∈	∈	PROPN
ejpam-5052	53	16	der(e	der(e	PROPN
ejpam-5052	53	17	)	)	PUNCT
ejpam-5052	53	18	.	.	PUNCT
ejpam-5052	54	1	if	if	SCONJ
ejpam-5052	54	2	y	y	PROPN
ejpam-5052	54	3	is	be	AUX
ejpam-5052	54	4	a	a	DET
ejpam-5052	54	5	proper	proper	ADJ
ejpam-5052	54	6	hyperideal	hyperideal	NOUN
ejpam-5052	54	7	of	of	ADP
ejpam-5052	54	8	e	e	NOUN
ejpam-5052	54	9	,	,	PUNCT
ejpam-5052	54	10	then	then	ADV
ejpam-5052	54	11	d	d	PROPN
ejpam-5052	54	12	is	be	AUX
ejpam-5052	54	13	nonzero	nonzero	NOUN
ejpam-5052	54	14	on	on	ADP
ejpam-5052	54	15	y	y	PROPN
ejpam-5052	54	16	.	.	PUNCT
ejpam-5052	55	1	proof	proof	NOUN
ejpam-5052	55	2	.	.	PUNCT
ejpam-5052	56	1	let	let	VERB
ejpam-5052	56	2	d(m	d(m	NOUN
ejpam-5052	56	3	)	)	PUNCT
ejpam-5052	57	1	=	=	SYM
ejpam-5052	57	2	0	0	NUM
ejpam-5052	57	3	,	,	PUNCT
ejpam-5052	57	4	∀	∀	X
ejpam-5052	57	5	0	0	NUM
ejpam-5052	58	1	̸=	̸=	PROPN
ejpam-5052	58	2	m	m	NOUN
ejpam-5052	58	3	∈	∈	PROPN
ejpam-5052	58	4	y	y	PROPN
ejpam-5052	58	5	.	.	PUNCT
ejpam-5052	59	1	as	as	SCONJ
ejpam-5052	59	2	y	y	PROPN
ejpam-5052	59	3	is	be	AUX
ejpam-5052	59	4	a	a	DET
ejpam-5052	59	5	hyperideal	hyperideal	NOUN
ejpam-5052	59	6	of	of	ADP
ejpam-5052	59	7	e	e	NOUN
ejpam-5052	59	8	,	,	PUNCT
ejpam-5052	59	9	m⊙	m⊙	PROPN
ejpam-5052	59	10	g	g	NOUN
ejpam-5052	59	11	∈	∈	PROPN
ejpam-5052	59	12	y	y	PROPN
ejpam-5052	59	13	,	,	PUNCT
ejpam-5052	59	14	∀	∀	VERB
ejpam-5052	59	15	g	g	PROPN
ejpam-5052	59	16	∈	∈	PROPN
ejpam-5052	59	17	e.	e.	PROPN
ejpam-5052	59	18	thus	thus	ADV
ejpam-5052	59	19	,	,	PUNCT
ejpam-5052	59	20	d(m⊙	d(m⊙	NOUN
ejpam-5052	59	21	g	g	NOUN
ejpam-5052	59	22	)	)	PUNCT
ejpam-5052	59	23	=	=	SYM
ejpam-5052	60	1	0	0	X
ejpam-5052	60	2	.	.	PUNCT
ejpam-5052	61	1	so	so	ADV
ejpam-5052	61	2	,	,	PUNCT
ejpam-5052	61	3	d(m⊙	d(m⊙	NOUN
ejpam-5052	61	4	g	g	NOUN
ejpam-5052	61	5	)	)	PUNCT
ejpam-5052	61	6	∈	∈	PROPN
ejpam-5052	61	7	d(m)⊙	d(m)⊙	PROPN
ejpam-5052	61	8	g	g	PROPN
ejpam-5052	61	9	⊕m⊙	⊕m⊙	PROPN
ejpam-5052	61	10	d(g	d(g	PROPN
ejpam-5052	61	11	)	)	PUNCT
ejpam-5052	61	12	=	=	SYM
ejpam-5052	61	13	0⊙	0⊙	NOUN
ejpam-5052	61	14	g	g	PROPN
ejpam-5052	61	15	⊕m⊙	⊕m⊙	PROPN
ejpam-5052	61	16	d(g	d(g	PROPN
ejpam-5052	61	17	)	)	PUNCT
ejpam-5052	61	18	=	=	SYM
ejpam-5052	61	19	0⊕m⊙	0⊕m⊙	X
ejpam-5052	62	1	d(g	d(g	NUM
ejpam-5052	62	2	)	)	PUNCT
ejpam-5052	63	1	=	=	SYM
ejpam-5052	63	2	m⊙	m⊙	PROPN
ejpam-5052	63	3	d(g	d(g	PROPN
ejpam-5052	63	4	)	)	PUNCT
ejpam-5052	63	5	.	.	PUNCT
ejpam-5052	64	1	hence	hence	ADV
ejpam-5052	64	2	,	,	PUNCT
ejpam-5052	64	3	m⊙	m⊙	PROPN
ejpam-5052	64	4	d(g	d(g	PROPN
ejpam-5052	64	5	)	)	PUNCT
ejpam-5052	64	6	=	=	SYM
ejpam-5052	64	7	d(m⊙	d(m⊙	NOUN
ejpam-5052	64	8	g	g	NOUN
ejpam-5052	64	9	)	)	PUNCT
ejpam-5052	64	10	=	=	SYM
ejpam-5052	65	1	0	0	X
ejpam-5052	65	2	.	.	PUNCT
ejpam-5052	65	3	by	by	ADP
ejpam-5052	65	4	hypothesis	hypothesis	NOUN
ejpam-5052	65	5	,	,	PUNCT
ejpam-5052	65	6	e	e	PROPN
ejpam-5052	65	7	has	have	VERB
ejpam-5052	65	8	no	no	DET
ejpam-5052	65	9	zero	zero	NUM
ejpam-5052	65	10	divisors	divisor	NOUN
ejpam-5052	65	11	.	.	PUNCT
ejpam-5052	66	1	thus	thus	ADV
ejpam-5052	66	2	,	,	PUNCT
ejpam-5052	66	3	d(g	d(g	PROPN
ejpam-5052	66	4	)	)	PUNCT
ejpam-5052	66	5	=	=	SYM
ejpam-5052	66	6	0	0	NUM
ejpam-5052	66	7	,	,	PUNCT
ejpam-5052	66	8	∀	∀	X
ejpam-5052	66	9	g	g	NOUN
ejpam-5052	66	10	∈	∈	PROPN
ejpam-5052	66	11	e	e	NOUN
ejpam-5052	66	12	a	a	DET
ejpam-5052	66	13	contradiction	contradiction	NOUN
ejpam-5052	66	14	.	.	PUNCT
ejpam-5052	67	1	therefore	therefore	ADV
ejpam-5052	67	2	,	,	PUNCT
ejpam-5052	67	3	d	d	PROPN
ejpam-5052	67	4	is	be	AUX
ejpam-5052	67	5	nonzero	nonzero	NOUN
ejpam-5052	67	6	on	on	ADP
ejpam-5052	67	7	y	y	PROPN
ejpam-5052	67	8	.	.	PUNCT
ejpam-5052	68	1	theorem	theorem	NOUN
ejpam-5052	68	2	2	2	NUM
ejpam-5052	68	3	.	.	X
ejpam-5052	69	1	let	let	VERB
ejpam-5052	69	2	(	(	PUNCT
ejpam-5052	69	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	69	4	)	)	PUNCT
ejpam-5052	69	5	∈	∈	NOUN
ejpam-5052	69	6	okh	okh	VERB
ejpam-5052	69	7	and	and	CCONJ
ejpam-5052	69	8	g	g	NOUN
ejpam-5052	69	9	∈	∈	PROPN
ejpam-5052	69	10	g	g	PROPN
ejpam-5052	69	11	⊕	⊕	PROPN
ejpam-5052	69	12	g,∀g	g,∀g	PROPN
ejpam-5052	70	1	∈	∈	PROPN
ejpam-5052	70	2	e.	e.	PROPN
ejpam-5052	70	3	r.	r.	PROPN
ejpam-5052	70	4	cai	cai	PROPN
ejpam-5052	70	5	,	,	PUNCT
ejpam-5052	70	6	m.	m.	NOUN
ejpam-5052	70	7	alsaeedi	alsaeedi	PROPN
ejpam-5052	70	8	,	,	PUNCT
ejpam-5052	70	9	m.	m.	NOUN
ejpam-5052	70	10	akhoundi	akhoundi	PROPN
ejpam-5052	70	11	/	/	SYM
ejpam-5052	70	12	eur	eur	PROPN
ejpam-5052	70	13	.	.	PUNCT
ejpam-5052	71	1	j.	j.	PROPN
ejpam-5052	71	2	pure	pure	PROPN
ejpam-5052	71	3	appl	appl	PROPN
ejpam-5052	71	4	.	.	PROPN
ejpam-5052	71	5	math	math	PROPN
ejpam-5052	71	6	,	,	PUNCT
ejpam-5052	71	7	17	17	NUM
ejpam-5052	71	8	(	(	PUNCT
ejpam-5052	71	9	2	2	NUM
ejpam-5052	71	10	)	)	PUNCT
ejpam-5052	71	11	(	(	PUNCT
ejpam-5052	71	12	2024	2024	NUM
ejpam-5052	71	13	)	)	PUNCT
ejpam-5052	71	14	,	,	PUNCT
ejpam-5052	71	15	604	604	NUM
ejpam-5052	71	16	-	-	SYM
ejpam-5052	71	17	615	615	NUM
ejpam-5052	71	18	607	607	NUM
ejpam-5052	71	19	ide(g	ide(g	PROPN
ejpam-5052	71	20	)	)	PUNCT
ejpam-5052	71	21	=	=	SYM
ejpam-5052	72	1	g	g	NOUN
ejpam-5052	72	2	for	for	ADP
ejpam-5052	72	3	any	any	DET
ejpam-5052	72	4	g	g	PROPN
ejpam-5052	72	5	∈	∈	PROPN
ejpam-5052	72	6	e	e	NOUN
ejpam-5052	72	7	,	,	PUNCT
ejpam-5052	72	8	is	be	AUX
ejpam-5052	72	9	a	a	DET
ejpam-5052	72	10	homomorphism	homomorphism	NOUN
ejpam-5052	72	11	iff	iff	PROPN
ejpam-5052	72	12	ide	ide	PROPN
ejpam-5052	72	13	∈	∈	PROPN
ejpam-5052	72	14	der(e	der(e	PROPN
ejpam-5052	72	15	)	)	PUNCT
ejpam-5052	72	16	.	.	PUNCT
ejpam-5052	73	1	proof	proof	NOUN
ejpam-5052	73	2	.	.	PUNCT
ejpam-5052	74	1	let	let	VERB
ejpam-5052	74	2	ide	ide	NOUN
ejpam-5052	74	3	be	be	AUX
ejpam-5052	74	4	a	a	DET
ejpam-5052	74	5	homomorphism	homomorphism	NOUN
ejpam-5052	74	6	and	and	CCONJ
ejpam-5052	74	7	g	g	NOUN
ejpam-5052	74	8	,	,	PUNCT
ejpam-5052	74	9	g′	g′	PROPN
ejpam-5052	74	10	∈	∈	PROPN
ejpam-5052	74	11	e.	e.	PROPN
ejpam-5052	74	12	then	then	ADV
ejpam-5052	74	13	,	,	PUNCT
ejpam-5052	74	14	ide(g	ide(g	PROPN
ejpam-5052	74	15	⊙	⊙	PROPN
ejpam-5052	74	16	g′	g′	PROPN
ejpam-5052	74	17	)	)	PUNCT
ejpam-5052	75	1	=	=	PRON
ejpam-5052	75	2	ide(g)⊙	ide(g)⊙	VERB
ejpam-5052	75	3	ide(g	ide(g	NOUN
ejpam-5052	75	4	′	′	NOUN
ejpam-5052	75	5	)	)	PUNCT
ejpam-5052	76	1	=	=	SYM
ejpam-5052	76	2	g	g	PROPN
ejpam-5052	76	3	⊙	⊙	PROPN
ejpam-5052	76	4	g′	g′	PROPN
ejpam-5052	76	5	∈	∈	PROPN
ejpam-5052	76	6	(	(	PUNCT
ejpam-5052	76	7	g	g	PROPN
ejpam-5052	76	8	⊙	⊙	PROPN
ejpam-5052	76	9	g′)⊕	g′)⊕	PROPN
ejpam-5052	76	10	(	(	PUNCT
ejpam-5052	76	11	g	g	PROPN
ejpam-5052	76	12	⊙	⊙	PROPN
ejpam-5052	76	13	g′	g′	PROPN
ejpam-5052	76	14	)	)	PUNCT
ejpam-5052	76	15	=	=	PUNCT
ejpam-5052	77	1	ide(g)⊙	ide(g)⊙	NOUN
ejpam-5052	77	2	g′	g′	NOUN
ejpam-5052	77	3	⊕	⊕	PROPN
ejpam-5052	77	4	g	g	PROPN
ejpam-5052	77	5	⊙	⊙	PROPN
ejpam-5052	77	6	ide(g	ide(g	PROPN
ejpam-5052	77	7	′	′	NUM
ejpam-5052	77	8	)	)	PUNCT
ejpam-5052	77	9	.	.	PUNCT
ejpam-5052	78	1	hence	hence	ADV
ejpam-5052	78	2	,	,	PUNCT
ejpam-5052	78	3	ide	ide	ADJ
ejpam-5052	78	4	∈	∈	PROPN
ejpam-5052	78	5	der(e	der(e	PROPN
ejpam-5052	78	6	)	)	PUNCT
ejpam-5052	78	7	.	.	PUNCT
ejpam-5052	79	1	conversely	conversely	ADV
ejpam-5052	79	2	,	,	PUNCT
ejpam-5052	79	3	let	let	VERB
ejpam-5052	79	4	g	g	NOUN
ejpam-5052	79	5	,	,	PUNCT
ejpam-5052	79	6	g′	g′	PROPN
ejpam-5052	79	7	∈	∈	PROPN
ejpam-5052	80	1	e.	e.	PROPN
ejpam-5052	80	2	then	then	ADV
ejpam-5052	80	3	ide(g	ide(g	PROPN
ejpam-5052	80	4	⊙	⊙	PROPN
ejpam-5052	80	5	g′	g′	PROPN
ejpam-5052	80	6	)	)	PUNCT
ejpam-5052	81	1	=	=	PUNCT
ejpam-5052	81	2	g	g	PROPN
ejpam-5052	81	3	⊙	⊙	PROPN
ejpam-5052	81	4	g′	g′	PROPN
ejpam-5052	82	1	=	=	PUNCT
ejpam-5052	82	2	ide(g)⊙	ide(g)⊙	VERB
ejpam-5052	82	3	ide(g	ide(g	PROPN
ejpam-5052	82	4	′	′	NOUN
ejpam-5052	82	5	)	)	PUNCT
ejpam-5052	82	6	.	.	PUNCT
ejpam-5052	83	1	so	so	ADV
ejpam-5052	83	2	,	,	PUNCT
ejpam-5052	83	3	ide	ide	NOUN
ejpam-5052	83	4	is	be	AUX
ejpam-5052	83	5	a	a	DET
ejpam-5052	83	6	homomorphism	homomorphism	NOUN
ejpam-5052	83	7	.	.	PUNCT
ejpam-5052	84	1	theorem	theorem	NOUN
ejpam-5052	84	2	3	3	X
ejpam-5052	84	3	.	.	PUNCT
ejpam-5052	85	1	let	let	VERB
ejpam-5052	85	2	(	(	PUNCT
ejpam-5052	85	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	85	4	)	)	PUNCT
ejpam-5052	85	5	∈	∈	PROPN
ejpam-5052	85	6	okh	okh	NOUN
ejpam-5052	85	7	be	be	AUX
ejpam-5052	85	8	commutative	commutative	ADJ
ejpam-5052	85	9	and	and	CCONJ
ejpam-5052	85	10	and	and	CCONJ
ejpam-5052	85	11	g	g	PROPN
ejpam-5052	85	12	∈	∈	PROPN
ejpam-5052	86	1	g	g	PROPN
ejpam-5052	86	2	⊕	⊕	PROPN
ejpam-5052	86	3	g,∀g	g,∀g	PROPN
ejpam-5052	87	1	∈	∈	PROPN
ejpam-5052	87	2	e.	e.	PROPN
ejpam-5052	87	3	for	for	ADP
ejpam-5052	87	4	a	a	DET
ejpam-5052	87	5	given	give	VERB
ejpam-5052	87	6	t	t	PROPN
ejpam-5052	87	7	∈	∈	PROPN
ejpam-5052	87	8	e	e	NOUN
ejpam-5052	87	9	,	,	PUNCT
ejpam-5052	87	10	we	we	PRON
ejpam-5052	87	11	set	set	VERB
ejpam-5052	87	12	dt(g	dt(g	NOUN
ejpam-5052	87	13	)	)	PUNCT
ejpam-5052	87	14	=	=	VERB
ejpam-5052	88	1	t⊙	t⊙	VERB
ejpam-5052	88	2	g	g	NOUN
ejpam-5052	88	3	,	,	PUNCT
ejpam-5052	88	4	∀g	∀g	X
ejpam-5052	88	5	∈	∈	PROPN
ejpam-5052	88	6	e.	e.	PROPN
ejpam-5052	89	1	then	then	ADV
ejpam-5052	89	2	dt	dt	X
ejpam-5052	89	3	∈	∈	PROPN
ejpam-5052	89	4	der(e	der(e	PROPN
ejpam-5052	89	5	)	)	PUNCT
ejpam-5052	89	6	.	.	PUNCT
ejpam-5052	90	1	proof	proof	NOUN
ejpam-5052	90	2	.	.	PUNCT
ejpam-5052	91	1	let	let	VERB
ejpam-5052	91	2	g	g	NOUN
ejpam-5052	91	3	,	,	PUNCT
ejpam-5052	91	4	g′	g′	PROPN
ejpam-5052	91	5	∈	∈	PROPN
ejpam-5052	91	6	e.	e.	PROPN
ejpam-5052	91	7	for	for	ADP
ejpam-5052	91	8	a	a	DET
ejpam-5052	91	9	given	give	VERB
ejpam-5052	91	10	t	t	PROPN
ejpam-5052	91	11	∈	∈	PROPN
ejpam-5052	91	12	e	e	NOUN
ejpam-5052	91	13	,	,	PUNCT
ejpam-5052	91	14	we	we	PRON
ejpam-5052	91	15	have	have	VERB
ejpam-5052	91	16	dt(g	dt(g	PUNCT
ejpam-5052	91	17	⊕	⊕	PROPN
ejpam-5052	91	18	g′	g′	NOUN
ejpam-5052	91	19	)	)	PUNCT
ejpam-5052	92	1	=	=	PUNCT
ejpam-5052	92	2	t⊙	t⊙	NOUN
ejpam-5052	92	3	(	(	PUNCT
ejpam-5052	92	4	g	g	PROPN
ejpam-5052	92	5	⊕	⊕	PROPN
ejpam-5052	92	6	g′	g′	PROPN
ejpam-5052	92	7	)	)	PUNCT
ejpam-5052	93	1	=	=	VERB
ejpam-5052	93	2	t⊙	t⊙	VERB
ejpam-5052	93	3	g	g	PROPN
ejpam-5052	93	4	⊕	⊕	PROPN
ejpam-5052	93	5	t⊙	t⊙	ADJ
ejpam-5052	93	6	g′	g′	NOUN
ejpam-5052	93	7	=	=	PUNCT
ejpam-5052	93	8	dt(g)⊕	dt(g)⊕	NOUN
ejpam-5052	93	9	dt(g	dt(g	NOUN
ejpam-5052	93	10	′	′	NOUN
ejpam-5052	93	11	)	)	PUNCT
ejpam-5052	93	12	,	,	PUNCT
ejpam-5052	93	13	and	and	CCONJ
ejpam-5052	93	14	dt(g	dt(g	PROPN
ejpam-5052	93	15	⊙	⊙	PROPN
ejpam-5052	93	16	g′	g′	PROPN
ejpam-5052	93	17	)	)	PUNCT
ejpam-5052	94	1	=	=	SYM
ejpam-5052	94	2	t⊙	t⊙	NOUN
ejpam-5052	94	3	(	(	PUNCT
ejpam-5052	94	4	g	g	PROPN
ejpam-5052	94	5	⊙	⊙	PROPN
ejpam-5052	94	6	g′	g′	PROPN
ejpam-5052	94	7	)	)	PUNCT
ejpam-5052	94	8	∈	∈	PROPN
ejpam-5052	94	9	t⊙	t⊙	NOUN
ejpam-5052	94	10	(	(	PUNCT
ejpam-5052	94	11	g	g	PROPN
ejpam-5052	94	12	⊙	⊙	PROPN
ejpam-5052	94	13	g′)⊕	g′)⊕	PROPN
ejpam-5052	94	14	t⊙	t⊙	PROPN
ejpam-5052	94	15	(	(	PUNCT
ejpam-5052	94	16	g	g	PROPN
ejpam-5052	94	17	⊙	⊙	PROPN
ejpam-5052	94	18	g′	g′	PROPN
ejpam-5052	94	19	)	)	PUNCT
ejpam-5052	94	20	=	=	PRON
ejpam-5052	94	21	(	(	PUNCT
ejpam-5052	94	22	t⊙	t⊙	VERB
ejpam-5052	94	23	g)⊙	g)⊙	PROPN
ejpam-5052	94	24	g′	g′	PROPN
ejpam-5052	94	25	⊕	⊕	PROPN
ejpam-5052	94	26	(	(	PUNCT
ejpam-5052	94	27	t⊙	t⊙	VERB
ejpam-5052	94	28	g)⊙	g)⊙	ADJ
ejpam-5052	94	29	g′	g′	NOUN
ejpam-5052	94	30	=	=	SYM
ejpam-5052	94	31	(	(	PUNCT
ejpam-5052	94	32	t⊙	t⊙	VERB
ejpam-5052	94	33	g)⊙	g)⊙	PROPN
ejpam-5052	94	34	g′	g′	PROPN
ejpam-5052	94	35	⊕	⊕	PROPN
ejpam-5052	94	36	(	(	PUNCT
ejpam-5052	94	37	g	g	PROPN
ejpam-5052	94	38	⊙	⊙	PROPN
ejpam-5052	94	39	t)⊙	t)⊙	VERB
ejpam-5052	94	40	g′	g′	NOUN
ejpam-5052	94	41	=	=	SYM
ejpam-5052	94	42	(	(	PUNCT
ejpam-5052	94	43	t⊙	t⊙	VERB
ejpam-5052	94	44	g)⊙	g)⊙	PROPN
ejpam-5052	94	45	g′	g′	PROPN
ejpam-5052	94	46	⊕	⊕	PROPN
ejpam-5052	95	1	g	g	PROPN
ejpam-5052	95	2	⊙	⊙	PROPN
ejpam-5052	95	3	(	(	PUNCT
ejpam-5052	95	4	t⊙	t⊙	PROPN
ejpam-5052	95	5	g′	g′	NOUN
ejpam-5052	95	6	)	)	PUNCT
ejpam-5052	95	7	=	=	SYM
ejpam-5052	95	8	dt(g)⊙	dt(g)⊙	NOUN
ejpam-5052	95	9	g′	g′	NOUN
ejpam-5052	95	10	⊕	⊕	PROPN
ejpam-5052	95	11	g	g	PROPN
ejpam-5052	95	12	⊙	⊙	PROPN
ejpam-5052	95	13	dt(g	dt(g	PUNCT
ejpam-5052	95	14	′	′	NOUN
ejpam-5052	95	15	)	)	PUNCT
ejpam-5052	95	16	.	.	PUNCT
ejpam-5052	96	1	let	let	VERB
ejpam-5052	96	2	g	g	NOUN
ejpam-5052	96	3	,	,	PUNCT
ejpam-5052	96	4	g′	g′	NOUN
ejpam-5052	96	5	∈	∈	PROPN
ejpam-5052	96	6	e	e	X
ejpam-5052	96	7	and	and	CCONJ
ejpam-5052	96	8	(	(	PUNCT
ejpam-5052	96	9	g	g	NOUN
ejpam-5052	96	10	,	,	PUNCT
ejpam-5052	96	11	g′	g′	NOUN
