id	sid	tid	token	lemma	pos
ejpam-6141	1	1	european	european	PROPN
ejpam-6141	1	2	journal	journal	PROPN
ejpam-6141	1	3	of	of	ADP
ejpam-6141	1	4	pure	pure	ADJ
ejpam-6141	1	5	and	and	CCONJ
ejpam-6141	1	6	applied	applied	ADJ
ejpam-6141	1	7	mathematics	mathematic	NOUN
ejpam-6141	1	8	2025	2025	NUM
ejpam-6141	1	9	,	,	PUNCT
ejpam-6141	1	10	vol	vol	NOUN
ejpam-6141	1	11	.	.	PROPN
ejpam-6141	1	12	18	18	NUM
ejpam-6141	1	13	,	,	PUNCT
ejpam-6141	1	14	issue	issue	NOUN
ejpam-6141	1	15	2	2	NUM
ejpam-6141	1	16	,	,	PUNCT
ejpam-6141	1	17	article	article	NOUN
ejpam-6141	1	18	number	number	NOUN
ejpam-6141	1	19	6141	6141	NUM
ejpam-6141	1	20	issn	issn	PROPN
ejpam-6141	1	21	1307	1307	NUM
ejpam-6141	1	22	-	-	SYM
ejpam-6141	1	23	5543	5543	NUM
ejpam-6141	1	24	–	–	PUNCT
ejpam-6141	1	25	ejpam.com	ejpam.com	X
ejpam-6141	1	26	published	publish	VERB
ejpam-6141	1	27	by	by	ADP
ejpam-6141	1	28	new	new	PROPN
ejpam-6141	1	29	york	york	PROPN
ejpam-6141	1	30	business	business	PROPN
ejpam-6141	1	31	global	global	ADJ
ejpam-6141	1	32	hypergroups	hypergroup	NOUN
ejpam-6141	1	33	obtained	obtain	VERB
ejpam-6141	1	34	from	from	ADP
ejpam-6141	1	35	a	a	DET
ejpam-6141	1	36	latin	latin	ADJ
ejpam-6141	1	37	square	square	PROPN
ejpam-6141	1	38	mohammad	mohammad	PROPN
ejpam-6141	1	39	ali	ali	PROPN
ejpam-6141	1	40	dehghanizadeh1,∗	dehghanizadeh1,∗	PROPN
ejpam-6141	1	41	,	,	PUNCT
ejpam-6141	1	42	saeed	saeed	NOUN
ejpam-6141	1	43	mirvakili2	mirvakili2	NOUN
ejpam-6141	1	44	1	1	NUM
ejpam-6141	1	45	department	department	NOUN
ejpam-6141	1	46	of	of	ADP
ejpam-6141	1	47	mathematics	mathematic	NOUN
ejpam-6141	1	48	,	,	PUNCT
ejpam-6141	1	49	national	national	ADJ
ejpam-6141	1	50	university	university	PROPN
ejpam-6141	1	51	of	of	ADP
ejpam-6141	1	52	skills(nus	skills(nus	PROPN
ejpam-6141	1	53	)	)	PUNCT
ejpam-6141	1	54	,	,	PUNCT
ejpam-6141	1	55	tehran	tehran	PROPN
ejpam-6141	1	56	,	,	PUNCT
ejpam-6141	1	57	iran	iran	PROPN
ejpam-6141	1	58	2	2	NUM
ejpam-6141	1	59	department	department	NOUN
ejpam-6141	1	60	of	of	ADP
ejpam-6141	1	61	mathematical	mathematical	ADJ
ejpam-6141	1	62	sciences	sciences	PROPN
ejpam-6141	1	63	,	,	PUNCT
ejpam-6141	1	64	yazd	yazd	PROPN
ejpam-6141	1	65	university	university	PROPN
ejpam-6141	1	66	,	,	PUNCT
ejpam-6141	1	67	yazd	yazd	PROPN
ejpam-6141	1	68	,	,	PUNCT
ejpam-6141	1	69	iran	iran	PROPN
ejpam-6141	1	70	”	"	PUNCT
ejpam-6141	1	71	this	this	DET
ejpam-6141	1	72	paper	paper	NOUN
ejpam-6141	1	73	is	be	AUX
ejpam-6141	1	74	dedicated	dedicate	VERB
ejpam-6141	1	75	to	to	ADP
ejpam-6141	1	76	professor	professor	PROPN
ejpam-6141	1	77	ali	ali	PROPN
ejpam-6141	1	78	akbar	akbar	PROPN
ejpam-6141	1	79	mohammadi	mohammadi	PROPN
ejpam-6141	1	80	hassanabadi	hassanabadi	NOUN
ejpam-6141	1	81	on	on	ADP
ejpam-6141	1	82	his	his	PRON
ejpam-6141	1	83	80th	80th	ADJ
ejpam-6141	1	84	birthday	birthday	NOUN
ejpam-6141	1	85	.	.	PUNCT
ejpam-6141	1	86	”	"	PUNCT
ejpam-6141	2	1	abstract	abstract	ADJ
ejpam-6141	2	2	.	.	PUNCT
ejpam-6141	3	1	in	in	ADP
ejpam-6141	3	2	this	this	DET
ejpam-6141	3	3	study	study	NOUN
ejpam-6141	3	4	,	,	PUNCT
ejpam-6141	3	5	we	we	PRON
ejpam-6141	3	6	explore	explore	VERB
ejpam-6141	3	7	the	the	DET
ejpam-6141	3	8	construction	construction	NOUN
ejpam-6141	3	9	of	of	ADP
ejpam-6141	3	10	a	a	DET
ejpam-6141	3	11	sequence	sequence	NOUN
ejpam-6141	3	12	of	of	ADP
ejpam-6141	3	13	hypergroupoids	hypergroupoid	NOUN
ejpam-6141	3	14	derived	derive	VERB
ejpam-6141	3	15	from	from	ADP
ejpam-6141	3	16	a	a	DET
ejpam-6141	3	17	quasigroup	quasigroup	NOUN
ejpam-6141	3	18	(	(	PUNCT
ejpam-6141	3	19	latin	latin	ADJ
ejpam-6141	3	20	square	square	NOUN
ejpam-6141	3	21	)	)	PUNCT
ejpam-6141	3	22	.	.	PUNCT
ejpam-6141	4	1	we	we	PRON
ejpam-6141	4	2	demonstrate	demonstrate	VERB
ejpam-6141	4	3	that	that	SCONJ
ejpam-6141	4	4	cyclic	cyclic	ADJ
ejpam-6141	4	5	groups	group	NOUN
ejpam-6141	4	6	yield	yield	VERB
ejpam-6141	4	7	sequences	sequence	NOUN
ejpam-6141	4	8	of	of	ADP
ejpam-6141	4	9	commutative	commutative	ADJ
ejpam-6141	4	10	hypergroups	hypergroup	NOUN
ejpam-6141	4	11	.	.	PUNCT
ejpam-6141	5	1	additionally	additionally	ADV
ejpam-6141	5	2	,	,	PUNCT
ejpam-6141	5	3	under	under	ADP
ejpam-6141	5	4	specific	specific	ADJ
ejpam-6141	5	5	conditions	condition	NOUN
ejpam-6141	5	6	,	,	PUNCT
ejpam-6141	5	7	we	we	PRON
ejpam-6141	5	8	establish	establish	VERB
ejpam-6141	5	9	the	the	DET
ejpam-6141	5	10	formation	formation	NOUN
ejpam-6141	5	11	of	of	ADP
ejpam-6141	5	12	hv	hv	NOUN
ejpam-6141	5	13	-	-	PUNCT
ejpam-6141	5	14	groups	group	NOUN
ejpam-6141	5	15	and	and	CCONJ
ejpam-6141	5	16	hypergroups	hypergroup	NOUN
ejpam-6141	5	17	.	.	PUNCT
ejpam-6141	6	1	various	various	ADJ
ejpam-6141	6	2	examples	example	NOUN
ejpam-6141	6	3	are	be	AUX
ejpam-6141	6	4	provided	provide	VERB
ejpam-6141	6	5	to	to	PART
ejpam-6141	6	6	illustrate	illustrate	VERB
ejpam-6141	6	7	and	and	CCONJ
ejpam-6141	6	8	support	support	VERB
ejpam-6141	6	9	the	the	DET
ejpam-6141	6	10	theoretical	theoretical	ADJ
ejpam-6141	6	11	concepts	concept	NOUN
ejpam-6141	6	12	presented	present	VERB
ejpam-6141	6	13	in	in	ADP
ejpam-6141	6	14	this	this	DET
ejpam-6141	6	15	paper	paper	NOUN
ejpam-6141	6	16	,	,	PUNCT
ejpam-6141	6	17	offering	offer	VERB
ejpam-6141	6	18	insights	insight	NOUN
ejpam-6141	6	19	into	into	ADP
ejpam-6141	6	20	their	their	PRON
ejpam-6141	6	21	structure	structure	NOUN
ejpam-6141	6	22	and	and	CCONJ
ejpam-6141	6	23	applicability	applicability	NOUN
ejpam-6141	6	24	.	.	PUNCT
ejpam-6141	7	1	2020	2020	NUM
ejpam-6141	7	2	mathematics	mathematic	NOUN
ejpam-6141	7	3	subject	subject	NOUN
ejpam-6141	7	4	classifications	classification	NOUN
ejpam-6141	7	5	:	:	PUNCT
ejpam-6141	7	6	20n20	20n20	NUM
ejpam-6141	7	7	,	,	PUNCT
ejpam-6141	7	8	05b15	05b15	VERB
ejpam-6141	7	9	key	key	ADJ
ejpam-6141	7	10	words	word	NOUN
ejpam-6141	7	11	and	and	CCONJ
ejpam-6141	7	12	phrases	phrase	NOUN
ejpam-6141	7	13	:	:	PUNCT
ejpam-6141	7	14	latin	latin	ADJ
ejpam-6141	7	15	square	square	PROPN
ejpam-6141	7	16	,	,	PUNCT
ejpam-6141	7	17	quasigroup	quasigroup	NOUN
ejpam-6141	7	18	,	,	PUNCT
ejpam-6141	7	19	quasihypergroup	quasihypergroup	NOUN
ejpam-6141	7	20	,	,	PUNCT
ejpam-6141	7	21	hypergroup	hypergroup	PROPN
ejpam-6141	7	22	,	,	PUNCT
ejpam-6141	7	23	hv	hv	PROPN
ejpam-6141	7	24	-	-	PUNCT
ejpam-6141	7	25	group	group	NOUN
ejpam-6141	7	26	1	1	NUM
ejpam-6141	7	27	.	.	PUNCT
ejpam-6141	8	1	introduction	introduction	NOUN
ejpam-6141	8	2	the	the	DET
ejpam-6141	8	3	linkage	linkage	NOUN
ejpam-6141	8	4	between	between	ADP
ejpam-6141	8	5	algebraic	algebraic	ADJ
ejpam-6141	8	6	structures	structure	NOUN
ejpam-6141	8	7	and	and	CCONJ
ejpam-6141	8	8	combined	combine	VERB
ejpam-6141	8	9	design	design	NOUN
ejpam-6141	8	10	problems	problem	NOUN
ejpam-6141	8	11	in	in	ADP
ejpam-6141	8	12	combinatorial	combinatorial	ADJ
ejpam-6141	8	13	models	model	NOUN
ejpam-6141	8	14	has	have	AUX
ejpam-6141	8	15	been	be	AUX
ejpam-6141	8	16	a	a	DET
ejpam-6141	8	17	field	field	NOUN
ejpam-6141	8	18	of	of	ADP
ejpam-6141	8	19	great	great	ADJ
ejpam-6141	8	20	interdisciplinary	interdisciplinary	ADJ
ejpam-6141	8	21	potential	potential	NOUN
ejpam-6141	8	22	,	,	PUNCT
ejpam-6141	8	23	both	both	CCONJ
ejpam-6141	8	24	in	in	ADP
ejpam-6141	8	25	abstract	abstract	ADJ
ejpam-6141	8	26	algebra	algebra	NOUN
ejpam-6141	8	27	theory	theory	NOUN
ejpam-6141	8	28	and	and	CCONJ
ejpam-6141	8	29	in	in	ADP
ejpam-6141	8	30	practical	practical	ADJ
ejpam-6141	8	31	applications	application	NOUN
ejpam-6141	8	32	ranging	range	VERB
ejpam-6141	8	33	from	from	ADP
ejpam-6141	8	34	coding	code	VERB
ejpam-6141	8	35	theory	theory	NOUN
ejpam-6141	8	36	,	,	PUNCT
ejpam-6141	8	37	cryptography	cryptography	NOUN
ejpam-6141	8	38	,	,	PUNCT
ejpam-6141	8	39	and	and	CCONJ
ejpam-6141	8	40	experimental	experimental	ADJ
ejpam-6141	8	41	design	design	NOUN
ejpam-6141	9	1	[	[	X
ejpam-6141	9	2	1	1	NUM
ejpam-6141	9	3	,	,	PUNCT
ejpam-6141	9	4	2	2	NUM
ejpam-6141	9	5	]	]	PUNCT
ejpam-6141	9	6	.	.	PUNCT
ejpam-6141	10	1	one	one	NUM
ejpam-6141	10	2	of	of	ADP
ejpam-6141	10	3	the	the	DET
ejpam-6141	10	4	fundamental	fundamental	ADJ
ejpam-6141	10	5	conductivities	conductivity	NOUN
ejpam-6141	10	6	is	be	AUX
ejpam-6141	10	7	the	the	DET
ejpam-6141	10	8	relation	relation	NOUN
ejpam-6141	10	9	between	between	ADP
ejpam-6141	10	10	quasigroups	quasigroup	NOUN
ejpam-6141	10	11	and	and	CCONJ
ejpam-6141	10	12	latin	latin	ADJ
ejpam-6141	10	13	squares	square	NOUN
ejpam-6141	10	14	.	.	PUNCT
ejpam-6141	11	1	in	in	ADP
ejpam-6141	11	2	recent	recent	ADJ
ejpam-6141	11	3	years	year	NOUN
ejpam-6141	11	4	,	,	PUNCT
ejpam-6141	11	5	the	the	DET
ejpam-6141	11	6	topic	topic	NOUN
ejpam-6141	11	7	has	have	AUX
ejpam-6141	11	8	also	also	ADV
ejpam-6141	11	9	been	be	AUX
ejpam-6141	11	10	extended	extend	VERB
ejpam-6141	11	11	to	to	ADP
ejpam-6141	11	12	hyperstructures	hyperstructure	NOUN
ejpam-6141	11	13	,	,	PUNCT
ejpam-6141	11	14	and	and	CCONJ
ejpam-6141	11	15	here	here	ADV
ejpam-6141	11	16	also	also	ADV
ejpam-6141	11	17	to	to	ADP
ejpam-6141	11	18	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	11	19	and	and	CCONJ
ejpam-6141	11	20	hypergroups	hypergroup	NOUN
ejpam-6141	11	21	,	,	PUNCT
ejpam-6141	11	22	providing	provide	VERB
ejpam-6141	11	23	new	new	ADJ
ejpam-6141	11	24	avenues	avenue	NOUN
ejpam-6141	11	25	for	for	ADP
ejpam-6141	11	26	algebraic	algebraic	ADJ
ejpam-6141	11	27	generalization	generalization	NOUN
ejpam-6141	11	28	.	.	PUNCT
ejpam-6141	12	1	the	the	DET
ejpam-6141	12	2	paper	paper	NOUN
ejpam-6141	12	3	by	by	ADP
ejpam-6141	12	4	iranmanesh	iranmanesh	NOUN
ejpam-6141	12	5	and	and	CCONJ
ejpam-6141	12	6	ashrafi	ashrafi	VERB
ejpam-6141	12	7	[	[	X
ejpam-6141	12	8	3	3	X
ejpam-6141	12	9	]	]	PUNCT
ejpam-6141	12	10	opens	open	VERB
ejpam-6141	12	11	new	new	ADJ
ejpam-6141	12	12	fields	field	NOUN
ejpam-6141	12	13	of	of	ADP
ejpam-6141	12	14	algebraic	algebraic	ADJ
ejpam-6141	12	15	generalization	generalization	NOUN
ejpam-6141	12	16	involving	involve	VERB
ejpam-6141	12	17	the	the	DET
ejpam-6141	12	18	connections	connection	NOUN
ejpam-6141	12	19	between	between	ADP
ejpam-6141	12	20	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	12	21	and	and	CCONJ
ejpam-6141	12	22	latin	latin	ADJ
ejpam-6141	12	23	squares	square	NOUN
ejpam-6141	12	24	with	with	ADP
ejpam-6141	12	25	their	their	PRON
ejpam-6141	12	26	hyperstructural	hyperstructural	ADJ
ejpam-6141	12	27	homologues	homologue	NOUN
ejpam-6141	12	28	.	.	PUNCT
ejpam-6141	13	1	the	the	DET
ejpam-6141	13	2	study	study	NOUN
ejpam-6141	13	3	of	of	ADP
ejpam-6141	13	4	latin	latin	ADJ
ejpam-6141	13	5	squares	square	NOUN
ejpam-6141	13	6	dates	date	VERB
ejpam-6141	13	7	back	back	ADV
ejpam-6141	13	8	to	to	ADP
ejpam-6141	13	9	ancient	ancient	ADJ
ejpam-6141	13	10	mathematical	mathematical	ADJ
ejpam-6141	13	11	traditions	tradition	NOUN
ejpam-6141	13	12	,	,	PUNCT
ejpam-6141	13	13	with	with	ADP
ejpam-6141	13	14	early	early	ADJ
ejpam-6141	13	15	examples	example	NOUN
ejpam-6141	13	16	in	in	ADP
ejpam-6141	13	17	arabic	arabic	ADJ
ejpam-6141	13	18	manuscripts	manuscript	NOUN
ejpam-6141	13	19	and	and	CCONJ
ejpam-6141	13	20	medieval	medieval	ADJ
ejpam-6141	13	21	combinatorial	combinatorial	ADJ
ejpam-6141	13	22	puzzles	puzzle	NOUN
ejpam-6141	13	23	.	.	PUNCT
ejpam-6141	14	1	however	however	ADV
ejpam-6141	14	2	,	,	PUNCT
ejpam-6141	14	3	formalization	formalization	NOUN
ejpam-6141	14	4	started	start	VERB
ejpam-6141	14	5	in	in	ADP
ejpam-6141	14	6	the	the	DET
ejpam-6141	14	7	18th	18th	ADJ
ejpam-6141	14	8	century	century	NOUN
ejpam-6141	14	9	,	,	PUNCT
ejpam-6141	14	10	beginning	begin	VERB
ejpam-6141	14	11	with	with	ADP
ejpam-6141	14	12	leonhard	leonhard	PROPN
ejpam-6141	14	13	euler	euler	PROPN
ejpam-6141	14	14	’s	’s	PART
ejpam-6141	14	15	famous	famous	ADJ
ejpam-6141	14	16	”	"	PUNCT
ejpam-6141	14	17	36	36	NUM
ejpam-6141	14	18	officers	officer	NOUN
ejpam-6141	14	19	problem	problem	NOUN
ejpam-6141	14	20	”	"	PUNCT
ejpam-6141	14	21	that	that	PRON
ejpam-6141	14	22	launched	launch	VERB
ejpam-6141	14	23	a	a	DET
ejpam-6141	14	24	systematic	systematic	ADJ
ejpam-6141	14	25	investigation	investigation	NOUN
ejpam-6141	14	26	of	of	ADP
ejpam-6141	14	27	their	their	PRON
ejpam-6141	14	28	properties	property	NOUN
ejpam-6141	14	29	.	.	PUNCT
ejpam-6141	15	1	a	a	DET
ejpam-6141	15	2	latin	latin	ADJ
ejpam-6141	15	3	square	square	NOUN
ejpam-6141	15	4	of	of	ADP
ejpam-6141	15	5	order	order	NOUN
ejpam-6141	15	6	n	n	X
ejpam-6141	15	7	is	be	AUX
ejpam-6141	15	8	a	a	DET
ejpam-6141	15	9	n	n	NUM
ejpam-6141	15	10	×	×	NOUN
ejpam-6141	15	11	n	n	PRON
ejpam-6141	15	12	grid	grid	NOUN
ejpam-6141	15	13	of	of	ADP
ejpam-6141	15	14	points	point	NOUN
ejpam-6141	15	15	,	,	PUNCT
ejpam-6141	15	16	whose	whose	DET
ejpam-6141	15	17	values	value	NOUN
ejpam-6141	15	18	are	be	AUX
ejpam-6141	15	19	described	describe	VERB
ejpam-6141	15	20	by	by	ADP
ejpam-6141	15	21	[	[	X
ejpam-6141	15	22	1	1	NUM
ejpam-6141	15	23	,	,	PUNCT
ejpam-6141	15	24	2	2	NUM
ejpam-6141	15	25	,	,	PUNCT
ejpam-6141	15	26	4	4	NUM
ejpam-6141	15	27	]	]	PUNCT
ejpam-6141	15	28	.	.	PUNCT
ejpam-6141	16	1	this	this	DET
ejpam-6141	16	2	set	set	NOUN
ejpam-6141	16	3	of	of	ADP
ejpam-6141	16	4	n	n	CCONJ
ejpam-6141	16	5	independent	independent	ADJ
ejpam-6141	16	6	symbols	symbol	NOUN
ejpam-6141	16	7	(	(	PUNCT
ejpam-6141	16	8	which	which	PRON
ejpam-6141	16	9	can	can	AUX
ejpam-6141	16	10	all	all	PRON
ejpam-6141	16	11	occur	occur	VERB
ejpam-6141	16	12	simultaneously	simultaneously	ADV
ejpam-6141	16	13	in	in	ADP
ejpam-6141	16	14	rows	row	NOUN
ejpam-6141	16	15	and	and	CCONJ
ejpam-6141	16	16	columns	column	NOUN
ejpam-6141	16	17	)	)	PUNCT
ejpam-6141	16	18	became	become	VERB
ejpam-6141	16	19	∗corresponding	∗corresponde	VERB
ejpam-6141	16	20	author	author	NOUN
ejpam-6141	16	21	.	.	PUNCT
ejpam-6141	17	1	doi	doi	NOUN
ejpam-6141	17	2	:	:	PUNCT
ejpam-6141	17	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6141	https://doi.org/10.29020/nybg.ejpam.v18i2.6141	ADJ
ejpam-6141	17	4	email	email	NOUN
ejpam-6141	17	5	addresses	address	NOUN
ejpam-6141	17	6	:	:	PUNCT
ejpam-6141	17	7	mdehghanizadeh@nus.ac.ir	mdehghanizadeh@nus.ac.ir	PROPN
ejpam-6141	17	8	(	(	PUNCT
ejpam-6141	17	9	m.	m.	NOUN
ejpam-6141	17	10	a.	a.	NOUN
ejpam-6141	17	11	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	17	12	)	)	PUNCT
ejpam-6141	17	13	,	,	PUNCT
ejpam-6141	17	14	saeedmirvakili@yazd.ac.ir	saeedmirvakili@yazd.ac.ir	NOUN
ejpam-6141	17	15	(	(	PUNCT
ejpam-6141	17	16	s.	s.	PROPN
ejpam-6141	17	17	mirvakili	mirvakili	PROPN
ejpam-6141	17	18	)	)	PUNCT
ejpam-6141	17	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6141	18	1	1	1	NUM
ejpam-6141	18	2	copyright	copyright	NOUN
ejpam-6141	18	3	:	:	PUNCT
ejpam-6141	18	4	©	©	PROPN
ejpam-6141	18	5	2025	2025	NUM
ejpam-6141	18	6	the	the	DET
ejpam-6141	18	7	author(s	author(s	NOUN
ejpam-6141	18	8	)	)	PUNCT
ejpam-6141	18	9	.	.	PUNCT
ejpam-6141	19	1	(	(	PUNCT
ejpam-6141	19	2	cc	cc	NOUN
ejpam-6141	19	3	by	by	ADP
ejpam-6141	19	4	-	-	PUNCT
ejpam-6141	19	5	nc	nc	PROPN
ejpam-6141	19	6	4.0	4.0	NUM
ejpam-6141	19	7	)	)	PUNCT
ejpam-6141	19	8	m.	m.	NOUN
ejpam-6141	19	9	a.	a.	NOUN
ejpam-6141	19	10	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	19	11	,	,	PUNCT
ejpam-6141	19	12	s.	s.	PROPN
ejpam-6141	19	13	mirvakili	mirvakili	PROPN
ejpam-6141	19	14	/	/	SYM
ejpam-6141	19	15	eur	eur	PROPN
ejpam-6141	19	16	.	.	PUNCT
ejpam-6141	20	1	j.	j.	PROPN
ejpam-6141	20	2	pure	pure	PROPN
ejpam-6141	20	3	appl	appl	PROPN
ejpam-6141	20	4	.	.	PROPN
ejpam-6141	20	5	math	math	PROPN
ejpam-6141	20	6	,	,	PUNCT
ejpam-6141	20	7	18	18	NUM
ejpam-6141	20	8	(	(	PUNCT
ejpam-6141	20	9	2	2	NUM
ejpam-6141	20	10	)	)	PUNCT
ejpam-6141	20	11	(	(	PUNCT
ejpam-6141	20	12	2025	2025	NUM
ejpam-6141	20	13	)	)	PUNCT
ejpam-6141	20	14	,	,	PUNCT
ejpam-6141	20	15	6141	6141	NUM
ejpam-6141	20	16	2	2	NUM
ejpam-6141	20	17	of	of	ADP
ejpam-6141	20	18	10	10	NUM
ejpam-6141	20	19	a	a	DET
ejpam-6141	20	20	key	key	ADJ
ejpam-6141	20	21	object	object	NOUN
ejpam-6141	20	22	of	of	ADP
ejpam-6141	20	23	design	design	NOUN
ejpam-6141	20	24	theory	theory	NOUN
ejpam-6141	20	25	.	.	PUNCT
ejpam-6141	21	1	by	by	ADP
ejpam-6141	21	2	the	the	DET
ejpam-6141	21	3	20th	20th	ADJ
ejpam-6141	21	4	century	century	NOUN
ejpam-6141	21	5	latin	latin	ADJ
ejpam-6141	21	6	squares	square	NOUN
ejpam-6141	21	7	had	have	VERB
ejpam-6141	21	8	rigorous	rigorous	ADJ
ejpam-6141	21	9	applications	application	NOUN
ejpam-6141	21	10	in	in	ADP
ejpam-6141	21	11	statistical	statistical	ADJ
ejpam-6141	21	12	experimental	experimental	ADJ
ejpam-6141	21	13	design	design	NOUN
ejpam-6141	21	14	(	(	PUNCT
ejpam-6141	21	15	through	through	ADP
ejpam-6141	21	16	r.	r.	PROPN
ejpam-6141	21	17	a.	a.	PROPN
ejpam-6141	21	18	fisher	fisher	PROPN
ejpam-6141	21	19	’s	’s	PART
ejpam-6141	21	20	work	work	NOUN
ejpam-6141	21	21	)	)	PUNCT
ejpam-6141	21	22	,	,	PUNCT
ejpam-6141	21	23	error	error	NOUN
ejpam-6141	21	24	-	-	PUNCT
ejpam-6141	21	25	correcting	correct	VERB
ejpam-6141	21	26	codes	code	NOUN
ejpam-6141	21	27	,	,	PUNCT
ejpam-6141	21	28	and	and	CCONJ
ejpam-6141	21	29	group	group	NOUN
ejpam-6141	21	30	theory	theory	NOUN
ejpam-6141	21	31	where	where	SCONJ
ejpam-6141	21	32	they	they	PRON
ejpam-6141	21	33	became	became	AUX
ejpam-6141	21	34	known	know	VERB
ejpam-6141	21	35	as	as	ADP
ejpam-6141	21	36	multiplication	multiplication	NOUN
ejpam-6141	21	37	tables	table	NOUN
ejpam-6141	21	38	of	of	ADP
ejpam-6141	21	39	quasigroups	quasigroup	NOUN
ejpam-6141	21	40	(	(	PUNCT
ejpam-6141	21	41	non	non	ADJ
ejpam-6141	21	42	-	-	ADJ
ejpam-6141	21	43	associative	associative	ADJ
ejpam-6141	21	44	algebraic	algebraic	ADJ
ejpam-6141	21	45	structures	structure	NOUN
ejpam-6141	21	46	satisfying	satisfy	VERB
ejpam-6141	21	47	the	the	DET
ejpam-6141	21	48	latin	latin	ADJ
ejpam-6141	21	49	square	square	NOUN
ejpam-6141	21	50	property)[1	property)[1	NOUN
ejpam-6141	21	51	,	,	PUNCT
ejpam-6141	21	52	2	2	NUM
ejpam-6141	21	53	,	,	PUNCT
ejpam-6141	21	54	4	4	NUM
ejpam-6141	21	55	]	]	PUNCT
ejpam-6141	21	56	.	.	PUNCT
ejpam-6141	22	1	the	the	DET
ejpam-6141	22	2	desire	desire	NOUN
ejpam-6141	22	3	to	to	PART
ejpam-6141	22	4	use	use	VERB
ejpam-6141	22	5	the	the	DET
ejpam-6141	22	6	problem	problem	NOUN
ejpam-6141	22	7	of	of	ADP
ejpam-6141	22	8	latin	latin	ADJ
ejpam-6141	22	9	squares	square	NOUN
ejpam-6141	22	10	for	for	ADP
ejpam-6141	22	11	applications	application	NOUN
ejpam-6141	22	12	outside	outside	ADP
ejpam-6141	22	13	of	of	ADP
ejpam-6141	22	14	algebra	algebra	NOUN
ejpam-6141	22	15	enabled	enable	VERB
ejpam-6141	22	16	a	a	DET
ejpam-6141	22	17	number	number	NOUN
ejpam-6141	22	18	of	of	ADP
ejpam-6141	22	19	generalizations	generalization	NOUN
ejpam-6141	22	20	,	,	PUNCT
ejpam-6141	22	21	for	for	ADP
ejpam-6141	22	22	example	example	NOUN
ejpam-6141	22	23	,	,	PUNCT
ejpam-6141	22	24	reduced	reduce	VERB
ejpam-6141	22	25	latin	latin	ADJ
ejpam-6141	22	26	squares	square	NOUN
ejpam-6141	22	27	,	,	PUNCT
ejpam-6141	22	28	orthogonal	orthogonal	NOUN
ejpam-6141	22	29	arrays	array	VERB
ejpam-6141	22	30	,	,	PUNCT
ejpam-6141	22	31	and	and	CCONJ
ejpam-6141	22	32	partial	partial	ADJ
ejpam-6141	22	33	latin	latin	ADJ
ejpam-6141	22	34	squares	square	NOUN
ejpam-6141	22	35	.	.	PUNCT
ejpam-6141	23	1	all	all	DET
ejpam-6141	23	2	three	three	NUM
ejpam-6141	23	3	variants	variant	NOUN
ejpam-6141	23	4	relaxed	relaxed	ADJ
ejpam-6141	23	5	or	or	CCONJ
ejpam-6141	23	6	extended	extend	VERB
ejpam-6141	23	7	classical	classical	ADJ
ejpam-6141	23	8	constraints	constraint	NOUN
ejpam-6141	23	9	in	in	ADP
ejpam-6141	23	10	some	some	DET
ejpam-6141	23	11	way	way	NOUN
ejpam-6141	23	12	.	.	PUNCT
ejpam-6141	24	1	they	they	PRON
ejpam-6141	24	2	proved	prove	VERB
ejpam-6141	24	3	helpful	helpful	ADJ
ejpam-6141	24	4	in	in	ADP
ejpam-6141	24	5	solving	solve	VERB
ejpam-6141	24	6	problems	problem	NOUN
ejpam-6141	24	7	in	in	ADP
ejpam-6141	24	8	graph	graph	NOUN
ejpam-6141	24	9	theory	theory	NOUN
ejpam-6141	24	10	,	,	PUNCT
ejpam-6141	24	11	finite	finite	ADJ
ejpam-6141	24	12	geometry	geometry	NOUN
ejpam-6141	24	13	,	,	PUNCT
ejpam-6141	24	14	and	and	CCONJ
ejpam-6141	24	15	cryptography	cryptography	NOUN
ejpam-6141	24	16	.	.	PUNCT
ejpam-6141	25	1	at	at	ADP
ejpam-6141	25	2	the	the	DET
ejpam-6141	25	3	same	same	ADJ
ejpam-6141	25	4	time	time	NOUN
ejpam-6141	25	5	,	,	PUNCT
ejpam-6141	25	6	quasigroups	quasigroup	NOUN
ejpam-6141	25	7	(	(	PUNCT
ejpam-6141	25	8	algebraic	algebraic	PROPN
ejpam-6141	25	9	systems	system	NOUN
ejpam-6141	25	10	with	with	ADP
ejpam-6141	25	11	multiplication	multiplication	NOUN
ejpam-6141	25	12	tables	table	NOUN
ejpam-6141	25	13	of	of	ADP
ejpam-6141	25	14	latin	latin	ADJ
ejpam-6141	25	15	squares	square	NOUN
ejpam-6141	25	16	)	)	PUNCT
ejpam-6141	25	17	developed	develop	VERB
ejpam-6141	25	18	as	as	ADP
ejpam-6141	25	19	the	the	DET
ejpam-6141	25	20	basis	basis	NOUN
ejpam-6141	25	21	of	of	ADP
ejpam-6141	25	22	non	non	ADJ
ejpam-6141	25	23	-	-	ADJ
ejpam-6141	25	24	associative	associative	ADJ
ejpam-6141	25	25	algebras	algebra	NOUN
ejpam-6141	25	26	and	and	CCONJ
ejpam-6141	25	27	mathematically	mathematically	ADV
ejpam-6141	25	28	relevant	relevant	ADJ
ejpam-6141	25	29	solutions	solution	NOUN
ejpam-6141	25	30	of	of	ADP
ejpam-6141	25	31	equations	equation	NOUN
ejpam-6141	25	32	.	.	PUNCT
ejpam-6141	26	1	quasigroups	quasigroup	NOUN
ejpam-6141	26	2	are	be	AUX
ejpam-6141	26	3	not	not	PART
ejpam-6141	26	4	associative	associative	ADJ
ejpam-6141	26	5	but	but	CCONJ
ejpam-6141	26	6	contain	contain	VERB
ejpam-6141	26	7	cancellativity	cancellativity	NOUN
ejpam-6141	26	8	in	in	ADP
ejpam-6141	26	9	their	their	PRON
ejpam-6141	26	10	behavior	behavior	NOUN
ejpam-6141	26	11	.	.	PUNCT
ejpam-6141	27	1	they	they	PRON
ejpam-6141	27	2	therefore	therefore	ADV
ejpam-6141	27	3	offer	offer	VERB
ejpam-6141	27	4	the	the	DET
ejpam-6141	27	5	bridge	bridge	NOUN
ejpam-6141	27	6	between	between	ADP
ejpam-6141	27	7	discrete	discrete	ADJ
ejpam-6141	27	8	mathematics	mathematic	NOUN
ejpam-6141	27	9	and	and	CCONJ
ejpam-6141	27	10	algebraic	algebraic	ADJ
ejpam-6141	27	11	abstraction	abstraction	NOUN
ejpam-6141	27	12	.	.	PUNCT
ejpam-6141	28	1	on	on	ADP
ejpam-6141	28	2	the	the	DET
ejpam-6141	28	3	other	other	ADJ
ejpam-6141	28	4	hand	hand	NOUN
ejpam-6141	28	5	,	,	PUNCT
ejpam-6141	28	6	the	the	DET
ejpam-6141	28	7	mid-20th	mid-20th	NUM
ejpam-6141	28	8	century	century	NOUN
ejpam-6141	28	9	also	also	ADV
ejpam-6141	28	10	brought	bring	VERB
ejpam-6141	28	11	about	about	ADP
ejpam-6141	28	12	the	the	DET
ejpam-6141	28	13	development	development	NOUN
ejpam-6141	28	14	of	of	ADP
ejpam-6141	28	15	hyperstructures	hyperstructure	NOUN