ejpam-5052	96	12	)	)	PUNCT
ejpam-5052	97	1	∈≤.	∈≤.	PROPN
ejpam-5052	97	2	then	then	ADV
ejpam-5052	97	3	r.	r.	PROPN
ejpam-5052	97	4	cai	cai	PROPN
ejpam-5052	97	5	,	,	PUNCT
ejpam-5052	97	6	m.	m.	NOUN
ejpam-5052	97	7	alsaeedi	alsaeedi	PROPN
ejpam-5052	97	8	,	,	PUNCT
ejpam-5052	97	9	m.	m.	NOUN
ejpam-5052	97	10	akhoundi	akhoundi	PROPN
ejpam-5052	97	11	/	/	SYM
ejpam-5052	97	12	eur	eur	PROPN
ejpam-5052	97	13	.	.	PUNCT
ejpam-5052	98	1	j.	j.	PROPN
ejpam-5052	98	2	pure	pure	PROPN
ejpam-5052	98	3	appl	appl	PROPN
ejpam-5052	98	4	.	.	PROPN
ejpam-5052	98	5	math	math	PROPN
ejpam-5052	98	6	,	,	PUNCT
ejpam-5052	98	7	17	17	NUM
ejpam-5052	98	8	(	(	PUNCT
ejpam-5052	98	9	2	2	NUM
ejpam-5052	98	10	)	)	PUNCT
ejpam-5052	98	11	(	(	PUNCT
ejpam-5052	98	12	2024	2024	NUM
ejpam-5052	98	13	)	)	PUNCT
ejpam-5052	98	14	,	,	PUNCT
ejpam-5052	98	15	604	604	NUM
ejpam-5052	98	16	-	-	SYM
ejpam-5052	98	17	615	615	NUM
ejpam-5052	98	18	608	608	NUM
ejpam-5052	98	19	dt(g	dt(g	NOUN
ejpam-5052	98	20	)	)	PUNCT
ejpam-5052	98	21	=	=	VERB
ejpam-5052	99	1	t⊙	t⊙	VERB
ejpam-5052	99	2	g	g	NOUN
ejpam-5052	99	3	≤	≤	ADJ
ejpam-5052	99	4	t⊙	t⊙	NOUN
ejpam-5052	99	5	g′	g′	NOUN
ejpam-5052	99	6	=	=	SYM
ejpam-5052	99	7	dt(g	dt(g	NUM
ejpam-5052	99	8	′	′	NOUN
ejpam-5052	99	9	)	)	PUNCT
ejpam-5052	99	10	by	by	ADP
ejpam-5052	99	11	definition	definition	NOUN
ejpam-5052	99	12	2	2	NUM
ejpam-5052	99	13	,	,	PUNCT
ejpam-5052	99	14	and	and	CCONJ
ejpam-5052	99	15	hence	hence	ADV
ejpam-5052	99	16	dt	dt	X
ejpam-5052	99	17	∈	∈	PROPN
ejpam-5052	99	18	der(e	der(e	PROPN
ejpam-5052	99	19	)	)	PUNCT
ejpam-5052	99	20	.	.	PUNCT
ejpam-5052	100	1	corollary	corollary	ADJ
ejpam-5052	100	2	1	1	NUM
ejpam-5052	100	3	.	.	PUNCT
ejpam-5052	101	1	let	let	VERB
ejpam-5052	101	2	(	(	PUNCT
ejpam-5052	101	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	101	4	)	)	PUNCT
ejpam-5052	101	5	∈	∈	PROPN
ejpam-5052	101	6	okh	okh	NOUN
ejpam-5052	101	7	be	be	AUX
ejpam-5052	101	8	commutative	commutative	ADJ
ejpam-5052	101	9	and	and	CCONJ
ejpam-5052	101	10	g	g	PROPN
ejpam-5052	101	11	∈	∈	PROPN
ejpam-5052	101	12	g	g	PROPN
ejpam-5052	101	13	⊕	⊕	PROPN
ejpam-5052	101	14	g,∀g	g,∀g	PROPN
ejpam-5052	102	1	∈	∈	PROPN
ejpam-5052	102	2	e.	e.	PROPN
ejpam-5052	102	3	then	then	ADV
ejpam-5052	102	4	,	,	PUNCT
ejpam-5052	102	5	the	the	DET
ejpam-5052	102	6	identity	identity	NOUN
ejpam-5052	102	7	function	function	NOUN
ejpam-5052	102	8	ide	ide	NOUN
ejpam-5052	102	9	defined	define	VERB
ejpam-5052	102	10	by	by	ADP
ejpam-5052	102	11	ide(g	ide(g	PROPN
ejpam-5052	102	12	)	)	PUNCT
ejpam-5052	102	13	=	=	SYM
ejpam-5052	102	14	g	g	NOUN
ejpam-5052	102	15	for	for	ADP
ejpam-5052	102	16	any	any	DET
ejpam-5052	102	17	g	g	PROPN
ejpam-5052	102	18	∈	∈	PROPN
ejpam-5052	102	19	e	e	NOUN
ejpam-5052	102	20	,	,	PUNCT
ejpam-5052	102	21	is	be	AUX
ejpam-5052	102	22	a	a	DET
ejpam-5052	102	23	homomorphism	homomorphism	NOUN
ejpam-5052	102	24	.	.	PUNCT
ejpam-5052	103	1	proof	proof	NOUN
ejpam-5052	103	2	.	.	PUNCT
ejpam-5052	104	1	we	we	PRON
ejpam-5052	104	2	have	have	VERB
ejpam-5052	104	3	d1(g	d1(g	PRON
ejpam-5052	104	4	)	)	PUNCT
ejpam-5052	104	5	=	=	PRON
ejpam-5052	105	1	1⊙	1⊙	NUM
ejpam-5052	105	2	g	g	NOUN
ejpam-5052	105	3	=	=	SYM
ejpam-5052	105	4	g	g	PROPN
ejpam-5052	105	5	=	=	SYM
ejpam-5052	105	6	ide(g	ide(g	PROPN
ejpam-5052	105	7	)	)	PUNCT
ejpam-5052	105	8	.	.	PUNCT
ejpam-5052	106	1	by	by	ADP
ejpam-5052	106	2	theorem	theorem	NOUN
ejpam-5052	106	3	3	3	NUM
ejpam-5052	106	4	,	,	PUNCT
ejpam-5052	106	5	ide	ide	ADJ
ejpam-5052	106	6	=	=	SYM
ejpam-5052	106	7	d1	d1	NOUN
ejpam-5052	106	8	∈	∈	PROPN
ejpam-5052	106	9	der(e	der(e	PROPN
ejpam-5052	106	10	)	)	PUNCT
ejpam-5052	106	11	.	.	PUNCT
ejpam-5052	107	1	now	now	ADV
ejpam-5052	107	2	,	,	PUNCT
ejpam-5052	107	3	by	by	ADP
ejpam-5052	107	4	theorem	theorem	NOUN
ejpam-5052	107	5	2	2	NUM
ejpam-5052	107	6	,	,	PUNCT
ejpam-5052	107	7	ide	ide	NOUN
ejpam-5052	107	8	is	be	AUX
ejpam-5052	107	9	a	a	DET
ejpam-5052	107	10	homomorphism	homomorphism	NOUN
ejpam-5052	107	11	.	.	PUNCT
ejpam-5052	108	1	corollary	corollary	ADJ
ejpam-5052	108	2	2	2	NUM
ejpam-5052	108	3	.	.	PUNCT
ejpam-5052	109	1	let	let	AUX
ejpam-5052	109	2	(	(	PUNCT
ejpam-5052	109	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	109	4	)	)	PUNCT
ejpam-5052	109	5	∈	∈	PROPN
ejpam-5052	109	6	okh	okh	NOUN
ejpam-5052	109	7	be	be	AUX
ejpam-5052	109	8	commutative	commutative	ADJ
ejpam-5052	109	9	and	and	CCONJ
ejpam-5052	109	10	g	g	PROPN
ejpam-5052	109	11	∈	∈	PROPN
ejpam-5052	110	1	g	g	PROPN
ejpam-5052	110	2	⊕	⊕	PROPN
ejpam-5052	110	3	g,∀g	g,∀g	PROPN
ejpam-5052	110	4	∈	∈	PROPN
ejpam-5052	110	5	e.	e.	PROPN
ejpam-5052	111	1	if	if	SCONJ
ejpam-5052	111	2	d	d	PROPN
ejpam-5052	111	3	=	=	SYM
ejpam-5052	111	4	dt	dt	PROPN
ejpam-5052	111	5	,	,	PUNCT
ejpam-5052	111	6	where	where	SCONJ
ejpam-5052	111	7	t	t	PROPN
ejpam-5052	111	8	∈	∈	PROPN
ejpam-5052	111	9	e	e	PROPN
ejpam-5052	111	10	,	,	PUNCT
ejpam-5052	111	11	satisfies	satisfy	VERB
ejpam-5052	111	12	the	the	DET
ejpam-5052	111	13	following	follow	VERB
ejpam-5052	111	14	condition	condition	NOUN
ejpam-5052	111	15	(	(	PUNCT
ejpam-5052	111	16	g′	g′	NOUN
ejpam-5052	111	17	,	,	PUNCT
ejpam-5052	111	18	g	g	NOUN
ejpam-5052	111	19	)	)	PUNCT
ejpam-5052	111	20	∈≤	∈≤	PROPN
ejpam-5052	111	21	and	and	CCONJ
ejpam-5052	111	22	d(g	d(g	PROPN
ejpam-5052	111	23	)	)	PUNCT
ejpam-5052	112	1	=	=	SYM
ejpam-5052	112	2	g	g	PROPN
ejpam-5052	112	3	⇒	⇒	NOUN
ejpam-5052	112	4	d(g′	d(g′	PRON
ejpam-5052	112	5	)	)	PUNCT
ejpam-5052	112	6	=	=	SYM
ejpam-5052	113	1	g′	g′	NOUN
ejpam-5052	113	2	,	,	PUNCT
ejpam-5052	113	3	then	then	ADV
ejpam-5052	113	4	fixd(e	fixd(e	PROPN
ejpam-5052	113	5	)	)	PUNCT
ejpam-5052	113	6	=	=	PRON
ejpam-5052	113	7	{	{	PUNCT
ejpam-5052	113	8	x	x	PUNCT
ejpam-5052	113	9	∈	∈	PROPN
ejpam-5052	113	10	e	e	NOUN
ejpam-5052	113	11	|	|	ADV
ejpam-5052	113	12	d(x	d(x	PROPN
ejpam-5052	113	13	)	)	PUNCT
ejpam-5052	113	14	=	=	PUNCT
ejpam-5052	114	1	x	x	X
ejpam-5052	114	2	}	}	PUNCT
ejpam-5052	114	3	is	be	AUX
ejpam-5052	114	4	a	a	DET
ejpam-5052	114	5	hyperideal	hyperideal	NOUN
ejpam-5052	114	6	of	of	ADP
ejpam-5052	114	7	e.	e.	PROPN
ejpam-5052	114	8	proof	proof	PROPN
ejpam-5052	114	9	.	.	PUNCT
ejpam-5052	115	1	by	by	ADP
ejpam-5052	115	2	theorem	theorem	NOUN
ejpam-5052	115	3	3	3	NUM
ejpam-5052	115	4	,	,	PUNCT
ejpam-5052	115	5	d(g	d(g	PROPN
ejpam-5052	115	6	)	)	PUNCT
ejpam-5052	115	7	=	=	SYM
ejpam-5052	115	8	dt(g	dt(g	X
ejpam-5052	115	9	)	)	PUNCT
ejpam-5052	115	10	=	=	VERB
ejpam-5052	116	1	t⊙	t⊙	VERB
ejpam-5052	116	2	g	g	NOUN
ejpam-5052	116	3	,	,	PUNCT
ejpam-5052	116	4	for	for	SCONJ
ejpam-5052	116	5	any	any	DET
ejpam-5052	116	6	g	g	PROPN
ejpam-5052	116	7	∈	∈	PROPN
ejpam-5052	116	8	e.	e.	PROPN
ejpam-5052	116	9	let	let	VERB
ejpam-5052	116	10	g	g	NOUN
ejpam-5052	116	11	,	,	PUNCT
ejpam-5052	116	12	g′	g′	NOUN
ejpam-5052	116	13	∈	∈	PROPN
ejpam-5052	116	14	fixd(e	fixd(e	PROPN
ejpam-5052	116	15	)	)	PUNCT
ejpam-5052	116	16	.	.	PUNCT
ejpam-5052	117	1	then	then	ADV
ejpam-5052	117	2	d(g	d(g	NUM
ejpam-5052	117	3	)	)	PUNCT
ejpam-5052	117	4	=	=	SYM
ejpam-5052	117	5	g	g	PROPN
ejpam-5052	117	6	and	and	CCONJ
ejpam-5052	117	7	d(g′	d(g′	PRON
ejpam-5052	117	8	)	)	PUNCT
ejpam-5052	118	1	=	=	NOUN
ejpam-5052	118	2	g′.	g′.	NOUN
ejpam-5052	118	3	we	we	PRON
ejpam-5052	118	4	have	have	VERB
ejpam-5052	118	5	d(g	d(g	PROPN
ejpam-5052	118	6	⊖	⊖	NOUN
ejpam-5052	118	7	g′	g′	NOUN
ejpam-5052	118	8	)	)	PUNCT
ejpam-5052	118	9	=	=	PUNCT
ejpam-5052	118	10	dt(g	dt(g	PROPN
ejpam-5052	118	11	⊖	⊖	PUNCT
ejpam-5052	118	12	g′	g′	NOUN
ejpam-5052	118	13	)	)	PUNCT
ejpam-5052	119	1	=	=	VERB
ejpam-5052	119	2	t⊙	t⊙	NOUN
ejpam-5052	119	3	(	(	PUNCT
ejpam-5052	119	4	g	g	PROPN
ejpam-5052	119	5	⊖	⊖	ADJ
ejpam-5052	119	6	g′	g′	NOUN
ejpam-5052	119	7	)	)	PUNCT
ejpam-5052	120	1	=	=	VERB
ejpam-5052	120	2	t⊙	t⊙	VERB
ejpam-5052	120	3	g	g	PROPN
ejpam-5052	120	4	⊖	⊖	AUX
ejpam-5052	120	5	t⊙	t⊙	NOUN
ejpam-5052	120	6	g′	g′	NOUN
ejpam-5052	120	7	=	=	PUNCT
ejpam-5052	120	8	dt(g)⊖	dt(g)⊖	X
ejpam-5052	120	9	dt(g	dt(g	NOUN
ejpam-5052	120	10	′	′	NUM
ejpam-5052	120	11	)	)	PUNCT
ejpam-5052	121	1	=	=	SYM
ejpam-5052	122	1	d(g)⊖	d(g)⊖	PROPN
ejpam-5052	122	2	d(g′	d(g′	PROPN
ejpam-5052	122	3	)	)	PUNCT
ejpam-5052	122	4	=	=	SYM
ejpam-5052	123	1	g	g	NOUN
ejpam-5052	123	2	⊖	⊖	NOUN
ejpam-5052	123	3	g′.	g′.	X
ejpam-5052	123	4	so	so	ADV
ejpam-5052	123	5	,	,	PUNCT
ejpam-5052	123	6	g	g	PROPN
ejpam-5052	123	7	⊖	⊖	AUX
ejpam-5052	123	8	g′	g′	NOUN
ejpam-5052	123	9	⊆	⊆	NUM
ejpam-5052	123	10	fixd(e	fixd(e	NOUN
ejpam-5052	123	11	)	)	PUNCT
ejpam-5052	123	12	.	.	PUNCT
ejpam-5052	124	1	r.	r.	PROPN
ejpam-5052	124	2	cai	cai	PROPN
ejpam-5052	124	3	,	,	PUNCT
ejpam-5052	124	4	m.	m.	NOUN
ejpam-5052	124	5	alsaeedi	alsaeedi	PROPN
ejpam-5052	124	6	,	,	PUNCT
ejpam-5052	124	7	m.	m.	NOUN
ejpam-5052	124	8	akhoundi	akhoundi	PROPN
ejpam-5052	124	9	/	/	SYM
ejpam-5052	124	10	eur	eur	PROPN
ejpam-5052	124	11	.	.	PUNCT
ejpam-5052	125	1	j.	j.	PROPN
ejpam-5052	125	2	pure	pure	PROPN
ejpam-5052	125	3	appl	appl	PROPN
ejpam-5052	125	4	.	.	PROPN
ejpam-5052	125	5	math	math	PROPN
ejpam-5052	125	6	,	,	PUNCT
ejpam-5052	125	7	17	17	NUM
ejpam-5052	125	8	(	(	PUNCT
ejpam-5052	125	9	2	2	NUM
ejpam-5052	125	10	)	)	PUNCT
ejpam-5052	125	11	(	(	PUNCT
ejpam-5052	125	12	2024	2024	NUM
ejpam-5052	125	13	)	)	PUNCT
ejpam-5052	125	14	,	,	PUNCT
ejpam-5052	125	15	604	604	NUM
ejpam-5052	125	16	-	-	SYM
ejpam-5052	125	17	615	615	NUM
ejpam-5052	125	18	609	609	NUM
ejpam-5052	125	19	now	now	ADV
ejpam-5052	125	20	,	,	PUNCT
ejpam-5052	125	21	let	let	VERB
ejpam-5052	125	22	g	g	PROPN
ejpam-5052	125	23	∈	∈	PROPN
ejpam-5052	125	24	fixd(e	fixd(e	PROPN
ejpam-5052	125	25	)	)	PUNCT
ejpam-5052	125	26	and	and	CCONJ
ejpam-5052	125	27	q	q	PROPN
ejpam-5052	125	28	∈	∈	PROPN
ejpam-5052	125	29	e.	e.	PROPN
ejpam-5052	125	30	then	then	ADV
ejpam-5052	125	31	,	,	PUNCT
ejpam-5052	125	32	d(g	d(g	PROPN
ejpam-5052	125	33	⊙	⊙	PROPN
ejpam-5052	125	34	q	q	NOUN
ejpam-5052	125	35	)	)	PUNCT
ejpam-5052	125	36	=	=	SYM
ejpam-5052	126	1	dt(g	dt(g	X
ejpam-5052	126	2	⊙	⊙	X
ejpam-5052	126	3	q	q	NOUN
ejpam-5052	126	4	)	)	PUNCT
ejpam-5052	126	5	=	=	VERB
ejpam-5052	126	6	t⊙	t⊙	NOUN
ejpam-5052	126	7	(	(	PUNCT
ejpam-5052	126	8	g	g	PROPN
ejpam-5052	126	9	⊙	⊙	PROPN
ejpam-5052	126	10	q	q	PROPN
ejpam-5052	126	11	)	)	PUNCT
ejpam-5052	126	12	=	=	SYM
ejpam-5052	126	13	(	(	PUNCT
ejpam-5052	126	14	t⊙	t⊙	PROPN
ejpam-5052	126	15	g)⊙	g)⊙	VERB
ejpam-5052	126	16	q	q	NOUN
ejpam-5052	126	17	=	=	PUNCT
ejpam-5052	126	18	dt(g)⊙	dt(g)⊙	NOUN
ejpam-5052	126	19	q	q	NOUN
ejpam-5052	127	1	=	=	PUNCT
ejpam-5052	127	2	d(g)⊙	d(g)⊙	NUM
ejpam-5052	127	3	q	q	NOUN
ejpam-5052	127	4	=	=	PUNCT
ejpam-5052	127	5	g	g	PROPN
ejpam-5052	127	6	⊙	⊙	PROPN
ejpam-5052	127	7	q.	q.	PROPN
ejpam-5052	128	1	so	so	ADV
ejpam-5052	128	2	,	,	PUNCT
ejpam-5052	128	3	g	g	PROPN
ejpam-5052	128	4	⊙	⊙	PROPN
ejpam-5052	128	5	q	q	PROPN
ejpam-5052	128	6	∈	∈	PROPN
ejpam-5052	128	7	fixd(e	fixd(e	PROPN
ejpam-5052	128	8	)	)	PUNCT
ejpam-5052	128	9	.	.	PUNCT
ejpam-5052	129	1	let	let	VERB
ejpam-5052	129	2	g	g	PROPN
ejpam-5052	129	3	∈	∈	PROPN
ejpam-5052	129	4	fixd(e	fixd(e	PROPN
ejpam-5052	129	5	)	)	PUNCT
ejpam-5052	129	6	,	,	PUNCT
ejpam-5052	129	7	q	q	NOUN
ejpam-5052	129	8	∈	∈	PROPN
ejpam-5052	129	9	e	e	NOUN
ejpam-5052	129	10	and	and	CCONJ
ejpam-5052	129	11	q	q	PROPN
ejpam-5052	129	12	≤	≤	PROPN
ejpam-5052	129	13	g.	g.	NOUN
ejpam-5052	129	14	then	then	ADV
ejpam-5052	129	15	,	,	PUNCT
ejpam-5052	129	16	d(q	d(q	PROPN
ejpam-5052	129	17	)	)	PUNCT
ejpam-5052	129	18	=	=	PUNCT
ejpam-5052	129	19	dt(q	dt(q	X
ejpam-5052	129	20	)	)	PUNCT
ejpam-5052	129	21	≤	≤	NOUN
ejpam-5052	129	22	dt(g	dt(g	NOUN
ejpam-5052	129	23	)	)	PUNCT
ejpam-5052	129	24	=	=	SYM
ejpam-5052	129	25	d(g	d(g	PROPN
ejpam-5052	129	26	)	)	PUNCT
ejpam-5052	129	27	=	=	SYM
ejpam-5052	130	1	g.	g.	NOUN
ejpam-5052	130	2	by	by	ADP
ejpam-5052	130	3	hypothesis	hypothesis	NOUN
ejpam-5052	130	4	,	,	PUNCT
ejpam-5052	130	5	d(q	d(q	PROPN
ejpam-5052	130	6	)	)	PUNCT
ejpam-5052	130	7	=	=	SYM
ejpam-5052	130	8	q.	q.	NOUN
ejpam-5052	131	1	so	so	ADV
ejpam-5052	131	2	,	,	PUNCT
ejpam-5052	131	3	q	q	PROPN
ejpam-5052	131	4	∈	∈	PROPN
ejpam-5052	131	5	fixd(e	fixd(e	NOUN
ejpam-5052	131	6	)	)	PUNCT
ejpam-5052	131	7	.	.	PUNCT
ejpam-5052	132	1	hence	hence	ADV
ejpam-5052	132	2	,	,	PUNCT
ejpam-5052	132	3	fixd(e	fixd(e	PROPN
ejpam-5052	132	4	)	)	PUNCT
ejpam-5052	132	5	is	be	AUX
ejpam-5052	132	6	a	a	DET
ejpam-5052	132	7	hyperideal	hyperideal	NOUN
ejpam-5052	132	8	of	of	ADP
ejpam-5052	132	9	e.	e.	PROPN
ejpam-5052	132	10	example	example	PROPN
ejpam-5052	133	1	1	1	X
ejpam-5052	133	2	.	.	PUNCT
ejpam-5052	134	1	let	let	VERB
ejpam-5052	134	2	e	e	NOUN