ejpam-6141	28	16	,	,	PUNCT
ejpam-6141	28	17	a	a	DET
ejpam-6141	28	18	generalization	generalization	NOUN
ejpam-6141	28	19	of	of	ADP
ejpam-6141	28	20	classical	classical	ADJ
ejpam-6141	28	21	algebraic	algebraic	ADJ
ejpam-6141	28	22	operations	operation	NOUN
ejpam-6141	28	23	by	by	ADP
ejpam-6141	28	24	changing	change	VERB
ejpam-6141	28	25	binary	binary	ADJ
ejpam-6141	28	26	operations	operation	NOUN
ejpam-6141	28	27	(	(	PUNCT
ejpam-6141	28	28	contrary	contrary	ADJ
ejpam-6141	28	29	to	to	ADP
ejpam-6141	28	30	traditional	traditional	ADJ
ejpam-6141	28	31	algebraic	algebraic	ADJ
ejpam-6141	28	32	operations	operation	NOUN
ejpam-6141	28	33	)	)	PUNCT
ejpam-6141	28	34	to	to	PART
ejpam-6141	28	35	set	set	VERB
ejpam-6141	28	36	-	-	PUNCT
ejpam-6141	28	37	valued	value	VERB
ejpam-6141	28	38	operations	operation	NOUN
ejpam-6141	28	39	.	.	PUNCT
ejpam-6141	29	1	the	the	DET
ejpam-6141	29	2	fields	field	NOUN
ejpam-6141	29	3	were	be	AUX
ejpam-6141	29	4	opened	open	VERB
ejpam-6141	29	5	by	by	ADP
ejpam-6141	29	6	the	the	DET
ejpam-6141	29	7	work	work	NOUN
ejpam-6141	29	8	of	of	ADP
ejpam-6141	29	9	f.	f.	PROPN
ejpam-6141	29	10	marty	marty	PROPN
ejpam-6141	29	11	(	(	PUNCT
ejpam-6141	29	12	1934	1934	NUM
ejpam-6141	29	13	)	)	PUNCT
ejpam-6141	29	14	in	in	ADP
ejpam-6141	29	15	the	the	DET
ejpam-6141	29	16	invention	invention	NOUN
ejpam-6141	29	17	of	of	ADP
ejpam-6141	29	18	hypergroups	hypergroup	NOUN
ejpam-6141	29	19	–	–	PUNCT
ejpam-6141	29	20	structures	structure	NOUN
ejpam-6141	29	21	in	in	ADP
ejpam-6141	29	22	which	which	PRON
ejpam-6141	29	23	the	the	DET
ejpam-6141	29	24	product	product	NOUN
ejpam-6141	29	25	of	of	ADP
ejpam-6141	29	26	two	two	NUM
ejpam-6141	29	27	variables	variable	NOUN
ejpam-6141	29	28	is	be	AUX
ejpam-6141	29	29	a	a	DET
ejpam-6141	29	30	nonempty	nonempty	ADJ
ejpam-6141	29	31	set	set	NOUN
ejpam-6141	29	32	—	—	PUNCT
ejpam-6141	29	33	in	in	ADP
ejpam-6141	29	34	the	the	DET
ejpam-6141	29	35	direction	direction	NOUN
ejpam-6141	29	36	of	of	ADP
ejpam-6141	29	37	work	work	NOUN
ejpam-6141	29	38	from	from	ADP
ejpam-6141	29	39	corsini	corsini	PROPN
ejpam-6141	29	40	,	,	PUNCT
ejpam-6141	29	41	davvaz	davvaz	NOUN
ejpam-6141	29	42	and	and	CCONJ
ejpam-6141	29	43	vougiouklis	vougioukli	VERB
ejpam-6141	30	1	[	[	X
ejpam-6141	30	2	5–8	5–8	NOUN
ejpam-6141	30	3	]	]	PUNCT
ejpam-6141	30	4	.	.	PUNCT
ejpam-6141	31	1	hyperstructures	hyperstructure	NOUN
ejpam-6141	31	2	and	and	CCONJ
ejpam-6141	31	3	their	their	PRON
ejpam-6141	31	4	variants	variant	NOUN
ejpam-6141	31	5	—	—	PUNCT
ejpam-6141	31	6	such	such	ADJ
ejpam-6141	31	7	as	as	ADP
ejpam-6141	31	8	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	31	9	and	and	CCONJ
ejpam-6141	31	10	hv	hv	NOUN
ejpam-6141	31	11	-	-	PUNCT
ejpam-6141	31	12	structures	structure	NOUN
ejpam-6141	31	13	—	—	PUNCT
ejpam-6141	31	14	have	have	AUX
ejpam-6141	31	15	been	be	AUX
ejpam-6141	31	16	used	use	VERB
ejpam-6141	31	17	for	for	ADP
ejpam-6141	31	18	modelling	model	VERB
ejpam-6141	31	19	uncertainty	uncertainty	NOUN
ejpam-6141	31	20	theory	theory	NOUN
ejpam-6141	31	21	,	,	PUNCT
ejpam-6141	31	22	granular	granular	ADJ
ejpam-6141	31	23	computing	computing	NOUN
ejpam-6141	31	24	,	,	PUNCT
ejpam-6141	31	25	and	and	CCONJ
ejpam-6141	31	26	non	non	ADJ
ejpam-6141	31	27	-	-	ADJ
ejpam-6141	31	28	deterministic	deterministic	ADJ
ejpam-6141	31	29	systems	system	NOUN
ejpam-6141	31	30	.	.	PUNCT
ejpam-6141	32	1	since	since	SCONJ
ejpam-6141	32	2	hyperstructures	hyperstructure	NOUN
ejpam-6141	32	3	are	be	AUX
ejpam-6141	32	4	compatible	compatible	ADJ
ejpam-6141	32	5	with	with	ADP
ejpam-6141	32	6	multivaluedness	multivaluedness	NOUN
ejpam-6141	32	7	,	,	PUNCT
ejpam-6141	32	8	they	they	PRON
ejpam-6141	32	9	offer	offer	VERB
ejpam-6141	32	10	more	more	ADV
ejpam-6141	32	11	powerful	powerful	ADJ
ejpam-6141	32	12	algebraic	algebraic	ADJ
ejpam-6141	32	13	representations	representation	NOUN
ejpam-6141	32	14	for	for	ADP
ejpam-6141	32	15	complex	complex	ADJ
ejpam-6141	32	16	relational	relational	ADJ
ejpam-6141	32	17	systems	system	NOUN
ejpam-6141	32	18	.	.	PUNCT
ejpam-6141	33	1	the	the	DET
ejpam-6141	33	2	construction	construction	NOUN
ejpam-6141	33	3	of	of	ADP
ejpam-6141	33	4	a	a	DET
ejpam-6141	33	5	sequence	sequence	NOUN
ejpam-6141	33	6	of	of	ADP
ejpam-6141	33	7	hypergroupoids	hypergroupoid	NOUN
ejpam-6141	33	8	derived	derive	VERB
ejpam-6141	33	9	from	from	ADP
ejpam-6141	33	10	a	a	DET
ejpam-6141	33	11	quasigroup	quasigroup	NOUN
ejpam-6141	33	12	(	(	PUNCT
ejpam-6141	33	13	latin	latin	ADJ
ejpam-6141	33	14	square	square	NOUN
ejpam-6141	33	15	)	)	PUNCT
ejpam-6141	33	16	is	be	AUX
ejpam-6141	33	17	investigated	investigate	VERB
ejpam-6141	33	18	here	here	ADV
ejpam-6141	33	19	.	.	PUNCT
ejpam-6141	34	1	we	we	PRON
ejpam-6141	34	2	prove	prove	VERB
ejpam-6141	34	3	that	that	SCONJ
ejpam-6141	34	4	cyclic	cyclic	ADJ
ejpam-6141	34	5	groups	group	NOUN
ejpam-6141	34	6	are	be	AUX
ejpam-6141	34	7	capable	capable	ADJ
ejpam-6141	34	8	of	of	ADP
ejpam-6141	34	9	yielding	yield	VERB
ejpam-6141	34	10	sequences	sequence	NOUN
ejpam-6141	34	11	of	of	ADP
ejpam-6141	34	12	commutative	commutative	ADJ
ejpam-6141	34	13	hypergroups	hypergroup	NOUN
ejpam-6141	34	14	.	.	PUNCT
ejpam-6141	35	1	in	in	ADP
ejpam-6141	35	2	addition	addition	NOUN
ejpam-6141	35	3	,	,	PUNCT
ejpam-6141	35	4	under	under	ADP
ejpam-6141	35	5	some	some	DET
ejpam-6141	35	6	special	special	ADJ
ejpam-6141	35	7	conditions	condition	NOUN
ejpam-6141	35	8	,	,	PUNCT
ejpam-6141	35	9	we	we	PRON
ejpam-6141	35	10	show	show	VERB
ejpam-6141	35	11	that	that	SCONJ
ejpam-6141	35	12	hv	hv	NOUN
ejpam-6141	35	13	-	-	PUNCT
ejpam-6141	35	14	groups	group	NOUN
ejpam-6141	35	15	and	and	CCONJ
ejpam-6141	35	16	hypergroups	hypergroup	NOUN
ejpam-6141	35	17	are	be	AUX
ejpam-6141	35	18	formed	form	VERB
ejpam-6141	35	19	.	.	PUNCT
ejpam-6141	36	1	experiments	experiment	NOUN
ejpam-6141	36	2	are	be	AUX
ejpam-6141	36	3	given	give	VERB
ejpam-6141	36	4	in	in	ADP
ejpam-6141	36	5	this	this	DET
ejpam-6141	36	6	paper	paper	NOUN
ejpam-6141	36	7	to	to	PART
ejpam-6141	36	8	show	show	VERB
ejpam-6141	36	9	and	and	CCONJ
ejpam-6141	36	10	support	support	VERB
ejpam-6141	36	11	the	the	DET
ejpam-6141	36	12	theoretical	theoretical	ADJ
ejpam-6141	36	13	notions	notion	NOUN
ejpam-6141	36	14	presented	present	VERB
ejpam-6141	36	15	,	,	PUNCT
ejpam-6141	36	16	and	and	CCONJ
ejpam-6141	36	17	to	to	PART
ejpam-6141	36	18	show	show	VERB
ejpam-6141	36	19	how	how	SCONJ
ejpam-6141	36	20	they	they	PRON
ejpam-6141	36	21	are	be	AUX
ejpam-6141	36	22	formulated	formulate	VERB
ejpam-6141	36	23	and	and	CCONJ
ejpam-6141	36	24	how	how	SCONJ
ejpam-6141	36	25	they	they	PRON
ejpam-6141	36	26	may	may	AUX
ejpam-6141	36	27	be	be	AUX
ejpam-6141	36	28	extended	extend	VERB
ejpam-6141	36	29	to	to	PART
ejpam-6141	36	30	practice	practice	VERB
ejpam-6141	36	31	.	.	PUNCT
ejpam-6141	37	1	2	2	X
ejpam-6141	37	2	.	.	X
ejpam-6141	37	3	main	main	ADJ
ejpam-6141	37	4	results	result	NOUN
ejpam-6141	37	5	a	a	DET
ejpam-6141	37	6	quasigroup	quasigroup	NOUN
ejpam-6141	37	7	(	(	PUNCT
ejpam-6141	37	8	q	q	ADJ
ejpam-6141	37	9	,	,	PUNCT
ejpam-6141	37	10	⋆	⋆	ADJ
ejpam-6141	37	11	)	)	PUNCT
ejpam-6141	37	12	is	be	AUX
ejpam-6141	37	13	a	a	DET
ejpam-6141	37	14	non	non	ADJ
ejpam-6141	37	15	-	-	ADJ
ejpam-6141	37	16	empty	empty	ADJ
ejpam-6141	37	17	set	set	NOUN
ejpam-6141	37	18	q	q	NOUN
ejpam-6141	37	19	with	with	ADP
ejpam-6141	37	20	a	a	DET
ejpam-6141	37	21	binary	binary	ADJ
ejpam-6141	37	22	operation	operation	NOUN
ejpam-6141	37	23	⋆	⋆	NOUN
ejpam-6141	37	24	,	,	PUNCT
ejpam-6141	37	25	obeying	obey	VERB
ejpam-6141	37	26	the	the	DET
ejpam-6141	37	27	latin	latin	ADJ
ejpam-6141	37	28	square	square	PROPN
ejpam-6141	37	29	property[4	property[4	PROPN
ejpam-6141	37	30	,	,	PUNCT
ejpam-6141	37	31	9	9	NUM
ejpam-6141	37	32	]	]	PUNCT
ejpam-6141	37	33	.	.	PUNCT
ejpam-6141	38	1	this	this	PRON
ejpam-6141	38	2	states	state	VERB
ejpam-6141	38	3	that	that	SCONJ
ejpam-6141	38	4	,	,	PUNCT
ejpam-6141	38	5	for	for	ADP
ejpam-6141	38	6	each	each	DET
ejpam-6141	38	7	a	a	PRON
ejpam-6141	38	8	and	and	CCONJ
ejpam-6141	38	9	b	b	NOUN
ejpam-6141	38	10	in	in	ADP
ejpam-6141	38	11	q	q	NOUN
ejpam-6141	38	12	,	,	PUNCT
ejpam-6141	38	13	there	there	PRON
ejpam-6141	38	14	exist	exist	VERB
ejpam-6141	38	15	unique	unique	ADJ
ejpam-6141	38	16	elements	element	NOUN
ejpam-6141	38	17	x	x	PUNCT
ejpam-6141	38	18	and	and	CCONJ
ejpam-6141	38	19	y	y	PROPN
ejpam-6141	38	20	in	in	ADP
ejpam-6141	38	21	q	q	NOUN
ejpam-6141	38	22	such	such	ADJ
ejpam-6141	38	23	that	that	SCONJ
ejpam-6141	38	24	both	both	DET
ejpam-6141	38	25	a	a	DET
ejpam-6141	38	26	⋆	⋆	NOUN
ejpam-6141	38	27	x	x	SYM
ejpam-6141	38	28	=	=	SYM
ejpam-6141	38	29	b	b	PROPN
ejpam-6141	38	30	,	,	PUNCT
ejpam-6141	38	31	y	y	PROPN
ejpam-6141	38	32	⋆	⋆	VERB
ejpam-6141	38	33	a	a	DET
ejpam-6141	38	34	=	=	X
ejpam-6141	38	35	b	b	NOUN
ejpam-6141	38	36	hold	hold	NOUN
ejpam-6141	38	37	.	.	PUNCT
ejpam-6141	39	1	in	in	ADP
ejpam-6141	39	2	other	other	ADJ
ejpam-6141	39	3	words	word	NOUN
ejpam-6141	39	4	,	,	PUNCT
ejpam-6141	39	5	each	each	DET
ejpam-6141	39	6	element	element	NOUN
ejpam-6141	39	7	of	of	ADP
ejpam-6141	39	8	the	the	DET
ejpam-6141	39	9	set	set	NOUN
ejpam-6141	39	10	occurs	occur	VERB
ejpam-6141	39	11	exactly	exactly	ADV
ejpam-6141	39	12	once	once	ADV
ejpam-6141	39	13	in	in	ADP
ejpam-6141	39	14	each	each	DET
ejpam-6141	39	15	row	row	NOUN
ejpam-6141	39	16	and	and	CCONJ
ejpam-6141	39	17	exactly	exactly	ADV
ejpam-6141	39	18	once	once	ADV
ejpam-6141	39	19	in	in	ADP
ejpam-6141	39	20	each	each	DET
ejpam-6141	39	21	column	column	NOUN
ejpam-6141	39	22	of	of	ADP
ejpam-6141	39	23	the	the	DET
ejpam-6141	39	24	quasigroup	quasigroup	NOUN
ejpam-6141	39	25	’s	’s	PART
ejpam-6141	39	26	multiplication	multiplication	NOUN
ejpam-6141	39	27	table	table	NOUN
ejpam-6141	39	28	,	,	PUNCT
ejpam-6141	39	29	or	or	CCONJ
ejpam-6141	39	30	cayley	cayley	ADJ
ejpam-6141	39	31	table	table	NOUN
ejpam-6141	39	32	.	.	PUNCT
ejpam-6141	40	1	this	this	DET
ejpam-6141	40	2	property	property	NOUN
ejpam-6141	40	3	ensures	ensure	VERB
ejpam-6141	40	4	that	that	SCONJ
ejpam-6141	40	5	the	the	DET
ejpam-6141	40	6	cayley	cayley	ADJ
ejpam-6141	40	7	table	table	NOUN
ejpam-6141	40	8	of	of	ADP
ejpam-6141	40	9	a	a	DET
ejpam-6141	40	10	finite	finite	ADJ
ejpam-6141	40	11	quasigroup	quasigroup	NOUN
ejpam-6141	40	12	,	,	PUNCT
ejpam-6141	40	13	and	and	CCONJ
ejpam-6141	40	14	,	,	PUNCT
ejpam-6141	40	15	in	in	ADP
ejpam-6141	40	16	particular	particular	ADJ
ejpam-6141	40	17	,	,	PUNCT
ejpam-6141	40	18	a	a	DET
ejpam-6141	40	19	finite	finite	ADJ
ejpam-6141	40	20	group	group	NOUN
ejpam-6141	40	21	,	,	PUNCT
ejpam-6141	40	22	is	be	AUX
ejpam-6141	40	23	a	a	DET
ejpam-6141	40	24	latin	latin	ADJ
ejpam-6141	40	25	square	square	NOUN
ejpam-6141	40	26	.	.	PUNCT
ejpam-6141	41	1	m.	m.	NOUN
ejpam-6141	41	2	a.	a.	PROPN
ejpam-6141	41	3	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	41	4	,	,	PUNCT
ejpam-6141	41	5	s.	s.	PROPN
ejpam-6141	41	6	mirvakili	mirvakili	PROPN
ejpam-6141	41	7	/	/	SYM
ejpam-6141	41	8	eur	eur	PROPN
ejpam-6141	41	9	.	.	PUNCT
ejpam-6141	42	1	j.	j.	PROPN
ejpam-6141	42	2	pure	pure	PROPN
ejpam-6141	42	3	appl	appl	PROPN
ejpam-6141	42	4	.	.	PROPN
ejpam-6141	42	5	math	math	PROPN
ejpam-6141	42	6	,	,	PUNCT
ejpam-6141	42	7	18	18	NUM
ejpam-6141	42	8	(	(	PUNCT
ejpam-6141	42	9	2	2	NUM
ejpam-6141	42	10	)	)	PUNCT
ejpam-6141	42	11	(	(	PUNCT
ejpam-6141	42	12	2025	2025	NUM
ejpam-6141	42	13	)	)	PUNCT
ejpam-6141	42	14	,	,	PUNCT
ejpam-6141	42	15	6141	6141	NUM
ejpam-6141	42	16	3	3	NUM
ejpam-6141	42	17	of	of	ADP
ejpam-6141	42	18	10	10	NUM
ejpam-6141	42	19	we	we	PRON
ejpam-6141	42	20	recall	recall	VERB
ejpam-6141	42	21	basic	basic	ADJ
ejpam-6141	42	22	definitions	definition	NOUN
ejpam-6141	42	23	from	from	ADP
ejpam-6141	42	24	[	[	X
ejpam-6141	42	25	8	8	NUM
ejpam-6141	42	26	]	]	PUNCT
ejpam-6141	42	27	.	.	PUNCT
ejpam-6141	43	1	a	a	DET
ejpam-6141	43	2	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	43	3	or	or	CCONJ
ejpam-6141	43	4	hyperstructure	hyperstructure	NOUN
ejpam-6141	43	5	is	be	AUX
ejpam-6141	43	6	a	a	DET
ejpam-6141	43	7	non	non	ADJ
ejpam-6141	43	8	-	-	ADJ
ejpam-6141	43	9	empty	empty	ADJ
ejpam-6141	43	10	set	set	ADJ
ejpam-6141	43	11	h	h	NOUN
ejpam-6141	43	12	with	with	ADP
ejpam-6141	43	13	a	a	DET
ejpam-6141	43	14	hyperoperation	hyperoperation	NOUN
ejpam-6141	43	15	◦	◦	NOUN
ejpam-6141	43	16	defined	define	VERB
ejpam-6141	43	17	on	on	ADP
ejpam-6141	43	18	h	h	NOUN
ejpam-6141	43	19	,	,	PUNCT
ejpam-6141	43	20	that	that	ADV
ejpam-6141	43	21	is	is	ADV
ejpam-6141	43	22	,	,	PUNCT
ejpam-6141	43	23	a	a	DET
ejpam-6141	43	24	mapping	mapping	NOUN
ejpam-6141	43	25	of	of	ADP
ejpam-6141	43	26	h	h	NOUN
ejpam-6141	43	27	×h	×h	PROPN
ejpam-6141	43	28	into	into	ADP
ejpam-6141	43	29	the	the	DET
ejpam-6141	43	30	family	family	NOUN
ejpam-6141	43	31	of	of	ADP
ejpam-6141	43	32	non	non	ADJ
ejpam-6141	43	33	-	-	ADJ
ejpam-6141	43	34	empty	empty	ADJ
ejpam-6141	43	35	subsets	subset	NOUN
ejpam-6141	43	36	of	of	ADP
ejpam-6141	43	37	h.	h.	PROPN
ejpam-6141	43	38	if	if	SCONJ
ejpam-6141	43	39	(	(	PUNCT
ejpam-6141	43	40	x	x	NOUN
ejpam-6141	43	41	,	,	PUNCT
ejpam-6141	43	42	y	y	NOUN
ejpam-6141	43	43	)	)	PUNCT
ejpam-6141	43	44	∈	∈	PROPN
ejpam-6141	43	45	h	h	NOUN
ejpam-6141	43	46	×	×	PROPN
ejpam-6141	43	47	h	h	NOUN
ejpam-6141	43	48	,	,	PUNCT
ejpam-6141	43	49	its	its	PRON
ejpam-6141	43	50	image	image	NOUN
ejpam-6141	43	51	under	under	ADP
ejpam-6141	43	52	◦	◦	NOUN
ejpam-6141	43	53	is	be	AUX
ejpam-6141	43	54	defined	define	VERB
ejpam-6141	43	55	by	by	ADP
ejpam-6141	43	56	x	x	X
ejpam-6141	43	57	◦	◦	NOUN
ejpam-6141	43	58	y.	y.	NOUN
ejpam-6141	43	59	if	if	SCONJ
ejpam-6141	43	60	a	a	DET
ejpam-6141	43	61	,	,	PUNCT
ejpam-6141	43	62	b	b	NOUN
ejpam-6141	43	63	are	be	AUX
ejpam-6141	43	64	non	non	ADJ
ejpam-6141	43	65	-	-	ADJ
ejpam-6141	43	66	empty	empty	ADJ
ejpam-6141	43	67	subsets	subset	NOUN
ejpam-6141	43	68	of	of	ADP
ejpam-6141	43	69	h	h	NOUN
ejpam-6141	43	70	then	then	ADV
ejpam-6141	43	71	a	a	DET
ejpam-6141	43	72	◦	◦	NOUN
ejpam-6141	43	73	b	b	NOUN
ejpam-6141	43	74	is	be	AUX
ejpam-6141	43	75	given	give	VERB
ejpam-6141	43	76	by	by	ADP
ejpam-6141	43	77	a	a	DET
ejpam-6141	43	78	◦	◦	NOUN
ejpam-6141	43	79	b	b	NOUN
ejpam-6141	43	80	=	=	X
ejpam-6141	43	81	⋃	⋃	NOUN
ejpam-6141	43	82	{	{	PUNCT
ejpam-6141	43	83	x	x	SYM
ejpam-6141	43	84	◦	◦	VERB
ejpam-6141	43	85	y|x	y|x	NOUN
ejpam-6141	43	86	∈	∈	PROPN
ejpam-6141	43	87	a	a	DET
ejpam-6141	43	88	,	,	PUNCT
ejpam-6141	43	89	y	y	PROPN
ejpam-6141	43	90	∈	∈	PROPN
ejpam-6141	43	91	b	b	PROPN
ejpam-6141	43	92	}	}	PUNCT
ejpam-6141	43	93	.	.	PUNCT
ejpam-6141	44	1	the	the	DET
ejpam-6141	44	2	notation	notation	NOUN
ejpam-6141	44	3	a	a	DET
ejpam-6141	44	4	◦	◦	NOUN
ejpam-6141	44	5	a	a	PRON
ejpam-6141	44	6	is	be	AUX
ejpam-6141	44	7	used	use	VERB
ejpam-6141	44	8	for	for	ADP
ejpam-6141	44	9	{	{	PUNCT
ejpam-6141	44	10	a	a	DET
ejpam-6141	44	11	}	}	PUNCT
ejpam-6141	44	12	◦	◦	NOUN
ejpam-6141	44	13	a	a	NOUN
ejpam-6141	44	14	,	,	PUNCT
ejpam-6141	44	15	and	and	CCONJ
ejpam-6141	44	16	a	a	DET
ejpam-6141	44	17	◦	◦	NOUN
ejpam-6141	44	18	a	a	PRON
ejpam-6141	44	19	for	for	ADP
ejpam-6141	44	20	a	a	DET
ejpam-6141	44	21	◦	◦	NOUN
ejpam-6141	44	22	{	{	PUNCT
ejpam-6141	44	23	a	a	NOUN
ejpam-6141	44	24	}	}	PUNCT
ejpam-6141	44	25	.	.	PUNCT
ejpam-6141	45	1	generally	generally	ADV
ejpam-6141	45	2	,	,	PUNCT
ejpam-6141	45	3	the	the	DET
ejpam-6141	45	4	singleton	singleton	NOUN
ejpam-6141	45	5	{	{	PUNCT
ejpam-6141	45	6	a	a	PRON
ejpam-6141	45	7	}	}	PUNCT
ejpam-6141	45	8	is	be	AUX
ejpam-6141	45	9	identified	identify	VERB
ejpam-6141	45	10	with	with	ADP
ejpam-6141	45	11	its	its	PRON
ejpam-6141	45	12	member	member	NOUN
ejpam-6141	45	13	a.	a.	NOUN
ejpam-6141	45	14	the	the	DET
ejpam-6141	45	15	relational	relational	ADJ
ejpam-6141	45	16	notation	notation	NOUN
ejpam-6141	45	17	a	a	DET
ejpam-6141	45	18	≈	≈	PROPN
ejpam-6141	45	19	b	b	PROPN
ejpam-6141	45	20	(	(	PUNCT
ejpam-6141	45	21	read	read	VERB
ejpam-6141	45	22	a	a	DET
ejpam-6141	45	23	meets	meet	NOUN
ejpam-6141	45	24	b	b	NOUN
ejpam-6141	45	25	)	)	PUNCT
ejpam-6141	45	26	is	be	AUX
ejpam-6141	45	27	used	use	VERB
ejpam-6141	45	28	to	to	PART
ejpam-6141	45	29	assert	assert	VERB
ejpam-6141	45	30	that	that	SCONJ
ejpam-6141	45	31	the	the	DET
ejpam-6141	45	32	sets	set	NOUN
ejpam-6141	45	33	a	a	PRON
ejpam-6141	45	34	and	and	CCONJ
ejpam-6141	45	35	b	b	NOUN
ejpam-6141	45	36	have	have	VERB
ejpam-6141	45	37	an	an	DET
ejpam-6141	45	38	element	element	NOUN
ejpam-6141	45	39	in	in	ADP
ejpam-6141	45	40	common	common	ADJ
ejpam-6141	45	41	,	,	PUNCT
ejpam-6141	45	42	that	that	ADV
ejpam-6141	45	43	is	is	ADV
ejpam-6141	45	44	,	,	PUNCT
ejpam-6141	45	45	a	a	DET
ejpam-6141	45	46	∩b	∩b	NOUN
ejpam-6141	45	47	̸=	̸=	PROPN
ejpam-6141	45	48	∅.	∅.	ADP
ejpam-6141	45	49	a	a	DET
ejpam-6141	45	50	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	45	51	(	(	PUNCT
ejpam-6141	45	52	h	h	NOUN
ejpam-6141	45	53	,	,	PUNCT
ejpam-6141	45	54	◦	◦	NOUN
ejpam-6141	45	55	)	)	PUNCT
ejpam-6141	45	56	is	be	AUX
ejpam-6141	45	57	called	call	VERB
ejpam-6141	45	58	a	a	DET
ejpam-6141	45	59	semihypergroup	semihypergroup	NOUN
ejpam-6141	45	60	if	if	SCONJ
ejpam-6141	45	61	for	for	ADP
ejpam-6141	45	62	all	all	DET
ejpam-6141	45	63	x	x	NOUN
ejpam-6141	45	64	,	,	PUNCT
ejpam-6141	45	65	y	y	PROPN
ejpam-6141	45	66	,	,	PUNCT
ejpam-6141	45	67	z	z	PROPN
ejpam-6141	45	68	∈	∈	PROPN
ejpam-6141	45	69	h	h	NOUN
ejpam-6141	45	70	we	we	PRON
ejpam-6141	45	71	have	have	VERB
ejpam-6141	45	72	x	x	PART
ejpam-6141	45	73	◦	◦	NOUN
ejpam-6141	45	74	(	(	PUNCT
ejpam-6141	45	75	y	y	PROPN
ejpam-6141	45	76	◦	◦	PROPN
ejpam-6141	45	77	z	z	PROPN
ejpam-6141	45	78	)	)	PUNCT
ejpam-6141	46	1	=	=	SYM
ejpam-6141	46	2	(	(	PUNCT
ejpam-6141	46	3	x	x	SYM
ejpam-6141	46	4	◦	◦	VERB
ejpam-6141	46	5	y	y	NOUN
ejpam-6141	46	6	)	)	PUNCT
ejpam-6141	46	7	◦	◦	NOUN
ejpam-6141	46	8	z.	z.	PROPN
ejpam-6141	46	9	moreover	moreover	ADV
ejpam-6141	46	10	,	,	PUNCT
ejpam-6141	46	11	a	a	DET
ejpam-6141	46	12	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	46	13	(	(	PUNCT
ejpam-6141	46	14	h	h	NOUN
ejpam-6141	46	15	,	,	PUNCT
ejpam-6141	46	16	◦	◦	NOUN
ejpam-6141	46	17	)	)	PUNCT
ejpam-6141	46	18	is	be	AUX
ejpam-6141	46	19	called	call	VERB
ejpam-6141	46	20	a	a	DET
ejpam-6141	46	21	hv	hv	NOUN
ejpam-6141	46	22	-	-	PUNCT
ejpam-6141	46	23	semigroup	semigroup	NOUN
ejpam-6141	46	24	if	if	SCONJ
ejpam-6141	46	25	for	for	ADP
ejpam-6141	46	26	all	all	DET
ejpam-6141	46	27	x	x	NOUN
ejpam-6141	46	28	,	,	PUNCT
ejpam-6141	46	29	y	y	PROPN
ejpam-6141	46	30	,	,	PUNCT
ejpam-6141	46	31	z	z	PROPN
ejpam-6141	46	32	∈	∈	PROPN
ejpam-6141	46	33	h	h	NOUN
ejpam-6141	46	34	we	we	PRON
ejpam-6141	46	35	have	have	VERB
ejpam-6141	47	1	x	x	PART
ejpam-6141	47	2	◦	◦	NOUN
ejpam-6141	47	3	(	(	PUNCT
ejpam-6141	47	4	y	y	PROPN
ejpam-6141	47	5	◦	◦	PROPN
ejpam-6141	47	6	z	z	PROPN
ejpam-6141	47	7	)	)	PUNCT
ejpam-6141	47	8	∩	∩	NOUN
ejpam-6141	47	9	(	(	PUNCT
ejpam-6141	47	10	x	x	SYM
ejpam-6141	47	11	◦	◦	VERB
ejpam-6141	47	12	y	y	NOUN
ejpam-6141	47	13	)	)	PUNCT
ejpam-6141	47	14	◦	◦	NOUN
ejpam-6141	47	15	z	z	NOUN
ejpam-6141	47	16	̸=	̸=	PROPN
ejpam-6141	47	17	∅	∅	NOUN
ejpam-6141	47	18	or	or	CCONJ
ejpam-6141	47	19	x	x	PART
ejpam-6141	47	20	◦	◦	NOUN
ejpam-6141	47	21	(	(	PUNCT
ejpam-6141	47	22	y	y	PROPN
ejpam-6141	47	23	◦	◦	PROPN
ejpam-6141	47	24	z	z	PROPN
ejpam-6141	47	25	)	)	PUNCT
ejpam-6141	48	1	≈	≈	PROPN
ejpam-6141	48	2	(	(	PUNCT
ejpam-6141	48	3	x	x	SYM
ejpam-6141	48	4	◦	◦	VERB
ejpam-6141	48	5	y	y	NOUN
ejpam-6141	48	6	)	)	PUNCT
ejpam-6141	48	7	◦	◦	NOUN
ejpam-6141	48	8	z.	z.	PROPN
ejpam-6141	49	1	a	a	PRON
ejpam-6141	49	2	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	49	3	(	(	PUNCT
ejpam-6141	49	4	h	h	NOUN
ejpam-6141	49	5	,	,	PUNCT
ejpam-6141	49	6	◦	◦	NOUN
ejpam-6141	49	7	)	)	PUNCT
ejpam-6141	49	8	is	be	AUX
ejpam-6141	49	9	called	call	VERB
ejpam-6141	49	10	a	a	DET
ejpam-6141	49	11	commutative	commutative	ADJ
ejpam-6141	49	12	hypergroupoid	hypergroupoid	NOUN
ejpam-6141	49	13	if	if	SCONJ
ejpam-6141	49	14	x	x	PART
ejpam-6141	49	15	◦	◦	VERB
ejpam-6141	49	16	y	y	NOUN
ejpam-6141	49	17	=	=	SYM
ejpam-6141	49	18	y	y	PROPN
ejpam-6141	49	19	◦	◦	NOUN
ejpam-6141	49	20	x	x	ADP
ejpam-6141	49	21	,	,	PUNCT
ejpam-6141	49	22	for	for	ADP
ejpam-6141	49	23	all	all	DET
ejpam-6141	49	24	x	x	NOUN
ejpam-6141	49	25	,	,	PUNCT
ejpam-6141	49	26	y	y	PROPN
ejpam-6141	49	27	∈	∈	PROPN
ejpam-6141	49	28	h.	h.	NOUN
ejpam-6141	50	1	moreover	moreover	ADV
ejpam-6141	50	2	it	it	PRON
ejpam-6141	50	3	is	be	AUX
ejpam-6141	50	4	called	call	VERB
ejpam-6141	50	5	weak	weak	ADJ
ejpam-6141	50	6	commutative	commutative	ADJ
ejpam-6141	50	7	if	if	SCONJ
ejpam-6141	50	8	x	x	PRON
ejpam-6141	50	9	◦	◦	NOUN
ejpam-6141	50	10	y	y	PROPN
ejpam-6141	50	11	∩	∩	NOUN
ejpam-6141	50	12	y	y	PROPN
ejpam-6141	50	13	◦	◦	NOUN
ejpam-6141	50	14	x	x	PUNCT
ejpam-6141	50	15	̸=	̸=	NOUN
ejpam-6141	50	16	∅	∅	NOUN
ejpam-6141	50	17	or	or	CCONJ
ejpam-6141	50	18	x	x	PART
ejpam-6141	50	19	◦	◦	NOUN
ejpam-6141	50	20	y	y	PROPN
ejpam-6141	50	21	≈	≈	PROPN
ejpam-6141	50	22	y	y	PROPN
ejpam-6141	50	23	◦	◦	NOUN
ejpam-6141	50	24	x	x	ADP
ejpam-6141	50	25	,	,	PUNCT
ejpam-6141	50	26	for	for	ADP
ejpam-6141	50	27	all	all	DET
ejpam-6141	50	28	x	x	NOUN
ejpam-6141	50	29	,	,	PUNCT
ejpam-6141	50	30	y	y	PROPN
ejpam-6141	50	31	∈	∈	PROPN
ejpam-6141	50	32	h.	h.	PROPN
ejpam-6141	50	33	a	a	DET
ejpam-6141	50	34	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	50	35	(	(	PUNCT
ejpam-6141	50	36	h	h	NOUN
ejpam-6141	50	37	,	,	PUNCT
ejpam-6141	50	38	◦	◦	NOUN
ejpam-6141	50	39	)	)	PUNCT
ejpam-6141	50	40	is	be	AUX
ejpam-6141	50	41	called	call	VERB
ejpam-6141	50	42	a	a	DET
ejpam-6141	50	43	quasihypergroup	quasihypergroup	NOUN
ejpam-6141	50	44	if	if	SCONJ
ejpam-6141	50	45	for	for	ADP
ejpam-6141	50	46	all	all	PRON
ejpam-6141	50	47	x	x	SYM
ejpam-6141	50	48	∈	∈	NOUN
ejpam-6141	50	49	h	h	NOUN
ejpam-6141	50	50	we	we	PRON
ejpam-6141	50	51	have	have	VERB
ejpam-6141	50	52	x	x	PART
ejpam-6141	50	53	◦	◦	NOUN
ejpam-6141	50	54	h	h	NOUN
ejpam-6141	50	55	=	=	NOUN
ejpam-6141	51	1	h	h	NOUN
ejpam-6141	52	1	◦	◦	NOUN
ejpam-6141	52	2	x	x	X
ejpam-6141	53	1	=	=	PUNCT
ejpam-6141	53	2	h.	h.	NOUN
ejpam-6141	53	3	we	we	PRON
ejpam-6141	53	4	defin	defin	VERB
ejpam-6141	53	5	two	two	NUM
ejpam-6141	53	6	hypercompositions	hypercomposition	NOUN
ejpam-6141	53	7	on	on	ADP
ejpam-6141	53	8	(	(	PUNCT
ejpam-6141	53	9	h	h	NOUN
ejpam-6141	53	10	,	,	PUNCT
ejpam-6141	53	11	◦	◦	NOUN
ejpam-6141	53	12	)	)	PUNCT
ejpam-6141	53	13	,	,	PUNCT
ejpam-6141	53	14	right	right	ADJ
ejpam-6141	53	15	extension	extension	NOUN
ejpam-6141	53	16	/	/	PUNCT
ejpam-6141	53	17	and	and	CCONJ
ejpam-6141	53	18	left	leave	VERB
ejpam-6141	53	19	extension	extension	NOUN
ejpam-6141	53	20	\	\	PROPN
ejpam-6141	53	21	,	,	PUNCT
ejpam-6141	53	22	each	each	PRON
ejpam-6141	53	23	an	an	DET
ejpam-6141	53	24	inverse	inverse	NOUN
ejpam-6141	53	25	to	to	ADP
ejpam-6141	53	26	·	·	PUNCT
ejpam-6141	53	27	,	,	PUNCT
ejpam-6141	53	28	are	be	AUX
ejpam-6141	53	29	defined	define	VERB
ejpam-6141	53	30	by	by	ADP
ejpam-6141	53	31	:	:	PUNCT
ejpam-6141	53	32	a	a	PROPN
ejpam-6141	53	33	/	/	SYM
ejpam-6141	53	34	b	b	NOUN
ejpam-6141	53	35	=	=	PRON
ejpam-6141	53	36	{	{	PUNCT
ejpam-6141	53	37	x	x	X
ejpam-6141	53	38	|	|	ADV
ejpam-6141	53	39	a	a	PRON
ejpam-6141	53	40	∈	∈	NOUN
ejpam-6141	53	41	x	x	PUNCT
ejpam-6141	53	42	◦	◦	NOUN
ejpam-6141	53	43	b	b	NOUN
ejpam-6141	53	44	}	}	PUNCT
ejpam-6141	53	45	and	and	CCONJ
ejpam-6141	53	46	b\a	b\a	NOUN
ejpam-6141	53	47	=	=	PUNCT
ejpam-6141	53	48	{	{	PUNCT
ejpam-6141	53	49	x	x	X
ejpam-6141	53	50	|	|	ADV
ejpam-6141	53	51	a	a	DET
ejpam-6141	53	52	∈	∈	PROPN
ejpam-6141	53	53	b	b	NOUN
ejpam-6141	53	54	◦	◦	NOUN
ejpam-6141	53	55	x	x	NOUN
ejpam-6141	53	56	}	}	PUNCT
ejpam-6141	53	57	.	.	PUNCT
ejpam-6141	54	1	hence	hence	ADV
ejpam-6141	54	2	,	,	PUNCT
ejpam-6141	54	3	x	x	PROPN
ejpam-6141	54	4	≈	≈	PROPN
ejpam-6141	54	5	a	a	PROPN
ejpam-6141	54	6	/	/	SYM
ejpam-6141	54	7	b	b	NOUN
ejpam-6141	54	8	if	if	SCONJ
ejpam-6141	54	9	and	and	CCONJ
ejpam-6141	54	10	only	only	ADV
ejpam-6141	54	11	if	if	SCONJ
ejpam-6141	54	12	a	a	DET
ejpam-6141	54	13	≈	≈	PROPN
ejpam-6141	54	14	x	x	PUNCT
ejpam-6141	54	15	◦	◦	NOUN
ejpam-6141	54	16	b	b	NUM
ejpam-6141	54	17	,	,	PUNCT
ejpam-6141	54	18	and	and	CCONJ
ejpam-6141	54	19	x	x	X
ejpam-6141	54	20	≈	≈	NOUN
ejpam-6141	54	21	b\a	b\a	NOUN
ejpam-6141	54	22	if	if	SCONJ
ejpam-6141	54	23	and	and	CCONJ
ejpam-6141	54	24	only	only	ADV
ejpam-6141	54	25	if	if	SCONJ
ejpam-6141	54	26	a	a	DET
ejpam-6141	54	27	≈	≈	PROPN
ejpam-6141	54	28	b	b	PROPN
ejpam-6141	54	29	◦	◦	NOUN
ejpam-6141	54	30	x.	x.	NOUN
ejpam-6141	54	31	definition	definition	NOUN
ejpam-6141	54	32	1	1	NUM
ejpam-6141	54	33	.	.	PUNCT
ejpam-6141	55	1	let	let	VERB
ejpam-6141	55	2	x	x	PRON
ejpam-6141	55	3	be	be	AUX
ejpam-6141	55	4	a	a	DET
ejpam-6141	55	5	n	n	ADV
ejpam-6141	55	6	-	-	PUNCT
ejpam-6141	55	7	set	set	VERB
ejpam-6141	55	8	and	and	CCONJ
ejpam-6141	55	9	let	let	VERB
ejpam-6141	55	10	a	a	PRON
ejpam-6141	55	11	=	=	PUNCT
ejpam-6141	56	1	[	[	X
ejpam-6141	56	2	aij	aij	X
ejpam-6141	56	3	]	]	PUNCT
ejpam-6141	56	4	be	be	AUX
ejpam-6141	56	5	a	a	DET
ejpam-6141	56	6	n×n	n×n	PROPN
ejpam-6141	56	7	matrix	matrix	NOUN
ejpam-6141	56	8	with	with	ADP
ejpam-6141	56	9	aij	aij	PROPN
ejpam-6141	56	10	⊆	⊆	NUM
ejpam-6141	56	11	x	x	NOUN
ejpam-6141	56	12	for	for	ADP
ejpam-6141	56	13	all	all	PRON
ejpam-6141	56	14	of	of	ADP
ejpam-6141	56	15	1	1	NUM
ejpam-6141	56	16	≤	≤	NUM
ejpam-6141	56	17	i	i	PRON
ejpam-6141	56	18	,	,	PUNCT
ejpam-6141	56	19	j	j	PROPN
ejpam-6141	56	20	≤	≤	PROPN
ejpam-6141	56	21	n.	n.	NOUN
ejpam-6141	56	22	a	a	PRON
ejpam-6141	56	23	is	be	AUX
ejpam-6141	56	24	called	call	VERB
ejpam-6141	56	25	a	a	DET
ejpam-6141	56	26	generalized	generalized	ADJ
ejpam-6141	56	27	latin	latin	ADJ
ejpam-6141	56	28	square	square	NOUN
ejpam-6141	56	29	on	on	ADP
ejpam-6141	56	30	n	n	ADV
ejpam-6141	56	31	-	-	PUNCT
ejpam-6141	56	32	set	set	VERB
ejpam-6141	56	33	x	x	NOUN
ejpam-6141	56	34	if	if	SCONJ
ejpam-6141	56	35	the	the	DET
ejpam-6141	56	36	following	follow	VERB
ejpam-6141	56	37	condition	condition	NOUN
ejpam-6141	56	38	is	be	AUX
ejpam-6141	56	39	satisfied	satisfied	ADJ
ejpam-6141	56	40	:	:	PUNCT
ejpam-6141	56	41	n⋃	n⋃	PROPN
ejpam-6141	56	42	i=1	i=1	PROPN
ejpam-6141	56	43	aij	aij	PROPN
ejpam-6141	57	1	=	=	SYM
ejpam-6141	57	2	x	x	SYM
ejpam-6141	57	3	=	=	NOUN
ejpam-6141	57	4	n⋃	n⋃	PRON
ejpam-6141	57	5	j=1	j=1	PROPN
ejpam-6141	57	6	aij	aij	PROPN
ejpam-6141	57	7	.	.	PUNCT
ejpam-6141	57	8	example	example	NOUN
ejpam-6141	57	9	1	1	NUM
ejpam-6141	57	10	.	.	PUNCT
ejpam-6141	57	11	let	let	VERB
ejpam-6141	57	12	n	n	NOUN
ejpam-6141	57	13	=	=	SYM
ejpam-6141	57	14	4	4	NUM
ejpam-6141	57	15	,	,	PUNCT
ejpam-6141	57	16	x	x	PUNCT
ejpam-6141	57	17	=	=	X
ejpam-6141	57	18	{	{	PUNCT
ejpam-6141	57	19	a	a	PRON
ejpam-6141	57	20	,	,	PUNCT
ejpam-6141	57	21	b	b	NOUN
ejpam-6141	57	22	,	,	PUNCT
ejpam-6141	57	23	c	c	NOUN
ejpam-6141	57	24	,	,	PUNCT
ejpam-6141	57	25	d	d	NOUN
ejpam-6141	57	26	}	}	PUNCT
ejpam-6141	57	27	and	and	CCONJ
ejpam-6141	57	28	aii	aii	PROPN
ejpam-6141	57	29	=	=	SYM
ejpam-6141	57	30	x	x	PROPN
ejpam-6141	57	31	and	and	CCONJ
ejpam-6141	57	32	aij	aij	PROPN
ejpam-6141	57	33	=	=	SYM
ejpam-6141	57	34	{	{	PUNCT
ejpam-6141	57	35	a	a	NOUN
ejpam-6141	57	36	}	}	PUNCT
ejpam-6141	57	37	,	,	PUNCT
ejpam-6141	57	38	where	where	SCONJ
ejpam-6141	57	39	i	i	PRON
ejpam-6141	57	40	̸=	̸=	PROPN
ejpam-6141	57	41	j.	j.	PROPN
ejpam-6141	57	42	then	then	ADV
ejpam-6141	57	43	a	a	PRON
ejpam-6141	57	44	=	=	X
ejpam-6141	58	1	[	[	X
ejpam-6141	58	2	aij	aij	X
ejpam-6141	58	3	]	]	PUNCT
ejpam-6141	58	4	is	be	AUX
ejpam-6141	58	5	a	a	DET
ejpam-6141	58	6	generalized	generalized	ADJ
ejpam-6141	58	7	latin	latin	ADJ
ejpam-6141	58	8	square	square	NOUN
ejpam-6141	58	9	.	.	PUNCT
ejpam-6141	59	1	in	in	ADP
ejpam-6141	59	2	fact	fact	NOUN
ejpam-6141	59	3	a	a	DET
ejpam-6141	59	4	=	=	X
ejpam-6141	59	5	x	x	X
ejpam-6141	59	6	a	a	DET
ejpam-6141	59	7	a	a	DET
ejpam-6141	59	8	a	a	DET
ejpam-6141	59	9	a	a	NOUN
ejpam-6141	59	10	x	x	NOUN
ejpam-6141	59	11	a	a	DET
ejpam-6141	59	12	a	a	DET
ejpam-6141	59	13	a	a	DET
ejpam-6141	59	14	a	a	NOUN
ejpam-6141	59	15	x	x	NOUN
ejpam-6141	59	16	a	a	DET
ejpam-6141	59	17	a	a	DET
ejpam-6141	59	18	a	a	DET
ejpam-6141	59	19	a	a	DET
ejpam-6141	59	20	x	x	NOUN
ejpam-6141	59	21	definition	definition	NOUN
ejpam-6141	59	22	2	2	NUM
ejpam-6141	59	23	.	.	PUNCT
ejpam-6141	60	1	let	let	VERB
ejpam-6141	60	2	x	x	PRON
ejpam-6141	60	3	be	be	AUX
ejpam-6141	60	4	a	a	DET
ejpam-6141	60	5	n	n	ADV
ejpam-6141	60	6	-	-	PUNCT
ejpam-6141	60	7	set	set	VERB
ejpam-6141	60	8	and	and	CCONJ
ejpam-6141	60	9	let	let	VERB
ejpam-6141	60	10	a	a	PRON
ejpam-6141	60	11	=	=	PUNCT
ejpam-6141	61	1	[	[	X
ejpam-6141	61	2	aij	aij	X
ejpam-6141	61	3	]	]	PUNCT
ejpam-6141	61	4	be	be	AUX
ejpam-6141	61	5	a	a	DET
ejpam-6141	61	6	n×	n×	PROPN
ejpam-6141	61	7	n	n	NOUN
ejpam-6141	61	8	matrix	matrix	NOUN
ejpam-6141	61	9	with	with	ADP
ejpam-6141	61	10	aij	aij	PROPN
ejpam-6141	61	11	⊆	⊆	NUM
ejpam-6141	61	12	x	x	NOUN
ejpam-6141	61	13	for	for	ADP
ejpam-6141	61	14	all	all	PRON
ejpam-6141	61	15	of	of	ADP
ejpam-6141	61	16	1	1	NUM
ejpam-6141	61	17	≤	≤	NUM
ejpam-6141	61	18	i	i	PRON
ejpam-6141	61	19	,	,	PUNCT
ejpam-6141	61	20	j	j	PROPN
ejpam-6141	61	21	≤	≤	PROPN
ejpam-6141	61	22	n.	n.	NOUN
ejpam-6141	61	23	a	a	PRON
ejpam-6141	61	24	is	be	AUX
ejpam-6141	61	25	called	call	VERB
ejpam-6141	61	26	a	a	DET
ejpam-6141	61	27	latin	latin	ADJ
ejpam-6141	61	28	k	k	NOUN
ejpam-6141	61	29	-	-	NOUN
ejpam-6141	61	30	hypersquare	hypersquare	NOUN
ejpam-6141	61	31	on	on	ADP
ejpam-6141	61	32	n	n	ADV
ejpam-6141	61	33	-	-	PUNCT
ejpam-6141	61	34	set	set	VERB
ejpam-6141	61	35	x	x	NOUN
ejpam-6141	61	36	if	if	SCONJ
ejpam-6141	61	37	the	the	DET
ejpam-6141	61	38	following	follow	VERB
ejpam-6141	61	39	condition	condition	NOUN
ejpam-6141	61	40	is	be	AUX
ejpam-6141	61	41	satisfied	satisfied	ADJ
ejpam-6141	61	42	:	:	PUNCT
ejpam-6141	61	43	(	(	PUNCT
ejpam-6141	61	44	1	1	X
ejpam-6141	61	45	)	)	PUNCT
ejpam-6141	61	46	|aij	|aij	NOUN
ejpam-6141	61	47	|	|	NOUN
ejpam-6141	61	48	=	=	PROPN
ejpam-6141	61	49	k.	k.	PROPN
ejpam-6141	61	50	(	(	PUNCT
ejpam-6141	61	51	2	2	X
ejpam-6141	61	52	)	)	PUNCT
ejpam-6141	61	53	equations	equation	NOUN
ejpam-6141	61	54	a	a	DET
ejpam-6141	61	55	·	·	PUNCT
ejpam-6141	61	56	x	x	PUNCT
ejpam-6141	61	57	=	=	PUNCT
ejpam-6141	61	58	c	c	PROPN
ejpam-6141	61	59	and	and	CCONJ
ejpam-6141	61	60	y	y	PROPN
ejpam-6141	62	1	·	·	PUNCT
ejpam-6141	62	2	b	b	X
ejpam-6141	62	3	=	=	SYM
ejpam-6141	62	4	d	d	NOUN
ejpam-6141	62	5	has	have	VERB
ejpam-6141	62	6	exactly	exactly	ADV
ejpam-6141	62	7	k	k	ADJ
ejpam-6141	62	8	solutions	solution	NOUN
ejpam-6141	62	9	in	in	ADP
ejpam-6141	62	10	x	x	NOUN
ejpam-6141	62	11	,	,	PUNCT
ejpam-6141	62	12	where	where	SCONJ
ejpam-6141	62	13	the	the	DET
ejpam-6141	62	14	hyperoperation	hyperoperation	NOUN
ejpam-6141	62	15	·	·	PUNCT
ejpam-6141	62	16	on	on	ADP
ejpam-6141	62	17	x	x	SYM
ejpam-6141	62	18	is	be	AUX
ejpam-6141	62	19	defined	define	VERB
ejpam-6141	62	20	as	as	ADP
ejpam-6141	62	21	x	x	X
ejpam-6141	62	22	·	·	PUNCT
ejpam-6141	62	23	y	y	PROPN
ejpam-6141	62	24	=	=	SYM
ejpam-6141	62	25	axy	axy	PROPN
ejpam-6141	62	26	.	.	PUNCT
ejpam-6141	62	27	m.	m.	PROPN
ejpam-6141	62	28	a.	a.	PROPN
ejpam-6141	62	29	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	62	30	,	,	PUNCT
ejpam-6141	62	31	s.	s.	PROPN
ejpam-6141	62	32	mirvakili	mirvakili	PROPN
ejpam-6141	62	33	/	/	SYM
ejpam-6141	62	34	eur	eur	PROPN
ejpam-6141	62	35	.	.	PUNCT
ejpam-6141	63	1	j.	j.	PROPN
ejpam-6141	63	2	pure	pure	PROPN
ejpam-6141	63	3	appl	appl	PROPN
ejpam-6141	63	4	.	.	PROPN
ejpam-6141	63	5	math	math	PROPN
ejpam-6141	63	6	,	,	PUNCT
ejpam-6141	63	7	18	18	NUM
ejpam-6141	63	8	(	(	PUNCT
ejpam-6141	63	9	2	2	NUM
ejpam-6141	63	10	)	)	PUNCT
ejpam-6141	63	11	(	(	PUNCT
ejpam-6141	63	12	2025	2025	NUM
ejpam-6141	63	13	)	)	PUNCT
ejpam-6141	63	14	,	,	PUNCT
ejpam-6141	63	15	6141	6141	NUM
ejpam-6141	63	16	4	4	NUM
ejpam-6141	63	17	of	of	ADP
ejpam-6141	63	18	10	10	NUM
ejpam-6141	63	19	example	example	NOUN
ejpam-6141	63	20	2	2	NUM
ejpam-6141	63	21	.	.	PUNCT
ejpam-6141	64	1	the	the	DET
ejpam-6141	64	2	generalized	generalized	ADJ
ejpam-6141	64	3	latin	latin	PROPN
ejpam-6141	64	4	square	square	PROPN
ejpam-6141	64	5	a	a	DET
ejpam-6141	64	6	in	in	ADP
ejpam-6141	64	7	example	example	NOUN
ejpam-6141	64	8	1	1	NUM
ejpam-6141	64	9	is	be	AUX
ejpam-6141	64	10	not	not	PART
ejpam-6141	64	11	a	a	DET
ejpam-6141	64	12	latin	latin	ADJ
ejpam-6141	64	13	k	k	NOUN
ejpam-6141	64	14	-	-	NOUN
ejpam-6141	64	15	hypersquare	hypersquare	NOUN
ejpam-6141	64	16	.	.	PUNCT
ejpam-6141	65	1	but	but	CCONJ
ejpam-6141	65	2	the	the	DET
ejpam-6141	65	3	generalized	generalized	ADJ
ejpam-6141	65	4	latin	latin	PROPN
ejpam-6141	65	5	square	square	PROPN
ejpam-6141	65	6	b	b	PROPN
ejpam-6141	65	7	is	be	AUX
ejpam-6141	65	8	a	a	PRON
ejpam-6141	65	9	is	be	AUX
ejpam-6141	65	10	not	not	PART
ejpam-6141	65	11	a	a	DET
ejpam-6141	65	12	latin	latin	ADJ
ejpam-6141	65	13	2	2	NUM
ejpam-6141	65	14	-	-	PUNCT
ejpam-6141	65	15	hypersquare	hypersquare	NOUN
ejpam-6141	65	16	,	,	PUNCT
ejpam-6141	65	17	where	where	SCONJ
ejpam-6141	65	18	b	b	X
ejpam-6141	65	19	=	=	SYM
ejpam-6141	65	20	e	e	NOUN
ejpam-6141	65	21	,	,	PUNCT
ejpam-6141	65	22	c	c	PROPN
ejpam-6141	65	23	e	e	PROPN
ejpam-6141	65	24	,	,	PUNCT
ejpam-6141	65	25	a	a	DET
ejpam-6141	65	26	a	a	NOUN
ejpam-6141	65	27	,	,	PUNCT
ejpam-6141	65	28	b	b	PROPN
ejpam-6141	65	29	b	b	PROPN
ejpam-6141	65	30	,	,	PUNCT
ejpam-6141	65	31	c	c	PROPN
ejpam-6141	65	32	e	e	PROPN
ejpam-6141	65	33	,	,	PUNCT
ejpam-6141	65	34	a	a	DET
ejpam-6141	65	35	a	a	NOUN
ejpam-6141	65	36	,	,	PUNCT
ejpam-6141	65	37	b	b	PROPN
ejpam-6141	65	38	b	b	PROPN
ejpam-6141	65	39	,	,	PUNCT
ejpam-6141	65	40	c	c	PROPN
ejpam-6141	65	41	e	e	PROPN
ejpam-6141	65	42	,	,	PUNCT
ejpam-6141	65	43	c	c	PROPN
ejpam-6141	65	44	b	b	PROPN
ejpam-6141	65	45	,	,	PUNCT
ejpam-6141	65	46	c	c	PROPN
ejpam-6141	65	47	e	e	PROPN
ejpam-6141	65	48	,	,	PUNCT
ejpam-6141	65	49	c	c	PROPN
ejpam-6141	65	50	e	e	PROPN
ejpam-6141	65	51	,	,	PUNCT
ejpam-6141	65	52	a	a	DET
ejpam-6141	65	53	a	a	NOUN
ejpam-6141	65	54	,	,	PUNCT
ejpam-6141	65	55	b	b	NOUN
ejpam-6141	65	56	a	a	NOUN
ejpam-6141	65	57	,	,	PUNCT
ejpam-6141	65	58	b	b	PROPN
ejpam-6141	65	59	b	b	PROPN
ejpam-6141	65	60	,	,	PUNCT
ejpam-6141	65	61	c	c	PROPN
ejpam-6141	65	62	e	e	PROPN
ejpam-6141	65	63	,	,	PUNCT
ejpam-6141	65	64	c	c	PROPN
ejpam-6141	65	65	e	e	NOUN
ejpam-6141	65	66	,	,	PUNCT
ejpam-6141	65	67	a	a	DET
ejpam-6141	65	68	let	let	NOUN
ejpam-6141	65	69	(	(	PUNCT
ejpam-6141	65	70	h	h	NOUN
ejpam-6141	65	71	,	,	PUNCT
ejpam-6141	65	72	◦	◦	NOUN
ejpam-6141	65	73	)	)	PUNCT
ejpam-6141	65	74	be	be	AUX
ejpam-6141	65	75	a	a	DET
ejpam-6141	65	76	semihypergroup	semihypergroup	NOUN
ejpam-6141	65	77	.	.	PUNCT
ejpam-6141	66	1	the	the	DET
ejpam-6141	66	2	relation	relation	NOUN
ejpam-6141	66	3	β∗	β∗	NOUN
ejpam-6141	66	4	is	be	AUX
ejpam-6141	66	5	the	the	DET
ejpam-6141	66	6	transitive	transitive	ADJ
ejpam-6141	66	7	closure	closure	NOUN
ejpam-6141	66	8	of	of	ADP
ejpam-6141	66	9	the	the	DET
ejpam-6141	66	10	relation	relation	NOUN
ejpam-6141	66	11	β	β	X
ejpam-6141	66	12	=	=	SYM
ejpam-6141	66	13	∪n≥1βn	∪n≥1βn	PROPN
ejpam-6141	66	14	,	,	PUNCT
ejpam-6141	66	15	where	where	SCONJ
ejpam-6141	66	16	β1	β1	PROPN
ejpam-6141	66	17	is	be	AUX
ejpam-6141	66	18	the	the	DET
ejpam-6141	66	19	diagonal	diagonal	ADJ
ejpam-6141	66	20	relation	relation	NOUN
ejpam-6141	66	21	and	and	CCONJ
ejpam-6141	66	22	,	,	PUNCT
ejpam-6141	66	23	for	for	ADP
ejpam-6141	66	24	every	every	DET
ejpam-6141	66	25	integer	integer	NOUN
ejpam-6141	66	26	n	n	PROPN
ejpam-6141	66	27	>	>	X
ejpam-6141	66	28	1	1	NUM
ejpam-6141	66	29	,	,	PUNCT
ejpam-6141	66	30	βn	βn	X
ejpam-6141	66	31	is	be	AUX
ejpam-6141	66	32	the	the	DET
ejpam-6141	66	33	relation	relation	NOUN
ejpam-6141	66	34	defined	define	VERB
ejpam-6141	66	35	as	as	SCONJ
ejpam-6141	66	36	follows	follow	VERB
ejpam-6141	66	37	:	:	PUNCT
ejpam-6141	66	38	xβny	xβny	PROPN
ejpam-6141	66	39	⇔	⇔	PROPN
ejpam-6141	66	40	∃(z1	∃(z1	PROPN
ejpam-6141	66	41	,	,	PUNCT
ejpam-6141	66	42	.	.	PUNCT
ejpam-6141	66	43	.	.	PUNCT
ejpam-6141	67	1	.	.	PUNCT
ejpam-6141	68	1	,	,	PUNCT
ejpam-6141	68	2	zn	zn	X
ejpam-6141	68	3	)	)	PUNCT
ejpam-6141	68	4	∈	∈	PROPN
ejpam-6141	69	1	hn	hn	INTJ
ejpam-6141	69	2	:	:	PUNCT
ejpam-6141	69	3	{	{	PUNCT
ejpam-6141	69	4	x	x	NOUN
ejpam-6141	69	5	,	,	PUNCT
ejpam-6141	69	6	y	y	PROPN
ejpam-6141	69	7	}	}	PUNCT
ejpam-6141	69	8	⊆	⊆	NUM
ejpam-6141	69	9	n∏	n∏	PROPN
ejpam-6141	69	10	i=1	i=1	PROPN
ejpam-6141	69	11	zi	zi	PROPN
ejpam-6141	69	12	.	.	PUNCT
ejpam-6141	70	1	β∗	β∗	PROPN
ejpam-6141	70	2	is	be	AUX
ejpam-6141	70	3	the	the	DET
ejpam-6141	70	4	smallest	small	ADJ
ejpam-6141	70	5	strongly	strongly	ADV
ejpam-6141	70	6	regular	regular	ADJ
ejpam-6141	70	7	equivalence	equivalence	NOUN
ejpam-6141	70	8	onh.moreover	onh.moreover	NUM
ejpam-6141	70	9	,	,	PUNCT
ejpam-6141	70	10	the	the	DET
ejpam-6141	70	11	canonical	canonical	ADJ
ejpam-6141	70	12	projection	projection	NOUN
ejpam-6141	70	13	ψ	ψ	NOUN
ejpam-6141	70	14	:	:	PUNCT
ejpam-6141	70	15	h	h	NOUN
ejpam-6141	70	16	→	→	SYM
ejpam-6141	70	17	h	h	X
ejpam-6141	70	18	/	/	SYM
ejpam-6141	70	19	β∗	β∗	NOUN
ejpam-6141	70	20	is	be	AUX
ejpam-6141	70	21	a	a	DET
ejpam-6141	70	22	homomorphism	homomorphism	NOUN
ejpam-6141	70	23	and	and	CCONJ
ejpam-6141	70	24	if	if	SCONJ
ejpam-6141	70	25	h	h	NOUN
ejpam-6141	70	26	is	be	AUX
ejpam-6141	70	27	a	a	DET
ejpam-6141	70	28	hypergroup	hypergroup	NOUN
ejpam-6141	70	29	,	,	PUNCT
ejpam-6141	70	30	the	the	DET
ejpam-6141	70	31	kernel	kernel	NOUN
ejpam-6141	70	32	of	of	ADP
ejpam-6141	70	33	ψ	ψ	PROPN
ejpam-6141	70	34	is	be	AUX
ejpam-6141	70	35	called	call	VERB
ejpam-6141	70	36	heart	heart	NOUN
ejpam-6141	70	37	of	of	ADP
ejpam-6141	70	38	h	h	NOUN
ejpam-6141	70	39	and	and	CCONJ
ejpam-6141	70	40	is	be	AUX
ejpam-6141	70	41	denoted	denote	VERB
ejpam-6141	70	42	with	with	ADP
ejpam-6141	70	43	ωh	ωh	INTJ
ejpam-6141	70	44	.	.	PUNCT
ejpam-6141	71	1	let	let	AUX
ejpam-6141	71	2	(	(	PUNCT
ejpam-6141	71	3	h	h	NOUN
ejpam-6141	71	4	,	,	PUNCT
ejpam-6141	71	5	◦	◦	NOUN
ejpam-6141	71	6	)	)	PUNCT
ejpam-6141	71	7	be	be	AUX
ejpam-6141	71	8	a	a	DET
ejpam-6141	71	9	hypergroupoid	hypergroupoid	NOUN
ejpam-6141	71	10	.	.	PUNCT
ejpam-6141	72	1	let	let	VERB
ejpam-6141	72	2	u	u	PRON
ejpam-6141	72	3	denote	denote	VERB
ejpam-6141	72	4	the	the	DET
ejpam-6141	72	5	set	set	NOUN
ejpam-6141	72	6	of	of	ADP
ejpam-6141	72	7	all	all	DET
ejpam-6141	72	8	finite	finite	ADJ
ejpam-6141	72	9	products	product	NOUN
ejpam-6141	72	10	of	of	ADP
ejpam-6141	72	11	elements	element	NOUN
ejpam-6141	72	12	of	of	ADP
ejpam-6141	72	13	h.	h.	PROPN
ejpam-6141	72	14	then	then	ADV
ejpam-6141	72	15	relation	relation	NOUN
ejpam-6141	72	16	β	β	PROPN
ejpam-6141	72	17	can	can	AUX
ejpam-6141	72	18	be	be	AUX
ejpam-6141	72	19	defined	define	VERB
ejpam-6141	72	20	on	on	ADP
ejpam-6141	72	21	h	h	NOUN
ejpam-6141	72	22	as	as	SCONJ
ejpam-6141	72	23	follows	follow	VERB
ejpam-6141	72	24	:	:	PUNCT
ejpam-6141	73	1	xβy	xβy	PROPN
ejpam-6141	73	2	⇔	⇔	PROPN
ejpam-6141	73	3	∃u	∃u	PROPN
ejpam-6141	73	4	∈	∈	PROPN
ejpam-6141	73	5	usuch	usuch	NOUN
ejpam-6141	73	6	that{x	that{x	PROPN
ejpam-6141	73	7	,	,	PUNCT
ejpam-6141	73	8	y	y	NOUN
ejpam-6141	73	9	}	}	PUNCT
ejpam-6141	73	10	⊆	⊆	NUM
ejpam-6141	73	11	u.	u.	NOUN
ejpam-6141	74	1	if	if	SCONJ
ejpam-6141	74	2	(	(	PUNCT
ejpam-6141	74	3	h	h	NOUN
ejpam-6141	74	4	,	,	PUNCT
ejpam-6141	74	5	◦	◦	NOUN
ejpam-6141	74	6	)	)	PUNCT
ejpam-6141	74	7	is	be	AUX
ejpam-6141	74	8	a	a	DET
ejpam-6141	74	9	hypergroupoid	hypergroupoid	NOUN
ejpam-6141	74	10	then	then	ADV
ejpam-6141	74	11	the	the	DET
ejpam-6141	74	12	relation	relation	NOUN
ejpam-6141	74	13	β∗	β∗	NOUN
ejpam-6141	74	14	is	be	AUX
ejpam-6141	74	15	the	the	DET
ejpam-6141	74	16	transitive	transitive	ADJ
ejpam-6141	74	17	closure	closure	NOUN
ejpam-6141	74	18	of	of	ADP
ejpam-6141	74	19	the	the	DET
ejpam-6141	74	20	relation	relation	NOUN
ejpam-6141	74	21	β	β	NOUN
ejpam-6141	74	22	.	.	PUNCT
ejpam-6141	75	1	theorem	theorem	NOUN
ejpam-6141	75	2	1	1	NUM
ejpam-6141	75	3	.	.	PUNCT
ejpam-6141	76	1	(	(	PUNCT
ejpam-6141	76	2	theorem	theorem	VERB
ejpam-6141	76	3	81	81	NUM
ejpam-6141	76	4	in	in	ADP
ejpam-6141	76	5	[	[	X
ejpam-6141	76	6	5	5	NUM
ejpam-6141	76	7	]	]	PUNCT
ejpam-6141	76	8	)	)	PUNCT
ejpam-6141	76	9	if	if	SCONJ
ejpam-6141	76	10	h	h	NOUN
ejpam-6141	76	11	is	be	AUX
ejpam-6141	76	12	a	a	DET
ejpam-6141	76	13	hypergroup	hypergroup	NOUN
ejpam-6141	76	14	then	then	ADV
ejpam-6141	76	15	β	β	PROPN
ejpam-6141	76	16	=	=	SYM
ejpam-6141	76	17	β∗.	β∗.	PUNCT
ejpam-6141	76	18	as	as	ADP
ejpam-6141	76	19	a	a	DET
ejpam-6141	76	20	consequence	consequence	NOUN
ejpam-6141	76	21	of	of	ADP
ejpam-6141	76	22	theorem	theorem	NOUN
ejpam-6141	76	23	1	1	NUM
ejpam-6141	76	24	,	,	PUNCT
ejpam-6141	76	25	in	in	ADP
ejpam-6141	76	26	every	every	DET
ejpam-6141	76	27	hypergroup	hypergroup	NOUN
ejpam-6141	76	28	the	the	DET
ejpam-6141	76	29	relation	relation	NOUN
ejpam-6141	76	30	β	β	PROPN
ejpam-6141	76	31	is	be	AUX
ejpam-6141	76	32	transitive	transitive	ADJ
ejpam-6141	76	33	.	.	PUNCT
ejpam-6141	77	1	but	but	CCONJ
ejpam-6141	77	2	in	in	ADP
ejpam-6141	77	3	semihypergroups	semihypergroup	NOUN
ejpam-6141	77	4	this	this	PRON
ejpam-6141	77	5	not	not	PART
ejpam-6141	77	6	true	true	ADJ
ejpam-6141	77	7	and	and	CCONJ
ejpam-6141	77	8	in	in	ADP
ejpam-6141	77	9	hv	hv	NOUN
ejpam-6141	77	10	-	-	PUNCT
ejpam-6141	77	11	groups	group	NOUN
ejpam-6141	77	12	this	this	PRON
ejpam-6141	77	13	is	be	AUX
ejpam-6141	77	14	an	an	DET
ejpam-6141	77	15	open	open	ADJ
ejpam-6141	77	16	problem	problem	NOUN
ejpam-6141	77	17	.	.	PUNCT
ejpam-6141	78	1	definition	definition	NOUN
ejpam-6141	78	2	3	3	X
ejpam-6141	78	3	.	.	PUNCT
ejpam-6141	79	1	let	let	AUX
ejpam-6141	79	2	(	(	PUNCT
ejpam-6141	79	3	h	h	NOUN
ejpam-6141	79	4	,	,	PUNCT
ejpam-6141	79	5	◦	◦	NOUN
ejpam-6141	79	6	)	)	PUNCT
ejpam-6141	79	7	be	be	AUX
ejpam-6141	79	8	a	a	DET
ejpam-6141	79	9	hypergroupoid	hypergroupoid	NOUN
ejpam-6141	79	10	.	.	PUNCT
ejpam-6141	80	1	the	the	DET
ejpam-6141	80	2	hyperoperation	hyperoperation	NOUN
ejpam-6141	80	3	◦	◦	NOUN
ejpam-6141	80	4	is	be	AUX
ejpam-6141	80	5	called	call	VERB
ejpam-6141	80	6	total	total	ADJ
ejpam-6141	80	7	associative	associative	NOUN
ejpam-6141	80	8	,	,	PUNCT
ejpam-6141	80	9	if	if	SCONJ
ejpam-6141	80	10	x	x	X
ejpam-6141	80	11	◦	◦	NOUN
ejpam-6141	80	12	(	(	PUNCT
ejpam-6141	80	13	y	y	PROPN
ejpam-6141	80	14	◦	◦	PROPN
ejpam-6141	80	15	z	z	PROPN
ejpam-6141	80	16	)	)	PUNCT
ejpam-6141	81	1	=	=	SYM
ejpam-6141	81	2	h	h	NOUN
ejpam-6141	81	3	=	=	SYM
ejpam-6141	82	1	(	(	PUNCT
ejpam-6141	82	2	x	x	SYM
ejpam-6141	82	3	◦	◦	VERB
ejpam-6141	82	4	y	y	NOUN
ejpam-6141	82	5	)	)	PUNCT
ejpam-6141	82	6	◦	◦	NOUN
ejpam-6141	82	7	z	z	NUM
ejpam-6141	82	8	,	,	PUNCT
ejpam-6141	82	9	∀x	∀x	NUM
ejpam-6141	82	10	,	,	PUNCT
ejpam-6141	82	11	y	y	PROPN
ejpam-6141	82	12	,	,	PUNCT
ejpam-6141	82	13	z	z	PROPN
ejpam-6141	82	14	∈	∈	PROPN
ejpam-6141	82	15	h.	h.	PROPN
ejpam-6141	82	16	example	example	NOUN
ejpam-6141	83	1	3	3	X
ejpam-6141	83	2	.	.	X
ejpam-6141	84	1	let	let	AUX
ejpam-6141	84	2	(	(	PUNCT
ejpam-6141	84	3	h	h	NOUN
ejpam-6141	84	4	,	,	PUNCT
ejpam-6141	84	5	◦	◦	NOUN
ejpam-6141	84	6	t	t	NOUN
ejpam-6141	84	7	)	)	PUNCT
ejpam-6141	84	8	be	be	AUX
ejpam-6141	84	9	a	a	DET
ejpam-6141	84	10	total	total	ADJ
ejpam-6141	84	11	hypergroup	hypergroup	NOUN
ejpam-6141	84	12	,	,	PUNCT
ejpam-6141	84	13	i.	i.	PROPN
ejpam-6141	84	14	e.	e.	PROPN
ejpam-6141	84	15	,	,	PUNCT
ejpam-6141	84	16	for	for	ADP
ejpam-6141	84	17	all	all	DET
ejpam-6141	84	18	x	x	NOUN
ejpam-6141	84	19	,	,	PUNCT
ejpam-6141	84	20	y	y	PROPN
ejpam-6141	84	21	∈	∈	PROPN
ejpam-6141	84	22	h	h	NOUN
ejpam-6141	84	23	,	,	PUNCT
ejpam-6141	84	24	x	x	PUNCT
ejpam-6141	85	1	◦	◦	NOUN
ejpam-6141	85	2	t	t	X
ejpam-6141	85	3	y	y	PROPN
ejpam-6141	85	4	=	=	SYM
ejpam-6141	85	5	h.	h.	PROPN
ejpam-6141	85	6	then	then	ADV
ejpam-6141	85	7	◦	◦	NOUN
ejpam-6141	85	8	is	be	AUX
ejpam-6141	85	9	a	a	DET
ejpam-6141	85	10	total	total	ADJ
ejpam-6141	85	11	associative	associative	ADJ
ejpam-6141	85	12	hyperoperation	hyperoperation	NOUN
ejpam-6141	85	13	.	.	PUNCT
ejpam-6141	86	1	example	example	NOUN
ejpam-6141	87	1	4	4	X
ejpam-6141	87	2	.	.	PUNCT
ejpam-6141	87	3	let	let	VERB
ejpam-6141	87	4	h	h	NOUN
ejpam-6141	87	5	̸=	̸=	PROPN
ejpam-6141	87	6	∅	∅	NOUN
ejpam-6141	87	7	and	and	CCONJ
ejpam-6141	87	8	|h|	|h|	X
ejpam-6141	87	9	>	>	X
ejpam-6141	87	10	2	2	X
ejpam-6141	87	11	.	.	PUNCT
ejpam-6141	88	1	for	for	ADP
ejpam-6141	88	2	every	every	DET
ejpam-6141	88	3	x	x	NOUN
ejpam-6141	88	4	,	,	PUNCT
ejpam-6141	88	5	y	y	PROPN
ejpam-6141	88	6	∈	∈	PROPN
ejpam-6141	88	7	h	h	NOUN
ejpam-6141	88	8	,	,	PUNCT
ejpam-6141	88	9	define	define	VERB
ejpam-6141	88	10	x	x	X
ejpam-6141	88	11	◦	◦	NOUN
ejpam-6141	88	12	y	y	NOUN
ejpam-6141	88	13	=	=	SYM
ejpam-6141	88	14	{	{	PUNCT
ejpam-6141	88	15	h	h	NOUN
ejpam-6141	88	16	−	−	PROPN
ejpam-6141	88	17	{	{	PUNCT