ejpam-5052	134	3	=	=	PUNCT
ejpam-5052	134	4	{	{	PUNCT
ejpam-5052	134	5	0	0	NUM
ejpam-5052	134	6	,	,	PUNCT
ejpam-5052	134	7	1	1	NUM
ejpam-5052	134	8	,	,	PUNCT
ejpam-5052	134	9	f	f	PROPN
ejpam-5052	134	10	,	,	PUNCT
ejpam-5052	134	11	f	f	PROPN
ejpam-5052	134	12	′	′	NOUN
ejpam-5052	134	13	}	}	PUNCT
ejpam-5052	134	14	and	and	CCONJ
ejpam-5052	134	15	⊕	⊕	PROPN
ejpam-5052	134	16	0	0	NUM
ejpam-5052	135	1	1	1	NUM
ejpam-5052	135	2	f	f	NOUN
ejpam-5052	135	3	f	f	NOUN
ejpam-5052	136	1	′	′	NOUN
ejpam-5052	136	2	0	0	NUM
ejpam-5052	136	3	0	0	NUM
ejpam-5052	136	4	1	1	NUM
ejpam-5052	136	5	f	f	NOUN
ejpam-5052	136	6	f	f	NOUN
ejpam-5052	137	1	′	′	NUM
ejpam-5052	137	2	1	1	NUM
ejpam-5052	137	3	1	1	NUM
ejpam-5052	137	4	{	{	PUNCT
ejpam-5052	137	5	0	0	NUM
ejpam-5052	137	6	,	,	PUNCT
ejpam-5052	137	7	f	f	X
ejpam-5052	137	8	}	}	PUNCT
ejpam-5052	137	9	{	{	PUNCT
ejpam-5052	137	10	1	1	NUM
ejpam-5052	137	11	,	,	PUNCT
ejpam-5052	137	12	f	f	PROPN
ejpam-5052	137	13	′	′	NOUN
ejpam-5052	137	14	}	}	PUNCT
ejpam-5052	137	15	f	f	PROPN
ejpam-5052	137	16	f	f	PROPN
ejpam-5052	137	17	f	f	PROPN
ejpam-5052	137	18	{	{	PUNCT
ejpam-5052	137	19	1	1	NUM
ejpam-5052	137	20	,	,	PUNCT
ejpam-5052	137	21	f	f	PROPN
ejpam-5052	137	22	′	′	NOUN
ejpam-5052	137	23	}	}	PUNCT
ejpam-5052	137	24	{	{	PUNCT
ejpam-5052	137	25	0	0	NUM
ejpam-5052	137	26	,	,	PUNCT
ejpam-5052	137	27	f	f	NOUN
ejpam-5052	137	28	}	}	SYM
ejpam-5052	137	29	1	1	NUM
ejpam-5052	137	30	f	f	NOUN
ejpam-5052	137	31	′	′	NUM
ejpam-5052	138	1	f	f	NOUN
ejpam-5052	138	2	′	′	NUM
ejpam-5052	139	1	f	f	NOUN
ejpam-5052	139	2	1	1	NUM
ejpam-5052	139	3	0	0	NUM
ejpam-5052	139	4	⊙	⊙	NOUN
ejpam-5052	139	5	0	0	NUM
ejpam-5052	140	1	1	1	NUM
ejpam-5052	140	2	f	f	NOUN
ejpam-5052	140	3	f	f	NOUN
ejpam-5052	141	1	′	′	NOUN
ejpam-5052	141	2	0	0	NUM
ejpam-5052	141	3	0	0	NUM
ejpam-5052	141	4	0	0	NUM
ejpam-5052	141	5	0	0	NUM
ejpam-5052	141	6	0	0	NUM
ejpam-5052	141	7	1	1	NUM
ejpam-5052	141	8	0	0	NUM
ejpam-5052	141	9	1	1	NUM
ejpam-5052	141	10	f	f	NOUN
ejpam-5052	141	11	f	f	NOUN
ejpam-5052	142	1	′	′	NUM
ejpam-5052	143	1	f	f	NOUN
ejpam-5052	143	2	0	0	PUNCT
ejpam-5052	144	1	f	f	PROPN
ejpam-5052	144	2	f	f	PROPN
ejpam-5052	144	3	0	0	PUNCT
ejpam-5052	145	1	f	f	NOUN
ejpam-5052	146	1	′	′	NOUN
ejpam-5052	146	2	0	0	NUM
ejpam-5052	147	1	f	f	NOUN
ejpam-5052	148	1	′	′	NOUN
ejpam-5052	148	2	0	0	NUM
ejpam-5052	149	1	f	f	NOUN
ejpam-5052	149	2	′	′	NUM
ejpam-5052	149	3	≤:=	≤:=	PROPN
ejpam-5052	149	4	{	{	PUNCT
ejpam-5052	149	5	(	(	PUNCT
ejpam-5052	149	6	z	z	NOUN
ejpam-5052	149	7	,	,	PUNCT
ejpam-5052	149	8	z	z	NOUN
ejpam-5052	149	9	)	)	PUNCT
ejpam-5052	150	1	|	|	ADV
ejpam-5052	150	2	z	z	NOUN
ejpam-5052	150	3	∈	∈	PROPN
ejpam-5052	150	4	e	e	X
ejpam-5052	150	5	}	}	PUNCT
ejpam-5052	150	6	∪	∪	X
ejpam-5052	150	7	{	{	PUNCT
ejpam-5052	150	8	(	(	PUNCT
ejpam-5052	150	9	0	0	NUM
ejpam-5052	150	10	,	,	PUNCT
ejpam-5052	150	11	f	f	NOUN
ejpam-5052	150	12	)	)	PUNCT
ejpam-5052	150	13	,	,	PUNCT
ejpam-5052	150	14	(	(	PUNCT
ejpam-5052	150	15	f	f	PROPN
ejpam-5052	150	16	′	′	NUM
ejpam-5052	150	17	,	,	PUNCT
ejpam-5052	150	18	1	1	NUM
ejpam-5052	150	19	)	)	PUNCT
ejpam-5052	150	20	}	}	PUNCT
ejpam-5052	150	21	.	.	PUNCT
ejpam-5052	151	1	then	then	ADV
ejpam-5052	151	2	(	(	PUNCT
ejpam-5052	151	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	151	4	)	)	PUNCT
ejpam-5052	151	5	∈	∈	NOUN
ejpam-5052	151	6	okh	okh	NOUN
ejpam-5052	151	7	.	.	PUNCT
ejpam-5052	152	1	we	we	PRON
ejpam-5052	152	2	set	set	VERB
ejpam-5052	152	3	d(z	d(z	NOUN
ejpam-5052	152	4	)	)	PUNCT
ejpam-5052	153	1	=	=	SYM
ejpam-5052	153	2	df	df	NOUN
ejpam-5052	153	3	(	(	PUNCT
ejpam-5052	153	4	z	z	NOUN
ejpam-5052	153	5	)	)	PUNCT
ejpam-5052	153	6	=	=	SYM
ejpam-5052	154	1			NOUN
ejpam-5052	154	2	0	0	NUM
ejpam-5052	154	3	,	,	PUNCT
ejpam-5052	154	4	z	z	NOUN
ejpam-5052	154	5	=	=	SYM
ejpam-5052	154	6	0	0	NUM
ejpam-5052	154	7	,	,	PUNCT
ejpam-5052	154	8	f	f	PROPN
ejpam-5052	154	9	′	′	NUM
ejpam-5052	155	1	f	f	X
ejpam-5052	155	2	,	,	PUNCT
ejpam-5052	155	3	z	z	NOUN
ejpam-5052	155	4	=	=	SYM
ejpam-5052	155	5	1	1	NUM
ejpam-5052	155	6	,	,	PUNCT
ejpam-5052	155	7	f.	f.	PROPN
ejpam-5052	155	8	then	then	ADV
ejpam-5052	155	9	,	,	PUNCT
ejpam-5052	155	10	d	d	PROPN
ejpam-5052	155	11	=	=	PUNCT
ejpam-5052	155	12	df	df	PROPN
ejpam-5052	155	13	∈	∈	PROPN
ejpam-5052	155	14	der(e	der(e	PROPN
ejpam-5052	155	15	)	)	PUNCT
ejpam-5052	155	16	.	.	PUNCT
ejpam-5052	156	1	indeed	indeed	ADV
ejpam-5052	156	2	:	:	PUNCT
ejpam-5052	156	3	df	df	PROPN
ejpam-5052	156	4	(	(	PUNCT
ejpam-5052	156	5	0	0	NUM
ejpam-5052	156	6	)	)	PUNCT
ejpam-5052	156	7	=	=	SYM
ejpam-5052	157	1	f	f	PROPN
ejpam-5052	157	2	⊙	⊙	X
ejpam-5052	157	3	0	0	PUNCT
ejpam-5052	158	1	=	=	SYM
ejpam-5052	158	2	0	0	PROPN
ejpam-5052	158	3	,	,	PUNCT
ejpam-5052	158	4	r.	r.	PROPN
ejpam-5052	158	5	cai	cai	PROPN
ejpam-5052	158	6	,	,	PUNCT
ejpam-5052	158	7	m.	m.	NOUN
ejpam-5052	158	8	alsaeedi	alsaeedi	PROPN
ejpam-5052	158	9	,	,	PUNCT
ejpam-5052	158	10	m.	m.	NOUN
ejpam-5052	158	11	akhoundi	akhoundi	PROPN
ejpam-5052	158	12	/	/	SYM
ejpam-5052	158	13	eur	eur	PROPN
ejpam-5052	158	14	.	.	PUNCT
ejpam-5052	159	1	j.	j.	PROPN
ejpam-5052	159	2	pure	pure	PROPN
ejpam-5052	159	3	appl	appl	PROPN
ejpam-5052	159	4	.	.	PROPN
ejpam-5052	159	5	math	math	PROPN
ejpam-5052	159	6	,	,	PUNCT
ejpam-5052	159	7	17	17	NUM
ejpam-5052	159	8	(	(	PUNCT
ejpam-5052	159	9	2	2	NUM
ejpam-5052	159	10	)	)	PUNCT
ejpam-5052	159	11	(	(	PUNCT
ejpam-5052	159	12	2024	2024	NUM
ejpam-5052	159	13	)	)	PUNCT
ejpam-5052	159	14	,	,	PUNCT
ejpam-5052	159	15	604	604	NUM
ejpam-5052	159	16	-	-	SYM
ejpam-5052	159	17	615	615	NUM
ejpam-5052	159	18	610	610	NUM
ejpam-5052	159	19	df	df	NOUN
ejpam-5052	159	20	(	(	PUNCT
ejpam-5052	159	21	1	1	NUM
ejpam-5052	159	22	)	)	PUNCT
ejpam-5052	159	23	=	=	SYM
ejpam-5052	160	1	f	f	PROPN
ejpam-5052	160	2	⊙	⊙	NOUN
ejpam-5052	160	3	1	1	NUM
ejpam-5052	160	4	=	=	SYM
ejpam-5052	160	5	f	f	PROPN
ejpam-5052	160	6	,	,	PUNCT
ejpam-5052	160	7	df	df	PROPN
ejpam-5052	160	8	(	(	PUNCT
ejpam-5052	160	9	f	f	X
ejpam-5052	160	10	)	)	PUNCT
ejpam-5052	160	11	=	=	SYM
ejpam-5052	161	1	f	f	PROPN
ejpam-5052	161	2	⊙	⊙	PROPN
ejpam-5052	161	3	f	f	PROPN
ejpam-5052	162	1	=	=	SYM
ejpam-5052	162	2	f	f	PROPN
ejpam-5052	162	3	,	,	PUNCT
ejpam-5052	162	4	df	df	PROPN
ejpam-5052	162	5	(	(	PUNCT
ejpam-5052	162	6	f	f	PROPN
ejpam-5052	162	7	′	′	NUM
ejpam-5052	162	8	)	)	PUNCT
ejpam-5052	163	1	=	=	SYM
ejpam-5052	163	2	f	f	PROPN
ejpam-5052	163	3	⊙	⊙	PROPN
ejpam-5052	164	1	f	f	PROPN
ejpam-5052	164	2	′	′	NUM
ejpam-5052	165	1	=	=	NOUN
ejpam-5052	165	2	0	0	X
ejpam-5052	165	3	.	.	PUNCT
ejpam-5052	166	1	clearly	clearly	ADV
ejpam-5052	166	2	,	,	PUNCT
ejpam-5052	166	3	fixd(e	fixd(e	PROPN
ejpam-5052	166	4	)	)	PUNCT
ejpam-5052	166	5	=	=	PUNCT
ejpam-5052	166	6	{	{	PUNCT
ejpam-5052	166	7	0	0	NUM
ejpam-5052	166	8	,	,	PUNCT
ejpam-5052	166	9	f	f	X
ejpam-5052	166	10	}	}	PUNCT
ejpam-5052	166	11	is	be	AUX
ejpam-5052	166	12	a	a	DET
ejpam-5052	166	13	hyperideal	hyperideal	NOUN
ejpam-5052	166	14	of	of	ADP
ejpam-5052	166	15	e.	e.	PROPN
ejpam-5052	166	16	theorem	theorem	PROPN
ejpam-5052	166	17	4	4	X
ejpam-5052	166	18	.	.	PUNCT
ejpam-5052	167	1	let	let	VERB
ejpam-5052	167	2	(	(	PUNCT
ejpam-5052	167	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	167	4	)	)	PUNCT
ejpam-5052	167	5	∈	∈	NOUN
ejpam-5052	167	6	okh	okh	VERB
ejpam-5052	167	7	and	and	CCONJ
ejpam-5052	167	8	d	d	PROPN
ejpam-5052	167	9	∈	∈	PROPN
ejpam-5052	167	10	der(e	der(e	PROPN
ejpam-5052	167	11	)	)	PUNCT
ejpam-5052	167	12	with	with	ADP
ejpam-5052	167	13	d(g	d(g	PROPN
ejpam-5052	167	14	)	)	PUNCT
ejpam-5052	167	15	=	=	VERB
ejpam-5052	168	1	d(1)⊙	d(1)⊙	X
ejpam-5052	168	2	g	g	NOUN
ejpam-5052	168	3	;	;	PUNCT
ejpam-5052	168	4	∀g	∀g	X
ejpam-5052	168	5	∈	∈	PROPN
ejpam-5052	168	6	e.	e.	PROPN
ejpam-5052	169	1	if	if	SCONJ
ejpam-5052	169	2	d	d	PROPN
ejpam-5052	169	3	is	be	AUX
ejpam-5052	169	4	a	a	DET
ejpam-5052	169	5	homomorphism	homomorphism	NOUN
ejpam-5052	169	6	,	,	PUNCT
ejpam-5052	169	7	then	then	ADV
ejpam-5052	169	8	d	d	PROPN
ejpam-5052	169	9	is	be	AUX
ejpam-5052	169	10	idempotent	idempotent	ADJ
ejpam-5052	169	11	.	.	PUNCT
ejpam-5052	170	1	proof	proof	NOUN
ejpam-5052	170	2	.	.	PUNCT
ejpam-5052	171	1	let	let	VERB
ejpam-5052	171	2	g	g	PROPN
ejpam-5052	171	3	∈	∈	PROPN
ejpam-5052	171	4	e.	e.	PROPN
ejpam-5052	171	5	we	we	PRON
ejpam-5052	171	6	have	have	VERB
ejpam-5052	171	7	d2(g	d2(g	NOUN
ejpam-5052	171	8	)	)	PUNCT
ejpam-5052	171	9	=	=	SYM
ejpam-5052	171	10	d(d(g	d(d(g	PROPN
ejpam-5052	171	11	)	)	PUNCT
ejpam-5052	171	12	)	)	PUNCT
ejpam-5052	172	1	=	=	SYM
ejpam-5052	173	1	d(1⊙	d(1⊙	PROPN
ejpam-5052	173	2	d(g	d(g	NUM
ejpam-5052	173	3	)	)	PUNCT
ejpam-5052	173	4	)	)	PUNCT
ejpam-5052	174	1	=	=	SYM
ejpam-5052	174	2	d(1)⊙	d(1)⊙	X
ejpam-5052	174	3	(	(	PUNCT
ejpam-5052	174	4	1⊙	1⊙	NUM
ejpam-5052	174	5	d(g	d(g	PROPN
ejpam-5052	174	6	)	)	PUNCT
ejpam-5052	174	7	)	)	PUNCT
ejpam-5052	175	1	=	=	PUNCT
ejpam-5052	175	2	(	(	PUNCT
ejpam-5052	175	3	d(1)⊙	d(1)⊙	X
ejpam-5052	175	4	1)⊙	1)⊙	PROPN
ejpam-5052	175	5	d(g	d(g	PROPN
ejpam-5052	175	6	)	)	PUNCT
ejpam-5052	175	7	=	=	SYM
ejpam-5052	176	1	d(1)⊙	d(1)⊙	X
ejpam-5052	176	2	d(g	d(g	PROPN
ejpam-5052	176	3	)	)	PUNCT
ejpam-5052	176	4	=	=	PUNCT
ejpam-5052	176	5	d(1⊙	d(1⊙	PROPN
ejpam-5052	176	6	g	g	NOUN
ejpam-5052	176	7	)	)	PUNCT
ejpam-5052	176	8	=	=	SYM
ejpam-5052	176	9	d(g	d(g	PROPN
ejpam-5052	176	10	)	)	PUNCT
ejpam-5052	176	11	.	.	PUNCT
ejpam-5052	177	1	hence	hence	ADV
ejpam-5052	177	2	,	,	PUNCT
ejpam-5052	177	3	d2	d2	PROPN
ejpam-5052	177	4	=	=	SYM
ejpam-5052	177	5	d.	d.	PROPN
ejpam-5052	177	6	example	example	NOUN
ejpam-5052	178	1	2	2	NUM
ejpam-5052	178	2	.	.	X
ejpam-5052	178	3	in	in	ADP
ejpam-5052	178	4	example	example	NOUN
ejpam-5052	178	5	1	1	NUM
ejpam-5052	178	6	,	,	PUNCT
ejpam-5052	178	7	d(1⊙	d(1⊙	PROPN
ejpam-5052	178	8	1	1	NUM
ejpam-5052	178	9	)	)	PUNCT
ejpam-5052	178	10	=	=	PUNCT
ejpam-5052	178	11	d(1	d(1	VERB
ejpam-5052	178	12	)	)	PUNCT
ejpam-5052	178	13	=	=	SYM
ejpam-5052	178	14	f	f	X
ejpam-5052	178	15	=	=	SYM
ejpam-5052	178	16	f	f	PROPN
ejpam-5052	178	17	⊙	⊙	PROPN
ejpam-5052	178	18	f	f	PROPN
ejpam-5052	179	1	=	=	X
ejpam-5052	179	2	d(1)⊙	d(1)⊙	X
ejpam-5052	179	3	d(1	d(1	PROPN
ejpam-5052	179	4	)	)	PUNCT
ejpam-5052	179	5	,	,	PUNCT
ejpam-5052	179	6	d(1⊙	d(1⊙	PROPN
ejpam-5052	179	7	f	f	X
ejpam-5052	179	8	)	)	PUNCT
ejpam-5052	179	9	=	=	SYM
ejpam-5052	179	10	d(f	d(f	NOUN
ejpam-5052	179	11	)	)	PUNCT
ejpam-5052	180	1	=	=	SYM
ejpam-5052	180	2	f	f	X
ejpam-5052	180	3	=	=	SYM
ejpam-5052	180	4	f	f	PROPN
ejpam-5052	180	5	⊙	⊙	PROPN
ejpam-5052	180	6	f	f	PROPN
ejpam-5052	181	1	=	=	X
ejpam-5052	181	2	d(1)⊙	d(1)⊙	X
ejpam-5052	181	3	d(f	d(f	PROPN
ejpam-5052	181	4	)	)	PUNCT
ejpam-5052	181	5	,	,	PUNCT
ejpam-5052	181	6	d(1⊙	d(1⊙	PROPN
ejpam-5052	181	7	f	f	PROPN
ejpam-5052	181	8	′	′	NUM
ejpam-5052	181	9	)	)	PUNCT
ejpam-5052	182	1	=	=	PUNCT
ejpam-5052	182	2	d(f	d(f	NOUN
ejpam-5052	182	3	′	′	NOUN
ejpam-5052	182	4	)	)	PUNCT
ejpam-5052	182	5	=	=	SYM
ejpam-5052	182	6	0	0	PUNCT
ejpam-5052	183	1	=	=	SYM
ejpam-5052	183	2	f	f	PROPN
ejpam-5052	183	3	⊙	⊙	X
ejpam-5052	183	4	0	0	PUNCT
ejpam-5052	184	1	=	=	SYM
ejpam-5052	184	2	d(1)⊙	d(1)⊙	X
ejpam-5052	184	3	d(f	d(f	PROPN
ejpam-5052	184	4	′	′	NUM
ejpam-5052	184	5	)	)	PUNCT
ejpam-5052	184	6	,	,	PUNCT
ejpam-5052	184	7	d(f	d(f	PROPN
ejpam-5052	184	8	⊙	⊙	NOUN
ejpam-5052	184	9	f	f	X
ejpam-5052	184	10	)	)	PUNCT
ejpam-5052	184	11	=	=	SYM
ejpam-5052	184	12	d(f	d(f	NOUN
ejpam-5052	184	13	)	)	PUNCT
ejpam-5052	185	1	=	=	SYM
ejpam-5052	185	2	f	f	X
ejpam-5052	185	3	=	=	SYM
ejpam-5052	185	4	f	f	PROPN
ejpam-5052	185	5	⊙	⊙	PROPN
ejpam-5052	185	6	f	f	PROPN
ejpam-5052	186	1	=	=	PUNCT
ejpam-5052	186	2	d(f)⊙	d(f)⊙	PROPN
ejpam-5052	186	3	d(f	d(f	NOUN
ejpam-5052	186	4	)	)	PUNCT
ejpam-5052	186	5	,	,	PUNCT
ejpam-5052	186	6	d(f	d(f	PROPN
ejpam-5052	186	7	⊙	⊙	PROPN
ejpam-5052	186	8	f	f	PROPN
ejpam-5052	186	9	′	′	PROPN
ejpam-5052	186	10	)	)	PUNCT
ejpam-5052	186	11	=	=	PUNCT
ejpam-5052	186	12	d(0	d(0	NOUN
ejpam-5052	186	13	)	)	PUNCT
ejpam-5052	186	14	=	=	SYM
ejpam-5052	186	15	0	0	PUNCT
ejpam-5052	187	1	=	=	SYM
ejpam-5052	187	2	f	f	PROPN
ejpam-5052	187	3	⊙	⊙	NOUN
ejpam-5052	187	4	0	0	PUNCT
ejpam-5052	188	1	=	=	PUNCT
ejpam-5052	188	2	d(f)⊙	d(f)⊙	X
ejpam-5052	188	3	d(f	d(f	NOUN
ejpam-5052	188	4	′	′	NOUN
ejpam-5052	188	5	)	)	PUNCT
ejpam-5052	188	6	.	.	PUNCT
ejpam-5052	189	1	hence	hence	ADV
ejpam-5052	189	2	,	,	PUNCT
ejpam-5052	189	3	d	d	PROPN
ejpam-5052	189	4	is	be	AUX
ejpam-5052	189	5	a	a	DET
ejpam-5052	189	6	homomorphism	homomorphism	NOUN
ejpam-5052	189	7	of	of	ADP
ejpam-5052	189	8	e.	e.	PROPN
ejpam-5052	189	9	also	also	ADV
ejpam-5052	189	10	,	,	PUNCT