ejpam-6141	88	18	y	y	NOUN
ejpam-6141	88	19	}	}	PUNCT
ejpam-6141	88	20	,	,	PUNCT
ejpam-6141	88	21	x	x	PUNCT
ejpam-6141	88	22	̸=	̸=	PROPN
ejpam-6141	88	23	y	y	PROPN
ejpam-6141	88	24	h	h	NOUN
ejpam-6141	88	25	,	,	PUNCT
ejpam-6141	88	26	x	x	X
ejpam-6141	89	1	=	=	PUNCT
ejpam-6141	89	2	y.	y.	NOUN
ejpam-6141	89	3	then	then	ADV
ejpam-6141	89	4	for	for	ADP
ejpam-6141	89	5	every	every	DET
ejpam-6141	89	6	x	x	PROPN
ejpam-6141	89	7	,	,	PUNCT
ejpam-6141	89	8	y	y	PROPN
ejpam-6141	89	9	,	,	PUNCT
ejpam-6141	89	10	z	z	PROPN
ejpam-6141	89	11	∈	∈	PROPN
ejpam-6141	89	12	h	h	NOUN
ejpam-6141	89	13	,	,	PUNCT
ejpam-6141	89	14	we	we	PRON
ejpam-6141	89	15	have	have	VERB
ejpam-6141	89	16	y	y	PROPN
ejpam-6141	89	17	◦	◦	NOUN
ejpam-6141	89	18	z	z	NOUN
ejpam-6141	89	19	=	=	SYM
ejpam-6141	89	20	h	h	NOUN
ejpam-6141	89	21	−	−	PROPN
ejpam-6141	90	1	{	{	PUNCT
ejpam-6141	90	2	z	z	NOUN
ejpam-6141	90	3	}	}	PUNCT
ejpam-6141	90	4	and	and	CCONJ
ejpam-6141	90	5	so	so	ADV
ejpam-6141	90	6	|h	|h	X
ejpam-6141	90	7	−	−	PROPN
ejpam-6141	90	8	{	{	PUNCT
ejpam-6141	90	9	z	z	NOUN
ejpam-6141	90	10	}	}	PUNCT
ejpam-6141	90	11	=	=	SYM
ejpam-6141	90	12	2	2	X
ejpam-6141	90	13	.	.	PUNCT
ejpam-6141	91	1	so	so	ADV
ejpam-6141	91	2	x	x	SYM
ejpam-6141	91	3	◦	◦	NOUN
ejpam-6141	91	4	(	(	PUNCT
ejpam-6141	91	5	y	y	PROPN
ejpam-6141	91	6	◦	◦	PROPN
ejpam-6141	91	7	z	z	PROPN
ejpam-6141	91	8	)	)	PUNCT
ejpam-6141	91	9	=	=	SYM
ejpam-6141	92	1	x	x	PUNCT
ejpam-6141	92	2	◦	◦	NOUN
ejpam-6141	92	3	(	(	PUNCT
ejpam-6141	92	4	h	h	NOUN
ejpam-6141	92	5	−	−	PROPN
ejpam-6141	92	6	{	{	PUNCT
ejpam-6141	92	7	z	z	NOUN
ejpam-6141	92	8	}	}	PUNCT
ejpam-6141	92	9	)	)	PUNCT
ejpam-6141	93	1	=	=	SYM
ejpam-6141	93	2	∪w∈h−{z}x	∪w∈h−{z}x	NOUN
ejpam-6141	93	3	◦	◦	VERB
ejpam-6141	93	4	w	w	NOUN
ejpam-6141	93	5	=	=	SYM
ejpam-6141	93	6	h.	h.	PROPN
ejpam-6141	93	7	in	in	ADP
ejpam-6141	93	8	the	the	DET
ejpam-6141	93	9	similar	similar	ADJ
ejpam-6141	93	10	way	way	NOUN
ejpam-6141	93	11	we	we	PRON
ejpam-6141	93	12	have	have	VERB
ejpam-6141	93	13	h	h	NOUN
ejpam-6141	93	14	=	=	SYM
ejpam-6141	93	15	(	(	PUNCT
ejpam-6141	93	16	x	x	SYM
ejpam-6141	93	17	◦	◦	VERB
ejpam-6141	93	18	y	y	NOUN
ejpam-6141	93	19	)	)	PUNCT
ejpam-6141	93	20	◦	◦	NOUN
ejpam-6141	93	21	z.	z.	PROPN
ejpam-6141	93	22	therefore	therefore	ADV
ejpam-6141	93	23	the	the	DET
ejpam-6141	93	24	hyperoperation	hyperoperation	NOUN
ejpam-6141	93	25	◦	◦	NOUN
ejpam-6141	93	26	is	be	AUX
ejpam-6141	93	27	total	total	ADJ
ejpam-6141	93	28	associative	associative	ADJ
ejpam-6141	93	29	m.	m.	NOUN
ejpam-6141	93	30	a.	a.	PROPN
ejpam-6141	93	31	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	93	32	,	,	PUNCT
ejpam-6141	93	33	s.	s.	PROPN
ejpam-6141	93	34	mirvakili	mirvakili	PROPN
ejpam-6141	93	35	/	/	SYM
ejpam-6141	93	36	eur	eur	PROPN
ejpam-6141	93	37	.	.	PUNCT
ejpam-6141	94	1	j.	j.	PROPN
ejpam-6141	94	2	pure	pure	PROPN
ejpam-6141	94	3	appl	appl	PROPN
ejpam-6141	94	4	.	.	PROPN
ejpam-6141	94	5	math	math	PROPN
ejpam-6141	94	6	,	,	PUNCT
ejpam-6141	94	7	18	18	NUM
ejpam-6141	94	8	(	(	PUNCT
ejpam-6141	94	9	2	2	NUM
ejpam-6141	94	10	)	)	PUNCT
ejpam-6141	94	11	(	(	PUNCT
ejpam-6141	94	12	2025	2025	NUM
ejpam-6141	94	13	)	)	PUNCT
ejpam-6141	94	14	,	,	PUNCT
ejpam-6141	94	15	6141	6141	NUM
ejpam-6141	94	16	5	5	NUM
ejpam-6141	94	17	of	of	ADP
ejpam-6141	94	18	10	10	NUM
ejpam-6141	94	19	now	now	ADV
ejpam-6141	94	20	,	,	PUNCT
ejpam-6141	94	21	we	we	PRON
ejpam-6141	94	22	construct	construct	VERB
ejpam-6141	94	23	some	some	DET
ejpam-6141	94	24	hyperoperations	hyperoperation	NOUN
ejpam-6141	94	25	from	from	ADP
ejpam-6141	94	26	a	a	DET
ejpam-6141	94	27	quasigroup	quasigroup	NOUN
ejpam-6141	94	28	as	as	SCONJ
ejpam-6141	94	29	follows	follow	VERB
ejpam-6141	94	30	:	:	PUNCT
ejpam-6141	94	31	definition	definition	NOUN
ejpam-6141	94	32	4	4	NUM
ejpam-6141	94	33	.	.	PUNCT
ejpam-6141	95	1	let	let	AUX
ejpam-6141	95	2	(	(	PUNCT
ejpam-6141	95	3	h	h	NOUN
ejpam-6141	95	4	,	,	PUNCT
ejpam-6141	95	5	⋆	⋆	ADJ
ejpam-6141	95	6	)	)	PUNCT
ejpam-6141	95	7	be	be	AUX
ejpam-6141	95	8	a	a	DET
ejpam-6141	95	9	finite	finite	ADJ
ejpam-6141	95	10	quasigroup	quasigroup	NOUN
ejpam-6141	95	11	.	.	PUNCT
ejpam-6141	96	1	let	let	VERB
ejpam-6141	96	2	h	h	NOUN
ejpam-6141	96	3	=	=	PRON
ejpam-6141	96	4	{	{	PUNCT
ejpam-6141	96	5	a0	a0	PROPN
ejpam-6141	96	6	,	,	PUNCT
ejpam-6141	96	7	a1	a1	NOUN
ejpam-6141	96	8	,	,	PUNCT
ejpam-6141	96	9	.	.	PUNCT
ejpam-6141	96	10	.	.	PUNCT
ejpam-6141	97	1	.	.	PUNCT
ejpam-6141	98	1	,	,	PUNCT
ejpam-6141	98	2	an−1	an−1	ADJ
ejpam-6141	98	3	}	}	PUNCT
ejpam-6141	98	4	and	and	CCONJ
ejpam-6141	98	5	ai	ai	VERB
ejpam-6141	98	6	⋆	⋆	VERB
ejpam-6141	98	7	aj	aj	PROPN
ejpam-6141	98	8	=	=	SYM
ejpam-6141	98	9	aij	aij	PROPN
ejpam-6141	98	10	,	,	PUNCT
ejpam-6141	98	11	for	for	ADP
ejpam-6141	98	12	every	every	DET
ejpam-6141	98	13	i	i	PROPN
ejpam-6141	98	14	,	,	PUNCT
ejpam-6141	98	15	j	j	PROPN
ejpam-6141	98	16	=	=	SYM
ejpam-6141	98	17	0	0	NUM
ejpam-6141	98	18	,	,	PUNCT
ejpam-6141	98	19	1	1	NUM
ejpam-6141	98	20	,	,	PUNCT
ejpam-6141	98	21	.	.	PUNCT
ejpam-6141	98	22	.	.	PUNCT
ejpam-6141	99	1	.	.	PUNCT
ejpam-6141	100	1	,	,	PUNCT
ejpam-6141	101	1	n	n	CCONJ
ejpam-6141	101	2	−	−	PROPN
ejpam-6141	101	3	1	1	NUM
ejpam-6141	101	4	.	.	PUNCT
ejpam-6141	102	1	for	for	ADP
ejpam-6141	102	2	k	k	PROPN
ejpam-6141	102	3	∈	∈	PROPN
ejpam-6141	102	4	{	{	PUNCT
ejpam-6141	102	5	0	0	NUM
ejpam-6141	102	6	,	,	PUNCT
ejpam-6141	102	7	1	1	NUM
ejpam-6141	102	8	,	,	PUNCT
ejpam-6141	102	9	.	.	PUNCT
ejpam-6141	102	10	.	.	PUNCT
ejpam-6141	102	11	.	.	PUNCT
ejpam-6141	103	1	,	,	PUNCT
ejpam-6141	103	2	n	n	CCONJ
ejpam-6141	103	3	−	−	PROPN
ejpam-6141	103	4	1	1	NUM
ejpam-6141	103	5	}	}	PUNCT
ejpam-6141	103	6	set	set	VERB
ejpam-6141	103	7	ai	ai	VERB
ejpam-6141	103	8	⋆	⋆	NOUN
ejpam-6141	103	9	c	c	PROPN
ejpam-6141	103	10	k	k	PROPN
ejpam-6141	103	11	aj	aj	PROPN
ejpam-6141	103	12	=	=	PROPN
ejpam-6141	103	13	aih	aih	PROPN
ejpam-6141	103	14	,	,	PUNCT
ejpam-6141	103	15	when	when	SCONJ
ejpam-6141	103	16	j	j	PROPN
ejpam-6141	103	17	−	−	PROPN
ejpam-6141	103	18	k	k	PROPN
ejpam-6141	103	19	≡	≡	PROPN
ejpam-6141	103	20	h	h	PROPN
ejpam-6141	103	21	mod	mod	PROPN
ejpam-6141	103	22	n.	n.	PROPN
ejpam-6141	103	23	it	it	PRON
ejpam-6141	103	24	easily	easily	ADV
ejpam-6141	103	25	to	to	PART
ejpam-6141	103	26	see	see	VERB
ejpam-6141	103	27	that	that	PRON
ejpam-6141	103	28	(	(	PUNCT
ejpam-6141	103	29	h	h	NOUN
ejpam-6141	103	30	,	,	PUNCT
ejpam-6141	103	31	⋆k	⋆k	NUM
ejpam-6141	103	32	)	)	PUNCT
ejpam-6141	103	33	is	be	AUX
ejpam-6141	103	34	a	a	DET
ejpam-6141	103	35	quasigroup	quasigroup	NOUN
ejpam-6141	103	36	.	.	PUNCT
ejpam-6141	104	1	now	now	ADV
ejpam-6141	104	2	for	for	ADP
ejpam-6141	104	3	every	every	DET
ejpam-6141	104	4	x	x	NOUN
ejpam-6141	104	5	,	,	PUNCT
ejpam-6141	104	6	y	y	PROPN
ejpam-6141	104	7	∈	∈	PROPN
ejpam-6141	104	8	h	h	NOUN
ejpam-6141	104	9	define	define	VERB
ejpam-6141	104	10	the	the	DET
ejpam-6141	104	11	hyperoperation	hyperoperation	NOUN
ejpam-6141	104	12	◦	◦	NOUN
ejpam-6141	104	13	ck	ck	PROPN
ejpam-6141	104	14	as	as	SCONJ
ejpam-6141	104	15	follows	follow	VERB
ejpam-6141	104	16	x	x	PUNCT
ejpam-6141	104	17	◦	◦	NOUN
ejpam-6141	104	18	ck	ck	ADJ
ejpam-6141	104	19	y	y	NOUN
ejpam-6141	104	20	=	=	PUNCT
ejpam-6141	104	21	{	{	PUNCT
ejpam-6141	104	22	x	x	INTJ
ejpam-6141	104	23	⋆cm	⋆cm	PROPN
ejpam-6141	104	24	y|m	y|m	NOUN
ejpam-6141	104	25	=	=	SYM
ejpam-6141	104	26	0	0	NUM
ejpam-6141	104	27	,	,	PUNCT
ejpam-6141	104	28	1	1	NUM
ejpam-6141	104	29	,	,	PUNCT
ejpam-6141	104	30	.	.	PUNCT
ejpam-6141	104	31	.	.	PUNCT
ejpam-6141	105	1	.	.	PUNCT
ejpam-6141	106	1	,	,	PUNCT
ejpam-6141	107	1	k	k	PROPN
ejpam-6141	108	1	−	−	PROPN
ejpam-6141	109	1	1	1	NUM
ejpam-6141	109	2	}	}	PUNCT
ejpam-6141	109	3	.	.	PUNCT
ejpam-6141	110	1	definition	definition	NOUN
ejpam-6141	110	2	5	5	NUM
ejpam-6141	110	3	.	.	PUNCT
ejpam-6141	111	1	let	let	AUX
ejpam-6141	111	2	(	(	PUNCT
ejpam-6141	111	3	h	h	NOUN
ejpam-6141	111	4	,	,	PUNCT
ejpam-6141	111	5	⋆	⋆	ADJ
ejpam-6141	111	6	)	)	PUNCT
ejpam-6141	111	7	be	be	AUX
ejpam-6141	111	8	a	a	DET
ejpam-6141	111	9	finite	finite	ADJ
ejpam-6141	111	10	quasigroup	quasigroup	NOUN
ejpam-6141	111	11	.	.	PUNCT
ejpam-6141	112	1	let	let	VERB
ejpam-6141	112	2	h	h	NOUN
ejpam-6141	112	3	=	=	PRON
ejpam-6141	112	4	{	{	PUNCT
ejpam-6141	112	5	a0	a0	PROPN
ejpam-6141	112	6	,	,	PUNCT
ejpam-6141	112	7	a1	a1	NOUN
ejpam-6141	112	8	,	,	PUNCT
ejpam-6141	112	9	.	.	PUNCT
ejpam-6141	112	10	.	.	PUNCT
ejpam-6141	113	1	.	.	PUNCT
ejpam-6141	114	1	,	,	PUNCT
ejpam-6141	114	2	an−1	an−1	ADJ
ejpam-6141	114	3	}	}	PUNCT
ejpam-6141	114	4	and	and	CCONJ
ejpam-6141	114	5	ai	ai	VERB
ejpam-6141	114	6	⋆	⋆	VERB
ejpam-6141	114	7	aj	aj	PROPN
ejpam-6141	114	8	=	=	SYM
ejpam-6141	114	9	aij	aij	PROPN
ejpam-6141	114	10	,	,	PUNCT
ejpam-6141	114	11	for	for	ADP
ejpam-6141	114	12	every	every	DET
ejpam-6141	114	13	i	i	PROPN
ejpam-6141	114	14	,	,	PUNCT
ejpam-6141	114	15	j	j	PROPN
ejpam-6141	114	16	=	=	SYM
ejpam-6141	114	17	0	0	NUM
ejpam-6141	114	18	,	,	PUNCT
ejpam-6141	114	19	1	1	NUM
ejpam-6141	114	20	,	,	PUNCT
ejpam-6141	114	21	.	.	PUNCT
ejpam-6141	114	22	.	.	PUNCT
ejpam-6141	115	1	.	.	PUNCT
ejpam-6141	116	1	,	,	PUNCT
ejpam-6141	116	2	n−1	n−1	PROPN
ejpam-6141	116	3	.	.	PROPN
ejpam-6141	117	1	for	for	ADP
ejpam-6141	117	2	k	k	PROPN
ejpam-6141	117	3	∈	∈	PROPN
ejpam-6141	117	4	{	{	PUNCT
ejpam-6141	117	5	0	0	NUM
ejpam-6141	117	6	,	,	PUNCT
ejpam-6141	117	7	1	1	NUM
ejpam-6141	117	8	,	,	PUNCT
ejpam-6141	117	9	.	.	PUNCT
ejpam-6141	117	10	.	.	PUNCT
ejpam-6141	117	11	.	.	PUNCT
ejpam-6141	118	1	,	,	PUNCT
ejpam-6141	118	2	n−1	n−1	PROPN
ejpam-6141	118	3	}	}	PUNCT
ejpam-6141	118	4	set	set	VERB
ejpam-6141	118	5	ai⋆	ai⋆	PROPN
ejpam-6141	118	6	r	r	NOUN
ejpam-6141	118	7	k	k	PROPN
ejpam-6141	118	8	aj	aj	PROPN
ejpam-6141	118	9	=	=	PROPN
ejpam-6141	118	10	ahj	ahj	PROPN
ejpam-6141	118	11	,	,	PUNCT
ejpam-6141	119	1	when	when	SCONJ
ejpam-6141	119	2	j−k	j−k	NOUN
ejpam-6141	119	3	≡	≡	PROPN
ejpam-6141	119	4	h	h	PROPN
ejpam-6141	119	5	mod	mod	PROPN
ejpam-6141	119	6	n.	n.	PROPN
ejpam-6141	119	7	it	it	PRON
ejpam-6141	119	8	easily	easily	ADV
ejpam-6141	119	9	to	to	PART
ejpam-6141	119	10	see	see	VERB
ejpam-6141	119	11	that	that	PRON
ejpam-6141	119	12	(	(	PUNCT
ejpam-6141	119	13	h	h	NOUN
ejpam-6141	119	14	,	,	PUNCT
ejpam-6141	119	15	⋆rk	⋆rk	PROPN
ejpam-6141	119	16	)	)	PUNCT
ejpam-6141	119	17	is	be	AUX
ejpam-6141	119	18	a	a	DET
ejpam-6141	119	19	quasihypergroup	quasihypergroup	NOUN
ejpam-6141	119	20	.	.	PUNCT
ejpam-6141	120	1	now	now	ADV
ejpam-6141	120	2	for	for	ADP
ejpam-6141	120	3	every	every	DET
ejpam-6141	120	4	x	x	NOUN
ejpam-6141	120	5	,	,	PUNCT
ejpam-6141	120	6	y	y	PROPN
ejpam-6141	120	7	∈	∈	PROPN
ejpam-6141	120	8	h	h	NOUN
ejpam-6141	120	9	define	define	VERB
ejpam-6141	120	10	the	the	DET
ejpam-6141	120	11	hyperoperation	hyperoperation	NOUN
ejpam-6141	120	12	◦	◦	NOUN
ejpam-6141	120	13	rk	rk	NOUN
ejpam-6141	120	14	as	as	SCONJ
ejpam-6141	120	15	follows	follow	VERB
ejpam-6141	120	16	x	x	PUNCT
ejpam-6141	120	17	◦	◦	VERB
ejpam-6141	120	18	rk	rk	NOUN
ejpam-6141	121	1	y	y	NOUN
ejpam-6141	121	2	=	=	PUNCT
ejpam-6141	121	3	{	{	PUNCT
ejpam-6141	121	4	x	x	INTJ
ejpam-6141	121	5	⋆rm	⋆rm	PROPN
ejpam-6141	121	6	y|m	y|m	VERB
ejpam-6141	121	7	=	=	SYM
ejpam-6141	121	8	0	0	NUM
ejpam-6141	121	9	,	,	PUNCT
ejpam-6141	121	10	1	1	NUM
ejpam-6141	121	11	,	,	PUNCT
ejpam-6141	121	12	.	.	PUNCT
ejpam-6141	121	13	.	.	PUNCT
ejpam-6141	121	14	.	.	PUNCT
ejpam-6141	122	1	,	,	PUNCT
ejpam-6141	123	1	k	k	PROPN
ejpam-6141	124	1	−	−	PROPN
ejpam-6141	124	2	1	1	NUM
ejpam-6141	124	3	}	}	PUNCT
ejpam-6141	124	4	.	.	PUNCT
ejpam-6141	125	1	proposition	proposition	NOUN
ejpam-6141	125	2	1	1	NUM
ejpam-6141	125	3	.	.	PUNCT
ejpam-6141	126	1	let	let	AUX
ejpam-6141	126	2	(	(	PUNCT
ejpam-6141	126	3	h	h	NOUN
ejpam-6141	126	4	,	,	PUNCT
ejpam-6141	126	5	⋆	⋆	ADJ
ejpam-6141	126	6	)	)	PUNCT
ejpam-6141	126	7	be	be	AUX
ejpam-6141	126	8	a	a	DET
ejpam-6141	126	9	finite	finite	ADJ
ejpam-6141	126	10	quasigroup	quasigroup	NOUN
ejpam-6141	126	11	and	and	CCONJ
ejpam-6141	126	12	◦	◦	NOUN
ejpam-6141	126	13	rk	rk	NOUN
ejpam-6141	126	14	and	and	CCONJ
ejpam-6141	126	15	◦	◦	VERB
ejpam-6141	126	16	ck	ck	ADV
ejpam-6141	126	17	be	be	VERB
ejpam-6141	126	18	the	the	DET
ejpam-6141	126	19	hyperoperations	hyperoperation	NOUN
ejpam-6141	126	20	in	in	ADP
ejpam-6141	126	21	definition	definition	NOUN
ejpam-6141	126	22	4	4	NUM
ejpam-6141	126	23	and	and	CCONJ
ejpam-6141	126	24	5	5	NUM
ejpam-6141	126	25	.	.	PUNCT
ejpam-6141	127	1	then	then	ADV
ejpam-6141	127	2	(	(	PUNCT
ejpam-6141	127	3	h	h	NOUN
ejpam-6141	127	4	,	,	PUNCT
ejpam-6141	127	5	◦	◦	NOUN
ejpam-6141	127	6	cn−1	cn−1	NOUN
ejpam-6141	127	7	)	)	PUNCT
ejpam-6141	127	8	and	and	CCONJ
ejpam-6141	127	9	(	(	PUNCT
ejpam-6141	127	10	h	h	NOUN
ejpam-6141	127	11	,	,	PUNCT
ejpam-6141	127	12	◦	◦	NOUN
ejpam-6141	127	13	rn−1	rn−1	NOUN
ejpam-6141	127	14	)	)	PUNCT
ejpam-6141	127	15	are	be	AUX
ejpam-6141	127	16	total	total	ADJ
ejpam-6141	127	17	hypergroup	hypergroup	NOUN
ejpam-6141	127	18	.	.	PUNCT
ejpam-6141	128	1	proof	proof	NOUN
ejpam-6141	128	2	.	.	PUNCT
ejpam-6141	129	1	leth	leth	PROPN
ejpam-6141	129	2	=	=	PROPN
ejpam-6141	129	3	{	{	PUNCT
ejpam-6141	129	4	a0	a0	PROPN
ejpam-6141	129	5	,	,	PUNCT
ejpam-6141	129	6	a1	a1	NOUN
ejpam-6141	129	7	,	,	PUNCT
ejpam-6141	129	8	.	.	PUNCT
ejpam-6141	129	9	.	.	PUNCT
ejpam-6141	129	10	.	.	PUNCT
ejpam-6141	130	1	,	,	PUNCT
ejpam-6141	130	2	an−1	an−1	ADJ
ejpam-6141	130	3	}	}	PUNCT
ejpam-6141	130	4	.	.	PUNCT
ejpam-6141	131	1	since	since	SCONJ
ejpam-6141	131	2	(	(	PUNCT
ejpam-6141	131	3	h	h	NOUN
ejpam-6141	131	4	,	,	PUNCT
ejpam-6141	131	5	⋆	⋆	ADJ
ejpam-6141	131	6	)	)	PUNCT
ejpam-6141	131	7	is	be	AUX
ejpam-6141	131	8	a	a	DET
ejpam-6141	131	9	quasigroup	quasigroup	NOUN
ejpam-6141	131	10	then	then	ADV
ejpam-6141	131	11	for	for	ADP
ejpam-6141	131	12	every	every	DET
ejpam-6141	131	13	x	x	NOUN
ejpam-6141	131	14	,	,	PUNCT
ejpam-6141	131	15	y	y	PROPN
ejpam-6141	131	16	∈	∈	PROPN
ejpam-6141	131	17	h	h	NOUN
ejpam-6141	131	18	,	,	PUNCT
ejpam-6141	131	19	|x	|x	NOUN
ejpam-6141	131	20	◦	◦	VERB
ejpam-6141	131	21	cn−1	cn−1	PROPN
ejpam-6141	131	22	y|	y|	NOUN
ejpam-6141	131	23	=	=	SYM
ejpam-6141	131	24	n	n	NOUN
ejpam-6141	131	25	and	and	CCONJ
ejpam-6141	131	26	x	x	PART
ejpam-6141	131	27	◦	◦	VERB
ejpam-6141	131	28	rn−1	rn−1	PROPN
ejpam-6141	131	29	y	y	PROPN
ejpam-6141	131	30	⊆	⊆	NUM
ejpam-6141	131	31	h.	h.	NOUN
ejpam-6141	131	32	so	so	ADV
ejpam-6141	131	33	for	for	ADP
ejpam-6141	131	34	every	every	DET
ejpam-6141	131	35	x	x	NOUN
ejpam-6141	131	36	,	,	PUNCT
ejpam-6141	131	37	y	y	PROPN
ejpam-6141	131	38	∈	∈	PROPN
ejpam-6141	131	39	h	h	NOUN
ejpam-6141	131	40	,	,	PUNCT
ejpam-6141	131	41	x	x	PUNCT
ejpam-6141	131	42	◦	◦	VERB
ejpam-6141	131	43	rn−1	rn−1	PROPN
ejpam-6141	131	44	y	y	PROPN
ejpam-6141	131	45	=	=	SYM
ejpam-6141	131	46	h.	h.	PROPN
ejpam-6141	131	47	proposition	proposition	NOUN
ejpam-6141	131	48	2	2	X
ejpam-6141	131	49	.	.	PUNCT
ejpam-6141	132	1	let	let	AUX
ejpam-6141	132	2	(	(	PUNCT
ejpam-6141	132	3	h	h	NOUN
ejpam-6141	132	4	,	,	PUNCT
ejpam-6141	132	5	⋆	⋆	ADJ
ejpam-6141	132	6	)	)	PUNCT
ejpam-6141	132	7	be	be	AUX
ejpam-6141	132	8	a	a	DET
ejpam-6141	132	9	finite	finite	ADJ
ejpam-6141	132	10	quasigroup	quasigroup	NOUN
ejpam-6141	132	11	and	and	CCONJ
ejpam-6141	132	12	◦	◦	NOUN
ejpam-6141	132	13	rk	rk	NOUN
ejpam-6141	132	14	and	and	CCONJ
ejpam-6141	132	15	◦	◦	VERB
ejpam-6141	132	16	ck	ck	ADV
ejpam-6141	132	17	be	be	VERB
ejpam-6141	132	18	the	the	DET
ejpam-6141	132	19	hyperoperations	hyperoperation	NOUN
ejpam-6141	132	20	in	in	ADP
ejpam-6141	132	21	definition	definition	NOUN
ejpam-6141	132	22	4	4	NUM
ejpam-6141	132	23	and	and	CCONJ
ejpam-6141	132	24	5	5	NUM
ejpam-6141	132	25	.	.	PUNCT
ejpam-6141	133	1	then	then	ADV
ejpam-6141	133	2	for	for	SCONJ
ejpam-6141	133	3	k	k	PROPN
ejpam-6141	133	4	≥	≥	X
ejpam-6141	133	5	|h|	|h|	PROPN
ejpam-6141	133	6	2	2	NUM
ejpam-6141	133	7	,	,	PUNCT
ejpam-6141	133	8	(	(	PUNCT
ejpam-6141	133	9	h	h	NOUN
ejpam-6141	133	10	,	,	PUNCT
ejpam-6141	133	11	◦	◦	NOUN
ejpam-6141	133	12	rk	rk	NOUN
ejpam-6141	133	13	)	)	PUNCT
ejpam-6141	133	14	and	and	CCONJ
ejpam-6141	133	15	(	(	PUNCT
ejpam-6141	133	16	h	h	NOUN
ejpam-6141	133	17	,	,	PUNCT
ejpam-6141	133	18	◦	◦	NOUN
ejpam-6141	133	19	ck	ck	NOUN
ejpam-6141	133	20	)	)	PUNCT
ejpam-6141	133	21	are	be	AUX
ejpam-6141	133	22	weak	weak	ADJ
ejpam-6141	133	23	commutative	commutative	ADJ
ejpam-6141	133	24	hypergroupoids	hypergroupoid	NOUN
ejpam-6141	133	25	.	.	PUNCT
ejpam-6141	134	1	proof	proof	NOUN
ejpam-6141	134	2	.	.	PUNCT
ejpam-6141	135	1	for	for	ADP
ejpam-6141	135	2	every	every	DET
ejpam-6141	135	3	x	x	NOUN
ejpam-6141	135	4	,	,	PUNCT
ejpam-6141	135	5	y	y	PROPN
ejpam-6141	135	6	∈	∈	PROPN
ejpam-6141	135	7	h	h	NOUN
ejpam-6141	135	8	,	,	PUNCT
ejpam-6141	135	9	|x	|x	NOUN
ejpam-6141	135	10	◦	◦	NOUN
ejpam-6141	135	11	ck	ck	PROPN
ejpam-6141	135	12	y|	y|	NOUN
ejpam-6141	136	1	=	=	PUNCT
ejpam-6141	136	2	k	k	NOUN
ejpam-6141	136	3	=	=	PUNCT
ejpam-6141	136	4	|y	|y	NOUN
ejpam-6141	136	5	◦	◦	NOUN
ejpam-6141	136	6	ck	ck	ADJ
ejpam-6141	136	7	x|	x|	NOUN
ejpam-6141	136	8	.	.	PUNCT
ejpam-6141	137	1	if	if	SCONJ
ejpam-6141	137	2	x	x	PUNCT
ejpam-6141	137	3	◦	◦	VERB
ejpam-6141	137	4	ck	ck	ADJ
ejpam-6141	137	5	y	y	PROPN
ejpam-6141	137	6	∩	∩	PROPN
ejpam-6141	137	7	y	y	PROPN
ejpam-6141	137	8	◦	◦	NOUN
ejpam-6141	137	9	ck	ck	NOUN
ejpam-6141	137	10	x	x	SYM
ejpam-6141	137	11	=	=	NOUN
ejpam-6141	137	12	∅	∅	NOUN
ejpam-6141	137	13	then	then	ADV
ejpam-6141	137	14	|x	|x	PROPN
ejpam-6141	137	15	◦	◦	NOUN
ejpam-6141	137	16	ck	ck	PROPN
ejpam-6141	137	17	y∪y	y∪y	NOUN
ejpam-6141	137	18	◦	◦	NOUN
ejpam-6141	137	19	ck	ck	NOUN
ejpam-6141	137	20	x|	x|	PROPN
ejpam-6141	137	21	=	=	SYM
ejpam-6141	137	22	k+k+2	k+k+2	PROPN
ejpam-6141	137	23	>	>	X
ejpam-6141	137	24	|h|	|h|	PROPN
ejpam-6141	137	25	and	and	CCONJ
ejpam-6141	137	26	this	this	PRON
ejpam-6141	137	27	is	be	AUX
ejpam-6141	137	28	a	a	DET
ejpam-6141	137	29	contradiction	contradiction	NOUN
ejpam-6141	137	30	.	.	PUNCT
ejpam-6141	138	1	therefore	therefore	ADV
ejpam-6141	138	2	x	x	X
ejpam-6141	138	3	◦	◦	NOUN
ejpam-6141	138	4	ck	ck	PRON
ejpam-6141	138	5	y∩y	y∩y	PROPN
ejpam-6141	138	6	◦	◦	NOUN
ejpam-6141	138	7	ck	ck	NOUN
ejpam-6141	138	8	x	x	X
ejpam-6141	138	9	̸=	̸=	PROPN
ejpam-6141	138	10	∅.	∅.	ADV
ejpam-6141	138	11	in	in	ADP
ejpam-6141	138	12	theorem	theorem	NOUN
ejpam-6141	138	13	2	2	NUM
ejpam-6141	138	14	,	,	PUNCT
ejpam-6141	138	15	the	the	DET
ejpam-6141	138	16	given	give	VERB
ejpam-6141	138	17	boundary	boundary	NOUN
ejpam-6141	138	18	for	for	ADP
ejpam-6141	138	19	k	k	PROPN
ejpam-6141	138	20	is	be	AUX
ejpam-6141	138	21	the	the	DET
ejpam-6141	138	22	best	good	ADJ
ejpam-6141	138	23	boundary	boundary	NOUN
ejpam-6141	138	24	.	.	PUNCT
ejpam-6141	139	1	see	see	VERB
ejpam-6141	139	2	the	the	DET
ejpam-6141	139	3	next	next	ADJ
ejpam-6141	139	4	example	example	NOUN
ejpam-6141	139	5	.	.	PUNCT
ejpam-6141	140	1	example	example	NOUN
ejpam-6141	141	1	5	5	NUM
ejpam-6141	141	2	.	.	PUNCT
ejpam-6141	142	1	let	let	AUX
ejpam-6141	142	2	(	(	PUNCT
ejpam-6141	142	3	h	h	NOUN
ejpam-6141	142	4	,	,	PUNCT
ejpam-6141	142	5	⋆	⋆	ADJ
ejpam-6141	142	6	)	)	PUNCT
ejpam-6141	142	7	be	be	AUX
ejpam-6141	142	8	a	a	DET
ejpam-6141	142	9	quasigroup	quasigroup	NOUN
ejpam-6141	142	10	.	.	PUNCT
ejpam-6141	143	1	⋆0	⋆0	NUM
ejpam-6141	143	2	e	e	X
ejpam-6141	143	3	a	a	DET
ejpam-6141	143	4	b	b	NOUN
ejpam-6141	143	5	c	c	NOUN
ejpam-6141	143	6	e	e	X
ejpam-6141	143	7	e	e	X
ejpam-6141	143	8	a	a	DET
ejpam-6141	143	9	b	b	X
ejpam-6141	143	10	c	c	ADP
ejpam-6141	143	11	a	a	DET
ejpam-6141	143	12	a	a	DET
ejpam-6141	143	13	b	b	NOUN
ejpam-6141	143	14	c	c	NOUN
ejpam-6141	143	15	e	e	NOUN
ejpam-6141	143	16	b	b	PROPN
ejpam-6141	143	17	c	c	PROPN
ejpam-6141	143	18	e	e	PROPN
ejpam-6141	143	19	a	a	PRON
ejpam-6141	143	20	b	b	NOUN
ejpam-6141	143	21	c	c	NOUN
ejpam-6141	143	22	b	b	PROPN
ejpam-6141	143	23	c	c	NOUN
ejpam-6141	143	24	e	e	X
ejpam-6141	143	25	a	a	DET
ejpam-6141	143	26	⋆0	⋆0	NUM
ejpam-6141	143	27	e	e	X
ejpam-6141	143	28	a	a	DET
ejpam-6141	143	29	b	b	NOUN
ejpam-6141	143	30	c	c	NOUN
ejpam-6141	143	31	e	e	X
ejpam-6141	143	32	e	e	X
ejpam-6141	143	33	a	a	DET
ejpam-6141	143	34	b	b	X
ejpam-6141	143	35	c	c	ADP
ejpam-6141	143	36	a	a	DET
ejpam-6141	143	37	a	a	DET
ejpam-6141	143	38	b	b	NOUN
ejpam-6141	143	39	c	c	NOUN
ejpam-6141	143	40	e	e	NOUN
ejpam-6141	143	41	b	b	PROPN
ejpam-6141	143	42	c	c	PROPN
ejpam-6141	143	43	e	e	PROPN
ejpam-6141	143	44	a	a	PRON
ejpam-6141	143	45	b	b	NOUN
ejpam-6141	143	46	c	c	NOUN
ejpam-6141	143	47	b	b	PROPN
ejpam-6141	143	48	c	c	NOUN
ejpam-6141	143	49	e	e	X
ejpam-6141	143	50	a	a	DET
ejpam-6141	143	51	⋆1	⋆1	PROPN
ejpam-6141	143	52	e	e	PROPN
ejpam-6141	143	53	a	a	DET
ejpam-6141	143	54	b	b	NOUN
ejpam-6141	143	55	c	c	NOUN
ejpam-6141	143	56	e	e	X
ejpam-6141	143	57	c	c	X
ejpam-6141	143	58	e	e	PROPN
ejpam-6141	143	59	a	a	DET
ejpam-6141	143	60	b	b	NOUN
ejpam-6141	143	61	a	a	DET
ejpam-6141	143	62	e	e	NOUN
ejpam-6141	143	63	a	a	DET
ejpam-6141	143	64	b	b	PROPN
ejpam-6141	143	65	c	c	PROPN
ejpam-6141	143	66	b	b	PROPN
ejpam-6141	143	67	b	b	PROPN
ejpam-6141	143	68	c	c	NOUN
ejpam-6141	143	69	e	e	PROPN
ejpam-6141	143	70	a	a	PROPN
ejpam-6141	143	71	c	c	NOUN
ejpam-6141	143	72	a	a	DET
ejpam-6141	143	73	b	b	NOUN
ejpam-6141	143	74	c	c	NOUN
ejpam-6141	143	75	e	e	NOUN
ejpam-6141	143	76	⋆2	⋆2	X
ejpam-6141	143	77	e	e	PROPN
ejpam-6141	143	78	a	a	DET
ejpam-6141	143	79	b	b	NOUN
ejpam-6141	143	80	c	c	NOUN
ejpam-6141	143	81	e	e	PROPN
ejpam-6141	143	82	b	b	PROPN
ejpam-6141	143	83	c	c	PROPN
ejpam-6141	143	84	e	e	PROPN
ejpam-6141	143	85	a	a	PRON
ejpam-6141	143	86	a	a	DET
ejpam-6141	143	87	c	c	NOUN
ejpam-6141	143	88	e	e	NOUN
ejpam-6141	143	89	a	a	DET
ejpam-6141	143	90	b	b	PROPN
ejpam-6141	143	91	b	b	PROPN
ejpam-6141	143	92	a	a	DET
ejpam-6141	143	93	b	b	NOUN
ejpam-6141	143	94	c	c	NOUN
ejpam-6141	143	95	e	e	X
ejpam-6141	143	96	c	c	X
ejpam-6141	143	97	e	e	PROPN
ejpam-6141	143	98	a	a	PRON
ejpam-6141	143	99	b	b	PROPN
ejpam-6141	143	100	c	c	NOUN
ejpam-6141	143	101	⋆3	⋆3	PROPN
ejpam-6141	143	102	e	e	NOUN
ejpam-6141	143	103	a	a	DET
ejpam-6141	143	104	b	b	NOUN
ejpam-6141	143	105	c	c	NOUN
ejpam-6141	143	106	e	e	PROPN
ejpam-6141	143	107	a	a	PRON
ejpam-6141	143	108	b	b	NOUN
ejpam-6141	143	109	c	c	NOUN
ejpam-6141	143	110	e	e	PROPN
ejpam-6141	143	111	a	a	PRON
ejpam-6141	143	112	b	b	NOUN
ejpam-6141	143	113	c	c	NOUN
ejpam-6141	143	114	e	e	PROPN
ejpam-6141	143	115	a	a	PRON
ejpam-6141	143	116	b	b	PROPN
ejpam-6141	143	117	e	e	NOUN
ejpam-6141	143	118	a	a	PRON
ejpam-6141	143	119	b	b	NOUN
ejpam-6141	143	120	c	c	NOUN
ejpam-6141	143	121	c	c	NOUN
ejpam-6141	143	122	c	c	NOUN
ejpam-6141	143	123	e	e	PROPN
ejpam-6141	143	124	a	a	DET
ejpam-6141	143	125	b	b	PROPN
ejpam-6141	143	126	m.	m.	NOUN
ejpam-6141	143	127	a.	a.	NOUN
ejpam-6141	143	128	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	143	129	,	,	PUNCT
ejpam-6141	143	130	s.	s.	PROPN
ejpam-6141	143	131	mirvakili	mirvakili	PROPN
ejpam-6141	143	132	/	/	SYM
ejpam-6141	143	133	eur	eur	PROPN
ejpam-6141	143	134	.	.	PUNCT
ejpam-6141	144	1	j.	j.	PROPN
ejpam-6141	144	2	pure	pure	PROPN
ejpam-6141	144	3	appl	appl	PROPN
ejpam-6141	144	4	.	.	PROPN
ejpam-6141	144	5	math	math	PROPN
ejpam-6141	144	6	,	,	PUNCT
ejpam-6141	144	7	18	18	NUM
ejpam-6141	144	8	(	(	PUNCT
ejpam-6141	144	9	2	2	NUM
ejpam-6141	144	10	)	)	PUNCT
ejpam-6141	144	11	(	(	PUNCT
ejpam-6141	144	12	2025	2025	NUM
ejpam-6141	144	13	)	)	PUNCT
ejpam-6141	144	14	,	,	PUNCT
ejpam-6141	144	15	6141	6141	NUM
ejpam-6141	144	16	6	6	NUM
ejpam-6141	144	17	of	of	ADP
ejpam-6141	144	18	10	10	NUM
ejpam-6141	144	19	◦	◦	NOUN
ejpam-6141	144	20	c0	c0	X
ejpam-6141	144	21	e	e	PROPN
ejpam-6141	144	22	a	a	PRON
ejpam-6141	144	23	b	b	X
ejpam-6141	144	24	c	c	NOUN
ejpam-6141	144	25	e	e	X
ejpam-6141	144	26	e	e	X
ejpam-6141	144	27	a	a	DET
ejpam-6141	144	28	b	b	X
ejpam-6141	144	29	c	c	ADP
ejpam-6141	144	30	a	a	DET
ejpam-6141	144	31	a	a	DET
ejpam-6141	144	32	b	b	NOUN
ejpam-6141	144	33	c	c	NOUN
ejpam-6141	144	34	e	e	NOUN
ejpam-6141	144	35	b	b	PROPN
ejpam-6141	144	36	c	c	PROPN
ejpam-6141	144	37	e	e	PROPN
ejpam-6141	144	38	a	a	PRON
ejpam-6141	144	39	b	b	NOUN
ejpam-6141	144	40	c	c	NOUN
ejpam-6141	144	41	b	b	PROPN
ejpam-6141	144	42	c	c	PROPN
ejpam-6141	144	43	e	e	PROPN
ejpam-6141	144	44	a	a	DET
ejpam-6141	144	45	◦	◦	NOUN
ejpam-6141	144	46	c1	c1	NOUN
ejpam-6141	144	47	e	e	NOUN
ejpam-6141	144	48	a	a	DET
ejpam-6141	144	49	b	b	NOUN
ejpam-6141	144	50	c	c	NOUN
ejpam-6141	144	51	e	e	X
ejpam-6141	144	52	e	e	PROPN
ejpam-6141	144	53	,	,	PUNCT
ejpam-6141	144	54	c	c	PROPN
ejpam-6141	144	55	e	e	PROPN
ejpam-6141	144	56	,	,	PUNCT
ejpam-6141	144	57	a	a	DET
ejpam-6141	144	58	a	a	NOUN
ejpam-6141	144	59	,	,	PUNCT
ejpam-6141	144	60	b	b	PROPN
ejpam-6141	144	61	b	b	PROPN
ejpam-6141	144	62	,	,	PUNCT
ejpam-6141	144	63	c	c	PROPN
ejpam-6141	144	64	a	a	DET
ejpam-6141	144	65	e	e	NOUN
ejpam-6141	144	66	,	,	PUNCT
ejpam-6141	144	67	a	a	DET
ejpam-6141	144	68	a	a	NOUN
ejpam-6141	144	69	,	,	PUNCT
ejpam-6141	144	70	b	b	PROPN
ejpam-6141	144	71	b	b	PROPN
ejpam-6141	144	72	,	,	PUNCT
ejpam-6141	144	73	c	c	PROPN
ejpam-6141	144	74	e	e	NOUN
ejpam-6141	144	75	,	,	PUNCT
ejpam-6141	144	76	c	c	PROPN
ejpam-6141	144	77	b	b	PROPN
ejpam-6141	144	78	b	b	PROPN
ejpam-6141	144	79	,	,	PUNCT
ejpam-6141	144	80	c	c	PROPN
ejpam-6141	144	81	e	e	PROPN
ejpam-6141	144	82	,	,	PUNCT
ejpam-6141	144	83	c	c	PROPN
ejpam-6141	144	84	e	e	PROPN
ejpam-6141	144	85	,	,	PUNCT
ejpam-6141	144	86	a	a	DET
ejpam-6141	144	87	a	a	NOUN
ejpam-6141	144	88	,	,	PUNCT
ejpam-6141	144	89	b	b	PROPN
ejpam-6141	144	90	c	c	PROPN
ejpam-6141	144	91	a	a	PRON
ejpam-6141	144	92	,	,	PUNCT
ejpam-6141	144	93	b	b	PROPN
ejpam-6141	144	94	b	b	PROPN
ejpam-6141	144	95	,	,	PUNCT
ejpam-6141	144	96	c	c	PROPN
ejpam-6141	144	97	e	e	PROPN
ejpam-6141	144	98	,	,	PUNCT
ejpam-6141	144	99	c	c	PROPN
ejpam-6141	144	100	e	e	PROPN
ejpam-6141	144	101	,	,	PUNCT
ejpam-6141	144	102	a	a	DET
ejpam-6141	144	103	◦	◦	NOUN
ejpam-6141	144	104	c2	c2	PROPN
ejpam-6141	144	105	e	e	PROPN
ejpam-6141	144	106	a	a	DET
ejpam-6141	144	107	b	b	NOUN
ejpam-6141	144	108	c	c	NOUN
ejpam-6141	144	109	e	e	X
ejpam-6141	144	110	e	e	PROPN
ejpam-6141	144	111	,	,	PUNCT
ejpam-6141	144	112	b	b	NOUN
ejpam-6141	144	113	,	,	PUNCT
ejpam-6141	144	114	c	c	PROPN
ejpam-6141	144	115	e	e	PROPN
ejpam-6141	144	116	,	,	PUNCT
ejpam-6141	144	117	a	a	PRON
ejpam-6141	144	118	,	,	PUNCT
ejpam-6141	144	119	c	c	PROPN
ejpam-6141	144	120	e	e	PROPN
ejpam-6141	144	121	,	,	PUNCT
ejpam-6141	144	122	a	a	PRON
ejpam-6141	144	123	,	,	PUNCT
ejpam-6141	144	124	b	b	NOUN
ejpam-6141	144	125	a	a	DET
ejpam-6141	144	126	,	,	PUNCT
ejpam-6141	144	127	b	b	NOUN
ejpam-6141	144	128	,	,	PUNCT
ejpam-6141	144	129	c	c	PROPN
ejpam-6141	144	130	a	a	DET
ejpam-6141	144	131	e	e	NOUN
ejpam-6141	144	132	,	,	PUNCT
ejpam-6141	144	133	a	a	PRON
ejpam-6141	144	134	,	,	PUNCT
ejpam-6141	144	135	c	c	PROPN
ejpam-6141	144	136	e	e	PROPN
ejpam-6141	144	137	,	,	PUNCT
ejpam-6141	144	138	a	a	PRON
ejpam-6141	144	139	,	,	PUNCT
ejpam-6141	144	140	b	b	NOUN
ejpam-6141	144	141	a	a	PRON
ejpam-6141	144	142	,	,	PUNCT
ejpam-6141	144	143	b	b	NOUN
ejpam-6141	144	144	,	,	PUNCT
ejpam-6141	144	145	c	c	PROPN
ejpam-6141	144	146	e	e	PROPN
ejpam-6141	144	147	,	,	PUNCT
ejpam-6141	144	148	b	b	PROPN
ejpam-6141	144	149	,	,	PUNCT
ejpam-6141	144	150	c	c	PROPN
ejpam-6141	144	151	b	b	PROPN
ejpam-6141	144	152	a	a	PRON
ejpam-6141	144	153	,	,	PUNCT
ejpam-6141	144	154	b	b	NOUN
ejpam-6141	144	155	,	,	PUNCT
ejpam-6141	144	156	c	c	PROPN
ejpam-6141	144	157	e	e	PROPN
ejpam-6141	144	158	,	,	PUNCT
ejpam-6141	144	159	b	b	PROPN
ejpam-6141	144	160	,	,	PUNCT
ejpam-6141	144	161	c	c	PROPN
ejpam-6141	144	162	e	e	PROPN
ejpam-6141	144	163	,	,	PUNCT
ejpam-6141	144	164	a	a	PRON
ejpam-6141	144	165	,	,	PUNCT
ejpam-6141	144	166	c	c	PROPN
ejpam-6141	144	167	e	e	PROPN
ejpam-6141	144	168	,	,	PUNCT
ejpam-6141	144	169	a	a	PRON
ejpam-6141	144	170	,	,	PUNCT
ejpam-6141	144	171	b	b	NOUN
ejpam-6141	144	172	c	c	NOUN
ejpam-6141	144	173	e	e	PROPN
ejpam-6141	144	174	,	,	PUNCT
ejpam-6141	144	175	a	a	PRON
ejpam-6141	144	176	,	,	PUNCT
ejpam-6141	144	177	b	b	NOUN
ejpam-6141	144	178	a	a	PRON
ejpam-6141	144	179	,	,	PUNCT
ejpam-6141	144	180	b	b	NOUN
ejpam-6141	144	181	,	,	PUNCT
ejpam-6141	144	182	c	c	PROPN
ejpam-6141	144	183	e	e	PROPN
ejpam-6141	144	184	,	,	PUNCT
ejpam-6141	144	185	b	b	PROPN
ejpam-6141	144	186	,	,	PUNCT
ejpam-6141	144	187	c	c	PROPN
ejpam-6141	144	188	e	e	PROPN
ejpam-6141	144	189	,	,	PUNCT
ejpam-6141	144	190	a	a	PRON
ejpam-6141	144	191	,	,	PUNCT
ejpam-6141	144	192	c	c	PROPN
ejpam-6141	144	193	(	(	PUNCT
ejpam-6141	144	194	h	h	NOUN
ejpam-6141	144	195	,	,	PUNCT
ejpam-6141	144	196	◦	◦	NOUN
ejpam-6141	144	197	c1	c1	NOUN
ejpam-6141	144	198	)	)	PUNCT
ejpam-6141	144	199	is	be	AUX
ejpam-6141	144	200	not	not	PART
ejpam-6141	144	201	weak	weak	ADJ
ejpam-6141	144	202	commutative	commutative	ADJ
ejpam-6141	144	203	.	.	PUNCT
ejpam-6141	145	1	proposition	proposition	NOUN
ejpam-6141	145	2	3	3	X
ejpam-6141	145	3	.	.	PUNCT
ejpam-6141	146	1	let	let	AUX
ejpam-6141	146	2	(	(	PUNCT
ejpam-6141	146	3	h	h	NOUN
ejpam-6141	146	4	,	,	PUNCT
ejpam-6141	146	5	⋆	⋆	ADJ
ejpam-6141	146	6	)	)	PUNCT
ejpam-6141	146	7	be	be	AUX
ejpam-6141	146	8	a	a	DET
ejpam-6141	146	9	finite	finite	ADJ
ejpam-6141	146	10	quasigroup	quasigroup	NOUN
ejpam-6141	146	11	and	and	CCONJ
ejpam-6141	146	12	◦	◦	NOUN
ejpam-6141	146	13	ck	ck	ADV
ejpam-6141	146	14	be	be	VERB
ejpam-6141	146	15	the	the	DET
ejpam-6141	146	16	hyperoperation	hyperoperation	NOUN
ejpam-6141	146	17	in	in	ADP
ejpam-6141	146	18	definition	definition	NOUN
ejpam-6141	146	19	4	4	NUM
ejpam-6141	146	20	.	.	PUNCT
ejpam-6141	147	1	if	if	SCONJ
ejpam-6141	147	2	⋆	⋆	ADJ
ejpam-6141	147	3	is	be	AUX
ejpam-6141	147	4	commutative	commutative	ADJ
ejpam-6141	147	5	then	then	ADV
ejpam-6141	147	6	◦	◦	NOUN
ejpam-6141	147	7	ck	ck	NOUN
ejpam-6141	147	8	is	be	AUX
ejpam-6141	147	9	weak	weak	ADJ
ejpam-6141	147	10	commutative	commutative	ADJ
ejpam-6141	147	11	,	,	PUNCT
ejpam-6141	147	12	for	for	ADP
ejpam-6141	147	13	all	all	DET
ejpam-6141	147	14	k.	k.	NOUN
ejpam-6141	147	15	proof	proof	NOUN
ejpam-6141	147	16	.	.	PUNCT
ejpam-6141	148	1	for	for	ADP
ejpam-6141	148	2	every	every	DET
ejpam-6141	148	3	x	x	NOUN
ejpam-6141	148	4	,	,	PUNCT
ejpam-6141	148	5	y	y	PROPN
ejpam-6141	148	6	∈	∈	PROPN
ejpam-6141	148	7	h	h	NOUN
ejpam-6141	148	8	,	,	PUNCT
ejpam-6141	148	9	x	x	PUNCT
ejpam-6141	148	10	⋆	⋆	VERB
ejpam-6141	148	11	y	y	PROPN
ejpam-6141	148	12	=	=	SYM
ejpam-6141	148	13	y	y	PROPN
ejpam-6141	148	14	⋆	⋆	VERB
ejpam-6141	148	15	x.	x.	NOUN
ejpam-6141	149	1	we	we	PRON
ejpam-6141	149	2	have	have	VERB
ejpam-6141	149	3	x	x	PART
ejpam-6141	149	4	⋆	⋆	VERB
ejpam-6141	149	5	y	y	PROPN
ejpam-6141	149	6	∈	∈	PROPN
ejpam-6141	149	7	x	x	PUNCT
ejpam-6141	149	8	◦	◦	VERB
ejpam-6141	149	9	ck	ck	PROPN
ejpam-6141	149	10	y	y	PROPN
ejpam-6141	149	11	and	and	CCONJ
ejpam-6141	149	12	y	y	PROPN
ejpam-6141	149	13	⋆	⋆	VERB
ejpam-6141	149	14	x	x	PUNCT
ejpam-6141	149	15	∈	∈	PROPN
ejpam-6141	149	16	y	y	PROPN
ejpam-6141	149	17	◦	◦	NOUN
ejpam-6141	149	18	ck	ck	PROPN
ejpam-6141	149	19	x.	x.	NOUN
ejpam-6141	149	20	therefore	therefore	ADV
ejpam-6141	149	21	x	x	PUNCT
ejpam-6141	149	22	◦	◦	NOUN
ejpam-6141	149	23	ck	ck	ADJ
ejpam-6141	149	24	y	y	PROPN
ejpam-6141	149	25	∩	∩	PROPN
ejpam-6141	149	26	y	y	PROPN
ejpam-6141	149	27	◦	◦	NOUN
ejpam-6141	149	28	ck	ck	PROPN
ejpam-6141	149	29	x	x	SYM
ejpam-6141	149	30	̸=	̸=	PROPN
ejpam-6141	149	31	∅	∅	NOUN
ejpam-6141	149	32	and	and	CCONJ
ejpam-6141	149	33	proof	proof	NOUN
ejpam-6141	149	34	is	be	AUX
ejpam-6141	149	35	complete	complete	ADJ
ejpam-6141	149	36	.	.	PUNCT
ejpam-6141	150	1	proposition	proposition	NOUN
ejpam-6141	150	2	4	4	NUM
ejpam-6141	150	3	.	.	PUNCT
ejpam-6141	151	1	let	let	AUX
ejpam-6141	151	2	(	(	PUNCT
ejpam-6141	151	3	h	h	NOUN
ejpam-6141	151	4	,	,	PUNCT
ejpam-6141	151	5	⋆	⋆	ADJ
ejpam-6141	151	6	)	)	PUNCT
ejpam-6141	151	7	be	be	AUX
ejpam-6141	151	8	a	a	DET
ejpam-6141	151	9	finite	finite	ADJ
ejpam-6141	151	10	quasigroup	quasigroup	NOUN
ejpam-6141	151	11	and	and	CCONJ
ejpam-6141	151	12	◦	◦	NOUN
ejpam-6141	151	13	ck	ck	ADV
ejpam-6141	151	14	be	be	VERB
ejpam-6141	151	15	the	the	DET
ejpam-6141	151	16	hyperoperation	hyperoperation	NOUN
ejpam-6141	151	17	in	in	ADP
ejpam-6141	151	18	definition	definition	NOUN
ejpam-6141	151	19	4	4	NUM
ejpam-6141	151	20	.	.	PUNCT
ejpam-6141	152	1	if	if	SCONJ
ejpam-6141	152	2	(	(	PUNCT
ejpam-6141	152	3	h	h	NOUN
ejpam-6141	152	4	,	,	PUNCT
ejpam-6141	152	5	⋆	⋆	ADJ
ejpam-6141	152	6	)	)	PUNCT
ejpam-6141	152	7	is	be	AUX
ejpam-6141	152	8	a	a	DET
ejpam-6141	152	9	cyclic	cyclic	ADJ
ejpam-6141	152	10	group	group	NOUN
ejpam-6141	152	11	,	,	PUNCT
ejpam-6141	152	12	then	then	ADV
ejpam-6141	152	13	for	for	ADP
ejpam-6141	152	14	every	every	DET
ejpam-6141	152	15	k	k	PROPN
ejpam-6141	152	16	,	,	PUNCT
ejpam-6141	152	17	◦	◦	NOUN
ejpam-6141	152	18	ck	ck	ADJ
ejpam-6141	152	19	is	be	AUX
ejpam-6141	152	20	commutative	commutative	ADJ
ejpam-6141	152	21	;	;	PUNCT
ejpam-6141	152	22	proof	proof	NOUN
ejpam-6141	152	23	.	.	PUNCT
ejpam-6141	153	1	let	let	VERB
ejpam-6141	153	2	(	(	PUNCT
ejpam-6141	153	3	h	h	NOUN
ejpam-6141	153	4	,	,	PUNCT
ejpam-6141	153	5	⋆	⋆	ADJ
ejpam-6141	153	6	)	)	PUNCT
ejpam-6141	153	7	is	be	AUX
ejpam-6141	153	8	a	a	DET
ejpam-6141	153	9	cyclic	cyclic	ADJ
ejpam-6141	153	10	group	group	NOUN
ejpam-6141	153	11	then	then	ADV
ejpam-6141	153	12	(	(	PUNCT
ejpam-6141	153	13	h	h	NOUN
ejpam-6141	153	14	,	,	PUNCT
ejpam-6141	153	15	⋆	⋆	NOUN
ejpam-6141	153	16	)	)	PUNCT
ejpam-6141	153	17	∼=	∼=	PROPN
ejpam-6141	153	18	(	(	PUNCT
ejpam-6141	153	19	z,+	z,+	NUM
ejpam-6141	153	20	)	)	PUNCT
ejpam-6141	153	21	or	or	CCONJ
ejpam-6141	153	22	(	(	PUNCT
ejpam-6141	153	23	h	h	NOUN
ejpam-6141	153	24	,	,	PUNCT
ejpam-6141	153	25	⋆	⋆	NOUN
ejpam-6141	153	26	)	)	PUNCT
ejpam-6141	153	27	∼=	∼=	PROPN
ejpam-6141	153	28	(	(	PUNCT
ejpam-6141	153	29	zn,+	zn,+	NUM
ejpam-6141	153	30	)	)	PUNCT
ejpam-6141	153	31	.	.	PUNCT
ejpam-6141	154	1	if	if	SCONJ
ejpam-6141	154	2	(	(	PUNCT
ejpam-6141	154	3	h	h	NOUN
ejpam-6141	154	4	,	,	PUNCT
ejpam-6141	154	5	⋆	⋆	NOUN
ejpam-6141	154	6	)	)	PUNCT
ejpam-6141	154	7	∼=	∼=	PROPN
ejpam-6141	154	8	(	(	PUNCT
ejpam-6141	154	9	zn,+	zn,+	NUM
ejpam-6141	154	10	)	)	PUNCT
ejpam-6141	154	11	then	then	ADV
ejpam-6141	154	12	for	for	ADP
ejpam-6141	154	13	every	every	DET
ejpam-6141	154	14	x	x	NOUN
ejpam-6141	154	15	,	,	PUNCT
ejpam-6141	154	16	y	y	PROPN
ejpam-6141	154	17	∈	∈	PROPN
ejpam-6141	154	18	zn	zn	PROPN
ejpam-6141	154	19	,	,	PUNCT
ejpam-6141	154	20	x	x	PUNCT
ejpam-6141	154	21	◦	◦	NOUN
ejpam-6141	154	22	ck	ck	ADJ
ejpam-6141	154	23	y	y	NOUN
ejpam-6141	154	24	=	=	SYM
ejpam-6141	154	25	{	{	PUNCT
ejpam-6141	154	26	x+	x+	PROPN
ejpam-6141	154	27	y	y	PROPN
ejpam-6141	154	28	,	,	PUNCT
ejpam-6141	154	29	x+	x+	PROPN
ejpam-6141	154	30	y	y	PROPN
ejpam-6141	154	31	−	−	PROPN
ejpam-6141	154	32	1	1	NUM
ejpam-6141	154	33	,	,	PUNCT
ejpam-6141	154	34	.	.	PUNCT
ejpam-6141	154	35	.	.	PUNCT
ejpam-6141	154	36	.	.	PUNCT
ejpam-6141	155	1	,	,	PUNCT
ejpam-6141	155	2	x+	x+	NUM
ejpam-6141	155	3	y	y	PROPN
ejpam-6141	156	1	−	−	PUNCT
ejpam-6141	157	1	k	k	NOUN
ejpam-6141	157	2	}	}	PUNCT
ejpam-6141	157	3	=	=	SYM
ejpam-6141	157	4	{	{	PUNCT
ejpam-6141	157	5	y	y	PROPN
ejpam-6141	157	6	+	+	NUM
ejpam-6141	157	7	x	x	PROPN
ejpam-6141	157	8	,	,	PUNCT
ejpam-6141	157	9	y	y	PROPN
ejpam-6141	157	10	+	+	CCONJ
ejpam-6141	157	11	x−	x−	PROPN
ejpam-6141	157	12	1	1	NUM
ejpam-6141	157	13	,	,	PUNCT
ejpam-6141	157	14	.	.	PUNCT
ejpam-6141	157	15	.	.	PUNCT
ejpam-6141	157	16	.	.	PUNCT
ejpam-6141	158	1	,	,	PUNCT
ejpam-6141	158	2	y	y	PROPN
ejpam-6141	158	3	+	+	NUM
ejpam-6141	158	4	x−	x−	PROPN
ejpam-6141	158	5	k	k	PROPN
ejpam-6141	158	6	}	}	PUNCT
ejpam-6141	158	7	=	=	SYM
ejpam-6141	158	8	x	x	SYM
ejpam-6141	158	9	◦	◦	NOUN
ejpam-6141	158	10	ck	ck	VERB
ejpam-6141	158	11	y.	y.	NOUN
ejpam-6141	159	1	therefore	therefore	ADV
ejpam-6141	159	2	(	(	PUNCT
ejpam-6141	159	3	h	h	NOUN
ejpam-6141	159	4	,	,	PUNCT
ejpam-6141	159	5	◦	◦	NOUN
ejpam-6141	159	6	ck	ck	NOUN
ejpam-6141	159	7	)	)	PUNCT
ejpam-6141	159	8	is	be	AUX
ejpam-6141	159	9	a	a	DET
ejpam-6141	159	10	commutative	commutative	ADJ
ejpam-6141	159	11	hypergroupoid	hypergroupoid	NOUN
ejpam-6141	159	12	.	.	PUNCT
ejpam-6141	160	1	lemma	lemma	PROPN
ejpam-6141	160	2	1	1	NUM
ejpam-6141	160	3	.	.	PUNCT
ejpam-6141	161	1	(	(	PUNCT
ejpam-6141	161	2	h	h	NOUN
ejpam-6141	161	3	,	,	PUNCT
ejpam-6141	161	4	◦	◦	NOUN
ejpam-6141	161	5	ck	ck	ADJ
ejpam-6141	161	6	)	)	PUNCT
ejpam-6141	161	7	and	and	CCONJ
ejpam-6141	161	8	(	(	PUNCT
ejpam-6141	161	9	h	h	NOUN
ejpam-6141	161	10	,	,	PUNCT
ejpam-6141	161	11	◦	◦	NOUN
ejpam-6141	161	12	rk	rk	NOUN
ejpam-6141	161	13	)	)	PUNCT
ejpam-6141	161	14	are	be	AUX
ejpam-6141	161	15	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	161	16	.	.	PUNCT
ejpam-6141	162	1	proof	proof	NOUN
ejpam-6141	162	2	.	.	PUNCT
ejpam-6141	163	1	for	for	ADP
ejpam-6141	163	2	every	every	DET
ejpam-6141	163	3	a	a	PROPN
ejpam-6141	163	4	,	,	PUNCT
ejpam-6141	163	5	b	b	PROPN
ejpam-6141	163	6	∈	∈	PROPN
ejpam-6141	163	7	h	h	NOUN
ejpam-6141	163	8	,	,	PUNCT
ejpam-6141	163	9	a	a	DET
ejpam-6141	163	10	⋆	⋆	NOUN
ejpam-6141	163	11	x	x	SYM
ejpam-6141	163	12	=	=	SYM
ejpam-6141	163	13	b	b	PROPN
ejpam-6141	163	14	and	and	CCONJ
ejpam-6141	163	15	y	y	PROPN
ejpam-6141	163	16	⋆	⋆	VERB
ejpam-6141	163	17	a	a	DET
ejpam-6141	163	18	=	=	SYM
ejpam-6141	163	19	b	b	NOUN
ejpam-6141	163	20	have	have	VERB
ejpam-6141	163	21	solutions	solution	NOUN
ejpam-6141	163	22	in	in	ADP
ejpam-6141	163	23	h.	h.	PROPN
ejpam-6141	163	24	since	since	SCONJ
ejpam-6141	163	25	for	for	ADP
ejpam-6141	163	26	every	every	DET
ejpam-6141	163	27	k	k	NOUN
ejpam-6141	163	28	,	,	PUNCT
ejpam-6141	163	29	a	a	DET
ejpam-6141	163	30	⋆x	⋆x	PROPN
ejpam-6141	163	31	⊆	⊆	NUM
ejpam-6141	163	32	a	a	DET
ejpam-6141	163	33	◦	◦	NOUN
ejpam-6141	163	34	ck	ck	NOUN
ejpam-6141	163	35	x	x	X
ejpam-6141	163	36	and	and	CCONJ
ejpam-6141	163	37	y	y	PROPN
ejpam-6141	163	38	⋆	⋆	VERB
ejpam-6141	163	39	a	a	DET
ejpam-6141	163	40	⊆	⊆	NUM
ejpam-6141	163	41	y	y	PROPN
ejpam-6141	163	42	◦	◦	NOUN
ejpam-6141	163	43	ck	ck	PROPN
ejpam-6141	163	44	a	a	DET
ejpam-6141	163	45	therefore	therefore	ADV
ejpam-6141	163	46	b	b	PROPN
ejpam-6141	163	47	∈	∈	PROPN
ejpam-6141	163	48	a	a	DET
ejpam-6141	163	49	◦	◦	NOUN
ejpam-6141	163	50	ck	ck	NOUN
ejpam-6141	163	51	x	x	X
ejpam-6141	163	52	and	and	CCONJ
ejpam-6141	163	53	b	b	X
ejpam-6141	163	54	∈	∈	PROPN
ejpam-6141	163	55	y	y	PROPN
ejpam-6141	163	56	◦	◦	NOUN
ejpam-6141	163	57	ck	ck	PROPN
ejpam-6141	163	58	a	a	DET
ejpam-6141	163	59	have	have	AUX
ejpam-6141	163	60	solutions	solution	NOUN
ejpam-6141	163	61	in	in	ADP
ejpam-6141	163	62	h.	h.	PROPN
ejpam-6141	163	63	lemma	lemma	PROPN
ejpam-6141	164	1	2	2	X
ejpam-6141	164	2	.	.	X
ejpam-6141	164	3	we	we	PRON
ejpam-6141	164	4	have	have	VERB
ejpam-6141	164	5	⋆	⋆	NOUN
ejpam-6141	164	6	=	=	SYM
ejpam-6141	164	7	◦	◦	PROPN
ejpam-6141	164	8	c0	c0	PROPN
ejpam-6141	164	9	⊂	⊂	PROPN
ejpam-6141	164	10	◦	◦	PROPN
ejpam-6141	164	11	c1	c1	PROPN
ejpam-6141	164	12	⊂	⊂	PROPN
ejpam-6141	164	13	.	.	PUNCT
ejpam-6141	164	14	.	.	PUNCT
ejpam-6141	164	15	.	.	PUNCT
ejpam-6141	165	1	⊂	⊂	PROPN
ejpam-6141	165	2	◦	◦	VERB
ejpam-6141	165	3	cn−2	cn−2	PROPN
ejpam-6141	165	4	⊂	⊂	PROPN
ejpam-6141	165	5	◦	◦	PROPN
ejpam-6141	165	6	cn−1	cn−1	PROPN
ejpam-6141	165	7	=	=	PUNCT
ejpam-6141	165	8	◦	◦	NOUN
ejpam-6141	165	9	t	t	NOUN
ejpam-6141	165	10	,	,	PUNCT
ejpam-6141	165	11	and	and	CCONJ
ejpam-6141	165	12	⋆	⋆	ADJ
ejpam-6141	165	13	=	=	SYM
ejpam-6141	165	14	◦	◦	PROPN
ejpam-6141	165	15	r0	r0	NOUN
ejpam-6141	165	16	⊂	⊂	PROPN
ejpam-6141	165	17	◦	◦	PROPN
ejpam-6141	165	18	r1	r1	PROPN
ejpam-6141	165	19	⊂	⊂	PROPN
ejpam-6141	165	20	.	.	PUNCT
ejpam-6141	165	21	.	.	PUNCT
ejpam-6141	165	22	.	.	PUNCT
ejpam-6141	166	1	⊂	⊂	PROPN
ejpam-6141	166	2	◦	◦	PROPN
ejpam-6141	166	3	rn−2	rn−2	PROPN
ejpam-6141	166	4	⊂	⊂	PROPN
ejpam-6141	166	5	◦	◦	NOUN
ejpam-6141	166	6	rn−1	rn−1	PROPN
ejpam-6141	166	7	=	=	SYM
ejpam-6141	166	8	◦	◦	NOUN
ejpam-6141	166	9	t	t	NOUN
ejpam-6141	166	10	.	.	PUNCT
ejpam-6141	167	1	when	when	SCONJ
ejpam-6141	167	2	⋆	⋆	NOUN
ejpam-6141	167	3	is	be	AUX
ejpam-6141	167	4	the	the	DET
ejpam-6141	167	5	operation	operation	NOUN
ejpam-6141	167	6	in	in	ADP
ejpam-6141	167	7	definition	definition	NOUN
ejpam-6141	167	8	5	5	NUM
ejpam-6141	167	9	and	and	CCONJ
ejpam-6141	167	10	◦	◦	NOUN
ejpam-6141	167	11	t	t	NOUN
ejpam-6141	167	12	is	be	AUX
ejpam-6141	167	13	the	the	DET
ejpam-6141	167	14	hyperoperation	hyperoperation	NOUN
ejpam-6141	167	15	in	in	ADP
ejpam-6141	167	16	example	example	NOUN
ejpam-6141	168	1	3	3	NUM
ejpam-6141	168	2	.	.	PUNCT
ejpam-6141	168	3	proof	proof	NOUN
ejpam-6141	168	4	.	.	PUNCT
ejpam-6141	169	1	it	it	PRON
ejpam-6141	169	2	is	be	AUX
ejpam-6141	169	3	straightforward	straightforward	ADJ
ejpam-6141	169	4	.	.	PUNCT
ejpam-6141	170	1	example	example	NOUN
ejpam-6141	171	1	6	6	NUM
ejpam-6141	171	2	.	.	PUNCT
ejpam-6141	172	1	let	let	AUX
ejpam-6141	172	2	(	(	PUNCT
ejpam-6141	172	3	h	h	NOUN
ejpam-6141	172	4	,	,	PUNCT
ejpam-6141	172	5	⋆	⋆	ADJ
ejpam-6141	172	6	)	)	PUNCT
ejpam-6141	172	7	be	be	AUX
ejpam-6141	172	8	a	a	DET
ejpam-6141	172	9	cycle	cycle	NOUN
ejpam-6141	172	10	group	group	NOUN
ejpam-6141	172	11	of	of	ADP
ejpam-6141	172	12	order	order	NOUN
ejpam-6141	172	13	3	3	NUM
ejpam-6141	172	14	by	by	ADP
ejpam-6141	172	15	the	the	DET
ejpam-6141	172	16	following	following	ADJ
ejpam-6141	172	17	cayley	cayley	ADJ
ejpam-6141	172	18	table	table	NOUN
ejpam-6141	172	19	⋆	⋆	VERB
ejpam-6141	172	20	a	a	DET
ejpam-6141	172	21	b	b	NOUN
ejpam-6141	172	22	c	c	NOUN
ejpam-6141	172	23	a	a	DET
ejpam-6141	172	24	a	a	DET
ejpam-6141	172	25	b	b	NOUN
ejpam-6141	172	26	c	c	NOUN
ejpam-6141	172	27	b	b	PROPN
ejpam-6141	172	28	b	b	PROPN
ejpam-6141	172	29	c	c	PROPN
ejpam-6141	172	30	a	a	DET
ejpam-6141	172	31	c	c	NOUN
ejpam-6141	172	32	c	c	PROPN
ejpam-6141	172	33	a	a	DET
ejpam-6141	172	34	b	b	PROPN
ejpam-6141	172	35	m.	m.	NOUN
ejpam-6141	172	36	a.	a.	NOUN
ejpam-6141	172	37	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	172	38	,	,	PUNCT
ejpam-6141	172	39	s.	s.	PROPN
ejpam-6141	172	40	mirvakili	mirvakili	PROPN
ejpam-6141	172	41	/	/	SYM
ejpam-6141	172	42	eur	eur	PROPN
ejpam-6141	172	43	.	.	PUNCT
ejpam-6141	173	1	j.	j.	PROPN
ejpam-6141	173	2	pure	pure	PROPN
ejpam-6141	173	3	appl	appl	PROPN
ejpam-6141	173	4	.	.	PROPN
ejpam-6141	173	5	math	math	PROPN
ejpam-6141	173	6	,	,	PUNCT
ejpam-6141	173	7	18	18	NUM
ejpam-6141	173	8	(	(	PUNCT
ejpam-6141	173	9	2	2	NUM
ejpam-6141	173	10	)	)	PUNCT
ejpam-6141	173	11	(	(	PUNCT
ejpam-6141	173	12	2025	2025	NUM
ejpam-6141	173	13	)	)	PUNCT
ejpam-6141	173	14	,	,	PUNCT
ejpam-6141	173	15	6141	6141	NUM
ejpam-6141	173	16	7	7	NUM
ejpam-6141	173	17	of	of	ADP
ejpam-6141	173	18	10	10	NUM
ejpam-6141	173	19	then	then	ADV
ejpam-6141	173	20	we	we	PRON
ejpam-6141	173	21	obtain	obtain	VERB
ejpam-6141	173	22	⋆0	⋆0	NUM
ejpam-6141	173	23	a	a	DET
ejpam-6141	173	24	b	b	NOUN
ejpam-6141	173	25	c	c	NOUN
ejpam-6141	173	26	a	a	DET
ejpam-6141	173	27	a	a	DET
ejpam-6141	173	28	b	b	NOUN
ejpam-6141	173	29	c	c	NOUN
ejpam-6141	173	30	b	b	PROPN
ejpam-6141	173	31	b	b	PROPN
ejpam-6141	173	32	c	c	PROPN
ejpam-6141	173	33	a	a	DET
ejpam-6141	173	34	c	c	NOUN
ejpam-6141	173	35	c	c	NOUN
ejpam-6141	173	36	a	a	DET
ejpam-6141	173	37	b	b	PROPN
ejpam-6141	173	38	⋆1	⋆1	ADP
ejpam-6141	173	39	a	a	DET
ejpam-6141	173	40	b	b	NOUN
ejpam-6141	173	41	c	c	NOUN
ejpam-6141	173	42	a	a	DET
ejpam-6141	173	43	c	c	NOUN
ejpam-6141	173	44	a	a	DET
ejpam-6141	173	45	b	b	PROPN
ejpam-6141	173	46	b	b	PROPN
ejpam-6141	173	47	a	a	DET
ejpam-6141	173	48	b	b	NOUN
ejpam-6141	173	49	c	c	NOUN
ejpam-6141	173	50	c	c	PROPN
ejpam-6141	173	51	b	b	PROPN
ejpam-6141	173	52	c	c	PROPN
ejpam-6141	173	53	a	a	DET
ejpam-6141	173	54	⋆3	⋆3	NUM
ejpam-6141	173	55	a	a	DET
ejpam-6141	173	56	b	b	NOUN
ejpam-6141	173	57	c	c	NOUN
ejpam-6141	173	58	a	a	DET
ejpam-6141	173	59	b	b	NOUN
ejpam-6141	173	60	c	c	NOUN
ejpam-6141	173	61	a	a	DET
ejpam-6141	173	62	b	b	NOUN
ejpam-6141	173	63	c	c	NOUN
ejpam-6141	173	64	a	a	DET
ejpam-6141	173	65	b	b	NOUN
ejpam-6141	173	66	c	c	NOUN
ejpam-6141	173	67	a	a	DET
ejpam-6141	173	68	b	b	NOUN
ejpam-6141	173	69	c	c	NOUN
ejpam-6141	173	70	and	and	CCONJ
ejpam-6141	173	71	therefore	therefore	ADV
ejpam-6141	173	72	◦	◦	VERB
ejpam-6141	173	73	c0	c0	PROPN
ejpam-6141	173	74	a	a	DET
ejpam-6141	173	75	b	b	X
ejpam-6141	173	76	c	c	ADP
ejpam-6141	173	77	a	a	DET
ejpam-6141	173	78	a	a	DET
ejpam-6141	173	79	b	b	NOUN
ejpam-6141	173	80	c	c	NOUN
ejpam-6141	173	81	b	b	PROPN
ejpam-6141	173	82	b	b	PROPN
ejpam-6141	173	83	c	c	PROPN
ejpam-6141	173	84	a	a	DET
ejpam-6141	173	85	c	c	NOUN
ejpam-6141	173	86	c	c	PROPN
ejpam-6141	173	87	a	a	DET
ejpam-6141	173	88	b	b	PROPN
ejpam-6141	173	89	◦	◦	NOUN
ejpam-6141	173	90	c1	c1	PROPN
ejpam-6141	173	91	a	a	DET
ejpam-6141	173	92	b	b	PROPN
ejpam-6141	173	93	c	c	PROPN
ejpam-6141	173	94	a	a	DET
ejpam-6141	173	95	a	a	NOUN
ejpam-6141	173	96	,	,	PUNCT
ejpam-6141	173	97	c	c	PROPN