ejpam-5052	189	11	d(g	d(g	PROPN
ejpam-5052	189	12	)	)	PUNCT
ejpam-5052	189	13	=	=	SYM
ejpam-5052	190	1	d(1)⊙	d(1)⊙	X
ejpam-5052	190	2	g	g	NOUN
ejpam-5052	190	3	;	;	PUNCT
ejpam-5052	190	4	∀g	∀g	PROPN
ejpam-5052	190	5	∈	∈	PROPN
ejpam-5052	190	6	e.	e.	PROPN
ejpam-5052	190	7	r.	r.	PROPN
ejpam-5052	190	8	cai	cai	PROPN
ejpam-5052	190	9	,	,	PUNCT
ejpam-5052	190	10	m.	m.	NOUN
ejpam-5052	190	11	alsaeedi	alsaeedi	PROPN
ejpam-5052	190	12	,	,	PUNCT
ejpam-5052	190	13	m.	m.	NOUN
ejpam-5052	190	14	akhoundi	akhoundi	PROPN
ejpam-5052	190	15	/	/	SYM
ejpam-5052	190	16	eur	eur	PROPN
ejpam-5052	190	17	.	.	PUNCT
ejpam-5052	191	1	j.	j.	PROPN
ejpam-5052	191	2	pure	pure	PROPN
ejpam-5052	191	3	appl	appl	PROPN
ejpam-5052	191	4	.	.	PROPN
ejpam-5052	191	5	math	math	PROPN
ejpam-5052	191	6	,	,	PUNCT
ejpam-5052	191	7	17	17	NUM
ejpam-5052	191	8	(	(	PUNCT
ejpam-5052	191	9	2	2	NUM
ejpam-5052	191	10	)	)	PUNCT
ejpam-5052	191	11	(	(	PUNCT
ejpam-5052	191	12	2024	2024	NUM
ejpam-5052	191	13	)	)	PUNCT
ejpam-5052	191	14	,	,	PUNCT
ejpam-5052	191	15	604	604	NUM
ejpam-5052	191	16	-	-	SYM
ejpam-5052	191	17	615	615	NUM
ejpam-5052	191	18	611	611	NUM
ejpam-5052	191	19	now	now	ADV
ejpam-5052	191	20	,	,	PUNCT
ejpam-5052	191	21	by	by	ADP
ejpam-5052	191	22	theorem	theorem	NOUN
ejpam-5052	191	23	4	4	NUM
ejpam-5052	191	24	,	,	PUNCT
ejpam-5052	191	25	d	d	PROPN
ejpam-5052	191	26	is	be	AUX
ejpam-5052	191	27	idempotent	idempotent	ADJ
ejpam-5052	191	28	.	.	PUNCT
ejpam-5052	192	1	definition	definition	NOUN
ejpam-5052	192	2	6	6	NUM
ejpam-5052	192	3	.	.	PUNCT
ejpam-5052	193	1	let	let	AUX
ejpam-5052	193	2	(	(	PUNCT
ejpam-5052	193	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	193	4	)	)	PUNCT
ejpam-5052	193	5	∈	∈	NOUN
ejpam-5052	193	6	okh	okh	VERB
ejpam-5052	193	7	and	and	CCONJ
ejpam-5052	193	8	d	d	PROPN
ejpam-5052	193	9	∈	∈	PROPN
ejpam-5052	193	10	der(e	der(e	PROPN
ejpam-5052	193	11	)	)	PUNCT
ejpam-5052	193	12	be	be	AUX
ejpam-5052	193	13	a	a	DET
ejpam-5052	193	14	homomorphism	homomorphism	NOUN
ejpam-5052	193	15	.	.	PUNCT
ejpam-5052	194	1	a	a	DET
ejpam-5052	194	2	proper	proper	ADJ
ejpam-5052	194	3	hyperideal	hyperideal	NOUN
ejpam-5052	194	4	w	w	NOUN
ejpam-5052	194	5	of	of	ADP
ejpam-5052	194	6	e	e	PROPN
ejpam-5052	194	7	is	be	AUX
ejpam-5052	194	8	said	say	VERB
ejpam-5052	194	9	to	to	PART
ejpam-5052	194	10	be	be	AUX
ejpam-5052	194	11	a	a	DET
ejpam-5052	194	12	prime	prime	ADJ
ejpam-5052	194	13	hyperideal	hyperideal	NOUN
ejpam-5052	194	14	associated	associate	VERB
ejpam-5052	194	15	to	to	ADP
ejpam-5052	194	16	d	d	PROPN
ejpam-5052	194	17	if	if	SCONJ
ejpam-5052	194	18	g	g	PROPN
ejpam-5052	194	19	⊙	⊙	PROPN
ejpam-5052	194	20	g′	g′	PROPN
ejpam-5052	194	21	∈	∈	PROPN
ejpam-5052	194	22	w	w	PROPN
ejpam-5052	194	23	⇒	⇒	NOUN
ejpam-5052	194	24	g	g	PROPN
ejpam-5052	194	25	∈	∈	PROPN
ejpam-5052	194	26	w	w	PROPN
ejpam-5052	194	27	or	or	CCONJ
ejpam-5052	194	28	d(g′	d(g′	NUM
ejpam-5052	194	29	)	)	PUNCT
ejpam-5052	194	30	∈	∈	PROPN
ejpam-5052	194	31	w	w	PROPN
ejpam-5052	194	32	,	,	PUNCT
ejpam-5052	194	33	∀g	∀g	NOUN
ejpam-5052	194	34	,	,	PUNCT
ejpam-5052	194	35	g′	g′	PROPN
ejpam-5052	194	36	∈	∈	PROPN
ejpam-5052	194	37	e.	e.	PROPN
ejpam-5052	194	38	theorem	theorem	VERB
ejpam-5052	194	39	5	5	X
ejpam-5052	194	40	.	.	PUNCT
ejpam-5052	195	1	let	let	VERB
ejpam-5052	195	2	(	(	PUNCT
ejpam-5052	195	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	195	4	)	)	PUNCT
ejpam-5052	195	5	∈	∈	NOUN
ejpam-5052	195	6	okh	okh	VERB
ejpam-5052	195	7	and	and	CCONJ
ejpam-5052	195	8	d	d	PROPN
ejpam-5052	195	9	∈	∈	PROPN
ejpam-5052	195	10	der(e	der(e	PROPN
ejpam-5052	195	11	)	)	PUNCT
ejpam-5052	195	12	be	be	AUX
ejpam-5052	195	13	a	a	DET
ejpam-5052	195	14	homomorphism	homomorphism	NOUN
ejpam-5052	195	15	.	.	PUNCT
ejpam-5052	196	1	then	then	ADV
ejpam-5052	196	2	y	y	PROPN
ejpam-5052	196	3	is	be	AUX
ejpam-5052	196	4	a	a	DET
ejpam-5052	196	5	prime	prime	ADJ
ejpam-5052	196	6	hyperideal	hyperideal	NOUN
ejpam-5052	196	7	of	of	ADP
ejpam-5052	196	8	e	e	NOUN
ejpam-5052	196	9	associated	associate	VERB
ejpam-5052	196	10	to	to	ADP
ejpam-5052	196	11	d	d	PROPN
ejpam-5052	196	12	iff	iff	PROPN
ejpam-5052	196	13	for	for	ADP
ejpam-5052	196	14	any	any	DET
ejpam-5052	196	15	hyperideals	hyperideal	NOUN
ejpam-5052	196	16	g	g	NOUN
ejpam-5052	196	17	and	and	CCONJ
ejpam-5052	196	18	g′	g′	NOUN
ejpam-5052	196	19	of	of	ADP
ejpam-5052	196	20	e	e	PROPN
ejpam-5052	196	21	,	,	PUNCT
ejpam-5052	196	22	we	we	PRON
ejpam-5052	196	23	have	have	AUX
ejpam-5052	196	24	g⊙g′	g⊙g′	VERB
ejpam-5052	196	25	⊆	⊆	NUM
ejpam-5052	196	26	y	y	PROPN
ejpam-5052	196	27	⇒	⇒	NOUN
ejpam-5052	196	28	g	g	PROPN
ejpam-5052	196	29	⊆	⊆	PROPN
ejpam-5052	196	30	y	y	PROPN
ejpam-5052	196	31	or	or	CCONJ
ejpam-5052	196	32	d(g′	d(g′	NOUN
ejpam-5052	196	33	)	)	PUNCT
ejpam-5052	196	34	⊆	⊆	NUM
ejpam-5052	196	35	y	y	PROPN
ejpam-5052	196	36	.	.	PUNCT
ejpam-5052	197	1	proof	proof	NOUN
ejpam-5052	197	2	.	.	PUNCT
ejpam-5052	198	1	(	(	PUNCT
ejpam-5052	198	2	⇒	⇒	NOUN
ejpam-5052	198	3	):	):	PUNCT
ejpam-5052	198	4	let	let	VERB
ejpam-5052	198	5	y	y	PRON
ejpam-5052	198	6	be	be	AUX
ejpam-5052	198	7	a	a	DET
ejpam-5052	198	8	prime	prime	ADJ
ejpam-5052	198	9	hyperideal	hyperideal	NOUN
ejpam-5052	198	10	of	of	ADP
ejpam-5052	198	11	e	e	NOUN
ejpam-5052	198	12	associated	associate	VERB
ejpam-5052	198	13	to	to	ADP
ejpam-5052	198	14	d	d	PROPN
ejpam-5052	198	15	,	,	PUNCT
ejpam-5052	198	16	g⊙g′	g⊙g′	VERB
ejpam-5052	198	17	⊆	⊆	NUM
ejpam-5052	198	18	y	y	PROPN
ejpam-5052	198	19	and	and	CCONJ
ejpam-5052	198	20	g	g	PROPN
ejpam-5052	198	21	⊈	⊈	PROPN
ejpam-5052	198	22	y	y	PROPN
ejpam-5052	198	23	,	,	PUNCT
ejpam-5052	198	24	where	where	SCONJ
ejpam-5052	198	25	g	g	NOUN
ejpam-5052	198	26	,	,	PUNCT
ejpam-5052	198	27	g′	g′	NOUN
ejpam-5052	198	28	are	be	AUX
ejpam-5052	198	29	hyperideals	hyperideal	NOUN
ejpam-5052	198	30	of	of	ADP
ejpam-5052	198	31	e.	e.	PROPN
ejpam-5052	198	32	as	as	ADP
ejpam-5052	198	33	g	g	PROPN
ejpam-5052	198	34	⊈	⊈	PROPN
ejpam-5052	198	35	y	y	PROPN
ejpam-5052	198	36	,	,	PUNCT
ejpam-5052	198	37	∃g	∃g	PROPN
ejpam-5052	198	38	∈	∈	PROPN
ejpam-5052	198	39	g	g	NOUN
ejpam-5052	198	40	such	such	ADJ
ejpam-5052	198	41	that	that	PRON
ejpam-5052	198	42	g	g	PROPN
ejpam-5052	198	43	/∈	/∈	PROPN
ejpam-5052	199	1	y	y	PROPN
ejpam-5052	199	2	.	.	PUNCT
ejpam-5052	200	1	take	take	VERB
ejpam-5052	200	2	any	any	DET
ejpam-5052	200	3	g′	g′	NOUN
ejpam-5052	200	4	∈	∈	PROPN
ejpam-5052	200	5	g′.	g′.	NOUN
ejpam-5052	200	6	then	then	ADV
ejpam-5052	200	7	,	,	PUNCT
ejpam-5052	200	8	g	g	PROPN
ejpam-5052	200	9	⊙	⊙	PROPN
ejpam-5052	200	10	g′	g′	PROPN
ejpam-5052	200	11	∈	∈	PROPN
ejpam-5052	200	12	g⊙g′	g⊙g′	VERB
ejpam-5052	200	13	⊆	⊆	NUM
ejpam-5052	200	14	y	y	PROPN
ejpam-5052	200	15	.	.	PUNCT
ejpam-5052	201	1	since	since	SCONJ
ejpam-5052	201	2	y	y	PROPN
ejpam-5052	201	3	is	be	AUX
ejpam-5052	201	4	a	a	DET
ejpam-5052	201	5	prime	prime	ADJ
ejpam-5052	201	6	hyperideal	hyperideal	NOUN
ejpam-5052	201	7	associated	associate	VERB
ejpam-5052	201	8	to	to	ADP
ejpam-5052	201	9	d	d	PROPN
ejpam-5052	201	10	and	and	CCONJ
ejpam-5052	201	11	g	g	PROPN
ejpam-5052	201	12	/∈	/∈	PROPN
ejpam-5052	202	1	y	y	PROPN
ejpam-5052	202	2	,	,	PUNCT
ejpam-5052	202	3	we	we	PRON
ejpam-5052	202	4	get	get	VERB
ejpam-5052	202	5	d(g′	d(g′	PRON
ejpam-5052	202	6	)	)	PUNCT
ejpam-5052	202	7	∈	∈	PROPN
ejpam-5052	202	8	y	y	PROPN
ejpam-5052	202	9	.	.	PUNCT
ejpam-5052	203	1	hence	hence	ADV
ejpam-5052	203	2	,	,	PUNCT
ejpam-5052	203	3	d(g′	d(g′	PROPN
ejpam-5052	203	4	)	)	PUNCT
ejpam-5052	203	5	⊆	⊆	NUM
ejpam-5052	203	6	y	y	PROPN
ejpam-5052	203	7	.	.	PUNCT
ejpam-5052	204	1	(	(	PUNCT
ejpam-5052	204	2	⇐	⇐	ADJ
ejpam-5052	204	3	):	):	PUNCT
ejpam-5052	204	4	suppose	suppose	VERB
ejpam-5052	204	5	that	that	SCONJ
ejpam-5052	204	6	g	g	PROPN
ejpam-5052	204	7	⊙	⊙	PROPN
ejpam-5052	204	8	g′	g′	PROPN
ejpam-5052	204	9	∈	∈	PROPN
ejpam-5052	204	10	y	y	PROPN
ejpam-5052	204	11	for	for	ADP
ejpam-5052	204	12	some	some	DET
ejpam-5052	204	13	g	g	NOUN
ejpam-5052	204	14	,	,	PUNCT
ejpam-5052	204	15	g′	g′	PROPN
ejpam-5052	204	16	∈	∈	PROPN
ejpam-5052	204	17	e.	e.	PROPN
ejpam-5052	204	18	then	then	ADV
ejpam-5052	204	19	<	<	X
ejpam-5052	204	20	g	g	PROPN
ejpam-5052	204	21	⊙	⊙	PROPN
ejpam-5052	204	22	g′	g′	PROPN
ejpam-5052	204	23	>	>	PROPN
ejpam-5052	204	24	⊆	⊆	NUM
ejpam-5052	204	25	y	y	NOUN
ejpam-5052	204	26	.	.	PUNCT
ejpam-5052	205	1	so	so	ADV
ejpam-5052	205	2	,	,	PUNCT
ejpam-5052	205	3	<	<	X
ejpam-5052	205	4	g	g	X
ejpam-5052	205	5	>	>	X
ejpam-5052	205	6	⊙	⊙	PROPN
ejpam-5052	205	7	<	<	X
ejpam-5052	205	8	g′	g′	X
ejpam-5052	205	9	>	>	PUNCT
ejpam-5052	205	10	⊆	⊆	X
ejpam-5052	205	11	<	<	X
ejpam-5052	205	12	g	g	PROPN
ejpam-5052	205	13	⊙	⊙	PROPN
ejpam-5052	205	14	g′	g′	PROPN
ejpam-5052	205	15	>	>	PROPN
ejpam-5052	205	16	⊆	⊆	NUM
ejpam-5052	205	17	y	y	PROPN
ejpam-5052	205	18	.	.	PUNCT
ejpam-5052	206	1	hence	hence	ADV
ejpam-5052	206	2	,	,	PUNCT
ejpam-5052	206	3	<	<	X
ejpam-5052	206	4	g	g	PROPN
ejpam-5052	206	5	>	>	SYM
ejpam-5052	206	6	⊆	⊆	NUM
ejpam-5052	206	7	y	y	PROPN
ejpam-5052	206	8	or	or	CCONJ
ejpam-5052	206	9	d	d	PROPN
ejpam-5052	206	10	(	(	PUNCT
ejpam-5052	206	11	<	<	X
ejpam-5052	206	12	g′	g′	NOUN
ejpam-5052	206	13	>	>	PUNCT
ejpam-5052	206	14	)	)	PUNCT
ejpam-5052	206	15	⊆	⊆	NUM
ejpam-5052	206	16	y	y	PROPN
ejpam-5052	206	17	.	.	PUNCT
ejpam-5052	207	1	thus	thus	ADV
ejpam-5052	207	2	,	,	PUNCT
ejpam-5052	207	3	g	g	PROPN
ejpam-5052	207	4	∈	∈	PROPN
ejpam-5052	207	5	y	y	PROPN
ejpam-5052	207	6	or	or	CCONJ
ejpam-5052	207	7	d(g′	d(g′	NUM
ejpam-5052	207	8	)	)	PUNCT
ejpam-5052	207	9	∈	∈	PROPN
ejpam-5052	207	10	y	y	PROPN
ejpam-5052	207	11	.	.	PUNCT
ejpam-5052	208	1	therefore	therefore	ADV
ejpam-5052	208	2	,	,	PUNCT
ejpam-5052	208	3	y	y	PROPN
ejpam-5052	208	4	is	be	AUX
ejpam-5052	208	5	a	a	DET
ejpam-5052	208	6	prime	prime	ADJ
ejpam-5052	208	7	hyperideal	hyperideal	NOUN
ejpam-5052	208	8	associated	associate	VERB
ejpam-5052	208	9	to	to	ADP
ejpam-5052	208	10	d.	d.	PROPN
ejpam-5052	208	11	example	example	NOUN
ejpam-5052	209	1	3	3	X
ejpam-5052	209	2	.	.	PUNCT
ejpam-5052	210	1	in	in	ADP
ejpam-5052	210	2	example	example	NOUN
ejpam-5052	210	3	1	1	NUM
ejpam-5052	210	4	,	,	PUNCT
ejpam-5052	210	5	y	y	NOUN
ejpam-5052	210	6	=	=	PUNCT
ejpam-5052	210	7	{	{	PUNCT
ejpam-5052	210	8	0	0	NUM
ejpam-5052	210	9	,	,	PUNCT
ejpam-5052	210	10	f	f	X
ejpam-5052	210	11	}	}	PUNCT
ejpam-5052	210	12	is	be	AUX
ejpam-5052	210	13	a	a	DET
ejpam-5052	210	14	prime	prime	ADJ
ejpam-5052	210	15	hyperideal	hyperideal	NOUN
ejpam-5052	210	16	associated	associate	VERB
ejpam-5052	210	17	to	to	ADP
ejpam-5052	210	18	d.	d.	PROPN
ejpam-5052	210	19	theorem	theorem	VERB
ejpam-5052	210	20	6	6	NUM
ejpam-5052	210	21	.	.	PUNCT
ejpam-5052	211	1	let	let	VERB
ejpam-5052	211	2	(	(	PUNCT
ejpam-5052	211	3	e,⊕,⊙,≤	e,⊕,⊙,≤	X
ejpam-5052	211	4	)	)	PUNCT
ejpam-5052	211	5	∈	∈	NOUN
ejpam-5052	211	6	okh	okh	VERB
ejpam-5052	211	7	and	and	CCONJ
ejpam-5052	211	8	d	d	PROPN
ejpam-5052	211	9	∈	∈	PROPN
ejpam-5052	211	10	der(e	der(e	PROPN
ejpam-5052	211	11	)	)	PUNCT
ejpam-5052	211	12	be	be	AUX
ejpam-5052	211	13	a	a	DET
ejpam-5052	211	14	homomorphism	homomorphism	NOUN
ejpam-5052	211	15	.	.	PUNCT
ejpam-5052	212	1	if	if	SCONJ
ejpam-5052	212	2	w	w	NOUN
ejpam-5052	212	3	is	be	AUX
ejpam-5052	212	4	a	a	DET
ejpam-5052	212	5	prime	prime	ADJ
ejpam-5052	212	6	hyperideal	hyperideal	NOUN
ejpam-5052	212	7	associated	associate	VERB
ejpam-5052	212	8	to	to	ADP
ejpam-5052	212	9	d	d	PROPN
ejpam-5052	212	10	,	,	PUNCT
ejpam-5052	212	11	then	then	ADV
ejpam-5052	212	12	√	√	VERB
ejpam-5052	212	13	w	w	NOUN
ejpam-5052	212	14	:	:	PUNCT
ejpam-5052	212	15	=	=	X
ejpam-5052	212	16	{	{	PUNCT
ejpam-5052	212	17	t	t	X
ejpam-5052	212	18	∈	∈	PROPN
ejpam-5052	212	19	e	e	NOUN
ejpam-5052	212	20	|	|	ADV
ejpam-5052	212	21	∃n	∃n	PROPN
ejpam-5052	212	22	∈	∈	PROPN
ejpam-5052	212	23	n	n	PRON
ejpam-5052	212	24	such	such	ADJ
ejpam-5052	212	25	that	that	SCONJ
ejpam-5052	212	26	tn	tn	PROPN
ejpam-5052	212	27	∈	∈	PROPN
ejpam-5052	212	28	w	w	PROPN
ejpam-5052	212	29	}	}	PUNCT
ejpam-5052	212	30	is	be	AUX
ejpam-5052	212	31	a	a	DET
ejpam-5052	212	32	prime	prime	ADJ
ejpam-5052	212	33	hyperideal	hyperideal	NOUN
ejpam-5052	212	34	of	of	ADP
ejpam-5052	212	35	e	e	NOUN
ejpam-5052	212	36	associated	associate	VERB
ejpam-5052	212	37	to	to	ADP
ejpam-5052	212	38	d.	d.	PROPN
ejpam-5052	212	39	proof	proof	PROPN
ejpam-5052	212	40	.	.	PUNCT
ejpam-5052	213	1	let	let	VERB
ejpam-5052	213	2	z	z	NOUN
ejpam-5052	213	3	,	,	PUNCT
ejpam-5052	213	4	z′	z′	NUM
ejpam-5052	213	5	∈	∈	NOUN
ejpam-5052	213	6	√	√	NUM
ejpam-5052	213	7	w	w	NOUN
ejpam-5052	213	8	.	.	PUNCT
ejpam-5052	214	1	by	by	ADP
ejpam-5052	214	2	the	the	DET