ejpam-6141	173	98	a	a	X
ejpam-6141	173	99	,	,	PUNCT
ejpam-6141	173	100	b	b	PROPN
ejpam-6141	173	101	b	b	PROPN
ejpam-6141	173	102	,	,	PUNCT
ejpam-6141	173	103	c	c	PROPN
ejpam-6141	173	104	b	b	PROPN
ejpam-6141	173	105	a	a	PRON
ejpam-6141	173	106	,	,	PUNCT
ejpam-6141	173	107	b	b	PROPN
ejpam-6141	173	108	b	b	PROPN
ejpam-6141	173	109	,	,	PUNCT
ejpam-6141	173	110	c	c	PROPN
ejpam-6141	173	111	a	a	X
ejpam-6141	173	112	,	,	PUNCT
ejpam-6141	173	113	c	c	PROPN
ejpam-6141	173	114	c	c	PROPN
ejpam-6141	173	115	b	b	PROPN
ejpam-6141	173	116	,	,	PUNCT
ejpam-6141	173	117	c	c	PROPN
ejpam-6141	173	118	a	a	X
ejpam-6141	173	119	,	,	PUNCT
ejpam-6141	173	120	c	c	X
ejpam-6141	173	121	,	,	PUNCT
ejpam-6141	173	122	a	a	DET
ejpam-6141	173	123	a	a	NOUN
ejpam-6141	173	124	,	,	PUNCT
ejpam-6141	173	125	b	b	NOUN
ejpam-6141	173	126	◦	◦	NOUN
ejpam-6141	173	127	c2	c2	PROPN
ejpam-6141	173	128	a	a	DET
ejpam-6141	173	129	b	b	PROPN
ejpam-6141	173	130	c	c	PROPN
ejpam-6141	173	131	a	a	DET
ejpam-6141	173	132	h	h	NOUN
ejpam-6141	173	133	h	h	NOUN
ejpam-6141	174	1	h	h	NOUN
ejpam-6141	175	1	b	b	PROPN
ejpam-6141	175	2	h	h	NOUN
ejpam-6141	175	3	h	h	NOUN
ejpam-6141	176	1	h	h	NOUN
ejpam-6141	177	1	c	c	NOUN
ejpam-6141	177	2	h	h	NOUN
ejpam-6141	177	3	h	h	NOUN
ejpam-6141	177	4	h	h	PROPN
ejpam-6141	177	5	.	.	PUNCT
ejpam-6141	178	1	(	(	PUNCT
ejpam-6141	178	2	h	h	NOUN
ejpam-6141	178	3	,	,	PUNCT
ejpam-6141	178	4	◦	◦	NOUN
ejpam-6141	178	5	ck	ck	NOUN
ejpam-6141	178	6	)	)	PUNCT
ejpam-6141	178	7	are	be	AUX
ejpam-6141	178	8	commutative	commutative	ADJ
ejpam-6141	178	9	hypergroups	hypergroup	NOUN
ejpam-6141	178	10	.	.	PUNCT
ejpam-6141	178	11	example	example	NOUN
ejpam-6141	179	1	7	7	NUM
ejpam-6141	179	2	.	.	PUNCT
ejpam-6141	180	1	let	let	AUX
ejpam-6141	180	2	(	(	PUNCT
ejpam-6141	180	3	h	h	NOUN
ejpam-6141	180	4	,	,	PUNCT
ejpam-6141	180	5	⋆	⋆	ADJ
ejpam-6141	180	6	)	)	PUNCT
ejpam-6141	180	7	be	be	AUX
ejpam-6141	180	8	a	a	DET
ejpam-6141	180	9	finite	finite	ADJ
ejpam-6141	180	10	quasigroup	quasigroup	NOUN
ejpam-6141	180	11	by	by	ADP
ejpam-6141	180	12	the	the	DET
ejpam-6141	180	13	following	following	ADJ
ejpam-6141	180	14	cayley	cayley	ADJ
ejpam-6141	180	15	table	table	NOUN
ejpam-6141	180	16	⋆	⋆	VERB
ejpam-6141	180	17	a	a	DET
ejpam-6141	180	18	b	b	NOUN
ejpam-6141	180	19	c	c	NOUN
ejpam-6141	180	20	a	a	DET
ejpam-6141	180	21	b	b	NOUN
ejpam-6141	180	22	c	c	NOUN
ejpam-6141	180	23	a	a	DET
ejpam-6141	180	24	b	b	NOUN
ejpam-6141	180	25	a	a	PRON
ejpam-6141	180	26	b	b	NOUN
ejpam-6141	180	27	c	c	NOUN
ejpam-6141	180	28	c	c	NOUN
ejpam-6141	180	29	c	c	PROPN
ejpam-6141	180	30	b	b	PROPN
ejpam-6141	180	31	a	a	PRON
ejpam-6141	180	32	then	then	ADV
ejpam-6141	180	33	we	we	PRON
ejpam-6141	180	34	obtain	obtain	VERB
ejpam-6141	180	35	⋆0	⋆0	NUM
ejpam-6141	180	36	a	a	DET
ejpam-6141	180	37	b	b	NOUN
ejpam-6141	180	38	c	c	NOUN
ejpam-6141	180	39	a	a	DET
ejpam-6141	180	40	b	b	NOUN
ejpam-6141	180	41	c	c	NOUN
ejpam-6141	180	42	a	a	DET
ejpam-6141	180	43	b	b	NOUN
ejpam-6141	180	44	a	a	DET
ejpam-6141	180	45	b	b	NOUN
ejpam-6141	180	46	c	c	NOUN
ejpam-6141	180	47	c	c	NOUN
ejpam-6141	180	48	c	c	PROPN
ejpam-6141	180	49	a	a	DET
ejpam-6141	180	50	b	b	PROPN
ejpam-6141	180	51	⋆1	⋆1	ADP
ejpam-6141	180	52	a	a	DET
ejpam-6141	180	53	b	b	NOUN
ejpam-6141	180	54	c	c	NOUN
ejpam-6141	180	55	a	a	DET
ejpam-6141	180	56	a	a	DET
ejpam-6141	180	57	b	b	NOUN
ejpam-6141	180	58	c	c	NOUN
ejpam-6141	180	59	b	b	PROPN
ejpam-6141	180	60	c	c	PROPN
ejpam-6141	180	61	a	a	DET
ejpam-6141	180	62	b	b	NOUN
ejpam-6141	180	63	c	c	NOUN
ejpam-6141	180	64	b	b	PROPN
ejpam-6141	180	65	c	c	PROPN
ejpam-6141	180	66	a	a	DET
ejpam-6141	180	67	⋆2	⋆2	PROPN
ejpam-6141	180	68	a	a	DET
ejpam-6141	180	69	b	b	NOUN
ejpam-6141	180	70	c	c	NOUN
ejpam-6141	180	71	a	a	DET
ejpam-6141	180	72	c	c	NOUN
ejpam-6141	180	73	a	a	DET
ejpam-6141	180	74	b	b	PROPN
ejpam-6141	180	75	b	b	PROPN
ejpam-6141	180	76	b	b	PROPN
ejpam-6141	180	77	c	c	PROPN
ejpam-6141	180	78	a	a	DET
ejpam-6141	180	79	c	c	NOUN
ejpam-6141	180	80	a	a	DET
ejpam-6141	180	81	b	b	NOUN
ejpam-6141	180	82	c	c	NOUN
ejpam-6141	180	83	and	and	CCONJ
ejpam-6141	180	84	therefore	therefore	ADV
ejpam-6141	180	85	◦	◦	VERB
ejpam-6141	180	86	c0	c0	PROPN
ejpam-6141	180	87	a	a	DET
ejpam-6141	180	88	b	b	X
ejpam-6141	180	89	c	c	PROPN
ejpam-6141	180	90	a	a	DET
ejpam-6141	180	91	b	b	NOUN
ejpam-6141	180	92	c	c	NOUN
ejpam-6141	180	93	a	a	DET
ejpam-6141	180	94	b	b	NOUN
ejpam-6141	180	95	a	a	PRON
ejpam-6141	180	96	b	b	NOUN
ejpam-6141	180	97	c	c	NOUN
ejpam-6141	180	98	c	c	NOUN
ejpam-6141	180	99	c	c	PROPN
ejpam-6141	180	100	a	a	DET
ejpam-6141	180	101	b	b	PROPN
ejpam-6141	180	102	◦	◦	NOUN
ejpam-6141	180	103	c1	c1	PROPN
ejpam-6141	180	104	a	a	DET
ejpam-6141	180	105	b	b	PROPN
ejpam-6141	180	106	c	c	PROPN
ejpam-6141	180	107	a	a	DET
ejpam-6141	180	108	a	a	PROPN
ejpam-6141	180	109	,	,	PUNCT
ejpam-6141	180	110	b	b	PROPN
ejpam-6141	180	111	b	b	PROPN
ejpam-6141	180	112	,	,	PUNCT
ejpam-6141	180	113	c	c	PROPN
ejpam-6141	180	114	a	a	X
ejpam-6141	180	115	,	,	PUNCT
ejpam-6141	180	116	c	c	PROPN
ejpam-6141	180	117	b	b	PROPN
ejpam-6141	180	118	a	a	X
ejpam-6141	180	119	,	,	PUNCT
ejpam-6141	180	120	c	c	PROPN
ejpam-6141	180	121	a	a	X
ejpam-6141	180	122	,	,	PUNCT
ejpam-6141	180	123	b	b	PROPN
ejpam-6141	180	124	b	b	PROPN
ejpam-6141	180	125	,	,	PUNCT
ejpam-6141	180	126	c	c	PROPN
ejpam-6141	180	127	c	c	PROPN
ejpam-6141	180	128	b	b	PROPN
ejpam-6141	180	129	,	,	PUNCT
ejpam-6141	180	130	c	c	PROPN
ejpam-6141	180	131	c	c	X
ejpam-6141	180	132	,	,	PUNCT
ejpam-6141	180	133	a	a	DET
ejpam-6141	180	134	b	b	NOUN
ejpam-6141	180	135	,	,	PUNCT
ejpam-6141	180	136	a	a	DET
ejpam-6141	180	137	◦	◦	NOUN
ejpam-6141	180	138	c2	c2	PROPN
ejpam-6141	180	139	a	a	DET
ejpam-6141	180	140	b	b	PROPN
ejpam-6141	180	141	c	c	PROPN
ejpam-6141	180	142	a	a	DET
ejpam-6141	180	143	h	h	NOUN
ejpam-6141	180	144	h	h	NOUN
ejpam-6141	181	1	h	h	NOUN
ejpam-6141	182	1	b	b	PROPN
ejpam-6141	182	2	h	h	NOUN
ejpam-6141	182	3	h	h	NOUN
ejpam-6141	183	1	h	h	NOUN
ejpam-6141	184	1	c	c	NOUN
ejpam-6141	184	2	h	h	NOUN
ejpam-6141	184	3	h	h	NOUN
ejpam-6141	184	4	h	h	PROPN
ejpam-6141	184	5	.	.	PUNCT
ejpam-6141	185	1	(	(	PUNCT
ejpam-6141	185	2	h	h	NOUN
ejpam-6141	185	3	,	,	PUNCT
ejpam-6141	185	4	◦	◦	NOUN
ejpam-6141	185	5	c0	c0	NOUN
ejpam-6141	185	6	)	)	PUNCT
ejpam-6141	185	7	is	be	AUX
ejpam-6141	185	8	neither	neither	CCONJ
ejpam-6141	185	9	commutative	commutative	ADJ
ejpam-6141	185	10	nor	nor	CCONJ
ejpam-6141	185	11	weak	weak	ADJ
ejpam-6141	185	12	commutative	commutative	ADJ
ejpam-6141	185	13	(	(	PUNCT
ejpam-6141	185	14	because	because	SCONJ
ejpam-6141	185	15	a	a	DET
ejpam-6141	185	16	◦	◦	NOUN
ejpam-6141	185	17	c0	c0	NOUN
ejpam-6141	185	18	c	c	PROPN
ejpam-6141	185	19	̸≈	̸≈	PROPN
ejpam-6141	185	20	c	c	PROPN
ejpam-6141	185	21	◦	◦	PROPN
ejpam-6141	185	22	c0	c0	PROPN
ejpam-6141	185	23	a	a	NOUN
ejpam-6141	185	24	)	)	PUNCT
ejpam-6141	185	25	.	.	PUNCT
ejpam-6141	186	1	(	(	PUNCT
ejpam-6141	186	2	h	h	NOUN
ejpam-6141	186	3	,	,	PUNCT
ejpam-6141	186	4	◦	◦	NOUN
ejpam-6141	186	5	c1	c1	NOUN
ejpam-6141	186	6	)	)	PUNCT
ejpam-6141	186	7	is	be	AUX
ejpam-6141	186	8	not	not	PART
ejpam-6141	186	9	commutative	commutative	ADJ
ejpam-6141	186	10	but	but	CCONJ
ejpam-6141	186	11	it	it	PRON
ejpam-6141	186	12	is	be	AUX
ejpam-6141	186	13	weak	weak	ADJ
ejpam-6141	186	14	commutative	commutative	ADJ
ejpam-6141	186	15	(	(	PUNCT
ejpam-6141	186	16	because	because	SCONJ
ejpam-6141	186	17	x	x	PART
ejpam-6141	186	18	◦	◦	NOUN
ejpam-6141	186	19	c1	c1	NOUN
ejpam-6141	186	20	y	y	PROPN
ejpam-6141	186	21	≈	≈	PROPN
ejpam-6141	186	22	y	y	PROPN
ejpam-6141	186	23	◦	◦	PROPN
ejpam-6141	186	24	c1	c1	PROPN
ejpam-6141	186	25	x	x	PUNCT
ejpam-6141	186	26	for	for	ADP
ejpam-6141	186	27	all	all	DET
ejpam-6141	186	28	x	x	NOUN
ejpam-6141	186	29	,	,	PUNCT
ejpam-6141	186	30	y	y	PROPN
ejpam-6141	186	31	∈	∈	PROPN
ejpam-6141	186	32	h	h	PROPN
ejpam-6141	186	33	)	)	PUNCT
ejpam-6141	186	34	.	.	PUNCT
ejpam-6141	187	1	theorem	theorem	NOUN
ejpam-6141	187	2	2	2	NUM
ejpam-6141	187	3	.	.	X
ejpam-6141	187	4	for	for	ADP
ejpam-6141	187	5	every	every	DET
ejpam-6141	187	6	x	x	NOUN
ejpam-6141	187	7	,	,	PUNCT
ejpam-6141	187	8	y	y	PROPN
ejpam-6141	187	9	∈	∈	PROPN
ejpam-6141	187	10	h	h	NOUN
ejpam-6141	187	11	,	,	PUNCT
ejpam-6141	187	12	(	(	PUNCT
ejpam-6141	187	13	1	1	X
ejpam-6141	187	14	)	)	PUNCT
ejpam-6141	187	15	|x	|x	NOUN
ejpam-6141	187	16	◦	◦	NOUN
ejpam-6141	187	17	ck	ck	PROPN
ejpam-6141	187	18	y|	y|	NOUN
ejpam-6141	188	1	=	=	PUNCT
ejpam-6141	188	2	k	k	PROPN
ejpam-6141	189	1	+	+	PROPN
ejpam-6141	189	2	1	1	NUM
ejpam-6141	189	3	;	;	PUNCT
ejpam-6141	189	4	(	(	PUNCT
ejpam-6141	189	5	2	2	X
ejpam-6141	189	6	)	)	PUNCT
ejpam-6141	189	7	|{u|x	|{u|x	ADJ
ejpam-6141	189	8	∈	∈	PROPN
ejpam-6141	189	9	u	u	NOUN
ejpam-6141	189	10	◦	◦	NOUN
ejpam-6141	189	11	ck	ck	NOUN
ejpam-6141	189	12	y}|	y}|	NOUN
ejpam-6141	190	1	=	=	PUNCT
ejpam-6141	190	2	k	k	PROPN
ejpam-6141	191	1	+	+	PROPN
ejpam-6141	191	2	1	1	NUM
ejpam-6141	191	3	;	;	PUNCT
ejpam-6141	191	4	(	(	PUNCT
ejpam-6141	191	5	3	3	X
ejpam-6141	191	6	)	)	PUNCT
ejpam-6141	191	7	|{u|x	|{u|x	NOUN
ejpam-6141	191	8	∈	∈	PROPN
ejpam-6141	191	9	y	y	PROPN
ejpam-6141	191	10	◦	◦	NOUN
ejpam-6141	191	11	ck	ck	NOUN
ejpam-6141	191	12	u}|	u}|	NOUN
ejpam-6141	192	1	=	=	PUNCT
ejpam-6141	192	2	k	k	PROPN
ejpam-6141	192	3	+	+	PROPN
ejpam-6141	192	4	1	1	X
ejpam-6141	192	5	.	.	X
ejpam-6141	192	6	m.	m.	NOUN
ejpam-6141	192	7	a.	a.	PROPN
ejpam-6141	192	8	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	192	9	,	,	PUNCT
ejpam-6141	192	10	s.	s.	PROPN
ejpam-6141	192	11	mirvakili	mirvakili	PROPN
ejpam-6141	192	12	/	/	SYM
ejpam-6141	192	13	eur	eur	PROPN
ejpam-6141	192	14	.	.	PUNCT
ejpam-6141	193	1	j.	j.	PROPN
ejpam-6141	193	2	pure	pure	PROPN
ejpam-6141	193	3	appl	appl	PROPN
ejpam-6141	193	4	.	.	PROPN
ejpam-6141	193	5	math	math	PROPN
ejpam-6141	193	6	,	,	PUNCT
ejpam-6141	193	7	18	18	NUM
ejpam-6141	193	8	(	(	PUNCT
ejpam-6141	193	9	2	2	NUM
ejpam-6141	193	10	)	)	PUNCT
ejpam-6141	193	11	(	(	PUNCT
ejpam-6141	193	12	2025	2025	NUM
ejpam-6141	193	13	)	)	PUNCT
ejpam-6141	193	14	,	,	PUNCT
ejpam-6141	193	15	6141	6141	NUM
ejpam-6141	193	16	8	8	NUM
ejpam-6141	193	17	of	of	ADP
ejpam-6141	193	18	10	10	NUM
ejpam-6141	193	19	proof	proof	NOUN
ejpam-6141	193	20	.	.	PUNCT
ejpam-6141	194	1	it	it	PRON
ejpam-6141	194	2	obtains	obtain	VERB
ejpam-6141	194	3	from	from	ADP
ejpam-6141	194	4	definition	definition	NOUN
ejpam-6141	194	5	◦	◦	NOUN
ejpam-6141	194	6	ck	ck	PROPN
ejpam-6141	194	7	.	.	PUNCT
ejpam-6141	195	1	corollary	corollary	ADJ
ejpam-6141	195	2	1	1	NUM
ejpam-6141	195	3	.	.	PUNCT
ejpam-6141	196	1	for	for	ADP
ejpam-6141	196	2	all	all	PRON
ejpam-6141	196	3	k	k	NOUN
ejpam-6141	196	4	=	=	SYM
ejpam-6141	196	5	1	1	NUM
ejpam-6141	196	6	,	,	PUNCT
ejpam-6141	196	7	2	2	NUM
ejpam-6141	196	8	,	,	PUNCT
ejpam-6141	196	9	.	.	PUNCT
ejpam-6141	196	10	.	.	PUNCT
ejpam-6141	196	11	.	.	PUNCT
ejpam-6141	197	1	,	,	PUNCT
ejpam-6141	197	2	n	n	CCONJ
ejpam-6141	197	3	,	,	PUNCT
ejpam-6141	197	4	the	the	DET
ejpam-6141	197	5	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	197	6	(	(	PUNCT
ejpam-6141	197	7	h	h	NOUN
ejpam-6141	197	8	,	,	PUNCT
ejpam-6141	197	9	◦	◦	NOUN
ejpam-6141	197	10	ck−1	ck−1	NOUN
ejpam-6141	197	11	)	)	PUNCT
ejpam-6141	197	12	are	be	AUX
ejpam-6141	197	13	latin	latin	ADJ
ejpam-6141	197	14	k	k	NOUN
ejpam-6141	197	15	-	-	NOUN
ejpam-6141	197	16	hypersquare	hypersquare	NOUN
ejpam-6141	197	17	.	.	PUNCT
ejpam-6141	198	1	in	in	ADP
ejpam-6141	198	2	the	the	DET
ejpam-6141	198	3	next	next	ADJ
ejpam-6141	198	4	theorem	theorem	NOUN
ejpam-6141	198	5	we	we	PRON
ejpam-6141	198	6	show	show	VERB
ejpam-6141	198	7	that	that	SCONJ
ejpam-6141	198	8	for	for	ADP
ejpam-6141	198	9	all	all	PRON
ejpam-6141	198	10	k	k	NOUN
ejpam-6141	198	11	=	=	PUNCT
ejpam-6141	198	12	|h|	|h|	PROPN
ejpam-6141	198	13	2	2	NUM
ejpam-6141	198	14	,	,	PUNCT
ejpam-6141	198	15	|h|	|h|	PROPN
ejpam-6141	198	16	2	2	NUM
ejpam-6141	198	17	+1	+1	PROPN
ejpam-6141	198	18	,	,	PUNCT
ejpam-6141	198	19	.	.	PUNCT
ejpam-6141	198	20	.	.	PUNCT
ejpam-6141	199	1	.	.	PUNCT
ejpam-6141	200	1	,	,	PUNCT
ejpam-6141	200	2	n	n	CCONJ
ejpam-6141	200	3	,	,	PUNCT
ejpam-6141	200	4	the	the	DET
ejpam-6141	200	5	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	200	6	(	(	PUNCT
ejpam-6141	200	7	h	h	NOUN
ejpam-6141	200	8	,	,	PUNCT
ejpam-6141	200	9	◦	◦	NOUN
ejpam-6141	200	10	ck	ck	NOUN
ejpam-6141	200	11	)	)	PUNCT
ejpam-6141	200	12	are	be	AUX
ejpam-6141	200	13	hypergroups	hypergroup	NOUN
ejpam-6141	200	14	,	,	PUNCT
ejpam-6141	200	15	theorem	theorem	VERB
ejpam-6141	200	16	3	3	NUM
ejpam-6141	200	17	.	.	PUNCT
ejpam-6141	201	1	if	if	SCONJ
ejpam-6141	201	2	k	k	PROPN
ejpam-6141	201	3	≥	≥	AUX
ejpam-6141	201	4	|h|	|h|	PROPN
ejpam-6141	201	5	2	2	NUM
ejpam-6141	201	6	then	then	ADV
ejpam-6141	201	7	◦	◦	VERB
ejpam-6141	201	8	ck	ck	NOUN
ejpam-6141	201	9	is	be	AUX
ejpam-6141	201	10	a	a	DET
ejpam-6141	201	11	total	total	ADJ
ejpam-6141	201	12	associative	associative	ADJ
ejpam-6141	201	13	hyperoperation	hyperoperation	NOUN
ejpam-6141	201	14	.	.	PUNCT
ejpam-6141	202	1	proof	proof	NOUN
ejpam-6141	202	2	.	.	PUNCT
ejpam-6141	203	1	let	let	VERB
ejpam-6141	203	2	h	h	NOUN
ejpam-6141	203	3	=	=	PRON
ejpam-6141	203	4	{	{	PUNCT
ejpam-6141	203	5	a1	a1	PROPN
ejpam-6141	203	6	,	,	PUNCT
ejpam-6141	203	7	a2	a2	PROPN
ejpam-6141	203	8	,	,	PUNCT
ejpam-6141	203	9	.	.	PUNCT
ejpam-6141	203	10	.	.	PUNCT
ejpam-6141	204	1	.	.	PUNCT
ejpam-6141	205	1	,	,	PUNCT
ejpam-6141	205	2	an	an	PRON
ejpam-6141	205	3	}	}	PUNCT
ejpam-6141	205	4	and	and	CCONJ
ejpam-6141	205	5	k	k	PROPN
ejpam-6141	205	6	≥	≥	NOUN
ejpam-6141	205	7	n	n	PRON
ejpam-6141	205	8	2	2	NUM
ejpam-6141	205	9	.	.	PUNCT
ejpam-6141	205	10	suppose	suppose	VERB
ejpam-6141	205	11	that	that	SCONJ
ejpam-6141	205	12	x	x	PROPN
ejpam-6141	205	13	,	,	PUNCT
ejpam-6141	205	14	y	y	PROPN
ejpam-6141	205	15	,	,	PUNCT
ejpam-6141	205	16	z	z	PROPN
ejpam-6141	205	17	∈	∈	PROPN
ejpam-6141	205	18	h.	h.	NOUN
ejpam-6141	205	19	then	then	ADV
ejpam-6141	205	20	by	by	ADP
ejpam-6141	205	21	part	part	NOUN
ejpam-6141	205	22	(	(	PUNCT
ejpam-6141	205	23	1	1	NUM
ejpam-6141	205	24	)	)	PUNCT
ejpam-6141	205	25	of	of	ADP
ejpam-6141	205	26	theorem	theorem	ADJ
ejpam-6141	205	27	2	2	NUM
ejpam-6141	205	28	,	,	PUNCT
ejpam-6141	205	29	|y	|y	ADJ
ejpam-6141	205	30	◦	◦	NOUN
ejpam-6141	205	31	ck	ck	PRON
ejpam-6141	205	32	z|	z|	NOUN
ejpam-6141	205	33	=	=	PUNCT
ejpam-6141	205	34	k	k	PROPN
ejpam-6141	206	1	+	+	CCONJ
ejpam-6141	206	2	1	1	NUM
ejpam-6141	206	3	>	>	SYM
ejpam-6141	206	4	n	n	NUM
ejpam-6141	206	5	2	2	NUM
ejpam-6141	206	6	.	.	PUNCT
ejpam-6141	207	1	so	so	ADV
ejpam-6141	207	2	we	we	PRON
ejpam-6141	207	3	have	have	VERB
ejpam-6141	207	4	y	y	PROPN
ejpam-6141	207	5	◦	◦	NOUN
ejpam-6141	207	6	ck	ck	PROPN
ejpam-6141	207	7	z	z	NOUN
ejpam-6141	207	8	=	=	SYM
ejpam-6141	207	9	{	{	PUNCT
ejpam-6141	207	10	ai0	ai0	PROPN
ejpam-6141	207	11	,	,	PUNCT
ejpam-6141	207	12	ai2	ai2	INTJ
ejpam-6141	207	13	,	,	PUNCT
ejpam-6141	207	14	.	.	PUNCT
ejpam-6141	207	15	.	.	PUNCT
ejpam-6141	208	1	.	.	PUNCT
ejpam-6141	209	1	,	,	PUNCT
ejpam-6141	209	2	aik	aik	NOUN
ejpam-6141	209	3	}	}	PUNCT
ejpam-6141	209	4	.	.	PUNCT
ejpam-6141	210	1	now	now	ADV
ejpam-6141	210	2	if	if	SCONJ
ejpam-6141	210	3	h	h	PROPN
ejpam-6141	210	4	∈	∈	PROPN
ejpam-6141	210	5	h	h	NOUN
ejpam-6141	210	6	then	then	ADV
ejpam-6141	210	7	by	by	ADP
ejpam-6141	210	8	part	part	NOUN
ejpam-6141	210	9	(	(	PUNCT
ejpam-6141	210	10	3	3	NUM
ejpam-6141	210	11	)	)	PUNCT
ejpam-6141	210	12	of	of	ADP
ejpam-6141	210	13	theorem	theorem	NOUN
ejpam-6141	210	14	2	2	NUM
ejpam-6141	210	15	,	,	PUNCT
ejpam-6141	210	16	there	there	PRON
ejpam-6141	210	17	exists	exist	VERB
ejpam-6141	210	18	j	j	PROPN
ejpam-6141	210	19	=	=	SYM
ejpam-6141	210	20	0	0	PROPN
ejpam-6141	210	21	,	,	PUNCT
ejpam-6141	210	22	2	2	NUM
ejpam-6141	210	23	,	,	PUNCT
ejpam-6141	210	24	.	.	PUNCT
ejpam-6141	210	25	.	.	PUNCT
ejpam-6141	211	1	.	.	PUNCT
ejpam-6141	212	1	,	,	PUNCT
ejpam-6141	213	1	k	k	X
ejpam-6141	213	2	such	such	ADJ
ejpam-6141	213	3	that	that	SCONJ
ejpam-6141	213	4	u	u	PROPN
ejpam-6141	213	5	∈	∈	PROPN
ejpam-6141	213	6	x	x	INTJ
ejpam-6141	213	7	◦	◦	NOUN
ejpam-6141	213	8	ck	ck	ADJ
ejpam-6141	213	9	aij	aij	PROPN
ejpam-6141	213	10	.	.	PUNCT
ejpam-6141	214	1	hence	hence	ADV
ejpam-6141	214	2	x	x	PUNCT
ejpam-6141	214	3	◦	◦	NOUN
ejpam-6141	214	4	ck	ck	PROPN
ejpam-6141	214	5	(	(	PUNCT
ejpam-6141	214	6	y	y	PROPN
ejpam-6141	214	7	◦	◦	NOUN
ejpam-6141	214	8	ck	ck	PROPN
ejpam-6141	214	9	z	z	NOUN
ejpam-6141	214	10	)	)	PUNCT
ejpam-6141	215	1	=	=	SYM
ejpam-6141	215	2	h.	h.	PROPN
ejpam-6141	215	3	in	in	ADP
ejpam-6141	215	4	the	the	DET
ejpam-6141	215	5	similar	similar	ADJ
ejpam-6141	215	6	way	way	NOUN
ejpam-6141	215	7	we	we	PRON
ejpam-6141	215	8	obtain	obtain	VERB
ejpam-6141	215	9	(	(	PUNCT
ejpam-6141	215	10	x	x	PUNCT
ejpam-6141	215	11	◦	◦	VERB
ejpam-6141	215	12	ck	ck	PROPN
ejpam-6141	215	13	y	y	NOUN
ejpam-6141	215	14	)	)	PUNCT
ejpam-6141	215	15	◦	◦	NOUN
ejpam-6141	215	16	ck	ck	PROPN
ejpam-6141	215	17	z	z	NOUN
ejpam-6141	215	18	=	=	SYM
ejpam-6141	215	19	h.	h.	PROPN
ejpam-6141	215	20	therefore	therefore	ADV
ejpam-6141	215	21	◦	◦	VERB
ejpam-6141	215	22	ck	ck	PROPN
ejpam-6141	215	23	is	be	AUX
ejpam-6141	215	24	a	a	DET
ejpam-6141	215	25	total	total	ADJ
ejpam-6141	215	26	associative	associative	ADJ
ejpam-6141	215	27	hyperoperation	hyperoperation	NOUN
ejpam-6141	215	28	.	.	PUNCT
ejpam-6141	216	1	theorem	theorem	ADJ
ejpam-6141	216	2	4	4	NUM
ejpam-6141	216	3	.	.	PUNCT
ejpam-6141	217	1	if	if	SCONJ
ejpam-6141	217	2	k	k	PROPN
ejpam-6141	217	3	≥	≥	AUX
ejpam-6141	217	4	|h|	|h|	PROPN
ejpam-6141	217	5	2	2	NUM
ejpam-6141	217	6	then	then	ADV
ejpam-6141	217	7	(	(	PUNCT
ejpam-6141	217	8	h	h	NOUN
ejpam-6141	217	9	,	,	PUNCT
ejpam-6141	217	10	◦	◦	NOUN
ejpam-6141	217	11	ck	ck	NOUN
ejpam-6141	217	12	)	)	PUNCT
ejpam-6141	217	13	is	be	AUX
ejpam-6141	217	14	a	a	DET
ejpam-6141	217	15	hypergroup	hypergroup	NOUN
ejpam-6141	217	16	.	.	PUNCT
ejpam-6141	218	1	proof	proof	NOUN
ejpam-6141	218	2	.	.	PUNCT
ejpam-6141	219	1	by	by	ADP
ejpam-6141	219	2	theorem	theorem	NOUN
ejpam-6141	219	3	3	3	NUM
ejpam-6141	219	4	(	(	PUNCT
ejpam-6141	219	5	h	h	NOUN
ejpam-6141	219	6	,	,	PUNCT
ejpam-6141	219	7	◦	◦	NOUN
ejpam-6141	219	8	ck	ck	NOUN
ejpam-6141	219	9	)	)	PUNCT
ejpam-6141	219	10	is	be	AUX
ejpam-6141	219	11	a	a	DET
ejpam-6141	219	12	semihypergroup	semihypergroup	NOUN
ejpam-6141	219	13	and	and	CCONJ
ejpam-6141	219	14	by	by	ADP
ejpam-6141	219	15	lemma	lemma	PROPN
ejpam-6141	219	16	1	1	NUM
ejpam-6141	219	17	(	(	PUNCT
ejpam-6141	219	18	h	h	NOUN
ejpam-6141	219	19	,	,	PUNCT
ejpam-6141	219	20	◦	◦	NOUN
ejpam-6141	219	21	ck	ck	NOUN
ejpam-6141	219	22	)	)	PUNCT
ejpam-6141	219	23	is	be	AUX
ejpam-6141	219	24	a	a	DET
ejpam-6141	219	25	quasihypergroup	quasihypergroup	NOUN
ejpam-6141	219	26	.	.	PUNCT
ejpam-6141	220	1	therefore	therefore	ADV
ejpam-6141	220	2	(	(	PUNCT
ejpam-6141	220	3	h	h	NOUN
ejpam-6141	220	4	,	,	PUNCT
ejpam-6141	220	5	◦	◦	NOUN
ejpam-6141	220	6	ck	ck	NOUN
ejpam-6141	220	7	)	)	PUNCT
ejpam-6141	220	8	is	be	AUX
ejpam-6141	220	9	a	a	DET
ejpam-6141	220	10	hypergroup	hypergroup	ADJ
ejpam-6141	220	11	example	example	NOUN
ejpam-6141	220	12	8	8	NUM
ejpam-6141	220	13	.	.	PUNCT
ejpam-6141	221	1	in	in	ADP
ejpam-6141	221	2	theorem	theorem	NOUN
ejpam-6141	221	3	4	4	NUM
ejpam-6141	221	4	,	,	PUNCT
ejpam-6141	221	5	the	the	DET
ejpam-6141	221	6	given	give	VERB
ejpam-6141	221	7	boundary	boundary	NOUN
ejpam-6141	221	8	for	for	ADP
ejpam-6141	221	9	k	k	PROPN
ejpam-6141	221	10	is	be	AUX
ejpam-6141	221	11	the	the	DET
ejpam-6141	221	12	best	good	ADJ
ejpam-6141	221	13	boundary	boundary	NOUN
ejpam-6141	221	14	.	.	PUNCT
ejpam-6141	222	1	for	for	ADP
ejpam-6141	222	2	example	example	NOUN
ejpam-6141	222	3	if	if	SCONJ
ejpam-6141	222	4	(	(	PUNCT
ejpam-6141	222	5	h	h	NOUN
ejpam-6141	222	6	,	,	PUNCT
ejpam-6141	222	7	⋆	⋆	ADJ
ejpam-6141	222	8	)	)	PUNCT
ejpam-6141	222	9	is	be	AUX
ejpam-6141	222	10	the	the	DET
ejpam-6141	222	11	quasigroup	quasigroup	NOUN
ejpam-6141	222	12	in	in	ADP
ejpam-6141	222	13	example	example	NOUN
ejpam-6141	222	14	7	7	NUM
ejpam-6141	222	15	then	then	ADV
ejpam-6141	222	16	(	(	PUNCT
ejpam-6141	222	17	h	h	NOUN
ejpam-6141	222	18	,	,	PUNCT
ejpam-6141	222	19	◦	◦	NOUN
ejpam-6141	222	20	c1	c1	NOUN
ejpam-6141	222	21	)	)	PUNCT
ejpam-6141	222	22	is	be	AUX
ejpam-6141	222	23	not	not	PART
ejpam-6141	222	24	hypergroup	hypergroup	NOUN
ejpam-6141	222	25	.	.	PUNCT
ejpam-6141	223	1	theorem	theorem	NOUN
ejpam-6141	223	2	5	5	NUM
ejpam-6141	223	3	.	.	PUNCT
ejpam-6141	224	1	let	let	AUX
ejpam-6141	224	2	(	(	PUNCT
ejpam-6141	224	3	h	h	NOUN
ejpam-6141	224	4	,	,	PUNCT
ejpam-6141	224	5	⋆	⋆	ADJ
ejpam-6141	224	6	)	)	PUNCT
ejpam-6141	224	7	be	be	AUX
ejpam-6141	224	8	a	a	DET
ejpam-6141	224	9	cyclic	cyclic	ADJ
ejpam-6141	224	10	group	group	NOUN
ejpam-6141	224	11	of	of	ADP
ejpam-6141	224	12	order	order	NOUN
ejpam-6141	224	13	n	n	CCONJ
ejpam-6141	224	14	,	,	PUNCT
ejpam-6141	224	15	i.	i.	PROPN
ejpam-6141	224	16	e.	e.	PROPN
ejpam-6141	224	17	,	,	PUNCT
ejpam-6141	224	18	(	(	PUNCT
ejpam-6141	224	19	h	h	NOUN
ejpam-6141	224	20	,	,	PUNCT
ejpam-6141	224	21	⋆	⋆	NOUN
ejpam-6141	224	22	)	)	PUNCT
ejpam-6141	224	23	∼=	∼=	PROPN
ejpam-6141	224	24	(	(	PUNCT
ejpam-6141	224	25	zn,+	zn,+	NUM
ejpam-6141	224	26	)	)	PUNCT
ejpam-6141	224	27	.	.	PUNCT
ejpam-6141	225	1	then	then	ADV
ejpam-6141	225	2	(	(	PUNCT
ejpam-6141	225	3	h	h	NOUN
ejpam-6141	225	4	,	,	PUNCT
ejpam-6141	225	5	◦	◦	NOUN
ejpam-6141	225	6	ck	ck	NOUN
ejpam-6141	225	7	)	)	PUNCT
ejpam-6141	225	8	is	be	AUX
ejpam-6141	225	9	a	a	DET
ejpam-6141	225	10	commutative	commutative	ADJ
ejpam-6141	225	11	hypergroup	hypergroup	NOUN
ejpam-6141	225	12	,	,	PUNCT
ejpam-6141	225	13	for	for	ADP
ejpam-6141	225	14	all	all	PRON
ejpam-6141	225	15	k	k	NOUN
ejpam-6141	225	16	=	=	SYM
ejpam-6141	225	17	0	0	NUM
ejpam-6141	225	18	,	,	PUNCT
ejpam-6141	225	19	1	1	NUM
ejpam-6141	225	20	,	,	PUNCT
ejpam-6141	225	21	.	.	PUNCT
ejpam-6141	225	22	.	.	PUNCT
ejpam-6141	226	1	.	.	PUNCT
ejpam-6141	227	1	,	,	PUNCT
ejpam-6141	227	2	n−	n−	NOUN
ejpam-6141	227	3	1	1	NUM
ejpam-6141	227	4	.	.	PUNCT
ejpam-6141	227	5	example	example	NOUN
ejpam-6141	228	1	9	9	NUM
ejpam-6141	228	2	.	.	PUNCT
ejpam-6141	229	1	let	let	VERB
ejpam-6141	229	2	(	(	PUNCT
ejpam-6141	229	3	h	h	NOUN
ejpam-6141	229	4	,	,	PUNCT
ejpam-6141	229	5	⋆	⋆	NOUN
ejpam-6141	229	6	)	)	PUNCT
ejpam-6141	229	7	∼=	∼=	PROPN
ejpam-6141	229	8	(	(	PUNCT
ejpam-6141	229	9	z2	z2	PROPN
ejpam-6141	229	10	×	×	PROPN
ejpam-6141	229	11	z2,+	z2,+	PROPN
ejpam-6141	229	12	)	)	PUNCT
ejpam-6141	229	13	.	.	PUNCT
ejpam-6141	230	1	⋆	⋆	X
ejpam-6141	230	2	e	e	PROPN
ejpam-6141	230	3	a	a	DET
ejpam-6141	230	4	b	b	NOUN
ejpam-6141	230	5	c	c	NOUN
ejpam-6141	230	6	e	e	X
ejpam-6141	230	7	e	e	X
ejpam-6141	230	8	a	a	PRON
ejpam-6141	230	9	b	b	X
ejpam-6141	230	10	c	c	NOUN
ejpam-6141	230	11	a	a	PRON
ejpam-6141	230	12	a	a	DET
ejpam-6141	230	13	e	e	NOUN
ejpam-6141	230	14	c	c	NOUN
ejpam-6141	230	15	b	b	PROPN
ejpam-6141	230	16	b	b	PROPN
ejpam-6141	230	17	b	b	PROPN
ejpam-6141	230	18	c	c	NOUN
ejpam-6141	230	19	e	e	X
ejpam-6141	230	20	a	a	X
ejpam-6141	230	21	c	c	NOUN
ejpam-6141	230	22	c	c	PROPN
ejpam-6141	230	23	b	b	PROPN
ejpam-6141	230	24	a	a	DET
ejpam-6141	230	25	e	e	NOUN
ejpam-6141	230	26	then	then	ADV
ejpam-6141	230	27	we	we	PRON
ejpam-6141	230	28	obtain	obtain	VERB
ejpam-6141	230	29	⋆0	⋆0	NUM
ejpam-6141	230	30	e	e	X
ejpam-6141	230	31	a	a	DET
ejpam-6141	230	32	b	b	NOUN
ejpam-6141	230	33	c	c	NOUN
ejpam-6141	230	34	e	e	X
ejpam-6141	230	35	e	e	X
ejpam-6141	230	36	a	a	PRON
ejpam-6141	230	37	b	b	X
ejpam-6141	230	38	c	c	NOUN
ejpam-6141	230	39	a	a	DET
ejpam-6141	230	40	a	a	DET
ejpam-6141	230	41	e	e	NOUN
ejpam-6141	230	42	c	c	NOUN
ejpam-6141	230	43	b	b	PROPN
ejpam-6141	230	44	b	b	PROPN
ejpam-6141	230	45	b	b	PROPN
ejpam-6141	230	46	c	c	NOUN
ejpam-6141	230	47	e	e	X
ejpam-6141	230	48	a	a	X
ejpam-6141	230	49	c	c	NOUN
ejpam-6141	230	50	c	c	PROPN
ejpam-6141	230	51	b	b	PROPN
ejpam-6141	230	52	a	a	DET
ejpam-6141	230	53	e	e	X
ejpam-6141	230	54	⋆1	⋆1	PROPN
ejpam-6141	230	55	e	e	PROPN
ejpam-6141	230	56	a	a	DET
ejpam-6141	230	57	b	b	NOUN
ejpam-6141	230	58	c	c	NOUN
ejpam-6141	230	59	e	e	X
ejpam-6141	230	60	c	c	X
ejpam-6141	230	61	e	e	PROPN
ejpam-6141	230	62	a	a	PRON
ejpam-6141	230	63	b	b	NOUN
ejpam-6141	230	64	a	a	DET
ejpam-6141	230	65	b	b	NOUN
ejpam-6141	230	66	a	a	DET
ejpam-6141	230	67	e	e	NOUN
ejpam-6141	230	68	c	c	NOUN
ejpam-6141	230	69	b	b	PROPN
ejpam-6141	230	70	a	a	DET
ejpam-6141	230	71	b	b	NOUN
ejpam-6141	230	72	c	c	NOUN
ejpam-6141	230	73	e	e	X
ejpam-6141	230	74	c	c	NOUN
ejpam-6141	230	75	e	e	PROPN
ejpam-6141	230	76	c	c	PROPN
ejpam-6141	230	77	b	b	PROPN
ejpam-6141	230	78	a	a	DET
ejpam-6141	230	79	⋆2	⋆2	X
ejpam-6141	230	80	e	e	PROPN
ejpam-6141	230	81	a	a	DET
ejpam-6141	230	82	b	b	NOUN
ejpam-6141	230	83	c	c	NOUN
ejpam-6141	230	84	e	e	PROPN
ejpam-6141	230	85	b	b	PROPN
ejpam-6141	230	86	c	c	PROPN
ejpam-6141	230	87	e	e	PROPN
ejpam-6141	230	88	a	a	PRON
ejpam-6141	230	89	a	a	DET
ejpam-6141	230	90	c	c	NOUN
ejpam-6141	230	91	b	b	PROPN
ejpam-6141	230	92	a	a	DET
ejpam-6141	230	93	e	e	X
ejpam-6141	230	94	b	b	PROPN
ejpam-6141	230	95	e	e	PROPN
ejpam-6141	230	96	a	a	PRON
ejpam-6141	230	97	b	b	NOUN
ejpam-6141	230	98	c	c	NOUN
ejpam-6141	230	99	c	c	NOUN
ejpam-6141	230	100	a	a	DET
ejpam-6141	230	101	e	e	NOUN
ejpam-6141	230	102	c	c	NOUN
ejpam-6141	230	103	b	b	X
ejpam-6141	230	104	⋆3	⋆3	NUM
ejpam-6141	230	105	e	e	NOUN
ejpam-6141	230	106	a	a	DET
ejpam-6141	230	107	b	b	NOUN
ejpam-6141	230	108	c	c	NOUN
ejpam-6141	230	109	e	e	PROPN
ejpam-6141	230	110	a	a	DET
ejpam-6141	230	111	b	b	NOUN
ejpam-6141	230	112	c	c	NOUN
ejpam-6141	230	113	e	e	X
ejpam-6141	230	114	a	a	X
ejpam-6141	230	115	e	e	NOUN
ejpam-6141	230	116	c	c	NOUN
ejpam-6141	230	117	b	b	PROPN
ejpam-6141	230	118	a	a	DET
ejpam-6141	230	119	b	b	NOUN
ejpam-6141	230	120	c	c	NOUN
ejpam-6141	230	121	e	e	PROPN
ejpam-6141	230	122	a	a	PRON
ejpam-6141	230	123	b	b	PROPN
ejpam-6141	230	124	c	c	PROPN
ejpam-6141	230	125	b	b	PROPN
ejpam-6141	230	126	a	a	DET
ejpam-6141	230	127	e	e	NOUN
ejpam-6141	230	128	c	c	NOUN
ejpam-6141	230	129	and	and	CCONJ
ejpam-6141	230	130	therefore	therefore	ADV
ejpam-6141	230	131	◦	◦	NOUN
ejpam-6141	230	132	c0	c0	PROPN
ejpam-6141	230	133	e	e	PROPN
ejpam-6141	230	134	a	a	DET
ejpam-6141	230	135	b	b	X
ejpam-6141	230	136	c	c	NOUN
ejpam-6141	230	137	e	e	X
ejpam-6141	230	138	e	e	X
ejpam-6141	230	139	a	a	PRON
ejpam-6141	230	140	b	b	X
ejpam-6141	230	141	c	c	NOUN
ejpam-6141	230	142	a	a	DET
ejpam-6141	230	143	a	a	DET
ejpam-6141	230	144	e	e	NOUN
ejpam-6141	230	145	c	c	NOUN
ejpam-6141	230	146	b	b	PROPN
ejpam-6141	230	147	b	b	PROPN
ejpam-6141	230	148	b	b	PROPN
ejpam-6141	230	149	c	c	NOUN
ejpam-6141	230	150	e	e	X
ejpam-6141	230	151	a	a	X
ejpam-6141	230	152	c	c	NOUN
ejpam-6141	230	153	c	c	PROPN
ejpam-6141	230	154	b	b	PROPN
ejpam-6141	230	155	a	a	DET
ejpam-6141	230	156	e	e	NOUN
ejpam-6141	230	157	◦	◦	PROPN
ejpam-6141	230	158	c1	c1	PROPN
ejpam-6141	230	159	e	e	NOUN
ejpam-6141	230	160	a	a	DET
ejpam-6141	230	161	b	b	NOUN
ejpam-6141	230	162	c	c	NOUN
ejpam-6141	230	163	e	e	X
ejpam-6141	230	164	e	e	PROPN
ejpam-6141	230	165	,	,	PUNCT
ejpam-6141	230	166	c	c	PROPN
ejpam-6141	230	167	e	e	PROPN
ejpam-6141	230	168	,	,	PUNCT
ejpam-6141	230	169	a	a	DET
ejpam-6141	230	170	a	a	NOUN
ejpam-6141	230	171	,	,	PUNCT
ejpam-6141	230	172	b	b	PROPN
ejpam-6141	230	173	b	b	PROPN
ejpam-6141	230	174	,	,	PUNCT
ejpam-6141	230	175	c	c	PROPN
ejpam-6141	230	176	a	a	DET
ejpam-6141	230	177	a	a	PROPN
ejpam-6141	230	178	,	,	PUNCT
ejpam-6141	230	179	b	b	PROPN
ejpam-6141	230	180	e	e	NOUN
ejpam-6141	230	181	,	,	PUNCT
ejpam-6141	230	182	a	a	DET
ejpam-6141	230	183	e	e	NOUN
ejpam-6141	230	184	,	,	PUNCT
ejpam-6141	230	185	c	c	PROPN
ejpam-6141	230	186	b	b	PROPN
ejpam-6141	230	187	,	,	PUNCT
ejpam-6141	230	188	c	c	PROPN
ejpam-6141	230	189	b	b	PROPN
ejpam-6141	230	190	a	a	PRON
ejpam-6141	230	191	,	,	PUNCT
ejpam-6141	230	192	b	b	PROPN
ejpam-6141	230	193	b	b	PROPN
ejpam-6141	230	194	,	,	PUNCT
ejpam-6141	230	195	c	c	PROPN
ejpam-6141	230	196	e	e	PROPN
ejpam-6141	230	197	,	,	PUNCT
ejpam-6141	230	198	c	c	PROPN
ejpam-6141	230	199	e	e	PROPN
ejpam-6141	230	200	,	,	PUNCT
ejpam-6141	230	201	a	a	DET
ejpam-6141	230	202	c	c	NOUN
ejpam-6141	230	203	e	e	NOUN
ejpam-6141	230	204	,	,	PUNCT
ejpam-6141	230	205	c	c	PROPN
ejpam-6141	230	206	c	c	X
ejpam-6141	230	207	,	,	PUNCT
ejpam-6141	230	208	b	b	PROPN
ejpam-6141	230	209	a	a	NOUN
ejpam-6141	230	210	,	,	PUNCT
ejpam-6141	230	211	b	b	PROPN
ejpam-6141	230	212	e	e	NOUN
ejpam-6141	230	213	,	,	PUNCT
ejpam-6141	230	214	a	a	DET
ejpam-6141	230	215	◦	◦	NOUN
ejpam-6141	230	216	c2	c2	PROPN
ejpam-6141	230	217	e	e	PROPN
ejpam-6141	230	218	a	a	DET
ejpam-6141	230	219	b	b	NOUN
ejpam-6141	230	220	c	c	NOUN
ejpam-6141	230	221	e	e	X
ejpam-6141	230	222	e	e	PROPN
ejpam-6141	230	223	,	,	PUNCT
ejpam-6141	230	224	b	b	NOUN
ejpam-6141	230	225	,	,	PUNCT
ejpam-6141	230	226	c	c	PROPN
ejpam-6141	230	227	e	e	PROPN
ejpam-6141	230	228	,	,	PUNCT
ejpam-6141	230	229	a	a	PRON
ejpam-6141	230	230	,	,	PUNCT
ejpam-6141	230	231	c	c	PROPN
ejpam-6141	230	232	e	e	PROPN
ejpam-6141	230	233	,	,	PUNCT
ejpam-6141	230	234	a	a	PRON
ejpam-6141	230	235	,	,	PUNCT
ejpam-6141	230	236	b	b	NOUN
ejpam-6141	230	237	a	a	DET
ejpam-6141	230	238	,	,	PUNCT
ejpam-6141	230	239	b	b	NOUN
ejpam-6141	230	240	,	,	PUNCT
ejpam-6141	230	241	c	c	PROPN
ejpam-6141	230	242	a	a	DET
ejpam-6141	230	243	e	e	NOUN
ejpam-6141	230	244	,	,	PUNCT
ejpam-6141	230	245	a	a	PRON
ejpam-6141	230	246	,	,	PUNCT
ejpam-6141	230	247	b	b	PROPN
ejpam-6141	230	248	e	e	NOUN
ejpam-6141	230	249	,	,	PUNCT
ejpam-6141	230	250	a	a	PRON
ejpam-6141	230	251	,	,	PUNCT
ejpam-6141	230	252	c	c	PROPN
ejpam-6141	230	253	e	e	PROPN
ejpam-6141	230	254	,	,	PUNCT
ejpam-6141	230	255	b	b	PROPN
ejpam-6141	230	256	,	,	PUNCT
ejpam-6141	230	257	c	c	PROPN
ejpam-6141	230	258	a	a	DET
ejpam-6141	230	259	,	,	PUNCT
ejpam-6141	230	260	b	b	NOUN
ejpam-6141	230	261	,	,	PUNCT
ejpam-6141	230	262	c	c	PROPN
ejpam-6141	230	263	b	b	PROPN
ejpam-6141	230	264	e	e	NOUN
ejpam-6141	230	265	,	,	PUNCT
ejpam-6141	230	266	a	a	PRON
ejpam-6141	230	267	,	,	PUNCT
ejpam-6141	230	268	b	b	NOUN
ejpam-6141	230	269	a	a	PRON
ejpam-6141	230	270	,	,	PUNCT
ejpam-6141	230	271	b	b	NOUN
ejpam-6141	230	272	,	,	PUNCT
ejpam-6141	230	273	c	c	PROPN
ejpam-6141	230	274	e	e	PROPN
ejpam-6141	230	275	,	,	PUNCT
ejpam-6141	230	276	b	b	PROPN
ejpam-6141	230	277	,	,	PUNCT
ejpam-6141	230	278	c	c	PROPN
ejpam-6141	230	279	e	e	PROPN
ejpam-6141	230	280	,	,	PUNCT
ejpam-6141	230	281	a	a	PRON
ejpam-6141	230	282	,	,	PUNCT
ejpam-6141	230	283	c	c	NOUN
ejpam-6141	230	284	c	c	PROPN
ejpam-6141	230	285	e	e	NOUN
ejpam-6141	230	286	,	,	PUNCT
ejpam-6141	230	287	a	a	PRON
ejpam-6141	230	288	,	,	PUNCT
ejpam-6141	230	289	c	c	PROPN
ejpam-6141	230	290	e	e	PROPN
ejpam-6141	230	291	,	,	PUNCT
ejpam-6141	230	292	b	b	PROPN
ejpam-6141	230	293	,	,	PUNCT
ejpam-6141	230	294	c	c	PROPN
ejpam-6141	230	295	a	a	PRON
ejpam-6141	230	296	,	,	PUNCT
ejpam-6141	230	297	b	b	NOUN
ejpam-6141	230	298	,	,	PUNCT
ejpam-6141	230	299	c	c	PROPN
ejpam-6141	230	300	e	e	PROPN
ejpam-6141	230	301	,	,	PUNCT
ejpam-6141	230	302	a	a	PRON
ejpam-6141	230	303	,	,	PUNCT
ejpam-6141	230	304	b	b	PROPN
ejpam-6141	230	305	m.	m.	NOUN
ejpam-6141	230	306	a.	a.	PROPN
ejpam-6141	230	307	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	230	308	,	,	PUNCT
ejpam-6141	230	309	s.	s.	PROPN
ejpam-6141	230	310	mirvakili	mirvakili	PROPN
ejpam-6141	230	311	/	/	SYM
ejpam-6141	230	312	eur	eur	PROPN
ejpam-6141	230	313	.	.	PUNCT
ejpam-6141	231	1	j.	j.	PROPN
ejpam-6141	231	2	pure	pure	PROPN
ejpam-6141	231	3	appl	appl	PROPN
ejpam-6141	231	4	.	.	PROPN
ejpam-6141	231	5	math	math	PROPN
ejpam-6141	231	6	,	,	PUNCT
ejpam-6141	231	7	18	18	NUM
ejpam-6141	231	8	(	(	PUNCT
ejpam-6141	231	9	2	2	NUM
ejpam-6141	231	10	)	)	PUNCT
ejpam-6141	231	11	(	(	PUNCT
ejpam-6141	231	12	2025	2025	NUM
ejpam-6141	231	13	)	)	PUNCT
ejpam-6141	231	14	,	,	PUNCT
ejpam-6141	231	15	6141	6141	NUM
ejpam-6141	231	16	9	9	NUM
ejpam-6141	231	17	of	of	ADP
ejpam-6141	231	18	10	10	NUM
ejpam-6141	231	19	we	we	PRON
ejpam-6141	231	20	have	have	VERB
ejpam-6141	231	21	(	(	PUNCT
ejpam-6141	231	22	h	h	NOUN
ejpam-6141	231	23	,	,	PUNCT
ejpam-6141	231	24	⋆	⋆	ADJ
ejpam-6141	231	25	)	)	PUNCT
ejpam-6141	231	26	is	be	AUX
ejpam-6141	231	27	commutative	commutative	ADJ
ejpam-6141	231	28	but	but	CCONJ
ejpam-6141	231	29	(	(	PUNCT
ejpam-6141	231	30	h	h	NOUN
ejpam-6141	231	31	,	,	PUNCT
ejpam-6141	231	32	◦	◦	NOUN
ejpam-6141	231	33	c1	c1	NOUN
ejpam-6141	231	34	)	)	PUNCT
ejpam-6141	232	1	and	and	CCONJ
ejpam-6141	232	2	(	(	PUNCT
ejpam-6141	232	3	h	h	NOUN
ejpam-6141	232	4	,	,	PUNCT
ejpam-6141	232	5	◦	◦	NOUN
ejpam-6141	232	6	c2	c2	PROPN
ejpam-6141	232	7	)	)	PUNCT
ejpam-6141	232	8	are	be	AUX
ejpam-6141	232	9	weak	weak	ADJ
ejpam-6141	232	10	commutative(are	commutative(are	NOUN
ejpam-6141	232	11	not	not	PART
ejpam-6141	232	12	commutative	commutative	ADJ
ejpam-6141	232	13	)	)	PUNCT
ejpam-6141	232	14	theorem	theorem	VERB
ejpam-6141	232	15	6	6	NUM
ejpam-6141	232	16	.	.	PUNCT
ejpam-6141	233	1	let	let	AUX
ejpam-6141	233	2	(	(	PUNCT
ejpam-6141	233	3	h	h	NOUN
ejpam-6141	233	4	,	,	PUNCT
ejpam-6141	233	5	⋆	⋆	ADJ
ejpam-6141	233	6	)	)	PUNCT
ejpam-6141	233	7	be	be	AUX
ejpam-6141	233	8	a	a	DET
ejpam-6141	233	9	group	group	NOUN
ejpam-6141	233	10	of	of	ADP
ejpam-6141	233	11	order	order	NOUN
ejpam-6141	233	12	n.	n.	NOUN
ejpam-6141	234	1	then	then	ADV
ejpam-6141	234	2	(	(	PUNCT
ejpam-6141	234	3	h	h	NOUN
ejpam-6141	234	4	,	,	PUNCT
ejpam-6141	234	5	◦	◦	NOUN
ejpam-6141	234	6	ck	ck	NOUN
ejpam-6141	234	7	)	)	PUNCT
ejpam-6141	234	8	is	be	AUX
ejpam-6141	234	9	an	an	DET
ejpam-6141	234	10	hv	hv	NOUN
ejpam-6141	234	11	-	-	PUNCT
ejpam-6141	234	12	group	group	NOUN
ejpam-6141	234	13	,	,	PUNCT
ejpam-6141	234	14	for	for	ADP
ejpam-6141	234	15	all	all	PRON
ejpam-6141	234	16	k	k	NOUN
ejpam-6141	234	17	=	=	SYM
ejpam-6141	234	18	0	0	NUM
ejpam-6141	234	19	,	,	PUNCT
ejpam-6141	234	20	1	1	NUM
ejpam-6141	234	21	,	,	PUNCT
ejpam-6141	234	22	.	.	PUNCT
ejpam-6141	234	23	.	.	PUNCT
ejpam-6141	235	1	.	.	PUNCT
ejpam-6141	236	1	,	,	PUNCT
ejpam-6141	236	2	n−	n−	NOUN
ejpam-6141	236	3	1	1	NUM
ejpam-6141	236	4	.	.	PUNCT
ejpam-6141	237	1	proof	proof	NOUN
ejpam-6141	237	2	.	.	PUNCT
ejpam-6141	238	1	for	for	ADP
ejpam-6141	238	2	every	every	DET
ejpam-6141	238	3	x	x	PROPN
ejpam-6141	238	4	,	,	PUNCT
ejpam-6141	238	5	y	y	PROPN
ejpam-6141	238	6	,	,	PUNCT
ejpam-6141	238	7	z	z	PROPN
ejpam-6141	238	8	∈	∈	PROPN
ejpam-6141	238	9	x	x	X
ejpam-6141	238	10	,	,	PUNCT
ejpam-6141	238	11	x	x	X
ejpam-6141	238	12	⋆	⋆	X
ejpam-6141	238	13	(	(	PUNCT
ejpam-6141	238	14	y	y	PROPN
ejpam-6141	238	15	⋆	⋆	PROPN
ejpam-6141	238	16	z	z	PROPN
ejpam-6141	238	17	)	)	PUNCT
ejpam-6141	238	18	=	=	SYM
ejpam-6141	239	1	(	(	PUNCT
ejpam-6141	239	2	x	x	PUNCT
ejpam-6141	239	3	⋆	⋆	NOUN
ejpam-6141	239	4	y	y	NOUN
ejpam-6141	239	5	)	)	PUNCT
ejpam-6141	239	6	⋆	⋆	VERB
ejpam-6141	239	7	z	z	NOUN
ejpam-6141	239	8	,	,	PUNCT
ejpam-6141	239	9	x	x	PUNCT
ejpam-6141	239	10	⋆	⋆	X
ejpam-6141	239	11	(	(	PUNCT
ejpam-6141	239	12	y	y	PROPN
ejpam-6141	239	13	⋆	⋆	PROPN
ejpam-6141	239	14	z	z	PROPN
ejpam-6141	239	15	)	)	PUNCT
ejpam-6141	239	16	∈	∈	PROPN
ejpam-6141	239	17	x	x	PUNCT
ejpam-6141	239	18	◦	◦	NOUN
ejpam-6141	239	19	ck	ck	PROPN
ejpam-6141	239	20	(	(	PUNCT
ejpam-6141	239	21	y	y	PROPN
ejpam-6141	239	22	◦	◦	NOUN
ejpam-6141	239	23	ck	ck	PROPN
ejpam-6141	239	24	z	z	NOUN
ejpam-6141	239	25	)	)	PUNCT
ejpam-6141	239	26	and	and	CCONJ
ejpam-6141	239	27	(	(	PUNCT
ejpam-6141	239	28	x	x	X
ejpam-6141	239	29	⋆	⋆	PROPN
ejpam-6141	239	30	y	y	NOUN
ejpam-6141	239	31	)	)	PUNCT
ejpam-6141	239	32	⋆	⋆	X
ejpam-6141	239	33	z	z	NOUN
ejpam-6141	239	34	)	)	PUNCT
ejpam-6141	239	35	∈	∈	PROPN
ejpam-6141	239	36	(	(	PUNCT
ejpam-6141	239	37	x	x	SYM
ejpam-6141	239	38	◦	◦	NOUN
ejpam-6141	239	39	ck	ck	PROPN
ejpam-6141	239	40	y	y	NOUN
ejpam-6141	239	41	)	)	PUNCT
ejpam-6141	239	42	◦	◦	NOUN
ejpam-6141	239	43	ck	ck	PROPN
ejpam-6141	239	44	z.	z.	PROPN
ejpam-6141	240	1	therefore	therefore	ADV
ejpam-6141	240	2	x	x	X
ejpam-6141	240	3	◦	◦	NOUN
ejpam-6141	240	4	ck	ck	PROPN
ejpam-6141	240	5	(	(	PUNCT
ejpam-6141	240	6	y	y	PROPN
ejpam-6141	240	7	◦	◦	NOUN
ejpam-6141	240	8	ck	ck	PROPN
ejpam-6141	240	9	z	z	NOUN
ejpam-6141	240	10	)	)	PUNCT
ejpam-6141	240	11	∩	∩	NOUN
ejpam-6141	240	12	(	(	PUNCT
ejpam-6141	240	13	x	x	SYM
ejpam-6141	240	14	◦	◦	NOUN
ejpam-6141	240	15	ck	ck	PROPN
ejpam-6141	240	16	y	y	NOUN
ejpam-6141	240	17	)	)	PUNCT
ejpam-6141	240	18	◦	◦	NOUN
ejpam-6141	240	19	ck	ck	AUX
ejpam-6141	240	20	z	z	NOUN
ejpam-6141	240	21	̸=	̸=	PROPN
ejpam-6141	240	22	∅.	∅.	ADV
ejpam-6141	240	23	theorem	theorem	VERB
ejpam-6141	240	24	7	7	NUM
ejpam-6141	240	25	.	.	PUNCT
ejpam-6141	241	1	let	let	AUX
ejpam-6141	241	2	(	(	PUNCT
ejpam-6141	241	3	h	h	NOUN
ejpam-6141	241	4	,	,	PUNCT
ejpam-6141	241	5	⋆	⋆	ADJ
ejpam-6141	241	6	)	)	PUNCT
ejpam-6141	241	7	be	be	AUX
ejpam-6141	241	8	a	a	DET
ejpam-6141	241	9	quasigroup	quasigroup	NOUN
ejpam-6141	241	10	.	.	PUNCT
ejpam-6141	242	1	(	(	PUNCT
ejpam-6141	242	2	1	1	X
ejpam-6141	242	3	)	)	PUNCT
ejpam-6141	242	4	if	if	SCONJ
ejpam-6141	242	5	k	k	PROPN
ejpam-6141	242	6	=	=	SYM
ejpam-6141	242	7	0	0	PROPN
ejpam-6141	242	8	,	,	PUNCT
ejpam-6141	242	9	then	then	ADV
ejpam-6141	242	10	β∗	β∗	NOUN
ejpam-6141	242	11	=	=	SYM
ejpam-6141	242	12	{	{	PUNCT
ejpam-6141	242	13	(	(	PUNCT
ejpam-6141	242	14	x	x	X
ejpam-6141	242	15	,	,	PUNCT
ejpam-6141	242	16	x)|x	x)|x	PROPN
ejpam-6141	242	17	∈	∈	PROPN
ejpam-6141	242	18	h	h	NOUN
ejpam-6141	242	19	}	}	PUNCT
ejpam-6141	242	20	;	;	PUNCT
ejpam-6141	242	21	(	(	PUNCT
ejpam-6141	242	22	2	2	X
ejpam-6141	242	23	)	)	PUNCT
ejpam-6141	242	24	if	if	SCONJ
ejpam-6141	242	25	k	k	PROPN
ejpam-6141	242	26	>	>	X
ejpam-6141	242	27	0	0	PROPN
ejpam-6141	242	28	,	,	PUNCT
ejpam-6141	242	29	then	then	ADV
ejpam-6141	242	30	β∗	β∗	NOUN
ejpam-6141	242	31	=	=	SYM
ejpam-6141	242	32	h	h	NOUN
ejpam-6141	242	33	×h	×h	NOUN
ejpam-6141	242	34	.	.	PUNCT
ejpam-6141	243	1	proof	proof	NOUN
ejpam-6141	243	2	.	.	PUNCT
ejpam-6141	244	1	if	if	SCONJ
ejpam-6141	244	2	k	k	PROPN
ejpam-6141	245	1	=	=	NOUN
ejpam-6141	245	2	0	0	PROPN
ejpam-6141	245	3	then	then	ADV
ejpam-6141	245	4	∏n	∏n	PROPN
ejpam-6141	245	5	i=1	i=1	PROPN
ejpam-6141	245	6	zi	zi	PROPN
ejpam-6141	245	7	is	be	AUX
ejpam-6141	245	8	singleton	singleton	PROPN
ejpam-6141	245	9	and	and	CCONJ
ejpam-6141	245	10	so	so	ADV
ejpam-6141	245	11	β	β	X
ejpam-6141	245	12	=	=	SYM
ejpam-6141	245	13	{	{	PUNCT
ejpam-6141	245	14	(	(	PUNCT
ejpam-6141	245	15	x	x	X
ejpam-6141	245	16	,	,	PUNCT
ejpam-6141	245	17	x)|x	x)|x	PROPN
ejpam-6141	246	1	∈	∈	PROPN
ejpam-6141	246	2	h	h	NOUN
ejpam-6141	246	3	}	}	PUNCT
ejpam-6141	246	4	.	.	PUNCT
ejpam-6141	247	1	now	now	ADV
ejpam-6141	247	2	,	,	PUNCT
ejpam-6141	247	3	let	let	VERB
ejpam-6141	247	4	k	k	PRON
ejpam-6141	247	5	>	>	X
ejpam-6141	247	6	0	0	PUNCT
ejpam-6141	248	1	and	and	CCONJ
ejpam-6141	248	2	x	x	NOUN
ejpam-6141	248	3	,	,	PUNCT
ejpam-6141	248	4	y	y	PROPN
ejpam-6141	248	5	∈	∈	PROPN
ejpam-6141	248	6	h.	h.	PROPN
ejpam-6141	248	7	consider	consider	VERB
ejpam-6141	248	8	(	(	PUNCT
ejpam-6141	248	9	a1	a1	VERB
ejpam-6141	248	10	⋆0	⋆0	NUM
ejpam-6141	248	11	a1	a1	NOUN
ejpam-6141	248	12	,	,	PUNCT
ejpam-6141	248	13	.	.	PUNCT
ejpam-6141	248	14	.	.	PUNCT
ejpam-6141	248	15	.	.	PUNCT
ejpam-6141	249	1	,	,	PUNCT
ejpam-6141	249	2	a1	a1	VERB
ejpam-6141	249	3	⋆0	⋆0	NUM
ejpam-6141	249	4	an	an	PRON
ejpam-6141	249	5	)	)	PUNCT
ejpam-6141	249	6	=	=	SYM
ejpam-6141	249	7	(	(	PUNCT
ejpam-6141	249	8	b1	b1	NOUN
ejpam-6141	249	9	,	,	PUNCT
ejpam-6141	249	10	.	.	PUNCT
ejpam-6141	249	11	.	.	PUNCT
ejpam-6141	250	1	.	.	PUNCT
ejpam-6141	251	1	,	,	PUNCT
ejpam-6141	251	2	bn	bn	X
ejpam-6141	251	3	)	)	PUNCT
ejpam-6141	252	1	so	so	ADV
ejpam-6141	252	2	(	(	PUNCT
ejpam-6141	252	3	a1	a1	NOUN
ejpam-6141	252	4	⋆1	⋆1	NOUN
ejpam-6141	252	5	a1	a1	NOUN
ejpam-6141	252	6	,	,	PUNCT
ejpam-6141	252	7	.	.	PUNCT
ejpam-6141	252	8	.	.	PUNCT
ejpam-6141	253	1	.	.	PUNCT
ejpam-6141	254	1	,	,	PUNCT
ejpam-6141	254	2	a1	a1	VERB
ejpam-6141	254	3	⋆1	⋆1	ADV
ejpam-6141	254	4	an	an	PRON
ejpam-6141	254	5	)	)	PUNCT
ejpam-6141	254	6	=	=	SYM
ejpam-6141	254	7	(	(	PUNCT
ejpam-6141	254	8	b2	b2	NOUN
ejpam-6141	254	9	,	,	PUNCT
ejpam-6141	254	10	.	.	PUNCT
ejpam-6141	254	11	.	.	PUNCT
ejpam-6141	255	1	.	.	PUNCT
ejpam-6141	256	1	,	,	PUNCT
ejpam-6141	256	2	bn	bn	X
ejpam-6141	256	3	,	,	PUNCT
ejpam-6141	256	4	b1	b1	NOUN
ejpam-6141	256	5	)	)	PUNCT
ejpam-6141	256	6	.	.	PUNCT
ejpam-6141	257	1	therefore	therefore	ADV
ejpam-6141	257	2	{	{	PUNCT
ejpam-6141	257	3	bi	bi	NOUN
ejpam-6141	257	4	,	,	PUNCT
ejpam-6141	257	5	bi+1	bi+1	NOUN
ejpam-6141	257	6	}	}	PUNCT
ejpam-6141	257	7	⊆	⊆	NUM
ejpam-6141	257	8	a1	a1	NOUN
ejpam-6141	257	9	◦	◦	NOUN
ejpam-6141	257	10	c2	c2	PROPN
ejpam-6141	257	11	ai	ai	VERB
ejpam-6141	257	12	⊆	⊆	NUM
ejpam-6141	257	13	a1	a1	NOUN
ejpam-6141	257	14	◦	◦	NOUN
ejpam-6141	257	15	ck	ck	NOUN
ejpam-6141	257	16	ai	ai	NOUN
ejpam-6141	257	17	.	.	PUNCT
ejpam-6141	258	1	since	since	SCONJ
ejpam-6141	258	2	h	h	NOUN
ejpam-6141	258	3	=	=	SYM
ejpam-6141	258	4	{	{	PUNCT
ejpam-6141	258	5	b1	b1	NOUN
ejpam-6141	258	6	,	,	PUNCT
ejpam-6141	258	7	.	.	PUNCT
ejpam-6141	258	8	.	.	PUNCT
ejpam-6141	258	9	.	.	PUNCT
ejpam-6141	259	1	,	,	PUNCT
ejpam-6141	259	2	bn	bn	X
ejpam-6141	259	3	}	}	PUNCT
ejpam-6141	259	4	then	then	ADV
ejpam-6141	259	5	for	for	ADP
ejpam-6141	259	6	every	every	DET
ejpam-6141	259	7	x	x	NOUN
ejpam-6141	259	8	,	,	PUNCT
ejpam-6141	259	9	y	y	PROPN
ejpam-6141	259	10	∈	∈	PROPN
ejpam-6141	259	11	h	h	NOUN
ejpam-6141	259	12	there	there	PRON
ejpam-6141	259	13	exist	exist	VERB
ejpam-6141	259	14	1	1	NUM
ejpam-6141	259	15	≤	≤	NOUN
ejpam-6141	260	1	i	i	PRON
ejpam-6141	260	2	,	,	PUNCT
ejpam-6141	260	3	j	j	PROPN
ejpam-6141	260	4	≤	≤	PROPN
ejpam-6141	260	5	n	n	PRON
ejpam-6141	260	6	such	such	ADJ
ejpam-6141	260	7	that	that	SCONJ
ejpam-6141	260	8	i	i	PRON
ejpam-6141	260	9	<	<	X
ejpam-6141	260	10	j	j	PROPN
ejpam-6141	260	11	and	and	CCONJ
ejpam-6141	260	12	bi	bi	NOUN
ejpam-6141	260	13	=	=	PROPN
ejpam-6141	260	14	x	x	PROPN
ejpam-6141	260	15	and	and	CCONJ
ejpam-6141	260	16	bj	bj	VERB
ejpam-6141	260	17	=	=	PUNCT
ejpam-6141	260	18	y.	y.	NOUN
ejpam-6141	260	19	x	x	PUNCT
ejpam-6141	260	20	=	=	PUNCT
ejpam-6141	260	21	biβbi+1β	biβbi+1β	PROPN
ejpam-6141	260	22	.	.	PUNCT
ejpam-6141	260	23	.	.	PUNCT
ejpam-6141	260	24	.	.	PUNCT
ejpam-6141	260	25	βbj	βbj	X
ejpam-6141	261	1	=	=	PUNCT
ejpam-6141	261	2	y.	y.	NOUN
ejpam-6141	261	3	and	and	CCONJ
ejpam-6141	261	4	therefore	therefore	ADV
ejpam-6141	261	5	xβ∗y	xβ∗y	PROPN
ejpam-6141	261	6	.	.	PUNCT
ejpam-6141	261	7	corollary	corollary	ADJ
ejpam-6141	261	8	2	2	NUM
ejpam-6141	261	9	.	.	PUNCT
ejpam-6141	261	10	for	for	ADP
ejpam-6141	261	11	quasihypergroups	quasihypergroup	NOUN
ejpam-6141	261	12	(	(	PUNCT
ejpam-6141	261	13	h	h	NOUN
ejpam-6141	261	14	,	,	PUNCT
ejpam-6141	261	15	◦	◦	NOUN
ejpam-6141	261	16	ck	ck	ADJ
ejpam-6141	261	17	)	)	PUNCT
ejpam-6141	261	18	,	,	PUNCT
ejpam-6141	261	19	k	k	PROPN
ejpam-6141	261	20	=	=	SYM
ejpam-6141	261	21	0	0	NUM
ejpam-6141	261	22	,	,	PUNCT
ejpam-6141	261	23	1	1	NUM
ejpam-6141	261	24	,	,	PUNCT
ejpam-6141	261	25	.	.	PUNCT
ejpam-6141	261	26	.	.	PUNCT
ejpam-6141	262	1	.	.	PUNCT
ejpam-6141	263	1	,	,	PUNCT
ejpam-6141	263	2	n−	n−	NOUN
ejpam-6141	263	3	1	1	NUM
ejpam-6141	263	4	,	,	PUNCT
ejpam-6141	263	5	we	we	PRON
ejpam-6141	263	6	have	have	VERB
ejpam-6141	263	7	(	(	PUNCT
ejpam-6141	263	8	1	1	X
ejpam-6141	263	9	)	)	PUNCT
ejpam-6141	263	10	if	if	SCONJ
ejpam-6141	263	11	k	k	PROPN
ejpam-6141	263	12	=	=	SYM
ejpam-6141	263	13	0	0	PROPN
ejpam-6141	263	14	,	,	PUNCT
ejpam-6141	263	15	then	then	ADV
ejpam-6141	263	16	the	the	DET
ejpam-6141	263	17	fundamental	fundamental	ADJ
ejpam-6141	263	18	quasigroup	quasigroup	NOUN
ejpam-6141	263	19	h	h	PROPN
ejpam-6141	263	20	β∗	β∗	PROPN
ejpam-6141	263	21	is	be	AUX
ejpam-6141	263	22	isomorphic	isomorphic	ADJ
ejpam-6141	263	23	to	to	ADP
ejpam-6141	263	24	h	h	NOUN
ejpam-6141	263	25	;	;	PUNCT
ejpam-6141	263	26	(	(	PUNCT
ejpam-6141	263	27	2	2	X
ejpam-6141	263	28	)	)	PUNCT
ejpam-6141	263	29	if	if	SCONJ
ejpam-6141	263	30	k	k	PROPN
ejpam-6141	263	31	>	>	X
ejpam-6141	263	32	0	0	PROPN
ejpam-6141	263	33	,	,	PUNCT
ejpam-6141	263	34	then	then	ADV
ejpam-6141	263	35	the	the	DET
ejpam-6141	263	36	fundamental	fundamental	ADJ
ejpam-6141	263	37	quasigroup	quasigroup	NOUN
ejpam-6141	263	38	h	h	PROPN
ejpam-6141	263	39	β∗	β∗	PROPN
ejpam-6141	263	40	is	be	AUX
ejpam-6141	263	41	trivial	trivial	ADJ
ejpam-6141	263	42	group	group	NOUN
ejpam-6141	263	43	.	.	PUNCT
ejpam-6141	264	1	definition	definition	NOUN
ejpam-6141	264	2	6	6	NUM
ejpam-6141	264	3	.	.	PUNCT
ejpam-6141	265	1	a	a	PRON
ejpam-6141	265	2	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	265	3	(	(	PUNCT
ejpam-6141	265	4	h	h	NOUN
ejpam-6141	265	5	,	,	PUNCT
ejpam-6141	265	6	◦	◦	NOUN
ejpam-6141	265	7	)	)	PUNCT
ejpam-6141	265	8	is	be	AUX
ejpam-6141	265	9	called	call	VERB
ejpam-6141	265	10	a	a	DET