ejpam-5052	214	3	proof	proof	NOUN
ejpam-5052	214	4	of	of	ADP
ejpam-5052	214	5	lemma	lemma	PROPN
ejpam-5052	214	6	3.19	3.19	NUM
ejpam-5052	214	7	in	in	ADP
ejpam-5052	214	8	[	[	X
ejpam-5052	214	9	17	17	NUM
ejpam-5052	214	10	]	]	PUNCT
ejpam-5052	214	11	,	,	PUNCT
ejpam-5052	214	12	z	z	PROPN
ejpam-5052	214	13	⊕	⊕	PROPN
ejpam-5052	214	14	z′	z′	NUM
ejpam-5052	214	15	⊆	⊆	NUM
ejpam-5052	214	16	√	√	PROPN
ejpam-5052	214	17	w	w	NOUN
ejpam-5052	214	18	and	and	CCONJ
ejpam-5052	214	19	⊖z	⊖z	ADV
ejpam-5052	214	20	∈	∈	PROPN
ejpam-5052	214	21	√	√	PROPN
ejpam-5052	214	22	w	w	NOUN
ejpam-5052	214	23	.	.	PUNCT
ejpam-5052	215	1	also	also	ADV
ejpam-5052	215	2	,	,	PUNCT
ejpam-5052	215	3	for	for	ADP
ejpam-5052	215	4	any	any	DET
ejpam-5052	215	5	t	t	NOUN
ejpam-5052	215	6	∈	∈	PROPN
ejpam-5052	215	7	e	e	NOUN
ejpam-5052	215	8	,	,	PUNCT
ejpam-5052	215	9	t⊙	t⊙	PROPN
ejpam-5052	215	10	z	z	PROPN
ejpam-5052	215	11	,	,	PUNCT
ejpam-5052	215	12	z	z	PROPN
ejpam-5052	215	13	⊙	⊙	PROPN
ejpam-5052	215	14	t	t	PROPN
ejpam-5052	215	15	∈	∈	PROPN
ejpam-5052	215	16	√	√	PROPN
ejpam-5052	215	17	w	w	NOUN
ejpam-5052	215	18	.	.	PUNCT
ejpam-5052	216	1	now	now	ADV
ejpam-5052	216	2	,	,	PUNCT
ejpam-5052	216	3	let	let	VERB
ejpam-5052	216	4	q	q	PROPN
ejpam-5052	216	5	∈	∈	PROPN
ejpam-5052	216	6	(	(	PUNCT
ejpam-5052	216	7	√	√	PROPN
ejpam-5052	216	8	w	w	ADP
ejpam-5052	216	9	]	]	PUNCT
ejpam-5052	216	10	.	.	PUNCT
ejpam-5052	217	1	then	then	ADV
ejpam-5052	217	2	q	q	X
ejpam-5052	217	3	≤	≤	ADJ
ejpam-5052	217	4	z	z	NOUN
ejpam-5052	217	5	for	for	ADP
ejpam-5052	217	6	some	some	DET
ejpam-5052	217	7	z	z	NOUN
ejpam-5052	217	8	∈	∈	PROPN
ejpam-5052	217	9	√	√	PROPN
ejpam-5052	217	10	w	w	NOUN
ejpam-5052	217	11	.	.	PUNCT
ejpam-5052	218	1	as	as	SCONJ
ejpam-5052	218	2	z	z	PROPN
ejpam-5052	218	3	∈	∈	PROPN
ejpam-5052	218	4	√	√	PROPN
ejpam-5052	218	5	w	w	NOUN
ejpam-5052	218	6	,	,	PUNCT
ejpam-5052	218	7	∃n	∃n	PROPN
ejpam-5052	218	8	∈	∈	PROPN
ejpam-5052	218	9	n	n	PRON
ejpam-5052	218	10	such	such	ADJ
ejpam-5052	218	11	that	that	SCONJ
ejpam-5052	218	12	zn	zn	PROPN
ejpam-5052	218	13	∈	∈	PROPN
ejpam-5052	218	14	w	w	PROPN
ejpam-5052	218	15	.	.	PUNCT
ejpam-5052	218	16	r.	r.	PROPN
ejpam-5052	218	17	cai	cai	PROPN
ejpam-5052	218	18	,	,	PUNCT
ejpam-5052	218	19	m.	m.	NOUN
ejpam-5052	218	20	alsaeedi	alsaeedi	PROPN
ejpam-5052	218	21	,	,	PUNCT
ejpam-5052	218	22	m.	m.	NOUN
ejpam-5052	218	23	akhoundi	akhoundi	PROPN
ejpam-5052	218	24	/	/	SYM
ejpam-5052	218	25	eur	eur	PROPN
ejpam-5052	218	26	.	.	PUNCT
ejpam-5052	219	1	j.	j.	PROPN
ejpam-5052	219	2	pure	pure	PROPN
ejpam-5052	219	3	appl	appl	PROPN
ejpam-5052	219	4	.	.	PROPN
ejpam-5052	219	5	math	math	PROPN
ejpam-5052	219	6	,	,	PUNCT
ejpam-5052	219	7	17	17	NUM
ejpam-5052	219	8	(	(	PUNCT
ejpam-5052	219	9	2	2	NUM
ejpam-5052	219	10	)	)	PUNCT
ejpam-5052	219	11	(	(	PUNCT
ejpam-5052	219	12	2024	2024	NUM
ejpam-5052	219	13	)	)	PUNCT
ejpam-5052	219	14	,	,	PUNCT
ejpam-5052	219	15	604	604	NUM
ejpam-5052	219	16	-	-	SYM
ejpam-5052	219	17	615	615	NUM
ejpam-5052	219	18	612	612	NUM
ejpam-5052	219	19	since	since	SCONJ
ejpam-5052	219	20	q	q	PROPN
ejpam-5052	219	21	≤	≤	PROPN
ejpam-5052	219	22	z	z	NOUN
ejpam-5052	219	23	,	,	PUNCT
ejpam-5052	219	24	we	we	PRON
ejpam-5052	219	25	get	get	VERB
ejpam-5052	219	26	qn	qn	PRON
ejpam-5052	219	27	≤	≤	NUM
ejpam-5052	219	28	zn	zn	NOUN
ejpam-5052	219	29	∈	∈	PROPN
ejpam-5052	219	30	w	w	PROPN
ejpam-5052	219	31	.	.	PUNCT
ejpam-5052	220	1	thus	thus	ADV
ejpam-5052	220	2	,	,	PUNCT
ejpam-5052	220	3	qn	qn	PROPN
ejpam-5052	220	4	∈	∈	PROPN
ejpam-5052	220	5	w	w	PROPN
ejpam-5052	220	6	.	.	PUNCT
ejpam-5052	221	1	so	so	ADV
ejpam-5052	221	2	,	,	PUNCT
ejpam-5052	221	3	q	q	PROPN
ejpam-5052	221	4	∈	∈	PROPN
ejpam-5052	221	5	√	√	PROPN
ejpam-5052	221	6	w	w	NOUN
ejpam-5052	221	7	and	and	CCONJ
ejpam-5052	221	8	hence	hence	ADV
ejpam-5052	221	9	(	(	PUNCT
ejpam-5052	221	10	√	√	PROPN
ejpam-5052	221	11	w	w	NOUN
ejpam-5052	221	12	]	]	PUNCT
ejpam-5052	221	13	⊆	⊆	NUM
ejpam-5052	221	14	√	√	NUM
ejpam-5052	221	15	w	w	NOUN
ejpam-5052	221	16	.	.	PUNCT
ejpam-5052	222	1	let	let	VERB
ejpam-5052	222	2	g	g	PROPN
ejpam-5052	222	3	⊙	⊙	PROPN
ejpam-5052	222	4	g′	g′	PROPN
ejpam-5052	222	5	∈	∈	PROPN
ejpam-5052	223	1	√	√	PROPN
ejpam-5052	223	2	w	w	NOUN
ejpam-5052	223	3	and	and	CCONJ
ejpam-5052	223	4	g	g	PROPN
ejpam-5052	223	5	/∈	/∈	PROPN
ejpam-5052	224	1	√	√	PROPN
ejpam-5052	224	2	w	w	NOUN
ejpam-5052	224	3	for	for	ADP
ejpam-5052	224	4	g	g	NOUN
ejpam-5052	224	5	,	,	PUNCT
ejpam-5052	224	6	g′	g′	PROPN
ejpam-5052	224	7	∈	∈	PROPN
ejpam-5052	224	8	e.	e.	PROPN
ejpam-5052	224	9	claim	claim	NOUN
ejpam-5052	224	10	:	:	PUNCT
ejpam-5052	224	11	d(g′	d(g′	X
ejpam-5052	224	12	)	)	PUNCT
ejpam-5052	224	13	∈	∈	PROPN
ejpam-5052	224	14	√	√	NUM
ejpam-5052	224	15	w	w	NOUN
ejpam-5052	224	16	.	.	PUNCT
ejpam-5052	225	1	as	as	SCONJ
ejpam-5052	225	2	g	g	PROPN
ejpam-5052	225	3	⊙	⊙	PROPN
ejpam-5052	225	4	g′	g′	PROPN
ejpam-5052	225	5	∈	∈	PROPN
ejpam-5052	225	6	√	√	PROPN
ejpam-5052	225	7	w	w	NOUN
ejpam-5052	225	8	,	,	PUNCT
ejpam-5052	225	9	∃n	∃n	PROPN
ejpam-5052	225	10	∈	∈	PROPN
ejpam-5052	225	11	n	n	PRON
ejpam-5052	225	12	such	such	ADJ
ejpam-5052	225	13	that	that	PRON
ejpam-5052	225	14	(	(	PUNCT
ejpam-5052	225	15	g	g	PROPN
ejpam-5052	225	16	⊙	⊙	PROPN
ejpam-5052	225	17	g′)n	g′)n	PROPN
ejpam-5052	225	18	∈	∈	PROPN
ejpam-5052	225	19	w	w	PROPN
ejpam-5052	225	20	.	.	PUNCT
ejpam-5052	226	1	so	so	ADV
ejpam-5052	226	2	,	,	PUNCT
ejpam-5052	226	3	gn	gn	PROPN
ejpam-5052	226	4	⊙	⊙	PROPN
ejpam-5052	226	5	g′n	g′n	PROPN
ejpam-5052	227	1	∈	∈	PROPN
ejpam-5052	228	1	w	w	PROPN
ejpam-5052	228	2	.	.	PUNCT
ejpam-5052	229	1	as	as	SCONJ
ejpam-5052	229	2	w	w	PROPN
ejpam-5052	229	3	is	be	AUX
ejpam-5052	229	4	a	a	DET
ejpam-5052	229	5	prime	prime	ADJ
ejpam-5052	229	6	hyperideal	hyperideal	NOUN
ejpam-5052	229	7	associated	associate	VERB
ejpam-5052	229	8	to	to	ADP
ejpam-5052	229	9	d	d	PROPN
ejpam-5052	229	10	and	and	CCONJ
ejpam-5052	229	11	gn	gn	INTJ
ejpam-5052	229	12	/∈	/∈	PUNCT
ejpam-5052	230	1	w	w	PROPN
ejpam-5052	230	2	,	,	PUNCT
ejpam-5052	230	3	d(g′n	d(g′n	PROPN
ejpam-5052	230	4	)	)	PUNCT
ejpam-5052	230	5	∈	∈	PROPN
ejpam-5052	230	6	w	w	PROPN
ejpam-5052	230	7	.	.	PUNCT
ejpam-5052	231	1	since	since	SCONJ
ejpam-5052	231	2	d	d	PROPN
ejpam-5052	231	3	is	be	AUX
ejpam-5052	231	4	a	a	DET
ejpam-5052	231	5	homomorphism	homomorphism	NOUN
ejpam-5052	231	6	of	of	ADP
ejpam-5052	231	7	t	t	PROPN
ejpam-5052	231	8	,	,	PUNCT
ejpam-5052	231	9	we	we	PRON
ejpam-5052	231	10	obtain	obtain	VERB
ejpam-5052	231	11	(	(	PUNCT
ejpam-5052	231	12	d(g′))n	d(g′))n	X
ejpam-5052	231	13	=	=	SYM
ejpam-5052	231	14	d(g′n	d(g′n	NOUN
ejpam-5052	231	15	)	)	PUNCT
ejpam-5052	231	16	∈	∈	PROPN
ejpam-5052	231	17	w	w	PROPN
ejpam-5052	231	18	.	.	PUNCT
ejpam-5052	232	1	thus	thus	ADV
ejpam-5052	232	2	,	,	PUNCT
ejpam-5052	232	3	d(g′	d(g′	PROPN
ejpam-5052	232	4	)	)	PUNCT
ejpam-5052	232	5	∈	∈	PROPN
ejpam-5052	232	6	√	√	NUM
ejpam-5052	232	7	w	w	NOUN
ejpam-5052	232	8	.	.	PUNCT
ejpam-5052	233	1	so	so	ADV
ejpam-5052	233	2	,	,	PUNCT
ejpam-5052	233	3	√	√	PROPN
ejpam-5052	233	4	w	w	NOUN
ejpam-5052	233	5	is	be	AUX
ejpam-5052	233	6	a	a	DET
ejpam-5052	233	7	prime	prime	ADJ
ejpam-5052	233	8	hyperideal	hyperideal	NOUN
ejpam-5052	233	9	associated	associate	VERB
ejpam-5052	233	10	to	to	ADP
ejpam-5052	233	11	d.	d.	PROPN
ejpam-5052	233	12	let	let	VERB
ejpam-5052	233	13	ω	ω	NUM
ejpam-5052	233	14	be	be	AUX
ejpam-5052	233	15	an	an	DET
ejpam-5052	233	16	index	index	NOUN
ejpam-5052	233	17	set	set	VERB
ejpam-5052	233	18	and	and	CCONJ
ejpam-5052	233	19	(	(	PUNCT
ejpam-5052	233	20	ti,⊕i,⊙i,≤i	ti,⊕i,⊙i,≤i	NOUN
ejpam-5052	233	21	)	)	PUNCT
ejpam-5052	233	22	∈	∈	NOUN
ejpam-5052	233	23	okh	okh	NOUN
ejpam-5052	233	24	,	,	PUNCT
ejpam-5052	233	25	for	for	ADP
ejpam-5052	233	26	all	all	DET
ejpam-5052	233	27	i	i	PRON
ejpam-5052	233	28	∈	∈	PROPN
ejpam-5052	233	29	ω	ω	X
ejpam-5052	233	30	.	.	PUNCT
ejpam-5052	234	1	then,∏	then,∏	VERB
ejpam-5052	234	2	i∈ω	i∈ω	NOUN
ejpam-5052	234	3	ti	ti	NOUN
ejpam-5052	234	4	=	=	SYM
ejpam-5052	234	5	{	{	PUNCT
ejpam-5052	234	6	(	(	PUNCT
ejpam-5052	234	7	ti)i∈ω	ti)i∈ω	NUM
ejpam-5052	234	8	|	|	CCONJ
ejpam-5052	234	9	ti	ti	NOUN
ejpam-5052	234	10	∈	∈	NOUN
ejpam-5052	234	11	ti	ti	NOUN
ejpam-5052	234	12	}	}	PUNCT
ejpam-5052	234	13	∈	∈	NOUN
ejpam-5052	234	14	okh	okh	NOUN
ejpam-5052	234	15	.	.	PUNCT
ejpam-5052	235	1	indeed	indeed	ADV
ejpam-5052	235	2	:	:	PUNCT
ejpam-5052	235	3	for	for	ADP
ejpam-5052	235	4	any	any	DET
ejpam-5052	235	5	(	(	PUNCT
ejpam-5052	235	6	wi)i∈ω	wi)i∈ω	NOUN
ejpam-5052	235	7	,	,	PUNCT
ejpam-5052	235	8	(	(	PUNCT
ejpam-5052	235	9	w	w	PROPN
ejpam-5052	235	10	′	′	NUM
ejpam-5052	235	11	i)i∈ω	i)i∈ω	PROPN
ejpam-5052	235	12	∈	∈	PROPN
ejpam-5052	235	13	∏	∏	PROPN
ejpam-5052	235	14	i∈ω	i∈ω	NOUN
ejpam-5052	235	15	ti	ti	PROPN
ejpam-5052	235	16	,	,	PUNCT
ejpam-5052	235	17	(	(	PUNCT
ejpam-5052	235	18	i	i	NOUN
ejpam-5052	235	19	)	)	PUNCT
ejpam-5052	235	20	(	(	PUNCT
ejpam-5052	235	21	wi)i∈ω	wi)i∈ω	PROPN
ejpam-5052	235	22	⊕	⊕	PROPN
ejpam-5052	235	23	(	(	PUNCT
ejpam-5052	235	24	w′	w′	PROPN
ejpam-5052	235	25	i)i∈ω	i)i∈ω	PROPN
ejpam-5052	235	26	=	=	SYM
ejpam-5052	235	27	{	{	PUNCT
ejpam-5052	235	28	(	(	PUNCT
ejpam-5052	235	29	ti)i∈ω	ti)i∈ω	NUM
ejpam-5052	235	30	|	|	ADV
ejpam-5052	235	31	ti	ti	NOUN
ejpam-5052	235	32	∈	∈	PROPN
ejpam-5052	235	33	wi	wi	PROPN
ejpam-5052	235	34	⊕i	⊕i	VERB
ejpam-5052	236	1	w	w	ADP
ejpam-5052	236	2	′	′	NUM
ejpam-5052	236	3	i	i	PROPN
ejpam-5052	236	4	}	}	PUNCT
ejpam-5052	236	5	;	;	PUNCT
ejpam-5052	236	6	(	(	PUNCT
ejpam-5052	236	7	ii	ii	NOUN
ejpam-5052	236	8	)	)	PUNCT
ejpam-5052	236	9	(	(	PUNCT
ejpam-5052	236	10	wi)i∈ω	wi)i∈ω	PROPN
ejpam-5052	236	11	⊙	⊙	NOUN
ejpam-5052	236	12	(	(	PUNCT
ejpam-5052	236	13	w′	w′	PROPN
ejpam-5052	236	14	i)i∈ω	i)i∈ω	PROPN
ejpam-5052	236	15	=	=	SYM
ejpam-5052	236	16	(	(	PUNCT
ejpam-5052	236	17	wi	wi	PROPN
ejpam-5052	236	18	⊙i	⊙i	PROPN
ejpam-5052	236	19	w	w	PROPN
ejpam-5052	236	20	′	′	NUM
ejpam-5052	236	21	i)i∈ω	i)i∈ω	NUM
ejpam-5052	236	22	;	;	PUNCT
ejpam-5052	236	23	(	(	PUNCT
ejpam-5052	236	24	iii	iii	X
ejpam-5052	236	25	)	)	PUNCT
ejpam-5052	236	26	(	(	PUNCT
ejpam-5052	236	27	wi)i∈ω	wi)i∈ω	NOUN
ejpam-5052	236	28	≤	≤	NOUN
ejpam-5052	236	29	(	(	PUNCT
ejpam-5052	236	30	w′	w′	PROPN
ejpam-5052	236	31	i)i∈ω	i)i∈ω	PROPN
ejpam-5052	236	32	⇔	⇔	PROPN
ejpam-5052	236	33	wi	wi	PROPN
ejpam-5052	236	34	≤i	≤i	PROPN
ejpam-5052	237	1	w	w	PROPN
ejpam-5052	237	2	′	′	NUM
ejpam-5052	238	1	i	i	NOUN
ejpam-5052	238	2	,	,	PUNCT
ejpam-5052	238	3	∀i	∀i	X
ejpam-5052	238	4	∈	∈	PROPN
ejpam-5052	238	5	ω	ω	NOUN
ejpam-5052	238	6	.	.	PUNCT
ejpam-5052	238	7	define	define	VERB
ejpam-5052	238	8	the	the	DET
ejpam-5052	238	9	map	map	NOUN
ejpam-5052	238	10	πi	πi	ADP
ejpam-5052	238	11	:	:	PUNCT
ejpam-5052	238	12	∏	∏	NUM
ejpam-5052	238	13	i∈ω	i∈ω	NOUN
ejpam-5052	238	14	ti	ti	NOUN
ejpam-5052	238	15	→	→	SYM
ejpam-5052	238	16	ti	ti	NOUN
ejpam-5052	238	17	by	by	ADP
ejpam-5052	238	18	πi((wi)i∈ω	πi((wi)i∈ω	PROPN
ejpam-5052	238	19	)	)	PUNCT
ejpam-5052	238	20	=	=	SYM
ejpam-5052	238	21	wi	wi	PROPN
ejpam-5052	238	22	,	,	PUNCT
ejpam-5052	238	23	for	for	ADP
ejpam-5052	238	24	each	each	PRON
ejpam-5052	238	25	(	(	PUNCT
ejpam-5052	238	26	wi)i∈ω	wi)i∈ω	PROPN
ejpam-5052	238	27	∈	∈	PROPN
ejpam-5052	238	28	∏	∏	PROPN
ejpam-5052	238	29	i∈ω	i∈ω	NOUN
ejpam-5052	238	30	ti	ti	NOUN
ejpam-5052	238	31	and	and	CCONJ
ejpam-5052	238	32	i	i	PROPN
ejpam-5052	238	33	∈	∈	PROPN
ejpam-5052	238	34	ω	ω	X
ejpam-5052	238	35	and	and	CCONJ
ejpam-5052	238	36	define	define	VERB
ejpam-5052	238	37	the	the	DET
ejpam-5052	238	38	map	map	NOUN
ejpam-5052	239	1	ρi	ρi	INTJ
ejpam-5052	239	2	:	:	PUNCT
ejpam-5052	239	3	ti	ti	PROPN
ejpam-5052	239	4	→	→	SYM
ejpam-5052	239	5	∏	∏	X
ejpam-5052	239	6	i∈ω	i∈ω	NOUN
ejpam-5052	239	7	ti	ti	NOUN
ejpam-5052	239	8	by	by	ADP
ejpam-5052	239	9	(	(	PUNCT
ejpam-5052	239	10	ρi(t))(j	ρi(t))(j	NOUN
ejpam-5052	239	11	)	)	PUNCT
ejpam-5052	239	12	=	=	PUNCT
ejpam-5052	240	1			NOUN
ejpam-5052	240	2	t	t	PROPN
ejpam-5052	240	3	,	,	PUNCT
ejpam-5052	240	4	if	if	SCONJ
ejpam-5052	240	5	i	i	PRON
ejpam-5052	240	6	=	=	SYM
ejpam-5052	240	7	j	j	PROPN
ejpam-5052	240	8	0j	0j	NOUN
ejpam-5052	240	9	,	,	PUNCT
ejpam-5052	240	10	otherwise	otherwise	ADV
ejpam-5052	240	11	for	for	ADP
ejpam-5052	240	12	each	each	DET
ejpam-5052	240	13	t	t	NOUN
ejpam-5052	240	14	∈	∈	PROPN
ejpam-5052	240	15	ti	ti	X
ejpam-5052	240	16	.	.	PUNCT
ejpam-5052	240	17	theorem	theorem	NOUN
ejpam-5052	240	18	7	7	NUM
ejpam-5052	240	19	.	.	PUNCT
ejpam-5052	241	1	let	let	VERB
ejpam-5052	241	2	ω	ω	NUM
ejpam-5052	241	3	be	be	AUX
ejpam-5052	241	4	an	an	DET
ejpam-5052	241	5	index	index	NOUN
ejpam-5052	241	6	set	set	VERB
ejpam-5052	241	7	and	and	CCONJ
ejpam-5052	241	8	(	(	PUNCT
ejpam-5052	241	9	ti,⊕i,⊙i,≤i	ti,⊕i,⊙i,≤i	NOUN
ejpam-5052	241	10	)	)	PUNCT
ejpam-5052	241	11	∈	∈	NOUN
ejpam-5052	241	12	okh	okh	NOUN
ejpam-5052	241	13	,	,	PUNCT
ejpam-5052	241	14	for	for	ADP
ejpam-5052	241	15	all	all	PRON
ejpam-5052	242	1	i	i	PRON
ejpam-5052	242	2	∈	∈	PROPN
ejpam-5052	242	3	ω	ω	INTJ
ejpam-5052	242	4	.	.	PUNCT
ejpam-5052	243	1	if	if	SCONJ
ejpam-5052	243	2	d	d	PROPN
ejpam-5052	243	3	∈	∈	PROPN
ejpam-5052	243	4	der	der	NOUN
ejpam-5052	243	5	(	(	PUNCT
ejpam-5052	243	6	∏	∏	PROPN
ejpam-5052	243	7	i∈ω	i∈ω	NOUN
ejpam-5052	243	8	ti	ti	NOUN
ejpam-5052	243	9	)	)	PUNCT
ejpam-5052	243	10	,	,	PUNCT
ejpam-5052	243	11	then	then	ADV
ejpam-5052	243	12	di	di	X
ejpam-5052	243	13	=	=	NOUN
ejpam-5052	243	14	πidρi	πidρi	PROPN
ejpam-5052	243	15	∈	∈	PROPN
ejpam-5052	243	16	der(ti	der(ti	NOUN
ejpam-5052	243	17	)	)	PUNCT
ejpam-5052	243	18	,	,	PUNCT
ejpam-5052	243	19	for	for	ADP
ejpam-5052	243	20	all	all	PRON
ejpam-5052	243	21	i	i	PRON
ejpam-5052	243	22	∈	∈	PROPN
ejpam-5052	243	23	ω	ω	PROPN
ejpam-5052	243	24	.	.	PUNCT
ejpam-5052	243	25	r.	r.	PROPN
ejpam-5052	243	26	cai	cai	PROPN
ejpam-5052	243	27	,	,	PUNCT
ejpam-5052	243	28	m.	m.	NOUN
ejpam-5052	243	29	alsaeedi	alsaeedi	PROPN
ejpam-5052	243	30	,	,	PUNCT
ejpam-5052	243	31	m.	m.	NOUN
ejpam-5052	243	32	akhoundi	akhoundi	PROPN
ejpam-5052	243	33	/	/	SYM
ejpam-5052	243	34	eur	eur	PROPN
ejpam-5052	243	35	.	.	PUNCT
ejpam-5052	244	1	j.	j.	PROPN
ejpam-5052	244	2	pure	pure	PROPN
ejpam-5052	244	3	appl	appl	PROPN
ejpam-5052	244	4	.	.	PROPN
ejpam-5052	244	5	math	math	PROPN
ejpam-5052	244	6	,	,	PUNCT
ejpam-5052	244	7	17	17	NUM
ejpam-5052	244	8	(	(	PUNCT
ejpam-5052	244	9	2	2	NUM
ejpam-5052	244	10	)	)	PUNCT
ejpam-5052	244	11	(	(	PUNCT
ejpam-5052	244	12	2024	2024	NUM
ejpam-5052	244	13	)	)	PUNCT
ejpam-5052	244	14	,	,	PUNCT
ejpam-5052	244	15	604	604	NUM
ejpam-5052	244	16	-	-	SYM
ejpam-5052	244	17	615	615	NUM
ejpam-5052	244	18	613	613	NUM
ejpam-5052	244	19	proof	proof	NOUN
ejpam-5052	244	20	.	.	PUNCT
ejpam-5052	245	1	let	let	VERB
ejpam-5052	245	2	d	d	X
ejpam-5052	245	3	∈	∈	PROPN
ejpam-5052	245	4	der	der	NOUN
ejpam-5052	245	5	(	(	PUNCT
ejpam-5052	245	6	∏	∏	PROPN
ejpam-5052	245	7	i∈ω	i∈ω	NOUN
ejpam-5052	245	8	ti	ti	NOUN
ejpam-5052	245	9	)	)	PUNCT
ejpam-5052	245	10	and	and	CCONJ
ejpam-5052	245	11	z	z	NOUN
ejpam-5052	245	12	,	,	PUNCT
ejpam-5052	245	13	z′	z′	PROPN
ejpam-5052	245	14	∈	∈	PROPN
ejpam-5052	245	15	ti	ti	NOUN
ejpam-5052	245	16	,	,	PUNCT
ejpam-5052	245	17	for	for	ADP
ejpam-5052	245	18	all	all	PRON
ejpam-5052	246	1	i	i	PRON
ejpam-5052	246	2	∈	∈	PROPN
ejpam-5052	246	3	ω	ω	X
ejpam-5052	246	4	.	.	PUNCT
ejpam-5052	247	1	then	then	ADV
ejpam-5052	247	2	,	,	PUNCT
ejpam-5052	247	3	di(z	di(z	X
ejpam-5052	247	4	⊕i	⊕i	X
ejpam-5052	247	5	z	z	NOUN
ejpam-5052	247	6	′	′	NOUN
ejpam-5052	247	7	)	)	PUNCT
ejpam-5052	248	1	=	=	PUNCT
ejpam-5052	248	2	πidρi(z	πidρi(z	X
ejpam-5052	248	3	⊕i	⊕i	NOUN
ejpam-5052	248	4	z	z	NOUN
ejpam-5052	248	5	′	′	NOUN
ejpam-5052	248	6	)	)	PUNCT
ejpam-5052	249	1	=	=	PUNCT
ejpam-5052	249	2	πid(ρi(z	πid(ρi(z	NOUN
ejpam-5052	249	3	⊕i	⊕i	NOUN
ejpam-5052	249	4	z	z	NOUN
ejpam-5052	249	5	′	′	NUM
ejpam-5052	249	6	)	)	PUNCT
ejpam-5052	249	7	)	)	PUNCT
ejpam-5052	250	1	=	=	SYM
ejpam-5052	250	2	πi(d(ρi(z)⊕i	πi(d(ρi(z)⊕i	NOUN
ejpam-5052	250	3	ρi(z	ρi(z	PART
ejpam-5052	250	4	′	′	NOUN
ejpam-5052	250	5	)	)	PUNCT
ejpam-5052	250	6	)	)	PUNCT
ejpam-5052	250	7	)	)	PUNCT
ejpam-5052	251	1	⊆	⊆	NUM
ejpam-5052	251	2	πi(d(ρi(z))⊕i	πi(d(ρi(z))⊕i	PROPN
ejpam-5052	251	3	d(ρi(z	d(ρi(z	ADV
ejpam-5052	251	4	′	′	NOUN
ejpam-5052	251	5	)	)	PUNCT
ejpam-5052	251	6	)	)	PUNCT
ejpam-5052	251	7	)	)	PUNCT
ejpam-5052	252	1	=	=	PUNCT
ejpam-5052	252	2	πidρi(z)⊕i	πidρi(z)⊕i	NOUN
ejpam-5052	252	3	πidρi(z	πidρi(z	NUM
ejpam-5052	252	4	′	′	NUM
ejpam-5052	252	5	)	)	PUNCT
ejpam-5052	252	6	=	=	SYM
ejpam-5052	252	7	di(z)⊕i	di(z)⊕i	NUM
ejpam-5052	252	8	di(z	di(z	NOUN
ejpam-5052	252	9	′	′	NUM
ejpam-5052	252	10	)	)	PUNCT
ejpam-5052	252	11	,	,	PUNCT
ejpam-5052	252	12	and	and	CCONJ
ejpam-5052	252	13	di(z	di(z	PUNCT
ejpam-5052	252	14	⊙i	⊙i	PROPN
ejpam-5052	252	15	z	z	NOUN
ejpam-5052	252	16	′	′	NOUN
ejpam-5052	252	17	)	)	PUNCT
ejpam-5052	252	18	=	=	PUNCT
ejpam-5052	253	1	πidρi(z	πidρi(z	NOUN
ejpam-5052	253	2	⊙i	⊙i	PROPN
ejpam-5052	253	3	z	z	NOUN
ejpam-5052	253	4	′	′	NOUN
ejpam-5052	253	5	)	)	PUNCT
ejpam-5052	254	1	=	=	PUNCT
ejpam-5052	254	2	πid(ρi(z	πid(ρi(z	PROPN
ejpam-5052	254	3	⊙i	⊙i	PROPN
ejpam-5052	254	4	z	z	NOUN
ejpam-5052	254	5	′	′	NUM
ejpam-5052	254	6	)	)	PUNCT
ejpam-5052	254	7	)	)	PUNCT
ejpam-5052	255	1	=	=	PUNCT
ejpam-5052	255	2	πi(d(ρi(z)⊙i	πi(d(ρi(z)⊙i	X
ejpam-5052	255	3	ρi(z	ρi(z	X
ejpam-5052	255	4	′	′	NOUN
ejpam-5052	255	5	)	)	PUNCT
ejpam-5052	255	6	)	)	PUNCT
ejpam-5052	255	7	)	)	PUNCT
ejpam-5052	256	1	∈	∈	PROPN
ejpam-5052	256	2	πi((d(ρi(z))⊙i	πi((d(ρi(z))⊙i	PROPN
ejpam-5052	256	3	ρi(z	ρi(z	PUNCT
ejpam-5052	256	4	′))⊕i	′))⊕i	PROPN
ejpam-5052	256	5	(	(	PUNCT
ejpam-5052	256	6	ρi(z)⊙i	ρi(z)⊙i	PROPN
ejpam-5052	256	7	d(ρi(z	d(ρi(z	ADV
ejpam-5052	256	8	′	′	NUM
ejpam-5052	256	9	)	)	PUNCT
ejpam-5052	256	10	)	)	PUNCT
ejpam-5052	256	11	)	)	PUNCT
ejpam-5052	257	1	=	=	PRON
ejpam-5052	257	2	(	(	PUNCT
ejpam-5052	257	3	πidρi(z)⊙i	πidρi(z)⊙i	PROPN
ejpam-5052	257	4	πiρi(z	πiρi(z	ADP
ejpam-5052	257	5	′))⊕i	′))⊕i	ADJ
ejpam-5052	257	6	(	(	PUNCT
ejpam-5052	257	7	πiρi(z)⊙i	πiρi(z)⊙i	PROPN
ejpam-5052	257	8	πidρi(z	πidρi(z	NUM
ejpam-5052	257	9	′	′	NUM
ejpam-5052	257	10	)	)	PUNCT
ejpam-5052	257	11	)	)	PUNCT
ejpam-5052	258	1	=	=	PRON
ejpam-5052	258	2	(	(	PUNCT
ejpam-5052	258	3	πidρi(z)⊙i	πidρi(z)⊙i	PROPN
ejpam-5052	258	4	z	z	NOUN
ejpam-5052	258	5	′)⊕i	′)⊕i	NOUN
ejpam-5052	258	6	(	(	PUNCT
ejpam-5052	258	7	z	z	NOUN
ejpam-5052	258	8	⊙i	⊙i	NOUN
ejpam-5052	258	9	πidρi(z	πidρi(z	NOUN
ejpam-5052	258	10	′	′	NUM
ejpam-5052	258	11	)	)	PUNCT
ejpam-5052	258	12	)	)	PUNCT
ejpam-5052	259	1	=	=	SYM
ejpam-5052	259	2	(	(	PUNCT
ejpam-5052	259	3	di(z)⊙i	di(z)⊙i	PROPN
ejpam-5052	259	4	z	z	PROPN
ejpam-5052	259	5	′)⊕i	′)⊕i	PROPN
ejpam-5052	259	6	(	(	PUNCT
ejpam-5052	259	7	z	z	NOUN
ejpam-5052	259	8	⊙i	⊙i	NOUN
ejpam-5052	259	9	di(z	di(z	ADJ
ejpam-5052	259	10	′	′	NOUN
ejpam-5052	259	11	)	)	PUNCT
ejpam-5052	259	12	)	)	PUNCT
ejpam-5052	259	13	.	.	PUNCT
ejpam-5052	260	1	since	since	SCONJ
ejpam-5052	260	2	d	d	PROPN
ejpam-5052	260	3	∈	∈	PROPN
ejpam-5052	260	4	der	der	NOUN
ejpam-5052	260	5	(	(	PUNCT
ejpam-5052	260	6	∏	∏	PROPN
ejpam-5052	260	7	i∈ω	i∈ω	NOUN
ejpam-5052	260	8	ti	ti	NOUN
ejpam-5052	260	9	)	)	PUNCT
ejpam-5052	260	10	,	,	PUNCT
ejpam-5052	260	11	it	it	PRON
ejpam-5052	260	12	follows	follow	VERB
ejpam-5052	260	13	that	that	SCONJ
ejpam-5052	260	14	d	d	NOUN
ejpam-5052	260	15	is	be	AUX
ejpam-5052	260	16	isotone	isotone	NOUN
ejpam-5052	260	17	.	.	PUNCT
ejpam-5052	261	1	also	also	ADV
ejpam-5052	261	2	,	,	PUNCT
ejpam-5052	261	3	since	since	SCONJ
ejpam-5052	261	4	πi	πi	ADV
ejpam-5052	261	5	and	and	CCONJ
ejpam-5052	261	6	ρi	ρi	PROPN
ejpam-5052	261	7	are	be	AUX
ejpam-5052	261	8	isotone	isotone	NOUN
ejpam-5052	261	9	,	,	PUNCT
ejpam-5052	261	10	we	we	PRON
ejpam-5052	261	11	get	get	VERB
ejpam-5052	261	12	πidρi	πidρi	ADV
ejpam-5052	261	13	is	be	AUX
ejpam-5052	261	14	isotone	isotone	NOUN
ejpam-5052	261	15	.	.	PUNCT
ejpam-5052	262	1	therefore	therefore	ADV
ejpam-5052	262	2	,	,	PUNCT
ejpam-5052	262	3	di	di	PROPN
ejpam-5052	262	4	∈	∈	PROPN
ejpam-5052	262	5	der(ti	der(ti	NOUN
ejpam-5052	262	6	)	)	PUNCT
ejpam-5052	262	7	,	,	PUNCT
ejpam-5052	262	8	for	for	ADP
ejpam-5052	262	9	all	all	PRON
ejpam-5052	262	10	i	i	PRON
ejpam-5052	262	11	∈	∈	PROPN
ejpam-5052	262	12	ω	ω	X
ejpam-5052	262	13	.	.	PUNCT
ejpam-5052	263	1	let	let	VERB
ejpam-5052	263	2	ω	ω	NUM
ejpam-5052	263	3	be	be	AUX
ejpam-5052	263	4	an	an	DET
ejpam-5052	263	5	index	index	NOUN
ejpam-5052	263	6	set	set	NOUN
ejpam-5052	263	7	,	,	PUNCT
ejpam-5052	263	8	(	(	PUNCT
ejpam-5052	263	9	ti,⊕i,⊙i,≤i	ti,⊕i,⊙i,≤i	NOUN
ejpam-5052	263	10	)	)	PUNCT
ejpam-5052	263	11	∈	∈	NOUN
ejpam-5052	263	12	okh	okh	VERB
ejpam-5052	263	13	and	and	CCONJ
ejpam-5052	263	14	di	di	NOUN
ejpam-5052	263	15	∈	∈	PROPN
ejpam-5052	263	16	der(ti	der(ti	NOUN
ejpam-5052	263	17	)	)	PUNCT
ejpam-5052	263	18	,	,	PUNCT
ejpam-5052	263	19	for	for	ADP
ejpam-5052	263	20	all	all	DET
ejpam-5052	263	21	i	i	PRON
ejpam-5052	263	22	∈	∈	PROPN
ejpam-5052	263	23	ω	ω	X
ejpam-5052	263	24	.	.	PUNCT
ejpam-5052	264	1	define∏	define∏	PROPN
ejpam-5052	264	2	i∈ω	i∈ω	PROPN
ejpam-5052	264	3	di	di	NOUN
ejpam-5052	264	4	:	:	PUNCT
ejpam-5052	264	5	∏	∏	NUM
ejpam-5052	264	6	i∈ω	i∈ω	NOUN
ejpam-5052	264	7	ti	ti	PROPN
ejpam-5052	264	8	→	→	SYM
ejpam-5052	264	9	∏	∏	X
ejpam-5052	264	10	i∈ω	i∈ω	NOUN
ejpam-5052	264	11	ti	ti	NOUN
ejpam-5052	264	12	by	by	ADP
ejpam-5052	264	13	(	(	PUNCT
ejpam-5052	264	14	∏	∏	PROPN
ejpam-5052	264	15	i∈ω	i∈ω	NOUN
ejpam-5052	264	16	di)((wi)i∈ω	di)((wi)i∈ω	NOUN
ejpam-5052	264	17	)	)	PUNCT
ejpam-5052	264	18	=	=	SYM
ejpam-5052	264	19	(	(	PUNCT
ejpam-5052	264	20	di(wi))i∈ω	di(wi))i∈ω	PROPN
ejpam-5052	264	21	,	,	PUNCT
ejpam-5052	264	22	for	for	ADP
ejpam-5052	264	23	each	each	DET
ejpam-5052	264	24	(	(	PUNCT
ejpam-5052	264	25	wi)i∈ω	wi)i∈ω	PROPN
ejpam-5052	264	26	∈	∈	PROPN
ejpam-5052	264	27	∏	∏	NUM
ejpam-5052	264	28	i∈ω	i∈ω	NOUN
ejpam-5052	264	29	ti	ti	PROPN
ejpam-5052	264	30	.	.	PROPN
ejpam-5052	264	31	corollary	corollary	ADJ
ejpam-5052	264	32	3	3	NUM
ejpam-5052	264	33	.	.	PUNCT
ejpam-5052	265	1	let	let	VERB
ejpam-5052	265	2	ω	ω	NUM
ejpam-5052	265	3	be	be	AUX
ejpam-5052	265	4	an	an	DET
ejpam-5052	265	5	index	index	NOUN
ejpam-5052	265	6	set	set	VERB
ejpam-5052	265	7	and	and	CCONJ
ejpam-5052	265	8	(	(	PUNCT
ejpam-5052	265	9	ti,⊕i,⊙i,≤i	ti,⊕i,⊙i,≤i	NOUN
ejpam-5052	265	10	)	)	PUNCT
ejpam-5052	265	11	∈	∈	NOUN
ejpam-5052	265	12	okh	okh	NOUN
ejpam-5052	265	13	,	,	PUNCT
ejpam-5052	265	14	for	for	ADP
ejpam-5052	265	15	all	all	PRON
ejpam-5052	266	1	i	i	PRON
ejpam-5052	266	2	∈	∈	PROPN
ejpam-5052	266	3	ω	ω	INTJ
ejpam-5052	266	4	.	.	PUNCT
ejpam-5052	267	1	if	if	SCONJ
ejpam-5052	267	2	d	d	PROPN
ejpam-5052	267	3	∈	∈	PROPN
ejpam-5052	267	4	der	der	NOUN
ejpam-5052	267	5	(	(	PUNCT
ejpam-5052	267	6	∏	∏	PROPN
ejpam-5052	267	7	i∈ω	i∈ω	NOUN
ejpam-5052	267	8	ti	ti	NOUN
ejpam-5052	267	9	)	)	PUNCT
ejpam-5052	267	10	,	,	PUNCT
ejpam-5052	267	11	then	then	ADV
ejpam-5052	267	12	d	d	PROPN
ejpam-5052	267	13	=	=	SYM
ejpam-5052	267	14	∏	∏	NUM
ejpam-5052	267	15	i∈ω	i∈ω	NOUN
ejpam-5052	267	16	πidρi	πidρi	PROPN
ejpam-5052	267	17	iff	iff	PROPN
ejpam-5052	267	18	d	d	PROPN
ejpam-5052	267	19	∈	∈	PROPN
ejpam-5052	267	20	∏	∏	PROPN
ejpam-5052	267	21	i∈ω	i∈ω	NOUN
ejpam-5052	267	22	der(ti	der(ti	NOUN
ejpam-5052	267	23	)	)	PUNCT
ejpam-5052	267	24	.	.	PUNCT
ejpam-5052	268	1	proof	proof	NOUN
ejpam-5052	268	2	.	.	PUNCT
ejpam-5052	269	1	(	(	PUNCT
ejpam-5052	269	2	⇒	⇒	NOUN
ejpam-5052	269	3	):	):	PUNCT
ejpam-5052	269	4	let	let	VERB
ejpam-5052	269	5	d	d	PROPN
ejpam-5052	269	6	∈	∈	PROPN
ejpam-5052	269	7	der	der	NOUN
ejpam-5052	269	8	(	(	PUNCT
ejpam-5052	269	9	∏	∏	PROPN
ejpam-5052	269	10	i∈ω	i∈ω	NOUN
ejpam-5052	269	11	ti	ti	NOUN
ejpam-5052	269	12	)	)	PUNCT
ejpam-5052	269	13	and	and	CCONJ
ejpam-5052	269	14	d	d	NOUN
ejpam-5052	269	15	=	=	SYM
ejpam-5052	269	16	∏	∏	PROPN
ejpam-5052	269	17	i∈ω	i∈ω	NOUN
ejpam-5052	269	18	πidρi	πidρi	NOUN
ejpam-5052	269	19	.	.	PUNCT
ejpam-5052	270	1	by	by	ADP
ejpam-5052	270	2	theorem	theorem	NOUN
ejpam-5052	270	3	7	7	NUM
ejpam-5052	270	4	,	,	PUNCT
ejpam-5052	270	5	we	we	PRON
ejpam-5052	270	6	have	have	VERB
ejpam-5052	270	7	πidρi	πidρi	ADJ
ejpam-5052	270	8	∈	∈	PROPN
ejpam-5052	270	9	der(ti	der(ti	NOUN
ejpam-5052	270	10	)	)	PUNCT
ejpam-5052	270	11	,	,	PUNCT
ejpam-5052	270	12	∀i	∀i	X
ejpam-5052	270	13	∈	∈	PROPN
ejpam-5052	270	14	ω	ω	NOUN
ejpam-5052	270	15	.	.	PUNCT
ejpam-5052	271	1	thus	thus	ADV
ejpam-5052	271	2	,	,	PUNCT
ejpam-5052	271	3	d	d	PROPN
ejpam-5052	271	4	∈	∈	PROPN
ejpam-5052	271	5	∏	∏	PROPN
ejpam-5052	271	6	i∈ω	i∈ω	NOUN
ejpam-5052	271	7	der(ti	der(ti	NOUN
ejpam-5052	271	8	)	)	PUNCT
ejpam-5052	271	9	.	.	PUNCT
ejpam-5052	272	1	references	reference	NOUN
ejpam-5052	272	2	614	614	NUM
ejpam-5052	272	3	(	(	PUNCT
ejpam-5052	272	4	⇐	⇐	ADJ
ejpam-5052	272	5	):	):	PUNCT
ejpam-5052	272	6	let	let	VERB
ejpam-5052	272	7	d	d	X
ejpam-5052	272	8	∈	∈	PROPN
ejpam-5052	272	9	∏	∏	PROPN
ejpam-5052	272	10	i∈ω	i∈ω	NOUN
ejpam-5052	272	11	der(ti	der(ti	NOUN
ejpam-5052	272	12	)	)	PUNCT
ejpam-5052	272	13	and	and	CCONJ
ejpam-5052	272	14	w	w	NOUN
ejpam-5052	272	15	∈	∈	PROPN
ejpam-5052	272	16	ti	ti	NOUN
ejpam-5052	272	17	.	.	PUNCT
ejpam-5052	273	1	then	then	ADV
ejpam-5052	273	2	(	(	PUNCT