ejpam-6141	265	11	transposition	transposition	NOUN
ejpam-6141	265	12	hypergroup	hypergroup	NOUN
ejpam-6141	265	13	if	if	SCONJ
ejpam-6141	265	14	it	it	PRON
ejpam-6141	265	15	satisfies	satisfy	VERB
ejpam-6141	265	16	the	the	DET
ejpam-6141	265	17	axiom	axiom	NOUN
ejpam-6141	265	18	,	,	PUNCT
ejpam-6141	265	19	(	(	PUNCT
ejpam-6141	265	20	transposition	transposition	NOUN
ejpam-6141	265	21	)	)	PUNCT
ejpam-6141	265	22	b	b	NOUN
ejpam-6141	265	23	\	\	PROPN
ejpam-6141	265	24	a	a	PRON
ejpam-6141	265	25	≈	≈	PROPN
ejpam-6141	265	26	c	c	PROPN
ejpam-6141	265	27	/	/	SYM
ejpam-6141	265	28	d	d	NOUN
ejpam-6141	265	29	=	=	NOUN
ejpam-6141	265	30	⇒	⇒	VERB
ejpam-6141	265	31	a	a	DET
ejpam-6141	265	32	◦	◦	NOUN
ejpam-6141	265	33	d	d	PROPN
ejpam-6141	265	34	≈	≈	PROPN
ejpam-6141	265	35	b	b	PROPN
ejpam-6141	265	36	◦	◦	NOUN
ejpam-6141	265	37	c	c	NOUN
ejpam-6141	265	38	for	for	ADP
ejpam-6141	265	39	all	all	DET
ejpam-6141	265	40	a	a	DET
ejpam-6141	265	41	,	,	PUNCT
ejpam-6141	265	42	b	b	NOUN
ejpam-6141	265	43	,	,	PUNCT
ejpam-6141	265	44	c	c	NOUN
ejpam-6141	265	45	,	,	PUNCT
ejpam-6141	265	46	d	d	PROPN
ejpam-6141	265	47	∈	∈	PROPN
ejpam-6141	265	48	h.	h.	NOUN
ejpam-6141	265	49	if	if	SCONJ
ejpam-6141	265	50	the	the	DET
ejpam-6141	265	51	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	265	52	(	(	PUNCT
ejpam-6141	265	53	h	h	NOUN
ejpam-6141	265	54	,	,	PUNCT
ejpam-6141	265	55	◦	◦	NOUN
ejpam-6141	265	56	)	)	PUNCT
ejpam-6141	265	57	is	be	AUX
ejpam-6141	265	58	commutative	commutative	ADJ
ejpam-6141	265	59	then	then	ADV
ejpam-6141	265	60	hyperoperation	hyperoperation	NOUN
ejpam-6141	265	61	\	\	PUNCT
ejpam-6141	266	1	=	=	PUNCT
ejpam-6141	266	2	/	/	SYM
ejpam-6141	266	3	and	and	CCONJ
ejpam-6141	266	4	a	a	DET
ejpam-6141	266	5	commutative	commutative	ADJ
ejpam-6141	266	6	transposition	transposition	NOUN
ejpam-6141	266	7	hypergroup	hypergroup	PROPN
ejpam-6141	266	8	is	be	AUX
ejpam-6141	266	9	called	call	VERB
ejpam-6141	266	10	a	a	DET
ejpam-6141	266	11	join	join	NOUN
ejpam-6141	266	12	space	space	NOUN
ejpam-6141	266	13	.	.	PUNCT
ejpam-6141	267	1	theorem	theorem	VERB
ejpam-6141	267	2	8	8	NUM
ejpam-6141	267	3	.	.	PUNCT
ejpam-6141	268	1	if	if	SCONJ
ejpam-6141	268	2	k	k	PROPN
ejpam-6141	268	3	=	=	SYM
ejpam-6141	268	4	|h|	|h|	PROPN
ejpam-6141	268	5	2	2	NUM
ejpam-6141	268	6	,	,	PUNCT
ejpam-6141	268	7	.	.	PUNCT
ejpam-6141	268	8	.	.	PUNCT
ejpam-6141	269	1	.	.	PUNCT
ejpam-6141	270	1	,	,	PUNCT
ejpam-6141	270	2	n	n	CCONJ
ejpam-6141	270	3	then	then	ADV
ejpam-6141	270	4	the	the	DET
ejpam-6141	270	5	quasihypergroup	quasihypergroup	NOUN
ejpam-6141	270	6	(	(	PUNCT
ejpam-6141	270	7	h	h	NOUN
ejpam-6141	270	8	,	,	PUNCT
ejpam-6141	270	9	◦	◦	NOUN
ejpam-6141	270	10	ck	ck	NOUN
ejpam-6141	270	11	)	)	PUNCT
ejpam-6141	270	12	is	be	AUX
ejpam-6141	270	13	a	a	DET
ejpam-6141	270	14	transposition	transposition	NOUN
ejpam-6141	270	15	hypergroupoid	hypergroupoid	PROPN
ejpam-6141	270	16	.	.	PUNCT
ejpam-6141	271	1	proof	proof	NOUN
ejpam-6141	271	2	.	.	PUNCT
ejpam-6141	272	1	let	let	VERB
ejpam-6141	272	2	a	a	DET
ejpam-6141	272	3	,	,	PUNCT
ejpam-6141	272	4	b	b	NOUN
ejpam-6141	272	5	,	,	PUNCT
ejpam-6141	272	6	c	c	NOUN
ejpam-6141	272	7	,	,	PUNCT
ejpam-6141	272	8	d	d	PROPN
ejpam-6141	272	9	∈	∈	PROPN
ejpam-6141	272	10	h	h	NOUN
ejpam-6141	272	11	and	and	CCONJ
ejpam-6141	272	12	b	b	NOUN
ejpam-6141	272	13	\	\	PROPN
ejpam-6141	272	14	a	a	DET
ejpam-6141	272	15	≈	≈	PROPN
ejpam-6141	272	16	c	c	PROPN
ejpam-6141	272	17	/	/	SYM
ejpam-6141	272	18	d.	d.	PROPN
ejpam-6141	272	19	since	since	SCONJ
ejpam-6141	272	20	|a	|a	PRON
ejpam-6141	272	21	◦	◦	VERB
ejpam-6141	272	22	ck	ck	PROPN
ejpam-6141	272	23	d|	d|	PROPN
ejpam-6141	272	24	=	=	PUNCT
ejpam-6141	273	1	k	k	PROPN
ejpam-6141	274	1	+	+	CCONJ
ejpam-6141	274	2	1	1	NUM
ejpam-6141	274	3	=	=	SYM
ejpam-6141	274	4	|b	|b	ADJ
ejpam-6141	274	5	◦	◦	NOUN
ejpam-6141	274	6	ck	ck	PROPN
ejpam-6141	274	7	c|	c|	PROPN
ejpam-6141	274	8	then	then	ADV
ejpam-6141	274	9	a	a	DET
ejpam-6141	274	10	◦	◦	NOUN
ejpam-6141	274	11	ck	ck	ADJ
ejpam-6141	274	12	d	d	NOUN
ejpam-6141	274	13	∩	∩	X
ejpam-6141	274	14	b	b	X
ejpam-6141	274	15	◦	◦	NOUN
ejpam-6141	274	16	ck	ck	NOUN
ejpam-6141	274	17	c	c	X
ejpam-6141	274	18	̸=	̸=	PROPN
ejpam-6141	274	19	∅.	∅.	PRON
ejpam-6141	274	20	corollary	corollary	ADJ
ejpam-6141	274	21	3	3	NUM
ejpam-6141	274	22	.	.	PUNCT
ejpam-6141	275	1	let	let	AUX
ejpam-6141	275	2	(	(	PUNCT
ejpam-6141	275	3	h	h	NOUN
ejpam-6141	275	4	,	,	PUNCT
ejpam-6141	275	5	⋆	⋆	ADJ
ejpam-6141	275	6	)	)	PUNCT
ejpam-6141	275	7	be	be	AUX
ejpam-6141	275	8	a	a	DET
ejpam-6141	275	9	cyclic	cyclic	ADJ
ejpam-6141	275	10	group	group	NOUN
ejpam-6141	275	11	of	of	ADP
ejpam-6141	275	12	order	order	NOUN
ejpam-6141	275	13	n.	n.	NOUN
ejpam-6141	275	14	then	then	ADV
ejpam-6141	275	15	(	(	PUNCT
ejpam-6141	275	16	h	h	NOUN
ejpam-6141	275	17	,	,	PUNCT
ejpam-6141	275	18	◦	◦	NOUN
ejpam-6141	275	19	ck	ck	NOUN
ejpam-6141	275	20	)	)	PUNCT
ejpam-6141	275	21	is	be	AUX
ejpam-6141	275	22	a	a	DET
ejpam-6141	275	23	join	join	NOUN
ejpam-6141	275	24	space	space	NOUN
ejpam-6141	275	25	.	.	PUNCT
ejpam-6141	276	1	proof	proof	NOUN
ejpam-6141	276	2	.	.	PUNCT
ejpam-6141	277	1	it	it	PRON
ejpam-6141	277	2	obtains	obtain	VERB
ejpam-6141	277	3	from	from	ADP
ejpam-6141	277	4	theorems	theorem	NOUN
ejpam-6141	277	5	5	5	NUM
ejpam-6141	277	6	and	and	CCONJ
ejpam-6141	277	7	8	8	NUM
ejpam-6141	277	8	.	.	PUNCT
ejpam-6141	277	9	remark	remark	NOUN
ejpam-6141	277	10	1	1	NUM
ejpam-6141	277	11	.	.	PUNCT
ejpam-6141	278	1	for	for	ADP
ejpam-6141	278	2	every	every	DET
ejpam-6141	278	3	result	result	NOUN
ejpam-6141	278	4	true	true	ADJ
ejpam-6141	278	5	for	for	ADP
ejpam-6141	278	6	◦	◦	NOUN
ejpam-6141	278	7	ck	ck	ADJ
ejpam-6141	278	8	then	then	ADV
ejpam-6141	278	9	it	it	PRON
ejpam-6141	278	10	also	also	ADV
ejpam-6141	278	11	holds	hold	VERB
ejpam-6141	278	12	for	for	ADP
ejpam-6141	278	13	◦	◦	NOUN
ejpam-6141	278	14	rk	rk	NOUN
ejpam-6141	278	15	.	.	PUNCT
ejpam-6141	279	1	m.	m.	NOUN
ejpam-6141	279	2	a.	a.	PROPN
ejpam-6141	279	3	dehghanizadeh	dehghanizadeh	PROPN
ejpam-6141	279	4	,	,	PUNCT
ejpam-6141	279	5	s.	s.	PROPN
ejpam-6141	279	6	mirvakili	mirvakili	PROPN
ejpam-6141	279	7	/	/	SYM
ejpam-6141	279	8	eur	eur	PROPN
ejpam-6141	279	9	.	.	PUNCT
ejpam-6141	280	1	j.	j.	PROPN
ejpam-6141	280	2	pure	pure	PROPN
ejpam-6141	280	3	appl	appl	PROPN
ejpam-6141	280	4	.	.	PROPN
ejpam-6141	280	5	math	math	PROPN
ejpam-6141	280	6	,	,	PUNCT
ejpam-6141	280	7	18	18	NUM
ejpam-6141	280	8	(	(	PUNCT
ejpam-6141	280	9	2	2	NUM
ejpam-6141	280	10	)	)	PUNCT
ejpam-6141	280	11	(	(	PUNCT
ejpam-6141	280	12	2025	2025	NUM
ejpam-6141	280	13	)	)	PUNCT
ejpam-6141	280	14	,	,	PUNCT
ejpam-6141	280	15	6141	6141	NUM
ejpam-6141	280	16	10	10	NUM
ejpam-6141	280	17	of	of	ADP
ejpam-6141	280	18	10	10	NUM
ejpam-6141	280	19	3	3	NUM
ejpam-6141	280	20	.	.	PUNCT
ejpam-6141	280	21	conclusion	conclusion	NOUN
ejpam-6141	280	22	in	in	ADP
ejpam-6141	280	23	this	this	DET
ejpam-6141	280	24	paper	paper	NOUN
ejpam-6141	280	25	,	,	PUNCT
ejpam-6141	280	26	we	we	PRON
ejpam-6141	280	27	initiated	initiate	VERB
ejpam-6141	280	28	the	the	DET
ejpam-6141	280	29	construction	construction	NOUN
ejpam-6141	280	30	of	of	ADP
ejpam-6141	280	31	sequences	sequence	NOUN
ejpam-6141	280	32	of	of	ADP
ejpam-6141	280	33	hypergroupoids	hypergroupoid	NOUN
ejpam-6141	280	34	derived	derive	VERB
ejpam-6141	280	35	from	from	ADP
ejpam-6141	280	36	quasigroups	quasigroup	NOUN
ejpam-6141	280	37	(	(	PUNCT
ejpam-6141	280	38	latin	latin	ADJ
ejpam-6141	280	39	squares	square	NOUN
ejpam-6141	280	40	)	)	PUNCT
ejpam-6141	280	41	.	.	PUNCT
ejpam-6141	281	1	our	our	PRON
ejpam-6141	281	2	findings	finding	NOUN
ejpam-6141	281	3	demonstrate	demonstrate	VERB
ejpam-6141	281	4	that	that	SCONJ
ejpam-6141	281	5	cyclic	cyclic	ADJ
ejpam-6141	281	6	groups	group	NOUN
ejpam-6141	281	7	can	can	AUX
ejpam-6141	281	8	generate	generate	VERB
ejpam-6141	281	9	sequences	sequence	NOUN
ejpam-6141	281	10	of	of	ADP
ejpam-6141	281	11	commutative	commutative	ADJ
ejpam-6141	281	12	hypergroups	hypergroup	NOUN
ejpam-6141	281	13	,	,	PUNCT
ejpam-6141	281	14	providing	provide	VERB
ejpam-6141	281	15	a	a	DET
ejpam-6141	281	16	foundational	foundational	ADJ
ejpam-6141	281	17	framework	framework	NOUN
ejpam-6141	281	18	for	for	ADP
ejpam-6141	281	19	further	further	ADJ
ejpam-6141	281	20	exploration	exploration	NOUN
ejpam-6141	281	21	.	.	PUNCT
ejpam-6141	282	1	furthermore	furthermore	ADV
ejpam-6141	282	2	,	,	PUNCT
ejpam-6141	282	3	under	under	ADP
ejpam-6141	282	4	specific	specific	ADJ
ejpam-6141	282	5	conditions	condition	NOUN
ejpam-6141	282	6	,	,	PUNCT
ejpam-6141	282	7	the	the	DET
ejpam-6141	282	8	formation	formation	NOUN
ejpam-6141	282	9	of	of	ADP
ejpam-6141	282	10	hv	hv	NOUN
ejpam-6141	282	11	-	-	PUNCT
ejpam-6141	282	12	groups	group	NOUN
ejpam-6141	282	13	and	and	CCONJ
ejpam-6141	282	14	hypergroups	hypergroup	NOUN
ejpam-6141	282	15	was	be	AUX
ejpam-6141	282	16	established	establish	VERB
ejpam-6141	282	17	,	,	PUNCT
ejpam-6141	282	18	enriching	enrich	VERB
ejpam-6141	282	19	the	the	DET
ejpam-6141	282	20	theoretical	theoretical	ADJ
ejpam-6141	282	21	understanding	understanding	NOUN
ejpam-6141	282	22	of	of	ADP
ejpam-6141	282	23	these	these	DET
ejpam-6141	282	24	structures	structure	NOUN
ejpam-6141	282	25	.	.	PUNCT
ejpam-6141	283	1	to	to	PART
ejpam-6141	283	2	bridge	bridge	VERB
ejpam-6141	283	3	theory	theory	NOUN
ejpam-6141	283	4	with	with	ADP
ejpam-6141	283	5	application	application	NOUN
ejpam-6141	283	6	,	,	PUNCT
ejpam-6141	283	7	we	we	PRON
ejpam-6141	283	8	conducted	conduct	VERB
ejpam-6141	283	9	experiments	experiment	NOUN
ejpam-6141	283	10	that	that	PRON
ejpam-6141	283	11	not	not	PART
ejpam-6141	283	12	only	only	ADV
ejpam-6141	283	13	corroborate	corroborate	VERB
ejpam-6141	283	14	the	the	DET
ejpam-6141	283	15	presented	present	VERB
ejpam-6141	283	16	theoretical	theoretical	ADJ
ejpam-6141	283	17	concepts	concept	NOUN
ejpam-6141	283	18	but	but	CCONJ
ejpam-6141	283	19	also	also	ADV
ejpam-6141	283	20	illustrate	illustrate	VERB
ejpam-6141	283	21	their	their	PRON
ejpam-6141	283	22	formulation	formulation	NOUN
ejpam-6141	283	23	and	and	CCONJ
ejpam-6141	283	24	potential	potential	ADJ
ejpam-6141	283	25	practical	practical	ADJ
ejpam-6141	283	26	extensions	extension	NOUN
ejpam-6141	283	27	.	.	PUNCT
ejpam-6141	284	1	these	these	DET
ejpam-6141	284	2	contributions	contribution	NOUN
ejpam-6141	284	3	pave	pave	VERB
ejpam-6141	284	4	the	the	DET
ejpam-6141	284	5	way	way	NOUN
ejpam-6141	284	6	for	for	ADP
ejpam-6141	284	7	further	further	ADJ
ejpam-6141	284	8	research	research	NOUN
ejpam-6141	284	9	in	in	ADP
ejpam-6141	284	10	hyperstructure	hyperstructure	PROPN
ejpam-6141	284	11	theory	theory	NOUN
ejpam-6141	284	12	and	and	CCONJ
ejpam-6141	284	13	its	its	PRON
ejpam-6141	284	14	real	real	ADJ
ejpam-6141	284	15	-	-	PUNCT
ejpam-6141	284	16	world	world	NOUN
ejpam-6141	284	17	applicability	applicability	NOUN
ejpam-6141	284	18	.	.	PUNCT
ejpam-6141	285	1	future	future	ADJ
ejpam-6141	285	2	work	work	NOUN
ejpam-6141	285	3	may	may	AUX
ejpam-6141	285	4	delve	delve	VERB
ejpam-6141	285	5	into	into	ADP
ejpam-6141	285	6	extending	extend	VERB
ejpam-6141	285	7	the	the	DET
ejpam-6141	285	8	current	current	ADJ
ejpam-6141	285	9	constructions	construction	NOUN
ejpam-6141	285	10	from	from	ADP
ejpam-6141	285	11	γ	γ	NOUN
ejpam-6141	285	12	-	-	PUNCT
ejpam-6141	285	13	structures	structure	NOUN
ejpam-6141	285	14	to	to	ADP
ejpam-6141	285	15	γhyperstructures	γhyperstructure	NOUN
ejpam-6141	285	16	,	,	PUNCT
ejpam-6141	285	17	further	far	ADV
ejpam-6141	285	18	enriching	enrich	VERB
ejpam-6141	285	19	the	the	DET
ejpam-6141	285	20	theoretical	theoretical	ADJ
ejpam-6141	285	21	framework	framework	NOUN
ejpam-6141	285	22	.	.	PUNCT
ejpam-6141	286	1	moreover	moreover	ADV
ejpam-6141	286	2	,	,	PUNCT
ejpam-6141	286	3	this	this	DET
ejpam-6141	286	4	method	method	NOUN
ejpam-6141	286	5	can	can	AUX
ejpam-6141	286	6	be	be	AUX
ejpam-6141	286	7	applied	apply	VERB
ejpam-6141	286	8	to	to	PART
ejpam-6141	286	9	explore	explore	VERB
ejpam-6141	286	10	fuzzy	fuzzy	ADJ
ejpam-6141	286	11	algebraic	algebraic	ADJ
ejpam-6141	286	12	structures	structure	NOUN
ejpam-6141	286	13	,	,	PUNCT
ejpam-6141	286	14	expanding	expand	VERB
ejpam-6141	286	15	its	its	PRON
ejpam-6141	286	16	applicability	applicability	NOUN
ejpam-6141	286	17	.	.	PUNCT
ejpam-6141	287	1	for	for	ADP
ejpam-6141	287	2	example	example	NOUN
ejpam-6141	287	3	,	,	PUNCT
ejpam-6141	287	4	recent	recent	ADJ
ejpam-6141	287	5	advancements	advancement	NOUN
ejpam-6141	287	6	in	in	ADP
ejpam-6141	287	7	the	the	DET
ejpam-6141	287	8	fuzzification	fuzzification	NOUN
ejpam-6141	287	9	of	of	ADP
ejpam-6141	287	10	n	n	CCONJ
ejpam-6141	287	11	-	-	PUNCT
ejpam-6141	287	12	lie	lie	NOUN
ejpam-6141	287	13	algebras	algebra	NOUN
ejpam-6141	288	1	[	[	X
ejpam-6141	288	2	10	10	NUM
ejpam-6141	288	3	]	]	PUNCT
ejpam-6141	288	4	and	and	CCONJ
ejpam-6141	288	5	the	the	DET
ejpam-6141	288	6	structural	structural	ADJ
ejpam-6141	288	7	aspects	aspect	NOUN
ejpam-6141	288	8	of	of	ADP
ejpam-6141	288	9	gamma	gamma	NOUN
ejpam-6141	288	10	rings	ring	NOUN
ejpam-6141	289	1	[	[	X
ejpam-6141	289	2	11	11	NUM
ejpam-6141	289	3	]	]	PUNCT
ejpam-6141	289	4	provide	provide	VERB
ejpam-6141	289	5	promising	promising	ADJ
ejpam-6141	289	6	directions	direction	NOUN
ejpam-6141	289	7	for	for	ADP
ejpam-6141	289	8	future	future	ADJ
ejpam-6141	289	9	research	research	NOUN
ejpam-6141	289	10	.	.	PUNCT
ejpam-6141	290	1	references	reference	NOUN
ejpam-6141	290	2	[	[	X
ejpam-6141	290	3	1	1	NUM
ejpam-6141	290	4	]	]	PUNCT
ejpam-6141	290	5	j	j	PROPN
ejpam-6141	290	6	denes	dene	NOUN
ejpam-6141	290	7	and	and	CCONJ
ejpam-6141	290	8	a	a	DET
ejpam-6141	290	9	d	d	NOUN
ejpam-6141	290	10	keedwell	keedwell	NOUN
ejpam-6141	290	11	.	.	PUNCT
ejpam-6141	291	1	latin	latin	ADJ
ejpam-6141	291	2	squares	square	NOUN
ejpam-6141	291	3	and	and	CCONJ
ejpam-6141	291	4	their	their	PRON
ejpam-6141	291	5	applications	application	NOUN
ejpam-6141	291	6	.	.	PUNCT
ejpam-6141	292	1	academic	academic	PROPN
ejpam-6141	292	2	press	press	PROPN
ejpam-6141	292	3	inc	inc	PROPN
ejpam-6141	292	4	,	,	PUNCT
ejpam-6141	292	5	1974	1974	NUM
ejpam-6141	292	6	.	.	PUNCT
ejpam-6141	293	1	[	[	X
ejpam-6141	293	2	2	2	NUM
ejpam-6141	293	3	]	]	PUNCT
ejpam-6141	293	4	v	v	ADJ
ejpam-6141	293	5	shcherbacov	shcherbacov	NOUN
ejpam-6141	293	6	.	.	PUNCT
ejpam-6141	294	1	elements	element	NOUN
ejpam-6141	294	2	of	of	ADP
ejpam-6141	294	3	quasigroup	quasigroup	NOUN
ejpam-6141	294	4	theory	theory	NOUN
ejpam-6141	294	5	and	and	CCONJ
ejpam-6141	294	6	applications	application	NOUN
ejpam-6141	294	7	.	.	PUNCT
ejpam-6141	295	1	chapman	chapman	NOUN
ejpam-6141	295	2	and	and	CCONJ
ejpam-6141	295	3	hall	hall	PROPN
ejpam-6141	295	4	/	/	SYM
ejpam-6141	295	5	crc	crc	PROPN
ejpam-6141	295	6	,	,	PUNCT
ejpam-6141	295	7	2017	2017	NUM
ejpam-6141	295	8	.	.	PUNCT
ejpam-6141	296	1	[	[	X
ejpam-6141	296	2	3	3	X
ejpam-6141	296	3	]	]	X
ejpam-6141	296	4	a	a	DET
ejpam-6141	296	5	iranmanesh	iranmanesh	NOUN
ejpam-6141	296	6	and	and	CCONJ
ejpam-6141	296	7	a	a	DET
ejpam-6141	296	8	r	r	NOUN
ejpam-6141	296	9	ashrafi	ashrafi	NOUN
ejpam-6141	296	10	.	.	PUNCT
ejpam-6141	297	1	generalized	generalized	ADJ
ejpam-6141	297	2	latin	latin	PROPN
ejpam-6141	297	3	square	square	PROPN
ejpam-6141	297	4	.	.	PUNCT
ejpam-6141	298	1	j.	j.	PROPN
ejpam-6141	298	2	appl	appl	PROPN
ejpam-6141	298	3	.	.	PROPN
ejpam-6141	298	4	math	math	PROPN
ejpam-6141	298	5	.	.	PUNCT
ejpam-6141	299	1	&	&	CCONJ
ejpam-6141	299	2	computing	computing	PROPN
ejpam-6141	299	3	,	,	PUNCT
ejpam-6141	299	4	22(1	22(1	NUM
ejpam-6141	299	5	-	-	SYM
ejpam-6141	299	6	2):285–293	2):285–293	NUM
ejpam-6141	299	7	,	,	PUNCT
ejpam-6141	299	8	2006	2006	NUM
ejpam-6141	299	9	.	.	PUNCT
ejpam-6141	300	1	[	[	X
ejpam-6141	300	2	4	4	X
ejpam-6141	300	3	]	]	PUNCT
ejpam-6141	300	4	h	h	NOUN
ejpam-6141	300	5	o	o	NOUN
ejpam-6141	300	6	pflugfelder	pflugfelder	NOUN
ejpam-6141	300	7	o	o	X
ejpam-6141	300	8	chein	chein	ADV
ejpam-6141	300	9	and	and	CCONJ
ejpam-6141	300	10	(	(	PUNCT
ejpam-6141	300	11	eds	ed	NOUN
ejpam-6141	300	12	)	)	PUNCT
ejpam-6141	300	13	j	j	PROPN
ejpam-6141	300	14	d	d	PROPN
ejpam-6141	300	15	h	h	PROPN
ejpam-6141	300	16	smith	smith	PROPN
ejpam-6141	300	17	.	.	PUNCT
ejpam-6141	301	1	quasigroups	quasigroups	PROPN
ejpam-6141	301	2	and	and	CCONJ
ejpam-6141	301	3	loops	loop	NOUN
ejpam-6141	301	4	:	:	PUNCT
ejpam-6141	301	5	theory	theory	NOUN
ejpam-6141	301	6	and	and	CCONJ
ejpam-6141	301	7	applications	application	NOUN
ejpam-6141	301	8	.	.	PUNCT
ejpam-6141	302	1	heldermann	heldermann	PROPN
ejpam-6141	302	2	,	,	PUNCT
ejpam-6141	302	3	berlin	berlin	PROPN
ejpam-6141	302	4	,	,	PUNCT
ejpam-6141	302	5	1990	1990	NUM
ejpam-6141	302	6	.	.	PUNCT
ejpam-6141	303	1	[	[	X
ejpam-6141	303	2	5	5	X
ejpam-6141	303	3	]	]	X
ejpam-6141	303	4	p	p	X
ejpam-6141	303	5	corsini	corsini	PROPN
ejpam-6141	303	6	.	.	PUNCT
ejpam-6141	304	1	prolegomena	prolegomenon	NOUN
ejpam-6141	304	2	of	of	ADP
ejpam-6141	304	3	hypergroup	hypergroup	PROPN
ejpam-6141	304	4	theory	theory	PROPN
ejpam-6141	304	5	.	.	PUNCT
ejpam-6141	305	1	aviani	aviani	PROPN
ejpam-6141	305	2	editore	editore	PROPN
ejpam-6141	305	3	,	,	PUNCT
ejpam-6141	305	4	aviani	aviani	X
ejpam-6141	305	5	editore	editore	NOUN
ejpam-6141	305	6	,	,	PUNCT
ejpam-6141	305	7	1993	1993	NUM
ejpam-6141	305	8	.	.	PUNCT
ejpam-6141	306	1	[	[	X
ejpam-6141	306	2	6	6	NUM
ejpam-6141	306	3	]	]	PUNCT
ejpam-6141	306	4	p	p	X
ejpam-6141	306	5	corsini	corsini	NOUN
ejpam-6141	306	6	and	and	CCONJ
ejpam-6141	306	7	v	v	ADP
ejpam-6141	306	8	leoreanu	leoreanu	NOUN
ejpam-6141	306	9	.	.	PUNCT
ejpam-6141	307	1	applications	application	NOUN
ejpam-6141	307	2	of	of	ADP
ejpam-6141	307	3	hyperstructure	hyperstructure	NOUN
ejpam-6141	307	4	theory	theory	PROPN
ejpam-6141	307	5	.	.	PUNCT
ejpam-6141	308	1	kluwer	kluwer	NOUN
ejpam-6141	308	2	academic	academic	ADJ
ejpam-6141	308	3	publishers	publisher	NOUN
ejpam-6141	308	4	,	,	PUNCT
ejpam-6141	308	5	advances	advance	NOUN
ejpam-6141	308	6	in	in	ADP
ejpam-6141	308	7	mathematics	mathematic	NOUN
ejpam-6141	308	8	,	,	PUNCT
ejpam-6141	308	9	2003	2003	NUM
ejpam-6141	308	10	.	.	PUNCT
ejpam-6141	309	1	[	[	X
ejpam-6141	309	2	7	7	NUM
ejpam-6141	309	3	]	]	SYM
ejpam-6141	309	4	b	b	X
ejpam-6141	309	5	davvaz	davvaz	NOUN
ejpam-6141	309	6	.	.	PUNCT
ejpam-6141	310	1	semihypergroup	semihypergroup	PROPN
ejpam-6141	310	2	theory	theory	NOUN
ejpam-6141	310	3	.	.	PUNCT
ejpam-6141	311	1	elsevier	elsevier	NOUN
ejpam-6141	311	2	,	,	PUNCT
ejpam-6141	311	3	2016	2016	NUM
ejpam-6141	311	4	.	.	PUNCT
ejpam-6141	312	1	[	[	X
ejpam-6141	312	2	8	8	NUM
ejpam-6141	312	3	]	]	SYM
ejpam-6141	312	4	b	b	X
ejpam-6141	312	5	davvaz	davvaz	NOUN
ejpam-6141	312	6	and	and	CCONJ
ejpam-6141	312	7	t	t	PROPN
ejpam-6141	312	8	vougiouklis	vougioukli	VERB
ejpam-6141	312	9	.	.	PUNCT
ejpam-6141	313	1	a	a	DET
ejpam-6141	313	2	walk	walk	NOUN
ejpam-6141	313	3	through	through	ADP
ejpam-6141	313	4	weak	weak	ADJ
ejpam-6141	313	5	hyperstructures	hyperstructure	NOUN
ejpam-6141	313	6	;	;	PUNCT
ejpam-6141	313	7	hv	hv	NOUN
ejpam-6141	313	8	-	-	NOUN
ejpam-6141	313	9	structure	structure	NOUN
ejpam-6141	313	10	.	.	PUNCT
ejpam-6141	314	1	world	world	NOUN
ejpam-6141	314	2	scientific	scientific	PROPN
ejpam-6141	314	3	publishing	publishing	PROPN
ejpam-6141	314	4	co.	co.	PROPN
ejpam-6141	314	5	pte	pte	PROPN
ejpam-6141	314	6	.	.	PROPN
ejpam-6141	314	7	ltd	ltd	PROPN
ejpam-6141	314	8	.	.	PROPN
ejpam-6141	314	9	,	,	PUNCT
ejpam-6141	314	10	hackensack	hackensack	PROPN
ejpam-6141	314	11	,	,	PUNCT
ejpam-6141	314	12	nj	nj	PROPN
ejpam-6141	314	13	.	.	PROPN
ejpam-6141	314	14	,	,	PUNCT
ejpam-6141	314	15	2019	2019	NUM
ejpam-6141	314	16	.	.	PUNCT
ejpam-6141	315	1	[	[	X
ejpam-6141	315	2	9	9	NUM
ejpam-6141	315	3	]	]	SYM
ejpam-6141	315	4	r	r	NOUN
ejpam-6141	315	5	h	h	NOUN
ejpam-6141	315	6	bruck	bruck	NOUN
ejpam-6141	315	7	.	.	PUNCT
ejpam-6141	316	1	a	a	DET
ejpam-6141	316	2	survey	survey	NOUN
ejpam-6141	316	3	of	of	ADP
ejpam-6141	316	4	binary	binary	ADJ
ejpam-6141	316	5	systems	system	NOUN
ejpam-6141	316	6	.	.	PUNCT
ejpam-6141	317	1	university	university	NOUN
ejpam-6141	317	2	of	of	ADP
ejpam-6141	317	3	michigan	michigan	PROPN
ejpam-6141	317	4	press	press	PROPN
ejpam-6141	317	5	,	,	PUNCT
ejpam-6141	317	6	springerverlag	springerverlag	NOUN
ejpam-6141	317	7	,	,	PUNCT
ejpam-6141	317	8	1971	1971	NUM
ejpam-6141	317	9	.	.	PUNCT
ejpam-6141	318	1	[	[	X
ejpam-6141	318	2	10	10	NUM
ejpam-6141	318	3	]	]	SYM
ejpam-6141	318	4	s	s	VERB
ejpam-6141	318	5	shaqaqha	shaqaqha	NOUN
ejpam-6141	318	6	and	and	CCONJ
ejpam-6141	318	7	m	m	PROPN
ejpam-6141	318	8	y	y	PROPN
ejpam-6141	318	9	al	al	PROPN
ejpam-6141	318	10	-	-	PUNCT
ejpam-6141	318	11	deiakeh	deiakeh	NOUN
ejpam-6141	318	12	.	.	PUNCT
ejpam-6141	319	1	on	on	ADP
ejpam-6141	319	2	lie	lie	NOUN
ejpam-6141	319	3	homomorphisms	homomorphism	NOUN
ejpam-6141	319	4	of	of	ADP
ejpam-6141	319	5	complex	complex	ADJ
ejpam-6141	319	6	intuitionistic	intuitionistic	ADJ
ejpam-6141	319	7	fuzzy	fuzzy	ADJ
ejpam-6141	319	8	lie	lie	NOUN
ejpam-6141	319	9	algebras	algebra	NOUN
ejpam-6141	319	10	.	.	PUNCT
ejpam-6141	320	1	european	european	PROPN
ejpam-6141	320	2	journal	journal	PROPN
ejpam-6141	320	3	of	of	ADP
ejpam-6141	320	4	pure	pure	ADJ
ejpam-6141	320	5	and	and	CCONJ
ejpam-6141	320	6	applied	applied	ADJ
ejpam-6141	320	7	mathematics	mathematic	NOUN
ejpam-6141	320	8	,	,	PUNCT
ejpam-6141	320	9	17(4):3291	17(4):3291	NUM
ejpam-6141	320	10	–	–	PUNCT
ejpam-6141	320	11	3303	3303	NUM
ejpam-6141	320	12	,	,	PUNCT
ejpam-6141	320	13	2024	2024	NUM
ejpam-6141	320	14	.	.	PUNCT
ejpam-6141	321	1	[	[	X
ejpam-6141	321	2	11	11	NUM
ejpam-6141	321	3	]	]	SYM
ejpam-6141	321	4	s	s	VERB
ejpam-6141	321	5	shaqaqha	shaqaqha	NOUN
ejpam-6141	321	6	and	and	CCONJ
ejpam-6141	321	7	a	a	DET
ejpam-6141	321	8	dagher	dagher	NOUN
ejpam-6141	321	9	.	.	PUNCT
ejpam-6141	322	1	grading	grading	NOUN
ejpam-6141	322	2	and	and	CCONJ
ejpam-6141	322	3	filtrations	filtration	NOUN
ejpam-6141	322	4	of	of	ADP
ejpam-6141	322	5	gamma	gamma	NOUN
ejpam-6141	322	6	rings	ring	NOUN
ejpam-6141	322	7	.	.	PUNCT
ejpam-6141	323	1	italian	italian	ADJ
ejpam-6141	323	2	journal	journal	NOUN
ejpam-6141	323	3	of	of	ADP
ejpam-6141	323	4	pure	pure	ADJ
ejpam-6141	323	5	and	and	CCONJ
ejpam-6141	323	6	applied	applied	ADJ
ejpam-6141	323	7	mathematics	mathematic	NOUN
ejpam-6141	323	8	,	,	PUNCT
ejpam-6141	323	9	47:958–970	47:958–970	NUM
ejpam-6141	323	10	,	,	PUNCT
ejpam-6141	323	11	2022	2022	NUM
ejpam-6141	323	12	.	.	PUNCT