ejpam-5052	273	3	πi	πi	PROPN
ejpam-5052	273	4	(	(	PUNCT
ejpam-5052	273	5	∏	∏	NUM
ejpam-5052	273	6	i∈ω	i∈ω	NOUN
ejpam-5052	273	7	di)ρi)(w	di)ρi)(w	NOUN
ejpam-5052	273	8	)	)	PUNCT
ejpam-5052	273	9	=	=	SYM
ejpam-5052	273	10	di(w	di(w	NOUN
ejpam-5052	273	11	)	)	PUNCT
ejpam-5052	273	12	,	,	PUNCT
ejpam-5052	273	13	where	where	SCONJ
ejpam-5052	273	14	di	di	NOUN
ejpam-5052	273	15	∈	∈	PROPN
ejpam-5052	273	16	der(ti	der(ti	NOUN
ejpam-5052	273	17	)	)	PUNCT
ejpam-5052	273	18	.	.	PUNCT
ejpam-5052	274	1	so	so	ADV
ejpam-5052	274	2	,	,	PUNCT
ejpam-5052	274	3	(	(	PUNCT
ejpam-5052	274	4	πi	πi	PROPN
ejpam-5052	274	5	(	(	PUNCT
ejpam-5052	274	6	∏	∏	PROPN
ejpam-5052	274	7	i∈ω	i∈ω	NOUN
ejpam-5052	274	8	di)ρi	di)ρi	PROPN
ejpam-5052	274	9	)	)	PUNCT
ejpam-5052	274	10	=	=	SYM
ejpam-5052	274	11	di	di	NOUN
ejpam-5052	274	12	.	.	PUNCT
ejpam-5052	275	1	thus	thus	ADV
ejpam-5052	275	2	,	,	PUNCT
ejpam-5052	275	3	d	d	PROPN
ejpam-5052	275	4	=	=	SYM
ejpam-5052	275	5	∏	∏	PROPN
ejpam-5052	275	6	i∈ω	i∈ω	NOUN
ejpam-5052	275	7	di	di	NOUN
ejpam-5052	275	8	for	for	ADP
ejpam-5052	275	9	some	some	DET
ejpam-5052	275	10	di	di	NOUN
ejpam-5052	275	11	∈	∈	PROPN
ejpam-5052	275	12	der(ti	der(ti	NOUN
ejpam-5052	275	13	)	)	PUNCT
ejpam-5052	275	14	.	.	PUNCT
ejpam-5052	276	1	hence	hence	ADV
ejpam-5052	276	2	,	,	PUNCT
ejpam-5052	276	3	d	d	PROPN
ejpam-5052	276	4	=	=	SYM
ejpam-5052	276	5	∏	∏	PROPN
ejpam-5052	276	6	i∈ω	i∈ω	NOUN
ejpam-5052	276	7	πidρi	πidρi	NOUN
ejpam-5052	276	8	.	.	PUNCT
ejpam-5052	277	1	4	4	X
ejpam-5052	277	2	.	.	X
ejpam-5052	277	3	conclusions	conclusion	NOUN
ejpam-5052	277	4	this	this	DET
ejpam-5052	277	5	study	study	NOUN
ejpam-5052	277	6	was	be	AUX
ejpam-5052	277	7	conducted	conduct	VERB
ejpam-5052	277	8	to	to	PART
ejpam-5052	277	9	investigate	investigate	VERB
ejpam-5052	277	10	the	the	DET
ejpam-5052	277	11	significant	significant	ADJ
ejpam-5052	277	12	relationship	relationship	NOUN
ejpam-5052	277	13	between	between	ADP
ejpam-5052	277	14	homomorphisms	homomorphism	NOUN
ejpam-5052	277	15	and	and	CCONJ
ejpam-5052	277	16	derivations	derivation	NOUN
ejpam-5052	277	17	in	in	ADP
ejpam-5052	277	18	ordered	order	VERB
ejpam-5052	277	19	hyperrings	hyperring	NOUN
ejpam-5052	277	20	.	.	PUNCT
ejpam-5052	278	1	moreover	moreover	ADV
ejpam-5052	278	2	,	,	PUNCT
ejpam-5052	278	3	we	we	PRON
ejpam-5052	278	4	investigated	investigate	VERB
ejpam-5052	278	5	the	the	DET
ejpam-5052	278	6	relation	relation	NOUN
ejpam-5052	278	7	between	between	ADP
ejpam-5052	278	8	derivations	derivation	NOUN
ejpam-5052	278	9	and	and	CCONJ
ejpam-5052	278	10	hyperideals	hyperideal	NOUN
ejpam-5052	278	11	on	on	ADP
ejpam-5052	278	12	ordered	order	VERB
ejpam-5052	278	13	hyperrings	hyperring	NOUN
ejpam-5052	278	14	with	with	ADP
ejpam-5052	278	15	no	no	DET
ejpam-5052	278	16	zero	zero	NUM
ejpam-5052	278	17	divisors	divisor	NOUN
ejpam-5052	278	18	.	.	PUNCT
ejpam-5052	279	1	furthermore	furthermore	ADV
ejpam-5052	279	2	,	,	PUNCT
ejpam-5052	279	3	we	we	PRON
ejpam-5052	279	4	described	describe	VERB
ejpam-5052	279	5	prime	prime	ADJ
ejpam-5052	279	6	hyperideals	hyperideal	NOUN
ejpam-5052	279	7	associated	associate	VERB
ejpam-5052	279	8	to	to	ADP
ejpam-5052	279	9	derivations	derivation	NOUN
ejpam-5052	279	10	on	on	ADP
ejpam-5052	279	11	ordered	order	VERB
ejpam-5052	279	12	hyperrings	hyperring	NOUN
ejpam-5052	279	13	and	and	CCONJ
ejpam-5052	279	14	derive	derive	VERB
ejpam-5052	279	15	several	several	ADJ
ejpam-5052	279	16	results	result	NOUN
ejpam-5052	279	17	about	about	ADP
ejpam-5052	279	18	homomorphisms	homomorphism	NOUN
ejpam-5052	279	19	and	and	CCONJ
ejpam-5052	279	20	derivations	derivation	NOUN
ejpam-5052	279	21	on	on	ADP
ejpam-5052	279	22	ordered	order	VERB
ejpam-5052	279	23	hyperrings	hyperring	NOUN
ejpam-5052	279	24	.	.	PUNCT
ejpam-5052	280	1	one	one	PRON
ejpam-5052	280	2	can	can	AUX
ejpam-5052	280	3	further	far	ADV
ejpam-5052	280	4	apply	apply	VERB
ejpam-5052	280	5	these	these	DET
ejpam-5052	280	6	notions	notion	NOUN
ejpam-5052	280	7	on	on	ADP
ejpam-5052	280	8	fuzzy	fuzzy	ADJ
ejpam-5052	280	9	prime	prime	ADJ
ejpam-5052	280	10	hyperideals	hyperideal	NOUN
ejpam-5052	280	11	associated	associate	VERB
ejpam-5052	280	12	to	to	ADP
ejpam-5052	280	13	derivations	derivation	NOUN
ejpam-5052	280	14	in	in	ADP
ejpam-5052	280	15	ordered	order	VERB
ejpam-5052	280	16	hyperrings	hyperring	NOUN
ejpam-5052	280	17	.	.	PUNCT
ejpam-5052	281	1	references	reference	NOUN
ejpam-5052	281	2	[	[	X
ejpam-5052	281	3	1	1	NUM
ejpam-5052	281	4	]	]	X
ejpam-5052	281	5	marty	marty	PROPN
ejpam-5052	281	6	,	,	PUNCT
ejpam-5052	281	7	f.	f.	PROPN
ejpam-5052	281	8	sur	sur	PROPN
ejpam-5052	281	9	une	une	PROPN
ejpam-5052	281	10	generalization	generalization	PROPN
ejpam-5052	281	11	de	de	X
ejpam-5052	281	12	la	la	PROPN
ejpam-5052	281	13	notion	notion	PROPN
ejpam-5052	281	14	de	de	X
ejpam-5052	281	15	groupe	groupe	X
ejpam-5052	281	16	;	;	PUNCT
ejpam-5052	281	17	8iem	8iem	NUM
ejpam-5052	281	18	congres	congre	NOUN
ejpam-5052	281	19	math	math	NOUN
ejpam-5052	281	20	.	.	PUNCT
ejpam-5052	282	1	scandinaves	scandinave	NOUN
ejpam-5052	282	2	:	:	PUNCT
ejpam-5052	282	3	stockholm	stockholm	PROPN
ejpam-5052	282	4	,	,	PUNCT
ejpam-5052	282	5	sweden	sweden	PROPN
ejpam-5052	282	6	,	,	PUNCT
ejpam-5052	282	7	1934	1934	NUM
ejpam-5052	282	8	;	;	PUNCT
ejpam-5052	282	9	pp	pp	PROPN
ejpam-5052	282	10	.	.	PUNCT
ejpam-5052	283	1	45–49	45–49	X
ejpam-5052	283	2	.	.	PUNCT
ejpam-5052	284	1	[	[	X
ejpam-5052	284	2	2	2	NUM
ejpam-5052	284	3	]	]	PUNCT
ejpam-5052	284	4	krasner	krasner	NOUN
ejpam-5052	284	5	,	,	PUNCT
ejpam-5052	284	6	m.	m.	NOUN
ejpam-5052	284	7	a	a	DET
ejpam-5052	284	8	class	class	NOUN
ejpam-5052	284	9	of	of	ADP
ejpam-5052	284	10	hyperrings	hyperring	NOUN
ejpam-5052	284	11	and	and	CCONJ
ejpam-5052	284	12	hyperfields	hyperfield	NOUN
ejpam-5052	284	13	.	.	PUNCT
ejpam-5052	285	1	intern	intern	PROPN
ejpam-5052	285	2	.	.	PUNCT
ejpam-5052	286	1	j.	j.	PROPN
ejpam-5052	286	2	math	math	PROPN
ejpam-5052	286	3	.	.	PUNCT
ejpam-5052	287	1	math	math	NOUN
ejpam-5052	287	2	.	.	PUNCT
ejpam-5052	288	1	sci	sci	PROPN
ejpam-5052	288	2	.	.	PROPN
ejpam-5052	288	3	1983	1983	NUM
ejpam-5052	288	4	,	,	PUNCT
ejpam-5052	288	5	6	6	NUM
ejpam-5052	288	6	,	,	PUNCT
ejpam-5052	288	7	307–312	307–312	NUM
ejpam-5052	288	8	.	.	PUNCT
ejpam-5052	289	1	[	[	X
ejpam-5052	289	2	3	3	NUM
ejpam-5052	289	3	]	]	X
ejpam-5052	289	4	heidari	heidari	X
ejpam-5052	289	5	,	,	PUNCT
ejpam-5052	289	6	d.	d.	PROPN
ejpam-5052	289	7	;	;	PUNCT
ejpam-5052	289	8	davvaz	davvaz	PROPN
ejpam-5052	289	9	,	,	PUNCT
ejpam-5052	289	10	b.	b.	PROPN
ejpam-5052	289	11	on	on	ADP
ejpam-5052	289	12	ordered	order	VERB
ejpam-5052	289	13	hyperstructures	hyperstructure	NOUN
ejpam-5052	289	14	.	.	PUNCT
ejpam-5052	290	1	politehn	politehn	PROPN
ejpam-5052	290	2	.	.	PUNCT
ejpam-5052	291	1	univ	univ	PROPN
ejpam-5052	291	2	.	.	PUNCT
ejpam-5052	292	1	bucharest	bucharest	PROPN
ejpam-5052	292	2	sci	sci	PROPN
ejpam-5052	292	3	.	.	PUNCT
ejpam-5052	292	4	bull	bull	PROPN
ejpam-5052	292	5	.	.	PUNCT
ejpam-5052	293	1	ser	ser	PROPN
ejpam-5052	293	2	.	.	PUNCT
ejpam-5052	294	1	a	a	DET
ejpam-5052	294	2	appl	appl	PROPN
ejpam-5052	294	3	.	.	PUNCT
ejpam-5052	294	4	math	math	NOUN
ejpam-5052	294	5	.	.	PUNCT
ejpam-5052	295	1	phys	phy	NOUN
ejpam-5052	295	2	.	.	PUNCT
ejpam-5052	296	1	2011	2011	NUM
ejpam-5052	296	2	,	,	PUNCT
ejpam-5052	296	3	73	73	NUM
ejpam-5052	296	4	,	,	PUNCT
ejpam-5052	296	5	85–96	85–96	NUM
ejpam-5052	296	6	.	.	PUNCT
ejpam-5052	297	1	[	[	X
ejpam-5052	297	2	4	4	NUM
ejpam-5052	297	3	]	]	X
ejpam-5052	297	4	davvaz	davvaz	NOUN
ejpam-5052	297	5	,	,	PUNCT
ejpam-5052	297	6	b.	b.	PROPN
ejpam-5052	297	7	;	;	PUNCT
ejpam-5052	297	8	corsini	corsini	PROPN
ejpam-5052	297	9	,	,	PUNCT
ejpam-5052	297	10	p.	p.	PROPN
ejpam-5052	297	11	;	;	PUNCT
ejpam-5052	297	12	changphas	changphas	PROPN
ejpam-5052	297	13	,	,	PUNCT
ejpam-5052	297	14	t.	t.	NOUN
ejpam-5052	297	15	relationship	relationship	NOUN
ejpam-5052	297	16	between	between	ADP
ejpam-5052	297	17	ordered	order	VERB
ejpam-5052	297	18	semihypergroups	semihypergroup	NOUN
ejpam-5052	297	19	and	and	CCONJ
ejpam-5052	297	20	ordered	order	VERB
ejpam-5052	297	21	semigroups	semigroup	NOUN
ejpam-5052	297	22	by	by	ADP
ejpam-5052	297	23	using	use	VERB
ejpam-5052	297	24	pseudoorder	pseudoorder	NOUN
ejpam-5052	297	25	.	.	PUNCT
ejpam-5052	298	1	eur	eur	PROPN
ejpam-5052	298	2	.	.	PUNCT
ejpam-5052	299	1	j.	j.	PROPN
ejpam-5052	299	2	combin	combin	PROPN
ejpam-5052	299	3	.	.	PROPN
ejpam-5052	300	1	2015	2015	NUM
ejpam-5052	300	2	,	,	PUNCT
ejpam-5052	300	3	44	44	NUM
ejpam-5052	300	4	,	,	PUNCT
ejpam-5052	300	5	208–217	208–217	NUM
ejpam-5052	300	6	.	.	PUNCT
ejpam-5052	301	1	[	[	X
ejpam-5052	301	2	5	5	NUM
ejpam-5052	301	3	]	]	SYM
ejpam-5052	301	4	gu	gu	NOUN
ejpam-5052	301	5	,	,	PUNCT
ejpam-5052	301	6	z.	z.	PROPN
ejpam-5052	301	7	;	;	PUNCT
ejpam-5052	301	8	tang	tang	PROPN
ejpam-5052	301	9	,	,	PUNCT
ejpam-5052	301	10	x.	x.	PROPN
ejpam-5052	301	11	ordered	order	VERB
ejpam-5052	301	12	regular	regular	ADJ
ejpam-5052	301	13	equivalence	equivalence	NOUN
ejpam-5052	301	14	relations	relation	NOUN
ejpam-5052	301	15	on	on	ADP
ejpam-5052	301	16	ordered	order	VERB
ejpam-5052	301	17	semihypergroups	semihypergroup	NOUN
ejpam-5052	301	18	.	.	PUNCT
ejpam-5052	302	1	j.	j.	PROPN
ejpam-5052	302	2	algebra	algebra	PROPN
ejpam-5052	302	3	2016	2016	NUM
ejpam-5052	302	4	,	,	PUNCT
ejpam-5052	302	5	450	450	NUM
ejpam-5052	302	6	,	,	PUNCT
ejpam-5052	302	7	384–397	384–397	NUM
ejpam-5052	302	8	.	.	PUNCT
ejpam-5052	303	1	[	[	X
ejpam-5052	303	2	6	6	NUM
ejpam-5052	303	3	]	]	SYM
ejpam-5052	303	4	tang	tang	PROPN
ejpam-5052	303	5	,	,	PUNCT
ejpam-5052	303	6	j.	j.	PROPN
ejpam-5052	303	7	;	;	PUNCT
ejpam-5052	303	8	feng	feng	PROPN
ejpam-5052	303	9	,	,	PUNCT
ejpam-5052	303	10	x.	x.	PROPN
ejpam-5052	303	11	;	;	PUNCT
ejpam-5052	303	12	davvaz	davvaz	PROPN
ejpam-5052	303	13	,	,	PUNCT
ejpam-5052	303	14	b.	b.	PROPN
ejpam-5052	303	15	;	;	PUNCT
ejpam-5052	303	16	xie	xie	PROPN
ejpam-5052	303	17	,	,	PUNCT
ejpam-5052	303	18	x.y	x.y	PROPN
ejpam-5052	303	19	.	.	PROPN
ejpam-5052	303	20	a	a	DET
ejpam-5052	303	21	further	further	ADJ
ejpam-5052	303	22	study	study	NOUN
ejpam-5052	303	23	on	on	ADP
ejpam-5052	303	24	ordered	order	VERB
ejpam-5052	303	25	regular	regular	ADJ
ejpam-5052	303	26	equivalence	equivalence	NOUN
ejpam-5052	303	27	relations	relation	NOUN
ejpam-5052	303	28	in	in	ADP
ejpam-5052	303	29	ordered	order	VERB
ejpam-5052	303	30	semihypergroups	semihypergroup	NOUN
ejpam-5052	303	31	.	.	PUNCT
ejpam-5052	304	1	open	open	ADJ
ejpam-5052	304	2	math	math	NOUN
ejpam-5052	304	3	.	.	PUNCT
ejpam-5052	305	1	2018	2018	NUM
ejpam-5052	305	2	,	,	PUNCT
ejpam-5052	305	3	16	16	NUM
ejpam-5052	305	4	,	,	PUNCT
ejpam-5052	305	5	168–184	168–184	NUM
ejpam-5052	305	6	.	.	PUNCT
ejpam-5052	306	1	[	[	X
ejpam-5052	306	2	7	7	NUM
ejpam-5052	306	3	]	]	X
ejpam-5052	306	4	al	al	PROPN
ejpam-5052	306	5	-	-	PUNCT
ejpam-5052	306	6	tahan	tahan	PROPN
ejpam-5052	306	7	,	,	PUNCT
ejpam-5052	306	8	m.	m.	NOUN
ejpam-5052	306	9	;	;	PUNCT
ejpam-5052	306	10	davvaz	davvaz	PROPN
ejpam-5052	306	11	,	,	PUNCT
ejpam-5052	306	12	b.	b.	PROPN
ejpam-5052	306	13	on	on	ADP
ejpam-5052	306	14	quasi	quasi	ADJ
ejpam-5052	306	15	-	-	ADJ
ejpam-5052	306	16	ordering	ordering	ADJ
ejpam-5052	306	17	hypergroups	hypergroup	NOUN
ejpam-5052	306	18	,	,	PUNCT
ejpam-5052	306	19	ordered	order	VERB
ejpam-5052	306	20	hyperstructures	hyperstructure	NOUN
ejpam-5052	306	21	and	and	CCONJ
ejpam-5052	306	22	their	their	PRON
ejpam-5052	306	23	applications	application	NOUN
ejpam-5052	306	24	in	in	ADP
ejpam-5052	306	25	genetics	genetic	NOUN
ejpam-5052	306	26	.	.	PUNCT
ejpam-5052	307	1	mathematics	mathematic	NOUN
ejpam-5052	307	2	interdisciplinary	interdisciplinary	ADJ
ejpam-5052	307	3	research	research	NOUN
ejpam-5052	307	4	.	.	PUNCT
ejpam-5052	308	1	2022	2022	NUM
ejpam-5052	308	2	,	,	PUNCT
ejpam-5052	308	3	7	7	NUM
ejpam-5052	308	4	,	,	PUNCT
ejpam-5052	308	5	1–19	1–19	NOUN
ejpam-5052	308	6	.	.	PUNCT
ejpam-5052	309	1	[	[	X
ejpam-5052	309	2	8	8	NUM
ejpam-5052	309	3	]	]	X
ejpam-5052	309	4	posner	posner	NOUN
ejpam-5052	309	5	,	,	PUNCT
ejpam-5052	309	6	e.c	e.c	PROPN
ejpam-5052	309	7	.	.	PROPN
ejpam-5052	309	8	derivations	derivation	NOUN
ejpam-5052	309	9	in	in	ADP
ejpam-5052	309	10	prime	prime	ADJ
ejpam-5052	309	11	rings	ring	NOUN
ejpam-5052	309	12	,	,	PUNCT
ejpam-5052	309	13	proc	proc	NOUN
ejpam-5052	309	14	.	.	PUNCT
ejpam-5052	309	15	am	be	AUX
ejpam-5052	309	16	.	.	PUNCT
ejpam-5052	310	1	math	math	NOUN
ejpam-5052	310	2	.	.	PUNCT
ejpam-5052	311	1	soc	soc	PROPN
ejpam-5052	311	2	.	.	PUNCT
ejpam-5052	312	1	1957	1957	NUM
ejpam-5052	312	2	,	,	PUNCT
ejpam-5052	312	3	8	8	NUM
ejpam-5052	312	4	,	,	PUNCT
ejpam-5052	312	5	1093–1100	1093–1100	NUM
ejpam-5052	312	6	.	.	PUNCT
ejpam-5052	313	1	[	[	X
ejpam-5052	313	2	9	9	NUM
ejpam-5052	313	3	]	]	SYM
ejpam-5052	313	4	asokkumar	asokkumar	PROPN
ejpam-5052	313	5	,	,	PUNCT
ejpam-5052	313	6	a.	a.	NOUN
ejpam-5052	313	7	derivations	derivation	NOUN
ejpam-5052	313	8	in	in	ADP
ejpam-5052	313	9	hyperrings	hyperring	NOUN
ejpam-5052	313	10	and	and	CCONJ
ejpam-5052	313	11	prime	prime	ADJ
ejpam-5052	313	12	hyperrings	hyperring	NOUN
ejpam-5052	313	13	.	.	PUNCT
ejpam-5052	314	1	iran	iran	PROPN
ejpam-5052	314	2	.	.	PUNCT
ejpam-5052	315	1	j.	j.	PROPN
ejpam-5052	315	2	math	math	PROPN
ejpam-5052	315	3	.	.	PUNCT
ejpam-5052	316	1	sci	sci	PROPN
ejpam-5052	316	2	.	.	PUNCT
ejpam-5052	316	3	inform	inform	NOUN
ejpam-5052	316	4	.	.	PUNCT
ejpam-5052	317	1	2013	2013	NUM
ejpam-5052	317	2	,	,	PUNCT
ejpam-5052	317	3	8	8	NUM
ejpam-5052	317	4	,	,	PUNCT
ejpam-5052	317	5	1–13	1–13	NOUN
ejpam-5052	317	6	.	.	PUNCT
ejpam-5052	318	1	references	reference	NOUN
ejpam-5052	318	2	615	615	NUM
ejpam-5052	318	3	[	[	X
ejpam-5052	318	4	10	10	NUM
ejpam-5052	318	5	]	]	X
ejpam-5052	318	6	kamali	kamali	PROPN
ejpam-5052	318	7	ardekani	ardekani	PROPN
ejpam-5052	318	8	,	,	PUNCT
ejpam-5052	318	9	l.	l.	PROPN
ejpam-5052	318	10	;	;	PUNCT
ejpam-5052	318	11	davvaz	davvaz	PROPN
ejpam-5052	318	12	,	,	PUNCT
ejpam-5052	318	13	b.	b.	PROPN
ejpam-5052	319	1	some	some	DET
ejpam-5052	319	2	notes	note	NOUN
ejpam-5052	319	3	on	on	ADP
ejpam-5052	319	4	differential	differential	ADJ
ejpam-5052	319	5	hyperrings	hyperring	NOUN
ejpam-5052	319	6	,	,	PUNCT
ejpam-5052	319	7	iran	iran	PROPN
ejpam-5052	319	8	.	.	PUNCT
ejpam-5052	320	1	j.	j.	PROPN
ejpam-5052	320	2	sci	sci	PROPN
ejpam-5052	320	3	.	.	PROPN
ejpam-5052	320	4	technol	technol	PROPN
ejpam-5052	320	5	.	.	PUNCT
ejpam-5052	320	6	trans	trans	PROPN
ejpam-5052	320	7	.	.	PUNCT
ejpam-5052	321	1	a	a	DET
ejpam-5052	321	2	sci	sci	PROPN
ejpam-5052	321	3	.	.	PROPN
ejpam-5052	321	4	2015	2015	NUM
ejpam-5052	321	5	,	,	PUNCT
ejpam-5052	321	6	39(1	39(1	NUM
ejpam-5052	321	7	)	)	PUNCT
ejpam-5052	321	8	,	,	PUNCT
ejpam-5052	321	9	101–111	101–111	NUM
ejpam-5052	321	10	.	.	PUNCT
ejpam-5052	322	1	[	[	X
ejpam-5052	322	2	11	11	NUM
ejpam-5052	322	3	]	]	SYM
ejpam-5052	322	4	rao	rao	NOUN
ejpam-5052	322	5	,	,	PUNCT
ejpam-5052	322	6	y.	y.	PROPN
ejpam-5052	322	7	;	;	PUNCT
ejpam-5052	322	8	kosari	kosari	X
ejpam-5052	322	9	,	,	PUNCT
ejpam-5052	322	10	s.	s.	PROPN
ejpam-5052	322	11	;	;	PUNCT
ejpam-5052	322	12	shao	shao	PROPN
ejpam-5052	322	13	,	,	PUNCT
ejpam-5052	322	14	z.	z.	PROPN
ejpam-5052	322	15	;	;	PUNCT
ejpam-5052	322	16	omidi	omidi	PROPN
ejpam-5052	322	17	,	,	PUNCT
ejpam-5052	322	18	s.	s.	PROPN
ejpam-5052	322	19	some	some	DET
ejpam-5052	322	20	properties	property	NOUN
ejpam-5052	322	21	of	of	ADP
ejpam-5052	322	22	derivations	derivation	NOUN
ejpam-5052	322	23	and	and	CCONJ
ejpam-5052	322	24	m	m	NOUN
ejpam-5052	322	25	-	-	PUNCT
ejpam-5052	322	26	khyperideals	khyperideal	NOUN
ejpam-5052	322	27	in	in	ADP
ejpam-5052	322	28	ordered	order	VERB
ejpam-5052	322	29	semihyperrings	semihyperring	NOUN
ejpam-5052	322	30	.	.	PUNCT
ejpam-5052	323	1	politehn	politehn	PROPN
ejpam-5052	323	2	.	.	PUNCT
ejpam-5052	324	1	univ	univ	PROPN
ejpam-5052	324	2	.	.	PUNCT
ejpam-5052	325	1	bucharest	bucharest	PROPN
ejpam-5052	325	2	sci	sci	PROPN
ejpam-5052	325	3	.	.	PUNCT
ejpam-5052	325	4	bull	bull	PROPN
ejpam-5052	325	5	.	.	PUNCT
ejpam-5052	326	1	ser	ser	PROPN
ejpam-5052	326	2	.	.	PUNCT
ejpam-5052	327	1	a	a	DET
ejpam-5052	327	2	appl	appl	PROPN
ejpam-5052	327	3	.	.	PUNCT
ejpam-5052	327	4	math	math	NOUN
ejpam-5052	327	5	.	.	PUNCT
ejpam-5052	328	1	phys	phy	NOUN
ejpam-5052	328	2	.	.	PUNCT
ejpam-5052	329	1	2021	2021	NUM
ejpam-5052	329	2	,	,	PUNCT
ejpam-5052	329	3	83	83	NUM
ejpam-5052	329	4	,	,	PUNCT
ejpam-5052	329	5	87–96	87–96	NUM
ejpam-5052	329	6	.	.	PUNCT
ejpam-5052	330	1	[	[	X
ejpam-5052	330	2	12	12	NUM
ejpam-5052	330	3	]	]	PUNCT
ejpam-5052	330	4	omidi	omidi	NOUN
ejpam-5052	330	5	,	,	PUNCT
ejpam-5052	330	6	s.	s.	PROPN
ejpam-5052	330	7	;	;	PUNCT
ejpam-5052	330	8	davvaz	davvaz	PROPN
ejpam-5052	330	9	,	,	PUNCT
ejpam-5052	330	10	b.	b.	PROPN
ejpam-5052	330	11	ordered	order	VERB
ejpam-5052	330	12	krasner	krasner	PROPN
ejpam-5052	330	13	hyperrings	hyperring	NOUN
ejpam-5052	330	14	,	,	PUNCT
ejpam-5052	330	15	iran	iran	PROPN
ejpam-5052	330	16	.	.	PUNCT
ejpam-5052	331	1	j.	j.	PROPN
ejpam-5052	331	2	math	math	PROPN
ejpam-5052	331	3	.	.	PUNCT
ejpam-5052	332	1	sci	sci	PROPN
ejpam-5052	332	2	.	.	PUNCT
ejpam-5052	332	3	inform	inform	NOUN
ejpam-5052	332	4	.	.	PUNCT
ejpam-5052	333	1	2017	2017	NUM
ejpam-5052	333	2	,	,	PUNCT
ejpam-5052	333	3	12	12	NUM
ejpam-5052	333	4	,	,	PUNCT
ejpam-5052	333	5	35–49	35–49	NUM
ejpam-5052	333	6	.	.	PUNCT
ejpam-5052	334	1	[	[	X
ejpam-5052	334	2	13	13	NUM
ejpam-5052	334	3	]	]	SYM
ejpam-5052	334	4	kosari	kosari	X
ejpam-5052	334	5	,	,	PUNCT
ejpam-5052	334	6	s.	s.	PROPN
ejpam-5052	334	7	;	;	PUNCT
ejpam-5052	334	8	gheisari	gheisari	PROPN
ejpam-5052	334	9	,	,	PUNCT
ejpam-5052	334	10	m.	m.	NOUN
ejpam-5052	334	11	;	;	PUNCT
ejpam-5052	334	12	maedeh	maedeh	ADJ
ejpam-5052	334	13	mirmohseni	mirmohseni	PROPN
ejpam-5052	334	14	,	,	PUNCT
ejpam-5052	334	15	s.	s.	PROPN
ejpam-5052	334	16	;	;	PUNCT
ejpam-5052	334	17	zavieh	zavieh	PROPN
ejpam-5052	334	18	,	,	PUNCT
ejpam-5052	334	19	h.	h.	PROPN
ejpam-5052	334	20	;	;	PUNCT
ejpam-5052	334	21	riskhan	riskhan	PROPN
ejpam-5052	334	22	,	,	PUNCT
ejpam-5052	334	23	b.	b.	PROPN
ejpam-5052	334	24	;	;	PUNCT
ejpam-5052	334	25	faizan	faizan	PROPN
ejpam-5052	334	26	khan	khan	PROPN
ejpam-5052	334	27	,	,	PUNCT
ejpam-5052	334	28	m.	m.	NOUN
ejpam-5052	334	29	;	;	PUNCT
ejpam-5052	334	30	liu	liu	PROPN
ejpam-5052	334	31	,	,	PUNCT
ejpam-5052	334	32	y.	y.	PROPN
ejpam-5052	334	33	a	a	DET
ejpam-5052	334	34	survey	survey	NOUN
ejpam-5052	334	35	on	on	ADP
ejpam-5052	334	36	weak	weak	ADJ
ejpam-5052	334	37	pseudoorders	pseudoorder	NOUN
ejpam-5052	334	38	in	in	ADP
ejpam-5052	334	39	ordered	order	VERB
ejpam-5052	334	40	hyperstructures	hyperstructure	NOUN
ejpam-5052	334	41	,	,	PUNCT
ejpam-5052	334	42	artificial	artificial	ADJ
ejpam-5052	334	43	intelligence	intelligence	NOUN
ejpam-5052	334	44	and	and	CCONJ
ejpam-5052	334	45	applications	application	NOUN
ejpam-5052	334	46	.	.	PUNCT
ejpam-5052	335	1	2023	2023	NUM
ejpam-5052	335	2	,	,	PUNCT
ejpam-5052	335	3	1–5	1–5	PROPN
ejpam-5052	335	4	.	.	PUNCT
ejpam-5052	335	5	https://doi.org/10.47852/bonviewaia3202535	https://doi.org/10.47852/bonviewaia3202535	PROPN
ejpam-5052	335	6	.	.	PUNCT
ejpam-5052	336	1	[	[	X
ejpam-5052	336	2	14	14	NUM
ejpam-5052	336	3	]	]	PUNCT
ejpam-5052	336	4	z.	z.	PROPN
ejpam-5052	336	5	shao	shao	PROPN
ejpam-5052	336	6	,	,	PUNCT
ejpam-5052	336	7	x.	x.	PROPN
ejpam-5052	336	8	chen	chen	PROPN
ejpam-5052	336	9	,	,	PUNCT
ejpam-5052	336	10	s.	s.	PROPN
ejpam-5052	336	11	kosari	kosari	PROPN
ejpam-5052	336	12	and	and	CCONJ
ejpam-5052	336	13	s.	s.	PROPN
ejpam-5052	336	14	omidi	omidi	PROPN
ejpam-5052	336	15	,	,	PUNCT
ejpam-5052	336	16	on	on	ADP
ejpam-5052	336	17	some	some	DET
ejpam-5052	336	18	properties	property	NOUN
ejpam-5052	336	19	of	of	ADP
ejpam-5052	336	20	right	right	ADJ
ejpam-5052	336	21	pure	pure	ADJ
ejpam-5052	336	22	(	(	PUNCT
ejpam-5052	336	23	bi	bi	NOUN
ejpam-5052	336	24	-	-	PUNCT
ejpam-5052	336	25	quasi)hyperideals	quasi)hyperideal	NOUN
ejpam-5052	336	26	in	in	ADP
ejpam-5052	336	27	ordered	order	VERB
ejpam-5052	336	28	semihyperrings	semihyperring	NOUN
ejpam-5052	336	29	,	,	PUNCT
ejpam-5052	336	30	politehn	politehn	PROPN
ejpam-5052	336	31	.	.	PUNCT
ejpam-5052	337	1	univ	univ	PROPN
ejpam-5052	337	2	.	.	PUNCT
ejpam-5052	338	1	bucharest	bucharest	PROPN
ejpam-5052	338	2	sci	sci	PROPN
ejpam-5052	338	3	.	.	PUNCT
ejpam-5052	338	4	bull	bull	PROPN
ejpam-5052	338	5	.	.	PUNCT
ejpam-5052	339	1	ser	ser	PROPN
ejpam-5052	339	2	.	.	PUNCT
ejpam-5052	340	1	a	a	DET
ejpam-5052	340	2	appl	appl	PROPN
ejpam-5052	340	3	.	.	PUNCT
ejpam-5052	340	4	math	math	NOUN
ejpam-5052	340	5	.	.	PUNCT
ejpam-5052	341	1	phys	phy	NOUN
ejpam-5052	341	2	.	.	PUNCT
ejpam-5052	342	1	83(4	83(4	NUM
ejpam-5052	342	2	)	)	PUNCT
ejpam-5052	342	3	(	(	PUNCT
ejpam-5052	342	4	2021	2021	NUM
ejpam-5052	342	5	)	)	PUNCT
ejpam-5052	342	6	,	,	PUNCT
ejpam-5052	343	1	95–104	95–104	NOUN
ejpam-5052	343	2	.	.	PUNCT
ejpam-5052	344	1	[	[	X
ejpam-5052	344	2	15	15	NUM
ejpam-5052	344	3	]	]	X
ejpam-5052	344	4	chen	chen	PROPN
ejpam-5052	344	5	,	,	PUNCT
ejpam-5052	344	6	c.	c.	PROPN
ejpam-5052	344	7	;	;	PUNCT
ejpam-5052	344	8	kosari	kosari	PROPN
ejpam-5052	344	9	,	,	PUNCT
ejpam-5052	344	10	s.	s.	PROPN
ejpam-5052	344	11	;	;	PUNCT
ejpam-5052	344	12	omidi	omidi	PROPN
ejpam-5052	344	13	,	,	PUNCT
ejpam-5052	344	14	s.	s.	PROPN
ejpam-5052	344	15	;	;	PUNCT
ejpam-5052	344	16	davvaz	davvaz	PROPN
ejpam-5052	344	17	,	,	PUNCT
ejpam-5052	344	18	b.	b.	PROPN
ejpam-5052	344	19	;	;	PUNCT
ejpam-5052	344	20	akhoundi	akhoundi	ADJ
ejpam-5052	344	21	,	,	PUNCT
ejpam-5052	344	22	m.	m.	NOUN
ejpam-5052	344	23	a	a	DET
ejpam-5052	344	24	study	study	NOUN
ejpam-5052	344	25	on	on	ADP
ejpam-5052	344	26	interior	interior	ADJ
ejpam-5052	344	27	hyperfilters	hyperfilter	NOUN
ejpam-5052	344	28	in	in	ADP
ejpam-5052	344	29	ordered	order	VERB
ejpam-5052	344	30	γ	γ	NOUN
ejpam-5052	344	31	-	-	PUNCT
ejpam-5052	344	32	semihypergroups	semihypergroup	NOUN
ejpam-5052	344	33	,	,	PUNCT
ejpam-5052	344	34	politehn	politehn	PROPN
ejpam-5052	344	35	.	.	PUNCT
ejpam-5052	345	1	univ	univ	PROPN
ejpam-5052	345	2	.	.	PUNCT
ejpam-5052	346	1	bucharest	bucharest	PROPN
ejpam-5052	346	2	sci	sci	PROPN
ejpam-5052	346	3	.	.	PUNCT
ejpam-5052	346	4	bull	bull	PROPN
ejpam-5052	346	5	.	.	PUNCT
ejpam-5052	347	1	ser	ser	PROPN
ejpam-5052	347	2	.	.	PUNCT
ejpam-5052	348	1	a	a	DET
ejpam-5052	348	2	appl	appl	PROPN
ejpam-5052	348	3	.	.	PUNCT
ejpam-5052	348	4	math	math	NOUN
ejpam-5052	348	5	.	.	PUNCT
ejpam-5052	349	1	phys	phy	NOUN
ejpam-5052	349	2	.	.	PUNCT
ejpam-5052	350	1	2022	2022	NUM
ejpam-5052	350	2	,	,	PUNCT
ejpam-5052	350	3	84(1	84(1	NUM
ejpam-5052	350	4	)	)	PUNCT
ejpam-5052	350	5	,	,	PUNCT
ejpam-5052	350	6	71–80	71–80	NUM
ejpam-5052	350	7	.	.	PUNCT
ejpam-5052	351	1	[	[	X
ejpam-5052	351	2	16	16	NUM
ejpam-5052	351	3	]	]	X
ejpam-5052	351	4	rao	rao	PROPN
ejpam-5052	351	5	,	,	PUNCT
ejpam-5052	351	6	y.	y.	PROPN
ejpam-5052	351	7	;	;	PUNCT
ejpam-5052	351	8	kosari	kosari	X
ejpam-5052	351	9	,	,	PUNCT
ejpam-5052	351	10	s.	s.	PROPN
ejpam-5052	351	11	;	;	PUNCT
ejpam-5052	351	12	shao	shao	PROPN
ejpam-5052	351	13	,	,	PUNCT
ejpam-5052	351	14	z.	z.	PROPN
ejpam-5052	351	15	;	;	PUNCT
ejpam-5052	351	16	akhoundi	akhoundi	ADJ
ejpam-5052	351	17	,	,	PUNCT
ejpam-5052	351	18	m.	m.	NOUN
ejpam-5052	351	19	;	;	PUNCT
ejpam-5052	351	20	omidi	omidi	PROPN
ejpam-5052	351	21	,	,	PUNCT
ejpam-5052	351	22	s.	s.	PROPN
ejpam-5052	351	23	a	a	DET
ejpam-5052	351	24	study	study	NOUN
ejpam-5052	351	25	on	on	ADP
ejpam-5052	351	26	a	a	DET
ejpam-5052	351	27	-	-	PUNCT
ejpam-5052	351	28	i	i	NOUN
ejpam-5052	351	29	-	-	PUNCT
ejpam-5052	351	30	γ	γ	NOUN
ejpam-5052	351	31	-	-	PUNCT
ejpam-5052	351	32	hyperideals	hyperideal	NOUN
ejpam-5052	351	33	and	and	CCONJ
ejpam-5052	351	34	(	(	PUNCT
ejpam-5052	351	35	m	m	PROPN
ejpam-5052	351	36	,	,	PUNCT
ejpam-5052	351	37	n)-γ	n)-γ	NOUN
ejpam-5052	351	38	-	-	NOUN
ejpam-5052	351	39	hyperfilters	hyperfilter	NOUN
ejpam-5052	351	40	in	in	ADP
ejpam-5052	351	41	ordered	order	VERB
ejpam-5052	351	42	γ	γ	NOUN
ejpam-5052	351	43	-	-	PUNCT
ejpam-5052	351	44	semihypergroups	semihypergroup	NOUN
ejpam-5052	351	45	.	.	PUNCT
ejpam-5052	351	46	discrete	discrete	ADJ
ejpam-5052	351	47	dyn	dyn	NOUN
ejpam-5052	351	48	.	.	PUNCT
ejpam-5052	352	1	nat	nat	PROPN
ejpam-5052	352	2	.	.	PUNCT
ejpam-5052	353	1	soc	soc	PROPN
ejpam-5052	353	2	.	.	PUNCT
ejpam-5052	354	1	2021	2021	NUM
ejpam-5052	354	2	,	,	PUNCT
ejpam-5052	354	3	10	10	NUM
ejpam-5052	354	4	.	.	PUNCT
ejpam-5052	355	1	[	[	X
ejpam-5052	355	2	17	17	NUM
ejpam-5052	355	3	]	]	X
ejpam-5052	355	4	jun	jun	PROPN
ejpam-5052	355	5	,	,	PUNCT
ejpam-5052	355	6	j.	j.	PROPN
ejpam-5052	355	7	algebraic	algebraic	PROPN
ejpam-5052	355	8	geometry	geometry	NOUN
ejpam-5052	355	9	over	over	ADP
ejpam-5052	355	10	hyperrings	hyperring	NOUN
ejpam-5052	355	11	,	,	PUNCT
ejpam-5052	355	12	adv	adv	PROPN
ejpam-5052	355	13	.	.	PUNCT
ejpam-5052	355	14	math	math	PROPN
ejpam-5052	355	15	.	.	PUNCT
ejpam-5052	356	1	2018	2018	NUM
ejpam-5052	356	2	,	,	PUNCT
ejpam-5052	356	3	323	323	NUM
ejpam-5052	356	4	,	,	PUNCT
ejpam-5052	356	5	142–192	142–192	NUM
ejpam-5052	356	6	.	.	PUNCT